LMFDB - Embedded newform 429.2.j.a.122.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(122,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("429.122");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			122.17
Character	$\chi$	$=$	429.122
Dual form			429.2.j.a.320.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.727121 - 0.727121i) q^{2} +(1.73181 + 0.0289503i) q^{3} -0.942589i q^{4} +(-1.91531 - 1.91531i) q^{5} +(-1.23818 - 1.28029i) q^{6} +(-1.22176 - 1.22176i) q^{7} +(-2.13962 + 2.13962i) q^{8} +(2.99832 + 0.100273i) q^{9} +O(q^{10})$	\(q+(-0.727121 - 0.727121i) q^{2} +(1.73181 + 0.0289503i) q^{3} -0.942589i q^{4} +(-1.91531 - 1.91531i) q^{5} +(-1.23818 - 1.28029i) q^{6} +(-1.22176 - 1.22176i) q^{7} +(-2.13962 + 2.13962i) q^{8} +(2.99832 + 0.100273i) q^{9} +2.78533i q^{10} +(0.707107 - 0.707107i) q^{11} +(0.0272883 - 1.63238i) q^{12} +(-2.66027 - 2.43371i) q^{13} +1.77674i q^{14} +(-3.26150 - 3.37240i) q^{15} +1.22635 q^{16} +0.685652 q^{17} +(-2.10723 - 2.25306i) q^{18} +(-4.75837 + 4.75837i) q^{19} +(-1.80535 + 1.80535i) q^{20} +(-2.08049 - 2.15123i) q^{21} -1.02830 q^{22} +0.584276 q^{23} +(-3.76735 + 3.64347i) q^{24} +2.33683i q^{25} +(0.164739 + 3.70394i) q^{26} +(5.18962 + 0.260456i) q^{27} +(-1.15162 + 1.15162i) q^{28} -9.07437i q^{29} +(-0.0806360 + 4.82365i) q^{30} +(0.834032 - 0.834032i) q^{31} +(3.38754 + 3.38754i) q^{32} +(1.24504 - 1.20410i) q^{33} +(-0.498552 - 0.498552i) q^{34} +4.68011i q^{35} +(0.0945161 - 2.82619i) q^{36} +(1.51615 + 1.51615i) q^{37} +6.91982 q^{38} +(-4.53663 - 4.29174i) q^{39} +8.19607 q^{40} +(-1.26787 - 1.26787i) q^{41} +(-0.0514371 + 3.07697i) q^{42} -4.40961i q^{43} +(-0.666511 - 0.666511i) q^{44} +(-5.55067 - 5.93477i) q^{45} +(-0.424839 - 0.424839i) q^{46} +(5.98819 - 5.98819i) q^{47} +(2.12380 + 0.0355031i) q^{48} -4.01460i q^{49} +(1.69916 - 1.69916i) q^{50} +(1.18742 + 0.0198498i) q^{51} +(-2.29399 + 2.50755i) q^{52} +7.83038i q^{53} +(-3.58410 - 3.96287i) q^{54} -2.70866 q^{55} +5.22821 q^{56} +(-8.37834 + 8.10283i) q^{57} +(-6.59817 + 6.59817i) q^{58} +(2.76308 - 2.76308i) q^{59} +(-3.17879 + 3.07426i) q^{60} +5.84125 q^{61} -1.21289 q^{62} +(-3.54073 - 3.78575i) q^{63} -7.37899i q^{64} +(0.433940 + 9.75656i) q^{65} +(-1.78083 - 0.0297697i) q^{66} +(-3.79321 + 3.79321i) q^{67} -0.646288i q^{68} +(1.01185 + 0.0169150i) q^{69} +(3.40300 - 3.40300i) q^{70} +(-6.18069 - 6.18069i) q^{71} +(-6.62982 + 6.20073i) q^{72} +(0.0228980 + 0.0228980i) q^{73} -2.20484i q^{74} +(-0.0676519 + 4.04694i) q^{75} +(4.48519 + 4.48519i) q^{76} -1.72783 q^{77} +(0.178067 + 6.41929i) q^{78} -7.85016 q^{79} +(-2.34883 - 2.34883i) q^{80} +(8.97989 + 0.601301i) q^{81} +1.84378i q^{82} +(7.43110 + 7.43110i) q^{83} +(-2.02773 + 1.96105i) q^{84} +(-1.31324 - 1.31324i) q^{85} +(-3.20632 + 3.20632i) q^{86} +(0.262706 - 15.7151i) q^{87} +3.02588i q^{88} +(11.0816 - 11.0816i) q^{89} +(-0.279292 + 8.35131i) q^{90} +(0.276807 + 6.22364i) q^{91} -0.550732i q^{92} +(1.46853 - 1.42024i) q^{93} -8.70828 q^{94} +18.2275 q^{95} +(5.76849 + 5.96464i) q^{96} +(13.2337 - 13.2337i) q^{97} +(-2.91910 + 2.91910i) q^{98} +(2.19104 - 2.04923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) $ 96 * q + 12 * q^6 - 16 * q^7	$ 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) $ 96 * q + 12 * q^6 - 16 * q^7 + 16 * q^13 - 16 * q^15 - 120 * q^16 - 28 * q^18 - 24 * q^19 + 24 * q^24 - 24 * q^27 + 56 * q^28 + 48 * q^31 - 16 * q^34 - 16 * q^37 + 80 * q^40 + 52 * q^42 + 4 * q^45 - 56 * q^46 + 28 * q^48 + 4 * q^54 + 4 * q^57 + 48 * q^58 + 4 * q^60 - 96 * q^61 - 36 * q^63 + 20 * q^66 - 16 * q^67 + 48 * q^70 - 16 * q^72 - 16 * q^73 - 88 * q^76 + 80 * q^78 + 16 * q^79 + 32 * q^81 + 52 * q^84 - 8 * q^85 - 48 * q^87 - 16 * q^91 - 36 * q^93 - 16 * q^94 - 108 * q^96 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.727121	−	0.727121i	−0.514152	−	0.514152i	0.401644	−	0.915796i	$-0.368439\pi$
$2$	−0.727121	−	0.727121i	−0.514152	−	0.514152i	−0.915796	+	0.401644i	$0.868439\pi$
$3$	1.73181	+	0.0289503i	0.999860	+	0.0167145i
$3$	1.73181	+	0.0289503i	0.999860	+	0.0167145i
$4$		−	0.942589i		−	0.471295i
$5$	−1.91531	−	1.91531i	−0.856553	−	0.856553i	0.134377	−	0.990930i	$-0.457097\pi$
$5$	−1.91531	−	1.91531i	−0.856553	−	0.856553i	−0.990930	+	0.134377i	$0.957097\pi$
$6$	−1.23818	−	1.28029i	−0.505487	−	0.522674i
$7$	−1.22176	−	1.22176i	−0.461783	−	0.461783i	0.437457	−	0.899239i	$-0.355879\pi$
$7$	−1.22176	−	1.22176i	−0.461783	−	0.461783i	−0.899239	+	0.437457i	$0.855879\pi$
$8$	−2.13962	+	2.13962i	−0.756470	+	0.756470i
$9$	2.99832	+	0.100273i	0.999441	+	0.0334243i
$10$			2.78533i			0.880797i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$12$	0.0272883	−	1.63238i	0.00787744	−	0.471229i
$13$	−2.66027	−	2.43371i	−0.737827	−	0.674990i
$13$	−2.66027	−	2.43371i	−0.737827	−	0.674990i
$14$			1.77674i			0.474853i
$15$	−3.26150	−	3.37240i	−0.842116	−	0.870750i
$16$	1.22635			0.306587
$17$	0.685652			0.166295			0.0831475	−	0.996537i	$-0.473503\pi$
$17$	0.685652			0.166295			0.0831475	+	0.996537i	$0.473503\pi$
$18$	−2.10723	−	2.25306i	−0.496680	−	0.531050i
$19$	−4.75837	+	4.75837i	−1.09164	+	1.09164i	−0.0962910	+	0.995353i	$0.530698\pi$
$19$	−4.75837	+	4.75837i	−1.09164	+	1.09164i	−0.995353	+	0.0962910i	$0.969302\pi$
$20$	−1.80535	+	1.80535i	−0.403689	+	0.403689i
$21$	−2.08049	−	2.15123i	−0.454000	−	0.469437i
$22$	−1.02830			−0.219235
$23$	0.584276			0.121830			0.0609149	−	0.998143i	$-0.480598\pi$
$23$	0.584276			0.121830			0.0609149	+	0.998143i	$0.480598\pi$
$24$	−3.76735	+	3.64347i	−0.769008	+	0.743720i
$25$			2.33683i			0.467366i
$26$	0.164739	+	3.70394i	0.0323081	+	0.726403i
$27$	5.18962	+	0.260456i	0.998743	+	0.0501247i
$28$	−1.15162	+	1.15162i	−0.217636	+	0.217636i
$29$		−	9.07437i		−	1.68507i	−0.538643	−	0.842534i	$-0.681063\pi$
$29$		−	9.07437i		−	1.68507i	0.538643	−	0.842534i	$-0.318937\pi$
$30$	−0.0806360	+	4.82365i	−0.0147221	+	0.880674i
$31$	0.834032	−	0.834032i	0.149797	−	0.149797i	−0.628231	−	0.778027i	$-0.716221\pi$
$31$	0.834032	−	0.834032i	0.149797	−	0.149797i	0.778027	+	0.628231i	$0.216221\pi$
$32$	3.38754	+	3.38754i	0.598837	+	0.598837i
$33$	1.24504	−	1.20410i	0.216734	−	0.209607i
$34$	−0.498552	−	0.498552i	−0.0855009	−	0.0855009i
$35$			4.68011i			0.791082i
$36$	0.0945161	−	2.82619i	0.0157527	−	0.471031i
$37$	1.51615	+	1.51615i	0.249253	+	0.249253i	0.820664	−	0.571411i	$-0.193604\pi$
$37$	1.51615	+	1.51615i	0.249253	+	0.249253i	−0.571411	+	0.820664i	$0.693604\pi$
$38$	6.91982			1.12254
$39$	−4.53663	−	4.29174i	−0.726442	−	0.687228i
$40$	8.19607			1.29591
$41$	−1.26787	−	1.26787i	−0.198007	−	0.198007i	0.601138	−	0.799145i	$-0.294714\pi$
$41$	−1.26787	−	1.26787i	−0.198007	−	0.198007i	−0.799145	+	0.601138i	$0.794714\pi$
$42$	−0.0514371	+	3.07697i	−0.00793692	+	0.474787i
$43$		−	4.40961i		−	0.672459i	−0.941780	−	0.336229i	$-0.890848\pi$
$43$		−	4.40961i		−	0.672459i	0.941780	−	0.336229i	$-0.109152\pi$
$44$	−0.666511	−	0.666511i	−0.100480	−	0.100480i
$45$	−5.55067	−	5.93477i	−0.827445	−	0.884704i
$46$	−0.424839	−	0.424839i	−0.0626391	−	0.0626391i
$47$	5.98819	−	5.98819i	0.873467	−	0.873467i	−0.119382	−	0.992848i	$-0.538091\pi$
$47$	5.98819	−	5.98819i	0.873467	−	0.873467i	0.992848	+	0.119382i	$0.0380912\pi$
$48$	2.12380	+	0.0355031i	0.306544	+	0.00512443i
$49$		−	4.01460i		−	0.573514i
$50$	1.69916	−	1.69916i	0.240297	−	0.240297i
$51$	1.18742	+	0.0198498i	0.166272	+	0.00277953i
$52$	−2.29399	+	2.50755i	−0.318119	+	0.347734i
$53$			7.83038i			1.07559i	0.843077	+	0.537793i	$0.180742\pi$
$53$			7.83038i			1.07559i	−0.843077	+	0.537793i	$0.819258\pi$
$54$	−3.58410	−	3.96287i	−0.487734	−	0.539278i
$55$	−2.70866			−0.365235
$56$	5.22821			0.698649
$57$	−8.37834	+	8.10283i	−1.10974	+	1.07325i
$58$	−6.59817	+	6.59817i	−0.866382	+	0.866382i
$59$	2.76308	−	2.76308i	0.359722	−	0.359722i	−0.503989	−	0.863710i	$-0.668135\pi$
$59$	2.76308	−	2.76308i	0.359722	−	0.359722i	0.863710	+	0.503989i	$0.168135\pi$
$60$	−3.17879	+	3.07426i	−0.410380	+	0.396885i
$61$	5.84125			0.747895			0.373948	−	0.927450i	$-0.378004\pi$
$61$	5.84125			0.747895			0.373948	+	0.927450i	$0.378004\pi$
$62$	−1.21289			−0.154037
$63$	−3.54073	−	3.78575i	−0.446090	−	0.476959i
$64$		−	7.37899i		−	0.922374i
$65$	0.433940	+	9.75656i	0.0538237	+	1.21015i
$66$	−1.78083	−	0.0297697i	−0.219205	−	0.00366440i
$67$	−3.79321	+	3.79321i	−0.463415	+	0.463415i	−0.899773	−	0.436358i	$-0.856268\pi$
$67$	−3.79321	+	3.79321i	−0.463415	+	0.463415i	0.436358	+	0.899773i	$0.356268\pi$
$68$		−	0.646288i		−	0.0783739i
$69$	1.01185	+	0.0169150i	0.121813	+	0.00203632i
