LMFDB - Embedded newform 630.2.bz.a.517.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(13,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9, 6]))

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

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

chi := DirichletCharacter("630.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bz (of order $12$, degree $4$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			517.10
Character	$\chi$	$=$	630.517
Dual form			630.2.bz.a.223.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.684818 + 1.59092i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.438930 - 2.19256i) q^{5} +(-1.35947 - 1.07324i) q^{6} +(1.82597 + 1.91464i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.06205 - 2.17898i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.684818 + 1.59092i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.438930 - 2.19256i) q^{5} +(-1.35947 - 1.07324i) q^{6} +(1.82597 + 1.91464i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.06205 - 2.17898i) q^{9} +(2.00425 + 0.991451i) q^{10} +(-2.30836 - 3.99819i) q^{11} +(1.38853 - 1.03537i) q^{12} +(-4.25820 + 1.14098i) q^{13} +(-2.32199 + 1.26820i) q^{14} +(3.18761 + 2.19981i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-5.57375 + 5.57375i) q^{17} +(2.63843 - 1.42783i) q^{18} -7.15216 q^{19} +(-1.47641 + 1.67935i) q^{20} +(-4.29649 + 1.59379i) q^{21} +(4.45940 - 1.19489i) q^{22} +(-1.29239 - 4.82325i) q^{23} +(0.640711 + 1.60919i) q^{24} +(-4.61468 - 1.92476i) q^{25} -4.40841i q^{26} +(4.87871 - 1.78835i) q^{27} +(-0.624016 - 2.57111i) q^{28} +(2.14969 - 1.24113i) q^{29} +(-2.94987 + 2.50964i) q^{30} +(-1.31816 - 0.761040i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(7.94160 - 0.934378i) q^{33} +(-3.94124 - 6.82642i) q^{34} +(4.99944 - 3.16316i) q^{35} +(0.696298 + 2.91808i) q^{36} +(3.17227 + 3.17227i) q^{37} +(1.85112 - 6.90846i) q^{38} +(1.10088 - 7.55581i) q^{39} +(-1.24001 - 1.86075i) q^{40} +(0.829548 + 0.478940i) q^{41} +(-0.427470 - 4.56259i) q^{42} +(-5.54209 - 1.48500i) q^{43} +4.61671i q^{44} +(-5.68265 + 3.56476i) q^{45} +4.99340 q^{46} +(8.74053 + 2.34202i) q^{47} +(-1.72019 + 0.202390i) q^{48} +(-0.331680 + 6.99214i) q^{49} +(3.05355 - 3.95927i) q^{50} +(-5.05039 - 12.6844i) q^{51} +(4.25820 + 1.14098i) q^{52} +(-0.426131 + 0.426131i) q^{53} +(0.464712 + 5.17533i) q^{54} +(-9.77950 + 3.30630i) q^{55} +(2.64501 + 0.0626993i) q^{56} +(4.89792 - 11.3785i) q^{57} +(0.642454 + 2.39767i) q^{58} +(2.62693 - 4.54998i) q^{59} +(-1.66064 - 3.49889i) q^{60} +(-4.46250 + 2.57643i) q^{61} +(1.07627 - 1.07627i) q^{62} +(0.406720 - 7.92683i) q^{63} -1.00000i q^{64} +(0.632624 + 9.83718i) q^{65} +(-1.15290 + 7.91283i) q^{66} +(-9.46912 + 2.53724i) q^{67} +(7.61389 - 2.04013i) q^{68} +(8.55846 + 1.24697i) q^{69} +(1.76143 + 5.64778i) q^{70} -2.91185 q^{71} +(-2.99886 - 0.0826817i) q^{72} +(1.32049 + 1.32049i) q^{73} +(-3.88523 + 2.24314i) q^{74} +(6.22236 - 6.02347i) q^{75} +(6.19395 + 3.57608i) q^{76} +(3.44010 - 11.7202i) q^{77} +(7.01342 + 3.01896i) q^{78} +(12.2857 - 7.09317i) q^{79} +(2.11828 - 0.716158i) q^{80} +(-0.495902 + 8.98633i) q^{81} +(-0.677323 + 0.677323i) q^{82} +(1.96877 - 7.34757i) q^{83} +(4.51777 + 0.767982i) q^{84} +(9.77433 + 14.6673i) q^{85} +(2.86880 - 4.96890i) q^{86} +(0.502384 + 4.26993i) q^{87} +(-4.45940 - 1.19489i) q^{88} +3.99287 q^{89} +(-1.97252 - 6.41164i) q^{90} +(-9.95989 - 6.06951i) q^{91} +(-1.29239 + 4.82325i) q^{92} +(2.11345 - 1.57591i) q^{93} +(-4.52443 + 7.83654i) q^{94} +(-3.13930 + 15.6816i) q^{95} +(0.249723 - 1.71395i) q^{96} +(-5.19226 - 1.39126i) q^{97} +(-6.66804 - 2.13008i) q^{98} +(-3.95203 + 13.2743i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 8 q^{11} + 24 q^{15} + 96 q^{16} - 8 q^{18} + 8 q^{23} + 48 q^{30} - 24 q^{35} + 8 q^{36} - 44 q^{42} + 48 q^{46} + 32 q^{50} - 160 q^{53} - 4 q^{56} + 88 q^{57} + 24 q^{58} + 8 q^{60} - 48 q^{63} - 8 q^{65} + 16 q^{71} + 16 q^{72} - 16 q^{77} - 16 q^{78} - 8 q^{81} - 16 q^{86} + 8 q^{92} - 120 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) $ 192 * q + 8 * q^11 + 24 * q^15 + 96 * q^16 - 8 * q^18 + 8 * q^23 + 48 * q^30 - 24 * q^35 + 8 * q^36 - 44 * q^42 + 48 * q^46 + 32 * q^50 - 160 * q^53 - 4 * q^56 + 88 * q^57 + 24 * q^58 + 8 * q^60 - 48 * q^63 - 8 * q^65 + 16 * q^71 + 16 * q^72 - 16 * q^77 - 16 * q^78 - 8 * q^81 - 16 * q^86 + 8 * q^92 - 120 * q^93 - 128 * q^95 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−0.684818	+	1.59092i	−0.395380	+	0.918518i
$3$	−0.684818	+	1.59092i	−0.395380	+	0.918518i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.438930	−	2.19256i	0.196295	−	0.980545i
$5$	0.438930	−	2.19256i	0.196295	−	0.980545i
$6$	−1.35947	−	1.07324i	−0.555000	−	0.438150i
$7$	1.82597	+	1.91464i	0.690151	+	0.723665i
$7$	1.82597	+	1.91464i	0.690151	+	0.723665i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.06205	−	2.17898i	−0.687350	−	0.726326i
$10$	2.00425	+	0.991451i	0.633800	+	0.313524i
$11$	−2.30836	−	3.99819i	−0.695996	−	1.20550i	−0.969844	−	0.243727i	$-0.921630\pi$
$11$	−2.30836	−	3.99819i	−0.695996	−	1.20550i	0.273848	−	0.961773i	$-0.411703\pi$
$12$	1.38853	−	1.03537i	0.400834	−	0.298885i
$13$	−4.25820	+	1.14098i	−1.18101	+	0.316451i	−0.795327	−	0.606180i	$-0.792701\pi$
$13$	−4.25820	+	1.14098i	−1.18101	+	0.316451i	−0.385684	+	0.922631i	$0.626034\pi$
$14$	−2.32199	+	1.26820i	−0.620579	+	0.338942i
$15$	3.18761	+	2.19981i	0.823037	+	0.567988i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−5.57375	+	5.57375i	−1.35183	+	1.35183i	−0.468223	+	0.883610i	$0.655106\pi$
$17$	−5.57375	+	5.57375i	−1.35183	+	1.35183i	−0.883610	+	0.468223i	$0.844894\pi$
$18$	2.63843	−	1.42783i	0.621884	−	0.336542i
$19$	−7.15216			−1.64082			−0.820409	−	0.571777i	$-0.806254\pi$
$19$	−7.15216			−1.64082			−0.820409	+	0.571777i	$0.806254\pi$
$20$	−1.47641	+	1.67935i	−0.330135	+	0.375515i
$21$	−4.29649	+	1.59379i	−0.937571	+	0.347794i
$22$	4.45940	−	1.19489i	0.950748	−	0.254752i
$23$	−1.29239	−	4.82325i	−0.269481	−	1.00572i	−0.959450	−	0.281879i	$-0.909042\pi$
$23$	−1.29239	−	4.82325i	−0.269481	−	1.00572i	0.689969	−	0.723839i	$-0.257624\pi$
$24$	0.640711	+	1.60919i	0.130785	+	0.328474i
$25$	−4.61468	−	1.92476i	−0.922936	−	0.384953i
$26$		−	4.40841i		−	0.864560i
$27$	4.87871	−	1.78835i	0.938908	−	0.344168i
$28$	−0.624016	−	2.57111i	−0.117928	−	0.485894i
$29$	2.14969	−	1.24113i	0.399188	−	0.230471i	−0.286946	−	0.957947i	$-0.592640\pi$
$29$	2.14969	−	1.24113i	0.399188	−	0.230471i	0.686133	+	0.727476i	$0.259307\pi$
$30$	−2.94987	+	2.50964i	−0.538569	+	0.458195i
$31$	−1.31816	−	0.761040i	−0.236749	−	0.136687i	0.376933	−	0.926241i	$-0.376979\pi$
$31$	−1.31816	−	0.761040i	−0.236749	−	0.136687i	−0.613681	+	0.789554i	$0.710312\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	7.94160	−	0.934378i	1.38246	−	0.162654i
$34$	−3.94124	−	6.82642i	−0.675917	−	1.17072i
$35$	4.99944	−	3.16316i	0.845060	−	0.534672i
$36$	0.696298	+	2.91808i	0.116050	+	0.486346i
$37$	3.17227	+	3.17227i	0.521519	+	0.521519i	0.918030	−	0.396511i	$-0.129779\pi$
$37$	3.17227	+	3.17227i	0.521519	+	0.521519i	−0.396511	+	0.918030i	$0.629779\pi$
$38$	1.85112	−	6.90846i	0.300291	−	1.12070i
$39$	1.10088	−	7.55581i	0.176282	−	1.20990i
$40$	−1.24001	−	1.86075i	−0.196062	−	0.294210i
$41$	0.829548	+	0.478940i	0.129554	+	0.0747978i	0.563376	−	0.826201i	$-0.309502\pi$
$41$	0.829548	+	0.478940i	0.129554	+	0.0747978i	−0.433823	+	0.900998i	$0.642836\pi$
$42$	−0.427470	−	4.56259i	−0.0659600	−	0.704024i
$43$	−5.54209	−	1.48500i	−0.845161	−	0.226460i	−0.189844	−	0.981814i	$-0.560798\pi$
$43$	−5.54209	−	1.48500i	−0.845161	−	0.226460i	−0.655317	+	0.755354i	$0.727465\pi$
$44$			4.61671i			0.695996i
$45$	−5.68265	+	3.56476i	−0.847119	+	0.531403i
$46$	4.99340			0.736237
$47$	8.74053	+	2.34202i	1.27494	+	0.341618i	0.831920	−	0.554895i	$-0.187242\pi$
$47$	8.74053	+	2.34202i	1.27494	+	0.341618i	0.443017	+	0.896513i	$0.353908\pi$
$48$	−1.72019	+	0.202390i	−0.248287	+	0.0292125i
$49$	−0.331680	+	6.99214i	−0.0473829	+	0.998877i
$50$	3.05355	−	3.95927i	0.431837	−	0.559926i
$51$	−5.05039	−	12.6844i	−0.707196	−	1.77617i
$52$	4.25820	+	1.14098i	0.590505	+	0.158225i
$53$	−0.426131	+	0.426131i	−0.0585337	+	0.0585337i	−0.735768	−	0.677234i	$-0.763178\pi$
$53$	−0.426131	+	0.426131i	−0.0585337	+	0.0585337i	0.677234	+	0.735768i	$0.263178\pi$
$54$	0.464712	+	5.17533i	0.0632394	+	0.704273i
$55$	−9.77950	+	3.30630i	−1.31867	+	0.445821i
$56$	2.64501	+	0.0626993i	0.353454	+	0.00837854i
$57$	4.89792	−	11.3785i	0.648746	−	1.50712i
$58$	0.642454	+	2.39767i	0.0843583	+	0.314830i
$59$	2.62693	−	4.54998i	0.341997	−	0.592357i	−0.642806	−	0.766029i	$-0.722230\pi$
$59$	2.62693	−	4.54998i	0.341997	−	0.592357i	0.984804	+	0.173672i	$0.0555632\pi$
$60$	−1.66064	−	3.49889i	−0.214388	−	0.451705i
$61$	−4.46250	+	2.57643i	−0.571365	+	0.329878i	−0.757694	−	0.652610i	$-0.773674\pi$
$61$	−4.46250	+	2.57643i	−0.571365	+	0.329878i	0.186330	+	0.982487i	$0.440341\pi$
$62$	1.07627	−	1.07627i	0.136687	−	0.136687i
$63$	0.406720	−	7.92683i	0.0512419	−	0.998686i
$64$		−	1.00000i		−	0.125000i
$65$	0.632624	+	9.83718i	0.0784674	+	1.22015i
$66$	−1.15290	+	7.91283i	−0.141912	+	0.974002i
$67$	−9.46912	+	2.53724i	−1.15684	+	0.309974i	−0.785702	−	0.618605i	$-0.787698\pi$
$67$	−9.46912	+	2.53724i	−1.15684	+	0.309974i	−0.371135	+	0.928579i	$0.621031\pi$
