LMFDB - Embedded newform 98.8.c.i.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,8,Mod(67,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("98.67");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not 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:	$30.6137324974$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{37})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 10x^{2} + 9x + 81 $ x^4 - x^3 + 10x^2 + 9x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$1.77069 - 3.06693i$ of defining polynomial
Character	$\chi$	$=$	98.67
Dual form			98.8.c.i.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.00000 - 6.92820i) q^{2} +(-24.3311 + 42.1426i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-121.655 - 210.713i) q^{5} +389.297 q^{6} +512.000 q^{8} +(-90.5000 - 156.751i) q^{9} +O(q^{10})$	\(q+(-4.00000 - 6.92820i) q^{2} +(-24.3311 + 42.1426i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-121.655 - 210.713i) q^{5} +389.297 q^{6} +512.000 q^{8} +(-90.5000 - 156.751i) q^{9} +(-973.242 + 1685.70i) q^{10} +(-790.000 + 1368.32i) q^{11} +(-1557.19 - 2697.13i) q^{12} +9878.41 q^{13} +11840.0 q^{15} +(-2048.00 - 3547.24i) q^{16} +(-10073.1 + 17447.0i) q^{17} +(-724.000 + 1254.00i) q^{18} +(27469.8 + 47579.0i) q^{19} +15571.9 q^{20} +12640.0 q^{22} +(-50076.0 - 86734.2i) q^{23} +(-12457.5 + 21577.0i) q^{24} +(9462.50 - 16389.5i) q^{25} +(-39513.6 - 68439.6i) q^{26} -97616.2 q^{27} +11594.0 q^{29} +(-47360.0 - 82029.9i) q^{30} +(32165.6 - 55712.5i) q^{31} +(-16384.0 + 28377.9i) q^{32} +(-38443.1 - 66585.3i) q^{33} +161169. q^{34} +11584.0 q^{36} +(-251529. - 435661. i) q^{37} +(219758. - 380632. i) q^{38} +(-240352. + 416302. i) q^{39} +(-62287.5 - 107885. i) q^{40} -447594. q^{41} -560516. q^{43} +(-50560.0 - 87572.5i) q^{44} +(-22019.6 + 38139.1i) q^{45} +(-400608. + 693873. i) q^{46} +(146522. + 253783. i) q^{47} +199320. q^{48} -151400. q^{50} +(-490176. - 849010. i) q^{51} +(-316109. + 547517. i) q^{52} +(-643999. + 1.11544e6i) q^{53} +(390465. + 676305. i) q^{54} +384431. q^{55} -2.67347e6 q^{57} +(-46376.0 - 80325.6i) q^{58} +(-986843. + 1.70926e6i) q^{59} +(-378880. + 656239. i) q^{60} +(-281486. - 487548. i) q^{61} -514650. q^{62} +262144. q^{64} +(-1.20176e6 - 2.08151e6i) q^{65} +(-307544. + 532683. i) q^{66} +(396250. - 686325. i) q^{67} +(-644676. - 1.11661e6i) q^{68} +4.87361e6 q^{69} -2.22990e6 q^{71} +(-46336.0 - 80256.3i) q^{72} +(3.02328e6 - 5.23647e6i) q^{73} +(-2.01223e6 + 3.48529e6i) q^{74} +(460465. + 797549. i) q^{75} -3.51613e6 q^{76} +3.84563e6 q^{78} +(-1.25654e6 - 2.17639e6i) q^{79} +(-498300. + 863081. i) q^{80} +(2.57303e6 - 4.45661e6i) q^{81} +(1.79038e6 + 3.10102e6i) q^{82} -5.31492e6 q^{83} +4.90176e6 q^{85} +(2.24206e6 + 3.88337e6i) q^{86} +(-282094. + 488601. i) q^{87} +(-404480. + 700580. i) q^{88} +(-4.02728e6 - 6.97545e6i) q^{89} +352314. q^{90} +6.40973e6 q^{92} +(1.56525e6 + 2.71109e6i) q^{93} +(1.17217e6 - 2.03026e6i) q^{94} +(6.68368e6 - 1.15765e7i) q^{95} +(-797280. - 1.38093e6i) q^{96} -9.09154e6 q^{97} +285980. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} - 128 q^{4} + 2048 q^{8} - 362 q^{9}+O(q^{10}) $ 4 * q - 16 * q^2 - 128 * q^4 + 2048 * q^8 - 362 * q^9	$ 4 q - 16 q^{2} - 128 q^{4} + 2048 q^{8} - 362 q^{9} - 3160 q^{11} + 47360 q^{15} - 8192 q^{16} - 2896 q^{18} + 50560 q^{22} - 200304 q^{23} + 37850 q^{25} + 46376 q^{29} - 189440 q^{30} - 65536 q^{32} + 46336 q^{36} - 1006116 q^{37} - 961408 q^{39} - 2242064 q^{43} - 202240 q^{44} - 1602432 q^{46} - 605600 q^{50} - 1960704 q^{51} - 2575996 q^{53} - 10693888 q^{57} - 185504 q^{58} - 1515520 q^{60} + 1048576 q^{64} - 4807040 q^{65} + 1585000 q^{67} - 8919616 q^{71} - 185344 q^{72} - 8048928 q^{74} + 15382528 q^{78} - 5026160 q^{79} + 10292110 q^{81} + 19607040 q^{85} + 8968256 q^{86} - 1617920 q^{88} + 25638912 q^{92} + 6260992 q^{93} + 26734720 q^{95} + 1143920 q^{99}+O(q^{100}) $ 4 * q - 16 * q^2 - 128 * q^4 + 2048 * q^8 - 362 * q^9 - 3160 * q^11 + 47360 * q^15 - 8192 * q^16 - 2896 * q^18 + 50560 * q^22 - 200304 * q^23 + 37850 * q^25 + 46376 * q^29 - 189440 * q^30 - 65536 * q^32 + 46336 * q^36 - 1006116 * q^37 - 961408 * q^39 - 2242064 * q^43 - 202240 * q^44 - 1602432 * q^46 - 605600 * q^50 - 1960704 * q^51 - 2575996 * q^53 - 10693888 * q^57 - 185504 * q^58 - 1515520 * q^60 + 1048576 * q^64 - 4807040 * q^65 + 1585000 * q^67 - 8919616 * q^71 - 185344 * q^72 - 8048928 * q^74 + 15382528 * q^78 - 5026160 * q^79 + 10292110 * q^81 + 19607040 * q^85 + 8968256 * q^86 - 1617920 * q^88 + 25638912 * q^92 + 6260992 * q^93 + 26734720 * q^95 + 1143920 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−4.00000	−	6.92820i	−0.353553	−	0.612372i
$2$	−4.00000	−	6.92820i	−0.353553	−	0.612372i
$3$	−24.3311	+	42.1426i	−0.520279	+	0.901150i	0.479443	+	0.877573i	$0.340839\pi$
$3$	−24.3311	+	42.1426i	−0.520279	+	0.901150i	−0.999722	+	0.0235769i	$0.992495\pi$
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	−121.655	−	210.713i	−0.435247	−	0.753870i	0.562069	−	0.827091i	$-0.310006\pi$
$5$	−121.655	−	210.713i	−0.435247	−	0.753870i	−0.997316	+	0.0732205i	$0.976672\pi$
$6$	389.297			0.735786
$7$		0			0
$7$		0			0
$8$	512.000			0.353553
$9$	−90.5000	−	156.751i	−0.0413809	−	0.0716738i
$10$	−973.242	+	1685.70i	−0.307766	+	0.533067i
$11$	−790.000	+	1368.32i	−0.178959	+	0.309965i	−0.941524	−	0.336946i	$-0.890606\pi$
$11$	−790.000	+	1368.32i	−0.178959	+	0.309965i	0.762565	+	0.646911i	$0.223939\pi$
$12$	−1557.19	−	2697.13i	−0.260140	−	0.450575i
$13$	9878.41			1.24705			0.623527	−	0.781802i	$-0.285699\pi$
$13$	9878.41			1.24705			0.623527	+	0.781802i	$0.285699\pi$
$14$		0			0
$15$	11840.0			0.905800
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	−10073.1	+	17447.0i	−0.497267	+	0.861292i	−0.999995	−	0.00315249i	$-0.998997\pi$
$17$	−10073.1	+	17447.0i	−0.497267	+	0.861292i	0.502728	+	0.864445i	$0.332330\pi$
$18$	−724.000	+	1254.00i	−0.0292607	+	0.0506810i
$19$	27469.8	+	47579.0i	0.918792	+	1.59139i	0.801253	+	0.598326i	$0.204167\pi$
$19$	27469.8	+	47579.0i	0.918792	+	1.59139i	0.117539	+	0.993068i	$0.462499\pi$
$20$	15571.9			0.435247
$21$		0			0
$22$	12640.0			0.253086
$23$	−50076.0	−	86734.2i	−0.858188	−	1.48642i	−0.873656	−	0.486544i	$-0.838257\pi$
$23$	−50076.0	−	86734.2i	−0.858188	−	1.48642i	0.0154685	−	0.999880i	$-0.495076\pi$
$24$	−12457.5	+	21577.0i	−0.183946	+	0.318605i
$25$	9462.50	−	16389.5i	0.121120	−	0.209786i
$26$	−39513.6	−	68439.6i	−0.440900	−	0.763661i
$27$	−97616.2			−0.954440
$28$		0			0
$29$	11594.0			0.0882755			0.0441378	−	0.999025i	$-0.485946\pi$
$29$	11594.0			0.0882755			0.0441378	+	0.999025i	$0.485946\pi$
$30$	−47360.0	−	82029.9i	−0.320249	−	0.554687i
$31$	32165.6	−	55712.5i	0.193922	−	0.335882i	−0.752625	−	0.658450i	$-0.771213\pi$
$31$	32165.6	−	55712.5i	0.193922	−	0.335882i	0.946546	+	0.322567i	$0.104546\pi$
$32$	−16384.0	+	28377.9i	−0.0883883	+	0.153093i
$33$	−38443.1	−	66585.3i	−0.186217	−	0.322537i
$34$	161169.			0.703242
$35$		0			0
$36$	11584.0			0.0413809
$37$	−251529.	−	435661.i	−0.816361	−	1.41398i	−0.908347	−	0.418218i	$-0.862655\pi$
$37$	−251529.	−	435661.i	−0.816361	−	1.41398i	0.0919862	−	0.995760i	$-0.470678\pi$
$38$	219758.	−	380632.i	0.649684	−	1.12529i
$39$	−240352.	+	416302.i	−0.648816	+	1.12378i
$40$	−62287.5	−	107885.i	−0.153883	−	0.266533i
$41$	−447594.			−1.01424			−0.507120	−	0.861875i	$-0.669290\pi$
$41$	−447594.			−1.01424			−0.507120	+	0.861875i	$0.669290\pi$
$42$		0			0
$43$	−560516.			−1.07510			−0.537549	−	0.843232i	$-0.680650\pi$
$43$	−560516.			−1.07510			−0.537549	+	0.843232i	$0.680650\pi$
$44$	−50560.0	−	87572.5i	−0.0894793	−	0.154983i
$45$	−22019.6	+	38139.1i	−0.0360218	+	0.0623916i
$46$	−400608.	+	693873.i	−0.606830	+	1.05106i
$47$	146522.	+	253783.i	0.205854	+	0.356549i	0.950404	−	0.311017i	$-0.100669\pi$
$47$	146522.	+	253783.i	0.205854	+	0.356549i	−0.744551	+	0.667566i	$0.767336\pi$
$48$	199320.			0.260140
$49$		0			0
$50$	−151400.			−0.171290
$51$	−490176.	−	849010.i	−0.517436	−	0.896225i
$52$	−316109.	+	547517.i	−0.311763	+	0.539990i
$53$	−643999.	+	1.11544e6i	−0.594182	+	1.02915i	0.399480	+	0.916742i	$0.369191\pi$
$53$	−643999.	+	1.11544e6i	−0.594182	+	1.02915i	−0.993662	+	0.112412i	$0.964142\pi$
$54$	390465.	+	676305.i	0.337445	+	0.584473i
$55$	384431.			0.311565
$56$		0			0
$57$	−2.67347e6			−1.91211
$58$	−46376.0	−	80325.6i	−0.0312101	−	0.0540575i
$59$	−986843.	+	1.70926e6i	−0.625556	+	1.08349i	0.362877	+	0.931837i	$0.381794\pi$
$59$	−986843.	+	1.70926e6i	−0.625556	+	1.08349i	−0.988433	+	0.151657i	$0.951539\pi$
