LMFDB - Embedded newform 225.2.e.c.76.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(76,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1223810289.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} - 2x^{5} + 23x^{4} - 8x^{3} + 37x^{2} + 15x + 9 $ x^8 - 2x^7 + 8x^6 - 2x^5 + 23x^4 - 8x^3 + 37x^2 + 15*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			76.2
Root			$0.736627 + 1.27588i$ of defining polynomial
Character	$\chi$	$=$	225.76
Dual form			225.2.e.c.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.736627 - 1.27588i) q^{2} +(1.69629 + 0.350156i) q^{3} +(-0.0852394 + 0.147639i) q^{4} +(-0.802776 - 2.42219i) q^{6} +(-1.93291 - 3.34791i) q^{7} -2.69535 q^{8} +(2.75478 + 1.18793i) q^{9} +(-0.130139 - 0.225407i) q^{11} +(-0.196287 + 0.220591i) q^{12} +(2.03940 - 3.53235i) q^{13} +(-2.84768 + 4.93232i) q^{14} +(2.15595 + 3.73421i) q^{16} +3.26028 q^{17} +(-0.513594 - 4.38982i) q^{18} +4.24928 q^{19} +(-2.10649 - 6.35583i) q^{21} +(-0.191728 + 0.332082i) q^{22} +(-4.34768 + 7.53039i) q^{23} +(-4.57209 - 0.943794i) q^{24} -6.00912 q^{26} +(4.25694 + 2.97968i) q^{27} +0.659042 q^{28} +(-2.11105 - 3.65644i) q^{29} +(-1.32643 + 2.29744i) q^{31} +(0.480909 - 0.832959i) q^{32} +(-0.141825 - 0.427924i) q^{33} +(-2.40161 - 4.15971i) q^{34} +(-0.410201 + 0.305455i) q^{36} -2.27559 q^{37} +(-3.13014 - 5.42156i) q^{38} +(4.69629 - 5.27777i) q^{39} +(-2.82093 + 4.88599i) q^{41} +(-6.55756 + 7.36950i) q^{42} +(4.53631 + 7.85712i) q^{43} +0.0443719 q^{44} +12.8105 q^{46} +(0.714441 + 1.23745i) q^{47} +(2.34955 + 7.08921i) q^{48} +(-3.97232 + 6.88026i) q^{49} +(5.53037 + 1.14161i) q^{51} +(0.347675 + 0.602191i) q^{52} +11.3816 q^{53} +(0.665919 - 7.62624i) q^{54} +(5.20988 + 9.02378i) q^{56} +(7.20801 + 1.48791i) q^{57} +(-3.11011 + 5.38687i) q^{58} +(3.56212 - 6.16977i) q^{59} +(-1.26244 - 2.18660i) q^{61} +3.90833 q^{62} +(-1.34768 - 11.5189i) q^{63} +7.20679 q^{64} +(-0.441506 + 0.496172i) q^{66} +(-5.64280 + 9.77361i) q^{67} +(-0.277904 + 0.481344i) q^{68} +(-10.0117 + 11.2513i) q^{69} -8.38158 q^{71} +(-7.42510 - 3.20189i) q^{72} +0.403568 q^{73} +(1.67626 + 2.90337i) q^{74} +(-0.362207 + 0.627360i) q^{76} +(-0.503095 + 0.871386i) q^{77} +(-10.1932 - 2.10413i) q^{78} +(1.52125 + 2.63488i) q^{79} +(6.17764 + 6.54498i) q^{81} +8.31189 q^{82} +(-2.29012 - 3.96660i) q^{83} +(1.11792 + 0.230768i) q^{84} +(6.68314 - 11.5755i) q^{86} +(-2.30062 - 6.94157i) q^{87} +(0.350770 + 0.607551i) q^{88} +7.17772 q^{89} -15.7680 q^{91} +(-0.741187 - 1.28377i) q^{92} +(-3.05446 + 3.43266i) q^{93} +(1.05255 - 1.82308i) q^{94} +(1.10743 - 1.24454i) q^{96} +(-1.55756 - 2.69777i) q^{97} +11.7045 q^{98} +(-0.0907360 - 0.775544i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + q^{3} - 4 q^{4} + 8 q^{6} + q^{7} + 18 q^{8} + 5 q^{9} + q^{11} + 11 q^{12} - 2 q^{13} - 3 q^{14} - 4 q^{16} + 22 q^{17} - 5 q^{18} + 4 q^{19} - 15 q^{21} - 3 q^{22} - 15 q^{23} - 33 q^{24}+ \cdots - 17 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + q^3 - 4 * q^4 + 8 * q^6 + q^7 + 18 * q^8 + 5 * q^9 + q^11 + 11 * q^12 - 2 * q^13 - 3 * q^14 - 4 * q^16 + 22 * q^17 - 5 * q^18 + 4 * q^19 - 15 * q^21 - 3 * q^22 - 15 * q^23 - 33 * q^24 - 20 * q^26 - 2 * q^27 - 8 * q^28 - q^29 + 4 * q^31 - 10 * q^32 - 28 * q^33 - 9 * q^34 - 14 * q^36 - 2 * q^37 - 23 * q^38 + 25 * q^39 + 5 * q^41 - 21 * q^42 + 10 * q^43 + 44 * q^44 - 20 * q^47 + 53 * q^48 + 3 * q^49 + 11 * q^51 - 17 * q^52 + 40 * q^53 + 26 * q^54 + 30 * q^56 - 8 * q^57 + 18 * q^58 - 17 * q^59 + 13 * q^61 - 12 * q^62 + 9 * q^63 + 38 * q^64 - 8 * q^66 - 17 * q^67 - 34 * q^68 - 27 * q^69 - 16 * q^71 + 18 * q^72 + 4 * q^73 - 40 * q^74 - 11 * q^76 - 12 * q^77 - 61 * q^78 + 7 * q^79 + 17 * q^81 + 24 * q^82 - 30 * q^83 + 27 * q^84 + 34 * q^86 - 23 * q^87 - 9 * q^88 - 18 * q^89 - 34 * q^91 + 12 * q^92 + 15 * q^93 - 3 * q^94 + 34 * q^96 + 19 * q^97 + 26 * q^98 - 17 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.736627	−	1.27588i	−0.520874	−	0.902180i	−0.999705	−	0.0242735i	$-0.992273\pi$
$2$	−0.736627	−	1.27588i	−0.520874	−	0.902180i	0.478831	−	0.877907i	$-0.341061\pi$
$3$	1.69629	+	0.350156i	0.979352	+	0.202163i
$3$	1.69629	+	0.350156i	0.979352	+	0.202163i
$4$	−0.0852394	+	0.147639i	−0.0426197	+	0.0738195i
$5$		0			0
$5$		0			0
$6$	−0.802776	−	2.42219i	−0.327732	−	0.988854i
$7$	−1.93291	−	3.34791i	−0.730573	−	1.26539i	−0.956639	−	0.291278i	$-0.905920\pi$
$7$	−1.93291	−	3.34791i	−0.730573	−	1.26539i	0.226066	−	0.974112i	$-0.427414\pi$
$8$	−2.69535			−0.952950
$9$	2.75478	+	1.18793i	0.918260	+	0.395977i
$10$		0			0
$11$	−0.130139	−	0.225407i	−0.0392384	−	0.0679628i	0.845739	−	0.533596i	$-0.179160\pi$
$11$	−0.130139	−	0.225407i	−0.0392384	−	0.0679628i	−0.884978	+	0.465634i	$0.845826\pi$
$12$	−0.196287	+	0.220591i	−0.0566633	+	0.0636792i
$13$	2.03940	−	3.53235i	0.565629	−	0.979697i	−0.431362	−	0.902179i	$-0.641967\pi$
$13$	2.03940	−	3.53235i	0.565629	−	0.979697i	0.996991	−	0.0775187i	$-0.0246997\pi$
$14$	−2.84768	+	4.93232i	−0.761073	+	1.31822i
$15$		0			0
$16$	2.15595	+	3.73421i	0.538987	+	0.933553i
$17$	3.26028			0.790734			0.395367	−	0.918523i	$-0.370617\pi$
$17$	3.26028			0.790734			0.395367	+	0.918523i	$0.370617\pi$
$18$	−0.513594	−	4.38982i	−0.121055	−	1.03469i
$19$	4.24928			0.974853			0.487426	−	0.873164i	$-0.337936\pi$
$19$	4.24928			0.974853			0.487426	+	0.873164i	$0.337936\pi$
$20$		0			0
$21$	−2.10649	−	6.35583i	−0.459673	−	1.38696i
$22$	−0.191728	+	0.332082i	−0.0408765	+	0.0708002i
$23$	−4.34768	+	7.53039i	−0.906553	+	1.57020i	−0.0877339	+	0.996144i	$0.527963\pi$
$23$	−4.34768	+	7.53039i	−0.906553	+	1.57020i	−0.818819	+	0.574052i	$0.805371\pi$
$24$	−4.57209	−	0.943794i	−0.933274	−	0.192651i
$25$		0			0
$26$	−6.00912			−1.17849
$27$	4.25694	+	2.97968i	0.819248	+	0.573439i
$28$	0.659042			0.124547
$29$	−2.11105	−	3.65644i	−0.392012	−	0.678984i	0.600703	−	0.799472i	$-0.294887\pi$
$29$	−2.11105	−	3.65644i	−0.392012	−	0.678984i	−0.992715	+	0.120488i	$0.961554\pi$
$30$		0			0
$31$	−1.32643	+	2.29744i	−0.238233	+	0.412632i	−0.960207	−	0.279288i	$-0.909902\pi$
$31$	−1.32643	+	2.29744i	−0.238233	+	0.412632i	0.721974	+	0.691920i	$0.243235\pi$
$32$	0.480909	−	0.832959i	0.0850135	−	0.147248i
$33$	−0.141825	−	0.427924i	−0.0246886	−	0.0744921i
$34$	−2.40161	−	4.15971i	−0.411873	−	0.713384i
$35$		0			0
$36$	−0.410201	+	0.305455i	−0.0683668	+	0.0509091i
$37$	−2.27559			−0.374104			−0.187052	−	0.982350i	$-0.559893\pi$
$37$	−2.27559			−0.374104			−0.187052	+	0.982350i	$0.559893\pi$
$38$	−3.13014	−	5.42156i	−0.507776	−	0.879493i
$39$	4.69629	−	5.27777i	0.752008	−	0.845120i
$40$		0			0
$41$	−2.82093	+	4.88599i	−0.440555	+	0.763064i	−0.997731	−	0.0673308i	$-0.978552\pi$
$41$	−2.82093	+	4.88599i	−0.440555	+	0.763064i	0.557176	+	0.830395i	$0.311885\pi$
$42$	−6.55756	+	7.36950i	−1.01185	+	1.13714i
$43$	4.53631	+	7.85712i	0.691780	+	1.19820i	0.971254	+	0.238046i	$0.0765068\pi$
$43$	4.53631	+	7.85712i	0.691780	+	1.19820i	−0.279474	+	0.960153i	$0.590160\pi$
$44$	0.0443719			0.00668931
$45$		0			0
$46$	12.8105			1.88880
$47$	0.714441	+	1.23745i	0.104212	+	0.180500i	0.913416	−	0.407027i	$-0.133435\pi$
$47$	0.714441	+	1.23745i	0.104212	+	0.180500i	−0.809204	+	0.587528i	$0.800101\pi$
$48$	2.34955	+	7.08921i	0.339128	+	1.02324i
$49$	−3.97232	+	6.88026i	−0.567474	+	0.982894i
$50$		0			0
$51$	5.53037	+	1.14161i	0.774406	+	0.159857i
$52$	0.347675	+	0.602191i	0.0482139	+	0.0835089i
$53$	11.3816			1.56338			0.781690	−	0.623667i	$-0.214358\pi$
$53$	11.3816			1.56338			0.781690	+	0.623667i	$0.214358\pi$
$54$	0.665919	−	7.62624i	0.0906201	−	1.03780i
$55$		0			0
$56$	5.20988	+	9.02378i	0.696200	+	1.20585i
$57$	7.20801	+	1.48791i	0.954724	+	0.197079i
$58$	−3.11011	+	5.38687i	−0.408378	+	0.707331i
$59$	3.56212	−	6.16977i	0.463748	−	0.803235i	−0.535396	−	0.844601i	$-0.679838\pi$
$59$	3.56212	−	6.16977i	0.463748	−	0.803235i	0.999144	+	0.0413660i	$0.0131710\pi$
$60$		0			0
$61$	−1.26244	−	2.18660i	−0.161638	−	0.279966i	0.773818	−	0.633408i	$-0.218344\pi$
$61$	−1.26244	−	2.18660i	−0.161638	−	0.279966i	−0.935456	+	0.353442i	$0.885011\pi$
$62$	3.90833			0.496358
$63$	−1.34768	−	11.5189i	−0.169791	−	1.45125i
$64$	7.20679			0.900848
$65$		0			0
