LMFDB - Embedded newform 546.2.z.b.131.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(131,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("546.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.z (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.10
Character	$\chi$	$=$	546.131
Dual form			546.2.z.b.521.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-1.12951 + 1.31309i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.63964 + 2.83994i) q^{5} +(-1.63473 + 0.572419i) q^{6} +(1.76715 + 1.96906i) q^{7} +1.00000i q^{8} +(-0.448430 - 2.96630i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-1.12951 + 1.31309i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.63964 + 2.83994i) q^{5} +(-1.63473 + 0.572419i) q^{6} +(1.76715 + 1.96906i) q^{7} +1.00000i q^{8} +(-0.448430 - 2.96630i) q^{9} +(-2.83994 + 1.63964i) q^{10} +(0.671287 - 0.387567i) q^{11} +(-1.70193 - 0.321635i) q^{12} +1.00000i q^{13} +(0.545863 + 2.58883i) q^{14} +(-1.87712 - 5.36073i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0317875 - 0.0550576i) q^{17} +(1.09480 - 2.79310i) q^{18} +(-0.489387 - 0.282548i) q^{19} -3.27928 q^{20} +(-4.58156 + 0.0963620i) q^{21} +0.775135 q^{22} +(-6.86731 - 3.96485i) q^{23} +(-1.31309 - 1.12951i) q^{24} +(-2.87683 - 4.98281i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(4.40153 + 2.76162i) q^{27} +(-0.821683 + 2.51492i) q^{28} +4.95860i q^{29} +(1.05473 - 5.58109i) q^{30} +(0.453945 - 0.262085i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.249310 + 1.31922i) q^{33} -0.0635751i q^{34} +(-8.48949 + 1.79004i) q^{35} +(2.34467 - 1.87150i) q^{36} +(4.48895 - 7.77509i) q^{37} +(-0.282548 - 0.489387i) q^{38} +(-1.31309 - 1.12951i) q^{39} +(-2.83994 - 1.63964i) q^{40} -0.420082 q^{41} +(-4.01593 - 2.20733i) q^{42} +8.44891 q^{43} +(0.671287 + 0.387567i) q^{44} +(9.15936 + 3.59014i) q^{45} +(-3.96485 - 6.86731i) q^{46} +(-6.63458 + 11.4914i) q^{47} +(-0.572419 - 1.63473i) q^{48} +(-0.754392 + 6.95923i) q^{49} -5.75366i q^{50} +(0.108200 + 0.0204479i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(-0.134600 + 0.0777115i) q^{53} +(2.43103 + 4.59240i) q^{54} +2.54188i q^{55} +(-1.96906 + 1.76715i) q^{56} +(0.923777 - 0.323471i) q^{57} +(-2.47930 + 4.29427i) q^{58} +(3.93512 + 6.81583i) q^{59} +(3.70396 - 4.30600i) q^{60} +(-1.98841 - 1.14801i) q^{61} +0.524170 q^{62} +(5.04837 - 6.12486i) q^{63} -1.00000 q^{64} +(-2.83994 - 1.63964i) q^{65} +(-0.875520 + 1.01782i) q^{66} +(5.40708 + 9.36534i) q^{67} +(0.0317875 - 0.0550576i) q^{68} +(12.9629 - 4.53911i) q^{69} +(-8.24713 - 2.69453i) q^{70} -0.904569i q^{71} +(2.96630 - 0.448430i) q^{72} +(12.4197 - 7.17052i) q^{73} +(7.77509 - 4.48895i) q^{74} +(9.79229 + 1.85057i) q^{75} -0.565095i q^{76} +(1.94940 + 0.636915i) q^{77} +(-0.572419 - 1.63473i) q^{78} +(-5.03979 + 8.72917i) q^{79} +(-1.63964 - 2.83994i) q^{80} +(-8.59782 + 2.66035i) q^{81} +(-0.363802 - 0.210041i) q^{82} +10.1924 q^{83} +(-2.37423 - 3.91957i) q^{84} +0.208480 q^{85} +(7.31697 + 4.22445i) q^{86} +(-6.51110 - 5.60077i) q^{87} +(0.387567 + 0.671287i) q^{88} +(2.77465 - 4.80584i) q^{89} +(6.13716 + 7.68883i) q^{90} +(-1.96906 + 1.76715i) q^{91} -7.92969i q^{92} +(-0.168591 + 0.892098i) q^{93} +(-11.4914 + 6.63458i) q^{94} +(1.60483 - 0.926552i) q^{95} +(0.321635 - 1.70193i) q^{96} +6.01856i q^{97} +(-4.13294 + 5.64967i) q^{98} +(-1.45066 - 1.81744i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} + 24 q^{11} - 4 q^{14} - 12 q^{15} - 16 q^{16} - 4 q^{17} - 24 q^{18} + 4 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} - 16 q^{26} + 6 q^{27} - 2 q^{28} - 8 q^{30} - 6 q^{31} + 14 q^{33} - 48 q^{35} + 4 q^{36} - 16 q^{38} - 6 q^{39} + 6 q^{40} - 16 q^{41} + 14 q^{42} + 32 q^{43} + 24 q^{44} + 20 q^{45} + 16 q^{46} - 20 q^{47} - 26 q^{49} - 46 q^{51} + 60 q^{53} + 6 q^{54} - 8 q^{56} - 8 q^{57} - 10 q^{58} - 8 q^{59} - 6 q^{60} + 36 q^{61} - 36 q^{62} + 84 q^{63} - 32 q^{64} + 6 q^{65} + 36 q^{66} + 4 q^{68} + 36 q^{69} - 18 q^{70} - 24 q^{72} - 48 q^{73} + 84 q^{74} - 2 q^{75} - 52 q^{77} + 18 q^{79} - 74 q^{81} - 24 q^{83} + 8 q^{84} - 32 q^{85} + 24 q^{86} + 14 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{90} - 8 q^{91} - 40 q^{93} + 72 q^{95} - 6 q^{96} - 32 q^{98}+O(q^{100}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 + 24 * q^11 - 4 * q^14 - 12 * q^15 - 16 * q^16 - 4 * q^17 - 24 * q^18 + 4 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 - 16 * q^26 + 6 * q^27 - 2 * q^28 - 8 * q^30 - 6 * q^31 + 14 * q^33 - 48 * q^35 + 4 * q^36 - 16 * q^38 - 6 * q^39 + 6 * q^40 - 16 * q^41 + 14 * q^42 + 32 * q^43 + 24 * q^44 + 20 * q^45 + 16 * q^46 - 20 * q^47 - 26 * q^49 - 46 * q^51 + 60 * q^53 + 6 * q^54 - 8 * q^56 - 8 * q^57 - 10 * q^58 - 8 * q^59 - 6 * q^60 + 36 * q^61 - 36 * q^62 + 84 * q^63 - 32 * q^64 + 6 * q^65 + 36 * q^66 + 4 * q^68 + 36 * q^69 - 18 * q^70 - 24 * q^72 - 48 * q^73 + 84 * q^74 - 2 * q^75 - 52 * q^77 + 18 * q^79 - 74 * q^81 - 24 * q^83 + 8 * q^84 - 32 * q^85 + 24 * q^86 + 14 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 40 * q^93 + 72 * q^95 - 6 * q^96 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−1.12951	+	1.31309i	−0.652121	+	0.758115i
$3$	−1.12951	+	1.31309i	−0.652121	+	0.758115i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.63964	+	2.83994i	−0.733269	+	1.27006i	0.222210	+	0.974999i	$0.428673\pi$
$5$	−1.63964	+	2.83994i	−0.733269	+	1.27006i	−0.955479	+	0.295060i	$0.904660\pi$
$6$	−1.63473	+	0.572419i	−0.667375	+	0.233689i
$7$	1.76715	+	1.96906i	0.667918	+	0.744235i
$7$	1.76715	+	1.96906i	0.667918	+	0.744235i
$8$			1.00000i			0.353553i
$9$	−0.448430	−	2.96630i	−0.149477	−	0.988765i
$10$	−2.83994	+	1.63964i	−0.898067	+	0.518499i
$11$	0.671287	−	0.387567i	0.202401	−	0.116856i	−0.395374	−	0.918520i	$-0.629385\pi$
$11$	0.671287	−	0.387567i	0.202401	−	0.116856i	0.597775	+	0.801664i	$0.296052\pi$
$12$	−1.70193	−	0.321635i	−0.491304	−	0.0928479i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	0.545863	+	2.58883i	0.145888	+	0.691894i
$15$	−1.87712	−	5.36073i	−0.484671	−	1.38413i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.0317875	−	0.0550576i	−0.00770961	−	0.0133534i	0.862145	−	0.506662i	$-0.169121\pi$
$17$	−0.0317875	−	0.0550576i	−0.00770961	−	0.0133534i	−0.869854	+	0.493308i	$0.835787\pi$
$18$	1.09480	−	2.79310i	0.258046	−	0.658341i
$19$	−0.489387	−	0.282548i	−0.112273	−	0.0648209i	0.442812	−	0.896615i	$-0.353981\pi$
$19$	−0.489387	−	0.282548i	−0.112273	−	0.0648209i	−0.555085	+	0.831794i	$0.687314\pi$
$20$	−3.27928			−0.733269
$21$	−4.58156	+	0.0963620i	−0.999779	+	0.0210279i
$22$	0.775135			0.165259
$23$	−6.86731	−	3.96485i	−1.43193	−	0.826728i	−0.434666	−	0.900592i	$-0.643133\pi$
$23$	−6.86731	−	3.96485i	−1.43193	−	0.826728i	−0.997268	+	0.0738643i	$0.976467\pi$
$24$	−1.31309	−	1.12951i	−0.268034	−	0.230560i
$25$	−2.87683	−	4.98281i	−0.575366	−	0.996562i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$	4.40153	+	2.76162i	0.847075	+	0.531474i
$28$	−0.821683	+	2.51492i	−0.155283	+	0.475276i
$29$			4.95860i			0.920788i	0.887715	+	0.460394i	$0.152292\pi$
$29$			4.95860i			0.920788i	−0.887715	+	0.460394i	$0.847708\pi$
$30$	1.05473	−	5.58109i	0.192566	−	1.01896i
$31$	0.453945	−	0.262085i	0.0815309	−	0.0470719i	−0.458680	−	0.888601i	$-0.651678\pi$
$31$	0.453945	−	0.262085i	0.0815309	−	0.0470719i	0.540211	+	0.841529i	$0.318344\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−0.249310	+	1.31922i	−0.0433993	+	0.229647i
$34$		−	0.0635751i		−	0.0109030i
$35$	−8.48949	+	1.79004i	−1.43498	+	0.302571i
$36$	2.34467	−	1.87150i	0.390779	−	0.311917i
$37$	4.48895	−	7.77509i	0.737979	−	1.27822i	−0.215426	−	0.976520i	$-0.569114\pi$
$37$	4.48895	−	7.77509i	0.737979	−	1.27822i	0.953404	−	0.301696i	$-0.0975528\pi$
$38$	−0.282548	−	0.489387i	−0.0458353	−	0.0793890i
$39$	−1.31309	−	1.12951i	−0.210263	−	0.180866i
$40$	−2.83994	−	1.63964i	−0.449033	−	0.259250i
$41$	−0.420082			−0.0656058			−0.0328029	−	0.999462i	$-0.510443\pi$
$41$	−0.420082			−0.0656058			−0.0328029	+	0.999462i	$0.510443\pi$
$42$	−4.01593	−	2.20733i	−0.619672	−	0.340598i
$43$	8.44891			1.28845			0.644223	−	0.764838i	$-0.277181\pi$
$43$	8.44891			1.28845			0.644223	+	0.764838i	$0.277181\pi$
$44$	0.671287	+	0.387567i	0.101200	+	0.0584280i
$45$	9.15936	+	3.59014i	1.36540	+	0.535186i
$46$	−3.96485	−	6.86731i	−0.584585	−	1.01253i
$47$	−6.63458	+	11.4914i	−0.967753	+	1.67620i	−0.265723	+	0.964050i	$0.585611\pi$
$47$	−6.63458	+	11.4914i	−0.967753	+	1.67620i	−0.702030	+	0.712147i	$0.747723\pi$
$48$	−0.572419	−	1.63473i	−0.0826216	−	0.235953i
$49$	−0.754392	+	6.95923i	−0.107770	+	0.994176i
$50$		−	5.75366i		−	0.813690i
$51$	0.108200	+	0.0204479i	0.0151510	+	0.00286328i
$52$	−0.866025	+	0.500000i	−0.120096	+	0.0693375i
$53$	−0.134600	+	0.0777115i	−0.0184888	+	0.0106745i	−0.509216	−	0.860639i	$-0.670065\pi$
$53$	−0.134600	+	0.0777115i	−0.0184888	+	0.0106745i	0.490727	+	0.871313i	$0.336731\pi$
$54$	2.43103	+	4.59240i	0.330821	+	0.624946i
$55$			2.54188i			0.342747i
$56$	−1.96906	+	1.76715i	−0.263127	+	0.236145i
$57$	0.923777	−	0.323471i	0.122357	−	0.0428448i
$58$	−2.47930	+	4.29427i	−0.325548	+	0.563865i
$59$	3.93512	+	6.81583i	0.512309	+	0.887345i	0.999898	+	0.0142719i	$0.00454303\pi$
