LMFDB - Embedded newform 2548.2.j.s.1145.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2548,2,Mod(1145,2548)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2548, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("2548.1145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.j (of order $3$, 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:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 10 x^{10} - 8 x^{9} + 80 x^{8} - 56 x^{7} + 220 x^{6} - 240 x^{5} + 484 x^{4} - 336 x^{3} + \cdots + 4 $ x^12 + 10x^10 - 8x^9 + 80x^8 - 56x^7 + 220x^6 - 240x^5 + 484x^4 - 336x^3 + 216x^2 - 32x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1145.4
Root			$1.23667 + 2.14198i$ of defining polynomial
Character	$\chi$	$=$	2548.1145
Dual form			2548.2.j.s.1353.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.529566 - 0.917235i) q^{3} +(2.04647 + 3.54459i) q^{5} +(0.939121 + 1.62660i) q^{9} +(-0.926874 + 1.60539i) q^{11} +1.00000 q^{13} +4.33496 q^{15} +(-2.46552 + 4.27041i) q^{17} +(0.788959 + 1.36652i) q^{19} +(-2.15007 - 3.72403i) q^{23} +(-5.87608 + 10.1777i) q^{25} +5.16670 q^{27} +2.35746 q^{29} +(1.14057 - 1.97552i) q^{31} +(0.981681 + 1.70032i) q^{33} +(-1.67023 - 2.89292i) q^{37} +(0.529566 - 0.917235i) q^{39} -10.6089 q^{41} -0.0759434 q^{43} +(-3.84377 + 6.65760i) q^{45} +(4.88190 + 8.45570i) q^{47} +(2.61131 + 4.52293i) q^{51} +(-0.984819 + 1.70576i) q^{53} -7.58728 q^{55} +1.67122 q^{57} +(5.64407 - 9.77581i) q^{59} +(-2.23817 - 3.87662i) q^{61} +(2.04647 + 3.54459i) q^{65} +(-4.86365 + 8.42409i) q^{67} -4.55441 q^{69} -12.4059 q^{71} +(5.48668 - 9.50322i) q^{73} +(6.22354 + 10.7795i) q^{75} +(3.07735 + 5.33012i) q^{79} +(-0.0812565 + 0.140740i) q^{81} +17.3928 q^{83} -20.1825 q^{85} +(1.24843 - 2.16234i) q^{87} +(-0.629405 - 1.09016i) q^{89} +(-1.20801 - 2.09234i) q^{93} +(-3.22916 + 5.59307i) q^{95} -6.51465 q^{97} -3.48179 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 10 q^{5} - 6 q^{9} + 4 q^{11} + 12 q^{13} + 8 q^{15} + 16 q^{17} + 10 q^{19} + 2 q^{23} - 12 q^{25} + 24 q^{27} + 4 q^{29} + 6 q^{31} + 28 q^{33} - 16 q^{37} - 16 q^{41} + 12 q^{43} + 34 q^{45} + 30 q^{47}+ \cdots - 104 q^{99}+O(q^{100}) $ 12 * q + 10 * q^5 - 6 * q^9 + 4 * q^11 + 12 * q^13 + 8 * q^15 + 16 * q^17 + 10 * q^19 + 2 * q^23 - 12 * q^25 + 24 * q^27 + 4 * q^29 + 6 * q^31 + 28 * q^33 - 16 * q^37 - 16 * q^41 + 12 * q^43 + 34 * q^45 + 30 * q^47 + 12 * q^51 + 6 * q^53 + 32 * q^55 - 24 * q^57 + 8 * q^59 + 16 * q^61 + 10 * q^65 - 8 * q^69 + 14 * q^73 + 28 * q^75 - 14 * q^79 - 14 * q^81 + 28 * q^83 + 48 * q^85 + 24 * q^87 + 30 * q^89 + 16 * q^93 + 10 * q^95 - 44 * q^97 - 104 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.529566	−	0.917235i	0.305745	−	0.529566i	−0.671682	−	0.740840i	$-0.734428\pi$
$3$	0.529566	−	0.917235i	0.305745	−	0.529566i	0.977427	+	0.211274i	$0.0677612\pi$
$4$		0			0
$5$	2.04647	+	3.54459i	0.915210	+	1.58519i	0.806594	+	0.591105i	$0.201308\pi$
$5$	2.04647	+	3.54459i	0.915210	+	1.58519i	0.108615	+	0.994084i	$0.465358\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	0.939121	+	1.62660i	0.313040	+	0.542202i
$10$		0			0
$11$	−0.926874	+	1.60539i	−0.279463	+	0.484044i	−0.971251	−	0.238056i	$-0.923490\pi$
$11$	−0.926874	+	1.60539i	−0.279463	+	0.484044i	0.691788	+	0.722100i	$0.256823\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$		0			0
$15$	4.33496			1.11928
$16$		0			0
$17$	−2.46552	+	4.27041i	−0.597977	+	1.03573i	0.395142	+	0.918620i	$0.370695\pi$
$17$	−2.46552	+	4.27041i	−0.597977	+	1.03573i	−0.993119	+	0.117107i	$0.962638\pi$
$18$		0			0
$19$	0.788959	+	1.36652i	0.181000	+	0.313500i	0.942221	−	0.334991i	$-0.108733\pi$
$19$	0.788959	+	1.36652i	0.181000	+	0.313500i	−0.761222	+	0.648492i	$0.775400\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.15007	−	3.72403i	−0.448320	−	0.776513i	0.549957	−	0.835193i	$-0.314644\pi$
$23$	−2.15007	−	3.72403i	−0.448320	−	0.776513i	−0.998277	+	0.0586799i	$0.981311\pi$
$24$		0			0
$25$	−5.87608	+	10.1777i	−1.17522	+	2.03554i
$26$		0			0
$27$	5.16670			0.994331
$28$		0			0
$29$	2.35746			0.437769			0.218884	−	0.975751i	$-0.429758\pi$
$29$	2.35746			0.437769			0.218884	+	0.975751i	$0.429758\pi$
$30$		0			0
$31$	1.14057	−	1.97552i	0.204852	−	0.354815i	−0.745233	−	0.666804i	$-0.767662\pi$
$31$	1.14057	−	1.97552i	0.204852	−	0.354815i	0.950086	+	0.311989i	$0.100995\pi$
$32$		0			0
$33$	0.981681	+	1.70032i	0.170889	+	0.295988i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.67023	−	2.89292i	−0.274584	−	0.475593i	0.695446	−	0.718578i	$-0.255207\pi$
$37$	−1.67023	−	2.89292i	−0.274584	−	0.475593i	−0.970030	+	0.242985i	$0.921873\pi$
$38$		0			0
$39$	0.529566	−	0.917235i	0.0847984	−	0.146875i
$40$		0			0
$41$	−10.6089			−1.65684			−0.828420	−	0.560108i	$-0.810760\pi$
$41$	−10.6089			−1.65684			−0.828420	+	0.560108i	$0.810760\pi$
$42$		0			0
$43$	−0.0759434			−0.0115813			−0.00579063	−	0.999983i	$-0.501843\pi$
$43$	−0.0759434			−0.0115813			−0.00579063	+	0.999983i	$0.501843\pi$
$44$		0			0
$45$	−3.84377	+	6.65760i	−0.572995	+	0.992456i
$46$		0			0
$47$	4.88190	+	8.45570i	0.712098	+	1.23339i	0.964068	+	0.265655i	$0.0855883\pi$
$47$	4.88190	+	8.45570i	0.712098	+	1.23339i	−0.251970	+	0.967735i	$0.581078\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	2.61131	+	4.52293i	0.365657	+	0.633337i
$52$		0			0
$53$	−0.984819	+	1.70576i	−0.135275	+	0.234304i	−0.925703	−	0.378252i	$-0.876525\pi$
$53$	−0.984819	+	1.70576i	−0.135275	+	0.234304i	0.790427	+	0.612556i	$0.209859\pi$
$54$		0			0
$55$	−7.58728			−1.02307
$56$		0			0
$57$	1.67122			0.221359
$58$		0			0
$59$	5.64407	−	9.77581i	0.734795	−	1.27270i	−0.220019	−	0.975496i	$-0.570612\pi$
$59$	5.64407	−	9.77581i	0.734795	−	1.27270i	0.954813	−	0.297206i	$-0.0960548\pi$
$60$		0			0
$61$	−2.23817	−	3.87662i	−0.286568	−	0.496351i	0.686420	−	0.727205i	$-0.259181\pi$
$61$	−2.23817	−	3.87662i	−0.286568	−	0.496351i	−0.972988	+	0.230855i	$0.925848\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.04647	+	3.54459i	0.253833	+	0.439652i
$66$		0			0
$67$	−4.86365	+	8.42409i	−0.594190	+	1.02917i	0.399471	+	0.916746i	$0.369194\pi$
$67$	−4.86365	+	8.42409i	−0.594190	+	1.02917i	−0.993661	+	0.112421i	$0.964140\pi$
