LMFDB - Embedded newform 770.2.m.f.43.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(43,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("770.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.m (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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.13
Character	$\chi$	$=$	770.43
Dual form			770.2.m.f.197.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.888243 - 0.888243i) q^{3} +1.00000i q^{4} +(1.38828 + 1.75290i) q^{5} -1.25616i q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.42205i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.888243 - 0.888243i) q^{3} +1.00000i q^{4} +(1.38828 + 1.75290i) q^{5} -1.25616i q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.42205i q^{9} +(-0.257823 + 2.22115i) q^{10} +(2.56981 - 2.09669i) q^{11} +(0.888243 - 0.888243i) q^{12} +(1.35377 - 1.35377i) q^{13} +1.00000i q^{14} +(0.323868 - 2.79014i) q^{15} -1.00000 q^{16} +(2.87993 + 2.87993i) q^{17} +(1.00554 - 1.00554i) q^{18} -1.47952 q^{19} +(-1.75290 + 1.38828i) q^{20} -1.25616i q^{21} +(3.29971 + 0.334548i) q^{22} +(4.72879 + 4.72879i) q^{23} +1.25616 q^{24} +(-1.14533 + 4.86705i) q^{25} +1.91453 q^{26} +(-3.92785 + 3.92785i) q^{27} +(-0.707107 + 0.707107i) q^{28} -8.86980 q^{29} +(2.20193 - 1.74391i) q^{30} +8.87900 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.14498 - 0.420247i) q^{33} +4.07283i q^{34} +(-0.257823 + 2.22115i) q^{35} +1.42205 q^{36} +(1.13673 - 1.13673i) q^{37} +(-1.04618 - 1.04618i) q^{38} -2.40496 q^{39} +(-2.22115 - 0.257823i) q^{40} +8.24941i q^{41} +(0.888243 - 0.888243i) q^{42} +(4.20653 - 4.20653i) q^{43} +(2.09669 + 2.56981i) q^{44} +(2.49271 - 1.97421i) q^{45} +6.68752i q^{46} +(8.69999 - 8.69999i) q^{47} +(0.888243 + 0.888243i) q^{48} +1.00000i q^{49} +(-4.25140 + 2.63166i) q^{50} -5.11615i q^{51} +(1.35377 + 1.35377i) q^{52} +(-0.533202 - 0.533202i) q^{53} -5.55482 q^{54} +(7.24291 + 1.59382i) q^{55} -1.00000 q^{56} +(1.31418 + 1.31418i) q^{57} +(-6.27190 - 6.27190i) q^{58} +9.93780i q^{59} +(2.79014 + 0.323868i) q^{60} -2.09421i q^{61} +(6.27840 + 6.27840i) q^{62} +(1.00554 - 1.00554i) q^{63} -1.00000i q^{64} +(4.25246 + 0.493609i) q^{65} +(-2.63378 - 3.22810i) q^{66} +(7.31404 - 7.31404i) q^{67} +(-2.87993 + 2.87993i) q^{68} -8.40062i q^{69} +(-1.75290 + 1.38828i) q^{70} -10.9434 q^{71} +(1.00554 + 1.00554i) q^{72} +(-10.4699 + 10.4699i) q^{73} +1.60758 q^{74} +(5.34046 - 3.30580i) q^{75} -1.47952i q^{76} +(3.29971 + 0.334548i) q^{77} +(-1.70056 - 1.70056i) q^{78} -12.8565 q^{79} +(-1.38828 - 1.75290i) q^{80} +2.71162 q^{81} +(-5.83322 + 5.83322i) q^{82} +(7.94643 - 7.94643i) q^{83} +1.25616 q^{84} +(-1.05007 + 9.04639i) q^{85} +5.94893 q^{86} +(7.87854 + 7.87854i) q^{87} +(-0.334548 + 3.29971i) q^{88} -8.22801i q^{89} +(3.15859 + 0.366637i) q^{90} +1.91453 q^{91} +(-4.72879 + 4.72879i) q^{92} +(-7.88671 - 7.88671i) q^{93} +12.3036 q^{94} +(-2.05400 - 2.59346i) q^{95} +1.25616i q^{96} +(1.76695 - 1.76695i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(-2.98159 - 3.65439i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{3}+O(q^{10}) $ 36 * q - 4 * q^3	$ 36 q - 4 q^{3} + 12 q^{11} + 4 q^{12} - 4 q^{15} - 36 q^{16} - 12 q^{20} - 12 q^{22} + 4 q^{23} + 12 q^{25} + 24 q^{26} + 56 q^{27} + 8 q^{31} - 44 q^{33} - 44 q^{36} - 28 q^{37} + 16 q^{38} + 4 q^{42} - 44 q^{45} + 12 q^{47} + 4 q^{48} + 28 q^{53} + 40 q^{55} - 36 q^{56} - 24 q^{58} + 12 q^{60} + 24 q^{66} + 12 q^{67} - 12 q^{70} - 112 q^{71} - 52 q^{75} - 12 q^{77} + 48 q^{78} + 4 q^{81} + 40 q^{82} + 32 q^{86} - 12 q^{88} + 24 q^{91} - 4 q^{92} - 80 q^{93} + 100 q^{97}+O(q^{100}) $ 36 * q - 4 * q^3 + 12 * q^11 + 4 * q^12 - 4 * q^15 - 36 * q^16 - 12 * q^20 - 12 * q^22 + 4 * q^23 + 12 * q^25 + 24 * q^26 + 56 * q^27 + 8 * q^31 - 44 * q^33 - 44 * q^36 - 28 * q^37 + 16 * q^38 + 4 * q^42 - 44 * q^45 + 12 * q^47 + 4 * q^48 + 28 * q^53 + 40 * q^55 - 36 * q^56 - 24 * q^58 + 12 * q^60 + 24 * q^66 + 12 * q^67 - 12 * q^70 - 112 * q^71 - 52 * q^75 - 12 * q^77 + 48 * q^78 + 4 * q^81 + 40 * q^82 + 32 * q^86 - 12 * q^88 + 24 * q^91 - 4 * q^92 - 80 * q^93 + 100 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−0.888243	−	0.888243i	−0.512827	−	0.512827i	0.402564	−	0.915392i	$-0.368119\pi$
$3$	−0.888243	−	0.888243i	−0.512827	−	0.512827i	−0.915392	+	0.402564i	$0.868119\pi$
$4$			1.00000i			0.500000i
$5$	1.38828	+	1.75290i	0.620860	+	0.783922i
$5$	1.38828	+	1.75290i	0.620860	+	0.783922i
$6$		−	1.25616i		−	0.512827i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		−	1.42205i		−	0.474017i
$10$	−0.257823	+	2.22115i	−0.0815308	+	0.702391i
$11$	2.56981	−	2.09669i	0.774826	−	0.632174i
$11$	2.56981	−	2.09669i	0.774826	−	0.632174i
$12$	0.888243	−	0.888243i	0.256414	−	0.256414i
$13$	1.35377	−	1.35377i	0.375469	−	0.375469i	−0.493995	−	0.869465i	$-0.664464\pi$
$13$	1.35377	−	1.35377i	0.375469	−	0.375469i	0.869465	+	0.493995i	$0.164464\pi$
$14$			1.00000i			0.267261i
$15$	0.323868	−	2.79014i	0.0836224	−	0.720410i
$16$	−1.00000			−0.250000
$17$	2.87993	+	2.87993i	0.698485	+	0.698485i	0.964084	−	0.265599i	$-0.0855696\pi$
$17$	2.87993	+	2.87993i	0.698485	+	0.698485i	−0.265599	+	0.964084i	$0.585570\pi$
$18$	1.00554	−	1.00554i	0.237008	−	0.237008i
$19$	−1.47952			−0.339426			−0.169713	−	0.985494i	$-0.554284\pi$
$19$	−1.47952			−0.339426			−0.169713	+	0.985494i	$0.554284\pi$
$20$	−1.75290	+	1.38828i	−0.391961	+	0.310430i
$21$		−	1.25616i		−	0.274118i
$22$	3.29971	+	0.334548i	0.703500	+	0.0713258i
$23$	4.72879	+	4.72879i	0.986020	+	0.986020i	0.999904	−	0.0138832i	$-0.00441930\pi$
$23$	4.72879	+	4.72879i	0.986020	+	0.986020i	−0.0138832	+	0.999904i	$0.504419\pi$
$24$	1.25616			0.256414
$25$	−1.14533	+	4.86705i	−0.229066	+	0.973411i
$26$	1.91453			0.375469
$27$	−3.92785	+	3.92785i	−0.755916	+	0.755916i
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$	−8.86980			−1.64708			−0.823541	−	0.567257i	$-0.808005\pi$
$29$	−8.86980			−1.64708			−0.823541	+	0.567257i	$0.808005\pi$
$30$	2.20193	−	1.74391i	0.402016	−	0.318394i
$31$	8.87900			1.59472			0.797358	−	0.603506i	$-0.206230\pi$
$31$	8.87900			1.59472			0.797358	+	0.603506i	$0.206230\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−4.14498	−	0.420247i	−0.721548	−	0.0731556i
$34$			4.07283i			0.698485i
$35$	−0.257823	+	2.22115i	−0.0435800	+	0.375444i
$36$	1.42205			0.237008
$37$	1.13673	−	1.13673i	0.186878	−	0.186878i	−0.607467	−	0.794345i	$-0.707814\pi$
$37$	1.13673	−	1.13673i	0.186878	−	0.186878i	0.794345	+	0.607467i	$0.207814\pi$
$38$	−1.04618	−	1.04618i	−0.169713	−	0.169713i
$39$	−2.40496			−0.385102
$40$	−2.22115	−	0.257823i	−0.351195	−	0.0407654i
$41$			8.24941i			1.28834i	0.764881	+	0.644171i	$0.222797\pi$
$41$			8.24941i			1.28834i	−0.764881	+	0.644171i	$0.777203\pi$
$42$	0.888243	−	0.888243i	0.137059	−	0.137059i
$43$	4.20653	−	4.20653i	0.641490	−	0.641490i	−0.309432	−	0.950922i	$-0.600139\pi$
$43$	4.20653	−	4.20653i	0.641490	−	0.641490i	0.950922	+	0.309432i	$0.100139\pi$
$44$	2.09669	+	2.56981i	0.316087	+	0.387413i
$45$	2.49271	−	1.97421i	0.371592	−	0.294298i
$46$			6.68752i			0.986020i
$47$	8.69999	−	8.69999i	1.26902	−	1.26902i	0.322431	−	0.946593i	$-0.395500\pi$
$47$	8.69999	−	8.69999i	1.26902	−	1.26902i	0.946593	−	0.322431i	$-0.104500\pi$
$48$	0.888243	+	0.888243i	0.128207	+	0.128207i
$49$			1.00000i			0.142857i
$50$	−4.25140	+	2.63166i	−0.601238	+	0.372172i
$51$		−	5.11615i		−	0.716404i
$52$	1.35377	+	1.35377i	0.187735	+	0.187735i
$53$	−0.533202	−	0.533202i	−0.0732409	−	0.0732409i	0.669537	−	0.742778i	$-0.266492\pi$
$53$	−0.533202	−	0.533202i	−0.0732409	−	0.0732409i	−0.742778	+	0.669537i	$0.766492\pi$
$54$	−5.55482			−0.755916
$55$	7.24291	+	1.59382i	0.976634	+	0.214911i
$56$	−1.00000			−0.133631
$57$	1.31418	+	1.31418i	0.174067	+	0.174067i
$58$	−6.27190	−	6.27190i	−0.823541	−	0.823541i
$59$			9.93780i			1.29379i	0.762579	+	0.646896i	$0.223933\pi$
$59$			9.93780i			1.29379i	−0.762579	+	0.646896i	$0.776067\pi$
$60$	2.79014	+	0.323868i	0.360205	+	0.0418112i
$61$		−	2.09421i		−	0.268136i	−0.990972	−	0.134068i	$-0.957196\pi$
$61$		−	2.09421i		−	0.268136i	0.990972	−	0.134068i	$-0.0428040\pi$
$62$	6.27840	+	6.27840i	0.797358	+	0.797358i
$63$	1.00554	−	1.00554i	0.126686	−	0.126686i
$64$		−	1.00000i		−	0.125000i
$65$	4.25246	+	0.493609i	0.527453	+	0.0612247i
$66$	−2.63378	−	3.22810i	−0.324196	−	0.397352i
$67$	7.31404	−	7.31404i	0.893552	−	0.893552i	−0.101303	−	0.994856i	$-0.532301\pi$