$68$	7.61389	−	2.04013i	0.923319	−	0.247403i
$69$	8.55846	+	1.24697i	1.03032	+	0.150117i
$70$	1.76143	+	5.64778i	0.210531	+	0.675038i
$71$	−2.91185			−0.345573			−0.172786	−	0.984959i	$-0.555277\pi$
$71$	−2.91185			−0.345573			−0.172786	+	0.984959i	$0.555277\pi$
$72$	−2.99886	−	0.0826817i	−0.353419	−	0.00974413i
$73$	1.32049	+	1.32049i	0.154552	+	0.154552i	0.780147	−	0.625596i	$-0.215144\pi$
$73$	1.32049	+	1.32049i	0.154552	+	0.154552i	−0.625596	+	0.780147i	$0.715144\pi$
$74$	−3.88523	+	2.24314i	−0.451648	+	0.260759i
$75$	6.22236	−	6.02347i	0.718496	−	0.695531i
$76$	6.19395	+	3.57608i	0.710495	+	0.410205i
$77$	3.44010	−	11.7202i	0.392036	−	1.33564i
$78$	7.01342	+	3.01896i	0.794114	+	0.341829i
$79$	12.2857	−	7.09317i	1.38225	−	0.798044i	0.389826	−	0.920888i	$-0.372535\pi$
$79$	12.2857	−	7.09317i	1.38225	−	0.798044i	0.992426	+	0.122845i	$0.0392017\pi$
$80$	2.11828	−	0.716158i	0.236831	−	0.0800689i
$81$	−0.495902	+	8.98633i	−0.0551002	+	0.998481i
$82$	−0.677323	+	0.677323i	−0.0747978	+	0.0747978i
$83$	1.96877	−	7.34757i	0.216101	−	0.806500i	−0.769675	−	0.638436i	$-0.779582\pi$
$83$	1.96877	−	7.34757i	0.216101	−	0.806500i	0.985776	−	0.168064i	$-0.0537516\pi$
$84$	4.51777	+	0.767982i	0.492929	+	0.0837937i
$85$	9.77433	+	14.6673i	1.06017	+	1.59089i
$86$	2.86880	−	4.96890i	0.309350	−	0.535810i
$87$	0.502384	+	4.26993i	0.0538612	+	0.457785i
$88$	−4.45940	−	1.19489i	−0.475374	−	0.127376i
$89$	3.99287			0.423244			0.211622	−	0.977352i	$-0.432125\pi$
$89$	3.99287			0.423244			0.211622	+	0.977352i	$0.432125\pi$
$90$	−1.97252	−	6.41164i	−0.207921	−	0.675847i
$91$	−9.95989	−	6.06951i	−1.04408	−	0.636258i
$92$	−1.29239	+	4.82325i	−0.134741	+	0.502859i
$93$	2.11345	−	1.57591i	0.219155	−	0.163415i
$94$	−4.52443	+	7.83654i	−0.466659	+	0.808278i
$95$	−3.13930	+	15.6816i	−0.322085	+	1.60890i
$96$	0.249723	−	1.71395i	0.0254872	−	0.174930i
$97$	−5.19226	−	1.39126i	−0.527194	−	0.141261i	−0.0146016	−	0.999893i	$-0.504648\pi$
$97$	−5.19226	−	1.39126i	−0.527194	−	0.141261i	−0.512592	+	0.858632i	$0.671315\pi$
$98$	−6.66804	−	2.13008i	−0.673574	−	0.215170i
$99$	−3.95203	+	13.2743i	−0.397194	+	1.33412i
$100$	3.03405	+	3.97424i	0.303405	+	0.397424i
$101$	−12.1753	+	7.02941i	−1.21149	+	0.699453i	−0.963083	−	0.269203i	$-0.913240\pi$
$101$	−12.1753	+	7.02941i	−1.21149	+	0.699453i	−0.248405	+	0.968656i	$0.579906\pi$
$102$	13.5593	−	1.59534i	1.34257	−	0.157962i
$103$	5.75993	−	1.54337i	0.567543	−	0.152073i	0.0363736	−	0.999338i	$-0.488419\pi$
$103$	5.75993	−	1.54337i	0.567543	−	0.152073i	0.531170	+	0.847266i	$0.321753\pi$
$104$	−2.20420	+	3.81779i	−0.216140	+	0.374365i
$105$	1.60863	+	10.1199i	0.156986	+	0.987601i
$106$	−0.301320	−	0.521902i	−0.0292668	−	0.0506916i
$107$	−9.01710	−	9.01710i	−0.871716	−	0.871716i	0.120944	−	0.992659i	$-0.461408\pi$
$107$	−9.01710	−	9.01710i	−0.871716	−	0.871716i	−0.992659	+	0.120944i	$0.961408\pi$
$108$	−5.11926	−	0.890596i	−0.492601	−	0.0856977i
$109$			6.41947i			0.614873i	0.951569	+	0.307437i	$0.0994712\pi$
$109$			6.41947i			0.614873i	−0.951569	+	0.307437i	$0.900529\pi$
$110$	−0.662517	−	10.3020i	−0.0631685	−	0.982257i
$111$	−7.21926	+	2.87440i	−0.685222	+	0.272826i
$112$	−0.745141	+	2.53865i	−0.0704092	+	0.239880i
$113$	−3.17853	−	11.8625i	−0.299011	−	1.11593i	−0.937979	−	0.346692i	$-0.887305\pi$
$113$	−3.17853	−	11.8625i	−0.299011	−	1.11593i	0.638968	−	0.769234i	$-0.279362\pi$
$114$	9.72312	+	7.67601i	0.910654	+	0.718924i
$115$	−11.1426	+	0.716573i	−1.03905	+	0.0668207i
$116$	−2.48225			−0.230471
$117$	11.2668	+	6.92576i	1.04161	+	0.640287i
$118$	3.71504	+	3.71504i	0.341997	+	0.341997i
$119$	−20.8492	−	0.494226i	−1.91124	−	0.0453056i
$120$	3.80948	−	0.698479i	0.347756	−	0.0637621i
$121$	−5.15702	+	8.93222i	−0.468820	+	0.812020i
$122$	−1.33366	−	4.97727i	−0.120744	−	0.450621i
$123$	−1.33004	+	0.991758i	−0.119926	+	0.0894238i
$124$	0.761040	+	1.31816i	0.0683434	+	0.118374i
$125$	−6.24569	+	9.27315i	−0.558632	+	0.829416i
$126$	7.55146	+	2.44448i	0.672737	+	0.217771i
$127$	9.48491	+	9.48491i	0.841650	+	0.841650i	0.989073	−	0.147424i	$-0.0470981\pi$
$127$	9.48491	+	9.48491i	0.841650	+	0.841650i	−0.147424	+	0.989073i	$0.547098\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	6.15783	−	7.80006i	0.542167	−	0.686757i
$130$	−9.66572	−	1.93498i	−0.847740	−	0.169709i
$131$	−5.00045	−	2.88701i	−0.436891	−	0.252239i	0.265387	−	0.964142i	$-0.414500\pi$
$131$	−5.00045	−	2.88701i	−0.436891	−	0.252239i	−0.702278	+	0.711903i	$0.747834\pi$
$132$	−7.34482	−	3.16161i	−0.639284	−	0.275182i
$133$	−13.0596	−	13.6938i	−1.13241	−	1.18740i
$134$		−	9.80315i		−	0.846863i
$135$	−1.77967	−	11.4818i	−0.153169	−	0.988200i
$136$			7.88248i			0.675917i
$137$	−0.134451	+	0.501778i	−0.0114869	+	0.0428698i	−0.971431	−	0.237320i	$-0.923731\pi$
$137$	−0.134451	+	0.501778i	−0.0114869	+	0.0428698i	0.959944	+	0.280190i	$0.0903975\pi$
$138$	−3.41957	+	7.94410i	−0.291093	+	0.676246i
$139$	−8.04729	+	13.9383i	−0.682562	+	1.18223i	0.291634	+	0.956530i	$0.405801\pi$
$139$	−8.04729	+	13.9383i	−0.682562	+	1.18223i	−0.974196	+	0.225703i	$0.927532\pi$
$140$	−5.91122	+	0.239658i	−0.499590	+	0.0202548i
$141$	−9.71163	+	12.3016i	−0.817867	+	1.03598i
$142$	0.753641	−	2.81263i	0.0632442	−	0.236030i
$143$	14.3913	+	14.3913i	1.20346	+	1.20346i
$144$	0.856027	−	2.87528i	0.0713355	−	0.239606i
$145$	−1.77768	−	5.25811i	−0.147629	−	0.436662i
$146$	−1.61726	+	0.933727i	−0.133846	+	0.0772758i
$147$	−10.8968	−	5.31602i	−0.898752	−	0.438458i
$148$	−1.16113	−	4.33341i	−0.0954446	−	0.356204i
$149$	11.3650	+	6.56156i	0.931054	+	0.537544i	0.887145	−	0.461491i	$-0.152685\pi$
$149$	11.3650	+	6.56156i	0.931054	+	0.537544i	0.0439091	+	0.999036i	$0.486019\pi$
$150$	4.20776	+	7.56933i	0.343563	+	0.618033i
$151$	1.64198	+	2.84400i	0.133623	+	0.231442i	0.925071	−	0.379795i	$-0.124006\pi$
$151$	1.64198	+	2.84400i	0.133623	+	0.231442i	−0.791448	+	0.611237i	$0.790672\pi$
$152$	−5.05734	+	5.05734i	−0.410205	+	0.410205i
$153$	23.6384	+	0.651737i	1.91105	+	0.0526898i
$154$	10.4305	+	6.35631i	0.840515	+	0.512206i
$155$	−2.24721	+	2.55611i	−0.180500	+	0.205312i
$156$	−4.73129	+	5.99308i	−0.378807	+	0.479831i
$157$	1.71048	+	6.38359i	0.136511	+	0.509466i	0.999987	+	0.00507638i	$0.00161587\pi$
$157$	1.71048	+	6.38359i	0.136511	+	0.509466i	−0.863476	+	0.504390i	$0.831717\pi$
$158$	3.67169	+	13.7029i	0.292104	+	1.09015i
$159$	−0.386119	−	0.969763i	−0.0306212	−	0.0769072i
$160$	0.143504	+	2.23146i	0.0113450	+	0.176412i
$161$	6.87493	−	11.2816i	0.541820	−	0.889112i
$162$	−8.55178	−	2.80484i	−0.671891	−	0.220369i
$163$	1.36935	−	1.36935i	0.107255	−	0.107255i	−0.651443	−	0.758698i	$-0.725836\pi$
$163$	1.36935	−	1.36935i	0.107255	−	0.107255i	0.758698	+	0.651443i	$0.225836\pi$
$164$	−0.478940	−	0.829548i	−0.0373989	−	0.0647768i
$165$	1.43712	−	17.8226i	0.111880	−	1.38749i
$166$	6.58765	+	3.80338i	0.511301	+	0.295200i
$167$	1.11596	+	4.16483i	0.0863557	+	0.322284i	0.995567	−	0.0940500i	$-0.0299814\pi$
$167$	1.11596	+	4.16483i	0.0863557	+	0.322284i	−0.909212	+	0.416334i	$0.863315\pi$
$168$	−1.91110	+	4.16506i	−0.147444	+	0.321341i
$169$	5.57206	−	3.21703i	0.428620	−	0.247464i
$170$	−16.6973	+	5.64510i	−1.28062	+	0.432959i
$171$	14.7481	+	15.5844i	1.12782	+	1.19177i
$172$	4.05709	+	4.05709i	0.309350	+	0.309350i
$173$	1.08818	−	4.06116i	0.0827331	−	0.308764i	−0.912142	−	0.409874i	$-0.865573\pi$
$173$	1.08818	−	4.06116i	0.0827331	−	0.308764i	0.994875	+	0.101110i	$0.0322394\pi$
$174$	−4.25446	−	0.619874i	−0.322530	−	0.0469926i
$175$	−4.74103	−	12.3500i	−0.358389	−	0.933573i
$176$	2.30836	−	3.99819i	0.173999	−	0.301375i
$177$	5.43968	+	7.29514i	0.408872	+	0.548337i
$178$	−1.03343	+	3.85682i	−0.0774590	+	0.289081i
$179$		−	5.43754i		−	0.406421i	−0.979135	−	0.203211i	$-0.934862\pi$
$179$		−	5.43754i		−	0.406421i	0.979135	−	0.203211i	$-0.0651376\pi$
$180$	6.70370	−	0.245848i	0.499664	−	0.0183244i
$181$		−	18.4709i		−	1.37293i	−0.727163	−	0.686465i	$-0.759162\pi$
$181$		−	18.4709i		−	1.37293i	0.727163	−	0.686465i	$-0.240838\pi$
$182$	8.44051	−	8.04961i	0.625652	−	0.596677i
$183$	−1.04289	−	8.86386i	−0.0770925	−	0.655235i
$184$	−4.32441	−	2.49670i	−0.318800	−	0.184059i
$185$	8.34782	−	5.56301i	0.613744	−	0.409001i
$186$	0.975213	+	2.44932i	0.0715061	+	0.179592i
$187$	35.1511	+	9.41872i	2.57051	+	0.688765i
$188$	−6.39851	−	6.39851i	−0.466659	−	0.466659i
$189$	12.3324	+	6.07549i	0.897051	+	0.441927i
$190$	−14.3347	−	7.09102i	−1.03995	−	0.514436i
$191$	7.66575	+	13.2775i	0.554675	+	0.960725i	0.997929	+	0.0643286i	$0.0204906\pi$
$191$	7.66575	+	13.2775i	0.554675	+	0.960725i	−0.443254	+	0.896396i	$0.646176\pi$
$192$	1.59092	+	0.684818i	0.114815	+	0.0494225i
$193$	3.60474	+	13.4531i	0.259475	+	0.968373i	0.965546	+	0.260232i	$0.0837991\pi$
$193$	3.60474	+	13.4531i	0.259475	+	0.968373i	−0.706071	+	0.708141i	$0.749534\pi$
$194$	2.68771	−	4.65525i	0.192966	−	0.334227i
$195$	−16.0834	−	5.73022i	−1.15176	−	0.410350i
$196$	3.78331	−	5.88953i	0.270237	−	0.420681i
$197$	−5.10508	−	5.10508i	−0.363722	−	0.363722i	0.501459	−	0.865181i	$-0.332797\pi$
$197$	−5.10508	−	5.10508i	−0.363722	−	0.363722i	−0.865181	+	0.501459i	$0.832797\pi$
$198$	−11.7992	−	7.25302i	−0.838530	−	0.515449i
$199$	−10.0687			−0.713748			−0.356874	−	0.934153i	$-0.616157\pi$
$199$	−10.0687			−0.713748			−0.356874	+	0.934153i	$0.616157\pi$
$200$	−4.62409	+	1.90206i	−0.326972	+	0.134496i
$201$	2.44807	−	16.8022i	0.172674	−	1.18513i