$68$		0			0
$69$	−4.55441			−0.548286
$70$		0			0
$71$	−12.4059			−1.47231			−0.736157	−	0.676811i	$-0.763362\pi$
$71$	−12.4059			−1.47231			−0.736157	+	0.676811i	$0.763362\pi$
$72$		0			0
$73$	5.48668	−	9.50322i	0.642168	−	1.11227i	−0.342780	−	0.939416i	$-0.611369\pi$
$73$	5.48668	−	9.50322i	0.642168	−	1.11227i	0.984948	−	0.172852i	$-0.0552981\pi$
$74$		0			0
$75$	6.22354	+	10.7795i	0.718633	+	1.24471i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	3.07735	+	5.33012i	0.346228	+	0.599685i	0.985576	−	0.169232i	$-0.0541289\pi$
$79$	3.07735	+	5.33012i	0.346228	+	0.599685i	−0.639348	+	0.768918i	$0.720796\pi$
$80$		0			0
$81$	−0.0812565	+	0.140740i	−0.00902850	+	0.0156378i
$82$		0			0
$83$	17.3928			1.90910			0.954552	−	0.298045i	$-0.0963346\pi$
$83$	17.3928			1.90910			0.954552	+	0.298045i	$0.0963346\pi$
$84$		0			0
$85$	−20.1825			−2.18910
$86$		0			0
$87$	1.24843	−	2.16234i	0.133845	−	0.231827i
$88$		0			0
$89$	−0.629405	−	1.09016i	−0.0667168	−	0.115557i	0.830737	−	0.556664i	$-0.187919\pi$
$89$	−0.629405	−	1.09016i	−0.0667168	−	0.115557i	−0.897454	+	0.441108i	$0.854586\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−1.20801	−	2.09234i	−0.125265	−	0.216965i
$94$		0			0
$95$	−3.22916	+	5.59307i	−0.331305	+	0.573837i
$96$		0			0
$97$	−6.51465			−0.661462			−0.330731	−	0.943725i	$-0.607295\pi$
$97$	−6.51465			−0.661462			−0.330731	+	0.943725i	$0.607295\pi$
$98$		0			0
$99$	−3.48179			−0.349933
$100$		0			0
$101$	−0.524655	+	0.908730i	−0.0522052	+	0.0904220i	−0.890947	−	0.454107i	$-0.849958\pi$
$101$	−0.524655	+	0.908730i	−0.0522052	+	0.0904220i	0.838742	+	0.544529i	$0.183292\pi$
$102$		0			0
$103$	−4.49293	−	7.78198i	−0.442701	−	0.766781i	0.555188	−	0.831725i	$-0.312646\pi$
$103$	−4.49293	−	7.78198i	−0.442701	−	0.766781i	−0.997889	+	0.0649440i	$0.979313\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.29230	+	14.3627i	0.801647	+	1.38849i	0.918532	+	0.395347i	$0.129376\pi$
$107$	8.29230	+	14.3627i	0.801647	+	1.38849i	−0.116885	+	0.993145i	$0.537291\pi$
$108$		0			0
$109$	−4.21792	+	7.30564i	−0.404003	+	0.699754i	−0.994205	−	0.107502i	$-0.965715\pi$
$109$	−4.21792	+	7.30564i	−0.404003	+	0.699754i	0.590202	+	0.807256i	$0.299048\pi$
$110$		0			0
$111$	−3.53798			−0.335810
$112$		0			0
$113$	−0.951842			−0.0895418			−0.0447709	−	0.998997i	$-0.514256\pi$
$113$	−0.951842			−0.0895418			−0.0447709	+	0.998997i	$0.514256\pi$
$114$		0			0
$115$	8.80010	−	15.2422i	0.820614	−	1.42134i
$116$		0			0
$117$	0.939121	+	1.62660i	0.0868217	+	0.150380i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	3.78181	+	6.55029i	0.343801	+	0.595480i
$122$		0			0
$123$	−5.61813	+	9.73089i	−0.506570	+	0.877405i
$124$		0			0
$125$	−27.6362			−2.47186
$126$		0			0
$127$	−15.6229			−1.38631			−0.693155	−	0.720789i	$-0.743780\pi$
$127$	−15.6229			−1.38631			−0.693155	+	0.720789i	$0.743780\pi$
$128$		0			0
$129$	−0.0402170	+	0.0696579i	−0.00354091	+	0.00613303i
$130$		0			0
$131$	−5.48466	−	9.49971i	−0.479197	−	0.829994i	0.520518	−	0.853851i	$-0.325739\pi$
$131$	−5.48466	−	9.49971i	−0.479197	−	0.829994i	−0.999715	+	0.0238568i	$0.992405\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	10.5735	+	18.3138i	0.910022	+	1.57620i
$136$		0			0
$137$	2.20743	−	3.82338i	0.188593	−	0.326653i	−0.756188	−	0.654354i	$-0.772941\pi$
$137$	2.20743	−	3.82338i	0.188593	−	0.326653i	0.944781	+	0.327701i	$0.106274\pi$
$138$		0			0
$139$	13.0801			1.10944			0.554720	−	0.832037i	$-0.312825\pi$
$139$	13.0801			1.10944			0.554720	+	0.832037i	$0.312825\pi$
$140$		0			0
$141$	10.3411			0.870882
$142$		0			0
$143$	−0.926874	+	1.60539i	−0.0775091	+	0.134250i
$144$		0			0
$145$	4.82446	+	8.35622i	0.400650	+	0.693946i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.56379	+	9.63677i	0.455803	+	0.789475i	0.998734	−	0.0503029i	$-0.0160187\pi$
$149$	5.56379	+	9.63677i	0.455803	+	0.789475i	−0.542931	+	0.839778i	$0.682685\pi$
$150$		0			0
$151$	9.32841	−	16.1573i	0.759135	−	1.31486i	−0.184157	−	0.982897i	$-0.558956\pi$
$151$	9.32841	−	16.1573i	0.759135	−	1.31486i	0.943292	−	0.331963i	$-0.107711\pi$
$152$		0			0
$153$	−9.26170			−0.748764
$154$		0			0
$155$	9.33657			0.749931
$156$		0			0
$157$	4.98148	−	8.62817i	0.397565	−	0.688603i	−0.595860	−	0.803088i	$-0.703189\pi$
$157$	4.98148	−	8.62817i	0.397565	−	0.688603i	0.993425	+	0.114486i	$0.0365220\pi$
$158$		0			0
$159$	1.04305	+	1.80662i	0.0827194	+	0.143274i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−9.38636	−	16.2576i	−0.735196	−	1.27340i	−0.954637	−	0.297771i	$-0.903757\pi$
$163$	−9.38636	−	16.2576i	−0.735196	−	1.27340i	0.219441	−	0.975626i	$-0.429577\pi$
$164$		0			0
$165$	−4.01796	+	6.95932i	−0.312798	+	0.541782i
$166$		0			0
$167$	9.39140			0.726729			0.363364	−	0.931647i	$-0.381628\pi$
$167$	9.39140			0.726729			0.363364	+	0.931647i	$0.381628\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	−1.48185	+	2.56665i	−0.113320	+	0.196276i
$172$		0			0
$173$	7.66362	+	13.2738i	0.582655	+	1.00919i	0.995163	+	0.0982337i	$0.0313193\pi$
$173$	7.66362	+	13.2738i	0.582655	+	1.00919i	−0.412509	+	0.910954i	$0.635347\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−5.97781	−	10.3539i	−0.449319	−	0.778244i
$178$		0			0
$179$	2.09691	−	3.63196i	0.156731	−	0.271466i	−0.776957	−	0.629554i	$-0.783238\pi$
$179$	2.09691	−	3.63196i	0.156731	−	0.271466i	0.933688	+	0.358088i	$0.116571\pi$
$180$		0			0
$181$	22.8843			1.70097			0.850487	−	0.525995i	$-0.176307\pi$
$181$	22.8843			1.70097			0.850487	+	0.525995i	$0.176307\pi$
$182$		0			0
$183$	−4.74103			−0.350467
$184$		0			0
$185$	6.83615	−	11.8406i	0.502604	−	0.870535i
$186$		0			0
$187$	−4.57046	−	7.91627i	−0.334225	−	0.578895i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.8669	+	22.2861i	0.931015	+	1.61257i	0.781590	+	0.623792i	$0.214409\pi$
$191$	12.8669	+	22.2861i	0.931015	+	1.61257i	0.149425	+	0.988773i	$0.452258\pi$
$192$		0			0
$193$	−5.79379	+	10.0351i	−0.417046	+	0.722345i	−0.995641	−	0.0932702i	$-0.970268\pi$
$193$	−5.79379	+	10.0351i	−0.417046	+	0.722345i	0.578595	+	0.815615i	$0.303601\pi$
$194$		0			0
$195$	4.33496			0.310433
$196$		0			0
$197$	−13.6986			−0.975983			−0.487992	−	0.872848i	$-0.662270\pi$
