LMFDB - Embedded newform 430.2.p.a.59.14

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			59.14
Character	$\chi$	$=$	430.59
Dual form			430.2.p.a.379.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.974928 - 0.222521i) q^{2} +(-1.83835 - 0.419592i) q^{3} +(0.900969 - 0.433884i) q^{4} +(-1.98399 + 1.03139i) q^{5} -1.88563 q^{6} -0.473994i q^{7} +(0.781831 - 0.623490i) q^{8} +(0.500573 + 0.241063i) q^{9} +O(q^{10})$	\(q+(0.974928 - 0.222521i) q^{2} +(-1.83835 - 0.419592i) q^{3} +(0.900969 - 0.433884i) q^{4} +(-1.98399 + 1.03139i) q^{5} -1.88563 q^{6} -0.473994i q^{7} +(0.781831 - 0.623490i) q^{8} +(0.500573 + 0.241063i) q^{9} +(-1.70474 + 1.44701i) q^{10} +(0.557882 + 0.268662i) q^{11} +(-1.83835 + 0.419592i) q^{12} +(-4.22925 + 3.37271i) q^{13} +(-0.105474 - 0.462110i) q^{14} +(4.08004 - 1.06359i) q^{15} +(0.623490 - 0.781831i) q^{16} +(-4.38565 - 3.49744i) q^{17} +(0.541664 + 0.123631i) q^{18} +(-7.04969 + 3.39495i) q^{19} +(-1.34001 + 1.79007i) q^{20} +(-0.198884 + 0.871367i) q^{21} +(0.603677 + 0.137785i) q^{22} +(-2.89434 + 6.01017i) q^{23} +(-1.69889 + 0.818143i) q^{24} +(2.87246 - 4.09255i) q^{25} +(-3.37271 + 4.22925i) q^{26} +(3.60365 + 2.87381i) q^{27} +(-0.205658 - 0.427054i) q^{28} +(0.714806 + 3.13177i) q^{29} +(3.74107 - 1.94482i) q^{30} +(-0.383484 - 1.68015i) q^{31} +(0.433884 - 0.900969i) q^{32} +(-0.912855 - 0.727977i) q^{33} +(-5.05394 - 2.43385i) q^{34} +(0.488873 + 0.940401i) q^{35} +0.555594 q^{36} -8.81997i q^{37} +(-6.11749 + 4.87854i) q^{38} +(9.19000 - 4.42567i) q^{39} +(-0.908087 + 2.04337i) q^{40} +(-0.327912 - 1.43668i) q^{41} +0.893776i q^{42} +(6.18062 + 2.19089i) q^{43} +0.619202 q^{44} +(-1.24176 + 0.0380186i) q^{45} +(-1.48439 + 6.50353i) q^{46} +(-4.16254 - 8.64361i) q^{47} +(-1.47424 + 1.17567i) q^{48} +6.77533 q^{49} +(1.88977 - 4.62912i) q^{50} +(6.59487 + 8.26970i) q^{51} +(-2.34705 + 4.87371i) q^{52} +(-3.86444 - 3.08179i) q^{53} +(4.15278 + 1.99987i) q^{54} +(-1.38393 + 0.0423713i) q^{55} +(-0.295530 - 0.370583i) q^{56} +(14.3843 - 3.28312i) q^{57} +(1.39377 + 2.89419i) q^{58} +(1.84595 - 2.31475i) q^{59} +(3.21452 - 2.72853i) q^{60} +(-0.257800 + 1.12949i) q^{61} +(-0.747738 - 1.55269i) q^{62} +(0.114262 - 0.237268i) q^{63} +(0.222521 - 0.974928i) q^{64} +(4.91221 - 11.0534i) q^{65} +(-1.05196 - 0.506596i) q^{66} +(4.47423 + 9.29084i) q^{67} +(-5.46881 - 1.24822i) q^{68} +(7.84264 - 9.83436i) q^{69} +(0.685875 + 0.808038i) q^{70} +(-14.1341 + 6.80661i) q^{71} +(0.541664 - 0.123631i) q^{72} +(6.79574 - 5.41942i) q^{73} +(-1.96263 - 8.59883i) q^{74} +(-6.99780 + 6.31828i) q^{75} +(-4.87854 + 6.11749i) q^{76} +(0.127344 - 0.264432i) q^{77} +(7.97478 - 6.35968i) q^{78} -7.48910 q^{79} +(-0.430626 + 2.19421i) q^{80} +(-6.45817 - 8.09829i) q^{81} +(-0.639381 - 1.32769i) q^{82} +(-11.8878 - 2.71331i) q^{83} +(0.198884 + 0.871367i) q^{84} +(12.3083 + 2.41557i) q^{85} +(6.51317 + 0.760641i) q^{86} -6.05722i q^{87} +(0.603677 - 0.137785i) q^{88} +(-1.14929 + 5.03538i) q^{89} +(-1.20217 + 0.313384i) q^{90} +(1.59864 + 2.00464i) q^{91} +6.67078i q^{92} +3.24962i q^{93} +(-5.98156 - 7.50064i) q^{94} +(10.4850 - 14.0066i) q^{95} +(-1.17567 + 1.47424i) q^{96} +(5.51211 - 11.4460i) q^{97} +(6.60546 - 1.50765i) q^{98} +(0.214496 + 0.268969i) 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
$3$	−1.83835	−	0.419592i	−1.06137	−	0.242251i	−0.344021	−	0.938962i	$-0.611789\pi$
$3$	−1.83835	−	0.419592i	−1.06137	−	0.242251i	−0.717352	+	0.696711i	$0.754646\pi$
$4$	0.900969	−	0.433884i	0.450484	−	0.216942i
$5$	−1.98399	+	1.03139i	−0.887269	+	0.461252i
$5$	−1.98399	+	1.03139i	−0.887269	+	0.461252i
$6$	−1.88563			−0.769805
$7$		−	0.473994i		−	0.179153i	−0.995980	−	0.0895764i	$-0.971449\pi$
$7$		−	0.473994i		−	0.179153i	0.995980	−	0.0895764i	$-0.0285513\pi$
$8$	0.781831	−	0.623490i	0.276419	−	0.220437i
$9$	0.500573	+	0.241063i	0.166858	+	0.0803544i
$10$	−1.70474	+	1.44701i	−0.539088	+	0.457586i
$11$	0.557882	+	0.268662i	0.168208	+	0.0810046i	0.516093	−	0.856533i	$-0.327386\pi$
$11$	0.557882	+	0.268662i	0.168208	+	0.0810046i	−0.347885	+	0.937537i	$0.613100\pi$
$12$	−1.83835	+	0.419592i	−0.530686	+	0.121126i
$13$	−4.22925	+	3.37271i	−1.17298	+	0.935422i	−0.998785	−	0.0492892i	$-0.984304\pi$
$13$	−4.22925	+	3.37271i	−1.17298	+	0.935422i	−0.174197	+	0.984711i	$0.555733\pi$
$14$	−0.105474	−	0.462110i	−0.0281890	−	0.123504i
$15$	4.08004	−	1.06359i	1.05346	−	0.274618i
$16$	0.623490	−	0.781831i	0.155872	−	0.195458i
$17$	−4.38565	−	3.49744i	−1.06368	−	0.848253i	−0.0748299	−	0.997196i	$-0.523841\pi$
$17$	−4.38565	−	3.49744i	−1.06368	−	0.848253i	−0.988846	+	0.148943i	$0.952413\pi$
$18$	0.541664	+	0.123631i	0.127671	+	0.0291402i
$19$	−7.04969	+	3.39495i	−1.61731	+	0.778856i	−0.999969	−	0.00784001i	$-0.997504\pi$
$19$	−7.04969	+	3.39495i	−1.61731	+	0.778856i	−0.617341	+	0.786696i	$0.711790\pi$
$20$	−1.34001	+	1.79007i	−0.299636	+	0.400273i
$21$	−0.198884	+	0.871367i	−0.0434000	+	0.190148i
$22$	0.603677	+	0.137785i	0.128704	+	0.0293759i
$23$	−2.89434	+	6.01017i	−0.603513	+	1.25321i	0.345633	+	0.938370i	$0.387664\pi$
$23$	−2.89434	+	6.01017i	−0.603513	+	1.25321i	−0.949146	+	0.314837i	$0.898050\pi$
$24$	−1.69889	+	0.818143i	−0.346785	+	0.167003i
$25$	2.87246	−	4.09255i	0.574493	−	0.818510i
$26$	−3.37271	+	4.22925i	−0.661443	+	0.829423i
$27$	3.60365	+	2.87381i	0.693523	+	0.553066i
$28$	−0.205658	−	0.427054i	−0.0388657	−	0.0807055i
$29$	0.714806	+	3.13177i	0.132736	+	0.581555i	0.996923	+	0.0783844i	$0.0249762\pi$
$29$	0.714806	+	3.13177i	0.132736	+	0.581555i	−0.864187	+	0.503171i	$0.832167\pi$
$30$	3.74107	−	1.94482i	0.683024	−	0.355074i
$31$	−0.383484	−	1.68015i	−0.0688757	−	0.301764i	0.928744	−	0.370722i	$-0.120890\pi$
$31$	−0.383484	−	1.68015i	−0.0688757	−	0.301764i	−0.997620	+	0.0689579i	$0.978033\pi$
$32$	0.433884	−	0.900969i	0.0767005	−	0.159270i
$33$	−0.912855	−	0.727977i	−0.158908	−	0.126725i
$34$	−5.05394	−	2.43385i	−0.866744	−	0.417402i
$35$	0.488873	+	0.940401i	0.0826346	+	0.158957i
$36$	0.555594			0.0925990
$37$		−	8.81997i		−	1.44999i	−0.688752	−	0.724997i	$-0.741841\pi$
$37$		−	8.81997i		−	1.44999i	0.688752	−	0.724997i	$-0.258159\pi$
$38$	−6.11749	+	4.87854i	−0.992389	+	0.791403i
$39$	9.19000	−	4.42567i	1.47158	−	0.708675i
$40$	−0.908087	+	2.04337i	−0.143581	+	0.323086i
$41$	−0.327912	−	1.43668i	−0.0512112	−	0.224371i	0.942846	−	0.333228i	$-0.108138\pi$
$41$	−0.327912	−	1.43668i	−0.0512112	−	0.224371i	−0.994057	+	0.108857i	$0.965281\pi$
$42$			0.893776i			0.137913i
$43$	6.18062	+	2.19089i	0.942535	+	0.334107i
$43$	6.18062	+	2.19089i	0.942535	+	0.334107i
$44$	0.619202			0.0933482
$45$	−1.24176	+	0.0380186i	−0.185111	+	0.00566748i
$46$	−1.48439	+	6.50353i	−0.218861	+	0.958894i
$47$	−4.16254	−	8.64361i	−0.607169	−	1.26080i	−0.947278	−	0.320414i	$-0.896178\pi$
$47$	−4.16254	−	8.64361i	−0.607169	−	1.26080i	0.340109	−	0.940386i	$-0.389536\pi$
$48$	−1.47424	+	1.17567i	−0.212789	+	0.169693i
$49$	6.77533			0.967904
$50$	1.88977	−	4.62912i	0.267253	−	0.654657i
$51$	6.59487	+	8.26970i	0.923466	+	1.15799i
$52$	−2.34705	+	4.87371i	−0.325478	+	0.675862i
$53$	−3.86444	−	3.08179i	−0.530821	−	0.423316i	0.321054	−	0.947061i	$-0.395963\pi$
$53$	−3.86444	−	3.08179i	−0.530821	−	0.423316i	−0.851875	+	0.523745i	$0.824534\pi$
$54$	4.15278	+	1.99987i	0.565122	+	0.272148i
$55$	−1.38393	+	0.0423713i	−0.186609	+	0.00571334i
$56$	−0.295530	−	0.370583i	−0.0394919	−	0.0495213i
$57$	14.3843	−	3.28312i	1.90525	−	0.434860i
$58$	1.39377	+	2.89419i	0.183011	+	0.380026i
$59$	1.84595	−	2.31475i	0.240322	−	0.301354i	−0.647014	−	0.762478i	$-0.723982\pi$
$59$	1.84595	−	2.31475i	0.240322	−	0.301354i	0.887336	+	0.461124i	$0.152554\pi$
$60$	3.21452	−	2.72853i	0.414992	−	0.352251i
$61$	−0.257800	+	1.12949i	−0.0330079	+	0.144617i	−0.988747	−	0.149600i	$-0.952202\pi$
$61$	−0.257800	+	1.12949i	−0.0330079	+	0.144617i	0.955739	+	0.294217i	$0.0950587\pi$
$62$	−0.747738	−	1.55269i	−0.0949628	−	0.197192i
$63$	0.114262	−	0.237268i	0.0143957	−	0.0298930i
$64$	0.222521	−	0.974928i	0.0278151	−	0.121866i
$65$	4.91221	−	11.0534i	0.609285	−	1.37101i
$66$	−1.05196	−	0.506596i	−0.129487	−	0.0623577i
$67$	4.47423	+	9.29084i	0.546614	+	1.13506i	0.973062	+	0.230544i	$0.0740507\pi$
$67$	4.47423	+	9.29084i	0.546614	+	1.13506i	−0.426447	+	0.904512i	$0.640235\pi$
$68$	−5.46881	−	1.24822i	−0.663191	−	0.151369i
$69$	7.84264	−	9.83436i	0.944143	−	1.18392i
$70$	0.685875	+	0.808038i	0.0819777	+	0.0965791i
$71$	−14.1341	+	6.80661i	−1.67740	+	0.807796i	−0.680204	+	0.733023i	$0.738109\pi$
$71$	−14.1341	+	6.80661i	−1.67740	+	0.807796i	−0.997201	+	0.0747727i	$0.976177\pi$
$72$	0.541664	−	0.123631i	0.0638357	−	0.0145701i
$73$	6.79574	−	5.41942i	0.795382	−	0.634296i	−0.139112	−	0.990277i	$-0.544425\pi$
$73$	6.79574	−	5.41942i	0.795382	−	0.634296i	0.934493	+	0.355981i	$0.115853\pi$
$74$	−1.96263	−	8.59883i	−0.228151	−	0.999594i
$75$	−6.99780	+	6.31828i	−0.808036	+	0.729572i
$76$	−4.87854	+	6.11749i	−0.559607	+	0.701725i
$77$	0.127344	−	0.264432i	0.0145122	−	0.0301349i
$78$	7.97478	−	6.35968i	0.902967	−	0.720092i
$79$	−7.48910			−0.842590			−0.421295	−	0.906924i	$-0.638424\pi$
