LMFDB - Embedded newform 13.7.f.a.7.3

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			7.3
Character	$\chi$	$=$	13.7
Dual form			13.7.f.a.2.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.77368 + 1.27910i) q^{2} +(4.54257 - 7.86796i) q^{3} +(-34.2737 + 19.7879i) q^{4} +(-109.630 - 109.630i) q^{5} +(-11.6208 + 43.3696i) q^{6} +(-504.391 - 135.151i) q^{7} +(361.954 - 361.954i) q^{8} +(323.230 + 559.851i) q^{9} +O(q^{10})$	\(q+(-4.77368 + 1.27910i) q^{2} +(4.54257 - 7.86796i) q^{3} +(-34.2737 + 19.7879i) q^{4} +(-109.630 - 109.630i) q^{5} +(-11.6208 + 43.3696i) q^{6} +(-504.391 - 135.151i) q^{7} +(361.954 - 361.954i) q^{8} +(323.230 + 559.851i) q^{9} +(663.567 + 383.110i) q^{10} +(246.492 + 919.919i) q^{11} +359.552i q^{12} +(300.508 - 2176.35i) q^{13} +2580.68 q^{14} +(-1360.56 + 364.562i) q^{15} +(1.54938 - 2.68361i) q^{16} +(-5348.10 + 3087.73i) q^{17} +(-2259.11 - 2259.11i) q^{18} +(1060.35 - 3957.28i) q^{19} +(5926.77 + 1588.07i) q^{20} +(-3354.60 + 3354.60i) q^{21} +(-2353.35 - 4076.12i) q^{22} +(-9993.12 - 5769.53i) q^{23} +(-1203.64 - 4492.04i) q^{24} +8412.42i q^{25} +(1349.25 + 10773.6i) q^{26} +12496.2 q^{27} +(19961.7 - 5348.72i) q^{28} +(-186.040 + 322.231i) q^{29} +(6028.59 - 3480.61i) q^{30} +(-10895.2 - 10895.2i) q^{31} +(-8482.96 + 31658.8i) q^{32} +(8357.59 + 2239.41i) q^{33} +(21580.6 - 21580.6i) q^{34} +(40479.7 + 70113.0i) q^{35} +(-22156.6 - 12792.1i) q^{36} +(-22349.7 - 83410.4i) q^{37} +20247.1i q^{38} +(-15758.4 - 12250.6i) q^{39} -79361.9 q^{40} +(1614.20 - 432.523i) q^{41} +(11722.9 - 20304.7i) q^{42} +(-88370.0 + 51020.4i) q^{43} +(-26651.5 - 26651.5i) q^{44} +(25940.7 - 96812.1i) q^{45} +(55083.8 + 14759.7i) q^{46} +(-27686.6 + 27686.6i) q^{47} +(-14.0764 - 24.3810i) q^{48} +(134258. + 77513.7i) q^{49} +(-10760.4 - 40158.3i) q^{50} +56104.9i q^{51} +(32765.9 + 80538.0i) q^{52} +239411. q^{53} +(-59653.1 + 15984.0i) q^{54} +(73827.8 - 127874. i) q^{55} +(-231485. + 133648. i) q^{56} +(-26319.0 - 26319.0i) q^{57} +(475.930 - 1776.20i) q^{58} +(120217. + 32212.1i) q^{59} +(39417.6 - 39417.6i) q^{60} +(38209.4 + 66180.6i) q^{61} +(65946.4 + 38074.2i) q^{62} +(-87369.9 - 326069. i) q^{63} -161782. i q^{64} +(-271538. + 205648. i) q^{65} -42761.0 q^{66} +(-354858. + 95083.9i) q^{67} +(122199. - 211656. i) q^{68} +(-90788.9 + 52417.0i) q^{69} +(-282919. - 282919. i) q^{70} +(-111837. + 417380. i) q^{71} +(319635. + 85645.9i) q^{72} +(343212. - 343212. i) q^{73} +(213381. + 369587. i) q^{74} +(66188.6 + 38214.0i) q^{75} +(41964.2 + 156613. i) q^{76} -497313. i q^{77} +(90895.3 + 38323.9i) q^{78} -559268. q^{79} +(-464.063 + 124.345i) q^{80} +(-178870. + 309811. i) q^{81} +(-7152.43 + 4129.46i) q^{82} +(-55181.9 - 55181.9i) q^{83} +(48593.9 - 181355. i) q^{84} +(924819. + 247805. i) q^{85} +(356590. - 356590. i) q^{86} +(1690.20 + 2927.52i) q^{87} +(422187. + 243750. i) q^{88} +(-189901. - 708722. i) q^{89} +495331. i q^{90} +(-445710. + 1.05712e6i) q^{91} +456668. q^{92} +(-135215. + 36230.8i) q^{93} +(96753.1 - 167581. i) q^{94} +(-550082. + 317590. i) q^{95} +(210556. + 210556. i) q^{96} +(328784. - 1.22704e6i) q^{97} +(-740052. - 198296. i) q^{98} +(-435344. + 435344. 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 $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−4.77368	+	1.27910i	−0.596711	+	0.159888i	−0.544518	−	0.838749i	$-0.683288\pi$
$2$	−4.77368	+	1.27910i	−0.596711	+	0.159888i	−0.0521922	+	0.998637i	$0.516621\pi$
$3$	4.54257	−	7.86796i	0.168243	−	0.291406i	−0.769559	−	0.638576i	$-0.779524\pi$
$3$	4.54257	−	7.86796i	0.168243	−	0.291406i	0.937802	+	0.347170i	$0.112857\pi$
$4$	−34.2737	+	19.7879i	−0.535526	+	0.309186i
$5$	−109.630	−	109.630i	−0.877039	−	0.877039i	0.116188	−	0.993227i	$-0.462932\pi$
$5$	−109.630	−	109.630i	−0.877039	−	0.877039i	−0.993227	+	0.116188i	$0.962932\pi$
$6$	−11.6208	+	43.3696i	−0.0538002	+	0.200785i
$7$	−504.391	−	135.151i	−1.47053	−	0.394027i	−0.567416	−	0.823431i	$-0.692057\pi$
$7$	−504.391	−	135.151i	−1.47053	−	0.394027i	−0.903112	+	0.429404i	$0.858724\pi$
$8$	361.954	−	361.954i	0.706941	−	0.706941i
$9$	323.230	+	559.851i	0.443388	+	0.767971i
$10$	663.567	+	383.110i	0.663567	+	0.383110i
$11$	246.492	+	919.919i	0.185193	+	0.691149i	0.994589	+	0.103886i	$0.0331278\pi$
$11$	246.492	+	919.919i	0.185193	+	0.691149i	−0.809396	+	0.587263i	$0.800206\pi$
$12$			359.552i			0.208074i
$13$	300.508	−	2176.35i	0.136781	−	0.990601i
$13$	300.508	−	2176.35i	0.136781	−	0.990601i
$14$	2580.68			0.940480
$15$	−1360.56	+	364.562i	−0.403130	+	0.108018i
$16$	1.54938	−	2.68361i	0.000378267	−	0.000655178i
$17$	−5348.10	+	3087.73i	−1.08856	+	0.628481i	−0.933193	−	0.359375i	$-0.882990\pi$
$17$	−5348.10	+	3087.73i	−1.08856	+	0.628481i	−0.155368	+	0.987857i	$0.549656\pi$
$18$	−2259.11	−	2259.11i	−0.387364	−	0.387364i
$19$	1060.35	−	3957.28i	0.154592	−	0.576947i	−0.844547	−	0.535481i	$-0.820130\pi$
$19$	1060.35	−	3957.28i	0.154592	−	0.576947i	0.999140	−	0.0414662i	$-0.0132029\pi$
$20$	5926.77	+	1588.07i	0.740846	+	0.198509i
$21$	−3354.60	+	3354.60i	−0.362228	+	0.362228i
$22$	−2353.35	−	4076.12i	−0.221013	−	0.382806i
$23$	−9993.12	−	5769.53i	−0.821330	−	0.474195i	0.0295450	−	0.999563i	$-0.490594\pi$
$23$	−9993.12	−	5769.53i	−0.821330	−	0.474195i	−0.850875	+	0.525368i	$0.823927\pi$
$24$	−1203.64	−	4492.04i	−0.0870687	−	0.324945i
$25$			8412.42i			0.538395i
$26$	1349.25	+	10773.6i	0.0767666	+	0.612972i
$27$	12496.2			0.634875
$28$	19961.7	−	5348.72i	0.909334	−	0.243655i
$29$	−186.040	+	322.231i	−0.00762804	+	0.0132122i	−0.869814	−	0.493379i	$-0.835761\pi$
$29$	−186.040	+	322.231i	−0.00762804	+	0.0132122i	0.862186	+	0.506592i	$0.169095\pi$
$30$	6028.59	−	3480.61i	0.223281	−	0.128911i
$31$	−10895.2	−	10895.2i	−0.365722	−	0.365722i	0.500193	−	0.865914i	$-0.333263\pi$
$31$	−10895.2	−	10895.2i	−0.365722	−	0.365722i	−0.865914	+	0.500193i	$0.833263\pi$
$32$	−8482.96	+	31658.8i	−0.258879	+	0.966151i
$33$	8357.59	+	2239.41i	0.232562	+	0.0623149i
$34$	21580.6	−	21580.6i	0.549069	−	0.549069i
$35$	40479.7	+	70113.0i	0.944134	+	1.63529i
$36$	−22156.6	−	12792.1i	−0.474892	−	0.274179i
$37$	−22349.7	−	83410.4i	−0.441232	−	1.64670i	−0.725696	−	0.688015i	$-0.758482\pi$
$37$	−22349.7	−	83410.4i	−0.441232	−	1.64670i	0.284464	−	0.958687i	$-0.408184\pi$
$38$			20247.1i			0.368988i
$39$	−15758.4	−	12250.6i	−0.265655	−	0.206521i
$40$	−79361.9			−1.24003
$41$	1614.20	−	432.523i	0.0234210	−	0.00627563i	−0.247090	−	0.968993i	$-0.579474\pi$
$41$	1614.20	−	432.523i	0.0234210	−	0.00627563i	0.270511	+	0.962717i	$0.412808\pi$
$42$	11722.9	−	20304.7i	0.158229	−	0.274061i
$43$	−88370.0	+	51020.4i	−1.11147	+	0.641710i	−0.939211	−	0.343341i	$-0.888441\pi$
$43$	−88370.0	+	51020.4i	−1.11147	+	0.641710i	−0.172264	+	0.985051i	$0.555108\pi$
$44$	−26651.5	−	26651.5i	−0.312869	−	0.312869i
$45$	25940.7	−	96812.1i	0.284672	−	1.06241i
$46$	55083.8	+	14759.7i	0.565914	+	0.151636i
$47$	−27686.6	+	27686.6i	−0.266671	+	0.266671i	−0.827758	−	0.561086i	$-0.810384\pi$
$47$	−27686.6	+	27686.6i	−0.266671	+	0.266671i	0.561086	+	0.827758i	$0.310384\pi$
$48$	−14.0764	−	24.3810i	−0.000127282	−	0.000220459i
$49$	134258.	+	77513.7i	1.14117	+	0.658856i
$50$	−10760.4	−	40158.3i	−0.0860830	−	0.321266i
$51$			56104.9i			0.422951i
$52$	32765.9	+	80538.0i	0.233030	+	0.572784i
$53$	239411.			1.60811			0.804056	−	0.594554i	$-0.202671\pi$
$53$	239411.			1.60811			0.804056	+	0.594554i	$0.202671\pi$
$54$	−59653.1	+	15984.0i	−0.378837	+	0.101509i
$55$	73827.8	−	127874.i	0.443743	−	0.768586i
$56$	−231485.	+	133648.i	−1.31813	+	0.761024i
$57$	−26319.0	−	26319.0i	−0.142117	−	0.142117i
$58$	475.930	−	1776.20i	0.00243927	−	0.00910347i
$59$	120217.	+	32212.1i	0.585344	+	0.156842i	0.539324	−	0.842098i	$-0.318680\pi$
$59$	120217.	+	32212.1i	0.585344	+	0.156842i	0.0460194	+	0.998941i	$0.485346\pi$
$60$	39417.6	−	39417.6i	0.182489	−	0.182489i
$61$	38209.4	+	66180.6i	0.168337	+	0.291569i	0.937835	−	0.347080i	$-0.112827\pi$
$61$	38209.4	+	66180.6i	0.168337	+	0.291569i	−0.769498	+	0.638649i	$0.779494\pi$
$62$	65946.4	+	38074.2i	0.276704	+	0.159755i
$63$	−87369.9	−	326069.i	−0.349414	−	1.30403i
$64$		−	161782.i		−	0.617148i
$65$	−271538.	+	205648.i	−0.988758	+	0.748834i
$66$	−42761.0			−0.148736
$67$	−354858.	+	95083.9i	−1.17986	+	0.316142i	−0.794870	−	0.606779i	$-0.792461\pi$
$67$	−354858.	+	95083.9i	−1.17986	+	0.316142i	−0.384988	+	0.922921i	$0.625795\pi$
$68$	122199.	−	211656.i	0.388635	−	0.673136i
$69$	−90788.9	+	52417.0i	−0.276366	+	0.159560i
$70$	−282919.	−	282919.i	−0.824838	−	0.824838i
$71$	−111837.	+	417380.i	−0.312470	+	1.16616i	0.613851	+	0.789422i	$0.289619\pi$
$71$	−111837.	+	417380.i	−0.312470	+	1.16616i	−0.926322	+	0.376734i	$0.877047\pi$
$72$	319635.	+	85645.9i	0.856360	+	0.229461i
$73$	343212.	−	343212.i	0.882256	−	0.882256i	−0.111508	−	0.993764i	$-0.535568\pi$
$73$	343212.	−	343212.i	0.882256	−	0.882256i	0.993764	+	0.111508i	$0.0355681\pi$
$74$	213381.	+	369587.i	0.526576	+	0.912057i
$75$	66188.6	+	38214.0i	0.156892	+	0.0905814i
$76$	41964.2	+	156613.i	0.0955957	+	0.356768i
$77$		−	497313.i		−	1.08933i
$78$	90895.3	+	38323.9i	0.191539	+	0.0807582i
$79$	−559268.			−1.13433			−0.567164	−	0.823605i	$-0.691959\pi$
$79$	−559268.			−1.13433			−0.567164	+	0.823605i	$0.691959\pi$
$80$	−464.063	+	124.345i	−0.000906372	+	0.000242862i
$81$	−178870.	+	309811.i	−0.336575	+	0.582965i