$60$	−378880.	+	656239.i	−0.226450	+	0.392223i
$61$	−281486.	−	487548.i	−0.158782	−	0.275019i	0.775647	−	0.631166i	$-0.217423\pi$
$61$	−281486.	−	487548.i	−0.158782	−	0.275019i	−0.934430	+	0.356147i	$0.884090\pi$
$62$	−514650.			−0.274247
$63$		0			0
$64$	262144.			0.125000
$65$	−1.20176e6	−	2.08151e6i	−0.542776	−	0.940116i
$66$	−307544.	+	532683.i	−0.131675	+	0.228068i
$67$	396250.	−	686325.i	0.160956	−	0.278784i	−0.774256	−	0.632873i	$-0.781876\pi$
$67$	396250.	−	686325.i	0.160956	−	0.278784i	0.935212	+	0.354089i	$0.115209\pi$
$68$	−644676.	−	1.11661e6i	−0.248634	−	0.430646i
$69$	4.87361e6			1.78599
$70$		0			0
$71$	−2.22990e6			−0.739404			−0.369702	−	0.929150i	$-0.620540\pi$
$71$	−2.22990e6			−0.739404			−0.369702	+	0.929150i	$0.620540\pi$
$72$	−46336.0	−	80256.3i	−0.0146304	−	0.0253405i
$73$	3.02328e6	−	5.23647e6i	0.909595	−	1.57547i	0.0949681	−	0.995480i	$-0.469725\pi$
$73$	3.02328e6	−	5.23647e6i	0.909595	−	1.57547i	0.814627	−	0.579985i	$-0.196942\pi$
$74$	−2.01223e6	+	3.48529e6i	−0.577254	+	0.999833i
$75$	460465.	+	797549.i	0.126032	+	0.218295i
$76$	−3.51613e6			−0.918792
$77$		0			0
$78$	3.84563e6			0.917565
$79$	−1.25654e6	−	2.17639e6i	−0.286736	−	0.496640i	0.686293	−	0.727325i	$-0.259237\pi$
$79$	−1.25654e6	−	2.17639e6i	−0.286736	−	0.496640i	−0.973029	+	0.230685i	$0.925903\pi$
$80$	−498300.	+	863081.i	−0.108812	+	0.188468i
$81$	2.57303e6	−	4.45661e6i	0.537956	−	0.931767i
$82$	1.79038e6	+	3.10102e6i	0.358588	+	0.621093i
$83$	−5.31492e6			−1.02029			−0.510145	−	0.860088i	$-0.670408\pi$
$83$	−5.31492e6			−1.02029			−0.510145	+	0.860088i	$0.670408\pi$
$84$		0			0
$85$	4.90176e6			0.865737
$86$	2.24206e6	+	3.88337e6i	0.380105	+	0.658361i
$87$	−282094.	+	488601.i	−0.0459279	+	0.0795495i
$88$	−404480.	+	700580.i	−0.0632714	+	0.109589i
$89$	−4.02728e6	−	6.97545e6i	−0.605545	−	1.04883i	−0.991965	−	0.126512i	$-0.959622\pi$
$89$	−4.02728e6	−	6.97545e6i	−0.605545	−	1.04883i	0.386420	−	0.922323i	$-0.373711\pi$
$90$	352314.			0.0509425
$91$		0			0
$92$	6.40973e6			0.858188
$93$	1.56525e6	+	2.71109e6i	0.201787	+	0.349505i
$94$	1.17217e6	−	2.03026e6i	0.145561	−	0.252119i
$95$	6.68368e6	−	1.15765e7i	0.799803	−	1.38530i
$96$	−797280.	−	1.38093e6i	−0.0919732	−	0.159302i
$97$	−9.09154e6			−1.01143			−0.505716	−	0.862700i	$-0.668772\pi$
$97$	−9.09154e6			−1.01143			−0.505716	+	0.862700i	$0.668772\pi$
$98$		0			0
$99$	285980.			0.0296219
$100$	605600.	+	1.04893e6i	0.0605600	+	0.104893i
$101$	−1.41298e6	+	2.44735e6i	−0.136462	+	0.236358i	−0.926155	−	0.377144i	$-0.876906\pi$
$101$	−1.41298e6	+	2.44735e6i	−0.136462	+	0.236358i	0.789693	+	0.613502i	$0.210240\pi$
$102$	−3.92141e6	+	6.79208e6i	−0.365882	+	0.633727i
$103$	5.21108e6	+	9.02585e6i	0.469891	+	0.813875i	0.999407	−	0.0344245i	$-0.0109598\pi$
$103$	5.21108e6	+	9.02585e6i	0.469891	+	0.813875i	−0.529516	+	0.848300i	$0.677626\pi$
$104$	5.05774e6			0.440900
$105$		0			0
$106$	1.03040e7			0.840301
$107$	4.76395e6	+	8.25140e6i	0.375945	+	0.651155i	0.990468	−	0.137743i	$-0.0439849\pi$
$107$	4.76395e6	+	8.25140e6i	0.375945	+	0.651155i	−0.614523	+	0.788899i	$0.710652\pi$
$108$	3.12372e6	−	5.41044e6i	0.238610	−	0.413285i
$109$	1.26550e7	−	2.19191e7i	0.935985	−	1.62117i	0.163116	−	0.986607i	$-0.447846\pi$
$109$	1.26550e7	−	2.19191e7i	0.935985	−	1.62117i	0.772869	−	0.634566i	$-0.218821\pi$
$110$	−1.53772e6	−	2.66341e6i	−0.110155	−	0.190794i
$111$	2.44799e7			1.69894
$112$		0			0
$113$	−1.65579e7			−1.07952			−0.539759	−	0.841820i	$-0.681484\pi$
$113$	−1.65579e7			−1.07952			−0.539759	+	0.841820i	$0.681484\pi$
$114$	1.06939e7	+	1.85224e7i	0.676034	+	1.17093i
$115$	−1.21840e7	+	2.11033e7i	−0.747047	+	1.29392i
$116$	−371008.	+	642605.i	−0.0220689	+	0.0382244i
$117$	−893996.	−	1.54845e6i	−0.0516042	−	0.0893811i
$118$	1.57895e7			0.884669
$119$		0			0
$120$	6.06208e6			0.320249
$121$	8.49539e6	+	1.47144e7i	0.435948	+	0.755083i
$122$	−2.25189e6	+	3.90038e6i	−0.112276	+	0.194468i
$123$	1.08904e7	−	1.88628e7i	0.527688	−	0.913982i
$124$	2.05860e6	+	3.56560e6i	0.0969608	+	0.167941i
$125$	−2.36133e7			−1.08136
$126$		0			0
$127$	−3.05915e6			−0.132522			−0.0662610	−	0.997802i	$-0.521107\pi$
$127$	−3.05915e6			−0.132522			−0.0662610	+	0.997802i	$0.521107\pi$
$128$	−1.04858e6	−	1.81619e6i	−0.0441942	−	0.0765466i
$129$	1.36379e7	−	2.36216e7i	0.559352	−	0.968825i
$130$	−9.61408e6	+	1.66521e7i	−0.383801	+	0.664763i
$131$	1.21139e7	+	2.09818e7i	0.470797	+	0.815444i	0.999442	−	0.0333990i	$-0.0106332\pi$
$131$	1.21139e7	+	2.09818e7i	0.470797	+	0.815444i	−0.528645	+	0.848843i	$0.677300\pi$
$132$	4.92071e6			0.186217
$133$		0			0
$134$	−6.34000e6			−0.227626
$135$	1.18755e7	+	2.05690e7i	0.415417	+	0.719524i
$136$	−5.15740e6	+	8.93289e6i	−0.175811	+	0.304513i
$137$	−9.62503e6	+	1.66710e7i	−0.319801	+	0.553912i	−0.980446	−	0.196786i	$-0.936949\pi$
$137$	−9.62503e6	+	1.66710e7i	−0.319801	+	0.553912i	0.660645	+	0.750698i	$0.270283\pi$
$138$	−1.94944e7	−	3.37653e7i	−0.631442	−	1.09369i
$139$	−1.93579e7			−0.611374			−0.305687	−	0.952132i	$-0.598886\pi$
$139$	−1.93579e7			−0.611374			−0.305687	+	0.952132i	$0.598886\pi$
$140$		0			0
$141$	−1.42601e7			−0.428406
$142$	8.91962e6	+	1.54492e7i	0.261419	+	0.452791i
$143$	−7.80394e6	+	1.35168e7i	−0.223171	+	0.386544i
$144$	−370688.	+	642050.i	−0.0103452	+	0.0179184i
$145$	−1.41047e6	−	2.44301e6i	−0.0384217	−	0.0665483i
$146$	−4.83725e7			−1.28636
$147$		0			0
$148$	3.21957e7			0.816361
$149$	−2.66975e7	−	4.62414e7i	−0.661178	−	1.14519i	−0.980306	−	0.197483i	$-0.936723\pi$
$149$	−2.66975e7	−	4.62414e7i	−0.661178	−	1.14519i	0.319128	−	0.947712i	$-0.396610\pi$
$150$	3.68372e6	−	6.38039e6i	0.0891184	−	0.154358i
$151$	−6.09624e6	+	1.05590e7i	−0.144093	+	0.249576i	−0.929034	−	0.369994i	$-0.879360\pi$
$151$	−6.09624e6	+	1.05590e7i	−0.144093	+	0.249576i	0.784941	+	0.619570i	$0.212693\pi$
$152$	1.40645e7	+	2.43605e7i	0.324842	+	0.562643i
$153$	3.64645e6			0.0823095
$154$		0			0
$155$	−1.56525e7			−0.337615
$156$	−1.53825e7	−	2.66433e7i	−0.324408	−	0.561891i
$157$	3.29690e7	−	5.71040e7i	0.679918	−	1.17765i	−0.295087	−	0.955471i	$-0.595349\pi$
$157$	3.29690e7	−	5.71040e7i	0.679918	−	1.17765i	0.975005	−	0.222183i	$-0.0713182\pi$
$158$	−1.00523e7	+	1.74111e7i	−0.202753	+	0.351178i
$159$	−3.13383e7	−	5.42796e7i	−0.618281	−	1.07089i
$160$	7.97280e6			0.153883
$161$		0			0
$162$	−4.11684e7			−0.760785
$163$	−2.56374e7	−	4.44054e7i	−0.463680	−	0.803117i	0.535461	−	0.844560i	$-0.320138\pi$
$163$	−2.56374e7	−	4.44054e7i	−0.463680	−	0.803117i	−0.999141	+	0.0414431i	$0.986804\pi$
$164$	1.43230e7	−	2.48082e7i	0.253560	−	0.439179i
$165$	−9.35360e6	+	1.62009e7i	−0.162101	+	0.280767i
$166$	2.12597e7	+	3.68229e7i	0.360727	+	0.624798i
$167$	9.55719e7			1.58790			0.793949	−	0.607985i	$-0.208022\pi$
$167$	9.55719e7			1.58790			0.793949	+	0.607985i	$0.208022\pi$
$168$		0			0
$169$	3.48344e7			0.555143
$170$	−1.96070e7	−	3.39604e7i	−0.306084	−	0.530153i
$171$	4.97203e6	−	8.61180e6i	0.0760409	−	0.131707i
$172$	1.79365e7	−	3.10670e7i	0.268775	−	0.465531i
$173$	3.65795e6	+	6.33576e6i	0.0537127	+	0.0930331i	0.891632	−	0.452762i	$-0.149561\pi$
$173$	3.65795e6	+	6.33576e6i	0.0537127	+	0.0930331i	−0.837919	+	0.545795i	$0.816228\pi$
$174$	4.51351e6			0.0649519
$175$		0			0
$176$	6.47168e6			0.0894793
$177$	−4.80219e7	−	8.31763e7i	−0.650927	−	1.12744i
$178$	−3.22182e7	+	5.58036e7i	−0.428185	+	0.741638i
$179$	−3.29616e7	+	5.70912e7i	−0.429559	+	0.744018i	−0.996834	−	0.0795105i	$-0.974664\pi$
$179$	−3.29616e7	+	5.70912e7i	−0.429559	+	0.744018i	0.567275	+	0.823528i	$0.307998\pi$
$180$	−1.40925e6	−	2.44090e6i	−0.0180109	−	0.0311958i
$181$	−7.17864e7			−0.899844			−0.449922	−	0.893068i	$-0.648548\pi$
$181$	−7.17864e7			−0.899844			−0.449922	+	0.893068i	$0.648548\pi$
$182$		0			0
$183$	2.73954e7			0.330445
$184$	−2.56389e7	−	4.44079e7i	−0.303415	−	0.525530i
$185$	−6.11996e7	+	1.06001e8i	−0.710637	+	1.23086i
$186$	1.25220e7	−	2.16887e7i	0.142685	−	0.247137i
$187$	−1.59154e7	−	2.75663e7i	−0.177981	−	0.308271i
$188$	−1.87548e7			−0.205854
$189$		0			0
$190$	−1.06939e8			−1.13109
$191$	−4.34465e7	−	7.52515e7i	−0.451168	−	0.781445i	0.547291	−	0.836942i	$-0.315659\pi$
$191$	−4.34465e7	−	7.52515e7i	−0.451168	−	0.781445i	−0.998459	+	0.0554970i	$0.982326\pi$
$192$	−6.37824e6	+	1.10474e7i	−0.0650349	+	0.112644i
$193$	−7.50848e7	+	1.30051e8i	−0.751799	+	1.30215i	0.195151	+	0.980773i	$0.437480\pi$
$193$	−7.50848e7	+	1.30051e8i	−0.751799	+	1.30215i	−0.946950	+	0.321381i	$0.895853\pi$
$194$	3.63662e7	+	6.29880e7i	0.357595	+	0.619373i
$195$	1.16960e8			1.12958
$196$		0			0
$197$	−3.40156e7			−0.316991			−0.158495	−	0.987360i	$-0.550664\pi$