$79$	−7.48910			−0.842590			−0.421295	+	0.906924i	$0.638424\pi$
$80$	−0.430626	+	2.19421i	−0.0481454	+	0.245320i
$81$	−6.45817	−	8.09829i	−0.717574	−	0.899810i
$82$	−0.639381	−	1.32769i	−0.0706078	−	0.146619i
$83$	−11.8878	−	2.71331i	−1.30485	−	0.297824i	−0.487077	−	0.873359i	$-0.661937\pi$
$83$	−11.8878	−	2.71331i	−1.30485	−	0.297824i	−0.817777	+	0.575535i	$0.804794\pi$
$84$	0.198884	+	0.871367i	0.0217000	+	0.0950740i
$85$	12.3083	+	2.41557i	1.33503	+	0.262006i
$86$	6.51317	+	0.760641i	0.702334	+	0.0820221i
$87$		−	6.05722i		−	0.649402i
$88$	0.603677	−	0.137785i	0.0643522	−	0.0146880i
$89$	−1.14929	+	5.03538i	−0.121825	+	0.533749i	0.876778	+	0.480896i	$0.159689\pi$
$89$	−1.14929	+	5.03538i	−0.121825	+	0.533749i	−0.998602	+	0.0528530i	$0.983169\pi$
$90$	−1.20217	+	0.313384i	−0.126720	+	0.0330336i
$91$	1.59864	+	2.00464i	0.167583	+	0.210143i
$92$			6.67078i			0.695477i
$93$			3.24962i			0.336969i
$94$	−5.98156	−	7.50064i	−0.616951	−	0.773632i
$95$	10.4850	−	14.0066i	1.07574	−	1.43704i
$96$	−1.17567	+	1.47424i	−0.119991	+	0.150464i
$97$	5.51211	−	11.4460i	0.559670	−	1.16217i	−0.408705	−	0.912666i	$-0.634020\pi$
$97$	5.51211	−	11.4460i	0.559670	−	1.16217i	0.968375	−	0.249500i	$-0.0802661\pi$
$98$	6.60546	−	1.50765i	0.667252	−	0.152296i
$99$	0.214496	+	0.268969i	0.0215577	+	0.0270325i
$100$	0.812310	−	4.93357i	0.0812310	−	0.493357i
$101$	−6.30357	+	3.03564i	−0.627229	+	0.302057i	−0.720364	−	0.693596i	$-0.756025\pi$
$101$	−6.30357	+	3.03564i	−0.627229	+	0.302057i	0.0931355	+	0.995653i	$0.470311\pi$
$102$	8.26970	+	6.59487i	0.818822	+	0.652989i
$103$	12.5553	+	10.0125i	1.23711	+	0.986565i	0.999886	+	0.0151105i	$0.00480999\pi$
$103$	12.5553	+	10.0125i	1.23711	+	0.986565i	0.237227	+	0.971454i	$0.423761\pi$
$104$	−1.20371	+	5.27378i	−0.118033	+	0.517137i
$105$	−0.504136	−	1.93391i	−0.0491987	−	0.188731i
$106$	−4.45331	−	2.14460i	−0.432544	−	0.208302i
$107$	5.19649	+	1.18607i	0.502364	+	0.114661i	0.466191	−	0.884684i	$-0.345626\pi$
$107$	5.19649	+	1.18607i	0.502364	+	0.114661i	0.0361731	+	0.999346i	$0.488483\pi$
$108$	4.49368	+	1.02565i	0.432404	+	0.0986935i
$109$	2.64092	+	1.27180i	0.252954	+	0.121816i	0.556065	−	0.831139i	$-0.312311\pi$
$109$	2.64092	+	1.27180i	0.252954	+	0.121816i	−0.303110	+	0.952956i	$0.598025\pi$
$110$	−1.33980	+	0.349262i	−0.127745	+	0.0333008i
$111$	−3.70079	+	16.2142i	−0.351263	+	1.53898i
$112$	−0.370583	−	0.295530i	−0.0350168	−	0.0279250i
$113$	3.01120	+	2.40135i	0.283270	+	0.225900i	0.754808	−	0.655945i	$-0.227730\pi$
$113$	3.01120	+	2.40135i	0.283270	+	0.225900i	−0.471539	+	0.881845i	$0.656301\pi$
$114$	13.2931	−	6.40162i	1.24501	−	0.599567i
$115$	−0.456474	−	14.9093i	−0.0425664	−	1.39030i
$116$	2.00284	+	2.51148i	0.185959	+	0.233185i
$117$	−2.93008	+	0.668772i	−0.270886	+	0.0618280i
$118$	1.28459	−	2.66747i	0.118256	−	0.245561i
$119$	−1.65776	+	2.07877i	−0.151967	+	0.190560i
$120$	2.52677	−	3.37541i	0.230661	−	0.308132i
$121$	−6.61933	−	8.30038i	−0.601758	−	0.754580i
$122$			1.15854i			0.104889i
$123$			2.77870i			0.250547i
$124$	−1.07450	−	1.34738i	−0.0964927	−	0.120998i
$125$	−1.47793	+	11.0822i	−0.132190	+	0.991224i
$126$	0.0586005	−	0.256745i	0.00522054	−	0.0228727i
$127$	4.18848	−	0.955992i	0.371667	−	0.0848306i	−0.0326075	−	0.999468i	$-0.510381\pi$
$127$	4.18848	−	0.955992i	0.371667	−	0.0848306i	0.404275	+	0.914638i	$0.367524\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−10.4429	−	6.62096i	−0.919443	−	0.582943i
$130$	2.32943	−	11.8694i	0.204305	−	1.04101i
$131$	1.00510	+	4.40362i	0.0878159	+	0.384746i	0.999668	−	0.0257727i	$-0.00820462\pi$
$131$	1.00510	+	4.40362i	0.0878159	+	0.384746i	−0.911852	+	0.410519i	$0.865347\pi$
$132$	−1.13831	−	0.259812i	−0.0990773	−	0.0226137i
$133$	1.60919	+	3.34151i	0.139534	+	0.289746i
$134$	6.42946	+	8.06229i	0.555421	+	0.696476i
$135$	−10.1136	−	1.98486i	−0.870444	−	0.170829i
$136$	−5.60945			−0.481007
$137$	−11.6960	+	9.32724i	−0.999256	+	0.796880i	−0.979196	−	0.202919i	$-0.934957\pi$
$137$	−11.6960	+	9.32724i	−0.999256	+	0.796880i	−0.0200601	+	0.999799i	$0.506386\pi$
$138$	5.45766	−	11.3329i	0.464587	−	0.964724i
$139$	−7.79921	+	9.77990i	−0.661521	+	0.829521i	−0.993508	−	0.113763i	$-0.963709\pi$
$139$	−7.79921	+	9.77990i	−0.661521	+	0.829521i	0.331987	+	0.943284i	$0.392281\pi$
$140$	0.848484	+	0.635158i	0.0717100	+	0.0536806i
$141$	4.02543	+	17.6366i	0.339002	+	1.48527i
$142$	−12.2651	+	9.78107i	−1.02926	+	0.820810i
$143$	−3.26554	+	0.745338i	−0.273078	+	0.0623283i
$144$	0.500573	−	0.241063i	0.0417144	−	0.0200886i
$145$	−4.64825	−	5.47617i	−0.386016	−	0.454771i
$146$	5.41942	−	6.79574i	0.448515	−	0.562420i
$147$	−12.4554	−	2.84287i	−1.02731	−	0.234476i
$148$	−3.82684	−	7.94651i	−0.314564	−	0.653200i
$149$	−4.57828	−	2.20478i	−0.375068	−	0.180623i	0.236847	−	0.971547i	$-0.423886\pi$
$149$	−4.57828	−	2.20478i	−0.375068	−	0.180623i	−0.611914	+	0.790924i	$0.709600\pi$
$150$	−5.41640	+	7.71702i	−0.442247	+	0.630092i
$151$	−0.933584	+	4.09030i	−0.0759740	+	0.332864i	−0.998604	−	0.0528226i	$-0.983178\pi$
$151$	−0.933584	+	4.09030i	−0.0759740	+	0.332864i	0.922630	+	0.385686i	$0.126035\pi$
$152$	−3.39495	+	7.04969i	−0.275367	+	0.571806i
$153$	−1.35223	−	2.80794i	−0.109322	−	0.227008i
$154$	0.0653094	−	0.286139i	0.00526278	−	0.0230578i
$155$	2.49372	+	2.93789i	0.200301	+	0.235977i
$156$	6.35968	−	7.97478i	0.509182	−	0.638494i
$157$	10.5990	+	22.0091i	0.845895	+	1.75652i	0.623957	+	0.781459i	$0.285524\pi$
$157$	10.5990	+	22.0091i	0.845895	+	1.75652i	0.221938	+	0.975061i	$0.428762\pi$
$158$	−7.30134	+	1.66648i	−0.580863	+	0.132578i
$159$	5.81110	+	7.28689i	0.460850	+	0.577888i
$160$	0.0684288	+	2.23502i	0.00540977	+	0.176694i
$161$	2.84878	+	1.37190i	0.224516	+	0.108121i
$162$	−8.09829	−	6.45817i	−0.636261	−	0.507402i
$163$	−0.109614	+	0.227615i	−0.00858561	+	0.0178282i	−0.905218	−	0.424948i	$-0.860292\pi$
$163$	−0.109614	+	0.227615i	−0.00858561	+	0.0178282i	0.896632	+	0.442777i	$0.146007\pi$
$164$	−0.918788	−	1.15212i	−0.0717453	−	0.0899658i
$165$	2.56193	+	0.502792i	0.199446	+	0.0391423i
$166$	−12.1935			−0.946399
$167$	−3.05089	+	2.43300i	−0.236085	+	0.188271i	−0.734385	−	0.678733i	$-0.762529\pi$
$167$	−3.05089	+	2.43300i	−0.236085	+	0.188271i	0.498300	+	0.867005i	$0.333958\pi$
$168$	0.387795	+	0.805264i	0.0299190	+	0.0621275i
$169$	3.61857	−	15.8540i	0.278351	−	1.21954i
$170$	12.5372	−	0.383848i	0.961563	−	0.0294398i
$171$	−4.34728			−0.332445
$172$	6.51913	−	0.707747i	0.497079	−	0.0539652i
$173$		−	16.1166i		−	1.22532i	−0.790345	−	0.612662i	$-0.790099\pi$
$173$		−	16.1166i		−	1.22532i	0.790345	−	0.612662i	$-0.209901\pi$
$174$	−1.34786	−	5.90535i	−0.102181	−	0.447684i
$175$	−1.93984	−	1.36153i	−0.146638	−	0.102922i
$176$	0.557882	−	0.268662i	0.0420519	−	0.0202511i
$177$	−4.36475	+	3.48077i	−0.328075	+	0.261631i
$178$			5.16487i			0.387124i
$179$	18.8664			1.41014			0.705071	−	0.709137i	$-0.250915\pi$
$179$	18.8664			1.41014			0.705071	+	0.709137i	$0.250915\pi$
$180$	−1.10229	+	0.573035i	−0.0821602	+	0.0427115i
$181$	−9.98978	−	4.81082i	−0.742534	−	0.357586i	0.0240660	−	0.999710i	$-0.492339\pi$
$181$	−9.98978	−	4.81082i	−0.742534	−	0.357586i	−0.766600	+	0.642125i	$0.778053\pi$
$182$	2.00464	+	1.59864i	0.148593	+	0.118499i
$183$	0.947853	−	1.96824i	0.0700673	−	0.145496i
$184$	1.48439	+	6.50353i	0.109431	+	0.479447i
$185$	9.09684	+	17.4988i	0.668813	+	1.28653i
$186$	0.723108	+	3.16814i	0.0530208	+	0.232299i
$187$	−1.50705	−	3.12941i	−0.110206	−	0.228845i
$188$	−7.50064	−	5.98156i	−0.547041	−	0.436250i
$189$	1.36217	−	1.70811i	0.0990833	−	0.124247i
$190$	7.10539	−	15.9885i	0.515479	−	1.15993i
$191$	−1.13752	+	0.547799i	−0.0823078	+	0.0396373i	−0.474585	−	0.880210i	$-0.657402\pi$
$191$	−1.13752	+	0.547799i	−0.0823078	+	0.0396373i	0.392277	+	0.919847i	$0.371687\pi$
$192$	−0.818143	+	1.69889i	−0.0590444	+	0.122607i
$193$	−17.8306	−	4.06972i	−1.28347	−	0.292945i	−0.474222	−	0.880405i	$-0.657271\pi$
$193$	−17.8306	−	4.06972i	−1.28347	−	0.292945i	−0.809253	+	0.587460i	$0.800128\pi$
$194$	2.82693	−	12.3856i	0.202962	−	0.889234i
$195$	−13.6683	+	18.2590i	−0.978808	+	1.30755i
$196$	6.10436	−	2.93971i	0.436026	−	0.209979i
$197$	−24.6262	−	5.62077i	−1.75455	−	0.400464i	−0.780202	−	0.625528i	$-0.784884\pi$
$197$	−24.6262	−	5.62077i	−1.75455	−	0.400464i	−0.974344	+	0.225065i	$0.927741\pi$
$198$	0.268969	+	0.214496i	0.0191148	+	0.0152436i
$199$	−1.06268	+	1.33256i	−0.0753313	+	0.0944625i	−0.818069	−	0.575120i	$-0.804955\pi$
$199$	−1.06268	+	1.33256i	−0.0753313	+	0.0944625i	0.742738	+	0.669582i	$0.233527\pi$
$200$	−0.305880	−	4.99063i	−0.0216290	−	0.352891i
$201$	−4.32685	−	18.9572i	−0.305193	−	1.33714i
$202$	−5.47003	+	4.36221i	−0.384870	+	0.306924i
$203$	1.48444	−	0.338814i	0.104187	−	0.0237801i
$204$	9.52986	+	4.58934i	0.667223	+	0.321318i
$205$	2.13235	+	2.51215i	0.148930	+	0.175456i
$206$	14.4685	+	6.96768i	1.00807	+	0.485461i
$207$	−2.89766	+	2.31081i	−0.201401	+	0.160612i
$208$			5.40941i			0.375075i
$209$	−4.84499			−0.335135
$210$	−0.921833	−	1.77325i	−0.0636125	−	0.122366i
