LMFDB - Embedded newform 603.2.z.c.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(10,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("603.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.z (of order $33$, degree $20$, 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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$5$ over $\Q(\zeta_{33})$
Twist minimal:	no (minimal twist has level 67)
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	603.19
Dual form			603.2.z.c.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.83066 - 0.943770i) q^{2} +(1.30049 + 1.82629i) q^{4} +(0.863926 + 0.997024i) q^{5} +(-0.0491040 - 1.03082i) q^{7} +(-0.0709360 - 0.493371i) q^{8} +O(q^{10})$	\(q+(-1.83066 - 0.943770i) q^{2} +(1.30049 + 1.82629i) q^{4} +(0.863926 + 0.997024i) q^{5} +(-0.0491040 - 1.03082i) q^{7} +(-0.0709360 - 0.493371i) q^{8} +(-0.640592 - 2.64056i) q^{10} +(-3.91359 + 0.754283i) q^{11} +(-3.67378 + 1.47076i) q^{13} +(-0.882963 + 1.93342i) q^{14} +(1.13081 - 3.26726i) q^{16} +(2.27094 - 3.18910i) q^{17} +(-0.0878936 + 1.84511i) q^{19} +(-0.697322 + 2.87440i) q^{20} +(7.87631 + 2.31269i) q^{22} +(-3.70668 - 3.53431i) q^{23} +(0.463886 - 3.22640i) q^{25} +(8.11349 + 0.774744i) q^{26} +(1.81871 - 1.43025i) q^{28} +(4.51973 - 7.82841i) q^{29} +(-0.984123 - 0.393984i) q^{31} +(-5.87515 + 5.60194i) q^{32} +(-7.16709 + 3.69489i) q^{34} +(0.985329 - 0.939509i) q^{35} +(-4.40654 - 7.63235i) q^{37} +(1.90227 - 3.29482i) q^{38} +(0.430619 - 0.496961i) q^{40} +(-10.4444 - 0.997319i) q^{41} +(0.310274 + 0.679406i) q^{43} +(-6.46713 - 6.16640i) q^{44} +(3.45008 + 9.96836i) q^{46} +(0.127195 - 0.524304i) q^{47} +(5.90813 - 0.564158i) q^{49} +(-3.89419 + 5.46863i) q^{50} +(-7.46375 - 4.79666i) q^{52} +(0.194412 - 0.425703i) q^{53} +(-4.13309 - 3.25030i) q^{55} +(-0.505093 + 0.0973486i) q^{56} +(-15.6623 + 10.0655i) q^{58} +(1.84843 + 12.8561i) q^{59} +(-6.41548 - 1.23648i) q^{61} +(1.42976 + 1.65003i) q^{62} +(9.40760 - 2.76232i) q^{64} +(-4.64026 - 2.39222i) q^{65} +(-7.61020 - 3.01410i) q^{67} +8.77755 q^{68} +(-2.69048 + 0.789996i) q^{70} +(-3.73448 - 5.24434i) q^{71} +(-14.2222 - 2.74110i) q^{73} +(0.863685 + 18.1310i) q^{74} +(-3.48401 + 2.23904i) q^{76} +(0.969702 + 3.99716i) q^{77} +(5.44259 + 4.28010i) q^{79} +(4.23447 - 1.69523i) q^{80} +(18.1789 + 11.6829i) q^{82} +(-1.59415 + 4.60598i) q^{83} +(5.14153 - 0.490957i) q^{85} +(0.0731967 - 1.53659i) q^{86} +(0.649755 + 1.87734i) q^{88} +(-7.32268 - 2.15013i) q^{89} +(1.69648 + 3.71478i) q^{91} +(1.63415 - 11.3658i) q^{92} +(-0.727673 + 0.839779i) q^{94} +(-1.91556 + 1.50641i) q^{95} +(2.28880 + 3.96432i) q^{97} +(-11.3482 - 4.54313i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8}+O(q^{10}) $ 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8	$ 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8} + 8 q^{10} + 24 q^{11} - 22 q^{13} + 32 q^{14} - 28 q^{16} - 17 q^{17} + 15 q^{20} + 49 q^{22} + 13 q^{23} - 34 q^{25} + 27 q^{26} + 22 q^{28} - 8 q^{29} + 10 q^{31} - 34 q^{32} - 50 q^{34} + q^{35} + 7 q^{37} - 50 q^{38} + 43 q^{40} + 5 q^{41} + 2 q^{43} + 19 q^{44} + 52 q^{46} + 6 q^{47} - 27 q^{49} - 134 q^{50} + 120 q^{52} + 52 q^{53} - 64 q^{55} + 124 q^{56} - 56 q^{58} - 27 q^{59} - 16 q^{61} + 74 q^{62} - 197 q^{64} + 92 q^{65} - 56 q^{67} - 16 q^{68} - 22 q^{70} + 113 q^{71} + q^{73} + 24 q^{74} - 144 q^{76} - 85 q^{77} + 36 q^{79} + 13 q^{80} - 20 q^{82} + 61 q^{83} - 6 q^{85} - 189 q^{86} + 129 q^{88} - 95 q^{89} + 42 q^{91} - 4 q^{92} + 70 q^{94} + 20 q^{95} + 53 q^{97} - q^{98}+O(q^{100}) $ 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8 + 8 * q^10 + 24 * q^11 - 22 * q^13 + 32 * q^14 - 28 * q^16 - 17 * q^17 + 15 * q^20 + 49 * q^22 + 13 * q^23 - 34 * q^25 + 27 * q^26 + 22 * q^28 - 8 * q^29 + 10 * q^31 - 34 * q^32 - 50 * q^34 + q^35 + 7 * q^37 - 50 * q^38 + 43 * q^40 + 5 * q^41 + 2 * q^43 + 19 * q^44 + 52 * q^46 + 6 * q^47 - 27 * q^49 - 134 * q^50 + 120 * q^52 + 52 * q^53 - 64 * q^55 + 124 * q^56 - 56 * q^58 - 27 * q^59 - 16 * q^61 + 74 * q^62 - 197 * q^64 + 92 * q^65 - 56 * q^67 - 16 * q^68 - 22 * q^70 + 113 * q^71 + q^73 + 24 * q^74 - 144 * q^76 - 85 * q^77 + 36 * q^79 + 13 * q^80 - 20 * q^82 + 61 * q^83 - 6 * q^85 - 189 * q^86 + 129 * q^88 - 95 * q^89 + 42 * q^91 - 4 * q^92 + 70 * q^94 + 20 * q^95 + 53 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{5}{33}\right)$	$1$

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 $

$2$	−1.83066	−	0.943770i	−1.29447	−	0.667346i	−0.333175	−	0.942865i	$-0.608120\pi$
$2$	−1.83066	−	0.943770i	−1.29447	−	0.667346i	−0.961296	+	0.275519i	$0.911150\pi$
$3$		0			0
$3$		0			0
$4$	1.30049	+	1.82629i	0.650246	+	0.913143i
$5$	0.863926	+	0.997024i	0.386360	+	0.445883i	0.915298	−	0.402778i	$-0.131955\pi$
$5$	0.863926	+	0.997024i	0.386360	+	0.445883i	−0.528938	+	0.848660i	$0.677410\pi$
$6$		0			0
$7$	−0.0491040	−	1.03082i	−0.0185596	−	0.389613i	−0.988967	−	0.148138i	$-0.952672\pi$
$7$	−0.0491040	−	1.03082i	−0.0185596	−	0.389613i	0.970407	−	0.241475i	$-0.0776311\pi$
$8$	−0.0709360	−	0.493371i	−0.0250797	−	0.174433i
$9$		0			0
$10$	−0.640592	−	2.64056i	−0.202573	−	0.835017i
$11$	−3.91359	+	0.754283i	−1.17999	+	0.227425i	−0.741275	−	0.671201i	$-0.765779\pi$
$11$	−3.91359	+	0.754283i	−1.17999	+	0.227425i	−0.438716	+	0.898626i	$0.644567\pi$
$12$		0			0
$13$	−3.67378	+	1.47076i	−1.01892	+	0.407915i	−0.820161	−	0.572133i	$-0.806116\pi$
$13$	−3.67378	+	1.47076i	−1.01892	+	0.407915i	−0.198762	+	0.980048i	$0.563692\pi$
$14$	−0.882963	+	1.93342i	−0.235982	+	0.516728i
$15$		0			0
$16$	1.13081	−	3.26726i	0.282702	−	0.816815i
$17$	2.27094	−	3.18910i	0.550785	−	0.773469i	−0.441525	−	0.897249i	$-0.645562\pi$
$17$	2.27094	−	3.18910i	0.550785	−	0.773469i	0.992310	+	0.123780i	$0.0395017\pi$
$18$		0			0
$19$	−0.0878936	+	1.84511i	−0.0201642	+	0.423298i	0.966105	+	0.258151i	$0.0831131\pi$
$19$	−0.0878936	+	1.84511i	−0.0201642	+	0.423298i	−0.986269	+	0.165148i	$0.947190\pi$
$20$	−0.697322	+	2.87440i	−0.155926	+	0.642735i
$21$		0			0
$22$	7.87631	+	2.31269i	1.67924	+	0.493068i
$23$	−3.70668	−	3.53431i	−0.772895	−	0.736954i	0.197019	−	0.980400i	$-0.436874\pi$
$23$	−3.70668	−	3.53431i	−0.772895	−	0.736954i	−0.969915	+	0.243445i	$0.921722\pi$
$24$		0			0
$25$	0.463886	−	3.22640i	0.0927772	−	0.645279i
$26$	8.11349	+	0.774744i	1.59119	+	0.151940i
$27$		0			0
$28$	1.81871	−	1.43025i	0.343704	−	0.270292i
$29$	4.51973	−	7.82841i	0.839293	−	1.45370i	−0.0511930	−	0.998689i	$-0.516302\pi$
$29$	4.51973	−	7.82841i	0.839293	−	1.45370i	0.890486	−	0.455010i	$-0.150364\pi$
$30$		0			0
$31$	−0.984123	−	0.393984i	−0.176754	−	0.0707615i	0.281598	−	0.959533i	$-0.409136\pi$
$31$	−0.984123	−	0.393984i	−0.176754	−	0.0707615i	−0.458351	+	0.888771i	$0.651560\pi$
$32$	−5.87515	+	5.60194i	−1.03859	+	0.990293i
$33$		0			0
$34$	−7.16709	+	3.69489i	−1.22915	+	0.633669i
$35$	0.985329	−	0.939509i	0.166551	−	0.158806i
$36$		0			0
$37$	−4.40654	−	7.63235i	−0.724430	−	1.25475i	−0.959208	−	0.282701i	$-0.908769\pi$
$37$	−4.40654	−	7.63235i	−0.724430	−	1.25475i	0.234778	−	0.972049i	$-0.424564\pi$
$38$	1.90227	−	3.29482i	0.308588	−	0.534490i
$39$		0			0
$40$	0.430619	−	0.496961i	0.0680868	−	0.0785764i
$41$	−10.4444	−	0.997319i	−1.63114	−	0.155755i	−0.761066	−	0.648675i	$-0.775324\pi$
$41$	−10.4444	−	0.997319i	−1.63114	−	0.155755i	−0.870075	+	0.492920i	$0.835930\pi$
$42$		0			0
$43$	0.310274	+	0.679406i	0.0473164	+	0.103608i	0.931814	−	0.362937i	$-0.118226\pi$
$43$	0.310274	+	0.679406i	0.0473164	+	0.103608i	−0.884497	+	0.466545i	$0.845499\pi$
$44$	−6.46713	−	6.16640i	−0.974956	−	0.929619i
$45$		0			0
$46$	3.45008	+	9.96836i	0.508687	+	1.46975i
$47$	0.127195	−	0.524304i	0.0185533	−	0.0764777i	−0.961782	−	0.273815i	$-0.911714\pi$
$47$	0.127195	−	0.524304i	0.0185533	−	0.0764777i	0.980336	+	0.197338i	$0.0632295\pi$
$48$		0			0
$49$	5.90813	−	0.564158i	0.844018	−	0.0805940i
$50$	−3.89419	+	5.46863i	−0.550722	+	0.773381i
$51$		0			0
$52$	−7.46375	−	4.79666i	−1.03504	−	0.665177i
$53$	0.194412	−	0.425703i	0.0267046	−	0.0584749i	−0.895810	−	0.444438i	$-0.853403\pi$
$53$	0.194412	−	0.425703i	0.0267046	−	0.0584749i	0.922514	+	0.385963i	$0.126131\pi$
