LMFDB - Embedded newform 225.2.k.c.124.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(49,225)]

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, 3]))

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

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

chi := DirichletCharacter("225.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.k (of order $6$, degree $2$, not 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 102x^{12} - 406x^{10} + 1167x^{8} - 1842x^{6} + 2023x^{4} - 441x^{2} + 81 $ x^16 - 12x^14 + 102x^12 - 406x^10 + 1167x^8 - 1842x^6 + 2023x^4 - 441*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.3
Root			$-1.27588 - 0.736627i$ of defining polynomial
Character	$\chi$	$=$	225.124
Dual form			225.2.k.c.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27588 - 0.736627i) q^{2} +(-0.350156 - 1.69629i) q^{3} +(0.0852394 + 0.147639i) q^{4} +(-0.802776 + 2.42219i) q^{6} +(-3.34791 - 1.93291i) q^{7} +2.69535i q^{8} +(-2.75478 + 1.18793i) q^{9} +O(q^{10})$	\(q+(-1.27588 - 0.736627i) q^{2} +(-0.350156 - 1.69629i) q^{3} +(0.0852394 + 0.147639i) q^{4} +(-0.802776 + 2.42219i) q^{6} +(-3.34791 - 1.93291i) q^{7} +2.69535i q^{8} +(-2.75478 + 1.18793i) q^{9} +(-0.130139 + 0.225407i) q^{11} +(0.220591 - 0.196287i) q^{12} +(3.53235 - 2.03940i) q^{13} +(2.84768 + 4.93232i) q^{14} +(2.15595 - 3.73421i) q^{16} +3.26028i q^{17} +(4.38982 + 0.513594i) q^{18} -4.24928 q^{19} +(-2.10649 + 6.35583i) q^{21} +(0.332082 - 0.191728i) q^{22} +(-7.53039 + 4.34768i) q^{23} +(4.57209 - 0.943794i) q^{24} -6.00912 q^{26} +(2.97968 + 4.25694i) q^{27} -0.659042i q^{28} +(2.11105 - 3.65644i) q^{29} +(-1.32643 - 2.29744i) q^{31} +(-0.832959 + 0.480909i) q^{32} +(0.427924 + 0.141825i) q^{33} +(2.40161 - 4.15971i) q^{34} +(-0.410201 - 0.305455i) q^{36} -2.27559i q^{37} +(5.42156 + 3.13014i) q^{38} +(-4.69629 - 5.27777i) q^{39} +(-2.82093 - 4.88599i) q^{41} +(7.36950 - 6.55756i) q^{42} +(-7.85712 - 4.53631i) q^{43} -0.0443719 q^{44} +12.8105 q^{46} +(1.23745 + 0.714441i) q^{47} +(-7.08921 - 2.34955i) q^{48} +(3.97232 + 6.88026i) q^{49} +(5.53037 - 1.14161i) q^{51} +(0.602191 + 0.347675i) q^{52} -11.3816i q^{53} +(-0.665919 - 7.62624i) q^{54} +(5.20988 - 9.02378i) q^{56} +(1.48791 + 7.20801i) q^{57} +(-5.38687 + 3.11011i) q^{58} +(-3.56212 - 6.16977i) q^{59} +(-1.26244 + 2.18660i) q^{61} +3.90833i q^{62} +(11.5189 + 1.34768i) q^{63} -7.20679 q^{64} +(-0.441506 - 0.496172i) q^{66} +(9.77361 - 5.64280i) q^{67} +(-0.481344 + 0.277904i) q^{68} +(10.0117 + 11.2513i) q^{69} -8.38158 q^{71} +(-3.20189 - 7.42510i) q^{72} -0.403568i q^{73} +(-1.67626 + 2.90337i) q^{74} +(-0.362207 - 0.627360i) q^{76} +(0.871386 - 0.503095i) q^{77} +(2.10413 + 10.1932i) q^{78} +(-1.52125 + 2.63488i) q^{79} +(6.17764 - 6.54498i) q^{81} +8.31189i q^{82} +(3.96660 + 2.29012i) q^{83} +(-1.11792 + 0.230768i) q^{84} +(6.68314 + 11.5755i) q^{86} +(-6.94157 - 2.30062i) q^{87} +(-0.607551 - 0.350770i) q^{88} -7.17772 q^{89} -15.7680 q^{91} +(-1.28377 - 0.741187i) q^{92} +(-3.43266 + 3.05446i) q^{93} +(-1.05255 - 1.82308i) q^{94} +(1.10743 + 1.24454i) q^{96} +(-2.69777 - 1.55756i) q^{97} -11.7045i q^{98} +(0.0907360 - 0.775544i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 16 * q^6 - 10 * q^9	$ 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9} + 2 q^{11} + 6 q^{14} - 8 q^{16} - 8 q^{19} - 30 q^{21} + 66 q^{24} - 40 q^{26} + 2 q^{29} + 8 q^{31} + 18 q^{34} - 28 q^{36} - 50 q^{39} + 10 q^{41} - 88 q^{44} - 6 q^{49} + 22 q^{51} - 52 q^{54} + 60 q^{56} + 34 q^{59} + 26 q^{61} - 76 q^{64} - 16 q^{66} + 54 q^{69} - 32 q^{71} + 80 q^{74} - 22 q^{76} - 14 q^{79} + 34 q^{81} - 54 q^{84} + 68 q^{86} + 36 q^{89} - 68 q^{91} + 6 q^{94} + 68 q^{96} + 34 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 16 * q^6 - 10 * q^9 + 2 * q^11 + 6 * q^14 - 8 * q^16 - 8 * q^19 - 30 * q^21 + 66 * q^24 - 40 * q^26 + 2 * q^29 + 8 * q^31 + 18 * q^34 - 28 * q^36 - 50 * q^39 + 10 * q^41 - 88 * q^44 - 6 * q^49 + 22 * q^51 - 52 * q^54 + 60 * q^56 + 34 * q^59 + 26 * q^61 - 76 * q^64 - 16 * q^66 + 54 * q^69 - 32 * q^71 + 80 * q^74 - 22 * q^76 - 14 * q^79 + 34 * q^81 - 54 * q^84 + 68 * q^86 + 36 * q^89 - 68 * q^91 + 6 * q^94 + 68 * q^96 + 34 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.27588	−	0.736627i	−0.902180	−	0.520874i	−0.0242735	−	0.999705i	$-0.507727\pi$
$2$	−1.27588	−	0.736627i	−0.902180	−	0.520874i	−0.877907	+	0.478831i	$0.841061\pi$
$3$	−0.350156	−	1.69629i	−0.202163	−	0.979352i
$3$	−0.350156	−	1.69629i	−0.202163	−	0.979352i
$4$	0.0852394	+	0.147639i	0.0426197	+	0.0738195i
$5$		0			0
$5$		0			0
$6$	−0.802776	+	2.42219i	−0.327732	+	0.988854i
$7$	−3.34791	−	1.93291i	−1.26539	−	0.730573i	−0.291278	−	0.956639i	$-0.594080\pi$
$7$	−3.34791	−	1.93291i	−1.26539	−	0.730573i	−0.974112	+	0.226066i	$0.927414\pi$
$8$			2.69535i			0.952950i
$9$	−2.75478	+	1.18793i	−0.918260	+	0.395977i
$10$		0			0
$11$	−0.130139	+	0.225407i	−0.0392384	+	0.0679628i	−0.884978	−	0.465634i	$-0.845826\pi$
$11$	−0.130139	+	0.225407i	−0.0392384	+	0.0679628i	0.845739	+	0.533596i	$0.179160\pi$
$12$	0.220591	−	0.196287i	0.0636792	−	0.0566633i
$13$	3.53235	−	2.03940i	0.979697	−	0.565629i	0.0775187	−	0.996991i	$-0.475300\pi$
$13$	3.53235	−	2.03940i	0.979697	−	0.565629i	0.902179	+	0.431362i	$0.141967\pi$
$14$	2.84768	+	4.93232i	0.761073	+	1.31822i
$15$		0			0
$16$	2.15595	−	3.73421i	0.538987	−	0.933553i
$17$			3.26028i			0.790734i	0.918523	+	0.395367i	$0.129383\pi$
$17$			3.26028i			0.790734i	−0.918523	+	0.395367i	$0.870617\pi$
$18$	4.38982	+	0.513594i	1.03469	+	0.121055i
$19$	−4.24928			−0.974853			−0.487426	−	0.873164i	$-0.662064\pi$
$19$	−4.24928			−0.974853			−0.487426	+	0.873164i	$0.662064\pi$
$20$		0			0
$21$	−2.10649	+	6.35583i	−0.459673	+	1.38696i
$22$	0.332082	−	0.191728i	0.0708002	−	0.0408765i
$23$	−7.53039	+	4.34768i	−1.57020	+	0.906553i	−0.574052	+	0.818819i	$0.694629\pi$
$23$	−7.53039	+	4.34768i	−1.57020	+	0.906553i	−0.996144	+	0.0877339i	$0.972037\pi$
$24$	4.57209	−	0.943794i	0.933274	−	0.192651i
$25$		0			0
$26$	−6.00912			−1.17849
$27$	2.97968	+	4.25694i	0.573439	+	0.819248i
$28$		−	0.659042i		−	0.124547i
$29$	2.11105	−	3.65644i	0.392012	−	0.678984i	−0.600703	−	0.799472i	$-0.705113\pi$
$29$	2.11105	−	3.65644i	0.392012	−	0.678984i	0.992715	+	0.120488i	$0.0384459\pi$
$30$		0			0
$31$	−1.32643	−	2.29744i	−0.238233	−	0.412632i	0.721974	−	0.691920i	$-0.243235\pi$
$31$	−1.32643	−	2.29744i	−0.238233	−	0.412632i	−0.960207	+	0.279288i	$0.909902\pi$
$32$	−0.832959	+	0.480909i	−0.147248	+	0.0850135i
$33$	0.427924	+	0.141825i	0.0744921	+	0.0246886i
$34$	2.40161	−	4.15971i	0.411873	−	0.713384i
$35$		0			0
$36$	−0.410201	−	0.305455i	−0.0683668	−	0.0509091i
$37$		−	2.27559i		−	0.374104i	−0.982350	−	0.187052i	$-0.940107\pi$
$37$		−	2.27559i		−	0.374104i	0.982350	−	0.187052i	$-0.0598933\pi$
$38$	5.42156	+	3.13014i	0.879493	+	0.507776i
$39$	−4.69629	−	5.27777i	−0.752008	−	0.845120i
$40$		0			0
$41$	−2.82093	−	4.88599i	−0.440555	−	0.763064i	0.557176	−	0.830395i	$-0.311885\pi$
$41$	−2.82093	−	4.88599i	−0.440555	−	0.763064i	−0.997731	+	0.0673308i	$0.978552\pi$
$42$	7.36950	−	6.55756i	1.13714	−	1.01185i
$43$	−7.85712	−	4.53631i	−1.19820	−	0.691780i	−0.238046	−	0.971254i	$-0.576507\pi$
$43$	−7.85712	−	4.53631i	−1.19820	−	0.691780i	−0.960153	+	0.279474i	$0.909840\pi$
$44$	−0.0443719			−0.00668931
$45$		0			0
$46$	12.8105			1.88880
$47$	1.23745	+	0.714441i	0.180500	+	0.104212i	0.587528	−	0.809204i	$-0.300101\pi$
$47$	1.23745	+	0.714441i	0.180500	+	0.104212i	−0.407027	+	0.913416i	$0.633435\pi$
$48$	−7.08921	−	2.34955i	−1.02324	−	0.339128i
$49$	3.97232	+	6.88026i	0.567474	+	0.982894i
$50$		0			0
$51$	5.53037	−	1.14161i	0.774406	−	0.159857i
$52$	0.602191	+	0.347675i	0.0835089	+	0.0482139i
$53$		−	11.3816i		−	1.56338i	−0.623667	−	0.781690i	$-0.714358\pi$
$53$		−	11.3816i		−	1.56338i	0.623667	−	0.781690i	$-0.285642\pi$
$54$	−0.665919	−	7.62624i	−0.0906201	−	1.03780i
$55$		0			0
$56$	5.20988	−	9.02378i	0.696200	−	1.20585i
$57$	1.48791	+	7.20801i	0.197079	+	0.954724i