$70$	3.40300	−	3.40300i	0.406737	−	0.406737i
$71$	−6.18069	−	6.18069i	−0.733513	−	0.733513i	0.237801	−	0.971314i	$-0.423573\pi$
$71$	−6.18069	−	6.18069i	−0.733513	−	0.733513i	−0.971314	+	0.237801i	$0.923573\pi$
$72$	−6.62982	+	6.20073i	−0.781331	+	0.730763i
$73$	0.0228980	+	0.0228980i	0.00268000	+	0.00268000i	0.708446	−	0.705766i	$-0.249397\pi$
$73$	0.0228980	+	0.0228980i	0.00268000	+	0.00268000i	−0.705766	+	0.708446i	$0.749397\pi$
$74$		−	2.20484i		−	0.256308i
$75$	−0.0676519	+	4.04694i	−0.00781177	+	0.467300i
$76$	4.48519	+	4.48519i	0.514486	+	0.514486i
$77$	−1.72783			−0.196905
$78$	0.178067	+	6.41929i	0.0201621	+	0.726842i
$79$	−7.85016			−0.883212			−0.441606	−	0.897209i	$-0.645591\pi$
$79$	−7.85016			−0.883212			−0.441606	+	0.897209i	$0.645591\pi$
$80$	−2.34883	−	2.34883i	−0.262608	−	0.262608i
$81$	8.97989	+	0.601301i	0.997766	+	0.0668112i
$82$			1.84378i			0.203612i
$83$	7.43110	+	7.43110i	0.815669	+	0.815669i	0.985477	−	0.169808i	$-0.0543148\pi$
$83$	7.43110	+	7.43110i	0.815669	+	0.815669i	−0.169808	+	0.985477i	$0.554315\pi$
$84$	−2.02773	+	1.96105i	−0.221243	+	0.213968i
$85$	−1.31324	−	1.31324i	−0.142440	−	0.142440i
$86$	−3.20632	+	3.20632i	−0.345746	+	0.345746i
$87$	0.262706	−	15.7151i	0.0281650	−	1.68483i
$88$			3.02588i			0.322560i
$89$	11.0816	−	11.0816i	1.17465	−	1.17465i	0.193557	−	0.981089i	$-0.437997\pi$
$89$	11.0816	−	11.0816i	1.17465	−	1.17465i	0.981089	−	0.193557i	$-0.0620026\pi$
$90$	−0.279292	+	8.35131i	−0.0294400	+	0.880305i
$91$	0.276807	+	6.22364i	0.0290173	+	0.652414i
$92$		−	0.550732i		−	0.0574178i
$93$	1.46853	−	1.42024i	0.152279	−	0.147272i
$94$	−8.70828			−0.898190
$95$	18.2275			1.87010
$96$	5.76849	+	5.96464i	0.588745	+	0.608763i
$97$	13.2337	−	13.2337i	1.34368	−	1.34368i	0.451307	−	0.892369i	$-0.350958\pi$
$97$	13.2337	−	13.2337i	1.34368	−	1.34368i	0.892369	−	0.451307i	$-0.149042\pi$
$98$	−2.91910	+	2.91910i	−0.294873	+	0.294873i
$99$	2.19104	−	2.04923i	0.220208	−	0.205956i
$100$	2.20267			0.220267
$101$	7.30068			0.726445			0.363222	−	0.931703i	$-0.381677\pi$
$101$	7.30068			0.726445			0.363222	+	0.931703i	$0.381677\pi$
$102$	−0.848963	−	0.877830i	−0.0840599	−	0.0869181i
$103$		−	2.68902i		−	0.264957i	−0.991186	−	0.132479i	$-0.957706\pi$
$103$		−	2.68902i		−	0.264957i	0.991186	−	0.132479i	$-0.0422936\pi$
$104$	10.8992	−	0.484760i	1.06875	−	0.0475347i
$105$	−0.135491	+	8.10505i	−0.0132225	+	0.790972i
$106$	5.69364	−	5.69364i	0.553015	−	0.553015i
$107$			9.24544i			0.893790i	0.894586	+	0.446895i	$0.147470\pi$
$107$			9.24544i			0.893790i	−0.894586	+	0.446895i	$0.852530\pi$
$108$	0.245503	−	4.89168i	0.0236235	−	0.470702i
$109$	11.0557	−	11.0557i	1.05894	−	1.05894i	0.0607907	−	0.998151i	$-0.480638\pi$
$109$	11.0557	−	11.0557i	1.05894	−	1.05894i	0.998151	−	0.0607907i	$-0.0193622\pi$
$110$	1.96952	+	1.96952i	0.187787	+	0.187787i
$111$	2.58178	+	2.66957i	0.245052	+	0.253384i
$112$	−1.49830	−	1.49830i	−0.141576	−	0.141576i
$113$			5.61081i			0.527820i	0.964547	+	0.263910i	$0.0850122\pi$
$113$			5.61081i			0.527820i	−0.964547	+	0.263910i	$0.914988\pi$
$114$	11.9838	+	0.200331i	1.12239	+	0.0187627i
$115$	−1.11907	−	1.11907i	−0.104354	−	0.104354i
$116$	−8.55340			−0.794164
$117$	−7.73233	−	7.56380i	−0.714854	−	0.699274i
$118$	−4.01818			−0.369904
$119$	−0.837703	−	0.837703i	−0.0767921	−	0.0767921i
$120$	14.1940	+	0.237279i	1.29573	+	0.0216605i
$121$		−	1.00000i		−	0.0909091i
$122$	−4.24730	−	4.24730i	−0.384532	−	0.384532i
$123$	−2.15900	−	2.23241i	−0.194670	−	0.201289i
$124$	−0.786150	−	0.786150i	−0.0705984	−	0.0705984i
$125$	−5.10080	+	5.10080i	−0.456229	+	0.456229i
$126$	−0.178158	+	5.32724i	−0.0158716	+	0.474588i
$127$			9.87847i			0.876573i	0.898835	+	0.438286i	$0.144414\pi$
$127$			9.87847i			0.876573i	−0.898835	+	0.438286i	$0.855586\pi$
$128$	1.40965	−	1.40965i	0.124597	−	0.124597i
$129$	0.127659	−	7.63660i	0.0112398	−	0.672365i
$130$	6.77867	−	7.40973i	0.594529	−	0.649876i
$131$			18.6591i			1.63025i	0.579282	+	0.815127i	$0.303333\pi$
$131$			18.6591i			1.63025i	−0.579282	+	0.815127i	$0.696667\pi$
$132$	−1.13497	−	1.17357i	−0.0987869	−	0.102146i
$133$	11.6272			1.00820
$134$	5.51625			0.476531
$135$	−9.44088	−	10.4386i	−0.812542	−	0.898411i
$136$	−1.46703	+	1.46703i	−0.125797	+	0.125797i
$137$	−7.42005	+	7.42005i	−0.633938	+	0.633938i	−0.949053	−	0.315116i	$-0.897957\pi$
$137$	−7.42005	+	7.42005i	−0.633938	+	0.633938i	0.315116	+	0.949053i	$0.397957\pi$
$138$	−0.723441	−	0.748039i	−0.0615834	−	0.0636773i
$139$	8.03319			0.681367			0.340683	−	0.940178i	$-0.389342\pi$
$139$	8.03319			0.681367			0.340683	+	0.940178i	$0.389342\pi$
$140$	4.41142			0.372833
$141$	10.5438	−	10.1970i	0.887944	−	0.858745i
$142$			8.98822i			0.754275i
$143$	−3.60199	+	0.160205i	−0.301214	+	0.0133970i
$144$	3.67698	+	0.122969i	0.306415	+	0.0102474i
$145$	−17.3802	+	17.3802i	−1.44335	+	1.44335i
$146$		−	0.0332992i		−	0.00275586i
$147$	0.116224	−	6.95251i	0.00958597	−	0.573434i
$148$	1.42910	−	1.42910i	0.117471	−	0.117471i
$149$	−0.713473	−	0.713473i	−0.0584500	−	0.0584500i	0.677278	−	0.735728i	$-0.263160\pi$
$149$	−0.713473	−	0.713473i	−0.0584500	−	0.0584500i	−0.735728	+	0.677278i	$0.763160\pi$
$150$	2.99181	−	2.89343i	0.244280	−	0.236247i
$151$	−0.536788	−	0.536788i	−0.0436832	−	0.0436832i	0.684928	−	0.728611i	$-0.259834\pi$
$151$	−0.536788	−	0.536788i	−0.0436832	−	0.0436832i	−0.728611	+	0.684928i	$0.759834\pi$
$152$		−	20.3622i		−	1.65159i
$153$	2.05581	+	0.0687522i	0.166202	+	0.00555829i
$154$	1.25634	+	1.25634i	0.101239	+	0.101239i
$155$	−3.19486			−0.256617
$156$	−4.04535	+	4.27618i	−0.323887	+	0.342368i
$157$	−8.38190			−0.668948			−0.334474	−	0.942405i	$-0.608559\pi$
$157$	−8.38190			−0.668948			−0.334474	+	0.942405i	$0.608559\pi$
$158$	5.70802	+	5.70802i	0.454105	+	0.454105i
$159$	−0.226692	+	13.5607i	−0.0179778	+	1.07544i
$160$		−	12.9764i		−	1.02587i
$161$	−0.713846	−	0.713846i	−0.0562589	−	0.0562589i
$162$	−6.09225	−	6.96669i	−0.478652	−	0.547355i
$163$	11.0927	+	11.0927i	0.868848	+	0.868848i	0.992345	−	0.123497i	$-0.0394110\pi$
$163$	11.0927	+	11.0927i	0.868848	+	0.868848i	−0.123497	+	0.992345i	$0.539411\pi$
$164$	−1.19508	+	1.19508i	−0.0933198	+	0.0933198i
$165$	−4.69088	−	0.0784165i	−0.365184	−	0.00610471i
$166$		−	10.8066i		−	0.838756i
$167$	14.5551	−	14.5551i	1.12631	−	1.12631i	0.135533	−	0.990773i	$-0.456725\pi$
$167$	14.5551	−	14.5551i	1.12631	−	1.12631i	0.990773	−	0.135533i	$-0.0432747\pi$
$168$	9.05426	+	0.151358i	0.698551	+	0.0116775i
$169$	1.15411	+	12.9487i	0.0887779	+	0.996051i
$170$			1.90976i			0.146472i
$171$	−14.7443	+	13.7900i	−1.12752	+	1.05455i
$172$	−4.15645			−0.316926
$173$	−0.214913			−0.0163396			−0.00816978	−	0.999967i	$-0.502601\pi$
$173$	−0.214913			−0.0163396			−0.00816978	+	0.999967i	$0.502601\pi$
$174$	−11.6178	+	11.2357i	−0.880742	+	0.851780i
$175$	2.85505	−	2.85505i	0.215821	−	0.215821i
$176$	0.867158	−	0.867158i	0.0653645	−	0.0653645i
$177$	4.86511	−	4.70513i	0.365684	−	0.353659i
$178$	−16.1153			−1.20789
$179$	−17.9288			−1.34006			−0.670029	−	0.742335i	$-0.733719\pi$
$179$	−17.9288			−1.34006			−0.670029	+	0.742335i	$0.733719\pi$
$180$	−5.59406	+	5.23200i	−0.416956	+	0.389970i
$181$			22.8739i			1.70020i	0.526618	+	0.850102i	$0.323460\pi$
$181$			22.8739i			1.70020i	−0.526618	+	0.850102i	$0.676540\pi$
$182$	4.32406	−	4.72661i	0.320521	−	0.350360i
$183$	10.1159	+	0.169106i	0.747791	+	0.0125007i
$184$	−1.25013	+	1.25013i	−0.0921606	+	0.0921606i
$185$		−	5.80778i		−	0.426996i
$186$	−2.10049	−	0.0351134i	−0.154015	−	0.00257464i
$187$	0.484829	−	0.484829i	0.0354542	−	0.0354542i
$188$	−5.64440	−	5.64440i	−0.411660	−	0.411660i
$189$	−6.02227	−	6.65870i	−0.438055	−	0.484349i
$190$	−13.2536	−	13.2536i	−0.961517	−	0.961517i
$191$		−	6.47533i		−	0.468538i	−0.972172	−	0.234269i	$-0.924730\pi$
$191$		−	6.47533i		−	0.468538i	0.972172	−	0.234269i	$-0.0752697\pi$
$192$	0.213624	−	12.7790i	0.0154170	−	0.922245i
$193$	7.46691	+	7.46691i	0.537480	+	0.537480i	0.922788	−	0.385308i	$-0.125905\pi$
$193$	7.46691	+	7.46691i	0.537480	+	0.537480i	−0.385308	+	0.922788i	$0.625905\pi$
$194$	−19.2450			−1.38171
$195$	0.469046	+	16.9091i	0.0335891	+	1.21088i
$196$	−3.78412			−0.270294
$197$	−15.5217	−	15.5217i	−1.10588	−	1.10588i	−0.993687	−	0.112189i	$-0.964214\pi$
$197$	−15.5217	−	15.5217i	−1.10588	−	1.10588i	−0.112189	−	0.993687i	$-0.535786\pi$
$198$	−3.08319	−	0.103111i	−0.219113	−	0.00732778i
$199$		−	27.1492i		−	1.92456i	−0.272066	−	0.962278i	$-0.587707\pi$
$199$		−	27.1492i		−	1.92456i	0.272066	−	0.962278i	$-0.412293\pi$
$200$	−4.99992	−	4.99992i	−0.353548	−	0.353548i
