LMFDB - Embedded newform 370.2.c.a.369.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(369,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("370.369");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 19x^{8} + 103x^{6} + 210x^{4} + 140x^{2} + 16 $ x^10 + 19x^8 + 103x^6 + 210x^4 + 140x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			369.6
Root			$0.377861i$ of defining polynomial
Character	$\chi$	$=$	370.369
Dual form			370.2.c.a.369.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.377861i q^{3} +1.00000 q^{4} +(1.04797 + 1.97529i) q^{5} -0.377861i q^{6} +0.631751i q^{7} -1.00000 q^{8} +2.85722 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.377861i q^{3} +1.00000 q^{4} +(1.04797 + 1.97529i) q^{5} -0.377861i q^{6} +0.631751i q^{7} -1.00000 q^{8} +2.85722 q^{9} +(-1.04797 - 1.97529i) q^{10} +1.24789 q^{11} +0.377861i q^{12} -3.34999 q^{13} -0.631751i q^{14} +(-0.746385 + 0.395986i) q^{15} +1.00000 q^{16} -3.10511 q^{17} -2.85722 q^{18} +5.97327i q^{19} +(1.04797 + 1.97529i) q^{20} -0.238714 q^{21} -1.24789 q^{22} +7.60706 q^{23} -0.377861i q^{24} +(-2.80353 + 4.14008i) q^{25} +3.34999 q^{26} +2.21322i q^{27} +0.631751i q^{28} -9.57629i q^{29} +(0.746385 - 0.395986i) q^{30} +7.26707i q^{31} -1.00000 q^{32} +0.471529i q^{33} +3.10511 q^{34} +(-1.24789 + 0.662054i) q^{35} +2.85722 q^{36} +(4.10511 + 4.48866i) q^{37} -5.97327i q^{38} -1.26583i q^{39} +(-1.04797 - 1.97529i) q^{40} -8.45510 q^{41} +0.238714 q^{42} +4.86640 q^{43} +1.24789 q^{44} +(2.99427 + 5.64384i) q^{45} -7.60706 q^{46} +13.1187i q^{47} +0.377861i q^{48} +6.60089 q^{49} +(2.80353 - 4.14008i) q^{50} -1.17330i q^{51} -3.34999 q^{52} -7.17340i q^{53} -2.21322i q^{54} +(1.30775 + 2.46494i) q^{55} -0.631751i q^{56} -2.25707 q^{57} +9.57629i q^{58} -4.36469i q^{59} +(-0.746385 + 0.395986i) q^{60} -2.14666i q^{61} -7.26707i q^{62} +1.80505i q^{63} +1.00000 q^{64} +(-3.51068 - 6.61720i) q^{65} -0.471529i q^{66} -11.3451i q^{67} -3.10511 q^{68} +2.87441i q^{69} +(1.24789 - 0.662054i) q^{70} -12.7183 q^{71} -2.85722 q^{72} -4.45836i q^{73} +(-4.10511 - 4.48866i) q^{74} +(-1.56437 - 1.05934i) q^{75} +5.97327i q^{76} +0.788355i q^{77} +1.26583i q^{78} -8.78679i q^{79} +(1.04797 + 1.97529i) q^{80} +7.73537 q^{81} +8.45510 q^{82} -6.63185i q^{83} -0.238714 q^{84} +(-3.25406 - 6.13349i) q^{85} -4.86640 q^{86} +3.61851 q^{87} -1.24789 q^{88} -13.7784i q^{89} +(-2.99427 - 5.64384i) q^{90} -2.11636i q^{91} +7.60706 q^{92} -2.74594 q^{93} -13.1187i q^{94} +(-11.7989 + 6.25979i) q^{95} -0.377861i q^{96} -11.0583 q^{97} -6.60089 q^{98} +3.56550 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} - 8 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 - 8 * q^9	$ 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} - 8 q^{9} + 3 q^{10} - 2 q^{13} - 10 q^{15} + 10 q^{16} + 18 q^{17} + 8 q^{18} - 3 q^{20} - 12 q^{21} + 10 q^{23} + 5 q^{25} + 2 q^{26} + 10 q^{30} - 10 q^{32} - 18 q^{34} - 8 q^{36} - 8 q^{37} + 3 q^{40} - 4 q^{41} + 12 q^{42} - 10 q^{43} + 20 q^{45} - 10 q^{46} - 8 q^{49} - 5 q^{50} - 2 q^{52} + 5 q^{55} + 12 q^{57} - 10 q^{60} + 10 q^{64} + 2 q^{65} + 18 q^{68} - 20 q^{71} + 8 q^{72} + 8 q^{74} + 25 q^{75} - 3 q^{80} + 58 q^{81} + 4 q^{82} - 12 q^{84} - 28 q^{85} + 10 q^{86} - 10 q^{87} - 20 q^{90} + 10 q^{92} - 32 q^{93} + 2 q^{95} + 2 q^{97} + 8 q^{98} - 82 q^{99}+O(q^{100}) $ 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 - 8 * q^9 + 3 * q^10 - 2 * q^13 - 10 * q^15 + 10 * q^16 + 18 * q^17 + 8 * q^18 - 3 * q^20 - 12 * q^21 + 10 * q^23 + 5 * q^25 + 2 * q^26 + 10 * q^30 - 10 * q^32 - 18 * q^34 - 8 * q^36 - 8 * q^37 + 3 * q^40 - 4 * q^41 + 12 * q^42 - 10 * q^43 + 20 * q^45 - 10 * q^46 - 8 * q^49 - 5 * q^50 - 2 * q^52 + 5 * q^55 + 12 * q^57 - 10 * q^60 + 10 * q^64 + 2 * q^65 + 18 * q^68 - 20 * q^71 + 8 * q^72 + 8 * q^74 + 25 * q^75 - 3 * q^80 + 58 * q^81 + 4 * q^82 - 12 * q^84 - 28 * q^85 + 10 * q^86 - 10 * q^87 - 20 * q^90 + 10 * q^92 - 32 * q^93 + 2 * q^95 + 2 * q^97 + 8 * q^98 - 82 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$			0.377861i			0.218158i	0.994033	+	0.109079i	$0.0347902\pi$
$3$			0.377861i			0.218158i	−0.994033	+	0.109079i	$0.965210\pi$
$4$	1.00000			0.500000
$5$	1.04797	+	1.97529i	0.468665	+	0.883376i
$5$	1.04797	+	1.97529i	0.468665	+	0.883376i
$6$		−	0.377861i		−	0.154261i
$7$			0.631751i			0.238779i	0.992847	+	0.119390i	$0.0380938\pi$
$7$			0.631751i			0.238779i	−0.992847	+	0.119390i	$0.961906\pi$
$8$	−1.00000			−0.353553
$9$	2.85722			0.952407
$10$	−1.04797	−	1.97529i	−0.331396	−	0.624641i
$11$	1.24789			0.376253			0.188126	−	0.982145i	$-0.439759\pi$
$11$	1.24789			0.376253			0.188126	+	0.982145i	$0.439759\pi$
$12$			0.377861i			0.109079i
$13$	−3.34999			−0.929120			−0.464560	−	0.885542i	$-0.653788\pi$
$13$	−3.34999			−0.929120			−0.464560	+	0.885542i	$0.653788\pi$
$14$		−	0.631751i		−	0.168843i
$15$	−0.746385	+	0.395986i	−0.192716	+	0.102243i
$16$	1.00000			0.250000
$17$	−3.10511			−0.753100			−0.376550	−	0.926396i	$-0.622890\pi$
$17$	−3.10511			−0.753100			−0.376550	+	0.926396i	$0.622890\pi$
$18$	−2.85722			−0.673453
$19$			5.97327i			1.37036i	0.728373	+	0.685181i	$0.240277\pi$
$19$			5.97327i			1.37036i	−0.728373	+	0.685181i	$0.759723\pi$
$20$	1.04797	+	1.97529i	0.234333	+	0.441688i
$21$	−0.238714			−0.0520917
$22$	−1.24789			−0.266051
$23$	7.60706			1.58618			0.793090	−	0.609104i	$-0.208471\pi$
$23$	7.60706			1.58618			0.793090	+	0.609104i	$0.208471\pi$
$24$		−	0.377861i		−	0.0771306i
$25$	−2.80353	+	4.14008i	−0.560706	+	0.828015i
$26$	3.34999			0.656987
$27$			2.21322i			0.425934i
$28$			0.631751i			0.119390i
$29$		−	9.57629i		−	1.77827i	−0.457643	−	0.889136i	$-0.651306\pi$
$29$		−	9.57629i		−	1.77827i	0.457643	−	0.889136i	$-0.348694\pi$
$30$	0.746385	−	0.395986i	0.136271	−	0.0722969i
$31$			7.26707i			1.30520i	0.757701	+	0.652602i	$0.226323\pi$
$31$			7.26707i			1.30520i	−0.757701	+	0.652602i	$0.773677\pi$
$32$	−1.00000			−0.176777
$33$			0.471529i			0.0820827i
$34$	3.10511			0.532522
$35$	−1.24789	+	0.662054i	−0.210932	+	0.111908i
$36$	2.85722			0.476203
$37$	4.10511	+	4.48866i	0.674876	+	0.737931i
$37$	4.10511	+	4.48866i	0.674876	+	0.737931i
$38$		−	5.97327i		−	0.968992i
$39$		−	1.26583i		−	0.202695i
$40$	−1.04797	−	1.97529i	−0.165698	−	0.312321i
$41$	−8.45510			−1.32046			−0.660232	−	0.751061i	$-0.729542\pi$
$41$	−8.45510			−1.32046			−0.660232	+	0.751061i	$0.729542\pi$
$42$	0.238714			0.0368344
$43$	4.86640			0.742119			0.371059	−	0.928609i	$-0.378995\pi$
$43$	4.86640			0.742119			0.371059	+	0.928609i	$0.378995\pi$
$44$	1.24789			0.188126
$45$	2.99427	+	5.64384i	0.446360	+	0.841333i
$46$	−7.60706			−1.12160
$47$			13.1187i			1.91356i	0.290815	+	0.956779i	$0.406074\pi$
$47$			13.1187i			1.91356i	−0.290815	+	0.956779i	$0.593926\pi$
$48$			0.377861i			0.0545396i
$49$	6.60089			0.942984
$50$	2.80353	−	4.14008i	0.396479	−	0.585495i
$51$		−	1.17330i		−	0.164295i
$52$	−3.34999			−0.464560
$53$		−	7.17340i		−	0.985343i	−0.870215	−	0.492671i	$-0.836020\pi$
$53$		−	7.17340i		−	0.985343i	0.870215	−	0.492671i	$-0.163980\pi$
$54$		−	2.21322i		−	0.301181i
$55$	1.30775	+	2.46494i	0.176337	+	0.332373i
$56$		−	0.631751i		−	0.0844213i
$57$	−2.25707			−0.298956
$58$			9.57629i			1.25743i
$59$		−	4.36469i		−	0.568234i	−0.958790	−	0.284117i	$-0.908300\pi$
