LMFDB - Embedded newform 430.2.p.a.59.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(59,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 8]))

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

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

chi := DirichletCharacter("430.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.p (of order $14$, degree $6$, 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:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			59.3
Character	$\chi$	$=$	430.59
Dual form			430.2.p.a.379.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.974928 + 0.222521i) q^{2} +(-2.18942 - 0.499720i) q^{3} +(0.900969 - 0.433884i) q^{4} +(2.05139 + 0.889832i) q^{5} +2.24572 q^{6} +1.14095i q^{7} +(-0.781831 + 0.623490i) q^{8} +(1.84092 + 0.886539i) q^{9} +O(q^{10})$	\(q+(-0.974928 + 0.222521i) q^{2} +(-2.18942 - 0.499720i) q^{3} +(0.900969 - 0.433884i) q^{4} +(2.05139 + 0.889832i) q^{5} +2.24572 q^{6} +1.14095i q^{7} +(-0.781831 + 0.623490i) q^{8} +(1.84092 + 0.886539i) q^{9} +(-2.19796 - 0.411045i) q^{10} +(-1.80460 - 0.869050i) q^{11} +(-2.18942 + 0.499720i) q^{12} +(0.422758 - 0.337138i) q^{13} +(-0.253885 - 1.11234i) q^{14} +(-4.04668 - 2.97333i) q^{15} +(0.623490 - 0.781831i) q^{16} +(1.76902 + 1.41075i) q^{17} +(-1.99203 - 0.454669i) q^{18} +(-0.428279 + 0.206248i) q^{19} +(2.23432 - 0.0883539i) q^{20} +(0.570155 - 2.49801i) q^{21} +(1.95274 + 0.445700i) q^{22} +(-1.14269 + 2.37282i) q^{23} +(2.02332 - 0.974382i) q^{24} +(3.41640 + 3.65078i) q^{25} +(-0.337138 + 0.422758i) q^{26} +(1.67981 + 1.33961i) q^{27} +(0.495039 + 1.02796i) q^{28} +(2.18692 + 9.58151i) q^{29} +(4.60685 + 1.99831i) q^{30} +(-0.255792 - 1.12070i) q^{31} +(-0.433884 + 0.900969i) q^{32} +(3.51674 + 2.80451i) q^{33} +(-2.03859 - 0.981732i) q^{34} +(-1.01525 + 2.34053i) q^{35} +2.04326 q^{36} +5.37416i q^{37} +(0.371647 - 0.296378i) q^{38} +(-1.09407 + 0.526875i) q^{39} +(-2.15864 + 0.583322i) q^{40} +(0.164189 + 0.719359i) q^{41} +2.56225i q^{42} +(4.24065 + 5.00169i) q^{43} -2.00296 q^{44} +(2.98757 + 3.45674i) q^{45} +(0.586039 - 2.56760i) q^{46} +(2.74930 + 5.70898i) q^{47} +(-1.75578 + 1.40018i) q^{48} +5.69824 q^{49} +(-4.14312 - 2.79903i) q^{50} +(-3.16814 - 3.97273i) q^{51} +(0.234613 - 0.487179i) q^{52} +(-0.489207 - 0.390130i) q^{53} +(-1.93579 - 0.932227i) q^{54} +(-2.92863 - 3.38855i) q^{55} +(-0.711370 - 0.892029i) q^{56} +(1.04075 - 0.237544i) q^{57} +(-4.26417 - 8.85465i) q^{58} +(-6.16442 + 7.72994i) q^{59} +(-4.93601 - 0.923092i) q^{60} +(1.32599 - 5.80953i) q^{61} +(0.498757 + 1.03568i) q^{62} +(-1.01149 + 2.10039i) q^{63} +(0.222521 - 0.974928i) q^{64} +(1.16724 - 0.315418i) q^{65} +(-4.05263 - 1.95164i) q^{66} +(-3.22869 - 6.70444i) q^{67} +(2.20593 + 0.503490i) q^{68} +(3.68757 - 4.62407i) q^{69} +(0.468981 - 2.50776i) q^{70} +(4.68255 - 2.25500i) q^{71} +(-1.99203 + 0.454669i) q^{72} +(-0.421091 + 0.335809i) q^{73} +(-1.19586 - 5.23942i) q^{74} +(-5.65555 - 9.70033i) q^{75} +(-0.296378 + 0.371647i) q^{76} +(0.991541 - 2.05896i) q^{77} +(0.949396 - 0.757118i) q^{78} +2.81076 q^{79} +(1.97472 - 1.04904i) q^{80} +(-6.83025 - 8.56486i) q^{81} +(-0.320145 - 0.664787i) q^{82} +(-6.70520 - 1.53042i) q^{83} +(-0.570155 - 2.49801i) q^{84} +(2.37362 + 4.46812i) q^{85} +(-5.24731 - 3.93266i) q^{86} -22.0708i q^{87} +(1.95274 - 0.445700i) q^{88} +(-3.13587 + 13.7391i) q^{89} +(-3.68186 - 2.70528i) q^{90} +(0.384657 + 0.482345i) q^{91} +2.63363i q^{92} +2.58150i q^{93} +(-3.95074 - 4.95407i) q^{94} +(-1.06209 + 0.0419994i) q^{95} +(1.40018 - 1.75578i) q^{96} +(5.97950 - 12.4166i) q^{97} +(-5.55537 + 1.26798i) q^{98} +(-2.55167 - 3.19970i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 22 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{9}+O(q^{10}) $ 132 * q + 22 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^9	$ 132 q + 22 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{9} + 8 q^{11} - 10 q^{14} - 20 q^{15} - 22 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} + 4 q^{24} - 16 q^{25} + 12 q^{26} + 40 q^{29} + 24 q^{31} - 4 q^{35} + 128 q^{36} - 56 q^{39} - 28 q^{41} - 8 q^{44} - 80 q^{45} - 12 q^{46} - 136 q^{49} - 56 q^{50} + 172 q^{51} + 16 q^{54} - 4 q^{56} + 16 q^{59} - 8 q^{60} - 44 q^{61} + 22 q^{64} + 42 q^{65} + 8 q^{66} - 62 q^{69} + 12 q^{70} - 8 q^{71} - 4 q^{74} - 122 q^{75} - 52 q^{76} - 64 q^{79} - 4 q^{80} - 56 q^{81} + 24 q^{84} - 72 q^{85} - 10 q^{86} + 16 q^{89} + 2 q^{90} - 24 q^{91} - 20 q^{94} + 106 q^{95} - 4 q^{96} - 104 q^{99}+O(q^{100}) $ 132 * q + 22 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^9 + 8 * q^11 - 10 * q^14 - 20 * q^15 - 22 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 + 4 * q^24 - 16 * q^25 + 12 * q^26 + 40 * q^29 + 24 * q^31 - 4 * q^35 + 128 * q^36 - 56 * q^39 - 28 * q^41 - 8 * q^44 - 80 * q^45 - 12 * q^46 - 136 * q^49 - 56 * q^50 + 172 * q^51 + 16 * q^54 - 4 * q^56 + 16 * q^59 - 8 * q^60 - 44 * q^61 + 22 * q^64 + 42 * q^65 + 8 * q^66 - 62 * q^69 + 12 * q^70 - 8 * q^71 - 4 * q^74 - 122 * q^75 - 52 * q^76 - 64 * q^79 - 4 * q^80 - 56 * q^81 + 24 * q^84 - 72 * q^85 - 10 * q^86 + 16 * q^89 + 2 * q^90 - 24 * q^91 - 20 * q^94 + 106 * q^95 - 4 * q^96 - 104 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$87$	$261$
$\chi(n)$	$-1$	$e\left(\frac{4}{7}\right)$

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 $

$2$	−0.974928	+	0.222521i	−0.689378	+	0.157346i
$2$	−0.974928	+	0.222521i	−0.689378	+	0.157346i
$3$	−2.18942	−	0.499720i	−1.26406	−	0.288513i	−0.462603	−	0.886566i	$-0.653084\pi$
$3$	−2.18942	−	0.499720i	−1.26406	−	0.288513i	−0.801457	+	0.598052i	$0.795942\pi$
$4$	0.900969	−	0.433884i	0.450484	−	0.216942i
$5$	2.05139	+	0.889832i	0.917409	+	0.397945i
$5$	2.05139	+	0.889832i	0.917409	+	0.397945i
$6$	2.24572			0.916812
$7$			1.14095i			0.431238i	0.976478	+	0.215619i	$0.0691769\pi$
$7$			1.14095i			0.431238i	−0.976478	+	0.215619i	$0.930823\pi$
$8$	−0.781831	+	0.623490i	−0.276419	+	0.220437i
$9$	1.84092	+	0.886539i	0.613639	+	0.295513i
$10$	−2.19796	−	0.411045i	−0.695057	−	0.129984i
$11$	−1.80460	−	0.869050i	−0.544108	−	0.262029i	0.141577	−	0.989927i	$-0.454783\pi$
$11$	−1.80460	−	0.869050i	−0.544108	−	0.262029i	−0.685685	+	0.727899i	$0.740497\pi$
$12$	−2.18942	+	0.499720i	−0.632030	+	0.144257i
$13$	0.422758	−	0.337138i	0.117252	−	0.0935053i	−0.563109	−	0.826383i	$-0.690395\pi$
$13$	0.422758	−	0.337138i	0.117252	−	0.0935053i	0.680360	+	0.732878i	$0.261823\pi$
$14$	−0.253885	−	1.11234i	−0.0678536	−	0.297286i
$15$	−4.04668	−	2.97333i	−1.04485	−	0.767711i
$16$	0.623490	−	0.781831i	0.155872	−	0.195458i
$17$	1.76902	+	1.41075i	0.429050	+	0.342156i	0.814085	−	0.580746i	$-0.197239\pi$
$17$	1.76902	+	1.41075i	0.429050	+	0.342156i	−0.385034	+	0.922902i	$0.625810\pi$
$18$	−1.99203	−	0.454669i	−0.469527	−	0.107166i
$19$	−0.428279	+	0.206248i	−0.0982540	+	0.0473166i	−0.482365	−	0.875970i	$-0.660222\pi$
$19$	−0.428279	+	0.206248i	−0.0982540	+	0.0473166i	0.384111	+	0.923287i	$0.374508\pi$
$20$	2.23432	−	0.0883539i	0.499610	−	0.0197565i
$21$	0.570155	−	2.49801i	0.124418	−	0.545111i
$22$	1.95274	+	0.445700i	0.416325	+	0.0950235i
$23$	−1.14269	+	2.37282i	−0.238268	+	0.494768i	−0.985474	−	0.169824i	$-0.945680\pi$
$23$	−1.14269	+	2.37282i	−0.238268	+	0.494768i	0.747207	+	0.664591i	$0.231394\pi$
$24$	2.02332	−	0.974382i	0.413009	−	0.198895i
$25$	3.41640	+	3.65078i	0.683280	+	0.730157i
$26$	−0.337138	+	0.422758i	−0.0661182	+	0.0829096i
$27$	1.67981	+	1.33961i	0.323281	+	0.257808i
$28$	0.495039	+	1.02796i	0.0935535	+	0.194266i
$29$	2.18692	+	9.58151i	0.406100	+	1.77924i	0.601872	+	0.798593i	$0.294422\pi$
$29$	2.18692	+	9.58151i	0.406100	+	1.77924i	−0.195771	+	0.980650i	$0.562721\pi$
$30$	4.60685	+	1.99831i	0.841092	+	0.364841i
$31$	−0.255792	−	1.12070i	−0.0459416	−	0.201283i	0.946749	−	0.321974i	$-0.104346\pi$
$31$	−0.255792	−	1.12070i	−0.0459416	−	0.201283i	−0.992690	+	0.120691i	$0.961489\pi$
$32$	−0.433884	+	0.900969i	−0.0767005	+	0.159270i
$33$	3.51674	+	2.80451i	0.612186	+	0.488202i
$34$	−2.03859	−	0.981732i	−0.349615	−	0.168366i
$35$	−1.01525	+	2.34053i	−0.171609	+	0.395622i
$36$	2.04326			0.340544
$37$			5.37416i			0.883507i	0.897137	+	0.441753i	$0.145643\pi$
$37$			5.37416i			0.883507i	−0.897137	+	0.441753i	$0.854357\pi$
$38$	0.371647	−	0.296378i	0.0602891	−	0.0480789i
$39$	−1.09407	+	0.526875i	−0.175191	+	0.0843675i
$40$	−2.15864	+	0.583322i	−0.341311	+	0.0922313i
$41$	0.164189	+	0.719359i	0.0256420	+	0.112345i	0.986129	−	0.165979i	$-0.0530783\pi$
$41$	0.164189	+	0.719359i	0.0256420	+	0.112345i	−0.960487	+	0.278324i	$0.910221\pi$
$42$			2.56225i			0.395364i
$43$	4.24065	+	5.00169i	0.646692	+	0.762751i
$43$	4.24065	+	5.00169i	0.646692	+	0.762751i
$44$	−2.00296			−0.301957
$45$	2.98757	+	3.45674i	0.445360	+	0.515301i
$46$	0.586039	−	2.56760i	0.0864067	−	0.378572i
$47$	2.74930	+	5.70898i	0.401027	+	0.832741i	0.999501	+	0.0315983i	$0.0100597\pi$
$47$	2.74930	+	5.70898i	0.401027	+	0.832741i	−0.598474	+	0.801142i	$0.704226\pi$
$48$	−1.75578	+	1.40018i	−0.253424	+	0.202099i
$49$	5.69824			0.814034
$50$	−4.14312	−	2.79903i	−0.585925	−	0.395843i
$51$	−3.16814	−	3.97273i	−0.443629	−	0.556293i
$52$	0.234613	−	0.487179i	0.0325349	−	0.0675595i
$53$	−0.489207	−	0.390130i	−0.0671978	−	0.0535884i	0.589315	−	0.807903i	$-0.299398\pi$
$53$	−0.489207	−	0.390130i	−0.0671978	−	0.0535884i	−0.656513	+	0.754315i	$0.727969\pi$
$54$	−1.93579	−	0.932227i	−0.263428	−	0.126860i
$55$	−2.92863	−	3.38855i	−0.394897	−	0.456912i
$56$	−0.711370	−	0.892029i	−0.0950607	−	0.119202i