$66$	−0.441506	+	0.496172i	−0.0543456	+	0.0610746i
$67$	−5.64280	+	9.77361i	−0.689377	+	1.19404i	0.282662	+	0.959219i	$0.408782\pi$
$67$	−5.64280	+	9.77361i	−0.689377	+	1.19404i	−0.972040	+	0.234817i	$0.924551\pi$
$68$	−0.277904	+	0.481344i	−0.0337008	+	0.0583716i
$69$	−10.0117	+	11.2513i	−1.20527	+	1.35450i
$70$		0			0
$71$	−8.38158			−0.994711			−0.497355	−	0.867547i	$-0.665695\pi$
$71$	−8.38158			−0.994711			−0.497355	+	0.867547i	$0.665695\pi$
$72$	−7.42510	−	3.20189i	−0.875056	−	0.377346i
$73$	0.403568			0.0472340			0.0236170	−	0.999721i	$-0.492482\pi$
$73$	0.403568			0.0472340			0.0236170	+	0.999721i	$0.492482\pi$
$74$	1.67626	+	2.90337i	0.194861	+	0.337509i
$75$		0			0
$76$	−0.362207	+	0.627360i	−0.0415480	+	0.0719632i
$77$	−0.503095	+	0.871386i	−0.0573330	+	0.0993036i
$78$	−10.1932	−	2.10413i	−1.15415	−	0.238246i
$79$	1.52125	+	2.63488i	0.171154	+	0.296447i	0.938824	−	0.344399i	$-0.111917\pi$
$79$	1.52125	+	2.63488i	0.171154	+	0.296447i	−0.767670	+	0.640846i	$0.778584\pi$
$80$		0			0
$81$	6.17764	+	6.54498i	0.686404	+	0.727220i
$82$	8.31189			0.917895
$83$	−2.29012	−	3.96660i	−0.251373	−	0.435391i	0.712531	−	0.701641i	$-0.247549\pi$
$83$	−2.29012	−	3.96660i	−0.251373	−	0.435391i	−0.963904	+	0.266250i	$0.914215\pi$
$84$	1.11792	+	0.230768i	0.121976	+	0.0251788i
$85$		0			0
$86$	6.68314	−	11.5755i	0.720661	−	1.24822i
$87$	−2.30062	−	6.94157i	−0.246652	−	0.744215i
$88$	0.350770	+	0.607551i	0.0373922	+	0.0647652i
$89$	7.17772			0.760837			0.380419	−	0.924814i	$-0.375780\pi$
$89$	7.17772			0.760837			0.380419	+	0.924814i	$0.375780\pi$
$90$		0			0
$91$	−15.7680			−1.65293
$92$	−0.741187	−	1.28377i	−0.0772741	−	0.133843i
$93$	−3.05446	+	3.43266i	−0.316733	+	0.355950i
$94$	1.05255	−	1.82308i	0.108563	−	0.188036i
$95$		0			0
$96$	1.10743	−	1.24454i	0.113026	−	0.127021i
$97$	−1.55756	−	2.69777i	−0.158146	−	0.273917i	0.776054	−	0.630666i	$-0.217218\pi$
$97$	−1.55756	−	2.69777i	−0.158146	−	0.273917i	−0.934200	+	0.356749i	$0.883885\pi$
$98$	11.7045			1.18233
$99$	−0.0907360	−	0.775544i	−0.00911931	−	0.0779451i
$100$		0			0
$101$	−1.92286	−	3.33049i	−0.191332	−	0.331396i	0.754360	−	0.656461i	$-0.227947\pi$
$101$	−1.92286	−	3.33049i	−0.191332	−	0.331396i	−0.945692	+	0.325065i	$0.894614\pi$
$102$	−2.61727	−	7.89700i	−0.259149	−	0.781920i
$103$	2.10339	−	3.64318i	0.207254	−	0.358974i	−0.743595	−	0.668630i	$-0.766881\pi$
$103$	2.10339	−	3.64318i	0.207254	−	0.358974i	0.950848	+	0.309657i	$0.100214\pi$
$104$	−5.49691	+	9.52092i	−0.539016	+	0.933603i
$105$		0			0
$106$	−8.38398	−	14.5215i	−0.814324	−	1.41045i
$107$	−1.62655			−0.157245			−0.0786223	−	0.996904i	$-0.525052\pi$
$107$	−1.62655			−0.157245			−0.0786223	+	0.996904i	$0.525052\pi$
$108$	−0.802776	+	0.374504i	−0.0772471	+	0.0360367i
$109$	−12.9021			−1.23580			−0.617900	−	0.786256i	$-0.712016\pi$
$109$	−12.9021			−1.23580			−0.617900	+	0.786256i	$0.712016\pi$
$110$		0			0
$111$	−3.86005	−	0.796811i	−0.366380	−	0.0756299i
$112$	8.33452	−	14.4358i	0.787539	−	1.36406i
$113$	−0.664539	+	1.15102i	−0.0625146	+	0.108278i	−0.895589	−	0.444883i	$-0.853245\pi$
$113$	−0.664539	+	1.15102i	−0.0625146	+	0.108278i	0.833074	+	0.553161i	$0.186579\pi$
$114$	−3.41122	−	10.2926i	−0.319490	−	0.963987i
$115$		0			0
$116$	0.719778			0.0668297
$117$	9.81430	−	7.30818i	0.907332	−	0.675641i
$118$	−10.4958			−0.966217
$119$	−6.30184	−	10.9151i	−0.577689	−	1.00059i
$120$		0			0
$121$	5.46613	−	9.46761i	0.496921	−	0.860692i
$122$	−1.85989	+	3.22142i	−0.168386	+	0.291654i
$123$	−6.49597	+	7.30028i	−0.585722	+	0.658244i
$124$	−0.226128	−	0.391665i	−0.0203069	−	0.0351725i
$125$		0			0
$126$	−13.7040	+	10.2046i	−1.22085	+	0.909099i
$127$	−1.65285			−0.146667			−0.0733335	−	0.997307i	$-0.523364\pi$
$127$	−1.65285			−0.146667			−0.0733335	+	0.997307i	$0.523364\pi$
$128$	−6.27053	−	10.8609i	−0.554242	−	0.959975i
$129$	4.94366	+	14.9163i	0.435265	+	1.31331i
$130$		0			0
$131$	6.58886	−	11.4122i	0.575672	−	0.997092i	−0.420297	−	0.907387i	$-0.638074\pi$
$131$	6.58886	−	11.4122i	0.575672	−	0.997092i	0.995968	−	0.0897057i	$-0.0285926\pi$
$132$	0.0752675	+	0.0155371i	0.00655119	+	0.00135233i
$133$	−8.21350	−	14.2262i	−0.712201	−	1.23357i
$134$	16.6266			1.43632
$135$		0			0
$136$	−8.78759			−0.753530
$137$	−10.1464	−	17.5741i	−0.866867	−	1.50146i	−0.865181	−	0.501459i	$-0.832797\pi$
$137$	−10.1464	−	17.5741i	−0.866867	−	1.50146i	−0.00168578	−	0.999999i	$-0.500537\pi$
$138$	21.7302	+	4.48566i	1.84980	+	0.381845i
$139$	−1.53440	+	2.65766i	−0.130146	+	0.225420i	−0.923733	−	0.383038i	$-0.874878\pi$
$139$	−1.53440	+	2.65766i	−0.130146	+	0.225420i	0.793587	+	0.608457i	$0.208211\pi$
$140$		0			0
$141$	0.778597	+	2.34923i	0.0655697	+	0.197841i
$142$	6.17410	+	10.6939i	0.518119	+	0.897409i
$143$	−1.06162			−0.0887774
$144$	1.50318	+	12.8480i	0.125265	+	1.07067i
$145$		0			0
$146$	−0.297279	−	0.514902i	−0.0246030	−	0.0426136i
$147$	−9.14736	+	10.2800i	−0.754461	+	0.847877i
$148$	0.193970	−	0.335965i	0.0159442	−	0.0276162i
$149$	−2.03081	+	3.51747i	−0.166371	+	0.288162i	−0.937141	−	0.348951i	$-0.886538\pi$
$149$	−2.03081	+	3.51747i	−0.166371	+	0.288162i	0.770771	+	0.637113i	$0.219871\pi$
$150$		0			0
$151$	6.80994	+	11.7952i	0.554185	+	0.959876i	0.997966	+	0.0637412i	$0.0203032\pi$
$151$	6.80994	+	11.7952i	0.554185	+	0.959876i	−0.443782	+	0.896135i	$0.646363\pi$
$152$	−11.4533			−0.928986
$153$	8.98135	+	3.87299i	0.726099	+	0.313112i
$154$	1.48237			0.119453
$155$		0			0
$156$	0.378896	+	1.14323i	0.0303360	+	0.0915316i
$157$	−1.03131	+	1.78627i	−0.0823071	+	0.142560i	−0.904241	−	0.427023i	$-0.859562\pi$
$157$	−1.03131	+	1.78627i	−0.0823071	+	0.142560i	0.821933	+	0.569584i	$0.192896\pi$
$158$	2.24119	−	3.88185i	0.178299	−	0.308823i
$159$	19.3064	+	3.98533i	1.53110	+	0.316057i
$160$		0			0
$161$	33.6147			2.64921
$162$	3.79996	−	12.7031i	0.298553	−	0.998051i
$163$	−3.50525			−0.274552			−0.137276	−	0.990533i	$-0.543835\pi$
$163$	−3.50525			−0.274552			−0.137276	+	0.990533i	$0.543835\pi$
$164$	−0.480909	−	0.832959i	−0.0375527	−	0.0650431i
$165$		0			0
$166$	−3.37393	+	5.84381i	−0.261868	+	0.453568i
$167$	−10.2674	+	17.7837i	−0.794518	+	1.37615i	0.128626	+	0.991693i	$0.458943\pi$
$167$	−10.2674	+	17.7837i	−0.794518	+	1.37615i	−0.923145	+	0.384453i	$0.874390\pi$
$168$	5.67772	+	17.1312i	0.438046	+	1.32170i
$169$	−1.81833	−	3.14944i	−0.139871	−	0.242264i
$170$		0			0
$171$	11.7058	+	5.04786i	0.895169	+	0.386019i
$172$	−1.54669			−0.117934
$173$	3.87589	+	6.71323i	0.294678	+	0.510397i	0.974910	−	0.222600i	$-0.0714542\pi$
$173$	3.87589	+	6.71323i	0.294678	+	0.510397i	−0.680232	+	0.732997i	$0.738121\pi$
$174$	−7.16189	+	8.04865i	−0.542941	+	0.610167i
$175$		0			0
$176$	0.561145	−	0.971932i	0.0422979	−	0.0732622i
$177$	8.20275	−	9.21840i	0.616557	−	0.692897i
$178$	−5.28731	−	9.15788i	−0.396300	−	0.686412i
$179$	−10.7632			−0.804477			−0.402238	−	0.915535i	$-0.631768\pi$
$179$	−10.7632			−0.804477			−0.402238	+	0.915535i	$0.631768\pi$
$180$		0			0
$181$	−7.84572			−0.583168			−0.291584	−	0.956545i	$-0.594182\pi$
$181$	−7.84572			−0.583168			−0.291584	+	0.956545i	$0.594182\pi$
$182$	11.6151	+	20.1180i	0.860970	+	1.49124i
$183$	−1.37580	−	4.15116i	−0.101702	−	0.306862i
$184$	11.7185	−	20.2970i	0.863900	−	1.49632i
$185$		0			0
$186$	6.62965	+	1.36852i	0.486109	+	0.100345i
$187$	−0.424289	−	0.734890i	−0.0310271	−	0.0537405i
$188$	−0.243594			−0.0177659
$189$	1.74738	−	20.0113i	0.127103	−	1.45561i
$190$		0			0
$191$	2.86627	+	4.96453i	0.207396	+	0.359221i	0.950894	−	0.309518i	$-0.100168\pi$
$191$	2.86627	+	4.96453i	0.207396	+	0.359221i	−0.743497	+	0.668739i	$0.766834\pi$
$192$	12.2248	+	2.52350i	0.882248	+	0.182118i
$193$	4.24119	−	7.34595i	0.305287	−	0.528773i	−0.672038	−	0.740517i	$-0.734581\pi$
$193$	4.24119	−	7.34595i	0.305287	−	0.528773i	0.977325	+	0.211744i	$0.0679142\pi$
$194$	−2.29468	+	3.97450i	−0.164748	+	0.285352i
$195$		0			0
$196$	−0.677196	−	1.17294i	−0.0483712	−	0.0837813i
$197$	10.6266			0.757110			0.378555	−	0.925579i	$-0.376421\pi$
$197$	10.6266			0.757110			0.378555	+	0.925579i	$0.376421\pi$
$198$	−0.922659	+	0.687055i	−0.0655705	+	0.0488268i
$199$	−18.5784			−1.31699			−0.658495	−	0.752585i	$-0.728807\pi$
