LMFDB - Embedded newform 315.2.k.b.256.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(16,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 2]))

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

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

chi := DirichletCharacter("315.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.k (of order $3$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			256.8
Character	$\chi$	$=$	315.256
Dual form			315.2.k.b.16.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.304907 - 0.528114i) q^{2} +(-1.22862 - 1.22086i) q^{3} +(0.814064 + 1.41000i) q^{4} -1.00000 q^{5} +(-1.01937 + 0.276604i) q^{6} +(1.83653 + 1.90451i) q^{7} +2.21248 q^{8} +(0.0190166 + 2.99994i) q^{9} +O(q^{10})$	\(q+(0.304907 - 0.528114i) q^{2} +(-1.22862 - 1.22086i) q^{3} +(0.814064 + 1.41000i) q^{4} -1.00000 q^{5} +(-1.01937 + 0.276604i) q^{6} +(1.83653 + 1.90451i) q^{7} +2.21248 q^{8} +(0.0190166 + 2.99994i) q^{9} +(-0.304907 + 0.528114i) q^{10} +2.59160 q^{11} +(0.721233 - 2.72621i) q^{12} +(0.424083 - 0.734533i) q^{13} +(1.56577 - 0.389202i) q^{14} +(1.22862 + 1.22086i) q^{15} +(-0.953527 + 1.65156i) q^{16} +(2.86094 - 4.95529i) q^{17} +(1.59011 + 0.904659i) q^{18} +(1.85316 + 3.20976i) q^{19} +(-0.814064 - 1.41000i) q^{20} +(0.0687288 - 4.58206i) q^{21} +(0.790197 - 1.36866i) q^{22} -0.821322 q^{23} +(-2.71830 - 2.70112i) q^{24} +1.00000 q^{25} +(-0.258611 - 0.447928i) q^{26} +(3.63913 - 3.70900i) q^{27} +(-1.19030 + 4.13990i) q^{28} +(-0.710523 - 1.23066i) q^{29} +(1.01937 - 0.276604i) q^{30} +(-1.28764 - 2.23026i) q^{31} +(2.79396 + 4.83927i) q^{32} +(-3.18409 - 3.16397i) q^{33} +(-1.74464 - 3.02180i) q^{34} +(-1.83653 - 1.90451i) q^{35} +(-4.21443 + 2.46896i) q^{36} +(3.88789 + 6.73402i) q^{37} +2.26016 q^{38} +(-1.41780 + 0.384718i) q^{39} -2.21248 q^{40} +(-5.02127 + 8.69709i) q^{41} +(-2.39889 - 1.43340i) q^{42} +(-4.78564 - 8.28897i) q^{43} +(2.10973 + 3.65416i) q^{44} +(-0.0190166 - 2.99994i) q^{45} +(-0.250427 + 0.433752i) q^{46} +(1.54651 - 2.67863i) q^{47} +(3.18784 - 0.865017i) q^{48} +(-0.254294 + 6.99538i) q^{49} +(0.304907 - 0.528114i) q^{50} +(-9.56471 + 2.59537i) q^{51} +1.38092 q^{52} +(1.63632 - 2.83418i) q^{53} +(-0.849181 - 3.05278i) q^{54} -2.59160 q^{55} +(4.06329 + 4.21369i) q^{56} +(1.64183 - 6.20602i) q^{57} -0.866573 q^{58} +(-2.84690 - 4.93098i) q^{59} +(-0.721233 + 2.72621i) q^{60} +(-0.503822 + 0.872646i) q^{61} -1.57044 q^{62} +(-5.67848 + 5.54571i) q^{63} -0.406523 q^{64} +(-0.424083 + 0.734533i) q^{65} +(-2.64179 + 0.716848i) q^{66} +(0.435403 + 0.754140i) q^{67} +9.31594 q^{68} +(1.00909 + 1.00272i) q^{69} +(-1.56577 + 0.389202i) q^{70} -10.3908 q^{71} +(0.0420739 + 6.63731i) q^{72} +(-7.98812 + 13.8358i) q^{73} +4.74178 q^{74} +(-1.22862 - 1.22086i) q^{75} +(-3.01718 + 5.22590i) q^{76} +(4.75956 + 4.93572i) q^{77} +(-0.229121 + 0.866061i) q^{78} +(4.88570 - 8.46228i) q^{79} +(0.953527 - 1.65156i) q^{80} +(-8.99928 + 0.114097i) q^{81} +(3.06204 + 5.30361i) q^{82} +(-7.18628 - 12.4470i) q^{83} +(6.51665 - 3.63318i) q^{84} +(-2.86094 + 4.95529i) q^{85} -5.83669 q^{86} +(-0.629499 + 2.37946i) q^{87} +5.73387 q^{88} +(1.48923 + 2.57942i) q^{89} +(-1.59011 - 0.904659i) q^{90} +(2.17776 - 0.541325i) q^{91} +(-0.668609 - 1.15806i) q^{92} +(-1.14081 + 4.31217i) q^{93} +(-0.943080 - 1.63346i) q^{94} +(-1.85316 - 3.20976i) q^{95} +(2.47535 - 9.35665i) q^{96} +(-6.02424 - 10.4343i) q^{97} +(3.61682 + 2.26724i) q^{98} +(0.0492835 + 7.77465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9} + q^{10} - 2 q^{11} - 16 q^{12} - 4 q^{13} - 13 q^{14} - q^{15} - 5 q^{16} - 7 q^{17} - 12 q^{18} - 2 q^{19} + 7 q^{20} - 5 q^{21} + 19 q^{22} - 2 q^{23} - 30 q^{24} + 24 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 3 q^{30} + 8 q^{31} + 17 q^{32} + q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} + 70 q^{38} - 8 q^{39} - 12 q^{40} + 20 q^{41} - 15 q^{42} + 31 q^{43} - 7 q^{44} - 9 q^{45} - 10 q^{46} - 31 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} - 37 q^{51} + 8 q^{52} + 8 q^{53} + 111 q^{54} + 2 q^{55} + 45 q^{56} + 5 q^{57} - 90 q^{58} - 21 q^{59} + 16 q^{60} + 5 q^{61} + 14 q^{62} - 9 q^{63} - 56 q^{64} + 4 q^{65} + 46 q^{66} + 43 q^{67} + 96 q^{68} + 26 q^{69} + 13 q^{70} + 24 q^{71} - 69 q^{72} - 18 q^{73} - 18 q^{74} + q^{75} - 13 q^{76} + 5 q^{77} + 19 q^{78} + 40 q^{79} + 5 q^{80} - 39 q^{81} + 5 q^{82} - 60 q^{83} + 47 q^{84} + 7 q^{85} - 24 q^{86} - 61 q^{87} - 100 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} - 8 q^{93} - 11 q^{94} + 2 q^{95} + 6 q^{96} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9 + q^10 - 2 * q^11 - 16 * q^12 - 4 * q^13 - 13 * q^14 - q^15 - 5 * q^16 - 7 * q^17 - 12 * q^18 - 2 * q^19 + 7 * q^20 - 5 * q^21 + 19 * q^22 - 2 * q^23 - 30 * q^24 + 24 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 3 * q^30 + 8 * q^31 + 17 * q^32 + q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 + 70 * q^38 - 8 * q^39 - 12 * q^40 + 20 * q^41 - 15 * q^42 + 31 * q^43 - 7 * q^44 - 9 * q^45 - 10 * q^46 - 31 * q^47 - 36 * q^48 - 11 * q^49 - q^50 - 37 * q^51 + 8 * q^52 + 8 * q^53 + 111 * q^54 + 2 * q^55 + 45 * q^56 + 5 * q^57 - 90 * q^58 - 21 * q^59 + 16 * q^60 + 5 * q^61 + 14 * q^62 - 9 * q^63 - 56 * q^64 + 4 * q^65 + 46 * q^66 + 43 * q^67 + 96 * q^68 + 26 * q^69 + 13 * q^70 + 24 * q^71 - 69 * q^72 - 18 * q^73 - 18 * q^74 + q^75 - 13 * q^76 + 5 * q^77 + 19 * q^78 + 40 * q^79 + 5 * q^80 - 39 * q^81 + 5 * q^82 - 60 * q^83 + 47 * q^84 + 7 * q^85 - 24 * q^86 - 61 * q^87 - 100 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 - 8 * q^93 - 11 * q^94 + 2 * q^95 + 6 * q^96 + 6 * q^97 - 15 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.304907	−	0.528114i	0.215602	−	0.373433i	−0.737857	−	0.674957i	$-0.764162\pi$
$2$	0.304907	−	0.528114i	0.215602	−	0.373433i	0.953459	+	0.301524i	$0.0974954\pi$
$3$	−1.22862	−	1.22086i	−0.709344	−	0.704862i
$3$	−1.22862	−	1.22086i	−0.709344	−	0.704862i
$4$	0.814064	+	1.41000i	0.407032	+	0.705000i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.01937	+	0.276604i	−0.416155	+	0.112923i
$7$	1.83653	+	1.90451i	0.694144	+	0.719836i
$7$	1.83653	+	1.90451i	0.694144	+	0.719836i
$8$	2.21248			0.782230
$9$	0.0190166	+	2.99994i	0.00633887	+	0.999980i
$10$	−0.304907	+	0.528114i	−0.0964200	+	0.167004i
$11$	2.59160			0.781397			0.390699	−	0.920519i	$-0.372233\pi$
$11$	2.59160			0.781397			0.390699	+	0.920519i	$0.372233\pi$
$12$	0.721233	−	2.72621i	0.208202	−	0.786989i
$13$	0.424083	−	0.734533i	0.117619	−	0.203723i	−0.801204	−	0.598391i	$-0.795807\pi$
$13$	0.424083	−	0.734533i	0.117619	−	0.203723i	0.918824	+	0.394668i	$0.129140\pi$
$14$	1.56577	−	0.389202i	0.418469	−	0.104019i
$15$	1.22862	+	1.22086i	0.317228	+	0.315224i
$16$	−0.953527	+	1.65156i	−0.238382	+	0.412889i
$17$	2.86094	−	4.95529i	0.693879	−	1.20183i	−0.276678	−	0.960963i	$-0.589233\pi$
$17$	2.86094	−	4.95529i	0.693879	−	1.20183i	0.970557	−	0.240872i	$-0.0774333\pi$
$18$	1.59011	+	0.904659i	0.374792	+	0.213230i
$19$	1.85316	+	3.20976i	0.425144	+	0.736370i	0.996434	−	0.0843777i	$-0.0268902\pi$
$19$	1.85316	+	3.20976i	0.425144	+	0.736370i	−0.571290	+	0.820748i	$0.693557\pi$
$20$	−0.814064	−	1.41000i	−0.182030	−	0.315285i
$21$	0.0687288	−	4.58206i	0.0149979	−	0.999888i
$22$	0.790197	−	1.36866i	0.168471	−	0.291800i
$23$	−0.821322			−0.171258			−0.0856288	−	0.996327i	$-0.527290\pi$
$23$	−0.821322			−0.171258			−0.0856288	+	0.996327i	$0.527290\pi$
$24$	−2.71830	−	2.70112i	−0.554871	−	0.551365i
$25$	1.00000			0.200000
$26$	−0.258611	−	0.447928i	−0.0507179	−	0.0878459i
$27$	3.63913	−	3.70900i	0.700351	−	0.713798i
$28$	−1.19030	+	4.13990i	−0.224945	+	0.782368i
$29$	−0.710523	−	1.23066i	−0.131941	−	0.228528i	0.792484	−	0.609893i	$-0.208788\pi$
$29$	−0.710523	−	1.23066i	−0.131941	−	0.228528i	−0.924425	+	0.381365i	$0.875454\pi$
$30$	1.01937	−	0.276604i	0.186110	−	0.0505008i
$31$	−1.28764	−	2.23026i	−0.231267	−	0.400566i	0.726914	−	0.686728i	$-0.240954\pi$
$31$	−1.28764	−	2.23026i	−0.231267	−	0.400566i	−0.958181	+	0.286162i	$0.907620\pi$
$32$	2.79396	+	4.83927i	0.493906	+	0.855471i
$33$	−3.18409	−	3.16397i	−0.554280	−	0.550777i
$34$	−1.74464	−	3.02180i	−0.299203	−	0.518235i
$35$	−1.83653	−	1.90451i	−0.310431	−	0.321920i
$36$	−4.21443	+	2.46896i	−0.702406	+	0.411493i
$37$	3.88789	+	6.73402i	0.639165	+	1.10707i	0.985616	+	0.168998i	$0.0540533\pi$
$37$	3.88789	+	6.73402i	0.639165	+	1.10707i	−0.346451	+	0.938068i	$0.612613\pi$
$38$	2.26016			0.366647
$39$	−1.41780	+	0.384718i	−0.227029	+	0.0616041i
$40$	−2.21248			−0.349824
$41$	−5.02127	+	8.69709i	−0.784191	+	1.35826i	0.145291	+	0.989389i	$0.453588\pi$
$41$	−5.02127	+	8.69709i	−0.784191	+	1.35826i	−0.929481	+	0.368869i	$0.879745\pi$
$42$	−2.39889	−	1.43340i	−0.370158	−	0.221178i
$43$	−4.78564	−	8.28897i	−0.729803	−	1.26406i	−0.956966	−	0.290199i	$-0.906278\pi$
$43$	−4.78564	−	8.28897i	−0.729803	−	1.26406i	0.227163	−	0.973857i	$-0.427055\pi$
$44$	2.10973	+	3.65416i	0.318053	+	0.550885i
$45$	−0.0190166	−	2.99994i	−0.00283483	−	0.447205i
$46$	−0.250427	+	0.433752i	−0.0369234	+	0.0639532i
$47$	1.54651	−	2.67863i	0.225581	−	0.390718i	−0.730913	−	0.682471i	$-0.760905\pi$
$47$	1.54651	−	2.67863i	0.225581	−	0.390718i	0.956494	+	0.291753i	$0.0942386\pi$
$48$	3.18784	−	0.865017i	0.460125	−	0.124854i
$49$	−0.254294	+	6.99538i	−0.0363278	+	0.999340i