$67$	7.31404	−	7.31404i	0.893552	−	0.893552i	0.994856	+	0.101303i	$0.0323013\pi$
$68$	−2.87993	+	2.87993i	−0.349243	+	0.349243i
$69$		−	8.40062i		−	1.01132i
$70$	−1.75290	+	1.38828i	−0.209512	+	0.165932i
$71$	−10.9434			−1.29874			−0.649371	−	0.760471i	$-0.724968\pi$
$71$	−10.9434			−1.29874			−0.649371	+	0.760471i	$0.724968\pi$
$72$	1.00554	+	1.00554i	0.118504	+	0.118504i
$73$	−10.4699	+	10.4699i	−1.22541	+	1.22541i	−0.259733	+	0.965680i	$0.583635\pi$
$73$	−10.4699	+	10.4699i	−1.22541	+	1.22541i	−0.965680	+	0.259733i	$0.916365\pi$
$74$	1.60758			0.186878
$75$	5.34046	−	3.30580i	0.616663	−	0.381720i
$76$		−	1.47952i		−	0.169713i
$77$	3.29971	+	0.334548i	0.376037	+	0.0381253i
$78$	−1.70056	−	1.70056i	−0.192551	−	0.192551i
$79$	−12.8565			−1.44646			−0.723232	−	0.690605i	$-0.757344\pi$
$79$	−12.8565			−1.44646			−0.723232	+	0.690605i	$0.757344\pi$
$80$	−1.38828	−	1.75290i	−0.155215	−	0.195980i
$81$	2.71162			0.301292
$82$	−5.83322	+	5.83322i	−0.644171	+	0.644171i
$83$	7.94643	−	7.94643i	0.872234	−	0.872234i	−0.120482	−	0.992716i	$-0.538444\pi$
$83$	7.94643	−	7.94643i	0.872234	−	0.872234i	0.992716	+	0.120482i	$0.0384439\pi$
$84$	1.25616			0.137059
$85$	−1.05007	+	9.04639i	−0.113896	+	0.981219i
$86$	5.94893			0.641490
$87$	7.87854	+	7.87854i	0.844668	+	0.844668i
$88$	−0.334548	+	3.29971i	−0.0356629	+	0.351750i
$89$		−	8.22801i		−	0.872167i	−0.899906	−	0.436084i	$-0.856365\pi$
$89$		−	8.22801i		−	0.872167i	0.899906	−	0.436084i	$-0.143635\pi$
$90$	3.15859	+	0.366637i	0.332945	+	0.0386470i
$91$	1.91453			0.200697
$92$	−4.72879	+	4.72879i	−0.493010	+	0.493010i
$93$	−7.88671	−	7.88671i	−0.817814	−	0.817814i
$94$	12.3036			1.26902
$95$	−2.05400	−	2.59346i	−0.210736	−	0.266083i
$96$			1.25616i			0.128207i
$97$	1.76695	−	1.76695i	0.179407	−	0.179407i	−0.611690	−	0.791097i	$-0.709510\pi$
$97$	1.76695	−	1.76695i	0.179407	−	0.179407i	0.791097	+	0.611690i	$0.209510\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$	−2.98159	−	3.65439i	−0.299661	−	0.367280i
$100$	−4.86705	−	1.14533i	−0.486705	−	0.114533i
$101$			1.82071i			0.181167i	0.995889	+	0.0905835i	$0.0288732\pi$
$101$			1.82071i			0.181167i	−0.995889	+	0.0905835i	$0.971127\pi$
$102$	3.61766	−	3.61766i	0.358202	−	0.358202i
$103$	−0.202934	−	0.202934i	−0.0199957	−	0.0199957i	0.697038	−	0.717034i	$-0.254501\pi$
$103$	−0.202934	−	0.202934i	−0.0199957	−	0.0199957i	−0.717034	+	0.697038i	$0.754501\pi$
$104$			1.91453i			0.187735i
$105$	2.20193	−	1.74391i	0.214887	−	0.170189i
$106$		−	0.754061i		−	0.0732409i
$107$	−7.06549	−	7.06549i	−0.683047	−	0.683047i	0.277639	−	0.960686i	$-0.410448\pi$
$107$	−7.06549	−	7.06549i	−0.683047	−	0.683047i	−0.960686	+	0.277639i	$0.910448\pi$
$108$	−3.92785	−	3.92785i	−0.377958	−	0.377958i
$109$	−8.35194			−0.799970			−0.399985	−	0.916522i	$-0.630985\pi$
$109$	−8.35194			−0.799970			−0.399985	+	0.916522i	$0.630985\pi$
$110$	3.99451	+	6.24851i	0.380861	+	0.595772i
$111$	−2.01939			−0.191672
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	−6.97441	−	6.97441i	−0.656098	−	0.656098i	0.298357	−	0.954454i	$-0.403561\pi$
$113$	−6.97441	−	6.97441i	−0.656098	−	0.656098i	−0.954454	+	0.298357i	$0.903561\pi$
$114$			1.85853i			0.174067i
$115$	−1.72420	+	14.8540i	−0.160782	+	1.38514i
$116$		−	8.86980i		−	0.823541i
$117$	−1.92513	−	1.92513i	−0.177979	−	0.177979i
$118$	−7.02708	+	7.02708i	−0.646896	+	0.646896i
$119$			4.07283i			0.373356i
$120$	1.74391	+	2.20193i	0.159197	+	0.201008i
$121$	2.20782	−	10.7762i	0.200711	−	0.979651i
$122$	1.48083	−	1.48083i	0.134068	−	0.134068i
$123$	7.32748	−	7.32748i	0.660697	−	0.660697i
$124$			8.87900i			0.797358i
$125$	−10.1215	+	4.74921i	−0.905296	+	0.424782i
$126$	1.42205			0.126686
$127$	−11.9485	−	11.9485i	−1.06026	−	1.06026i	−0.998064	−	0.0621978i	$-0.980189\pi$
$127$	−11.9485	−	11.9485i	−1.06026	−	1.06026i	−0.0621978	−	0.998064i	$-0.519811\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−7.47284			−0.657947
$130$	2.65791	+	3.35598i	0.233114	+	0.294339i
$131$		−	6.02808i		−	0.526676i	−0.964704	−	0.263338i	$-0.915177\pi$
$131$		−	6.02808i		−	0.526676i	0.964704	−	0.263338i	$-0.0848234\pi$
$132$	0.420247	−	4.14498i	0.0365778	−	0.360774i
$133$	−1.04618	−	1.04618i	−0.0907154	−	0.0907154i
$134$	10.3436			0.893552
$135$	−12.3381	−	1.43216i	−1.06190	−	0.123261i
$136$	−4.07283			−0.349243
$137$	2.39805	−	2.39805i	0.204879	−	0.204879i	−0.597207	−	0.802087i	$-0.703723\pi$
$137$	2.39805	−	2.39805i	0.204879	−	0.204879i	0.802087	+	0.597207i	$0.203723\pi$
$138$	5.94014	−	5.94014i	0.505658	−	0.505658i
$139$	3.78375			0.320933			0.160467	−	0.987041i	$-0.448700\pi$
$139$	3.78375			0.320933			0.160467	+	0.987041i	$0.448700\pi$
$140$	−2.22115	−	0.257823i	−0.187722	−	0.0217900i
$141$	−15.4554			−1.30158
$142$	−7.73815	−	7.73815i	−0.649371	−	0.649371i
$143$	0.640500	−	6.31738i	0.0535613	−	0.528286i
$144$			1.42205i			0.118504i
$145$	−12.3138	−	15.5479i	−1.02261	−	1.29118i
$146$	−14.8067			−1.22541
$147$	0.888243	−	0.888243i	0.0732610	−	0.0732610i
$148$	1.13673	+	1.13673i	0.0934389	+	0.0934389i
$149$	0.493471			0.0404267			0.0202134	−	0.999796i	$-0.493565\pi$
$149$	0.493471			0.0404267			0.0202134	+	0.999796i	$0.493565\pi$
$150$	6.11382	+	1.43872i	0.499192	+	0.117471i
$151$		−	19.0310i		−	1.54872i	−0.632746	−	0.774359i	$-0.718072\pi$
$151$		−	19.0310i		−	1.54872i	0.632746	−	0.774359i	$-0.281928\pi$
$152$	1.04618	−	1.04618i	0.0848565	−	0.0848565i
$153$	4.09540	−	4.09540i	0.331094	−	0.331094i
$154$	2.09669	+	2.56981i	0.168956	+	0.207081i
$155$	12.3266	+	15.5640i	0.990095	+	1.25013i
$156$		−	2.40496i		−	0.192551i
$157$	−12.7843	+	12.7843i	−1.02030	+	1.02030i	−0.0205125	+	0.999790i	$0.506530\pi$
$157$	−12.7843	+	12.7843i	−1.02030	+	1.02030i	−0.999790	+	0.0205125i	$0.993470\pi$
$158$	−9.09089	−	9.09089i	−0.723232	−	0.723232i
$159$			0.947225i			0.0751198i
$160$	0.257823	−	2.22115i	0.0203827	−	0.175598i
$161$			6.68752i			0.527050i
$162$	1.91741	+	1.91741i	0.150646	+	0.150646i
$163$	−1.69054	−	1.69054i	−0.132413	−	0.132413i	0.637794	−	0.770207i	$-0.279847\pi$
$163$	−1.69054	−	1.69054i	−0.132413	−	0.132413i	−0.770207	+	0.637794i	$0.779847\pi$
$164$	−8.24941			−0.644171
$165$	−5.01776	−	7.84916i	−0.390632	−	0.611056i
$166$	11.2379			0.872234
$167$	15.3944	+	15.3944i	1.19126	+	1.19126i	0.976715	+	0.214542i	$0.0688259\pi$
$167$	15.3944	+	15.3944i	1.19126	+	1.19126i	0.214542	+	0.976715i	$0.431174\pi$
$168$	0.888243	+	0.888243i	0.0685294	+	0.0685294i
$169$			9.33459i			0.718045i
$170$	−7.13928	+	5.65425i	−0.547558	+	0.433661i
$171$			2.10396i			0.160894i
$172$	4.20653	+	4.20653i	0.320745	+	0.320745i
$173$	5.59818	−	5.59818i	0.425622	−	0.425622i	−0.461512	−	0.887134i	$-0.652693\pi$
$173$	5.59818	−	5.59818i	0.425622	−	0.425622i	0.887134	+	0.461512i	$0.152693\pi$
$174$			11.1419i			0.844668i
$175$	−4.25140	+	2.63166i	−0.321375	+	0.198935i
$176$	−2.56981	+	2.09669i	−0.193707	+	0.158044i
$177$	8.82718	−	8.82718i	0.663491	−	0.663491i
$178$	5.81808	−	5.81808i	0.436084	−	0.436084i
$179$		−	1.60494i		−	0.119959i	−0.998200	−	0.0599794i	$-0.980897\pi$
$179$		−	1.60494i		−	0.119959i	0.998200	−	0.0599794i	$-0.0191035\pi$
$180$	1.97421	+	2.49271i	0.147149	+	0.185796i
$181$	−24.0351			−1.78652			−0.893258	−	0.449544i	$-0.851586\pi$
$181$	−24.0351			−1.78652			−0.893258	+	0.449544i	$0.851586\pi$
$182$	1.35377	+	1.35377i	0.100348	+	0.100348i
$183$	−1.86016	+	1.86016i	−0.137507	+	0.137507i
$184$	−6.68752			−0.493010
$185$	3.57069	+	0.414472i	0.262523	+	0.0304726i
$186$		−	11.1535i		−	0.817814i
$187$	13.4392	+	1.36256i	0.982769	+	0.0996401i
$188$	8.69999	+	8.69999i	0.634512	+	0.634512i
$189$	−5.55482			−0.404054
$190$	0.381455	−	3.28625i	0.0276737	−	0.238410i
$191$	−5.76500			−0.417141			−0.208570	−	0.978007i	$-0.566881\pi$
$191$	−5.76500			−0.417141			−0.208570	+	0.978007i	$0.566881\pi$
$192$	−0.888243	+	0.888243i	−0.0641034	+	0.0641034i
$193$	−2.53288	+	2.53288i	−0.182321	+	0.182321i	−0.792366	−	0.610046i	$-0.791151\pi$
$193$	−2.53288	+	2.53288i	−0.182321	+	0.182321i	0.610046	+	0.792366i	$0.291151\pi$
$194$	2.49885			0.179407
$195$	−3.33877	−	4.21566i	−0.239094	−	0.301890i
$196$	−1.00000			−0.0714286
$197$	9.40601	+	9.40601i	0.670150	+	0.670150i	0.957751	−	0.287600i	$-0.0928575\pi$
$197$	9.40601	+	9.40601i	0.670150	+	0.670150i	−0.287600	+	0.957751i	$0.592857\pi$
$198$	0.475744	−	4.69235i	0.0338096	−	0.333471i
$199$		−	9.67486i		−	0.685833i	−0.939366	−	0.342916i	$-0.888585\pi$
$199$		−	9.67486i		−	0.685833i	0.939366	−	0.342916i	$-0.111415\pi$
$200$	−2.63166	−	4.25140i	−0.186086	−	0.300619i