$197$	−3.40156e7			−0.316991			−0.158495	+	0.987360i	$0.550664\pi$
$198$	−1.14392e6	−	1.98133e6i	−0.0104729	−	0.0181396i
$199$	−4.93749e7	+	8.55198e7i	−0.444140	+	0.769273i	−0.997992	−	0.0633420i	$-0.979824\pi$
$199$	−4.93749e7	+	8.55198e7i	−0.444140	+	0.769273i	0.553852	+	0.832615i	$0.313157\pi$
$200$	4.84480e6	−	8.39144e6i	0.0428224	−	0.0741705i
$201$	1.92824e7	+	3.33980e7i	0.167484	+	0.290091i
$202$	2.26076e7			0.192986
$203$		0			0
$204$	6.27425e7			0.517436
$205$	5.44522e7	+	9.43139e7i	0.441445	+	0.764605i
$206$	4.16886e7	−	7.22068e7i	0.332263	−	0.575497i
$207$	−9.06376e6	+	1.56989e7i	−0.0710251	+	0.123019i
$208$	−2.02310e7	−	3.50411e7i	−0.155882	−	0.269995i
$209$	−8.68044e7			−0.657703
$210$		0			0
$211$	1.03289e8			0.756946			0.378473	−	0.925612i	$-0.376449\pi$
$211$	1.03289e8			0.756946			0.378473	+	0.925612i	$0.376449\pi$
$212$	−4.12159e7	−	7.13881e7i	−0.297091	−	0.514577i
$213$	5.42559e7	−	9.39740e7i	0.384697	−	0.666314i
$214$	3.81116e7	−	6.60112e7i	0.265833	−	0.460436i
$215$	6.81897e7	+	1.18108e8i	0.467934	+	0.810485i
$216$	−4.99795e7			−0.337445
$217$		0			0
$218$	−2.02480e8			−1.32368
$219$	1.47119e8	+	2.54818e8i	0.946487	+	1.63936i
$220$	−1.23018e7	+	2.13073e7i	−0.0778912	+	0.134912i
$221$	−9.95057e7	+	1.72349e8i	−0.620119	+	1.07408i
$222$	−9.79194e7	−	1.69601e8i	−0.600667	−	1.04039i
$223$	−1.64092e8			−0.990878			−0.495439	−	0.868643i	$-0.664993\pi$
$223$	−1.64092e8			−0.990878			−0.495439	+	0.868643i	$0.664993\pi$
$224$		0			0
$225$	−3.42542e6			−0.0200482
$226$	6.62314e7	+	1.14716e8i	0.381667	+	0.661066i
$227$	1.51175e8	−	2.61843e8i	0.857809	−	1.48577i	−0.0162057	−	0.999869i	$-0.505159\pi$
$227$	1.51175e8	−	2.61843e8i	0.857809	−	1.48577i	0.874015	−	0.485900i	$-0.161508\pi$
$228$	8.55511e7	−	1.48179e8i	0.478028	−	0.827969i
$229$	−3.27573e7	−	5.67372e7i	−0.180253	−	0.312208i	0.761713	−	0.647914i	$-0.224358\pi$
$229$	−3.27573e7	−	5.67372e7i	−0.180253	−	0.312208i	−0.941967	+	0.335706i	$0.891025\pi$
$230$	1.94944e8			1.05648
$231$		0			0
$232$	5.93613e6			0.0312101
$233$	−4.21297e7	−	7.29708e7i	−0.218194	−	0.377923i	0.736062	−	0.676914i	$-0.236683\pi$
$233$	−4.21297e7	−	7.29708e7i	−0.218194	−	0.377923i	−0.954256	+	0.298991i	$0.903350\pi$
$234$	−7.15197e6	+	1.23876e7i	−0.0364897	+	0.0632020i
$235$	3.56502e7	−	6.17480e7i	0.179195	−	0.310374i
$236$	−6.31580e7	−	1.09393e8i	−0.312778	−	0.541747i
$237$	1.22292e8			0.596730
$238$		0			0
$239$	3.48515e7			0.165131			0.0825655	−	0.996586i	$-0.473689\pi$
$239$	3.48515e7			0.165131			0.0825655	+	0.996586i	$0.473689\pi$
$240$	−2.42483e7	−	4.19993e7i	−0.113225	−	0.196111i
$241$	−2.14707e7	+	3.71884e7i	−0.0988069	+	0.171139i	−0.911191	−	0.411984i	$-0.864836\pi$
$241$	−2.14707e7	+	3.71884e7i	−0.0988069	+	0.171139i	0.812384	+	0.583123i	$0.198169\pi$
$242$	6.79631e7	−	1.17716e8i	0.308262	−	0.533925i
$243$	1.84656e7	+	3.19834e7i	0.0825548	+	0.142989i
$244$	3.60302e7			0.158782
$245$		0			0
$246$	−1.74247e8			−0.746264
$247$	2.71357e8	+	4.70005e8i	1.14578	+	1.98455i
$248$	1.64688e7	−	2.85248e7i	0.0685617	−	0.118752i
$249$	1.29318e8	−	2.23985e8i	0.530836	−	0.919434i
$250$	9.44531e7	+	1.63598e8i	0.382319	+	0.662197i
$251$	−3.78052e8			−1.50901			−0.754507	−	0.656292i	$-0.772124\pi$
$251$	−3.78052e8			−1.50901			−0.754507	+	0.656292i	$0.772124\pi$
$252$		0			0
$253$	1.58240e8			0.614320
$254$	1.22366e7	+	2.11944e7i	0.0468536	+	0.0811528i
$255$	−1.19265e8	+	2.06573e8i	−0.450425	+	0.780159i
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	−3.64012e7	−	6.30487e7i	−0.133767	−	0.231692i	0.791359	−	0.611352i	$-0.209374\pi$
$257$	−3.64012e7	−	6.30487e7i	−0.133767	−	0.231692i	−0.925126	+	0.379661i	$0.876041\pi$
$258$	−2.18207e8			−0.791043
$259$		0			0
$260$	1.53825e8			0.542776
$261$	−1.04926e6	−	1.81737e6i	−0.00365292	−	0.00632704i
$262$	9.69110e7	−	1.67855e8i	0.332904	−	0.576606i
$263$	1.56843e8	−	2.71660e8i	0.531643	−	0.920832i	−0.467675	−	0.883900i	$-0.654908\pi$
$263$	1.56843e8	−	2.71660e8i	0.531643	−	0.920832i	0.999318	−	0.0369318i	$-0.0117584\pi$
$264$	−1.96828e7	−	3.40917e7i	−0.0658376	−	0.114034i
$265$	3.13383e8			1.03446
$266$		0			0
$267$	3.91951e8			1.26021
$268$	2.53600e7	+	4.39248e7i	0.0804781	+	0.139392i
$269$	−2.20120e8	+	3.81259e8i	−0.689487	+	1.19423i	0.282517	+	0.959262i	$0.408831\pi$
$269$	−2.20120e8	+	3.81259e8i	−0.689487	+	1.19423i	−0.972004	+	0.234965i	$0.924503\pi$
$270$	9.50042e7	−	1.64552e8i	0.293744	−	0.508780i
$271$	−2.34789e7	−	4.06666e7i	−0.0716613	−	0.124121i	0.827968	−	0.560775i	$-0.189497\pi$
$271$	−2.34789e7	−	4.06666e7i	−0.0716613	−	0.124121i	−0.899630	+	0.436654i	$0.856163\pi$
$272$	8.25185e7			0.248634
$273$		0			0
$274$	1.54000e8			0.452267
$275$	1.49508e7	+	2.58955e7i	0.0433509	+	0.0750860i
$276$	−1.55955e8	+	2.70123e8i	−0.446497	+	0.773356i
$277$	−1.50782e8	+	2.61162e8i	−0.426256	+	0.738297i	−0.996537	−	0.0831529i	$-0.973501\pi$
$277$	−1.50782e8	+	2.61162e8i	−0.426256	+	0.738297i	0.570281	+	0.821450i	$0.306834\pi$
$278$	7.74317e7	+	1.34116e8i	0.216153	+	0.374389i
$279$	−1.16440e7			−0.0320986
$280$		0			0
$281$	−2.24765e7			−0.0604306			−0.0302153	−	0.999543i	$-0.509619\pi$
$281$	−2.24765e7			−0.0604306			−0.0302153	+	0.999543i	$0.509619\pi$
$282$	5.70404e7	+	9.87968e7i	0.151464	+	0.262344i
$283$	1.16825e8	−	2.02347e8i	0.306396	−	0.530694i	−0.671175	−	0.741299i	$-0.734210\pi$
$283$	1.16825e8	−	2.02347e8i	0.306396	−	0.530694i	0.977571	+	0.210605i	$0.0675434\pi$
$284$	7.13569e7	−	1.23594e8i	0.184851	−	0.320171i
$285$	3.25242e8	+	5.63336e8i	0.832242	+	1.44148i
$286$	1.24863e8			0.315612
$287$		0			0
$288$	5.93101e6			0.0146304
$289$	2.23647e6	+	3.87368e6i	0.00545031	+	0.00944021i
$290$	−1.12838e7	+	1.95441e7i	−0.0271682	+	0.0470567i
$291$	2.21207e8	−	3.83141e8i	0.526227	−	0.911451i
$292$	1.93490e8	+	3.35134e8i	0.454798	+	0.787733i
$293$	7.24171e8			1.68192			0.840959	−	0.541099i	$-0.181992\pi$
$293$	7.24171e8			1.68192			0.840959	+	0.541099i	$0.181992\pi$
$294$		0			0
$295$	4.80219e8			1.08909
$296$	−1.28783e8	−	2.23058e8i	−0.288627	−	0.499917i
$297$	7.71168e7	−	1.33570e8i	0.170805	−	0.295843i
$298$	−2.13580e8	+	3.69931e8i	−0.467524	+	0.809774i
$299$	−4.94671e8	−	8.56795e8i	−1.07021	−	1.85365i
$300$	−5.89395e7			−0.126032
$301$		0			0
$302$	9.75398e7			0.203778
$303$	−6.87584e7	−	1.19093e8i	−0.141996	−	0.245945i
$304$	1.12516e8	−	1.94884e8i	0.229698	−	0.397849i
$305$	−6.84885e7	+	1.18626e8i	−0.138219	+	0.239403i
$306$	−1.45858e7	−	2.52633e7i	−0.0291008	−	0.0504040i
$307$	−8.91138e7			−0.175776			−0.0878882	−	0.996130i	$-0.528012\pi$
$307$	−8.91138e7			−0.175776			−0.0878882	+	0.996130i	$0.528012\pi$
$308$		0			0
$309$	−5.07164e8			−0.977898
$310$	6.26099e7	+	1.08444e8i	0.119365	+	0.206746i
$311$	1.08529e8	−	1.87977e8i	0.204590	−	0.354359i	−0.745412	−	0.666604i	$-0.767747\pi$
$311$	1.08529e8	−	1.87977e8i	0.204590	−	0.354359i	0.950002	+	0.312244i	$0.101081\pi$
$312$	−1.23060e8	+	2.13147e8i	−0.229391	+	0.397317i
$313$	−4.38278e8	−	7.59119e8i	−0.807875	−	1.39928i	−0.914333	−	0.404963i	$-0.867284\pi$
$313$	−4.38278e8	−	7.59119e8i	−0.807875	−	1.39928i	0.106458	−	0.994317i	$-0.466049\pi$
$314$	−5.27504e8			−0.961550
$315$		0			0
$316$	1.60837e8			0.286736
$317$	−5.51976e8	−	9.56051e8i	−0.973224	−	1.68567i	−0.685675	−	0.727908i	$-0.740493\pi$
$317$	−5.51976e8	−	9.56051e8i	−0.973224	−	1.68567i	−0.287549	−	0.957766i	$-0.592841\pi$
$318$	−2.50707e8	+	4.34237e8i	−0.437191	+	0.757237i
$319$	−9.15926e6	+	1.58643e7i	−0.0157977	+	0.0273624i
$320$	−3.18912e7	−	5.52372e7i	−0.0544059	−	0.0942338i
$321$	−4.63648e8			−0.782385
$322$		0			0
$323$	−1.10682e9			−1.82754
$324$	1.64674e8	+	2.85223e8i	0.268978	+	0.465884i
$325$	9.34744e7	−	1.61902e8i	0.151043	−	0.261614i
$326$	−2.05100e8	+	3.55243e8i	−0.327871	+	0.567889i
$327$	6.15818e8	+	1.06663e9i	0.973947	+	1.68692i
$328$	−2.29168e8			−0.358588
$329$		0			0
$330$	1.49658e8			0.229245
$331$	1.74266e8	+	3.01838e8i	0.264129	+	0.457484i	0.967335	−	0.253502i	$-0.0815824\pi$
$331$	1.74266e8	+	3.01838e8i	0.264129	+	0.457484i	−0.703206	+	0.710986i	$0.748249\pi$
$332$	1.70078e8	−	2.94583e8i	0.255073	−	0.441799i
$333$	−4.55267e7	+	7.88546e7i	−0.0675635	+	0.117023i
$334$	−3.82288e8	−	6.62141e8i	−0.561407	−	0.972385i
$335$	−1.92824e8			−0.280223
$336$		0			0
$337$	−4.12629e8			−0.587294			−0.293647	−	0.955914i	$-0.594869\pi$
$337$	−4.12629e8			−0.587294			−0.293647	+	0.955914i	$0.594869\pi$
$338$	−1.39338e8	−	2.41340e8i	−0.196273	−	0.339954i
$339$	4.02870e8	−	6.97791e8i	0.561650	−	0.972807i
$340$	−1.56856e8	+	2.71683e8i	−0.216434	+	0.374875i
$341$	5.08217e7	+	8.80258e7i	0.0694079	+	0.120218i
