LMFDB - Embedded newform 430.2.l.a.7.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(7,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("430.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.l (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.15
Character	$\chi$	$=$	430.7
Dual form			430.2.l.a.123.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.356683 + 1.33116i) q^{3} -1.00000i q^{4} +(-2.17879 - 0.502846i) q^{5} +(0.689058 + 1.19348i) q^{6} +(0.982140 + 3.66540i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.953316 + 0.550397i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.356683 + 1.33116i) q^{3} -1.00000i q^{4} +(-2.17879 - 0.502846i) q^{5} +(0.689058 + 1.19348i) q^{6} +(0.982140 + 3.66540i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.953316 + 0.550397i) q^{9} +(-1.89621 + 1.18507i) q^{10} -3.08561 q^{11} +(1.33116 + 0.356683i) q^{12} +(0.926064 + 3.45612i) q^{13} +(3.28630 + 1.89735i) q^{14} +(1.44651 - 2.72096i) q^{15} -1.00000 q^{16} +(-5.28586 + 1.41634i) q^{17} +(1.06329 - 0.284907i) q^{18} +(1.41091 + 2.44376i) q^{19} +(-0.502846 + 2.17879i) q^{20} -5.22953 q^{21} +(-2.18186 + 2.18186i) q^{22} +(5.99981 + 1.60764i) q^{23} +(1.19348 - 0.689058i) q^{24} +(4.49429 + 2.19120i) q^{25} +(3.09867 + 1.78902i) q^{26} +(-3.99612 + 3.99612i) q^{27} +(3.66540 - 0.982140i) q^{28} +(2.57370 - 4.45777i) q^{29} +(-0.901178 - 2.94685i) q^{30} +(0.770423 + 1.33441i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.10059 - 4.10744i) q^{33} +(-2.73616 + 4.73918i) q^{34} +(-0.296750 - 8.48001i) q^{35} +(0.550397 - 0.953316i) q^{36} +(-2.01924 - 0.541054i) q^{37} +(2.72567 + 0.730340i) q^{38} -4.93095 q^{39} +(1.18507 + 1.89621i) q^{40} -5.14804 q^{41} +(-3.69784 + 3.69784i) q^{42} +(6.18280 + 2.18471i) q^{43} +3.08561i q^{44} +(-1.80031 - 1.67857i) q^{45} +(5.37928 - 3.10573i) q^{46} +(0.934631 + 0.934631i) q^{47} +(0.356683 - 1.33116i) q^{48} +(-6.40835 + 3.69986i) q^{49} +(4.72735 - 1.62853i) q^{50} -7.54151i q^{51} +(3.45612 - 0.926064i) q^{52} +(-5.74837 - 1.54027i) q^{53} +5.65137i q^{54} +(6.72292 + 1.55159i) q^{55} +(1.89735 - 3.28630i) q^{56} +(-3.75628 + 1.00649i) q^{57} +(-1.33224 - 4.97200i) q^{58} -11.4272i q^{59} +(-2.72096 - 1.44651i) q^{60} +(-8.42126 - 4.86202i) q^{61} +(1.48834 + 0.398801i) q^{62} +(-1.08113 + 4.03485i) q^{63} +1.00000i q^{64} +(-0.279807 - 7.99584i) q^{65} +(-2.12617 - 3.68263i) q^{66} +(3.31052 - 12.3550i) q^{67} +(1.41634 + 5.28586i) q^{68} +(-4.28006 + 7.41327i) q^{69} +(-6.20611 - 5.78644i) q^{70} +(4.81086 + 2.77755i) q^{71} +(-0.284907 - 1.06329i) q^{72} +(10.6716 - 2.85944i) q^{73} +(-1.81040 + 1.04524i) q^{74} +(-4.51987 + 5.20105i) q^{75} +(2.44376 - 1.41091i) q^{76} +(-3.03050 - 11.3100i) q^{77} +(-3.48671 + 3.48671i) q^{78} +(-0.130872 - 0.0755588i) q^{79} +(2.17879 + 0.502846i) q^{80} +(-2.24293 - 3.88488i) q^{81} +(-3.64021 + 3.64021i) q^{82} +(6.50323 + 1.74253i) q^{83} +5.22953i q^{84} +(12.2290 - 0.427943i) q^{85} +(5.91672 - 2.82708i) q^{86} +(5.01601 + 5.01601i) q^{87} +(2.18186 + 2.18186i) q^{88} +(8.18633 + 14.1791i) q^{89} +(-2.45995 + 0.0860836i) q^{90} +(-11.7585 + 6.78878i) q^{91} +(1.60764 - 5.99981i) q^{92} +(-2.05111 + 0.549594i) q^{93} +1.32177 q^{94} +(-1.84524 - 6.03393i) q^{95} +(-0.689058 - 1.19348i) q^{96} +(5.41942 + 5.41942i) q^{97} +(-1.91519 + 7.14758i) q^{98} +(-2.94157 - 1.69831i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{6} + 12 q^{7}+O(q^{10}) $ 88 * q + 4 * q^6 + 12 * q^7	$ 88 q + 4 q^{6} + 12 q^{7} + 16 q^{13} - 88 q^{16} + 4 q^{17} - 16 q^{21} + 12 q^{23} - 8 q^{25} + 12 q^{28} - 36 q^{30} - 40 q^{31} + 12 q^{33} - 40 q^{35} - 40 q^{36} + 16 q^{38} - 56 q^{41} - 56 q^{43} + 24 q^{46} + 72 q^{47} + 24 q^{50} - 16 q^{52} + 20 q^{53} + 24 q^{55} - 8 q^{56} + 20 q^{57} + 8 q^{60} + 72 q^{61} + 36 q^{62} - 40 q^{66} - 16 q^{67} + 4 q^{68} + 24 q^{71} + 60 q^{73} - 48 q^{76} - 48 q^{77} + 40 q^{78} + 28 q^{81} + 20 q^{86} - 64 q^{87} - 8 q^{90} + 48 q^{91} - 12 q^{92} - 108 q^{93} + 4 q^{95} - 4 q^{96} - 48 q^{97} - 96 q^{98}+O(q^{100}) $ 88 * q + 4 * q^6 + 12 * q^7 + 16 * q^13 - 88 * q^16 + 4 * q^17 - 16 * q^21 + 12 * q^23 - 8 * q^25 + 12 * q^28 - 36 * q^30 - 40 * q^31 + 12 * q^33 - 40 * q^35 - 40 * q^36 + 16 * q^38 - 56 * q^41 - 56 * q^43 + 24 * q^46 + 72 * q^47 + 24 * q^50 - 16 * q^52 + 20 * q^53 + 24 * q^55 - 8 * q^56 + 20 * q^57 + 8 * q^60 + 72 * q^61 + 36 * q^62 - 40 * q^66 - 16 * q^67 + 4 * q^68 + 24 * q^71 + 60 * q^73 - 48 * q^76 - 48 * q^77 + 40 * q^78 + 28 * q^81 + 20 * q^86 - 64 * q^87 - 8 * q^90 + 48 * q^91 - 12 * q^92 - 108 * q^93 + 4 * q^95 - 4 * q^96 - 48 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.356683	+	1.33116i	−0.205931	+	0.768545i	0.783233	+	0.621728i	$0.213569\pi$
$3$	−0.356683	+	1.33116i	−0.205931	+	0.768545i	−0.989164	+	0.146816i	$0.953097\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−2.17879	−	0.502846i	−0.974387	−	0.224880i
$5$	−2.17879	−	0.502846i	−0.974387	−	0.224880i
$6$	0.689058	+	1.19348i	0.281307	+	0.487238i
$7$	0.982140	+	3.66540i	0.371214	+	1.38539i	0.858799	+	0.512314i	$0.171211\pi$
$7$	0.982140	+	3.66540i	0.371214	+	1.38539i	−0.487585	+	0.873076i	$0.662122\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.953316	+	0.550397i	0.317772	+	0.183466i
$10$	−1.89621	+	1.18507i	−0.599633	+	0.374753i
$11$	−3.08561			−0.930348			−0.465174	−	0.885219i	$-0.654008\pi$
$11$	−3.08561			−0.930348			−0.465174	+	0.885219i	$0.654008\pi$
$12$	1.33116	+	0.356683i	0.384272	+	0.102965i
$13$	0.926064	+	3.45612i	0.256844	+	0.958555i	0.967055	+	0.254566i	$0.0819327\pi$
$13$	0.926064	+	3.45612i	0.256844	+	0.958555i	−0.710211	+	0.703988i	$0.751401\pi$
$14$	3.28630	+	1.89735i	0.878302	+	0.507088i
$15$	1.44651	−	2.72096i	0.373486	−	0.702550i
$16$	−1.00000			−0.250000
$17$	−5.28586	+	1.41634i	−1.28201	+	0.343514i	−0.834621	−	0.550825i	$-0.814313\pi$
$17$	−5.28586	+	1.41634i	−1.28201	+	0.343514i	−0.447390	+	0.894339i	$0.647646\pi$
$18$	1.06329	−	0.284907i	0.250619	−	0.0671531i
$19$	1.41091	+	2.44376i	0.323685	+	0.560638i	0.981245	−	0.192763i	$-0.0617450\pi$
$19$	1.41091	+	2.44376i	0.323685	+	0.560638i	−0.657561	+	0.753402i	$0.728412\pi$
$20$	−0.502846	+	2.17879i	−0.112440	+	0.487193i
$21$	−5.22953			−1.14118
$22$	−2.18186	+	2.18186i	−0.465174	+	0.465174i
$23$	5.99981	+	1.60764i	1.25105	+	0.335217i	0.822740	−	0.568417i	$-0.192444\pi$
$23$	5.99981	+	1.60764i	1.25105	+	0.335217i	0.428305	+	0.903634i	$0.359111\pi$
$24$	1.19348	−	0.689058i	0.243619	−	0.140653i
$25$	4.49429	+	2.19120i	0.898858	+	0.438239i
$26$	3.09867	+	1.78902i	0.607699	+	0.350855i
$27$	−3.99612	+	3.99612i	−0.769054	+	0.769054i
$28$	3.66540	−	0.982140i	0.692695	−	0.185607i
$29$	2.57370	−	4.45777i	0.477923	−	0.827787i	−0.521757	−	0.853094i	$-0.674723\pi$
$29$	2.57370	−	4.45777i	0.477923	−	0.827787i	0.999680	+	0.0253072i	$0.00805639\pi$
$30$	−0.901178	−	2.94685i	−0.164532	−	0.538018i
$31$	0.770423	+	1.33441i	0.138372	+	0.239668i	0.926881	−	0.375356i	$-0.122480\pi$
$31$	0.770423	+	1.33441i	0.138372	+	0.239668i	−0.788508	+	0.615024i	$0.789146\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	1.10059	−	4.10744i	0.191587	−	0.715014i
$34$	−2.73616	+	4.73918i	−0.469248	+	0.812762i
$35$	−0.296750	−	8.48001i	−0.0501599	−	1.43338i
$36$	0.550397	−	0.953316i	0.0917329	−	0.158886i
$37$	−2.01924	−	0.541054i	−0.331961	−	0.0889488i	0.0889886	−	0.996033i	$-0.471637\pi$
$37$	−2.01924	−	0.541054i	−0.331961	−	0.0889488i	−0.420950	+	0.907084i	$0.638303\pi$
$38$	2.72567	+	0.730340i	0.442161	+	0.118477i
$39$	−4.93095			−0.789584
$40$	1.18507	+	1.89621i	0.187377	+	0.299817i
$41$	−5.14804			−0.803989			−0.401994	−	0.915642i	$-0.631683\pi$
$41$	−5.14804			−0.803989			−0.401994	+	0.915642i	$0.631683\pi$
$42$	−3.69784	+	3.69784i	−0.570589	+	0.570589i
$43$	6.18280	+	2.18471i	0.942869	+	0.333165i
$43$	6.18280	+	2.18471i	0.942869	+	0.333165i
$44$			3.08561i			0.465174i
$45$	−1.80031	−	1.67857i	−0.268375	−	0.250227i
$46$	5.37928	−	3.10573i	0.793131	−	0.457915i
$47$	0.934631	+	0.934631i	0.136330	+	0.136330i	0.771979	−	0.635649i	$-0.219267\pi$
$47$	0.934631	+	0.934631i	0.136330	+	0.136330i	−0.635649	+	0.771979i	$0.719267\pi$
$48$	0.356683	−	1.33116i	0.0514827	−	0.192136i
$49$	−6.40835	+	3.69986i	−0.915478	+	0.528552i
$50$	4.72735	−	1.62853i	0.668549	−	0.230309i
$51$		−	7.54151i		−	1.05602i
$52$	3.45612	−	0.926064i	0.479277	−	0.128422i
$53$	−5.74837	−	1.54027i	−0.789599	−	0.211572i	−0.158586	−	0.987345i	$-0.550694\pi$
$53$	−5.74837	−	1.54027i	−0.789599	−	0.211572i	−0.631012	+	0.775773i	$0.717360\pi$
$54$			5.65137i			0.769054i
$55$	6.72292	+	1.55159i	0.906518	+	0.209216i
$56$	1.89735	−	3.28630i	0.253544	−	0.439151i
$57$	−3.75628	+	1.00649i	−0.497532	+	0.133313i
$58$	−1.33224	−	4.97200i	−0.174932	−	0.652855i
$59$		−	11.4272i		−	1.48770i	−0.668346	−	0.743850i	$-0.732998\pi$
$59$		−	11.4272i		−	1.48770i	0.668346	−	0.743850i	$-0.267002\pi$
$60$	−2.72096	−	1.44651i	−0.351275	−	0.186743i
$61$	−8.42126	−	4.86202i	−1.07823	−	0.622517i	−0.147813	−	0.989015i	$-0.547223\pi$
$61$	−8.42126	−	4.86202i	−1.07823	−	0.622517i	−0.930419	+	0.366498i	$0.880557\pi$
$62$	1.48834	+	0.398801i	0.189020	+	0.0506477i
$63$	−1.08113	+	4.03485i	−0.136210	+	0.508343i
$64$			1.00000i			0.125000i
$65$	−0.279807	−	7.99584i	−0.0347058	−	0.991762i
