LMFDB - Embedded newform 403.2.c.b.311.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(311,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("403.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			311.13
Character	$\chi$	$=$	403.311
Dual form			403.2.c.b.311.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.937316i q^{2} +1.68575 q^{3} +1.12144 q^{4} +0.290760i q^{5} -1.58008i q^{6} +3.85549i q^{7} -2.92577i q^{8} -0.158249 q^{9} +O(q^{10})$	\(q-0.937316i q^{2} +1.68575 q^{3} +1.12144 q^{4} +0.290760i q^{5} -1.58008i q^{6} +3.85549i q^{7} -2.92577i q^{8} -0.158249 q^{9} +0.272534 q^{10} -2.09645i q^{11} +1.89046 q^{12} +(2.07708 - 2.94716i) q^{13} +3.61382 q^{14} +0.490148i q^{15} -0.499499 q^{16} +5.29143 q^{17} +0.148329i q^{18} +3.22555i q^{19} +0.326069i q^{20} +6.49940i q^{21} -1.96504 q^{22} -6.80143 q^{23} -4.93212i q^{24} +4.91546 q^{25} +(-2.76242 - 1.94688i) q^{26} -5.32402 q^{27} +4.32370i q^{28} -4.52320 q^{29} +0.459424 q^{30} -1.00000i q^{31} -5.38336i q^{32} -3.53409i q^{33} -4.95974i q^{34} -1.12102 q^{35} -0.177466 q^{36} +4.81693i q^{37} +3.02336 q^{38} +(3.50143 - 4.96818i) q^{39} +0.850698 q^{40} +6.15845i q^{41} +6.09199 q^{42} -7.12251 q^{43} -2.35104i q^{44} -0.0460124i q^{45} +6.37509i q^{46} -4.76874i q^{47} -0.842031 q^{48} -7.86484 q^{49} -4.60734i q^{50} +8.92003 q^{51} +(2.32931 - 3.30506i) q^{52} -5.08219 q^{53} +4.99029i q^{54} +0.609564 q^{55} +11.2803 q^{56} +5.43746i q^{57} +4.23967i q^{58} -9.83912i q^{59} +0.549671i q^{60} -9.60411 q^{61} -0.937316 q^{62} -0.610127i q^{63} -6.04491 q^{64} +(0.856916 + 0.603930i) q^{65} -3.31256 q^{66} +6.38630i q^{67} +5.93402 q^{68} -11.4655 q^{69} +1.05075i q^{70} -3.60967i q^{71} +0.463000i q^{72} -8.21949i q^{73} +4.51499 q^{74} +8.28623 q^{75} +3.61725i q^{76} +8.08285 q^{77} +(-4.65675 - 3.28195i) q^{78} -4.16666 q^{79} -0.145234i q^{80} -8.50021 q^{81} +5.77241 q^{82} +5.60314i q^{83} +7.28867i q^{84} +1.53854i q^{85} +6.67605i q^{86} -7.62499 q^{87} -6.13374 q^{88} +5.99295i q^{89} -0.0431282 q^{90} +(11.3628 + 8.00815i) q^{91} -7.62739 q^{92} -1.68575i q^{93} -4.46982 q^{94} -0.937859 q^{95} -9.07500i q^{96} +1.49758i q^{97} +7.37184i q^{98} +0.331761i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9}+O(q^{10}) $ 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9	$ 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9} + 4 q^{10} - 16 q^{12} + 10 q^{13} - 16 q^{14} + 28 q^{16} - 8 q^{17} - 16 q^{22} - 8 q^{23} + 4 q^{25} + 18 q^{26} + 20 q^{27} - 16 q^{29} + 40 q^{30} - 4 q^{35} - 44 q^{36} + 12 q^{38} + 4 q^{39} + 28 q^{40} + 28 q^{42} - 32 q^{43} - 64 q^{49} - 64 q^{52} - 12 q^{53} + 44 q^{55} + 8 q^{56} + 16 q^{61} + 8 q^{62} - 76 q^{64} - 66 q^{65} - 68 q^{66} + 64 q^{68} + 20 q^{69} + 16 q^{74} - 32 q^{77} - 20 q^{78} + 64 q^{79} - 16 q^{81} + 12 q^{82} - 72 q^{87} + 80 q^{88} + 68 q^{90} + 22 q^{91} + 28 q^{92} + 88 q^{94} + 4 q^{95}+O(q^{100}) $ 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9 + 4 * q^10 - 16 * q^12 + 10 * q^13 - 16 * q^14 + 28 * q^16 - 8 * q^17 - 16 * q^22 - 8 * q^23 + 4 * q^25 + 18 * q^26 + 20 * q^27 - 16 * q^29 + 40 * q^30 - 4 * q^35 - 44 * q^36 + 12 * q^38 + 4 * q^39 + 28 * q^40 + 28 * q^42 - 32 * q^43 - 64 * q^49 - 64 * q^52 - 12 * q^53 + 44 * q^55 + 8 * q^56 + 16 * q^61 + 8 * q^62 - 76 * q^64 - 66 * q^65 - 68 * q^66 + 64 * q^68 + 20 * q^69 + 16 * q^74 - 32 * q^77 - 20 * q^78 + 64 * q^79 - 16 * q^81 + 12 * q^82 - 72 * q^87 + 80 * q^88 + 68 * q^90 + 22 * q^91 + 28 * q^92 + 88 * q^94 + 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	0.937316i		−	0.662783i	−0.943493	−	0.331391i	$-0.892482\pi$
$2$		−	0.937316i		−	0.662783i	0.943493	−	0.331391i	$-0.107518\pi$
$3$	1.68575			0.973268			0.486634	−	0.873606i	$-0.338225\pi$
$3$	1.68575			0.973268			0.486634	+	0.873606i	$0.338225\pi$
$4$	1.12144			0.560719
$5$			0.290760i			0.130032i	0.997884	+	0.0650159i	$0.0207098\pi$
$5$			0.290760i			0.130032i	−0.997884	+	0.0650159i	$0.979290\pi$
$6$		−	1.58008i		−	0.645065i
$7$			3.85549i			1.45724i	0.684918	+	0.728620i	$0.259838\pi$
$7$			3.85549i			1.45724i	−0.684918	+	0.728620i	$0.740162\pi$
$8$		−	2.92577i		−	1.03442i
$9$	−0.158249			−0.0527496
$10$	0.272534			0.0861828
$11$		−	2.09645i		−	0.632104i	−0.948742	−	0.316052i	$-0.897643\pi$
$11$		−	2.09645i		−	0.632104i	0.948742	−	0.316052i	$-0.102357\pi$
$12$	1.89046			0.545730
$13$	2.07708	−	2.94716i	0.576077	−	0.817395i
$13$	2.07708	−	2.94716i	0.576077	−	0.817395i
$14$	3.61382			0.965833
$15$			0.490148i			0.126556i
$16$	−0.499499			−0.124875
$17$	5.29143			1.28336			0.641680	−	0.766972i	$-0.278238\pi$
$17$	5.29143			1.28336			0.641680	+	0.766972i	$0.278238\pi$
$18$			0.148329i			0.0349615i
$19$			3.22555i			0.739991i	0.929034	+	0.369996i	$0.120641\pi$
$19$			3.22555i			0.739991i	−0.929034	+	0.369996i	$0.879359\pi$
$20$			0.326069i			0.0729113i
$21$			6.49940i			1.41828i
$22$	−1.96504			−0.418947
$23$	−6.80143			−1.41820			−0.709098	−	0.705110i	$-0.750898\pi$
$23$	−6.80143			−1.41820			−0.709098	+	0.705110i	$0.750898\pi$
$24$		−	4.93212i		−	1.00677i
$25$	4.91546			0.983092
$26$	−2.76242	−	1.94688i	−0.541755	−	0.381814i
$27$	−5.32402			−1.02461
$28$			4.32370i			0.817102i
$29$	−4.52320			−0.839938			−0.419969	−	0.907539i	$-0.637959\pi$
$29$	−4.52320			−0.839938			−0.419969	+	0.907539i	$0.637959\pi$
$30$	0.459424			0.0838789
$31$		−	1.00000i		−	0.179605i
$31$		−	1.00000i		−	0.179605i
$32$		−	5.38336i		−	0.951653i
$33$		−	3.53409i		−	0.615206i
$34$		−	4.95974i		−	0.850589i
$35$	−1.12102			−0.189487
$36$	−0.177466			−0.0295777
$37$			4.81693i			0.791899i	0.918272	+	0.395950i	$0.129584\pi$
$37$			4.81693i			0.791899i	−0.918272	+	0.395950i	$0.870416\pi$
$38$	3.02336			0.490453
$39$	3.50143	−	4.96818i	0.560677	−	0.795545i
$40$	0.850698			0.134507
$41$			6.15845i			0.961788i	0.876779	+	0.480894i	$0.159688\pi$
$41$			6.15845i			0.961788i	−0.876779	+	0.480894i	$0.840312\pi$
$42$	6.09199			0.940015
$43$	−7.12251			−1.08617			−0.543087	−	0.839677i	$-0.682744\pi$
$43$	−7.12251			−1.08617			−0.543087	+	0.839677i	$0.682744\pi$
$44$		−	2.35104i		−	0.354433i
$45$		−	0.0460124i		−	0.00685912i
$46$			6.37509i			0.939956i
$47$		−	4.76874i		−	0.695592i	−0.937570	−	0.347796i	$-0.886930\pi$
$47$		−	4.76874i		−	0.695592i	0.937570	−	0.347796i	$-0.113070\pi$
$48$	−0.842031			−0.121537
$49$	−7.86484			−1.12355
$50$		−	4.60734i		−	0.651576i
$51$	8.92003			1.24905
$52$	2.32931	−	3.30506i	0.323017	−	0.458329i
$53$	−5.08219			−0.698093			−0.349046	−	0.937105i	$-0.613494\pi$
$53$	−5.08219			−0.698093			−0.349046	+	0.937105i	$0.613494\pi$
$54$			4.99029i			0.679092i
$55$	0.609564			0.0821936
$56$	11.2803			1.50739
$57$			5.43746i			0.720210i
$58$			4.23967i			0.556696i
$59$		−	9.83912i		−	1.28094i	−0.767981	−	0.640472i	$-0.778739\pi$