$342$	−7.95524e7			−0.107538
$343$		0			0
$344$	−2.86984e8			−0.380105
$345$	−5.92900e8	−	1.02693e9i	−0.777346	−	1.34640i
$346$	2.92636e7	−	5.06861e7i	0.0379806	−	0.0657843i
$347$	2.53882e8	−	4.39736e8i	0.326196	−	0.564988i	−0.655558	−	0.755145i	$-0.727566\pi$
$347$	2.53882e8	−	4.39736e8i	0.326196	−	0.564988i	0.981754	+	0.190157i	$0.0608997\pi$
$348$	−1.80540e7	−	3.12705e7i	−0.0229640	−	0.0397747i
$349$	1.28301e8			0.161563			0.0807814	−	0.996732i	$-0.474258\pi$
$349$	1.28301e8			0.161563			0.0807814	+	0.996732i	$0.474258\pi$
$350$		0			0
$351$	−9.64292e8			−1.19024
$352$	−2.58867e7	−	4.48371e7i	−0.0316357	−	0.0547947i
$353$	−3.99614e8	+	6.92153e8i	−0.483537	+	0.837511i	−0.999821	−	0.0189067i	$-0.993981\pi$
$353$	−3.99614e8	+	6.92153e8i	−0.483537	+	0.837511i	0.516284	+	0.856417i	$0.327315\pi$
$354$	−3.84175e8	+	6.65410e8i	−0.460275	+	0.797220i
$355$	2.71280e8	+	4.69870e8i	0.321824	+	0.557415i
$356$	5.15491e8			0.605545
$357$		0			0
$358$	5.27386e8			0.607488
$359$	2.61657e8	+	4.53203e8i	0.298470	+	0.516966i	0.975786	−	0.218726i	$-0.0701902\pi$
$359$	2.61657e8	+	4.53203e8i	0.298470	+	0.516966i	−0.677316	+	0.735692i	$0.736857\pi$
$360$	−1.12740e7	+	1.95272e7i	−0.0127356	+	0.0220588i
$361$	−1.06224e9	+	1.83985e9i	−1.18836	+	2.05830i
$362$	2.87146e8	+	4.97351e8i	0.318143	+	0.551039i
$363$	−8.26807e8			−0.907258
$364$		0			0
$365$	−1.47119e9			−1.58359
$366$	−1.09582e8	−	1.89801e8i	−0.116830	−	0.202355i
$367$	−3.16062e8	+	5.47436e8i	−0.333765	+	0.578099i	−0.983247	−	0.182279i	$-0.941653\pi$
$367$	−3.16062e8	+	5.47436e8i	−0.333765	+	0.578099i	0.649481	+	0.760377i	$0.274986\pi$
$368$	−2.05111e8	+	3.55263e8i	−0.214547	+	0.371606i
$369$	4.05073e7	+	7.01606e7i	0.0419702	+	0.0726944i
$370$	9.79194e8			1.00499
$371$		0			0
$372$	−2.00352e8			−0.201787
$373$	−7.60278e8	−	1.31684e9i	−0.758563	−	1.31387i	−0.943584	−	0.331135i	$-0.892569\pi$
$373$	−7.60278e8	−	1.31684e9i	−0.758563	−	1.31387i	0.185021	−	0.982735i	$-0.440765\pi$
$374$	−1.27323e8	+	2.20531e8i	−0.125851	+	0.217981i
$375$	5.74536e8	−	9.95126e8i	0.562610	−	0.974470i
$376$	7.50191e7	+	1.29937e8i	0.0727803	+	0.126059i
$377$	1.14530e8			0.110084
$378$		0			0
$379$	1.88756e9			1.78100			0.890498	−	0.454987i	$-0.150356\pi$
$379$	1.88756e9			1.78100			0.890498	+	0.454987i	$0.150356\pi$
$380$	4.27756e8	+	7.40894e8i	0.399902	+	0.692650i
$381$	7.44324e7	−	1.28921e8i	0.0689484	−	0.119422i
$382$	−3.47572e8	+	6.02012e8i	−0.319024	+	0.552565i
$383$	−5.98467e8	−	1.03658e9i	−0.544308	−	0.942769i	−0.998650	−	0.0519417i	$-0.983459\pi$
$383$	−5.98467e8	−	1.03658e9i	−0.544308	−	0.942769i	0.454342	−	0.890827i	$-0.349874\pi$
$384$	1.02052e8			0.0919732
$385$		0			0
$386$	1.20136e9			1.06320
$387$	5.07267e7	+	8.78612e7i	0.0444885	+	0.0770564i
$388$	2.90929e8	−	5.03904e8i	0.252858	−	0.437963i
$389$	3.16271e8	−	5.47798e8i	0.272418	−	0.471842i	−0.697062	−	0.717011i	$-0.745510\pi$
$389$	3.16271e8	−	5.47798e8i	0.272418	−	0.471842i	0.969481	+	0.245168i	$0.0788432\pi$
$390$	−4.67841e8	−	8.10325e8i	−0.399367	−	0.691724i
$391$	2.01767e9			1.70699
$392$		0			0
$393$	−1.17897e9			−0.979783
$394$	1.36062e8	+	2.35667e8i	0.112073	+	0.194116i
$395$	−3.05729e8	+	5.29539e8i	−0.249602	+	0.432323i
$396$	−9.15136e6	+	1.58506e7i	−0.00740547	+	0.0128266i
$397$	7.43941e8	+	1.28854e9i	0.596722	+	1.03355i	0.993301	+	0.115552i	$0.0368636\pi$
$397$	7.43941e8	+	1.28854e9i	0.596722	+	1.03355i	−0.396580	+	0.918000i	$0.629803\pi$
$398$	7.89998e8			0.628109
$399$		0			0
$400$	−7.75168e7			−0.0605600
$401$	−1.24639e8	−	2.15881e8i	−0.0965267	−	0.167189i	0.813718	−	0.581260i	$-0.197440\pi$
$401$	−1.24639e8	−	2.15881e8i	−0.0965267	−	0.167189i	−0.910245	+	0.414071i	$0.864107\pi$
$402$	1.54259e8	−	2.67184e8i	0.118429	−	0.205125i
$403$	3.17745e8	−	5.50351e8i	0.241831	−	0.418863i
$404$	−9.04305e7	−	1.56630e8i	−0.0682308	−	0.118179i
$405$	−1.25209e9			−0.936575
$406$		0			0
$407$	7.94832e8			0.584379
$408$	−2.50970e8	−	4.34693e8i	−0.182941	−	0.316863i
$409$	−1.09560e9	+	1.89763e9i	−0.791806	+	1.37145i	0.133042	+	0.991110i	$0.457525\pi$
$409$	−1.09560e9	+	1.89763e9i	−0.791806	+	1.37145i	−0.924848	+	0.380337i	$0.875808\pi$
$410$	4.35617e8	−	7.54511e8i	0.312149	−	0.540657i
$411$	−4.68374e8	−	8.11248e8i	−0.332772	−	0.576378i
$412$	−6.67018e8			−0.469891
$413$		0			0
$414$	1.45020e8			0.100445
$415$	6.46588e8	+	1.11992e9i	0.444078	+	0.769166i
$416$	−1.61848e8	+	2.80329e8i	−0.110225	+	0.190915i
$417$	4.70999e8	−	8.15794e8i	0.318085	−	0.550940i
$418$	3.47218e8	+	6.01399e8i	0.232533	+	0.402759i
$419$	−5.82428e8			−0.386806			−0.193403	−	0.981119i	$-0.561953\pi$
$419$	−5.82428e8			−0.386806			−0.193403	+	0.981119i	$0.561953\pi$
$420$		0			0
$421$	2.11025e9			1.37831			0.689153	−	0.724616i	$-0.257983\pi$
$421$	2.11025e9			1.37831			0.689153	+	0.724616i	$0.257983\pi$
$422$	−4.13155e8	−	7.15606e8i	−0.267621	−	0.463533i
$423$	2.65204e7	−	4.59347e7i	0.0170368	−	0.0295087i
$424$	−3.29727e8	+	5.71105e8i	−0.210075	+	0.363861i
$425$	1.90633e8	+	3.30185e8i	0.120458	+	0.208639i
$426$	−8.68094e8			−0.544043
$427$		0			0
$428$	−6.09786e8			−0.375945
$429$	−3.79756e8	−	6.57757e8i	−0.232223	−	0.402221i
$430$	5.45518e8	−	9.44864e8i	0.330879	−	0.573099i
$431$	1.22596e9	−	2.12342e9i	0.737573	−	1.27751i	−0.216012	−	0.976391i	$-0.569305\pi$
$431$	1.22596e9	−	2.12342e9i	0.737573	−	1.27751i	0.953585	−	0.301123i	$-0.0973615\pi$
$432$	1.99918e8	+	3.46268e8i	0.119305	+	0.206642i
$433$	−2.52472e9			−1.49453			−0.747267	−	0.664524i	$-0.768634\pi$
$433$	−2.52472e9			−1.49453			−0.747267	+	0.664524i	$0.768634\pi$
$434$		0			0
$435$	1.37273e8			0.0799600
$436$	8.09919e8	+	1.40282e9i	0.467992	+	0.810586i
$437$	2.75115e9	−	4.76513e9i	1.57699	−	2.73143i
$438$	1.17695e9	−	2.03854e9i	0.669267	−	1.15921i
$439$	−3.86119e8	−	6.68777e8i	−0.217819	−	0.377273i	0.736322	−	0.676631i	$-0.236561\pi$
$439$	−3.86119e8	−	6.68777e8i	−0.217819	−	0.377273i	−0.954141	+	0.299358i	$0.903227\pi$
$440$	1.96828e8			0.110155
$441$		0			0
$442$	1.59209e9			0.876981
$443$	1.47110e9	+	2.54802e9i	0.803951	+	1.39248i	0.916997	+	0.398894i	$0.130606\pi$
$443$	1.47110e9	+	2.54802e9i	0.803951	+	1.39248i	−0.113046	+	0.993590i	$0.536061\pi$
$444$	−7.83355e8	+	1.35681e9i	−0.424735	+	0.735663i
$445$	−9.79878e8	+	1.69720e9i	−0.527123	+	0.913004i
$446$	6.56368e8	+	1.13686e9i	0.350328	+	0.606786i
$447$	2.59831e9			1.37599
$448$		0			0
$449$	−3.98879e8			−0.207959			−0.103980	−	0.994579i	$-0.533158\pi$
$449$	−3.98879e8			−0.207959			−0.103980	+	0.994579i	$0.533158\pi$
$450$	1.37017e7	+	2.37320e7i	0.00708811	+	0.0122770i
$451$	3.53599e8	−	6.12452e8i	0.181507	−	0.314379i
$452$	5.29851e8	−	9.17729e8i	0.269879	−	0.467445i
$453$	−2.96656e8	−	5.13823e8i	−0.149937	−	0.259699i
$454$	−2.41881e9			−1.21312
$455$		0			0
$456$	−1.36882e9			−0.676034
$457$	2.85310e8	+	4.94171e8i	0.139833	+	0.242198i	0.927433	−	0.373989i	$-0.122010\pi$
$457$	2.85310e8	+	4.94171e8i	0.139833	+	0.242198i	−0.787600	+	0.616187i	$0.788677\pi$
$458$	−2.62058e8	+	4.53898e8i	−0.127458	+	0.220764i
$459$	9.83293e8	−	1.70311e9i	0.474612	−	0.822052i
$460$	−7.79777e8	−	1.35061e9i	−0.373524	−	0.646962i
$461$	7.31588e8			0.347787			0.173894	−	0.984764i	$-0.444365\pi$
$461$	7.31588e8			0.347787			0.173894	+	0.984764i	$0.444365\pi$
$462$		0			0
$463$	2.31515e9			1.08404			0.542020	−	0.840366i	$-0.317660\pi$
$463$	2.31515e9			1.08404			0.542020	+	0.840366i	$0.317660\pi$
$464$	−2.37445e7	−	4.11267e7i	−0.0110344	−	0.0191122i
$465$	3.80841e8	−	6.59636e8i	0.175654	−	0.304242i
$466$	−3.37038e8	+	5.83766e8i	−0.154286	+	0.267232i
$467$	1.37267e9	+	2.37754e9i	0.623675	+	1.08024i	0.988795	+	0.149277i	$0.0476945\pi$
$467$	1.37267e9	+	2.37754e9i	0.623675	+	1.08024i	−0.365120	+	0.930960i	$0.618972\pi$
$468$	1.14431e8			0.0516042
$469$		0			0
$470$	−5.70404e8			−0.253419
$471$	1.60434e9	+	2.77880e9i	0.707495	+	1.22542i
$472$	−5.05264e8	+	8.75142e8i	−0.221167	+	0.383073i
$473$	4.42808e8	−	7.66965e8i	0.192398	−	0.333244i
$474$	−4.89167e8	−	8.47262e8i	−0.210976	−	0.365421i
$475$	1.03973e9			0.445136
$476$		0			0
$477$	2.33128e8			0.0983511
$478$	−1.39406e8	−	2.41458e8i	−0.0583827	−	0.101122i
$479$	−1.88198e9	+	3.25969e9i	−0.782422	+	1.35519i	0.148105	+	0.988972i	$0.452683\pi$
$479$	−1.88198e9	+	3.25969e9i	−0.782422	+	1.35519i	−0.930527	+	0.366223i	$0.880651\pi$
$480$	−1.93987e8	+	3.35995e8i	−0.0800622	+	0.138672i
$481$	−2.48471e9	−	4.30364e9i	−1.01805	−	1.76331i
$482$	3.43532e8			0.139734
$483$		0			0
$484$	−1.08741e9			−0.435948
$485$	1.10603e9	+	1.91571e9i	0.440222	+	0.762488i
$486$	1.47725e8	−	2.55867e8i	0.0583751	−	0.101109i
