LMFDB - Embedded newform 74.6.f.a.7.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,6,Mod(7,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("74.7");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	74.f (of order $9$, degree $6$, 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:	$11.8684026662$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			7.7
Character	$\chi$	$=$	74.7
Dual form			74.6.f.a.53.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.75877 + 1.36808i) q^{2} +(13.8016 + 5.02336i) q^{3} +(12.2567 - 10.2846i) q^{4} +(19.0297 + 107.923i) q^{5} -58.7493 q^{6} +(6.51125 + 36.9271i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-20.8996 - 17.5369i) q^{9} +O(q^{10})$	\(q+(-3.75877 + 1.36808i) q^{2} +(13.8016 + 5.02336i) q^{3} +(12.2567 - 10.2846i) q^{4} +(19.0297 + 107.923i) q^{5} -58.7493 q^{6} +(6.51125 + 36.9271i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-20.8996 - 17.5369i) q^{9} +(-219.175 - 379.623i) q^{10} +(-188.083 + 325.770i) q^{11} +(220.825 - 80.3738i) q^{12} +(635.350 - 533.122i) q^{13} +(-74.9935 - 129.893i) q^{14} +(-279.495 + 1585.10i) q^{15} +(44.4539 - 252.111i) q^{16} +(24.1218 + 20.2406i) q^{17} +(102.549 + 37.3247i) q^{18} +(-1526.55 - 555.618i) q^{19} +(1343.18 + 1127.07i) q^{20} +(-95.6328 + 542.360i) q^{21} +(261.283 - 1481.81i) q^{22} +(1086.21 + 1881.38i) q^{23} +(-720.073 + 604.213i) q^{24} +(-8348.67 + 3038.67i) q^{25} +(-1658.78 + 2873.09i) q^{26} +(-1984.86 - 3437.88i) q^{27} +(459.587 + 385.639i) q^{28} +(-3357.10 + 5814.67i) q^{29} +(-1117.98 - 6340.39i) q^{30} +3950.03 q^{31} +(177.816 + 1008.44i) q^{32} +(-4232.30 + 3551.33i) q^{33} +(-118.359 - 43.0792i) q^{34} +(-3861.37 + 1405.42i) q^{35} -436.521 q^{36} +(8325.10 + 191.540i) q^{37} +6498.07 q^{38} +(11446.9 - 4166.33i) q^{39} +(-6590.64 - 2398.80i) q^{40} +(-9768.97 + 8197.14i) q^{41} +(-382.531 - 2169.44i) q^{42} +12978.5 q^{43} +(1045.13 + 5927.23i) q^{44} +(1494.92 - 2589.27i) q^{45} +(-6656.71 - 5585.64i) q^{46} +(5714.57 + 9897.93i) q^{47} +(1879.98 - 3256.22i) q^{48} +(14472.2 - 5267.45i) q^{49} +(27223.6 - 22843.3i) q^{50} +(231.243 + 400.524i) q^{51} +(2304.35 - 13068.6i) q^{52} +(5365.20 - 30427.6i) q^{53} +(12163.9 + 10206.8i) q^{54} +(-38737.2 - 14099.2i) q^{55} +(-2255.07 - 820.778i) q^{56} +(-18277.7 - 15336.8i) q^{57} +(4663.64 - 26448.8i) q^{58} +(4428.01 - 25112.5i) q^{59} +(12876.4 + 22302.6i) q^{60} +(-19052.9 + 15987.2i) q^{61} +(-14847.3 + 5403.96i) q^{62} +(511.504 - 885.951i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(69626.5 + 58423.6i) q^{65} +(11049.8 - 19138.7i) q^{66} +(6243.21 + 35407.0i) q^{67} +503.820 q^{68} +(5540.62 + 31422.4i) q^{69} +(12591.3 - 10565.3i) q^{70} +(54936.4 + 19995.2i) q^{71} +(1640.78 - 597.196i) q^{72} -1212.22 q^{73} +(-31554.2 + 10669.5i) q^{74} -130489. q^{75} +(-24424.8 + 8889.88i) q^{76} +(-13254.4 - 4824.21i) q^{77} +(-37326.3 + 31320.5i) q^{78} +(-2017.16 - 11439.9i) q^{79} +28054.5 q^{80} +(-8973.27 - 50889.9i) q^{81} +(25505.0 - 44175.9i) q^{82} +(24805.7 + 20814.5i) q^{83} +(4405.82 + 7631.10i) q^{84} +(-1725.39 + 2988.47i) q^{85} +(-48783.2 + 17755.6i) q^{86} +(-75542.5 + 63387.7i) q^{87} +(-12037.3 - 20849.3i) q^{88} +(15564.2 - 88268.7i) q^{89} +(-2076.72 + 11777.6i) q^{90} +(23823.6 + 19990.3i) q^{91} +(32662.6 + 11888.2i) q^{92} +(54516.6 + 19842.4i) q^{93} +(-35020.9 - 29386.0i) q^{94} +(30914.1 - 175323. i) q^{95} +(-2611.64 + 14811.3i) q^{96} +(-6004.97 - 10400.9i) q^{97} +(-47191.4 + 39598.3i) q^{98} +(9643.86 - 3510.08i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 3 q^{3} - 72 q^{5} + 114 q^{7} - 1536 q^{8} - 93 q^{9}+O(q^{10}) $ 48 * q - 3 * q^3 - 72 * q^5 + 114 * q^7 - 1536 * q^8 - 93 * q^9	\( 48 q - 3 q^{3} - 72 q^{5} + 114 q^{7} - 1536 q^{8} - 93 q^{9} - 648 q^{10} - 9 q^{11} - 48 q^{12} + 288 q^{13} - 660 q^{14} - 3678 q^{15} - 2475 q^{17} + 744 q^{18} + 945 q^{19} - 1152 q^{20} - 2073 q^{21} - 60 q^{22} - 5739 q^{23} - 192 q^{24} - 3834 q^{25} - 5304 q^{26} - 1077 q^{27} - 5232 q^{28} - 11640 q^{29} - 14712 q^{30} - 20394 q^{31} - 62013 q^{33} + 7812 q^{34} + 27999 q^{35} + 62208 q^{36} + 13605 q^{37} + 60696 q^{38} + 25590 q^{39} + 9216 q^{40} - 18267 q^{41} - 8292 q^{42} + 2208 q^{43} - 240 q^{44} - 48132 q^{45} - 40308 q^{46} - 663 q^{47} + 58326 q^{49} + 61776 q^{50} + 8748 q^{51} - 31536 q^{52} + 20940 q^{53} + 37836 q^{54} - 158868 q^{55} + 13632 q^{56} + 164910 q^{57} - 28068 q^{58} + 111258 q^{59} - 31824 q^{60} + 88758 q^{61} + 116100 q^{62} - 202488 q^{63} - 98304 q^{64} + 155997 q^{65} - 53532 q^{66} + 52503 q^{67} + 32544 q^{68} + 298758 q^{69} - 5760 q^{70} + 160434 q^{71} + 11904 q^{72} - 477210 q^{73} + 8844 q^{74} + 808230 q^{75} + 15120 q^{76} - 510765 q^{77} + 26004 q^{78} - 378768 q^{79} + 82944 q^{80} + 55476 q^{81} - 149064 q^{82} - 230082 q^{83} - 42336 q^{84} + 55653 q^{85} - 149904 q^{86} - 453051 q^{87} - 576 q^{88} + 492789 q^{89} + 12276 q^{90} + 220839 q^{91} + 176160 q^{92} - 109767 q^{93} - 6768 q^{94} - 630843 q^{95} + 6144 q^{96} - 632190 q^{97} - 194628 q^{98} - 414765 q^{99}+O(q^{100}) \) 48 * q - 3 * q^3 - 72 * q^5 + 114 * q^7 - 1536 * q^8 - 93 * q^9 - 648 * q^10 - 9 * q^11 - 48 * q^12 + 288 * q^13 - 660 * q^14 - 3678 * q^15 - 2475 * q^17 + 744 * q^18 + 945 * q^19 - 1152 * q^20 - 2073 * q^21 - 60 * q^22 - 5739 * q^23 - 192 * q^24 - 3834 * q^25 - 5304 * q^26 - 1077 * q^27 - 5232 * q^28 - 11640 * q^29 - 14712 * q^30 - 20394 * q^31 - 62013 * q^33 + 7812 * q^34 + 27999 * q^35 + 62208 * q^36 + 13605 * q^37 + 60696 * q^38 + 25590 * q^39 + 9216 * q^40 - 18267 * q^41 - 8292 * q^42 + 2208 * q^43 - 240 * q^44 - 48132 * q^45 - 40308 * q^46 - 663 * q^47 + 58326 * q^49 + 61776 * q^50 + 8748 * q^51 - 31536 * q^52 + 20940 * q^53 + 37836 * q^54 - 158868 * q^55 + 13632 * q^56 + 164910 * q^57 - 28068 * q^58 + 111258 * q^59 - 31824 * q^60 + 88758 * q^61 + 116100 * q^62 - 202488 * q^63 - 98304 * q^64 + 155997 * q^65 - 53532 * q^66 + 52503 * q^67 + 32544 * q^68 + 298758 * q^69 - 5760 * q^70 + 160434 * q^71 + 11904 * q^72 - 477210 * q^73 + 8844 * q^74 + 808230 * q^75 + 15120 * q^76 - 510765 * q^77 + 26004 * q^78 - 378768 * q^79 + 82944 * q^80 + 55476 * q^81 - 149064 * q^82 - 230082 * q^83 - 42336 * q^84 + 55653 * q^85 - 149904 * q^86 - 453051 * q^87 - 576 * q^88 + 492789 * q^89 + 12276 * q^90 + 220839 * q^91 + 176160 * q^92 - 109767 * q^93 - 6768 * q^94 - 630843 * q^95 + 6144 * q^96 - 632190 * q^97 - 194628 * q^98 - 414765 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−3.75877	+	1.36808i	−0.664463	+	0.241845i
$2$	−3.75877	+	1.36808i	−0.664463	+	0.241845i
$3$	13.8016	+	5.02336i	0.885371	+	0.322249i	0.744375	−	0.667761i	$-0.232747\pi$
$3$	13.8016	+	5.02336i	0.885371	+	0.322249i	0.140996	+	0.990010i	$0.454970\pi$
$4$	12.2567	−	10.2846i	0.383022	−	0.321394i
$5$	19.0297	+	107.923i	0.340414	+	1.93058i	0.365295	+	0.930892i	$0.380968\pi$
$5$	19.0297	+	107.923i	0.340414	+	1.93058i	−0.0248817	+	0.999690i	$0.507921\pi$
$6$	−58.7493			−0.666230
$7$	6.51125	+	36.9271i	0.0502249	+	0.284839i	0.999568	−	0.0294030i	$-0.00936061\pi$
$7$	6.51125	+	36.9271i	0.0502249	+	0.284839i	−0.949343	+	0.314242i	$0.898250\pi$
$8$	−32.0000	+	55.4256i	−0.176777	+	0.306186i
$9$	−20.8996	−	17.5369i	−0.0860068	−	0.0721683i
$10$	−219.175	−	379.623i	−0.693093	−	1.20047i
$11$	−188.083	+	325.770i	−0.468672	+	0.811763i	−0.999359	−	0.0358048i	$-0.988601\pi$
$11$	−188.083	+	325.770i	−0.468672	+	0.811763i	0.530687	+	0.847568i	$0.321934\pi$
$12$	220.825	−	80.3738i	0.442686	−	0.161124i
$13$	635.350	−	533.122i	1.04269	−	0.874919i	0.0503822	−	0.998730i	$-0.483956\pi$
$13$	635.350	−	533.122i	1.04269	−	0.874919i	0.992306	+	0.123811i	$0.0395116\pi$
$14$	−74.9935	−	129.893i	−0.102260	−	0.177119i
$15$	−279.495	+	1585.10i	−0.320735	+	1.81898i
$16$	44.4539	−	252.111i	0.0434120	−	0.246202i
$17$	24.1218	+	20.2406i	0.0202436	+	0.0169864i	0.652853	−	0.757484i	$-0.273572\pi$
$17$	24.1218	+	20.2406i	0.0202436	+	0.0169864i	−0.632610	+	0.774471i	$0.718016\pi$
$18$	102.549	+	37.3247i	0.0746018	+	0.0271528i
$19$	−1526.55	−	555.618i	−0.970122	−	0.353095i	−0.192130	−	0.981370i	$-0.561539\pi$
$19$	−1526.55	−	555.618i	−0.970122	−	0.353095i	−0.777992	+	0.628274i	$0.783762\pi$
$20$	1343.18	+	1127.07i	0.750863	+	0.630049i
$21$	−95.6328	+	542.360i	−0.0473215	+	0.268374i
$22$	261.283	−	1481.81i	0.115094	−	0.652732i
$23$	1086.21	+	1881.38i	0.428150	+	0.741577i	0.996709	−	0.0810652i	$-0.0258322\pi$
$23$	1086.21	+	1881.38i	0.428150	+	0.741577i	−0.568559	+	0.822643i	$0.692499\pi$
$24$	−720.073	+	604.213i	−0.255181	+	0.214122i
$25$	−8348.67	+	3038.67i	−2.67157	+	0.972373i
$26$	−1658.78	+	2873.09i	−0.481233	+	0.833520i
$27$	−1984.86	−	3437.88i	−0.523988	−	0.907574i
$28$	459.587	+	385.639i	0.110783	+	0.0929579i
$29$	−3357.10	+	5814.67i	−0.741258	+	1.28390i	0.210664	+	0.977558i	$0.432437\pi$
$29$	−3357.10	+	5814.67i	−0.741258	+	1.28390i	−0.951923	+	0.306339i	$0.900896\pi$
$30$	−1117.98	−	6340.39i	−0.226794	−	1.28621i
$31$	3950.03			0.738237			0.369119	−	0.929382i	$-0.379660\pi$
$31$	3950.03			0.738237			0.369119	+	0.929382i	$0.379660\pi$
$32$	177.816	+	1008.44i	0.0306970	+	0.174091i
$33$	−4232.30	+	3551.33i	−0.676538	+	0.567683i
$34$	−118.359	−	43.0792i	−0.0175592	−	0.00639102i
$35$	−3861.37	+	1405.42i	−0.532809	+	0.193927i
$36$	−436.521			−0.0561369
$37$	8325.10	+	191.540i	0.999735	+	0.0230014i
$37$	8325.10	+	191.540i	0.999735	+	0.0230014i
$38$	6498.07			0.730004
$39$	11446.9	−	4166.33i	1.20511	−	0.438623i
$40$	−6590.64	−	2398.80i	−0.651295	−	0.237052i
$41$	−9768.97	+	8197.14i	−0.907588	+	0.761557i	−0.971659	−	0.236388i	$-0.924036\pi$
$41$	−9768.97	+	8197.14i	−0.907588	+	0.761557i	0.0640703	+	0.997945i	$0.479592\pi$
$42$	−382.531	−	2169.44i	−0.0334614	−	0.189769i
$43$	12978.5			1.07042			0.535209	−	0.844720i	$-0.320233\pi$
$43$	12978.5			1.07042			0.535209	+	0.844720i	$0.320233\pi$
$44$	1045.13	+	5927.23i	0.0813840	+	0.461551i
$45$	1494.92	−	2589.27i	0.110049	−	0.190610i
$46$	−6656.71	−	5585.64i	−0.463836	−	0.389205i
$47$	5714.57	+	9897.93i	0.377345	+	0.653581i	0.990675	−	0.136246i	$-0.0435036\pi$
