LMFDB - Embedded newform 13.7.f.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,7,Mod(2,13)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("13.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	13.f (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.99070308706$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	13.11
Dual form			13.7.f.a.6.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.397723 + 1.48432i) q^{2} +(-0.503519 - 0.872121i) q^{3} +(53.3806 + 30.8193i) q^{4} +(84.5480 + 84.5480i) q^{5} +(1.49477 - 0.400522i) q^{6} +(41.0022 + 153.022i) q^{7} +(-136.519 + 136.519i) q^{8} +(363.993 - 630.454i) q^{9} +O(q^{10})$	\(q+(-0.397723 + 1.48432i) q^{2} +(-0.503519 - 0.872121i) q^{3} +(53.3806 + 30.8193i) q^{4} +(84.5480 + 84.5480i) q^{5} +(1.49477 - 0.400522i) q^{6} +(41.0022 + 153.022i) q^{7} +(-136.519 + 136.519i) q^{8} +(363.993 - 630.454i) q^{9} +(-159.123 + 91.8697i) q^{10} +(-1010.62 - 270.795i) q^{11} -62.0725i q^{12} +(-1383.55 - 1706.63i) q^{13} -243.442 q^{14} +(31.1645 - 116.308i) q^{15} +(1824.09 + 3159.42i) q^{16} +(-1495.03 - 863.153i) q^{17} +(791.028 + 791.028i) q^{18} +(6576.65 - 1762.21i) q^{19} +(1907.51 + 7118.93i) q^{20} +(112.809 - 112.809i) q^{21} +(803.894 - 1392.38i) q^{22} +(-3373.09 + 1947.46i) q^{23} +(187.801 + 50.3210i) q^{24} -1328.27i q^{25} +(3083.46 - 1374.87i) q^{26} -1467.24 q^{27} +(-2527.32 + 9432.09i) q^{28} +(-17563.9 - 30421.6i) q^{29} +(160.243 + 92.5164i) q^{30} +(-12140.0 - 12140.0i) q^{31} +(-17350.3 + 4649.00i) q^{32} +(272.701 + 1017.73i) q^{33} +(1875.80 - 1875.80i) q^{34} +(-9471.08 + 16404.4i) q^{35} +(38860.3 - 22436.0i) q^{36} +(55534.6 + 14880.5i) q^{37} +10462.7i q^{38} +(-791.747 + 2065.95i) q^{39} -23084.8 q^{40} +(-19534.1 + 72902.3i) q^{41} +(122.578 + 212.311i) q^{42} +(56257.3 + 32480.2i) q^{43} +(-45601.9 - 45601.9i) q^{44} +(84078.5 - 22528.8i) q^{45} +(-1549.09 - 5781.30i) q^{46} +(-64283.9 + 64283.9i) q^{47} +(1836.93 - 3181.66i) q^{48} +(80152.3 - 46276.0i) q^{49} +(1971.58 + 528.282i) q^{50} +1738.46i q^{51} +(-21257.5 - 133741. i) q^{52} -272670. q^{53} +(583.555 - 2177.86i) q^{54} +(-62550.8 - 108341. i) q^{55} +(-26488.0 - 15292.9i) q^{56} +(-4848.33 - 4848.33i) q^{57} +(52141.0 - 13971.2i) q^{58} +(74113.8 + 276596. i) q^{59} +(5248.10 - 5248.10i) q^{60} +(98976.0 - 171431. i) q^{61} +(22848.1 - 13191.3i) q^{62} +(111398. + 29849.1i) q^{63} +205882. i q^{64} +(27316.1 - 261269. i) q^{65} -1619.10 q^{66} +(-149296. + 557182. i) q^{67} +(-53203.6 - 92151.3i) q^{68} +(3396.84 + 1961.16i) q^{69} +(-20582.5 - 20582.5i) q^{70} +(366966. - 98328.2i) q^{71} +(36376.9 + 135761. i) q^{72} +(188403. - 188403. i) q^{73} +(-44174.7 + 76512.9i) q^{74} +(-1158.41 + 668.809i) q^{75} +(405376. + 108620. i) q^{76} -165751. i q^{77} +(-2751.63 - 1996.88i) q^{78} -716299. q^{79} +(-112899. + 421347. i) q^{80} +(-264612. - 458322. i) q^{81} +(-100441. - 57989.8i) q^{82} +(-406773. - 406773. i) q^{83} +(9498.48 - 2545.11i) q^{84} +(-53423.5 - 199379. i) q^{85} +(-70585.8 + 70585.8i) q^{86} +(-17687.6 + 30635.8i) q^{87} +(174937. - 101000. i) q^{88} +(270869. + 72579.1i) q^{89} +133760. i q^{90} +(204425. - 281690. i) q^{91} -240077. q^{92} +(-4474.84 + 16700.3i) q^{93} +(-69850.7 - 120985. i) q^{94} +(705034. + 407052. i) q^{95} +(12790.7 + 12790.7i) q^{96} +(-254823. + 68279.7i) q^{97} +(36810.0 + 137377. i) q^{98} +(-538583. + 538583. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} - 2 q^{3} - 6 q^{4} - 114 q^{5} + 634 q^{6} + 316 q^{7} - 1398 q^{8} - 1946 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 - 2 * q^3 - 6 * q^4 - 114 * q^5 + 634 * q^6 + 316 * q^7 - 1398 * q^8 - 1946 * q^9	\( 24 q - 12 q^{2} - 2 q^{3} - 6 q^{4} - 114 q^{5} + 634 q^{6} + 316 q^{7} - 1398 q^{8} - 1946 q^{9} + 4674 q^{10} + 228 q^{11} - 1552 q^{13} - 14616 q^{14} + 7486 q^{15} - 2138 q^{16} + 20898 q^{17} - 5630 q^{18} - 14036 q^{19} - 14634 q^{20} - 314 q^{21} + 37852 q^{22} + 29634 q^{23} + 47154 q^{24} + 510 q^{26} - 107060 q^{27} - 40572 q^{28} + 1026 q^{29} - 247734 q^{30} - 118116 q^{31} + 180876 q^{32} + 306046 q^{33} + 101898 q^{34} + 104862 q^{35} + 105066 q^{36} - 31470 q^{37} + 28510 q^{39} - 275328 q^{40} - 357216 q^{41} - 25636 q^{42} - 480486 q^{43} - 797712 q^{44} + 464248 q^{45} + 1012050 q^{46} + 140028 q^{47} + 676102 q^{48} + 854562 q^{49} + 756714 q^{50} - 771704 q^{52} - 1397076 q^{53} - 1271048 q^{54} - 205490 q^{55} - 1461108 q^{56} - 1483394 q^{57} + 1133806 q^{58} + 1568052 q^{59} + 886808 q^{60} + 768676 q^{61} + 3741966 q^{62} + 1336264 q^{63} - 946968 q^{65} - 5076928 q^{66} - 1489892 q^{67} - 569052 q^{68} - 1475766 q^{69} - 2626556 q^{70} + 2136948 q^{71} + 4787052 q^{72} + 326326 q^{73} + 2159718 q^{74} + 3466008 q^{75} + 1522158 q^{76} - 1573544 q^{78} - 1734344 q^{79} - 5214300 q^{80} - 773072 q^{81} - 3540426 q^{82} - 3642132 q^{83} + 2952364 q^{84} + 3509916 q^{85} - 132324 q^{86} + 531698 q^{87} + 4478052 q^{88} + 632754 q^{89} - 2946788 q^{91} - 1656060 q^{92} - 295514 q^{93} + 1552210 q^{94} - 2753718 q^{95} - 3979208 q^{96} + 2258214 q^{97} + 4984308 q^{98} + 4336480 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 - 2 * q^3 - 6 * q^4 - 114 * q^5 + 634 * q^6 + 316 * q^7 - 1398 * q^8 - 1946 * q^9 + 4674 * q^10 + 228 * q^11 - 1552 * q^13 - 14616 * q^14 + 7486 * q^15 - 2138 * q^16 + 20898 * q^17 - 5630 * q^18 - 14036 * q^19 - 14634 * q^20 - 314 * q^21 + 37852 * q^22 + 29634 * q^23 + 47154 * q^24 + 510 * q^26 - 107060 * q^27 - 40572 * q^28 + 1026 * q^29 - 247734 * q^30 - 118116 * q^31 + 180876 * q^32 + 306046 * q^33 + 101898 * q^34 + 104862 * q^35 + 105066 * q^36 - 31470 * q^37 + 28510 * q^39 - 275328 * q^40 - 357216 * q^41 - 25636 * q^42 - 480486 * q^43 - 797712 * q^44 + 464248 * q^45 + 1012050 * q^46 + 140028 * q^47 + 676102 * q^48 + 854562 * q^49 + 756714 * q^50 - 771704 * q^52 - 1397076 * q^53 - 1271048 * q^54 - 205490 * q^55 - 1461108 * q^56 - 1483394 * q^57 + 1133806 * q^58 + 1568052 * q^59 + 886808 * q^60 + 768676 * q^61 + 3741966 * q^62 + 1336264 * q^63 - 946968 * q^65 - 5076928 * q^66 - 1489892 * q^67 - 569052 * q^68 - 1475766 * q^69 - 2626556 * q^70 + 2136948 * q^71 + 4787052 * q^72 + 326326 * q^73 + 2159718 * q^74 + 3466008 * q^75 + 1522158 * q^76 - 1573544 * q^78 - 1734344 * q^79 - 5214300 * q^80 - 773072 * q^81 - 3540426 * q^82 - 3642132 * q^83 + 2952364 * q^84 + 3509916 * q^85 - 132324 * q^86 + 531698 * q^87 + 4478052 * q^88 + 632754 * q^89 - 2946788 * q^91 - 1656060 * q^92 - 295514 * q^93 + 1552210 * q^94 - 2753718 * q^95 - 3979208 * q^96 + 2258214 * q^97 + 4984308 * q^98 + 4336480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.397723	+	1.48432i	−0.0497153	+	0.185540i	−0.986318	−	0.164853i	$-0.947285\pi$
$2$	−0.397723	+	1.48432i	−0.0497153	+	0.185540i	0.936603	+	0.350393i	$0.113952\pi$
$3$	−0.503519	−	0.872121i	−0.0186489	−	0.0323008i	0.856550	−	0.516063i	$-0.172603\pi$
$3$	−0.503519	−	0.872121i	−0.0186489	−	0.0323008i	−0.875199	+	0.483763i	$0.839270\pi$
$4$	53.3806	+	30.8193i	0.834072	+	0.481552i
$5$	84.5480	+	84.5480i	0.676384	+	0.676384i	0.959180	−	0.282796i	$-0.0912619\pi$
$5$	84.5480	+	84.5480i	0.676384	+	0.676384i	−0.282796	+	0.959180i	$0.591262\pi$
$6$	1.49477	−	0.400522i	0.00692023	−	0.00185427i
$7$	41.0022	+	153.022i	0.119540	+	0.446130i	0.999586	−	0.0287583i	$-0.00915530\pi$
$7$	41.0022	+	153.022i	0.119540	+	0.446130i	−0.880046	+	0.474888i	$0.842489\pi$
$8$	−136.519	+	136.519i	−0.266638	+	0.266638i
$9$	363.993	−	630.454i	0.499304	−	0.864821i
$10$	−159.123	+	91.8697i	−0.159123	+	0.0918697i
$11$	−1010.62	−	270.795i	−0.759295	−	0.203452i	−0.141658	−	0.989916i	$-0.545243\pi$
$11$	−1010.62	−	270.795i	−0.759295	−	0.203452i	−0.617637	+	0.786463i	$0.711910\pi$
$12$		−	62.0725i		−	0.0359216i
$13$	−1383.55	−	1706.63i	−0.629745	−	0.776802i
$13$	−1383.55	−	1706.63i	−0.629745	−	0.776802i
$14$	−243.442			−0.0887179
$15$	31.1645	−	116.308i	0.00923394	−	0.0344615i
$16$	1824.09	+	3159.42i	0.445336	+	0.771344i
$17$	−1495.03	−	863.153i	−0.304300	−	0.175688i	0.340073	−	0.940399i	$-0.389548\pi$
$17$	−1495.03	−	863.153i	−0.304300	−	0.175688i	−0.644373	+	0.764711i	$0.722882\pi$
$18$	791.028	+	791.028i	0.135636	+	0.135636i
$19$	6576.65	−	1762.21i	0.958835	−	0.256919i	0.254728	−	0.967013i	$-0.418014\pi$
$19$	6576.65	−	1762.21i	0.958835	−	0.256919i	0.704107	+	0.710094i	$0.251347\pi$
$20$	1907.51	+	7118.93i	0.238439	+	0.889867i
$21$	112.809	−	112.809i	0.0121810	−	0.0121810i
$22$	803.894	−	1392.38i	0.0754972	−	0.130765i
$23$	−3373.09	+	1947.46i	−0.277233	+	0.160061i	−0.632170	−	0.774830i	$-0.717836\pi$
$23$	−3373.09	+	1947.46i	−0.277233	+	0.160061i	0.354937	+	0.934890i	$0.384502\pi$
$24$	187.801	+	50.3210i	0.0135851	+	0.00364012i
$25$		−	1328.27i		−	0.0850092i
$26$	3083.46	−	1374.87i	0.175436	−	0.0782240i
$27$	−1467.24			−0.0745436
$28$	−2527.32	+	9432.09i	−0.115129	+	0.429669i
$29$	−17563.9	−	30421.6i	−0.720158	−	1.24735i	−0.960936	−	0.276770i	$-0.910736\pi$
$29$	−17563.9	−	30421.6i	−0.720158	−	1.24735i	0.240778	−	0.970580i	$-0.422598\pi$
$30$	160.243	+	92.5164i	0.00593493	+	0.00342653i
$31$	−12140.0	−	12140.0i	−0.407507	−	0.407507i	0.473361	−	0.880868i	$-0.343041\pi$
$31$	−12140.0	−	12140.0i	−0.407507	−	0.407507i	−0.880868	+	0.473361i	$0.843041\pi$
$32$	−17350.3	+	4649.00i	−0.529490	+	0.141876i
$33$	272.701	+	1017.73i	0.00758831	+	0.0283200i
$34$	1875.80	−	1875.80i	0.0477255	−	0.0477255i
$35$	−9471.08	+	16404.4i	−0.220900	+	0.382610i
$36$	38860.3	−	22436.0i	0.832912	−	0.480882i
$37$	55534.6	+	14880.5i	1.09637	+	0.293773i	0.761287	−	0.648415i	$-0.224568\pi$
$37$	55534.6	+	14880.5i	1.09637	+	0.293773i	0.335087	+	0.942187i	$0.391234\pi$
$38$			10462.7i			0.190675i
$39$	−791.747	+	2065.95i	−0.0133473	+	0.0348277i
$40$	−23084.8			−0.360699
$41$	−19534.1	+	72902.3i	−0.283428	+	1.05777i	0.666553	+	0.745458i	$0.267769\pi$
$41$	−19534.1	+	72902.3i	−0.283428	+	1.05777i	−0.949981	+	0.312309i	$0.898898\pi$
$42$	122.578	+	212.311i	0.00165449	+	0.00286566i
$43$	56257.3	+	32480.2i	0.707577	+	0.408520i	0.810163	−	0.586204i	$-0.199378\pi$
$43$	56257.3	+	32480.2i	0.707577	+	0.408520i	−0.102586	+	0.994724i	$0.532712\pi$
$44$	−45601.9	−	45601.9i	−0.535334	−	0.535334i
$45$	84078.5	−	22528.8i	0.922672	−	0.247229i