$487$	−2.08450e9	+	3.61047e9i	−0.817808	+	1.41648i	0.0894862	+	0.995988i	$0.471477\pi$
$487$	−2.08450e9	+	3.61047e9i	−0.817808	+	1.41648i	−0.907294	+	0.420497i	$0.861856\pi$
$488$	−1.44121e8	−	2.49625e8i	−0.0561380	−	0.0972339i
$489$	2.49514e9			0.964972
$490$		0			0
$491$	1.29041e8			0.0491975			0.0245987	−	0.999697i	$-0.492169\pi$
$491$	1.29041e8			0.0491975			0.0245987	+	0.999697i	$0.492169\pi$
$492$	6.96988e8	+	1.20722e9i	0.263844	+	0.456991i
$493$	−1.16787e8	+	2.02281e8i	−0.0438965	+	0.0760310i
$494$	2.17086e9	−	3.76004e9i	0.810191	−	1.40329i
$495$	−3.47910e7	−	6.02597e7i	−0.0128928	−	0.0223310i
$496$	−2.63501e8			−0.0969608
$497$		0			0
$498$	−2.06908e9			−0.750715
$499$	1.27564e9	+	2.20947e9i	0.459596	+	0.796043i	0.998939	−	0.0460428i	$-0.0146611\pi$
$499$	1.27564e9	+	2.20947e9i	0.459596	+	0.796043i	−0.539344	+	0.842086i	$0.681328\pi$
$500$	7.55625e8	−	1.30878e9i	0.270341	−	0.468244i
$501$	−2.32536e9	+	4.02765e9i	−0.826150	+	1.43093i
$502$	1.51221e9	+	2.61922e9i	0.533517	+	0.924078i
$503$	−7.40127e8			−0.259309			−0.129655	−	0.991559i	$-0.541387\pi$
$503$	−7.40127e8			−0.259309			−0.129655	+	0.991559i	$0.541387\pi$
$504$		0			0
$505$	6.87584e8			0.237578
$506$	−6.32961e8	−	1.09632e9i	−0.217195	−	0.376193i
$507$	−8.47557e8	+	1.46801e9i	−0.288829	+	0.500267i
$508$	9.78929e7	−	1.69555e8i	0.0331305	−	0.0573837i
$509$	1.41720e9	+	2.45467e9i	0.476343	+	0.825050i	0.999633	−	0.0271047i	$-0.00862875\pi$
$509$	1.41720e9	+	2.45467e9i	0.476343	+	0.825050i	−0.523290	+	0.852155i	$0.675295\pi$
$510$	1.90824e9			0.636997
$511$		0			0
$512$	1.34218e8			0.0441942
$513$	−2.68149e9	−	4.64448e9i	−0.876932	−	1.51889i
$514$	−2.91210e8	+	5.04390e8i	−0.0945877	+	0.163831i
$515$	1.26791e9	−	2.19608e9i	0.409038	−	0.708474i
$516$	8.72828e8	+	1.51178e9i	0.279676	+	0.484413i
$517$	−4.63008e8			−0.147357
$518$		0			0
$519$	−3.56007e8			−0.111782
$520$	−6.15301e8	−	1.06573e9i	−0.191900	−	0.332381i
$521$	−9.83101e8	+	1.70278e9i	−0.304555	+	0.527505i	−0.977162	−	0.212495i	$-0.931841\pi$
$521$	−9.83101e8	+	1.70278e9i	−0.304555	+	0.527505i	0.672607	+	0.740000i	$0.265174\pi$
$522$	−8.39406e6	+	1.45389e7i	−0.00258300	+	0.00447389i
$523$	1.89665e9	+	3.28509e9i	0.579737	+	1.00413i	0.995509	+	0.0946651i	$0.0301780\pi$
$523$	1.89665e9	+	3.28509e9i	0.579737	+	1.00413i	−0.415772	+	0.909469i	$0.636489\pi$
$524$	−1.55058e9			−0.470797
$525$		0			0
$526$	−2.50949e9			−0.751856
$527$	6.48013e8	+	1.12239e9i	0.192862	+	0.334047i
$528$	−1.57463e8	+	2.72734e8i	−0.0465542	+	0.0806343i
$529$	−3.31280e9	+	5.73794e9i	−0.972972	+	1.68524i
$530$	−1.25353e9	−	2.17118e9i	−0.365738	−	0.633477i
$531$	3.57237e8			0.103544
$532$		0			0
$533$	−4.42152e9			−1.26481
$534$	−1.56781e9	−	2.71552e9i	−0.445551	−	0.771718i
$535$	1.15912e9	−	2.00765e9i	0.327258	−	0.566827i
$536$	2.02880e8	−	3.51398e8i	0.0569066	−	0.0985651i
$537$	−1.60398e9	−	2.77818e9i	−0.446981	−	0.774194i
$538$	3.52192e9			0.975082
$539$		0			0
$540$	−1.52007e9			−0.415417
$541$	−5.95765e8	−	1.03190e9i	−0.161765	−	0.280185i	0.773737	−	0.633507i	$-0.218385\pi$
$541$	−5.95765e8	−	1.03190e9i	−0.161765	−	0.280185i	−0.935502	+	0.353322i	$0.885052\pi$
$542$	−1.87831e8	+	3.25333e8i	−0.0506722	+	0.0877668i
$543$	1.74664e9	−	3.02527e9i	0.468170	−	0.810894i
$544$	−3.30074e8	−	5.71705e8i	−0.0879053	−	0.152256i
$545$	−6.15818e9			−1.62954
$546$		0			0
$547$	4.67708e9			1.22185			0.610927	−	0.791687i	$-0.290797\pi$
$547$	4.67708e9			1.22185			0.610927	+	0.791687i	$0.290797\pi$
$548$	−6.16002e8	−	1.06695e9i	−0.159901	−	0.276956i
$549$	−5.09490e7	+	8.82462e7i	−0.0131411	+	0.0227611i
$550$	1.19606e8	−	2.07164e8i	0.0306537	−	0.0530938i
$551$	3.18484e8	+	5.51631e8i	0.0811068	+	0.140481i
$552$	2.49529e9			0.631442
$553$		0			0
$554$	2.41251e9			0.602817
$555$	−2.97810e9	−	5.15823e9i	−0.739459	−	1.28078i
$556$	6.19454e8	−	1.07293e9i	0.152844	−	0.264733i
$557$	−4.79545e8	+	8.30597e8i	−0.117581	+	0.203656i	−0.918808	−	0.394704i	$-0.870847\pi$
$557$	−4.79545e8	+	8.30597e8i	−0.117581	+	0.203656i	0.801228	+	0.598360i	$0.204181\pi$
$558$	4.65759e7	+	8.06718e7i	0.0113486	+	0.0196563i
$559$	−5.53700e9			−1.34071
$560$		0			0
$561$	1.54896e9			0.370398
$562$	8.99061e7	+	1.55722e8i	0.0213654	+	0.0370060i
$563$	−3.54539e8	+	6.14080e8i	−0.0837308	+	0.145026i	−0.904850	−	0.425731i	$-0.860017\pi$
$563$	−3.54539e8	+	6.14080e8i	−0.0837308	+	0.145026i	0.821119	+	0.570757i	$0.193350\pi$
$564$	4.56323e8	−	7.90375e8i	0.107102	−	0.185505i
$565$	2.01435e9	+	3.48896e9i	0.469857	+	0.813816i
$566$	−1.86920e9			−0.433310
$567$		0			0
$568$	−1.14171e9			−0.261419
$569$	−2.51099e9	−	4.34916e9i	−0.571415	−	0.989720i	−0.996421	−	0.0845291i	$-0.973061\pi$
$569$	−2.51099e9	−	4.34916e9i	−0.571415	−	0.989720i	0.425006	−	0.905190i	$-0.360272\pi$
$570$	2.60194e9	−	4.50668e9i	0.588484	−	1.01928i
$571$	−4.30863e9	+	7.46277e9i	−0.968530	+	1.67754i	−0.268715	+	0.963220i	$0.586599\pi$
$571$	−4.30863e9	+	7.46277e9i	−0.968530	+	1.67754i	−0.699815	+	0.714324i	$0.746734\pi$
$572$	−4.99452e8	−	8.65077e8i	−0.111586	−	0.193272i
$573$	4.22840e9			0.938933
$574$		0			0
$575$	−1.89538e9			−0.415775
$576$	−2.37240e7	−	4.10912e7i	−0.00517261	−	0.00895922i
$577$	1.08597e9	−	1.88096e9i	0.235344	−	0.407629i	−0.724028	−	0.689770i	$-0.757711\pi$
$577$	1.08597e9	−	1.88096e9i	0.235344	−	0.407629i	0.959373	+	0.282142i	$0.0910448\pi$
$578$	1.78918e7	−	3.09895e7i	0.00385395	−	0.00667524i
$579$	−3.65379e9	−	6.32854e9i	−0.782291	−	1.35497i
$580$	1.80540e8			0.0384217
$581$		0			0
$582$	−3.53931e9			−0.744197
$583$	−1.01752e9	−	1.76239e9i	−0.212668	−	0.368352i
$584$	1.54792e9	−	2.68107e9i	0.321591	−	0.557011i
$585$	−2.17519e8	+	3.76753e8i	−0.0449211	+	0.0778057i
$586$	−2.89669e9	−	5.01721e9i	−0.594648	−	1.02996i
$587$	1.89864e9			0.387444			0.193722	−	0.981056i	$-0.437944\pi$
$587$	1.89864e9			0.387444			0.193722	+	0.981056i	$0.437944\pi$
$588$		0			0
$589$	3.53433e9			0.712695
$590$	−1.92087e9	−	3.32705e9i	−0.385050	−	0.666926i
$591$	8.27635e8	−	1.43351e9i	0.164924	−	0.285656i
$592$	−1.03026e9	+	1.78447e9i	−0.204090	+	0.353495i
$593$	−2.62958e9	−	4.55457e9i	−0.517839	−	0.896924i	−0.999785	−	0.0207230i	$-0.993403\pi$
$593$	−2.62958e9	−	4.55457e9i	−0.517839	−	0.896924i	0.481946	−	0.876201i	$-0.339930\pi$
$594$	−1.23387e9			−0.241555
$595$		0			0
$596$	3.41728e9			0.661178
$597$	−2.40268e9	−	4.16157e9i	−0.462154	−	0.800474i
$598$	−3.95737e9	+	6.85436e9i	−0.756750	+	1.31073i
$599$	−1.38783e9	+	2.40380e9i	−0.263842	+	0.456988i	−0.967260	−	0.253789i	$-0.918323\pi$
$599$	−1.38783e9	+	2.40380e9i	−0.263842	+	0.456988i	0.703418	+	0.710777i	$0.251656\pi$
$600$	2.35758e8	+	4.08345e8i	0.0445592	+	0.0771788i
$601$	1.17814e9			0.221378			0.110689	−	0.993855i	$-0.464694\pi$
$601$	1.17814e9			0.221378			0.110689	+	0.993855i	$0.464694\pi$
$602$		0			0
$603$	−1.43443e8			−0.0266420
$604$	−3.90159e8	−	6.75775e8i	−0.0720464	−	0.124788i
$605$	2.06702e9	−	3.58018e9i	0.379490	−	0.657296i
$606$	−5.50067e8	+	9.52745e8i	−0.100406	+	0.173909i
$607$	3.52861e9	+	6.11174e9i	0.640388	+	1.10919i	0.985346	+	0.170567i	$0.0545600\pi$
$607$	3.52861e9	+	6.11174e9i	0.640388	+	1.10919i	−0.344958	+	0.938618i	$0.612107\pi$
$608$	−1.80026e9			−0.324842
$609$		0			0
$610$	1.09582e9			0.195471
$611$	1.44740e9	+	2.50697e9i	0.256711	+	0.444636i
$612$	−1.16686e8	+	2.02107e8i	−0.0205774	+	0.0356410i
$613$	2.41837e9	−	4.18874e9i	0.424045	−	0.734467i	−0.572286	−	0.820054i	$-0.693943\pi$
$613$	2.41837e9	−	4.18874e9i	0.424045	−	0.734467i	0.996331	+	0.0855873i	$0.0272767\pi$
$614$	3.56455e8	+	6.17398e8i	0.0621463	+	0.107641i
$615$	−5.29951e9			−0.918699
$616$		0			0
$617$	−1.39798e9			−0.239609			−0.119804	−	0.992798i	$-0.538227\pi$
$617$	−1.39798e9			−0.239609			−0.119804	+	0.992798i	$0.538227\pi$
$618$	2.02866e9	+	3.51374e9i	0.345739	+	0.598838i
$619$	−9.10088e8	+	1.57632e9i	−0.154229	+	0.267133i	−0.932778	−	0.360451i	$-0.882623\pi$
$619$	−9.10088e8	+	1.57632e9i	−0.154229	+	0.267133i	0.778549	+	0.627584i	$0.215956\pi$
$620$	5.00879e8	−	8.67548e8i	0.0844038	−	0.146192i
$621$	4.88823e9	+	8.46666e9i	0.819088	+	1.41870i
$622$	−1.73646e9			−0.289333
$623$		0			0
$624$	1.96896e9			0.324408
$625$	2.13342e9	+	3.69520e9i	0.349540	+	0.605421i
$626$	−3.50622e9	+	6.07295e9i	−0.571254	+	0.989441i
$627$	2.11204e9	−	3.65817e9i	0.342189	−	0.592689i
$628$	2.11002e9	+	3.65465e9i	0.339959	+	0.588827i
$629$	1.01347e10			1.62380
$630$		0			0
$631$	−3.89745e9			−0.617559			−0.308779	−	0.951134i	$-0.599920\pi$
$631$	−3.89745e9			−0.617559			−0.308779	+	0.951134i	$0.599920\pi$
$632$	−6.43348e8	−	1.11431e9i	−0.101376	−	0.175589i
$633$	−2.51312e9	+	4.35286e9i	−0.393823	+	0.682121i