$59$	3.93512	+	6.81583i	0.512309	+	0.887345i	−0.487589	+	0.873073i	$0.662124\pi$
$60$	3.70396	−	4.30600i	0.478180	−	0.555902i
$61$	−1.98841	−	1.14801i	−0.254590	−	0.146987i	0.367274	−	0.930113i	$-0.380291\pi$
$61$	−1.98841	−	1.14801i	−0.254590	−	0.146987i	−0.621864	+	0.783125i	$0.713624\pi$
$62$	0.524170			0.0665697
$63$	5.04837	−	6.12486i	0.636035	−	0.771660i
$64$	−1.00000			−0.125000
$65$	−2.83994	−	1.63964i	−0.352251	−	0.203372i
$66$	−0.875520	+	1.01782i	−0.107769	+	0.125286i
$67$	5.40708	+	9.36534i	0.660580	+	1.14416i	0.980463	+	0.196701i	$0.0630229\pi$
$67$	5.40708	+	9.36534i	0.660580	+	1.14416i	−0.319884	+	0.947457i	$0.603644\pi$
$68$	0.0317875	−	0.0550576i	0.00385481	−	0.00667672i
$69$	12.9629	−	4.53911i	1.56055	−	0.546444i
$70$	−8.24713	−	2.69453i	−0.985720	−	0.322057i
$71$		−	0.904569i		−	0.107353i	−0.998558	−	0.0536763i	$-0.982906\pi$
$71$		−	0.904569i		−	0.107353i	0.998558	−	0.0536763i	$-0.0170939\pi$
$72$	2.96630	−	0.448430i	0.349581	−	0.0528480i
$73$	12.4197	−	7.17052i	1.45362	−	0.839246i	0.454933	−	0.890526i	$-0.349663\pi$
$73$	12.4197	−	7.17052i	1.45362	−	0.839246i	0.998684	+	0.0512797i	$0.0163300\pi$
$74$	7.77509	−	4.48895i	0.903835	−	0.521830i
$75$	9.79229	+	1.85057i	1.13072	+	0.213686i
$76$		−	0.565095i		−	0.0648209i
$77$	1.94940	+	0.636915i	0.222155	+	0.0725832i
$78$	−0.572419	−	1.63473i	−0.0648137	−	0.185097i
$79$	−5.03979	+	8.72917i	−0.567021	+	0.982108i	0.429838	+	0.902906i	$0.358571\pi$
$79$	−5.03979	+	8.72917i	−0.567021	+	0.982108i	−0.996859	+	0.0792024i	$0.974763\pi$
$80$	−1.63964	−	2.83994i	−0.183317	−	0.317515i
$81$	−8.59782	+	2.66035i	−0.955313	+	0.295595i
$82$	−0.363802	−	0.210041i	−0.0401752	−	0.0231952i
$83$	10.1924			1.11876			0.559382	−	0.828910i	$-0.311038\pi$
$83$	10.1924			1.11876			0.559382	+	0.828910i	$0.311038\pi$
$84$	−2.37423	−	3.91957i	−0.259050	−	0.427660i
$85$	0.208480			0.0226129
$86$	7.31697	+	4.22445i	0.789009	+	0.455535i
$87$	−6.51110	−	5.60077i	−0.698063	−	0.600465i
$88$	0.387567	+	0.671287i	0.0413148	+	0.0715594i
$89$	2.77465	−	4.80584i	0.294113	−	0.509418i	−0.680665	−	0.732594i	$-0.738309\pi$
$89$	2.77465	−	4.80584i	0.294113	−	0.509418i	0.974778	+	0.223176i	$0.0716426\pi$
$90$	6.13716	+	7.68883i	0.646914	+	0.810474i
$91$	−1.96906	+	1.76715i	−0.206414	+	0.185247i
$92$		−	7.92969i		−	0.826728i
$93$	−0.168591	+	0.892098i	−0.0174821	+	0.0925063i
$94$	−11.4914	+	6.63458i	−1.18525	+	0.684304i
$95$	1.60483	−	0.926552i	0.164653	−	0.0950622i
$96$	0.321635	−	1.70193i	0.0328267	−	0.173702i
$97$			6.01856i			0.611092i	0.952177	+	0.305546i	$0.0988390\pi$
$97$			6.01856i			0.611092i	−0.952177	+	0.305546i	$0.901161\pi$
$98$	−4.13294	+	5.64967i	−0.417490	+	0.570703i
$99$	−1.45066	−	1.81744i	−0.145797	−	0.182659i
$100$	2.87683	−	4.98281i	0.287683	−	0.498281i
$101$	−0.513004	−	0.888549i	−0.0510458	−	0.0884139i	0.839373	−	0.543555i	$-0.182922\pi$
$101$	−0.513004	−	0.888549i	−0.0510458	−	0.0884139i	−0.890419	+	0.455141i	$0.849589\pi$
$102$	0.0834800	+	0.0718085i	0.00826575	+	0.00711010i
$103$	−16.5108	−	9.53254i	−1.62686	−	0.939269i	−0.985022	−	0.172430i	$-0.944838\pi$
$103$	−16.5108	−	9.53254i	−1.62686	−	0.939269i	−0.641840	−	0.766839i	$-0.721829\pi$
$104$	−1.00000			−0.0980581
$105$	7.23844	−	13.1693i	0.706400	−	1.28520i
$106$	−0.155423			−0.0150960
$107$	9.92883	+	5.73241i	0.959857	+	0.554173i	0.896129	−	0.443794i	$-0.146368\pi$
$107$	9.92883	+	5.73241i	0.959857	+	0.554173i	0.0637277	+	0.997967i	$0.479701\pi$
$108$	−0.190869	+	5.19265i	−0.0183664	+	0.499663i
$109$	−5.09789	−	8.82981i	−0.488289	−	0.845742i	0.511620	−	0.859212i	$-0.329046\pi$
$109$	−5.09789	−	8.82981i	−0.488289	−	0.845742i	−0.999909	+	0.0134699i	$0.995712\pi$
$110$	−1.27094	+	2.20133i	−0.121179	+	0.209889i
$111$	5.13912	+	14.6764i	0.487784	+	1.39302i
$112$	−2.58883	+	0.545863i	−0.244621	+	0.0515792i
$113$		−	7.78444i		−	0.732299i	−0.930556	−	0.366149i	$-0.880676\pi$
$113$		−	7.78444i		−	0.732299i	0.930556	−	0.366149i	$-0.119324\pi$
$114$	0.961750	+	0.181754i	0.0900761	+	0.0170228i
$115$	22.5198	−	13.0018i	2.09998	−	1.21243i
$116$	−4.29427	+	2.47930i	−0.398713	+	0.230197i
$117$	2.96630	−	0.448430i	0.274234	−	0.0414574i
$118$			7.87024i			0.724514i
$119$	0.0522385	−	0.159886i	0.00478870	−	0.0146568i
$120$	5.36073	−	1.87712i	0.489365	−	0.171357i
$121$	−5.19958	+	9.00594i	−0.472689	+	0.818722i
$122$	−1.14801	−	1.98841i	−0.103936	−	0.180022i
$123$	0.474486	−	0.551607i	0.0427829	−	0.0497367i
$124$	0.453945	+	0.262085i	0.0407654	+	0.0235359i
$125$	2.47144			0.221053
$126$	7.43445	−	2.78010i	0.662313	−	0.247671i
$127$	16.3753			1.45307			0.726536	−	0.687128i	$-0.241129\pi$
$127$	16.3753			1.45307			0.726536	+	0.687128i	$0.241129\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−9.54310	+	11.0942i	−0.840223	+	0.976790i
$130$	−1.63964	−	2.83994i	−0.143806	−	0.249079i
$131$	−5.12731	+	8.88075i	−0.447975	+	0.775915i	−0.998254	−	0.0590656i	$-0.981188\pi$
$131$	−5.12731	+	8.88075i	−0.447975	+	0.775915i	0.550279	+	0.834981i	$0.314521\pi$
$132$	−1.26713	+	0.443702i	−0.110290	+	0.0386193i
$133$	−0.308465	−	1.46293i	−0.0267473	−	0.126853i
$134$			10.8142i			0.934201i
$135$	−15.0597	+	7.97201i	−1.29614	+	0.686121i
$136$	0.0550576	−	0.0317875i	0.00472115	−	0.00272576i
$137$	3.07137	−	1.77325i	0.262405	−	0.151499i	−0.363026	−	0.931779i	$-0.618257\pi$
$137$	3.07137	−	1.77325i	0.262405	−	0.151499i	0.625431	+	0.780280i	$0.284923\pi$
$138$	13.4957	+	2.55046i	1.14883	+	0.217110i
$139$			20.2499i			1.71757i	0.512335	+	0.858785i	$0.328780\pi$
$139$			20.2499i			1.71757i	−0.512335	+	0.858785i	$0.671220\pi$
$140$	−5.79496	−	6.45709i	−0.489763	−	0.545724i
$141$	−7.59552	−	21.6915i	−0.639658	−	1.82675i
$142$	0.452285	−	0.783380i	0.0379549	−	0.0657398i
$143$	0.387567	+	0.671287i	0.0324100	+	0.0561358i
$144$	2.79310	+	1.09480i	0.232759	+	0.0912330i
$145$	−14.0821	−	8.13030i	−1.16945	−	0.675185i
$146$	14.3410			1.18687
$147$	−8.28603	−	8.85108i	−0.683420	−	0.730025i
$148$	8.97790			0.737979
$149$	3.65805	+	2.11197i	0.299679	+	0.173020i	0.642299	−	0.766454i	$-0.277981\pi$
$149$	3.65805	+	2.11197i	0.299679	+	0.173020i	−0.342620	+	0.939474i	$0.611314\pi$
$150$	7.55509	+	6.49879i	0.616870	+	0.530624i
$151$	7.84022	+	13.5797i	0.638028	+	1.10510i	0.985865	+	0.167542i	$0.0535830\pi$
$151$	7.84022	+	13.5797i	0.638028	+	1.10510i	−0.347837	+	0.937555i	$0.613084\pi$
$152$	0.282548	−	0.489387i	0.0229176	−	0.0396945i
$153$	−0.149063	+	0.118981i	−0.0120510	+	0.00961902i
$154$	1.36978	+	1.52629i	0.110380	+	0.122992i
$155$			1.71890i			0.138065i
$156$	0.321635	−	1.70193i	0.0257514	−	0.136263i
$157$	13.9664	−	8.06348i	1.11464	−	0.643536i	0.174610	−	0.984638i	$-0.444133\pi$
$157$	13.9664	−	8.06348i	1.11464	−	0.643536i	0.940026	+	0.341102i	$0.110800\pi$
$158$	−8.72917	+	5.03979i	−0.694455	+	0.400944i
$159$	0.0499894	−	0.264519i	0.00396442	−	0.0209777i
$160$		−	3.27928i		−	0.259250i
$161$	−4.32853	−	20.5286i	−0.341136	−	1.61788i
$162$	−8.77611	−	1.99498i	−0.689516	−	0.156740i
$163$	−3.85465	+	6.67646i	−0.301920	+	0.522941i	−0.976571	−	0.215196i	$-0.930961\pi$
$163$	−3.85465	+	6.67646i	−0.301920	+	0.522941i	0.674651	+	0.738137i	$0.264294\pi$
$164$	−0.210041	−	0.363802i	−0.0164015	−	0.0284081i
$165$	−3.33773	−	2.87107i	−0.259842	−	0.223513i
$166$	8.82690	+	5.09621i	0.685100	+	0.395543i
$167$	−2.69769			−0.208753			−0.104377	−	0.994538i	$-0.533285\pi$
$167$	−2.69769			−0.208753			−0.104377	+	0.994538i	$0.533285\pi$
$168$	−0.0963620	−	4.58156i	−0.00743449	−	0.353475i
$169$	−1.00000			−0.0769231
$170$	0.180549	+	0.104240i	0.0138475	+	0.00799485i
$171$	−0.618664	+	1.57837i	−0.0473104	+	0.120701i
$172$	4.22445	+	7.31697i	0.322112	+	0.557914i
$173$	1.62741	−	2.81875i	0.123729	−	0.214306i	−0.797506	−	0.603311i	$-0.793848\pi$
$173$	1.62741	−	2.81875i	0.123729	−	0.214306i	0.921236	+	0.389005i	$0.127181\pi$
$174$	−2.83840	−	8.10596i	−0.215178	−	0.614511i
$175$	4.72768	−	14.4700i	0.357379	−	1.09383i
$176$			0.775135i			0.0584280i
$177$	−13.3946	−	2.53134i	−1.00680	−	0.190267i
$178$	4.80584	−	2.77465i	0.360213	−	0.207969i
$179$	5.31458	−	3.06838i	0.397230	−	0.229341i	−0.288058	−	0.957613i	$-0.593010\pi$
$179$	5.31458	−	3.06838i	0.397230	−	0.229341i	0.685288	+	0.728272i	$0.259676\pi$
$180$	1.47053	+	9.72730i	0.109607	+	0.725030i
$181$		−	16.4415i		−	1.22209i	−0.791598	−	0.611043i	$-0.790750\pi$
$181$		−	16.4415i		−	1.22209i	0.791598	−	0.611043i	$-0.209250\pi$
$182$	−2.58883	+	0.545863i	−0.191897	+	0.0404621i
$183$	3.75336	−	1.31428i	0.277456	−	0.0971546i
$184$	3.96485	−	6.86731i	0.292292	−	0.506265i
$185$	14.7205	+	25.4967i	1.08227	+	1.87455i
$186$	−0.592054	+	0.688284i	−0.0434115	+	0.0504675i
$187$	−0.0426771	−	0.0246396i	−0.00312086	−	0.00180183i
$188$	−13.2692			−0.967753
$189$	2.34035	+	13.5471i	0.170235	+	0.985403i
$190$	1.85310			0.134438
$191$	−10.6198	−	6.13132i	−0.768418	−	0.443647i	0.0638917	−	0.997957i	$-0.479649\pi$
$191$	−10.6198	−	6.13132i	−0.768418	−	0.443647i	−0.832310	+	0.554310i	$0.812982\pi$
$192$	1.12951	−	1.31309i	0.0815151	−	0.0947644i
$193$	2.19040	+	3.79389i	0.157669	+	0.273090i	0.934028	−	0.357201i	$-0.116269\pi$
$193$	2.19040	+	3.79389i	0.157669	+	0.273090i	−0.776359	+	0.630291i	$0.782936\pi$
$194$	−3.00928	+	5.21223i	−0.216054	+	0.374216i
$195$	5.36073	−	1.87712i	0.383890	−	0.134423i