$201$	−6.67893	+	6.45930i	−0.471096	+	0.455604i
$202$	−5.30848	−	5.30848i	−0.373503	−	0.373503i
$203$	−11.0867	+	11.0867i	−0.778135	+	0.778135i
$204$	0.0187102	−	1.11925i	0.00130998	−	0.0783630i
$205$			4.85671i			0.339208i
$206$	−1.95525	+	1.95525i	−0.136228	+	0.136228i
$207$	1.75185	+	0.0585869i	0.121762	+	0.00407207i
$208$	−3.26242	−	2.98457i	−0.226208	−	0.206943i
$209$			6.72935i			0.465479i
$210$	5.99187	−	5.79484i	0.413478	−	0.399882i
$211$	8.42661			0.580112			0.290056	−	0.957010i	$-0.406326\pi$
$211$	8.42661			0.580112			0.290056	+	0.957010i	$0.406326\pi$
$212$	7.38084			0.506918
$213$	−10.5248	−	10.8827i	−0.721150	−	0.745671i
$214$	6.72255	−	6.72255i	0.459544	−	0.459544i
$215$	−8.44577	+	8.44577i	−0.575996	+	0.575996i
$216$	−11.6611	+	10.5465i	−0.793437	+	0.717601i
$217$	−2.03798			−0.138347
$218$	−16.0776			−1.08891
$219$	0.0389920	+	0.0403178i	0.00263483	+	0.00272442i
$220$			2.55315i			0.172134i
$221$	−1.82402	−	1.66868i	−0.122697	−	0.112247i
$222$	0.0638309	−	3.81837i	0.00428405	−	0.256272i
$223$	−8.12647	+	8.12647i	−0.544189	+	0.544189i	−0.924754	−	0.380565i	$-0.875729\pi$
$223$	−8.12647	+	8.12647i	−0.544189	+	0.544189i	0.380565	+	0.924754i	$0.375729\pi$
$224$		−	8.27753i		−	0.553065i
$225$	−0.234320	+	7.00657i	−0.0156214	+	0.467105i
$226$	4.07974	−	4.07974i	0.271380	−	0.271380i
$227$	−7.97654	−	7.97654i	−0.529422	−	0.529422i	0.390978	−	0.920400i	$-0.372137\pi$
$227$	−7.97654	−	7.97654i	−0.529422	−	0.529422i	−0.920400	+	0.390978i	$0.872137\pi$
$228$	7.63764	+	7.89733i	0.505815	+	0.523014i
$229$	12.1956	+	12.1956i	0.805909	+	0.805909i	0.984012	−	0.178103i	$-0.0569961\pi$
$229$	12.1956	+	12.1956i	0.805909	+	0.805909i	−0.178103	+	0.984012i	$0.556996\pi$
$230$			1.62740i			0.107307i
$231$	−2.99228	−	0.0500213i	−0.196877	−	0.00329116i
$232$	19.4157	+	19.4157i	1.27470	+	1.27470i
$233$	−21.6214			−1.41646			−0.708232	−	0.705980i	$-0.750507\pi$
$233$	−21.6214			−1.41646			−0.708232	+	0.705980i	$0.750507\pi$
$234$	0.122537	+	11.1221i	0.00801052	+	0.727077i
$235$	−22.9385			−1.49634
$236$	−2.60445	−	2.60445i	−0.169535	−	0.169535i
$237$	−13.5950	−	0.227264i	−0.883088	−	0.0147624i
$238$			1.21822i			0.0789657i
$239$	−4.18358	−	4.18358i	−0.270613	−	0.270613i	0.558734	−	0.829347i	$-0.311287\pi$
$239$	−4.18358	−	4.18358i	−0.270613	−	0.270613i	−0.829347	+	0.558734i	$0.811287\pi$
$240$	−3.99973	−	4.13573i	−0.258182	−	0.266960i
$241$	−20.0354	−	20.0354i	−1.29059	−	1.29059i	−0.934420	−	0.356173i	$-0.884081\pi$
$241$	−20.0354	−	20.0354i	−1.29059	−	1.29059i	−0.356173	−	0.934420i	$-0.615919\pi$
$242$	−0.727121	+	0.727121i	−0.0467411	+	0.0467411i
$243$	15.5340	+	1.30131i	0.996510	+	0.0834790i
$244$		−	5.50590i		−	0.352479i
$245$	−7.68920	+	7.68920i	−0.491245	+	0.491245i
$246$	−0.0533781	+	3.19308i	−0.00340326	+	0.203583i
$247$	24.2390	−	1.07807i	1.54229	−	0.0685962i
$248$			3.56902i			0.226633i
$249$	12.6541	+	13.0844i	0.801921	+	0.829188i
$250$	7.41780			0.469143
$251$	17.2322			1.08769			0.543845	−	0.839186i	$-0.316968\pi$
$251$	17.2322			1.08769			0.543845	+	0.839186i	$0.316968\pi$
$252$	−3.56841	+	3.33745i	−0.224788	+	0.210240i
$253$	0.413145	−	0.413145i	0.0259742	−	0.0259742i
$254$	7.18285	−	7.18285i	0.450692	−	0.450692i
$255$	−2.23625	−	2.31229i	−0.140040	−	0.144801i
$256$	−16.8080			−1.05050
$257$	−26.3716			−1.64502			−0.822509	−	0.568752i	$-0.807426\pi$
$257$	−26.3716			−1.64502			−0.822509	+	0.568752i	$0.807426\pi$
$258$	−5.64555	+	5.45991i	−0.351477	+	0.339919i
$259$		−	3.70474i		−	0.230201i
$260$	9.19643	−	0.409027i	0.570338	−	0.0253668i
$261$	0.909912	−	27.2079i	0.0563221	−	1.68413i
$262$	13.5674	−	13.5674i	0.838199	−	0.838199i
$263$			16.5928i			1.02315i	0.859238	+	0.511577i	$0.170938\pi$
$263$			16.5928i			1.02315i	−0.859238	+	0.511577i	$0.829062\pi$
$264$	−0.0876001	+	5.24024i	−0.00539141	+	0.322515i
$265$	14.9976	−	14.9976i	0.921296	−	0.921296i
$266$	−8.45437	−	8.45437i	−0.518371	−	0.518371i
$267$	19.5120	−	18.8704i	1.19412	−	1.15485i
$268$	3.57544	+	3.57544i	0.218405	+	0.218405i
$269$		−	24.0266i		−	1.46493i	−0.680805	−	0.732465i	$-0.738370\pi$
$269$		−	24.0266i		−	1.46493i	0.680805	−	0.732465i	$-0.261630\pi$
$270$	−0.725454	+	14.4548i	−0.0441497	+	0.879690i
$271$	4.26290	+	4.26290i	0.258953	+	0.258953i	0.824628	−	0.565675i	$-0.191384\pi$
$271$	4.26290	+	4.26290i	0.258953	+	0.258953i	−0.565675	+	0.824628i	$0.691384\pi$
$272$	0.840846			0.0509838
$273$	0.299201	+	10.7862i	0.0181085	+	0.652808i
$274$	10.7906			0.651881
$275$	1.65239	+	1.65239i	0.0996427	+	0.0996427i
$276$	0.0159439	−	0.953763i	0.000959707	−	0.0574098i
$277$		−	1.71001i		−	0.102744i	−0.998680	−	0.0513722i	$-0.983641\pi$
$277$		−	1.71001i		−	0.102744i	0.998680	−	0.0513722i	$-0.0163595\pi$
$278$	−5.84111	−	5.84111i	−0.350326	−	0.350326i
$279$	2.58433	−	2.41707i	0.154720	−	0.144706i
$280$	−10.0136	−	10.0136i	−0.598430	−	0.598430i
$281$	−10.2191	+	10.2191i	−0.609623	+	0.609623i	−0.942848	−	0.333224i	$-0.891863\pi$
$281$	−10.2191	+	10.2191i	−0.609623	+	0.609623i	0.333224	+	0.942848i	$0.391863\pi$
$282$	−15.0811	−	0.252107i	−0.898065	−	0.0150128i
$283$			7.27577i			0.432500i	0.976338	+	0.216250i	$0.0693826\pi$
$283$			7.27577i			0.432500i	−0.976338	+	0.216250i	$0.930617\pi$
$284$	−5.82585	+	5.82585i	−0.345701	+	0.345701i
$285$	31.5665	+	0.527692i	1.86984	+	0.0312578i
$286$	2.73557	+	2.50260i	0.161758	+	0.147982i
$287$			3.09806i			0.182873i
$288$	9.81725	+	10.4966i	0.578487	+	0.618519i
$289$	−16.5299			−0.972346
$290$	25.2751			1.48420
$291$	23.3013	−	22.5351i	1.36595	−	1.32103i
$292$	0.0215834	−	0.0215834i	0.00126307	−	0.00126307i
$293$	−9.78840	+	9.78840i	−0.571844	+	0.571844i	−0.932643	−	0.360799i	$-0.882504\pi$
$293$	−9.78840	+	9.78840i	−0.571844	+	0.571844i	0.360799	+	0.932643i	$0.382504\pi$
$294$	−5.13983	+	4.97081i	−0.299761	+	0.289904i
$295$	−10.5843			−0.616241
$296$	−6.48795			−0.377104
$297$	3.85379	−	3.48545i	0.223619	−	0.202246i
$298$			1.03756i			0.0601044i
$299$	−1.55433	−	1.42196i	−0.0898894	−	0.0822339i
$300$	3.81460	+	0.0637680i	0.220236	+	0.00368165i
$301$	−5.38749	+	5.38749i	−0.310530	+	0.310530i
$302$			0.780620i			0.0449196i
$303$	12.6434	+	0.211357i	0.726343	+	0.0121421i
$304$	−5.83540	+	5.83540i	−0.334683	+	0.334683i
$305$	−11.1878	−	11.1878i	−0.640612	−	0.640612i
$306$	−1.44483	−	1.54481i	−0.0825954	−	0.0883110i
$307$	13.9978	+	13.9978i	0.798896	+	0.798896i	0.982921	−	0.184026i	$-0.0589130\pi$
$307$	13.9978	+	13.9978i	0.798896	+	0.798896i	−0.184026	+	0.982921i	$0.558913\pi$
$308$			1.62864i			0.0928002i
$309$	0.0778481	−	4.65688i	0.00442862	−	0.264920i
$310$	2.32305	+	2.32305i	0.131940	+	0.131940i
$311$	29.2802			1.66033			0.830163	−	0.557521i	$-0.188247\pi$
$311$	29.2802			1.66033			0.830163	+	0.557521i	$0.188247\pi$
$312$	18.8893	−	0.523978i	1.06940	−	0.0296644i
$313$	−4.47160			−0.252750			−0.126375	−	0.991983i	$-0.540334\pi$
$313$	−4.47160			−0.252750			−0.126375	+	0.991983i	$0.540334\pi$
$314$	6.09465	+	6.09465i	0.343941	+	0.343941i
$315$	−0.469287	+	14.0325i	−0.0264413	+	0.790640i
$316$			7.39948i			0.416253i
$317$	15.5975	+	15.5975i	0.876043	+	0.876043i	0.993123	−	0.117079i	$-0.0373531\pi$
$317$	15.5975	+	15.5975i	0.876043	+	0.876043i	−0.117079	+	0.993123i	$0.537353\pi$
$318$	10.0251	−	9.69546i	0.562181	−	0.543694i
$319$	−6.41655	−	6.41655i	−0.359258	−	0.359258i
$320$	−14.1331	+	14.1331i	−0.790062	+	0.790062i
$321$	−0.267658	+	16.0113i	−0.0149392	+	0.893665i
$322$			1.03810i			0.0578513i
$323$	−3.26258	+	3.26258i	−0.181535	+	0.181535i
$324$	0.566780	−	8.46435i	0.0314878	−	0.470242i
$325$	5.68716	−	6.21660i	0.315467	−	0.344835i
$326$		−	16.1315i		−	0.893440i
$327$	19.4664	−	18.8262i	1.07649	−	1.04109i
$328$	5.42550			0.299573
$329$	−14.6323			−0.806704
$330$	3.35382	+	3.46786i	0.184622	+	0.190899i
$331$	3.92428	−	3.92428i	0.215698	−	0.215698i	−0.590985	−	0.806683i	$-0.701261\pi$
$331$	3.92428	−	3.92428i	0.215698	−	0.215698i	0.806683	+	0.590985i	$0.201261\pi$
$332$	7.00447	−	7.00447i	0.384420	−	0.384420i
$333$	4.39387	+	4.69792i	0.240782	+	0.257445i
$334$	−21.1666			−1.15819
$335$	14.5304			0.793878
$336$	−2.55140	−	2.63815i	−0.139190	−	0.143923i
$337$			6.66716i			0.363183i	0.983374	+	0.181592i	$0.0581249\pi$
$337$			6.66716i			0.363183i	−0.983374	+	0.181592i	$0.941875\pi$
$338$	8.57607	−	10.2544i	0.466477	−	0.557768i
$339$	−0.162435	+	9.71684i	−0.00882223	+	0.527747i
$340$	−1.23784	+	1.23784i	−0.0671314	+	0.0671314i
$341$		−	1.17950i		−	0.0638735i
$342$	20.7479	+	0.693869i	1.12192	+	0.0375202i
$343$	−13.4572	+	13.4572i	−0.726621	+	0.726621i
$344$	9.43488	+	9.43488i	0.508695	+	0.508695i
$345$	−1.90562	−	1.97041i	−0.102595	−	0.106083i
