LMFDB - Embedded newform 115.2.e.a.22.4

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			22.4
Root			$-0.0985483 + 2.23390i$ of defining polynomial
Character	$\chi$	$=$	115.22
Dual form			115.2.e.a.68.4

$q$-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 $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

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

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	0.355029	−	0.934855i	$-0.384471\pi$
$2$	−0.819998	−	0.819998i	−0.579826	−	0.579826i	−0.934855	+	0.355029i	$0.884471\pi$
$3$	1.37823	−	1.37823i	0.795721	−	0.795721i	−0.186696	−	0.982418i	$-0.559778\pi$
$3$	1.37823	−	1.37823i	0.795721	−	0.795721i	0.982418	+	0.186696i	$0.0597781\pi$
$4$		−	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	−0.958785	−	0.284134i	$-0.908294\pi$
$7$	−1.78496	+	1.78496i	−0.674651	+	0.674651i	0.284134	+	0.958785i	$0.408294\pi$
$8$	−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	$-0.909346\pi$
$11$		−	1.86370i		−	0.561927i	0.959718	−	0.280964i	$-0.0906541\pi$
$12$	−0.903025	−	0.903025i	−0.260681	−	0.260681i
$13$	1.52206	−	1.52206i	0.422143	−	0.422143i	−0.463798	−	0.885941i	$-0.653514\pi$
$13$	1.52206	−	1.52206i	0.422143	−	0.422143i	0.885941	+	0.463798i	$0.153514\pi$
$14$	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	−0.302400	+	0.953181i	$0.597788\pi$
$17$	−5.17689	+	5.17689i	−1.25558	+	1.25558i	−0.953181	+	0.302400i	$0.902212\pi$
$18$	−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	$0.153489\pi$
$29$			4.99452i			0.927460i	−0.885977	+	0.463730i	$0.846511\pi$
$30$	−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	−0.415430	−	0.909625i	$-0.636369\pi$
$37$	3.00607	−	3.00607i	0.494195	−	0.494195i	0.909625	+	0.415430i	$0.136369\pi$
$38$	−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	0.521937	−	0.852984i	$-0.325210\pi$
$43$	−2.17082	−	2.17082i	−0.331048	−	0.331048i	−0.852984	+	0.521937i	$0.825210\pi$
$44$	−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	−0.975581	−	0.219639i	$-0.929512\pi$
$47$	−8.19401	−	8.19401i	−1.19522	−	1.19522i	−0.219639	−	0.975581i	$-0.570488\pi$
$48$	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	0.990624	−	0.136616i	$-0.0436227\pi$
$53$	6.21727	+	6.21727i	0.854008	+	0.854008i	−0.136616	+	0.990624i	$0.543623\pi$
$54$		−	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	$-0.954398\pi$
$59$		−	2.19330i		−	0.285544i	0.989756	−	0.142772i	$-0.0456015\pi$
$60$	−2.10626	−	1.92827i	−0.271916	−	0.248939i
$61$		−	12.5637i		−	1.60861i	−0.594213	−	0.804307i	$-0.702537\pi$
$61$		−	12.5637i		−	1.60861i	0.594213	−	0.804307i	$-0.297463\pi$
$62$	−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	−0.773436	−	0.633874i	$-0.781464\pi$
$67$	−1.14237	+	1.14237i	−0.139562	+	0.139562i	0.633874	+	0.773436i	$0.281464\pi$
$68$	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	−0.979010	−	0.203811i	$-0.934667\pi$
$73$	−6.62331	+	6.62331i	−0.775200	+	0.775200i	0.203811	+	0.979010i	$0.434667\pi$
$74$	−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	0.721056	−	0.692877i	$-0.243657\pi$
$83$	0.256727	+	0.256727i	0.0281794	+	0.0281794i	−0.692877	+	0.721056i	$0.743657\pi$
$84$	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	−0.0149577	+	0.999888i	$0.504761\pi$