$50$	0.304907	−	0.528114i	0.0431203	−	0.0746866i
$51$	−9.56471	+	2.59537i	−1.33933	+	0.363425i
$52$	1.38092			0.191499
$53$	1.63632	−	2.83418i	0.224765	−	0.389305i	−0.731484	−	0.681859i	$-0.761172\pi$
$53$	1.63632	−	2.83418i	0.224765	−	0.389305i	0.956249	+	0.292554i	$0.0945051\pi$
$54$	−0.849181	−	3.05278i	−0.115559	−	0.415430i
$55$	−2.59160			−0.349451
$56$	4.06329	+	4.21369i	0.542981	+	0.563078i
$57$	1.64183	−	6.20602i	0.217466	−	0.822008i
$58$	−0.866573			−0.113787
$59$	−2.84690	−	4.93098i	−0.370635	−	0.641959i	0.619028	−	0.785369i	$-0.287527\pi$
$59$	−2.84690	−	4.93098i	−0.370635	−	0.641959i	−0.989663	+	0.143410i	$0.954193\pi$
$60$	−0.721233	+	2.72621i	−0.0931107	+	0.351952i
$61$	−0.503822	+	0.872646i	−0.0645078	+	0.111731i	−0.896476	−	0.443093i	$-0.853881\pi$
$61$	−0.503822	+	0.872646i	−0.0645078	+	0.111731i	0.831968	+	0.554824i	$0.187214\pi$
$62$	−1.57044			−0.199446
$63$	−5.67848	+	5.54571i	−0.715421	+	0.698693i
$64$	−0.406523			−0.0508153
$65$	−0.424083	+	0.734533i	−0.0526010	+	0.0911075i
$66$	−2.64179	+	0.716848i	−0.325182	+	0.0882379i
$67$	0.435403	+	0.754140i	0.0531929	+	0.0921328i	0.891396	−	0.453226i	$-0.149727\pi$
$67$	0.435403	+	0.754140i	0.0531929	+	0.0921328i	−0.838203	+	0.545359i	$0.816394\pi$
$68$	9.31594			1.12972
$69$	1.00909	+	1.00272i	0.121481	+	0.120713i
$70$	−1.56577	+	0.389202i	−0.187145	+	0.0465185i
$71$	−10.3908			−1.23316			−0.616581	−	0.787292i	$-0.711483\pi$
$71$	−10.3908			−1.23316			−0.616581	+	0.787292i	$0.711483\pi$
$72$	0.0420739	+	6.63731i	0.00495846	+	0.782215i
$73$	−7.98812	+	13.8358i	−0.934939	+	1.61936i	−0.160195	+	0.987085i	$0.551212\pi$
$73$	−7.98812	+	13.8358i	−0.934939	+	1.61936i	−0.774743	+	0.632276i	$0.782121\pi$
$74$	4.74178			0.551220
$75$	−1.22862	−	1.22086i	−0.141869	−	0.140972i
$76$	−3.01718	+	5.22590i	−0.346094	+	0.599452i
$77$	4.75956	+	4.93572i	0.542402	+	0.562478i
$78$	−0.229121	+	0.866061i	−0.0259428	+	0.0980621i
$79$	4.88570	−	8.46228i	0.549684	−	0.952081i	−0.448612	−	0.893727i	$-0.648081\pi$
$79$	4.88570	−	8.46228i	0.549684	−	0.952081i	0.998296	−	0.0583542i	$-0.0185853\pi$
$80$	0.953527	−	1.65156i	0.106608	−	0.184650i
$81$	−8.99928	+	0.114097i	−0.999920	+	0.0126775i
$82$	3.06204	+	5.30361i	0.338146	+	0.585685i
$83$	−7.18628	−	12.4470i	−0.788797	−	1.36624i	−0.926704	−	0.375791i	$-0.877371\pi$
$83$	−7.18628	−	12.4470i	−0.788797	−	1.36624i	0.137907	−	0.990445i	$-0.455962\pi$
$84$	6.51665	−	3.63318i	0.711025	−	0.396413i
$85$	−2.86094	+	4.95529i	−0.310312	+	0.537477i
$86$	−5.83669			−0.629387
$87$	−0.629499	+	2.37946i	−0.0674894	+	0.255105i
$88$	5.73387			0.611233
$89$	1.48923	+	2.57942i	0.157858	+	0.273418i	0.934096	−	0.357022i	$-0.116208\pi$
$89$	1.48923	+	2.57942i	0.157858	+	0.273418i	−0.776238	+	0.630440i	$0.782875\pi$
$90$	−1.59011	−	0.904659i	−0.167612	−	0.0953594i
$91$	2.17776	−	0.541325i	0.228292	−	0.0567463i
$92$	−0.668609	−	1.15806i	−0.0697073	−	0.120737i
$93$	−1.14081	+	4.31217i	−0.118296	+	0.447151i
$94$	−0.943080	−	1.63346i	−0.0972713	−	0.168479i
$95$	−1.85316	−	3.20976i	−0.190130	−	0.329315i
$96$	2.47535	−	9.35665i	0.252639	−	0.954959i
$97$	−6.02424	−	10.4343i	−0.611668	−	1.05944i	−0.990959	−	0.134163i	$-0.957165\pi$
$97$	−6.02424	−	10.4343i	−0.611668	−	1.05944i	0.379291	−	0.925278i	$-0.376168\pi$
$98$	3.61682	+	2.26724i	0.365354	+	0.229025i
$99$	0.0492835	+	7.77465i	0.00495317	+	0.781381i
$100$	0.814064	+	1.41000i	0.0814064	+	0.141000i
$101$	−0.183389			−0.0182479			−0.00912394	−	0.999958i	$-0.502904\pi$
$101$	−0.183389			−0.0182479			−0.00912394	+	0.999958i	$0.502904\pi$
$102$	−1.54569	+	5.84260i	−0.153046	+	0.578504i
$103$	−10.0259			−0.987884			−0.493942	−	0.869495i	$-0.664444\pi$
$103$	−10.0259			−0.987884			−0.493942	+	0.869495i	$0.664444\pi$
$104$	0.938275	−	1.62514i	0.0920054	−	0.159358i
$105$	−0.0687288	+	4.58206i	−0.00670725	+	0.447163i
$106$	−0.997848	−	1.72832i	−0.0969195	−	0.167870i
$107$	−0.753244	−	1.30466i	−0.0728189	−	0.126126i	0.827317	−	0.561736i	$-0.189866\pi$
$107$	−0.753244	−	1.30466i	−0.0728189	−	0.126126i	−0.900136	+	0.435610i	$0.856533\pi$
$108$	8.19218	+	2.11181i	0.788293	+	0.203209i
$109$	7.48045	−	12.9565i	0.716497	−	1.24101i	−0.245883	−	0.969300i	$-0.579078\pi$
$109$	7.48045	−	12.9565i	0.716497	−	1.24101i	0.962379	−	0.271709i	$-0.0875889\pi$
$110$	−0.790197	+	1.36866i	−0.0753423	+	0.130497i
$111$	3.44454	−	13.0201i	0.326941	−	1.23581i
$112$	−4.89658	+	1.21714i	−0.462684	+	0.115009i
$113$	6.34240	−	10.9854i	0.596643	−	1.03342i	−0.396670	−	0.917961i	$-0.629834\pi$
$113$	6.34240	−	10.9854i	0.596643	−	1.03342i	0.993313	−	0.115455i	$-0.0368325\pi$
$114$	−2.77688	−	2.75933i	−0.260079	−	0.258435i
$115$	0.821322			0.0765887
$116$	1.15682	−	2.00367i	0.107408	−	0.186036i
$117$	2.21162	+	1.25825i	0.204464	+	0.116326i
$118$	−3.47216			−0.319638
$119$	14.6916	−	3.65188i	1.34678	−	0.334767i
$120$	2.71830	+	2.70112i	0.248146	+	0.246578i
$121$	−4.28360			−0.389419
$122$	0.307238	+	0.532151i	0.0278160	+	0.0481787i
$123$	16.7871	−	4.55518i	1.51365	−	0.410726i
$124$	2.09644	−	3.63114i	0.188266	−	0.326086i
$125$	−1.00000			−0.0894427
$126$	1.19736	+	4.68981i	0.106669	+	0.417801i
$127$	12.2153			1.08393			0.541964	−	0.840401i	$-0.317681\pi$
$127$	12.2153			1.08393			0.541964	+	0.840401i	$0.317681\pi$
$128$	−5.71186	+	9.89323i	−0.504862	+	0.874447i
$129$	−4.23991	+	16.0266i	−0.373303	+	1.41106i
$130$	0.258611	+	0.447928i	0.0226817	+	0.0392859i
$131$	14.5615			1.27225			0.636123	−	0.771588i	$-0.280537\pi$
$131$	14.5615			1.27225			0.636123	+	0.771588i	$0.280537\pi$
$132$	1.86915	−	7.06525i	0.162688	−	0.614951i
$133$	−2.70963	+	9.42419i	−0.234955	+	0.817181i
$134$	0.531029			0.0458739
$135$	−3.63913	+	3.70900i	−0.313207	+	0.319220i
$136$	6.32977	−	10.9635i	0.542774	−	0.940111i
$137$	−20.8786			−1.78378			−0.891890	−	0.452253i	$-0.850620\pi$
$137$	−20.8786			−1.78378			−0.891890	+	0.452253i	$0.850620\pi$
$138$	0.837229	−	0.227181i	0.0712696	−	0.0193389i
$139$	9.91507	−	17.1734i	0.840986	−	1.45663i	−0.0480768	−	0.998844i	$-0.515309\pi$
$139$	9.91507	−	17.1734i	0.840986	−	1.45663i	0.889062	−	0.457786i	$-0.151357\pi$
$140$	1.19030	−	4.13990i	0.100599	−	0.349885i
$141$	−5.17029	+	1.40295i	−0.435417	+	0.118150i
$142$	−3.16823	+	5.48753i	−0.265872	+	0.460503i
$143$	1.09905	−	1.90362i	0.0919074	−	0.159188i
$144$	−4.97270	−	2.82912i	−0.414392	−	0.235760i
$145$	0.710523	+	1.23066i	0.0590057	+	0.102201i
$146$	4.87126	+	8.43728i	0.403149	+	0.698274i
$147$	8.85279	−	8.28421i	0.730166	−	0.683270i
$148$	−6.32998	+	10.9638i	−0.520321	+	0.901223i
$149$	−14.3192			−1.17307			−0.586536	−	0.809923i	$-0.699509\pi$
$149$	−14.3192			−1.17307			−0.586536	+	0.809923i	$0.699509\pi$
$150$	−1.01937	+	0.276604i	−0.0832309	+	0.0225846i
$151$	11.1701			0.909011			0.454505	−	0.890744i	$-0.349816\pi$
$151$	11.1701			0.909011			0.454505	+	0.890744i	$0.349816\pi$
$152$	4.10008	+	7.10154i	0.332560	+	0.576011i
$153$	14.9200	+	8.48841i	1.20621	+	0.686247i
$154$	4.05785	−	1.00866i	0.326991	−	0.0812798i
$155$	1.28764	+	2.23026i	0.103426	+	0.179139i
$156$	−1.69663	−	1.68591i	−0.135839	−	0.134981i
$157$	−1.37931	−	2.38904i	−0.110081	−	0.190666i	0.805722	−	0.592294i	$-0.201778\pi$
$157$	−1.37931	−	2.38904i	−0.110081	−	0.190666i	−0.915803	+	0.401628i	$0.868444\pi$
$158$	−2.97937	−	5.16041i	−0.237026	−	0.410541i
$159$	−5.47054	+	1.48443i	−0.433842	+	0.117723i
$160$	−2.79396	−	4.83927i	−0.220882	−	0.382578i
$161$	−1.50839	−	1.56421i	−0.118877	−	0.123277i
$162$	−2.68368	+	4.78743i	−0.210850	+	0.376136i
$163$	−7.91058	−	13.7015i	−0.619604	−	1.07319i	−0.989558	−	0.144136i	$-0.953960\pi$
$163$	−7.91058	−	13.7015i	−0.619604	−	1.07319i	0.369954	−	0.929050i	$-0.379373\pi$
$164$	−16.3505			−1.27676
$165$	3.18409	+	3.16397i	0.247881	+	0.246315i
$166$	−8.76459			−0.680264
$167$	−8.28485	+	14.3498i	−0.641101	+	1.11042i	0.344086	+	0.938938i	$0.388189\pi$
$167$	−8.28485	+	14.3498i	−0.641101	+	1.11042i	−0.985187	+	0.171482i	$0.945145\pi$
$168$	0.152061	−	10.1377i	0.0117318	−	0.782142i
$169$	6.14031	+	10.6353i	0.472331	+	0.818102i
$170$	1.74464	+	3.02180i	0.133808	+	0.231762i
$171$	−9.59386	+	5.62040i	−0.733661	+	0.429803i
$172$	7.79163	−	13.4955i	0.594106	−	1.02902i
$173$	0.523964	−	0.907533i	0.0398363	−	0.0689985i	−0.845420	−	0.534102i	$-0.820650\pi$
$173$	0.523964	−	0.907533i	0.0398363	−	0.0689985i	0.885256	+	0.465104i	$0.153983\pi$
$174$	1.06469	+	1.05796i	0.0807139	+	0.0802038i
$175$	1.83653	+	1.90451i	0.138829	+	0.143967i
$176$	−2.47116	+	4.28018i	−0.186271	+	0.322630i
$177$	−2.52226	+	9.53397i	−0.189585	+	0.716617i
$178$	1.81630			0.136138
$179$	0.924721	−	1.60166i	0.0691169	−	0.119714i	−0.829396	−	0.558661i	$-0.811315\pi$
$179$	0.924721	−	1.60166i	0.0691169	−	0.119714i	0.898513	+	0.438947i	$0.144649\pi$
$180$	4.21443	−	2.46896i	0.314125	−	0.184025i
$181$	17.5376			1.30356			0.651780	−	0.758408i	$-0.274022\pi$
$181$	17.5376			1.30356			0.651780	+	0.758408i	$0.274022\pi$
$182$	0.378134	−	1.31516i	0.0280291	−	0.0974863i
$183$	1.68438	−	0.457056i	0.124513	−	0.0337865i
$184$	−1.81716			−0.133963
$185$	−3.88789	−	6.73402i	−0.285843	−	0.495095i
$186$	1.92948	+	1.91728i	0.141476	+	0.140582i
$187$	7.41441	−	12.8421i	0.542195	−	0.939110i
$188$	5.03582			0.367275
$189$	13.7472	+	0.119047i	0.999963	+	0.00865940i
$190$	−2.26016			−0.163969
$191$	−7.32816	+	12.6927i	−0.530247	+	0.918414i	0.469130	+	0.883129i	$0.344567\pi$