$54$		0			0
$55$	−4.13309	−	3.25030i	−0.557306	−	0.438270i
$56$	−0.505093	+	0.0973486i	−0.0674958	+	0.0130088i
$57$		0			0
$58$	−15.6623	+	10.0655i	−2.05656	+	1.32167i
$59$	1.84843	+	12.8561i	0.240645	+	1.67372i	0.648915	+	0.760861i	$0.275223\pi$
$59$	1.84843	+	12.8561i	0.240645	+	1.67372i	−0.408270	+	0.912861i	$0.633868\pi$
$60$		0			0
$61$	−6.41548	−	1.23648i	−0.821418	−	0.158315i	−0.238808	−	0.971067i	$-0.576756\pi$
$61$	−6.41548	−	1.23648i	−0.821418	−	0.158315i	−0.582610	+	0.812752i	$0.697969\pi$
$62$	1.42976	+	1.65003i	0.181580	+	0.209555i
$63$		0			0
$64$	9.40760	−	2.76232i	1.17595	−	0.345290i
$65$	−4.64026	−	2.39222i	−0.575553	−	0.296718i
$66$		0			0
$67$	−7.61020	−	3.01410i	−0.929734	−	0.368231i
$67$	−7.61020	−	3.01410i	−0.929734	−	0.368231i
$68$	8.77755			1.06443
$69$		0			0
$70$	−2.69048	+	0.789996i	−0.321574	+	0.0944226i
$71$	−3.73448	−	5.24434i	−0.443201	−	0.622388i	0.531189	−	0.847253i	$-0.321745\pi$
$71$	−3.73448	−	5.24434i	−0.443201	−	0.622388i	−0.974390	+	0.224865i	$0.927806\pi$
$72$		0			0
$73$	−14.2222	−	2.74110i	−1.66458	−	0.320821i	−0.731867	−	0.681447i	$-0.761351\pi$
$73$	−14.2222	−	2.74110i	−1.66458	−	0.320821i	−0.932710	+	0.360626i	$0.882563\pi$
$74$	0.863685	+	18.1310i	0.100401	+	2.10768i
$75$		0			0
$76$	−3.48401	+	2.23904i	−0.399643	+	0.256835i
$77$	0.969702	+	3.99716i	0.110508	+	0.455519i
$78$		0			0
$79$	5.44259	+	4.28010i	0.612339	+	0.481549i	0.875510	−	0.483201i	$-0.160526\pi$
$79$	5.44259	+	4.28010i	0.612339	+	0.481549i	−0.263171	+	0.964749i	$0.584768\pi$
$80$	4.23447	−	1.69523i	0.473428	−	0.189532i
$81$		0			0
$82$	18.1789	+	11.6829i	2.00752	+	1.29016i
$83$	−1.59415	+	4.60598i	−0.174980	+	0.505572i	−0.998054	−	0.0623628i	$-0.980136\pi$
$83$	−1.59415	+	4.60598i	−0.174980	+	0.505572i	0.823073	+	0.567935i	$0.192258\pi$
$84$		0			0
$85$	5.14153	−	0.490957i	0.557678	−	0.0532517i
$86$	0.0731967	−	1.53659i	0.00789300	−	0.165695i
$87$		0			0
$88$	0.649755	+	1.87734i	0.0692641	+	0.200126i
$89$	−7.32268	−	2.15013i	−0.776203	−	0.227914i	−0.130444	−	0.991456i	$-0.541640\pi$
$89$	−7.32268	−	2.15013i	−0.776203	−	0.227914i	−0.645758	+	0.763542i	$0.723459\pi$
$90$		0			0
$91$	1.69648	+	3.71478i	0.177840	+	0.389415i
$92$	1.63415	−	11.3658i	0.170372	−	1.18497i
$93$		0			0
$94$	−0.727673	+	0.839779i	−0.0750537	+	0.0866166i
$95$	−1.91556	+	1.50641i	−0.196532	+	0.154554i
$96$		0			0
$97$	2.28880	+	3.96432i	0.232393	+	0.402516i	0.958512	−	0.285053i	$-0.0920112\pi$
$97$	2.28880	+	3.96432i	0.232393	+	0.402516i	−0.726119	+	0.687569i	$0.758678\pi$
$98$	−11.3482	−	4.54313i	−1.14634	−	0.458926i
$99$		0			0
$100$	6.49560	−	3.34872i	0.649560	−	0.334872i
$101$	1.64220	−	0.846614i	0.163405	−	0.0842412i	−0.374584	−	0.927193i	$-0.622214\pi$
$101$	1.64220	−	0.846614i	0.163405	−	0.0842412i	0.537989	+	0.842952i	$0.319184\pi$
$102$		0			0
$103$	−2.38420	−	0.954489i	−0.234922	−	0.0940486i	0.251215	−	0.967931i	$-0.419170\pi$
$103$	−2.38420	−	0.954489i	−0.234922	−	0.0940486i	−0.486137	+	0.873883i	$0.661594\pi$
$104$	0.986232	+	1.70820i	0.0967080	+	0.167503i
$105$		0			0
$106$	−0.757668	+	0.595837i	−0.0735912	+	0.0578728i
$107$	10.5186	−	12.1392i	1.01687	−	1.17354i	0.0321385	−	0.999483i	$-0.489768\pi$
$107$	10.5186	−	12.1392i	1.01687	−	1.17354i	0.984736	−	0.174053i	$-0.0556863\pi$
$108$		0			0
$109$	0.328781	−	2.28672i	0.0314915	−	0.219028i	−0.967999	−	0.250955i	$-0.919255\pi$
$109$	0.328781	−	2.28672i	0.0314915	−	0.219028i	0.999490	+	0.0319269i	$0.0101644\pi$
$110$	4.49874	+	9.85087i	0.428938	+	0.939243i
$111$		0			0
$112$	−3.42348	−	1.00522i	−0.323489	−	0.0949848i
$113$	−5.12299	−	14.8019i	−0.481930	−	1.39245i	−0.879949	−	0.475068i	$-0.842423\pi$
$113$	−5.12299	−	14.8019i	−0.481930	−	1.39245i	0.398019	−	0.917377i	$-0.369698\pi$
$114$		0			0
$115$	0.321496	−	6.74903i	0.0299796	−	0.629350i
$116$	20.1748	−	1.92646i	1.87318	−	0.178867i
$117$		0			0
$118$	8.74936	−	25.2796i	0.805444	−	2.32718i
$119$	−3.39889	−	2.18434i	−0.311576	−	0.200238i
$120$		0			0
$121$	4.53519	−	1.81562i	0.412290	−	0.165056i
$122$	10.5776	+	8.31831i	0.957650	+	0.753104i
$123$		0			0
$124$	−0.560318	−	2.30966i	−0.0503181	−	0.207414i
$125$	9.16668	−	5.89107i	0.819893	−	0.526913i
$126$		0			0
$127$	0.445147	+	9.34478i	0.0395004	+	0.829215i	0.928506	+	0.371318i	$0.121094\pi$
$127$	0.445147	+	9.34478i	0.0395004	+	0.829215i	−0.889005	+	0.457897i	$0.848603\pi$
$128$	−3.88683	−	0.749125i	−0.343550	−	0.0662139i
$129$		0			0
$130$	6.23702	+	8.75866i	0.547023	+	0.768186i
$131$	−11.1427	+	3.27180i	−0.973545	+	0.285859i	−0.729557	−	0.683920i	$-0.760274\pi$
$131$	−11.1427	+	3.27180i	−0.973545	+	0.285859i	−0.243988	+	0.969778i	$0.578456\pi$
$132$		0			0
$133$	1.90629			0.165297
$134$	11.0871	+	12.7001i	0.957776	+	1.09712i
$135$		0			0
$136$	−1.73450	−	0.894196i	−0.148732	−	0.0766766i
$137$	−0.849173	+	0.249340i	−0.0725498	+	0.0213025i	−0.317806	−	0.948156i	$-0.602946\pi$
$137$	−0.849173	+	0.249340i	−0.0725498	+	0.0213025i	0.245256	+	0.969458i	$0.421128\pi$
$138$		0			0
$139$	12.3453	+	14.2472i	1.04711	+	1.20843i	0.977517	+	0.210857i	$0.0676255\pi$
$139$	12.3453	+	14.2472i	1.04711	+	1.20843i	0.0695957	+	0.997575i	$0.477829\pi$
$140$	2.99723	+	0.577668i	0.253312	+	0.0488219i
$141$		0			0
$142$	1.88710	+	13.1251i	0.158362	+	1.10143i
$143$	13.2683	−	8.52701i	1.10955	−	0.713065i
$144$		0			0
$145$	11.7098	−	2.25688i	0.972448	−	0.187424i
$146$	23.4489	+	18.4404i	1.94065	+	1.52614i
$147$		0			0
$148$	8.20818	−	17.9734i	0.674708	−	1.47741i
$149$	17.6111	+	11.3180i	1.44276	+	0.927204i	0.999526	+	0.0307967i	$0.00980444\pi$
$149$	17.6111	+	11.3180i	1.44276	+	0.927204i	0.443232	+	0.896407i	$0.353832\pi$
$150$		0			0
$151$	−0.348748	+	0.489748i	−0.0283807	+	0.0398551i	−0.828523	−	0.559956i	$-0.810818\pi$
$151$	−0.348748	+	0.489748i	−0.0283807	+	0.0398551i	0.800142	+	0.599811i	$0.204758\pi$
$152$	0.916560	−	0.0875209i	0.0743428	−	0.00709888i
$153$		0			0
$154$	1.99721	−	8.23261i	0.160940	−	0.663403i
$155$	−0.457399	−	1.32157i	−0.0367392	−	0.106151i
$156$		0			0
$157$	1.55477	+	1.48247i	0.124084	+	0.118314i	0.749581	−	0.661913i	$-0.230255\pi$
$157$	1.55477	+	1.48247i	0.124084	+	0.118314i	−0.625497	+	0.780227i	$0.715104\pi$
$158$	−5.92409	−	12.9719i	−0.471295	−	1.03199i
$159$		0			0
$160$	−10.6610	−	1.01800i	−0.842823	−	0.0804799i
$161$	−3.46122	+	3.99446i	−0.272782	+	0.314808i
$162$		0			0
$163$	11.1029	−	19.2307i	0.869643	−	1.50627i	0.00728093	−	0.999973i	$-0.497682\pi$
$163$	11.1029	−	19.2307i	0.869643	−	1.50627i	0.862362	−	0.506292i	$-0.168984\pi$
$164$	−11.7615	−	20.3715i	−0.918417	−	1.59074i
$165$		0			0
$166$	7.26532	−	6.92747i	0.563899	−	0.537676i
$167$	−5.55626	+	2.86445i	−0.429956	+	0.221658i	−0.659600	−	0.751617i	$-0.729274\pi$
$167$	−5.55626	+	2.86445i	−0.429956	+	0.221658i	0.229644	+	0.973275i	$0.426244\pi$
$168$		0			0
$169$	1.92497	−	1.83546i	0.148075	−	0.141189i
$170$	−9.87574	−	3.95365i	−0.757434	−	0.303231i
$171$		0			0
$172$	−0.837281	+	1.45021i	−0.0638421	+	0.110578i
$173$	4.98896	−	3.92336i	0.379304	−	0.298288i	−0.410245	−	0.911975i	$-0.634557\pi$
$173$	4.98896	−	3.92336i	0.379304	−	0.298288i	0.789549	+	0.613687i	$0.210314\pi$
$174$		0			0
$175$	−3.34861	−	0.319753i	−0.253131	−	0.0241711i
$176$	−1.96109	+	13.6397i	−0.147823	+	1.02813i
$177$		0			0
$178$	11.3761	+	10.8471i	0.852674	+	0.813023i
$179$	10.3667	+	3.04394i	0.774845	+	0.227515i	0.645167	−	0.764041i	$-0.276788\pi$
$179$	10.3667	+	3.04394i	0.774845	+	0.227515i	0.129677	+	0.991556i	$0.458606\pi$
$180$		0			0
$181$	−1.92265	+	7.92525i	−0.142909	+	0.589079i	0.854647	+	0.519209i	$0.173774\pi$
$181$	−1.92265	+	7.92525i	−0.142909	+	0.589079i	−0.997556	+	0.0698699i	$0.977742\pi$
$182$	0.400217	−	8.40158i	0.0296660	−	0.622767i
$183$		0			0
$184$	−1.48079	+	2.07947i	−0.109165	+	0.153301i
$185$	3.80271	−	10.9872i	0.279581	−	0.807796i
$186$		0			0
$187$	−6.48207	+	14.1937i	−0.474016	+	1.03795i
$188$	1.12295	−	0.449560i	0.0818993	−	0.0327875i
$189$		0			0
$190$	4.92843	−	0.949877i	0.357546	−	0.0689113i
$191$	3.86675	+	15.9389i	0.279788	+	1.15330i	0.922129	+	0.386883i	$0.126448\pi$
$191$	3.86675	+	15.9389i	0.279788	+	1.15330i	−0.642341	+	0.766419i	$0.722037\pi$
