LMFDB - Embedded newform 546.2.bv.a.515.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(317,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("546.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			515.33
Character	$\chi$	$=$	546.515
Dual form			546.2.bv.a.317.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(1.59559 - 0.673858i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.579405 + 0.155251i) q^{5} +(1.71563 - 0.237927i) q^{6} +(0.0183841 + 2.64569i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.09183 - 2.15041i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(1.59559 - 0.673858i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.579405 + 0.155251i) q^{5} +(1.71563 - 0.237927i) q^{6} +(0.0183841 + 2.64569i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.09183 - 2.15041i) q^{9} +(0.519481 + 0.299922i) q^{10} +(-3.10273 + 0.831373i) q^{11} +(1.71875 + 0.214218i) q^{12} +(3.60424 + 0.0973883i) q^{13} +(-0.666997 + 2.56030i) q^{14} +(1.02911 - 0.142719i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.59410 + 4.49310i) q^{17} +(2.57712 - 1.53573i) q^{18} +(2.15080 - 8.02689i) q^{19} +(0.424154 + 0.424154i) q^{20} +(1.81215 + 4.20905i) q^{21} -3.21218 q^{22} +(0.637898 + 1.10487i) q^{23} +(1.60474 + 0.651764i) q^{24} +(-4.01852 - 2.32009i) q^{25} +(3.45622 + 1.02691i) q^{26} +(1.88864 - 4.84077i) q^{27} +(-1.30692 + 2.30042i) q^{28} -4.10654i q^{29} +(1.03098 + 0.128497i) q^{30} +(-5.29917 + 1.41991i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-4.39046 + 3.41733i) q^{33} +(-3.66860 + 3.66860i) q^{34} +(-0.400094 + 1.53578i) q^{35} +(2.88678 - 0.816391i) q^{36} +(3.77455 + 1.01139i) q^{37} +(4.15502 - 7.19671i) q^{38} +(5.81652 - 2.27335i) q^{39} +(0.299922 + 0.519481i) q^{40} +(-5.19752 + 5.19752i) q^{41} +(0.661022 + 4.53465i) q^{42} -9.47120i q^{43} +(-3.10273 - 0.831373i) q^{44} +(1.54587 - 0.921198i) q^{45} +(0.330201 + 1.23233i) q^{46} +(1.48819 - 5.55402i) q^{47} +(1.38137 + 1.04489i) q^{48} +(-6.99932 + 0.0972771i) q^{49} +(-3.28111 - 3.28111i) q^{50} +(-1.11140 + 8.91722i) q^{51} +(3.07267 + 1.88646i) q^{52} +(1.48181 + 0.855522i) q^{53} +(3.07717 - 4.18701i) q^{54} -1.92681 q^{55} +(-1.85778 + 1.88378i) q^{56} +(-1.97719 - 14.2570i) q^{57} +(1.06285 - 3.96661i) q^{58} +(-3.14252 + 0.842037i) q^{59} +(0.962597 + 0.390957i) q^{60} +(0.398128 + 0.689579i) q^{61} -5.48610 q^{62} +(5.72776 + 5.49480i) q^{63} +1.00000i q^{64} +(2.07319 + 0.615989i) q^{65} +(-5.12533 + 2.16455i) q^{66} +(6.42620 - 1.72190i) q^{67} +(-4.49310 + 2.59410i) q^{68} +(1.76235 + 1.33307i) q^{69} +(-0.783950 + 1.37990i) q^{70} +(-8.81512 + 8.81512i) q^{71} +(2.99971 - 0.0414195i) q^{72} +(1.65075 + 6.16069i) q^{73} +(3.38417 + 1.95385i) q^{74} +(-7.97533 - 0.994011i) q^{75} +(5.87609 - 5.87609i) q^{76} +(-2.25659 - 8.19356i) q^{77} +(6.20671 - 0.690464i) q^{78} +(-2.17550 - 3.76807i) q^{79} +(0.155251 + 0.579405i) q^{80} +(-0.248493 - 8.99657i) q^{81} +(-6.36563 + 3.67520i) q^{82} +(-9.60558 + 9.60558i) q^{83} +(-0.535156 + 4.55122i) q^{84} +(-2.20059 + 2.20059i) q^{85} +(2.45133 - 9.14848i) q^{86} +(-2.76723 - 6.55236i) q^{87} +(-2.78183 - 1.60609i) q^{88} +(-3.10650 + 11.5936i) q^{89} +(1.73162 - 0.489708i) q^{90} +(-0.191398 + 9.53747i) q^{91} +1.27580i q^{92} +(-7.49849 + 5.83648i) q^{93} +(2.87497 - 4.97960i) q^{94} +(2.49237 - 4.31691i) q^{95} +(1.06387 + 1.36682i) q^{96} +(9.09518 + 9.09518i) q^{97} +(-6.78601 - 1.71760i) q^{98} +(-4.70259 + 8.41121i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{7}+O(q^{10}) $ 144 * q - 16 * q^7	$ 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) $ 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	1.59559	−	0.673858i	0.921216	−	0.389052i
$3$	1.59559	−	0.673858i	0.921216	−	0.389052i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	0.579405	+	0.155251i	0.259118	+	0.0694304i	0.386039	−	0.922482i	$-0.373843\pi$
$5$	0.579405	+	0.155251i	0.259118	+	0.0694304i	−0.126921	+	0.991913i	$0.540510\pi$
$6$	1.71563	−	0.237927i	0.700404	−	0.0971334i
$7$	0.0183841	+	2.64569i	0.00694853	+	0.999976i
$7$	0.0183841	+	2.64569i	0.00694853	+	0.999976i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.09183	−	2.15041i	0.697277	−	0.716802i
$10$	0.519481	+	0.299922i	0.164274	+	0.0948438i
$11$	−3.10273	+	0.831373i	−0.935507	+	0.250668i	−0.694201	−	0.719781i	$-0.744242\pi$
$11$	−3.10273	+	0.831373i	−0.935507	+	0.250668i	−0.241306	+	0.970449i	$0.577576\pi$
$12$	1.71875	+	0.214218i	0.496161	+	0.0618394i
$13$	3.60424	+	0.0973883i	0.999635	+	0.0270106i
$13$	3.60424	+	0.0973883i	0.999635	+	0.0270106i
$14$	−0.666997	+	2.56030i	−0.178262	+	0.684268i
$15$	1.02911	−	0.142719i	0.265716	−	0.0368500i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.59410	+	4.49310i	−0.629160	+	1.08974i	0.358560	+	0.933507i	$0.383268\pi$
$17$	−2.59410	+	4.49310i	−0.629160	+	1.08974i	−0.987721	+	0.156231i	$0.950066\pi$
$18$	2.57712	−	1.53573i	0.607433	−	0.361974i
$19$	2.15080	−	8.02689i	0.493427	−	1.84149i	−0.0452411	−	0.998976i	$-0.514406\pi$
$19$	2.15080	−	8.02689i	0.493427	−	1.84149i	0.538668	−	0.842518i	$-0.318928\pi$
$20$	0.424154	+	0.424154i	0.0948438	+	0.0948438i
$21$	1.81215	+	4.20905i	0.395444	+	0.918490i
$22$	−3.21218			−0.684839
$23$	0.637898	+	1.10487i	0.133011	+	0.230382i	0.924836	−	0.380366i	$-0.124202\pi$
$23$	0.637898	+	1.10487i	0.133011	+	0.230382i	−0.791825	+	0.610748i	$0.790869\pi$
$24$	1.60474	+	0.651764i	0.327567	+	0.133041i
$25$	−4.01852	−	2.32009i	−0.803704	−	0.464019i
$26$	3.45622	+	1.02691i	0.677820	+	0.201395i
$27$	1.88864	−	4.84077i	0.363469	−	0.931606i
$28$	−1.30692	+	2.30042i	−0.246985	+	0.434739i
$29$		−	4.10654i		−	0.762565i	−0.924459	−	0.381283i	$-0.875483\pi$
$29$		−	4.10654i		−	0.762565i	0.924459	−	0.381283i	$-0.124517\pi$
$30$	1.03098	+	0.128497i	0.188231	+	0.0234603i
$31$	−5.29917	+	1.41991i	−0.951758	+	0.255023i	−0.701108	−	0.713055i	$-0.747311\pi$
$31$	−5.29917	+	1.41991i	−0.951758	+	0.255023i	−0.250650	+	0.968078i	$0.580644\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−4.39046	+	3.41733i	−0.764281	+	0.594881i
$34$	−3.66860	+	3.66860i	−0.629160	+	0.629160i
$35$	−0.400094	+	1.53578i	−0.0676283	+	0.259594i
$36$	2.88678	−	0.816391i	0.481130	−	0.136065i
$37$	3.77455	+	1.01139i	0.620532	+	0.166271i	0.555370	−	0.831604i	$-0.312577\pi$
$37$	3.77455	+	1.01139i	0.620532	+	0.166271i	0.0651624	+	0.997875i	$0.479243\pi$
$38$	4.15502	−	7.19671i	0.674034	−	1.16746i
$39$	5.81652	−	2.27335i	0.931388	−	0.364028i
$40$	0.299922	+	0.519481i	0.0474219	+	0.0821371i
$41$	−5.19752	+	5.19752i	−0.811716	+	0.811716i	−0.984891	−	0.173175i	$-0.944597\pi$
$41$	−5.19752	+	5.19752i	−0.811716	+	0.811716i	0.173175	+	0.984891i	$0.444597\pi$
$42$	0.661022	+	4.53465i	0.101998	+	0.699712i
$43$		−	9.47120i		−	1.44434i	−0.691713	−	0.722172i	$-0.743144\pi$
$43$		−	9.47120i		−	1.44434i	0.691713	−	0.722172i	$-0.256856\pi$
$44$	−3.10273	−	0.831373i	−0.467754	−	0.125334i
$45$	1.54587	−	0.921198i	0.230445	−	0.137324i
$46$	0.330201	+	1.23233i	0.0486854	+	0.181696i
$47$	1.48819	−	5.55402i	0.217075	−	0.810137i	−0.768350	−	0.640030i	$-0.778922\pi$
$47$	1.48819	−	5.55402i	0.217075	−	0.810137i	0.985426	−	0.170107i	$-0.0544113\pi$
$48$	1.38137	+	1.04489i	0.199384	+	0.150818i
$49$	−6.99932	+	0.0972771i	−0.999903	+	0.0138967i
$50$	−3.28111	−	3.28111i	−0.464019	−	0.464019i
$51$	−1.11140	+	8.91722i	−0.155628	+	1.24866i
$52$	3.07267	+	1.88646i	0.426102	+	0.261605i
$53$	1.48181	+	0.855522i	0.203542	+	0.117515i	0.598306	−	0.801267i	$-0.295841\pi$
$53$	1.48181	+	0.855522i	0.203542	+	0.117515i	−0.394765	+	0.918782i	$0.629174\pi$
$54$	3.07717	−	4.18701i	0.418750	−	0.569780i
$55$	−1.92681			−0.259811
$56$	−1.85778	+	1.88378i	−0.248257	+	0.251731i
$57$	−1.97719	−	14.2570i	−0.261885	−	1.88838i
$58$	1.06285	−	3.96661i	0.139559	−	0.520842i
$59$	−3.14252	+	0.842037i	−0.409122	+	0.109624i	−0.457509	−	0.889205i	$-0.651258\pi$
$59$	−3.14252	+	0.842037i	−0.409122	+	0.109624i	0.0483876	+	0.998829i	$0.484592\pi$
$60$	0.962597	+	0.390957i	0.124271	+	0.0504724i
$61$	0.398128	+	0.689579i	0.0509751	+	0.0882915i	0.890387	−	0.455204i	$-0.150434\pi$
$61$	0.398128	+	0.689579i	0.0509751	+	0.0882915i	−0.839412	+	0.543496i	$0.817100\pi$
$62$	−5.48610			−0.696736
$63$	5.72776	+	5.49480i	0.721630	+	0.692279i
$64$			1.00000i			0.125000i
$65$	2.07319	+	0.615989i	0.257148	+	0.0764041i
$66$	−5.12533	+	2.16455i	−0.630884	+	0.266438i
$67$	6.42620	−	1.72190i	0.785085	−	0.210363i	0.156060	−	0.987748i	$-0.450121\pi$
$67$	6.42620	−	1.72190i	0.785085	−	0.210363i	0.629026	+	0.777385i	$0.283454\pi$
$68$	−4.49310	+	2.59410i	−0.544869	+	0.314580i
$69$	1.76235	+	1.33307i	0.212162	+	0.160483i
$70$	−0.783950	+	1.37990i	−0.0937000	+	0.164929i
$71$	−8.81512	+	8.81512i	−1.04616	+	1.04616i	−0.0472805	+	0.998882i	$0.515055\pi$
$71$	−8.81512	+	8.81512i	−1.04616	+	1.04616i	−0.998882	+	0.0472805i	$0.984945\pi$
$72$	2.99971	−	0.0414195i	0.353520	−	0.00488133i
$73$	1.65075	+	6.16069i	0.193206	+	0.721054i	0.992724	+	0.120412i	$0.0384216\pi$
$73$	1.65075	+	6.16069i	0.193206	+	0.721054i	−0.799518	+	0.600642i	$0.794912\pi$
$74$	3.38417	+	1.95385i	0.393401	+	0.227130i
$75$	−7.97533	−	0.994011i	−0.920912	−	0.114778i
$76$	5.87609	−	5.87609i	0.674034	−	0.674034i
$77$	−2.25659	−	8.19356i	−0.257163	−	0.933743i
$78$	6.20671	−	0.690464i	0.702772	−	0.0781797i
