LMFDB - Embedded newform 450.2.f.b.143.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(107,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("450.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.f (of order $4$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			143.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	450.143
Dual form			450.2.f.b.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.00000 + 2.00000i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.00000 + 2.00000i) q^{7} +(0.707107 - 0.707107i) q^{8} -2.82843i q^{11} +(3.00000 + 3.00000i) q^{13} +2.82843 q^{14} -1.00000 q^{16} +(2.82843 + 2.82843i) q^{17} +8.00000i q^{19} +(-2.00000 + 2.00000i) q^{22} +(-2.82843 + 2.82843i) q^{23} -4.24264i q^{26} +(-2.00000 - 2.00000i) q^{28} +1.41421 q^{29} +4.00000 q^{31} +(0.707107 + 0.707107i) q^{32} -4.00000i q^{34} +(3.00000 - 3.00000i) q^{37} +(5.65685 - 5.65685i) q^{38} +9.89949i q^{41} +2.82843 q^{44} +4.00000 q^{46} -1.00000i q^{49} +(-3.00000 + 3.00000i) q^{52} +(2.82843 - 2.82843i) q^{53} +2.82843i q^{56} +(-1.00000 - 1.00000i) q^{58} -2.82843 q^{59} +(-2.82843 - 2.82843i) q^{62} -1.00000i q^{64} +(4.00000 - 4.00000i) q^{67} +(-2.82843 + 2.82843i) q^{68} -5.65685i q^{71} +(-1.00000 - 1.00000i) q^{73} -4.24264 q^{74} -8.00000 q^{76} +(5.65685 + 5.65685i) q^{77} -12.0000i q^{79} +(7.00000 - 7.00000i) q^{82} +(-8.48528 + 8.48528i) q^{83} +(-2.00000 - 2.00000i) q^{88} -9.89949 q^{89} -12.0000 q^{91} +(-2.82843 - 2.82843i) q^{92} +(3.00000 - 3.00000i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{7}+O(q^{10}) $ 4 * q - 8 * q^7	$ 4 q - 8 q^{7} + 12 q^{13} - 4 q^{16} - 8 q^{22} - 8 q^{28} + 16 q^{31} + 12 q^{37} + 16 q^{46} - 12 q^{52} - 4 q^{58} + 16 q^{67} - 4 q^{73} - 32 q^{76} + 28 q^{82} - 8 q^{88} - 48 q^{91} + 12 q^{97}+O(q^{100}) $ 4 * q - 8 * q^7 + 12 * q^13 - 4 * q^16 - 8 * q^22 - 8 * q^28 + 16 * q^31 + 12 * q^37 + 16 * q^46 - 12 * q^52 - 4 * q^58 + 16 * q^67 - 4 * q^73 - 32 * q^76 + 28 * q^82 - 8 * q^88 - 48 * q^91 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.00000	+	2.00000i	−0.755929	+	0.755929i	−0.975579	−	0.219650i	$-0.929509\pi$
$7$	−2.00000	+	2.00000i	−0.755929	+	0.755929i	0.219650	+	0.975579i	$0.429509\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$		−	2.82843i		−	0.852803i	−0.904534	−	0.426401i	$-0.859781\pi$
$11$		−	2.82843i		−	0.852803i	0.904534	−	0.426401i	$-0.140219\pi$
$12$		0			0
$13$	3.00000	+	3.00000i	0.832050	+	0.832050i	0.987797	−	0.155747i	$-0.0497784\pi$
$13$	3.00000	+	3.00000i	0.832050	+	0.832050i	−0.155747	+	0.987797i	$0.549778\pi$
$14$	2.82843			0.755929
$15$		0			0
$16$	−1.00000			−0.250000
$17$	2.82843	+	2.82843i	0.685994	+	0.685994i	0.961344	−	0.275350i	$-0.0887937\pi$
$17$	2.82843	+	2.82843i	0.685994	+	0.685994i	−0.275350	+	0.961344i	$0.588794\pi$
$18$		0			0
$19$			8.00000i			1.83533i	0.397360	+	0.917663i	$0.369927\pi$
$19$			8.00000i			1.83533i	−0.397360	+	0.917663i	$0.630073\pi$
$20$		0			0
$21$		0			0
$22$	−2.00000	+	2.00000i	−0.426401	+	0.426401i
$23$	−2.82843	+	2.82843i	−0.589768	+	0.589768i	−0.937568	−	0.347801i	$-0.886929\pi$
$23$	−2.82843	+	2.82843i	−0.589768	+	0.589768i	0.347801	+	0.937568i	$0.386929\pi$
$24$		0			0
$25$		0			0
$26$		−	4.24264i		−	0.832050i
$27$		0			0
$28$	−2.00000	−	2.00000i	−0.377964	−	0.377964i
$29$	1.41421			0.262613			0.131306	−	0.991342i	$-0.458083\pi$
$29$	1.41421			0.262613			0.131306	+	0.991342i	$0.458083\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$		−	4.00000i		−	0.685994i
$35$		0			0
$36$		0			0
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	−0.416115	−	0.909312i	$-0.636609\pi$
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	0.909312	+	0.416115i	$0.136609\pi$
$38$	5.65685	−	5.65685i	0.917663	−	0.917663i
$39$		0			0
$40$		0			0
$41$			9.89949i			1.54604i	0.634381	+	0.773021i	$0.281255\pi$
$41$			9.89949i			1.54604i	−0.634381	+	0.773021i	$0.718745\pi$
$42$		0			0
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$	2.82843			0.426401
$45$		0			0
$46$	4.00000			0.589768
$47$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$47$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$		0			0
$52$	−3.00000	+	3.00000i	−0.416025	+	0.416025i
$53$	2.82843	−	2.82843i	0.388514	−	0.388514i	−0.485643	−	0.874157i	$-0.661414\pi$
$53$	2.82843	−	2.82843i	0.388514	−	0.388514i	0.874157	+	0.485643i	$0.161414\pi$
$54$		0			0
$55$		0			0
$56$			2.82843i			0.377964i
$57$		0			0
$58$	−1.00000	−	1.00000i	−0.131306	−	0.131306i
$59$	−2.82843			−0.368230			−0.184115	−	0.982905i	$-0.558942\pi$
$59$	−2.82843			−0.368230			−0.184115	+	0.982905i	$0.558942\pi$
$60$		0			0
$61$		0			0			−	1.00000i	$-0.5\pi$
$61$		0			0				1.00000i	$0.5\pi$
$62$	−2.82843	−	2.82843i	−0.359211	−	0.359211i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$		0			0
$67$	4.00000	−	4.00000i	0.488678	−	0.488678i	−0.419211	−	0.907889i	$-0.637693\pi$
$67$	4.00000	−	4.00000i	0.488678	−	0.488678i	0.907889	+	0.419211i	$0.137693\pi$
$68$	−2.82843	+	2.82843i	−0.342997	+	0.342997i
$69$		0			0
$70$		0			0
$71$		−	5.65685i		−	0.671345i	−0.941979	−	0.335673i	$-0.891036\pi$
$71$		−	5.65685i		−	0.671345i	0.941979	−	0.335673i	$-0.108964\pi$
$72$		0			0
$73$	−1.00000	−	1.00000i	−0.117041	−	0.117041i	0.646160	−	0.763202i	$-0.276374\pi$
$73$	−1.00000	−	1.00000i	−0.117041	−	0.117041i	−0.763202	+	0.646160i	$0.776374\pi$
$74$	−4.24264			−0.493197
$75$		0			0
$76$	−8.00000			−0.917663
$77$	5.65685	+	5.65685i	0.644658	+	0.644658i
$78$		0			0
$79$		−	12.0000i		−	1.35011i	−0.737769	−	0.675053i	$-0.764121\pi$
$79$		−	12.0000i		−	1.35011i	0.737769	−	0.675053i	$-0.235879\pi$
$80$		0			0
$81$		0			0
$82$	7.00000	−	7.00000i	0.773021	−	0.773021i
$83$	−8.48528	+	8.48528i	−0.931381	+	0.931381i	−0.997792	−	0.0664117i	$-0.978845\pi$
$83$	−8.48528	+	8.48528i	−0.931381	+	0.931381i	0.0664117	+	0.997792i	$0.478845\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−2.00000	−	2.00000i	−0.213201	−	0.213201i
$89$	−9.89949			−1.04934			−0.524672	−	0.851304i	$-0.675812\pi$
$89$	−9.89949			−1.04934			−0.524672	+	0.851304i	$0.675812\pi$
