LMFDB - Embedded newform 115.2.e.a.68.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(22,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("115.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.e (of order $4$, degree $2$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{18} + 3 x^{16} + 80 x^{14} - 600 x^{12} + 3500 x^{10} - 15000 x^{8} + 50000 x^{6} + \cdots + 9765625 $ x^20 - 6x^18 + 3x^16 + 80x^14 - 600x^12 + 3500x^10 - 15000x^8 + 50000x^6 + 46875x^4 - 2343750*x^2 + 9765625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			68.4
Root			$-0.0985483 - 2.23390i$ of defining polynomial
Character	$\chi$	$=$	115.68
Dual form			115.2.e.a.22.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.819998 + 0.819998i) q^{2} +(1.37823 + 1.37823i) q^{3} +0.655207i q^{4} +(2.23390 + 0.0985483i) q^{5} -2.26029 q^{6} +(-1.78496 - 1.78496i) q^{7} +(-2.17726 - 2.17726i) q^{8} +0.799034i q^{9} +O(q^{10})$	\(q+(-0.819998 + 0.819998i) q^{2} +(1.37823 + 1.37823i) q^{3} +0.655207i q^{4} +(2.23390 + 0.0985483i) q^{5} -2.26029 q^{6} +(-1.78496 - 1.78496i) q^{7} +(-2.17726 - 2.17726i) q^{8} +0.799034i q^{9} +(-1.91260 + 1.75098i) q^{10} +1.86370i q^{11} +(-0.903025 + 0.903025i) q^{12} +(1.52206 + 1.52206i) q^{13} +2.92733 q^{14} +(2.94300 + 3.21464i) q^{15} +2.26029 q^{16} +(-5.17689 - 5.17689i) q^{17} +(-0.655207 - 0.655207i) q^{18} +3.69906 q^{19} +(-0.0645695 + 1.46366i) q^{20} -4.92017i q^{21} +(-1.52823 - 1.52823i) q^{22} +(-4.03621 + 2.59017i) q^{23} -6.00154i q^{24} +(4.98058 + 0.440293i) q^{25} -2.49617 q^{26} +(3.03344 - 3.03344i) q^{27} +(1.16952 - 1.16952i) q^{28} -4.99452i q^{29} +(-5.04925 - 0.222748i) q^{30} +0.833946 q^{31} +(2.50109 - 2.50109i) q^{32} +(-2.56861 + 2.56861i) q^{33} +8.49009 q^{34} +(-3.81151 - 4.16332i) q^{35} -0.523533 q^{36} +(3.00607 + 3.00607i) q^{37} +(-3.03322 + 3.03322i) q^{38} +4.19549i q^{39} +(-4.64921 - 5.07835i) q^{40} +0.310413 q^{41} +(4.03453 + 4.03453i) q^{42} +(-2.17082 + 2.17082i) q^{43} -1.22111 q^{44} +(-0.0787435 + 1.78496i) q^{45} +(1.18576 - 5.43362i) q^{46} +(-8.19401 + 8.19401i) q^{47} +(3.11520 + 3.11520i) q^{48} -0.627842i q^{49} +(-4.44510 + 3.72302i) q^{50} -14.2699i q^{51} +(-0.997262 + 0.997262i) q^{52} +(6.21727 - 6.21727i) q^{53} +4.97482i q^{54} +(-0.183665 + 4.16332i) q^{55} +7.77265i q^{56} +(5.09815 + 5.09815i) q^{57} +(4.09550 + 4.09550i) q^{58} +2.19330i q^{59} +(-2.10626 + 1.92827i) q^{60} +12.5637i q^{61} +(-0.683834 + 0.683834i) q^{62} +(1.42624 - 1.42624i) q^{63} +8.62237i q^{64} +(3.25012 + 3.55011i) q^{65} -4.21251i q^{66} +(-1.14237 - 1.14237i) q^{67} +(3.39193 - 3.39193i) q^{68} +(-9.13268 - 1.99298i) q^{69} +(6.53934 + 0.288483i) q^{70} -13.5516 q^{71} +(1.73971 - 1.73971i) q^{72} +(-6.62331 - 6.62331i) q^{73} -4.92994 q^{74} +(6.25755 + 7.47120i) q^{75} +2.42365i q^{76} +(3.32663 - 3.32663i) q^{77} +(-3.44029 - 3.44029i) q^{78} +1.36002 q^{79} +(5.04925 + 0.222748i) q^{80} +10.7586 q^{81} +(-0.254538 + 0.254538i) q^{82} +(0.256727 - 0.256727i) q^{83} +3.22373 q^{84} +(-11.0545 - 12.0748i) q^{85} -3.56014i q^{86} +(6.88360 - 6.88360i) q^{87} +(4.05777 - 4.05777i) q^{88} -10.8389 q^{89} +(-1.39909 - 1.52823i) q^{90} -5.43362i q^{91} +(-1.69710 - 2.64455i) q^{92} +(1.14937 + 1.14937i) q^{93} -13.4382i q^{94} +(8.26331 + 0.364536i) q^{95} +6.89416 q^{96} +(-9.99507 - 9.99507i) q^{97} +(0.514829 + 0.514829i) q^{98} -1.48916 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8}+O(q^{10}) $ 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8	$ 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8} - 16 q^{12} + 4 q^{13} + 8 q^{16} + 8 q^{18} - 12 q^{25} - 16 q^{26} + 4 q^{27} - 4 q^{31} + 24 q^{32} - 8 q^{35} - 32 q^{36} - 36 q^{41} + 32 q^{46} - 8 q^{47} + 4 q^{48} + 60 q^{50} + 40 q^{52} - 12 q^{55} + 36 q^{58} - 60 q^{62} - 76 q^{70} + 44 q^{71} + 72 q^{72} - 56 q^{73} + 28 q^{75} - 12 q^{77} - 44 q^{78} + 92 q^{81} + 28 q^{82} - 4 q^{85} + 24 q^{87} - 72 q^{92} - 8 q^{93} + 64 q^{95} - 104 q^{96} - 60 q^{98}+O(q^{100}) $ 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8 - 16 * q^12 + 4 * q^13 + 8 * q^16 + 8 * q^18 - 12 * q^25 - 16 * q^26 + 4 * q^27 - 4 * q^31 + 24 * q^32 - 8 * q^35 - 32 * q^36 - 36 * q^41 + 32 * q^46 - 8 * q^47 + 4 * q^48 + 60 * q^50 + 40 * q^52 - 12 * q^55 + 36 * q^58 - 60 * q^62 - 76 * q^70 + 44 * q^71 + 72 * q^72 - 56 * q^73 + 28 * q^75 - 12 * q^77 - 44 * q^78 + 92 * q^81 + 28 * q^82 - 4 * q^85 + 24 * q^87 - 72 * q^92 - 8 * q^93 + 64 * q^95 - 104 * q^96 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.819998	+	0.819998i	−0.579826	+	0.579826i	−0.934855	−	0.355029i	$-0.884471\pi$
$2$	−0.819998	+	0.819998i	−0.579826	+	0.579826i	0.355029	+	0.934855i	$0.384471\pi$
$3$	1.37823	+	1.37823i	0.795721	+	0.795721i	0.982418	−	0.186696i	$-0.0597781\pi$
$3$	1.37823	+	1.37823i	0.795721	+	0.795721i	−0.186696	+	0.982418i	$0.559778\pi$
$4$			0.655207i			0.327603i
$5$	2.23390	+	0.0985483i	0.999028	+	0.0440721i
$5$	2.23390	+	0.0985483i	0.999028	+	0.0440721i
$6$	−2.26029			−0.922760
$7$	−1.78496	−	1.78496i	−0.674651	−	0.674651i	0.284134	−	0.958785i	$-0.408294\pi$
$7$	−1.78496	−	1.78496i	−0.674651	−	0.674651i	−0.958785	+	0.284134i	$0.908294\pi$
$8$	−2.17726	−	2.17726i	−0.769779	−	0.769779i
$9$			0.799034i			0.266345i
$10$	−1.91260	+	1.75098i	−0.604817	+	0.553709i
$11$			1.86370i			0.561927i	0.959718	+	0.280964i	$0.0906541\pi$
$11$			1.86370i			0.561927i	−0.959718	+	0.280964i	$0.909346\pi$
$12$	−0.903025	+	0.903025i	−0.260681	+	0.260681i
$13$	1.52206	+	1.52206i	0.422143	+	0.422143i	0.885941	−	0.463798i	$-0.153514\pi$
$13$	1.52206	+	1.52206i	0.422143	+	0.422143i	−0.463798	+	0.885941i	$0.653514\pi$
$14$	2.92733			0.782361
$15$	2.94300	+	3.21464i	0.759879	+	0.830017i
$16$	2.26029			0.565073
$17$	−5.17689	−	5.17689i	−1.25558	−	1.25558i	−0.953181	−	0.302400i	$-0.902212\pi$
$17$	−5.17689	−	5.17689i	−1.25558	−	1.25558i	−0.302400	−	0.953181i	$-0.597788\pi$
$18$	−0.655207	−	0.655207i	−0.154434	−	0.154434i
$19$	3.69906			0.848622			0.424311	−	0.905517i	$-0.360516\pi$
$19$	3.69906			0.848622			0.424311	+	0.905517i	$0.360516\pi$
$20$	−0.0645695	+	1.46366i	−0.0144382	+	0.327285i
$21$		−	4.92017i		−	1.07367i
$22$	−1.52823	−	1.52823i	−0.325820	−	0.325820i
$23$	−4.03621	+	2.59017i	−0.841609	+	0.540087i
$23$	−4.03621	+	2.59017i	−0.841609	+	0.540087i
$24$		−	6.00154i		−	1.22506i
$25$	4.98058	+	0.440293i	0.996115	+	0.0880586i
$26$	−2.49617			−0.489539
$27$	3.03344	−	3.03344i	0.583785	−	0.583785i
$28$	1.16952	−	1.16952i	0.221018	−	0.221018i
$29$		−	4.99452i		−	0.927460i	−0.885977	−	0.463730i	$-0.846511\pi$
$29$		−	4.99452i		−	0.927460i	0.885977	−	0.463730i	$-0.153489\pi$
$30$	−5.04925	−	0.222748i	−0.921863	−	0.0406680i
$31$	0.833946			0.149781			0.0748905	−	0.997192i	$-0.476139\pi$
$31$	0.833946			0.149781			0.0748905	+	0.997192i	$0.476139\pi$
$32$	2.50109	−	2.50109i	0.442135	−	0.442135i
$33$	−2.56861	+	2.56861i	−0.447138	+	0.447138i
$34$	8.49009			1.45604
$35$	−3.81151	−	4.16332i	−0.644262	−	0.703729i
$36$	−0.523533			−0.0872554
$37$	3.00607	+	3.00607i	0.494195	+	0.494195i	0.909625	−	0.415430i	$-0.136369\pi$
$37$	3.00607	+	3.00607i	0.494195	+	0.494195i	−0.415430	+	0.909625i	$0.636369\pi$
$38$	−3.03322	+	3.03322i	−0.492053	+	0.492053i
$39$			4.19549i			0.671816i
$40$	−4.64921	−	5.07835i	−0.735105	−	0.802957i
$41$	0.310413			0.0484784			0.0242392	−	0.999706i	$-0.492284\pi$
$41$	0.310413			0.0484784			0.0242392	+	0.999706i	$0.492284\pi$
$42$	4.03453	+	4.03453i	0.622541	+	0.622541i
$43$	−2.17082	+	2.17082i	−0.331048	+	0.331048i	−0.852984	−	0.521937i	$-0.825210\pi$
$43$	−2.17082	+	2.17082i	−0.331048	+	0.331048i	0.521937	+	0.852984i	$0.325210\pi$
$44$	−1.22111			−0.184089
$45$	−0.0787435	+	1.78496i	−0.0117384	+	0.266086i
$46$	1.18576	−	5.43362i	0.174830	−	0.801144i
$47$	−8.19401	+	8.19401i	−1.19522	+	1.19522i	−0.219639	+	0.975581i	$0.570488\pi$
$47$	−8.19401	+	8.19401i	−1.19522	+	1.19522i	−0.975581	+	0.219639i	$0.929512\pi$
$48$	3.11520	+	3.11520i	0.449640	+	0.449640i
$49$		−	0.627842i		−	0.0896917i
$50$	−4.44510	+	3.72302i	−0.628632	+	0.526515i
$51$		−	14.2699i		−	1.99819i
$52$	−0.997262	+	0.997262i	−0.138295	+	0.138295i
$53$	6.21727	−	6.21727i	0.854008	−	0.854008i	−0.136616	−	0.990624i	$-0.543623\pi$
$53$	6.21727	−	6.21727i	0.854008	−	0.854008i	0.990624	+	0.136616i	$0.0436227\pi$
$54$			4.97482i			0.676988i
$55$	−0.183665	+	4.16332i	−0.0247653	+	0.561381i
$56$			7.77265i			1.03866i
$57$	5.09815	+	5.09815i	0.675267	+	0.675267i
$58$	4.09550	+	4.09550i	0.537765	+	0.537765i
$59$			2.19330i			0.285544i	0.989756	+	0.142772i	$0.0456015\pi$