$66$	−2.12617	−	3.68263i	−0.261713	−	0.453301i
$67$	3.31052	−	12.3550i	0.404445	−	1.50941i	−0.400632	−	0.916239i	$-0.631210\pi$
$67$	3.31052	−	12.3550i	0.404445	−	1.50941i	0.805077	−	0.593170i	$-0.202124\pi$
$68$	1.41634	+	5.28586i	0.171757	+	0.641005i
$69$	−4.28006	+	7.41327i	−0.515258	+	0.892453i
$70$	−6.20611	−	5.78644i	−0.741772	−	0.691612i
$71$	4.81086	+	2.77755i	0.570944	+	0.329635i	0.757526	−	0.652805i	$-0.226408\pi$
$71$	4.81086	+	2.77755i	0.570944	+	0.329635i	−0.186582	+	0.982439i	$0.559741\pi$
$72$	−0.284907	−	1.06329i	−0.0335766	−	0.125309i
$73$	10.6716	−	2.85944i	1.24901	−	0.334672i	0.427057	−	0.904225i	$-0.359550\pi$
$73$	10.6716	−	2.85944i	1.24901	−	0.334672i	0.821954	+	0.569553i	$0.192884\pi$
$74$	−1.81040	+	1.04524i	−0.210455	+	0.121506i
$75$	−4.51987	+	5.20105i	−0.521909	+	0.600566i
$76$	2.44376	−	1.41091i	0.280319	−	0.161842i
$77$	−3.03050	−	11.3100i	−0.345358	−	1.28889i
$78$	−3.48671	+	3.48671i	−0.394792	+	0.394792i
$79$	−0.130872	−	0.0755588i	−0.0147242	−	0.00850103i	0.492620	−	0.870245i	$-0.336039\pi$
$79$	−0.130872	−	0.0755588i	−0.0147242	−	0.00850103i	−0.507344	+	0.861744i	$0.669373\pi$
$80$	2.17879	+	0.502846i	0.243597	+	0.0562199i
$81$	−2.24293	−	3.88488i	−0.249215	−	0.431653i
$82$	−3.64021	+	3.64021i	−0.401994	+	0.401994i
$83$	6.50323	+	1.74253i	0.713822	+	0.191268i	0.597413	−	0.801933i	$-0.296195\pi$
$83$	6.50323	+	1.74253i	0.713822	+	0.191268i	0.116408	+	0.993201i	$0.462862\pi$
$84$			5.22953i			0.570589i
$85$	12.2290	−	0.427943i	1.32642	−	0.0464170i
$86$	5.91672	−	2.82708i	0.638017	−	0.304852i
$87$	5.01601	+	5.01601i	0.537772	+	0.537772i
$88$	2.18186	+	2.18186i	0.232587	+	0.232587i
$89$	8.18633	+	14.1791i	0.867749	+	1.50298i	0.864292	+	0.502991i	$0.167767\pi$
$89$	8.18633	+	14.1791i	0.867749	+	1.50298i	0.00345698	+	0.999994i	$0.498900\pi$
$90$	−2.45995	+	0.0860836i	−0.259301	+	0.00907400i
$91$	−11.7585	+	6.78878i	−1.23263	+	0.711658i
$92$	1.60764	−	5.99981i	0.167608	−	0.625523i
$93$	−2.05111	+	0.549594i	−0.212690	+	0.0569902i
$94$	1.32177			0.136330
$95$	−1.84524	−	6.03393i	−0.189318	−	0.619068i
$96$	−0.689058	−	1.19348i	−0.0703267	−	0.121809i
$97$	5.41942	+	5.41942i	0.550259	+	0.550259i	0.926516	−	0.376256i	$-0.122789\pi$
$97$	5.41942	+	5.41942i	0.550259	+	0.550259i	−0.376256	+	0.926516i	$0.622789\pi$
$98$	−1.91519	+	7.14758i	−0.193463	+	0.722015i
$99$	−2.94157	−	1.69831i	−0.295638	−	0.170687i
$100$	2.19120	−	4.49429i	0.219120	−	0.449429i
$101$	2.50329	−	4.33582i	0.249086	−	0.431430i	−0.714186	−	0.699956i	$-0.753203\pi$
$101$	2.50329	−	4.33582i	0.249086	−	0.431430i	0.963273	+	0.268525i	$0.0865363\pi$
$102$	−5.33265	−	5.33265i	−0.528011	−	0.528011i
$103$	−4.93106	−	18.4030i	−0.485872	−	1.81330i	−0.576103	−	0.817377i	$-0.695427\pi$
$103$	−4.93106	−	18.4030i	−0.485872	−	1.81330i	0.0902308	−	0.995921i	$-0.471240\pi$
$104$	1.78902	−	3.09867i	0.175428	−	0.303850i
$105$	11.3941	+	2.62965i	1.11195	+	0.256628i
$106$	−5.15384	+	2.97557i	−0.500586	+	0.289013i
$107$	11.3309	+	11.3309i	1.09540	+	1.09540i	0.994941	+	0.100457i	$0.0320306\pi$
$107$	11.3309	+	11.3309i	1.09540	+	1.09540i	0.100457	+	0.994941i	$0.467969\pi$
$108$	3.99612	+	3.99612i	0.384527	+	0.384527i
$109$	−0.412546	+	0.238184i	−0.0395148	+	0.0228139i	−0.519627	−	0.854393i	$-0.673929\pi$
$109$	−0.412546	+	0.238184i	−0.0395148	+	0.0228139i	0.480112	+	0.877207i	$0.340596\pi$
$110$	5.85096	−	3.65668i	0.557867	−	0.348651i
$111$	1.44046	−	2.49495i	0.136722	−	0.236810i
$112$	−0.982140	−	3.66540i	−0.0928035	−	0.346347i
$113$	2.50734	+	2.50734i	0.235871	+	0.235871i	0.815138	−	0.579267i	$-0.196661\pi$
$113$	2.50734	+	2.50734i	0.235871	+	0.235871i	−0.579267	+	0.815138i	$0.696661\pi$
$114$	−1.94440	+	3.36779i	−0.182109	+	0.315423i
$115$	−12.2639	−	6.51970i	−1.14362	−	0.607965i
$116$	−4.45777	−	2.57370i	−0.413894	−	0.238962i
$117$	−1.01941	+	3.80448i	−0.0942441	+	0.351724i
$118$	−8.08028	−	8.08028i	−0.743850	−	0.743850i
$119$	−10.3829	−	17.9837i	−0.951800	−	1.64857i
$120$	−2.94685	+	0.901178i	−0.269009	+	0.0822659i
$121$	−1.47898			−0.134453
$122$	−9.39269	+	2.51676i	−0.850374	+	0.227857i
$123$	1.83622	−	6.85286i	0.165566	−	0.617901i
$124$	1.33441	−	0.770423i	0.119834	−	0.0691861i
$125$	−8.69030	−	7.03411i	−0.777284	−	0.629150i
$126$	2.08859	+	3.61754i	0.186066	+	0.322276i
$127$	6.62157	+	6.62157i	0.587570	+	0.587570i	0.936973	−	0.349403i	$-0.113616\pi$
$127$	6.62157	+	6.62157i	0.587570	+	0.587570i	−0.349403	+	0.936973i	$0.613616\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−5.11349	+	7.45104i	−0.450218	+	0.656028i
$130$	−5.85177	−	5.45606i	−0.513234	−	0.478528i
$131$			7.65046i			0.668424i	0.942498	+	0.334212i	$0.108470\pi$
$131$			7.65046i			0.668424i	−0.942498	+	0.334212i	$0.891530\pi$
$132$	−4.10744	−	1.10059i	−0.357507	−	0.0957937i
$133$	−7.57165	+	7.57165i	−0.656546	+	0.656546i
$134$	−6.39544	−	11.0772i	−0.552482	−	0.956927i
$135$	10.7162	−	6.69730i	0.922301	−	0.576412i
$136$	4.73918	+	2.73616i	0.406381	+	0.234624i
$137$	−5.69838	+	5.69838i	−0.486845	+	0.486845i	−0.907309	−	0.420464i	$-0.861867\pi$
$137$	−5.69838	+	5.69838i	−0.486845	+	0.486845i	0.420464	+	0.907309i	$0.361867\pi$
$138$	2.21552	+	8.26843i	0.188598	+	0.703856i
$139$	−13.3233	+	7.69222i	−1.13007	+	0.652446i	−0.943952	−	0.330082i	$-0.892924\pi$
$139$	−13.3233	+	7.69222i	−1.13007	+	0.652446i	−0.186117	+	0.982528i	$0.559590\pi$
$140$	−8.48001	+	0.296750i	−0.716692	+	0.0250800i
$141$	−1.57751	+	0.910775i	−0.132850	+	0.0767011i
$142$	5.36582	−	1.43777i	0.450289	−	0.120655i
$143$	−2.85748	−	10.6642i	−0.238954	−	0.891789i
$144$	−0.953316	−	0.550397i	−0.0794430	−	0.0458664i
$145$	−7.84913	+	8.41839i	−0.651834	+	0.699110i
$146$	5.52400	−	9.56786i	0.457170	−	0.791841i
$147$	−2.63935	−	9.85020i	−0.217690	−	0.812431i
$148$	−0.541054	+	2.01924i	−0.0444744	+	0.165981i
$149$	7.44505	+	12.8952i	0.609922	+	1.05642i	0.991253	+	0.131978i	$0.0421328\pi$
$149$	7.44505	+	12.8952i	0.609922	+	1.05642i	−0.381330	+	0.924439i	$0.624534\pi$
$150$	0.481670	+	6.87373i	0.0393282	+	0.561238i
$151$		−	2.00303i		−	0.163004i	−0.996673	−	0.0815020i	$-0.974028\pi$
$151$		−	2.00303i		−	0.163004i	0.996673	−	0.0815020i	$-0.0259717\pi$
$152$	0.730340	−	2.72567i	0.0592384	−	0.221081i
$153$	−5.81865	−	1.55910i	−0.470410	−	0.126046i
$154$	−10.1403	−	5.85449i	−0.817126	−	0.471768i
$155$	−1.00759	−	3.29482i	−0.0809316	−	0.264646i
$156$			4.93095i			0.394792i
$157$	3.82484	+	14.2745i	0.305256	+	1.13923i	0.932725	+	0.360588i	$0.117424\pi$
$157$	3.82484	+	14.2745i	0.305256	+	1.13923i	−0.627470	+	0.778641i	$0.715909\pi$
$158$	−0.145968	+	0.0391121i	−0.0116126	+	0.00311159i
$159$	4.10069	−	7.10260i	0.325206	−	0.563273i
$160$	1.89621	−	1.18507i	0.149908	−	0.0936884i
$161$			23.5706i			1.85762i
$162$	−4.33302	−	1.16103i	−0.340434	−	0.0912190i
$163$	11.3824	−	3.04991i	0.891539	−	0.238887i	0.216160	−	0.976358i	$-0.430647\pi$
$163$	11.3824	−	3.04991i	0.891539	−	0.238887i	0.675379	+	0.737471i	$0.263980\pi$
$164$			5.14804i			0.401994i
$165$	−4.46336	+	8.39585i	−0.347472	+	0.653616i
$166$	5.83063	−	3.36632i	0.452545	−	0.261277i
$167$	0.768359	−	2.86755i	0.0594574	−	0.221898i	−0.929804	−	0.368055i	$-0.880024\pi$
$167$	0.768359	−	2.86755i	0.0594574	−	0.221898i	0.989261	+	0.146157i	$0.0466905\pi$
$168$	3.69784	+	3.69784i	0.285295	+	0.285295i
$169$	0.171172	−	0.0988262i	0.0131671	−	0.00760201i
$170$	8.34462	−	8.94982i	0.640003	−	0.686420i
$171$			3.10624i			0.237540i
$172$	2.18471	−	6.18280i	0.166582	−	0.471434i
$173$	−11.1981	+	11.1981i	−0.851378	+	0.851378i	−0.990303	−	0.138925i	$-0.955635\pi$
$173$	−11.1981	+	11.1981i	−0.851378	+	0.851378i	0.138925	+	0.990303i	$0.455635\pi$
$174$	7.09370			0.537772
$175$	−3.61758	+	18.6254i	−0.273464	+	1.40795i
$176$	3.08561			0.232587
$177$	15.2115	+	4.07590i	1.14336	+	0.306364i
$178$	15.8148	+	4.23755i	1.18537	+	0.317618i
$179$	10.9405	−	18.9495i	0.817732	−	1.41635i	−0.0896172	−	0.995976i	$-0.528564\pi$
$179$	10.9405	−	18.9495i	0.817732	−	1.41635i	0.907349	−	0.420377i	$-0.138102\pi$
$180$	−1.67857	+	1.80031i	−0.125113	+	0.134187i
$181$	−0.841674	+	1.45782i	−0.0625611	+	0.108359i	−0.895610	−	0.444841i	$-0.853260\pi$
$181$	−0.841674	+	1.45782i	−0.0625611	+	0.108359i	0.833048	+	0.553200i	$0.186594\pi$
$182$	−3.51413	+	13.1149i	−0.260485	+	0.972143i
$183$	9.47583	−	9.47583i	0.700474	−	0.700474i
$184$	−3.10573	−	5.37928i	−0.228957	−	0.396566i
$185$	4.12745	+	2.19421i	0.303456	+	0.161322i
$186$	−1.06173	+	1.83898i	−0.0778501	+	0.134840i
$187$	16.3101	−	4.37029i	1.19272	−	0.319587i
$188$	0.934631	−	0.934631i	0.0681650	−	0.0681650i
$189$	−18.5721	−	10.7226i	−1.35092	−	0.779956i
$190$	−5.57142	−	2.96185i	−0.404193	−	0.214875i
$191$	−5.90159	+	3.40728i	−0.427024	+	0.246542i	−0.698078	−	0.716022i	$-0.745961\pi$
$191$	−5.90159	+	3.40728i	−0.427024	+	0.246542i	0.271054	+	0.962564i	$0.412628\pi$
$192$	−1.33116	−	0.356683i	−0.0960681	−	0.0257414i
$193$	8.31762	−	8.31762i	0.598715	−	0.598715i	−0.341255	−	0.939971i	$-0.610852\pi$
$193$	8.31762	−	8.31762i	0.598715	−	0.598715i	0.939971	+	0.341255i	$0.110852\pi$
$194$	7.66422			0.550259
$195$	10.7435	+	2.47951i	0.769360	+	0.177561i
$196$	3.69986	+	6.40835i	0.264276	+	0.457739i
$197$	−12.7799	+	3.42437i	−0.910531	+	0.243976i	−0.683534	−	0.729919i	$-0.739558\pi$
$197$	−12.7799	+	3.42437i	−0.910531	+	0.243976i	−0.226998	+	0.973895i	$0.572891\pi$