$97$	−9.99507	+	9.99507i	−1.01485	+	1.01485i	−0.999888	+	0.0149577i	$0.995239\pi$
$98$	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	0.549407	−	0.835555i	$-0.314854\pi$
$103$	−2.90408	−	2.90408i	−0.286148	−	0.286148i	−0.835555	+	0.549407i	$0.814854\pi$
$104$			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	0.112766	−	0.993622i	$-0.464029\pi$
$107$	11.4446	−	11.4446i	1.10639	−	1.10639i	0.993622	−	0.112766i	$-0.0359710\pi$
$108$	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	0.916326	−	0.400433i	$-0.131140\pi$
$113$	5.48402	+	5.48402i	0.515893	+	0.515893i	−0.400433	+	0.916326i	$0.631140\pi$
$114$	−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	0.108248	−	0.994124i	$-0.465476\pi$
$127$	−9.98331	−	9.98331i	−0.885876	−	0.885876i	−0.994124	+	0.108248i	$0.965476\pi$
$128$	−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	−0.235487	−	0.971877i	$-0.575669\pi$
$137$	8.61922	−	8.61922i	0.736390	−	0.736390i	0.971877	+	0.235487i	$0.0756686\pi$
$138$	9.12302	+	5.85453i	0.776603	+	0.498371i
$139$			12.3554i			1.04797i	0.851727	+	0.523987i	$0.175556\pi$
$139$			12.3554i			1.04797i	−0.851727	+	0.523987i	$0.824444\pi$
$140$	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	−0.220955	−	0.975284i	$-0.570917\pi$
$157$	9.45172	−	9.45172i	0.754329	−	0.754329i	0.975284	+	0.220955i	$0.0709173\pi$
$158$	−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	−0.183703	−	0.982982i	$-0.558808\pi$
$163$	10.2045	−	10.2045i	0.799279	−	0.799279i	0.982982	+	0.183703i	$0.0588084\pi$
$164$		−	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	0.582058	−	0.813147i	$-0.302248\pi$
$167$	−2.98633	−	2.98633i	−0.231089	−	0.231089i	−0.813147	+	0.582058i	$0.802248\pi$
$168$	−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	−0.349746	−	0.936845i	$-0.613732\pi$
$173$	7.72208	−	7.72208i	0.587099	−	0.587099i	0.936845	+	0.349746i	$0.113732\pi$
$174$		−	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	$-0.841463\pi$
$179$		−	12.7829i		−	0.955442i	0.878512	−	0.477721i	$-0.158537\pi$
$180$	−1.16952	+	0.0515932i	−0.0871706	+	0.00384553i
$181$			2.65927i			0.197662i	0.995104	+	0.0988311i	$0.0315104\pi$
$181$			2.65927i			0.197662i	−0.995104	+	0.0988311i	$0.968490\pi$
$182$	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	$0.369245\pi$
$191$			25.3411i			1.83362i	−0.399325	+	0.916809i	$0.630755\pi$
$192$	−11.8836	−	11.8836i	−0.857625	−	0.857625i
$193$	4.70486	−	4.70486i	0.338663	−	0.338663i	−0.517201	−	0.855864i	$-0.673026\pi$
$193$	4.70486	−	4.70486i	0.338663	−	0.338663i	0.855864	+	0.517201i	$0.173026\pi$
$194$	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	0.980691	−	0.195565i	$-0.0626540\pi$
$197$	11.0198	+	11.0198i	0.785126	+	0.785126i	−0.195565	+	0.980691i	$0.562654\pi$
$198$	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	−0.365533	−	0.930798i	$-0.619113\pi$
$223$	8.44122	−	8.44122i	0.565266	−	0.565266i	0.930798	+	0.365533i	$0.119113\pi$
$224$	−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	−0.605607	−	0.795764i	$-0.707070\pi$
$227$	2.86501	−	2.86501i	0.190157	−	0.190157i	0.795764	+	0.605607i	$0.207070\pi$
$228$	−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	−0.408514	−	0.912752i	$-0.633953\pi$
$233$	7.69686	−	7.69686i	0.504238	−	0.504238i	0.912752	+	0.408514i	$0.133953\pi$