$79$	−2.17550	−	3.76807i	−0.244763	−	0.423942i	0.717302	−	0.696762i	$-0.245377\pi$
$79$	−2.17550	−	3.76807i	−0.244763	−	0.423942i	−0.962065	+	0.272821i	$0.912043\pi$
$80$	0.155251	+	0.579405i	0.0173576	+	0.0647795i
$81$	−0.248493	−	8.99657i	−0.0276104	−	0.999619i
$82$	−6.36563	+	3.67520i	−0.702966	+	0.405858i
$83$	−9.60558	+	9.60558i	−1.05435	+	1.05435i	−0.0559134	+	0.998436i	$0.517807\pi$
$83$	−9.60558	+	9.60558i	−1.05435	+	1.05435i	−0.998436	+	0.0559134i	$0.982193\pi$
$84$	−0.535156	+	4.55122i	−0.0583903	+	0.496579i
$85$	−2.20059	+	2.20059i	−0.238688	+	0.238688i
$86$	2.45133	−	9.14848i	0.264333	−	0.986506i
$87$	−2.76723	−	6.55236i	−0.296678	−	0.702487i
$88$	−2.78183	−	1.60609i	−0.296544	−	0.171210i
$89$	−3.10650	+	11.5936i	−0.329288	+	1.22892i	0.580642	+	0.814159i	$0.302802\pi$
$89$	−3.10650	+	11.5936i	−0.329288	+	1.22892i	−0.909930	+	0.414762i	$0.863865\pi$
$90$	1.73162	−	0.489708i	0.182529	−	0.0516197i
$91$	−0.191398	+	9.53747i	−0.0200640	+	0.999799i
$92$			1.27580i			0.133011i
$93$	−7.49849	+	5.83648i	−0.777558	+	0.605215i
$94$	2.87497	−	4.97960i	0.296531	−	0.513606i
$95$	2.49237	−	4.31691i	0.255712	−	0.442905i
$96$	1.06387	+	1.36682i	0.108580	+	0.139500i
$97$	9.09518	+	9.09518i	0.923475	+	0.923475i	0.997273	−	0.0737979i	$-0.0235120\pi$
$97$	9.09518	+	9.09518i	0.923475	+	0.923475i	−0.0737979	+	0.997273i	$0.523512\pi$
$98$	−6.78601	−	1.71760i	−0.685490	−	0.173503i
$99$	−4.70259	+	8.41121i	−0.472628	+	0.845359i
$100$	−2.32009	−	4.01852i	−0.232009	−	0.401852i
$101$	5.76486	−	9.98503i	0.573625	−	0.993548i	−0.422564	−	0.906333i	$-0.638870\pi$
$101$	5.76486	−	9.98503i	0.573625	−	0.993548i	0.996190	−	0.0872149i	$-0.0277967\pi$
$102$	−3.38148	+	8.32572i	−0.334816	+	0.824369i
$103$	0.364990	−	0.210727i	0.0359636	−	0.0207636i	−0.481910	−	0.876220i	$-0.660057\pi$
$103$	0.364990	−	0.210727i	0.0359636	−	0.0207636i	0.517874	+	0.855457i	$0.326724\pi$
$104$	2.47972	+	2.61744i	0.243156	+	0.256661i
$105$	0.396510	+	2.72009i	0.0386954	+	0.265453i
$106$	1.20989	+	1.20989i	0.117515	+	0.117515i
$107$	11.0489	−	6.37909i	1.06814	−	0.616690i	0.140466	−	0.990086i	$-0.455140\pi$
$107$	11.0489	−	6.37909i	1.06814	−	0.616690i	0.927672	+	0.373396i	$0.121807\pi$
$108$	4.05599	−	3.24791i	0.390288	−	0.312530i
$109$	−6.59696	+	1.76765i	−0.631874	+	0.169310i	−0.560520	−	0.828141i	$-0.689399\pi$
$109$	−6.59696	+	1.76765i	−0.631874	+	0.169310i	−0.0713542	+	0.997451i	$0.522732\pi$
$110$	−1.86115	−	0.498695i	−0.177454	−	0.0475487i
$111$	6.70417	−	0.929749i	0.636332	−	0.0882479i
$112$	−2.28204	+	1.33876i	−0.215633	+	0.126501i
$113$		−	16.8438i		−	1.58453i	−0.610175	−	0.792267i	$-0.708901\pi$
$113$		−	16.8438i		−	1.58453i	0.610175	−	0.792267i	$-0.291099\pi$
$114$	1.78016	−	14.2829i	0.166727	−	1.33772i
$115$	0.198069	+	0.739204i	0.0184700	+	0.0689311i
$116$	2.05327	−	3.55637i	0.190641	−	0.330200i
$117$	7.74887	−	7.54685i	0.716384	−	0.697707i
$118$	−3.25338			−0.299498
$119$	−11.9350	−	6.78056i	−1.09408	−	0.621573i
$120$	0.828610	+	0.626774i	0.0756414	+	0.0572164i
$121$	−0.590549	+	0.340954i	−0.0536863	+	0.0309958i
$122$	0.206086	+	0.769125i	0.0186582	+	0.0696333i
$123$	−4.79073	+	11.7955i	−0.431965	+	1.06357i
$124$	−5.29917	−	1.41991i	−0.475879	−	0.127511i
$125$	−4.08893	−	4.08893i	−0.365725	−	0.365725i
$126$	4.11043	+	6.79002i	0.366186	+	0.604903i
$127$		−	2.45849i		−	0.218155i	−0.994033	−	0.109078i	$-0.965210\pi$
$127$		−	2.45849i		−	0.218155i	0.994033	−	0.109078i	$-0.0347897\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	−6.38225	−	15.1122i	−0.561925	−	1.33055i
$130$	1.84312	+	1.13158i	0.161652	+	0.0992463i
$131$	−18.1910	+	10.5026i	−1.58936	+	0.917616i	−0.595944	+	0.803026i	$0.703222\pi$
$131$	−18.1910	+	10.5026i	−1.58936	+	0.917616i	−0.993413	+	0.114590i	$0.963445\pi$
$132$	−5.51091	+	0.764265i	−0.479664	+	0.0665208i
$133$	21.2762	+	5.54277i	1.84488	+	0.480619i
$134$	6.65289			0.574722
$135$	1.84582	−	2.51155i	0.158863	−	0.216160i
$136$	−5.01141	+	1.34280i	−0.429725	+	0.115144i
$137$	5.66907	−	1.51902i	0.484342	−	0.129779i	−0.00838191	−	0.999965i	$-0.502668\pi$
$137$	5.66907	−	1.51902i	0.484342	−	0.129779i	0.492723	+	0.870186i	$0.336001\pi$
$138$	1.35728	+	1.74378i	0.115539	+	0.148440i
$139$	3.39367			0.287847			0.143923	−	0.989589i	$-0.454028\pi$
$139$	3.39367			0.287847			0.143923	+	0.989589i	$0.454028\pi$
$140$	−1.11438	+	1.12998i	−0.0941824	+	0.0955005i
$141$	−1.36807	−	9.86478i	−0.115212	−	0.830764i
$142$	−10.7963	+	6.23323i	−0.906003	+	0.523081i
$143$	−11.2639	+	2.69430i	−0.941937	+	0.225308i
$144$	2.90822	+	0.736375i	0.242352	+	0.0613646i
$145$	0.637545	−	2.37935i	0.0529452	−	0.197594i
$146$			6.37801i			0.527848i
$147$	−11.1025	+	4.87177i	−0.915720	+	0.401817i
$148$	2.76316	+	2.76316i	0.227130	+	0.227130i
$149$	21.0577	+	5.64239i	1.72511	+	0.462242i	0.979048	−	0.203631i	$-0.0652743\pi$
$149$	21.0577	+	5.64239i	1.72511	+	0.462242i	0.746065	+	0.665873i	$0.231941\pi$
$150$	−7.44631	−	3.02431i	−0.607989	−	0.246934i
$151$	−2.93466	−	10.9523i	−0.238819	−	0.891286i	−0.976390	−	0.216016i	$-0.930694\pi$
$151$	−2.93466	−	10.9523i	−0.238819	−	0.891286i	0.737571	−	0.675270i	$-0.235973\pi$
$152$	7.19671	−	4.15502i	0.583730	−	0.337017i
$153$	4.23559	+	14.9772i	0.342427	+	1.21083i
$154$	−0.0590530	−	8.49842i	−0.00475862	−	0.684822i
$155$	−3.29081			−0.264324
$156$	6.17393	+	0.939478i	0.494310	+	0.0752184i
$157$	−11.9352	+	20.6724i	−0.952533	+	1.64984i	−0.212619	+	0.977135i	$0.568199\pi$
$157$	−11.9352	+	20.6724i	−0.952533	+	1.64984i	−0.739915	+	0.672701i	$0.765134\pi$
$158$	−1.12612	−	4.20274i	−0.0895894	−	0.334352i
$159$	2.94086	+	0.366536i	0.233225	+	0.0290682i
$160$			0.599845i			0.0474219i
$161$	−2.91142	+	1.70799i	−0.229452	+	0.134609i
$162$	2.08846	−	8.75433i	0.164085	−	0.687805i
$163$	−1.30429	−	0.349483i	−0.102160	−	0.0273737i	0.207377	−	0.978261i	$-0.433507\pi$
$163$	−1.30429	−	0.349483i	−0.102160	−	0.0273737i	−0.309537	+	0.950887i	$0.600174\pi$
$164$	−7.09994	+	1.90242i	−0.554412	+	0.148554i
$165$	−3.07440	+	1.29840i	−0.239342	+	0.101080i
$166$	−11.7644	+	6.79217i	−0.913093	+	0.527175i
$167$	−0.236454	−	0.236454i	−0.0182973	−	0.0182973i	0.697899	−	0.716196i	$-0.254118\pi$
$167$	−0.236454	−	0.236454i	−0.0182973	−	0.0182973i	−0.716196	+	0.697899i	$0.754118\pi$
$168$	−1.69486	+	4.25763i	−0.130762	+	0.328484i
$169$	12.9810	+	0.702021i	0.998541	+	0.0540016i
$170$	−2.69516	+	1.55605i	−0.206710	+	0.119344i
$171$	−12.7620	−	21.4160i	−0.975932	−	1.63772i
$172$	4.73560	−	8.20230i	0.361086	−	0.625420i
$173$	−12.6750	−	21.9538i	−0.963663	−	1.66911i	−0.713166	−	0.700996i	$-0.752739\pi$
$173$	−12.6750	−	21.9538i	−0.963663	−	1.66911i	−0.250497	−	0.968117i	$-0.580594\pi$
$174$	−0.977058	−	7.04531i	−0.0740706	−	0.534103i
$175$	6.06436	−	10.6744i	0.458423	−	0.806909i
$176$	−2.27135	−	2.27135i	−0.171210	−	0.171210i
$177$	−4.44678	+	3.46116i	−0.334240	+	0.260157i
$178$	−6.00130	+	10.3946i	−0.449816	+	0.779105i
$179$	1.48007	−	2.56356i	0.110626	−	0.191609i	−0.805397	−	0.592736i	$-0.798048\pi$
$179$	1.48007	−	2.56356i	0.110626	−	0.191609i	0.916023	+	0.401126i	$0.131381\pi$
$180$	1.79936	−	0.0248453i	0.134117	−	0.00185186i
$181$			0.717545i			0.0533347i	0.999644	+	0.0266674i	$0.00848949\pi$
$181$			0.717545i			0.0533347i	−0.999644	+	0.0266674i	$0.991511\pi$
$182$	−2.65336	+	9.16295i	−0.196680	+	0.679203i
$183$	1.09993	+	0.832004i	0.0813091	+	0.0615035i
$184$	−0.330201	+	1.23233i	−0.0243427	+	0.0908482i
$185$	2.02997	+	1.17201i	0.149247	+	0.0861676i
$186$	−8.75358	+	3.69685i	−0.641844	+	0.271067i
$187$	4.31332	−	16.0975i	0.315421	−	1.17717i
$188$	4.06582	−	4.06582i	0.296531	−	0.296531i
$189$	12.8419	+	4.90776i	0.934109	+	0.356987i
$190$	3.52474	−	3.52474i	0.255712	−	0.255712i
$191$	12.6313	−	7.29268i	0.913968	−	0.527680i	0.0322624	−	0.999479i	$-0.489729\pi$
$191$	12.6313	−	7.29268i	0.913968	−	0.527680i	0.881706	+	0.471800i	$0.156395\pi$
$192$	0.673858	+	1.59559i	0.0486315	+	0.115152i
$193$	5.24169	+	19.5623i	0.377305	+	1.40812i	0.849947	+	0.526868i	$0.176634\pi$
$193$	5.24169	+	19.5623i	0.377305	+	1.40812i	−0.472642	+	0.881255i	$0.656699\pi$
$194$	6.43126	+	11.1393i	0.461738	+	0.799753i
$195$	3.72306	−	0.414171i	0.266614	−	0.0296594i
$196$	−6.11023	−	3.41542i	−0.436445	−	0.243958i
$197$	0.904894	−	0.904894i	0.0644710	−	0.0644710i	−0.674136	−	0.738607i	$-0.735484\pi$
$197$	0.904894	−	0.904894i	0.0644710	−	0.0644710i	0.738607	+	0.674136i	$0.235484\pi$
$198$	−6.71933	+	6.90749i	−0.477522	+	0.490894i
$199$	−2.41271	−	1.39298i	−0.171032	−	0.0987456i	0.412040	−	0.911166i	$-0.364816\pi$
$199$	−2.41271	−	1.39298i	−0.171032	−	0.0987456i	−0.583073	+	0.812420i	$0.698150\pi$
$200$	−1.20097	−	4.48208i	−0.0849213	−	0.316931i
$201$	9.09328	−	7.07779i	0.641391	−	0.499229i
$202$	8.15274	−	8.15274i	0.573625	−	0.573625i
$203$	10.8646	−	0.0754949i	0.762547	−	0.00529871i
$204$	−5.42111	+	7.16683i	−0.379554	+	0.501779i
$205$	−3.81839	+	2.20455i	−0.266688	+	0.153972i
$206$	0.407094	−	0.109080i	0.0283636	−	0.00760000i
$207$	3.71030	+	0.939465i	0.257884	+	0.0652973i
$208$	1.71778	+	3.17005i	0.119106	+	0.219804i
$209$			26.6934i			1.84642i
$210$	−0.321010	+	2.73002i	−0.0221518	+	0.188390i
$211$	2.68634			0.184935			0.0924677	−	0.995716i	$-0.470524\pi$
$211$	2.68634			0.184935			0.0924677	+	0.995716i	$0.470524\pi$
$212$	0.855522	+	1.48181i	0.0587575	+	0.101771i
$213$	−8.12520	+	20.0055i	−0.556729	+	1.37075i
