LMFDB - Embedded newform 324.10.e.e.217.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,10,Mod(109,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("324.109");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	324.e (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:	$166.871610917$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 4)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			217.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	324.217
Dual form			324.10.e.e.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(333.000 + 576.773i) q^{5} +(3164.00 - 5480.21i) q^{7} +O(q^{10})$	$q+(333.000 + 576.773i) q^{5} +(3164.00 - 5480.21i) q^{7} +(15210.0 - 26344.5i) q^{11} +(16169.0 + 28005.5i) q^{13} +590994. q^{17} +34676.0 q^{19} +(-524268. - 908059. i) q^{23} +(754784. - 1.30733e6i) q^{25} +(-2.20470e6 + 3.81866e6i) q^{29} +(3.70059e6 + 6.40961e6i) q^{31} +4.21445e6 q^{35} +1.02345e7 q^{37} +(-9.17637e6 - 1.58939e7i) q^{41} +(126170. - 218533. i) q^{43} +(2.47586e7 - 4.28831e7i) q^{47} +(155012. + 268488. i) q^{49} -6.63969e7 q^{53} +2.02597e7 q^{55} +(3.07619e7 + 5.32811e7i) q^{59} +(-1.78193e7 + 3.08640e7i) q^{61} +(-1.07686e7 + 1.86517e7i) q^{65} +(-9.08712e7 - 1.57394e8i) q^{67} +9.09050e7 q^{71} -2.62979e8 q^{73} +(-9.62489e7 - 1.66708e8i) q^{77} +(5.82514e7 - 1.00894e8i) q^{79} +(4.78186e6 - 8.28243e6i) q^{83} +(1.96801e8 + 3.40869e8i) q^{85} +6.11827e8 q^{89} +2.04635e8 q^{91} +(1.15471e7 + 2.00002e7i) q^{95} +(1.29656e8 - 2.24571e8i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 666 q^{5} + 6328 q^{7}+O(q^{10}) $ 2 * q + 666 * q^5 + 6328 * q^7	$ 2 q + 666 q^{5} + 6328 q^{7} + 30420 q^{11} + 32338 q^{13} + 1181988 q^{17} + 69352 q^{19} - 1048536 q^{23} + 1509569 q^{25} - 4409406 q^{29} + 7401184 q^{31} + 8428896 q^{35} + 20469004 q^{37} - 18352746 q^{41} + 252340 q^{43} + 49517136 q^{47} + 310023 q^{49} - 132793812 q^{53} + 40519440 q^{55} + 61523748 q^{59} - 35638622 q^{61} - 21537108 q^{65} - 181742372 q^{67} + 181809936 q^{71} - 525957356 q^{73} - 192497760 q^{77} + 116502832 q^{79} + 9563724 q^{83} + 393602004 q^{85} + 1223653428 q^{89} + 409269728 q^{91} + 23094216 q^{95} + 259312798 q^{97}+O(q^{100}) $ 2 * q + 666 * q^5 + 6328 * q^7 + 30420 * q^11 + 32338 * q^13 + 1181988 * q^17 + 69352 * q^19 - 1048536 * q^23 + 1509569 * q^25 - 4409406 * q^29 + 7401184 * q^31 + 8428896 * q^35 + 20469004 * q^37 - 18352746 * q^41 + 252340 * q^43 + 49517136 * q^47 + 310023 * q^49 - 132793812 * q^53 + 40519440 * q^55 + 61523748 * q^59 - 35638622 * q^61 - 21537108 * q^65 - 181742372 * q^67 + 181809936 * q^71 - 525957356 * q^73 - 192497760 * q^77 + 116502832 * q^79 + 9563724 * q^83 + 393602004 * q^85 + 1223653428 * q^89 + 409269728 * q^91 + 23094216 * q^95 + 259312798 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	333.000	+	576.773i	0.238275	+	0.412705i	0.960220	−	0.279246i	$-0.0900846\pi$
$5$	333.000	+	576.773i	0.238275	+	0.412705i	−0.721944	+	0.691951i	$0.756751\pi$
$6$		0			0
$7$	3164.00	−	5480.21i	0.498076	−	0.862692i	−0.501922	−	0.864913i	$-0.667374\pi$
$7$	3164.00	−	5480.21i	0.498076	−	0.862692i	0.999998	+	0.00222065i	$0.000706854\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	15210.0	−	26344.5i	0.313229	−	0.542529i	−0.665830	−	0.746103i	$-0.731923\pi$
$11$	15210.0	−	26344.5i	0.313229	−	0.542529i	0.979059	+	0.203574i	$0.0652559\pi$
$12$		0			0
$13$	16169.0	+	28005.5i	0.157014	+	0.271956i	0.933791	−	0.357820i	$-0.116480\pi$