$59$		−	4.36469i		−	0.568234i	0.958790	−	0.284117i	$-0.0917004\pi$
$60$	−0.746385	+	0.395986i	−0.0963579	+	0.0511216i
$61$		−	2.14666i		−	0.274852i	−0.990512	−	0.137426i	$-0.956117\pi$
$61$		−	2.14666i		−	0.274852i	0.990512	−	0.137426i	$-0.0438829\pi$
$62$		−	7.26707i		−	0.922919i
$63$			1.80505i			0.227415i
$64$	1.00000			0.125000
$65$	−3.51068	−	6.61720i	−0.435446	−	0.820762i
$66$		−	0.471529i		−	0.0580412i
$67$		−	11.3451i		−	1.38602i	−0.720926	−	0.693012i	$-0.756283\pi$
$67$		−	11.3451i		−	1.38602i	0.720926	−	0.693012i	$-0.243717\pi$
$68$	−3.10511			−0.376550
$69$			2.87441i			0.346038i
$70$	1.24789	−	0.662054i	0.149151	−	0.0791306i
$71$	−12.7183			−1.50939			−0.754694	−	0.656077i	$-0.772215\pi$
$71$	−12.7183			−1.50939			−0.754694	+	0.656077i	$0.772215\pi$
$72$	−2.85722			−0.336727
$73$		−	4.45836i		−	0.521811i	−0.965364	−	0.260906i	$-0.915979\pi$
$73$		−	4.45836i		−	0.521811i	0.965364	−	0.260906i	$-0.0840211\pi$
$74$	−4.10511	−	4.48866i	−0.477209	−	0.521796i
$75$	−1.56437	−	1.05934i	−0.180638	−	0.122323i
$76$			5.97327i			0.685181i
$77$			0.788355i			0.0898414i
$78$			1.26583i			0.143327i
$79$		−	8.78679i		−	0.988592i	−0.869294	−	0.494296i	$-0.835426\pi$
$79$		−	8.78679i		−	0.988592i	0.869294	−	0.494296i	$-0.164574\pi$
$80$	1.04797	+	1.97529i	0.117166	+	0.220844i
$81$	7.73537			0.859486
$82$	8.45510			0.933710
$83$		−	6.63185i		−	0.727941i	−0.931411	−	0.363970i	$-0.881421\pi$
$83$		−	6.63185i		−	0.727941i	0.931411	−	0.363970i	$-0.118579\pi$
$84$	−0.238714			−0.0260458
$85$	−3.25406	−	6.13349i	−0.352952	−	0.665270i
$86$	−4.86640			−0.524757
$87$	3.61851			0.387945
$88$	−1.24789			−0.133026
$89$		−	13.7784i		−	1.46051i	−0.683175	−	0.730255i	$-0.739401\pi$
$89$		−	13.7784i		−	1.46051i	0.683175	−	0.730255i	$-0.260599\pi$
$90$	−2.99427	−	5.64384i	−0.315624	−	0.594912i
$91$		−	2.11636i		−	0.221855i
$92$	7.60706			0.793090
$93$	−2.74594			−0.284741
$94$		−	13.1187i		−	1.35309i
$95$	−11.7989	+	6.25979i	−1.21054	+	0.642241i
$96$		−	0.377861i		−	0.0385653i
$97$	−11.0583			−1.12280			−0.561398	−	0.827546i	$-0.689736\pi$
$97$	−11.0583			−1.12280			−0.561398	+	0.827546i	$0.689736\pi$
$98$	−6.60089			−0.666791
$99$	3.56550			0.358346
$100$	−2.80353	+	4.14008i	−0.280353	+	0.414008i
$101$	8.65314			0.861019			0.430510	−	0.902586i	$-0.358334\pi$
$101$	8.65314			0.861019			0.430510	+	0.902586i	$0.358334\pi$
$102$			1.17330i			0.116174i
$103$	4.57336			0.450627			0.225313	−	0.974286i	$-0.427659\pi$
$103$	4.57336			0.450627			0.225313	+	0.974286i	$0.427659\pi$
$104$	3.34999			0.328494
$105$	−0.250165	−	0.471529i	−0.0244136	−	0.0460165i
$106$			7.17340i			0.696743i
$107$		−	11.4715i		−	1.10900i	−0.832185	−	0.554498i	$-0.812910\pi$
$107$		−	11.4715i		−	1.10900i	0.832185	−	0.554498i	$-0.187090\pi$
$108$			2.21322i			0.212967i
$109$			0.727748i			0.0697057i	0.999392	+	0.0348528i	$0.0110962\pi$
$109$			0.727748i			0.0697057i	−0.999392	+	0.0348528i	$0.988904\pi$
$110$	−1.30775	−	2.46494i	−0.124689	−	0.235023i
$111$	−1.69609	+	1.55116i	−0.160986	+	0.147230i
$112$			0.631751i			0.0596948i
$113$	17.9970			1.69301			0.846506	−	0.532379i	$-0.178702\pi$
$113$	17.9970			1.69301			0.846506	+	0.532379i	$0.178702\pi$
$114$	2.25707			0.211394
$115$	7.97195	+	15.0261i	0.743388	+	1.40119i
$116$		−	9.57629i		−	0.889136i
$117$	−9.57166			−0.884901
$118$			4.36469i			0.401802i
$119$		−	1.96166i		−	0.179825i
$120$	0.746385	−	0.395986i	0.0681353	−	0.0361484i
$121$	−9.44277			−0.858434
$122$			2.14666i			0.194350i
$123$		−	3.19485i		−	0.288070i
$124$			7.26707i			0.652602i
$125$	−11.1159	−	1.19911i	−0.994232	−	0.107252i
$126$		−	1.80505i		−	0.160807i
$127$			15.4830i			1.37389i	0.726707	+	0.686947i	$0.241050\pi$
$127$			15.4830i			1.37389i	−0.726707	+	0.686947i	$0.758950\pi$
$128$	−1.00000			−0.0883883
$129$			1.83882i			0.161899i
$130$	3.51068	+	6.61720i	0.307907	+	0.580367i
$131$		−	6.22121i		−	0.543550i	−0.962361	−	0.271775i	$-0.912389\pi$
$131$		−	6.22121i		−	0.543550i	0.962361	−	0.271775i	$-0.0876106\pi$
$132$			0.471529i			0.0410413i
$133$	−3.77362			−0.327214
$134$			11.3451i			0.980066i
$135$	−4.37174	+	2.31938i	−0.376260	+	0.199620i
$136$	3.10511			0.266261
$137$		−	14.1258i		−	1.20685i	−0.797419	−	0.603426i	$-0.793802\pi$
$137$		−	14.1258i		−	1.20685i	0.797419	−	0.603426i	$-0.206198\pi$
$138$		−	2.87441i		−	0.244686i
$139$	8.43675			0.715596			0.357798	−	0.933799i	$-0.383528\pi$
$139$	8.43675			0.715596			0.357798	+	0.933799i	$0.383528\pi$
$140$	−1.24789	+	0.662054i	−0.105466	+	0.0559538i
$141$	−4.95705			−0.417459
$142$	12.7183			1.06730
$143$	−4.18042			−0.349584
$144$	2.85722			0.238102
$145$	18.9159	−	10.0356i	1.57088	−	0.833414i
$146$			4.45836i			0.368976i
$147$			2.49422i			0.205720i
$148$	4.10511	+	4.48866i	0.337438	+	0.368966i
$149$	13.6447			1.11782			0.558909	−	0.829229i	$-0.311220\pi$
$149$	13.6447			1.11782			0.558909	+	0.829229i	$0.311220\pi$
$150$	1.56437	+	1.05934i	0.127731	+	0.0864951i
$151$	−3.17741			−0.258574			−0.129287	−	0.991607i	$-0.541269\pi$
$151$	−3.17741			−0.258574			−0.129287	+	0.991607i	$0.541269\pi$
$152$		−	5.97327i		−	0.484496i
$153$	−8.87199			−0.717258
$154$		−	0.788355i		−	0.0635275i
$155$	−14.3546	+	7.61566i	−1.15299	+	0.611704i
$156$		−	1.26583i		−	0.101348i
$157$			0.215310i			0.0171836i	0.999963	+	0.00859180i	$0.00273489\pi$
$157$			0.215310i			0.0171836i	−0.999963	+	0.00859180i	$0.997265\pi$
$158$			8.78679i			0.699040i
$159$	2.71055			0.214961
$160$	−1.04797	−	1.97529i	−0.0828491	−	0.156160i
$161$			4.80576i			0.378747i
$162$	−7.73537			−0.607748
$163$	−1.66609			−0.130498			−0.0652490	−	0.997869i	$-0.520784\pi$
$163$	−1.66609			−0.130498			−0.0652490	+	0.997869i	$0.520784\pi$
$164$	−8.45510			−0.660232
$165$	−0.931406	+	0.494147i	−0.0725099	+	0.0384693i
$166$			6.63185i			0.514732i
$167$	5.92242			0.458290			0.229145	−	0.973392i	$-0.426407\pi$
$167$	5.92242			0.458290			0.229145	+	0.973392i	$0.426407\pi$
$168$	0.238714			0.0184172
$169$	−1.77756			−0.136736
$170$	3.25406	+	6.13349i	0.249575	+	0.470417i
$171$			17.0669i			1.30514i
$172$	4.86640			0.371059
$173$		−	2.88008i		−	0.218968i	−0.993989	−	0.109484i	$-0.965080\pi$
$173$		−	2.88008i		−	0.218968i	0.993989	−	0.109484i	$-0.0349199\pi$
$174$	−3.61851			−0.274318
$175$	−2.61550	−	1.77113i	−0.197713	−	0.133885i
$176$	1.24789			0.0940632
$177$	1.64925			0.123965
$178$			13.7784i			1.03274i
$179$			4.46182i			0.333492i	0.986000	+	0.166746i	$0.0533260\pi$
$179$			4.46182i			0.333492i	−0.986000	+	0.166746i	$0.946674\pi$
$180$	2.99427	+	5.64384i	0.223180	+	0.420667i
$181$	3.93480			0.292472			0.146236	−	0.989250i	$-0.453284\pi$
$181$	3.93480			0.292472			0.146236	+	0.989250i	$0.453284\pi$
$182$			2.11636i			0.156875i
$183$	0.811140			0.0599612
$184$	−7.60706			−0.560800
$185$	−4.56437	+	12.8127i	−0.335579	+	0.942012i
$186$	2.74594			0.201342
$187$	−3.87484			−0.283356
$188$			13.1187i			0.956779i
$189$	−1.39820			−0.101704
$190$	11.7989	−	6.25979i	0.855984	−	0.454133i
$191$			7.76296i			0.561708i	0.959751	+	0.280854i	$0.0906177\pi$
$191$			7.76296i			0.561708i	−0.959751	+	0.280854i	$0.909382\pi$
$192$			0.377861i			0.0272698i
$193$	−3.49189			−0.251352			−0.125676	−	0.992071i	$-0.540110\pi$
$193$	−3.49189			−0.251352			−0.125676	+	0.992071i	$0.540110\pi$
$194$	11.0583			0.793937
$195$	2.50038	−	1.32655i	0.179056	−	0.0949962i