$201$	−12.9933			−0.916476
$202$	−1.28743	+	1.28743i	−0.0905835	+	0.0905835i
$203$	−6.27190	−	6.27190i	−0.440201	−	0.440201i
$204$	5.11615			0.358202
$205$	−14.4604	+	11.4525i	−1.00996	+	0.799880i
$206$		−	0.286992i		−	0.0199957i
$207$	6.72457	−	6.72457i	0.467390	−	0.467390i
$208$	−1.35377	+	1.35377i	−0.0938674	+	0.0938674i
$209$	−3.80209	+	3.10210i	−0.262996	+	0.214577i
$210$	2.79014	+	0.323868i	0.192538	+	0.0223490i
$211$		−	11.1990i		−	0.770971i	−0.922714	−	0.385485i	$-0.874034\pi$
$211$		−	11.1990i		−	0.770971i	0.922714	−	0.385485i	$-0.125966\pi$
$212$	0.533202	−	0.533202i	0.0366204	−	0.0366204i
$213$	9.72040	+	9.72040i	0.666031	+	0.666031i
$214$		−	9.99212i		−	0.683047i
$215$	13.2135	+	1.53377i	0.901153	+	0.104602i
$216$		−	5.55482i		−	0.377958i
$217$	6.27840	+	6.27840i	0.426206	+	0.426206i
$218$	−5.90571	−	5.90571i	−0.399985	−	0.399985i
$219$	18.5997			1.25685
$220$	−1.59382	+	7.24291i	−0.107456	+	0.488317i
$221$	7.79755			0.524520
$222$	−1.42792	−	1.42792i	−0.0958360	−	0.0958360i
$223$	1.71338	+	1.71338i	0.114736	+	0.114736i	0.762144	−	0.647408i	$-0.224147\pi$
$223$	1.71338	+	1.71338i	0.114736	+	0.114736i	−0.647408	+	0.762144i	$0.724147\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	6.92119	+	1.62872i	0.461413	+	0.108581i
$226$		−	9.86331i		−	0.656098i
$227$	−5.86091	−	5.86091i	−0.389002	−	0.389002i	0.485329	−	0.874332i	$-0.338700\pi$
$227$	−5.86091	−	5.86091i	−0.389002	−	0.389002i	−0.874332	+	0.485329i	$0.838700\pi$
$228$	−1.31418	+	1.31418i	−0.0870335	+	0.0870335i
$229$		−	1.08317i		−	0.0715777i	−0.999359	−	0.0357888i	$-0.988606\pi$
$229$		−	1.08317i		−	0.0715777i	0.999359	−	0.0357888i	$-0.0113944\pi$
$230$	−11.7226	+	9.28418i	−0.772963	+	0.612181i
$231$	−2.63378	−	3.22810i	−0.173290	−	0.212394i
$232$	6.27190	−	6.27190i	0.411770	−	0.411770i
$233$	13.0962	−	13.0962i	0.857963	−	0.857963i	−0.133135	−	0.991098i	$-0.542504\pi$
$233$	13.0962	−	13.0962i	0.857963	−	0.857963i	0.991098	+	0.133135i	$0.0425043\pi$
$234$		−	2.72255i		−	0.177979i
$235$	27.3283	+	3.17216i	1.78270	+	0.206929i
$236$	−9.93780			−0.646896
$237$	11.4197	+	11.4197i	0.741786	+	0.741786i
$238$	−2.87993	+	2.87993i	−0.186678	+	0.186678i
$239$	27.4149			1.77332			0.886661	−	0.462419i	$-0.153018\pi$
$239$	27.4149			1.77332			0.886661	+	0.462419i	$0.153018\pi$
$240$	−0.323868	+	2.79014i	−0.0209056	+	0.180103i
$241$		−	1.81865i		−	0.117149i	−0.998283	−	0.0585747i	$-0.981344\pi$
$241$		−	1.81865i		−	0.117149i	0.998283	−	0.0585747i	$-0.0186556\pi$
$242$	9.18106	−	6.05873i	0.590181	−	0.389470i
$243$	9.37498	+	9.37498i	0.601405	+	0.601405i
$244$	2.09421			0.134068
$245$	−1.75290	+	1.38828i	−0.111989	+	0.0886943i
$246$	10.3626			0.660697
$247$	−2.00294	+	2.00294i	−0.127444	+	0.127444i
$248$	−6.27840	+	6.27840i	−0.398679	+	0.398679i
$249$	−14.1167			−0.894610
$250$	−10.5152	−	3.79879i	−0.665039	−	0.240257i
$251$	−11.0968			−0.700423			−0.350212	−	0.936671i	$-0.613890\pi$
$251$	−11.0968			−0.700423			−0.350212	+	0.936671i	$0.613890\pi$
$252$	1.00554	+	1.00554i	0.0633431	+	0.0633431i
$253$	22.0669	+	2.23729i	1.38733	+	0.140657i
$254$		−	16.8978i		−	1.06026i
$255$	8.96811	−	7.10267i	0.561605	−	0.444787i
$256$	1.00000			0.0625000
$257$	−3.77824	+	3.77824i	−0.235680	+	0.235680i	−0.815059	−	0.579378i	$-0.803295\pi$
$257$	−3.77824	+	3.77824i	−0.235680	+	0.235680i	0.579378	+	0.815059i	$0.303295\pi$
$258$	−5.28409	−	5.28409i	−0.328973	−	0.328973i
$259$	1.60758			0.0998904
$260$	−0.493609	+	4.25246i	−0.0306123	+	0.263726i
$261$			12.6133i			0.780744i
$262$	4.26249	−	4.26249i	0.263338	−	0.263338i
$263$	−17.0224	+	17.0224i	−1.04965	+	1.04965i	−0.0509451	+	0.998701i	$0.516223\pi$
$263$	−17.0224	+	17.0224i	−1.04965	+	1.04965i	−0.998701	+	0.0509451i	$0.983777\pi$
$264$	3.22810	−	2.63378i	0.198676	−	0.162098i
$265$	0.194414	−	1.67489i	0.0119428	−	0.102887i
$266$		−	1.47952i		−	0.0907154i
$267$	−7.30847	+	7.30847i	−0.447271	+	0.447271i
$268$	7.31404	+	7.31404i	0.446776	+	0.446776i
$269$		−	21.8470i		−	1.33204i	−0.745936	−	0.666018i	$-0.767997\pi$
$269$		−	21.8470i		−	1.33204i	0.745936	−	0.666018i	$-0.232003\pi$
$270$	−7.71168	−	9.73706i	−0.469318	−	0.592579i
$271$			11.6241i			0.706114i	0.935602	+	0.353057i	$0.114858\pi$
$271$			11.6241i			0.706114i	−0.935602	+	0.353057i	$0.885142\pi$
$272$	−2.87993	−	2.87993i	−0.174621	−	0.174621i
$273$	−1.70056	−	1.70056i	−0.102923	−	0.102923i
$274$	3.39136			0.204879
$275$	7.26141	+	14.9088i	0.437879	+	0.899034i
$276$	8.40062			0.505658
$277$	−20.9515	−	20.9515i	−1.25885	−	1.25885i	−0.951641	−	0.307213i	$-0.900604\pi$
$277$	−20.9515	−	20.9515i	−1.25885	−	1.25885i	−0.307213	−	0.951641i	$-0.599396\pi$
$278$	2.67551	+	2.67551i	0.160467	+	0.160467i
$279$		−	12.6264i		−	0.755922i
$280$	−1.38828	−	1.75290i	−0.0829659	−	0.104756i
$281$			12.0990i			0.721763i	0.932612	+	0.360881i	$0.117524\pi$
$281$			12.0990i			0.721763i	−0.932612	+	0.360881i	$0.882476\pi$
$282$	−10.9286	−	10.9286i	−0.650790	−	0.650790i
$283$	−11.0577	+	11.0577i	−0.657315	+	0.657315i	−0.954744	−	0.297429i	$-0.903871\pi$
$283$	−11.0577	+	11.0577i	−0.657315	+	0.657315i	0.297429	+	0.954744i	$0.403871\pi$
$284$		−	10.9434i		−	0.649371i
$285$	−0.479171	+	4.12807i	−0.0283836	+	0.244526i
$286$	4.91996	−	4.01416i	0.290924	−	0.237362i
$287$	−5.83322	+	5.83322i	−0.344324	+	0.344324i
$288$	−1.00554	+	1.00554i	−0.0592521	+	0.0592521i
$289$		−	0.412027i		−	0.0242369i
$290$	2.28684	−	19.7012i	0.134288	−	1.15689i
$291$	−3.13897			−0.184010
$292$	−10.4699	−	10.4699i	−0.612707	−	0.612707i
$293$	19.5279	−	19.5279i	1.14083	−	1.14083i	0.152533	−	0.988298i	$-0.451257\pi$
$293$	19.5279	−	19.5279i	1.14083	−	1.14083i	0.988298	−	0.152533i	$-0.0487429\pi$
$294$	1.25616			0.0732610
$295$	−17.4200	+	13.7965i	−1.01423	+	0.803263i
$296$			1.60758i			0.0934389i
$297$	−1.85835	+	18.3293i	−0.107833	+	1.06357i
$298$	0.348937	+	0.348937i	0.0202134	+	0.0202134i
$299$	12.8034			0.740441
$300$	3.30580	+	5.34046i	0.190860	+	0.308331i
$301$	5.94893			0.342891
$302$	13.4569	−	13.4569i	0.774359	−	0.774359i
$303$	1.61723	−	1.61723i	0.0929074	−	0.0929074i
$304$	1.47952			0.0848565
$305$	3.67094	−	2.90735i	0.210197	−	0.166475i
$306$	5.79177			0.331094
$307$	12.1977	+	12.1977i	0.696157	+	0.696157i	0.963579	−	0.267422i	$-0.0861718\pi$
$307$	12.1977	+	12.1977i	0.696157	+	0.696157i	−0.267422	+	0.963579i	$0.586172\pi$
$308$	−0.334548	+	3.29971i	−0.0190626	+	0.188018i
$309$			0.360509i			0.0205086i
$310$	−2.28921	+	19.7216i	−0.130019	+	1.12011i
$311$	−28.6968			−1.62725			−0.813623	−	0.581393i	$-0.802508\pi$
$311$	−28.6968			−1.62725			−0.813623	+	0.581393i	$0.802508\pi$
$312$	1.70056	−	1.70056i	0.0962755	−	0.0962755i
$313$	−8.12218	−	8.12218i	−0.459093	−	0.459093i	0.439265	−	0.898358i	$-0.355239\pi$
$313$	−8.12218	−	8.12218i	−0.459093	−	0.459093i	−0.898358	+	0.439265i	$0.855239\pi$
$314$	−18.0798			−1.02030
$315$	3.15859	+	0.366637i	0.177967	+	0.0206577i
$316$		−	12.8565i		−	0.723232i
$317$	9.80486	−	9.80486i	0.550696	−	0.550696i	−0.375946	−	0.926642i	$-0.622682\pi$
$317$	9.80486	−	9.80486i	0.550696	−	0.550696i	0.926642	+	0.375946i	$0.122682\pi$
$318$	−0.669789	+	0.669789i	−0.0375599	+	0.0375599i
$319$	−22.7937	+	18.5972i	−1.27620	+	1.04124i
$320$	1.75290	−	1.38828i	0.0979902	−	0.0776075i
$321$			12.5517i			0.700570i
$322$	−4.72879	+	4.72879i	−0.263525	+	0.263525i
$323$	−4.26092	−	4.26092i	−0.237084	−	0.237084i
$324$			2.71162i			0.150646i
$325$	5.03838	+	8.13941i	0.279479	+	0.451493i
$326$		−	2.39078i		−	0.132413i
$327$	7.41855	+	7.41855i	0.410247	+	0.410247i
$328$	−5.83322	−	5.83322i	−0.322086	−	0.322086i
$329$	12.3036			0.678322
$330$	2.00210	−	9.09829i	0.110212	−	0.500844i
$331$	5.87481			0.322909			0.161454	−	0.986880i	$-0.448382\pi$
$331$	5.87481			0.322909			0.161454	+	0.986880i	$0.448382\pi$
$332$	7.94643	+	7.94643i	0.436117	+	0.436117i
$333$	−1.61649	−	1.61649i	−0.0885832	−	0.0885832i
$334$			21.7710i			1.19126i
$335$	22.9748	+	2.66682i	1.25525	+	0.145704i
$336$			1.25616i			0.0685294i
$337$	12.0573	+	12.0573i	0.656805	+	0.656805i	0.954623	−	0.297818i	$-0.0962589\pi$
$337$	12.0573	+	12.0573i	0.656805	+	0.656805i	−0.297818	+	0.954623i	$0.596259\pi$
$338$	−6.60055	+	6.60055i	−0.359023	+	0.359023i
$339$			12.3899i			0.672929i
$340$	−9.04639	−	1.05007i	−0.490610	−	0.0569481i
$341$	22.8173	−	18.6165i	1.23563	−	1.00814i
$342$	−1.48772	+	1.48772i	−0.0804468	+	0.0804468i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$			5.94893i			0.320745i
$345$	14.7255	−	11.6625i	0.792792	−	0.627886i
