LMFDB - Embedded newform 225.2.e.e.76.3

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			76.3
Root			$0.736627 + 1.27588i$ of defining polynomial
Character	$\chi$	$=$	225.76
Dual form			225.2.e.e.151.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.736627 + 1.27588i) q^{2} +(-1.69629 - 0.350156i) q^{3} +(-0.0852394 + 0.147639i) q^{4} +(-0.802776 - 2.42219i) q^{6} +(1.93291 + 3.34791i) q^{7} +2.69535 q^{8} +(2.75478 + 1.18793i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 8 * q + 2 * q^2 - q^3 - 4 * q^4 + 8 * q^6 - q^7 - 18 * q^8 + 5 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$0.00772725\pi$
$2$	0.736627	+	1.27588i	0.520874	+	0.902180i	−0.478831	+	0.877907i	$0.658939\pi$
$3$	−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	$0.0940803\pi$
$7$	1.93291	+	3.34791i	0.730573	+	1.26539i	−0.226066	+	0.974112i	$0.572586\pi$
$8$	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	$0.358033\pi$
$13$	−2.03940	+	3.53235i	−0.565629	+	0.979697i	−0.996991	+	0.0775187i	$0.975300\pi$
$14$	−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	$-0.629383\pi$
$17$	−3.26028			−0.790734			−0.395367	+	0.918523i	$0.629383\pi$
$18$	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	$-0.472037\pi$
$23$	4.34768	−	7.53039i	0.906553	−	1.57020i	0.818819	−	0.574052i	$-0.194629\pi$
$24$	−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	$-0.440107\pi$
$37$	2.27559			0.374104			0.187052	+	0.982350i	$0.440107\pi$
$38$	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	$-0.923493\pi$
$43$	−4.53631	−	7.85712i	−0.691780	−	1.19820i	0.279474	−	0.960153i	$-0.409840\pi$
$44$	0.0443719			0.00668931
$45$		0			0
$46$	12.8105			1.88880
$47$	−0.714441	−	1.23745i	−0.104212	−	0.180500i	0.809204	−	0.587528i	$-0.199899\pi$
$47$	−0.714441	−	1.23745i	−0.104212	−	0.180500i	−0.913416	+	0.407027i	$0.866565\pi$
$48$	−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	$-0.785642\pi$
$53$	−11.3816			−1.56338			−0.781690	+	0.623667i	$0.785642\pi$
$54$	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	$-0.591218\pi$
$67$	5.64280	−	9.77361i	0.689377	−	1.19404i	0.972040	−	0.234817i	$-0.0754491\pi$
$68$	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	$-0.507518\pi$
$73$	−0.403568			−0.0472340			−0.0236170	+	0.999721i	$0.507518\pi$
$74$	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	0.963904	−	0.266250i	$-0.0857845\pi$
$83$	2.29012	+	3.96660i	0.251373	+	0.435391i	−0.712531	+	0.701641i	$0.752451\pi$
$84$	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	0.934200	−	0.356749i	$-0.116115\pi$
$97$	1.55756	+	2.69777i	0.158146	+	0.273917i	−0.776054	+	0.630666i	$0.782782\pi$
$98$	−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	−0.950848	−	0.309657i	$-0.899786\pi$
$103$	−2.10339	+	3.64318i	−0.207254	+	0.358974i	0.743595	+	0.668630i	$0.233119\pi$
$104$	−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	$-0.474948\pi$
$107$	1.62655			0.157245			0.0786223	+	0.996904i	$0.474948\pi$
$108$	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	−0.833074	−	0.553161i	$-0.813421\pi$
$113$	0.664539	−	1.15102i	0.0625146	−	0.108278i	0.895589	+	0.444883i	$0.146755\pi$
$114$	−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	$-0.476636\pi$
$127$	1.65285			0.146667			0.0733335	+	0.997307i	$0.476636\pi$
$128$	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	$0.167203\pi$
$137$	10.1464	+	17.5741i	0.866867	+	1.50146i	0.00168578	+	0.999999i	$0.499463\pi$