$46$	−1549.09	−	5781.30i	−0.0159149	−	0.0593953i
$47$	−64283.9	+	64283.9i	−0.619168	+	0.619168i	−0.945318	−	0.326150i	$-0.894248\pi$
$47$	−64283.9	+	64283.9i	−0.619168	+	0.619168i	0.326150	+	0.945318i	$0.394248\pi$
$48$	1836.93	−	3181.66i	0.0166100	−	0.0287694i
$49$	80152.3	−	46276.0i	0.681284	−	0.393339i
$50$	1971.58	+	528.282i	0.0157726	+	0.00422626i
$51$			1738.46i			0.0131055i
$52$	−21257.5	−	133741.i	−0.151183	−	0.951163i
$53$	−272670.			−1.83151			−0.915756	−	0.401735i	$-0.868407\pi$
$53$	−272670.			−1.83151			−0.915756	+	0.401735i	$0.868407\pi$
$54$	583.555	−	2177.86i	0.00370596	−	0.0138308i
$55$	−62550.8	−	108341.i	−0.375963	−	0.651187i
$56$	−26488.0	−	15292.9i	−0.150829	−	0.0870812i
$57$	−4848.33	−	4848.33i	−0.0261799	−	0.0261799i
$58$	52141.0	−	13971.2i	0.267236	−	0.0716058i
$59$	74113.8	+	276596.i	0.360863	+	1.34676i	0.872943	+	0.487822i	$0.162209\pi$
$59$	74113.8	+	276596.i	0.360863	+	1.34676i	−0.512080	+	0.858938i	$0.671125\pi$
$60$	5248.10	−	5248.10i	0.0242968	−	0.0242968i
$61$	98976.0	−	171431.i	0.436054	−	0.755268i	−0.561327	−	0.827594i	$-0.689709\pi$
$61$	98976.0	−	171431.i	0.436054	−	0.755268i	0.997381	+	0.0723264i	$0.0230423\pi$
$62$	22848.1	−	13191.3i	0.0958682	−	0.0553496i
$63$	111398.	+	29849.1i	0.445509	+	0.119374i
$64$			205882.i			0.785376i
$65$	27316.1	−	261269.i	0.0994668	−	0.951366i
$66$	−1619.10			−0.00563175
$67$	−149296.	+	557182.i	−0.496392	+	1.85256i	0.0256948	+	0.999670i	$0.491820\pi$
$67$	−149296.	+	557182.i	−0.496392	+	1.85256i	−0.522087	+	0.852892i	$0.674846\pi$
$68$	−53203.6	−	92151.3i	−0.169205	−	0.293072i
$69$	3396.84	+	1961.16i	0.0103402	+	0.00596990i
$70$	−20582.5	−	20582.5i	−0.0600074	−	0.0600074i
$71$	366966.	−	98328.2i	1.02530	−	0.274728i	0.293290	−	0.956023i	$-0.405250\pi$
$71$	366966.	−	98328.2i	1.02530	−	0.274728i	0.732009	+	0.681295i	$0.238583\pi$
$72$	36376.9	+	135761.i	0.0974605	+	0.363728i
$73$	188403.	−	188403.i	0.484306	−	0.484306i	−0.422197	−	0.906504i	$-0.638741\pi$
$73$	188403.	−	188403.i	0.484306	−	0.484306i	0.906504	+	0.422197i	$0.138741\pi$
$74$	−44174.7	+	76512.9i	−0.109013	+	0.188816i
$75$	−1158.41	+	668.809i	−0.00274586	+	0.00158532i
$76$	405376.	+	108620.i	0.923457	+	0.247440i
$77$		−	165751.i		−	0.363065i
$78$	−2751.63	−	1996.88i	−0.00579838	−	0.00420793i
$79$	−716299.			−1.45282			−0.726412	−	0.687260i	$-0.758813\pi$
$79$	−716299.			−1.45282			−0.726412	+	0.687260i	$0.758813\pi$
$80$	−112899.	+	421347.i	−0.220507	+	0.822943i
$81$	−264612.	−	458322.i	−0.497914	−	0.862413i
$82$	−100441.	−	57989.8i	−0.182167	−	0.105174i
$83$	−406773.	−	406773.i	−0.711406	−	0.711406i	0.255423	−	0.966829i	$-0.417785\pi$
$83$	−406773.	−	406773.i	−0.711406	−	0.711406i	−0.966829	+	0.255423i	$0.917785\pi$
$84$	9498.48	−	2545.11i	0.0160257	−	0.00429407i
$85$	−53423.5	−	199379.i	−0.0869913	−	0.324656i
$86$	−70585.8	+	70585.8i	−0.110974	+	0.110974i
$87$	−17687.6	+	30635.8i	−0.0268603	+	0.0465234i
$88$	174937.	−	101000.i	0.256705	−	0.148209i
$89$	270869.	+	72579.1i	0.384228	+	0.102954i	0.445762	−	0.895151i	$-0.352933\pi$
$89$	270869.	+	72579.1i	0.384228	+	0.102954i	−0.0615341	+	0.998105i	$0.519599\pi$
$90$			133760.i			0.183484i
$91$	204425.	−	281690.i	0.271274	−	0.373807i
$92$	−240077.			−0.308310
$93$	−4474.84	+	16700.3i	−0.00556325	+	0.0207623i
$94$	−69850.7	−	120985.i	−0.0840983	−	0.145663i
$95$	705034.	+	407052.i	0.822317	+	0.474765i
$96$	12790.7	+	12790.7i	0.0144571	+	0.0144571i
$97$	−254823.	+	68279.7i	−0.279206	+	0.0748129i	−0.395704	−	0.918378i	$-0.629500\pi$
$97$	−254823.	+	68279.7i	−0.279206	+	0.0748129i	0.116499	+	0.993191i	$0.462833\pi$
$98$	36810.0	+	137377.i	0.0391100	+	0.145960i
$99$	−538583.	+	538583.i	−0.555069	+	0.555069i
$100$	40936.3	−	70903.8i	0.0409363	−	0.0709038i
$101$	1.06736e6	−	616242.i	1.03597	−	0.598118i	0.117282	−	0.993099i	$-0.462582\pi$
$101$	1.06736e6	−	616242.i	1.03597	−	0.598118i	0.918690	+	0.394980i	$0.129249\pi$
$102$	−2580.43	−	691.424i	−0.00243160	−	0.000651544i
$103$			1.27482e6i			1.16664i	0.812243	+	0.583319i	$0.198246\pi$
$103$			1.27482e6i			1.16664i	−0.812243	+	0.583319i	$0.801754\pi$
$104$	421868.	+	44106.9i	0.375039	+	0.0392109i
$105$	19075.5			0.0164781
$106$	108447.	−	404730.i	0.0910542	−	0.339819i
$107$	312612.	+	541461.i	0.255185	+	0.441993i	0.964946	−	0.262450i	$-0.0845303\pi$
$107$	312612.	+	541461.i	0.255185	+	0.441993i	−0.709761	+	0.704443i	$0.751197\pi$
$108$	−78322.2	−	45219.4i	−0.0621747	−	0.0358966i
$109$	205640.	+	205640.i	0.158792	+	0.158792i	0.782031	−	0.623239i	$-0.214184\pi$
$109$	205640.	+	205640.i	0.158792	+	0.158792i	−0.623239	+	0.782031i	$0.714184\pi$
$110$	185691.	−	49755.7i	0.139512	−	0.0373822i
$111$	−14985.2	−	55925.5i	−0.0109570	−	0.0408923i
$112$	−408671.	+	408671.i	−0.290884	+	0.290884i
$113$	40925.7	−	70885.4i	0.0283636	−	0.0491271i	−0.851495	−	0.524362i	$-0.824304\pi$
$113$	40925.7	−	70885.4i	0.0283636	−	0.0491271i	0.879859	+	0.475235i	$0.157637\pi$
$114$	9124.77	−	5268.19i	0.00615896	−	0.00355588i
$115$	−449842.	−	120535.i	−0.295778	−	0.0792536i
$116$		−	2.16523e6i		−	1.38717i
$117$	−1.57956e6	+	251062.i	−0.986229	+	0.156756i
$118$	−440034.			−0.267818
$119$	70782.5	−	264164.i	0.0420034	−	0.156759i
$120$	11623.6	+	20132.7i	0.00672664	+	0.0116509i
$121$	−586191.	−	338438.i	−0.330890	−	0.191039i
$122$	215094.	+	215094.i	0.118454	+	0.118454i
$123$	73415.5	−	19671.6i	0.0394523	−	0.0105712i
$124$	−273895.	−	1.02219e6i	−0.143654	−	0.536126i
$125$	1.43337e6	−	1.43337e6i	0.733883	−	0.733883i
$126$	−88611.1	+	153479.i	−0.0442972	+	0.0767251i
$127$	−2.65501e6	+	1.53287e6i	−1.29615	+	0.748332i	−0.979737	−	0.200290i	$-0.935812\pi$
$127$	−2.65501e6	+	1.53287e6i	−1.29615	+	0.748332i	−0.316412	+	0.948622i	$0.602478\pi$
$128$	−1.41601e6	−	379420.i	−0.675208	−	0.180922i
$129$		−	65417.6i		−	0.0304737i
$130$	376943.	+	144458.i	0.171572	+	0.0657525i
$131$	3.63996e6			1.61913			0.809567	−	0.587028i	$-0.199702\pi$
$131$	3.63996e6			1.61913			0.809567	+	0.587028i	$0.199702\pi$
$132$	−16808.9	+	62731.8i	−0.00730833	+	0.0272751i
$133$	539315.	+	934121.i	0.229238	+	0.397053i
$134$	−767658.	−	443208.i	−0.319046	−	0.184201i
$135$	−124052.	−	124052.i	−0.0504201	−	0.0504201i
$136$	321936.	−	86262.4i	0.127983	−	0.0342929i
$137$	640244.	+	2.38942e6i	0.248991	+	0.929247i	0.971335	+	0.237714i	$0.0763980\pi$
$137$	640244.	+	2.38942e6i	0.248991	+	0.929247i	−0.722344	+	0.691534i	$0.756935\pi$
$138$	−4262.00	+	4262.00i	−0.00162172	+	0.00162172i
$139$	−22648.9	+	39229.0i	−0.00843339	+	0.0146071i	−0.870211	−	0.492679i	$-0.836018\pi$
$139$	−22648.9	+	39229.0i	−0.00843339	+	0.0146071i	0.861778	+	0.507286i	$0.169351\pi$
$140$	−1.01114e6	+	583784.i	−0.368493	+	0.212749i
$141$	88431.5	+	23695.1i	0.0315464	+	0.00845283i
$142$			583802.i			0.203892i
$143$	936097.	+	2.09942e6i	0.320120	+	0.717945i
$144$	2.65583e6			0.889432
$145$	1.08709e6	−	4.05709e6i	0.356585	−	1.33079i
$146$	204719.	+	354583.i	0.0657808	+	0.113936i
$147$	−80716.5	−	46601.7i	−0.0254103	−	0.0146707i
$148$	2.50587e6	+	2.50587e6i	0.772988	+	0.772988i
$149$	−4.59923e6	+	1.23236e6i	−1.39036	+	0.372545i	−0.874872	−	0.484354i	$-0.839055\pi$
$149$	−4.59923e6	+	1.23236e6i	−1.39036	+	0.372545i	−0.515485	+	0.856899i	$0.672388\pi$
$150$	−532.001	−	1985.45i	−0.000157630	−	0.000588283i
$151$	1.85287e6	−	1.85287e6i	0.538163	−	0.538163i	−0.384826	−	0.922989i	$-0.625739\pi$
$151$	1.85287e6	−	1.85287e6i	0.538163	−	0.538163i	0.922989	+	0.384826i	$0.125739\pi$
$152$	−657261.	+	1.13841e6i	−0.187158	+	0.324166i
$153$	−1.08836e6	+	628364.i	−0.303877	+	0.175443i
$154$	246028.	+	65922.9i	0.0673630	+	0.0180499i
$155$		−	2.05283e6i		−	0.551263i
$156$	−105935.	+	85880.4i	−0.0279039	+	0.0226214i
$157$	1.39574e6			0.360665			0.180333	−	0.983606i	$-0.442283\pi$
$157$	1.39574e6			0.360665			0.180333	+	0.983606i	$0.442283\pi$
$158$	284888.	−	1.06322e6i	0.0722276	−	0.269557i
$159$	137295.	+	237801.i	0.0341556	+	0.0591593i
$160$	−1.86000e6	−	1.07387e6i	−0.454101	−	0.262175i
$161$	−436309.	−	436309.i	−0.104548	−	0.104548i
$162$	785538.	−	210484.i	0.184766	−	0.0495079i
$163$	−1.72601e6	−	6.44157e6i	−0.398548	−	1.48740i	−0.815651	−	0.578544i	$-0.803621\pi$
$163$	−1.72601e6	−	6.44157e6i	−0.398548	−	1.48740i	0.417103	−	0.908859i	$-0.363045\pi$
$164$	−3.28954e6	+	3.28954e6i	−0.745768	+	0.745768i
$165$	−62991.1	+	109104.i	−0.0140226	+	0.0242878i
$166$	765564.	−	441998.i	0.167362	−	0.0966266i
$167$	−8.35095e6	−	2.23763e6i	−1.79302	−	0.480440i	−0.800171	−	0.599773i	$-0.795258\pi$
$167$	−8.35095e6	−	2.23763e6i	−1.79302	−	0.480440i	−0.992854	+	0.119333i	$0.961924\pi$
$168$			30801.0i			0.00649586i
$169$	−998387.	+	4.72243e6i	−0.206842	+	0.978374i
$170$	317191.			0.0645615
$171$	1.28286e6	−	4.78771e6i	0.256562	−	0.957501i
$172$	2.00203e6	+	3.46762e6i	0.393447	+	0.681470i
$173$	2.56885e6	+	1.48313e6i	0.496135	+	0.286444i	0.727116	−	0.686514i	$-0.240860\pi$
$173$	2.56885e6	+	1.48313e6i	0.496135	+	0.286444i	−0.230981	+	0.972958i	$0.574193\pi$
$174$	−38438.6	−	38438.6i	−0.00729658	−	0.00729658i
$175$	203255.	−	54462.0i	0.0379251	−	0.0101620i
$176$	−987912.	−	3.68694e6i	−0.181209	−	0.676282i
$177$	203908.	−	203908.i	0.0367717	−	0.0367717i
$178$	−215461.	+	373190.i	−0.0382041	+	0.0661714i
$179$	2.29060e6	−	1.32248e6i	0.399384	−	0.230584i	−0.286834	−	0.957980i	$-0.592603\pi$
$179$	2.29060e6	−	1.32248e6i	0.399384	−	0.230584i	0.686218	+	0.727396i	$0.259270\pi$
$180$	5.18248e6	+	1.38864e6i	0.888629	+	0.238107i
$181$			1.21255e6i			0.204486i	0.994759	+	0.102243i	$0.0326019\pi$
$181$			1.21255e6i			0.204486i	−0.994759	+	0.102243i	$0.967398\pi$
$182$	336814.	+	415466.i	0.0558697	+	0.0689162i
$183$	−199345.			−0.0325277
$184$	194626.	−	726355.i	0.0312426	−	0.116599i
$185$	3.43723e6	+	5.95346e6i	0.542867	+	0.940273i
$186$	−23008.9	−	13284.2i	−0.00357567	−	0.00206441i
$187$	1.27717e6	+	1.27717e6i	0.195309	+	0.195309i
$188$	−5.41269e6	+	1.45033e6i	−0.814592	+	0.218269i
$189$	−60160.2	−	224521.i	−0.00891094	−	0.0332561i
$190$	−884603.	+	884603.i	−0.128970	+	0.128970i
$191$	503963.	−	872890.i	0.0723267	−	0.125274i	−0.827594	−	0.561327i	$-0.810291\pi$
$191$	503963.	−	872890.i	0.0723267	−	0.125274i	0.899921	+	0.436054i	$0.143624\pi$
$192$	179554.	−	103665.i	0.0253683	−	0.0146464i
$193$	199106.	+	53350.3i	0.0276957	+	0.00742104i	0.272640	−	0.962116i	$-0.412103\pi$