$192$		0			0
$193$	−2.19934	−	15.2968i	−0.158312	−	1.10108i	−0.901743	−	0.432272i	$-0.857712\pi$
$193$	−2.19934	−	15.2968i	−0.158312	−	1.10108i	0.743431	−	0.668812i	$-0.233197\pi$
$194$	−0.448607	−	9.41742i	−0.0322081	−	0.676132i
$195$		0			0
$196$	8.71379	+	10.0562i	0.622413	+	0.718303i
$197$	−0.0405888	−	0.0569990i	−0.00289183	−	0.00406101i	0.813128	−	0.582086i	$-0.197763\pi$
$197$	−0.0405888	−	0.0569990i	−0.00289183	−	0.00406101i	−0.816019	+	0.578025i	$0.803824\pi$
$198$		0			0
$199$	−7.73311	−	3.98670i	−0.548186	−	0.282609i	0.161802	−	0.986823i	$-0.448269\pi$
$199$	−7.73311	−	3.98670i	−0.548186	−	0.282609i	−0.709988	+	0.704214i	$0.751300\pi$
$200$	−1.62472			−0.114885
$201$		0			0
$202$	−3.80532			−0.267741
$203$	−8.29161	−	4.27462i	−0.581957	−	0.300020i
$204$		0			0
$205$	−8.02884	−	11.2749i	−0.560758	−	0.787475i
$206$	3.46383	+	3.99748i	0.241337	+	0.278517i
$207$		0			0
$208$	0.651008	+	13.6663i	0.0451393	+	0.947590i
$209$	−1.04776	−	7.28731i	−0.0724749	−	0.504074i
$210$		0			0
$211$	1.70993	+	7.04843i	0.117716	+	0.485234i	0.999897	+	0.0143232i	$0.00455937\pi$
$211$	1.70993	+	7.04843i	0.117716	+	0.485234i	−0.882181	+	0.470910i	$0.843925\pi$
$212$	1.03029	−	0.198572i	0.0707605	−	0.0136380i
$213$		0			0
$214$	−30.7126	+	12.2955i	−2.09947	+	0.840501i
$215$	−0.409330	+	0.896308i	−0.0279161	+	0.0611277i
$216$		0			0
$217$	−0.357801	+	1.03380i	−0.0242891	+	0.0701789i
$218$	−2.76003	+	3.87591i	−0.186933	+	0.262510i
$219$		0			0
$220$	0.560922	−	11.7752i	0.0378173	−	0.793883i
$221$	−3.65256	+	15.0560i	−0.245698	+	1.01278i
$222$		0			0
$223$	−24.4994	−	7.19366i	−1.64060	−	0.481723i	−0.674152	−	0.738592i	$-0.735491\pi$
$223$	−24.4994	−	7.19366i	−1.64060	−	0.481723i	−0.966446	+	0.256869i	$0.917309\pi$
$224$	6.06308	+	5.78114i	0.405107	+	0.386268i
$225$		0			0
$226$	−4.59115	+	31.9321i	−0.305398	+	2.12409i
$227$	−12.0016	−	1.14601i	−0.796573	−	0.0760635i	−0.311171	−	0.950354i	$-0.600721\pi$
$227$	−12.0016	−	1.14601i	−0.796573	−	0.0760635i	−0.485403	+	0.874291i	$0.661327\pi$
$228$		0			0
$229$	22.4631	−	17.6652i	1.48440	−	1.16735i	0.538619	−	0.842550i	$-0.318946\pi$
$229$	22.4631	−	17.6652i	1.48440	−	1.16735i	0.945784	−	0.324797i	$-0.105296\pi$
$230$	−6.95807	+	12.0517i	−0.458802	+	0.794668i
$231$		0			0
$232$	−4.18292	−	1.67459i	−0.274622	−	0.109942i
$233$	5.42868	−	5.17623i	0.355644	−	0.339106i	−0.491103	−	0.871102i	$-0.663406\pi$
$233$	5.42868	−	5.17623i	0.355644	−	0.339106i	0.846747	+	0.531995i	$0.178558\pi$
$234$		0			0
$235$	0.632631	−	0.326144i	0.0412683	−	0.0212753i
$236$	−21.0751	+	20.0950i	−1.37187	+	1.30807i
$237$		0			0
$238$	4.16070	+	7.20654i	0.269698	+	0.467131i
$239$	−4.84829	+	8.39748i	−0.313610	+	0.543188i	−0.979141	−	0.203182i	$-0.934872\pi$
$239$	−4.84829	+	8.39748i	−0.313610	+	0.543188i	0.665531	+	0.746370i	$0.268205\pi$
$240$		0			0
$241$	2.75134	−	3.17521i	0.177229	−	0.204534i	−0.660184	−	0.751104i	$-0.729522\pi$
$241$	2.75134	−	3.17521i	0.177229	−	0.204534i	0.837413	+	0.546571i	$0.184067\pi$
$242$	−10.0159	−	0.956404i	−0.643847	−	0.0614799i
$243$		0			0
$244$	−6.08511	−	13.3245i	−0.389559	−	0.853016i
$245$	5.66666	+	5.40315i	0.362030	+	0.345195i
$246$		0			0
$247$	−2.39082	−	6.90781i	−0.152124	−	0.439533i
$248$	−0.124570	+	0.513485i	−0.00791021	+	0.0326063i
$249$		0			0
$250$	−22.3409	+	2.13329i	−1.41296	+	0.134921i
$251$	2.36562	−	3.32205i	0.149317	−	0.209686i	−0.733142	−	0.680075i	$-0.761947\pi$
$251$	2.36562	−	3.32205i	0.149317	−	0.209686i	0.882459	+	0.470389i	$0.155886\pi$
$252$		0			0
$253$	17.1723	+	11.0360i	1.07961	+	0.693824i
$254$	8.00441	−	17.5272i	0.502241	−	1.09975i
$255$		0			0
$256$	−9.00567	−	7.08214i	−0.562855	−	0.442634i
$257$	−5.98400	+	1.15332i	−0.373272	+	0.0719422i	−0.372437	−	0.928057i	$-0.621478\pi$
$257$	−5.98400	+	1.15332i	−0.373272	+	0.0719422i	−0.000834648		1.00000i	$0.500266\pi$
$258$		0			0
$259$	−7.65119	+	4.91712i	−0.475422	+	0.305535i
$260$	−1.66574	−	11.5855i	−0.103305	−	0.718502i
$261$		0			0
$262$	23.4864	+	4.52663i	1.45099	+	0.279656i
$263$	9.17320	+	10.5864i	0.565644	+	0.652788i	0.964456	−	0.264245i	$-0.0851228\pi$
$263$	9.17320	+	10.5864i	0.565644	+	0.652788i	−0.398812	+	0.917033i	$0.630577\pi$
$264$		0			0
$265$	0.592394	−	0.173943i	0.0363905	−	0.0106852i
$266$	−3.48977	−	1.79910i	−0.213972	−	0.110310i
$267$		0			0
$268$	−4.39240	−	17.8182i	−0.268309	−	1.08842i
$269$	−20.7654			−1.26609			−0.633045	−	0.774115i	$-0.718195\pi$
$269$	−20.7654			−1.26609			−0.633045	+	0.774115i	$0.718195\pi$
$270$		0			0
$271$	2.66373	−	0.782142i	0.161810	−	0.0475117i	−0.199824	−	0.979832i	$-0.564037\pi$
$271$	2.66373	−	0.782142i	0.161810	−	0.0475117i	0.361634	+	0.932320i	$0.382219\pi$
$272$	−7.85160	−	11.0260i	−0.476073	−	0.668551i
$273$		0			0
$274$	1.78986	+	0.344968i	0.108130	+	0.0208403i
$275$	0.618156	+	12.9767i	0.0372762	+	0.782524i
$276$		0			0
$277$	−10.3017	+	6.62049i	−0.618968	+	0.397787i	−0.812211	−	0.583364i	$-0.801736\pi$
$277$	−10.3017	+	6.62049i	−0.618968	+	0.397787i	0.193242	+	0.981151i	$0.438100\pi$
$278$	−9.15389	−	37.7329i	−0.549014	−	2.26307i
$279$		0			0
$280$	−0.533422	−	0.419487i	−0.0318780	−	0.0250692i
$281$	−8.24434	+	3.30054i	−0.491816	+	0.196894i	−0.604295	−	0.796761i	$-0.706545\pi$
$281$	−8.24434	+	3.30054i	−0.491816	+	0.196894i	0.112479	+	0.993654i	$0.464121\pi$
$282$		0			0
$283$	11.0205	+	7.08247i	0.655103	+	0.421009i	0.825528	−	0.564362i	$-0.190878\pi$
$283$	11.0205	+	7.08247i	0.655103	+	0.421009i	−0.170425	+	0.985371i	$0.554514\pi$
$284$	4.72100	−	13.6404i	0.280140	−	0.809411i
$285$		0			0
$286$	−32.3372	+	3.08783i	−1.91214	+	0.182587i
$287$	−0.515194	+	10.8153i	−0.0304109	+	0.638404i
$288$		0			0
$289$	0.547015	+	1.58050i	0.0321774	+	0.0929704i
$290$	−23.5667	−	6.91980i	−1.38388	−	0.406344i
$291$		0			0
$292$	−13.4898	−	29.5385i	−0.789430	−	1.72861i
$293$	−1.07136	+	7.45149i	−0.0625897	+	0.435321i	0.934298	+	0.356492i	$0.116027\pi$
$293$	−1.07136	+	7.45149i	−0.0625897	+	0.435321i	−0.996888	+	0.0788291i	$0.974882\pi$
$294$		0			0
$295$	−11.2209	+	12.9497i	−0.653308	+	0.753958i
$296$	−3.45299	+	2.71546i	−0.200701	+	0.157833i
$297$		0			0
$298$	−21.5583	−	37.3401i	−1.24884	−	2.16306i
$299$	18.8156	+	7.53264i	1.08814	+	0.435624i
$300$		0			0
$301$	0.685109	−	0.353198i	0.0394890	−	0.0203580i
$302$	1.10065	−	0.567423i	0.0633351	−	0.0326515i
$303$		0			0
$304$	5.92908	+	2.37364i	0.340056	+	0.136138i
$305$	−4.30970	−	7.46462i	−0.246773	−	0.427423i
$306$		0			0
$307$	−6.59067	+	5.18296i	−0.376149	+	0.295807i	−0.788279	−	0.615318i	$-0.789028\pi$
$307$	−6.59067	+	5.18296i	−0.376149	+	0.295807i	0.412129	+	0.911125i	$0.364785\pi$
$308$	−6.03888	+	6.96923i	−0.344097	+	0.397109i
$309$		0			0
$310$	−0.409914	+	2.85102i	−0.0232816	+	0.161927i
$311$	−12.4260	−	27.2092i	−0.704614	−	1.54289i	−0.834285	−	0.551333i	$-0.814119\pi$
$311$	−12.4260	−	27.2092i	−0.704614	−	1.54289i	0.129671	−	0.991557i	$-0.458608\pi$
$312$		0			0
$313$	13.2501	+	3.89059i	0.748942	+	0.219909i	0.633861	−	0.773447i	$-0.281469\pi$
$313$	13.2501	+	3.89059i	0.748942	+	0.219909i	0.115081	+	0.993356i	$0.463287\pi$
$314$	−1.44714	−	4.18124i	−0.0816669	−	0.235961i
$315$		0			0
$316$	−0.738640	+	15.5060i	−0.0415517	+	0.872278i
$317$	19.7342	−	1.88439i	1.10838	−	0.105838i	0.475227	−	0.879863i	$-0.342366\pi$
$317$	19.7342	−	1.88439i	1.10838	−	0.105838i	0.633154	+	0.774026i	$0.281760\pi$
$318$		0			0
$319$	−11.7835	+	34.0463i	−0.659752	+	1.90623i
$320$	10.8816	+	6.99316i	0.608298	+	0.390929i
$321$		0			0
$322$	10.1062	−	4.04590i	0.563194	−	0.225469i
$323$	5.68464	+	4.47045i	0.316302	+	0.248743i
$324$		0			0
$325$	3.04104	+	12.5353i	0.168686	+	0.695335i
$326$	−38.4749	+	24.7263i	−2.13093	+	1.36946i
$327$		0			0
$328$	0.248836	+	5.22370i	0.0137397	+	0.288431i
$329$	−0.546709	−	0.105369i	−0.0301410	−	0.00580921i
$330$		0			0
$331$	18.3244	+	25.7331i	1.00720	+	1.41442i	0.907816	+	0.419368i	$0.137748\pi$
$331$	18.3244	+	25.7331i	1.00720	+	1.41442i	0.0993851	+	0.995049i	$0.468312\pi$
$332$	−10.4850	+	3.07868i	−0.575440	+	0.168965i
$333$		0			0
$334$	12.8750			0.704488
$335$	−3.56952	−	10.1915i	−0.195024	−	0.556822i
$336$		0			0