$197$	−13.6986			−0.975983			−0.487992	+	0.872848i	$0.662270\pi$
$198$		0			0
$199$	4.67455	−	8.09656i	0.331370	−	0.573950i	−0.651411	−	0.758725i	$-0.725822\pi$
$199$	4.67455	−	8.09656i	0.331370	−	0.573950i	0.982781	+	0.184775i	$0.0591558\pi$
$200$		0			0
$201$	5.15124	+	8.92222i	0.363341	+	0.629325i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−21.7109	−	37.6044i	−1.51636	−	2.62640i
$206$		0			0
$207$	4.03835	−	6.99462i	0.280684	−	0.486160i
$208$		0			0
$209$	−2.92506			−0.202331
$210$		0			0
$211$	−1.71265			−0.117904			−0.0589518	−	0.998261i	$-0.518776\pi$
$211$	−1.71265			−0.117904			−0.0589518	+	0.998261i	$0.518776\pi$
$212$		0			0
$213$	−6.56976	+	11.3792i	−0.450152	+	0.779687i
$214$		0			0
$215$	−0.155416	−	0.269188i	−0.0105993	−	0.0183585i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−5.81112	−	10.0652i	−0.392679	−	0.680140i
$220$		0			0
$221$	−2.46552	+	4.27041i	−0.165849	+	0.287259i
$222$		0			0
$223$	14.3065			0.958033			0.479017	−	0.877806i	$-0.340993\pi$
$223$	14.3065			0.958033			0.479017	+	0.877806i	$0.340993\pi$
$224$		0			0
$225$	−22.0734			−1.47156
$226$		0			0
$227$	−5.69936	+	9.87158i	−0.378280	+	0.655200i	−0.990812	−	0.135246i	$-0.956818\pi$
$227$	−5.69936	+	9.87158i	−0.378280	+	0.655200i	0.612532	+	0.790446i	$0.290151\pi$
$228$		0			0
$229$	11.6079	+	20.1055i	0.767074	+	1.32861i	0.939143	+	0.343527i	$0.111622\pi$
$229$	11.6079	+	20.1055i	0.767074	+	1.32861i	−0.172069	+	0.985085i	$0.555045\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	14.1264	+	24.4676i	0.925451	+	1.60293i	0.790834	+	0.612031i	$0.209647\pi$
$233$	14.1264	+	24.4676i	0.925451	+	1.60293i	0.134617	+	0.990898i	$0.457019\pi$
$234$		0			0
$235$	−19.9813	+	34.6087i	−1.30344	+	2.25762i
$236$		0			0
$237$	6.51863			0.423430
$238$		0			0
$239$	27.2744			1.76424			0.882118	−	0.471028i	$-0.156117\pi$
$239$	27.2744			1.76424			0.882118	+	0.471028i	$0.156117\pi$
$240$		0			0
$241$	−7.60842	+	13.1782i	−0.490101	+	0.848880i	−0.999935	−	0.0113926i	$-0.996374\pi$
$241$	−7.60842	+	13.1782i	−0.490101	+	0.848880i	0.509834	+	0.860273i	$0.329707\pi$
$242$		0			0
$243$	7.83611	+	13.5725i	0.502687	+	0.870679i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.788959	+	1.36652i	0.0502002	+	0.0869494i
$248$		0			0
$249$	9.21061	−	15.9532i	0.583699	−	1.01100i
$250$		0			0
$251$	24.6393			1.55522			0.777611	−	0.628746i	$-0.216432\pi$
$251$	24.6393			1.55522			0.777611	+	0.628746i	$0.216432\pi$
$252$		0			0
$253$	7.97137			0.501156
$254$		0			0
$255$	−10.6880	+	18.5121i	−0.669306	+	1.15927i
$256$		0			0
$257$	12.8435	+	22.2456i	0.801155	+	1.38764i	0.918856	+	0.394592i	$0.129114\pi$
$257$	12.8435	+	22.2456i	0.801155	+	1.38764i	−0.117702	+	0.993049i	$0.537553\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	2.21393	+	3.83465i	0.137039	+	0.237359i
$262$		0			0
$263$	4.91364	−	8.51068i	0.302988	−	0.524791i	−0.673823	−	0.738893i	$-0.735349\pi$
$263$	4.91364	−	8.51068i	0.302988	−	0.524791i	0.976811	+	0.214102i	$0.0686824\pi$
$264$		0			0
$265$	−8.06161			−0.495221
$266$		0			0
$267$	−1.33325			−0.0815933
$268$		0			0
$269$	12.6669	−	21.9398i	0.772316	−	1.33769i	−0.163975	−	0.986465i	$-0.552432\pi$
$269$	12.6669	−	21.9398i	0.772316	−	1.33769i	0.936291	−	0.351226i	$-0.114235\pi$
$270$		0			0
$271$	2.91243	+	5.04447i	0.176917	+	0.306430i	0.940823	−	0.338898i	$-0.110054\pi$
$271$	2.91243	+	5.04447i	0.176917	+	0.306430i	−0.763906	+	0.645328i	$0.776721\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−10.8928	−	18.8668i	−0.656859	−	1.13771i
$276$		0			0
$277$	4.95442	−	8.58130i	0.297682	−	0.515600i	−0.677923	−	0.735133i	$-0.737120\pi$
$277$	4.95442	−	8.58130i	0.297682	−	0.515600i	0.975605	+	0.219532i	$0.0704532\pi$
$278$		0			0
$279$	4.28453			0.256508
$280$		0			0
$281$	1.88907			0.112693			0.0563463	−	0.998411i	$-0.482055\pi$
$281$	1.88907			0.112693			0.0563463	+	0.998411i	$0.482055\pi$
$282$		0			0
$283$	12.1615	−	21.0643i	0.722924	−	1.25214i	−0.236898	−	0.971534i	$-0.576131\pi$
$283$	12.1615	−	21.0643i	0.722924	−	1.25214i	0.959823	−	0.280607i	$-0.0905359\pi$
$284$		0			0
$285$	3.42011	+	5.92380i	0.202590	+	0.350895i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−3.65762	−	6.33518i	−0.215154	−	0.372658i
$290$		0			0
$291$	−3.44993	+	5.97546i	−0.202239	+	0.350288i
$292$		0			0
$293$	−22.2794			−1.30158			−0.650789	−	0.759258i	$-0.725562\pi$
$293$	−22.2794			−1.30158			−0.650789	+	0.759258i	$0.725562\pi$
$294$		0			0
$295$	46.2017			2.68996
$296$		0			0
$297$	−4.78888	+	8.29458i	−0.277879	+	0.481300i
$298$		0			0
$299$	−2.15007	−	3.72403i	−0.124342	−	0.215366i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	0.555679	+	0.962464i	0.0319229	+	0.0552921i
$304$		0			0
$305$	9.16069	−	15.8668i	0.524540	−	0.908530i
$306$		0			0
$307$	−26.5004			−1.51246			−0.756228	−	0.654308i	$-0.772960\pi$
$307$	−26.5004			−1.51246			−0.756228	+	0.654308i	$0.772960\pi$
$308$		0			0
$309$	−9.51720			−0.541415
$310$		0			0
$311$	−7.60511	+	13.1724i	−0.431246	+	0.746940i	−0.996981	−	0.0776473i	$-0.975259\pi$
$311$	−7.60511	+	13.1724i	−0.431246	+	0.746940i	0.565735	+	0.824587i	$0.308593\pi$
$312$		0			0
$313$	−11.5772	−	20.0523i	−0.654383	−	1.13342i	−0.982048	−	0.188630i	$-0.939595\pi$
$313$	−11.5772	−	20.0523i	−0.654383	−	1.13342i	0.327665	−	0.944794i	$-0.393738\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.27873	+	16.0712i	0.521146	+	0.902651i	0.999698	+	0.0245915i	$0.00782850\pi$
$317$	9.27873	+	16.0712i	0.521146	+	0.902651i	−0.478552	+	0.878059i	$0.658838\pi$
$318$		0			0
$319$	−2.18506	+	3.78464i	−0.122340	+	0.211899i
$320$		0			0
$321$	17.5653			0.980397
$322$		0			0
$323$	−7.78079			−0.432935
$324$		0			0
$325$	−5.87608	+	10.1777i	−0.325947	+	0.564556i
$326$		0			0
$327$	4.46733	+	7.73763i	0.247044	+	0.427892i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−11.4393	−	19.8134i	−0.628761	−	1.08905i	−0.987801	−	0.155723i	$-0.950229\pi$
$331$	−11.4393	−	19.8134i	−0.628761	−	1.08905i	0.359040	−	0.933322i	$-0.383104\pi$
$332$		0			0
$333$	3.13709	−	5.43360i	0.171912	−	0.297760i
$334$		0			0
$335$	−39.8133			−2.17523
$336$		0			0
$337$	10.9953			0.598950			0.299475	−	0.954104i	$-0.403188\pi$