$82$	−7152.43	+	4129.46i	−0.0129721	+	0.00748947i
$83$	−55181.9	−	55181.9i	−0.0965078	−	0.0965078i	0.657205	−	0.753712i	$-0.271739\pi$
$83$	−55181.9	−	55181.9i	−0.0965078	−	0.0965078i	−0.753712	+	0.657205i	$0.771739\pi$
$84$	48593.9	−	181355.i	0.0819867	−	0.305979i
$85$	924819.	+	247805.i	1.50591	+	0.403508i
$86$	356590.	−	356590.i	0.560627	−	0.560627i
$87$	1690.20	+	2927.52i	0.00256673	+	0.00444571i
$88$	422187.	+	243750.i	0.619522	+	0.357681i
$89$	−189901.	−	708722.i	−0.269376	−	1.00532i	−0.959517	−	0.281649i	$-0.909119\pi$
$89$	−189901.	−	708722.i	−0.269376	−	1.00532i	0.690142	−	0.723674i	$-0.257548\pi$
$90$			495331.i			0.679467i
$91$	−445710.	+	1.05712e6i	−0.591464	+	1.40281i
$92$	456668.			0.586458
$93$	−135215.	+	36230.8i	−0.168104	+	0.0450432i
$94$	96753.1	−	167581.i	0.116488	−	0.201763i
$95$	−550082.	+	317590.i	−0.641589	+	0.370421i
$96$	210556.	+	210556.i	0.237987	+	0.237987i
$97$	328784.	−	1.22704e6i	0.360243	−	1.34444i	−0.513514	−	0.858081i	$-0.671657\pi$
$97$	328784.	−	1.22704e6i	0.360243	−	1.34444i	0.873757	−	0.486363i	$-0.161677\pi$
$98$	−740052.	−	198296.i	−0.786293	−	0.210686i
$99$	−435344.	+	435344.i	−0.448670	+	0.448670i
$100$	−166464.	−	288325.i	−0.166464	−	0.288325i
$101$	−304548.	−	175831.i	−0.295591	−	0.170660i	0.344869	−	0.938651i	$-0.387923\pi$
$101$	−304548.	−	175831.i	−0.295591	−	0.170660i	−0.640461	+	0.767991i	$0.721257\pi$
$102$	−71764.0	−	267827.i	−0.0676248	−	0.252379i
$103$			272950.i			0.249788i	0.992170	+	0.124894i	$0.0398591\pi$
$103$			272950.i			0.249788i	−0.992170	+	0.124894i	$0.960141\pi$
$104$	−678969.	−	896509.i	−0.603601	−	0.796993i
$105$	735528.			0.635377
$106$	−1.14287e6	+	306232.i	−0.959577	+	0.257118i
$107$	635277.	−	1.10033e6i	0.518575	−	0.898199i	−0.481192	−	0.876615i	$-0.659796\pi$
$107$	635277.	−	1.10033e6i	0.518575	−	0.898199i	0.999767	−	0.0215836i	$-0.00687080\pi$
$108$	−428292.	+	247275.i	−0.339992	+	0.196295i
$109$	201347.	+	201347.i	0.155477	+	0.155477i	0.780559	−	0.625082i	$-0.214935\pi$
$109$	201347.	+	201347.i	0.155477	+	0.155477i	−0.625082	+	0.780559i	$0.714935\pi$
$110$	−188867.	+	704861.i	−0.141899	+	0.529573i
$111$	−757795.	−	203050.i	−0.554093	−	0.148469i
$112$	−1144.19	+	1144.19i	−0.000814411	+	0.000814411i
$113$	186229.	+	322559.i	0.129066	+	0.223549i	0.923315	−	0.384043i	$-0.125469\pi$
$113$	186229.	+	322559.i	0.129066	+	0.223549i	−0.794249	+	0.607593i	$0.792135\pi$
$114$	159303.	+	91973.8i	0.107525	+	0.0620797i
$115$	463032.	+	1.72806e6i	0.304451	+	1.13623i
$116$		−	14725.4i		−	0.00943394i
$117$	1.31557e6	−	535222.i	0.821401	−	0.334177i
$118$	−615082.			−0.374358
$119$	3.11485e6	−	834621.i	1.84840	−	0.495277i
$120$	−360507.	+	624417.i	−0.208627	+	0.361352i
$121$	748723.	−	432276.i	0.422635	−	0.244008i
$122$	−267052.	−	267052.i	−0.147067	−	0.147067i
$123$	3929.53	−	14665.2i	0.00211167	−	0.00788084i
$124$	589012.	+	157825.i	0.308930	+	0.0827774i
$125$	−790714.	+	790714.i	−0.404846	+	0.404846i
$126$	834153.	+	1.44480e6i	0.416998	+	0.722262i
$127$	281444.	+	162492.i	0.137398	+	0.0793270i	0.567123	−	0.823633i	$-0.308056\pi$
$127$	281444.	+	162492.i	0.137398	+	0.0793270i	−0.429725	+	0.902960i	$0.641390\pi$
$128$	−335974.	−	1.25387e6i	−0.160205	−	0.597893i
$129$			927055.i			0.431854i
$130$	1.03319e6	−	1.32903e6i	0.470273	−	0.604928i
$131$	−855957.			−0.380748			−0.190374	−	0.981712i	$-0.560970\pi$
$131$	−855957.			−0.380748			−0.190374	+	0.981712i	$0.560970\pi$
$132$	−330759.	+	88626.5i	−0.143810	+	0.0385338i
$133$	−1.06966e6	+	1.85271e6i	−0.454665	+	0.787503i
$134$	1.57236e6	−	907801.i	0.653487	−	0.377291i
$135$	−1.36996e6	−	1.36996e6i	−0.556810	−	0.556810i
$136$	−818151.	+	3.05338e6i	−0.325250	+	1.21385i
$137$	−1.84280e6	−	493778.i	−0.716667	−	0.192030i	−0.117983	−	0.993016i	$-0.537643\pi$
$137$	−1.84280e6	−	493778.i	−0.716667	−	0.192030i	−0.598684	+	0.800985i	$0.704309\pi$
$138$	366351.	−	366351.i	0.139399	−	0.139399i
$139$	−2.06373e6	−	3.57448e6i	−0.768437	−	1.33097i	−0.938410	−	0.345523i	$-0.887702\pi$
$139$	−2.06373e6	−	3.57448e6i	−0.768437	−	1.33097i	0.169973	−	0.985449i	$-0.445632\pi$
$140$	−2.77478e6	−	1.60202e6i	−1.01122	−	0.583826i
$141$	92068.9	+	343606.i	0.0328440	+	0.122575i
$142$		−	2.13549e6i		−	0.745818i
$143$	2.07614e6	−	260009.i	0.709984	−	0.0889161i
$144$	2003.23			0.000670877
$145$	55721.8	−	14930.6i	0.0182777	−	0.00489749i
$146$	−1.19938e6	+	2.07739e6i	−0.385389	+	0.667513i
$147$	1.21975e6	−	704223.i	0.383989	−	0.221696i
$148$	2.41653e6	+	2.41653e6i	0.745429	+	0.745429i
$149$	176765.	−	659697.i	0.0534366	−	0.199428i	−0.934047	−	0.357150i	$-0.883748\pi$
$149$	176765.	−	659697.i	0.0534366	−	0.199428i	0.987484	+	0.157722i	$0.0504151\pi$
$150$	−364843.	−	97759.5i	−0.108102	−	0.0289658i
$151$	−3.13486e6	+	3.13486e6i	−0.910515	+	0.910515i	−0.996313	−	0.0857972i	$-0.972656\pi$
$151$	−3.13486e6	+	3.13486e6i	−0.910515	+	0.910515i	0.0857972	+	0.996313i	$0.472656\pi$
$152$	−1.04856e6	−	1.81615e6i	−0.298580	−	0.517155i
$153$	−3.45734e6	−	1.99609e6i	−0.965311	−	0.557323i
$154$	636116.	+	2.37402e6i	0.174170	+	0.650012i
$155$			2.38888e6i			0.641504i
$156$	782511.	+	108048.i	0.206118	+	0.0284606i
$157$	3.83603e6			0.991250			0.495625	−	0.868537i	$-0.334939\pi$
$157$	3.83603e6			0.991250			0.495625	+	0.868537i	$0.334939\pi$
$158$	2.66977e6	−	715362.i	0.676865	−	0.181366i
$159$	1.08754e6	−	1.88367e6i	0.270554	−	0.468613i
$160$	4.40074e6	−	2.54077e6i	1.07440	−	0.620305i
$161$	4.26068e6	+	4.26068e6i	1.02094	+	1.02094i
$162$	457586.	−	1.70774e6i	0.107629	−	0.401676i
$163$	−4.52726e6	−	1.21308e6i	−1.04538	−	0.280108i	−0.305036	−	0.952341i	$-0.598669\pi$
$163$	−4.52726e6	−	1.21308e6i	−1.04538	−	0.280108i	−0.740340	+	0.672233i	$0.765335\pi$
$164$	−46765.7	+	46765.7i	−0.0106022	+	0.0106022i
$165$	−670736.	−	1.16175e6i	−0.149314	−	0.258619i
$166$	334004.	+	192837.i	0.0730176	+	0.0421568i
$167$	1.65611e6	+	6.18070e6i	0.355582	+	1.32705i	0.879750	+	0.475437i	$0.157710\pi$
$167$	1.65611e6	+	6.18070e6i	0.355582	+	1.32705i	−0.524167	+	0.851615i	$0.675623\pi$
$168$			2.42842e6i			0.512148i
$169$	−4.64620e6	−	1.30802e6i	−0.962582	−	0.270991i
$170$	−4.73176e6			−0.963111
$171$	2.55822e6	−	685474.i	0.511623	−	0.137089i
$172$	2.01918e6	−	3.49732e6i	0.396816	−	0.687305i
$173$	−1.88157e6	+	1.08632e6i	−0.363397	+	0.209807i	−0.670570	−	0.741846i	$-0.733950\pi$
$173$	−1.88157e6	+	1.08632e6i	−0.363397	+	0.209807i	0.307173	+	0.951654i	$0.400617\pi$
$174$	−11813.1	−	11813.1i	−0.00224241	−	0.00224241i
$175$	1.13695e6	−	4.24315e6i	0.212142	−	0.791725i
$176$	2850.62	+	763.820i	0.000522878	+	0.000140105i
$177$	799539.	−	799539.i	0.144185	−	0.144185i
$178$	1.81306e6	+	3.14031e6i	0.321479	+	0.556817i
$179$	7.13572e6	+	4.11981e6i	1.24417	+	0.718320i	0.969940	−	0.243345i	$-0.0782447\pi$
$179$	7.13572e6	+	4.11981e6i	1.24417	+	0.718320i	0.274227	+	0.961665i	$0.411578\pi$
$180$	1.02663e6	+	3.83142e6i	0.176033	+	0.656965i
$181$		−	6.89585e6i		−	1.16293i	−0.813573	−	0.581463i	$-0.802481\pi$
$181$		−	6.89585e6i		−	1.16293i	0.813573	−	0.581463i	$-0.197519\pi$
$182$	775515.	−	5.61646e6i	0.128640	−	0.931641i
$183$	694275.			0.113287
$184$	−5.70535e6	+	1.52875e6i	−0.915860	+	0.245404i
$185$	−6.69407e6	+	1.15945e7i	−1.05724	+	1.83120i
$186$	599132.	−	345909.i	0.0931073	−	0.0537555i
$187$	−4.15872e6	−	4.15872e6i	−0.635968	−	0.635968i
$188$	401062.	−	1.49678e6i	0.0603584	−	0.225261i
$189$	−6.30300e6	−	1.68888e6i	−0.933602	−	0.250158i
$190$	2.21969e6	−	2.21969e6i	0.323617	−	0.323617i
$191$	−3.49255e6	−	6.04927e6i	−0.501236	−	0.868166i	−0.999999	−	0.00142767i	$-0.999546\pi$
$191$	−3.49255e6	−	6.04927e6i	−0.501236	−	0.868166i	0.498763	−	0.866738i	$-0.333788\pi$
$192$	−1.27289e6	−	734904.i	−0.179841	−	0.103831i
$193$	−170632.	−	636806.i	−0.0237349	−	0.0885799i	0.953042	−	0.302837i	$-0.0979337\pi$
$193$	−170632.	−	636806.i	−0.0237349	−	0.0885799i	−0.976777	+	0.214257i	$0.931267\pi$
$194$			6.27804e6i			0.859842i
$195$	384554.	+	3.07062e6i	0.0518626	+	0.414116i
$196$	−6.13534e6			−0.814836
$197$	−3.13085e6	+	838909.i	−0.409509	+	0.109728i	−0.457692	−	0.889111i	$-0.651324\pi$
$197$	−3.13085e6	+	838909.i	−0.409509	+	0.109728i	0.0481825	+	0.998839i	$0.484657\pi$
$198$	1.52135e6	−	2.63505e6i	0.195989	−	0.339463i
$199$	1.17491e7	−	6.78336e6i	1.49089	−	0.860767i	0.490947	−	0.871190i	$-0.336651\pi$
$199$	1.17491e7	−	6.78336e6i	1.49089	−	0.860767i	0.999946	+	0.0104224i	$0.00331760\pi$
$200$	3.04491e6	+	3.04491e6i	0.380614	+	0.380614i
$201$	−863850.	+	3.22393e6i	−0.106378	+	0.397007i
$202$	1.67872e6	+	449813.i	0.203669	+	0.0545730i
$203$	137387.	−	137387.i	0.0164232	−	0.0164232i
$204$	−1.11020e6	−	1.92292e6i	−0.130771	−	0.226501i
$205$	−224382.	−	129547.i	−0.0260451	−	0.0150371i
$206$	−349132.	−	1.30298e6i	−0.0399381	−	0.149051i
$207$		−	7.45954e6i		−	0.841010i
$208$	−5374.88	−	4178.45i	−0.000597281	−	0.000464328i
$209$	3.90175e6			0.427386
$210$	−3.51118e6	+	940818.i	−0.379136	+	0.101589i
$211$	−167666.	+	290406.i	−0.0178483	+	0.0309142i	−0.874812	−	0.484463i	$-0.839015\pi$
$211$	−167666.	+	290406.i	−0.0178483	+	0.0309142i	0.856963	+	0.515377i	$0.172348\pi$
$212$	−8.20549e6	+	4.73744e6i	−0.861186	+	0.497206i
$213$	2.77590e6	+	2.77590e6i	0.287253	+	0.287253i
$214$	−1.62517e6	+	6.06523e6i	−0.165828	+	0.618879i
$215$	1.52814e7	+	4.09463e6i	1.53761	+	0.412002i
$216$	4.52307e6	−	4.52307e6i	0.448819	−	0.448819i
$217$	4.02295e6	+	6.96795e6i	0.393700	+	0.681908i