$199$	−18.5784			−1.31699			−0.658495	+	0.752585i	$0.728807\pi$
$200$		0			0
$201$	−12.9941	+	14.6030i	−0.916533	+	1.03002i
$202$	−2.83286	+	4.90666i	−0.199319	+	0.345231i
$203$	−8.16095	+	14.1352i	−0.572786	+	0.992095i
$204$	−0.639951	+	0.719188i	−0.0448055	+	0.0503533i
$205$		0			0
$206$	−6.19767			−0.431812
$207$	−20.9225	+	15.5799i	−1.45421	+	1.08287i
$208$	17.5874			1.21947
$209$	−0.552997	−	0.957820i	−0.0382516	−	0.0662538i
$210$		0			0
$211$	−5.22666	+	9.05283i	−0.359818	+	0.623223i	−0.987930	−	0.154900i	$-0.950494\pi$
$211$	−5.22666	+	9.05283i	−0.359818	+	0.623223i	0.628112	+	0.778123i	$0.283828\pi$
$212$	−0.970160	+	1.68037i	−0.0666308	+	0.115408i
$213$	−14.2176	−	2.93486i	−0.974172	−	0.201093i
$214$	1.19816	+	2.07528i	0.0819046	+	0.141863i
$215$		0			0
$216$	−11.4739	−	8.03127i	−0.780703	−	0.546459i
$217$	10.2555			0.696187
$218$	9.50407	+	16.4615i	0.643697	+	1.11492i
$219$	0.684567	+	0.141312i	0.0462587	+	0.00954896i
$220$		0			0
$221$	6.64902	−	11.5164i	0.447261	−	0.774680i
$222$	1.82679	+	5.51190i	0.122606	+	0.369934i
$223$	−1.96560	−	3.40452i	−0.131626	−	0.227983i	0.792677	−	0.609641i	$-0.208687\pi$
$223$	−1.96560	−	3.40452i	−0.131626	−	0.227983i	−0.924304	+	0.381658i	$0.875353\pi$
$224$	−3.71822			−0.248434
$225$		0			0
$226$	1.95807			0.130249
$227$	−2.41570	−	4.18411i	−0.160335	−	0.277709i	0.774654	−	0.632386i	$-0.217924\pi$
$227$	−2.41570	−	4.18411i	−0.160335	−	0.277709i	−0.934989	+	0.354677i	$0.884591\pi$
$228$	−0.834081	+	0.937354i	−0.0552383	+	0.0620778i
$229$	9.42648	−	16.3271i	0.622919	−	1.07893i	−0.366020	−	0.930607i	$-0.619280\pi$
$229$	9.42648	−	16.3271i	0.622919	−	1.07893i	0.988939	−	0.148321i	$-0.0473869\pi$
$230$		0			0
$231$	−1.15851	+	1.30196i	−0.0762247	+	0.0856626i
$232$	5.69001	+	9.85539i	0.373568	+	0.647038i
$233$	−11.9021			−0.779735			−0.389867	−	0.920871i	$-0.627479\pi$
$233$	−11.9021			−0.779735			−0.389867	+	0.920871i	$0.627479\pi$
$234$	−16.5538	−	7.13842i	−1.08216	−	0.466653i
$235$		0			0
$236$	0.607266	+	1.05181i	0.0395296	+	0.0684673i
$237$	1.65786	+	5.00219i	0.107689	+	0.324927i
$238$	−9.28421	+	16.0807i	−0.601806	+	1.04236i
$239$	10.8147	−	18.7317i	0.699547	−	1.21165i	−0.269076	−	0.963119i	$-0.586718\pi$
$239$	10.8147	−	18.7317i	0.699547	−	1.21165i	0.968624	−	0.248533i	$-0.0799483\pi$
$240$		0			0
$241$	−1.94916	−	3.37604i	−0.125556	−	0.217470i	0.796394	−	0.604778i	$-0.206738\pi$
$241$	−1.94916	−	3.37604i	−0.125556	−	0.217470i	−0.921950	+	0.387308i	$0.873405\pi$
$242$	−16.1060			−1.03533
$243$	8.18729	+	13.2653i	0.525215	+	0.850970i
$244$	0.430437			0.0275559
$245$		0			0
$246$	14.0994	+	2.91046i	0.898942	+	0.185564i
$247$	8.66600	−	15.0100i	0.551405	−	0.955061i
$248$	3.57518	−	6.19240i	0.227024	−	0.393218i
$249$	−2.49577	−	7.53039i	−0.158163	−	0.477219i
$250$		0			0
$251$	−30.1033			−1.90010			−0.950052	−	0.312092i	$-0.898970\pi$
$251$	−30.1033			−1.90010			−0.950052	+	0.312092i	$0.898970\pi$
$252$	1.81552	+	0.782897i	0.114367	+	0.0493179i
$253$	2.26321			0.142287
$254$	1.21754	+	2.10883i	0.0763950	+	0.132320i
$255$		0			0
$256$	−2.03131	+	3.51832i	−0.126957	+	0.219895i
$257$	8.20707	−	14.2151i	0.511943	−	0.886711i	−0.487961	−	0.872865i	$-0.662259\pi$
$257$	8.20707	−	14.2151i	0.511943	−	0.886711i	0.999904	−	0.0138459i	$-0.00440744\pi$
$258$	15.3898	−	17.2953i	0.958125	−	1.07676i
$259$	4.39851	+	7.61845i	0.273310	+	0.473388i
$260$		0			0
$261$	−1.47187	−	12.5805i	−0.0911067	−	0.778712i
$262$	−19.4141			−1.19941
$263$	−12.9036	−	22.3497i	−0.795670	−	1.37814i	−0.922413	−	0.386206i	$-0.873786\pi$
$263$	−12.9036	−	22.3497i	−0.795670	−	1.37814i	0.126743	−	0.991936i	$-0.459548\pi$
$264$	0.382269	+	1.15341i	0.0235270	+	0.0709872i
$265$		0			0
$266$	−12.1006	+	20.9588i	−0.741934	+	1.28507i
$267$	12.1755	+	2.51332i	0.745127	+	0.153813i
$268$	−0.961978	−	1.66619i	−0.0587621	−	0.101779i
$269$	−12.5206			−0.763392			−0.381696	−	0.924288i	$-0.624660\pi$
$269$	−12.5206			−0.763392			−0.381696	+	0.924288i	$0.624660\pi$
$270$		0			0
$271$	19.6462			1.19342			0.596710	−	0.802457i	$-0.296474\pi$
$271$	19.6462			1.19342			0.596710	+	0.802457i	$0.296474\pi$
$272$	7.02899	+	12.1746i	0.426195	+	0.738191i
$273$	−26.7470	−	5.52125i	−1.61880	−	0.334161i
$274$	−14.9483	+	25.8911i	−0.903057	+	1.56414i
$275$		0			0
$276$	−0.807745	−	2.43718i	−0.0486205	−	0.146701i
$277$	10.4150	+	18.0394i	0.625779	+	1.08388i	0.988390	+	0.151941i	$0.0485523\pi$
$277$	10.4150	+	18.0394i	0.625779	+	1.08388i	−0.362610	+	0.931941i	$0.618114\pi$
$278$	4.52112			0.271159
$279$	−6.38321	+	4.75324i	−0.382153	+	0.284569i
$280$		0			0
$281$	−2.36221	−	4.09146i	−0.140917	−	0.244076i	0.786925	−	0.617049i	$-0.211672\pi$
$281$	−2.36221	−	4.09146i	−0.140917	−	0.244076i	−0.927842	+	0.372973i	$0.878339\pi$
$282$	2.42380	−	2.72390i	0.144335	−	0.162206i
$283$	−11.5762	+	20.0506i	−0.688136	+	1.19189i	0.284304	+	0.958734i	$0.408237\pi$
$283$	−11.5762	+	20.0506i	−0.688136	+	1.19189i	−0.972440	+	0.233152i	$0.925096\pi$
$284$	0.714441	−	1.23745i	0.0423943	−	0.0734291i
$285$		0			0
$286$	0.782020	+	1.35450i	0.0462418	+	0.0800932i
$287$	21.8105			1.28743
$288$	2.31430	−	1.72333i	0.136371	−	0.101548i
$289$	−6.37059			−0.374740
$290$		0			0
$291$	−1.69742	−	5.12158i	−0.0995048	−	0.300232i
$292$	−0.0343999	+	0.0595824i	−0.00201310	+	0.00348679i
$293$	8.43963	−	14.6179i	0.493049	−	0.853985i	−0.506919	−	0.861993i	$-0.669216\pi$
$293$	8.43963	−	14.6179i	0.493049	−	0.853985i	0.999968	+	0.00800832i	$0.00254915\pi$
$294$	19.8541	+	4.09839i	1.15792	+	0.239023i
$295$		0			0
$296$	6.13350			0.356503
$297$	0.117647	−	1.34732i	0.00682657	−	0.0781792i
$298$	5.98380			0.346632
$299$	17.7333	+	30.7150i	1.02554	+	1.77630i
$300$		0			0
$301$	17.5366	−	30.3743i	1.01079	−	1.75074i
$302$	10.0328	−	17.3773i	0.577321	−	0.999949i
$303$	−2.09553	−	6.32277i	−0.120385	−	0.363233i
$304$	9.16123	+	15.8677i	0.525433	+	0.910076i
$305$		0			0
$306$	−1.67446	−	14.3120i	−0.0957225	−	0.818165i
$307$	−22.7177			−1.29657			−0.648285	−	0.761398i	$-0.724513\pi$
$307$	−22.7177			−1.29657			−0.648285	+	0.761398i	$0.724513\pi$
$308$	−0.0857671	−	0.148553i	−0.00488703	−	0.00846459i
$309$	4.84364	−	5.44337i	0.275545	−	0.309663i
$310$		0			0
$311$	−15.7968	+	27.3608i	−0.895754	+	1.55149i	−0.0628843	+	0.998021i	$0.520030\pi$
$311$	−15.7968	+	27.3608i	−0.895754	+	1.55149i	−0.832869	+	0.553470i	$0.813303\pi$
$312$	−12.6581	+	14.2254i	−0.716626	+	0.805357i
$313$	15.2498	+	26.4134i	0.861970	+	1.49298i	0.870024	+	0.493009i	$0.164103\pi$
$313$	15.2498	+	26.4134i	0.861970	+	1.49298i	−0.00805392	+	0.999968i	$0.502564\pi$
$314$	3.03875			0.171487
$315$		0			0
$316$	−0.518682			−0.0291781
$317$	−11.0445	−	19.1296i	−0.620320	−	1.07443i	−0.989426	−	0.145039i	$-0.953669\pi$
$317$	−11.0445	−	19.1296i	−0.620320	−	1.07443i	0.369106	−	0.929387i	$-0.379664\pi$
$318$	−9.13686	−	27.5683i	−0.512369	−	1.54595i
$319$	−0.549459	+	0.951691i	−0.0307638	+	0.0532845i
$320$		0			0
$321$	−2.75910	−	0.569547i	−0.153998	−	0.0317890i
$322$	−24.7615	−	42.8882i	−1.37991	−	2.39007i
$323$	13.8538			0.770849
$324$	−1.49287	+	0.354170i	−0.0829374	+	0.0196761i
$325$		0			0
$326$	2.58206	+	4.47226i	0.143007	+	0.247696i
$327$	−21.8857	−	4.51776i	−1.21028	−	0.249833i
$328$	7.60339	−	13.1695i	0.419827	−	0.727162i
$329$	2.76191	−	4.78377i	0.152269	−	0.263738i
$330$		0			0
$331$	14.8024	+	25.6385i	0.813612	+	1.40922i	0.910321	+	0.413904i	$0.135835\pi$
$331$	14.8024	+	25.6385i	0.813612	+	1.40922i	−0.0967089	+	0.995313i	$0.530832\pi$
$332$	0.780834			0.0428538
$333$	−6.26874	−	2.70324i	−0.343525	−	0.148137i
$334$	30.2531			1.65538
$335$		0			0
$336$	19.1925	−	21.5689i	1.04704	−	1.17668i
$337$	−6.26553	+	10.8522i	−0.341305	+	0.591158i	−0.984675	−	0.174397i	$-0.944202\pi$
$337$	−6.26553	+	10.8522i	−0.341305	+	0.591158i	0.643370	+	0.765555i	$0.277536\pi$
$338$	−2.67886	+	4.63992i	−0.145711	+	0.252379i
$339$	−1.53028	+	1.71976i	−0.0831136	+	0.0934045i
$340$		0			0
$341$	0.690479			0.0373915
$342$	−2.18241	−	18.6536i	−0.118011	−	1.00867i
$343$	3.65180			0.197179
$344$	−12.2269	−	21.1777i	−0.659232	−	1.14182i
$345$		0			0
$346$	5.71017	−	9.89030i	0.306980	−	0.531706i
$347$	8.54872	−	14.8068i	0.458919	−	0.794872i	−0.539985	−	0.841675i	$-0.681570\pi$