$90$		0			0
$91$	−12.0000			−1.25794
$92$	−2.82843	−	2.82843i	−0.294884	−	0.294884i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.00000	−	3.00000i	0.304604	−	0.304604i	−0.538208	−	0.842812i	$-0.680899\pi$
$97$	3.00000	−	3.00000i	0.304604	−	0.304604i	0.842812	+	0.538208i	$0.180899\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$		0			0
$100$		0			0
$101$		−	1.41421i		−	0.140720i	−0.997522	−	0.0703598i	$-0.977585\pi$
$101$		−	1.41421i		−	0.140720i	0.997522	−	0.0703598i	$-0.0224147\pi$
$102$		0			0
$103$	2.00000	+	2.00000i	0.197066	+	0.197066i	0.798741	−	0.601675i	$-0.205500\pi$
$103$	2.00000	+	2.00000i	0.197066	+	0.197066i	−0.601675	+	0.798741i	$0.705500\pi$
$104$	4.24264			0.416025
$105$		0			0
$106$	−4.00000			−0.388514
$107$	−14.1421	−	14.1421i	−1.36717	−	1.36717i	−0.864446	−	0.502726i	$-0.832330\pi$
$107$	−14.1421	−	14.1421i	−1.36717	−	1.36717i	−0.502726	−	0.864446i	$-0.667670\pi$
$108$		0			0
$109$		−	8.00000i		−	0.766261i	−0.923694	−	0.383131i	$-0.874846\pi$
$109$		−	8.00000i		−	0.766261i	0.923694	−	0.383131i	$-0.125154\pi$
$110$		0			0
$111$		0			0
$112$	2.00000	−	2.00000i	0.188982	−	0.188982i
$113$	−1.41421	+	1.41421i	−0.133038	+	0.133038i	−0.770490	−	0.637452i	$-0.779988\pi$
$113$	−1.41421	+	1.41421i	−0.133038	+	0.133038i	0.637452	+	0.770490i	$0.279988\pi$
$114$		0			0
$115$		0			0
$116$			1.41421i			0.131306i
$117$		0			0
$118$	2.00000	+	2.00000i	0.184115	+	0.184115i
$119$	−11.3137			−1.03713
$120$		0			0
$121$	3.00000			0.272727
$122$		0			0
$123$		0			0
$124$			4.00000i			0.359211i
$125$		0			0
$126$		0			0
$127$	−14.0000	+	14.0000i	−1.24230	+	1.24230i	−0.283254	+	0.959045i	$0.591414\pi$
$127$	−14.0000	+	14.0000i	−1.24230	+	1.24230i	−0.959045	+	0.283254i	$0.908586\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$			14.1421i			1.23560i	0.786334	+	0.617802i	$0.211977\pi$
$131$			14.1421i			1.23560i	−0.786334	+	0.617802i	$0.788023\pi$
$132$		0			0
$133$	−16.0000	−	16.0000i	−1.38738	−	1.38738i
$134$	−5.65685			−0.488678
$135$		0			0
$136$	4.00000			0.342997
$137$	−4.24264	−	4.24264i	−0.362473	−	0.362473i	0.502249	−	0.864723i	$-0.332506\pi$
$137$	−4.24264	−	4.24264i	−0.362473	−	0.362473i	−0.864723	+	0.502249i	$0.832506\pi$
$138$		0			0
$139$			4.00000i			0.339276i	0.985506	+	0.169638i	$0.0542598\pi$
$139$			4.00000i			0.339276i	−0.985506	+	0.169638i	$0.945740\pi$
$140$		0			0
$141$		0			0
$142$	−4.00000	+	4.00000i	−0.335673	+	0.335673i
$143$	8.48528	−	8.48528i	0.709575	−	0.709575i
$144$		0			0
$145$		0			0
$146$			1.41421i			0.117041i
$147$		0			0
$148$	3.00000	+	3.00000i	0.246598	+	0.246598i
$149$	21.2132			1.73785			0.868927	−	0.494941i	$-0.164810\pi$
$149$	21.2132			1.73785			0.868927	+	0.494941i	$0.164810\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$	5.65685	+	5.65685i	0.458831	+	0.458831i
$153$		0			0
$154$		−	8.00000i		−	0.644658i
$155$		0			0
$156$		0			0
$157$	9.00000	−	9.00000i	0.718278	−	0.718278i	−0.249974	−	0.968252i	$-0.580422\pi$
$157$	9.00000	−	9.00000i	0.718278	−	0.718278i	0.968252	+	0.249974i	$0.0804222\pi$
$158$	−8.48528	+	8.48528i	−0.675053	+	0.675053i
$159$		0			0
$160$		0			0
$161$		−	11.3137i		−	0.891645i
$162$		0			0
$163$	16.0000	+	16.0000i	1.25322	+	1.25322i	0.954270	+	0.298947i	$0.0966354\pi$
$163$	16.0000	+	16.0000i	1.25322	+	1.25322i	0.298947	+	0.954270i	$0.403365\pi$
$164$	−9.89949			−0.773021
$165$		0			0
$166$	12.0000			0.931381
$167$	−2.82843	−	2.82843i	−0.218870	−	0.218870i	0.589152	−	0.808022i	$-0.299462\pi$
$167$	−2.82843	−	2.82843i	−0.218870	−	0.218870i	−0.808022	+	0.589152i	$0.799462\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.89949	−	9.89949i	0.752645	−	0.752645i	−0.222327	−	0.974972i	$-0.571365\pi$
$173$	9.89949	−	9.89949i	0.752645	−	0.752645i	0.974972	+	0.222327i	$0.0713654\pi$
$174$		0			0
$175$		0			0
$176$			2.82843i			0.213201i
$177$		0			0
$178$	7.00000	+	7.00000i	0.524672	+	0.524672i
$179$	2.82843			0.211407			0.105703	−	0.994398i	$-0.466291\pi$
$179$	2.82843			0.211407			0.105703	+	0.994398i	$0.466291\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	8.48528	+	8.48528i	0.628971	+	0.628971i
$183$		0			0
$184$			4.00000i			0.294884i
$185$		0			0
$186$		0			0
$187$	8.00000	−	8.00000i	0.585018	−	0.585018i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	22.6274i		−	1.63726i	−0.574320	−	0.818631i	$-0.694733\pi$
$191$		−	22.6274i		−	1.63726i	0.574320	−	0.818631i	$-0.305267\pi$
$192$		0			0
$193$	−9.00000	−	9.00000i	−0.647834	−	0.647834i	0.304635	−	0.952469i	$-0.401466\pi$
$193$	−9.00000	−	9.00000i	−0.647834	−	0.647834i	−0.952469	+	0.304635i	$0.901466\pi$
$194$	−4.24264			−0.304604
$195$		0			0
$196$	1.00000			0.0714286
$197$	12.7279	+	12.7279i	0.906827	+	0.906827i	0.996015	−	0.0891879i	$-0.0284272\pi$
$197$	12.7279	+	12.7279i	0.906827	+	0.906827i	−0.0891879	+	0.996015i	$0.528427\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$		0			0
$201$		0			0
$202$	−1.00000	+	1.00000i	−0.0703598	+	0.0703598i
$203$	−2.82843	+	2.82843i	−0.198517	+	0.198517i
$204$		0			0
$205$		0			0
$206$		−	2.82843i		−	0.197066i
$207$		0			0
$208$	−3.00000	−	3.00000i	−0.208013	−	0.208013i
$209$	22.6274			1.56517
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	2.82843	+	2.82843i	0.194257	+	0.194257i
$213$		0			0
$214$			20.0000i			1.36717i
$215$		0			0
$216$		0			0
$217$	−8.00000	+	8.00000i	−0.543075	+	0.543075i
$218$	−5.65685	+	5.65685i	−0.383131	+	0.383131i
$219$		0			0
$220$		0			0
$221$			16.9706i			1.14156i
$222$		0			0
$223$	−6.00000	−	6.00000i	−0.401790	−	0.401790i	0.477074	−	0.878863i	$-0.341698\pi$
$223$	−6.00000	−	6.00000i	−0.401790	−	0.401790i	−0.878863	+	0.477074i	$0.841698\pi$
$224$	−2.82843			−0.188982
$225$		0			0
$226$	2.00000			0.133038
$227$	5.65685	+	5.65685i	0.375459	+	0.375459i	0.869461	−	0.494002i	$-0.164466\pi$
$227$	5.65685	+	5.65685i	0.375459	+	0.375459i	−0.494002	+	0.869461i	$0.664466\pi$
$228$		0			0
$229$			6.00000i			0.396491i	0.980152	+	0.198246i	$0.0635244\pi$
$229$			6.00000i			0.396491i	−0.980152	+	0.198246i	$0.936476\pi$
$230$		0			0
$231$		0			0