$57$	1.04075	−	0.237544i	0.137850	−	0.0314635i
$58$	−4.26417	−	8.85465i	−0.559914	−	1.16267i
$59$	−6.16442	+	7.72994i	−0.802539	+	1.00635i	0.197123	+	0.980379i	$0.436840\pi$
$59$	−6.16442	+	7.72994i	−0.802539	+	1.00635i	−0.999663	+	0.0259736i	$0.991731\pi$
$60$	−4.93601	−	0.923092i	−0.637236	−	0.119171i
$61$	1.32599	−	5.80953i	0.169775	−	0.743834i	−0.816313	−	0.577610i	$-0.803985\pi$
$61$	1.32599	−	5.80953i	0.169775	−	0.743834i	0.986088	−	0.166224i	$-0.0531575\pi$
$62$	0.498757	+	1.03568i	0.0633422	+	0.131532i
$63$	−1.01149	+	2.10039i	−0.127436	+	0.264624i
$64$	0.222521	−	0.974928i	0.0278151	−	0.121866i
$65$	1.16724	−	0.315418i	0.144778	−	0.0391228i
$66$	−4.05263	−	1.95164i	−0.498845	−	0.240231i
$67$	−3.22869	−	6.70444i	−0.394447	−	0.819078i	−0.999734	−	0.0230703i	$-0.992656\pi$
$67$	−3.22869	−	6.70444i	−0.394447	−	0.819078i	0.605287	−	0.796008i	$-0.293058\pi$
$68$	2.20593	+	0.503490i	0.267509	+	0.0610571i
$69$	3.68757	−	4.62407i	0.443932	−	0.556673i
$70$	0.468981	−	2.50776i	0.0560539	−	0.299735i
$71$	4.68255	−	2.25500i	0.555716	−	0.267619i	−0.134877	−	0.990862i	$-0.543064\pi$
$71$	4.68255	−	2.25500i	0.555716	−	0.267619i	0.690593	+	0.723244i	$0.257350\pi$
$72$	−1.99203	+	0.454669i	−0.234763	+	0.0535832i
$73$	−0.421091	+	0.335809i	−0.0492850	+	0.0393035i	−0.647823	−	0.761791i	$-0.724320\pi$
$73$	−0.421091	+	0.335809i	−0.0492850	+	0.0393035i	0.598538	+	0.801095i	$0.295749\pi$
$74$	−1.19586	−	5.23942i	−0.139016	−	0.609070i
$75$	−5.65555	−	9.70033i	−0.653047	−	1.12010i
$76$	−0.296378	+	0.371647i	−0.0339969	+	0.0426308i
$77$	0.991541	−	2.05896i	0.112997	−	0.234640i
$78$	0.949396	−	0.757118i	0.107498	−	0.0857267i
$79$	2.81076			0.316235			0.158117	−	0.987420i	$-0.449458\pi$
$79$	2.81076			0.316235			0.158117	+	0.987420i	$0.449458\pi$
$80$	1.97472	−	1.04904i	0.220780	−	0.117286i
$81$	−6.83025	−	8.56486i	−0.758916	−	0.951651i
$82$	−0.320145	−	0.664787i	−0.0353541	−	0.0734135i
$83$	−6.70520	−	1.53042i	−0.735991	−	0.167985i	−0.161936	−	0.986801i	$-0.551774\pi$
$83$	−6.70520	−	1.53042i	−0.735991	−	0.167985i	−0.574056	+	0.818816i	$0.694631\pi$
$84$	−0.570155	−	2.49801i	−0.0622090	−	0.272555i
$85$	2.37362	+	4.46812i	0.257456	+	0.484636i
$86$	−5.24731	−	3.93266i	−0.565831	−	0.424069i
$87$		−	22.0708i		−	2.36623i
$88$	1.95274	−	0.445700i	0.208163	−	0.0475118i
$89$	−3.13587	+	13.7391i	−0.332401	+	1.45635i	0.482065	+	0.876135i	$0.339887\pi$
$89$	−3.13587	+	13.7391i	−0.332401	+	1.45635i	−0.814467	+	0.580210i	$0.802970\pi$
$90$	−3.68186	−	2.70528i	−0.388102	−	0.285161i
$91$	0.384657	+	0.482345i	0.0403230	+	0.0505635i
$92$			2.63363i			0.274575i
$93$			2.58150i			0.267689i
$94$	−3.95074	−	4.95407i	−0.407487	−	0.510973i
$95$	−1.06209	+	0.0419994i	−0.108969	+	0.00430905i
$96$	1.40018	−	1.75578i	0.142906	−	0.179198i
$97$	5.97950	−	12.4166i	0.607126	−	1.26071i	−0.340174	−	0.940363i	$-0.610486\pi$
$97$	5.97950	−	12.4166i	0.607126	−	1.26071i	0.947300	−	0.320348i	$-0.103800\pi$
$98$	−5.55537	+	1.26798i	−0.561177	+	0.128085i
$99$	−2.55167	−	3.19970i	−0.256453	−	0.321582i
$100$	4.66208	+	1.80692i	0.466208	+	0.180692i
$101$	1.27992	−	0.616377i	0.127357	−	0.0613318i	−0.369120	−	0.929382i	$-0.620341\pi$
$101$	1.27992	−	0.616377i	0.127357	−	0.0613318i	0.496477	+	0.868050i	$0.334627\pi$
$102$	3.97273	+	3.16814i	0.393359	+	0.313693i
$103$	4.89063	+	3.90015i	0.481888	+	0.384293i	0.834088	−	0.551632i	$-0.185995\pi$
$103$	4.89063	+	3.90015i	0.481888	+	0.384293i	−0.352200	+	0.935925i	$0.614566\pi$
$104$	−0.120323	+	0.527170i	−0.0117987	+	0.0516933i
$105$	3.39242	−	4.61705i	0.331066	−	0.450578i
$106$	0.563754	+	0.271490i	0.0547566	+	0.0263694i
$107$	−12.5203	−	2.85769i	−1.21039	−	0.276263i	−0.430737	−	0.902478i	$-0.641746\pi$
$107$	−12.5203	−	2.85769i	−1.21039	−	0.276263i	−0.779651	+	0.626215i	$0.784603\pi$
$108$	2.09469	+	0.478100i	0.201562	+	0.0460052i
$109$	−8.30706	−	4.00047i	−0.795672	−	0.383176i	−0.00854305	−	0.999964i	$-0.502719\pi$
$109$	−8.30706	−	4.00047i	−0.795672	−	0.383176i	−0.787129	+	0.616788i	$0.788434\pi$
$110$	3.60923	+	2.65191i	0.344127	+	0.252850i
$111$	2.68558	−	11.7663i	0.254904	−	1.11681i
$112$	0.892029	+	0.711370i	0.0842888	+	0.0672181i
$113$	7.30960	+	5.82921i	0.687630	+	0.548366i	0.903782	−	0.427993i	$-0.140779\pi$
$113$	7.30960	+	5.82921i	0.687630	+	0.548366i	−0.216152	+	0.976360i	$0.569351\pi$
$114$	−0.961796	+	0.463176i	−0.0900804	+	0.0433805i
$115$	−4.45552	+	3.85078i	−0.415479	+	0.359087i
$116$	6.12761	+	7.68378i	0.568934	+	0.713421i
$117$	1.07715	−	0.245852i	0.0995823	−	0.0227290i
$118$	4.28979	−	8.90785i	0.394907	−	0.820034i
$119$	−1.60959	+	2.01836i	−0.147551	+	0.185023i
$120$	5.01766	−	0.198418i	0.458048	−	0.0181130i
$121$	−4.35705	−	5.46357i	−0.396095	−	0.496688i
$122$			5.95893i			0.539496i
$123$		−	1.65702i		−	0.149409i
$124$	−0.716713	−	0.898730i	−0.0643627	−	0.0807083i
$125$	3.75978	+	10.5292i	0.336285	+	0.941760i
$126$	0.518754	−	2.27281i	0.0462142	−	0.202478i
$127$	4.04981	−	0.924344i	0.359363	−	0.0820222i	−0.0390276	−	0.999238i	$-0.512426\pi$
$127$	4.04981	−	0.924344i	0.359363	−	0.0820222i	0.398390	+	0.917216i	$0.369569\pi$
$128$			1.00000i			0.0883883i
$129$	−6.78509	−	13.0699i	−0.597394	−	1.15074i
$130$	−1.06778	+	0.567245i	−0.0936509	+	0.0497506i
$131$	2.99784	+	13.1344i	0.261922	+	1.14756i	0.919163	+	0.393876i	$0.128866\pi$
$131$	2.99784	+	13.1344i	0.261922	+	1.14756i	−0.657241	+	0.753680i	$0.728277\pi$
$132$	4.38531	+	1.00092i	0.381692	+	0.0871187i
$133$	−0.235319	−	0.488644i	−0.0204047	−	0.0423709i
$134$	4.63962	+	5.81790i	0.400802	+	0.502590i
$135$	2.25393	+	4.24281i	0.193987	+	0.365163i
$136$	−2.26266			−0.194022
$137$	2.56358	−	2.04438i	0.219021	−	0.174663i	−0.507833	−	0.861456i	$-0.669553\pi$
$137$	2.56358	−	2.04438i	0.219021	−	0.174663i	0.726854	+	0.686792i	$0.240982\pi$
$138$	−2.56617	+	5.32870i	−0.218446	+	0.453609i
$139$	−2.60450	+	3.26593i	−0.220910	+	0.277013i	−0.879920	−	0.475121i	$-0.842404\pi$
$139$	−2.60450	+	3.26593i	−0.220910	+	0.277013i	0.659010	+	0.752134i	$0.270976\pi$
$140$	0.100807	+	2.54925i	0.00851977	+	0.215451i
$141$	−3.16647	−	13.8732i	−0.266665	−	1.16834i
$142$	−4.06336	+	3.24042i	−0.340990	+	0.271930i
$143$	−1.05590	+	0.241002i	−0.0882987	+	0.0201536i
$144$	1.84092	−	0.886539i	0.153410	−	0.0738782i
$145$	−4.03971	+	21.6014i	−0.335480	+	1.79390i
$146$	0.335809	−	0.421091i	0.0277918	−	0.0348498i
$147$	−12.4758	−	2.84752i	−1.02899	−	0.234860i
$148$	2.33176	+	4.84195i	0.191670	+	0.398006i
$149$	14.4791	+	6.97278i	1.18618	+	0.571232i	0.919705	−	0.392610i	$-0.128428\pi$
$149$	14.4791	+	6.97278i	1.18618	+	0.571232i	0.266472	+	0.963843i	$0.414142\pi$
$150$	7.67228	+	8.19864i	0.626439	+	0.669416i
$151$	3.26937	−	14.3241i	0.266058	−	1.16568i	−0.648498	−	0.761216i	$-0.724603\pi$
$151$	3.26937	−	14.3241i	0.266058	−	1.16568i	0.914556	−	0.404459i	$-0.132540\pi$
$152$	0.206248	−	0.428279i	0.0167290	−	0.0347380i
$153$	2.00594	+	4.16537i	0.162170	+	0.336750i
$154$	−0.508520	+	2.22797i	−0.0409777	+	0.179535i
$155$	0.472503	−	2.52660i	0.0379524	−	0.202941i
$156$	−0.757118	+	0.949396i	−0.0606179	+	0.0760125i
$157$	−5.72272	−	11.8834i	−0.456723	−	0.948395i	−0.994443	−	0.105272i	$-0.966429\pi$
$157$	−5.72272	−	11.8834i	−0.456723	−	0.948395i	0.537720	−	0.843123i	$-0.319286\pi$
$158$	−2.74028	+	0.625452i	−0.218005	+	0.0497583i
$159$	0.876123	+	1.09862i	0.0694810	+	0.0871265i
$160$	−1.69178	+	1.46215i	−0.133747	+	0.115593i
$161$	−2.70727	−	1.30375i	−0.213363	−	0.102750i
$162$	8.56486	+	6.83025i	0.672919	+	0.536635i
$163$	3.85540	−	8.00583i	0.301979	−	0.627065i	−0.693666	−	0.720297i	$-0.744006\pi$
$163$	3.85540	−	8.00583i	0.301979	−	0.627065i	0.995644	+	0.0932320i	$0.0297198\pi$
$164$	0.460047	+	0.576881i	0.0359236	+	0.0450468i
$165$	4.71867	+	8.88245i	0.367348	+	0.691498i
$166$	6.87764			0.533808
$167$	−10.0612	+	8.02356i	−0.778561	+	0.620882i	−0.929989	−	0.367587i	$-0.880184\pi$
$167$	−10.0612	+	8.02356i	−0.778561	+	0.620882i	0.151428	+	0.988468i	$0.451613\pi$
$168$	1.11172	+	2.30851i	0.0857710	+	0.178105i
$169$	−2.82771	+	12.3890i	−0.217516	+	0.953001i
$170$	−3.30836	−	3.82792i	−0.253740	−	0.293588i
$171$	−0.971274			−0.0742752
$172$	5.99084	+	2.66642i	0.456797	+	0.203313i
$173$		−	23.9248i		−	1.81897i	−0.415736	−	0.909485i	$-0.636476\pi$
$173$		−	23.9248i		−	1.81897i	0.415736	−	0.909485i	$-0.363524\pi$
$174$	4.91121	+	21.5174i	0.372318	+	1.63123i
$175$	−4.16535	+	3.89793i	−0.314871	+	0.294656i
$176$	−1.80460	+	0.869050i	−0.136027	+	0.0655071i
$177$	17.3593	−	13.8436i	1.30480	−	1.04055i
$178$		−	14.0925i		−	1.05628i
$179$	−10.3172			−0.771147			−0.385573	−	0.922677i	$-0.625996\pi$
$179$	−10.3172			−0.771147			−0.385573	+	0.922677i	$0.625996\pi$
$180$	4.19153	+	1.81816i	0.312418	+	0.135518i
$181$	−13.6885	−	6.59204i	−1.01746	−	0.489982i	−0.150631	−	0.988590i	$-0.548131\pi$
$181$	−13.6885	−	6.59204i	−1.01746	−	0.489982i	−0.866828	+	0.498608i	$0.833845\pi$
$182$	−0.482345	−	0.384657i	−0.0357538	−	0.0285127i
$183$	−5.80628	+	12.0569i	−0.429212	+	0.891269i
$184$	−0.586039	−	2.56760i	−0.0432033	−	0.189286i
$185$	−4.78210	+	11.0245i	−0.351587	+	0.810537i
$186$	−0.574437	−	2.51677i	−0.0421198	−	0.184539i
$187$	−1.96637	−	4.08320i	−0.143795	−	0.298593i
$188$	4.95407	+	3.95074i	0.361313	+	0.288137i
$189$	−1.52842	+	1.91658i	−0.111176	+	0.139411i
$190$	1.02612	−	0.277285i	0.0744425	−	0.0201163i
$191$	17.8390	−	8.59082i	1.29079	−	0.621610i	0.342647	−	0.939464i	$-0.388677\pi$
$191$	17.8390	−	8.59082i	1.29079	−	0.621610i	0.948140	+	0.317854i	$0.102962\pi$
$192$	−0.974382	+	2.02332i	−0.0703200	+	0.146021i
$193$	−6.71834	−	1.53342i	−0.483597	−	0.110378i	−0.0262300	−	0.999656i	$-0.508350\pi$