$59$			2.19330i			0.285544i	−0.989756	+	0.142772i	$0.954398\pi$
$60$	−2.10626	+	1.92827i	−0.271916	+	0.248939i
$61$			12.5637i			1.60861i	0.594213	+	0.804307i	$0.297463\pi$
$61$			12.5637i			1.60861i	−0.594213	+	0.804307i	$0.702537\pi$
$62$	−0.683834	+	0.683834i	−0.0868470	+	0.0868470i
$63$	1.42624	−	1.42624i	0.179690	−	0.179690i
$64$			8.62237i			1.07780i
$65$	3.25012	+	3.55011i	0.403128	+	0.440337i
$66$		−	4.21251i		−	0.518524i
$67$	−1.14237	−	1.14237i	−0.139562	−	0.139562i	0.633874	−	0.773436i	$-0.281464\pi$
$67$	−1.14237	−	1.14237i	−0.139562	−	0.139562i	−0.773436	+	0.633874i	$0.781464\pi$
$68$	3.39193	−	3.39193i	0.411333	−	0.411333i
$69$	−9.13268	−	1.99298i	−1.09945	−	0.239927i
$70$	6.53934	+	0.288483i	0.781601	+	0.0344803i
$71$	−13.5516			−1.60827			−0.804137	−	0.594444i	$-0.797372\pi$
$71$	−13.5516			−1.60827			−0.804137	+	0.594444i	$0.797372\pi$
$72$	1.73971	−	1.73971i	0.205027	−	0.205027i
$73$	−6.62331	−	6.62331i	−0.775200	−	0.775200i	0.203811	−	0.979010i	$-0.434667\pi$
$73$	−6.62331	−	6.62331i	−0.775200	−	0.775200i	−0.979010	+	0.203811i	$0.934667\pi$
$74$	−4.92994			−0.573094
$75$	6.25755	+	7.47120i	0.722560	+	0.862700i
$76$			2.42365i			0.278011i
$77$	3.32663	−	3.32663i	0.379105	−	0.379105i
$78$	−3.44029	−	3.44029i	−0.389537	−	0.389537i
$79$	1.36002			0.153015			0.0765073	−	0.997069i	$-0.475623\pi$
$79$	1.36002			0.153015			0.0765073	+	0.997069i	$0.475623\pi$
$80$	5.04925	+	0.222748i	0.564524	+	0.0249040i
$81$	10.7586			1.19541
$82$	−0.254538	+	0.254538i	−0.0281090	+	0.0281090i
$83$	0.256727	−	0.256727i	0.0281794	−	0.0281794i	−0.692877	−	0.721056i	$-0.743657\pi$
$83$	0.256727	−	0.256727i	0.0281794	−	0.0281794i	0.721056	+	0.692877i	$0.243657\pi$
$84$	3.22373			0.351737
$85$	−11.0545	−	12.0748i	−1.19903	−	1.30970i
$86$		−	3.56014i		−	0.383900i
$87$	6.88360	−	6.88360i	0.738000	−	0.738000i
$88$	4.05777	−	4.05777i	0.432560	−	0.432560i
$89$	−10.8389			−1.14892			−0.574460	−	0.818533i	$-0.694788\pi$
$89$	−10.8389			−1.14892			−0.574460	+	0.818533i	$0.694788\pi$
$90$	−1.39909	−	1.52823i	−0.147477	−	0.161090i
$91$		−	5.43362i		−	0.569598i
$92$	−1.69710	−	2.64455i	−0.176934	−	0.275714i
$93$	1.14937	+	1.14937i	0.119184	+	0.119184i
$94$		−	13.4382i		−	1.38604i
$95$	8.26331	+	0.364536i	0.847797	+	0.0374006i
$96$	6.89416			0.703633
$97$	−9.99507	−	9.99507i	−1.01485	−	1.01485i	−0.999888	−	0.0149577i	$-0.995239\pi$
$97$	−9.99507	−	9.99507i	−1.01485	−	1.01485i	−0.0149577	−	0.999888i	$-0.504761\pi$
$98$	0.514829	+	0.514829i	0.0520056	+	0.0520056i
$99$	−1.48916			−0.149666
$100$	−0.288483	+	3.26331i	−0.0288483	+	0.326331i
$101$	−7.07389			−0.703878			−0.351939	−	0.936023i	$-0.614478\pi$
$101$	−7.07389			−0.703878			−0.351939	+	0.936023i	$0.614478\pi$
$102$	11.7013	+	11.7013i	1.15860	+	1.15860i
$103$	−2.90408	+	2.90408i	−0.286148	+	0.286148i	−0.835555	−	0.549407i	$-0.814854\pi$
$103$	−2.90408	+	2.90408i	−0.286148	+	0.286148i	0.549407	+	0.835555i	$0.314854\pi$
$104$		−	6.62784i		−	0.649913i
$105$	0.484874	−	10.9911i	0.0473189	−	1.07263i
$106$			10.1963i			0.990352i
$107$	11.4446	+	11.4446i	1.10639	+	1.10639i	0.993622	+	0.112766i	$0.0359710\pi$
$107$	11.4446	+	11.4446i	1.10639	+	1.10639i	0.112766	+	0.993622i	$0.464029\pi$
$108$	1.98753	+	1.98753i	0.191250	+	0.191250i
$109$	−0.846570			−0.0810867			−0.0405433	−	0.999178i	$-0.512909\pi$
$109$	−0.846570			−0.0810867			−0.0405433	+	0.999178i	$0.512909\pi$
$110$	−3.26331	−	3.56452i	−0.311144	−	0.339863i
$111$			8.28611i			0.786483i
$112$	−4.03453	−	4.03453i	−0.381227	−	0.381227i
$113$	5.48402	−	5.48402i	0.515893	−	0.515893i	−0.400433	−	0.916326i	$-0.631140\pi$
$113$	5.48402	−	5.48402i	0.515893	−	0.515893i	0.916326	+	0.400433i	$0.131140\pi$
$114$	−8.36095			−0.783074
$115$	−9.27174	+	5.38840i	−0.864594	+	0.502471i
$116$	3.27244			0.303839
$117$	−1.21618	+	1.21618i	−0.112436	+	0.112436i
$118$	−1.79850	−	1.79850i	−0.165566	−	0.165566i
$119$			18.4811i			1.69416i
$120$	0.591442	−	13.4068i	0.0539910	−	1.22387i
$121$	7.52661			0.684238
$122$	−10.3022	−	10.3022i	−0.932717	−	0.932717i
$123$	0.427821	+	0.427821i	0.0385753	+	0.0385753i
$124$			0.546407i			0.0490688i
$125$	11.0827	+	1.47440i	0.991266	+	0.131874i
$126$			2.33903i			0.208378i
$127$	−9.98331	+	9.98331i	−0.885876	+	0.885876i	−0.994124	−	0.108248i	$-0.965476\pi$
$127$	−9.98331	+	9.98331i	−0.885876	+	0.885876i	0.108248	+	0.994124i	$0.465476\pi$
$128$	−2.06814	−	2.06814i	−0.182799	−	0.182799i
$129$	−5.98379			−0.526843
$130$	−5.57618	−	0.245993i	−0.489063	−	0.0215750i
$131$	12.2649			1.07159			0.535794	−	0.844349i	$-0.320012\pi$
$131$	12.2649			1.07159			0.535794	+	0.844349i	$0.320012\pi$
$132$	−1.68297	−	1.68297i	−0.146484	−	0.146484i
$133$	−6.60267	−	6.60267i	−0.572524	−	0.572524i
$134$	1.87348			0.161844
$135$	7.07532	−	6.47744i	0.608947	−	0.557489i
$136$			22.5429i			1.93304i
$137$	8.61922	+	8.61922i	0.736390	+	0.736390i	0.971877	−	0.235487i	$-0.0756686\pi$
$137$	8.61922	+	8.61922i	0.736390	+	0.736390i	−0.235487	+	0.971877i	$0.575669\pi$
$138$	9.12302	−	5.85453i	0.776603	−	0.498371i
$139$		−	12.3554i		−	1.04797i	−0.851727	−	0.523987i	$-0.824444\pi$
$139$		−	12.3554i		−	1.04797i	0.851727	−	0.523987i	$-0.175556\pi$
$140$	2.72783	−	2.49732i	0.230544	−	0.211062i
$141$	−22.5865			−1.90212
$142$	11.1123	−	11.1123i	0.932519	−	0.932519i
$143$	−2.83666	+	2.83666i	−0.237214	+	0.237214i
$144$			1.80605i			0.150504i
$145$	0.492202	−	11.1572i	0.0408751	−	0.926559i
$146$	10.8622			0.898962
$147$	0.865311	−	0.865311i	0.0713696	−	0.0713696i
$148$	−1.96960	+	1.96960i	−0.161900	+	0.161900i
$149$	−22.1174			−1.81193			−0.905964	−	0.423355i	$-0.860852\pi$
$149$	−22.1174			−1.81193			−0.905964	+	0.423355i	$0.860852\pi$
$150$	−11.2576	−	0.995191i	−0.919175	−	0.0812570i
$151$	−11.5971			−0.943757			−0.471879	−	0.881664i	$-0.656424\pi$
$151$	−11.5971			−0.943757			−0.471879	+	0.881664i	$0.656424\pi$
$152$	−8.05382	−	8.05382i	−0.653251	−	0.653251i
$153$	4.13652	−	4.13652i	0.334418	−	0.334418i
$154$			5.45566i			0.439630i
$155$	1.86295	+	0.0821839i	0.149636	+	0.00660117i
$156$	−2.74891			−0.220089
$157$	9.45172	+	9.45172i	0.754329	+	0.754329i	0.975284	−	0.220955i	$-0.0709173\pi$
$157$	9.45172	+	9.45172i	0.754329	+	0.754329i	−0.220955	+	0.975284i	$0.570917\pi$
$158$	−1.11522	+	1.11522i	−0.0887219	+	0.0887219i
$159$	17.1377			1.35910
$160$	5.83366	−	5.34070i	0.461191	−	0.422220i
$161$	11.8278	+	2.58113i	0.932163	+	0.203422i
$162$	−8.82207	+	8.82207i	−0.693127	+	0.693127i
$163$	10.2045	+	10.2045i	0.799279	+	0.799279i	0.982982	−	0.183703i	$-0.0588084\pi$
$163$	10.2045	+	10.2045i	0.799279	+	0.799279i	−0.183703	+	0.982982i	$0.558808\pi$
$164$			0.203385i			0.0158817i
$165$	−5.99114	+	5.48487i	−0.466410	+	0.426997i
$166$			0.421031i			0.0326783i
$167$	−2.98633	+	2.98633i	−0.231089	+	0.231089i	−0.813147	−	0.582058i	$-0.802248\pi$
$167$	−2.98633	+	2.98633i	−0.231089	+	0.231089i	0.582058	+	0.813147i	$0.302248\pi$
$168$	−10.7125	+	10.7125i	−0.826488	+	0.826488i
$169$		−	8.36668i		−	0.643591i
$170$	18.9660	+	0.836684i	1.45462	+	0.0641707i
$171$			2.95567i			0.226026i
$172$	−1.42234	−	1.42234i	−0.108452	−	0.108452i
$173$	7.72208	+	7.72208i	0.587099	+	0.587099i	0.936845	−	0.349746i	$-0.113732\pi$
$173$	7.72208	+	7.72208i	0.587099	+	0.587099i	−0.349746	+	0.936845i	$0.613732\pi$
$174$			11.2891i			0.855823i
$175$	−8.10422	−	9.67603i	−0.612621	−	0.731439i
$176$			4.21251i			0.317530i
$177$	−3.02287	+	3.02287i	−0.227213	+	0.227213i
$178$	8.88787	−	8.88787i	0.666174	−	0.666174i
$179$			12.7829i			0.955442i	0.878512	+	0.477721i	$0.158537\pi$
$179$			12.7829i			0.955442i	−0.878512	+	0.477721i	$0.841463\pi$
$180$	−1.16952	−	0.0515932i	−0.0871706	−	0.00384553i
$181$		−	2.65927i		−	0.197662i	−0.995104	−	0.0988311i	$-0.968490\pi$
$181$		−	2.65927i		−	0.197662i	0.995104	−	0.0988311i	$-0.0315104\pi$
$182$	4.45556	+	4.45556i	0.330268	+	0.330268i
$183$	−17.3156	+	17.3156i	−1.28001	+	1.28001i
$184$	14.4274	+	3.14842i	1.06360	+	0.232105i
$185$	6.41900	+	7.01149i	0.471934	+	0.515495i
$186$	−1.88496			−0.138212
$187$	9.64819	−	9.64819i	0.705546	−	0.705546i
$188$	−5.36877	−	5.36877i	−0.391558	−	0.391558i
$189$	−10.8291			−0.787703
$190$	−7.07481	+	6.47698i	−0.513261	+	0.469889i
$191$		−	25.3411i		−	1.83362i	−0.399325	−	0.916809i	$-0.630755\pi$
$191$		−	25.3411i		−	1.83362i	0.399325	−	0.916809i	$-0.369245\pi$
$192$	−11.8836	+	11.8836i	−0.857625	+	0.857625i
$193$	4.70486	+	4.70486i	0.338663	+	0.338663i	0.855864	−	0.517201i	$-0.173026\pi$
$193$	4.70486	+	4.70486i	0.338663	+	0.338663i	−0.517201	+	0.855864i	$0.673026\pi$
$194$	16.3919			1.17687