$59$		−	9.83912i		−	1.28094i	0.767981	−	0.640472i	$-0.221261\pi$
$60$			0.549671i			0.0709622i
$61$	−9.60411			−1.22968			−0.614840	−	0.788652i	$-0.710780\pi$
$61$	−9.60411			−1.22968			−0.614840	+	0.788652i	$0.710780\pi$
$62$	−0.937316			−0.119039
$63$		−	0.610127i		−	0.0768688i
$64$	−6.04491			−0.755614
$65$	0.856916	+	0.603930i	0.106287	+	0.0749083i
$66$	−3.31256			−0.407748
$67$			6.38630i			0.780210i	0.920770	+	0.390105i	$0.127561\pi$
$67$			6.38630i			0.780210i	−0.920770	+	0.390105i	$0.872439\pi$
$68$	5.93402			0.719605
$69$	−11.4655			−1.38029
$70$			1.05075i			0.125589i
$71$		−	3.60967i		−	0.428389i	−0.976791	−	0.214194i	$-0.931287\pi$
$71$		−	3.60967i		−	0.428389i	0.976791	−	0.214194i	$-0.0687126\pi$
$72$			0.463000i			0.0545651i
$73$		−	8.21949i		−	0.962018i	−0.876716	−	0.481009i	$-0.840270\pi$
$73$		−	8.21949i		−	0.962018i	0.876716	−	0.481009i	$-0.159730\pi$
$74$	4.51499			0.524857
$75$	8.28623			0.956812
$76$			3.61725i			0.414927i
$77$	8.08285			0.921127
$78$	−4.65675	−	3.28195i	−0.527273	−	0.371607i
$79$	−4.16666			−0.468786			−0.234393	−	0.972142i	$-0.575310\pi$
$79$	−4.16666			−0.468786			−0.234393	+	0.972142i	$0.575310\pi$
$80$		−	0.145234i		−	0.0162377i
$81$	−8.50021			−0.944468
$82$	5.77241			0.637456
$83$			5.60314i			0.615024i	0.951544	+	0.307512i	$0.0994964\pi$
$83$			5.60314i			0.615024i	−0.951544	+	0.307512i	$0.900504\pi$
$84$			7.28867i			0.795260i
$85$			1.53854i			0.166878i
$86$			6.67605i			0.719897i
$87$	−7.62499			−0.817484
$88$	−6.13374			−0.653859
$89$			5.99295i			0.635251i	0.948216	+	0.317626i	$0.102885\pi$
$89$			5.99295i			0.635251i	−0.948216	+	0.317626i	$0.897115\pi$
$90$	−0.0431282			−0.00454611
$91$	11.3628	+	8.00815i	1.19114	+	0.839483i
$92$	−7.62739			−0.795210
$93$		−	1.68575i		−	0.174804i
$94$	−4.46982			−0.461026
$95$	−0.937859			−0.0962224
$96$		−	9.07500i		−	0.926213i
$97$			1.49758i			0.152056i	0.997106	+	0.0760282i	$0.0242239\pi$
$97$			1.49758i			0.152056i	−0.997106	+	0.0760282i	$0.975776\pi$
$98$			7.37184i			0.744668i
$99$			0.331761i			0.0333432i
$100$	5.51238			0.551238
$101$	6.72002			0.668667			0.334333	−	0.942455i	$-0.391489\pi$
$101$	6.72002			0.668667			0.334333	+	0.942455i	$0.391489\pi$
$102$		−	8.36089i		−	0.827851i
$103$	−10.1453			−0.999647			−0.499824	−	0.866127i	$-0.666602\pi$
$103$	−10.1453			−0.999647			−0.499824	+	0.866127i	$0.666602\pi$
$104$	−8.62273	−	6.07705i	−0.845528	−	0.595904i
$105$	−1.88976			−0.184422
$106$			4.76362i			0.462684i
$107$	−13.0831			−1.26479			−0.632397	−	0.774644i	$-0.717929\pi$
$107$	−13.0831			−1.26479			−0.632397	+	0.774644i	$0.717929\pi$
$108$	−5.97056			−0.574517
$109$			8.14852i			0.780486i	0.920712	+	0.390243i	$0.127609\pi$
$109$			8.14852i			0.780486i	−0.920712	+	0.390243i	$0.872391\pi$
$110$		−	0.571354i		−	0.0544765i
$111$			8.12014i			0.770730i
$112$		−	1.92582i		−	0.181973i
$113$	20.6286			1.94057			0.970287	−	0.241958i	$-0.0777895\pi$
$113$	20.6286			1.94057			0.970287	+	0.241958i	$0.0777895\pi$
$114$	5.09662			0.477342
$115$		−	1.97758i		−	0.184411i
$116$	−5.07249			−0.470969
$117$	−0.328695	+	0.466385i	−0.0303878	+	0.0431173i
$118$	−9.22237			−0.848988
$119$			20.4011i			1.87016i
$120$	1.43406			0.130911
$121$	6.60489			0.600445
$122$			9.00209i			0.815011i
$123$			10.3816i			0.936077i
$124$		−	1.12144i		−	0.100708i
$125$			2.88302i			0.257865i
$126$	−0.571882			−0.0509473
$127$	1.36933			0.121509			0.0607544	−	0.998153i	$-0.480649\pi$
$127$	1.36933			0.121509			0.0607544	+	0.998153i	$0.480649\pi$
$128$		−	5.10073i		−	0.450845i
$129$	−12.0068			−1.05714
$130$	0.566074	−	0.803201i	0.0496479	−	0.0704454i
$131$	9.73999			0.850987			0.425494	−	0.904961i	$-0.360100\pi$
$131$	9.73999			0.850987			0.425494	+	0.904961i	$0.360100\pi$
$132$		−	3.96327i		−	0.344958i
$133$	−12.4361			−1.07834
$134$	5.98598			0.517110
$135$		−	1.54801i		−	0.133232i
$136$		−	15.4815i		−	1.32753i
$137$			11.0632i			0.945191i	0.881280	+	0.472595i	$0.156683\pi$
$137$			11.0632i			0.945191i	−0.881280	+	0.472595i	$0.843317\pi$
$138$			10.7468i			0.914829i
$139$	15.7894			1.33924			0.669620	−	0.742704i	$-0.266457\pi$
$139$	15.7894			1.33924			0.669620	+	0.742704i	$0.266457\pi$
$140$	−1.25716			−0.106249
$141$		−	8.03890i		−	0.676998i
$142$	−3.38340			−0.283929
$143$	−6.17858	−	4.35449i	−0.516679	−	0.364140i
$144$	0.0790451			0.00658709
$145$		−	1.31517i		−	0.109219i
$146$	−7.70426			−0.637609
$147$	−13.2581			−1.09351
$148$			5.40189i			0.444033i
$149$			2.97069i			0.243368i	0.992569	+	0.121684i	$0.0388295\pi$
$149$			2.97069i			0.243368i	−0.992569	+	0.121684i	$0.961171\pi$
$150$		−	7.76682i		−	0.634158i
$151$		−	20.1243i		−	1.63770i	−0.574011	−	0.818848i	$-0.694613\pi$
$151$		−	20.1243i		−	1.63770i	0.574011	−	0.818848i	$-0.305387\pi$
$152$	9.43722			0.765460
$153$	−0.837363			−0.0676967
$154$		−	7.57619i		−	0.610507i
$155$	0.290760			0.0233544
$156$	3.92664	−	5.57150i	0.314383	−	0.446077i
$157$	18.9740			1.51429			0.757147	−	0.653245i	$-0.226593\pi$
$157$	18.9740			1.51429			0.757147	+	0.653245i	$0.226593\pi$
$158$			3.90548i			0.310703i
$159$	−8.56730			−0.679431
$160$	1.56527			0.123745
$161$		−	26.2229i		−	2.06665i
$162$			7.96739i			0.625977i
$163$			19.5049i			1.52774i	0.645369	+	0.763871i	$0.276704\pi$
$163$			19.5049i			1.52774i	−0.645369	+	0.763871i	$0.723296\pi$
$164$			6.90632i			0.539293i
$165$	1.02757			0.0799964
$166$	5.25191			0.407627
$167$		−	23.5293i		−	1.82075i	−0.413785	−	0.910375i	$-0.635793\pi$
$167$		−	23.5293i		−	1.82075i	0.413785	−	0.910375i	$-0.364207\pi$
$168$	19.0158			1.46710
$169$	−4.37152	−	12.2430i	−0.336270	−	0.941765i
$170$	1.44209			0.110604
$171$		−	0.510439i		−	0.0390342i
$172$	−7.98746			−0.609038
$173$	11.3779			0.865043			0.432522	−	0.901624i	$-0.357624\pi$
$173$	11.3779			0.865043			0.432522	+	0.901624i	$0.357624\pi$
$174$			7.14702i			0.541814i
$175$			18.9515i			1.43260i
$176$			1.04718i			0.0789338i
$177$		−	16.5863i		−	1.24670i
$178$	5.61729			0.421033
$179$	20.7125			1.54813			0.774063	−	0.633108i	$-0.218221\pi$
$179$	20.7125			1.54813			0.774063	+	0.633108i	$0.218221\pi$
$180$		−	0.0516001i		−	0.00384604i
$181$	2.21171			0.164395			0.0821975	−	0.996616i	$-0.473806\pi$
$181$	2.21171			0.164395			0.0821975	+	0.996616i	$0.473806\pi$
$182$	7.50617	−	10.6505i	0.556394	−	0.789468i
$183$	−16.1901			−1.19681
$184$			19.8995i			1.46701i
$185$	−1.40057			−0.102972
$186$	−1.58008			−0.115857
$187$		−	11.0932i		−	0.811217i
$188$		−	5.34785i		−	0.390032i
$189$		−	20.5267i		−	1.49310i
$190$			0.879071i			0.0637745i
$191$	−5.93737			−0.429613			−0.214806	−	0.976657i	$-0.568912\pi$
$191$	−5.93737			−0.429613			−0.214806	+	0.976657i	$0.568912\pi$
$192$	−10.1902			−0.735415
$193$		−	7.67380i		−	0.552372i	−0.961104	−	0.276186i	$-0.910929\pi$
$193$		−	7.67380i		−	0.552372i	0.961104	−	0.276186i	$-0.0890706\pi$