$198$	−3.28089	+	0.879112i	−0.233163	+	0.0624758i
$199$	−14.8453			−1.05235			−0.526177	−	0.850375i	$-0.676375\pi$
$199$	−14.8453			−1.05235			−0.526177	+	0.850375i	$0.676375\pi$
$200$	−1.62853	−	4.72735i	−0.115155	−	0.334274i
$201$	15.2657	+	8.81366i	1.07676	+	0.621668i
$202$	−1.29580	−	4.83598i	−0.0911720	−	0.340258i
$203$	18.8672	+	5.05546i	1.32422	+	0.354823i
$204$	−7.54151			−0.528011
$205$	11.2165	+	2.58867i	0.783396	+	0.180801i
$206$	−16.4996	−	9.52608i	−1.14959	−	0.663713i
$207$	4.83487	+	4.83487i	0.336046	+	0.336046i
$208$	−0.926064	−	3.45612i	−0.0642110	−	0.239639i
$209$	−4.35352	−	7.54052i	−0.301139	−	0.521588i
$210$	9.91628	−	6.19739i	0.684288	−	0.427660i
$211$			2.46597i			0.169765i	0.996391	+	0.0848823i	$0.0270514\pi$
$211$			2.46597i			0.169765i	−0.996391	+	0.0848823i	$0.972949\pi$
$212$	−1.54027	+	5.74837i	−0.105786	+	0.394799i
$213$	−5.41331	+	5.41331i	−0.370914	+	0.370914i
$214$	16.0243			1.09540
$215$	−12.3725	−	7.86903i	−0.843797	−	0.536663i
$216$	5.65137			0.384527
$217$	−4.13449	+	4.13449i	−0.280667	+	0.280667i
$218$	−0.123293	+	0.460136i	−0.00835046	+	0.0311643i
$219$			15.2254i			1.02884i
$220$	1.55159	−	6.72292i	0.104608	−	0.453259i
$221$	−9.79010	−	16.9569i	−0.658553	−	1.14065i
$222$	−0.745636	−	2.78275i	−0.0500438	−	0.186766i
$223$	18.7017	+	18.7017i	1.25236	+	1.25236i	0.954659	+	0.297700i	$0.0962196\pi$
$223$	18.7017	+	18.7017i	1.25236	+	1.25236i	0.297700	+	0.954659i	$0.403780\pi$
$224$	−3.28630	−	1.89735i	−0.219575	−	0.126772i
$225$	3.07845	+	4.56255i	0.205230	+	0.304170i
$226$	3.54591			0.235871
$227$	23.4394	+	6.28056i	1.55572	+	0.416855i	0.931307	−	0.364235i	$-0.118670\pi$
$227$	23.4394	+	6.28056i	1.55572	+	0.416855i	0.624418	+	0.781091i	$0.285336\pi$
$228$	1.00649	+	3.75628i	0.0666567	+	0.248766i
$229$	14.5186	+	8.38232i	0.959416	+	0.553919i	0.895993	−	0.444068i	$-0.146465\pi$
$229$	14.5186	+	8.38232i	0.959416	+	0.553919i	0.0634229	+	0.997987i	$0.479798\pi$
$230$	−13.2820	+	4.06179i	−0.875792	+	0.267827i
$231$	16.1363			1.06169
$232$	−4.97200	+	1.33224i	−0.326428	+	0.0874660i
$233$	18.7606	−	5.02689i	1.22905	−	0.329322i	0.414839	−	0.909895i	$-0.363838\pi$
$233$	18.7606	−	5.02689i	1.22905	−	0.329322i	0.814209	+	0.580572i	$0.197171\pi$
$234$	1.96934	+	3.41100i	0.128740	+	0.222984i
$235$	−1.56639	−	2.50634i	−0.102180	−	0.163496i
$236$	−11.4272			−0.743850
$237$	0.147260	−	0.147260i	0.00956559	−	0.00956559i
$238$	−20.0583	−	5.37459i	−1.30018	−	0.348383i
$239$	7.09029	−	4.09358i	0.458633	−	0.264792i	−0.252836	−	0.967509i	$-0.581363\pi$
$239$	7.09029	−	4.09358i	0.458633	−	0.264792i	0.711469	+	0.702717i	$0.248030\pi$
$240$	−1.44651	+	2.72096i	−0.0933716	+	0.175637i
$241$	12.5779	+	7.26185i	0.810213	+	0.467777i	0.847030	−	0.531545i	$-0.178388\pi$
$241$	12.5779	+	7.26185i	0.810213	+	0.467777i	−0.0368166	+	0.999322i	$0.511722\pi$
$242$	−1.04580	+	1.04580i	−0.0672264	+	0.0672264i
$243$	−10.4050	+	2.78802i	−0.667482	+	0.178851i
$244$	−4.86202	+	8.42126i	−0.311259	+	0.539116i
$245$	15.8229	−	4.83882i	1.01089	−	0.309141i
$246$	−3.54730	−	6.14410i	−0.226168	−	0.391734i
$247$	−7.13935	+	7.13935i	−0.454266	+	0.454266i
$248$	0.398801	−	1.48834i	0.0253239	−	0.0945099i
$249$	−4.63918	+	8.03529i	−0.293996	+	0.509216i
$250$	−11.1188	+	1.17111i	−0.703217	+	0.0740673i
$251$	4.08032	−	7.06732i	0.257547	−	0.446085i	−0.708037	−	0.706175i	$-0.750419\pi$
$251$	4.08032	−	7.06732i	0.257547	−	0.446085i	0.965584	+	0.260090i	$0.0837523\pi$
$252$	4.03485	+	1.08113i	0.254171	+	0.0681050i
$253$	−18.5131	−	4.96057i	−1.16391	−	0.311868i
$254$	9.36432			0.587570
$255$	−3.79222	+	16.4314i	−0.237478	+	1.02897i
$256$	1.00000			0.0625000
$257$	2.70407	−	2.70407i	0.168675	−	0.168675i	−0.617722	−	0.786397i	$-0.711944\pi$
$257$	2.70407	−	2.70407i	0.168675	−	0.168675i	0.786397	+	0.617722i	$0.211944\pi$
$258$	1.65290	+	8.88447i	0.102905	+	0.553123i
$259$		−	7.93271i		−	0.492915i
$260$	−7.99584	+	0.279807i	−0.495881	+	0.0173529i
$261$	4.90709	−	2.83311i	0.303741	−	0.175365i
$262$	5.40969	+	5.40969i	0.334212	+	0.334212i
$263$	−5.82651	+	21.7448i	−0.359278	+	1.34084i	0.515736	+	0.856748i	$0.327519\pi$
$263$	−5.82651	+	21.7448i	−0.359278	+	1.34084i	−0.875014	+	0.484097i	$0.839148\pi$
$264$	−3.68263	+	2.12617i	−0.226650	+	0.130857i
$265$	11.7500	+	6.24648i	0.721796	+	0.383718i
$266$			10.7079i			0.656546i
$267$	−21.7946	+	5.83984i	−1.33381	+	0.357393i
$268$	−12.3550	−	3.31052i	−0.754704	−	0.202222i
$269$		−	29.1326i		−	1.77624i	−0.459608	−	0.888122i	$-0.652010\pi$
$269$		−	29.1326i		−	1.77624i	0.459608	−	0.888122i	$-0.347990\pi$
$270$	2.84177	−	12.3132i	0.172945	−	0.749356i
$271$	6.09376	−	10.5547i	0.370169	−	0.641152i	−0.619422	−	0.785058i	$-0.712633\pi$
$271$	6.09376	−	10.5547i	0.370169	−	0.641152i	0.989591	+	0.143906i	$0.0459663\pi$
$272$	5.28586	−	1.41634i	0.320503	−	0.0858784i
$273$	−4.84288	−	18.0739i	−0.293105	−	1.09388i
$274$			8.05872i			0.486845i
$275$	−13.8677	−	6.76119i	−0.836251	−	0.407715i
$276$	7.41327	+	4.28006i	0.446227	+	0.257629i
$277$	−28.1867	−	7.55261i	−1.69358	−	0.453793i	−0.722268	−	0.691614i	$-0.756900\pi$
$277$	−28.1867	−	7.55261i	−1.69358	−	0.453793i	−0.971309	+	0.237821i	$0.923567\pi$
$278$	−3.98179	+	14.8602i	−0.238812	+	0.891258i
$279$			1.69616i			0.101546i
$280$	−5.78644	+	6.20611i	−0.345806	+	0.370886i
$281$	−11.5979	−	20.0882i	−0.691875	−	1.19836i	−0.971223	−	0.238173i	$-0.923452\pi$
$281$	−11.5979	−	20.0882i	−0.691875	−	1.19836i	0.279348	−	0.960190i	$-0.409882\pi$
$282$	−0.471452	+	1.75948i	−0.0280745	+	0.104776i
$283$	−5.92963	−	22.1297i	−0.352480	−	1.31547i	−0.883626	−	0.468193i	$-0.844905\pi$
$283$	−5.92963	−	22.1297i	−0.352480	−	1.31547i	0.531146	−	0.847280i	$-0.321761\pi$
$284$	2.77755	−	4.81086i	0.164817	−	0.285472i
$285$	8.69028	−	0.304109i	0.514768	−	0.0180138i
$286$	−9.56130	−	5.52022i	−0.565372	−	0.326418i
$287$	−5.05609	−	18.8696i	−0.298452	−	1.11384i
$288$	−1.06329	+	0.284907i	−0.0626547	+	0.0167883i
$289$	11.2119	−	6.47320i	0.659524	−	0.380776i
$290$	0.402533	+	11.5029i	0.0236375	+	0.675472i
$291$	−9.14713	+	5.28110i	−0.536214	+	0.309583i
$292$	−2.85944	−	10.6716i	−0.167336	−	0.624506i
$293$	2.20023	−	2.20023i	0.128539	−	0.128539i	−0.639910	−	0.768450i	$-0.721029\pi$
$293$	2.20023	−	2.20023i	0.128539	−	0.128539i	0.768450	+	0.639910i	$0.221029\pi$
$294$	−8.83145	−	5.09884i	−0.515061	−	0.297370i
$295$	−5.74615	+	24.8976i	−0.334554	+	1.44960i
$296$	1.04524	+	1.81040i	0.0607531	+	0.105228i
$297$	12.3305	−	12.3305i	0.715488	−	0.715488i
$298$	14.3827	+	3.85384i	0.833170	+	0.223247i
$299$			22.2248i			1.28529i
$300$	5.20105	+	4.51987i	0.300283	+	0.260955i
$301$	−1.93544	+	24.8081i	−0.111557	+	1.42992i
$302$	−1.41635	−	1.41635i	−0.0815020	−	0.0815020i
$303$	4.87879	+	4.87879i	0.280279	+	0.280279i
$304$	−1.41091	−	2.44376i	−0.0809211	−	0.140160i
$305$	15.9033	+	14.8279i	0.910623	+	0.849045i
$306$	−5.21686	+	3.01195i	−0.298228	+	0.172182i
$307$	−0.709924	+	2.64947i	−0.0405175	+	0.151213i	−0.983221	−	0.182418i	$-0.941607\pi$
$307$	−0.709924	+	2.64947i	−0.0405175	+	0.151213i	0.942704	+	0.333632i	$0.108274\pi$
$308$	−11.3100	+	3.03050i	−0.644447	+	0.172679i
$309$	26.2561			1.49366
$310$	−3.04226	−	1.61731i	−0.172789	−	0.0918572i
$311$	−3.02217	−	5.23455i	−0.171371	−	0.296824i	0.767528	−	0.641015i	$-0.221486\pi$
$311$	−3.02217	−	5.23455i	−0.171371	−	0.296824i	−0.938900	+	0.344191i	$0.888153\pi$
$312$	3.48671	+	3.48671i	0.197396	+	0.197396i
$313$	−7.17581	+	26.7805i	−0.405601	+	1.51372i	0.397345	+	0.917670i	$0.369932\pi$
$313$	−7.17581	+	26.7805i	−0.405601	+	1.51372i	−0.802945	+	0.596053i	$0.796735\pi$
$314$	12.7982	+	7.38903i	0.722242	+	0.416987i
$315$	4.38448	−	8.24746i	0.247037	−	0.464692i
$316$	−0.0755588	+	0.130872i	−0.00425051	+	0.00736211i
$317$	−24.1062	−	24.1062i	−1.35394	−	1.35394i	−0.881203	−	0.472737i	$-0.843266\pi$
$317$	−24.1062	−	24.1062i	−1.35394	−	1.35394i	−0.472737	−	0.881203i	$-0.656734\pi$
$318$	−2.12267	−	7.92192i	−0.119034	−	0.444239i
$319$	−7.94143	+	13.7550i	−0.444635	+	0.770130i
$320$	0.502846	−	2.17879i	0.0281100	−	0.121798i
$321$	−19.1247	+	11.0417i	−1.06744	+	0.616286i
$322$	16.6669	+	16.6669i	0.928811	+	0.928811i
$323$	−10.9191	−	10.9191i	−0.607554	−	0.607554i
$324$	−3.88488	+	2.24293i	−0.215826	+	0.124607i
$325$	−3.41104	+	17.5620i	−0.189210	+	0.974164i
$326$	5.89197	−	10.2052i	0.326326	−	0.565213i
$327$	−0.169912	−	0.634121i	−0.00939616	−	0.0350670i
$328$	3.64021	+	3.64021i	0.200997	+	0.200997i
$329$	−2.50785	+	4.34373i	−0.138262	+	0.239478i
$330$	2.78069	+	9.09283i	0.153072	+	0.500544i
$331$	26.3418	+	15.2084i	1.44787	+	0.835931i	0.998355	−	0.0573392i	$-0.0182617\pi$
$331$	26.3418	+	15.2084i	1.44787	+	0.835931i	0.449520	+	0.893270i	$0.351595\pi$
$332$	1.74253	−	6.50323i	0.0956340	−	0.356911i
$333$	−1.62718	−	1.62718i	−0.0891689	−	0.0891689i
$334$	−1.48436	−	2.57098i	−0.0812203	−	0.140678i
$335$	−13.4256	+	25.2544i	−0.733521	+	1.37980i
$336$	5.22953			0.285295
$337$	−7.44719	+	1.99547i	−0.405674	+	0.108700i	−0.455885	−	0.890039i	$-0.650677\pi$
$337$	−7.44719	+	1.99547i	−0.405674	+	0.108700i	0.0502110	+	0.998739i	$0.484011\pi$
$338$	0.0511562	−	0.190917i	0.00278253	−	0.0103845i
$339$	−4.23199	+	2.44334i	−0.229850	+	0.132704i
$340$	−0.427943	−	12.2290i	−0.0232085	−	0.663211i
$341$	−2.37723	−	4.11748i	−0.128734	−	0.222974i
$342$	2.19644	+	2.19644i	0.118770	+	0.118770i