$193$	−6.71834	−	1.53342i	−0.483597	−	0.110378i	−0.457367	+	0.889278i	$0.651207\pi$
$194$	−3.06664	+	13.4358i	−0.220172	+	0.964635i
$195$	−2.71319	+	0.107290i	−0.194295	+	0.00768321i
$196$	5.13393	−	2.47237i	0.366710	−	0.176598i
$197$	−12.9864	−	2.96405i	−0.925240	−	0.211180i	−0.266747	−	0.963767i	$-0.585949\pi$
$197$	−12.9864	−	2.96405i	−0.925240	−	0.211180i	−0.658493	+	0.752586i	$0.728806\pi$
$198$	3.19970	+	2.55167i	0.227393	+	0.181340i
$199$	11.4013	−	14.2967i	0.808213	−	1.01347i	−0.191277	−	0.981536i	$-0.561263\pi$
$199$	11.4013	−	14.2967i	0.808213	−	1.01347i	0.999490	−	0.0319313i	$-0.0101658\pi$
$200$	−4.94727	−	0.724207i	−0.349825	−	0.0512092i
$201$	3.71860	+	16.2923i	0.262290	+	1.14917i
$202$	−1.11067	+	0.885733i	−0.0781467	+	0.0623199i
$203$	−10.9320	+	2.49516i	−0.767277	+	0.175126i
$204$	−4.57810	−	2.20470i	−0.320531	−	0.154360i
$205$	−0.303293	+	1.62179i	−0.0211829	+	0.113270i
$206$	−5.63587	−	2.71409i	−0.392670	−	0.189100i
$207$	−4.20720	+	3.35513i	−0.292420	+	0.233198i
$208$		−	0.540727i		−	0.0374927i
$209$	0.952114			0.0658591
$210$	−2.27997	+	5.25618i	−0.157333	+	0.362711i
$211$	8.85936	−	4.26644i	0.609904	−	0.293714i	−0.103323	−	0.994648i	$-0.532947\pi$
$211$	8.85936	−	4.26644i	0.609904	−	0.293714i	0.713226	+	0.700934i	$0.247233\pi$
$212$	−0.610031	−	0.139236i	−0.0418971	−	0.00956275i
$213$	−11.3789	+	2.59716i	−0.779670	+	0.177955i
$214$	12.8423			0.877884
$215$	4.24855	+	14.0339i	0.289749	+	0.957103i
$216$	−2.14856			−0.146191
$217$	1.27866	−	0.291845i	0.0868009	−	0.0198117i
$218$	8.98898	+	2.05168i	0.608810	+	0.138957i
$219$	1.08975	−	0.524798i	0.0736388	−	0.0354626i
$220$	−4.10884	−	1.78229i	−0.277018	−	0.120162i
$221$	1.22348			0.0823004
$222$			12.0689i			0.810009i
$223$	0.733885	−	0.585254i	0.0491446	−	0.0391915i	−0.598609	−	0.801041i	$-0.704280\pi$
$223$	0.733885	−	0.585254i	0.0491446	−	0.0391915i	0.647754	+	0.761849i	$0.275708\pi$
$224$	−1.02796	−	0.495039i	−0.0686834	−	0.0330762i
$225$	3.05274	+	9.74956i	0.203516	+	0.649970i
$226$	−8.42346	−	4.05652i	−0.560320	−	0.269836i
$227$	−5.71139	+	1.30359i	−0.379078	+	0.0865221i	−0.407814	−	0.913065i	$-0.633709\pi$
$227$	−5.71139	+	1.30359i	−0.379078	+	0.0865221i	0.0287361	+	0.999587i	$0.490852\pi$
$228$	0.834615	−	0.665583i	0.0552737	−	0.0440793i
$229$	0.920829	+	4.03442i	0.0608501	+	0.266602i	0.996197	−	0.0871303i	$-0.0277696\pi$
$229$	0.920829	+	4.03442i	0.0608501	+	0.266602i	−0.935347	+	0.353732i	$0.884913\pi$
$230$	3.48693	−	4.74568i	0.229921	−	0.312921i
$231$	−3.19980	+	4.01242i	−0.210531	+	0.263998i
$232$	−7.68378	−	6.12761i	−0.504465	−	0.402297i
$233$	−13.3822	−	3.05441i	−0.876700	−	0.200101i	−0.239590	−	0.970874i	$-0.577013\pi$
$233$	−13.3822	−	3.05441i	−0.876700	−	0.200101i	−0.637110	+	0.770773i	$0.719870\pi$
$234$	−0.995434	+	0.479376i	−0.0650736	+	0.0313378i
$235$	0.559854	+	14.1578i	0.0365208	+	0.923550i
$236$	−2.20006	+	9.63908i	−0.143211	+	0.627450i
$237$	−6.15391	−	1.40459i	−0.399740	−	0.0912380i
$238$	1.12011	−	2.32592i	0.0726057	−	0.150767i
$239$	20.8801	−	10.0553i	1.35062	−	0.650424i	0.388094	−	0.921620i	$-0.373133\pi$
$239$	20.8801	−	10.0553i	1.35062	−	0.650424i	0.962524	+	0.271196i	$0.0874192\pi$
$240$	−4.84771	+	1.30998i	−0.312918	+	0.0845588i
$241$	1.42719	−	1.78963i	0.0919331	−	0.115280i	−0.733737	−	0.679433i	$-0.762226\pi$
$241$	1.42719	−	1.78963i	0.0919331	−	0.115280i	0.825670	+	0.564153i	$0.190797\pi$
$242$	5.46357	+	4.35705i	0.351211	+	0.280082i
$243$	7.87754	+	16.3579i	0.505344	+	1.04936i
$244$	−1.32599	−	5.80953i	−0.0848876	−	0.371917i
$245$	11.6893	+	5.07047i	0.746802	+	0.323941i
$246$	0.368723	+	1.61548i	0.0235089	+	0.102999i
$247$	−0.111524	+	0.231582i	−0.00709611	+	0.0147352i
$248$	0.898730	+	0.716713i	0.0570694	+	0.0455113i
$249$	13.9157	+	6.70145i	0.881871	+	0.424687i
$250$	−6.00848	−	9.42858i	−0.380010	−	0.596316i
$251$	26.0386			1.64354			0.821771	−	0.569818i	$-0.192986\pi$
$251$	26.0386			1.64354			0.821771	+	0.569818i	$0.192986\pi$
$252$			2.33126i			0.146855i
$253$	4.12420	−	3.28894i	0.259286	−	0.206774i
$254$	−3.74259	+	1.80234i	−0.234831	+	0.113089i
$255$	−2.96404	−	10.9687i	−0.185615	−	0.686888i
$256$	−0.222521	−	0.974928i	−0.0139076	−	0.0609330i
$257$			23.9732i			1.49541i	0.664033	+	0.747703i	$0.268843\pi$
$257$			23.9732i			1.49541i	−0.664033	+	0.747703i	$0.731157\pi$
$258$	9.52331	+	11.2324i	0.592895	+	0.699299i
$259$	−6.13164			−0.381002
$260$	0.914789	−	0.790627i	0.0567328	−	0.0490326i
$261$	−4.46845	+	19.5776i	−0.276590	+	1.21182i
$262$	−5.84535	−	12.1380i	−0.361127	−	0.749888i
$263$	12.0451	−	9.60568i	0.742736	−	0.592312i	−0.177295	−	0.984158i	$-0.556735\pi$
$263$	12.0451	−	9.60568i	0.742736	−	0.592312i	0.920031	+	0.391846i	$0.128163\pi$
$264$	−4.49808			−0.276838
$265$	−0.656405	−	1.23562i	−0.0403226	−	0.0759035i
$266$	0.338152	+	0.424030i	0.0207335	+	0.0259989i
$267$	13.7314	−	28.5136i	0.840351	−	1.74501i
$268$	−5.81790	−	4.63962i	−0.355385	−	0.283410i
$269$	1.43603	+	0.691557i	0.0875565	+	0.0421650i	0.477149	−	0.878822i	$-0.341670\pi$
$269$	1.43603	+	0.691557i	0.0875565	+	0.0421650i	−0.389593	+	0.920987i	$0.627384\pi$
$270$	−3.14153	−	3.63489i	−0.191188	−	0.221212i
$271$	18.5052	+	23.2047i	1.12411	+	1.40959i	0.900472	+	0.434915i	$0.143221\pi$
$271$	18.5052	+	23.2047i	1.12411	+	1.40959i	0.223636	+	0.974673i	$0.428207\pi$
$272$	2.20593	−	0.503490i	0.133754	−	0.0305285i
$273$	−0.601137	−	1.24827i	−0.0363825	−	0.0755490i
$274$	−2.04438	+	2.56358i	−0.123506	+	0.154871i
$275$	−2.99252	−	9.55723i	−0.180456	−	0.576323i
$276$	1.31608	−	5.76612i	0.0792187	−	0.347080i
$277$	8.77302	+	18.2174i	0.527120	+	1.09458i	0.979256	+	0.202627i	$0.0649478\pi$
$277$	8.77302	+	18.2174i	0.527120	+	1.09458i	−0.452136	+	0.891949i	$0.649338\pi$
$278$	1.81246	−	3.76360i	0.108704	−	0.225726i
$279$	0.522650	−	2.28988i	0.0312902	−	0.137092i
$280$	−0.665540	−	2.46290i	−0.0397736	−	0.147186i
$281$	−24.6995	−	11.8947i	−1.47345	−	0.709576i	−0.486964	−	0.873422i	$-0.661896\pi$
$281$	−24.6995	−	11.8947i	−1.47345	−	0.709576i	−0.986486	+	0.163846i	$0.947610\pi$
$282$	6.17416	+	12.8208i	0.367666	+	0.763466i
$283$	−7.93616	−	1.81138i	−0.471756	−	0.107675i	−0.0199681	−	0.999801i	$-0.506356\pi$
$283$	−7.93616	−	1.81138i	−0.471756	−	0.107675i	−0.451788	+	0.892125i	$0.649214\pi$
$284$	3.24042	−	4.06336i	0.192284	−	0.241116i
$285$	2.34635	+	0.438795i	0.138986	+	0.0259920i
$286$	0.975798	−	0.469919i	0.0577001	−	0.0277869i
$287$	−0.820751	+	0.187331i	−0.0484474	+	0.0110578i
$288$	−1.59749	+	1.27395i	−0.0941329	+	0.0750684i
$289$	−2.64363	−	11.5825i	−0.155508	−	0.681323i
$290$	−0.868335	−	21.9587i	−0.0509904	−	1.28946i
$291$	−19.2964	+	24.1969i	−1.13118	+	1.41845i
$292$	−0.233688	+	0.485258i	−0.0136756	+	0.0283976i
$293$	11.3926	−	9.08526i	0.665560	−	0.530767i	−0.231411	−	0.972856i	$-0.574334\pi$
$293$	11.3926	−	9.08526i	0.665560	−	0.530767i	0.896971	+	0.442090i	$0.145763\pi$
$294$	12.7967			0.746316
$295$	−19.5240	+	10.3718i	−1.13673	+	0.603871i
$296$	−3.35073	−	4.20169i	−0.194757	−	0.244218i
$297$	−1.86721	−	3.87730i	−0.108347	−	0.224984i
$298$	−15.6677	−	3.57605i	−0.907605	−	0.207155i
$299$	0.316887	+	1.38837i	0.0183261	+	0.0802917i
$300$	−9.30429	−	6.28584i	−0.537183	−	0.362913i
$301$	−5.70667	+	4.83836i	−0.328927	+	0.278878i
$302$			14.6924i			0.845454i
$303$	−3.11029	+	0.709905i	−0.178682	+	0.0407829i
$304$	−0.105776	+	0.463436i	−0.00606668	+	0.0265799i
$305$	7.88962	−	10.7377i	0.451758	−	0.614839i
$306$	−2.88253	−	3.61457i	−0.164783	−	0.206631i
$307$			1.67978i			0.0958703i	0.998850	+	0.0479351i	$0.0152641\pi$
$307$			1.67978i			0.0958703i	−0.998850	+	0.0479351i	$0.984736\pi$
$308$		−	2.28527i		−	0.130215i
$309$	−8.75864	−	10.9830i	−0.498262	−	0.624800i
$310$	0.101564	+	2.56839i	0.00576847	+	0.145875i
$311$	−8.46633	+	10.6164i	−0.480081	+	0.602003i	−0.961607	−	0.274429i	$-0.911511\pi$
$311$	−8.46633	+	10.6164i	−0.480081	+	0.602003i	0.481526	+	0.876432i	$0.340083\pi$
$312$	0.526875	−	1.09407i	0.0298284	−	0.0619394i
$313$	32.8180	−	7.49049i	1.85498	−	0.423387i	0.858924	−	0.512103i	$-0.171133\pi$
$313$	32.8180	−	7.49049i	1.85498	−	0.423387i	0.996057	+	0.0887156i	$0.0282762\pi$
$314$	8.22354	+	10.3120i	0.464081	+	0.581939i
$315$	−3.94396	+	3.40866i	−0.222217	+	0.192056i
$316$	2.53240	−	1.21954i	0.142459	−	0.0686045i
$317$	−14.2540	−	11.3672i	−0.800584	−	0.638444i	0.135280	−	0.990807i	$-0.456807\pi$
$317$	−14.2540	−	11.3672i	−0.800584	−	0.638444i	−0.935863	+	0.352363i	$0.885378\pi$
$318$	−1.09862	−	0.876123i	−0.0616077	−	0.0491305i
$319$	4.38030	−	19.1914i	0.245250	−	1.07451i
$320$	1.32400	−	1.80195i	0.0740138	−	0.100732i
$321$	25.9842	+	12.5133i	1.45030	+	0.698426i
$322$	2.92950	+	0.668640i	0.163255	+	0.0372618i
$323$	−1.04860	−	0.239336i	−0.0583456	−	0.0133170i
$324$	−9.86999	−	4.75314i	−0.548333	−	0.264063i
$325$	2.67513	+	0.391599i	0.148389	+	0.0217220i
$326$	−1.97728	+	8.66302i	−0.109511	+	0.479800i
$327$	16.1885	+	12.9099i	0.895226	+	0.713919i
$328$	−0.576881	−	0.460047i	−0.0318529	−	0.0254019i
$329$	−6.51365	+	3.13681i	−0.359109	+	0.172938i
$330$	−6.57689	−	7.60974i	−0.362046	−	0.418903i
$331$	9.05357	+	11.3528i	0.497629	+	0.624008i	0.965693	−	0.259687i	$-0.0836195\pi$
$331$	9.05357	+	11.3528i	0.497629	+	0.624008i	−0.468063	+	0.883695i	$0.655048\pi$
$332$	−6.70520	+	1.53042i	−0.367996	+	0.0839926i
$333$	−4.76440	+	9.89338i	−0.261088	+	0.542154i
$334$	8.02356	−	10.0612i	0.439030	−	0.550526i
$335$	−0.657474	−	16.6264i	−0.0359216	−	0.908398i
$336$	−1.59754	−	2.00325i	−0.0871528	−	0.109286i
$337$			9.76500i			0.531934i	0.963982	+	0.265967i	$0.0856912\pi$