$211$	−5.62106	+	2.70696i	−0.386970	+	0.186355i	−0.617245	−	0.786771i	$-0.711751\pi$
$211$	−5.62106	+	2.70696i	−0.386970	+	0.186355i	0.230276	+	0.973125i	$0.426037\pi$
$212$	−4.81887	−	1.09988i	−0.330962	−	0.0755398i
$213$	28.8394	−	6.58240i	1.97604	−	0.451019i
$214$	5.33013			0.364360
$215$	−14.5220	+	2.02793i	−0.990390	+	0.138303i
$216$	4.60924			0.313619
$217$	−0.796381	+	0.181769i	−0.0540619	+	0.0123393i
$218$	2.85771	+	0.652254i	0.193549	+	0.0441762i
$219$	−14.7669	+	7.11137i	−0.997855	+	0.480542i
$220$	−1.22849	+	0.638640i	−0.0828250	+	0.0430571i
$221$	30.3438			2.04115
$222$			16.6312i			1.11621i
$223$	−5.82252	+	4.64331i	−0.389905	+	0.310939i	−0.798748	−	0.601666i	$-0.794504\pi$
$223$	−5.82252	+	4.64331i	−0.389905	+	0.310939i	0.408843	+	0.912605i	$0.365932\pi$
$224$	−0.427054	−	0.205658i	−0.0285337	−	0.0137411i
$225$	2.42444	−	1.35617i	0.161629	−	0.0904116i
$226$	3.47005	+	1.67109i	0.230825	+	0.111159i
$227$	3.29207	−	0.751393i	0.218502	−	0.0498717i	−0.111868	−	0.993723i	$-0.535683\pi$
$227$	3.29207	−	0.751393i	0.218502	−	0.0498717i	0.330370	+	0.943851i	$0.392826\pi$
$228$	11.5353	−	9.19911i	0.763945	−	0.609226i
$229$	0.571143	+	2.50234i	0.0377422	+	0.165359i	0.990287	−	0.139040i	$-0.0444015\pi$
$229$	0.571143	+	2.50234i	0.0377422	+	0.165359i	−0.952545	+	0.304399i	$0.901544\pi$
$230$	−3.76267	−	14.4340i	−0.248103	−	0.951747i
$231$	−0.345057	+	0.432687i	−0.0227031	+	0.0284687i
$232$	2.51148	+	2.00284i	0.164887	+	0.131493i
$233$	−3.52340	−	0.804193i	−0.230825	−	0.0526844i	0.105543	−	0.994415i	$-0.466342\pi$
$233$	−3.52340	−	0.804193i	−0.230825	−	0.0526844i	−0.336369	+	0.941730i	$0.609199\pi$
$234$	−2.70780	+	1.30401i	−0.177015	+	0.0852457i
$235$	17.1734	+	12.8557i	1.12027	+	0.838610i
$236$	0.658811	−	2.88644i	0.0428850	−	0.187891i
$237$	13.7676	+	3.14237i	0.894302	+	0.204119i
$238$	−1.15363	+	2.39554i	−0.0747787	+	0.155280i
$239$	−13.6906	+	6.59305i	−0.885572	+	0.426469i	−0.820656	−	0.571422i	$-0.806392\pi$
$239$	−13.6906	+	6.59305i	−0.885572	+	0.426469i	−0.0649153	+	0.997891i	$0.520678\pi$
$240$	1.71231	−	3.85304i	0.110529	−	0.248713i
$241$	11.1731	−	14.0106i	0.719722	−	0.902503i	−0.278600	−	0.960407i	$-0.589870\pi$
$241$	11.1731	−	14.0106i	0.719722	−	0.902503i	0.998322	+	0.0579045i	$0.0184419\pi$
$242$	−8.30038	−	6.61933i	−0.533569	−	0.425507i
$243$	2.47478	+	5.13894i	0.158758	+	0.329663i
$244$	0.257800	+	1.12949i	0.0165039	+	0.0723085i
$245$	−13.4422	+	6.98802i	−0.858792	+	0.446448i
$246$	0.618320	+	2.70904i	0.0394226	+	0.172722i
$247$	18.3647	−	38.1347i	1.16852	−	2.42645i
$248$	−1.34738	−	1.07450i	−0.0855585	−	0.0682306i
$249$	20.7154	+	9.97603i	1.31279	+	0.632205i
$250$	1.02515	+	11.1332i	0.0648362	+	0.704128i
$251$	1.68422			0.106307			0.0531534	−	0.998586i	$-0.483073\pi$
$251$	1.68422			0.106307			0.0531534	+	0.998586i	$0.483073\pi$
$252$		−	0.263348i		−	0.0165894i
$253$	−3.22940	+	2.57536i	−0.203031	+	0.161912i
$254$	3.87073	−	1.86405i	0.242871	−	0.116961i
$255$	−21.6135	−	9.60515i	−1.35349	−	0.601498i
$256$	−0.222521	−	0.974928i	−0.0139076	−	0.0609330i
$257$			23.1077i			1.44142i	0.693239	+	0.720708i	$0.256183\pi$
$257$			23.1077i			1.44142i	−0.693239	+	0.720708i	$0.743817\pi$
$258$	−11.6543	−	4.13120i	−0.725568	−	0.257197i
$259$	−4.18061			−0.259770
$260$	−0.370159	−	12.0901i	−0.0229563	−	0.749799i
$261$	−0.397142	+	1.73999i	−0.0245825	+	0.107703i
$262$	1.95980	+	4.06956i	0.121077	+	0.251418i
$263$	−6.97473	+	5.56216i	−0.430080	+	0.342978i	−0.814482	−	0.580188i	$-0.802979\pi$
$263$	−6.97473	+	5.56216i	−0.430080	+	0.342978i	0.384402	+	0.923166i	$0.374408\pi$
$264$	−1.16758			−0.0718599
$265$	10.8455	+	2.12850i	0.666237	+	0.130753i
$266$	2.31240	+	2.89965i	0.141782	+	0.177789i
$267$	4.22561	−	8.77456i	0.258603	−	0.536995i
$268$	8.06229	+	6.42946i	0.492483	+	0.392742i
$269$	−10.5513	−	5.08125i	−0.643326	−	0.309810i	0.0836265	−	0.996497i	$-0.473350\pi$
$269$	−10.5513	−	5.08125i	−0.643326	−	0.309810i	−0.726953	+	0.686688i	$0.759064\pi$
$270$	−10.3017	+	0.315405i	−0.626945	+	0.0191949i
$271$	8.86633	+	11.1180i	0.538591	+	0.675372i	0.974440	−	0.224648i	$-0.0721232\pi$
$271$	8.86633	+	11.1180i	0.538591	+	0.675372i	−0.435849	+	0.900020i	$0.643552\pi$
$272$	−5.46881	+	1.24822i	−0.331595	+	0.0756845i
$273$	−2.09774	−	4.35600i	−0.126961	−	0.263637i
$274$	−9.32724	+	11.6960i	−0.563479	+	0.706580i
$275$	2.70201	−	1.51144i	0.162937	−	0.0911431i
$276$	2.79901	−	12.2632i	0.168480	−	0.738161i
$277$	−8.04937	−	16.7147i	−0.483640	−	1.00429i	−0.989882	−	0.141896i	$-0.954680\pi$
$277$	−8.04937	−	16.7147i	−0.483640	−	1.00429i	0.506242	−	0.862391i	$-0.331034\pi$
$278$	−5.42744	+	11.2702i	−0.325516	+	0.675941i
$279$	0.213061	−	0.933482i	0.0127556	−	0.0558861i
$280$	0.968547	+	0.430428i	0.0578817	+	0.0257230i
$281$	−17.1365	−	8.25249i	−1.02228	−	0.492302i	−0.153836	−	0.988096i	$-0.549163\pi$
$281$	−17.1365	−	8.25249i	−1.02228	−	0.492302i	−0.868440	+	0.495794i	$0.834877\pi$
$282$	7.84901	+	16.2986i	0.467402	+	0.970569i
$283$	−13.9582	−	3.18586i	−0.829727	−	0.189380i	−0.213495	−	0.976944i	$-0.568485\pi$
$283$	−13.9582	−	3.18586i	−0.829727	−	0.189380i	−0.616232	+	0.787564i	$0.711342\pi$
$284$	−9.78107	+	12.2651i	−0.580400	+	0.727799i
$285$	−25.1522	+	21.3495i	−1.48989	+	1.26464i
$286$	−3.01781	+	1.45330i	−0.178447	+	0.0859355i
$287$	−0.680975	+	0.155428i	−0.0401967	+	0.00917463i
$288$	0.434381	−	0.346407i	0.0255961	−	0.0204122i
$289$	3.21898	+	14.1033i	0.189352	+	0.829604i
$290$	−5.75027	−	4.30454i	−0.337668	−	0.252771i
$291$	−14.9358	+	18.7290i	−0.875554	+	1.09791i
$292$	3.77135	−	7.83129i	0.220702	−	0.458292i
$293$	−8.18857	+	6.53017i	−0.478382	+	0.381497i	−0.832785	−	0.553596i	$-0.813255\pi$
$293$	−8.18857	+	6.53017i	−0.478382	+	0.381497i	0.354404	+	0.935092i	$0.384684\pi$
$294$	−12.7758			−0.745097
$295$	−1.27494	+	6.49634i	−0.0742299	+	0.378231i
$296$	−5.49916	−	6.89573i	−0.319632	−	0.400806i
$297$	1.23833	+	2.57141i	0.0718550	+	0.149208i
$298$	−4.95411	−	1.13074i	−0.286984	−	0.0655022i
$299$	−8.02967	−	35.1803i	−0.464368	−	2.03453i
$300$	−3.56340	+	8.72881i	−0.205733	+	0.503958i
$301$	1.03847	−	2.92957i	0.0598563	−	0.168858i
$302$			4.19549i			0.241423i
$303$	12.8619	−	2.93565i	0.738897	−	0.168648i
$304$	−1.74113	+	7.62839i	−0.0998607	+	0.437518i
$305$	−0.653478	−	2.50680i	−0.0374180	−	0.143539i
$306$	−1.94315	−	2.43664i	−0.111083	−	0.139293i
$307$		−	10.6781i		−	0.609429i	−0.952444	−	0.304715i	$-0.901439\pi$
$307$		−	10.6781i		−	0.609429i	0.952444	−	0.304715i	$-0.0985611\pi$
$308$		−	0.293498i		−	0.0167236i
$309$	−18.8799	−	23.6747i	−1.07404	−	1.34681i
$310$	3.08494	+	2.30932i	0.175213	+	0.131161i
$311$	−7.13495	+	8.94695i	−0.404586	+	0.507335i	−0.941829	−	0.336093i	$-0.890894\pi$
$311$	−7.13495	+	8.94695i	−0.404586	+	0.507335i	0.537243	+	0.843428i	$0.319466\pi$
$312$	4.42567	−	9.19000i	0.250554	−	0.520281i
$313$	−7.29710	+	1.66551i	−0.412456	+	0.0941405i	−0.423714	−	0.905796i	$-0.639274\pi$
$313$	−7.29710	+	1.66551i	−0.412456	+	0.0941405i	0.0112574	+	0.999937i	$0.496417\pi$
$314$	15.2308	+	19.0988i	0.859523	+	1.07781i
$315$	0.0180206	+	0.588588i	0.00101535	+	0.0331632i
$316$	−6.74745	+	3.24940i	−0.379574	+	0.182793i
$317$	1.12294	+	0.895512i	0.0630704	+	0.0502970i	0.654518	−	0.756047i	$-0.272872\pi$
$317$	1.12294	+	0.895512i	0.0630704	+	0.0502970i	−0.591447	+	0.806344i	$0.701443\pi$
$318$	7.28689	+	5.81110i	0.408629	+	0.325870i
$319$	−0.442609	+	1.93920i	−0.0247814	+	0.108574i
$320$	0.564052	+	2.16376i	0.0315315	+	0.120958i
$321$	−9.05532	−	4.36081i	−0.505418	−	0.243397i
$322$	3.08263	+	0.703591i	0.171788	+	0.0392096i
$323$	42.7911	+	9.76679i	2.38096	+	0.543439i
$324$	−9.33232	−	4.49421i	−0.518462	−	0.249678i
$325$	1.65463	+	26.9964i	0.0917822	+	1.49749i
$326$	−0.0562163	+	0.246300i	−0.00311353	+	0.0136413i
$327$	−4.32131	−	3.44613i	−0.238969	−	0.190571i
$328$	−1.15212	−	0.918788i	−0.0636154	−	0.0507316i
$329$	−4.09702	+	1.97302i	−0.225876	+	0.108776i
$330$	2.60958	−	0.0798965i	0.143652	−	0.00439816i
$331$	12.5181	+	15.6972i	0.688056	+	0.862795i	0.996068	−	0.0885872i	$-0.0282352\pi$
$331$	12.5181	+	15.6972i	0.688056	+	0.862795i	−0.308012	+	0.951382i	$0.599664\pi$
$332$	−11.8878	+	2.71331i	−0.652427	+	0.148912i
$333$	2.12617	−	4.41504i	0.116513	−	0.241942i
$334$	−2.43300	+	3.05089i	−0.133128	+	0.166937i
$335$	−18.4593	−	13.8183i	−1.00854	−	0.754973i
$336$	0.557260	+	0.698782i	0.0304010	+	0.0381217i
$337$		−	0.710269i		−	0.0386908i	−0.999813	−	0.0193454i	$-0.993842\pi$
$337$		−	0.710269i		−	0.0386908i	0.999813	−	0.0193454i	$-0.00615822\pi$
$338$		−	16.2617i		−	0.884520i
$339$	−4.52806	−	5.67800i	−0.245930	−	0.308387i
$340$	12.1375	−	3.16402i	0.658248	−	0.171593i
$341$	0.237454	−	1.04035i	0.0128588	−	0.0563383i
$342$	−4.23829	+	0.967361i	−0.229180	+	0.0523089i
$343$		−	6.52942i		−	0.352556i
$344$	6.19820	−	2.14065i	0.334184	−	0.115416i
$345$	−5.41668	+	27.6001i	−0.291624	+	1.48594i
$346$	−3.58628	−	15.7125i	−0.192800	−	0.844711i
$347$	6.36655	+	1.45312i	0.341774	+	0.0780078i	0.389963	−	0.920830i	$-0.372488\pi$
$347$	6.36655	+	1.45312i	0.341774	+	0.0780078i	−0.0481887	+	0.998838i	$0.515345\pi$
$348$	−2.62813	−	5.45737i	−0.140883	−	0.292546i