$196$	−6.40407	+	2.82629i	−0.457433	+	0.201878i
$197$		−	21.3903i		−	1.52400i	−0.647578	−	0.761999i	$-0.724218\pi$
$197$		−	21.3903i		−	1.52400i	0.647578	−	0.761999i	$-0.275782\pi$
$198$	−0.347594	−	2.29928i	−0.0247024	−	0.163403i
$199$	−11.4613	+	6.61717i	−0.812468	+	0.469079i	−0.847812	−	0.530296i	$-0.822081\pi$
$199$	−11.4613	+	6.61717i	−0.812468	+	0.469079i	0.0353440	+	0.999375i	$0.488747\pi$
$200$	4.98281	−	2.87683i	0.352338	−	0.203422i
$201$	−18.4049	−	3.47821i	−1.29818	−	0.245334i
$202$		−	1.02601i		−	0.0721896i
$203$	−9.76377	+	8.76256i	−0.685282	+	0.615011i
$204$	0.0363916	+	0.103928i	0.00254792	+	0.00727641i
$205$	0.688783	−	1.19301i	0.0481067	−	0.0833232i
$206$	−9.53254	−	16.5108i	−0.664163	−	1.15036i
$207$	−8.68140	+	22.1484i	−0.603399	+	1.53942i
$208$	−0.866025	−	0.500000i	−0.0600481	−	0.0346688i
$209$	−0.438025			−0.0302988
$210$	12.8533	−	7.78577i	0.886965	−	0.537269i
$211$	−11.5454			−0.794816			−0.397408	−	0.917642i	$-0.630090\pi$
$211$	−11.5454			−0.794816			−0.397408	+	0.917642i	$0.630090\pi$
$212$	−0.134600	−	0.0777115i	−0.00924439	−	0.00533725i
$213$	1.18778	+	1.02172i	0.0813856	+	0.0700069i
$214$	5.73241	+	9.92883i	0.391860	+	0.678721i
$215$	−13.8532	+	23.9944i	−0.944777	+	1.63640i
$216$	−2.76162	+	4.40153i	−0.187904	+	0.299486i
$217$	1.31825	+	0.430702i	0.0894885	+	0.0292379i
$218$		−	10.1958i		−	0.690545i
$219$	−4.61258	+	24.4074i	−0.311689	+	1.64930i
$220$	−2.20133	+	1.27094i	−0.148414	+	0.0856868i
$221$	0.0550576	−	0.0317875i	0.00370358	−	0.00213826i
$222$	−2.88760	+	15.2797i	−0.193803	+	1.02551i
$223$		−	24.9699i		−	1.67211i	−0.548649	−	0.836053i	$-0.684858\pi$
$223$		−	24.9699i		−	1.67211i	0.548649	−	0.836053i	$-0.315142\pi$
$224$	−2.51492	−	0.821683i	−0.168035	−	0.0549010i
$225$	−13.4904	+	10.7680i	−0.899363	+	0.717864i
$226$	3.89222	−	6.74152i	0.258907	−	0.448440i
$227$	−7.48692	−	12.9677i	−0.496925	−	0.860699i	0.503069	−	0.864246i	$-0.332204\pi$
$227$	−7.48692	−	12.9677i	−0.496925	−	0.860699i	−0.999994	+	0.00354752i	$0.998871\pi$
$228$	0.742023	+	0.638279i	0.0491417	+	0.0422710i
$229$	−8.63673	−	4.98642i	−0.570731	−	0.329512i	0.186710	−	0.982415i	$-0.440217\pi$
$229$	−8.63673	−	4.98642i	−0.570731	−	0.329512i	−0.757441	+	0.652903i	$0.773551\pi$
$230$	26.0037			1.71463
$231$	−3.03819	+	1.84035i	−0.199899	+	0.121086i
$232$	−4.95860			−0.325548
$233$	25.2675	+	14.5882i	1.65533	+	0.955705i	0.974828	+	0.222958i	$0.0715712\pi$
$233$	25.2675	+	14.5882i	1.65533	+	0.955705i	0.680501	+	0.732747i	$0.261762\pi$
$234$	2.79310	+	1.09480i	0.182591	+	0.0715691i
$235$	−21.7566	−	37.6836i	−1.41925	−	2.45820i
$236$	−3.93512	+	6.81583i	−0.256154	+	0.443673i
$237$	−5.76974	−	16.4774i	−0.374785	−	1.07032i
$238$	0.125183	−	0.112346i	0.00811442	−	0.00728234i
$239$			3.76036i			0.243237i	0.992577	+	0.121619i	$0.0388085\pi$
$239$			3.76036i			0.243237i	−0.992577	+	0.121619i	$0.961191\pi$
$240$	5.58109	+	1.05473i	0.360258	+	0.0680824i
$241$	−1.74550	+	1.00776i	−0.112437	+	0.0649158i	−0.555164	−	0.831741i	$-0.687345\pi$
$241$	−1.74550	+	1.00776i	−0.112437	+	0.0649158i	0.442727	+	0.896657i	$0.354011\pi$
$242$	−9.00594	+	5.19958i	−0.578924	+	0.334242i
$243$	6.21800	−	14.2946i	0.398885	−	0.917001i
$244$		−	2.29602i		−	0.146987i
$245$	−18.5268	−	13.5530i	−1.18364	−	0.865872i
$246$	0.686720	−	0.240463i	0.0437837	−	0.0153314i
$247$	0.282548	−	0.489387i	0.0179781	−	0.0311389i
$248$	0.262085	+	0.453945i	0.0166424	+	0.0288255i
$249$	−11.5124	+	13.3836i	−0.729570	+	0.848152i
$250$	2.14033	+	1.23572i	0.135367	+	0.0781539i
$251$	17.5688			1.10893			0.554467	−	0.832206i	$-0.312922\pi$
$251$	17.5688			1.10893			0.554467	+	0.832206i	$0.312922\pi$
$252$	7.82847	+	1.30959i	0.493147	+	0.0824963i
$253$	−6.14658			−0.386432
$254$	14.1814	+	8.18765i	0.889822	+	0.513739i
$255$	−0.235480	+	0.273754i	−0.0147463	+	0.0171431i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.28209	−	16.0771i	0.579001	−	1.00286i	−0.416593	−	0.909093i	$-0.636776\pi$
$257$	9.28209	−	16.0771i	0.579001	−	1.00286i	0.995594	−	0.0937659i	$-0.0298905\pi$
$258$	−13.8117	+	4.83632i	−0.859877	+	0.301096i
$259$	23.2422	−	4.90070i	1.44420	−	0.304515i
$260$		−	3.27928i		−	0.203372i
$261$	14.7087	−	2.22358i	0.910443	−	0.137636i
$262$	−8.88075	+	5.12731i	−0.548655	+	0.316766i
$263$	5.98281	−	3.45417i	0.368916	−	0.212994i	−0.304069	−	0.952650i	$-0.598345\pi$
$263$	5.98281	−	3.45417i	0.368916	−	0.212994i	0.672985	+	0.739656i	$0.265012\pi$
$264$	−1.31922	−	0.249310i	−0.0811925	−	0.0153440i
$265$		−	0.509675i		−	0.0313091i
$266$	0.464329	−	1.42117i	0.0284698	−	0.0871376i
$267$	3.17653	+	9.07161i	0.194400	+	0.555173i
$268$	−5.40708	+	9.36534i	−0.330290	+	0.572079i
$269$	15.4949	+	26.8379i	0.944738	+	1.63633i	0.756275	+	0.654254i	$0.227017\pi$
$269$	15.4949	+	26.8379i	0.944738	+	1.63633i	0.188464	+	0.982080i	$0.439649\pi$
$270$	−17.0281	−	0.625912i	−1.03630	−	0.0380918i
$271$	−3.39550	−	1.96040i	−0.206262	−	0.119086i	0.393311	−	0.919406i	$-0.371330\pi$
$271$	−3.39550	−	1.96040i	−0.206262	−	0.119086i	−0.599573	+	0.800320i	$0.704663\pi$
$272$	0.0635751			0.00385481
$273$	−0.0963620	−	4.58156i	−0.00583210	−	0.277289i
$274$	3.54651			0.214252
$275$	−3.86235	−	2.22993i	−0.232909	−	0.134470i
$276$	10.4124	+	8.95664i	0.626755	+	0.539126i
$277$	13.6130	+	23.5784i	0.817926	+	1.41669i	0.907208	+	0.420683i	$0.138209\pi$
$277$	13.6130	+	23.5784i	0.817926	+	1.41669i	−0.0892822	+	0.996006i	$0.528457\pi$
$278$	−10.1249	+	17.5369i	−0.607253	+	1.05179i
$279$	−0.980984	−	1.22901i	−0.0587300	−	0.0735787i
$280$	−1.79004	−	8.48949i	−0.106975	−	0.507344i
$281$		−	26.6249i		−	1.58831i	−0.607717	−	0.794153i	$-0.707915\pi$
$281$		−	26.6249i		−	1.58831i	0.607717	−	0.794153i	$-0.292085\pi$
$282$	4.26782	−	22.5831i	0.254145	−	1.34481i
$283$	−9.67441	+	5.58552i	−0.575084	+	0.332025i	−0.759177	−	0.650884i	$-0.774398\pi$
$283$	−9.67441	+	5.58552i	−0.575084	+	0.332025i	0.184093	+	0.982909i	$0.441065\pi$
$284$	0.783380	−	0.452285i	0.0464851	−	0.0268382i
$285$	−0.596022	+	3.15384i	−0.0353053	+	0.186818i
$286$			0.775135i			0.0458347i
$287$	−0.742346	−	0.827167i	−0.0438193	−	0.0488261i
$288$	1.87150	+	2.34467i	0.110279	+	0.138161i
$289$	8.49798	−	14.7189i	0.499881	−	0.865820i
$290$	−8.13030	−	14.0821i	−0.477428	−	0.826929i
$291$	−7.90294	−	6.79801i	−0.463278	−	0.398506i
$292$	12.4197	+	7.17052i	0.726808	+	0.419623i
$293$	0.00282466			0.000165019			8.25093e−5	−	1.00000i	$-0.499974\pi$
$293$	0.00282466			0.000165019			8.25093e−5		1.00000i	$0.499974\pi$
$294$	−2.75037	−	11.8083i	−0.160405	−	0.688673i
$295$	−25.8087			−1.50264
$296$	7.77509	+	4.48895i	0.451918	+	0.260915i
$297$	4.02500	+	0.147949i	0.233554	+	0.00858488i
$298$	2.11197	+	3.65805i	0.122343	+	0.211905i
$299$	3.96485	−	6.86731i	0.229293	−	0.397147i
$300$	3.29350	+	9.40566i	0.190150	+	0.543036i
$301$	14.9305	+	16.6364i	0.860577	+	0.958906i
$302$			15.6804i			0.902308i
$303$	1.74619	+	0.330000i	0.100316	+	0.0189580i
$304$	0.489387	−	0.282548i	0.0280683	−	0.0162052i
$305$	6.52054	−	3.76463i	0.373365	−	0.215562i
$306$	−0.188582	+	0.0285090i	−0.0107805	+	0.00162975i
$307$			11.3486i			0.647699i	0.946109	+	0.323849i	$0.104977\pi$
$307$			11.3486i			0.647699i	−0.946109	+	0.323849i	$0.895023\pi$
$308$	0.423118	+	2.00669i	0.0241094	+	0.114342i
$309$	31.1662	−	10.9132i	1.77298	−	0.620831i
$310$	−0.859449	+	1.48861i	−0.0488134	+	0.0845474i
$311$	−14.1139	−	24.4460i	−0.800325	−	1.38620i	−0.919402	−	0.393318i	$-0.871327\pi$
$311$	−14.1139	−	24.4460i	−0.800325	−	1.38620i	0.119077	−	0.992885i	$-0.462006\pi$
$312$	1.12951	−	1.31309i	0.0639457	−	0.0743393i
$313$	1.24068	+	0.716308i	0.0701275	+	0.0404881i	0.534654	−	0.845071i	$-0.320442\pi$
$313$	1.24068	+	0.716308i	0.0701275	+	0.0404881i	−0.464526	+	0.885559i	$0.653775\pi$
$314$	16.1270			0.910097
$315$	9.11672	+	24.3796i	0.513669	+	1.37364i
$316$	−10.0796			−0.567021
$317$	−23.9114	−	13.8053i	−1.34300	−	0.775380i	−0.355752	−	0.934580i	$-0.615775\pi$
$317$	−23.9114	−	13.8053i	−1.34300	−	0.775380i	−0.987246	+	0.159200i	$0.949108\pi$
$318$	0.175551	−	0.204085i	0.00984443	−	0.0114445i
$319$	1.92179	+	3.32864i	0.107600	+	0.186368i
$320$	1.63964	−	2.83994i	0.0916586	−	0.158757i
$321$	−18.7419	+	6.56269i	−1.04607	+	0.366294i
$322$	6.51569	−	19.9426i	0.363105	−	1.11136i
$323$			0.0359260i			0.00199897i
$324$	−6.60284	−	6.11576i	−0.366825	−	0.339764i
$325$	4.98281	−	2.87683i	0.276397	−	0.159578i
$326$	−6.67646	+	3.85465i	−0.369775	+	0.213490i
$327$	17.3525	+	3.27932i	0.959593	+	0.181347i
$328$		−	0.420082i		−	0.0231952i
$329$	−34.3516	+	7.24314i	−1.89386	+	0.399328i
$330$	−1.45502	−	4.15529i	−0.0800963	−	0.228741i
$331$	3.30352	−	5.72187i	0.181578	−	0.314502i	−0.760840	−	0.648939i	$-0.775213\pi$
$331$	3.30352	−	5.72187i	0.181578	−	0.314502i	0.942418	+	0.334437i	$0.108546\pi$
$332$	5.09621	+	8.82690i	0.279691	+	0.484439i
$333$	−25.0762	−	9.82897i	−1.37417	−	0.538624i
$334$	−2.33626	−	1.34884i	−0.127835	−	0.0738054i
$335$	−35.4626			−1.93753
$336$	2.20733	−	4.01593i	0.120420	−	0.219087i
$337$	5.23466			0.285150			0.142575	−	0.989784i	$-0.454462\pi$
$337$	5.23466			0.285150			0.142575	+	0.989784i	$0.454462\pi$
$338$	−0.866025	−	0.500000i	−0.0471056	−	0.0271964i
$339$	10.2217	+	8.79258i	0.555167	+	0.477547i
$340$	0.104240	+	0.180549i	0.00565321	+	0.00979166i
