LMFDB - Embedded newform 37.7.g.a.8.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,7,Mod(8,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, 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("37.8");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	37.g (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:	$8.51200109393$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			8.9
Character	$\chi$	$=$	37.8
Dual form			37.7.g.a.14.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.34959 - 0.629570i) q^{2} +(32.2680 + 18.6299i) q^{3} +(-50.3014 - 29.0415i) q^{4} +(85.5401 - 22.9204i) q^{5} +(-64.0877 - 64.0877i) q^{6} +(207.449 - 359.312i) q^{7} +(209.985 + 209.985i) q^{8} +(329.649 + 570.970i) q^{9} +O(q^{10})$	\(q+(-2.34959 - 0.629570i) q^{2} +(32.2680 + 18.6299i) q^{3} +(-50.3014 - 29.0415i) q^{4} +(85.5401 - 22.9204i) q^{5} +(-64.0877 - 64.0877i) q^{6} +(207.449 - 359.312i) q^{7} +(209.985 + 209.985i) q^{8} +(329.649 + 570.970i) q^{9} -215.414 q^{10} +1086.08i q^{11} +(-1082.08 - 1874.23i) q^{12} +(2749.12 - 736.623i) q^{13} +(-713.632 + 713.632i) q^{14} +(3187.21 + 854.011i) q^{15} +(1497.48 + 2593.71i) q^{16} +(700.628 - 2614.78i) q^{17} +(-415.075 - 1549.08i) q^{18} +(9822.17 - 2631.84i) q^{19} +(-4968.43 - 1331.29i) q^{20} +(13387.9 - 7729.52i) q^{21} +(683.764 - 2551.84i) q^{22} +(-2113.08 - 2113.08i) q^{23} +(2863.79 + 10687.8i) q^{24} +(-6739.89 + 3891.28i) q^{25} -6923.05 q^{26} -2597.06i q^{27} +(-20870.0 + 12049.3i) q^{28} +(-26325.0 + 26325.0i) q^{29} +(-6950.98 - 4013.15i) q^{30} +(-18055.4 + 18055.4i) q^{31} +(-6804.57 - 25395.0i) q^{32} +(-20233.6 + 35045.7i) q^{33} +(-3292.37 + 5702.56i) q^{34} +(9509.62 - 35490.4i) q^{35} -38294.1i q^{36} +(-7402.67 - 50109.2i) q^{37} -24735.0 q^{38} +(102432. + 27446.5i) q^{39} +(22775.1 + 13149.2i) q^{40} +(27700.1 + 15992.7i) q^{41} +(-36322.4 + 9732.56i) q^{42} +(-14263.8 - 14263.8i) q^{43} +(31541.5 - 54631.4i) q^{44} +(41285.1 + 41285.1i) q^{45} +(3634.53 + 6295.19i) q^{46} -206904. q^{47} +111592. i q^{48} +(-27245.7 - 47190.9i) q^{49} +(18285.8 - 4899.66i) q^{50} +(71321.0 - 71321.0i) q^{51} +(-159677. - 42785.4i) q^{52} +(73561.4 + 127412. i) q^{53} +(-1635.03 + 6102.01i) q^{54} +(24893.4 + 92903.4i) q^{55} +(119011. - 31889.0i) q^{56} +(365973. + 98062.2i) q^{57} +(78426.2 - 45279.4i) q^{58} +(1273.56 - 4753.00i) q^{59} +(-135520. - 135520. i) q^{60} +(-34102.2 - 127271. i) q^{61} +(53789.7 - 31055.5i) q^{62} +273542. q^{63} -127726. i q^{64} +(218276. - 126022. i) q^{65} +(69604.4 - 69604.4i) q^{66} +(-142156. - 82073.6i) q^{67} +(-111180. + 111180. i) q^{68} +(-28818.3 - 107551. i) q^{69} +(-44687.4 + 77400.8i) q^{70} +(-209467. + 362807. i) q^{71} +(-50673.6 + 189117. i) q^{72} -19064.6i q^{73} +(-14154.0 + 122396. i) q^{74} -289977. q^{75} +(-570502. - 152866. i) q^{76} +(390242. + 225306. i) q^{77} +(-223393. - 128976. i) q^{78} +(88214.2 - 23636.9i) q^{79} +(187543. + 187543. i) q^{80} +(288697. - 500039. i) q^{81} +(-55015.4 - 55015.4i) q^{82} +(417764. + 723588. i) q^{83} -897909. q^{84} -239727. i q^{85} +(24533.9 + 42494.0i) q^{86} +(-1.33989e6 + 359021. i) q^{87} +(-228061. + 228061. i) q^{88} +(196318. + 52603.2i) q^{89} +(-71011.1 - 122995. i) q^{90} +(305624. - 1.14060e6i) q^{91} +(44923.8 + 167658. i) q^{92} +(-918980. + 246240. i) q^{93} +(486139. + 130260. i) q^{94} +(779866. - 450256. i) q^{95} +(253537. - 946215. i) q^{96} +(327480. + 327480. i) q^{97} +(34306.1 + 128032. i) q^{98} +(-620119. + 358026. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{2} - 6 q^{3} + 264 q^{4} + 52 q^{5} - 132 q^{6} - 2 q^{7} - 1968 q^{8} + 8094 q^{9}+O(q^{10}) $ 72 * q - 2 * q^2 - 6 * q^3 + 264 * q^4 + 52 * q^5 - 132 * q^6 - 2 * q^7 - 1968 * q^8 + 8094 * q^9	\( 72 q - 2 q^{2} - 6 q^{3} + 264 q^{4} + 52 q^{5} - 132 q^{6} - 2 q^{7} - 1968 q^{8} + 8094 q^{9} + 1864 q^{10} + 1178 q^{12} + 2898 q^{13} + 10168 q^{14} + 1418 q^{15} + 23668 q^{16} - 16734 q^{17} + 30222 q^{18} - 20756 q^{19} + 27910 q^{20} - 22326 q^{21} + 40188 q^{22} + 23388 q^{23} + 51426 q^{24} - 54060 q^{25} + 31064 q^{26} - 84486 q^{28} - 101426 q^{29} - 280062 q^{30} - 112740 q^{31} + 66416 q^{32} + 27376 q^{33} + 45094 q^{34} + 152710 q^{35} - 23168 q^{37} - 67600 q^{38} + 386674 q^{39} - 473862 q^{40} - 566622 q^{41} - 569640 q^{42} - 33332 q^{43} + 667736 q^{44} + 399362 q^{45} + 303310 q^{46} + 352424 q^{47} - 402226 q^{49} - 190836 q^{50} - 525822 q^{51} - 290936 q^{52} + 365094 q^{53} + 1191884 q^{54} - 343392 q^{55} + 2217442 q^{56} + 73378 q^{57} - 581028 q^{58} - 576604 q^{59} + 2105904 q^{60} - 213462 q^{61} - 423156 q^{62} - 1483688 q^{63} + 2273880 q^{65} - 846680 q^{66} + 1591698 q^{67} - 3165948 q^{68} + 2464258 q^{69} + 2158358 q^{70} - 1388114 q^{71} + 1672988 q^{72} - 3228324 q^{74} + 1857268 q^{75} - 3488628 q^{76} + 846288 q^{77} - 6537300 q^{78} - 781076 q^{79} - 3635536 q^{80} - 2236868 q^{81} + 3720360 q^{82} - 944002 q^{83} + 6632744 q^{84} - 1174862 q^{86} - 1073982 q^{87} - 427452 q^{88} + 3381078 q^{89} + 412204 q^{90} - 2879114 q^{91} + 696698 q^{92} - 543710 q^{93} - 3545780 q^{94} - 268230 q^{95} - 9026178 q^{96} - 1842138 q^{97} - 7266130 q^{98} + 8295480 q^{99}+O(q^{100}) \) 72 * q - 2 * q^2 - 6 * q^3 + 264 * q^4 + 52 * q^5 - 132 * q^6 - 2 * q^7 - 1968 * q^8 + 8094 * q^9 + 1864 * q^10 + 1178 * q^12 + 2898 * q^13 + 10168 * q^14 + 1418 * q^15 + 23668 * q^16 - 16734 * q^17 + 30222 * q^18 - 20756 * q^19 + 27910 * q^20 - 22326 * q^21 + 40188 * q^22 + 23388 * q^23 + 51426 * q^24 - 54060 * q^25 + 31064 * q^26 - 84486 * q^28 - 101426 * q^29 - 280062 * q^30 - 112740 * q^31 + 66416 * q^32 + 27376 * q^33 + 45094 * q^34 + 152710 * q^35 - 23168 * q^37 - 67600 * q^38 + 386674 * q^39 - 473862 * q^40 - 566622 * q^41 - 569640 * q^42 - 33332 * q^43 + 667736 * q^44 + 399362 * q^45 + 303310 * q^46 + 352424 * q^47 - 402226 * q^49 - 190836 * q^50 - 525822 * q^51 - 290936 * q^52 + 365094 * q^53 + 1191884 * q^54 - 343392 * q^55 + 2217442 * q^56 + 73378 * q^57 - 581028 * q^58 - 576604 * q^59 + 2105904 * q^60 - 213462 * q^61 - 423156 * q^62 - 1483688 * q^63 + 2273880 * q^65 - 846680 * q^66 + 1591698 * q^67 - 3165948 * q^68 + 2464258 * q^69 + 2158358 * q^70 - 1388114 * q^71 + 1672988 * q^72 - 3228324 * q^74 + 1857268 * q^75 - 3488628 * q^76 + 846288 * q^77 - 6537300 * q^78 - 781076 * q^79 - 3635536 * q^80 - 2236868 * q^81 + 3720360 * q^82 - 944002 * q^83 + 6632744 * q^84 - 1174862 * q^86 - 1073982 * q^87 - 427452 * q^88 + 3381078 * q^89 + 412204 * q^90 - 2879114 * q^91 + 696698 * q^92 - 543710 * q^93 - 3545780 * q^94 - 268230 * q^95 - 9026178 * q^96 - 1842138 * q^97 - 7266130 * q^98 + 8295480 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−2.34959	−	0.629570i	−0.293698	−	0.0786963i	0.108961	−	0.994046i	$-0.465248\pi$
$2$	−2.34959	−	0.629570i	−0.293698	−	0.0786963i	−0.402660	+	0.915350i	$0.631914\pi$
$3$	32.2680	+	18.6299i	1.19511	+	0.689998i	0.959461	−	0.281840i	$-0.0909448\pi$
$3$	32.2680	+	18.6299i	1.19511	+	0.689998i	0.235650	+	0.971838i	$0.424278\pi$
$4$	−50.3014	−	29.0415i	−0.785960	−	0.453774i
$5$	85.5401	−	22.9204i	0.684320	−	0.183363i	0.100123	−	0.994975i	$-0.468076\pi$
$5$	85.5401	−	22.9204i	0.684320	−	0.183363i	0.584197	+	0.811612i	$0.301410\pi$
$6$	−64.0877	−	64.0877i	−0.296702	−	0.296702i
$7$	207.449	−	359.312i	0.604808	−	1.04756i	−0.387274	−	0.921965i	$-0.626583\pi$
$7$	207.449	−	359.312i	0.604808	−	1.04756i	0.992082	−	0.125593i	$-0.0400833\pi$
$8$	209.985	+	209.985i	0.410127	+	0.410127i
$9$	329.649	+	570.970i	0.452194	+	0.783223i
$10$	−215.414			−0.215414
$11$			1086.08i			0.815989i	0.912984	+	0.407994i	$0.133772\pi$
$11$			1086.08i			0.815989i	−0.912984	+	0.407994i	$0.866228\pi$
$12$	−1082.08	−	1874.23i	−0.626206	−	1.08462i
$13$	2749.12	−	736.623i	1.25130	−	0.335286i	0.428464	−	0.903559i	$-0.359055\pi$
$13$	2749.12	−	736.623i	1.25130	−	0.335286i	0.822840	+	0.568273i	$0.192388\pi$
$14$	−713.632	+	713.632i	−0.260070	+	0.260070i
$15$	3187.21	+	854.011i	0.944359	+	0.253040i
$16$	1497.48	+	2593.71i	0.365596	+	0.633231i
$17$	700.628	−	2614.78i	0.142607	−	0.532216i	−0.857243	−	0.514912i	$-0.827825\pi$
$17$	700.628	−	2614.78i	0.142607	−	0.532216i	0.999850	−	0.0173048i	$-0.00550856\pi$
$18$	−415.075	−	1549.08i	−0.0711720	−	0.265617i
$19$	9822.17	−	2631.84i	1.43201	−	0.383707i	0.542283	−	0.840196i	$-0.317560\pi$
$19$	9822.17	−	2631.84i	1.43201	−	0.383707i	0.889729	+	0.456489i	$0.150893\pi$
$20$	−4968.43	−	1331.29i	−0.621054	−	0.166411i
$21$	13387.9	−	7729.52i	1.44562	−	0.834632i
$22$	683.764	−	2551.84i	0.0642153	−	0.239655i
$23$	−2113.08	−	2113.08i	−0.173673	−	0.173673i	0.614918	−	0.788591i	$-0.289189\pi$
$23$	−2113.08	−	2113.08i	−0.173673	−	0.173673i	−0.788591	+	0.614918i	$0.789189\pi$
$24$	2863.79	+	10687.8i	0.207161	+	0.773134i
$25$	−6739.89	+	3891.28i	−0.431353	+	0.249042i
$26$	−6923.05			−0.393892
$27$		−	2597.06i		−	0.131944i
$28$	−20870.0	+	12049.3i	−0.950709	+	0.548892i
$29$	−26325.0	+	26325.0i	−1.07938	+	1.07938i	−0.0828130	+	0.996565i	$0.526390\pi$
$29$	−26325.0	+	26325.0i	−1.07938	+	1.07938i	−0.996565	+	0.0828130i	$0.973610\pi$
$30$	−6950.98	−	4013.15i	−0.257444	−	0.148635i
$31$	−18055.4	+	18055.4i	−0.606067	+	0.606067i	−0.941916	−	0.335849i	$-0.890977\pi$
$31$	−18055.4	+	18055.4i	−0.606067	+	0.606067i	0.335849	+	0.941916i	$0.390977\pi$
$32$	−6804.57	−	25395.0i	−0.207659	−	0.774994i
$33$	−20233.6	+	35045.7i	−0.563030	+	0.975197i
$34$	−3292.37	+	5702.56i	−0.0837669	+	0.145088i
$35$	9509.62	−	35490.4i	0.221799	−	0.827764i
$36$		−	38294.1i		−	0.820776i
$37$	−7402.67	−	50109.2i	−0.146145	−	0.989263i
$37$	−7402.67	−	50109.2i	−0.146145	−	0.989263i
$38$	−24735.0			−0.450776
$39$	102432.	+	27446.5i	1.72679	+	0.462693i
$40$	22775.1	+	13149.2i	0.355861	+	0.205456i
$41$	27700.1	+	15992.7i	0.401912	+	0.232044i	0.687308	−	0.726366i	$-0.258792\pi$
$41$	27700.1	+	15992.7i	0.401912	+	0.232044i	−0.285397	+	0.958409i	$0.592125\pi$
$42$	−36322.4	+	9732.56i	−0.490260	+	0.131365i
$43$	−14263.8	−	14263.8i	−0.179403	−	0.179403i	0.611693	−	0.791095i	$-0.290489\pi$
$43$	−14263.8	−	14263.8i	−0.179403	−	0.179403i	−0.791095	+	0.611693i	$0.790489\pi$
$44$	31541.5	−	54631.4i	0.370274	−	0.641334i