$337$			9.76500i			0.531934i	−0.963982	+	0.265967i	$0.914309\pi$
$338$		−	12.7076i		−	0.691203i
$339$	−13.0908	−	16.4153i	−0.710994	−	0.891558i
$340$	4.07721	+	2.99576i	0.221118	+	0.162468i
$341$	−0.512340	+	2.24471i	−0.0277448	+	0.121558i
$342$	0.946922	−	0.216129i	0.0512037	−	0.0116869i
$343$			14.4880i			0.782280i
$344$	−6.43397	−	1.26648i	−0.346897	−	0.0682841i
$345$	11.6793	−	6.20445i	0.628792	−	0.334036i
$346$	5.32377	+	23.3250i	0.286208	+	1.25396i
$347$	−15.2305	−	3.47627i	−0.817617	−	0.186616i	−0.206796	−	0.978384i	$-0.566304\pi$
$347$	−15.2305	−	3.47627i	−0.817617	−	0.186616i	−0.610821	+	0.791768i	$0.709161\pi$
$348$	−9.57615	−	19.8851i	−0.513335	−	1.06595i
$349$	−1.47700	−	1.85210i	−0.0790619	−	0.0991405i	0.740728	−	0.671806i	$-0.234481\pi$
$349$	−1.47700	−	1.85210i	−0.0790619	−	0.0991405i	−0.819789	+	0.572665i	$0.805910\pi$
$350$	3.19355	−	4.72708i	0.170702	−	0.252673i
$351$	1.16179			0.0620116
$352$	1.56597	−	1.24882i	0.0834667	−	0.0665625i
$353$	13.9541	−	28.9759i	0.742700	−	1.54223i	−0.0946160	−	0.995514i	$-0.530162\pi$
$353$	13.9541	−	28.9759i	0.742700	−	1.54223i	0.837316	−	0.546719i	$-0.184123\pi$
$354$	−13.8436	+	17.3593i	−0.735777	+	0.922636i
$355$	11.6123	−	0.459196i	0.616317	−	0.0243716i
$356$	3.13587	+	13.7391i	0.166201	+	0.728173i
$357$	4.53267	−	3.61469i	0.239895	−	0.191310i
$358$	10.0586	−	2.29580i	0.531612	−	0.121337i
$359$	−2.09676	+	1.00975i	−0.110663	+	0.0532923i	−0.488396	−	0.872622i	$-0.662418\pi$
$359$	−2.09676	+	1.00975i	−0.110663	+	0.0532923i	0.377733	+	0.925914i	$0.376704\pi$
$360$	−4.49102	−	0.839872i	−0.236697	−	0.0442652i
$361$	−11.7054	+	14.6781i	−0.616075	+	0.772533i
$362$	14.8122	+	3.38078i	0.778511	+	0.177690i
$363$	6.80914	+	14.1393i	0.357387	+	0.742122i
$364$	0.555845	+	0.267681i	0.0291342	+	0.0140303i
$365$	−1.16264	+	0.314175i	−0.0608551	+	0.0164447i
$366$	2.97780	−	13.0466i	0.155652	−	0.681956i
$367$	−5.42943	+	11.2743i	−0.283414	+	0.588515i	−0.993269	−	0.115833i	$-0.963046\pi$
$367$	−5.42943	+	11.2743i	−0.283414	+	0.588515i	0.709855	+	0.704348i	$0.248761\pi$
$368$	1.14269	+	2.37282i	0.0595669	+	0.123692i
$369$	−0.335481	+	1.46984i	−0.0174645	+	0.0765168i
$370$	2.20902	−	11.8122i	0.114841	−	0.614087i
$371$	0.445118	−	0.558160i	0.0231094	−	0.0289782i
$372$	1.12007	+	2.32585i	0.0580729	+	0.120590i
$373$	−33.2460	+	7.58818i	−1.72141	+	0.392901i	−0.965218	−	0.261447i	$-0.915800\pi$
$373$	−33.2460	+	7.58818i	−1.72141	+	0.392901i	−0.756194	+	0.654348i	$0.772943\pi$
$374$	2.82566	+	3.54327i	0.146112	+	0.183218i
$375$	−2.97008	−	24.9316i	−0.153374	−	1.28746i
$376$	−5.70898	−	2.74930i	−0.294418	−	0.141784i
$377$	4.15483	+	3.31337i	0.213985	+	0.170647i
$378$	1.06362	−	2.20864i	0.0547068	−	0.113600i
$379$	−20.3491	−	25.5170i	−1.04526	−	1.31072i	−0.948970	−	0.315365i	$-0.897873\pi$
$379$	−20.3491	−	25.5170i	−1.04526	−	1.31072i	−0.0962925	−	0.995353i	$-0.530698\pi$
$380$	−0.938691	+	0.498666i	−0.0481538	+	0.0255810i
$381$	−9.32864			−0.477921
$382$	−15.4801	+	12.3450i	−0.792032	+	0.631624i
$383$	−4.67406	−	9.70578i	−0.238833	−	0.495942i	0.746756	−	0.665098i	$-0.231610\pi$
$383$	−4.67406	−	9.70578i	−0.238833	−	0.495942i	−0.985589	+	0.169156i	$0.945896\pi$
$384$	0.499720	−	2.18942i	0.0255012	−	0.111728i
$385$	3.86616	−	3.34142i	0.197038	−	0.170294i
$386$	6.89112			0.350749
$387$	3.37248	+	12.9672i	0.171433	+	0.659160i
$388$		−	13.7813i		−	0.699641i
$389$	−4.29794	−	18.8305i	−0.217914	−	0.954746i	−0.959016	−	0.283352i	$-0.908553\pi$
$389$	−4.29794	−	18.8305i	−0.217914	−	0.954746i	0.741101	−	0.671393i	$-0.234304\pi$
$390$	2.62129	−	0.708341i	0.132734	−	0.0358683i
$391$	−5.36889	+	2.58552i	−0.271517	+	0.130756i
$392$	−4.45506	+	3.55279i	−0.225015	+	0.179443i
$393$		−	30.2547i		−	1.52615i
$394$	13.3203			0.671069
$395$	5.76595	+	2.50110i	0.290117	+	0.125844i
$396$	−3.68728	−	1.77570i	−0.185293	−	0.0892322i
$397$	20.4061	+	16.2733i	1.02415	+	0.816735i	0.983220	−	0.182426i	$-0.0583951\pi$
$397$	20.4061	+	16.2733i	1.02415	+	0.816735i	0.0409344	+	0.999162i	$0.486967\pi$
$398$	−7.93408	+	16.4753i	−0.397699	+	0.825831i
$399$	0.271025	+	1.18744i	0.0135682	+	0.0594463i
$400$	4.98439	−	0.394822i	0.249219	−	0.0197411i
$401$	−4.43997	−	19.4528i	−0.221722	−	0.971426i	−0.956182	−	0.292774i	$-0.905422\pi$
$401$	−4.43997	−	19.4528i	−0.221722	−	0.971426i	0.734460	−	0.678652i	$-0.237436\pi$
$402$	−7.25073	−	15.0563i	−0.361634	−	0.750940i
$403$	−0.485968	−	0.387546i	−0.0242078	−	0.0193051i
$404$	0.885733	−	1.11067i	0.0440668	−	0.0552581i
$405$	−6.39021	−	23.6476i	−0.317532	−	1.17506i
$406$	10.1027	−	4.86520i	0.501388	−	0.241456i
$407$	4.67042	−	9.69822i	0.231504	−	0.480723i
$408$	4.95391	+	1.13070i	0.245255	+	0.0559779i
$409$	2.93888	−	12.8761i	0.145318	−	0.636681i	−0.848831	−	0.528665i	$-0.822693\pi$
$409$	2.93888	−	12.8761i	0.145318	−	0.636681i	0.994149	−	0.108016i	$-0.0344499\pi$
$410$	−0.0651927	−	1.64861i	−0.00321964	−	0.0814192i
$411$	−6.63435	+	3.19494i	−0.327248	+	0.157595i
$412$	6.09851	+	1.39195i	0.300452	+	0.0685763i
$413$	−8.81946	−	7.03328i	−0.433977	−	0.346085i
$414$	3.35513	−	4.20720i	0.164896	−	0.206772i
$415$	−12.3932	−	9.10599i	−0.608357	−	0.446995i
$416$	0.120323	+	0.527170i	0.00589933	+	0.0258466i
$417$	7.33438	−	5.84897i	0.359166	−	0.286425i
$418$	−0.928242	+	0.211865i	−0.0454018	+	0.0103627i
$419$	−23.6917	−	11.4093i	−1.15741	−	0.557381i	−0.246161	−	0.969229i	$-0.579169\pi$
$419$	−23.6917	−	11.4093i	−1.15741	−	0.557381i	−0.911253	+	0.411848i	$0.864884\pi$
$420$	1.05320	−	5.63173i	0.0513909	−	0.274800i
$421$	−31.5659	−	15.2014i	−1.53843	−	0.740869i	−0.543309	−	0.839533i	$-0.682829\pi$
$421$	−31.5659	−	15.2014i	−1.53843	−	0.740869i	−0.995121	+	0.0986636i	$0.968543\pi$
$422$	−7.68787	+	6.13087i	−0.374240	+	0.298446i
$423$			12.9471i			0.629510i
$424$	0.625719			0.0303876
$425$	0.893349	+	11.2780i	0.0433338	+	0.547063i
$426$	10.5157	−	5.06409i	0.509487	−	0.245356i
$427$	6.62837	+	1.51288i	0.320769	+	0.0732135i
$428$	−12.5203	+	2.85769i	−0.605194	+	0.138132i
$429$	2.43224			0.117429
$430$	−7.26487	−	12.7366i	−0.350343	−	0.614215i
$431$	−34.3306			−1.65365			−0.826824	−	0.562460i	$-0.809855\pi$
$431$	−34.3306			−1.65365			−0.826824	+	0.562460i	$0.809855\pi$
$432$	2.09469	−	0.478100i	0.100781	−	0.0230026i
$433$	17.0161	+	3.88381i	0.817740	+	0.186644i	0.610876	−	0.791726i	$-0.290817\pi$
$433$	17.0161	+	3.88381i	0.817740	+	0.186644i	0.206864	+	0.978370i	$0.433674\pi$
$434$	−1.18166	+	0.569056i	−0.0567214	+	0.0273156i
$435$	19.6393	−	45.2757i	0.941631	−	2.17081i
$436$	−9.22015			−0.441565
$437$		−	1.25191i		−	0.0598869i
$438$	−0.945653	+	0.754133i	−0.0451851	+	0.0360339i
$439$	14.3780	+	6.92409i	0.686225	+	0.330469i	0.744302	−	0.667843i	$-0.232782\pi$
$439$	14.3780	+	6.92409i	0.686225	+	0.330469i	−0.0580764	+	0.998312i	$0.518497\pi$
$440$	4.40243	+	0.823305i	0.209877	+	0.0392495i
$441$	10.4900	+	5.05171i	0.499523	+	0.240558i
$442$	−1.19281	+	0.272251i	−0.0567361	+	0.0129496i
$443$	26.8331	−	21.3987i	1.27488	−	1.01668i	0.276430	−	0.961034i	$-0.410849\pi$
$443$	26.8331	−	21.3987i	1.27488	−	1.01668i	0.998450	−	0.0556493i	$-0.0177229\pi$
$444$	−2.68558	−	11.7663i	−0.127452	−	0.558403i
$445$	−18.6584	+	25.3939i	−0.884494	+	1.20379i
$446$	−0.585254	+	0.733885i	−0.0277126	+	0.0347505i
$447$	−28.2164	−	22.5018i	−1.33459	−	1.06430i
$448$	1.11234	+	0.253885i	0.0525532	+	0.0119949i
$449$	−7.04620	+	3.39327i	−0.332531	+	0.160138i	−0.592697	−	0.805426i	$-0.701937\pi$
$449$	−7.04620	+	3.39327i	−0.332531	+	0.160138i	0.260166	+	0.965564i	$0.416223\pi$
$450$	−5.14569	−	8.82582i	−0.242570	−	0.416053i
$451$	0.328863	−	1.44084i	0.0154856	−	0.0678467i
$452$	9.11493	+	2.08042i	0.428730	+	0.0978548i
$453$	−14.3160	+	29.7275i	−0.672626	+	1.39672i
$454$	5.27812	−	2.54181i	0.247714	−	0.119293i
$455$	0.359876	+	1.33176i	0.0168712	+	0.0624337i
$456$	−0.665583	+	0.834615i	−0.0311688	+	0.0390844i
$457$	8.71448	+	6.94957i	0.407646	+	0.325087i	0.805753	−	0.592252i	$-0.201761\pi$
$457$	8.71448	+	6.94957i	0.407646	+	0.325087i	−0.398106	+	0.917339i	$0.630332\pi$
$458$	−1.79548	−	3.72836i	−0.0838974	−	0.174215i
$459$	1.08178	+	4.73959i	0.0504932	+	0.221225i
$460$	−2.34349	+	5.40261i	−0.109266	+	0.251898i
$461$	3.30458	+	14.4783i	0.153909	+	0.674321i	0.991726	+	0.128370i	$0.0409745\pi$
$461$	3.30458	+	14.4783i	0.153909	+	0.674321i	−0.837817	+	0.545951i	$0.816168\pi$
$462$	2.22673	−	4.62384i	0.103597	−	0.215121i
$463$	17.4390	+	13.9071i	0.810458	+	0.646319i	0.938434	−	0.345458i	$-0.112277\pi$
$463$	17.4390	+	13.9071i	0.810458	+	0.646319i	−0.127976	+	0.991777i	$0.540848\pi$
$464$	8.85465	+	4.26417i	0.411067	+	0.197959i
$465$	−2.29710	+	5.29566i	−0.106525	+	0.245580i
$466$	13.7264			0.635863
$467$			35.4601i			1.64090i	0.571720	+	0.820449i	$0.306276\pi$
$467$			35.4601i			1.64090i	−0.571720	+	0.820449i	$0.693724\pi$
$468$	0.863805	−	0.688862i	0.0399294	−	0.0318426i
$469$	7.64942	−	3.68377i	0.353217	−	0.170101i
$470$	−3.69622	−	13.6782i	−0.170494	−	0.630929i
$471$	6.59107	+	28.8774i	0.303701	+	1.33060i
$472$		−	9.88696i		−	0.455084i
$473$	−3.30595	−	12.7114i	−0.152008	−	0.584471i
$474$	6.31217			0.289928
$475$	−2.21614	−	0.858928i	−0.101684	−	0.0394103i
$476$	−0.574456	+	2.51685i	−0.0263301	+	0.115360i
$477$	−0.554725	−	1.15190i	−0.0253991	−	0.0527418i
$478$	−18.1190	+	14.4494i	−0.828745	+	0.660902i
$479$	19.5796			0.894615			0.447307	−	0.894380i	$-0.352383\pi$
$479$	19.5796			0.894615			0.447307	+	0.894380i	$0.352383\pi$
$480$	4.43467	−	2.35585i	0.202414	−	0.107529i
$481$	1.81183	+	2.27197i	0.0826125	+	0.103593i
$482$	−0.993172	+	2.06234i	−0.0452377	+	0.0939371i