$341$	0.203151	−	0.351868i	0.0110013	−	0.0190547i
$342$	−1.32496	+	1.05758i	−0.0716458	+	0.0571871i
$343$	−15.0363	+	10.8125i	−0.811882	+	0.583822i
$344$			8.44891i			0.455535i
$345$	−8.36367	+	44.2563i	−0.450285	+	2.38268i
$346$	2.81875	−	1.62741i	0.151537	−	0.0874900i
$347$	0.456848	−	0.263761i	0.0245249	−	0.0141594i	−0.487687	−	0.873018i	$-0.662159\pi$
$347$	0.456848	−	0.263761i	0.0245249	−	0.0141594i	0.512212	+	0.858859i	$0.328826\pi$
$348$	1.59486	−	8.43916i	0.0854932	−	0.452387i
$349$			9.59298i			0.513500i	0.966478	+	0.256750i	$0.0826518\pi$
$349$			9.59298i			0.513500i	−0.966478	+	0.256750i	$0.917348\pi$
$350$	11.3293	−	10.1675i	0.605576	−	0.543478i
$351$	−2.76162	+	4.40153i	−0.147404	+	0.234936i
$352$	−0.387567	+	0.671287i	−0.0206574	+	0.0357797i
$353$	−14.5492	−	25.2000i	−0.774378	−	1.34126i	−0.935143	−	0.354270i	$-0.884729\pi$
$353$	−14.5492	−	25.2000i	−0.774378	−	1.34126i	0.160765	−	0.986993i	$-0.448604\pi$
$354$	−10.3344	−	8.88949i	−0.549265	−	0.472471i
$355$	2.56892	+	1.48317i	0.136344	+	0.0787183i
$356$	5.54931			0.294113
$357$	0.150942	+	0.249187i	0.00798870	+	0.0131884i
$358$	6.13675			0.324337
$359$	31.5163	+	18.1959i	1.66336	+	0.960344i	0.971091	+	0.238708i	$0.0767240\pi$
$359$	31.5163	+	18.1959i	1.66336	+	0.960344i	0.692273	+	0.721636i	$0.256609\pi$
$360$	−3.59014	+	9.15936i	−0.189217	+	0.482740i
$361$	−9.34033	−	16.1779i	−0.491597	−	0.851470i
$362$	8.22074	−	14.2387i	0.432072	−	0.748371i
$363$	−5.95268	−	16.9998i	−0.312435	−	0.892259i
$364$	−2.51492	−	0.821683i	−0.131818	−	0.0430679i
$365$			47.0283i			2.46157i
$366$	3.90765	+	0.738478i	0.204256	+	0.0386009i
$367$	−19.5725	+	11.3002i	−1.02167	+	0.589864i	−0.914588	−	0.404386i	$-0.867485\pi$
$367$	−19.5725	+	11.3002i	−1.02167	+	0.589864i	−0.107085	+	0.994250i	$0.534152\pi$
$368$	6.86731	−	3.96485i	0.357984	−	0.206682i
$369$	0.188377	+	1.24609i	0.00980653	+	0.0648687i
$370$			29.4410i			1.53057i
$371$	−0.390877	−	0.127708i	−0.0202933	−	0.00663029i
$372$	−0.856876	+	0.300045i	−0.0444269	+	0.0155566i
$373$	−2.77610	+	4.80834i	−0.143741	+	0.248966i	−0.928902	−	0.370324i	$-0.879247\pi$
$373$	−2.77610	+	4.80834i	−0.143741	+	0.248966i	0.785162	+	0.619291i	$0.212580\pi$
$374$	−0.0246396	−	0.0426771i	−0.00127408	−	0.00220678i
$375$	−2.79151	+	3.24524i	−0.144153	+	0.167583i
$376$	−11.4914	−	6.63458i	−0.592625	−	0.342152i
$377$	−4.95860			−0.255381
$378$	−4.74673	+	12.9023i	−0.244145	+	0.663621i
$379$	13.5561			0.696331			0.348166	−	0.937433i	$-0.386805\pi$
$379$	13.5561			0.696331			0.348166	+	0.937433i	$0.386805\pi$
$380$	1.60483	+	0.926552i	0.0823263	+	0.0475311i
$381$	−18.4960	+	21.5023i	−0.947579	+	1.10160i
$382$	−6.13132	−	10.6198i	−0.313706	−	0.543354i
$383$	7.98157	−	13.8245i	0.407839	−	0.706398i	−0.586808	−	0.809726i	$-0.699616\pi$
$383$	7.98157	−	13.8245i	0.407839	−	0.706398i	0.994647	+	0.103328i	$0.0329490\pi$
$384$	1.63473	−	0.572419i	0.0834219	−	0.0292111i
$385$	−5.00512	+	4.49188i	−0.255084	+	0.228927i
$386$			4.38080i			0.222977i
$387$	−3.78874	−	25.0620i	−0.192593	−	1.27397i
$388$	−5.21223	+	3.00928i	−0.264611	+	0.152773i
$389$	−3.28024	+	1.89385i	−0.166315	+	0.0960220i	−0.580847	−	0.814013i	$-0.697279\pi$
$389$	−3.28024	+	1.89385i	−0.166315	+	0.0960220i	0.414532	+	0.910035i	$0.363945\pi$
$390$	5.58109	+	1.05473i	0.282609	+	0.0534083i
$391$			0.504131i			0.0254950i
$392$	−6.95923	−	0.754392i	−0.351494	−	0.0381025i
$393$	−5.86994	−	16.7635i	−0.296099	−	0.845607i
$394$	10.6952	−	18.5246i	0.538815	−	0.933255i
$395$	−16.5269	−	28.6254i	−0.831557	−	1.44030i
$396$	0.848615	−	2.16503i	0.0426445	−	0.108797i
$397$	−1.96197	−	1.13274i	−0.0984682	−	0.0568507i	0.449957	−	0.893050i	$-0.351439\pi$
$397$	−1.96197	−	1.13274i	−0.0984682	−	0.0568507i	−0.548425	+	0.836199i	$0.684773\pi$
$398$	−13.2343			−0.663378
$399$	2.26938	+	1.24735i	0.113611	+	0.0624457i
$400$	5.75366			0.287683
$401$	3.06792	+	1.77127i	0.153205	+	0.0884528i	0.574643	−	0.818404i	$-0.305141\pi$
$401$	3.06792	+	1.77127i	0.153205	+	0.0884528i	−0.421438	+	0.906857i	$0.638474\pi$
$402$	−14.2000	−	12.2147i	−0.708232	−	0.609212i
$403$	0.262085	+	0.453945i	0.0130554	+	0.0226126i
$404$	0.513004	−	0.888549i	0.0255229	−	0.0442070i
$405$	6.54209	−	28.7793i	0.325079	−	1.43005i
$406$	−12.8370	+	2.70672i	−0.637087	+	0.134332i
$407$		−	6.95908i		−	0.344949i
$408$	−0.0204479	+	0.108200i	−0.00101232	+	0.00535670i
$409$	−11.4284	+	6.59821i	−0.565100	+	0.326261i	−0.755190	−	0.655506i	$-0.772455\pi$
$409$	−11.4284	+	6.59821i	−0.565100	+	0.326261i	0.190090	+	0.981767i	$0.439122\pi$
$410$	1.19301	−	0.688783i	0.0589184	−	0.0340166i
$411$	−1.14068	+	6.03589i	−0.0562656	+	0.297729i
$412$		−	19.0651i		−	0.939269i
$413$	−6.46684	+	19.7930i	−0.318212	+	0.973952i
$414$	−18.5925	+	14.8404i	−0.913773	+	0.729367i
$415$	−16.7119	+	28.9458i	−0.820355	+	1.42090i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	−26.5900	−	22.8724i	−1.30212	−	1.12006i
$418$	−0.379341	−	0.219012i	−0.0185542	−	0.0107123i
$419$	26.8712			1.31275			0.656373	−	0.754437i	$-0.272090\pi$
$419$	26.8712			1.31275			0.656373	+	0.754437i	$0.272090\pi$
$420$	15.0242	−	0.315998i	0.733106	−	0.0154191i
$421$	14.0176			0.683178			0.341589	−	0.939849i	$-0.389035\pi$
$421$	14.0176			0.683178			0.341589	+	0.939849i	$0.389035\pi$
$422$	−9.99859	−	5.77269i	−0.486724	−	0.281010i
$423$	37.0621	+	14.5270i	1.80202	+	0.706328i
$424$	−0.0777115	−	0.134600i	−0.00377401	−	0.00653677i
$425$	−0.182895	+	0.316783i	−0.00887169	+	0.0153662i
$426$	0.517793	+	1.47873i	0.0250871	+	0.0716445i
$427$	−1.25331	−	5.94399i	−0.0606519	−	0.287650i
$428$			11.4648i			0.554173i
$429$	−1.31922	−	0.249310i	−0.0636926	−	0.0120368i
$430$	−23.9944	+	13.8532i	−1.15711	+	0.668058i
$431$	20.7067	−	11.9550i	0.997404	−	0.575852i	0.0899250	−	0.995949i	$-0.471337\pi$
$431$	20.7067	−	11.9550i	0.997404	−	0.575852i	0.907479	+	0.420097i	$0.138004\pi$
$432$	−4.59240	+	2.43103i	−0.220952	+	0.116963i
$433$			6.69816i			0.321893i	0.986963	+	0.160947i	$0.0514547\pi$
$433$			6.69816i			0.321893i	−0.986963	+	0.160947i	$0.948545\pi$
$434$	0.926285	+	1.03212i	0.0444631	+	0.0495434i
$435$	26.5817	−	9.30788i	1.27449	−	0.446279i
$436$	5.09789	−	8.82981i	0.244145	−	0.422871i
$437$	2.24052	+	3.88069i	0.107178	+	0.185638i
$438$	−16.1983	+	18.8311i	−0.773985	+	0.899786i
$439$	−7.83044	−	4.52091i	−0.373727	−	0.215771i	0.301359	−	0.953511i	$-0.402560\pi$
$439$	−7.83044	−	4.52091i	−0.373727	−	0.215771i	−0.675085	+	0.737740i	$0.735893\pi$
$440$	−2.54188			−0.121179
$441$	20.9814	−	0.882977i	0.999116	−	0.0420465i
$442$	0.0635751			0.00302396
$443$	22.6779	+	13.0931i	1.07746	+	0.622073i	0.930210	−	0.367027i	$-0.119624\pi$
$443$	22.6779	+	13.0931i	1.07746	+	0.622073i	0.147251	+	0.989099i	$0.452958\pi$
$444$	−10.1406	+	11.7888i	−0.481251	+	0.559473i
$445$	9.09885	+	15.7597i	0.431327	+	0.747080i
$446$	12.4849	−	21.6245i	0.591178	−	1.02395i
$447$	−6.90501	+	2.41787i	−0.326596	+	0.114361i
$448$	−1.76715	−	1.96906i	−0.0834898	−	0.0930293i
$449$		−	5.49646i		−	0.259394i	−0.991554	−	0.129697i	$-0.958600\pi$
$449$		−	5.49646i		−	0.259394i	0.991554	−	0.129697i	$-0.0414005\pi$
$450$	−17.0670	+	2.58011i	−0.804548	+	0.121628i
$451$	−0.281995	+	0.162810i	−0.0132786	+	0.00766643i
$452$	6.74152	−	3.89222i	0.317095	−	0.183075i
$453$	−26.6870	−	5.04337i	−1.25386	−	0.236958i
$454$		−	14.9738i		−	0.702758i
$455$	−1.79004	−	8.48949i	−0.0839182	−	0.397993i
$456$	0.323471	+	0.923777i	0.0151479	+	0.0432598i
$457$	16.3520	−	28.3226i	0.764916	−	1.32487i	−0.175375	−	0.984502i	$-0.556114\pi$
$457$	16.3520	−	28.3226i	0.764916	−	1.32487i	0.940291	−	0.340372i	$-0.110553\pi$
$458$	−4.98642	−	8.63673i	−0.233000	−	0.403568i
$459$	0.0121345	−	0.330123i	0.000566390	−	0.0154088i
$460$	22.5198	+	13.0018i	1.04999	+	0.606213i
$461$	21.6678			1.00917			0.504585	−	0.863362i	$-0.331646\pi$
$461$	21.6678			1.00917			0.504585	+	0.863362i	$0.331646\pi$
$462$	−3.55133	+	0.0746936i	−0.165223	+	0.00347506i
$463$	27.3020			1.26883			0.634415	−	0.772992i	$-0.281241\pi$
$463$	27.3020			1.26883			0.634415	+	0.772992i	$0.281241\pi$
$464$	−4.29427	−	2.47930i	−0.199356	−	0.115099i
$465$	−2.25707	−	1.94151i	−0.104669	−	0.0900352i
$466$	14.5882	+	25.2675i	0.675785	+	1.17049i
$467$	8.36005	−	14.4800i	0.386857	−	0.670056i	−0.605168	−	0.796098i	$-0.706894\pi$
$467$	8.36005	−	14.4800i	0.386857	−	0.670056i	0.992025	+	0.126042i	$0.0402274\pi$
$468$	1.87150	+	2.34467i	0.0865101	+	0.108383i
$469$	−8.88581	+	27.1968i	−0.410309	+	1.25583i
$470$		−	43.5132i		−	2.00712i
$471$	−5.18699	+	27.4469i	−0.239004	+	1.26469i
$472$	−6.81583	+	3.93512i	−0.313724	+	0.181129i
$473$	5.67164	−	3.27452i	0.260782	−	0.150563i
$474$	3.24194	−	17.1547i	0.148907	−	0.787941i
$475$			3.25136i			0.149183i
$476$	0.164585	−	0.0347033i	0.00754374	−	0.00159062i
$477$	0.290874	+	0.364416i	0.0133182	+	0.0166855i
$478$	−1.88018	+	3.25657i	−0.0859974	+	0.148952i
$479$	−11.7404	−	20.3349i	−0.536431	−	0.929125i	−0.999093	−	0.0425904i	$-0.986439\pi$
$479$	−11.7404	−	20.3349i	−0.536431	−	0.929125i	0.462662	−	0.886535i	$-0.346894\pi$
$480$	4.30600	+	3.70396i	0.196541	+	0.169062i
$481$	7.77509	+	4.48895i	0.354513	+	0.204678i
$482$	−2.01553			−0.0918048
$483$	31.8451	+	17.5034i	1.44900	+	0.796434i
$484$	−10.3992			−0.472689
$485$	−17.0923	−	9.86827i	−0.776123	−	0.448095i