$634$	−4.41581e9	+	7.64841e9i	−0.688173	+	1.19195i
$635$	3.72162e8	+	6.44603e8i	0.0576798	+	0.0999044i
$636$	4.01131e9			0.618281
$637$		0			0
$638$	1.46548e8			0.0223413
$639$	2.01806e8	+	3.49539e8i	0.0305972	+	0.0529959i
$640$	−2.55130e8	+	4.41897e8i	−0.0384708	+	0.0666333i
$641$	2.21272e8	−	3.83254e8i	0.0331835	−	0.0574756i	−0.848957	−	0.528462i	$-0.822769\pi$
$641$	2.21272e8	−	3.83254e8i	0.0331835	−	0.0574756i	0.882140	+	0.470987i	$0.156102\pi$
$642$	1.85459e9	+	3.21224e9i	0.276615	+	0.479111i
$643$	2.08316e9			0.309018			0.154509	−	0.987991i	$-0.450620\pi$
$643$	2.08316e9			0.309018			0.154509	+	0.987991i	$0.450620\pi$
$644$		0			0
$645$	−6.63651e9			−0.973825
$646$	4.42727e9	+	7.66826e9i	0.646133	+	1.11914i
$647$	−5.93712e6	+	1.02834e7i	−0.000861808	+	0.00149270i	−0.866456	−	0.499253i	$-0.833608\pi$
$647$	−5.93712e6	+	1.02834e7i	−0.000861808	+	0.00149270i	0.865594	+	0.500746i	$0.166941\pi$
$648$	1.31739e9	−	2.28179e9i	0.190196	−	0.329430i
$649$	−1.55921e9	−	2.70063e9i	−0.223897	−	0.387801i
$650$	−1.49559e9			−0.213607
$651$		0			0
$652$	3.28159e9			0.463680
$653$	2.74219e9	+	4.74961e9i	0.385391	+	0.667516i	0.991823	−	0.127619i	$-0.0407334\pi$
$653$	2.74219e9	+	4.74961e9i	0.385391	+	0.667516i	−0.606433	+	0.795135i	$0.707400\pi$
$654$	4.92654e9	−	8.53302e9i	0.688684	−	1.19284i
$655$	2.94743e9	−	5.10510e9i	0.409826	−	0.709839i
$656$	9.16673e8	+	1.58772e9i	0.126780	+	0.219589i
$657$	−1.09443e9			−0.150559
$658$		0			0
$659$	−3.99439e9			−0.543691			−0.271845	−	0.962341i	$-0.587634\pi$
$659$	−3.99439e9			−0.543691			−0.271845	+	0.962341i	$0.587634\pi$
$660$	−5.98630e8	−	1.03686e9i	−0.0810504	−	0.140383i
$661$	−1.20560e9	+	2.08815e9i	−0.162367	+	0.281227i	−0.935717	−	0.352752i	$-0.885246\pi$
$661$	−1.20560e9	+	2.08815e9i	−0.162367	+	0.281227i	0.773350	+	0.633979i	$0.218579\pi$
$662$	1.39413e9	−	2.41470e9i	0.186767	−	0.323490i
$663$	−4.84216e9	−	8.38686e9i	−0.645270	−	1.11764i
$664$	−2.72124e9			−0.360727
$665$		0			0
$666$	7.28428e8			0.0955491
$667$	−5.80581e8	−	1.00560e9i	−0.0757570	−	0.131215i
$668$	−3.05830e9	+	5.29713e9i	−0.396974	+	0.687580i
$669$	3.99253e9	−	6.91526e9i	0.515533	−	0.892930i
$670$	7.71294e8	+	1.33592e9i	0.0990737	+	0.171601i
$671$	8.89496e8			0.113662
$672$		0			0
$673$	−1.34332e9			−0.169874			−0.0849372	−	0.996386i	$-0.527069\pi$
$673$	−1.34332e9			−0.169874			−0.0849372	+	0.996386i	$0.527069\pi$
$674$	1.65052e9	+	2.85878e9i	0.207640	+	0.359642i
$675$	−9.23693e8	+	1.59988e9i	−0.115602	+	0.200228i
$676$	−1.11470e9	+	1.93072e9i	−0.138786	+	0.240384i
$677$	−2.20251e9	−	3.81486e9i	−0.272808	−	0.472518i	0.696772	−	0.717293i	$-0.254619\pi$
$677$	−2.20251e9	−	3.81486e9i	−0.272808	−	0.472518i	−0.969580	+	0.244775i	$0.921286\pi$
$678$	−6.44592e9			−0.794293
$679$		0			0
$680$	2.50970e9			0.306084
$681$	7.35651e9	+	1.27418e10i	0.892600	+	1.54603i
$682$	4.06574e8	−	7.04206e8i	0.0490788	−	0.0850070i
$683$	4.64213e9	−	8.04041e9i	0.557500	−	0.965619i	−0.440204	−	0.897898i	$-0.645094\pi$
$683$	4.64213e9	−	8.04041e9i	0.557500	−	0.965619i	0.997704	−	0.0677212i	$-0.0215728\pi$
$684$	3.18210e8	+	5.51155e8i	0.0380204	+	0.0658533i
$685$	4.68374e9			0.556770
$686$		0			0
$687$	3.18807e9			0.375128
$688$	1.14794e9	+	1.98828e9i	0.134387	+	0.232766i
$689$	−6.36168e9	+	1.10188e10i	−0.740977	+	1.28341i
$690$	−4.74320e9	+	8.21546e9i	−0.549667	+	0.952051i
$691$	−3.29229e9	−	5.70241e9i	−0.379598	−	0.657484i	0.611405	−	0.791317i	$-0.290604\pi$
$691$	−3.29229e9	−	5.70241e9i	−0.379598	−	0.657484i	−0.991004	+	0.133834i	$0.957271\pi$
$692$	−4.68218e8			−0.0537127
$693$		0			0
$694$	−4.06211e9			−0.461311
$695$	2.35499e9	+	4.07897e9i	0.266099	+	0.460897i
$696$	−1.44432e8	+	2.50164e8i	−0.0162380	+	0.0281250i
$697$	4.50864e9	−	7.80919e9i	0.504348	−	0.873557i
$698$	−5.13204e8	−	8.88896e8i	−0.0571211	−	0.0989366i
$699$	4.10024e9			0.454087
$700$		0			0
$701$	−2.90253e9			−0.318247			−0.159123	−	0.987259i	$-0.550867\pi$
$701$	−2.90253e9			−0.318247			−0.159123	+	0.987259i	$0.550867\pi$
$702$	3.85717e9	+	6.68081e9i	0.420813	+	0.728869i
$703$	1.38189e10	−	2.39350e10i	1.50013	−	2.59830i
$704$	−2.07094e8	+	3.58697e8i	−0.0223698	+	0.0387457i
$705$	1.73482e9	+	3.00479e9i	0.186462	+	0.322962i
$706$	6.39383e9			0.683825
$707$		0			0
$708$	6.14680e9			0.650927
$709$	−1.53364e9	−	2.65635e9i	−0.161608	−	0.279913i	0.773838	−	0.633384i	$-0.218335\pi$
$709$	−1.53364e9	−	2.65635e9i	−0.161608	−	0.279913i	−0.935445	+	0.353471i	$0.885001\pi$
$710$	2.17024e9	−	3.75896e9i	0.227564	−	0.394152i
$711$	−2.27434e8	+	3.93927e8i	−0.0237307	+	0.0411028i
$712$	−2.06197e9	−	3.57143e9i	−0.214092	−	0.370819i
$713$	−6.44291e9			−0.665685
$714$		0			0
$715$	3.79756e9			0.388538
$716$	−2.10954e9	−	3.65384e9i	−0.214779	−	0.372009i
$717$	−8.47974e8	+	1.46873e9i	−0.0859143	+	0.148808i
$718$	2.09325e9	−	3.62562e9i	0.211050	−	0.365550i
$719$	6.43770e8	+	1.11504e9i	0.0645921	+	0.111877i	0.896513	−	0.443017i	$-0.146092\pi$
$719$	6.43770e8	+	1.11504e9i	0.0645921	+	0.111877i	−0.831921	+	0.554894i	$0.812759\pi$
$720$	1.80385e8			0.0180109
$721$		0			0
$722$	1.69958e10			1.68059
$723$	−1.04481e9	−	1.80967e9i	−0.102814	−	0.178080i
$724$	2.29716e9	−	3.97880e9i	0.224961	−	0.389644i
$725$	1.09708e8	−	1.90020e8i	0.0106919	−	0.0185190i
$726$	3.30723e9	+	5.72828e9i	0.320764	+	0.555580i
$727$	−7.44359e9			−0.718476			−0.359238	−	0.933246i	$-0.616963\pi$
$727$	−7.44359e9			−0.718476			−0.359238	+	0.933246i	$0.616963\pi$
$728$		0			0
$729$	9.45727e9			0.904106
$730$	5.88476e9	+	1.01927e10i	0.559885	+	0.969750i
$731$	5.64611e9	−	9.77935e9i	0.534612	−	0.925974i
$732$	−8.76653e8	+	1.51841e9i	−0.0826112	+	0.143087i
$733$	1.18991e9	+	2.06098e9i	0.111596	+	0.193290i	0.916414	−	0.400232i	$-0.131070\pi$
$733$	1.18991e9	+	2.06098e9i	0.111596	+	0.193290i	−0.804818	+	0.593522i	$0.797737\pi$
$734$	5.05700e9			0.472016
$735$		0			0
$736$	3.28178e9			0.303415
$737$	6.26075e8	+	1.08439e9i	0.0576090	+	0.0997817i
$738$	3.24058e8	−	5.61285e8i	0.0296774	−	0.0514027i
$739$	4.23678e9	−	7.33832e9i	0.386172	−	0.668869i	−0.605759	−	0.795648i	$-0.707130\pi$
$739$	4.23678e9	−	7.33832e9i	0.386172	−	0.668869i	0.991931	+	0.126779i	$0.0404638\pi$
$740$	−3.91678e9	−	6.78406e9i	−0.355319	−	0.615430i
$741$	−2.64096e10			−2.38451
$742$		0			0
$743$	−1.74485e10			−1.56062			−0.780311	−	0.625391i	$-0.784939\pi$
$743$	−1.74485e10			−1.56062			−0.780311	+	0.625391i	$0.784939\pi$
$744$	8.01407e8	+	1.38808e9i	0.0713424	+	0.123569i
$745$	−6.49578e9	+	1.12510e10i	−0.575552	+	0.996885i
$746$	−6.08222e9	+	1.05347e10i	−0.536385	+	0.929046i
$747$	4.81001e8	+	8.33117e8i	0.0422205	+	0.0731281i
$748$	2.03717e9			0.177981
$749$		0			0
$750$	−9.19258e9			−0.795651
$751$	−4.75533e7	−	8.23648e7i	−0.00409677	−	0.00709581i	0.863970	−	0.503544i	$-0.167971\pi$
$751$	−4.75533e7	−	8.23648e7i	−0.00409677	−	0.00709581i	−0.868067	+	0.496448i	$0.834637\pi$
$752$	6.00152e8	−	1.03949e9i	0.0514635	−	0.0891374i
$753$	9.19840e9	−	1.59321e10i	0.785108	−	1.35985i
$754$	−4.58121e8	−	7.93489e8i	−0.0389207	−	0.0674126i
$755$	2.96656e9			0.250864
$756$		0			0
$757$	2.26187e10			1.89510			0.947548	−	0.319614i	$-0.103553\pi$
$757$	2.26187e10			1.89510			0.947548	+	0.319614i	$0.103553\pi$
$758$	−7.55023e9	−	1.30774e10i	−0.629677	−	1.09063i
$759$	−3.85015e9	+	6.66865e9i	−0.319618	+	0.553595i
$760$	3.42204e9	−	5.92715e9i	0.282773	−	0.489777i
$761$	8.54898e9	+	1.48073e10i	0.703183	+	1.21795i	0.967343	+	0.253469i	$0.0815717\pi$
$761$	8.54898e9	+	1.48073e10i	0.703183	+	1.21795i	−0.264161	+	0.964479i	$0.585095\pi$
$762$	−1.19092e9			−0.0975078
$763$		0			0
$764$	5.56115e9			0.451168
$765$	−4.43609e8	−	7.68354e8i	−0.0358250	−	0.0620506i
$766$	−4.78774e9	+	8.29260e9i	−0.384884	+	0.666638i
$767$	−9.74844e9	+	1.68848e10i	−0.780102	+	1.35118i
$768$	−4.08207e8	−	7.07036e8i	−0.0325174	−	0.0563219i
$769$	1.77666e10			1.40884			0.704422	−	0.709781i	$-0.251206\pi$
$769$	1.77666e10			1.40884			0.704422	+	0.709781i	$0.251206\pi$
$770$		0			0
$771$	3.54272e9			0.278385
$772$	−4.80543e9	−	8.32325e9i	−0.375899	−	0.651077i
$773$	6.03550e9	−	1.04538e10i	0.469986	−	0.814040i	−0.529425	−	0.848357i	$-0.677592\pi$
$773$	6.03550e9	−	1.04538e10i	0.469986	−	0.814040i	0.999411	+	0.0343171i	$0.0109256\pi$
$774$	4.05814e8	−	7.02890e8i	0.0314582	−	0.0544871i
$775$	−6.08735e8	−	1.05436e9i	−0.0469756	−	0.0813641i
$776$	−4.65487e9			−0.357595
$777$		0			0
$778$	−5.06034e9			−0.385258
$779$	−1.22953e10	−	2.12961e10i	−0.931876	−	1.61406i
$780$	−3.74273e9	+	6.48260e9i	−0.282395	+	0.489123i
$781$	1.76162e9	−	3.05122e9i	0.132323	−	0.229190i
$782$	−8.07069e9	−	1.39788e10i	−0.603514	−	1.04532i