$195$	−0.413458	+	9.37228i	−0.0296084	+	0.671163i
$196$	0.411366			0.0293833
$197$	11.0198	−	11.0198i	0.785126	−	0.785126i	−0.195565	−	0.980691i	$-0.562654\pi$
$197$	11.0198	−	11.0198i	0.785126	−	0.785126i	0.980691	+	0.195565i	$0.0626540\pi$
$198$	1.22111	−	1.22111i	0.0867805	−	0.0867805i
$199$	14.2416			1.00956			0.504778	−	0.863249i	$-0.331574\pi$
$199$	14.2416			1.00956			0.504778	+	0.863249i	$0.331574\pi$
$200$	−9.88540	−	11.8027i	−0.699003	−	0.834574i
$201$		−	3.14889i		−	0.222105i
$202$	5.80057	−	5.80057i	0.408127	−	0.408127i
$203$	−8.91502	+	8.91502i	−0.625712	+	0.625712i
$204$	9.34973			0.654612
$205$	0.693430	+	0.0305907i	0.0484313	+	0.00213655i
$206$		−	4.76268i		−	0.331832i
$207$	−2.06963	−	3.22507i	−0.143849	−	0.224158i
$208$	3.44029	+	3.44029i	0.238541	+	0.238541i
$209$			6.89394i			0.476864i
$210$	8.61512	+	9.41031i	0.594499	+	0.649373i
$211$	−0.547276			−0.0376760			−0.0188380	−	0.999823i	$-0.505997\pi$
$211$	−0.547276			−0.0376760			−0.0188380	+	0.999823i	$0.505997\pi$
$212$	4.07360	+	4.07360i	0.279776	+	0.279776i
$213$	−18.6772	−	18.6772i	−1.27974	−	1.27974i
$214$	−18.7690			−1.28302
$215$	−5.06333	+	4.63546i	−0.345316	+	0.316136i
$216$	−13.2092			−0.898771
$217$	−1.48856	−	1.48856i	−0.101050	−	0.101050i
$218$	0.694186	−	0.694186i	0.0470162	−	0.0470162i
$219$		−	18.2569i		−	1.23369i
$220$	−2.72783	−	0.120338i	−0.183910	−	0.00811321i
$221$		−	15.7591i		−	1.06007i
$222$	−6.79459	−	6.79459i	−0.456023	−	0.456023i
$223$	8.44122	+	8.44122i	0.565266	+	0.565266i	0.930798	−	0.365533i	$-0.119113\pi$
$223$	8.44122	+	8.44122i	0.565266	+	0.565266i	−0.365533	+	0.930798i	$0.619113\pi$
$224$	−8.92870			−0.596574
$225$	−0.351809	+	3.97965i	−0.0234540	+	0.265310i
$226$			8.99376i			0.598256i
$227$	2.86501	+	2.86501i	0.190157	+	0.190157i	0.795764	−	0.605607i	$-0.207070\pi$
$227$	2.86501	+	2.86501i	0.190157	+	0.190157i	−0.605607	+	0.795764i	$0.707070\pi$
$228$	−3.34034	+	3.34034i	−0.221220	+	0.221220i
$229$	16.8510			1.11355			0.556774	−	0.830664i	$-0.312039\pi$
$229$	16.8510			1.11355			0.556774	+	0.830664i	$0.312039\pi$
$230$	3.18433	−	12.0213i	0.209968	−	0.792660i
$231$	9.16973			0.603324
$232$	−10.8744	+	10.8744i	−0.713939	+	0.713939i
$233$	7.69686	+	7.69686i	0.504238	+	0.504238i	0.912752	−	0.408514i	$-0.133953\pi$
$233$	7.69686	+	7.69686i	0.504238	+	0.504238i	−0.408514	+	0.912752i	$0.633953\pi$
$234$		−	1.99452i		−	0.130386i
$235$	−19.1121	+	17.4971i	−1.24673	+	1.14138i
$236$	−1.43707			−0.0935450
$237$	1.87442	+	1.87442i	0.121757	+	0.121757i
$238$	−15.1545	−	15.1545i	−0.982317	−	0.982317i
$239$		−	18.8007i		−	1.21612i	−0.793892	−	0.608058i	$-0.791949\pi$
$239$		−	18.8007i		−	1.21612i	0.793892	−	0.608058i	$-0.208051\pi$
$240$	6.65203	+	7.26603i	0.429387	+	0.469020i
$241$		−	2.15033i		−	0.138515i	−0.997599	−	0.0692574i	$-0.977937\pi$
$241$		−	2.15033i		−	0.138515i	0.997599	−	0.0692574i	$-0.0220630\pi$
$242$	−6.17181	+	6.17181i	−0.396739	+	0.396739i
$243$	5.72758	+	5.72758i	0.367424	+	0.367424i
$244$	−8.23181			−0.526987
$245$	0.0618728	−	1.40253i	0.00395291	−	0.0896046i
$246$	−0.701624			−0.0447339
$247$	5.63018	+	5.63018i	0.358240	+	0.358240i
$248$	−1.81572	−	1.81572i	−0.115298	−	0.115298i
$249$	0.707657			0.0448459
$250$	−10.2968	+	7.87879i	−0.651226	+	0.498298i
$251$		−	3.83797i		−	0.242251i	−0.992637	−	0.121125i	$-0.961350\pi$
$251$		−	3.83797i		−	0.242251i	0.992637	−	0.121125i	$-0.0386503\pi$
$252$	0.934484	+	0.934484i	0.0588670	+	0.0588670i
$253$	−4.82730	−	7.52230i	−0.303490	−	0.472923i
$254$		−	16.3726i		−	1.02731i
$255$	1.40627	−	31.8775i	0.0880643	−	1.99624i
$256$	−13.8530			−0.865812
$257$	16.6728	−	16.6728i	1.04002	−	1.04002i	0.0408546	−	0.999165i	$-0.486992\pi$
$257$	16.6728	−	16.6728i	1.04002	−	1.04002i	0.999165	−	0.0408546i	$-0.0130081\pi$
$258$	4.90670	−	4.90670i	0.305478	−	0.305478i
$259$		−	10.7314i		−	0.666818i
$260$	−2.32606	+	2.12950i	−0.144256	+	0.132066i
$261$	3.99080			0.247024
$262$	−10.0572	+	10.0572i	−0.621335	+	0.621335i
$263$	9.73835	−	9.73835i	0.600492	−	0.600492i	−0.339951	−	0.940443i	$-0.610410\pi$
$263$	9.73835	−	9.73835i	0.600492	−	0.600492i	0.940443	+	0.339951i	$0.110410\pi$
$264$	11.1851			0.688394
$265$	14.5014	−	13.2760i	0.890816	−	0.815540i
$266$	10.8283			0.663928
$267$	−14.9385	−	14.9385i	−0.914220	−	0.914220i
$268$	0.748486	−	0.748486i	0.0457211	−	0.0457211i
$269$			10.3305i			0.629860i	0.949115	+	0.314930i	$0.101981\pi$
$269$			10.3305i			0.629860i	−0.949115	+	0.314930i	$0.898019\pi$
$270$	−0.490260	+	11.1132i	−0.0298363	+	0.676330i
$271$	6.83506			0.415200			0.207600	−	0.978214i	$-0.433435\pi$
$271$	6.83506			0.415200			0.207600	+	0.978214i	$0.433435\pi$
$272$	−11.7013	−	11.7013i	−0.709495	−	0.709495i
$273$	7.48878	−	7.48878i	0.453241	−	0.453241i
$274$	−14.1355			−0.853956
$275$	−0.820576	+	9.28231i	−0.0494826	+	0.559745i
$276$	1.30582	−	5.98379i	0.0786009	−	0.360182i
$277$	−4.78771	+	4.78771i	−0.287665	+	0.287665i	−0.836156	−	0.548491i	$-0.815203\pi$
$277$	−4.78771	+	4.78771i	−0.287665	+	0.287665i	0.548491	+	0.836156i	$0.315203\pi$
$278$	10.1314	+	10.1314i	0.607642	+	0.607642i
$279$			0.666351i			0.0398934i
$280$	−0.765982	+	17.3633i	−0.0457762	+	1.03766i
$281$			18.7407i			1.11798i	0.829176	+	0.558988i	$0.188810\pi$
$281$			18.7407i			1.11798i	−0.829176	+	0.558988i	$0.811190\pi$
$282$	18.5209	−	18.5209i	1.10290	−	1.10290i
$283$	9.03344	−	9.03344i	0.536982	−	0.536982i	−0.385659	−	0.922641i	$-0.626026\pi$
$283$	9.03344	−	9.03344i	0.536982	−	0.536982i	0.922641	+	0.385659i	$0.126026\pi$
$284$		−	8.87907i		−	0.526876i
$285$	10.8863	+	11.8911i	0.644850	+	0.704371i
$286$		−	4.65212i		−	0.275085i
$287$	−0.554075	−	0.554075i	−0.0327060	−	0.0327060i
$288$	1.99846	+	1.99846i	0.117760	+	0.117760i
$289$			36.6005i			2.15297i
$290$	8.74531	+	9.55252i	0.513542	+	0.560943i
$291$		−	27.5510i		−	1.61507i
$292$	4.33964	−	4.33964i	0.253958	−	0.253958i
$293$	−7.41003	+	7.41003i	−0.432899	+	0.432899i	−0.889613	−	0.456715i	$-0.849026\pi$
$293$	−7.41003	+	7.41003i	−0.432899	+	0.432899i	0.456715	+	0.889613i	$0.349026\pi$
$294$			1.41911i			0.0827640i
$295$	−0.216146	+	4.89961i	−0.0125845	+	0.285266i
$296$		−	13.0900i		−	0.760842i
$297$	5.65342	+	5.65342i	0.328045	+	0.328045i
$298$	18.1362	−	18.1362i	1.05060	−	1.05060i
$299$	−10.0857	−	2.20097i	−0.583273	−	0.127285i
$300$	−4.89518	+	4.09999i	−0.282623	+	0.236713i
$301$	7.74967			0.446683
$302$	9.50958	−	9.50958i	0.547215	−	0.547215i
$303$	−9.74944	−	9.74944i	−0.560091	−	0.560091i
$304$	8.36095			0.479533
$305$	−1.23813	+	28.0660i	−0.0708951	+	1.60705i
$306$			6.78387i			0.387808i
$307$	−7.54028	+	7.54028i	−0.430347	+	0.430347i	−0.888746	−	0.458400i	$-0.848423\pi$
$307$	−7.54028	+	7.54028i	−0.430347	+	0.430347i	0.458400	+	0.888746i	$0.348423\pi$
$308$	2.17963	+	2.17963i	0.124196	+	0.124196i
$309$	−8.00498			−0.455387
$310$	−1.59500	+	1.46022i	−0.0905901	+	0.0829351i
$311$	0.679491			0.0385304			0.0192652	−	0.999814i	$-0.493867\pi$
$311$	0.679491			0.0385304			0.0192652	+	0.999814i	$0.493867\pi$
$312$	9.13469	−	9.13469i	0.517150	−	0.517150i
$313$	4.45436	−	4.45436i	0.251775	−	0.251775i	−0.569923	−	0.821698i	$-0.693027\pi$
$313$	4.45436	−	4.45436i	0.251775	−	0.251775i	0.821698	+	0.569923i	$0.193027\pi$
$314$	−15.5008			−0.874760
$315$	3.32663	−	3.04552i	0.187435	−	0.171596i
$316$			0.891096i			0.0501281i
$317$	−13.4899	+	13.4899i	−0.757670	+	0.757670i	−0.975898	−	0.218228i	$-0.929972\pi$
$317$	−13.4899	+	13.4899i	−0.757670	+	0.757670i	0.218228	+	0.975898i	$0.429972\pi$
$318$	−14.0528	+	14.0528i	−0.788044	+	0.788044i
$319$	9.30831			0.521165
$320$	−0.849720	+	19.2615i	−0.0475008	+	1.07675i
$321$			31.5465i			1.76075i
$322$	−11.8153	+	7.58227i	−0.658442	+	0.422543i
$323$	−19.1496	−	19.1496i	−1.06551	−	1.06551i
$324$			7.04914i			0.391619i
$325$	6.91057	+	8.25088i	0.383330	+	0.457676i
$326$	−16.7354			−0.926886
$327$	−1.16677	−	1.16677i	−0.0645224	−	0.0645224i
$328$	−0.675851	−	0.675851i	−0.0373176	−	0.0373176i
$329$	29.2520			1.61271
$330$	0.415136	−	9.41031i	0.0228525	−	0.518020i
$331$	−15.2719			−0.839420			−0.419710	−	0.907658i	$-0.637868\pi$
$331$	−15.2719			−0.839420			−0.419710	+	0.907658i	$0.637868\pi$
$332$	0.168209	+	0.168209i	0.00923167	+	0.00923167i
$333$	−2.40195	+	2.40195i	−0.131626	+	0.131626i
$334$		−	4.89757i		−	0.267983i
$335$	−2.43935	−	2.66451i	−0.133276	−	0.145578i
$336$		−	11.1210i		−	0.606701i
$337$	−5.81558	−	5.81558i	−0.316795	−	0.316795i	0.530740	−	0.847535i	$-0.321914\pi$
$337$	−5.81558	−	5.81558i	−0.316795	−	0.316795i	−0.847535	+	0.530740i	$0.821914\pi$
$338$	6.86066	+	6.86066i	0.373171	+	0.373171i