$486$	12.5323	−	9.27051i	0.568475	−	0.420519i
$487$	−8.37385	−	14.5039i	−0.379455	−	0.657236i	0.611528	−	0.791223i	$-0.290555\pi$
$487$	−8.37385	−	14.5039i	−0.379455	−	0.657236i	−0.990983	+	0.133987i	$0.957222\pi$
$488$	1.14801	−	1.98841i	0.0519679	−	0.0900110i
$489$	−4.41296	−	12.6026i	−0.199561	−	0.569910i
$490$	−9.26820	−	21.0007i	−0.418694	−	0.948715i
$491$		−	4.91806i		−	0.221949i	−0.993823	−	0.110974i	$-0.964603\pi$
$491$		−	4.91806i		−	0.221949i	0.993823	−	0.110974i	$-0.0353972\pi$
$492$	0.714949	+	0.135113i	0.0322324	+	0.00609136i
$493$	0.273009	−	0.157622i	0.0122957	−	0.00709892i
$494$	0.489387	−	0.282548i	0.0220186	−	0.0127124i
$495$	7.53997	−	1.13986i	0.338897	−	0.0512327i
$496$			0.524170i			0.0235359i
$497$	1.78115	−	1.59851i	0.0798955	−	0.0717028i
$498$	−16.6618	+	5.83434i	−0.746635	+	0.261443i
$499$	14.1854	−	24.5697i	0.635024	−	1.09989i	−0.351487	−	0.936193i	$-0.614324\pi$
$499$	14.1854	−	24.5697i	0.635024	−	1.09989i	0.986510	−	0.163700i	$-0.0523429\pi$
$500$	1.23572	+	2.14033i	0.0552632	+	0.0957186i
$501$	3.04705	−	3.54231i	0.136132	−	0.158259i
$502$	15.2150	+	8.78441i	0.679081	+	0.392067i
$503$	21.0263			0.937518			0.468759	−	0.883326i	$-0.344701\pi$
$503$	21.0263			0.937518			0.468759	+	0.883326i	$0.344701\pi$
$504$	6.12486	+	5.04837i	0.272823	+	0.224872i
$505$	3.36456			0.149721
$506$	−5.32310	−	3.07329i	−0.236640	−	0.136624i
$507$	1.12951	−	1.31309i	0.0501631	−	0.0583165i
$508$	8.18765	+	14.1814i	0.363268	+	0.629199i
$509$	−5.11529	+	8.85994i	−0.226731	+	0.392710i	−0.956837	−	0.290624i	$-0.906137\pi$
$509$	−5.11529	+	8.85994i	−0.226731	+	0.392710i	0.730106	+	0.683334i	$0.239471\pi$
$510$	−0.340809	+	0.119338i	−0.0150913	+	0.00528438i
$511$	36.0666	+	11.7838i	1.59549	+	0.521284i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.37376	−	2.59514i	−0.0606530	−	0.114578i
$514$	16.0771	−	9.28209i	0.709128	−	0.409415i
$515$	54.1436	−	31.2598i	2.38585	−	1.37747i
$516$	−14.3794	−	2.71746i	−0.633018	−	0.119630i
$517$			10.2854i			0.452351i
$518$	22.5787	+	7.37698i	0.992052	+	0.324126i
$519$	1.86312	+	5.32074i	0.0817818	+	0.233554i
$520$	1.63964	−	2.83994i	0.0719029	−	0.124539i
$521$	9.52485	+	16.4975i	0.417291	+	0.722770i	0.995666	−	0.0930014i	$-0.0296461\pi$
$521$	9.52485	+	16.4975i	0.417291	+	0.722770i	−0.578375	+	0.815771i	$0.696313\pi$
$522$	13.8499	+	5.42865i	0.606192	+	0.237606i
$523$	−3.66053	−	2.11341i	−0.160064	−	0.0924128i	0.417829	−	0.908526i	$-0.362791\pi$
$523$	−3.66053	−	2.11341i	−0.160064	−	0.0924128i	−0.577892	+	0.816113i	$0.696125\pi$
$524$	−10.2546			−0.447975
$525$	13.6605	+	22.5518i	0.596194	+	0.984243i
$526$	6.90835			0.301218
$527$	−0.0288596	−	0.0166621i	−0.00125714	−	0.000725811i
$528$	−1.01782	−	0.875520i	−0.0442951	−	0.0381021i
$529$	19.9400	+	34.5371i	0.866957	+	1.50161i
$530$	0.254838	−	0.441392i	0.0110694	−	0.0191728i
$531$	18.4531	−	14.7291i	0.800798	−	0.639191i
$532$	1.11271	−	0.998605i	0.0482419	−	0.0432950i
$533$		−	0.420082i		−	0.0181958i
$534$	−1.78485	+	9.44451i	−0.0772379	+	0.408704i
$535$	−32.5594	+	18.7982i	−1.40767	+	0.812716i
$536$	−9.36534	+	5.40708i	−0.404521	+	0.233550i
$537$	−1.97379	+	10.4443i	−0.0851754	+	0.450705i
$538$			30.9897i			1.33606i
$539$	2.19076	+	4.96402i	0.0943626	+	0.213815i
$540$	−14.4338	−	9.05612i	−0.621133	−	0.389713i
$541$	6.14135	−	10.6371i	0.264037	−	0.457326i	−0.703274	−	0.710919i	$-0.748279\pi$
$541$	6.14135	−	10.6371i	0.264037	−	0.457326i	0.967311	+	0.253593i	$0.0816125\pi$
$542$	−1.96040	−	3.39550i	−0.0842062	−	0.145849i
$543$	21.5892	+	18.5708i	0.926481	+	0.796947i
$544$	0.0550576	+	0.0317875i	0.00236058	+	0.00136288i
$545$	33.4348			1.43219
$546$	2.20733	−	4.01593i	0.0944650	−	0.171866i
$547$	−22.8684			−0.977784			−0.488892	−	0.872344i	$-0.662599\pi$
$547$	−22.8684			−0.977784			−0.488892	+	0.872344i	$0.662599\pi$
$548$	3.07137	+	1.77325i	0.131202	+	0.0757497i
$549$	−2.51367	+	6.41301i	−0.107281	+	0.273700i
$550$	−2.22993	−	3.86235i	−0.0950845	−	0.164691i
$551$	1.40104	−	2.42667i	0.0596863	−	0.103380i
$552$	4.53911	+	12.9629i	0.193197	+	0.551737i
$553$	−26.0943	+	5.50207i	−1.10964	+	0.233972i
$554$			27.2260i			1.15672i
$555$	−50.1064	−	9.46925i	−2.12690	−	0.401947i
$556$	−17.5369	+	10.1249i	−0.743730	+	0.429393i
$557$	−7.50850	+	4.33503i	−0.318145	+	0.183681i	−0.650566	−	0.759450i	$-0.725468\pi$
$557$	−7.50850	+	4.33503i	−0.318145	+	0.183681i	0.332420	+	0.943131i	$0.392135\pi$
$558$	−0.235054	−	1.55484i	−0.00995061	−	0.0658218i
$559$			8.44891i			0.357351i
$560$	2.69453	−	8.24713i	0.113864	−	0.348505i
$561$	0.0805582	−	0.0282084i	0.00340117	−	0.00119096i
$562$	13.3124	−	23.0578i	0.561551	−	0.972635i
$563$	1.98331	+	3.43520i	0.0835867	+	0.144776i	0.904788	−	0.425862i	$-0.140029\pi$
$563$	1.98331	+	3.43520i	0.0835867	+	0.144776i	−0.821201	+	0.570638i	$0.806696\pi$
$564$	14.9876	−	17.4236i	0.631092	−	0.733668i
$565$	22.1073	+	12.7637i	0.930062	+	0.536972i
$566$	−11.1710			−0.469554
$567$	−20.4320	−	12.2284i	−0.858063	−	0.513544i
$568$	0.904569			0.0379549
$569$	13.0722	+	7.54725i	0.548016	+	0.316397i	0.748321	−	0.663336i	$-0.230860\pi$
$569$	13.0722	+	7.54725i	0.548016	+	0.316397i	−0.200306	+	0.979733i	$0.564194\pi$
$570$	−2.09309	+	2.43330i	−0.0876700	+	0.101920i
$571$	7.87788	+	13.6449i	0.329679	+	0.571021i	0.982448	−	0.186536i	$-0.0597262\pi$
$571$	7.87788	+	13.6449i	0.329679	+	0.571021i	−0.652769	+	0.757557i	$0.726393\pi$
$572$	−0.387567	+	0.671287i	−0.0162050	+	0.0280679i
$573$	20.0461	−	7.01937i	0.837437	−	0.293238i
$574$	−0.229307	−	1.08752i	−0.00957111	−	0.0453922i
$575$			45.6247i			1.90268i
$576$	0.448430	+	2.96630i	0.0186846	+	0.123596i
$577$	17.2803	−	9.97681i	0.719390	−	0.415340i	−0.0951379	−	0.995464i	$-0.530329\pi$
$577$	17.2803	−	9.97681i	0.719390	−	0.415340i	0.814528	+	0.580124i	$0.196996\pi$
$578$	14.7189	−	8.49798i	0.612227	−	0.353469i
$579$	−7.45580	−	1.40902i	−0.309852	−	0.0585568i
$580$		−	16.2606i		−	0.675185i
$581$	18.0115	+	20.0695i	0.747243	+	0.832623i
$582$	−3.44514	−	9.83871i	−0.142806	−	0.407828i
$583$	−0.0602369	+	0.104333i	−0.00249476	+	0.00432105i
$584$	7.17052	+	12.4197i	0.296718	+	0.513931i
$585$	−3.59014	+	9.15936i	−0.148434	+	0.378693i
$586$	0.00244623	+	0.00141233i	0.000101053	+	5.83429e-5i
$587$	−35.8969			−1.48162			−0.740812	−	0.671713i	$-0.765559\pi$
$587$	−35.8969			−1.48162			−0.740812	+	0.671713i	$0.765559\pi$
$588$	3.52225	−	11.6015i	0.145255	−	0.478436i
$589$	−0.296206			−0.0122050
$590$	−22.3510	−	12.9043i	−0.920175	−	0.531263i
$591$	28.0875	+	24.1605i	1.15537	+	0.993831i
$592$	4.48895	+	7.77509i	0.184495	+	0.319554i
$593$	18.0525	−	31.2679i	0.741327	−	1.28402i	−0.210564	−	0.977580i	$-0.567530\pi$
$593$	18.0525	−	31.2679i	0.741327	−	1.28402i	0.951891	−	0.306437i	$-0.0991367\pi$
$594$	3.41178	+	2.14063i	0.139987	+	0.0878310i
$595$	0.368415	+	0.410510i	0.0151035	+	0.0168293i
$596$			4.22395i			0.173020i
$597$	4.25662	−	22.5239i	0.174212	−	0.921841i
$598$	6.86731	−	3.96485i	0.280825	−	0.162135i
$599$	34.0580	−	19.6634i	1.39157	−	0.803424i	0.398082	−	0.917350i	$-0.369676\pi$
$599$	34.0580	−	19.6634i	1.39157	−	0.803424i	0.993489	+	0.113926i	$0.0363427\pi$
$600$	−1.85057	+	9.79229i	−0.0755494	+	0.399769i
$601$		−	16.2190i		−	0.661585i	−0.943703	−	0.330793i	$-0.892684\pi$
$601$		−	16.2190i		−	0.661585i	0.943703	−	0.330793i	$-0.107316\pi$
$602$	4.61195	+	21.8728i	0.187969	+	0.891468i
$603$	25.3557	−	20.2387i	1.03256	−	0.824183i
$604$	−7.84022	+	13.5797i	−0.319014	+	0.552549i
$605$	−17.0509	−	29.5330i	−0.693216	−	1.20069i
$606$	1.34724	+	1.15888i	0.0547281	+	0.0470764i
$607$	7.16275	+	4.13542i	0.290727	+	0.167851i	0.638270	−	0.769813i	$-0.279650\pi$
$607$	7.16275	+	4.13542i	0.290727	+	0.167851i	−0.347543	+	0.937664i	$0.612984\pi$
$608$	0.565095			0.0229176
$609$	−0.477820	−	22.7181i	−0.0193623	−	0.920585i
$610$	7.52927			0.304851
$611$	−11.4914	−	6.63458i	−0.464893	−	0.268406i
$612$	−0.177572	−	0.0696018i	−0.00717791	−	0.00281348i
$613$	13.2273	+	22.9103i	0.534245	+	0.925339i	0.999199	+	0.0400046i	$0.0127373\pi$
$613$	13.2273	+	22.9103i	0.534245	+	0.925339i	−0.464955	+	0.885334i	$0.653929\pi$
$614$	−5.67430	+	9.82817i	−0.228996	+	0.396633i
$615$	0.788545	+	2.25195i	0.0317972	+	0.0908072i
$616$	−0.636915	+	1.94940i	−0.0256620	+	0.0785437i
$617$			28.3865i			1.14280i	0.820673	+	0.571398i	$0.193599\pi$
$617$			28.3865i			1.14280i	−0.820673	+	0.571398i	$0.806401\pi$
$618$	32.4473	+	6.13199i	1.30522	+	0.246665i
$619$	18.2085	−	10.5127i	0.731860	−	0.422539i	−0.0872424	−	0.996187i	$-0.527805\pi$
$619$	18.2085	−	10.5127i	0.731860	−	0.422539i	0.819102	+	0.573648i	$0.194472\pi$
$620$	−1.48861	+	0.859449i	−0.0597840	+	0.0345163i
$621$	−19.2773	−	36.4163i	−0.773571	−	1.46134i
$622$		−	28.2278i		−	1.13183i
$623$	14.3662	−	3.02916i	0.575570	−	0.121361i
$624$	1.63473	−	0.572419i	0.0654415	−	0.0229151i
$625$	10.3319	−	17.8953i	0.413275	−	0.715813i
$626$	0.716308	+	1.24068i	0.0286294	+	0.0495876i
$627$	0.494752	−	0.575168i	0.0197585	−	0.0229700i
$628$	13.9664	+	8.06348i	0.557318	+	0.321768i
$629$	−0.570770			−0.0227581
$630$	−4.29450	+	25.6717i	−0.171097	+	1.02279i
$631$	−17.2982			−0.688632			−0.344316	−	0.938854i	$-0.611889\pi$
$631$	−17.2982			−0.688632			−0.344316	+	0.938854i	$0.611889\pi$
$632$	−8.72917	−	5.03979i	−0.347228	−	0.200472i