$346$	0.156268	+	0.156268i	0.00840103	+	0.00840103i
$347$		−	31.6363i		−	1.69833i	−0.528131	−	0.849163i	$-0.677107\pi$
$347$		−	31.6363i		−	1.69833i	0.528131	−	0.849163i	$-0.322893\pi$
$348$	−14.8129	−	0.247624i	−0.794053	−	0.0132740i
$349$	−19.7840	−	19.7840i	−1.05902	−	1.05902i	−0.998146	−	0.0608700i	$-0.980613\pi$
$349$	−19.7840	−	19.7840i	−1.05902	−	1.05902i	−0.0608700	−	0.998146i	$-0.519387\pi$
$350$	−4.15193			−0.221930
$351$	−13.1719	−	13.3229i	−0.703066	−	0.711125i
$352$	4.79070			0.255345
$353$	−2.07918	−	2.07918i	−0.110664	−	0.110664i	0.649607	−	0.760270i	$-0.274934\pi$
$353$	−2.07918	−	2.07918i	−0.110664	−	0.110664i	−0.760270	+	0.649607i	$0.774934\pi$
$354$	−6.95872	−	0.116328i	−0.369852	−	0.00618274i
$355$			23.6759i			1.25659i
$356$	−10.4454	−	10.4454i	−0.553605	−	0.553605i
$357$	−1.42649	−	1.47499i	−0.0754978	−	0.0780649i
$358$	13.0364	+	13.0364i	0.688994	+	0.688994i
$359$	−2.89554	+	2.89554i	−0.152821	+	0.152821i	−0.779377	−	0.626556i	$-0.784464\pi$
$359$	−2.89554	+	2.89554i	−0.152821	+	0.152821i	0.626556	+	0.779377i	$0.284464\pi$
$360$	24.5745	+	0.821843i	1.29519	+	0.0433149i
$361$		−	26.2841i		−	1.38337i
$362$	16.6321	−	16.6321i	0.874164	−	0.874164i
$363$	0.0289503	−	1.73181i	0.00151950	−	0.0908964i
$364$	5.86633	−	0.260915i	0.307479	−	0.0136757i
$365$		−	0.0877134i		−	0.00459113i
$366$	−7.23254	−	7.47847i	−0.378051	−	0.390906i
$367$	−13.1256			−0.685150			−0.342575	−	0.939491i	$-0.611299\pi$
$367$	−13.1256			−0.685150			−0.342575	+	0.939491i	$0.611299\pi$
$368$	0.716524			0.0373514
$369$	−3.67434	−	3.92861i	−0.191279	−	0.204515i
$370$	−4.22296	+	4.22296i	−0.219541	+	0.219541i
$371$	9.56686	−	9.56686i	0.496687	−	0.496687i
$372$	−1.33870	−	1.38422i	−0.0694085	−	0.0717685i
$373$	15.5262			0.803918			0.401959	−	0.915658i	$-0.368329\pi$
$373$	15.5262			0.803918			0.401959	+	0.915658i	$0.368329\pi$
$374$	−0.705059			−0.0364577
$375$	−8.98128	+	8.68594i	−0.463791	+	0.448540i
$376$			25.6249i			1.32150i
$377$	−22.0844	+	24.1403i	−1.13740	+	1.24329i
$378$	−0.462761	+	9.22060i	−0.0238019	+	0.474256i
$379$	3.63325	−	3.63325i	0.186627	−	0.186627i	−0.607609	−	0.794236i	$-0.707871\pi$
$379$	3.63325	−	3.63325i	0.186627	−	0.186627i	0.794236	+	0.607609i	$0.207871\pi$
$380$		−	17.1811i		−	0.881369i
$381$	−0.285985	+	17.1076i	−0.0146514	+	0.876450i
$382$	−4.70835	+	4.70835i	−0.240900	+	0.240900i
$383$	18.0993	+	18.0993i	0.924830	+	0.924830i	0.997366	−	0.0725360i	$-0.0231092\pi$
$383$	18.0993	+	18.0993i	0.924830	+	0.924830i	−0.0725360	+	0.997366i	$0.523109\pi$
$384$	2.48206	−	2.40044i	0.126662	−	0.122497i
$385$	3.30934	+	3.30934i	0.168659	+	0.168659i
$386$		−	10.8587i		−	0.552693i
$387$	0.442164	−	13.2214i	0.0224764	−	0.672083i
$388$	−12.4739	−	12.4739i	−0.633267	−	0.633267i
$389$	16.5998			0.841643			0.420821	−	0.907143i	$-0.361742\pi$
$389$	16.5998			0.841643			0.420821	+	0.907143i	$0.361742\pi$
$390$	11.9539	−	12.6360i	0.605308	−	0.639848i
$391$	0.400609			0.0202597
$392$	8.58971	+	8.58971i	0.433846	+	0.433846i
$393$	−0.540187	+	32.3140i	−0.0272488	+	1.63003i
$394$			22.5723i			1.13718i
$395$	15.0355	+	15.0355i	0.756518	+	0.756518i
$396$	−1.93158	−	2.06525i	−0.0970658	−	0.103783i
$397$	14.3747	+	14.3747i	0.721448	+	0.721448i	0.968900	−	0.247452i	$-0.0795933\pi$
$397$	14.3747	+	14.3747i	0.721448	+	0.721448i	−0.247452	+	0.968900i	$0.579593\pi$
$398$	−19.7408	+	19.7408i	−0.989515	+	0.989515i
$399$	20.1361	+	0.336610i	1.00806	+	0.0168516i
$400$			2.86576i			0.143288i
$401$	3.53303	−	3.53303i	0.176431	−	0.176431i	−0.613367	−	0.789798i	$-0.710185\pi$
$401$	3.53303	−	3.53303i	0.176431	−	0.176431i	0.789798	+	0.613367i	$0.210185\pi$
$402$	9.55309	+	0.159697i	0.476465	+	0.00796497i
$403$	−4.24855	+	0.188962i	−0.211635	+	0.00941285i
$404$		−	6.88154i		−	0.342369i
$405$	−16.0476	−	18.3510i	−0.797412	−	0.911866i
$406$	16.1228			0.800160
$407$	2.14415			0.106282
$408$	−2.58309	+	2.49815i	−0.127882	+	0.123677i
$409$	20.0298	−	20.0298i	0.990412	−	0.990412i	−0.00954215	−	0.999954i	$-0.503037\pi$
$409$	20.0298	−	20.0298i	0.990412	−	0.990412i	0.999954	+	0.00954215i	$0.00303741\pi$
$410$	3.53142	−	3.53142i	0.174404	−	0.174404i
$411$	−13.0649	+	12.6353i	−0.644445	+	0.623253i
$412$	−2.53465			−0.124873
$413$	−6.75164			−0.332227
$414$	−1.23121	−	1.31641i	−0.0605105	−	0.0646978i
$415$		−	28.4657i		−	1.39733i
$416$	−0.767493	−	17.2561i	−0.0376295	−	0.846048i
$417$	13.9120	+	0.232563i	0.681271	+	0.0113887i
$418$	4.89305	−	4.89305i	0.239327	−	0.239327i
$419$			34.6003i			1.69034i	0.534501	+	0.845168i	$0.320500\pi$
$419$			34.6003i			1.69034i	−0.534501	+	0.845168i	$0.679500\pi$
$420$	7.63974	+	0.127712i	0.372781	+	0.00623170i
$421$	−23.6936	+	23.6936i	−1.15475	+	1.15475i	−0.169165	+	0.985588i	$0.554107\pi$
$421$	−23.6936	+	23.6936i	−1.15475	+	1.15475i	−0.985588	+	0.169165i	$0.945893\pi$
$422$	−6.12717	−	6.12717i	−0.298266	−	0.298266i
$423$	18.5550	−	17.3541i	0.902174	−	0.843784i
$424$	−16.7540	−	16.7540i	−0.813648	−	0.813648i
$425$			1.60225i			0.0777206i
$426$	−0.260212	+	15.5659i	−0.0126073	+	0.754170i
$427$	−7.13662	−	7.13662i	−0.345365	−	0.345365i
$428$	8.71465			0.421239
$429$	−6.24260	+	0.173166i	−0.301395	+	0.00836051i
$430$	12.2822			0.592300
$431$	18.7333	+	18.7333i	0.902353	+	0.902353i	0.995639	−	0.0932860i	$-0.0297371\pi$
$431$	18.7333	+	18.7333i	0.902353	+	0.902353i	−0.0932860	+	0.995639i	$0.529737\pi$
$432$	6.36427	+	0.319409i	0.306201	+	0.0153676i
$433$			0.814028i			0.0391197i	0.999809	+	0.0195598i	$0.00622649\pi$
$433$			0.814028i			0.0391197i	−0.999809	+	0.0195598i	$0.993774\pi$
$434$	1.48186	+	1.48186i	0.0711314	+	0.0711314i
$435$	−30.6024	+	29.5961i	−1.46727	+	1.41902i
$436$	−10.4210	−	10.4210i	−0.499073	−	0.499073i
$437$	−2.78020	+	2.78020i	−0.132995	+	0.132995i
$438$	0.000964022	−	0.0576678i	4.60627e−5	−	0.00275548i
$439$			7.32147i			0.349435i	0.984619	+	0.174717i	$0.0559011\pi$
$439$			7.32147i			0.349435i	−0.984619	+	0.174717i	$0.944099\pi$
$440$	5.79550	−	5.79550i	0.276289	−	0.276289i
$441$	0.402555	−	12.0371i	0.0191693	−	0.573193i
$442$	0.112954	+	2.53961i	0.00537267	+	0.120797i
$443$			37.4045i			1.77714i	0.458740	+	0.888571i	$0.348301\pi$
$443$			37.4045i			1.77714i	−0.458740	+	0.888571i	$0.651699\pi$
$444$	2.51631	−	2.43356i	0.119419	−	0.115492i
$445$	−42.4494			−2.01229
$446$	11.8179			0.559592
$447$	−1.21494	−	1.25625i	−0.0574649	−	0.0594188i
$448$	−9.01537	+	9.01537i	−0.425936	+	0.425936i
$449$	−12.0219	+	12.0219i	−0.567349	+	0.567349i	−0.931385	−	0.364036i	$-0.881399\pi$
$449$	−12.0219	+	12.0219i	−0.567349	+	0.567349i	0.364036	+	0.931385i	$0.381399\pi$
$450$	5.26500	−	4.92425i	0.248195	−	0.232131i
$451$	−1.79303			−0.0844306
$452$	5.28869			0.248759
$453$	−0.914074	−	0.945154i	−0.0429469	−	0.0444072i
$454$			11.5998i			0.544407i
$455$	11.3900	−	12.4504i	0.533972	−	0.583682i
$456$	0.589491	−	35.2634i	0.0276055	−	1.65136i
$457$	6.60130	−	6.60130i	0.308796	−	0.308796i	−0.535646	−	0.844442i	$-0.679932\pi$
$457$	6.60130	−	6.60130i	0.308796	−	0.308796i	0.844442	+	0.535646i	$0.179932\pi$
$458$		−	17.7354i		−	0.828720i
$459$	3.55827	+	0.178582i	0.166086	+	0.00833549i
$460$	−1.05482	+	1.05482i	−0.0491814	+	0.0491814i
$461$	−18.4537	−	18.4537i	−0.859476	−	0.859476i	0.131800	−	0.991276i	$-0.457924\pi$
$461$	−18.4537	−	18.4537i	−0.859476	−	0.859476i	−0.991276	+	0.131800i	$0.957924\pi$
$462$	2.13938	+	2.21212i	0.0995327	+	0.102917i
$463$	−16.0851	−	16.0851i	−0.747538	−	0.747538i	0.226478	−	0.974016i	$-0.427279\pi$
$463$	−16.0851	−	16.0851i	−0.747538	−	0.747538i	−0.974016	+	0.226478i	$0.927279\pi$
$464$		−	11.1283i		−	0.516619i
$465$	−5.53289	−	0.0924922i	−0.256582	−	0.00428922i
$466$	15.7214	+	15.7214i	0.728278	+	0.728278i
$467$	−2.58769			−0.119744			−0.0598720	−	0.998206i	$-0.519069\pi$
$467$	−2.58769			−0.119744			−0.0598720	+	0.998206i	$0.519069\pi$
$468$	−7.12956	+	7.28841i	−0.329564	+	0.336907i
$469$	9.26880			0.427994
$470$	16.6791	+	16.6791i	0.769347	+	0.769347i
$471$	−14.5158	−	0.242658i	−0.668855	−	0.0111811i
$472$			11.8239i			0.544237i
$473$	−3.11806	−	3.11806i	−0.143369	−	0.143369i
$474$	9.71995	+	10.0504i	0.446452	+	0.461632i
$475$	−11.1195	−	11.1195i	−0.510197	−	0.510197i
$476$	−0.789610	+	0.789610i	−0.0361917	+	0.0361917i
$477$	−0.785174	+	23.4780i	−0.0359507	+	1.07498i
$478$			6.08393i			0.278273i
$479$	26.6716	−	26.6716i	1.21865	−	1.21865i	0.250552	−	0.968103i	$-0.419388\pi$
$479$	26.6716	−	26.6716i	1.21865	−	1.21865i	0.968103	−	0.250552i	$-0.0806120\pi$
$480$	0.375670	−	22.4726i	0.0171469	−	1.02573i
$481$	−0.343504	−	7.72322i	−0.0156624	−	0.352148i
$482$			29.1363i			1.32712i