$339$	15.1165			0.821014
$340$	7.91150	−	7.24296i	0.429061	−	0.392805i
$341$			1.55423i			0.0841661i
$342$	−2.42365	−	2.42365i	−0.131056	−	0.131056i
$343$	−13.6154	+	13.6154i	−0.735162	+	0.735162i
$344$	9.45292			0.509667
$345$	−20.2050	−	5.35213i	−1.08780	−	0.288149i
$346$	−12.6642			−0.680830
$347$	−8.76600	+	8.76600i	−0.470584	+	0.470584i	−0.902103	−	0.431520i	$-0.857977\pi$
$347$	−8.76600	+	8.76600i	−0.470584	+	0.470584i	0.431520	+	0.902103i	$0.357977\pi$
$348$	4.51018	+	4.51018i	0.241771	+	0.241771i
$349$			11.0595i			0.592004i	0.955187	+	0.296002i	$0.0956535\pi$
$349$			11.0595i			0.592004i	−0.955187	+	0.296002i	$0.904346\pi$
$350$	14.5798	+	1.28888i	0.779321	+	0.0688936i
$351$	9.23413			0.492881
$352$	4.66130	+	4.66130i	0.248448	+	0.248448i
$353$	22.3279	+	22.3279i	1.18839	+	1.18839i	0.977512	+	0.210881i	$0.0676333\pi$
$353$	22.3279	+	22.3279i	1.18839	+	1.18839i	0.210881	+	0.977512i	$0.432367\pi$
$354$		−	4.95750i		−	0.263488i
$355$	−30.2728	−	1.33548i	−1.60671	−	0.0708801i
$356$		−	7.10171i		−	0.376390i
$357$	−25.4712	+	25.4712i	−1.34808	+	1.34808i
$358$	−10.4820	−	10.4820i	−0.553990	−	0.553990i
$359$	19.7035			1.03991			0.519956	−	0.854193i	$-0.325948\pi$
$359$	19.7035			1.03991			0.519956	+	0.854193i	$0.325948\pi$
$360$	4.05777	−	3.71488i	0.213863	−	0.195791i
$361$	−5.31698			−0.279841
$362$	2.18060	+	2.18060i	0.114610	+	0.114610i
$363$	10.3734	+	10.3734i	0.544462	+	0.544462i
$364$	3.56014			0.186602
$365$	−14.1431	−	15.4485i	−0.740282	−	0.808611i
$366$		−	28.3976i		−	1.48437i
$367$	−25.8561	−	25.8561i	−1.34968	−	1.34968i	−0.886007	−	0.463671i	$-0.846532\pi$
$367$	−25.8561	−	25.8561i	−1.34968	−	1.34968i	−0.463671	−	0.886007i	$-0.653468\pi$
$368$	−9.12302	+	5.85453i	−0.475570	+	0.305189i
$369$			0.248031i			0.0129120i
$370$	−11.0130	−	0.485837i	−0.572537	−	0.0252575i
$371$	−22.1952			−1.15231
$372$	−0.753074	+	0.753074i	−0.0390451	+	0.0390451i
$373$	−17.3315	+	17.3315i	−0.897389	+	0.897389i	−0.995205	−	0.0978153i	$-0.968815\pi$
$373$	−17.3315	+	17.3315i	−0.897389	+	0.897389i	0.0978153	+	0.995205i	$0.468815\pi$
$374$			15.8230i			0.818188i
$375$	13.2424	+	17.3066i	0.683837	+	0.893707i
$376$	35.6811			1.84011
$377$	7.60195	−	7.60195i	0.391520	−	0.391520i
$378$	8.87986	−	8.87986i	0.456731	−	0.456731i
$379$	26.0488			1.33804			0.669018	−	0.743246i	$-0.266715\pi$
$379$	26.0488			1.33804			0.669018	+	0.743246i	$0.266715\pi$
$380$	−0.238846	+	5.41417i	−0.0122526	+	0.277741i
$381$	−27.5186			−1.40982
$382$	20.7797	+	20.7797i	1.06318	+	1.06318i
$383$	−1.04098	+	1.04098i	−0.0531917	+	0.0531917i	−0.733202	−	0.680011i	$-0.761975\pi$
$383$	−1.04098	+	1.04098i	−0.0531917	+	0.0531917i	0.680011	+	0.733202i	$0.261975\pi$
$384$		−	5.70073i		−	0.290914i
$385$	7.75918	−	7.10352i	0.395445	−	0.362029i
$386$	−7.71596			−0.392732
$387$	−1.73456	−	1.73456i	−0.0881728	−	0.0881728i
$388$	6.54884	−	6.54884i	0.332467	−	0.332467i
$389$	−11.1720			−0.566443			−0.283222	−	0.959054i	$-0.591403\pi$
$389$	−11.1720			−0.566443			−0.283222	+	0.959054i	$0.591403\pi$
$390$	−7.34622	−	8.02429i	−0.371990	−	0.406326i
$391$	34.3041	+	7.48603i	1.73483	+	0.378585i
$392$	−1.36698	+	1.36698i	−0.0690428	+	0.0690428i
$393$	16.9038	+	16.9038i	0.852686	+	0.852686i
$394$			18.0724i			0.910473i
$395$	3.03815	+	0.134028i	0.152866	+	0.00674368i
$396$		−	0.975709i		−	0.0490312i
$397$	4.79153	−	4.79153i	0.240480	−	0.240480i	−0.576569	−	0.817049i	$-0.695609\pi$
$397$	4.79153	−	4.79153i	0.240480	−	0.240480i	0.817049	+	0.576569i	$0.195609\pi$
$398$	−11.6780	+	11.6780i	−0.585367	+	0.585367i
$399$		−	18.2000i		−	0.911139i
$400$	11.2576	+	0.995191i	0.562878	+	0.0497595i
$401$		−	12.0884i		−	0.603663i	−0.953361	−	0.301832i	$-0.902402\pi$
$401$		−	12.0884i		−	0.603663i	0.953361	−	0.301832i	$-0.0975981\pi$
$402$	2.58208	+	2.58208i	0.128783	+	0.128783i
$403$	1.26931	+	1.26931i	0.0632290	+	0.0632290i
$404$		−	4.63486i		−	0.230593i
$405$	24.0337	+	1.06025i	1.19424	+	0.0526841i
$406$		−	14.6206i		−	0.725608i
$407$	−5.60242	+	5.60242i	−0.277702	+	0.277702i
$408$	−31.0693	+	31.0693i	−1.53816	+	1.53816i
$409$		−	27.9704i		−	1.38305i	−0.722353	−	0.691524i	$-0.756939\pi$
$409$		−	27.9704i		−	1.38305i	0.722353	−	0.691524i	$-0.243061\pi$
$410$	−0.593696	+	0.543527i	−0.0293205	+	0.0268429i
$411$			23.7585i			1.17192i
$412$	−1.90277	−	1.90277i	−0.0937429	−	0.0937429i
$413$	3.91495	−	3.91495i	0.192642	−	0.192642i
$414$	4.34165	+	0.947459i	0.213380	+	0.0465651i
$415$	0.598801	−	0.548201i	0.0293940	−	0.0269101i
$416$	7.61362			0.373288
$417$	17.0286	−	17.0286i	0.833895	−	0.833895i
$418$	−5.65302	−	5.65302i	−0.276498	−	0.276498i
$419$	12.4527			0.608354			0.304177	−	0.952616i	$-0.401619\pi$
$419$	12.4527			0.608354			0.304177	+	0.952616i	$0.401619\pi$
$420$	7.20147	+	0.317693i	0.351396	+	0.0155018i
$421$			27.8660i			1.35811i	0.734090	+	0.679053i	$0.237609\pi$
$421$			27.8660i			1.35811i	−0.734090	+	0.679053i	$0.762391\pi$
$422$	0.448765	−	0.448765i	0.0218455	−	0.0218455i
$423$	−6.54730	−	6.54730i	−0.318341	−	0.318341i
$424$	−27.0733			−1.31479
$425$	−23.5046	−	28.0633i	−1.14014	−	1.36127i
$426$	30.6305			1.48405
$427$	22.4257	−	22.4257i	1.08525	−	1.08525i
$428$	−7.49855	+	7.49855i	−0.362456	+	0.362456i
$429$	−7.81915			−0.377512
$430$	0.350846	−	7.95299i	0.0169193	−	0.383527i
$431$			8.73549i			0.420774i	0.977618	+	0.210387i	$0.0674723\pi$
$431$			8.73549i			0.420774i	−0.977618	+	0.210387i	$0.932528\pi$
$432$	6.85645	−	6.85645i	0.329881	−	0.329881i
$433$	24.7415	−	24.7415i	1.18900	−	1.18900i	0.211656	−	0.977344i	$-0.432114\pi$
$433$	24.7415	−	24.7415i	1.18900	−	1.18900i	0.977344	−	0.211656i	$-0.0678858\pi$
$434$	2.44123			0.117183
$435$	16.0556	−	14.6989i	0.769808	−	0.704757i
$436$		−	0.554678i		−	0.0265643i
$437$	−14.9302	+	9.58118i	−0.714208	+	0.458330i
$438$	14.9706	+	14.9706i	0.715323	+	0.715323i
$439$		−	26.8462i		−	1.28130i	−0.767833	−	0.640650i	$-0.778665\pi$
$439$		−	26.8462i		−	1.28130i	0.767833	−	0.640650i	$-0.221335\pi$
$440$	9.46453	−	8.66475i	0.451204	−	0.413076i
$441$	0.501668			0.0238889
$442$	12.9224	+	12.9224i	0.614656	+	0.614656i
$443$	−22.9288	−	22.9288i	−1.08938	−	1.08938i	−0.995592	−	0.0937869i	$-0.970103\pi$
$443$	−22.9288	−	22.9288i	−1.08938	−	1.08938i	−0.0937869	−	0.995592i	$-0.529897\pi$
$444$	−5.42911			−0.257654
$445$	−24.2130	−	1.06815i	−1.14780	−	0.0506354i
$446$	−13.8436			−0.655512
$447$	−30.4828	−	30.4828i	−1.44179	−	1.44179i
$448$	15.3906	−	15.3906i	0.727136	−	0.727136i
$449$		−	7.68005i		−	0.362444i	−0.983442	−	0.181222i	$-0.941995\pi$
$449$		−	7.68005i		−	0.362444i	0.983442	−	0.181222i	$-0.0580052\pi$
$450$	−2.97482	−	3.55179i	−0.140235	−	0.167433i
$451$			0.578518i			0.0272413i
$452$	3.59316	+	3.59316i	0.169008	+	0.169008i
$453$	−15.9834	−	15.9834i	−0.750968	−	0.750968i
$454$	−4.69861			−0.220516
$455$	0.535474	−	12.1381i	0.0251034	−	0.569045i
$456$		−	22.2000i		−	1.03961i
$457$	−0.788754	−	0.788754i	−0.0368964	−	0.0368964i	0.688418	−	0.725314i	$-0.258306\pi$
$457$	−0.788754	−	0.788754i	−0.0368964	−	0.0368964i	−0.725314	+	0.688418i	$0.758306\pi$
$458$	−13.8178	+	13.8178i	−0.645664	+	0.645664i
$459$	−31.4076			−1.46598
$460$	−3.53052	−	6.07490i	−0.164611	−	0.283244i
$461$	28.3501			1.32040			0.660198	−	0.751092i	$-0.270473\pi$
$461$	28.3501			1.32040			0.660198	+	0.751092i	$0.270473\pi$
$462$	−7.51916	+	7.51916i	−0.349823	+	0.349823i
$463$	−19.3363	−	19.3363i	−0.898632	−	0.898632i	0.0966834	−	0.995315i	$-0.469177\pi$
$463$	−19.3363	−	19.3363i	−0.898632	−	0.898632i	−0.995315	+	0.0966834i	$0.969177\pi$
$464$		−	11.2891i		−	0.524082i
$465$	2.45430	+	2.68084i	0.113815	+	0.124321i
$466$	−12.6228			−0.584741
$467$	14.6609	+	14.6609i	0.678424	+	0.678424i	0.959643	−	0.281219i	$-0.0907389\pi$
$467$	14.6609	+	14.6609i	0.678424	+	0.678424i	−0.281219	+	0.959643i	$0.590739\pi$
$468$	−0.796847	−	0.796847i	−0.0368342	−	0.0368342i
$469$			4.07816i			0.188312i
$470$	1.32431	−	30.0194i	0.0610857	−	1.38469i
$471$			26.0533i			1.20047i
$472$	4.77540	−	4.77540i	0.219806	−	0.219806i
$473$	−4.04577	−	4.04577i	−0.186025	−	0.186025i
$474$	−3.07405			−0.141196
$475$	18.4234	+	1.62867i	0.845325	+	0.0747285i
$476$	−12.1089			−0.555012
$477$	4.96781	+	4.96781i	0.227461	+	0.227461i
$478$	15.4165	+	15.4165i	0.705136	+	0.705136i
$479$	−18.4596			−0.843439			−0.421719	−	0.906726i	$-0.638573\pi$
$479$	−18.4596			−0.843439			−0.421719	+	0.906726i	$0.638573\pi$
$480$	15.4008	+	0.679408i	0.702949	+	0.0310106i
$481$			9.15082i			0.417241i
$482$	1.76327	+	1.76327i	0.0803145	+	0.0803145i
$483$	12.7441	+	19.8589i	0.579875	+	0.903609i
$484$			4.93149i			0.224158i