$346$	7.91702			0.425622
$347$	11.5264	+	11.5264i	0.618768	+	0.618768i	0.945215	−	0.326447i	$-0.105852\pi$
$347$	11.5264	+	11.5264i	0.618768	+	0.618768i	−0.326447	+	0.945215i	$0.605852\pi$
$348$	−7.87854	+	7.87854i	−0.422334	+	0.422334i
$349$	−33.2970			−1.78235			−0.891175	−	0.453661i	$-0.850118\pi$
$349$	−33.2970			−1.78235			−0.891175	+	0.453661i	$0.850118\pi$
$350$	−4.86705	−	1.14533i	−0.260155	−	0.0612204i
$351$			10.6349i			0.567647i
$352$	−3.29971	−	0.334548i	−0.175875	−	0.0178315i
$353$	20.8810	+	20.8810i	1.11138	+	1.11138i	0.992964	+	0.118420i	$0.0377830\pi$
$353$	20.8810	+	20.8810i	1.11138	+	1.11138i	0.118420	+	0.992964i	$0.462217\pi$
$354$	12.4835			0.663491
$355$	−15.1926	−	19.1827i	−0.806337	−	1.01811i
$356$	8.22801			0.436084
$357$	3.61766	−	3.61766i	0.191467	−	0.191467i
$358$	1.13486	−	1.13486i	0.0599794	−	0.0599794i
$359$	−24.4482			−1.29032			−0.645162	−	0.764046i	$-0.723210\pi$
$359$	−24.4482			−1.29032			−0.645162	+	0.764046i	$0.723210\pi$
$360$	−0.366637	+	3.15859i	−0.0193235	+	0.166472i
$361$	−16.8110			−0.884790
$362$	−16.9954	−	16.9954i	−0.893258	−	0.893258i
$363$	−11.5329	+	7.61076i	−0.605321	+	0.399461i
$364$			1.91453i			0.100348i
$365$	−32.8880	−	3.81752i	−1.72144	−	0.199818i
$366$	−2.63067			−0.137507
$367$	−17.6498	+	17.6498i	−0.921310	+	0.921310i	−0.997122	−	0.0758120i	$-0.975845\pi$
$367$	−17.6498	+	17.6498i	−0.921310	+	0.921310i	0.0758120	+	0.997122i	$0.475845\pi$
$368$	−4.72879	−	4.72879i	−0.246505	−	0.246505i
$369$	11.7311			0.610696
$370$	2.23178	+	2.81794i	0.116025	+	0.146498i
$371$		−	0.754061i		−	0.0391489i
$372$	7.88671	−	7.88671i	0.408907	−	0.408907i
$373$	−3.47802	+	3.47802i	−0.180085	+	0.180085i	−0.791393	−	0.611308i	$-0.790644\pi$
$373$	−3.47802	+	3.47802i	−0.180085	+	0.180085i	0.611308	+	0.791393i	$0.290644\pi$
$374$	8.53945	+	10.4664i	0.441564	+	0.541205i
$375$	13.2088	+	4.77191i	0.682100	+	0.246420i
$376$			12.3036i			0.634512i
$377$	−12.0077	+	12.0077i	−0.618429	+	0.618429i
$378$	−3.92785	−	3.92785i	−0.202027	−	0.202027i
$379$			20.7313i			1.06490i	0.846463	+	0.532448i	$0.178728\pi$
$379$			20.7313i			1.06490i	−0.846463	+	0.532448i	$0.821272\pi$
$380$	2.59346	−	2.05400i	0.133042	−	0.105368i
$381$			21.2264i			1.08746i
$382$	−4.07647	−	4.07647i	−0.208570	−	0.208570i
$383$	−0.806297	−	0.806297i	−0.0411998	−	0.0411998i	0.686207	−	0.727407i	$-0.259275\pi$
$383$	−0.806297	−	0.806297i	−0.0411998	−	0.0411998i	−0.727407	+	0.686207i	$0.759275\pi$
$384$	−1.25616			−0.0641034
$385$	3.99451	+	6.24851i	0.203579	+	0.318454i
$386$	−3.58203			−0.182321
$387$	−5.98189	−	5.98189i	−0.304077	−	0.304077i
$388$	1.76695	+	1.76695i	0.0897035	+	0.0897035i
$389$		−	35.0385i		−	1.77652i	−0.459340	−	0.888260i	$-0.651914\pi$
$389$		−	35.0385i		−	1.77652i	0.459340	−	0.888260i	$-0.348086\pi$
$390$	0.620054	−	5.34179i	0.0313977	−	0.270492i
$391$			27.2371i			1.37744i
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$	−5.35440	+	5.35440i	−0.270094	+	0.270094i
$394$			13.3021i			0.670150i
$395$	−17.8484	−	22.5361i	−0.898052	−	1.13391i
$396$	3.65439	−	2.98159i	0.183640	−	0.149831i
$397$	0.531094	−	0.531094i	0.0266548	−	0.0266548i	−0.693654	−	0.720309i	$-0.744000\pi$
$397$	0.531094	−	0.531094i	0.0266548	−	0.0266548i	0.720309	+	0.693654i	$0.244000\pi$
$398$	6.84116	−	6.84116i	0.342916	−	0.342916i
$399$			1.85853i			0.0930427i
$400$	1.14533	−	4.86705i	0.0572665	−	0.243353i
$401$	−11.5324			−0.575903			−0.287951	−	0.957645i	$-0.592974\pi$
$401$	−11.5324			−0.575903			−0.287951	+	0.957645i	$0.592974\pi$
$402$	−9.18764	−	9.18764i	−0.458238	−	0.458238i
$403$	12.0202	−	12.0202i	0.598767	−	0.598767i
$404$	−1.82071			−0.0905835
$405$	3.76451	+	4.75321i	0.187060	+	0.236189i
$406$		−	8.86980i		−	0.440201i
$407$	0.537814	−	5.30456i	0.0266584	−	0.262937i
$408$	3.61766	+	3.61766i	0.179101	+	0.179101i
$409$	9.69828			0.479549			0.239775	−	0.970829i	$-0.422926\pi$
$409$	9.69828			0.479549			0.239775	+	0.970829i	$0.422926\pi$
$410$	−18.3232	−	2.12689i	−0.904919	−	0.105040i
$411$	−4.26011			−0.210136
$412$	0.202934	−	0.202934i	0.00999784	−	0.00999784i
$413$	−7.02708	+	7.02708i	−0.345780	+	0.345780i
$414$	9.50998			0.467390
$415$	24.9612	+	2.89740i	1.22530	+	0.142228i
$416$	−1.91453			−0.0938674
$417$	−3.36089	−	3.36089i	−0.164583	−	0.164583i
$418$	−4.88200	−	0.494971i	−0.238786	−	0.0242098i
$419$		−	28.3703i		−	1.38598i	−0.720946	−	0.692991i	$-0.756292\pi$
$419$		−	28.3703i		−	1.38598i	0.720946	−	0.692991i	$-0.243708\pi$
$420$	1.74391	+	2.20193i	0.0850943	+	0.107443i
$421$	−6.66942			−0.325048			−0.162524	−	0.986705i	$-0.551963\pi$
$421$	−6.66942			−0.325048			−0.162524	+	0.986705i	$0.551963\pi$
$422$	7.91889	−	7.91889i	0.385485	−	0.385485i
$423$	−12.3718	−	12.3718i	−0.601538	−	0.601538i
$424$	0.754061			0.0366204
$425$	−17.3152	+	10.7183i	−0.839912	+	0.519914i
$426$			13.7467i			0.666031i
$427$	1.48083	−	1.48083i	0.0716623	−	0.0716623i
$428$	7.06549	−	7.06549i	0.341524	−	0.341524i
$429$	−6.18029	+	5.04245i	−0.298387	+	0.243452i
$430$	8.25881	+	10.4279i	0.398275	+	0.502878i
$431$		−	0.660707i		−	0.0318251i	−0.999873	−	0.0159126i	$-0.994935\pi$
$431$		−	0.660707i		−	0.0318251i	0.999873	−	0.0159126i	$-0.00506534\pi$
$432$	3.92785	−	3.92785i	0.188979	−	0.188979i
$433$	−0.909235	−	0.909235i	−0.0436950	−	0.0436950i	0.684922	−	0.728617i	$-0.259836\pi$
$433$	−0.909235	−	0.909235i	−0.0436950	−	0.0436950i	−0.728617	+	0.684922i	$0.759836\pi$
$434$			8.87900i			0.426206i
$435$	−2.87265	+	24.7480i	−0.137733	+	1.18657i
$436$		−	8.35194i		−	0.399985i
$437$	−6.99636	−	6.99636i	−0.334681	−	0.334681i
$438$	13.1520	+	13.1520i	0.628425	+	0.628425i
$439$	3.74444			0.178712			0.0893562	−	0.996000i	$-0.471519\pi$
$439$	3.74444			0.178712			0.0893562	+	0.996000i	$0.471519\pi$
$440$	−6.24851	+	3.99451i	−0.297886	+	0.190431i
$441$	1.42205			0.0677167
$442$	5.51370	+	5.51370i	0.262260	+	0.262260i
$443$	13.7718	+	13.7718i	0.654319	+	0.654319i	0.954030	−	0.299711i	$-0.0968902\pi$
$443$	13.7718	+	13.7718i	0.654319	+	0.654319i	−0.299711	+	0.954030i	$0.596890\pi$
$444$		−	2.01939i		−	0.0958360i
$445$	14.4229	−	11.4228i	0.683711	−	0.541494i
$446$			2.42308i			0.114736i
$447$	−0.438322	−	0.438322i	−0.0207319	−	0.0207319i
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$			31.7894i			1.50023i	0.661305	+	0.750117i	$0.270003\pi$
$449$			31.7894i			1.50023i	−0.661305	+	0.750117i	$0.729997\pi$
$450$	3.74235	+	6.04570i	0.176416	+	0.284997i
$451$	17.2964	+	21.1994i	0.814457	+	0.998241i
$452$	6.97441	−	6.97441i	0.328049	−	0.328049i
$453$	−16.9041	+	16.9041i	−0.794225	+	0.794225i
$454$		−	8.28858i		−	0.389002i
$455$	2.65791	+	3.35598i	0.124605	+	0.157331i
$456$	−1.85853			−0.0870335
$457$	2.54612	+	2.54612i	0.119102	+	0.119102i	0.764146	−	0.645044i	$-0.223161\pi$
$457$	2.54612	+	2.54612i	0.119102	+	0.119102i	−0.645044	+	0.764146i	$0.723161\pi$
$458$	0.765915	−	0.765915i	0.0357888	−	0.0357888i
$459$	−22.6239			−1.05599
$460$	−14.8540	−	1.72420i	−0.692572	−	0.0803910i
$461$			14.4788i			0.674343i	0.941443	+	0.337172i	$0.109470\pi$
$461$			14.4788i			0.674343i	−0.941443	+	0.337172i	$0.890530\pi$
$462$	0.420247	−	4.14498i	0.0195517	−	0.192842i
$463$	18.1240	+	18.1240i	0.842292	+	0.842292i	0.989157	−	0.146865i	$-0.0469183\pi$
$463$	18.1240	+	18.1240i	0.842292	+	0.842292i	−0.146865	+	0.989157i	$0.546918\pi$
$464$	8.86980			0.411770
$465$	2.87563	−	24.7736i	0.133354	−	1.14885i
$466$	18.5209			0.857963
$467$	14.5407	−	14.5407i	0.672866	−	0.672866i	−0.285510	−	0.958376i	$-0.592163\pi$
$467$	14.5407	−	14.5407i	0.672866	−	0.672866i	0.958376	+	0.285510i	$0.0921630\pi$
$468$	1.92513	−	1.92513i	0.0889894	−	0.0889894i
$469$	10.3436			0.477624
$470$	17.0810	+	21.5671i	0.787886	+	0.994815i
$471$	22.7112			1.04648
$472$	−7.02708	−	7.02708i	−0.323448	−	0.323448i
$473$	1.99020	−	19.6297i	0.0915095	−	0.902576i
$474$			16.1498i			0.741786i
$475$	1.69454	−	7.20092i	0.0777510	−	0.330401i
$476$	−4.07283			−0.186678
$477$	−0.758239	+	0.758239i	−0.0347174	+	0.0347174i
$478$	19.3853	+	19.3853i	0.886661	+	0.886661i
$479$	38.0893			1.74035			0.870173	−	0.492747i	$-0.164007\pi$
$479$	38.0893			1.74035			0.870173	+	0.492747i	$0.164007\pi$
$480$	−2.20193	+	1.74391i	−0.100504	+	0.0795985i
$481$		−	3.07776i		−	0.140334i
$482$	1.28598	−	1.28598i	0.0585747	−	0.0585747i
$483$	5.94014	−	5.94014i	0.270286	−	0.270286i
$484$	10.7762	+	2.20782i	0.489825	+	0.100355i
$485$	5.55033	+	0.644261i	0.252028	+	0.0292544i
$486$			13.2582i			0.601405i