$483$	−1.21558	−	1.25691i	−0.0553107	−	0.0571914i
$484$	−0.942589			−0.0428450
$485$	−50.6932			−2.30186
$486$	−10.3489	−	12.2413i	−0.469437	−	0.555279i
$487$	−11.2647	+	11.2647i	−0.510453	+	0.510453i	−0.914665	−	0.404212i	$-0.867546\pi$
$487$	−11.2647	+	11.2647i	−0.510453	+	0.510453i	0.404212	+	0.914665i	$0.367546\pi$
$488$	−12.4980	+	12.4980i	−0.565760	+	0.565760i
$489$	18.8893	+	19.5316i	0.854204	+	0.883249i
$490$	11.1820			0.505149
$491$	28.0090			1.26403			0.632013	−	0.774957i	$-0.282229\pi$
$491$	28.0090			1.26403			0.632013	+	0.774957i	$0.282229\pi$
$492$	−2.10424	+	2.03505i	−0.0948666	+	0.0917470i
$493$		−	6.22186i		−	0.280218i
$494$	−18.4086	−	16.8408i	−0.828243	−	0.757705i
$495$	−8.12143	−	0.271605i	−0.365031	−	0.0122077i
$496$	1.02281	−	1.02281i	0.0459256	−	0.0459256i
$497$			15.1027i			0.677447i
$498$	0.312855	−	18.7150i	0.0140194	−	0.838639i
$499$	19.0643	−	19.0643i	0.853437	−	0.853437i	−0.137118	−	0.990555i	$-0.543784\pi$
$499$	19.0643	−	19.0643i	0.853437	−	0.853437i	0.990555	+	0.137118i	$0.0437839\pi$
$500$	4.80796	+	4.80796i	0.215019	+	0.215019i
$501$	25.6280	−	24.7852i	1.14497	−	1.10732i
$502$	−12.5299	−	12.5299i	−0.559238	−	0.559238i
$503$			5.59799i			0.249602i	0.992182	+	0.124801i	$0.0398292\pi$
$503$			5.59799i			0.249602i	−0.992182	+	0.124801i	$0.960171\pi$
$504$	15.6759	+	0.524247i	0.698259	+	0.0233518i
$505$	−13.9831	−	13.9831i	−0.622238	−	0.622238i
$506$	−0.600813			−0.0267094
$507$	1.62383	+	22.4580i	0.0721170	+	0.997396i
$508$	9.31134			0.413124
$509$	−15.7946	−	15.7946i	−0.700084	−	0.700084i	0.264345	−	0.964428i	$-0.414844\pi$
$509$	−15.7946	−	15.7946i	−0.700084	−	0.700084i	−0.964428	+	0.264345i	$0.914844\pi$
$510$	−0.0552882	+	3.30734i	−0.00244820	+	0.146452i
$511$		−	0.0559517i		−	0.00247516i
$512$	9.40212	+	9.40212i	0.415519	+	0.415519i
$513$	−25.9335	+	23.4548i	−1.14499	+	1.03555i
$514$	19.1754	+	19.1754i	0.845790	+	0.845790i
$515$	−5.15032	+	5.15032i	−0.226950	+	0.226950i
$516$	−7.19818	−	0.120330i	−0.316882	−	0.00529725i
$517$		−	8.46858i		−	0.372448i
$518$	−2.69379	+	2.69379i	−0.118358	+	0.118358i
$519$	−0.372189	−	0.00622181i	−0.0163373	−	0.000273107i
$520$	−21.8038	−	19.9469i	−0.956159	−	0.874728i
$521$		−	30.0308i		−	1.31567i	−0.753161	−	0.657836i	$-0.771472\pi$
$521$		−	30.0308i		−	1.31567i	0.753161	−	0.657836i	$-0.228528\pi$
$522$	−20.4451	+	19.1218i	−0.894856	+	0.836939i
$523$	32.6628			1.42824			0.714122	−	0.700021i	$-0.246826\pi$
$523$	32.6628			1.42824			0.714122	+	0.700021i	$0.246826\pi$
$524$	17.5879			0.768330
$525$	5.02705	−	4.86174i	0.219399	−	0.212184i
$526$	12.0649	−	12.0649i	0.526057	−	0.526057i
$527$	0.571856	−	0.571856i	0.0249104	−	0.0249104i
$528$	1.52686	−	1.47665i	0.0664479	−	0.0642628i
$529$	−22.6586			−0.985157
$530$	−21.8102			−0.947373
$531$	8.56166	−	8.00753i	0.371544	−	0.347497i
$532$		−	10.9597i		−	0.475162i
$533$	0.287253	+	6.45849i	0.0124423	+	0.279748i
$534$	−27.9087	−	0.466543i	−1.20773	−	0.0201893i
$535$	17.7079	−	17.7079i	0.765579	−	0.765579i
$536$		−	16.2321i		−	0.701118i
$537$	−31.0492	−	0.519043i	−1.33987	−	0.0223984i
$538$	−17.4703	+	17.4703i	−0.753197	+	0.753197i
$539$	−2.83875	−	2.83875i	−0.122274	−	0.122274i
$540$	−9.83930	+	8.89888i	−0.423416	+	0.382947i
$541$	22.4593	+	22.4593i	0.965599	+	0.965599i	0.999428	−	0.0338290i	$-0.0107701\pi$
$541$	22.4593	+	22.4593i	0.965599	+	0.965599i	−0.0338290	+	0.999428i	$0.510770\pi$
$542$		−	6.19929i		−	0.266282i
$543$	−0.662206	+	39.6132i	−0.0284180	+	1.69997i
$544$	2.32267	+	2.32267i	0.0995836	+	0.0995836i
$545$	−42.3501			−1.81408
$546$	7.62529	−	8.06040i	0.326332	−	0.344953i
$547$	−7.05352			−0.301587			−0.150793	−	0.988565i	$-0.548183\pi$
$547$	−7.05352			−0.301587			−0.150793	+	0.988565i	$0.548183\pi$
$548$	6.99406	+	6.99406i	0.298771	+	0.298771i
$549$	17.5140	+	0.585718i	0.747477	+	0.0249978i
$550$		−	2.40297i		−	0.102463i
$551$	43.1792	+	43.1792i	1.83949	+	1.83949i
$552$	−2.20117	+	2.12879i	−0.0936881	+	0.0906073i
$553$	9.59102	+	9.59102i	0.407852	+	0.407852i
$554$	−1.24338	+	1.24338i	−0.0528262	+	0.0528262i
$555$	0.168137	−	10.0580i	0.00713701	−	0.426937i
$556$		−	7.57200i		−	0.321125i
$557$	−7.62592	+	7.62592i	−0.323121	+	0.323121i	−0.849963	−	0.526842i	$-0.823376\pi$
$557$	−7.62592	+	7.62592i	−0.323121	+	0.323121i	0.526842	+	0.849963i	$0.323376\pi$
$558$	−3.63662	−	0.121619i	−0.153951	−	0.00514856i
$559$	−10.7317	+	11.7308i	−0.453903	+	0.496158i
$560$			5.73943i			0.242535i
$561$	0.853667	−	0.825595i	0.0360418	−	0.0348567i
$562$	14.8611			0.626879
$563$	34.9632			1.47352			0.736761	−	0.676153i	$-0.236354\pi$
$563$	34.9632			1.47352			0.736761	+	0.676153i	$0.236354\pi$
$564$	−9.61162	−	9.93843i	−0.404722	−	0.418483i
$565$	10.7464	−	10.7464i	0.452106	−	0.452106i
$566$	5.29037	−	5.29037i	0.222371	−	0.222371i
$567$	−10.2366	−	11.7059i	−0.429899	−	0.491603i
$568$	26.4487			1.10976
$569$	20.6038			0.863755			0.431877	−	0.901932i	$-0.357851\pi$
$569$	20.6038			0.863755			0.431877	+	0.901932i	$0.357851\pi$
$570$	−22.5690	−	23.3364i	−0.945312	−	0.977454i
$571$		−	11.8056i		−	0.494049i	−0.969009	−	0.247025i	$-0.920547\pi$
$571$		−	11.8056i		−	0.494049i	0.969009	−	0.247025i	$-0.0794529\pi$
$572$	0.151007	+	3.39520i	0.00631394	+	0.141960i
$573$	0.187463	−	11.2140i	0.00783137	−	0.468473i
$574$	2.25267	−	2.25267i	0.0940244	−	0.0940244i
$575$			1.36535i			0.0569391i
$576$	0.739912	−	22.1246i	0.0308297	−	0.921859i
$577$	−27.8072	+	27.8072i	−1.15763	+	1.15763i	−0.172643	+	0.984984i	$0.555231\pi$
$577$	−27.8072	+	27.8072i	−1.15763	+	1.15763i	−0.984984	+	0.172643i	$0.944769\pi$
$578$	12.0192	+	12.0192i	0.499934	+	0.499934i
$579$	12.7151	+	13.1474i	0.528421	+	0.546388i
$580$	16.3824	+	16.3824i	0.680243	+	0.680243i
$581$		−	18.1581i		−	0.753323i
$582$	−33.3286	−	0.557148i	−1.38152	−	0.0230945i
$583$	5.53692	+	5.53692i	0.229316	+	0.229316i
$584$	−0.0979859			−0.00405468
$585$	0.322776	+	29.2968i	0.0133451	+	1.21128i
$586$	14.2347			0.588030
$587$	19.8062	+	19.8062i	0.817491	+	0.817491i	0.985744	−	0.168253i	$-0.0538126\pi$
$587$	19.8062	+	19.8062i	0.817491	+	0.817491i	−0.168253	+	0.985744i	$0.553813\pi$
$588$	−6.55337	−	0.109551i	−0.270256	−	0.00451782i
$589$			7.93726i			0.327049i
$590$	7.69607	+	7.69607i	0.316842	+	0.316842i
$591$	−26.4313	−	27.3300i	−1.08724	−	1.12421i
$592$	1.85932	+	1.85932i	0.0764175	+	0.0764175i
$593$	25.6794	−	25.6794i	1.05453	−	1.05453i	0.0561035	−	0.998425i	$-0.482132\pi$
$593$	25.6794	−	25.6794i	1.05453	−	1.05453i	0.998425	−	0.0561035i	$-0.0178677\pi$
$594$	−5.33651	−	0.267828i	−0.218960	−	0.0109891i
$595$			3.20892i			0.131553i
$596$	−0.672512	+	0.672512i	−0.0275472	+	0.0275472i
$597$	0.785978	−	47.0173i	0.0321679	−	1.92429i
$598$	0.0962532	+	2.16412i	0.00393609	+	0.0884976i
$599$			14.6311i			0.597811i	0.954283	+	0.298906i	$0.0966215\pi$
$599$			14.6311i			0.597811i	−0.954283	+	0.298906i	$0.903378\pi$
$600$	−8.51416	−	8.80366i	−0.347589	−	0.359408i
$601$	24.8110			1.01206			0.506031	−	0.862515i	$-0.331112\pi$
$601$	24.8110			1.01206			0.506031	+	0.862515i	$0.331112\pi$
$602$	7.83472			0.319319
$603$	−11.7536	+	10.9929i	−0.478645	+	0.447666i
$604$	−0.505971	+	0.505971i	−0.0205877	+	0.0205877i
$605$	−1.91531	+	1.91531i	−0.0778684	+	0.0778684i
$606$	−9.03959	−	9.34695i	−0.367208	−	0.379694i
$607$	−8.90410			−0.361406			−0.180703	−	0.983538i	$-0.557837\pi$
$607$	−8.90410			−0.361406			−0.180703	+	0.983538i	$0.557837\pi$
$608$	−32.2383			−1.30743
$609$	−19.5210	+	18.8791i	−0.791032	+	0.765020i
$610$			16.2698i			0.658744i
$611$	−30.5037	+	1.35671i	−1.23405	+	0.0548865i
$612$	0.0648051	−	1.93778i	0.00261959	−	0.0783301i
$613$	10.1007	−	10.1007i	0.407964	−	0.407964i	−0.473064	−	0.881028i	$-0.656852\pi$
$613$	10.1007	−	10.1007i	0.407964	−	0.407964i	0.881028	+	0.473064i	$0.156852\pi$
$614$		−	20.3562i		−	0.821508i
$615$	−0.140603	+	8.41090i	−0.00566967	+	0.339160i
$616$	3.69690	−	3.69690i	0.148952	−	0.148952i
$617$	5.81382	+	5.81382i	0.234056	+	0.234056i	0.814383	−	0.580328i	$-0.197075\pi$
$617$	5.81382	+	5.81382i	0.234056	+	0.234056i	−0.580328	+	0.814383i	$0.697075\pi$
$618$	−3.44272	+	3.32951i	−0.138486	+	0.133932i
$619$	8.83244	+	8.83244i	0.355006	+	0.355006i	0.861968	−	0.506962i	$-0.169232\pi$
$619$	8.83244	+	8.83244i	0.355006	+	0.355006i	−0.506962	+	0.861968i	$0.669232\pi$
$620$			3.01144i			0.120942i
$621$	3.03217	+	0.152178i	0.121677	+	0.00610669i
$622$	−21.2902	−	21.2902i	−0.853660	−	0.853660i
$623$	−27.0781			−1.08486
$624$	−5.56348	−	5.26315i	−0.222717	−	0.210695i
$625$	31.2234			1.24894
$626$	3.25140	+	3.25140i	0.129952	+	0.129952i
$627$	−0.194817	+	11.6539i	−0.00778023	+	0.465414i