$214$	12.3235	−	3.30206i	0.842414	−	0.225724i
$215$	1.47042	−	5.48766i	0.100281	−	0.374256i
$216$	4.75841	−	2.08747i	0.323769	−	0.142034i
$217$	−3.85405	−	13.9938i	−0.261630	−	0.949963i
$218$	−6.82968			−0.462564
$219$	6.78536	+	8.71757i	0.458512	+	0.589079i
$220$	−1.66866	−	0.963404i	−0.112501	−	0.0649527i
$221$	−9.78731	+	15.9416i	−0.658365	+	1.07235i
$222$	6.71637	+	0.837099i	0.450773	+	0.0561824i
$223$	2.18383	+	2.18383i	0.146240	+	0.146240i	0.776436	−	0.630196i	$-0.217025\pi$
$223$	2.18383	+	2.18383i	0.146240	+	0.146240i	−0.630196	+	0.776436i	$0.717025\pi$
$224$	−2.55078	+	0.702512i	−0.170431	+	0.0469386i
$225$	−13.3952	+	3.78821i	−0.893014	+	0.252547i
$226$	4.35950	−	16.2699i	0.289990	−	1.08226i
$227$	−5.50302	−	20.5375i	−0.365248	−	1.36312i	−0.867084	−	0.498162i	$-0.834009\pi$
$227$	−5.50302	−	20.5375i	−0.365248	−	1.36312i	0.501836	−	0.864963i	$-0.332658\pi$
$228$	5.41619	−	13.3355i	0.358696	−	0.883165i
$229$	4.13582	+	1.10819i	0.273303	+	0.0732312i	0.392867	−	0.919595i	$-0.371483\pi$
$229$	4.13582	+	1.10819i	0.273303	+	0.0732312i	−0.119565	+	0.992826i	$0.538150\pi$
$230$			0.765280i			0.0504611i
$231$	−9.12190	−	11.5530i	−0.600177	−	0.760129i
$232$	2.90376	−	2.90376i	0.190641	−	0.190641i
$233$	7.18694	+	12.4481i	0.470832	+	0.815505i	0.999443	−	0.0333591i	$-0.0106205\pi$
$233$	7.18694	+	12.4481i	0.470832	+	0.815505i	−0.528612	+	0.848864i	$0.677287\pi$
$234$	9.43811	−	5.28414i	0.616988	−	0.345435i
$235$	1.72454	−	2.98698i	0.112496	−	0.194849i
$236$	−3.14252	−	0.842037i	−0.204561	−	0.0548119i
$237$	−6.01036	−	4.54633i	−0.390415	−	0.295316i
$238$	−9.77342	−	9.63854i	−0.633517	−	0.624774i
$239$	7.07117	−	7.07117i	0.457396	−	0.457396i	−0.440404	−	0.897800i	$-0.645165\pi$
$239$	7.07117	−	7.07117i	0.457396	−	0.457396i	0.897800	+	0.440404i	$0.145165\pi$
$240$	0.638155	+	0.819878i	0.0411927	+	0.0529229i
$241$	2.14060	+	7.98882i	0.137888	+	0.514605i	0.999969	+	0.00783522i	$0.00249405\pi$
$241$	2.14060	+	7.98882i	0.137888	+	0.514605i	−0.862081	+	0.506770i	$0.830839\pi$
$242$	−0.658672	+	0.176491i	−0.0423411	+	0.0113453i
$243$	−6.45891	−	14.1874i	−0.414339	−	0.910123i
$244$			0.796257i			0.0509751i
$245$	−4.07055	−	1.03029i	−0.260058	−	0.0658229i
$246$	−7.68039	+	10.1537i	−0.489684	+	0.647373i
$247$	8.53371	−	28.7213i	0.542987	−	1.82749i
$248$	−4.75110	−	2.74305i	−0.301695	−	0.174184i
$249$	−8.85379	+	21.7994i	−0.561086	+	1.38148i
$250$	−2.89131	−	5.00789i	−0.182862	−	0.316727i
$251$	25.4886			1.60882			0.804412	−	0.594071i	$-0.202480\pi$
$251$	25.4886			1.60882			0.804412	+	0.594071i	$0.202480\pi$
$252$	2.21299	+	7.62251i	0.139405	+	0.480173i
$253$	−2.89779	−	2.89779i	−0.182182	−	0.182182i
$254$	0.636303	−	2.37472i	0.0399252	−	0.149003i
$255$	−2.02836	+	4.99414i	−0.127021	+	0.312745i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.50252	+	11.2627i	0.405616	+	0.702548i	0.994393	−	0.105748i	$-0.0337236\pi$
$257$	6.50252	+	11.2627i	0.405616	+	0.702548i	−0.588777	+	0.808296i	$0.700390\pi$
$258$	−2.25346	−	16.2491i	−0.140294	−	1.01162i
$259$	−2.60642	+	10.0049i	−0.161955	+	0.621672i
$260$	1.48744	+	1.57006i	0.0922474	+	0.0973709i
$261$	−8.83073	−	8.59018i	−0.546608	−	0.531719i
$262$	−20.2894	+	5.43654i	−1.25349	+	0.335871i
$263$	−7.46602	−	4.31051i	−0.460375	−	0.265797i	0.251827	−	0.967772i	$-0.418969\pi$
$263$	−7.46602	−	4.31051i	−0.460375	−	0.265797i	−0.712202	+	0.701975i	$0.752302\pi$
$264$	−5.52094	−	0.688106i	−0.339790	−	0.0423500i
$265$	0.725746	+	0.725746i	0.0445822	+	0.0445822i
$266$	19.1166	+	10.8606i	1.17212	+	0.665905i
$267$	2.85575	+	20.5920i	0.174769	+	1.26021i
$268$	6.42620	+	1.72190i	0.392543	+	0.105181i
$269$	19.8943	+	11.4860i	1.21298	+	0.700313i	0.963407	−	0.268044i	$-0.0863772\pi$
$269$	19.8943	+	11.4860i	1.21298	+	0.700313i	0.249571	+	0.968357i	$0.419710\pi$
$270$	2.43297	−	1.94824i	0.148066	−	0.118566i
$271$	19.2021	+	5.14519i	1.16645	+	0.312548i	0.789538	−	0.613702i	$-0.210320\pi$
$271$	19.2021	+	5.14519i	1.16645	+	0.312548i	0.376909	+	0.926250i	$0.376987\pi$
$272$	−5.18819			−0.314580
$273$	6.12151	+	15.3469i	0.370491	+	0.928836i
$274$	5.86906			0.354563
$275$	14.3972	+	3.85773i	0.868186	+	0.232630i
$276$	0.859706	+	2.03565i	0.0517482	+	0.122532i
$277$	12.9397	+	7.47073i	0.777470	+	0.448872i	0.835533	−	0.549440i	$-0.185159\pi$
$277$	12.9397	+	7.47073i	0.777470	+	0.448872i	−0.0580630	+	0.998313i	$0.518492\pi$
$278$	3.27803	+	0.878345i	0.196603	+	0.0526796i
$279$	−8.03158	+	14.3656i	−0.480838	+	0.860044i
$280$	−1.36887	+	0.803051i	−0.0818056	+	0.0479915i
$281$	0.842761	+	0.842761i	0.0502749	+	0.0502749i	0.731797	−	0.681522i	$-0.238682\pi$
$281$	0.842761	+	0.842761i	0.0502749	+	0.0502749i	−0.681522	+	0.731797i	$0.738682\pi$
$282$	1.23174	−	9.88273i	0.0733491	−	0.588508i
$283$	4.36513	+	2.52021i	0.259480	+	0.149811i	0.624097	−	0.781346i	$-0.285467\pi$
$283$	4.36513	+	2.52021i	0.259480	+	0.149811i	−0.364617	+	0.931158i	$0.618800\pi$
$284$	−12.0417	+	3.22656i	−0.714542	+	0.191461i
$285$	1.06782	−	8.56753i	0.0632522	−	0.507497i
$286$	−11.5774	−	0.312829i	−0.684589	−	0.0184979i
$287$	−13.8466	−	13.6555i	−0.817336	−	0.806056i
$288$	2.61854	+	1.46399i	0.154299	+	0.0862662i
$289$	−4.95866	−	8.58865i	−0.291686	−	0.505215i
$290$	1.23164	−	2.13327i	0.0723245	−	0.125270i
$291$	20.6411	+	8.38334i	1.21000	+	0.491440i
$292$	−1.65075	+	6.16069i	−0.0966029	+	0.360527i
$293$	4.76090	+	4.76090i	0.278135	+	0.278135i	0.832364	−	0.554229i	$-0.186987\pi$
$293$	4.76090	+	4.76090i	0.278135	+	0.278135i	−0.554229	+	0.832364i	$0.686987\pi$
$294$	−11.9851	+	1.83222i	−0.698986	+	0.106857i
$295$	−1.95152			−0.113622
$296$	1.95385	+	3.38417i	0.113565	+	0.196701i
$297$	−1.83545	+	16.5897i	−0.106503	+	0.962635i
$298$	18.8798	+	10.9003i	1.09368	+	0.631435i
$299$	2.19153	+	4.04434i	0.126740	+	0.233891i
$300$	−6.40984	−	4.84850i	−0.370072	−	0.279929i
$301$	25.0578	−	0.174119i	1.44431	−	0.0100361i
$302$		−	11.3387i		−	0.652466i
$303$	2.46987	−	19.8167i	0.141890	−	1.13844i
$304$	8.02689	−	2.15080i	0.460374	−	0.123357i
$305$	0.123620	+	0.461355i	0.00707845	+	0.0264171i
$306$	0.214892	+	15.5631i	0.0122846	+	0.889682i
$307$	−17.3519	+	17.3519i	−0.990324	+	0.990324i	−0.999954	−	0.00962922i	$-0.996935\pi$
$307$	−17.3519	+	17.3519i	−0.990324	+	0.990324i	0.00962922	+	0.999954i	$0.496935\pi$
$308$	2.14251	−	8.22413i	0.122081	−	0.468613i
$309$	0.440376	−	0.582187i	0.0250521	−	0.0331194i
$310$	−3.17868	−	0.851724i	−0.180537	−	0.0483747i
$311$	−12.1990	+	21.1294i	−0.691744	+	1.19814i	0.279521	+	0.960139i	$0.409824\pi$
$311$	−12.1990	+	21.1294i	−0.691744	+	1.19814i	−0.971266	+	0.237997i	$0.923509\pi$
$312$	5.72040	+	2.50540i	0.323854	+	0.141840i
$313$	12.9180	+	22.3747i	0.730171	+	1.26469i	0.956810	+	0.290714i	$0.0938930\pi$
$313$	12.9180	+	22.3747i	0.730171	+	1.26469i	−0.226639	+	0.973979i	$0.572774\pi$
$314$	−16.8789	+	16.8789i	−0.952533	+	0.952533i
$315$	2.46562	+	4.07296i	0.138922	+	0.229485i
$316$		−	4.35100i		−	0.244763i
$317$	14.2207	+	3.81041i	0.798712	+	0.214014i	0.635018	−	0.772497i	$-0.280993\pi$
$317$	14.2207	+	3.81041i	0.798712	+	0.214014i	0.163693	+	0.986511i	$0.447659\pi$
$318$	2.74579	+	1.11520i	0.153976	+	0.0625372i
$319$	3.41407	+	12.7415i	0.191151	+	0.713385i
$320$	−0.155251	+	0.579405i	−0.00867881	+	0.0323897i
$321$	13.3310	−	17.6238i	0.744061	−	0.983666i
$322$	−3.25428	+	0.896263i	−0.181354	+	0.0499468i
$323$	30.4863	+	30.4863i	1.69630	+	1.69630i
$324$	4.28308	−	7.91550i	0.237949	−	0.439750i
$325$	−14.2577	−	8.75352i	−0.790877	−	0.485558i
$326$	−1.16939	−	0.675150i	−0.0647668	−	0.0373931i
$327$	−9.33491	+	7.26587i	−0.516222	+	0.401803i
$328$	−7.35040			−0.405858
$329$	14.7216	+	3.83519i	0.811626	+	0.211441i
$330$	−3.30569	+	0.458440i	−0.181972	+	0.0252363i
$331$	0.769457	−	2.87165i	0.0422932	−	0.157840i	−0.941550	−	0.336874i	$-0.890630\pi$
$331$	0.769457	−	2.87165i	0.0422932	−	0.157840i	0.983843	+	0.179034i	$0.0572971\pi$
$332$	−13.1215	+	3.51589i	−0.720134	+	0.192959i
$333$	10.0706	−	6.00116i	0.551866	−	0.328862i
$334$	−0.167198	−	0.289596i	−0.00914867	−	0.0158460i
$335$	3.99070			0.218035
$336$	−2.73907	+	3.67389i	−0.149428	+	0.200427i
$337$			13.9931i			0.762255i	0.924523	+	0.381127i	$0.124464\pi$
$337$			13.9931i			0.762255i	−0.924523	+	0.381127i	$0.875536\pi$
$338$	12.3570	+	4.03784i	0.672133	+	0.219629i
$339$	−11.3503	−	26.8759i	−0.616466	−	1.45970i
$340$	−3.00607	+	0.805473i	−0.163027	+	0.0436829i
$341$	15.2614	−	8.81117i	0.826451	−	0.477152i
$342$	−6.78425	−	23.9893i	−0.366850	−	1.29719i
$343$	−0.386041	−	18.5162i	−0.0208442	−	0.999783i
$344$	6.69715	−	6.69715i	0.361086	−	0.361086i
$345$	0.814156	+	1.04600i	0.0438327	+	0.0563146i
$346$	−6.56107	−	24.4862i	−0.352725	−	1.31639i
$347$	−8.62184	−	4.97782i	−0.462845	−	0.267224i	0.250395	−	0.968144i	$-0.419440\pi$
$347$	−8.62184	−	4.97782i	−0.462845	−	0.267224i	−0.713240	+	0.700920i	$0.752773\pi$
$348$	0.879694	−	7.05812i	0.0471565	−	0.378355i
$349$	13.9690	−	13.9690i	0.747742	−	0.747742i	−0.226313	−	0.974055i	$-0.572667\pi$
$349$	13.9690	−	13.9690i	0.747742	−	0.747742i	0.974055	+	0.226313i	$0.0726672\pi$
$350$	8.62046	−	8.74110i	0.460783	−	0.467232i
$351$	7.27854	−	17.2633i	0.388499	−	0.921449i
$352$	−1.60609	−	2.78183i	−0.0856049	−	0.148272i
$353$	−3.84065	−	14.3335i	−0.204417	−	0.762896i	−0.989626	−	0.143665i	$-0.954111\pi$
$353$	−3.84065	−	14.3335i	−0.204417	−	0.762896i	0.785209	−	0.619231i	$-0.212556\pi$