$232$	1.00000	−	1.00000i	0.0656532	−	0.0656532i
$233$	8.48528	−	8.48528i	0.555889	−	0.555889i	−0.372245	−	0.928134i	$-0.621412\pi$
$233$	8.48528	−	8.48528i	0.555889	−	0.555889i	0.928134	+	0.372245i	$0.121412\pi$
$234$		0			0
$235$		0			0
$236$		−	2.82843i		−	0.184115i
$237$		0			0
$238$	8.00000	+	8.00000i	0.518563	+	0.518563i
$239$	16.9706			1.09773			0.548867	−	0.835910i	$-0.315059\pi$
$239$	16.9706			1.09773			0.548867	+	0.835910i	$0.315059\pi$
$240$		0			0
$241$	22.0000			1.41714			0.708572	−	0.705638i	$-0.249340\pi$
$241$	22.0000			1.41714			0.708572	+	0.705638i	$0.249340\pi$
$242$	−2.12132	−	2.12132i	−0.136364	−	0.136364i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−24.0000	+	24.0000i	−1.52708	+	1.52708i
$248$	2.82843	−	2.82843i	0.179605	−	0.179605i
$249$		0			0
$250$		0			0
$251$		−	8.48528i		−	0.535586i	−0.963476	−	0.267793i	$-0.913706\pi$
$251$		−	8.48528i		−	0.535586i	0.963476	−	0.267793i	$-0.0862944\pi$
$252$		0			0
$253$	8.00000	+	8.00000i	0.502956	+	0.502956i
$254$	19.7990			1.24230
$255$		0			0
$256$	1.00000			0.0625000
$257$	9.89949	+	9.89949i	0.617514	+	0.617514i	0.944893	−	0.327379i	$-0.106166\pi$
$257$	9.89949	+	9.89949i	0.617514	+	0.617514i	−0.327379	+	0.944893i	$0.606166\pi$
$258$		0			0
$259$			12.0000i			0.745644i
$260$		0			0
$261$		0			0
$262$	10.0000	−	10.0000i	0.617802	−	0.617802i
$263$	19.7990	−	19.7990i	1.22086	−	1.22086i	0.253531	−	0.967327i	$-0.418408\pi$
$263$	19.7990	−	19.7990i	1.22086	−	1.22086i	0.967327	−	0.253531i	$-0.0815919\pi$
$264$		0			0
$265$		0			0
$266$			22.6274i			1.38738i
$267$		0			0
$268$	4.00000	+	4.00000i	0.244339	+	0.244339i
$269$	−15.5563			−0.948487			−0.474244	−	0.880394i	$-0.657278\pi$
$269$	−15.5563			−0.948487			−0.474244	+	0.880394i	$0.657278\pi$
$270$		0			0
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$	−2.82843	−	2.82843i	−0.171499	−	0.171499i
$273$		0			0
$274$			6.00000i			0.362473i
$275$		0			0
$276$		0			0
$277$	−9.00000	+	9.00000i	−0.540758	+	0.540758i	−0.923751	−	0.382993i	$-0.874893\pi$
$277$	−9.00000	+	9.00000i	−0.540758	+	0.540758i	0.382993	+	0.923751i	$0.374893\pi$
$278$	2.82843	−	2.82843i	0.169638	−	0.169638i
$279$		0			0
$280$		0			0
$281$			12.7279i			0.759284i	0.925133	+	0.379642i	$0.123953\pi$
$281$			12.7279i			0.759284i	−0.925133	+	0.379642i	$0.876047\pi$
$282$		0			0
$283$	−8.00000	−	8.00000i	−0.475551	−	0.475551i	0.428155	−	0.903705i	$-0.359164\pi$
$283$	−8.00000	−	8.00000i	−0.475551	−	0.475551i	−0.903705	+	0.428155i	$0.859164\pi$
$284$	5.65685			0.335673
$285$		0			0
$286$	−12.0000			−0.709575
$287$	−19.7990	−	19.7990i	−1.16870	−	1.16870i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$		0			0
$291$		0			0
$292$	1.00000	−	1.00000i	0.0585206	−	0.0585206i
$293$	−12.7279	+	12.7279i	−0.743573	+	0.743573i	−0.973264	−	0.229691i	$-0.926229\pi$
$293$	−12.7279	+	12.7279i	−0.743573	+	0.743573i	0.229691	+	0.973264i	$0.426229\pi$
$294$		0			0
$295$		0			0
$296$		−	4.24264i		−	0.246598i
$297$		0			0
$298$	−15.0000	−	15.0000i	−0.868927	−	0.868927i
$299$	−16.9706			−0.981433
$300$		0			0
$301$		0			0
$302$	5.65685	+	5.65685i	0.325515	+	0.325515i
$303$		0			0
$304$		−	8.00000i		−	0.458831i
$305$		0			0
$306$		0			0
$307$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$307$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$308$	−5.65685	+	5.65685i	−0.322329	+	0.322329i
$309$		0			0
$310$		0			0
$311$		−	22.6274i		−	1.28308i	−0.767088	−	0.641542i	$-0.778295\pi$
$311$		−	22.6274i		−	1.28308i	0.767088	−	0.641542i	$-0.221705\pi$
$312$		0			0
$313$	21.0000	+	21.0000i	1.18699	+	1.18699i	0.977895	+	0.209095i	$0.0670517\pi$
$313$	21.0000	+	21.0000i	1.18699	+	1.18699i	0.209095	+	0.977895i	$0.432948\pi$
$314$	−12.7279			−0.718278
$315$		0			0
$316$	12.0000			0.675053
$317$	−8.48528	−	8.48528i	−0.476581	−	0.476581i	0.427456	−	0.904036i	$-0.359410\pi$
$317$	−8.48528	−	8.48528i	−0.476581	−	0.476581i	−0.904036	+	0.427456i	$0.859410\pi$
$318$		0			0
$319$		−	4.00000i		−	0.223957i
$320$		0			0
$321$		0			0
$322$	−8.00000	+	8.00000i	−0.445823	+	0.445823i
$323$	−22.6274	+	22.6274i	−1.25902	+	1.25902i
$324$		0			0
$325$		0			0
$326$		−	22.6274i		−	1.25322i
$327$		0			0
$328$	7.00000	+	7.00000i	0.386510	+	0.386510i
$329$		0			0
$330$		0			0
$331$	16.0000			0.879440			0.439720	−	0.898135i	$-0.355078\pi$
$331$	16.0000			0.879440			0.439720	+	0.898135i	$0.355078\pi$
$332$	−8.48528	−	8.48528i	−0.465690	−	0.465690i
$333$		0			0
$334$			4.00000i			0.218870i
$335$		0			0
$336$		0			0
$337$	21.0000	−	21.0000i	1.14394	−	1.14394i	0.156221	−	0.987722i	$-0.450069\pi$
$337$	21.0000	−	21.0000i	1.14394	−	1.14394i	0.987722	−	0.156221i	$-0.0499311\pi$
$338$	3.53553	−	3.53553i	0.192308	−	0.192308i
$339$		0			0
$340$		0			0
$341$		−	11.3137i		−	0.612672i
$342$		0			0
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$		0			0
$345$		0			0
$346$	−14.0000			−0.752645
$347$	11.3137	+	11.3137i	0.607352	+	0.607352i	0.942253	−	0.334901i	$-0.108703\pi$
$347$	11.3137	+	11.3137i	0.607352	+	0.607352i	−0.334901	+	0.942253i	$0.608703\pi$
$348$		0			0
$349$		−	16.0000i		−	0.856460i	−0.903670	−	0.428230i	$-0.859137\pi$
$349$		−	16.0000i		−	0.856460i	0.903670	−	0.428230i	$-0.140863\pi$
$350$		0			0
$351$		0			0
$352$	2.00000	−	2.00000i	0.106600	−	0.106600i
$353$	8.48528	−	8.48528i	0.451626	−	0.451626i	−0.444268	−	0.895894i	$-0.646536\pi$
$353$	8.48528	−	8.48528i	0.451626	−	0.451626i	0.895894	+	0.444268i	$0.146536\pi$
$354$		0			0
$355$		0			0
$356$		−	9.89949i		−	0.524672i
$357$		0			0
$358$	−2.00000	−	2.00000i	−0.105703	−	0.105703i
$359$	11.3137			0.597115			0.298557	−	0.954392i	$-0.403495\pi$
$359$	11.3137			0.597115			0.298557	+	0.954392i	$0.403495\pi$
$360$		0			0
$361$	−45.0000			−2.36842
$362$	−5.65685	−	5.65685i	−0.297318	−	0.297318i
$363$		0			0
$364$		−	12.0000i		−	0.628971i
$365$		0			0
$366$		0			0
$367$	22.0000	−	22.0000i	1.14839	−	1.14839i	0.161521	−	0.986869i	$-0.448360\pi$
$367$	22.0000	−	22.0000i	1.14839	−	1.14839i	0.986869	−	0.161521i	$-0.0516401\pi$
$368$	2.82843	−	2.82843i	0.147442	−	0.147442i
$369$		0			0
$370$		0			0