$628$			7.90069i			0.315272i
$629$	1.03955	+	1.03955i	0.0414495	+	0.0414495i
$630$	10.5445	−	9.86208i	0.420105	−	0.392915i
$631$	18.1091	+	18.1091i	0.720913	+	0.720913i	0.968791	−	0.247878i	$-0.0797333\pi$
$631$	18.1091	+	18.1091i	0.720913	+	0.720913i	−0.247878	+	0.968791i	$0.579733\pi$
$632$	16.7963	−	16.7963i	0.668123	−	0.668123i
$633$	14.5933	+	0.243953i	0.580031	+	0.00969626i
$634$		−	22.6826i		−	0.900840i
$635$	18.9203	−	18.9203i	0.750831	−	0.750831i
$636$	12.7822	+	0.213677i	0.506847	+	0.00847286i
$637$	−9.77036	+	10.6799i	−0.387116	+	0.423154i
$638$			9.33122i			0.369426i
$639$	−17.9120	−	19.1515i	−0.708586	−	0.757620i
$640$	−5.39984			−0.213447
$641$	0.285956			0.0112946			0.00564729	−	0.999984i	$-0.498202\pi$
$641$	0.285956			0.0112946			0.00564729	+	0.999984i	$0.498202\pi$
$642$	11.8368	−	11.4476i	0.467161	−	0.451799i
$643$	26.4640	−	26.4640i	1.04364	−	1.04364i	0.0446337	−	0.999003i	$-0.485788\pi$
$643$	26.4640	−	26.4640i	1.04364	−	1.04364i	0.999003	−	0.0446337i	$-0.0142121\pi$
$644$	−0.672863	+	0.672863i	−0.0265145	+	0.0265145i
$645$	−14.8710	+	14.3819i	−0.585543	+	0.566289i
$646$	4.74459			0.186673
$647$	−27.0120			−1.06195			−0.530976	−	0.847387i	$-0.678175\pi$
$647$	−27.0120			−1.06195			−0.530976	+	0.847387i	$0.678175\pi$
$648$	−20.5001	+	17.9270i	−0.805320	+	0.704239i
$649$		−	3.90758i		−	0.153386i
$650$	−8.65548	+	0.384968i	−0.339496	+	0.0150997i
$651$	−3.52939	−	0.0590001i	−0.138328	−	0.00231240i
$652$	10.4559	−	10.4559i	0.409483	−	0.409483i
$653$		−	2.67027i		−	0.104496i	−0.998634	−	0.0522478i	$-0.983361\pi$
$653$		−	2.67027i		−	0.104496i	0.998634	−	0.0522478i	$-0.0166386\pi$
$654$	−27.8434	−	0.465452i	−1.08876	−	0.0182006i
$655$	35.7380	−	35.7380i	1.39640	−	1.39640i
$656$	−1.55484	−	1.55484i	−0.0607064	−	0.0607064i
$657$	0.0663595	+	0.0709516i	0.00258893	+	0.00276808i
$658$	10.6394	+	10.6394i	0.414769	+	0.414769i
$659$		−	29.6624i		−	1.15548i	−0.816220	−	0.577741i	$-0.803934\pi$
$659$		−	29.6624i		−	1.15548i	0.816220	−	0.577741i	$-0.196066\pi$
$660$	−0.0739145	+	4.42157i	−0.00287712	+	0.172109i
$661$	−16.2307	−	16.2307i	−0.631302	−	0.631302i	0.317093	−	0.948395i	$-0.397293\pi$
$661$	−16.2307	−	16.2307i	−0.631302	−	0.631302i	−0.948395	+	0.317093i	$0.897293\pi$
$662$	−5.70685			−0.221803
$663$	−3.11055	−	2.94264i	−0.120804	−	0.114283i
$664$	−31.7994			−1.23406
$665$	−22.2697	−	22.2697i	−0.863581	−	0.863581i
$666$	0.221086	−	6.61083i	0.00856690	−	0.256165i
$667$		−	5.30193i		−	0.205292i
$668$	−13.7195	−	13.7195i	−0.530822	−	0.530822i
$669$	−14.3088	+	13.8382i	−0.553209	+	0.535017i
$670$	−10.5653	−	10.5653i	−0.408174	−	0.408174i
$671$	4.13039	−	4.13039i	0.159452	−	0.159452i
$672$	0.239637	−	14.3351i	0.00924419	−	0.552988i
$673$		−	41.9656i		−	1.61765i	−0.588047	−	0.808827i	$-0.700103\pi$
$673$		−	41.9656i		−	1.61765i	0.588047	−	0.808827i	$-0.299897\pi$
$674$	4.84783	−	4.84783i	0.186732	−	0.186732i
$675$	−0.608640	+	12.1273i	−0.0234266	+	0.466778i
$676$	12.2053	−	1.08785i	0.469434	−	0.0418406i
$677$			9.22634i			0.354597i	0.984157	+	0.177299i	$0.0567358\pi$
$677$			9.22634i			0.354597i	−0.984157	+	0.177299i	$0.943264\pi$
$678$	7.18343	−	6.94721i	0.275878	−	0.266806i
$679$	−32.3368			−1.24097
$680$	5.61965			0.215504
$681$	−13.5829	−	14.0448i	−0.520499	−	0.538197i
$682$	−0.857639	+	0.857639i	−0.0328407	+	0.0328407i
$683$	−18.4406	+	18.4406i	−0.705608	+	0.705608i	−0.965609	−	0.260000i	$-0.916277\pi$
$683$	−18.4406	+	18.4406i	−0.705608	+	0.705608i	0.260000	+	0.965609i	$0.416277\pi$
$684$	12.9983	+	13.8978i	0.497002	+	0.531395i
$685$	28.4234			1.08600
$686$	19.5701			0.747188
$687$	20.7674	+	21.4735i	0.792326	+	0.819266i
$688$		−	5.40770i		−	0.206167i
$689$	19.0569	−	20.8310i	0.726009	−	0.793596i
$690$	−0.0471137	+	2.81834i	−0.00179359	+	0.107292i
$691$	−8.75732	+	8.75732i	−0.333144	+	0.333144i	−0.853779	−	0.520635i	$-0.825695\pi$
$691$	−8.75732	+	8.75732i	−0.333144	+	0.333144i	0.520635	+	0.853779i	$0.325695\pi$
$692$			0.202575i			0.00770075i
$693$	−5.18060	−	0.173255i	−0.196795	−	0.00658140i
$694$	−23.0034	+	23.0034i	−0.873198	+	0.873198i
$695$	−15.3861	−	15.3861i	−0.583627	−	0.583627i
$696$	33.0622	+	34.1864i	1.25322	+	1.29583i
$697$	−0.869314	−	0.869314i	−0.0329276	−	0.0329276i
$698$			28.7708i			1.08899i
$699$	−37.4441	−	0.625946i	−1.41627	−	0.0236754i
$700$	−2.69114	−	2.69114i	−0.101715	−	0.101715i
$701$	−21.1184			−0.797633			−0.398816	−	0.917031i	$-0.630579\pi$
$701$	−21.1184			−0.797633			−0.398816	+	0.917031i	$0.630579\pi$
$702$	−0.109778	+	19.2650i	−0.00414330	+	0.727109i
$703$	−14.4287			−0.544191
$704$	−5.21773	−	5.21773i	−0.196651	−	0.196651i
$705$	−39.7251	−	0.664076i	−1.49613	−	0.0250105i
$706$			3.02364i			0.113796i
$707$	−8.91969	−	8.91969i	−0.335459	−	0.335459i
$708$	−4.43500	−	4.58580i	−0.166678	−	0.172345i
$709$	−9.59182	−	9.59182i	−0.360228	−	0.360228i	0.503669	−	0.863897i	$-0.331983\pi$
$709$	−9.59182	−	9.59182i	−0.360228	−	0.360228i	−0.863897	+	0.503669i	$0.831983\pi$
$710$	17.2152	−	17.2152i	0.646076	−	0.646076i
$711$	−23.5373	−	0.787157i	−0.882718	−	0.0295207i
$712$			47.4208i			1.77717i
$713$	0.487305	−	0.487305i	0.0182497	−	0.0182497i
$714$	−0.0352679	+	2.10973i	−0.00131987	+	0.0789547i
$715$	7.20577	+	6.59209i	0.269481	+	0.246530i
$716$			16.8995i			0.631563i
$717$	−7.12404	−	7.36627i	−0.266052	−	0.275098i
$718$	4.21082			0.157146
$719$	−21.7294			−0.810369			−0.405184	−	0.914235i	$-0.632793\pi$
$719$	−21.7294			−0.810369			−0.405184	+	0.914235i	$0.632793\pi$
$720$	−6.80704	−	7.27809i	−0.253683	−	0.271238i
$721$	−3.28535	+	3.28535i	−0.122353	+	0.122353i
$722$	−19.1117	+	19.1117i	−0.711265	+	0.711265i
$723$	−34.1174	−	35.2775i	−1.26884	−	1.31198i
$724$	21.5607			0.801297
$725$	21.2052			0.787543
$726$	−1.28029	+	1.23818i	−0.0475158	+	0.0459533i
$727$			11.4506i			0.424678i	0.977196	+	0.212339i	$0.0681082\pi$
$727$			11.4506i			0.424678i	−0.977196	+	0.212339i	$0.931892\pi$
$728$	−13.9085	−	12.7239i	−0.515482	−	0.471581i
$729$	26.8643	+	2.70333i	0.994975	+	0.100123i
$730$	−0.0637783	+	0.0637783i	−0.00236054	+	0.00236054i
$731$		−	3.02345i		−	0.111826i
$732$	0.159397	−	9.53517i	0.00589150	−	0.352430i
$733$	−19.5460	+	19.5460i	−0.721946	+	0.721946i	−0.969001	−	0.247055i	$-0.920537\pi$
$733$	−19.5460	+	19.5460i	−0.721946	+	0.721946i	0.247055	+	0.969001i	$0.420537\pi$
$734$	9.54389	+	9.54389i	0.352271	+	0.352271i
$735$	−13.5388	+	13.0936i	−0.499387	+	0.482965i
$736$	1.97925	+	1.97925i	0.0729563	+	0.0729563i
$737$			5.36441i			0.197601i
$738$	−0.184881	+	5.52826i	−0.00680558	+	0.203498i
$739$	−8.15738	−	8.15738i	−0.300074	−	0.300074i	0.540969	−	0.841043i	$-0.318058\pi$
$739$	−8.15738	−	8.15738i	−0.300074	−	0.300074i	−0.841043	+	0.540969i	$0.818058\pi$
$740$	−5.47435			−0.201241
$741$	42.0086	−	1.16529i	1.54322	−	0.0428080i
$742$	−13.9125			−0.510745
$743$	16.5927	+	16.5927i	0.608726	+	0.608726i	0.942613	−	0.333887i	$-0.108360\pi$
$743$	16.5927	+	16.5927i	0.608726	+	0.608726i	−0.333887	+	0.942613i	$0.608360\pi$
$744$	−0.103324	+	6.18087i	−0.00378805	+	0.226602i
$745$			2.73304i			0.100131i
$746$	−11.2895	−	11.2895i	−0.413336	−	0.413336i
$747$	21.5357	+	23.0260i	0.787950	+	0.842476i
$748$	−0.456995	−	0.456995i	−0.0167094	−	0.0167094i
$749$	11.2957	−	11.2957i	0.412737	−	0.412737i
$750$	12.8462	+	0.214748i	0.469077	+	0.00784147i
$751$			5.91830i			0.215962i	0.994153	+	0.107981i	$0.0344386\pi$
$751$			5.91830i			0.215962i	−0.994153	+	0.107981i	$0.965561\pi$
$752$	7.34359	−	7.34359i	0.267793	−	0.267793i
$753$	29.8430	+	0.498879i	1.08754	+	0.0181802i
$754$	33.6109	−	1.49491i	1.22404	−	0.0544413i
$755$			2.05623i			0.0748339i
$756$	−6.27642	+	5.67652i	−0.228271	+	0.206453i
$757$	27.3635			0.994542			0.497271	−	0.867595i	$-0.334336\pi$
$757$	27.3635			0.994542			0.497271	+	0.867595i	$0.334336\pi$
$758$	−5.28362			−0.191910
$759$	0.727449	−	0.703528i	0.0264047	−	0.0255364i
$760$	−38.9999	+	38.9999i	−1.41468	+	1.41468i
$761$	26.9789	−	26.9789i	0.977985	−	0.977985i	−0.0217776	−	0.999763i	$-0.506933\pi$
$761$	26.9789	−	26.9789i	0.977985	−	0.977985i	0.999763	+	0.0217776i	$0.00693257\pi$
$762$	12.6473	−	12.2314i	0.458162	−	0.443096i
$763$	−27.0148			−0.978001
$764$	−6.10358			−0.220820
$765$	−3.80582	−	4.06919i	−0.137600	−	0.147122i
$766$		−	26.3207i		−	0.951007i
$767$	−14.0751	+	0.626013i	−0.508221	+	0.0226040i
$768$	−29.1082	−	0.486595i	−1.05035	−	0.0175585i
$769$	−4.99745	+	4.99745i	−0.180213	+	0.180213i	−0.791449	−	0.611236i	$-0.790673\pi$
$769$	−4.99745	+	4.99745i	−0.180213	+	0.180213i	0.611236	+	0.791449i	$0.290673\pi$
$770$		−	4.81258i		−	0.173433i
$771$	−45.6706	−	0.763467i	−1.64479	−	0.0274956i