$783$	−1.13176e9			−0.0842537
$784$		0			0
$785$	−1.60434e10			−1.18373
$786$	4.71589e9	+	8.16816e9i	0.346406	+	0.599992i
$787$	−1.21545e10	+	2.10522e10i	−0.888842	+	1.53952i	−0.0475959	+	0.998867i	$0.515156\pi$
$787$	−1.21545e10	+	2.10522e10i	−0.888842	+	1.53952i	−0.841246	+	0.540653i	$0.818177\pi$
$788$	1.08850e9	−	1.88534e9i	0.0792476	−	0.137261i
$789$	7.63231e9	+	1.32195e10i	0.553205	+	0.958180i
$790$	4.89167e9			0.352990
$791$		0			0
$792$	1.46422e8			0.0104729
$793$	−2.78063e9	−	4.81620e9i	−0.198010	−	0.342964i
$794$	5.95153e9	−	1.03083e10i	0.421946	−	0.730832i
$795$	−7.62495e9	+	1.32068e10i	−0.538210	+	0.932207i
$796$	−3.15999e9	−	5.47326e9i	−0.222070	−	0.384637i
$797$	1.54740e10			1.08267			0.541337	−	0.840805i	$-0.317918\pi$
$797$	1.54740e10			1.08267			0.541337	+	0.840805i	$0.317918\pi$
$798$		0			0
$799$	−5.90368e9			−0.409458
$800$	3.10067e8	+	5.37052e8i	0.0214112	+	0.0370853i
$801$	−7.28937e8	+	1.26256e9i	−0.0501160	+	0.0868034i
$802$	−9.97109e8	+	1.72704e9i	−0.0682547	+	0.118221i
$803$	4.77678e9	+	8.27363e9i	0.325560	+	0.563886i
$804$	−2.46814e9			−0.167484
$805$		0			0
$806$	−5.08393e9			−0.342000
$807$	−1.07115e10	−	1.85529e10i	−0.717452	−	1.24266i
$808$	−7.23444e8	+	1.25304e9i	−0.0482464	+	0.0835653i
$809$	−4.85543e9	+	8.40985e9i	−0.322409	+	0.558429i	−0.980985	−	0.194085i	$-0.937826\pi$
$809$	−4.85543e9	+	8.40985e9i	−0.322409	+	0.558429i	0.658575	+	0.752515i	$0.271159\pi$
$810$	5.00836e9	+	8.67473e9i	0.331129	+	0.573533i
$811$	−8.26711e8			−0.0544228			−0.0272114	−	0.999630i	$-0.508663\pi$
$811$	−8.26711e8			−0.0544228			−0.0272114	+	0.999630i	$0.508663\pi$
$812$		0			0
$813$	2.28506e9			0.149136
$814$	−3.17933e9	−	5.50676e9i	−0.206609	−	0.357858i
$815$	−6.23786e9	+	1.08043e10i	−0.403630	+	0.699108i
$816$	−2.00776e9	+	3.47754e9i	−0.129359	+	0.224056i
$817$	−1.53972e10	−	2.66688e10i	−0.987792	−	1.71091i
$818$	1.75295e10			1.11978
$819$		0			0
$820$	−6.96988e9			−0.441445
$821$	1.35967e10	+	2.35503e10i	0.857500	+	1.48523i	0.874306	+	0.485374i	$0.161317\pi$
$821$	1.35967e10	+	2.35503e10i	0.857500	+	1.48523i	−0.0168068	+	0.999859i	$0.505350\pi$
$822$	−3.74699e9	+	6.48998e9i	−0.235305	+	0.407560i
$823$	5.18409e8	−	8.97911e8i	0.0324170	−	0.0561480i	−0.849362	−	0.527811i	$-0.823013\pi$
$823$	5.18409e8	−	8.97911e8i	0.0324170	−	0.0561480i	0.881779	+	0.471663i	$0.156346\pi$
$824$	2.66807e9	+	4.62124e9i	0.166132	+	0.287748i
$825$	−1.45507e9			−0.0902184
$826$		0			0
$827$	−1.82384e9			−0.112129			−0.0560645	−	0.998427i	$-0.517855\pi$
$827$	−1.82384e9			−0.112129			−0.0560645	+	0.998427i	$0.517855\pi$
$828$	−5.80080e8	−	1.00473e9i	−0.0355126	−	0.0615096i
$829$	8.27954e9	−	1.43406e10i	0.504737	−	0.874231i	−0.495248	−	0.868752i	$-0.664923\pi$
$829$	8.27954e9	−	1.43406e10i	0.504737	−	0.874231i	0.999985	−	0.00547881i	$-0.00174397\pi$
$830$	5.17271e9	−	8.95939e9i	0.314011	−	0.543883i
$831$	−7.33737e9	−	1.27087e10i	−0.443544	−	0.768241i
$832$	2.58956e9			0.155882
$833$		0			0
$834$	−7.53598e9			−0.449841
$835$	−1.16268e10	−	2.01382e10i	−0.691128	−	1.19707i
$836$	2.77774e9	−	4.81119e9i	0.164426	−	0.284794i
$837$	−3.13989e9	+	5.43844e9i	−0.185087	+	0.320579i
$838$	2.32971e9	+	4.03518e9i	0.136757	+	0.236869i
$839$	−1.18110e9			−0.0690429			−0.0345215	−	0.999404i	$-0.510991\pi$
$839$	−1.18110e9			−0.0690429			−0.0345215	+	0.999404i	$0.510991\pi$
$840$		0			0
$841$	−1.71155e10			−0.992207
$842$	−8.44099e9	−	1.46202e10i	−0.487305	−	0.844037i
$843$	5.46877e8	−	9.47219e8i	0.0314408	−	0.0544570i
$844$	−3.30524e9	+	5.72485e9i	−0.189236	+	0.327767i
$845$	−4.23779e9	−	7.34006e9i	−0.241624	−	0.418506i
$846$	−4.24327e8			−0.0240937
$847$		0			0
$848$	5.27564e9			0.297091
$849$	5.68495e9	+	9.84663e9i	0.318823	+	0.552218i
$850$	1.52506e9	−	2.64148e9i	0.0851767	−	0.147530i
$851$	−2.51911e10	+	4.36323e10i	−1.40118	+	2.42692i
$852$	3.47238e9	+	6.01434e9i	0.192348	+	0.333157i
$853$	−9.29772e9			−0.512926			−0.256463	−	0.966554i	$-0.582557\pi$
$853$	−9.29772e9			−0.512926			−0.256463	+	0.966554i	$0.582557\pi$
$854$		0			0
$855$	−2.41949e9			−0.132386
$856$	2.43914e9	+	4.22472e9i	0.132917	+	0.230218i
$857$	1.31335e10	−	2.27480e10i	0.712769	−	1.23455i	−0.251044	−	0.967976i	$-0.580774\pi$
$857$	1.31335e10	−	2.27480e10i	0.712769	−	1.23455i	0.963814	−	0.266577i	$-0.0858927\pi$
$858$	−3.03805e9	+	5.26206e9i	−0.164206	+	0.284413i
$859$	1.73260e10	+	3.00094e10i	0.932656	+	1.61541i	0.778762	+	0.627319i	$0.215848\pi$
$859$	1.73260e10	+	3.00094e10i	0.932656	+	1.61541i	0.153894	+	0.988087i	$0.450819\pi$
$860$	−8.72828e9			−0.467934
$861$		0			0
$862$	−1.96153e10			−1.04309
$863$	1.52753e9	+	2.64576e9i	0.0809007	+	0.140124i	0.903637	−	0.428299i	$-0.140887\pi$
$863$	1.52753e9	+	2.64576e9i	0.0809007	+	0.140124i	−0.822736	+	0.568423i	$0.807554\pi$
$864$	1.59934e9	−	2.77014e9i	0.0843614	−	0.146118i
$865$	8.90019e8	−	1.54156e9i	0.0467566	−	0.0809848i
$866$	1.00989e10	+	1.74918e10i	0.528397	+	0.915211i
$867$	−2.17663e8			−0.0113427
$868$		0			0
$869$	3.97067e9			0.205255
$870$	−5.49092e8	−	9.51055e8i	−0.0282701	−	0.0489653i
$871$	3.91432e9	−	6.77980e9i	0.200721	−	0.347659i
$872$	6.47935e9	−	1.12226e10i	0.330921	−	0.573171i
$873$	8.22784e8	+	1.42510e9i	0.0418539	+	0.0724931i
$874$	−4.40184e10			−2.23020
$875$		0			0
$876$	−1.88312e10			−0.946487
$877$	−4.36306e9	−	7.55705e9i	−0.218420	−	0.378315i	0.735905	−	0.677085i	$-0.236757\pi$
$877$	−4.36306e9	−	7.55705e9i	−0.218420	−	0.378315i	−0.954325	+	0.298770i	$0.903424\pi$
$878$	−3.08895e9	+	5.35022e9i	−0.154021	+	0.266772i
$879$	−1.76198e10	+	3.05185e10i	−0.875067	+	1.51566i
$880$	−7.87314e8	−	1.36367e9i	−0.0389456	−	0.0674558i
$881$	−6.67328e9			−0.328794			−0.164397	−	0.986394i	$-0.552568\pi$
$881$	−6.67328e9			−0.328794			−0.164397	+	0.986394i	$0.552568\pi$
$882$		0			0
$883$	−2.31023e9			−0.112925			−0.0564627	−	0.998405i	$-0.517982\pi$
$883$	−2.31023e9			−0.112925			−0.0564627	+	0.998405i	$0.517982\pi$
$884$	−6.36837e9	−	1.10303e10i	−0.310060	−	0.537039i
$885$	−1.16842e10	+	2.02377e10i	−0.566628	+	0.981429i
$886$	1.17688e10	−	2.03842e10i	0.568479	−	0.984635i
$887$	−1.54471e10	−	2.67551e10i	−0.743213	−	1.28728i	−0.951025	−	0.309114i	$-0.899968\pi$
$887$	−1.54471e10	−	2.67551e10i	−0.743213	−	1.28728i	0.207812	−	0.978169i	$-0.433366\pi$
$888$	1.25337e10			0.600667
$889$		0			0
$890$	1.56781e10			0.745465
$891$	4.06538e9	+	7.04145e9i	0.192544	+	0.333496i
$892$	5.25094e9	−	9.09490e9i	0.247719	−	0.429063i
$893$	−8.04982e9	+	1.39427e10i	−0.378274	+	0.655189i
$894$	−1.03932e10	−	1.80016e10i	−0.486486	−	0.842618i
$895$	1.60398e10			0.747857
$896$		0			0
$897$	4.81435e10			2.22722
$898$	1.59551e9	+	2.76351e9i	0.0735247	+	0.127349i
$899$	3.72929e8	−	6.45931e8i	0.0171185	−	0.0296502i
$900$	1.09614e8	−	1.89856e8i	0.00501205	−	0.00868113i
$901$	−1.29741e10	−	2.24718e10i	−0.590935	−	1.02353i
$902$	−5.65759e9			−0.256690
$903$		0			0
$904$	−8.47762e9			−0.381667
$905$	8.73319e9	+	1.51263e10i	0.391654	+	0.678365i
$906$	−2.37325e9	+	4.11058e9i	−0.106021	+	0.183635i
$907$	1.69547e10	−	2.93663e10i	0.754508	−	1.30685i	−0.191111	−	0.981568i	$-0.561209\pi$
$907$	1.69547e10	−	2.93663e10i	0.754508	−	1.30685i	0.945619	−	0.325277i	$-0.105458\pi$
$908$	9.67522e9	+	1.67580e10i	0.428904	+	0.742884i
$909$	5.11498e8			0.0225876
$910$		0			0
$911$	−2.69204e10			−1.17969			−0.589844	−	0.807518i	$-0.700811\pi$
$911$	−2.69204e10			−1.17969			−0.589844	+	0.807518i	$0.700811\pi$
$912$	5.47527e9	+	9.48345e9i	0.239014	+	0.413985i
$913$	4.19879e9	−	7.27252e9i	0.182590	−	0.316255i
$914$	2.28248e9	−	3.95337e9i	0.0988769	−	0.171260i
$915$	−3.33279e9	−	5.77257e9i	−0.143825	−	0.249112i
$916$	4.19293e9			0.180253
$917$		0			0
$918$	−1.57327e10			−0.671203
$919$	2.15783e9	+	3.73746e9i	0.0917091	+	0.158845i	0.908230	−	0.418471i	$-0.137434\pi$
$919$	2.15783e9	+	3.73746e9i	0.0917091	+	0.158845i	−0.816521	+	0.577315i	$0.804100\pi$
$920$	−6.23822e9	+	1.08049e10i	−0.264121	+	0.457471i
$921$	2.16823e9	−	3.75549e9i	0.0914528	−	0.158401i
$922$	−2.92635e9	−	5.06859e9i	−0.122961	−	0.212975i
$923$	−2.20279e10			−0.922077
$924$		0			0
$925$	−9.52037e9			−0.395510
$926$	−9.26059e9	−	1.60398e10i	−0.383266	−	0.663836i
$927$	9.43205e8	−	1.63368e9i	0.0388890	−	0.0673578i
$928$	−1.89956e8	+	3.29014e8i	−0.00780253	+	0.0135144i
$929$	1.75319e9	+	3.03661e9i	0.0717421	+	0.124261i	0.899665	−	0.436581i	$-0.143811\pi$
$929$	1.75319e9	+	3.03661e9i	0.0717421	+	0.124261i	−0.827923	+	0.560842i	$0.810477\pi$
$930$	−6.09346e9			−0.248413
$931$		0			0
$932$	5.39260e9			0.218194
$933$	5.28124e9	+	9.14737e9i	0.212887	+	0.368732i
$934$	1.09814e10	−	1.90203e10i	0.441005	−	0.763843i