$337$	10.9953			0.598950			0.299475	+	0.954104i	$0.403188\pi$
$338$		0			0
$339$	−0.504063	+	0.873063i	−0.0273769	+	0.0474182i
$340$		0			0
$341$	2.11433	+	3.66212i	0.114497	+	0.198315i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−9.32046	−	16.1435i	−0.501797	−	0.869138i
$346$		0			0
$347$	−2.86219	+	4.95746i	−0.153650	+	0.266130i	−0.932567	−	0.360998i	$-0.882436\pi$
$347$	−2.86219	+	4.95746i	−0.153650	+	0.266130i	0.778916	+	0.627128i	$0.215770\pi$
$348$		0			0
$349$	11.2570			0.602575			0.301287	−	0.953533i	$-0.402584\pi$
$349$	11.2570			0.602575			0.301287	+	0.953533i	$0.402584\pi$
$350$		0			0
$351$	5.16670			0.275778
$352$		0			0
$353$	6.62507	−	11.4750i	0.352617	−	0.610750i	−0.634090	−	0.773259i	$-0.718625\pi$
$353$	6.62507	−	11.4750i	0.352617	−	0.610750i	0.986707	+	0.162509i	$0.0519586\pi$
$354$		0			0
$355$	−25.3884	−	43.9740i	−1.34748	−	2.33390i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.12057	−	3.67294i	−0.111919	−	0.193850i	0.804625	−	0.593784i	$-0.202367\pi$
$359$	−2.12057	−	3.67294i	−0.111919	−	0.193850i	−0.916544	+	0.399934i	$0.869033\pi$
$360$		0			0
$361$	8.25509	−	14.2982i	0.434478	−	0.752539i
$362$		0			0
$363$	8.01086			0.420461
$364$		0			0
$365$	44.9133			2.35087
$366$		0			0
$367$	−5.10148	+	8.83602i	−0.266295	+	0.461237i	−0.967902	−	0.251328i	$-0.919133\pi$
$367$	−5.10148	+	8.83602i	−0.266295	+	0.461237i	0.701607	+	0.712564i	$0.252466\pi$
$368$		0			0
$369$	−9.96308	−	17.2566i	−0.518657	−	0.898341i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−8.80991	−	15.2592i	−0.456160	−	0.790092i	0.542594	−	0.839995i	$-0.317442\pi$
$373$	−8.80991	−	15.2592i	−0.456160	−	0.790092i	−0.998754	+	0.0499028i	$0.984109\pi$
$374$		0			0
$375$	−14.6352	+	25.3489i	−0.755758	+	1.30901i
$376$		0			0
$377$	2.35746			0.121415
$378$		0			0
$379$	−23.5661			−1.21051			−0.605255	−	0.796032i	$-0.706929\pi$
$379$	−23.5661			−1.21051			−0.605255	+	0.796032i	$0.706929\pi$
$380$		0			0
$381$	−8.27336	+	14.3299i	−0.423857	+	0.734142i
$382$		0			0
$383$	−3.65908	−	6.33771i	−0.186970	−	0.323842i	0.757269	−	0.653104i	$-0.226533\pi$
$383$	−3.65908	−	6.33771i	−0.186970	−	0.323842i	−0.944239	+	0.329262i	$0.893200\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.0713200	−	0.123530i	−0.00362540	−	0.00627937i
$388$		0			0
$389$	17.6488	−	30.5686i	0.894830	−	1.54989i	0.0608152	−	0.998149i	$-0.480630\pi$
$389$	17.6488	−	30.5686i	0.894830	−	1.54989i	0.834015	−	0.551742i	$-0.186037\pi$
$390$		0			0
$391$	21.2042			1.07234
$392$		0			0
$393$	−11.6180			−0.586048
$394$		0			0
$395$	−12.5954	+	21.8159i	−0.633743	+	1.09768i
$396$		0			0
$397$	9.70140	+	16.8033i	0.486899	+	0.843334i	0.999887	−	0.0150620i	$-0.00479456\pi$
$397$	9.70140	+	16.8033i	0.486899	+	0.843334i	−0.512987	+	0.858396i	$0.671461\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.66322	−	15.0051i	−0.432621	−	0.749321i	0.564478	−	0.825448i	$-0.309078\pi$
$401$	−8.66322	−	15.0051i	−0.432621	−	0.749321i	−0.997098	+	0.0761277i	$0.975744\pi$
$402$		0			0
$403$	1.14057	−	1.97552i	0.0568158	−	0.0984078i
$404$		0			0
$405$	−0.665156			−0.0330519
$406$		0			0
$407$	6.19237			0.306944
$408$		0			0
$409$	−0.189328	+	0.327925i	−0.00936166	+	0.0162149i	−0.870668	−	0.491871i	$-0.836313\pi$
$409$	−0.189328	+	0.327925i	−0.00936166	+	0.0162149i	0.861307	+	0.508086i	$0.169647\pi$
$410$		0			0
$411$	−2.33795	−	4.04946i	−0.115323	−	0.199745i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	35.5938	+	61.6502i	1.74723	+	3.02629i
$416$		0			0
$417$	6.92678	−	11.9975i	0.339206	−	0.587521i
$418$		0			0
$419$	−13.0797			−0.638986			−0.319493	−	0.947589i	$-0.603513\pi$
$419$	−13.0797			−0.638986			−0.319493	+	0.947589i	$0.603513\pi$
$420$		0			0
$421$	−15.5509			−0.757904			−0.378952	−	0.925416i	$-0.623715\pi$
$421$	−15.5509			−0.757904			−0.378952	+	0.925416i	$0.623715\pi$
$422$		0			0
$423$	−9.16939	+	15.8818i	−0.445831	+	0.772202i
$424$		0			0
$425$	−28.9753	−	50.1866i	−1.40551	−	2.43441i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	0.981681	+	1.70032i	0.0473960	+	0.0820923i
$430$		0			0
$431$	1.87660	−	3.25036i	0.0903925	−	0.156564i	−0.817284	−	0.576235i	$-0.804521\pi$
$431$	1.87660	−	3.25036i	0.0903925	−	0.156564i	0.907676	+	0.419671i	$0.137855\pi$
$432$		0			0
$433$	22.8084			1.09610			0.548051	−	0.836445i	$-0.315370\pi$
$433$	22.8084			1.09610			0.548051	+	0.836445i	$0.315370\pi$
$434$		0			0
$435$	10.2195			0.489987
$436$		0			0
$437$	3.39263	−	5.87621i	0.162291	−	0.281097i
$438$		0			0
$439$	−11.2076	−	19.4121i	−0.534908	−	0.926488i	−0.999168	−	0.0407886i	$-0.987013\pi$
$439$	−11.2076	−	19.4121i	−0.534908	−	0.926488i	0.464260	−	0.885699i	$-0.346320\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.38208	−	4.12589i	−0.113176	−	0.196027i	0.803873	−	0.594801i	$-0.202769\pi$
$443$	−2.38208	−	4.12589i	−0.113176	−	0.196027i	−0.917049	+	0.398774i	$0.869436\pi$
$444$		0			0
$445$	2.57612	−	4.46197i	0.122120	−	0.211518i
$446$		0			0
$447$	11.7856			0.557438
$448$		0			0
$449$	−38.0709			−1.79668			−0.898338	−	0.439305i	$-0.855225\pi$
$449$	−38.0709			−1.79668			−0.898338	+	0.439305i	$0.855225\pi$
$450$		0			0
$451$	9.83316	−	17.0315i	0.463025	−	0.801983i
$452$		0			0
$453$	−9.88001	−	17.1127i	−0.464203	−	0.804023i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.297125	−	0.514636i	−0.0138989	−	0.0240737i	0.858992	−	0.511989i	$-0.171091\pi$
$457$	−0.297125	−	0.514636i	−0.0138989	−	0.0240737i	−0.872891	+	0.487915i	$0.837758\pi$
$458$		0			0
$459$	−12.7386	+	22.0639i	−0.594588	+	1.02986i
$460$		0			0
$461$	−20.5070			−0.955106			−0.477553	−	0.878603i	$-0.658476\pi$
$461$	−20.5070			−0.955106			−0.477553	+	0.878603i	$0.658476\pi$
$462$		0			0
$463$	−4.95253			−0.230164			−0.115082	−	0.993356i	$-0.536713\pi$
$463$	−4.95253			−0.230164			−0.115082	+	0.993356i	$0.536713\pi$
$464$		0			0
$465$	4.94432	−	8.56382i	0.229288	−	0.397138i
$466$		0			0
$467$	−0.763766	−	1.32288i	−0.0353429	−	0.0612157i	0.847813	−	0.530295i	$-0.177919\pi$
$467$	−0.763766	−	1.32288i	−0.0353429	−	0.0612157i	−0.883156	+	0.469080i	$0.844586\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−5.27604	−	9.13836i	−0.243107	−	0.421074i
$472$		0			0
$473$	0.0703899	−	0.121919i	0.00323653	−	0.00560584i