$349$	15.4581	+	19.3838i	0.827451	+	1.03759i	0.998629	+	0.0523505i	$0.0166713\pi$
$349$	15.4581	+	19.3838i	0.827451	+	1.03759i	−0.171178	+	0.985240i	$0.554757\pi$
$350$	−2.19418	−	0.895738i	−0.117284	−	0.0478792i
$351$	−24.9333			−1.33084
$352$	0.484112	−	0.386066i	0.0258032	−	0.0205774i
$353$	6.44534	−	13.3839i	0.343051	−	0.712352i	−0.656051	−	0.754716i	$-0.727775\pi$
$353$	6.44534	−	13.3839i	0.343051	−	0.712352i	0.999102	+	0.0423639i	$0.0134889\pi$
$354$	−3.48077	+	4.36475i	−0.185001	+	0.231984i
$355$	21.0216	−	28.0820i	1.11571	−	1.49044i
$356$	1.14929	+	5.03538i	0.0609124	+	0.266875i
$357$	3.91979	−	3.12593i	0.207457	−	0.165442i
$358$	18.3934	−	4.19817i	0.972121	−	0.221880i
$359$	30.3042	−	14.5937i	1.59939	−	0.770227i	0.599839	−	0.800121i	$-0.295231\pi$
$359$	30.3042	−	14.5937i	1.59939	−	0.770227i	0.999553	+	0.0298939i	$0.00951695\pi$
$360$	−0.947146	+	0.803951i	−0.0499190	+	0.0423720i
$361$	26.3262	−	33.0119i	1.38559	−	1.73747i
$362$	−10.8098	−	2.46727i	−0.568152	−	0.129677i
$363$	8.68589	+	18.0364i	0.455891	+	0.946668i
$364$	2.31011	+	1.11249i	0.121083	+	0.0583103i
$365$	−7.89316	+	17.7612i	−0.413147	+	0.929662i
$366$	0.486114	−	2.12981i	0.0254096	−	0.111327i
$367$	2.98803	−	6.20470i	0.155974	−	0.323883i	−0.808309	−	0.588759i	$-0.799617\pi$
$367$	2.98803	−	6.20470i	0.155974	−	0.323883i	0.964282	+	0.264876i	$0.0853311\pi$
$368$	2.89434	+	6.01017i	0.150878	+	0.313302i
$369$	0.182186	−	0.798208i	0.00948421	−	0.0415531i
$370$	12.7626	+	15.0358i	0.663496	+	0.781674i
$371$	−1.46075	+	1.83172i	−0.0758382	+	0.0950981i
$372$	1.40996	+	2.92780i	0.0731028	+	0.151799i
$373$	−33.1534	+	7.56705i	−1.71662	+	0.391807i	−0.963843	−	0.266470i	$-0.914143\pi$
$373$	−33.1534	+	7.56705i	−1.71662	+	0.391807i	−0.752775	+	0.658277i	$0.771285\pi$
$374$	−2.16562	−	2.71560i	−0.111982	−	0.140420i
$375$	7.36697	−	19.7529i	0.380429	−	1.02004i
$376$	−8.64361	−	4.16254i	−0.445760	−	0.214667i
$377$	−13.5856	−	10.8342i	−0.699696	−	0.557989i
$378$	0.947928	−	1.96839i	0.0487562	−	0.101243i
$379$	−8.11445	−	10.1752i	−0.416811	−	0.522665i	0.528457	−	0.848960i	$-0.322771\pi$
$379$	−8.11445	−	10.1752i	−0.416811	−	0.522665i	−0.945268	+	0.326296i	$0.894199\pi$
$380$	3.36946	−	17.1688i	0.172850	−	0.880738i
$381$	−8.10102			−0.415028
$382$	−0.987100	+	0.787186i	−0.0505044	+	0.0402759i
$383$	5.49185	+	11.4039i	0.280620	+	0.582714i	0.992869	−	0.119214i	$-0.0380373\pi$
$383$	5.49185	+	11.4039i	0.280620	+	0.582714i	−0.712248	+	0.701927i	$0.752323\pi$
$384$	−0.419592	+	1.83835i	−0.0214122	+	0.0938130i
$385$	0.0200837	+	0.655974i	0.00102356	+	0.0334315i
$386$	−18.2892			−0.930893
$387$	2.56571	+	2.58662i	0.130422	+	0.131485i
$388$		−	12.7041i		−	0.644953i
$389$	7.93717	+	34.7750i	0.402431	+	1.76316i	0.617506	+	0.786566i	$0.288143\pi$
$389$	7.93717	+	34.7750i	0.402431	+	1.76316i	−0.215076	+	0.976597i	$0.569000\pi$
$390$	−9.26261	+	20.8427i	−0.469030	+	1.05541i
$391$	33.7138	−	16.2357i	1.70498	−	0.821074i
$392$	5.29717	−	4.22435i	0.267547	−	0.213362i
$393$		−	8.51714i		−	0.429633i
$394$	−25.2595			−1.27256
$395$	14.8583	−	7.72420i	0.747604	−	0.388647i
$396$	0.309956	+	0.149267i	0.0155759	+	0.00750094i
$397$	15.9177	+	12.6939i	0.798886	+	0.637091i	0.935417	−	0.353545i	$-0.115024\pi$
$397$	15.9177	+	12.6939i	0.798886	+	0.637091i	−0.136531	+	0.990636i	$0.543595\pi$
$398$	−0.739514	+	1.53562i	−0.0370685	+	0.0769735i
$399$	−1.55618	−	6.81807i	−0.0779065	−	0.341331i
$400$	−1.40873	−	4.79744i	−0.0704366	−	0.239872i
$401$	−4.42331	−	19.3798i	−0.220889	−	0.967780i	−0.956811	−	0.290712i	$-0.906108\pi$
$401$	−4.42331	−	19.3798i	−0.220889	−	0.967780i	0.735921	−	0.677067i	$-0.236749\pi$
$402$	−8.43674	−	17.5191i	−0.420786	−	0.873772i
$403$	7.28851	+	5.81239i	0.363067	+	0.289536i
$404$	−4.36221	+	5.47003i	−0.217028	+	0.272144i
$405$	21.1655	+	9.40605i	1.05172	+	0.467390i
$406$	1.37183	−	0.660638i	0.0680827	−	0.0327869i
$407$	2.36959	−	4.92050i	0.117456	−	0.243900i
$408$	10.3121	+	2.35368i	0.510527	+	0.116525i
$409$	2.21483	−	9.70381i	0.109516	−	0.479822i	−0.890190	−	0.455589i	$-0.849429\pi$
$409$	2.21483	−	9.70381i	0.109516	−	0.479822i	0.999706	−	0.0242329i	$-0.00771434\pi$
$410$	2.63789	+	1.97467i	0.130276	+	0.0975221i
$411$	25.4150	−	12.2392i	1.25363	−	0.603715i
$412$	15.6562	+	3.57343i	0.771327	+	0.176050i
$413$	−1.09717	−	0.874968i	−0.0539884	−	0.0430543i
$414$	−2.31081	+	2.89766i	−0.113570	+	0.142412i
$415$	26.3838	−	6.87777i	1.29513	−	0.337616i
$416$	1.20371	+	5.27378i	0.0590166	+	0.258568i
$417$	18.4413	−	14.7064i	0.903073	−	0.720176i
$418$	−4.72351	+	1.07811i	−0.231035	+	0.0527322i
$419$	−4.99401	−	2.40499i	−0.243973	−	0.117491i	0.307902	−	0.951418i	$-0.400373\pi$
$419$	−4.99401	−	2.40499i	−0.243973	−	0.117491i	−0.551875	+	0.833927i	$0.686087\pi$
$420$	−1.29330	−	1.52366i	−0.0631068	−	0.0743470i
$421$	26.1233	+	12.5803i	1.27317	+	0.613127i	0.943626	−	0.331013i	$-0.107390\pi$
$421$	26.1233	+	12.5803i	1.27317	+	0.613127i	0.329545	+	0.944140i	$0.393105\pi$
$422$	−4.87777	+	3.88989i	−0.237446	+	0.189357i
$423$		−	5.33019i		−	0.259163i
$424$	−4.94280			−0.240044
$425$	−26.9110	+	7.90221i	−1.30538	+	0.383314i
$426$	26.6516	−	12.8347i	1.29127	−	0.621845i
$427$	0.535373	+	0.122195i	0.0259085	+	0.00591345i
$428$	5.19649	−	1.18607i	0.251182	−	0.0573306i
$429$	6.31594			0.304937
$430$	−13.7066	+	5.20852i	−0.660992	+	0.251177i
$431$	22.2177			1.07019			0.535094	−	0.844792i	$-0.320276\pi$
$431$	22.2177			1.07019			0.535094	+	0.844792i	$0.320276\pi$
$432$	4.49368	−	1.02565i	0.216202	−	0.0493467i
$433$	23.2256	+	5.30108i	1.11615	+	0.254754i	0.740532	−	0.672021i	$-0.234574\pi$
$433$	23.2256	+	5.30108i	1.11615	+	0.254754i	0.375617	+	0.926775i	$0.377431\pi$
$434$	−0.735967	+	0.354423i	−0.0353275	+	0.0170128i
$435$	6.24737	+	12.0175i	0.299538	+	0.576195i
$436$	2.93120			0.140379
$437$		−	52.1960i		−	2.49687i
$438$	−12.8142	+	10.2190i	−0.612288	+	0.488284i
$439$	11.9789	+	5.76872i	0.571720	+	0.275326i	0.697326	−	0.716754i	$-0.254373\pi$
$439$	11.9789	+	5.76872i	0.571720	+	0.275326i	−0.125606	+	0.992080i	$0.540087\pi$
$440$	−1.05558	+	0.895993i	−0.0503229	+	0.0427148i
$441$	3.39155	+	1.63328i	0.161502	+	0.0777754i
$442$	29.5830	−	6.75214i	1.40712	−	0.321166i
$443$	−23.3305	+	18.6054i	−1.10847	+	0.883972i	−0.993992	−	0.109455i	$-0.965090\pi$
$443$	−23.3305	+	18.6054i	−1.10847	+	0.883972i	−0.114473	+	0.993426i	$0.536518\pi$
$444$	3.70079	+	16.2142i	0.175631	+	0.769492i
$445$	−2.91326	−	11.1755i	−0.138102	−	0.529771i
$446$	−4.64331	+	5.82252i	−0.219867	+	0.275705i
$447$	7.49138	+	5.97418i	0.354330	+	0.282569i
$448$	−0.462110	−	0.105474i	−0.0218326	−	0.00498316i
$449$	6.85719	−	3.30225i	0.323611	−	0.155843i	−0.265024	−	0.964242i	$-0.585380\pi$
$449$	6.85719	−	3.30225i	0.323611	−	0.155843i	0.588635	+	0.808399i	$0.299666\pi$
$450$	2.06188	−	1.86166i	0.0971978	−	0.0877595i
$451$	0.203044	−	0.889592i	0.00956095	−	0.0418893i
$452$	3.75490	+	0.857032i	0.176616	+	0.0403114i
$453$	3.43251	−	7.12768i	0.161273	−	0.334888i
$454$	3.04233	−	1.46511i	0.142784	−	0.0687609i
$455$	−5.23926	−	2.32836i	−0.245620	−	0.109155i
$456$	9.19911	−	11.5353i	0.430788	−	0.540191i
$457$	25.6943	+	20.4905i	1.20193	+	0.958505i	0.999783	−	0.0208510i	$-0.00663757\pi$
$457$	25.6943	+	20.4905i	1.20193	+	0.958505i	0.202144	+	0.979356i	$0.435209\pi$
$458$	1.11365	+	2.31251i	0.0520373	+	0.108057i
$459$	−5.75335	−	25.2071i	−0.268543	−	1.17657i
$460$	−6.88019	−	13.2348i	−0.320790	−	0.617076i
$461$	−6.81175	−	29.8442i	−0.317255	−	1.38998i	−0.842345	−	0.538938i	$-0.818826\pi$
$461$	−6.81175	−	29.8442i	−0.317255	−	1.38998i	0.525090	−	0.851047i	$-0.324032\pi$
$462$	−0.240123	+	0.498621i	−0.0111716	+	0.0231980i
$463$	−24.4574	−	19.5041i	−1.13663	−	0.906433i	−0.140140	−	0.990132i	$-0.544755\pi$
$463$	−24.4574	−	19.5041i	−1.13663	−	0.906433i	−0.996491	+	0.0836981i	$0.973327\pi$
$464$	2.89419	+	1.39377i	0.134359	+	0.0647041i
$465$	−3.35163	−	6.44722i	−0.155428	−	0.298983i
$466$	−3.61401			−0.167416
$467$		−	2.13928i		−	0.0989943i	−0.998774	−	0.0494971i	$-0.984238\pi$
$467$		−	2.13928i		−	0.0989943i	0.998774	−	0.0494971i	$-0.0157619\pi$
$468$	−2.34974	+	1.87386i	−0.108617	+	0.0866191i
$469$	4.40380	−	2.12076i	0.203349	−	0.0979275i
$470$	19.6035	+	8.71190i	0.904241	+	0.401850i
$471$	−10.2499	−	44.9078i	−0.472291	−	2.06924i
$472$		−	2.96067i		−	0.136276i
$473$	2.85945	+	2.88275i	0.131477	+	0.132549i
$474$	14.1217			0.648630
$475$	−6.35598	+	38.6031i	−0.291632	+	1.77123i
$476$	−0.591649	+	2.59218i	−0.0271182	+	0.118813i
$477$	−1.19153	−	2.47423i	−0.0545563	−	0.113287i
$478$	−11.8803	+	9.47419i	−0.543391	+	0.433340i
$479$	35.5888			1.62609			0.813046	−	0.582200i	$-0.197808\pi$
$479$	35.5888			1.62609			0.813046	+	0.582200i	$0.197808\pi$
$480$	0.812000	−	4.13747i	0.0370626	−	0.188849i
$481$	29.7472	+	37.3018i	1.35636	+	1.70082i
$482$	7.77530	−	16.1456i	0.354155	−	0.735411i
$483$	−4.66143	−	3.71736i	−0.212102	−	0.169146i
$484$	−9.56522	−	4.60637i	−0.434783	−	0.209380i
$485$	0.869327	+	28.3939i	0.0394741	+	1.28930i
$486$	3.55626	+	4.45941i	0.161315	+	0.202283i
$487$	−8.63298	+	1.97042i	−0.391198	+	0.0892883i	−0.413595	−	0.910461i	$-0.635727\pi$