$485$	−21.3429	−	23.3129i	−0.969133	−	1.05859i
$486$	−9.39321			−0.426084
$487$	4.06167	−	4.06167i	0.184052	−	0.184052i	−0.609067	−	0.793119i	$-0.708456\pi$
$487$	4.06167	−	4.06167i	0.184052	−	0.184052i	0.793119	+	0.609067i	$0.208456\pi$
$488$	27.3545	−	27.3545i	1.23828	−	1.23828i
$489$			28.1283i			1.27201i
$490$	1.09934	+	1.20081i	0.0496631	+	0.0542471i
$491$	−14.8576			−0.670514			−0.335257	−	0.942127i	$-0.608823\pi$
$491$	−14.8576			−0.670514			−0.335257	+	0.942127i	$0.608823\pi$
$492$	−0.280311	+	0.280311i	−0.0126374	+	0.0126374i
$493$	−25.8561	+	25.8561i	−1.16450	+	1.16450i
$494$	−9.23347			−0.415433
$495$	−3.32663	−	0.146754i	−0.149521	−	0.00659612i
$496$	1.88496			0.0846372
$497$	24.1890	+	24.1890i	1.08502	+	1.08502i
$498$	−0.580277	+	0.580277i	−0.0260028	+	0.0260028i
$499$		−	3.58013i		−	0.160269i	−0.996784	−	0.0801343i	$-0.974465\pi$
$499$		−	3.58013i		−	0.160269i	0.996784	−	0.0801343i	$-0.0255349\pi$
$500$	−0.966034	+	7.26146i	−0.0432024	+	0.324742i
$501$	−8.23170			−0.367765
$502$	3.14713	+	3.14713i	0.140463	+	0.140463i
$503$	−6.36498	+	6.36498i	−0.283801	+	0.283801i	−0.834623	−	0.550822i	$-0.814314\pi$
$503$	−6.36498	+	6.36498i	−0.283801	+	0.283801i	0.550822	+	0.834623i	$0.314314\pi$
$504$	−6.21062			−0.276643
$505$	−15.8023	−	0.697120i	−0.703194	−	0.0310214i
$506$	10.1267	+	2.20989i	0.450185	+	0.0982418i
$507$	11.5312	−	11.5312i	0.512119	−	0.512119i
$508$	−6.54113	−	6.54113i	−0.290216	−	0.290216i
$509$			15.6300i			0.692789i	0.938089	+	0.346394i	$0.112594\pi$
$509$			15.6300i			0.692789i	−0.938089	+	0.346394i	$0.887406\pi$
$510$	24.9863	+	27.2926i	1.10641	+	1.20854i
$511$			23.6447i			1.04598i
$512$	15.4957	−	15.4957i	0.684820	−	0.684820i
$513$	11.2209	−	11.2209i	0.495413	−	0.495413i
$514$			27.3433i			1.20606i
$515$	−6.77360	+	6.20122i	−0.298481	+	0.273258i
$516$		−	3.92062i		−	0.172596i
$517$	−15.2712	−	15.2712i	−0.671627	−	0.671627i
$518$	8.79974	+	8.79974i	0.386639	+	0.386639i
$519$			21.2856i			0.934334i
$520$	0.653163	−	14.8059i	0.0286431	−	0.649282i
$521$			10.2971i			0.451124i	0.974229	+	0.225562i	$0.0724218\pi$
$521$			10.2971i			0.451124i	−0.974229	+	0.225562i	$0.927578\pi$
$522$	−3.27244	+	3.27244i	−0.143231	+	0.143231i
$523$	28.9495	−	28.9495i	1.26587	−	1.26587i	0.317674	−	0.948200i	$-0.397098\pi$
$523$	28.9495	−	28.9495i	1.26587	−	1.26587i	0.948200	−	0.317674i	$-0.102902\pi$
$524$			8.03604i			0.351056i
$525$	2.16632	−	24.5053i	0.0945458	−	1.06950i
$526$			15.9708i			0.696362i
$527$	−4.31725	−	4.31725i	−0.188062	−	0.188062i
$528$	−5.80581	+	5.80581i	−0.252665	+	0.252665i
$529$	9.58206	−	20.9090i	0.416611	−	0.909085i
$530$	−1.00483	+	22.7775i	−0.0436470	+	0.989390i
$531$	−1.75252			−0.0760531
$532$	4.32611	−	4.32611i	0.187561	−	0.187561i
$533$	0.472467	+	0.472467i	0.0204648	+	0.0204648i
$534$	24.4991			1.06018
$535$	24.4381	+	26.6938i	1.05655	+	1.15407i
$536$			4.97447i			0.214864i
$537$	−17.6178	+	17.6178i	−0.760266	+	0.760266i
$538$	−8.47097	−	8.47097i	−0.365209	−	0.365209i
$539$	1.17011			0.0504003
$540$	4.24406	+	4.63580i	0.182635	+	0.199493i
$541$	−22.3203			−0.959625			−0.479812	−	0.877371i	$-0.659295\pi$
$541$	−22.3203			−0.959625			−0.479812	+	0.877371i	$0.659295\pi$
$542$	−5.60474	+	5.60474i	−0.240744	+	0.240744i
$543$	3.66509	−	3.66509i	0.157284	−	0.157284i
$544$	−25.8958			−1.11027
$545$	−1.89115	−	0.0834280i	−0.0810079	−	0.00357366i
$546$			12.2816i			0.525602i
$547$	−19.4194	+	19.4194i	−0.830314	+	0.830314i	−0.987560	−	0.157245i	$-0.949739\pi$
$547$	−19.4194	+	19.4194i	−0.830314	+	0.830314i	0.157245	+	0.987560i	$0.449739\pi$
$548$	−5.64737	+	5.64737i	−0.241244	+	0.241244i
$549$	−10.0388			−0.428446
$550$	−6.93861	−	8.28435i	−0.295863	−	0.353246i
$551$		−	18.4750i		−	0.787063i
$552$	15.5450	+	24.2235i	0.661639	+	1.03102i
$553$	−2.42759	−	2.42759i	−0.103231	−	0.103231i
$554$		−	7.85182i		−	0.333592i
$555$	−0.816582	+	18.5103i	−0.0346620	+	0.785718i
$556$	8.09535			0.343319
$557$	24.7614	+	24.7614i	1.04917	+	1.04917i	0.998727	+	0.0504476i	$0.0160648\pi$
$557$	24.7614	+	24.7614i	1.04917	+	1.04917i	0.0504476	+	0.998727i	$0.483935\pi$
$558$	−0.546407	−	0.546407i	−0.0231312	−	0.0231312i
$559$	−6.60824			−0.279499
$560$	−8.61512	−	9.41031i	−0.364055	−	0.397658i
$561$	26.5948			1.12284
$562$	−15.3673	−	15.3673i	−0.648232	−	0.648232i
$563$	6.83152	−	6.83152i	0.287914	−	0.287914i	−0.548341	−	0.836255i	$-0.684740\pi$
$563$	6.83152	−	6.83152i	0.287914	−	0.287914i	0.836255	+	0.548341i	$0.184740\pi$
$564$		−	14.7988i		−	0.623142i
$565$	12.7912	−	11.7103i	0.538128	−	0.492655i
$566$			14.8148i			0.622713i
$567$	−19.2037	−	19.2037i	−0.806481	−	0.806481i
$568$	29.5053	+	29.5053i	1.23802	+	1.23802i
$569$	−23.5370			−0.986722			−0.493361	−	0.869825i	$-0.664232\pi$
$569$	−23.5370			−0.986722			−0.493361	+	0.869825i	$0.664232\pi$
$570$	−18.6775	−	0.823957i	−0.782314	−	0.0345118i
$571$		−	23.7543i		−	0.994085i	−0.867726	−	0.497043i	$-0.834419\pi$
$571$		−	23.7543i		−	0.994085i	0.867726	−	0.497043i	$-0.165581\pi$
$572$	−1.85860	−	1.85860i	−0.0777120	−	0.0777120i
$573$	34.9259	−	34.9259i	1.45905	−	1.45905i
$574$	0.908680			0.0379276
$575$	−21.2431	+	11.1234i	−0.885899	+	0.463878i
$576$	−6.88957			−0.287065
$577$	−16.4059	+	16.4059i	−0.682986	+	0.682986i	−0.960672	−	0.277686i	$-0.910433\pi$
$577$	−16.4059	+	16.4059i	−0.682986	+	0.682986i	0.277686	+	0.960672i	$0.410433\pi$
$578$	−30.0123	−	30.0123i	−1.24835	−	1.24835i
$579$			12.9688i			0.538963i
$580$	7.31030	+	0.322494i	0.303544	+	0.0133908i
$581$	−0.916493			−0.0380225
$582$	22.5918	+	22.5918i	0.936459	+	0.936459i
$583$	11.5871	+	11.5871i	0.479891	+	0.479891i
$584$			28.8414i			1.19347i
$585$	−2.83666	+	2.59696i	−0.117282	+	0.107371i
$586$		−	12.1524i		−	0.502012i
$587$	−0.365946	+	0.365946i	−0.0151042	+	0.0151042i	−0.714619	−	0.699514i	$-0.753400\pi$
$587$	−0.365946	+	0.365946i	−0.0151042	+	0.0151042i	0.699514	+	0.714619i	$0.253400\pi$
$588$	0.566957	+	0.566957i	0.0233809	+	0.0233809i
$589$	3.08481			0.127107
$590$	−3.84043	−	4.19491i	−0.158108	−	0.172702i
$591$	30.3755			1.24948
$592$	6.79459	+	6.79459i	0.279256	+	0.279256i
$593$	−6.14484	−	6.14484i	−0.252338	−	0.252338i	0.569590	−	0.821929i	$-0.307102\pi$
$593$	−6.14484	−	6.14484i	−0.252338	−	0.252338i	−0.821929	+	0.569590i	$0.807102\pi$
$594$	−9.27159			−0.380418
$595$	−1.82128	+	41.2848i	−0.0746652	+	1.69251i
$596$		−	14.4915i		−	0.593593i
$597$	19.6281	+	19.6281i	0.803326	+	0.803326i
$598$	10.0751	−	6.46550i	0.412000	−	0.264394i
$599$			22.3478i			0.913105i	0.889697	+	0.456552i	$0.150916\pi$
$599$			22.3478i			0.913105i	−0.889697	+	0.456552i	$0.849084\pi$
$600$	2.64244	−	29.8911i	0.107877	−	1.22030i
$601$	5.68719			0.231985			0.115993	−	0.993250i	$-0.462995\pi$
$601$	5.68719			0.231985			0.115993	+	0.993250i	$0.462995\pi$
$602$	−6.35471	+	6.35471i	−0.258999	+	0.258999i
$603$	0.912790	−	0.912790i	0.0371717	−	0.0371717i
$604$		−	7.59848i		−	0.309178i
$605$	16.8137	+	0.741735i	0.683573	+	0.0301558i
$606$	15.9890			0.649511
$607$	29.8093	−	29.8093i	1.20992	−	1.20992i	0.238872	−	0.971051i	$-0.423222\pi$
$607$	29.8093	−	29.8093i	1.20992	−	1.20992i	0.971051	−	0.238872i	$-0.0767777\pi$
$608$	9.25169	−	9.25169i	0.375206	−	0.375206i
$609$	−24.5739			−0.995784
$610$	−21.9988	−	24.0293i	−0.890704	−	0.972917i
$611$	−24.9435			−1.00911
$612$	2.71027	+	2.71027i	0.109556	+	0.109556i
$613$	11.5614	−	11.5614i	0.466962	−	0.466962i	−0.433967	−	0.900929i	$-0.642887\pi$
$613$	11.5614	−	11.5614i	0.466962	−	0.466962i	0.900929	+	0.433967i	$0.142887\pi$
$614$		−	12.3660i		−	0.499053i
$615$	0.913545	+	0.997867i	0.0368377	+	0.0402379i
$616$	−14.4859			−0.583654
$617$	−20.2525	−	20.2525i	−0.815335	−	0.815335i	0.170093	−	0.985428i	$-0.445593\pi$
$617$	−20.2525	−	20.2525i	−0.815335	−	0.815335i	−0.985428	+	0.170093i	$0.945593\pi$
$618$	6.56407	−	6.56407i	0.264046	−	0.264046i
$619$	−23.4050			−0.940725			−0.470363	−	0.882473i	$-0.655877\pi$
$619$	−23.4050			−0.940725			−0.470363	+	0.882473i	$0.655877\pi$
$620$	−0.0538475	+	1.22062i	−0.00216257	+	0.0490211i
$621$	−4.38649	+	20.1007i	−0.176024	+	0.806614i
$622$	−0.557181	+	0.557181i	−0.0223409	+	0.0223409i
$623$	19.3470	+	19.3470i	0.775120	+	0.775120i
$624$			9.48303i			0.379625i
$625$	24.6123	+	4.38583i	0.984491	+	0.175433i
$626$			7.30513i			0.291972i
$627$	−9.50144	+	9.50144i	−0.379451	+	0.379451i
$628$	−6.19283	+	6.19283i	−0.247121	+	0.247121i
$629$		−	31.1242i		−	1.24100i
$630$	−0.230508	+	5.22516i	−0.00918365	+	0.208175i
$631$			0.768430i			0.0305907i	0.999883	+	0.0152954i	$0.00486885\pi$
$631$			0.768430i			0.0305907i	−0.999883	+	0.0152954i	$0.995131\pi$