$772$	7.03823	−	7.03823i	0.253311	−	0.253311i
$773$	35.3707	+	35.3707i	1.27219	+	1.27219i	0.944934	+	0.327260i	$0.106125\pi$
$773$	35.3707	+	35.3707i	1.27219	+	1.27219i	0.327260	+	0.944934i	$0.393875\pi$
$774$	−9.93509	+	9.29207i	−0.357109	+	0.333997i
$775$	1.94899	+	1.94899i	0.0700098	+	0.0700098i
$776$			56.6300i			2.03290i
$777$	0.107253	−	6.41590i	0.00384769	−	0.230169i
$778$	−12.0701	−	12.0701i	−0.432733	−	0.432733i
$779$	12.0659			0.432307
$780$	15.9383	−	0.442118i	0.570683	−	0.0158304i
$781$	−8.74082			−0.312771
$782$	−0.291292	−	0.291292i	−0.0104166	−	0.0104166i
$783$	2.36347	−	47.0925i	0.0844636	−	1.68295i
$784$		−	4.92328i		−	0.175832i
$785$	16.0539	+	16.0539i	0.572989	+	0.572989i
$786$	23.8890	−	23.1034i	0.852092	−	0.824072i
$787$	10.2861	+	10.2861i	0.366660	+	0.366660i	0.866258	−	0.499598i	$-0.166519\pi$
$787$	10.2861	+	10.2861i	0.366660	+	0.366660i	−0.499598	+	0.866258i	$0.666519\pi$
$788$	−14.6306	+	14.6306i	−0.521194	+	0.521194i
$789$	−0.480365	+	28.7355i	−0.0171015	+	1.02301i
$790$		−	21.8652i		−	0.777931i
$791$	6.85507	−	6.85507i	0.243738	−	0.243738i
$792$	−0.303413	+	9.07256i	−0.0107813	+	0.322380i
$793$	−15.5393	−	14.2159i	−0.551818	−	0.504822i
$794$		−	20.9044i		−	0.741868i
$795$	26.4072	−	25.5388i	0.936566	−	0.905768i
$796$	−25.5906			−0.907034
$797$	12.7719			0.452405			0.226202	−	0.974080i	$-0.427369\pi$
$797$	12.7719			0.452405			0.226202	+	0.974080i	$0.427369\pi$
$798$	−14.3966	−	14.8861i	−0.509634	−	0.526963i
$799$	4.10581	−	4.10581i	0.145253	−	0.145253i
$800$	−7.91609	+	7.91609i	−0.279876	+	0.279876i
$801$	34.3374	−	32.1150i	1.21325	−	1.13473i
$802$	−5.13789			−0.181425
$803$	0.0323826			0.00114276
$804$	6.08847	+	6.29549i	0.214724	+	0.222025i
$805$			2.73447i			0.0963775i
$806$	3.22661	+	2.95181i	0.113652	+	0.103973i
$807$	0.695578	−	41.6095i	0.0244855	−	1.46473i
$808$	−15.6207	+	15.6207i	−0.549533	+	0.549533i
$809$			8.40724i			0.295583i	0.989019	+	0.147791i	$0.0472164\pi$
$809$			8.40724i			0.295583i	−0.989019	+	0.147791i	$0.952784\pi$
$810$	−1.67482	+	25.0119i	−0.0588471	+	0.878829i
$811$	−20.9038	+	20.9038i	−0.734031	+	0.734031i	−0.971416	−	0.237385i	$-0.923710\pi$
$811$	−20.9038	+	20.9038i	−0.734031	+	0.734031i	0.237385	+	0.971416i	$0.423710\pi$
$812$	10.4502	+	10.4502i	0.366731	+	0.366731i
$813$	7.25911	+	7.50593i	0.254588	+	0.263245i
$814$	−1.55906	−	1.55906i	−0.0546450	−	0.0546450i
$815$		−	42.4920i		−	1.48843i
$816$	1.45618	+	0.0243428i	0.0509767	+	0.000852167i
$817$	20.9825	+	20.9825i	0.734086	+	0.734086i
$818$	−29.1283			−1.01845
$819$	0.205896	+	18.6882i	0.00719460	+	0.653020i
$820$	4.57789			0.159867
$821$	2.67158	+	2.67158i	0.0932389	+	0.0932389i	0.752188	−	0.658949i	$-0.228999\pi$
$821$	2.67158	+	2.67158i	0.0932389	+	0.0932389i	−0.658949	+	0.752188i	$0.728999\pi$
$822$	18.6872	+	0.312390i	0.651790	+	0.0108958i
$823$			25.1518i			0.876735i	0.898796	+	0.438367i	$0.144443\pi$
$823$			25.1518i			0.876735i	−0.898796	+	0.438367i	$0.855557\pi$
$824$	5.75349	+	5.75349i	0.200432	+	0.200432i
$825$	2.81378	+	2.90946i	0.0979633	+	0.101294i
$826$	4.90926	+	4.90926i	0.170815	+	0.170815i
$827$	21.6744	−	21.6744i	0.753693	−	0.753693i	−0.221474	−	0.975166i	$-0.571087\pi$
$827$	21.6744	−	21.6744i	0.753693	−	0.753693i	0.975166	+	0.221474i	$0.0710867\pi$
$828$	0.0552234	−	1.65127i	0.00191915	−	0.0573857i
$829$			27.1668i			0.943541i	0.881721	+	0.471770i	$0.156385\pi$
$829$			27.1668i			0.943541i	−0.881721	+	0.471770i	$0.843615\pi$
$830$	−20.6980	+	20.6980i	−0.718439	+	0.718439i
$831$	0.0495052	−	2.96140i	0.00171732	−	0.102730i
$832$	−17.9583	+	19.6301i	−0.622593	+	0.680553i
$833$		−	2.75261i		−	0.0953724i
$834$	−9.94658	−	10.2848i	−0.344422	−	0.356133i
$835$	−55.7550			−1.92948
$836$	6.34301			0.219378
$837$	4.54554	−	4.11108i	0.157117	−	0.142100i
$838$	25.1586	−	25.1586i	0.869090	−	0.869090i
$839$	11.4698	−	11.4698i	0.395981	−	0.395981i	−0.480832	−	0.876813i	$-0.659665\pi$
$839$	11.4698	−	11.4698i	0.395981	−	0.395981i	0.876813	+	0.480832i	$0.159665\pi$
$840$	−17.0518	−	17.6316i	−0.588344	−	0.608349i
$841$	−53.3442			−1.83945
$842$	34.4562			1.18744
$843$	−17.9935	+	17.4018i	−0.619728	+	0.599349i
$844$		−	7.94284i		−	0.273404i
$845$	22.5902	−	27.0112i	0.777128	−	0.929214i
$846$	−26.1102	−	0.873203i	−0.897688	−	0.0300213i
$847$	−1.22176	+	1.22176i	−0.0419802	+	0.0419802i
$848$			9.60276i			0.329760i
$849$	−0.210636	+	12.6003i	−0.00722900	+	0.432439i
$850$	1.16503	−	1.16503i	0.0399602	−	0.0399602i
$851$	0.885847	+	0.885847i	0.0303664	+	0.0303664i
$852$	−10.2579	+	9.92061i	−0.351431	+	0.339874i
$853$	−14.5399	−	14.5399i	−0.497836	−	0.497836i	0.412928	−	0.910764i	$-0.364506\pi$
$853$	−14.5399	−	14.5399i	−0.497836	−	0.497836i	−0.910764	+	0.412928i	$0.864506\pi$
$854$			10.3784i			0.355140i
$855$	54.6519	+	1.82772i	1.86906	+	0.0625068i
$856$	−19.7817	−	19.7817i	−0.676125	−	0.676125i
$857$	−6.90315			−0.235807			−0.117904	−	0.993025i	$-0.537617\pi$
$857$	−6.90315			−0.235807			−0.117904	+	0.993025i	$0.537617\pi$
$858$	4.66504	+	4.41321i	0.159262	+	0.150665i
$859$	−17.2360			−0.588083			−0.294042	−	0.955793i	$-0.595000\pi$
$859$	−17.2360			−0.588083			−0.294042	+	0.955793i	$0.595000\pi$
$860$	7.96089	+	7.96089i	0.271464	+	0.271464i
$861$	−0.0896898	+	5.36525i	−0.00305662	+	0.182847i
$862$		−	27.2428i		−	0.927894i
$863$	7.71634	+	7.71634i	0.262667	+	0.262667i	0.826137	−	0.563470i	$-0.190534\pi$
$863$	7.71634	+	7.71634i	0.262667	+	0.262667i	−0.563470	+	0.826137i	$0.690534\pi$
$864$	16.6977	+	18.4623i	0.568068	+	0.628101i
$865$	0.411626	+	0.411626i	0.0139957	+	0.0139957i
$866$	0.591897	−	0.591897i	0.0201135	−	0.0201135i
$867$	−28.6266	−	0.478545i	−0.972210	−	0.0162522i
$868$			1.92098i			0.0652022i
$869$	−5.55090	+	5.55090i	−0.188301	+	0.188301i
$870$	43.7716	+	0.731721i	1.48400	+	0.0248077i
$871$	19.3226	−	0.859405i	0.654720	−	0.0291198i
$872$			47.3099i			1.60211i
$873$	41.0058	−	38.3519i	1.38784	−	1.29801i
$874$	4.04308			0.136759
$875$	12.4639			0.421358
$876$	0.0380031	−	0.0367534i	0.00128401	−	0.00124178i
$877$	−21.1702	+	21.1702i	−0.714868	+	0.714868i	−0.967549	−	0.252682i	$-0.918687\pi$
$877$	−21.1702	+	21.1702i	−0.714868	+	0.714868i	0.252682	+	0.967549i	$0.418687\pi$
$878$	5.32359	−	5.32359i	0.179663	−	0.179663i
$879$	−17.2350	+	16.6683i	−0.581322	+	0.562206i
$880$	−3.32175			−0.111976
$881$	47.4750			1.59947			0.799737	−	0.600351i	$-0.204972\pi$
$881$	47.4750			1.59947			0.799737	+	0.600351i	$0.204972\pi$
$882$	−9.04511	+	8.45969i	−0.304565	+	0.284853i
$883$		−	27.0499i		−	0.910301i	−0.890414	−	0.455151i	$-0.849585\pi$
$883$		−	27.0499i		−	0.910301i	0.890414	−	0.455151i	$-0.150415\pi$
$884$	−1.57288	+	1.71930i	−0.0529016	+	0.0578264i
$885$	−18.3300	−	0.306419i	−0.616155	−	0.0103001i
$886$	27.1976	−	27.1976i	0.913721	−	0.913721i
$887$		−	30.6604i		−	1.02948i	−0.857348	−	0.514738i	$-0.827889\pi$
$887$		−	30.6604i		−	1.02948i	0.857348	−	0.514738i	$-0.172111\pi$
$888$	−11.2359	−	0.187828i	−0.377052	−	0.00630310i
$889$	12.0691	−	12.0691i	0.404786	−	0.404786i
$890$	30.8658	+	30.8658i	1.03463	+	1.03463i
$891$	6.77493	−	5.92456i	0.226969	−	0.198480i
$892$	7.65993	+	7.65993i	0.256473	+	0.256473i
$893$			56.9880i			1.90703i
$894$	−0.0300378	+	1.79686i	−0.00100461	+	0.0600960i
$895$	34.3392	+	34.3392i	1.14783	+	1.14783i
$896$	−3.44452			−0.115073
$897$	−2.65064	−	2.50756i	−0.0885023	−	0.0837249i
$898$	17.4828			0.583408
$899$	−7.56832	−	7.56832i	−0.252417	−	0.252417i
$900$	6.60432	+	0.220868i	0.220144	+	0.00736226i
$901$			5.36891i			0.178864i
$902$	1.30375	+	1.30375i	0.0434102	+	0.0434102i
$903$	−9.48607	+	9.17413i	−0.315677	+	0.305296i
$904$	−12.0050	−	12.0050i	−0.399280	−	0.399280i
$905$	43.8106	−	43.8106i	1.45631	−	1.45631i
$906$	−0.0225992	+	1.35188i	−0.000750808	+	0.0449134i
$907$		−	46.5127i		−	1.54443i	−0.635362	−	0.772215i	$-0.719149\pi$
$907$		−	46.5127i		−	1.54443i	0.635362	−	0.772215i	$-0.280851\pi$
$908$	−7.51860	+	7.51860i	−0.249514	+	0.249514i
$909$	21.8898	+	0.732059i	0.726039	+	0.0242809i
$910$	−17.3349	+	0.770998i	−0.574645	+	0.0255583i
$911$		−	30.0304i		−	0.994950i	−0.867478	−	0.497475i	$-0.834261\pi$
$911$		−	30.0304i		−	0.994950i	0.867478	−	0.497475i	$-0.165739\pi$
$912$	−10.2747	+	9.93687i	−0.340231	+	0.329043i
$913$	10.5092			0.347802
$914$	−9.59990			−0.317536
$915$	−19.0513	−	19.6990i	−0.629815	−	0.651230i
$916$	11.4955	−	11.4955i	0.379820	−	0.379820i
$917$	22.7970	−	22.7970i	0.752823	−	0.752823i
$918$	−2.45744	−	2.71715i	−0.0811077	−	0.0896792i
$919$	34.3152			1.13195			0.565976	−	0.824422i	$-0.308499\pi$
$919$	34.3152			1.13195			0.565976	+	0.824422i	$0.308499\pi$
