LMFDB - Embedded newform 2548.2.j.r.1145.3

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			1145.3
Root			$1.23667 + 2.14198i$ of defining polynomial
Character	$\chi$	$=$	2548.1145
Dual form			2548.2.j.r.1353.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.529566 + 0.917235i) q^{3} +(-2.04647 - 3.54459i) q^{5} +(0.939121 + 1.62660i) q^{9} +(-0.926874 + 1.60539i) q^{11} -1.00000 q^{13} +4.33496 q^{15} +(2.46552 - 4.27041i) q^{17} +(-0.788959 - 1.36652i) q^{19} +(-2.15007 - 3.72403i) q^{23} +(-5.87608 + 10.1777i) q^{25} -5.16670 q^{27} +2.35746 q^{29} +(-1.14057 + 1.97552i) q^{31} +(-0.981681 - 1.70032i) q^{33} +(-1.67023 - 2.89292i) q^{37} +(0.529566 - 0.917235i) q^{39} +10.6089 q^{41} -0.0759434 q^{43} +(3.84377 - 6.65760i) q^{45} +(-4.88190 - 8.45570i) q^{47} +(2.61131 + 4.52293i) q^{51} +(-0.984819 + 1.70576i) q^{53} +7.58728 q^{55} +1.67122 q^{57} +(-5.64407 + 9.77581i) q^{59} +(2.23817 + 3.87662i) q^{61} +(2.04647 + 3.54459i) q^{65} +(-4.86365 + 8.42409i) q^{67} +4.55441 q^{69} -12.4059 q^{71} +(-5.48668 + 9.50322i) q^{73} +(-6.22354 - 10.7795i) q^{75} +(3.07735 + 5.33012i) q^{79} +(-0.0812565 + 0.140740i) q^{81} -17.3928 q^{83} -20.1825 q^{85} +(-1.24843 + 2.16234i) q^{87} +(0.629405 + 1.09016i) q^{89} +(-1.20801 - 2.09234i) q^{93} +(-3.22916 + 5.59307i) q^{95} +6.51465 q^{97} -3.48179 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.977427	−	0.211274i	$-0.932239\pi$
$3$	−0.529566	+	0.917235i	−0.305745	+	0.529566i	0.671682	+	0.740840i	$0.265572\pi$
$4$		0			0
$5$	−2.04647	−	3.54459i	−0.915210	−	1.58519i	−0.806594	−	0.591105i	$-0.798692\pi$
$5$	−2.04647	−	3.54459i	−0.915210	−	1.58519i	−0.108615	−	0.994084i	$-0.534642\pi$
$6$		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	$-0.629305\pi$
$17$	2.46552	−	4.27041i	0.597977	−	1.03573i	0.993119	−	0.117107i	$-0.0373621\pi$
$18$		0			0
$19$	−0.788959	−	1.36652i	−0.181000	−	0.313500i	0.761222	−	0.648492i	$-0.224600\pi$
$19$	−0.788959	−	1.36652i	−0.181000	−	0.313500i	−0.942221	+	0.334991i	$0.891267\pi$
$20$		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	−0.950086	−	0.311989i	$-0.899005\pi$
$31$	−1.14057	+	1.97552i	−0.204852	+	0.354815i	0.745233	+	0.666804i	$0.232338\pi$
$32$		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	$-0.189240\pi$
$41$	10.6089			1.65684			0.828420	+	0.560108i	$0.189240\pi$
$42$		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	$-0.914412\pi$
$47$	−4.88190	−	8.45570i	−0.712098	−	1.23339i	0.251970	−	0.967735i	$-0.418922\pi$
$48$		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	$0.429388\pi$
$59$	−5.64407	+	9.77581i	−0.734795	+	1.27270i	−0.954813	+	0.297206i	$0.903945\pi$
$60$		0			0
$61$	2.23817	+	3.87662i	0.286568	+	0.496351i	0.972988	−	0.230855i	$-0.0741522\pi$
$61$	2.23817	+	3.87662i	0.286568	+	0.496351i	−0.686420	+	0.727205i	$0.740819\pi$
$62$		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	$0.388631\pi$
$73$	−5.48668	+	9.50322i	−0.642168	+	1.11227i	−0.984948	+	0.172852i	$0.944702\pi$
$74$		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	$-0.903665\pi$
$83$	−17.3928			−1.90910			−0.954552	+	0.298045i	$0.903665\pi$
$84$		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	0.897454	−	0.441108i	$-0.145414\pi$