$371$			11.3137i			0.587378i
$372$		0			0
$373$	5.00000	+	5.00000i	0.258890	+	0.258890i	0.824603	−	0.565712i	$-0.191399\pi$
$373$	5.00000	+	5.00000i	0.258890	+	0.258890i	−0.565712	+	0.824603i	$0.691399\pi$
$374$	−11.3137			−0.585018
$375$		0			0
$376$		0			0
$377$	4.24264	+	4.24264i	0.218507	+	0.218507i
$378$		0			0
$379$			20.0000i			1.02733i	0.857991	+	0.513665i	$0.171713\pi$
$379$			20.0000i			1.02733i	−0.857991	+	0.513665i	$0.828287\pi$
$380$		0			0
$381$		0			0
$382$	−16.0000	+	16.0000i	−0.818631	+	0.818631i
$383$	−16.9706	+	16.9706i	−0.867155	+	0.867155i	−0.992157	−	0.125001i	$-0.960106\pi$
$383$	−16.9706	+	16.9706i	−0.867155	+	0.867155i	0.125001	+	0.992157i	$0.460106\pi$
$384$		0			0
$385$		0			0
$386$			12.7279i			0.647834i
$387$		0			0
$388$	3.00000	+	3.00000i	0.152302	+	0.152302i
$389$	−21.2132			−1.07555			−0.537776	−	0.843088i	$-0.680735\pi$
$389$	−21.2132			−1.07555			−0.537776	+	0.843088i	$0.680735\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$		0			0
$394$		−	18.0000i		−	0.906827i
$395$		0			0
$396$		0			0
$397$	−7.00000	+	7.00000i	−0.351320	+	0.351320i	−0.860601	−	0.509281i	$-0.829912\pi$
$397$	−7.00000	+	7.00000i	−0.351320	+	0.351320i	0.509281	+	0.860601i	$0.329912\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			12.7279i			0.635602i	0.948157	+	0.317801i	$0.102944\pi$
$401$			12.7279i			0.635602i	−0.948157	+	0.317801i	$0.897056\pi$
$402$		0			0
$403$	12.0000	+	12.0000i	0.597763	+	0.597763i
$404$	1.41421			0.0703598
$405$		0			0
$406$	4.00000			0.198517
$407$	−8.48528	−	8.48528i	−0.420600	−	0.420600i
$408$		0			0
$409$		−	24.0000i		−	1.18672i	−0.804936	−	0.593362i	$-0.797800\pi$
$409$		−	24.0000i		−	1.18672i	0.804936	−	0.593362i	$-0.202200\pi$
$410$		0			0
$411$		0			0
$412$	−2.00000	+	2.00000i	−0.0985329	+	0.0985329i
$413$	5.65685	−	5.65685i	0.278356	−	0.278356i
$414$		0			0
$415$		0			0
$416$			4.24264i			0.208013i
$417$		0			0
$418$	−16.0000	−	16.0000i	−0.782586	−	0.782586i
$419$	−25.4558			−1.24360			−0.621800	−	0.783176i	$-0.713598\pi$
$419$	−25.4558			−1.24360			−0.621800	+	0.783176i	$0.713598\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	2.82843	+	2.82843i	0.137686	+	0.137686i
$423$		0			0
$424$		−	4.00000i		−	0.194257i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	14.1421	−	14.1421i	0.683586	−	0.683586i
$429$		0			0
$430$		0			0
$431$			39.5980i			1.90737i	0.300811	+	0.953684i	$0.402743\pi$
$431$			39.5980i			1.90737i	−0.300811	+	0.953684i	$0.597257\pi$
$432$		0			0
$433$	−23.0000	−	23.0000i	−1.10531	−	1.10531i	−0.993759	−	0.111551i	$-0.964418\pi$
$433$	−23.0000	−	23.0000i	−1.10531	−	1.10531i	−0.111551	−	0.993759i	$-0.535582\pi$
$434$	11.3137			0.543075
$435$		0			0
$436$	8.00000			0.383131
$437$	−22.6274	−	22.6274i	−1.08242	−	1.08242i
$438$		0			0
$439$		−	8.00000i		−	0.381819i	−0.981608	−	0.190910i	$-0.938856\pi$
$439$		−	8.00000i		−	0.381819i	0.981608	−	0.190910i	$-0.0611437\pi$
$440$		0			0
$441$		0			0
$442$	12.0000	−	12.0000i	0.570782	−	0.570782i
$443$	−16.9706	+	16.9706i	−0.806296	+	0.806296i	−0.984071	−	0.177775i	$-0.943110\pi$
$443$	−16.9706	+	16.9706i	−0.806296	+	0.806296i	0.177775	+	0.984071i	$0.443110\pi$
$444$		0			0
$445$		0			0
$446$			8.48528i			0.401790i
$447$		0			0
$448$	2.00000	+	2.00000i	0.0944911	+	0.0944911i
$449$	1.41421			0.0667409			0.0333704	−	0.999443i	$-0.489376\pi$
$449$	1.41421			0.0667409			0.0333704	+	0.999443i	$0.489376\pi$
$450$		0			0
$451$	28.0000			1.31847
$452$	−1.41421	−	1.41421i	−0.0665190	−	0.0665190i
$453$		0			0
$454$		−	8.00000i		−	0.375459i
$455$		0			0
$456$		0			0
$457$	15.0000	−	15.0000i	0.701670	−	0.701670i	−0.263099	−	0.964769i	$-0.584744\pi$
$457$	15.0000	−	15.0000i	0.701670	−	0.701670i	0.964769	+	0.263099i	$0.0847444\pi$
$458$	4.24264	−	4.24264i	0.198246	−	0.198246i
$459$		0			0
$460$		0			0
$461$			18.3848i			0.856264i	0.903716	+	0.428132i	$0.140828\pi$
$461$			18.3848i			0.856264i	−0.903716	+	0.428132i	$0.859172\pi$
$462$		0			0
$463$	−14.0000	−	14.0000i	−0.650635	−	0.650635i	0.302511	−	0.953146i	$-0.402175\pi$
$463$	−14.0000	−	14.0000i	−0.650635	−	0.650635i	−0.953146	+	0.302511i	$0.902175\pi$
$464$	−1.41421			−0.0656532
$465$		0			0
$466$	−12.0000			−0.555889
$467$	19.7990	+	19.7990i	0.916188	+	0.916188i	0.996750	−	0.0805616i	$-0.0256714\pi$
$467$	19.7990	+	19.7990i	0.916188	+	0.916188i	−0.0805616	+	0.996750i	$0.525671\pi$
$468$		0			0
$469$			16.0000i			0.738811i
$470$		0			0
$471$		0			0
$472$	−2.00000	+	2.00000i	−0.0920575	+	0.0920575i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		−	11.3137i		−	0.518563i
$477$		0			0
$478$	−12.0000	−	12.0000i	−0.548867	−	0.548867i
$479$	5.65685			0.258468			0.129234	−	0.991614i	$-0.458748\pi$
$479$	5.65685			0.258468			0.129234	+	0.991614i	$0.458748\pi$
$480$		0			0
$481$	18.0000			0.820729
$482$	−15.5563	−	15.5563i	−0.708572	−	0.708572i
$483$		0			0
$484$			3.00000i			0.136364i
$485$		0			0
$486$		0			0
$487$	18.0000	−	18.0000i	0.815658	−	0.815658i	−0.169818	−	0.985476i	$-0.554318\pi$
$487$	18.0000	−	18.0000i	0.815658	−	0.815658i	0.985476	+	0.169818i	$0.0543179\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			2.82843i			0.127645i	0.997961	+	0.0638226i	$0.0203292\pi$
$491$			2.82843i			0.127645i	−0.997961	+	0.0638226i	$0.979671\pi$
$492$		0			0
$493$	4.00000	+	4.00000i	0.180151	+	0.180151i
$494$	33.9411			1.52708
$495$		0			0
$496$	−4.00000			−0.179605
$497$	11.3137	+	11.3137i	0.507489	+	0.507489i
$498$		0			0
$499$		−	32.0000i		−	1.43252i	−0.697835	−	0.716258i	$-0.745853\pi$
$499$		−	32.0000i		−	1.43252i	0.697835	−	0.716258i	$-0.254147\pi$
$500$		0			0
$501$		0			0
$502$	−6.00000	+	6.00000i	−0.267793	+	0.267793i
$503$	16.9706	−	16.9706i	0.756680	−	0.756680i	−0.219037	−	0.975717i	$-0.570291\pi$
$503$	16.9706	−	16.9706i	0.756680	−	0.756680i	0.975717	+	0.219037i	$0.0702914\pi$
$504$		0			0
$505$		0			0
$506$		−	11.3137i		−	0.502956i
$507$		0			0
$508$	−14.0000	−	14.0000i	−0.621150	−	0.621150i
$509$	−24.0416			−1.06563			−0.532813	−	0.846233i	$-0.678865\pi$
$509$	−24.0416			−1.06563			−0.532813	+	0.846233i	$0.678865\pi$