$347$	8.54872	−	14.8068i	0.458919	−	0.794872i	0.998904	+	0.0468031i	$0.0149033\pi$
$348$	1.22095	+	0.252035i	0.0654498	+	0.0135105i
$349$	9.20231	+	15.9389i	0.492588	+	0.853188i	0.999964	−	0.00853709i	$-0.00271747\pi$
$349$	9.20231	+	15.9389i	0.492588	+	0.853188i	−0.507375	+	0.861725i	$0.669384\pi$
$350$		0			0
$351$	19.2069	−	8.96024i	1.02519	−	0.478262i
$352$	−0.250340			−0.0133432
$353$	15.8594	+	27.4693i	0.844110	+	1.46204i	0.886391	+	0.462936i	$0.153204\pi$
$353$	15.8594	+	27.4693i	0.844110	+	1.46204i	−0.0422810	+	0.999106i	$0.513462\pi$
$354$	−17.8039	−	3.67517i	−0.946267	−	0.195333i
$355$		0			0
$356$	−0.611825	+	1.05971i	−0.0324267	+	0.0561646i
$357$	−6.86774	−	20.7218i	−0.363479	−	1.09671i
$358$	7.92844	+	13.7325i	0.419031	+	0.725783i
$359$	−11.4533			−0.604483			−0.302241	−	0.953231i	$-0.597735\pi$
$359$	−11.4533			−0.604483			−0.302241	+	0.953231i	$0.597735\pi$
$360$		0			0
$361$	−0.943580			−0.0496621
$362$	5.77937	+	10.0102i	0.303757	+	0.526122i
$363$	12.5873	−	14.1458i	0.660660	−	0.742461i
$364$	1.34405	−	2.32797i	0.0704475	−	0.122019i
$365$		0			0
$366$	−4.28291	+	4.81321i	−0.223871	+	0.251590i
$367$	−1.24619	−	2.15846i	−0.0650506	−	0.112671i	0.831666	−	0.555276i	$-0.187388\pi$
$367$	−1.24619	−	2.15846i	−0.0650506	−	0.112671i	−0.896716	+	0.442606i	$0.854054\pi$
$368$	−37.4934			−1.95448
$369$	−13.5753	+	10.1088i	−0.706700	+	0.526242i
$370$		0			0
$371$	−21.9996	−	38.1045i	−1.14216	−	1.97829i
$372$	−0.246434	−	0.743556i	−0.0127770	−	0.0385516i
$373$	7.51868	−	13.0227i	0.389303	−	0.674292i	−0.603053	−	0.797701i	$-0.706049\pi$
$373$	7.51868	−	13.0227i	0.389303	−	0.674292i	0.992356	+	0.123409i	$0.0393827\pi$
$374$	−0.625086	+	1.08268i	−0.0323224	+	0.0559841i
$375$		0			0
$376$	−1.92567	−	3.33536i	−0.0993088	−	0.172008i
$377$	−17.2211			−0.886932
$378$	−26.8191	+	12.5114i	−1.37943	+	0.643518i
$379$	6.27273			0.322208			0.161104	−	0.986937i	$-0.448495\pi$
$379$	6.27273			0.322208			0.161104	+	0.986937i	$0.448495\pi$
$380$		0			0
$381$	−2.80371	−	0.578757i	−0.143639	−	0.0296506i
$382$	4.22275	−	7.31402i	0.216055	−	0.374218i
$383$	11.0944	−	19.2161i	0.566897	−	0.981894i	−0.429973	−	0.902842i	$-0.641477\pi$
$383$	11.0944	−	19.2161i	0.566897	−	0.981894i	0.996870	−	0.0790528i	$-0.0251896\pi$
$384$	−6.83362	−	20.6188i	−0.348727	−	1.05220i
$385$		0			0
$386$	−12.4967			−0.636065
$387$	3.16282	+	27.0335i	0.160775	+	1.37419i
$388$	0.531061			0.0269605
$389$	15.0461	+	26.0606i	0.762869	+	1.32133i	0.941366	+	0.337387i	$0.109543\pi$
$389$	15.0461	+	26.0606i	0.762869	+	1.32133i	−0.178498	+	0.983940i	$0.557124\pi$
$390$		0			0
$391$	−14.1746	+	24.5512i	−0.716842	+	1.24161i
$392$	10.7068	−	18.5447i	0.540774	−	0.936649i
$393$	15.1727	−	17.0513i	0.765360	−	0.860125i
$394$	−7.82781	−	13.5582i	−0.394359	−	0.683050i
$395$		0			0
$396$	0.122235	+	0.0527107i	0.00614253	+	0.00264881i
$397$	29.2313			1.46708			0.733538	−	0.679648i	$-0.237868\pi$
$397$	29.2313			1.46708			0.733538	+	0.679648i	$0.237868\pi$
$398$	13.6854	+	23.7038i	0.685986	+	1.18816i
$399$	−8.95107	−	27.0077i	−0.448114	−	1.35208i
$400$		0			0
$401$	−12.1171	+	20.9874i	−0.605098	+	1.04806i	0.386938	+	0.922106i	$0.373533\pi$
$401$	−12.1171	+	20.9874i	−0.605098	+	1.04806i	−0.992036	+	0.125954i	$0.959801\pi$
$402$	28.2034	+	5.82189i	1.40666	+	0.290369i
$403$	5.41024	+	9.37080i	0.269503	+	0.466793i
$404$	0.655614			0.0326180
$405$		0			0
$406$	24.0463			1.19340
$407$	0.296142	+	0.512934i	0.0146792	+	0.0254252i
$408$	−14.9063	−	3.07703i	−0.737971	−	0.152336i
$409$	−1.16995	+	2.02642i	−0.0578504	+	0.100200i	−0.893500	−	0.449063i	$-0.851758\pi$
$409$	−1.16995	+	2.02642i	−0.0578504	+	0.100200i	0.835650	+	0.549263i	$0.185091\pi$
$410$		0			0
$411$	−11.0576	−	33.3636i	−0.545429	−	1.64570i
$412$	0.358584	+	0.621086i	0.0176662	+	0.0305987i
$413$	−27.5411			−1.35521
$414$	35.2900	+	15.2179i	1.73441	+	0.747921i
$415$		0			0
$416$	−1.96153	−	3.39748i	−0.0961721	−	0.166575i
$417$	−3.53338	+	3.97087i	−0.173030	+	0.194454i
$418$	−0.814706	+	1.41111i	−0.0398486	+	0.0690197i
$419$	−11.4212	+	19.7821i	−0.557964	+	0.966421i	0.439703	+	0.898143i	$0.355084\pi$
$419$	−11.4212	+	19.7821i	−0.557964	+	0.966421i	−0.997666	+	0.0682778i	$0.978250\pi$
$420$		0			0
$421$	−5.93792	−	10.2848i	−0.289396	−	0.501249i	0.684269	−	0.729229i	$-0.260121\pi$
$421$	−5.93792	−	10.2848i	−0.289396	−	0.501249i	−0.973666	+	0.227980i	$0.926788\pi$
$422$	15.4004			0.749679
$423$	0.498126	+	4.25761i	0.0242197	+	0.207012i
$424$	−30.6773			−1.48982
$425$		0			0
$426$	6.72853	+	20.3018i	0.325998	+	0.983623i
$427$	−4.88036	+	8.45303i	−0.236177	+	0.409071i
$428$	0.138646	−	0.240142i	0.00670172	−	0.0116077i
$429$	−1.80082	−	0.371734i	−0.0869443	−	0.0179475i
$430$		0			0
$431$	8.86916			0.427212			0.213606	−	0.976920i	$-0.431479\pi$
$431$	8.86916			0.427212			0.213606	+	0.976920i	$0.431479\pi$
$432$	−1.94900	+	22.3203i	−0.0937713	+	1.07389i
$433$	9.37059			0.450322			0.225161	−	0.974322i	$-0.427709\pi$
$433$	9.37059			0.450322			0.225161	+	0.974322i	$0.427709\pi$
$434$	−7.55446	−	13.0847i	−0.362626	−	0.628086i
$435$		0			0
$436$	1.09977	−	1.90486i	0.0526695	−	0.0912262i
$437$	−18.4745	+	31.9988i	−0.883756	+	1.53071i
$438$	−0.323974	−	0.977517i	−0.0154801	−	0.0467075i
$439$	−9.71155	−	16.8209i	−0.463507	−	0.802817i	0.535626	−	0.844455i	$-0.320076\pi$
$439$	−9.71155	−	16.8209i	−0.463507	−	0.802817i	−0.999133	+	0.0416380i	$0.986742\pi$
$440$		0			0
$441$	−19.1161	+	14.2348i	−0.910292	+	0.677846i
$442$	−19.5914			−0.931868
$443$	−5.43963	−	9.42172i	−0.258445	−	0.447639i	0.707381	−	0.706833i	$-0.249877\pi$
$443$	−5.43963	−	9.42172i	−0.258445	−	0.447639i	−0.965825	+	0.259193i	$0.916543\pi$
$444$	0.446669	−	0.501974i	0.0211980	−	0.0238226i
$445$		0			0
$446$	−2.89583	+	5.01572i	−0.137121	+	0.237501i
$447$	−4.67650	+	5.25554i	−0.221191	+	0.248578i
$448$	−13.9301	−	24.1276i	−0.658136	−	1.13992i
$449$	1.34014			0.0632451			0.0316225	−	0.999500i	$-0.489933\pi$
$449$	1.34014			0.0632451			0.0316225	+	0.999500i	$0.489933\pi$
$450$		0			0
$451$	1.46845			0.0691467
$452$	−0.113290	−	0.196224i	−0.00532871	−	0.00922959i
$453$	7.42146	+	22.3925i	0.348691	+	1.05209i
$454$	−3.55894	+	6.16426i	−0.167029	+	0.289303i
$455$		0			0
$456$	−19.4281	−	4.01045i	−0.909804	−	0.187806i
$457$	−10.0556	−	17.4169i	−0.470383	−	0.814728i	0.529043	−	0.848595i	$-0.322551\pi$
$457$	−10.0556	−	17.4169i	−0.470383	−	0.814728i	−0.999426	+	0.0338671i	$0.989218\pi$
$458$	−27.7752			−1.29785
$459$	13.8788	+	9.71457i	0.647807	+	0.453437i
$460$		0			0
$461$	16.8766	+	29.2312i	0.786024	+	1.36143i	0.928386	+	0.371618i	$0.121197\pi$
$461$	16.8766	+	29.2312i	0.786024	+	1.36143i	−0.142362	+	0.989815i	$0.545470\pi$
$462$	2.51453	+	0.519062i	0.116987	+	0.0241490i
$463$	2.62268	−	4.54262i	0.121886	−	0.211114i	−0.798625	−	0.601829i	$-0.794439\pi$
$463$	2.62268	−	4.54262i	0.121886	−	0.211114i	0.920512	+	0.390715i	$0.127772\pi$
$464$	9.10262	−	15.7662i	0.422578	−	0.731927i
$465$		0			0
$466$	8.76744	+	15.1856i	0.406144	+	0.703462i
$467$	14.2120			0.657652			0.328826	−	0.944390i	$-0.393347\pi$
$467$	14.2120			0.657652			0.328826	+	0.944390i	$0.393347\pi$
$468$	0.242408	+	2.07192i	0.0112053	+	0.0957745i
$469$	43.6282			2.01456
$470$		0			0
$471$	−2.37486	+	2.66891i	−0.109428	+	0.122977i
$472$	−9.60115	+	16.6297i	−0.441929	+	0.765443i
$473$	1.18070	−	2.04503i	0.0542887	−	0.0940307i
$474$	5.16095	−	5.79997i	0.237050	−	0.266401i
$475$		0			0
$476$	2.14866			0.0984837
$477$	31.3538	+	13.5205i	1.43559	+	0.619063i
$478$	−31.8657			−1.45750
$479$	−10.2417	−	17.7391i	−0.467954	−	0.810519i	0.531376	−	0.847136i	$-0.321675\pi$
$479$	−10.2417	−	17.7391i	−0.467954	−	0.810519i	−0.999329	+	0.0366168i	$0.988342\pi$
$480$		0			0
$481$	−4.64084	+	8.03817i	−0.211604	+	0.366509i
$482$	−2.87161	+	4.97377i	−0.130798	+	0.226549i
$483$	57.0203	+	11.7704i	2.59451	+	0.535572i
$484$	0.931859	+	1.61403i	0.0423572	+	0.0733649i
$485$		0			0
$486$	10.8939	−	20.2175i	0.494158	−	0.917087i
$487$	31.3554			1.42085			0.710425	−	0.703772i	$-0.248503\pi$
$487$	31.3554			1.42085			0.710425	+	0.703772i	$0.248503\pi$
$488$	3.40271	+	5.89366i	0.154033	+	0.266793i
$489$	−5.94591	−	1.22738i	−0.268883	−	0.0555042i
$490$		0			0