$632$	−2.96113	−	2.96113i	−0.117787	−	0.117787i
$633$	−0.754272	−	0.754272i	−0.0299796	−	0.0299796i
$634$		−	22.1234i		−	0.878634i
$635$	−23.2855	+	21.3178i	−0.924058	+	0.845973i
$636$			11.2287i			0.445247i
$637$	0.955612	−	0.955612i	0.0378627	−	0.0378627i
$638$	−7.63279	+	7.63279i	−0.302185	+	0.302185i
$639$		−	10.8282i		−	0.428355i
$640$	−4.41619	−	4.82381i	−0.174565	−	0.190678i
$641$			24.6345i			0.973002i	0.873680	+	0.486501i	$0.161727\pi$
$641$			24.6345i			0.973002i	−0.873680	+	0.486501i	$0.838273\pi$
$642$	−25.8680	−	25.8680i	−1.02093	−	1.02093i
$643$	11.9143	−	11.9143i	0.469853	−	0.469853i	−0.432014	−	0.901867i	$-0.642197\pi$
$643$	11.9143	−	11.9143i	0.469853	−	0.469853i	0.901867	+	0.432014i	$0.142197\pi$
$644$	−1.69118	+	7.74967i	−0.0666417	+	0.305380i
$645$	−13.3672	−	0.589692i	−0.526331	−	0.0232191i
$646$	31.4053			1.23563
$647$	15.5990	−	15.5990i	0.613260	−	0.613260i	−0.330534	−	0.943794i	$-0.607229\pi$
$647$	15.5990	−	15.5990i	0.613260	−	0.613260i	0.943794	+	0.330534i	$0.107229\pi$
$648$	−23.4244	−	23.4244i	−0.920198	−	0.920198i
$649$	−4.08766			−0.160455
$650$	−12.4324	−	1.09905i	−0.487637	−	0.0431081i
$651$		−	4.10315i		−	0.160815i
$652$	−6.68606	+	6.68606i	−0.261846	+	0.261846i
$653$	2.42246	+	2.42246i	0.0947982	+	0.0947982i	0.752915	−	0.658117i	$-0.228647\pi$
$653$	2.42246	+	2.42246i	0.0947982	+	0.0947982i	−0.658117	+	0.752915i	$0.728647\pi$
$654$	1.91349			0.0748236
$655$	27.3985	+	1.20868i	1.07055	+	0.0472272i
$656$	0.701624			0.0273938
$657$	5.29225	−	5.29225i	0.206470	−	0.206470i
$658$	−23.9866	+	23.9866i	−0.935093	+	0.935093i
$659$	12.1720			0.474153			0.237077	−	0.971491i	$-0.423811\pi$
$659$	12.1720			0.474153			0.237077	+	0.971491i	$0.423811\pi$
$660$	−3.59373	−	3.92543i	−0.139886	−	0.152797i
$661$		−	42.6358i		−	1.65834i	−0.558995	−	0.829171i	$-0.688813\pi$
$661$		−	42.6358i		−	1.65834i	0.558995	−	0.829171i	$-0.311187\pi$
$662$	12.5229	−	12.5229i	0.486718	−	0.486718i
$663$	21.7196	−	21.7196i	0.843520	−	0.843520i
$664$	−1.11792			−0.0433839
$665$	−14.0990	−	15.4003i	−0.546735	−	0.597200i
$666$		−	3.93919i		−	0.152641i
$667$	12.9367	+	20.1590i	0.500909	+	0.780558i
$668$	−1.95666	−	1.95666i	−0.0757056	−	0.0757056i
$669$			23.2679i			0.899588i
$670$	4.18515	+	0.184628i	0.161686	+	0.00713280i
$671$	−23.4150			−0.903925
$672$	−12.3058	−	12.3058i	−0.474707	−	0.474707i
$673$	−1.88228	−	1.88228i	−0.0725567	−	0.0725567i	0.669897	−	0.742454i	$-0.266338\pi$
$673$	−1.88228	−	1.88228i	−0.0725567	−	0.0725567i	−0.742454	+	0.669897i	$0.766338\pi$
$674$	9.53753			0.367372
$675$	16.4439	−	13.7727i	0.632925	−	0.530110i
$676$	5.48190			0.210842
$677$	25.4073	+	25.4073i	0.976483	+	0.976483i	0.999730	−	0.0232465i	$-0.00740024\pi$
$677$	25.4073	+	25.4073i	0.976483	+	0.976483i	−0.0232465	+	0.999730i	$0.507400\pi$
$678$	−12.3955	+	12.3955i	−0.476045	+	0.476045i
$679$			35.6816i			1.36933i
$680$	−2.22157	+	50.3585i	−0.0851932	+	1.93116i
$681$			7.89729i			0.302625i
$682$	−1.27446	−	1.27446i	−0.0488017	−	0.0488017i
$683$	−9.66884	−	9.66884i	−0.369968	−	0.369968i	0.497498	−	0.867465i	$-0.334252\pi$
$683$	−9.66884	−	9.66884i	−0.369968	−	0.369968i	−0.867465	+	0.497498i	$0.834252\pi$
$684$	−1.93658			−0.0740469
$685$	18.4050	+	20.1039i	0.703220	+	0.768129i
$686$		−	22.3292i		−	0.852532i
$687$	23.2246	+	23.2246i	0.886073	+	0.886073i
$688$	−4.90670	+	4.90670i	−0.187066	+	0.187066i
$689$	18.9261			0.721027
$690$	20.9568	−	12.1794i	0.797813	−	0.463660i
$691$	15.0902			0.574059			0.287030	−	0.957922i	$-0.407332\pi$
$691$	15.0902			0.574059			0.287030	+	0.957922i	$0.407332\pi$
$692$	−5.05956	+	5.05956i	−0.192335	+	0.192335i
$693$	2.65809	+	2.65809i	0.100973	+	0.100973i
$694$		−	14.3762i		−	0.545713i
$695$	1.21761	−	27.6007i	0.0461864	−	1.04695i
$696$	−29.9748			−1.13619
$697$	−1.60698	−	1.60698i	−0.0608686	−	0.0608686i
$698$	−9.06881	−	9.06881i	−0.343259	−	0.343259i
$699$			21.2161i			0.802466i
$700$	6.33980	−	5.30994i	0.239622	−	0.200697i
$701$		−	26.7926i		−	1.01194i	−0.862550	−	0.505971i	$-0.831134\pi$
$701$		−	26.7926i		−	1.01194i	0.862550	−	0.505971i	$-0.168866\pi$
$702$	−7.57197	+	7.57197i	−0.285785	+	0.285785i
$703$	11.1196	+	11.1196i	0.419384	+	0.419384i
$704$	−16.0695			−0.605643
$705$	−50.4558	−	2.22586i	−1.90028	−	0.0838307i
$706$	−36.6176			−1.37812
$707$	12.6266	+	12.6266i	0.474872	+	0.474872i
$708$	−1.98061	−	1.98061i	−0.0744358	−	0.0744358i
$709$	−16.2692			−0.611003			−0.305502	−	0.952192i	$-0.598824\pi$
$709$	−16.2692			−0.611003			−0.305502	+	0.952192i	$0.598824\pi$
$710$	25.9187	−	23.7285i	0.972711	−	0.890515i
$711$			1.08671i			0.0407546i
$712$	23.5991	+	23.5991i	0.884415	+	0.884415i
$713$	−3.36598	+	2.16006i	−0.126057	+	0.0808949i
$714$		−	41.7726i		−	1.56330i
$715$	−6.61636	+	6.05726i	−0.247438	+	0.226529i
$716$	−8.37547			−0.313006
$717$	25.9117	−	25.9117i	0.967690	−	0.967690i
$718$	−16.1568	+	16.1568i	−0.602968	+	0.602968i
$719$		−	33.1573i		−	1.23656i	−0.785958	−	0.618280i	$-0.787830\pi$
$719$		−	33.1573i		−	1.23656i	0.785958	−	0.618280i	$-0.212170\pi$
$720$	−0.177983	+	4.03453i	−0.00663304	+	0.150358i
$721$	10.3673			0.386100
$722$	4.35991	−	4.35991i	0.162259	−	0.162259i
$723$	2.96365	−	2.96365i	0.110219	−	0.110219i
$724$	1.74237			0.0647548
$725$	2.19906	−	24.8756i	0.0816709	−	0.923857i
$726$	−17.0123			−0.631387
$727$	−21.5242	−	21.5242i	−0.798290	−	0.798290i	0.184536	−	0.982826i	$-0.440922\pi$
$727$	−21.5242	−	21.5242i	−0.798290	−	0.798290i	−0.982826	+	0.184536i	$0.940922\pi$
$728$	−11.8304	+	11.8304i	−0.438465	+	0.438465i
$729$		−	16.4881i		−	0.610671i
$730$	24.2650	+	1.07045i	0.898089	+	0.0396192i
$731$	22.4763			0.831314
$732$	−11.3453	−	11.3453i	−0.419335	−	0.419335i
$733$	−31.6457	+	31.6457i	−1.16886	+	1.16886i	−0.186384	+	0.982477i	$0.559677\pi$
$733$	−31.6457	+	31.6457i	−1.16886	+	1.16886i	−0.982477	+	0.186384i	$0.940323\pi$
$734$	42.4039			1.56516
$735$	2.01829	−	1.84774i	0.0744457	−	0.0681549i
$736$	−3.61670	+	16.5732i	−0.133313	+	0.610896i
$737$	2.12903	−	2.12903i	0.0784239	−	0.0784239i
$738$	−0.203385	−	0.203385i	−0.00748669	−	0.00748669i
$739$			25.3398i			0.932141i	0.884748	+	0.466071i	$0.154331\pi$
$739$			25.3398i			0.932141i	−0.884748	+	0.466071i	$0.845669\pi$
$740$	−4.59397	+	4.20577i	−0.168878	+	0.154607i
$741$			15.5194i			0.570118i
$742$	18.2000	−	18.2000i	0.668142	−	0.668142i
$743$	−13.6789	+	13.6789i	−0.501830	+	0.501830i	−0.912006	−	0.410176i	$-0.865467\pi$
$743$	−13.6789	+	13.6789i	−0.501830	+	0.501830i	0.410176	+	0.912006i	$0.365467\pi$
$744$		−	5.00496i		−	0.183491i
$745$	−49.4079	−	2.17963i	−1.81017	−	0.0798555i
$746$		−	28.4235i		−	1.04066i
$747$	0.205133	+	0.205133i	0.00750544	+	0.00750544i
$748$	6.32156	+	6.32156i	0.231139	+	0.231139i
$749$		−	40.8561i		−	1.49285i
$750$	−25.0501	−	3.33257i	−0.914701	−	0.121688i
$751$		−	15.6373i		−	0.570613i	−0.958436	−	0.285307i	$-0.907905\pi$
$751$		−	15.6373i		−	0.570613i	0.958436	−	0.285307i	$-0.0920954\pi$
$752$	−18.5209	+	18.5209i	−0.675386	+	0.675386i
$753$	5.28960	−	5.28960i	0.192764	−	0.192764i
$754$			12.4672i			0.454028i
$755$	−25.9067	−	1.14287i	−0.942840	−	0.0415934i
$756$		−	7.09531i		−	0.258054i
$757$	−4.50831	−	4.50831i	−0.163857	−	0.163857i	0.620416	−	0.784273i	$-0.286964\pi$
$757$	−4.50831	−	4.50831i	−0.163857	−	0.163857i	−0.784273	+	0.620416i	$0.786964\pi$
$758$	−21.3599	+	21.3599i	−0.775828	+	0.775828i
$759$	3.71433	−	17.0206i	0.134822	−	0.617808i
$760$	−17.1977	−	18.7851i	−0.623826	−	0.681407i
$761$	21.8465			0.791934			0.395967	−	0.918265i	$-0.370409\pi$
$761$	21.8465			0.791934			0.395967	+	0.918265i	$0.370409\pi$
$762$	22.5652	−	22.5652i	0.817451	−	0.817451i
$763$	1.51109	+	1.51109i	0.0547052	+	0.0547052i
$764$	16.6037			0.600700
$765$	9.64819	−	8.83290i	0.348831	−	0.319354i
$766$		−	1.70721i		−	0.0616838i
$767$	−3.33833	+	3.33833i	−0.120540	+	0.120540i
$768$	−19.0926	−	19.0926i	−0.688945	−	0.688945i
$769$	−3.09789			−0.111713			−0.0558564	−	0.998439i	$-0.517789\pi$
$769$	−3.09789			−0.111713			−0.0558564	+	0.998439i	$0.517789\pi$
$770$	−0.537647	+	12.1874i	−0.0193754	+	0.439203i
$771$	45.9579			1.65513
$772$	−3.08266	+	3.08266i	−0.110947	+	0.110947i
$773$	4.26685	−	4.26685i	0.153468	−	0.153468i	−0.626197	−	0.779665i	$-0.715389\pi$
$773$	4.26685	−	4.26685i	0.153468	−	0.153468i	0.779665	+	0.626197i	$0.215389\pi$
$774$	2.84468			0.102250
$775$	4.15353	+	0.367181i	0.149199	+	0.0131895i
$776$			43.5238i			1.56241i
$777$	14.7904	−	14.7904i	0.530601	−	0.530601i
$778$	9.16103	−	9.16103i	0.328439	−	0.328439i
$779$	1.14824			0.0411398
$780$	−6.14078	−	0.270901i	−0.219875	−	0.00969980i