$337$	−8.90260	−	4.58961i	−0.484956	−	0.250012i	0.198368	−	0.980128i	$-0.436436\pi$
$337$	−8.90260	−	4.58961i	−0.484956	−	0.250012i	−0.683324	+	0.730116i	$0.739466\pi$
$338$	−5.25622	+	1.54336i	−0.285900	+	0.0839480i
$339$		0			0
$340$	7.58315	+	8.75142i	0.411254	+	0.474613i
$341$	4.14863	+	0.799583i	0.224661	+	0.0432998i
$342$		0			0
$343$	−1.89973	−	13.2129i	−0.102576	−	0.713429i
$344$	0.313189	−	0.201275i	0.0168860	−	0.0108520i
$345$		0			0
$346$	−12.8358	+	2.47390i	−0.690059	+	0.132998i
$347$	−24.5117	−	19.2762i	−1.31585	−	1.03480i	−0.996185	−	0.0872704i	$-0.972186\pi$
$347$	−24.5117	−	19.2762i	−1.31585	−	1.03480i	−0.319670	−	0.947529i	$-0.603572\pi$
$348$		0			0
$349$	−10.4247	+	22.8268i	−0.558019	+	1.22189i	0.394916	+	0.918717i	$0.370774\pi$
$349$	−10.4247	+	22.8268i	−0.558019	+	1.22189i	−0.952935	+	0.303175i	$0.901953\pi$
$350$	5.82838	+	3.74568i	0.311540	+	0.200215i
$351$		0			0
$352$	18.7675	−	26.3552i	1.00031	−	1.40474i
$353$	−6.21452	+	0.593414i	−0.330765	+	0.0315843i	−0.259118	−	0.965846i	$-0.583432\pi$
$353$	−6.21452	+	0.593414i	−0.330765	+	0.0315843i	−0.0716476	+	0.997430i	$0.522826\pi$
$354$		0			0
$355$	2.00242	−	8.25408i	0.106277	−	0.438081i
$356$	−5.59633	−	16.1695i	−0.296605	−	0.856984i
$357$		0			0
$358$	−16.1051	−	15.3562i	−0.851183	−	0.811601i
$359$	6.43293	+	14.0862i	0.339517	+	0.743439i	0.999972	−	0.00742662i	$-0.00236399\pi$
$359$	6.43293	+	14.0862i	0.339517	+	0.743439i	−0.660455	+	0.750865i	$0.729637\pi$
$360$		0			0
$361$	15.5172	+	1.48172i	0.816697	+	0.0779851i
$362$	10.9993	−	12.6939i	0.578111	−	0.667176i
$363$		0			0
$364$	−4.57799	+	7.92931i	−0.239952	+	0.415609i
$365$	−9.55396	−	16.5479i	−0.500077	−	0.866159i
$366$		0			0
$367$	26.2108	−	24.9920i	1.36819	−	1.30457i	0.458857	−	0.888510i	$-0.348259\pi$
$367$	26.2108	−	24.9920i	1.36819	−	1.30457i	0.909337	−	0.416061i	$-0.136590\pi$
$368$	−15.7390	+	8.11404i	−0.820455	+	0.422974i
$369$		0			0
$370$	−17.3309	+	16.5249i	−0.900988	+	0.859091i
$371$	−0.448370	−	0.179500i	−0.0232782	−	0.00931918i
$372$		0			0
$373$	7.37087	−	12.7667i	0.381649	−	0.661035i	−0.609649	−	0.792671i	$-0.708690\pi$
$373$	7.37087	−	12.7667i	0.381649	−	0.661035i	0.991298	+	0.131636i	$0.0420230\pi$
$374$	25.2621	−	19.8663i	1.30627	−	1.02726i
$375$		0			0
$376$	−0.267699	−	0.0255622i	−0.0138055	−	0.00131827i
$377$	−5.09080	+	35.4073i	−0.262189	+	1.82357i
$378$		0			0
$379$	−23.4082	−	22.3197i	−1.20240	−	1.14648i	−0.985390	−	0.170315i	$-0.945521\pi$
$379$	−23.4082	−	22.3197i	−1.20240	−	1.14648i	−0.217009	−	0.976170i	$-0.569630\pi$
$380$	−5.24230	−	1.53928i	−0.268924	−	0.0789633i
$381$		0			0
$382$	7.96400	−	32.8281i	0.407474	−	1.67963i
$383$	1.37813	−	28.9305i	0.0704190	−	1.47828i	−0.636661	−	0.771144i	$-0.719685\pi$
$383$	1.37813	−	28.9305i	0.0704190	−	1.47828i	0.707080	−	0.707134i	$-0.250012\pi$
$384$		0			0
$385$	−3.14752	+	4.42007i	−0.160412	+	0.225268i
$386$	−10.4104	+	30.0788i	−0.529874	+	1.53097i
$387$		0			0
$388$	−4.26342	+	9.33559i	−0.216442	+	0.473943i
$389$	20.2192	−	8.09456i	1.02516	−	0.410410i	0.202701	−	0.979241i	$-0.435028\pi$
$389$	20.2192	−	8.09456i	1.02516	−	0.410410i	0.822455	+	0.568830i	$0.192604\pi$
$390$		0			0
$391$	−19.6889	+	3.79472i	−0.995711	+	0.191907i
$392$	−0.697438	−	2.87488i	−0.0352259	−	0.145203i
$393$		0			0
$394$	0.0205103	+	0.142652i	0.00103329	+	0.00718671i
$395$	0.434633	+	9.12408i	0.0218688	+	0.459082i
$396$		0			0
$397$	−0.748015	−	0.863255i	−0.0375418	−	0.0433255i	0.736668	−	0.676254i	$-0.236398\pi$
$397$	−0.748015	−	0.863255i	−0.0375418	−	0.0433255i	−0.774210	+	0.632929i	$0.781853\pi$
$398$	10.3942	+	14.5965i	0.521012	+	0.731659i
$399$		0			0
$400$	−10.0169	−	5.16408i	−0.500846	−	0.258204i
$401$	2.38063			0.118883			0.0594416	−	0.998232i	$-0.481068\pi$
$401$	2.38063			0.118883			0.0594416	+	0.998232i	$0.481068\pi$
$402$		0			0
$403$	4.19491			0.208963
$404$	3.68183	+	1.89812i	0.183178	+	0.0944348i
$405$		0			0
$406$	11.1448	+	15.6507i	0.553109	+	0.776733i
$407$	23.0023	+	26.5461i	1.14018	+	1.31584i
$408$		0			0
$409$	0.0359794	+	0.755301i	0.00177907	+	0.0373472i	0.999582	−	0.0289000i	$-0.00920043\pi$
$409$	0.0359794	+	0.755301i	0.00177907	+	0.0373472i	−0.997803	+	0.0662472i	$0.978897\pi$
$410$	4.05712	+	28.2179i	0.200367	+	1.39358i
$411$		0			0
$412$	−1.35746	−	5.59554i	−0.0668774	−	0.275672i
$413$	13.1616	−	2.53668i	0.647638	−	0.124822i
$414$		0			0
$415$	−5.96950	+	2.38983i	−0.293031	+	0.117312i
$416$	13.3449	−	29.2212i	0.654287	−	1.43269i
$417$		0			0
$418$	−4.95946	+	14.3294i	−0.242575	+	0.700875i
$419$	−7.27618	+	10.2180i	−0.355465	+	0.499180i	−0.953128	−	0.302567i	$-0.902156\pi$
$419$	−7.27618	+	10.2180i	−0.355465	+	0.499180i	0.597664	+	0.801747i	$0.296096\pi$
$420$		0			0
$421$	−0.594249	+	12.4748i	−0.0289619	+	0.607986i	0.937004	+	0.349318i	$0.113587\pi$
$421$	−0.594249	+	12.4748i	−0.0289619	+	0.607986i	−0.965966	+	0.258668i	$0.916716\pi$
$422$	3.52179	−	14.5170i	0.171438	−	0.706678i
$423$		0			0
$424$	−0.223820	−	0.0657196i	−0.0108697	−	0.00319163i
$425$	−9.23583	−	8.80634i	−0.448003	−	0.427170i
$426$		0			0
$427$	−0.959564	+	6.67391i	−0.0464366	+	0.322973i
$428$	35.8490	+	3.42316i	1.73283	+	0.165465i
$429$		0			0
$430$	1.59525	−	1.25452i	0.0769299	−	0.0604983i
$431$	−7.91023	+	13.7009i	−0.381022	+	0.659950i	−0.991209	−	0.132308i	$-0.957761\pi$
$431$	−7.91023	+	13.7009i	−0.381022	+	0.659950i	0.610186	+	0.792258i	$0.291095\pi$
$432$		0			0
$433$	−11.8344	−	4.73777i	−0.568724	−	0.227683i	0.0694359	−	0.997586i	$-0.477880\pi$
$433$	−11.8344	−	4.73777i	−0.568724	−	0.227683i	−0.638160	+	0.769904i	$0.720304\pi$
$434$	1.63068	−	1.55485i	0.0782751	−	0.0746352i
$435$		0			0
$436$	4.60379	−	2.37342i	0.220481	−	0.113666i
$437$	6.84699	−	6.52860i	0.327536	−	0.312305i
$438$		0			0
$439$	−6.34178	−	10.9843i	−0.302676	−	0.524251i	0.674065	−	0.738672i	$-0.264547\pi$
$439$	−6.34178	−	10.9843i	−0.302676	−	0.524251i	−0.976741	+	0.214421i	$0.931213\pi$
$440$	−1.31042	+	2.26971i	−0.0624717	+	0.108204i
$441$		0			0
$442$	20.8960	−	24.1153i	0.993922	−	1.14705i
$443$	−15.2095	−	1.45233i	−0.722627	−	0.0690025i	−0.272739	−	0.962088i	$-0.587930\pi$
$443$	−15.2095	−	1.45233i	−0.722627	−	0.0690025i	−0.449887	+	0.893085i	$0.648536\pi$
$444$		0			0
$445$	−4.18252	−	9.15844i	−0.198271	−	0.434152i
$446$	38.0608	+	36.2909i	1.80223	+	1.71842i
$447$		0			0
$448$	−3.30940	−	9.56189i	−0.156355	−	0.451757i
$449$	8.79434	−	36.2508i	0.415031	−	1.71078i	−0.253706	−	0.967281i	$-0.581650\pi$
$449$	8.79434	−	36.2508i	0.415031	−	1.71078i	0.668737	−	0.743499i	$-0.266835\pi$
$450$		0			0
$451$	41.6273	−	3.97493i	1.96016	−	0.187172i
$452$	20.3701	−	28.6058i	0.958128	−	1.34550i
$453$		0			0
$454$	20.8892	+	13.4247i	0.980380	+	0.630052i
$455$	−2.23809	+	4.90073i	−0.104923	+	0.229750i
$456$		0			0
$457$	23.4785	+	18.4637i	1.09828	+	0.863696i	0.991438	−	0.130580i	$-0.0416840\pi$
$457$	23.4785	+	18.4637i	1.09828	+	0.863696i	0.106841	+	0.994276i	$0.465926\pi$
$458$	−57.7941	+	11.1389i	−2.70054	+	0.520486i
$459$		0			0
$460$	12.7438	−	8.18992i	0.594181	−	0.381857i
$461$	0.926999	+	6.44742i	0.0431746	+	0.300286i	0.999955	+	0.00947507i	$0.00301605\pi$
$461$	0.926999	+	6.44742i	0.0431746	+	0.300286i	−0.956780	+	0.290811i	$0.906075\pi$
$462$		0			0
$463$	32.8797	+	6.33703i	1.52805	+	0.294507i	0.882904	−	0.469554i	$-0.155585\pi$
$463$	32.8797	+	6.33703i	1.52805	+	0.294507i	0.645144	+	0.764061i	$0.276797\pi$
$464$	−20.4665	−	23.6196i	−0.950133	−	1.09651i
$465$		0			0
$466$	−14.8232	+	4.35249i	−0.686672	+	0.201625i
$467$	8.27547	+	4.26630i	0.382943	+	0.197421i	0.638940	−	0.769257i	$-0.279373\pi$
$467$	8.27547	+	4.26630i	0.382943	+	0.197421i	−0.255997	+	0.966678i	$0.582404\pi$
$468$		0			0
$469$	−2.73330	+	7.99275i	−0.126212	+	0.369071i
$470$	−1.46594			−0.0676186
$471$		0			0
$472$	6.21170	−	1.82392i	0.285917	−	0.0839528i
$473$	−1.72675	−	2.42488i	−0.0793961	−	0.111496i
$474$		0			0
$475$	5.91230	+	1.13950i	0.271275	+	0.0522839i
$476$	−0.431012	−	9.04806i	−0.0197554	−	0.414717i
$477$		0			0
$478$	16.8008	−	10.7972i	0.768452	−	0.493854i
$479$	3.09896	+	12.7741i	0.141595	+	0.583663i	0.997756	+	0.0669536i	$0.0213279\pi$
$479$	3.09896	+	12.7741i	0.141595	+	0.583663i	−0.856161	+	0.516709i	$0.827157\pi$