$633$	13.0406	−	15.1602i	0.518316	−	0.602562i
$634$	−13.8053	−	23.9114i	−0.548277	−	0.949643i
$635$	−26.8496	+	46.5048i	−1.06549	+	1.84549i
$636$	0.254075	−	0.0889672i	0.0100747	−	0.00352778i
$637$	−6.95923	−	0.754392i	−0.275735	−	0.0298901i
$638$			3.84358i			0.152169i
$639$	−2.68322	+	0.405636i	−0.106147	+	0.0160467i
$640$	2.83994	−	1.63964i	0.112258	−	0.0648124i
$641$	−31.5222	+	18.1993i	−1.24505	+	0.718830i	−0.970118	−	0.242633i	$-0.921989\pi$
$641$	−31.5222	+	18.1993i	−1.24505	+	0.718830i	−0.274932	+	0.961464i	$0.588655\pi$
$642$	−19.5123	−	3.68749i	−0.770089	−	0.145533i
$643$		−	33.3355i		−	1.31462i	−0.753619	−	0.657312i	$-0.771694\pi$
$643$		−	33.3355i		−	1.31462i	0.753619	−	0.657312i	$-0.228306\pi$
$644$	15.6140	−	14.0129i	0.615279	−	0.552186i
$645$	−15.8596	−	45.2923i	−0.624472	−	1.78338i
$646$	−0.0179630	+	0.0311128i	−0.000706744	+	0.00122412i
$647$	−6.90781	−	11.9647i	−0.271574	−	0.470380i	0.697691	−	0.716399i	$-0.254211\pi$
$647$	−6.90781	−	11.9647i	−0.271574	−	0.470380i	−0.969265	+	0.246019i	$0.920877\pi$
$648$	−2.66035	−	8.59782i	−0.104508	−	0.337754i
$649$	5.28318	+	3.05025i	0.207383	+	0.119733i
$650$	5.75366			0.225677
$651$	−2.05452	+	1.24450i	−0.0805230	+	0.0487759i
$652$	−7.70931			−0.301920
$653$	−19.1703	−	11.0680i	−0.750191	−	0.433123i	0.0755719	−	0.997140i	$-0.475922\pi$
$653$	−19.1703	−	11.0680i	−0.750191	−	0.433123i	−0.825763	+	0.564017i	$0.809255\pi$
$654$	13.3880	+	11.5162i	0.523513	+	0.450319i
$655$	−16.8139	−	29.1224i	−0.656972	−	1.13791i
$656$	0.210041	−	0.363802i	0.00820073	−	0.0142041i
$657$	−26.8393	−	33.6251i	−1.04710	−	1.31184i
$658$	−33.3709	−	10.9030i	−1.30093	−	0.425045i
$659$			39.8621i			1.55281i	0.630235	+	0.776404i	$0.282958\pi$
$659$			39.8621i			1.55281i	−0.630235	+	0.776404i	$0.717042\pi$
$660$	0.817557	−	4.32609i	0.0318234	−	0.168393i
$661$	22.4684	−	12.9722i	0.873921	−	0.504559i	0.00527195	−	0.999986i	$-0.498322\pi$
$661$	22.4684	−	12.9722i	0.873921	−	0.504559i	0.868649	+	0.495427i	$0.164989\pi$
$662$	5.72187	−	3.30352i	0.222387	−	0.128395i
$663$	−0.0204479	+	0.108200i	−0.000794132	+	0.00420214i
$664$			10.1924i			0.395543i
$665$	4.66041	+	1.52266i	0.180723	+	0.0590463i
$666$	−16.8021	−	21.0502i	−0.651069	−	0.815680i
$667$	19.6601	−	34.0522i	0.761241	−	1.31851i
$668$	−1.34884	−	2.33626i	−0.0521883	−	0.0903928i
$669$	32.7878	+	28.2036i	1.26765	+	1.09041i
$670$	−30.7115	−	17.7313i	−1.18649	−	0.685020i
$671$	−1.77972			−0.0687054
$672$	3.91957	−	2.37423i	0.151201	−	0.0915880i
$673$	−35.1761			−1.35594			−0.677970	−	0.735090i	$-0.737140\pi$
$673$	−35.1761			−1.35594			−0.677970	+	0.735090i	$0.737140\pi$
$674$	4.53335	+	2.61733i	0.174618	+	0.100816i
$675$	1.09819	−	29.8767i	0.0422695	−	1.14995i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	2.60892	−	4.51879i	0.100269	−	0.173671i	−0.811526	−	0.584316i	$-0.801363\pi$
$677$	2.60892	−	4.51879i	0.100269	−	0.173671i	0.911796	+	0.410645i	$0.134696\pi$
$678$	4.45596	+	12.7254i	0.171130	+	0.488718i
$679$	−11.8509	+	10.6357i	−0.454796	+	0.408160i
$680$			0.208480i			0.00799485i
$681$	25.4844	+	4.81611i	0.976563	+	0.184554i
$682$	0.351868	−	0.203151i	0.0134737	−	0.00777906i
$683$	−13.1375	+	7.58494i	−0.502693	+	0.290230i	−0.729825	−	0.683634i	$-0.760398\pi$
$683$	−13.1375	+	7.58494i	−0.502693	+	0.290230i	0.227132	+	0.973864i	$0.427065\pi$
$684$	−1.67624	+	0.253406i	−0.0640926	+	0.00968920i
$685$			11.6300i			0.444359i
$686$	−18.4281	+	1.84580i	−0.703586	+	0.0704729i
$687$	16.3029	−	5.70864i	0.621993	−	0.217798i
$688$	−4.22445	+	7.31697i	−0.161056	+	0.278957i
$689$	−0.0777115	−	0.134600i	−0.00296057	−	0.00512786i
$690$	−29.3713	+	34.1452i	−1.11815	+	1.29989i
$691$	−45.2319	−	26.1146i	−1.72070	−	0.993448i	−0.917494	−	0.397749i	$-0.869791\pi$
$691$	−45.2319	−	26.1146i	−1.72070	−	0.993448i	−0.803208	−	0.595698i	$-0.796875\pi$
$692$	3.25481			0.123729
$693$	1.01511	−	6.06812i	0.0385607	−	0.230509i
$694$	0.527523			0.0200245
$695$	−57.5083	−	33.2025i	−2.18142	−	1.25944i
$696$	5.60077	−	6.51110i	0.212297	−	0.246803i
$697$	0.0133534	+	0.0231287i	0.000505795	+	0.000876063i
$698$	−4.79649	+	8.30776i	−0.181550	+	0.314454i
$699$	−47.6955	+	16.7011i	−1.80401	+	0.631695i
$700$	14.8952	−	3.14071i	0.562987	−	0.118708i
$701$			35.9314i			1.35711i	0.734549	+	0.678556i	$0.237394\pi$
$701$			35.9314i			1.35711i	−0.734549	+	0.678556i	$0.762606\pi$
$702$	−4.59240	+	2.43103i	−0.173329	+	0.0917531i
$703$	−4.39366	+	2.53668i	−0.165710	+	0.0956728i
$704$	−0.671287	+	0.387567i	−0.0253001	+	0.0146070i
$705$	74.0563	+	13.9954i	2.78912	+	0.527096i
$706$		−	29.0985i		−	1.09514i
$707$	0.843053	−	2.58033i	0.0317063	−	0.0970433i
$708$	−4.50508	−	12.8657i	−0.169311	−	0.483523i
$709$	−17.2180	+	29.8224i	−0.646634	+	1.12000i	0.337288	+	0.941402i	$0.390490\pi$
$709$	−17.2180	+	29.8224i	−0.646634	+	1.12000i	−0.983922	+	0.178601i	$0.942843\pi$
$710$	1.48317	+	2.56892i	0.0556623	+	0.0964098i
$711$	28.1533	+	11.0351i	1.05583	+	0.413848i
$712$	4.80584	+	2.77465i	0.180106	+	0.103985i
$713$	−4.15651			−0.155662
$714$	0.00612622	+	0.291273i	0.000229268	+	0.0109006i
$715$	−2.54188			−0.0950610
$716$	5.31458	+	3.06838i	0.198615	+	0.114671i
$717$	−4.93771	−	4.24735i	−0.184402	−	0.158620i
$718$	18.1959	+	31.5163i	0.679066	+	1.17618i
$719$	−7.08672	+	12.2746i	−0.264290	+	0.457764i	−0.967377	−	0.253340i	$-0.918471\pi$
$719$	−7.08672	+	12.2746i	−0.264290	+	0.457764i	0.703087	+	0.711104i	$0.251804\pi$
$720$	−7.68883	+	6.13716i	−0.286546	+	0.228719i
$721$	−10.4069	−	49.3562i	−0.387574	−	1.83812i
$722$		−	18.6807i		−	0.695222i
$723$	0.648264	−	3.43028i	0.0241092	−	0.127573i
$724$	14.2387	−	8.22074i	0.529179	−	0.305521i
$725$	24.7077	−	14.2650i	0.917623	−	0.529790i
$726$	3.34473	−	17.6986i	0.124135	−	0.656857i
$727$			22.1410i			0.821162i	0.911824	+	0.410581i	$0.134674\pi$
$727$			22.1410i			0.821162i	−0.911824	+	0.410581i	$0.865326\pi$
$728$	−1.76715	−	1.96906i	−0.0654948	−	0.0729782i
$729$	11.7469	+	24.3107i	0.435071	+	0.900396i
$730$	−23.5141	+	40.7277i	−0.870297	+	1.50740i
$731$	−0.268570	−	0.465177i	−0.00993342	−	0.0172052i
$732$	3.01488	+	2.59336i	0.111433	+	0.0958535i
$733$	−0.401905	−	0.232040i	−0.0148447	−	0.00857058i	0.492559	−	0.870279i	$-0.336061\pi$
$733$	−0.401905	−	0.232040i	−0.0148447	−	0.00857058i	−0.507404	+	0.861708i	$0.669395\pi$
$734$	−22.6003			−0.834193
$735$	38.7226	−	9.01923i	1.42831	−	0.332679i
$736$	7.92969			0.292292
$737$	7.25940	+	4.19122i	0.267403	+	0.154385i
$738$	−0.459904	+	1.17333i	−0.0169293	+	0.0431910i
$739$	−11.0538	−	19.1458i	−0.406622	−	0.704291i	0.587886	−	0.808943i	$-0.299960\pi$
$739$	−11.0538	−	19.1458i	−0.406622	−	0.704291i	−0.994509	+	0.104653i	$0.966627\pi$
$740$	−14.7205	+	25.4967i	−0.541136	+	0.937276i
$741$	0.323471	+	0.923777i	0.0118830	+	0.0339358i
$742$	−0.274655	−	0.306037i	−0.0100829	−	0.0112350i
$743$			44.7176i			1.64053i	0.571983	+	0.820265i	$0.306174\pi$
$743$			44.7176i			1.64053i	−0.571983	+	0.820265i	$0.693826\pi$
$744$	−0.892098	−	0.168591i	−0.0327059	−	0.00618085i
$745$	−11.9957	+	6.92575i	−0.439490	+	0.253740i
$746$	−4.80834	+	2.77610i	−0.176046	+	0.101640i
$747$	−4.57059	−	30.2338i	−0.167229	−	1.10620i
$748$		−	0.0492793i		−	0.00180183i
$749$	6.25823	+	29.6805i	0.228671	+	1.08450i
$750$	−4.04014	+	1.41470i	−0.147525	+	0.0516576i
$751$	−22.4137	+	38.8217i	−0.817888	+	1.41662i	0.0893474	+	0.996001i	$0.471522\pi$
$751$	−22.4137	+	38.8217i	−0.817888	+	1.41662i	−0.907235	+	0.420623i	$0.861811\pi$
$752$	−6.63458	−	11.4914i	−0.241938	−	0.419049i
$753$	−19.8441	+	23.0695i	−0.723159	+	0.840699i
$754$	−4.29427	−	2.47930i	−0.156388	−	0.0902907i
$755$	−51.4205			−1.87138
$756$	−10.5619	+	8.80033i	−0.384133	+	0.320065i
$757$	−17.1283			−0.622540			−0.311270	−	0.950322i	$-0.600754\pi$
$757$	−17.1283			−0.622540			−0.311270	+	0.950322i	$0.600754\pi$
$758$	11.7399	+	6.77806i	0.426414	+	0.246190i
$759$	6.94260	−	8.07104i	0.252001	−	0.292960i
$760$	0.926552	+	1.60483i	0.0336096	+	0.0582135i
$761$	−11.2812	+	19.5396i	−0.408944	+	0.708312i	−0.994772	−	0.102124i	$-0.967436\pi$
$761$	−11.2812	+	19.5396i	−0.408944	+	0.708312i	0.585828	+	0.810436i	$0.300770\pi$
$762$	−26.7692	+	9.37353i	−0.969744	+	0.339567i
$763$	8.37770	−	25.6416i	0.303293	−	0.928288i
$764$		−	12.2626i		−	0.443647i
$765$	−0.0934888	−	0.618414i	−0.00338009	−	0.0223588i
$766$	13.8245	−	7.98157i	0.499499	−	0.288386i
$767$	−6.81583	+	3.93512i	−0.246105	+	0.142089i
$768$	1.70193	+	0.321635i	0.0614130	+	0.0116060i
$769$		−	22.9531i		−	0.827711i	−0.910343	−	0.413856i	$-0.864182\pi$
$769$		−	22.9531i		−	0.827711i	0.910343	−	0.413856i	$-0.135818\pi$
$770$	−6.58050	+	1.38752i	−0.237145	+	0.0500027i
$771$	10.6265	+	30.3474i	0.382704	+	1.09293i
$772$	−2.19040	+	3.79389i	−0.0788343	+	0.136545i
$773$	0.115663	+	0.200334i	0.00416011	+	0.00720552i	0.868098	−	0.496393i	$-0.165342\pi$
$773$	0.115663	+	0.200334i	0.00416011	+	0.00720552i	−0.863938	+	0.503598i	$0.832009\pi$
$774$	9.24983	−	23.5987i	0.332478	−	0.848236i
$775$	−2.61184	−	1.50795i	−0.0938201	−	0.0541671i
$776$	−6.01856			−0.216054
$777$	−19.8172	+	36.0546i	−0.710937	+	1.29345i
$778$	−3.78770			−0.135796
$779$	0.205583	+	0.118693i	0.00736576	+	0.00425262i
$780$	4.30600	+	3.70396i	0.154179	+	0.132623i
$781$	−0.350582	−	0.607225i	−0.0125448	−	0.0217282i
$782$	−0.252065	+	0.436590i	−0.00901384	+	0.0156124i