$193$	199106.	+	53350.3i	0.0276957	+	0.00742104i	−0.244945	+	0.969537i	$0.578770\pi$
$194$		−	405396.i		−	0.0555232i
$195$	−241612.	+	107731.i	−0.0325848	+	0.0145290i
$196$	5.70477e6			0.757653
$197$	−361964.	+	1.35087e6i	−0.0473442	+	0.176691i	−0.985549	−	0.169389i	$-0.945821\pi$
$197$	−361964.	+	1.35087e6i	−0.0473442	+	0.176691i	0.938205	+	0.346080i	$0.112487\pi$
$198$	−585223.	−	1.01364e6i	−0.0753921	−	0.130583i
$199$	7.29852e6	+	4.21380e6i	0.926138	+	0.534706i	0.885588	−	0.464472i	$-0.153756\pi$
$199$	7.29852e6	+	4.21380e6i	0.926138	+	0.534706i	0.0405496	+	0.999178i	$0.487089\pi$
$200$	181333.	+	181333.i	0.0226667	+	0.0226667i
$201$	561104.	−	150347.i	0.0690964	−	0.0185143i
$202$	490187.	+	1.82940e6i	0.0594713	+	0.221950i
$203$	3.93503e6	−	3.93503e6i	0.470392	−	0.470392i
$204$	−53578.1	+	92799.9i	−0.00631098	+	0.0109309i
$205$	−7.81532e6	+	4.51218e6i	−0.907162	+	0.523750i
$206$	−1.89224e6	−	507023.i	−0.216458	−	0.0579998i
$207$			2.83544e6i			0.319676i
$208$	2.86825e6	−	7.48428e6i	0.318733	−	0.831688i
$209$	−7.12370e6			−0.780309
$210$	−7586.76	+	28314.2i	−0.000819216	+	0.00305735i
$211$	−6.18071e6	−	1.07053e7i	−0.657947	−	1.13960i	−0.981146	−	0.193266i	$-0.938092\pi$
$211$	−6.18071e6	−	1.07053e7i	−0.657947	−	1.13960i	0.323200	−	0.946331i	$-0.395241\pi$
$212$	−1.45553e7	−	8.40350e6i	−1.52761	−	0.881967i
$213$	−270529.	−	270529.i	−0.0279946	−	0.0279946i
$214$	−928034.	+	248666.i	−0.0946940	+	0.0253732i
$215$	2.01031e6	+	7.50258e6i	0.202277	+	0.754910i
$216$	200306.	−	200306.i	0.0198762	−	0.0198762i
$217$	1.35993e6	−	2.35547e6i	0.133088	−	0.230514i
$218$	−387023.	+	223448.i	−0.0373566	+	0.0215678i
$219$	−259175.	−	69445.8i	−0.0246752	−	0.00661171i
$220$		−	7.71109e6i		−	0.724182i
$221$	595356.	+	3.74568e6i	0.0551569	+	0.347019i
$222$	88971.4			0.00813189
$223$	−1.45822e6	+	5.44215e6i	−0.131495	+	0.490745i	−0.999988	−	0.00495630i	$-0.998422\pi$
$223$	−1.45822e6	+	5.44215e6i	−0.131495	+	0.490745i	0.868493	+	0.495702i	$0.165089\pi$
$224$	−1.42280e6	−	2.46437e6i	−0.126590	−	0.219261i
$225$	−837412.	−	483480.i	−0.0735177	−	0.0424455i
$226$	88939.6	+	88939.6i	0.00770495	+	0.00770495i
$227$	1.73975e7	−	4.66164e6i	1.48733	−	0.398530i	0.578499	−	0.815683i	$-0.303639\pi$
$227$	1.73975e7	−	4.66164e6i	1.48733	−	0.398530i	0.908836	+	0.417153i	$0.136972\pi$
$228$	−109385.	−	408229.i	−0.00922894	−	0.0344429i
$229$	2.46115e6	−	2.46115e6i	0.204942	−	0.204942i	−0.597171	−	0.802114i	$-0.703709\pi$
$229$	2.46115e6	−	2.46115e6i	0.204942	−	0.204942i	0.802114	+	0.597171i	$0.203709\pi$
$230$	357825.	−	619770.i	0.0294094	−	0.0509386i
$231$	−144555.	+	83458.8i	−0.0117273	+	0.00677074i
$232$	6.55093e6	+	1.75532e6i	0.524613	+	0.140570i
$233$			7.92328e6i			0.626379i	0.949691	+	0.313189i	$0.101397\pi$
$233$			7.92328e6i			0.626379i	−0.949691	+	0.313189i	$0.898603\pi$
$234$	255568.	−	2.44442e6i	0.0199462	−	0.190778i
$235$	−1.08701e7			−0.837590
$236$	−4.56827e6	+	1.70490e7i	−0.347549	+	1.29707i
$237$	360670.	+	624699.i	0.0270935	+	0.0469273i
$238$	363952.	+	210128.i	0.0269969	+	0.0155866i
$239$	−4.71743e6	−	4.71743e6i	−0.345551	−	0.345551i	0.512898	−	0.858449i	$-0.328572\pi$
$239$	−4.71743e6	−	4.71743e6i	−0.345551	−	0.345551i	−0.858449	+	0.512898i	$0.828572\pi$
$240$	424312.	−	113694.i	0.0306939	−	0.00822440i
$241$	3.92690e6	+	1.46554e7i	0.280542	+	1.04700i	0.952036	+	0.305987i	$0.0989865\pi$
$241$	3.92690e6	+	1.46554e7i	0.280542	+	1.04700i	−0.671493	+	0.741010i	$0.734347\pi$
$242$	735492.	−	735492.i	0.0518957	−	0.0518957i
$243$	−801284.	+	1.38786e6i	−0.0558429	+	0.0967227i
$244$	1.05668e7	−	6.10074e6i	0.727401	−	0.419965i
$245$	1.06893e7	+	2.86418e6i	0.726858	+	0.194761i
$246$			116796.i			0.00784553i
$247$	−1.21066e7	−	8.78583e6i	−0.803397	−	0.583031i
$248$	3.31469e6			0.217314
$249$	−149937.	+	559573.i	−0.00971206	+	0.0362459i
$250$	1.55749e6	+	2.69766e6i	0.0996795	+	0.172650i
$251$	1.46092e7	+	8.43462e6i	0.923857	+	0.533389i	0.884864	−	0.465850i	$-0.154251\pi$
$251$	1.46092e7	+	8.43462e6i	0.923857	+	0.533389i	0.0389938	+	0.999239i	$0.487585\pi$
$252$	5.02657e6	+	5.02657e6i	0.314102	+	0.314102i
$253$	3.93628e6	−	1.05472e6i	0.243066	−	0.0651294i
$254$	−1.21931e6	−	4.55054e6i	−0.0744071	−	0.277691i
$255$	−146983.	+	146983.i	−0.00886435	+	0.00886435i
$256$	−5.46185e6	+	9.46020e6i	−0.325552	+	0.563872i
$257$	1.40648e7	−	8.12030e6i	0.828578	−	0.478380i	−0.0247877	−	0.999693i	$-0.507891\pi$
$257$	1.40648e7	−	8.12030e6i	0.828578	−	0.478380i	0.853365	+	0.521313i	$0.174558\pi$
$258$	97100.7	+	26018.0i	0.00565410	+	0.00151501i
$259$			9.10818e6i			0.524242i
$260$	9.51027e6	−	1.31048e7i	0.541094	−	0.745609i
$261$	−2.55726e7			−1.43831
$262$	−1.44769e6	+	5.40287e6i	−0.0804957	+	0.300414i
$263$	−8.94641e6	−	1.54956e7i	−0.491792	−	0.851809i	0.508163	−	0.861261i	$-0.330325\pi$
$263$	−8.94641e6	−	1.54956e7i	−0.491792	−	0.851809i	−0.999955	+	0.00945184i	$0.996991\pi$
$264$	−176169.	−	101711.i	−0.00957452	−	0.00552785i
$265$	−2.30537e7	−	2.30537e7i	−1.23881	−	1.23881i
$266$	−1.60103e6	+	428995.i	−0.0850658	+	0.0227933i
$267$	−73090.0	−	272776.i	−0.00383994	−	0.0143308i
$268$	−2.51415e7	+	2.51415e7i	−1.30613	+	1.30613i
$269$	1.39538e7	−	2.41688e7i	0.716864	−	1.24165i	−0.245372	−	0.969429i	$-0.578910\pi$
$269$	1.39538e7	−	2.41688e7i	0.716864	−	1.24165i	0.962236	−	0.272216i	$-0.0877566\pi$
$270$	233472.	−	134795.i	0.0118616	−	0.00684830i
$271$	−4.43066e6	−	1.18719e6i	−0.222618	−	0.0596503i	0.145786	−	0.989316i	$-0.453429\pi$
$271$	−4.43066e6	−	1.18719e6i	−0.222618	−	0.0596503i	−0.368404	+	0.929666i	$0.620096\pi$
$272$		−	6.29789e6i		−	0.312960i
$273$	−348600.	−	36446.6i	−0.0171332	−	0.00179130i
$274$	−3.80131e6			−0.184791
$275$	−359689.	+	1.34238e6i	−0.0172953	+	0.0645470i
$276$	120883.	+	209376.i	0.00574963	+	0.00995864i
$277$	1.19929e7	+	6.92409e6i	0.564266	+	0.325779i	0.754856	−	0.655891i	$-0.227707\pi$
$277$	1.19929e7	+	6.92409e6i	0.564266	+	0.325779i	−0.190590	+	0.981670i	$0.561040\pi$
$278$	−49220.5	−	49220.5i	−0.00229093	−	0.00229093i
$279$	−1.20726e7	+	3.23485e6i	−0.555891	+	0.148950i
$280$	−946527.	−	3.53249e6i	−0.0431180	−	0.160919i
$281$	−2.60746e6	+	2.60746e6i	−0.117517	+	0.117517i	−0.763419	−	0.645903i	$-0.776481\pi$
$281$	−2.60746e6	+	2.60746e6i	−0.117517	+	0.117517i	0.645903	+	0.763419i	$0.276481\pi$
$282$	−70342.4	+	121837.i	−0.00313668	+	0.00543288i
$283$	2.12903e7	−	1.22920e7i	0.939339	−	0.542328i	0.0495859	−	0.998770i	$-0.484210\pi$
$283$	2.12903e7	−	1.22920e7i	0.939339	−	0.542328i	0.889753	+	0.456442i	$0.150877\pi$
$284$	2.26193e7	+	6.06081e6i	0.987469	+	0.264591i
$285$		−	819833.i		−	0.0354153i
$286$	−3.48852e6	+	554482.i	−0.149122	+	0.0237022i
$287$	−1.19566e7			−0.505782
$288$	−3.38441e6	+	1.26308e7i	−0.141679	+	0.528753i
$289$	−1.05787e7	−	1.83229e7i	−0.438268	−	0.759102i
$290$	5.58965e6	+	3.22719e6i	0.229188	+	0.132321i
$291$	187857.	+	187857.i	0.00762338	+	0.00762338i
$292$	1.58636e7	−	4.25063e6i	0.637165	−	0.170728i
$293$	2.10986e6	+	7.87411e6i	0.0838786	+	0.313039i	0.995099	−	0.0988789i	$-0.0315256\pi$
$293$	2.10986e6	+	7.87411e6i	0.0838786	+	0.313039i	−0.911221	+	0.411918i	$0.864859\pi$
$294$	101275.	−	101275.i	0.00398528	−	0.00398528i
$295$	−1.71195e7	+	2.96518e7i	−0.666845	+	1.15501i
$296$	−9.61298e6	+	5.55005e6i	−0.370666	+	0.214004i
$297$	1.48283e6	+	397322.i	0.0566006	+	0.0151661i
$298$		−	7.31687e6i		−	0.276488i
$299$	7.99044e6	+	3.06223e6i	0.298921	+	0.114558i
$300$	−82448.9			−0.00305366
$301$	−2.66352e6	+	9.94039e6i	−0.0976689	+	0.364505i
$302$	2.01332e6	+	3.48718e6i	0.0730958	+	0.126606i
$303$	−1.07488e6	−	620580.i	−0.0386394	−	0.0223085i
$304$	1.75640e7	+	1.75640e7i	0.625176	+	0.625176i
$305$	2.28624e7	−	6.12596e6i	0.805791	−	0.215911i
$306$	−499829.	−	1.86539e6i	−0.0174444	−	0.0651035i
$307$	3.47630e7	−	3.47630e7i	1.20144	−	1.20144i	0.227712	−	0.973729i	$-0.426876\pi$
$307$	3.47630e7	−	3.47630e7i	1.20144	−	1.20144i	0.973729	−	0.227712i	$-0.0731244\pi$
$308$	5.10833e6	−	8.84789e6i	0.174834	−	0.302822i
$309$	1.11179e6	−	641895.i	0.0376833	−	0.0217565i
$310$	3.04706e6	+	816458.i	0.102281	+	0.0274062i
$311$			4.30507e7i			1.43119i	0.698513	+	0.715597i	$0.253845\pi$
$311$			4.30507e7i			1.43119i	−0.698513	+	0.715597i	$0.746155\pi$
$312$	−173952.	−	390129.i	−0.00572751	−	0.0128453i
$313$	1.32699e7			0.432748			0.216374	−	0.976311i	$-0.430577\pi$
$313$	1.32699e7			0.432748			0.216374	+	0.976311i	$0.430577\pi$
$314$	−555116.	+	2.07172e6i	−0.0179306	+	0.0669179i
$315$	6.89482e6	+	1.19422e7i	0.220593	+	0.382078i
$316$	−3.82365e7	−	2.20758e7i	−1.21176	−	0.699610i
$317$	−2.15384e7	−	2.15384e7i	−0.676139	−	0.676139i	0.282985	−	0.959124i	$-0.408675\pi$
$317$	−2.15384e7	−	2.15384e7i	−0.676139	−	0.676139i	−0.959124	+	0.282985i	$0.908675\pi$
$318$	−407578.	+	109210.i	−0.0126745	+	0.00339611i
$319$	9.51246e6	+	3.55010e7i	0.293036	+	1.09362i
$320$	−1.74069e7	+	1.74069e7i	−0.531216	+	0.531216i
$321$	314813.	−	545272.i	0.00951782	−	0.0164853i
$322$	821152.	−	474093.i	0.0245955	−	0.0142002i
$323$	−1.13533e7	−	3.04211e6i	−0.336911	−	0.0902751i
$324$		−	3.26206e7i		−	0.959086i
$325$	−2.26687e6	+	1.83773e6i	−0.0660353	+	0.0535341i
$326$	1.02478e7			0.295787
$327$	75799.2	−	282887.i	0.00216781	−	0.00809038i
$328$	−7.28576e6	−	1.26193e7i	−0.206468	−	0.357613i
$329$	−1.24727e7	−	7.20109e6i	−0.350244	−	0.202214i
$330$	−136892.	−	136892.i	−0.00380922	−	0.00380922i
$331$	−2.58957e7	+	6.93873e6i	−0.714075	+	0.191336i	−0.597526	−	0.801849i	$-0.703850\pi$
$331$	−2.58957e7	+	6.93873e6i	−0.714075	+	0.191336i	−0.116548	+	0.993185i	$0.537183\pi$
$332$	−9.17732e6	−	3.42502e7i	−0.250785	−	0.935942i
$333$	2.95957e7	−	2.95957e7i	0.801485	−	0.801485i
$334$	6.64272e6	−	1.15055e7i	0.178282	−	0.308793i
$335$	−5.97314e7	+	3.44859e7i	−1.58880	+	0.917291i
$336$	562184.	+	150637.i	0.0148204	+	0.00397112i
$337$		−	1.33912e7i		−	0.349888i	−0.984578	−	0.174944i	$-0.944025\pi$
$337$		−	1.33912e7i		−	0.349888i	0.984578	−	0.174944i	$-0.0559745\pi$
$338$	−6.61251e6	−	3.36014e6i	−0.171244	−	0.0870177i
$339$	−82427.6			−0.00211579
$340$	3.29295e6	−	1.22895e7i	0.0837816	−	0.312677i
$341$	8.98152e6	+	1.55565e7i	0.226510	+	0.392326i
$342$	6.59627e6	+	3.80836e6i	0.164900	+	0.0952050i
$343$	2.35468e7	+	2.35468e7i	0.583510	+	0.583510i