$510$		0			0
$511$	4.00000			0.176950
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	14.0000i		−	0.617514i
$515$		0			0
$516$		0			0
$517$		0			0
$518$	8.48528	−	8.48528i	0.372822	−	0.372822i
$519$		0			0
$520$		0			0
$521$		−	29.6985i		−	1.30111i	−0.759457	−	0.650557i	$-0.774535\pi$
$521$		−	29.6985i		−	1.30111i	0.759457	−	0.650557i	$-0.225465\pi$
$522$		0			0
$523$	24.0000	+	24.0000i	1.04945	+	1.04945i	0.998712	+	0.0507346i	$0.0161562\pi$
$523$	24.0000	+	24.0000i	1.04945	+	1.04945i	0.0507346	+	0.998712i	$0.483844\pi$
$524$	−14.1421			−0.617802
$525$		0			0
$526$	−28.0000			−1.22086
$527$	11.3137	+	11.3137i	0.492833	+	0.492833i
$528$		0			0
$529$			7.00000i			0.304348i
$530$		0			0
$531$		0			0
$532$	16.0000	−	16.0000i	0.693688	−	0.693688i
$533$	−29.6985	+	29.6985i	−1.28638	+	1.28638i
$534$		0			0
$535$		0			0
$536$		−	5.65685i		−	0.244339i
$537$		0			0
$538$	11.0000	+	11.0000i	0.474244	+	0.474244i
$539$	−2.82843			−0.121829
$540$		0			0
$541$	−8.00000			−0.343947			−0.171973	−	0.985102i	$-0.555014\pi$
$541$	−8.00000			−0.343947			−0.171973	+	0.985102i	$0.555014\pi$
$542$		0			0
$543$		0			0
$544$			4.00000i			0.171499i
$545$		0			0
$546$		0			0
$547$	−12.0000	+	12.0000i	−0.513083	+	0.513083i	−0.915470	−	0.402387i	$-0.868181\pi$
$547$	−12.0000	+	12.0000i	−0.513083	+	0.513083i	0.402387	+	0.915470i	$0.368181\pi$
$548$	4.24264	−	4.24264i	0.181237	−	0.181237i
$549$		0			0
$550$		0			0
$551$			11.3137i			0.481980i
$552$		0			0
$553$	24.0000	+	24.0000i	1.02058	+	1.02058i
$554$	12.7279			0.540758
$555$		0			0
$556$	−4.00000			−0.169638
$557$	8.48528	+	8.48528i	0.359533	+	0.359533i	0.863641	−	0.504108i	$-0.168179\pi$
$557$	8.48528	+	8.48528i	0.359533	+	0.359533i	−0.504108	+	0.863641i	$0.668179\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	9.00000	−	9.00000i	0.379642	−	0.379642i
$563$	16.9706	−	16.9706i	0.715224	−	0.715224i	−0.252399	−	0.967623i	$-0.581220\pi$
$563$	16.9706	−	16.9706i	0.715224	−	0.715224i	0.967623	+	0.252399i	$0.0812196\pi$
$564$		0			0
$565$		0			0
$566$			11.3137i			0.475551i
$567$		0			0
$568$	−4.00000	−	4.00000i	−0.167836	−	0.167836i
$569$	−18.3848			−0.770730			−0.385365	−	0.922764i	$-0.625924\pi$
$569$	−18.3848			−0.770730			−0.385365	+	0.922764i	$0.625924\pi$
$570$		0			0
$571$	8.00000			0.334790			0.167395	−	0.985890i	$-0.446465\pi$
$571$	8.00000			0.334790			0.167395	+	0.985890i	$0.446465\pi$
$572$	8.48528	+	8.48528i	0.354787	+	0.354787i
$573$		0			0
$574$			28.0000i			1.16870i
$575$		0			0
$576$		0			0
$577$	−31.0000	+	31.0000i	−1.29055	+	1.29055i	−0.356098	+	0.934448i	$0.615893\pi$
$577$	−31.0000	+	31.0000i	−1.29055	+	1.29055i	−0.934448	+	0.356098i	$0.884107\pi$
$578$	−0.707107	+	0.707107i	−0.0294118	+	0.0294118i
$579$		0			0
$580$		0			0
$581$		−	33.9411i		−	1.40812i
$582$		0			0
$583$	−8.00000	−	8.00000i	−0.331326	−	0.331326i
$584$	−1.41421			−0.0585206
$585$		0			0
$586$	18.0000			0.743573
$587$	25.4558	+	25.4558i	1.05068	+	1.05068i	0.998646	+	0.0520296i	$0.0165690\pi$
$587$	25.4558	+	25.4558i	1.05068	+	1.05068i	0.0520296	+	0.998646i	$0.483431\pi$
$588$		0			0
$589$			32.0000i			1.31854i
$590$		0			0
$591$		0			0
$592$	−3.00000	+	3.00000i	−0.123299	+	0.123299i
$593$	−24.0416	+	24.0416i	−0.987271	+	0.987271i	−0.999920	−	0.0126486i	$-0.995974\pi$
$593$	−24.0416	+	24.0416i	−0.987271	+	0.987271i	0.0126486	+	0.999920i	$0.495974\pi$
$594$		0			0
$595$		0			0
$596$			21.2132i			0.868927i
$597$		0			0
$598$	12.0000	+	12.0000i	0.490716	+	0.490716i
$599$	39.5980			1.61793			0.808965	−	0.587857i	$-0.200028\pi$
$599$	39.5980			1.61793			0.808965	+	0.587857i	$0.200028\pi$
$600$		0			0
$601$	8.00000			0.326327			0.163163	−	0.986599i	$-0.447830\pi$
$601$	8.00000			0.326327			0.163163	+	0.986599i	$0.447830\pi$
$602$		0			0
$603$		0			0
$604$		−	8.00000i		−	0.325515i
$605$		0			0
$606$		0			0
$607$	6.00000	−	6.00000i	0.243532	−	0.243532i	−0.574777	−	0.818310i	$-0.694911\pi$
$607$	6.00000	−	6.00000i	0.243532	−	0.243532i	0.818310	+	0.574777i	$0.194911\pi$
$608$	−5.65685	+	5.65685i	−0.229416	+	0.229416i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	3.00000	+	3.00000i	0.121169	+	0.121169i	0.765091	−	0.643922i	$-0.222694\pi$
$613$	3.00000	+	3.00000i	0.121169	+	0.121169i	−0.643922	+	0.765091i	$0.722694\pi$
$614$		0			0
$615$		0			0
$616$	8.00000			0.322329
$617$	−25.4558	−	25.4558i	−1.02481	−	1.02481i	−0.999684	−	0.0251295i	$-0.992000\pi$
$617$	−25.4558	−	25.4558i	−1.02481	−	1.02481i	−0.0251295	−	0.999684i	$-0.508000\pi$
$618$		0			0
$619$			12.0000i			0.482321i	0.970485	+	0.241160i	$0.0775280\pi$
$619$			12.0000i			0.482321i	−0.970485	+	0.241160i	$0.922472\pi$
$620$		0			0
$621$		0			0
$622$	−16.0000	+	16.0000i	−0.641542	+	0.641542i
$623$	19.7990	−	19.7990i	0.793230	−	0.793230i
$624$		0			0
$625$		0			0
$626$		−	29.6985i		−	1.18699i
$627$		0			0
$628$	9.00000	+	9.00000i	0.359139	+	0.359139i
$629$	16.9706			0.676661
$630$		0			0
$631$	−20.0000			−0.796187			−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000			−0.796187			−0.398094	+	0.917345i	$0.630328\pi$
$632$	−8.48528	−	8.48528i	−0.337526	−	0.337526i
$633$		0			0
$634$			12.0000i			0.476581i
$635$		0			0
$636$		0			0
$637$	3.00000	−	3.00000i	0.118864	−	0.118864i
$638$	−2.82843	+	2.82843i	−0.111979	+	0.111979i
$639$		0			0
$640$		0			0
$641$		−	18.3848i		−	0.726155i	−0.931759	−	0.363078i	$-0.881726\pi$
$641$		−	18.3848i		−	0.726155i	0.931759	−	0.363078i	$-0.118274\pi$
$642$		0			0
$643$	−12.0000	−	12.0000i	−0.473234	−	0.473234i	0.429726	−	0.902959i	$-0.358610\pi$
$643$	−12.0000	−	12.0000i	−0.473234	−	0.473234i	−0.902959	+	0.429726i	$0.858610\pi$
$644$	11.3137			0.445823
$645$		0			0
$646$	32.0000			1.25902
$647$	−11.3137	−	11.3137i	−0.444788	−	0.444788i	0.448830	−	0.893617i	$-0.351841\pi$
$647$	−11.3137	−	11.3137i	−0.444788	−	0.444788i	−0.893617	+	0.448830i	$0.851841\pi$
$648$		0			0
$649$			8.00000i			0.314027i
$650$		0			0
$651$		0			0
$652$	−16.0000	+	16.0000i	−0.626608	+	0.626608i
$653$	25.4558	−	25.4558i	0.996164	−	0.996164i	−0.00382851	−	0.999993i	$-0.501219\pi$