$58$	−5.38687	+	3.11011i	−0.707331	+	0.408378i
$59$	−3.56212	−	6.16977i	−0.463748	−	0.803235i	0.535396	−	0.844601i	$-0.320162\pi$
$59$	−3.56212	−	6.16977i	−0.463748	−	0.803235i	−0.999144	+	0.0413660i	$0.986829\pi$
$60$		0			0
$61$	−1.26244	+	2.18660i	−0.161638	+	0.279966i	−0.935456	−	0.353442i	$-0.885011\pi$
$61$	−1.26244	+	2.18660i	−0.161638	+	0.279966i	0.773818	+	0.633408i	$0.218344\pi$
$62$			3.90833i			0.496358i
$63$	11.5189	+	1.34768i	1.45125	+	0.169791i
$64$	−7.20679			−0.900848
$65$		0			0
$66$	−0.441506	−	0.496172i	−0.0543456	−	0.0610746i
$67$	9.77361	−	5.64280i	1.19404	−	0.689377i	0.234817	−	0.972040i	$-0.424551\pi$
$67$	9.77361	−	5.64280i	1.19404	−	0.689377i	0.959219	+	0.282662i	$0.0912176\pi$
$68$	−0.481344	+	0.277904i	−0.0583716	+	0.0337008i
$69$	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	$0.665695\pi$
$72$	−3.20189	−	7.42510i	−0.377346	−	0.875056i
$73$		−	0.403568i		−	0.0472340i	−0.999721	−	0.0236170i	$-0.992482\pi$
$73$		−	0.403568i		−	0.0472340i	0.999721	−	0.0236170i	$-0.00751823\pi$
$74$	−1.67626	+	2.90337i	−0.194861	+	0.337509i
$75$		0			0
$76$	−0.362207	−	0.627360i	−0.0415480	−	0.0719632i
$77$	0.871386	−	0.503095i	0.0993036	−	0.0573330i
$78$	2.10413	+	10.1932i	0.238246	+	1.15415i
$79$	−1.52125	+	2.63488i	−0.171154	+	0.296447i	−0.938824	−	0.344399i	$-0.888083\pi$
$79$	−1.52125	+	2.63488i	−0.171154	+	0.296447i	0.767670	+	0.640846i	$0.221416\pi$
$80$		0			0
$81$	6.17764	−	6.54498i	0.686404	−	0.727220i
$82$			8.31189i			0.917895i
$83$	3.96660	+	2.29012i	0.435391	+	0.251373i	0.701641	−	0.712531i	$-0.252451\pi$
$83$	3.96660	+	2.29012i	0.435391	+	0.251373i	−0.266250	+	0.963904i	$0.585785\pi$
$84$	−1.11792	+	0.230768i	−0.121976	+	0.0251788i
$85$		0			0
$86$	6.68314	+	11.5755i	0.720661	+	1.24822i
$87$	−6.94157	−	2.30062i	−0.744215	−	0.246652i
$88$	−0.607551	−	0.350770i	−0.0647652	−	0.0373922i
$89$	−7.17772			−0.760837			−0.380419	−	0.924814i	$-0.624220\pi$
$89$	−7.17772			−0.760837			−0.380419	+	0.924814i	$0.624220\pi$
$90$		0			0
$91$	−15.7680			−1.65293
$92$	−1.28377	−	0.741187i	−0.133843	−	0.0772741i
$93$	−3.43266	+	3.05446i	−0.355950	+	0.316733i
$94$	−1.05255	−	1.82308i	−0.108563	−	0.188036i
$95$		0			0
$96$	1.10743	+	1.24454i	0.113026	+	0.127021i
$97$	−2.69777	−	1.55756i	−0.273917	−	0.158146i	0.356749	−	0.934200i	$-0.383885\pi$
$97$	−2.69777	−	1.55756i	−0.273917	−	0.158146i	−0.630666	+	0.776054i	$0.717218\pi$
$98$		−	11.7045i		−	1.18233i
$99$	0.0907360	−	0.775544i	0.00911931	−	0.0779451i
$100$		0			0
$101$	−1.92286	+	3.33049i	−0.191332	+	0.331396i	−0.945692	−	0.325065i	$-0.894614\pi$
$101$	−1.92286	+	3.33049i	−0.191332	+	0.331396i	0.754360	+	0.656461i	$0.227947\pi$
$102$	−7.89700	−	2.61727i	−0.781920	−	0.259149i
$103$	3.64318	−	2.10339i	0.358974	−	0.207254i	−0.309657	−	0.950848i	$-0.600214\pi$
$103$	3.64318	−	2.10339i	0.358974	−	0.207254i	0.668630	+	0.743595i	$0.266881\pi$
$104$	5.49691	+	9.52092i	0.539016	+	0.933603i
$105$		0			0
$106$	−8.38398	+	14.5215i	−0.814324	+	1.41045i
$107$		−	1.62655i		−	0.157245i	−0.996904	−	0.0786223i	$-0.974948\pi$
$107$		−	1.62655i		−	0.157245i	0.996904	−	0.0786223i	$-0.0250521\pi$
$108$	−0.374504	+	0.802776i	−0.0360367	+	0.0772471i
$109$	12.9021			1.23580			0.617900	−	0.786256i	$-0.287984\pi$
$109$	12.9021			1.23580			0.617900	+	0.786256i	$0.287984\pi$
$110$		0			0
$111$	−3.86005	+	0.796811i	−0.366380	+	0.0756299i
$112$	−14.4358	+	8.33452i	−1.36406	+	0.787539i
$113$	−1.15102	+	0.664539i	−0.108278	+	0.0625146i	−0.553161	−	0.833074i	$-0.686579\pi$
$113$	−1.15102	+	0.664539i	−0.108278	+	0.0625146i	0.444883	+	0.895589i	$0.353245\pi$
$114$	3.41122	−	10.2926i	0.319490	−	0.963987i
$115$		0			0
$116$	0.719778			0.0668297
$117$	−7.30818	+	9.81430i	−0.675641	+	0.907332i
$118$			10.4958i			0.966217i
$119$	6.30184	−	10.9151i	0.577689	−	1.00059i
$120$		0			0
$121$	5.46613	+	9.46761i	0.496921	+	0.860692i
$122$	3.22142	−	1.85989i	0.291654	−	0.168386i
$123$	−7.30028	+	6.49597i	−0.658244	+	0.585722i
$124$	0.226128	−	0.391665i	0.0203069	−	0.0351725i
$125$		0			0
$126$	−13.7040	−	10.2046i	−1.22085	−	0.909099i
$127$		−	1.65285i		−	0.146667i	−0.997307	−	0.0733335i	$-0.976636\pi$
$127$		−	1.65285i		−	0.146667i	0.997307	−	0.0733335i	$-0.0233637\pi$
$128$	10.8609	+	6.27053i	0.959975	+	0.554242i
$129$	−4.94366	+	14.9163i	−0.435265	+	1.31331i
$130$		0			0
$131$	6.58886	+	11.4122i	0.575672	+	0.997092i	0.995968	+	0.0897057i	$0.0285926\pi$
$131$	6.58886	+	11.4122i	0.575672	+	0.997092i	−0.420297	+	0.907387i	$0.638074\pi$
$132$	0.0155371	+	0.0752675i	0.00135233	+	0.00655119i
$133$	14.2262	+	8.21350i	1.23357	+	0.712201i
$134$	−16.6266			−1.43632
$135$		0			0
$136$	−8.78759			−0.753530
$137$	−17.5741	−	10.1464i	−1.50146	−	0.866867i	−0.999999	−	0.00168578i	$-0.999463\pi$
$137$	−17.5741	−	10.1464i	−1.50146	−	0.866867i	−0.501459	−	0.865181i	$-0.667203\pi$
$138$	−4.48566	−	21.7302i	−0.381845	−	1.84980i
$139$	1.53440	+	2.65766i	0.130146	+	0.225420i	0.923733	−	0.383038i	$-0.125122\pi$
$139$	1.53440	+	2.65766i	0.130146	+	0.225420i	−0.793587	+	0.608457i	$0.791789\pi$
$140$		0			0
$141$	0.778597	−	2.34923i	0.0655697	−	0.197841i
$142$	10.6939	+	6.17410i	0.897409	+	0.518119i
$143$			1.06162i			0.0887774i
$144$	−1.50318	+	12.8480i	−0.125265	+	1.07067i
$145$		0			0
$146$	−0.297279	+	0.514902i	−0.0246030	+	0.0426136i
$147$	10.2800	−	9.14736i	0.847877	−	0.754461i
$148$	0.335965	−	0.193970i	0.0276162	−	0.0159442i
$149$	2.03081	+	3.51747i	0.166371	+	0.288162i	0.937141	−	0.348951i	$-0.113462\pi$
$149$	2.03081	+	3.51747i	0.166371	+	0.288162i	−0.770771	+	0.637113i	$0.780129\pi$
$150$		0			0
$151$	6.80994	−	11.7952i	0.554185	−	0.959876i	−0.443782	−	0.896135i	$-0.646363\pi$
$151$	6.80994	−	11.7952i	0.554185	−	0.959876i	0.997966	−	0.0637412i	$-0.0203032\pi$
$152$		−	11.4533i		−	0.928986i
$153$	−3.87299	−	8.98135i	−0.313112	−	0.726099i
$154$	−1.48237			−0.119453
$155$		0			0
$156$	0.378896	−	1.14323i	0.0303360	−	0.0915316i
$157$	1.78627	−	1.03131i	0.142560	−	0.0823071i	−0.427023	−	0.904241i	$-0.640438\pi$
$157$	1.78627	−	1.03131i	0.142560	−	0.0823071i	0.569584	+	0.821933i	$0.307104\pi$
$158$	3.88185	−	2.24119i	0.308823	−	0.178299i
$159$	−19.3064	+	3.98533i	−1.53110	+	0.316057i
$160$		0			0
$161$	33.6147			2.64921
$162$	−12.7031	+	3.79996i	−0.998051	+	0.298553i
$163$			3.50525i			0.274552i	0.990533	+	0.137276i	$0.0438347\pi$
$163$			3.50525i			0.274552i	−0.990533	+	0.137276i	$0.956165\pi$
$164$	0.480909	−	0.832959i	0.0375527	−	0.0650431i
$165$		0			0
$166$	−3.37393	−	5.84381i	−0.261868	−	0.453568i
$167$	17.7837	−	10.2674i	1.37615	−	0.794518i	0.384453	−	0.923145i	$-0.374390\pi$
$167$	17.7837	−	10.2674i	1.37615	−	0.794518i	0.991693	+	0.128626i	$0.0410568\pi$
$168$	−17.1312	−	5.67772i	−1.32170	−	0.438046i
$169$	1.81833	−	3.14944i	0.139871	−	0.242264i
$170$		0			0
$171$	11.7058	−	5.04786i	0.895169	−	0.386019i
$172$		−	1.54669i		−	0.117934i
$173$	−6.71323	−	3.87589i	−0.510397	−	0.294678i	0.222600	−	0.974910i	$-0.428546\pi$
$173$	−6.71323	−	3.87589i	−0.510397	−	0.294678i	−0.732997	+	0.680232i	$0.761879\pi$
$174$	7.16189	+	8.04865i	0.542941	+	0.610167i
$175$		0			0
$176$	0.561145	+	0.971932i	0.0422979	+	0.0732622i
$177$	−9.21840	+	8.20275i	−0.692897	+	0.616557i
$178$	9.15788	+	5.28731i	0.686412	+	0.396300i
$179$	10.7632			0.804477			0.402238	−	0.915535i	$-0.368232\pi$
$179$	10.7632			0.804477			0.402238	+	0.915535i	$0.368232\pi$
$180$		0			0
$181$	−7.84572			−0.583168			−0.291584	−	0.956545i	$-0.594182\pi$
$181$	−7.84572			−0.583168			−0.291584	+	0.956545i	$0.594182\pi$
$182$	20.1180	+	11.6151i	1.49124	+	0.860970i
$183$	4.15116	+	1.37580i	0.306862	+	0.101702i
$184$	−11.7185	−	20.2970i	−0.863900	−	1.49632i
$185$		0			0
$186$	6.62965	−	1.36852i	0.486109	−	0.100345i
$187$	−0.734890	−	0.424289i	−0.0537405	−	0.0310271i
$188$			0.243594i			0.0177659i
$189$	−1.74738	−	20.0113i	−0.127103	−	1.45561i
$190$		0			0
$191$	2.86627	−	4.96453i	0.207396	−	0.359221i	−0.743497	−	0.668739i	$-0.766834\pi$
$191$	2.86627	−	4.96453i	0.207396	−	0.359221i	0.950894	+	0.309518i	$0.100168\pi$
$192$	2.52350	+	12.2248i	0.182118	+	0.882248i