$474$		0			0
$475$	−18.5440			−0.850855
$476$		0			0
$477$	−3.69945			−0.169386
$478$		0			0
$479$	8.85321	−	15.3342i	0.404514	−	0.700638i	−0.589751	−	0.807585i	$-0.700774\pi$
$479$	8.85321	−	15.3342i	0.404514	−	0.700638i	0.994265	+	0.106947i	$0.0341075\pi$
$480$		0			0
$481$	−1.67023	−	2.89292i	−0.0761559	−	0.131906i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−13.3320	−	23.0918i	−0.605377	−	1.04854i
$486$		0			0
$487$	5.34073	−	9.25042i	0.242012	−	0.419177i	−0.719275	−	0.694725i	$-0.755526\pi$
$487$	5.34073	−	9.25042i	0.242012	−	0.419177i	0.961287	+	0.275548i	$0.0888594\pi$
$488$		0			0
$489$	−19.8828			−0.899130
$490$		0			0
$491$	26.1047			1.17809			0.589045	−	0.808101i	$-0.299504\pi$
$491$	26.1047			1.17809			0.589045	+	0.808101i	$0.299504\pi$
$492$		0			0
$493$	−5.81236	+	10.0673i	−0.261776	+	0.453409i
$494$		0			0
$495$	−7.12537	−	12.3415i	−0.320262	−	0.554710i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	14.3821	+	24.9105i	0.643830	+	1.11515i	0.984570	+	0.174989i	$0.0559889\pi$
$499$	14.3821	+	24.9105i	0.643830	+	1.11515i	−0.340740	+	0.940157i	$0.610678\pi$
$500$		0			0
$501$	4.97336	−	8.61412i	0.222194	−	0.384851i
$502$		0			0
$503$	−15.9492			−0.711138			−0.355569	−	0.934650i	$-0.615713\pi$
$503$	−15.9492			−0.711138			−0.355569	+	0.934650i	$0.615713\pi$
$504$		0			0
$505$	−4.29477			−0.191115
$506$		0			0
$507$	0.529566	−	0.917235i	0.0235188	−	0.0407358i
$508$		0			0
$509$	−4.02583	−	6.97294i	−0.178442	−	0.309070i	0.762905	−	0.646510i	$-0.223772\pi$
$509$	−4.02583	−	6.97294i	−0.178442	−	0.309070i	−0.941347	+	0.337440i	$0.890439\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	4.07631	+	7.06038i	0.179974	+	0.311723i
$514$		0			0
$515$	18.3893	−	31.8512i	0.810329	−	1.40353i
$516$		0			0
$517$	−18.0996			−0.796021
$518$		0			0
$519$	16.2336			0.712574
$520$		0			0
$521$	18.0748	−	31.3065i	0.791873	−	1.37156i	−0.132933	−	0.991125i	$-0.542440\pi$
$521$	18.0748	−	31.3065i	0.791873	−	1.37156i	0.924806	−	0.380439i	$-0.124227\pi$
$522$		0			0
$523$	−20.8748	−	36.1563i	−0.912793	−	1.58100i	−0.810101	−	0.586290i	$-0.800588\pi$
$523$	−20.8748	−	36.1563i	−0.912793	−	1.58100i	−0.102692	−	0.994713i	$-0.532746\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.62420	+	9.74140i	0.244994	+	0.424342i
$528$		0			0
$529$	2.25442	−	3.90477i	0.0980182	−	0.169772i
$530$		0			0
$531$	21.2018			0.920081
$532$		0			0
$533$	−10.6089			−0.459525
$534$		0			0
$535$	−33.9399	+	58.7856i	−1.46735	+	2.54152i
$536$		0			0
$537$	−2.22091	−	3.84673i	−0.0958392	−	0.165998i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	5.32904	+	9.23017i	0.229113	+	0.396836i	0.957546	−	0.288282i	$-0.0930840\pi$
$541$	5.32904	+	9.23017i	0.229113	+	0.396836i	−0.728432	+	0.685118i	$0.759751\pi$
$542$		0			0
$543$	12.1187	−	20.9902i	0.520064	−	0.900778i
$544$		0			0
$545$	−34.5274			−1.47899
$546$		0			0
$547$	−36.4994			−1.56060			−0.780301	−	0.625404i	$-0.784934\pi$
$547$	−36.4994			−1.56060			−0.780301	+	0.625404i	$0.784934\pi$
$548$		0			0
$549$	4.20382	−	7.28123i	0.179415	−	0.310755i
$550$		0			0
$551$	1.85994	+	3.22150i	0.0792359	+	0.137241i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−7.24038	−	12.5407i	−0.307337	−	0.532323i
$556$		0			0
$557$	13.4844	−	23.3556i	0.571352	−	0.989610i	−0.425076	−	0.905158i	$-0.639753\pi$
$557$	13.4844	−	23.3556i	0.571352	−	0.989610i	0.996428	−	0.0844522i	$-0.0269140\pi$
$558$		0			0
$559$	−0.0759434			−0.00321206
$560$		0			0
$561$	−9.68144			−0.408751
$562$		0			0
$563$	3.83407	−	6.64080i	0.161587	−	0.279877i	−0.773851	−	0.633368i	$-0.781672\pi$
$563$	3.83407	−	6.64080i	0.161587	−	0.279877i	0.935438	+	0.353491i	$0.115005\pi$
$564$		0			0
$565$	−1.94792	−	3.37389i	−0.0819495	−	0.141941i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−22.4284	−	38.8472i	−0.940249	−	1.62856i	−0.764996	−	0.644035i	$-0.777259\pi$
$569$	−22.4284	−	38.8472i	−0.940249	−	1.62856i	−0.175253	−	0.984524i	$-0.556074\pi$
$570$		0			0
$571$	−14.3661	+	24.8827i	−0.601201	+	1.04131i	0.391439	+	0.920204i	$0.371977\pi$
$571$	−14.3661	+	24.8827i	−0.601201	+	1.04131i	−0.992640	+	0.121106i	$0.961356\pi$
$572$		0			0
$573$	27.2554			1.13861
$574$		0			0
$575$	50.5359			2.10749
$576$		0			0
$577$	−7.92616	+	13.7285i	−0.329970	+	0.571526i	−0.982506	−	0.186233i	$-0.940372\pi$
$577$	−7.92616	+	13.7285i	−0.329970	+	0.571526i	0.652535	+	0.757758i	$0.273705\pi$
$578$		0			0
$579$	6.13638	+	10.6285i	0.255019	+	0.441706i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.82561	−	3.16204i	−0.0756089	−	0.130958i
$584$		0			0
$585$	−3.84377	+	6.65760i	−0.158920	+	0.275258i
$586$		0			0
$587$	−13.7379			−0.567023			−0.283511	−	0.958969i	$-0.591499\pi$
$587$	−13.7379			−0.567023			−0.283511	+	0.958969i	$0.591499\pi$
$588$		0			0
$589$	3.59945			0.148313
$590$		0			0
$591$	−7.25430	+	12.5648i	−0.298402	+	0.516847i
$592$		0			0
$593$	12.3698	+	21.4252i	0.507969	+	0.879828i	0.999957	+	0.00922599i	$0.00293676\pi$
$593$	12.3698	+	21.4252i	0.507969	+	0.879828i	−0.491989	+	0.870602i	$0.663730\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.95096	−	8.57532i	−0.202629	−	0.350964i
$598$		0			0
$599$	3.79554	−	6.57407i	0.155082	−	0.268609i	−0.778007	−	0.628255i	$-0.783769\pi$
$599$	3.79554	−	6.57407i	0.155082	−	0.268609i	0.933089	+	0.359646i	$0.117103\pi$
$600$		0			0
$601$	13.8456			0.564772			0.282386	−	0.959301i	$-0.408874\pi$
$601$	13.8456			0.564772			0.282386	+	0.959301i	$0.408874\pi$
$602$		0			0
$603$	−18.2702			−0.744021
$604$		0			0
$605$	−15.4787	+	26.8099i	−0.629300	+	1.08998i
$606$		0			0
$607$	−5.17955	−	8.97125i	−0.210232	−	0.364132i	0.741555	−	0.670892i	$-0.234088\pi$
$607$	−5.17955	−	8.97125i	−0.210232	−	0.364132i	−0.951787	+	0.306760i	$0.900755\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	4.88190	+	8.45570i	0.197501	+	0.342081i
$612$		0			0
$613$	−8.69396	+	15.0584i	−0.351146	+	0.608202i	−0.986450	−	0.164059i	$-0.947541\pi$
$613$	−8.69396	+	15.0584i	−0.351146	+	0.608202i	0.635305	+	0.772262i	$0.280875\pi$
$614$		0			0
$615$	−45.9894			−1.85447
$616$		0			0
$617$	−11.9371			−0.480571			−0.240285	−	0.970702i	$-0.577241\pi$
$617$	−11.9371			−0.480571			−0.240285	+	0.970702i	$0.577241\pi$