$487$	−8.63298	+	1.97042i	−0.391198	+	0.0892883i	0.0223977	+	0.999749i	$0.492870\pi$
$488$	0.502672	+	1.04381i	0.0227549	+	0.0472510i
$489$	0.297014	−	0.372444i	0.0134314	−	0.0168425i
$490$	−11.5502	+	9.80399i	−0.521785	+	0.442899i
$491$	0.0466035	−	0.204183i	0.00210319	−	0.00921466i	−0.973865	−	0.227126i	$-0.927067\pi$
$491$	0.0466035	−	0.204183i	0.00210319	−	0.00921466i	0.975969	+	0.217911i	$0.0699243\pi$
$492$	1.20563	+	2.50353i	0.0543542	+	0.112868i
$493$	7.81828	−	16.2348i	0.352118	−	0.731180i
$494$	9.41848	−	41.2651i	0.423758	−	1.85660i
$495$	−0.702972	−	0.312405i	−0.0315962	−	0.0140415i
$496$	−1.55269	−	0.747738i	−0.0697180	−	0.0335744i
$497$	3.22629	+	6.69946i	0.144719	+	0.300512i
$498$	22.4159	+	5.11629i	1.00448	+	0.229267i
$499$	−19.8853	+	24.9353i	−0.890186	+	1.11626i	0.102403	+	0.994743i	$0.467347\pi$
$499$	−19.8853	+	24.9353i	−0.890186	+	1.11626i	−0.992590	+	0.121515i	$0.961225\pi$
$500$	3.47683	+	10.6260i	0.155488	+	0.475209i
$501$	6.62947	−	3.19258i	0.296183	−	0.142634i
$502$	1.64199	−	0.374773i	0.0732855	−	0.0167269i
$503$	−5.71637	+	4.55865i	−0.254880	+	0.203260i	−0.742591	−	0.669745i	$-0.766403\pi$
$503$	−5.71637	+	4.55865i	−0.254880	+	0.203260i	0.487711	+	0.873005i	$0.337832\pi$
$504$	−0.0586005	−	0.256745i	−0.00261027	−	0.0114363i
$505$	9.37531	−	12.5241i	0.417196	−	0.557317i
$506$	−2.57536	+	3.22940i	−0.114489	+	0.143565i
$507$	−13.3044	+	27.6269i	−0.590869	+	1.22695i
$508$	3.35890	−	2.67863i	0.149027	−	0.118845i
$509$	−20.2913			−0.899395			−0.449697	−	0.893181i	$-0.648468\pi$
$509$	−20.2913			−0.899395			−0.449697	+	0.893181i	$0.648468\pi$
$510$	−23.2089	−	4.55488i	−1.02771	−	0.201693i
$511$	−2.56877	−	3.22114i	−0.113636	−	0.142495i
$512$	−0.433884	−	0.900969i	−0.0191751	−	0.0398176i
$513$	−35.1611	−	8.02529i	−1.55240	−	0.354325i
$514$	5.14194	+	22.5283i	0.226801	+	0.993681i
$515$	−35.2365	−	6.91536i	−1.55271	−	0.304727i
$516$	−12.2814	−	1.43429i	−0.540660	−	0.0631410i
$517$		−	5.94043i		−	0.261260i
$518$	−4.07579	+	0.930273i	−0.179080	+	0.0408738i
$519$	−6.76240	+	29.6280i	−0.296836	+	1.30053i
$520$	−3.05119	−	11.7046i	−0.133803	−	0.513283i
$521$	−18.6386	−	23.3720i	−0.816571	−	1.02395i	−0.999169	−	0.0407599i	$-0.987022\pi$
$521$	−18.6386	−	23.3720i	−0.816571	−	1.02395i	0.182598	−	0.983188i	$-0.441549\pi$
$522$			1.78474i			0.0781159i
$523$			38.8211i			1.69753i	0.528773	+	0.848763i	$0.322652\pi$
$523$			38.8211i			1.69753i	−0.528773	+	0.848763i	$0.677348\pi$
$524$	2.81622	+	3.53143i	0.123027	+	0.154271i
$525$	2.99483	+	3.31691i	0.130705	+	0.144762i
$526$	−5.56216	+	6.97473i	−0.242522	+	0.304113i
$527$	−4.19440	+	8.70976i	−0.182711	+	0.379403i
$528$	−1.13831	+	0.259812i	−0.0495386	+	0.0113069i
$529$	−13.4046	−	16.8089i	−0.582810	−	0.730821i
$530$	11.0473	−	0.338230i	0.479862	−	0.0146918i
$531$	1.48203	−	0.713709i	0.0643147	−	0.0309723i
$532$	2.89965	+	2.31240i	0.125716	+	0.100255i
$533$	6.23231	+	4.97010i	0.269951	+	0.215279i
$534$	2.16714	−	9.49485i	0.0937813	−	0.410883i
$535$	−11.5331	+	3.00647i	−0.498620	+	0.129981i
$536$	9.29084	+	4.47423i	0.401303	+	0.193257i
$537$	−34.6831	−	7.91619i	−1.49669	−	0.341609i
$538$	−11.4175	−	2.60596i	−0.492242	−	0.112351i
$539$	3.77983	+	1.82027i	0.162809	+	0.0784047i
$540$	−9.97328	+	2.59985i	−0.429182	+	0.111880i
$541$	2.71115	−	11.8783i	0.116561	−	0.510689i	−0.882614	−	0.470098i	$-0.844219\pi$
$541$	2.71115	−	11.8783i	0.116561	−	0.510689i	0.999176	−	0.0405913i	$-0.0129242\pi$
$542$	11.1180	+	8.86633i	0.477560	+	0.380841i
$543$	16.3461	+	13.0356i	0.701480	+	0.559412i
$544$	−5.05394	+	2.43385i	−0.216686	+	0.104350i
$545$	−6.55130	+	0.200579i	−0.280627	+	0.00859185i
$546$	−3.01445	−	3.78000i	−0.129006	−	0.161769i
$547$	−2.03791	+	0.465140i	−0.0871349	+	0.0198880i	−0.265866	−	0.964010i	$-0.585658\pi$
$547$	−2.03791	+	0.465140i	−0.0871349	+	0.0198880i	0.178731	+	0.983898i	$0.442801\pi$
$548$	−6.49078	+	13.4782i	−0.277273	+	0.575762i
$549$	−0.401327	+	0.503248i	−0.0171282	+	0.0214781i
$550$	2.29793	−	2.07480i	0.0979843	−	0.0884696i
$551$	−15.6714	−	19.6513i	−0.667623	−	0.837173i
$552$		−	12.5786i		−	0.535382i
$553$			3.54979i			0.150952i
$554$	−11.5669	−	14.5045i	−0.491431	−	0.616235i
$555$	−9.38085	−	35.9858i	−0.398195	−	1.52751i
$556$	−2.78351	+	12.1953i	−0.118047	+	0.517198i
$557$	16.4444	−	3.75334i	0.696773	−	0.159034i	0.140558	−	0.990072i	$-0.455110\pi$
$557$	16.4444	−	3.75334i	0.696773	−	0.159034i	0.556215	+	0.831038i	$0.312253\pi$
$558$		−	0.957488i		−	0.0405337i
$559$	−33.5286	+	11.5796i	−1.41811	+	0.489766i
$560$	1.04004	+	0.204114i	0.0439498	+	0.00862539i
$561$	1.45740	+	6.38530i	0.0615316	+	0.269588i
$562$	−18.5432	−	4.23236i	−0.782197	−	0.178531i
$563$	−3.46500	−	7.19514i	−0.146032	−	0.303239i	0.815103	−	0.579315i	$-0.196680\pi$
$563$	−3.46500	−	7.19514i	−0.146032	−	0.303239i	−0.961136	+	0.276076i	$0.910966\pi$
$564$	11.2790	+	14.1434i	0.474932	+	0.595545i
$565$	−8.45093	−	1.65854i	−0.355533	−	0.0697754i
$566$	−14.3171			−0.601794
$567$	−3.83854	+	3.06113i	−0.161203	+	0.128555i
$568$	−6.80661	+	14.1341i	−0.285599	+	0.593052i
$569$	−6.47384	+	8.11794i	−0.271398	+	0.340322i	−0.898788	−	0.438383i	$-0.855551\pi$
$569$	−6.47384	+	8.11794i	−0.271398	+	0.340322i	0.627391	+	0.778705i	$0.284123\pi$
$570$	−19.7709	+	26.4112i	−0.828110	+	1.10624i
$571$	−9.67661	−	42.3960i	−0.404954	−	1.77422i	−0.606855	−	0.794812i	$-0.707569\pi$
$571$	−9.67661	−	42.3960i	−0.404954	−	1.77422i	0.201902	−	0.979406i	$-0.435288\pi$
$572$	−2.61876	+	2.08839i	−0.109496	+	0.0873199i
$573$	2.32101	−	0.529755i	0.0969615	−	0.0221308i
$574$	−0.629316	+	0.303062i	−0.0262671	+	0.0126496i
$575$	16.2830	+	29.1092i	0.679048	+	1.21394i
$576$	0.346407	−	0.434381i	0.0144336	−	0.0180992i
$577$	0.428848	+	0.0978817i	0.0178532	+	0.00407487i	0.231438	−	0.972850i	$-0.425657\pi$
$577$	0.428848	+	0.0978817i	0.0178532	+	0.00407487i	−0.213585	+	0.976924i	$0.568514\pi$
$578$	6.27655	+	13.0334i	0.261070	+	0.542117i
$579$	31.0713	+	14.9631i	1.29128	+	0.621847i
$580$	−6.56395	−	2.91706i	−0.272553	−	0.121124i
$581$	−1.28609	+	5.63474i	−0.0533561	+	0.233768i
$582$	−10.3938	+	21.5829i	−0.430836	+	0.894641i
$583$	−1.32794	−	2.75750i	−0.0549977	−	0.114204i
$584$	1.93417	−	8.47415i	0.0800365	−	0.350663i
$585$	5.12350	−	4.34890i	0.211831	−	0.179805i
$586$	−6.53017	+	8.18857i	−0.269759	+	0.338267i
$587$	−5.44915	−	11.3153i	−0.224910	−	0.467031i	0.757726	−	0.652573i	$-0.226310\pi$
$587$	−5.44915	−	11.3153i	−0.224910	−	0.467031i	−0.982636	+	0.185542i	$0.940596\pi$
$588$	−12.4554	+	2.84287i	−0.513654	+	0.117238i
$589$	8.40748	+	10.5426i	0.346424	+	0.434402i
$590$	0.202595	+	6.61716i	0.00834071	+	0.272424i
$591$	42.9132	+	20.6659i	1.76521	+	0.850082i
$592$	−6.89573	−	5.49916i	−0.283413	−	0.226014i
$593$	10.2935	−	21.3747i	0.422704	−	0.877754i	−0.575497	−	0.817804i	$-0.695191\pi$
$593$	10.2935	−	21.3747i	0.422704	−	0.877754i	0.998201	−	0.0599504i	$-0.0190943\pi$
$594$	1.77947	+	2.23139i	0.0730126	+	0.0915549i
$595$	1.14497	−	5.83407i	0.0469391	−	0.239173i
$596$	−5.08151			−0.208147
$597$	2.51271	−	2.00382i	0.102838	−	0.0820108i
$598$	−15.6567	−	32.5115i	−0.640250	−	1.32949i
$599$	−0.986987	+	4.32427i	−0.0403272	+	0.176685i	−0.991081	−	0.133263i	$-0.957455\pi$
$599$	−0.986987	+	4.32427i	−0.0403272	+	0.176685i	0.950754	+	0.309948i	$0.100312\pi$
$600$	−1.53171	+	9.30289i	−0.0625320	+	0.379789i
$601$	−12.5869			−0.513430			−0.256715	−	0.966487i	$-0.582640\pi$
$601$	−12.5869			−0.513430			−0.256715	+	0.966487i	$0.582640\pi$
$602$	0.360539	−	3.08720i	0.0146945	−	0.125825i
$603$			5.72931i			0.233316i
$604$	0.933584	+	4.09030i	0.0379870	+	0.166432i
$605$	21.6937	+	9.64079i	0.881973	+	0.391954i
$606$	11.8862	−	5.72409i	0.482844	−	0.232525i
$607$	−19.6862	+	15.6992i	−0.799038	+	0.637212i	−0.935457	−	0.353439i	$-0.885012\pi$
$607$	−19.6862	+	15.6992i	−0.799038	+	0.637212i	0.136419	+	0.990651i	$0.456441\pi$
$608$			7.82457i			0.317328i
$609$	−2.87108			−0.116342
$610$	−1.19491	−	2.29854i	−0.0483805	−	0.0930651i
$611$	46.7568	+	22.5169i	1.89158	+	0.910936i
$612$	−2.43664	−	1.94315i	−0.0984953	−	0.0785474i
$613$	4.92112	−	10.2188i	0.198762	−	0.412734i	−0.777635	−	0.628716i	$-0.783581\pi$
$613$	4.92112	−	10.2188i	0.198762	−	0.412734i	0.976397	+	0.215982i	$0.0692952\pi$
$614$	−2.37609	−	10.4103i	−0.0958913	−	0.420127i
$615$	−2.86593	−	5.51293i	−0.115565	−	0.222303i
$616$	−0.0653094	−	0.286139i	−0.00263139	−	0.0115289i
$617$	20.5086	+	42.5865i	0.825645	+	1.71447i	0.690119	+	0.723696i	$0.257558\pi$
$617$	20.5086	+	42.5865i	0.825645	+	1.71447i	0.135526	+	0.990774i	$0.456728\pi$
$618$	−23.6747	−	18.8799i	−0.952335	−	0.759462i
$619$	12.8765	−	16.1466i	0.517550	−	0.648987i	−0.452537	−	0.891746i	$-0.649481\pi$
$619$	12.8765	−	16.1466i	0.517550	−	0.648987i	0.970087	+	0.242759i	$0.0780524\pi$
$620$	3.52147	+	1.56496i	0.141426	+	0.0628503i
$621$	−27.7023	+	13.3407i	−1.11166	+	0.535345i
$622$	−4.96518	+	10.3103i	−0.199086	+	0.413406i
$623$	2.38674	+	0.544757i	0.0956227	+	0.0218252i
$624$	2.26974	−	9.94439i	0.0908624	−	0.398094i
$625$	−8.49791	−	23.5114i	−0.339916	−	0.940456i