$196$	6.60089			0.471492
$197$			1.07617i			0.0766736i	0.999265	+	0.0383368i	$0.0122060\pi$
$197$			1.07617i			0.0766736i	−0.999265	+	0.0383368i	$0.987794\pi$
$198$	−3.56550			−0.253389
$199$		−	5.71343i		−	0.405014i	−0.979281	−	0.202507i	$-0.935091\pi$
$199$		−	5.71343i		−	0.405014i	0.979281	−	0.202507i	$-0.0649090\pi$
$200$	2.80353	−	4.14008i	0.198239	−	0.292748i
$201$	4.28687			0.302372
$202$	−8.65314			−0.608833
$203$	6.04983			0.424615
$204$		−	1.17330i		−	0.0821475i
$205$	−8.86067	−	16.7013i	−0.618856	−	1.16647i
$206$	−4.57336			−0.318641
$207$	21.7350			1.51069
$208$	−3.34999			−0.232280
$209$			7.45398i			0.515603i
$210$	0.250165	+	0.471529i	0.0172630	+	0.0325386i
$211$	22.8397			1.57235			0.786176	−	0.618003i	$-0.212058\pi$
$211$	22.8397			1.57235			0.786176	+	0.618003i	$0.212058\pi$
$212$		−	7.17340i		−	0.492671i
$213$		−	4.80576i		−	0.329286i
$214$			11.4715i			0.784178i
$215$	5.09983	+	9.61254i	0.347805	+	0.655570i
$216$		−	2.21322i		−	0.150590i
$217$	−4.59098			−0.311656
$218$		−	0.727748i		−	0.0492893i
$219$	1.68464			0.113837
$220$	1.30775	+	2.46494i	0.0881684	+	0.166186i
$221$	10.4021			0.699720
$222$	1.69609	−	1.55116i	0.113834	−	0.104107i
$223$		−	3.32116i		−	0.222401i	−0.993798	−	0.111201i	$-0.964530\pi$
$223$		−	3.32116i		−	0.222401i	0.993798	−	0.111201i	$-0.0354696\pi$
$224$		−	0.631751i		−	0.0422106i
$225$	−8.01030	+	11.8291i	−0.534020	+	0.788607i
$226$	−17.9970			−1.19714
$227$	5.62938			0.373635			0.186818	−	0.982395i	$-0.440183\pi$
$227$	5.62938			0.373635			0.186818	+	0.982395i	$0.440183\pi$
$228$	−2.25707			−0.149478
$229$	−0.973208			−0.0643114			−0.0321557	−	0.999483i	$-0.510237\pi$
$229$	−0.973208			−0.0643114			−0.0321557	+	0.999483i	$0.510237\pi$
$230$	−7.97195	−	15.0261i	−0.525655	−	0.990794i
$231$	−0.297889			−0.0195997
$232$			9.57629i			0.628714i
$233$		−	14.4150i		−	0.944357i	−0.881503	−	0.472178i	$-0.843468\pi$
$233$		−	14.4150i		−	0.944357i	0.881503	−	0.472178i	$-0.156532\pi$
$234$	9.57166			0.625719
$235$	−25.9132	+	13.7480i	−1.69039	+	0.896819i
$236$		−	4.36469i		−	0.284117i
$237$	3.32019			0.215669
$238$			1.96166i			0.127155i
$239$			8.43344i			0.545514i	0.962083	+	0.272757i	$0.0879355\pi$
$239$			8.43344i			0.545514i	−0.962083	+	0.272757i	$0.912065\pi$
$240$	−0.746385	+	0.395986i	−0.0481789	+	0.0255608i
$241$			18.6567i			1.20178i	0.799331	+	0.600891i	$0.205188\pi$
$241$			18.6567i			1.20178i	−0.799331	+	0.600891i	$0.794812\pi$
$242$	9.44277			0.607004
$243$			9.56255i			0.613438i
$244$		−	2.14666i		−	0.137426i
$245$	6.91752	+	13.0387i	0.441944	+	0.833010i
$246$			3.19485i			0.203696i
$247$		−	20.0104i		−	1.27323i
$248$		−	7.26707i		−	0.461460i
$249$	2.50592			0.158806
$250$	11.1159	+	1.19911i	0.703028	+	0.0758385i
$251$		−	25.1189i		−	1.58549i	−0.609553	−	0.792746i	$-0.708651\pi$
$251$		−	25.1189i		−	1.58549i	0.609553	−	0.792746i	$-0.291349\pi$
$252$			1.80505i			0.113708i
$253$	9.49277			0.596805
$254$		−	15.4830i		−	0.971490i
$255$	2.31761	−	1.22958i	0.145134	−	0.0769994i
$256$	1.00000			0.0625000
$257$	−20.3552			−1.26973			−0.634863	−	0.772625i	$-0.718943\pi$
$257$	−20.3552			−1.26973			−0.634863	+	0.772625i	$0.718943\pi$
$258$		−	1.83882i		−	0.114480i
$259$	−2.83571	+	2.59341i	−0.176203	+	0.161146i
$260$	−3.51068	−	6.61720i	−0.217723	−	0.410381i
$261$		−	27.3616i		−	1.69364i
$262$			6.22121i			0.384348i
$263$			22.2211i			1.37021i	0.728443	+	0.685107i	$0.240244\pi$
$263$			22.2211i			1.37021i	−0.728443	+	0.685107i	$0.759756\pi$
$264$		−	0.471529i		−	0.0290206i
$265$	14.1695	−	7.51750i	0.870428	−	0.461796i
$266$	3.77362			0.231375
$267$	5.20633			0.318622
$268$		−	11.3451i		−	0.693012i
$269$	−15.8411			−0.965850			−0.482925	−	0.875662i	$-0.660426\pi$
$269$	−15.8411			−0.965850			−0.482925	+	0.875662i	$0.660426\pi$
$270$	4.37174	−	2.31938i	0.266056	−	0.141153i
$271$	−2.00602			−0.121857			−0.0609285	−	0.998142i	$-0.519406\pi$
$271$	−2.00602			−0.121857			−0.0609285	+	0.998142i	$0.519406\pi$
$272$	−3.10511			−0.188275
$273$	0.799690			0.0483994
$274$			14.1258i			0.853373i
$275$	−3.49849	+	5.16636i	−0.210967	+	0.311543i
$276$			2.87441i			0.173019i
$277$	−11.5671			−0.695000			−0.347500	−	0.937680i	$-0.612969\pi$
$277$	−11.5671			−0.695000			−0.347500	+	0.937680i	$0.612969\pi$
$278$	−8.43675			−0.506003
$279$			20.7636i			1.24309i
$280$	1.24789	−	0.662054i	0.0745757	−	0.0395653i
$281$		−	14.2909i		−	0.852521i	−0.904600	−	0.426261i	$-0.859831\pi$
$281$		−	14.2909i		−	0.852521i	0.904600	−	0.426261i	$-0.140169\pi$
$282$	4.95705			0.295188
$283$	−12.3837			−0.736137			−0.368068	−	0.929799i	$-0.619981\pi$
$283$	−12.3837			−0.736137			−0.368068	+	0.929799i	$0.619981\pi$
$284$	−12.7183			−0.754694
$285$	−2.36533	−	4.45836i	−0.140110	−	0.264090i
$286$	4.18042			0.247193
$287$		−	5.34152i		−	0.315300i
$288$	−2.85722			−0.168363
$289$	−7.35829			−0.432840
$290$	−18.9159	+	10.0356i	−1.11078	+	0.589313i
$291$		−	4.17849i		−	0.244947i
$292$		−	4.45836i		−	0.260906i
$293$		−	27.8374i		−	1.62628i	−0.582068	−	0.813140i	$-0.697756\pi$
$293$		−	27.8374i		−	1.62628i	0.582068	−	0.813140i	$-0.302244\pi$
$294$		−	2.49422i		−	0.145466i
$295$	8.62152	−	4.57405i	0.501964	−	0.266312i
$296$	−4.10511	−	4.48866i	−0.238605	−	0.260898i
$297$			2.76185i			0.160259i
$298$	−13.6447			−0.790416
$299$	−25.4836			−1.47375
$300$	−1.56437	−	1.05934i	−0.0903192	−	0.0611613i
$301$			3.07435i			0.177203i
$302$	3.17741			0.182839
$303$			3.26968i			0.187838i
$304$			5.97327i			0.342590i
$305$	4.24028	−	2.24963i	0.242798	−	0.128814i
$306$	8.87199			0.507178
$307$		−	19.9411i		−	1.13810i	−0.822304	−	0.569049i	$-0.807312\pi$
$307$		−	19.9411i		−	1.13810i	0.822304	−	0.569049i	$-0.192688\pi$
$308$			0.788355i			0.0449207i
$309$			1.72810i			0.0983080i
$310$	14.3546	−	7.61566i	0.815284	−	0.432540i
$311$		−	4.96832i		−	0.281727i	−0.990029	−	0.140864i	$-0.955012\pi$
$311$		−	4.96832i		−	0.281727i	0.990029	−	0.140864i	$-0.0449879\pi$
$312$			1.26583i			0.0716636i
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$		−	0.215310i		−	0.0121506i
$315$	−3.56550	+	1.89164i	−0.200893	+	0.106582i
$316$		−	8.78679i		−	0.494296i
$317$			22.9198i			1.28730i	0.765319	+	0.643651i	$0.222581\pi$
$317$			22.9198i			1.28730i	−0.765319	+	0.643651i	$0.777419\pi$
$318$	−2.71055			−0.152000
$319$		−	11.9502i		−	0.669080i
$320$	1.04797	+	1.97529i	0.0585832	+	0.110422i
$321$	4.33465			0.241937
$322$		−	4.80576i		−	0.267815i
$323$		−	18.5477i		−	1.03202i
$324$	7.73537			0.429743
$325$	9.39179	−	13.8692i	0.520963	−	0.769326i
$326$	1.66609			0.0922760
$327$	−0.274988			−0.0152069
$328$	8.45510			0.466855
$329$	−8.28775			−0.456918
$330$	0.931406	−	0.494147i	0.0512722	−	0.0272019i
$331$			5.54265i			0.304651i	0.988330	+	0.152326i	$0.0486763\pi$
$331$			5.54265i			0.304651i	−0.988330	+	0.152326i	$0.951324\pi$
$332$		−	6.63185i		−	0.363970i
$333$	11.7292	+	12.8251i	0.642757	+	0.702811i
$334$	−5.92242			−0.324060
$335$	22.4098	−	11.8893i	1.22438	−	0.649581i
$336$	−0.238714			−0.0130229
$337$			25.6348i			1.39642i	0.715894	+	0.698209i	$0.246019\pi$
$337$			25.6348i			1.39642i	−0.715894	+	0.698209i	$0.753981\pi$
$338$	1.77756			0.0966867
$339$			6.80035i			0.369344i
$340$	−3.25406	−	6.13349i	−0.176476	−	0.332635i
$341$			9.06851i			0.491087i
$342$		−	17.0669i		−	0.922875i
$343$			8.59237i			0.463945i