$483$	5.27582	+	4.20733i	0.240058	+	0.191440i
$484$	−6.29612	−	3.03205i	−0.286187	−	0.137820i
$485$	23.3149	−	20.1504i	1.05868	−	0.914985i
$486$	−11.3200	−	14.1948i	−0.513486	−	0.643891i
$487$	19.1834	−	4.37849i	0.869283	−	0.198408i	0.235458	−	0.971885i	$-0.424341\pi$
$487$	19.1834	−	4.37849i	0.869283	−	0.198408i	0.633825	+	0.773476i	$0.281484\pi$
$488$	2.58548	+	5.36881i	0.117039	+	0.243035i
$489$	−12.4418	+	15.6015i	−0.562636	+	0.705523i
$490$	−12.5245	−	2.34223i	−0.565800	−	0.105811i
$491$	3.27199	−	14.3355i	0.147663	−	0.646954i	−0.845868	−	0.533392i	$-0.820917\pi$
$491$	3.27199	−	14.3355i	0.147663	−	0.646954i	0.993531	−	0.113561i	$-0.0362259\pi$
$492$	−0.718956	−	1.49293i	−0.0324130	−	0.0673064i
$493$	−9.64838	+	20.0351i	−0.434541	+	0.902334i
$494$	0.0571961	−	0.250593i	0.00257338	−	0.0112747i
$495$	−2.38729	−	8.83439i	−0.107300	−	0.397076i
$496$	−1.03568	−	0.498757i	−0.0465034	−	0.0223949i
$497$	2.57283	+	5.34254i	0.115407	+	0.239646i
$498$	−15.0580	−	3.43689i	−0.674766	−	0.154011i
$499$	−15.4077	+	19.3207i	−0.689744	+	0.864911i	−0.996211	−	0.0869700i	$-0.972282\pi$
$499$	−15.4077	+	19.3207i	−0.689744	+	0.864911i	0.306467	+	0.951881i	$0.400853\pi$
$500$	7.95590	+	7.85517i	0.355798	+	0.351294i
$501$	26.0377	−	12.5391i	1.16328	−	0.560206i
$502$	−25.3858	+	5.79413i	−1.13302	+	0.258605i
$503$	−12.3937	+	9.88367i	−0.552609	+	0.440691i	−0.859560	−	0.511034i	$-0.829263\pi$
$503$	−12.3937	+	9.88367i	−0.552609	+	0.440691i	0.306951	+	0.951725i	$0.400691\pi$
$504$	−0.518754	−	2.27281i	−0.0231071	−	0.101239i
$505$	3.17409	−	0.125516i	0.141245	−	0.00558539i
$506$	−3.28894	+	4.12420i	−0.146211	+	0.183343i
$507$	12.3821	−	25.7116i	0.549907	−	1.14189i
$508$	3.24770	−	2.58995i	0.144093	−	0.114911i
$509$	−9.64252			−0.427397			−0.213699	−	0.976900i	$-0.568551\pi$
$509$	−9.64252			−0.427397			−0.213699	+	0.976900i	$0.568551\pi$
$510$	5.33049	+	10.0342i	0.236038	+	0.444320i
$511$	−0.383141	−	0.480443i	−0.0169491	−	0.0212536i
$512$	0.433884	+	0.900969i	0.0191751	+	0.0398176i
$513$	−0.995722	−	0.227267i	−0.0439622	−	0.0100341i
$514$	−5.33454	−	23.3721i	−0.235296	−	1.03090i
$515$	6.56211	+	12.3526i	0.289161	+	0.544319i
$516$	−11.7840	−	8.83165i	−0.518761	−	0.388792i
$517$		−	12.6917i		−	0.558181i
$518$	5.97791	−	1.36442i	0.262654	−	0.0599491i
$519$	−11.9557	+	52.3814i	−0.524797	+	2.29929i
$520$	−0.715922	+	0.974364i	−0.0313953	+	0.0427287i
$521$	19.8296	+	24.8656i	0.868752	+	1.08938i	0.995244	+	0.0974133i	$0.0310569\pi$
$521$	19.8296	+	24.8656i	0.868752	+	1.08938i	−0.126492	+	0.991968i	$0.540372\pi$
$522$		−	20.0810i		−	0.878923i
$523$			14.4549i			0.632070i	0.948747	+	0.316035i	$0.102352\pi$
$523$			14.4549i			0.632070i	−0.948747	+	0.316035i	$0.897648\pi$
$524$	8.39976	+	10.5330i	0.366945	+	0.460135i
$525$	11.0676	−	6.45269i	0.483028	−	0.281618i
$526$	−9.60568	+	12.0451i	−0.418828	+	0.525193i
$527$	1.12852	−	2.34339i	0.0491591	−	0.102080i
$528$	4.38531	−	1.00092i	0.190846	−	0.0435593i
$529$	10.0157	+	12.5593i	0.435466	+	0.546057i
$530$	0.914899	+	1.05858i	0.0397407	+	0.0459816i
$531$	−18.2011	+	8.76518i	−0.789859	+	0.380376i
$532$	−0.424030	−	0.338152i	−0.0183840	−	0.0146608i
$533$	0.311935	+	0.248760i	0.0135114	+	0.0107750i
$534$	−7.04229	+	30.8543i	−0.304750	+	1.33520i
$535$	−23.1412	−	17.0032i	−1.00048	−	0.735114i
$536$	6.70444	+	3.22869i	0.289588	+	0.139458i
$537$	22.5887	+	5.15573i	0.974776	+	0.222486i
$538$	−1.55391	−	0.354671i	−0.0669940	−	0.0152909i
$539$	−10.2830	−	4.95206i	−0.442922	−	0.213300i
$540$	3.87161	+	2.84470i	0.166607	+	0.122416i
$541$	−1.43900	+	6.30467i	−0.0618674	+	0.271059i	−0.996395	−	0.0848309i	$-0.972965\pi$
$541$	−1.43900	+	6.30467i	−0.0618674	+	0.271059i	0.934528	+	0.355890i	$0.115822\pi$
$542$	−23.2047	−	18.5052i	−0.996729	−	0.794865i
$543$	26.6757	+	21.2731i	1.14476	+	0.912918i
$544$	−2.03859	+	0.981732i	−0.0874037	+	0.0420914i
$545$	−13.4813	−	15.5984i	−0.577475	−	0.668163i
$546$	0.863832	+	1.08321i	0.0369686	+	0.0463572i
$547$	−2.97921	+	0.679984i	−0.127382	+	0.0290740i	−0.285736	−	0.958308i	$-0.592238\pi$
$547$	−2.97921	+	0.679984i	−0.127382	+	0.0290740i	0.158355	+	0.987382i	$0.449381\pi$
$548$	1.42268	−	2.95422i	0.0607737	−	0.126198i
$549$	7.59141	−	9.51932i	0.323993	−	0.406275i
$550$	5.04418	+	8.65171i	0.215085	+	0.368910i
$551$	−2.91278	−	3.65252i	−0.124089	−	0.155602i
$552$			5.91441i			0.251734i
$553$			3.20693i			0.136372i
$554$	−12.6068	−	15.8084i	−0.535612	−	0.671636i
$555$	15.9792	−	21.7475i	0.678278	−	0.923130i
$556$	−0.929534	+	4.07255i	−0.0394210	+	0.172715i
$557$	−23.3810	+	5.33655i	−0.990684	+	0.226117i	−0.687001	−	0.726656i	$-0.741073\pi$
$557$	−23.3810	+	5.33655i	−0.990684	+	0.226117i	−0.303682	+	0.952773i	$0.598216\pi$
$558$			2.34877i			0.0994313i
$559$	3.47903	+	0.684821i	0.147147	+	0.0289648i
$560$	1.19690	+	2.25305i	0.0505783	+	0.0952088i
$561$	2.26474	+	9.92246i	0.0956173	+	0.418927i
$562$	26.7271	+	6.10028i	1.12741	+	0.257325i
$563$	19.4411	+	40.3699i	0.819346	+	1.70139i	0.706427	+	0.707786i	$0.250306\pi$
$563$	19.4411	+	40.3699i	0.819346	+	1.70139i	0.112919	+	0.993604i	$0.463980\pi$
$564$	−8.87225	−	11.1255i	−0.373589	−	0.468466i
$565$	9.80782	+	18.4623i	0.412618	+	0.776715i
$566$	8.14026			0.342161
$567$	9.77206	−	7.79296i	0.410388	−	0.327273i
$568$	−2.25500	+	4.68255i	−0.0946175	+	0.196475i
$569$	−5.36088	+	6.72233i	−0.224740	+	0.281815i	−0.881399	−	0.472373i	$-0.843398\pi$
$569$	−5.36088	+	6.72233i	−0.224740	+	0.281815i	0.656659	+	0.754188i	$0.271969\pi$
$570$	−2.38517	+	0.0943189i	−0.0999037	+	0.00395059i
$571$	8.26429	+	36.2082i	0.345850	+	1.51527i	0.786502	+	0.617588i	$0.211890\pi$
$571$	8.26429	+	36.2082i	0.345850	+	1.51527i	−0.440652	+	0.897678i	$0.645253\pi$
$572$	−0.846765	+	0.675273i	−0.0354050	+	0.0282346i
$573$	−43.3500	+	9.89436i	−1.81097	+	0.413343i
$574$	0.758488	−	0.365269i	0.0316587	−	0.0152460i
$575$	−12.5665	+	3.93479i	−0.524061	+	0.164092i
$576$	1.27395	−	1.59749i	0.0530814	−	0.0665620i
$577$	31.7152	+	7.23878i	1.32032	+	0.301354i	0.823903	−	0.566730i	$-0.191792\pi$
$577$	31.7152	+	7.23878i	1.32032	+	0.301354i	0.496416	+	0.868085i	$0.334649\pi$
$578$	5.15470	+	10.7038i	0.214407	+	0.445221i
$579$	13.9430	+	6.71458i	0.579450	+	0.279048i
$580$	5.73284	+	21.2150i	0.238043	+	0.880903i
$581$	1.74613	−	7.65029i	0.0724416	−	0.317387i
$582$	13.4283	−	27.8841i	0.556620	−	1.15583i
$583$	0.543782	+	1.12917i	0.0225211	+	0.0467656i
$584$	0.119849	−	0.525092i	0.00495938	−	0.0217285i
$585$	2.42842	+	0.454142i	0.100403	+	0.0187765i
$586$	−9.08526	+	11.3926i	−0.375309	+	0.470622i
$587$	−6.45967	−	13.4136i	−0.266619	−	0.553640i	0.724079	−	0.689717i	$-0.242265\pi$
$587$	−6.45967	−	13.4136i	−0.266619	−	0.553640i	−0.990698	+	0.136077i	$0.956551\pi$
$588$	−12.4758	+	2.84752i	−0.514494	+	0.117430i
$589$	0.340692	+	0.427215i	0.0140380	+	0.0176031i
$590$	16.7265	−	14.4563i	0.688620	−	0.595155i
$591$	26.9514	+	12.9791i	1.10863	+	0.533889i
$592$	4.20169	+	3.35073i	0.172688	+	0.137714i
$593$	9.63805	−	20.0136i	0.395787	−	0.821861i	−0.603905	−	0.797056i	$-0.706389\pi$
$593$	9.63805	−	20.0136i	0.395787	−	0.821861i	0.999692	−	0.0248046i	$-0.00789636\pi$
$594$	2.68318	+	3.36460i	0.110092	+	0.138051i
$595$	−5.09789	+	2.70818i	−0.208993	+	0.111025i
$596$	16.0706			0.658278
$597$	−32.1064	+	25.6040i	−1.31403	+	1.04790i
$598$	−0.617884	−	1.28305i	−0.0252672	−	0.0524678i
$599$	−0.416398	+	1.82436i	−0.0170136	+	0.0745413i	−0.982722	−	0.185088i	$-0.940743\pi$
$599$	−0.416398	+	1.82436i	−0.0170136	+	0.0745413i	0.965708	+	0.259629i	$0.0836002\pi$
$600$	10.4697	+	4.05784i	0.427425	+	0.165661i
$601$	−4.82688			−0.196892			−0.0984462	−	0.995142i	$-0.531387\pi$
$601$	−4.82688			−0.196892			−0.0984462	+	0.995142i	$0.531387\pi$
$602$	4.48696	−	5.98690i	0.182875	−	0.244008i
$603$		−	15.2047i		−	0.619182i
$604$	−3.26937	−	14.3241i	−0.133029	−	0.582838i
$605$	−4.07635	−	15.0849i	−0.165727	−	0.613290i
$606$	2.87434	−	1.38421i	0.116762	−	0.0562297i
$607$	−14.6329	+	11.6694i	−0.593933	+	0.473646i	−0.873728	−	0.486414i	$-0.838305\pi$
$607$	−14.6329	+	11.6694i	−0.593933	+	0.473646i	0.279796	+	0.960060i	$0.409733\pi$
$608$		−	0.475354i		−	0.0192782i
$609$	25.1816			1.02041
$610$	−5.30245	+	12.2241i	−0.214690	+	0.494939i
$611$	3.08700	+	1.48662i	0.124887	+	0.0601423i
$612$	3.61457	+	2.88253i	0.146110	+	0.116519i
$613$	6.97327	−	14.4801i	0.281648	−	0.584848i	−0.711369	−	0.702818i	$-0.751925\pi$
$613$	6.97327	−	14.4801i	0.281648	−	0.584848i	0.993017	+	0.117971i	$0.0376389\pi$
$614$	−0.373787	−	1.63767i	−0.0150848	−	0.0660909i
$615$	1.47447	−	3.39920i	0.0594565	−	0.137069i
$616$	0.508520	+	2.22797i	0.0204889	+	0.0897676i
$617$	−8.30189	−	17.2391i	−0.334222	−	0.694018i	0.664352	−	0.747420i	$-0.268708\pi$
$617$	−8.30189	−	17.2391i	−0.334222	−	0.694018i	−0.998573	+	0.0534020i	$0.982994\pi$
$618$	10.9830	+	8.75864i	0.441801	+	0.352324i
$619$	20.2065	−	25.3382i	0.812169	−	1.01843i	−0.187179	−	0.982326i	$-0.559935\pi$
$619$	20.2065	−	25.3382i	0.812169	−	1.01843i	0.999348	−	0.0361016i	$-0.0114940\pi$
$620$	−0.670539	−	2.48140i	−0.0269295	−	0.0996554i
$621$	−5.09816	+	2.45514i	−0.204582	+	0.0985216i
$622$	5.89168	−	12.2342i	0.236235	−	0.490547i
$623$	−15.6756	−	3.57786i	−0.628031	−	0.143344i
$624$	−0.270212	+	1.18388i	−0.0108171	+	0.0473930i
$625$	−1.65644	+	24.9451i	−0.0662575	+	0.997803i
$626$	−30.3284	+	14.6054i	−1.21217	+	0.583748i
$627$	−2.08457	−	0.475790i	−0.0832498	−	0.0190012i
$628$	−10.3120	−	8.22354i	−0.411493	−	0.328155i
$629$	−7.58158	+	9.50700i	−0.302297	+	0.379069i
$630$	3.08658	−	4.20081i	0.122972	−	0.167364i