$344$	−1.21143e7	+	3.24602e6i	−0.297594	+	0.0797400i
$345$	121383.	+	453008.i	0.00295598	+	0.0110319i
$346$	−3.22312e6	+	3.22312e6i	−0.0778123	+	0.0778123i
$347$	1.22247e7	−	2.11738e7i	0.292583	−	0.506769i	−0.681837	−	0.731504i	$-0.738819\pi$
$347$	1.22247e7	−	2.11738e7i	0.292583	−	0.506769i	0.974420	+	0.224736i	$0.0721519\pi$
$348$	−1.88835e6	+	1.09024e6i	−0.0448068	+	0.0258692i
$349$	−4.40479e7	−	1.18026e7i	−1.03621	−	0.277653i	−0.299670	−	0.954043i	$-0.596877\pi$
$349$	−4.40479e7	−	1.18026e7i	−1.03621	−	0.277653i	−0.736543	+	0.676390i	$0.763543\pi$
$350$			323356.i			0.00754183i
$351$	2.03000e6	+	2.50404e6i	0.0469435	+	0.0579056i
$352$	1.87935e7			0.430904
$353$	1.25723e7	−	4.69204e7i	0.285818	−	1.06669i	−0.662421	−	0.749131i	$-0.730471\pi$
$353$	1.25723e7	−	4.69204e7i	0.285818	−	1.06669i	0.948239	−	0.317556i	$-0.102862\pi$
$354$	221566.	+	383763.i	0.00499451	+	0.00865075i
$355$	3.93397e7	+	2.27128e7i	0.879318	+	0.507674i
$356$	1.22223e7	+	1.22223e7i	0.270897	+	0.270897i
$357$	−266023.	+	71280.7i	−0.00584675	+	0.00156663i
$358$	1.05196e6	+	3.92597e6i	0.0229271	+	0.0855653i
$359$	−3.07062e7	+	3.07062e7i	−0.663656	+	0.663656i	−0.956240	−	0.292584i	$-0.905485\pi$
$359$	−3.07062e7	+	3.07062e7i	−0.663656	+	0.663656i	0.292584	+	0.956240i	$0.405485\pi$
$360$	−8.40269e6	+	1.45539e7i	−0.180099	+	0.311940i
$361$	−595963.	+	344079.i	−0.0126677	+	0.00731370i
$362$	−1.79981e6	−	482258.i	−0.0379403	−	0.0101661i
$363$			681640.i			0.0142507i
$364$	1.95938e7	−	8.73656e6i	0.406270	−	0.181149i
$365$	3.18583e7			0.655154
$366$	79284.1	−	295892.i	0.00161712	−	0.00603518i
$367$	3.17736e7	+	5.50335e7i	0.642788	+	1.11334i	0.984808	+	0.173649i	$0.0555559\pi$
$367$	3.17736e7	+	5.50335e7i	0.642788	+	1.11334i	−0.342019	+	0.939693i	$0.611111\pi$
$368$	−1.23057e7	−	7.10469e6i	−0.246923	−	0.142561i
$369$	3.88513e7	+	3.88513e7i	0.773262	+	0.773262i
$370$	−1.02039e7	+	2.73413e6i	−0.201447	+	0.0539776i
$371$	−1.11801e7	−	4.17246e7i	−0.218939	−	0.817091i
$372$	−753562.	+	753562.i	−0.0146383	+	0.0146383i
$373$	−5.95820e6	+	1.03199e7i	−0.114812	+	0.198861i	−0.917705	−	0.397263i	$-0.869960\pi$
$373$	−5.95820e6	+	1.03199e7i	−0.114812	+	0.198861i	0.802892	+	0.596124i	$0.203293\pi$
$374$	−2.40368e6	+	1.38777e6i	−0.0459476	+	0.0265278i
$375$	−1.97180e6	−	528341.i	−0.0373911	−	0.0100189i
$376$		−	1.75519e7i		−	0.330187i
$377$	−2.76180e7	+	7.20651e7i	−0.515428	+	1.34493i
$378$	357188.			0.00661335
$379$	1.93903e7	−	7.23656e7i	0.356178	−	1.32927i	−0.522818	−	0.852445i	$-0.675119\pi$
$379$	1.93903e7	−	7.23656e7i	0.356178	−	1.32927i	0.878996	−	0.476830i	$-0.158214\pi$
$380$	2.50901e7	+	4.34573e7i	0.457248	+	0.791976i
$381$	2.67370e6	+	1.54366e6i	0.0483434	+	0.0279111i
$382$	1.09521e6	+	1.09521e6i	0.0196475	+	0.0196475i
$383$	−1.14935e7	+	3.07968e6i	−0.204577	+	0.0548163i	−0.359652	−	0.933086i	$-0.617105\pi$
$383$	−1.14935e7	+	3.07968e6i	−0.204577	+	0.0548163i	0.155075	+	0.987903i	$0.450438\pi$
$384$	382091.	+	1.42598e6i	0.00674796	+	0.0251837i
$385$	1.40139e7	−	1.40139e7i	0.245571	−	0.245571i
$386$	−158378.	+	274319.i	−0.00275380	+	0.00476973i
$387$	4.09545e7	−	2.36451e7i	0.706592	−	0.407951i
$388$	−1.57070e7	−	4.20867e6i	−0.268904	−	0.0720525i
$389$			3.78373e7i			0.642794i	0.946945	+	0.321397i	$0.104152\pi$
$389$			3.78373e7i			0.642794i	−0.946945	+	0.321397i	$0.895848\pi$
$390$	−63812.7	−	401477.i	−0.00107576	−	0.00676810i
$391$	6.72382e6			0.112483
$392$	−4.62476e6	+	1.72598e7i	−0.0767769	+	0.286535i
$393$	−1.83279e6	−	3.17449e6i	−0.0301950	−	0.0522993i
$394$	−1.86116e6	−	1.07454e6i	−0.0304295	−	0.0175685i
$395$	−6.05616e7	−	6.05616e7i	−0.982667	−	0.982667i
$396$	−4.53486e7	+	1.21511e7i	−0.730262	+	0.195673i
$397$	−2.79128e7	−	1.04172e8i	−0.446100	−	1.66487i	−0.713015	−	0.701149i	$-0.752671\pi$
$397$	−2.79128e7	−	1.04172e8i	−0.446100	−	1.66487i	0.266915	−	0.963720i	$-0.413996\pi$
$398$	−9.15742e6	+	9.15742e6i	−0.145253	+	0.145253i
$399$	543111.	−	940696.i	0.00855007	−	0.0148092i
$400$	4.19656e6	−	2.42289e6i	0.0655713	−	0.0378576i
$401$	−4.23629e7	−	1.13511e7i	−0.656981	−	0.176038i	−0.0850980	−	0.996373i	$-0.527120\pi$
$401$	−4.23629e7	−	1.13511e7i	−0.656981	−	0.176038i	−0.571883	+	0.820335i	$0.693787\pi$
$402$			892655.i			0.0137406i
$403$	−3.92225e6	+	3.75150e7i	−0.0599266	+	0.573178i
$404$	7.59686e7			1.15210
$405$	1.63778e7	−	6.11226e7i	0.246541	−	0.920104i
$406$	4.27580e6	+	7.40590e6i	0.0638909	+	0.110662i
$407$	−5.20949e7	−	3.00770e7i	−0.772702	−	0.446120i
$408$	−237332.	−	237332.i	−0.00349443	−	0.00349443i
$409$	−3.15517e7	+	8.45425e6i	−0.461161	+	0.123568i	−0.481917	−	0.876217i	$-0.660059\pi$
$409$	−3.15517e7	+	8.45425e6i	−0.461161	+	0.123568i	0.0207560	+	0.999785i	$0.493393\pi$
$410$	−3.58919e6	−	1.33950e7i	−0.0520768	−	0.194353i
$411$	1.76149e6	−	1.76149e6i	0.0253720	−	0.0253720i
$412$	−3.92890e7	+	6.80505e7i	−0.561796	+	0.973060i
$413$	−3.92866e7	+	2.26821e7i	−0.557692	+	0.321984i
$414$	−4.20871e6	−	1.12772e6i	−0.0593127	−	0.0158928i
$415$		−	6.87836e7i		−	0.962367i
$416$	3.19392e7	+	2.31785e7i	0.443653	+	0.321963i
$417$	45616.6			0.000629093
$418$	2.83326e6	−	1.05739e7i	0.0387933	−	0.144779i
$419$	−3.53659e7	−	6.12555e7i	−0.480775	−	0.832727i	0.518981	−	0.854785i	$-0.326311\pi$
$419$	−3.53659e7	−	6.12555e7i	−0.480775	−	0.832727i	−0.999757	+	0.0220584i	$0.992978\pi$
$420$	1.01826e6	+	587894.i	0.0137439	+	0.00793507i
$421$	6.36893e7	+	6.36893e7i	0.853533	+	0.853533i	0.990566	−	0.137033i	$-0.0437567\pi$
$421$	6.36893e7	+	6.36893e7i	0.853533	+	0.853533i	−0.137033	+	0.990566i	$0.543757\pi$
$422$	1.83483e7	−	4.91641e6i	0.244151	−	0.0654201i
$423$	1.71292e7	+	6.39269e7i	0.226316	+	0.844622i
$424$	3.72245e7	−	3.72245e7i	0.488351	−	0.488351i
$425$	−1.14650e6	+	1.98580e6i	−0.0149351	+	0.0258683i
$426$	509146.	−	293956.i	0.00658588	−	0.00380236i
$427$	3.02911e7	+	8.11647e6i	0.389073	+	0.104252i
$428$			3.85380e7i			0.491539i
$429$	1.35960e6	−	1.87349e6i	0.0172203	−	0.0237290i
$430$	−1.19358e7			−0.150122
$431$	255099.	−	952044.i	0.00318623	−	0.0118912i	−0.964314	−	0.264760i	$-0.914707\pi$
$431$	255099.	−	952044.i	0.00318623	−	0.0118912i	0.967501	+	0.252869i	$0.0813740\pi$
$432$	−2.67639e6	−	4.63564e6i	−0.0331969	−	0.0574987i
$433$	4.92899e7	+	2.84576e7i	0.607148	+	0.350537i	0.771848	−	0.635807i	$-0.219332\pi$
$433$	4.92899e7	+	2.84576e7i	0.607148	+	0.350537i	−0.164700	+	0.986344i	$0.552666\pi$
$434$	2.95539e6	+	2.95539e6i	0.0361532	+	0.0361532i
$435$	−4.08564e6	+	1.09474e6i	−0.0496355	+	0.0132998i
$436$	4.63950e6	+	1.73149e7i	0.0559773	+	0.208910i
$437$	−1.87518e7	+	1.87518e7i	−0.224698	+	0.224698i
$438$	206160.	−	357079.i	0.00245348	−	0.00424954i
$439$	−8.79431e7	+	5.07740e7i	−1.03946	+	0.600133i	−0.919681	−	0.392667i	$-0.871552\pi$
$439$	−8.79431e7	+	5.07740e7i	−1.03946	+	0.600133i	−0.119781	+	0.992800i	$0.538219\pi$
$440$	2.33300e7	+	6.25124e6i	0.273877	+	0.0733852i
$441$		−	6.73765e7i		−	0.785584i
$442$	−5.79657e6	−	606041.i	−0.0671281	−	0.00701835i
$443$	1.09735e8			1.26222			0.631109	−	0.775694i	$-0.282600\pi$
$443$	1.09735e8			1.26222			0.631109	+	0.775694i	$0.282600\pi$
$444$	923667.	−	3.44717e6i	0.0105528	−	0.0393835i
$445$	1.67650e7	+	2.90379e7i	0.190250	+	0.329522i
$446$	−7.49793e6	−	4.32893e6i	−0.0845156	−	0.0487951i
$447$	3.39057e6	+	3.39057e6i	0.0379621	+	0.0379621i
$448$	−3.15045e7	+	8.44161e6i	−0.350380	+	0.0938839i
$449$	1.78438e7	+	6.65939e7i	0.197128	+	0.735691i	0.991706	+	0.128529i	$0.0410254\pi$
$449$	1.78438e7	+	6.65939e7i	0.197128	+	0.735691i	−0.794578	+	0.607162i	$0.792308\pi$
$450$	1.05070e6	−	1.05070e6i	0.0115303	−	0.0115303i
$451$	3.94832e7	−	6.83869e7i	0.430410	−	0.745493i
$452$	4.36928e6	−	2.52260e6i	0.0473145	−	0.0273170i
$453$	−2.54888e6	−	682971.i	−0.0274192	−	0.00734695i
$454$			2.76775e7i			0.295773i
$455$	4.11000e7	−	6.53264e6i	0.436323	−	0.0693513i
$456$	1.32378e6			0.0139611
$457$	−2.91466e7	+	1.08776e8i	−0.305379	+	1.13969i	0.627240	+	0.778826i	$0.284184\pi$
$457$	−2.91466e7	+	1.08776e8i	−0.305379	+	1.13969i	−0.932619	+	0.360863i	$0.882482\pi$
$458$	2.67428e6	+	4.63199e6i	0.0278363	+	0.0482138i
$459$	2.19356e6	+	1.26645e6i	0.0226836	+	0.0130964i
$460$	−2.02980e7	−	2.02980e7i	−0.208536	−	0.208536i
$461$	9.98675e7	−	2.67594e7i	1.01934	−	0.273133i	0.289816	−	0.957082i	$-0.406406\pi$
$461$	9.98675e7	−	2.67594e7i	1.01934	−	0.273133i	0.729529	+	0.683950i	$0.239739\pi$
$462$	−66386.9	−	247759.i	−0.000673219	−	0.00251249i
$463$	6.63536e6	−	6.63536e6i	0.0668531	−	0.0668531i	−0.672890	−	0.739743i	$-0.734947\pi$
$463$	6.63536e6	−	6.63536e6i	0.0668531	−	0.0668531i	0.739743	+	0.672890i	$0.234947\pi$
$464$	6.40766e7	−	1.10984e8i	0.641424	−	1.11098i
$465$	−1.79032e6	+	1.03364e6i	−0.0178062	+	0.0102804i
$466$	−1.17607e7	−	3.15127e6i	−0.116218	−	0.0311406i
$467$			5.57195e6i			0.0547087i	0.999626	+	0.0273544i	$0.00870825\pi$
$467$			5.57195e6i			0.0547087i	−0.999626	+	0.0273544i	$0.991292\pi$
$468$	−9.20553e7	−	3.52790e7i	−0.898072	−	0.344174i
$469$	−9.13828e7			−0.885821
$470$	4.32330e6	−	1.61348e7i	0.0416411	−	0.155407i
$471$	−702781.	−	1.21725e6i	−0.00672600	−	0.0116498i
$472$	−4.78785e7	−	2.76427e7i	−0.455317	−	0.262878i
$473$	−4.80594e7	−	4.80594e7i	−0.454145	−	0.454145i
$474$	−1.07070e6	+	286893.i	−0.0100539	+	0.00269393i
$475$	−2.34069e6	−	8.73556e6i	−0.0218405	−	0.0815098i
$476$	1.19198e7	−	1.19198e7i	0.110521	−	0.110521i
$477$	−9.92499e7	+	1.71906e8i	−0.914482	+	1.58393i
$478$	8.87841e6	−	5.12595e6i	0.0812927	−	0.0469344i
$479$	−8.77395e7	−	2.35097e7i	−0.798341	−	0.213915i	−0.163486	−	0.986546i	$-0.552274\pi$
$479$	−8.77395e7	−	2.35097e7i	−0.798341	−	0.213915i	−0.634856	+	0.772631i	$0.718940\pi$
$480$			2.16286e6i			0.0195571i
$481$	−5.14394e7	−	1.15365e8i	−0.462233	−	1.03667i
$482$	−2.33151e7			−0.208207
$483$	−160824.	+	600204.i	−0.00142728	+	0.00532669i
$484$	−2.08608e7	−	3.61320e7i	−0.183991	−	0.318681i
$485$	−2.73177e7	−	1.57719e7i	−0.239452	−	0.138248i
$486$	−1.74135e6	−	1.74135e6i	−0.0151697	−	0.0151697i
$487$	1.06893e7	−	2.86420e6i	0.0925474	−	0.0247980i	−0.212248	−	0.977216i	$-0.568079\pi$
$487$	1.06893e7	−	2.86420e6i	0.0925474	−	0.0247980i	0.304796	+	0.952418i	$0.401412\pi$
$488$	9.89152e6	+	3.69157e7i	0.0851145	+	0.317652i
$489$	−4.74875e6	+	4.74875e6i	−0.0406118	+	0.0406118i