$138$	−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	−0.821933	−	0.569584i	$-0.807104\pi$
$157$	1.03131	−	1.78627i	0.0823071	−	0.142560i	0.904241	+	0.427023i	$0.140438\pi$
$158$	−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	$-0.456165\pi$
$163$	3.50525			0.274552			0.137276	+	0.990533i	$0.456165\pi$
$164$	−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	$-0.541057\pi$
$167$	10.2674	−	17.7837i	0.794518	−	1.37615i	0.923145	−	0.384453i	$-0.125610\pi$
$168$	−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	0.680232	−	0.732997i	$-0.261879\pi$
$173$	−3.87589	−	6.71323i	−0.294678	−	0.510397i	−0.974910	+	0.222600i	$0.928546\pi$
$174$	−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	−0.977325	−	0.211744i	$-0.932086\pi$
$193$	−4.24119	+	7.34595i	−0.305287	+	0.528773i	0.672038	+	0.740517i	$0.265419\pi$
$194$	−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	$-0.623579\pi$
$197$	−10.6266			−0.757110			−0.378555	+	0.925579i	$0.623579\pi$
$198$	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	0.924304	−	0.381658i	$-0.124647\pi$
$223$	1.96560	+	3.40452i	0.131626	+	0.227983i	−0.792677	+	0.609641i	$0.791313\pi$
$224$	−3.71822			−0.248434
$225$		0			0
$226$	1.95807			0.130249
$227$	2.41570	+	4.18411i	0.160335	+	0.277709i	0.934989	−	0.354677i	$-0.115409\pi$
$227$	2.41570	+	4.18411i	0.160335	+	0.277709i	−0.774654	+	0.632386i	$0.782076\pi$
$228$	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	$-0.372521\pi$
$233$	11.9021			0.779735			0.389867	+	0.920871i	$0.372521\pi$
$234$	−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	$0.337741\pi$
$257$	−8.20707	+	14.2151i	−0.511943	+	0.886711i	−0.999904	+	0.0138459i	$0.995593\pi$
$258$	−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	$0.126214\pi$
$263$	12.9036	+	22.3497i	0.795670	+	1.37814i	−0.126743	+	0.991936i	$0.540452\pi$
$264$	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	$-0.951448\pi$
$277$	−10.4150	−	18.0394i	−0.625779	−	1.08388i	0.362610	−	0.931941i	$-0.381886\pi$
$278$	−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	$-0.591763\pi$
$283$	11.5762	−	20.0506i	0.688136	−	1.19189i	0.972440	−	0.233152i	$-0.0749041\pi$
$284$	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	−0.999968	−	0.00800832i	$-0.997451\pi$
$293$	−8.43963	+	14.6179i	−0.493049	+	0.853985i	0.506919	+	0.861993i	$0.330784\pi$
$294$	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	$-0.275487\pi$
$307$	22.7177			1.29657			0.648285	+	0.761398i	$0.275487\pi$
$308$	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	$-0.835897\pi$
$313$	−15.2498	−	26.4134i	−0.861970	−	1.49298i	0.00805392	−	0.999968i	$-0.497436\pi$
$314$	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	$0.0463307\pi$
$317$	11.0445	+	19.1296i	0.620320	+	1.07443i	−0.369106	+	0.929387i	$0.620336\pi$
$318$	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	−0.643370	−	0.765555i	$-0.722464\pi$
$337$	6.26553	−	10.8522i	0.341305	−	0.591158i	0.984675	+	0.174397i	$0.0557977\pi$
$338$	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	−0.998904	−	0.0468031i	$-0.985097\pi$
$347$	−8.54872	+	14.8068i	−0.458919	+	0.794872i	0.539985	+	0.841675i	$0.318430\pi$
$348$	−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	$-0.846796\pi$
$353$	−15.8594	−	27.4693i	−0.844110	−	1.46204i	0.0422810	−	0.999106i	$-0.486538\pi$
$354$	−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	0.896716	−	0.442606i	$-0.145946\pi$