$487$	−19.6660	+	19.6660i	−0.891152	+	0.891152i	−0.994632	−	0.103480i	$-0.967002\pi$
$487$	−19.6660	+	19.6660i	−0.891152	+	0.891152i	0.103480	+	0.994632i	$0.467002\pi$
$488$	1.48083	+	1.48083i	0.0670339	+	0.0670339i
$489$			3.00322i			0.135810i
$490$	−2.22115	−	0.257823i	−0.100342	−	0.0116473i
$491$		−	6.03773i		−	0.272479i	−0.990676	−	0.136240i	$-0.956498\pi$
$491$		−	6.03773i		−	0.272479i	0.990676	−	0.136240i	$-0.0435017\pi$
$492$	7.32748	+	7.32748i	0.330348	+	0.330348i
$493$	−25.5444	−	25.5444i	−1.15046	−	1.15046i
$494$	−2.83259			−0.127444
$495$	2.26650	−	10.2998i	0.101871	−	0.462941i
$496$	−8.87900			−0.398679
$497$	−7.73815	−	7.73815i	−0.347104	−	0.347104i
$498$	−9.98202	−	9.98202i	−0.447305	−	0.447305i
$499$		−	12.4443i		−	0.557081i	−0.960424	−	0.278541i	$-0.910149\pi$
$499$		−	12.4443i		−	0.557081i	0.960424	−	0.278541i	$-0.0898507\pi$
$500$	−4.74921	−	10.1215i	−0.212391	−	0.452648i
$501$		−	27.3480i		−	1.22182i
$502$	−7.84662	−	7.84662i	−0.350212	−	0.350212i
$503$	−8.83489	+	8.83489i	−0.393928	+	0.393928i	−0.876085	−	0.482157i	$-0.839854\pi$
$503$	−8.83489	+	8.83489i	−0.393928	+	0.393928i	0.482157	+	0.876085i	$0.339854\pi$
$504$			1.42205i			0.0633431i
$505$	−3.19152	+	2.52766i	−0.142021	+	0.112479i
$506$	14.0216	+	17.1856i	0.623337	+	0.763994i
$507$	8.29138	−	8.29138i	0.368233	−	0.368233i
$508$	11.9485	−	11.9485i	0.530131	−	0.530131i
$509$			1.45865i			0.0646534i	0.999477	+	0.0323267i	$0.0102917\pi$
$509$			1.45865i			0.0646534i	−0.999477	+	0.0323267i	$0.989708\pi$
$510$	11.3638	+	1.31906i	0.503196	+	0.0584090i
$511$	−14.8067			−0.655011
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	5.81135	−	5.81135i	0.256578	−	0.256578i
$514$	−5.34324			−0.235680
$515$	0.0739931	−	0.637453i	0.00326053	−	0.0280895i
$516$		−	7.47284i		−	0.328973i
$517$	4.11616	−	40.5984i	0.181028	−	1.78552i
$518$	1.13673	+	1.13673i	0.0499452	+	0.0499452i
$519$	−9.94508			−0.436541
$520$	−3.35598	+	2.65791i	−0.147169	+	0.116557i
$521$	28.3008			1.23988			0.619941	−	0.784648i	$-0.287157\pi$
$521$	28.3008			1.23988			0.619941	+	0.784648i	$0.287157\pi$
$522$	−8.91895	+	8.91895i	−0.390372	+	0.390372i
$523$	5.44347	−	5.44347i	0.238026	−	0.238026i	−0.578006	−	0.816032i	$-0.696169\pi$
$523$	5.44347	−	5.44347i	0.238026	−	0.238026i	0.816032	+	0.578006i	$0.196169\pi$
$524$	6.02808			0.263338
$525$	6.11382	+	1.43872i	0.266829	+	0.0627910i
$526$	−24.0733			−1.04965
$527$	25.5709	+	25.5709i	1.11389	+	1.11389i
$528$	4.14498	+	0.420247i	0.180387	+	0.0182889i
$529$			21.7229i			0.944473i
$530$	1.32179	−	1.04685i	0.0574151	−	0.0454723i
$531$	14.1320			0.613278
$532$	1.04618	−	1.04618i	0.0453577	−	0.0453577i
$533$	11.1678	+	11.1678i	0.483733	+	0.483733i
$534$	−10.3357			−0.447271
$535$	2.57620	−	22.1940i	0.111379	−	0.959532i
$536$			10.3436i			0.446776i
$537$	−1.42557	+	1.42557i	−0.0615181	+	0.0615181i
$538$	15.4482	−	15.4482i	0.666018	−	0.666018i
$539$	2.09669	+	2.56981i	0.0903106	+	0.110689i
$540$	1.43216	−	12.3381i	0.0616304	−	0.530948i
$541$			38.4666i			1.65381i	0.562344	+	0.826903i	$0.309900\pi$
$541$			38.4666i			1.65381i	−0.562344	+	0.826903i	$0.690100\pi$
$542$	−8.21948	+	8.21948i	−0.353057	+	0.353057i
$543$	21.3490	+	21.3490i	0.916174	+	0.916174i
$544$		−	4.07283i		−	0.174621i
$545$	−11.5949	−	14.6401i	−0.496670	−	0.627114i
$546$		−	2.40496i		−	0.102923i
$547$	−16.7490	−	16.7490i	−0.716137	−	0.716137i	0.251675	−	0.967812i	$-0.419019\pi$
$547$	−16.7490	−	16.7490i	−0.716137	−	0.716137i	−0.967812	+	0.251675i	$0.919019\pi$
$548$	2.39805	+	2.39805i	0.102440	+	0.102440i
$549$	−2.97807			−0.127101
$550$	−5.40752	+	15.6767i	−0.230577	+	0.668457i
$551$	13.1231			0.559062
$552$	5.94014	+	5.94014i	0.252829	+	0.252829i
$553$	−9.09089	−	9.09089i	−0.386584	−	0.386584i
$554$		−	29.6299i		−	1.25885i
$555$	−2.80349	−	3.53979i	−0.119002	−	0.150256i
$556$			3.78375i			0.160467i
$557$	28.2389	+	28.2389i	1.19652	+	1.19652i	0.975201	+	0.221319i	$0.0710362\pi$
$557$	28.2389	+	28.2389i	1.19652	+	1.19652i	0.221319	+	0.975201i	$0.428964\pi$
$558$	8.92820	−	8.92820i	0.377961	−	0.377961i
$559$		−	11.3894i		−	0.481720i
$560$	0.257823	−	2.22115i	0.0108950	−	0.0938609i
$561$	−10.7270	−	13.1475i	−0.452893	−	0.555089i
$562$	−8.55525	+	8.55525i	−0.360881	+	0.360881i
$563$	3.94828	−	3.94828i	0.166400	−	0.166400i	−0.618995	−	0.785395i	$-0.712460\pi$
$563$	3.94828	−	3.94828i	0.166400	−	0.166400i	0.785395	+	0.618995i	$0.212460\pi$
$564$		−	15.4554i		−	0.650790i
$565$	2.54299	−	21.9079i	0.106984	−	0.921674i
$566$	−15.6380			−0.657315
$567$	1.91741	+	1.91741i	0.0805236	+	0.0805236i
$568$	7.73815	−	7.73815i	0.324686	−	0.324686i
$569$	30.6319			1.28416			0.642079	−	0.766639i	$-0.278072\pi$
$569$	30.6319			1.28416			0.642079	+	0.766639i	$0.278072\pi$
$570$	−3.25781	+	2.58016i	−0.136455	+	0.108071i
$571$			15.1172i			0.632635i	0.948653	+	0.316318i	$0.102447\pi$
$571$			15.1172i			0.632635i	−0.948653	+	0.316318i	$0.897553\pi$
$572$	6.31738	+	0.640500i	0.264143	+	0.0267807i
$573$	5.12072	+	5.12072i	0.213921	+	0.213921i
$574$	−8.24941			−0.344324
$575$	−28.4313	+	17.5992i	−1.18567	+	0.733939i
$576$	−1.42205			−0.0592521
$577$	−24.9260	+	24.9260i	−1.03768	+	1.03768i	−0.0384196	+	0.999262i	$0.512232\pi$
$577$	−24.9260	+	24.9260i	−1.03768	+	1.03768i	−0.999262	+	0.0384196i	$0.987768\pi$
$578$	0.291347	−	0.291347i	0.0121185	−	0.0121185i
$579$	4.49962			0.186998
$580$	15.5479	−	12.3138i	0.645591	−	0.511303i
$581$	11.2379			0.466229
$582$	−2.21959	−	2.21959i	−0.0920048	−	0.0920048i
$583$	−2.48818	−	0.252269i	−0.103050	−	0.0104479i
$584$		−	14.8067i		−	0.612707i
$585$	0.701937	−	6.04721i	0.0290215	−	0.250021i
$586$	27.6166			1.14083
$587$	9.40740	−	9.40740i	0.388285	−	0.388285i	−0.485790	−	0.874075i	$-0.661468\pi$
$587$	9.40740	−	9.40740i	0.388285	−	0.388285i	0.874075	+	0.485790i	$0.161468\pi$
$588$	0.888243	+	0.888243i	0.0366305	+	0.0366305i
$589$	−13.1367			−0.541288
$590$	−22.0734	−	2.56219i	−0.908747	−	0.105484i
$591$		−	16.7096i		−	0.687342i
$592$	−1.13673	+	1.13673i	−0.0467195	+	0.0467195i
$593$	7.99804	−	7.99804i	0.328440	−	0.328440i	−0.523553	−	0.851993i	$-0.675394\pi$
$593$	7.99804	−	7.99804i	0.328440	−	0.328440i	0.851993	+	0.523553i	$0.175394\pi$
$594$	−14.2748	+	11.6467i	−0.585703	+	0.477871i
$595$	−7.13928	+	5.65425i	−0.292682	+	0.231802i
$596$			0.493471i			0.0202134i
$597$	−8.59362	+	8.59362i	−0.351714	+	0.351714i
$598$	9.05339	+	9.05339i	0.370221	+	0.370221i
$599$		−	14.1834i		−	0.579518i	−0.957100	−	0.289759i	$-0.906425\pi$
$599$		−	14.1834i		−	0.579518i	0.957100	−	0.289759i	$-0.0935752\pi$
$600$	−1.43872	+	6.11382i	−0.0587356	+	0.249596i
$601$			22.0502i			0.899447i	0.893168	+	0.449724i	$0.148478\pi$
$601$			22.0502i			0.899447i	−0.893168	+	0.449724i	$0.851522\pi$
$602$	4.20653	+	4.20653i	0.171445	+	0.171445i
$603$	−10.4009	−	10.4009i	−0.423559	−	0.423559i
$604$	19.0310			0.774359
$605$	21.9546	−	11.0903i	0.892582	−	0.450884i
$606$	2.28711			0.0929074
$607$	−20.1106	−	20.1106i	−0.816265	−	0.816265i	0.169299	−	0.985565i	$-0.445850\pi$
$607$	−20.1106	−	20.1106i	−0.816265	−	0.816265i	−0.985565	+	0.169299i	$0.945850\pi$
$608$	1.04618	+	1.04618i	0.0424283	+	0.0424283i
$609$			11.1419i			0.451494i
$610$	4.65156	+	0.539935i	0.188336	+	0.0218613i
$611$		−	23.5556i		−	0.952959i
$612$	4.09540	+	4.09540i	0.165547	+	0.165547i
$613$	7.51374	−	7.51374i	0.303477	−	0.303477i	−0.538895	−	0.842373i	$-0.681158\pi$
$613$	7.51374	−	7.51374i	0.303477	−	0.303477i	0.842373	+	0.538895i	$0.181158\pi$
$614$			17.2501i			0.696157i
$615$	23.0170	+	2.67172i	0.928135	+	0.107734i
$616$	−2.56981	+	2.09669i	−0.103540	+	0.0844779i
$617$	13.3597	−	13.3597i	0.537841	−	0.537841i	−0.385054	−	0.922894i	$-0.625817\pi$
$617$	13.3597	−	13.3597i	0.537841	−	0.537841i	0.922894	+	0.385054i	$0.125817\pi$
$618$	−0.254918	+	0.254918i	−0.0102543	+	0.0102543i
$619$			11.1084i			0.446484i	0.974763	+	0.223242i	$0.0716640\pi$
$619$			11.1084i			0.446484i	−0.974763	+	0.223242i	$0.928336\pi$
$620$	−15.5640	+	12.3266i	−0.625066	+	0.495048i
$621$	−37.1480			−1.49070
$622$	−20.2917	−	20.2917i	−0.813623	−	0.813623i
$623$	5.81808	−	5.81808i	0.233096	−	0.233096i
$624$	2.40496			0.0962755
$625$	−22.3764	−	11.1488i	−0.895058	−	0.445951i
$626$		−	11.4865i		−	0.459093i
$627$	6.13260	+	0.621766i	0.244912	+	0.0248309i
$628$	−12.7843	−	12.7843i	−0.510151	−	0.510151i
$629$	6.54742			0.261063
$630$	1.97421	+	2.49271i	0.0786544	+	0.0993121i
$631$	43.0780			1.71491			0.857454	−	0.514561i	$-0.172045\pi$
$631$	43.0780			1.71491			0.857454	+	0.514561i	$0.172045\pi$