$191$	−7.32816	+	12.6927i	−0.530247	+	0.918414i	−0.999377	+	0.0352855i	$0.988766\pi$
$192$	0.499462	+	0.496306i	0.0360456	+	0.0358178i
$193$	9.68857	+	16.7811i	0.697398	+	1.20793i	0.969365	+	0.245623i	$0.0789925\pi$
$193$	9.68857	+	16.7811i	0.697398	+	1.20793i	−0.271967	+	0.962307i	$0.587674\pi$
$194$	−7.34732			−0.527507
$195$	1.41780	−	0.384718i	0.101530	−	0.0275502i
$196$	−10.0705	+	5.33613i	−0.719321	+	0.381152i
$197$	14.1208			1.00607			0.503034	−	0.864267i	$-0.332217\pi$
$197$	14.1208			1.00607			0.503034	+	0.864267i	$0.332217\pi$
$198$	4.12093	+	2.34452i	0.292862	+	0.166617i
$199$	−7.44208	+	12.8901i	−0.527555	+	0.913752i	0.471929	+	0.881636i	$0.343558\pi$
$199$	−7.44208	+	12.8901i	−0.527555	+	0.913752i	−0.999484	+	0.0321156i	$0.989776\pi$
$200$	2.21248			0.156446
$201$	0.385752	−	1.45812i	0.0272088	−	0.102848i
$202$	−0.0559165	+	0.0968503i	−0.00393427	+	0.00681436i
$203$	1.03891	−	3.61335i	0.0729168	−	0.253607i
$204$	−11.4458	−	11.3734i	−0.801363	−	0.796300i
$205$	5.02127	−	8.69709i	0.350701	−	0.607431i
$206$	−3.05697	+	5.29483i	−0.212989	+	0.368908i
$207$	−0.0156188	−	2.46392i	−0.00108558	−	0.171254i
$208$	0.808748	+	1.40079i	0.0560766	+	0.0971275i
$209$	4.80265	+	8.31843i	0.332206	+	0.575398i
$210$	2.39889	+	1.43340i	0.165539	+	0.0989139i
$211$	9.98630	−	17.2968i	0.687485	−	1.19076i	−0.285164	−	0.958479i	$-0.592048\pi$
$211$	9.98630	−	17.2968i	0.687485	−	1.19076i	0.972649	−	0.232280i	$-0.0746187\pi$
$212$	5.32826			0.365946
$213$	12.7663	+	12.6857i	0.874736	+	0.869208i
$214$	−0.918677			−0.0627995
$215$	4.78564	+	8.28897i	0.326378	+	0.565303i
$216$	8.05151	−	8.20610i	0.547836	−	0.558355i
$217$	1.88275	−	6.54826i	0.127809	−	0.444525i
$218$	−4.56168	−	7.90106i	−0.308956	−	0.535127i
$219$	26.7059	−	7.24663i	1.80462	−	0.489682i
$220$	−2.10973	−	3.65416i	−0.142238	−	0.246363i
$221$	−2.42655	−	4.20290i	−0.163227	−	0.282718i
$222$	−5.82584	−	5.78903i	−0.391005	−	0.388534i
$223$	−12.7041	−	22.0042i	−0.850731	−	1.47351i	−0.880550	−	0.473954i	$-0.842826\pi$
$223$	−12.7041	−	22.0042i	−0.850731	−	1.47351i	0.0298185	−	0.999555i	$-0.490507\pi$
$224$	−4.08524	+	14.2086i	−0.272956	+	0.949351i
$225$	0.0190166	+	2.99994i	0.00126777	+	0.199996i
$226$	−3.86768	−	6.69902i	−0.257274	−	0.445612i
$227$	12.6054			0.836652			0.418326	−	0.908297i	$-0.362617\pi$
$227$	12.6054			0.836652			0.418326	+	0.908297i	$0.362617\pi$
$228$	10.0870	−	2.73711i	0.668031	−	0.181270i
$229$	−8.28392			−0.547417			−0.273708	−	0.961813i	$-0.588250\pi$
$229$	−8.28392			−0.547417			−0.273708	+	0.961813i	$0.588250\pi$
$230$	0.250427	−	0.433752i	0.0165127	−	0.0286008i
$231$	0.178118	−	11.8749i	0.0117193	−	0.781309i
$232$	−1.57202	−	2.72282i	−0.103208	−	0.178762i
$233$	−7.23136	−	12.5251i	−0.473742	−	0.820546i	0.525806	−	0.850605i	$-0.323764\pi$
$233$	−7.23136	−	12.5251i	−0.473742	−	0.820546i	−0.999548	+	0.0300589i	$0.990430\pi$
$234$	1.33884	−	0.784336i	0.0875226	−	0.0512737i
$235$	−1.54651	+	2.67863i	−0.100883	+	0.174734i
$236$	4.63512	−	8.02827i	0.301721	−	0.522596i
$237$	−16.3339	+	4.43219i	−1.06100	+	0.287902i
$238$	2.55096	−	8.87232i	0.165354	−	0.575107i
$239$	−4.79788	+	8.31018i	−0.310349	+	0.537541i	−0.978438	−	0.206541i	$-0.933779\pi$
$239$	−4.79788	+	8.31018i	−0.310349	+	0.537541i	0.668089	+	0.744082i	$0.267113\pi$
$240$	−3.18784	+	0.865017i	−0.205774	+	0.0558366i
$241$	6.32334			0.407322			0.203661	−	0.979041i	$-0.434716\pi$
$241$	6.32334			0.407322			0.203661	+	0.979041i	$0.434716\pi$
$242$	−1.30610	+	2.26223i	−0.0839593	+	0.145422i
$243$	11.1960	+	10.8466i	0.718223	+	0.695813i
$244$	−1.64057			−0.105027
$245$	0.254294	−	6.99538i	0.0162463	−	0.446918i
$246$	2.71286	−	10.2544i	0.172966	−	0.653799i
$247$	3.14357			0.200020
$248$	−2.84888	−	4.93440i	−0.180904	−	0.313335i
$249$	−6.36680	+	24.0661i	−0.403480	+	1.52513i
$250$	−0.304907	+	0.528114i	−0.0192840	+	0.0334009i
$251$	−23.2432			−1.46710			−0.733548	−	0.679638i	$-0.762137\pi$
$251$	−23.2432			−1.46710			−0.733548	+	0.679638i	$0.762137\pi$
$252$	−12.4421	−	3.49210i	−0.783778	−	0.219982i
$253$	−2.12854			−0.133820
$254$	3.72452	−	6.45105i	0.233697	−	0.404775i
$255$	9.56471	−	2.59537i	0.598965	−	0.162529i
$256$	3.07665	+	5.32891i	0.192291	+	0.333057i
$257$	−10.0789			−0.628702			−0.314351	−	0.949307i	$-0.601787\pi$
$257$	−10.0789			−0.628702			−0.314351	+	0.949307i	$0.601787\pi$
$258$	7.17108	+	7.12577i	0.446452	+	0.443631i
$259$	−5.68476	+	19.7718i	−0.353234	+	1.22856i
$260$	−1.38092			−0.0856411
$261$	3.67840	−	2.15493i	0.227687	−	0.133387i
$262$	4.43991	−	7.69014i	0.274298	−	0.475099i
$263$	−21.6265			−1.33355			−0.666774	−	0.745260i	$-0.732325\pi$
$263$	−21.6265			−1.33355			−0.666774	+	0.745260i	$0.732325\pi$
$264$	−7.04475	−	7.00023i	−0.433574	−	0.430835i
$265$	−1.63632	+	2.83418i	−0.100518	+	0.174102i
$266$	4.15086	+	4.30450i	0.254506	+	0.263926i
$267$	1.31941	−	4.98726i	0.0807463	−	0.305216i
$268$	−0.708891	+	1.22784i	−0.0433024	+	0.0750020i
$269$	−9.66852	+	16.7464i	−0.589500	+	1.02104i	0.404798	+	0.914406i	$0.367342\pi$
$269$	−9.66852	+	16.7464i	−0.589500	+	1.02104i	−0.994298	+	0.106638i	$0.965991\pi$
$270$	0.849181	+	3.05278i	0.0516795	+	0.185786i
$271$	11.3865	+	19.7220i	0.691681	+	1.19803i	0.971287	+	0.237912i	$0.0764629\pi$
$271$	11.3865	+	19.7220i	0.691681	+	1.19803i	−0.279606	+	0.960115i	$0.590204\pi$
$272$	5.45596	+	9.45000i	0.330816	+	0.572991i
$273$	−3.33653	−	1.99366i	−0.201936	−	0.120662i
$274$	−6.36603	+	11.0263i	−0.384586	+	0.666122i
$275$	2.59160			0.156279
$276$	−0.592364	+	2.23910i	−0.0356561	+	0.134778i
$277$	13.0057			0.781440			0.390720	−	0.920510i	$-0.372226\pi$
$277$	13.0057			0.781440			0.390720	+	0.920510i	$0.372226\pi$
$278$	−6.04635	−	10.4726i	−0.362636	−	0.628104i
$279$	6.66615	−	3.90525i	0.399092	−	0.233801i
$280$	−4.06329	−	4.21369i	−0.242828	−	0.251816i
$281$	2.44922	+	4.24218i	0.146108	+	0.253067i	0.929786	−	0.368101i	$-0.119992\pi$
$281$	2.44922	+	4.24218i	0.146108	+	0.253067i	−0.783677	+	0.621168i	$0.786658\pi$
$282$	−0.835537	+	3.15827i	−0.0497555	+	0.188072i
$283$	−5.33651	−	9.24310i	−0.317222	−	0.549445i	0.662685	−	0.748898i	$-0.269417\pi$
$283$	−5.33651	−	9.24310i	−0.317222	−	0.549445i	−0.979907	+	0.199453i	$0.936084\pi$
$284$	−8.45877	−	14.6510i	−0.501936	−	0.869378i
$285$	−1.64183	+	6.20602i	−0.0972539	+	0.367613i
$286$	−0.670217	−	1.16085i	−0.0396308	−	0.0686425i
$287$	−25.7854	+	6.40946i	−1.52206	+	0.378338i
$288$	−14.4644	+	8.47372i	−0.852323	+	0.499319i
$289$	−7.86993	−	13.6311i	−0.462937	−	0.801831i
$290$	0.866573			0.0508869
$291$	−5.33727	+	20.1745i	−0.312876	+	1.18265i
$292$	−26.0113			−1.52220
$293$	−4.44394	+	7.69713i	−0.259618	+	0.449671i	−0.966140	−	0.258020i	$-0.916930\pi$
$293$	−4.44394	+	7.69713i	−0.259618	+	0.449671i	0.706522	+	0.707691i	$0.250263\pi$
$294$	−1.67573	−	7.20119i	−0.0977307	−	0.419982i
$295$	2.84690	+	4.93098i	0.165753	+	0.287093i
$296$	8.60188	+	14.8989i	0.499974	+	0.865981i
$297$	9.43118	−	9.61226i	0.547253	−	0.557760i
$298$	−4.36601	+	7.56216i	−0.252916	+	0.438064i
$299$	−0.348308	+	0.603288i	−0.0201432	+	0.0348890i
$300$	0.721233	−	2.72621i	0.0416404	−	0.157398i
$301$	6.99742	−	24.3372i	0.403324	−	1.40278i
$302$	3.40584	−	5.89909i	0.195984	−	0.339455i
$303$	0.225315	+	0.223892i	0.0129440	+	0.0128622i
$304$	−7.06814			−0.405386
$305$	0.503822	−	0.872646i	0.0288488	−	0.0499676i
$306$	9.03205	−	5.29128i	0.516328	−	0.302482i
$307$	−29.1276			−1.66240			−0.831199	−	0.555975i	$-0.812345\pi$
$307$	−29.1276			−1.66240			−0.831199	+	0.555975i	$0.812345\pi$
$308$	−3.08478	+	10.7290i	−0.175772	+	0.611340i
$309$	12.3181	+	12.2402i	0.700750	+	0.696322i
$310$	1.57044			0.0891951
$311$	7.44944	+	12.9028i	0.422419	+	0.731651i	0.996176	−	0.0873749i	$-0.0278478\pi$
$311$	7.44944	+	12.9028i	0.422419	+	0.731651i	−0.573757	+	0.819026i	$0.694514\pi$
$312$	−3.13685	+	0.851181i	−0.177589	+	0.0481886i
$313$	−6.84997	+	11.8645i	−0.387183	+	0.670621i	−0.992069	−	0.125691i	$-0.959885\pi$
$313$	−6.84997	+	11.8645i	−0.387183	+	0.670621i	0.604886	+	0.796312i	$0.293218\pi$
$314$	−1.68225			−0.0949348
$315$	5.67848	−	5.54571i	0.319946	−	0.312465i
$316$	15.9091			0.894956
$317$	−9.30783	+	16.1216i	−0.522780	+	0.905481i	0.476869	+	0.878974i	$0.341772\pi$
$317$	−9.30783	+	16.1216i	−0.522780	+	0.905481i	−0.999649	+	0.0265067i	$0.991562\pi$
$318$	−0.884059	+	3.34168i	−0.0495756	+	0.187392i
$319$	−1.84139	−	3.18938i	−0.103098	−	0.178571i
$320$	0.406523			0.0227253
$321$	−0.667349	+	2.52253i	−0.0372478	+	0.140794i
$322$	−1.28600	+	0.319660i	−0.0716660	+	0.0178140i
$323$	21.2071			1.17999
$324$	−7.48686	−	12.5961i	−0.415937	−	0.699783i
$325$	0.424083	−	0.734533i	0.0235239	−	0.0407445i
$326$	−9.64795			−0.534351
$327$	−25.0087	+	6.78608i	−1.38298	+	0.375271i
$328$	−11.1095	+	19.2422i	−0.613418	+	1.06247i
$329$	7.94167	−	1.97405i	0.437838	−	0.108833i
$330$	2.64179	−	0.716848i	0.145426	−	0.0394612i
$331$	12.6664	−	21.9389i	0.696211	−	1.20587i	−0.273560	−	0.961855i	$-0.588201\pi$
$331$	12.6664	−	21.9389i	0.696211	−	1.20587i	0.969771	−	0.244017i	$-0.0784654\pi$
$332$	11.7002	−	20.2653i	0.642131	−	1.11220i
$333$	−20.1277	+	11.7915i	−1.10299	+	0.646170i
$334$	5.05222	+	8.75069i	0.276445	+	0.478817i
$335$	−0.435403	−	0.754140i	−0.0237886	−	0.0412031i
$336$	7.50200	+	4.48263i	0.409267	+	0.244547i
$337$	0.447094	−	0.774389i	0.0243548	−	0.0421837i	−0.853591	−	0.520944i	$-0.825580\pi$