$218$	−1.21871e6	−	703624.i	−0.117634	−	0.0679158i
$219$	−1.14132e6	−	4.25945e6i	−0.108661	−	0.405528i
$220$			5.84359e6i			0.548797i
$221$	5.11283e6	+	1.25672e7i	0.473680	+	1.16429i
$222$	3.87720e6			0.354372
$223$	7.94252e6	−	2.12819e6i	0.716215	−	0.191909i	0.117733	−	0.993045i	$-0.462437\pi$
$223$	7.94252e6	−	2.12819e6i	0.716215	−	0.191909i	0.598482	+	0.801136i	$0.295771\pi$
$224$	8.55747e6	−	1.48220e7i	0.761379	−	1.31875i
$225$	−4.70970e6	+	2.71915e6i	−0.413472	+	0.238718i
$226$	−1.30159e6	−	1.30159e6i	−0.112758	−	0.112758i
$227$	−1.76030e6	+	6.56953e6i	−0.150490	+	0.561638i	0.848959	+	0.528459i	$0.177230\pi$
$227$	−1.76030e6	+	6.56953e6i	−0.150490	+	0.561638i	−0.999449	+	0.0331793i	$0.989437\pi$
$228$	1.42285e6	+	381251.i	0.120048	+	0.0321667i
$229$	−7.40252e6	+	7.40252e6i	−0.616415	+	0.616415i	−0.944610	−	0.328195i	$-0.893560\pi$
$229$	−7.40252e6	+	7.40252e6i	−0.616415	+	0.616415i	0.328195	+	0.944610i	$0.393560\pi$
$230$	−4.42073e6	−	7.65694e6i	−0.363338	−	0.629320i
$231$	−3.91284e6	−	2.25908e6i	−0.317436	−	0.183272i
$232$	49294.9	+	183971.i	0.00394764	+	0.0147328i
$233$		−	2.35159e7i		−	1.85906i	−0.368745	−	0.929531i	$-0.620212\pi$
$233$		−	2.35159e7i		−	1.85906i	0.368745	−	0.929531i	$-0.379788\pi$
$234$	−5.59549e6	+	4.23773e6i	−0.436707	+	0.330739i
$235$	6.07057e6			0.467763
$236$	−4.75770e6	+	1.27482e6i	−0.361960	+	0.0969870i
$237$	−2.54051e6	+	4.40030e6i	−0.190843	+	0.330550i
$238$	−1.38017e7	+	7.96843e6i	−1.02377	+	0.591074i
$239$	−1.42176e7	−	1.42176e7i	−1.04144	−	1.04144i	−0.999103	−	0.0423355i	$-0.986520\pi$
$239$	−1.42176e7	−	1.42176e7i	−1.04144	−	1.04144i	−0.0423355	−	0.999103i	$-0.513480\pi$
$240$	−1129.69	+	4216.07i	−8.17197e−5	+	0.000304982i
$241$	3.44530e6	+	923165.i	0.246136	+	0.0659520i	0.379778	−	0.925078i	$-0.376000\pi$
$241$	3.44530e6	+	923165.i	0.246136	+	0.0659520i	−0.133642	+	0.991030i	$0.542667\pi$
$242$	−3.02124e6	+	3.02124e6i	−0.213177	+	0.213177i
$243$	6.17994e6	+	1.07040e7i	0.430690	+	0.745978i
$244$	−2.61915e6	−	1.51217e6i	−0.180298	−	0.104095i
$245$	−6.22084e6	−	2.32165e7i	−0.423010	−	1.57869i
$246$			75033.3i			0.00504021i
$247$	−8.29378e6	−	3.49689e6i	−0.550379	−	0.232055i
$248$	−7.88713e6			−0.517087
$249$	−684836.	+	183501.i	−0.0443597	+	0.0118861i
$250$	2.76321e6	−	4.78602e6i	0.176846	−	0.306306i
$251$	−6.54138e6	+	3.77667e6i	−0.413665	+	0.238829i	−0.692363	−	0.721549i	$-0.743430\pi$
$251$	−6.54138e6	+	3.77667e6i	−0.413665	+	0.238829i	0.278699	+	0.960379i	$0.410097\pi$
$252$	9.44671e6	+	9.44671e6i	0.590309	+	0.590309i
$253$	2.84428e6	−	1.06150e7i	0.175635	−	0.655479i
$254$	−1.55137e6	−	415689.i	−0.0946705	−	0.0253669i
$255$	6.15077e6	−	6.15077e6i	0.370945	−	0.370945i
$256$	8.38468e6	+	1.45227e7i	0.499766	+	0.865620i
$257$	2.36040e7	+	1.36278e7i	1.39055	+	0.802834i	0.993376	−	0.114910i	$-0.0366580\pi$
$257$	2.36040e7	+	1.36278e7i	1.39055	+	0.802834i	0.397173	+	0.917744i	$0.369991\pi$
$258$	−1.18580e6	−	4.42547e6i	−0.0690483	−	0.257692i
$259$			4.50921e7i			2.59538i
$260$	5.23724e6	−	1.24215e7i	0.297977	−	0.706730i
$261$	−240535.			−0.0135287
$262$	4.08607e6	−	1.09486e6i	0.227197	−	0.0608771i
$263$	−1.21155e6	+	2.09846e6i	−0.0665998	+	0.115354i	−0.897403	−	0.441213i	$-0.854548\pi$
$263$	−1.21155e6	+	2.09846e6i	−0.0665998	+	0.115354i	0.830803	+	0.556567i	$0.187882\pi$
$264$	3.83563e6	−	2.21450e6i	0.208461	−	0.120355i
$265$	−2.62466e7	−	2.62466e7i	−1.41038	−	1.41038i
$266$	2.73642e6	−	1.02125e7i	0.145391	−	0.542607i
$267$	−6.43884e6	−	1.72528e6i	−0.338278	−	0.0906413i
$268$	1.02808e7	−	1.02808e7i	0.534098	−	0.534098i
$269$	1.25867e7	+	2.18008e7i	0.646628	+	1.11999i	0.983923	+	0.178594i	$0.0571548\pi$
$269$	1.25867e7	+	2.18008e7i	0.646628	+	1.11999i	−0.337295	+	0.941399i	$0.609512\pi$
$270$	8.29209e6	+	4.78744e6i	0.421282	+	0.243227i
$271$	−3.19870e6	−	1.19377e7i	−0.160719	−	0.599810i	−0.998548	−	0.0538771i	$-0.982842\pi$
$271$	−3.19870e6	−	1.19377e7i	−0.160719	−	0.599810i	0.837829	−	0.545933i	$-0.183825\pi$
$272$			19136.3i			0.000950936i
$273$	6.29270e6	+	8.30886e6i	0.309278	+	0.408370i
$274$	9.42855e6			0.458346
$275$	−7.73875e6	+	2.07359e6i	−0.372111	+	0.0997069i
$276$	2.07444e6	−	3.59304e6i	0.0986676	−	0.170897i
$277$	−3.22905e7	+	1.86429e7i	−1.51927	+	0.877153i	−0.519530	+	0.854452i	$0.673893\pi$
$277$	−3.22905e7	+	1.86429e7i	−1.51927	+	0.877153i	−0.999742	+	0.0227006i	$0.992774\pi$
$278$	1.44237e7	+	1.44237e7i	0.671341	+	0.671341i
$279$	2.57803e6	−	9.62136e6i	0.118707	−	0.443020i
$280$	4.00295e7	+	1.07259e7i	1.82350	+	0.488605i
$281$	1.19883e7	−	1.19883e7i	0.540304	−	0.540304i	−0.383314	−	0.923618i	$-0.625217\pi$
$281$	1.19883e7	−	1.19883e7i	0.540304	−	0.540304i	0.923618	+	0.383314i	$0.125217\pi$
$282$	−879016.	−	1.52250e6i	−0.0391967	−	0.0678906i
$283$	1.22628e6	+	707994.i	0.0541042	+	0.0312371i	0.526808	−	0.849984i	$-0.323389\pi$
$283$	1.22628e6	+	707994.i	0.0541042	+	0.0312371i	−0.472704	+	0.881221i	$0.656722\pi$
$284$	−4.42603e6	−	1.65182e7i	−0.193223	−	0.721118i
$285$			5.77070e6i			0.249284i
$286$	−9.57826e6	+	3.89680e6i	−0.409438	+	0.166575i
$287$	−872643.			−0.0369140
$288$	−2.04662e7	+	5.48390e6i	−0.856761	+	0.229568i
$289$	6.99935e6	−	1.21232e7i	0.289977	−	0.502256i
$290$	−246900.	+	142548.i	−0.0101234	+	0.00584476i
$291$	−8.16076e6	−	8.16076e6i	−0.331170	−	0.331170i
$292$	−4.97169e6	+	1.85546e7i	−0.199690	+	0.745252i
$293$	−2.35256e7	−	6.30367e6i	−0.935273	−	0.250606i	−0.241171	−	0.970483i	$-0.577531\pi$
$293$	−2.35256e7	−	6.30367e6i	−0.935273	−	0.250606i	−0.694102	+	0.719877i	$0.744198\pi$
$294$	−4.92193e6	+	4.92193e6i	−0.193684	+	0.193684i
$295$	−9.64800e6	−	1.67108e7i	−0.375812	−	0.650926i
$296$	−3.82803e7	−	2.21011e7i	−1.47605	−	0.852196i
$297$	3.08022e6	+	1.14955e7i	0.117574	+	0.438793i
$298$			3.37529e6i			0.127545i
$299$	−1.55595e7	+	2.00147e7i	−0.582081	+	0.748749i
$300$	−3.02470e6			−0.112026
$301$	5.14685e7	−	1.37910e7i	1.88731	−	0.505702i
$302$	1.09550e7	−	1.89746e7i	0.397734	−	0.688895i
$303$	−2.76686e6	+	1.59745e6i	−0.0994626	+	0.0574247i
$304$	−8976.91	−	8976.91i	−0.000319526	−	0.000319526i
$305$	3.06648e6	−	1.14443e7i	0.108079	−	0.403356i
$306$	1.90574e7	+	5.10643e6i	0.665121	+	0.178219i
$307$	−1.63598e7	+	1.63598e7i	−0.565410	+	0.565410i	−0.930839	−	0.365429i	$-0.880922\pi$
$307$	−1.63598e7	+	1.63598e7i	−0.565410	+	0.565410i	0.365429	+	0.930839i	$0.380922\pi$
$308$	9.84079e6	+	1.70447e7i	0.336804	+	0.583362i
$309$	2.14756e6	+	1.23989e6i	0.0727897	+	0.0420251i
$310$	−3.05563e6	−	1.14038e7i	−0.102569	−	0.382792i
$311$		−	5.07520e7i		−	1.68722i	−0.536957	−	0.843610i	$-0.680426\pi$
$311$		−	5.07520e7i		−	1.68722i	0.536957	−	0.843610i	$-0.319574\pi$
$312$	−1.01380e7	+	1.26964e6i	−0.333800	+	0.0418041i
$313$	−2.28509e6			−0.0745197			−0.0372599	−	0.999306i	$-0.511863\pi$
$313$	−2.28509e6			−0.0745197			−0.0372599	+	0.999306i	$0.511863\pi$
$314$	−1.83120e7	+	4.90669e6i	−0.591489	+	0.158489i
$315$	−2.61686e7	+	4.53253e7i	−0.837236	+	1.45014i
$316$	1.91682e7	−	1.10667e7i	0.607462	−	0.350718i
$317$	7.52499e6	+	7.52499e6i	0.236226	+	0.236226i	0.815285	−	0.579059i	$-0.196580\pi$
$317$	7.52499e6	+	7.52499e6i	0.236226	+	0.236226i	−0.579059	+	0.815285i	$0.696580\pi$
$318$	−2.78216e6	+	1.03831e7i	−0.0865167	+	0.322885i
$319$	−342284.	−	91714.8i	−0.0105442	−	0.00282532i
$320$	−1.77361e7	+	1.77361e7i	−0.541263	+	0.541263i
$321$	−5.77158e6	−	9.99667e6i	−0.174494	−	0.302232i
$322$	−2.57890e7	−	1.48893e7i	−0.772444	−	0.445971i
$323$	6.54814e6	+	2.44380e7i	0.194317	+	0.725201i
$324$		−	1.41578e7i		−	0.416257i
$325$	1.83084e7	+	2.52800e6i	0.533335	+	0.0736423i
$326$	2.31634e7			0.668573
$327$	2.49882e6	−	669558.i	0.0714649	−	0.0191489i
$328$	427712.	−	740819.i	0.0121208	−	0.0209938i
$329$	1.77068e7	−	1.02230e7i	0.497224	−	0.287072i
$330$	4.68788e6	+	4.68788e6i	0.130447	+	0.130447i
$331$	−2.71683e6	+	1.01394e7i	−0.0749168	+	0.279593i	−0.993214	−	0.116297i	$-0.962897\pi$
$331$	−2.71683e6	+	1.01394e7i	−0.0749168	+	0.279593i	0.918298	+	0.395891i	$0.129564\pi$
$332$	2.98322e6	+	799351.i	0.0815213	+	0.0218436i
$333$	3.94733e7	−	3.94733e7i	1.06898	−	1.06898i
$334$	−1.58115e7	−	2.73863e7i	−0.424360	−	0.735012i
$335$	4.93271e7	+	2.84790e7i	1.31205	+	0.757513i
$336$	3804.87	+	14200.0i	0.000100305	+	0.000374343i
$337$			6.33481e6i			0.165518i	0.996570	+	0.0827588i	$0.0263731\pi$
$337$			6.33481e6i			0.165518i	−0.996570	+	0.0827588i	$0.973627\pi$
$338$	2.38526e7	+	301113.i	0.617711	+	0.00779794i
$339$	3.38384e6			0.0868581
$340$	−3.66005e7	+	9.80707e6i	−0.931215	+	0.249518i
$341$	7.33714e6	−	1.27083e7i	0.185039	−	0.320497i
$342$	−1.13354e7	+	6.54447e6i	−0.283372	+	0.163605i
$343$	−1.38016e7	−	1.38016e7i	−0.342017	−	0.342017i
$344$	−1.35188e7	+	5.04529e7i	−0.332096	+	1.23940i
$345$	1.56996e7	+	4.20671e6i	0.382325	+	0.102444i
$346$	7.59248e6	−	7.59248e6i	0.183297	−	0.183297i
$347$	1.00637e7	+	1.74308e7i	0.240862	+	0.417186i	0.960960	−	0.276687i	$-0.0892365\pi$
$347$	1.00637e7	+	1.74308e7i	0.240862	+	0.417186i	−0.720098	+	0.693872i	$0.755903\pi$
$348$	−115859.	−	66891.1i	−0.00274911	−	0.00158720i
$349$	1.03111e7	+	3.84816e7i	0.242566	+	0.905268i	0.974591	+	0.223991i	$0.0719086\pi$
$349$	1.03111e7	+	3.84816e7i	0.242566	+	0.905268i	−0.732025	+	0.681277i	$0.761425\pi$
$350$			2.17098e7i			0.506350i
$351$	3.75522e6	−	2.71962e7i	0.0868389	−	0.628908i
$352$	−3.12146e7			−0.715697
$353$	−1.26671e7	+	3.39413e6i	−0.287973	+	0.0771622i	−0.399914	−	0.916553i	$-0.630960\pi$