$367$	1.24619	+	2.15846i	0.0650506	+	0.112671i	−0.831666	+	0.555276i	$0.812612\pi$
$368$	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	−0.992356	−	0.123409i	$-0.960617\pi$
$373$	−7.51868	+	13.0227i	−0.389303	+	0.674292i	0.603053	+	0.797701i	$0.293951\pi$
$374$	−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	$0.358523\pi$
$383$	−11.0944	+	19.2161i	−0.566897	+	0.981894i	−0.996870	+	0.0790528i	$0.974810\pi$
$384$	−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	$-0.762132\pi$
$397$	−29.2313			−1.46708			−0.733538	+	0.679648i	$0.762132\pi$
$398$	−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	$-0.572291\pi$
$433$	−9.37059			−0.450322			−0.225161	+	0.974322i	$0.572291\pi$
$434$	−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	0.965825	−	0.259193i	$-0.0834567\pi$
$443$	5.43963	+	9.42172i	0.258445	+	0.447639i	−0.707381	+	0.706833i	$0.750123\pi$
$444$	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	0.999426	−	0.0338671i	$-0.0107823\pi$
$457$	10.0556	+	17.4169i	0.470383	+	0.814728i	−0.529043	+	0.848595i	$0.677449\pi$
$458$	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	−0.920512	−	0.390715i	$-0.872228\pi$
$463$	−2.62268	+	4.54262i	−0.121886	+	0.211114i	0.798625	+	0.601829i	$0.205561\pi$
$464$	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	$-0.606653\pi$
$467$	−14.2120			−0.657652			−0.328826	+	0.944390i	$0.606653\pi$
$468$	−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	$-0.751497\pi$
$487$	−31.3554			−1.42085			−0.710425	+	0.703772i	$0.751497\pi$
$488$	−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	$-0.507114\pi$
$503$	−1.00236			−0.0446931			−0.0223466	+	0.999750i	$0.507114\pi$
$504$	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	$-0.426986\pi$
$523$	10.3998			0.454749			0.227375	+	0.973807i	$0.426986\pi$
$524$	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	0.999890	−	0.0148294i	$-0.00472053\pi$
$547$	11.3924	+	19.7322i	0.487102	+	0.843686i	−0.512788	+	0.858515i	$0.671387\pi$
$548$	−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	$-0.373752\pi$
$557$	18.2341			0.772605			0.386303	+	0.922372i	$0.373752\pi$
$558$	−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	$-0.663688\pi$
$563$	12.0556	−	20.8809i	0.508083	−	0.880025i	0.999956	−	0.00935862i	$-0.00297898\pi$
$564$	−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	$-0.236191\pi$
$577$	35.4119			1.47422			0.737108	+	0.675775i	$0.236191\pi$
$578$	−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	$-0.933673\pi$
$587$	−16.1925	−	28.0463i	−0.668338	−	1.15759i	0.310031	−	0.950726i	$-0.399661\pi$
$588$	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	$-0.705066\pi$
$593$	−29.2504			−1.20117			−0.600585	+	0.799561i	$0.705066\pi$
$594$	−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	$0.478890\pi$
$607$	−20.4733	+	35.4608i	−0.830987	+	1.43931i	−0.897257	+	0.441509i	$0.854443\pi$
$608$	−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	$-0.264507\pi$
$613$	33.3827			1.34831			0.674157	+	0.738588i	$0.264507\pi$
$614$	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	−0.842504	−	0.538689i	$-0.818920\pi$
$617$	1.12440	−	1.94752i	0.0452666	−	0.0784040i	0.887771	+	0.460285i	$0.152253\pi$
$618$	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	$-0.653188\pi$
$643$	13.5970	−	23.5506i	0.536212	−	0.928746i	0.999104	−	0.0423312i	$-0.0134785\pi$
$644$	−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	$-0.606676\pi$