$193$	7.34595	−	4.24119i	0.528773	−	0.305287i	−0.211744	−	0.977325i	$-0.567914\pi$
$193$	7.34595	−	4.24119i	0.528773	−	0.305287i	0.740517	+	0.672038i	$0.234581\pi$
$194$	2.29468	+	3.97450i	0.164748	+	0.285352i
$195$		0			0
$196$	−0.677196	+	1.17294i	−0.0483712	+	0.0837813i
$197$			10.6266i			0.757110i	0.925579	+	0.378555i	$0.123579\pi$
$197$			10.6266i			0.757110i	−0.925579	+	0.378555i	$0.876421\pi$
$198$	−0.687055	+	0.922659i	−0.0488268	+	0.0655705i
$199$	18.5784			1.31699			0.658495	−	0.752585i	$-0.271193\pi$
$199$	18.5784			1.31699			0.658495	+	0.752585i	$0.271193\pi$
$200$		0			0
$201$	−12.9941	−	14.6030i	−0.916533	−	1.03002i
$202$	4.90666	−	2.83286i	0.345231	−	0.199319i
$203$	−14.1352	+	8.16095i	−0.992095	+	0.572786i
$204$	0.639951	+	0.719188i	0.0448055	+	0.0503533i
$205$		0			0
$206$	−6.19767			−0.431812
$207$	15.5799	−	20.9225i	1.08287	−	1.45421i
$208$		−	17.5874i		−	1.21947i
$209$	0.552997	−	0.957820i	0.0382516	−	0.0662538i
$210$		0			0
$211$	−5.22666	−	9.05283i	−0.359818	−	0.623223i	0.628112	−	0.778123i	$-0.283828\pi$
$211$	−5.22666	−	9.05283i	−0.359818	−	0.623223i	−0.987930	+	0.154900i	$0.950494\pi$
$212$	1.68037	−	0.970160i	0.115408	−	0.0666308i
$213$	2.93486	+	14.2176i	0.201093	+	0.974172i
$214$	−1.19816	+	2.07528i	−0.0819046	+	0.141863i
$215$		0			0
$216$	−11.4739	+	8.03127i	−0.780703	+	0.546459i
$217$			10.2555i			0.696187i
$218$	−16.4615	−	9.50407i	−1.11492	−	0.643697i
$219$	−0.684567	+	0.141312i	−0.0462587	+	0.00954896i
$220$		0			0
$221$	6.64902	+	11.5164i	0.447261	+	0.774680i
$222$	5.51190	+	1.82679i	0.369934	+	0.122606i
$223$	3.40452	+	1.96560i	0.227983	+	0.131626i	0.609641	−	0.792677i	$-0.291313\pi$
$223$	3.40452	+	1.96560i	0.227983	+	0.131626i	−0.381658	+	0.924304i	$0.624647\pi$
$224$	3.71822			0.248434
$225$		0			0
$226$	1.95807			0.130249
$227$	−4.18411	−	2.41570i	−0.277709	−	0.160335i	0.354677	−	0.934989i	$-0.384591\pi$
$227$	−4.18411	−	2.41570i	−0.277709	−	0.160335i	−0.632386	+	0.774654i	$0.717924\pi$
$228$	−0.937354	+	0.834081i	−0.0620778	+	0.0552383i
$229$	−9.42648	−	16.3271i	−0.622919	−	1.07893i	−0.988939	−	0.148321i	$-0.952613\pi$
$229$	−9.42648	−	16.3271i	−0.622919	−	1.07893i	0.366020	−	0.930607i	$-0.380720\pi$
$230$		0			0
$231$	−1.15851	−	1.30196i	−0.0762247	−	0.0856626i
$232$	9.85539	+	5.69001i	0.647038	+	0.373568i
$233$			11.9021i			0.779735i	0.920871	+	0.389867i	$0.127479\pi$
$233$			11.9021i			0.779735i	−0.920871	+	0.389867i	$0.872521\pi$
$234$	16.5538	−	7.13842i	1.08216	−	0.466653i
$235$		0			0
$236$	0.607266	−	1.05181i	0.0395296	−	0.0684673i
$237$	5.00219	+	1.65786i	0.324927	+	0.107689i
$238$	−16.0807	+	9.28421i	−1.04236	+	0.601806i
$239$	−10.8147	−	18.7317i	−0.699547	−	1.21165i	−0.968624	−	0.248533i	$-0.920052\pi$
$239$	−10.8147	−	18.7317i	−0.699547	−	1.21165i	0.269076	−	0.963119i	$-0.413282\pi$
$240$		0			0
$241$	−1.94916	+	3.37604i	−0.125556	+	0.217470i	−0.921950	−	0.387308i	$-0.873405\pi$
$241$	−1.94916	+	3.37604i	−0.125556	+	0.217470i	0.796394	+	0.604778i	$0.206738\pi$
$242$		−	16.1060i		−	1.03533i
$243$	−13.2653	−	8.18729i	−0.850970	−	0.525215i
$244$	−0.430437			−0.0275559
$245$		0			0
$246$	14.0994	−	2.91046i	0.898942	−	0.185564i
$247$	−15.0100	+	8.66600i	−0.955061	+	0.551405i
$248$	6.19240	−	3.57518i	0.393218	−	0.227024i
$249$	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	$0.898970\pi$
$252$	0.782897	+	1.81552i	0.0493179	+	0.114367i
$253$		−	2.26321i		−	0.142287i
$254$	−1.21754	+	2.10883i	−0.0763950	+	0.132320i
$255$		0			0
$256$	−2.03131	−	3.51832i	−0.126957	−	0.219895i
$257$	−14.2151	+	8.20707i	−0.886711	+	0.511943i	−0.872865	−	0.487961i	$-0.837741\pi$
$257$	−14.2151	+	8.20707i	−0.886711	+	0.511943i	−0.0138459	+	0.999904i	$0.504407\pi$
$258$	17.2953	−	15.3898i	1.07676	−	0.958125i
$259$	−4.39851	+	7.61845i	−0.273310	+	0.473388i
$260$		0			0
$261$	−1.47187	+	12.5805i	−0.0911067	+	0.778712i
$262$		−	19.4141i		−	1.19941i
$263$	22.3497	+	12.9036i	1.37814	+	0.795670i	0.991936	−	0.126743i	$-0.0404522\pi$
$263$	22.3497	+	12.9036i	1.37814	+	0.795670i	0.386206	+	0.922413i	$0.373786\pi$
$264$	−0.382269	+	1.15341i	−0.0235270	+	0.0709872i
$265$		0			0
$266$	−12.1006	−	20.9588i	−0.741934	−	1.28507i
$267$	2.51332	+	12.1755i	0.153813	+	0.745127i
$268$	1.66619	+	0.961978i	0.101779	+	0.0587621i
$269$	12.5206			0.763392			0.381696	−	0.924288i	$-0.375340\pi$
$269$	12.5206			0.763392			0.381696	+	0.924288i	$0.375340\pi$
$270$		0			0
$271$	19.6462			1.19342			0.596710	−	0.802457i	$-0.296474\pi$
$271$	19.6462			1.19342			0.596710	+	0.802457i	$0.296474\pi$
$272$	12.1746	+	7.02899i	0.738191	+	0.426195i
$273$	5.52125	+	26.7470i	0.334161	+	1.61880i
$274$	14.9483	+	25.8911i	0.903057	+	1.56414i
$275$		0			0
$276$	−0.807745	+	2.43718i	−0.0486205	+	0.146701i
$277$	18.0394	+	10.4150i	1.08388	+	0.625779i	0.931941	−	0.362610i	$-0.118114\pi$
$277$	18.0394	+	10.4150i	1.08388	+	0.625779i	0.151941	+	0.988390i	$0.451448\pi$
$278$		−	4.52112i		−	0.271159i
$279$	6.38321	+	4.75324i	0.382153	+	0.284569i
$280$		0			0
$281$	−2.36221	+	4.09146i	−0.140917	+	0.244076i	−0.927842	−	0.372973i	$-0.878339\pi$
$281$	−2.36221	+	4.09146i	−0.140917	+	0.244076i	0.786925	+	0.617049i	$0.211672\pi$
$282$	−2.72390	+	2.42380i	−0.162206	+	0.144335i
$283$	−20.0506	+	11.5762i	−1.19189	+	0.688136i	−0.958734	−	0.284304i	$-0.908237\pi$
$283$	−20.0506	+	11.5762i	−1.19189	+	0.688136i	−0.233152	+	0.972440i	$0.574904\pi$
$284$	−0.714441	−	1.23745i	−0.0423943	−	0.0734291i
$285$		0			0
$286$	0.782020	−	1.35450i	0.0462418	−	0.0800932i
$287$			21.8105i			1.28743i
$288$	1.72333	−	2.31430i	0.101548	−	0.136371i
$289$	6.37059			0.374740
$290$		0			0
$291$	−1.69742	+	5.12158i	−0.0995048	+	0.300232i
$292$	0.0595824	−	0.0343999i	0.00348679	−	0.00201310i
$293$	14.6179	−	8.43963i	0.853985	−	0.493049i	−0.00800832	−	0.999968i	$-0.502549\pi$
$293$	14.6179	−	8.43963i	0.853985	−	0.493049i	0.861993	+	0.506919i	$0.169216\pi$
$294$	−19.8541	+	4.09839i	−1.15792	+	0.239023i
$295$		0			0
$296$	6.13350			0.356503
$297$	−1.34732	+	0.117647i	−0.0781792	+	0.00682657i
$298$		−	5.98380i		−	0.346632i
$299$	−17.7333	+	30.7150i	−1.02554	+	1.77630i
$300$		0			0
$301$	17.5366	+	30.3743i	1.01079	+	1.75074i
$302$	−17.3773	+	10.0328i	−0.999949	+	0.577321i
$303$	6.32277	+	2.09553i	0.363233	+	0.120385i
$304$	−9.16123	+	15.8677i	−0.525433	+	0.910076i
$305$		0			0
$306$	−1.67446	+	14.3120i	−0.0957225	+	0.818165i
$307$		−	22.7177i		−	1.29657i	−0.761398	−	0.648285i	$-0.775487\pi$
$307$		−	22.7177i		−	1.29657i	0.761398	−	0.648285i	$-0.224513\pi$
$308$	0.148553	+	0.0857671i	0.00846459	+	0.00488703i
$309$	−4.84364	−	5.44337i	−0.275545	−	0.309663i
$310$		0			0
$311$	−15.7968	−	27.3608i	−0.895754	−	1.55149i	−0.832869	−	0.553470i	$-0.813303\pi$
$311$	−15.7968	−	27.3608i	−0.895754	−	1.55149i	−0.0628843	−	0.998021i	$-0.520030\pi$
$312$	14.2254	−	12.6581i	0.805357	−	0.716626i
$313$	−26.4134	−	15.2498i	−1.49298	−	0.861970i	−0.493009	−	0.870024i	$-0.664103\pi$
$313$	−26.4134	−	15.2498i	−1.49298	−	0.861970i	−0.999968	+	0.00805392i	$0.997436\pi$
$314$	−3.03875			−0.171487
$315$		0			0
$316$	−0.518682			−0.0291781
$317$	−19.1296	−	11.0445i	−1.07443	−	0.620320i	−0.145039	−	0.989426i	$-0.546331\pi$
$317$	−19.1296	−	11.0445i	−1.07443	−	0.620320i	−0.929387	+	0.369106i	$0.879664\pi$
$318$	27.5683	+	9.13686i	1.54595	+	0.512369i
$319$	0.549459	+	0.951691i	0.0307638	+	0.0532845i
$320$		0			0
$321$	−2.75910	+	0.569547i	−0.153998	+	0.0317890i
$322$	−42.8882	−	24.7615i	−2.39007	−	1.37991i
$323$		−	13.8538i		−	0.770849i
$324$	1.49287	+	0.354170i	0.0829374	+	0.0196761i
$325$		0			0
$326$	2.58206	−	4.47226i	0.143007	−	0.247696i
$327$	−4.51776	−	21.8857i	−0.249833	−	1.21028i
$328$	13.1695	−	7.60339i	0.727162	−	0.419827i
$329$	−2.76191	−	4.78377i	−0.152269	−	0.263738i
$330$		0			0
$331$	14.8024	−	25.6385i	0.813612	−	1.40922i	−0.0967089	−	0.995313i	$-0.530832\pi$
$331$	14.8024	−	25.6385i	0.813612	−	1.40922i	0.910321	−	0.413904i	$-0.135835\pi$
$332$			0.780834i			0.0428538i
$333$	2.70324	+	6.26874i	0.148137	+	0.343525i
$334$	−30.2531			−1.65538
$335$		0			0