$353$	−1.26671e7	+	3.39413e6i	−0.287973	+	0.0771622i	0.111941	+	0.993715i	$0.464293\pi$
$354$	−2.79405e6	+	4.83944e6i	−0.0629832	+	0.109090i
$355$	5.80179e7	−	3.34967e7i	1.29681	−	0.748715i
$356$	2.05327e7	+	2.05327e7i	0.455090	+	0.455090i
$357$	7.58264e6	−	2.82988e7i	0.166654	−	0.621961i
$358$	−3.93333e7	−	1.05393e7i	−0.857258	−	0.229702i
$359$	−1.46920e7	+	1.46920e7i	−0.317538	+	0.317538i	−0.847821	−	0.530283i	$-0.822086\pi$
$359$	−1.46920e7	+	1.46920e7i	−0.317538	+	0.317538i	0.530283	+	0.847821i	$0.322086\pi$
$360$	−2.56522e7	−	4.44309e7i	−0.549815	−	0.952308i
$361$	2.62072e7	+	1.51307e7i	0.557056	+	0.321617i
$362$	8.82052e6	+	3.29186e7i	0.185938	+	0.693930i
$363$		−	7.85457e6i		−	0.164211i
$364$	−5.64204e6	−	4.50510e7i	−0.116986	−	0.934115i
$365$	−7.52527e7			−1.54755
$366$	−3.31425e6	+	888051.i	−0.0675993	+	0.0181132i
$367$	−1.81304e7	+	3.14028e7i	−0.366784	+	0.635288i	−0.989061	−	0.147509i	$-0.952874\pi$
$367$	−1.81304e7	+	3.14028e7i	−0.366784	+	0.635288i	0.622277	+	0.782797i	$0.286208\pi$
$368$	−30966.3	+	17878.4i	−0.000621365	+	0.000358745i
$369$	763906.	+	763906.i	0.0152041	+	0.0152041i
$370$	1.71248e7	−	6.39108e7i	0.338081	−	1.26174i
$371$	−1.20757e8	−	3.23567e7i	−2.36477	−	0.633639i
$372$	3.91739e6	−	3.91739e6i	0.0760971	−	0.0760971i
$373$	−2.08755e7	−	3.61574e7i	−0.402263	−	0.696740i	0.591735	−	0.806132i	$-0.298443\pi$
$373$	−2.08755e7	−	3.61574e7i	−0.402263	−	0.696740i	−0.993999	+	0.109392i	$0.965110\pi$
$374$	2.51719e7	+	1.45330e7i	0.481173	+	0.277805i
$375$	2.62943e6	+	9.81318e6i	0.0498618	+	0.186087i
$376$			2.00426e7i			0.377042i
$377$	645382.	+	501722.i	0.0120446	+	0.00936352i
$378$	3.22488e7			0.597087
$379$	−4.40128e6	+	1.17932e6i	−0.0808466	+	0.0216628i	−0.299016	−	0.954248i	$-0.596658\pi$
$379$	−4.40128e6	+	1.17932e6i	−0.0808466	+	0.0216628i	0.218169	+	0.975911i	$0.429992\pi$
$380$	1.25689e7	−	2.17700e7i	0.229058	−	0.396741i
$381$	2.55696e6	−	1.47626e6i	0.0462327	−	0.0266925i
$382$	2.44100e7	+	2.44100e7i	0.437902	+	0.437902i
$383$	−2.73848e6	+	1.02201e7i	−0.0487431	+	0.181912i	−0.986005	−	0.166713i	$-0.946685\pi$
$383$	−2.73848e6	+	1.02201e7i	−0.0487431	+	0.181912i	0.937262	+	0.348625i	$0.113351\pi$
$384$	−1.13916e7	−	3.05237e6i	−0.201183	−	0.0539068i
$385$	−5.45204e7	+	5.45204e7i	−0.955381	+	0.955381i
$386$	1.62908e6	+	2.82165e6i	0.0283257	+	0.0490616i
$387$	−5.71277e7	−	3.29827e7i	−0.985630	−	0.569054i
$388$	1.30119e7	+	4.85610e7i	0.222764	+	0.831367i
$389$		−	3.79607e7i		−	0.644889i	−0.946588	−	0.322445i	$-0.895495\pi$
$389$		−	3.79607e7i		−	0.644889i	0.946588	−	0.322445i	$-0.104505\pi$
$390$	−5.76339e6	−	1.41663e7i	−0.0971592	−	0.238815i
$391$	7.12590e7			1.19209
$392$	7.66515e7	−	2.05387e7i	1.27251	−	0.340969i
$393$	−3.88824e6	+	6.73463e6i	−0.0640583	+	0.110952i
$394$	1.38726e7	−	8.00938e6i	0.226814	−	0.130951i
$395$	6.13125e7	+	6.13125e7i	0.994850	+	0.994850i
$396$	6.30629e6	−	2.35354e7i	0.101552	−	0.378997i
$397$	4.47978e7	+	1.20035e7i	0.715954	+	0.191839i	0.598366	−	0.801223i	$-0.295817\pi$
$397$	4.47978e7	+	1.20035e7i	0.715954	+	0.191839i	0.117588	+	0.993062i	$0.462484\pi$
$398$	−4.74100e7	+	4.74100e7i	−0.752005	+	0.752005i
$399$	9.71803e6	+	1.68321e7i	0.152989	+	0.264984i
$400$	22575.7	+	13034.1i	0.000352745	+	0.000203657i
$401$	−1.78451e6	−	6.65990e6i	−0.0276750	−	0.103284i	0.950707	−	0.310091i	$-0.100360\pi$
$401$	−1.78451e6	−	6.65990e6i	−0.0276750	−	0.103284i	−0.978382	+	0.206807i	$0.933693\pi$
$402$		−	1.64950e7i		−	0.253907i
$403$	−2.69859e7	+	2.04377e7i	−0.412308	+	0.312260i
$404$	1.39173e7			0.211063
$405$	5.35741e7	−	1.43551e7i	0.806472	−	0.216094i
$406$	−480110.	+	831575.i	−0.00717402	+	0.0124258i
$407$	7.12218e7	−	4.11199e7i	1.05640	−	0.609915i
$408$	2.03074e7	+	2.03074e7i	0.299002	+	0.299002i
$409$	−1.04813e7	+	3.91166e7i	−0.153195	+	0.571730i	0.846058	+	0.533090i	$0.178969\pi$
$409$	−1.04813e7	+	3.91166e7i	−0.153195	+	0.571730i	−0.999253	+	0.0386403i	$0.987697\pi$
$410$	1.23683e6	+	331408.i	0.0179456	+	0.00480852i
$411$	−1.22561e7	+	1.22561e7i	−0.176533	+	0.176533i
$412$	−5.40111e6	−	9.35500e6i	−0.0772309	−	0.133768i
$413$	−5.62830e7	−	3.24950e7i	−0.798964	−	0.461282i
$414$	9.54154e6	+	3.56095e7i	0.134468	+	0.501840i
$415$			1.20992e7i			0.169282i
$416$	6.63516e7	+	2.79756e7i	0.921661	+	0.388598i
$417$	−3.74985e7			−0.517137
$418$	−1.86257e7	+	4.99074e6i	−0.255026	+	0.0683339i
$419$	−1.96125e7	+	3.39698e7i	−0.266619	+	0.461797i	−0.967986	−	0.251002i	$-0.919240\pi$
$419$	−1.96125e7	+	3.39698e7i	−0.266619	+	0.461797i	0.701368	+	0.712800i	$0.252573\pi$
$420$	−2.52092e7	+	1.45546e7i	−0.340261	+	0.196450i
$421$	−2.96788e7	−	2.96788e7i	−0.397740	−	0.397740i	0.479695	−	0.877435i	$-0.340747\pi$
$421$	−2.96788e7	−	2.96788e7i	−0.397740	−	0.397740i	−0.877435	+	0.479695i	$0.840747\pi$
$422$	428925.	−	1.60077e6i	0.00570747	−	0.0213006i
$423$	−2.44495e7	−	6.55124e6i	−0.323035	−	0.0865570i
$424$	8.66557e7	−	8.66557e7i	1.13684	−	1.13684i
$425$	−2.59753e7	−	4.49905e7i	−0.338371	−	0.586076i
$426$	−1.68019e7	−	9.70061e6i	−0.217336	−	0.125479i
$427$	−1.03281e7	−	3.85450e7i	−0.132659	−	0.495090i
$428$			5.02832e7i			0.641345i
$429$	7.38527e6	−	1.75161e7i	0.0935394	−	0.221853i
$430$	−7.81858e7			−0.983383
$431$	4.23018e6	−	1.13347e6i	0.0528357	−	0.0141573i	−0.232304	−	0.972643i	$-0.574627\pi$
$431$	4.23018e6	−	1.13347e6i	0.0528357	−	0.0141573i	0.285140	+	0.958486i	$0.407960\pi$
$432$	19361.5	−	33535.0i	0.000240152	−	0.000415956i
$433$	7.46948e7	−	4.31251e7i	0.920082	−	0.531210i	0.0364211	−	0.999337i	$-0.488404\pi$
$433$	7.46948e7	−	4.31251e7i	0.920082	−	0.531210i	0.883661	+	0.468127i	$0.155071\pi$
$434$	−2.81170e7	−	2.81170e7i	−0.343954	−	0.343954i
$435$	135647.	−	506240.i	0.00164794	−	0.00615019i
$436$	−1.08851e7	−	2.91667e6i	−0.131333	−	0.0351906i
$437$	−3.34278e7	+	3.34278e7i	−0.400557	+	0.400557i
$438$	1.08966e7	+	1.88734e7i	0.129678	+	0.224609i
$439$	−8.03083e7	−	4.63660e7i	−0.949220	−	0.548032i	−0.0563814	−	0.998409i	$-0.517956\pi$
$439$	−8.03083e7	−	4.63660e7i	−0.949220	−	0.548032i	−0.892839	+	0.450377i	$0.851290\pi$
$440$	−1.95621e7	−	7.30066e7i	−0.229645	−	0.857046i
$441$			1.00219e8i			1.16852i
$442$	−4.04819e7	−	5.34522e7i	−0.468807	−	0.619011i
$443$	−5.32456e6			−0.0612453			−0.0306226	−	0.999531i	$-0.509749\pi$
$443$	−5.32456e6			−0.0612453			−0.0306226	+	0.999531i	$0.509749\pi$
$444$	2.99903e7	−	8.03589e6i	0.342636	−	0.0918090i
$445$	−5.68782e7	+	9.85160e7i	−0.645455	+	1.11796i
$446$	−3.51929e7	+	2.03186e7i	−0.396689	+	0.229029i
$447$	−4.38750e6	−	4.38750e6i	−0.0491241	−	0.0491241i
$448$	−2.18650e7	+	8.16012e7i	−0.243173	+	0.907534i
$449$	1.37952e7	+	3.69642e6i	0.152402	+	0.0408360i	0.334213	−	0.942497i	$-0.391529\pi$
$449$	1.37952e7	+	3.69642e6i	0.152402	+	0.0408360i	−0.181811	+	0.983333i	$0.558196\pi$
$450$	1.90046e7	−	1.90046e7i	0.208555	−	0.208555i
$451$	795772.	+	1.37832e6i	0.00867479	+	0.0150252i
$452$	−1.27655e7	−	7.37018e6i	−0.138237	−	0.0798110i
$453$	1.04246e7	+	3.89053e7i	0.112141	+	0.418518i
$454$		−	3.36125e7i		−	0.359197i
$455$	1.64755e8	−	6.70286e7i	1.74906	−	0.711584i
$456$	−1.90525e7			−0.200936
$457$	−2.19469e7	+	5.88065e6i	−0.229945	+	0.0616137i	−0.371952	−	0.928252i	$-0.621311\pi$
$457$	−2.19469e7	+	5.88065e6i	−0.229945	+	0.0616137i	0.142006	+	0.989866i	$0.454645\pi$
$458$	2.58687e7	−	4.48059e7i	0.269264	−	0.466379i
$459$	−6.68312e7	+	3.85850e7i	−0.691100	+	0.399007i
$460$	−5.00644e7	−	5.00644e7i	−0.514347	−	0.514347i
$461$	−6.59036e6	+	2.45955e7i	−0.0672676	+	0.251046i	−0.991369	−	0.131101i	$-0.958149\pi$
$461$	−6.59036e6	+	2.45955e7i	−0.0672676	+	0.251046i	0.924101	+	0.382147i	$0.124815\pi$
$462$	2.15683e7	+	5.77920e6i	0.218720	+	0.0586059i
$463$	6.94735e7	−	6.94735e7i	0.699965	−	0.699965i	−0.264438	−	0.964403i	$-0.585186\pi$
$463$	6.94735e7	−	6.94735e7i	0.699965	−	0.699965i	0.964403	+	0.264438i	$0.0851864\pi$
$464$	576.495	+	998.519i	5.77088e−6	+	9.99546e-6i
$465$	1.87956e7	+	1.08517e7i	0.186938	+	0.107929i
$466$	3.00793e7	+	1.12257e8i	0.297242	+	1.10932i
$467$		−	3.86547e7i		−	0.379534i	−0.981829	−	0.189767i	$-0.939227\pi$
$467$		−	3.86547e7i		−	0.379534i	0.981829	−	0.189767i	$-0.0607733\pi$
$468$	−3.44983e7	+	4.43763e7i	−0.336558	+	0.432926i
$469$	1.91838e8			1.85958
$470$	−2.89790e7	+	7.76489e6i	−0.279119	+	0.0747897i
$471$	1.74254e7	−	3.01817e7i	0.166771	−	0.288856i
$472$	5.51724e7	−	3.18538e7i	0.524682	−	0.302925i
$473$	−6.87172e7	−	6.87172e7i	−0.649354	−	0.649354i
$474$	6.49916e6	−	2.42552e7i	0.0610271	−	0.227756i
$475$	3.32903e7	+	8.92011e6i	0.310625	+	0.0832318i
$476$	−9.02418e7	+	9.02418e7i	−0.836733	+	0.836733i
$477$	7.73848e7	+	1.34034e8i	0.713018	+	1.23498i
$478$	8.60564e7	+	4.96847e7i	0.787951	+	0.454924i
$479$	−4.41084e7	−	1.64615e8i	−0.401342	−	1.49783i	−0.810704	−	0.585457i	$-0.800915\pi$
$479$	−4.41084e7	−	1.64615e8i	−0.401342	−	1.49783i	0.409361	−	0.912372i	$-0.365752\pi$
$480$		−	4.61665e7i		−	0.417449i
$481$	−1.88247e8	+	2.35754e7i	−1.69158	+	0.211848i
$482$	−1.76276e7			−0.157417
$483$	5.28773e7	−	1.41684e7i	0.469276	−	0.125742i
$484$	−1.71077e7	+	2.96313e7i	−0.150888	+	0.261346i
$485$	−1.70564e8	+	9.84755e7i	−1.49508	+	0.863183i
$486$	−4.31926e7	−	4.31926e7i	−0.376271	−	0.376271i
$487$	2.56860e7	−	9.58613e7i	0.222387	−	0.829959i	−0.761048	−	0.648696i	$-0.775315\pi$
$487$	2.56860e7	−	9.58613e7i	0.222387	−	0.829959i	0.983435	−	0.181263i	$-0.0580185\pi$