$647$	−16.7316			−0.657787			−0.328893	+	0.944367i	$0.606676\pi$
$648$	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	$0.519375\pi$
$653$	−22.8666	+	39.6060i	−0.894837	+	1.54990i	−0.834006	+	0.551756i	$0.813958\pi$
$654$	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	$0.246093\pi$
$673$	24.9740	+	43.2562i	0.962676	+	1.66740i	0.246944	+	0.969030i	$0.420574\pi$
$674$	18.4614			0.711108
$675$		0			0
$676$	0.619973			0.0238451
$677$	5.41553	+	9.37998i	0.208136	+	0.360502i	0.951127	−	0.308799i	$-0.0999271\pi$
$677$	5.41553	+	9.37998i	0.208136	+	0.360502i	−0.742991	+	0.669301i	$0.766594\pi$
$678$	−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	$-0.502618\pi$
$683$	−0.429870			−0.0164485			−0.00822426	+	0.999966i	$0.502618\pi$
$684$	−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	0.999895	−	0.0145126i	$-0.00461966\pi$
$727$	13.1412	+	22.7612i	0.487379	+	0.844165i	−0.512516	+	0.858678i	$0.671286\pi$
$728$	−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	$-0.490713\pi$
$733$	23.8317	−	41.2777i	0.880243	−	1.52462i	0.851071	−	0.525050i	$-0.175954\pi$
$734$	−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	−0.780123	−	0.625627i	$-0.784843\pi$
$743$	4.13633	−	7.16433i	0.151747	−	0.262834i	0.931870	+	0.362793i	$0.118177\pi$
$744$	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	$-0.348059\pi$
$757$	25.2804			0.918830			0.459415	+	0.888222i	$0.348059\pi$
$758$	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	$-0.622345\pi$
$773$	−20.8502			−0.749930			−0.374965	+	0.927039i	$0.622345\pi$
$774$	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	$0.455328\pi$
$787$	−22.0941	+	38.2682i	−0.787571	+	1.36411i	−0.927451	+	0.373945i	$0.878005\pi$
$788$	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	$-0.648075\pi$
$797$	15.5187	−	26.8792i	0.549701	−	0.952110i	0.998295	−	0.0583744i	$-0.0185917\pi$
$798$	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	−0.891475	−	0.453069i	$-0.850329\pi$
$823$	−1.53102	+	2.65181i	−0.0533680	+	0.0924362i	0.838107	+	0.545506i	$0.183662\pi$
$824$	−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	$-0.540372\pi$
$827$	−7.27526			−0.252985			−0.126493	+	0.991968i	$0.540372\pi$
$828$	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	0.941716	−	0.336408i	$-0.109212\pi$
$853$	5.24309	+	9.08131i	0.179520	+	0.310938i	−0.762196	+	0.647346i	$0.775879\pi$
$854$	14.3800			0.492074
$855$		0			0
$856$	4.38412			0.149846
$857$	−4.42038	−	7.65631i	−0.150997	−	0.261535i	0.780597	−	0.625034i	$-0.214915\pi$
$857$	−4.42038	−	7.65631i	−0.150997	−	0.261535i	−0.931594	+	0.363500i	$0.881582\pi$
$858$	−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	$-0.375238\pi$
$863$	22.4434			0.763984			0.381992	+	0.924166i	$0.375238\pi$
$864$	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	−0.528505	−	0.848930i	$-0.677247\pi$
$877$	13.9466	−	24.1562i	0.470943	−	0.815697i	0.999448	+	0.0332332i	$0.0105804\pi$
$878$	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	$-0.810856\pi$
$883$	−49.2436			−1.65718			−0.828589	+	0.559858i	$0.810856\pi$
$884$	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	−0.761368	−	0.648320i	$-0.775472\pi$
$887$	5.38403	−	9.32542i	0.180778	−	0.313117i	0.942146	+	0.335203i	$0.108805\pi$
$888$	−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	$-0.988566\pi$
$907$	−15.9852	−	27.6871i	−0.530779	−	0.919336i	0.468576	−	0.883423i	$-0.344767\pi$