$343$	−1.07256	−	1.07256i	−0.0579127	−	0.0579127i
$344$	−2.82708	−	5.91672i	−0.152426	−	0.319008i
$345$	13.0531	−	13.9998i	0.702755	−	0.753723i
$346$			15.8366i			0.851378i
$347$	−3.98708	−	1.06833i	−0.214038	−	0.0573512i	0.150207	−	0.988655i	$-0.452006\pi$
$347$	−3.98708	−	1.06833i	−0.214038	−	0.0573512i	−0.364244	+	0.931303i	$0.618673\pi$
$348$	5.01601	−	5.01601i	0.268886	−	0.268886i
$349$	−15.0356	−	26.0424i	−0.804836	−	1.39402i	−0.916402	−	0.400260i	$-0.868920\pi$
$349$	−15.0356	−	26.0424i	−0.804836	−	1.39402i	0.111566	−	0.993757i	$-0.464413\pi$
$350$	10.6121	+	15.7282i	0.567243	+	0.840706i
$351$	−17.5117	−	10.1104i	−0.934708	−	0.539654i
$352$	2.18186	−	2.18186i	0.116293	−	0.116293i
$353$	3.77288	+	14.0806i	0.200810	+	0.749433i	0.990686	+	0.136166i	$0.0434781\pi$
$353$	3.77288	+	14.0806i	0.200810	+	0.749433i	−0.789876	+	0.613266i	$0.789855\pi$
$354$	13.6382	−	7.87404i	0.724864	−	0.418500i
$355$	−9.08520	−	8.47084i	−0.482192	−	0.449585i
$356$	14.1791	−	8.18633i	0.751492	−	0.433874i
$357$	27.6426	−	7.40682i	1.46300	−	0.392010i
$358$	−5.66322	−	21.1354i	−0.299311	−	1.11704i
$359$	1.45269	+	0.838714i	0.0766703	+	0.0442656i	0.537845	−	0.843044i	$-0.319239\pi$
$359$	1.45269	+	0.838714i	0.0766703	+	0.0442656i	−0.461175	+	0.887309i	$0.652572\pi$
$360$	0.0860836	+	2.45995i	0.00453700	+	0.129650i
$361$	5.51868	−	9.55863i	0.290457	−	0.503086i
$362$	0.435683	+	1.62599i	0.0228990	+	0.0854601i
$363$	0.527527	−	1.96876i	0.0276880	−	0.103333i
$364$	6.78878	+	11.7585i	0.355829	+	0.616314i
$365$	−24.6890	+	0.863969i	−1.29228	+	0.0452222i
$366$		−	13.4008i		−	0.700474i
$367$	−0.849225	+	3.16935i	−0.0443292	+	0.165439i	−0.984542	−	0.175149i	$-0.943959\pi$
$367$	−0.849225	+	3.16935i	−0.0443292	+	0.165439i	0.940213	+	0.340588i	$0.110626\pi$
$368$	−5.99981	−	1.60764i	−0.312761	−	0.0838042i
$369$	−4.90771	−	2.83347i	−0.255485	−	0.147504i
$370$	4.47009	−	1.36700i	0.232389	−	0.0710670i
$371$		−	22.5828i		−	1.17244i
$372$	0.549594	+	2.05111i	0.0284951	+	0.106345i
$373$	−28.4214	+	7.61549i	−1.47160	+	0.394315i	−0.903481	−	0.428629i	$-0.858997\pi$
$373$	−28.4214	+	7.61549i	−1.47160	+	0.394315i	−0.568123	+	0.822944i	$0.692330\pi$
$374$	8.44275	−	14.6233i	0.436564	−	0.756151i
$375$	12.4632	−	9.05922i	0.643597	−	0.467816i
$376$		−	1.32177i		−	0.0681650i
$377$	17.7900	+	4.76681i	0.916231	+	0.245503i
$378$	−20.7145	+	5.55044i	−1.06544	+	0.285484i
$379$		−	8.88071i		−	0.456171i	−0.973641	−	0.228086i	$-0.926753\pi$
$379$		−	8.88071i		−	0.456171i	0.973641	−	0.228086i	$-0.0732466\pi$
$380$	−6.03393	+	1.84524i	−0.309534	+	0.0946589i
$381$	−11.1762	+	6.45256i	−0.572572	+	0.330575i
$382$	−1.76374	+	6.58237i	−0.0902408	+	0.336783i
$383$	−13.3782	−	13.3782i	−0.683594	−	0.683594i	0.277215	−	0.960808i	$-0.410589\pi$
$383$	−13.3782	−	13.3782i	−0.683594	−	0.683594i	−0.960808	+	0.277215i	$0.910589\pi$
$384$	−1.19348	+	0.689058i	−0.0609047	+	0.0351634i
$385$	0.915657	+	26.1660i	0.0466662	+	1.33354i
$386$		−	11.7629i		−	0.598715i
$387$	4.69171	+	5.48571i	0.238493	+	0.278854i
$388$	5.41942	−	5.41942i	0.275130	−	0.275130i
$389$	−15.8425			−0.803244			−0.401622	−	0.915805i	$-0.631554\pi$
$389$	−15.8425			−0.803244			−0.401622	+	0.915805i	$0.631554\pi$
$390$	9.35010	−	5.84355i	0.473461	−	0.295899i
$391$	−33.9911			−1.71901
$392$	7.14758	+	1.91519i	0.361007	+	0.0967317i
$393$	−10.1840	−	2.72879i	−0.513714	−	0.137649i
$394$	−6.61537	+	11.4582i	−0.333278	+	0.577254i
$395$	0.247148	+	0.230435i	0.0124354	+	0.0115945i
$396$	−1.69831	+	2.94157i	−0.0853435	+	0.147819i
$397$	1.72508	−	6.43809i	0.0865793	−	0.323118i	−0.909029	−	0.416732i	$-0.863175\pi$
$397$	1.72508	−	6.43809i	0.0865793	−	0.323118i	0.995609	+	0.0936138i	$0.0298419\pi$
$398$	−10.4972	+	10.4972i	−0.526177	+	0.526177i
$399$	−7.37839	−	12.7798i	−0.369382	−	0.639788i
$400$	−4.49429	−	2.19120i	−0.224715	−	0.109560i
$401$	11.6637	−	20.2021i	0.582458	−	1.00885i	−0.412729	−	0.910854i	$-0.635424\pi$
$401$	11.6637	−	20.2021i	0.582458	−	1.00885i	0.995187	−	0.0979928i	$-0.0312422\pi$
$402$	17.0267	−	4.56229i	0.849214	−	0.227546i
$403$	−3.89843	+	3.89843i	−0.194194	+	0.194194i
$404$	−4.33582	−	2.50329i	−0.215715	−	0.124543i
$405$	2.93340	+	9.59220i	0.145762	+	0.476640i
$406$	16.9159	−	9.76639i	0.839521	−	0.484698i
$407$	6.23060	+	1.66948i	0.308839	+	0.0827533i
$408$	−5.33265	+	5.33265i	−0.264006	+	0.264006i
$409$	−3.35018			−0.165656			−0.0828278	−	0.996564i	$-0.526395\pi$
$409$	−3.35018			−0.165656			−0.0828278	+	0.996564i	$0.526395\pi$
$410$	9.76174	−	6.10081i	0.482098	−	0.301297i
$411$	−5.55293	−	9.61795i	−0.273906	−	0.474419i
$412$	−18.4030	+	4.93106i	−0.906649	+	0.242936i
$413$	41.8854	−	11.2232i	2.06104	−	0.552255i
$414$	6.83753			0.336046
$415$	−13.2930	−	7.06675i	−0.652526	−	0.346893i
$416$	−3.09867	−	1.78902i	−0.151925	−	0.0877138i
$417$	−5.48737	−	20.4791i	−0.268718	−	1.00287i
$418$	−8.41035	−	2.25355i	−0.411364	−	0.110225i
$419$	22.3837			1.09351			0.546757	−	0.837291i	$-0.315862\pi$
$419$	22.3837			1.09351			0.546757	+	0.837291i	$0.315862\pi$
$420$	2.62965	−	11.3941i	0.128314	−	0.555974i
$421$	6.32970	+	3.65445i	0.308491	+	0.178107i	0.646251	−	0.763125i	$-0.276336\pi$
$421$	6.32970	+	3.65445i	0.308491	+	0.178107i	−0.337760	+	0.941232i	$0.609669\pi$
$422$	1.74371	+	1.74371i	0.0848823	+	0.0848823i
$423$	0.376580	+	1.40542i	0.0183100	+	0.0683337i
$424$	2.97557	+	5.15384i	0.144507	+	0.250293i
$425$	−26.8597	−	5.21691i	−1.30289	−	0.253058i
$426$			7.65558i			0.370914i
$427$	9.55036	−	35.6424i	0.462174	−	1.72486i
$428$	11.3309	−	11.3309i	0.547699	−	0.547699i
$429$	15.2150			0.734588
$430$	−14.3129	+	3.18443i	−0.690230	+	0.153567i
$431$	24.9556			1.20207			0.601034	−	0.799224i	$-0.294756\pi$
$431$	24.9556			1.20207			0.601034	+	0.799224i	$0.294756\pi$
$432$	3.99612	−	3.99612i	0.192264	−	0.192264i
$433$	7.53473	−	28.1200i	0.362096	−	1.35136i	−0.509219	−	0.860637i	$-0.670066\pi$
$433$	7.53473	−	28.1200i	0.362096	−	1.35136i	0.871315	−	0.490724i	$-0.163268\pi$
$434$			5.84705i			0.280667i
$435$	−8.40657	−	13.4511i	−0.403064	−	0.644932i
$436$	0.238184	+	0.412546i	0.0114069	+	0.0197574i
$437$	4.53647	+	16.9303i	0.217009	+	0.809888i
$438$	10.7660	+	10.7660i	0.514420	+	0.514420i
$439$	1.56334	+	0.902595i	0.0746141	+	0.0430785i	0.536843	−	0.843682i	$-0.319617\pi$
$439$	1.56334	+	0.902595i	0.0746141	+	0.0430785i	−0.462229	+	0.886761i	$0.652950\pi$
$440$	−3.65668	−	5.85096i	−0.174326	−	0.278934i
$441$	−8.14557			−0.387884
$442$	−18.9130	−	5.06773i	−0.899601	−	0.241047i
$443$	−5.21841	−	19.4754i	−0.247934	−	0.925302i	−0.971886	−	0.235452i	$-0.924343\pi$
$443$	−5.21841	−	19.4754i	−0.247934	−	0.925302i	0.723952	−	0.689850i	$-0.242324\pi$
$444$	−2.49495	−	1.44046i	−0.118405	−	0.0683611i
$445$	−10.7064	−	35.0099i	−0.507532	−	1.65963i
$446$	26.4482			1.25236
$447$	−19.8211	+	5.31104i	−0.937505	+	0.251204i
$448$	−3.66540	+	0.982140i	−0.173174	+	0.0464017i
$449$	−7.50951	−	13.0068i	−0.354395	−	0.613831i	0.632619	−	0.774463i	$-0.281980\pi$
$449$	−7.50951	−	13.0068i	−0.354395	−	0.613831i	−0.987014	+	0.160632i	$0.948647\pi$
$450$	5.40300	+	1.04942i	0.254700	+	0.0494699i
$451$	15.8849			0.747989
$452$	2.50734	−	2.50734i	0.117935	−	0.117935i
$453$	2.66634	+	0.714445i	0.125276	+	0.0335676i
$454$	21.0151	−	12.1331i	0.986290	−	0.569435i
$455$	29.0331	−	8.87864i	1.36109	−	0.416237i
$456$	3.36779	+	1.94440i	0.157711	+	0.0910547i
$457$	17.7443	−	17.7443i	0.830042	−	0.830042i	−0.157480	−	0.987522i	$-0.550337\pi$
$457$	17.7443	−	17.7443i	0.830042	−	0.830042i	0.987522	+	0.157480i	$0.0503371\pi$
$458$	16.1934	−	4.33901i	0.756668	−	0.202749i
$459$	15.4631	−	26.7829i	0.721755	−	1.25012i
$460$	−6.51970	+	12.2639i	−0.303983	+	0.571809i
$461$	7.84548	+	13.5888i	0.365400	+	0.632892i	0.988840	−	0.148979i	$-0.0475987\pi$
$461$	7.84548	+	13.5888i	0.365400	+	0.632892i	−0.623440	+	0.781871i	$0.714265\pi$
$462$	11.4101	−	11.4101i	0.530846	−	0.530846i
$463$	−2.11367	+	7.88832i	−0.0982305	+	0.366601i	−0.997489	−	0.0708155i	$-0.977440\pi$
$463$	−2.11367	+	7.88832i	−0.0982305	+	0.366601i	0.899259	+	0.437417i	$0.144106\pi$
$464$	−2.57370	+	4.45777i	−0.119481	+	0.206947i
$465$	4.74531	−	0.166058i	0.220059	−	0.00770075i
$466$	9.71120	−	16.8203i	0.449863	−	0.779185i
$467$	16.8680	+	4.51978i	0.780560	+	0.209150i	0.627032	−	0.778994i	$-0.284270\pi$
$467$	16.8680	+	4.51978i	0.780560	+	0.209150i	0.153528	+	0.988144i	$0.450936\pi$
$468$	3.80448	+	1.01941i	0.175862	+	0.0471221i
$469$	48.5375			2.24125
$470$	−2.87986	−	0.664646i	−0.132838	−	0.0306578i
$471$	−20.3659			−0.938410
$472$	−8.08028	+	8.08028i	−0.371925	+	0.371925i
$473$	−19.0777	−	6.74116i	−0.877196	−	0.309959i
$474$		−	0.208258i		−	0.00956559i
$475$	0.986261	+	14.0746i	0.0452528	+	0.645785i
$476$	−17.9837	+	10.3829i	−0.824283	+	0.475900i
$477$	−4.63225	−	4.63225i	−0.212096	−	0.212096i
$478$	2.11899	−	7.90819i	0.0969205	−	0.361712i
$479$	−26.2625	+	15.1627i	−1.19997	+	0.692801i	−0.960548	−	0.278116i	$-0.910290\pi$
$479$	−26.2625	+	15.1627i	−1.19997	+	0.692801i	−0.239419	+	0.970916i	$0.576957\pi$
$480$	0.901178	+	2.94685i	0.0411329	+	0.134505i
$481$		−	7.47979i		−	0.341049i
$482$	14.0288	−	3.75901i	0.638995	−	0.171218i
$483$	−31.3762	−	8.40722i	−1.42767	−	0.382542i
$484$			1.47898i			0.0672264i
$485$	−9.08267	−	14.5329i	−0.412423	−	0.659907i
$486$	−5.38603	+	9.32889i	−0.244315	+	0.423167i