$47$	5714.57	+	9897.93i	0.377345	+	0.653581i	−0.613330	+	0.789827i	$0.710170\pi$
$48$	1879.98	−	3256.22i	0.117774	−	0.203991i
$49$	14472.2	−	5267.45i	0.861082	−	0.313408i
$50$	27223.6	−	22843.3i	1.54000	−	1.29221i
$51$	231.243	+	400.524i	0.0124492	+	0.0215627i
$52$	2304.35	−	13068.6i	0.118179	−	0.670227i
$53$	5365.20	−	30427.6i	0.262359	−	1.48791i	−0.514091	−	0.857736i	$-0.671871\pi$
$53$	5365.20	−	30427.6i	0.262359	−	1.48791i	0.776451	−	0.630178i	$-0.217018\pi$
$54$	12163.9	+	10206.8i	0.567663	+	0.476325i
$55$	−38737.2	−	14099.2i	−1.72672	−	0.628474i
$56$	−2255.07	−	820.778i	−0.0960925	−	0.0349748i
$57$	−18277.7	−	15336.8i	−0.745133	−	0.625241i
$58$	4663.64	−	26448.8i	0.182035	−	1.03237i
$59$	4428.01	−	25112.5i	0.165607	−	0.939203i	−0.782830	−	0.622236i	$-0.786224\pi$
$59$	4428.01	−	25112.5i	0.165607	−	0.939203i	0.948437	−	0.316967i	$-0.102664\pi$
$60$	12876.4	+	22302.6i	0.461760	+	0.799792i
$61$	−19052.9	+	15987.2i	−0.655595	+	0.550109i	−0.908763	−	0.417313i	$-0.862972\pi$
$61$	−19052.9	+	15987.2i	−0.655595	+	0.550109i	0.253168	+	0.967422i	$0.418527\pi$
$62$	−14847.3	+	5403.96i	−0.490531	+	0.178539i
$63$	511.504	−	885.951i	0.0162367	−	0.0281228i
$64$	−2048.00	−	3547.24i	−0.0625000	−	0.108253i
$65$	69626.5	+	58423.6i	2.04405	+	1.71516i
$66$	11049.8	−	19138.7i	0.312243	−	0.540821i
$67$	6243.21	+	35407.0i	0.169911	+	0.963612i	0.943855	+	0.330359i	$0.107170\pi$
$67$	6243.21	+	35407.0i	0.169911	+	0.963612i	−0.773944	+	0.633253i	$0.781719\pi$
$68$	503.820			0.0132131
$69$	5540.62	+	31422.4i	0.140099	+	0.794542i
$70$	12591.3	−	10565.3i	0.307132	−	0.257714i
$71$	54936.4	+	19995.2i	1.29334	+	0.470739i	0.894823	−	0.446421i	$-0.147302\pi$
$71$	54936.4	+	19995.2i	1.29334	+	0.470739i	0.398521	+	0.917159i	$0.369524\pi$
$72$	1640.78	−	597.196i	0.0373009	−	0.0135764i
$73$	−1212.22			−0.0266241			−0.0133120	−	0.999911i	$-0.504237\pi$
$73$	−1212.22			−0.0266241			−0.0133120	+	0.999911i	$0.504237\pi$
$74$	−31554.2	+	10669.5i	−0.669850	+	0.226497i
$75$	−130489.			−2.67868
$76$	−24424.8	+	8889.88i	−0.485061	+	0.176548i
$77$	−13254.4	−	4824.21i	−0.254761	−	0.0927255i
$78$	−37326.3	+	31320.5i	−0.694671	+	0.582898i
$79$	−2017.16	−	11439.9i	−0.0363641	−	0.206231i	0.961212	−	0.275809i	$-0.0889458\pi$
$79$	−2017.16	−	11439.9i	−0.0363641	−	0.206231i	−0.997576	+	0.0695783i	$0.977835\pi$
$80$	28054.5			0.490091
$81$	−8973.27	−	50889.9i	−0.151963	−	0.861826i
$82$	25505.0	−	44175.9i	0.418880	−	0.725522i
$83$	24805.7	+	20814.5i	0.395236	+	0.331643i	0.818649	−	0.574294i	$-0.194723\pi$
$83$	24805.7	+	20814.5i	0.395236	+	0.331643i	−0.423413	+	0.905937i	$0.639168\pi$
$84$	4405.82	+	7631.10i	0.0681284	+	0.118002i
$85$	−1725.39	+	2988.47i	−0.0259024	+	0.0448643i
$86$	−48783.2	+	17755.6i	−0.711253	+	0.258875i
$87$	−75542.5	+	63387.7i	−1.07002	+	0.897856i
$88$	−12037.3	−	20849.3i	−0.165700	−	0.287002i
$89$	15564.2	−	88268.7i	0.208281	−	1.18122i	−0.683910	−	0.729566i	$-0.739722\pi$
$89$	15564.2	−	88268.7i	0.208281	−	1.18122i	0.892192	−	0.451657i	$-0.149167\pi$
$90$	−2076.72	+	11777.6i	−0.0270253	+	0.153268i
$91$	23823.6	+	19990.3i	0.301580	+	0.253056i
$92$	32662.6	+	11888.2i	0.402329	+	0.146436i
$93$	54516.6	+	19842.4i	0.653614	+	0.237896i
$94$	−35020.9	−	29386.0i	−0.408797	−	0.343022i
$95$	30914.1	−	175323.i	0.351437	−	1.99310i
$96$	−2611.64	+	14811.3i	−0.0289224	+	0.164027i
$97$	−6004.97	−	10400.9i	−0.0648009	−	0.112238i	0.831805	−	0.555068i	$-0.187308\pi$
$97$	−6004.97	−	10400.9i	−0.0648009	−	0.112238i	−0.896606	+	0.442830i	$0.853975\pi$
$98$	−47191.4	+	39598.3i	−0.496361	+	0.416496i
$99$	9643.86	−	3510.08i	0.0988924	−	0.0359939i
$100$	−71075.7	+	123107.i	−0.710757	+	1.23107i
$101$	24885.1	+	43102.3i	0.242737	+	0.420434i	0.961493	−	0.274829i	$-0.0886213\pi$
$101$	24885.1	+	43102.3i	0.242737	+	0.420434i	−0.718756	+	0.695263i	$0.755288\pi$
$102$	−1417.14	−	1189.12i	−0.0134869	−	0.0113168i
$103$	19693.1	−	34109.4i	0.182903	−	0.316797i	−0.759965	−	0.649964i	$-0.774784\pi$
$103$	19693.1	−	34109.4i	0.182903	−	0.316797i	0.942868	+	0.333167i	$0.108117\pi$
$104$	9217.41	+	52274.5i	0.0835652	+	0.473922i
$105$	−60352.9			−0.534226
$106$	21460.8	+	121710.i	0.185516	+	1.05211i
$107$	−71231.1	+	59770.0i	−0.601465	+	0.504689i	−0.891916	−	0.452201i	$-0.850639\pi$
$107$	−71231.1	+	59770.0i	−0.601465	+	0.504689i	0.290451	+	0.956890i	$0.406195\pi$
$108$	−59685.2	−	21723.6i	−0.492388	−	0.179214i
$109$	−20659.9	+	7519.58i	−0.166556	+	0.0606216i	−0.423953	−	0.905684i	$-0.639358\pi$
$109$	−20659.9	+	7519.58i	−0.166556	+	0.0606216i	0.257396	+	0.966306i	$0.417135\pi$
$110$	164893.			1.29933
$111$	113937.	+	44463.5i	0.877725	+	0.342528i
$112$	9599.17			0.0723084
$113$	184050.	−	66988.6i	1.35593	−	0.493520i	0.441140	−	0.897439i	$-0.354574\pi$
$113$	184050.	−	66988.6i	1.35593	−	0.493520i	0.914795	+	0.403919i	$0.132352\pi$
$114$	89683.6	+	32642.1i	0.646325	+	0.235243i
$115$	−182373.	+	153029.i	−1.28593	+	1.07902i
$116$	18654.5	+	105795.i	0.128718	+	0.729997i
$117$	−22627.9			−0.152820
$118$	17712.0	+	100450.i	0.117102	+	0.664117i
$119$	−590.364	+	1022.54i	−0.00382166	+	0.00661931i
$120$	−78911.2	−	66214.3i	−0.500248	−	0.419758i
$121$	9774.82	+	16930.5i	0.0606940	+	0.105125i
$122$	49743.5	−	86158.2i	0.302577	−	0.524079i
$123$	−176004.	+	64060.3i	−1.04896	+	0.381791i
$124$	48414.4	−	40624.5i	0.282761	−	0.237265i
$125$	−315583.	−	546606.i	−1.80650	−	3.12896i
$126$	−710.574	+	4029.86i	−0.00398733	+	0.0226133i
$127$	−1114.26	+	6319.27i	−0.00613022	+	0.0347662i	−0.987719	−	0.156238i	$-0.950063\pi$
$127$	−1114.26	+	6319.27i	−0.00613022	+	0.0347662i	0.981589	+	0.191004i	$0.0611744\pi$
$128$	12550.9	+	10531.4i	0.0677094	+	0.0568149i
$129$	179124.	+	65195.7i	0.947717	+	0.344941i
$130$	−341638.	−	124346.i	−1.77300	−	0.645318i
$131$	92629.3	+	77725.2i	0.471596	+	0.395716i	0.847376	−	0.530993i	$-0.178181\pi$
$131$	92629.3	+	77725.2i	0.471596	+	0.395716i	−0.375780	+	0.926709i	$0.622625\pi$
$132$	−15350.2	+	87055.1i	−0.0766793	+	0.434870i
$133$	10577.6	−	59988.7i	0.0518513	−	0.294063i
$134$	−71906.5	−	124546.i	−0.345944	−	0.599193i
$135$	333255.	−	279634.i	1.57377	−	1.32055i
$136$	−1893.75	+	689.267i	−0.00877959	+	0.00319551i
$137$	50836.6	−	88051.6i	0.231406	−	0.400807i	−0.726816	−	0.686832i	$-0.759001\pi$
$137$	50836.6	−	88051.6i	0.231406	−	0.400807i	0.958222	+	0.286025i	$0.0923340\pi$
$138$	−63814.3	−	110530.i	−0.285246	−	0.494061i
$139$	289287.	+	242740.i	1.26996	+	1.06563i	0.994546	+	0.104301i	$0.0332607\pi$
$139$	289287.	+	242740.i	1.26996	+	1.06563i	0.275418	+	0.961325i	$0.411184\pi$
$140$	−32873.5	+	56938.5i	−0.141751	+	0.245520i
$141$	29149.2	+	165313.i	0.123475	+	0.700261i
$142$	−233848.			−0.973225
$143$	54176.3	+	307249.i	0.221549	+	1.25647i
$144$	−5350.31	+	4489.44i	−0.0215017	+	0.0180421i
$145$	−691420.	−	251656.i	−2.73100	−	0.994004i
$146$	4556.46	−	1658.42i	0.0176907	−	0.00643890i
$147$	226199.			0.863372
$148$	104008.	−	83272.7i	0.390313	−	0.312499i
$149$	321569.			1.18661			0.593306	−	0.804977i	$-0.297823\pi$
$149$	321569.			1.18661			0.593306	+	0.804977i	$0.297823\pi$
$150$	490478.	−	178519.i	1.77988	−	0.647825i
$151$	190027.	+	69164.0i	0.678222	+	0.246853i	0.658084	−	0.752944i	$-0.271367\pi$
$151$	190027.	+	69164.0i	0.678222	+	0.246853i	0.0201383	+	0.999797i	$0.493589\pi$
$152$	79645.0	−	66830.1i	0.279608	−	0.234619i
$153$	−149.180	−	846.043i	−0.000515208	−	0.00292189i
$154$	56420.1			0.191705
$155$	75167.9	+	426298.i	0.251306	+	1.42523i
$156$	97452.2	−	168792.i	0.320612	−	0.555317i
$157$	−189359.	−	158891.i	−0.613106	−	0.514457i	0.282522	−	0.959261i	$-0.408829\pi$
$157$	−189359.	−	158891.i	−0.613106	−	0.514457i	−0.895628	+	0.444804i	$0.853273\pi$
$158$	23232.7	+	40240.2i	0.0740384	+	0.128238i
$159$	226897.	−	392997.i	0.711764	−	1.23281i
$160$	−105450.	+	38380.8i	−0.325647	+	0.118526i
$161$	−62401.2	+	52360.9i	−0.189727	+	0.159200i
$162$	103350.	+	179007.i	0.309402	+	0.535900i
$163$	1679.36	−	9524.13i	0.00495080	−	0.0280774i	−0.982232	−	0.187669i	$-0.939907\pi$
$163$	1679.36	−	9524.13i	0.00495080	−	0.0280774i	0.987183	+	0.159592i	$0.0510178\pi$
$164$	−35431.1	+	200940.i	−0.102867	+	0.583387i
$165$	−463809.	−	389182.i	−1.32626	−	1.11286i
$166$	−121715.	−	44300.6i	−0.342826	−	0.124778i
$167$	584091.	+	212592.i	1.62065	+	0.589868i	0.983506	−	0.180877i	$-0.0578936\pi$
$167$	584091.	+	212592.i	1.62065	+	0.589868i	0.637144	+	0.770745i	$0.280116\pi$
$168$	−27000.4	−	22656.0i	−0.0738069	−	0.0619314i
$169$	54976.1	−	311785.i	0.148067	−	0.839728i
$170$	2396.89	−	13593.4i	0.00636100	−	0.0360750i
$171$	22160.5	+	38383.1i	0.0579548	+	0.100381i
$172$	159074.	−	133479.i	0.409994	−	0.344026i
$173$	−193618.	+	70471.2i	−0.491848	+	0.179018i	−0.576024	−	0.817433i	$-0.695396\pi$
$173$	−193618.	+	70471.2i	−0.491848	+	0.179018i	0.0841761	+	0.996451i	$0.473174\pi$
$174$	197227.	−	341608.i	0.493849	−	0.855371i
$175$	−166569.	−	288507.i	−0.411150	−	0.712132i
$176$	73769.1	+	61899.6i	0.179512	+	0.150628i
$177$	187262.	−	324348.i	0.449280	−	0.778176i
$178$	62256.6	+	353075.i	0.147277	+	0.835251i
$179$	−634526.			−1.48019			−0.740094	−	0.672504i	$-0.765219\pi$
$179$	−634526.			−1.48019			−0.740094	+	0.672504i	$0.765219\pi$
$180$	−8306.86	−	47110.6i	−0.0191098	−	0.108377i
$181$	−93235.3	+	78233.7i	−0.211536	+	0.177500i	−0.742399	−	0.669958i	$-0.766312\pi$
$181$	−93235.3	+	78233.7i	−0.211536	+	0.177500i	0.530863	+	0.847457i	$0.321868\pi$
$182$	−116896.	−	42546.5i	−0.261589	−	0.0952107i
$183$	−343269.	+	124940.i	−0.757717	+	0.275786i
$184$	−139035.			−0.302748
$185$	137753.	+	902113.i	0.295917	+	1.93790i
$186$	−232061.			−0.491836
$187$	−11130.7	+	4051.24i	−0.0232765	+	0.00847196i
$188$	171838.	+	62544.0i	0.354589	+	0.129060i
$189$	114027.	−	95680.2i	0.232196	−	0.194835i
$190$	123656.	+	701290.i	0.248503	+	1.40933i
$191$	−658916.			−1.30691			−0.653457	−	0.756964i	$-0.726682\pi$
$191$	−658916.			−1.30691			−0.653457	+	0.756964i	$0.726682\pi$
$192$	−10446.5	−	59245.3i	−0.0204512	−	0.115985i
$193$	−336.909	+	583.544i	−0.000651058	+	0.00112767i	−0.866351	−	0.499436i	$-0.833541\pi$