$626$	−6.74353	+	3.24751i	−0.269526	+	0.129797i
$627$	8.90679	+	2.03292i	0.355703	+	0.0811869i
$628$	19.0988	+	15.2308i	0.762125	+	0.607775i
$629$	−30.8473	+	38.6813i	−1.22996	+	1.54232i
$630$	0.148542	+	0.569821i	0.00591806	+	0.0227022i
$631$	−4.46319	−	19.5545i	−0.177677	−	0.778453i	−0.982699	−	0.185208i	$-0.940704\pi$
$631$	−4.46319	−	19.5545i	−0.177677	−	0.778453i	0.805023	−	0.593244i	$-0.202153\pi$
$632$	−5.85522	+	4.66938i	−0.232908	+	0.185738i
$633$	11.4693	−	2.61779i	0.455864	−	0.104048i
$634$	1.29405	+	0.623183i	0.0513934	+	0.0247498i
$635$	−7.32391	+	6.21664i	−0.290640	+	0.246700i
$636$	8.39729	+	4.04392i	0.332974	+	0.160352i
$637$	−28.6545	+	22.8512i	−1.13533	+	0.905399i
$638$			1.98907i			0.0787480i
$639$	−8.71595			−0.344798
$640$	1.03139	+	1.98399i	0.0407693	+	0.0784242i
$641$	−12.4462	+	5.99376i	−0.491594	+	0.236739i	−0.663222	−	0.748423i	$-0.730812\pi$
$641$	−12.4462	+	5.99376i	−0.491594	+	0.236739i	0.171628	+	0.985162i	$0.445097\pi$
$642$	−9.79865	−	2.23648i	−0.386722	−	0.0882668i
$643$	−36.8376	+	8.40793i	−1.45273	+	0.331577i	−0.874790	−	0.484502i	$-0.839001\pi$
$643$	−36.8376	+	8.40793i	−1.45273	+	0.331577i	−0.577941	+	0.816078i	$0.696144\pi$
$644$	3.16191			0.124597
$645$	27.5474	+	2.36526i	1.08468	+	0.0931319i
$646$	43.8915			1.72689
$647$	−29.3551	+	6.70010i	−1.15407	+	0.263408i	−0.756392	−	0.654118i	$-0.773040\pi$
$647$	−29.3551	+	6.70010i	−1.15407	+	0.263408i	−0.397675	+	0.917526i	$0.630183\pi$
$648$	−10.0984	−	2.30489i	−0.396703	−	0.0905448i
$649$	1.65170	−	0.795419i	0.0648351	−	0.0312229i
$650$	7.62040	+	25.9513i	0.298897	+	1.01790i
$651$	1.54030			0.0603690
$652$			0.252634i			0.00989391i
$653$	3.59975	−	2.87070i	0.140869	−	0.112339i	−0.550520	−	0.834822i	$-0.685571\pi$
$653$	3.59975	−	2.87070i	0.140869	−	0.112339i	0.691389	+	0.722483i	$0.256999\pi$
$654$	−4.97980	−	2.39814i	−0.194725	−	0.0937748i
$655$	−6.53597	−	7.70011i	−0.255381	−	0.300868i
$656$	−1.32769	−	0.639381i	−0.0518375	−	0.0249636i
$657$	4.70819	−	1.07461i	0.183684	−	0.0419247i
$658$	−3.55526	+	2.83522i	−0.138598	+	0.110528i
$659$	−10.1116	−	44.3019i	−0.393893	−	1.72576i	−0.650736	−	0.759304i	$-0.725539\pi$
$659$	−10.1116	−	44.3019i	−0.393893	−	1.72576i	0.256843	−	0.966453i	$-0.417318\pi$
$660$	2.52637	−	0.658579i	0.0983388	−	0.0256351i
$661$	−13.0372	+	16.3481i	−0.507088	+	0.635868i	−0.967812	−	0.251676i	$-0.919018\pi$
$661$	−13.0372	+	16.3481i	−0.507088	+	0.635868i	0.460724	+	0.887543i	$0.347590\pi$
$662$	15.6972	+	12.5181i	0.610088	+	0.486529i
$663$	−55.7826	−	12.7320i	−2.16642	−	0.494471i
$664$	−10.9860	+	5.29056i	−0.426338	+	0.205314i
$665$	−6.63902	−	4.96983i	−0.257450	−	0.192722i
$666$	1.09042	−	4.77746i	0.0422531	−	0.185123i
$667$	−20.8914	−	4.76832i	−0.808917	−	0.184630i
$668$	−1.69311	+	3.51579i	−0.0655086	+	0.136030i
$669$	12.6521	−	6.09295i	0.489160	−	0.235567i
$670$	−21.0714	−	9.36424i	−0.814059	−	0.361772i
$671$	−0.447274	+	0.560863i	−0.0172668	+	0.0216519i
$672$	0.698782	+	0.557260i	0.0269561	+	0.0214968i
$673$	−13.5133	−	28.0606i	−0.520899	−	1.08166i	−0.981039	−	0.193811i	$-0.937915\pi$
$673$	−13.5133	−	28.0606i	−0.520899	−	1.08166i	0.460140	−	0.887846i	$-0.347799\pi$
$674$	−0.158050	−	0.692461i	−0.00608785	−	0.0266726i
$675$	22.1126	−	6.49318i	0.851114	−	0.249923i
$676$	−3.61857	−	15.8540i	−0.139176	−	0.609768i
$677$	−14.5106	+	30.1316i	−0.557689	+	1.15805i	0.411426	+	0.911443i	$0.365031\pi$
$677$	−14.5106	+	30.1316i	−0.557689	+	1.15805i	−0.969115	+	0.246609i	$0.920684\pi$
$678$	−5.67800	−	4.52806i	−0.218062	−	0.173899i
$679$	−5.42534	−	2.61270i	−0.208205	−	0.100266i
$680$	11.1291	−	5.78554i	0.426782	−	0.221865i
$681$	−6.36726			−0.243994
$682$		−	1.06711i		−	0.0408617i
$683$	2.88883	−	2.30377i	0.110538	−	0.0881511i	−0.566661	−	0.823951i	$-0.691765\pi$
$683$	2.88883	−	2.30377i	0.110538	−	0.0881511i	0.677199	+	0.735800i	$0.263194\pi$
$684$	−3.91677	+	1.88622i	−0.149761	+	0.0721212i
$685$	13.5847	−	30.5683i	0.519046	−	1.16796i
$686$	−1.45293	−	6.36571i	−0.0554732	−	0.243044i
$687$		−	4.83983i		−	0.184651i
$688$	5.56646	−	3.46620i	0.212219	−	0.132148i
$689$	26.7376			1.01862
$690$	0.860740	+	28.1135i	0.0327678	+	1.07026i
$691$	2.26668	−	9.93098i	0.0862286	−	0.377792i	−0.913339	−	0.407200i	$-0.866505\pi$
$691$	2.26668	−	9.93098i	0.0862286	−	0.377792i	0.999567	+	0.0294081i	$0.00936224\pi$
$692$	−6.99274	−	14.5206i	−0.265824	−	0.551989i
$693$	0.127490	−	0.101670i	0.00484294	−	0.00386212i
$694$	6.53028			0.247886
$695$	5.38668	−	27.4473i	0.204329	−	1.04114i
$696$	−3.77662	−	4.73573i	−0.143152	−	0.179507i
$697$	−3.58658	+	7.44760i	−0.135851	+	0.282098i
$698$	19.3838	+	15.4581i	0.733687	+	0.585096i
$699$	6.13981	+	2.95678i	0.232229	+	0.111836i
$700$	−2.33848	−	0.385030i	−0.0883864	−	0.0145528i
$701$	−6.47209	−	8.11574i	−0.244447	−	0.306527i	0.644438	−	0.764656i	$-0.277091\pi$
$701$	−6.47209	−	8.11574i	−0.244447	−	0.306527i	−0.888886	+	0.458129i	$0.848520\pi$
$702$	−24.3081	+	5.54817i	−0.917452	+	0.209402i
$703$	29.9434	+	62.1780i	1.12934	+	2.34509i
$704$	0.386066	−	0.484112i	0.0145504	−	0.0182456i
$705$	−26.1766	−	30.8390i	−0.985869	−	1.16147i
$706$	3.30555	−	14.4825i	0.124406	−	0.545058i
$707$	1.43887	+	2.98785i	0.0541144	+	0.112370i
$708$	−2.42225	+	5.02986i	−0.0910338	+	0.189034i
$709$	−9.94300	+	43.5631i	−0.373417	+	1.63605i	0.343689	+	0.939084i	$0.388323\pi$
$709$	−9.94300	+	43.5631i	−0.373417	+	1.63605i	−0.717106	+	0.696964i	$0.754534\pi$
$710$	14.2457	−	32.0557i	0.534633	−	1.20303i
$711$	−3.74884	−	1.80535i	−0.140593	−	0.0677058i
$712$	2.24095	+	4.65339i	0.0839833	+	0.174393i
$713$	11.2079	+	2.55814i	0.419740	+	0.0958030i
$714$	3.12593	−	3.91979i	0.116985	−	0.146694i
$715$	5.71007	−	4.84679i	0.213545	−	0.181260i
$716$	16.9980	−	8.18583i	0.635247	−	0.305919i
$717$	27.9345	−	6.37588i	1.04323	−	0.238111i
$718$	26.2970	−	20.9711i	0.981394	−	0.782636i
$719$	3.38717	+	14.8401i	0.126320	+	0.553444i	0.997991	+	0.0633529i	$0.0201794\pi$
$719$	3.38717	+	14.8401i	0.126320	+	0.553444i	−0.871671	+	0.490091i	$0.836963\pi$
$720$	−0.744503	+	0.994554i	−0.0277460	+	0.0370649i
$721$	4.74588	−	5.95115i	0.176746	−	0.221632i
$722$	18.3202	−	38.0424i	0.681809	−	1.41579i
$723$	−26.4188	+	21.0683i	−0.982526	+	0.783538i
$724$	−11.0878			−0.412075
$725$	14.8702	+	6.07052i	0.552264	+	0.225453i
$726$	12.4816	+	15.6514i	0.463236	+	0.580879i
$727$	5.25966	+	10.9218i	0.195070	+	0.405067i	0.975444	−	0.220246i	$-0.0706859\pi$
$727$	5.25966	+	10.9218i	0.195070	+	0.405067i	−0.780375	+	0.625312i	$0.784972\pi$
$728$	2.49974	+	0.570549i	0.0926465	+	0.0211460i
$729$	4.52141	+	19.8096i	0.167460	+	0.733689i
$730$	−3.74303	+	19.0723i	−0.138536	+	0.705896i
$731$	−19.4435	−	31.2248i	−0.719144	−	1.15489i
$732$		−	2.18458i		−	0.0807443i
$733$	1.22581	−	0.279782i	0.0452762	−	0.0103340i	−0.199823	−	0.979832i	$-0.564037\pi$
$733$	1.22581	−	0.279782i	0.0452762	−	0.0103340i	0.245099	+	0.969498i	$0.421180\pi$
$734$	1.53243	−	6.71403i	0.0565632	−	0.247820i
$735$	27.6436	−	7.20619i	1.01965	−	0.265804i
$736$	4.15917	+	5.21543i	0.153309	+	0.192243i
$737$			6.38524i			0.235204i
$738$		−	0.818736i		−	0.0301381i
$739$	−12.4020	−	15.5516i	−0.456214	−	0.572074i	0.499521	−	0.866301i	$-0.333509\pi$
$739$	−12.4020	−	15.5516i	−0.456214	−	0.572074i	−0.955735	+	0.294227i	$0.904938\pi$
$740$	15.7884	+	11.8189i	0.580393	+	0.434470i
$741$	−49.7617	+	62.3992i	−1.82804	+	2.29229i
$742$	−1.01653	+	2.11084i	−0.0373179	+	0.0774914i
$743$	35.7946	−	8.16988i	1.31318	−	0.299724i	0.492098	−	0.870540i	$-0.336230\pi$
$743$	35.7946	−	8.16988i	1.31318	−	0.299724i	0.821078	+	0.570816i	$0.193373\pi$
$744$	2.02610	+	2.54065i	0.0742805	+	0.0931448i
$745$	11.3573	−	0.347722i	0.416099	−	0.0127395i
$746$	−30.6384	+	14.7547i	−1.12175	+	0.540206i
$747$	−5.29662	−	4.22392i	−0.193793	−	0.154545i
$748$	−2.71560	−	2.16562i	−0.0992922	−	0.0791829i
$749$	0.562188	−	2.46310i	0.0205419	−	0.0899999i
$750$	2.78683	−	20.8970i	0.101761	−	0.763049i
$751$	23.3506	+	11.2451i	0.852077	+	0.410339i	0.808348	−	0.588705i	$-0.200362\pi$
$751$	23.3506	+	11.2451i	0.852077	+	0.410339i	0.0437289	+	0.999043i	$0.486076\pi$
$752$	−9.35315	−	2.13479i	−0.341074	−	0.0778480i
$753$	−3.09618	−	0.706683i	−0.112831	−	0.0257530i
$754$	−15.6559	−	7.53946i	−0.570153	−	0.274571i
$755$	−2.36647	−	9.07802i	−0.0861248	−	0.330383i
$756$	0.486153	−	2.12998i	0.0176812	−	0.0774664i
$757$	10.7938	+	8.60775i	0.392307	+	0.312854i	0.799701	−	0.600398i	$-0.204991\pi$
$757$	10.7938	+	8.60775i	0.392307	+	0.312854i	−0.407395	+	0.913252i	$0.633563\pi$
$758$	−10.1752	−	8.11445i	−0.369580	−	0.294730i
$759$	7.01738	−	3.37939i	0.254715	−	0.122664i
$760$	−0.535426	−	17.4881i	−0.0194219	−	0.634359i
$761$	24.2664	+	30.4292i	0.879658	+	1.10306i	0.993974	+	0.109612i	$0.0349608\pi$
$761$	24.2664	+	30.4292i	0.879658	+	1.10306i	−0.114317	+	0.993444i	$0.536468\pi$
$762$	−7.89791	+	1.80265i	−0.286111	+	0.0653030i
$763$	0.602826	−	1.25178i	0.0218238	−	0.0453175i
$764$	−0.787186	+	0.987100i	−0.0284794	+	0.0357120i
$765$	5.57891	+	4.17625i	0.201706	+	0.150993i
$766$	7.89177	+	9.89596i	0.285141	+	0.357556i
$767$			16.0155i			0.578285i
$768$			1.88563i			0.0680417i