$336$	19.1925	+	21.5689i	1.04704	+	1.17668i
$337$	10.8522	−	6.26553i	0.591158	−	0.341305i	−0.174397	−	0.984675i	$-0.555798\pi$
$337$	10.8522	−	6.26553i	0.591158	−	0.341305i	0.765555	+	0.643370i	$0.222464\pi$
$338$	−4.63992	+	2.67886i	−0.252379	+	0.145711i
$339$	1.53028	+	1.71976i	0.0831136	+	0.0934045i
$340$		0			0
$341$	0.690479			0.0373915
$342$	−18.6536	−	2.18241i	−1.00867	−	0.118011i
$343$		−	3.65180i		−	0.197179i
$344$	12.2269	−	21.1777i	0.659232	−	1.14182i
$345$		0			0
$346$	5.71017	+	9.89030i	0.306980	+	0.531706i
$347$	−14.8068	+	8.54872i	−0.794872	+	0.458919i	−0.841675	−	0.539985i	$-0.818430\pi$
$347$	−14.8068	+	8.54872i	−0.794872	+	0.458919i	0.0468031	+	0.998904i	$0.485097\pi$
$348$	−0.252035	−	1.22095i	−0.0135105	−	0.0654498i
$349$	−9.20231	+	15.9389i	−0.492588	+	0.853188i	−0.999964	−	0.00853709i	$-0.997283\pi$
$349$	−9.20231	+	15.9389i	−0.492588	+	0.853188i	0.507375	+	0.861725i	$0.330616\pi$
$350$		0			0
$351$	19.2069	+	8.96024i	1.02519	+	0.478262i
$352$		−	0.250340i		−	0.0133432i
$353$	−27.4693	−	15.8594i	−1.46204	−	0.844110i	−0.462936	−	0.886391i	$-0.653204\pi$
$353$	−27.4693	−	15.8594i	−1.46204	−	0.844110i	−0.999106	+	0.0422810i	$0.986538\pi$
$354$	17.8039	−	3.67517i	0.946267	−	0.195333i
$355$		0			0
$356$	−0.611825	−	1.05971i	−0.0324267	−	0.0561646i
$357$	−20.7218	−	6.86774i	−1.09671	−	0.363479i
$358$	−13.7325	−	7.92844i	−0.725783	−	0.419031i
$359$	11.4533			0.604483			0.302241	−	0.953231i	$-0.402265\pi$
$359$	11.4533			0.604483			0.302241	+	0.953231i	$0.402265\pi$
$360$		0			0
$361$	−0.943580			−0.0496621
$362$	10.0102	+	5.77937i	0.526122	+	0.303757i
$363$	14.1458	−	12.5873i	0.742461	−	0.660660i
$364$	−1.34405	−	2.32797i	−0.0704475	−	0.122019i
$365$		0			0
$366$	−4.28291	−	4.81321i	−0.223871	−	0.251590i
$367$	−2.15846	−	1.24619i	−0.112671	−	0.0650506i	0.442606	−	0.896716i	$-0.354054\pi$
$367$	−2.15846	−	1.24619i	−0.112671	−	0.0650506i	−0.555276	+	0.831666i	$0.687388\pi$
$368$			37.4934i			1.95448i
$369$	13.5753	+	10.1088i	0.706700	+	0.526242i
$370$		0			0
$371$	−21.9996	+	38.1045i	−1.14216	+	1.97829i
$372$	−0.743556	−	0.246434i	−0.0385516	−	0.0127770i
$373$	13.0227	−	7.51868i	0.674292	−	0.389303i	−0.123409	−	0.992356i	$-0.539383\pi$
$373$	13.0227	−	7.51868i	0.674292	−	0.389303i	0.797701	+	0.603053i	$0.206049\pi$
$374$	0.625086	+	1.08268i	0.0323224	+	0.0559841i
$375$		0			0
$376$	−1.92567	+	3.33536i	−0.0993088	+	0.172008i
$377$		−	17.2211i		−	0.886932i
$378$	−12.5114	+	26.8191i	−0.643518	+	1.37943i
$379$	−6.27273			−0.322208			−0.161104	−	0.986937i	$-0.551505\pi$
$379$	−6.27273			−0.322208			−0.161104	+	0.986937i	$0.551505\pi$
$380$		0			0
$381$	−2.80371	+	0.578757i	−0.143639	+	0.0296506i
$382$	−7.31402	+	4.22275i	−0.374218	+	0.216055i
$383$	19.2161	−	11.0944i	0.981894	−	0.566897i	0.0790528	−	0.996870i	$-0.474810\pi$
$383$	19.2161	−	11.0944i	0.981894	−	0.566897i	0.902842	+	0.429973i	$0.141477\pi$
$384$	6.83362	−	20.6188i	0.348727	−	1.05220i
$385$		0			0
$386$	−12.4967			−0.636065
$387$	27.0335	+	3.16282i	1.37419	+	0.160775i
$388$		−	0.531061i		−	0.0269605i
$389$	−15.0461	+	26.0606i	−0.762869	+	1.32133i	0.178498	+	0.983940i	$0.442876\pi$
$389$	−15.0461	+	26.0606i	−0.762869	+	1.32133i	−0.941366	+	0.337387i	$0.890457\pi$
$390$		0			0
$391$	−14.1746	−	24.5512i	−0.716842	−	1.24161i
$392$	−18.5447	+	10.7068i	−0.936649	+	0.540774i
$393$	17.0513	−	15.1727i	0.860125	−	0.765360i
$394$	7.82781	−	13.5582i	0.394359	−	0.683050i
$395$		0			0
$396$	0.122235	−	0.0527107i	0.00614253	−	0.00264881i
$397$			29.2313i			1.46708i	0.679648	+	0.733538i	$0.262132\pi$
$397$			29.2313i			1.46708i	−0.679648	+	0.733538i	$0.737868\pi$
$398$	−23.7038	−	13.6854i	−1.18816	−	0.685986i
$399$	8.95107	−	27.0077i	0.448114	−	1.35208i
$400$		0			0
$401$	−12.1171	−	20.9874i	−0.605098	−	1.04806i	−0.992036	−	0.125954i	$-0.959801\pi$
$401$	−12.1171	−	20.9874i	−0.605098	−	1.04806i	0.386938	−	0.922106i	$-0.373533\pi$
$402$	5.82189	+	28.2034i	0.290369	+	1.40666i
$403$	−9.37080	−	5.41024i	−0.466793	−	0.269503i
$404$	−0.655614			−0.0326180
$405$		0			0
$406$	24.0463			1.19340
$407$	0.512934	+	0.296142i	0.0254252	+	0.0146792i
$408$	3.07703	+	14.9063i	0.152336	+	0.737971i
$409$	1.16995	+	2.02642i	0.0578504	+	0.100200i	0.893500	−	0.449063i	$-0.148242\pi$
$409$	1.16995	+	2.02642i	0.0578504	+	0.100200i	−0.835650	+	0.549263i	$0.814909\pi$
$410$		0			0
$411$	−11.0576	+	33.3636i	−0.545429	+	1.64570i
$412$	0.621086	+	0.358584i	0.0305987	+	0.0176662i
$413$			27.5411i			1.35521i
$414$	−35.2900	+	15.2179i	−1.73441	+	0.747921i
$415$		0			0
$416$	−1.96153	+	3.39748i	−0.0961721	+	0.166575i
$417$	3.97087	−	3.53338i	0.194454	−	0.173030i
$418$	−1.41111	+	0.814706i	−0.0690197	+	0.0398486i
$419$	11.4212	+	19.7821i	0.557964	+	0.966421i	0.997666	+	0.0682778i	$0.0217504\pi$
$419$	11.4212	+	19.7821i	0.557964	+	0.966421i	−0.439703	+	0.898143i	$0.644916\pi$
$420$		0			0
$421$	−5.93792	+	10.2848i	−0.289396	+	0.501249i	−0.973666	−	0.227980i	$-0.926788\pi$
$421$	−5.93792	+	10.2848i	−0.289396	+	0.501249i	0.684269	+	0.729229i	$0.260121\pi$
$422$			15.4004i			0.749679i
$423$	−4.25761	−	0.498126i	−0.207012	−	0.0242197i
$424$	30.6773			1.48982
$425$		0			0
$426$	6.72853	−	20.3018i	0.325998	−	0.983623i
$427$	8.45303	−	4.88036i	0.409071	−	0.236177i
$428$	0.240142	−	0.138646i	0.0116077	−	0.00670172i
$429$	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	$0.431479\pi$
$432$	22.3203	−	1.94900i	1.07389	−	0.0937713i
$433$		−	9.37059i		−	0.450322i	−0.974322	−	0.225161i	$-0.927709\pi$
$433$		−	9.37059i		−	0.450322i	0.974322	−	0.225161i	$-0.0722908\pi$
$434$	7.55446	−	13.0847i	0.362626	−	0.628086i
$435$		0			0
$436$	1.09977	+	1.90486i	0.0526695	+	0.0912262i
$437$	31.9988	−	18.4745i	1.53071	−	0.883756i
$438$	0.977517	+	0.323974i	0.0467075	+	0.0154801i
$439$	9.71155	−	16.8209i	0.463507	−	0.802817i	−0.535626	−	0.844455i	$-0.679924\pi$
$439$	9.71155	−	16.8209i	0.463507	−	0.802817i	0.999133	+	0.0416380i	$0.0132576\pi$
$440$		0			0
$441$	−19.1161	−	14.2348i	−0.910292	−	0.677846i
$442$		−	19.5914i		−	0.931868i
$443$	9.42172	+	5.43963i	0.447639	+	0.258445i	0.706833	−	0.707381i	$-0.250123\pi$
$443$	9.42172	+	5.43963i	0.447639	+	0.258445i	−0.259193	+	0.965825i	$0.583457\pi$
$444$	−0.446669	−	0.501974i	−0.0211980	−	0.0238226i
$445$		0			0
$446$	−2.89583	−	5.01572i	−0.137121	−	0.237501i
$447$	5.25554	−	4.67650i	0.248578	−	0.221191i
$448$	24.1276	+	13.9301i	1.13992	+	0.658136i
$449$	−1.34014			−0.0632451			−0.0316225	−	0.999500i	$-0.510067\pi$
$449$	−1.34014			−0.0632451			−0.0316225	+	0.999500i	$0.510067\pi$
$450$		0			0
$451$	1.46845			0.0691467
$452$	−0.196224	−	0.113290i	−0.00922959	−	0.00532871i
$453$	−22.3925	−	7.42146i	−1.05209	−	0.348691i
$454$	3.55894	+	6.16426i	0.167029	+	0.289303i
$455$		0			0
$456$	−19.4281	+	4.01045i	−0.909804	+	0.187806i
$457$	−17.4169	−	10.0556i	−0.814728	−	0.470383i	0.0338671	−	0.999426i	$-0.489218\pi$
$457$	−17.4169	−	10.0556i	−0.814728	−	0.470383i	−0.848595	+	0.529043i	$0.822551\pi$
$458$			27.7752i			1.29785i
$459$	−13.8788	+	9.71457i	−0.647807	+	0.453437i
$460$		0			0
$461$	16.8766	−	29.2312i	0.786024	−	1.36143i	−0.142362	−	0.989815i	$-0.545470\pi$
$461$	16.8766	−	29.2312i	0.786024	−	1.36143i	0.928386	−	0.371618i	$-0.121197\pi$
$462$	0.519062	+	2.51453i	0.0241490	+	0.116987i
$463$	4.54262	−	2.62268i	0.211114	−	0.121886i	−0.390715	−	0.920512i	$-0.627772\pi$
$463$	4.54262	−	2.62268i	0.211114	−	0.121886i	0.601829	+	0.798625i	$0.294439\pi$
$464$	−9.10262	−	15.7662i	−0.422578	−	0.731927i
$465$		0			0
$466$	8.76744	−	15.1856i	0.406144	−	0.703462i
$467$			14.2120i			0.657652i	0.944390	+	0.328826i	$0.106653\pi$
$467$			14.2120i			0.657652i	−0.944390	+	0.328826i	$0.893347\pi$
$468$	−2.07192	−	0.242408i	−0.0957745	−	0.0112053i
$469$	−43.6282			−2.01456
$470$		0			0
$471$	−2.37486	−	2.66891i	−0.109428	−	0.122977i
$472$	16.6297	−	9.60115i	0.765443	−	0.441929i
$473$	2.04503	−	1.18070i	0.0940307	−	0.0542887i
$474$	−5.16095	−	5.79997i	−0.237050	−	0.266401i
$475$		0			0
$476$	2.14866			0.0984837
$477$	13.5205	+	31.3538i	0.619063	+	1.43559i