$488$	3.77844e7	+	1.01243e7i	0.325127	+	0.0871175i
$489$	−3.01098e7	+	3.01098e7i	−0.257502	+	0.257502i
$490$	5.93926e7	+	1.02871e8i	0.504829	+	0.874390i
$491$	1.91410e8	+	1.10511e8i	1.61704	+	0.933599i	0.987680	+	0.156486i	$0.0500165\pi$
$491$	1.91410e8	+	1.10511e8i	1.61704	+	0.933599i	0.629361	+	0.777113i	$0.283317\pi$
$492$	155514.	+	580388.i	0.00130580	+	0.00487330i
$493$		−	2.29777e6i		−	0.0191763i
$494$	4.40648e7	+	6.08442e6i	0.365520	+	0.0504706i
$495$	9.54535e7			0.787003
$496$	−46119.4	+	12357.6i	−0.000377953	+	0.000101272i
$497$	1.12819e8	−	1.95408e8i	0.918993	−	1.59174i
$498$	3.03447e6	−	1.75195e6i	0.0245695	−	0.0141852i
$499$	1.58111e8	+	1.58111e8i	1.27251	+	1.27251i	0.944768	+	0.327739i	$0.106287\pi$
$499$	1.58111e8	+	1.58111e8i	1.27251	+	1.27251i	0.327739	+	0.944768i	$0.393713\pi$
$500$	1.14541e7	−	4.27472e7i	0.0916327	−	0.341978i
$501$	5.61525e7	+	1.50460e7i	0.446535	+	0.119649i
$502$	2.63957e7	−	2.63957e7i	0.208652	−	0.208652i
$503$	−8.01396e7	−	1.38806e8i	−0.629713	−	1.09070i	−0.987609	−	0.156934i	$-0.949839\pi$
$503$	−8.01396e7	−	1.38806e8i	−0.629713	−	1.09070i	0.357896	−	0.933762i	$-0.383494\pi$
$504$	−1.49646e8	−	8.63981e7i	−1.16889	−	0.674858i
$505$	1.41113e7	+	5.26639e7i	0.109570	+	0.408921i
$506$			5.43108e7i			0.419213i
$507$	−3.13971e7	+	3.06143e7i	−0.240916	+	0.234910i
$508$	−1.28615e7			−0.0981072
$509$	−1.30303e8	+	3.49146e7i	−0.988100	+	0.264760i	−0.716452	−	0.697636i	$-0.754235\pi$
$509$	−1.30303e8	+	3.49146e7i	−0.988100	+	0.264760i	−0.271648	+	0.962397i	$0.587568\pi$
$510$	−2.14944e7	+	3.72293e7i	−0.162037	+	0.280656i
$511$	−2.19499e8	+	1.26728e8i	−1.64501	+	0.949750i
$512$	143600.	+	143600.i	0.00106990	+	0.00106990i
$513$	1.32504e7	−	4.94511e7i	0.0981469	−	0.366289i
$514$	−1.30109e8	−	3.48627e7i	−0.958119	−	0.256727i
$515$	2.99235e7	−	2.99235e7i	0.219074	−	0.219074i
$516$	−1.83445e7	−	3.17736e7i	−0.133523	−	0.231269i
$517$	−3.22940e7	−	1.86449e7i	−0.233695	−	0.134924i
$518$	−5.76775e7	−	2.15255e8i	−0.414970	−	1.54869i
$519$			1.97388e7i			0.141195i
$520$	−2.38489e7	+	1.72719e8i	−0.169613	+	1.22838i
$521$	−1.31409e8			−0.929203			−0.464602	−	0.885520i	$-0.653802\pi$
$521$	−1.31409e8			−0.929203			−0.464602	+	0.885520i	$0.653802\pi$
$522$	1.14824e6	−	307670.i	0.00807274	−	0.00216309i
$523$	1.29159e8	−	2.23710e8i	0.902857	−	1.56379i	0.0790898	−	0.996867i	$-0.474799\pi$
$523$	1.29159e8	−	2.23710e8i	0.902857	−	1.56379i	0.823768	−	0.566927i	$-0.191868\pi$
$524$	2.93368e7	−	1.69376e7i	0.203901	−	0.117722i
$525$	−2.82203e7	−	2.82203e7i	−0.195022	−	0.195022i
$526$	3.09939e6	−	1.15671e7i	0.0212970	−	0.0794816i
$527$	9.19102e7	+	2.46273e7i	0.627960	+	0.168261i
$528$	18958.8	−	18958.8i	0.000128798	−	0.000128798i
$529$	−7.44298e6	−	1.28916e7i	−0.0502782	−	0.0870844i
$530$	1.58865e8	+	9.17208e7i	1.06709	+	0.616084i
$531$	2.08239e7	+	7.77157e7i	0.139084	+	0.519069i
$532$		−	8.46655e7i		−	0.562305i
$533$	−456242.	−	3.64304e6i	−0.00301310	−	0.0240592i
$534$	3.29438e7			0.216346
$535$	−1.90275e8	+	5.09839e7i	−1.24257	+	0.332945i
$536$	−9.40262e7	+	1.62858e8i	−0.610597	+	1.05758i
$537$	6.48290e7	−	3.74290e7i	0.418645	−	0.241705i
$538$	−8.79704e7	−	8.79704e7i	−0.564924	−	0.564924i
$539$	−3.82130e7	+	1.42613e8i	−0.244031	+	0.910735i
$540$	7.40623e7	+	1.98449e7i	0.470344	+	0.126028i
$541$	5.85677e7	−	5.85677e7i	0.369885	−	0.369885i	−0.497550	−	0.867435i	$-0.665767\pi$
$541$	5.85677e7	−	5.85677e7i	0.369885	−	0.369885i	0.867435	+	0.497550i	$0.165767\pi$
$542$	3.05392e7	+	5.28954e7i	0.191805	+	0.332216i
$543$	−5.42563e7	−	3.13249e7i	−0.338883	−	0.195654i
$544$	−5.23862e7	−	1.95508e8i	−0.325402	−	1.21442i
$545$		−	4.41473e7i		−	0.272719i
$546$	−4.06673e7	−	3.16149e7i	−0.249843	−	0.194229i
$547$	−2.34576e8			−1.43325			−0.716623	−	0.697461i	$-0.754313\pi$
$547$	−2.34576e8			−1.43325			−0.716623	+	0.697461i	$0.754313\pi$
$548$	7.29304e7	−	1.95417e7i	0.443167	−	0.118746i
$549$	−2.47009e7	+	4.27831e7i	−0.149278	+	0.258557i
$550$	3.42900e7	−	1.97974e7i	0.206101	−	0.118992i
$551$	1.07789e6	+	1.07789e6i	0.00644348	+	0.00644348i
$552$	−1.38889e7	+	5.18339e7i	−0.0825751	+	0.308175i
$553$	2.82090e8	+	7.55858e7i	1.66806	+	0.446956i
$554$	1.30298e8	−	1.30298e8i	0.766320	−	0.766320i
$555$	6.08165e7	+	1.05337e8i	0.355748	+	0.616174i
$556$	1.41463e8	+	8.16738e7i	0.823036	+	0.475180i
$557$	−4.49513e7	−	1.67761e8i	−0.260122	−	0.970788i	−0.965169	−	0.261627i	$-0.915741\pi$
$557$	−4.49513e7	−	1.67761e8i	−0.260122	−	0.970788i	0.705047	−	0.709160i	$-0.250926\pi$
$558$			4.92269e7i			0.283335i
$559$	8.44825e7	+	2.07656e8i	0.483650	+	1.18880i
$560$	250875.			0.00142854
$561$	−5.16120e7	+	1.38294e7i	−0.292322	+	0.0783275i
$562$	−4.18941e7	+	7.25626e7i	−0.236017	+	0.408794i
$563$	9.12800e6	−	5.27005e6i	0.0511505	−	0.0295318i	−0.474207	−	0.880414i	$-0.657265\pi$
$563$	9.12800e6	−	5.27005e6i	0.0511505	−	0.0295318i	0.525357	+	0.850882i	$0.323932\pi$
$564$	−9.95478e6	−	9.95478e6i	−0.0554874	−	0.0554874i
$565$	1.49458e7	−	5.57784e7i	0.0828653	−	0.309258i
$566$	−6.75948e6	−	1.81120e6i	−0.0372790	−	0.00998888i
$567$	1.32092e8	−	1.32092e8i	0.724647	−	0.724647i
$568$	1.10593e8	+	1.91552e8i	0.603505	+	1.04530i
$569$	1.67525e8	+	9.67207e7i	0.909376	+	0.525028i	0.880230	−	0.474547i	$-0.157388\pi$
$569$	1.67525e8	+	9.67207e7i	0.909376	+	0.525028i	0.0291456	+	0.999575i	$0.490721\pi$
$570$	−7.38133e6	−	2.75475e7i	−0.0398575	−	0.148750i
$571$		−	2.47411e6i		−	0.0132896i	−0.999978	−	0.00664479i	$-0.997885\pi$
$571$		−	2.47411e6i		−	0.0132896i	0.999978	−	0.00664479i	$-0.00211512\pi$
$572$	−6.60119e7	+	4.99939e7i	−0.352723	+	0.267134i
$573$	−6.34605e7			−0.337318
$574$	4.16572e6	−	1.11620e6i	0.0220270	−	0.00590211i
$575$	4.85357e7	−	8.40664e7i	0.255304	−	0.442200i
$576$	9.05736e7	−	5.22927e7i	0.473952	−	0.273636i
$577$	−2.77747e7	−	2.77747e7i	−0.144584	−	0.144584i	0.631109	−	0.775694i	$-0.282600\pi$
$577$	−2.77747e7	−	2.77747e7i	−0.144584	−	0.144584i	−0.775694	+	0.631109i	$0.782600\pi$
$578$	−1.79058e7	+	6.68254e7i	−0.0927279	+	0.346065i
$579$	−5.78547e6	−	1.55021e6i	−0.0298059	−	0.00798648i
$580$	−1.61434e6	+	1.61434e6i	−0.00827393	+	0.00827393i
$581$	2.03754e7	+	3.52912e7i	0.103891	+	0.179944i
$582$	4.93953e7	+	2.85184e7i	0.250563	+	0.144663i
$583$	5.90128e7	+	2.20239e8i	0.297811	+	1.11144i
$584$		−	2.48454e8i		−	1.24741i
$585$	−2.02902e8	−	8.55489e7i	−1.01349	−	0.427314i
$586$	1.20367e8			0.598156
$587$	2.88532e6	−	773119.i	0.0142653	−	0.00382236i	−0.251679	−	0.967811i	$-0.580983\pi$
$587$	2.88532e6	−	773119.i	0.0142653	−	0.00382236i	0.265945	+	0.963988i	$0.414316\pi$
$588$	−2.78702e7	+	4.82726e7i	−0.137091	+	0.237448i
$589$	−5.46681e7	+	3.15627e7i	−0.267540	+	0.154464i
$590$	6.74314e7	+	6.74314e7i	0.328327	+	0.328327i
$591$	−7.62161e6	+	2.84442e7i	−0.0369219	+	0.137794i
$592$	−258469.	−	69256.6i	−0.00124579	−	0.000333808i
$593$	−2.70643e8	+	2.70643e8i	−1.29787	+	1.29787i	−0.368079	+	0.929795i	$0.619984\pi$
$593$	−2.70643e8	+	2.70643e8i	−1.29787	+	1.29787i	−0.929795	+	0.368079i	$0.880016\pi$
$594$	−2.94080e7	−	5.09361e7i	−0.140316	−	0.243034i
$595$	−4.32980e8	−	2.49981e8i	−2.05550	−	1.18674i
$596$	6.99564e6	+	2.61081e7i	0.0330437	+	0.123321i
$597$		−	1.23256e8i		−	0.579273i
$598$	4.86754e7	−	1.15446e8i	0.227618	−	0.539854i
$599$	1.05246e6			0.00489697			0.00244848	−	0.999997i	$-0.499221\pi$
$599$	1.05246e6			0.00489697			0.00244848	+	0.999997i	$0.499221\pi$
$600$	3.77889e7	−	1.01255e7i	0.174949	−	0.0468774i
$601$	6.30053e7	−	1.09128e8i	0.290238	−	0.502706i	−0.683628	−	0.729831i	$-0.739599\pi$
$601$	6.30053e7	−	1.09128e8i	0.290238	−	0.502706i	0.973866	+	0.227124i	$0.0729323\pi$
$602$	−2.28054e8	+	1.31667e8i	−1.04532	+	0.603516i
$603$	−1.67934e8	−	1.67934e8i	−0.765924	−	0.765924i
$604$	4.54108e7	−	1.69476e8i	0.206086	−	0.769124i
$605$	−1.29473e8	−	3.46921e7i	−0.584672	−	0.156662i
$606$	1.11648e7	−	1.11648e7i	0.0501688	−	0.0501688i
$607$	−1.44340e8	−	2.50004e8i	−0.645387	−	1.11784i	−0.984212	−	0.176994i	$-0.943363\pi$
$607$	−1.44340e8	−	2.50004e8i	−0.645387	−	1.11784i	0.338825	−	0.940850i	$-0.389971\pi$
$608$	1.16288e8	+	6.71389e7i	0.517397	+	0.298719i
$609$	−456866.	−	1.70505e6i	−0.00202272	−	0.00754891i
$610$			5.85537e7i			0.257967i
$611$	5.19358e7	+	6.85759e7i	0.227689	+	0.300641i
$612$	1.57994e8			0.689266
$613$	3.95247e7	−	1.05906e7i	0.171588	−	0.0459769i	−0.172002	−	0.985097i	$-0.555024\pi$
$613$	3.95247e7	−	1.05906e7i	0.171588	−	0.0459769i	0.343590	+	0.939120i	$0.388357\pi$
$614$	5.71707e7	−	9.90226e7i	0.246984	−	0.427789i
$615$	−2.03854e6	+	1.17695e6i	−0.00876382	+	0.00505979i
$616$	−1.80004e8	−	1.80004e8i	−0.770089	−	0.770089i
$617$	−8.63032e7	+	3.22088e8i	−0.367427	+	1.37126i	0.496673	+	0.867938i	$0.334555\pi$
$617$	−8.63032e7	+	3.22088e8i	−0.367427	+	1.37126i	−0.864100	+	0.503319i	$0.832112\pi$
$618$	−1.18377e7	−	3.17191e6i	−0.0501537	−	0.0134386i
$619$	1.42624e8	−	1.42624e8i	0.601341	−	0.601341i	−0.339327	−	0.940668i	$-0.610199\pi$
$619$	1.42624e8	−	1.42624e8i	0.601341	−	0.601341i	0.940668	+	0.339327i	$0.110199\pi$
$620$	−4.72710e7	−	8.18757e7i	−0.198344	−	0.343542i
$621$	−1.24876e8	−	7.20975e7i	−0.521442	−	0.301055i
$622$	6.49171e7	+	2.42274e8i	0.269766	+	1.00678i
$623$			3.83139e8i			1.58450i
$624$	−57291.6	+	23308.4i	−0.000235796	+	9.59310e-5i
$625$	3.04816e8			1.24853
$626$	1.09083e7	−	2.92288e6i	0.0444667	−	0.0119148i
$627$	1.77239e7	−	3.06988e7i	0.0719048	−	0.124543i
$628$	−1.31475e8	+	7.59071e7i	−0.530840	+	0.306481i