$632$	9.09089	−	9.09089i	0.361616	−	0.361616i
$633$	−9.94743	+	9.94743i	−0.395375	+	0.395375i
$634$	13.8662			0.550696
$635$	4.35664	−	37.5326i	0.172888	−	1.48944i
$636$	−0.947225			−0.0375599
$637$	1.35377	+	1.35377i	0.0536385	+	0.0536385i
$638$	−29.2678	−	2.96737i	−1.15872	−	0.117479i
$639$			15.5621i			0.615626i
$640$	2.22115	+	0.257823i	0.0877988	+	0.0101914i
$641$	−18.9643			−0.749044			−0.374522	−	0.927218i	$-0.622193\pi$
$641$	−18.9643			−0.749044			−0.374522	+	0.927218i	$0.622193\pi$
$642$	−8.87542	+	8.87542i	−0.350285	+	0.350285i
$643$	−16.1431	−	16.1431i	−0.636622	−	0.636622i	0.313099	−	0.949721i	$-0.398633\pi$
$643$	−16.1431	−	16.1431i	−0.636622	−	0.636622i	−0.949721	+	0.313099i	$0.898633\pi$
$644$	−6.68752			−0.263525
$645$	−10.3744	−	13.0991i	−0.408493	−	0.515778i
$646$		−	6.02586i		−	0.237084i
$647$	−20.7235	+	20.7235i	−0.814725	+	0.814725i	−0.985338	−	0.170613i	$-0.945425\pi$
$647$	−20.7235	+	20.7235i	−0.814725	+	0.814725i	0.170613	+	0.985338i	$0.445425\pi$
$648$	−1.91741	+	1.91741i	−0.0753229	+	0.0753229i
$649$	20.8364	+	25.5382i	0.817902	+	1.00246i
$650$	−2.19276	+	9.31810i	−0.0860073	+	0.365486i
$651$		−	11.1535i		−	0.437140i
$652$	1.69054	−	1.69054i	0.0662066	−	0.0662066i
$653$	2.78208	+	2.78208i	0.108871	+	0.108871i	0.759444	−	0.650573i	$-0.225471\pi$
$653$	2.78208	+	2.78208i	0.108871	+	0.108871i	−0.650573	+	0.759444i	$0.725471\pi$
$654$			10.4914i			0.410247i
$655$	10.5666	−	8.36869i	0.412872	−	0.326992i
$656$		−	8.24941i		−	0.322086i
$657$	14.8888	+	14.8888i	0.580866	+	0.580866i
$658$	8.69999	+	8.69999i	0.339161	+	0.339161i
$659$	−34.4321			−1.34128			−0.670642	−	0.741781i	$-0.733981\pi$
$659$	−34.4321			−1.34128			−0.670642	+	0.741781i	$0.733981\pi$
$660$	7.84916	−	5.01776i	0.305528	−	0.195316i
$661$	−28.1721			−1.09577			−0.547884	−	0.836554i	$-0.684567\pi$
$661$	−28.1721			−1.09577			−0.547884	+	0.836554i	$0.684567\pi$
$662$	4.15412	+	4.15412i	0.161454	+	0.161454i
$663$	−6.92611	−	6.92611i	−0.268988	−	0.268988i
$664$			11.2379i			0.436117i
$665$	0.381455	−	3.28625i	0.0147922	−	0.127435i
$666$		−	2.28606i		−	0.0885832i
$667$	−41.9434	−	41.9434i	−1.62406	−	1.62406i
$668$	−15.3944	+	15.3944i	−0.595628	+	0.595628i
$669$		−	3.04379i		−	0.117680i
$670$	14.3599	+	18.1313i	0.554771	+	0.700475i
$671$	−4.39089	−	5.38171i	−0.169508	−	0.207758i
$672$	−0.888243	+	0.888243i	−0.0342647	+	0.0342647i
$673$	−25.6689	+	25.6689i	−0.989465	+	0.989465i	−0.999945	−	0.0104805i	$-0.996664\pi$
$673$	−25.6689	+	25.6689i	−0.989465	+	0.989465i	0.0104805	+	0.999945i	$0.496664\pi$
$674$			17.0516i			0.656805i
$675$	−14.6184	−	23.6158i	−0.562662	−	0.908971i
$676$	−9.33459			−0.359023
$677$	1.67884	+	1.67884i	0.0645231	+	0.0645231i	0.738632	−	0.674109i	$-0.235472\pi$
$677$	1.67884	+	1.67884i	0.0645231	+	0.0645231i	−0.674109	+	0.738632i	$0.735472\pi$
$678$	−8.76101	+	8.76101i	−0.336465	+	0.336465i
$679$	2.49885			0.0958971
$680$	−5.65425	−	7.13928i	−0.216831	−	0.273779i
$681$			10.4118i			0.398982i
$682$	29.2981	+	2.97045i	1.12188	+	0.113744i
$683$	−8.58431	−	8.58431i	−0.328470	−	0.328470i	0.523535	−	0.852004i	$-0.324613\pi$
$683$	−8.58431	−	8.58431i	−0.328470	−	0.328470i	−0.852004	+	0.523535i	$0.824613\pi$
$684$	−2.10396			−0.0804468
$685$	7.53273	+	0.874371i	0.287811	+	0.0334080i
$686$	−1.00000			−0.0381802
$687$	−0.962115	+	0.962115i	−0.0367070	+	0.0367070i
$688$	−4.20653	+	4.20653i	−0.160372	+	0.160372i
$689$	−1.44367			−0.0549994
$690$	18.6591	+	2.16587i	0.710339	+	0.0824534i
$691$	8.46405			0.321988			0.160994	−	0.986955i	$-0.448530\pi$
$691$	8.46405			0.321988			0.160994	+	0.986955i	$0.448530\pi$
$692$	5.59818	+	5.59818i	0.212811	+	0.212811i
$693$	0.475744	−	4.69235i	0.0180720	−	0.178248i
$694$			16.3007i			0.618768i
$695$	5.25292	+	6.63254i	0.199255	+	0.251587i
$696$	−11.1419			−0.422334
$697$	−23.7577	+	23.7577i	−0.899888	+	0.899888i
$698$	−23.5446	−	23.5446i	−0.891175	−	0.891175i
$699$	−23.2653			−0.879974
$700$	−2.63166	−	4.25140i	−0.0994673	−	0.160688i
$701$		−	8.58739i		−	0.324341i	−0.986763	−	0.162171i	$-0.948151\pi$
$701$		−	8.58739i		−	0.324341i	0.986763	−	0.162171i	$-0.0518495\pi$
$702$	−7.51998	+	7.51998i	−0.283823	+	0.283823i
$703$	−1.68182	+	1.68182i	−0.0634312	+	0.0634312i
$704$	−2.09669	−	2.56981i	−0.0790218	−	0.0968533i
$705$	−21.4565	−	27.0918i	−0.808099	−	1.02034i
$706$			29.5302i			1.11138i
$707$	−1.28743	+	1.28743i	−0.0484189	+	0.0484189i
$708$	8.82718	+	8.82718i	0.331746	+	0.331746i
$709$		−	9.13828i		−	0.343195i	−0.985167	−	0.171598i	$-0.945107\pi$
$709$		−	9.13828i		−	0.343195i	0.985167	−	0.171598i	$-0.0548929\pi$
$710$	2.82146	−	24.3070i	0.105888	−	0.912225i
$711$			18.2825i			0.685648i
$712$	5.81808	+	5.81808i	0.218042	+	0.218042i
$713$	41.9869	+	41.9869i	1.57242	+	1.57242i
$714$	5.11615			0.191467
$715$	11.9629	−	7.64759i	0.447389	−	0.286004i
$716$	1.60494			0.0599794
$717$	−24.3511	−	24.3511i	−0.909408	−	0.909408i
$718$	−17.2875	−	17.2875i	−0.645162	−	0.645162i
$719$		−	17.4983i		−	0.652578i	−0.945270	−	0.326289i	$-0.894202\pi$
$719$		−	17.4983i		−	0.652578i	0.945270	−	0.326289i	$-0.105798\pi$
$720$	−2.49271	+	1.97421i	−0.0928980	+	0.0735745i
$721$		−	0.286992i		−	0.0106881i
$722$	−11.8872	−	11.8872i	−0.442395	−	0.442395i
$723$	−1.61540	+	1.61540i	−0.0600774	+	0.0600774i
$724$		−	24.0351i		−	0.893258i
$725$	10.1589	−	43.1698i	0.377290	−	1.60329i
$726$	−13.5366	−	2.77339i	−0.502391	−	0.102930i
$727$	−27.3661	+	27.3661i	−1.01495	+	1.01495i	−0.0150668	+	0.999886i	$0.504796\pi$
$727$	−27.3661	+	27.3661i	−1.01495	+	1.01495i	−0.999886	+	0.0150668i	$0.995204\pi$
$728$	−1.35377	+	1.35377i	−0.0501742	+	0.0501742i
$729$		−	24.7894i		−	0.918126i
$730$	−20.5560	−	25.9547i	−0.760810	−	0.960628i
$731$	24.2290			0.896142
$732$	−1.86016	−	1.86016i	−0.0687536	−	0.0687536i
$733$	−0.449878	+	0.449878i	−0.0166166	+	0.0166166i	−0.715366	−	0.698750i	$-0.753740\pi$
$733$	−0.449878	+	0.449878i	−0.0166166	+	0.0166166i	0.698750	+	0.715366i	$0.253740\pi$
$734$	−24.9605			−0.921310
$735$	2.79014	+	0.323868i	0.102916	+	0.0119461i
$736$		−	6.68752i		−	0.246505i
$737$	3.46043	−	34.1309i	0.127467	−	1.25723i
$738$	8.29512	+	8.29512i	0.305348	+	0.305348i
$739$	−6.02634			−0.221683			−0.110841	−	0.993838i	$-0.535355\pi$
$739$	−6.02634			−0.221683			−0.110841	+	0.993838i	$0.535355\pi$
$740$	−0.414472	+	3.57069i	−0.0152363	+	0.131261i
$741$	3.55820			0.130714
$742$	0.533202	−	0.533202i	0.0195744	−	0.0195744i
$743$	−20.6171	+	20.6171i	−0.756368	+	0.756368i	−0.975659	−	0.219291i	$-0.929625\pi$
$743$	−20.6171	+	20.6171i	−0.756368	+	0.756368i	0.219291	+	0.975659i	$0.429625\pi$
$744$	11.1535			0.408907
$745$	0.685078	+	0.865006i	0.0250993	+	0.0316914i
$746$	−4.91867			−0.180085
$747$	−11.3002	−	11.3002i	−0.413453	−	0.413453i
$748$	−1.36256	+	13.4392i	−0.0498200	+	0.491385i
$749$		−	9.99212i		−	0.365104i
$750$	5.96579	+	12.7143i	0.217840	+	0.464260i
$751$	24.6959			0.901166			0.450583	−	0.892734i	$-0.351216\pi$
$751$	24.6959			0.901166			0.450583	+	0.892734i	$0.351216\pi$
$752$	−8.69999	+	8.69999i	−0.317256	+	0.317256i
$753$	9.85664	+	9.85664i	0.359196	+	0.359196i
$754$	−16.9815			−0.618429
$755$	33.3594	−	26.4204i	1.21407	−	0.961537i
$756$		−	5.55482i		−	0.202027i
$757$	24.1915	−	24.1915i	0.879256	−	0.879256i	−0.114202	−	0.993458i	$-0.536431\pi$
$757$	24.1915	−	24.1915i	0.879256	−	0.879256i	0.993458	+	0.114202i	$0.0364311\pi$
$758$	−14.6592	+	14.6592i	−0.532448	+	0.532448i
$759$	−17.6135	−	21.5880i	−0.639328	−	0.783594i
$760$	3.28625	+	0.381455i	0.119205	+	0.0138368i
$761$		−	18.9888i		−	0.688344i	−0.938907	−	0.344172i	$-0.888160\pi$
$761$		−	18.9888i		−	0.688344i	0.938907	−	0.344172i	$-0.111840\pi$
$762$	−15.0093	+	15.0093i	−0.543731	+	0.543731i
$763$	−5.90571	−	5.90571i	−0.213801	−	0.213801i
$764$		−	5.76500i		−	0.208570i
$765$	12.8644	+	1.49325i	0.465114	+	0.0539887i
$766$		−	1.14028i		−	0.0411998i
$767$	13.4535	+	13.4535i	0.485779	+	0.485779i
$768$	−0.888243	−	0.888243i	−0.0320517	−	0.0320517i
$769$	−17.1249			−0.617538			−0.308769	−	0.951137i	$-0.599917\pi$
$769$	−17.1249			−0.617538			−0.308769	+	0.951137i	$0.599917\pi$
$770$	−1.59382	+	7.24291i	−0.0574374	+	0.261016i
$771$	6.71200			0.241727
$772$	−2.53288	−	2.53288i	−0.0911603	−	0.0911603i
$773$	21.8670	+	21.8670i	0.786502	+	0.786502i	0.980919	−	0.194417i	$-0.0622815\pi$
$773$	21.8670	+	21.8670i	0.786502	+	0.786502i	−0.194417	+	0.980919i	$0.562282\pi$
$774$		−	8.45967i		−	0.304077i
$775$	−10.1694	+	43.2146i	−0.365295	+	1.55231i
$776$			2.49885i			0.0897035i