$89$	0.629405	+	1.09016i	0.0667168	+	0.115557i	−0.830737	+	0.556664i	$0.812081\pi$
$90$		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	$-0.392705\pi$
$97$	6.51465			0.661462			0.330731	+	0.943725i	$0.392705\pi$
$98$		0			0
$99$	−3.48179			−0.349933
$100$		0			0
$101$	0.524655	−	0.908730i	0.0522052	−	0.0904220i	−0.838742	−	0.544529i	$-0.816708\pi$
$101$	0.524655	−	0.908730i	0.0522052	−	0.0904220i	0.890947	+	0.454107i	$0.150042\pi$
$102$		0			0
$103$	4.49293	+	7.78198i	0.442701	+	0.766781i	0.997889	−	0.0649440i	$-0.0206869\pi$
$103$	4.49293	+	7.78198i	0.442701	+	0.766781i	−0.555188	+	0.831725i	$0.687354\pi$
$104$		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	0.999715	−	0.0238568i	$-0.00759458\pi$
$131$	5.48466	+	9.49971i	0.479197	+	0.829994i	−0.520518	+	0.853851i	$0.674261\pi$
$132$		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	$-0.687175\pi$
$139$	−13.0801			−1.10944			−0.554720	+	0.832037i	$0.687175\pi$
$140$		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	−0.993425	−	0.114486i	$-0.963478\pi$
$157$	−4.98148	+	8.62817i	−0.397565	+	0.688603i	0.595860	+	0.803088i	$0.296811\pi$
$158$		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	$-0.618372\pi$
$167$	−9.39140			−0.726729			−0.363364	+	0.931647i	$0.618372\pi$
$168$		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	$-0.968681\pi$
$173$	−7.66362	−	13.2738i	−0.582655	−	1.00919i	0.412509	−	0.910954i	$-0.364653\pi$
$174$		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	$-0.823693\pi$
$181$	−22.8843			−1.70097			−0.850487	+	0.525995i	$0.823693\pi$
$182$		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	−0.982781	−	0.184775i	$-0.940844\pi$
$199$	−4.67455	+	8.09656i	−0.331370	+	0.573950i	0.651411	+	0.758725i	$0.274178\pi$
$200$		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	$-0.659007\pi$
$223$	−14.3065			−0.958033			−0.479017	+	0.877806i	$0.659007\pi$
$224$		0			0
$225$	−22.0734			−1.47156
$226$		0			0
$227$	5.69936	−	9.87158i	0.378280	−	0.655200i	−0.612532	−	0.790446i	$-0.709849\pi$
$227$	5.69936	−	9.87158i	0.378280	−	0.655200i	0.990812	+	0.135246i	$0.0431824\pi$
$228$		0			0
$229$	−11.6079	−	20.1055i	−0.767074	−	1.32861i	−0.939143	−	0.343527i	$-0.888378\pi$
$229$	−11.6079	−	20.1055i	−0.767074	−	1.32861i	0.172069	−	0.985085i	$-0.444955\pi$
$230$		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	−0.509834	−	0.860273i	$-0.670293\pi$
$241$	7.60842	−	13.1782i	0.490101	−	0.848880i	0.999935	+	0.0113926i	$0.00362645\pi$
$242$		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	$-0.783568\pi$
$251$	−24.6393			−1.55522			−0.777611	+	0.628746i	$0.783568\pi$
$252$		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	$-0.870886\pi$
$257$	−12.8435	−	22.2456i	−0.801155	−	1.38764i	0.117702	−	0.993049i	$-0.462447\pi$
$258$		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	$0.447568\pi$
$269$	−12.6669	+	21.9398i	−0.772316	+	1.33769i	−0.936291	+	0.351226i	$0.885765\pi$
$270$		0			0
$271$	−2.91243	−	5.04447i	−0.176917	−	0.306430i	0.763906	−	0.645328i	$-0.223279\pi$
$271$	−2.91243	−	5.04447i	−0.176917	−	0.306430i	−0.940823	+	0.338898i	$0.889946\pi$
$272$		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	$0.423869\pi$