$618$		0			0
$619$	−6.82038	+	11.8133i	−0.274134	+	0.474815i	−0.969916	−	0.243438i	$-0.921725\pi$
$619$	−6.82038	+	11.8133i	−0.274134	+	0.474815i	0.695782	+	0.718253i	$0.255058\pi$
$620$		0			0
$621$	−11.1087	−	19.2409i	−0.445779	−	0.772111i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−27.1763	−	47.0708i	−1.08705	−	1.88283i
$626$		0			0
$627$	−1.54901	+	2.68297i	−0.0618616	+	0.107147i
$628$		0			0
$629$	16.4720			0.656780
$630$		0			0
$631$	19.7012			0.784293			0.392146	−	0.919903i	$-0.371733\pi$
$631$	19.7012			0.784293			0.392146	+	0.919903i	$0.371733\pi$
$632$		0			0
$633$	−0.906960	+	1.57090i	−0.0360484	+	0.0624377i
$634$		0			0
$635$	−31.9718	−	55.3768i	−1.26876	−	2.19756i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−11.6507	−	20.1796i	−0.460893	−	0.798291i
$640$		0			0
$641$	−5.79181	+	10.0317i	−0.228763	+	0.396229i	−0.957442	−	0.288627i	$-0.906801\pi$
$641$	−5.79181	+	10.0317i	−0.228763	+	0.396229i	0.728679	+	0.684856i	$0.240135\pi$
$642$		0			0
$643$	40.5221			1.59803			0.799017	−	0.601308i	$-0.205354\pi$
$643$	40.5221			1.59803			0.799017	+	0.601308i	$0.205354\pi$
$644$		0			0
$645$	−0.329212			−0.0129627
$646$		0			0
$647$	10.3842	−	17.9859i	0.408244	−	0.707100i	−0.586449	−	0.809986i	$-0.699475\pi$
$647$	10.3842	−	17.9859i	0.408244	−	0.707100i	0.994693	+	0.102887i	$0.0328079\pi$
$648$		0			0
$649$	10.4627	+	18.1219i	0.410696	+	0.711346i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−6.59800	−	11.4281i	−0.258200	−	0.447215i	0.707560	−	0.706653i	$-0.249796\pi$
$653$	−6.59800	−	11.4281i	−0.258200	−	0.447215i	−0.965760	+	0.259438i	$0.916463\pi$
$654$		0			0
$655$	22.4484	−	38.8818i	0.877131	−	1.51924i
$656$		0			0
$657$	20.6106			0.804097
$658$		0			0
$659$	39.0259			1.52023			0.760117	−	0.649787i	$-0.225142\pi$
$659$	39.0259			1.52023			0.760117	+	0.649787i	$0.225142\pi$
$660$		0			0
$661$	15.6248	−	27.0630i	0.607736	−	1.05263i	−0.383877	−	0.923384i	$-0.625411\pi$
$661$	15.6248	−	27.0630i	0.607736	−	1.05263i	0.991613	−	0.129245i	$-0.0412553\pi$
$662$		0			0
$663$	2.61131	+	4.52293i	0.101415	+	0.175656i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.06869	−	8.77923i	−0.196260	−	0.339933i
$668$		0			0
$669$	7.57622	−	13.1224i	0.292914	−	0.507341i
$670$		0			0
$671$	8.29800			0.320341
$672$		0			0
$673$	−10.7294			−0.413589			−0.206795	−	0.978384i	$-0.566303\pi$
$673$	−10.7294			−0.413589			−0.206795	+	0.978384i	$0.566303\pi$
$674$		0			0
$675$	−30.3599	+	52.5850i	−1.16855	+	2.02400i
$676$		0			0
$677$	1.72736	+	2.99188i	0.0663880	+	0.114987i	0.897309	−	0.441403i	$-0.145519\pi$
$677$	1.72736	+	2.99188i	0.0663880	+	0.114987i	−0.830921	+	0.556391i	$0.812186\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	6.03637	+	10.4553i	0.231314	+	0.400648i
$682$		0			0
$683$	21.3342	−	36.9519i	0.816329	−	1.41392i	−0.0920400	−	0.995755i	$-0.529339\pi$
$683$	21.3342	−	36.9519i	0.816329	−	1.41392i	0.908369	−	0.418169i	$-0.137328\pi$
$684$		0			0
$685$	18.0697			0.690409
$686$		0			0
$687$	24.5887			0.938116
$688$		0			0
$689$	−0.984819	+	1.70576i	−0.0375186	+	0.0649841i
$690$		0			0
$691$	−11.2766	−	19.5317i	−0.428983	−	0.743021i	0.567800	−	0.823167i	$-0.307795\pi$
$691$	−11.2766	−	19.5317i	−0.428983	−	0.743021i	−0.996783	+	0.0801457i	$0.974461\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	26.7681	+	46.3636i	1.01537	+	1.75867i
$696$		0			0
$697$	26.1566	−	45.3046i	0.990753	−	1.71603i
$698$		0			0
$699$	29.9234			1.13181
$700$		0			0
$701$	17.6163			0.665358			0.332679	−	0.943040i	$-0.392047\pi$
$701$	17.6163			0.665358			0.332679	+	0.943040i	$0.392047\pi$
$702$		0			0
$703$	2.63548	−	4.56479i	0.0993991	−	0.172164i
$704$		0			0
$705$	21.1629	+	36.6551i	0.797039	+	1.38051i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−3.74412	−	6.48501i	−0.140614	−	0.243550i	0.787114	−	0.616807i	$-0.211574\pi$
$709$	−3.74412	−	6.48501i	−0.140614	−	0.243550i	−0.927728	+	0.373257i	$0.878241\pi$
$710$		0			0
$711$	−5.78000	+	10.0112i	−0.216767	+	0.375451i
$712$		0			0
$713$	−9.80920			−0.367358
$714$		0			0
$715$	−7.58728			−0.283748
$716$		0			0
$717$	14.4436	−	25.0171i	0.539406	−	0.934279i
$718$		0			0
$719$	22.4592	+	38.9005i	0.837588	+	1.45074i	0.891906	+	0.452220i	$0.149368\pi$
$719$	22.4592	+	38.9005i	0.837588	+	1.45074i	−0.0543187	+	0.998524i	$0.517299\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	8.05831	+	13.9574i	0.299692	+	0.519082i
$724$		0			0
$725$	−13.8526	+	23.9934i	−0.514473	+	0.891093i
$726$		0			0
$727$	−30.1822			−1.11939			−0.559697	−	0.828697i	$-0.689083\pi$
$727$	−30.1822			−1.11939			−0.559697	+	0.828697i	$0.689083\pi$
$728$		0			0
$729$	16.1114			0.596718
$730$		0			0
$731$	0.187240	−	0.324310i	0.00692533	−	0.0119950i
$732$		0			0
$733$	23.8346	+	41.2827i	0.880350	+	1.52481i	0.850952	+	0.525243i	$0.176025\pi$
$733$	23.8346	+	41.2827i	0.880350	+	1.52481i	0.0293973	+	0.999568i	$0.490641\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−9.01598	−	15.6161i	−0.332108	−	0.575228i
$738$		0			0
$739$	1.62084	−	2.80737i	0.0596234	−	0.103271i	−0.834673	−	0.550746i	$-0.814343\pi$
$739$	1.62084	−	2.80737i	0.0596234	−	0.103271i	0.894296	+	0.447475i	$0.147677\pi$
$740$		0			0
$741$	1.67122			0.0613939
$742$		0			0
$743$	13.5278			0.496286			0.248143	−	0.968723i	$-0.420180\pi$
$743$	13.5278			0.496286			0.248143	+	0.968723i	$0.420180\pi$
$744$		0			0
$745$	−22.7723	+	39.4427i	−0.834311	+	1.44507i
$746$		0			0
$747$	16.3339	+	28.2911i	0.597626	+	1.03512i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	7.29338	+	12.6325i	0.266139	+	0.460966i	0.967861	−	0.251484i	$-0.0809186\pi$
$751$	7.29338	+	12.6325i	0.266139	+	0.460966i	−0.701722	+	0.712451i	$0.747585\pi$
$752$		0			0
$753$	13.0481	−	22.6001i	0.475501	−	0.823592i
$754$		0			0
$755$	76.3612			2.77907
$756$		0			0
$757$	15.6796			0.569884			0.284942	−	0.958545i	$-0.408026\pi$
$757$	15.6796			0.569884			0.284942	+	0.958545i	$0.408026\pi$
$758$		0			0
$759$	4.22136	−	7.31161i	0.153226	−	0.265395i
$760$		0			0
$761$	−17.5026	−	30.3154i	−0.634468	−	1.09893i	−0.986628	−	0.162991i	$-0.947886\pi$
$761$	−17.5026	−	30.3154i	−0.634468	−	1.09893i	0.352160	−	0.935940i	$-0.385447\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−18.9538	−	32.8289i	−0.685276	−	1.18693i