$193$	−336.909	+	583.544i	−0.000651058	+	0.00112767i	0.865700	+	0.500564i	$0.166874\pi$
$194$	36800.6	+	30879.3i	0.0702021	+	0.0589066i
$195$	667472.	+	1.15610e6i	1.25703	+	2.17725i
$196$	123208.	−	213402.i	0.229086	−	0.396789i
$197$	−83745.9	+	30481.0i	−0.153744	+	0.0559582i	−0.417746	−	0.908564i	$-0.637180\pi$
$197$	−83745.9	+	30481.0i	−0.153744	+	0.0559582i	0.264002	+	0.964522i	$0.414957\pi$
$198$	−31447.0	+	26387.2i	−0.0570054	+	0.0478332i
$199$	−46022.4	−	79713.2i	−0.0823829	−	0.142691i	0.821890	−	0.569646i	$-0.192920\pi$
$199$	−46022.4	−	79713.2i	−0.0823829	−	0.142691i	−0.904273	+	0.426955i	$0.859586\pi$
$200$	98737.3	−	559967.i	0.174545	−	0.989892i
$201$	−91696.1	+	520034.i	−0.160089	+	0.907908i
$202$	−152505.	−	127967.i	−0.262970	−	0.220658i
$203$	−236578.	−	86107.3i	−0.402934	−	0.146656i
$204$	6953.51	+	2530.87i	0.0116985	+	0.00425789i
$205$	−1.07056e6	−	898305.i	−1.77920	−	1.49293i
$206$	−27357.3	+	155151.i	−0.0449164	+	0.254734i
$207$	10292.0	−	58368.9i	0.0166946	−	0.0946795i
$208$	−106162.	−	183878.i	−0.170142	−	0.294694i
$209$	468122.	−	392801.i	0.741298	−	0.622023i
$210$	226853.	−	82567.7i	0.354973	−	0.129200i
$211$	−568170.	+	984099.i	−0.878561	+	1.52171i	−0.0256402	+	0.999671i	$0.508162\pi$
$211$	−568170.	+	984099.i	−0.878561	+	1.52171i	−0.852921	+	0.522041i	$0.825171\pi$
$212$	−247176.	−	428121.i	−0.377717	−	0.654225i
$213$	657765.	+	551930.i	0.993394	+	0.833557i
$214$	185971.	−	322112.i	0.277595	−	0.480809i
$215$	246977.	+	1.40068e6i	0.364385	+	2.06653i
$216$	254063.			0.370515
$217$	25719.6	+	145863.i	0.0370779	+	0.210279i
$218$	67368.3	−	56528.7i	0.0960096	−	0.0805616i
$219$	−16730.6	−	6089.42i	−0.0235722	−	0.00857958i
$220$	−619795.	+	225587.i	−0.863359	+	0.314237i
$221$	26116.5			0.0359695
$222$	−489094.	−	11252.8i	−0.666054	−	0.0153243i
$223$	785777.			1.05812			0.529062	−	0.848583i	$-0.322544\pi$
$223$	785777.			1.05812			0.529062	+	0.848583i	$0.322544\pi$
$224$	−36081.1	+	13132.4i	−0.0480463	+	0.0174874i
$225$	227773.	+	82902.6i	0.299948	+	0.109172i
$226$	−600154.	+	503589.i	−0.781613	+	0.655851i
$227$	−131830.	−	747645.i	−0.169805	−	0.963010i	−0.943971	−	0.330028i	$-0.892942\pi$
$227$	−131830.	−	747645.i	−0.169805	−	0.963010i	0.774166	−	0.632982i	$-0.218169\pi$
$228$	−381757.			−0.486351
$229$	−189501.	−	1.07471e6i	−0.238793	−	1.35426i	−0.834476	−	0.551044i	$-0.814230\pi$
$229$	−189501.	−	1.07471e6i	−0.238793	−	1.35426i	0.595683	−	0.803219i	$-0.296881\pi$
$230$	476143.	−	824703.i	0.593496	−	1.02796i
$231$	−158698.	−	133163.i	−0.195677	−	0.164193i
$232$	−214855.	−	372139.i	−0.262074	−	0.453926i
$233$	−4016.61	+	6956.97i	−0.00484696	+	0.00839519i	−0.868439	−	0.495797i	$-0.834876\pi$
$233$	−4016.61	+	6956.97i	−0.00484696	+	0.00839519i	0.863592	+	0.504192i	$0.168210\pi$
$234$	85053.0	−	30956.8i	0.101543	−	0.0369586i
$235$	−959466.	+	805087.i	−1.13334	+	0.950984i
$236$	−203999.	−	353337.i	−0.238423	−	0.412961i
$237$	29626.7	−	168021.i	0.0342619	−	0.194309i
$238$	820.125	−	4651.16i	0.000938507	−	0.00532254i
$239$	−899877.	−	755086.i	−1.01903	−	0.855070i	−0.0295275	−	0.999564i	$-0.509400\pi$
$239$	−899877.	−	755086.i	−1.01903	−	0.855070i	−0.989506	+	0.144494i	$0.953845\pi$
$240$	387195.	+	140928.i	0.433912	+	0.157931i
$241$	−752832.	−	274008.i	−0.834940	−	0.303893i	−0.111055	−	0.993814i	$-0.535423\pi$
$241$	−752832.	−	274008.i	−0.834940	−	0.303893i	−0.723885	+	0.689921i	$0.757645\pi$
$242$	−59903.6	−	50265.1i	−0.0657528	−	0.0551732i
$243$	−35715.3	+	202552.i	−0.0388006	+	0.220049i
$244$	−69102.9	+	391902.i	−0.0743056	+	0.421408i
$245$	843880.	+	1.46164e6i	0.898184	+	1.55570i
$246$	573920.	−	481576.i	0.604663	−	0.507373i
$247$	−1.26610e6	+	460824.i	−1.32046	+	0.480610i
$248$	−126401.	+	218933.i	−0.130503	+	0.226038i
$249$	237799.	+	411881.i	0.243059	+	0.420991i
$250$	1.93401e6	+	1.62282e6i	1.95708	+	1.64218i
$251$	855560.	−	1.48187e6i	0.857169	−	1.48466i	−0.0174498	−	0.999848i	$-0.505555\pi$
$251$	855560.	−	1.48187e6i	0.857169	−	1.48466i	0.874618	−	0.484812i	$-0.161112\pi$
$252$	−2842.29	−	16119.5i	−0.00281947	−	0.0159900i
$253$	−817195.			−0.802647
$254$	−4457.03	−	25277.1i	−0.00433472	−	0.0245834i
$255$	−38825.2	+	32578.2i	−0.0373907	+	0.0313745i
$256$	−61583.7	−	22414.6i	−0.0587308	−	0.0213763i
$257$	843776.	−	307109.i	0.796882	−	0.290041i	0.0886884	−	0.996059i	$-0.471732\pi$
$257$	843776.	−	307109.i	0.796882	−	0.290041i	0.708194	+	0.706018i	$0.249510\pi$
$258$	−762477.			−0.713145
$259$	47133.7	+	308669.i	0.0436599	+	0.285919i
$260$	1.45426e6			1.33416
$261$	172133.	−	62651.5i	0.156410	−	0.0569285i
$262$	−454507.	−	165427.i	−0.409060	−	0.148886i
$263$	−1.00644e6	+	844503.i	−0.897218	+	0.752856i	−0.969645	−	0.244518i	$-0.921370\pi$
$263$	−1.00644e6	+	844503.i	−0.897218	+	0.752856i	0.0724264	+	0.997374i	$0.476926\pi$
$264$	−61400.7	−	348221.i	−0.0542205	−	0.307500i
$265$	3.38593e6			2.96185
$266$	42310.5	+	239955.i	0.0366644	+	0.207934i
$267$	658215.	−	1.14006e6i	0.565054	−	0.978702i
$268$	440668.	+	369765.i	0.374779	+	0.314477i
$269$	−9371.17	−	16231.3i	−0.00789611	−	0.0136765i	0.862050	−	0.506823i	$-0.169180\pi$
$269$	−9371.17	−	16231.3i	−0.00789611	−	0.0136765i	−0.869946	+	0.493146i	$0.835847\pi$
$270$	−870067.	+	1.50700e6i	−0.726345	+	1.25807i
$271$	1.62822e6	−	592622.i	1.34676	−	0.490179i	0.434822	−	0.900517i	$-0.356811\pi$
$271$	1.62822e6	−	592622.i	1.34676	−	0.490179i	0.911934	+	0.410338i	$0.134589\pi$
$272$	6175.18	−	5181.59i	0.00506090	−	0.00424660i
$273$	228384.	+	395572.i	0.185464	+	0.321232i
$274$	−70621.4	+	400514.i	−0.0568277	+	0.322286i
$275$	580339.	−	3.29127e6i	0.462754	−	2.62441i
$276$	391077.	+	328152.i	0.309022	+	0.259300i
$277$	−439130.	−	159830.i	−0.343870	−	0.125158i	0.164311	−	0.986409i	$-0.447460\pi$
$277$	−439130.	−	159830.i	−0.343870	−	0.125158i	−0.508181	+	0.861250i	$0.669682\pi$
$278$	−1.41945e6	−	516638.i	−1.10156	−	0.400935i
$279$	−82554.2	−	69271.2i	−0.0634934	−	0.0532773i
$280$	45667.4	−	258992.i	0.0348105	−	0.197420i
$281$	216352.	−	1.22699e6i	0.163454	−	0.926991i	−0.787191	−	0.616709i	$-0.788465\pi$
$281$	216352.	−	1.22699e6i	0.163454	−	0.926991i	0.950645	−	0.310282i	$-0.100424\pi$
$282$	−335727.	−	581496.i	−0.251399	−	0.435436i
$283$	−1.54627e6	+	1.29747e6i	−1.14767	+	0.963013i	−0.999663	−	0.0259724i	$-0.991732\pi$
$283$	−1.54627e6	+	1.29747e6i	−1.14767	+	0.963013i	−0.148012	+	0.988986i	$0.547287\pi$
$284$	878982.	−	319923.i	0.646672	−	0.235369i
$285$	1.30737e6	−	2.26443e6i	0.953425	−	1.65138i
$286$	−623978.	−	1.08076e6i	−0.451080	−	0.781294i
$287$	−366305.	−	307366.i	−0.262505	−	0.220268i
$288$	13968.7	−	24194.4i	0.00992370	−	0.0171884i
$289$	−246383.	−	1.39731e6i	−0.173527	−	0.984120i
$290$	2.94318e6			2.05505
$291$	−30630.5	−	173714.i	−0.0212042	−	0.120255i
$292$	−14857.8	+	12467.2i	−0.0101976	+	0.00855682i
$293$	−1.91383e6	−	696578.i	−1.30237	−	0.474024i	−0.404603	−	0.914492i	$-0.632590\pi$
$293$	−1.91383e6	−	696578.i	−1.30237	−	0.474024i	−0.897768	+	0.440468i	$0.854812\pi$
$294$	−850231.	+	309459.i	−0.573679	+	0.208802i
$295$	2.79447e6			1.86958
$296$	−277019.	+	455295.i	−0.183773	+	0.302039i
$297$	1.49328e6			0.982313
$298$	−1.20870e6	+	439932.i	−0.788459	+	0.286976i
$299$	1.69313e6	+	616249.i	1.09525	+	0.398637i
$300$	−1.59937e6	+	1.34203e6i	−1.02599	+	0.860911i
$301$	84506.2	+	479258.i	0.0537616	+	0.304897i
$302$	−808888.			−0.510354
$303$	126935.	+	719887.i	0.0794285	+	0.450461i
$304$	−207938.	+	360160.i	−0.129048	+	0.223517i
$305$	−2.08796e6	−	1.75201e6i	−1.28520	−	1.07841i
$306$	1718.19	+	2975.99i	0.00104898	+	0.00181689i
$307$	887922.	−	1.53793e6i	0.537686	−	0.931300i	−0.461342	−	0.887222i	$-0.652632\pi$
$307$	887922.	−	1.53793e6i	0.537686	−	0.931300i	0.999028	−	0.0440774i	$-0.0140348\pi$
$308$	−212070.	+	77187.3i	−0.127381	+	0.0463627i
$309$	443139.	−	371838.i	0.264024	−	0.221543i
$310$	−865749.	−	1.49952e6i	−0.511667	−	0.886234i
$311$	−226353.	+	1.28371e6i	−0.132705	+	0.752605i	0.843726	+	0.536774i	$0.180357\pi$
$311$	−226353.	+	1.28371e6i	−0.132705	+	0.752605i	−0.976431	+	0.215831i	$0.930754\pi$
$312$	−135379.	+	767773.i	−0.0787345	+	0.446526i
$313$	504725.	+	423514.i	0.291202	+	0.244347i	0.776671	−	0.629907i	$-0.216907\pi$
$313$	504725.	+	423514.i	0.291202	+	0.244347i	−0.485469	+	0.874254i	$0.661351\pi$
$314$	929130.	+	338176.i	0.531805	+	0.193561i
$315$	105348.	+	38343.6i	0.0598205	+	0.0217729i
$316$	−142378.	−	119470.i	−0.0802095	−	0.0673038i
$317$	−466942.	+	2.64816e6i	−0.260985	+	1.48012i	0.519246	+	0.854625i	$0.326213\pi$
$317$	−466942.	+	2.64816e6i	−0.260985	+	1.48012i	−0.780231	+	0.625492i	$0.784898\pi$
$318$	−315202.	+	1.78760e6i	−0.174792	+	0.991294i
$319$	−1.26283e6	−	2.18729e6i	−0.694813	−	1.20345i
$320$	343855.	−	288529.i	0.187716	−	0.157512i
$321$	−1.28335e6	+	467100.i	−0.695155	+	0.253016i
$322$	162918.	−	282182.i	0.0875648	−	0.151667i
$323$	−25577.0	−	44300.7i	−0.0136409	−	0.0236268i
$324$	−633366.	−	531457.i	−0.335191	−	0.281258i
$325$	−3.68434e6	+	6.38147e6i	−1.93487	+	3.35129i
$326$	6717.44	+	38096.5i	0.00350074	+	0.0198537i
$327$	−322912.			−0.166999
$328$	−141724.	−	803759.i	−0.0727378	−	0.412517i
$329$	−328293.	+	275470.i	−0.167214	+	0.140309i
$330$	2.27578e6	+	828317.i	1.15039	+	0.418708i
$331$	3.23490e6	−	1.17741e6i	1.62290	−	0.590687i	0.638967	−	0.769234i	$-0.279362\pi$
$331$	3.23490e6	−	1.17741e6i	1.62290	−	0.590687i	0.983931	+	0.178548i	$0.0571399\pi$
$332$	518105.			0.257972
$333$	−170633.	−	149999.i	−0.0843241	−	0.0741274i
$334$	−2.48630e6			−1.21952
$335$	−3.70242e6	+	1.34757e6i	−1.80249	+	0.656054i
$336$	132484.	+	48220.1i	0.0640198	+	0.0233013i
$337$	1.19284e6	−	1.00091e6i	0.572148	−	0.480089i	−0.310210	−	0.950668i	$-0.600399\pi$
$337$	1.19284e6	−	1.00091e6i	0.572148	−	0.480089i	0.882358	+	0.470579i	$0.155955\pi$
$338$	219904.	+	1.24714e6i	0.104699	+	0.593777i
$339$	2.87668e6			1.35954
$340$	9587.55	+	54373.7i	0.00449791	+	0.0255089i
$341$	−742935.	+	1.28680e6i	−0.345991	+	0.599274i
$342$	−135807.	−	113956.i	−0.0627853	−	0.0526831i
$343$	603848.	+	1.04590e6i	0.277136	+	0.480013i
$344$	−415312.	+	719341.i	−0.189225	+	0.327747i
$345$	−3.28576e6	+	1.19592e6i	−1.48624	+	0.540946i