$194$	1.40371			0.100780
$195$	1.44455	+	1.01807i	0.103446	+	0.0729059i
$196$	−8.81993			−0.629995
$197$		−	10.6398i		−	0.758057i	−0.925385	−	0.379029i	$-0.876258\pi$
$197$		−	10.6398i		−	0.758057i	0.925385	−	0.379029i	$-0.123742\pi$
$198$	0.310965			0.0220993
$199$	−21.8838			−1.55130			−0.775650	−	0.631163i	$-0.782578\pi$
$199$	−21.8838			−1.55130			−0.775650	+	0.631163i	$0.782578\pi$
$200$		−	14.3815i		−	1.01693i
$201$			10.7657i			0.759354i
$202$		−	6.29878i		−	0.443181i
$203$		−	17.4392i		−	1.22399i
$204$	10.0033			0.700368
$205$	−1.79063			−0.125063
$206$			9.50936i			0.662549i
$207$	1.07632			0.0748093
$208$	−1.03750	+	1.47210i	−0.0719375	+	0.102072i
$209$	6.76220			0.467751
$210$			1.77131i			0.122232i
$211$	27.2902			1.87873			0.939366	−	0.342917i	$-0.111415\pi$
$211$	27.2902			1.87873			0.939366	+	0.342917i	$0.111415\pi$
$212$	−5.69937			−0.391434
$213$		−	6.08500i		−	0.416937i
$214$			12.2630i			0.838284i
$215$		−	2.07094i		−	0.141237i
$216$			15.5769i			1.05987i
$217$	3.85549			0.261728
$218$	7.63774			0.517293
$219$		−	13.8560i		−	0.936302i
$220$	0.683588			0.0460875
$221$	10.9907	−	15.5947i	0.739315	−	1.04901i
$222$	7.61114			0.510826
$223$			23.9038i			1.60071i	0.599524	+	0.800357i	$0.295357\pi$
$223$			23.9038i			1.60071i	−0.599524	+	0.800357i	$0.704643\pi$
$224$	20.7555			1.38679
$225$	−0.777865			−0.0518577
$226$		−	19.3355i		−	1.28618i
$227$			14.9621i			0.993072i	0.868016	+	0.496536i	$0.165395\pi$
$227$			14.9621i			0.993072i	−0.868016	+	0.496536i	$0.834605\pi$
$228$			6.09778i			0.403835i
$229$			13.2617i			0.876355i	0.898888	+	0.438178i	$0.144376\pi$
$229$			13.2617i			0.876355i	−0.898888	+	0.438178i	$0.855624\pi$
$230$	−1.85362			−0.122224
$231$	13.6257			0.896503
$232$			13.2339i			0.868846i
$233$	−0.641941			−0.0420549			−0.0210275	−	0.999779i	$-0.506694\pi$
$233$	−0.641941			−0.0420549			−0.0210275	+	0.999779i	$0.506694\pi$
$234$	0.437150	+	0.308091i	0.0285774	+	0.0201405i
$235$	1.38656			0.0904491
$236$		−	11.0340i		−	0.718250i
$237$	−7.02395			−0.456254
$238$	19.1223			1.23951
$239$		−	4.79323i		−	0.310048i	−0.987911	−	0.155024i	$-0.950454\pi$
$239$		−	4.79323i		−	0.310048i	0.987911	−	0.155024i	$-0.0495455\pi$
$240$		−	0.244829i		−	0.0158036i
$241$		−	20.2887i		−	1.30691i	−0.756966	−	0.653454i	$-0.773319\pi$
$241$		−	20.2887i		−	1.30691i	0.756966	−	0.653454i	$-0.226681\pi$
$242$		−	6.19087i		−	0.397964i
$243$	1.64282			0.105387
$244$	−10.7704			−0.689506
$245$		−	2.28678i		−	0.146097i
$246$	9.73084			0.620416
$247$	9.50620	+	6.69970i	0.604865	+	0.426292i
$248$	−2.92577			−0.185787
$249$			9.44548i			0.598583i
$250$	2.70230			0.170908
$251$	−21.8713			−1.38050			−0.690251	−	0.723570i	$-0.742500\pi$
$251$	−21.8713			−1.38050			−0.690251	+	0.723570i	$0.742500\pi$
$252$		−	0.684220i		−	0.0431018i
$253$			14.2589i			0.896447i
$254$		−	1.28350i		−	0.0805339i
$255$			2.59359i			0.162417i
$256$	−16.8708			−1.05443
$257$	−15.8299			−0.987444			−0.493722	−	0.869620i	$-0.664364\pi$
$257$	−15.8299			−0.987444			−0.493722	+	0.869620i	$0.664364\pi$
$258$			11.2541i			0.700652i
$259$	−18.5717			−1.15399
$260$	0.960979	+	0.677270i	0.0595974	+	0.0420025i
$261$	0.715791			0.0443064
$262$		−	9.12945i		−	0.564020i
$263$	3.06797			0.189179			0.0945897	−	0.995516i	$-0.469846\pi$
$263$	3.06797			0.189179			0.0945897	+	0.995516i	$0.469846\pi$
$264$	−10.3400			−0.636380
$265$		−	1.47770i		−	0.0907742i
$266$			11.6565i			0.714708i
$267$			10.1026i			0.618269i
$268$			7.16184i			0.437479i
$269$	6.90791			0.421183			0.210591	−	0.977574i	$-0.432461\pi$
$269$	6.90791			0.421183			0.210591	+	0.977574i	$0.432461\pi$
$270$	−1.45098			−0.0883035
$271$		−	32.2346i		−	1.95811i	−0.203597	−	0.979055i	$-0.565263\pi$
$271$		−	32.2346i		−	1.95811i	0.203597	−	0.979055i	$-0.434737\pi$
$272$	−2.64307			−0.160259
$273$	19.1548	+	13.4997i	1.15930	+	0.817041i
$274$	10.3697			0.626456
$275$		−	10.3050i		−	0.621416i
$276$	−12.8579			−0.773952
$277$	16.2761			0.977938			0.488969	−	0.872301i	$-0.337373\pi$
$277$	16.2761			0.977938			0.488969	+	0.872301i	$0.337373\pi$
$278$		−	14.7997i		−	0.887625i
$279$			0.158249i			0.00947410i
$280$			3.27986i			0.196009i
$281$		−	22.5291i		−	1.34397i	−0.740563	−	0.671987i	$-0.765441\pi$
$281$		−	22.5291i		−	1.34397i	0.740563	−	0.671987i	$-0.234559\pi$
$282$	−7.53499			−0.448702
$283$	−11.1486			−0.662718			−0.331359	−	0.943505i	$-0.607507\pi$
$283$	−11.1486			−0.662718			−0.331359	+	0.943505i	$0.607507\pi$
$284$		−	4.04802i		−	0.240206i
$285$	−1.58100			−0.0936501
$286$	−4.08153	+	5.79128i	−0.241346	+	0.342446i
$287$	−23.7439			−1.40156
$288$			0.851910i			0.0501993i
$289$	10.9993			0.647015
$290$	−1.23273			−0.0723882
$291$			2.52455i			0.147992i
$292$		−	9.21765i		−	0.539422i
$293$			29.1854i			1.70503i	0.522705	+	0.852514i	$0.324923\pi$
$293$			29.1854i			1.70503i	−0.522705	+	0.852514i	$0.675077\pi$
$294$			12.4271i			0.724762i
$295$	2.86082			0.166564
$296$	14.0933			0.819154
$297$			11.1615i			0.647658i
$298$	2.78447			0.161300
$299$	−14.1271	+	20.0449i	−0.816991	+	1.15923i
$300$	9.29250			0.536503
$301$		−	27.4608i		−	1.58281i
$302$	−18.8629			−1.08544
$303$	11.3283			0.650792
$304$		−	1.61116i		−	0.0924062i
$305$		−	2.79249i		−	0.159898i
$306$			0.784873i			0.0448682i
$307$			10.2881i			0.587175i	0.955932	+	0.293588i	$0.0948493\pi$
$307$			10.2881i			0.587175i	−0.955932	+	0.293588i	$0.905151\pi$
$308$	9.06442			0.516493
$309$	−17.1025			−0.972925
$310$		−	0.272534i		−	0.0154789i
$311$	6.14155			0.348256			0.174128	−	0.984723i	$-0.444289\pi$
$311$	6.14155			0.348256			0.174128	+	0.984723i	$0.444289\pi$
$312$	−14.5358	−	10.2444i	−0.822925	−	0.579974i
$313$	8.55769			0.483709			0.241855	−	0.970313i	$-0.422244\pi$
$313$	8.55769			0.483709			0.241855	+	0.970313i	$0.422244\pi$
$314$		−	17.7847i		−	1.00365i
$315$	0.177401			0.00999539
$316$	−4.67265			−0.262857
$317$			14.4222i			0.810032i	0.914310	+	0.405016i	$0.132734\pi$
$317$			14.4222i			0.810032i	−0.914310	+	0.405016i	$0.867266\pi$
$318$			8.03027i			0.450315i
$319$			9.48267i			0.530928i
$320$		−	1.75762i		−	0.0982538i
$321$	−22.0549			−1.23098
$322$	−24.5791			−1.36974
$323$			17.0678i			0.949676i
$324$	−9.53246			−0.529581
$325$	10.2098	−	14.4866i	0.566337	−	0.803575i
$326$	18.2823			1.01256
$327$			13.7364i			0.759622i
$328$	18.0182			0.994890
$329$	18.3859			1.01364
$330$		−	0.963160i		−	0.0530202i
$331$			21.6554i			1.19029i	0.803620	+	0.595143i	$0.202905\pi$
$331$			21.6554i			1.19029i	−0.803620	+	0.595143i	$0.797095\pi$
$332$			6.28357i			0.344856i
$333$		−	0.762274i		−	0.0417723i
$334$	−22.0544			−1.20676
$335$	−1.85688			−0.101452
$336$		−	3.24644i		−	0.177108i
$337$	14.4456			0.786904			0.393452	−	0.919345i	$-0.371281\pi$
$337$	14.4456			0.786904			0.393452	+	0.919345i	$0.371281\pi$