$480$		0			0
$481$	27.4140	+	21.5586i	1.24997	+	0.982988i
$482$	−8.03343	+	3.21610i	−0.365913	+	0.146489i
$483$		0			0
$484$	9.21382	+	5.92136i	0.418810	+	0.269153i
$485$	−1.97517	+	5.70688i	−0.0896878	+	0.259136i
$486$		0			0
$487$	−10.4485	+	0.997714i	−0.473468	+	0.0452107i	−0.329063	−	0.944308i	$-0.606733\pi$
$487$	−10.4485	+	0.997714i	−0.473468	+	0.0452107i	−0.144405	+	0.989519i	$0.546127\pi$
$488$	−0.154956	+	3.25292i	−0.00701451	+	0.147253i
$489$		0			0
$490$	−5.27439	−	15.2393i	−0.238273	−	0.688444i
$491$	3.24867	+	0.953895i	0.146610	+	0.0430487i	0.354214	−	0.935164i	$-0.384748\pi$
$491$	3.24867	+	0.953895i	0.146610	+	0.0430487i	−0.207604	+	0.978213i	$0.566567\pi$
$492$		0			0
$493$	−14.7015	−	32.1917i	−0.662121	−	1.44984i
$494$	−2.14261	+	14.9022i	−0.0964008	+	0.670482i
$495$		0			0
$496$	−2.40010	+	2.76987i	−0.107768	+	0.124371i
$497$	−5.22259	+	4.10709i	−0.234265	+	0.184228i
$498$		0			0
$499$	−9.94203	−	17.2201i	−0.445067	−	0.770878i	0.552990	−	0.833188i	$-0.313487\pi$
$499$	−9.94203	−	17.2201i	−0.445067	−	0.770878i	−0.998057	+	0.0623098i	$0.980153\pi$
$500$	22.6800	+	9.07970i	1.01428	+	0.406056i
$501$		0			0
$502$	−7.46590	+	3.84894i	−0.333219	+	0.171787i
$503$	−19.8911	+	10.2546i	−0.886899	+	0.457228i	−0.840573	−	0.541698i	$-0.817782\pi$
$503$	−19.8911	+	10.2546i	−0.886899	+	0.457228i	−0.0463259	+	0.998926i	$0.514751\pi$
$504$		0			0
$505$	2.26284	+	0.905903i	0.100695	+	0.0403121i
$506$	−21.0212	−	36.4097i	−0.934505	−	1.61861i
$507$		0			0
$508$	−16.4873	+	12.9658i	−0.731507	+	0.575264i
$509$	24.3102	−	28.0554i	1.07753	−	1.24354i	0.109158	−	0.994024i	$-0.465185\pi$
$509$	24.3102	−	28.0554i	1.07753	−	1.24354i	0.968372	−	0.249511i	$-0.0802699\pi$
$510$		0			0
$511$	−2.12721	+	14.7951i	−0.0941022	+	0.654495i
$512$	13.0911	+	28.6656i	0.578551	+	1.26685i
$513$		0			0
$514$	12.0431	+	3.53618i	0.531200	+	0.155974i
$515$	−1.10812	−	3.20171i	−0.0488297	−	0.141084i
$516$		0			0
$517$	−0.102315	+	2.14785i	−0.00449980	+	0.0944625i
$518$	18.6473	−	1.78061i	0.819317	−	0.0782353i
$519$		0			0
$520$	−0.851089	+	2.45906i	−0.0373227	+	0.107837i
$521$	36.0401	+	23.1616i	1.57895	+	1.01473i	0.976220	+	0.216781i	$0.0695557\pi$
$521$	36.0401	+	23.1616i	1.57895	+	1.01473i	0.602727	+	0.797947i	$0.294081\pi$
$522$		0			0
$523$	−23.8771	+	9.55895i	−1.04407	+	0.417984i	−0.829372	−	0.558696i	$-0.811302\pi$
$523$	−23.8771	+	9.55895i	−1.04407	+	0.417984i	−0.214701	+	0.976680i	$0.568878\pi$
$524$	−20.4663	−	16.0949i	−0.894074	−	0.703108i
$525$		0			0
$526$	−6.80183	−	28.0375i	−0.296574	−	1.22249i
$527$	−3.49134	+	2.24375i	−0.152085	+	0.0977392i
$528$		0			0
$529$	0.153727	+	3.22712i	0.00668378	+	0.140310i
$530$	−1.24863	−	0.240654i	−0.0542372	−	0.0104534i
$531$		0			0
$532$	2.47912	+	3.48144i	0.107484	+	0.150940i
$533$	39.8372	−	11.6973i	1.72554	−	0.506665i
$534$		0			0
$535$	21.1904			0.916139
$536$	−0.947232	+	3.96846i	−0.0409142	+	0.171411i
$537$		0			0
$538$	38.0144	+	19.5978i	1.63892	+	0.844920i
$539$	−22.6964	+	6.66428i	−0.977605	+	0.287051i
$540$		0			0
$541$	−14.4578	−	16.6852i	−0.621589	−	0.717351i	0.354419	−	0.935087i	$-0.384679\pi$
$541$	−14.4578	−	16.6852i	−0.621589	−	0.717351i	−0.976008	+	0.217735i	$0.930133\pi$
$542$	−5.61454	−	1.08211i	−0.241165	−	0.0464808i
$543$		0			0
$544$	4.52299	+	31.4581i	0.193922	+	1.34876i
$545$	2.56396	−	1.64776i	0.109828	−	0.0705822i
$546$		0			0
$547$	8.84274	−	1.70430i	0.378088	−	0.0728705i	0.00333329	−	0.999994i	$-0.498939\pi$
$547$	8.84274	−	1.70430i	0.378088	−	0.0728705i	0.374755	+	0.927124i	$0.377727\pi$
$548$	−1.55971	−	1.22657i	−0.0666275	−	0.0523964i
$549$		0			0
$550$	11.1154	−	24.3393i	0.473961	−	1.03783i
$551$	14.0470	+	9.02749i	0.598424	+	0.384584i
$552$		0			0
$553$	4.14475	−	5.82049i	0.176253	−	0.247512i
$554$	25.1071	−	2.39743i	1.06670	−	0.101857i
$555$		0			0
$556$	−9.96454	+	41.0744i	−0.422591	+	1.74194i
$557$	−7.43353	−	21.4778i	−0.314969	−	0.910043i	−0.985725	−	0.168365i	$-0.946151\pi$
$557$	−7.43353	−	21.4778i	−0.314969	−	0.910043i	0.670756	−	0.741678i	$-0.265970\pi$
$558$		0			0
$559$	−2.13912	−	2.03965i	−0.0904752	−	0.0862680i
$560$	−1.95540	−	4.28173i	−0.0826308	−	0.180936i
$561$		0			0
$562$	18.2075	+	1.73861i	0.768038	+	0.0733387i
$563$	−23.8707	+	27.5482i	−1.00603	+	1.16102i	−0.0191077	+	0.999817i	$0.506083\pi$
$563$	−23.8707	+	27.5482i	−1.00603	+	1.16102i	−0.986921	+	0.161202i	$0.948463\pi$
$564$		0			0
$565$	10.3320	−	17.8955i	0.434669	−	0.752869i
$566$	−13.4906	−	23.3664i	−0.567053	−	0.982164i
$567$		0			0
$568$	−2.32249	+	2.21449i	−0.0974497	+	0.0929181i
$569$	23.2079	−	11.9645i	0.972926	−	0.501578i	0.102957	−	0.994686i	$-0.467169\pi$
$569$	23.2079	−	11.9645i	0.972926	−	0.501578i	0.869968	+	0.493108i	$0.164139\pi$
$570$		0			0
$571$	−12.0867	+	11.5246i	−0.505811	+	0.482290i	−0.899480	−	0.436963i	$-0.856054\pi$
$571$	−12.0867	+	11.5246i	−0.505811	+	0.482290i	0.393669	+	0.919252i	$0.371206\pi$
$572$	32.8281	+	13.1424i	1.37261	+	0.549511i
$573$		0			0
$574$	11.1503	−	19.3128i	0.465403	−	0.806101i
$575$	−13.1226	+	10.3197i	−0.547248	+	0.430361i
$576$		0			0
$577$	−30.7945	−	2.94052i	−1.28199	−	0.122415i	−0.568268	−	0.822844i	$-0.692386\pi$
$577$	−30.7945	−	2.94052i	−1.28199	−	0.122415i	−0.713723	+	0.700428i	$0.752992\pi$
$578$	0.490227	−	3.40961i	0.0203908	−	0.141821i
$579$		0			0
$580$	19.3503	+	18.4504i	0.803476	+	0.766113i
$581$	4.82621	+	1.41710i	0.200225	+	0.0587914i
$582$		0			0
$583$	−0.439749	+	1.81267i	−0.0182125	+	0.0750731i
$584$	−0.343514	+	7.21124i	−0.0142147	+	0.298403i
$585$		0			0
$586$	8.99379	−	12.6300i	0.371530	−	0.521741i
$587$	3.60090	−	10.4041i	0.148625	−	0.429424i	−0.845973	−	0.533226i	$-0.820980\pi$
$587$	3.60090	−	10.4041i	0.148625	−	0.429424i	0.994598	+	0.103802i	$0.0331007\pi$
$588$		0			0
$589$	0.813443	−	1.78119i	0.0335173	−	0.0733927i
$590$	32.7632	−	13.1164i	1.34884	−	0.539994i
$591$		0			0
$592$	−29.9198	+	5.76657i	−1.22970	+	0.237005i
$593$	2.09895	+	8.65201i	0.0861937	+	0.355295i	0.998533	−	0.0541387i	$-0.0172413\pi$
$593$	2.09895	+	8.65201i	0.0861937	+	0.355295i	−0.912340	+	0.409434i	$0.865726\pi$
$594$		0			0
$595$	−0.758557	−	5.27588i	−0.0310978	−	0.216290i
$596$	2.23326	+	46.8818i	0.0914778	+	1.92035i
$597$		0			0
$598$	−27.3359	−	31.5473i	−1.11785	−	1.29006i
$599$	9.41243	+	13.2179i	0.384581	+	0.540069i	0.960806	−	0.277223i	$-0.0894139\pi$
$599$	9.41243	+	13.2179i	0.384581	+	0.540069i	−0.576224	+	0.817292i	$0.695475\pi$
$600$		0			0
$601$	−24.8735	−	12.8232i	−1.01461	−	0.523069i	−0.131046	−	0.991376i	$-0.541834\pi$
$601$	−24.8735	−	12.8232i	−1.01461	−	0.523069i	−0.883566	+	0.468307i	$0.844864\pi$
$602$	−1.58754			−0.0647032
$603$		0			0
$604$	−1.34796			−0.0548479
$605$	5.72829	+	2.95314i	0.232888	+	0.120062i
$606$		0			0
$607$	21.1469	+	29.6967i	0.858327	+	1.20535i	0.977174	+	0.212439i	$0.0681406\pi$
$607$	21.1469	+	29.6967i	0.858327	+	1.20535i	−0.118848	+	0.992912i	$0.537920\pi$
$608$	−9.81983	−	11.3327i	−0.398247	−	0.459601i
$609$		0			0
$610$	0.844704	+	17.7325i	0.0342011	+	0.717969i
$611$	0.303840	+	2.11325i	0.0122920	+	0.0854930i
$612$		0			0
$613$	1.18523	+	4.88557i	0.0478709	+	0.197327i	0.990726	−	0.135878i	$-0.0433854\pi$
$613$	1.18523	+	4.88557i	0.0478709	+	0.197327i	−0.942855	+	0.333204i	$0.891870\pi$
$614$	16.9568	−	3.26815i	0.684320	−	0.131892i
$615$		0			0
$616$	1.90330	−	0.761965i	0.0766860	−	0.0307004i
$617$	−2.08724	+	4.57042i	−0.0840291	+	0.183998i	−0.946982	−	0.321286i	$-0.895885\pi$
$617$	−2.08724	+	4.57042i	−0.0840291	+	0.183998i	0.862953	+	0.505284i	$0.168612\pi$
$618$		0			0
$619$	9.15824	−	26.4610i	0.368101	−	1.06356i	−0.597127	−	0.802147i	$-0.703691\pi$
$619$	9.15824	−	26.4610i	0.368101	−	1.06356i	0.965228	−	0.261411i	$-0.0841876\pi$
$620$	1.81872	−	2.55403i	0.0730414	−	0.102572i
$621$		0			0
$622$	−2.93141	+	61.5379i	−0.117539	+	2.46745i
$623$	−1.85683	+	7.65394i	−0.0743921	+	0.306649i
$624$		0			0
$625$	−1.84482	−	0.541688i	−0.0737927	−	0.0216675i
$626$	−20.5847	−	19.6274i	−0.822728	−	0.784470i
$627$		0			0
$628$	−0.685448	+	4.76739i	−0.0273523	+	0.190240i
$629$	−34.3473	−	3.27977i	−1.36952	−	0.130773i
$630$		0			0