$354$	−5.19107	+	2.19232i	−0.275902	+	0.116520i
$355$	−6.47608	+	3.73897i	−0.343715	+	0.198444i
$356$	−8.48711	+	8.48711i	−0.449816	+	0.449816i
$357$	−23.6126	−	2.77649i	−1.24971	−	0.146947i
$358$	2.09314	−	2.09314i	0.110626	−	0.110626i
$359$	3.87962	−	14.4789i	0.204759	−	0.764169i	−0.784764	−	0.619794i	$-0.787216\pi$
$359$	3.87962	−	14.4789i	0.204759	−	0.764169i	0.989523	−	0.144375i	$-0.0461172\pi$
$360$	1.74448	+	0.441711i	0.0919422	+	0.0232802i
$361$	−43.3505	−	25.0284i	−2.28161	−	1.31729i
$362$	−0.185714	+	0.693096i	−0.00976093	+	0.0364283i
$363$	−0.712522	+	0.941970i	−0.0373977	+	0.0494406i
$364$	−4.93449	+	8.16399i	−0.258638	+	0.427910i
$365$			3.82582i			0.200252i
$366$	0.847111	+	1.08834i	0.0442792	+	0.0568883i
$367$	−6.15961	+	10.6688i	−0.321529	+	0.556905i	−0.980804	−	0.194998i	$-0.937530\pi$
$367$	−6.15961	+	10.6688i	−0.321529	+	0.556905i	0.659275	+	0.751902i	$0.270863\pi$
$368$	−0.637898	+	1.10487i	−0.0332528	+	0.0575955i
$369$	0.304450	+	22.0491i	0.0158490	+	1.14783i
$370$	1.65747	+	1.65747i	0.0861676	+	0.0861676i
$371$	−2.23620	+	3.93613i	−0.116098	+	0.204354i
$372$	−9.41213	+	1.30529i	−0.487996	+	0.0676763i
$373$	−2.52756	−	4.37786i	−0.130872	−	0.226677i	0.793141	−	0.609038i	$-0.208444\pi$
$373$	−2.52756	−	4.37786i	−0.130872	−	0.226677i	−0.924013	+	0.382361i	$0.875111\pi$
$374$	8.33270	−	14.4327i	0.430874	−	0.746295i
$375$	−9.27961	−	3.76890i	−0.479197	−	0.194625i
$376$	4.97960	−	2.87497i	0.256803	−	0.148265i
$377$	0.399929	−	14.8009i	0.0205974	−	0.762287i
$378$	11.1341	+	8.06425i	0.572676	+	0.414780i
$379$	−1.20575	−	1.20575i	−0.0619353	−	0.0619353i	0.675461	−	0.737396i	$-0.263945\pi$
$379$	−1.20575	−	1.20575i	−0.0619353	−	0.0619353i	−0.737396	+	0.675461i	$0.763945\pi$
$380$	4.31691	−	2.49237i	0.221453	−	0.127856i
$381$	−1.65667	−	3.92274i	−0.0848739	−	0.200968i
$382$	14.0884	−	3.77497i	0.720824	−	0.193144i
$383$	17.5705	+	4.70799i	0.897808	+	0.240567i	0.678075	−	0.734993i	$-0.262815\pi$
$383$	17.5705	+	4.70799i	0.897808	+	0.240567i	0.219734	+	0.975560i	$0.429481\pi$
$384$	0.237927	+	1.71563i	0.0121417	+	0.0875504i
$385$	−0.0354226	−	5.09773i	−0.00180530	−	0.259804i
$386$			20.2524i			1.03082i
$387$	−20.3669	−	19.8121i	−1.03531	−	1.00711i
$388$	3.32907	+	12.4242i	0.169008	+	0.630745i
$389$	15.4549	−	26.7687i	0.783595	−	1.35723i	−0.146240	−	0.989249i	$-0.546717\pi$
$389$	15.4549	−	26.7687i	0.783595	−	1.35723i	0.929835	−	0.367977i	$-0.119949\pi$
$390$	3.70340	+	0.563541i	0.187529	+	0.0285360i
$391$	−6.61908			−0.334741
$392$	−5.01805	−	4.88048i	−0.253450	−	0.246502i
$393$	−21.9482	+	29.0160i	−1.10714	+	1.46366i
$394$	1.10826	−	0.639857i	0.0558336	−	0.0322355i
$395$	−0.675498	−	2.52099i	−0.0339880	−	0.126845i
$396$	−8.27817	+	4.93303i	−0.415994	+	0.247894i
$397$	6.56445	+	1.75894i	0.329461	+	0.0882787i	0.419758	−	0.907636i	$-0.362115\pi$
$397$	6.56445	+	1.75894i	0.329461	+	0.0882787i	−0.0902972	+	0.995915i	$0.528782\pi$
$398$	−1.96997	−	1.96997i	−0.0987456	−	0.0987456i
$399$	37.6831	−	5.49312i	1.88652	−	0.275000i
$400$		−	4.64019i		−	0.232009i
$401$	−6.13006	+	22.8777i	−0.306121	+	1.14246i	0.625856	+	0.779939i	$0.284750\pi$
$401$	−6.13006	+	22.8777i	−0.306121	+	1.14246i	−0.931976	+	0.362519i	$0.881917\pi$
$402$	10.6153	−	4.48311i	0.529443	−	0.223597i
$403$	−19.2377	+	4.60160i	−0.958299	+	0.229222i
$404$	9.98503	−	5.76486i	0.496774	−	0.286813i
$405$	1.25275	−	5.25124i	0.0622496	−	0.260936i
$406$	10.5140	+	2.73905i	0.521799	+	0.135937i
$407$	−12.5522			−0.622191
$408$	−7.09130	+	5.51954i	−0.351072	+	0.273258i
$409$	−2.45363	+	0.657447i	−0.121324	+	0.0325087i	−0.318970	−	0.947765i	$-0.603337\pi$
$409$	−2.45363	+	0.657447i	−0.121324	+	0.0325087i	0.197646	+	0.980273i	$0.436670\pi$
$410$	−4.25886	+	1.14116i	−0.210330	+	0.0563578i
$411$	8.02192	−	6.24389i	0.395692	−	0.307989i
$412$	0.421455			0.0207636
$413$	−2.28554	−	8.29866i	−0.112464	−	0.408350i
$414$	3.34072	+	1.86775i	0.164188	+	0.0917949i
$415$	−7.05680	+	4.07425i	−0.346405	+	0.199997i
$416$	0.838775	+	3.50663i	0.0411243	+	0.171927i
$417$	5.41491	−	2.28685i	0.265169	−	0.111987i
$418$	−6.90875	+	25.7838i	−0.337918	+	1.26113i
$419$		−	3.88080i		−	0.189590i	−0.995497	−	0.0947948i	$-0.969781\pi$
$419$		−	3.88080i		−	0.189590i	0.995497	−	0.0947948i	$-0.0302195\pi$
$420$	−1.01665	+	2.55392i	−0.0496077	+	0.124618i
$421$	0.262070	+	0.262070i	0.0127725	+	0.0127725i	0.713464	−	0.700692i	$-0.247125\pi$
$421$	0.262070	+	0.262070i	0.0127725	+	0.0127725i	−0.700692	+	0.713464i	$0.747125\pi$
$422$	2.59481	+	0.695277i	0.126313	+	0.0338455i
$423$	−8.83034	−	14.8183i	−0.429346	−	0.720490i
$424$	0.442851	+	1.65274i	0.0215067	+	0.0802642i
$425$	20.8488	−	12.0371i	1.01132	−	0.583884i
$426$	−13.0261	+	17.2209i	−0.631118	+	0.834353i
$427$	−1.81709	+	1.06600i	−0.0879352	+	0.0515874i
$428$	12.7582			0.616690
$429$	−16.1571	+	11.8893i	−0.780070	+	0.574020i
$430$	2.84062	−	4.92011i	0.136987	−	0.237269i
$431$	−3.75773	−	14.0240i	−0.181004	−	0.675514i	−0.995451	−	0.0952769i	$-0.969626\pi$
$431$	−3.75773	−	14.0240i	−0.181004	−	0.675514i	0.814447	−	0.580238i	$-0.197040\pi$
$432$	5.13655	−	0.784775i	0.247132	−	0.0377575i
$433$		−	9.24282i		−	0.444182i	−0.975026	−	0.222091i	$-0.928712\pi$
$433$		−	9.24282i		−	0.444182i	0.975026	−	0.222091i	$-0.0712881\pi$
$434$	−0.100857	−	14.5145i	−0.00484129	−	0.696719i
$435$	−0.586083	−	4.22609i	−0.0281005	−	0.202625i
$436$	−6.59696	−	1.76765i	−0.315937	−	0.0846551i
$437$	10.2407	−	2.74398i	0.489878	−	0.131262i
$438$	4.29788	+	10.1767i	0.205360	+	0.486262i
$439$	5.46918	−	3.15763i	0.261030	−	0.150705i	−0.363775	−	0.931487i	$-0.618512\pi$
$439$	5.46918	−	3.15763i	0.261030	−	0.150705i	0.624804	+	0.780782i	$0.285179\pi$
$440$	−1.36246	−	1.36246i	−0.0649527	−	0.0649527i
$441$	−14.4322	+	15.2549i	−0.687248	+	0.726423i
$442$	−13.5798	+	12.8652i	−0.645925	+	0.611937i
$443$	−13.0061	+	7.50906i	−0.617937	+	0.356766i	−0.776065	−	0.630652i	$-0.782787\pi$
$443$	−13.0061	+	7.50906i	−0.617937	+	0.356766i	0.158128	+	0.987419i	$0.449454\pi$
$444$	6.27086	+	2.54690i	0.297602	+	0.120871i
$445$	−3.59985	+	6.23511i	−0.170649	+	0.295573i
$446$	1.54420	+	2.67463i	0.0731200	+	0.126648i
$447$	37.4016	−	5.18694i	1.76904	−	0.245334i
$448$	−2.64569	+	0.0183841i	−0.124997	+	0.000868566i
$449$	−11.2960	−	11.2960i	−0.533091	−	0.533091i	0.388400	−	0.921491i	$-0.373028\pi$
$449$	−11.2960	−	11.2960i	−0.533091	−	0.533091i	−0.921491	+	0.388400i	$0.873028\pi$
$450$	−13.9192	+	0.192194i	−0.656159	+	0.00906012i
$451$	11.8054	−	20.4475i	0.555894	−	0.962837i
$452$	8.42191	−	14.5872i	0.396133	−	0.686123i
$453$	−12.0628	−	15.4979i	−0.566761	−	0.728153i
$454$		−	21.2620i		−	0.997877i
$455$	−1.59160	+	5.49635i	−0.0746154	+	0.257673i
$456$	8.68312	−	11.4793i	0.406624	−	0.537567i
$457$	−4.29015	+	16.0111i	−0.200685	+	0.748966i	0.790037	+	0.613059i	$0.210061\pi$
$457$	−4.29015	+	16.0111i	−0.200685	+	0.748966i	−0.990722	+	0.135907i	$0.956605\pi$
$458$	3.70807	+	2.14086i	0.173267	+	0.100036i
$459$	16.8508	+	21.0433i	0.786527	+	0.982216i
$460$	−0.198069	+	0.739204i	−0.00923501	+	0.0344655i
$461$	12.3842	−	12.3842i	0.576788	−	0.576788i	−0.357229	−	0.934017i	$-0.616278\pi$
$461$	12.3842	−	12.3842i	0.576788	−	0.576788i	0.934017	+	0.357229i	$0.116278\pi$
$462$	−5.82096	−	13.5202i	−0.270815	−	0.629018i
$463$	15.3743	−	15.3743i	0.714503	−	0.714503i	−0.252971	−	0.967474i	$-0.581408\pi$
$463$	15.3743	−	15.3743i	0.714503	−	0.714503i	0.967474	+	0.252971i	$0.0814076\pi$
$464$	3.55637	−	2.05327i	0.165100	−	0.0953206i
$465$	−5.25079	+	2.21754i	−0.243499	+	0.102836i
$466$	3.72023	+	13.8841i	0.172336	+	0.643168i
$467$	−2.94747	−	5.10517i	−0.136393	−	0.236239i	0.789736	−	0.613447i	$-0.210218\pi$
$467$	−2.94747	−	5.10517i	−0.136393	−	0.236239i	−0.926129	+	0.377208i	$0.876884\pi$
$468$	10.4841	−	2.66133i	0.484630	−	0.123020i
$469$	4.67374	+	16.9701i	0.215813	+	0.783605i
$470$	2.43886	−	2.43886i	0.112496	−	0.112496i
$471$	−5.11347	+	41.0273i	−0.235616	+	1.89044i
$472$	−2.81751	−	1.62669i	−0.129686	−	0.0748745i
$473$	7.87410	+	29.3865i	0.362052	+	1.35119i
$474$	−4.62888	−	5.94702i	−0.212612	−	0.273156i
$475$	−27.2662	+	27.2662i	−1.25106	+	1.25106i
$476$	−6.94577	−	11.8397i	−0.318359	−	0.542670i
$477$	4.93941	−	1.39688i	0.226160	−	0.0639588i
$478$	8.66038	−	5.00007i	0.396117	−	0.228698i
$479$	−17.4615	+	4.67881i	−0.797838	+	0.213780i	−0.634635	−	0.772812i	$-0.718849\pi$
$479$	−17.4615	+	4.67881i	−0.797838	+	0.213780i	−0.163204	+	0.986592i	$0.552183\pi$
$480$	0.404210	+	0.957107i	0.0184496	+	0.0436858i
$481$	13.5059	+	4.01287i	0.615814	+	0.182971i
$482$			8.27064i			0.376717i
$483$	−3.49450	+	4.68714i	−0.159005	+	0.213272i
$484$	−0.681908			−0.0309958
$485$	3.85776	+	6.68183i	0.175172	+	0.303406i
$486$	−2.56685	−	15.3757i	−0.116435	−	0.697455i
$487$	−37.4584	+	10.0369i	−1.69740	+	0.454817i	−0.972283	−	0.233807i	$-0.924882\pi$
$487$	−37.4584	+	10.0369i	−1.69740	+	0.454817i	−0.725118	+	0.688624i	$0.758215\pi$
$488$	−0.206086	+	0.769125i	−0.00932909	+	0.0348167i
$489$	−2.31662	+	0.321273i	−0.104761	+	0.0145285i
$490$	−3.66519	−	2.04872i	−0.165576	−	0.0925517i
$491$	−9.27442			−0.418549			−0.209274	−	0.977857i	$-0.567110\pi$
$491$	−9.27442			−0.418549			−0.209274	+	0.977857i	$0.567110\pi$
$492$	−10.0466	+	7.81984i	−0.452938	+	0.352546i
$493$	18.4511	+	10.6528i	0.830996	+	0.479776i