$202$	−3.63869	−	13.5798i	−0.256018	−	0.955470i
$203$	6.30158	+	1.84963i	0.442284	+	0.129818i
$204$	−1.96843	+	13.5102i	−0.137818	+	0.945903i
$205$	1.41422	−	1.60862i	0.0987734	−	0.112351i
$206$			5.96312i			0.415470i
$207$	−7.84480	+	12.7619i	−0.545252	+	0.887012i
$208$	−3.11722	−	3.11722i	−0.216140	−	0.216140i
$209$	16.5097	+	28.5957i	1.14200	+	1.97801i
$210$	−10.1914	−	1.06540i	−0.703274	−	0.0735198i
$211$	0.548186	−	0.949486i	0.0377387	−	0.0653653i	−0.846539	−	0.532326i	$-0.821318\pi$
$211$	0.548186	−	0.949486i	0.0377387	−	0.0653653i	0.884278	+	0.466961i	$0.154651\pi$
$212$	0.582106	−	0.155975i	0.0399792	−	0.0107124i
$213$	1.99408	−	4.63251i	0.136632	−	0.317415i
$214$	11.0436	−	6.37605i	0.754928	−	0.435858i
$215$	−5.68854	+	11.4996i	−0.387955	+	0.784265i
$216$	2.18521	−	4.71432i	0.148685	−	0.320769i
$217$	−0.949802	−	3.91344i	−0.0644768	−	0.265661i
$218$	−6.20073	−	1.66148i	−0.419966	−	0.112530i
$219$	−3.00509	+	1.19650i	−0.203065	+	0.0808518i
$220$	10.1224	+	2.02641i	0.682455	+	0.136621i
$221$	17.3746	−	30.0937i	1.16874	−	2.02432i
$222$	−0.907978	−	7.71722i	−0.0609395	−	0.517946i
$223$	−1.23147	+	4.59592i	−0.0824655	+	0.307765i	−0.994822	−	0.101631i	$-0.967594\pi$
$223$	−1.23147	+	4.59592i	−0.0824655	+	0.307765i	0.912357	+	0.409396i	$0.134261\pi$
$224$	−2.25929	−	1.37680i	−0.150955	−	0.0919915i
$225$	5.32168	+	14.0243i	0.354779	+	0.934950i
$226$	12.2809			0.816914
$227$	−11.9592	−	3.20446i	−0.793760	−	0.212687i	−0.160917	−	0.986968i	$-0.551445\pi$
$227$	−11.9592	−	3.20446i	−0.793760	−	0.212687i	−0.632843	+	0.774281i	$0.718112\pi$
$228$	−9.93098	+	7.40512i	−0.657695	+	0.490416i
$229$	12.3058	−	21.3143i	0.813191	−	1.40849i	−0.0974290	−	0.995242i	$-0.531062\pi$
$229$	12.3058	−	21.3143i	0.813191	−	1.40849i	0.910620	−	0.413245i	$-0.135605\pi$
$230$	2.19175	−	10.9484i	0.144520	−	0.721913i
$231$	16.2901	+	13.4992i	1.07181	+	0.888179i
$232$	0.642454	−	2.39767i	0.0421792	−	0.157415i
$233$	−15.5262	+	15.5262i	−1.01716	+	1.01716i	−0.0173079	+	0.999850i	$0.505510\pi$
$233$	−15.5262	+	15.5262i	−1.01716	+	1.01716i	−0.999850	+	0.0173079i	$0.994490\pi$
$234$	−9.60583	+	9.09036i	−0.627953	+	0.594255i
$235$	8.97150	−	18.1362i	0.585236	−	1.18307i
$236$	−4.54998	+	2.62693i	−0.296178	+	0.170999i
$237$	2.87118	+	24.4031i	0.186503	+	1.58515i
$238$	5.87356	−	20.0109i	0.380726	−	1.29711i
$239$	−22.0785	−	12.7470i	−1.42814	−	0.824535i	−0.431163	−	0.902274i	$-0.641897\pi$
$239$	−22.0785	−	12.7470i	−1.42814	−	0.824535i	−0.996974	+	0.0777388i	$0.975230\pi$
$240$	−0.311287	+	3.86045i	−0.0200935	+	0.249191i
$241$	−15.0522	+	8.69040i	−0.969598	+	0.559798i	−0.899114	−	0.437715i	$-0.855788\pi$
$241$	−15.0522	+	8.69040i	−0.969598	+	0.559798i	−0.0704845	+	0.997513i	$0.522455\pi$
$242$	−7.29312	−	7.29312i	−0.468820	−	0.468820i
$243$	−13.9569	−	6.94294i	−0.895337	−	0.445389i
$244$	5.15285			0.329878
$245$	15.1851	+	3.79629i	0.970142	+	0.242536i
$246$	−0.613724	−	1.54141i	−0.0391296	−	0.0982767i
$247$	30.4553	−	8.16047i	1.93782	−	0.519238i
$248$	−1.47022	+	0.393943i	−0.0933588	+	0.0250154i
$249$	10.3411	+	8.16390i	0.655343	+	0.517366i
$250$	−7.34067	−	8.43294i	−0.464265	−	0.533346i
$251$		−	10.7321i		−	0.677401i	−0.940894	−	0.338701i	$-0.890013\pi$
$251$		−	10.7321i		−	0.677401i	0.940894	−	0.338701i	$-0.109987\pi$
$252$	−4.31564	+	6.66147i	−0.271860	+	0.419633i
$253$	−16.3010	+	16.3010i	−1.02483	+	1.02483i
$254$	−11.6166	+	6.70684i	−0.728890	+	0.420825i
$255$	−30.0281	+	5.50574i	−1.88043	+	0.344783i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.95020	−	7.27823i	−0.121650	−	0.454004i	0.878048	−	0.478572i	$-0.158845\pi$
$257$	−1.95020	−	7.27823i	−0.121650	−	0.454004i	−0.999698	+	0.0245685i	$0.992179\pi$
$258$	5.94052	+	7.96682i	0.369841	+	0.495992i
$259$	−0.281286	+	11.8662i	−0.0174783	+	0.737332i
$260$	4.37072	−	8.83556i	0.271061	−	0.547958i
$261$	−7.13716	−	2.12487i	−0.441779	−	0.131526i
$262$	4.08285	−	4.08285i	0.252239	−	0.252239i
$263$	10.0428	+	2.69097i	0.619267	+	0.165932i	0.554795	−	0.831987i	$-0.312797\pi$
$263$	10.0428	+	2.69097i	0.619267	+	0.165932i	0.0644724	+	0.997919i	$0.479464\pi$
$264$	4.95486	−	6.27627i	0.304950	−	0.386277i
$265$	0.747279	+	1.12136i	0.0459050	+	0.0688848i
$266$	16.6073	−	9.07040i	1.01826	−	0.556142i
$267$	−2.73439	+	6.35234i	−0.167342	+	0.388757i
$268$	9.46912	+	2.53724i	0.578418	+	0.154987i
$269$	−9.63676			−0.587563			−0.293782	−	0.955873i	$-0.594914\pi$
$269$	−9.63676			−0.587563			−0.293782	+	0.955873i	$0.594914\pi$
$270$	11.5512	+	1.25269i	0.702985	+	0.0762365i
$271$		−	17.8487i		−	1.08423i	−0.840304	−	0.542116i	$-0.817623\pi$
$271$		−	17.8487i		−	1.08423i	0.840304	−	0.542116i	$-0.182377\pi$
$272$	−7.61389	−	2.04013i	−0.461660	−	0.123701i
$273$	16.4768	−	11.6889i	0.997222	−	0.707443i
$274$	−0.449882	−	0.259740i	−0.0271784	−	0.0156914i
$275$	2.95676	+	22.8934i	0.178299	+	1.38052i
$276$	−6.78836	−	5.35913i	−0.408611	−	0.322582i
$277$	−4.36487	+	16.2899i	−0.262259	+	0.978766i	0.701647	+	0.712525i	$0.252448\pi$
$277$	−4.36487	+	16.2899i	−0.262259	+	0.978766i	−0.963907	+	0.266241i	$0.914218\pi$
$278$	−11.3806	−	11.3806i	−0.682562	−	0.682562i
$279$	1.05982	+	4.44155i	0.0634498	+	0.265908i
$280$	1.29845	−	5.77183i	0.0775969	−	0.344933i
$281$	6.11133	+	10.5851i	0.364571	+	0.631456i	0.988707	−	0.149860i	$-0.0478823\pi$
$281$	6.11133	+	10.5851i	0.364571	+	0.631456i	−0.624136	+	0.781316i	$0.714549\pi$
$282$	−9.36890	−	12.5646i	−0.557910	−	0.748212i
$283$	3.54022	−	0.948599i	0.210444	−	0.0563884i	−0.152057	−	0.988372i	$-0.548590\pi$
$283$	3.54022	−	0.948599i	0.210444	−	0.0563884i	0.362501	+	0.931983i	$0.381923\pi$
$284$	2.52173	+	1.45592i	0.149637	+	0.0863931i
$285$	−22.7983	−	15.7334i	−1.35045	−	0.931965i
$286$	−17.6257	+	10.1762i	−1.04223	+	0.601730i
$287$	0.597732	+	2.46281i	0.0352830	+	0.145375i
$288$	2.55575	+	1.57103i	0.150599	+	0.0925741i
$289$		−	45.1334i		−	2.65491i
$290$	5.53904	−	0.356213i	0.325264	−	0.0209175i
$291$	5.76913	−	7.30770i	0.338192	−	0.428385i
$292$	−0.483333	−	1.80382i	−0.0282849	−	0.105561i
$293$	8.50141	−	2.27794i	0.496657	−	0.133079i	−0.00179086	−	0.999998i	$-0.500570\pi$
$293$	8.50141	−	2.27794i	0.496657	−	0.133079i	0.498448	+	0.866919i	$0.333903\pi$
$294$	7.95517	−	9.14960i	0.463955	−	0.533616i
$295$	−8.82309	−	7.75684i	−0.513700	−	0.451621i
$296$	4.48627			0.260759
$297$	−18.4120	−	15.3779i	−1.06837	−	0.892314i
$298$	−9.27945	+	9.27945i	−0.537544	+	0.537544i
$299$	11.0065	+	19.0638i	0.636521	+	1.10249i
$300$	−8.40046	+	2.10530i	−0.485001	+	0.121550i
$301$	−7.27644	−	13.3227i	−0.419407	−	0.767905i
$302$	−3.17207	+	0.849954i	−0.182532	+	0.0489094i
$303$	−2.84537	−	24.1838i	−0.163462	−	1.38932i
$304$	−3.57608	−	6.19395i	−0.205102	−	0.355248i
$305$	3.69026	+	10.9152i	0.211303	+	0.625002i
$306$	−6.74761	+	22.6643i	−0.385735	+	1.29563i
$307$	−2.89985	+	2.89985i	−0.165503	+	0.165503i	−0.785000	−	0.619496i	$-0.787337\pi$
$307$	−2.89985	+	2.89985i	−0.165503	+	0.165503i	0.619496	+	0.785000i	$0.287337\pi$
$308$	−8.83934	+	8.42997i	−0.503668	+	0.480342i
$309$	−1.48913	+	10.2205i	−0.0847135	+	0.581425i
$310$	−1.88739	−	2.83221i	−0.107197	−	0.160859i
$311$	−20.9144	−	12.0750i	−1.18595	−	0.684708i	−0.228566	−	0.973529i	$-0.573404\pi$
$311$	−20.9144	−	12.0750i	−1.18595	−	0.684708i	−0.957383	+	0.288821i	$0.906737\pi$
$312$	−4.56432	−	6.12120i	−0.258404	−	0.346545i
$313$	−1.66599	+	6.21756i	−0.0941673	+	0.351437i	−0.996892	−	0.0787818i	$-0.974897\pi$
$313$	−1.66599	+	6.21756i	−0.0941673	+	0.351437i	0.902725	+	0.430219i	$0.141564\pi$
$314$	−6.60878			−0.372955
$315$	−17.2016	−	4.37108i	−0.969198	−	0.246282i
$316$	−14.1863			−0.798044
$317$	1.67886	−	6.26559i	0.0942941	−	0.351910i	−0.902617	−	0.430444i	$-0.858357\pi$
$317$	1.67886	−	6.26559i	0.0942941	−	0.351910i	0.996911	+	0.0785334i	$0.0250237\pi$
$318$	1.03665	−	0.121969i	0.0581327	−	0.00683966i
$319$	−9.92451	−	5.72992i	−0.555666	−	0.320814i
$320$	−2.19256	−	0.438930i	−0.122568	−	0.0245369i
$321$	20.5205	−	8.17041i	1.14534	−	0.456028i
$322$	9.11779	+	9.56056i	0.508115	+	0.532789i
$323$	39.8644	−	39.8644i	2.21811	−	2.21811i
$324$	4.92263	−	7.53444i	0.273479	−	0.418580i
$325$	21.8463	+	2.93076i	1.21182	+	0.162569i
$326$	0.968274	+	1.67710i	0.0536277	+	0.0928859i
$327$	−10.2129	−	4.39616i	−0.564772	−	0.243108i
$328$	0.925241	−	0.247917i	0.0510879	−	0.0136890i
$329$	11.4758	+	21.0114i	0.632682	+	1.15840i
$330$	16.8434	+	6.00098i	0.927196	+	0.330343i
$331$	14.5561	+	25.2119i	0.800074	+	1.38577i	0.919567	+	0.392934i	$0.128540\pi$
$331$	14.5561	+	25.2119i	0.800074	+	1.38577i	−0.119492	+	0.992835i	$0.538127\pi$
$332$	−5.37879	+	5.37879i	−0.295200	+	0.295200i
$333$	0.370933	−	13.4537i	0.0203270	−	0.737259i
$334$	−4.31175			−0.235928
$335$	1.40679	+	21.8753i	0.0768612	+	1.19518i
$336$	−3.52851	−	2.92397i	−0.192496	−	0.159516i
$337$	−22.3022	+	5.97585i	−1.21488	+	0.325525i	−0.808674	−	0.588257i	$-0.799814\pi$
$337$	−22.3022	+	5.97585i	−1.21488	+	0.325525i	−0.406203	+	0.913783i	$0.633148\pi$
$338$	1.66526	+	6.21483i	0.0905781	+	0.338042i
$339$	21.0489	+	3.06682i	1.14322	+	0.166567i
$340$	−1.13117	−	17.5894i	−0.0613461	−	0.953920i
$341$			7.02701i			0.380534i
$342$	−18.8705	+	10.2120i	−1.02040	+	0.552204i
$343$	−13.9931	+	12.1324i	−0.755554	+	0.655087i
$344$	−4.96890	+	2.86880i	−0.267905	+	0.154675i
$345$	6.49061	−	18.2176i	0.349443	−	0.980805i
$346$	3.64113	+	2.10221i	0.195749	+	0.113015i