$337$	0.447094	−	0.774389i	0.0243548	−	0.0421837i	0.877946	+	0.478760i	$0.158914\pi$
$338$	7.48889			0.407342
$339$	−21.2040	+	5.75368i	−1.15164	+	0.312497i
$340$	−9.31594			−0.505228
$341$	−3.33705	−	5.77994i	−0.180711	−	0.313001i
$342$	0.0429806	+	6.78035i	0.00232413	+	0.366639i
$343$	−13.7898	+	12.3629i	−0.744578	+	0.667536i
$344$	−10.5881	−	18.3392i	−0.570874	−	0.988783i
$345$	−1.00909	−	1.00272i	−0.0543278	−	0.0539845i
$346$	−0.319521	−	0.553426i	−0.0171775	−	0.0297524i
$347$	−5.11830	−	8.86516i	−0.274765	−	0.475907i	0.695311	−	0.718709i	$-0.255267\pi$
$347$	−5.11830	−	8.86516i	−0.274765	−	0.475907i	−0.970076	+	0.242802i	$0.921933\pi$
$348$	−3.86749	+	1.04944i	−0.207319	+	0.0562559i
$349$	8.59290	+	14.8833i	0.459967	+	0.796687i	0.998959	−	0.0456246i	$-0.0145278\pi$
$349$	8.59290	+	14.8833i	0.459967	+	0.796687i	−0.538991	+	0.842311i	$0.681194\pi$
$350$	1.56577	−	0.389202i	0.0836938	−	0.0208037i
$351$	−1.18109	−	4.24599i	−0.0630420	−	0.226634i
$352$	7.24082	+	12.5415i	0.385937	+	0.668462i
$353$	−19.7286			−1.05005			−0.525025	−	0.851087i	$-0.675944\pi$
$353$	−19.7286			−1.05005			−0.525025	+	0.851087i	$0.675944\pi$
$354$	4.26597	+	4.23901i	0.226734	+	0.225301i
$355$	10.3908			0.551486
$356$	−2.42465	+	4.19962i	−0.128506	+	0.222580i
$357$	−22.5088	−	13.4496i	−1.19129	−	0.711826i
$358$	−0.563908	−	0.976717i	−0.0298035	−	0.0516211i
$359$	−11.2039	−	19.4056i	−0.591317	−	1.02419i	−0.994055	−	0.108876i	$-0.965275\pi$
$359$	−11.2039	−	19.4056i	−0.591317	−	1.02419i	0.402739	−	0.915315i	$-0.368058\pi$
$360$	−0.0420739	−	6.63731i	−0.00221749	−	0.349817i
$361$	2.63161	−	4.55808i	0.138506	−	0.239899i
$362$	5.34734	−	9.26186i	0.281050	−	0.486793i
$363$	5.26292	+	5.22967i	0.276232	+	0.274486i
$364$	2.53611	+	2.62997i	0.132928	+	0.137848i
$365$	7.98812	−	13.8358i	0.418117	−	0.724200i
$366$	0.272202	−	1.02891i	0.0142282	−	0.0537817i
$367$	18.5225			0.966867			0.483434	−	0.875381i	$-0.339389\pi$
$367$	18.5225			0.966867			0.483434	+	0.875381i	$0.339389\pi$
$368$	0.783153	−	1.35646i	0.0408247	−	0.0707104i
$369$	−26.1862	−	14.8981i	−1.36320	−	0.775565i
$370$	−4.74178			−0.246513
$371$	8.40287	−	2.08869i	0.436255	−	0.108440i
$372$	−7.00884	+	1.90184i	−0.363391	+	0.0986059i
$373$	11.0195			0.570566			0.285283	−	0.958443i	$-0.407912\pi$
$373$	11.0195			0.570566			0.285283	+	0.958443i	$0.407912\pi$
$374$	−4.52141	−	7.83131i	−0.233796	−	0.404947i
$375$	1.22862	+	1.22086i	0.0634457	+	0.0630448i
$376$	3.42162	−	5.92641i	0.176456	−	0.305631i
$377$	−1.20528			−0.0620751
$378$	4.25449	−	7.22380i	0.218827	−	0.371552i
$379$	−13.3492			−0.685702			−0.342851	−	0.939390i	$-0.611393\pi$
$379$	−13.3492			−0.685702			−0.342851	+	0.939390i	$0.611393\pi$
$380$	3.01718	−	5.22590i	0.154778	−	0.268083i
$381$	−15.0079	−	14.9131i	−0.768879	−	0.764020i
$382$	4.46881	+	7.74021i	0.228644	+	0.396023i
$383$	26.8424			1.37158			0.685792	−	0.727798i	$-0.259456\pi$
$383$	26.8424			1.37158			0.685792	+	0.727798i	$0.259456\pi$
$384$	19.0959	−	5.18166i	0.974485	−	0.264426i
$385$	−4.75956	−	4.93572i	−0.242570	−	0.251548i
$386$	11.8164			0.601441
$387$	24.7754	−	14.5143i	1.25940	−	0.737801i
$388$	9.80822	−	16.9883i	0.497937	−	0.862452i
$389$	27.6951			1.40419			0.702097	−	0.712081i	$-0.252247\pi$
$389$	27.6951			1.40419			0.702097	+	0.712081i	$0.252247\pi$
$390$	0.229121	−	0.866061i	0.0116020	−	0.0438547i
$391$	−2.34975	+	4.06989i	−0.118832	+	0.205823i
$392$	−0.562622	+	15.4771i	−0.0284167	+	0.781714i
$393$	−17.8906	−	17.7775i	−0.902460	−	0.896758i
$394$	4.30554	−	7.45741i	0.216910	−	0.375699i
$395$	−4.88570	+	8.46228i	−0.245826	+	0.425784i
$396$	−10.9221	+	6.39855i	−0.548858	+	0.321539i
$397$	8.58155	+	14.8637i	0.430696	+	0.745987i	0.996933	−	0.0782551i	$-0.0249349\pi$
$397$	8.58155	+	14.8637i	0.430696	+	0.745987i	−0.566238	+	0.824242i	$0.691602\pi$
$398$	4.53828	+	7.86053i	0.227484	+	0.394013i
$399$	14.8347	−	8.27068i	0.742664	−	0.414052i
$400$	−0.953527	+	1.65156i	−0.0476763	+	0.0825778i
$401$	32.4100			1.61848			0.809239	−	0.587479i	$-0.199880\pi$
$401$	32.4100			1.61848			0.809239	+	0.587479i	$0.199880\pi$
$402$	−0.652433	−	0.648311i	−0.0325404	−	0.0323348i
$403$	−2.18426			−0.108806
$404$	−0.149290	−	0.258578i	−0.00742747	−	0.0128647i
$405$	8.99928	−	0.114097i	0.447178	−	0.00566954i
$406$	−1.59149	−	1.65039i	−0.0789843	−	0.0819077i
$407$	10.0759	+	17.4519i	0.499442	+	0.865059i
$408$	−21.1617	+	5.74222i	−1.04766	+	0.284282i
$409$	2.00476	+	3.47234i	0.0991289	+	0.171696i	0.911324	−	0.411689i	$-0.135061\pi$
$409$	2.00476	+	3.47234i	0.0991289	+	0.171696i	−0.812195	+	0.583385i	$0.801728\pi$
$410$	−3.06204	−	5.30361i	−0.151223	−	0.261926i
$411$	25.6519	+	25.4898i	1.26531	+	1.25732i
$412$	−8.16174	−	14.1365i	−0.402100	−	0.696458i
$413$	4.16266	−	14.4779i	0.204831	−	0.712409i
$414$	−1.30599	−	0.743017i	−0.0641860	−	0.0365173i
$415$	7.18628	+	12.4470i	0.352761	+	0.610999i
$416$	4.73947			0.232372
$417$	−33.1481	+	8.99472i	−1.62327	+	0.440473i
$418$	5.85744			0.286497
$419$	−8.65843	+	14.9968i	−0.422992	+	0.732644i	−0.996231	−	0.0867448i	$-0.972354\pi$
$419$	−8.65843	+	14.9968i	−0.422992	+	0.732644i	0.573238	+	0.819389i	$0.305687\pi$
$420$	−6.51665	+	3.63318i	−0.317980	+	0.177281i
$421$	14.6623	+	25.3959i	0.714598	+	1.23772i	0.963114	+	0.269092i	$0.0867236\pi$
$421$	14.6623	+	25.3959i	0.714598	+	1.23772i	−0.248517	+	0.968628i	$0.579943\pi$
$422$	−6.08978	−	10.5478i	−0.296446	−	0.513459i
$423$	8.06513	+	4.58849i	0.392140	+	0.223100i
$424$	3.62032	−	6.27057i	0.175818	−	0.304526i
$425$	2.86094	−	4.95529i	0.138776	−	0.240367i
$426$	10.5920	−	2.87414i	0.513186	−	0.139252i
$427$	−2.58725	+	0.643110i	−0.125206	+	0.0311223i
$428$	1.22638	−	2.12415i	0.0592792	−	0.102675i
$429$	−3.67436	+	0.997034i	−0.177400	+	0.0481373i
$430$	5.83669			0.281470
$431$	11.6728	−	20.2178i	0.562258	−	0.973859i	−0.435041	−	0.900411i	$-0.643266\pi$
$431$	11.6728	−	20.2178i	0.562258	−	0.973859i	0.997299	−	0.0734485i	$-0.0234005\pi$
$432$	2.65562	+	9.54687i	0.127769	+	0.459324i
$433$	−4.00111			−0.192281			−0.0961406	−	0.995368i	$-0.530650\pi$
$433$	−4.00111			−0.192281			−0.0961406	+	0.995368i	$0.530650\pi$
$434$	−2.88417	−	2.99092i	−0.138444	−	0.143569i
$435$	0.629499	−	2.37946i	0.0301822	−	0.114086i
$436$	24.3582			1.16655
$437$	−1.52204	−	2.63625i	−0.0728091	−	0.126109i
$438$	4.31577	−	16.3133i	0.206216	−	0.779481i
$439$	2.07375	−	3.59183i	0.0989745	−	0.171429i	−0.812286	−	0.583259i	$-0.801777\pi$
$439$	2.07375	−	3.59183i	0.0989745	−	0.171429i	0.911260	+	0.411831i	$0.135110\pi$
$440$	−5.73387			−0.273351
$441$	−20.9906	−	0.629839i	−0.999550	−	0.0299923i
$442$	−2.95948			−0.140768
$443$	10.9253	−	18.9231i	0.519075	−	0.899064i	−0.480680	−	0.876896i	$-0.659610\pi$
$443$	10.9253	−	18.9231i	0.519075	−	0.899064i	0.999754	−	0.0221673i	$-0.00705664\pi$
$444$	21.1624	−	5.74241i	1.00432	−	0.272523i
$445$	−1.48923	−	2.57942i	−0.0705962	−	0.122276i
$446$	−15.4943			−0.733676
$447$	17.5928	+	17.4817i	0.832112	+	0.826854i
$448$	−0.746592	−	0.774225i	−0.0352732	−	0.0365787i
$449$	6.28701			0.296702			0.148351	−	0.988935i	$-0.452603\pi$
$449$	6.28701			0.296702			0.148351	+	0.988935i	$0.452603\pi$
$450$	1.59011	+	0.904659i	0.0749584	+	0.0426460i
$451$	−13.0131	+	22.5394i	−0.612764	+	1.06134i
$452$	20.6525			0.971411
$453$	−13.7238	−	13.6371i	−0.644802	−	0.640727i
$454$	3.84348	−	6.65710i	0.180384	−	0.312433i
$455$	−2.17776	+	0.541325i	−0.102095	+	0.0253777i
$456$	3.63253	−	13.7307i	0.170109	−	0.642999i
$457$	−11.4016	+	19.7481i	−0.533343	+	0.923778i	0.465898	+	0.884838i	$0.345731\pi$
$457$	−11.4016	+	19.7481i	−0.533343	+	0.923778i	−0.999242	+	0.0389393i	$0.987602\pi$
$458$	−2.52582	+	4.37486i	−0.118024	+	0.204424i
$459$	−7.96786	−	28.6442i	−0.371908	−	1.33700i
$460$	0.668609	+	1.15806i	0.0311740	+	0.0539950i
$461$	−0.276239	−	0.478459i	−0.0128657	−	0.0222841i	0.859521	−	0.511101i	$-0.170762\pi$
$461$	−0.276239	−	0.478459i	−0.0128657	−	0.0222841i	−0.872387	+	0.488817i	$0.837429\pi$
$462$	−6.21698	−	3.71480i	−0.289240	−	0.172828i
$463$	4.80357	−	8.32002i	0.223241	−	0.386664i	−0.732550	−	0.680714i	$-0.761670\pi$
$463$	4.80357	−	8.32002i	0.223241	−	0.386664i	0.955790	+	0.294050i	$0.0950031\pi$
$464$	2.71001			0.125809
$465$	1.14081	−	4.31217i	0.0529036	−	0.199972i
$466$	−8.81957			−0.408559
$467$	9.57895	+	16.5912i	0.443261	+	0.767750i	0.997929	−	0.0643211i	$-0.0204882\pi$
$467$	9.57895	+	16.5912i	0.443261	+	0.767750i	−0.554668	+	0.832072i	$0.687155\pi$
$468$	0.0262604	+	4.14268i	0.00121389	+	0.191495i
$469$	−0.636633	+	2.21423i	−0.0293970	+	0.102244i
$470$	0.943080	+	1.63346i	0.0435010	+	0.0753460i
$471$	−1.22203	+	4.61917i	−0.0563080	+	0.212840i
$472$	−6.29872	−	10.9097i	−0.289922	−	0.502160i
$473$	−12.4025	−	21.4817i	−0.570266	−	0.987730i
$474$	−2.63962	+	9.97757i	−0.121242	+	0.458285i
$475$	1.85316	+	3.20976i	0.0850287	+	0.147274i
$476$	17.1090	+	17.7423i	0.784191	+	0.813216i
$477$	8.53349	+	4.85495i	0.390722	+	0.222293i
$478$	2.92582	+	5.06766i	0.133824	+	0.231789i
$479$	37.6979			1.72246			0.861231	−	0.508213i	$-0.169694\pi$
$479$	37.6979			1.72246			0.861231	+	0.508213i	$0.169694\pi$
$480$	−2.47535	+	9.35665i	−0.112984	+	0.427071i
$481$	6.59514			0.300713
$482$	1.92803	−	3.33944i	0.0878193	−	0.152108i
$483$	−0.0564485	+	3.76335i	−0.00256850	+	0.171238i
$484$	−3.48713	−	6.03988i	−0.158506	−	0.274540i
$485$	6.02424	+	10.4343i	0.273546	+	0.473796i