$494$	15.6766	−	25.5340i	0.705322	−	1.14883i
$495$	−4.03056	+	4.14342i	−0.181160	+	0.186233i
$496$	−3.87926	−	3.87926i	−0.174184	−	0.174184i
$497$	−23.4841	−	23.1600i	−1.05341	−	1.03887i
$498$	−14.1942	+	18.7651i	−0.636057	+	0.840882i
$499$	−9.84950	+	36.7588i	−0.440924	+	1.64555i	0.285555	+	0.958362i	$0.407822\pi$
$499$	−9.84950	+	36.7588i	−0.440924	+	1.64555i	−0.726479	+	0.687189i	$0.758845\pi$
$500$	−1.49665	−	5.58558i	−0.0669322	−	0.249795i
$501$	−0.536620	−	0.217948i	−0.0239744	−	0.00973718i
$502$	24.6201	+	6.59693i	1.09885	+	0.294435i
$503$			13.4961i			0.601763i	0.953662	+	0.300882i	$0.0972809\pi$
$503$			13.4961i			0.601763i	−0.953662	+	0.300882i	$0.902719\pi$
$504$	0.164730	+	7.93554i	0.00733766	+	0.353477i
$505$	4.89038	−	4.89038i	0.217619	−	0.217619i
$506$	−2.04904	−	3.54905i	−0.0910911	−	0.157774i
$507$	21.1855	−	7.62724i	0.940881	−	0.338737i
$508$	1.22924	−	2.12911i	0.0545389	−	0.0944641i
$509$	−40.8332	−	10.9412i	−1.80990	−	0.484961i	−0.814449	−	0.580235i	$-0.802961\pi$
$509$	−40.8332	−	10.9412i	−1.80990	−	0.484961i	−0.995451	+	0.0952733i	$0.969627\pi$
$510$	−3.25182	+	4.29899i	−0.143993	+	0.190362i
$511$	−16.2689	+	4.48063i	−0.719694	+	0.198211i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−34.7942	−	25.5714i	−1.53620	−	1.12901i
$514$	3.36595	+	12.5619i	0.148466	+	0.554082i
$515$	0.244193	−	0.0654313i	0.0107604	−	0.00288325i
$516$	2.02890	−	16.2787i	0.0893173	−	0.716628i
$517$			18.4698i			0.812303i
$518$	−5.10706	+	8.98937i	−0.224391	+	0.394970i
$519$	−35.0179	−	26.4881i	−1.53711	−	1.16270i
$520$	1.03040	+	1.90154i	0.0451860	+	0.0833880i
$521$	23.0923	+	13.3323i	1.01169	+	0.584099i	0.911686	−	0.410888i	$-0.134781\pi$
$521$	23.0923	+	13.3323i	1.01169	+	0.584099i	0.100004	+	0.994987i	$0.468114\pi$
$522$	−6.30652	−	10.5830i	−0.276029	−	0.463207i
$523$	−9.51589	−	16.4820i	−0.416101	−	0.720708i	0.579443	−	0.815013i	$-0.303270\pi$
$523$	−9.51589	−	16.4820i	−0.416101	−	0.720708i	−0.995543	+	0.0943055i	$0.969937\pi$
$524$	−21.0052			−0.917616
$525$	2.48322	−	21.1185i	0.108377	−	0.921687i
$526$	−6.09598	−	6.09598i	−0.265797	−	0.265797i
$527$	7.36675	−	27.4931i	0.320901	−	1.19762i
$528$	−5.15472	−	2.09358i	−0.224331	−	0.0911115i
$529$	10.6862	−	18.5090i	0.464616	−	0.804739i
$530$	0.513180	+	0.888854i	0.0222911	+	0.0386094i
$531$	−4.76291	+	8.51910i	−0.206693	+	0.369698i
$532$	15.6543	+	15.4383i	0.678701	+	0.669334i
$533$	−19.2393	+	18.2269i	−0.833345	+	0.789495i
$534$	−2.57117	+	20.6295i	−0.111265	+	0.892725i
$535$	7.39216	−	1.98072i	0.319591	−	0.0856341i
$536$	5.76157	+	3.32645i	0.248862	+	0.143681i
$537$	0.634115	−	5.08775i	0.0273641	−	0.219553i
$538$	16.2436	+	16.2436i	0.700313	+	0.700313i
$539$	21.6361	−	6.12087i	0.931933	−	0.263645i
$540$	2.85431	−	1.25216i	0.122830	−	0.0538843i
$541$	−43.3634	−	11.6192i	−1.86434	−	0.499547i	−0.864342	−	0.502905i	$-0.832265\pi$
$541$	−43.3634	−	11.6192i	−1.86434	−	0.499547i	−0.999994	+	0.00335721i	$0.998931\pi$
$542$	17.2162	+	9.93975i	0.739497	+	0.426949i
$543$	0.483524	+	1.14491i	0.0207500	+	0.0491328i
$544$	−5.01141	−	1.34280i	−0.214862	−	0.0575722i
$545$	−4.09674			−0.175485
$546$	1.94086	+	16.4083i	0.0830610	+	0.702211i
$547$	−10.8785			−0.465131			−0.232566	−	0.972581i	$-0.574712\pi$
$547$	−10.8785			−0.465131			−0.232566	+	0.972581i	$0.574712\pi$
$548$	5.66907	+	1.51902i	0.242171	+	0.0648895i
$549$	2.31569	+	0.586344i	0.0988313	+	0.0250245i
$550$	12.9082	+	7.45255i	0.550408	+	0.317778i
$551$	−32.9627	−	8.83234i	−1.40426	−	0.376270i
$552$	0.303547	+	2.18880i	0.0129198	+	0.0931614i
$553$	9.92915	−	5.82496i	0.422231	−	0.247703i
$554$	10.5652	+	10.5652i	0.448872	+	0.448872i
$555$	4.02878	+	0.502129i	0.171012	+	0.0213142i
$556$	2.93900	+	1.69683i	0.124641	+	0.0719617i
$557$	−36.3533	+	9.74083i	−1.54034	+	0.412732i	−0.926375	−	0.376603i	$-0.877092\pi$
$557$	−36.3533	+	9.74083i	−1.54034	+	0.412732i	−0.613963	+	0.789335i	$0.710426\pi$
$558$	−11.4760	+	11.7973i	−0.485817	+	0.499421i
$559$	0.922384	−	34.1364i	0.0390127	−	1.44382i
$560$	−1.53007	+	0.421398i	−0.0646573	+	0.0178073i
$561$	−3.96515	−	28.5917i	−0.167409	−	1.20714i
$562$	0.595922	+	1.03217i	0.0251375	+	0.0435393i
$563$	6.20164	−	10.7416i	0.261368	−	0.452703i	−0.705238	−	0.708971i	$-0.749160\pi$
$563$	6.20164	−	10.7416i	0.261368	−	0.452703i	0.966606	+	0.256268i	$0.0824931\pi$
$564$	3.74761	−	9.22719i	0.157803	−	0.388535i
$565$	2.61502	−	9.75940i	0.110015	−	0.410581i
$566$	3.56412	+	3.56412i	0.149811	+	0.149811i
$567$	23.7975	−	0.822829i	0.999403	−	0.0345556i
$568$	−12.4665			−0.523081
$569$	−13.3186	−	23.0685i	−0.558344	−	0.967081i	−0.997635	−	0.0687356i	$-0.978104\pi$
$569$	−13.3186	−	23.0685i	−0.558344	−	0.967081i	0.439291	−	0.898345i	$-0.355230\pi$
$570$	3.24887	−	7.99922i	0.136080	−	0.335051i
$571$	−38.6796	−	22.3317i	−1.61869	−	0.934552i	−0.987259	−	0.159121i	$-0.949134\pi$
$571$	−38.6796	−	22.3317i	−1.61869	−	0.934552i	−0.631432	−	0.775431i	$-0.717533\pi$
$572$	−11.1020	−	3.29863i	−0.464198	−	0.137923i
$573$	15.2402	−	20.1478i	0.636667	−	0.841688i
$574$	−9.84045	−	16.7739i	−0.410733	−	0.700129i
$575$		−	5.91994i		−	0.246878i
$576$	2.15041	+	2.09183i	0.0896003	+	0.0871596i
$577$	10.4543	−	2.80122i	0.435218	−	0.116616i	−0.0345564	−	0.999403i	$-0.511002\pi$
$577$	10.4543	−	2.80122i	0.435218	−	0.116616i	0.469775	+	0.882786i	$0.344335\pi$
$578$	−2.56679	−	9.57939i	−0.106764	−	0.398450i
$579$	21.5458	+	27.6812i	0.895413	+	1.15039i
$580$	1.74181	−	1.74181i	0.0723245	−	0.0723245i
$581$	−25.5899	−	25.2368i	−1.06165	−	1.04700i
$582$	17.7680	+	13.4400i	0.736506	+	0.557105i
$583$	−5.30890	−	1.42252i	−0.219872	−	0.0589146i
$584$	−3.18901	+	5.52352i	−0.131962	+	0.228565i
$585$	5.66140	−	3.16966i	0.234070	−	0.131049i
$586$	3.36646	+	5.83089i	0.139067	+	0.240872i
$587$	−9.59239	+	9.59239i	−0.395920	+	0.395920i	−0.876791	−	0.480871i	$-0.840321\pi$
$587$	−9.59239	+	9.59239i	−0.395920	+	0.395920i	0.480871	+	0.876791i	$0.340321\pi$
$588$	−12.0509	−	1.33218i	−0.496973	−	0.0549384i
$589$			45.5897i			1.87849i
$590$	−1.88503	−	0.505091i	−0.0776053	−	0.0207943i
$591$	0.834072	−	2.05361i	0.0343091	−	0.0844743i
$592$	1.01139	+	3.77455i	0.0415678	+	0.155133i
$593$	−5.39354	+	20.1290i	−0.221486	+	0.826598i	0.762295	+	0.647229i	$0.224072\pi$
$593$	−5.39354	+	20.1290i	−0.221486	+	0.826598i	−0.983782	+	0.179369i	$0.942594\pi$
$594$	−6.06665	+	15.5494i	−0.248918	+	0.638000i
$595$	−5.86254	−	5.78162i	−0.240341	−	0.237023i
$596$	15.4153	+	15.4153i	0.631435	+	0.631435i
$597$	−4.78837	−	0.596802i	−0.195975	−	0.0244255i
$598$	1.07011	+	4.47375i	0.0437599	+	0.182945i
$599$	20.0588	+	11.5809i	0.819579	+	0.473184i	0.850271	−	0.526345i	$-0.176438\pi$
$599$	20.0588	+	11.5809i	0.819579	+	0.473184i	−0.0306925	+	0.999529i	$0.509771\pi$
$600$	−4.93654	−	6.34228i	−0.201533	−	0.258923i
$601$	−4.85103			−0.197877			−0.0989387	−	0.995094i	$-0.531545\pi$
$601$	−4.85103			−0.197877			−0.0989387	+	0.995094i	$0.531545\pi$
$602$	24.2491	+	6.31726i	0.988319	+	0.257472i
$603$	9.73975	−	17.4209i	0.396633	−	0.709432i
$604$	2.93466	−	10.9523i	0.119410	−	0.445643i
$605$	−0.395101	+	0.105867i	−0.0160631	+	0.00430411i
$606$	7.51466	−	18.5022i	0.305262	−	0.751603i
$607$	−17.4499	−	30.2241i	−0.708268	−	1.22676i	−0.965499	−	0.260407i	$-0.916143\pi$
$607$	−17.4499	−	30.2241i	−0.708268	−	1.22676i	0.257231	−	0.966350i	$-0.417190\pi$
$608$	8.31005			0.337017
$609$	17.2846	−	7.44167i	0.700409	−	0.301552i
$610$			0.477630i			0.0193387i
$611$	5.90470	−	19.8731i	0.238879	−	0.803978i
$612$	−3.82045	+	15.0884i	−0.154433	+	0.609913i
$613$	18.8091	−	5.03987i	0.759691	−	0.203559i	0.141879	−	0.989884i	$-0.454686\pi$
$613$	18.8091	−	5.03987i	0.759691	−	0.203559i	0.617812	+	0.786325i	$0.288019\pi$
$614$	−21.2516	+	12.2696i	−0.857646	+	0.495162i
$615$	−4.60704	+	6.09061i	−0.185774	+	0.245597i
$616$	4.19807	−	7.38937i	0.169145	−	0.297726i
$617$	7.75021	−	7.75021i	0.312012	−	0.312012i	−0.533677	−	0.845688i	$-0.679190\pi$
$617$	7.75021	−	7.75021i	0.312012	−	0.312012i	0.845688	+	0.533677i	$0.179190\pi$
$618$	0.576051	−	0.448372i	0.0231722	−	0.0180362i
$619$	−10.8113	−	40.3484i	−0.434544	−	1.62174i	−0.742156	−	0.670228i	$-0.766196\pi$
$619$	−10.8113	−	40.3484i	−0.434544	−	1.62174i	0.307612	−	0.951512i	$-0.400470\pi$
$620$	−2.84992	−	1.64540i	−0.114456	−	0.0660810i
$621$	6.55319	−	1.00121i	0.262971	−	0.0401773i
$622$	−17.2521	+	17.2521i	−0.691744	+	0.691744i
$623$	−30.7302	−	8.00569i	−1.23118	−	0.320741i
$624$	4.87704	+	3.90058i	0.195238	+	0.156148i
$625$	9.86613	+	17.0886i	0.394645	+	0.683546i
$626$	6.68687	+	24.9557i	0.267261	+	0.997432i
$627$	17.9875	+	42.5917i	0.718353	+	1.70095i
$628$	−20.6724	+	11.9352i	−0.824918	+	0.476267i
$629$	−14.3358	+	14.3358i	−0.571606	+	0.571606i
$630$	1.32745	+	4.57232i	0.0528868	+	0.182166i
$631$	−2.77766	+	2.77766i	−0.110577	+	0.110577i	−0.760230	−	0.649653i	$-0.774914\pi$
$631$	−2.77766	+	2.77766i	−0.110577	+	0.110577i	0.649653	+	0.760230i	$0.274914\pi$
$632$	1.12612	−	4.20274i	0.0447947	−	0.167176i
$633$	4.28631	−	1.81021i	0.170365	−	0.0719496i
$634$	12.7499	+	7.36115i	0.506363	+	0.292349i
$635$	0.381683	−	1.42446i	0.0151466	−	0.0565280i
$636$	2.36359	+	1.78786i	0.0937225	+	0.0708933i
$637$	−25.2367	−	0.331043i	−0.999914	−	0.0131164i
$638$			13.1909i			0.522234i
$639$	0.516354	+	37.3958i	0.0204267	+	1.47936i
$640$	−0.299922	+	0.519481i	−0.0118555	+	0.0205343i