$283$	−12.1615	+	21.0643i	−0.722924	+	1.25214i	−0.959823	+	0.280607i	$0.909464\pi$
$284$		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	$-0.274438\pi$
$293$	22.2794			1.30158			0.650789	+	0.759258i	$0.274438\pi$
$294$		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	$-0.227040\pi$
$307$	26.5004			1.51246			0.756228	+	0.654308i	$0.227040\pi$
$308$		0			0
$309$	−9.51720			−0.541415
$310$		0			0
$311$	7.60511	−	13.1724i	0.431246	−	0.746940i	−0.565735	−	0.824587i	$-0.691407\pi$
$311$	7.60511	−	13.1724i	0.431246	−	0.746940i	0.996981	+	0.0776473i	$0.0247408\pi$
$312$		0			0
$313$	11.5772	+	20.0523i	0.654383	+	1.13342i	0.982048	+	0.188630i	$0.0604048\pi$
$313$	11.5772	+	20.0523i	0.654383	+	1.13342i	−0.327665	+	0.944794i	$0.606262\pi$
$314$		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	$-0.597416\pi$
$349$	−11.2570			−0.602575			−0.301287	+	0.953533i	$0.597416\pi$
$350$		0			0
$351$	5.16670			0.275778
$352$		0			0
$353$	−6.62507	+	11.4750i	−0.352617	+	0.610750i	−0.986707	−	0.162509i	$-0.948041\pi$
$353$	−6.62507	+	11.4750i	−0.352617	+	0.610750i	0.634090	+	0.773259i	$0.281375\pi$
$354$		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	−0.701607	−	0.712564i	$-0.747534\pi$
$367$	5.10148	−	8.83602i	0.266295	−	0.461237i	0.967902	+	0.251328i	$0.0808671\pi$
$368$		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	0.944239	−	0.329262i	$-0.106800\pi$
$383$	3.65908	+	6.33771i	0.186970	+	0.323842i	−0.757269	+	0.653104i	$0.773467\pi$
$384$		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	0.512987	−	0.858396i	$-0.328539\pi$
$397$	−9.70140	−	16.8033i	−0.486899	−	0.843334i	−0.999887	+	0.0150620i	$0.995205\pi$
$398$		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	−0.861307	−	0.508086i	$-0.830353\pi$
$409$	0.189328	−	0.327925i	0.00936166	−	0.0162149i	0.870668	+	0.491871i	$0.163687\pi$
$410$		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	$-0.396487\pi$
$419$	13.0797			0.638986			0.319493	+	0.947589i	$0.396487\pi$
$420$		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	$-0.684630\pi$
$433$	−22.8084			−1.09610			−0.548051	+	0.836445i	$0.684630\pi$
$434$		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	$0.0129870\pi$
$439$	11.2076	+	19.4121i	0.534908	+	0.926488i	−0.464260	+	0.885699i	$0.653680\pi$
$440$		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	$-0.341524\pi$
$461$	20.5070			0.955106			0.477553	+	0.878603i	$0.341524\pi$
$462$		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	0.883156	−	0.469080i	$-0.155414\pi$
$467$	0.763766	+	1.32288i	0.0353429	+	0.0612157i	−0.847813	+	0.530295i	$0.822081\pi$
$468$		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	−0.994265	−	0.106947i	$-0.965893\pi$
$479$	−8.85321	+	15.3342i	−0.404514	+	0.700638i	0.589751	+	0.807585i	$0.299226\pi$
$480$		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	$-0.384287\pi$
$503$	15.9492			0.711138			0.355569	+	0.934650i	$0.384287\pi$
$504$		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	0.941347	−	0.337440i	$-0.109561\pi$
$509$	4.02583	+	6.97294i	0.178442	+	0.309070i	−0.762905	+	0.646510i	$0.776228\pi$
$510$		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	$0.457560\pi$