$653$	25.4558	−	25.4558i	0.996164	−	0.996164i	0.999993	+	0.00382851i	$0.00121866\pi$
$654$		0			0
$655$		0			0
$656$		−	9.89949i		−	0.386510i
$657$		0			0
$658$		0			0
$659$	2.82843			0.110180			0.0550899	−	0.998481i	$-0.482455\pi$
$659$	2.82843			0.110180			0.0550899	+	0.998481i	$0.482455\pi$
$660$		0			0
$661$	32.0000			1.24466			0.622328	−	0.782757i	$-0.286187\pi$
$661$	32.0000			1.24466			0.622328	+	0.782757i	$0.286187\pi$
$662$	−11.3137	−	11.3137i	−0.439720	−	0.439720i
$663$		0			0
$664$			12.0000i			0.465690i
$665$		0			0
$666$		0			0
$667$	−4.00000	+	4.00000i	−0.154881	+	0.154881i
$668$	2.82843	−	2.82843i	0.109435	−	0.109435i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−25.0000	−	25.0000i	−0.963679	−	0.963679i	0.0356839	−	0.999363i	$-0.488639\pi$
$673$	−25.0000	−	25.0000i	−0.963679	−	0.963679i	−0.999363	+	0.0356839i	$0.988639\pi$
$674$	−29.6985			−1.14394
$675$		0			0
$676$	−5.00000			−0.192308
$677$	−14.1421	−	14.1421i	−0.543526	−	0.543526i	0.381034	−	0.924561i	$-0.375568\pi$
$677$	−14.1421	−	14.1421i	−0.543526	−	0.543526i	−0.924561	+	0.381034i	$0.875568\pi$
$678$		0			0
$679$			12.0000i			0.460518i
$680$		0			0
$681$		0			0
$682$	−8.00000	+	8.00000i	−0.306336	+	0.306336i
$683$	−8.48528	+	8.48528i	−0.324680	+	0.324680i	−0.850559	−	0.525879i	$-0.823736\pi$
$683$	−8.48528	+	8.48528i	−0.324680	+	0.324680i	0.525879	+	0.850559i	$0.323736\pi$
$684$		0			0
$685$		0			0
$686$			16.9706i			0.647939i
$687$		0			0
$688$		0			0
$689$	16.9706			0.646527
$690$		0			0
$691$		0			0			−	1.00000i	$-0.5\pi$
$691$		0			0				1.00000i	$0.5\pi$
$692$	9.89949	+	9.89949i	0.376322	+	0.376322i
$693$		0			0
$694$		−	16.0000i		−	0.607352i
$695$		0			0
$696$		0			0
$697$	−28.0000	+	28.0000i	−1.06058	+	1.06058i
$698$	−11.3137	+	11.3137i	−0.428230	+	0.428230i
$699$		0			0
$700$		0			0
$701$			35.3553i			1.33535i	0.744452	+	0.667676i	$0.232711\pi$
$701$			35.3553i			1.33535i	−0.744452	+	0.667676i	$0.767289\pi$
$702$		0			0
$703$	24.0000	+	24.0000i	0.905177	+	0.905177i
$704$	−2.82843			−0.106600
$705$		0			0
$706$	−12.0000			−0.451626
$707$	2.82843	+	2.82843i	0.106374	+	0.106374i
$708$		0			0
$709$			26.0000i			0.976450i	0.872718	+	0.488225i	$0.162356\pi$
$709$			26.0000i			0.976450i	−0.872718	+	0.488225i	$0.837644\pi$
$710$		0			0
$711$		0			0
$712$	−7.00000	+	7.00000i	−0.262336	+	0.262336i
$713$	−11.3137	+	11.3137i	−0.423702	+	0.423702i
$714$		0			0
$715$		0			0
$716$			2.82843i			0.105703i
$717$		0			0
$718$	−8.00000	−	8.00000i	−0.298557	−	0.298557i
$719$	22.6274			0.843860			0.421930	−	0.906628i	$-0.361353\pi$
$719$	22.6274			0.843860			0.421930	+	0.906628i	$0.361353\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$	31.8198	+	31.8198i	1.18421	+	1.18421i
$723$		0			0
$724$			8.00000i			0.297318i
$725$		0			0
$726$		0			0
$727$	6.00000	−	6.00000i	0.222528	−	0.222528i	−0.587034	−	0.809562i	$-0.699705\pi$
$727$	6.00000	−	6.00000i	0.222528	−	0.222528i	0.809562	+	0.587034i	$0.199705\pi$
$728$	−8.48528	+	8.48528i	−0.314485	+	0.314485i
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	11.0000	+	11.0000i	0.406294	+	0.406294i	0.880444	−	0.474150i	$-0.157245\pi$
$733$	11.0000	+	11.0000i	0.406294	+	0.406294i	−0.474150	+	0.880444i	$0.657245\pi$
$734$	−31.1127			−1.14839
$735$		0			0
$736$	−4.00000			−0.147442
$737$	−11.3137	−	11.3137i	−0.416746	−	0.416746i
$738$		0			0
$739$		−	8.00000i		−	0.294285i	−0.989115	−	0.147142i	$-0.952992\pi$
$739$		−	8.00000i		−	0.294285i	0.989115	−	0.147142i	$-0.0470076\pi$
$740$		0			0
$741$		0			0
$742$	8.00000	−	8.00000i	0.293689	−	0.293689i
$743$	28.2843	−	28.2843i	1.03765	−	1.03765i	0.0383863	−	0.999263i	$-0.487778\pi$
$743$	28.2843	−	28.2843i	1.03765	−	1.03765i	0.999263	−	0.0383863i	$-0.0122217\pi$
$744$		0			0
$745$		0			0
$746$		−	7.07107i		−	0.258890i
$747$		0			0
$748$	8.00000	+	8.00000i	0.292509	+	0.292509i
$749$	56.5685			2.06697
$750$		0			0
$751$	−12.0000			−0.437886			−0.218943	−	0.975738i	$-0.570261\pi$
$751$	−12.0000			−0.437886			−0.218943	+	0.975738i	$0.570261\pi$
$752$		0			0
$753$		0			0
$754$		−	6.00000i		−	0.218507i
$755$		0			0
$756$		0			0
$757$	−15.0000	+	15.0000i	−0.545184	+	0.545184i	−0.925044	−	0.379860i	$-0.875972\pi$
$757$	−15.0000	+	15.0000i	−0.545184	+	0.545184i	0.379860	+	0.925044i	$0.375972\pi$
$758$	14.1421	−	14.1421i	0.513665	−	0.513665i
$759$		0			0
$760$		0			0
$761$		−	41.0122i		−	1.48669i	−0.668908	−	0.743345i	$-0.733238\pi$
$761$		−	41.0122i		−	1.48669i	0.668908	−	0.743345i	$-0.266762\pi$
$762$		0			0
$763$	16.0000	+	16.0000i	0.579239	+	0.579239i
$764$	22.6274			0.818631
$765$		0			0
$766$	24.0000			0.867155
$767$	−8.48528	−	8.48528i	−0.306386	−	0.306386i
$768$		0			0
$769$			40.0000i			1.44244i	0.692708	+	0.721218i	$0.256418\pi$
$769$			40.0000i			1.44244i	−0.692708	+	0.721218i	$0.743582\pi$
$770$		0			0
$771$		0			0
$772$	9.00000	−	9.00000i	0.323917	−	0.323917i
$773$	−8.48528	+	8.48528i	−0.305194	+	0.305194i	−0.843042	−	0.537848i	$-0.819238\pi$
$773$	−8.48528	+	8.48528i	−0.305194	+	0.305194i	0.537848	+	0.843042i	$0.319238\pi$
$774$		0			0
$775$		0			0
$776$		−	4.24264i		−	0.152302i
$777$		0			0
$778$	15.0000	+	15.0000i	0.537776	+	0.537776i
$779$	−79.1960			−2.83749
$780$		0			0
$781$	−16.0000			−0.572525
$782$	11.3137	+	11.3137i	0.404577	+	0.404577i
$783$		0			0
$784$			1.00000i			0.0357143i
$785$		0			0
$786$		0			0
$787$	20.0000	−	20.0000i	0.712923	−	0.712923i	−0.254223	−	0.967146i	$-0.581820\pi$
$787$	20.0000	−	20.0000i	0.712923	−	0.712923i	0.967146	+	0.254223i	$0.0818196\pi$
$788$	−12.7279	+	12.7279i	−0.453413	+	0.453413i
$789$		0			0
$790$		0			0
$791$		−	5.65685i		−	0.201135i
$792$		0			0
$793$		0			0
$794$	9.89949			0.351320
$795$		0			0
$796$		0			0
$797$	21.2132	+	21.2132i	0.751410	+	0.751410i	0.974742	−	0.223332i	$-0.0716935\pi$
$797$	21.2132	+	21.2132i	0.751410	+	0.751410i	−0.223332	+	0.974742i	$0.571693\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$	9.00000	−	9.00000i	0.317801	−	0.317801i
$803$	−2.82843	+	2.82843i	−0.0998130	+	0.0998130i
$804$		0			0
$805$		0			0
$806$		−	16.9706i		−	0.597763i
$807$		0			0