$45$	41285.1	+	41285.1i	0.453060	+	0.453060i
$46$	3634.53	+	6295.19i	0.0373400	+	0.0646748i
$47$	−206904.			−1.99285			−0.996425	−	0.0844780i	$-0.973078\pi$
$47$	−206904.			−1.99285			−0.996425	+	0.0844780i	$0.973078\pi$
$48$			111592.i			1.00904i
$49$	−27245.7	−	47190.9i	−0.231584	−	0.401116i
$50$	18285.8	−	4899.66i	0.146286	−	0.0391973i
$51$	71321.0	−	71321.0i	0.537659	−	0.537659i
$52$	−159677.	−	42785.4i	−1.13562	−	0.304288i
$53$	73561.4	+	127412.i	0.494108	+	0.855821i	0.999977	−	0.00678969i	$-0.00216124\pi$
$53$	73561.4	+	127412.i	0.494108	+	0.855821i	−0.505869	+	0.862611i	$0.668828\pi$
$54$	−1635.03	+	6102.01i	−0.0103835	+	0.0387518i
$55$	24893.4	+	92903.4i	0.149622	+	0.558398i
$56$	119011.	−	31889.0i	0.677680	−	0.181584i
$57$	365973.	+	98062.2i	1.97617	+	0.529513i
$58$	78426.2	−	45279.4i	0.401955	−	0.232069i
$59$	1273.56	−	4753.00i	0.00620103	−	0.0231426i	−0.962756	−	0.270372i	$-0.912853\pi$
$59$	1273.56	−	4753.00i	0.00620103	−	0.0231426i	0.968957	+	0.247229i	$0.0795201\pi$
$60$	−135520.	−	135520.i	−0.627405	−	0.627405i
$61$	−34102.2	−	127271.i	−0.150242	−	0.560712i	−0.999466	−	0.0326787i	$-0.989596\pi$
$61$	−34102.2	−	127271.i	−0.150242	−	0.560712i	0.849223	−	0.528034i	$-0.177070\pi$
$62$	53789.7	−	31055.5i	0.225696	−	0.130306i
$63$	273542.			1.09396
$64$		−	127726.i		−	0.487235i
$65$	218276.	−	126022.i	0.794814	−	0.458886i
$66$	69604.4	−	69604.4i	0.242106	−	0.242106i
$67$	−142156.	−	82073.6i	−0.472650	−	0.272885i	0.244698	−	0.969599i	$-0.421311\pi$
$67$	−142156.	−	82073.6i	−0.472650	−	0.272885i	−0.717348	+	0.696715i	$0.754644\pi$
$68$	−111180.	+	111180.i	−0.353589	+	0.353589i
$69$	−28818.3	−	107551.i	−0.0877245	−	0.327392i
$70$	−44687.4	+	77400.8i	−0.130284	+	0.225658i
$71$	−209467.	+	362807.i	−0.585249	+	1.01368i	0.409596	+	0.912267i	$0.365670\pi$
$71$	−209467.	+	362807.i	−0.585249	+	1.01368i	−0.994844	+	0.101413i	$0.967664\pi$
$72$	−50673.6	+	189117.i	−0.135764	+	0.506678i
$73$		−	19064.6i		−	0.0490071i	−0.999700	−	0.0245036i	$-0.992199\pi$
$73$		−	19064.6i		−	0.0490071i	0.999700	−	0.0245036i	$-0.00780050\pi$
$74$	−14154.0	+	122396.i	−0.0349289	+	0.302046i
$75$	−289977.			−0.687353
$76$	−570502.	−	152866.i	−1.29962	−	0.348232i
$77$	390242.	+	225306.i	0.854795	+	0.493516i
$78$	−223393.	−	128976.i	−0.470745	−	0.271785i
$79$	88214.2	−	23636.9i	0.178919	−	0.0479413i	−0.168247	−	0.985745i	$-0.553811\pi$
$79$	88214.2	−	23636.9i	0.178919	−	0.0479413i	0.347166	+	0.937804i	$0.387144\pi$
$80$	187543.	+	187543.i	0.366296	+	0.366296i
$81$	288697.	−	500039.i	0.543235	−	0.940911i
$82$	−55015.4	−	55015.4i	−0.0997798	−	0.0997798i
$83$	417764.	+	723588.i	0.730629	+	1.26549i	0.956615	+	0.291355i	$0.0941062\pi$
$83$	417764.	+	723588.i	0.730629	+	1.26549i	−0.225986	+	0.974130i	$0.572560\pi$
$84$	−897909.			−1.51494
$85$		−	239727.i		−	0.390355i
$86$	24533.9	+	42494.0i	0.0385720	+	0.0668086i
$87$	−1.33989e6	+	359021.i	−2.03475	+	0.545208i
$88$	−228061.	+	228061.i	−0.334659	+	0.334659i
$89$	196318.	+	52603.2i	0.278477	+	0.0746177i	0.395354	−	0.918529i	$-0.370622\pi$
$89$	196318.	+	52603.2i	0.278477	+	0.0746177i	−0.116877	+	0.993146i	$0.537288\pi$
$90$	−71011.1	−	122995.i	−0.0974089	−	0.168717i
$91$	305624.	−	1.14060e6i	0.405567	−	1.51360i
$92$	44923.8	+	167658.i	0.0576916	+	0.215308i
$93$	−918980.	+	246240.i	−1.14250	+	0.306133i
$94$	486139.	+	130260.i	0.585297	+	0.156830i
$95$	779866.	−	450256.i	0.909598	−	0.525157i
$96$	253537.	−	946215.i	0.286568	−	1.06949i
$97$	327480.	+	327480.i	0.358814	+	0.358814i	0.863376	−	0.504562i	$-0.168346\pi$
$97$	327480.	+	327480.i	0.358814	+	0.358814i	−0.504562	+	0.863376i	$0.668346\pi$
$98$	34306.1	+	128032.i	0.0364496	+	0.136032i
$99$	−620119.	+	358026.i	−0.639101	+	0.368985i
$100$	452035.			0.452035
$101$			338207.i			0.328260i	0.986439	+	0.164130i	$0.0524817\pi$
$101$			338207.i			0.328260i	−0.986439	+	0.164130i	$0.947518\pi$
$102$	−212477.	+	122673.i	−0.200221	+	0.115598i
$103$	−1.14918e6	+	1.14918e6i	−1.05166	+	1.05166i	−0.0530723	+	0.998591i	$0.516901\pi$
$103$	−1.14918e6	+	1.14918e6i	−1.05166	+	1.05166i	−0.998591	+	0.0530723i	$0.983099\pi$
$104$	731953.	+	422593.i	0.650704	+	0.375684i
$105$	968041.	−	968041.i	0.836230	−	0.836230i
$106$	−92624.1	−	345678.i	−0.0777690	−	0.290238i
$107$	484185.	−	838633.i	0.395239	−	0.684574i	−0.597892	−	0.801576i	$-0.703995\pi$
$107$	484185.	−	838633.i	0.395239	−	0.684574i	0.993132	+	0.117002i	$0.0373284\pi$
$108$	−75422.5	+	130636.i	−0.0598728	+	0.103703i
$109$	−559814.	+	2.08925e6i	−0.432279	+	1.61329i	0.315217	+	0.949020i	$0.397923\pi$
$109$	−559814.	+	2.08925e6i	−0.432279	+	1.61329i	−0.747495	+	0.664267i	$0.768744\pi$
$110$		−	233957.i		−	0.175775i
$111$	694661.	−	1.75483e6i	0.507930	−	1.28312i
$112$	1.24260e6			0.884460
$113$	−1.02202e6	−	273849.i	−0.708309	−	0.189791i	−0.113360	−	0.993554i	$-0.536161\pi$
$113$	−1.02202e6	−	273849.i	−0.708309	−	0.189791i	−0.594949	+	0.803763i	$0.702828\pi$
$114$	−798149.	−	460811.i	−0.538728	−	0.311035i
$115$	−229185.	−	132320.i	−0.150693	−	0.0870027i
$116$	2.08870e6	−	559665.i	1.33814	−	0.358554i
$117$	1.32683e6	+	1.32683e6i	0.828436	+	0.828436i
$118$	−5984.69	+	10365.8i	−0.00364247	+	0.00630894i
$119$	−794177.	−	794177.i	−0.471277	−	0.471277i
$120$	489937.	+	848597.i	0.283529	+	0.491086i
$121$	591989.			0.334163
$122$			320504.i			0.176504i
$123$	595886.	+	1.03210e6i	0.320219	+	0.554636i
$124$	1.43257e6	−	383855.i	0.751362	−	0.201327i
$125$	−1.46577e6	+	1.46577e6i	−0.750476	+	0.750476i
$126$	−642710.	−	172214.i	−0.321295	−	0.0860907i
$127$	−1.45829e6	−	2.52584e6i	−0.711924	−	1.23309i	−0.964134	−	0.265416i	$-0.914491\pi$
$127$	−1.45829e6	−	2.52584e6i	−0.711924	−	1.23309i	0.252210	−	0.967673i	$-0.418843\pi$
$128$	−515905.	+	1.92538e6i	−0.246003	+	0.918094i
$129$	−194530.	−	725997.i	−0.0906187	−	0.338194i
$130$	−592198.	+	158679.i	−0.269548	+	0.0722253i
$131$	3.13736e6	+	840654.i	1.39557	+	0.373941i	0.876751	−	0.480945i	$-0.159706\pi$
$131$	3.13736e6	+	840654.i	1.39557	+	0.373941i	0.518816	+	0.854886i	$0.326373\pi$
$132$	2.03556e6	−	1.17523e6i	0.885038	−	0.510977i
$133$	1.09195e6	−	4.07520e6i	0.464137	−	1.73218i
$134$	282336.	+	282336.i	0.117342	+	0.117342i
$135$	−59525.6	−	222152.i	−0.0241937	−	0.0902921i
$136$	696186.	−	401943.i	0.276763	−	0.159789i
$137$	1.35279e6			0.526101			0.263050	−	0.964782i	$-0.415271\pi$
$137$	1.35279e6			0.526101			0.263050	+	0.964782i	$0.415271\pi$
$138$			270844.i			0.103058i
$139$	−1.23858e6	+	715094.i	−0.461190	+	0.266268i	−0.712544	−	0.701627i	$-0.752457\pi$
$139$	−1.23858e6	+	715094.i	−0.461190	+	0.266268i	0.251355	+	0.967895i	$0.419124\pi$
$140$	−1.50904e6	+	1.50904e6i	−0.549943	+	0.549943i
$141$	−6.67637e6	−	3.85460e6i	−2.38168	−	1.37506i
$142$	720574.	−	720574.i	0.251660	−	0.251660i
$143$	800032.	+	2.98576e6i	0.273590	+	1.02105i
$144$	−987287.	+	1.71003e6i	−0.330640	+	0.572686i
$145$	−1.64846e6	+	2.85522e6i	−0.540722	+	0.936559i
$146$	−12002.5	+	44794.0i	−0.00385668	+	0.0143933i
$147$		−	2.03034e6i		−	0.639171i
$148$	−1.08288e6	+	2.73555e6i	−0.334038	+	0.843838i
$149$	−4.20404e6			−1.27089			−0.635445	−	0.772146i	$-0.719183\pi$
$149$	−4.20404e6			−1.27089			−0.635445	+	0.772146i	$0.719183\pi$
$150$	681327.	+	182561.i	0.201875	+	0.0540921i
$151$	3.64193e6	+	2.10267e6i	1.05779	+	0.610717i	0.924821	−	0.380403i	$-0.124215\pi$
$151$	3.64193e6	+	2.10267e6i	1.05779	+	0.610717i	0.132972	+	0.991120i	$0.457548\pi$
$152$	2.61516e6	+	1.50986e6i	0.744676	+	0.429939i
$153$	1.72392e6	−	461923.i	0.481330	−	0.128972i
$154$	−775062.	−	775062.i	−0.212214	−	0.212214i
$155$	−1.13062e6	+	1.95829e6i	−0.303614	+	0.525875i
$156$	−4.35537e6	−	4.35537e6i	−1.14723	−	1.14723i
$157$	−2.90095e6	−	5.02459e6i	−0.749620	−	1.29838i	−0.948005	−	0.318256i	$-0.896903\pi$
$157$	−2.90095e6	−	5.02459e6i	−0.749620	−	1.29838i	0.198385	−	0.980124i	$-0.436431\pi$
$158$	−222148.			−0.0563211
$159$			5.48178e6i			1.36373i
$160$	−1.16413e6	−	2.01633e6i	−0.284211	−	0.492267i
$161$	−1.19761e6	+	320899.i	−0.286971	+	0.0768936i
$162$	−993129.	+	993129.i	−0.233594	+	0.233594i
$163$	−6.74692e6	−	1.80783e6i	−1.55791	−	0.417441i	−0.625910	−	0.779896i	$-0.715272\pi$
$163$	−6.74692e6	−	1.80783e6i	−1.55791	−	0.417441i	−0.932001	+	0.362455i	$0.881939\pi$
$164$	−928905.	−	1.60891e6i	−0.210591	−	0.364754i
$165$	−927525.	+	3.46157e6i	−0.206478	+	0.770586i
$166$	−526023.	−	1.96315e6i	−0.114995	−	0.429169i
$167$	202465.	−	54250.2i	0.0434710	−	0.0116480i	−0.237018	−	0.971505i	$-0.576170\pi$
$167$	202465.	−	54250.2i	0.0434710	−	0.0116480i	0.280489	+	0.959857i	$0.409503\pi$
$168$	4.43435e6	+	1.18818e6i	0.935195	+	0.250585i
$169$	2.83488e6	−	1.63672e6i	0.587321	−	0.339090i
$170$	−150925.	+	563260.i	−0.0307195	+	0.114647i
$171$	4.74058e6	+	4.74058e6i	0.948075	+	0.948075i
$172$	303246.	+	1.13173e6i	0.0595950	+	0.222412i
$173$	2.73241e6	−	1.57756e6i	0.527725	−	0.304682i	−0.212365	−	0.977190i	$-0.568117\pi$
$173$	2.73241e6	−	1.57756e6i	0.527725	−	0.304682i	0.740089	+	0.672509i	$0.234783\pi$
$174$	3.37421e6			0.640508
$175$			3.22897e6i			0.602489i
$176$	−2.81698e6	+	1.62638e6i	−0.516709	+	0.298322i
$177$	129643.	−	129643.i	0.0233792	−	0.0233792i
$178$	−428148.	−	247192.i	−0.0759162	−	0.0438302i
$179$	6.30946e6	−	6.30946e6i	1.10010	−	1.10010i	0.105704	−	0.994398i	$-0.466290\pi$
$179$	6.30946e6	−	6.30946e6i	1.10010	−	1.10010i	0.994398	−	0.105704i	$-0.0337098\pi$
$180$	−877716.	−	3.27568e6i	−0.150500	−	0.561674i
$181$	1.04984e6	−	1.81838e6i	0.177047	−	0.306655i	−0.763821	−	0.645428i	$-0.776679\pi$
$181$	1.04984e6	−	1.81838e6i	0.177047	−	0.306655i	0.940868	+	0.338774i	$0.110012\pi$
$182$	−1.43618e6	+	2.48753e6i	−0.238229	+	0.412624i
$183$	1.27064e6	−	4.74210e6i	0.207334	−	0.773781i
$184$		−	887429.i		−	0.142456i
$185$	−1.78175e6	−	4.11667e6i	−0.281404	−	0.650176i
$186$	2.31425e6			0.359643
$187$	2.83986e6	+	760938.i	0.434282	+	0.116366i
$188$	1.04076e7	+	6.00880e6i	1.56630	+	0.904304i
$189$	−933154.	−	538757.i	−0.138219	−	0.0798008i
$190$	−2.11583e6	+	566936.i	−0.308475	+	0.0826557i
$191$	6.87193e6	+	6.87193e6i	0.986231	+	0.986231i	0.999906	−	0.0136753i	$-0.00435313\pi$
$191$	6.87193e6	+	6.87193e6i	0.986231	+	0.986231i	−0.0136753	+	0.999906i	$0.504353\pi$