$338$	−11.4755	+	4.09749i	−0.624186	+	0.222874i
$339$	34.7746			1.88870
$340$			1.72537i			0.0935715i
$341$	−2.09645			−0.113529
$342$	−0.478442			−0.0258712
$343$		−	3.33438i		−	0.180039i
$344$			20.8389i			1.12356i
$345$		−	3.33371i		−	0.179481i
$346$		−	10.6647i		−	0.573335i
$347$	−9.70087			−0.520770			−0.260385	−	0.965505i	$-0.583849\pi$
$347$	−9.70087			−0.520770			−0.260385	+	0.965505i	$0.583849\pi$
$348$	−8.55095			−0.458379
$349$			2.05208i			0.109845i	0.998491	+	0.0549227i	$0.0174912\pi$
$349$			2.05208i			0.109845i	−0.998491	+	0.0549227i	$0.982509\pi$
$350$	17.7636			0.949503
$351$	−11.0584	+	15.6907i	−0.590253	+	0.837509i
$352$	−11.2860			−0.601543
$353$			11.7324i			0.624452i	0.950008	+	0.312226i	$0.101075\pi$
$353$			11.7324i			0.624452i	−0.950008	+	0.312226i	$0.898925\pi$
$354$	−15.5466			−0.826293
$355$	1.04955			0.0557042
$356$			6.72072i			0.356197i
$357$			34.3911i			1.82017i
$358$		−	19.4142i		−	1.02607i
$359$		−	24.9325i		−	1.31588i	−0.753068	−	0.657942i	$-0.771427\pi$
$359$		−	24.9325i		−	1.31588i	0.753068	−	0.657942i	$-0.228573\pi$
$360$	−0.134622			−0.00709520
$361$	8.59585			0.452413
$362$		−	2.07307i		−	0.108958i
$363$	11.1342			0.584394
$364$	12.7426	+	8.98065i	0.667896	+	0.470714i
$365$	2.38990			0.125093
$366$			15.1753i			0.793224i
$367$	13.7018			0.715230			0.357615	−	0.933869i	$-0.383590\pi$
$367$	13.7018			0.715230			0.357615	+	0.933869i	$0.383590\pi$
$368$	3.39731			0.177097
$369$		−	0.974566i		−	0.0507339i
$370$			1.31278i			0.0682481i
$371$		−	19.5944i		−	1.01729i
$372$		−	1.89046i		−	0.0980160i
$373$	−9.22059			−0.477424			−0.238712	−	0.971090i	$-0.576725\pi$
$373$	−9.22059			−0.477424			−0.238712	+	0.971090i	$0.576725\pi$
$374$	−10.3979			−0.537661
$375$			4.86005i			0.250972i
$376$	−13.9523			−0.719533
$377$	−9.39503	+	13.3306i	−0.483869	+	0.686561i
$378$	−19.2400			−0.989600
$379$		−	7.66126i		−	0.393532i	−0.980450	−	0.196766i	$-0.936956\pi$
$379$		−	7.66126i		−	0.393532i	0.980450	−	0.196766i	$-0.0630440\pi$
$380$	−1.05175			−0.0539537
$381$	2.30835			0.118261
$382$			5.56519i			0.284740i
$383$			3.77098i			0.192688i	0.995348	+	0.0963440i	$0.0307149\pi$
$383$			3.77098i			0.192688i	−0.995348	+	0.0963440i	$0.969285\pi$
$384$		−	8.59855i		−	0.438793i
$385$			2.35017i			0.119776i
$386$	−7.19278			−0.366103
$387$	1.12713			0.0572952
$388$			1.67944i			0.0852609i
$389$	−1.98742			−0.100766			−0.0503831	−	0.998730i	$-0.516044\pi$
$389$	−1.98742			−0.100766			−0.0503831	+	0.998730i	$0.516044\pi$
$390$	0.954258	−	1.35400i	0.0483207	−	0.0685623i
$391$	−35.9893			−1.82006
$392$			23.0107i			1.16222i
$393$	16.4192			0.828239
$394$	−9.97289			−0.502427
$395$		−	1.21150i		−	0.0609571i
$396$			0.372049i			0.0186962i
$397$			7.83722i			0.393339i	0.980470	+	0.196669i	$0.0630126\pi$
$397$			7.83722i			0.393339i	−0.980470	+	0.196669i	$0.936987\pi$
$398$			20.5120i			1.02817i
$399$	−20.9641			−1.04952
$400$	−2.45527			−0.122763
$401$		−	23.9276i		−	1.19489i	−0.801911	−	0.597444i	$-0.796183\pi$
$401$		−	23.9276i		−	1.19489i	0.801911	−	0.597444i	$-0.203817\pi$
$402$	10.0909			0.503286
$403$	−2.94716	−	2.07708i	−0.146809	−	0.103466i
$404$	7.53609			0.374934
$405$		−	2.47152i		−	0.122811i
$406$	−16.3460			−0.811240
$407$	10.0985			0.500562
$408$		−	26.0980i		−	1.29204i
$409$		−	26.7159i		−	1.32101i	−0.750820	−	0.660507i	$-0.770341\pi$
$409$		−	26.7159i		−	1.32101i	0.750820	−	0.660507i	$-0.229659\pi$
$410$			1.67839i			0.0828896i
$411$			18.6497i			0.919924i
$412$	−11.3773			−0.560521
$413$	37.9347			1.86664
$414$		−	1.00885i		−	0.0495823i
$415$	−1.62917			−0.0799727
$416$	−15.8656	−	11.1816i	−0.777877	−	0.548225i
$417$	26.6170			1.30344
$418$		−	6.33832i		−	0.310017i
$419$	−17.5555			−0.857641			−0.428821	−	0.903390i	$-0.641071\pi$
$419$	−17.5555			−0.857641			−0.428821	+	0.903390i	$0.641071\pi$
$420$	−2.11925			−0.103409
$421$		−	27.6416i		−	1.34717i	−0.739110	−	0.673585i	$-0.764754\pi$
$421$		−	27.6416i		−	1.34717i	0.739110	−	0.673585i	$-0.235246\pi$
$422$		−	25.5795i		−	1.24519i
$423$			0.754647i			0.0366922i
$424$			14.8693i			0.722119i
$425$	26.0098			1.26166
$426$	−5.70357			−0.276339
$427$		−	37.0286i		−	1.79194i
$428$	−14.6719			−0.709195
$429$	−10.4155	−	7.34057i	−0.502867	−	0.354406i
$430$	−1.94113			−0.0936094
$431$			23.6042i			1.13697i	0.822692	+	0.568487i	$0.192471\pi$
$431$			23.6042i			1.13697i	−0.822692	+	0.568487i	$0.807529\pi$
$432$	2.65934			0.127948
$433$	−17.3815			−0.835303			−0.417651	−	0.908607i	$-0.637147\pi$
$433$	−17.3815			−0.835303			−0.417651	+	0.908607i	$0.637147\pi$
$434$		−	3.61382i		−	0.173469i
$435$		−	2.21704i		−	0.106299i
$436$			9.13806i			0.437634i
$437$		−	21.9383i		−	1.04945i
$438$	−12.9875			−0.620565
$439$	−20.9810			−1.00137			−0.500684	−	0.865630i	$-0.666918\pi$
$439$	−20.9810			−1.00137			−0.500684	+	0.865630i	$0.666918\pi$
$440$		−	1.78345i		−	0.0850225i
$441$	1.24460			0.0592667
$442$	−14.6172	−	10.3018i	−0.695268	−	0.490005i
$443$	−32.4721			−1.54280			−0.771399	−	0.636352i	$-0.780443\pi$
$443$	−32.4721			−1.54280			−0.771399	+	0.636352i	$0.780443\pi$
$444$			9.10624i			0.432163i
$445$	−1.74251			−0.0826028
$446$	22.4054			1.06093
$447$			5.00783i			0.236862i
$448$		−	23.3061i		−	1.10111i
$449$			22.2111i			1.04821i	0.851655	+	0.524103i	$0.175599\pi$
$449$			22.2111i			1.04821i	−0.851655	+	0.524103i	$0.824401\pi$
$450$			0.729106i			0.0343704i
$451$	12.9109			0.607950
$452$	23.1337			1.08812
$453$		−	33.9246i		−	1.59392i
$454$	14.0243			0.658191
$455$	−2.32845	+	3.30384i	−0.109159	+	0.154886i
$456$	15.9088			0.744997
$457$		−	24.7016i		−	1.15549i	−0.816216	−	0.577747i	$-0.803932\pi$
$457$		−	24.7016i		−	1.15549i	0.816216	−	0.577747i	$-0.196068\pi$
$458$	12.4304			0.580833
$459$	−28.1717			−1.31494
$460$		−	2.21774i		−	0.103403i
$461$			1.87166i			0.0871720i	0.999050	+	0.0435860i	$0.0138783\pi$
$461$			1.87166i			0.0871720i	−0.999050	+	0.0435860i	$0.986122\pi$
$462$		−	12.7716i		−	0.594187i
$463$			33.6330i			1.56306i	0.623869	+	0.781529i	$0.285560\pi$
$463$			33.6330i			1.56306i	−0.623869	+	0.781529i	$0.714440\pi$
$464$	2.25934			0.104887
$465$	0.490148			0.0227301
$466$			0.601701i			0.0278733i
$467$	−11.9042			−0.550861			−0.275430	−	0.961321i	$-0.588820\pi$
$467$	−11.9042			−0.550861			−0.275430	+	0.961321i	$0.588820\pi$
$468$	−0.368611	+	0.523022i	−0.0170390	+	0.0241767i
$469$	−24.6223			−1.13695
$470$		−	1.29964i		−	0.0599481i
$471$	31.9855			1.47381
$472$	−28.7871			−1.32503
$473$			14.9320i			0.686574i
$474$			6.58366i			0.302397i
$475$			15.8550i			0.727479i
$476$			22.8786i			1.04864i
$477$	0.804251			0.0368241
$478$	−4.49277			−0.205495
$479$			9.00430i			0.411417i	0.978613	+	0.205708i	$0.0659499\pi$
$479$			9.00430i			0.411417i	−0.978613	+	0.205708i	$0.934050\pi$
$480$	2.63865			0.120437