$347$	32.1948	−	8.62656i	1.72831	−	0.463098i	0.748514	−	0.663119i	$-0.230768\pi$
$347$	32.1948	−	8.62656i	1.72831	−	0.463098i	0.979792	+	0.200021i	$0.0641011\pi$
$348$	1.69989	−	3.94906i	0.0911236	−	0.211692i
$349$	−5.12603	−	8.87854i	−0.274390	−	0.475257i	0.695591	−	0.718438i	$-0.255143\pi$
$349$	−5.12603	−	8.87854i	−0.274390	−	0.475257i	−0.969981	+	0.243181i	$0.921809\pi$
$350$	13.1563	−	1.38307i	0.703232	−	0.0739283i
$351$	−18.7340	+	13.1817i	−0.999948	+	0.703585i
$352$	3.26451	+	3.26451i	0.173999	+	0.173999i
$353$	−1.19020	+	4.44187i	−0.0633477	+	0.236417i	−0.990339	−	0.138665i	$-0.955719\pi$
$353$	−1.19020	+	4.44187i	−0.0633477	+	0.236417i	0.926992	+	0.375082i	$0.122385\pi$
$354$	−8.45446	+	3.36621i	−0.449350	+	0.178912i
$355$	−1.27810	+	6.38441i	−0.0678343	+	0.338849i
$356$	−3.45793	−	1.99644i	−0.183270	−	0.105811i
$357$	15.0642	−	32.8310i	0.797281	−	1.73760i
$358$	5.25226	+	1.40734i	0.277591	+	0.0743802i
$359$		−	7.09032i		−	0.374213i	−0.982340	−	0.187106i	$-0.940089\pi$
$359$		−	7.09032i		−	0.374213i	0.982340	−	0.187106i	$-0.0599109\pi$
$360$	−1.49757	+	6.53890i	−0.0789291	+	0.344631i
$361$	32.1534			1.69228
$362$	17.8415	+	4.78062i	0.937729	+	0.251264i
$363$	−10.6788	−	14.3213i	−0.560493	−	0.751675i
$364$	5.59077	+	10.2363i	0.293036	+	0.536528i
$365$	3.47486	−	2.31566i	0.181883	−	0.121207i
$366$	8.83175	+	1.28678i	0.461643	+	0.0672613i
$367$	−1.91087	−	0.512015i	−0.0997465	−	0.0267270i	0.208601	−	0.978001i	$-0.433109\pi$
$367$	−1.91087	−	0.512015i	−0.0997465	−	0.0267270i	−0.308347	+	0.951274i	$0.599776\pi$
$368$	3.53087	−	3.53087i	0.184059	−	0.184059i
$369$	−0.666969	−	2.79517i	−0.0347210	−	0.145511i
$370$	3.21288	+	9.50319i	0.167030	+	0.494047i
$371$	−1.59399	−	0.0377852i	−0.0827559	−	0.00196171i
$372$	−2.61826	+	0.308054i	−0.135750	+	0.0159719i
$373$	−4.71418	−	17.5935i	−0.244091	−	0.910959i	−0.973838	−	0.227243i	$-0.927029\pi$
$373$	−4.71418	−	17.5935i	−0.244091	−	0.910959i	0.729747	−	0.683717i	$-0.239638\pi$
$374$	−18.1956	+	31.5156i	−0.940870	+	1.62963i
$375$	−10.4757	−	16.2868i	−0.540962	−	0.841047i
$376$	7.83654	−	4.52443i	0.404139	−	0.233330i
$377$	−7.73771	+	7.73771i	−0.398512	+	0.398512i
$378$	−9.06034	+	10.3397i	−0.466013	+	0.531819i
$379$		−	34.4387i		−	1.76900i	−0.466545	−	0.884498i	$-0.654501\pi$
$379$		−	34.4387i		−	1.76900i	0.466545	−	0.884498i	$-0.345499\pi$
$380$	10.5595	−	12.0110i	0.541691	−	0.616151i
$381$	−21.5852	+	8.59430i	−1.10584	+	0.440299i
$382$	−14.8091	+	3.96809i	−0.757700	+	0.203025i
$383$	−32.4365	+	8.69134i	−1.65743	+	0.444107i	−0.961679	−	0.274177i	$-0.911594\pi$
$383$	−32.4365	+	8.69134i	−1.65743	+	0.444107i	−0.695750	+	0.718284i	$0.744928\pi$
$384$	−1.07324	+	1.35947i	−0.0547687	+	0.0693750i
$385$	−24.1874	−	12.6870i	−1.23270	−	0.646590i
$386$	−13.9276			−0.708898
$387$	8.19228	+	15.1382i	0.416437	+	0.769520i
$388$	3.80099	+	3.80099i	0.192966	+	0.192966i
$389$	−11.1478	+	6.43616i	−0.565214	+	0.326326i	−0.755236	−	0.655453i	$-0.772478\pi$
$389$	−11.1478	+	6.43616i	−0.565214	+	0.326326i	0.190022	+	0.981780i	$0.439144\pi$
$390$	9.69766	−	14.0523i	0.491060	−	0.711565i
$391$	34.0871	+	19.6802i	1.72386	+	0.995269i
$392$	4.70965	+	5.17872i	0.237873	+	0.261565i
$393$	8.01740	−	5.97823i	0.404424	−	0.301562i
$394$	6.25242	−	3.60984i	0.314992	−	0.181861i
$395$	−10.1597	−	30.0507i	−0.511188	−	1.51201i
$396$	10.0597	−	9.51989i	0.505520	−	0.478393i
$397$	−7.41281	+	7.41281i	−0.372038	+	0.372038i	−0.868219	−	0.496181i	$-0.834735\pi$
$397$	−7.41281	+	7.41281i	−0.372038	+	0.372038i	0.496181	+	0.868219i	$0.334735\pi$
$398$	2.60596	−	9.72557i	0.130625	−	0.487499i
$399$	30.7292	−	11.3990i	1.53838	−	0.570666i
$400$	−0.640446	−	4.95881i	−0.0320223	−	0.247941i
$401$	−15.3968	+	26.6680i	−0.768879	+	1.33174i	0.169292	+	0.985566i	$0.445852\pi$
$401$	−15.3968	+	26.6680i	−0.768879	+	1.33174i	−0.938171	+	0.346172i	$0.887481\pi$
$402$	15.5960	+	6.71337i	0.777859	+	0.334833i
$403$	6.48132	+	1.73666i	0.322857	+	0.0865094i
$404$	14.0588			0.699453
$405$	19.4854	+	5.03166i	0.968239	+	0.250025i
$406$	−3.41757	+	5.60814i	−0.169611	+	0.278327i
$407$	5.36062	−	20.0061i	0.265716	−	0.991666i
$408$	−12.5404	−	5.39806i	−0.620842	−	0.267244i
$409$	14.0321	−	24.3044i	0.693845	−	1.20177i	−0.276724	−	0.960949i	$-0.589249\pi$
$409$	14.0321	−	24.3044i	0.693845	−	1.20177i	0.970569	−	0.240825i	$-0.0774179\pi$
$410$	1.18778	+	1.78237i	0.0586602	+	0.0880251i
$411$	−0.706215	−	0.557528i	−0.0348350	−	0.0275008i
$412$	−5.75993	−	1.54337i	−0.283772	−	0.0760364i
$413$	13.5083	−	3.27849i	0.664698	−	0.161324i
$414$	−10.2966	−	10.8805i	−0.506052	−	0.534748i
$415$	−15.2459	−	7.54173i	−0.748390	−	0.370209i
$416$	3.81779	−	2.20420i	0.187183	−	0.108070i
$417$	−16.6638	−	22.3478i	−0.816030	−	1.09438i
$418$	−31.8944	+	8.54607i	−1.56000	+	0.418002i
$419$	13.8784	−	24.0381i	0.678005	−	1.17434i	−0.297576	−	0.954698i	$-0.596178\pi$
$419$	13.8784	−	24.0381i	0.678005	−	1.17434i	0.975581	−	0.219641i	$-0.0704885\pi$
$420$	3.66683	−	9.56840i	0.178923	−	0.466890i
$421$	−6.47717	−	11.2188i	−0.315678	−	0.546770i	0.663903	−	0.747818i	$-0.268899\pi$
$421$	−6.47717	−	11.2188i	−0.315678	−	0.546770i	−0.979581	+	0.201048i	$0.935565\pi$
$422$	0.775252	+	0.775252i	0.0377387	+	0.0377387i
$423$	−12.9202	−	23.8748i	−0.628202	−	1.16083i
$424$			0.602641i			0.0292668i
$425$	36.4492	−	14.9929i	1.76805	−	0.727264i
$426$	3.95856	+	3.12512i	0.191793	+	0.151413i
$427$	−13.0813	−	3.83960i	−0.633049	−	0.185811i
$428$	3.30049	+	12.3176i	0.159535	+	0.595393i
$429$	−32.7508	+	13.0400i	−1.58122	+	0.629576i
$430$	−9.63544	−	8.47102i	−0.464662	−	0.408509i
$431$	−30.1744			−1.45345			−0.726724	−	0.686929i	$-0.758958\pi$
$431$	−30.1744			−1.45345			−0.726724	+	0.686929i	$0.758958\pi$
$432$	3.98811	+	3.33091i	0.191878	+	0.160258i
$433$	14.2795	+	14.2795i	0.686228	+	0.686228i	0.961396	−	0.275168i	$-0.0887335\pi$
$433$	14.2795	+	14.2795i	0.686228	+	0.686228i	−0.275168	+	0.961396i	$0.588734\pi$
$434$	4.02591	+	0.0954333i	0.193250	+	0.00458095i
$435$	9.58261	+	0.772692i	0.459451	+	0.0370477i
$436$	3.20973	−	5.55942i	0.153718	−	0.266248i
$437$	9.24336	+	34.4967i	0.442170	+	1.65020i
$438$	−0.377955	−	3.21237i	−0.0180594	−	0.153493i
$439$	−3.15034	−	5.45654i	−0.150357	−	0.260427i	0.781002	−	0.624529i	$-0.214709\pi$
$439$	−3.15034	−	5.45654i	−0.150357	−	0.260427i	−0.931359	+	0.364103i	$0.881376\pi$
$440$	−4.57725	+	9.25305i	−0.218212	+	0.441122i
$441$	15.9197	−	13.6954i	0.758079	−	0.652162i
$442$	24.5714	+	24.5714i	1.16874	+	1.16874i
$443$	−20.4634	−	5.48314i	−0.972243	−	0.260512i	−0.262468	−	0.964941i	$-0.584537\pi$
$443$	−20.4634	−	5.48314i	−0.972243	−	0.260512i	−0.709775	+	0.704429i	$0.751203\pi$
$444$	7.68927	+	1.12032i	0.364916	+	0.0531683i
$445$	1.75259	−	8.75463i	0.0830808	−	0.415009i
$446$	−4.12059	−	2.37902i	−0.195115	−	0.112650i
$447$	−18.2218	+	13.5873i	−0.861864	+	0.642656i
$448$	1.91464	−	1.82597i	0.0904582	−	0.0862689i
$449$		−	13.9136i		−	0.656625i	−0.944569	−	0.328313i	$-0.893520\pi$
$449$		−	13.9136i		−	0.656625i	0.944569	−	0.328313i	$-0.106480\pi$
$450$	−14.9237	+	1.51061i	−0.703512	+	0.0712106i
$451$		−	4.42225i		−	0.208236i
$452$	−3.17853	+	11.8625i	−0.149506	+	0.557963i
$453$	−5.64904	+	0.664644i	−0.265415	+	0.0312277i
$454$	6.19054	−	10.7223i	0.290536	−	0.503224i
$455$	−17.6795	+	19.1736i	−0.828827	+	0.898873i
$456$	−4.58247	−	11.5092i	−0.214594	−	0.538967i
$457$	−10.8787	+	40.6000i	−0.508886	+	1.89919i	−0.0775750	+	0.996987i	$0.524718\pi$
$457$	−10.8787	+	40.6000i	−0.508886	+	1.89919i	−0.431311	+	0.902203i	$0.641949\pi$
$458$	17.4030	+	17.4030i	0.813191	+	0.813191i
$459$	−17.2249	+	37.1605i	−0.803989	+	1.73451i
$460$	10.0080	+	4.95071i	0.466627	+	0.230828i
$461$	1.36961	−	0.790747i	0.0637893	−	0.0368288i	−0.467766	−	0.883852i	$-0.654941\pi$
$461$	1.36961	−	0.790747i	0.0637893	−	0.0368288i	0.531555	+	0.847024i	$0.321608\pi$
$462$	−17.2554	+	12.2412i	−0.802792	+	0.569512i
$463$	1.35165	+	5.04444i	0.0628167	+	0.234435i	0.990195	−	0.139689i	$-0.0446102\pi$
$463$	1.35165	+	5.04444i	0.0628167	+	0.234435i	−0.927379	+	0.374124i	$0.877944\pi$
$464$	2.14969	+	1.24113i	0.0997970	+	0.0576178i
$465$	−2.52763	−	5.32560i	−0.117216	−	0.246969i
$466$	−10.9787	−	19.0157i	−0.508579	−	0.880885i
$467$	0.0281666	−	0.0281666i	0.00130340	−	0.00130340i	−0.706455	−	0.707758i	$-0.749707\pi$
$467$	0.0281666	−	0.0281666i	0.00130340	−	0.00130340i	0.707758	+	0.706455i	$0.249707\pi$
$468$	−6.29444	−	11.6313i	−0.290961	−	0.537656i
$469$	−22.1482	−	13.4970i	−1.02271	−	0.623234i
$470$	15.1962	+	13.3598i	0.700950	+	0.616242i
$471$	−11.3271	−	1.65036i	−0.521927	−	0.0760447i
$472$	−1.35980	−	5.07484i	−0.0625899	−	0.233589i
$473$	6.85581	+	25.5862i	0.315231	+	1.17646i
$474$	−24.3147	−	3.54265i	−1.11681	−	0.162719i
$475$	33.0049	+	13.7662i	1.51437	+	0.631637i
$476$	17.8088	+	10.8526i	0.816267	+	0.497429i
$477$	1.80724	+	0.0498274i	0.0827477	+	0.00228144i
$478$	18.0270	−	18.0270i	0.824535	−	0.824535i
$479$	−2.03857	−	3.53091i	−0.0931448	−	0.161331i	0.815688	−	0.578492i	$-0.196359\pi$
$479$	−2.03857	−	3.53091i	−0.0931448	−	0.161331i	−0.908833	+	0.417161i	$0.863025\pi$
$480$	−3.64834	−	1.29984i	−0.166523	−	0.0593292i
$481$	−17.1277	−	9.88866i	−0.780954	−	0.450884i
$482$	−4.49848	−	16.7886i	−0.204900	−	0.764698i
$483$	13.2400	+	18.6633i	0.602440	+	0.849208i
$484$	8.93222	−	5.15702i	0.406010	−	0.234410i
$485$	−5.32946	+	10.7737i	−0.241999	+	0.489208i
$486$	10.3187	−	11.6844i	0.468065	−	0.530015i