$346$	631355.	−	529770.i	0.283520	−	0.237902i
$347$	−109582.	−	189802.i	−0.0488558	−	0.0846207i	0.840563	−	0.541713i	$-0.182224\pi$
$347$	−109582.	−	189802.i	−0.0488558	−	0.0846207i	−0.889419	+	0.457093i	$0.848891\pi$
$348$	−273985.	+	1.55385e6i	−0.121277	+	0.687797i
$349$	706941.	−	4.00926e6i	0.310685	−	1.76198i	−0.284775	−	0.958594i	$-0.591919\pi$
$349$	706941.	−	4.00926e6i	0.310685	−	1.76198i	0.595459	−	0.803385i	$-0.296970\pi$
$350$	1.02080e6	+	856550.i	0.445419	+	0.373751i
$351$	−3.09389e6	−	1.12608e6i	−1.34041	−	0.487869i
$352$	−361965.	−	131744.i	−0.155707	−	0.0566729i
$353$	−1.50526e6	−	1.26307e6i	−0.642948	−	0.539498i	0.261974	−	0.965075i	$-0.415627\pi$
$353$	−1.50526e6	−	1.26307e6i	−0.642948	−	0.539498i	−0.904922	+	0.425577i	$0.860071\pi$
$354$	−260142.	+	1.47534e6i	−0.110332	+	0.625726i
$355$	−1.11252e6	+	6.30939e6i	−0.468528	+	2.65715i
$356$	−717043.	−	1.24196e6i	−0.299861	−	0.519375i
$357$	−13284.5	+	11147.0i	−0.00551665	+	0.00462902i
$358$	2.38504e6	−	868082.i	0.983530	−	0.357976i
$359$	205883.	−	356600.i	0.0843112	−	0.146031i	−0.820786	−	0.571235i	$-0.806464\pi$
$359$	205883.	−	356600.i	0.0843112	−	0.146031i	0.905097	+	0.425204i	$0.139798\pi$
$360$	95674.6	+	165713.i	0.0389081	+	0.0673909i
$361$	124833.	+	104747.i	0.0504152	+	0.0423034i
$362$	243420.	−	421616.i	0.0976304	−	0.169101i
$363$	49859.9	+	282770.i	0.0198603	+	0.112633i
$364$	497591.			0.196843
$365$	−23068.2	−	130826.i	−0.00906320	−	0.0514000i
$366$	1.11934e6	−	939239.i	0.436777	−	0.366500i
$367$	513773.	+	186998.i	0.199116	+	0.0724724i	0.439653	−	0.898168i	$-0.355101\pi$
$367$	513773.	+	186998.i	0.199116	+	0.0724724i	−0.240537	+	0.970640i	$0.577324\pi$
$368$	522602.	−	190212.i	0.201165	−	0.0732179i
$369$	347920.			0.133019
$370$	−1.75194e6	−	3.20238e6i	−0.665298	−	1.21610i
$371$	1.15854e6			0.436994
$372$	872265.	−	317479.i	0.326807	−	0.118948i
$373$	−2.08681e6	−	759538.i	−0.776625	−	0.282669i	−0.0768607	−	0.997042i	$-0.524490\pi$
$373$	−2.08681e6	−	759538.i	−0.776625	−	0.282669i	−0.699765	+	0.714373i	$0.746712\pi$
$374$	36295.3	−	30455.3i	0.0134175	−	0.0112586i
$375$	−1.60974e6	−	9.12931e6i	−0.591124	−	3.35243i
$376$	−731465.			−0.266823
$377$	966994.	+	5.48409e6i	0.350405	+	1.98725i
$378$	−297704.	+	515638.i	−0.107165	+	0.185616i
$379$	4.00246e6	+	3.35847e6i	1.43130	+	1.20100i	0.944942	+	0.327237i	$0.106118\pi$
$379$	4.00246e6	+	3.35847e6i	1.43130	+	1.20100i	0.486353	+	0.873762i	$0.338327\pi$
$380$	−1.42422e6	−	2.46682e6i	−0.505961	−	0.876350i
$381$	−47122.4	+	81618.5i	−0.0166309	+	0.0288055i
$382$	2.47671e6	−	901450.i	0.868395	−	0.316070i
$383$	−3.87257e6	+	3.24947e6i	−1.34897	+	1.13192i	−0.369748	+	0.929132i	$0.620556\pi$
$383$	−3.87257e6	+	3.24947e6i	−1.34897	+	1.13192i	−0.979223	+	0.202788i	$0.935000\pi$
$384$	120319.	+	208398.i	0.0416394	+	0.0721216i
$385$	268415.	−	1.52226e6i	0.0922899	−	0.523402i
$386$	468.030	−	2654.33i	0.000159884	−	0.000906748i
$387$	−271246.	−	227602.i	−0.0920632	−	0.0772502i
$388$	−180570.	−	65722.2i	−0.0608930	−	0.0221632i
$389$	2.59080e6	+	942973.i	0.868080	+	0.315955i	0.737389	−	0.675468i	$-0.236058\pi$
$389$	2.59080e6	+	942973.i	0.868080	+	0.315955i	0.130690	+	0.991423i	$0.458281\pi$
$390$	−4.09051e6	−	3.43234e6i	−1.36181	−	1.14269i
$391$	−11878.8	+	67367.8i	−0.00392943	+	0.0222849i
$392$	−171159.	+	970689.i	−0.0562579	+	0.319055i
$393$	887988.	+	1.53804e6i	0.290019	+	0.502327i
$394$	273081.	−	229142.i	0.0886240	−	0.0743643i
$395$	1.19624e6	−	435395.i	0.385767	−	0.140408i
$396$	82102.3	−	142205.i	0.0263098	−	0.0455699i
$397$	−867409.	−	1.50240e6i	−0.276215	−	0.478419i	0.694226	−	0.719757i	$-0.255747\pi$
$397$	−867409.	−	1.50240e6i	−0.276215	−	0.478419i	−0.970441	+	0.241339i	$0.922414\pi$
$398$	282042.	+	236661.i	0.0892495	+	0.0748892i
$399$	447333.	−	774803.i	0.140669	−	0.243646i
$400$	394949.	+	2.23987e6i	0.123422	+	0.699959i
$401$	5.86353e6			1.82095			0.910475	−	0.413564i	$-0.135716\pi$
$401$	5.86353e6			1.82095			0.910475	+	0.413564i	$0.135716\pi$
$402$	−366784.	−	2.08014e6i	−0.113200	−	0.641988i
$403$	2.50965e6	−	2.10585e6i	0.769751	−	0.645898i
$404$	748300.	+	272359.i	0.228099	+	0.0830211i
$405$	5.32143e6	−	1.93684e6i	1.61209	−	0.586755i
$406$	1.00704e6			0.303203
$407$	−1.62821e6	+	2.67604e6i	−0.487219	+	0.800768i
$408$	−29599.1			−0.00880294
$409$	−5.61235e6	+	2.04273e6i	−1.65896	+	0.603812i	−0.990199	−	0.139664i	$-0.955398\pi$
$409$	−5.61235e6	+	2.04273e6i	−1.65896	+	0.603812i	−0.668762	+	0.743476i	$0.733176\pi$
$410$	5.25294e6	+	1.91191e6i	1.54327	+	0.561705i
$411$	1.14394e6	−	959879.i	0.334040	−	0.280293i
$412$	−109429.	−	620604.i	−0.0317607	−	0.180124i
$413$	956163.			0.275840
$414$	41168.1	+	233476.i	0.0118048	+	0.0669485i
$415$	−1.77431e6	+	3.07320e6i	−0.505720	+	0.875932i
$416$	650598.	+	545917.i	0.184323	+	0.154665i
$417$	2.77324e6	+	4.80339e6i	0.780992	+	1.35272i
$418$	−1.22218e6	+	2.11688e6i	−0.342132	+	0.592590i
$419$	−1.75212e6	+	637721.i	−0.487562	+	0.177458i	−0.574091	−	0.818791i	$-0.694645\pi$
$419$	−1.75212e6	+	637721.i	−0.487562	+	0.177458i	0.0865294	+	0.996249i	$0.472422\pi$
$420$	−739728.	+	620706.i	−0.204620	+	0.171697i
$421$	−1.78843e6	−	3.09764e6i	−0.491774	−	0.851778i	0.508181	−	0.861250i	$-0.330318\pi$
$421$	−1.78843e6	−	3.09764e6i	−0.491774	−	0.851778i	−0.999955	+	0.00947251i	$0.996985\pi$
$422$	789293.	−	4.47630e6i	0.215753	−	1.22360i
$423$	54146.3	−	307079.i	0.0147136	−	0.0834448i
$424$	1.51478e6	+	1.27105e6i	0.409200	+	0.343359i
$425$	−262889.	−	95683.9i	−0.0705993	−	0.0256960i
$426$	−3.22747e6	−	1.17470e6i	−0.861665	−	0.313620i
$427$	−714420.	−	599470.i	−0.189620	−	0.159110i
$428$	−258349.	+	1.46517e6i	−0.0681705	+	0.386614i
$429$	−795705.	+	4.51267e6i	−0.208741	+	1.18383i
$430$	−2.84457e6	−	4.92693e6i	−0.741899	−	1.28501i
$431$	−1.45563e6	+	1.22142e6i	−0.377448	+	0.316716i	−0.811699	−	0.584075i	$-0.801457\pi$
$431$	−1.45563e6	+	1.22142e6i	−0.377448	+	0.316716i	0.434252	+	0.900792i	$0.357013\pi$
$432$	−954963.	+	347578.i	−0.246194	+	0.0896072i
$433$	−1.32650e6	+	2.29757e6i	−0.340008	+	0.588911i	−0.984434	−	0.175756i	$-0.943763\pi$
$433$	−1.32650e6	+	2.29757e6i	−0.340008	+	0.588911i	0.644426	+	0.764667i	$0.277096\pi$
$434$	−296227.	−	513080.i	−0.0754918	−	0.130756i
$435$	−8.27852e6	−	6.94651e6i	−2.09763	−	1.76012i
$436$	−175886.	+	304644.i	−0.0443114	+	0.0767496i
$437$	−612830.	−	3.47553e6i	−0.153510	−	0.870598i
$438$	71217.1			0.0177378
$439$	−813979.	−	4.61631e6i	−0.201582	−	1.14323i	−0.902728	−	0.430211i	$-0.858439\pi$
$439$	−813979.	−	4.61631e6i	−0.201582	−	1.14323i	0.701146	−	0.713018i	$-0.252672\pi$
$440$	2.02105e6	−	1.69586e6i	0.497673	−	0.417598i
$441$	−394839.	−	143709.i	−0.0966770	−	0.0351875i
$442$	−98165.8	+	35729.4i	−0.0239004	+	0.00869902i
$443$	−3.57528e6			−0.865568			−0.432784	−	0.901498i	$-0.642469\pi$
$443$	−3.57528e6			−0.865568			−0.432784	+	0.901498i	$0.642469\pi$
$444$	1.85379e6	−	626823.i	0.446274	−	0.150899i
$445$	9.82239e6			2.35135
$446$	−2.95355e6	+	1.07501e6i	−0.703085	+	0.255902i
$447$	4.43816e6	+	1.61536e6i	1.05059	+	0.382384i
$448$	117654.	−	98723.7i	0.0276957	−	0.0232395i
$449$	−1.11770e6	−	6.33881e6i	−0.261644	−	1.48386i	−0.778425	−	0.627738i	$-0.783981\pi$
$449$	−1.11770e6	−	6.33881e6i	−0.261644	−	1.48386i	0.516781	−	0.856118i	$-0.327130\pi$
$450$	−969563.			−0.225707
$451$	−833000.	−	4.72418e6i	−0.192843	−	1.09367i
$452$	1.56689e6	−	2.71394e6i	0.360739	−	0.624818i
$453$	2.27523e6	+	1.90914e6i	0.520930	+	0.437113i
$454$	1.51836e6	+	2.62987e6i	0.345728	+	0.598818i
$455$	−1.70406e6	+	2.95152e6i	−0.385883	+	0.668370i
$456$	1.43494e6	−	522274.i	0.323162	−	0.117621i
$457$	700895.	−	588120.i	0.156986	−	0.131727i	−0.560911	−	0.827876i	$-0.689549\pi$
$457$	700895.	−	588120.i	0.156986	−	0.131727i	0.717898	+	0.696149i	$0.245105\pi$
$458$	2.18258e6	+	3.78034e6i	0.486191	+	0.842107i
$459$	21706.3	−	123103.i	0.00480900	−	0.0272732i
$460$	−661451.	+	3.75127e6i	−0.145748	+	0.826578i
$461$	−4.67275e6	−	3.92090e6i	−1.02405	−	0.859278i	−0.0339172	−	0.999425i	$-0.510798\pi$
$461$	−4.67275e6	−	3.92090e6i	−1.02405	−	0.859278i	−0.990131	+	0.140146i	$0.955243\pi$
$462$	778686.	+	283419.i	0.169730	+	0.0617765i
$463$	3.25325e6	+	1.18409e6i	0.705286	+	0.256703i	0.669666	−	0.742662i	$-0.266437\pi$
$463$	3.25325e6	+	1.18409e6i	0.705286	+	0.256703i	0.0356197	+	0.999365i	$0.488660\pi$
$464$	1.31670e6	+	1.10485e6i	0.283918	+	0.238236i
$465$	−1.10401e6	+	6.26118e6i	−0.236779	+	1.34284i
$466$	5579.82	−	31644.7i	0.00119030	−	0.00675051i
$467$	1.15018e6	+	1.99217e6i	0.244048	+	0.422703i	0.961863	−	0.273530i	$-0.0881913\pi$
$467$	1.15018e6	+	1.99217e6i	0.244048	+	0.422703i	−0.717816	+	0.696233i	$0.754858\pi$
$468$	−277343.	+	232719.i	−0.0585333	+	0.0491153i
$469$	−1.26683e6	+	461088.i	−0.265941	+	0.0967947i
$470$	2.50499e6	−	4.33877e6i	0.523071	−	0.905986i
$471$	−1.81528e6	−	3.14416e6i	−0.377043	−	0.653058i
$472$	1.25018e6	+	1.04902e6i	0.258296	+	0.216736i
$473$	−2.44104e6	+	4.22800e6i	−0.501674	+	0.868925i
$474$	118507.	+	672084.i	0.0242268	+	0.137397i
$475$	1.44330e7			2.93509
$476$	3280.50	+	18604.6i	0.000663624	+	0.00376360i
$477$	−645736.	+	541837.i	−0.129945	+	0.109037i
$478$	4.41545e6	+	1.60709e6i	0.883904	+	0.321715i
$479$	−4.80588e6	+	1.74920e6i	−0.957049	+	0.348337i	−0.772876	−	0.634557i	$-0.781183\pi$
$479$	−4.80588e6	+	1.74920e6i	−0.957049	+	0.348337i	−0.184173	+	0.982894i	$0.558961\pi$
$480$	−1.64818e6			−0.326514
$481$	5.39146e6	−	4.31660e6i	1.06254	−	0.850704i
$482$	3.20459e6			0.628282
$483$	−1.12426e6	+	409198.i	−0.219280	+	0.0798115i
$484$	293931.	+	106982.i	0.0570337	+	0.0207586i
$485$	1.00822e6	−	845999.i	0.194627	−	0.163311i
$486$	−142861.	−	810206.i	−0.0274362	−	0.155598i
$487$	−3.29907e6			−0.630332			−0.315166	−	0.949037i	$-0.602060\pi$
$487$	−3.29907e6			−0.630332			−0.315166	+	0.949037i	$0.602060\pi$
$488$	−276412.	−	1.56761e6i	−0.0525420	−	0.297981i
$489$	71021.0	−	123012.i	0.0134312	−	0.0232635i
$490$	−5.17159e6	−	4.33948e6i	−0.973048	−	0.816484i
$491$	−2.86299e6	−	4.95884e6i	−0.535939	−	0.928274i	−0.999117	−	0.0420087i	$-0.986624\pi$