$234$			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	$0.208051\pi$
$239$			18.8007i			1.21612i	−0.793892	+	0.608058i	$0.791949\pi$
$240$	6.65203	−	7.26603i	0.429387	−	0.469020i
$241$			2.15033i			0.138515i	0.997599	+	0.0692574i	$0.0220630\pi$
$241$			2.15033i			0.138515i	−0.997599	+	0.0692574i	$0.977937\pi$
$242$	−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	$0.0386503\pi$
$251$			3.83797i			0.242251i	−0.992637	+	0.121125i	$0.961350\pi$
$252$	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	0.999165	+	0.0408546i	$0.0130081\pi$
$257$	16.6728	+	16.6728i	1.04002	+	1.04002i	0.0408546	+	0.999165i	$0.486992\pi$
$258$	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	0.940443	−	0.339951i	$-0.110410\pi$
$263$	9.73835	+	9.73835i	0.600492	+	0.600492i	−0.339951	+	0.940443i	$0.610410\pi$
$264$	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	$-0.898019\pi$
$269$		−	10.3305i		−	0.629860i	0.949115	−	0.314930i	$-0.101981\pi$
$270$	−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	0.548491	−	0.836156i	$-0.315203\pi$
$277$	−4.78771	−	4.78771i	−0.287665	−	0.287665i	−0.836156	+	0.548491i	$0.815203\pi$
$278$	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	$-0.811190\pi$
$281$		−	18.7407i		−	1.11798i	0.829176	−	0.558988i	$-0.188810\pi$
$282$	18.5209	+	18.5209i	1.10290	+	1.10290i
$283$	9.03344	+	9.03344i	0.536982	+	0.536982i	0.922641	−	0.385659i	$-0.126026\pi$
$283$	9.03344	+	9.03344i	0.536982	+	0.536982i	−0.385659	+	0.922641i	$0.626026\pi$
$284$			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	0.456715	−	0.889613i	$-0.349026\pi$
$293$	−7.41003	−	7.41003i	−0.432899	−	0.432899i	−0.889613	+	0.456715i	$0.849026\pi$
$294$		−	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	0.458400	−	0.888746i	$-0.348423\pi$
$307$	−7.54028	−	7.54028i	−0.430347	−	0.430347i	−0.888746	+	0.458400i	$0.848423\pi$
$308$	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	0.821698	−	0.569923i	$-0.193027\pi$
$313$	4.45436	+	4.45436i	0.251775	+	0.251775i	−0.569923	+	0.821698i	$0.693027\pi$
$314$	−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	0.218228	−	0.975898i	$-0.429972\pi$
$317$	−13.4899	−	13.4899i	−0.757670	−	0.757670i	−0.975898	+	0.218228i	$0.929972\pi$
$318$	−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	−0.847535	−	0.530740i	$-0.821914\pi$
$337$	−5.81558	+	5.81558i	−0.316795	+	0.316795i	0.530740	+	0.847535i	$0.321914\pi$
$338$	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	0.431520	−	0.902103i	$-0.357977\pi$
$347$	−8.76600	−	8.76600i	−0.470584	−	0.470584i	−0.902103	+	0.431520i	$0.857977\pi$
$348$	4.51018	−	4.51018i	0.241771	−	0.241771i
$349$		−	11.0595i		−	0.592004i	−0.955187	−	0.296002i	$-0.904346\pi$
$349$		−	11.0595i		−	0.592004i	0.955187	−	0.296002i	$-0.0956535\pi$
$350$	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	0.210881	−	0.977512i	$-0.432367\pi$
$353$	22.3279	−	22.3279i	1.18839	−	1.18839i	0.977512	−	0.210881i	$-0.0676333\pi$
$354$			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	−0.463671	+	0.886007i	$0.653468\pi$
$367$	−25.8561	+	25.8561i	−1.34968	+	1.34968i	−0.886007	+	0.463671i	$0.846532\pi$
$368$	−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	0.0978153	−	0.995205i	$-0.468815\pi$