$344$	−4.86640			−0.262379
$345$	−5.67779	+	3.01229i	−0.305682	+	0.162176i
$346$			2.88008i			0.154834i
$347$	19.6225			1.05339			0.526696	−	0.850054i	$-0.323431\pi$
$347$	19.6225			1.05339			0.526696	+	0.850054i	$0.323431\pi$
$348$	3.61851			0.193972
$349$	−15.6263			−0.836459			−0.418230	−	0.908341i	$-0.637349\pi$
$349$	−15.6263			−0.836459			−0.418230	+	0.908341i	$0.637349\pi$
$350$	2.61550	+	1.77113i	0.139804	+	0.0946709i
$351$		−	7.41425i		−	0.395744i
$352$	−1.24789			−0.0665128
$353$	23.5724			1.25463			0.627316	−	0.778765i	$-0.284153\pi$
$353$	23.5724			1.25463			0.627316	+	0.778765i	$0.284153\pi$
$354$	−1.64925			−0.0876564
$355$	−13.3284	−	25.1224i	−0.707398	−	1.33336i
$356$		−	13.7784i		−	0.730255i
$357$	0.741234			0.0392302
$358$		−	4.46182i		−	0.235815i
$359$	−9.34905			−0.493424			−0.246712	−	0.969089i	$-0.579350\pi$
$359$	−9.34905			−0.493424			−0.246712	+	0.969089i	$0.579350\pi$
$360$	−2.99427	−	5.64384i	−0.157812	−	0.297456i
$361$	−16.6799			−0.877891
$362$	−3.93480			−0.206809
$363$		−	3.56806i		−	0.187274i
$364$		−	2.11636i		−	0.110927i
$365$	8.80654	−	4.67221i	0.460955	−	0.244555i
$366$	−0.811140			−0.0423990
$367$		−	12.2379i		−	0.638811i	−0.947618	−	0.319406i	$-0.896517\pi$
$367$		−	12.2379i		−	0.638811i	0.947618	−	0.319406i	$-0.103483\pi$
$368$	7.60706			0.396545
$369$	−24.1581			−1.25762
$370$	4.56437	−	12.8127i	0.237291	−	0.666103i
$371$	4.53180			0.235280
$372$	−2.74594			−0.142371
$373$			10.1918i			0.527712i	0.964562	+	0.263856i	$0.0849943\pi$
$373$			10.1918i			0.527712i	−0.964562	+	0.263856i	$0.915006\pi$
$374$	3.87484			0.200363
$375$	0.453098	−	4.20025i	0.0233979	−	0.216900i
$376$		−	13.1187i		−	0.676545i
$377$			32.0805i			1.65223i
$378$	1.39820			0.0719157
$379$	20.7538			1.06605			0.533025	−	0.846099i	$-0.321055\pi$
$379$	20.7538			1.06605			0.533025	+	0.846099i	$0.321055\pi$
$380$	−11.7989	+	6.25979i	−0.605272	+	0.321120i
$381$	−5.85042			−0.299726
$382$		−	7.76296i		−	0.397188i
$383$	17.7328			0.906103			0.453052	−	0.891484i	$-0.350335\pi$
$383$	17.7328			0.906103			0.453052	+	0.891484i	$0.350335\pi$
$384$		−	0.377861i		−	0.0192826i
$385$	−1.55723	+	0.826171i	−0.0793638	+	0.0421056i
$386$	3.49189			0.177732
$387$	13.9044			0.706799
$388$	−11.0583			−0.561398
$389$			10.9054i			0.552923i	0.961025	+	0.276462i	$0.0891619\pi$
$389$			10.9054i			0.552923i	−0.961025	+	0.276462i	$0.910838\pi$
$390$	−2.50038	+	1.32655i	−0.126612	+	0.0671725i
$391$	−23.6208			−1.19455
$392$	−6.60089			−0.333395
$393$	2.35075			0.118580
$394$		−	1.07617i		−	0.0542164i
$395$	17.3565	−	9.20827i	0.873298	−	0.463319i
$396$	3.56550			0.179173
$397$		−	23.0106i		−	1.15487i	−0.816437	−	0.577435i	$-0.804054\pi$
$397$		−	23.0106i		−	1.15487i	0.816437	−	0.577435i	$-0.195946\pi$
$398$			5.71343i			0.286388i
$399$		−	1.42590i		−	0.0713844i
$400$	−2.80353	+	4.14008i	−0.140176	+	0.207004i
$401$		−	16.5769i		−	0.827809i	−0.910320	−	0.413904i	$-0.864165\pi$
$401$		−	16.5769i		−	0.827809i	0.910320	−	0.413904i	$-0.135835\pi$
$402$	−4.28687			−0.213810
$403$		−	24.3446i		−	1.21269i
$404$	8.65314			0.430510
$405$	8.10642	+	15.2796i	0.402811	+	0.759249i
$406$	−6.04983			−0.300248
$407$	5.12273	+	5.60135i	0.253924	+	0.277649i
$408$			1.17330i			0.0580870i
$409$			5.05401i			0.249905i	0.992163	+	0.124952i	$0.0398778\pi$
$409$			5.05401i			0.249905i	−0.992163	+	0.124952i	$0.960122\pi$
$410$	8.86067	+	16.7013i	0.437597	+	0.824817i
$411$	5.33760			0.263285
$412$	4.57336			0.225313
$413$	2.75740			0.135683
$414$	−21.7350			−1.06822
$415$	13.0998	−	6.94997i	0.643045	−	0.341161i
$416$	3.34999			0.164247
$417$			3.18792i			0.156113i
$418$		−	7.45398i		−	0.364586i
$419$	−24.2194			−1.18319			−0.591597	−	0.806234i	$-0.701502\pi$
$419$	−24.2194			−1.18319			−0.591597	+	0.806234i	$0.701502\pi$
$420$	−0.250165	−	0.471529i	−0.0122068	−	0.0230083i
$421$			20.8487i			1.01611i	0.861326	+	0.508053i	$0.169635\pi$
$421$			20.8487i			1.01611i	−0.861326	+	0.508053i	$0.830365\pi$
$422$	−22.8397			−1.11182
$423$			37.4830i			1.82249i
$424$			7.17340i			0.348371i
$425$	8.70527	−	12.8554i	0.422267	−	0.623578i
$426$			4.80576i			0.232840i
$427$	1.35616			0.0656290
$428$		−	11.4715i		−	0.554498i
$429$		−	1.57962i		−	0.0762647i
$430$	−5.09983	−	9.61254i	−0.245935	−	0.463558i
$431$			28.2298i			1.35978i	0.733314	+	0.679890i	$0.237973\pi$
$431$			28.2298i			1.35978i	−0.733314	+	0.679890i	$0.762027\pi$
$432$			2.21322i			0.106483i
$433$		−	30.3997i		−	1.46091i	−0.682958	−	0.730457i	$-0.739307\pi$
$433$		−	30.3997i		−	1.46091i	0.682958	−	0.730457i	$-0.260693\pi$
$434$	4.59098			0.220374
$435$	3.79208	+	7.14759i	0.181816	+	0.342701i
$436$			0.727748i			0.0348528i
$437$			45.4390i			2.17364i
$438$	−1.68464			−0.0804952
$439$			33.7591i			1.61123i	0.592438	+	0.805616i	$0.298166\pi$
$439$			33.7591i			1.61123i	−0.592438	+	0.805616i	$0.701834\pi$
$440$	−1.30775	−	2.46494i	−0.0623444	−	0.117512i
$441$	18.8602			0.898105
$442$	−10.4021			−0.494777
$443$			15.5413i			0.738388i	0.929352	+	0.369194i	$0.120366\pi$
$443$			15.5413i			0.738388i	−0.929352	+	0.369194i	$0.879634\pi$
$444$	−1.69609	+	1.55116i	−0.0804929	+	0.0736149i
$445$	27.2164	−	14.4393i	1.29018	−	0.684490i
$446$			3.32116i			0.157261i
$447$			5.15580i			0.243861i
$448$			0.631751i			0.0298474i
$449$			14.2184i			0.671006i	0.942039	+	0.335503i	$0.108906\pi$
$449$			14.2184i			0.671006i	−0.942039	+	0.335503i	$0.891094\pi$
$450$	8.01030	−	11.8291i	0.377609	−	0.557630i
$451$	−10.5510			−0.496829
$452$	17.9970			0.846506
$453$		−	1.20062i		−	0.0564100i
$454$	−5.62938			−0.264200
$455$	4.18042	−	2.21788i	0.195981	−	0.103976i
$456$	2.25707			0.105697
$457$	9.17031			0.428969			0.214484	−	0.976727i	$-0.431193\pi$
$457$	9.17031			0.428969			0.214484	+	0.976727i	$0.431193\pi$
$458$	0.973208			0.0454750
$459$		−	6.87228i		−	0.320771i
$460$	7.97195	+	15.0261i	0.371694	+	0.700597i
$461$			10.3300i			0.481114i	0.970635	+	0.240557i	$0.0773301\pi$
$461$			10.3300i			0.481114i	−0.970635	+	0.240557i	$0.922670\pi$
$462$	0.297889			0.0138590
$463$	−25.8049			−1.19926			−0.599629	−	0.800278i	$-0.704685\pi$
$463$	−25.8049			−1.19926			−0.599629	+	0.800278i	$0.704685\pi$
$464$		−	9.57629i		−	0.444568i
$465$	−2.87766	−	5.42403i	−0.133448	−	0.251533i
$466$			14.4150i			0.667761i
$467$	−34.4582			−1.59454			−0.797268	−	0.603625i	$-0.793722\pi$
$467$	−34.4582			−1.59454			−0.797268	+	0.603625i	$0.793722\pi$
$468$	−9.57166			−0.442450
$469$	7.16727			0.330954
$470$	25.9132	−	13.7480i	1.19529	−	0.634147i
$471$	−0.0813572			−0.00374874
$472$			4.36469i			0.200901i
$473$	6.07273			0.279224
$474$	−3.32019			−0.152501
$475$	−24.7298	−	16.7462i	−1.13468	−	0.768369i
$476$		−	1.96166i		−	0.0899124i
$477$		−	20.4960i		−	0.938448i
$478$		−	8.43344i		−	0.385737i
$479$			29.6039i			1.35264i	0.736610	+	0.676318i	$0.236426\pi$
$479$			29.6039i			1.35264i	−0.736610	+	0.676318i	$0.763574\pi$
$480$	0.746385	−	0.395986i	0.0340676	−	0.0180742i
$481$	−13.7521	−	15.0370i	−0.627041	−	0.685627i
$482$		−	18.6567i		−	0.849789i
$483$	−1.81591			−0.0826268
$484$	−9.44277			−0.429217
$485$	−11.5887	−	21.8433i	−0.526216	−	0.991852i
$486$		−	9.56255i		−	0.433766i
$487$	−27.0961			−1.22784			−0.613920	−	0.789369i	$-0.710408\pi$
$487$	−27.0961			−1.22784			−0.613920	+	0.789369i	$0.710408\pi$
$488$			2.14666i			0.0971749i