$486$	9.14200	−	2.60554i	0.414690	−	0.118190i
$487$	0.455759	−	0.789397i	0.0206524	−	0.0357710i	−0.855514	−	0.517779i	$-0.826759\pi$
$487$	0.455759	−	0.789397i	0.0206524	−	0.0357710i	0.876167	+	0.482008i	$0.160092\pi$
$488$	−1.11470	+	1.93071i	−0.0504600	+	0.0873993i
$489$	−7.00850	+	26.4916i	−0.316935	+	1.19799i
$490$	−3.61682	−	2.26724i	−0.163391	−	0.102423i
$491$	−13.5035	+	23.3887i	−0.609403	+	1.05552i	0.381935	+	0.924189i	$0.375258\pi$
$491$	−13.5035	+	23.3887i	−0.609403	+	1.05552i	−0.991339	+	0.131329i	$0.958076\pi$
$492$	20.0886	+	19.9617i	0.905664	+	0.899941i
$493$	−8.13105			−0.366204
$494$	0.958495	−	1.66016i	0.0431247	−	0.0746943i
$495$	−0.0492835	−	7.77465i	−0.00221513	−	0.349444i
$496$	4.91120			0.220519
$497$	−19.0830	−	19.7894i	−0.855992	−	0.887674i
$498$	10.7683	+	10.7003i	0.482541	+	0.479492i
$499$	−15.6527			−0.700709			−0.350355	−	0.936617i	$-0.613939\pi$
$499$	−15.6527			−0.700709			−0.350355	+	0.936617i	$0.613939\pi$
$500$	−0.814064	−	1.41000i	−0.0364060	−	0.0630571i
$501$	27.6980	−	7.51582i	1.23745	−	0.335782i
$502$	−7.08700	+	12.2750i	−0.316308	+	0.547862i
$503$	21.7298			0.968882			0.484441	−	0.874824i	$-0.339023\pi$
$503$	21.7298			0.968882			0.484441	+	0.874824i	$0.339023\pi$
$504$	−12.5635	+	12.2698i	−0.559624	+	0.546539i
$505$	0.183389			0.00816070
$506$	−0.649006	+	1.12411i	−0.0288518	+	0.0499729i
$507$	5.44010	−	20.5632i	0.241603	−	0.913244i
$508$	9.94400	+	17.2235i	0.441194	+	0.764170i
$509$	17.7242			0.785611			0.392805	−	0.919622i	$-0.371505\pi$
$509$	17.7242			0.785611			0.392805	+	0.919622i	$0.371505\pi$
$510$	1.54569	−	5.84260i	0.0684443	−	0.258715i
$511$	−41.0209	+	10.1965i	−1.81466	+	0.451068i
$512$	−19.0951			−0.843891
$513$	18.6489	+	4.80739i	0.823370	+	0.212251i
$514$	−3.07311	+	5.32279i	−0.135549	+	0.234778i
$515$	10.0259			0.441795
$516$	−26.0490	+	7.06838i	−1.14674	+	0.311168i
$517$	4.00793	−	6.94193i	0.176268	−	0.305306i
$518$	8.70843	+	9.03075i	0.382626	+	0.396788i
$519$	−1.75172	+	0.475328i	−0.0768920	+	0.0208646i
$520$	−0.938275	+	1.62514i	−0.0411461	+	0.0712671i
$521$	17.8247	−	30.8733i	0.780915	−	1.35259i	−0.150494	−	0.988611i	$-0.548086\pi$
$521$	17.8247	−	30.8733i	0.780915	−	1.35259i	0.931409	−	0.363974i	$-0.118580\pi$
$522$	−0.0164793	−	2.59967i	−0.000721278	−	0.113784i
$523$	−7.63530	−	13.2247i	−0.333868	−	0.578277i	0.649399	−	0.760448i	$-0.275021\pi$
$523$	−7.63530	−	13.2247i	−0.333868	−	0.578277i	−0.983267	+	0.182171i	$0.941687\pi$
$524$	11.8540	+	20.5317i	0.517844	+	0.896933i
$525$	0.0687288	−	4.58206i	0.00299957	−	0.199978i
$526$	−6.59407	+	11.4213i	−0.287515	+	0.497991i
$527$	−14.7354			−0.641886
$528$	8.26160	−	2.24178i	0.359540	−	0.0975609i
$529$	−22.3254			−0.970671
$530$	0.997848	+	1.72832i	0.0433437	+	0.0750735i
$531$	14.7385	−	8.63431i	0.639597	−	0.374697i
$532$	−15.4939	+	3.85131i	−0.671747	+	0.166975i
$533$	4.25887	+	7.37657i	0.184472	+	0.319515i
$534$	−2.23155	−	2.21745i	−0.0965686	−	0.0959583i
$535$	0.753244	+	1.30466i	0.0325656	+	0.0564053i
$536$	0.963321	+	1.66852i	0.0416091	+	0.0720691i
$537$	−3.09153	+	0.838885i	−0.133410	+	0.0362006i
$538$	5.89600	+	10.2122i	0.254194	+	0.440278i
$539$	−0.659029	+	18.1292i	−0.0283864	+	0.780881i
$540$	−8.19218	−	2.11181i	−0.352535	−	0.0908779i
$541$	−18.3417	−	31.7688i	−0.788573	−	1.36585i	−0.926841	−	0.375453i	$-0.877487\pi$
$541$	−18.3417	−	31.7688i	−0.788573	−	1.36585i	0.138269	−	0.990395i	$-0.455846\pi$
$542$	13.8873			0.596510
$543$	−21.5471	−	21.4109i	−0.924674	−	0.918831i
$544$	31.9733			1.37085
$545$	−7.48045	+	12.9565i	−0.320427	+	0.554996i
$546$	−2.07021	+	1.15419i	−0.0885967	+	0.0493946i
$547$	10.7334	+	18.5908i	0.458928	+	0.794887i	0.998905	−	0.0467935i	$-0.0149003\pi$
$547$	10.7334	+	18.5908i	0.458928	+	0.794887i	−0.539977	+	0.841680i	$0.681567\pi$
$548$	−16.9965	−	29.4388i	−0.726055	−	1.25756i
$549$	−2.62747	−	1.49484i	−0.112138	−	0.0637983i
$550$	0.790197	−	1.36866i	0.0336941	−	0.0583599i
$551$	2.63342	−	4.56122i	0.112188	−	0.194315i
$552$	2.23260	+	2.21849i	0.0950258	+	0.0944253i
$553$	25.0892	−	6.23641i	1.06690	−	0.265199i
$554$	3.96554	−	6.86852i	0.168480	−	0.291815i
$555$	−3.44454	+	13.0201i	−0.146212	+	0.552673i
$556$	32.2860			1.36923
$557$	−20.8397	+	36.0954i	−0.883006	+	1.52941i	−0.0350230	+	0.999387i	$0.511150\pi$
$557$	−20.8397	+	36.0954i	−0.883006	+	1.52941i	−0.847983	+	0.530024i	$0.822183\pi$
$558$	−0.0298645	−	4.71123i	−0.00126426	−	0.199442i
$559$	−8.11802			−0.343356
$560$	4.89658	−	1.21714i	0.206918	−	0.0514335i
$561$	−24.7879	+	6.72618i	−1.04655	+	0.283979i
$562$	2.98714			0.126005
$563$	15.8164	+	27.3948i	0.666582	+	1.15455i	0.978854	+	0.204561i	$0.0655766\pi$
$563$	15.8164	+	27.3948i	0.666582	+	1.15455i	−0.312272	+	0.949993i	$0.601090\pi$
$564$	−6.18711	−	6.14801i	−0.260524	−	0.258878i
$565$	−6.34240	+	10.9854i	−0.266827	+	0.462158i
$566$	−6.50855			−0.273575
$567$	−16.7448	−	16.9296i	−0.703214	−	0.710978i
$568$	−22.9895			−0.964616
$569$	8.54530	−	14.8009i	0.358237	−	0.620486i	−0.629429	−	0.777058i	$-0.716711\pi$
$569$	8.54530	−	14.8009i	0.358237	−	0.620486i	0.987666	+	0.156572i	$0.0500445\pi$
$570$	2.77688	+	2.75933i	0.116311	+	0.115576i
$571$	−4.79354	−	8.30265i	−0.200603	−	0.347455i	0.748120	−	0.663564i	$-0.230957\pi$
$571$	−4.79354	−	8.30265i	−0.200603	−	0.347455i	−0.948723	+	0.316109i	$0.897624\pi$
$572$	3.57880			0.149637
$573$	24.4995	−	6.64793i	1.02348	−	0.277721i
$574$	−4.47722	+	15.5719i	−0.186876	+	0.649960i
$575$	−0.821322			−0.0342515
$576$	−0.00773068	−	1.21954i	−0.000322112	−	0.0508143i
$577$	−1.38408	+	2.39729i	−0.0576199	+	0.0998007i	−0.893397	−	0.449269i	$-0.851684\pi$
$577$	−1.38408	+	2.39729i	−0.0576199	+	0.0998007i	0.835777	+	0.549070i	$0.185018\pi$
$578$	−9.59839			−0.399240
$579$	8.58374	−	32.4459i	0.356728	−	1.34841i
$580$	−1.15682	+	2.00367i	−0.0480344	+	0.0831980i
$581$	10.5076	−	36.5457i	0.435927	−	1.51617i
$582$	9.02707	+	8.97003i	0.374184	+	0.371820i
$583$	4.24068	−	7.34507i	0.175631	−	0.304202i
$584$	−17.6736	+	30.6115i	−0.731337	+	1.26671i
$585$	−2.21162	−	1.25825i	−0.0914391	−	0.0520224i
$586$	2.70998	+	4.69382i	0.111948	+	0.193900i
$587$	−3.93124	−	6.80910i	−0.162260	−	0.281042i	0.773419	−	0.633895i	$-0.218545\pi$
$587$	−3.93124	−	6.80910i	−0.162260	−	0.281042i	−0.935679	+	0.352853i	$0.885212\pi$
$588$	18.8875	+	5.73856i	0.778906	+	0.236654i
$589$	4.77240	−	8.26604i	0.196643	−	0.340596i
$590$	3.47216			0.142947
$591$	−17.3491	−	17.2395i	−0.713648	−	0.709139i
$592$	−14.8288			−0.609461
$593$	−13.2930	−	23.0242i	−0.545878	−	0.945489i	−0.998551	−	0.0538121i	$-0.982863\pi$
$593$	−13.2930	−	23.0242i	−0.545878	−	0.945489i	0.452673	−	0.891677i	$-0.350471\pi$
$594$	−2.20074	−	7.91158i	−0.0902974	−	0.324616i
$595$	−14.6916	+	3.65188i	−0.602297	+	0.149712i
$596$	−11.6567	−	20.1900i	−0.477478	−	0.827016i
$597$	24.8804	−	6.75128i	1.01829	−	0.276311i
$598$	0.212403	+	0.367893i	0.00868582	+	0.0150443i
$599$	−1.52743	−	2.64558i	−0.0624090	−	0.108096i	0.833133	−	0.553073i	$-0.186545\pi$
$599$	−1.52743	−	2.64558i	−0.0624090	−	0.108096i	−0.895542	+	0.444978i	$0.853212\pi$
$600$	−2.71830	−	2.70112i	−0.110974	−	0.110273i
$601$	6.02622	+	10.4377i	0.245815	+	0.425764i	0.962360	−	0.271777i	$-0.0876112\pi$
$601$	6.02622	+	10.4377i	0.245815	+	0.425764i	−0.716546	+	0.697540i	$0.754278\pi$
$602$	−10.7193	−	11.1160i	−0.436885	−	0.453055i
$603$	−2.25409	+	1.32052i	−0.0917938	+	0.0537759i
$604$	9.09318	+	15.7499i	0.369996	+	0.640852i
$605$	4.28360			0.174153
$606$	0.186940	−	0.0507261i	0.00759394	−	0.00206061i
$607$	2.58423			0.104891			0.0524454	−	0.998624i	$-0.483298\pi$
$607$	2.58423			0.104891			0.0524454	+	0.998624i	$0.483298\pi$
$608$	−10.3553	+	17.9359i	−0.419962	+	0.727396i
$609$	−5.68780	+	3.17108i	−0.230481	+	0.128498i
$610$	−0.307238	−	0.532151i	−0.0124397	−	0.0215462i
$611$	−1.31169	−	2.27192i	−0.0530654	−	0.0919119i
$612$	0.177158	+	27.9473i	0.00716117	+	1.12970i
$613$	22.7845	−	39.4640i	0.920259	−	1.59393i	0.121244	−	0.992623i	$-0.461312\pi$
$613$	22.7845	−	39.4640i	0.920259	−	1.59393i	0.799014	−	0.601312i	$-0.205355\pi$
$614$	−8.88119	+	15.3827i	−0.358416	+	0.620794i
$615$	−16.7871	+	4.55518i	−0.676923	+	0.183682i
$616$	10.5304	+	10.9202i	0.424283	+	0.439987i
$617$	3.71170	−	6.42886i	0.149428	−	0.258816i	−0.781588	−	0.623794i	$-0.785590\pi$
$617$	3.71170	−	6.42886i	0.149428	−	0.258816i	0.931016	+	0.364978i	$0.118924\pi$
$618$	10.2201	−	2.77321i	0.411112	−	0.111555i
$619$	−7.36782			−0.296138			−0.148069	−	0.988977i	$-0.547306\pi$
$619$	−7.36782			−0.296138			−0.148069	+	0.988977i	$0.547306\pi$
$620$	−2.09644	+	3.63114i	−0.0841951	+	0.145830i
$621$	−2.98890	+	3.04629i	−0.119940	+	0.122243i
$622$	9.08554			0.364297
$623$	−2.17751	+	7.57344i	−0.0872399	+	0.303423i
$624$	0.716523	−	2.70841i	0.0286839	−	0.108423i
$625$	1.00000			0.0400000
$626$	4.17720	+	7.23513i	0.166955	+	0.289174i
$627$	4.25498	−	16.0835i	0.169928	−	0.642315i
$628$	2.24570	−	3.88967i	0.0896132	−	0.155215i
$629$	44.4920			1.77401
$630$	−1.19736	−	4.68981i	−0.0477039	−	0.186846i
$631$	−37.8581			−1.50711			−0.753554	−	0.657386i	$-0.771662\pi$
$631$	−37.8581			−1.50711			−0.753554	+	0.657386i	$0.771662\pi$
$632$	10.8095	−	18.7226i	0.429980	−	0.744747i
$633$	−33.3863	+	9.05933i	−1.32698	+	0.360076i
$634$	5.67604	+	9.83119i	0.225424	+	0.390447i
$635$	−12.2153			−0.484748
$636$	−6.54641	−	6.50504i	−0.259582	−	0.257942i