$487$	−40.1565	+	10.7599i	−1.81967	+	0.487578i	−0.996748	−	0.0805814i	$-0.974322\pi$
$487$	−40.1565	+	10.7599i	−1.81967	+	0.487578i	−0.822918	+	0.568160i	$0.807656\pi$
$488$	2.51676	+	9.39269i	0.113929	+	0.425187i
$489$			16.2396i			0.734382i
$490$	7.76694	−	14.6101i	0.350875	−	0.660016i
$491$	12.3219	+	7.11408i	0.556082	+	0.321054i	0.751571	−	0.659652i	$-0.229296\pi$
$491$	12.3219	+	7.11408i	0.556082	+	0.321054i	−0.195490	+	0.980706i	$0.562630\pi$
$492$	−6.85286	−	1.83622i	−0.308951	−	0.0827831i
$493$	−7.29047	+	27.2084i	−0.328346	+	1.22541i
$494$			10.0966i			0.454266i
$495$	5.55508	+	5.17943i	0.249682	+	0.232798i
$496$	−0.770423	−	1.33441i	−0.0345930	−	0.0599169i
$497$	−5.45589	+	20.3617i	−0.244730	+	0.913345i
$498$	2.40142	+	8.96221i	0.107610	+	0.401606i
$499$	7.64744	−	13.2458i	0.342347	−	0.592962i	−0.642521	−	0.766268i	$-0.722112\pi$
$499$	7.64744	−	13.2458i	0.342347	−	0.592962i	0.984868	+	0.173306i	$0.0554450\pi$
$500$	−7.03411	+	8.69030i	−0.314575	+	0.388642i
$501$	3.54311	+	2.04561i	0.158294	+	0.0913913i
$502$	−2.11213	−	7.88257i	−0.0942689	−	0.351816i
$503$	11.5272	−	3.08871i	0.513973	−	0.137719i	0.00749583	−	0.999972i	$-0.497614\pi$
$503$	11.5272	−	3.08871i	0.513973	−	0.137719i	0.506478	+	0.862253i	$0.330947\pi$
$504$	3.61754	−	2.08859i	0.161138	−	0.0930332i
$505$	−7.63440	+	8.18810i	−0.339726	+	0.364366i
$506$	−16.5984	+	9.58308i	−0.737888	+	0.426020i
$507$	0.0704992	+	0.263107i	0.00313098	+	0.0116850i
$508$	6.62157	−	6.62157i	0.293785	−	0.293785i
$509$	32.8390	+	18.9596i	1.45556	+	0.840369i	0.998788	−	0.0492132i	$-0.0156714\pi$
$509$	32.8390	+	18.9596i	1.45556	+	0.840369i	0.456774	+	0.889583i	$0.349005\pi$
$510$	8.93725	+	14.3003i	0.395748	+	0.633226i
$511$	20.9619	+	36.3071i	0.927301	+	1.60613i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−15.4038	−	4.12742i	−0.680092	−	0.182230i
$514$		−	3.82413i		−	0.168675i
$515$	1.48990	+	42.5758i	0.0656530	+	1.87612i
$516$	7.45104	+	5.11349i	0.328014	+	0.225109i
$517$	−2.88391	−	2.88391i	−0.126834	−	0.126834i
$518$	−5.60927	−	5.60927i	−0.246457	−	0.246457i
$519$	−10.9123	−	18.9007i	−0.478997	−	0.829648i
$520$	−5.45606	+	5.85177i	−0.239264	+	0.256617i
$521$	−24.8560	+	14.3506i	−1.08896	+	0.628712i	−0.933300	−	0.359098i	$-0.883084\pi$
$521$	−24.8560	+	14.3506i	−1.08896	+	0.628712i	−0.155662	+	0.987810i	$0.549751\pi$
$522$	1.46653	−	5.47315i	0.0641881	−	0.239553i
$523$	−10.7183	+	2.87197i	−0.468680	+	0.125582i	−0.485427	−	0.874277i	$-0.661336\pi$
$523$	−10.7183	+	2.87197i	−0.468680	+	0.125582i	0.0167470	+	0.999860i	$0.494669\pi$
$524$	7.65046			0.334212
$525$	−23.5031	−	11.4589i	−1.02576	−	0.500109i
$526$	11.2560	+	19.4959i	0.490783	+	0.850062i
$527$	−5.96234	−	5.96234i	−0.259724	−	0.259724i
$528$	−1.10059	+	4.10744i	−0.0478969	+	0.178753i
$529$	13.4946	+	7.79109i	0.586720	+	0.338743i
$530$	12.7254	−	3.89157i	0.552757	−	0.169039i
$531$	6.28952	−	10.8938i	0.272942	−	0.472750i
$532$	7.57165	+	7.57165i	0.328273	+	0.328273i
$533$	−4.76741	−	17.7922i	−0.206500	−	0.770667i
$534$	−11.2817	+	19.5405i	−0.488207	+	0.845600i
$535$	−18.9900	−	30.3854i	−0.821009	−	1.31367i
$536$	−11.0772	+	6.39544i	−0.478463	+	0.276241i
$537$	21.3225	+	21.3225i	0.920135	+	0.920135i
$538$	−20.5998	−	20.5998i	−0.888122	−	0.888122i
$539$	19.7737	−	11.4163i	0.851713	−	0.491737i
$540$	−6.69730	−	10.7162i	−0.288206	−	0.461151i
$541$	3.23653	−	5.60584i	0.139149	−	0.241014i	−0.788025	−	0.615643i	$-0.788896\pi$
$541$	3.23653	−	5.60584i	0.139149	−	0.241014i	0.927175	+	0.374629i	$0.122230\pi$
$542$	−3.15436	−	11.7722i	−0.135491	−	0.505661i
$543$	−1.64038	−	1.64038i	−0.0703955	−	0.0703955i
$544$	2.73616	−	4.73918i	0.117312	−	0.203191i
$545$	1.01862	−	0.311506i	0.0436331	−	0.0133435i
$546$	−16.2046	−	9.35573i	−0.693493	−	0.400388i
$547$	−5.59773	+	20.8910i	−0.239342	+	0.893235i	0.736802	+	0.676109i	$0.236335\pi$
$547$	−5.59773	+	20.8910i	−0.239342	+	0.893235i	−0.976143	+	0.217126i	$0.930332\pi$
$548$	5.69838	+	5.69838i	0.243423	+	0.243423i
$549$	−5.35208	−	9.27007i	−0.228421	−	0.395637i
$550$	−14.5868	+	5.02503i	−0.621983	+	0.214268i
$551$	14.5250			0.618785
$552$	8.26843	−	2.21552i	0.351928	−	0.0942988i
$553$	0.148419	−	0.553906i	0.00631140	−	0.0235545i
$554$	−25.2715	+	14.5905i	−1.07368	+	0.619892i
$555$	−4.39304	+	4.71165i	−0.186474	+	0.199998i
$556$	7.69222	+	13.3233i	0.326223	+	0.565035i
$557$	−25.0449	−	25.0449i	−1.06119	−	1.06119i	−0.998002	−	0.0631859i	$-0.979874\pi$
$557$	−25.0449	−	25.0449i	−1.06119	−	1.06119i	−0.0631859	−	0.998002i	$-0.520126\pi$
$558$	1.19936	+	1.19936i	0.0507731	+	0.0507731i
$559$	−1.82493	+	23.3917i	−0.0771864	+	0.989363i
$560$	0.296750	+	8.48001i	0.0125400	+	0.358346i
$561$			23.2702i			0.982468i
$562$	−22.4055	−	6.00353i	−0.945119	−	0.253244i
$563$	−15.4917	+	15.4917i	−0.652898	+	0.652898i	−0.953690	−	0.300792i	$-0.902749\pi$
$563$	−15.4917	+	15.4917i	−0.652898	+	0.652898i	0.300792	+	0.953690i	$0.402749\pi$
$564$	0.910775	+	1.57751i	0.0383505	+	0.0664251i
$565$	−4.20217	−	6.72379i	−0.176787	−	0.282872i
$566$	−19.8409	−	11.4552i	−0.833976	−	0.481497i
$567$	12.0367	−	12.0367i	0.505495	−	0.505495i
$568$	−1.43777	−	5.36582i	−0.0603273	−	0.225145i
$569$	−3.15681	+	1.82259i	−0.132340	+	0.0764068i	−0.564709	−	0.825290i	$-0.691011\pi$
$569$	−3.15681	+	1.82259i	−0.132340	+	0.0764068i	0.432368	+	0.901697i	$0.357678\pi$
$570$	5.92992	−	6.36000i	0.248377	−	0.266391i
$571$	−15.5434	+	8.97397i	−0.650470	+	0.375549i	−0.788636	−	0.614860i	$-0.789213\pi$
$571$	−15.5434	+	8.97397i	−0.650470	+	0.375549i	0.138166	+	0.990409i	$0.455879\pi$
$572$	−10.6642	+	2.85748i	−0.445895	+	0.119477i
$573$	−2.43064	−	9.07127i	−0.101541	−	0.378958i
$574$	−16.9180	−	9.76762i	−0.706144	−	0.407693i
$575$	23.4422	+	20.3720i	0.977608	+	0.849570i
$576$	−0.550397	+	0.953316i	−0.0229332	+	0.0397215i
$577$	−11.9754	−	44.6928i	−0.498543	−	1.86059i	−0.509206	−	0.860644i	$-0.670061\pi$
$577$	−11.9754	−	44.6928i	−0.498543	−	1.86059i	0.0106634	−	0.999943i	$-0.496606\pi$
$578$	3.35077	−	12.5053i	0.139374	−	0.520150i
$579$	8.10532	+	14.0388i	0.336846	+	0.583434i
$580$	8.41839	+	7.84913i	0.349555	+	0.325917i
$581$			25.5483i			1.05992i
$582$	−2.73370	+	10.2023i	−0.113315	+	0.422899i
$583$	17.7372	+	4.75268i	0.734601	+	0.196836i
$584$	−9.56786	−	5.52400i	−0.395921	−	0.228585i
$585$	4.13414	−	7.77657i	0.170926	−	0.321521i
$586$		−	3.11160i		−	0.128539i
$587$	7.05908	+	26.3448i	0.291359	+	1.08737i	0.944066	+	0.329757i	$0.106967\pi$
$587$	7.05908	+	26.3448i	0.291359	+	1.08737i	−0.652707	+	0.757611i	$0.726367\pi$
$588$	−9.85020	+	2.63935i	−0.406216	+	0.108845i
$589$	−2.17399	+	3.76547i	−0.0895778	+	0.155153i
$590$	13.5421	+	21.6684i	0.557521	+	0.892075i
$591$		−	18.2335i		−	0.750026i
$592$	2.01924	+	0.541054i	0.0829903	+	0.0222372i
$593$	−4.87335	+	1.30581i	−0.200125	+	0.0536232i	−0.357489	−	0.933917i	$-0.616367\pi$
$593$	−4.87335	+	1.30581i	−0.200125	+	0.0536232i	0.157364	+	0.987541i	$0.449700\pi$
$594$		−	17.4380i		−	0.715488i
$595$	13.5792	+	44.4039i	0.556692	+	1.82038i
$596$	12.8952	−	7.44505i	0.528208	−	0.304961i
$597$	5.29505	−	19.7614i	0.216712	−	0.808781i
$598$	15.7153	+	15.7153i	0.642647	+	0.642647i
$599$	24.2316	−	13.9901i	0.990077	−	0.571621i	0.0847797	−	0.996400i	$-0.472981\pi$
$599$	24.2316	−	13.9901i	0.990077	−	0.571621i	0.905297	+	0.424778i	$0.139648\pi$
$600$	6.87373	−	0.481670i	0.280619	−	0.0196641i
$601$		−	12.9764i		−	0.529319i	−0.964342	−	0.264660i	$-0.914740\pi$
$601$		−	12.9764i		−	0.529319i	0.964342	−	0.264660i	$-0.0852596\pi$
$602$	16.1734	+	18.9105i	0.659179	+	0.770736i
$603$	9.95616	−	9.95616i	0.405446	−	0.405446i
$604$	−2.00303			−0.0815020
$605$	3.22240	+	0.743700i	0.131009	+	0.0302357i
$606$	6.89965			0.280279
$607$	−19.2595	−	5.16057i	−0.781720	−	0.209461i	−0.154177	−	0.988043i	$-0.549273\pi$
$607$	−19.2595	−	5.16057i	−0.781720	−	0.209461i	−0.627543	+	0.778582i	$0.715939\pi$
$608$	−2.72567	−	0.730340i	−0.110540	−	0.0296192i
$609$	−13.4592	+	23.3121i	−0.545395	+	0.944653i
$610$	21.7303	−	0.760432i	0.879834	−	0.0307890i
$611$	−2.36467	+	4.09572i	−0.0956642	+	0.165695i
$612$	−1.55910	+	5.81865i	−0.0630230	+	0.235205i
$613$	28.7893	−	28.7893i	1.16279	−	1.16279i	0.178926	−	0.983862i	$-0.442738\pi$
$613$	28.7893	−	28.7893i	1.16279	−	1.16279i	0.983862	−	0.178926i	$-0.0572623\pi$
$614$	1.37147	+	2.37545i	0.0553479	+	0.0958654i
$615$	−7.44667	+	14.0076i	−0.300279	+	0.564842i
$616$	−5.85449	+	10.1403i	−0.235884	+	0.408563i
$617$	−38.6574	+	10.3582i	−1.55629	+	0.417007i	−0.931487	−	0.363776i	$-0.881488\pi$
$617$	−38.6574	+	10.3582i	−1.55629	+	0.417007i	−0.624803	+	0.780782i	$0.714821\pi$
$618$	18.5659	−	18.5659i	0.746828	−	0.746828i
$619$	15.1742	+	8.76081i	0.609902	+	0.352127i	0.772927	−	0.634495i	$-0.218792\pi$
$619$	15.1742	+	8.76081i	0.609902	+	0.352127i	−0.163025	+	0.986622i	$0.552125\pi$
$620$	−3.29482	+	1.00759i	−0.132323	+	0.0404658i
$621$	−30.4003	+	17.5516i	−1.21992	+	0.704322i
$622$	−5.83838	−	1.56439i	−0.234098	−	0.0627263i
$623$	−43.9320	+	43.9320i	−1.76010	+	1.76010i
$624$	4.93095			0.197396
$625$	15.3973	+	19.6958i	0.615892	+	0.787830i
$626$	13.8626	+	24.0107i	0.554061	+	0.959662i
$627$	11.5904	−	3.10565i	0.462878	−	0.124028i
$628$	14.2745	−	3.82484i	0.569615	−	0.152628i
$629$	11.4398			0.456133
$630$	−2.73154	−	8.93213i	−0.108827	−	0.355864i