$491$	5.19604	−	8.99980i	0.234494	−	0.406155i	−0.724632	−	0.689136i	$-0.757990\pi$
$491$	5.19604	−	8.99980i	0.234494	−	0.406155i	0.959125	+	0.282981i	$0.0913234\pi$
$492$	−0.524094	−	1.58133i	−0.0236280	−	0.0712919i
$493$	−6.88260	−	11.9210i	−0.309977	−	0.536896i
$494$	−25.5345			−1.14885
$495$		0			0
$496$	−11.4388			−0.513618
$497$	16.2009	+	28.0607i	0.726709	+	1.25870i
$498$	−7.76940	+	8.73138i	−0.348155	+	0.391263i
$499$	1.91285	−	3.31316i	0.0856310	−	0.148317i	−0.820029	−	0.572322i	$-0.806043\pi$
$499$	1.91285	−	3.31316i	0.0856310	−	0.148317i	0.905660	+	0.424005i	$0.139376\pi$
$500$		0			0
$501$	−23.6436	+	26.5711i	−1.05632	+	1.18711i
$502$	22.1749	+	38.4081i	0.989715	+	1.71424i
$503$	1.00236			0.0446931			0.0223466	−	0.999750i	$-0.492886\pi$
$503$	1.00236			0.0446931			0.0223466	+	0.999750i	$0.492886\pi$
$504$	3.63246	+	31.0475i	0.161802	+	1.38297i
$505$		0			0
$506$	−1.66714	−	2.88757i	−0.0741134	−	0.128368i
$507$	−1.98161	−	5.97905i	−0.0880065	−	0.265539i
$508$	0.140888	−	0.244026i	0.00625090	−	0.0108269i
$509$	−2.28161	+	3.95187i	−0.101131	+	0.175163i	−0.912151	−	0.409855i	$-0.865579\pi$
$509$	−2.28161	+	3.95187i	−0.101131	+	0.175163i	0.811020	+	0.585018i	$0.198913\pi$
$510$		0			0
$511$	−0.780062	−	1.35111i	−0.0345079	−	0.0597695i
$512$	−19.0969			−0.843971
$513$	18.0889	+	12.6615i	0.798646	+	0.559019i
$514$	−24.1822			−1.06663
$515$		0			0
$516$	−2.62363	−	0.541583i	−0.115499	−	0.0238419i
$517$	0.185953	−	0.322080i	0.00817822	−	0.0141651i
$518$	6.48013	−	11.2239i	0.284721	−	0.493151i
$519$	4.22394	+	12.7447i	0.185410	+	0.559432i
$520$		0			0
$521$	39.3708			1.72486			0.862432	−	0.506173i	$-0.168940\pi$
$521$	39.3708			1.72486			0.862432	+	0.506173i	$0.168940\pi$
$522$	−14.9669	+	11.1451i	−0.655084	+	0.487806i
$523$	−10.3998			−0.454749			−0.227375	−	0.973807i	$-0.573014\pi$
$523$	−10.3998			−0.454749			−0.227375	+	0.973807i	$0.573014\pi$
$524$	1.12326	+	1.94555i	0.0490699	+	0.0849916i
$525$		0			0
$526$	−19.0103	+	32.9268i	−0.828888	+	1.43568i
$527$	−4.32452	+	7.49029i	−0.188379	+	0.326282i
$528$	1.29219	−	1.45219i	0.0562354	−	0.0631984i
$529$	−26.3046	−	45.5608i	−1.14368	−	1.98091i
$530$		0			0
$531$	17.1421	−	12.7648i	0.743904	−	0.553946i
$532$	2.80046			0.121415
$533$	11.5060	+	19.9290i	0.498381	+	0.863222i
$534$	−5.76210	−	17.3858i	−0.249351	−	0.752357i
$535$		0			0
$536$	15.2093	−	26.3433i	0.656942	−	1.13786i
$537$	−18.2574	−	3.76879i	−0.787866	−	0.162635i
$538$	9.22298	+	15.9747i	0.397631	+	0.688717i
$539$	2.06781			0.0890670
$540$		0			0
$541$	13.7093			0.589408			0.294704	−	0.955589i	$-0.404779\pi$
$541$	13.7093			0.589408			0.294704	+	0.955589i	$0.404779\pi$
$542$	−14.4719	−	25.0661i	−0.621622	−	1.07668i
$543$	−13.3086	−	2.74723i	−0.571126	−	0.117895i
$544$	1.56790	−	2.71568i	0.0672230	−	0.116434i
$545$		0			0
$546$	12.6581	+	38.1930i	0.541718	+	1.63451i
$547$	−11.3924	−	19.7322i	−0.487102	−	0.843686i	0.512788	−	0.858515i	$-0.328613\pi$
$547$	−11.3924	−	19.7322i	−0.487102	−	0.843686i	−0.999890	+	0.0148294i	$0.995279\pi$
$548$	3.45950			0.147783
$549$	−0.880201	−	7.52330i	−0.0375661	−	0.321087i
$550$		0			0
$551$	−8.97044	−	15.5373i	−0.382154	−	0.661910i
$552$	26.9851	−	30.3263i	1.14856	−	1.29077i
$553$	5.88089	−	10.1860i	0.250081	−	0.433153i
$554$	15.3440	−	26.5766i	0.651905	−	1.12913i
$555$		0			0
$556$	−0.261583	−	0.453075i	−0.0110936	−	0.0192146i
$557$	−18.2341			−0.772605			−0.386303	−	0.922372i	$-0.626248\pi$
$557$	−18.2341			−0.772605			−0.386303	+	0.922372i	$0.626248\pi$
$558$	10.7666	+	4.64282i	0.455786	+	0.196546i
$559$	37.0054			1.56516
$560$		0			0
$561$	−0.462390	−	1.39515i	−0.0195221	−	0.0589034i
$562$	−3.48013	+	6.02776i	−0.146800	+	0.254266i
$563$	−12.0556	+	20.8809i	−0.508083	+	0.880025i	0.491873	+	0.870667i	$0.336312\pi$
$563$	−12.0556	+	20.8809i	−0.508083	+	0.880025i	−0.999956	+	0.00935862i	$0.997021\pi$
$564$	−0.413206	−	0.0852961i	−0.0173991	−	0.00359161i
$565$		0			0
$566$	34.1095			1.43373
$567$	9.97113	−	33.3330i	0.418748	−	1.39986i
$568$	22.5913			0.947910
$569$	16.0024	+	27.7170i	0.670857	+	1.16196i	0.977661	+	0.210186i	$0.0674069\pi$
$569$	16.0024	+	27.7170i	0.670857	+	1.16196i	−0.306804	+	0.951773i	$0.599260\pi$
$570$		0			0
$571$	9.89042	−	17.1307i	0.413901	−	0.716898i	−0.581411	−	0.813610i	$-0.697499\pi$
$571$	9.89042	−	17.1307i	0.413901	−	0.716898i	0.995312	+	0.0967121i	$0.0308326\pi$
$572$	0.0904921	−	0.156737i	0.00378367	−	0.00655350i
$573$	3.12366	+	9.42491i	0.130493	+	0.393731i
$574$	−16.0662	−	27.8274i	−0.670589	−	1.16150i
$575$		0			0
$576$	19.8531	+	8.56117i	0.827213	+	0.356715i
$577$	−35.4119			−1.47422			−0.737108	−	0.675775i	$-0.763809\pi$
$577$	−35.4119			−1.47422			−0.737108	+	0.675775i	$0.763809\pi$
$578$	4.69275	+	8.12808i	0.195193	+	0.338084i
$579$	9.76650	−	10.9758i	0.405882	−	0.456137i
$580$		0			0
$581$	−8.85321	+	15.3342i	−0.367293	+	0.636170i
$582$	−5.28413	+	5.93840i	−0.219034	+	0.246154i
$583$	−1.48119	−	2.56549i	−0.0613445	−	0.106252i
$584$	−1.08776			−0.0450117
$585$		0			0
$586$	−24.8675			−1.02726
$587$	16.1925	+	28.0463i	0.668338	+	1.15759i	0.978369	+	0.206868i	$0.0663272\pi$
$587$	16.1925	+	28.0463i	0.668338	+	1.15759i	−0.310031	+	0.950726i	$0.600339\pi$
$588$	−0.738008	−	2.22676i	−0.0304349	−	0.0918302i
$589$	−5.63636	+	9.76247i	−0.232242	+	0.402255i
$590$		0			0
$591$	18.0257	+	3.72095i	0.741478	+	0.153060i
$592$	−4.90605	−	8.49752i	−0.201637	−	0.349246i
$593$	29.2504			1.20117			0.600585	−	0.799561i	$-0.294934\pi$
$593$	29.2504			1.20117			0.600585	+	0.799561i	$0.294934\pi$
$594$	−1.80567	+	0.842367i	−0.0740876	+	0.0345627i
$595$		0			0
$596$	−0.346210	−	0.599654i	−0.0141813	−	0.0245628i
$597$	−31.5144	−	6.50535i	−1.28980	−	0.266246i
$598$	26.1257	−	45.2510i	1.06836	−	1.85045i
$599$	−2.03081	+	3.51747i	−0.0829767	+	0.143720i	−0.904527	−	0.426416i	$-0.859776\pi$
$599$	−2.03081	+	3.51747i	−0.0829767	+	0.143720i	0.821551	+	0.570136i	$0.193109\pi$
$600$		0			0
$601$	−23.4538	−	40.6232i	−0.956700	−	1.65705i	−0.730429	−	0.682989i	$-0.760680\pi$
$601$	−23.4538	−	40.6232i	−0.956700	−	1.65705i	−0.226271	−	0.974064i	$-0.572653\pi$
$602$	−51.6717			−2.10598
$603$	−27.1550	+	20.2209i	−1.10584	+	0.823459i
$604$	−2.32190			−0.0944768
$605$		0			0
$606$	−6.52344	+	7.33116i	−0.264997	+	0.297808i
$607$	20.4733	−	35.4608i	0.830987	−	1.43931i	−0.0662702	−	0.997802i	$-0.521110\pi$
$607$	20.4733	−	35.4608i	0.830987	−	1.43931i	0.897257	−	0.441509i	$-0.145557\pi$
$608$	2.04352	−	3.53948i	0.0828756	−	0.143545i
$609$	−18.7928	+	21.1197i	−0.761524	+	0.855814i
$610$		0			0
$611$	5.82813			0.235781
$612$	−1.33737	+	0.995867i	−0.0540599	+	0.0402555i
$613$	−33.3827			−1.34831			−0.674157	−	0.738588i	$-0.735493\pi$
$613$	−33.3827			−1.34831			−0.674157	+	0.738588i	$0.735493\pi$
$614$	16.7345	+	28.9850i	0.675350	+	1.16974i
$615$		0			0
$616$	1.35602	−	2.34869i	0.0546355	−	0.0946314i
$617$	−1.12440	+	1.94752i	−0.0452666	+	0.0784040i	−0.887771	−	0.460285i	$-0.847747\pi$
$617$	−1.12440	+	1.94752i	−0.0452666	+	0.0784040i	0.842504	+	0.538689i	$0.181080\pi$
$618$	−10.5130	−	2.17015i	−0.422896	−	0.0872963i
$619$	17.1467	+	29.6990i	0.689184	+	1.19370i	0.972102	+	0.234558i	$0.0753642\pi$
$619$	17.1467	+	29.6990i	0.689184	+	1.19370i	−0.282918	+	0.959144i	$0.591302\pi$
$620$		0			0
$621$	−40.9459	+	19.1018i	−1.64310	+	0.766527i
$622$	46.5454			1.86630
$623$	−13.8739	−	24.0303i	−0.555847	−	0.962756i
$624$	29.8333	+	6.15833i	1.19429	+	0.246531i
$625$		0			0
$626$	22.4669	−	38.9137i	0.897956	−	1.55531i
$627$	−0.602656	−	1.81837i	−0.0240678	−	0.0726188i
$628$	−0.175816	−	0.304522i	−0.00701581	−	0.0121517i
$629$	−7.41904			−0.295817
$630$		0			0
$631$	−18.7552			−0.746633			−0.373316	−	0.927704i	$-0.621779\pi$
$631$	−18.7552			−0.746633			−0.373316	+	0.927704i	$0.621779\pi$
$632$	−4.10030	−	7.10193i	−0.163101	−	0.282499i
$633$	−12.0358	+	13.5261i	−0.478381	+	0.537613i
$634$	−16.2713	+	28.1828i	−0.646218	+	1.11928i
$635$		0			0
$636$	−2.23406	+	2.51068i	−0.0885862	+	0.0995548i
$637$	16.2023	+	28.0632i	0.641959	+	1.11191i
$638$	1.61899			0.0640963
$639$	−23.0894	−	9.95674i	−0.913403	−	0.393883i
$640$		0			0
$641$	−10.3175	−	17.8704i	−0.407517	−	0.705840i	0.587094	−	0.809519i	$-0.300272\pi$