$637$	5.03049	+	3.15341i	0.199315	+	0.124942i
$638$	−2.24581			−0.0889125
$639$	−0.197598	−	31.1718i	−0.00781685	−	1.23314i
$640$	5.71186	−	9.89323i	0.225781	−	0.391064i
$641$	−7.61475			−0.300765			−0.150382	−	0.988628i	$-0.548050\pi$
$641$	−7.61475			−0.300765			−0.150382	+	0.988628i	$0.548050\pi$
$642$	1.12871	+	1.12157i	0.0445465	+	0.0442650i
$643$	8.97170	−	15.5394i	0.353809	−	0.612815i	−0.633104	−	0.774067i	$-0.718220\pi$
$643$	8.97170	−	15.5394i	0.353809	−	0.612815i	0.986913	+	0.161251i	$0.0515529\pi$
$644$	0.977620	−	3.40019i	0.0385236	−	0.133986i
$645$	4.23991	−	16.0266i	0.166946	−	0.631046i
$646$	6.46618	−	11.1998i	0.254409	−	0.440649i
$647$	17.2402	−	29.8610i	0.677784	−	1.17396i	−0.297863	−	0.954609i	$-0.596274\pi$
$647$	17.2402	−	29.8610i	0.677784	−	1.17396i	0.975647	−	0.219347i	$-0.0703928\pi$
$648$	−19.9107	+	0.252438i	−0.782167	+	0.00991671i
$649$	−7.37804	−	12.7791i	−0.289613	−	0.501625i
$650$	−0.258611	−	0.447928i	−0.0101436	−	0.0175692i
$651$	−10.3077	+	5.74676i	−0.403990	+	0.225233i
$652$	12.8794	−	22.3078i	0.504397	−	0.873642i
$653$	−12.1011			−0.473551			−0.236775	−	0.971564i	$-0.576091\pi$
$653$	−12.1011			−0.473551			−0.236775	+	0.971564i	$0.576091\pi$
$654$	−4.04149	+	15.2766i	−0.158035	+	0.597361i
$655$	−14.5615			−0.568965
$656$	−9.57583	−	16.5858i	−0.373873	−	0.647568i
$657$	−41.6586	−	23.7008i	−1.62526	−	0.924655i
$658$	1.37894	−	4.79601i	0.0537568	−	0.186968i
$659$	−4.89965	−	8.48645i	−0.190863	−	0.330585i	0.754673	−	0.656101i	$-0.227795\pi$
$659$	−4.89965	−	8.48645i	−0.190863	−	0.330585i	−0.945537	+	0.325516i	$0.894462\pi$
$660$	−1.86915	+	7.06525i	−0.0727564	+	0.275014i
$661$	11.6204	+	20.1271i	0.451981	+	0.782853i	0.998509	−	0.0545871i	$-0.0173843\pi$
$661$	11.6204	+	20.1271i	0.451981	+	0.782853i	−0.546528	+	0.837441i	$0.684051\pi$
$662$	−7.72417	−	13.3787i	−0.300208	−	0.519976i
$663$	−2.14984	+	8.12624i	−0.0834928	+	0.315597i
$664$	−15.8995	−	27.5388i	−0.617021	−	1.06871i
$665$	2.70963	−	9.42419i	0.105075	−	0.365454i
$666$	0.0901725	+	14.2250i	0.00349411	+	0.551209i
$667$	0.583568	+	1.01077i	0.0225958	+	0.0391372i
$668$	−26.9776			−1.04379
$669$	−11.2554	+	42.5447i	−0.435160	+	1.64487i
$670$	−0.531029			−0.0205154
$671$	−1.30571	+	2.26155i	−0.0504062	+	0.0873062i
$672$	22.3659	−	12.4695i	0.862782	−	0.481020i
$673$	25.6329	+	44.3975i	0.988076	+	1.71140i	0.627376	+	0.778716i	$0.284129\pi$
$673$	25.6329	+	44.3975i	0.988076	+	1.71140i	0.360700	+	0.932682i	$0.382538\pi$
$674$	−0.272644	−	0.472233i	−0.0105019	−	0.0181897i
$675$	3.63913	−	3.70900i	0.140070	−	0.142760i
$676$	−9.99720	+	17.3157i	−0.384508	+	0.665987i
$677$	−3.65588	+	6.33218i	−0.140507	+	0.243365i	−0.927688	−	0.373357i	$-0.878207\pi$
$677$	−3.65588	+	6.33218i	−0.140507	+	0.243365i	0.787181	+	0.616722i	$0.211540\pi$
$678$	−3.42664	+	12.9524i	−0.131599	+	0.497436i
$679$	8.80846	−	30.6361i	0.338038	−	1.17571i
$680$	−6.32977	+	10.9635i	−0.242736	+	0.420431i
$681$	−15.4873	−	15.3894i	−0.593474	−	0.589724i
$682$	−4.06996			−0.155847
$683$	−4.08644	+	7.07792i	−0.156363	+	0.270829i	−0.933555	−	0.358435i	$-0.883310\pi$
$683$	−4.08644	+	7.07792i	−0.156363	+	0.270829i	0.777191	+	0.629264i	$0.216644\pi$
$684$	−15.7348	−	8.95197i	−0.601634	−	0.342287i
$685$	20.8786			0.797730
$686$	2.32445	+	11.0521i	0.0887478	+	0.421972i
$687$	10.1778	+	10.1135i	0.388307	+	0.385853i
$688$	18.2529			0.695887
$689$	−1.38787	−	2.40385i	−0.0528735	−	0.0915795i
$690$	−0.837229	+	0.227181i	−0.0318727	+	0.00864864i
$691$	−16.9543	+	29.3657i	−0.644973	+	1.11713i	0.339335	+	0.940666i	$0.389798\pi$
$691$	−16.9543	+	29.3657i	−0.644973	+	1.11713i	−0.984308	+	0.176460i	$0.943535\pi$
$692$	1.70616			0.0648585
$693$	−14.7164	+	14.3723i	−0.559028	+	0.545957i
$694$	−6.24242			−0.236959
$695$	−9.91507	+	17.1734i	−0.376100	+	0.651425i
$696$	−1.39275	+	5.26452i	−0.0527922	+	0.199551i
$697$	28.7311	+	49.7637i	1.08827	+	1.88493i
$698$	10.4801			0.396679
$699$	−6.40674	+	24.2170i	−0.242325	+	0.915972i
$700$	−1.19030	+	4.13990i	−0.0449891	+	0.156474i
$701$	−17.5312			−0.662144			−0.331072	−	0.943606i	$-0.607410\pi$
$701$	−17.5312			−0.662144			−0.331072	+	0.943606i	$0.607410\pi$
$702$	−2.60249	−	0.670879i	−0.0982246	−	0.0253207i
$703$	−14.4097	+	24.9584i	−0.543474	+	0.941325i
$704$	−1.05354			−0.0397069
$705$	5.17029	−	1.40295i	0.194724	−	0.0528383i
$706$	−6.01540	+	10.4190i	−0.226392	+	0.392123i
$707$	−0.336800	−	0.349265i	−0.0126667	−	0.0131355i
$708$	−15.4962	+	4.20487i	−0.582382	+	0.158029i
$709$	−9.53461	+	16.5144i	−0.358080	+	0.620212i	−0.987640	−	0.156739i	$-0.949902\pi$
$709$	−9.53461	+	16.5144i	−0.358080	+	0.620212i	0.629560	+	0.776952i	$0.283235\pi$
$710$	3.16823	−	5.48753i	0.118901	−	0.205943i
$711$	25.4792	+	14.4959i	0.955546	+	0.543638i
$712$	3.29489	+	5.70692i	0.123481	+	0.213876i
$713$	1.05757	+	1.83176i	0.0396062	+	0.0686000i
$714$	−13.9660	+	7.78636i	−0.522664	+	0.291397i
$715$	−1.09905	+	1.90362i	−0.0411022	+	0.0711912i
$716$	3.01113			0.112531
$717$	16.0403	−	4.35253i	0.599037	−	0.162548i
$718$	−13.6645			−0.509956
$719$	15.5912	+	27.0047i	0.581452	+	1.00710i	0.995308	+	0.0967619i	$0.0308485\pi$
$719$	15.5912	+	27.0047i	0.581452	+	1.00710i	−0.413856	+	0.910343i	$0.635818\pi$
$720$	4.97270	+	2.82912i	0.185322	+	0.105435i
$721$	−18.4129	−	19.0944i	−0.685734	−	0.711114i
$722$	−1.60479	−	2.77958i	−0.0597242	−	0.103445i
$723$	−7.76898	−	7.71989i	−0.288932	−	0.287106i
$724$	14.2767	+	24.7280i	0.530591	+	0.919010i
$725$	−0.710523	−	1.23066i	−0.0263881	−	0.0457056i
$726$	4.36656	−	1.18486i	0.162058	−	0.0439744i
$727$	−7.47472	−	12.9466i	−0.277222	−	0.480162i	0.693471	−	0.720484i	$-0.256080\pi$
$727$	−7.47472	−	12.9466i	−0.277222	−	0.480162i	−0.970693	+	0.240322i	$0.922747\pi$
$728$	4.81826	−	1.19767i	0.178577	−	0.0443887i
$729$	−0.513421	−	26.9951i	−0.0190156	−	0.999819i
$730$	−4.87126	−	8.43728i	−0.180294	−	0.312278i
$731$	−54.7657			−2.02558
$732$	2.01564	+	2.00291i	0.0745003	+	0.0740295i
$733$	−42.6811			−1.57646			−0.788231	−	0.615380i	$-0.789003\pi$
$733$	−42.6811			−1.57646			−0.788231	+	0.615380i	$0.789003\pi$
$734$	5.64764	−	9.78200i	0.208458	−	0.361060i
$735$	−8.85279	+	8.28421i	−0.326540	+	0.305568i
$736$	−2.29474	−	3.97460i	−0.0845852	−	0.146506i
$737$	1.12839	+	1.95443i	0.0415648	+	0.0719923i
$738$	−15.8523	+	9.28679i	−0.583530	+	0.341851i
$739$	20.0227	−	34.6804i	0.736548	−	1.27574i	−0.217493	−	0.976062i	$-0.569788\pi$
$739$	20.0227	−	34.6804i	0.736548	−	1.27574i	0.954041	−	0.299676i	$-0.0968786\pi$
$740$	6.32998	−	10.9638i	0.232695	−	0.403039i
$741$	−3.86225	−	3.83785i	−0.141883	−	0.140987i
$742$	1.45902	−	5.07453i	0.0535624	−	0.186292i
$743$	−13.8153	+	23.9289i	−0.506836	+	0.877865i	0.493133	+	0.869954i	$0.335852\pi$
$743$	−13.8153	+	23.9289i	−0.506836	+	0.877865i	−0.999969	+	0.00791113i	$0.997482\pi$
$744$	−2.52401	+	9.54059i	−0.0925347	+	0.349775i
$745$	14.3192			0.524614
$746$	3.35991	−	5.81953i	0.123015	−	0.213068i
$747$	37.2036	−	21.7951i	1.36121	−	0.797441i
$748$	24.1432			0.882763
$749$	1.10137	−	3.83061i	0.0402432	−	0.139967i
$750$	1.01937	−	0.276604i	0.0372220	−	0.0101002i
$751$	−15.1895			−0.554274			−0.277137	−	0.960830i	$-0.589386\pi$
$751$	−15.1895			−0.554274			−0.277137	+	0.960830i	$0.589386\pi$
$752$	2.94927	+	5.10828i	0.107549	+	0.186280i
$753$	28.5570	+	28.3766i	1.04068	+	1.03410i
$754$	−0.367498	+	0.636526i	−0.0133835	+	0.0231809i
$755$	−11.1701			−0.406522
$756$	11.0232	+	19.4805i	0.400912	+	0.708498i
$757$	−3.51810			−0.127867			−0.0639337	−	0.997954i	$-0.520365\pi$
$757$	−3.51810			−0.127867			−0.0639337	+	0.997954i	$0.520365\pi$
$758$	−4.07026	+	7.04989i	−0.147838	+	0.256064i
$759$	2.61517	+	2.59864i	0.0949246	+	0.0943248i
$760$	−4.10008	−	7.10154i	−0.148725	−	0.257600i
$761$	−14.4881			−0.525195			−0.262597	−	0.964906i	$-0.584579\pi$
$761$	−14.4881			−0.525195			−0.262597	+	0.964906i	$0.584579\pi$
$762$	−12.4518	+	3.37879i	−0.451082	+	0.122401i
$763$	38.4139	−	9.54850i	1.39068	−	0.345679i
$764$	−23.8623			−0.863309
$765$	−14.9200	−	8.48841i	−0.539433	−	0.306899i
$766$	8.18444	−	14.1759i	0.295716	−	0.512195i
$767$	−4.82929			−0.174375
$768$	2.72581	−	10.3034i	0.0983590	−	0.371790i
$769$	3.48120	−	6.02962i	0.125535	−	0.217434i	−0.796407	−	0.604761i	$-0.793268\pi$
$769$	3.48120	−	6.02962i	0.125535	−	0.217434i	0.921942	+	0.387328i	$0.126602\pi$
$770$	−4.05785	+	1.00866i	−0.146235	+	0.0363494i
$771$	12.3831	+	12.3048i	0.445966	+	0.443148i
$772$	−15.7742	+	27.3218i	−0.567727	+	0.983331i
$773$	−4.97387	+	8.61499i	−0.178898	+	0.309860i	−0.941503	−	0.337004i	$-0.890586\pi$
$773$	−4.97387	+	8.61499i	−0.178898	+	0.309860i	0.762606	+	0.646864i	$0.223920\pi$
$774$	−0.110994	−	17.5097i	−0.00398960	−	0.629374i
$775$	−1.28764	−	2.23026i	−0.0462534	−	0.0801132i
$776$	−13.3285	−	23.0857i	−0.478466	−	0.828727i
$777$	31.1229	−	17.3517i	1.11653	−	0.622490i
$778$	8.44441	−	14.6261i	0.302747	−	0.524373i
$779$	−37.2208			−1.33357
$780$	1.69663	+	1.68591i	0.0607490	+	0.0603651i
$781$	−26.9288			−0.963588
$782$	1.43291	+	2.48187i	0.0512408	+	0.0887517i
$783$	−7.15021	−	1.84321i	−0.255528	−	0.0658709i
$784$	−11.3108	−	7.09026i	−0.403957	−	0.253224i
$785$	1.37931	+	2.38904i	0.0492298	+	0.0852686i
$786$	−14.8435	+	4.02778i	−0.529451	+	0.143666i
$787$	2.65264	+	4.59451i	0.0945565	+	0.163777i	0.909423	−	0.415871i	$-0.136523\pi$
$787$	2.65264	+	4.59451i	0.0945565	+	0.163777i	−0.814867	+	0.579648i	$0.803190\pi$