$192$	2.37952e6	−	4.12146e6i	0.336191	−	0.582300i
$193$	−8.24594e6	−	8.24594e6i	−1.14701	−	1.14701i	−0.987137	−	0.159875i	$-0.948891\pi$
$193$	−8.24594e6	−	8.24594e6i	−1.14701	−	1.14701i	−0.159875	−	0.987137i	$-0.551109\pi$
$194$	−563271.	−	975614.i	−0.0771458	−	0.133620i
$195$	9.39110e6			1.26652
$196$			3.16502e6i			0.420348i
$197$	−6.44755e6	−	1.11675e7i	−0.843326	−	1.46068i	−0.887067	−	0.461641i	$-0.847261\pi$
$197$	−6.44755e6	−	1.11675e7i	−0.843326	−	1.46068i	0.0437402	−	0.999043i	$-0.486073\pi$
$198$	1.68243e6	−	450805.i	0.216741	−	0.0580755i
$199$	−7.09853e6	+	7.09853e6i	−0.900761	+	0.900761i	−0.995502	−	0.0947411i	$-0.969798\pi$
$199$	−7.09853e6	+	7.09853e6i	−0.900761	+	0.900761i	0.0947411	+	0.995502i	$0.469798\pi$
$200$	−2.23239e6	−	598166.i	−0.279048	−	0.0747708i
$201$	−3.05805e6	−	5.29670e6i	−0.376580	−	0.652255i
$202$	212925.	−	794646.i	0.0258328	−	0.0964095i
$203$	3.99779e6	+	1.49200e7i	0.477894	+	1.78353i
$204$	−5.65882e6	+	1.51628e6i	−0.666554	+	0.178603i
$205$	2.73603e6	+	733117.i	0.317585	+	0.0850965i
$206$	3.42359e6	−	1.97661e6i	0.391634	−	0.226110i
$207$	509928.	−	1.90308e6i	0.0574907	−	0.214558i
$208$	6.02734e6	+	6.02734e6i	0.669785	+	0.669785i
$209$	2.85839e6	+	1.06677e7i	0.313100	+	1.16851i
$210$	−2.88395e6	+	1.66505e6i	−0.311408	+	0.179791i
$211$	495815.			0.0527804			0.0263902	−	0.999652i	$-0.491599\pi$
$211$	495815.			0.0527804			0.0263902	+	0.999652i	$0.491599\pi$
$212$		−	8.54534e6i		−	0.896854i
$213$	−1.35182e7	+	7.80471e6i	−1.39887	+	0.807641i
$214$	−1.66561e6	+	1.66561e6i	−0.169955	+	0.169955i
$215$	−1.54705e6	−	893193.i	−0.155665	−	0.0898731i
$216$	545343.	−	545343.i	0.0541139	−	0.0541139i
$217$	2.74194e6	+	1.02331e7i	0.268336	+	1.00144i
$218$	2.63066e6	−	4.55644e6i	0.253919	−	0.439801i
$219$	355172.	−	615177.i	0.0338148	−	0.0585690i
$220$	1.44589e6	−	5.39612e6i	0.135789	−	0.506773i
$221$		−	7.70443e6i		−	0.713779i
$222$	−2.73696e6	+	3.68580e6i	−0.250155	+	0.336878i
$223$	1.85435e7			1.67215			0.836077	−	0.548613i	$-0.184844\pi$
$223$	1.85435e7			1.67215			0.836077	+	0.548613i	$0.184844\pi$
$224$	−1.05363e7	−	2.82320e6i	−0.937444	−	0.251187i
$225$	−4.44360e6	−	2.56551e6i	−0.390110	−	0.225230i
$226$	2.22891e6	+	1.28686e6i	0.193093	+	0.111483i
$227$	3.19387e6	−	855795.i	0.273048	−	0.0731631i	−0.119697	−	0.992811i	$-0.538192\pi$
$227$	3.19387e6	−	855795.i	0.273048	−	0.0731631i	0.392745	+	0.919647i	$0.371526\pi$
$228$	−1.55611e7	−	1.55611e7i	−1.31291	−	1.31291i
$229$	8.93229e6	−	1.54712e7i	0.743801	−	1.28830i	−0.206953	−	0.978351i	$-0.566355\pi$
$229$	8.93229e6	−	1.54712e7i	0.743801	−	1.28830i	0.950753	−	0.309949i	$-0.100312\pi$
$230$	455186.	+	455186.i	0.0374115	+	0.0374115i
$231$	8.39489e6	+	1.45404e7i	0.681050	+	1.17961i
$232$	−1.10557e7			−0.885364
$233$		−	1.49237e7i		−	1.17980i	−0.807476	−	0.589900i	$-0.799167\pi$
$233$		−	1.49237e7i		−	1.17980i	0.807476	−	0.589900i	$-0.200833\pi$
$234$	−2.28218e6	−	3.95285e6i	−0.178116	−	0.308505i
$235$	−1.76986e7	+	4.74231e6i	−1.36375	+	0.365415i
$236$	−202096.	+	202096.i	−0.0153753	+	0.0153753i
$237$	3.28685e6	+	880709.i	0.246908	+	0.0661587i
$238$	1.36600e6	+	2.36598e6i	0.101326	+	0.175501i
$239$	−3.35398e6	+	1.25172e7i	−0.245678	+	0.916883i	0.727363	+	0.686252i	$0.240745\pi$
$239$	−3.35398e6	+	1.25172e7i	−0.245678	+	0.916883i	−0.973041	+	0.230630i	$0.925921\pi$
$240$	2.55773e6	+	9.54558e6i	0.185021	+	0.690508i
$241$	−9.45369e6	+	2.53311e6i	−0.675383	+	0.180968i	−0.580178	−	0.814489i	$-0.697017\pi$
$241$	−9.45369e6	+	2.53311e6i	−0.675383	+	0.180968i	−0.0952045	+	0.995458i	$0.530350\pi$
$242$	−1.39093e6	−	372699.i	−0.0981431	−	0.0262974i
$243$	1.69918e7	−	9.81021e6i	1.18419	−	0.683690i
$244$	−1.98076e6	+	7.39229e6i	−0.136352	+	0.508873i
$245$	−3.41223e6	−	3.41223e6i	−0.232028	−	0.232028i
$246$	−750304.	−	2.80017e6i	−0.0504001	−	0.188096i
$247$	2.50636e7	−	1.44705e7i	1.66323	−	0.960268i
$248$	−7.58271e6			−0.497129
$249$			3.11317e7i			2.01653i
$250$	4.36677e6	−	2.52116e6i	0.279473	−	0.161354i
$251$	−8.99767e6	+	8.99767e6i	−0.568996	+	0.568996i	−0.931847	−	0.362851i	$-0.881803\pi$
$251$	−8.99767e6	+	8.99767e6i	−0.568996	+	0.568996i	0.362851	+	0.931847i	$0.381803\pi$
$252$	−1.37595e7	−	7.94407e6i	−0.859810	−	0.496411i
$253$	2.29497e6	−	2.29497e6i	0.141715	−	0.141715i
$254$	1.83620e6	+	6.85278e6i	0.112052	+	0.418182i
$255$	4.46610e6	−	7.73551e6i	0.269344	−	0.466518i
$256$	−1.66290e6	+	2.88022e6i	−0.0991164	+	0.171675i
$257$	−3.57294e6	+	1.33344e7i	−0.210487	+	0.785550i	0.777219	+	0.629230i	$0.216630\pi$
$257$	−3.57294e6	+	1.33344e7i	−0.210487	+	0.785550i	−0.987707	+	0.156320i	$0.950037\pi$
$258$			1.82826e6i			0.106458i
$259$	−1.95405e7	−	7.73522e6i	−1.12470	−	0.445219i
$260$	−1.46394e7			−0.832923
$261$	−2.37088e7	−	6.35274e6i	−1.33348	−	0.357305i
$262$	−6.84226e6	−	3.95038e6i	−0.380448	−	0.219652i
$263$	−1.13330e7	−	6.54311e6i	−0.622985	−	0.359681i	0.155045	−	0.987907i	$-0.450448\pi$
$263$	−1.13330e7	−	6.54311e6i	−0.622985	−	0.359681i	−0.778030	+	0.628227i	$0.783781\pi$
$264$	−1.16078e7	+	3.11031e6i	−0.630869	+	0.169041i
$265$	9.21278e6	+	9.21278e6i	0.495055	+	0.495055i
$266$	−5.13125e6	+	8.88758e6i	−0.272633	+	0.472214i
$267$	5.35479e6	+	5.35479e6i	0.281325	+	0.281325i
$268$	4.76709e6	+	8.25684e6i	0.247656	+	0.428953i
$269$	6.79936e6			0.349310			0.174655	−	0.984630i	$-0.444119\pi$
$269$	6.79936e6			0.349310			0.174655	+	0.984630i	$0.444119\pi$
$270$			559442.i			0.0284226i
$271$	1.23831e7	+	2.14482e7i	0.622189	+	1.07766i	0.989077	+	0.147398i	$0.0470900\pi$
$271$	1.23831e7	+	2.14482e7i	0.622189	+	1.07766i	−0.366888	+	0.930265i	$0.619577\pi$
$272$	7.83116e6	−	2.09835e6i	0.389152	−	0.104273i
$273$	3.11112e7	−	3.11112e7i	1.52908	−	1.52908i
$274$	−3.17850e6	−	851677.i	−0.154515	−	0.0414022i
$275$	−4.22624e6	−	7.32006e6i	−0.203215	−	0.351979i
$276$	−1.67385e6	+	6.24691e6i	−0.0796142	+	0.297124i
$277$	590948.	+	2.20545e6i	0.0278042	+	0.103767i	0.978433	−	0.206562i	$-0.0662275\pi$
$277$	590948.	+	2.20545e6i	0.0278042	+	0.103767i	−0.950629	+	0.310329i	$0.899561\pi$
$278$	3.36035e6	−	900404.i	0.156405	−	0.0419086i
$279$	−1.62610e7	−	4.35712e6i	−0.748746	−	0.200626i
$280$	9.44933e6	−	5.45557e6i	0.430454	−	0.248523i
$281$	−600567.	+	2.24135e6i	−0.0270672	+	0.101016i	−0.978138	−	0.207957i	$-0.933319\pi$
$281$	−600567.	+	2.24135e6i	−0.0270672	+	0.101016i	0.951071	+	0.308973i	$0.0999853\pi$
$282$	1.32600e7	+	1.32600e7i	0.591283	+	0.591283i
$283$	−6.66209e6	−	2.48633e7i	−0.293935	−	1.09698i	−0.942059	−	0.335446i	$-0.891113\pi$
$283$	−6.66209e6	−	2.48633e7i	−0.293935	−	1.09698i	0.648124	−	0.761534i	$-0.275554\pi$
$284$	2.10730e7	−	1.21665e7i	0.919964	−	0.531141i
$285$	3.35530e7			1.44943
$286$		−	7.51899e6i		−	0.321411i
$287$	1.14927e7	−	6.63533e6i	0.486158	−	0.280684i
$288$	1.22566e7	−	1.22566e7i	0.513091	−	0.513091i
$289$	1.45576e7	+	8.40481e6i	0.603108	+	0.348205i
$290$	5.67076e6	−	5.67076e6i	0.232513	−	0.232513i
$291$	4.46619e6	+	1.66680e7i	0.181242	+	0.676403i
$292$	−553665.	+	958976.i	−0.0222382	+	0.0385176i
$293$	1.79060e7	−	3.10141e7i	0.711862	−	1.23298i	−0.252296	−	0.967650i	$-0.581186\pi$
$293$	1.79060e7	−	3.10141e7i	0.711862	−	1.23298i	0.964158	−	0.265330i	$-0.0854810\pi$
$294$	−1.27824e6	+	4.77046e6i	−0.0503003	+	0.187723i
$295$		−	435762.i		−	0.0169740i
$296$	8.96772e6	−	1.20766e7i	0.345786	−	0.465662i
$297$	2.82061e6			0.107665
$298$	9.87777e6	+	2.64674e6i	0.373259	+	0.100014i
$299$	−7.36563e6	−	4.25255e6i	−0.275548	−	0.159087i
$300$	1.45863e7	+	8.42138e6i	0.540232	+	0.311903i
$301$	−8.08415e6	+	2.16614e6i	−0.296439	+	0.0794305i
$302$	−7.23326e6	−	7.23326e6i	−0.262611	−	0.262611i
$303$	−6.30077e6	+	1.09133e7i	−0.226499	+	0.392307i
$304$	2.15348e7	+	2.15348e7i	0.766513	+	0.766513i
$305$	−5.83420e6	−	1.01051e7i	−0.205628	−	0.356158i
$306$	−4.34132e6			−0.151516
$307$			3.51477e7i			1.21474i	0.794421	+	0.607368i	$0.207775\pi$
$307$			3.51477e7i			1.21474i	−0.794421	+	0.607368i	$0.792225\pi$
$308$	−1.30865e7	−	2.26665e7i	−0.447890	−	0.775767i
$309$	−5.84909e7	+	1.56726e7i	−1.98250	+	0.531209i
$310$	3.88937e6	−	3.88937e6i	0.130555	−	0.130555i
$311$	−1.11299e7	−	2.98224e6i	−0.370006	−	0.0991428i	0.0690245	−	0.997615i	$-0.478011\pi$
$311$	−1.11299e7	−	2.98224e6i	−0.370006	−	0.0991428i	−0.439031	+	0.898472i	$0.644678\pi$
$312$	1.57458e7	+	2.72725e7i	0.518442	+	0.897968i
$313$	2.43364e6	−	9.08246e6i	0.0793639	−	0.296190i	−0.914823	−	0.403854i	$-0.867670\pi$
$313$	2.43364e6	−	9.08246e6i	0.0793639	−	0.296190i	0.994187	+	0.107664i	$0.0343370\pi$
$314$	3.65270e6	+	1.36321e7i	0.117985	+	0.440325i
$315$	2.33988e7	−	6.26968e6i	0.748620	−	0.200592i
$316$	−5.12375e6	−	1.37290e6i	−0.162378	−	0.0435090i
$317$	−2.01525e7	+	1.16350e7i	−0.632631	+	0.365249i	−0.781770	−	0.623567i	$-0.785683\pi$
$317$	−2.01525e7	+	1.16350e7i	−0.632631	+	0.365249i	0.149140	+	0.988816i	$0.452350\pi$
$318$	3.45116e6	−	1.28799e7i	0.107321	−	0.400527i
$319$	−2.85910e7	−	2.85910e7i	−0.880760	−	0.880760i
$320$	−2.92752e6	−	1.09257e7i	−0.0893410	−	0.333425i
$321$	3.12474e7	−	1.80407e7i	0.944710	−	0.545428i
$322$	3.01592e6			0.0903341
$323$		−	2.75268e7i		−	0.816860i
$324$	−2.90438e7	+	1.67684e7i	−0.853922	+	0.493012i
$325$	−1.56623e7	+	1.56623e7i	−0.456254	+	0.456254i
$326$	1.47143e7	+	8.49532e6i	0.424705	+	0.245204i
$327$	−5.69867e7	+	5.69867e7i	−1.62979	+	1.62979i
$328$	2.45839e6	+	9.17484e6i	0.0696674	+	0.260002i
$329$	−4.29220e7	+	7.43430e7i	−1.20529	+	2.08763i
$330$	4.35860e6	−	7.54932e6i	0.121285	−	0.210071i
$331$	−1.44363e6	+	5.38770e6i	−0.0398081	+	0.148566i	−0.982969	−	0.183770i	$-0.941170\pi$
$331$	−1.44363e6	+	5.38770e6i	−0.0398081	+	0.148566i	0.943161	+	0.332336i	$0.107837\pi$
$332$		−	4.85300e7i		−	1.32616i
$333$	2.61705e7	−	2.07451e7i	0.708728	−	0.561803i
$334$	−509863.			−0.0136840
$335$	−1.40412e7	−	3.76232e6i	−0.373481	−	0.100074i
$336$	4.00963e7	+	2.31496e7i	1.05703	+	0.610276i
$337$	2.23071e7	+	1.28790e7i	0.582845	+	0.336506i	0.762263	−	0.647267i	$-0.224088\pi$
$337$	2.23071e7	+	1.28790e7i	0.582845	+	0.336506i	−0.179418	+	0.983773i	$0.557422\pi$
$338$	−7.69124e6	+	2.06086e6i	−0.199180	+	0.0533702i
$339$	−2.78767e7	−	2.78767e7i	−0.715553	−	0.715553i
$340$	−6.96204e6	+	1.20586e7i	−0.177133	+	0.306804i