$631$	−6.75788	−	29.6082i	−0.269027	−	1.17868i	−0.911147	−	0.412081i	$-0.864802\pi$
$631$	−6.75788	−	29.6082i	−0.269027	−	1.17868i	0.642120	−	0.766604i	$-0.278055\pi$
$632$	−2.19754	+	1.75248i	−0.0874133	+	0.0697098i
$633$	−21.5289	+	4.91382i	−0.855695	+	0.195307i
$634$	16.4260	+	7.91037i	0.652362	+	0.314161i
$635$	9.13026	+	1.70746i	0.362323	+	0.0677586i
$636$	1.26603	+	0.609690i	0.0502015	+	0.0241758i
$637$	2.40897	−	1.92109i	0.0954470	−	0.0761165i
$638$			19.6849i			0.779333i
$639$	10.6193			0.420094
$640$	−0.889832	+	2.05139i	−0.0351737	+	0.0810883i
$641$	41.2189	−	19.8500i	1.62805	−	0.784027i	0.628065	−	0.778161i	$-0.283847\pi$
$641$	41.2189	−	19.8500i	1.62805	−	0.784027i	0.999983	−	0.00586595i	$-0.00186720\pi$
$642$	−28.1172	−	6.41757i	−1.10970	−	0.253281i
$643$	−7.17184	+	1.63693i	−0.282830	+	0.0645540i	−0.361582	−	0.932340i	$-0.617763\pi$
$643$	−7.17184	+	1.63693i	−0.282830	+	0.0645540i	0.0787528	+	0.996894i	$0.474906\pi$
$644$	−3.00484			−0.118407
$645$	−2.28884	−	32.8491i	−0.0901230	−	1.29343i
$646$	1.07557			0.0423176
$647$	24.6372	−	5.62328i	0.968589	−	0.221074i	0.291170	−	0.956671i	$-0.405956\pi$
$647$	24.6372	−	5.62328i	0.968589	−	0.221074i	0.677419	+	0.735597i	$0.263098\pi$
$648$	10.6802	+	2.43769i	0.419558	+	0.0957614i
$649$	17.8420	−	8.59227i	0.700361	−	0.337276i
$650$	−2.69519	+	0.213491i	−0.105714	+	0.00837381i
$651$	−2.94535			−0.115438
$652$		−	8.88580i		−	0.347995i
$653$	−20.0086	+	15.9563i	−0.782998	+	0.624420i	−0.931188	−	0.364539i	$-0.881227\pi$
$653$	−20.0086	+	15.9563i	−0.782998	+	0.624420i	0.148190	+	0.988959i	$0.452655\pi$
$654$	−18.6554	−	8.98394i	−0.729482	−	0.351300i
$655$	−5.53766	+	29.6113i	−0.216374	+	1.15701i
$656$	0.664787	+	0.320145i	0.0259556	+	0.0124996i
$657$	−1.07290	+	0.244883i	−0.0418579	+	0.00955379i
$658$	5.65233	−	4.50759i	0.220351	−	0.175724i
$659$	1.18992	+	5.21338i	0.0463527	+	0.203084i	0.992802	−	0.119768i	$-0.0382152\pi$
$659$	1.18992	+	5.21338i	0.0463527	+	0.203084i	−0.946449	+	0.322853i	$0.895358\pi$
$660$	8.10532	+	5.95546i	0.315499	+	0.231816i
$661$	13.9906	−	17.5437i	0.544171	−	0.682369i	−0.431373	−	0.902174i	$-0.641971\pi$
$661$	13.9906	−	17.5437i	0.544171	−	0.682369i	0.975544	+	0.219805i	$0.0705421\pi$
$662$	−11.3528	−	9.05357i	−0.441240	−	0.351877i
$663$	−2.67871	−	0.611399i	−0.104033	−	0.0237448i
$664$	6.19654	−	2.98410i	0.240472	−	0.115805i
$665$	−0.0479191	−	1.21179i	−0.00185822	−	0.0469914i
$666$	2.44346	−	10.7055i	0.0946823	−	0.414830i
$667$	−25.2342	−	5.75954i	−0.977072	−	0.223010i
$668$	−5.58356	+	11.5944i	−0.216034	+	0.448600i
$669$	−1.89924	+	0.914627i	−0.0734290	+	0.0353615i
$670$	4.34071	+	16.0633i	0.167696	+	0.620578i
$671$	−7.44165	+	9.33154i	−0.287282	+	0.360240i
$672$	2.00325	+	1.59754i	0.0772770	+	0.0616263i
$673$	0.303547	+	0.630321i	0.0117009	+	0.0242971i	0.906737	−	0.421696i	$-0.138565\pi$
$673$	0.303547	+	0.630321i	0.0117009	+	0.0242971i	−0.895037	+	0.445993i	$0.852851\pi$
$674$	−2.17292	−	9.52018i	−0.0836977	−	0.366703i
$675$	0.848301	+	10.7093i	0.0326511	+	0.412200i
$676$	2.82771	+	12.3890i	0.108758	+	0.476500i
$677$	4.03650	−	8.38187i	0.155135	−	0.322142i	−0.808887	−	0.587965i	$-0.799929\pi$
$677$	4.03650	−	8.38187i	0.155135	−	0.322142i	0.964022	+	0.265823i	$0.0856437\pi$
$678$	16.4153	+	13.0908i	0.630427	+	0.502749i
$679$	14.1666	+	6.82230i	0.543666	+	0.261816i
$680$	−4.64160	−	2.01339i	−0.177997	−	0.0772099i
$681$	13.1560			0.504140
$682$		−	2.30244i		−	0.0881648i
$683$	18.1745	−	14.4937i	0.695428	−	0.554585i	−0.210720	−	0.977546i	$-0.567581\pi$
$683$	18.1745	−	14.4937i	0.695428	−	0.554585i	0.906148	+	0.422961i	$0.139009\pi$
$684$	−0.875087	+	0.421420i	−0.0334598	+	0.0161134i
$685$	7.07805	−	1.91268i	0.270438	−	0.0730796i
$686$	−3.22389	−	14.1248i	−0.123089	−	0.539287i
$687$		−	9.29317i		−	0.354557i
$688$	6.55448	−	0.196967i	0.249887	−	0.00750929i
$689$	−0.338344			−0.0128899
$690$	−10.0058	+	8.64778i	−0.380916	+	0.329215i
$691$	−8.06922	+	35.3536i	−0.306968	+	1.34491i	0.552410	+	0.833572i	$0.313708\pi$
$691$	−8.06922	+	35.3536i	−0.306968	+	1.34491i	−0.859378	+	0.511341i	$0.829149\pi$
$692$	−10.3806	−	21.5555i	−0.394611	−	0.819418i
$693$	3.65069	−	2.91133i	0.138678	−	0.110592i
$694$	15.6222			0.593011
$695$	−8.24897	+	4.38214i	−0.312901	+	0.166224i
$696$	13.7609	+	17.2556i	0.521605	+	0.654073i
$697$	−0.724379	+	1.50419i	−0.0274378	+	0.0569752i
$698$	1.85210	+	1.47700i	0.0701029	+	0.0559052i
$699$	27.7729	+	13.3747i	1.05047	+	0.505879i
$700$	−2.06160	+	5.31920i	−0.0779213	+	0.201047i
$701$	−2.74047	−	3.43644i	−0.103506	−	0.129793i	0.727380	−	0.686235i	$-0.240738\pi$
$701$	−2.74047	−	3.43644i	−0.103506	−	0.129793i	−0.830887	+	0.556442i	$0.812166\pi$
$702$	−1.13266	+	0.258522i	−0.0427495	+	0.00975728i
$703$	−1.10841	−	2.30164i	−0.0418046	−	0.0868081i
$704$	−1.24882	+	1.56597i	−0.0470668	+	0.0590199i
$705$	5.84916	−	31.2770i	0.220292	−	1.17796i
$706$	−7.15646	+	31.3545i	−0.269337	+	1.18004i
$707$	0.703255	+	1.46032i	0.0264486	+	0.0549211i
$708$	9.63368	−	20.0045i	0.362056	−	0.751817i
$709$	4.98824	−	21.8549i	0.187337	−	0.820779i	−0.790676	−	0.612235i	$-0.790270\pi$
$709$	4.98824	−	21.8549i	0.187337	−	0.820779i	0.978013	−	0.208544i	$-0.0668724\pi$
$710$	−11.2190	+	3.03166i	−0.421040	+	0.113776i
$711$	5.17437	+	2.49184i	0.194054	+	0.0934514i
$712$	−6.11449	−	12.6969i	−0.229150	−	0.475835i
$713$	2.95151	+	0.673662i	0.110535	+	0.0252288i
$714$	−3.61469	+	4.53267i	−0.135276	+	0.169631i
$715$	−2.38051	−	0.445183i	−0.0890261	−	0.0166489i
$716$	−9.29551	+	4.47648i	−0.347390	+	0.167294i
$717$	−50.7400	+	11.5811i	−1.89492	+	0.432503i
$718$	1.81950	−	1.45100i	0.0679031	−	0.0541509i
$719$	3.72736	+	16.3306i	0.139007	+	0.609029i	0.995654	+	0.0931268i	$0.0296862\pi$
$719$	3.72736	+	16.3306i	0.139007	+	0.609029i	−0.856647	+	0.515903i	$0.827457\pi$
$720$	4.56531	−	0.180530i	0.170139	−	0.00672797i
$721$	−4.44986	+	5.57995i	−0.165722	+	0.207808i
$722$	8.14575	−	16.9148i	0.303153	−	0.629505i
$723$	−4.01902	+	3.20506i	−0.149469	+	0.119197i
$724$	−15.1931			−0.564647
$725$	−27.5086	+	40.7182i	−1.02165	+	1.51224i
$726$	−9.78472	−	12.2696i	−0.363145	−	0.455369i
$727$	−13.2399	−	27.4929i	−0.491040	−	1.01966i	−0.988366	−	0.152092i	$-0.951399\pi$
$727$	−13.2399	−	27.4929i	−0.491040	−	1.01966i	0.497326	−	0.867564i	$-0.334315\pi$
$728$	−0.601474	−	0.137282i	−0.0222921	−	0.00508803i
$729$	−1.75979	−	7.71017i	−0.0651776	−	0.285562i
$730$	1.06358	−	0.565009i	0.0393647	−	0.0209119i
$731$	0.445669	+	14.8306i	0.0164837	+	0.548529i
$732$			13.3821i			0.494617i
$733$	−35.4242	+	8.08535i	−1.30842	+	0.298639i	−0.819194	−	0.573516i	$-0.805579\pi$
$733$	−35.4242	+	8.08535i	−1.30842	+	0.298639i	−0.489229	+	0.872155i	$0.662722\pi$
$734$	2.78453	−	12.1998i	0.102779	−	0.450304i
$735$	−23.0589	−	16.9428i	−0.850542	−	0.624943i
$736$	−1.64204	−	2.05906i	−0.0605265	−	0.0758979i
$737$			14.9047i			0.549023i
$738$		−	1.50764i		−	0.0554970i
$739$	−23.1672	−	29.0508i	−0.852221	−	1.06865i	−0.996861	−	0.0791667i	$-0.974774\pi$
$739$	−23.1672	−	29.0508i	−0.852221	−	1.06865i	0.144641	−	0.989484i	$-0.453797\pi$
$740$	0.474828	+	12.0076i	0.0174550	+	0.441408i
$741$	0.359899	−	0.451299i	0.0132212	−	0.0165789i
$742$	−0.309755	+	0.643214i	−0.0113715	+	0.0236131i
$743$	40.3190	−	9.20255i	1.47916	−	0.337609i	0.594595	−	0.804025i	$-0.297312\pi$
$743$	40.3190	−	9.20255i	1.47916	−	0.337609i	0.884565	+	0.466417i	$0.154455\pi$
$744$	−1.60954	−	2.01830i	−0.0590085	−	0.0739943i
$745$	23.4977	+	27.1879i	0.860890	+	0.996087i
$746$	30.7239	−	14.7959i	1.12488	−	0.541715i
$747$	−10.9869	−	8.76179i	−0.401991	−	0.320577i
$748$	−3.54327	−	2.82566i	−0.129555	−	0.103317i
$749$	3.26047	−	14.2851i	0.119135	−	0.521965i
$750$	8.44342	+	23.6456i	0.308310	+	0.863417i
$751$	−7.18442	−	3.45983i	−0.262163	−	0.126251i	0.298186	−	0.954508i	$-0.403619\pi$
$751$	−7.18442	−	3.45983i	−0.262163	−	0.126251i	−0.560349	+	0.828257i	$0.689333\pi$
$752$	6.17762	+	1.41000i	0.225275	+	0.0514175i
$753$	−57.0093	−	13.0120i	−2.07754	−	0.474184i
$754$	−4.78795	−	2.30576i	−0.174367	−	0.0839707i
$755$	19.4528	−	26.4750i	0.707958	−	0.963525i
$756$	−0.545488	+	2.38994i	−0.0198392	+	0.0869212i
$757$	−18.8073	−	14.9983i	−0.683562	−	0.545122i	0.218977	−	0.975730i	$-0.429728\pi$
$757$	−18.8073	−	14.9983i	−0.683562	−	0.545122i	−0.902539	+	0.430608i	$0.858299\pi$
$758$	25.5170	+	20.3491i	0.926818	+	0.739112i
$759$	−10.6731	+	5.13992i	−0.387411	+	0.186567i
$760$	0.804192	−	0.695041i	0.0291711	−	0.0252118i
$761$	−7.80996	−	9.79338i	−0.283111	−	0.355010i	0.619859	−	0.784713i	$-0.287190\pi$
$761$	−7.80996	−	9.79338i	−0.283111	−	0.355010i	−0.902970	+	0.429703i	$0.858618\pi$
$762$	9.09475	−	2.07582i	0.329468	−	0.0751989i
$763$	4.56433	−	9.47793i	0.165240	−	0.343124i
$764$	12.3450	−	15.4801i	0.446626	−	0.560051i
$765$	0.408479	+	10.3297i	0.0147686	+	0.373473i
$766$	6.71661	+	8.42236i	0.242681	+	0.304312i
$767$			5.34615i			0.193038i
$768$			2.24572i			0.0810355i
$769$	13.1998	+	16.5520i	0.475997	+	0.596882i	0.960628	−	0.277837i	$-0.0896175\pi$
$769$	13.1998	+	16.5520i	0.475997	+	0.596882i	−0.484631	+	0.874719i	$0.661046\pi$
$770$	−3.02569	+	4.11794i	−0.109038	+	0.148400i
$771$	11.9799	−	52.4873i	0.431445	−	1.89028i
$772$	−6.71834	+	1.53342i	−0.241798	+	0.0551889i
$773$			1.44239i			0.0518790i	0.999664	+	0.0259395i	$0.00825772\pi$
$773$			1.44239i			0.0518790i	−0.999664	+	0.0259395i	$0.991742\pi$
$774$	−6.17340	−	11.8916i	−0.221898	−	0.427436i
$775$	3.21754	−	4.76259i	0.115577	−	0.171077i
$776$	3.06664	+	13.4358i	0.110086	+	0.482317i
$777$	13.4247	+	3.06410i	0.481609	+	0.109924i
$778$	8.38037	+	17.4020i	0.300451	+	0.623893i