$489$		−	0.629549i		−	0.0284692i
$490$	−6.91752	−	13.0387i	−0.312502	−	0.589027i
$491$	2.46033			0.111033			0.0555166	−	0.998458i	$-0.482319\pi$
$491$	2.46033			0.111033			0.0555166	+	0.998458i	$0.482319\pi$
$492$		−	3.19485i		−	0.144035i
$493$			29.7354i			1.33922i
$494$			20.0104i			0.900310i
$495$	3.73653	+	7.04289i	0.167944	+	0.316554i
$496$			7.26707i			0.326301i
$497$		−	8.03482i		−	0.360411i
$498$	−2.50592			−0.112293
$499$		−	31.4091i		−	1.40606i	−0.711158	−	0.703032i	$-0.751829\pi$
$499$		−	31.4091i		−	1.40606i	0.711158	−	0.703032i	$-0.248171\pi$
$500$	−11.1159	−	1.19911i	−0.497116	−	0.0536259i
$501$			2.23785i			0.0999798i
$502$			25.1189i			1.12111i
$503$	1.78145			0.0794311			0.0397156	−	0.999211i	$-0.487355\pi$
$503$	1.78145			0.0794311			0.0397156	+	0.999211i	$0.487355\pi$
$504$		−	1.80505i		−	0.0804034i
$505$	9.06821	+	17.0924i	0.403530	+	0.760604i
$506$	−9.49277			−0.422005
$507$		−	0.671672i		−	0.0298300i
$508$			15.4830i			0.686947i
$509$	21.2370			0.941314			0.470657	−	0.882316i	$-0.344017\pi$
$509$	21.2370			0.941314			0.470657	+	0.882316i	$0.344017\pi$
$510$	−2.31761	+	1.22958i	−0.102625	+	0.0544468i
$511$	2.81657			0.124598
$512$	−1.00000			−0.0441942
$513$	−13.2201			−0.583683
$514$	20.3552			0.897831
$515$	4.79274	+	9.03371i	0.211193	+	0.398073i
$516$			1.83882i			0.0809496i
$517$			16.3707i			0.719982i
$518$	2.83571	−	2.59341i	0.124594	−	0.113948i
$519$	1.08827			0.0477698
$520$	3.51068	+	6.61720i	0.153954	+	0.290183i
$521$	2.52950			0.110819			0.0554097	−	0.998464i	$-0.482354\pi$
$521$	2.52950			0.110819			0.0554097	+	0.998464i	$0.482354\pi$
$522$			27.3616i			1.19758i
$523$	−1.60848			−0.0703338			−0.0351669	−	0.999381i	$-0.511196\pi$
$523$	−1.60848			−0.0703338			−0.0351669	+	0.999381i	$0.511196\pi$
$524$		−	6.22121i		−	0.271775i
$525$	0.669242	−	0.988294i	0.0292081	−	0.0431327i
$526$		−	22.2211i		−	0.968887i
$527$		−	22.5651i		−	0.982950i
$528$			0.471529i			0.0205207i
$529$	34.8673			1.51597
$530$	−14.1695	+	7.51750i	−0.615486	+	0.326539i
$531$		−	12.4709i		−	0.541190i
$532$	−3.77362			−0.163607
$533$	28.3245			1.22687
$534$	−5.20633			−0.225300
$535$	22.6596	−	12.0218i	0.979660	−	0.519748i
$536$			11.3451i			0.490033i
$537$	−1.68595			−0.0727541
$538$	15.8411			0.682959
$539$	8.23719			0.354801
$540$	−4.37174	+	2.31938i	−0.188130	+	0.0998102i
$541$		−	3.12463i		−	0.134338i	−0.997742	−	0.0671692i	$-0.978603\pi$
$541$		−	3.12463i		−	0.134338i	0.997742	−	0.0671692i	$-0.0213967\pi$
$542$	2.00602			0.0861660
$543$			1.48681i			0.0638051i
$544$	3.10511			0.133131
$545$	−1.43751	+	0.762657i	−0.0615763	+	0.0326686i
$546$	−0.799690			−0.0342236
$547$	5.44201			0.232683			0.116342	−	0.993209i	$-0.462883\pi$
$547$	5.44201			0.232683			0.116342	+	0.993209i	$0.462883\pi$
$548$		−	14.1258i		−	0.603426i
$549$		−	6.13349i		−	0.261771i
$550$	3.49849	−	5.16636i	0.149176	−	0.220294i
$551$	57.2017			2.43688
$552$		−	2.87441i		−	0.122343i
$553$	5.55106			0.236055
$554$	11.5671			0.491440
$555$	−4.84144	−	1.72470i	−0.205508	−	0.0732094i
$556$	8.43675			0.357798
$557$	−36.3451			−1.53999			−0.769995	−	0.638050i	$-0.779741\pi$
$557$	−36.3451			−1.53999			−0.769995	+	0.638050i	$0.779741\pi$
$558$		−	20.7636i		−	0.878995i
$559$	−16.3024			−0.689517
$560$	−1.24789	+	0.662054i	−0.0527330	+	0.0279769i
$561$		−	1.46415i		−	0.0618165i
$562$			14.2909i			0.602824i
$563$	−38.4949			−1.62237			−0.811184	−	0.584791i	$-0.801177\pi$
$563$	−38.4949			−1.62237			−0.811184	+	0.584791i	$0.801177\pi$
$564$	−4.95705			−0.208729
$565$	18.8602	+	35.5492i	0.793456	+	1.49557i
$566$	12.3837			0.520527
$567$			4.88683i			0.205228i
$568$	12.7183			0.533649
$569$			41.2793i			1.73052i	0.501324	+	0.865260i	$0.332846\pi$
$569$			41.2793i			1.73052i	−0.501324	+	0.865260i	$0.667154\pi$
$570$	2.36533	+	4.45836i	0.0990728	+	0.186740i
$571$	−26.0635			−1.09072			−0.545362	−	0.838200i	$-0.683608\pi$
$571$	−26.0635			−1.09072			−0.545362	+	0.838200i	$0.683608\pi$
$572$	−4.18042			−0.174792
$573$	−2.93332			−0.122541
$574$			5.34152i			0.222951i
$575$	−21.3266	+	31.4938i	−0.889381	+	1.31338i
$576$	2.85722			0.119051
$577$	11.8411			0.492952			0.246476	−	0.969149i	$-0.420727\pi$
$577$	11.8411			0.492952			0.246476	+	0.969149i	$0.420727\pi$
$578$	7.35829			0.306064
$579$		−	1.31945i		−	0.0548344i
$580$	18.9159	−	10.0356i	0.785441	−	0.416707i
$581$	4.18968			0.173817
$582$			4.17849i			0.173204i
$583$		−	8.95162i		−	0.370738i
$584$			4.45836i			0.184488i
$585$	−10.0308	−	18.9068i	−0.414722	−	0.781700i
$586$			27.8374i			1.14995i
$587$	−26.7315			−1.10333			−0.551663	−	0.834067i	$-0.686006\pi$
$587$	−26.7315			−1.10333			−0.551663	+	0.834067i	$0.686006\pi$
$588$			2.49422i			0.102860i
$589$	−43.4082			−1.78860
$590$	−8.62152	+	4.57405i	−0.354942	+	0.188311i
$591$	−0.406641			−0.0167270
$592$	4.10511	+	4.48866i	0.168719	+	0.184483i
$593$		−	22.6119i		−	0.928560i	−0.885688	−	0.464280i	$-0.846313\pi$
$593$		−	22.6119i		−	0.928560i	0.885688	−	0.464280i	$-0.153687\pi$
$594$		−	2.76185i		−	0.113320i
$595$	3.87484	−	2.05575i	0.158853	−	0.0842776i
$596$	13.6447			0.558909
$597$	2.15888			0.0883572
$598$	25.4836			1.04210
$599$	14.3406			0.585942			0.292971	−	0.956121i	$-0.405356\pi$
$599$	14.3406			0.585942			0.292971	+	0.956121i	$0.405356\pi$
$600$	1.56437	+	1.05934i	0.0638653	+	0.0432476i
$601$	15.0845			0.615308			0.307654	−	0.951498i	$-0.400456\pi$
$601$	15.0845			0.615308			0.307654	+	0.951498i	$0.400456\pi$
$602$		−	3.07435i		−	0.125301i
$603$		−	32.4154i		−	1.32006i
$604$	−3.17741			−0.129287
$605$	−9.89572	−	18.6522i	−0.402318	−	0.758320i
$606$		−	3.26968i		−	0.132822i
$607$	41.5964			1.68835			0.844174	−	0.536070i	$-0.180092\pi$
$607$	41.5964			1.68835			0.844174	+	0.536070i	$0.180092\pi$
$608$		−	5.97327i		−	0.242248i
$609$			2.28599i			0.0926332i
$610$	−4.24028	+	2.24963i	−0.171684	+	0.0910850i
$611$		−	43.9475i		−	1.77793i
$612$	−8.87199			−0.358629
$613$			30.4369i			1.22934i	0.788786	+	0.614668i	$0.210710\pi$
$613$			30.4369i			1.22934i	−0.788786	+	0.614668i	$0.789290\pi$
$614$			19.9411i			0.804756i
$615$	6.31076	−	3.34810i	0.254474	−	0.135009i
$616$		−	0.788355i		−	0.0317637i
$617$			39.8195i			1.60307i	0.597946	+	0.801536i	$0.295984\pi$
$617$			39.8195i			1.60307i	−0.597946	+	0.801536i	$0.704016\pi$
$618$		−	1.72810i		−	0.0695142i
$619$	39.4011			1.58367			0.791833	−	0.610738i	$-0.209127\pi$
$619$	39.4011			1.58367			0.791833	+	0.610738i	$0.209127\pi$
$620$	−14.3546	+	7.61566i	−0.576493	+	0.305852i
$621$			16.8361i			0.675608i
$622$			4.96832i			0.199211i
$623$	8.70453			0.348740
$624$		−	1.26583i		−	0.0506738i
$625$	−9.28046	−	23.2136i	−0.371218	−	0.928546i
$626$	10.0000			0.399680
$627$	−2.81657			−0.112483
$628$			0.215310i			0.00859180i
$629$	−12.7468	−	13.9378i	−0.508249	−	0.555736i
$630$	3.56550	−	1.89164i	0.142053	−	0.0753646i
$631$		−	0.114985i		−	0.00457750i	−0.999997	−	0.00228875i	$-0.999271\pi$
$631$		−	0.114985i		−	0.00457750i	0.999997	−	0.00228875i	$-0.000728532\pi$
$632$			8.78679i			0.349520i
$633$			8.63024i			0.343021i
$634$		−	22.9198i		−	0.910260i
$635$	−30.5834	+	16.2257i	−1.21366	+	0.643897i
$636$	2.71055			0.107480
$637$	−22.1129			−0.876146
$638$			11.9502i			0.473111i
$639$	−36.3391			−1.43755
$640$	−1.04797	−	1.97529i	−0.0414246	−	0.0780801i