$641$	8.54841	−	14.8063i	0.337642	−	0.584813i	−0.646347	−	0.763044i	$-0.723704\pi$
$641$	8.54841	−	14.8063i	0.337642	−	0.584813i	0.983989	+	0.178231i	$0.0570373\pi$
$642$	17.4381	−	13.5730i	0.688227	−	0.535684i
$643$	15.2523	+	15.2523i	0.601493	+	0.601493i	0.940709	−	0.339215i	$-0.110162\pi$
$643$	15.2523	+	15.2523i	0.601493	+	0.601493i	−0.339215	+	0.940709i	$0.610162\pi$
$644$	−3.37536	+	0.0234544i	−0.133008	+	0.000924231i
$645$	−1.35172	−	9.74693i	−0.0532241	−	0.383785i
$646$	21.5570	+	37.3379i	0.848151	+	1.46904i
$647$	−6.39763	+	11.0810i	−0.251517	+	0.435640i	−0.963944	−	0.266106i	$-0.914263\pi$
$647$	−6.39763	+	11.0810i	−0.251517	+	0.435640i	0.712427	+	0.701746i	$0.247596\pi$
$648$	6.18582	−	6.53725i	0.243002	−	0.256807i
$649$	9.05035	−	5.22522i	0.355257	−	0.205108i
$650$	−11.5063	−	12.1454i	−0.451316	−	0.476383i
$651$	−15.5794	−	19.7314i	−0.610603	−	0.773333i
$652$	−0.954807	−	0.954807i	−0.0373931	−	0.0373931i
$653$	−9.47898	+	5.47269i	−0.370941	+	0.214163i	−0.673870	−	0.738850i	$-0.735369\pi$
$653$	−9.47898	+	5.47269i	−0.370941	+	0.214163i	0.302928	+	0.953013i	$0.402036\pi$
$654$	−10.8974	+	4.60223i	−0.426121	+	0.179962i
$655$	−12.1705	+	3.26108i	−0.475541	+	0.127421i
$656$	−7.09994	−	1.90242i	−0.277206	−	0.0742771i
$657$	16.7011	+	9.33733i	0.651571	+	0.364284i
$658$	13.2273	+	7.51473i	0.515654	+	0.292955i
$659$			19.1808i			0.747177i	0.927595	+	0.373588i	$0.121873\pi$
$659$			19.1808i			0.747177i	−0.927595	+	0.373588i	$0.878127\pi$
$660$	−3.31171	−	0.412757i	−0.128908	−	0.0160665i
$661$	−0.274549	−	1.02463i	−0.0106787	−	0.0398535i	0.960381	−	0.278691i	$-0.0899004\pi$
$661$	−0.274549	−	1.02463i	−0.0106787	−	0.0398535i	−0.971060	+	0.238837i	$0.923234\pi$
$662$	1.48648	−	2.57465i	0.0577735	−	0.100067i
$663$	−4.87419	+	32.0315i	−0.189298	+	1.24400i
$664$	−13.5843			−0.527175
$665$	11.4670	+	6.51466i	0.444672	+	0.252628i
$666$	11.2807	−	3.19021i	0.437117	−	0.123618i
$667$	4.53720	−	2.61955i	0.175681	−	0.101430i
$668$	−0.0865481	−	0.323002i	−0.00334865	−	0.0124973i
$669$	4.95609	+	2.01291i	0.191614	+	0.0778236i
$670$	3.85472	+	1.03287i	0.148921	+	0.0399032i
$671$	−1.80858	−	1.80858i	−0.0698195	−	0.0698195i
$672$	−3.59661	+	2.83979i	−0.138742	+	0.109547i
$673$		−	20.6567i		−	0.796258i	−0.917329	−	0.398129i	$-0.869660\pi$
$673$		−	20.6567i		−	0.796258i	0.917329	−	0.398129i	$-0.130340\pi$
$674$	−3.62169	+	13.5163i	−0.139502	+	0.520630i
$675$	−18.8206	+	15.0709i	−0.724404	+	0.580079i
$676$	10.8909	+	7.09848i	0.418880	+	0.273019i
$677$	−16.6890	+	9.63538i	−0.641409	+	0.370318i	−0.785157	−	0.619297i	$-0.787418\pi$
$677$	−16.6890	+	9.63538i	−0.641409	+	0.370318i	0.143748	+	0.989614i	$0.454084\pi$
$678$	−4.00761	−	28.8978i	−0.153911	−	1.10981i
$679$	−23.8958	+	24.2302i	−0.917036	+	0.929870i
$680$	−3.11211			−0.119344
$681$	−22.6200	−	29.0613i	−0.866799	−	1.11363i
$682$	17.0219	−	4.56100i	0.651801	−	0.174650i
$683$	−23.0006	+	6.16299i	−0.880093	+	0.235820i	−0.670447	−	0.741957i	$-0.733898\pi$
$683$	−23.0006	+	6.16299i	−0.880093	+	0.235820i	−0.209646	+	0.977777i	$0.567231\pi$
$684$	−0.344198	−	24.9278i	−0.0131607	−	0.953137i
$685$	3.52052			0.134512
$686$	4.41947	−	17.9852i	0.168736	−	0.686679i
$687$	7.34585	−	1.01874i	0.280261	−	0.0388673i
$688$	8.20230	−	4.73560i	0.312710	−	0.180543i
$689$	5.25746	+	3.22781i	0.200293	+	0.122970i
$690$	0.515690	+	1.22107i	0.0196320	+	0.0464855i
$691$	1.29565	−	4.83543i	0.0492888	−	0.183948i	−0.936893	−	0.349617i	$-0.886312\pi$
$691$	1.29565	−	4.83543i	0.0492888	−	0.183948i	0.986181	+	0.165669i	$0.0529783\pi$
$692$		−	25.3500i		−	0.963663i
$693$	−22.3399	−	12.2869i	−0.848622	−	0.466742i
$694$	−7.03971	−	7.03971i	−0.267224	−	0.267224i
$695$	1.96631	+	0.526871i	0.0745863	+	0.0199853i
$696$	2.67650	−	6.58994i	0.101452	−	0.249791i
$697$	−9.87013	−	36.8358i	−0.373858	−	1.39526i
$698$	17.1084	−	9.87755i	0.647563	−	0.373871i
$699$	19.8557	+	15.0192i	0.751012	+	0.568078i
$700$	10.5891	−	6.21212i	0.400230	−	0.234796i
$701$	12.9949			0.490810			0.245405	−	0.969421i	$-0.421079\pi$
$701$	12.9949			0.490810			0.245405	+	0.969421i	$0.421079\pi$
$702$	11.4986	−	14.7913i	0.433987	−	0.558261i
$703$	16.2366	−	28.1226i	0.612374	−	1.06066i
$704$	−0.831373	−	3.10273i	−0.0313336	−	0.116938i
$705$	0.738853	−	5.92810i	0.0278268	−	0.223265i
$706$		−	14.8391i		−	0.558479i
$707$	26.5233	+	15.0685i	0.997510	+	0.566708i
$708$	−5.58160	+	0.774068i	−0.209769	+	0.0290913i
$709$	42.1942	+	11.3059i	1.58464	+	0.424602i	0.940358	−	0.340187i	$-0.110490\pi$
$709$	42.1942	+	11.3059i	1.58464	+	0.424602i	0.644280	+	0.764789i	$0.277157\pi$
$710$	−7.22313	+	1.93543i	−0.271079	+	0.0726355i
$711$	−12.6537	−	3.20397i	−0.474550	−	0.120158i
$712$	−10.3946	+	6.00130i	−0.389552	+	0.224908i
$713$	−4.94915	−	4.94915i	−0.185347	−	0.185347i
$714$	−22.0894	−	8.79327i	−0.826675	−	0.329080i
$715$	−6.94467	−	0.187648i	−0.259716	−	0.00701766i
$716$	2.56356	−	1.48007i	0.0958047	−	0.0553129i
$717$	6.51774	−	16.0477i	0.243409	−	0.599311i
$718$	7.49485	−	12.9815i	0.279705	−	0.484464i
$719$	15.7316	+	27.2479i	0.586690	+	1.01618i	0.994662	+	0.103182i	$0.0329025\pi$
$719$	15.7316	+	27.2479i	0.586690	+	1.01618i	−0.407973	+	0.912994i	$0.633764\pi$
$720$	1.57072	+	0.878164i	0.0585371	+	0.0327273i
$721$	0.564229	+	0.961777i	0.0210130	+	0.0358184i
$722$	−35.3955	−	35.3955i	−1.31729	−	1.31729i
$723$	8.79886	+	11.3044i	0.327233	+	0.420417i
$724$	−0.358773	+	0.621412i	−0.0133337	+	0.0230946i
$725$	−9.52755	+	16.5022i	−0.353844	+	0.612877i
$726$	−0.932043	+	0.725459i	−0.0345913	+	0.0269243i
$727$		−	42.0789i		−	1.56062i	−0.625393	−	0.780310i	$-0.715061\pi$
$727$		−	42.0789i		−	1.56062i	0.625393	−	0.780310i	$-0.284939\pi$
$728$	−6.87935	+	6.60867i	−0.254966	+	0.244934i
$729$	−19.8661	−	18.2849i	−0.735781	−	0.677220i
$730$	−0.990194	+	3.69545i	−0.0366487	+	0.136775i
$731$	42.5551	+	24.5692i	1.57396	+	0.908724i
$732$	0.536564	+	1.27050i	0.0198320	+	0.0469591i
$733$	5.35665	−	19.9913i	0.197852	−	0.738395i	−0.793658	−	0.608365i	$-0.791826\pi$
$733$	5.35665	−	19.9913i	0.197852	−	0.738395i	0.991510	−	0.130030i	$-0.0415075\pi$
$734$	−8.71100	+	8.71100i	−0.321529	+	0.321529i
$735$	−7.18921	+	1.09905i	−0.265178	+	0.0405390i
$736$	−0.902125	+	0.902125i	−0.0332528	+	0.0332528i
$737$	−18.5072	+	10.6851i	−0.681722	+	0.393592i
$738$	−5.41265	+	21.3766i	−0.199242	+	0.786883i
$739$	9.97235	+	37.2173i	0.366839	+	1.36906i	0.864911	+	0.501925i	$0.167375\pi$
$739$	9.97235	+	37.2173i	0.366839	+	1.36906i	−0.498072	+	0.867136i	$0.665959\pi$
$740$	1.17201	+	2.02997i	0.0430838	+	0.0746233i
$741$	−5.73779	−	51.5780i	−0.210783	−	1.89477i
$742$	−3.17875	+	3.22323i	−0.116696	+	0.118329i
$743$	1.60617	−	1.60617i	0.0589248	−	0.0589248i	−0.677030	−	0.735955i	$-0.736733\pi$
$743$	1.60617	−	1.60617i	0.0589248	−	0.0589248i	0.735955	+	0.677030i	$0.236733\pi$
$744$	−9.42925	−	1.17522i	−0.345693	−	0.0430857i
$745$	11.3249	+	6.53846i	0.414914	+	0.239551i
$746$	−1.30836	−	4.88287i	−0.0479025	−	0.178775i
$747$	0.562656	+	40.7491i	0.0205865	+	1.49093i
$748$	11.7842	−	11.7842i	0.430874	−	0.430874i
$749$	17.0802	+	29.1147i	0.624097	+	1.06383i
$750$	−7.98796	−	6.04222i	−0.291679	−	0.220631i
$751$	1.80427	−	1.04170i	0.0658387	−	0.0380120i	−0.466719	−	0.884406i	$-0.654564\pi$
$751$	1.80427	−	1.04170i	0.0658387	−	0.0380120i	0.532558	+	0.846394i	$0.321231\pi$
$752$	5.55402	−	1.48819i	0.202534	−	0.0542689i
$753$	40.6694	−	17.1757i	1.48207	−	0.625917i
$754$	4.21707	−	14.1931i	0.153576	−	0.516882i
$755$		−	6.80143i		−	0.247529i
$756$	8.66752	+	10.6712i	0.315235	+	0.388107i
$757$	−10.9645			−0.398510			−0.199255	−	0.979948i	$-0.563852\pi$
$757$	−10.9645			−0.398510			−0.199255	+	0.979948i	$0.563852\pi$
$758$	−0.852595	−	1.47674i	−0.0309676	−	0.0536375i
$759$	−6.57638	−	2.67099i	−0.238708	−	0.0969507i
$760$	4.81488	−	1.29014i	0.174654	−	0.0467985i
$761$	5.57308	−	20.7990i	0.202024	−	0.753964i	−0.788312	−	0.615276i	$-0.789045\pi$
$761$	5.57308	−	20.7990i	0.202024	−	0.753964i	0.990336	−	0.138688i	$-0.0442886\pi$
$762$	−0.584941	−	4.21786i	−0.0211902	−	0.152797i
$763$	−4.79793	−	17.4210i	−0.173697	−	0.630683i
$764$	14.5854			0.527680
$765$	0.128902	+	9.33543i	0.00466046	+	0.337523i
$766$	15.7532	+	9.09514i	0.569188	+	0.328621i
$767$	−11.4084	+	2.72885i	−0.411934	+	0.0985332i
$768$	−0.214218	+	1.71875i	−0.00772992	+	0.0620201i
$769$	15.9582	+	15.9582i	0.575466	+	0.575466i	0.933651	−	0.358185i	$-0.116604\pi$
$769$	15.9582	+	15.9582i	0.575466	+	0.575466i	−0.358185	+	0.933651i	$0.616604\pi$
$770$	1.28517	−	4.93320i	0.0463145	−	0.177780i
$771$	17.9648	+	13.5889i	0.646988	+	0.489392i
$772$	−5.24169	+	19.5623i	−0.188653	+	0.704061i
$773$	7.23162	+	26.9888i	0.260103	+	0.970719i	0.965180	+	0.261588i	$0.0842461\pi$
$773$	7.23162	+	26.9888i	0.260103	+	0.970719i	−0.705076	+	0.709131i	$0.749087\pi$
$774$	−14.5452	−	24.4084i	−0.522816	−	0.877342i
$775$	24.5891	+	6.58864i	0.883267	+	0.236671i
$776$			12.8625i			0.461738i
$777$	2.58307	+	17.7201i	0.0926673	+	0.635703i
$778$	21.8565	−	21.8565i	0.783595	−	0.783595i
$779$	30.5411	+	52.8987i	1.09425	+	1.89529i
$780$	3.43135	+	1.50285i	0.122862	+	0.0538106i
$781$	20.0222	−	34.6796i	0.716452	−	1.24093i
$782$	−6.39354	−	1.71314i	−0.228632	−	0.0612619i
$783$	−19.8788	−	7.75577i	−0.710411	−	0.277169i
$784$	−3.58391	−	6.01295i	−0.127997	−	0.214748i
$785$	−10.1247	+	10.1247i	−0.361367	+	0.361367i