$373$	−17.3315	−	17.3315i	−0.897389	−	0.897389i	−0.995205	+	0.0978153i	$0.968815\pi$
$374$		−	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	0.680011	−	0.733202i	$-0.261975\pi$
$383$	−1.04098	−	1.04098i	−0.0531917	−	0.0531917i	−0.733202	+	0.680011i	$0.761975\pi$
$384$			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	0.817049	−	0.576569i	$-0.195609\pi$
$397$	4.79153	+	4.79153i	0.240480	+	0.240480i	−0.576569	+	0.817049i	$0.695609\pi$
$398$	−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	$0.0975981\pi$
$401$			12.0884i			0.603663i	−0.953361	+	0.301832i	$0.902402\pi$
$402$	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	$0.243061\pi$
$409$			27.9704i			1.38305i	−0.722353	+	0.691524i	$0.756939\pi$
$410$	−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	$-0.762391\pi$
$421$		−	27.8660i		−	1.35811i	0.734090	−	0.679053i	$-0.237609\pi$
$422$	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	$-0.932528\pi$
$431$		−	8.73549i		−	0.420774i	0.977618	−	0.210387i	$-0.0674723\pi$
$432$	6.85645	+	6.85645i	0.329881	+	0.329881i
$433$	24.7415	+	24.7415i	1.18900	+	1.18900i	0.977344	+	0.211656i	$0.0678858\pi$
$433$	24.7415	+	24.7415i	1.18900	+	1.18900i	0.211656	+	0.977344i	$0.432114\pi$
$434$	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	$0.221335\pi$
$439$			26.8462i			1.28130i	−0.767833	+	0.640650i	$0.778665\pi$
$440$	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	−0.0937869	+	0.995592i	$0.529897\pi$
$443$	−22.9288	+	22.9288i	−1.08938	+	1.08938i	−0.995592	+	0.0937869i	$0.970103\pi$
$444$	−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	$0.0580052\pi$
$449$			7.68005i			0.362444i	−0.983442	+	0.181222i	$0.941995\pi$
$450$	−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	−0.725314	−	0.688418i	$-0.758306\pi$
$457$	−0.788754	+	0.788754i	−0.0368964	+	0.0368964i	0.688418	+	0.725314i	$0.258306\pi$
$458$	−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	−0.995315	−	0.0966834i	$-0.969177\pi$
$463$	−19.3363	+	19.3363i	−0.898632	+	0.898632i	0.0966834	+	0.995315i	$0.469177\pi$
$464$			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	−0.281219	−	0.959643i	$-0.590739\pi$
$467$	14.6609	−	14.6609i	0.678424	−	0.678424i	0.959643	+	0.281219i	$0.0907389\pi$
$468$	−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	0.793119	−	0.609067i	$-0.208456\pi$
$487$	4.06167	+	4.06167i	0.184052	+	0.184052i	−0.609067	+	0.793119i	$0.708456\pi$
$488$	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	$0.0255349\pi$
$499$			3.58013i			0.160269i	−0.996784	+	0.0801343i	$0.974465\pi$
$500$	−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	0.550822	−	0.834623i	$-0.314314\pi$
$503$	−6.36498	−	6.36498i	−0.283801	−	0.283801i	−0.834623	+	0.550822i	$0.814314\pi$
$504$	−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	$-0.887406\pi$
$509$		−	15.6300i		−	0.692789i	0.938089	−	0.346394i	$-0.112594\pi$
$510$	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	$-0.927578\pi$
$521$		−	10.2971i		−	0.451124i	0.974229	−	0.225562i	$-0.0724218\pi$
$522$	−3.27244	−	3.27244i	−0.143231	−	0.143231i
$523$	28.9495	+	28.9495i	1.26587	+	1.26587i	0.948200	+	0.317674i	$0.102902\pi$
$523$	28.9495	+	28.9495i	1.26587	+	1.26587i	0.317674	+	0.948200i	$0.397098\pi$
$524$		−	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	0.157245	−	0.987560i	$-0.449739\pi$