$490$	−8.50272e6	+	1.47271e7i	−0.0722719	+	0.125179i
$491$	1.53346e8	−	8.85343e7i	1.29547	−	0.747940i	0.315852	−	0.948808i	$-0.397710\pi$
$491$	1.53346e8	−	8.85343e7i	1.29547	−	0.747940i	0.979618	+	0.200868i	$0.0643762\pi$
$492$	4.52523e6	+	1.21253e6i	0.0379966	+	0.0101812i
$493$			6.06415e7i			0.506092i
$494$	1.78560e7	−	1.44757e7i	0.148117	−	0.120077i
$495$	−9.10722e7			−0.750880
$496$	1.62110e7	−	6.05001e7i	0.132851	−	0.495805i
$497$	3.00928e7	+	5.21223e7i	0.245129	+	0.424575i
$498$	−770952.	−	445110.i	−0.00624223	−	0.00360395i
$499$	5.94289e7	+	5.94289e7i	0.478295	+	0.478295i	0.904586	−	0.426291i	$-0.140180\pi$
$499$	5.94289e7	+	5.94289e7i	0.478295	+	0.478295i	−0.426291	+	0.904586i	$0.640180\pi$
$500$	1.20689e8	−	3.23386e7i	0.965514	−	0.258709i
$501$	2.25338e6	+	8.40973e6i	0.0179193	+	0.0668758i
$502$	−1.83301e7	+	1.83301e7i	−0.144895	+	0.144895i
$503$	9.88201e7	−	1.71161e8i	0.776500	−	1.34494i	−0.157447	−	0.987527i	$-0.550326\pi$
$503$	9.88201e7	−	1.71161e8i	0.776500	−	1.34494i	0.933948	−	0.357410i	$-0.116340\pi$
$504$	−1.92829e7	+	1.11330e7i	−0.150619	+	0.0869600i
$505$	1.42345e8	+	3.81413e7i	1.10527	+	0.296157i
$506$			6.26219e6i			0.0483365i
$507$	4.62124e6	−	1.50712e6i	0.0354596	−	0.0115644i
$508$	−1.88968e8			−1.44144
$509$	−6.19958e7	+	2.31372e8i	−0.470121	+	1.75451i	0.169208	+	0.985580i	$0.445879\pi$
$509$	−6.19958e7	+	2.31372e8i	−0.470121	+	1.75451i	−0.639329	+	0.768933i	$0.720788\pi$
$510$	−159712.	−	276629.i	−0.00120400	−	0.00208539i
$511$	3.65549e7	+	2.11050e7i	0.273957	+	0.158169i
$512$	−7.82117e7	−	7.82117e7i	−0.582723	−	0.582723i
$513$	−9.64953e6	+	2.58559e6i	−0.0714750	+	0.0191517i
$514$	6.45925e6	+	2.41063e7i	0.0475656	+	0.177517i
$515$	−1.07783e8	+	1.07783e8i	−0.789095	+	0.789095i
$516$	2.01612e6	−	3.49203e6i	0.0146747	−	0.0254173i
$517$	8.23744e7	−	4.75589e7i	0.596102	−	0.344160i
$518$	−1.35195e7	−	3.62253e6i	−0.0972680	−	0.0260629i
$519$		−	2.98713e6i		−	0.0213674i
$520$	3.19389e7	+	3.93972e7i	0.227149	+	0.280192i
$521$	3.39064e7			0.239756			0.119878	−	0.992789i	$-0.461750\pi$
$521$	3.39064e7			0.239756			0.119878	+	0.992789i	$0.461750\pi$
$522$	1.01708e7	−	3.79579e7i	0.0715062	−	0.266865i
$523$	−7.00345e7	−	1.21303e8i	−0.489561	−	0.847945i	0.510367	−	0.859957i	$-0.329510\pi$
$523$	−7.00345e7	−	1.21303e8i	−0.489561	−	0.847945i	−0.999928	+	0.0120119i	$0.996176\pi$
$524$	1.94303e8	+	1.12181e8i	1.35047	+	0.779697i
$525$	−149840.	−	149840.i	−0.00103550	−	0.00103550i
$526$	2.65587e7	−	7.11638e6i	0.182494	−	0.0488992i
$527$	7.67096e6	+	2.86284e7i	0.0524104	+	0.195598i
$528$	−2.71802e6	+	2.71802e6i	−0.0184651	+	0.0184651i
$529$	−6.64328e7	+	1.15065e8i	−0.448761	+	0.777277i
$530$	4.33881e7	−	2.50501e7i	0.291436	−	0.168260i
$531$	2.01358e8	+	5.39538e7i	1.34489	+	0.360361i
$532$			6.64852e7i			0.441561i
$533$	1.51444e8	−	6.75264e7i	1.00016	−	0.445956i
$534$	433956.			0.00284985
$535$	−1.93487e7	+	7.22102e7i	−0.126354	+	0.471560i
$536$	−5.56840e7	−	9.64475e7i	−0.361606	−	0.626321i
$537$	−2.30672e6	−	1.33179e6i	−0.0148961	−	0.00860027i
$538$	3.03244e7	+	3.03244e7i	0.194736	+	0.194736i
$539$	−9.35350e7	+	2.50626e7i	−0.597321	+	0.160052i
$540$	−2.79878e6	−	1.04452e7i	−0.0177741	−	0.0663339i
$541$	3.54479e7	−	3.54479e7i	0.223872	−	0.223872i	−0.586255	−	0.810127i	$-0.699398\pi$
$541$	3.54479e7	−	3.54479e7i	0.223872	−	0.223872i	0.810127	+	0.586255i	$0.199398\pi$
$542$	3.52435e6	−	6.10435e6i	0.0221351	−	0.0383390i
$543$	1.05749e6	−	610542.i	0.00660506	−	0.00381343i
$544$	2.99520e7	+	8.02561e6i	0.186050	+	0.0498518i
$545$			3.47729e7i			0.214808i
$546$	192744.	−	502938.i	0.00118414	−	0.00308984i
$547$	−1.61004e8			−0.983725			−0.491862	−	0.870673i	$-0.663684\pi$
$547$	−1.61004e8			−0.983725			−0.491862	+	0.870673i	$0.663684\pi$
$548$	−3.94637e7	+	1.47281e8i	−0.239804	+	0.894961i
$549$	−7.20531e7	−	1.24800e8i	−0.435447	−	0.754217i
$550$	−1.84946e6	−	1.06779e6i	−0.0111162	−	0.00641795i
$551$	−1.69121e8	−	1.69121e8i	−1.01098	−	1.01098i
$552$	−731467.	+	195996.i	−0.00434888	+	0.00116528i
$553$	−2.93699e7	−	1.09610e8i	−0.173671	−	0.648148i
$554$	−1.50474e7	+	1.50474e7i	−0.0884977	+	0.0884977i
$555$	3.46142e6	−	5.99536e6i	0.0202477	−	0.0350700i
$556$	−2.41802e6	+	1.39605e6i	−0.0140681	+	0.00812223i
$557$	−1.05515e6	−	282727.i	−0.00610589	−	0.00163607i	0.255765	−	0.966739i	$-0.417673\pi$
$557$	−1.05515e6	−	282727.i	−0.00610589	−	0.00163607i	−0.261871	+	0.965103i	$0.584339\pi$
$558$		−	1.92062e7i		−	0.110545i
$559$	−2.24030e7	−	1.40949e8i	−0.128254	−	0.806910i
$560$	−6.91046e7			−0.393498
$561$	470766.	−	1.75692e6i	0.00266635	−	0.00995094i
$562$	−2.83326e6	−	4.90735e6i	−0.0159617	−	0.0276464i
$563$	−1.70250e8	−	9.82938e7i	−0.954029	−	0.550809i	−0.0596987	−	0.998216i	$-0.519014\pi$
$563$	−1.70250e8	−	9.82938e7i	−0.954029	−	0.550809i	−0.894330	+	0.447408i	$0.852347\pi$
$564$	3.99026e6	+	3.99026e6i	0.0222415	+	0.0222415i
$565$	9.45341e6	−	2.53303e6i	0.0524135	−	0.0140442i
$566$	9.77758e6	+	3.64904e7i	0.0539240	+	0.201247i
$567$	5.92838e7	−	5.92838e7i	0.325227	−	0.325227i
$568$	−3.66741e7	+	6.35213e7i	−0.200131	+	0.346637i
$569$	2.79573e6	−	1.61412e6i	0.0151760	−	0.00876189i	−0.492393	−	0.870373i	$-0.663878\pi$
$569$	2.79573e6	−	1.61412e6i	0.0151760	−	0.00876189i	0.507569	+	0.861611i	$0.330544\pi$
$570$	1.21690e6	+	326066.i	0.00657096	+	0.00176068i
$571$		−	5.73160e7i		−	0.307870i	−0.988081	−	0.153935i	$-0.950805\pi$
$571$		−	5.73160e7i		−	0.307870i	0.988081	−	0.153935i	$-0.0491946\pi$
$572$	−1.47332e7	+	1.40918e8i	−0.0787244	+	0.752972i
$573$	−1.01502e6			−0.00539525
$574$	4.75542e6	−	1.77475e7i	0.0251451	−	0.0938428i
$575$	2.58674e6	+	4.48037e6i	0.0136066	+	0.0235673i
$576$	1.29799e8	+	7.49395e7i	0.679210	+	0.392142i
$577$	−7.62964e7	−	7.62964e7i	−0.397170	−	0.397170i	0.480064	−	0.877234i	$-0.340614\pi$
$577$	−7.62964e7	−	7.62964e7i	−0.397170	−	0.397170i	−0.877234	+	0.480064i	$0.840614\pi$
$578$	3.14044e7	−	8.41479e6i	0.162632	−	0.0435772i
$579$	−53725.8	−	200508.i	−0.000276788	−	0.00103299i
$580$	1.83066e8	−	1.83066e8i	0.938262	−	0.938262i
$581$	4.55668e7	−	7.89239e7i	0.232338	−	0.402421i
$582$	−353554.	+	204125.i	−0.00179344	+	0.00103544i
$583$	2.75566e8	+	7.38377e7i	1.39066	+	0.372625i
$584$			5.14412e7i			0.258269i
$585$	−1.54775e8	−	1.12322e8i	−0.773097	−	0.561042i
$586$	−1.25268e7			−0.0622514
$587$	−6.86741e7	+	2.56295e8i	−0.339530	+	1.26714i	0.559343	+	0.828936i	$0.311053\pi$
$587$	−6.86741e7	+	2.56295e8i	−0.339530	+	1.26714i	−0.898873	+	0.438208i	$0.855613\pi$
$588$	−2.87246e6	−	4.97525e6i	−0.0141294	−	0.0244728i
$589$	−1.01234e8	−	5.84475e7i	−0.495428	−	0.286036i
$590$	−3.72040e7	−	3.72040e7i	−0.181148	−	0.181148i
$591$	1.36038e6	−	364512.i	0.00659018	−	0.00176583i
$592$	5.42867e7	+	2.02601e8i	0.261655	+	0.976509i
$593$	−9.62915e7	+	9.62915e7i	−0.461768	+	0.461768i	−0.899235	−	0.437467i	$-0.855876\pi$
$593$	−9.62915e7	+	9.62915e7i	−0.461768	+	0.461768i	0.437467	+	0.899235i	$0.355876\pi$
$594$	−1.17951e6	+	2.04296e6i	−0.00562783	+	0.00974769i
$595$	2.83190e7	−	1.63500e7i	0.134440	−	0.0776188i
$596$	−2.83490e8	−	7.59610e7i	−1.33906	−	0.358799i
$597$		−	8.48692e6i		−	0.0398866i
$598$	−7.72331e6	+	1.06425e7i	−0.0361160	+	0.0497666i
$599$	8.14581e7			0.379013			0.189506	−	0.981879i	$-0.439311\pi$
$599$	8.14581e7			0.379013			0.189506	+	0.981879i	$0.439311\pi$
$600$	66839.8	−	249450.i	0.000309444	−	0.00115486i
$601$	8.68715e7	+	1.50466e8i	0.400178	+	0.693129i	0.993747	−	0.111654i	$-0.0356148\pi$
$601$	8.68715e7	+	1.50466e8i	0.400178	+	0.693129i	−0.593569	+	0.804783i	$0.702281\pi$
$602$	−1.36954e7	−	7.90703e6i	−0.0627747	−	0.0362430i
$603$	2.96935e8	+	2.96935e8i	1.35428	+	1.35428i
$604$	1.56011e8	−	4.18031e7i	0.708020	−	0.189713i
$605$	−2.09471e7	−	7.81756e7i	−0.0945926	−	0.353024i
$606$	1.34864e6	−	1.34864e6i	0.00606008	−	0.00606008i
$607$	2.02330e7	−	3.50446e7i	0.0904678	−	0.156695i	−0.817240	−	0.576297i	$-0.804497\pi$
$607$	2.02330e7	−	3.50446e7i	0.0904678	−	0.156695i	0.907708	+	0.419602i	$0.137830\pi$
$608$	−1.05914e8	+	6.11497e7i	−0.471243	+	0.272072i
$609$	−5.41319e6	−	1.45046e6i	−0.0239663	−	0.00642176i
$610$			3.63716e7i			0.160241i
$611$	1.98649e8	+	2.07691e7i	0.870889	+	0.0910528i
$612$	−7.74629e7			−0.337940
$613$	5.62710e7	−	2.10006e8i	0.244289	−	0.911698i	−0.729451	−	0.684033i	$-0.760224\pi$
$613$	5.62710e7	−	2.10006e8i	0.244289	−	0.911698i	0.973740	−	0.227665i	$-0.0731090\pi$
$614$	3.77734e7	+	6.54255e7i	0.163185	+	0.282645i
$615$	7.87033e6	+	4.54394e6i	0.0338351	+	0.0195347i
$616$	2.26281e7	+	2.26281e7i	0.0968068	+	0.0968068i
$617$	2.53229e8	−	6.78525e7i	1.07810	−	0.288875i	0.324281	−	0.945961i	$-0.394878\pi$
$617$	2.53229e8	−	6.78525e7i	1.07810	−	0.288875i	0.753816	+	0.657086i	$0.228211\pi$
$618$	510592.	+	1.90556e6i	0.00216326	+	0.00807339i
$619$	−2.25903e8	+	2.25903e8i	−0.952466	+	0.952466i	−0.998920	−	0.0464548i	$-0.985208\pi$
$619$	−2.25903e8	+	2.25903e8i	−0.952466	+	0.952466i	0.0464548	+	0.998920i	$0.485208\pi$
$620$	6.32669e7	−	1.09581e8i	0.265461	−	0.459793i
$621$	4.94914e6	−	2.85739e6i	0.0206659	−	0.0119315i
$622$	−6.39010e7	−	1.71222e7i	−0.265544	−	0.0711523i
$623$			4.44250e7i			0.183723i
$624$	−7.97142e6	+	1.26702e6i	−0.0328082	+	0.00521469i
$625$	2.21622e8			0.907764
$626$	−5.27774e6	+	1.96968e7i	−0.0215142	+	0.0802921i
$627$	3.58692e6	+	6.21273e6i	0.0145519	+	0.0252046i
$628$	7.45053e7	+	4.30156e7i	0.300821	+	0.173679i
$629$	−7.01816e7	−	7.01816e7i	−0.282014	−	0.282014i
$630$	−2.04682e7	+	5.48445e6i	−0.0818576	+	0.0219337i
$631$	6.35382e7	+	2.37128e8i	0.252899	+	0.943832i	0.969247	+	0.246089i	$0.0791455\pi$
$631$	6.35382e7	+	2.37128e8i	0.252899	+	0.943832i	−0.716348	+	0.697743i	$0.754188\pi$
$632$	9.77882e7	−	9.77882e7i	0.387378	−	0.387378i
$633$	−6.22421e6	+	1.07806e7i	−0.0245399	+	0.0425044i
$634$	4.05362e7	−	2.34036e7i	0.159065	−	0.0918364i
$635$	−3.54077e8	−	9.48746e7i	−1.38285	−	0.370535i
$636$			1.69253e7i			0.0657908i
$637$	−1.89871e8	−	7.27655e7i	−0.734582	−	0.281519i
$638$	−5.64782e7			−0.217480
$639$	7.15815e7	−	2.67146e8i	0.274346	−	1.02387i
$640$	−8.76420e7	−	1.51800e8i	−0.334328	−	0.579073i
$641$	−1.69848e8	−	9.80620e7i	−0.644892	−	0.372329i	0.141604	−	0.989923i	$-0.454774\pi$
$641$	−1.69848e8	−	9.80620e7i	−0.644892	−	0.372329i	−0.786497	+	0.617595i	$0.788107\pi$