$631$	7.02531	−	5.52477i	0.279673	−	0.219937i	−0.468462	−	0.883484i	$-0.655192\pi$
$631$	7.02531	−	5.52477i	0.279673	−	0.219937i	0.748135	+	0.663546i	$0.230949\pi$
$632$	1.72560	−	2.98883i	0.0686406	−	0.118889i
$633$		0			0
$634$	−37.9049	−	15.1748i	−1.50540	−	0.602670i
$635$	−8.93240	+	8.51702i	−0.354471	+	0.337988i
$636$		0			0
$637$	−20.8754	+	10.7620i	−0.827114	+	0.426407i
$638$	53.7035	−	51.2062i	2.12614	−	2.02727i
$639$		0			0
$640$	−2.61104	−	4.52245i	−0.103210	−	0.178765i
$641$	−4.94729	+	8.56896i	−0.195406	+	0.338454i	−0.947034	−	0.321134i	$-0.895936\pi$
$641$	−4.94729	+	8.56896i	−0.195406	+	0.338454i	0.751627	+	0.659588i	$0.229269\pi$
$642$		0			0
$643$	−3.64677	+	4.20860i	−0.143815	+	0.165971i	−0.823087	−	0.567915i	$-0.807750\pi$
$643$	−3.64677	+	4.20860i	−0.143815	+	0.165971i	0.679272	+	0.733886i	$0.262296\pi$
$644$	−11.7963	−	1.12641i	−0.464840	−	0.0443868i
$645$		0			0
$646$	−6.18756	−	13.5489i	−0.243446	−	0.533073i
$647$	5.65110	+	5.38831i	0.222168	+	0.211837i	0.792986	−	0.609240i	$-0.208525\pi$
$647$	5.65110	+	5.38831i	0.222168	+	0.211837i	−0.570818	+	0.821077i	$0.693374\pi$
$648$		0			0
$649$	−16.9311	−	48.9193i	−0.664605	−	1.92025i
$650$	6.26336	−	25.8179i	0.245669	−	1.01266i
$651$		0			0
$652$	49.5600	−	4.73240i	1.94092	−	0.185335i
$653$	−8.66565	+	12.1692i	−0.339113	+	0.476217i	−0.948555	−	0.316613i	$-0.897454\pi$
$653$	−8.66565	+	12.1692i	−0.339113	+	0.476217i	0.609442	+	0.792831i	$0.291394\pi$
$654$		0			0
$655$	−12.8886	−	8.28298i	−0.503598	−	0.323643i
$656$	−15.0691	+	32.9968i	−0.588350	+	1.28831i
$657$		0			0
$658$	0.901392	+	0.708863i	0.0351399	+	0.0276343i
$659$	−2.43061	+	0.468463i	−0.0946833	+	0.0182487i	−0.236373	−	0.971662i	$-0.575959\pi$
$659$	−2.43061	+	0.468463i	−0.0946833	+	0.0182487i	0.141690	+	0.989911i	$0.454747\pi$
$660$		0			0
$661$	−29.7394	+	19.1124i	−1.15673	+	0.743385i	−0.970968	−	0.239209i	$-0.923112\pi$
$661$	−29.7394	+	19.1124i	−1.15673	+	0.743385i	−0.185762	+	0.982595i	$0.559475\pi$
$662$	−9.25967	−	64.4025i	−0.359887	−	2.50307i
$663$		0			0
$664$	2.38554	+	0.459775i	0.0925769	+	0.0178427i
$665$	1.64690	+	1.90062i	0.0638640	+	0.0737029i
$666$		0			0
$667$	−44.4212	+	13.0432i	−1.72000	+	0.505036i
$668$	−12.4572	−	6.42212i	−0.481983	−	0.248479i
$669$		0			0
$670$	−3.08387	+	22.0260i	−0.119140	+	0.850938i
$671$	26.0402			1.00527
$672$		0			0
$673$	6.54768	−	1.92257i	0.252394	−	0.0741097i	−0.153088	−	0.988213i	$-0.548922\pi$
$673$	6.54768	−	1.92257i	0.252394	−	0.0741097i	0.405482	+	0.914103i	$0.367104\pi$
$674$	11.9661	+	16.8040i	0.460916	+	0.647266i
$675$		0			0
$676$	5.85548	+	1.12855i	0.225211	+	0.0434059i
$677$	0.134202	+	2.81724i	0.00515780	+	0.108276i	0.999978	+	0.00662578i	$0.00210907\pi$
$677$	0.134202	+	2.81724i	0.00515780	+	0.108276i	−0.994820	+	0.101650i	$0.967588\pi$
$678$		0			0
$679$	3.97411	−	2.55401i	0.152512	−	0.0980138i
$680$	−0.606943	−	2.50185i	−0.0232752	−	0.0959418i
$681$		0			0
$682$	−6.84010	−	5.37911i	−0.261921	−	0.205977i
$683$	−14.2250	+	5.69484i	−0.544306	+	0.217907i	−0.627487	−	0.778627i	$-0.715916\pi$
$683$	−14.2250	+	5.69484i	−0.544306	+	0.217907i	0.0831810	+	0.996534i	$0.473492\pi$
$684$		0			0
$685$	−0.982221	−	0.631235i	−0.0375287	−	0.0241182i
$686$	−8.99218	+	25.9812i	−0.343323	+	0.991966i
$687$		0			0
$688$	2.57066	−	0.245468i	0.0980054	−	0.00935838i
$689$	−0.0881203	+	1.84987i	−0.00335712	+	0.0704746i
$690$		0			0
$691$	−6.05959	−	17.5080i	−0.230518	−	0.666037i	−0.999637	−	0.0269319i	$-0.991426\pi$
$691$	−6.05959	−	17.5080i	−0.230518	−	0.666037i	0.769120	−	0.639105i	$-0.220695\pi$
$692$	13.6533	+	4.00897i	0.519020	+	0.152398i
$693$		0			0
$694$	26.6802	+	58.4214i	1.01277	+	2.21765i
$695$	−3.53940	+	24.6171i	−0.134257	+	0.933779i
$696$		0			0
$697$	−26.8992	+	31.0433i	−1.01888	+	1.17585i
$698$	40.6272	−	31.9496i	1.53776	−	1.20931i
$699$		0			0
$700$	−3.77088	−	6.53136i	−0.142526	−	0.246862i
$701$	−23.1530	−	9.26905i	−0.874475	−	0.350087i	−0.109377	−	0.994000i	$-0.534885\pi$
$701$	−23.1530	−	9.26905i	−0.874475	−	0.350087i	−0.765098	+	0.643913i	$0.777310\pi$
$702$		0			0
$703$	14.4699	−	7.45973i	0.545741	−	0.281349i
$704$	−34.7339	+	17.9066i	−1.30908	+	0.674879i
$705$		0			0
$706$	11.9367	+	4.77873i	0.449244	+	0.179850i
$707$	−0.953344	−	1.65124i	−0.0358542	−	0.0621013i
$708$		0			0
$709$	19.2729	−	15.1563i	0.723807	−	0.569208i	−0.186841	−	0.982390i	$-0.559825\pi$
$709$	19.2729	−	15.1563i	0.723807	−	0.569208i	0.910649	+	0.413182i	$0.135583\pi$
$710$	−11.4557	+	13.2206i	−0.429925	+	0.496159i
$711$		0			0
$712$	−0.541371	+	3.76532i	−0.0202887	+	0.141111i
$713$	2.25537	+	4.93856i	0.0844642	+	0.184951i
$714$		0			0
$715$	19.9645	+	5.86210i	0.746629	+	0.219230i
$716$	7.92273	+	22.8912i	0.296086	+	0.855485i
$717$		0			0
$718$	1.51759	−	31.8581i	0.0566359	−	1.18893i
$719$	−7.16898	+	0.684554i	−0.267358	+	0.0255296i	−0.227874	−	0.973691i	$-0.573177\pi$
$719$	−7.16898	+	0.684554i	−0.267358	+	0.0255296i	−0.0394838	+	0.999220i	$0.512571\pi$
$720$		0			0
$721$	−0.866832	+	2.50455i	−0.0322825	+	0.0932742i
$722$	−27.0084	−	17.3572i	−1.00515	−	0.645969i
$723$		0			0
$724$	−16.9742	+	6.79543i	−0.630840	+	0.252550i
$725$	−23.1609	−	18.2139i	−0.860175	−	0.676449i
$726$		0			0
$727$	−8.72886	−	35.9809i	−0.323736	−	1.33446i	−0.868426	−	0.495819i	$-0.834868\pi$
$727$	−8.72886	−	35.9809i	−0.323736	−	1.33446i	0.544690	−	0.838637i	$-0.316647\pi$
$728$	1.71242	−	1.10051i	0.0634666	−	0.0407875i
$729$		0			0
$730$	1.87258	+	39.3103i	0.0693074	+	1.45494i
$731$	2.87131	+	0.553399i	0.106199	+	0.0204682i
$732$		0			0
$733$	−1.80318	−	2.53221i	−0.0666019	−	0.0935293i	0.779932	−	0.625865i	$-0.215254\pi$
$733$	−1.80318	−	2.53221i	−0.0666019	−	0.0935293i	−0.846533	+	0.532336i	$0.821314\pi$
$734$	−71.5697	+	21.0148i	−2.64169	+	0.775669i
$735$		0			0
$736$	41.5763			1.53252
$737$	32.0567	+	6.05571i	1.18082	+	0.223065i
$738$		0			0
$739$	2.79002	+	1.43835i	0.102632	+	0.0529107i	0.508778	−	0.860898i	$-0.330097\pi$
$739$	2.79002	+	1.43835i	0.102632	+	0.0529107i	−0.406146	+	0.913808i	$0.633128\pi$
$740$	25.0112	−	7.34395i	0.919430	−	0.269969i
$741$		0			0
$742$	0.651404	+	0.751761i	0.0239138	+	0.0275980i
$743$	−40.2376	−	7.75517i	−1.47618	−	0.284509i	−0.613269	−	0.789874i	$-0.710146\pi$
$743$	−40.2376	−	7.75517i	−1.47618	−	0.284509i	−0.862906	+	0.505364i	$0.831358\pi$
$744$		0			0
$745$	3.93041	+	27.3366i	0.143999	+	1.00153i
$746$	−25.5424	+	16.4151i	−0.935173	+	0.600999i
$747$		0			0
$748$	−34.3517	+	6.62075i	−1.25602	+	0.242079i
$749$	−13.0298	−	10.2467i	−0.476098	−	0.374407i
$750$		0			0
$751$	−13.7846	+	30.1840i	−0.503006	+	1.10143i	0.472475	+	0.881344i	$0.343361\pi$
$751$	−13.7846	+	30.1840i	−0.503006	+	1.10143i	−0.975481	+	0.220085i	$0.929366\pi$
$752$	−1.56921	−	1.00847i	−0.0572230	−	0.0367750i
$753$		0			0
$754$	42.7358	−	60.0141i	1.55635	−	2.18558i
$755$	−0.789583	+	0.0753960i	−0.0287359	+	0.00274394i
$756$		0			0
$757$	5.64742	−	23.2790i	0.205259	−	0.846089i	−0.772271	−	0.635293i	$-0.780879\pi$
$757$	5.64742	−	23.2790i	0.205259	−	0.846089i	0.977530	−	0.210796i	$-0.0676055\pi$
$758$	21.7878	+	62.9516i	0.791367	+	2.28651i
$759$		0			0
$760$	0.879100	+	0.838221i	0.0318883	+	0.0304055i
$761$	−0.440125	−	0.963739i	−0.0159545	−	0.0349355i	0.901487	−	0.432806i	$-0.142477\pi$
$761$	−0.440125	−	0.963739i	−0.0159545	−	0.0349355i	−0.917442	+	0.397871i	$0.869749\pi$
$762$		0			0
$763$	−2.37334	−	0.226627i	−0.0859207	−	0.00820444i
$764$	−24.0804	+	27.7903i	−0.871198	+	1.00542i
$765$		0			0
$766$	−29.8266	+	51.6611i	−1.07768	+	1.86659i
$767$	−25.6989	−	44.5119i	−0.927935	−	1.60723i
$768$		0			0
$769$	−24.2506	+	23.1229i	−0.874500	+	0.833834i	−0.987149	−	0.159801i	$-0.948915\pi$
$769$	−24.2506	+	23.1229i	−0.874500	+	0.833834i	0.112649	+	0.993635i	$0.464066\pi$
$770$	9.93356	−	5.12110i	0.357981	−	0.184552i
$771$		0			0
$772$	25.0760	−	23.9099i	0.902506	−	0.860538i
$773$	−6.10074	−	2.44237i	−0.219428	−	0.0878459i	0.259344	−	0.965785i	$-0.416494\pi$
$773$	−6.10074	−	2.44237i	−0.219428	−	0.0878459i	−0.478772	+	0.877939i	$0.658918\pi$
$774$		0			0
$775$	−1.72767	+	2.99241i	−0.0620597	+	0.107491i
$776$	1.79352	−	1.41044i	0.0643837	−	0.0506319i
$777$		0			0