$481$	14.1963	+	10.0051i	0.647295	+	0.456195i
$482$	−19.0169			−0.866196
$483$		−	44.2052i		−	2.01141i
$484$	7.40698			0.336681
$485$	−0.435436			−0.0197722
$486$		−	1.53984i		−	0.0698487i
$487$			36.5025i			1.65409i	0.562139	+	0.827043i	$0.309979\pi$
$487$			36.5025i			1.65409i	−0.562139	+	0.827043i	$0.690021\pi$
$488$			28.0995i			1.27200i
$489$			32.8804i			1.48690i
$490$	−2.14344			−0.0968305
$491$	9.04853			0.408355			0.204177	−	0.978934i	$-0.434548\pi$
$491$	9.04853			0.408355			0.204177	+	0.978934i	$0.434548\pi$
$492$			11.6423i			0.524876i
$493$	−23.9342			−1.07794
$494$	6.27974	−	8.91032i	0.282539	−	0.400894i
$495$	−0.0964627			−0.00433568
$496$			0.499499i			0.0224282i
$497$	13.9171			0.624265
$498$	8.85340			0.396731
$499$		−	26.1949i		−	1.17264i	−0.810078	−	0.586322i	$-0.800575\pi$
$499$		−	26.1949i		−	1.17264i	0.810078	−	0.586322i	$-0.199425\pi$
$500$			3.23313i			0.144590i
$501$		−	39.6645i		−	1.77208i
$502$			20.5003i			0.914972i
$503$	−19.4070			−0.865315			−0.432657	−	0.901558i	$-0.642424\pi$
$503$	−19.4070			−0.865315			−0.432657	+	0.901558i	$0.642424\pi$
$504$	−1.78509			−0.0795144
$505$			1.95391i			0.0869479i
$506$	13.3651			0.594150
$507$	−7.36928	−	20.6385i	−0.327281	−	0.916590i
$508$	1.53562			0.0681323
$509$			2.27885i			0.101008i	0.998724	+	0.0505041i	$0.0160828\pi$
$509$			2.27885i			0.101008i	−0.998724	+	0.0505041i	$0.983917\pi$
$510$	2.43101			0.107647
$511$	31.6902			1.40189
$512$			5.61183i			0.248010i
$513$		−	17.1729i		−	0.758200i
$514$			14.8376i			0.654460i
$515$		−	2.94985i		−	0.129986i
$516$	−13.4649			−0.592757
$517$	−9.99743			−0.439686
$518$			17.4075i			0.764842i
$519$	19.1802			0.841919
$520$	1.76696	−	2.50714i	0.0774865	−	0.109946i
$521$	29.5904			1.29638			0.648189	−	0.761479i	$-0.275527\pi$
$521$	29.5904			1.29638			0.648189	+	0.761479i	$0.275527\pi$
$522$		−	0.670923i		−	0.0293655i
$523$	31.9338			1.39637			0.698183	−	0.715919i	$-0.253992\pi$
$523$	31.9338			1.39637			0.698183	+	0.715919i	$0.253992\pi$
$524$	10.9228			0.477165
$525$			31.9475i			1.39430i
$526$		−	2.87566i		−	0.125385i
$527$		−	5.29143i		−	0.230498i
$528$			1.76528i			0.0768238i
$529$	23.2595			1.01128
$530$	−1.38507			−0.0601636
$531$			1.55703i			0.0675693i
$532$	−13.9463			−0.604649
$533$	18.1499	+	12.7916i	0.786161	+	0.554064i
$534$	9.46934			0.409778
$535$		−	3.80405i		−	0.164464i
$536$	18.6849			0.807063
$537$	34.9161			1.50674
$538$		−	6.47490i		−	0.279153i
$539$			16.4882i			0.710199i
$540$		−	1.73600i		−	0.0747055i
$541$			14.7693i			0.634983i	0.948261	+	0.317491i	$0.102840\pi$
$541$			14.7693i			0.634983i	−0.948261	+	0.317491i	$0.897160\pi$
$542$	−30.2140			−1.29780
$543$	3.72839			0.160000
$544$		−	28.4857i		−	1.22131i
$545$	−2.36926			−0.101488
$546$	12.6535	−	17.9541i	0.541521	−	0.768364i
$547$	11.1112			0.475082			0.237541	−	0.971377i	$-0.423659\pi$
$547$	11.1112			0.475082			0.237541	+	0.971377i	$0.423659\pi$
$548$			12.4067i			0.529987i
$549$	1.51984			0.0648651
$550$	−9.65906			−0.411864
$551$		−	14.5898i		−	0.621546i
$552$			33.5455i			1.42779i
$553$		−	16.0645i		−	0.683134i
$554$		−	15.2559i		−	0.648160i
$555$	−2.36101			−0.100219
$556$	17.7069			0.750938
$557$			22.7023i			0.961925i	0.876741	+	0.480963i	$0.159713\pi$
$557$			22.7023i			0.961925i	−0.876741	+	0.480963i	$0.840287\pi$
$558$	0.148329			0.00627927
$559$	−14.7940	+	20.9912i	−0.625719	+	0.887833i
$560$	0.559950			0.0236622
$561$		−	18.7004i		−	0.789532i
$562$	−21.1169			−0.890762
$563$	−1.26121			−0.0531536			−0.0265768	−	0.999647i	$-0.508461\pi$
$563$	−1.26121			−0.0531536			−0.0265768	+	0.999647i	$0.508461\pi$
$564$		−	9.01513i		−	0.379606i
$565$			5.99796i			0.252336i
$566$			10.4498i			0.439238i
$567$		−	32.7725i		−	1.37632i
$568$	−10.5611			−0.443133
$569$	−5.71226			−0.239470			−0.119735	−	0.992806i	$-0.538205\pi$
$569$	−5.71226			−0.239470			−0.119735	+	0.992806i	$0.538205\pi$
$570$			1.48189i			0.0620697i
$571$	10.4480			0.437234			0.218617	−	0.975811i	$-0.429846\pi$
$571$	10.4480			0.437234			0.218617	+	0.975811i	$0.429846\pi$
$572$	−6.92889	−	4.88329i	−0.289712	−	0.204181i
$573$	−10.0089			−0.418128
$574$			22.2555i			0.928927i
$575$	−33.4322			−1.39422
$576$	0.956599			0.0398583
$577$			15.5655i			0.647999i	0.946057	+	0.324000i	$0.105028\pi$
$577$			15.5655i			0.647999i	−0.946057	+	0.324000i	$0.894972\pi$
$578$		−	10.3098i		−	0.428830i
$579$		−	12.9361i		−	0.537606i
$580$		−	1.47488i		−	0.0612410i
$581$	−21.6029			−0.896238
$582$	2.36630			0.0980862
$583$			10.6546i			0.441267i
$584$	−24.0484			−0.995129
$585$	−0.135606	−	0.0955712i	−0.00560661	−	0.00395138i
$586$	27.3559			1.13006
$587$			10.6110i			0.437962i	0.975729	+	0.218981i	$0.0702733\pi$
$587$			10.6110i			0.437962i	−0.975729	+	0.218981i	$0.929727\pi$
$588$	−14.8682			−0.613154
$589$	3.22555			0.132906
$590$		−	2.68149i		−	0.110395i
$591$		−	17.9361i		−	0.737793i
$592$		−	2.40605i		−	0.0988882i
$593$		−	46.0558i		−	1.89129i	−0.325206	−	0.945643i	$-0.605434\pi$
$593$		−	46.0558i		−	1.89129i	0.325206	−	0.945643i	$-0.394566\pi$
$594$	10.4619			0.429257
$595$	−5.93182			−0.243181
$596$			3.33144i			0.136461i
$597$	−36.8906			−1.50983
$598$	18.7884	+	13.2415i	0.768316	+	0.541487i
$599$	−8.40314			−0.343343			−0.171672	−	0.985154i	$-0.554917\pi$
$599$	−8.40314			−0.343343			−0.171672	+	0.985154i	$0.554917\pi$
$600$		−	24.2436i		−	0.989743i
$601$	44.1276			1.80000			0.900001	−	0.435888i	$-0.143566\pi$
$601$	44.1276			1.80000			0.900001	+	0.435888i	$0.143566\pi$
$602$	−25.7395			−1.04906
$603$		−	1.01062i		−	0.0411558i
$604$		−	22.5682i		−	0.918287i
$605$			1.92044i			0.0780769i
$606$		−	10.6182i		−	0.431334i
$607$	10.1399			0.411564			0.205782	−	0.978598i	$-0.434026\pi$
$607$	10.1399			0.411564			0.205782	+	0.978598i	$0.434026\pi$
$608$	17.3643			0.704215
$609$		−	29.3981i		−	1.19127i
$610$	−2.61745			−0.105977
$611$	−14.0542	−	9.90503i	−0.568574	−	0.400715i
$612$	−0.939050			−0.0379589
$613$			0.969289i			0.0391492i	0.999808	+	0.0195746i	$0.00623119\pi$
$613$			0.969289i			0.0391492i	−0.999808	+	0.0195746i	$0.993769\pi$
$614$	9.64325			0.389170
$615$	−3.01855			−0.121720
$616$		−	23.6486i		−	0.952830i
$617$		−	8.86561i		−	0.356916i	−0.983948	−	0.178458i	$-0.942889\pi$
$617$		−	8.86561i		−	0.356916i	0.983948	−	0.178458i	$-0.0571108\pi$
$618$			16.0304i			0.644838i
$619$		−	23.1571i		−	0.930763i	−0.885110	−	0.465381i	$-0.845917\pi$
$619$		−	23.1571i		−	0.930763i	0.885110	−	0.465381i	$-0.154083\pi$
$620$	0.326069			0.0130953
$621$	36.2109			1.45309
$622$		−	5.75658i		−	0.230818i
$623$	−23.1058			−0.925713
$624$	−1.74896	+	2.48160i	−0.0700145	+	0.0993435i
$625$	23.7390			0.949561
$626$		−	8.02126i		−	0.320594i
$627$	11.3994			0.455247
$628$	21.2782			0.849094
$629$			25.4885i			1.01629i
$630$		−	0.166280i		−	0.00662477i