$642$	684150.	+	684150.i	0.00258551	+	0.00258551i
$643$	−3.56549e8	+	9.55371e7i	−1.34118	+	0.359368i	−0.856871	−	0.515531i	$-0.827595\pi$
$643$	−3.56549e8	+	9.55371e7i	−1.34118	+	0.359368i	−0.484307	+	0.874898i	$0.660928\pi$
$644$	−9.84370e6	−	3.67372e7i	−0.0368554	−	0.137546i
$645$	5.53093e6	−	5.53093e6i	0.0206119	−	0.0206119i
$646$	9.03094e6	−	1.56421e7i	0.0334993	−	0.0580225i
$647$	−2.14030e8	+	1.23571e8i	−0.790247	+	0.456249i	−0.840049	−	0.542510i	$-0.817474\pi$
$647$	−2.14030e8	+	1.23571e8i	−0.790247	+	0.456249i	0.0498027	+	0.998759i	$0.484141\pi$
$648$	9.86939e7	+	2.64450e7i	0.362715	+	0.0971892i
$649$		−	2.99604e8i		−	1.09601i
$650$	−1.82619e6	−	4.09566e6i	−0.00664976	−	0.0149137i
$651$	−2.73900e6			−0.00992773
$652$	1.06389e8	−	3.97049e8i	0.383843	−	1.43252i
$653$	1.72426e8	+	2.98651e8i	0.619246	+	1.07257i	0.989624	+	0.143684i	$0.0458950\pi$
$653$	1.72426e8	+	2.98651e8i	0.619246	+	1.07257i	−0.370378	+	0.928881i	$0.620772\pi$
$654$	389747.	+	225021.i	0.00139332	+	0.000804432i
$655$	3.07751e8	+	3.07751e8i	1.09516	+	1.09516i
$656$	−2.65961e8	+	7.12642e7i	−0.942122	+	0.252441i
$657$	−5.02022e7	−	1.87357e8i	−0.177022	−	0.660655i
$658$	1.56494e7	−	1.56494e7i	0.0549313	−	0.0549313i
$659$	−2.05050e7	+	3.55158e7i	−0.0716480	+	0.124098i	−0.899624	−	0.436666i	$-0.856159\pi$
$659$	−2.05050e7	+	3.55158e7i	−0.0716480	+	0.124098i	0.827976	+	0.560764i	$0.189492\pi$
$660$	−6.72501e6	+	3.88268e6i	−0.0233917	+	0.0135052i
$661$	−6.81872e7	−	1.82707e7i	−0.236101	−	0.0632631i	0.138828	−	0.990316i	$-0.455666\pi$
$661$	−6.81872e7	−	1.82707e7i	−0.236101	−	0.0632631i	−0.374929	+	0.927053i	$0.622333\pi$
$662$		−	4.11972e7i		−	0.142002i
$663$	2.96691e6	−	2.40524e6i	0.0101804	−	0.00825313i
$664$	1.11064e8			0.379376
$665$	−3.33801e7	+	1.24576e8i	−0.113507	+	0.423613i
$666$	3.21586e7	+	5.57003e7i	0.108862	+	0.188554i
$667$	1.18490e8	+	6.84100e7i	0.399303	+	0.230538i
$668$	−3.76816e8	−	3.76816e8i	−1.26416	−	1.26416i
$669$	5.48046e6	−	1.46848e6i	0.0183037	−	0.00490446i
$670$	−2.74317e7	−	1.02376e8i	−0.0912069	−	0.340389i
$671$	−1.46450e8	+	1.46450e8i	−0.484755	+	0.484755i
$672$	−1.43282e6	+	2.48171e6i	−0.00472154	+	0.00817794i
$673$	6.56515e7	−	3.79039e7i	0.215377	−	0.124348i	−0.388431	−	0.921478i	$-0.626983\pi$
$673$	6.56515e7	−	3.79039e7i	0.215377	−	0.124348i	0.603808	+	0.797130i	$0.293649\pi$
$674$	1.98768e7	+	5.32598e6i	0.0649183	+	0.0173948i
$675$			1.94889e6i			0.00633689i
$676$	−1.98836e8	+	2.21316e8i	−0.643659	+	0.716429i
$677$	5.03333e8			1.62214			0.811072	−	0.584947i	$-0.198885\pi$
$677$	5.03333e8			1.62214			0.811072	+	0.584947i	$0.198885\pi$
$678$	32783.3	−	122349.i	0.000105187	−	0.000392565i
$679$	−2.08967e7	−	3.61941e7i	−0.0667525	−	0.115619i
$680$	3.45123e7	+	1.99257e7i	0.109761	+	0.0633704i
$681$	−1.28255e7	−	1.28255e7i	−0.0406099	−	0.0406099i
$682$	−2.66629e7	+	7.14431e6i	−0.0840532	+	0.0225220i
$683$	−7.04794e7	−	2.63033e8i	−0.221208	−	0.825559i	−0.983888	−	0.178783i	$-0.942784\pi$
$683$	−7.04794e7	−	2.63033e8i	−0.221208	−	0.825559i	0.762681	−	0.646775i	$-0.223883\pi$
$684$	2.16034e8	−	2.16034e8i	0.675077	−	0.675077i
$685$	−1.47890e8	+	2.56152e8i	−0.460115	+	0.796942i
$686$	−4.43160e7	+	2.55859e7i	−0.137274	+	0.0792552i
$687$	−3.38566e6	−	907185.i	−0.0104417	−	0.00279786i
$688$			2.36988e8i			0.727713i
$689$	3.77253e8	+	4.65348e8i	1.15339	+	1.42272i
$690$	−720686.			−0.00219381
$691$	1.21826e6	−	4.54662e6i	0.00369238	−	0.0137802i	−0.964055	−	0.265703i	$-0.914396\pi$
$691$	1.21826e6	−	4.54662e6i	0.00369238	−	0.0137802i	0.967747	+	0.251922i	$0.0810628\pi$
$692$	9.14178e7	+	1.58340e8i	0.275875	+	0.477829i
$693$	−1.04498e8	−	6.03322e7i	−0.313986	−	0.181280i
$694$	2.65666e7	+	2.65666e7i	0.0794800	+	0.0794800i
$695$	−5.23165e6	+	1.40182e6i	−0.0155842	+	0.00417577i
$696$	−1.76767e6	−	6.59704e6i	−0.00524293	−	0.0195669i
$697$	9.21299e7	−	9.21299e7i	0.272084	−	0.272084i
$698$	3.50377e7	−	6.06871e7i	0.103031	−	0.178456i
$699$	6.91006e6	−	3.98952e6i	0.0202325	−	0.0116813i
$700$	1.25283e7	+	3.35696e6i	0.0365258	+	0.00978706i
$701$		−	1.17358e8i		−	0.340689i	−0.985385	−	0.170344i	$-0.945512\pi$
$701$		−	1.17358e8i		−	0.340689i	0.985385	−	0.170344i	$-0.0544880\pi$
$702$	−4.52418e6	+	2.01726e6i	−0.0130776	+	0.00583110i
$703$	3.91454e8			1.12672
$704$	5.57518e7	−	2.08068e8i	0.159787	−	0.596332i
$705$	5.47333e6	+	9.48008e6i	0.0156201	+	0.0270548i
$706$	6.46446e7	+	3.73226e7i	0.183704	+	0.106061i
$707$	1.38063e8	+	1.38063e8i	0.390678	+	0.390678i
$708$	1.71690e7	−	4.60042e6i	0.0483777	−	0.0129628i
$709$	−8.01441e7	−	2.99102e8i	−0.224871	−	0.839229i	−0.982456	−	0.186493i	$-0.940288\pi$
$709$	−8.01441e7	−	2.99102e8i	−0.224871	−	0.839229i	0.757585	−	0.652736i	$-0.226379\pi$
$710$	−4.93593e7	+	4.93593e7i	−0.137909	+	0.137909i
$711$	−2.60728e8	+	4.51594e8i	−0.725401	+	1.25643i
$712$	−4.68871e7	+	2.70703e7i	−0.129901	+	0.0749985i
$713$	6.45917e7	+	1.73073e7i	0.178200	+	0.0477486i
$714$		−	423214.i		−	0.00116269i
$715$	−9.83566e7	+	2.56647e8i	−0.269082	+	0.702130i
$716$	1.63032e8			0.444153
$717$	−1.73885e6	+	6.48949e6i	−0.00471743	+	0.0176057i
$718$	−3.33653e7	−	5.77904e7i	−0.0901409	−	0.156129i
$719$	7.91977e7	+	4.57248e7i	0.213072	+	0.123017i	0.602738	−	0.797939i	$-0.294076\pi$
$719$	7.91977e7	+	4.57248e7i	0.213072	+	0.123017i	−0.389666	+	0.920956i	$0.627410\pi$
$720$	2.24545e8	+	2.24545e8i	0.601598	+	0.601598i
$721$	−1.95075e8	+	5.22703e7i	−0.520471	+	0.139460i
$722$	−273696.	−	1.02145e6i	−0.000727205	−	0.00271397i
$723$	1.08040e7	−	1.08040e7i	0.0285871	−	0.0285871i
$724$	−3.73699e7	+	6.47266e7i	−0.0984706	+	0.170556i
$725$	−4.04081e7	+	2.33296e7i	−0.106036	+	0.0612201i
$726$	−1.01177e6	−	271104.i	−0.00264407	−	0.000708476i
$727$		−	6.46738e8i		−	1.68316i	−0.540134	−	0.841579i	$-0.681626\pi$
$727$		−	6.46738e8i		−	1.68316i	0.540134	−	0.841579i	$-0.318374\pi$
$728$	1.05482e7	+	6.63637e7i	0.0273390	+	0.172003i
$729$	−3.84191e8			−0.991663
$730$	−1.26708e7	+	4.72879e7i	−0.0325712	+	0.121557i
$731$	−5.60707e7	−	9.71174e7i	−0.143544	−	0.248625i
$732$	−1.06412e7	−	6.14368e6i	−0.0271304	−	0.0156637i
$733$	−2.74415e7	−	2.74415e7i	−0.0696781	−	0.0696781i	0.671409	−	0.741087i	$-0.265689\pi$
$733$	−2.74415e7	−	2.74415e7i	−0.0696781	−	0.0696781i	−0.741087	+	0.671409i	$0.765689\pi$
$734$	−9.43244e7	+	2.52741e7i	−0.238526	+	0.0639129i
$735$	−2.88434e6	−	1.07645e7i	−0.00726414	−	0.0271102i
$736$	4.94705e7	−	4.94705e7i	0.124083	−	0.124083i
$737$	3.01764e8	−	5.22671e8i	0.753816	−	1.30565i
$738$	−7.31198e7	+	4.22158e7i	−0.181914	+	0.105028i
$739$	−1.43432e8	−	3.84325e7i	−0.355396	−	0.0952281i	0.0767035	−	0.997054i	$-0.475561\pi$
$739$	−1.43432e8	−	3.84325e7i	−0.355396	−	0.0952281i	−0.432100	+	0.901826i	$0.642227\pi$
$740$			4.23732e8i			1.04567i
$741$	−1.56642e6	+	1.49822e7i	−0.00384993	+	0.0368232i
$742$	6.63793e7			0.162488
$743$	1.72605e8	−	6.44171e8i	0.420811	−	1.57049i	−0.352093	−	0.935965i	$-0.614530\pi$
$743$	1.72605e8	−	6.44171e8i	0.420811	−	1.57049i	0.772904	−	0.634523i	$-0.218803\pi$
$744$	−1.66901e6	−	2.89081e6i	−0.00405266	−	0.00701941i
$745$	−4.93049e8	−	2.84662e8i	−1.19240	−	0.688432i
$746$	−1.29483e7	−	1.29483e7i	−0.0311887	−	0.0311887i
$747$	−4.04514e8	+	1.08389e8i	−0.970447	+	0.260030i
$748$	2.88145e7	+	1.07537e8i	0.0688505	+	0.256953i
$749$	−7.00378e7	+	7.00378e7i	−0.166681	+	0.166681i
$750$	1.56845e6	−	2.71664e6i	0.00371782	−	0.00643945i
$751$	−2.62130e8	+	1.51341e8i	−0.618866	+	0.357302i	−0.776427	−	0.630207i	$-0.782970\pi$
$751$	−2.62130e8	+	1.51341e8i	−0.618866	+	0.357302i	0.157561	+	0.987509i	$0.449637\pi$
$752$	−3.20360e8	−	8.58402e7i	−0.753329	−	0.201854i
$753$		−	1.69880e7i		−	0.0397884i
$754$	−9.59834e7	−	6.96559e7i	−0.223914	−	0.162496i
$755$	3.13313e8			0.728009
$756$	3.70819e6	−	1.38392e7i	0.00858216	−	0.0320291i
$757$	1.13017e8	+	1.95751e8i	0.260529	+	0.451250i	0.966383	−	0.257108i	$-0.0827697\pi$
$757$	1.13017e8	+	1.95751e8i	0.260529	+	0.451250i	−0.705854	+	0.708358i	$0.749436\pi$
$758$	9.97018e7	+	5.75629e7i	0.228926	+	0.132171i
$759$	−2.90184e6	−	2.90184e6i	−0.00663664	−	0.00663664i
$760$	−1.51820e8	+	4.06802e7i	−0.345851	+	0.0926706i
$761$	−2.47488e7	−	9.23639e7i	−0.0561566	−	0.209579i	0.932147	−	0.362081i	$-0.117934\pi$
$761$	−2.47488e7	−	9.23639e7i	−0.0561566	−	0.209579i	−0.988303	+	0.152502i	$0.951267\pi$
$762$	−3.35468e6	+	3.35468e6i	−0.00758203	+	0.00758203i
$763$	−2.30358e7	+	3.98992e7i	−0.0518597	+	0.0898236i
$764$	5.38037e7	−	3.10636e7i	0.120651	−	0.0696581i
$765$	−1.45145e8	−	3.88916e7i	−0.324204	−	0.0868703i
$766$		−	1.82849e7i		−	0.0406825i
$767$	3.69508e8	−	5.09170e8i	0.818914	−	1.12844i
$768$	1.10006e7			0.0242847
$769$	−1.13874e6	+	4.24984e6i	−0.00250407	+	0.00934530i	−0.967167	−	0.254143i	$-0.918206\pi$
$769$	−1.13874e6	+	4.24984e6i	−0.00250407	+	0.00934530i	0.964662	+	0.263489i	$0.0848732\pi$
$770$	1.52275e7	+	2.63748e7i	0.0333546	+	0.0577719i
$771$	−1.41638e7	−	8.17746e6i	−0.0309041	−	0.0178425i
$772$	8.98418e6	+	8.98418e6i	0.0195266	+	0.0195266i
$773$	7.14801e8	−	1.91530e8i	1.54756	−	0.414667i	0.618858	−	0.785503i	$-0.287596\pi$
$773$	7.14801e8	−	1.91530e8i	1.54756	−	0.414667i	0.928698	+	0.370836i	$0.120929\pi$
$774$	1.88084e7	+	7.01938e7i	0.0405629	+	0.151383i
$775$	−1.61252e7	+	1.61252e7i	−0.0346418	+	0.0346418i
$776$	2.54667e7	−	4.41096e7i	0.0544988	−	0.0943948i
$777$	7.94343e6	−	4.58614e6i	0.0169334	−	0.00977653i
$778$	−5.61627e7	−	1.50488e7i	−0.119264	−	0.0319567i
$779$			5.13876e8i			1.08704i
$780$	−1.62176e7	−	1.69558e6i	−0.0341746	−	0.00357300i
$781$	−3.97490e8			−0.834398
$782$	−2.67421e6	+	9.98030e6i	−0.00559211	+	0.0208700i
$783$	2.57705e7	+	4.46359e7i	0.0536832	+	0.0929820i
$784$	2.92411e8	+	1.68824e8i	0.606800	+	0.350336i
$785$	1.18007e8	+	1.18007e8i	0.243948	+	0.243948i
$786$	5.44090e6	−	1.45788e6i	0.0112048	−	0.00300231i
$787$	1.13954e8	+	4.25284e8i	0.233780	+	0.872479i	0.978695	+	0.205319i	$0.0658233\pi$
$787$	1.13954e8	+	4.25284e8i	0.233780	+	0.872479i	−0.744915	+	0.667159i	$0.767510\pi$
$788$	−6.09547e7	+	6.09547e7i	−0.124574	+	0.124574i
$789$	−9.00938e6	+	1.56047e7i	−0.0183427	+	0.0317705i
$790$	1.13980e8	−	6.58062e7i	0.231178	−	0.133471i
$791$	1.25251e7	+	3.35609e6i	0.0253077	+	0.00678117i
$792$		−	1.47053e8i		−	0.296005i
$793$	−4.29509e8	+	6.82682e7i	−0.861296	+	0.136899i