$478$			31.8657i			1.45750i
$479$	10.2417	−	17.7391i	0.467954	−	0.810519i	−0.531376	−	0.847136i	$-0.678325\pi$
$479$	10.2417	−	17.7391i	0.467954	−	0.810519i	0.999329	+	0.0366168i	$0.0116581\pi$
$480$		0			0
$481$	−4.64084	−	8.03817i	−0.211604	−	0.366509i
$482$	4.97377	−	2.87161i	0.226549	−	0.130798i
$483$	−11.7704	−	57.0203i	−0.535572	−	2.59451i
$484$	−0.931859	+	1.61403i	−0.0423572	+	0.0733649i
$485$		0			0
$486$	10.8939	+	20.2175i	0.494158	+	0.917087i
$487$			31.3554i			1.42085i	0.703772	+	0.710425i	$0.251497\pi$
$487$			31.3554i			1.42085i	−0.703772	+	0.710425i	$0.748503\pi$
$488$	−5.89366	−	3.40271i	−0.266793	−	0.154033i
$489$	5.94591	−	1.22738i	0.268883	−	0.0555042i
$490$		0			0
$491$	5.19604	+	8.99980i	0.234494	+	0.406155i	0.959125	−	0.282981i	$-0.0913234\pi$
$491$	5.19604	+	8.99980i	0.234494	+	0.406155i	−0.724632	+	0.689136i	$0.757990\pi$
$492$	−1.58133	−	0.524094i	−0.0712919	−	0.0236280i
$493$	11.9210	+	6.88260i	0.536896	+	0.309977i
$494$	25.5345			1.14885
$495$		0			0
$496$	−11.4388			−0.513618
$497$	28.0607	+	16.2009i	1.25870	+	0.726709i
$498$	−8.73138	+	7.76940i	−0.391263	+	0.348155i
$499$	−1.91285	−	3.31316i	−0.0856310	−	0.148317i	0.820029	−	0.572322i	$-0.193957\pi$
$499$	−1.91285	−	3.31316i	−0.0856310	−	0.148317i	−0.905660	+	0.424005i	$0.860624\pi$
$500$		0			0
$501$	−23.6436	−	26.5711i	−1.05632	−	1.18711i
$502$	38.4081	+	22.1749i	1.71424	+	0.989715i
$503$		−	1.00236i		−	0.0446931i	−0.999750	−	0.0223466i	$-0.992886\pi$
$503$		−	1.00236i		−	0.0446931i	0.999750	−	0.0223466i	$-0.00711372\pi$
$504$	−3.63246	+	31.0475i	−0.161802	+	1.38297i
$505$		0			0
$506$	−1.66714	+	2.88757i	−0.0741134	+	0.128368i
$507$	−5.97905	−	1.98161i	−0.265539	−	0.0880065i
$508$	0.244026	−	0.140888i	0.0108269	−	0.00625090i
$509$	2.28161	+	3.95187i	0.101131	+	0.175163i	0.912151	−	0.409855i	$-0.134421\pi$
$509$	2.28161	+	3.95187i	0.101131	+	0.175163i	−0.811020	+	0.585018i	$0.801087\pi$
$510$		0			0
$511$	−0.780062	+	1.35111i	−0.0345079	+	0.0597695i
$512$		−	19.0969i		−	0.843971i
$513$	−12.6615	−	18.0889i	−0.559019	−	0.798646i
$514$	24.1822			1.06663
$515$		0			0
$516$	−2.62363	+	0.541583i	−0.115499	+	0.0238419i
$517$	−0.322080	+	0.185953i	−0.0141651	+	0.00817822i
$518$	11.2239	−	6.48013i	0.493151	−	0.284721i
$519$	−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	$0.168940\pi$
$522$	11.1451	−	14.9669i	0.487806	−	0.655084i
$523$			10.3998i			0.454749i	0.973807	+	0.227375i	$0.0730142\pi$
$523$			10.3998i			0.454749i	−0.973807	+	0.227375i	$0.926986\pi$
$524$	−1.12326	+	1.94555i	−0.0490699	+	0.0849916i
$525$		0			0
$526$	−19.0103	−	32.9268i	−0.828888	−	1.43568i
$527$	7.49029	−	4.32452i	0.326282	−	0.188379i
$528$	1.45219	−	1.29219i	0.0631984	−	0.0562354i
$529$	26.3046	−	45.5608i	1.14368	−	1.98091i
$530$		0			0
$531$	17.1421	+	12.7648i	0.743904	+	0.553946i
$532$			2.80046i			0.121415i
$533$	−19.9290	−	11.5060i	−0.863222	−	0.498381i
$534$	5.76210	−	17.3858i	0.249351	−	0.752357i
$535$		0			0
$536$	15.2093	+	26.3433i	0.656942	+	1.13786i
$537$	−3.76879	−	18.2574i	−0.162635	−	0.787866i
$538$	−15.9747	−	9.22298i	−0.688717	−	0.397631i
$539$	−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	$0.404779\pi$
$542$	−25.0661	−	14.4719i	−1.07668	−	0.621622i
$543$	2.74723	+	13.3086i	0.117895	+	0.571126i
$544$	−1.56790	−	2.71568i	−0.0672230	−	0.116434i
$545$		0			0
$546$	12.6581	−	38.1930i	0.541718	−	1.63451i
$547$	−19.7322	−	11.3924i	−0.843686	−	0.487102i	0.0148294	−	0.999890i	$-0.495279\pi$
$547$	−19.7322	−	11.3924i	−0.843686	−	0.487102i	−0.858515	+	0.512788i	$0.828613\pi$
$548$		−	3.45950i		−	0.147783i
$549$	0.880201	−	7.52330i	0.0375661	−	0.321087i
$550$		0			0
$551$	−8.97044	+	15.5373i	−0.382154	+	0.661910i
$552$	−30.3263	+	26.9851i	−1.29077	+	1.14856i
$553$	10.1860	−	5.88089i	0.433153	−	0.250081i
$554$	−15.3440	−	26.5766i	−0.651905	−	1.12913i
$555$		0			0
$556$	−0.261583	+	0.453075i	−0.0110936	+	0.0192146i
$557$		−	18.2341i		−	0.772605i	−0.922372	−	0.386303i	$-0.873752\pi$
$557$		−	18.2341i		−	0.772605i	0.922372	−	0.386303i	$-0.126248\pi$
$558$	−4.64282	−	10.7666i	−0.196546	−	0.455786i
$559$	−37.0054			−1.56516
$560$		0			0
$561$	−0.462390	+	1.39515i	−0.0195221	+	0.0589034i
$562$	6.02776	−	3.48013i	0.254266	−	0.146800i
$563$	−20.8809	+	12.0556i	−0.880025	+	0.508083i	−0.870667	−	0.491873i	$-0.836312\pi$
$563$	−20.8809	+	12.0556i	−0.880025	+	0.508083i	−0.00935862	+	0.999956i	$0.502979\pi$
$564$	0.413206	−	0.0852961i	0.0173991	−	0.00359161i
$565$		0			0
$566$	34.1095			1.43373
$567$	−33.3330	+	9.97113i	−1.39986	+	0.418748i
$568$		−	22.5913i		−	0.947910i
$569$	−16.0024	+	27.7170i	−0.670857	+	1.16196i	0.306804	+	0.951773i	$0.400740\pi$
$569$	−16.0024	+	27.7170i	−0.670857	+	1.16196i	−0.977661	+	0.210186i	$0.932593\pi$
$570$		0			0
$571$	9.89042	+	17.1307i	0.413901	+	0.716898i	0.995312	−	0.0967121i	$-0.0308326\pi$
$571$	9.89042	+	17.1307i	0.413901	+	0.716898i	−0.581411	+	0.813610i	$0.697499\pi$
$572$	−0.156737	+	0.0904921i	−0.00655350	+	0.00378367i
$573$	−9.42491	−	3.12366i	−0.393731	−	0.130493i
$574$	16.0662	−	27.8274i	0.670589	−	1.16150i
$575$		0			0
$576$	19.8531	−	8.56117i	0.827213	−	0.356715i
$577$		−	35.4119i		−	1.47422i	−0.675775	−	0.737108i	$-0.736191\pi$
$577$		−	35.4119i		−	1.47422i	0.675775	−	0.737108i	$-0.263809\pi$
$578$	−8.12808	−	4.69275i	−0.338084	−	0.195193i
$579$	−9.76650	−	10.9758i	−0.405882	−	0.456137i
$580$		0			0
$581$	−8.85321	−	15.3342i	−0.367293	−	0.636170i
$582$	5.93840	−	5.28413i	0.246154	−	0.219034i
$583$	2.56549	+	1.48119i	0.106252	+	0.0613445i
$584$	1.08776			0.0450117
$585$		0			0
$586$	−24.8675			−1.02726
$587$	28.0463	+	16.1925i	1.15759	+	0.668338i	0.950726	−	0.310031i	$-0.100339\pi$
$587$	28.0463	+	16.1925i	1.15759	+	0.668338i	0.206868	+	0.978369i	$0.433673\pi$
$588$	2.22676	+	0.738008i	0.0918302	+	0.0304349i
$589$	5.63636	+	9.76247i	0.232242	+	0.402255i
$590$		0			0
$591$	18.0257	−	3.72095i	0.741478	−	0.153060i
$592$	−8.49752	−	4.90605i	−0.349246	−	0.201637i
$593$		−	29.2504i		−	1.20117i	−0.799561	−	0.600585i	$-0.794934\pi$
$593$		−	29.2504i		−	1.20117i	0.799561	−	0.600585i	$-0.205066\pi$
$594$	1.80567	+	0.842367i	0.0740876	+	0.0345627i
$595$		0			0
$596$	−0.346210	+	0.599654i	−0.0141813	+	0.0245628i
$597$	−6.50535	−	31.5144i	−0.266246	−	1.28980i
$598$	45.2510	−	26.1257i	1.85045	−	1.06836i
$599$	2.03081	+	3.51747i	0.0829767	+	0.143720i	0.904527	−	0.426416i	$-0.140224\pi$
$599$	2.03081	+	3.51747i	0.0829767	+	0.143720i	−0.821551	+	0.570136i	$0.806891\pi$
$600$		0			0
$601$	−23.4538	+	40.6232i	−0.956700	+	1.65705i	−0.226271	+	0.974064i	$0.572653\pi$
$601$	−23.4538	+	40.6232i	−0.956700	+	1.65705i	−0.730429	+	0.682989i	$0.760680\pi$
$602$		−	51.6717i		−	2.10598i
$603$	−20.2209	+	27.1550i	−0.823459	+	1.10584i
$604$	2.32190			0.0944768
$605$		0			0
$606$	−6.52344	−	7.33116i	−0.264997	−	0.297808i
$607$	−35.4608	+	20.4733i	−1.43931	+	0.830987i	−0.997802	−	0.0662702i	$-0.978890\pi$
$607$	−35.4608	+	20.4733i	−1.43931	+	0.830987i	−0.441509	+	0.897257i	$0.645557\pi$
$608$	3.53948	−	2.04352i	0.143545	−	0.0828756i
$609$	18.7928	+	21.1197i	0.761524	+	0.855814i
$610$		0			0
$611$	5.82813			0.235781
$612$	0.995867	−	1.33737i	0.0402555	−	0.0540599i
$613$			33.3827i			1.34831i	0.738588	+	0.674157i	$0.235493\pi$
$613$			33.3827i			1.34831i	−0.738588	+	0.674157i	$0.764507\pi$
$614$	−16.7345	+	28.9850i	−0.675350	+	1.16974i
$615$		0			0
$616$	1.35602	+	2.34869i	0.0546355	+	0.0946314i
$617$	1.94752	−	1.12440i	0.0784040	−	0.0452666i	−0.460285	−	0.887771i	$-0.652253\pi$
$617$	1.94752	−	1.12440i	0.0784040	−	0.0452666i	0.538689	+	0.842504i	$0.318920\pi$
$618$	2.17015	+	10.5130i	0.0872963	+	0.422896i
$619$	−17.1467	+	29.6990i	−0.689184	+	1.19370i	0.282918	+	0.959144i	$0.408698\pi$
$619$	−17.1467	+	29.6990i	−0.689184	+	1.19370i	−0.972102	+	0.234558i	$0.924636\pi$
$620$		0			0
$621$	−40.9459	−	19.1018i	−1.64310	−	0.766527i
$622$			46.5454i			1.86630i
$623$	24.0303	+	13.8739i	0.962756	+	0.555847i
$624$	−29.8333	+	6.15833i	−1.19429	+	0.246531i
$625$		0			0
$626$	22.4669	+	38.9137i	0.897956	+	1.55531i