$777$	−1.42792	−	1.42792i	−0.0512265	−	0.0512265i
$778$	24.7759	−	24.7759i	0.888260	−	0.888260i
$779$		−	12.2052i		−	0.437297i
$780$	4.21566	−	3.33877i	0.150945	−	0.119547i
$781$	−28.1224	+	22.9449i	−1.00630	+	0.821032i
$782$	−19.2596	+	19.2596i	−0.688721	+	0.688721i
$783$	34.8393	−	34.8393i	1.24505	−	1.24505i
$784$		−	1.00000i		−	0.0357143i
$785$	−40.1580	−	4.66139i	−1.43330	−	0.166372i
$786$	−7.57226			−0.270094
$787$	7.04060	+	7.04060i	0.250970	+	0.250970i	0.821368	−	0.570398i	$-0.193211\pi$
$787$	7.04060	+	7.04060i	0.250970	+	0.250970i	−0.570398	+	0.821368i	$0.693211\pi$
$788$	−9.40601	+	9.40601i	−0.335075	+	0.335075i
$789$	30.2401			1.07657
$790$	3.31469	−	28.5562i	0.117931	−	1.01598i
$791$		−	9.86331i		−	0.350699i
$792$	4.69235	+	0.475744i	0.166735	+	0.0169048i
$793$	−2.83508	−	2.83508i	−0.100677	−	0.100677i
$794$	0.751080			0.0266548
$795$	−1.66039	+	1.31502i	−0.0588880	+	0.0466389i
$796$	9.67486			0.342916
$797$	−16.2064	+	16.2064i	−0.574059	+	0.574059i	−0.933260	−	0.359201i	$-0.883049\pi$
$797$	−16.2064	+	16.2064i	−0.574059	+	0.574059i	0.359201	+	0.933260i	$0.383049\pi$
$798$	−1.31418	+	1.31418i	−0.0465213	+	0.0465213i
$799$	50.1107			1.77279
$800$	4.25140	−	2.63166i	0.150310	−	0.0930431i
$801$	−11.7006			−0.413422
$802$	−8.15467	−	8.15467i	−0.287951	−	0.287951i
$803$	−4.95356	+	48.8579i	−0.174807	+	1.72416i
$804$		−	12.9933i		−	0.458238i
$805$	−11.7226	+	9.28418i	−0.413166	+	0.327224i
$806$	16.9991			0.598767
$807$	−19.4055	+	19.4055i	−0.683104	+	0.683104i
$808$	−1.28743	−	1.28743i	−0.0452918	−	0.0452918i
$809$	−1.28331			−0.0451188			−0.0225594	−	0.999746i	$-0.507181\pi$
$809$	−1.28331			−0.0451188			−0.0225594	+	0.999746i	$0.507181\pi$
$810$	−0.699119	+	6.02294i	−0.0245646	+	0.211624i
$811$		−	38.2967i		−	1.34478i	−0.740198	−	0.672389i	$-0.765268\pi$
$811$		−	38.2967i		−	1.34478i	0.740198	−	0.672389i	$-0.234732\pi$
$812$	6.27190	−	6.27190i	0.220101	−	0.220101i
$813$	10.3250	−	10.3250i	0.362115	−	0.362115i
$814$	4.13118	−	3.37060i	0.144798	−	0.118139i
$815$	0.616399	−	5.31030i	0.0215915	−	0.186012i
$816$			5.11615i			0.179101i
$817$	−6.22366	+	6.22366i	−0.217738	+	0.217738i
$818$	6.85772	+	6.85772i	0.239775	+	0.239775i
$819$		−	2.72255i		−	0.0951337i
$820$	−11.4525	−	14.4604i	−0.399940	−	0.504980i
$821$		−	4.69422i		−	0.163829i	−0.996639	−	0.0819147i	$-0.973897\pi$
$821$		−	4.69422i		−	0.163829i	0.996639	−	0.0819147i	$-0.0261035\pi$
$822$	−3.01235	−	3.01235i	−0.105068	−	0.105068i
$823$	−33.8017	−	33.8017i	−1.17825	−	1.17825i	−0.980189	−	0.198065i	$-0.936534\pi$
$823$	−33.8017	−	33.8017i	−1.17825	−	1.17825i	−0.198065	−	0.980189i	$-0.563466\pi$
$824$	0.286992			0.00999784
$825$	6.79273	−	19.6925i	0.236493	−	0.685605i
$826$	−9.93780			−0.345780
$827$	−19.0259	−	19.0259i	−0.661594	−	0.661594i	0.294161	−	0.955756i	$-0.404960\pi$
$827$	−19.0259	−	19.0259i	−0.661594	−	0.661594i	−0.955756	+	0.294161i	$0.904960\pi$
$828$	6.72457	+	6.72457i	0.233695	+	0.233695i
$829$		−	0.385397i		−	0.0133854i	−0.999978	−	0.00669270i	$-0.997870\pi$
$829$		−	0.385397i		−	0.0133854i	0.999978	−	0.00669270i	$-0.00213037\pi$
$830$	15.6015	+	19.6990i	0.541535	+	0.683763i
$831$			37.2200i			1.29115i
$832$	−1.35377	−	1.35377i	−0.0469337	−	0.0469337i
$833$	−2.87993	+	2.87993i	−0.0997836	+	0.0997836i
$834$		−	4.75301i		−	0.164583i
$835$	−5.61307	+	48.3568i	−0.194248	+	1.67346i
$836$	−3.10210	−	3.80209i	−0.107288	−	0.131498i
$837$	−34.8754	+	34.8754i	−1.20547	+	1.20547i
$838$	20.0609	−	20.0609i	0.692991	−	0.692991i
$839$		−	18.6298i		−	0.643173i	−0.946880	−	0.321587i	$-0.895784\pi$
$839$		−	18.6298i		−	0.643173i	0.946880	−	0.321587i	$-0.104216\pi$
$840$	−0.323868	+	2.79014i	−0.0111745	+	0.0962688i
$841$	49.6734			1.71288
$842$	−4.71599	−	4.71599i	−0.162524	−	0.162524i
$843$	10.7468	−	10.7468i	0.370140	−	0.370140i
$844$	11.1990			0.385485
$845$	−16.3626	+	12.9591i	−0.562891	+	0.445806i
$846$		−	17.4964i		−	0.601538i
$847$	9.18106	−	6.05873i	0.315465	−	0.208180i
$848$	0.533202	+	0.533202i	0.0183102	+	0.0183102i
$849$	19.6439			0.674178
$850$	−19.8227	−	4.66474i	−0.679913	−	0.159999i
$851$	10.7507			0.368531
$852$	−9.72040	+	9.72040i	−0.333015	+	0.333015i
$853$	10.2175	−	10.2175i	0.349842	−	0.349842i	−0.510209	−	0.860051i	$-0.670432\pi$
$853$	10.2175	−	10.2175i	0.349842	−	0.349842i	0.860051	+	0.510209i	$0.170432\pi$
$854$	2.09421			0.0716623
$855$	−3.68803	+	2.92089i	−0.126128	+	0.0998924i
$856$	9.99212			0.341524
$857$	−34.2775	−	34.2775i	−1.17090	−	1.17090i	−0.981996	−	0.188903i	$-0.939507\pi$
$857$	−34.2775	−	34.2775i	−1.17090	−	1.17090i	−0.188903	−	0.981996i	$-0.560493\pi$
$858$	−7.93567	−	0.804574i	−0.270919	−	0.0274677i
$859$		−	13.2629i		−	0.452525i	−0.974066	−	0.226263i	$-0.927349\pi$
$859$		−	13.2629i		−	0.452525i	0.974066	−	0.226263i	$-0.0726508\pi$
$860$	−1.53377	+	13.2135i	−0.0523012	+	0.450576i
$861$	10.3626			0.353157
$862$	0.467190	−	0.467190i	0.0159126	−	0.0159126i
$863$	−21.1845	−	21.1845i	−0.721129	−	0.721129i	0.247706	−	0.968835i	$-0.420323\pi$
$863$	−21.1845	−	21.1845i	−0.721129	−	0.721129i	−0.968835	+	0.247706i	$0.920323\pi$
$864$	5.55482			0.188979
$865$	17.5849	+	2.04119i	0.597905	+	0.0694025i
$866$		−	1.28585i		−	0.0436950i
$867$	−0.365980	+	0.365980i	−0.0124293	+	0.0124293i
$868$	−6.27840	+	6.27840i	−0.213103	+	0.213103i
$869$	−33.0386	+	26.9560i	−1.12076	+	0.914418i
$870$	−19.5307	+	15.4682i	−0.662153	+	0.524421i
$871$		−	19.8031i		−	0.671003i
$872$	5.90571	−	5.90571i	0.199993	−	0.199993i
$873$	−2.51270	−	2.51270i	−0.0850419	−	0.0850419i
$874$		−	9.89434i		−	0.334681i
$875$	−10.5152	−	3.79879i	−0.355478	−	0.128423i
$876$			18.5997i			0.628425i
$877$	−21.2067	−	21.2067i	−0.716099	−	0.716099i	0.251705	−	0.967804i	$-0.419009\pi$
$877$	−21.2067	−	21.2067i	−0.716099	−	0.716099i	−0.967804	+	0.251705i	$0.919009\pi$
$878$	2.64772	+	2.64772i	0.0893562	+	0.0893562i
$879$	−34.6910			−1.17010
$880$	−7.24291	−	1.59382i	−0.244158	−	0.0537278i
$881$	3.46287			0.116667			0.0583335	−	0.998297i	$-0.481421\pi$
$881$	3.46287			0.116667			0.0583335	+	0.998297i	$0.481421\pi$
$882$	1.00554	+	1.00554i	0.0338583	+	0.0338583i
$883$	−26.2872	−	26.2872i	−0.884634	−	0.884634i	0.109368	−	0.994001i	$-0.465117\pi$
$883$	−26.2872	−	26.2872i	−0.884634	−	0.884634i	−0.994001	+	0.109368i	$0.965117\pi$
$884$			7.79755i			0.262260i
$885$	27.7278	+	3.21854i	0.932060	+	0.108190i
$886$			19.4763i			0.654319i
$887$	13.2703	+	13.2703i	0.445573	+	0.445573i	0.893880	−	0.448307i	$-0.147973\pi$
$887$	13.2703	+	13.2703i	0.445573	+	0.445573i	−0.448307	+	0.893880i	$0.647973\pi$
$888$	1.42792	−	1.42792i	0.0479180	−	0.0479180i
$889$		−	16.8978i		−	0.566734i
$890$	18.2757	+	2.12137i	0.612602	+	0.0711085i
$891$	6.96835	−	5.68542i	0.233449	−	0.190469i
$892$	−1.71338	+	1.71338i	−0.0573681	+	0.0573681i
$893$	−12.8718	+	12.8718i	−0.430740	+	0.430740i
$894$		−	0.619881i		−	0.0207319i
$895$	2.81330	−	2.22811i	0.0940382	−	0.0744776i
$896$	1.00000			0.0334077
$897$	−11.3725	−	11.3725i	−0.379718	−	0.379718i
$898$	−22.4785	+	22.4785i	−0.750117	+	0.750117i
$899$	−78.7550			−2.62663
$900$	−1.62872	+	6.92119i	−0.0542905	+	0.230706i
$901$		−	3.07116i		−	0.102315i
$902$	−2.75982	+	27.2207i	−0.0918920	+	0.906349i
$903$	−5.28409	−	5.28409i	−0.175844	−	0.175844i
$904$	9.86331			0.328049
$905$	−33.3676	−	42.1312i	−1.10918	−	1.40049i
$906$	−23.9060			−0.794225
$907$	12.1339	−	12.1339i	0.402899	−	0.402899i	−0.476355	−	0.879253i	$-0.658042\pi$
$907$	12.1339	−	12.1339i	0.402899	−	0.402899i	0.879253	+	0.476355i	$0.158042\pi$
$908$	5.86091	−	5.86091i	0.194501	−	0.194501i
$909$	2.58914			0.0858762
$910$	−0.493609	+	4.25246i	−0.0163630	+	0.140968i
$911$	−16.8498			−0.558259			−0.279130	−	0.960253i	$-0.590046\pi$
$911$	−16.8498			−0.558259			−0.279130	+	0.960253i	$0.590046\pi$
$912$	−1.31418	−	1.31418i	−0.0435167	−	0.0435167i
$913$	3.75963	−	37.0819i	0.124426	−	1.22723i
$914$			3.60075i			0.119102i
$915$	−5.84312	−	0.678247i	−0.193168	−	0.0224222i
$916$	1.08317			0.0357888
$917$	4.26249	−	4.26249i	0.140760	−	0.140760i
$918$	−15.9975	−	15.9975i	−0.527996	−	0.527996i
$919$	25.4965			0.841051			0.420526	−	0.907281i	$-0.361846\pi$
$919$	25.4965			0.841051			0.420526	+	0.907281i	$0.361846\pi$
$920$	−9.28418	−	11.7226i	−0.306090	−	0.386481i
$921$		−	21.6690i		−	0.714017i
$922$	−10.2380	+	10.2380i	−0.337172	+	0.337172i
$923$	−14.8149	+	14.8149i	−0.487638	+	0.487638i
$924$	3.22810	−	2.63378i	0.106197	−	0.0866451i
$925$	4.23061	+	6.83448i	0.139102	+	0.224716i
$926$			25.6311i			0.842292i
$927$	−0.288582	+	0.288582i	−0.00947828	+	0.00947828i