$935$	−3.87239e9	+	6.70718e9i	−0.154931	+	0.268348i
$936$	−4.57726e8	−	7.92804e8i	−0.0182448	−	0.0316010i
$937$	−1.32324e10			−0.525474			−0.262737	−	0.964868i	$-0.584625\pi$
$937$	−1.32324e10			−0.525474			−0.262737	+	0.964868i	$0.584625\pi$
$938$		0			0
$939$	4.26550e10			1.68128
$940$	2.28162e9	+	3.95187e9i	0.0895973	+	0.155187i
$941$	1.55966e9	−	2.70141e9i	0.0610192	−	0.105688i	−0.833902	−	0.551912i	$-0.813898\pi$
$941$	1.55966e9	−	2.70141e9i	0.0610192	−	0.105688i	0.894921	+	0.446224i	$0.147232\pi$
$942$	1.28347e10	−	2.22304e10i	0.500274	−	0.866501i
$943$	2.24137e10	+	3.88217e10i	0.870408	+	1.50759i
$944$	8.08422e9			0.312778
$945$		0			0
$946$	−7.08492e9			−0.272092
$947$	−8.78840e9	−	1.52220e10i	−0.336268	−	0.582432i	0.647460	−	0.762099i	$-0.275831\pi$
$947$	−8.78840e9	−	1.52220e10i	−0.336268	−	0.582432i	−0.983727	+	0.179667i	$0.942498\pi$
$948$	−3.91334e9	+	6.77810e9i	−0.149183	+	0.258392i
$949$	2.98652e10	−	5.17280e10i	1.13431	−	1.96469i
$950$	−4.15892e9	−	7.20346e9i	−0.157379	−	0.272589i
$951$	5.37206e10			2.02539
$952$		0			0
$953$	4.05868e10			1.51901			0.759504	−	0.650503i	$-0.225442\pi$
$953$	4.05868e10			1.51901			0.759504	+	0.650503i	$0.225442\pi$
$954$	−9.32511e8	−	1.61516e9i	−0.0347724	−	0.0602275i
$955$	−1.05710e10	+	1.83095e10i	−0.392739	+	0.680243i
$956$	−1.11525e9	+	1.93167e9i	−0.0412828	+	0.0715039i
$957$	−4.45709e8	−	7.71990e8i	−0.0164384	−	0.0284721i
$958$	3.01117e10			1.10651
$959$		0			0
$960$	3.10378e9			0.113225
$961$	1.16870e10	+	2.02426e10i	0.424789	+	0.735756i
$962$	−1.98776e10	+	3.44291e10i	−0.719867	+	1.24685i
$963$	8.62275e8	−	1.49350e9i	0.0311139	−	0.0538908i
$964$	−1.37413e9	−	2.38006e9i	−0.0494035	−	0.0855693i
$965$	3.65379e10			1.30887
$966$		0			0
$967$	9.54269e8			0.0339374			0.0169687	−	0.999856i	$-0.494598\pi$
$967$	9.54269e8			0.0339374			0.0169687	+	0.999856i	$0.494598\pi$
$968$	4.34964e9	+	7.53379e9i	0.154131	+	0.266962i
$969$	2.69300e10	−	4.66442e10i	0.950832	−	1.64689i
$970$	8.84827e9	−	1.53257e10i	0.311284	−	0.539160i
$971$	4.17200e9	+	7.22611e9i	0.146244	+	0.253301i	0.929836	−	0.367974i	$-0.119948\pi$
$971$	4.17200e9	+	7.22611e9i	0.146244	+	0.253301i	−0.783593	+	0.621275i	$0.786615\pi$
$972$	−2.36360e9			−0.0825548
$973$		0			0
$974$	3.33521e10			1.15655
$975$	4.54866e9	+	7.87851e9i	0.157169	+	0.272225i
$976$	−1.15297e9	+	1.99700e9i	−0.0396956	+	0.0687548i
$977$	−3.09430e9	+	5.35948e9i	−0.106153	+	0.183862i	−0.914209	−	0.405244i	$-0.867187\pi$
$977$	−3.09430e9	+	5.35948e9i	−0.106153	+	0.183862i	0.808056	+	0.589106i	$0.200520\pi$
$978$	−9.98057e9	−	1.72869e10i	−0.341169	−	0.590922i
$979$	1.27262e10			0.433470
$980$		0			0
$981$	−4.58110e9			−0.154927
$982$	−5.16164e8	−	8.94023e8i	−0.0173939	−	0.0301272i
$983$	−2.14116e10	+	3.70860e10i	−0.718972	+	1.24530i	0.242435	+	0.970168i	$0.422054\pi$
$983$	−2.14116e10	+	3.70860e10i	−0.718972	+	1.24530i	−0.961407	+	0.275129i	$0.911279\pi$
$984$	5.57590e9	−	9.65774e9i	0.186566	−	0.323142i
$985$	4.13818e9	+	7.16753e9i	0.137969	+	0.238970i
$986$	1.86859e9			0.0620791
$987$		0			0
$988$	−3.47337e10			−1.14578
$989$	2.80684e10	+	4.86159e10i	0.922636	+	1.59805i
$990$	−2.78328e8	+	4.82078e8i	−0.00911661	+	0.0157904i
$991$	−5.75291e9	+	9.96433e9i	−0.187771	+	0.325230i	−0.944507	−	0.328491i	$-0.893460\pi$
$991$	−5.75291e9	+	9.96433e9i	−0.187771	+	0.325230i	0.756735	+	0.653721i	$0.226793\pi$
$992$	1.05400e9	+	1.82559e9i	0.0342808	+	0.0593761i
$993$	−1.69603e10			−0.549682
$994$		0			0
$995$	2.40268e10			0.773243
$996$	8.27633e9	+	1.43350e10i	0.265418	+	0.459717i
$997$	−2.37843e10	+	4.11957e10i	−0.760077	+	1.31649i	0.182733	+	0.983163i	$0.441506\pi$
$997$	−2.37843e10	+	4.11957e10i	−0.760077	+	1.31649i	−0.942810	+	0.333330i	$0.891828\pi$
$998$	1.02051e10	−	1.76758e10i	0.324983	−	0.562887i
$999$	2.45533e10	+	4.25276e10i	0.779167	+	1.34956i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.8.c.i.67.1		4
7.2	even	3	inner	98.8.c.i.79.1		4
7.3	odd	6		98.8.a.j.1.1	✓	2
7.4	even	3		98.8.a.j.1.2	yes	2
7.5	odd	6	inner	98.8.c.i.79.2		4
7.6	odd	2	inner	98.8.c.i.67.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.8.a.j.1.1	✓	2	7.3	odd	6
98.8.a.j.1.2	yes	2	7.4	even	3
98.8.c.i.67.1		4	1.1	even	1	trivial
98.8.c.i.67.2		4	7.6	odd	2	inner
98.8.c.i.79.1		4	7.2	even	3	inner
98.8.c.i.79.2		4	7.5	odd	6	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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 - 6.92820i) q^{2} +(-24.3311 + 42.1426i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-121.655 - 210.713i) q^{5} +389.297 q^{6} +512.000 q^{8} +(-90.5000 - 156.751i) q^{9} +O(q^{10})\)	\(q+(-4.00000 - 6.92820i) q^{2} +(-24.3311 + 42.1426i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-121.655 - 210.713i) q^{5} +389.297 q^{6} +512.000 q^{8} +(-90.5000 - 156.751i) q^{9} +(-973.242 + 1685.70i) q^{10} +(-790.000 + 1368.32i) q^{11} +(-1557.19 - 2697.13i) q^{12} +9878.41 q^{13} +11840.0 q^{15} +(-2048.00 - 3547.24i) q^{16} +(-10073.1 + 17447.0i) q^{17} +(-724.000 + 1254.00i) q^{18} +(27469.8 + 47579.0i) q^{19} +15571.9 q^{20} +12640.0 q^{22} +(-50076.0 - 86734.2i) q^{23} +(-12457.5 + 21577.0i) q^{24} +(9462.50 - 16389.5i) q^{25} +(-39513.6 - 68439.6i) q^{26} -97616.2 q^{27} +11594.0 q^{29} +(-47360.0 - 82029.9i) q^{30} +(32165.6 - 55712.5i) q^{31} +(-16384.0 + 28377.9i) q^{32} +(-38443.1 - 66585.3i) q^{33} +161169. q^{34} +11584.0 q^{36} +(-251529. - 435661. i) q^{37} +(219758. - 380632. i) q^{38} +(-240352. + 416302. i) q^{39} +(-62287.5 - 107885. i) q^{40} -447594. q^{41} -560516. q^{43} +(-50560.0 - 87572.5i) q^{44} +(-22019.6 + 38139.1i) q^{45} +(-400608. + 693873. i) q^{46} +(146522. + 253783. i) q^{47} +199320. q^{48} -151400. q^{50} +(-490176. - 849010. i) q^{51} +(-316109. + 547517. i) q^{52} +(-643999. + 1.11544e6i) q^{53} +(390465. + 676305. i) q^{54} +384431. q^{55} -2.67347e6 q^{57} +(-46376.0 - 80325.6i) q^{58} +(-986843. + 1.70926e6i) q^{59} +(-378880. + 656239. i) q^{60} +(-281486. - 487548. i) q^{61} -514650. q^{62} +262144. q^{64} +(-1.20176e6 - 2.08151e6i) q^{65} +(-307544. + 532683. i) q^{66} +(396250. - 686325. i) q^{67} +(-644676. - 1.11661e6i) q^{68} +4.87361e6 q^{69} -2.22990e6 q^{71} +(-46336.0 - 80256.3i) q^{72} +(3.02328e6 - 5.23647e6i) q^{73} +(-2.01223e6 + 3.48529e6i) q^{74} +(460465. + 797549. i) q^{75} -3.51613e6 q^{76} +3.84563e6 q^{78} +(-1.25654e6 - 2.17639e6i) q^{79} +(-498300. + 863081. i) q^{80} +(2.57303e6 - 4.45661e6i) q^{81} +(1.79038e6 + 3.10102e6i) q^{82} -5.31492e6 q^{83} +4.90176e6 q^{85} +(2.24206e6 + 3.88337e6i) q^{86} +(-282094. + 488601. i) q^{87} +(-404480. + 700580. i) q^{88} +(-4.02728e6 - 6.97545e6i) q^{89} +352314. q^{90} +6.40973e6 q^{92} +(1.56525e6 + 2.71109e6i) q^{93} +(1.17217e6 - 2.03026e6i) q^{94} +(6.68368e6 - 1.15765e7i) q^{95} +(-797280. - 1.38093e6i) q^{96} -9.09154e6 q^{97} +285980. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} - 128 q^{4} + 2048 q^{8} - 362 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 - 128 * q^4 + 2048 * q^8 - 362 * q^9	\( 4 q - 16 q^{2} - 128 q^{4} + 2048 q^{8} - 362 q^{9} - 3160 q^{11} + 47360 q^{15} - 8192 q^{16} - 2896 q^{18} + 50560 q^{22} - 200304 q^{23} + 37850 q^{25} + 46376 q^{29} - 189440 q^{30} - 65536 q^{32} + 46336 q^{36} - 1006116 q^{37} - 961408 q^{39} - 2242064 q^{43} - 202240 q^{44} - 1602432 q^{46} - 605600 q^{50} - 1960704 q^{51} - 2575996 q^{53} - 10693888 q^{57} - 185504 q^{58} - 1515520 q^{60} + 1048576 q^{64} - 4807040 q^{65} + 1585000 q^{67} - 8919616 q^{71} - 185344 q^{72} - 8048928 q^{74} + 15382528 q^{78} - 5026160 q^{79} + 10292110 q^{81} + 19607040 q^{85} + 8968256 q^{86} - 1617920 q^{88} + 25638912 q^{92} + 6260992 q^{93} + 26734720 q^{95} + 1143920 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 - 128 * q^4 + 2048 * q^8 - 362 * q^9 - 3160 * q^11 + 47360 * q^15 - 8192 * q^16 - 2896 * q^18 + 50560 * q^22 - 200304 * q^23 + 37850 * q^25 + 46376 * q^29 - 189440 * q^30 - 65536 * q^32 + 46336 * q^36 - 1006116 * q^37 - 961408 * q^39 - 2242064 * q^43 - 202240 * q^44 - 1602432 * q^46 - 605600 * q^50 - 1960704 * q^51 - 2575996 * q^53 - 10693888 * q^57 - 185504 * q^58 - 1515520 * q^60 + 1048576 * q^64 - 4807040 * q^65 + 1585000 * q^67 - 8919616 * q^71 - 185344 * q^72 - 8048928 * q^74 + 15382528 * q^78 - 5026160 * q^79 + 10292110 * q^81 + 19607040 * q^85 + 8968256 * q^86 - 1617920 * q^88 + 25638912 * q^92 + 6260992 * q^93 + 26734720 * q^95 + 1143920 * q^99

Introduction

L-functions

Modular forms

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Database

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