$487$	9.53230	+	9.53230i	0.431950	+	0.431950i	0.889291	−	0.457342i	$-0.151198\pi$
$487$	9.53230	+	9.53230i	0.431950	+	0.431950i	−0.457342	+	0.889291i	$0.651198\pi$
$488$	−1.33366	+	4.97727i	−0.0603718	+	0.225311i
$489$	1.24077	+	3.11627i	0.0561094	+	0.140923i
$490$	−7.59713	+	13.6852i	−0.343204	+	0.618232i
$491$	9.83603	−	17.0365i	0.443894	−	0.768847i	−0.554080	−	0.832463i	$-0.686930\pi$
$491$	9.83603	−	17.0365i	0.443894	−	0.768847i	0.997974	+	0.0636162i	$0.0202634\pi$
$492$	1.64773	−	0.193866i	0.0742854	−	0.00874013i
$493$	−5.06413	+	18.8996i	−0.228077	+	0.851194i
$494$			31.5296i			1.41859i
$495$	27.3702	+	14.4916i	1.23020	+	0.651348i
$496$		−	1.52208i		−	0.0683434i
$497$	−5.31694	−	5.57513i	−0.238497	−	0.250079i
$498$	−10.5622	+	7.87580i	−0.473304	+	0.352923i
$499$	11.8005	+	6.81305i	0.528265	+	0.304994i	0.740310	−	0.672266i	$-0.234679\pi$
$499$	11.8005	+	6.81305i	0.528265	+	0.304994i	−0.212045	+	0.977260i	$0.568012\pi$
$500$	10.0455	−	4.90794i	0.449249	−	0.219490i
$501$	−7.39014	−	1.07674i	−0.330167	−	0.0481052i
$502$	10.3664	+	2.77766i	0.462674	+	0.123973i
$503$	−5.65314	−	5.65314i	−0.252061	−	0.252061i	0.569754	−	0.821815i	$-0.307038\pi$
$503$	−5.65314	−	5.65314i	−0.252061	−	0.252061i	−0.821815	+	0.569754i	$0.807038\pi$
$504$	−5.31752	−	5.89271i	−0.236861	−	0.262482i
$505$	10.0683	+	29.7806i	0.448035	+	1.32522i
$506$	−11.5265	−	19.9646i	−0.512417	−	0.887533i
$507$	1.30219	+	11.0678i	0.0578324	+	0.491537i
$508$	−3.47172	−	12.9566i	−0.154033	−	0.574857i
$509$	−11.9631	+	20.7207i	−0.530256	+	0.918429i	0.469121	+	0.883134i	$0.344571\pi$
$509$	−11.9631	+	20.7207i	−0.530256	+	0.918429i	−0.999377	+	0.0352958i	$0.988763\pi$
$510$	2.45371	−	30.4299i	0.108652	−	1.34746i
$511$	−0.117088	+	4.93943i	−0.00517967	+	0.218508i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−34.8933	+	12.7906i	−1.54058	+	0.564718i
$514$	7.53498			0.332354
$515$	−0.855732	−	13.3065i	−0.0377080	−	0.586353i
$516$	−9.23287	+	3.67614i	−0.406455	+	0.161833i
$517$	−10.8124	−	40.3525i	−0.475530	−	1.77470i
$518$	−11.3891	−	3.34291i	−0.500408	−	0.146879i
$519$	5.71577	+	4.51236i	0.250894	+	0.198071i
$520$	7.40327	+	6.50860i	0.324655	+	0.285421i
$521$			23.9113i			1.04757i	0.851849	+	0.523787i	$0.175481\pi$
$521$			23.9113i			1.04757i	−0.851849	+	0.523787i	$0.824519\pi$
$522$	3.89970	−	6.34401i	0.170685	−	0.277670i
$523$	22.7595	+	22.7595i	0.995204	+	0.995204i	0.999989	−	0.00478458i	$-0.00152299\pi$
$523$	22.7595	+	22.7595i	0.995204	+	0.995204i	−0.00478458	+	0.999989i	$0.501523\pi$
$524$	2.88701	+	5.00045i	0.126120	+	0.218446i
$525$	22.8946	+	0.914895i	0.999203	+	0.0399293i
$526$	−5.19855	+	9.00415i	−0.226667	+	0.392600i
$527$	11.5889	−	3.10525i	0.504822	−	0.135267i
$528$	4.78000	+	6.41044i	0.208023	+	0.278979i
$529$	−1.67493	+	0.967022i	−0.0728231	+	0.0420444i
$530$	−1.27656	+	0.431586i	−0.0554504	+	0.0187469i
$531$	−15.3312	+	3.65825i	−0.665316	+	0.158755i
$532$	4.46306	+	18.3890i	0.193498	+	0.797264i
$533$	−4.07884	−	1.09292i	−0.176674	−	0.0473397i
$534$	−5.42818	−	4.28532i	−0.234900	−	0.185444i
$535$	−23.7284	+	15.8127i	−1.02587	+	0.683643i
$536$	−4.90158	+	8.48978i	−0.211716	+	0.366703i
$537$	8.65069	+	3.72372i	0.373305	+	0.160691i
$538$	2.49418	−	9.30839i	0.107532	−	0.401313i
$539$	28.7215	−	14.8142i	1.23712	−	0.638094i
$540$	−4.19969	+	10.8334i	−0.180726	+	0.466195i
$541$	−5.77666			−0.248358			−0.124179	−	0.992260i	$-0.539630\pi$
$541$	−5.77666			−0.248358			−0.124179	+	0.992260i	$0.539630\pi$
$542$	17.2405	+	4.61958i	0.740544	+	0.198428i
$543$	29.3857	+	12.6492i	1.26106	+	0.542829i
$544$	3.94124	−	6.82642i	0.168979	−	0.292681i
$545$	14.0751	+	2.81770i	0.602911	+	0.120697i
$546$	7.02608	+	18.9407i	0.300688	+	0.810586i
$547$	6.28386	−	23.4517i	0.268678	−	1.00272i	−0.691282	−	0.722585i	$-0.742954\pi$
$547$	6.28386	−	23.4517i	0.268678	−	1.00272i	0.959960	−	0.280136i	$-0.0903796\pi$
$548$	0.367327	−	0.367327i	0.0156914	−	0.0156914i
$549$	14.8159	+	4.41098i	0.632326	+	0.188256i
$550$	−22.8786	−	3.06924i	−0.975547	−	0.130873i
$551$	−15.3749	+	8.87673i	−0.654995	+	0.378161i
$552$	6.93348	−	5.17001i	0.295109	−	0.220050i
$553$	36.0142	+	10.5708i	1.53148	+	0.449517i
$554$	−14.6051	−	8.43228i	−0.620512	−	0.358253i
$555$	3.13357	+	17.0904i	0.133013	+	0.725446i
$556$	13.9383	−	8.04729i	0.591116	−	0.341281i
$557$	−6.52661	−	6.52661i	−0.276541	−	0.276541i	0.555185	−	0.831727i	$-0.312647\pi$
$557$	−6.52661	−	6.52661i	−0.276541	−	0.276541i	−0.831727	+	0.555185i	$0.812647\pi$
$558$	−4.56451	−	0.125848i	−0.193231	−	0.00532758i
$559$	25.2937			1.06981
$560$	5.23910	+	2.74806i	0.221392	+	0.116127i
$561$	−39.0565	+	49.4725i	−1.64897	+	2.08873i
$562$	−11.8062	+	3.16346i	−0.498013	+	0.133442i
$563$	−16.1318	+	4.32250i	−0.679874	+	0.182172i	−0.582199	−	0.813047i	$-0.697807\pi$
$563$	−16.1318	+	4.32250i	−0.679874	+	0.182172i	−0.0976757	+	0.995218i	$0.531141\pi$
$564$	14.5613	−	5.79770i	0.613143	−	0.244127i
$565$	−27.4043	+	1.76236i	−1.15291	+	0.0741430i
$566$			3.66511i			0.154056i
$567$	−18.1111	+	15.4593i	−0.760593	+	0.649229i
$568$	−2.05899	+	2.05899i	−0.0863931	+	0.0863931i
$569$	−5.27814	+	3.04734i	−0.221271	+	0.127751i	−0.606539	−	0.795054i	$-0.707443\pi$
$569$	−5.27814	+	3.04734i	−0.221271	+	0.127751i	0.385267	+	0.922805i	$0.374109\pi$
$570$	21.0979	−	17.9493i	0.883694	−	0.751815i
$571$	10.1901	−	17.6498i	0.426444	−	0.738623i	−0.570110	−	0.821568i	$-0.693099\pi$
$571$	10.1901	−	17.6498i	0.426444	−	0.738623i	0.996554	+	0.0829455i	$0.0264328\pi$
$572$	−5.26758	−	19.6589i	−0.220248	−	0.821978i
$573$	−26.3730	+	3.10295i	−1.10175	+	0.129628i
$574$	−2.53360	−	0.0600584i	−0.105750	−	0.00250679i
$575$	−3.31967	+	24.7453i	−0.138440	+	1.03195i
$576$	−2.17898	+	2.06205i	−0.0907908	+	0.0859187i
$577$	−9.25925	+	9.25925i	−0.385468	+	0.385468i	−0.873067	−	0.487600i	$-0.837873\pi$
$577$	−9.25925	+	9.25925i	−0.385468	+	0.385468i	0.487600	+	0.873067i	$0.337873\pi$
$578$	43.5955	+	11.6814i	1.81334	+	0.485882i
$579$	−23.8713	−	3.47805i	−0.992059	−	0.144543i
$580$	−1.08953	+	5.44250i	−0.0452404	+	0.225987i
$581$	17.6629	−	9.64693i	0.732779	−	0.400222i
$582$	5.56554	+	7.46392i	0.230699	+	0.309390i
$583$	2.68742	+	0.720092i	0.111301	+	0.0298231i
$584$	1.86745			0.0772758
$585$	20.1305	−	21.6632i	0.832294	−	0.895664i
$586$			8.80130i			0.363578i
$587$	−2.21477	−	0.593445i	−0.0914133	−	0.0244941i	0.212822	−	0.977091i	$-0.431734\pi$
$587$	−2.21477	−	0.593445i	−0.0914133	−	0.0244941i	−0.304236	+	0.952597i	$0.598401\pi$
$588$	6.77889	+	10.0522i	0.279557	+	0.414546i
$589$	9.42769	+	5.44308i	0.388461	+	0.224278i
$590$	9.77612	−	6.51483i	0.402476	−	0.268211i
$591$	11.6178	−	4.62572i	0.477893	−	0.190277i
$592$	−1.16113	+	4.33341i	−0.0477223	+	0.178102i
$593$	−15.7590	−	15.7590i	−0.647146	−	0.647146i	0.305157	−	0.952302i	$-0.401291\pi$
$593$	−15.7590	−	15.7590i	−0.647146	−	0.647146i	−0.952302	+	0.305157i	$0.901291\pi$
$594$	19.6192	−	13.8045i	0.804987	−	0.566406i
$595$	−10.2350	+	45.4963i	−0.419593	+	1.86517i
$596$	−6.56156	−	11.3650i	−0.268772	−	0.465527i
$597$	6.89519	−	16.0184i	0.282201	−	0.655590i
$598$	−21.2629	+	5.69737i	−0.869504	+	0.232983i
$599$	−2.06758	−	1.19372i	−0.0844789	−	0.0487739i	0.457165	−	0.889382i	$-0.348865\pi$
$599$	−2.06758	−	1.19372i	−0.0844789	−	0.0487739i	−0.541644	+	0.840608i	$0.682198\pi$
$600$	0.140633	−	8.65911i	0.00574131	−	0.353507i
$601$	13.9564	−	8.05771i	0.569292	−	0.328681i	−0.187575	−	0.982250i	$-0.560063\pi$
$601$	13.9564	−	8.05771i	0.569292	−	0.328681i	0.756866	+	0.653570i	$0.226729\pi$
$602$	14.7520	−	3.58035i	0.601246	−	0.145924i
$603$	25.0544	+	15.4011i	1.02029	+	0.627181i
$604$		−	3.28397i		−	0.133623i
$605$	17.3209	+	15.2277i	0.704195	+	0.619095i
$606$	24.0962	+	3.51081i	0.978841	+	0.142617i
$607$	−3.02566	−	11.2919i	−0.122808	−	0.458325i	0.876944	−	0.480592i	$-0.159578\pi$
$607$	−3.02566	−	11.2919i	−0.122808	−	0.458325i	−0.999752	+	0.0222669i	$0.992912\pi$
$608$	6.90846	−	1.85112i	0.280175	−	0.0750726i
$609$	−7.25804	+	8.75864i	−0.294111	+	0.354918i
$610$	−11.4984	+	0.739455i	−0.465556	+	0.0299396i
$611$	−39.8911			−1.61382
$612$	−20.1456	−	12.3836i	−0.814339	−	0.500579i
$613$	11.0269	−	11.0269i	0.445374	−	0.445374i	−0.448440	−	0.893813i	$-0.648020\pi$
$613$	11.0269	−	11.0269i	0.445374	−	0.445374i	0.893813	+	0.448440i	$0.148020\pi$
$614$	−2.05050	−	3.55158i	−0.0827516	−	0.143330i
$615$	1.59070	+	3.35152i	0.0641431	+	0.135146i
$616$	−5.85494	−	10.7200i	−0.235902	−	0.431920i
$617$	32.4923	−	8.70627i	1.30809	−	0.350501i	0.463586	−	0.886052i	$-0.346563\pi$
$617$	32.4923	−	8.70627i	1.30809	−	0.350501i	0.844503	+	0.535551i	$0.179896\pi$
$618$	−9.48685	−	4.08365i	−0.381617	−	0.164269i
$619$	−20.9823	−	36.3425i	−0.843352	−	1.46073i	−0.887045	−	0.461683i	$-0.847246\pi$
$619$	−20.9823	−	36.3425i	−0.843352	−	1.46073i	0.0436934	−	0.999045i	$-0.486088\pi$
$620$	3.22419	−	1.09005i	0.129487	−	0.0437775i
$621$	−14.9309	−	21.2200i	−0.599155	−	0.851530i
$622$	17.0766	−	17.0766i	0.684708	−	0.684708i
$623$	7.29086	+	7.64491i	0.292102	+	0.306287i
$624$	7.09396	−	2.82451i	0.283986	−	0.113071i
$625$	17.5906	+	17.7643i	0.703623	+	0.710574i
$626$	−5.57451	−	3.21844i	−0.222802	−	0.128635i
$627$	−56.7996	+	6.68282i	−2.26836	+	0.266886i
$628$	1.71048	−	6.38359i	0.0682555	−	0.254733i
$629$	−35.3629			−1.41001
$630$	8.67423	−	15.4841i	0.345590	−	0.616902i
$631$	−30.7177			−1.22285			−0.611426	−	0.791302i	$-0.709404\pi$