$779$	−0.218685	−	0.274223i	−0.00783522	−	0.00982505i
$780$	−2.39795	+	1.27387i	−0.0858603	+	0.0456120i
$781$	−10.4098			−0.372493
$782$	4.65895	−	3.71539i	0.166604	−	0.132862i
$783$	−9.16185	+	19.0248i	−0.327418	+	0.679890i
$784$	3.55279	−	4.45506i	0.126885	−	0.159109i
$785$	−1.16535	−	29.4697i	−0.0415930	−	1.05182i
$786$	6.73231	+	29.4962i	0.240134	+	1.05209i
$787$	18.5134	−	14.7639i	0.659931	−	0.526277i	−0.235276	−	0.971929i	$-0.575599\pi$
$787$	18.5134	−	14.7639i	0.659931	−	0.526277i	0.895207	+	0.445651i	$0.147028\pi$
$788$	−12.9864	+	2.96405i	−0.462620	+	0.105590i
$789$	−31.1720	+	15.0116i	−1.10975	+	0.534429i
$790$	−6.17794	−	1.15535i	−0.219801	−	0.0411054i
$791$	−6.65083	+	8.33988i	−0.236476	+	0.296532i
$792$	3.98996	+	0.910682i	0.141777	+	0.0323597i
$793$	−1.39804	−	2.90306i	−0.0496459	−	0.103091i
$794$	−23.5157	−	11.3245i	−0.834539	−	0.401893i
$795$	0.819679	+	3.03331i	0.0290710	+	0.107580i
$796$	4.06906	−	17.8277i	0.144224	−	0.631887i
$797$	−6.79533	+	14.1107i	−0.240703	+	0.499825i	−0.985966	−	0.166945i	$-0.946610\pi$
$797$	−6.79533	+	14.1107i	−0.240703	+	0.499825i	0.745263	+	0.666771i	$0.232324\pi$
$798$	−0.528460	−	1.09736i	−0.0187073	−	0.0388461i
$799$	−3.19036	+	13.9779i	−0.112867	+	0.494502i
$800$	−4.77156	+	1.49405i	−0.168700	+	0.0528228i
$801$	−17.9532	+	22.5125i	−0.634343	+	0.795441i
$802$	8.65731	+	17.9771i	0.305700	+	0.634793i
$803$	1.05174	−	0.240052i	0.0371150	−	0.00847125i
$804$	10.4193	+	13.0654i	0.367460	+	0.460780i
$805$	−4.39354	−	5.08351i	−0.154852	−	0.179170i
$806$	0.560021	+	0.269692i	0.0197259	+	0.00949949i
$807$	−2.79849	−	2.23172i	−0.0985114	−	0.0785603i
$808$	−0.616377	+	1.27992i	−0.0216841	+	0.0450275i
$809$	−11.3460	−	14.2274i	−0.398904	−	0.500210i	0.541296	−	0.840832i	$-0.317934\pi$
$809$	−11.3460	−	14.2274i	−0.398904	−	0.500210i	−0.940200	+	0.340622i	$0.889362\pi$
$810$	11.4921	+	21.6328i	0.403791	+	0.760098i
$811$	−0.746699			−0.0262202			−0.0131101	−	0.999914i	$-0.504173\pi$
$811$	−0.746699			−0.0262202			−0.0131101	+	0.999914i	$0.504173\pi$
$812$	−8.76679	+	6.99128i	−0.307654	+	0.245346i
$813$	−28.9196	−	60.0522i	−1.01426	−	2.10612i
$814$	−2.39526	+	10.4943i	−0.0839539	+	0.367826i
$815$	15.0328	−	12.9924i	0.526575	−	0.455104i
$816$	−5.08131			−0.177881
$817$	−2.84777	−	1.26749i	−0.0996309	−	0.0443440i
$818$			13.2072i			0.461779i
$819$	0.280504	+	1.22897i	0.00980161	+	0.0429437i
$820$	0.430409	+	1.59277i	0.0150305	+	0.0556220i
$821$	15.9470	−	7.67968i	0.556555	−	0.268023i	−0.134392	−	0.990928i	$-0.542908\pi$
$821$	15.9470	−	7.67968i	0.556555	−	0.268023i	0.690947	+	0.722905i	$0.257194\pi$
$822$	5.75707	−	4.59111i	0.200801	−	0.160133i
$823$		−	38.2955i		−	1.33490i	−0.744656	−	0.667448i	$-0.767387\pi$
$823$		−	38.2955i		−	1.33490i	0.744656	−	0.667448i	$-0.232613\pi$
$824$	−6.25535			−0.217915
$825$	1.77594	+	22.4202i	0.0618304	+	0.780571i
$826$	10.1634	+	4.89443i	0.353630	+	0.170299i
$827$	42.3886	+	33.8038i	1.47400	+	1.17547i	0.945098	+	0.326788i	$0.105966\pi$
$827$	42.3886	+	33.8038i	1.47400	+	1.17547i	0.528898	+	0.848685i	$0.322605\pi$
$828$	−2.33482	+	4.84830i	−0.0811406	+	0.168490i
$829$	−2.55719	−	11.2038i	−0.0888148	−	0.389123i	0.910909	−	0.412606i	$-0.135382\pi$
$829$	−2.55719	−	11.2038i	−0.0888148	−	0.389123i	−0.999724	+	0.0234832i	$0.992524\pi$
$830$	14.1087	+	6.11994i	0.489721	+	0.212426i
$831$	−10.1042	−	44.2695i	−0.350511	−	1.53569i
$832$	−0.234613	−	0.487179i	−0.00813374	−	0.0168899i
$833$	10.0803	+	8.03877i	0.349262	+	0.278527i
$834$	−5.84897	+	7.33438i	−0.202533	+	0.253969i
$835$	−27.7791	+	7.50665i	−0.961336	+	0.259778i
$836$	0.857825	−	0.413107i	0.0296685	−	0.0142876i
$837$	1.07161	−	2.22523i	0.0370403	−	0.0769150i
$838$	25.6365	+	5.85136i	0.885598	+	0.202132i
$839$	−7.07002	+	30.9758i	−0.244084	+	1.06940i	0.693175	+	0.720769i	$0.256211\pi$
$839$	−7.07002	+	30.9758i	−0.244084	+	1.06940i	−0.937259	+	0.348633i	$0.886646\pi$
$840$	0.226385	+	5.72489i	0.00781102	+	0.197528i
$841$	−60.8947	+	29.3253i	−2.09982	+	1.01122i
$842$	34.1571	+	7.79615i	1.17713	+	0.268673i
$843$	48.1335	+	38.3852i	1.65781	+	1.32206i
$844$	6.13087	−	7.68787i	0.211033	−	0.264627i
$845$	−16.8249	+	22.8985i	−0.578793	+	0.787732i
$846$	−2.88101	−	12.6225i	−0.0990510	−	0.433971i
$847$	6.23365	−	4.97117i	0.214191	−	0.170811i
$848$	−0.610031	+	0.139236i	−0.0209486	+	0.00478137i
$849$	16.4704	+	7.93172i	0.565262	+	0.272216i
$850$	−3.38054	−	10.7964i	−0.115952	−	0.370315i
$851$	−12.7519	−	6.14101i	−0.437131	−	0.210511i
$852$	−9.12518	+	7.27709i	−0.312623	+	0.249309i
$853$		−	4.68269i		−	0.160332i	−0.996782	−	0.0801662i	$-0.974455\pi$
$853$		−	4.68269i		−	0.160332i	0.996782	−	0.0801662i	$-0.0255451\pi$
$854$	−6.79883			−0.232651
$855$	−1.99246	−	0.864270i	−0.0681407	−	0.0295574i
$856$	11.5705	−	5.57208i	0.395473	−	0.190450i
$857$	4.17427	+	0.952751i	0.142590	+	0.0325453i	0.293220	−	0.956045i	$-0.405273\pi$
$857$	4.17427	+	0.952751i	0.142590	+	0.0325453i	−0.150630	+	0.988590i	$0.548130\pi$
$858$	−2.37125	+	0.541223i	−0.0809533	+	0.0184771i
$859$	46.8192			1.59745			0.798726	−	0.601695i	$-0.205508\pi$
$859$	46.8192			1.59745			0.798726	+	0.601695i	$0.205508\pi$
$860$	9.91689	+	10.8007i	0.338163	+	0.368301i
$861$	1.89058			0.0644307
$862$	33.4699	−	7.63929i	1.13999	−	0.260195i
$863$	38.7285	+	8.83953i	1.31833	+	0.300901i	0.823119	−	0.567869i	$-0.192232\pi$
$863$	38.7285	+	8.83953i	1.31833	+	0.300901i	0.495216	+	0.868770i	$0.335089\pi$
$864$	−1.93579	+	0.932227i	−0.0658569	+	0.0317150i
$865$	21.2891	−	49.0791i	0.723850	−	1.66874i
$866$	−17.4537			−0.593100
$867$			26.6800i			0.906100i
$868$	1.02540	−	0.817732i	0.0348045	−	0.0277556i
$869$	−5.07229	−	2.44269i	−0.172066	−	0.0828625i
$870$	−9.07207	+	48.5107i	−0.307572	+	1.64467i
$871$	−3.62527	−	1.74584i	−0.122838	−	0.0591555i
$872$	8.98898	−	2.05168i	0.304405	−	0.0694785i
$873$	22.0155	−	17.5568i	0.745112	−	0.594207i
$874$	0.278576	+	1.22052i	0.00942297	+	0.0412847i
$875$	−12.0133	+	4.28972i	−0.406123	+	0.145019i
$876$	0.754133	−	0.945653i	0.0254798	−	0.0319507i
$877$	−5.58542	−	4.45422i	−0.188606	−	0.150408i	0.524635	−	0.851327i	$-0.324202\pi$
$877$	−5.58542	−	4.45422i	−0.188606	−	0.150408i	−0.713241	+	0.700919i	$0.752773\pi$
$878$	−15.5583	−	3.55108i	−0.525067	−	0.119843i
$879$	−29.4831	+	14.1983i	−0.994441	+	0.478898i
$880$	−4.47525	+	0.176969i	−0.150861	+	0.00596563i
$881$	7.47519	−	32.7510i	0.251846	−	1.10341i	−0.677885	−	0.735168i	$-0.737103\pi$
$881$	7.47519	−	32.7510i	0.251846	−	1.10341i	0.929731	−	0.368240i	$-0.120040\pi$
$882$	−11.3511	−	2.59081i	−0.382211	−	0.0872371i
$883$	−17.0885	+	35.4847i	−0.575075	+	1.19416i	0.387179	+	0.922004i	$0.373449\pi$
$883$	−17.0885	+	35.4847i	−0.575075	+	1.19416i	−0.962254	+	0.272151i	$0.912265\pi$
$884$	1.10232	−	0.530849i	0.0370750	−	0.0178544i
$885$	47.9291	−	12.9517i	1.61112	−	0.435367i
$886$	−21.3987	+	26.8331i	−0.718904	+	0.901477i
$887$	22.3552	+	17.8276i	0.750613	+	0.598594i	0.922262	−	0.386564i	$-0.126338\pi$
$887$	22.3552	+	17.8276i	0.750613	+	0.598594i	−0.171650	+	0.985158i	$0.554910\pi$
$888$	5.23649	+	10.8737i	0.175725	+	0.364897i
$889$	1.05463	+	4.62063i	0.0353711	+	0.154971i
$890$	12.5399	−	28.9091i	0.420339	−	0.969037i
$891$	4.88258	+	21.3920i	0.163573	+	0.716658i
$892$	0.407276	−	0.845716i	0.0136366	−	0.0283167i
$893$	−2.35494	−	1.87800i	−0.0788050	−	0.0628449i
$894$	32.5161	+	15.6589i	1.08750	+	0.523713i
$895$	−21.1647	−	9.18061i	−0.707457	−	0.306874i
$896$	−1.14095			−0.0381164
$897$		−	3.19808i		−	0.106781i
$898$	6.11446	−	4.87612i	0.204042	−	0.162718i
$899$	10.1786	−	4.90175i	0.339475	−	0.163482i
$900$	6.98060	+	7.45951i	0.232687	+	0.248650i
$901$	−0.315043	−	1.38029i	−0.0104956	−	0.0459843i
$902$			1.47790i			0.0492086i
$903$	14.9121	−	7.74144i	0.496244	−	0.257619i
$904$	−9.34933			−0.310954
$905$	−22.2147	−	25.7033i	−0.738440	−	0.854407i
$906$	7.34210	−	32.1678i	0.243925	−	1.06870i
$907$	10.6299	+	22.0731i	0.352958	+	0.732926i	0.999553	−	0.0299083i	$-0.00952154\pi$
$907$	10.6299	+	22.0731i	0.352958	+	0.732926i	−0.646594	+	0.762834i	$0.723807\pi$
$908$	−4.58018	+	3.65257i	−0.151999	+	0.121215i
$909$	2.90267			0.0962755
$910$	−0.647197	−	1.21829i	−0.0214544	−	0.0403858i
$911$	−34.7071	−	43.5213i	−1.14990	−	1.44193i	−0.877394	−	0.479771i	$-0.840720\pi$
$911$	−34.7071	−	43.5213i	−1.14990	−	1.44193i	−0.272504	−	0.962155i	$-0.587852\pi$
$912$	0.463176	−	0.961796i	0.0153373	−	0.0318482i
$913$	10.7702	+	8.58895i	0.356442	+	0.284253i
$914$	−10.0424	−	4.83617i	−0.332174	−	0.159966i
$915$	−22.6395	+	19.5667i	−0.748439	+	0.646855i
$916$	2.58011	+	3.23535i	0.0852491	+	0.106899i
$917$	−14.9857	+	3.42038i	−0.494870	+	0.112951i
$918$	−2.10931	−	4.38004i	−0.0696177	−	0.144563i
$919$	33.2297	−	41.6687i	1.09615	−	1.37452i	0.175338	−	0.984508i	$-0.443898\pi$
$919$	33.2297	−	41.6687i	1.09615	−	1.37452i	0.920808	−	0.390016i	$-0.127530\pi$
$920$	1.08254	−	5.78863i	0.0356903	−	0.190846i
$921$	0.839421	−	3.67774i	0.0276599	−	0.121186i
$922$	−6.44345	−	13.3800i	−0.212204	−	0.440645i
$923$	1.21934	−	2.53198i	0.0401350	−	0.0833412i
$924$	−1.14199	+	5.00341i	−0.0375689	+	0.164600i
$925$	−19.6199	+	18.3603i	−0.645098	+	0.603682i
$926$	−20.0964	−	9.67791i	−0.660408	−	0.318036i
$927$	5.54561	+	11.5156i	0.182142	+	0.378221i
$928$	−9.58151	−	2.18692i	−0.314529	−	0.0717891i
$929$	−10.8217	+	13.5700i	−0.355049	+	0.445218i	−0.926995	−	0.375074i	$-0.877617\pi$
$929$	−10.8217	+	13.5700i	−0.355049	+	0.445218i	0.571946	+	0.820291i	$0.306189\pi$
$930$	1.06111	−	5.67404i	0.0347952	−	0.186059i
$931$	−2.44044	+	1.17525i	−0.0799821	+	0.0385173i