$769$	−29.3988	−	36.8649i	−1.06015	−	1.32938i	−0.941712	−	0.336419i	$-0.890784\pi$
$769$	−29.3988	−	36.8649i	−1.06015	−	1.32938i	−0.118434	−	0.992962i	$-0.537787\pi$
$770$	0.165548	+	0.635058i	0.00596594	+	0.0228859i
$771$	9.69578	−	42.4800i	0.349185	−	1.52988i
$772$	−17.8306	+	4.06972i	−0.641737	+	0.146472i
$773$		−	39.5080i		−	1.42100i	−0.703695	−	0.710502i	$-0.748468\pi$
$773$		−	39.5080i		−	1.42100i	0.703695	−	0.710502i	$-0.251532\pi$
$774$	3.07695	+	1.95084i	0.110599	+	0.0701216i
$775$	−7.97764	−	3.25675i	−0.286565	−	0.116986i
$776$	−2.82693	−	12.3856i	−0.101481	−	0.444617i
$777$	7.68543	+	1.75415i	0.275713	+	0.0629297i
$778$	15.4763	+	32.1369i	0.554854	+	1.15217i
$779$	7.18912	+	9.01487i	0.257577	+	0.322991i
$780$	−4.39244	+	22.3812i	−0.157275	+	0.801377i
$781$	−9.71381			−0.347587
$782$	29.2557	−	23.3306i	1.04618	−	0.834302i
$783$	−6.42422	+	13.3400i	−0.229583	+	0.476734i
$784$	4.22435	−	5.29717i	0.150870	−	0.189185i
$785$	−43.7284	−	32.7342i	−1.56074	−	1.16833i
$786$	−1.89524	−	8.30360i	−0.0676011	−	0.296180i
$787$	23.6607	−	18.8688i	0.843412	−	0.672599i	−0.103310	−	0.994649i	$-0.532943\pi$
$787$	23.6607	−	18.8688i	0.843412	−	0.672599i	0.946723	+	0.322050i	$0.104372\pi$
$788$	−24.6262	+	5.62077i	−0.877273	+	0.200232i
$789$	15.1558	−	7.29867i	0.539562	−	0.259840i
$790$	12.7670	−	10.8368i	0.454230	−	0.385557i
$791$	1.13823	−	1.42729i	0.0404706	−	0.0507486i
$792$	0.335399	+	0.0765527i	0.0119179	+	0.00272018i
$793$	−2.71916	−	5.64639i	−0.0965602	−	0.200509i
$794$	18.3433	+	8.83366i	0.650978	+	0.313495i
$795$	−19.0448	−	8.46363i	−0.675450	−	0.300174i
$796$	−0.379266	+	1.66167i	−0.0134427	+	0.0588964i
$797$	−20.1739	+	41.8916i	−0.714597	+	1.48388i	0.153849	+	0.988094i	$0.450833\pi$
$797$	−20.1739	+	41.8916i	−0.714597	+	1.48388i	−0.868447	+	0.495782i	$0.834881\pi$
$798$	−3.03433	−	6.30085i	−0.107414	−	0.223048i
$799$	−11.9750	+	52.4660i	−0.423646	+	1.85612i
$800$	−2.44094	−	4.36369i	−0.0863004	−	0.154280i
$801$	−1.78915	+	2.24352i	−0.0632165	+	0.0792710i
$802$	−8.62481	−	17.9096i	−0.304553	−	0.632410i
$803$	5.24721	−	1.19764i	0.185170	−	0.0422639i
$804$	−12.1236	−	15.2025i	−0.427565	−	0.536150i
$805$	−7.06693	+	0.216366i	−0.249077	+	0.00762589i
$806$	8.39915	+	4.04482i	0.295848	+	0.142473i
$807$	17.2650	+	13.7684i	0.607757	+	0.484670i
$808$	−3.03564	+	6.30357i	−0.106793	+	0.221759i
$809$	−7.54219	−	9.45761i	−0.265169	−	0.332512i	0.631365	−	0.775486i	$-0.282495\pi$
$809$	−7.54219	−	9.45761i	−0.265169	−	0.332512i	−0.896535	+	0.442974i	$0.853923\pi$
$810$	22.7278	+	4.46046i	0.798575	+	0.156725i
$811$	−18.2406			−0.640515			−0.320258	−	0.947330i	$-0.603769\pi$
$811$	−18.2406			−0.640515			−0.320258	+	0.947330i	$0.603769\pi$
$812$	1.19043	−	0.949335i	0.0417758	−	0.0333151i
$813$	−11.6344	−	24.1591i	−0.408036	−	0.847296i
$814$	1.21526	−	5.32441i	0.0425949	−	0.186621i
$815$	−0.0172874	−	0.564642i	−0.000605553	−	0.0197785i
$816$	10.5773			0.370281
$817$	−51.0094	+	5.53781i	−1.78459	+	0.193744i
$818$		−	9.95336i		−	0.348011i
$819$	0.316994	+	1.38884i	0.0110767	+	0.0485300i
$820$	3.01116	+	1.33818i	0.105154	+	0.0467312i
$821$	−32.2510	+	15.5313i	−1.12557	+	0.542045i	−0.901608	−	0.432553i	$-0.857613\pi$
$821$	−32.2510	+	15.5313i	−1.12557	+	0.542045i	−0.223960	+	0.974598i	$0.571898\pi$
$822$	22.0543	−	17.5877i	0.769231	−	0.613442i
$823$			13.1256i			0.457531i	0.973482	+	0.228766i	$0.0734689\pi$
$823$			13.1256i			0.457531i	−0.973482	+	0.228766i	$0.926531\pi$
$824$	16.0589			0.559437
$825$	−5.60142	+	1.64481i	−0.195017	+	0.0572651i
$826$	−1.26436	−	0.608886i	−0.0439929	−	0.0211859i
$827$	−13.3182	−	10.6209i	−0.463120	−	0.369326i	0.363956	−	0.931416i	$-0.381426\pi$
$827$	−13.3182	−	10.6209i	−0.463120	−	0.369326i	−0.827076	+	0.562090i	$0.809997\pi$
$828$	−1.60808	+	3.33921i	−0.0558847	+	0.116046i
$829$	−0.173683	−	0.760953i	−0.00603225	−	0.0264290i	0.971822	−	0.235715i	$-0.0757432\pi$
$829$	−0.173683	−	0.760953i	−0.00603225	−	0.0264290i	−0.977854	+	0.209286i	$0.932886\pi$
$830$	24.1918	−	12.5763i	0.839711	−	0.436529i
$831$	7.78422	+	34.1049i	0.270032	+	1.18309i
$832$	2.34705	+	4.87371i	0.0813695	+	0.168965i
$833$	−29.7142	−	23.6963i	−1.02954	−	0.821028i
$834$	14.7064	−	18.4413i	0.509242	−	0.638569i
$835$	3.54356	−	7.97372i	0.122630	−	0.275942i
$836$	−4.36518	+	2.10216i	−0.150973	+	0.0727048i
$837$	3.44650	−	7.15674i	0.119129	−	0.247373i
$838$	−5.40396	−	1.23342i	−0.186677	−	0.0426077i
$839$	1.38035	−	6.04773i	0.0476551	−	0.208791i	−0.945495	−	0.325637i	$-0.894421\pi$
$839$	1.38035	−	6.04773i	0.0476551	−	0.208791i	0.993150	+	0.116846i	$0.0372784\pi$
$840$	−1.59993	−	1.19767i	−0.0552027	−	0.0413236i
$841$	16.8311	−	8.10541i	0.580381	−	0.279497i
$842$	28.2677	+	6.45192i	0.974170	+	0.222348i
$843$	28.0402	+	22.3613i	0.965755	+	0.770164i
$844$	−3.88989	+	4.87777i	−0.133896	+	0.167900i
$845$	9.17244	+	35.1864i	0.315542	+	1.21045i
$846$	−1.18608	−	5.19655i	−0.0407782	−	0.178661i
$847$	−3.93433	+	3.13752i	−0.135185	+	0.107807i
$848$	−4.81887	+	1.09988i	−0.165481	+	0.0377699i
$849$	24.3233	+	11.7135i	0.834772	+	0.402005i
$850$	−24.4779	+	13.6924i	−0.839586	+	0.469644i
$851$	53.0095	+	25.5280i	1.81714	+	0.875089i
$852$	23.1274	−	18.4435i	0.792331	−	0.631863i
$853$		−	14.8149i		−	0.507253i	−0.967302	−	0.253626i	$-0.918377\pi$
$853$		−	14.8149i		−	0.507253i	0.967302	−	0.253626i	$-0.0816233\pi$
$854$	0.549141			0.0187912
$855$	8.62498	−	4.48375i	0.294968	−	0.153341i
$856$	4.80228	−	2.31266i	0.164139	−	0.0790450i
$857$	0.00951881	+	0.00217261i	0.000325156	+	7.42148e-5i	0.222684	−	0.974891i	$-0.428518\pi$
$857$	0.00951881	+	0.00217261i	0.000325156	+	7.42148e-5i	−0.222358	+	0.974965i	$0.571375\pi$
$858$	6.15759	−	1.40543i	0.210217	−	0.0479806i
$859$	−31.3714			−1.07038			−0.535189	−	0.844732i	$-0.679760\pi$
$859$	−31.3714			−1.07038			−0.535189	+	0.844732i	$0.679760\pi$
$860$	−12.2040	+	8.12794i	−0.416151	+	0.277161i
$861$	1.31709			0.0448862
$862$	21.6606	−	4.94390i	0.737764	−	0.168390i
$863$	16.4709	+	3.75937i	0.560675	+	0.127970i	0.493461	−	0.869768i	$-0.335732\pi$
$863$	16.4709	+	3.75937i	0.560675	+	0.127970i	0.0672145	+	0.997739i	$0.478589\pi$
$864$	4.15278	−	1.99987i	0.141281	−	0.0680371i
$865$	16.6225	+	31.9753i	0.565183	+	1.08719i
$866$	23.8229			0.809534
$867$		−	27.2774i		−	0.926390i
$868$	−0.638648	+	0.509305i	−0.0216771	+	0.0172869i
$869$	−4.17803	−	2.01204i	−0.141730	−	0.0682536i
$870$	8.76487	+	10.3260i	0.297157	+	0.350085i
$871$	−50.2579	−	24.2029i	−1.70293	−	0.820086i
$872$	2.85771	−	0.652254i	0.0967743	−	0.0220881i
$873$	5.51842	−	4.40079i	0.186770	−	0.148944i
$874$	−11.6147	−	50.8873i	−0.392873	−	1.72129i
$875$	5.25291	+	0.700530i	0.177581	+	0.0236822i
$876$	−10.2190	+	12.8142i	−0.345269	+	0.432953i
$877$	−24.2429	−	19.3331i	−0.818625	−	0.652831i	0.121906	−	0.992542i	$-0.461100\pi$
$877$	−24.2429	−	19.3331i	−0.818625	−	0.652831i	−0.940530	+	0.339710i	$0.889671\pi$
$878$	12.9622	+	2.95854i	0.437453	+	0.0998458i
$879$	17.7935	−	8.56889i	0.600159	−	0.289021i
$880$	−0.829739	+	1.10842i	−0.0279705	+	0.0373648i
$881$	−7.22222	+	31.6426i	−0.243323	+	1.06607i	0.694647	+	0.719351i	$0.255561\pi$
$881$	−7.22222	+	31.6426i	−0.243323	+	1.06607i	−0.937970	+	0.346717i	$0.887297\pi$
$882$	3.66995	+	0.837643i	0.123574	+	0.0282049i
$883$	23.5226	−	48.8453i	0.791600	−	1.64377i	0.0266833	−	0.999644i	$-0.491505\pi$
$883$	23.5226	−	48.8453i	0.791600	−	1.64377i	0.764916	−	0.644130i	$-0.222780\pi$
$884$	27.3388	−	13.1657i	0.919505	−	0.442810i
$885$	5.06960	−	11.4076i	0.170413	−	0.383462i
$886$	−18.6054	+	23.3305i	−0.625062	+	0.783803i
$887$	5.14066	+	4.09954i	0.172606	+	0.137649i	0.705983	−	0.708229i	$-0.250506\pi$
$887$	5.14066	+	4.09954i	0.172606	+	0.137649i	−0.533376	+	0.845878i	$0.679077\pi$
$888$	7.21600	+	14.9842i	0.242153	+	0.502836i
$889$	−0.453134	−	1.98531i	−0.0151976	−	0.0665852i
$890$	−5.32701	−	10.2471i	−0.178562	−	0.343483i
$891$	−1.42719	−	6.25295i	−0.0478128	−	0.209482i
$892$	−3.23126	+	6.70977i	−0.108190	+	0.224660i
$893$	58.6893	+	46.8031i	1.96396	+	1.56621i
$894$	8.63294	+	4.15740i	0.288729	+	0.139044i
$895$	−37.4308	+	19.4586i	−1.25117	+	0.650431i
$896$	−0.473994			−0.0158350
$897$			68.0429i			2.27189i
$898$	5.95045	−	4.74532i	0.198569	−	0.158353i
$899$	4.98773	−	2.40196i	0.166350	−	0.0801100i
$900$	1.59592	−	2.27380i	0.0531974	−	0.0757932i
$901$	6.16971	+	27.0312i	0.205543	+	0.900541i
$902$		−	0.912470i		−	0.0303819i
$903$	−3.13829	+	4.94985i	−0.104436	+	0.164721i
$904$	3.85147			0.128098
$905$	24.7815	−	0.758726i	0.823765	−	0.0252209i
$906$	1.76039	−	7.71278i	0.0584851	−	0.256240i
$907$	−3.51503	−	7.29902i	−0.116714	−	0.242360i	0.834425	−	0.551121i	$-0.185800\pi$
$907$	−3.51503	−	7.29902i	−0.116714	−	0.242360i	−0.951140	+	0.308761i	$0.900086\pi$
$908$	2.64003	−	2.10536i	0.0876126	−	0.0698687i
$909$	−3.88718			−0.128930
$910$	−5.62601	−	1.10414i	−0.186501	−	0.0366017i
$911$	−11.6946	−	14.6646i	−0.387460	−	0.485860i	0.549402	−	0.835558i	$-0.314855\pi$
$911$	−11.6946	−	14.6646i	−0.387460	−	0.485860i	−0.936862	+	0.349698i	$0.886284\pi$
$912$	6.40162	−	13.2931i	0.211979	−	0.440178i