$928$	6.27190	+	6.27190i	0.205885	+	0.205885i
$929$		−	12.7297i		−	0.417648i	−0.977953	−	0.208824i	$-0.933036\pi$
$929$		−	12.7297i		−	0.417648i	0.977953	−	0.208824i	$-0.0669637\pi$
$930$	19.5510	−	15.4842i	0.641102	−	0.507748i
$931$		−	1.47952i		−	0.0484894i
$932$	13.0962	+	13.0962i	0.428982	+	0.428982i
$933$	25.4897	+	25.4897i	0.834496	+	0.834496i
$934$	20.5637			0.672866
$935$	16.2690	+	25.4492i	0.532052	+	0.832276i
$936$	2.72255			0.0889894
$937$	12.4492	+	12.4492i	0.406698	+	0.406698i	0.880585	−	0.473888i	$-0.157150\pi$
$937$	12.4492	+	12.4492i	0.406698	+	0.406698i	−0.473888	+	0.880585i	$0.657150\pi$
$938$	7.31404	+	7.31404i	0.238812	+	0.238812i
$939$			14.4289i			0.470870i
$940$	−3.17216	+	27.3283i	−0.103465	+	0.891351i
$941$			47.8865i			1.56106i	0.625121	+	0.780528i	$0.285050\pi$
$941$			47.8865i			1.56106i	−0.625121	+	0.780528i	$0.714950\pi$
$942$	16.0592	+	16.0592i	0.523239	+	0.523239i
$943$	−39.0097	+	39.0097i	−1.27033	+	1.27033i
$944$		−	9.93780i		−	0.323448i
$945$	−7.71168	−	9.73706i	−0.250861	−	0.316747i
$946$	15.2876	−	12.4730i	0.497043	−	0.405533i
$947$	−17.4772	+	17.4772i	−0.567932	+	0.567932i	−0.931549	−	0.363617i	$-0.881542\pi$
$947$	−17.4772	+	17.4772i	−0.567932	+	0.567932i	0.363617	+	0.931549i	$0.381542\pi$
$948$	−11.4197	+	11.4197i	−0.370893	+	0.370893i
$949$			28.3479i			0.920211i
$950$	6.29005	−	3.89360i	0.204076	−	0.126325i
$951$	−17.4182			−0.564824
$952$	−2.87993	−	2.87993i	−0.0933390	−	0.0933390i
$953$	3.85767	−	3.85767i	0.124962	−	0.124962i	−0.641860	−	0.766822i	$-0.721837\pi$
$953$	3.85767	−	3.85767i	0.124962	−	0.124962i	0.766822	+	0.641860i	$0.221837\pi$
$954$	−1.07231			−0.0347174
$955$	−8.00346	−	10.1055i	−0.258986	−	0.327006i
$956$			27.4149i			0.886661i
$957$	36.7651	+	3.72751i	1.18845	+	0.120493i
$958$	26.9332	+	26.9332i	0.870173	+	0.870173i
$959$	3.39136			0.109513
$960$	−2.79014	−	0.323868i	−0.0900513	−	0.0104528i
$961$	47.8367			1.54312
$962$	2.17631	−	2.17631i	0.0701669	−	0.0701669i
$963$	−10.0475	+	10.0475i	−0.323776	+	0.323776i
$964$	1.81865			0.0585747
$965$	−7.95624	−	0.923530i	−0.256121	−	0.0297295i
$966$	8.40062			0.270286
$967$	32.6022	+	32.6022i	1.04842	+	1.04842i	0.998767	+	0.0496495i	$0.0158104\pi$
$967$	32.6022	+	32.6022i	1.04842	+	1.04842i	0.0496495	+	0.998767i	$0.484190\pi$
$968$	6.05873	+	9.18106i	0.194735	+	0.295090i
$969$			7.56947i			0.243166i
$970$	3.46912	+	4.38024i	0.111387	+	0.140641i
$971$	24.9573			0.800919			0.400460	−	0.916314i	$-0.368851\pi$
$971$	24.9573			0.800919			0.400460	+	0.916314i	$0.368851\pi$
$972$	−9.37498	+	9.37498i	−0.300703	+	0.300703i
$973$	2.67551	+	2.67551i	0.0857731	+	0.0857731i
$974$	−27.8119			−0.891152
$975$	2.75447	−	11.7051i	0.0882137	−	0.374862i
$976$			2.09421i			0.0670339i
$977$	26.9726	−	26.9726i	0.862931	−	0.862931i	−0.128746	−	0.991678i	$-0.541095\pi$
$977$	26.9726	−	26.9726i	0.862931	−	0.862931i	0.991678	+	0.128746i	$0.0410953\pi$
$978$	−2.12360	+	2.12360i	−0.0679051	+	0.0679051i
$979$	−17.2515	−	21.1444i	−0.551362	−	0.675778i
$980$	−1.38828	−	1.75290i	−0.0443471	−	0.0559944i
$981$			11.8769i			0.379199i
$982$	4.26932	−	4.26932i	0.136240	−	0.136240i
$983$	1.63673	+	1.63673i	0.0522037	+	0.0522037i	0.732727	−	0.680523i	$-0.238247\pi$
$983$	1.63673	+	1.63673i	0.0522037	+	0.0522037i	−0.680523	+	0.732727i	$0.738247\pi$
$984$			10.3626i			0.330348i
$985$	−3.42959	+	29.5460i	−0.109276	+	0.941414i
$986$		−	36.1252i		−	1.15046i
$987$	−10.9286	−	10.9286i	−0.347862	−	0.347862i
$988$	−2.00294	−	2.00294i	−0.0637221	−	0.0637221i
$989$	39.7836			1.26504
$990$	8.88570	−	5.68039i	0.282406	−	0.180535i
$991$	−5.70763			−0.181309			−0.0906543	−	0.995882i	$-0.528896\pi$
$991$	−5.70763			−0.181309			−0.0906543	+	0.995882i	$0.528896\pi$
$992$	−6.27840	−	6.27840i	−0.199340	−	0.199340i
$993$	−5.21826	−	5.21826i	−0.165596	−	0.165596i
$994$		−	10.9434i		−	0.347104i
$995$	16.9591	−	13.4315i	0.537639	−	0.425806i
$996$		−	14.1167i		−	0.447305i
$997$	1.75802	+	1.75802i	0.0556771	+	0.0556771i	0.734397	−	0.678720i	$-0.237465\pi$
$997$	1.75802	+	1.75802i	0.0556771	+	0.0556771i	−0.678720	+	0.734397i	$0.737465\pi$
$998$	8.79942	−	8.79942i	0.278541	−	0.278541i
$999$			8.92985i			0.282528i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.m.f.43.13	yes	36
5.2	odd	4	inner	770.2.m.f.197.4	yes	36
11.10	odd	2	inner	770.2.m.f.43.4	✓	36
55.32	even	4	inner	770.2.m.f.197.13	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.m.f.43.4	✓	36	11.10	odd	2	inner
770.2.m.f.43.13	yes	36	1.1	even	1	trivial
770.2.m.f.197.4	yes	36	5.2	odd	4	inner
770.2.m.f.197.13	yes	36	55.32	even	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.888243 - 0.888243i) q^{3} +1.00000i q^{4} +(1.38828 + 1.75290i) q^{5} -1.25616i q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.42205i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.888243 - 0.888243i) q^{3} +1.00000i q^{4} +(1.38828 + 1.75290i) q^{5} -1.25616i q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.42205i q^{9} +(-0.257823 + 2.22115i) q^{10} +(2.56981 - 2.09669i) q^{11} +(0.888243 - 0.888243i) q^{12} +(1.35377 - 1.35377i) q^{13} +1.00000i q^{14} +(0.323868 - 2.79014i) q^{15} -1.00000 q^{16} +(2.87993 + 2.87993i) q^{17} +(1.00554 - 1.00554i) q^{18} -1.47952 q^{19} +(-1.75290 + 1.38828i) q^{20} -1.25616i q^{21} +(3.29971 + 0.334548i) q^{22} +(4.72879 + 4.72879i) q^{23} +1.25616 q^{24} +(-1.14533 + 4.86705i) q^{25} +1.91453 q^{26} +(-3.92785 + 3.92785i) q^{27} +(-0.707107 + 0.707107i) q^{28} -8.86980 q^{29} +(2.20193 - 1.74391i) q^{30} +8.87900 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.14498 - 0.420247i) q^{33} +4.07283i q^{34} +(-0.257823 + 2.22115i) q^{35} +1.42205 q^{36} +(1.13673 - 1.13673i) q^{37} +(-1.04618 - 1.04618i) q^{38} -2.40496 q^{39} +(-2.22115 - 0.257823i) q^{40} +8.24941i q^{41} +(0.888243 - 0.888243i) q^{42} +(4.20653 - 4.20653i) q^{43} +(2.09669 + 2.56981i) q^{44} +(2.49271 - 1.97421i) q^{45} +6.68752i q^{46} +(8.69999 - 8.69999i) q^{47} +(0.888243 + 0.888243i) q^{48} +1.00000i q^{49} +(-4.25140 + 2.63166i) q^{50} -5.11615i q^{51} +(1.35377 + 1.35377i) q^{52} +(-0.533202 - 0.533202i) q^{53} -5.55482 q^{54} +(7.24291 + 1.59382i) q^{55} -1.00000 q^{56} +(1.31418 + 1.31418i) q^{57} +(-6.27190 - 6.27190i) q^{58} +9.93780i q^{59} +(2.79014 + 0.323868i) q^{60} -2.09421i q^{61} +(6.27840 + 6.27840i) q^{62} +(1.00554 - 1.00554i) q^{63} -1.00000i q^{64} +(4.25246 + 0.493609i) q^{65} +(-2.63378 - 3.22810i) q^{66} +(7.31404 - 7.31404i) q^{67} +(-2.87993 + 2.87993i) q^{68} -8.40062i q^{69} +(-1.75290 + 1.38828i) q^{70} -10.9434 q^{71} +(1.00554 + 1.00554i) q^{72} +(-10.4699 + 10.4699i) q^{73} +1.60758 q^{74} +(5.34046 - 3.30580i) q^{75} -1.47952i q^{76} +(3.29971 + 0.334548i) q^{77} +(-1.70056 - 1.70056i) q^{78} -12.8565 q^{79} +(-1.38828 - 1.75290i) q^{80} +2.71162 q^{81} +(-5.83322 + 5.83322i) q^{82} +(7.94643 - 7.94643i) q^{83} +1.25616 q^{84} +(-1.05007 + 9.04639i) q^{85} +5.94893 q^{86} +(7.87854 + 7.87854i) q^{87} +(-0.334548 + 3.29971i) q^{88} -8.22801i q^{89} +(3.15859 + 0.366637i) q^{90} +1.91453 q^{91} +(-4.72879 + 4.72879i) q^{92} +(-7.88671 - 7.88671i) q^{93} +12.3036 q^{94} +(-2.05400 - 2.59346i) q^{95} +1.25616i q^{96} +(1.76695 - 1.76695i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(-2.98159 - 3.65439i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{3}+O(q^{10}) \) 36 * q - 4 * q^3	\( 36 q - 4 q^{3} + 12 q^{11} + 4 q^{12} - 4 q^{15} - 36 q^{16} - 12 q^{20} - 12 q^{22} + 4 q^{23} + 12 q^{25} + 24 q^{26} + 56 q^{27} + 8 q^{31} - 44 q^{33} - 44 q^{36} - 28 q^{37} + 16 q^{38} + 4 q^{42} - 44 q^{45} + 12 q^{47} + 4 q^{48} + 28 q^{53} + 40 q^{55} - 36 q^{56} - 24 q^{58} + 12 q^{60} + 24 q^{66} + 12 q^{67} - 12 q^{70} - 112 q^{71} - 52 q^{75} - 12 q^{77} + 48 q^{78} + 4 q^{81} + 40 q^{82} + 32 q^{86} - 12 q^{88} + 24 q^{91} - 4 q^{92} - 80 q^{93} + 100 q^{97}+O(q^{100}) \) 36 * q - 4 * q^3 + 12 * q^11 + 4 * q^12 - 4 * q^15 - 36 * q^16 - 12 * q^20 - 12 * q^22 + 4 * q^23 + 12 * q^25 + 24 * q^26 + 56 * q^27 + 8 * q^31 - 44 * q^33 - 44 * q^36 - 28 * q^37 + 16 * q^38 + 4 * q^42 - 44 * q^45 + 12 * q^47 + 4 * q^48 + 28 * q^53 + 40 * q^55 - 36 * q^56 - 24 * q^58 + 12 * q^60 + 24 * q^66 + 12 * q^67 - 12 * q^70 - 112 * q^71 - 52 * q^75 - 12 * q^77 + 48 * q^78 + 4 * q^81 + 40 * q^82 + 32 * q^86 - 12 * q^88 + 24 * q^91 - 4 * q^92 - 80 * q^93 + 100 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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