$641$	34.9774			1.38153			0.690763	−	0.723081i	$-0.257275\pi$
$641$	34.9774			1.38153			0.690763	+	0.723081i	$0.257275\pi$
$642$	−4.33465			−0.171075
$643$	−25.2868			−0.997216			−0.498608	−	0.866828i	$-0.666155\pi$
$643$	−25.2868			−0.997216			−0.498608	+	0.866828i	$0.666155\pi$
$644$			4.80576i			0.189374i
$645$	−3.63220	+	1.92703i	−0.143018	+	0.0758766i
$646$			18.5477i			0.729748i
$647$	23.5824			0.927120			0.463560	−	0.886066i	$-0.346572\pi$
$647$	23.5824			0.927120			0.463560	+	0.886066i	$0.346572\pi$
$648$	−7.73537			−0.303874
$649$		−	5.44665i		−	0.213800i
$650$	−9.39179	+	13.8692i	−0.368376	+	0.543995i
$651$		−	1.73475i		−	0.0679903i
$652$	−1.66609			−0.0652490
$653$	−9.89261			−0.387128			−0.193564	−	0.981088i	$-0.562005\pi$
$653$	−9.89261			−0.387128			−0.193564	+	0.981088i	$0.562005\pi$
$654$	0.274988			0.0107529
$655$	12.2887	−	6.51963i	0.480159	−	0.254743i
$656$	−8.45510			−0.330116
$657$		−	12.7385i		−	0.496977i
$658$	8.28775			0.323090
$659$	−25.4137			−0.989976			−0.494988	−	0.868900i	$-0.664827\pi$
$659$	−25.4137			−0.989976			−0.494988	+	0.868900i	$0.664827\pi$
$660$	−0.931406	+	0.494147i	−0.0362549	+	0.0192347i
$661$			28.4574i			1.10687i	0.832894	+	0.553433i	$0.186682\pi$
$661$			28.4574i			1.10687i	−0.832894	+	0.553433i	$0.813318\pi$
$662$		−	5.54265i		−	0.215421i
$663$			3.93055i			0.152650i
$664$			6.63185i			0.257366i
$665$	−3.95463	−	7.45398i	−0.153354	−	0.289053i
$666$	−11.7292	−	12.8251i	−0.454498	−	0.496962i
$667$		−	72.8474i		−	2.82066i
$668$	5.92242			0.229145
$669$	1.25494			0.0485186
$670$	−22.4098	+	11.8893i	−0.865767	+	0.459323i
$671$		−	2.67880i		−	0.103414i
$672$	0.238714			0.00920860
$673$			20.4187i			0.787082i	0.919307	+	0.393541i	$0.128750\pi$
$673$			20.4187i			0.787082i	−0.919307	+	0.393541i	$0.871250\pi$
$674$		−	25.6348i		−	0.987416i
$675$	−9.16288	−	6.20481i	−0.352680	−	0.238823i
$676$	−1.77756			−0.0683678
$677$		−	18.5163i		−	0.711641i	−0.934554	−	0.355821i	$-0.884201\pi$
$677$		−	18.5163i		−	0.711641i	0.934554	−	0.355821i	$-0.115799\pi$
$678$		−	6.80035i		−	0.261166i
$679$		−	6.98607i		−	0.268101i
$680$	3.25406	+	6.13349i	0.124787	+	0.235209i
$681$			2.12713i			0.0815116i
$682$		−	9.06851i		−	0.347251i
$683$	−32.0667			−1.22700			−0.613499	−	0.789695i	$-0.710239\pi$
$683$	−32.0667			−1.22700			−0.613499	+	0.789695i	$0.710239\pi$
$684$			17.0669i			0.652571i
$685$	27.9026	−	14.8034i	1.06610	−	0.565609i
$686$		−	8.59237i		−	0.328058i
$687$		−	0.367738i		−	0.0140301i
$688$	4.86640			0.185530
$689$			24.0308i			0.915502i
$690$	5.67779	−	3.01229i	0.216150	−	0.114676i
$691$	−6.57629			−0.250174			−0.125087	−	0.992146i	$-0.539921\pi$
$691$	−6.57629			−0.250174			−0.125087	+	0.992146i	$0.539921\pi$
$692$		−	2.88008i		−	0.109484i
$693$			2.25251i			0.0855656i
$694$	−19.6225			−0.744860
$695$	8.84144	+	16.6650i	0.335375	+	0.632140i
$696$	−3.61851			−0.137159
$697$	26.2540			0.994442
$698$	15.6263			0.591466
$699$	5.44686			0.206019
$700$	−2.61550	−	1.77113i	−0.0988565	−	0.0669425i
$701$		−	9.62168i		−	0.363406i	−0.983353	−	0.181703i	$-0.941839\pi$
$701$		−	9.62168i		−	0.363406i	0.983353	−	0.181703i	$-0.0581609\pi$
$702$			7.41425i			0.279833i
$703$	−26.8120	+	24.5209i	−1.01123	+	0.924824i
$704$	1.24789			0.0470316
$705$	−5.19482	−	9.79160i	−0.195648	−	0.368773i
$706$	−23.5724			−0.887159
$707$			5.46663i			0.205594i
$708$	1.64925			0.0619825
$709$		−	8.65759i		−	0.325142i	−0.986697	−	0.162571i	$-0.948021\pi$
$709$		−	8.65759i		−	0.325142i	0.986697	−	0.162571i	$-0.0519787\pi$
$710$	13.3284	+	25.1224i	0.500206	+	0.942826i
$711$		−	25.1058i		−	0.941541i
$712$			13.7784i			0.516368i
$713$			55.2810i			2.07029i
$714$	−0.741234			−0.0277400
$715$	−4.38094	−	8.25753i	−0.163838	−	0.308814i
$716$			4.46182i			0.166746i
$717$	−3.18667			−0.119008
$718$	9.34905			0.348904
$719$	51.5303			1.92176			0.960878	−	0.276972i	$-0.0893310\pi$
$719$	51.5303			1.92176			0.960878	+	0.276972i	$0.0893310\pi$
$720$	2.99427	+	5.64384i	0.111590	+	0.210333i
$721$			2.88923i			0.107600i
$722$	16.6799			0.620763
$723$	−7.04964			−0.262179
$724$	3.93480			0.146236
$725$	39.6466	+	26.8474i	1.47244	+	0.997087i
$726$			3.56806i			0.132423i
$727$	11.3224			0.419924			0.209962	−	0.977710i	$-0.432666\pi$
$727$	11.3224			0.419924			0.209962	+	0.977710i	$0.432666\pi$
$728$			2.11636i			0.0784375i
$729$	19.5928			0.725660
$730$	−8.80654	+	4.67221i	−0.325945	+	0.172926i
$731$	−15.1107			−0.558890
$732$	0.811140			0.0299806
$733$		−	2.74231i		−	0.101290i	−0.998717	−	0.0506448i	$-0.983872\pi$
$733$		−	2.74231i		−	0.101290i	0.998717	−	0.0506448i	$-0.0161276\pi$
$734$			12.2379i			0.451708i
$735$	−4.92680	+	2.61386i	−0.181728	+	0.0964137i
$736$	−7.60706			−0.280400
$737$		−	14.1574i		−	0.521495i
$738$	24.1581			0.889272
$739$	8.18878			0.301229			0.150614	−	0.988593i	$-0.451875\pi$
$739$	8.18878			0.301229			0.150614	+	0.988593i	$0.451875\pi$
$740$	−4.56437	+	12.8127i	−0.167790	+	0.471006i
$741$	7.56115			0.277766
$742$	−4.53180			−0.166368
$743$			22.1217i			0.811567i	0.913969	+	0.405784i	$0.133001\pi$
$743$			22.1217i			0.811567i	−0.913969	+	0.405784i	$0.866999\pi$
$744$	2.74594			0.100671
$745$	14.2992	+	26.9522i	0.523882	+	0.987453i
$746$		−	10.1918i		−	0.373149i
$747$		−	18.9487i		−	0.693296i
$748$	−3.87484			−0.141678
$749$	7.24715			0.264805
$750$	−0.453098	+	4.20025i	−0.0165448	+	0.153371i
$751$	−19.0818			−0.696306			−0.348153	−	0.937438i	$-0.613191\pi$
$751$	−19.0818			−0.696306			−0.348153	+	0.937438i	$0.613191\pi$
$752$			13.1187i			0.478390i
$753$	9.49146			0.345888
$754$		−	32.0805i		−	1.16830i
$755$	−3.32982	−	6.27630i	−0.121185	−	0.228418i
$756$	−1.39820			−0.0508521
$757$	31.2209			1.13474			0.567372	−	0.823462i	$-0.307960\pi$
$757$	31.2209			1.13474			0.567372	+	0.823462i	$0.307960\pi$
$758$	−20.7538			−0.753811
$759$			3.58695i			0.130198i
$760$	11.7989	−	6.25979i	0.427992	−	0.227066i
$761$	−29.3163			−1.06271			−0.531357	−	0.847148i	$-0.678318\pi$
$761$	−29.3163			−1.06271			−0.531357	+	0.847148i	$0.678318\pi$
$762$	5.85042			0.211939
$763$	−0.459756			−0.0166443
$764$			7.76296i			0.280854i
$765$	−9.29756	−	17.5247i	−0.336154	−	0.633608i
$766$	−17.7328			−0.640712
$767$			14.6217i			0.527958i
$768$			0.377861i			0.0136349i
$769$		−	29.0289i		−	1.04681i	−0.852084	−	0.523404i	$-0.824662\pi$
$769$		−	29.0289i		−	1.04681i	0.852084	−	0.523404i	$-0.175338\pi$
$770$	1.55723	−	0.826171i	0.0561187	−	0.0297731i
$771$		−	7.69146i		−	0.277001i
$772$	−3.49189			−0.125676
$773$		−	43.4153i		−	1.56154i	−0.624819	−	0.780769i	$-0.714827\pi$
$773$		−	43.4153i		−	1.56154i	0.624819	−	0.780769i	$-0.285173\pi$
$774$	−13.9044			−0.499782
$775$	−30.0862	−	20.3734i	−1.08073	−	0.731836i
$776$	11.0583			0.396969
$777$	−0.979948	−	1.07151i	−0.0351554	−	0.0384401i
$778$		−	10.9054i		−	0.390976i
$779$		−	50.5046i		−	1.80951i
$780$	2.50038	−	1.32655i	0.0895280	−	0.0474981i
$781$	−15.8711			−0.567912
$782$	23.6208			0.844676
$783$	21.1944			0.757426
$784$	6.60089			0.235746
$785$	−0.425299	+	0.225638i	−0.0151796	+	0.00805336i
$786$	−2.35075			−0.0838486
$787$		−	18.9119i		−	0.674136i	−0.941480	−	0.337068i	$-0.890565\pi$
$787$		−	18.9119i		−	0.674136i	0.941480	−	0.337068i	$-0.109435\pi$
$788$			1.07617i			0.0383368i
$789$	−8.39650			−0.298923
$790$	−17.3565	+	9.20827i	−0.617515	+	0.327616i
$791$			11.3696i			0.404256i