$341$	−1.96096e7	−	1.96096e7i	−0.494544	−	0.494544i
$342$	−8.15388e6	−	1.41229e7i	−0.203838	−	0.353058i
$343$	2.62040e7			0.649359
$344$		−	5.99036e6i		−	0.147156i
$345$	−4.93023e6	−	8.53942e6i	−0.120063	−	0.207956i
$346$	−7.41322e6	+	1.98637e6i	−0.178969	+	0.0479547i
$347$	6.52073e6	−	6.52073e6i	0.156066	−	0.156066i	−0.624755	−	0.780821i	$-0.714801\pi$
$347$	6.52073e6	−	6.52073e6i	0.156066	−	0.156066i	0.780821	+	0.624755i	$0.214801\pi$
$348$	7.78247e7	+	2.08531e7i	1.84663	+	0.494803i
$349$	−3.54161e7	−	6.13426e7i	−0.833153	−	1.44306i	−0.895525	−	0.445011i	$-0.853200\pi$
$349$	−3.54161e7	−	6.13426e7i	−0.833153	−	1.44306i	0.0623718	−	0.998053i	$-0.480134\pi$
$350$	2.03286e6	−	7.58674e6i	0.0474137	−	0.176950i
$351$	−1.91305e6	−	7.13961e6i	−0.0442390	−	0.165102i
$352$	2.75810e7	−	7.39031e6i	0.632386	−	0.169447i
$353$	−7.75259e7	−	2.07730e7i	−1.76247	−	0.472254i	−0.775259	−	0.631643i	$-0.782381\pi$
$353$	−7.75259e7	−	2.07730e7i	−1.76247	−	0.472254i	−0.987216	+	0.159390i	$0.949047\pi$
$354$	−386228.	+	222989.i	−0.00870631	+	0.00502659i
$355$	−9.60213e6	+	3.58356e7i	−0.214626	+	0.800995i
$356$	−8.34739e6	−	8.34739e6i	−0.185012	−	0.185012i
$357$	−1.08310e7	−	4.04220e7i	−0.238049	−	0.888409i
$358$	−1.87969e7	+	1.08524e7i	−0.409672	+	0.236524i
$359$	6.90226e6			0.149179			0.0745896	−	0.997214i	$-0.476235\pi$
$359$	6.90226e6			0.149179			0.0745896	+	0.997214i	$0.476235\pi$
$360$			1.73385e7i			0.371624i
$361$	4.88056e7	−	2.81779e7i	1.03740	−	0.598945i
$362$	−3.61150e6	+	3.61150e6i	−0.0761310	+	0.0761310i
$363$	1.91023e7	+	1.10287e7i	0.399362	+	0.230571i
$364$	−4.84982e7	+	4.84982e7i	−1.00559	+	1.00559i
$365$	−436968.	−	1.63079e6i	−0.00898610	−	0.0335366i
$366$	−5.97097e6	+	1.03420e7i	−0.121787	+	0.210942i
$367$	−2.07085e7	+	3.58683e7i	−0.418940	+	0.725625i	−0.995833	−	0.0911947i	$-0.970931\pi$
$367$	−2.07085e7	+	3.58683e7i	−0.418940	+	0.725625i	0.576893	+	0.816819i	$0.304265\pi$
$368$	2.31642e6	−	8.64500e6i	0.0464809	−	0.173469i
$369$			2.10879e7i			0.419715i
$370$	1.59464e6	+	1.07942e7i	0.0314816	+	0.213101i
$371$	6.10409e7			1.19536
$372$	5.33772e7	+	1.43024e7i	1.03688	+	0.277830i
$373$	−7.72445e6	−	4.45972e6i	−0.148847	−	0.0859371i	0.423727	−	0.905790i	$-0.360722\pi$
$373$	−7.72445e6	−	4.45972e6i	−0.148847	−	0.0859371i	−0.572574	+	0.819853i	$0.694055\pi$
$374$	−6.19344e6	−	3.57578e6i	−0.118391	−	0.0683528i
$375$	−7.46049e7	+	1.99903e7i	−1.41473	+	0.379075i
$376$	−4.34467e7	−	4.34467e7i	−0.817322	−	0.817322i
$377$	−5.29788e7	+	9.17619e7i	−0.988730	+	1.71253i
$378$	1.85334e6	+	1.85334e6i	0.0343147	+	0.0343147i
$379$	2.18388e7	+	3.78259e7i	0.401154	+	0.694819i	0.993865	−	0.110596i	$-0.0352759\pi$
$379$	2.18388e7	+	3.78259e7i	0.401154	+	0.694819i	−0.592711	+	0.805415i	$0.701943\pi$
$380$	−5.23045e7			−0.953210
$381$		−	1.08672e8i		−	1.96490i
$382$	−1.18198e7	−	2.04726e7i	−0.212042	−	0.367267i
$383$	5.55503e7	−	1.48847e7i	0.988758	−	0.264937i	0.272029	−	0.962289i	$-0.412305\pi$
$383$	5.55503e7	−	1.48847e7i	0.988758	−	0.264937i	0.716729	+	0.697352i	$0.245639\pi$
$384$	−5.25170e7	+	5.25170e7i	−0.927483	+	0.927483i
$385$	3.85454e7	+	1.03282e7i	0.675446	+	0.180985i
$386$	1.41832e7	+	2.45660e7i	0.246610	+	0.427141i
$387$	3.44213e6	−	1.28462e7i	0.0593875	−	0.221637i
$388$	−6.96218e6	−	2.59832e7i	−0.119193	−	0.444834i
$389$	1.46314e7	−	3.92047e6i	0.248563	−	0.0666024i	−0.132386	−	0.991198i	$-0.542264\pi$
$389$	1.46314e7	−	3.92047e6i	0.248563	−	0.0666024i	0.380949	+	0.924596i	$0.375597\pi$
$390$	−2.20652e7	−	5.91236e6i	−0.371976	−	0.0996706i
$391$	−7.00571e6	+	4.04475e6i	−0.117198	+	0.0676645i
$392$	4.18820e6	−	1.56306e7i	0.0695294	−	0.259487i
$393$	8.55751e7	+	8.55751e7i	1.40984	+	1.40984i
$394$	8.11836e6	+	3.02981e7i	0.132733	+	0.495367i
$395$	7.00408e6	−	4.04381e6i	0.113647	−	0.0656144i
$396$	4.15905e7			0.669744
$397$		−	1.01555e8i		−	1.62304i	−0.584327	−	0.811518i	$-0.698642\pi$
$397$		−	1.01555e8i		−	1.62304i	0.584327	−	0.811518i	$-0.301358\pi$
$398$	2.11477e7	−	1.22096e7i	0.335439	−	0.193666i
$399$	1.11156e8	−	1.11156e8i	1.74990	−	1.74990i
$400$	−2.01857e7	−	1.16542e7i	−0.315402	−	0.182097i
$401$	2.56443e6	−	2.56443e6i	0.0397703	−	0.0397703i	−0.686942	−	0.726712i	$-0.741047\pi$
$401$	2.56443e6	−	2.56443e6i	0.0397703	−	0.0397703i	0.726712	+	0.686942i	$0.241047\pi$
$402$	3.85052e6	+	1.43703e7i	0.0592708	+	0.221202i
$403$	−3.63363e7	+	6.29362e7i	−0.555169	+	0.961581i
$404$	9.82204e6	−	1.70123e7i	0.148956	−	0.257999i
$405$	1.32341e7	−	4.93904e7i	0.199219	−	0.743494i
$406$		−	3.75726e7i		−	0.561428i
$407$	5.44226e7	−	8.03989e6i	0.807228	−	0.119252i
$408$	2.99527e7			0.441017
$409$	6.85249e7	+	1.83612e7i	1.00156	+	0.268368i	0.722101	−	0.691788i	$-0.243177\pi$
$409$	6.85249e7	+	1.83612e7i	1.00156	+	0.268368i	0.279463	+	0.960156i	$0.409843\pi$
$410$	−5.96700e6	−	3.44505e6i	−0.0865773	−	0.0499854i
$411$	4.36519e7	+	2.52024e7i	0.628749	+	0.363008i
$412$	9.11794e7	−	2.44314e7i	1.30378	−	0.349347i
$413$	−1.44361e6	−	1.44361e6i	−0.0204927	−	0.0204927i
$414$	−2.39624e6	+	4.15041e6i	−0.0337699	+	0.0584911i
$415$	5.23205e7	+	5.23205e7i	0.732028	+	0.732028i
$416$	−3.74131e7	−	6.48014e7i	−0.519689	−	0.900128i
$417$	−5.32886e7			−0.734897
$418$		−	2.68642e7i		−	0.367828i
$419$	6.87940e7	+	1.19155e8i	0.935209	+	1.61983i	0.774261	+	0.632866i	$0.218122\pi$
$419$	6.87940e7	+	1.19155e8i	0.935209	+	1.61983i	0.160948	+	0.986963i	$0.448545\pi$
$420$	−7.68072e7	+	2.05804e7i	−1.03670	+	0.277784i
$421$	−2.41774e7	+	2.41774e7i	−0.324013	+	0.324013i	−0.850304	−	0.526291i	$-0.823582\pi$
$421$	−2.41774e7	+	2.41774e7i	−0.324013	+	0.324013i	0.526291	+	0.850304i	$0.323582\pi$
$422$	−1.16496e6	−	312151.i	−0.0155015	−	0.00415362i
$423$	−6.82057e7	−	1.18136e8i	−0.901155	−	1.56085i
$424$	−1.13078e7	+	4.22014e7i	−0.148348	+	0.553643i
$425$	5.45267e6	+	2.03497e7i	0.0710301	+	0.265088i
$426$	3.66757e7	−	9.82723e6i	0.474406	−	0.127117i
$427$	−5.28045e7	−	1.41489e7i	−0.678246	−	0.181735i
$428$	−4.87104e7	+	2.81230e7i	−0.621284	+	0.358699i
$429$	−2.98091e7	+	1.11249e8i	−0.377552	+	1.40904i
$430$	3.07261e6	+	3.07261e6i	0.0386458	+	0.0386458i
$431$	−2.17361e7	−	8.11202e7i	−0.271487	−	1.01320i	−0.958159	−	0.286237i	$-0.907596\pi$
$431$	−2.17361e7	−	8.11202e7i	−0.271487	−	1.01320i	0.686672	−	0.726968i	$-0.259071\pi$
$432$	6.73602e6	−	3.88904e6i	0.0835511	−	0.0482382i
$433$	8.00524e7			0.986077			0.493038	−	0.870008i	$-0.335886\pi$
$433$	8.00524e7			0.986077			0.493038	+	0.870008i	$0.335886\pi$
$434$		−	2.57697e7i		−	0.315240i
$435$	−1.06385e8	+	6.14214e7i	−1.29245	+	0.746195i
$436$	8.88345e7	−	8.88345e7i	1.07182	−	1.07182i
$437$	−2.63163e7	−	1.51937e7i	−0.315341	−	0.182062i
$438$	−1.22181e6	+	1.22181e6i	−0.0145405	+	0.0145405i
$439$	−5.72372e6	−	2.13612e7i	−0.0676526	−	0.252483i	0.923814	−	0.382841i	$-0.125054\pi$
$439$	−5.72372e6	−	2.13612e7i	−0.0676526	−	0.252483i	−0.991467	+	0.130358i	$0.958387\pi$
$440$	−1.42811e7	+	2.47356e7i	−0.167650	+	0.290378i
$441$	1.79630e7	−	3.11129e7i	0.209442	−	0.362764i
$442$	−4.85048e6	+	1.81022e7i	−0.0561717	+	0.209636i
$443$		−	1.17997e7i		−	0.135725i	−0.997695	−	0.0678627i	$-0.978382\pi$
$443$		−	1.17997e7i		−	0.135725i	0.997695	−	0.0678627i	$-0.0216180\pi$
$444$	−8.59055e7	+	6.80966e7i	−0.981459	+	0.777994i
$445$	1.79987e7			0.204250
$446$	−4.35695e7	−	1.16744e7i	−0.491109	−	0.131592i
$447$	−1.35656e8	−	7.83210e7i	−1.51886	−	0.876912i
$448$	−4.58934e7	−	2.64966e7i	−0.510407	−	0.294683i
$449$	1.02803e8	−	2.75460e7i	1.13571	−	0.304312i	0.358483	−	0.933536i	$-0.383294\pi$
$449$	1.02803e8	−	2.75460e7i	1.13571	−	0.304312i	0.777224	+	0.629224i	$0.216627\pi$
$450$	8.82546e6	+	8.82546e6i	0.0968500	+	0.0968500i
$451$	−1.73694e7	+	3.00846e7i	−0.189345	+	0.327955i
$452$	4.34559e7	+	4.34559e7i	0.470580	+	0.470580i
$453$	7.83452e7	+	1.35698e8i	0.842787	+	1.45975i
$454$	−8.04306e6			−0.0859516
$455$		−	1.04572e8i		−	1.11015i
$456$	5.62573e7	+	9.74405e7i	0.593313	+	1.02765i
$457$	−1.47416e8	+	3.94999e7i	−1.54453	+	0.413855i	−0.927725	−	0.373264i	$-0.878238\pi$
$457$	−1.47416e8	+	3.94999e7i	−1.54453	+	0.413855i	−0.616801	+	0.787119i	$0.711572\pi$
$458$	−3.07274e7	+	3.07274e7i	−0.319838	+	0.319838i
$459$	−6.79073e6	−	1.81957e6i	−0.0702228	−	0.0188162i
$460$	7.68556e6	+	1.33118e7i	0.0789591	+	0.136761i
$461$	−3.60355e7	+	1.34486e8i	−0.367814	+	1.37270i	0.495752	+	0.868464i	$0.334892\pi$
$461$	−3.60355e7	+	1.34486e8i	−0.367814	+	1.37270i	−0.863566	+	0.504236i	$0.831774\pi$
$462$	−1.05703e7	−	3.94491e7i	−0.107192	−	0.400047i
$463$	1.66389e8	−	4.45838e7i	1.67641	−	0.449194i	0.709586	−	0.704619i	$-0.248882\pi$
$463$	1.66389e8	−	4.45838e7i	1.67641	−	0.449194i	0.966829	+	0.255425i	$0.0822154\pi$
$464$	−1.07700e8	−	2.88582e7i	−1.07811	−	0.288879i
$465$	−7.29657e7	+	4.21268e7i	−0.725705	+	0.418986i
$466$	−9.39551e6	+	3.50645e7i	−0.0928459	+	0.346506i
$467$	6.91456e7	+	6.91456e7i	0.678912	+	0.678912i	0.959754	−	0.280842i	$-0.0906136\pi$
$467$	6.91456e7	+	6.91456e7i	0.678912	+	0.678912i	−0.280842	+	0.959754i	$0.590614\pi$
$468$	−2.82083e7	−	1.05275e8i	−0.275195	−	1.02704i
$469$	−5.89801e7	+	3.40522e7i	−0.571725	+	0.330085i
$470$	4.45699e7			0.429288
$471$		−	2.16178e8i		−	2.06895i
$472$	1.26549e6	−	730630.i	0.0120346	−	0.00694818i
$473$	1.54916e7	−	1.54916e7i	0.146391	−	0.146391i
$474$	−7.16827e6	−	4.13860e6i	−0.0673100	−	0.0388614i
$475$	−5.59591e7	+	5.59591e7i	−0.522144	+	0.522144i
$476$	1.68841e7	+	6.30124e7i	0.156552	+	0.584258i
$477$	−4.84989e7	+	8.40026e7i	−0.446866	+	0.773994i
$478$	1.57609e7	−	2.72987e7i	0.144311	−	0.249953i
$479$	−2.60489e7	+	9.72159e7i	−0.237019	+	0.884567i	0.740209	+	0.672377i	$0.234726\pi$
$479$	−2.60489e7	+	9.72159e7i	−0.237019	+	0.884567i	−0.977228	+	0.212191i	$0.931940\pi$
$480$		−	8.67504e7i		−	0.784419i
$481$	−5.72624e7	−	1.32303e8i	−0.514558	−	1.18887i
$482$	2.38070e7			0.212600
$483$	−4.46228e7	−	1.19566e7i	−0.396018	−	0.106113i
$484$	−2.97779e7	−	1.71923e7i	−0.262638	−	0.151634i
$485$	3.55186e7	+	2.05067e7i	0.311337	+	0.179750i
$486$	−4.60999e7	+	1.23524e7i	−0.401598	+	0.107608i
$487$	−1.01581e7	−	1.01581e7i	−0.0879476	−	0.0879476i	0.661764	−	0.749712i	$-0.269808\pi$
$487$	−1.01581e7	−	1.01581e7i	−0.0879476	−	0.0879476i	−0.749712	+	0.661764i	$0.769808\pi$