$631$		−	0.538705i		−	0.0214455i	−0.999943	−	0.0107228i	$-0.996587\pi$
$631$		−	0.538705i		−	0.0214455i	0.999943	−	0.0107228i	$-0.00341323\pi$
$632$			12.1907i			0.484921i
$633$	46.0044			1.82851
$634$	13.5182			0.536875
$635$			0.398147i			0.0158000i
$636$	−9.60770			−0.380970
$637$	−16.3359	+	23.1789i	−0.647250	+	0.918383i
$638$	8.88826			0.351890
$639$			0.571226i			0.0225973i
$640$	1.48309			0.0586242
$641$	−10.1422			−0.400593			−0.200296	−	0.979735i	$-0.564191\pi$
$641$	−10.1422			−0.400593			−0.200296	+	0.979735i	$0.564191\pi$
$642$			20.6724i			0.815875i
$643$		−	40.0663i		−	1.58006i	−0.613068	−	0.790030i	$-0.710065\pi$
$643$		−	40.0663i		−	1.58006i	0.613068	−	0.790030i	$-0.289935\pi$
$644$		−	29.4074i		−	1.15881i
$645$		−	3.49109i		−	0.137461i
$646$	15.9979			0.629428
$647$	−9.30740			−0.365912			−0.182956	−	0.983121i	$-0.558567\pi$
$647$	−9.30740			−0.365912			−0.182956	+	0.983121i	$0.558567\pi$
$648$			24.8697i			0.976974i
$649$	−20.6272			−0.809690
$650$	−13.5786	−	9.56979i	−0.532595	−	0.375358i
$651$	6.49940			0.254731
$652$			21.8735i			0.856634i
$653$	−18.5912			−0.727530			−0.363765	−	0.931491i	$-0.618509\pi$
$653$	−18.5912			−0.727530			−0.363765	+	0.931491i	$0.618509\pi$
$654$	12.8753			0.503464
$655$			2.83200i			0.110655i
$656$		−	3.07614i		−	0.120103i
$657$			1.30072i			0.0507461i
$658$		−	17.2334i		−	0.671826i
$659$	46.6156			1.81589			0.907944	−	0.419092i	$-0.137651\pi$
$659$	46.6156			1.81589			0.907944	+	0.419092i	$0.137651\pi$
$660$	1.15236			0.0448555
$661$			11.4634i			0.445874i	0.974833	+	0.222937i	$0.0715645\pi$
$661$			11.4634i			0.445874i	−0.974833	+	0.222937i	$0.928436\pi$
$662$	20.2979			0.788901
$663$	18.5276	−	26.2888i	0.719551	−	1.02097i
$664$	16.3935			0.636192
$665$		−	3.61591i		−	0.140219i
$666$	−0.714491			−0.0276860
$667$	30.7643			1.19120
$668$		−	26.3866i		−	1.02093i
$669$			40.2957i			1.55792i
$670$			1.74048i			0.0672407i
$671$			20.1346i			0.777286i
$672$	34.9886			1.34971
$673$	21.9979			0.847957			0.423978	−	0.905672i	$-0.360633\pi$
$673$	21.9979			0.847957			0.423978	+	0.905672i	$0.360633\pi$
$674$		−	13.5401i		−	0.521546i
$675$	−26.1700			−1.00728
$676$	−4.90239	−	13.7297i	−0.188553	−	0.528066i
$677$	−21.3442			−0.820325			−0.410162	−	0.912013i	$-0.634528\pi$
$677$	−21.3442			−0.820325			−0.410162	+	0.912013i	$0.634528\pi$
$678$		−	32.5948i		−	1.25180i
$679$	−5.77392			−0.221583
$680$	4.50141			0.172621
$681$			25.2224i			0.966525i
$682$			1.96504i			0.0752452i
$683$			51.2441i			1.96080i	0.197019	+	0.980400i	$0.436874\pi$
$683$			51.2441i			1.96080i	−0.197019	+	0.980400i	$0.563126\pi$
$684$		−	0.572426i		−	0.0218872i
$685$	−3.21673			−0.122905
$686$	−3.12537			−0.119327
$687$			22.3558i			0.852928i
$688$	3.55769			0.135636
$689$	−10.5561	+	14.9780i	−0.402155	+	0.570618i
$690$	−3.12474			−0.118957
$691$			1.09848i			0.0417883i	0.999782	+	0.0208942i	$0.00665130\pi$
$691$			1.09848i			0.0417883i	−0.999782	+	0.0208942i	$0.993349\pi$
$692$	12.7596			0.485046
$693$	−1.27910			−0.0485891
$694$			9.09278i			0.345157i
$695$			4.59093i			0.174144i
$696$			22.3090i			0.845620i
$697$			32.5870i			1.23432i
$698$	1.92345			0.0728036
$699$	−1.08215			−0.0409307
$700$			21.2530i			0.803287i
$701$	−15.7633			−0.595372			−0.297686	−	0.954664i	$-0.596215\pi$
$701$	−15.7633			−0.595372			−0.297686	+	0.954664i	$0.596215\pi$
$702$	14.7072	+	10.3652i	0.555087	+	0.391209i
$703$	−15.5372			−0.585998
$704$			12.6729i			0.477626i
$705$	2.33739			0.0880312
$706$	10.9970			0.413876
$707$			25.9090i			0.974408i
$708$		−	18.6005i		−	0.699050i
$709$			16.6481i			0.625233i	0.949879	+	0.312617i	$0.101206\pi$
$709$			16.6481i			0.625233i	−0.949879	+	0.312617i	$0.898794\pi$
$710$		−	0.983757i		−	0.0369198i
$711$	0.659369			0.0247283
$712$	17.5340			0.657115
$713$			6.80143i			0.254716i
$714$	32.2354			1.20638
$715$	1.26611	−	1.79648i	0.0473498	−	0.0671846i
$716$	23.2278			0.868064
$717$		−	8.08018i		−	0.301760i
$718$	−23.3696			−0.872145
$719$	−20.8992			−0.779408			−0.389704	−	0.920940i	$-0.627423\pi$
$719$	−20.8992			−0.779408			−0.389704	+	0.920940i	$0.627423\pi$
$720$			0.0229831i			0.000856531i
$721$		−	39.1152i		−	1.45673i
$722$		−	8.05703i		−	0.299852i
$723$		−	34.2016i		−	1.27197i
$724$	2.48029			0.0921794
$725$	−22.2336			−0.825736
$726$		−	10.4363i		−	0.387326i
$727$	−12.5078			−0.463889			−0.231945	−	0.972729i	$-0.574509\pi$
$727$	−12.5078			−0.463889			−0.231945	+	0.972729i	$0.574509\pi$
$728$	23.4301	−	33.2449i	0.868375	−	1.23214i
$729$	28.2700			1.04704
$730$		−	2.24009i		−	0.0829094i
$731$	−37.6883			−1.39395
$732$	−18.1562			−0.671074
$733$		−	21.1736i		−	0.782064i	−0.920377	−	0.391032i	$-0.872118\pi$
$733$		−	21.1736i		−	0.782064i	0.920377	−	0.391032i	$-0.127882\pi$
$734$		−	12.8429i		−	0.474042i
$735$		−	3.85494i		−	0.142191i
$736$			36.6146i			1.34963i
$737$	13.3886			0.493174
$738$	−0.913477			−0.0336255
$739$		−	23.8513i		−	0.877385i	−0.898637	−	0.438693i	$-0.855442\pi$
$739$		−	23.8513i		−	0.877385i	0.898637	−	0.438693i	$-0.144558\pi$
$740$	−1.57065			−0.0577384
$741$	16.0251	+	11.2940i	0.588696	+	0.414896i
$742$	−18.3661			−0.674241
$743$			10.3245i			0.378771i	0.981903	+	0.189385i	$0.0606496\pi$
$743$			10.3245i			0.378771i	−0.981903	+	0.189385i	$0.939350\pi$
$744$	−4.93212			−0.180820
$745$	−0.863756			−0.0316456
$746$			8.64260i			0.316428i
$747$		−	0.886689i		−	0.0324423i
$748$		−	12.4404i		−	0.454865i
$749$		−	50.4420i		−	1.84311i
$750$	4.55540			0.166340
$751$	43.3903			1.58333			0.791667	−	0.610953i	$-0.209213\pi$
$751$	43.3903			1.58333			0.791667	+	0.610953i	$0.209213\pi$
$752$			2.38198i			0.0868619i
$753$	−36.8695			−1.34360
$754$	12.4950	+	8.80612i	0.455041	+	0.320700i
$755$	5.85135			0.212952
$756$		−	23.0194i		−	0.837209i
$757$	14.4887			0.526600			0.263300	−	0.964714i	$-0.415189\pi$
$757$	14.4887			0.526600			0.263300	+	0.964714i	$0.415189\pi$
$758$	−7.18102			−0.260826
$759$			24.0369i			0.872483i
$760$			2.74397i			0.0995341i
$761$		−	45.1186i		−	1.63555i	−0.575541	−	0.817773i	$-0.695208\pi$
$761$		−	45.1186i		−	1.63555i	0.575541	−	0.817773i	$-0.304792\pi$
$762$		−	2.16366i		−	0.0783811i
$763$	−31.4166			−1.13736
$764$	−6.65839			−0.240892
$765$		−	0.243471i		−	0.00880273i
$766$	3.53460			0.127710
$767$	−28.9975	−	20.4366i	−1.04704	−	0.737923i
$768$	−28.4400			−1.02624
$769$		−	13.9625i		−	0.503502i	−0.967792	−	0.251751i	$-0.918994\pi$
$769$		−	13.9625i		−	0.503502i	0.967792	−	0.251751i	$-0.0810064\pi$
$770$	2.20285			0.0793853
$771$	−26.6853			−0.961047
$772$		−	8.60569i		−	0.309726i
$773$		−	20.2617i		−	0.728762i	−0.931250	−	0.364381i	$-0.881281\pi$
$773$		−	20.2617i		−	0.728762i	0.931250	−	0.364381i	$-0.118719\pi$
$774$		−	1.05648i		−	0.0379743i
$775$		−	4.91546i		−	0.176568i
$776$	4.38158			0.157290
$777$	−31.3072			−1.12314