$766$		0			0
$767$	5.64407	−	9.77581i	0.203795	−	0.352984i
$768$		0			0
$769$	−12.5842			−0.453797			−0.226899	−	0.973918i	$-0.572859\pi$
$769$	−12.5842			−0.453797			−0.226899	+	0.973918i	$0.572859\pi$
$770$		0			0
$771$	27.2059			0.979796
$772$		0			0
$773$	11.7129	−	20.2873i	0.421283	−	0.729683i	−0.574783	−	0.818306i	$-0.694913\pi$
$773$	11.7129	−	20.2873i	0.421283	−	0.729683i	0.996065	+	0.0886233i	$0.0282467\pi$
$774$		0			0
$775$	13.4042	+	23.2167i	0.481492	+	0.833968i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−8.37002	−	14.4973i	−0.299887	−	0.519420i
$780$		0			0
$781$	11.4987	−	19.9164i	0.411457	−	0.712665i
$782$		0			0
$783$	12.1803			0.435287
$784$		0			0
$785$	40.7778			1.45542
$786$		0			0
$787$	−1.11136	+	1.92494i	−0.0396158	+	0.0686166i	−0.885153	−	0.465299i	$-0.845947\pi$
$787$	−1.11136	+	1.92494i	−0.0396158	+	0.0686166i	0.845538	+	0.533916i	$0.179280\pi$
$788$		0			0
$789$	−5.20419	−	9.01392i	−0.185274	−	0.320904i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−2.23817	−	3.87662i	−0.0794797	−	0.137663i
$794$		0			0
$795$	−4.26915	+	7.39439i	−0.151411	+	0.262252i
$796$		0			0
$797$	24.4865			0.867355			0.433678	−	0.901068i	$-0.357216\pi$
$797$	24.4865			0.867355			0.433678	+	0.901068i	$0.357216\pi$
$798$		0			0
$799$	−48.1458			−1.70327
$800$		0			0
$801$	1.18217	−	2.04759i	0.0417701	−	0.0723479i
$802$		0			0
$803$	10.1709	+	17.6166i	0.358924	+	0.621675i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−13.4159	−	23.2371i	−0.472263	−	0.817984i
$808$		0			0
$809$	−14.2010	+	24.5968i	−0.499279	+	0.864777i	−1.00000		0.000831996i	$-0.999735\pi$
$809$	−14.2010	+	24.5968i	−0.499279	+	0.864777i	0.500720	+	0.865609i	$0.333069\pi$
$810$		0			0
$811$	−7.34230			−0.257823			−0.128912	−	0.991656i	$-0.541148\pi$
$811$	−7.34230			−0.257823			−0.128912	+	0.991656i	$0.541148\pi$
$812$		0			0
$813$	6.16928			0.216366
$814$		0			0
$815$	38.4178	−	66.5416i	1.34572	−	2.33085i
$816$		0			0
$817$	−0.0599162	−	0.103778i	−0.00209620	−	0.00363073i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	10.0207	+	17.3564i	0.349726	+	0.605744i	0.986201	−	0.165554i	$-0.0529412\pi$
$821$	10.0207	+	17.3564i	0.349726	+	0.605744i	−0.636474	+	0.771298i	$0.719608\pi$
$822$		0			0
$823$	6.35704	−	11.0107i	0.221593	−	0.383810i	−0.733699	−	0.679474i	$-0.762208\pi$
$823$	6.35704	−	11.0107i	0.221593	−	0.383810i	0.955292	+	0.295665i	$0.0955412\pi$
$824$		0			0
$825$	−23.0738			−0.803325
$826$		0			0
$827$	13.4132			0.466423			0.233212	−	0.972426i	$-0.425076\pi$
$827$	13.4132			0.466423			0.233212	+	0.972426i	$0.425076\pi$
$828$		0			0
$829$	−17.7630	+	30.7665i	−0.616936	+	1.06856i	0.373106	+	0.927789i	$0.378293\pi$
$829$	−17.7630	+	30.7665i	−0.616936	+	1.06856i	−0.990042	+	0.140775i	$0.955041\pi$
$830$		0			0
$831$	−5.24738	−	9.08872i	−0.182029	−	0.315284i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	19.2192	+	33.2887i	0.665109	+	1.15200i
$836$		0			0
$837$	5.89298	−	10.2069i	0.203691	−	0.352803i
$838$		0			0
$839$	43.6914			1.50840			0.754198	−	0.656647i	$-0.228026\pi$
$839$	43.6914			1.50840			0.754198	+	0.656647i	$0.228026\pi$
$840$		0			0
$841$	−23.4424			−0.808359
$842$		0			0
$843$	1.00039	−	1.73272i	0.0344552	−	0.0596781i
$844$		0			0
$845$	2.04647	+	3.54459i	0.0704007	+	0.121938i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−12.8806	−	22.3098i	−0.442061	−	0.765672i
$850$		0			0
$851$	−7.18221	+	12.4400i	−0.246203	+	0.426436i
$852$		0			0
$853$	−19.7458			−0.676082			−0.338041	−	0.941131i	$-0.609764\pi$
$853$	−19.7458			−0.676082			−0.338041	+	0.941131i	$0.609764\pi$
$854$		0			0
$855$	−12.1303			−0.414847
$856$		0			0
$857$	−17.1319	+	29.6732i	−0.585213	+	1.01362i	0.409636	+	0.912249i	$0.365656\pi$
$857$	−17.1319	+	29.6732i	−0.585213	+	1.01362i	−0.994849	+	0.101369i	$0.967678\pi$
$858$		0			0
$859$	0.506046	+	0.876497i	0.0172661	+	0.0299057i	0.874529	−	0.484973i	$-0.161170\pi$
$859$	0.506046	+	0.876497i	0.0172661	+	0.0299057i	−0.857263	+	0.514878i	$0.827837\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−10.2149	−	17.6928i	−0.347720	−	0.602268i	0.638124	−	0.769933i	$-0.279711\pi$
$863$	−10.2149	−	17.6928i	−0.347720	−	0.602268i	−0.985844	+	0.167665i	$0.946377\pi$
$864$		0			0
$865$	−31.3668	+	54.3288i	−1.06650	+	1.84724i
$866$		0			0
$867$	−7.74780			−0.263129
$868$		0			0
$869$	−11.4092			−0.387032
$870$		0			0
$871$	−4.86365	+	8.42409i	−0.164799	+	0.285439i
$872$		0			0
$873$	−6.11804	−	10.5968i	−0.207064	−	0.358646i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−4.53799	−	7.86002i	−0.153237	−	0.265414i	0.779179	−	0.626802i	$-0.215636\pi$
$877$	−4.53799	−	7.86002i	−0.153237	−	0.265414i	−0.932416	+	0.361388i	$0.882303\pi$
$878$		0			0
$879$	−11.7984	+	20.4355i	−0.397951	+	0.689271i
$880$		0			0
$881$	51.7776			1.74443			0.872215	−	0.489122i	$-0.162683\pi$
$881$	51.7776			1.74443			0.872215	+	0.489122i	$0.162683\pi$
$882$		0			0
$883$	−35.7639			−1.20355			−0.601776	−	0.798665i	$-0.705540\pi$
$883$	−35.7639			−1.20355			−0.601776	+	0.798665i	$0.705540\pi$
$884$		0			0
$885$	24.4668	−	42.3778i	0.822443	−	1.42451i
$886$		0			0
$887$	10.1538	+	17.5869i	0.340932	+	0.590512i	0.984606	−	0.174788i	$-0.0559240\pi$
$887$	10.1538	+	17.5869i	0.340932	+	0.590512i	−0.643674	+	0.765300i	$0.722591\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.150629	−	0.260897i	−0.00504627	−	0.00874039i
$892$		0			0
$893$	−7.70324	+	13.3424i	−0.257779	+	0.446486i
$894$		0			0
$895$	17.1651			0.573766
$896$		0			0
$897$	−4.55441			−0.152067
$898$		0			0
$899$	2.68884	−	4.65721i	0.0896779	−	0.155327i
$900$		0			0
$901$	−4.85619	−	8.41117i	−0.161783	−	0.280217i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	46.8320	+	81.1154i	1.55675	+	2.69637i
$906$		0			0
$907$	−23.4334	+	40.5878i	−0.778092	+	1.34770i	0.154948	+	0.987923i	$0.450479\pi$
$907$	−23.4334	+	40.5878i	−0.778092	+	1.34770i	−0.933040	+	0.359773i	$0.882854\pi$
$908$		0			0
$909$	−1.97086			−0.0653693
$910$		0			0
$911$	−8.34268			−0.276405			−0.138203	−	0.990404i	$-0.544133\pi$
$911$	−8.34268			−0.276405			−0.138203	+	0.990404i	$0.544133\pi$
$912$		0			0