$488$	1.95641e7	−	3.38860e7i	0.168345	−	0.291582i
$489$	−1.84030e8	−	1.84030e8i	−1.57384	−	1.57384i
$490$	5.86909e6	+	1.01656e7i	0.0498865	+	0.0864059i
$491$	1.98385e8			1.67596			0.837981	−	0.545700i	$-0.183736\pi$
$491$	1.98385e8			1.67596			0.837981	+	0.545700i	$0.183736\pi$
$492$		−	6.92217e7i		−	0.581229i
$493$	5.03899e7	+	8.72779e7i	0.420536	+	0.728389i
$494$	−6.79994e7	+	1.82204e7i	−0.564058	+	0.151139i
$495$	−4.48389e7	+	4.48389e7i	−0.369692	+	0.369692i
$496$	−7.38679e7	−	1.97929e7i	−0.605356	−	0.162205i
$497$	8.69074e7	+	1.50528e8i	0.707926	+	1.22616i
$498$	1.95996e7	−	7.31466e7i	0.158693	−	0.592251i
$499$	−3.07817e7	−	1.14879e8i	−0.247737	−	0.924566i	−0.971988	−	0.235030i	$-0.924481\pi$
$499$	−3.07817e7	−	1.14879e8i	−0.247737	−	0.924566i	0.724251	−	0.689536i	$-0.242185\pi$
$500$	1.16299e8	−	3.11622e7i	0.930390	−	0.249297i
$501$	7.54381e6	+	2.02136e6i	0.0599898	+	0.0160742i
$502$	2.68055e7	−	1.54762e7i	0.211891	−	0.122335i
$503$	−2.17301e7	+	8.10978e7i	−0.170749	+	0.637243i	0.826488	+	0.562954i	$0.190335\pi$
$503$	−2.17301e7	+	8.10978e7i	−0.170749	+	0.637243i	−0.997237	+	0.0742886i	$0.976331\pi$
$504$	5.74397e7	+	5.74397e7i	0.448663	+	0.448663i
$505$	7.75183e6	+	2.89302e7i	0.0601908	+	0.224635i
$506$	−6.83708e6	+	3.94739e6i	−0.0527739	+	0.0304690i
$507$	1.21968e8			0.935885
$508$			1.69404e8i			1.29221i
$509$	2.87108e6	−	1.65762e6i	0.0217716	−	0.0125699i	−0.489075	−	0.872242i	$-0.662665\pi$
$509$	2.87108e6	−	1.65762e6i	0.0217716	−	0.0125699i	0.510846	+	0.859672i	$0.329332\pi$
$510$	−1.53635e7	+	1.53635e7i	−0.115819	+	0.115819i
$511$	−6.85014e6	−	3.95493e6i	−0.0513378	−	0.0296399i
$512$	9.59270e7	−	9.59270e7i	0.714712	−	0.714712i
$513$	−6.83505e6	−	2.55087e7i	−0.0506278	−	0.188946i
$514$	1.67899e7	−	2.90809e7i	0.123640	−	0.214150i
$515$	−7.19613e7	+	1.24641e8i	−0.526838	+	0.912511i
$516$	−1.12989e7	+	4.21681e7i	−0.0822408	+	0.306927i
$517$		−	2.24714e8i		−	1.62614i
$518$	4.10423e7	+	3.04767e7i	0.295285	+	0.219270i
$519$	1.17559e8			0.840920
$520$	7.22973e7	+	1.93720e7i	0.514176	+	0.137773i
$521$	6.68481e7	+	3.85948e7i	0.472690	+	0.272908i	0.717365	−	0.696698i	$-0.245348\pi$
$521$	6.68481e7	+	3.85948e7i	0.472690	+	0.272908i	−0.244675	+	0.969605i	$0.578681\pi$
$522$	5.17063e7	+	2.98526e7i	0.363523	+	0.209880i
$523$	−8.20692e7	+	2.19904e7i	−0.573687	+	0.153719i	−0.533987	−	0.845493i	$-0.679307\pi$
$523$	−8.20692e7	+	2.19904e7i	−0.573687	+	0.153719i	−0.0396999	+	0.999212i	$0.512640\pi$
$524$	−1.33400e8	−	1.33400e8i	−0.927175	−	0.927175i
$525$	−6.01554e7	+	1.04192e8i	−0.415716	+	0.720042i
$526$	2.25085e7	+	2.25085e7i	0.154664	+	0.154664i
$527$	3.45607e7	+	5.98608e7i	0.236130	+	0.408988i
$528$	−1.21198e8			−0.823366
$529$		−	1.39106e8i		−	0.939676i
$530$	−1.58461e7	−	2.74463e7i	−0.106438	−	0.184356i
$531$	3.13365e6	−	839658.i	0.0209299	−	0.00560814i
$532$	−1.73277e8	+	1.73277e8i	−1.15081	+	1.15081i
$533$	8.79315e7	+	2.35612e7i	0.580715	+	0.155602i
$534$	−9.21033e6	−	1.59528e7i	−0.0604855	−	0.104764i
$535$	2.21954e7	−	8.28344e7i	0.144945	−	0.540941i
$536$	−1.26163e7	−	4.70848e7i	−0.0819292	−	0.305764i
$537$	3.21138e8	−	8.60488e7i	2.07381	−	0.555676i
$538$	−1.59757e7	−	4.28067e6i	−0.102592	−	0.0274894i
$539$	5.12531e7	−	2.95910e7i	0.327306	−	0.188970i
$540$	−3.45743e6	+	1.29033e7i	−0.0219569	+	0.0819444i
$541$	−2.38493e7	−	2.38493e7i	−0.150621	−	0.150621i	0.627775	−	0.778395i	$-0.283966\pi$
$541$	−2.38493e7	−	2.38493e7i	−0.150621	−	0.150621i	−0.778395	+	0.627775i	$0.783966\pi$
$542$	−1.55921e7	−	5.81905e7i	−0.0979280	−	0.365472i
$543$	6.77527e7	−	3.91170e7i	0.423182	−	0.244324i
$544$	−7.11698e7			−0.442078
$545$			1.91546e8i			1.18327i
$546$	−9.26852e7	+	5.35119e7i	−0.569420	+	0.328755i
$547$	8.00317e7	−	8.00317e7i	0.488990	−	0.488990i	−0.418997	−	0.907987i	$-0.637618\pi$
$547$	8.00317e7	−	8.00317e7i	0.488990	−	0.488990i	0.907987	+	0.418997i	$0.137618\pi$
$548$	−6.80473e7	−	3.92871e7i	−0.413494	−	0.238731i
$549$	6.14261e7	−	6.14261e7i	0.371224	−	0.371224i
$550$	5.32143e6	+	1.98598e7i	0.0319846	+	0.119368i
$551$	−1.89285e8	+	3.27851e8i	−1.13152	+	1.95985i
$552$	1.65328e7	−	2.86356e7i	0.0982942	−	0.170251i
$553$	9.80691e6	−	3.65999e7i	0.0579905	−	0.216423i
$554$		−	5.55394e6i		−	0.0326642i
$555$	1.91999e7	−	1.66030e8i	0.112310	−	0.971200i
$556$	8.30697e7			0.483302
$557$	1.40508e8	+	3.76489e7i	0.813083	+	0.217865i	0.641320	−	0.767274i	$-0.278387\pi$
$557$	1.40508e8	+	3.76489e7i	0.813083	+	0.217865i	0.171763	+	0.985138i	$0.445054\pi$
$558$	3.54635e7	+	2.04749e7i	0.204117	+	0.117847i
$559$	−4.97198e7	−	2.87057e7i	−0.284639	−	0.164336i
$560$	1.06292e8	−	2.84810e7i	0.605254	−	0.162177i
$561$	7.74604e7	+	7.74604e7i	0.438724	+	0.438724i
$562$	2.82217e6	−	4.88814e6i	0.0158992	−	0.0275382i
$563$	−1.33534e8	−	1.33534e8i	−0.748287	−	0.748287i	0.225870	−	0.974157i	$-0.427477\pi$
$563$	−1.33534e8	−	1.33534e8i	−0.748287	−	0.748287i	−0.974157	+	0.225870i	$0.927477\pi$
$564$	2.23887e8	+	3.87784e8i	1.24794	+	2.16149i
$565$	−9.37001e7			−0.519511
$566$			6.26127e7i			0.345313i
$567$	−1.19780e8	−	2.07465e8i	−0.657105	−	1.13814i
$568$	−1.20169e8	+	3.21992e7i	−0.655764	+	0.175711i
$569$	1.84261e8	−	1.84261e8i	1.00022	−	1.00022i	0.000223024	−	1.00000i	$-0.499929\pi$
$569$	1.84261e8	−	1.84261e8i	1.00022	−	1.00022i	1.00000		0.000223024i	$-7.09906e-5\pi$
$570$	−7.88357e7	−	2.11240e7i	−0.425695	−	0.114065i
$571$	2.79711e6	+	4.84474e6i	0.0150246	+	0.0260233i	0.873440	−	0.486932i	$-0.161884\pi$
$571$	2.79711e6	+	4.84474e6i	0.0150246	+	0.0260233i	−0.858415	+	0.512955i	$0.828551\pi$
$572$	4.64683e7	−	1.73422e8i	0.248296	−	0.926652i
$573$	9.37198e7	+	3.49767e8i	0.498159	+	1.85915i
$574$	−3.11806e7	+	8.35482e6i	−0.164873	+	0.0441775i
$575$	2.24645e7	+	6.01934e6i	0.118166	+	0.0316625i
$576$	7.29275e7	−	4.21047e7i	0.381614	−	0.220325i
$577$	3.25895e7	−	1.21626e8i	0.169649	−	0.633137i	−0.827753	−	0.561093i	$-0.810381\pi$
$577$	3.25895e7	−	1.21626e8i	0.169649	−	0.633137i	0.997401	−	0.0720443i	$-0.0229523\pi$
$578$	−2.89128e7	−	2.89128e7i	−0.149729	−	0.149729i
$579$	−1.12459e8	−	4.19701e8i	−0.579371	−	2.16224i
$580$	1.65840e8	−	9.57476e7i	0.849972	−	0.490732i
$581$	3.46659e8			1.76756
$582$		−	4.19748e7i		−	0.212922i
$583$	−1.38380e8	+	7.98936e7i	−0.698340	+	0.403187i
$584$	4.00328e6	−	4.00328e6i	0.0200991	−	0.0200991i
$585$	1.43909e8	+	8.30859e7i	0.718820	+	0.415011i
$586$	−6.15973e7	+	6.15973e7i	−0.306104	+	0.306104i
$587$	5.78918e7	+	2.16055e8i	0.286222	+	1.06819i	0.947942	+	0.318443i	$0.103160\pi$
$587$	5.78918e7	+	2.16055e8i	0.286222	+	1.06819i	−0.661720	+	0.749751i	$0.730173\pi$
$588$	−5.89642e7	+	1.02129e8i	−0.290039	+	0.502362i
$589$	−1.29824e8	+	2.24862e8i	−0.635344	+	1.10045i
$590$	−274343.	+	1.02386e6i	−0.00133579	+	0.00498523i
$591$		−	4.80470e8i		−	2.32757i
$592$	1.18883e8	−	9.42379e7i	0.573002	−	0.454214i
$593$	−1.99866e8			−0.958461			−0.479230	−	0.877689i	$-0.659084\pi$
$593$	−1.99866e8			−0.958461			−0.479230	+	0.877689i	$0.659084\pi$
$594$	−6.62728e6	−	1.77577e6i	−0.0316210	−	0.00847283i
$595$	−8.61368e7	−	4.97311e7i	−0.408920	−	0.236090i
$596$	2.11469e8	+	1.22092e8i	0.998869	+	0.576697i
$597$	−3.61301e8	+	9.68103e7i	−1.69803	+	0.454986i
$598$	1.46289e7	+	1.46289e7i	0.0684083	+	0.0684083i
$599$	−1.89526e8	+	3.28269e8i	−0.881838	+	1.52739i	−0.0325426	+	0.999470i	$0.510360\pi$
$599$	−1.89526e8	+	3.28269e8i	−0.881838	+	1.52739i	−0.849295	+	0.527918i	$0.822973\pi$
$600$	−6.08908e7	−	6.08908e7i	−0.281902	−	0.281902i
$601$	−1.96487e7	−	3.40326e7i	−0.0905131	−	0.156773i	0.817214	−	0.576334i	$-0.195517\pi$
$601$	−1.96487e7	−	3.40326e7i	−0.0905131	−	0.156773i	−0.907727	+	0.419561i	$0.862184\pi$
$602$	2.03582e7			0.0933145
$603$		−	1.08222e8i		−	0.493587i
$604$	−1.22129e8	−	2.11534e8i	−0.554255	−	0.959998i
$605$	5.06388e7	−	1.35686e7i	0.228674	−	0.0612731i
$606$	2.16749e7	−	2.16749e7i	0.0973954	−	0.0973954i
$607$	−3.41058e8	−	9.13863e7i	−1.52497	−	0.408616i	−0.603599	−	0.797288i	$-0.706267\pi$
$607$	−3.41058e8	−	9.13863e7i	−1.52497	−	0.408616i	−0.921376	+	0.388673i	$0.872934\pi$
$608$	−1.33671e8	−	2.31526e8i	−0.594741	−	1.03012i
$609$	−1.48957e8	+	5.55916e8i	−0.659492	+	2.46126i
$610$	7.34608e6	+	2.74160e7i	0.0323643	+	0.120785i
$611$	−5.68802e8	+	1.52410e8i	−2.49366	+	0.668175i
$612$	−1.00131e8	−	2.68299e7i	−0.436830	−	0.117048i
$613$	3.51134e8	−	2.02727e8i	1.52437	−	0.880098i	0.524790	−	0.851231i	$-0.324144\pi$
$613$	3.51134e8	−	2.02727e8i	1.52437	−	0.880098i	0.999583	−	0.0288661i	$-0.00918963\pi$
$614$	2.21280e7	−	8.25826e7i	0.0955952	−	0.356766i
$615$	7.46283e7	+	7.46283e7i	0.320833	+	0.320833i
$616$	3.46340e7	+	1.29256e8i	0.148170	+	0.552979i
$617$	−6.46079e7	+	3.73014e7i	−0.275062	+	0.158807i	−0.631186	−	0.775632i	$-0.717431\pi$
$617$	−6.46079e7	+	3.73014e7i	−0.275062	+	0.158807i	0.356124	+	0.934439i	$0.384098\pi$
$618$	1.47297e8			0.624061
$619$		−	6.63101e7i		−	0.279581i	−0.990181	−	0.139791i	$-0.955357\pi$
$619$		−	6.63101e7i		−	0.279581i	0.990181	−	0.139791i	$-0.0446429\pi$
$620$	1.13744e8	−	6.56699e7i	0.477257	−	0.275544i
$621$	−5.48778e6	+	5.48778e6i	−0.0229151	+	0.0229151i
$622$	2.42731e7	+	1.40141e7i	0.100868	+	0.0582362i
$623$	5.96269e7	−	5.96269e7i	0.246591	−	0.246591i
$624$	8.22012e7	+	3.06779e8i	0.338317	+	1.26262i
$625$	−3.09850e7	+	5.36677e7i	−0.126915	+	0.219823i
$626$	−1.14361e7	+	1.98079e7i	−0.0466181	+	0.0807449i
$627$	−1.06503e8	+	3.97476e8i	−0.432077	+	1.61253i
$628$			3.36992e8i			1.36063i
$629$	−1.36211e8	−	1.57515e7i	−0.547343	−	0.0632952i
$630$	−5.89247e7			−0.235654
$631$	−1.44589e8	−	3.87426e7i	−0.575504	−	0.154206i	−0.0406843	−	0.999172i	$-0.512954\pi$
$631$	−1.44589e8	−	3.87426e7i	−0.575504	−	0.154206i	−0.534820	+	0.844966i	$0.679620\pi$
$632$	2.34871e7	+	1.35603e7i	0.0930416	+	0.0537176i
$633$	1.59990e7	+	9.23701e6i	0.0630784	+	0.0364184i
$634$	5.46750e7	−	1.46501e7i	0.214546	−	0.0574875i
$635$	−1.82636e8	−	1.82636e8i	−0.713287	−	0.713287i
$636$	1.59199e8	−	2.75741e8i	0.618828	−	1.07184i
$637$	−1.09663e8	−	1.09663e8i	−0.424271	−	0.424271i
$638$	4.91771e7	+	8.51772e7i	0.189365	+	0.327990i
$639$	−2.76203e8			−1.05858
$640$			1.76522e8i			0.673378i
$641$	−2.49881e8	−	4.32806e8i	−0.948764	−	1.64331i	−0.748033	−	0.663662i	$-0.769001\pi$