$491$	−2.86299e6	−	4.95884e6i	−0.535939	−	0.928274i	0.463178	−	0.886265i	$-0.346709\pi$
$492$	−1.49840e6	+	2.59530e6i	−0.279071	+	0.483365i
$493$	−198672.	+	72310.6i	−0.0368145	+	0.0133994i
$494$	4.12855e6	−	3.46426e6i	0.761167	−	0.638695i
$495$	562338.	+	973997.i	0.103154	+	0.178667i
$496$	175594.	−	995845.i	0.0320484	−	0.181755i
$497$	−380661.	+	2.15883e6i	−0.0691269	+	0.392038i
$498$	−1.45732e6	−	1.22284e6i	−0.263319	−	0.220950i
$499$	−2.12650e6	−	773982.i	−0.382308	−	0.139149i	0.143715	−	0.989619i	$-0.454095\pi$
$499$	−2.12650e6	−	773982.i	−0.382308	−	0.139149i	−0.526023	+	0.850470i	$0.676317\pi$
$500$	−9.48964e6	−	3.45395e6i	−1.69756	−	0.617861i
$501$	6.99344e6	+	5.86819e6i	1.24479	+	1.04450i
$502$	−1.18853e6	+	6.74050e6i	−0.210500	+	1.19380i
$503$	1.74562e6	−	9.89992e6i	0.307631	−	1.74466i	−0.303223	−	0.952920i	$-0.598063\pi$
$503$	1.74562e6	−	9.89992e6i	0.307631	−	1.74466i	0.610854	−	0.791743i	$-0.290826\pi$
$504$	32736.2	+	56700.8i	0.00574054	+	0.00994290i
$505$	−4.17817e6	+	3.50590e6i	−0.729050	+	0.611746i
$506$	3.07165e6	−	1.11799e6i	0.533329	−	0.194116i
$507$	2.32497e6	−	4.02696e6i	0.401695	−	0.695756i
$508$	51334.0	+	88913.1i	0.00882563	+	0.0152864i
$509$	3.41804e6	+	2.86808e6i	0.584767	+	0.490678i	0.886509	−	0.462712i	$-0.153124\pi$
$509$	3.41804e6	+	2.86808e6i	0.584767	+	0.490678i	−0.301742	+	0.953390i	$0.597568\pi$
$510$	101366.	−	175570.i	0.0172570	−	0.0298900i
$511$	−7893.07	−	44763.8i	−0.00133719	−	0.00758359i
$512$	262144.			0.0441942
$513$	1.11984e6	+	6.35092e6i	0.187872	+	1.06547i
$514$	−2.75141e6	+	2.30871e6i	−0.459354	+	0.385444i
$515$	4.05593e6	+	1.47624e6i	0.673865	+	0.245267i
$516$	2.86598e6	−	1.04313e6i	0.473858	−	0.172470i
$517$	−4.29926e6			−0.707404
$518$	−599449.	−	1.09573e6i	−0.0981585	−	0.179424i
$519$	−3.02623e6			−0.493156
$520$	−5.46621e6	+	1.98954e6i	−0.886499	+	0.322659i
$521$	986474.	+	359047.i	0.159218	+	0.0579505i	0.420399	−	0.907339i	$-0.361890\pi$
$521$	986474.	+	359047.i	0.159218	+	0.0579505i	−0.261182	+	0.965290i	$0.584112\pi$
$522$	−561298.	+	470985.i	−0.0901607	+	0.0756538i
$523$	733954.	+	4.16246e6i	0.117332	+	0.665420i	0.985569	+	0.169272i	$0.0541417\pi$
$523$	733954.	+	4.16246e6i	0.117332	+	0.665420i	−0.868238	+	0.496148i	$0.834747\pi$
$524$	1.93470e6			0.307813
$525$	−849646.	−	4.81858e6i	−0.134536	−	0.762994i
$526$	2.62763e6	−	4.55118e6i	0.414094	−	0.717232i
$527$	95281.8	+	79950.9i	0.0149446	+	0.0125400i
$528$	707185.	+	1.22488e6i	0.110395	+	0.191209i
$529$	858450.	−	1.48688e6i	0.133375	−	0.231013i
$530$	−1.27269e7	+	4.63222e6i	−1.96804	+	0.716308i
$531$	−532938.	+	447188.i	−0.0820239	+	0.0688263i
$532$	−487313.	−	844051.i	−0.0746499	−	0.129297i
$533$	−1.83664e6	+	1.04161e7i	−0.280031	+	1.58813i
$534$	−914383.	+	5.18572e6i	−0.138763	+	0.786967i
$535$	−7.80606e6	−	6.55006e6i	−1.17909	−	0.989375i
$536$	−2.16224e6	−	786991.i	−0.325081	−	0.118320i
$537$	−8.75745e6	−	3.18745e6i	−1.31052	−	0.476988i
$538$	57429.9	+	48189.4i	0.00855426	+	0.00717787i
$539$	−1.00600e6	+	5.70533e6i	−0.149151	+	0.845880i
$540$	1.20868e6	−	6.85479e6i	0.178373	−	1.01160i
$541$	−23467.6	−	40647.1i	−0.00344728	−	0.00597086i	0.864297	−	0.502982i	$-0.167764\pi$
$541$	−23467.6	−	40647.1i	−0.00344728	−	0.00597086i	−0.867744	+	0.497012i	$0.834431\pi$
$542$	−5.30933e6	+	4.45506e6i	−0.776322	+	0.651411i
$543$	−1.67979e6	+	611393.i	−0.244487	+	0.0889859i
$544$	−16122.3	+	27924.6i	−0.00233576	+	0.00404566i
$545$	−1.20469e6	−	2.08658e6i	−0.173733	−	0.300914i
$546$	−1.39962e6	−	1.17442e6i	−0.200922	−	0.168594i
$547$	1.21689e6	−	2.10772e6i	0.173894	−	0.301193i	−0.765884	−	0.642979i	$-0.777698\pi$
$547$	1.21689e6	−	2.10772e6i	0.173894	−	0.301193i	0.939778	+	0.341786i	$0.111032\pi$
$548$	−282486.	−	1.60206e6i	−0.0401833	−	0.227891i
$549$	678564.			0.0960860
$550$	2.32136e6	+	1.31651e7i	0.327216	+	1.85574i
$551$	8.35551e6	−	7.01110e6i	1.17245	−	0.983801i
$552$	−1.91891e6	−	698425.i	−0.268044	−	0.0975600i
$553$	409307.	−	148976.i	0.0569163	−	0.0207158i
$554$	1.86925e6			0.258758
$555$	−2.63044e6	+	1.31426e7i	−0.362489	+	1.81112i
$556$	6.04219e6			0.828910
$557$	1.67211e6	−	608597.i	0.228363	−	0.0831174i	−0.225304	−	0.974288i	$-0.572338\pi$
$557$	1.67211e6	−	608597.i	0.228363	−	0.0831174i	0.453667	+	0.891171i	$0.350115\pi$
$558$	405071.	+	147434.i	0.0550739	+	0.0200452i
$559$	8.24588e6	−	6.91912e6i	1.11611	−	0.936529i
$560$	182669.	+	1.03597e6i	0.0246148	+	0.139597i
$561$	−173972.			−0.0233384
$562$	865407.	+	4.90797e6i	0.115579	+	0.655482i
$563$	−3.79224e6	+	6.56835e6i	−0.504226	+	0.873344i	0.495763	+	0.868458i	$0.334889\pi$
$563$	−3.79224e6	+	6.56835e6i	−0.504226	+	0.873344i	−0.999988	+	0.00488611i	$0.998445\pi$
$564$	2.05745e6	+	1.72641e6i	0.272353	+	0.228531i
$565$	1.07320e7	+	1.85884e7i	1.41436	+	2.44974i
$566$	4.03702e6	−	6.99232e6i	0.529688	−	0.917446i
$567$	1.82079e6	−	662714.i	0.237850	−	0.0865702i
$568$	−2.86621e6	+	2.40504e6i	−0.372767	+	0.312788i
$569$	−709469.	−	1.22884e6i	−0.0918656	−	0.159116i	0.816431	−	0.577444i	$-0.195950\pi$
$569$	−709469.	−	1.22884e6i	−0.0918656	−	0.159116i	−0.908296	+	0.418328i	$0.862616\pi$
$570$	−1.81618e6	+	1.03001e7i	−0.234138	+	1.32786i
$571$	978859.	−	5.55139e6i	0.125641	−	0.712543i	−0.855285	−	0.518158i	$-0.826618\pi$
$571$	978859.	−	5.55139e6i	0.125641	−	0.712543i	0.980925	−	0.194385i	$-0.0622711\pi$
$572$	3.82396e6	+	3.20868e6i	0.488678	+	0.410050i
$573$	−9.09408e6	−	3.30997e6i	−1.15710	−	0.421151i
$574$	1.79736e6	+	654184.i	0.227696	+	0.0828744i
$575$	−1.47853e7	−	1.24064e7i	−1.86492	−	1.56486i
$576$	−19405.1	+	110052.i	−0.00243702	+	0.0138210i
$577$	2.32914e6	−	1.32092e7i	0.291243	−	1.65172i	−0.390848	−	0.920455i	$-0.627818\pi$
$577$	2.32914e6	−	1.32092e7i	0.291243	−	1.65172i	0.682092	−	0.731267i	$-0.261071\pi$
$578$	2.83773e6	+	4.91509e6i	0.353306	+	0.611945i
$579$	−7581.23	+	6361.41i	−0.000939817	+	0.000788600i
$580$	−1.10627e7	+	4.02650e6i	−1.36550	+	0.497002i
$581$	−607103.	+	1.05153e6i	−0.0746142	+	0.129236i
$582$	352787.	+	611046.i	0.0431724	+	0.0747767i
$583$	8.90328e6	+	7.47074e6i	1.08487	+	0.910316i
$584$	38791.1	−	67188.1i	0.00470652	−	0.00815193i
$585$	−430602.	−	2.44206e6i	−0.0520219	−	0.295031i
$586$	8.14663e6			0.980018
$587$	1.61829e6	+	9.17778e6i	0.193848	+	1.09937i	0.914050	+	0.405602i	$0.132938\pi$
$587$	1.61829e6	+	9.17778e6i	0.193848	+	1.09937i	−0.720202	+	0.693764i	$0.755951\pi$
$588$	2.77246e6	−	2.32637e6i	0.330691	−	0.277482i
$589$	−6.02990e6	−	2.19471e6i	−0.716180	−	0.260668i
$590$	−1.05038e7	+	3.82306e6i	−1.24227	+	0.452149i
$591$	−1.30894e6			−0.154153
$592$	418373.	−	2.09033e6i	0.0490636	−	0.245138i
$593$	−9.27831e6			−1.08351			−0.541754	−	0.840537i	$-0.682240\pi$
$593$	−9.27831e6			−1.08351			−0.541754	+	0.840537i	$0.682240\pi$
$594$	−5.61289e6	+	2.04293e6i	−0.652711	+	0.237567i
$595$	−121590.	−	44255.1i	−0.0140801	−	0.00512473i
$596$	3.94138e6	−	3.30721e6i	0.454499	−	0.381370i
$597$	−234754.	−	1.33135e6i	−0.0269573	−	0.152883i
$598$	−7.20716e6			−0.824159
$599$	−1.98547e6	−	1.12602e7i	−0.226098	−	1.28227i	−0.860575	−	0.509324i	$-0.829896\pi$
$599$	−1.98547e6	−	1.12602e7i	−0.226098	−	1.28227i	0.634477	−	0.772942i	$-0.281215\pi$
$600$	4.17565e6	−	7.23243e6i	0.473528	−	0.820175i
$601$	−3.86745e6	−	3.24518e6i	−0.436756	−	0.366482i	0.397738	−	0.917499i	$-0.369795\pi$
$601$	−3.86745e6	−	3.24518e6i	−0.436756	−	0.366482i	−0.834494	+	0.551017i	$0.814240\pi$
$602$	−973303.	−	1.68581e6i	−0.109460	−	0.189591i
$603$	490448.	−	849481.i	0.0549287	−	0.0951394i
$604$	3.04043e6	−	1.10662e6i	0.339111	−	0.123426i
$605$	−1.64117e6	+	1.37711e6i	−0.182291	+	0.152961i
$606$	−1.46198e6	−	2.53223e6i	−0.161719	−	0.280106i
$607$	−244884.	+	1.38880e6i	−0.0269766	+	0.152992i	−0.995321	−	0.0966275i	$-0.969194\pi$
$607$	−244884.	+	1.38880e6i	−0.0269766	+	0.152992i	0.968344	+	0.249620i	$0.0803056\pi$
$608$	288865.	−	1.63823e6i	0.0316910	−	0.179728i
$609$	−2.83260e6	−	2.37683e6i	−0.309487	−	0.259690i
$610$	1.02450e7	+	3.72889e6i	1.11478	+	0.405747i
$611$	8.90755e6	+	3.24208e6i	0.965284	+	0.351335i
$612$	−10529.7	−	8835.44i	−0.00113641	−	0.000953564i
$613$	−251108.	+	1.42411e6i	−0.0269905	+	0.153070i	−0.995324	−	0.0965877i	$-0.969207\pi$
$613$	−251108.	+	1.42411e6i	−0.0269905	+	0.153070i	0.968334	+	0.249658i	$0.0803183\pi$
$614$	−1.23349e6	+	6.99546e6i	−0.132043	+	0.748851i
$615$	−1.02629e7	−	1.77758e7i	−1.09416	−	1.89514i
$616$	691525.	−	580259.i	0.0734271	−	0.0616126i
$617$	−1.79859e6	+	654632.i	−0.190203	+	0.0692284i	−0.435366	−	0.900254i	$-0.643381\pi$
$617$	−1.79859e6	+	654632.i	−0.190203	+	0.0692284i	0.245162	+	0.969482i	$0.421159\pi$
$618$	−1.15695e6	+	2.00390e6i	−0.121855	+	0.211060i
$619$	224957.	+	389637.i	0.0235979	+	0.0408727i	0.877583	−	0.479424i	$-0.159155\pi$
$619$	224957.	+	389637.i	0.0235979	+	0.0408727i	−0.853985	+	0.520297i	$0.825821\pi$
$620$	5.30562e6	+	4.45194e6i	0.554315	+	0.465126i
$621$	4.31197e6	−	7.46856e6i	0.448691	−	0.777155i
$622$	−905413.	−	5.13485e6i	−0.0938363	−	0.532172i
$623$	3.36085e6			0.346920
$624$	−541516.	−	3.07109e6i	−0.0556737	−	0.315741i
$625$	3.17174e7	−	2.66141e7i	3.24786	−	2.72528i
$626$	−2.47655e6	−	901389.i	−0.252587	−	0.0919341i
$627$	8.43399e6	−	3.06972e6i	0.856770	−	0.311839i
$628$	−3.95504e6			−0.400177
$629$	196939.	+	173125.i	0.0198475	+	0.0174475i
$630$	−448436.			−0.0450142
$631$	1.58705e7	−	5.77639e6i	1.58678	−	0.577542i	0.610118	−	0.792311i	$-0.291122\pi$
$631$	1.58705e7	−	5.77639e6i	1.58678	−	0.577542i	0.976665	+	0.214769i	$0.0688999\pi$
$632$	698611.	+	254274.i	0.0695733	+	0.0253226i
$633$	−1.27851e7	+	1.07280e7i	−1.26822	+	1.06416i
$634$	−1.86777e6	−	1.05926e7i	−0.184544	−	1.04660i
$635$	−703197.			−0.0692058
$636$	−1.26081e6	−	7.15040e6i	−0.123596	−	0.700950i
$637$	6.38671e6	−	1.10621e7i	0.623633	−	1.08016i
$638$	7.73907e6	+	6.49385e6i	0.752726	+	0.631612i
$639$	−797497.	−	1.38131e6i	−0.0772639	−	0.133825i
$640$	−897742.	+	1.55494e6i	−0.0866367	+	0.150059i
$641$	−1.19455e7	+	4.34781e6i	−1.14831	+	0.417951i	−0.844908	−	0.534911i	$-0.820345\pi$
$641$	−1.19455e7	+	4.34781e6i	−1.14831	+	0.417951i	−0.303403	+	0.952862i	$0.598123\pi$
$642$	4.18478e6	−	3.51145e6i	0.400714	−	0.336239i