$641$	−10.3175	−	17.8704i	−0.407517	−	0.705840i	−0.994611	+	0.103679i	$0.966939\pi$
$642$	1.30576	+	3.93981i	0.0515340	+	0.155492i
$643$	−13.5970	+	23.5506i	−0.536212	+	0.928746i	0.462892	+	0.886415i	$0.346812\pi$
$643$	−13.5970	+	23.5506i	−0.536212	+	0.928746i	−0.999104	+	0.0423312i	$0.986522\pi$
$644$	−2.86530	+	4.96285i	−0.112909	+	0.195564i
$645$		0			0
$646$	−10.2051	−	17.6758i	−0.401515	−	0.695445i
$647$	16.7316			0.657787			0.328893	−	0.944367i	$-0.393324\pi$
$647$	16.7316			0.657787			0.328893	+	0.944367i	$0.393324\pi$
$648$	−16.6509	−	17.6410i	−0.654109	−	0.693004i
$649$	−1.85428			−0.0727869
$650$		0			0
$651$	17.3962	+	3.59102i	0.681812	+	0.140743i
$652$	0.298785	−	0.517511i	0.0117013	−	0.0202673i
$653$	22.8666	−	39.6060i	0.894837	−	1.54990i	0.0608319	−	0.998148i	$-0.480625\pi$
$653$	22.8666	−	39.6060i	0.894837	−	1.54990i	0.834006	−	0.551756i	$-0.186042\pi$
$654$	10.3575	+	31.2514i	0.405011	+	1.22203i
$655$		0			0
$656$	−24.3271			−0.949814
$657$	1.11174	+	0.479411i	0.0433731	+	0.0187036i
$658$	−8.13799			−0.317252
$659$	−9.30543	−	16.1175i	−0.362488	−	0.627848i	0.625882	−	0.779918i	$-0.284739\pi$
$659$	−9.30543	−	16.1175i	−0.362488	−	0.627848i	−0.988370	+	0.152070i	$0.951406\pi$
$660$		0			0
$661$	−8.39799	+	14.5457i	−0.326644	+	0.565764i	−0.981844	−	0.189692i	$-0.939251\pi$
$661$	−8.39799	+	14.5457i	−0.326644	+	0.565764i	0.655200	+	0.755456i	$0.272584\pi$
$662$	21.8077	−	37.7720i	0.847579	−	1.46805i
$663$	15.3112	−	17.2070i	0.594638	−	0.668264i
$664$	6.17267	+	10.6914i	0.239546	+	0.414906i
$665$		0			0
$666$	1.16873	+	9.98942i	0.0452873	+	0.387082i
$667$	36.7126			1.42152
$668$	−1.75038	−	3.03175i	−0.0677243	−	0.117302i
$669$	−2.14211	−	6.46331i	−0.0828187	−	0.249886i
$670$		0			0
$671$	−0.328584	+	0.569124i	−0.0126848	+	0.0219708i
$672$	−6.30718	−	1.30196i	−0.243305	−	0.0502242i
$673$	−24.9740	−	43.2562i	−0.962676	−	1.66740i	−0.715733	−	0.698374i	$-0.753907\pi$
$673$	−24.9740	−	43.2562i	−0.962676	−	1.66740i	−0.246944	−	0.969030i	$-0.579426\pi$
$674$	18.4614			0.711108
$675$		0			0
$676$	0.619973			0.0238451
$677$	−5.41553	−	9.37998i	−0.208136	−	0.360502i	0.742991	−	0.669301i	$-0.233406\pi$
$677$	−5.41553	−	9.37998i	−0.208136	−	0.360502i	−0.951127	+	0.308799i	$0.900073\pi$
$678$	3.32145	+	0.685630i	0.127559	+	0.0263315i
$679$	−6.02125	+	10.4291i	−0.231074	+	0.400232i
$680$		0			0
$681$	−2.63262	−	7.94333i	−0.100882	−	0.304389i
$682$	−0.508625	−	0.880965i	−0.0194763	−	0.0337339i
$683$	0.429870			0.0164485			0.00822426	−	0.999966i	$-0.497382\pi$
$683$	0.429870			0.0164485			0.00822426	+	0.999966i	$0.497382\pi$
$684$	−1.74306	+	1.29796i	−0.0666476	+	0.0496289i
$685$		0			0
$686$	−2.69001	−	4.65924i	−0.102705	−	0.177891i
$687$	21.7071	−	24.3948i	0.828176	−	0.930719i
$688$	−19.5601	+	33.8791i	−0.745721	+	1.29163i
$689$	23.2116	−	40.2037i	0.884293	−	1.53164i
$690$		0			0
$691$	−17.3518	−	30.0542i	−0.660093	−	1.14331i	−0.980591	−	0.196065i	$-0.937184\pi$
$691$	−17.3518	−	30.0542i	−0.660093	−	1.14331i	0.320498	−	0.947249i	$-0.396150\pi$
$692$	−1.32151			−0.0502364
$693$	−2.42106	+	1.80284i	−0.0919686	+	0.0684841i
$694$	−25.1889			−0.956157
$695$		0			0
$696$	6.20097	+	18.7100i	0.235047	+	0.709200i
$697$	−9.19701	+	15.9297i	−0.348362	+	0.603380i
$698$	13.5573	−	23.4820i	0.513153	−	0.888807i
$699$	−20.1894	−	4.16761i	−0.763635	−	0.157633i
$700$		0			0
$701$	1.84808			0.0698010			0.0349005	−	0.999391i	$-0.488889\pi$
$701$	1.84808			0.0698010			0.0349005	+	0.999391i	$0.488889\pi$
$702$	−25.5805	−	17.9052i	−0.965472	−	0.675789i
$703$	−9.66962			−0.364696
$704$	−0.937884	−	1.62446i	−0.0353478	−	0.0612242i
$705$		0			0
$706$	23.3649	−	40.4692i	0.879351	−	1.52308i
$707$	−7.43344	+	12.8751i	−0.279563	+	0.484218i
$708$	0.661797	+	1.99682i	0.0248719	+	0.0750450i
$709$	3.15338	+	5.46181i	0.118428	+	0.205123i	0.919145	−	0.393920i	$-0.128881\pi$
$709$	3.15338	+	5.46181i	0.118428	+	0.205123i	−0.800717	+	0.599043i	$0.795548\pi$
$710$		0			0
$711$	1.06065	+	9.06566i	0.0397775	+	0.339989i
$712$	−19.3465			−0.725040
$713$	−11.5337	−	19.9770i	−0.431942	−	0.748145i
$714$	−21.3795	+	24.0266i	−0.800106	+	0.899173i
$715$		0			0
$716$	0.917446	−	1.58906i	0.0342866	−	0.0593861i
$717$	24.9039	−	27.9875i	0.930054	−	1.04521i
$718$	8.43682	+	14.6130i	0.314859	+	0.545352i
$719$	18.0129			0.671770			0.335885	−	0.941903i	$-0.390965\pi$
$719$	18.0129			0.671770			0.335885	+	0.941903i	$0.390965\pi$
$720$		0			0
$721$	−16.2627			−0.605655
$722$	0.695067	+	1.20389i	0.0258677	+	0.0448042i
$723$	−2.12419	−	6.40925i	−0.0789996	−	0.238363i
$724$	0.668765	−	1.15833i	0.0248544	−	0.0430491i
$725$		0			0
$726$	−27.3204	−	5.63961i	−1.01395	−	0.209306i
$727$	−13.1412	−	22.7612i	−0.487379	−	0.844165i	0.512516	−	0.858678i	$-0.328714\pi$
$727$	−13.1412	−	22.7612i	−0.487379	−	0.844165i	−0.999895	+	0.0145126i	$0.995380\pi$
$728$	42.5002			1.57516
$729$	9.24306	+	25.3686i	0.342336	+	0.939578i
$730$		0			0
$731$	14.7896	+	25.6164i	0.547014	+	0.947456i
$732$	0.730145	+	0.150720i	0.0269869	+	0.00557078i
$733$	−23.8317	+	41.2777i	−0.880243	+	1.52462i	−0.0291714	+	0.999574i	$0.509287\pi$
$733$	−23.8317	+	41.2777i	−0.880243	+	1.52462i	−0.851071	+	0.525050i	$0.824046\pi$
$734$	−1.83595	+	3.17997i	−0.0677663	+	0.117375i
$735$		0			0
$736$	4.18167	+	7.24287i	0.154138	+	0.266976i
$737$	2.93739			0.108200
$738$	22.8975	+	9.87396i	0.842867	+	0.363465i
$739$	−10.0273			−0.368859			−0.184429	−	0.982846i	$-0.559044\pi$
$739$	−10.0273			−0.368859			−0.184429	+	0.982846i	$0.559044\pi$
$740$		0			0
$741$	19.9559	−	22.4267i	0.733097	−	0.823867i
$742$	−32.4110	+	56.1376i	−1.18985	+	2.06088i
$743$	−4.13633	+	7.16433i	−0.151747	+	0.262834i	−0.931870	−	0.362793i	$-0.881823\pi$
$743$	−4.13633	+	7.16433i	−0.151747	+	0.262834i	0.780123	+	0.625627i	$0.215157\pi$
$744$	8.23285	−	9.25222i	0.301831	−	0.339203i
$745$		0			0
$746$	−22.1539			−0.811111
$747$	−1.59673	−	13.6476i	−0.0584212	−	0.499340i
$748$	0.144665			0.00528946
$749$	3.14398	+	5.44554i	0.114879	+	0.198976i
$750$		0			0
$751$	2.89880	−	5.02087i	0.105779	−	0.183214i	−0.808277	−	0.588802i	$-0.799600\pi$
$751$	2.89880	−	5.02087i	0.105779	−	0.183214i	0.914056	+	0.405588i	$0.132933\pi$
$752$	−3.08060	+	5.33575i	−0.112338	+	0.194575i
$753$	−51.0638	−	10.5409i	−1.86087	−	0.384130i
$754$	12.6855	+	21.9720i	0.461980	+	0.800173i
$755$		0			0
$756$	2.80550	+	1.96373i	0.102035	+	0.0714203i
$757$	−25.2804			−0.918830			−0.459415	−	0.888222i	$-0.651941\pi$
$757$	−25.2804			−0.918830			−0.459415	+	0.888222i	$0.651941\pi$
$758$	−4.62066	−	8.00322i	−0.167830	−	0.290690i
$759$	3.83905	+	0.792476i	0.139349	+	0.0287651i
$760$		0			0
$761$	−9.73190	+	16.8561i	−0.352781	+	0.611035i	−0.986736	−	0.162335i	$-0.948097\pi$
$761$	−9.73190	+	16.8561i	−0.352781	+	0.611035i	0.633954	+	0.773370i	$0.281431\pi$
$762$	1.32687	+	4.00352i	0.0480674	+	0.145032i
$763$	24.9387	+	43.1951i	0.902843	+	1.56377i
$764$	−0.977278			−0.0353567
$765$		0			0
$766$	−32.6897			−1.18113
$767$	−14.5292	−	25.1653i	−0.524618	−	0.908666i
$768$	−4.67764	+	5.25681i	−0.168790	+	0.189689i
$769$	24.6715	−	42.7324i	0.889678	−	1.54097i	0.0494224	−	0.998778i	$-0.484262\pi$
$769$	24.6715	−	42.7324i	0.889678	−	1.54097i	0.840256	−	0.542190i	$-0.182405\pi$
$770$		0			0
$771$	18.8990	−	21.2391i	0.680632	−	0.764907i
$772$	0.723033	+	1.25233i	0.0260225	+	0.0450723i
$773$	20.8502			0.749930			0.374965	−	0.927039i	$-0.377655\pi$
$773$	20.8502			0.749930			0.374965	+	0.927039i	$0.377655\pi$
$774$	32.1615	−	23.9490i	1.15602	−	0.860827i
$775$		0			0
$776$	4.19816	+	7.27143i	0.150705	+	0.261029i
$777$	4.79350	+	14.4632i	0.171966	+	0.518866i
$778$	22.1668	−	38.3940i	0.794717	−	1.37649i
$779$	−11.9869	+	20.7620i	−0.429476	+	0.743875i
$780$		0			0
$781$	1.09077	+	1.88927i	0.0390308	+	0.0676034i
$782$	41.7657			1.49354
$783$	1.90841	−	21.8555i	0.0682010	−	0.781052i
$784$	−34.2564			−1.22344
$785$		0			0
$786$	−32.9320	−	6.79798i	−1.17464	−	0.242476i
$787$	22.0941	−	38.2682i	0.787571	−	1.36411i	−0.139880	−	0.990169i	$-0.544672\pi$
$787$	22.0941	−	38.2682i	0.787571	−	1.36411i	0.927451	−	0.373945i	$-0.121995\pi$
$788$	−0.905801	+	1.56889i	−0.0322678	+	0.0558895i
$789$	−14.0623	−	42.4298i	−0.500632	−	1.51054i