$788$	11.4953	+	19.9104i	0.409501	+	0.709277i
$789$	26.5708	+	26.4029i	0.945944	+	0.939967i
$790$	2.97937	+	5.16041i	0.106001	+	0.183599i
$791$	32.5697	−	8.09583i	1.15805	−	0.287855i
$792$	0.109039	+	17.2013i	0.00387452	+	0.611220i
$793$	0.427324	+	0.740148i	0.0151747	+	0.0262834i
$794$	10.4663			0.371435
$795$	5.47054	−	1.48443i	0.194020	−	0.0526472i
$796$	−24.2333			−0.858927
$797$	22.7137	−	39.3413i	0.804561	−	1.39354i	−0.112025	−	0.993705i	$-0.535734\pi$
$797$	22.7137	−	39.3413i	0.804561	−	1.39354i	0.916587	−	0.399836i	$-0.130933\pi$
$798$	0.155338	−	10.3562i	0.00549892	−	0.366606i
$799$	−8.84891	−	15.3268i	−0.313052	−	0.542222i
$800$	2.79396	+	4.83927i	0.0987812	+	0.171094i
$801$	−7.70978	+	4.51665i	−0.272412	+	0.159588i
$802$	9.88203	−	17.1162i	0.348947	−	0.604393i
$803$	−20.7020	+	35.8569i	−0.730558	+	1.26536i
$804$	2.36997	−	0.643089i	0.0835824	−	0.0226800i
$805$	1.50839	+	1.56421i	0.0531636	+	0.0551313i
$806$	−0.665997	+	1.15354i	−0.0234587	+	0.0406317i
$807$	32.3239	−	8.77105i	1.13785	−	0.308756i
$808$	−0.405745			−0.0142740
$809$	−15.7751	+	27.3232i	−0.554622	+	0.960633i	0.443311	+	0.896368i	$0.353804\pi$
$809$	−15.7751	+	27.3232i	−0.554622	+	0.960633i	−0.997933	+	0.0642652i	$0.979530\pi$
$810$	2.68368	−	4.78743i	0.0942951	−	0.168213i
$811$	0.692971			0.0243335			0.0121668	−	0.999926i	$-0.496127\pi$
$811$	0.692971			0.0243335			0.0121668	+	0.999926i	$0.496127\pi$
$812$	5.94055	−	1.47664i	0.208472	−	0.0518198i
$813$	10.0881	−	38.1322i	0.353804	−	1.33735i
$814$	12.2888			0.430722
$815$	7.91058	+	13.7015i	0.277095	+	0.479943i
$816$	4.83379	−	18.2714i	0.169217	−	0.639627i
$817$	17.7371	−	30.7215i	0.620542	−	1.07481i
$818$	2.44506			0.0854895
$819$	1.66536	+	6.52287i	0.0581922	+	0.227927i
$820$	16.3505			0.570985
$821$	−16.3083	+	28.2468i	−0.569163	+	0.985818i	0.427487	+	0.904022i	$0.359399\pi$
$821$	−16.3083	+	28.2468i	−0.569163	+	0.985818i	−0.996649	+	0.0817967i	$0.973934\pi$
$822$	21.2829	−	5.77511i	0.742328	−	0.201430i
$823$	−11.2374	−	19.4638i	−0.391711	−	0.678464i	0.600964	−	0.799276i	$-0.294783\pi$
$823$	−11.2374	−	19.4638i	−0.391711	−	0.678464i	−0.992675	+	0.120812i	$0.961450\pi$
$824$	−22.1822			−0.772753
$825$	−3.18409	−	3.16397i	−0.110856	−	0.110155i
$826$	−6.37674	−	6.61276i	−0.221875	−	0.230087i
$827$	2.64312			0.0919105			0.0459552	−	0.998944i	$-0.485367\pi$
$827$	2.64312			0.0919105			0.0459552	+	0.998944i	$0.485367\pi$
$828$	3.46141	−	2.02781i	0.120292	−	0.0704712i
$829$	−4.44867	+	7.70532i	−0.154509	+	0.267617i	−0.932880	−	0.360187i	$-0.882713\pi$
$829$	−4.44867	+	7.70532i	−0.154509	+	0.267617i	0.778371	+	0.627804i	$0.216046\pi$
$830$	8.76459			0.304223
$831$	−15.9791	−	15.8782i	−0.554310	−	0.550807i
$832$	−0.172399	+	0.298604i	−0.00597686	+	0.0103522i
$833$	33.9366	+	21.2735i	1.17583	+	0.737081i
$834$	−5.35686	+	20.2486i	−0.185493	+	0.701150i
$835$	8.28485	−	14.3498i	0.286709	−	0.496595i
$836$	−7.81932	+	13.5435i	−0.270437	+	0.468410i
$837$	−12.9579	−	3.34034i	−0.447892	−	0.115459i
$838$	5.28003	+	9.14528i	0.182396	+	0.315918i
$839$	−1.64205	−	2.84412i	−0.0566900	−	0.0981900i	0.836288	−	0.548291i	$-0.184721\pi$
$839$	−1.64205	−	2.84412i	−0.0566900	−	0.0981900i	−0.892978	+	0.450101i	$0.851388\pi$
$840$	−0.152061	+	10.1377i	−0.00524661	+	0.349785i
$841$	13.4903	−	23.3659i	0.465183	−	0.805721i
$842$	17.8826			0.616274
$843$	2.16993	−	8.20218i	0.0747363	−	0.282498i
$844$	32.5179			1.11931
$845$	−6.14031	−	10.6353i	−0.211233	−	0.365866i
$846$	4.88236	−	2.86025i	0.167859	−	0.0983373i
$847$	−7.86698	−	8.15815i	−0.270313	−	0.280318i
$848$	3.12054	+	5.40494i	0.107160	+	0.185606i
$849$	−4.72796	+	17.8714i	−0.162263	+	0.613344i
$850$	−1.74464	−	3.02180i	−0.0598406	−	0.103647i
$851$	−3.19321	−	5.53080i	−0.109462	−	0.189593i
$852$	−7.49418	+	28.3275i	−0.256746	+	0.970484i
$853$	9.58073	+	16.5943i	0.328038	+	0.568178i	0.982122	−	0.188243i	$-0.0602793\pi$
$853$	9.58073	+	16.5943i	0.328038	+	0.568178i	−0.654084	+	0.756421i	$0.726946\pi$
$854$	−0.449234	+	1.56245i	−0.0153725	+	0.0534659i
$855$	9.59386	−	5.62040i	0.328103	−	0.192214i
$856$	−1.66654	−	2.88653i	−0.0569611	−	0.0986596i
$857$	−42.6645			−1.45739			−0.728695	−	0.684838i	$-0.759873\pi$
$857$	−42.6645			−1.45739			−0.728695	+	0.684838i	$0.759873\pi$
$858$	−0.593790	+	2.24448i	−0.0202716	+	0.0766254i
$859$	−39.5162			−1.34828			−0.674138	−	0.738606i	$-0.735485\pi$
$859$	−39.5162			−1.34828			−0.674138	+	0.738606i	$0.735485\pi$
$860$	−7.79163	+	13.4955i	−0.265692	+	0.460193i
$861$	39.5055	+	23.6055i	1.34634	+	0.804473i
$862$	−7.11822	−	12.3291i	−0.242447	−	0.419931i
$863$	7.46972	+	12.9379i	0.254272	+	0.440412i	0.964698	−	0.263360i	$-0.0848307\pi$
$863$	7.46972	+	12.9379i	0.254272	+	0.440412i	−0.710425	+	0.703773i	$0.751497\pi$
$864$	28.1165	+	7.24796i	0.956541	+	0.246581i
$865$	−0.523964	+	0.907533i	−0.0178153	+	0.0308570i
$866$	−1.21997	+	2.11304i	−0.0414562	+	0.0718042i
$867$	−6.97249	+	26.3555i	−0.236798	+	0.895081i
$868$	10.7657	−	2.67603i	0.365412	−	0.0908303i
$869$	12.6618	−	21.9309i	0.429522	−	0.743953i
$870$	−1.06469	−	1.05796i	−0.0360963	−	0.0358683i
$871$	0.738587			0.0250261
$872$	16.5504	−	28.6660i	0.560466	−	0.970755i
$873$	31.1877	−	18.2708i	1.05554	−	0.618372i
$874$	−1.85632			−0.0627910
$875$	−1.83653	−	1.90451i	−0.0620861	−	0.0643841i
$876$	31.9581	+	31.7561i	1.07976	+	1.07294i
$877$	−16.3600			−0.552437			−0.276219	−	0.961095i	$-0.589081\pi$
$877$	−16.3600			−0.552437			−0.276219	+	0.961095i	$0.589081\pi$
$878$	−1.26460	−	2.19035i	−0.0426781	−	0.0739207i
$879$	14.8570	−	4.03144i	0.501115	−	0.135977i
$880$	2.47116	−	4.28018i	0.0833028	−	0.144285i
$881$	−16.4786			−0.555177			−0.277588	−	0.960700i	$-0.589535\pi$
$881$	−16.4786			−0.555177			−0.277588	+	0.960700i	$0.589535\pi$
$882$	−6.73279	+	10.8934i	−0.226705	+	0.366799i
$883$	5.23072			0.176028			0.0880139	−	0.996119i	$-0.471948\pi$
$883$	5.23072			0.176028			0.0880139	+	0.996119i	$0.471948\pi$
$884$	3.95073	−	6.84286i	0.132877	−	0.230150i
$885$	2.52226	−	9.53397i	0.0847848	−	0.320481i
$886$	−6.66237	−	11.5396i	−0.223827	−	0.387679i
$887$	7.56572			0.254032			0.127016	−	0.991901i	$-0.459460\pi$
$887$	7.56572			0.254032			0.127016	+	0.991901i	$0.459460\pi$
$888$	7.62097	−	28.8068i	0.255743	−	0.966692i
$889$	22.4337	+	23.2640i	0.752403	+	0.780251i
$890$	−1.81630			−0.0608827
$891$	−23.3225	+	0.295695i	−0.781334	+	0.00990615i
$892$	20.6839	−	35.8256i	0.692549	−	1.19953i
$893$	11.4637			0.383617
$894$	14.5965	−	3.96074i	0.488179	−	0.132467i
$895$	−0.924721	+	1.60166i	−0.0309100	+	0.0535377i
$896$	−29.3318	+	7.29097i	−0.979905	+	0.243574i
$897$	1.16447	−	0.315977i	0.0388804	−	0.0105502i
$898$	1.91695	−	3.32026i	0.0639695	−	0.110798i
$899$	−1.82979	+	3.16930i	−0.0610271	+	0.105702i
$900$	−4.21443	+	2.46896i	−0.140481	+	0.0822985i
$901$	−9.36280	−	16.2168i	−0.311920	−	0.540261i
$902$	7.93558	+	13.7448i	0.264226	+	0.457653i
$903$	−38.3095	+	21.3584i	−1.27486	+	0.710763i
$904$	14.0324	−	24.3049i	0.466712	−	0.808369i
$905$	−17.5376			−0.582970
$906$	−11.3864	+	3.08970i	−0.378289	+	0.102648i
$907$	−9.31228			−0.309209			−0.154605	−	0.987976i	$-0.549410\pi$
$907$	−9.31228			−0.309209			−0.154605	+	0.987976i	$0.549410\pi$
$908$	10.2616	+	17.7736i	0.340544	+	0.589839i
$909$	−0.00348743	−	0.550156i	−0.000115671	−	0.0182475i
$910$	−0.378134	+	1.31516i	−0.0125350	+	0.0435972i
$911$	−1.89020	−	3.27392i	−0.0626251	−	0.108470i	0.833013	−	0.553253i	$-0.186614\pi$
$911$	−1.89020	−	3.27392i	−0.0626251	−	0.108470i	−0.895638	+	0.444784i	$0.853281\pi$
$912$	8.68406	+	8.62919i	0.287558	+	0.285741i
$913$	−18.6240	−	32.2577i	−0.616364	−	1.06757i
$914$	6.95284	+	12.0427i	0.229979	+	0.398336i
$915$	−1.68438	+	0.457056i	−0.0556840	+	0.0151098i
$916$	−6.74364	−	11.6803i	−0.222816	−	0.385929i
$917$	26.7427	+	27.7325i	0.883122	+	0.915808i
$918$	−17.5569	−	4.52587i	−0.579463	−	0.149376i
$919$	7.78230	+	13.4793i	0.256714	+	0.444642i	0.965360	−	0.260923i	$-0.0840267\pi$
$919$	7.78230	+	13.4793i	0.256714	+	0.444642i	−0.708645	+	0.705565i	$0.750693\pi$
$920$	1.81716			0.0599100
$921$	35.7867	+	35.5606i	1.17921	+	1.17176i
$922$	−0.336908			−0.0110955
$923$	−4.40656	+	7.63238i	−0.145044	+	0.251223i
$924$	16.8886	−	9.41576i	0.555593	−	0.309756i
$925$	3.88789	+	6.73402i	0.127833	+	0.221413i
$926$	−2.92928	−	5.07366i	−0.0962621	−	0.166731i
$927$	−0.190659	−	30.0772i	−0.00626207	−	0.987864i
$928$	3.97034	−	6.87682i	0.130333	−	0.225743i
$929$	21.2375	−	36.7845i	0.696780	−	1.20686i	−0.272796	−	0.962072i	$-0.587949\pi$
$929$	21.2375	−	36.7845i	0.696780	−	1.20686i	0.969577	−	0.244787i	$-0.0787181\pi$
$930$	−1.92948	−	1.91728i	−0.0632700	−	0.0628702i
$931$	−22.9248	+	12.1473i	−0.751329	+	0.398112i
$932$	11.7736	−	20.3924i	0.385656	−	0.667976i
$933$	6.59995	−	24.9474i	0.216073	−	0.816740i
$934$	11.6827			0.382271
$935$	−7.41441	+	12.8421i	−0.242477	+	0.419983i
$936$	4.89316	+	2.78386i	0.159938	+	0.0909934i
$937$	−35.8902			−1.17248			−0.586241	−	0.810137i	$-0.699393\pi$
$937$	−35.8902			−1.17248			−0.586241	+	0.810137i	$0.699393\pi$
$938$	0.975252	+	1.01135i	0.0318431	+	0.0330217i
$939$	22.9009	−	6.21413i	0.747341	−	0.202790i
$940$	−5.03582			−0.164250
$941$	−0.135411	−	0.234539i	−0.00441428	−	0.00764575i	0.863810	−	0.503818i	$-0.168072\pi$
$941$	−0.135411	−	0.234539i	−0.00441428	−	0.00764575i	−0.868224	+	0.496172i	$0.834738\pi$