$641$	−2.49881e8	−	4.32806e8i	−0.948764	−	1.64331i	−0.200732	−	0.979646i	$-0.564332\pi$
$642$	−8.47763e7	+	2.27157e7i	−0.320383	+	0.0858464i
$643$	−3.40032e7	+	3.40032e7i	−0.127905	+	0.127905i	−0.768161	−	0.640256i	$-0.778828\pi$
$643$	−3.40032e7	+	3.40032e7i	−0.127905	+	0.127905i	0.640256	+	0.768161i	$0.278828\pi$
$644$	6.95609e7	+	1.86388e7i	0.260440	+	0.0697846i
$645$	−3.32802e7	−	5.76431e7i	−0.124024	−	0.214817i
$646$	−1.73300e7	+	6.46765e7i	−0.0642838	+	0.239910i
$647$	−1.29453e7	−	4.83123e7i	−0.0477967	−	0.178380i	0.937901	−	0.346903i	$-0.112767\pi$
$647$	−1.29453e7	−	4.83123e7i	−0.0477967	−	0.178380i	−0.985698	+	0.168524i	$0.946100\pi$
$648$	1.65623e8	−	4.43785e7i	0.608688	−	0.163098i
$649$	5.16214e6	+	1.38319e6i	0.0188841	+	0.00505997i
$650$	4.66606e7	−	2.69395e7i	0.169906	−	0.0980955i
$651$	−1.02164e8	+	3.81283e8i	−0.370303	+	1.38199i
$652$	2.86877e8	+	2.86877e8i	1.03503	+	1.03503i
$653$	−1.29738e8	−	4.84190e8i	−0.465939	−	1.73891i	−0.653758	−	0.756704i	$-0.726808\pi$
$653$	−1.29738e8	−	4.84190e8i	−0.465939	−	1.73891i	0.187819	−	0.982204i	$-0.439858\pi$
$654$	1.69772e8	−	9.80182e7i	0.606924	−	0.350408i
$655$	2.87638e8			1.02358
$656$			9.57949e7i			0.339337i
$657$	1.08853e7	−	6.28463e6i	0.0383835	−	0.0221607i
$658$	1.47653e8	−	1.47653e8i	0.518281	−	0.518281i
$659$	1.61505e8	+	9.32447e7i	0.564324	+	0.325813i	0.754879	−	0.655864i	$-0.227695\pi$
$659$	1.61505e8	+	9.32447e7i	0.564324	+	0.325813i	−0.190555	+	0.981676i	$0.561029\pi$
$660$	1.47185e8	−	1.47185e8i	0.511956	−	0.511956i
$661$	−3.67011e7	−	1.36970e8i	−0.127079	−	0.474266i	0.872826	−	0.488032i	$-0.162285\pi$
$661$	−3.67011e7	−	1.36970e8i	−0.127079	−	0.474266i	−0.999905	+	0.0137652i	$0.995618\pi$
$662$	6.78387e6	−	1.17500e7i	0.0233832	−	0.0405008i
$663$	1.43533e8	−	2.48607e8i	0.492506	−	0.853045i
$664$	−6.42186e7	+	2.39667e8i	−0.219359	+	0.818661i
$665$		−	3.73621e8i		−	1.27047i
$666$	−7.45505e7	+	3.22664e7i	−0.252364	+	0.109226i
$667$	1.11253e8			0.374917
$668$	−1.17598e7	−	3.15102e6i	−0.0394520	−	0.0105711i
$669$	5.98360e8	+	3.45464e8i	1.99841	+	1.15378i
$670$	3.06223e7	+	1.76798e7i	0.101815	+	0.0587831i
$671$	1.38227e8	−	3.70377e7i	0.457535	−	0.122596i
$672$	−2.87390e8	−	2.87390e8i	−0.947031	−	0.947031i
$673$	3.73376e7	−	6.46706e7i	0.122490	−	0.212159i	−0.798259	−	0.602314i	$-0.794245\pi$
$673$	3.73376e7	−	6.46706e7i	0.122490	−	0.212159i	0.920749	+	0.390155i	$0.127579\pi$
$674$	−4.43042e7	−	4.43042e7i	−0.144699	−	0.144699i
$675$	1.01059e7	+	1.75039e7i	0.0328596	+	0.0569145i
$676$	−1.90132e8			−0.615480
$677$			3.76311e8i			1.21278i	0.795169	+	0.606388i	$0.207382\pi$
$677$			3.76311e8i			1.21278i	−0.795169	+	0.606388i	$0.792618\pi$
$678$	4.79483e7	+	8.30490e7i	0.153845	+	0.266468i
$679$	1.85603e8	−	4.97321e7i	0.592891	−	0.158865i
$680$	5.03391e7	−	5.03391e7i	0.160095	−	0.160095i
$681$	1.19003e8	+	3.18868e7i	0.376806	+	0.100965i
$682$	3.37288e7	+	5.84200e7i	0.106328	+	0.184166i
$683$	−4.72396e7	+	1.76301e8i	−0.148267	+	0.553340i	0.851321	+	0.524645i	$0.175802\pi$
$683$	−4.72396e7	+	1.76301e8i	−0.148267	+	0.553340i	−0.999588	+	0.0286949i	$0.990865\pi$
$684$	−1.00784e8	−	3.76131e8i	−0.314937	−	1.17536i
$685$	1.15718e8	−	3.10065e7i	0.360022	−	0.0964675i
$686$	−6.15686e7	−	1.64973e7i	−0.190716	−	0.0511022i
$687$	5.76455e8	−	3.32816e8i	1.77785	−	1.02644i
$688$	1.56364e7	−	5.83558e7i	0.0480144	−	0.179192i
$689$	2.96083e8	+	2.96083e8i	0.905225	+	0.905225i
$690$	6.20786e6	+	2.31680e7i	0.0188971	+	0.0705248i
$691$	2.53423e8	−	1.46314e8i	0.768089	−	0.443456i	−0.0641035	−	0.997943i	$-0.520419\pi$
$691$	2.53423e8	−	1.46314e8i	0.768089	−	0.443456i	0.832192	+	0.554487i	$0.187085\pi$
$692$	−1.83259e8			−0.553027
$693$			2.97088e8i			0.892660i
$694$	−1.94263e7	+	1.12158e7i	−0.0581181	+	0.0335545i
$695$	−8.95579e7	+	8.95579e7i	−0.266778	+	0.266778i
$696$	−3.56745e8	−	2.05967e8i	−1.05811	−	0.610899i
$697$	6.12248e7	−	6.12248e7i	0.180813	−	0.180813i
$698$	4.45939e7	+	1.66427e8i	0.131132	+	0.489392i
$699$	2.78027e8	−	4.81558e8i	0.814060	−	1.40999i
$700$	9.37741e7	−	1.62422e8i	0.273394	−	0.473532i
$701$	−1.21102e8	+	4.51960e8i	−0.351559	+	1.31204i	0.533201	+	0.845988i	$0.320989\pi$
$701$	−1.21102e8	+	4.51960e8i	−0.351559	+	1.31204i	−0.884760	+	0.466047i	$0.845678\pi$
$702$			1.79795e7i			0.0519717i
$703$	−2.04590e8	−	4.72698e8i	−0.588868	−	1.36056i
$704$	1.38720e8			0.397578
$705$	−6.59446e8	−	1.76698e8i	−1.88197	−	0.504272i
$706$	1.69076e8	+	9.76160e7i	0.480472	+	0.277400i
$707$	1.21522e8	+	7.01606e7i	0.343871	+	0.198534i
$708$	−1.02863e7	+	2.75620e6i	−0.0289840	+	0.00776625i
$709$	1.76921e8	+	1.76921e8i	0.496410	+	0.496410i	0.910318	−	0.413909i	$-0.135837\pi$
$709$	1.76921e8	+	1.76921e8i	0.496410	+	0.496410i	−0.413909	+	0.910318i	$0.635837\pi$
$710$	4.51221e7	−	7.81537e7i	0.126071	−	0.218361i
$711$	4.25757e7	+	4.25757e7i	0.118455	+	0.118455i
$712$	3.01779e7	+	5.22697e7i	0.0836083	+	0.144814i
$713$	7.63047e7			0.210515
$714$			1.01794e8i			0.279658i
$715$	1.36870e8	+	2.37065e8i	0.374446	+	0.648559i
$716$	−5.00611e8	+	1.34138e8i	−1.36383	+	0.365438i
$717$	−3.41421e8	+	3.41421e8i	−0.926260	+	0.926260i
$718$	−1.62175e7	−	4.34546e6i	−0.0438137	−	0.0117398i
$719$	−1.86271e8	−	3.22631e8i	−0.501140	−	0.868000i	−0.999999	−	0.00131668i	$-0.999581\pi$
$719$	−1.86271e8	−	3.22631e8i	−0.501140	−	0.868000i	0.498859	−	0.866683i	$-0.333752\pi$
$720$	−4.52580e7	+	1.68905e8i	−0.121255	+	0.452528i
$721$	1.74518e8	+	6.51311e8i	0.465624	+	1.73773i
$722$	−1.32413e8	+	3.54799e7i	−0.351819	+	0.0942695i
$723$	−3.52243e8	−	9.43833e7i	−0.932025	−	0.249735i
$724$	−1.05617e8	+	6.09781e7i	−0.278304	+	0.160679i
$725$	7.49896e7	−	2.79865e8i	0.196783	−	0.734403i
$726$	−3.79392e7	−	3.79392e7i	−0.0991468	−	0.0991468i
$727$	1.59490e8	+	5.95224e8i	0.415078	+	1.54909i	0.784679	+	0.619902i	$0.212828\pi$
$727$	1.59490e8	+	5.95224e8i	0.415078	+	1.54909i	−0.369601	+	0.929191i	$0.620506\pi$
$728$	3.03686e8	−	1.75333e8i	0.787101	−	0.454433i
$729$	3.10133e8			0.800508
$730$			4.10678e6i			0.0105568i
$731$	−4.72902e7	+	2.73030e7i	−0.121065	+	0.0698970i
$732$	−2.01633e8	+	2.01633e8i	−0.514078	+	0.514078i
$733$	−1.30773e8	−	7.55021e7i	−0.332053	−	0.191711i	0.324699	−	0.945817i	$-0.394737\pi$
$733$	−1.30773e8	−	7.55021e7i	−0.332053	−	0.191711i	−0.656752	+	0.754106i	$0.728070\pi$
$734$	7.12381e7	−	7.12381e7i	0.180146	−	0.180146i
$735$	−4.65362e7	−	1.73675e8i	−0.117200	−	0.437398i
$736$	−3.92830e7	+	6.80402e7i	−0.0985306	+	0.170660i
$737$	8.91386e7	−	1.54393e8i	0.222671	−	0.385677i
$738$	1.32763e7	−	4.95479e7i	0.0330300	−	0.123270i
$739$		−	2.31144e8i		−	0.572730i	−0.958121	−	0.286365i	$-0.907553\pi$
$739$		−	2.31144e8i		−	0.572730i	0.958121	−	0.286365i	$-0.0924470\pi$
$740$	−2.99300e7	+	2.58819e8i	−0.0738604	+	0.638706i
$741$	1.07834e9			2.65033
$742$	−1.43421e8	−	3.84296e7i	−0.351076	−	0.0940705i
$743$	−4.28324e8	−	2.47293e8i	−1.04425	−	0.602901i	−0.123219	−	0.992379i	$-0.539322\pi$
$743$	−4.28324e8	−	2.47293e8i	−1.04425	−	0.602901i	−0.921035	+	0.389479i	$0.872655\pi$
$744$	−2.44679e8	−	1.41265e8i	−0.594125	−	0.343018i
$745$	−3.59614e8	+	9.63583e7i	−0.869697	+	0.233034i
$746$	1.53416e7	+	1.53416e7i	0.0369533	+	0.0369533i
$747$	−2.75431e8	+	4.77061e8i	−0.660772	+	1.14449i
$748$	−1.20750e8	−	1.20750e8i	−0.288525	−	0.288525i
$749$	−2.00887e8	−	3.47947e8i	−0.478087	−	0.828072i
$750$	1.87876e8			0.445336
$751$		−	4.13182e8i		−	0.975488i	−0.872987	−	0.487744i	$-0.837820\pi$
$751$		−	4.13182e8i		−	0.975488i	0.872987	−	0.487744i	$-0.162180\pi$
$752$	−3.09834e8	−	5.36649e8i	−0.728578	−	1.26193i
$753$	−4.57963e8	+	1.22711e8i	−1.07262	+	0.287407i
$754$	1.82249e8	−	1.82249e8i	0.425158	−	0.425158i
$755$	3.59725e8	+	9.63880e7i	0.835852	+	0.223966i
$756$	3.12927e7	+	5.42005e7i	0.0724231	+	0.125440i
$757$	2.14291e7	−	7.99746e7i	0.0493988	−	0.184359i	−0.936818	−	0.349817i	$-0.886244\pi$
$757$	2.14291e7	−	7.99746e7i	0.0493988	−	0.184359i	0.986217	+	0.165458i	$0.0529103\pi$
$758$	−2.74981e7	−	1.02624e8i	−0.0631386	−	0.235637i
$759$	1.16809e8	−	3.12990e7i	0.267148	−	0.0715822i
$760$	2.58307e8	+	6.92133e7i	0.588432	+	0.157670i
$761$	2.26034e8	−	1.30501e8i	0.512884	−	0.296114i	−0.221134	−	0.975243i	$-0.570976\pi$
$761$	2.26034e8	−	1.30501e8i	0.512884	−	0.296114i	0.734018	+	0.679130i	$0.237643\pi$
$762$	−6.84165e7	+	2.55334e8i	−0.154631	+	0.577090i
$763$	6.34561e8	+	6.34561e8i	1.42856	+	1.42856i
$764$	−1.46096e8	−	5.45239e8i	−0.327612	−	1.22266i
$765$	1.36877e8	−	7.90259e7i	0.305735	−	0.176516i
$766$	−1.39891e8			−0.311246
$767$		−	1.40047e7i		−	0.0310375i
$768$	−1.07317e8	+	6.19593e7i	−0.236910	+	0.136780i
$769$	−3.28551e8	+	3.28551e8i	−0.722477	+	0.722477i	−0.969109	−	0.246632i	$-0.920676\pi$
$769$	−3.28551e8	+	3.28551e8i	−0.722477	+	0.722477i	0.246632	+	0.969109i	$0.420676\pi$
$770$	−8.40636e7	−	4.85341e7i	−0.184135	−	0.106310i
$771$	−3.63710e8	+	3.63710e8i	−0.793583	+	0.793583i
$772$	1.75308e8	+	6.54257e8i	0.381021	+	1.42199i
$773$	2.43967e8	−	4.22563e8i	0.528193	−	0.914858i	−0.471267	−	0.881991i	$-0.656203\pi$
$773$	2.43967e8	−	4.22563e8i	0.528193	−	0.914858i	0.999460	−	0.0328667i	$-0.0104637\pi$
$774$	−1.61752e7	+	2.80163e7i	−0.0348840	+	0.0604209i
$775$	5.14327e7	−	1.91949e8i	0.110493	−	0.412365i
$776$			1.37532e8i			0.294319i
$777$	−4.86426e8	−	6.13639e8i	−1.03694	−	1.30813i
$778$	−3.68460e7			−0.0782441
$779$	3.14166e8	+	8.41805e7i	0.664579	+	0.178073i
$780$	−4.72386e8	−	2.72732e8i	−0.995435	−	0.574715i
$781$	−3.94038e8	−	2.27498e8i	−0.827152	−	0.477556i
$782$	1.90070e7	−	5.09291e6i	0.0397459	−	0.0106499i
$783$	6.83674e7	+	6.83674e7i	0.142418	+	0.142418i
$784$	8.15997e7	−	1.41335e8i	0.169333	−	0.293292i
$785$	−3.63313e8	−	3.63313e8i	−0.751056	−	0.751056i
$786$	−1.47191e8	−	2.54942e8i	−0.303119	−	0.525017i
$787$	2.10061e8			0.430945			0.215473	−	0.976510i	$-0.430871\pi$
$787$	2.10061e8			0.430945			0.215473	+	0.976510i	$0.430871\pi$
$788$			7.48987e8i			1.53072i
$789$	−2.43796e8	−	4.22266e8i	−0.496358	−	0.859717i
$790$	−1.90026e7	+	5.09172e6i	−0.0385417	+	0.0103272i
$791$	−3.10413e8	+	3.10413e8i	−0.627207	+	0.627207i
$792$	−2.05396e8	−	5.50356e7i	−0.413443	−	0.110782i
$793$	−1.87502e8	−	3.24762e8i	−0.375998	−	0.651248i