$790$		0			0
$791$	5.13799			0.182686
$792$	0.244565	+	2.09036i	0.00869025	+	0.0742778i
$793$	−10.2985			−0.365709
$794$	−21.5326	−	37.2955i	−0.764162	−	1.32357i
$795$		0			0
$796$	1.58362	−	2.74290i	0.0561297	−	0.0972196i
$797$	−15.5187	+	26.8792i	−0.549701	+	0.952110i	0.448594	+	0.893736i	$0.351925\pi$
$797$	−15.5187	+	26.8792i	−0.549701	+	0.952110i	−0.998295	+	0.0583744i	$0.981408\pi$
$798$	−27.8649	+	31.3151i	−0.986408	+	1.10854i
$799$	2.32928	+	4.03443i	0.0824039	+	0.142728i
$800$		0			0
$801$	19.7731	+	8.52664i	0.698647	+	0.301274i
$802$	35.7031			1.26072
$803$	−0.0525199	−	0.0909671i	−0.00185339	−	0.00321016i
$804$	−1.04836	−	3.16319i	−0.0369729	−	0.111557i
$805$		0			0
$806$	7.97065	−	13.8056i	0.280754	−	0.486281i
$807$	−21.2385	−	4.38415i	−0.747629	−	0.154329i
$808$	5.18278	+	8.97683i	0.182329	+	0.315804i
$809$	14.6229			0.514114			0.257057	−	0.966396i	$-0.417247\pi$
$809$	14.6229			0.514114			0.257057	+	0.966396i	$0.417247\pi$
$810$		0			0
$811$	26.7177			0.938187			0.469093	−	0.883149i	$-0.344581\pi$
$811$	26.7177			0.938187			0.469093	+	0.883149i	$0.344581\pi$
$812$	−1.39127	−	2.40975i	−0.0488240	−	0.0845656i
$813$	33.3256	+	6.87923i	1.16878	+	0.241265i
$814$	0.436293	−	0.755682i	0.0152921	−	0.0264866i
$815$		0			0
$816$	7.66018	+	23.1128i	0.268160	+	0.809110i
$817$	19.2761	+	33.3871i	0.674384	+	1.16807i
$818$	3.44727			0.120531
$819$	−43.4373	−	18.7313i	−1.51782	−	0.654523i
$820$		0			0
$821$	9.29903	+	16.1064i	0.324538	+	0.562117i	0.981419	−	0.191878i	$-0.0614577\pi$
$821$	9.29903	+	16.1064i	0.324538	+	0.562117i	−0.656881	+	0.753995i	$0.728124\pi$
$822$	−34.4225	+	38.6846i	−1.20062	+	1.34928i
$823$	1.53102	−	2.65181i	0.0533680	−	0.0924362i	−0.838107	−	0.545506i	$-0.816338\pi$
$823$	1.53102	−	2.65181i	0.0533680	−	0.0924362i	0.891475	+	0.453069i	$0.149671\pi$
$824$	−5.66938	+	9.81966i	−0.197502	+	0.342084i
$825$		0			0
$826$	20.2875	+	35.1390i	0.705892	+	1.22264i
$827$	7.27526			0.252985			0.126493	−	0.991968i	$-0.459628\pi$
$827$	7.27526			0.252985			0.126493	+	0.991968i	$0.459628\pi$
$828$	−0.516773	−	4.41699i	−0.0179591	−	0.153501i
$829$	10.5211			0.365411			0.182706	−	0.983168i	$-0.441514\pi$
$829$	10.5211			0.365411			0.182706	+	0.983168i	$0.441514\pi$
$830$		0			0
$831$	11.3503	+	34.2469i	0.393738	+	1.18801i
$832$	14.6975	−	25.4569i	0.509546	−	0.882559i
$833$	−12.9509	+	22.4315i	−0.448721	+	0.777207i
$834$	7.66912	+	1.58310i	0.265560	+	0.0548182i
$835$		0			0
$836$	0.188549			0.00652109
$837$	−12.4921	+	5.82773i	−0.431791	+	0.201436i
$838$	33.6528			1.16252
$839$	−7.59033	−	13.1468i	−0.262047	−	0.453879i	0.704739	−	0.709467i	$-0.251064\pi$
$839$	−7.59033	−	13.1468i	−0.262047	−	0.453879i	−0.966786	+	0.255588i	$0.917731\pi$
$840$		0			0
$841$	5.58695	−	9.67689i	0.192654	−	0.333686i
$842$	−8.74806	+	15.1521i	−0.301478	+	0.522176i
$843$	−2.57433	−	7.76744i	−0.0886646	−	0.267525i
$844$	−0.891034	−	1.54332i	−0.0306707	−	0.0531232i
$845$		0			0
$846$	5.06525	−	3.77182i	0.174147	−	0.129678i
$847$	−42.2622			−1.45215
$848$	24.5381	+	42.5012i	0.842641	+	1.45950i
$849$	−26.6575	+	29.9581i	−0.914882	+	1.02816i
$850$		0			0
$851$	9.89351	−	17.1361i	0.339145	−	0.587417i
$852$	1.64520	−	1.84890i	0.0563636	−	0.0633424i
$853$	−5.24309	−	9.08131i	−0.179520	−	0.310938i	0.762196	−	0.647346i	$-0.224121\pi$
$853$	−5.24309	−	9.08131i	−0.179520	−	0.310938i	−0.941716	+	0.336408i	$0.890788\pi$
$854$	14.3800			0.492074
$855$		0			0
$856$	4.38412			0.149846
$857$	4.42038	+	7.65631i	0.150997	+	0.261535i	0.931594	−	0.363500i	$-0.118418\pi$
$857$	4.42038	+	7.65631i	0.150997	+	0.261535i	−0.780597	+	0.625034i	$0.785085\pi$
$858$	0.852245	+	2.57145i	0.0290952	+	0.0877878i
$859$	1.03416	−	1.79121i	0.0352849	−	0.0611153i	−0.847844	−	0.530246i	$-0.822099\pi$
$859$	1.03416	−	1.79121i	0.0352849	−	0.0611153i	0.883129	+	0.469131i	$0.155433\pi$
$860$		0			0
$861$	36.9968	+	7.63707i	1.26085	+	0.260271i
$862$	−6.53326	−	11.3159i	−0.222524	−	0.385423i
$863$	−22.4434			−0.763984			−0.381992	−	0.924166i	$-0.624762\pi$
$863$	−22.4434			−0.763984			−0.381992	+	0.924166i	$0.624762\pi$
$864$	4.52915	−	2.11290i	0.154085	−	0.0718824i
$865$		0			0
$866$	−6.90263	−	11.9557i	−0.234561	−	0.406271i
$867$	−10.8063	−	2.23070i	−0.367003	−	0.0757586i
$868$	−0.874171	+	1.51411i	−0.0296713	+	0.0513922i
$869$	0.395947	−	0.685801i	0.0134316	−	0.0232642i
$870$		0			0
$871$	23.0159	+	39.8647i	0.779863	+	1.35076i
$872$	34.7758			1.17766
$873$	−1.08597	−	9.28203i	−0.0367544	−	0.314149i
$874$	54.4353			1.84130
$875$		0			0
$876$	−0.0792152	+	0.0890235i	−0.00267643	+	0.00300782i
$877$	−13.9466	+	24.1562i	−0.470943	+	0.815697i	−0.999448	−	0.0332332i	$-0.989420\pi$
$877$	−13.9466	+	24.1562i	−0.470943	+	0.815697i	0.528505	+	0.848930i	$0.322753\pi$
$878$	−14.3076	+	24.7815i	−0.482857	+	0.836334i
$879$	19.4346	−	21.8409i	0.655512	−	0.736676i
$880$		0			0
$881$	−9.22153			−0.310681			−0.155341	−	0.987861i	$-0.549647\pi$
$881$	−9.22153			−0.310681			−0.155341	+	0.987861i	$0.549647\pi$
$882$	32.2433	+	13.9041i	1.08569	+	0.468175i
$883$	49.2436			1.65718			0.828589	−	0.559858i	$-0.189144\pi$
$883$	49.2436			1.65718			0.828589	+	0.559858i	$0.189144\pi$
$884$	1.13352	+	1.96331i	0.0381243	+	0.0660333i
$885$		0			0
$886$	−8.01396	+	13.8806i	−0.269234	+	0.466328i
$887$	−5.38403	+	9.32542i	−0.180778	+	0.313117i	−0.942146	−	0.335203i	$-0.891195\pi$
$887$	−5.38403	+	9.32542i	−0.180778	+	0.313117i	0.761368	+	0.648320i	$0.224528\pi$
$888$	10.4042	+	2.14768i	0.349142	+	0.0720716i
$889$	3.19482	+	5.53360i	0.107151	+	0.185591i
$890$		0			0
$891$	0.671335	−	2.24424i	0.0224906	−	0.0751849i
$892$	0.670187			0.0224395
$893$	3.03586	+	5.25827i	0.101591	+	0.175961i
$894$	10.1503	+	2.09527i	0.339475	+	0.0700762i
$895$		0			0
$896$	−24.2408	+	41.9863i	−0.809829	+	1.40266i
$897$	19.3258	+	58.3109i	0.645268	+	1.94695i
$898$	−0.987183	−	1.70985i	−0.0329427	−	0.0570585i
$899$	11.2006			0.373561
$900$		0			0
$901$	37.1071			1.23622
$902$	−1.08170	−	1.87356i	−0.0360167	−	0.0623828i
$903$	40.3828	−	45.3829i	1.34386	−	1.51025i
$904$	1.79116	−	3.10239i	0.0595733	−	0.103184i
$905$		0			0
$906$	23.1032	−	25.9638i	0.767553	−	0.862590i
$907$	15.9852	+	27.6871i	0.530779	+	0.919336i	0.999355	+	0.0359130i	$0.0114339\pi$
$907$	15.9852	+	27.6871i	0.530779	+	0.919336i	−0.468576	+	0.883423i	$0.655233\pi$
$908$	0.823651			0.0273338
$909$	−1.34066	−	11.4590i	−0.0444670	−	0.380071i
$910$		0			0
$911$	5.04010	+	8.72970i	0.166986	+	0.289228i	0.937359	−	0.348366i	$-0.113263\pi$
$911$	5.04010	+	8.72970i	0.166986	+	0.289228i	−0.770373	+	0.637594i	$0.779930\pi$
$912$	9.98390	+	30.1241i	0.330600	+	0.997508i
$913$	−0.596067	+	1.03242i	−0.0197269	+	0.0341681i
$914$	−14.8145	+	25.6595i	−0.490021	+	0.848741i
$915$		0			0
$916$	1.60702	+	2.78343i	0.0530973	+	0.0919672i
$917$	−50.9428			−1.68228
$918$	2.17108	−	24.8636i	0.0716564	−	0.820623i
$919$	−29.7976			−0.982932			−0.491466	−	0.870897i	$-0.663539\pi$
$919$	−29.7976			−0.982932			−0.491466	+	0.870897i	$0.663539\pi$
$920$		0			0
$921$	−38.5358	−	7.95476i	−1.26980	−	0.262118i
$922$	24.8636	−	43.0650i	0.818839	−	1.41827i
$923$	−17.0934	+	29.6067i	−0.562637	+	0.974516i
$924$	−0.0934688	−	0.282020i	−0.00307490	−	0.00927779i
$925$		0			0
$926$	−7.72776			−0.253950
$927$	10.1222	−	7.53749i	0.332458	−	0.247564i
$928$	−4.06089			−0.133305
$929$	6.19275	+	10.7262i	0.203178	+	0.351914i	0.949551	−	0.313614i	$-0.101540\pi$
$929$	6.19275	+	10.7262i	0.203178	+	0.351914i	−0.746373	+	0.665528i	$0.768206\pi$
$930$		0			0
$931$	−16.8795	+	29.2362i	−0.553204	+	0.958177i
$932$	1.01453	−	1.75722i	0.0332321	−	0.0575597i
$933$	−36.3765	+	40.8805i	−1.19091	+	1.33837i
$934$	−10.4689	−	18.1327i	−0.342554	−	0.593321i
$935$		0			0
$936$	−26.4530	+	19.6981i	−0.864642	+	0.643853i
$937$	−44.4280			−1.45140			−0.725699	−	0.688012i	$-0.758484\pi$
$937$	−44.4280			−1.45140			−0.725699	+	0.688012i	$0.758484\pi$
$938$	−32.1377	−	55.6641i	−1.04933	−	1.81750i
$939$	16.6192	+	50.1446i	0.542348	+	1.63641i
$940$		0			0
$941$	−7.66617	+	13.2782i	−0.249910	+	0.432857i	−0.963501	−	0.267706i	$-0.913734\pi$
$941$	−7.66617	+	13.2782i	−0.249910	+	0.432857i	0.713591	+	0.700563i	$0.247068\pi$
$942$	5.15459	+	1.06404i	0.167946	+	0.0346682i