$627$	−1.81837	−	0.602656i	−0.0726188	−	0.0240678i
$628$	0.304522	+	0.175816i	0.0121517	+	0.00701581i
$629$	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	$0.621779\pi$
$632$	−7.10193	−	4.10030i	−0.282499	−	0.163101i
$633$	−13.5261	+	12.0358i	−0.537613	+	0.478381i
$634$	16.2713	+	28.1828i	0.646218	+	1.11928i
$635$		0			0
$636$	−2.23406	−	2.51068i	−0.0885862	−	0.0995548i
$637$	28.0632	+	16.2023i	1.11191	+	0.641959i
$638$		−	1.61899i		−	0.0640963i
$639$	23.0894	−	9.95674i	0.913403	−	0.393883i
$640$		0			0
$641$	−10.3175	+	17.8704i	−0.407517	+	0.705840i	−0.994611	−	0.103679i	$-0.966939\pi$
$641$	−10.3175	+	17.8704i	−0.407517	+	0.705840i	0.587094	+	0.809519i	$0.300272\pi$
$642$	3.93981	+	1.30576i	0.155492	+	0.0515340i
$643$	−23.5506	+	13.5970i	−0.928746	+	0.536212i	−0.886415	−	0.462892i	$-0.846812\pi$
$643$	−23.5506	+	13.5970i	−0.928746	+	0.536212i	−0.0423312	+	0.999104i	$0.513478\pi$
$644$	2.86530	+	4.96285i	0.112909	+	0.195564i
$645$		0			0
$646$	−10.2051	+	17.6758i	−0.401515	+	0.695445i
$647$			16.7316i			0.657787i	0.944367	+	0.328893i	$0.106676\pi$
$647$			16.7316i			0.657787i	−0.944367	+	0.328893i	$0.893324\pi$
$648$	17.6410	+	16.6509i	0.693004	+	0.654109i
$649$	1.85428			0.0727869
$650$		0			0
$651$	17.3962	−	3.59102i	0.681812	−	0.140743i
$652$	−0.517511	+	0.298785i	−0.0202673	+	0.0117013i
$653$	39.6060	−	22.8666i	1.54990	−	0.894837i	0.551756	−	0.834006i	$-0.313958\pi$
$653$	39.6060	−	22.8666i	1.54990	−	0.894837i	0.998148	−	0.0608319i	$-0.0193754\pi$
$654$	−10.3575	+	31.2514i	−0.405011	+	1.22203i
$655$		0			0
$656$	−24.3271			−0.949814
$657$	0.479411	+	1.11174i	0.0187036	+	0.0433731i
$658$			8.13799i			0.317252i
$659$	9.30543	−	16.1175i	0.362488	−	0.627848i	−0.625882	−	0.779918i	$-0.715261\pi$
$659$	9.30543	−	16.1175i	0.362488	−	0.627848i	0.988370	+	0.152070i	$0.0485941\pi$
$660$		0			0
$661$	−8.39799	−	14.5457i	−0.326644	−	0.565764i	0.655200	−	0.755456i	$-0.272584\pi$
$661$	−8.39799	−	14.5457i	−0.326644	−	0.565764i	−0.981844	+	0.189692i	$0.939251\pi$
$662$	−37.7720	+	21.8077i	−1.46805	+	0.847579i
$663$	17.2070	−	15.3112i	0.668264	−	0.594638i
$664$	−6.17267	+	10.6914i	−0.239546	+	0.414906i
$665$		0			0
$666$	1.16873	−	9.98942i	0.0452873	−	0.387082i
$667$			36.7126i			1.42152i
$668$	3.03175	+	1.75038i	0.117302	+	0.0677243i
$669$	2.14211	−	6.46331i	0.0828187	−	0.249886i
$670$		0			0
$671$	−0.328584	−	0.569124i	−0.0126848	−	0.0219708i
$672$	−1.30196	−	6.30718i	−0.0502242	−	0.243305i
$673$	43.2562	+	24.9740i	1.66740	+	0.962676i	0.969030	+	0.246944i	$0.0794262\pi$
$673$	43.2562	+	24.9740i	1.66740	+	0.962676i	0.698374	+	0.715733i	$0.253907\pi$
$674$	−18.4614			−0.711108
$675$		0			0
$676$	0.619973			0.0238451
$677$	−9.37998	−	5.41553i	−0.360502	−	0.208136i	0.308799	−	0.951127i	$-0.400073\pi$
$677$	−9.37998	−	5.41553i	−0.360502	−	0.208136i	−0.669301	+	0.742991i	$0.733406\pi$
$678$	−0.685630	−	3.32145i	−0.0263315	−	0.127559i
$679$	6.02125	+	10.4291i	0.231074	+	0.400232i
$680$		0			0
$681$	−2.63262	+	7.94333i	−0.100882	+	0.304389i
$682$	−0.880965	−	0.508625i	−0.0337339	−	0.0194763i
$683$		−	0.429870i		−	0.0164485i	−0.999966	−	0.00822426i	$-0.997382\pi$
$683$		−	0.429870i		−	0.0164485i	0.999966	−	0.00822426i	$-0.00261789\pi$
$684$	1.74306	+	1.29796i	0.0666476	+	0.0496289i
$685$		0			0
$686$	−2.69001	+	4.65924i	−0.102705	+	0.177891i
$687$	−24.3948	+	21.7071i	−0.930719	+	0.828176i
$688$	−33.8791	+	19.5601i	−1.29163	+	0.745721i
$689$	−23.2116	−	40.2037i	−0.884293	−	1.53164i
$690$		0			0
$691$	−17.3518	+	30.0542i	−0.660093	+	1.14331i	0.320498	+	0.947249i	$0.396150\pi$
$691$	−17.3518	+	30.0542i	−0.660093	+	1.14331i	−0.980591	+	0.196065i	$0.937184\pi$
$692$		−	1.32151i		−	0.0502364i
$693$	−1.80284	+	2.42106i	−0.0684841	+	0.0919686i
$694$	25.1889			0.956157
$695$		0			0
$696$	6.20097	−	18.7100i	0.235047	−	0.709200i
$697$	15.9297	−	9.19701i	0.603380	−	0.348362i
$698$	23.4820	−	13.5573i	0.888807	−	0.513153i
$699$	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	$0.488889\pi$
$702$	−17.9052	−	25.5805i	−0.675789	−	0.965472i
$703$			9.66962i			0.364696i
$704$	0.937884	−	1.62446i	0.0353478	−	0.0612242i
$705$		0			0
$706$	23.3649	+	40.4692i	0.879351	+	1.52308i
$707$	12.8751	−	7.43344i	0.484218	−	0.279563i
$708$	−1.99682	−	0.661797i	−0.0750450	−	0.0248719i
$709$	−3.15338	+	5.46181i	−0.118428	+	0.205123i	−0.919145	−	0.393920i	$-0.871119\pi$
$709$	−3.15338	+	5.46181i	−0.118428	+	0.205123i	0.800717	+	0.599043i	$0.204452\pi$
$710$		0			0
$711$	1.06065	−	9.06566i	0.0397775	−	0.339989i
$712$		−	19.3465i		−	0.725040i
$713$	19.9770	+	11.5337i	0.748145	+	0.431942i
$714$	21.3795	+	24.0266i	0.800106	+	0.899173i
$715$		0			0
$716$	0.917446	+	1.58906i	0.0342866	+	0.0593861i
$717$	−27.9875	+	24.9039i	−1.04521	+	0.930054i
$718$	−14.6130	−	8.43682i	−0.545352	−	0.314859i
$719$	−18.0129			−0.671770			−0.335885	−	0.941903i	$-0.609035\pi$
$719$	−18.0129			−0.671770			−0.335885	+	0.941903i	$0.609035\pi$
$720$		0			0
$721$	−16.2627			−0.605655
$722$	1.20389	+	0.695067i	0.0448042	+	0.0258677i
$723$	6.40925	+	2.12419i	0.238363	+	0.0789996i
$724$	−0.668765	−	1.15833i	−0.0248544	−	0.0430491i
$725$		0			0
$726$	−27.3204	+	5.63961i	−1.01395	+	0.209306i
$727$	−22.7612	−	13.1412i	−0.844165	−	0.487379i	0.0145126	−	0.999895i	$-0.495380\pi$
$727$	−22.7612	−	13.1412i	−0.844165	−	0.487379i	−0.858678	+	0.512516i	$0.828714\pi$
$728$		−	42.5002i		−	1.57516i
$729$	−9.24306	+	25.3686i	−0.342336	+	0.939578i
$730$		0			0
$731$	14.7896	−	25.6164i	0.547014	−	0.947456i
$732$	0.150720	+	0.730145i	0.00557078	+	0.0269869i
$733$	−41.2777	+	23.8317i	−1.52462	+	0.880243i	−0.525050	+	0.851071i	$0.675954\pi$
$733$	−41.2777	+	23.8317i	−1.52462	+	0.880243i	−0.999574	+	0.0291714i	$0.990713\pi$
$734$	1.83595	+	3.17997i	0.0677663	+	0.117375i
$735$		0			0
$736$	4.18167	−	7.24287i	0.154138	−	0.266976i
$737$			2.93739i			0.108200i
$738$	−9.87396	−	22.8975i	−0.363465	−	0.842867i
$739$	10.0273			0.368859			0.184429	−	0.982846i	$-0.440956\pi$
$739$	10.0273			0.368859			0.184429	+	0.982846i	$0.440956\pi$
$740$		0			0
$741$	19.9559	+	22.4267i	0.733097	+	0.823867i
$742$	56.1376	−	32.4110i	2.06088	−	1.18985i
$743$	−7.16433	+	4.13633i	−0.262834	+	0.151747i	−0.625627	−	0.780123i	$-0.715157\pi$
$743$	−7.16433	+	4.13633i	−0.262834	+	0.151747i	0.362793	+	0.931870i	$0.381823\pi$
$744$	−8.23285	−	9.25222i	−0.301831	−	0.339203i
$745$		0			0
$746$	−22.1539			−0.811111
$747$	−13.6476	−	1.59673i	−0.499340	−	0.0584212i
$748$		−	0.144665i		−	0.00528946i
$749$	−3.14398	+	5.44554i	−0.114879	+	0.198976i
$750$		0			0
$751$	2.89880	+	5.02087i	0.105779	+	0.183214i	0.914056	−	0.405588i	$-0.132933\pi$
$751$	2.89880	+	5.02087i	0.105779	+	0.183214i	−0.808277	+	0.588802i	$0.799600\pi$
$752$	5.33575	−	3.08060i	0.194575	−	0.112338i
$753$	10.5409	+	51.0638i	0.384130	+	1.86087i
$754$	−12.6855	+	21.9720i	−0.461980	+	0.800173i
$755$		0			0
$756$	2.80550	−	1.96373i	0.102035	−	0.0714203i
$757$		−	25.2804i		−	0.918830i	−0.888222	−	0.459415i	$-0.848059\pi$
$757$		−	25.2804i		−	0.918830i	0.888222	−	0.459415i	$-0.151941\pi$
$758$	8.00322	+	4.62066i	0.290690	+	0.167830i
$759$	−3.83905	+	0.792476i	−0.139349	+	0.0287651i
$760$		0			0
$761$	−9.73190	−	16.8561i	−0.352781	−	0.611035i	0.633954	−	0.773370i	$-0.281431\pi$
$761$	−9.73190	−	16.8561i	−0.352781	−	0.611035i	−0.986736	+	0.162335i	$0.948097\pi$
$762$	4.00352	+	1.32687i	0.145032	+	0.0480674i
$763$	−43.1951	−	24.9387i	−1.56377	−	0.902843i
$764$	0.977278			0.0353567
$765$		0			0
$766$	−32.6897			−1.18113
$767$	−25.1653	−	14.5292i	−0.908666	−	0.524618i
$768$	−5.25681	+	4.67764i	−0.189689	+	0.168790i
$769$	−24.6715	−	42.7324i	−0.889678	−	1.54097i	−0.840256	−	0.542190i	$-0.817595\pi$
$769$	−24.6715	−	42.7324i	−0.889678	−	1.54097i	−0.0494224	−	0.998778i	$-0.515738\pi$
$770$		0			0
$771$	18.8990	+	21.2391i	0.680632	+	0.764907i
$772$	1.25233	+	0.723033i	0.0450723	+	0.0260225i
$773$		−	20.8502i		−	0.749930i	−0.927039	−	0.374965i	$-0.877655\pi$
$773$		−	20.8502i		−	0.749930i	0.927039	−	0.374965i	$-0.122345\pi$
$774$	−32.1615	−	23.9490i	−1.15602	−	0.860827i
$775$		0			0