$778$	−44.6539	−	4.26393i	−1.60092	−	0.152869i
$779$	2.75816	−	19.1834i	0.0988214	−	0.687318i
$780$		0			0
$781$	18.5709	+	17.7073i	0.664520	+	0.633618i
$782$	39.6250	+	11.6349i	1.41699	+	0.416065i
$783$		0			0
$784$	4.83772	−	19.9413i	0.172776	−	0.712191i
$785$	−0.134852	+	2.83089i	−0.00481307	+	0.101039i
$786$		0			0
$787$	−11.6421	+	16.3490i	−0.414996	+	0.582780i	−0.968173	−	0.250284i	$-0.919476\pi$
$787$	−11.6421	+	16.3490i	−0.414996	+	0.582780i	0.553176	+	0.833064i	$0.313416\pi$
$788$	0.0513110	−	0.148253i	0.00182788	−	0.00528131i
$789$		0			0
$790$	7.81536	−	17.1133i	0.278058	−	0.608862i
$791$	−15.0065	+	6.00770i	−0.533570	+	0.213609i
$792$		0			0
$793$	25.3876	−	4.89306i	0.901541	−	0.173758i
$794$	0.554645	+	2.28628i	0.0196836	+	0.0811370i
$795$		0			0
$796$	−2.77601	−	19.3075i	−0.0983929	−	0.684338i
$797$	1.52536	+	32.0211i	0.0540309	+	1.13425i	0.849273	+	0.527955i	$0.177041\pi$
$797$	1.52536	+	32.0211i	0.0540309	+	1.13425i	−0.795242	+	0.606293i	$0.792656\pi$
$798$		0			0
$799$	−1.38320	−	1.59630i	−0.0489343	−	0.0564731i
$800$	15.3487	+	21.5542i	0.542658	+	0.762057i
$801$		0			0
$802$	−4.35813	−	2.24677i	−0.153891	−	0.0793362i
$803$	57.7272			2.03715
$804$		0			0
$805$	−6.97281			−0.245759
$806$	−7.67944	−	3.95902i	−0.270497	−	0.139451i
$807$		0			0
$808$	−0.534186	−	0.750159i	−0.0187926	−	0.0263905i
$809$	−8.53177	−	9.84618i	−0.299961	−	0.346173i	0.585681	−	0.810541i	$-0.300827\pi$
$809$	−8.53177	−	9.84618i	−0.299961	−	0.346173i	−0.885642	+	0.464368i	$0.846282\pi$
$810$		0			0
$811$	0.189740	+	3.98314i	0.00666268	+	0.139867i	0.999748	+	0.0224683i	$0.00715249\pi$
$811$	0.189740	+	3.98314i	0.00666268	+	0.139867i	−0.993085	+	0.117399i	$0.962544\pi$
$812$	−2.97649	−	20.7020i	−0.104454	−	0.726496i
$813$		0			0
$814$	−17.0560	−	70.3057i	−0.597812	−	2.46421i
$815$	28.7655	−	5.54410i	1.00761	−	0.194201i
$816$		0			0
$817$	−1.28085	+	0.512776i	−0.0448114	+	0.0179398i
$818$	0.646964	−	1.41665i	0.0226206	−	0.0495321i
$819$		0			0
$820$	10.1498	−	29.3259i	0.354446	−	1.02411i
$821$	20.1885	−	28.3507i	0.704583	−	0.989448i	−0.294843	−	0.955546i	$-0.595267\pi$
$821$	20.1885	−	28.3507i	0.704583	−	0.989448i	0.999425	−	0.0339020i	$-0.0107934\pi$
$822$		0			0
$823$	0.362271	−	7.60500i	0.0126280	−	0.265094i	−0.983720	−	0.179708i	$-0.942485\pi$
$823$	0.362271	−	7.60500i	0.0126280	−	0.265094i	0.996348	−	0.0853857i	$-0.0272122\pi$
$824$	−0.301791	+	1.24400i	−0.0105134	+	0.0433368i
$825$		0			0
$826$	−26.4883	−	7.77768i	−0.921647	−	0.270620i
$827$	−5.34026	−	5.09193i	−0.185699	−	0.177064i	0.591527	−	0.806285i	$-0.298525\pi$
$827$	−5.34026	−	5.09193i	−0.185699	−	0.177064i	−0.777226	+	0.629222i	$0.783374\pi$
$828$		0			0
$829$	−5.78626	+	40.2443i	−0.200965	+	1.39774i	0.600463	+	0.799653i	$0.294983\pi$
$829$	−5.78626	+	40.2443i	−0.200965	+	1.39774i	−0.801428	+	0.598091i	$0.795926\pi$
$830$	13.1836	+	1.25888i	0.457608	+	0.0436963i
$831$		0			0
$832$	−30.4987	+	23.9845i	−1.05735	+	0.831511i
$833$	11.6179	−	20.1228i	0.402536	−	0.697212i
$834$		0			0
$835$	−7.65612	−	3.06505i	−0.264951	−	0.106070i
$836$	11.9461	−	11.3906i	0.413165	−	0.393952i
$837$		0			0
$838$	22.9636	−	11.8386i	0.793264	−	0.408956i
$839$	1.61375	−	1.53871i	0.0557130	−	0.0531222i	−0.661711	−	0.749759i	$-0.730169\pi$
$839$	1.61375	−	1.53871i	0.0557130	−	0.0531222i	0.717424	+	0.696637i	$0.245321\pi$
$840$		0			0
$841$	−26.3560	−	45.6499i	−0.908827	−	1.57413i
$842$	12.8612	−	22.2763i	0.443227	−	0.767692i
$843$		0			0
$844$	−10.6487	+	12.2892i	−0.366543	+	0.423013i
$845$	3.49303	+	0.333544i	0.120164	+	0.0114743i
$846$		0			0
$847$	−2.09427	−	4.58581i	−0.0719599	−	0.157570i
$848$	−1.17104	−	1.11658i	−0.0402137	−	0.0383437i
$849$		0			0
$850$	8.59648	+	24.8379i	0.294857	+	0.851933i
$851$	−10.6415	+	43.8647i	−0.364785	+	1.50366i
$852$		0			0
$853$	50.8419	−	4.85482i	1.74079	−	0.166226i	0.824268	−	0.566200i	$-0.191587\pi$
$853$	50.8419	−	4.85482i	1.74079	−	0.166226i	0.916526	+	0.399974i	$0.130981\pi$
$854$	8.05527	−	11.3120i	0.275646	−	0.387090i
$855$		0			0
$856$	−6.73525	−	4.32848i	−0.230206	−	0.147945i
$857$	−2.83269	+	6.20273i	−0.0967630	+	0.211881i	−0.951823	−	0.306647i	$-0.900793\pi$
$857$	−2.83269	+	6.20273i	−0.0967630	+	0.211881i	0.855060	+	0.518529i	$0.173520\pi$
$858$		0			0
$859$	−18.0169	−	14.1687i	−0.614730	−	0.483429i	0.261577	−	0.965183i	$-0.415758\pi$
$859$	−18.0169	−	14.1687i	−0.614730	−	0.483429i	−0.876307	+	0.481754i	$0.840000\pi$
$860$	−2.16925	+	0.418088i	−0.0739707	+	0.0142567i
$861$		0			0
$862$	27.4114	−	17.6163i	0.933637	−	0.600012i
$863$	1.30736	+	9.09286i	0.0445029	+	0.309524i	0.999899	+	0.0141977i	$0.00451941\pi$
$863$	1.30736	+	9.09286i	0.0445029	+	0.309524i	−0.955396	+	0.295327i	$0.904571\pi$
$864$		0			0
$865$	8.22178	+	1.58462i	0.279549	+	0.0538787i
$866$	17.1933	+	19.8422i	0.584254	+	0.674265i
$867$		0			0
$868$	−2.35333	+	0.691000i	−0.0798773	+	0.0234541i
$869$	−24.5285	−	12.6453i	−0.832071	−	0.428962i
$870$		0			0
$871$	32.3912	−	0.119636i	1.09753	−	0.00405371i
$872$	−1.15152			−0.0389955
$873$		0			0
$874$	−18.6960	+	5.48964i	−0.632401	+	0.185690i
$875$	−6.52275	−	9.15992i	−0.220509	−	0.309662i
$876$		0			0
$877$	53.2121	+	10.2558i	1.79684	+	0.346313i	0.974795	−	0.223103i	$-0.0716187\pi$
$877$	53.2121	+	10.2558i	1.79684	+	0.346313i	0.822049	+	0.569417i	$0.192831\pi$
$878$	1.24299	+	26.0936i	0.0419490	+	0.880617i
$879$		0			0
$880$	−15.2933	+	9.82841i	−0.515537	+	0.331316i
$881$	−7.28649	−	30.0353i	−0.245488	−	1.01192i	−0.952458	−	0.304671i	$-0.901453\pi$
$881$	−7.28649	−	30.0353i	−0.245488	−	1.01192i	0.706970	−	0.707244i	$-0.250062\pi$
$882$		0			0
$883$	−4.48356	−	3.52591i	−0.150884	−	0.118656i	0.539863	−	0.841753i	$-0.318476\pi$
$883$	−4.48356	−	3.52591i	−0.150884	−	0.118656i	−0.690747	+	0.723096i	$0.742718\pi$
$884$	−32.2468	+	12.9097i	−1.08458	+	0.434199i
$885$		0			0
$886$	26.4728	+	17.0130i	0.889370	+	0.571564i
$887$	7.73781	−	22.3569i	0.259810	−	0.750673i	−0.737360	−	0.675500i	$-0.763928\pi$
$887$	7.73781	−	22.3569i	0.259810	−	0.750673i	0.997171	−	0.0751729i	$-0.0239509\pi$
$888$		0			0
$889$	9.61092	−	0.917731i	0.322340	−	0.0307797i
$890$	−0.986697	+	20.7133i	−0.0330741	+	0.694312i
$891$		0			0
$892$	−18.7236	−	54.0981i	−0.626911	−	1.81134i
$893$	0.956222	+	0.280772i	0.0319987	+	0.00939568i
$894$		0			0
$895$	5.92119	+	12.9656i	0.197924	+	0.433392i
$896$	−0.581353	+	4.04340i	−0.0194216	+	0.135081i
$897$		0			0
$898$	−50.3118	+	58.0629i	−1.67893	+	1.93759i
$899$	−7.53224	+	5.92342i	−0.251214	+	0.197557i
$900$		0			0
$901$	−0.916109	−	1.58675i	−0.0305200	−	0.0528622i
$902$	−79.9568	−	32.0099i	−2.66227	−	1.06581i
$903$		0			0
$904$	−6.93942	+	3.57752i	−0.230802	+	0.118986i
$905$	−9.56269	+	4.92991i	−0.317875	+	0.163876i
$906$		0			0
$907$	−25.1150	−	10.0545i	−0.833929	−	0.333855i	−0.0848980	−	0.996390i	$-0.527056\pi$
$907$	−25.1150	−	10.0545i	−0.833929	−	0.333855i	−0.749031	+	0.662535i	$0.769481\pi$
$908$	−13.5150	−	23.4087i	−0.448512	−	0.776846i
$909$		0			0
$910$	8.72234	−	6.85932i	0.289143	−	0.227384i
$911$	25.5392	−	29.4738i	0.846152	−	0.976511i	−0.153781	−	0.988105i	$-0.549145\pi$
$911$	25.5392	−	29.4738i	0.846152	−	0.976511i	0.999933	+	0.0115939i	$0.00369053\pi$
$912$		0			0
$913$	2.76462	−	19.2284i	0.0914956	−	0.636366i
$914$	−25.5556	−	55.9590i	−0.845305	−	1.85096i
$915$		0			0
$916$	61.4747	+	18.0506i	2.03118	+	0.596409i
$917$	3.91979	+	11.3255i	0.129443	+	0.374000i
$918$		0			0
$919$	2.46688	−	51.7862i	0.0813749	−	1.70827i	−0.477183	−	0.878804i	$-0.658342\pi$
$919$	2.46688	−	51.7862i	0.0813749	−	1.70827i	0.558558	−	0.829466i	$-0.311355\pi$
$920$	−3.35258	+	0.320132i	−0.110531	+	0.0105544i
$921$		0			0
$922$	4.38786	−	12.6779i	0.144506	−	0.417524i
$923$	21.4328	+	13.7740i	0.705469	+	0.453377i
$924$		0			0
$925$	−26.6691	+	10.6767i	−0.876875	+	0.351048i
$926$	−54.2107	−	42.6318i	−1.78147	−	1.40097i
$927$		0			0
$928$	17.3002	+	71.3123i	0.567906	+	2.34094i
$929$	−22.5037	+	14.4622i	−0.738322	+	0.474491i	−0.854967	−	0.518683i	$-0.826422\pi$
$929$	−22.5037	+	14.4622i	−0.738322	+	0.474491i	0.116645	+	0.993174i	$0.462786\pi$
$930$		0			0
$931$	0.521649	+	10.9508i	0.0170963	+	0.358896i