$920$	4.78876			0.157881
$921$	23.8362	+	24.6467i	0.785431	+	0.812137i
$922$			26.8362i			0.883803i
$923$	1.40032	+	31.4843i	0.0460921	+	1.03632i
$924$	−0.0471495	+	2.82049i	−0.00155111	+	0.0927872i
$925$	−3.54297	+	3.54297i	−0.116492	+	0.116492i
$926$			23.3916i			0.768697i
$927$	0.269636	−	8.06256i	0.00885601	−	0.264809i
$928$	30.7398	−	30.7398i	1.00908	−	1.00908i
$929$	3.31771	+	3.31771i	0.108851	+	0.108851i	0.759434	−	0.650584i	$-0.225476\pi$
$929$	3.31771	+	3.31771i	0.108851	+	0.108851i	−0.650584	+	0.759434i	$0.725476\pi$
$930$	3.95583	+	4.09033i	0.129717	+	0.134127i
$931$	19.1029	+	19.1029i	0.626073	+	0.626073i
$932$			20.3801i			0.667572i
$933$	50.7077	+	0.847670i	1.66009	+	0.0277515i
$934$	1.88156	+	1.88156i	0.0615666	+	0.0615666i
$935$	−1.85720			−0.0607368
$936$	32.7279	−	0.360577i	1.06974	−	0.0117858i
$937$	37.4029			1.22190			0.610950	−	0.791669i	$-0.290788\pi$
$937$	37.4029			1.22190			0.610950	+	0.791669i	$0.290788\pi$
$938$	−6.73954	−	6.73954i	−0.220054	−	0.220054i
$939$	−7.74396	−	0.129454i	−0.252715	−	0.00422458i
$940$			21.6216i			0.705218i
$941$	−30.8012	−	30.8012i	−1.00409	−	1.00409i	−0.999992	−	0.00409963i	$-0.998695\pi$
$941$	−30.8012	−	30.8012i	−1.00409	−	1.00409i	−0.00409963	−	0.999992i	$-0.501305\pi$
$942$	10.3783	+	10.7312i	0.338144	+	0.349642i
$943$	−0.740783	−	0.740783i	−0.0241232	−	0.0241232i
$944$	3.38849	−	3.38849i	0.110286	−	0.110286i
$945$	−1.21896	+	24.2880i	−0.0396528	+	0.790088i
$946$			4.53442i			0.147427i
$947$	12.2407	−	12.2407i	0.397769	−	0.397769i	−0.479676	−	0.877446i	$-0.659246\pi$
$947$	12.2407	−	12.2407i	0.397769	−	0.397769i	0.877446	+	0.479676i	$0.159246\pi$
$948$	−0.214217	+	12.8145i	−0.00695745	+	0.416195i
$949$	−0.00518785	−	0.116642i	−0.000168405	−	0.00378635i
$950$			16.1704i			0.524638i
$951$	26.5604	+	27.4635i	0.861278	+	0.890564i
$952$	3.58473			0.116182
$953$	−43.1228			−1.39688			−0.698442	−	0.715667i	$-0.746123\pi$
$953$	−43.1228			−1.39688			−0.698442	+	0.715667i	$0.746123\pi$
$954$	17.6423	−	16.5005i	0.571190	−	0.534222i
$955$	−12.4023	+	12.4023i	−0.401328	+	0.401328i
$956$	−3.94339	+	3.94339i	−0.127538	+	0.127538i
$957$	−10.9265	−	11.2980i	−0.353203	−	0.365212i
$958$	−38.7869			−1.25315
$959$	18.1311			0.585483
$960$	−24.8849	+	24.0666i	−0.803157	+	0.776746i
$961$			29.6088i			0.955122i
$962$	−5.36595	+	5.86548i	−0.173005	+	0.189111i
$963$	−0.927066	+	27.7208i	−0.0298743	+	0.893291i
$964$	−18.8851	+	18.8851i	−0.608250	+	0.608250i
$965$		−	28.6029i		−	0.920760i
$966$	−0.0300534	+	1.79780i	−0.000966954	+	0.0578432i
$967$	−5.30573	+	5.30573i	−0.170621	+	0.170621i	−0.787252	−	0.616631i	$-0.788497\pi$
$967$	−5.30573	+	5.30573i	−0.170621	+	0.170621i	0.616631	+	0.787252i	$0.288497\pi$
$968$	2.13962	+	2.13962i	0.0687700	+	0.0687700i
$969$	−5.74462	+	5.55572i	−0.184544	+	0.178475i
$970$	36.8601	+	36.8601i	1.18351	+	1.18351i
$971$			15.8717i			0.509349i	0.967027	+	0.254674i	$0.0819683\pi$
$971$			15.8717i			0.509349i	−0.967027	+	0.254674i	$0.918032\pi$
$972$	1.22660	−	14.6422i	0.0393432	−	0.469650i
$973$	−9.81465	−	9.81465i	−0.314643	−	0.314643i
$974$	16.3816			0.524901
$975$	10.0291	−	10.6013i	0.321187	−	0.339514i
$976$	7.16339			0.229295
$977$	−10.6376	−	10.6376i	−0.340326	−	0.340326i	0.516164	−	0.856490i	$-0.327360\pi$
$977$	−10.6376	−	10.6376i	−0.340326	−	0.340326i	−0.856490	+	0.516164i	$0.827360\pi$
$978$	0.467011	−	27.9366i	0.0149334	−	0.893315i
$979$		−	15.6717i		−	0.500871i
$980$	7.24776	+	7.24776i	0.231521	+	0.231521i
$981$	34.2571	−	32.0399i	1.09374	−	1.02296i
$982$	−20.3659	−	20.3659i	−0.649902	−	0.649902i
$983$	−14.2143	+	14.2143i	−0.453366	+	0.453366i	−0.896470	−	0.443104i	$-0.853877\pi$
$983$	−14.2143	+	14.2143i	−0.453366	+	0.453366i	0.443104	+	0.896470i	$0.353877\pi$
$984$	9.39593	+	0.157070i	0.299531	+	0.00500721i
$985$			59.4578i			1.89448i
$986$	−4.52404	+	4.52404i	−0.144075	+	0.144075i
$987$	−25.3403	−	0.423609i	−0.806591	−	0.0134836i
$988$	−1.01618	−	22.8475i	−0.0323290	−	0.726875i
$989$		−	2.57643i		−	0.0819256i
$990$	5.70778	+	6.10276i	0.181405	+	0.193958i
$991$	−33.5182			−1.06474			−0.532370	−	0.846512i	$-0.678699\pi$
$991$	−33.5182			−1.06474			−0.532370	+	0.846512i	$0.678699\pi$
$992$	5.65063			0.179408
$993$	6.90971	−	6.68249i	0.219273	−	0.212063i
$994$	10.9815	−	10.9815i	0.348311	−	0.348311i
$995$	−51.9992	+	51.9992i	−1.64848	+	1.64848i
$996$	12.3332	−	11.9276i	0.390792	−	0.377941i
$997$	26.8741			0.851112			0.425556	−	0.904932i	$-0.360079\pi$
$997$	26.8741			0.851112			0.425556	+	0.904932i	$0.360079\pi$
$998$	−27.7242			−0.877593
$999$	7.47333	+	8.26311i	0.236446	+	0.261433i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.j.a.122.17	✓	96
3.2	odd	2	inner	429.2.j.a.122.32	yes	96
13.8	odd	4	inner	429.2.j.a.320.32	yes	96
39.8	even	4	inner	429.2.j.a.320.17	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.j.a.122.17	✓	96	1.1	even	1	trivial
429.2.j.a.122.32	yes	96	3.2	odd	2	inner
429.2.j.a.320.17	yes	96	39.8	even	4	inner
429.2.j.a.320.32	yes	96	13.8	odd	4	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.727121 - 0.727121i) q^{2} +(1.73181 + 0.0289503i) q^{3} -0.942589i q^{4} +(-1.91531 - 1.91531i) q^{5} +(-1.23818 - 1.28029i) q^{6} +(-1.22176 - 1.22176i) q^{7} +(-2.13962 + 2.13962i) q^{8} +(2.99832 + 0.100273i) q^{9} +O(q^{10})\)	\(q+(-0.727121 - 0.727121i) q^{2} +(1.73181 + 0.0289503i) q^{3} -0.942589i q^{4} +(-1.91531 - 1.91531i) q^{5} +(-1.23818 - 1.28029i) q^{6} +(-1.22176 - 1.22176i) q^{7} +(-2.13962 + 2.13962i) q^{8} +(2.99832 + 0.100273i) q^{9} +2.78533i q^{10} +(0.707107 - 0.707107i) q^{11} +(0.0272883 - 1.63238i) q^{12} +(-2.66027 - 2.43371i) q^{13} +1.77674i q^{14} +(-3.26150 - 3.37240i) q^{15} +1.22635 q^{16} +0.685652 q^{17} +(-2.10723 - 2.25306i) q^{18} +(-4.75837 + 4.75837i) q^{19} +(-1.80535 + 1.80535i) q^{20} +(-2.08049 - 2.15123i) q^{21} -1.02830 q^{22} +0.584276 q^{23} +(-3.76735 + 3.64347i) q^{24} +2.33683i q^{25} +(0.164739 + 3.70394i) q^{26} +(5.18962 + 0.260456i) q^{27} +(-1.15162 + 1.15162i) q^{28} -9.07437i q^{29} +(-0.0806360 + 4.82365i) q^{30} +(0.834032 - 0.834032i) q^{31} +(3.38754 + 3.38754i) q^{32} +(1.24504 - 1.20410i) q^{33} +(-0.498552 - 0.498552i) q^{34} +4.68011i q^{35} +(0.0945161 - 2.82619i) q^{36} +(1.51615 + 1.51615i) q^{37} +6.91982 q^{38} +(-4.53663 - 4.29174i) q^{39} +8.19607 q^{40} +(-1.26787 - 1.26787i) q^{41} +(-0.0514371 + 3.07697i) q^{42} -4.40961i q^{43} +(-0.666511 - 0.666511i) q^{44} +(-5.55067 - 5.93477i) q^{45} +(-0.424839 - 0.424839i) q^{46} +(5.98819 - 5.98819i) q^{47} +(2.12380 + 0.0355031i) q^{48} -4.01460i q^{49} +(1.69916 - 1.69916i) q^{50} +(1.18742 + 0.0198498i) q^{51} +(-2.29399 + 2.50755i) q^{52} +7.83038i q^{53} +(-3.58410 - 3.96287i) q^{54} -2.70866 q^{55} +5.22821 q^{56} +(-8.37834 + 8.10283i) q^{57} +(-6.59817 + 6.59817i) q^{58} +(2.76308 - 2.76308i) q^{59} +(-3.17879 + 3.07426i) q^{60} +5.84125 q^{61} -1.21289 q^{62} +(-3.54073 - 3.78575i) q^{63} -7.37899i q^{64} +(0.433940 + 9.75656i) q^{65} +(-1.78083 - 0.0297697i) q^{66} +(-3.79321 + 3.79321i) q^{67} -0.646288i q^{68} +(1.01185 + 0.0169150i) q^{69} +(3.40300 - 3.40300i) q^{70} +(-6.18069 - 6.18069i) q^{71} +(-6.62982 + 6.20073i) q^{72} +(0.0228980 + 0.0228980i) q^{73} -2.20484i q^{74} +(-0.0676519 + 4.04694i) q^{75} +(4.48519 + 4.48519i) q^{76} -1.72783 q^{77} +(0.178067 + 6.41929i) q^{78} -7.85016 q^{79} +(-2.34883 - 2.34883i) q^{80} +(8.97989 + 0.601301i) q^{81} +1.84378i q^{82} +(7.43110 + 7.43110i) q^{83} +(-2.02773 + 1.96105i) q^{84} +(-1.31324 - 1.31324i) q^{85} +(-3.20632 + 3.20632i) q^{86} +(0.262706 - 15.7151i) q^{87} +3.02588i q^{88} +(11.0816 - 11.0816i) q^{89} +(-0.279292 + 8.35131i) q^{90} +(0.276807 + 6.22364i) q^{91} -0.550732i q^{92} +(1.46853 - 1.42024i) q^{93} -8.70828 q^{94} +18.2275 q^{95} +(5.76849 + 5.96464i) q^{96} +(13.2337 - 13.2337i) q^{97} +(-2.91910 + 2.91910i) q^{98} +(2.19104 - 2.04923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) \) 96 * q + 12 * q^6 - 16 * q^7	\( 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) \) 96 * q + 12 * q^6 - 16 * q^7 + 16 * q^13 - 16 * q^15 - 120 * q^16 - 28 * q^18 - 24 * q^19 + 24 * q^24 - 24 * q^27 + 56 * q^28 + 48 * q^31 - 16 * q^34 - 16 * q^37 + 80 * q^40 + 52 * q^42 + 4 * q^45 - 56 * q^46 + 28 * q^48 + 4 * q^54 + 4 * q^57 + 48 * q^58 + 4 * q^60 - 96 * q^61 - 36 * q^63 + 20 * q^66 - 16 * q^67 + 48 * q^70 - 16 * q^72 - 16 * q^73 - 88 * q^76 + 80 * q^78 + 16 * q^79 + 32 * q^81 + 52 * q^84 - 8 * q^85 - 48 * q^87 - 16 * q^91 - 36 * q^93 - 16 * q^94 - 108 * q^96 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more