$908$	−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	$-0.241516\pi$
$937$	44.4280			1.45140			0.725699	+	0.688012i	$0.241516\pi$
$938$	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	0.634127	−	0.773229i	$-0.281360\pi$
$947$	−10.8498	−	18.7925i	−0.352572	−	0.610673i	−0.986699	+	0.162556i	$0.948026\pi$
$948$	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	$-0.296036\pi$
$953$	36.9099			1.19563			0.597815	+	0.801634i	$0.296036\pi$
$954$	−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	−0.641911	−	0.766779i	$-0.721858\pi$
$967$	10.6691	−	18.4794i	0.343095	−	0.594258i	0.985006	+	0.172521i	$0.0551914\pi$
$968$	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	$0.452902\pi$
$977$	−24.4696	+	42.3826i	−0.782852	+	1.35594i	−0.930274	+	0.366865i	$0.880431\pi$
$978$	−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	$0.0286613\pi$
$983$	18.0545	+	31.2712i	0.575848	+	0.997398i	−0.420101	+	0.907477i	$0.638005\pi$
$984$	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	$0.139223\pi$
$997$	25.8840	+	44.8324i	0.819754	+	1.41986i	−0.0861095	+	0.996286i	$0.527443\pi$
$998$	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.e.76.3	yes	8
3.2	odd	2		675.2.e.c.226.2		8
5.2	odd	4		225.2.k.c.49.3		16
5.3	odd	4		225.2.k.c.49.6		16
5.4	even	2		225.2.e.c.76.2	✓	8
9.2	odd	6		675.2.e.c.451.2		8
9.4	even	3		2025.2.a.q.1.2		4
9.5	odd	6		2025.2.a.z.1.3		4
9.7	even	3	inner	225.2.e.e.151.3	yes	8
15.2	even	4		675.2.k.c.199.6		16
15.8	even	4		675.2.k.c.199.3		16
15.14	odd	2		675.2.e.e.226.3		8
45.2	even	12		675.2.k.c.424.3		16
45.4	even	6		2025.2.a.y.1.3		4
45.7	odd	12		225.2.k.c.124.6		16
45.13	odd	12		2025.2.b.n.649.6		8
45.14	odd	6		2025.2.a.p.1.2		4
45.22	odd	12		2025.2.b.n.649.3		8
45.23	even	12		2025.2.b.o.649.3		8
45.29	odd	6		675.2.e.e.451.3		8
45.32	even	12		2025.2.b.o.649.6		8
45.34	even	6		225.2.e.c.151.2	yes	8
45.38	even	12		675.2.k.c.424.6		16
45.43	odd	12		225.2.k.c.124.3		16

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

\(f(q)\)	\(=\)	\(q+(0.736627 + 1.27588i) q^{2} +(-1.69629 - 0.350156i) q^{3} +(-0.0852394 + 0.147639i) q^{4} +(-0.802776 - 2.42219i) q^{6} +(1.93291 + 3.34791i) q^{7} +2.69535 q^{8} +(2.75478 + 1.18793i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - q^{3} - 4 q^{4} + 8 q^{6} - q^{7} - 18 q^{8} + 5 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - q^3 - 4 * q^4 + 8 * q^6 - q^7 - 18 * q^8 + 5 * q^9	\( 8 q + 2 q^{2} - q^{3} - 4 q^{4} + 8 q^{6} - q^{7} - 18 q^{8} + 5 q^{9} + q^{11} - 11 q^{12} + 2 q^{13} - 3 q^{14} - 4 q^{16} - 22 q^{17} + 5 q^{18} + 4 q^{19} - 15 q^{21} + 3 q^{22} + 15 q^{23} - 33 q^{24} - 20 q^{26} + 2 q^{27} + 8 q^{28} - q^{29} + 4 q^{31} + 10 q^{32} + 28 q^{33} - 9 q^{34} - 14 q^{36} + 2 q^{37} + 23 q^{38} + 25 q^{39} + 5 q^{41} + 21 q^{42} - 10 q^{43} + 44 q^{44} + 20 q^{47} - 53 q^{48} + 3 q^{49} + 11 q^{51} + 17 q^{52} - 40 q^{53} + 26 q^{54} + 30 q^{56} + 8 q^{57} - 18 q^{58} - 17 q^{59} + 13 q^{61} + 12 q^{62} - 9 q^{63} + 38 q^{64} - 8 q^{66} + 17 q^{67} + 34 q^{68} - 27 q^{69} - 16 q^{71} - 18 q^{72} - 4 q^{73} - 40 q^{74} - 11 q^{76} + 12 q^{77} + 61 q^{78} + 7 q^{79} + 17 q^{81} - 24 q^{82} + 30 q^{83} + 27 q^{84} + 34 q^{86} + 23 q^{87} + 9 q^{88} - 18 q^{89} - 34 q^{91} - 12 q^{92} - 15 q^{93} - 3 q^{94} + 34 q^{96} - 19 q^{97} - 26 q^{98} - 17 q^{99}+O(q^{100}) \) 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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