$781$		−	25.2561i		−	0.903733i
$782$	−34.2678	+	21.9907i	−1.22541	+	0.786388i
$783$	−15.1506	−	15.1506i	−0.541437	−	0.541437i
$784$		−	1.41911i		−	0.0506824i
$785$	20.1827	+	22.0456i	0.720352	+	0.786841i
$786$	−27.7222			−0.988819
$787$	−19.8446	−	19.8446i	−0.707383	−	0.707383i	0.258601	−	0.965984i	$-0.416738\pi$
$787$	−19.8446	−	19.8446i	−0.707383	−	0.707383i	−0.965984	+	0.258601i	$0.916738\pi$
$788$	7.22022	+	7.22022i	0.257210	+	0.257210i
$789$	26.8434			0.955649
$790$	−2.60118	+	2.38137i	−0.0925458	+	0.0847255i
$791$	−19.5775			−0.696095
$792$	3.24230	+	3.24230i	0.115210	+	0.115210i
$793$	−19.1226	+	19.1226i	−0.679065	+	0.679065i
$794$			7.85809i			0.278873i
$795$	38.2837	+	1.68889i	1.35778	+	0.0598987i
$796$			9.33116i			0.330734i
$797$	−8.00378	−	8.00378i	−0.283509	−	0.283509i	0.550998	−	0.834507i	$-0.314247\pi$
$797$	−8.00378	−	8.00378i	−0.283509	−	0.283509i	−0.834507	+	0.550998i	$0.814247\pi$
$798$	14.9239	+	14.9239i	0.528302	+	0.528302i
$799$	84.8391			3.00139
$800$	13.5581	−	11.3557i	0.479351	−	0.401484i
$801$		−	8.66065i		−	0.306009i
$802$	9.91242	+	9.91242i	0.350020	+	0.350020i
$803$	12.3439	−	12.3439i	0.435606	−	0.435606i
$804$	2.06317			0.0727625
$805$	26.1678	+	6.93159i	0.922292	+	0.244307i
$806$	−2.08167			−0.0733237
$807$	−14.2378	+	14.2378i	−0.501193	+	0.501193i
$808$	15.4017	+	15.4017i	0.541831	+	0.541831i
$809$			2.43398i			0.0855741i	0.999084	+	0.0427871i	$0.0136237\pi$
$809$			2.43398i			0.0855741i	−0.999084	+	0.0427871i	$0.986376\pi$
$810$	−20.5770	+	18.8382i	−0.723001	+	0.661906i
$811$	−30.3188			−1.06464			−0.532319	−	0.846544i	$-0.678679\pi$
$811$	−30.3188			−1.06464			−0.532319	+	0.846544i	$0.678679\pi$
$812$	−5.84118	−	5.84118i	−0.204985	−	0.204985i
$813$	9.42028	+	9.42028i	0.330384	+	0.330384i
$814$		−	9.18794i		−	0.322037i
$815$	21.7902	+	23.8014i	0.763276	+	0.833728i
$816$		−	32.2541i		−	1.12912i
$817$	−8.03000	+	8.03000i	−0.280934	+	0.280934i
$818$	22.9357	+	22.9357i	0.801928	+	0.801928i
$819$	4.34165			0.151710
$820$	−0.0200432	+	0.454340i	−0.000699940	+	0.0158662i
$821$	51.4053			1.79406			0.897028	−	0.441973i	$-0.145721\pi$
$821$	51.4053			1.79406			0.897028	+	0.441973i	$0.145721\pi$
$822$	−19.4820	−	19.4820i	−0.679511	−	0.679511i
$823$	−2.89805	−	2.89805i	−0.101020	−	0.101020i	0.654791	−	0.755810i	$-0.272757\pi$
$823$	−2.89805	−	2.89805i	−0.101020	−	0.101020i	−0.755810	+	0.654791i	$0.772757\pi$
$824$	12.6459			0.440541
$825$	−13.9241	+	11.6622i	−0.484775	+	0.406026i
$826$			6.42051i			0.223398i
$827$	−24.4729	−	24.4729i	−0.851004	−	0.851004i	0.139252	−	0.990257i	$-0.455530\pi$
$827$	−24.4729	−	24.4729i	−0.851004	−	0.851004i	−0.990257	+	0.139252i	$0.955530\pi$
$828$	2.11309	−	1.35604i	0.0734349	−	0.0471256i
$829$			36.4441i			1.26576i	0.774251	+	0.632878i	$0.218127\pi$
$829$			36.4441i			1.26576i	−0.774251	+	0.632878i	$0.781873\pi$
$830$	−0.0414919	+	0.940539i	−0.00144020	+	0.0326466i
$831$	−13.1971			−0.457803
$832$	−13.1237	+	13.1237i	−0.454984	+	0.454984i
$833$	−3.25027	+	3.25027i	−0.112615	+	0.112615i
$834$			27.9268i			0.967028i
$835$	−6.96545	+	6.37685i	−0.241049	+	0.220680i
$836$	−4.51696			−0.156222
$837$	2.52972	−	2.52972i	0.0874400	−	0.0874400i
$838$	−10.2112	+	10.2112i	−0.352739	+	0.352739i
$839$	−26.5753			−0.917481			−0.458741	−	0.888570i	$-0.651699\pi$
$839$	−26.5753			−0.917481			−0.458741	+	0.888570i	$0.651699\pi$
$840$	−24.9863	+	22.8749i	−0.862110	+	0.789259i
$841$	4.05473			0.139818
$842$	−22.8501	−	22.8501i	−0.787465	−	0.787465i
$843$	−25.8290	+	25.8290i	−0.889597	+	0.889597i
$844$		−	0.358579i		−	0.0123428i
$845$	0.824522	−	18.6903i	0.0283644	−	0.642966i
$846$	10.7375			0.369164
$847$	−13.4347	−	13.4347i	−0.461622	−	0.461622i
$848$	14.0528	−	14.0528i	0.482577	−	0.482577i
$849$	24.9003			0.854576
$850$	42.2855	+	3.73813i	1.45038	+	0.128217i
$851$	−19.9194	−	4.34692i	−0.682827	−	0.149010i
$852$	12.2374	−	12.2374i	0.419246	−	0.419246i
$853$	−6.91723	−	6.91723i	−0.236841	−	0.236841i	0.578699	−	0.815541i	$-0.303560\pi$
$853$	−6.91723	−	6.91723i	−0.236841	−	0.236841i	−0.815541	+	0.578699i	$0.803560\pi$
$854$			36.7780i			1.25852i
$855$	−0.291277	+	6.60267i	−0.00996145	+	0.225806i
$856$		−	49.8357i		−	1.70335i
$857$	11.5433	−	11.5433i	0.394312	−	0.394312i	−0.481909	−	0.876221i	$-0.660057\pi$
$857$	11.5433	−	11.5433i	0.394312	−	0.394312i	0.876221	+	0.481909i	$0.160057\pi$
$858$	6.41168	−	6.41168i	0.218891	−	0.218891i
$859$		−	4.02478i		−	0.137324i	−0.997640	−	0.0686618i	$-0.978127\pi$
$859$		−	4.02478i		−	0.137324i	0.997640	−	0.0686618i	$-0.0218729\pi$
$860$	−3.03719	−	3.31752i	−0.103567	−	0.113127i
$861$		−	1.52728i		−	0.0520497i
$862$	−7.16308	−	7.16308i	−0.243976	−	0.243976i
$863$	−1.24478	−	1.24478i	−0.0423729	−	0.0423729i	0.685603	−	0.727976i	$-0.259539\pi$
$863$	−1.24478	−	1.24478i	−0.0423729	−	0.0423729i	−0.727976	+	0.685603i	$0.759539\pi$
$864$		−	15.1738i		−	0.516224i
$865$	16.4893	+	18.0113i	0.560654	+	0.612403i
$866$			40.5760i			1.37883i
$867$	−50.4438	+	50.4438i	−1.71316	+	1.71316i
$868$	0.975314	−	0.975314i	0.0331043	−	0.0331043i
$869$			2.53468i			0.0859831i
$870$	−1.11252	+	25.2186i	−0.0377180	+	0.854991i
$871$		−	3.47750i		−	0.117830i
$872$	1.84321	+	1.84321i	0.0624188	+	0.0624188i
$873$	7.98641	−	7.98641i	0.270299	−	0.270299i
$874$	4.38618	−	20.0993i	0.148365	−	0.679868i
$875$	−17.1504	−	22.4139i	−0.579790	−	0.757728i
$876$	11.9620			0.404160
$877$	−6.27788	+	6.27788i	−0.211989	+	0.211989i	−0.805112	−	0.593123i	$-0.797895\pi$
$877$	−6.27788	+	6.27788i	−0.211989	+	0.211989i	0.593123	+	0.805112i	$0.297895\pi$
$878$	22.0139	+	22.0139i	0.742932	+	0.742932i
$879$	−20.4255			−0.688934
$880$	−0.415136	+	9.41031i	−0.0139942	+	0.317221i
$881$			18.4565i			0.621814i	0.950440	+	0.310907i	$0.100633\pi$
$881$			18.4565i			0.621814i	−0.950440	+	0.310907i	$0.899367\pi$
$882$	−0.411366	+	0.411366i	−0.0138514	+	0.0138514i
$883$	3.42570	+	3.42570i	0.115284	+	0.115284i	0.762395	−	0.647111i	$-0.224023\pi$
$883$	3.42570	+	3.42570i	0.115284	+	0.115284i	−0.647111	+	0.762395i	$0.724023\pi$
$884$	10.3254			0.347282
$885$	−7.05068	+	6.45489i	−0.237006	+	0.216979i
$886$	37.6031			1.26330
$887$	−32.7858	+	32.7858i	−1.10084	+	1.10084i	−0.106528	+	0.994310i	$0.533973\pi$
$887$	−32.7858	+	32.7858i	−1.10084	+	1.10084i	−0.994310	+	0.106528i	$0.966027\pi$
$888$	18.0410	−	18.0410i	0.605418	−	0.605418i
$889$	35.6396			1.19531
$890$	20.7305	−	18.9787i	0.694887	−	0.636167i
$891$			20.0509i			0.671731i
$892$	−5.53074	+	5.53074i	−0.185183	+	0.185183i
$893$	−30.3101	+	30.3101i	−1.01429	+	1.01429i
$894$	49.9917			1.67197
$895$	−1.25974	+	28.5558i	−0.0421084	+	0.954514i
$896$			7.38307i			0.246651i
$897$	−10.8670	−	16.9339i	−0.362839	−	0.565406i
$898$	6.29762	+	6.29762i	0.210154	+	0.210154i
$899$		−	4.16516i		−	0.138916i
$900$	−2.60749	−	0.230508i	−0.0869165	−	0.00768359i
$901$	−64.3723			−2.14455
$902$	−0.474383	−	0.474383i	−0.0157952	−	0.0157952i
$903$	10.6808	+	10.6808i	0.355435	+	0.355435i
$904$	−23.8803			−0.794247
$905$	0.262067	−	5.94054i	0.00871140	−	0.197470i
$906$	26.2128			0.870861
$907$	0.435105	+	0.435105i	0.0144474	+	0.0144474i	0.714294	−	0.699846i	$-0.246748\pi$
$907$	0.435105	+	0.435105i	0.0144474	+	0.0144474i	−0.699846	+	0.714294i	$0.746748\pi$
$908$	−1.87717	+	1.87717i	−0.0622962	+	0.0622962i
$909$		−	5.65228i		−	0.187474i
$910$	9.51416	+	10.3923i	0.315391	+	0.344503i
$911$			16.4896i			0.546324i	0.961968	+	0.273162i	$0.0880695\pi$
$911$			16.4896i			0.546324i	−0.961968	+	0.273162i	$0.911931\pi$
$912$	11.5233	+	11.5233i	0.381575	+	0.381575i
$913$	0.478462	+	0.478462i	0.0158348	+	0.0158348i
$914$	1.29355			0.0427869
$915$	−40.3878	+	36.9749i	−1.33518	+	1.22235i
$916$			11.0409i			0.364802i
$917$	−21.8923	−	21.8923i	−0.722948	−	0.722948i
$918$	25.7541	−	25.7541i	0.850013	−	0.850013i
$919$	−22.8467			−0.753643			−0.376822	−	0.926286i	$-0.622983\pi$
$919$	−22.8467			−0.753643			−0.376822	+	0.926286i	$0.622983\pi$
$920$	31.9190	+	8.45505i	1.05234	+	0.278755i
$921$	−20.7845			−0.684872
$922$	−23.2470	+	23.2470i	−0.765600	+	0.765600i
$923$	−20.6263	−	20.6263i	−0.678921	−	0.678921i
$924$			6.00807i			0.197651i
$925$	13.6484	+	16.2955i	0.448757	+	0.535793i
$926$	31.7114			1.04210
$927$	−2.32046	−	2.32046i	−0.0762139	−	0.0762139i
$928$	−12.4918	−	12.4918i	−0.410063	−	0.410063i
$929$			44.1020i			1.44694i	0.690355	+	0.723470i	$0.257454\pi$
$929$			44.1020i			1.44694i	−0.690355	+	0.723470i	$0.742546\pi$
$930$	−4.21080	−	0.185760i	−0.138078	−	0.00609130i
$931$		−	2.32242i		−	0.0761144i
$932$	−5.04303	+	5.04303i	−0.165190	+	0.165190i
$933$	0.936494	+	0.936494i	0.0306594	+	0.0306594i