$786$	−28.7102	+	22.3467i	−1.02406	+	0.797081i
$787$	4.16696	+	15.5513i	0.148536	+	0.554344i	0.999572	+	0.0292373i	$0.00930784\pi$
$787$	4.16696	+	15.5513i	0.148536	+	0.554344i	−0.851037	+	0.525106i	$0.824025\pi$
$788$	1.23611	−	0.331214i	0.0440345	−	0.0117990i
$789$	−14.8174	−	1.84678i	−0.527514	−	0.0657470i
$790$		−	2.60992i		−	0.0928569i
$791$	44.5635	−	0.309658i	1.58450	−	0.0110102i
$792$	−9.27286	+	2.62239i	−0.329497	+	0.0931827i
$793$	1.36779	+	2.52418i	0.0485717	+	0.0896362i
$794$	5.88553	+	3.39801i	0.208870	+	0.120591i
$795$	1.64705	+	0.668945i	0.0584147	+	0.0237250i
$796$	−1.39298	−	2.41271i	−0.0493728	−	0.0855162i
$797$	36.5440			1.29446			0.647228	−	0.762297i	$-0.275928\pi$
$797$	36.5440			1.29446			0.647228	+	0.762297i	$0.275928\pi$
$798$	37.8208	+	4.44717i	1.33884	+	0.157428i
$799$	21.0943	+	21.0943i	0.746261	+	0.746261i
$800$	1.20097	−	4.48208i	0.0424607	−	0.158465i
$801$	18.4327	+	30.9321i	0.651288	+	1.09293i
$802$	−11.8424	+	20.5116i	−0.418169	+	0.724289i
$803$	−10.2437	−	17.7425i	−0.361491	−	0.626120i
$804$	11.4139	−	1.58291i	0.402538	−	0.0558248i
$805$	−1.95206	+	0.537618i	−0.0688011	+	0.0189486i
$806$	−19.7732	−	0.534282i	−0.696481	−	0.0188193i
$807$	39.4831	+	4.92101i	1.38987	+	0.173228i
$808$	11.1369	−	2.98411i	0.391793	−	0.104981i
$809$	−34.2469	−	19.7725i	−1.20406	−	0.695163i	−0.242603	−	0.970126i	$-0.578001\pi$
$809$	−34.2469	−	19.7725i	−1.20406	−	0.695163i	−0.961455	+	0.274963i	$0.911335\pi$
$810$	2.56918	−	4.74807i	0.0902719	−	0.166830i
$811$	12.9524	+	12.9524i	0.454821	+	0.454821i	0.896951	−	0.442130i	$-0.145777\pi$
$811$	12.9524	+	12.9524i	0.454821	+	0.454821i	−0.442130	+	0.896951i	$0.645777\pi$
$812$	9.44678	+	5.36693i	0.331517	+	0.188342i
$813$	34.1059	−	4.72988i	1.19615	−	0.165884i
$814$	−12.1245	−	3.24876i	−0.424964	−	0.113869i
$815$	−0.701455	−	0.404985i	−0.0245709	−	0.0141860i
$816$	−8.27824	+	3.49610i	−0.289796	+	0.122388i
$817$	−76.0243	−	20.3706i	−2.65975	−	0.712678i
$818$	−2.54018			−0.0888153
$819$	20.1091	+	20.3624i	0.702668	+	0.711518i
$820$	−4.40910			−0.153972
$821$	−49.2090	−	13.1855i	−1.71741	−	0.460178i	−0.740186	−	0.672402i	$-0.765263\pi$
$821$	−49.2090	−	13.1855i	−1.71741	−	0.460178i	−0.977221	+	0.212224i	$0.931929\pi$
$822$	9.36462	−	3.95491i	0.326629	−	0.137943i
$823$	24.0663	+	13.8947i	0.838897	+	0.484337i	0.856889	−	0.515501i	$-0.172394\pi$
$823$	24.0663	+	13.8947i	0.838897	+	0.484337i	−0.0179923	+	0.999838i	$0.505727\pi$
$824$	0.407094	+	0.109080i	0.0141818	+	0.00380000i
$825$	25.5717	−	3.54633i	0.890291	−	0.123467i
$826$	−0.0598104	−	8.60743i	−0.00208107	−	0.299491i
$827$	−28.9331	−	28.9331i	−1.00610	−	1.00610i	−0.999981	−	0.00612059i	$-0.998052\pi$
$827$	−28.9331	−	28.9331i	−1.00610	−	1.00610i	−0.00612059	−	0.999981i	$-0.501948\pi$
$828$	2.74348	+	2.66875i	0.0953426	+	0.0927455i
$829$	11.7669	+	6.79364i	0.408682	+	0.235953i	0.690223	−	0.723596i	$-0.257512\pi$
$829$	11.7669	+	6.79364i	0.408682	+	0.235953i	−0.281541	+	0.959549i	$0.590846\pi$
$830$	−7.87084	+	2.10898i	−0.273201	+	0.0732039i
$831$	25.6807	+	3.20073i	0.890852	+	0.111032i
$832$	−0.0973883	+	3.60424i	−0.00337633	+	0.124954i
$833$	17.7198	−	31.7010i	0.613956	−	1.09838i
$834$	5.82228	−	0.807446i	0.201609	−	0.0279596i
$835$	−0.100293	−	0.173712i	−0.00347078	−	0.00601157i
$836$	−13.3467	+	23.1171i	−0.461604	+	0.799522i
$837$	−3.13477	+	28.3337i	−0.108354	+	0.979357i
$838$	1.00443	−	3.74857i	0.0346973	−	0.129492i
$839$	−10.8590	−	10.8590i	−0.374896	−	0.374896i	0.494361	−	0.869257i	$-0.335402\pi$
$839$	−10.8590	−	10.8590i	−0.374896	−	0.374896i	−0.869257	+	0.494361i	$0.835402\pi$
$840$	−1.64302	+	2.20377i	−0.0566894	+	0.0760371i
$841$	12.1363			0.418494
$842$	0.185312	+	0.320969i	0.00638627	+	0.0110613i
$843$	1.91260	+	0.776802i	0.0658736	+	0.0267545i
$844$	2.32644	+	1.34317i	0.0800794	+	0.0462339i
$845$	7.41229	+	2.42208i	0.254991	+	0.0833219i
$846$	−4.69420	−	16.5988i	−0.161390	−	0.570679i
$847$	−0.912914	−	1.55614i	−0.0313681	−	0.0534696i
$848$			1.71104i			0.0587575i
$849$	8.66324	+	1.07975i	0.297322	+	0.0370569i
$850$	23.2539	−	6.23085i	0.797601	−	0.213717i
$851$	1.29032	+	4.81556i	0.0442318	+	0.165075i
$852$	−17.0394	+	13.2627i	−0.583759	+	0.454371i
$853$	−17.7621	+	17.7621i	−0.608162	+	0.608162i	−0.942465	−	0.334304i	$-0.891499\pi$
$853$	−17.7621	+	17.7621i	−0.608162	+	0.608162i	0.334304	+	0.942465i	$0.391499\pi$
$854$	−2.03108	+	0.559380i	−0.0695020	+	0.0191416i
$855$	−4.06949	−	14.3898i	−0.139174	−	0.492122i
$856$	12.3235	+	3.30206i	0.421207	+	0.112862i
$857$	−2.75343	+	4.76907i	−0.0940553	+	0.162908i	−0.909214	−	0.416329i	$-0.863316\pi$
$857$	−2.75343	+	4.76907i	−0.0940553	+	0.162908i	0.815159	+	0.579238i	$0.196650\pi$
$858$	−18.6837	+	7.30241i	−0.637851	+	0.249300i
$859$	20.8680	+	36.1445i	0.712008	+	1.23323i	0.964102	+	0.265531i	$0.0855472\pi$
$859$	20.8680	+	36.1445i	0.712008	+	1.23323i	−0.252095	+	0.967703i	$0.581119\pi$
$860$	4.01725	−	4.01725i	0.136987	−	0.136987i
$861$	−31.2953	−	12.4579i	−1.06654	−	0.424565i
$862$		−	14.5188i		−	0.494511i
$863$	−0.943703	−	0.252864i	−0.0321240	−	0.00860761i	0.242721	−	0.970096i	$-0.421960\pi$
$863$	−0.943703	−	0.252864i	−0.0321240	−	0.00860761i	−0.274845	+	0.961488i	$0.588627\pi$
$864$	5.16464	+	0.571402i	0.175705	+	0.0194395i
$865$	−3.93562	−	14.6879i	−0.133815	−	0.499405i
$866$	2.39222	−	8.92788i	0.0812909	−	0.303382i
$867$	−13.6995	−	10.3625i	−0.465260	−	0.351931i
$868$	3.65921	−	14.0460i	0.124202	−	0.476754i
$869$	9.88265	+	9.88265i	0.335246	+	0.335246i
$870$	0.527680	−	4.23378i	0.0178900	−	0.143539i
$871$	23.3292	−	5.58028i	0.790481	−	0.189081i
$872$	−5.91467	−	3.41484i	−0.200296	−	0.115641i
$873$	38.5839	−	0.532759i	1.30587	−	0.0180312i
$874$	10.6019			0.358616
$875$	10.7428	−	10.8932i	0.363175	−	0.368257i
$876$	1.51750	+	10.9423i	0.0512717	+	0.369707i
$877$	5.91791	−	22.0859i	0.199833	−	0.745789i	−0.791129	−	0.611649i	$-0.790506\pi$
$877$	5.91791	−	22.0859i	0.199833	−	0.745789i	0.990962	−	0.134139i	$-0.0428270\pi$
$878$	6.10007	−	1.63451i	0.205867	−	0.0551620i
$879$	10.8046	+	4.38828i	0.364431	+	0.148013i
$880$	−0.963404	−	1.66866i	−0.0324763	−	0.0562507i
$881$	−8.65737			−0.291674			−0.145837	−	0.989309i	$-0.546588\pi$
$881$	−8.65737			−0.291674			−0.145837	+	0.989309i	$0.546588\pi$
$882$	−17.8887	+	10.9997i	−0.602344	+	0.370381i
$883$			32.3230i			1.08776i	0.839164	+	0.543878i	$0.183045\pi$
$883$			32.3230i			1.08776i	−0.839164	+	0.543878i	$0.816955\pi$
$884$	−16.4468	+	8.91215i	−0.553167	+	0.299748i
$885$	−3.11384	+	1.31505i	−0.104670	+	0.0442049i
$886$	−14.5064	+	3.88698i	−0.487352	+	0.130586i
$887$	31.4819	−	18.1761i	1.05706	−	0.610292i	0.132440	−	0.991191i	$-0.457719\pi$
$887$	31.4819	−	18.1761i	1.05706	−	0.610292i	0.924617	+	0.380899i	$0.124385\pi$
$888$	5.39800	+	4.08313i	0.181145	+	0.137021i
$889$	6.50439	−	0.0451970i	0.218150	−	0.00151586i
$890$	−5.09095	+	5.09095i	−0.170649	+	0.170649i
$891$	8.25051	+	27.7073i	0.276403	+	0.928230i
$892$	0.799337	+	2.98317i	0.0267638	+	0.0998838i
$893$	−41.3807	−	23.8911i	−1.38475	−	0.799487i
$894$	37.4697	+	4.67006i	1.25317	+	0.156190i
$895$	1.25556	−	1.25556i	0.0419686	−	0.0419686i
$896$	−2.56030	−	0.666997i	−0.0855335	−	0.0222828i
$897$	6.22211	+	4.97634i	0.207750	+	0.166155i
$898$	−7.98748	−	13.8347i	−0.266546	−	0.461671i
$899$	5.83090	+	21.7612i	0.194472	+	0.725778i
$900$	−13.4947	−	3.41692i	−0.449823	−	0.113897i
$901$	−7.68790	+	4.43861i	−0.256121	+	0.147872i
$902$	16.6954	−	16.6954i	0.555894	−	0.555894i
$903$	39.8648	−	17.1633i	1.32662	−	0.571157i
$904$	11.9104	−	11.9104i	0.396133	−	0.396133i
$905$	−0.111400	+	0.415750i	−0.00370305	+	0.0138200i
$906$	−7.64065	−	18.0919i	−0.253843	−	0.601062i
$907$	−0.583687	−	0.336992i	−0.0193810	−	0.0111896i	0.490278	−	0.871566i	$-0.336895\pi$
$907$	−0.583687	−	0.336992i	−0.0193810	−	0.0111896i	−0.509659	+	0.860376i	$0.670229\pi$
$908$	5.50302	−	20.5375i	0.182624	−	0.681562i
$909$	−9.41276	−	33.2838i	−0.312202	−	1.10395i
$910$	−2.95993	+	4.89713i	−0.0981207	+	0.162338i
$911$			12.7937i			0.423875i	0.977283	+	0.211937i	$0.0679772\pi$
$911$			12.7937i			0.423875i	−0.977283	+	0.211937i	$0.932023\pi$
$912$	11.3583	−	8.84078i	0.376111	−	0.292748i
$913$	21.8177	−	37.7893i	0.722059	−	1.25064i
$914$	−8.28794	+	14.3551i	−0.274141	+	0.474825i
$915$	0.508135	+	0.652833i	0.0167984	+	0.0215820i
$916$	3.02763	+	3.02763i	0.100036	+	0.100036i
$917$	−28.1210	−	47.9347i	−0.928637	−	1.58294i
$918$	10.8302	+	24.6875i	0.357450	+	0.814810i
$919$	18.3696	+	31.8172i	0.605959	+	1.04955i	0.991899	+	0.127027i	$0.0405436\pi$
$919$	18.3696	+	31.8172i	0.605959	+	1.04955i	−0.385941	+	0.922524i	$0.626123\pi$
$920$	−0.382640	+	0.662752i	−0.0126153	+	0.0218503i
$921$	−15.9938	+	39.3792i	−0.527014	+	1.29759i
$922$	15.1674	−	8.75692i	0.499513	−	0.288394i
$923$	−32.6303	+	30.9133i	−1.07404	+	1.01752i
$924$	−2.12332	−	14.5661i	−0.0698521	−	0.479190i
$925$	−12.8216	−	12.8216i	−0.421571	−	0.421571i
$926$	18.8296	−	10.8713i	0.618778	−	0.357252i
$927$	0.310349	−	1.22568i	0.0101932	−	0.0402567i
$928$	3.96661	−	1.06285i	0.130210	−	0.0348898i
$929$	−10.1081	−	2.70847i	−0.331638	−	0.0888620i	0.0891581	−	0.996017i	$-0.471582\pi$
$929$	−10.1081	−	2.70847i	−0.331638	−	0.0888620i	−0.420796	+	0.907155i	$0.638249\pi$
$930$	−5.64581	+	0.782973i	−0.185133	+	0.0256747i
$931$	−14.2733	+	56.3920i	−0.467789	+	1.84817i
$932$			14.3739i			0.470832i