$808$	−1.00000	−	1.00000i	−0.0351799	−	0.0351799i
$809$	−1.41421			−0.0497211			−0.0248606	−	0.999691i	$-0.507914\pi$
$809$	−1.41421			−0.0497211			−0.0248606	+	0.999691i	$0.507914\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	−2.82843	−	2.82843i	−0.0992583	−	0.0992583i
$813$		0			0
$814$			12.0000i			0.420600i
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−16.9706	+	16.9706i	−0.593362	+	0.593362i
$819$		0			0
$820$		0			0
$821$		−	41.0122i		−	1.43134i	−0.698441	−	0.715668i	$-0.746123\pi$
$821$		−	41.0122i		−	1.43134i	0.698441	−	0.715668i	$-0.253877\pi$
$822$		0			0
$823$	−38.0000	−	38.0000i	−1.32460	−	1.32460i	−0.910010	−	0.414587i	$-0.863926\pi$
$823$	−38.0000	−	38.0000i	−1.32460	−	1.32460i	−0.414587	−	0.910010i	$-0.636074\pi$
$824$	2.82843			0.0985329
$825$		0			0
$826$	−8.00000			−0.278356
$827$	33.9411	+	33.9411i	1.18025	+	1.18025i	0.979680	+	0.200569i	$0.0642791\pi$
$827$	33.9411	+	33.9411i	1.18025	+	1.18025i	0.200569	+	0.979680i	$0.435721\pi$
$828$		0			0
$829$		−	56.0000i		−	1.94496i	−0.232986	−	0.972480i	$-0.574849\pi$
$829$		−	56.0000i		−	1.94496i	0.232986	−	0.972480i	$-0.425151\pi$
$830$		0			0
$831$		0			0
$832$	3.00000	−	3.00000i	0.104006	−	0.104006i
$833$	2.82843	−	2.82843i	0.0979992	−	0.0979992i
$834$		0			0
$835$		0			0
$836$			22.6274i			0.782586i
$837$		0			0
$838$	18.0000	+	18.0000i	0.621800	+	0.621800i
$839$	45.2548			1.56237			0.781185	−	0.624299i	$-0.214615\pi$
$839$	45.2548			1.56237			0.781185	+	0.624299i	$0.214615\pi$
$840$		0			0
$841$	−27.0000			−0.931034
$842$	7.07107	+	7.07107i	0.243685	+	0.243685i
$843$		0			0
$844$		−	4.00000i		−	0.137686i
$845$		0			0
$846$		0			0
$847$	−6.00000	+	6.00000i	−0.206162	+	0.206162i
$848$	−2.82843	+	2.82843i	−0.0971286	+	0.0971286i
$849$		0			0
$850$		0			0
$851$			16.9706i			0.581743i
$852$		0			0
$853$	−19.0000	−	19.0000i	−0.650548	−	0.650548i	0.302577	−	0.953125i	$-0.402153\pi$
$853$	−19.0000	−	19.0000i	−0.650548	−	0.650548i	−0.953125	+	0.302577i	$0.902153\pi$
$854$		0			0
$855$		0			0
$856$	−20.0000			−0.683586
$857$	−8.48528	−	8.48528i	−0.289852	−	0.289852i	0.547170	−	0.837022i	$-0.315705\pi$
$857$	−8.48528	−	8.48528i	−0.289852	−	0.289852i	−0.837022	+	0.547170i	$0.815705\pi$
$858$		0			0
$859$		−	44.0000i		−	1.50126i	−0.660722	−	0.750630i	$-0.729750\pi$
$859$		−	44.0000i		−	1.50126i	0.660722	−	0.750630i	$-0.270250\pi$
$860$		0			0
$861$		0			0
$862$	28.0000	−	28.0000i	0.953684	−	0.953684i
$863$	31.1127	−	31.1127i	1.05909	−	1.05909i	0.0609476	−	0.998141i	$-0.480588\pi$
$863$	31.1127	−	31.1127i	1.05909	−	1.05909i	0.998141	−	0.0609476i	$-0.0194123\pi$
$864$		0			0
$865$		0			0
$866$			32.5269i			1.10531i
$867$		0			0
$868$	−8.00000	−	8.00000i	−0.271538	−	0.271538i
$869$	−33.9411			−1.15137
$870$		0			0
$871$	24.0000			0.813209
$872$	−5.65685	−	5.65685i	−0.191565	−	0.191565i
$873$		0			0
$874$			32.0000i			1.08242i
$875$		0			0
$876$		0			0
$877$	15.0000	−	15.0000i	0.506514	−	0.506514i	−0.406941	−	0.913455i	$-0.633404\pi$
$877$	15.0000	−	15.0000i	0.506514	−	0.506514i	0.913455	+	0.406941i	$0.133404\pi$
$878$	−5.65685	+	5.65685i	−0.190910	+	0.190910i
$879$		0			0
$880$		0			0
$881$			52.3259i			1.76290i	0.472273	+	0.881452i	$0.343434\pi$
$881$			52.3259i			1.76290i	−0.472273	+	0.881452i	$0.656566\pi$
$882$		0			0
$883$	−16.0000	−	16.0000i	−0.538443	−	0.538443i	0.384629	−	0.923071i	$-0.374330\pi$
$883$	−16.0000	−	16.0000i	−0.538443	−	0.538443i	−0.923071	+	0.384629i	$0.874330\pi$
$884$	−16.9706			−0.570782
$885$		0			0
$886$	24.0000			0.806296
$887$	−25.4558	−	25.4558i	−0.854724	−	0.854724i	0.135987	−	0.990711i	$-0.456579\pi$
$887$	−25.4558	−	25.4558i	−0.854724	−	0.854724i	−0.990711	+	0.135987i	$0.956579\pi$
$888$		0			0
$889$		−	56.0000i		−	1.87818i
$890$		0			0
$891$		0			0
$892$	6.00000	−	6.00000i	0.200895	−	0.200895i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		−	2.82843i		−	0.0944911i
$897$		0			0
$898$	−1.00000	−	1.00000i	−0.0333704	−	0.0333704i
$899$	5.65685			0.188667
$900$		0			0
$901$	16.0000			0.533037
$902$	−19.7990	−	19.7990i	−0.659234	−	0.659234i
$903$		0			0
$904$			2.00000i			0.0665190i
$905$		0			0
$906$		0			0
$907$	−4.00000	+	4.00000i	−0.132818	+	0.132818i	−0.770390	−	0.637573i	$-0.779939\pi$
$907$	−4.00000	+	4.00000i	−0.132818	+	0.132818i	0.637573	+	0.770390i	$0.279939\pi$
$908$	−5.65685	+	5.65685i	−0.187729	+	0.187729i
$909$		0			0
$910$		0			0
$911$			11.3137i			0.374840i	0.982280	+	0.187420i	$0.0600125\pi$
$911$			11.3137i			0.374840i	−0.982280	+	0.187420i	$0.939987\pi$
$912$		0			0
$913$	24.0000	+	24.0000i	0.794284	+	0.794284i
$914$	−21.2132			−0.701670
$915$		0			0
$916$	−6.00000			−0.198246
$917$	−28.2843	−	28.2843i	−0.934029	−	0.934029i
$918$		0			0
$919$		−	20.0000i		−	0.659739i	−0.944027	−	0.329870i	$-0.892995\pi$
$919$		−	20.0000i		−	0.659739i	0.944027	−	0.329870i	$-0.107005\pi$
$920$		0			0
$921$		0			0
$922$	13.0000	−	13.0000i	0.428132	−	0.428132i
$923$	16.9706	−	16.9706i	0.558593	−	0.558593i
$924$		0			0
$925$		0			0
$926$			19.7990i			0.650635i
$927$		0			0
$928$	1.00000	+	1.00000i	0.0328266	+	0.0328266i
$929$	−32.5269			−1.06717			−0.533587	−	0.845745i	$-0.679156\pi$
$929$	−32.5269			−1.06717			−0.533587	+	0.845745i	$0.679156\pi$
$930$		0			0
$931$	8.00000			0.262189
$932$	8.48528	+	8.48528i	0.277945	+	0.277945i
$933$		0			0
$934$		−	28.0000i		−	0.916188i
$935$		0			0
$936$		0			0
$937$	11.0000	−	11.0000i	0.359354	−	0.359354i	−0.504221	−	0.863575i	$-0.668220\pi$
$937$	11.0000	−	11.0000i	0.359354	−	0.359354i	0.863575	+	0.504221i	$0.168220\pi$
$938$	11.3137	−	11.3137i	0.369406	−	0.369406i
$939$		0			0
$940$		0			0
$941$		−	29.6985i		−	0.968143i	−0.875028	−	0.484071i	$-0.839157\pi$
$941$		−	29.6985i		−	0.968143i	0.875028	−	0.484071i	$-0.160843\pi$
$942$		0			0
$943$	−28.0000	−	28.0000i	−0.911805	−	0.911805i
$944$	2.82843			0.0920575
$945$		0			0
$946$		0			0
$947$	5.65685	+	5.65685i	0.183823	+	0.183823i	0.793019	−	0.609196i	$-0.208508\pi$
$947$	5.65685	+	5.65685i	0.183823	+	0.183823i	−0.609196	+	0.793019i	$0.708508\pi$
$948$		0			0
$949$		−	6.00000i		−	0.194768i
$950$		0			0
$951$		0			0