$643$	−2.45531e6	−	4.25271e6i	−0.234195	−	0.405638i	0.724843	−	0.688914i	$-0.241912\pi$
$643$	−2.45531e6	−	4.25271e6i	−0.234195	−	0.405638i	−0.959039	+	0.283276i	$0.908579\pi$
$644$	−226323.	+	1.28354e6i	−0.0215038	+	0.121954i
$645$	−3.62743e6	+	2.05722e7i	−0.343320	+	1.94707i
$646$	156745.	+	131525.i	0.0147779	+	0.0124001i
$647$	7.15621e6	+	2.60465e6i	0.672082	+	0.244618i	0.655444	−	0.755244i	$-0.272481\pi$
$647$	7.15621e6	+	2.60465e6i	0.672082	+	0.244618i	0.0166382	+	0.999862i	$0.494704\pi$
$648$	3.10775e6	+	1.13113e6i	0.290743	+	0.105822i
$649$	7.34805e6	+	6.16575e6i	0.684795	+	0.574611i
$650$	5.11824e6	−	2.90270e7i	0.475157	−	2.69475i
$651$	−377752.	+	2.14234e6i	−0.0349345	+	0.198123i
$652$	−77368.4	−	134006.i	−0.00712763	−	0.0123454i
$653$	7.29634e6	−	6.12236e6i	0.669610	−	0.561870i	−0.243340	−	0.969941i	$-0.578243\pi$
$653$	7.29634e6	−	6.12236e6i	0.669610	−	0.561870i	0.912950	+	0.408071i	$0.133799\pi$
$654$	1.21375e6	−	441770.i	0.110965	−	0.0403879i
$655$	−6.62562e6	+	1.14759e7i	−0.603425	+	1.04516i
$656$	1.63232e6	+	2.82726e6i	0.148097	+	0.256511i
$657$	25335.0	+	21258.6i	0.00228985	+	0.00192141i
$658$	857112.	−	1.48456e6i	0.0771743	−	0.133670i
$659$	3.82437e6	+	2.16891e7i	0.343041	+	1.94548i	0.325208	+	0.945642i	$0.394566\pi$
$659$	3.82437e6	+	2.16891e7i	0.343041	+	1.94548i	0.0178329	+	0.999841i	$0.494323\pi$
$660$	−9.68734e6			−0.865655
$661$	2.82554e6	+	1.60244e7i	0.251534	+	1.42652i	0.804814	+	0.593527i	$0.202265\pi$
$661$	2.82554e6	+	1.60244e7i	0.251534	+	1.42652i	−0.553280	+	0.832995i	$0.686624\pi$
$662$	−1.05485e7	+	8.85122e6i	−0.935501	+	0.784979i
$663$	360448.	+	131192.i	0.0318463	+	0.0115911i
$664$	−1.94744e6	+	708810.i	−0.171413	+	0.0623892i
$665$	6.67544e6			0.585364
$666$	846580.	+	330374.i	0.0739576	+	0.0288616i
$667$	−1.45861e7			−1.26948
$668$	9.34545e6	−	3.40147e6i	0.810325	−	0.294934i
$669$	1.08449e7	+	3.94724e6i	0.936833	+	0.340979i
$670$	1.20730e7	−	1.01304e7i	1.03903	−	0.871847i
$671$	−1.62464e6	−	9.21378e6i	−0.139300	−	0.790008i
$672$	−563945.			−0.0481741
$673$	933776.	+	5.29570e6i	0.0794703	+	0.450699i	0.998413	+	0.0563084i	$0.0179330\pi$
$673$	933776.	+	5.29570e6i	0.0794703	+	0.450699i	−0.918943	+	0.394390i	$0.870956\pi$
$674$	−3.11429e6	+	5.39411e6i	−0.264064	+	0.457372i
$675$	2.70175e7	+	2.26704e7i	2.28237	+	1.91514i
$676$	−2.53276e6	−	4.38687e6i	−0.213171	−	0.369222i
$677$	2.24426e6	−	3.88718e6i	0.188192	−	0.325959i	−0.756455	−	0.654046i	$-0.773070\pi$
$677$	2.24426e6	−	3.88718e6i	0.188192	−	0.325959i	0.944648	+	0.328087i	$0.106404\pi$
$678$	−1.08128e7	+	3.93553e6i	−0.903365	+	0.328798i
$679$	344976.	−	289469.i	0.0287153	−	0.0240950i
$680$	−110425.	−	191262.i	−0.00915789	−	0.0158619i
$681$	1.93623e6	−	1.09809e7i	0.159989	−	0.907341i
$682$	1.03207e6	−	5.85318e6i	0.0849669	−	0.481871i
$683$	6.43306e6	+	5.39798e6i	0.527674	+	0.442771i	0.867297	−	0.497791i	$-0.165855\pi$
$683$	6.43306e6	+	5.39798e6i	0.527674	+	0.442771i	−0.339623	+	0.940562i	$0.610300\pi$
$684$	666370.	+	242539.i	0.0544597	+	0.0198217i
$685$	1.04702e7	+	3.81083e6i	0.852565	+	0.310308i
$686$	−3.70059e6	−	3.10517e6i	−0.300235	−	0.251927i
$687$	2.78326e6	−	1.57846e7i	0.224989	−	1.27598i
$688$	576945.	−	3.27202e6i	0.0464690	−	0.263539i
$689$	−1.28128e7	−	2.21925e7i	−1.02825	−	1.78097i
$690$	1.07143e7	−	8.99037e6i	0.856724	−	0.718877i
$691$	−1.72588e7	+	6.28167e6i	−1.37504	+	0.500472i	−0.920670	−	0.390342i	$-0.872357\pi$
$691$	−1.72588e7	+	6.28167e6i	−1.37504	+	0.500472i	−0.454367	+	0.890815i	$0.650134\pi$
$692$	−1.64835e6	+	2.85503e6i	−0.130853	+	0.226645i
$693$	192411.	+	333265.i	0.0152193	+	0.0263607i
$694$	671558.	+	563504.i	0.0529279	+	0.0444118i
$695$	−2.06922e7	+	3.58399e7i	−1.62497	+	2.81452i
$696$	−1.09594e6	−	6.21539e6i	−0.0857560	−	0.486346i
$697$	−401560.			−0.0313089
$698$	2.82776e6	+	1.60371e7i	0.219687	+	1.24591i
$699$	−90382.9	+	75840.2i	−0.00699670	+	0.00587093i
$700$	−5.00877e6	−	1.82304e6i	−0.386354	−	0.140621i
$701$	2.52244e6	−	918092.i	0.193876	−	0.0705653i	−0.243257	−	0.969962i	$-0.578216\pi$
$701$	2.52244e6	−	918092.i	0.193876	−	0.0705653i	0.437134	+	0.899397i	$0.355994\pi$
$702$	1.31698e7			1.00864
$703$	−1.26022e7	−	4.91797e6i	−0.961743	−	0.375316i
$704$	1.54078e6			0.117168
$705$	−1.72864e7	+	6.29173e6i	−1.30988	+	0.476757i
$706$	7.38592e6	+	2.68825e6i	0.557690	+	0.202983i
$707$	−1.42961e6	+	1.19959e6i	−0.107565	+	0.0902574i
$708$	−1.04057e6	−	5.90136e6i	−0.0780167	−	0.442455i
$709$	−7.10003e6			−0.530450			−0.265225	−	0.964187i	$-0.585446\pi$
$709$	−7.10003e6			−0.530450			−0.265225	+	0.964187i	$0.585446\pi$
$710$	−4.45006e6	−	2.52376e7i	−0.331299	−	1.87889i
$711$	−158462.	+	274464.i	−0.0117558	+	0.0203616i
$712$	4.39430e6	+	3.68725e6i	0.324855	+	0.272586i
$713$	4.29058e6	+	7.43150e6i	0.316076	+	0.547460i
$714$	34683.4	−	60073.5i	0.00254611	−	0.00440999i
$715$	−3.21282e7	+	1.16937e7i	−2.35029	+	0.855436i
$716$	−7.77720e6	+	6.52584e6i	−0.566945	+	0.475723i
$717$	−8.62664e6	−	1.49418e7i	−0.626677	−	1.08544i
$718$	−286010.	+	1.62204e6i	−0.0207048	+	0.117423i
$719$	−1.43986e6	+	8.16584e6i	−0.103872	+	0.589086i	0.887793	+	0.460243i	$0.152238\pi$
$719$	−1.43986e6	+	8.16584e6i	−0.103872	+	0.589086i	−0.991665	+	0.128843i	$0.958874\pi$
$720$	−586328.	−	491988.i	−0.0421512	−	0.0353690i
$721$	1.38779e6	+	505113.i	0.0994225	+	0.0361868i
$722$	−612522.	−	222940.i	−0.0437299	−	0.0159164i
$723$	−9.01382e6	−	7.56349e6i	−0.641303	−	0.538117i
$724$	−338156.	+	1.91778e6i	−0.0239756	+	0.135973i
$725$	1.03585e7	−	5.87459e7i	0.731899	−	4.15080i
$726$	−574264.	−	994654.i	−0.0404362	−	0.0700375i
$727$	1.51772e7	−	1.27351e7i	1.06501	−	0.893651i	0.0704205	−	0.997517i	$-0.477566\pi$
$727$	1.51772e7	−	1.27351e7i	1.06501	−	0.893651i	0.994591	+	0.103866i	$0.0331215\pi$
$728$	−1.87033e6	+	680745.i	−0.130795	+	0.0476054i
$729$	−7.78893e6	+	1.34908e7i	−0.542824	+	0.940199i
$730$	265689.	+	460187.i	0.0184530	+	0.0319615i
$731$	313065.	+	262692.i	0.0216691	+	0.0181825i
$732$	−2.92239e6	+	5.06173e6i	−0.201586	+	0.349158i
$733$	−1.45739e6	−	8.26525e6i	−0.100188	−	0.568193i	−0.993034	−	0.117831i	$-0.962406\pi$
$733$	−1.45739e6	−	8.26525e6i	−0.100188	−	0.568193i	0.892846	−	0.450362i	$-0.148705\pi$
$734$	−2.18699e6			−0.149832
$735$	4.30451e6	+	2.44121e7i	0.293904	+	1.66681i
$736$	−1.70412e6	+	1.42992e6i	−0.115959	+	0.0973012i
$737$	−1.27088e7	−	4.62562e6i	−0.861857	−	0.313690i
$738$	−1.30775e6	+	475983.i	−0.0883862	+	0.0321700i
$739$	9.68391e6			0.652288			0.326144	−	0.945320i	$-0.394251\pi$
$739$	9.68391e6			0.652288			0.326144	+	0.945320i	$0.394251\pi$
$740$	1.09663e7	+	9.64021e6i	0.736172	+	0.647153i
$741$	−1.97891e7			−1.32398
$742$	−4.35467e6	+	1.58497e6i	−0.290366	+	0.105685i
$743$	2.46978e6	+	898925.i	0.164129	+	0.0597381i	0.422778	−	0.906233i	$-0.361055\pi$
$743$	2.46978e6	+	898925.i	0.164129	+	0.0597381i	−0.258649	+	0.965971i	$0.583277\pi$
$744$	−2.84431e6	+	2.38666e6i	−0.188384	+	0.158073i
$745$	6.11936e6	+	3.47046e7i	0.403939	+	2.29085i
$746$	8.88296e6			0.584401
$747$	−153410.	−	870031.i	−0.0100589	−	0.0570470i
$748$	−94760.2	+	164129.i	−0.00619259	+	0.0107259i
$749$	−2.67094e6	−	2.24118e6i	−0.173964	−	0.145973i
$750$	1.85403e7	+	3.21127e7i	1.20355	+	2.08461i
$751$	−4.39640e6	+	7.61480e6i	−0.284445	+	0.492673i	−0.972474	−	0.233010i	$-0.925143\pi$
$751$	−4.39640e6	+	7.61480e6i	−0.284445	+	0.492673i	0.688030	+	0.725683i	$0.258476\pi$
$752$	2.74941e6	−	1.00070e6i	0.177294	−	0.0645299i
$753$	1.92521e7	−	1.61544e7i	1.23734	−	1.03825i
$754$	−1.11374e7	−	1.92905e7i	−0.713436	−	1.23571i
$755$	−3.84823e6	+	2.18244e7i	−0.245693	+	1.39340i
$756$	413566.	−	2.34545e6i	0.0263172	−	0.149252i
$757$	6.41505e6	+	5.38287e6i	0.406874	+	0.341408i	0.823144	−	0.567833i	$-0.192218\pi$
$757$	6.41505e6	+	5.38287e6i	0.406874	+	0.341408i	−0.416269	+	0.909241i	$0.636663\pi$
$758$	−1.96390e7	−	7.14801e6i	−1.24150	−	0.451868i
$759$	−1.12786e7	−	4.10506e6i	−0.710640	−	0.258652i
$760$	8.72811e6	+	7.32375e6i	0.548133	+	0.459938i
$761$	297191.	−	1.68545e6i	0.0186026	−	0.105501i	−0.974093	−	0.226149i	$-0.927386\pi$
$761$	297191.	−	1.68545e6i	0.0186026	−	0.105501i	0.992695	+	0.120649i	$0.0384974\pi$
$762$	65461.8	−	371252.i	0.00408414	−	0.0231623i
$763$	−412198.	−	713947.i	−0.0256327	−	0.0443971i
$764$	−8.07614e6	+	6.77669e6i	−0.500577	+	0.420034i
$765$	88468.4	−	32199.9i	0.00546556	−	0.00198930i
$766$	1.01106e7	−	1.75120e7i	0.622592	−	1.07836i
$767$	−1.05747e7	−	1.83159e7i	−0.649050	−	1.12419i
$768$	−737355.	−	618714.i	−0.0451101	−	0.0378518i
$769$	−6.50694e6	+	1.12704e7i	−0.396790	+	0.687261i	−0.993328	−	0.115324i	$-0.963209\pi$
$769$	−6.50694e6	+	1.12704e7i	−0.396790	+	0.687261i	0.596538	+	0.802585i	$0.296543\pi$
$770$	1.07366e6	+	6.08902e6i	0.0652588	+	0.370101i
$771$	1.31881e7			0.799002
$772$	1872.12	+	10617.3i	0.000113055	+	0.000641167i
$773$	−1.41528e7	+	1.18756e7i	−0.851910	+	0.714837i	−0.960209	−	0.279281i	$-0.909904\pi$
$773$	−1.41528e7	+	1.18756e7i	−0.851910	+	0.714837i	0.108300	+	0.994118i	$0.465459\pi$
$774$	1.33093e6	+	484419.i	0.0798551	+	0.0290649i
$775$	−3.29775e7	+	1.20028e7i	−1.97225	+	0.717842i
$776$	768636.			0.0458212
$777$	−900036.	+	4.49689e6i	−0.0534820	+	0.267214i
$778$	−1.10283e7			−0.653219
$779$	1.94673e7	−	7.08550e6i	1.14937	−	0.418338i
$780$	2.00710e7	+	7.30525e6i	1.18122	+	0.429931i
$781$	−1.68464e7	+	1.41358e7i	−0.988282	+	0.829267i
$782$	−47515.1	−	269471.i	−0.00277853	−	0.0157578i
$783$	2.66536e7			1.55364
$784$	−684635.	−	3.88276e6i	−0.0397804	−	0.225606i
$785$	1.35445e7	−	2.34597e7i	0.784492	−	1.35878i
$786$	−5.44191e6	−	4.56630e6i	−0.314192	−	0.263638i
$787$	2.14462e6	+	3.71459e6i	0.123428	+	0.213784i	0.921117	−	0.389285i	$-0.127278\pi$
$787$	2.14462e6	+	3.71459e6i	0.123428	+	0.213784i	−0.797689	+	0.603069i	$0.793945\pi$
$788$	−712964.	+	1.23489e6i	−0.0409027	+	0.0708456i
$789$	−1.81327e7	+	6.59976e6i	−1.03698	+	0.377429i
$790$	−3.90073e6	+	3.27310e6i	−0.222371	+	0.186591i
$791$	3.67209e6	+	6.36024e6i	0.208676	+	0.361437i
$792$	−114055.	+	646840.i	−0.00646104	+	0.0366424i
$793$	−3.58208e6	+	2.03150e7i	−0.202280	+	1.14718i