$783$	−13.6938	+	21.8254i	−0.489375	+	0.779976i
$784$	−5.64967	−	4.13294i	−0.201774	−	0.147605i
$785$			52.8848i			1.88754i
$786$	3.29824	−	17.4526i	0.117644	−	0.622513i
$787$	11.6700	−	6.73765i	0.415989	−	0.240171i	−0.277371	−	0.960763i	$-0.589463\pi$
$787$	11.6700	−	6.73765i	0.415989	−	0.240171i	0.693360	+	0.720592i	$0.256130\pi$
$788$	18.5246	−	10.6952i	0.659911	−	0.381000i
$789$	−2.22196	+	11.7575i	−0.0791040	+	0.418578i
$790$		−	33.0537i		−	1.17600i
$791$	15.3280	−	13.7562i	0.545002	−	0.489116i
$792$	1.81744	−	1.45066i	0.0645798	−	0.0515471i
$793$	1.14801	−	1.98841i	0.0407669	−	0.0706104i
$794$	−1.13274	−	1.96197i	−0.0401995	−	0.0696276i
$795$	0.669251	+	0.575682i	0.0237359	+	0.0204173i
$796$	−11.4613	−	6.61717i	−0.406234	−	0.234539i
$797$	22.6270			0.801491			0.400745	−	0.916190i	$-0.368751\pi$
$797$	22.6270			0.801491			0.400745	+	0.916190i	$0.368751\pi$
$798$	1.34167	+	2.21493i	0.0474945	+	0.0784076i
$799$	0.843588			0.0298440
$800$	4.98281	+	2.87683i	0.176169	+	0.101711i
$801$	−15.4998	−	6.07536i	−0.547658	−	0.214662i
$802$	1.77127	+	3.06792i	0.0625456	+	0.108332i
$803$	5.55812	−	9.62695i	0.196142	−	0.339728i
$804$	−6.19023	−	17.6782i	−0.218313	−	0.623462i
$805$	65.3972	+	21.3668i	2.30495	+	0.753079i
$806$			0.524170i			0.0184631i
$807$	−52.7422	−	9.96736i	−1.85661	−	0.350868i
$808$	0.888549	−	0.513004i	0.0312590	−	0.0180474i
$809$	−4.35883	+	2.51657i	−0.153248	+	0.0884780i	−0.574663	−	0.818390i	$-0.694867\pi$
$809$	−4.35883	+	2.51657i	−0.153248	+	0.0884780i	0.421415	+	0.906868i	$0.361534\pi$
$810$	20.0553	−	21.6525i	0.704670	−	0.760793i
$811$			45.0640i			1.58241i	0.611551	+	0.791205i	$0.290546\pi$
$811$			45.0640i			1.58241i	−0.611551	+	0.791205i	$0.709454\pi$
$812$	−12.4705	−	4.07439i	−0.437628	−	0.142983i
$813$	6.40943	−	2.24434i	0.224788	−	0.0787123i
$814$	3.47954	−	6.02674i	0.121958	−	0.211237i
$815$	−12.6405	−	21.8940i	−0.442777	−	0.766912i
$816$	−0.0718085	+	0.0834800i	−0.00251380	+	0.00292239i
$817$	−4.13478	−	2.38722i	−0.144658	−	0.0835182i
$818$	−13.1964			−0.461402
$819$	6.12486	+	5.04837i	0.214020	+	0.176404i
$820$	1.37757			0.0481067
$821$	−31.0231	−	17.9112i	−1.08271	−	0.625105i	−0.151087	−	0.988521i	$-0.548277\pi$
$821$	−31.0231	−	17.9112i	−1.08271	−	0.625105i	−0.931627	+	0.363416i	$0.881611\pi$
$822$	−4.00580	+	4.65690i	−0.139718	+	0.162428i
$823$	−19.2405	−	33.3254i	−0.670680	−	1.16165i	−0.977712	−	0.209953i	$-0.932669\pi$
$823$	−19.2405	−	33.3254i	−0.670680	−	1.16165i	0.307032	−	0.951699i	$-0.400664\pi$
$824$	9.53254	−	16.5108i	0.332082	−	0.575182i
$825$	7.29066	−	2.55291i	0.253828	−	0.0888809i
$826$	−15.4970	+	13.9079i	−0.539209	+	0.483916i
$827$		−	9.60510i		−	0.334002i	−0.985957	−	0.167001i	$-0.946592\pi$
$827$		−	9.60510i		−	0.334002i	0.985957	−	0.167001i	$-0.0534083\pi$
$828$	−23.5218	+	3.55591i	−0.817439	+	0.123576i
$829$	−6.43512	+	3.71532i	−0.223501	+	0.129038i	−0.607570	−	0.794266i	$-0.707856\pi$
$829$	−6.43512	+	3.71532i	−0.223501	+	0.129038i	0.384069	+	0.923304i	$0.374522\pi$
$830$	−28.9458	+	16.7119i	−1.00473	+	0.580078i
$831$	−46.3366	−	8.75682i	−1.60740	−	0.303771i
$832$		−	1.00000i		−	0.0346688i
$833$	0.407139	−	0.179682i	0.0141065	−	0.00622560i
$834$	−11.5914	−	33.1030i	−0.401378	−	1.14626i
$835$	4.42323	−	7.66126i	0.153072	−	0.265129i
$836$	−0.219012	−	0.379341i	−0.00757471	−	0.0131198i
$837$	2.72183	+	0.100048i	0.0940802	+	0.00345815i
$838$	23.2712	+	13.4356i	0.803889	+	0.464126i
$839$	−30.1877			−1.04219			−0.521097	−	0.853497i	$-0.674477\pi$
$839$	−30.1877			−1.04219			−0.521097	+	0.853497i	$0.674477\pi$
$840$	13.1693	+	7.23844i	0.454386	+	0.249750i
$841$	4.41233			0.152149
$842$	12.1396	+	7.00882i	0.418360	+	0.241540i
$843$	34.9610	+	30.0730i	1.20412	+	1.03577i
$844$	−5.77269	−	9.99859i	−0.198704	−	0.344166i
$845$	1.63964	−	2.83994i	0.0564053	−	0.0976968i
$846$	24.8332	+	31.1118i	0.853784	+	1.06965i
$847$	−26.9217	+	5.67652i	−0.925039	+	0.195048i
$848$		−	0.155423i		−	0.00533725i
$849$	3.59299	−	19.0123i	0.123311	−	0.652500i
$850$	−0.316783	+	0.182895i	−0.0108656	+	0.00627323i
$851$	−61.6540	+	35.5960i	−2.11347	+	1.22021i
$852$	−0.290941	+	1.53951i	−0.00996747	+	0.0527427i
$853$		−	3.08780i		−	0.105724i	−0.998602	−	0.0528621i	$-0.983166\pi$
$853$		−	3.08780i		−	0.105724i	0.998602	−	0.0528621i	$-0.0168344\pi$
$854$	1.88660	−	5.77430i	0.0645580	−	0.197593i
$855$	−3.46808	−	4.34492i	−0.118606	−	0.148593i
$856$	−5.73241	+	9.92883i	−0.195930	+	0.339361i
$857$	−22.0602	−	38.2094i	−0.753563	−	1.30521i	−0.946086	−	0.323917i	$-0.895000\pi$
$857$	−22.0602	−	38.2094i	−0.753563	−	1.30521i	0.192523	−	0.981293i	$-0.438333\pi$
$858$	−1.01782	−	0.875520i	−0.0347480	−	0.0298898i
$859$	18.6113	+	10.7453i	0.635011	+	0.366624i	0.782690	−	0.622412i	$-0.213847\pi$
$859$	18.6113	+	10.7453i	0.635011	+	0.366624i	−0.147679	+	0.989035i	$0.547180\pi$
$860$	−27.7063			−0.944777
$861$	1.92463	−	0.0404800i	0.0655913	−	0.00137955i
$862$	23.9100			0.814377
$863$	32.5710	+	18.8049i	1.10873	+	0.640125i	0.938500	−	0.345280i	$-0.112216\pi$
$863$	32.5710	+	18.8049i	1.10873	+	0.640125i	0.170229	+	0.985405i	$0.445549\pi$
$864$	−5.19265	−	0.190869i	−0.176657	−	0.00649349i
$865$	5.33672	+	9.24347i	0.181454	+	0.314287i
$866$	−3.34908	+	5.80078i	−0.113806	+	0.197118i
$867$	9.72881	+	27.7838i	0.330408	+	0.943586i
$868$	0.286125	+	1.35699i	0.00971172	+	0.0460591i
$869$			7.81303i			0.265039i
$870$	27.6743	+	5.22997i	0.938248	+	0.177313i
$871$	−9.36534	+	5.40708i	−0.317332	+	0.183212i
$872$	8.82981	−	5.09789i	0.299015	−	0.172636i
$873$	17.8528	−	2.69890i	0.604227	−	0.0913440i
$874$			4.48103i			0.151573i
$875$	4.36740	+	4.86642i	0.147645	+	0.164515i
$876$	−23.4437	+	8.20909i	−0.792090	+	0.277359i
$877$	2.71113	−	4.69582i	0.0915485	−	0.158567i	−0.816614	−	0.577184i	$-0.804152\pi$
$877$	2.71113	−	4.69582i	0.0915485	−	0.158567i	0.908163	+	0.418617i	$0.137485\pi$
$878$	−4.52091	−	7.83044i	−0.152573	−	0.264265i
$879$	−0.00319048	+	0.00370905i	−0.000107612	+	0.000125103i
$880$	−2.20133	−	1.27094i	−0.0742070	−	0.0428434i
$881$	−50.7448			−1.70963			−0.854817	−	0.518929i	$-0.826331\pi$
$881$	−50.7448			−1.70963			−0.854817	+	0.518929i	$0.826331\pi$
$882$	18.6119	+	9.72603i	0.626697	+	0.327493i
$883$	−37.1977			−1.25180			−0.625900	−	0.779903i	$-0.715268\pi$
$883$	−37.1977			−1.25180			−0.625900	+	0.779903i	$0.715268\pi$
$884$	0.0550576	+	0.0317875i	0.00185179	+	0.00106913i
$885$	29.1511	−	33.8892i	0.979903	−	1.13917i
$886$	13.0931	+	22.6779i	0.439872	+	0.761880i
$887$	14.7459	−	25.5407i	0.495120	−	0.857573i	−0.504864	−	0.863199i	$-0.668457\pi$
$887$	14.7459	−	25.5407i	0.495120	−	0.857573i	0.999984	+	0.00562569i	$0.00179072\pi$
$888$	−14.6764	+	5.13912i	−0.492508	+	0.172458i
$889$	28.9375	+	32.2439i	0.970534	+	1.08143i
$890$			18.1977i			0.609989i
$891$	−4.74054	+	5.11809i	−0.158814	+	0.171463i
$892$	21.6245	−	12.4849i	0.724043	−	0.418026i
$893$	6.49375	−	3.74917i	0.217305	−	0.125461i
$894$	−7.18885	−	1.35857i	−0.240431	−	0.0454373i
$895$			20.1241i			0.672675i
$896$	−0.545863	−	2.58883i	−0.0182360	−	0.0864867i
$897$	4.53911	+	12.9629i	0.151556	+	0.432818i
$898$	2.74823	−	4.76008i	0.0917096	−	0.158846i
$899$	1.29957	+	2.25093i	0.0433432	+	0.0750726i
$900$	−16.0705	−	6.29908i	−0.535685	−	0.209969i
$901$	0.00855723	+	0.00494052i	0.000285083	+	0.000164592i
$902$	−0.325620			−0.0108420
$903$	−38.7092	+	0.814154i	−1.28816	+	0.0270933i
$904$	7.78444			0.258907
$905$	46.6928	+	26.9581i	1.55212	+	0.896117i
$906$	−20.5899	−	17.7112i	−0.684053	−	0.588414i
$907$	−20.7483	−	35.9370i	−0.688935	−	1.19327i	−0.972183	−	0.234223i	$-0.924745\pi$
$907$	−20.7483	−	35.9370i	−0.688935	−	1.19327i	0.283248	−	0.959047i	$-0.408588\pi$
$908$	7.48692	−	12.9677i	0.248462	−	0.430349i
$909$	−2.40565	+	1.92017i	−0.0797904	+	0.0636881i
$910$	2.69453	−	8.24713i	0.0893226	−	0.273390i
$911$		−	7.92533i		−	0.262578i	−0.991344	−	0.131289i	$-0.958088\pi$
$911$		−	7.92533i		−	0.262578i	0.991344	−	0.131289i	$-0.0419116\pi$
$912$	−0.181754	+	0.961750i	−0.00601848	+	0.0318467i
$913$	6.84204	−	3.95025i	0.226438	−	0.130734i
$914$	28.3226	−	16.3520i	0.936827	−	0.540877i
$915$	−2.42167	+	12.8143i	−0.0800580	+	0.423626i
$916$		−	9.97283i		−	0.329512i
$917$	−26.5474	+	5.59762i	−0.876673	+	0.184850i
$918$	0.175570	−	0.279828i	0.00579468	−	0.00923568i
$919$	−1.89226	+	3.27749i	−0.0624198	+	0.108114i	−0.895547	−	0.444968i	$-0.853215\pi$
$919$	−1.89226	+	3.27749i	−0.0624198	+	0.108114i	0.833127	+	0.553082i	$0.186548\pi$
$920$	13.0018	+	22.5198i	0.428658	+	0.742457i
$921$	−14.9018	−	12.8183i	−0.491030	−	0.422378i
$922$	18.7649	+	10.8339i	0.617988	+	0.356795i
$923$	0.904569			0.0297743
$924$	−3.11289	−	1.71098i	−0.102406	−	0.0562870i
$925$	−51.6557			−1.69843
$926$	23.6442	+	13.6510i	0.776997	+	0.448599i
$927$	−20.8724	+	53.2507i	−0.685539	+	1.74898i
$928$	−2.47930	−	4.29427i	−0.0813869	−	0.140966i
$929$	21.6760	−	37.5440i	0.711167	−	1.23178i	−0.253252	−	0.967400i	$-0.581500\pi$
$929$	21.6760	−	37.5440i	0.711167	−	1.23178i	0.964419	−	0.264378i	$-0.0851665\pi$
$930$	−0.983931	−	2.80993i	−0.0322644	−	0.0921413i
$931$	2.33550	−	3.19260i	0.0765430	−	0.104633i
$932$			29.1764i			0.955705i
$933$	48.0416	+	9.07903i	1.57281	+	0.297234i
$934$	14.4800	−	8.36005i	0.473801	−	0.273549i