$943$	−24.5290	−	42.4854i	−0.798773	−	1.38352i
$944$	30.7189			0.999816
$945$		0			0
$946$	−3.47894			−0.113110
$947$	10.8498	+	18.7925i	0.352572	+	0.610673i	0.986699	−	0.162556i	$-0.0519738\pi$
$947$	10.8498	+	18.7925i	0.352572	+	0.610673i	−0.634127	+	0.773229i	$0.718640\pi$
$948$	−0.879833	−	0.181620i	−0.0285756	−	0.00589873i
$949$	0.823037	−	1.42554i	0.0267169	−	0.0462751i
$950$		0			0
$951$	−12.0363	−	36.3166i	−0.390303	−	1.17765i
$952$	16.9857	+	29.4200i	0.550508	+	0.953509i
$953$	−36.9099			−1.19563			−0.597815	−	0.801634i	$-0.703964\pi$
$953$	−36.9099			−1.19563			−0.597815	+	0.801634i	$0.703964\pi$
$954$	−5.84552	−	49.9631i	−0.189256	−	1.61762i
$955$		0			0
$956$	1.84368	+	3.19336i	0.0596290	+	0.103281i
$957$	−1.26528	+	1.42194i	−0.0409007	+	0.0459649i
$958$	−15.0886	+	26.1342i	−0.487490	+	0.844357i
$959$	−39.2243	+	67.9385i	−1.26662	+	2.19385i
$960$		0			0
$961$	11.9812	+	20.7520i	0.386490	+	0.669420i
$962$	13.6743			0.440876
$963$	−4.48079	−	1.93223i	−0.144391	−	0.0622652i
$964$	0.664581			0.0214047
$965$		0			0
$966$	−26.9851	−	81.4212i	−0.868231	−	2.61968i
$967$	−10.6691	+	18.4794i	−0.343095	+	0.594258i	−0.985006	−	0.172521i	$-0.944809\pi$
$967$	−10.6691	+	18.4794i	−0.343095	+	0.594258i	0.641911	+	0.766779i	$0.278142\pi$
$968$	−14.7331	+	25.5185i	−0.473541	+	0.820197i
$969$	23.5001	+	4.85101i	0.754932	+	0.155837i
$970$		0			0
$971$	−42.5851			−1.36662			−0.683311	−	0.730128i	$-0.739460\pi$
$971$	−42.5851			−1.36662			−0.683311	+	0.730128i	$0.739460\pi$
$972$	−2.65636	+	0.0780359i	−0.0852027	+	0.00250300i
$973$	11.8635			0.380325
$974$	−23.0973	−	40.0057i	−0.740085	−	1.28186i
$975$		0			0
$976$	5.44349	−	9.42840i	0.174242	−	0.301796i
$977$	24.4696	−	42.3826i	0.782852	−	1.35594i	−0.147423	−	0.989074i	$-0.547098\pi$
$977$	24.4696	−	42.3826i	0.782852	−	1.35594i	0.930274	−	0.366865i	$-0.119569\pi$
$978$	2.81393	+	8.49036i	0.0899795	+	0.271492i
$979$	−0.934101	−	1.61791i	−0.0298540	−	0.0517087i
$980$		0			0
$981$	−35.5426	−	15.3268i	−1.13479	−	0.489349i
$982$	−15.3102			−0.488567
$983$	−18.0545	−	31.2712i	−0.575848	−	0.997398i	−0.995949	−	0.0899205i	$-0.971339\pi$
$983$	−18.0545	−	31.2712i	−0.575848	−	0.997398i	0.420101	−	0.907477i	$-0.361995\pi$
$984$	17.5089	−	19.6768i	0.558164	−	0.627274i
$985$		0			0
$986$	−10.1398	+	17.5627i	−0.322918	+	0.559310i
$987$	6.36005	−	7.14754i	0.202443	−	0.227509i
$988$	1.47737	+	2.55888i	0.0470014	+	0.0814088i
$989$	−78.8896			−2.50854
$990$		0			0
$991$	32.0054			1.01669			0.508343	−	0.861155i	$-0.330258\pi$
$991$	32.0054			1.01669			0.508343	+	0.861155i	$0.330258\pi$
$992$	1.27578	+	2.20972i	0.0405061	+	0.0701586i
$993$	16.1316	+	48.6733i	0.511921	+	1.54460i
$994$	23.8680	−	41.3406i	0.757048	−	1.31125i
$995$		0			0
$996$	1.32452	+	0.273414i	0.0419690	+	0.00866345i
$997$	−25.8840	−	44.8324i	−0.819754	−	1.41986i	−0.905863	−	0.423570i	$-0.860777\pi$
$997$	−25.8840	−	44.8324i	−0.819754	−	1.41986i	0.0861095	−	0.996286i	$-0.472557\pi$
$998$	−5.63624			−0.178412
$999$	−9.68703	−	6.78051i	−0.306484	−	0.214526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.e.c.76.2	✓	8
3.2	odd	2		675.2.e.e.226.3		8
5.2	odd	4		225.2.k.c.49.6		16
5.3	odd	4		225.2.k.c.49.3		16
5.4	even	2		225.2.e.e.76.3	yes	8
9.2	odd	6		675.2.e.e.451.3		8
9.4	even	3		2025.2.a.y.1.3		4
9.5	odd	6		2025.2.a.p.1.2		4
9.7	even	3	inner	225.2.e.c.151.2	yes	8
15.2	even	4		675.2.k.c.199.3		16
15.8	even	4		675.2.k.c.199.6		16
15.14	odd	2		675.2.e.c.226.2		8
45.2	even	12		675.2.k.c.424.6		16
45.4	even	6		2025.2.a.q.1.2		4
45.7	odd	12		225.2.k.c.124.3		16
45.13	odd	12		2025.2.b.n.649.3		8
45.14	odd	6		2025.2.a.z.1.3		4
45.22	odd	12		2025.2.b.n.649.6		8
45.23	even	12		2025.2.b.o.649.6		8
45.29	odd	6		675.2.e.c.451.2		8
45.32	even	12		2025.2.b.o.649.3		8
45.34	even	6		225.2.e.e.151.3	yes	8
45.38	even	12		675.2.k.c.424.3		16
45.43	odd	12		225.2.k.c.124.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.e.c.76.2	✓	8	1.1	even	1	trivial
225.2.e.c.151.2	yes	8	9.7	even	3	inner
225.2.e.e.76.3	yes	8	5.4	even	2
225.2.e.e.151.3	yes	8	45.34	even	6
225.2.k.c.49.3		16	5.3	odd	4
225.2.k.c.49.6		16	5.2	odd	4
225.2.k.c.124.3		16	45.7	odd	12
225.2.k.c.124.6		16	45.43	odd	12
675.2.e.c.226.2		8	15.14	odd	2
675.2.e.c.451.2		8	45.29	odd	6
675.2.e.e.226.3		8	3.2	odd	2
675.2.e.e.451.3		8	9.2	odd	6
675.2.k.c.199.3		16	15.2	even	4
675.2.k.c.199.6		16	15.8	even	4
675.2.k.c.424.3		16	45.38	even	12
675.2.k.c.424.6		16	45.2	even	12
2025.2.a.p.1.2		4	9.5	odd	6
2025.2.a.q.1.2		4	45.4	even	6
2025.2.a.y.1.3		4	9.4	even	3
2025.2.a.z.1.3		4	45.14	odd	6
2025.2.b.n.649.3		8	45.13	odd	12
2025.2.b.n.649.6		8	45.22	odd	12
2025.2.b.o.649.3		8	45.32	even	12
2025.2.b.o.649.6		8	45.23	even	12

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.736627 - 1.27588i) q^{2} +(1.69629 + 0.350156i) q^{3} +(-0.0852394 + 0.147639i) q^{4} +(-0.802776 - 2.42219i) q^{6} +(-1.93291 - 3.34791i) q^{7} -2.69535 q^{8} +(2.75478 + 1.18793i) q^{9} +(-0.130139 - 0.225407i) q^{11} +(-0.196287 + 0.220591i) q^{12} +(2.03940 - 3.53235i) q^{13} +(-2.84768 + 4.93232i) q^{14} +(2.15595 + 3.73421i) q^{16} +3.26028 q^{17} +(-0.513594 - 4.38982i) q^{18} +4.24928 q^{19} +(-2.10649 - 6.35583i) q^{21} +(-0.191728 + 0.332082i) q^{22} +(-4.34768 + 7.53039i) q^{23} +(-4.57209 - 0.943794i) q^{24} -6.00912 q^{26} +(4.25694 + 2.97968i) q^{27} +0.659042 q^{28} +(-2.11105 - 3.65644i) q^{29} +(-1.32643 + 2.29744i) q^{31} +(0.480909 - 0.832959i) q^{32} +(-0.141825 - 0.427924i) q^{33} +(-2.40161 - 4.15971i) q^{34} +(-0.410201 + 0.305455i) q^{36} -2.27559 q^{37} +(-3.13014 - 5.42156i) q^{38} +(4.69629 - 5.27777i) q^{39} +(-2.82093 + 4.88599i) q^{41} +(-6.55756 + 7.36950i) q^{42} +(4.53631 + 7.85712i) q^{43} +0.0443719 q^{44} +12.8105 q^{46} +(0.714441 + 1.23745i) q^{47} +(2.34955 + 7.08921i) q^{48} +(-3.97232 + 6.88026i) q^{49} +(5.53037 + 1.14161i) q^{51} +(0.347675 + 0.602191i) q^{52} +11.3816 q^{53} +(0.665919 - 7.62624i) q^{54} +(5.20988 + 9.02378i) q^{56} +(7.20801 + 1.48791i) q^{57} +(-3.11011 + 5.38687i) q^{58} +(3.56212 - 6.16977i) q^{59} +(-1.26244 - 2.18660i) q^{61} +3.90833 q^{62} +(-1.34768 - 11.5189i) q^{63} +7.20679 q^{64} +(-0.441506 + 0.496172i) q^{66} +(-5.64280 + 9.77361i) q^{67} +(-0.277904 + 0.481344i) q^{68} +(-10.0117 + 11.2513i) q^{69} -8.38158 q^{71} +(-7.42510 - 3.20189i) q^{72} +0.403568 q^{73} +(1.67626 + 2.90337i) q^{74} +(-0.362207 + 0.627360i) q^{76} +(-0.503095 + 0.871386i) q^{77} +(-10.1932 - 2.10413i) q^{78} +(1.52125 + 2.63488i) q^{79} +(6.17764 + 6.54498i) q^{81} +8.31189 q^{82} +(-2.29012 - 3.96660i) q^{83} +(1.11792 + 0.230768i) q^{84} +(6.68314 - 11.5755i) q^{86} +(-2.30062 - 6.94157i) q^{87} +(0.350770 + 0.607551i) q^{88} +7.17772 q^{89} -15.7680 q^{91} +(-0.741187 - 1.28377i) q^{92} +(-3.05446 + 3.43266i) q^{93} +(1.05255 - 1.82308i) q^{94} +(1.10743 - 1.24454i) q^{96} +(-1.55756 - 2.69777i) q^{97} +11.7045 q^{98} +(-0.0907360 - 0.775544i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + q^{3} - 4 q^{4} + 8 q^{6} + q^{7} + 18 q^{8} + 5 q^{9} + q^{11} + 11 q^{12} - 2 q^{13} - 3 q^{14} - 4 q^{16} + 22 q^{17} - 5 q^{18} + 4 q^{19} - 15 q^{21} - 3 q^{22} - 15 q^{23} - 33 q^{24}+ \cdots - 17 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + q^3 - 4 * q^4 + 8 * q^6 + q^7 + 18 * q^8 + 5 * q^9 + q^11 + 11 * q^12 - 2 * q^13 - 3 * q^14 - 4 * q^16 + 22 * q^17 - 5 * q^18 + 4 * q^19 - 15 * q^21 - 3 * q^22 - 15 * q^23 - 33 * q^24 - 20 * q^26 - 2 * q^27 - 8 * q^28 - q^29 + 4 * q^31 - 10 * q^32 - 28 * q^33 - 9 * q^34 - 14 * q^36 - 2 * q^37 - 23 * q^38 + 25 * q^39 + 5 * q^41 - 21 * q^42 + 10 * q^43 + 44 * q^44 - 20 * q^47 + 53 * q^48 + 3 * q^49 + 11 * q^51 - 17 * q^52 + 40 * q^53 + 26 * q^54 + 30 * q^56 - 8 * q^57 + 18 * q^58 - 17 * q^59 + 13 * q^61 - 12 * q^62 + 9 * q^63 + 38 * q^64 - 8 * q^66 - 17 * q^67 - 34 * q^68 - 27 * q^69 - 16 * q^71 + 18 * q^72 + 4 * q^73 - 40 * q^74 - 11 * q^76 - 12 * q^77 - 61 * q^78 + 7 * q^79 + 17 * q^81 + 24 * q^82 - 30 * q^83 + 27 * q^84 + 34 * q^86 - 23 * q^87 - 9 * q^88 - 18 * q^89 - 34 * q^91 + 12 * q^92 + 15 * q^93 - 3 * q^94 + 34 * q^96 + 19 * q^97 + 26 * q^98 - 17 * q^99

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