$631$	−30.7177			−1.22285			−0.611426	+	0.791302i	$0.709404\pi$
$632$	3.67169	−	13.7029i	0.146052	−	0.545074i
$633$	1.13515	+	1.52234i	0.0451181	+	0.0605077i
$634$	5.61757	+	3.24331i	0.223102	+	0.128808i
$635$	24.9595	−	16.6331i	0.990487	−	0.660063i
$636$	−0.150493	+	1.03290i	−0.00596744	+	0.0409571i
$637$	−6.56553	−	30.1523i	−0.260136	−	1.19468i
$638$	8.10333	−	8.10333i	0.320814	−	0.320814i
$639$	6.00437	+	6.34485i	0.237529	+	0.250998i
$640$	0.991451	−	2.00425i	0.0391905	−	0.0792250i
$641$	0.486131	+	0.842004i	0.0192010	+	0.0332572i	0.875466	−	0.483279i	$-0.160554\pi$
$641$	0.486131	+	0.842004i	0.0192010	+	0.0332572i	−0.856265	+	0.516536i	$0.827221\pi$
$642$	2.58090	+	21.9360i	0.101860	+	0.865744i
$643$	8.23414	−	2.20633i	0.324723	−	0.0870093i	−0.0927750	−	0.995687i	$-0.529574\pi$
$643$	8.23414	−	2.20633i	0.324723	−	0.0870093i	0.417498	+	0.908678i	$0.362907\pi$
$644$	−11.5946	+	6.33265i	−0.456893	+	0.249542i
$645$	−14.3993	−	16.9251i	−0.566972	−	0.666426i
$646$	28.1884	+	48.8237i	1.10906	+	1.92094i
$647$	30.5787	−	30.5787i	1.20217	−	1.20217i	0.228671	−	0.973504i	$-0.426562\pi$
$647$	30.5787	−	30.5787i	1.20217	−	1.20217i	0.973504	−	0.228671i	$-0.0734379\pi$
$648$	6.00364	+	6.70495i	0.235845	+	0.263395i
$649$	−24.2556			−0.952115
$650$	−8.48515	+	20.3434i	−0.332815	+	0.797934i
$651$	6.87640	+	1.16893i	0.269507	+	0.0458140i
$652$	−1.87056	+	0.501215i	−0.0732568	+	0.0196291i
$653$	10.9782	+	40.9711i	0.429610	+	1.60332i	0.753646	+	0.657280i	$0.228293\pi$
$653$	10.9782	+	40.9711i	0.429610	+	1.60332i	−0.324037	+	0.946044i	$0.605040\pi$
$654$	6.88965	−	8.72705i	0.269407	−	0.341255i
$655$	−8.52480	+	9.69661i	−0.333092	+	0.378878i
$656$			0.957880i			0.0373989i
$657$	0.154404	−	5.60023i	0.00602389	−	0.218486i
$658$	−23.2656	+	5.64663i	−0.906988	+	0.220129i
$659$	−12.6865	+	7.32456i	−0.494196	+	0.285324i	−0.726314	−	0.687364i	$-0.758768\pi$
$659$	−12.6865	+	7.32456i	−0.494196	+	0.285324i	0.232117	+	0.972688i	$0.425435\pi$
$660$	−10.1559	+	14.7163i	−0.395317	+	0.572830i
$661$	22.7860	+	13.1555i	0.886273	+	0.511690i	0.872722	−	0.488218i	$-0.162353\pi$
$661$	22.7860	+	13.1555i	0.886273	+	0.511690i	0.0135513	+	0.999908i	$0.495686\pi$
$662$	−28.1202	+	7.53478i	−1.09292	+	0.292847i
$663$	35.9782	+	48.2502i	1.39728	+	1.87388i
$664$	−3.80338	−	6.58765i	−0.147600	−	0.255650i
$665$	−35.7568	+	22.6234i	−1.38659	+	0.877299i
$666$	12.8993	+	3.84037i	0.499837	+	0.148811i
$667$	−8.76450	−	8.76450i	−0.339363	−	0.339363i
$668$	1.11596	−	4.16483i	0.0431779	−	0.161142i
$669$	−6.46840	−	5.10654i	−0.250083	−	0.197430i
$670$	−21.4940	−	4.30290i	−0.830387	−	0.166235i
$671$	20.6021	+	11.8946i	0.795335	+	0.459187i
$672$	3.73759	−	2.65150i	0.144181	−	0.102284i
$673$	−1.70695	−	0.457376i	−0.0657981	−	0.0176306i	0.225770	−	0.974181i	$-0.427510\pi$
$673$	−1.70695	−	0.457376i	−0.0657981	−	0.0176306i	−0.291568	+	0.956550i	$0.594177\pi$
$674$		−	23.0889i		−	0.889352i
$675$	−25.9558	−	1.13769i	−0.999041	−	0.0437897i
$676$	−6.43406			−0.247464
$677$	−34.1728	−	9.15658i	−1.31337	−	0.351916i	−0.466879	−	0.884321i	$-0.654622\pi$
$677$	−34.1728	−	9.15658i	−1.31337	−	0.351916i	−0.846490	+	0.532405i	$0.821288\pi$
$678$	−8.41019	+	19.5379i	−0.322991	+	0.750350i
$679$	−6.81713	−	12.4817i	−0.261618	−	0.479003i
$680$	17.2828	+	3.45985i	0.662767	+	0.132679i
$681$	13.2879	−	16.8317i	0.509194	−	0.644990i
$682$	−6.78757	−	1.81872i	−0.259909	−	0.0696425i
$683$	−33.5428	+	33.5428i	−1.28348	+	1.28348i	−0.344802	+	0.938675i	$0.612054\pi$
$683$	−33.5428	+	33.5428i	−1.28348	+	1.28348i	−0.938675	+	0.344802i	$0.887946\pi$
$684$	−4.98003	−	20.8705i	−0.190416	−	0.798005i
$685$	1.04117	+	0.515038i	0.0397810	+	0.0196786i
$686$	−8.09730	−	16.6563i	−0.309157	−	0.635942i
$687$	25.4821	+	34.1740i	0.972202	+	1.30382i
$688$	−1.48500	−	5.54209i	−0.0566150	−	0.211290i
$689$	1.32834	−	2.30076i	0.0506059	−	0.0876519i
$690$	15.9170	+	10.9845i	0.605950	+	0.418174i
$691$	−8.66899	+	5.00504i	−0.329784	+	0.190401i	−0.655745	−	0.754982i	$-0.727645\pi$
$691$	−8.66899	+	5.00504i	−0.329784	+	0.190401i	0.325961	+	0.945383i	$0.394312\pi$
$692$	−2.97297	+	2.97297i	−0.113015	+	0.113015i
$693$	−32.6318	+	16.6718i	−1.23958	+	0.633309i
$694$			33.3305i			1.26521i
$695$	27.0285	+	23.7621i	1.02525	+	0.901350i
$696$	3.37454	+	2.66406i	0.127911	+	0.100981i
$697$	−7.29319	+	1.95420i	−0.276249	+	0.0740207i
$698$	9.90273	−	2.65343i	0.374824	−	0.100434i
$699$	−14.0684	−	35.3337i	−0.532114	−	1.33644i
$700$	−2.06915	+	13.0659i	−0.0782063	+	0.493846i
$701$	4.08393			0.154248			0.0771239	−	0.997022i	$-0.475426\pi$
$701$	4.08393			0.154248			0.0771239	+	0.997022i	$0.475426\pi$
$702$	−7.88378	−	21.5073i	−0.297554	−	0.811742i
$703$	−22.6886	−	22.6886i	−0.855717	−	0.855717i
$704$	−3.99819	+	2.30836i	−0.150687	+	0.0869995i
$705$	22.7094	+	26.6929i	0.855285	+	1.00531i
$706$	−3.98247	−	2.29928i	−0.149882	−	0.0865346i
$707$	−35.6905	−	10.4758i	−1.34228	−	0.393984i
$708$	−1.06333	−	9.03762i	−0.0399624	−	0.339655i
$709$	33.6638	−	19.4358i	1.26427	−	0.729926i	0.290372	−	0.956914i	$-0.406221\pi$
$709$	33.6638	−	19.4358i	1.26427	−	0.729926i	0.973898	+	0.226988i	$0.0728877\pi$
$710$	−5.83607	−	2.88695i	−0.219024	−	0.108345i
$711$	−40.7896	−	12.1439i	−1.52973	−	0.455431i
$712$	2.82339	−	2.82339i	0.105811	−	0.105811i
$713$	−1.96712	+	7.34138i	−0.0736691	+	0.274937i
$714$	27.8134	+	23.0482i	1.04089	+	0.862556i
$715$	37.8706	−	25.2371i	1.41628	−	0.943813i
$716$	−2.71877	+	4.70905i	−0.101605	+	0.175985i
$717$	35.3992	−	26.3957i	1.32201	−	0.985765i
$718$	6.84872	+	1.83511i	0.255592	+	0.0684857i
$719$	5.40655			0.201630			0.100815	−	0.994905i	$-0.467855\pi$
$719$	5.40655			0.201630			0.100815	+	0.994905i	$0.467855\pi$
$720$	−5.92850	−	3.13894i	−0.220942	−	0.116981i
$721$	13.4725	+	8.21005i	0.501740	+	0.305758i
$722$	−8.32191	+	31.0578i	−0.309709	+	1.15585i
$723$	−3.51771	−	29.8982i	−0.130825	−	1.11193i
$724$	−9.23544	+	15.9963i	−0.343232	+	0.594496i
$725$	−12.3090	+	1.58975i	−0.457145	+	0.0590418i
$726$	16.5972	−	6.60831i	0.615981	−	0.245258i
$727$	36.9817	+	9.90922i	1.37158	+	0.367513i	0.868054	−	0.496470i	$-0.165371\pi$
$727$	36.9817	+	9.90922i	1.37158	+	0.367513i	0.503522	+	0.863983i	$0.332037\pi$
$728$	−11.3345	+	2.75092i	−0.420085	+	0.101956i
$729$	20.6036	−	17.4497i	0.763096	−	0.646285i
$730$	1.33739	+	3.95579i	0.0494991	+	0.146410i
$731$	39.1672	−	22.6132i	1.44865	−	0.836380i
$732$	−3.52876	+	8.19777i	−0.130427	+	0.302998i
$733$	30.0145	−	8.04236i	1.10861	−	0.297051i	0.342344	−	0.939575i	$-0.388779\pi$
$733$	30.0145	−	8.04236i	1.10861	−	0.297051i	0.766266	+	0.642523i	$0.222112\pi$
$734$	0.989138	−	1.71324i	0.0365097	−	0.0632367i
$735$	−16.4386	+	21.5586i	−0.606348	+	0.795199i
$736$	2.49670	+	4.32441i	0.0920296	+	0.159400i
$737$	32.0025	+	32.0025i	1.17883	+	1.17883i
$738$	2.87255	+	0.0791991i	0.105740	+	0.00291536i
$739$		−	14.8835i		−	0.547499i	−0.961801	−	0.273750i	$-0.911736\pi$
$739$		−	14.8835i		−	0.547499i	0.961801	−	0.273750i	$-0.0882639\pi$
$740$	−10.0109	+	0.643798i	−0.368009	+	0.0236665i
$741$	−7.87367	+	54.0404i	−0.289246	+	1.98522i
$742$	0.449053	−	1.52990i	0.0164852	−	0.0561643i
$743$	−5.23665	−	19.5434i	−0.192114	−	0.716979i	−0.992995	−	0.118156i	$-0.962302\pi$
$743$	−5.23665	−	19.5434i	−0.192114	−	0.716979i	0.800881	−	0.598823i	$-0.204365\pi$
$744$	0.380098	−	2.60878i	0.0139351	−	0.0956424i
$745$	19.3751	−	22.0383i	0.709848	−	0.807423i
$746$	18.2142			0.666869
$747$	−20.0699	+	10.8611i	−0.734319	+	0.397388i
$748$	−25.7324	−	25.7324i	−0.940870	−	0.940870i
$749$	0.799548	−	33.7294i	0.0292148	−	1.23245i
$750$	18.4432	−	5.90339i	0.673449	−	0.215561i
$751$	18.2989	−	31.6946i	0.667735	−	1.15655i	−0.310801	−	0.950475i	$-0.600597\pi$
$751$	18.2989	−	31.6946i	0.667735	−	1.15655i	0.978536	−	0.206076i	$-0.0660695\pi$
$752$	2.34202	+	8.74053i	0.0854046	+	0.318734i
$753$	17.0738	+	7.34950i	0.622205	+	0.267831i
$754$	−5.47139	−	9.47672i	−0.199256	−	0.345122i
$755$	6.95637	−	2.35184i	0.253168	−	0.0855923i
$756$	−7.64244	−	11.4277i	−0.277953	−	0.415623i
$757$	−10.3158	−	10.3158i	−0.374935	−	0.374935i	0.494336	−	0.869271i	$-0.335411\pi$
$757$	−10.3158	−	10.3158i	−0.374935	−	0.374935i	−0.869271	+	0.494336i	$0.835411\pi$
$758$	33.2652	+	8.91338i	1.20825	+	0.323749i
$759$	−14.7704	−	37.0968i	−0.536130	−	1.34653i
$760$	8.86873	+	13.3084i	0.321703	+	0.482745i
$761$	34.1435	+	19.7128i	1.23770	+	0.714587i	0.968624	−	0.248532i	$-0.0799481\pi$
$761$	34.1435	+	19.7128i	1.23770	+	0.714587i	0.269077	+	0.963119i	$0.413281\pi$
$762$	−2.71480	−	23.0740i	−0.0983469	−	0.835884i
$763$	−12.2910	+	11.7217i	−0.444963	+	0.424356i
$764$		−	15.3315i		−	0.554675i
$765$	11.8046	−	51.5428i	0.426796	−	1.86353i
$766$		−	33.5808i		−	1.21332i
$767$	−5.99455	+	22.3720i	−0.216451	+	0.807805i
$768$	−1.03537	−	1.38853i	−0.0373606	−	0.0501042i
$769$	−20.0702	+	34.7625i	−0.723749	+	1.25357i	0.235738	+	0.971817i	$0.424249\pi$
$769$	−20.0702	+	34.7625i	−0.723749	+	1.25357i	−0.959487	+	0.281753i	$0.909084\pi$
$770$	18.5149	−	20.0796i	0.667230	−	0.723619i
$771$	12.9146	+	1.88166i	0.465108	+	0.0677662i
$772$	3.60474	−	13.4531i	0.129737	−	0.484187i
$773$	18.2480	+	18.2480i	0.656336	+	0.656336i	0.954511	−	0.298175i	$-0.0963779\pi$
$773$	18.2480	+	18.2480i	0.656336	+	0.656336i	−0.298175	+	0.954511i	$0.596378\pi$
$774$	−16.7427	+	3.99507i	−0.601805	+	0.143600i
$775$	4.61807	+	6.04910i	0.165886	+	0.217290i
$776$	−4.65525	+	2.68771i	−0.167114	+	0.0964831i