$547$	−19.4194	−	19.4194i	−0.830314	−	0.830314i	−0.987560	+	0.157245i	$0.949739\pi$
$548$	−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	0.0504476	−	0.998727i	$-0.483935\pi$
$557$	24.7614	−	24.7614i	1.04917	−	1.04917i	0.998727	−	0.0504476i	$-0.0160648\pi$
$558$	−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	0.836255	−	0.548341i	$-0.184740\pi$
$563$	6.83152	+	6.83152i	0.287914	+	0.287914i	−0.548341	+	0.836255i	$0.684740\pi$
$564$			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	$0.165581\pi$
$571$			23.7543i			0.994085i	−0.867726	+	0.497043i	$0.834419\pi$
$572$	−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	0.277686	−	0.960672i	$-0.410433\pi$
$577$	−16.4059	−	16.4059i	−0.682986	−	0.682986i	−0.960672	+	0.277686i	$0.910433\pi$
$578$	−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	0.699514	−	0.714619i	$-0.253400\pi$
$587$	−0.365946	−	0.365946i	−0.0151042	−	0.0151042i	−0.714619	+	0.699514i	$0.753400\pi$
$588$	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	−0.821929	−	0.569590i	$-0.807102\pi$
$593$	−6.14484	+	6.14484i	−0.252338	+	0.252338i	0.569590	+	0.821929i	$0.307102\pi$
$594$	−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	$-0.849084\pi$
$599$		−	22.3478i		−	0.913105i	0.889697	−	0.456552i	$-0.150916\pi$
$600$	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	0.971051	+	0.238872i	$0.0767777\pi$
$607$	29.8093	+	29.8093i	1.20992	+	1.20992i	0.238872	+	0.971051i	$0.423222\pi$
$608$	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	0.900929	−	0.433967i	$-0.142887\pi$
$613$	11.5614	+	11.5614i	0.466962	+	0.466962i	−0.433967	+	0.900929i	$0.642887\pi$
$614$			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	−0.985428	−	0.170093i	$-0.945593\pi$
$617$	−20.2525	+	20.2525i	−0.815335	+	0.815335i	0.170093	+	0.985428i	$0.445593\pi$
$618$	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	$-0.995131\pi$
$631$		−	0.768430i		−	0.0305907i	0.999883	−	0.0152954i	$-0.00486885\pi$
$632$	−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	$-0.838273\pi$
$641$		−	24.6345i		−	0.973002i	0.873680	−	0.486501i	$-0.161727\pi$
$642$	−25.8680	+	25.8680i	−1.02093	+	1.02093i
$643$	11.9143	+	11.9143i	0.469853	+	0.469853i	0.901867	−	0.432014i	$-0.142197\pi$
$643$	11.9143	+	11.9143i	0.469853	+	0.469853i	−0.432014	+	0.901867i	$0.642197\pi$
$644$	−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	0.943794	−	0.330534i	$-0.107229\pi$
$647$	15.5990	+	15.5990i	0.613260	+	0.613260i	−0.330534	+	0.943794i	$0.607229\pi$
$648$	−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	−0.658117	−	0.752915i	$-0.728647\pi$
$653$	2.42246	−	2.42246i	0.0947982	−	0.0947982i	0.752915	+	0.658117i	$0.228647\pi$
$654$	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	$0.311187\pi$
$661$			42.6358i			1.65834i	−0.558995	+	0.829171i	$0.688813\pi$
$662$	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	−0.742454	−	0.669897i	$-0.766338\pi$
$673$	−1.88228	+	1.88228i	−0.0725567	+	0.0725567i	0.669897	+	0.742454i	$0.266338\pi$
$674$	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	−0.0232465	−	0.999730i	$-0.507400\pi$
$677$	25.4073	−	25.4073i	0.976483	−	0.976483i	0.999730	+	0.0232465i	$0.00740024\pi$