$932$	16.5132	+	3.18267i	0.540909	+	0.104252i
$933$		0			0
$934$	−11.1231	−	15.6203i	−0.363960	−	0.511111i
$935$	−19.7515	+	5.79957i	−0.645944	+	0.189666i
$936$		0			0
$937$	−24.8991			−0.813418			−0.406709	−	0.913558i	$-0.633324\pi$
$937$	−24.8991			−0.813418			−0.406709	+	0.913558i	$0.633324\pi$
$938$	12.5471	−	12.0524i	0.409676	−	0.393524i
$939$		0			0
$940$	1.41836	+	0.731218i	0.0462619	+	0.0238497i
$941$	11.8213	−	3.47106i	0.385365	−	0.113153i	−0.0833110	−	0.996524i	$-0.526550\pi$
$941$	11.8213	−	3.47106i	0.385365	−	0.113153i	0.468676	+	0.883370i	$0.344731\pi$
$942$		0			0
$943$	35.1892	+	40.6105i	1.14592	+	1.32246i
$944$	44.0944	+	8.49851i	1.43515	+	0.276603i
$945$		0			0
$946$	0.872560	+	6.06879i	0.0283694	+	0.197313i
$947$	−10.1980	+	6.55388i	−0.331391	+	0.212972i	−0.695746	−	0.718288i	$-0.744926\pi$
$947$	−10.1980	+	6.55388i	−0.331391	+	0.212972i	0.364354	+	0.931260i	$0.381290\pi$
$948$		0			0
$949$	56.2805	−	10.8472i	1.82694	−	0.352115i
$950$	−9.74796	−	7.66588i	−0.316266	−	0.248714i
$951$		0			0
$952$	−0.836583	+	1.83186i	−0.0271138	+	0.0593710i
$953$	16.0587	+	10.3203i	0.520193	+	0.334308i	0.774248	−	0.632882i	$-0.218128\pi$
$953$	16.0587	+	10.3203i	0.520193	+	0.334308i	−0.254055	+	0.967190i	$0.581765\pi$
$954$		0			0
$955$	−12.5509	+	17.6253i	−0.406138	+	0.570342i
$956$	−21.6414	+	2.06650i	−0.699931	+	0.0668354i
$957$		0			0
$958$	6.38266	−	26.3097i	0.206214	−	0.850027i
$959$	0.298722	+	0.863100i	0.00964624	+	0.0278710i
$960$		0			0
$961$	−21.6225	−	20.6170i	−0.697499	−	0.665064i
$962$	−29.8393	−	65.3389i	−0.962057	−	2.10661i
$963$		0			0
$964$	9.37695	+	0.895390i	0.302011	+	0.0288386i
$965$	13.3512	−	15.4081i	0.429789	−	0.496003i
$966$		0			0
$967$	13.2483	−	22.9468i	0.426037	−	0.737918i	−0.570480	−	0.821312i	$-0.693243\pi$
$967$	13.2483	−	22.9468i	0.426037	−	0.737918i	0.996517	+	0.0833940i	$0.0265760\pi$
$968$	−1.21748	−	2.10874i	−0.0391313	−	0.0677774i
$969$		0			0
$970$	9.00183	−	8.58323i	0.289031	−	0.275591i
$971$	21.3329	−	10.9979i	0.684604	−	0.352938i	−0.0805813	−	0.996748i	$-0.525678\pi$
$971$	21.3329	−	10.9979i	0.684604	−	0.352938i	0.765185	+	0.643810i	$0.222647\pi$
$972$		0			0
$973$	14.0801	−	13.4253i	0.451387	−	0.430397i
$974$	20.0693	+	8.03453i	0.643062	+	0.257443i
$975$		0			0
$976$	−11.2946	+	19.5628i	−0.361531	+	0.626190i
$977$	15.4221	−	12.1281i	0.493397	−	0.388012i	−0.340227	−	0.940343i	$-0.610504\pi$
$977$	15.4221	−	12.1281i	0.493397	−	0.388012i	0.833625	+	0.552331i	$0.186262\pi$
$978$		0			0
$979$	30.2798	+	2.89137i	0.967746	+	0.0924085i
$980$	−2.49825	+	17.3757i	−0.0798037	+	0.555047i
$981$		0			0
$982$	−5.04694	−	4.81225i	−0.161054	−	0.153565i
$983$	4.87381	+	1.43108i	0.155450	+	0.0456443i	0.358532	−	0.933518i	$-0.383277\pi$
$983$	4.87381	+	1.43108i	0.155450	+	0.0456443i	−0.203082	+	0.979162i	$0.565096\pi$
$984$		0			0
$985$	0.0217636	−	0.0897109i	0.000693447	−	0.00285843i
$986$	−3.46822	+	72.8069i	−0.110451	+	2.31864i
$987$		0			0
$988$	9.50640	−	13.3499i	0.302439	−	0.424716i
$989$	1.25114	−	3.61494i	0.0397841	−	0.114949i
$990$		0			0
$991$	−16.6529	+	36.4648i	−0.528997	+	1.15834i	0.436923	+	0.899499i	$0.356068\pi$
$991$	−16.6529	+	36.4648i	−0.528997	+	1.15834i	−0.965920	+	0.258842i	$0.916659\pi$
$992$	7.98894	−	3.19829i	0.253649	−	0.101546i
$993$		0			0
$994$	13.4369	−	2.58975i	0.426193	−	0.0821419i
$995$	−2.70601	−	11.1543i	−0.0857861	−	0.353615i
$996$		0			0
$997$	2.63935	+	18.3571i	0.0835890	+	0.581374i	0.987970	+	0.154648i	$0.0494242\pi$
$997$	2.63935	+	18.3571i	0.0835890	+	0.581374i	−0.904381	+	0.426727i	$0.859667\pi$
$998$	1.94865	+	40.9071i	0.0616833	+	1.29489i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.z.c.19.1		100
3.2	odd	2		67.2.g.a.19.5	✓	100
67.60	even	33	inner	603.2.z.c.127.1		100
201.23	odd	66		4489.2.a.p.1.10		50
201.44	even	66		4489.2.a.q.1.41		50
201.194	odd	66		67.2.g.a.60.5	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.g.a.19.5	✓	100	3.2	odd	2
67.2.g.a.60.5	yes	100	201.194	odd	66
603.2.z.c.19.1		100	1.1	even	1	trivial
603.2.z.c.127.1		100	67.60	even	33	inner
4489.2.a.p.1.10		50	201.23	odd	66
4489.2.a.q.1.41		50	201.44	even	66

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.z (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.83066 - 0.943770i) q^{2} +(1.30049 + 1.82629i) q^{4} +(0.863926 + 0.997024i) q^{5} +(-0.0491040 - 1.03082i) q^{7} +(-0.0709360 - 0.493371i) q^{8} +O(q^{10})\)	\(q+(-1.83066 - 0.943770i) q^{2} +(1.30049 + 1.82629i) q^{4} +(0.863926 + 0.997024i) q^{5} +(-0.0491040 - 1.03082i) q^{7} +(-0.0709360 - 0.493371i) q^{8} +(-0.640592 - 2.64056i) q^{10} +(-3.91359 + 0.754283i) q^{11} +(-3.67378 + 1.47076i) q^{13} +(-0.882963 + 1.93342i) q^{14} +(1.13081 - 3.26726i) q^{16} +(2.27094 - 3.18910i) q^{17} +(-0.0878936 + 1.84511i) q^{19} +(-0.697322 + 2.87440i) q^{20} +(7.87631 + 2.31269i) q^{22} +(-3.70668 - 3.53431i) q^{23} +(0.463886 - 3.22640i) q^{25} +(8.11349 + 0.774744i) q^{26} +(1.81871 - 1.43025i) q^{28} +(4.51973 - 7.82841i) q^{29} +(-0.984123 - 0.393984i) q^{31} +(-5.87515 + 5.60194i) q^{32} +(-7.16709 + 3.69489i) q^{34} +(0.985329 - 0.939509i) q^{35} +(-4.40654 - 7.63235i) q^{37} +(1.90227 - 3.29482i) q^{38} +(0.430619 - 0.496961i) q^{40} +(-10.4444 - 0.997319i) q^{41} +(0.310274 + 0.679406i) q^{43} +(-6.46713 - 6.16640i) q^{44} +(3.45008 + 9.96836i) q^{46} +(0.127195 - 0.524304i) q^{47} +(5.90813 - 0.564158i) q^{49} +(-3.89419 + 5.46863i) q^{50} +(-7.46375 - 4.79666i) q^{52} +(0.194412 - 0.425703i) q^{53} +(-4.13309 - 3.25030i) q^{55} +(-0.505093 + 0.0973486i) q^{56} +(-15.6623 + 10.0655i) q^{58} +(1.84843 + 12.8561i) q^{59} +(-6.41548 - 1.23648i) q^{61} +(1.42976 + 1.65003i) q^{62} +(9.40760 - 2.76232i) q^{64} +(-4.64026 - 2.39222i) q^{65} +(-7.61020 - 3.01410i) q^{67} +8.77755 q^{68} +(-2.69048 + 0.789996i) q^{70} +(-3.73448 - 5.24434i) q^{71} +(-14.2222 - 2.74110i) q^{73} +(0.863685 + 18.1310i) q^{74} +(-3.48401 + 2.23904i) q^{76} +(0.969702 + 3.99716i) q^{77} +(5.44259 + 4.28010i) q^{79} +(4.23447 - 1.69523i) q^{80} +(18.1789 + 11.6829i) q^{82} +(-1.59415 + 4.60598i) q^{83} +(5.14153 - 0.490957i) q^{85} +(0.0731967 - 1.53659i) q^{86} +(0.649755 + 1.87734i) q^{88} +(-7.32268 - 2.15013i) q^{89} +(1.69648 + 3.71478i) q^{91} +(1.63415 - 11.3658i) q^{92} +(-0.727673 + 0.839779i) q^{94} +(-1.91556 + 1.50641i) q^{95} +(2.28880 + 3.96432i) q^{97} +(-11.3482 - 4.54313i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8}+O(q^{10}) \) 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8	\( 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8} + 8 q^{10} + 24 q^{11} - 22 q^{13} + 32 q^{14} - 28 q^{16} - 17 q^{17} + 15 q^{20} + 49 q^{22} + 13 q^{23} - 34 q^{25} + 27 q^{26} + 22 q^{28} - 8 q^{29} + 10 q^{31} - 34 q^{32} - 50 q^{34} + q^{35} + 7 q^{37} - 50 q^{38} + 43 q^{40} + 5 q^{41} + 2 q^{43} + 19 q^{44} + 52 q^{46} + 6 q^{47} - 27 q^{49} - 134 q^{50} + 120 q^{52} + 52 q^{53} - 64 q^{55} + 124 q^{56} - 56 q^{58} - 27 q^{59} - 16 q^{61} + 74 q^{62} - 197 q^{64} + 92 q^{65} - 56 q^{67} - 16 q^{68} - 22 q^{70} + 113 q^{71} + q^{73} + 24 q^{74} - 144 q^{76} - 85 q^{77} + 36 q^{79} + 13 q^{80} - 20 q^{82} + 61 q^{83} - 6 q^{85} - 189 q^{86} + 129 q^{88} - 95 q^{89} + 42 q^{91} - 4 q^{92} + 70 q^{94} + 20 q^{95} + 53 q^{97} - q^{98}+O(q^{100}) \) 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8 + 8 * q^10 + 24 * q^11 - 22 * q^13 + 32 * q^14 - 28 * q^16 - 17 * q^17 + 15 * q^20 + 49 * q^22 + 13 * q^23 - 34 * q^25 + 27 * q^26 + 22 * q^28 - 8 * q^29 + 10 * q^31 - 34 * q^32 - 50 * q^34 + q^35 + 7 * q^37 - 50 * q^38 + 43 * q^40 + 5 * q^41 + 2 * q^43 + 19 * q^44 + 52 * q^46 + 6 * q^47 - 27 * q^49 - 134 * q^50 + 120 * q^52 + 52 * q^53 - 64 * q^55 + 124 * q^56 - 56 * q^58 - 27 * q^59 - 16 * q^61 + 74 * q^62 - 197 * q^64 + 92 * q^65 - 56 * q^67 - 16 * q^68 - 22 * q^70 + 113 * q^71 + q^73 + 24 * q^74 - 144 * q^76 - 85 * q^77 + 36 * q^79 + 13 * q^80 - 20 * q^82 + 61 * q^83 - 6 * q^85 - 189 * q^86 + 129 * q^88 - 95 * q^89 + 42 * q^91 - 4 * q^92 + 70 * q^94 + 20 * q^95 + 53 * q^97 - q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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