$629$	3.77077e8	+	3.77077e8i	1.51523	+	1.51523i
$630$	6.69446e7	−	2.49841e8i	0.267728	−	0.999175i
$631$	−2.27876e7	−	6.10592e6i	−0.0907006	−	0.0243032i	0.213183	−	0.977012i	$-0.431617\pi$
$631$	−2.27876e7	−	6.10592e6i	−0.0907006	−	0.0243032i	−0.303884	+	0.952709i	$0.598284\pi$
$632$	−2.02429e8	+	2.02429e8i	−0.801903	+	0.801903i
$633$	1.52327e6	+	2.63838e6i	0.00600572	+	0.0104022i
$634$	−4.55472e7	−	2.62967e7i	−0.178729	−	0.103189i
$635$	−1.30407e7	−	4.86687e7i	−0.0509309	−	0.190077i
$636$			8.60806e7i			0.334606i
$637$	2.09043e8	−	2.68898e8i	0.808754	−	1.04033i
$638$	1.75127e6			0.00674359
$639$	−2.69819e8	+	7.22979e7i	−1.03412	+	0.277091i
$640$	−1.00629e8	+	1.74295e8i	−0.383869	+	0.664881i
$641$	1.99071e8	−	1.14934e8i	0.755849	−	0.436389i	−0.0719545	−	0.997408i	$-0.522924\pi$
$641$	1.99071e8	−	1.14934e8i	0.755849	−	0.436389i	0.827803	+	0.561018i	$0.189590\pi$
$642$	4.03385e7	+	4.03385e7i	0.152445	+	0.152445i
$643$	7.17624e7	−	2.67821e8i	0.269938	−	1.00742i	−0.689220	−	0.724552i	$-0.742047\pi$
$643$	7.17624e7	−	2.67821e8i	0.269938	−	1.00742i	0.959158	−	0.282871i	$-0.0912867\pi$
$644$	−2.30339e8	−	6.17192e7i	−0.862403	−	0.231080i
$645$	1.01633e8	−	1.01633e8i	0.378752	−	0.378752i
$646$	−6.25175e7	−	1.08284e8i	−0.231902	−	0.401666i
$647$	1.76730e8	+	1.02035e8i	0.652524	+	0.376735i	0.789422	−	0.613850i	$-0.210380\pi$
$647$	1.76730e8	+	1.02035e8i	0.652524	+	0.376735i	−0.136899	+	0.990585i	$0.543714\pi$
$648$	4.73949e7	+	1.76880e8i	0.174183	+	0.650061i
$649$			1.18530e8i			0.433606i
$650$	−9.06320e7	+	1.13505e7i	−0.330021	+	0.0413308i
$651$	7.30981e7			0.264949
$652$	1.79170e8	−	4.80085e7i	0.646431	−	0.173211i
$653$	8.95105e7	−	1.55037e8i	0.321465	−	0.556795i	−0.659325	−	0.751858i	$-0.729158\pi$
$653$	8.95105e7	−	1.55037e8i	0.321465	−	0.556795i	0.980791	+	0.195063i	$0.0624913\pi$
$654$	−1.10722e7	+	6.39252e6i	−0.0395821	+	0.0228528i
$655$	9.38385e7	+	9.38385e7i	0.333931	+	0.333931i
$656$	1340.29	−	5002.02i	4.74773e−6	−	1.77188e-5i
$657$	3.03084e8	+	8.12112e7i	1.06873	+	0.286365i
$658$	−7.14503e7	+	7.14503e7i	−0.250799	+	0.250799i
$659$	1.25284e8	+	2.16998e8i	0.437763	+	0.758227i	0.997517	−	0.0704316i	$-0.0224376\pi$
$659$	1.25284e8	+	2.16998e8i	0.437763	+	0.758227i	−0.559754	+	0.828659i	$0.689104\pi$
$660$	4.59771e7	+	2.65449e7i	0.159923	+	0.0923314i
$661$	−4.96236e7	−	1.85198e8i	−0.171824	−	0.641256i	−0.997071	−	0.0764838i	$-0.975631\pi$
$661$	−4.96236e7	−	1.85198e8i	−0.171824	−	0.641256i	0.825247	−	0.564772i	$-0.191036\pi$
$662$		−	5.18772e7i		−	0.178815i
$663$	1.22104e8	+	1.68600e7i	0.418976	+	0.0578517i
$664$	−3.99466e7			−0.136451
$665$	3.20379e8	−	8.58454e7i	1.08943	−	0.291912i
$666$	−1.37943e8	+	2.38923e8i	−0.466955	+	0.808791i
$667$	3.71825e6	−	2.14673e6i	0.0125303	−	0.00723436i
$668$	−1.79064e8	−	1.79064e8i	−0.600730	−	0.600730i
$669$	1.93349e7	−	7.21589e7i	0.0645749	−	0.240997i
$670$	−2.71899e8	−	7.28552e7i	−0.904032	−	0.242235i
$671$	−5.14625e7	+	5.14625e7i	−0.170343	+	0.170343i
$672$	−7.77457e7	−	1.34660e8i	−0.256194	−	0.443741i
$673$	−3.11179e8	−	1.79659e8i	−1.02086	−	0.589392i	−0.106505	−	0.994312i	$-0.533966\pi$
$673$	−3.11179e8	−	1.79659e8i	−1.02086	−	0.589392i	−0.914352	+	0.404920i	$0.867299\pi$
$674$	−8.10289e6	−	3.02404e7i	−0.0264643	−	0.0987661i
$675$			1.05124e8i			0.341814i
$676$	1.85125e8	−	4.71078e7i	0.599274	−	0.152494i
$677$	−3.39447e8			−1.09397			−0.546985	−	0.837142i	$-0.684225\pi$
$677$	−3.39447e8			−1.09397			−0.546985	+	0.837142i	$0.684225\pi$
$678$	−1.61534e7	+	4.32828e6i	−0.0518291	+	0.0138876i
$679$	−3.31671e8	+	5.74471e8i	−1.05949	+	1.83510i
$680$	4.24436e8	−	2.45048e8i	1.34985	−	0.779336i
$681$	4.36925e7	+	4.36925e7i	0.138346	+	0.138346i
$682$	−1.87699e7	+	7.00504e7i	−0.0591711	+	0.220830i
$683$	−4.37240e8	−	1.17158e8i	−1.37233	−	0.367714i	−0.503999	−	0.863704i	$-0.668139\pi$
$683$	−4.37240e8	−	1.17158e8i	−1.37233	−	0.367714i	−0.868328	+	0.495990i	$0.834805\pi$
$684$	−7.41156e7	+	7.41156e7i	−0.231602	+	0.231602i
$685$	1.47893e8	+	2.56159e8i	0.460127	+	0.796963i
$686$	8.35384e7	+	4.82309e7i	0.258770	+	0.149401i
$687$	2.46163e7	+	9.18692e7i	0.0759193	+	0.283335i
$688$			316201.i			0.000970952i
$689$	7.19449e7	−	5.21042e8i	0.219959	−	1.59300i
$690$	−8.03259e7			−0.244517
$691$	4.02652e8	−	1.07890e8i	1.22038	−	0.327000i	0.409554	−	0.912286i	$-0.365684\pi$
$691$	4.02652e8	−	1.07890e8i	1.22038	−	0.327000i	0.810827	+	0.585286i	$0.199018\pi$
$692$	4.29921e7	−	7.44645e7i	0.129739	−	0.224715i
$693$	2.78421e8	−	1.60747e8i	0.836571	−	0.482994i
$694$	−7.03367e7	−	7.03367e7i	−0.210428	−	0.210428i
$695$	−1.65624e8	+	6.18116e8i	−0.493365	+	1.84126i
$696$	1.67140e6	+	447851.i	0.00495739	+	0.00132833i
$697$	−7.29738e6	+	7.29738e6i	−0.0215511	+	0.0215511i
$698$	−9.84441e7	−	1.70510e8i	−0.289483	−	0.501400i
$699$	−1.85022e8	−	1.06823e8i	−0.541741	−	0.312775i
$700$	4.49957e7	+	1.67926e8i	0.131183	+	0.489581i
$701$		−	5.12960e8i		−	1.48912i	−0.667556	−	0.744560i	$-0.732659\pi$
$701$		−	5.12960e8i		−	1.48912i	0.667556	−	0.744560i	$-0.267341\pi$
$702$	1.68606e7	+	1.34629e8i	0.0487372	+	0.389161i
$703$	−3.53777e8			−1.01827
$704$	1.48826e8	−	3.98778e7i	0.426541	−	0.114291i
$705$	2.75760e7	−	4.77630e7i	0.0786979	−	0.136309i
$706$	5.61271e7	−	3.24050e7i	0.159499	−	0.0920870i
$707$	1.29848e8	+	1.29848e8i	0.367431	+	0.367431i
$708$	−1.15819e7	+	4.32243e7i	−0.0326348	+	0.121795i
$709$	−5.53793e6	−	1.48388e6i	−0.0155385	−	0.00416353i	0.251041	−	0.967976i	$-0.419227\pi$
$709$	−5.53793e6	−	1.48388e6i	−0.0155385	−	0.00416353i	−0.266580	+	0.963813i	$0.585894\pi$
$710$	−2.34114e8	+	2.34114e8i	−0.654111	+	0.654111i
$711$	−1.80772e8	−	3.13107e8i	−0.502948	−	0.871131i
$712$	−3.25260e8	−	1.87789e8i	−0.901138	−	0.520272i
$713$	4.60169e7	+	1.71737e8i	0.126955	+	0.473801i
$714$			1.44789e8i			0.397777i
$715$	−2.56112e8	−	1.99102e8i	−0.700667	−	0.544701i
$716$	−3.26090e8			−0.888378
$717$	−1.76448e8	+	4.72792e7i	−0.478697	+	0.128266i
$718$	5.13422e7	−	8.89273e7i	0.138708	−	0.240249i
$719$	2.99105e8	−	1.72689e8i	0.804707	−	0.464598i	−0.0404077	−	0.999183i	$-0.512866\pi$
$719$	2.99105e8	−	1.72689e8i	0.804707	−	0.464598i	0.845114	+	0.534586i	$0.179532\pi$
$720$	−219614.	−	219614.i	−0.000588386	−	0.000588386i
$721$	3.68895e7	−	1.37674e8i	0.0984232	−	0.367320i
$722$	−1.44459e8	−	3.87076e7i	−0.383824	−	0.102845i
$723$	2.29139e7	−	2.29139e7i	0.0606296	−	0.0606296i
$724$	1.36454e8	+	2.36346e8i	0.359561	+	0.622777i
$725$	−2.71075e6	−	1.56505e6i	−0.00711336	−	0.00410690i
$726$	1.00468e7	+	3.74952e7i	0.0262554	+	0.0979865i
$727$			5.82836e8i			1.51685i	0.651759	+	0.758426i	$0.274031\pi$
$727$			5.82836e8i			1.51685i	−0.651759	+	0.758426i	$0.725969\pi$
$728$	2.21302e8	+	5.43955e8i	0.573575	+	1.40984i
$729$	−1.48501e8			−0.383307
$730$	3.59233e8	−	9.62561e7i	0.923437	−	0.247434i
$731$	3.15075e8	−	5.45725e8i	0.806605	−	1.39708i
$732$	−2.37954e7	+	1.37383e7i	−0.0606679	+	0.0350266i
$733$	5.00617e8	+	5.00617e8i	1.27114	+	1.27114i	0.945491	+	0.325649i	$0.105583\pi$
$733$	5.00617e8	+	5.00617e8i	1.27114	+	1.27114i	0.325649	+	0.945491i	$0.394417\pi$
$734$	4.63815e7	−	1.73098e8i	0.117289	−	0.437727i
$735$	−2.10925e8	−	5.65172e7i	−0.531210	−	0.142337i
$736$	2.67428e8	−	2.67428e8i	0.670770	−	0.670770i
$737$	−1.74939e8	−	3.03003e8i	−0.437003	−	0.756911i
$738$	−4.62376e6	−	2.66953e6i	−0.0115034	−	0.00664149i
$739$	−3.66647e7	−	1.36834e8i	−0.0908478	−	0.339049i	0.905509	−	0.424326i	$-0.139489\pi$
$739$	−3.66647e7	−	1.36834e8i	−0.0908478	−	0.339049i	−0.996357	+	0.0852775i	$0.972822\pi$
$740$		−	5.29847e8i		−	1.30754i
$741$	−6.51885e7	+	4.93703e7i	−0.160220	+	0.121342i
$742$	6.17842e8			1.51240
$743$	−4.36580e8	+	1.16981e8i	−1.06438	+	0.285200i	−0.748182	−	0.663493i	$-0.769073\pi$
$743$	−4.36580e8	+	1.16981e8i	−1.06438	+	0.285200i	−0.316198	+	0.948693i	$0.602407\pi$
$744$	−3.58278e7	+	6.20556e7i	−0.0869965	+	0.150682i
$745$	−9.17013e7	+	5.29438e7i	−0.221772	+	0.128040i
$746$	1.45902e8	+	1.45902e8i	0.351435	+	0.351435i
$747$	1.30572e7	−	4.87301e7i	0.0313248	−	0.116906i
$748$	2.24827e8	+	6.02423e7i	0.537210	+	0.143945i
$749$	−4.69140e8	+	4.69140e8i	−1.11649	+	1.11649i
$750$	−2.51042e7	−	4.34817e7i	−0.0595062	−	0.103068i
$751$	1.58016e8	+	9.12306e7i	0.373062	+	0.215388i	0.674795	−	0.738005i	$-0.264232\pi$
$751$	1.58016e8	+	9.12306e7i	0.373062	+	0.215388i	−0.301733	+	0.953392i	$0.597565\pi$
$752$	31402.9	+	117197.i	7.38442e−5	+	0.000275590i
$753$			6.86231e7i			0.160726i
$754$	−3.72260e6	−	1.56955e6i	−0.00868426	−	0.00366152i
$755$	6.87349e8			1.59712
$756$	2.49446e8	−	6.68389e7i	0.577314	−	0.154691i
$757$	−3.53297e8	+	6.11929e8i	−0.814428	+	1.41063i	0.0953102	+	0.995448i	$0.469616\pi$
$757$	−3.53297e8	+	6.11929e8i	−0.814428	+	1.41063i	−0.909738	+	0.415183i	$0.863718\pi$
$758$	1.95019e7	−	1.12594e7i	0.0447784	−	0.0258528i
$759$	−7.05981e7	−	7.05981e7i	−0.161461	−	0.161461i
$760$	−8.41514e7	+	3.14057e8i	−0.191699	+	0.715432i
$761$	−2.31789e7	−	6.21078e6i	−0.0525944	−	0.0140926i	0.232426	−	0.972614i	$-0.425334\pi$
$761$	−2.31789e7	−	6.21078e6i	−0.0525944	−	0.0140926i	−0.285020	+	0.958521i	$0.592000\pi$
$762$	−1.03178e7	+	1.03178e7i	−0.0233197	+	0.0233197i
$763$	−7.43454e7	−	1.28770e8i	−0.167371	−	0.289895i
$764$	2.39405e8	+	1.38220e8i	0.536850	+	0.309950i
$765$	1.60196e8	+	5.97859e8i	0.357822	+	1.33541i
$766$		−	5.22906e7i		−	0.116342i
$767$	1.06231e8	−	2.51955e8i	0.235432	−	0.558389i