$794$	−6.39358e7	+	2.38612e8i	−0.127727	+	0.476683i
$795$	1.25644e8	+	4.68912e8i	0.250059	+	0.933232i
$796$	5.63219e8	−	1.50914e8i	1.11670	−	0.299220i
$797$	4.32538e8	+	1.15898e8i	0.854376	+	0.228929i	0.659320	−	0.751863i	$-0.270844\pi$
$797$	4.32538e8	+	1.15898e8i	0.854376	+	0.228929i	0.195056	+	0.980792i	$0.437511\pi$
$798$	−3.31150e8	+	1.91190e8i	−0.651653	+	0.376232i
$799$	−1.44963e8	+	5.41007e8i	−0.284194	+	1.06063i
$800$	1.44681e8	+	1.44681e8i	0.282580	+	0.282580i
$801$	3.46812e7	+	1.29432e8i	0.0674834	+	0.251851i
$802$	−7.63986e6	+	4.41087e6i	−0.0148102	+	0.00855070i
$803$	2.07057e7			0.0399892
$804$			3.55242e8i			0.683528i
$805$	−9.50885e7	+	5.48994e7i	−0.182281	+	0.105240i
$806$	1.24998e8	−	1.24998e8i	0.238725	−	0.238725i
$807$	2.19402e8	+	1.26672e8i	0.417464	+	0.241023i
$808$	−7.10183e7	+	7.10183e7i	−0.134628	+	0.134628i
$809$	−1.55754e7	−	5.81282e7i	−0.0294167	−	0.109785i	0.949656	−	0.313293i	$-0.101432\pi$
$809$	−1.55754e7	−	5.81282e7i	−0.0294167	−	0.109785i	−0.979073	+	0.203508i	$0.934766\pi$
$810$	−6.21894e7	+	1.07715e8i	−0.117020	+	0.202685i
$811$	−4.32795e8	+	7.49623e8i	−0.811371	+	1.40534i	0.100534	+	0.994934i	$0.467945\pi$
$811$	−4.32795e8	+	7.49623e8i	−0.811371	+	1.40534i	−0.911905	+	0.410402i	$0.865388\pi$
$812$	2.32204e8	−	8.66597e8i	0.433712	−	1.61864i
$813$			9.22788e8i			1.71724i
$814$	−1.32932e8	−	1.53724e7i	−0.246466	−	0.0285015i
$815$	−6.18568e8			−1.14265
$816$	2.91788e8	+	7.81844e7i	0.537028	+	0.143896i
$817$	−1.77641e8	−	1.02561e8i	−0.325745	−	0.188069i
$818$	−1.49446e8	−	8.62825e7i	−0.273038	−	0.157639i
$819$	7.51998e8	−	2.01497e8i	1.36888	−	0.366790i
$820$	−1.16335e8	−	1.16335e8i	−0.210994	−	0.210994i
$821$	−3.03636e8	+	5.25913e8i	−0.548686	+	0.950351i	0.449679	+	0.893190i	$0.351538\pi$
$821$	−3.03636e8	+	5.25913e8i	−0.548686	+	0.950351i	−0.998365	+	0.0571612i	$0.981795\pi$
$822$	−8.66972e7	−	8.66972e7i	−0.156095	−	0.156095i
$823$	−3.41663e7	−	5.91777e7i	−0.0612912	−	0.106160i	0.833752	−	0.552140i	$-0.186189\pi$
$823$	−3.41663e7	−	5.91777e7i	−0.0612912	−	0.106160i	−0.895043	+	0.445980i	$0.852855\pi$
$824$	−4.82621e8			−0.862631
$825$		−	3.14938e8i		−	0.560872i
$826$	2.48304e6	+	4.30075e6i	0.00440598	+	0.00763139i
$827$	5.01803e8	−	1.34458e8i	0.887190	−	0.237722i	0.213683	−	0.976903i	$-0.431454\pi$
$827$	5.01803e8	−	1.34458e8i	0.887190	−	0.237722i	0.673507	+	0.739181i	$0.264787\pi$
$828$	−8.09184e7	+	8.09184e7i	−0.142546	+	0.142546i
$829$	1.67391e8	+	4.48523e7i	0.293811	+	0.0787264i	0.402714	−	0.915326i	$-0.368067\pi$
$829$	1.67391e8	+	4.48523e7i	0.293811	+	0.0787264i	−0.108903	+	0.994052i	$0.534734\pi$
$830$	−8.99922e7	−	1.55871e8i	−0.157388	−	0.272603i
$831$	−2.20187e7	+	8.21747e7i	−0.0383696	+	0.143197i
$832$	−9.40858e7	−	3.51133e8i	−0.163363	−	0.609679i
$833$	−1.42483e8	+	3.81781e7i	−0.246506	+	0.0660511i
$834$	1.25206e8	+	3.35489e7i	0.215838	+	0.0578337i
$835$	1.60754e7	−	9.28113e6i	0.0276123	−	0.0159420i
$836$	1.66024e8	−	6.19611e8i	0.284153	−	1.06048i
$837$	4.68908e7	+	4.68908e7i	0.0799670	+	0.0799670i
$838$	−8.66213e7	−	3.23275e8i	−0.147195	−	0.549339i
$839$	8.33089e8	−	4.80984e8i	1.41061	−	0.814414i	0.415161	−	0.909748i	$-0.363725\pi$
$839$	8.33089e8	−	4.80984e8i	1.41061	−	0.814414i	0.995445	+	0.0953345i	$0.0303921\pi$
$840$	4.06548e8			0.685921
$841$		−	7.91183e8i		−	1.33011i
$842$	7.20282e7	−	4.15855e7i	0.120661	−	0.0696636i
$843$	−6.11353e7	+	6.11353e7i	−0.102049	+	0.102049i
$844$	−2.49402e7	−	1.43992e7i	−0.0414833	−	0.0239504i
$845$	2.04982e8	−	2.04982e8i	0.339739	−	0.339739i
$846$	8.58805e7	+	3.20511e8i	0.141835	+	0.529336i
$847$	1.22808e8	−	2.12709e8i	0.202104	−	0.350055i
$848$	−2.20313e8	+	3.81594e8i	−0.361288	+	0.625769i
$849$	2.48229e8	−	9.26402e8i	0.405629	−	1.51383i
$850$		−	5.12461e7i		−	0.0834458i
$851$	−9.02421e7	+	1.21527e8i	−0.146427	+	0.197189i
$852$	9.06643e8			1.46595
$853$	9.02182e7	+	2.41739e7i	0.145361	+	0.0389493i	0.330766	−	0.943713i	$-0.392693\pi$
$853$	9.02182e7	+	2.41739e7i	0.145361	+	0.0389493i	−0.185405	+	0.982662i	$0.559360\pi$
$854$	1.15161e8	+	6.64883e7i	0.184898	+	0.106751i
$855$	5.14165e8	+	2.96853e8i	0.822629	+	0.474945i
$856$	2.77772e8	−	7.44288e7i	0.442861	−	0.118664i
$857$	−2.79857e8	−	2.79857e8i	−0.444624	−	0.444624i	0.448938	−	0.893563i	$-0.351802\pi$
$857$	−2.79857e8	−	2.79857e8i	−0.444624	−	0.444624i	−0.893563	+	0.448938i	$0.851802\pi$
$858$	1.40078e8	−	2.42623e8i	0.221773	−	0.384122i
$859$	4.08888e7	+	4.08888e7i	0.0645098	+	0.0645098i	0.738626	−	0.674116i	$-0.235475\pi$
$859$	4.08888e7	+	4.08888e7i	0.0645098	+	0.0645098i	−0.674116	+	0.738626i	$0.735475\pi$
$860$	5.18794e7	+	8.98577e7i	0.0815642	+	0.141273i
$861$	4.94463e8			0.774684
$862$			2.04283e8i			0.318942i
$863$	3.83920e8	+	6.64968e8i	0.597321	+	1.03459i	0.993215	+	0.116294i	$0.0371016\pi$
$863$	3.83920e8	+	6.64968e8i	0.597321	+	1.03459i	−0.395893	+	0.918296i	$0.629565\pi$
$864$	−6.59523e7	+	1.76719e7i	−0.102256	+	0.0273994i
$865$	1.97572e8	−	1.97572e8i	0.305265	−	0.305265i
$866$	−1.88090e8	−	5.03986e7i	−0.289609	−	0.0776006i
$867$	3.13162e8	+	5.42413e8i	0.480521	+	0.832286i
$868$	1.59261e8	−	5.94368e8i	0.243528	−	0.908859i
$869$	2.56716e7	+	9.58077e7i	0.0391195	+	0.145996i
$870$	2.88630e8	−	7.73382e7i	0.438312	−	0.117445i
$871$	−4.51260e8	−	1.20915e8i	−0.682924	−	0.182989i
$872$	−5.56264e8	+	3.21159e8i	−0.838942	+	0.484363i
$873$	−7.90275e7	+	2.94934e8i	−0.118778	+	0.443285i
$874$	5.22669e7	+	5.22669e7i	0.0782876	+	0.0782876i
$875$	2.22597e8	+	8.30743e8i	0.332273	+	1.24006i
$876$	−3.57313e7	+	2.06295e7i	−0.0531541	+	0.0306886i
$877$	7.72728e8			1.14559			0.572793	−	0.819700i	$-0.305860\pi$
$877$	7.72728e8			1.14559			0.572793	+	0.819700i	$0.305860\pi$
$878$			5.37935e7i			0.0794779i
$879$	1.15558e9	−	6.67175e8i	1.70151	−	0.982366i
$880$	−2.03687e8	+	2.03687e8i	−0.298893	+	0.298893i
$881$	−4.80567e8	−	2.77455e8i	−0.702791	−	0.405757i	0.105595	−	0.994409i	$-0.466325\pi$
$881$	−4.80567e8	−	2.77455e8i	−0.702791	−	0.405757i	−0.808386	+	0.588653i	$0.799659\pi$
$882$	−6.17935e7	+	6.17935e7i	−0.0900610	+	0.0900610i
$883$	6.11811e7	+	2.28331e8i	0.0888659	+	0.331652i	0.996018	−	0.0891506i	$-0.0284152\pi$
$883$	6.11811e7	+	2.28331e8i	0.0888659	+	0.331652i	−0.907152	+	0.420802i	$0.861749\pi$
$884$	−2.23748e8	+	3.87544e8i	−0.323894	+	0.561001i
$885$	8.11823e6	−	1.40612e7i	0.0117120	−	0.0202858i
$886$	−7.42876e6	+	2.77245e7i	−0.0106811	+	0.0398624i
$887$			1.82074e8i			0.260902i	0.991455	+	0.130451i	$0.0416426\pi$
$887$			1.82074e8i			0.260902i	−0.991455	+	0.130451i	$0.958357\pi$
$888$	5.14357e8	−	2.22620e8i	0.734558	−	0.317926i
$889$	−1.21009e9			−1.72231
$890$	−4.22896e7	−	1.13315e7i	−0.0599878	−	0.0160737i
$891$	5.43082e8	+	3.13549e8i	0.767773	+	0.443274i
$892$	−9.32762e8	−	5.38531e8i	−1.31425	−	0.758780i
$893$	−2.03224e9	+	5.44538e8i	−2.85379	+	0.764670i
$894$	2.69427e8	+	2.69427e8i	0.377076	+	0.377076i
$895$	3.95096e8	−	6.84327e8i	0.551104	−	0.954541i
$896$	5.84790e8	+	5.84790e8i	0.812972	+	0.812972i
$897$	−1.58450e8	−	2.74443e8i	−0.219540	−	0.380254i
$898$	−2.58887e8			−0.357504
$899$		−	9.50613e8i		−	1.30835i
$900$	1.49013e8	+	2.58098e8i	0.204407	+	0.354044i
$901$	3.84693e8	−	1.03078e8i	0.525945	−	0.140927i
$902$	5.97512e7	−	5.97512e7i	0.0814192	−	0.0814192i
$903$	−3.01214e8	−	8.07102e7i	−0.409084	−	0.109614i
$904$	−1.57104e8	−	2.72112e8i	−0.212658	−	0.368335i
$905$	4.81256e7	−	1.79607e8i	0.0649278	−	0.242314i
$906$	−9.86476e7	−	3.68158e8i	−0.132648	−	0.495050i
$907$	3.70095e8	−	9.91667e7i	0.496011	−	0.132906i	−0.00213693	−	0.999998i	$-0.500680\pi$
$907$	3.70095e8	−	9.91667e7i	0.496011	−	0.132906i	0.498148	+	0.867092i	$0.334014\pi$
$908$	−1.85510e8	−	4.97072e7i	−0.247805	−	0.0663990i
$909$	−1.93106e8	+	1.11490e8i	−0.257101	+	0.148437i
$910$	−6.58356e7	+	2.45702e8i	−0.0873648	+	0.326050i
$911$	−8.43618e8	−	8.43618e8i	−1.11581	−	1.11581i	−0.992349	−	0.123462i	$-0.960600\pi$
$911$	−8.43618e8	−	8.43618e8i	−1.11581	−	1.11581i	−0.123462	−	0.992349i	$-0.539400\pi$
$912$	2.93692e8	+	1.09607e9i	0.387176	+	1.44496i
$913$	−7.85875e8	+	4.53725e8i	−1.03262	+	0.596185i
$914$	3.71234e8			0.486194
$915$		−	4.34764e8i		−	0.567531i
$916$	−8.98614e8	+	5.18815e8i	−1.16919	+	0.675035i
$917$	9.52900e8	−	9.52900e8i	1.23577	−	1.23577i
$918$	1.48099e7	+	8.55048e6i	0.0191436	+	0.0110526i
$919$	−6.59914e8	+	6.59914e8i	−0.850238	+	0.850238i	−0.990162	−	0.139924i	$-0.955314\pi$
$919$	−6.59914e8	+	6.59914e8i	−0.850238	+	0.850238i	0.139924	+	0.990162i	$0.455314\pi$
$920$	−2.03402e7	−	7.59107e7i	−0.0261211	−	0.0974854i
$921$	−6.54800e8	+	1.13415e9i	−0.838165	+	1.45174i
$922$	1.69337e8	−	2.93301e8i	0.216053	−	0.374214i
$923$	−3.08596e8	+	1.15170e9i	−0.392451	+	1.46465i
$924$		−	9.75202e8i		−	1.23617i
$925$	2.44882e8	+	3.08924e8i	0.309408	+	0.390325i
$926$	−4.19014e8			−0.527710
$927$	−1.03497e9	−	2.77320e8i	−1.29924	−	0.348131i
$928$	8.47652e8	+	4.89392e8i	1.06065	+	0.612369i
$929$	9.71663e8	+	5.60990e8i	1.21191	+	0.699694i	0.963174	−	0.268879i	$-0.0866531\pi$
$929$	9.71663e8	+	5.60990e8i	1.21191	+	0.699694i	0.248731	+	0.968573i	$0.419986\pi$
$930$	1.97961e8	−	5.30435e7i	0.246111	−	0.0659453i
$931$	−3.91811e8	−	3.91811e8i	−0.485542	−	0.485542i
$932$	−4.33407e8	+	7.50683e8i	−0.535363	+	0.927275i
$933$	−3.03580e8	−	3.03580e8i	−0.373790	−	0.373790i
$934$	−1.18932e8	−	2.05996e8i	−0.145968	−	0.252823i
$935$	2.60363e8			0.318526
$936$			5.57231e8i			0.679528i
$937$	2.82499e8	+	4.89302e8i	0.343398	+	0.594783i	0.985061	−	0.172203i	$-0.0550887\pi$
$937$	2.82499e8	+	4.89302e8i	0.343398	+	0.594783i	−0.641663	+	0.766986i	$0.721755\pi$
$938$	1.60017e8	−	4.28765e7i	0.193891	−	0.0519530i
$939$	2.47734e8	−	2.47734e8i	0.299219	−	0.299219i
$940$	1.02799e9	+	2.75448e8i	1.23767	+	0.331632i
$941$	−4.60649e8	−	7.97868e8i	−0.552842	−	0.957551i	−0.998068	−	0.0621327i	$-0.980210\pi$
$941$	−4.60649e8	−	7.97868e8i	−0.552842	−	0.957551i	0.445225	−	0.895419i	$-0.353124\pi$
$942$	−1.36099e8	+	5.07929e8i	−0.162818	+	0.607646i
$943$	−2.47388e7	−	9.23263e7i	−0.0295014	−	0.110101i
$944$	1.42350e7	−	3.81427e6i	0.0169217	−	0.00453414i
$945$	−9.21706e7	−	2.46970e7i	−0.109219	−	0.0292651i
$946$	−4.61519e7	+	2.66458e7i	−0.0545151	+	0.0314743i