$932$	−13.3822	+	3.05441i	−0.438350	+	0.100050i
$933$	23.8416	−	19.0130i	0.780538	−	0.622458i
$934$	−7.89061	−	34.5710i	−0.258189	−	1.13120i
$935$	−0.400421	−	10.1260i	−0.0130952	−	0.331155i
$936$	−0.688862	+	0.863805i	−0.0225161	+	0.0282344i
$937$	−1.63773	+	3.40078i	−0.0535023	+	0.111099i	−0.926006	−	0.377509i	$-0.876781\pi$
$937$	−1.63773	+	3.40078i	−0.0535023	+	0.111099i	0.872504	+	0.488608i	$0.162495\pi$
$938$	−6.63792	+	5.29356i	−0.216736	+	0.172841i
$939$	−75.5953			−2.46696
$940$	6.64723	+	12.5128i	0.216809	+	0.408122i
$941$	−26.6210	−	33.3817i	−0.867820	−	1.08821i	−0.995345	−	0.0963768i	$-0.969275\pi$
$941$	−26.6210	−	33.3817i	−0.867820	−	1.08821i	0.127525	−	0.991835i	$-0.459297\pi$
$942$	−12.8516	−	26.6867i	−0.418729	−	0.869500i
$943$	−1.89453	−	0.432414i	−0.0616943	−	0.0140813i
$944$	2.20006	+	9.63908i	0.0716057	+	0.313725i
$945$	−4.84083	+	2.57162i	−0.157472	+	0.0836547i
$946$	6.05162	+	11.6571i	0.196755	+	0.379003i
$947$		−	5.76760i		−	0.187422i	−0.995599	−	0.0937109i	$-0.970127\pi$
$947$		−	5.76760i		−	0.187422i	0.995599	−	0.0937109i	$-0.0298729\pi$
$948$	−6.15391	+	1.40459i	−0.199870	+	0.0456190i
$949$	−0.0648056	+	0.283932i	−0.00210368	+	0.00921681i
$950$	2.35171	+	0.344255i	0.0762995	+	0.0111691i
$951$	25.5275	+	32.0105i	0.827786	+	1.03801i
$952$		−	2.58158i		−	0.0836695i
$953$		−	54.4323i		−	1.76324i	−0.471964	−	0.881618i	$-0.656455\pi$
$953$		−	54.4323i		−	1.76324i	0.471964	−	0.881618i	$-0.343545\pi$
$954$	0.797138	+	0.999579i	0.0258083	+	0.0323626i
$955$	44.2392	−	1.74939i	1.43155	−	0.0566090i
$956$	14.4494	−	18.1190i	0.467328	−	0.586011i
$957$	−19.1806	+	39.8289i	−0.620021	+	1.28749i
$958$	−19.0887	+	4.35687i	−0.616728	+	0.140764i
$959$	2.33253	+	2.92491i	0.0753215	+	0.0944501i
$960$	−3.79926	+	3.28359i	−0.122620	+	0.105977i
$961$	26.7395	−	12.8771i	0.862565	−	0.415389i
$962$	−2.27197	−	1.81183i	−0.0732512	−	0.0584159i
$963$	−20.5155	−	16.3605i	−0.661102	−	0.527211i
$964$	0.509357	−	2.23164i	0.0164053	−	0.0718762i
$965$	−12.4175	−	9.12383i	−0.399732	−	0.293707i
$966$	−6.07977	−	2.92786i	−0.195613	−	0.0942024i
$967$	2.58516	+	0.590046i	0.0831331	+	0.0189746i	0.263885	−	0.964554i	$-0.414996\pi$
$967$	2.58516	+	0.590046i	0.0831331	+	0.0189746i	−0.180752	+	0.983529i	$0.557853\pi$
$968$	6.81296	+	1.55501i	0.218977	+	0.0499800i
$969$	2.17622	+	1.04801i	0.0699102	+	0.0336670i
$970$	−18.2465	+	24.8333i	−0.585859	+	0.797349i
$971$	8.92876	−	39.1195i	0.286538	−	1.25540i	−0.602704	−	0.797965i	$-0.705910\pi$
$971$	8.92876	−	39.1195i	0.286538	−	1.25540i	0.889241	−	0.457438i	$-0.151233\pi$
$972$	14.1948	+	11.3200i	0.455300	+	0.363089i
$973$	−3.72626	−	2.97159i	−0.119458	−	0.0952649i
$974$	−17.7281	+	8.53742i	−0.568046	+	0.273557i
$975$	−5.66128	−	2.19419i	−0.181306	−	0.0702702i
$976$	−3.71533	−	4.65888i	−0.118925	−	0.149127i
$977$	30.6115	−	6.98687i	0.979347	−	0.223530i	0.297257	−	0.954798i	$-0.403928\pi$
$977$	30.6115	−	6.98687i	0.979347	−	0.223530i	0.682090	+	0.731268i	$0.261071\pi$
$978$	8.65816	−	17.9789i	0.276858	−	0.574901i
$979$	17.5990	−	22.0684i	0.562466	−	0.705311i
$980$	12.7317	−	0.503462i	0.406699	−	0.0160825i
$981$	−11.7460	−	14.7291i	−0.375022	−	0.470263i
$982$			14.7042i			0.469230i
$983$		−	12.7059i		−	0.405254i	−0.979256	−	0.202627i	$-0.935052\pi$
$983$		−	12.7059i		−	0.405254i	0.979256	−	0.202627i	$-0.0649480\pi$
$984$	1.03314	+	1.29551i	0.0329352	+	0.0412995i
$985$	−24.0026	−	17.6361i	−0.764786	−	0.561933i
$986$	4.94826	−	21.6797i	0.157585	−	0.690423i
$987$	15.8286	−	3.61278i	0.503831	−	0.114996i
$988$			0.257037i			0.00817744i
$989$	−16.7139	+	4.34691i	−0.531470	+	0.138224i
$990$	4.29327	+	8.08167i	0.136449	+	0.256852i
$991$	−8.21457	−	35.9904i	−0.260944	−	1.14327i	−0.920230	−	0.391379i	$-0.871998\pi$
$991$	−8.21457	−	35.9904i	−0.260944	−	1.14327i	0.659285	−	0.751893i	$-0.270859\pi$
$992$	1.12070	+	0.255792i	0.0355822	+	0.00812140i
$993$	−14.1488	−	29.3803i	−0.448999	−	0.932356i
$994$	−3.69715	−	4.63608i	−0.117267	−	0.147048i
$995$	36.1101	−	19.1829i	1.14477	−	0.608140i
$996$	15.4453			0.489402
$997$	−26.5449	+	21.1688i	−0.840684	+	0.670423i	−0.946054	−	0.324010i	$-0.894969\pi$
$997$	−26.5449	+	21.1688i	−0.840684	+	0.670423i	0.105370	+	0.994433i	$0.466397\pi$
$998$	10.7222	−	22.2648i	0.339404	−	0.704779i
$999$	−7.19927	+	9.02760i	−0.227775	+	0.285620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.p.a.59.3	✓	132
5.4	even	2	inner	430.2.p.a.59.20	yes	132
43.35	even	7	inner	430.2.p.a.379.20	yes	132
215.164	even	14	inner	430.2.p.a.379.3	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.p.a.59.3	✓	132	1.1	even	1	trivial
430.2.p.a.59.20	yes	132	5.4	even	2	inner
430.2.p.a.379.3	yes	132	215.164	even	14	inner
430.2.p.a.379.20	yes	132	43.35	even	7	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.p (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.974928 + 0.222521i) q^{2} +(-2.18942 - 0.499720i) q^{3} +(0.900969 - 0.433884i) q^{4} +(2.05139 + 0.889832i) q^{5} +2.24572 q^{6} +1.14095i q^{7} +(-0.781831 + 0.623490i) q^{8} +(1.84092 + 0.886539i) q^{9} +O(q^{10})\)	\(q+(-0.974928 + 0.222521i) q^{2} +(-2.18942 - 0.499720i) q^{3} +(0.900969 - 0.433884i) q^{4} +(2.05139 + 0.889832i) q^{5} +2.24572 q^{6} +1.14095i q^{7} +(-0.781831 + 0.623490i) q^{8} +(1.84092 + 0.886539i) q^{9} +(-2.19796 - 0.411045i) q^{10} +(-1.80460 - 0.869050i) q^{11} +(-2.18942 + 0.499720i) q^{12} +(0.422758 - 0.337138i) q^{13} +(-0.253885 - 1.11234i) q^{14} +(-4.04668 - 2.97333i) q^{15} +(0.623490 - 0.781831i) q^{16} +(1.76902 + 1.41075i) q^{17} +(-1.99203 - 0.454669i) q^{18} +(-0.428279 + 0.206248i) q^{19} +(2.23432 - 0.0883539i) q^{20} +(0.570155 - 2.49801i) q^{21} +(1.95274 + 0.445700i) q^{22} +(-1.14269 + 2.37282i) q^{23} +(2.02332 - 0.974382i) q^{24} +(3.41640 + 3.65078i) q^{25} +(-0.337138 + 0.422758i) q^{26} +(1.67981 + 1.33961i) q^{27} +(0.495039 + 1.02796i) q^{28} +(2.18692 + 9.58151i) q^{29} +(4.60685 + 1.99831i) q^{30} +(-0.255792 - 1.12070i) q^{31} +(-0.433884 + 0.900969i) q^{32} +(3.51674 + 2.80451i) q^{33} +(-2.03859 - 0.981732i) q^{34} +(-1.01525 + 2.34053i) q^{35} +2.04326 q^{36} +5.37416i q^{37} +(0.371647 - 0.296378i) q^{38} +(-1.09407 + 0.526875i) q^{39} +(-2.15864 + 0.583322i) q^{40} +(0.164189 + 0.719359i) q^{41} +2.56225i q^{42} +(4.24065 + 5.00169i) q^{43} -2.00296 q^{44} +(2.98757 + 3.45674i) q^{45} +(0.586039 - 2.56760i) q^{46} +(2.74930 + 5.70898i) q^{47} +(-1.75578 + 1.40018i) q^{48} +5.69824 q^{49} +(-4.14312 - 2.79903i) q^{50} +(-3.16814 - 3.97273i) q^{51} +(0.234613 - 0.487179i) q^{52} +(-0.489207 - 0.390130i) q^{53} +(-1.93579 - 0.932227i) q^{54} +(-2.92863 - 3.38855i) q^{55} +(-0.711370 - 0.892029i) q^{56} +(1.04075 - 0.237544i) q^{57} +(-4.26417 - 8.85465i) q^{58} +(-6.16442 + 7.72994i) q^{59} +(-4.93601 - 0.923092i) q^{60} +(1.32599 - 5.80953i) q^{61} +(0.498757 + 1.03568i) q^{62} +(-1.01149 + 2.10039i) q^{63} +(0.222521 - 0.974928i) q^{64} +(1.16724 - 0.315418i) q^{65} +(-4.05263 - 1.95164i) q^{66} +(-3.22869 - 6.70444i) q^{67} +(2.20593 + 0.503490i) q^{68} +(3.68757 - 4.62407i) q^{69} +(0.468981 - 2.50776i) q^{70} +(4.68255 - 2.25500i) q^{71} +(-1.99203 + 0.454669i) q^{72} +(-0.421091 + 0.335809i) q^{73} +(-1.19586 - 5.23942i) q^{74} +(-5.65555 - 9.70033i) q^{75} +(-0.296378 + 0.371647i) q^{76} +(0.991541 - 2.05896i) q^{77} +(0.949396 - 0.757118i) q^{78} +2.81076 q^{79} +(1.97472 - 1.04904i) q^{80} +(-6.83025 - 8.56486i) q^{81} +(-0.320145 - 0.664787i) q^{82} +(-6.70520 - 1.53042i) q^{83} +(-0.570155 - 2.49801i) q^{84} +(2.37362 + 4.46812i) q^{85} +(-5.24731 - 3.93266i) q^{86} -22.0708i q^{87} +(1.95274 - 0.445700i) q^{88} +(-3.13587 + 13.7391i) q^{89} +(-3.68186 - 2.70528i) q^{90} +(0.384657 + 0.482345i) q^{91} +2.63363i q^{92} +2.58150i q^{93} +(-3.95074 - 4.95407i) q^{94} +(-1.06209 + 0.0419994i) q^{95} +(1.40018 - 1.75578i) q^{96} +(5.97950 - 12.4166i) q^{97} +(-5.55537 + 1.26798i) q^{98} +(-2.55167 - 3.19970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 22 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{9}+O(q^{10}) \) 132 * q + 22 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^9	\( 132 q + 22 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{9} + 8 q^{11} - 10 q^{14} - 20 q^{15} - 22 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} + 4 q^{24} - 16 q^{25} + 12 q^{26} + 40 q^{29} + 24 q^{31} - 4 q^{35} + 128 q^{36} - 56 q^{39} - 28 q^{41} - 8 q^{44} - 80 q^{45} - 12 q^{46} - 136 q^{49} - 56 q^{50} + 172 q^{51} + 16 q^{54} - 4 q^{56} + 16 q^{59} - 8 q^{60} - 44 q^{61} + 22 q^{64} + 42 q^{65} + 8 q^{66} - 62 q^{69} + 12 q^{70} - 8 q^{71} - 4 q^{74} - 122 q^{75} - 52 q^{76} - 64 q^{79} - 4 q^{80} - 56 q^{81} + 24 q^{84} - 72 q^{85} - 10 q^{86} + 16 q^{89} + 2 q^{90} - 24 q^{91} - 20 q^{94} + 106 q^{95} - 4 q^{96} - 104 q^{99}+O(q^{100}) \) 132 * q + 22 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^9 + 8 * q^11 - 10 * q^14 - 20 * q^15 - 22 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 + 4 * q^24 - 16 * q^25 + 12 * q^26 + 40 * q^29 + 24 * q^31 - 4 * q^35 + 128 * q^36 - 56 * q^39 - 28 * q^41 - 8 * q^44 - 80 * q^45 - 12 * q^46 - 136 * q^49 - 56 * q^50 + 172 * q^51 + 16 * q^54 - 4 * q^56 + 16 * q^59 - 8 * q^60 - 44 * q^61 + 22 * q^64 + 42 * q^65 + 8 * q^66 - 62 * q^69 + 12 * q^70 - 8 * q^71 - 4 * q^74 - 122 * q^75 - 52 * q^76 - 64 * q^79 - 4 * q^80 - 56 * q^81 + 24 * q^84 - 72 * q^85 - 10 * q^86 + 16 * q^89 + 2 * q^90 - 24 * q^91 - 20 * q^94 + 106 * q^95 - 4 * q^96 - 104 * q^99

Introduction

L-functions

Modular forms

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