$631$	−2.18575	−	1.26194i	−0.0870134	−	0.0502372i	0.455862	−	0.890050i	$-0.349331\pi$
$631$	−2.18575	−	1.26194i	−0.0870134	−	0.0502372i	−0.542875	+	0.839813i	$0.682664\pi$
$632$	0.0391121	+	0.145968i	0.00155580	+	0.00580631i
$633$	−3.28260	−	0.879570i	−0.130472	−	0.0349598i
$634$	−34.0914			−1.35394
$635$	−11.0974	−	17.7567i	−0.440387	−	0.704652i
$636$	−7.10260	−	4.10069i	−0.281636	−	0.162603i
$637$	−18.7217	−	18.7217i	−0.741781	−	0.741781i
$638$	4.11079	+	15.3417i	0.162748	+	0.607382i
$639$	3.05751	+	5.29577i	0.120953	+	0.209497i
$640$	−1.18507	−	1.89621i	−0.0468442	−	0.0749541i
$641$			27.8310i			1.09926i	0.835409	+	0.549629i	$0.185231\pi$
$641$			27.8310i			1.09926i	−0.835409	+	0.549629i	$0.814769\pi$
$642$	−5.71559	+	21.3309i	−0.225576	+	0.841863i
$643$	−10.8574	+	10.8574i	−0.428175	+	0.428175i	−0.888006	−	0.459831i	$-0.847910\pi$
$643$	−10.8574	+	10.8574i	−0.428175	+	0.428175i	0.459831	+	0.888006i	$0.347910\pi$
$644$	23.5706			0.928811
$645$	14.8880	−	13.6630i	0.586213	−	0.537980i
$646$	−15.4419			−0.607554
$647$	27.4961	−	27.4961i	1.08098	−	1.08098i	0.0845660	−	0.996418i	$-0.473050\pi$
$647$	27.4961	−	27.4961i	1.08098	−	1.08098i	0.996418	−	0.0845660i	$-0.0269504\pi$
$648$	−1.16103	+	4.33302i	−0.0456095	+	0.170217i
$649$			35.2601i			1.38408i
$650$	10.0062	+	14.8302i	0.392477	+	0.581687i
$651$	−4.02896	−	6.97836i	−0.157907	−	0.273503i
$652$	−3.04991	−	11.3824i	−0.119444	−	0.445769i
$653$	12.2215	+	12.2215i	0.478264	+	0.478264i	0.904576	−	0.426312i	$-0.140188\pi$
$653$	12.2215	+	12.2215i	0.478264	+	0.478264i	−0.426312	+	0.904576i	$0.640188\pi$
$654$	−0.568537	−	0.328245i	−0.0222316	−	0.0128354i
$655$	3.84701	−	16.6688i	0.150315	−	0.651303i
$656$	5.14804			0.200997
$657$	11.7472	+	3.14765i	0.458302	+	0.122802i
$658$	1.29816	+	4.84480i	0.0506076	+	0.188870i
$659$	−28.5057	−	16.4578i	−1.11042	−	0.641104i	−0.171485	−	0.985187i	$-0.554857\pi$
$659$	−28.5057	−	16.4578i	−1.11042	−	0.641104i	−0.938939	+	0.344083i	$0.888190\pi$
$660$	8.39585	+	4.46336i	0.326808	+	0.173736i
$661$	−8.96561			−0.348722			−0.174361	−	0.984682i	$-0.555786\pi$
$661$	−8.96561			−0.348722			−0.174361	+	0.984682i	$0.555786\pi$
$662$	29.3804	−	7.87246i	1.14190	−	0.305972i
$663$	26.0643	−	6.98392i	1.01226	−	0.271233i
$664$	−3.36632	−	5.83063i	−0.130638	−	0.226272i
$665$	20.3045	−	12.6897i	0.787373	−	0.492086i
$666$	−2.30118			−0.0891689
$667$	22.6082	−	22.6082i	0.875392	−	0.875392i
$668$	−2.86755	−	0.768359i	−0.110949	−	0.0297287i
$669$	−31.5655	+	18.2244i	−1.22039	+	0.704595i
$670$	8.36421	+	27.3509i	0.323138	+	1.05666i
$671$	25.9848	+	15.0023i	1.00313	+	0.579158i
$672$	3.69784	−	3.69784i	0.142647	−	0.142647i
$673$	10.5146	−	2.81737i	0.405307	−	0.108602i	−0.0504050	−	0.998729i	$-0.516051\pi$
$673$	10.5146	−	2.81737i	0.405307	−	0.108602i	0.455712	+	0.890127i	$0.349385\pi$
$674$	−3.85495	+	6.67697i	−0.148487	+	0.257187i
$675$	−26.7160	+	9.20345i	−1.02830	+	0.354241i
$676$	−0.0988262	−	0.171172i	−0.00380101	−	0.00658354i
$677$	−6.19708	+	6.19708i	−0.238173	+	0.238173i	−0.816093	−	0.577920i	$-0.803864\pi$
$677$	−6.19708	+	6.19708i	−0.238173	+	0.238173i	0.577920	+	0.816093i	$0.303864\pi$
$678$	−1.26477	+	4.72017i	−0.0485731	+	0.181277i
$679$	−14.5417	+	25.1870i	−0.558059	+	0.966587i
$680$	−8.94982	−	8.34462i	−0.343210	−	0.320002i
$681$	−16.7208	+	28.9613i	−0.640744	+	1.10980i
$682$	−4.59246	−	1.23054i	−0.175854	−	0.0471200i
$683$	−35.6108	−	9.54190i	−1.36261	−	0.365111i	−0.497836	−	0.867271i	$-0.665872\pi$
$683$	−35.6108	−	9.54190i	−1.36261	−	0.365111i	−0.864774	+	0.502160i	$0.832539\pi$
$684$	3.10624			0.118770
$685$	15.2810	−	9.55018i	0.583857	−	0.364894i
$686$	−1.51683			−0.0579127
$687$	−16.3367	+	16.3367i	−0.623285	+	0.623285i
$688$	−6.18280	−	2.18471i	−0.235717	−	0.0832912i
$689$		−	21.2934i		−	0.811215i
$690$	−0.669412	−	19.1293i	−0.0254841	−	0.728239i
$691$	−6.91419	+	3.99191i	−0.263028	+	0.151859i	−0.625715	−	0.780052i	$-0.715193\pi$
$691$	−6.91419	+	3.99191i	−0.263028	+	0.151859i	0.362687	+	0.931911i	$0.381859\pi$
$692$	11.1981	+	11.1981i	0.425689	+	0.425689i
$693$	3.33596	−	12.4500i	0.126723	−	0.472936i
$694$	−3.57472	+	2.06386i	−0.135694	+	0.0783432i
$695$	32.8968	−	10.0602i	1.24785	−	0.381605i
$696$		−	7.09370i		−	0.268886i
$697$	27.2118	−	7.29139i	1.03072	−	0.276181i
$698$	−29.0465	−	7.78299i	−1.09943	−	0.294590i
$699$			26.7663i			1.01240i
$700$	18.6254	+	3.61758i	0.703975	+	0.136732i
$701$	11.6811	−	20.2322i	0.441188	−	0.764160i	−0.556590	−	0.830787i	$-0.687891\pi$
$701$	11.6811	−	20.2322i	0.441188	−	0.764160i	0.997778	+	0.0666273i	$0.0212239\pi$
$702$	−19.5318	+	5.23353i	−0.737181	+	0.197527i
$703$	−1.52676	−	5.69793i	−0.0575827	−	0.214901i
$704$		−	3.08561i		−	0.116293i
$705$	3.89505	−	1.19115i	0.146696	−	0.0448612i
$706$	12.6243	+	7.28864i	0.475121	+	0.274311i
$707$	18.3511	+	4.91716i	0.690163	+	0.184929i
$708$	4.07590	−	15.2115i	0.153182	−	0.571682i
$709$			14.8385i			0.557271i	0.960397	+	0.278635i	$0.0898821\pi$
$709$			14.8385i			0.557271i	−0.960397	+	0.278635i	$0.910118\pi$
$710$	−12.4140	+	0.434416i	−0.465889	+	0.0163034i
$711$	−0.0831747	−	0.144063i	−0.00311929	−	0.00540278i
$712$	4.23755	−	15.8148i	0.158809	−	0.592683i
$713$	2.47713	+	9.24478i	0.0927693	+	0.346220i
$714$	14.3089	−	24.7837i	0.535496	−	0.927506i
$715$	0.863377	+	24.6721i	0.0322885	+	0.922683i
$716$	−18.9495	−	10.9405i	−0.708177	−	0.408866i
$717$	2.92022	+	10.8984i	0.109058	+	0.407009i
$718$	1.62027	−	0.434150i	0.0604680	−	0.0162023i
$719$	8.98622	−	5.18820i	0.335130	−	0.193487i	−0.322987	−	0.946404i	$-0.604687\pi$
$719$	8.98622	−	5.18820i	0.335130	−	0.193487i	0.658116	+	0.752916i	$0.271354\pi$
$720$	1.80031	+	1.67857i	0.0670937	+	0.0625567i
$721$	62.6112	−	36.1486i	2.33176	−	1.34624i
$722$	−2.85668	−	10.6613i	−0.106315	−	0.396771i
$723$	−14.1530	+	14.1530i	−0.526356	+	0.526356i
$724$	1.45782	+	0.841674i	0.0541795	+	0.0312806i
$725$	21.3348	−	14.3950i	0.792354	−	0.534619i
$726$	−1.01910	−	1.76514i	−0.0378225	−	0.0655105i
$727$	−3.11527	+	3.11527i	−0.115539	+	0.115539i	−0.762513	−	0.646973i	$-0.776034\pi$
$727$	−3.11527	+	3.11527i	−0.115539	+	0.115539i	0.646973	+	0.762513i	$0.276034\pi$
$728$	13.1149	+	3.51413i	0.486071	+	0.130242i
$729$		−	28.3028i		−	1.04825i
$730$	−16.8468	+	18.0687i	−0.623529	+	0.668751i
$731$	−35.7758	−	2.79109i	−1.32321	−	0.103232i
$732$	−9.47583	−	9.47583i	−0.350237	−	0.350237i
$733$	36.6603	+	36.6603i	1.35408	+	1.35408i	0.881041	+	0.473039i	$0.156843\pi$
$733$	36.6603	+	36.6603i	1.35408	+	1.35408i	0.473039	+	0.881041i	$0.343157\pi$
$734$	1.64058	+	2.84156i	0.0605548	+	0.104884i
$735$	0.797472	+	22.7888i	0.0294152	+	0.840576i
$736$	−5.37928	+	3.10573i	−0.198283	+	0.114479i
$737$	−10.2150	+	38.1229i	−0.376274	+	1.40428i
$738$	−5.47384	+	1.46671i	−0.201495	+	0.0539903i
$739$	16.6375			0.612021			0.306010	−	0.952028i	$-0.401006\pi$
$739$	16.6375			0.612021			0.306010	+	0.952028i	$0.401006\pi$
$740$	2.19421	−	4.12745i	0.0806609	−	0.151728i
$741$	−6.95712	−	12.0501i	−0.255576	−	0.442671i
$742$	−15.9684	−	15.9684i	−0.586220	−	0.586220i
$743$	−1.19537	+	4.46119i	−0.0438540	+	0.163665i	−0.984380	−	0.176056i	$-0.943666\pi$
$743$	−1.19537	+	4.46119i	−0.0438540	+	0.163665i	0.940526	+	0.339721i	$0.110333\pi$
$744$	1.83898	+	1.06173i	0.0674201	+	0.0389250i
$745$	−9.73693	−	31.8397i	−0.356734	−	1.16652i
$746$	−14.7120	+	25.4819i	−0.538644	+	0.932959i
$747$	5.24054	+	5.24054i	0.191741	+	0.191741i
$748$	−4.37029	−	16.3101i	−0.159794	−	0.596358i
$749$	−30.4037	+	52.6607i	−1.11093	+	1.92418i
$750$	2.40697	−	15.2186i	0.0878901	−	0.555706i
$751$	5.32690	−	3.07549i	0.194381	−	0.112226i	−0.399651	−	0.916668i	$-0.630869\pi$
$751$	5.32690	−	3.07549i	0.194381	−	0.112226i	0.594032	+	0.804441i	$0.297535\pi$
$752$	−0.934631	−	0.934631i	−0.0340825	−	0.0340825i
$753$	7.95234	+	7.95234i	0.289799	+	0.289799i
$754$	15.9501	−	9.20878i	0.580867	−	0.335364i
$755$	−1.00721	+	4.36418i	−0.0366563	+	0.158829i
$756$	−10.7226	+	18.5721i	−0.389978	+	0.675462i
$757$	−8.71960	−	32.5420i	−0.316919	−	1.18276i	−0.922189	−	0.386739i	$-0.873602\pi$
$757$	−8.71960	−	32.5420i	−0.316919	−	1.18276i	0.605270	−	0.796020i	$-0.293065\pi$
$758$	−6.27961	−	6.27961i	−0.228086	−	0.228086i
$759$	13.2066	−	22.8745i	0.479369	−	0.830292i
$760$	−2.96185	+	5.57142i	−0.107438	+	0.202097i
$761$	14.4090	+	8.31902i	0.522325	+	0.301564i	0.737885	−	0.674926i	$-0.235825\pi$
$761$	14.4090	+	8.31902i	0.522325	+	0.301564i	−0.215561	+	0.976490i	$0.569158\pi$
$762$	−3.34009	+	12.4654i	−0.120999	+	0.451574i
$763$	−1.27822	−	1.27822i	−0.0462745	−	0.0462745i
$764$	3.40728	+	5.90159i	0.123271	+	0.213512i
$765$	11.8937	+	6.32285i	0.430016	+	0.228603i
$766$	−18.9196			−0.683594
$767$	39.4939	−	10.5824i	1.42604	−	0.382107i
$768$	−0.356683	+	1.33116i	−0.0128707	+	0.0480340i
$769$	19.7660	−	11.4119i	0.712780	−	0.411524i	−0.0993094	−	0.995057i	$-0.531663\pi$
$769$	19.7660	−	11.4119i	0.712780	−	0.411524i	0.812090	+	0.583533i	$0.198330\pi$
$770$	19.1497	+	17.8547i	0.690106	+	0.643439i
$771$	2.63505	+	4.56404i	0.0948990	+	0.164370i
$772$	−8.31762	−	8.31762i	−0.299358	−	0.299358i
$773$	−24.5698	−	24.5698i	−0.883715	−	0.883715i	0.110195	−	0.993910i	$-0.464853\pi$
$773$	−24.5698	−	24.5698i	−0.883715	−	0.883715i	−0.993910	+	0.110195i	$0.964853\pi$
$774$	7.19652	+	0.561446i	0.258674	+	0.0201808i
$775$	0.538546	+	7.68539i	0.0193451	+	0.276067i