$678$	−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	−0.867465	−	0.497498i	$-0.834252\pi$
$683$	−9.66884	+	9.66884i	−0.369968	+	0.369968i	0.497498	+	0.867465i	$0.334252\pi$
$684$	−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	$0.168866\pi$
$701$			26.7926i			1.01194i	−0.862550	+	0.505971i	$0.831134\pi$
$702$	−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	$0.212170\pi$
$719$			33.1573i			1.23656i	−0.785958	+	0.618280i	$0.787830\pi$
$720$	−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	−0.982826	−	0.184536i	$-0.940922\pi$
$727$	−21.5242	+	21.5242i	−0.798290	+	0.798290i	0.184536	+	0.982826i	$0.440922\pi$
$728$	−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	−0.982477	−	0.186384i	$-0.940323\pi$
$733$	−31.6457	−	31.6457i	−1.16886	−	1.16886i	−0.186384	−	0.982477i	$-0.559677\pi$
$734$	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	$-0.845669\pi$
$739$		−	25.3398i		−	0.932141i	0.884748	−	0.466071i	$-0.154331\pi$
$740$	−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	0.410176	−	0.912006i	$-0.365467\pi$
$743$	−13.6789	−	13.6789i	−0.501830	−	0.501830i	−0.912006	+	0.410176i	$0.865467\pi$
$744$			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	$0.0920954\pi$
$751$			15.6373i			0.570613i	−0.958436	+	0.285307i	$0.907905\pi$
$752$	−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	−0.784273	−	0.620416i	$-0.786964\pi$
$757$	−4.50831	+	4.50831i	−0.163857	+	0.163857i	0.620416	+	0.784273i	$0.286964\pi$
$758$	−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	0.779665	−	0.626197i	$-0.215389\pi$
$773$	4.26685	+	4.26685i	0.153468	+	0.153468i	−0.626197	+	0.779665i	$0.715389\pi$
$774$	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	−0.965984	−	0.258601i	$-0.916738\pi$
$787$	−19.8446	+	19.8446i	−0.707383	+	0.707383i	0.258601	+	0.965984i	$0.416738\pi$
$788$	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	−0.834507	−	0.550998i	$-0.814247\pi$
$797$	−8.00378	+	8.00378i	−0.283509	+	0.283509i	0.550998	+	0.834507i	$0.314247\pi$
$798$	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	$-0.986376\pi$
$809$		−	2.43398i		−	0.0855741i	0.999084	−	0.0427871i	$-0.0136237\pi$
$810$	−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	−0.755810	−	0.654791i	$-0.772757\pi$
$823$	−2.89805	+	2.89805i	−0.101020	+	0.101020i	0.654791	+	0.755810i	$0.272757\pi$
$824$	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	−0.990257	−	0.139252i	$-0.955530\pi$
$827$	−24.4729	+	24.4729i	−0.851004	+	0.851004i	0.139252	+	0.990257i	$0.455530\pi$
$828$	2.11309	+	1.35604i	0.0734349	+	0.0471256i
$829$		−	36.4441i		−	1.26576i	−0.774251	−	0.632878i	$-0.781873\pi$
$829$		−	36.4441i		−	1.26576i	0.774251	−	0.632878i	$-0.218127\pi$
$830$	−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	−0.815541	−	0.578699i	$-0.803560\pi$
$853$	−6.91723	+	6.91723i	−0.236841	+	0.236841i	0.578699	+	0.815541i	$0.303560\pi$
$854$		−	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	0.876221	−	0.481909i	$-0.160057\pi$
$857$	11.5433	+	11.5433i	0.394312	+	0.394312i	−0.481909	+	0.876221i	$0.660057\pi$
$858$	6.41168	+	6.41168i	0.218891	+	0.218891i
$859$			4.02478i			0.137324i	0.997640	+	0.0686618i	$0.0218729\pi$
$859$			4.02478i			0.137324i	−0.997640	+	0.0686618i	$0.978127\pi$
$860$	−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	−0.727976	−	0.685603i	$-0.759539\pi$