$952$	−8.00000	+	8.00000i	−0.259281	+	0.259281i
$953$	−4.24264	+	4.24264i	−0.137433	+	0.137433i	−0.772476	−	0.635044i	$-0.780982\pi$
$953$	−4.24264	+	4.24264i	−0.137433	+	0.137433i	0.635044	+	0.772476i	$0.280982\pi$
$954$		0			0
$955$		0			0
$956$			16.9706i			0.548867i
$957$		0			0
$958$	−4.00000	−	4.00000i	−0.129234	−	0.129234i
$959$	16.9706			0.548008
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−12.7279	−	12.7279i	−0.410365	−	0.410365i
$963$		0			0
$964$			22.0000i			0.708572i
$965$		0			0
$966$		0			0
$967$	−10.0000	+	10.0000i	−0.321578	+	0.321578i	−0.849372	−	0.527794i	$-0.823019\pi$
$967$	−10.0000	+	10.0000i	−0.321578	+	0.321578i	0.527794	+	0.849372i	$0.323019\pi$
$968$	2.12132	−	2.12132i	0.0681818	−	0.0681818i
$969$		0			0
$970$		0			0
$971$			36.7696i			1.17999i	0.807406	+	0.589996i	$0.200871\pi$
$971$			36.7696i			1.17999i	−0.807406	+	0.589996i	$0.799129\pi$
$972$		0			0
$973$	−8.00000	−	8.00000i	−0.256468	−	0.256468i
$974$	−25.4558			−0.815658
$975$		0			0
$976$		0			0
$977$	−8.48528	−	8.48528i	−0.271468	−	0.271468i	0.558223	−	0.829691i	$-0.311483\pi$
$977$	−8.48528	−	8.48528i	−0.271468	−	0.271468i	−0.829691	+	0.558223i	$0.811483\pi$
$978$		0			0
$979$			28.0000i			0.894884i
$980$		0			0
$981$		0			0
$982$	2.00000	−	2.00000i	0.0638226	−	0.0638226i
$983$	−5.65685	+	5.65685i	−0.180426	+	0.180426i	−0.791541	−	0.611116i	$-0.790721\pi$
$983$	−5.65685	+	5.65685i	−0.180426	+	0.180426i	0.611116	+	0.791541i	$0.290721\pi$
$984$		0			0
$985$		0			0
$986$		−	5.65685i		−	0.180151i
$987$		0			0
$988$	−24.0000	−	24.0000i	−0.763542	−	0.763542i
$989$		0			0
$990$		0			0
$991$	−32.0000			−1.01651			−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000			−1.01651			−0.508257	+	0.861206i	$0.669710\pi$
$992$	2.82843	+	2.82843i	0.0898027	+	0.0898027i
$993$		0			0
$994$		−	16.0000i		−	0.507489i
$995$		0			0
$996$		0			0
$997$	−13.0000	+	13.0000i	−0.411714	+	0.411714i	−0.882335	−	0.470621i	$-0.844030\pi$
$997$	−13.0000	+	13.0000i	−0.411714	+	0.411714i	0.470621	+	0.882335i	$0.344030\pi$
$998$	−22.6274	+	22.6274i	−0.716258	+	0.716258i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.f.b.143.1		4
3.2	odd	2	inner	450.2.f.b.143.2		4
4.3	odd	2		3600.2.w.g.593.2		4
5.2	odd	4	inner	450.2.f.b.107.2		4
5.3	odd	4		90.2.f.a.17.1	✓	4
5.4	even	2		90.2.f.a.53.2	yes	4
12.11	even	2		3600.2.w.g.593.1		4
15.2	even	4	inner	450.2.f.b.107.1		4
15.8	even	4		90.2.f.a.17.2	yes	4
15.14	odd	2		90.2.f.a.53.1	yes	4
20.3	even	4		720.2.w.a.17.2		4
20.7	even	4		3600.2.w.g.1457.2		4
20.19	odd	2		720.2.w.a.593.1		4
40.3	even	4		2880.2.w.c.2177.1		4
40.13	odd	4		2880.2.w.l.2177.1		4
40.19	odd	2		2880.2.w.c.2753.2		4
40.29	even	2		2880.2.w.l.2753.2		4
45.4	even	6		810.2.m.c.593.1		8
45.13	odd	12		810.2.m.c.107.1		8
45.14	odd	6		810.2.m.c.593.2		8
45.23	even	12		810.2.m.c.107.2		8
45.29	odd	6		810.2.m.c.53.1		8
45.34	even	6		810.2.m.c.53.2		8
45.38	even	12		810.2.m.c.377.1		8
45.43	odd	12		810.2.m.c.377.2		8
60.23	odd	4		720.2.w.a.17.1		4
60.47	odd	4		3600.2.w.g.1457.1		4
60.59	even	2		720.2.w.a.593.2		4
120.29	odd	2		2880.2.w.l.2753.1		4
120.53	even	4		2880.2.w.l.2177.2		4
120.59	even	2		2880.2.w.c.2753.1		4
120.83	odd	4		2880.2.w.c.2177.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.f.a.17.1	✓	4	5.3	odd	4
90.2.f.a.17.2	yes	4	15.8	even	4
90.2.f.a.53.1	yes	4	15.14	odd	2
90.2.f.a.53.2	yes	4	5.4	even	2
450.2.f.b.107.1		4	15.2	even	4	inner
450.2.f.b.107.2		4	5.2	odd	4	inner
450.2.f.b.143.1		4	1.1	even	1	trivial
450.2.f.b.143.2		4	3.2	odd	2	inner
720.2.w.a.17.1		4	60.23	odd	4
720.2.w.a.17.2		4	20.3	even	4
720.2.w.a.593.1		4	20.19	odd	2
720.2.w.a.593.2		4	60.59	even	2
810.2.m.c.53.1		8	45.29	odd	6
810.2.m.c.53.2		8	45.34	even	6
810.2.m.c.107.1		8	45.13	odd	12
810.2.m.c.107.2		8	45.23	even	12
810.2.m.c.377.1		8	45.38	even	12
810.2.m.c.377.2		8	45.43	odd	12
810.2.m.c.593.1		8	45.4	even	6
810.2.m.c.593.2		8	45.14	odd	6
2880.2.w.c.2177.1		4	40.3	even	4
2880.2.w.c.2177.2		4	120.83	odd	4
2880.2.w.c.2753.1		4	120.59	even	2
2880.2.w.c.2753.2		4	40.19	odd	2
2880.2.w.l.2177.1		4	40.13	odd	4
2880.2.w.l.2177.2		4	120.53	even	4
2880.2.w.l.2753.1		4	120.29	odd	2
2880.2.w.l.2753.2		4	40.29	even	2
3600.2.w.g.593.1		4	12.11	even	2
3600.2.w.g.593.2		4	4.3	odd	2
3600.2.w.g.1457.1		4	60.47	odd	4
3600.2.w.g.1457.2		4	20.7	even	4

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.00000 + 2.00000i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-2.00000 + 2.00000i) q^{7} +(0.707107 - 0.707107i) q^{8} -2.82843i q^{11} +(3.00000 + 3.00000i) q^{13} +2.82843 q^{14} -1.00000 q^{16} +(2.82843 + 2.82843i) q^{17} +8.00000i q^{19} +(-2.00000 + 2.00000i) q^{22} +(-2.82843 + 2.82843i) q^{23} -4.24264i q^{26} +(-2.00000 - 2.00000i) q^{28} +1.41421 q^{29} +4.00000 q^{31} +(0.707107 + 0.707107i) q^{32} -4.00000i q^{34} +(3.00000 - 3.00000i) q^{37} +(5.65685 - 5.65685i) q^{38} +9.89949i q^{41} +2.82843 q^{44} +4.00000 q^{46} -1.00000i q^{49} +(-3.00000 + 3.00000i) q^{52} +(2.82843 - 2.82843i) q^{53} +2.82843i q^{56} +(-1.00000 - 1.00000i) q^{58} -2.82843 q^{59} +(-2.82843 - 2.82843i) q^{62} -1.00000i q^{64} +(4.00000 - 4.00000i) q^{67} +(-2.82843 + 2.82843i) q^{68} -5.65685i q^{71} +(-1.00000 - 1.00000i) q^{73} -4.24264 q^{74} -8.00000 q^{76} +(5.65685 + 5.65685i) q^{77} -12.0000i q^{79} +(7.00000 - 7.00000i) q^{82} +(-8.48528 + 8.48528i) q^{83} +(-2.00000 - 2.00000i) q^{88} -9.89949 q^{89} -12.0000 q^{91} +(-2.82843 - 2.82843i) q^{92} +(3.00000 - 3.00000i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{7}+O(q^{10}) \) 4 * q - 8 * q^7	\( 4 q - 8 q^{7} + 12 q^{13} - 4 q^{16} - 8 q^{22} - 8 q^{28} + 16 q^{31} + 12 q^{37} + 16 q^{46} - 12 q^{52} - 4 q^{58} + 16 q^{67} - 4 q^{73} - 32 q^{76} + 28 q^{82} - 8 q^{88} - 48 q^{91} + 12 q^{97}+O(q^{100}) \) 4 * q - 8 * q^7 + 12 * q^13 - 4 * q^16 - 8 * q^22 - 8 * q^28 + 16 * q^31 + 12 * q^37 + 16 * q^46 - 12 * q^52 - 4 * q^58 + 16 * q^67 - 4 * q^73 - 32 * q^76 + 28 * q^82 - 8 * q^88 - 48 * q^91 + 12 * q^97

Introduction

L-functions

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