$933$	−5.22651	+	41.9343i	−0.171108	+	1.37287i
$934$	−1.52572	−	5.69408i	−0.0499232	−	0.186316i
$935$	4.99832	−	8.65735i	0.163463	−	0.283126i
$936$	10.8157	+	0.142851i	0.353523	+	0.00466924i
$937$	−22.8370			−0.746052			−0.373026	−	0.927821i	$-0.621680\pi$
$937$	−22.8370			−0.746052			−0.373026	+	0.927821i	$0.621680\pi$
$938$	0.122307	+	17.6015i	0.00399348	+	0.574708i
$939$	35.6893	+	26.9960i	1.16468	+	0.880981i
$940$	2.98698	−	1.72454i	0.0974247	−	0.0562482i
$941$	12.3909	+	46.2433i	0.403930	+	1.50749i	0.806020	+	0.591888i	$0.201617\pi$
$941$	12.3909	+	46.2433i	0.403930	+	1.50749i	−0.402090	+	0.915600i	$0.631716\pi$
$942$	−15.5579	+	38.3059i	−0.506903	+	1.24807i
$943$	−9.05808	−	2.42711i	−0.294972	−	0.0790374i
$944$	−2.30049	−	2.30049i	−0.0748745	−	0.0748745i
$945$	6.67872	+	4.83730i	0.217259	+	0.157357i
$946$			30.4232i			0.989143i
$947$	10.1022	−	37.7018i	0.328276	−	1.22514i	−0.582701	−	0.812687i	$-0.698004\pi$
$947$	10.1022	−	37.7018i	0.328276	−	1.22514i	0.910977	−	0.412457i	$-0.135329\pi$
$948$	−2.93196	−	6.94242i	−0.0952255	−	0.225479i
$949$	5.34972	+	22.3653i	0.173659	+	0.726009i
$950$	−33.3941	+	19.2801i	−1.08345	+	0.625528i
$951$	25.2580	−	3.50284i	0.819048	−	0.113587i
$952$	−3.64477	−	13.2339i	−0.118128	−	0.428914i
$953$	16.5271			0.535364			0.267682	−	0.963507i	$-0.413742\pi$
$953$	16.5271			0.535364			0.267682	+	0.963507i	$0.413742\pi$
$954$	5.13264	−	0.0708705i	0.166175	−	0.00229452i
$955$	8.45084	−	2.26439i	0.273463	−	0.0732741i
$956$	9.65940	−	2.58823i	0.312407	−	0.0837093i
$957$	14.0334	+	18.0296i	0.453635	+	0.582814i
$958$	−18.0775			−0.584058
$959$	4.12308	+	14.9707i	0.133141	+	0.483428i
$960$	0.142719	+	1.02911i	0.00460625	+	0.0332145i
$961$	−0.781758	+	0.451348i	−0.0252180	+	0.0145596i
$962$	12.0071	+	7.37171i	0.387123	+	0.237674i
$963$	9.39480	−	37.1036i	0.302743	−	1.19565i
$964$	−2.14060	+	7.98882i	−0.0689440	+	0.257303i
$965$			12.1483i			0.391066i
$966$	−4.58855	+	3.62299i	−0.147634	+	0.116568i
$967$	−9.49989	−	9.49989i	−0.305496	−	0.305496i	0.537664	−	0.843160i	$-0.319307\pi$
$967$	−9.49989	−	9.49989i	−0.305496	−	0.305496i	−0.843160	+	0.537664i	$0.819307\pi$
$968$	−0.658672	−	0.176491i	−0.0211705	−	0.00567263i
$969$	69.1871	+	28.1002i	2.22261	+	0.902710i
$970$	1.99692	+	7.45261i	0.0641173	+	0.239289i
$971$	−17.2979	+	9.98695i	−0.555116	+	0.320496i	−0.751183	−	0.660094i	$-0.770516\pi$
$971$	−17.2979	+	9.98695i	−0.555116	+	0.320496i	0.196067	+	0.980591i	$0.437183\pi$
$972$	1.50013	−	15.5161i	0.0481166	−	0.497679i
$973$	0.0623894	+	8.97858i	0.00200011	+	0.287840i
$974$	−38.7798			−1.24258
$975$	−28.6482	−	4.35935i	−0.917476	−	0.139611i
$976$	−0.398128	+	0.689579i	−0.0127438	+	0.0220729i
$977$	−0.219237	−	0.818205i	−0.00701403	−	0.0261767i	0.962330	−	0.271884i	$-0.0876466\pi$
$977$	−0.219237	−	0.818205i	−0.00701403	−	0.0261767i	−0.969344	+	0.245707i	$0.920980\pi$
$978$	−2.32083	−	0.289258i	−0.0742120	−	0.00924947i
$979$		−	38.5545i		−	1.23221i
$980$	−3.01005	−	2.92753i	−0.0961526	−	0.0935166i
$981$	−9.99856	+	17.8838i	−0.319229	+	0.570985i
$982$	−8.95841	−	2.40040i	−0.285874	−	0.0765998i
$983$	9.53265	−	2.55427i	0.304044	−	0.0814685i	−0.103571	−	0.994622i	$-0.533027\pi$
$983$	9.53265	−	2.55427i	0.304044	−	0.0814685i	0.407616	+	0.913154i	$0.366360\pi$
$984$	−11.7282	+	4.95313i	−0.373883	+	0.157900i
$985$	0.664787	−	0.383815i	0.0211819	−	0.0122294i
$986$	15.0653	+	15.0653i	0.479776	+	0.479776i
$987$	26.0740	−	3.80084i	0.829944	−	0.120982i
$988$	21.7511	−	20.6065i	0.691994	−	0.655582i
$989$	10.4645	−	6.04166i	0.332751	−	0.192114i
$990$	−4.96561	+	2.95905i	−0.157818	+	0.0940448i
$991$	2.30625	−	3.99454i	0.0732605	−	0.126891i	−0.827068	−	0.562102i	$-0.809993\pi$
$991$	2.30625	−	3.99454i	0.0732605	−	0.126891i	0.900328	+	0.435211i	$0.143326\pi$
$992$	−2.74305	−	4.75110i	−0.0870919	−	0.150848i
$993$	−0.707347	−	5.10049i	−0.0224470	−	0.161859i
$994$	−16.6897	−	28.4490i	−0.529364	−	0.902346i
$995$	−1.18168	−	1.18168i	−0.0374616	−	0.0374616i
$996$	−18.5673	+	14.4519i	−0.588327	+	0.457927i
$997$	−23.8097	+	41.2397i	−0.754062	+	1.30607i	0.191777	+	0.981439i	$0.438575\pi$
$997$	−23.8097	+	41.2397i	−0.754062	+	1.30607i	−0.945839	+	0.324635i	$0.894758\pi$
$998$	−19.0278	+	32.9571i	−0.602313	+	1.04324i
$999$	12.0247	−	16.3616i	0.380443	−	0.517657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bv.a.515.33	yes	144
3.2	odd	2	inner	546.2.bv.a.515.9	yes	144
7.2	even	3	inner	546.2.bv.a.359.9	yes	144
13.5	odd	4	inner	546.2.bv.a.473.33	yes	144
21.2	odd	6	inner	546.2.bv.a.359.33	yes	144
39.5	even	4	inner	546.2.bv.a.473.9	yes	144
91.44	odd	12	inner	546.2.bv.a.317.9	✓	144
273.44	even	12	inner	546.2.bv.a.317.33	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bv.a.317.9	✓	144	91.44	odd	12	inner
546.2.bv.a.317.33	yes	144	273.44	even	12	inner
546.2.bv.a.359.9	yes	144	7.2	even	3	inner
546.2.bv.a.359.33	yes	144	21.2	odd	6	inner
546.2.bv.a.473.9	yes	144	39.5	even	4	inner
546.2.bv.a.473.33	yes	144	13.5	odd	4	inner
546.2.bv.a.515.9	yes	144	3.2	odd	2	inner
546.2.bv.a.515.33	yes	144	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(1.59559 - 0.673858i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.579405 + 0.155251i) q^{5} +(1.71563 - 0.237927i) q^{6} +(0.0183841 + 2.64569i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.09183 - 2.15041i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(1.59559 - 0.673858i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.579405 + 0.155251i) q^{5} +(1.71563 - 0.237927i) q^{6} +(0.0183841 + 2.64569i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.09183 - 2.15041i) q^{9} +(0.519481 + 0.299922i) q^{10} +(-3.10273 + 0.831373i) q^{11} +(1.71875 + 0.214218i) q^{12} +(3.60424 + 0.0973883i) q^{13} +(-0.666997 + 2.56030i) q^{14} +(1.02911 - 0.142719i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.59410 + 4.49310i) q^{17} +(2.57712 - 1.53573i) q^{18} +(2.15080 - 8.02689i) q^{19} +(0.424154 + 0.424154i) q^{20} +(1.81215 + 4.20905i) q^{21} -3.21218 q^{22} +(0.637898 + 1.10487i) q^{23} +(1.60474 + 0.651764i) q^{24} +(-4.01852 - 2.32009i) q^{25} +(3.45622 + 1.02691i) q^{26} +(1.88864 - 4.84077i) q^{27} +(-1.30692 + 2.30042i) q^{28} -4.10654i q^{29} +(1.03098 + 0.128497i) q^{30} +(-5.29917 + 1.41991i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-4.39046 + 3.41733i) q^{33} +(-3.66860 + 3.66860i) q^{34} +(-0.400094 + 1.53578i) q^{35} +(2.88678 - 0.816391i) q^{36} +(3.77455 + 1.01139i) q^{37} +(4.15502 - 7.19671i) q^{38} +(5.81652 - 2.27335i) q^{39} +(0.299922 + 0.519481i) q^{40} +(-5.19752 + 5.19752i) q^{41} +(0.661022 + 4.53465i) q^{42} -9.47120i q^{43} +(-3.10273 - 0.831373i) q^{44} +(1.54587 - 0.921198i) q^{45} +(0.330201 + 1.23233i) q^{46} +(1.48819 - 5.55402i) q^{47} +(1.38137 + 1.04489i) q^{48} +(-6.99932 + 0.0972771i) q^{49} +(-3.28111 - 3.28111i) q^{50} +(-1.11140 + 8.91722i) q^{51} +(3.07267 + 1.88646i) q^{52} +(1.48181 + 0.855522i) q^{53} +(3.07717 - 4.18701i) q^{54} -1.92681 q^{55} +(-1.85778 + 1.88378i) q^{56} +(-1.97719 - 14.2570i) q^{57} +(1.06285 - 3.96661i) q^{58} +(-3.14252 + 0.842037i) q^{59} +(0.962597 + 0.390957i) q^{60} +(0.398128 + 0.689579i) q^{61} -5.48610 q^{62} +(5.72776 + 5.49480i) q^{63} +1.00000i q^{64} +(2.07319 + 0.615989i) q^{65} +(-5.12533 + 2.16455i) q^{66} +(6.42620 - 1.72190i) q^{67} +(-4.49310 + 2.59410i) q^{68} +(1.76235 + 1.33307i) q^{69} +(-0.783950 + 1.37990i) q^{70} +(-8.81512 + 8.81512i) q^{71} +(2.99971 - 0.0414195i) q^{72} +(1.65075 + 6.16069i) q^{73} +(3.38417 + 1.95385i) q^{74} +(-7.97533 - 0.994011i) q^{75} +(5.87609 - 5.87609i) q^{76} +(-2.25659 - 8.19356i) q^{77} +(6.20671 - 0.690464i) q^{78} +(-2.17550 - 3.76807i) q^{79} +(0.155251 + 0.579405i) q^{80} +(-0.248493 - 8.99657i) q^{81} +(-6.36563 + 3.67520i) q^{82} +(-9.60558 + 9.60558i) q^{83} +(-0.535156 + 4.55122i) q^{84} +(-2.20059 + 2.20059i) q^{85} +(2.45133 - 9.14848i) q^{86} +(-2.76723 - 6.55236i) q^{87} +(-2.78183 - 1.60609i) q^{88} +(-3.10650 + 11.5936i) q^{89} +(1.73162 - 0.489708i) q^{90} +(-0.191398 + 9.53747i) q^{91} +1.27580i q^{92} +(-7.49849 + 5.83648i) q^{93} +(2.87497 - 4.97960i) q^{94} +(2.49237 - 4.31691i) q^{95} +(1.06387 + 1.36682i) q^{96} +(9.09518 + 9.09518i) q^{97} +(-6.78601 - 1.71760i) q^{98} +(-4.70259 + 8.41121i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{7}+O(q^{10}) \) 144 * q - 16 * q^7	\( 144 q - 16 q^{7} + 72 q^{16} + 16 q^{18} + 8 q^{19} + 8 q^{21} + 24 q^{27} - 8 q^{28} - 8 q^{31} + 12 q^{33} - 8 q^{37} + 16 q^{39} - 40 q^{45} + 8 q^{46} + 8 q^{52} - 12 q^{54} - 32 q^{55} + 16 q^{57} + 8 q^{58} - 32 q^{61} - 40 q^{63} - 32 q^{66} - 8 q^{67} + 16 q^{72} + 80 q^{73} - 16 q^{76} + 16 q^{78} - 112 q^{79} - 48 q^{81} + 16 q^{84} - 80 q^{85} + 96 q^{87} - 32 q^{91} + 36 q^{93} - 64 q^{94} - 144 q^{97} - 32 q^{99}+O(q^{100}) \) 144 * q - 16 * q^7 + 72 * q^16 + 16 * q^18 + 8 * q^19 + 8 * q^21 + 24 * q^27 - 8 * q^28 - 8 * q^31 + 12 * q^33 - 8 * q^37 + 16 * q^39 - 40 * q^45 + 8 * q^46 + 8 * q^52 - 12 * q^54 - 32 * q^55 + 16 * q^57 + 8 * q^58 - 32 * q^61 - 40 * q^63 - 32 * q^66 - 8 * q^67 + 16 * q^72 + 80 * q^73 - 16 * q^76 + 16 * q^78 - 112 * q^79 - 48 * q^81 + 16 * q^84 - 80 * q^85 + 96 * q^87 - 32 * q^91 + 36 * q^93 - 64 * q^94 - 144 * q^97 - 32 * q^99

Introduction

L-functions

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