$768$	1.52352e8			0.336329
$769$	−4.99378e8	+	1.33808e8i	−1.09812	+	0.294241i	−0.761999	−	0.647578i	$-0.775782\pi$
$769$	−4.99378e8	+	1.33808e8i	−1.09812	+	0.294241i	−0.336122	+	0.941818i	$0.609115\pi$
$770$	1.90526e8	−	3.30000e8i	0.417332	−	0.722840i
$771$	2.14446e8	−	1.23810e8i	0.467901	−	0.270143i
$772$	1.84492e7	+	1.84492e7i	0.0400983	+	0.0400983i
$773$	1.21473e8	−	4.53345e8i	0.262992	−	0.981501i	−0.700475	−	0.713676i	$-0.747029\pi$
$773$	1.21473e8	−	4.53345e8i	0.262992	−	0.981501i	0.963468	−	0.267824i	$-0.0863046\pi$
$774$	3.14898e8	+	8.43766e7i	0.679121	+	0.181970i
$775$	9.16551e7	−	9.16551e7i	0.196903	−	0.196903i
$776$	−3.25126e8	−	5.63136e8i	−0.695772	−	1.20511i
$777$	3.54783e8	+	2.04834e8i	0.756309	+	0.436655i
$778$	4.85557e7	+	1.81212e8i	0.103110	+	0.384812i
$779$		−	6.84646e6i		−	0.0144828i
$780$	−7.39413e7	−	9.76319e7i	−0.155813	−	0.205735i
$781$	−4.11523e8			−0.863854
$782$	−3.40168e8	+	9.11477e7i	−0.711333	+	0.190601i
$783$	−2.32481e6	+	4.02668e6i	−0.00484285	+	0.00838807i
$784$	416033.	−	240197.i	0.000863336	−	0.000498447i
$785$	−4.20544e8	−	4.20544e8i	−0.869365	−	0.869365i
$786$	9.94694e6	−	3.71225e7i	0.0204843	−	0.0764486i
$787$	−2.68622e8	−	7.19769e7i	−0.551083	−	0.147662i	−0.0274763	−	0.999622i	$-0.508747\pi$
$787$	−2.68622e8	−	7.19769e7i	−0.551083	−	0.147662i	−0.523606	+	0.851960i	$0.675414\pi$
$788$	9.07055e7	−	9.07055e7i	0.185377	−	0.185377i
$789$	1.10071e7	+	1.90648e7i	0.0224099	+	0.0388151i
$790$	−3.71111e8	−	2.14261e8i	−0.752702	−	0.434573i
$791$	−5.03382e7	−	1.87865e8i	−0.101711	−	0.379591i
$792$			3.15149e8i			0.634367i
$793$	1.55515e8	−	6.32692e7i	0.311854	−	0.126874i
$794$	−2.29204e8			−0.457890
$795$	−3.25734e8	+	8.72801e7i	−0.648278	+	0.173706i
$796$	−2.68457e8	+	4.64981e8i	−0.532275	+	0.921927i
$797$	−6.94980e8	+	4.01247e8i	−1.37277	+	0.792568i	−0.991276	−	0.131803i	$-0.957923\pi$
$797$	−6.94980e8	+	4.01247e8i	−1.37277	+	0.792568i	−0.381493	+	0.924372i	$0.624590\pi$
$798$	−6.79209e7	−	6.79209e7i	−0.133658	−	0.133658i
$799$	6.25821e7	−	2.33560e8i	0.122690	−	0.457886i
$800$	−2.66328e8	−	7.13623e7i	−0.520171	−	0.139379i
$801$	3.35397e8	−	3.35397e8i	0.652622	−	0.652622i
$802$	1.70374e7	+	2.95097e7i	0.0330279	+	0.0572060i
$803$	4.00327e8	+	2.31129e8i	0.773157	+	0.446383i
$804$	−3.41876e7	−	1.27590e8i	−0.0657809	−	0.245498i
$805$		−	9.34197e8i		−	1.79081i
$806$	1.02680e8	−	1.32081e8i	0.196102	−	0.252252i
$807$	2.28704e8			0.435163
$808$	−1.73875e8	+	4.65897e7i	−0.329612	+	0.0883194i
$809$	−5.09890e7	+	8.83156e7i	−0.0963011	+	0.166798i	−0.910151	−	0.414277i	$-0.864034\pi$
$809$	−5.09890e7	+	8.83156e7i	−0.0963011	+	0.166798i	0.813850	+	0.581075i	$0.197368\pi$
$810$	−2.37384e8	+	1.37054e8i	−0.446680	+	0.257891i
$811$	−1.91379e8	−	1.91379e8i	−0.358782	−	0.358782i	0.504582	−	0.863364i	$-0.331647\pi$
$811$	−1.91379e8	−	1.91379e8i	−0.358782	−	0.358782i	−0.863364	+	0.504582i	$0.831647\pi$
$812$	−1.99016e6	+	7.42736e6i	−0.00371723	+	0.0138729i
$813$	−1.08456e8	−	2.90606e7i	−0.201828	−	0.0540796i
$814$	−2.87394e8	+	2.87394e8i	−0.532849	+	0.532849i
$815$	3.63334e8	+	6.29312e8i	0.671170	+	1.16250i
$816$	150564.	+	86927.9i	0.000277108	+	0.000159989i
$817$	1.08199e8	+	4.03804e8i	0.198407	+	0.740465i
$818$		−	2.00137e8i		−	0.365652i
$819$	−7.35896e8	+	9.21612e7i	−1.33957	+	0.167763i
$820$	1.02538e7			0.0185971
$821$	5.88198e8	−	1.57607e8i	1.06290	−	0.284804i	0.315329	−	0.948982i	$-0.397885\pi$
$821$	5.88198e8	−	1.57607e8i	1.06290	−	0.284804i	0.747574	+	0.664178i	$0.231218\pi$
$822$	4.28298e7	−	7.41835e7i	0.0771136	−	0.133565i
$823$	1.30451e8	−	7.53157e7i	0.234016	−	0.135109i	−0.378407	−	0.925639i	$-0.623528\pi$
$823$	1.30451e8	−	7.53157e7i	0.234016	−	0.135109i	0.612424	+	0.790530i	$0.290195\pi$
$824$	9.87953e7	+	9.87953e7i	0.176585	+	0.176585i
$825$	−1.88389e7	+	7.03076e7i	−0.0335500	+	0.125210i
$826$	3.10242e8	+	8.31291e7i	0.550504	+	0.147507i
$827$	5.54788e8	−	5.54788e8i	0.980867	−	0.980867i	−0.0189529	−	0.999820i	$-0.506033\pi$
$827$	5.54788e8	−	5.54788e8i	0.980867	−	0.980867i	0.999820	+	0.0189529i	$0.00603326\pi$
$828$	1.47609e8	+	2.55666e8i	0.260029	+	0.450383i
$829$	3.70301e8	+	2.13793e8i	0.649967	+	0.375259i	0.788444	−	0.615107i	$-0.210887\pi$
$829$	3.70301e8	+	2.13793e8i	0.649967	+	0.375259i	−0.138477	+	0.990366i	$0.544221\pi$
$830$	−1.54761e7	−	5.77576e7i	−0.0270662	−	0.101012i
$831$			3.38747e8i			0.590300i
$832$	−3.52094e8	−	4.86167e7i	−0.611348	−	0.0844142i
$833$	−9.57366e8			−1.65631
$834$	1.79006e8	−	4.79645e7i	0.308581	−	0.0826841i
$835$	4.96030e8	−	8.59148e8i	0.852017	−	1.47574i
$836$	−1.33727e8	+	7.72074e7i	−0.228876	+	0.132142i
$837$	−1.36149e8	−	1.36149e8i	−0.232187	−	0.232187i
$838$	5.01729e7	−	1.87248e8i	0.0852584	−	0.318189i
$839$	1.03728e9	+	2.77939e8i	1.75635	+	0.470613i	0.985963	−	0.166964i	$-0.0533962\pi$
$839$	1.03728e9	+	2.77939e8i	1.75635	+	0.470613i	0.770387	+	0.637576i	$0.220063\pi$
$840$	2.66227e8	−	2.66227e8i	0.449174	−	0.449174i
$841$	2.97342e8	+	5.15012e8i	0.499884	+	0.865824i
$842$	1.79639e8	+	1.03715e8i	0.300930	+	0.173742i
$843$	−3.98658e7	−	1.48781e8i	−0.0665453	−	0.248350i
$844$		−	1.32710e7i		−	0.0220738i
$845$	3.65964e8	+	6.52761e8i	0.606552	+	1.08189i
$846$	1.25094e8			0.206598
$847$	−4.36072e8	+	1.16845e8i	−0.717642	+	0.192292i
$848$	370939.	−	642485.i	0.000608296	−	0.00105360i
$849$	1.11409e7	−	6.43222e6i	0.0182053	−	0.0105109i
$850$	1.81545e8	+	1.81545e8i	0.295616	+	0.295616i
$851$	−2.57895e8	+	9.62477e8i	−0.418460	+	1.56172i
$852$	−1.50070e8	−	4.02110e7i	−0.242647	−	0.0650169i
$853$	4.41336e8	−	4.41336e8i	0.711086	−	0.711086i	−0.255676	−	0.966763i	$-0.582298\pi$
$853$	4.41336e8	−	4.41336e8i	0.711086	−	0.711086i	0.966763	+	0.255676i	$0.0822980\pi$
$854$	9.86062e7	+	1.70791e8i	0.158318	+	0.274215i
$855$	−3.55606e8	−	2.05309e8i	−0.568946	−	0.328481i
$856$	−1.68329e8	−	6.28211e8i	−0.268372	−	1.00158i
$857$			3.43869e8i			0.546325i	0.961968	+	0.273162i	$0.0880696\pi$
$857$			3.43869e8i			0.546325i	−0.961968	+	0.273162i	$0.911930\pi$
$858$	−1.28500e7	+	9.30628e7i	−0.0203443	+	0.147338i
$859$	7.87640e8			1.24265			0.621324	−	0.783554i	$-0.286595\pi$
$859$	7.87640e8			1.24265			0.621324	+	0.783554i	$0.286595\pi$
$860$	−6.04772e8	+	1.62048e8i	−0.950816	+	0.254770i
$861$	−3.96404e6	+	6.86592e6i	−0.00621053	+	0.0107570i
$862$	−1.87437e7	+	1.08217e7i	−0.0292640	+	0.0168956i
$863$	−3.37935e8	−	3.37935e8i	−0.525776	−	0.525776i	0.393534	−	0.919310i	$-0.371252\pi$
$863$	−3.37935e8	−	3.37935e8i	−0.525776	−	0.525776i	−0.919310	+	0.393534i	$0.871252\pi$
$864$	−1.06005e8	+	3.95617e8i	−0.164356	+	0.613385i
$865$	3.25369e8	+	8.71825e7i	0.502723	+	0.134704i
$866$	−3.01408e8	+	3.01408e8i	−0.464089	+	0.464089i
$867$	−6.35900e7	−	1.10141e8i	−0.0975735	−	0.169002i
$868$	−2.75762e8	−	1.59212e8i	−0.421673	−	0.243453i
$869$	−1.37855e8	−	5.14481e8i	−0.210069	−	0.783990i
$870$			2.59014e6i			0.00393337i
$871$	1.00298e8	+	8.00869e8i	0.151788	+	1.21201i
$872$	1.45757e8			0.219826
$873$	7.93231e8	−	2.12546e8i	1.19222	−	0.319455i
$874$	1.16816e8	−	2.02332e8i	0.174972	−	0.303061i
$875$	5.05695e8	−	2.91963e8i	0.754857	−	0.435817i
$876$	1.23403e8	+	1.23403e8i	0.183574	+	0.183574i
$877$	3.32800e7	−	1.24202e8i	0.0493383	−	0.184133i	−0.936859	−	0.349707i	$-0.886281\pi$
$877$	3.32800e7	−	1.24202e8i	0.0493383	−	0.184133i	0.986197	+	0.165574i	$0.0529477\pi$
$878$	4.42673e8	+	1.18614e8i	0.654033	+	0.175248i
$879$	−1.56464e8	+	1.56464e8i	−0.230381	+	0.230381i
$880$	−228775.	−	396250.i	−0.000335707	−	0.000581462i
$881$	−8.09632e8	−	4.67441e8i	−1.18402	−	0.683595i	−0.227080	−	0.973876i	$-0.572918\pi$
$881$	−8.09632e8	−	4.67441e8i	−1.18402	−	0.683595i	−0.956942	+	0.290281i	$0.906251\pi$
$882$	−1.28191e8	−	4.78414e8i	−0.186832	−	0.697266i
$883$		−	1.56594e8i		−	0.227454i	−0.993512	−	0.113727i	$-0.963721\pi$
$883$		−	1.56594e8i		−	0.227454i	0.993512	−	0.113727i	$-0.0362789\pi$
$884$	−4.23915e8	−	3.29553e8i	−0.613652	−	0.477055i
$885$	−1.75307e8			−0.252912
$886$	2.54178e7	−	6.81067e6i	0.0365457	−	0.00979239i
$887$	−1.03733e8	+	1.79671e8i	−0.148644	+	0.257458i	−0.930726	−	0.365716i	$-0.880824\pi$
$887$	−1.03733e8	+	1.79671e8i	−0.148644	+	0.257458i	0.782083	+	0.623174i	$0.214157\pi$
$888$	−3.47782e8	+	2.00792e8i	−0.496670	+	0.286753i
$889$	−1.19997e8	−	1.19997e8i	−0.170791	−	0.170791i
$890$	1.45506e8	−	5.43037e8i	0.206401	−	0.770300i
$891$	−3.29091e8	−	8.81798e7i	−0.465247	−	0.124663i
$892$	−2.30107e8	+	2.30107e8i	−0.324216	+	0.324216i
$893$	8.02062e7	+	1.38921e8i	0.112630	+	0.195081i
$894$	2.65566e7	+	1.53325e7i	0.0371673	+	0.0214585i
$895$	−3.30634e8	−	1.23394e9i	−0.461188	−	1.72118i
$896$			6.77849e8i			0.942343i
$897$	8.67949e7	+	2.13340e8i	0.120259	+	0.295594i
$898$	−7.05823e7			−0.0974690
$899$	5.53773e6	−	1.48383e6i	0.00762171	−	0.00204223i
$900$	1.07613e8	−	1.86390e8i	0.147617	−	0.255680i
$901$	−1.28039e9	+	7.39235e8i	−1.75053	+	1.01067i
$902$	−5.56178e6	−	5.56178e6i	−0.00757869	−	0.00757869i
$903$	1.25293e8	−	4.67599e8i	0.170162	−	0.635053i
$904$	1.84158e8	+	4.93449e7i	0.249278	+	0.0667940i
$905$	−7.55991e8	+	7.55991e8i	−1.01993	+	1.01993i
$906$	−9.95278e7	−	1.72387e8i	−0.133832	−	0.231804i
$907$	4.21792e8	+	2.43521e8i	0.565296	+	0.326374i	0.755268	−	0.655416i	$-0.227506\pi$
$907$	4.21792e8	+	2.43521e8i	0.565296	+	0.326374i	−0.189972	+	0.981789i	$0.560840\pi$
$908$	−6.96653e7	−	2.59994e8i	−0.0930591	−	0.347301i
$909$		−	2.27336e8i		−	0.302674i