$776$	4.19816	−	7.27143i	0.150705	−	0.261029i
$777$	14.4632	+	4.79350i	0.518866	+	0.171966i
$778$	38.3940	−	22.1668i	1.37649	−	0.794717i
$779$	11.9869	+	20.7620i	0.429476	+	0.743875i
$780$		0			0
$781$	1.09077	−	1.88927i	0.0390308	−	0.0676034i
$782$			41.7657i			1.49354i
$783$	21.8555	−	1.90841i	0.781052	−	0.0682010i
$784$	34.2564			1.22344
$785$		0			0
$786$	−32.9320	+	6.79798i	−1.17464	+	0.242476i
$787$	−38.2682	+	22.0941i	−1.36411	+	0.787571i	−0.990169	−	0.139880i	$-0.955328\pi$
$787$	−38.2682	+	22.0941i	−1.36411	+	0.787571i	−0.373945	+	0.927451i	$0.621995\pi$
$788$	−1.56889	+	0.905801i	−0.0558895	+	0.0322678i
$789$	14.0623	−	42.4298i	0.500632	−	1.51054i
$790$		0			0
$791$	5.13799			0.182686
$792$	2.09036	+	0.244565i	0.0742778	+	0.00869025i
$793$			10.2985i			0.365709i
$794$	21.5326	−	37.2955i	0.764162	−	1.32357i
$795$		0			0
$796$	1.58362	+	2.74290i	0.0561297	+	0.0972196i
$797$	26.8792	−	15.5187i	0.952110	−	0.549701i	0.0583744	−	0.998295i	$-0.481408\pi$
$797$	26.8792	−	15.5187i	0.952110	−	0.549701i	0.893736	+	0.448594i	$0.148075\pi$
$798$	−31.3151	+	27.8649i	−1.10854	+	0.986408i
$799$	−2.32928	+	4.03443i	−0.0824039	+	0.142728i
$800$		0			0
$801$	19.7731	−	8.52664i	0.698647	−	0.301274i
$802$			35.7031i			1.26072i
$803$	0.0909671	+	0.0525199i	0.00321016	+	0.00185339i
$804$	1.04836	−	3.16319i	0.0369729	−	0.111557i
$805$		0			0
$806$	7.97065	+	13.8056i	0.280754	+	0.486281i
$807$	−4.38415	−	21.2385i	−0.154329	−	0.747629i
$808$	−8.97683	−	5.18278i	−0.315804	−	0.182329i
$809$	−14.6229			−0.514114			−0.257057	−	0.966396i	$-0.582753\pi$
$809$	−14.6229			−0.514114			−0.257057	+	0.966396i	$0.582753\pi$
$810$		0			0
$811$	26.7177			0.938187			0.469093	−	0.883149i	$-0.344581\pi$
$811$	26.7177			0.938187			0.469093	+	0.883149i	$0.344581\pi$
$812$	−2.40975	−	1.39127i	−0.0845656	−	0.0488240i
$813$	−6.87923	−	33.3256i	−0.241265	−	1.16878i
$814$	−0.436293	−	0.755682i	−0.0152921	−	0.0264866i
$815$		0			0
$816$	7.66018	−	23.1128i	0.268160	−	0.809110i
$817$	33.3871	+	19.2761i	1.16807	+	0.674384i
$818$		−	3.44727i		−	0.120531i
$819$	43.4373	−	18.7313i	1.51782	−	0.654523i
$820$		0			0
$821$	9.29903	−	16.1064i	0.324538	−	0.562117i	−0.656881	−	0.753995i	$-0.728124\pi$
$821$	9.29903	−	16.1064i	0.324538	−	0.562117i	0.981419	+	0.191878i	$0.0614577\pi$
$822$	38.6846	−	34.4225i	1.34928	−	1.20062i
$823$	2.65181	−	1.53102i	0.0924362	−	0.0533680i	−0.453069	−	0.891475i	$-0.649671\pi$
$823$	2.65181	−	1.53102i	0.0924362	−	0.0533680i	0.545506	+	0.838107i	$0.316338\pi$
$824$	5.66938	+	9.81966i	0.197502	+	0.342084i
$825$		0			0
$826$	20.2875	−	35.1390i	0.705892	−	1.22264i
$827$			7.27526i			0.252985i	0.991968	+	0.126493i	$0.0403720\pi$
$827$			7.27526i			0.252985i	−0.991968	+	0.126493i	$0.959628\pi$
$828$	4.41699	+	0.516773i	0.153501	+	0.0179591i
$829$	−10.5211			−0.365411			−0.182706	−	0.983168i	$-0.558486\pi$
$829$	−10.5211			−0.365411			−0.182706	+	0.983168i	$0.558486\pi$
$830$		0			0
$831$	11.3503	−	34.2469i	0.393738	−	1.18801i
$832$	−25.4569	+	14.6975i	−0.882559	+	0.509546i
$833$	−22.4315	+	12.9509i	−0.777207	+	0.448721i
$834$	−7.66912	+	1.58310i	−0.265560	+	0.0548182i
$835$		0			0
$836$	0.188549			0.00652109
$837$	5.82773	−	12.4921i	0.201436	−	0.431791i
$838$		−	33.6528i		−	1.16252i
$839$	7.59033	−	13.1468i	0.262047	−	0.453879i	−0.704739	−	0.709467i	$-0.748936\pi$
$839$	7.59033	−	13.1468i	0.262047	−	0.453879i	0.966786	+	0.255588i	$0.0822691\pi$
$840$		0			0
$841$	5.58695	+	9.67689i	0.192654	+	0.333686i
$842$	15.1521	−	8.74806i	0.522176	−	0.301478i
$843$	7.76744	+	2.57433i	0.267525	+	0.0886646i
$844$	0.891034	−	1.54332i	0.0306707	−	0.0531232i
$845$		0			0
$846$	5.06525	+	3.77182i	0.174147	+	0.129678i
$847$		−	42.2622i		−	1.45215i
$848$	−42.5012	−	24.5381i	−1.45950	−	0.842641i
$849$	26.6575	+	29.9581i	0.914882	+	1.02816i
$850$		0			0
$851$	9.89351	+	17.1361i	0.339145	+	0.587417i
$852$	−1.84890	+	1.64520i	−0.0633424	+	0.0563636i
$853$	9.08131	+	5.24309i	0.310938	+	0.179520i	0.647346	−	0.762196i	$-0.275879\pi$
$853$	9.08131	+	5.24309i	0.310938	+	0.179520i	−0.336408	+	0.941716i	$0.609212\pi$
$854$	−14.3800			−0.492074
$855$		0			0
$856$	4.38412			0.149846
$857$	7.65631	+	4.42038i	0.261535	+	0.150997i	0.625034	−	0.780597i	$-0.285085\pi$
$857$	7.65631	+	4.42038i	0.261535	+	0.150997i	−0.363500	+	0.931594i	$0.618418\pi$
$858$	−2.57145	−	0.852245i	−0.0877878	−	0.0290952i
$859$	−1.03416	−	1.79121i	−0.0352849	−	0.0611153i	0.847844	−	0.530246i	$-0.177901\pi$
$859$	−1.03416	−	1.79121i	−0.0352849	−	0.0611153i	−0.883129	+	0.469131i	$0.844567\pi$
$860$		0			0
$861$	36.9968	−	7.63707i	1.26085	−	0.260271i
$862$	−11.3159	−	6.53326i	−0.385423	−	0.222524i
$863$			22.4434i			0.763984i	0.924166	+	0.381992i	$0.124762\pi$
$863$			22.4434i			0.763984i	−0.924166	+	0.381992i	$0.875238\pi$
$864$	−4.52915	−	2.11290i	−0.154085	−	0.0718824i
$865$		0			0
$866$	−6.90263	+	11.9557i	−0.234561	+	0.406271i
$867$	−2.23070	−	10.8063i	−0.0757586	−	0.367003i
$868$	−1.51411	+	0.874171i	−0.0513922	+	0.0296713i
$869$	−0.395947	−	0.685801i	−0.0134316	−	0.0232642i
$870$		0			0
$871$	23.0159	−	39.8647i	0.779863	−	1.35076i
$872$			34.7758i			1.17766i
$873$	9.28203	+	1.08597i	0.314149	+	0.0367544i
$874$	−54.4353			−1.84130
$875$		0			0
$876$	−0.0792152	−	0.0890235i	−0.00267643	−	0.00300782i
$877$	24.1562	−	13.9466i	0.815697	−	0.470943i	−0.0332332	−	0.999448i	$-0.510580\pi$
$877$	24.1562	−	13.9466i	0.815697	−	0.470943i	0.848930	+	0.528505i	$0.177247\pi$
$878$	−24.7815	+	14.3076i	−0.836334	+	0.482857i
$879$	−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	$0.549647\pi$
$882$	13.9041	+	32.2433i	0.468175	+	1.08569i
$883$		−	49.2436i		−	1.65718i	−0.559858	−	0.828589i	$-0.689144\pi$
$883$		−	49.2436i		−	1.65718i	0.559858	−	0.828589i	$-0.310856\pi$
$884$	−1.13352	+	1.96331i	−0.0381243	+	0.0660333i
$885$		0			0
$886$	−8.01396	−	13.8806i	−0.269234	−	0.466328i
$887$	9.32542	−	5.38403i	0.313117	−	0.180778i	−0.335203	−	0.942146i	$-0.608805\pi$
$887$	9.32542	−	5.38403i	0.313117	−	0.180778i	0.648320	+	0.761368i	$0.275472\pi$
$888$	−2.14768	−	10.4042i	−0.0720716	−	0.349142i
$889$	−3.19482	+	5.53360i	−0.107151	+	0.185591i
$890$		0			0
$891$	0.671335	+	2.24424i	0.0224906	+	0.0751849i
$892$			0.670187i			0.0224395i
$893$	−5.25827	−	3.03586i	−0.175961	−	0.101591i
$894$	−10.1503	+	2.09527i	−0.339475	+	0.0700762i
$895$		0			0
$896$	−24.2408	−	41.9863i	−0.809829	−	1.40266i
$897$	58.3109	+	19.3258i	1.94695	+	0.645268i
$898$	1.70985	+	0.987183i	0.0570585	+	0.0329427i
$899$	−11.2006			−0.373561
$900$		0			0
$901$	37.1071			1.23622
$902$	−1.87356	−	1.08170i	−0.0623828	−	0.0360167i
$903$	45.3829	−	40.3828i	1.51025	−	1.34386i
$904$	−1.79116	−	3.10239i	−0.0595733	−	0.103184i
$905$		0			0
$906$	23.1032	+	25.9638i	0.767553	+	0.862590i
$907$	27.6871	+	15.9852i	0.919336	+	0.530779i	0.883423	−	0.468576i	$-0.155233\pi$
$907$	27.6871	+	15.9852i	0.919336	+	0.530779i	0.0359130	+	0.999355i	$0.488566\pi$
$908$		−	0.823651i		−	0.0273338i
$909$	1.34066	−	11.4590i	0.0444670	−	0.380071i
$910$		0			0
$911$	5.04010	−	8.72970i	0.166986	−	0.289228i	−0.770373	−	0.637594i	$-0.779930\pi$
$911$	5.04010	−	8.72970i	0.166986	−	0.289228i	0.937359	+	0.348366i	$0.113263\pi$
$912$	30.1241	+	9.98390i	0.997508	+	0.330600i
$913$	−1.03242	+	0.596067i	−0.0341681	+	0.0197269i
$914$	14.8145	+	25.6595i	0.490021	+	0.848741i
$915$		0			0
$916$	1.60702	−	2.78343i	0.0530973	−	0.0919672i
$917$		−	50.9428i		−	1.68228i
$918$	24.8636	−	2.17108i	0.820623	−	0.0716564i
$919$	29.7976			0.982932			0.491466	−	0.870897i	$-0.336461\pi$
$919$	29.7976			0.982932			0.491466	+	0.870897i	$0.336461\pi$
$920$		0			0
$921$	−38.5358	+	7.95476i	−1.26980	+	0.262118i
$922$	−43.0650	+	24.8636i	−1.41827	+	0.818839i
$923$	−29.6067	+	17.0934i	−0.974516	+	0.562637i
$924$	0.0934688	−	0.282020i	0.00307490	−	0.00927779i
$925$		0			0
$926$	−7.72776			−0.253950
$927$	−7.53749	+	10.1222i	−0.247564	+	0.332458i
$928$			4.06089i			0.133305i
$929$	−6.19275	+	10.7262i	−0.203178	+	0.351914i	−0.949551	−	0.313614i	$-0.898460\pi$