$934$	−24.0438			−0.786736
$935$	22.5039	−	20.6022i	0.735955	−	0.673765i
$936$	5.29587			0.173101
$937$	1.75039	+	1.75039i	0.0571827	+	0.0571827i	0.735120	−	0.677937i	$-0.237126\pi$
$937$	1.75039	+	1.75039i	0.0571827	+	0.0571827i	−0.677937	+	0.735120i	$0.737126\pi$
$938$	−3.34408	−	3.34408i	−0.109188	−	0.109188i
$939$	12.2783			0.400686
$940$	−11.4642	−	12.5224i	−0.373921	−	0.408434i
$941$		−	0.294994i		−	0.00961654i	−0.999988	−	0.00480827i	$-0.998469\pi$
$941$		−	0.294994i		−	0.00961654i	0.999988	−	0.00480827i	$-0.00153053\pi$
$942$	−21.3636	−	21.3636i	−0.696065	−	0.696065i
$943$	−1.25289	+	0.804022i	−0.0407998	+	0.0261826i
$944$			4.95750i			0.161353i
$945$	−24.1911	−	1.06719i	−0.786937	−	0.0347157i
$946$	6.63505			0.215724
$947$	21.6094	−	21.6094i	0.702212	−	0.702212i	−0.262673	−	0.964885i	$-0.584604\pi$
$947$	21.6094	−	21.6094i	0.702212	−	0.702212i	0.964885	+	0.262673i	$0.0846041\pi$
$948$	−1.22814	+	1.22814i	−0.0398880	+	0.0398880i
$949$		−	20.1621i		−	0.654490i
$950$	−16.4427	+	13.7717i	−0.533471	+	0.446812i
$951$	−37.1844			−1.20579
$952$	40.2382	−	40.2382i	1.30413	−	1.30413i
$953$	22.4603	−	22.4603i	0.727560	−	0.727560i	−0.242573	−	0.970133i	$-0.577991\pi$
$953$	22.4603	−	22.4603i	0.727560	−	0.727560i	0.970133	+	0.242573i	$0.0779915\pi$
$954$	−8.14719			−0.263775
$955$	2.49732	−	56.6094i	0.0808115	−	1.83184i
$956$	12.3183			0.398404
$957$	12.8290	+	12.8290i	0.414702	+	0.414702i
$958$	15.1368	−	15.1368i	0.489048	−	0.489048i
$959$		−	30.7699i		−	0.993613i
$960$	−27.7178	+	25.3756i	−0.894589	+	0.818994i
$961$	−30.3045			−0.977566
$962$	−7.50365	−	7.50365i	−0.241928	−	0.241928i
$963$	−9.14460	+	9.14460i	−0.294681	+	0.294681i
$964$	1.40891			0.0453779
$965$	10.0465	+	10.9738i	0.323409	+	0.353260i
$966$	−26.7343	−	5.83411i	−0.860163	−	0.187710i
$967$	−13.3362	+	13.3362i	−0.428863	+	0.428863i	−0.888241	−	0.459378i	$-0.848072\pi$
$967$	−13.3362	+	13.3362i	−0.428863	+	0.428863i	0.459378	+	0.888241i	$0.348072\pi$
$968$	−16.3874	−	16.3874i	−0.526712	−	0.526712i
$969$		−	52.7852i		−	1.69570i
$970$	36.6177	+	1.61539i	1.17572	+	0.0518671i
$971$		−	38.1082i		−	1.22295i	−0.791263	−	0.611475i	$-0.790576\pi$
$971$		−	38.1082i		−	1.22295i	0.791263	−	0.611475i	$-0.209424\pi$
$972$	−3.75275	+	3.75275i	−0.120369	+	0.120369i
$973$	−22.0539	+	22.0539i	−0.707016	+	0.707016i
$974$			6.66112i			0.213436i
$975$	−1.84725	+	20.8960i	−0.0591592	+	0.669206i
$976$			28.3976i			0.908984i
$977$	−19.6996	−	19.6996i	−0.630246	−	0.630246i	0.317883	−	0.948130i	$-0.397028\pi$
$977$	−19.6996	−	19.6996i	−0.630246	−	0.630246i	−0.948130	+	0.317883i	$0.897028\pi$
$978$	−23.0652	−	23.0652i	−0.737543	−	0.737543i
$979$		−	20.2005i		−	0.645610i
$980$	0.918949	+	0.0405395i	0.0293548	+	0.00129499i
$981$		−	0.676438i		−	0.0215970i
$982$	12.1832	−	12.1832i	0.388781	−	0.388781i
$983$	15.6702	−	15.6702i	0.499801	−	0.499801i	−0.411575	−	0.911376i	$-0.635021\pi$
$983$	15.6702	−	15.6702i	0.499801	−	0.499801i	0.911376	+	0.411575i	$0.135021\pi$
$984$		−	1.86296i		−	0.0593889i
$985$	25.7030	−	23.5310i	0.818965	−	0.749761i
$986$		−	42.4039i		−	1.35042i
$987$	40.3159	+	40.3159i	1.28327	+	1.28327i
$988$	−3.68893	+	3.68893i	−0.117360	+	0.117360i
$989$	3.13911	−	14.3847i	0.0998180	−	0.457407i
$990$	2.84817	−	2.60749i	0.0905208	−	0.0828716i
$991$	16.6072			0.527545			0.263773	−	0.964585i	$-0.415033\pi$
$991$	16.6072			0.527545			0.263773	+	0.964585i	$0.415033\pi$
$992$	2.08578	−	2.08578i	0.0662235	−	0.0662235i
$993$	−21.0482	−	21.0482i	−0.667944	−	0.667944i
$994$	−39.6698			−1.25825
$995$	31.8141	+	1.40348i	1.00858	+	0.0444933i
$996$			0.463661i			0.0146917i
$997$	16.3178	−	16.3178i	0.516788	−	0.516788i	−0.399810	−	0.916598i	$-0.630924\pi$
$997$	16.3178	−	16.3178i	0.516788	−	0.516788i	0.916598	+	0.399810i	$0.130924\pi$
$998$	2.93570	+	2.93570i	0.0929279	+	0.0929279i
$999$	18.2374			0.577007

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.e.a.68.4	yes	20
5.2	odd	4	inner	115.2.e.a.22.3	✓	20
5.3	odd	4		575.2.e.d.482.7		20
5.4	even	2		575.2.e.d.68.8		20
23.22	odd	2	inner	115.2.e.a.68.3	yes	20
115.22	even	4	inner	115.2.e.a.22.4	yes	20
115.68	even	4		575.2.e.d.482.8		20
115.114	odd	2		575.2.e.d.68.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.e.a.22.3	✓	20	5.2	odd	4	inner
115.2.e.a.22.4	yes	20	115.22	even	4	inner
115.2.e.a.68.3	yes	20	23.22	odd	2	inner
115.2.e.a.68.4	yes	20	1.1	even	1	trivial
575.2.e.d.68.7		20	115.114	odd	2
575.2.e.d.68.8		20	5.4	even	2
575.2.e.d.482.7		20	5.3	odd	4
575.2.e.d.482.8		20	115.68	even	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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.819998 + 0.819998i) q^{2} +(1.37823 + 1.37823i) q^{3} +0.655207i q^{4} +(2.23390 + 0.0985483i) q^{5} -2.26029 q^{6} +(-1.78496 - 1.78496i) q^{7} +(-2.17726 - 2.17726i) q^{8} +0.799034i q^{9} +O(q^{10})\)	\(q+(-0.819998 + 0.819998i) q^{2} +(1.37823 + 1.37823i) q^{3} +0.655207i q^{4} +(2.23390 + 0.0985483i) q^{5} -2.26029 q^{6} +(-1.78496 - 1.78496i) q^{7} +(-2.17726 - 2.17726i) q^{8} +0.799034i q^{9} +(-1.91260 + 1.75098i) q^{10} +1.86370i q^{11} +(-0.903025 + 0.903025i) q^{12} +(1.52206 + 1.52206i) q^{13} +2.92733 q^{14} +(2.94300 + 3.21464i) q^{15} +2.26029 q^{16} +(-5.17689 - 5.17689i) q^{17} +(-0.655207 - 0.655207i) q^{18} +3.69906 q^{19} +(-0.0645695 + 1.46366i) q^{20} -4.92017i q^{21} +(-1.52823 - 1.52823i) q^{22} +(-4.03621 + 2.59017i) q^{23} -6.00154i q^{24} +(4.98058 + 0.440293i) q^{25} -2.49617 q^{26} +(3.03344 - 3.03344i) q^{27} +(1.16952 - 1.16952i) q^{28} -4.99452i q^{29} +(-5.04925 - 0.222748i) q^{30} +0.833946 q^{31} +(2.50109 - 2.50109i) q^{32} +(-2.56861 + 2.56861i) q^{33} +8.49009 q^{34} +(-3.81151 - 4.16332i) q^{35} -0.523533 q^{36} +(3.00607 + 3.00607i) q^{37} +(-3.03322 + 3.03322i) q^{38} +4.19549i q^{39} +(-4.64921 - 5.07835i) q^{40} +0.310413 q^{41} +(4.03453 + 4.03453i) q^{42} +(-2.17082 + 2.17082i) q^{43} -1.22111 q^{44} +(-0.0787435 + 1.78496i) q^{45} +(1.18576 - 5.43362i) q^{46} +(-8.19401 + 8.19401i) q^{47} +(3.11520 + 3.11520i) q^{48} -0.627842i q^{49} +(-4.44510 + 3.72302i) q^{50} -14.2699i q^{51} +(-0.997262 + 0.997262i) q^{52} +(6.21727 - 6.21727i) q^{53} +4.97482i q^{54} +(-0.183665 + 4.16332i) q^{55} +7.77265i q^{56} +(5.09815 + 5.09815i) q^{57} +(4.09550 + 4.09550i) q^{58} +2.19330i q^{59} +(-2.10626 + 1.92827i) q^{60} +12.5637i q^{61} +(-0.683834 + 0.683834i) q^{62} +(1.42624 - 1.42624i) q^{63} +8.62237i q^{64} +(3.25012 + 3.55011i) q^{65} -4.21251i q^{66} +(-1.14237 - 1.14237i) q^{67} +(3.39193 - 3.39193i) q^{68} +(-9.13268 - 1.99298i) q^{69} +(6.53934 + 0.288483i) q^{70} -13.5516 q^{71} +(1.73971 - 1.73971i) q^{72} +(-6.62331 - 6.62331i) q^{73} -4.92994 q^{74} +(6.25755 + 7.47120i) q^{75} +2.42365i q^{76} +(3.32663 - 3.32663i) q^{77} +(-3.44029 - 3.44029i) q^{78} +1.36002 q^{79} +(5.04925 + 0.222748i) q^{80} +10.7586 q^{81} +(-0.254538 + 0.254538i) q^{82} +(0.256727 - 0.256727i) q^{83} +3.22373 q^{84} +(-11.0545 - 12.0748i) q^{85} -3.56014i q^{86} +(6.88360 - 6.88360i) q^{87} +(4.05777 - 4.05777i) q^{88} -10.8389 q^{89} +(-1.39909 - 1.52823i) q^{90} -5.43362i q^{91} +(-1.69710 - 2.64455i) q^{92} +(1.14937 + 1.14937i) q^{93} -13.4382i q^{94} +(8.26331 + 0.364536i) q^{95} +6.89416 q^{96} +(-9.99507 - 9.99507i) q^{97} +(0.514829 + 0.514829i) q^{98} -1.48916 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8}+O(q^{10}) \) 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8	\( 20 q - 4 q^{2} - 8 q^{3} - 8 q^{6} + 4 q^{8} - 16 q^{12} + 4 q^{13} + 8 q^{16} + 8 q^{18} - 12 q^{25} - 16 q^{26} + 4 q^{27} - 4 q^{31} + 24 q^{32} - 8 q^{35} - 32 q^{36} - 36 q^{41} + 32 q^{46} - 8 q^{47} + 4 q^{48} + 60 q^{50} + 40 q^{52} - 12 q^{55} + 36 q^{58} - 60 q^{62} - 76 q^{70} + 44 q^{71} + 72 q^{72} - 56 q^{73} + 28 q^{75} - 12 q^{77} - 44 q^{78} + 92 q^{81} + 28 q^{82} - 4 q^{85} + 24 q^{87} - 72 q^{92} - 8 q^{93} + 64 q^{95} - 104 q^{96} - 60 q^{98}+O(q^{100}) \) 20 * q - 4 * q^2 - 8 * q^3 - 8 * q^6 + 4 * q^8 - 16 * q^12 + 4 * q^13 + 8 * q^16 + 8 * q^18 - 12 * q^25 - 16 * q^26 + 4 * q^27 - 4 * q^31 + 24 * q^32 - 8 * q^35 - 32 * q^36 - 36 * q^41 + 32 * q^46 - 8 * q^47 + 4 * q^48 + 60 * q^50 + 40 * q^52 - 12 * q^55 + 36 * q^58 - 60 * q^62 - 76 * q^70 + 44 * q^71 + 72 * q^72 - 56 * q^73 + 28 * q^75 - 12 * q^77 - 44 * q^78 + 92 * q^81 + 28 * q^82 - 4 * q^85 + 24 * q^87 - 72 * q^92 - 8 * q^93 + 64 * q^95 - 104 * q^96 - 60 * q^98

Introduction

L-functions

Modular forms

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Database

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