$776$		−	7.66422i		−	0.275130i
$777$	10.5597	+	2.82946i	0.378827	+	0.101506i
$778$	−11.2023	+	11.2023i	−0.401622	+	0.401622i
$779$	−7.26341	−	12.5806i	−0.260239	−	0.450747i
$780$	2.47951	−	10.7435i	0.0887807	−	0.384680i
$781$	−14.8445	−	8.57045i	−0.531177	−	0.306675i
$782$	−24.0354	+	24.0354i	−0.859503	+	0.859503i
$783$	7.52900	+	28.0986i	0.269065	+	1.00416i
$784$	6.40835	−	3.69986i	0.228870	−	0.132138i
$785$	−1.15566	−	33.0245i	−0.0412474	−	1.17870i
$786$	−9.13071	+	5.27162i	−0.325682	+	0.188032i
$787$	−26.9602	+	7.22396i	−0.961027	+	0.257506i	−0.705035	−	0.709173i	$-0.749069\pi$
$787$	−26.9602	+	7.22396i	−0.961027	+	0.257506i	−0.255992	+	0.966679i	$0.582402\pi$
$788$	3.42437	+	12.7799i	0.121988	+	0.455266i
$789$	−26.8676	−	15.5120i	−0.956513	−	0.552243i
$790$	0.337702	−	0.0118176i	0.0120149	−	0.000420451i
$791$	−6.72783	+	11.6530i	−0.239214	+	0.414331i
$792$	0.879112	+	3.28089i	0.0312379	+	0.116581i
$793$	9.00508	−	33.6074i	0.319780	−	1.19343i
$794$	−3.33260	−	5.77223i	−0.118270	−	0.204849i
$795$	−12.5061	+	13.4131i	−0.443545	+	0.475713i
$796$			14.8453i			0.526177i
$797$	−13.0117	+	48.5605i	−0.460899	+	1.72010i	0.209240	+	0.977864i	$0.432901\pi$
$797$	−13.0117	+	48.5605i	−0.460899	+	1.72010i	−0.670139	+	0.742235i	$0.733766\pi$
$798$	−14.2540	−	3.81934i	−0.504585	−	0.135203i
$799$	−6.26409	−	3.61657i	−0.221608	−	0.127945i
$800$	−4.72735	+	1.62853i	−0.167137	+	0.0575773i
$801$			18.0229i			0.636809i
$802$	−6.03758	−	22.5326i	−0.213194	−	0.795652i
$803$	−32.9283	+	8.82312i	−1.16202	+	0.311361i
$804$	8.81366	−	15.2657i	0.310834	−	0.538380i
$805$	11.8524	−	51.3555i	0.417742	−	1.81004i
$806$			5.51321i			0.194194i
$807$	38.7801	+	10.3911i	1.36512	+	0.365784i
$808$	−4.83598	+	1.29580i	−0.170129	+	0.0455860i
$809$			15.9553i			0.560958i	0.959860	+	0.280479i	$0.0904933\pi$
$809$			15.9553i			0.560958i	−0.959860	+	0.280479i	$0.909507\pi$
$810$	8.85693	+	4.70848i	0.311201	+	0.165439i
$811$	44.8270	−	25.8809i	1.57409	−	0.908801i	0.578431	−	0.815732i	$-0.303665\pi$
$811$	44.8270	−	25.8809i	1.57409	−	0.908801i	0.995660	−	0.0930698i	$-0.0296680\pi$
$812$	5.05546	−	18.8672i	0.177412	−	0.662110i
$813$	11.8764	+	11.8764i	0.416525	+	0.416525i
$814$	5.58621	−	3.22520i	0.195796	−	0.113043i
$815$	−26.3336	+	0.921519i	−0.922424	+	0.0322794i
$816$			7.54151i			0.264006i
$817$	3.38446	+	18.1917i	0.118407	+	0.636448i
$818$	−2.36893	+	2.36893i	−0.0828278	+	0.0828278i
$819$	−14.9461			−0.522259
$820$	2.58867	−	11.2165i	0.0904003	−	0.391698i
$821$	−23.9730			−0.836664			−0.418332	−	0.908294i	$-0.637385\pi$
$821$	−23.9730			−0.836664			−0.418332	+	0.908294i	$0.637385\pi$
$822$	−10.7274	−	2.87441i	−0.374162	−	0.100256i
$823$	29.2799	+	7.84552i	1.02063	+	0.273478i	0.730065	−	0.683377i	$-0.239490\pi$
$823$	29.2799	+	7.84552i	1.02063	+	0.273478i	0.290567	+	0.956855i	$0.406156\pi$
$824$	−9.52608	+	16.4996i	−0.331857	+	0.574793i
$825$	13.9466	−	16.0484i	0.485557	−	0.558735i
$826$	21.6815	−	37.5534i	0.754395	−	1.30665i
$827$	−14.3068	+	53.3938i	−0.497497	+	1.85668i	0.0180717	+	0.999837i	$0.494247\pi$
$827$	−14.3068	+	53.3938i	−0.497497	+	1.85668i	−0.515569	+	0.856848i	$0.672419\pi$
$828$	4.83487	−	4.83487i	0.168023	−	0.168023i
$829$	−24.1086	−	41.7573i	−0.837325	−	1.45029i	−0.892123	−	0.451793i	$-0.850785\pi$
$829$	−24.1086	−	41.7573i	−0.837325	−	1.45029i	0.0547977	−	0.998497i	$-0.482549\pi$
$830$	−14.3965	+	4.40260i	−0.499710	+	0.152817i
$831$	20.1074	−	34.8271i	0.697520	−	1.20814i
$832$	−3.45612	+	0.926064i	−0.119819	+	0.0321055i
$833$	28.6334	−	28.6334i	0.992088	−	0.992088i
$834$	−18.3611	−	10.6008i	−0.635793	−	0.367075i
$835$	−3.11603	+	5.86144i	−0.107835	+	0.202844i
$836$	−7.54052	+	4.35352i	−0.260794	+	0.150570i
$837$	−8.41119	−	2.25377i	−0.290733	−	0.0779017i
$838$	15.8277	−	15.8277i	0.546757	−	0.546757i
$839$	−1.45650			−0.0502839			−0.0251420	−	0.999684i	$-0.508004\pi$
$839$	−1.45650			−0.0502839			−0.0251420	+	0.999684i	$0.508004\pi$
$840$	−6.19739	−	9.91628i	−0.213830	−	0.342144i
$841$	1.25219	+	2.16885i	0.0431789	+	0.0747880i
$842$	7.05986	−	1.89168i	0.243299	−	0.0651918i
$843$	30.8774	−	8.27357i	1.06347	−	0.284957i
$844$	2.46597			0.0848823
$845$	−0.422643	+	0.129249i	−0.0145394	+	0.00444629i
$846$	1.26006	+	0.727497i	0.0433218	+	0.0250119i
$847$	−1.45257	−	5.42105i	−0.0499108	−	0.186270i
$848$	5.74837	+	1.54027i	0.197400	+	0.0528931i
$849$	31.5731			1.08359
$850$	−22.6816	+	15.3038i	−0.777972	+	0.524915i
$851$	−11.2452	−	6.49244i	−0.385482	−	0.222558i
$852$	5.41331	+	5.41331i	0.185457	+	0.185457i
$853$	3.22877	+	12.0499i	0.110551	+	0.412581i	0.998916	−	0.0465569i	$-0.0148249\pi$
$853$	3.22877	+	12.0499i	0.110551	+	0.412581i	−0.888365	+	0.459138i	$0.848158\pi$
$854$	−18.4499	−	31.9561i	−0.631342	−	1.09352i
$855$	1.56196	−	6.76786i	0.0534179	−	0.231456i
$856$		−	16.0243i		−	0.547699i
$857$	−0.867717	+	3.23836i	−0.0296406	+	0.110620i	−0.979161	−	0.203084i	$-0.934903\pi$
$857$	−0.867717	+	3.23836i	−0.0296406	+	0.110620i	0.949521	+	0.313705i	$0.101570\pi$
$858$	10.7586	−	10.7586i	0.367294	−	0.367294i
$859$	−13.5550			−0.462492			−0.231246	−	0.972895i	$-0.574280\pi$
$859$	−13.5550			−0.462492			−0.231246	+	0.972895i	$0.574280\pi$
$860$	−7.86903	+	12.3725i	−0.268332	+	0.421898i
$861$	26.9218			0.917494
$862$	17.6462	−	17.6462i	0.601034	−	0.601034i
$863$	−6.86684	+	25.6274i	−0.233750	+	0.872367i	0.744958	+	0.667111i	$0.232469\pi$
$863$	−6.86684	+	25.6274i	−0.233750	+	0.872367i	−0.978708	+	0.205256i	$0.934197\pi$
$864$		−	5.65137i		−	0.192264i
$865$	30.0294	−	18.7675i	1.02103	−	0.638114i
$866$	−14.5560	−	25.2117i	−0.494633	−	0.856729i
$867$	4.61776	+	17.2337i	0.156827	+	0.585287i
$868$	4.13449	+	4.13449i	0.140334	+	0.140334i
$869$	0.403820	+	0.233145i	0.0136986	+	0.00790891i
$870$	−15.4557	−	3.56704i	−0.523998	−	0.120934i
$871$	45.7663			1.55073
$872$	0.460136	+	0.123293i	0.0155822	+	0.00417523i
$873$	2.18359	+	8.14926i	0.0739032	+	0.275811i
$874$	15.1793	+	8.76379i	0.513449	+	0.296440i
$875$	17.2477	−	38.7619i	0.583078	−	1.31039i
$876$	15.2254			0.514420
$877$	16.4462	−	4.40673i	0.555347	−	0.148805i	0.0297793	−	0.999556i	$-0.490520\pi$
$877$	16.4462	−	4.40673i	0.555347	−	0.148805i	0.525568	+	0.850752i	$0.323853\pi$
$878$	1.74368	−	0.467217i	0.0588463	−	0.0157678i
$879$	2.14408	+	3.71365i	0.0723179	+	0.125258i
$880$	−6.72292	−	1.55159i	−0.226630	−	0.0523041i
$881$	−45.5400			−1.53428			−0.767141	−	0.641478i	$-0.778321\pi$
$881$	−45.5400			−1.53428			−0.767141	+	0.641478i	$0.778321\pi$
$882$	−5.75979	+	5.75979i	−0.193942	+	0.193942i
$883$	8.60209	+	2.30492i	0.289483	+	0.0775668i	0.400638	−	0.916236i	$-0.368788\pi$
$883$	8.60209	+	2.30492i	0.289483	+	0.0775668i	−0.111155	+	0.993803i	$0.535455\pi$
$884$	−16.9569	+	9.79010i	−0.570324	+	0.329277i
$885$	−31.0931	−	16.5296i	−1.04518	−	0.555636i
$886$	−17.4611	−	10.0812i	−0.586618	−	0.338684i
$887$	−7.75093	+	7.75093i	−0.260251	+	0.260251i	−0.825156	−	0.564905i	$-0.808913\pi$
$887$	−7.75093	+	7.75093i	−0.260251	+	0.260251i	0.564905	+	0.825156i	$0.308913\pi$
$888$	−2.78275	+	0.745636i	−0.0933830	+	0.0250219i
$889$	−17.7674	+	30.7740i	−0.595899	+	1.03213i
$890$	−32.3263	−	17.1852i	−1.08358	−	0.576048i
$891$	6.92083	+	11.9872i	0.231857	+	0.401587i
$892$	18.7017	−	18.7017i	0.626180	−	0.626180i
$893$	−0.965339	+	3.60270i	−0.0323039	+	0.120560i
$894$	−10.2602	+	17.7711i	−0.343151	+	0.594355i
$895$	−33.3658	+	35.7857i	−1.11530	+	1.19618i
$896$	−1.89735	+	3.28630i	−0.0633860	+	0.109788i
$897$	−29.5848	−	7.92721i	−0.987806	−	0.264682i
$898$	−14.5073	−	3.88721i	−0.484113	−	0.129718i
$899$	7.93134			0.264525
$900$	4.56255	−	3.07845i	0.152085	−	0.102615i
$901$	32.5666			1.08495
$902$	11.2323	−	11.2323i	0.373994	−	0.373994i
$903$	−32.3332	−	11.4250i	−1.07598	−	0.380200i
$904$		−	3.54591i		−	0.117935i
$905$	2.56690	−	2.75306i	0.0853265	−	0.0915149i
$906$	2.39058	−	1.38020i	0.0794217	−	0.0458541i
$907$	5.93729	+	5.93729i	0.197145	+	0.197145i	0.798775	−	0.601630i	$-0.205482\pi$
$907$	5.93729	+	5.93729i	0.197145	+	0.197145i	−0.601630	+	0.798775i	$0.705482\pi$
$908$	6.28056	−	23.4394i	0.208428	−	0.777862i
$909$	4.77285	−	2.75561i	0.158305	−	0.0913977i
$910$	14.2514	−	26.8076i	0.472428	−	0.888665i
$911$		−	20.5960i		−	0.682375i	−0.939995	−	0.341187i	$-0.889171\pi$
$911$		−	20.5960i		−	0.682375i	0.939995	−	0.341187i	$-0.110829\pi$
$912$	3.75628	−	1.00649i	0.124383	−	0.0333283i
$913$	−20.0665	−	5.37679i	−0.664103	−	0.177946i
$914$		−	25.0942i		−	0.830042i
$915$	−25.4108	+	15.8810i	−0.840054	+	0.525010i
$916$	8.38232	−	14.5186i	0.276960	−	0.479708i
$917$	−28.0420	+	7.51382i	−0.926028	+	0.248128i
$918$	−8.00428	−	29.8724i	−0.264181	−	0.985936i
$919$		−	29.2435i		−	0.964652i	−0.875992	−	0.482326i	$-0.839792\pi$
$919$		−	29.2435i		−	0.964652i	0.875992	−	0.482326i	$-0.160208\pi$
$920$	4.06179	+	13.2820i	0.133913	+	0.437896i
$921$	−3.27365	−	1.89004i	−0.107870	−	0.0622790i
$922$	15.1563	+	4.06112i	0.499146	+	0.133746i
$923$	−5.14438	+	19.1991i	−0.169329	+	0.631946i
$924$		−	16.1363i		−	0.530846i
$925$	−7.88950	−	6.85621i	−0.259405	−	0.225431i
$926$	4.08329	+	7.07247i	0.134185	+	0.232416i
$927$	5.42808	−	20.2579i	0.178282	−	0.665356i
$928$	1.33224	+	4.97200i	0.0437330	+	0.163214i
$929$	19.9838	−	34.6129i	0.655646	−	1.13561i	−0.326085	−	0.945340i	$-0.605730\pi$