$910$	−7.00752e8	+	5.30712e8i	−0.929908	+	0.704263i
$911$	1.95215e7			0.0258202			0.0129101	−	0.999917i	$-0.495890\pi$
$911$	1.95215e7			0.0258202			0.0129101	+	0.999917i	$0.495890\pi$
$912$	−111408.	+	29851.7i	−0.000146870	+	3.93536e-5i
$913$	3.71610e7	−	6.43648e7i	0.0488287	−	0.0845738i
$914$	9.72456e7	−	5.61448e7i	0.127359	−	0.0735310i
$915$	−7.61133e7	−	7.61133e7i	−0.0993567	−	0.0993567i
$916$	1.07231e8	−	4.00192e8i	0.139519	−	0.520693i
$917$	4.31737e8	+	1.15684e8i	0.559901	+	0.150025i
$918$	2.69677e8	−	2.69677e8i	0.348590	−	0.348590i
$919$	−3.88963e8	−	6.73704e8i	−0.501144	−	0.868006i	−0.999999	−	0.00132100i	$-0.999580\pi$
$919$	−3.88963e8	−	6.73704e8i	−0.501144	−	0.868006i	0.498856	−	0.866685i	$-0.333754\pi$
$920$	7.93073e8	+	4.57881e8i	1.01847	+	0.588016i
$921$	5.44028e7	+	2.03034e8i	0.0696374	+	0.259890i
$922$		−	1.25841e8i		−	0.160557i
$923$	8.74757e8	+	3.68822e8i	1.11245	+	0.469042i
$924$	1.78810e8			0.226660
$925$	7.01683e8	−	1.88016e8i	0.886576	−	0.237557i
$926$	−2.42781e8	+	4.20509e8i	−0.305760	+	0.529593i
$927$	−1.52811e8	+	8.82257e7i	−0.191830	+	0.110753i
$928$	−8.62330e6	−	8.62330e6i	−0.0107902	−	0.0107902i
$929$	7.71909e7	−	2.88080e8i	0.0962762	−	0.359308i	−0.900934	−	0.433957i	$-0.857117\pi$
$929$	7.71909e7	−	2.88080e8i	0.0962762	−	0.359308i	0.997210	+	0.0746492i	$0.0237837\pi$
$930$	−1.03605e8	−	2.77608e7i	−0.128804	−	0.0345131i
$931$	4.49104e8	−	4.49104e8i	0.556542	−	0.556542i
$932$	4.65330e8	+	8.05976e8i	0.574796	+	0.995576i
$933$	−3.99314e8	−	2.30544e8i	−0.491666	−	0.283863i
$934$	4.94434e7	+	1.84525e8i	0.0606830	+	0.226472i
$935$			9.11841e8i			1.11554i
$936$	2.82448e8	−	6.69900e8i	0.344438	−	0.816926i
$937$	−5.91150e8			−0.718586			−0.359293	−	0.933225i	$-0.616982\pi$
$937$	−5.91150e8			−0.718586			−0.359293	+	0.933225i	$0.616982\pi$
$938$	−9.15774e8	+	2.45381e8i	−1.10963	+	0.297325i
$939$	−1.03802e7	+	1.79790e7i	−0.0125374	+	0.0217155i
$940$	−2.08061e8	+	1.20124e8i	−0.250499	+	0.144626i
$941$	−2.56138e8	−	2.56138e8i	−0.307401	−	0.307401i	0.536500	−	0.843900i	$-0.319746\pi$
$941$	−2.56138e8	−	2.56138e8i	−0.307401	−	0.307401i	−0.843900	+	0.536500i	$0.819746\pi$
$942$	−4.45779e7	+	1.66367e8i	−0.0533295	+	0.199028i
$943$	−1.86263e7	−	4.99091e6i	−0.0222122	−	0.00595175i
$944$	272707.	−	272707.i	0.000324176	−	0.000324176i
$945$	5.05845e8	+	8.76149e8i	0.599407	+	1.03820i
$946$	4.15930e8	+	2.40138e8i	0.491301	+	0.283653i
$947$	−2.81691e8	−	1.05128e9i	−0.331683	−	1.23786i	−0.907421	−	0.420222i	$-0.861952\pi$
$947$	−2.81691e8	−	1.05128e9i	−0.331683	−	1.23786i	0.575739	−	0.817634i	$-0.304715\pi$
$948$		−	2.01086e8i		−	0.236024i
$949$	−6.43812e8	−	8.50089e8i	−0.753288	−	0.994639i
$950$	−1.70327e8			−0.198661
$951$	9.33891e7	−	2.50235e7i	0.108581	−	0.0290942i
$952$	8.25337e8	−	1.42953e9i	0.956578	−	1.65684i
$953$	−1.22342e9	+	7.06339e8i	−1.41350	+	0.816084i	−0.995716	−	0.0924638i	$-0.970526\pi$
$953$	−1.22342e9	+	7.06339e8i	−1.41350	+	0.816084i	−0.417782	+	0.908547i	$0.637192\pi$
$954$	−5.40855e8	−	5.40855e8i	−0.622924	−	0.622924i
$955$	−2.80293e8	+	1.04607e9i	−0.321812	+	1.20102i
$956$	7.68628e8	+	2.05953e8i	0.879716	+	0.235719i
$957$	−2.27646e6	+	2.27646e6i	−0.00259731	+	0.00259731i
$958$	4.21119e8	+	7.29400e8i	0.478970	+	0.829601i
$959$	8.62759e8	+	4.98114e8i	0.978214	+	0.564772i
$960$	5.89795e7	+	2.20114e8i	0.0666633	+	0.248791i
$961$		−	6.50092e8i		−	0.732495i
$962$	8.68474e8	−	3.53329e8i	0.975510	−	0.396875i
$963$	8.21363e8			0.919721
$964$	−1.36351e8	+	3.65350e7i	−0.152204	+	0.0407829i
$965$	−5.11066e7	+	8.85193e7i	−0.0568716	+	0.0985045i
$966$	−2.34297e8	+	1.35271e8i	−0.259917	+	0.150063i
$967$	−5.20123e8	−	5.20123e8i	−0.575210	−	0.575210i	0.358370	−	0.933580i	$-0.383333\pi$
$967$	−5.20123e8	−	5.20123e8i	−0.575210	−	0.575210i	−0.933580	+	0.358370i	$0.883333\pi$
$968$	1.14540e8	−	4.27467e8i	0.126278	−	0.471278i
$969$	2.22023e8	+	5.94908e7i	0.244020	+	0.0653850i
$970$	6.88261e8	−	6.88261e8i	0.754115	−	0.754115i
$971$	6.26795e7	+	1.08564e8i	0.0684649	+	0.118585i	0.898226	−	0.439534i	$-0.144857\pi$
$971$	6.26795e7	+	1.08564e8i	0.0684649	+	0.118585i	−0.829761	+	0.558119i	$0.811523\pi$
$972$	−4.23618e8	−	2.44576e8i	−0.461292	−	0.266327i
$973$	5.57831e8	+	2.08185e9i	0.605570	+	2.26002i
$974$			4.90467e8i			0.530802i
$975$	1.03057e8	−	1.32566e8i	0.111190	−	0.143027i
$976$	236804.			0.000254706
$977$	7.75343e8	−	2.07753e8i	0.831401	−	0.222773i	0.182076	−	0.983284i	$-0.441718\pi$
$977$	7.75343e8	−	2.07753e8i	0.831401	−	0.222773i	0.649325	+	0.760511i	$0.275052\pi$
$978$	1.05221e8	−	1.82248e8i	0.112483	−	0.194826i
$979$	6.05158e8	−	3.49388e8i	0.644942	−	0.372357i
$980$	6.72617e8	+	6.72617e8i	0.714643	+	0.714643i
$981$	−4.76429e7	+	1.77806e8i	−0.0504652	+	0.188339i
$982$	−1.05509e9	−	2.82710e8i	−1.11418	−	0.298543i
$983$	−4.58540e8	+	4.58540e8i	−0.482744	+	0.482744i	−0.906007	−	0.423263i	$-0.860885\pi$
$983$	−4.58540e8	+	4.58540e8i	−0.482744	+	0.482744i	0.423263	+	0.906007i	$0.360885\pi$
$984$	−3.88582e6	−	6.73044e6i	−0.00407847	−	0.00706412i
$985$	4.35205e8	+	2.51265e8i	0.455391	+	0.262920i
$986$	2.93909e6	+	1.09688e7i	0.00306607	+	0.0114427i
$987$		−	1.85755e8i		−	0.193192i
$988$	3.53455e8	−	4.42655e7i	0.366491	−	0.0458981i
$989$	1.17746e9			1.21718
$990$	−4.55665e8	+	1.22095e8i	−0.469613	+	0.125832i
$991$	−6.28778e8	+	1.08908e9i	−0.646065	+	1.11902i	0.337989	+	0.941150i	$0.390253\pi$
$991$	−6.28778e8	+	1.08908e9i	−0.646065	+	1.11902i	−0.984054	+	0.177868i	$0.943080\pi$
$992$	4.37354e8	−	2.52506e8i	0.448020	−	0.258665i
$993$	6.74347e7	+	6.74347e7i	0.0688709	+	0.0688709i
$994$	−2.88614e8	+	1.07712e9i	−0.293872	+	1.09675i
$995$	−2.03171e9	−	5.44396e8i	−2.06250	−	0.552645i
$996$	1.98407e7	−	1.98407e7i	0.0200807	−	0.0200807i
$997$	−4.46374e8	−	7.73142e8i	−0.450415	−	0.780142i	0.547997	−	0.836481i	$-0.315391\pi$
$997$	−4.46374e8	−	7.73142e8i	−0.450415	−	0.780142i	−0.998412	+	0.0563386i	$0.982057\pi$
$998$	−9.57012e8	−	5.52531e8i	−0.962777	−	0.555860i
$999$	−2.79288e8	−	1.04232e9i	−0.280127	−	1.04545i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.7.f.a.7.3	yes	24
13.2	odd	12	inner	13.7.f.a.2.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.7.f.a.2.3	✓	24	13.2	odd	12	inner
13.7.f.a.7.3	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)

\(f(q)\)	\(=\)	\(q+(-4.77368 + 1.27910i) q^{2} +(4.54257 - 7.86796i) q^{3} +(-34.2737 + 19.7879i) q^{4} +(-109.630 - 109.630i) q^{5} +(-11.6208 + 43.3696i) q^{6} +(-504.391 - 135.151i) q^{7} +(361.954 - 361.954i) q^{8} +(323.230 + 559.851i) q^{9} +O(q^{10})\)	\(q+(-4.77368 + 1.27910i) q^{2} +(4.54257 - 7.86796i) q^{3} +(-34.2737 + 19.7879i) q^{4} +(-109.630 - 109.630i) q^{5} +(-11.6208 + 43.3696i) q^{6} +(-504.391 - 135.151i) q^{7} +(361.954 - 361.954i) q^{8} +(323.230 + 559.851i) q^{9} +(663.567 + 383.110i) q^{10} +(246.492 + 919.919i) q^{11} +359.552i q^{12} +(300.508 - 2176.35i) q^{13} +2580.68 q^{14} +(-1360.56 + 364.562i) q^{15} +(1.54938 - 2.68361i) q^{16} +(-5348.10 + 3087.73i) q^{17} +(-2259.11 - 2259.11i) q^{18} +(1060.35 - 3957.28i) q^{19} +(5926.77 + 1588.07i) q^{20} +(-3354.60 + 3354.60i) q^{21} +(-2353.35 - 4076.12i) q^{22} +(-9993.12 - 5769.53i) q^{23} +(-1203.64 - 4492.04i) q^{24} +8412.42i q^{25} +(1349.25 + 10773.6i) q^{26} +12496.2 q^{27} +(19961.7 - 5348.72i) q^{28} +(-186.040 + 322.231i) q^{29} +(6028.59 - 3480.61i) q^{30} +(-10895.2 - 10895.2i) q^{31} +(-8482.96 + 31658.8i) q^{32} +(8357.59 + 2239.41i) q^{33} +(21580.6 - 21580.6i) q^{34} +(40479.7 + 70113.0i) q^{35} +(-22156.6 - 12792.1i) q^{36} +(-22349.7 - 83410.4i) q^{37} +20247.1i q^{38} +(-15758.4 - 12250.6i) q^{39} -79361.9 q^{40} +(1614.20 - 432.523i) q^{41} +(11722.9 - 20304.7i) q^{42} +(-88370.0 + 51020.4i) q^{43} +(-26651.5 - 26651.5i) q^{44} +(25940.7 - 96812.1i) q^{45} +(55083.8 + 14759.7i) q^{46} +(-27686.6 + 27686.6i) q^{47} +(-14.0764 - 24.3810i) q^{48} +(134258. + 77513.7i) q^{49} +(-10760.4 - 40158.3i) q^{50} +56104.9i q^{51} +(32765.9 + 80538.0i) q^{52} +239411. q^{53} +(-59653.1 + 15984.0i) q^{54} +(73827.8 - 127874. i) q^{55} +(-231485. + 133648. i) q^{56} +(-26319.0 - 26319.0i) q^{57} +(475.930 - 1776.20i) q^{58} +(120217. + 32212.1i) q^{59} +(39417.6 - 39417.6i) q^{60} +(38209.4 + 66180.6i) q^{61} +(65946.4 + 38074.2i) q^{62} +(-87369.9 - 326069. i) q^{63} -161782. i q^{64} +(-271538. + 205648. i) q^{65} -42761.0 q^{66} +(-354858. + 95083.9i) q^{67} +(122199. - 211656. i) q^{68} +(-90788.9 + 52417.0i) q^{69} +(-282919. - 282919. i) q^{70} +(-111837. + 417380. i) q^{71} +(319635. + 85645.9i) q^{72} +(343212. - 343212. i) q^{73} +(213381. + 369587. i) q^{74} +(66188.6 + 38214.0i) q^{75} +(41964.2 + 156613. i) q^{76} -497313. i q^{77} +(90895.3 + 38323.9i) q^{78} -559268. q^{79} +(-464.063 + 124.345i) q^{80} +(-178870. + 309811. i) q^{81} +(-7152.43 + 4129.46i) q^{82} +(-55181.9 - 55181.9i) q^{83} +(48593.9 - 181355. i) q^{84} +(924819. + 247805. i) q^{85} +(356590. - 356590. i) q^{86} +(1690.20 + 2927.52i) q^{87} +(422187. + 243750. i) q^{88} +(-189901. - 708722. i) q^{89} +495331. i q^{90} +(-445710. + 1.05712e6i) q^{91} +456668. q^{92} +(-135215. + 36230.8i) q^{93} +(96753.1 - 167581. i) q^{94} +(-550082. + 317590. i) q^{95} +(210556. + 210556. i) q^{96} +(328784. - 1.22704e6i) q^{97} +(-740052. - 198296. i) q^{98} +(-435344. + 435344. 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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