$792$	−3.56550			−0.126694
$793$			7.19130i			0.255371i
$794$			23.0106i			0.816616i
$795$	2.84057	+	5.35412i	0.100745	+	0.189891i
$796$		−	5.71343i		−	0.202507i
$797$	6.65779			0.235831			0.117916	−	0.993024i	$-0.462379\pi$
$797$	6.65779			0.235831			0.117916	+	0.993024i	$0.462379\pi$
$798$			1.42590i			0.0504764i
$799$		−	40.7350i		−	1.44110i
$800$	2.80353	−	4.14008i	0.0991197	−	0.146374i
$801$		−	39.3680i		−	1.39100i
$802$			16.5769i			0.585349i
$803$		−	5.56354i		−	0.196333i
$804$	4.28687			0.151186
$805$	−9.49277	+	5.03628i	−0.334576	+	0.177506i
$806$			24.3446i			0.857503i
$807$		−	5.98574i		−	0.210708i
$808$	−8.65314			−0.304416
$809$		−	35.3855i		−	1.24409i	−0.782982	−	0.622044i	$-0.786302\pi$
$809$		−	35.3855i		−	1.24409i	0.782982	−	0.622044i	$-0.213698\pi$
$810$	−8.10642	−	15.2796i	−0.284831	−	0.536870i
$811$	34.1205			1.19813			0.599067	−	0.800699i	$-0.295538\pi$
$811$	34.1205			1.19813			0.599067	+	0.800699i	$0.295538\pi$
$812$	6.04983			0.212307
$813$		−	0.757997i		−	0.0265841i
$814$	−5.12273	−	5.60135i	−0.179551	−	0.196327i
$815$	−1.74600	−	3.29100i	−0.0611599	−	0.115279i
$816$		−	1.17330i		−	0.0410737i
$817$			29.0683i			1.01697i
$818$		−	5.05401i		−	0.176709i
$819$		−	6.04691i		−	0.211296i
$820$	−8.86067	−	16.7013i	−0.309428	−	0.583233i
$821$	−50.1981			−1.75193			−0.875963	−	0.482378i	$-0.839773\pi$
$821$	−50.1981			−1.75193			−0.875963	+	0.482378i	$0.839773\pi$
$822$	−5.33760			−0.186170
$823$		−	47.6713i		−	1.66172i	−0.556483	−	0.830859i	$-0.687850\pi$
$823$		−	47.6713i		−	1.66172i	0.556483	−	0.830859i	$-0.312150\pi$
$824$	−4.57336			−0.159321
$825$	−1.95217	−	1.32195i	−0.0679657	−	0.0460242i
$826$	−2.75740			−0.0959420
$827$	−3.77813			−0.131378			−0.0656892	−	0.997840i	$-0.520925\pi$
$827$	−3.77813			−0.131378			−0.0656892	+	0.997840i	$0.520925\pi$
$828$	21.7350			0.755345
$829$		−	11.9862i		−	0.416297i	−0.978097	−	0.208149i	$-0.933256\pi$
$829$		−	11.9862i		−	0.416297i	0.978097	−	0.208149i	$-0.0667438\pi$
$830$	−13.0998	+	6.94997i	−0.454702	+	0.241237i
$831$		−	4.37076i		−	0.151620i
$832$	−3.34999			−0.116140
$833$	−20.4965			−0.710162
$834$		−	3.18792i		−	0.110389i
$835$	6.20650	+	11.6985i	0.214785	+	0.404843i
$836$			7.45398i			0.257801i
$837$	−16.0836			−0.555931
$838$	24.2194			0.836644
$839$	−54.1303			−1.86879			−0.934393	−	0.356243i	$-0.884058\pi$
$839$	−54.1303			−1.86879			−0.934393	+	0.356243i	$0.884058\pi$
$840$	0.250165	+	0.471529i	0.00863150	+	0.0162693i
$841$	−62.7053			−2.16225
$842$		−	20.8487i		−	0.718495i
$843$	5.39996			0.185985
$844$	22.8397			0.786176
$845$	−1.86283	−	3.51120i	−0.0640833	−	0.120789i
$846$		−	37.4830i		−	1.28869i
$847$		−	5.96548i		−	0.204976i
$848$		−	7.17340i		−	0.246336i
$849$		−	4.67933i		−	0.160594i
$850$	−8.70527	+	12.8554i	−0.298588	+	0.440936i
$851$	31.2278	+	34.1455i	1.07048	+	1.17049i
$852$		−	4.80576i		−	0.164643i
$853$	54.7590			1.87491			0.937457	−	0.348101i	$-0.113173\pi$
$853$	54.7590			1.87491			0.937457	+	0.348101i	$0.113173\pi$
$854$	−1.35616			−0.0464067
$855$	−33.7121	+	17.8856i	−1.15293	+	0.611675i
$856$			11.4715i			0.392089i
$857$	−13.8273			−0.472331			−0.236165	−	0.971713i	$-0.575891\pi$
$857$	−13.8273			−0.472331			−0.236165	+	0.971713i	$0.575891\pi$
$858$			1.57962i			0.0539273i
$859$			27.9420i			0.953368i	0.879075	+	0.476684i	$0.158161\pi$
$859$			27.9420i			0.953368i	−0.879075	+	0.476684i	$0.841839\pi$
$860$	5.09983	+	9.61254i	0.173903	+	0.327785i
$861$	2.01835			0.0687852
$862$		−	28.2298i		−	0.961510i
$863$			0.665448i			0.0226521i	0.999936	+	0.0113261i	$0.00360527\pi$
$863$			0.665448i			0.0226521i	−0.999936	+	0.0113261i	$0.996395\pi$
$864$		−	2.21322i		−	0.0752951i
$865$	5.68899	−	3.01823i	0.193431	−	0.102623i
$866$			30.3997i			1.03302i
$867$		−	2.78041i		−	0.0944277i
$868$	−4.59098			−0.155828
$869$		−	10.9650i		−	0.371961i
$870$	−3.79208	−	7.14759i	−0.128563	−	0.242326i
$871$			38.0059i			1.28778i
$872$		−	0.727748i		−	0.0246447i
$873$	−31.5959			−1.06936
$874$		−	45.4390i		−	1.53700i
$875$	0.757540	−	7.02245i	0.0256095	−	0.237402i
$876$	1.68464			0.0569187
$877$		−	2.04026i		−	0.0688948i	−0.999407	−	0.0344474i	$-0.989033\pi$
$877$		−	2.04026i		−	0.0688948i	0.999407	−	0.0344474i	$-0.0109671\pi$
$878$		−	33.7591i		−	1.13931i
$879$	10.5187			0.354786
$880$	1.30775	+	2.46494i	0.0440842	+	0.0830932i
$881$	19.5251			0.657816			0.328908	−	0.944362i	$-0.393319\pi$
$881$	19.5251			0.657816			0.328908	+	0.944362i	$0.393319\pi$
$882$	−18.8602			−0.635056
$883$	21.6799			0.729586			0.364793	−	0.931089i	$-0.381140\pi$
$883$	21.6799			0.729586			0.364793	+	0.931089i	$0.381140\pi$
$884$	10.4021			0.349860
$885$	1.72836	+	3.25774i	0.0580981	+	0.109508i
$886$		−	15.5413i		−	0.522119i
$887$		−	35.0252i		−	1.17603i	−0.808850	−	0.588015i	$-0.799910\pi$
$887$		−	35.0252i		−	1.17603i	0.808850	−	0.588015i	$-0.200090\pi$
$888$	1.69609	−	1.55116i	0.0569171	−	0.0520536i
$889$	−9.78140			−0.328058
$890$	−27.2164	+	14.4393i	−0.912294	+	0.484008i
$891$	9.65290			0.323384
$892$		−	3.32116i		−	0.111201i
$893$	−78.3615			−2.62227
$894$		−	5.15580i		−	0.172436i
$895$	−8.81339	+	4.67585i	−0.294599	+	0.156296i
$896$		−	0.631751i		−	0.0211053i
$897$		−	9.62925i		−	0.321511i
$898$		−	14.2184i		−	0.474473i
$899$	69.5916			2.32101
$900$	−8.01030	+	11.8291i	−0.267010	+	0.394304i
$901$			22.2742i			0.742062i
$902$	10.5510			0.351311
$903$	−1.16168			−0.0386582
$904$	−17.9970			−0.598570
$905$	4.12355	+	7.77237i	0.137071	+	0.258362i
$906$			1.20062i			0.0398879i
$907$	19.4042			0.644307			0.322153	−	0.946688i	$-0.395593\pi$
$907$	19.4042			0.644307			0.322153	+	0.946688i	$0.395593\pi$
$908$	5.62938			0.186818
$909$	24.7239			0.820041
$910$	−4.18042	+	2.21788i	−0.138580	+	0.0735219i
$911$		−	7.46474i		−	0.247318i	−0.992325	−	0.123659i	$-0.960537\pi$
$911$		−	7.46474i		−	0.247318i	0.992325	−	0.123659i	$-0.0394629\pi$
$912$	−2.25707			−0.0747389
$913$		−	8.27583i		−	0.273890i
$914$	−9.17031			−0.303327
$915$	0.850049	+	1.60224i	0.0281017	+	0.0529683i
$916$	−0.973208			−0.0321557
$917$	3.93025			0.129788
$918$			6.87228i			0.226819i
$919$		−	27.8014i		−	0.917083i	−0.888673	−	0.458541i	$-0.848372\pi$
$919$		−	27.8014i		−	0.917083i	0.888673	−	0.458541i	$-0.151628\pi$
$920$	−7.97195	−	15.0261i	−0.262827	−	0.495397i
$921$	7.53496			0.248285
$922$		−	10.3300i		−	0.340199i
$923$	42.6063			1.40240
$924$	−0.297889			−0.00979983
$925$	−30.0922	+	4.41139i	−0.989425	+	0.145046i
$926$	25.8049			0.848003
$927$	13.0671			0.429180
$928$			9.57629i			0.314357i
$929$	19.4503			0.638145			0.319072	−	0.947730i	$-0.396629\pi$
$929$	19.4503			0.638145			0.319072	+	0.947730i	$0.396629\pi$
$930$	2.87766	+	5.42403i	0.0943622	+	0.177861i
$931$			39.4289i			1.29223i
$932$		−	14.4150i		−	0.472178i
$933$	1.87733			0.0614611
$934$	34.4582			1.12751
$935$	−4.06070	−	7.65392i	−0.132799	−	0.250310i
$936$	9.57166			0.312860
$937$			14.2786i			0.466463i	0.972421	+	0.233231i	$0.0749299\pi$
$937$			14.2786i			0.466463i	−0.972421	+	0.233231i	$0.925070\pi$
$938$	−7.16727			−0.234020
$939$		−	3.77861i		−	0.123310i
$940$	−25.9132	+	13.7480i	−0.845196	+	0.448409i
$941$	−18.0266			−0.587649			−0.293825	−	0.955859i	$-0.594928\pi$
$941$	−18.0266			−0.587649			−0.293825	+	0.955859i	$0.594928\pi$
$942$	0.0813572			0.00265076
$943$	−64.3184			−2.09450