$942$	2.06685	+	2.05379i	0.0673415	+	0.0669160i
$943$	4.12408	−	7.14312i	0.134299	−	0.232612i
$944$	10.8584			0.353411
$945$	−13.7472	−	0.119047i	−0.447197	−	0.00387260i
$946$	−15.1264			−0.491801
$947$	−18.5709	+	32.1657i	−0.603472	+	1.04524i	0.388819	+	0.921314i	$0.372883\pi$
$947$	−18.5709	+	32.1657i	−0.603472	+	1.04524i	−0.992291	+	0.123930i	$0.960450\pi$
$948$	−19.5462	−	19.4227i	−0.634832	−	0.630820i
$949$	6.77524	+	11.7351i	0.219934	+	0.380936i
$950$	2.26016			0.0733293
$951$	31.1180	−	8.44384i	1.00907	−	0.273810i
$952$	32.5049	−	8.07971i	1.05349	−	0.261865i
$953$	−2.96964			−0.0961960			−0.0480980	−	0.998843i	$-0.515316\pi$
$953$	−2.96964			−0.0961960			−0.0480980	+	0.998843i	$0.515316\pi$
$954$	5.16589	−	3.02635i	0.167252	−	0.0979817i
$955$	7.32816	−	12.6927i	0.237134	−	0.410727i
$956$	−15.6231			−0.505288
$957$	−1.63141	+	6.16662i	−0.0527360	+	0.199338i
$958$	11.4944	−	19.9088i	0.371366	−	0.643224i
$959$	−38.3442	−	39.7634i	−1.23820	−	1.28403i
$960$	−0.499462	−	0.496306i	−0.0161201	−	0.0160182i
$961$	12.1840	−	21.1032i	0.393031	−	0.680750i
$962$	2.01090	−	3.48299i	0.0648342	−	0.112296i
$963$	3.89957	−	2.28450i	0.125662	−	0.0736169i
$964$	5.14760	+	8.91591i	0.165793	+	0.287162i
$965$	−9.68857	−	16.7811i	−0.311886	−	0.540202i
$966$	1.97027	+	1.17728i	0.0633923	+	0.0378784i
$967$	8.85857	−	15.3435i	0.284872	−	0.493413i	−0.687706	−	0.725989i	$-0.741382\pi$
$967$	8.85857	−	15.3435i	0.284872	−	0.493413i	0.972578	+	0.232576i	$0.0747154\pi$
$968$	−9.47740			−0.304615
$969$	−26.0555	−	25.8908i	−0.837022	−	0.831733i
$970$	7.34732			0.235908
$971$	2.00281	+	3.46897i	0.0642733	+	0.111325i	0.896371	−	0.443304i	$-0.146194\pi$
$971$	2.00281	+	3.46897i	0.0642733	+	0.111325i	−0.832098	+	0.554629i	$0.812860\pi$
$972$	−6.17952	+	24.6162i	−0.198208	+	0.789565i
$973$	50.9162	−	12.6562i	1.63230	−	0.405739i
$974$	−0.277928	−	0.481385i	−0.00890538	−	0.0154246i
$975$	−1.41780	+	0.384718i	−0.0454058	+	0.0123208i
$976$	−0.960816	−	1.66418i	−0.0307550	−	0.0532692i
$977$	19.9749	+	34.5975i	0.639052	+	1.10687i	0.985641	+	0.168854i	$0.0540065\pi$
$977$	19.9749	+	34.5975i	0.639052	+	1.10687i	−0.346589	+	0.938017i	$0.612660\pi$
$978$	11.8537	+	11.7788i	0.379039	+	0.376644i
$979$	3.85949	+	6.68483i	0.123350	+	0.213648i
$980$	10.0705	−	5.33613i	0.321690	−	0.170456i
$981$	39.0110	+	22.1945i	1.24553	+	0.708616i
$982$	8.23461	+	14.2628i	0.262777	+	0.455143i
$983$	41.9390			1.33765			0.668823	−	0.743422i	$-0.266798\pi$
$983$	41.9390			1.33765			0.668823	+	0.743422i	$0.266798\pi$
$984$	37.1412	−	10.0782i	1.18402	−	0.321283i
$985$	−14.1208			−0.449927
$986$	−2.47921	+	4.29412i	−0.0789542	+	0.136753i
$987$	−12.1673	−	7.27028i	−0.387291	−	0.231416i
$988$	2.55906	+	4.43243i	0.0814147	+	0.141014i
$989$	3.93055	+	6.80792i	0.124984	+	0.216479i
$990$	−4.12093	−	2.34452i	−0.130972	−	0.0745136i
$991$	−1.22348	+	2.11912i	−0.0388650	+	0.0673162i	−0.884804	−	0.465964i	$-0.845708\pi$
$991$	−1.22348	+	2.11912i	−0.0388650	+	0.0673162i	0.845939	+	0.533280i	$0.179041\pi$
$992$	7.19522	−	12.4625i	0.228448	−	0.395684i
$993$	−42.3465	+	11.4907i	−1.34383	+	0.364646i
$994$	−16.2696	+	4.04412i	−0.516040	+	0.128272i
$995$	7.44208	−	12.8901i	0.235930	−	0.408642i
$996$	−39.1161	+	10.6141i	−1.23944	+	0.336321i
$997$	−3.97420			−0.125864			−0.0629321	−	0.998018i	$-0.520045\pi$
$997$	−3.97420			−0.125864			−0.0629321	+	0.998018i	$0.520045\pi$
$998$	−4.77260	+	8.26639i	−0.151074	+	0.261668i
$999$	39.1251	+	10.0858i	1.23786	+	0.319101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.b.256.8	yes	24
3.2	odd	2		945.2.k.b.361.5		24
7.2	even	3		315.2.l.b.121.5	yes	24
9.2	odd	6		945.2.l.b.46.8		24
9.7	even	3		315.2.l.b.151.5	yes	24
21.2	odd	6		945.2.l.b.226.8		24
63.2	odd	6		945.2.k.b.856.5		24
63.16	even	3	inner	315.2.k.b.16.8	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.b.16.8	✓	24	63.16	even	3	inner
315.2.k.b.256.8	yes	24	1.1	even	1	trivial
315.2.l.b.121.5	yes	24	7.2	even	3
315.2.l.b.151.5	yes	24	9.7	even	3
945.2.k.b.361.5		24	3.2	odd	2
945.2.k.b.856.5		24	63.2	odd	6
945.2.l.b.46.8		24	9.2	odd	6
945.2.l.b.226.8		24	21.2	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.304907 - 0.528114i) q^{2} +(-1.22862 - 1.22086i) q^{3} +(0.814064 + 1.41000i) q^{4} -1.00000 q^{5} +(-1.01937 + 0.276604i) q^{6} +(1.83653 + 1.90451i) q^{7} +2.21248 q^{8} +(0.0190166 + 2.99994i) q^{9} +O(q^{10})\)	\(q+(0.304907 - 0.528114i) q^{2} +(-1.22862 - 1.22086i) q^{3} +(0.814064 + 1.41000i) q^{4} -1.00000 q^{5} +(-1.01937 + 0.276604i) q^{6} +(1.83653 + 1.90451i) q^{7} +2.21248 q^{8} +(0.0190166 + 2.99994i) q^{9} +(-0.304907 + 0.528114i) q^{10} +2.59160 q^{11} +(0.721233 - 2.72621i) q^{12} +(0.424083 - 0.734533i) q^{13} +(1.56577 - 0.389202i) q^{14} +(1.22862 + 1.22086i) q^{15} +(-0.953527 + 1.65156i) q^{16} +(2.86094 - 4.95529i) q^{17} +(1.59011 + 0.904659i) q^{18} +(1.85316 + 3.20976i) q^{19} +(-0.814064 - 1.41000i) q^{20} +(0.0687288 - 4.58206i) q^{21} +(0.790197 - 1.36866i) q^{22} -0.821322 q^{23} +(-2.71830 - 2.70112i) q^{24} +1.00000 q^{25} +(-0.258611 - 0.447928i) q^{26} +(3.63913 - 3.70900i) q^{27} +(-1.19030 + 4.13990i) q^{28} +(-0.710523 - 1.23066i) q^{29} +(1.01937 - 0.276604i) q^{30} +(-1.28764 - 2.23026i) q^{31} +(2.79396 + 4.83927i) q^{32} +(-3.18409 - 3.16397i) q^{33} +(-1.74464 - 3.02180i) q^{34} +(-1.83653 - 1.90451i) q^{35} +(-4.21443 + 2.46896i) q^{36} +(3.88789 + 6.73402i) q^{37} +2.26016 q^{38} +(-1.41780 + 0.384718i) q^{39} -2.21248 q^{40} +(-5.02127 + 8.69709i) q^{41} +(-2.39889 - 1.43340i) q^{42} +(-4.78564 - 8.28897i) q^{43} +(2.10973 + 3.65416i) q^{44} +(-0.0190166 - 2.99994i) q^{45} +(-0.250427 + 0.433752i) q^{46} +(1.54651 - 2.67863i) q^{47} +(3.18784 - 0.865017i) q^{48} +(-0.254294 + 6.99538i) q^{49} +(0.304907 - 0.528114i) q^{50} +(-9.56471 + 2.59537i) q^{51} +1.38092 q^{52} +(1.63632 - 2.83418i) q^{53} +(-0.849181 - 3.05278i) q^{54} -2.59160 q^{55} +(4.06329 + 4.21369i) q^{56} +(1.64183 - 6.20602i) q^{57} -0.866573 q^{58} +(-2.84690 - 4.93098i) q^{59} +(-0.721233 + 2.72621i) q^{60} +(-0.503822 + 0.872646i) q^{61} -1.57044 q^{62} +(-5.67848 + 5.54571i) q^{63} -0.406523 q^{64} +(-0.424083 + 0.734533i) q^{65} +(-2.64179 + 0.716848i) q^{66} +(0.435403 + 0.754140i) q^{67} +9.31594 q^{68} +(1.00909 + 1.00272i) q^{69} +(-1.56577 + 0.389202i) q^{70} -10.3908 q^{71} +(0.0420739 + 6.63731i) q^{72} +(-7.98812 + 13.8358i) q^{73} +4.74178 q^{74} +(-1.22862 - 1.22086i) q^{75} +(-3.01718 + 5.22590i) q^{76} +(4.75956 + 4.93572i) q^{77} +(-0.229121 + 0.866061i) q^{78} +(4.88570 - 8.46228i) q^{79} +(0.953527 - 1.65156i) q^{80} +(-8.99928 + 0.114097i) q^{81} +(3.06204 + 5.30361i) q^{82} +(-7.18628 - 12.4470i) q^{83} +(6.51665 - 3.63318i) q^{84} +(-2.86094 + 4.95529i) q^{85} -5.83669 q^{86} +(-0.629499 + 2.37946i) q^{87} +5.73387 q^{88} +(1.48923 + 2.57942i) q^{89} +(-1.59011 - 0.904659i) q^{90} +(2.17776 - 0.541325i) q^{91} +(-0.668609 - 1.15806i) q^{92} +(-1.14081 + 4.31217i) q^{93} +(-0.943080 - 1.63346i) q^{94} +(-1.85316 - 3.20976i) q^{95} +(2.47535 - 9.35665i) q^{96} +(-6.02424 - 10.4343i) q^{97} +(3.61682 + 2.26724i) q^{98} +(0.0492835 + 7.77465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9} + q^{10} - 2 q^{11} - 16 q^{12} - 4 q^{13} - 13 q^{14} - q^{15} - 5 q^{16} - 7 q^{17} - 12 q^{18} - 2 q^{19} + 7 q^{20} - 5 q^{21} + 19 q^{22} - 2 q^{23} - 30 q^{24} + 24 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 3 q^{30} + 8 q^{31} + 17 q^{32} + q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} + 70 q^{38} - 8 q^{39} - 12 q^{40} + 20 q^{41} - 15 q^{42} + 31 q^{43} - 7 q^{44} - 9 q^{45} - 10 q^{46} - 31 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} - 37 q^{51} + 8 q^{52} + 8 q^{53} + 111 q^{54} + 2 q^{55} + 45 q^{56} + 5 q^{57} - 90 q^{58} - 21 q^{59} + 16 q^{60} + 5 q^{61} + 14 q^{62} - 9 q^{63} - 56 q^{64} + 4 q^{65} + 46 q^{66} + 43 q^{67} + 96 q^{68} + 26 q^{69} + 13 q^{70} + 24 q^{71} - 69 q^{72} - 18 q^{73} - 18 q^{74} + q^{75} - 13 q^{76} + 5 q^{77} + 19 q^{78} + 40 q^{79} + 5 q^{80} - 39 q^{81} + 5 q^{82} - 60 q^{83} + 47 q^{84} + 7 q^{85} - 24 q^{86} - 61 q^{87} - 100 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} - 8 q^{93} - 11 q^{94} + 2 q^{95} + 6 q^{96} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9 + q^10 - 2 * q^11 - 16 * q^12 - 4 * q^13 - 13 * q^14 - q^15 - 5 * q^16 - 7 * q^17 - 12 * q^18 - 2 * q^19 + 7 * q^20 - 5 * q^21 + 19 * q^22 - 2 * q^23 - 30 * q^24 + 24 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 3 * q^30 + 8 * q^31 + 17 * q^32 + q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 + 70 * q^38 - 8 * q^39 - 12 * q^40 + 20 * q^41 - 15 * q^42 + 31 * q^43 - 7 * q^44 - 9 * q^45 - 10 * q^46 - 31 * q^47 - 36 * q^48 - 11 * q^49 - q^50 - 37 * q^51 + 8 * q^52 + 8 * q^53 + 111 * q^54 + 2 * q^55 + 45 * q^56 + 5 * q^57 - 90 * q^58 - 21 * q^59 + 16 * q^60 + 5 * q^61 + 14 * q^62 - 9 * q^63 - 56 * q^64 + 4 * q^65 + 46 * q^66 + 43 * q^67 + 96 * q^68 + 26 * q^69 + 13 * q^70 + 24 * q^71 - 69 * q^72 - 18 * q^73 - 18 * q^74 + q^75 - 13 * q^76 + 5 * q^77 + 19 * q^78 + 40 * q^79 + 5 * q^80 - 39 * q^81 + 5 * q^82 - 60 * q^83 + 47 * q^84 + 7 * q^85 - 24 * q^86 - 61 * q^87 - 100 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 - 8 * q^93 - 11 * q^94 + 2 * q^95 + 6 * q^96 + 6 * q^97 - 15 * q^98 - q^99

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