$794$	1.65726e8			0.331078
$795$	−8.49764e6	+	3.17136e7i	−0.0169121	+	0.0631167i
$796$	2.59733e8	+	4.49871e8i	0.514977	+	0.891966i
$797$	−1.66629e8	−	9.62034e7i	−0.329137	−	0.190027i	0.326321	−	0.945259i	$-0.394191\pi$
$797$	−1.66629e8	−	9.62034e7i	−0.329137	−	0.190027i	−0.655458	+	0.755232i	$0.727524\pi$
$798$	1.18029e6	+	1.18029e6i	0.00232262	+	0.00232262i
$799$	1.51593e8	−	4.06192e7i	0.297193	−	0.0796326i
$800$	6.17512e6	+	2.30459e7i	0.0120608	+	0.0450115i
$801$	1.44352e8	−	1.44352e8i	0.280883	−	0.280883i
$802$	3.36974e7	−	5.83656e7i	0.0653241	−	0.113145i
$803$	−2.41423e8	+	1.39386e8i	−0.466265	+	0.269198i
$804$	3.45857e7	+	9.26720e6i	0.0665469	+	0.0178312i
$805$		−	7.37781e7i		−	0.141429i
$806$	−5.41243e7	−	2.07424e7i	−0.103368	−	0.0396145i
$807$	−2.81041e7			−0.0534748
$808$	−6.15864e7	+	2.29843e8i	−0.116748	+	0.435710i
$809$	2.42457e8	+	4.19949e8i	0.457920	+	0.793141i	0.998851	−	0.0479260i	$-0.0152612\pi$
$809$	2.42457e8	+	4.19949e8i	0.457920	+	0.793141i	−0.540931	+	0.841067i	$0.681928\pi$
$810$	8.42117e7	+	4.86197e7i	0.158459	+	0.0914865i
$811$	8.76833e7	+	8.76833e7i	0.164382	+	0.164382i	0.784505	−	0.620123i	$-0.212917\pi$
$811$	8.76833e7	+	8.76833e7i	0.164382	+	0.164382i	−0.620123	+	0.784505i	$0.712917\pi$
$812$	3.31329e8	−	8.87794e7i	0.618859	−	0.165823i
$813$	1.19555e6	+	4.46185e6i	0.00222482	+	0.00830315i
$814$	6.53633e7	−	6.53633e7i	0.121188	−	0.121188i
$815$	3.98691e8	−	6.90552e8i	0.736484	−	1.27563i
$816$	−5.49253e6	+	3.17111e6i	−0.0101088	+	0.00583635i
$817$	4.27222e8	+	1.14474e8i	0.783406	+	0.209913i
$818$		−	5.01953e7i		−	0.0917071i
$819$	−1.03184e8	−	2.31414e8i	−0.187827	−	0.421247i
$820$	−5.56248e8			−1.00885
$821$	−2.26346e8	+	8.44736e8i	−0.409019	+	1.52648i	0.387501	+	0.921869i	$0.373339\pi$
$821$	−2.26346e8	+	8.44736e8i	−0.409019	+	1.52648i	−0.796520	+	0.604612i	$0.793328\pi$
$822$	1.91403e6	+	3.31520e6i	0.00344615	+	0.00596890i
$823$	2.88097e8	+	1.66333e8i	0.516820	+	0.298386i	0.735633	−	0.677381i	$-0.236885\pi$
$823$	2.88097e8	+	1.66333e8i	0.516820	+	0.298386i	−0.218813	+	0.975767i	$0.570218\pi$
$824$	−1.74036e8	−	1.74036e8i	−0.311070	−	0.311070i
$825$	1.35182e6	−	362220.i	0.00240746	−	0.000645076i
$826$	−1.80424e7	−	6.73351e7i	−0.0320150	−	0.119482i
$827$	−1.08746e8	+	1.08746e8i	−0.192263	+	0.192263i	−0.796673	−	0.604410i	$-0.793409\pi$
$827$	−1.08746e8	+	1.08746e8i	−0.192263	+	0.192263i	0.604410	+	0.796673i	$0.293409\pi$
$828$	−8.73863e7	+	1.51358e8i	−0.153940	+	0.266633i
$829$	2.29108e8	−	1.32275e8i	0.402139	−	0.232175i	−0.285268	−	0.958448i	$-0.592083\pi$
$829$	2.29108e8	−	1.32275e8i	0.402139	−	0.232175i	0.687406	+	0.726273i	$0.258749\pi$
$830$	1.02097e8	+	2.73568e7i	0.178558	+	0.0478444i
$831$		−	1.39456e7i		−	0.0243016i
$832$	3.51365e8	−	2.84848e8i	0.610082	−	0.494587i
$833$	−1.59773e8			−0.276419
$834$	−18142.8	+	67709.7i	−3.12756e−5	+	0.000116722i
$835$	−5.16869e8	−	8.95243e8i	−0.887812	−	1.53774i
$836$	−3.80267e8	−	2.19548e8i	−0.650834	−	0.375759i
$837$	1.78124e7	+	1.78124e7i	0.0303770	+	0.0303770i
$838$	1.04989e8	−	2.81316e7i	0.178406	−	0.0478038i
$839$	−5.57409e7	−	2.08028e8i	−0.0943817	−	0.352237i	0.902543	−	0.430599i	$-0.141698\pi$
$839$	−5.57409e7	−	2.08028e8i	−0.0943817	−	0.352237i	−0.996925	+	0.0783619i	$0.975031\pi$
$840$	−2.60416e6	+	2.60416e6i	−0.00439370	+	0.00439370i
$841$	−3.19572e8	+	5.53516e8i	−0.537256	+	0.930555i
$842$	−1.19866e8	+	6.92047e7i	−0.200798	+	0.115931i
$843$	3.58693e6	+	961115.i	0.00598743	+	0.00160433i
$844$		−	7.61940e8i		−	1.26734i
$845$	−4.83683e8	+	3.14860e8i	−0.801662	+	0.521852i
$846$	−1.01701e8			−0.167963
$847$	2.77534e7	−	1.03577e8i	0.0456737	−	0.170457i
$848$	−4.97376e8	−	8.61480e8i	−0.815637	−	1.41273i
$849$	−2.14402e7	−	1.23785e7i	−0.0350352	−	0.0202276i
$850$	−2.49157e6	−	2.49157e6i	−0.00405710	−	0.00405710i
$851$	−2.16303e8	+	5.79581e7i	−0.350972	+	0.0940428i
$852$	−6.10347e6	−	2.27785e7i	−0.00986866	−	0.0368304i
$853$	5.01340e7	−	5.01340e7i	0.0807766	−	0.0807766i	−0.665564	−	0.746341i	$-0.731809\pi$
$853$	5.01340e7	−	5.01340e7i	0.0807766	−	0.0807766i	0.746341	+	0.665564i	$0.231809\pi$
$854$	−2.40949e7	+	4.17336e7i	−0.0386858	+	0.0670058i
$855$	5.13255e8	−	2.96328e8i	0.821173	−	0.474104i
$856$	−1.16597e8	−	3.12421e7i	−0.185894	−	0.0498102i
$857$			8.31708e8i			1.32138i	0.750658	+	0.660691i	$0.229737\pi$
$857$			8.31708e8i			1.32138i	−0.750658	+	0.660691i	$0.770263\pi$
$858$	2.24011e6	+	2.76322e6i	0.00354656	+	0.00437475i
$859$	−4.48498e8			−0.707589			−0.353795	−	0.935323i	$-0.615109\pi$
$859$	−4.48498e8			−0.707589			−0.353795	+	0.935323i	$0.615109\pi$
$860$	−1.23913e8	+	4.62448e8i	−0.194814	+	0.727056i
$861$	6.02040e6	+	1.04276e7i	0.00943226	+	0.0163372i
$862$	1.31168e6	+	757299.i	0.00204789	+	0.00118235i
$863$	−6.64442e8	−	6.64442e8i	−1.03377	−	1.03377i	−0.999409	−	0.0343632i	$-0.989060\pi$
$863$	−6.64442e8	−	6.64442e8i	−1.03377	−	1.03377i	−0.0343632	−	0.999409i	$-0.510940\pi$
$864$	2.54571e7	−	6.82121e6i	0.0394700	−	0.0105760i
$865$	9.17957e7	+	3.42586e8i	0.141832	+	0.529324i
$866$	−6.18439e7	+	6.18439e7i	−0.0952232	+	0.0952232i
$867$	−1.06532e7	+	1.84518e7i	−0.0163464	+	0.0283128i
$868$	1.45188e8	−	8.38242e7i	0.222009	−	0.128177i
$869$	7.23907e8	+	1.93970e8i	1.10312	+	0.295581i
$870$		−	6.49981e6i		−	0.00987058i
$871$	1.15746e9	−	5.16095e8i	1.75167	−	0.781043i
$872$	−5.61474e7			−0.0846798
$873$	−4.97067e7	+	1.85508e8i	−0.0747088	+	0.278817i
$874$	−2.03757e7	−	3.52918e7i	−0.0305196	−	0.0528615i
$875$	2.78108e8	+	1.60566e8i	0.415135	+	0.239678i
$876$	−1.16947e7	−	1.16947e7i	−0.0173970	−	0.0173970i
$877$	−1.59390e8	+	4.27083e7i	−0.236299	+	0.0633160i	−0.375025	−	0.927015i	$-0.622366\pi$
$877$	−1.59390e8	+	4.27083e7i	−0.236299	+	0.0633160i	0.138726	+	0.990331i	$0.455699\pi$
$878$	−4.03879e7	−	1.50730e8i	−0.0596716	−	0.222698i
$879$	5.80482e6	−	5.80482e6i	0.00854717	−	0.00854717i
$880$	2.28197e8	−	3.95249e8i	0.334859	−	0.579993i
$881$	3.68288e8	−	2.12631e8i	0.538592	−	0.310956i	−0.205916	−	0.978570i	$-0.566017\pi$
$881$	3.68288e8	−	2.12631e8i	0.538592	−	0.310956i	0.744508	+	0.667614i	$0.232684\pi$
$882$	1.00008e8	+	2.67972e7i	0.145757	+	0.0390556i
$883$			1.18261e9i			1.71775i	0.512187	+	0.858874i	$0.328835\pi$
$883$			1.18261e9i			1.71775i	−0.512187	+	0.858874i	$0.671165\pi$
$884$	−8.36587e7	+	2.18295e8i	−0.121103	+	0.316000i
$885$	3.44800e7			0.0497436
$886$	−4.36441e7	+	1.62882e8i	−0.0627516	+	0.234192i
$887$	−4.98447e8	−	8.63336e8i	−0.714247	−	1.23711i	−0.963249	−	0.268609i	$-0.913436\pi$
$887$	−4.98447e8	−	8.63336e8i	−0.714247	−	1.23711i	0.249002	−	0.968503i	$-0.419897\pi$
$888$	9.68064e6	+	5.58912e6i	0.0138250	+	0.00798187i
$889$	−3.43425e8	−	3.43425e8i	−0.488795	−	0.488795i
$890$	−4.97693e7	+	1.33357e7i	−0.0705979	+	0.0189166i
$891$	1.43311e8	+	5.34845e8i	0.202604	+	0.756127i
$892$	−2.45564e8	+	2.45564e8i	−0.345995	+	0.345995i
$893$	−3.09491e8	+	5.36054e8i	−0.434604	+	0.752756i
$894$	−6.38120e6	+	3.68419e6i	−0.00893079	+	0.00515619i
$895$	3.05479e8	+	8.18528e7i	0.426100	+	0.114173i
$896$		−	2.32239e8i		−	0.322858i
$897$	−1.35270e6	−	8.51052e6i	−0.00187424	−	0.0117918i
$898$	−1.05944e8			−0.146300
$899$	−1.56093e8	+	5.82547e8i	−0.214835	+	0.801774i
$900$	−2.98010e7	−	5.16169e7i	−0.0408794	−	0.0708051i
$901$	4.07649e8	+	2.35356e8i	0.557329	+	0.321774i
$902$	8.58047e7	+	8.58047e7i	0.116921	+	0.116921i
$903$	1.00104e7	−	2.68227e6i	0.0135952	−	0.00364283i
$904$	4.09006e6	+	1.52643e7i	0.00553636	+	0.0206620i
$905$	−1.02519e8	+	1.02519e8i	−0.138311	+	0.138311i
$906$	2.02749e6	−	3.51172e6i	0.00272631	−	0.00472211i
$907$	4.90070e8	−	2.82942e8i	0.656805	−	0.379206i	−0.134254	−	0.990947i	$-0.542864\pi$
$907$	4.90070e8	−	2.82942e8i	0.656805	−	0.379206i	0.791058	+	0.611741i	$0.209530\pi$
$908$	1.07236e9	+	2.87337e8i	1.43246	+	0.383826i
$909$		−	8.97231e8i		−	1.19457i
$910$	−6.64988e6	+	6.36038e7i	−0.00882448	+	0.0844032i
$911$	−3.50495e8			−0.463582			−0.231791	−	0.972766i	$-0.574458\pi$
$911$	−3.50495e8			−0.463582			−0.231791	+	0.972766i	$0.574458\pi$
$912$	6.47412e6	−	2.41617e7i	0.00853486	−	0.0318525i
$913$	3.00941e8	+	5.21245e8i	0.395430	+	0.684904i
$914$	−1.49867e8	−	8.65257e7i	−0.196276	−	0.113320i
$915$	−1.68543e7	−	1.68543e7i	−0.0220012	−	0.0220012i
$916$	2.07229e8	−	5.55268e7i	0.269627	−	0.0722464i
$917$	1.49247e8	+	5.56996e8i	0.193551	+	0.722343i
$918$	−2.75225e6	+	2.75225e6i	−0.00355763	+	0.00355763i
$919$	1.00136e8	−	1.73441e8i	0.129016	−	0.223462i	−0.794280	−	0.607552i	$-0.792151\pi$
$919$	1.00136e8	−	1.73441e8i	0.129016	−	0.223462i	0.923296	+	0.384090i	$0.125485\pi$
$920$	7.78671e7	−	4.49566e7i	0.0999978	−	0.0577338i
$921$	−4.78214e7	−	1.28137e7i	−0.0612130	−	0.0164020i
$922$			1.58878e8i			0.202708i
$923$	−6.75526e8	−	4.90234e8i	−0.859086	−	0.623446i
$924$	−1.02886e7			−0.0130418
$925$	1.97652e7	−	7.37649e7i	0.0249734	−	0.0932018i
$926$	7.20997e6	+	1.24880e7i	0.00908031	+	0.0157276i
$927$	8.03713e8	+	4.64024e8i	1.00893	+	0.582507i
$928$	4.46170e8	+	4.46170e8i	0.558286	+	0.558286i
$929$	1.10734e9	−	2.96711e8i	1.38113	−	0.370072i	0.509597	−	0.860413i	$-0.329794\pi$
$929$	1.10734e9	−	2.96711e8i	1.38113	−	0.370072i	0.871531	+	0.490341i	$0.163128\pi$
$930$	−822205.	−	3.06851e6i	−0.00102219	−	0.00381486i
$931$	4.45586e8	−	4.45586e8i	0.552182	−	0.552182i
$932$	−2.44190e8	+	4.22949e8i	−0.301634	+	0.522445i
$933$	3.75454e7	−	2.16768e7i	0.0462287	−	0.0266902i
$934$	−8.27056e6	−	2.21609e6i	−0.0101507	−	0.00271986i
$935$			2.15964e8i			0.264208i
$936$	1.81364e8	−	2.49914e8i	0.221169	−	0.304763i
$937$	−1.31881e9			−1.60311			−0.801554	−	0.597922i	$-0.795993\pi$
$937$	−1.31881e9			−1.60311			−0.801554	+	0.597922i	$0.795993\pi$
$938$	3.63450e7	−	1.35641e8i	0.0440389	−	0.164355i
$939$	−6.68166e6	−	1.15730e7i	−0.00807026	−	0.0139781i
$940$	−5.80255e8	−	3.35010e8i	−0.698611	−	0.403343i
$941$	−6.60638e8	−	6.60638e8i	−0.792856	−	0.792856i	0.189101	−	0.981958i	$-0.439443\pi$
$941$	−6.60638e8	−	6.60638e8i	−0.792856	−	0.792856i	−0.981958	+	0.189101i	$0.939443\pi$
$942$	2.08630e6	−	559023.i	0.00249589	−	0.000668771i
$943$	−7.60837e7	−	2.83948e8i	−0.0907312	−	0.338613i
$944$	−7.38695e8	+	7.38695e8i	−0.878110	+	0.878110i
$945$	1.38964e7	−	2.40692e7i	0.0164667	−	0.0285211i
$946$	9.04498e7	−	5.22212e7i	0.106840	−	0.0616841i