$929$	−6.19275	+	10.7262i	−0.203178	+	0.351914i	0.746373	+	0.665528i	$0.231794\pi$
$930$		0			0
$931$	−16.8795	−	29.2362i	−0.553204	−	0.958177i
$932$	−1.75722	+	1.01453i	−0.0575597	+	0.0332321i
$933$	−40.8805	+	36.3765i	−1.33837	+	1.19091i
$934$	10.4689	−	18.1327i	0.342554	−	0.593321i
$935$		0			0
$936$	−26.4530	−	19.6981i	−0.864642	−	0.643853i
$937$		−	44.4280i		−	1.45140i	−0.688012	−	0.725699i	$-0.741516\pi$
$937$		−	44.4280i		−	1.45140i	0.688012	−	0.725699i	$-0.258484\pi$
$938$	55.6641	+	32.1377i	1.81750	+	1.04933i
$939$	−16.6192	+	50.1446i	−0.542348	+	1.63641i
$940$		0			0
$941$	−7.66617	−	13.2782i	−0.249910	−	0.432857i	0.713591	−	0.700563i	$-0.247068\pi$
$941$	−7.66617	−	13.2782i	−0.249910	−	0.432857i	−0.963501	+	0.267706i	$0.913734\pi$
$942$	1.06404	+	5.15459i	0.0346682	+	0.167946i
$943$	42.4854	+	24.5290i	1.38352	+	0.798773i
$944$	−30.7189			−0.999816
$945$		0			0
$946$	−3.47894			−0.113110
$947$	18.7925	+	10.8498i	0.610673	+	0.352572i	0.773229	−	0.634127i	$-0.218640\pi$
$947$	18.7925	+	10.8498i	0.610673	+	0.352572i	−0.162556	+	0.986699i	$0.551974\pi$
$948$	0.181620	+	0.879833i	0.00589873	+	0.0285756i
$949$	−0.823037	−	1.42554i	−0.0267169	−	0.0462751i
$950$		0			0
$951$	−12.0363	+	36.3166i	−0.390303	+	1.17765i
$952$	29.4200	+	16.9857i	0.953509	+	0.550508i
$953$			36.9099i			1.19563i	0.801634	+	0.597815i	$0.203964\pi$
$953$			36.9099i			1.19563i	−0.801634	+	0.597815i	$0.796036\pi$
$954$	5.84552	−	49.9631i	0.189256	−	1.61762i
$955$		0			0
$956$	1.84368	−	3.19336i	0.0596290	−	0.103281i
$957$	1.42194	−	1.26528i	0.0459649	−	0.0409007i
$958$	−26.1342	+	15.0886i	−0.844357	+	0.487490i
$959$	39.2243	+	67.9385i	1.26662	+	2.19385i
$960$		0			0
$961$	11.9812	−	20.7520i	0.386490	−	0.669420i
$962$			13.6743i			0.440876i
$963$	1.93223	+	4.48079i	0.0622652	+	0.144391i
$964$	−0.664581			−0.0214047
$965$		0			0
$966$	−26.9851	+	81.4212i	−0.868231	+	2.61968i
$967$	18.4794	−	10.6691i	0.594258	−	0.343095i	−0.172521	−	0.985006i	$-0.555191\pi$
$967$	18.4794	−	10.6691i	0.594258	−	0.343095i	0.766779	+	0.641911i	$0.221858\pi$
$968$	−25.5185	+	14.7331i	−0.820197	+	0.473541i
$969$	−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	$0.739460\pi$
$972$	0.0780359	−	2.65636i	0.00250300	−	0.0852027i
$973$		−	11.8635i		−	0.380325i
$974$	23.0973	−	40.0057i	0.740085	−	1.28186i
$975$		0			0
$976$	5.44349	+	9.42840i	0.174242	+	0.301796i
$977$	−42.3826	+	24.4696i	−1.35594	+	0.782852i	−0.989074	−	0.147423i	$-0.952902\pi$
$977$	−42.3826	+	24.4696i	−1.35594	+	0.782852i	−0.366865	+	0.930274i	$0.619569\pi$
$978$	−8.49036	−	2.81393i	−0.271492	−	0.0899795i
$979$	0.934101	−	1.61791i	0.0298540	−	0.0517087i
$980$		0			0
$981$	−35.5426	+	15.3268i	−1.13479	+	0.489349i
$982$		−	15.3102i		−	0.488567i
$983$	31.2712	+	18.0545i	0.997398	+	0.575848i	0.907477	−	0.420101i	$-0.138005\pi$
$983$	31.2712	+	18.0545i	0.997398	+	0.575848i	0.0899205	+	0.995949i	$0.471339\pi$
$984$	−17.5089	−	19.6768i	−0.558164	−	0.627274i
$985$		0			0
$986$	−10.1398	−	17.5627i	−0.322918	−	0.559310i
$987$	−7.14754	+	6.36005i	−0.227509	+	0.202443i
$988$	−2.55888	−	1.47737i	−0.0814088	−	0.0470014i
$989$	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	$0.330258\pi$
$992$	2.20972	+	1.27578i	0.0701586	+	0.0405061i
$993$	−48.6733	−	16.1316i	−1.54460	−	0.511921i
$994$	−23.8680	−	41.3406i	−0.757048	−	1.31125i
$995$		0			0
$996$	1.32452	−	0.273414i	0.0419690	−	0.00866345i
$997$	−44.8324	−	25.8840i	−1.41986	−	0.819754i	−0.423570	−	0.905863i	$-0.639223\pi$
$997$	−44.8324	−	25.8840i	−1.41986	−	0.819754i	−0.996286	+	0.0861095i	$0.972557\pi$
$998$			5.63624i			0.178412i
$999$	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.k.c.124.3		16
3.2	odd	2		675.2.k.c.424.6		16
5.2	odd	4		225.2.e.e.151.3	yes	8
5.3	odd	4		225.2.e.c.151.2	yes	8
5.4	even	2	inner	225.2.k.c.124.6		16
9.2	odd	6		2025.2.b.o.649.3		8
9.4	even	3	inner	225.2.k.c.49.6		16
9.5	odd	6		675.2.k.c.199.3		16
9.7	even	3		2025.2.b.n.649.6		8
15.2	even	4		675.2.e.c.451.2		8
15.8	even	4		675.2.e.e.451.3		8
15.14	odd	2		675.2.k.c.424.3		16
45.2	even	12		2025.2.a.z.1.3		4
45.4	even	6	inner	225.2.k.c.49.3		16
45.7	odd	12		2025.2.a.q.1.2		4
45.13	odd	12		225.2.e.c.76.2	✓	8
45.14	odd	6		675.2.k.c.199.6		16
45.22	odd	12		225.2.e.e.76.3	yes	8
45.23	even	12		675.2.e.e.226.3		8
45.29	odd	6		2025.2.b.o.649.6		8
45.32	even	12		675.2.e.c.226.2		8
45.34	even	6		2025.2.b.n.649.3		8
45.38	even	12		2025.2.a.p.1.2		4
45.43	odd	12		2025.2.a.y.1.3		4

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

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.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.27588 - 0.736627i) q^{2} +(-0.350156 - 1.69629i) q^{3} +(0.0852394 + 0.147639i) q^{4} +(-0.802776 + 2.42219i) q^{6} +(-3.34791 - 1.93291i) q^{7} +2.69535i q^{8} +(-2.75478 + 1.18793i) q^{9} +O(q^{10})\)	\(q+(-1.27588 - 0.736627i) q^{2} +(-0.350156 - 1.69629i) q^{3} +(0.0852394 + 0.147639i) q^{4} +(-0.802776 + 2.42219i) q^{6} +(-3.34791 - 1.93291i) q^{7} +2.69535i q^{8} +(-2.75478 + 1.18793i) q^{9} +(-0.130139 + 0.225407i) q^{11} +(0.220591 - 0.196287i) q^{12} +(3.53235 - 2.03940i) q^{13} +(2.84768 + 4.93232i) q^{14} +(2.15595 - 3.73421i) q^{16} +3.26028i q^{17} +(4.38982 + 0.513594i) q^{18} -4.24928 q^{19} +(-2.10649 + 6.35583i) q^{21} +(0.332082 - 0.191728i) q^{22} +(-7.53039 + 4.34768i) q^{23} +(4.57209 - 0.943794i) q^{24} -6.00912 q^{26} +(2.97968 + 4.25694i) q^{27} -0.659042i q^{28} +(2.11105 - 3.65644i) q^{29} +(-1.32643 - 2.29744i) q^{31} +(-0.832959 + 0.480909i) q^{32} +(0.427924 + 0.141825i) q^{33} +(2.40161 - 4.15971i) q^{34} +(-0.410201 - 0.305455i) q^{36} -2.27559i q^{37} +(5.42156 + 3.13014i) q^{38} +(-4.69629 - 5.27777i) q^{39} +(-2.82093 - 4.88599i) q^{41} +(7.36950 - 6.55756i) q^{42} +(-7.85712 - 4.53631i) q^{43} -0.0443719 q^{44} +12.8105 q^{46} +(1.23745 + 0.714441i) q^{47} +(-7.08921 - 2.34955i) q^{48} +(3.97232 + 6.88026i) q^{49} +(5.53037 - 1.14161i) q^{51} +(0.602191 + 0.347675i) q^{52} -11.3816i q^{53} +(-0.665919 - 7.62624i) q^{54} +(5.20988 - 9.02378i) q^{56} +(1.48791 + 7.20801i) q^{57} +(-5.38687 + 3.11011i) q^{58} +(-3.56212 - 6.16977i) q^{59} +(-1.26244 + 2.18660i) q^{61} +3.90833i q^{62} +(11.5189 + 1.34768i) q^{63} -7.20679 q^{64} +(-0.441506 - 0.496172i) q^{66} +(9.77361 - 5.64280i) q^{67} +(-0.481344 + 0.277904i) q^{68} +(10.0117 + 11.2513i) q^{69} -8.38158 q^{71} +(-3.20189 - 7.42510i) q^{72} -0.403568i q^{73} +(-1.67626 + 2.90337i) q^{74} +(-0.362207 - 0.627360i) q^{76} +(0.871386 - 0.503095i) q^{77} +(2.10413 + 10.1932i) q^{78} +(-1.52125 + 2.63488i) q^{79} +(6.17764 - 6.54498i) q^{81} +8.31189i q^{82} +(3.96660 + 2.29012i) q^{83} +(-1.11792 + 0.230768i) q^{84} +(6.68314 + 11.5755i) q^{86} +(-6.94157 - 2.30062i) q^{87} +(-0.607551 - 0.350770i) q^{88} -7.17772 q^{89} -15.7680 q^{91} +(-1.28377 - 0.741187i) q^{92} +(-3.43266 + 3.05446i) q^{93} +(-1.05255 - 1.82308i) q^{94} +(1.10743 + 1.24454i) q^{96} +(-2.69777 - 1.55756i) q^{97} -11.7045i q^{98} +(0.0907360 - 0.775544i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 16 * q^6 - 10 * q^9	\( 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9} + 2 q^{11} + 6 q^{14} - 8 q^{16} - 8 q^{19} - 30 q^{21} + 66 q^{24} - 40 q^{26} + 2 q^{29} + 8 q^{31} + 18 q^{34} - 28 q^{36} - 50 q^{39} + 10 q^{41} - 88 q^{44} - 6 q^{49} + 22 q^{51} - 52 q^{54} + 60 q^{56} + 34 q^{59} + 26 q^{61} - 76 q^{64} - 16 q^{66} + 54 q^{69} - 32 q^{71} + 80 q^{74} - 22 q^{76} - 14 q^{79} + 34 q^{81} - 54 q^{84} + 68 q^{86} + 36 q^{89} - 68 q^{91} + 6 q^{94} + 68 q^{96} + 34 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 16 * q^6 - 10 * q^9 + 2 * q^11 + 6 * q^14 - 8 * q^16 - 8 * q^19 - 30 * q^21 + 66 * q^24 - 40 * q^26 + 2 * q^29 + 8 * q^31 + 18 * q^34 - 28 * q^36 - 50 * q^39 + 10 * q^41 - 88 * q^44 - 6 * q^49 + 22 * q^51 - 52 * q^54 + 60 * q^56 + 34 * q^59 + 26 * q^61 - 76 * q^64 - 16 * q^66 + 54 * q^69 - 32 * q^71 + 80 * q^74 - 22 * q^76 - 14 * q^79 + 34 * q^81 - 54 * q^84 + 68 * q^86 + 36 * q^89 - 68 * q^91 + 6 * q^94 + 68 * q^96 + 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more