$913$	−5.90302	−	4.70750i	−0.195361	−	0.155795i
$914$	29.6096	+	14.2592i	0.979399	+	0.471654i
$915$	0.149488	+	4.88258i	0.00494192	+	0.161413i
$916$	1.60031	+	2.00672i	0.0528757	+	0.0663040i
$917$	2.08729	−	0.476410i	0.0689284	−	0.0157325i
$918$	−11.2182	−	23.2948i	−0.370256	−	0.768844i
$919$	−20.8024	+	26.0854i	−0.686209	+	0.860479i	−0.995910	−	0.0903553i	$-0.971200\pi$
$919$	−20.8024	+	26.0854i	−0.686209	+	0.860479i	0.309701	+	0.950834i	$0.399771\pi$
$920$	−9.65271	−	11.3720i	−0.318240	−	0.374923i
$921$	−4.48043	+	19.6300i	−0.147635	+	0.646832i
$922$	−13.2819	−	27.5802i	−0.437417	−	0.908306i
$923$	36.8197	−	76.4569i	1.21194	−	2.51661i
$924$	−0.123149	+	0.539552i	−0.00405131	+	0.0177500i
$925$	−36.0961	−	25.3350i	−1.18683	−	0.833011i
$926$	−28.1843	−	13.5728i	−0.926193	−	0.446031i
$927$	3.87120	+	8.03863i	0.127147	+	0.264023i
$928$	3.13177	+	0.714806i	0.102805	+	0.0234647i
$929$	17.7316	−	22.2347i	0.581756	−	0.729498i	−0.400656	−	0.916229i	$-0.631218\pi$
$929$	17.7316	−	22.2347i	0.581756	−	0.729498i	0.982411	+	0.186730i	$0.0597891\pi$
$930$	−4.70223	−	5.53977i	−0.154192	−	0.181656i
$931$	−47.7640	+	23.0019i	−1.56540	+	0.753858i
$932$	−3.52340	+	0.804193i	−0.115413	+	0.0263422i
$933$	16.8706	−	13.4539i	0.552319	−	0.440460i
$934$	−0.476035	−	2.08565i	−0.0155764	−	0.0682445i
$935$	6.21762	+	4.65438i	0.203338	+	0.152215i
$936$	−1.87386	+	2.34974i	−0.0612490	+	0.0768038i
$937$	−8.84509	+	18.3670i	−0.288956	+	0.600024i	−0.994030	−	0.109110i	$-0.965200\pi$
$937$	−8.84509	+	18.3670i	−0.288956	+	0.600024i	0.705073	+	0.709134i	$0.250914\pi$
$938$	3.82147	−	3.04752i	0.124776	−	0.0995052i
$939$	14.1135			0.460576
$940$	21.0506	+	4.13129i	0.686594	+	0.134748i
$941$	22.1220	+	27.7401i	0.721156	+	0.904302i	0.998403	−	0.0564973i	$-0.0179932\pi$
$941$	22.1220	+	27.7401i	0.721156	+	0.904302i	−0.277246	+	0.960799i	$0.589422\pi$
$942$	−19.9858	−	41.5010i	−0.651174	−	1.35218i
$943$	9.58375	+	2.18743i	0.312090	+	0.0712325i
$944$	−0.658811	−	2.88644i	−0.0214425	−	0.0939456i
$945$	−0.940810	+	4.79381i	−0.0306046	+	0.155943i
$946$	3.42923	+	2.17419i	0.111494	+	0.0706890i
$947$			2.37183i			0.0770741i	0.999257	+	0.0385370i	$0.0122698\pi$
$947$			2.37183i			0.0770741i	−0.999257	+	0.0385370i	$0.987730\pi$
$948$	13.7676	−	3.14237i	0.447151	−	0.102059i
$949$	−10.4627	+	45.8401i	−0.339634	+	1.48803i
$950$	2.39338	+	39.0496i	0.0776514	+	1.26694i
$951$	−1.68860	−	2.11744i	−0.0547567	−	0.0686627i
$952$			2.65885i			0.0861737i
$953$			35.5452i			1.15142i	0.817653	+	0.575711i	$0.195275\pi$
$953$			35.5452i			1.15142i	−0.817653	+	0.575711i	$0.804725\pi$
$954$	−1.71222	−	2.14706i	−0.0554352	−	0.0695136i
$955$	1.69183	−	2.26005i	0.0547463	−	0.0731336i
$956$	−9.47419	+	11.8803i	−0.306417	+	0.384235i
$957$	1.62734	−	3.37921i	0.0526045	−	0.109234i
$958$	34.6965	−	7.91924i	1.12099	−	0.255859i
$959$	4.42105	+	5.54382i	0.142763	+	0.179019i
$960$	−0.129031	−	4.21442i	−0.00416447	−	0.136020i
$961$	25.2542	−	12.1618i	0.814651	−	0.392315i
$962$	37.3018	+	29.7472i	1.20266	+	0.959088i
$963$	2.31531	+	1.84639i	0.0746097	+	0.0594992i
$964$	3.98763	−	17.4709i	0.128433	−	0.562701i
$965$	39.5733	−	10.3160i	1.27391	−	0.332085i
$966$	−5.37174	−	2.58690i	−0.172833	−	0.0832320i
$967$	33.5011	+	7.64640i	1.07732	+	0.245892i	0.724133	−	0.689660i	$-0.242240\pi$
$967$	33.5011	+	7.64640i	1.07732	+	0.245892i	0.353189	+	0.935552i	$0.385097\pi$
$968$	−10.3504	−	2.36241i	−0.332675	−	0.0759308i
$969$	−74.5670	−	35.9096i	−2.39544	−	1.15358i
$970$	7.16578	+	27.4886i	0.230079	+	0.882606i
$971$	4.27524	−	18.7311i	0.137199	−	0.601109i	−0.858844	−	0.512237i	$-0.828817\pi$
$971$	4.27524	−	18.7311i	0.137199	−	0.601109i	0.996043	−	0.0888713i	$-0.0283260\pi$
$972$	4.45941	+	3.55626i	0.143036	+	0.114067i
$973$	4.63561	+	3.69678i	0.148611	+	0.118513i
$974$	−7.97807	+	3.84204i	−0.255634	+	0.123107i
$975$	8.28567	−	50.3231i	0.265354	−	1.61163i
$976$	0.722339	+	0.905784i	0.0231215	+	0.0289934i
$977$	34.1046	−	7.78416i	1.09110	−	0.249037i	0.361132	−	0.932515i	$-0.382390\pi$
$977$	34.1046	−	7.78416i	1.09110	−	0.249037i	0.729972	+	0.683477i	$0.239533\pi$
$978$	0.206691	−	0.429198i	0.00660924	−	0.0137242i
$979$	−1.99398	+	2.50038i	−0.0637280	+	0.0799124i
$980$	−9.07903	+	12.1283i	−0.290019	+	0.387426i
$981$	1.01539	+	1.27326i	0.0324189	+	0.0406520i
$982$		−	0.209434i		−	0.00668332i
$983$		−	24.7444i		−	0.789224i	−0.918848	−	0.394612i	$-0.870879\pi$
$983$		−	24.7444i		−	0.789224i	0.918848	−	0.394612i	$-0.129121\pi$
$984$	1.73249	+	2.17248i	0.0552299	+	0.0692561i
$985$	54.6555	−	14.2477i	1.74147	−	0.453969i
$986$	4.00967	−	17.5675i	0.127694	−	0.559464i
$987$	8.35962	−	1.90803i	0.266090	−	0.0607332i
$988$		−	42.3263i		−	1.34658i
$989$	−31.0564	+	30.8054i	−0.987537	+	0.979553i
$990$	−0.754863	−	0.148146i	−0.0239911	−	0.00470839i
$991$	−9.02042	−	39.5210i	−0.286543	−	1.25543i	−0.889234	−	0.457453i	$-0.848762\pi$
$991$	−9.02042	−	39.5210i	−0.286543	−	1.25543i	0.602691	−	0.797975i	$-0.294095\pi$
$992$	−1.68015	−	0.383484i	−0.0533449	−	0.0121756i
$993$	−16.4262	−	34.1094i	−0.521271	−	1.08243i
$994$	4.63617	+	5.81357i	0.147050	+	0.184395i
$995$	0.733961	−	3.73982i	0.0232681	−	0.118560i
$996$	22.9924			0.728542
$997$	31.6524	−	25.2420i	1.00244	−	0.799421i	0.0227118	−	0.999742i	$-0.492770\pi$
$997$	31.6524	−	25.2420i	1.00244	−	0.799421i	0.979730	+	0.200321i	$0.0641985\pi$
$998$	−13.8381	+	28.7350i	−0.438036	+	0.909591i
$999$	25.3469	−	31.7841i	0.801942	−	1.00560i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.p.a.59.14	yes	132
5.4	even	2	inner	430.2.p.a.59.9	✓	132
43.35	even	7	inner	430.2.p.a.379.9	yes	132
215.164	even	14	inner	430.2.p.a.379.14	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.p.a.59.9	✓	132	5.4	even	2	inner
430.2.p.a.59.14	yes	132	1.1	even	1	trivial
430.2.p.a.379.9	yes	132	43.35	even	7	inner
430.2.p.a.379.14	yes	132	215.164	even	14	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)

\(f(q)\)	\(=\)	\(q+(0.974928 - 0.222521i) q^{2} +(-1.83835 - 0.419592i) q^{3} +(0.900969 - 0.433884i) q^{4} +(-1.98399 + 1.03139i) q^{5} -1.88563 q^{6} -0.473994i q^{7} +(0.781831 - 0.623490i) q^{8} +(0.500573 + 0.241063i) q^{9} +O(q^{10})\)	\(q+(0.974928 - 0.222521i) q^{2} +(-1.83835 - 0.419592i) q^{3} +(0.900969 - 0.433884i) q^{4} +(-1.98399 + 1.03139i) q^{5} -1.88563 q^{6} -0.473994i q^{7} +(0.781831 - 0.623490i) q^{8} +(0.500573 + 0.241063i) q^{9} +(-1.70474 + 1.44701i) q^{10} +(0.557882 + 0.268662i) q^{11} +(-1.83835 + 0.419592i) q^{12} +(-4.22925 + 3.37271i) q^{13} +(-0.105474 - 0.462110i) q^{14} +(4.08004 - 1.06359i) q^{15} +(0.623490 - 0.781831i) q^{16} +(-4.38565 - 3.49744i) q^{17} +(0.541664 + 0.123631i) q^{18} +(-7.04969 + 3.39495i) q^{19} +(-1.34001 + 1.79007i) q^{20} +(-0.198884 + 0.871367i) q^{21} +(0.603677 + 0.137785i) q^{22} +(-2.89434 + 6.01017i) q^{23} +(-1.69889 + 0.818143i) q^{24} +(2.87246 - 4.09255i) q^{25} +(-3.37271 + 4.22925i) q^{26} +(3.60365 + 2.87381i) q^{27} +(-0.205658 - 0.427054i) q^{28} +(0.714806 + 3.13177i) q^{29} +(3.74107 - 1.94482i) q^{30} +(-0.383484 - 1.68015i) q^{31} +(0.433884 - 0.900969i) q^{32} +(-0.912855 - 0.727977i) q^{33} +(-5.05394 - 2.43385i) q^{34} +(0.488873 + 0.940401i) q^{35} +0.555594 q^{36} -8.81997i q^{37} +(-6.11749 + 4.87854i) q^{38} +(9.19000 - 4.42567i) q^{39} +(-0.908087 + 2.04337i) q^{40} +(-0.327912 - 1.43668i) q^{41} +0.893776i q^{42} +(6.18062 + 2.19089i) q^{43} +0.619202 q^{44} +(-1.24176 + 0.0380186i) q^{45} +(-1.48439 + 6.50353i) q^{46} +(-4.16254 - 8.64361i) q^{47} +(-1.47424 + 1.17567i) q^{48} +6.77533 q^{49} +(1.88977 - 4.62912i) q^{50} +(6.59487 + 8.26970i) q^{51} +(-2.34705 + 4.87371i) q^{52} +(-3.86444 - 3.08179i) q^{53} +(4.15278 + 1.99987i) q^{54} +(-1.38393 + 0.0423713i) q^{55} +(-0.295530 - 0.370583i) q^{56} +(14.3843 - 3.28312i) q^{57} +(1.39377 + 2.89419i) q^{58} +(1.84595 - 2.31475i) q^{59} +(3.21452 - 2.72853i) q^{60} +(-0.257800 + 1.12949i) q^{61} +(-0.747738 - 1.55269i) q^{62} +(0.114262 - 0.237268i) q^{63} +(0.222521 - 0.974928i) q^{64} +(4.91221 - 11.0534i) q^{65} +(-1.05196 - 0.506596i) q^{66} +(4.47423 + 9.29084i) q^{67} +(-5.46881 - 1.24822i) q^{68} +(7.84264 - 9.83436i) q^{69} +(0.685875 + 0.808038i) q^{70} +(-14.1341 + 6.80661i) q^{71} +(0.541664 - 0.123631i) q^{72} +(6.79574 - 5.41942i) q^{73} +(-1.96263 - 8.59883i) q^{74} +(-6.99780 + 6.31828i) q^{75} +(-4.87854 + 6.11749i) q^{76} +(0.127344 - 0.264432i) q^{77} +(7.97478 - 6.35968i) q^{78} -7.48910 q^{79} +(-0.430626 + 2.19421i) q^{80} +(-6.45817 - 8.09829i) q^{81} +(-0.639381 - 1.32769i) q^{82} +(-11.8878 - 2.71331i) q^{83} +(0.198884 + 0.871367i) q^{84} +(12.3083 + 2.41557i) q^{85} +(6.51317 + 0.760641i) q^{86} -6.05722i q^{87} +(0.603677 - 0.137785i) q^{88} +(-1.14929 + 5.03538i) q^{89} +(-1.20217 + 0.313384i) q^{90} +(1.59864 + 2.00464i) q^{91} +6.67078i q^{92} +3.24962i q^{93} +(-5.98156 - 7.50064i) q^{94} +(10.4850 - 14.0066i) q^{95} +(-1.17567 + 1.47424i) q^{96} +(5.51211 - 11.4460i) q^{97} +(6.60546 - 1.50765i) q^{98} +(0.214496 + 0.268969i) 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

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