$778$			1.86284i			0.0667860i
$779$	−19.8644			−0.711714
$780$	1.61997	+	1.14171i	0.0580042	+	0.0408797i
$781$	−7.56749			−0.270786
$782$			33.7334i			1.20630i
$783$	24.0816			0.860606
$784$	3.92848			0.140303
$785$			5.51689i			0.196906i
$786$		−	15.3900i		−	0.548942i
$787$			39.5845i			1.41103i	0.708693	+	0.705517i	$0.249285\pi$
$787$			39.5845i			1.41103i	−0.708693	+	0.705517i	$0.750715\pi$
$788$		−	11.9319i		−	0.425057i
$789$	5.17184			0.184122
$790$	−1.13556			−0.0404013
$791$			79.5334i			2.82788i
$792$	0.970657			0.0344908
$793$	−19.9485	+	28.3049i	−0.708391	+	1.00514i
$794$	7.34596			0.260698
$795$		−	2.49103i		−	0.0883477i
$796$	−24.5413			−0.869844
$797$	−47.8024			−1.69325			−0.846625	−	0.532190i	$-0.821369\pi$
$797$	−47.8024			−1.69325			−0.846625	+	0.532190i	$0.821369\pi$
$798$			19.6500i			0.695602i
$799$		−	25.2335i		−	0.892696i
$800$		−	26.4617i		−	0.935562i
$801$		−	0.948376i		−	0.0335092i
$802$	−22.4277			−0.791951
$803$	−17.2318			−0.608095
$804$			12.0731i			0.425784i
$805$	7.62456			0.268731
$806$	−1.94688	+	2.76242i	−0.0685758	+	0.0973022i
$807$	11.6450			0.409924
$808$		−	19.6613i		−	0.691681i
$809$	−26.7287			−0.939730			−0.469865	−	0.882738i	$-0.655697\pi$
$809$	−26.7287			−0.939730			−0.469865	+	0.882738i	$0.655697\pi$
$810$	−2.31660			−0.0813969
$811$			27.4420i			0.963621i	0.876276	+	0.481810i	$0.160021\pi$
$811$			27.4420i			0.963621i	−0.876276	+	0.481810i	$0.839979\pi$
$812$		−	19.5570i		−	0.686315i
$813$		−	54.3394i		−	1.90577i
$814$		−	9.46545i		−	0.331764i
$815$	−5.67124			−0.198655
$816$	−4.45555			−0.155975
$817$		−	22.9740i		−	0.803759i
$818$	−25.0412			−0.875545
$819$	−1.79814	−	1.26728i	−0.0628322	−	0.0442824i
$820$	−2.00808			−0.0701252
$821$			30.2439i			1.05552i	0.849394	+	0.527759i	$0.176968\pi$
$821$			30.2439i			1.05552i	−0.849394	+	0.527759i	$0.823032\pi$
$822$	17.4807			0.609710
$823$	−17.3317			−0.604144			−0.302072	−	0.953285i	$-0.597678\pi$
$823$	−17.3317			−0.604144			−0.302072	+	0.953285i	$0.597678\pi$
$824$			29.6829i			1.03405i
$825$		−	17.3717i		−	0.604804i
$826$		−	35.5568i		−	1.23718i
$827$		−	5.96729i		−	0.207503i	−0.994603	−	0.103751i	$-0.966915\pi$
$827$		−	5.96729i		−	0.207503i	0.994603	−	0.103751i	$-0.0330847\pi$
$828$	1.20702			0.0419470
$829$	−9.28049			−0.322325			−0.161162	−	0.986928i	$-0.551524\pi$
$829$	−9.28049			−0.322325			−0.161162	+	0.986928i	$0.551524\pi$
$830$			1.52704i			0.0530045i
$831$	27.4375			0.951795
$832$	−12.5557	+	17.8153i	−0.435292	+	0.617635i
$833$	−41.6163			−1.44192
$834$		−	24.9485i		−	0.863897i
$835$	6.84137			0.236755
$836$	7.58339			0.262277
$837$			5.32402i			0.184025i
$838$			16.4550i			0.568430i
$839$			47.4252i			1.63730i	0.574294	+	0.818649i	$0.305277\pi$
$839$			47.4252i			1.63730i	−0.574294	+	0.818649i	$0.694723\pi$
$840$			5.52902i			0.190769i
$841$	−8.54064			−0.294505
$842$	−25.9089			−0.892880
$843$		−	37.9784i		−	1.30805i
$844$	30.6042			1.05344
$845$	3.55976	−	1.27106i	0.122459	−	0.0437258i
$846$	0.707343			0.0243190
$847$			25.4651i			0.874992i
$848$	2.53855			0.0871742
$849$	−18.7938			−0.645002
$850$		−	24.3794i		−	0.836207i
$851$		−	32.7620i		−	1.12307i
$852$		−	6.82395i		−	0.233785i
$853$			28.2350i			0.966747i	0.875414	+	0.483374i	$0.160589\pi$
$853$			28.2350i			0.966747i	−0.875414	+	0.483374i	$0.839411\pi$
$854$	−34.7075			−1.18767
$855$	0.148415			0.00507569
$856$			38.2783i			1.30833i
$857$	−36.1912			−1.23627			−0.618133	−	0.786073i	$-0.712111\pi$
$857$	−36.1912			−1.23627			−0.618133	+	0.786073i	$0.712111\pi$
$858$	−6.88044	+	9.76265i	−0.234894	+	0.333291i
$859$	−29.9776			−1.02282			−0.511411	−	0.859336i	$-0.670877\pi$
$859$	−29.9776			−1.02282			−0.511411	+	0.859336i	$0.670877\pi$
$860$		−	2.32243i		−	0.0791943i
$861$	−40.0262			−1.36409
$862$	22.1246			0.753567
$863$			28.1898i			0.959591i	0.877380	+	0.479795i	$0.159289\pi$
$863$			28.1898i			0.959591i	−0.877380	+	0.479795i	$0.840711\pi$
$864$			28.6611i			0.975070i
$865$			3.30823i			0.112483i
$866$			16.2920i			0.553624i
$867$	18.5420			0.629719
$868$	4.32370			0.146756
$869$			8.73520i			0.296321i
$870$	−2.07807			−0.0704531
$871$	18.8214	+	13.2648i	0.637740	+	0.449461i
$872$	23.8407			0.807349
$873$		−	0.236990i		−	0.00802091i
$874$	−20.5632			−0.695559
$875$	−11.1155			−0.375771
$876$		−	15.5387i		−	0.525002i
$877$		−	5.32985i		−	0.179976i	−0.995943	−	0.0899882i	$-0.971317\pi$
$877$		−	5.32985i		−	0.179976i	0.995943	−	0.0899882i	$-0.0286829\pi$
$878$			19.6658i			0.663689i
$879$			49.1992i			1.65945i
$880$	−0.304477			−0.0102639
$881$	−10.7814			−0.363235			−0.181618	−	0.983369i	$-0.558133\pi$
$881$	−10.7814			−0.363235			−0.181618	+	0.983369i	$0.558133\pi$
$882$		−	1.16658i		−	0.0392809i
$883$	17.5068			0.589149			0.294575	−	0.955628i	$-0.404822\pi$
$883$	17.5068			0.589149			0.294575	+	0.955628i	$0.404822\pi$
$884$	12.3254	−	17.4885i	0.414548	−	0.588202i
$885$	4.82263			0.162111
$886$			30.4367i			1.02254i
$887$	−15.1926			−0.510119			−0.255060	−	0.966925i	$-0.582095\pi$
$887$	−15.1926			−0.510119			−0.255060	+	0.966925i	$0.582095\pi$
$888$	23.7577			0.797257
$889$			5.27946i			0.177067i
$890$			1.63328i			0.0547477i
$891$			17.8203i			0.597002i
$892$			26.8066i			0.897551i
$893$	15.3818			0.514732
$894$	4.69392			0.156988
$895$			6.02237i			0.201306i
$896$	19.6658			0.656989
$897$	−23.8147	+	33.7907i	−0.795151	+	1.12824i
$898$	20.8188			0.694733
$899$			4.52320i			0.150857i
$900$	−0.872328			−0.0290776
$901$	−26.8921			−0.895905
$902$		−	12.1016i		−	0.402938i
$903$		−	46.2921i		−	1.54050i
$904$		−	60.3546i		−	2.00736i
$905$			0.643076i			0.0213766i
$906$	−31.7981			−1.05642
$907$	23.0972			0.766928			0.383464	−	0.923556i	$-0.374731\pi$
$907$	23.0972			0.766928			0.383464	+	0.923556i	$0.374731\pi$
$908$			16.7791i			0.556834i
$909$	−1.06343			−0.0352719
$910$	3.09674	+	2.18249i	0.102656	+	0.0723490i
$911$	45.8733			1.51985			0.759926	−	0.650010i	$-0.225235\pi$
$911$	45.8733			1.51985			0.759926	+	0.650010i	$0.225235\pi$
$912$		−	2.71601i		−	0.0899360i
$913$	11.7467			0.388759
$914$	−23.1532			−0.765841
$915$		−	4.70744i		−	0.155623i
$916$			14.8721i			0.491389i
$917$			37.5525i			1.24009i
$918$			26.4058i			0.871520i
$919$	11.6629			0.384723			0.192362	−	0.981324i	$-0.438385\pi$
$919$	11.6629			0.384723			0.192362	+	0.981324i	$0.438385\pi$
$920$	−5.78596			−0.190758
$921$			17.3432i			0.571479i
$922$	1.75434			0.0577761
$923$	−10.6383	−	7.49755i	−0.350163	−	0.246785i
$924$	15.2803			0.502686
$925$			23.6774i			0.778509i
$926$	31.5247			1.03597
$927$	1.60548			0.0527310
$928$			24.3500i			0.799329i
$929$		−	32.8627i		−	1.07819i	−0.842244	−	0.539096i	$-0.818766\pi$
$929$		−	32.8627i		−	1.07819i	0.842244	−	0.539096i	$-0.181234\pi$
$930$		−	0.459424i		−	0.0150651i
$931$		−	25.3684i		−	0.831416i