$521$	−18.0748	+	31.3065i	−0.791873	+	1.37156i	−0.924806	+	0.380439i	$0.875773\pi$
$522$		0			0
$523$	20.8748	+	36.1563i	0.912793	+	1.58100i	0.810101	+	0.586290i	$0.199412\pi$
$523$	20.8748	+	36.1563i	0.912793	+	1.58100i	0.102692	+	0.994713i	$0.467254\pi$
$524$		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	−0.935438	−	0.353491i	$-0.884995\pi$
$563$	−3.83407	+	6.64080i	−0.161587	+	0.279877i	0.773851	+	0.633368i	$0.218328\pi$
$564$		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	−0.652535	−	0.757758i	$-0.726295\pi$
$577$	7.92616	−	13.7285i	0.329970	−	0.571526i	0.982506	+	0.186233i	$0.0596279\pi$
$578$		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	$-0.408501\pi$
$587$	13.7379			0.567023			0.283511	+	0.958969i	$0.408501\pi$
$588$		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	$-0.997063\pi$
$593$	−12.3698	−	21.4252i	−0.507969	−	0.879828i	0.491989	−	0.870602i	$-0.336270\pi$
$594$		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	$-0.591126\pi$
$601$	−13.8456			−0.564772			−0.282386	+	0.959301i	$0.591126\pi$
$602$		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	0.951787	−	0.306760i	$-0.0992449\pi$
$607$	5.17955	+	8.97125i	0.210232	+	0.364132i	−0.741555	+	0.670892i	$0.765912\pi$
$608$		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	−0.695782	−	0.718253i	$-0.744942\pi$
$619$	6.82038	−	11.8133i	0.274134	−	0.474815i	0.969916	+	0.243438i	$0.0782754\pi$
$620$		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	$-0.794646\pi$
$643$	−40.5221			−1.59803			−0.799017	+	0.601308i	$0.794646\pi$
$644$		0			0
$645$	−0.329212			−0.0129627
$646$		0			0
$647$	−10.3842	+	17.9859i	−0.408244	+	0.707100i	−0.994693	−	0.102887i	$-0.967192\pi$
$647$	−10.3842	+	17.9859i	−0.408244	+	0.707100i	0.586449	+	0.809986i	$0.300525\pi$
$648$		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	$0.374589\pi$
$661$	−15.6248	+	27.0630i	−0.607736	+	1.05263i	−0.991613	+	0.129245i	$0.958745\pi$
$662$		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	0.830921	−	0.556391i	$-0.187814\pi$
$677$	−1.72736	−	2.99188i	−0.0663880	−	0.114987i	−0.897309	+	0.441403i	$0.854481\pi$
$678$		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	0.996783	−	0.0801457i	$-0.0255386\pi$
$691$	11.2766	+	19.5317i	0.428983	+	0.743021i	−0.567800	+	0.823167i	$0.692205\pi$
$692$		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	$-0.850632\pi$
$719$	−22.4592	−	38.9005i	−0.837588	−	1.45074i	0.0543187	−	0.998524i	$-0.482701\pi$
$720$		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	$-0.310917\pi$
$727$	30.1822			1.11939			0.559697	+	0.828697i	$0.310917\pi$
$728$		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	$-0.823975\pi$
$733$	−23.8346	−	41.2827i	−0.880350	−	1.52481i	−0.0293973	−	0.999568i	$-0.509359\pi$
$734$		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	$0.0521141\pi$
$761$	17.5026	+	30.3154i	0.634468	+	1.09893i	−0.352160	+	0.935940i	$0.614553\pi$
$762$		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	$-0.427141\pi$
$769$	12.5842			0.453797			0.226899	+	0.973918i	$0.427141\pi$
$770$		0			0
$771$	27.2059			0.979796
$772$		0			0
$773$	−11.7129	+	20.2873i	−0.421283	+	0.729683i	−0.996065	−	0.0886233i	$-0.971753\pi$