$947$	−1.47704e9	−	3.95771e8i	−1.73917	−	0.466009i	−0.756908	−	0.653521i	$-0.773291\pi$
$947$	−1.47704e9	−	3.95771e8i	−1.73917	−	0.466009i	−0.982262	+	0.187512i	$0.939958\pi$
$948$			4.44624e7i			0.0521877i
$949$	−5.82201e8	−	6.08700e7i	−0.681200	−	0.0712205i
$950$	1.38973e7			0.0162091
$951$	−7.93910e6	+	2.96291e7i	−0.00923059	+	0.0344490i
$952$	2.64002e7	+	4.57264e7i	0.0305982	+	0.0529976i
$953$	−2.98183e8	−	1.72156e8i	−0.344512	−	0.198904i	0.317754	−	0.948173i	$-0.397071\pi$
$953$	−2.98183e8	−	1.72156e8i	−0.344512	−	0.198904i	−0.662265	+	0.749269i	$0.730405\pi$
$954$	−2.15690e8	−	2.15690e8i	−0.248419	−	0.248419i
$955$	1.16410e8	−	3.11920e7i	0.133654	−	0.0358124i
$956$	−1.06431e8	−	3.97207e8i	−0.121814	−	0.454615i
$957$	2.61715e7	−	2.61715e7i	0.0298602	−	0.0298602i
$958$	6.97919e7	−	1.20883e8i	0.0793796	−	0.137489i
$959$	−3.39384e8	+	1.95943e8i	−0.384800	+	0.222165i
$960$	2.39456e7	+	6.41621e6i	0.0270653	+	0.00725212i
$961$		−	5.92742e8i		−	0.667876i
$962$	1.91697e8	−	3.04693e7i	0.215323	−	0.0342245i
$963$	4.55155e8			0.509660
$964$	−2.42048e8	+	9.03337e8i	−0.270191	+	1.00837i
$965$	1.23234e7	+	2.13447e7i	0.0137135	+	0.0237524i
$966$	−826932.	−	477430.i	−0.000917357	−	0.000529637i
$967$	1.10118e8	+	1.10118e8i	0.121781	+	0.121781i	0.765371	−	0.643590i	$-0.222556\pi$
$967$	1.10118e8	+	1.10118e8i	0.121781	+	0.121781i	−0.643590	+	0.765371i	$0.722556\pi$
$968$	1.26229e8	−	3.38230e7i	0.139166	−	0.0372895i
$969$	3.06353e6	+	1.14332e7i	0.00336705	+	0.0125660i
$970$	3.42754e7	−	3.42754e7i	0.0375550	−	0.0375550i
$971$	7.00341e8	−	1.21303e9i	0.764983	−	1.32499i	−0.175273	−	0.984520i	$-0.556081\pi$
$971$	7.00341e8	−	1.21303e9i	0.764983	−	1.32499i	0.940256	−	0.340469i	$-0.110586\pi$
$972$	−8.55461e7	+	4.93900e7i	−0.0931539	+	0.0537824i
$973$	−6.93157e6	−	1.85731e6i	−0.00752477	−	0.00201626i
$974$			1.70056e7i			0.0184041i
$975$	2.74413e6	+	1.05165e6i	0.00296068	+	0.00113464i
$976$	7.22166e8			0.776762
$977$	5.17641e7	−	1.93186e8i	0.0555067	−	0.207154i	−0.932603	−	0.360904i	$-0.882468\pi$
$977$	5.17641e7	−	1.93186e8i	0.0555067	−	0.207154i	0.988110	+	0.153750i	$0.0491350\pi$
$978$	−5.15998e6	−	8.93734e6i	−0.00551609	−	0.00955415i
$979$	−2.54092e8	−	1.46700e8i	−0.270796	−	0.156344i
$980$	4.82327e8	+	4.82327e8i	0.512464	+	0.512464i
$981$	2.04498e8	−	5.47951e7i	0.216612	−	0.0580409i
$982$	7.04242e7	+	2.62827e8i	0.0743682	+	0.277546i
$983$	−2.37296e8	+	2.37296e8i	−0.249821	+	0.249821i	−0.820897	−	0.571076i	$-0.806526\pi$
$983$	−2.37296e8	+	2.37296e8i	−0.249821	+	0.249821i	0.571076	+	0.820897i	$0.306526\pi$
$984$	−7.33704e6	+	1.27081e7i	−0.00770080	+	0.0133382i
$985$	−1.44817e8	+	8.36099e7i	−0.151534	+	0.0874881i
$986$	−9.00114e7	−	2.41185e7i	−0.0939003	−	0.0251605i
$987$			1.45036e7i			0.0150842i
$988$	−3.75483e8	−	8.42109e8i	−0.389331	−	0.873167i
$989$	−2.53015e8			−0.261552
$990$	3.62215e7	−	1.35180e8i	0.0373302	−	0.139318i
$991$	1.32203e7	+	2.28983e7i	0.0135838	+	0.0235279i	0.872737	−	0.488190i	$-0.162343\pi$
$991$	1.32203e7	+	2.28983e7i	0.0135838	+	0.0235279i	−0.859154	+	0.511718i	$0.829009\pi$
$992$	2.67073e8	+	1.54194e8i	0.273586	+	0.157955i
$993$	1.90904e7	+	1.90904e7i	0.0194970	+	0.0194970i
$994$	−8.93349e7	+	2.39372e7i	−0.0909624	+	0.0243733i
$995$	2.60807e8	+	9.73344e8i	0.264758	+	0.988091i
$996$	−2.52494e7	+	2.52494e7i	−0.0255548	+	0.0255548i
$997$	1.27675e8	−	2.21140e8i	0.128831	−	0.223142i	−0.794393	−	0.607404i	$-0.792211\pi$
$997$	1.27675e8	−	2.21140e8i	0.128831	−	0.223142i	0.923224	+	0.384262i	$0.125544\pi$
$998$	−1.11848e8	+	6.45753e7i	−0.112522	+	0.0649643i
$999$	−8.14827e7	−	2.18332e7i	−0.0817276	−	0.0218989i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.7.f.a.11.3	yes	24
13.6	odd	12	inner	13.7.f.a.6.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.7.f.a.6.3	✓	24	13.6	odd	12	inner
13.7.f.a.11.3	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	13.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.397723 + 1.48432i) q^{2} +(-0.503519 - 0.872121i) q^{3} +(53.3806 + 30.8193i) q^{4} +(84.5480 + 84.5480i) q^{5} +(1.49477 - 0.400522i) q^{6} +(41.0022 + 153.022i) q^{7} +(-136.519 + 136.519i) q^{8} +(363.993 - 630.454i) q^{9} +O(q^{10})\)	\(q+(-0.397723 + 1.48432i) q^{2} +(-0.503519 - 0.872121i) q^{3} +(53.3806 + 30.8193i) q^{4} +(84.5480 + 84.5480i) q^{5} +(1.49477 - 0.400522i) q^{6} +(41.0022 + 153.022i) q^{7} +(-136.519 + 136.519i) q^{8} +(363.993 - 630.454i) q^{9} +(-159.123 + 91.8697i) q^{10} +(-1010.62 - 270.795i) q^{11} -62.0725i q^{12} +(-1383.55 - 1706.63i) q^{13} -243.442 q^{14} +(31.1645 - 116.308i) q^{15} +(1824.09 + 3159.42i) q^{16} +(-1495.03 - 863.153i) q^{17} +(791.028 + 791.028i) q^{18} +(6576.65 - 1762.21i) q^{19} +(1907.51 + 7118.93i) q^{20} +(112.809 - 112.809i) q^{21} +(803.894 - 1392.38i) q^{22} +(-3373.09 + 1947.46i) q^{23} +(187.801 + 50.3210i) q^{24} -1328.27i q^{25} +(3083.46 - 1374.87i) q^{26} -1467.24 q^{27} +(-2527.32 + 9432.09i) q^{28} +(-17563.9 - 30421.6i) q^{29} +(160.243 + 92.5164i) q^{30} +(-12140.0 - 12140.0i) q^{31} +(-17350.3 + 4649.00i) q^{32} +(272.701 + 1017.73i) q^{33} +(1875.80 - 1875.80i) q^{34} +(-9471.08 + 16404.4i) q^{35} +(38860.3 - 22436.0i) q^{36} +(55534.6 + 14880.5i) q^{37} +10462.7i q^{38} +(-791.747 + 2065.95i) q^{39} -23084.8 q^{40} +(-19534.1 + 72902.3i) q^{41} +(122.578 + 212.311i) q^{42} +(56257.3 + 32480.2i) q^{43} +(-45601.9 - 45601.9i) q^{44} +(84078.5 - 22528.8i) q^{45} +(-1549.09 - 5781.30i) q^{46} +(-64283.9 + 64283.9i) q^{47} +(1836.93 - 3181.66i) q^{48} +(80152.3 - 46276.0i) q^{49} +(1971.58 + 528.282i) q^{50} +1738.46i q^{51} +(-21257.5 - 133741. i) q^{52} -272670. q^{53} +(583.555 - 2177.86i) q^{54} +(-62550.8 - 108341. i) q^{55} +(-26488.0 - 15292.9i) q^{56} +(-4848.33 - 4848.33i) q^{57} +(52141.0 - 13971.2i) q^{58} +(74113.8 + 276596. i) q^{59} +(5248.10 - 5248.10i) q^{60} +(98976.0 - 171431. i) q^{61} +(22848.1 - 13191.3i) q^{62} +(111398. + 29849.1i) q^{63} +205882. i q^{64} +(27316.1 - 261269. i) q^{65} -1619.10 q^{66} +(-149296. + 557182. i) q^{67} +(-53203.6 - 92151.3i) q^{68} +(3396.84 + 1961.16i) q^{69} +(-20582.5 - 20582.5i) q^{70} +(366966. - 98328.2i) q^{71} +(36376.9 + 135761. i) q^{72} +(188403. - 188403. i) q^{73} +(-44174.7 + 76512.9i) q^{74} +(-1158.41 + 668.809i) q^{75} +(405376. + 108620. i) q^{76} -165751. i q^{77} +(-2751.63 - 1996.88i) q^{78} -716299. q^{79} +(-112899. + 421347. i) q^{80} +(-264612. - 458322. i) q^{81} +(-100441. - 57989.8i) q^{82} +(-406773. - 406773. i) q^{83} +(9498.48 - 2545.11i) q^{84} +(-53423.5 - 199379. i) q^{85} +(-70585.8 + 70585.8i) q^{86} +(-17687.6 + 30635.8i) q^{87} +(174937. - 101000. i) q^{88} +(270869. + 72579.1i) q^{89} +133760. i q^{90} +(204425. - 281690. i) q^{91} -240077. q^{92} +(-4474.84 + 16700.3i) q^{93} +(-69850.7 - 120985. i) q^{94} +(705034. + 407052. i) q^{95} +(12790.7 + 12790.7i) q^{96} +(-254823. + 68279.7i) q^{97} +(36810.0 + 137377. i) q^{98} +(-538583. + 538583. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 2 q^{3} - 6 q^{4} - 114 q^{5} + 634 q^{6} + 316 q^{7} - 1398 q^{8} - 1946 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 - 2 * q^3 - 6 * q^4 - 114 * q^5 + 634 * q^6 + 316 * q^7 - 1398 * q^8 - 1946 * q^9	\( 24 q - 12 q^{2} - 2 q^{3} - 6 q^{4} - 114 q^{5} + 634 q^{6} + 316 q^{7} - 1398 q^{8} - 1946 q^{9} + 4674 q^{10} + 228 q^{11} - 1552 q^{13} - 14616 q^{14} + 7486 q^{15} - 2138 q^{16} + 20898 q^{17} - 5630 q^{18} - 14036 q^{19} - 14634 q^{20} - 314 q^{21} + 37852 q^{22} + 29634 q^{23} + 47154 q^{24} + 510 q^{26} - 107060 q^{27} - 40572 q^{28} + 1026 q^{29} - 247734 q^{30} - 118116 q^{31} + 180876 q^{32} + 306046 q^{33} + 101898 q^{34} + 104862 q^{35} + 105066 q^{36} - 31470 q^{37} + 28510 q^{39} - 275328 q^{40} - 357216 q^{41} - 25636 q^{42} - 480486 q^{43} - 797712 q^{44} + 464248 q^{45} + 1012050 q^{46} + 140028 q^{47} + 676102 q^{48} + 854562 q^{49} + 756714 q^{50} - 771704 q^{52} - 1397076 q^{53} - 1271048 q^{54} - 205490 q^{55} - 1461108 q^{56} - 1483394 q^{57} + 1133806 q^{58} + 1568052 q^{59} + 886808 q^{60} + 768676 q^{61} + 3741966 q^{62} + 1336264 q^{63} - 946968 q^{65} - 5076928 q^{66} - 1489892 q^{67} - 569052 q^{68} - 1475766 q^{69} - 2626556 q^{70} + 2136948 q^{71} + 4787052 q^{72} + 326326 q^{73} + 2159718 q^{74} + 3466008 q^{75} + 1522158 q^{76} - 1573544 q^{78} - 1734344 q^{79} - 5214300 q^{80} - 773072 q^{81} - 3540426 q^{82} - 3642132 q^{83} + 2952364 q^{84} + 3509916 q^{85} - 132324 q^{86} + 531698 q^{87} + 4478052 q^{88} + 632754 q^{89} - 2946788 q^{91} - 1656060 q^{92} - 295514 q^{93} + 1552210 q^{94} - 2753718 q^{95} - 3979208 q^{96} + 2258214 q^{97} + 4984308 q^{98} + 4336480 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 - 2 * q^3 - 6 * q^4 - 114 * q^5 + 634 * q^6 + 316 * q^7 - 1398 * q^8 - 1946 * q^9 + 4674 * q^10 + 228 * q^11 - 1552 * q^13 - 14616 * q^14 + 7486 * q^15 - 2138 * q^16 + 20898 * q^17 - 5630 * q^18 - 14036 * q^19 - 14634 * q^20 - 314 * q^21 + 37852 * q^22 + 29634 * q^23 + 47154 * q^24 + 510 * q^26 - 107060 * q^27 - 40572 * q^28 + 1026 * q^29 - 247734 * q^30 - 118116 * q^31 + 180876 * q^32 + 306046 * q^33 + 101898 * q^34 + 104862 * q^35 + 105066 * q^36 - 31470 * q^37 + 28510 * q^39 - 275328 * q^40 - 357216 * q^41 - 25636 * q^42 - 480486 * q^43 - 797712 * q^44 + 464248 * q^45 + 1012050 * q^46 + 140028 * q^47 + 676102 * q^48 + 854562 * q^49 + 756714 * q^50 - 771704 * q^52 - 1397076 * q^53 - 1271048 * q^54 - 205490 * q^55 - 1461108 * q^56 - 1483394 * q^57 + 1133806 * q^58 + 1568052 * q^59 + 886808 * q^60 + 768676 * q^61 + 3741966 * q^62 + 1336264 * q^63 - 946968 * q^65 - 5076928 * q^66 - 1489892 * q^67 - 569052 * q^68 - 1475766 * q^69 - 2626556 * q^70 + 2136948 * q^71 + 4787052 * q^72 + 326326 * q^73 + 2159718 * q^74 + 3466008 * q^75 + 1522158 * q^76 - 1573544 * q^78 - 1734344 * q^79 - 5214300 * q^80 - 773072 * q^81 - 3540426 * q^82 - 3642132 * q^83 + 2952364 * q^84 + 3509916 * q^85 - 132324 * q^86 + 531698 * q^87 + 4478052 * q^88 + 632754 * q^89 - 2946788 * q^91 - 1656060 * q^92 - 295514 * q^93 + 1552210 * q^94 - 2753718 * q^95 - 3979208 * q^96 + 2258214 * q^97 + 4984308 * q^98 + 4336480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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