$794$	5.31579e6	+	4.46048e6i	0.299238	+	0.251090i
$795$	4.67311e7	+	1.70087e7i	2.62234	+	0.954452i
$796$	−1.38390e6	−	503699.i	−0.0774146	−	0.0281766i
$797$	−3.14639e6	−	2.64013e6i	−0.175455	−	0.147225i	0.550831	−	0.834617i	$-0.314311\pi$
$797$	−3.14639e6	−	2.64013e6i	−0.175455	−	0.147225i	−0.726286	+	0.687392i	$0.758755\pi$
$798$	−621428.	+	3.52430e6i	−0.0345449	+	0.195914i
$799$	−62494.2	+	354422.i	−0.00346316	+	0.0196406i
$800$	−4.54885e6	−	7.87883e6i	−0.251291	−	0.435248i
$801$	−1.87324e6	+	1.57184e6i	−0.103160	+	0.0865619i
$802$	−2.20397e7	+	8.02178e6i	−1.20995	+	0.440387i
$803$	227999.	−	394905.i	0.0124780	−	0.0216124i
$804$	4.22445e6	+	7.31697e6i	0.230479	+	0.399201i
$805$	−6.83841e6	−	5.73811e6i	−0.371934	−	0.312089i
$806$	−6.55223e6	+	1.13488e7i	−0.355264	+	0.615336i
$807$	−47801.0	−	271093.i	−0.00258376	−	0.0146533i
$808$	−3.18530e6			−0.171641
$809$	286027.	+	1.62214e6i	0.0153651	+	0.0871399i	0.991526	−	0.129908i	$-0.0414683\pi$
$809$	286027.	+	1.62214e6i	0.0153651	+	0.0871399i	−0.976161	+	0.217048i	$0.930357\pi$
$810$	−1.73523e7	+	1.45603e7i	−0.929274	+	0.779753i
$811$	1.77140e7	+	6.44737e6i	0.945724	+	0.344215i	0.768424	−	0.639942i	$-0.221041\pi$
$811$	1.77140e7	+	6.44737e6i	0.945724	+	0.344215i	0.177300	+	0.984157i	$0.443264\pi$
$812$	−3.78525e6	+	1.37772e6i	−0.201467	+	0.0733280i
$813$	2.54489e7			1.35034
$814$	2.45903e6	−	1.22861e7i	0.130078	−	0.649912i
$815$	1.05983e6			0.0558910
$816$	111256.	−	40493.9i	0.00584923	−	0.00212895i
$817$	−1.98123e7	−	7.21108e6i	−1.03844	−	0.377959i
$818$	1.83009e7	−	1.53563e7i	0.956289	−	0.802422i
$819$	−147336.	−	835582.i	−0.00767535	−	0.0435291i
$820$	−2.23602e7			−1.16129
$821$	−2.02929e6	−	1.15087e7i	−0.105072	−	0.595891i	−0.991192	−	0.132435i	$-0.957720\pi$
$821$	−2.02929e6	−	1.15087e7i	−0.105072	−	0.595891i	0.886120	−	0.463456i	$-0.153391\pi$
$822$	−2.98661e6	+	5.17297e6i	−0.154170	+	0.267030i
$823$	−2.36411e7	−	1.98372e7i	−1.21666	−	1.02089i	−0.998993	−	0.0448709i	$-0.985712\pi$
$823$	−2.36411e7	−	1.98372e7i	−1.21666	−	1.02089i	−0.217662	−	0.976024i	$-0.569843\pi$
$824$	1.26036e6	+	2.18300e6i	0.0646659	+	0.112005i
$825$	2.45428e7	−	4.25094e7i	1.25542	−	2.17445i
$826$	−3.59400e6	+	1.30811e6i	−0.183285	+	0.0667104i
$827$	2.14833e7	−	1.80266e7i	1.09229	−	0.916539i	0.0954055	−	0.995438i	$-0.469585\pi$
$827$	2.14833e7	−	1.80266e7i	1.09229	−	0.916539i	0.996883	+	0.0789000i	$0.0251408\pi$
$828$	−474155.	−	821261.i	−0.0240350	−	0.0416299i
$829$	4.92744e6	−	2.79449e7i	0.249021	−	1.41227i	−0.561946	−	0.827174i	$-0.689947\pi$
$829$	4.92744e6	−	2.79449e7i	0.249021	−	1.41227i	0.810967	−	0.585092i	$-0.198942\pi$
$830$	2.46485e6	−	1.39789e7i	0.124192	−	0.704330i
$831$	−5.25780e6	−	4.41182e6i	−0.264120	−	0.221623i
$832$	−3.19231e6	−	1.16190e6i	−0.159881	−	0.0581918i
$833$	455712.	+	165866.i	0.0227550	+	0.00828216i
$834$	−1.69954e7	−	1.42608e7i	−0.846089	−	0.709953i
$835$	−1.18284e7	+	6.70823e7i	−0.587098	+	3.32960i
$836$	1.69783e6	−	9.62889e6i	0.0840193	−	0.476497i
$837$	−7.84027e6	−	1.35797e7i	−0.386827	−	0.670005i
$838$	5.71338e6	−	4.79409e6i	0.281050	−	0.235829i
$839$	7.21262e6	−	2.62518e6i	0.353743	−	0.128752i	−0.159035	−	0.987273i	$-0.550838\pi$
$839$	7.21262e6	−	2.62518e6i	0.353743	−	0.128752i	0.512779	+	0.858521i	$0.328616\pi$
$840$	1.93129e6	−	3.34510e6i	0.0944387	−	0.163573i
$841$	−1.22847e7	−	2.12777e7i	−0.598928	−	1.03737i
$842$	1.09601e7	+	9.19662e6i	0.532764	+	0.447042i
$843$	9.14961e6	−	1.58476e7i	0.443439	−	0.768059i
$844$	3.15717e6	+	1.79052e7i	0.152560	+	0.865213i
$845$	3.46949e7			1.67157
$846$	216585.	+	1.22832e6i	0.0104041	+	0.0590044i
$847$	−561548.	+	471195.i	−0.0268954	+	0.0225679i
$848$	−7.43262e6	−	2.70525e6i	−0.354938	−	0.129187i
$849$	−2.78586e7	+	1.01397e7i	−1.32645	+	0.482787i
$850$	1.11904e6			0.0531251
$851$	8.68248e6	+	1.58707e7i	0.410979	+	0.751229i
$852$	1.37384e7			0.648392
$853$	−2.22992e6	+	811624.i	−0.104934	+	0.0381929i	−0.393954	−	0.919130i	$-0.628893\pi$
$853$	−2.22992e6	+	811624.i	−0.104934	+	0.0381929i	0.289020	+	0.957323i	$0.406671\pi$
$854$	3.50547e6	+	1.27589e6i	0.164475	+	0.0598642i
$855$	−3.72070e6	+	3.12204e6i	−0.174064	+	0.146057i
$856$	−1.03339e6	−	5.86067e6i	−0.0482039	−	0.273378i
$857$	−3.75216e6			−0.174514			−0.0872569	−	0.996186i	$-0.527810\pi$
$857$	−3.75216e6			−0.174514			−0.0872569	+	0.996186i	$0.527810\pi$
$858$	−3.18282e6	−	1.80507e7i	−0.147603	−	0.837095i
$859$	1.61803e7	−	2.80251e7i	0.748174	−	1.29588i	−0.200522	−	0.979689i	$-0.564264\pi$
$859$	1.61803e7	−	2.80251e7i	0.748174	−	1.29588i	0.948697	−	0.316187i	$-0.102403\pi$
$860$	1.74325e7	+	1.46276e7i	0.803737	+	0.674415i
$861$	−3.51157e6	−	6.08221e6i	−0.161433	−	0.279611i
$862$	3.80037e6	−	6.58243e6i	0.174204	−	0.301730i
$863$	−2.51641e7	+	9.15898e6i	−1.15015	+	0.418620i	−0.845569	−	0.533866i	$-0.820739\pi$
$863$	−2.51641e7	+	9.15898e6i	−1.15015	+	0.418620i	−0.304581	+	0.952486i	$0.598516\pi$
$864$	3.11397e6	−	2.61293e6i	0.141916	−	0.119081i
$865$	−1.12899e7	−	1.95548e7i	−0.513040	−	0.888612i
$866$	1.84276e6	−	1.04508e7i	0.0834976	−	0.473538i
$867$	3.61871e6	−	2.05227e7i	0.163496	−	0.927230i
$868$	1.81538e6	+	1.52329e6i	0.0817841	+	0.0686250i
$869$	4.10616e6	+	1.49452e6i	0.184453	+	0.0671355i
$870$	4.06205e7	+	1.47846e7i	1.81948	+	0.662236i
$871$	2.28429e7	+	1.91674e7i	1.02025	+	0.856089i
$872$	244339.	−	1.38571e6i	0.0108818	−	0.0617138i
$873$	−56897.8	+	322684.i	−0.00252674	+	0.0143298i
$874$	7.05829e6	+	1.22253e7i	0.312551	+	0.541355i
$875$	1.81297e7	−	1.52127e7i	0.800519	−	0.671715i
$876$	−267689.	+	97430.8i	−0.0117861	+	0.00428979i
$877$	−3.50004e6	+	6.06224e6i	−0.153664	+	0.266155i	−0.932572	−	0.360984i	$-0.882441\pi$
$877$	−3.50004e6	+	6.06224e6i	−0.153664	+	0.266155i	0.778907	+	0.627139i	$0.215774\pi$
$878$	9.37504e6	+	1.62380e7i	0.410428	+	0.710882i
$879$	−2.29147e7	−	1.92277e7i	−1.00033	−	0.839375i
$880$	−5.27657e6	+	9.13930e6i	−0.229692	+	0.397838i
$881$	5.77619e6	+	3.27584e7i	0.250727	+	1.42194i	0.806807	+	0.590816i	$0.201194\pi$
$881$	5.77619e6	+	3.27584e7i	0.250727	+	1.42194i	−0.556079	+	0.831129i	$0.687695\pi$
$882$	1.68071e6			0.0727482
$883$	−1.41928e6	−	8.04915e6i	−0.0612586	−	0.347415i	−0.999996	−	0.00278175i	$-0.999115\pi$
$883$	−1.41928e6	−	8.04915e6i	−0.0612586	−	0.347415i	0.938738	−	0.344633i	$-0.111997\pi$
$884$	320102.	−	268598.i	0.0137771	−	0.0115604i
$885$	3.85681e7	+	1.40376e7i	1.65527	+	0.602471i
$886$	1.34387e7	−	4.89127e6i	0.575138	−	0.209333i
$887$	2.10786e7			0.899565			0.449782	−	0.893138i	$-0.351502\pi$
$887$	2.10786e7			0.899565			0.449782	+	0.893138i	$0.351502\pi$
$888$	−6.11041e6	+	4.89221e6i	−0.260039	+	0.208196i
$889$	−240607.			−0.0102107
$890$	−3.69201e7	+	1.34378e7i	−1.56238	+	0.568662i
$891$	1.82661e7	+	6.64833e6i	0.770819	+	0.280555i
$892$	9.63104e6	−	8.08140e6i	0.405285	−	0.340075i
$893$	−3.22410e6	−	1.82848e7i	−0.135294	−	0.767292i
$894$	−1.88920e7			−0.790557
$895$	−1.20748e7	−	6.84798e7i	−0.503876	−	2.85762i
$896$	−307174.	+	532040.i	−0.0127824	+	0.0221398i
$897$	2.02722e7	+	1.70104e7i	0.841240	+	0.705884i
$898$	1.28732e7	+	2.22970e7i	0.532715	+	0.922690i
$899$	−1.32606e7	+	2.29681e7i	−0.547225	+	0.947821i
$900$	3.64437e6	−	1.32644e6i	0.149974	−	0.0545860i
$901$	745291.	−	625373.i	0.0305854	−	0.0256642i
$902$	9.59411e6	+	1.66175e7i	0.392635	+	0.680063i
$903$	−1.24117e6	+	7.03902e6i	−0.0506538	+	0.287272i
$904$	−2.17670e6	+	1.23447e7i	−0.0885887	+	0.502411i
$905$	−1.02174e7	−	8.57345e6i	−0.414687	−	0.347964i
$906$	−1.11639e7	−	4.06334e6i	−0.451852	−	0.164461i
$907$	−2.54043e7	−	9.24642e6i	−1.02539	−	0.373212i	−0.226067	−	0.974112i	$-0.572587\pi$
$907$	−2.54043e7	−	9.24642e6i	−1.02539	−	0.373212i	−0.799324	+	0.600900i	$0.794809\pi$
$908$	−9.30504e6	−	7.80785e6i	−0.374545	−	0.314280i
$909$	235790.	−	1.33723e6i	0.00946489	−	0.0536781i
$910$	2.36725e6	−	1.34254e7i	0.0947635	−	0.537431i
$911$	1.41531e7	+	2.45139e7i	0.565010	+	0.978627i	0.997049	+	0.0767714i	$0.0244612\pi$
$911$	1.41531e7	+	2.45139e7i	0.565010	+	0.978627i	−0.432038	+	0.901855i	$0.642205\pi$
$912$	−4.67909e6	+	3.92622e6i	−0.186283	+	0.156310i
$913$	−1.14463e7	+	4.16610e6i	−0.454451	+	0.165407i
$914$	−1.82991e6	+	3.16949e6i	−0.0724542	+	0.125494i
$915$	−2.00161e7	−	3.46690e7i	−0.790365	−	1.36895i
$916$	−1.33756e7	−	1.12235e7i	−0.526715	−	0.441966i
$917$	−2.26704e6	+	3.92662e6i	−0.0890297	+	0.154204i
$918$	86825.4	+	492411.i	0.00340048	+	0.0192851i
$919$	2.76338e7			1.07932			0.539662	−	0.841882i	$-0.318552\pi$
$919$	2.76338e7			1.07932			0.539662	+	0.841882i	$0.318552\pi$
$920$	−2.64580e6	−	1.50051e7i	−0.103059	−	0.584479i
$921$	1.99803e7	−	1.67654e7i	0.776162	−	0.651277i
$922$	2.29279e7	+	8.34508e6i	0.888254	+	0.323298i
$923$	4.55637e7	−	1.65838e7i	1.76041	−	0.640738i
$924$	−3.31464e6			−0.127719
$925$	−7.00855e7	+	2.36981e7i	−2.69323	+	0.910666i
$926$	−1.38481e7			−0.530718
$927$	−1.00975e6	+	367519.i	−0.0385935	+	0.0140469i
$928$	−6.46071e6	−	2.35151e6i	−0.246269	−	0.0896347i
$929$	1.66184e7	−	1.39445e7i	0.631755	−	0.530106i	−0.269718	−	0.962939i	$-0.586931\pi$
$929$	1.66184e7	−	1.39445e7i	0.631755	−	0.530106i	0.901474	+	0.432833i	$0.142486\pi$
$930$	−4.41606e6	−	2.50447e7i	−0.167428	−	0.949530i
$931$	−2.50192e7			−0.946017
$932$	22319.3	+	126579.i	0.000841667	+	0.00477333i
$933$	−9.57258e6	+	1.65802e7i	−0.360019	+	0.623571i
$934$	−7.04873e6	−	5.91459e6i	−0.264389	−	0.221849i
$935$	−649035.	−	1.12416e6i	−0.0242794	−	0.0420532i
$936$	724092.	−	1.25416e6i	0.0270150	−	0.0467913i
$937$	2.16939e7	−	7.89592e6i	0.807212	−	0.293801i	0.0947405	−	0.995502i	$-0.469798\pi$
$937$	2.16939e7	−	7.89592e6i	0.807212	−	0.293801i	0.712472	+	0.701701i	$0.247576\pi$
$938$	4.13091e6	−	3.46625e6i	0.153299	−	0.128633i
$939$	4.83853e6	+	8.38058e6i	0.179081	+	0.310177i
$940$	−3.47989e6	+	1.97354e7i	−0.128454	+	0.728496i
$941$	−4.61640e6	+	2.61809e7i	−0.169953	+	0.963853i	0.773856	+	0.633362i	$0.218325\pi$
$941$	−4.61640e6	+	2.61809e7i	−0.169953	+	0.963853i	−0.943809	+	0.330491i	$0.892786\pi$
$942$	1.11247e7	+	9.33471e6i	0.408470	+	0.342747i
$943$	−2.60331e7	−	9.47527e6i	−0.953337	−	0.346986i