$932$	−0.719897			−0.0235810
$933$	10.3531			0.338946
$934$			11.1580i			0.365101i
$935$	3.22547			0.105484
$936$	1.36454	+	0.961686i	0.0446013	+	0.0314337i
$937$	−51.2949			−1.67573			−0.837865	−	0.545877i	$-0.816197\pi$
$937$	−51.2949			−1.67573			−0.837865	+	0.545877i	$0.816197\pi$
$938$			23.0789i			0.753553i
$939$	14.4261			0.470779
$940$	1.55494			0.0507165
$941$			41.9245i			1.36670i	0.730091	+	0.683350i	$0.239478\pi$
$941$			41.9245i			1.36670i	−0.730091	+	0.683350i	$0.760522\pi$
$942$		−	29.9805i		−	0.976818i
$943$		−	41.8863i		−	1.36400i
$944$			4.91463i			0.159958i
$945$	5.96835			0.194150
$946$	13.9960			0.455049
$947$			26.4877i			0.860736i	0.902654	+	0.430368i	$0.141616\pi$
$947$			26.4877i			0.860736i	−0.902654	+	0.430368i	$0.858384\pi$
$948$	−7.87692			−0.255831
$949$	−24.2242	−	17.0725i	−0.786349	−	0.554197i
$950$	14.8612			0.482161
$951$			24.3122i			0.788378i
$952$	59.6890			1.93453
$953$	−45.6327			−1.47819			−0.739094	−	0.673603i	$-0.764746\pi$
$953$	−45.6327			−1.47819			−0.739094	+	0.673603i	$0.764746\pi$
$954$		−	0.753837i		−	0.0244064i
$955$		−	1.72635i		−	0.0558633i
$956$		−	5.37531i		−	0.173850i
$957$			15.9854i			0.516735i
$958$	8.43987			0.272680
$959$	−42.6540			−1.37737
$960$		−	2.96290i		−	0.0956273i
$961$	−1.00000			−0.0322581
$962$	9.37797	−	13.3064i	0.302358	−	0.429016i
$963$	2.07039			0.0667174
$964$		−	22.7525i		−	0.732809i
$965$	2.23123			0.0718259
$966$	−41.4343			−1.33313
$967$		−	11.1815i		−	0.359571i	−0.983706	−	0.179786i	$-0.942460\pi$
$967$		−	11.1815i		−	0.359571i	0.983706	−	0.179786i	$-0.0575404\pi$
$968$		−	19.3244i		−	0.621111i
$969$			28.7720i			0.924289i
$970$			0.408142i			0.0131046i
$971$	−1.14584			−0.0367716			−0.0183858	−	0.999831i	$-0.505853\pi$
$971$	−1.14584			−0.0367716			−0.0183858	+	0.999831i	$0.505853\pi$
$972$	1.84232			0.0590926
$973$			60.8760i			1.95159i
$974$	34.2144			1.09630
$975$	17.2111	−	24.4209i	0.551197	−	0.782093i
$976$	4.79725			0.153556
$977$		−	60.2613i		−	1.92793i	−0.266031	−	0.963964i	$-0.585712\pi$
$977$		−	60.2613i		−	1.92793i	0.266031	−	0.963964i	$-0.414288\pi$
$978$	30.8193			0.985493
$979$	12.5639			0.401545
$980$		−	2.56448i		−	0.0819194i
$981$		−	1.28949i		−	0.0411703i
$982$		−	8.48134i		−	0.270650i
$983$			0.0739659i			0.00235915i	0.999999	+	0.00117957i	$0.000375470\pi$
$983$			0.0739659i			0.00235915i	−0.999999	+	0.00117957i	$0.999625\pi$
$984$	30.3742			0.968295
$985$	3.09364			0.0985715
$986$			22.4339i			0.714442i
$987$	30.9939			0.986548
$988$	10.6606	+	7.51330i	0.339160	+	0.239030i
$989$	48.4433			1.54041
$990$			0.0904161i			0.00287361i
$991$	8.14285			0.258666			0.129333	−	0.991601i	$-0.458716\pi$
$991$	8.14285			0.258666			0.129333	+	0.991601i	$0.458716\pi$
$992$	−5.38336			−0.170922
$993$			36.5055i			1.15847i
$994$		−	13.0447i		−	0.413752i
$995$		−	6.36293i		−	0.201718i
$996$			10.5925i			0.335637i
$997$	−58.8159			−1.86272			−0.931359	−	0.364102i	$-0.881376\pi$
$997$	−58.8159			−1.86272			−0.931359	+	0.364102i	$0.881376\pi$
$998$	−24.5529			−0.777208
$999$		−	25.6454i		−	0.811386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.c.b.311.13	✓	32
13.5	odd	4		5239.2.a.l.1.6		16
13.8	odd	4		5239.2.a.k.1.11		16
13.12	even	2	inner	403.2.c.b.311.20	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.c.b.311.13	✓	32	1.1	even	1	trivial
403.2.c.b.311.20	yes	32	13.12	even	2	inner
5239.2.a.k.1.11		16	13.8	odd	4
5239.2.a.l.1.6		16	13.5	odd	4

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.937316i q^{2} +1.68575 q^{3} +1.12144 q^{4} +0.290760i q^{5} -1.58008i q^{6} +3.85549i q^{7} -2.92577i q^{8} -0.158249 q^{9} +O(q^{10})\)	\(q-0.937316i q^{2} +1.68575 q^{3} +1.12144 q^{4} +0.290760i q^{5} -1.58008i q^{6} +3.85549i q^{7} -2.92577i q^{8} -0.158249 q^{9} +0.272534 q^{10} -2.09645i q^{11} +1.89046 q^{12} +(2.07708 - 2.94716i) q^{13} +3.61382 q^{14} +0.490148i q^{15} -0.499499 q^{16} +5.29143 q^{17} +0.148329i q^{18} +3.22555i q^{19} +0.326069i q^{20} +6.49940i q^{21} -1.96504 q^{22} -6.80143 q^{23} -4.93212i q^{24} +4.91546 q^{25} +(-2.76242 - 1.94688i) q^{26} -5.32402 q^{27} +4.32370i q^{28} -4.52320 q^{29} +0.459424 q^{30} -1.00000i q^{31} -5.38336i q^{32} -3.53409i q^{33} -4.95974i q^{34} -1.12102 q^{35} -0.177466 q^{36} +4.81693i q^{37} +3.02336 q^{38} +(3.50143 - 4.96818i) q^{39} +0.850698 q^{40} +6.15845i q^{41} +6.09199 q^{42} -7.12251 q^{43} -2.35104i q^{44} -0.0460124i q^{45} +6.37509i q^{46} -4.76874i q^{47} -0.842031 q^{48} -7.86484 q^{49} -4.60734i q^{50} +8.92003 q^{51} +(2.32931 - 3.30506i) q^{52} -5.08219 q^{53} +4.99029i q^{54} +0.609564 q^{55} +11.2803 q^{56} +5.43746i q^{57} +4.23967i q^{58} -9.83912i q^{59} +0.549671i q^{60} -9.60411 q^{61} -0.937316 q^{62} -0.610127i q^{63} -6.04491 q^{64} +(0.856916 + 0.603930i) q^{65} -3.31256 q^{66} +6.38630i q^{67} +5.93402 q^{68} -11.4655 q^{69} +1.05075i q^{70} -3.60967i q^{71} +0.463000i q^{72} -8.21949i q^{73} +4.51499 q^{74} +8.28623 q^{75} +3.61725i q^{76} +8.08285 q^{77} +(-4.65675 - 3.28195i) q^{78} -4.16666 q^{79} -0.145234i q^{80} -8.50021 q^{81} +5.77241 q^{82} +5.60314i q^{83} +7.28867i q^{84} +1.53854i q^{85} +6.67605i q^{86} -7.62499 q^{87} -6.13374 q^{88} +5.99295i q^{89} -0.0431282 q^{90} +(11.3628 + 8.00815i) q^{91} -7.62739 q^{92} -1.68575i q^{93} -4.46982 q^{94} -0.937859 q^{95} -9.07500i q^{96} +1.49758i q^{97} +7.37184i q^{98} +0.331761i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9}+O(q^{10}) \) 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9	\( 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9} + 4 q^{10} - 16 q^{12} + 10 q^{13} - 16 q^{14} + 28 q^{16} - 8 q^{17} - 16 q^{22} - 8 q^{23} + 4 q^{25} + 18 q^{26} + 20 q^{27} - 16 q^{29} + 40 q^{30} - 4 q^{35} - 44 q^{36} + 12 q^{38} + 4 q^{39} + 28 q^{40} + 28 q^{42} - 32 q^{43} - 64 q^{49} - 64 q^{52} - 12 q^{53} + 44 q^{55} + 8 q^{56} + 16 q^{61} + 8 q^{62} - 76 q^{64} - 66 q^{65} - 68 q^{66} + 64 q^{68} + 20 q^{69} + 16 q^{74} - 32 q^{77} - 20 q^{78} + 64 q^{79} - 16 q^{81} + 12 q^{82} - 72 q^{87} + 80 q^{88} + 68 q^{90} + 22 q^{91} + 28 q^{92} + 88 q^{94} + 4 q^{95}+O(q^{100}) \) 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9 + 4 * q^10 - 16 * q^12 + 10 * q^13 - 16 * q^14 + 28 * q^16 - 8 * q^17 - 16 * q^22 - 8 * q^23 + 4 * q^25 + 18 * q^26 + 20 * q^27 - 16 * q^29 + 40 * q^30 - 4 * q^35 - 44 * q^36 + 12 * q^38 + 4 * q^39 + 28 * q^40 + 28 * q^42 - 32 * q^43 - 64 * q^49 - 64 * q^52 - 12 * q^53 + 44 * q^55 + 8 * q^56 + 16 * q^61 + 8 * q^62 - 76 * q^64 - 66 * q^65 - 68 * q^66 + 64 * q^68 + 20 * q^69 + 16 * q^74 - 32 * q^77 - 20 * q^78 + 64 * q^79 - 16 * q^81 + 12 * q^82 - 72 * q^87 + 80 * q^88 + 68 * q^90 + 22 * q^91 + 28 * q^92 + 88 * q^94 + 4 * q^95

Introduction

L-functions

Modular forms

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