$944$		−	4.36469i		−	0.142058i
$945$	−1.46527	−	2.76185i	−0.0476652	−	0.0898430i
$946$	−6.07273			−0.197441
$947$	−20.7621			−0.674679			−0.337339	−	0.941383i	$-0.609527\pi$
$947$	−20.7621			−0.674679			−0.337339	+	0.941383i	$0.609527\pi$
$948$	3.32019			0.107835
$949$			14.9354i			0.484825i
$950$	24.7298	+	16.7462i	0.802340	+	0.543319i
$951$	−8.66049			−0.280836
$952$			1.96166i			0.0635776i
$953$			40.9858i			1.32766i	0.747883	+	0.663831i	$0.231071\pi$
$953$			40.9858i			1.32766i	−0.747883	+	0.663831i	$0.768929\pi$
$954$			20.4960i			0.663583i
$955$	−15.3341	+	8.13533i	−0.496199	+	0.263253i
$956$			8.43344i			0.272757i
$957$	4.51550			0.145965
$958$		−	29.6039i		−	0.956458i
$959$	8.92401			0.288171
$960$	−0.746385	+	0.395986i	−0.0240895	+	0.0127804i
$961$	−21.8103			−0.703560
$962$	13.7521	+	15.0370i	0.443385	+	0.484811i
$963$		−	32.7767i		−	1.05622i
$964$			18.6567i			0.600891i
$965$	−3.65939	−	6.89749i	−0.117800	−	0.222038i
$966$	1.81591			0.0584260
$967$	25.1227			0.807892			0.403946	−	0.914783i	$-0.367638\pi$
$967$	25.1227			0.807892			0.403946	+	0.914783i	$0.367638\pi$
$968$	9.44277			0.303502
$969$	7.00844			0.225144
$970$	11.5887	+	21.8433i	0.372091	+	0.701345i
$971$	−10.0012			−0.320953			−0.160476	−	0.987040i	$-0.551303\pi$
$971$	−10.0012			−0.320953			−0.160476	+	0.987040i	$0.551303\pi$
$972$			9.56255i			0.306719i
$973$			5.32992i			0.170869i
$974$	27.0961			0.868214
$975$	5.24064	+	3.54879i	0.167835	+	0.113652i
$976$		−	2.14666i		−	0.0687130i
$977$	−49.4636			−1.58248			−0.791240	−	0.611505i	$-0.790564\pi$
$977$	−49.4636			−1.58248			−0.791240	+	0.611505i	$0.790564\pi$
$978$			0.629549i			0.0201308i
$979$		−	17.1940i		−	0.549521i
$980$	6.91752	+	13.0387i	0.220972	+	0.416505i
$981$			2.07934i			0.0663882i
$982$	−2.46033			−0.0785123
$983$			36.4329i			1.16203i	0.813894	+	0.581014i	$0.197344\pi$
$983$			36.4329i			1.16203i	−0.813894	+	0.581014i	$0.802656\pi$
$984$			3.19485i			0.101848i
$985$	−2.12574	+	1.12779i	−0.0677316	+	0.0359343i
$986$		−	29.7354i		−	0.946969i
$987$		−	3.13162i		−	0.0996805i
$988$		−	20.0104i		−	0.636615i
$989$	37.0190			1.17713
$990$	−3.73653	−	7.04289i	−0.118755	−	0.223838i
$991$		−	49.5991i		−	1.57557i	−0.615953	−	0.787783i	$-0.711229\pi$
$991$		−	49.5991i		−	1.57557i	0.615953	−	0.787783i	$-0.288771\pi$
$992$		−	7.26707i		−	0.230730i
$993$	−2.09435			−0.0664622
$994$			8.03482i			0.254849i
$995$	11.2857	−	5.98749i	0.357780	−	0.189816i
$996$	2.50592			0.0794031
$997$	3.21866			0.101936			0.0509680	−	0.998700i	$-0.483769\pi$
$997$	3.21866			0.101936			0.0509680	+	0.998700i	$0.483769\pi$
$998$			31.4091i			0.994238i
$999$	−9.93437	+	9.08550i	−0.314310	+	0.287452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.c.a.369.6	yes	10
3.2	odd	2		3330.2.e.d.739.3		10
5.2	odd	4		1850.2.d.i.1701.6		20
5.3	odd	4		1850.2.d.i.1701.15		20
5.4	even	2		370.2.c.b.369.5	yes	10
15.14	odd	2		3330.2.e.c.739.7		10
37.36	even	2		370.2.c.b.369.6	yes	10
111.110	odd	2		3330.2.e.c.739.8		10
185.73	odd	4		1850.2.d.i.1701.5		20
185.147	odd	4		1850.2.d.i.1701.16		20
185.184	even	2	inner	370.2.c.a.369.5	✓	10
555.554	odd	2		3330.2.e.d.739.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.c.a.369.5	✓	10	185.184	even	2	inner
370.2.c.a.369.6	yes	10	1.1	even	1	trivial
370.2.c.b.369.5	yes	10	5.4	even	2
370.2.c.b.369.6	yes	10	37.36	even	2
1850.2.d.i.1701.5		20	185.73	odd	4
1850.2.d.i.1701.6		20	5.2	odd	4
1850.2.d.i.1701.15		20	5.3	odd	4
1850.2.d.i.1701.16		20	185.147	odd	4
3330.2.e.c.739.7		10	15.14	odd	2
3330.2.e.c.739.8		10	111.110	odd	2
3330.2.e.d.739.3		10	3.2	odd	2
3330.2.e.d.739.4		10	555.554	odd	2

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.377861i q^{3} +1.00000 q^{4} +(1.04797 + 1.97529i) q^{5} -0.377861i q^{6} +0.631751i q^{7} -1.00000 q^{8} +2.85722 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.377861i q^{3} +1.00000 q^{4} +(1.04797 + 1.97529i) q^{5} -0.377861i q^{6} +0.631751i q^{7} -1.00000 q^{8} +2.85722 q^{9} +(-1.04797 - 1.97529i) q^{10} +1.24789 q^{11} +0.377861i q^{12} -3.34999 q^{13} -0.631751i q^{14} +(-0.746385 + 0.395986i) q^{15} +1.00000 q^{16} -3.10511 q^{17} -2.85722 q^{18} +5.97327i q^{19} +(1.04797 + 1.97529i) q^{20} -0.238714 q^{21} -1.24789 q^{22} +7.60706 q^{23} -0.377861i q^{24} +(-2.80353 + 4.14008i) q^{25} +3.34999 q^{26} +2.21322i q^{27} +0.631751i q^{28} -9.57629i q^{29} +(0.746385 - 0.395986i) q^{30} +7.26707i q^{31} -1.00000 q^{32} +0.471529i q^{33} +3.10511 q^{34} +(-1.24789 + 0.662054i) q^{35} +2.85722 q^{36} +(4.10511 + 4.48866i) q^{37} -5.97327i q^{38} -1.26583i q^{39} +(-1.04797 - 1.97529i) q^{40} -8.45510 q^{41} +0.238714 q^{42} +4.86640 q^{43} +1.24789 q^{44} +(2.99427 + 5.64384i) q^{45} -7.60706 q^{46} +13.1187i q^{47} +0.377861i q^{48} +6.60089 q^{49} +(2.80353 - 4.14008i) q^{50} -1.17330i q^{51} -3.34999 q^{52} -7.17340i q^{53} -2.21322i q^{54} +(1.30775 + 2.46494i) q^{55} -0.631751i q^{56} -2.25707 q^{57} +9.57629i q^{58} -4.36469i q^{59} +(-0.746385 + 0.395986i) q^{60} -2.14666i q^{61} -7.26707i q^{62} +1.80505i q^{63} +1.00000 q^{64} +(-3.51068 - 6.61720i) q^{65} -0.471529i q^{66} -11.3451i q^{67} -3.10511 q^{68} +2.87441i q^{69} +(1.24789 - 0.662054i) q^{70} -12.7183 q^{71} -2.85722 q^{72} -4.45836i q^{73} +(-4.10511 - 4.48866i) q^{74} +(-1.56437 - 1.05934i) q^{75} +5.97327i q^{76} +0.788355i q^{77} +1.26583i q^{78} -8.78679i q^{79} +(1.04797 + 1.97529i) q^{80} +7.73537 q^{81} +8.45510 q^{82} -6.63185i q^{83} -0.238714 q^{84} +(-3.25406 - 6.13349i) q^{85} -4.86640 q^{86} +3.61851 q^{87} -1.24789 q^{88} -13.7784i q^{89} +(-2.99427 - 5.64384i) q^{90} -2.11636i q^{91} +7.60706 q^{92} -2.74594 q^{93} -13.1187i q^{94} +(-11.7989 + 6.25979i) q^{95} -0.377861i q^{96} -11.0583 q^{97} -6.60089 q^{98} +3.56550 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} - 8 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 - 8 * q^9	\( 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} - 8 q^{9} + 3 q^{10} - 2 q^{13} - 10 q^{15} + 10 q^{16} + 18 q^{17} + 8 q^{18} - 3 q^{20} - 12 q^{21} + 10 q^{23} + 5 q^{25} + 2 q^{26} + 10 q^{30} - 10 q^{32} - 18 q^{34} - 8 q^{36} - 8 q^{37} + 3 q^{40} - 4 q^{41} + 12 q^{42} - 10 q^{43} + 20 q^{45} - 10 q^{46} - 8 q^{49} - 5 q^{50} - 2 q^{52} + 5 q^{55} + 12 q^{57} - 10 q^{60} + 10 q^{64} + 2 q^{65} + 18 q^{68} - 20 q^{71} + 8 q^{72} + 8 q^{74} + 25 q^{75} - 3 q^{80} + 58 q^{81} + 4 q^{82} - 12 q^{84} - 28 q^{85} + 10 q^{86} - 10 q^{87} - 20 q^{90} + 10 q^{92} - 32 q^{93} + 2 q^{95} + 2 q^{97} + 8 q^{98} - 82 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 - 8 * q^9 + 3 * q^10 - 2 * q^13 - 10 * q^15 + 10 * q^16 + 18 * q^17 + 8 * q^18 - 3 * q^20 - 12 * q^21 + 10 * q^23 + 5 * q^25 + 2 * q^26 + 10 * q^30 - 10 * q^32 - 18 * q^34 - 8 * q^36 - 8 * q^37 + 3 * q^40 - 4 * q^41 + 12 * q^42 - 10 * q^43 + 20 * q^45 - 10 * q^46 - 8 * q^49 - 5 * q^50 - 2 * q^52 + 5 * q^55 + 12 * q^57 - 10 * q^60 + 10 * q^64 + 2 * q^65 + 18 * q^68 - 20 * q^71 + 8 * q^72 + 8 * q^74 + 25 * q^75 - 3 * q^80 + 58 * q^81 + 4 * q^82 - 12 * q^84 - 28 * q^85 + 10 * q^86 - 10 * q^87 - 20 * q^90 + 10 * q^92 - 32 * q^93 + 2 * q^95 + 2 * q^97 + 8 * q^98 - 82 * q^99

Introduction

L-functions

Modular forms

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Database

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