$944$	−6.13428e6	−	2.23270e6i	−0.224044	−	0.0815454i
$945$	1.24960e7	+	1.04854e7i	0.455188	+	0.381948i
$946$	3.39105e6	−	1.92316e7i	0.123199	−	0.698696i
$947$	7.41215e6	−	4.20364e7i	0.268577	−	1.52318i	−0.490074	−	0.871681i	$-0.663030\pi$
$947$	7.41215e6	−	4.20364e7i	0.268577	−	1.52318i	0.758652	−	0.651497i	$-0.225859\pi$
$948$	−1.36490e6	−	2.36408e6i	−0.0493266	−	0.0854363i
$949$	−770184.	+	646261.i	−0.0277606	+	0.0232939i
$950$	−5.42502e7	+	1.97455e7i	−1.95026	+	0.709836i
$951$	−1.97472e7	+	3.42031e7i	−0.708034	+	1.22635i
$952$	−37783.3	−	65442.5i	−0.00135116	−	0.00234028i
$953$	3.43836e7	+	2.88513e7i	1.22636	+	1.02904i	0.998467	+	0.0553570i	$0.0176297\pi$
$953$	3.43836e7	+	2.88513e7i	1.22636	+	1.02904i	0.227898	+	0.973685i	$0.426815\pi$
$954$	1.68590e6	−	2.92006e6i	0.0599736	−	0.103877i
$955$	−1.25390e7	−	7.11121e7i	−0.444891	−	2.52310i
$956$	−1.87953e7			−0.665127
$957$	−6.44151e6	−	3.65316e7i	−0.227357	−	1.28940i
$958$	1.56712e7	−	1.31497e7i	0.551680	−	0.462915i
$959$	3.58250e6	+	1.30392e6i	0.125788	+	0.0457831i
$960$	6.19513e6	−	2.25484e6i	0.216956	−	0.0789656i
$961$	−1.30264e7			−0.455006
$962$	−1.43598e7	+	2.36010e7i	−0.500278	+	0.822231i
$963$	2.53689e6			0.0881526
$964$	−1.20453e7	+	4.38414e6i	−0.417470	+	0.151947i
$965$	−69389.0	−	25255.5i	−0.00239868	−	0.000873049i
$966$	3.66603e6	−	3.07616e6i	0.126402	−	0.106064i
$967$	4.17143e6	+	2.36574e7i	0.143456	+	0.813580i	0.968594	+	0.248648i	$0.0799863\pi$
$967$	4.17143e6	+	2.36574e7i	0.143456	+	0.813580i	−0.825138	+	0.564931i	$0.808903\pi$
$968$	−1.25118e6			−0.0429171
$969$	−130465.	−	739902.i	−0.00446358	−	0.0253142i
$970$	−2.63228e6	+	4.55925e6i	−0.0898262	+	0.155584i
$971$	2.07823e7	+	1.74384e7i	0.707368	+	0.593552i	0.923859	−	0.382733i	$-0.125017\pi$
$971$	2.07823e7	+	1.74384e7i	0.707368	+	0.593552i	−0.216492	+	0.976284i	$0.569461\pi$
$972$	1.64541e6	+	2.84993e6i	0.0558610	+	0.0967540i
$973$	−7.08008e6	+	1.22631e7i	−0.239749	+	0.415257i
$974$	1.24005e7	−	4.51340e6i	0.418832	−	0.152443i
$975$	−8.29061e7	+	6.95665e7i	−2.79303	+	2.34363i
$976$	3.18358e6	+	5.51413e6i	0.106977	+	0.185290i
$977$	2.37631e6	−	1.34767e7i	0.0796464	−	0.451697i	−0.918738	−	0.394869i	$-0.870790\pi$
$977$	2.37631e6	−	1.34767e7i	0.0796464	−	0.451697i	0.998384	−	0.0568284i	$-0.0180988\pi$
$978$	−98661.3	+	559536.i	−0.00329837	+	0.0187060i
$979$	2.58279e7	+	2.16722e7i	0.861257	+	0.722681i
$980$	2.53756e7	+	9.23596e6i	0.844017	+	0.307197i
$981$	563654.	+	205153.i	0.0186999	+	0.00680622i
$982$	1.75454e7	+	1.47223e7i	0.580610	+	0.487190i
$983$	−8.62019e6	+	4.88875e7i	−0.284533	+	1.61367i	0.422415	+	0.906403i	$0.361183\pi$
$983$	−8.62019e6	+	4.88875e7i	−0.284533	+	1.61367i	−0.706948	+	0.707265i	$0.749929\pi$
$984$	2.08155e6	−	1.18051e7i	0.0685330	−	0.388670i
$985$	−4.88326e6	−	8.45805e6i	−0.160368	−	0.277766i
$986$	647835.	−	543598.i	0.0212213	−	0.0178068i
$987$	−5.91474e6	+	2.15279e6i	−0.193261	+	0.0703411i
$988$	−1.07789e7	+	1.86695e7i	−0.351302	+	0.608473i
$989$	1.40974e7	+	2.44175e7i	0.458299	+	0.793797i
$990$	−3.44620e6	−	2.89171e6i	−0.111751	−	0.0937706i
$991$	−4.81939e6	+	8.34742e6i	−0.155886	+	0.270003i	−0.933381	−	0.358886i	$-0.883157\pi$
$991$	−4.81939e6	+	8.34742e6i	−0.155886	+	0.270003i	0.777495	+	0.628889i	$0.216490\pi$
$992$	702377.	+	3.98338e6i	0.0226616	+	0.128521i
$993$	5.05613e7			1.62722
$994$	−1.52264e6	−	8.63534e6i	−0.0488801	−	0.277213i
$995$	7.72708e6	−	6.48379e6i	0.247433	−	0.207621i
$996$	7.15067e6	+	2.60263e6i	0.228401	+	0.0831312i
$997$	3.01773e7	−	1.09836e7i	0.961484	−	0.349952i	0.186869	−	0.982385i	$-0.440166\pi$
$997$	3.01773e7	−	1.09836e7i	0.961484	−	0.349952i	0.774615	+	0.632433i	$0.217944\pi$
$998$	9.05189e6			0.287682
$999$	−1.58657e7	−	2.90009e7i	−0.502974	−	0.919386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.f.a.7.7	✓	48
37.16	even	9	inner	74.6.f.a.53.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.f.a.7.7	✓	48	1.1	even	1	trivial
74.6.f.a.53.7	yes	48	37.16	even	9	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.75877 + 1.36808i) q^{2} +(13.8016 + 5.02336i) q^{3} +(12.2567 - 10.2846i) q^{4} +(19.0297 + 107.923i) q^{5} -58.7493 q^{6} +(6.51125 + 36.9271i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-20.8996 - 17.5369i) q^{9} +O(q^{10})\)	\(q+(-3.75877 + 1.36808i) q^{2} +(13.8016 + 5.02336i) q^{3} +(12.2567 - 10.2846i) q^{4} +(19.0297 + 107.923i) q^{5} -58.7493 q^{6} +(6.51125 + 36.9271i) q^{7} +(-32.0000 + 55.4256i) q^{8} +(-20.8996 - 17.5369i) q^{9} +(-219.175 - 379.623i) q^{10} +(-188.083 + 325.770i) q^{11} +(220.825 - 80.3738i) q^{12} +(635.350 - 533.122i) q^{13} +(-74.9935 - 129.893i) q^{14} +(-279.495 + 1585.10i) q^{15} +(44.4539 - 252.111i) q^{16} +(24.1218 + 20.2406i) q^{17} +(102.549 + 37.3247i) q^{18} +(-1526.55 - 555.618i) q^{19} +(1343.18 + 1127.07i) q^{20} +(-95.6328 + 542.360i) q^{21} +(261.283 - 1481.81i) q^{22} +(1086.21 + 1881.38i) q^{23} +(-720.073 + 604.213i) q^{24} +(-8348.67 + 3038.67i) q^{25} +(-1658.78 + 2873.09i) q^{26} +(-1984.86 - 3437.88i) q^{27} +(459.587 + 385.639i) q^{28} +(-3357.10 + 5814.67i) q^{29} +(-1117.98 - 6340.39i) q^{30} +3950.03 q^{31} +(177.816 + 1008.44i) q^{32} +(-4232.30 + 3551.33i) q^{33} +(-118.359 - 43.0792i) q^{34} +(-3861.37 + 1405.42i) q^{35} -436.521 q^{36} +(8325.10 + 191.540i) q^{37} +6498.07 q^{38} +(11446.9 - 4166.33i) q^{39} +(-6590.64 - 2398.80i) q^{40} +(-9768.97 + 8197.14i) q^{41} +(-382.531 - 2169.44i) q^{42} +12978.5 q^{43} +(1045.13 + 5927.23i) q^{44} +(1494.92 - 2589.27i) q^{45} +(-6656.71 - 5585.64i) q^{46} +(5714.57 + 9897.93i) q^{47} +(1879.98 - 3256.22i) q^{48} +(14472.2 - 5267.45i) q^{49} +(27223.6 - 22843.3i) q^{50} +(231.243 + 400.524i) q^{51} +(2304.35 - 13068.6i) q^{52} +(5365.20 - 30427.6i) q^{53} +(12163.9 + 10206.8i) q^{54} +(-38737.2 - 14099.2i) q^{55} +(-2255.07 - 820.778i) q^{56} +(-18277.7 - 15336.8i) q^{57} +(4663.64 - 26448.8i) q^{58} +(4428.01 - 25112.5i) q^{59} +(12876.4 + 22302.6i) q^{60} +(-19052.9 + 15987.2i) q^{61} +(-14847.3 + 5403.96i) q^{62} +(511.504 - 885.951i) q^{63} +(-2048.00 - 3547.24i) q^{64} +(69626.5 + 58423.6i) q^{65} +(11049.8 - 19138.7i) q^{66} +(6243.21 + 35407.0i) q^{67} +503.820 q^{68} +(5540.62 + 31422.4i) q^{69} +(12591.3 - 10565.3i) q^{70} +(54936.4 + 19995.2i) q^{71} +(1640.78 - 597.196i) q^{72} -1212.22 q^{73} +(-31554.2 + 10669.5i) q^{74} -130489. q^{75} +(-24424.8 + 8889.88i) q^{76} +(-13254.4 - 4824.21i) q^{77} +(-37326.3 + 31320.5i) q^{78} +(-2017.16 - 11439.9i) q^{79} +28054.5 q^{80} +(-8973.27 - 50889.9i) q^{81} +(25505.0 - 44175.9i) q^{82} +(24805.7 + 20814.5i) q^{83} +(4405.82 + 7631.10i) q^{84} +(-1725.39 + 2988.47i) q^{85} +(-48783.2 + 17755.6i) q^{86} +(-75542.5 + 63387.7i) q^{87} +(-12037.3 - 20849.3i) q^{88} +(15564.2 - 88268.7i) q^{89} +(-2076.72 + 11777.6i) q^{90} +(23823.6 + 19990.3i) q^{91} +(32662.6 + 11888.2i) q^{92} +(54516.6 + 19842.4i) q^{93} +(-35020.9 - 29386.0i) q^{94} +(30914.1 - 175323. i) q^{95} +(-2611.64 + 14811.3i) q^{96} +(-6004.97 - 10400.9i) q^{97} +(-47191.4 + 39598.3i) q^{98} +(9643.86 - 3510.08i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 3 q^{3} - 72 q^{5} + 114 q^{7} - 1536 q^{8} - 93 q^{9}+O(q^{10}) \) 48 * q - 3 * q^3 - 72 * q^5 + 114 * q^7 - 1536 * q^8 - 93 * q^9	\( 48 q - 3 q^{3} - 72 q^{5} + 114 q^{7} - 1536 q^{8} - 93 q^{9} - 648 q^{10} - 9 q^{11} - 48 q^{12} + 288 q^{13} - 660 q^{14} - 3678 q^{15} - 2475 q^{17} + 744 q^{18} + 945 q^{19} - 1152 q^{20} - 2073 q^{21} - 60 q^{22} - 5739 q^{23} - 192 q^{24} - 3834 q^{25} - 5304 q^{26} - 1077 q^{27} - 5232 q^{28} - 11640 q^{29} - 14712 q^{30} - 20394 q^{31} - 62013 q^{33} + 7812 q^{34} + 27999 q^{35} + 62208 q^{36} + 13605 q^{37} + 60696 q^{38} + 25590 q^{39} + 9216 q^{40} - 18267 q^{41} - 8292 q^{42} + 2208 q^{43} - 240 q^{44} - 48132 q^{45} - 40308 q^{46} - 663 q^{47} + 58326 q^{49} + 61776 q^{50} + 8748 q^{51} - 31536 q^{52} + 20940 q^{53} + 37836 q^{54} - 158868 q^{55} + 13632 q^{56} + 164910 q^{57} - 28068 q^{58} + 111258 q^{59} - 31824 q^{60} + 88758 q^{61} + 116100 q^{62} - 202488 q^{63} - 98304 q^{64} + 155997 q^{65} - 53532 q^{66} + 52503 q^{67} + 32544 q^{68} + 298758 q^{69} - 5760 q^{70} + 160434 q^{71} + 11904 q^{72} - 477210 q^{73} + 8844 q^{74} + 808230 q^{75} + 15120 q^{76} - 510765 q^{77} + 26004 q^{78} - 378768 q^{79} + 82944 q^{80} + 55476 q^{81} - 149064 q^{82} - 230082 q^{83} - 42336 q^{84} + 55653 q^{85} - 149904 q^{86} - 453051 q^{87} - 576 q^{88} + 492789 q^{89} + 12276 q^{90} + 220839 q^{91} + 176160 q^{92} - 109767 q^{93} - 6768 q^{94} - 630843 q^{95} + 6144 q^{96} - 632190 q^{97} - 194628 q^{98} - 414765 q^{99}+O(q^{100}) \) 48 * q - 3 * q^3 - 72 * q^5 + 114 * q^7 - 1536 * q^8 - 93 * q^9 - 648 * q^10 - 9 * q^11 - 48 * q^12 + 288 * q^13 - 660 * q^14 - 3678 * q^15 - 2475 * q^17 + 744 * q^18 + 945 * q^19 - 1152 * q^20 - 2073 * q^21 - 60 * q^22 - 5739 * q^23 - 192 * q^24 - 3834 * q^25 - 5304 * q^26 - 1077 * q^27 - 5232 * q^28 - 11640 * q^29 - 14712 * q^30 - 20394 * q^31 - 62013 * q^33 + 7812 * q^34 + 27999 * q^35 + 62208 * q^36 + 13605 * q^37 + 60696 * q^38 + 25590 * q^39 + 9216 * q^40 - 18267 * q^41 - 8292 * q^42 + 2208 * q^43 - 240 * q^44 - 48132 * q^45 - 40308 * q^46 - 663 * q^47 + 58326 * q^49 + 61776 * q^50 + 8748 * q^51 - 31536 * q^52 + 20940 * q^53 + 37836 * q^54 - 158868 * q^55 + 13632 * q^56 + 164910 * q^57 - 28068 * q^58 + 111258 * q^59 - 31824 * q^60 + 88758 * q^61 + 116100 * q^62 - 202488 * q^63 - 98304 * q^64 + 155997 * q^65 - 53532 * q^66 + 52503 * q^67 + 32544 * q^68 + 298758 * q^69 - 5760 * q^70 + 160434 * q^71 + 11904 * q^72 - 477210 * q^73 + 8844 * q^74 + 808230 * q^75 + 15120 * q^76 - 510765 * q^77 + 26004 * q^78 - 378768 * q^79 + 82944 * q^80 + 55476 * q^81 - 149064 * q^82 - 230082 * q^83 - 42336 * q^84 + 55653 * q^85 - 149904 * q^86 - 453051 * q^87 - 576 * q^88 + 492789 * q^89 + 12276 * q^90 + 220839 * q^91 + 176160 * q^92 - 109767 * q^93 - 6768 * q^94 - 630843 * q^95 + 6144 * q^96 - 632190 * q^97 - 194628 * q^98 - 414765 * q^99

Introduction

L-functions

Modular forms

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