$913$	−16.1209	+	27.9222i	−0.533524	+	0.924091i
$914$		0			0
$915$	−9.70238	−	16.8050i	−0.320751	−	0.555557i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−15.1506	−	26.2416i	−0.499772	−	0.865630i	0.500228	−	0.865894i	$-0.333249\pi$
$919$	−15.1506	−	26.2416i	−0.499772	−	0.865630i	−1.00000		0.000263625i	$0.999916\pi$
$920$		0			0
$921$	−14.0337	+	24.3071i	−0.462426	+	0.800945i
$922$		0			0
$923$	−12.4059			−0.408346
$924$		0			0
$925$	39.2576			1.29078
$926$		0			0
$927$	8.43880	−	14.6164i	0.277167	−	0.480067i
$928$		0			0
$929$	−2.42971	−	4.20839i	−0.0797163	−	0.138073i	0.823411	−	0.567445i	$-0.192068\pi$
$929$	−2.42971	−	4.20839i	−0.0797163	−	0.138073i	−0.903128	+	0.429372i	$0.858735\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	8.05480	+	13.9513i	0.263702	+	0.456746i
$934$		0			0
$935$	18.7066	−	32.4008i	0.611772	−	1.05962i
$936$		0			0
$937$	−46.8284			−1.52982			−0.764909	−	0.644139i	$-0.777216\pi$
$937$	−46.8284			−1.52982			−0.764909	+	0.644139i	$0.777216\pi$
$938$		0			0
$939$	−24.5236			−0.800297
$940$		0			0
$941$	−6.23344	+	10.7966i	−0.203204	+	0.351960i	−0.949559	−	0.313588i	$-0.898469\pi$
$941$	−6.23344	+	10.7966i	−0.203204	+	0.351960i	0.746355	+	0.665548i	$0.231802\pi$
$942$		0			0
$943$	22.8100	+	39.5080i	0.742794	+	1.28656i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−28.1950	−	48.8352i	−0.916215	−	1.58693i	−0.805113	−	0.593121i	$-0.797895\pi$
$947$	−28.1950	−	48.8352i	−0.916215	−	1.58693i	−0.111101	−	0.993809i	$-0.535438\pi$
$948$		0			0
$949$	5.48668	−	9.50322i	0.178105	−	0.308487i
$950$		0			0
$951$	19.6548			0.637350
$952$		0			0
$953$	−11.8704			−0.384521			−0.192260	−	0.981344i	$-0.561582\pi$
$953$	−11.8704			−0.384521			−0.192260	+	0.981344i	$0.561582\pi$
$954$		0			0
$955$	−52.6634	+	91.2157i	−1.70415	+	2.95167i
$956$		0			0
$957$	2.31427	+	4.00843i	0.0748097	+	0.129574i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	12.8982	+	22.3403i	0.416071	+	0.720656i
$962$		0			0
$963$	−15.5749	+	26.9766i	−0.501895	+	0.869308i
$964$		0			0
$965$	−47.4273			−1.52674
$966$		0			0
$967$	−56.7542			−1.82509			−0.912546	−	0.408973i	$-0.865887\pi$
$967$	−56.7542			−1.82509			−0.912546	+	0.408973i	$0.865887\pi$
$968$		0			0
$969$	−4.12044	+	7.13681i	−0.132368	+	0.229267i
$970$		0			0
$971$	9.76952	+	16.9213i	0.313519	+	0.543031i	0.979122	−	0.203276i	$-0.0651588\pi$
$971$	9.76952	+	16.9213i	0.313519	+	0.543031i	−0.665603	+	0.746306i	$0.731825\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	6.22354	+	10.7795i	0.199313	+	0.345220i
$976$		0			0
$977$	12.4128	−	21.4996i	0.397121	−	0.687833i	−0.596249	−	0.802800i	$-0.703343\pi$
$977$	12.4128	−	21.4996i	0.397121	−	0.687833i	0.993369	+	0.114967i	$0.0366761\pi$
$978$		0			0
$979$	2.33352			0.0745796
$980$		0			0
$981$	−15.8445			−0.505877
$982$		0			0
$983$	0.608688	−	1.05428i	0.0194141	−	0.0336263i	−0.856155	−	0.516719i	$-0.827153\pi$
$983$	0.608688	−	1.05428i	0.0194141	−	0.0336263i	0.875569	+	0.483093i	$0.160487\pi$
$984$		0			0
$985$	−28.0337	−	48.5559i	−0.893229	−	1.54712i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.163283	+	0.282815i	0.00519211	+	0.00899300i
$990$		0			0
$991$	27.2971	−	47.2799i	0.867120	−	1.50190i	0.00219393	−	0.999998i	$-0.499302\pi$
$991$	27.2971	−	47.2799i	0.867120	−	1.50190i	0.864926	−	0.501899i	$-0.167365\pi$
$992$		0			0
$993$	−24.2314			−0.768961
$994$		0			0
$995$	38.2653			1.21309
$996$		0			0
$997$	−13.7445	+	23.8062i	−0.435294	+	0.753951i	−0.997320	−	0.0731687i	$-0.976689\pi$
$997$	−13.7445	+	23.8062i	−0.435294	+	0.753951i	0.562026	+	0.827120i	$0.310022\pi$
$998$		0			0
$999$	−8.62957	−	14.9468i	−0.273027	−	0.472897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.j.s.1145.4		12
7.2	even	3	inner	2548.2.j.s.1353.4		12
7.3	odd	6		2548.2.a.s.1.4	yes	6
7.4	even	3		2548.2.a.r.1.3	✓	6
7.5	odd	6		2548.2.j.r.1353.3		12
7.6	odd	2		2548.2.j.r.1145.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2548.2.a.r.1.3	✓	6	7.4	even	3
2548.2.a.s.1.4	yes	6	7.3	odd	6
2548.2.j.r.1145.3		12	7.6	odd	2
2548.2.j.r.1353.3		12	7.5	odd	6
2548.2.j.s.1145.4		12	1.1	even	1	trivial
2548.2.j.s.1353.4		12	7.2	even	3	inner

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:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.j (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.529566 - 0.917235i) q^{3} +(2.04647 + 3.54459i) q^{5} +(0.939121 + 1.62660i) q^{9} +(-0.926874 + 1.60539i) q^{11} +1.00000 q^{13} +4.33496 q^{15} +(-2.46552 + 4.27041i) q^{17} +(0.788959 + 1.36652i) q^{19} +(-2.15007 - 3.72403i) q^{23} +(-5.87608 + 10.1777i) q^{25} +5.16670 q^{27} +2.35746 q^{29} +(1.14057 - 1.97552i) q^{31} +(0.981681 + 1.70032i) q^{33} +(-1.67023 - 2.89292i) q^{37} +(0.529566 - 0.917235i) q^{39} -10.6089 q^{41} -0.0759434 q^{43} +(-3.84377 + 6.65760i) q^{45} +(4.88190 + 8.45570i) q^{47} +(2.61131 + 4.52293i) q^{51} +(-0.984819 + 1.70576i) q^{53} -7.58728 q^{55} +1.67122 q^{57} +(5.64407 - 9.77581i) q^{59} +(-2.23817 - 3.87662i) q^{61} +(2.04647 + 3.54459i) q^{65} +(-4.86365 + 8.42409i) q^{67} -4.55441 q^{69} -12.4059 q^{71} +(5.48668 - 9.50322i) q^{73} +(6.22354 + 10.7795i) q^{75} +(3.07735 + 5.33012i) q^{79} +(-0.0812565 + 0.140740i) q^{81} +17.3928 q^{83} -20.1825 q^{85} +(1.24843 - 2.16234i) q^{87} +(-0.629405 - 1.09016i) q^{89} +(-1.20801 - 2.09234i) q^{93} +(-3.22916 + 5.59307i) q^{95} -6.51465 q^{97} -3.48179 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 10 q^{5} - 6 q^{9} + 4 q^{11} + 12 q^{13} + 8 q^{15} + 16 q^{17} + 10 q^{19} + 2 q^{23} - 12 q^{25} + 24 q^{27} + 4 q^{29} + 6 q^{31} + 28 q^{33} - 16 q^{37} - 16 q^{41} + 12 q^{43} + 34 q^{45} + 30 q^{47}+ \cdots - 104 q^{99}+O(q^{100}) \) 12 * q + 10 * q^5 - 6 * q^9 + 4 * q^11 + 12 * q^13 + 8 * q^15 + 16 * q^17 + 10 * q^19 + 2 * q^23 - 12 * q^25 + 24 * q^27 + 4 * q^29 + 6 * q^31 + 28 * q^33 - 16 * q^37 - 16 * q^41 + 12 * q^43 + 34 * q^45 + 30 * q^47 + 12 * q^51 + 6 * q^53 + 32 * q^55 - 24 * q^57 + 8 * q^59 + 16 * q^61 + 10 * q^65 - 8 * q^69 + 14 * q^73 + 28 * q^75 - 14 * q^79 - 14 * q^81 + 28 * q^83 + 48 * q^85 + 24 * q^87 + 30 * q^89 + 16 * q^93 + 10 * q^95 - 44 * q^97 - 104 * q^99

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