$863$	−1.24478	+	1.24478i	−0.0423729	+	0.0423729i	0.685603	+	0.727976i	$0.259539\pi$
$864$			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	0.593123	−	0.805112i	$-0.297895\pi$
$877$	−6.27788	−	6.27788i	−0.211989	−	0.211989i	−0.805112	+	0.593123i	$0.797895\pi$
$878$	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	$-0.899367\pi$
$881$		−	18.4565i		−	0.621814i	0.950440	−	0.310907i	$-0.100633\pi$
$882$	−0.411366	−	0.411366i	−0.0138514	−	0.0138514i
$883$	3.42570	−	3.42570i	0.115284	−	0.115284i	−0.647111	−	0.762395i	$-0.724023\pi$
$883$	3.42570	−	3.42570i	0.115284	−	0.115284i	0.762395	+	0.647111i	$0.224023\pi$
$884$	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	−0.994310	−	0.106528i	$-0.966027\pi$
$887$	−32.7858	−	32.7858i	−1.10084	−	1.10084i	−0.106528	−	0.994310i	$-0.533973\pi$
$888$	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	−0.699846	−	0.714294i	$-0.746748\pi$
$907$	0.435105	−	0.435105i	0.0144474	−	0.0144474i	0.714294	+	0.699846i	$0.246748\pi$
$908$	−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	$-0.911931\pi$
$911$		−	16.4896i		−	0.546324i	0.961968	−	0.273162i	$-0.0880695\pi$
$912$	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	$-0.742546\pi$
$929$		−	44.1020i		−	1.44694i	0.690355	−	0.723470i	$-0.257454\pi$
$930$	−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	−0.677937	−	0.735120i	$-0.737126\pi$
$937$	1.75039	−	1.75039i	0.0571827	−	0.0571827i	0.735120	+	0.677937i	$0.237126\pi$
$938$	−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	$0.00153053\pi$
$941$			0.294994i			0.00961654i	−0.999988	+	0.00480827i	$0.998469\pi$
$942$	−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	0.964885	−	0.262673i	$-0.0846041\pi$
$947$	21.6094	+	21.6094i	0.702212	+	0.702212i	−0.262673	+	0.964885i	$0.584604\pi$
$948$	−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	0.970133	−	0.242573i	$-0.0779915\pi$
$953$	22.4603	+	22.4603i	0.727560	+	0.727560i	−0.242573	+	0.970133i	$0.577991\pi$
$954$	−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	0.459378	−	0.888241i	$-0.348072\pi$
$967$	−13.3362	−	13.3362i	−0.428863	−	0.428863i	−0.888241	+	0.459378i	$0.848072\pi$
$968$	−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	$0.209424\pi$
$971$			38.1082i			1.22295i	−0.791263	+	0.611475i	$0.790576\pi$
$972$	−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	−0.948130	−	0.317883i	$-0.897028\pi$
$977$	−19.6996	+	19.6996i	−0.630246	+	0.630246i	0.317883	+	0.948130i	$0.397028\pi$
$978$	−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	0.911376	−	0.411575i	$-0.135021\pi$
$983$	15.6702	+	15.6702i	0.499801	+	0.499801i	−0.411575	+	0.911376i	$0.635021\pi$
$984$			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	0.916598	−	0.399810i	$-0.130924\pi$
$997$	16.3178	+	16.3178i	0.516788	+	0.516788i	−0.399810	+	0.916598i	$0.630924\pi$
$998$	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.22.4	yes	20
5.2	odd	4		575.2.e.d.68.7		20
5.3	odd	4	inner	115.2.e.a.68.3	yes	20
5.4	even	2		575.2.e.d.482.8		20
23.22	odd	2	inner	115.2.e.a.22.3	✓	20
115.22	even	4		575.2.e.d.68.8		20
115.68	even	4	inner	115.2.e.a.68.4	yes	20
115.114	odd	2		575.2.e.d.482.7		20

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more