$947$	2.09223e8	−	7.80832e8i	0.246354	−	0.919406i	−0.726344	−	0.687332i	$-0.758782\pi$
$947$	2.09223e8	−	7.80832e8i	0.246354	−	0.919406i	0.972698	−	0.232075i	$-0.0745514\pi$
$948$	−1.39756e8	−	1.39756e8i	−0.164038	−	0.164038i
$949$	−1.40434e7	−	5.24108e7i	−0.0164314	−	0.0613228i
$950$	1.66711e8	−	9.62507e7i	0.194444	−	0.112262i
$951$	−8.67039e8			−1.00809
$952$		−	3.33531e8i		−	0.386567i
$953$	−4.38199e8	+	2.52994e8i	−0.506282	+	0.292302i	−0.731304	−	0.682052i	$-0.761088\pi$
$953$	−4.38199e8	+	2.52994e8i	−0.506282	+	0.292302i	0.225022	+	0.974354i	$0.427755\pi$
$954$	1.66838e8	−	1.66838e8i	0.192154	−	0.192154i
$955$	7.45333e8	+	4.30318e8i	0.855737	+	0.494060i
$956$	5.32229e8	−	5.32229e8i	0.609151	−	0.609151i
$957$	−3.89926e8	−	1.45522e9i	−0.444884	−	1.66033i
$958$	1.22408e8	−	2.12018e8i	0.139224	−	0.241144i
$959$	2.80635e8	−	4.86074e8i	0.318190	−	0.551121i
$960$	1.09079e8	−	4.07089e8i	0.123290	−	0.460125i
$961$			2.35512e8i			0.265365i
$962$	5.12490e7	+	3.46908e8i	0.0575652	+	0.389663i
$963$	6.38445e8			0.714899
$964$	5.49099e8	+	1.47131e8i	0.612942	+	0.164237i
$965$	−8.94358e8	−	5.16358e8i	−0.995244	−	0.574604i
$966$	9.73176e7	+	5.61864e7i	0.107959	+	0.0623304i
$967$	1.06639e9	−	2.85738e8i	1.17933	−	0.316001i	0.384670	−	0.923054i	$-0.374315\pi$
$967$	1.06639e9	−	2.85738e8i	1.17933	−	0.316001i	0.794661	+	0.607053i	$0.207649\pi$
$968$	1.24309e8	+	1.24309e8i	0.137049	+	0.137049i
$969$	5.12822e8	−	8.88233e8i	0.563631	−	0.976238i
$970$	−7.05437e7	−	7.05437e7i	−0.0772935	−	0.0772935i
$971$	1.44783e8	+	2.50771e8i	0.158146	+	0.273917i	0.934200	−	0.356749i	$-0.116115\pi$
$971$	1.44783e8	+	2.50771e8i	0.158146	+	0.273917i	−0.776054	+	0.630666i	$0.782782\pi$
$972$	−1.13961e9			−1.24096
$973$			5.93382e8i			0.644163i
$974$	1.74720e7	+	3.02625e7i	0.0189089	+	0.0327512i
$975$	−7.97180e8	+	2.13604e8i	−0.860088	+	0.230460i
$976$	2.79037e8	−	2.79037e8i	0.300132	−	0.300132i
$977$	4.58333e8	+	1.22810e8i	0.491471	+	0.131689i	0.496039	−	0.868300i	$-0.334787\pi$
$977$	4.58333e8	+	1.22810e8i	0.491471	+	0.131689i	−0.00456805	+	0.999990i	$0.501454\pi$
$978$	3.16535e8	+	5.48254e8i	0.338380	+	0.586091i
$979$	−5.71313e7	+	2.13217e8i	−0.0608872	+	0.227234i
$980$	7.25436e7	+	2.70736e8i	0.0770763	+	0.287653i
$981$	−1.37744e9	+	3.69085e8i	−1.45904	+	0.390948i
$982$	−4.66123e8	−	1.24897e8i	−0.492227	−	0.131892i
$983$	−2.97978e8	+	1.72038e8i	−0.313707	+	0.181119i	−0.648584	−	0.761143i	$-0.724639\pi$
$983$	−2.97978e8	+	1.72038e8i	−0.313707	+	0.181119i	0.334877	+	0.942262i	$0.391305\pi$
$984$	−9.15994e7	+	3.41854e8i	−0.0961407	+	0.358802i
$985$	−8.07486e8	−	8.07486e8i	−0.844941	−	0.844941i
$986$	−6.34480e7	−	2.36791e8i	−0.0661892	−	0.247021i
$987$	−2.77001e9	+	1.59927e9i	−2.88091	+	1.66330i
$988$	−1.68098e9			−1.74298
$989$			6.02809e7i			0.0623147i
$990$	1.33582e8	−	7.71238e7i	0.137671	−	0.0794845i
$991$	−2.74572e7	+	2.74572e7i	−0.0282120	+	0.0282120i	−0.721072	−	0.692860i	$-0.756350\pi$
$991$	−2.74572e7	+	2.74572e7i	−0.0282120	+	0.0282120i	0.692860	+	0.721072i	$0.256350\pi$
$992$	5.81375e8	+	3.35657e8i	0.595554	+	0.343843i
$993$	−1.46956e8	+	1.46956e8i	−0.150085	+	0.150085i
$994$	−1.09429e8	−	4.08393e8i	−0.111422	−	0.415833i
$995$	−4.44508e8	+	7.69910e8i	−0.451243	+	0.781575i
$996$	9.04112e8	−	1.56597e9i	0.915048	−	1.58491i
$997$	−1.57149e8	+	5.86488e8i	−0.158572	+	0.591799i	0.840201	+	0.542275i	$0.182437\pi$
$997$	−1.57149e8	+	5.86488e8i	−0.158572	+	0.591799i	−0.998773	+	0.0495235i	$0.984230\pi$
$998$			2.89297e8i			0.291040i
$999$	−1.30136e8	+	1.92251e7i	−0.130528	+	0.0192829i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.7.g.a.8.9	✓	72
37.14	odd	12	inner	37.7.g.a.14.9	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.7.g.a.8.9	✓	72	1.1	even	1	trivial
37.7.g.a.14.9	yes	72	37.14	odd	12	inner

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	37.g (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.34959 - 0.629570i) q^{2} +(32.2680 + 18.6299i) q^{3} +(-50.3014 - 29.0415i) q^{4} +(85.5401 - 22.9204i) q^{5} +(-64.0877 - 64.0877i) q^{6} +(207.449 - 359.312i) q^{7} +(209.985 + 209.985i) q^{8} +(329.649 + 570.970i) q^{9} +O(q^{10})\)	\(q+(-2.34959 - 0.629570i) q^{2} +(32.2680 + 18.6299i) q^{3} +(-50.3014 - 29.0415i) q^{4} +(85.5401 - 22.9204i) q^{5} +(-64.0877 - 64.0877i) q^{6} +(207.449 - 359.312i) q^{7} +(209.985 + 209.985i) q^{8} +(329.649 + 570.970i) q^{9} -215.414 q^{10} +1086.08i q^{11} +(-1082.08 - 1874.23i) q^{12} +(2749.12 - 736.623i) q^{13} +(-713.632 + 713.632i) q^{14} +(3187.21 + 854.011i) q^{15} +(1497.48 + 2593.71i) q^{16} +(700.628 - 2614.78i) q^{17} +(-415.075 - 1549.08i) q^{18} +(9822.17 - 2631.84i) q^{19} +(-4968.43 - 1331.29i) q^{20} +(13387.9 - 7729.52i) q^{21} +(683.764 - 2551.84i) q^{22} +(-2113.08 - 2113.08i) q^{23} +(2863.79 + 10687.8i) q^{24} +(-6739.89 + 3891.28i) q^{25} -6923.05 q^{26} -2597.06i q^{27} +(-20870.0 + 12049.3i) q^{28} +(-26325.0 + 26325.0i) q^{29} +(-6950.98 - 4013.15i) q^{30} +(-18055.4 + 18055.4i) q^{31} +(-6804.57 - 25395.0i) q^{32} +(-20233.6 + 35045.7i) q^{33} +(-3292.37 + 5702.56i) q^{34} +(9509.62 - 35490.4i) q^{35} -38294.1i q^{36} +(-7402.67 - 50109.2i) q^{37} -24735.0 q^{38} +(102432. + 27446.5i) q^{39} +(22775.1 + 13149.2i) q^{40} +(27700.1 + 15992.7i) q^{41} +(-36322.4 + 9732.56i) q^{42} +(-14263.8 - 14263.8i) q^{43} +(31541.5 - 54631.4i) q^{44} +(41285.1 + 41285.1i) q^{45} +(3634.53 + 6295.19i) q^{46} -206904. q^{47} +111592. i q^{48} +(-27245.7 - 47190.9i) q^{49} +(18285.8 - 4899.66i) q^{50} +(71321.0 - 71321.0i) q^{51} +(-159677. - 42785.4i) q^{52} +(73561.4 + 127412. i) q^{53} +(-1635.03 + 6102.01i) q^{54} +(24893.4 + 92903.4i) q^{55} +(119011. - 31889.0i) q^{56} +(365973. + 98062.2i) q^{57} +(78426.2 - 45279.4i) q^{58} +(1273.56 - 4753.00i) q^{59} +(-135520. - 135520. i) q^{60} +(-34102.2 - 127271. i) q^{61} +(53789.7 - 31055.5i) q^{62} +273542. q^{63} -127726. i q^{64} +(218276. - 126022. i) q^{65} +(69604.4 - 69604.4i) q^{66} +(-142156. - 82073.6i) q^{67} +(-111180. + 111180. i) q^{68} +(-28818.3 - 107551. i) q^{69} +(-44687.4 + 77400.8i) q^{70} +(-209467. + 362807. i) q^{71} +(-50673.6 + 189117. i) q^{72} -19064.6i q^{73} +(-14154.0 + 122396. i) q^{74} -289977. q^{75} +(-570502. - 152866. i) q^{76} +(390242. + 225306. i) q^{77} +(-223393. - 128976. i) q^{78} +(88214.2 - 23636.9i) q^{79} +(187543. + 187543. i) q^{80} +(288697. - 500039. i) q^{81} +(-55015.4 - 55015.4i) q^{82} +(417764. + 723588. i) q^{83} -897909. q^{84} -239727. i q^{85} +(24533.9 + 42494.0i) q^{86} +(-1.33989e6 + 359021. i) q^{87} +(-228061. + 228061. i) q^{88} +(196318. + 52603.2i) q^{89} +(-71011.1 - 122995. i) q^{90} +(305624. - 1.14060e6i) q^{91} +(44923.8 + 167658. i) q^{92} +(-918980. + 246240. i) q^{93} +(486139. + 130260. i) q^{94} +(779866. - 450256. i) q^{95} +(253537. - 946215. i) q^{96} +(327480. + 327480. i) q^{97} +(34306.1 + 128032. i) q^{98} +(-620119. + 358026. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{2} - 6 q^{3} + 264 q^{4} + 52 q^{5} - 132 q^{6} - 2 q^{7} - 1968 q^{8} + 8094 q^{9}+O(q^{10}) \) 72 * q - 2 * q^2 - 6 * q^3 + 264 * q^4 + 52 * q^5 - 132 * q^6 - 2 * q^7 - 1968 * q^8 + 8094 * q^9	\( 72 q - 2 q^{2} - 6 q^{3} + 264 q^{4} + 52 q^{5} - 132 q^{6} - 2 q^{7} - 1968 q^{8} + 8094 q^{9} + 1864 q^{10} + 1178 q^{12} + 2898 q^{13} + 10168 q^{14} + 1418 q^{15} + 23668 q^{16} - 16734 q^{17} + 30222 q^{18} - 20756 q^{19} + 27910 q^{20} - 22326 q^{21} + 40188 q^{22} + 23388 q^{23} + 51426 q^{24} - 54060 q^{25} + 31064 q^{26} - 84486 q^{28} - 101426 q^{29} - 280062 q^{30} - 112740 q^{31} + 66416 q^{32} + 27376 q^{33} + 45094 q^{34} + 152710 q^{35} - 23168 q^{37} - 67600 q^{38} + 386674 q^{39} - 473862 q^{40} - 566622 q^{41} - 569640 q^{42} - 33332 q^{43} + 667736 q^{44} + 399362 q^{45} + 303310 q^{46} + 352424 q^{47} - 402226 q^{49} - 190836 q^{50} - 525822 q^{51} - 290936 q^{52} + 365094 q^{53} + 1191884 q^{54} - 343392 q^{55} + 2217442 q^{56} + 73378 q^{57} - 581028 q^{58} - 576604 q^{59} + 2105904 q^{60} - 213462 q^{61} - 423156 q^{62} - 1483688 q^{63} + 2273880 q^{65} - 846680 q^{66} + 1591698 q^{67} - 3165948 q^{68} + 2464258 q^{69} + 2158358 q^{70} - 1388114 q^{71} + 1672988 q^{72} - 3228324 q^{74} + 1857268 q^{75} - 3488628 q^{76} + 846288 q^{77} - 6537300 q^{78} - 781076 q^{79} - 3635536 q^{80} - 2236868 q^{81} + 3720360 q^{82} - 944002 q^{83} + 6632744 q^{84} - 1174862 q^{86} - 1073982 q^{87} - 427452 q^{88} + 3381078 q^{89} + 412204 q^{90} - 2879114 q^{91} + 696698 q^{92} - 543710 q^{93} - 3545780 q^{94} - 268230 q^{95} - 9026178 q^{96} - 1842138 q^{97} - 7266130 q^{98} + 8295480 q^{99}+O(q^{100}) \) 72 * q - 2 * q^2 - 6 * q^3 + 264 * q^4 + 52 * q^5 - 132 * q^6 - 2 * q^7 - 1968 * q^8 + 8094 * q^9 + 1864 * q^10 + 1178 * q^12 + 2898 * q^13 + 10168 * q^14 + 1418 * q^15 + 23668 * q^16 - 16734 * q^17 + 30222 * q^18 - 20756 * q^19 + 27910 * q^20 - 22326 * q^21 + 40188 * q^22 + 23388 * q^23 + 51426 * q^24 - 54060 * q^25 + 31064 * q^26 - 84486 * q^28 - 101426 * q^29 - 280062 * q^30 - 112740 * q^31 + 66416 * q^32 + 27376 * q^33 + 45094 * q^34 + 152710 * q^35 - 23168 * q^37 - 67600 * q^38 + 386674 * q^39 - 473862 * q^40 - 566622 * q^41 - 569640 * q^42 - 33332 * q^43 + 667736 * q^44 + 399362 * q^45 + 303310 * q^46 + 352424 * q^47 - 402226 * q^49 - 190836 * q^50 - 525822 * q^51 - 290936 * q^52 + 365094 * q^53 + 1191884 * q^54 - 343392 * q^55 + 2217442 * q^56 + 73378 * q^57 - 581028 * q^58 - 576604 * q^59 + 2105904 * q^60 - 213462 * q^61 - 423156 * q^62 - 1483688 * q^63 + 2273880 * q^65 - 846680 * q^66 + 1591698 * q^67 - 3165948 * q^68 + 2464258 * q^69 + 2158358 * q^70 - 1388114 * q^71 + 1672988 * q^72 - 3228324 * q^74 + 1857268 * q^75 - 3488628 * q^76 + 846288 * q^77 - 6537300 * q^78 - 781076 * q^79 - 3635536 * q^80 - 2236868 * q^81 + 3720360 * q^82 - 944002 * q^83 + 6632744 * q^84 - 1174862 * q^86 - 1073982 * q^87 - 427452 * q^88 + 3381078 * q^89 + 412204 * q^90 - 2879114 * q^91 + 696698 * q^92 - 543710 * q^93 - 3545780 * q^94 - 268230 * q^95 - 9026178 * q^96 - 1842138 * q^97 - 7266130 * q^98 + 8295480 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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