$773$	−11.7129	+	20.2873i	−0.421283	+	0.729683i	0.574783	+	0.818306i	$0.305087\pi$
$774$		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	−0.845538	−	0.533916i	$-0.820720\pi$
$787$	1.11136	−	1.92494i	0.0396158	−	0.0686166i	0.885153	+	0.465299i	$0.154053\pi$
$788$		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	$-0.642784\pi$
$797$	−24.4865			−0.867355			−0.433678	+	0.901068i	$0.642784\pi$
$798$		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	$-0.458852\pi$
$811$	7.34230			0.257823			0.128912	+	0.991656i	$0.458852\pi$
$812$		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	$-0.621707\pi$
$829$	17.7630	−	30.7665i	0.616936	−	1.06856i	0.990042	−	0.140775i	$-0.0449595\pi$
$830$		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	$-0.771974\pi$
$839$	−43.6914			−1.50840			−0.754198	+	0.656647i	$0.771974\pi$
$840$		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	$-0.390236\pi$
$853$	19.7458			0.676082			0.338041	+	0.941131i	$0.390236\pi$
$854$		0			0
$855$	−12.1303			−0.414847
$856$		0			0
$857$	17.1319	−	29.6732i	0.585213	−	1.01362i	−0.409636	−	0.912249i	$-0.634344\pi$
$857$	17.1319	−	29.6732i	0.585213	−	1.01362i	0.994849	−	0.101369i	$-0.0323224\pi$
$858$		0			0
$859$	−0.506046	−	0.876497i	−0.0172661	−	0.0299057i	0.857263	−	0.514878i	$-0.172163\pi$
$859$	−0.506046	−	0.876497i	−0.0172661	−	0.0299057i	−0.874529	+	0.484973i	$0.838830\pi$
$860$		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	$-0.837317\pi$
$881$	−51.7776			−1.74443			−0.872215	+	0.489122i	$0.837317\pi$
$882$		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	0.643674	−	0.765300i	$-0.277409\pi$
$887$	−10.1538	−	17.5869i	−0.340932	−	0.590512i	−0.984606	+	0.174788i	$0.944076\pi$
$888$		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	0.903128	−	0.429372i	$-0.141265\pi$
$929$	2.42971	+	4.20839i	0.0797163	+	0.138073i	−0.823411	+	0.567445i	$0.807932\pi$
$930$		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	$-0.222784\pi$
$937$	46.8284			1.52982			0.764909	+	0.644139i	$0.222784\pi$
$938$		0			0
$939$	−24.5236			−0.800297
$940$		0			0
$941$	6.23344	−	10.7966i	0.203204	−	0.351960i	−0.746355	−	0.665548i	$-0.768198\pi$
$941$	6.23344	−	10.7966i	0.203204	−	0.351960i	0.949559	+	0.313588i	$0.101531\pi$
$942$		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	0.665603	−	0.746306i	$-0.268175\pi$
$971$	−9.76952	−	16.9213i	−0.313519	−	0.543031i	−0.979122	+	0.203276i	$0.934841\pi$
$972$		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	−0.875569	−	0.483093i	$-0.839513\pi$
$983$	−0.608688	+	1.05428i	−0.0194141	+	0.0336263i	0.856155	+	0.516719i	$0.172847\pi$
$984$		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	−0.562026	−	0.827120i	$-0.689978\pi$
$997$	13.7445	−	23.8062i	0.435294	−	0.753951i	0.997320	+	0.0731687i	$0.0233111\pi$
$998$		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.r.1145.3		12
7.2	even	3	inner	2548.2.j.r.1353.3		12
7.3	odd	6		2548.2.a.r.1.3	✓	6
7.4	even	3		2548.2.a.s.1.4	yes	6
7.5	odd	6		2548.2.j.s.1353.4		12
7.6	odd	2		2548.2.j.s.1145.4		12

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
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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