$777$	−18.6856	−	8.57371i	−0.670342	−	0.307580i
$778$	−3.33160	−	12.4337i	−0.119444	−	0.445770i
$779$	−5.93306	−	3.42545i	−0.212574	−	0.122730i
$780$	11.0635	+	13.0042i	0.396137	+	0.465625i
$781$	6.72158	+	11.6421i	0.240517	+	0.416588i
$782$	−27.8320	+	27.8320i	−0.995269	+	0.995269i
$783$	8.26815	−	9.89949i	0.295480	−	0.353779i
$784$	−6.22121	+	3.20883i	−0.222186	+	0.114601i
$785$	14.7472	−	0.948386i	0.526351	−	0.0338494i
$786$	3.69948	+	9.29149i	0.131956	+	0.331416i
$787$	2.11280	+	7.88509i	0.0753133	+	0.281073i	0.993304	−	0.115528i	$-0.0368561\pi$
$787$	2.11280	+	7.88509i	0.0753133	+	0.281073i	−0.917991	+	0.396602i	$0.870189\pi$
$788$	1.86859	+	6.97367i	0.0665657	+	0.248427i
$789$	−11.1586	+	14.1345i	−0.397257	+	0.503202i
$790$	31.6562	−	2.03580i	1.12628	−	0.0724303i
$791$	16.9084	−	27.7462i	0.601194	−	0.986541i
$792$	6.59186	+	12.1809i	0.234232	+	0.432829i
$793$	16.0625	−	16.0625i	0.570398	−	0.570398i
$794$	−5.24165	−	9.07880i	−0.186019	−	0.322194i
$795$	−2.29575	+	0.420932i	−0.0814218	+	0.0149289i
$796$	8.71971	+	5.03433i	0.309062	+	0.178437i
$797$	−8.58694	−	32.0469i	−0.304165	−	1.13516i	−0.933662	−	0.358156i	$-0.883405\pi$
$797$	−8.58694	−	32.0469i	−0.304165	−	1.13516i	0.629497	−	0.777003i	$-0.283261\pi$
$798$	3.05733	+	32.6324i	0.108228	+	1.15517i
$799$	−61.7714	+	35.6637i	−2.18531	+	1.26169i
$800$	4.95561	+	0.664812i	0.175207	+	0.0235046i
$801$	−8.23350	−	8.70039i	−0.290916	−	0.307413i
$802$	−21.7744	−	21.7744i	−0.768879	−	0.768879i
$803$	2.23141	−	8.32773i	0.0787447	−	0.293879i
$804$	−10.5212	+	13.3271i	−0.371053	+	0.470009i
$805$	−21.7179	−	20.0255i	−0.765457	−	0.705808i
$806$	−3.35498	+	5.81099i	−0.118174	+	0.204683i
$807$	6.59942	−	15.3313i	0.232311	−	0.539687i
$808$	−3.63869	+	13.5798i	−0.128009	+	0.477735i
$809$			30.3069i			1.06553i	0.846262	+	0.532767i	$0.178848\pi$
$809$			30.3069i			1.06553i	−0.846262	+	0.532767i	$0.821152\pi$
$810$	−9.90342	+	17.5192i	−0.347971	+	0.615562i
$811$			14.1785i			0.497876i	0.968519	+	0.248938i	$0.0800815\pi$
$811$			14.1785i			0.497876i	−0.968519	+	0.248938i	$0.919918\pi$
$812$	−4.53251	−	4.75261i	−0.159060	−	0.166784i
$813$	28.3958	+	12.2231i	0.995886	+	0.428683i
$814$	17.9370	+	10.3559i	0.628691	+	0.362975i
$815$	−2.40133	−	3.60343i	−0.0841150	−	0.126222i
$816$	8.45981	−	10.7160i	0.296153	−	0.375134i
$817$	39.6379	+	10.6209i	1.38675	+	0.371580i
$818$	19.8444	+	19.8444i	0.693845	+	0.693845i
$819$	7.31246	+	34.2180i	0.255518	+	1.19567i
$820$	−2.02906	+	0.685993i	−0.0708578	+	0.0239559i
$821$	−15.0411	−	26.0520i	−0.524940	−	0.909222i	−0.999578	−	0.0290414i	$-0.990755\pi$
$821$	−15.0411	−	26.0520i	−0.524940	−	0.909222i	0.474639	−	0.880181i	$-0.342579\pi$
$822$	0.721312	−	0.537852i	0.0251587	−	0.0187597i
$823$	10.4200	+	38.8881i	0.363219	+	1.35555i	0.869819	+	0.493371i	$0.164236\pi$
$823$	10.4200	+	38.8881i	0.363219	+	1.35555i	−0.506600	+	0.862181i	$0.669098\pi$
$824$	2.98156	−	5.16422i	0.103868	−	0.179904i
$825$	−38.4464	−	10.9739i	−1.33853	−	0.382061i
$826$	−0.329414	+	13.8965i	−0.0114618	+	0.483522i
$827$	14.4960	+	14.4960i	0.504076	+	0.504076i	0.912702	−	0.408626i	$-0.133992\pi$
$827$	14.4960	+	14.4960i	0.504076	+	0.504076i	−0.408626	+	0.912702i	$0.633992\pi$
$828$	13.1747	−	7.12971i	0.457854	−	0.247774i
$829$	19.0841			0.662818			0.331409	−	0.943487i	$-0.392476\pi$
$829$	19.0841			0.662818			0.331409	+	0.943487i	$0.392476\pi$
$830$	11.2307	−	12.7744i	0.389822	−	0.443407i
$831$	−22.9268	−	18.0998i	−0.795322	−	0.627874i
$832$	1.14098	+	4.25820i	0.0395564	+	0.147626i
$833$	−37.1237	−	40.8211i	−1.28626	−	1.41437i
$834$	25.8992	−	10.3120i	0.896817	−	0.357074i
$835$	9.62148	−	0.618753i	0.332965	−	0.0214128i
$836$		−	33.0195i		−	1.14200i
$837$	−7.79193	−	1.35556i	−0.269328	−	0.0468550i
$838$	19.6270	+	19.6270i	0.678005	+	0.678005i
$839$	−20.3543	−	35.2547i	−0.702708	−	1.21713i	−0.967512	−	0.252824i	$-0.918641\pi$
$839$	−20.3543	−	35.2547i	−0.702708	−	1.21713i	0.264804	−	0.964302i	$-0.414693\pi$
$840$	8.29332	+	6.01837i	0.286147	+	0.207654i
$841$	−11.4192	+	19.7787i	−0.393766	+	0.682023i
$842$	12.5129	−	3.35283i	0.431224	−	0.115546i
$843$	−21.0252	+	2.47375i	−0.724147	+	0.0852004i
$844$	−0.949486	+	0.548186i	−0.0326826	+	0.0188693i
$845$	−4.60781	−	13.6292i	−0.158513	−	0.468857i
$846$	26.4053	−	6.30070i	0.907832	−	0.216623i
$847$	−26.5185	+	6.43612i	−0.911187	+	0.221148i
$848$	−0.582106	−	0.155975i	−0.0199896	−	0.00535620i
$849$	−0.915260	+	6.28182i	−0.0314117	+	0.215592i
$850$	5.04830	+	39.0877i	0.173155	+	1.34070i
$851$	11.2009	−	19.4005i	0.383961	−	0.665040i
$852$	−4.04318	+	3.01483i	−0.138517	+	0.103286i
$853$	−12.3681	+	46.1583i	−0.423475	+	1.58043i	0.343755	+	0.939059i	$0.388301\pi$
$853$	−12.3681	+	46.1583i	−0.423475	+	1.58043i	−0.767230	+	0.641372i	$0.778366\pi$
$854$	7.09446	−	11.6418i	0.242768	−	0.398375i
$855$	40.6432	−	25.4957i	1.38997	−	0.871935i
$856$	−12.7521			−0.435858
$857$	−48.1665	−	12.9062i	−1.64534	−	0.440866i	−0.687034	−	0.726625i	$-0.741088\pi$
$857$	−48.1665	−	12.9062i	−1.64534	−	0.440866i	−0.958302	+	0.285759i	$0.907754\pi$
$858$	−4.11912	−	35.0098i	−0.140624	−	1.19522i
$859$	−15.7580	+	27.2936i	−0.537656	+	0.931247i	0.461374	+	0.887206i	$0.347357\pi$
$859$	−15.7580	+	27.2936i	−0.537656	+	0.931247i	−0.999030	+	0.0440413i	$0.985977\pi$
$860$	10.6762	−	7.11466i	0.364056	−	0.242608i
$861$	−4.32747	−	0.735635i	−0.147480	−	0.0250704i
$862$	7.80970	−	29.1462i	0.266000	−	0.992724i
$863$	−17.6202	+	17.6202i	−0.599800	+	0.599800i	−0.940259	−	0.340459i	$-0.889417\pi$
$863$	−17.6202	+	17.6202i	−0.599800	+	0.599800i	0.340459	+	0.940259i	$0.389417\pi$
$864$	−4.24961	+	2.99012i	−0.144575	+	0.101726i
$865$	−8.42671	−	4.16848i	−0.286517	−	0.141732i
$866$	−17.4887	+	10.0971i	−0.594291	+	0.343114i
$867$	71.8036	+	30.9082i	2.43858	+	1.04970i
$868$	−1.13416	+	3.86404i	−0.0384961	+	0.131154i
$869$	−56.7197	−	32.7471i	−1.92408	−	1.11087i
$870$	−3.22653	+	9.05611i	−0.109389	+	0.307031i
$871$	37.4264	−	21.6081i	1.26815	−	0.732164i
$872$	4.53925	+	4.53925i	0.153718	+	0.153718i
$873$	7.67516	+	14.1827i	0.259765	+	0.480010i
$874$	−35.7136			−1.20803
$875$	−29.1592	+	4.97424i	−0.985760	+	0.168160i
$876$	3.20073	+	0.466346i	0.108143	+	0.0157564i
$877$	−47.9110	+	12.8377i	−1.61784	+	0.433499i	−0.950366	−	0.311135i	$-0.899291\pi$
$877$	−47.9110	+	12.8377i	−1.61784	+	0.433499i	−0.667474	+	0.744633i	$0.732624\pi$
$878$	6.08598	−	1.63073i	0.205392	−	0.0550346i
$879$	−2.19789	+	15.0850i	−0.0741328	+	0.508805i
$880$	−7.75309	−	6.81615i	−0.261356	−	0.229772i
$881$		−	56.9318i		−	1.91808i	−0.283268	−	0.959041i	$-0.591418\pi$
$881$		−	56.9318i		−	1.91808i	0.283268	−	0.959041i	$-0.408582\pi$
$882$	9.10844	+	18.9218i	0.306697	+	0.637132i
$883$	14.9738	−	14.9738i	0.503909	−	0.503909i	−0.408741	−	0.912650i	$-0.634032\pi$
$883$	14.9738	−	14.9738i	0.503909	−	0.503909i	0.912650	+	0.408741i	$0.134032\pi$
$884$	−30.0937	+	17.3746i	−1.01216	+	0.584371i
$885$	18.3827	−	8.72480i	0.617928	−	0.293281i
$886$	10.5926	−	18.3469i	0.355866	−	0.616377i
$887$	−13.3647	−	49.8777i	−0.448743	−	1.67473i	−0.705861	−	0.708350i	$-0.749440\pi$
$887$	−13.3647	−	49.8777i	−0.448743	−	1.67473i	0.257119	−	0.966380i	$-0.417227\pi$
$888$	−3.07228	+	7.13730i	−0.103099	+	0.239512i
$889$	−0.841029	+	35.4793i	−0.0282072	+	1.18994i
$890$	8.00272	+	3.95874i	0.268252	+	0.132697i
$891$	37.0738	−	18.7609i	1.24202	−	0.628515i
$892$	3.36444	−	3.36444i	0.112650	−	0.112650i
$893$	−62.5137	−	16.7505i	−2.09194	−	0.560534i
$894$	−8.40813	−	21.1176i	−0.281210	−	0.706278i
$895$	−11.9222	−	2.38670i	−0.398514	−	0.0797786i
$896$	1.26820	+	2.32199i	0.0423678	+	0.0775724i
$897$	−37.8664	+	4.45521i	−1.26432	+	0.148755i
$898$	13.4395	+	3.60112i	0.448483	+	0.120171i
$899$	−3.77818			−0.126010
$900$	2.40342	−	14.8062i	0.0801139	−	0.493540i
$901$		−	4.75030i		−	0.158256i
$902$	4.27157	+	1.14456i	0.142228	+	0.0381098i
$903$	26.1783	−	2.45265i	0.871160	−	0.0816190i
$904$	−10.6356	−	6.14046i	−0.353734	−	0.204229i
$905$	−40.4986	−	8.10742i	−1.34622	−	0.269500i
$906$	0.820082	−	5.62857i	0.0272454	−	0.186997i
$907$	2.22831	−	8.31615i	0.0739897	−	0.276133i	−0.919013	−	0.394228i	$-0.871012\pi$
$907$	2.22831	−	8.31615i	0.0739897	−	0.276133i	0.993002	+	0.118095i	$0.0376787\pi$
$908$	8.75474	+	8.75474i	0.290536	+	0.290536i
$909$	40.4230	+	12.0347i	1.34075	+	0.399167i
$910$	−13.9445	−	22.0396i	−0.462256	−	0.730605i
$911$	−12.9764	−	22.4757i	−0.429926	−	0.744653i	0.566941	−	0.823759i	$-0.308127\pi$
$911$	−12.9764	−	22.4757i	−0.429926	−	0.744653i	−0.996866	+	0.0791055i	$0.974794\pi$
$912$	12.3030	−	1.44753i	0.407394	−	0.0479324i
$913$	−33.9216	+	9.08927i	−1.12264	+	0.300811i
$914$	−36.4010	−	21.0161i	−1.20404	−	0.695152i
$915$	−19.8923	−	1.60401i	−0.657621	−	0.0530271i
$916$	−21.3143	+	12.3058i	−0.704244	+	0.406595i
$917$	−3.60308	−	14.8456i	−0.118984	−	0.490246i
$918$	−31.4362	−	26.2558i	−1.03755	−	0.866571i
$919$			31.3823i			1.03521i	0.855620	+	0.517604i	$0.173176\pi$
$919$			31.3823i			1.03521i	−0.855620	+	0.517604i	$0.826824\pi$
$920$	−7.37229	+	8.38568i	−0.243057	+	0.276468i
$921$	−2.62756	−	6.59930i	−0.0865811	−	0.217454i
$922$	0.409321	+	1.52761i	0.0134803	+	0.0503090i
$923$	12.3992	−	3.32236i	0.408125	−	0.109357i
$924$	−7.35807	−	19.8357i	−0.242063	−	0.652545i
$925$	−8.53316	−	20.7449i	−0.280568	−	0.682089i
$926$	−5.22239			−0.171618
$927$	−15.2402	−	9.36827i	−0.500555	−	0.307694i
$928$	−1.75522	+	1.75522i	−0.0576178	+	0.0576178i