$929$	19.9838	−	34.6129i	0.655646	−	1.13561i	0.981731	−	0.190272i	$-0.0609370\pi$
$930$	3.23802	−	3.47286i	0.106179	−	0.113880i
$931$	−18.0832	−	10.4403i	−0.592652	−	0.342168i
$932$	−5.02689	−	18.7606i	−0.164661	−	0.614524i
$933$	8.04597	−	2.15591i	0.263413	−	0.0705814i
$934$	15.1235	−	8.73154i	0.494855	−	0.285705i
$935$	−37.7340	+	1.32047i	−1.23403	+	0.0431839i
$936$	3.41100	−	1.96934i	0.111492	−	0.0643699i
$937$	8.00876	+	29.8891i	0.261635	+	0.976435i	0.964278	+	0.264892i	$0.0853364\pi$
$937$	8.00876	+	29.8891i	0.261635	+	0.976435i	−0.702643	+	0.711542i	$0.747997\pi$
$938$	34.3212	−	34.3212i	1.12063	−	1.12063i
$939$	−33.0896	−	19.1043i	−1.07984	−	0.623445i
$940$	−2.50634	+	1.56639i	−0.0817479	+	0.0510901i
$941$	−18.5148	−	32.0687i	−0.603567	−	1.04541i	−0.992276	−	0.124048i	$-0.960412\pi$
$941$	−18.5148	−	32.0687i	−0.603567	−	1.04541i	0.388710	−	0.921360i	$-0.372921\pi$
$942$	−14.4009	+	14.4009i	−0.469205	+	0.469205i
$943$	−30.8872	−	8.27621i	−1.00583	−	0.269510i
$944$			11.4272i			0.371925i
$945$	35.0730	+	32.7013i	1.14093	+	1.06377i
$946$	−18.2567	+	8.72328i	−0.593577	+	0.283618i
$947$	30.3228	+	30.3228i	0.985359	+	0.985359i	0.999894	−	0.0145354i	$-0.00462694\pi$
$947$	30.3228	+	30.3228i	0.985359	+	0.985359i	−0.0145354	+	0.999894i	$0.504627\pi$
$948$	−0.147260	−	0.147260i	−0.00478280	−	0.00478280i
$949$	19.7651	+	34.2341i	0.641602	+	1.11129i
$950$	10.6496	+	9.25483i	0.345519	+	0.300266i
$951$	40.6875	−	23.4909i	1.31938	−	0.761746i
$952$	−5.37459	+	20.0583i	−0.174192	+	0.650092i
$953$	−3.76156	+	1.00791i	−0.121849	+	0.0326493i	−0.319228	−	0.947678i	$-0.603424\pi$
$953$	−3.76156	+	1.00791i	−0.121849	+	0.0326493i	0.197379	+	0.980327i	$0.436757\pi$
$954$	−6.55099			−0.212096
$955$	14.5717	−	4.45618i	0.471529	−	0.144199i
$956$	−4.09358	−	7.09029i	−0.132396	−	0.229316i
$957$	−15.4775	−	15.4775i	−0.500315	−	0.500315i
$958$	−7.84878	+	29.2921i	−0.253583	+	0.946384i
$959$	−26.4834	−	15.2902i	−0.855194	−	0.493746i
$960$	2.72096	+	1.44651i	0.0878187	+	0.0466858i
$961$	14.3129	−	24.7907i	0.461706	−	0.799699i
$962$	−5.28901	−	5.28901i	−0.170525	−	0.170525i
$963$	4.56543	+	17.0384i	0.147119	+	0.549055i
$964$	7.26185	−	12.5779i	0.233888	−	0.405107i
$965$	−22.3049	+	13.9399i	−0.718019	+	0.448741i
$966$	−28.1311	+	16.2415i	−0.905104	+	0.522562i
$967$	−17.5925	−	17.5925i	−0.565737	−	0.565737i	0.365194	−	0.930931i	$-0.381003\pi$
$967$	−17.5925	−	17.5925i	−0.565737	−	0.565737i	−0.930931	+	0.365194i	$0.881003\pi$
$968$	1.04580	+	1.04580i	0.0336132	+	0.0336132i
$969$	18.4297	−	10.6404i	0.592046	−	0.341818i
$970$	−16.6988	−	3.85393i	−0.536165	−	0.123742i
$971$	11.5542	−	20.0125i	0.370793	−	0.642231i	−0.618895	−	0.785474i	$-0.712419\pi$
$971$	11.5542	−	20.0125i	0.370793	−	0.642231i	0.989688	+	0.143242i	$0.0457528\pi$
$972$	2.78802	+	10.4050i	0.0894257	+	0.333741i
$973$	−41.2804	−	41.2804i	−1.32339	−	1.32339i
$974$	−20.7866	+	36.0034i	−0.666044	+	1.15362i
$975$	−22.1611	−	10.8047i	−0.709724	−	0.346027i
$976$	8.42126	+	4.86202i	0.269558	+	0.155629i
$977$	−3.77556	+	14.0906i	−0.120791	+	0.450797i	−0.999655	−	0.0262751i	$-0.991635\pi$
$977$	−3.77556	+	14.0906i	−0.120791	+	0.450797i	0.878864	+	0.477072i	$0.158302\pi$
$978$	11.4832	+	11.4832i	0.367191	+	0.367191i
$979$	−25.2598	−	43.7513i	−0.807308	−	1.39830i
$980$	−4.83882	−	15.8229i	−0.154571	−	0.505445i
$981$	−0.524383			−0.0167423
$982$	13.7433	−	3.68252i	0.438568	−	0.117514i
$983$	2.53158	−	9.44800i	0.0807450	−	0.301344i	−0.913730	−	0.406323i	$-0.866811\pi$
$983$	2.53158	−	9.44800i	0.0807450	−	0.301344i	0.994474	+	0.104979i	$0.0334774\pi$
$984$	−6.14410	+	3.54730i	−0.195867	+	0.113084i
$985$	29.5667	−	1.03466i	0.942075	−	0.0329671i
$986$	14.0841	+	24.3944i	0.448529	+	0.776876i
$987$	−4.88768	−	4.88768i	−0.155577	−	0.155577i
$988$	7.13935	+	7.13935i	0.227133	+	0.227133i
$989$	33.5834	+	23.0476i	1.06789	+	0.732870i
$990$	7.59044	−	0.265621i	0.241240	−	0.00844198i
$991$			6.86164i			0.217967i	0.994044	+	0.108984i	$0.0347596\pi$
$991$			6.86164i			0.217967i	−0.994044	+	0.108984i	$0.965240\pi$
$992$	−1.48834	−	0.398801i	−0.0472550	−	0.0126619i
$993$	−29.6405	+	29.6405i	−0.940613	+	0.940613i
$994$	10.5400	+	18.2558i	0.334307	+	0.579037i
$995$	32.3448	+	7.46489i	1.02540	+	0.236653i
$996$	8.03529	+	4.63918i	0.254608	+	0.146998i
$997$	−23.3699	+	23.3699i	−0.740133	+	0.740133i	−0.972603	−	0.232470i	$-0.925319\pi$
$997$	−23.3699	+	23.3699i	−0.740133	+	0.740133i	0.232470	+	0.972603i	$0.425319\pi$
$998$	−3.95861	−	14.7737i	−0.125308	−	0.467654i
$999$	10.2313	−	5.90702i	0.323703	−	0.186890i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.l.a.7.15	✓	88
5.3	odd	4	inner	430.2.l.a.93.4	yes	88
43.37	odd	6	inner	430.2.l.a.37.4	yes	88
215.123	even	12	inner	430.2.l.a.123.15	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.l.a.7.15	✓	88	1.1	even	1	trivial
430.2.l.a.37.4	yes	88	43.37	odd	6	inner
430.2.l.a.93.4	yes	88	5.3	odd	4	inner
430.2.l.a.123.15	yes	88	215.123	even	12	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.356683 + 1.33116i) q^{3} -1.00000i q^{4} +(-2.17879 - 0.502846i) q^{5} +(0.689058 + 1.19348i) q^{6} +(0.982140 + 3.66540i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.953316 + 0.550397i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.356683 + 1.33116i) q^{3} -1.00000i q^{4} +(-2.17879 - 0.502846i) q^{5} +(0.689058 + 1.19348i) q^{6} +(0.982140 + 3.66540i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.953316 + 0.550397i) q^{9} +(-1.89621 + 1.18507i) q^{10} -3.08561 q^{11} +(1.33116 + 0.356683i) q^{12} +(0.926064 + 3.45612i) q^{13} +(3.28630 + 1.89735i) q^{14} +(1.44651 - 2.72096i) q^{15} -1.00000 q^{16} +(-5.28586 + 1.41634i) q^{17} +(1.06329 - 0.284907i) q^{18} +(1.41091 + 2.44376i) q^{19} +(-0.502846 + 2.17879i) q^{20} -5.22953 q^{21} +(-2.18186 + 2.18186i) q^{22} +(5.99981 + 1.60764i) q^{23} +(1.19348 - 0.689058i) q^{24} +(4.49429 + 2.19120i) q^{25} +(3.09867 + 1.78902i) q^{26} +(-3.99612 + 3.99612i) q^{27} +(3.66540 - 0.982140i) q^{28} +(2.57370 - 4.45777i) q^{29} +(-0.901178 - 2.94685i) q^{30} +(0.770423 + 1.33441i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.10059 - 4.10744i) q^{33} +(-2.73616 + 4.73918i) q^{34} +(-0.296750 - 8.48001i) q^{35} +(0.550397 - 0.953316i) q^{36} +(-2.01924 - 0.541054i) q^{37} +(2.72567 + 0.730340i) q^{38} -4.93095 q^{39} +(1.18507 + 1.89621i) q^{40} -5.14804 q^{41} +(-3.69784 + 3.69784i) q^{42} +(6.18280 + 2.18471i) q^{43} +3.08561i q^{44} +(-1.80031 - 1.67857i) q^{45} +(5.37928 - 3.10573i) q^{46} +(0.934631 + 0.934631i) q^{47} +(0.356683 - 1.33116i) q^{48} +(-6.40835 + 3.69986i) q^{49} +(4.72735 - 1.62853i) q^{50} -7.54151i q^{51} +(3.45612 - 0.926064i) q^{52} +(-5.74837 - 1.54027i) q^{53} +5.65137i q^{54} +(6.72292 + 1.55159i) q^{55} +(1.89735 - 3.28630i) q^{56} +(-3.75628 + 1.00649i) q^{57} +(-1.33224 - 4.97200i) q^{58} -11.4272i q^{59} +(-2.72096 - 1.44651i) q^{60} +(-8.42126 - 4.86202i) q^{61} +(1.48834 + 0.398801i) q^{62} +(-1.08113 + 4.03485i) q^{63} +1.00000i q^{64} +(-0.279807 - 7.99584i) q^{65} +(-2.12617 - 3.68263i) q^{66} +(3.31052 - 12.3550i) q^{67} +(1.41634 + 5.28586i) q^{68} +(-4.28006 + 7.41327i) q^{69} +(-6.20611 - 5.78644i) q^{70} +(4.81086 + 2.77755i) q^{71} +(-0.284907 - 1.06329i) q^{72} +(10.6716 - 2.85944i) q^{73} +(-1.81040 + 1.04524i) q^{74} +(-4.51987 + 5.20105i) q^{75} +(2.44376 - 1.41091i) q^{76} +(-3.03050 - 11.3100i) q^{77} +(-3.48671 + 3.48671i) q^{78} +(-0.130872 - 0.0755588i) q^{79} +(2.17879 + 0.502846i) q^{80} +(-2.24293 - 3.88488i) q^{81} +(-3.64021 + 3.64021i) q^{82} +(6.50323 + 1.74253i) q^{83} +5.22953i q^{84} +(12.2290 - 0.427943i) q^{85} +(5.91672 - 2.82708i) q^{86} +(5.01601 + 5.01601i) q^{87} +(2.18186 + 2.18186i) q^{88} +(8.18633 + 14.1791i) q^{89} +(-2.45995 + 0.0860836i) q^{90} +(-11.7585 + 6.78878i) q^{91} +(1.60764 - 5.99981i) q^{92} +(-2.05111 + 0.549594i) q^{93} +1.32177 q^{94} +(-1.84524 - 6.03393i) q^{95} +(-0.689058 - 1.19348i) q^{96} +(5.41942 + 5.41942i) q^{97} +(-1.91519 + 7.14758i) q^{98} +(-2.94157 - 1.69831i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{6} + 12 q^{7}+O(q^{10}) \) 88 * q + 4 * q^6 + 12 * q^7	\( 88 q + 4 q^{6} + 12 q^{7} + 16 q^{13} - 88 q^{16} + 4 q^{17} - 16 q^{21} + 12 q^{23} - 8 q^{25} + 12 q^{28} - 36 q^{30} - 40 q^{31} + 12 q^{33} - 40 q^{35} - 40 q^{36} + 16 q^{38} - 56 q^{41} - 56 q^{43} + 24 q^{46} + 72 q^{47} + 24 q^{50} - 16 q^{52} + 20 q^{53} + 24 q^{55} - 8 q^{56} + 20 q^{57} + 8 q^{60} + 72 q^{61} + 36 q^{62} - 40 q^{66} - 16 q^{67} + 4 q^{68} + 24 q^{71} + 60 q^{73} - 48 q^{76} - 48 q^{77} + 40 q^{78} + 28 q^{81} + 20 q^{86} - 64 q^{87} - 8 q^{90} + 48 q^{91} - 12 q^{92} - 108 q^{93} + 4 q^{95} - 4 q^{96} - 48 q^{97} - 96 q^{98}+O(q^{100}) \) 88 * q + 4 * q^6 + 12 * q^7 + 16 * q^13 - 88 * q^16 + 4 * q^17 - 16 * q^21 + 12 * q^23 - 8 * q^25 + 12 * q^28 - 36 * q^30 - 40 * q^31 + 12 * q^33 - 40 * q^35 - 40 * q^36 + 16 * q^38 - 56 * q^41 - 56 * q^43 + 24 * q^46 + 72 * q^47 + 24 * q^50 - 16 * q^52 + 20 * q^53 + 24 * q^55 - 8 * q^56 + 20 * q^57 + 8 * q^60 + 72 * q^61 + 36 * q^62 - 40 * q^66 - 16 * q^67 + 4 * q^68 + 24 * q^71 + 60 * q^73 - 48 * q^76 - 48 * q^77 + 40 * q^78 + 28 * q^81 + 20 * q^86 - 64 * q^87 - 8 * q^90 + 48 * q^91 - 12 * q^92 - 108 * q^93 + 4 * q^95 - 4 * q^96 - 48 * q^97 - 96 * q^98

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