$935$	0.139950	−	0.0808002i	0.00457685	−	0.00264245i
$936$	0.448430	+	2.96630i	0.0146574	+	0.0969564i
$937$			32.1821i			1.05134i	0.850687	+	0.525672i	$0.176186\pi$
$937$			32.1821i			1.05134i	−0.850687	+	0.525672i	$0.823814\pi$
$938$	−21.2937	+	19.1102i	−0.695265	+	0.623970i
$939$	−2.34194	+	0.820056i	−0.0764262	+	0.0267615i
$940$	21.7566	−	37.6836i	0.709623	−	1.22910i
$941$	−4.61669	−	7.99634i	−0.150500	−	0.260673i	0.780912	−	0.624642i	$-0.214755\pi$
$941$	−4.61669	−	7.99634i	−0.150500	−	0.260673i	−0.931411	+	0.363968i	$0.881422\pi$
$942$	−18.2155	+	21.1762i	−0.593493	+	0.689958i
$943$	2.88484	+	1.66556i	0.0939432	+	0.0542381i
$944$	−7.87024			−0.256154
$945$	−42.3101	−	15.5658i	−1.37635	−	0.506357i
$946$	6.54904			0.212928
$947$	13.8715	+	8.00874i	0.450764	+	0.260249i	0.708153	−	0.706059i	$-0.249529\pi$
$947$	13.8715	+	8.00874i	0.450764	+	0.260249i	−0.257389	+	0.966308i	$0.582862\pi$
$948$	11.3849	−	13.2354i	0.369766	−	0.429867i
$949$	7.17052	+	12.4197i	0.232765	+	0.403161i
$950$	−1.62568	+	2.81576i	−0.0527441	+	0.0913554i
$951$	45.1357	−	15.8048i	1.46362	−	0.512505i
$952$	0.159886	+	0.0522385i	0.00518195	+	0.00169306i
$953$		−	43.6220i		−	1.41305i	−0.707686	−	0.706527i	$-0.750261\pi$
$953$		−	43.6220i		−	1.41305i	0.707686	−	0.706527i	$-0.249739\pi$
$954$	0.0696964	+	0.461031i	0.00225650	+	0.0149264i
$955$	34.8251	−	20.1063i	1.12691	−	0.650624i
$956$	−3.25657	+	1.88018i	−0.105325	+	0.0608094i
$957$	−6.54149	−	1.23623i	−0.211456	−	0.0399616i
$958$		−	23.4807i		−	0.758628i
$959$	8.91920	+	2.91411i	0.288016	+	0.0941014i
$960$	1.87712	+	5.36073i	0.0605838	+	0.173017i
$961$	−15.3626	+	26.6088i	−0.495568	+	0.858350i
$962$	4.48895	+	7.77509i	0.144730	+	0.250679i
$963$	12.5517	−	32.0224i	0.404471	−	1.03191i
$964$	−1.74550	−	1.00776i	−0.0562187	−	0.0324579i
$965$	−14.3659			−0.462453
$966$	18.8269	+	31.0810i	0.605747	+	1.00001i
$967$	−8.32521			−0.267721			−0.133860	−	0.991000i	$-0.542737\pi$
$967$	−8.32521			−0.267721			−0.133860	+	0.991000i	$0.542737\pi$
$968$	−9.00594	−	5.19958i	−0.289462	−	0.167121i
$969$	−0.0471742	−	0.0405786i	−0.00151545	−	0.00130357i
$970$	−9.86827	−	17.0923i	−0.316851	−	0.548802i
$971$	−16.2057	+	28.0690i	−0.520065	+	0.900778i	0.479663	+	0.877453i	$0.340759\pi$
$971$	−16.2057	+	28.0690i	−0.520065	+	0.900778i	−0.999728	+	0.0233256i	$0.992575\pi$
$972$	15.4885	−	1.76236i	0.496794	−	0.0565279i
$973$	−39.8732	+	35.7845i	−1.27828	+	1.14720i
$974$		−	16.7477i		−	0.536631i
$975$	−1.85057	+	9.79229i	−0.0592658	+	0.313604i
$976$	1.98841	−	1.14801i	0.0636474	−	0.0367468i
$977$	12.7139	−	7.34038i	0.406754	−	0.234840i	−0.282640	−	0.959226i	$-0.591210\pi$
$977$	12.7139	−	7.34038i	0.406754	−	0.234840i	0.689394	+	0.724386i	$0.257877\pi$
$978$	2.47958	−	13.1207i	0.0792882	−	0.419553i
$979$		−	4.30146i		−	0.137475i
$980$	2.47386	−	22.8212i	0.0790246	−	0.728998i
$981$	−23.9058	+	19.0814i	−0.763252	+	0.609222i
$982$	2.45903	−	4.25916i	0.0784708	−	0.135915i
$983$	29.0073	+	50.2421i	0.925189	+	1.60247i	0.791257	+	0.611483i	$0.209427\pi$
$983$	29.0073	+	50.2421i	0.925189	+	1.60247i	0.133931	+	0.990991i	$0.457240\pi$
$984$	0.551607	+	0.474486i	0.0175846	+	0.0151260i
$985$	60.7472	+	35.0724i	1.93557	+	1.11750i
$986$	0.315243			0.0100394
$987$	29.2894	−	53.2880i	0.932292	−	1.69618i
$988$	0.565095			0.0179781
$989$	−58.0213	−	33.4986i	−1.84497	−	1.06519i
$990$	7.09974	+	2.78284i	0.225644	+	0.0884445i
$991$	−24.6887	−	42.7620i	−0.784261	−	1.35838i	−0.929439	−	0.368975i	$-0.879709\pi$
$991$	−24.6887	−	42.7620i	−0.784261	−	1.35838i	0.145178	−	0.989406i	$-0.453625\pi$
$992$	−0.262085	+	0.453945i	−0.00832121	+	0.0144128i
$993$	3.78200	+	10.8007i	0.120018	+	0.342751i
$994$	2.34178	−	0.493771i	0.0742766	−	0.0156615i
$995$		−	43.3991i		−	1.37584i
$996$	−17.3468	−	3.27824i	−0.549653	−	0.103875i
$997$	14.7839	−	8.53551i	0.468212	−	0.270322i	−0.247279	−	0.968944i	$-0.579536\pi$
$997$	14.7839	−	8.53551i	0.468212	−	0.270322i	0.715491	+	0.698622i	$0.246203\pi$
$998$	24.5697	−	14.1854i	0.777742	−	0.449029i
$999$	41.2301	−	21.8255i	1.30446	−	0.690528i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.z.b.131.10	yes	32
3.2	odd	2		546.2.z.a.131.1	✓	32
7.3	odd	6		546.2.z.a.521.1	yes	32
21.17	even	6	inner	546.2.z.b.521.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.z.a.131.1	✓	32	3.2	odd	2
546.2.z.a.521.1	yes	32	7.3	odd	6
546.2.z.b.131.10	yes	32	1.1	even	1	trivial
546.2.z.b.521.10	yes	32	21.17	even	6	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.12951 + 1.31309i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.63964 + 2.83994i) q^{5} +(-1.63473 + 0.572419i) q^{6} +(1.76715 + 1.96906i) q^{7} +1.00000i q^{8} +(-0.448430 - 2.96630i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.12951 + 1.31309i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.63964 + 2.83994i) q^{5} +(-1.63473 + 0.572419i) q^{6} +(1.76715 + 1.96906i) q^{7} +1.00000i q^{8} +(-0.448430 - 2.96630i) q^{9} +(-2.83994 + 1.63964i) q^{10} +(0.671287 - 0.387567i) q^{11} +(-1.70193 - 0.321635i) q^{12} +1.00000i q^{13} +(0.545863 + 2.58883i) q^{14} +(-1.87712 - 5.36073i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0317875 - 0.0550576i) q^{17} +(1.09480 - 2.79310i) q^{18} +(-0.489387 - 0.282548i) q^{19} -3.27928 q^{20} +(-4.58156 + 0.0963620i) q^{21} +0.775135 q^{22} +(-6.86731 - 3.96485i) q^{23} +(-1.31309 - 1.12951i) q^{24} +(-2.87683 - 4.98281i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(4.40153 + 2.76162i) q^{27} +(-0.821683 + 2.51492i) q^{28} +4.95860i q^{29} +(1.05473 - 5.58109i) q^{30} +(0.453945 - 0.262085i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.249310 + 1.31922i) q^{33} -0.0635751i q^{34} +(-8.48949 + 1.79004i) q^{35} +(2.34467 - 1.87150i) q^{36} +(4.48895 - 7.77509i) q^{37} +(-0.282548 - 0.489387i) q^{38} +(-1.31309 - 1.12951i) q^{39} +(-2.83994 - 1.63964i) q^{40} -0.420082 q^{41} +(-4.01593 - 2.20733i) q^{42} +8.44891 q^{43} +(0.671287 + 0.387567i) q^{44} +(9.15936 + 3.59014i) q^{45} +(-3.96485 - 6.86731i) q^{46} +(-6.63458 + 11.4914i) q^{47} +(-0.572419 - 1.63473i) q^{48} +(-0.754392 + 6.95923i) q^{49} -5.75366i q^{50} +(0.108200 + 0.0204479i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(-0.134600 + 0.0777115i) q^{53} +(2.43103 + 4.59240i) q^{54} +2.54188i q^{55} +(-1.96906 + 1.76715i) q^{56} +(0.923777 - 0.323471i) q^{57} +(-2.47930 + 4.29427i) q^{58} +(3.93512 + 6.81583i) q^{59} +(3.70396 - 4.30600i) q^{60} +(-1.98841 - 1.14801i) q^{61} +0.524170 q^{62} +(5.04837 - 6.12486i) q^{63} -1.00000 q^{64} +(-2.83994 - 1.63964i) q^{65} +(-0.875520 + 1.01782i) q^{66} +(5.40708 + 9.36534i) q^{67} +(0.0317875 - 0.0550576i) q^{68} +(12.9629 - 4.53911i) q^{69} +(-8.24713 - 2.69453i) q^{70} -0.904569i q^{71} +(2.96630 - 0.448430i) q^{72} +(12.4197 - 7.17052i) q^{73} +(7.77509 - 4.48895i) q^{74} +(9.79229 + 1.85057i) q^{75} -0.565095i q^{76} +(1.94940 + 0.636915i) q^{77} +(-0.572419 - 1.63473i) q^{78} +(-5.03979 + 8.72917i) q^{79} +(-1.63964 - 2.83994i) q^{80} +(-8.59782 + 2.66035i) q^{81} +(-0.363802 - 0.210041i) q^{82} +10.1924 q^{83} +(-2.37423 - 3.91957i) q^{84} +0.208480 q^{85} +(7.31697 + 4.22445i) q^{86} +(-6.51110 - 5.60077i) q^{87} +(0.387567 + 0.671287i) q^{88} +(2.77465 - 4.80584i) q^{89} +(6.13716 + 7.68883i) q^{90} +(-1.96906 + 1.76715i) q^{91} -7.92969i q^{92} +(-0.168591 + 0.892098i) q^{93} +(-11.4914 + 6.63458i) q^{94} +(1.60483 - 0.926552i) q^{95} +(0.321635 - 1.70193i) q^{96} +6.01856i q^{97} +(-4.13294 + 5.64967i) q^{98} +(-1.45066 - 1.81744i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} + 24 q^{11} - 4 q^{14} - 12 q^{15} - 16 q^{16} - 4 q^{17} - 24 q^{18} + 4 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} - 16 q^{26} + 6 q^{27} - 2 q^{28} - 8 q^{30} - 6 q^{31} + 14 q^{33} - 48 q^{35} + 4 q^{36} - 16 q^{38} - 6 q^{39} + 6 q^{40} - 16 q^{41} + 14 q^{42} + 32 q^{43} + 24 q^{44} + 20 q^{45} + 16 q^{46} - 20 q^{47} - 26 q^{49} - 46 q^{51} + 60 q^{53} + 6 q^{54} - 8 q^{56} - 8 q^{57} - 10 q^{58} - 8 q^{59} - 6 q^{60} + 36 q^{61} - 36 q^{62} + 84 q^{63} - 32 q^{64} + 6 q^{65} + 36 q^{66} + 4 q^{68} + 36 q^{69} - 18 q^{70} - 24 q^{72} - 48 q^{73} + 84 q^{74} - 2 q^{75} - 52 q^{77} + 18 q^{79} - 74 q^{81} - 24 q^{83} + 8 q^{84} - 32 q^{85} + 24 q^{86} + 14 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{90} - 8 q^{91} - 40 q^{93} + 72 q^{95} - 6 q^{96} - 32 q^{98}+O(q^{100}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 + 24 * q^11 - 4 * q^14 - 12 * q^15 - 16 * q^16 - 4 * q^17 - 24 * q^18 + 4 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 - 16 * q^26 + 6 * q^27 - 2 * q^28 - 8 * q^30 - 6 * q^31 + 14 * q^33 - 48 * q^35 + 4 * q^36 - 16 * q^38 - 6 * q^39 + 6 * q^40 - 16 * q^41 + 14 * q^42 + 32 * q^43 + 24 * q^44 + 20 * q^45 + 16 * q^46 - 20 * q^47 - 26 * q^49 - 46 * q^51 + 60 * q^53 + 6 * q^54 - 8 * q^56 - 8 * q^57 - 10 * q^58 - 8 * q^59 - 6 * q^60 + 36 * q^61 - 36 * q^62 + 84 * q^63 - 32 * q^64 + 6 * q^65 + 36 * q^66 + 4 * q^68 + 36 * q^69 - 18 * q^70 - 24 * q^72 - 48 * q^73 + 84 * q^74 - 2 * q^75 - 52 * q^77 + 18 * q^79 - 74 * q^81 - 24 * q^83 + 8 * q^84 - 32 * q^85 + 24 * q^86 + 14 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 40 * q^93 + 72 * q^95 - 6 * q^96 - 32 * q^98

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