$929$	−4.49717	−	7.78933i	−0.147547	−	0.255560i	0.782773	−	0.622307i	$-0.213805\pi$
$929$	−4.49717	−	7.78933i	−0.147547	−	0.255560i	−0.930320	+	0.366748i	$0.880471\pi$
$930$	5.79833	−	1.06314i	0.190135	−	0.0348618i
$931$	2.37223	−	50.0089i	0.0777467	−	1.63898i
$932$	21.2092	−	5.68300i	0.694732	−	0.186153i
$933$	33.5329	−	25.0040i	1.09782	−	0.818596i
$934$	0.0199168	+	0.0344969i	0.000651698	+	0.00112877i
$935$	36.0800	−	72.9370i	1.17994	−	2.38529i
$936$	12.8641	−	3.06956i	0.420475	−	0.100332i
$937$	−11.7084	+	11.7084i	−0.382497	+	0.382497i	−0.872001	−	0.489504i	$-0.837178\pi$
$937$	−11.7084	+	11.7084i	−0.382497	+	0.382497i	0.489504	+	0.872001i	$0.337178\pi$
$938$	18.7695	−	17.9002i	0.612846	−	0.584464i
$939$	−8.75074	−	6.90835i	−0.285569	−	0.225445i
$940$	−16.8376	+	11.2207i	−0.549184	+	0.365977i
$941$	−11.9133	−	6.87815i	−0.388363	−	0.224221i	0.293088	−	0.956086i	$-0.405317\pi$
$941$	−11.9133	−	6.87815i	−0.388363	−	0.224221i	−0.681451	+	0.731864i	$0.738651\pi$
$942$	4.52581	−	10.5140i	0.147459	−	0.342566i
$943$	1.23795	−	4.62010i	0.0403132	−	0.150451i
$944$	5.25386			0.170999
$945$	18.7340	−	24.3729i	0.609416	−	0.792851i
$946$	−26.4888			−0.861226
$947$	1.75490	−	6.54936i	0.0570265	−	0.212826i	−0.931533	−	0.363656i	$-0.881528\pi$
$947$	1.75490	−	6.54936i	0.0570265	−	0.212826i	0.988560	+	0.150831i	$0.0481949\pi$
$948$	9.71505	−	22.5693i	0.315530	−	0.733017i
$949$	−7.12955	−	4.11625i	−0.231435	−	0.133619i
$950$	−21.8395	+	28.3174i	−0.708565	+	0.918737i
$951$	8.81833	+	6.96171i	0.285954	+	0.225749i
$952$	−15.0921	+	14.3931i	−0.489137	+	0.466485i
$953$	15.6428	−	15.6428i	0.506720	−	0.506720i	−0.406798	−	0.913518i	$-0.633355\pi$
$953$	15.6428	−	15.6428i	0.506720	−	0.506720i	0.913518	+	0.406798i	$0.133355\pi$
$954$	−0.515877	+	1.73276i	−0.0167021	+	0.0561002i
$955$	32.4765	−	10.9798i	1.05091	−	0.355298i
$956$	12.7470	+	22.0785i	0.412268	+	0.714068i
$957$	15.9123	−	11.8651i	0.514372	−	0.383546i
$958$	3.93822	−	1.05524i	0.127238	−	0.0340934i
$959$	−1.20623	+	0.658806i	−0.0389511	+	0.0212740i
$960$	2.19981	−	3.18761i	0.0709985	−	0.102880i
$961$	−14.3416	−	24.8404i	−0.462633	−	0.801305i
$962$	13.9847	−	13.9847i	0.450884	−	0.450884i
$963$	−1.05437	+	38.2418i	−0.0339765	+	1.23232i
$964$	17.3808			0.559798
$965$	31.0790	−	1.99867i	1.00047	−	0.0643395i
$966$	−21.4541	+	7.95843i	−0.690274	+	0.256058i
$967$	36.3949	−	9.75197i	1.17038	−	0.313602i	0.379276	−	0.925284i	$-0.376173\pi$
$967$	36.3949	−	9.75197i	1.17038	−	0.313602i	0.791104	+	0.611681i	$0.209507\pi$
$968$	2.66947	+	9.96259i	0.0858000	+	0.320210i
$969$	36.1212	+	90.7208i	1.16038	+	2.91437i
$970$	−9.02722	−	7.93630i	−0.289847	−	0.254819i
$971$			35.1514i			1.12806i	0.825754	+	0.564031i	$0.190750\pi$
$971$			35.1514i			1.12806i	−0.825754	+	0.564031i	$0.809250\pi$
$972$	8.61558	+	12.9912i	0.276345	+	0.416694i
$973$	−41.3809	+	10.0433i	−1.32661	+	0.321972i
$974$	−11.6746	+	6.74035i	−0.374079	+	0.215975i
$975$	−19.6234	+	32.7487i	−0.628450	+	1.04880i
$976$	−4.46250	−	2.57643i	−0.142841	−	0.0824694i
$977$	−14.0879	+	3.77485i	−0.450713	+	0.120768i	−0.477033	−	0.878885i	$-0.658288\pi$
$977$	−14.0879	+	3.77485i	−0.450713	+	0.120768i	0.0263200	+	0.999654i	$0.491621\pi$
$978$	−3.33122	+	0.391938i	−0.106521	+	0.0125328i
$979$	−9.21697	−	15.9643i	−0.294576	−	0.510220i
$980$	−11.2526	−	10.8802i	−0.359450	−	0.347557i
$981$	13.9879	−	13.2373i	0.446599	−	0.422633i
$982$	13.9103	+	13.9103i	0.443894	+	0.443894i
$983$	14.7589	−	55.0809i	0.470735	−	1.75681i	−0.166403	−	0.986058i	$-0.553215\pi$
$983$	14.7589	−	55.0809i	0.470735	−	1.75681i	0.637138	−	0.770750i	$-0.280118\pi$
$984$	−0.239204	+	1.64176i	−0.00762555	+	0.0523374i
$985$	−13.4340	+	8.95244i	−0.428042	+	0.285249i
$986$	−16.9449	−	9.78314i	−0.539635	−	0.311559i
$987$	−41.2863	+	3.86811i	−1.31416	+	0.123123i
$988$	−30.4553	−	8.16047i	−0.968912	−	0.259619i
$989$			28.6501i			0.911020i
$990$	−21.0817	+	22.6869i	−0.670021	+	0.721035i
$991$	35.8029			1.13732			0.568658	−	0.822574i	$-0.307463\pi$
$991$	35.8029			1.13732			0.568658	+	0.822574i	$0.307463\pi$
$992$	1.47022	+	0.393943i	0.0466794	+	0.0125077i
$993$	−50.0783	+	5.89202i	−1.58919	+	0.186978i
$994$	6.76129	−	3.69282i	0.214455	−	0.117129i
$995$	−4.41943	+	22.0762i	−0.140105	+	0.699862i
$996$	−4.87373	−	12.2407i	−0.154430	−	0.387862i
$997$	−24.6417	−	6.60273i	−0.780411	−	0.209111i	−0.153445	−	0.988157i	$-0.549037\pi$
$997$	−24.6417	−	6.60273i	−0.780411	−	0.209111i	−0.626966	+	0.779047i	$0.715704\pi$
$998$	−9.63511	+	9.63511i	−0.304994	+	0.304994i
$999$	21.1497	+	9.80346i	0.669148	+	0.310168i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bz.a.517.10	yes	192
5.3	odd	4	inner	630.2.bz.a.13.27	✓	192
7.6	odd	2	inner	630.2.bz.a.517.15	yes	192
9.7	even	3	inner	630.2.bz.a.97.46	yes	192
35.13	even	4	inner	630.2.bz.a.13.46	yes	192
45.43	odd	12	inner	630.2.bz.a.223.15	yes	192
63.34	odd	6	inner	630.2.bz.a.97.27	yes	192
315.223	even	12	inner	630.2.bz.a.223.10	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bz.a.13.27	✓	192	5.3	odd	4	inner
630.2.bz.a.13.46	yes	192	35.13	even	4	inner
630.2.bz.a.97.27	yes	192	63.34	odd	6	inner
630.2.bz.a.97.46	yes	192	9.7	even	3	inner
630.2.bz.a.223.10	yes	192	315.223	even	12	inner
630.2.bz.a.223.15	yes	192	45.43	odd	12	inner
630.2.bz.a.517.10	yes	192	1.1	even	1	trivial
630.2.bz.a.517.15	yes	192	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.684818 + 1.59092i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.438930 - 2.19256i) q^{5} +(-1.35947 - 1.07324i) q^{6} +(1.82597 + 1.91464i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.06205 - 2.17898i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.684818 + 1.59092i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.438930 - 2.19256i) q^{5} +(-1.35947 - 1.07324i) q^{6} +(1.82597 + 1.91464i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.06205 - 2.17898i) q^{9} +(2.00425 + 0.991451i) q^{10} +(-2.30836 - 3.99819i) q^{11} +(1.38853 - 1.03537i) q^{12} +(-4.25820 + 1.14098i) q^{13} +(-2.32199 + 1.26820i) q^{14} +(3.18761 + 2.19981i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-5.57375 + 5.57375i) q^{17} +(2.63843 - 1.42783i) q^{18} -7.15216 q^{19} +(-1.47641 + 1.67935i) q^{20} +(-4.29649 + 1.59379i) q^{21} +(4.45940 - 1.19489i) q^{22} +(-1.29239 - 4.82325i) q^{23} +(0.640711 + 1.60919i) q^{24} +(-4.61468 - 1.92476i) q^{25} -4.40841i q^{26} +(4.87871 - 1.78835i) q^{27} +(-0.624016 - 2.57111i) q^{28} +(2.14969 - 1.24113i) q^{29} +(-2.94987 + 2.50964i) q^{30} +(-1.31816 - 0.761040i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(7.94160 - 0.934378i) q^{33} +(-3.94124 - 6.82642i) q^{34} +(4.99944 - 3.16316i) q^{35} +(0.696298 + 2.91808i) q^{36} +(3.17227 + 3.17227i) q^{37} +(1.85112 - 6.90846i) q^{38} +(1.10088 - 7.55581i) q^{39} +(-1.24001 - 1.86075i) q^{40} +(0.829548 + 0.478940i) q^{41} +(-0.427470 - 4.56259i) q^{42} +(-5.54209 - 1.48500i) q^{43} +4.61671i q^{44} +(-5.68265 + 3.56476i) q^{45} +4.99340 q^{46} +(8.74053 + 2.34202i) q^{47} +(-1.72019 + 0.202390i) q^{48} +(-0.331680 + 6.99214i) q^{49} +(3.05355 - 3.95927i) q^{50} +(-5.05039 - 12.6844i) q^{51} +(4.25820 + 1.14098i) q^{52} +(-0.426131 + 0.426131i) q^{53} +(0.464712 + 5.17533i) q^{54} +(-9.77950 + 3.30630i) q^{55} +(2.64501 + 0.0626993i) q^{56} +(4.89792 - 11.3785i) q^{57} +(0.642454 + 2.39767i) q^{58} +(2.62693 - 4.54998i) q^{59} +(-1.66064 - 3.49889i) q^{60} +(-4.46250 + 2.57643i) q^{61} +(1.07627 - 1.07627i) q^{62} +(0.406720 - 7.92683i) q^{63} -1.00000i q^{64} +(0.632624 + 9.83718i) q^{65} +(-1.15290 + 7.91283i) q^{66} +(-9.46912 + 2.53724i) q^{67} +(7.61389 - 2.04013i) q^{68} +(8.55846 + 1.24697i) q^{69} +(1.76143 + 5.64778i) q^{70} -2.91185 q^{71} +(-2.99886 - 0.0826817i) q^{72} +(1.32049 + 1.32049i) q^{73} +(-3.88523 + 2.24314i) q^{74} +(6.22236 - 6.02347i) q^{75} +(6.19395 + 3.57608i) q^{76} +(3.44010 - 11.7202i) q^{77} +(7.01342 + 3.01896i) q^{78} +(12.2857 - 7.09317i) q^{79} +(2.11828 - 0.716158i) q^{80} +(-0.495902 + 8.98633i) q^{81} +(-0.677323 + 0.677323i) q^{82} +(1.96877 - 7.34757i) q^{83} +(4.51777 + 0.767982i) q^{84} +(9.77433 + 14.6673i) q^{85} +(2.86880 - 4.96890i) q^{86} +(0.502384 + 4.26993i) q^{87} +(-4.45940 - 1.19489i) q^{88} +3.99287 q^{89} +(-1.97252 - 6.41164i) q^{90} +(-9.95989 - 6.06951i) q^{91} +(-1.29239 + 4.82325i) q^{92} +(2.11345 - 1.57591i) q^{93} +(-4.52443 + 7.83654i) q^{94} +(-3.13930 + 15.6816i) q^{95} +(0.249723 - 1.71395i) q^{96} +(-5.19226 - 1.39126i) q^{97} +(-6.66804 - 2.13008i) q^{98} +(-3.95203 + 13.2743i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 8 q^{11} + 24 q^{15} + 96 q^{16} - 8 q^{18} + 8 q^{23} + 48 q^{30} - 24 q^{35} + 8 q^{36} - 44 q^{42} + 48 q^{46} + 32 q^{50} - 160 q^{53} - 4 q^{56} + 88 q^{57} + 24 q^{58} + 8 q^{60} - 48 q^{63} - 8 q^{65} + 16 q^{71} + 16 q^{72} - 16 q^{77} - 16 q^{78} - 8 q^{81} - 16 q^{86} + 8 q^{92} - 120 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) \) 192 * q + 8 * q^11 + 24 * q^15 + 96 * q^16 - 8 * q^18 + 8 * q^23 + 48 * q^30 - 24 * q^35 + 8 * q^36 - 44 * q^42 + 48 * q^46 + 32 * q^50 - 160 * q^53 - 4 * q^56 + 88 * q^57 + 24 * q^58 + 8 * q^60 - 48 * q^63 - 8 * q^65 + 16 * q^71 + 16 * q^72 - 16 * q^77 - 16 * q^78 - 8 * q^81 - 16 * q^86 + 8 * q^92 - 120 * q^93 - 128 * q^95 - 48 * q^98

Introduction

L-functions

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