$13$	16169.0	+	28005.5i	0.157014	+	0.271956i	−0.776777	+	0.629776i	$0.783147\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	590994.			1.71618			0.858090	−	0.513499i	$-0.171651\pi$
$17$	590994.			1.71618			0.858090	+	0.513499i	$0.171651\pi$
$18$		0			0
$19$	34676.0			0.0610433			0.0305216	−	0.999534i	$-0.490283\pi$
$19$	34676.0			0.0610433			0.0305216	+	0.999534i	$0.490283\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−524268.	−	908059.i	−0.390641	−	0.676610i	0.601893	−	0.798577i	$-0.294413\pi$
$23$	−524268.	−	908059.i	−0.390641	−	0.676610i	−0.992534	+	0.121966i	$0.961080\pi$
$24$		0			0
$25$	754784.	−	1.30733e6i	0.386450	−	0.669350i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.20470e6	+	3.81866e6i	−0.578841	+	1.00258i	0.416772	+	0.909011i	$0.363161\pi$
$29$	−2.20470e6	+	3.81866e6i	−0.578841	+	1.00258i	−0.995613	+	0.0935705i	$0.970172\pi$
$30$		0			0
$31$	3.70059e6	+	6.40961e6i	0.719687	+	1.24653i	0.961124	+	0.276118i	$0.0890480\pi$
$31$	3.70059e6	+	6.40961e6i	0.719687	+	1.24653i	−0.241437	+	0.970417i	$0.577619\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.21445e6			0.474717
$36$		0			0
$37$	1.02345e7			0.897757			0.448879	−	0.893593i	$-0.351824\pi$
$37$	1.02345e7			0.897757			0.448879	+	0.893593i	$0.351824\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−9.17637e6	−	1.58939e7i	−0.507158	−	0.878424i	−0.999966	−	0.00828574i	$-0.997363\pi$
$41$	−9.17637e6	−	1.58939e7i	−0.507158	−	0.878424i	0.492807	−	0.870139i	$-0.335971\pi$
$42$		0			0
$43$	126170.	−	218533.i	0.00562792	−	0.00974785i	−0.863198	−	0.504866i	$-0.831542\pi$
$43$	126170.	−	218533.i	0.00562792	−	0.00974785i	0.868826	+	0.495118i	$0.164875\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.47586e7	−	4.28831e7i	0.740091	−	1.28188i	−0.212362	−	0.977191i	$-0.568116\pi$
$47$	2.47586e7	−	4.28831e7i	0.740091	−	1.28188i	0.952453	−	0.304684i	$-0.0985510\pi$
$48$		0			0
$49$	155012.	+	268488.i	0.00384133	+	0.00665338i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.63969e7			−1.15586			−0.577932	−	0.816085i	$-0.696140\pi$
$53$	−6.63969e7			−1.15586			−0.577932	+	0.816085i	$0.696140\pi$
$54$		0			0
$55$	2.02597e7			0.298539
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.07619e7	+	5.32811e7i	0.330506	+	0.572452i	0.982611	−	0.185676i	$-0.0594474\pi$
$59$	3.07619e7	+	5.32811e7i	0.330506	+	0.572452i	−0.652106	+	0.758128i	$0.726114\pi$
$60$		0			0
$61$	−1.78193e7	+	3.08640e7i	−0.164781	+	0.285409i	−0.936577	−	0.350461i	$-0.886025\pi$
$61$	−1.78193e7	+	3.08640e7i	−0.164781	+	0.285409i	0.771797	+	0.635869i	$0.219358\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.07686e7	+	1.86517e7i	−0.0748251	+	0.129601i
$66$		0			0
$67$	−9.08712e7	−	1.57394e8i	−0.550921	−	0.954224i	−0.998208	−	0.0598333i	$-0.980943\pi$
$67$	−9.08712e7	−	1.57394e8i	−0.550921	−	0.954224i	0.447287	−	0.894390i	$-0.352390\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	9.09050e7			0.424546			0.212273	−	0.977210i	$-0.431913\pi$
$71$	9.09050e7			0.424546			0.212273	+	0.977210i	$0.431913\pi$
$72$		0			0
$73$	−2.62979e8			−1.08385			−0.541923	−	0.840428i	$-0.682304\pi$
$73$	−2.62979e8			−1.08385			−0.541923	+	0.840428i	$0.682304\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−9.62489e7	−	1.66708e8i	−0.312024	−	0.540441i
$78$		0			0
$79$	5.82514e7	−	1.00894e8i	0.168261	−	0.291437i	−0.769547	−	0.638590i	$-0.779518\pi$
$79$	5.82514e7	−	1.00894e8i	0.168261	−	0.291437i	0.937809	+	0.347153i	$0.112851\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.78186e6	−	8.28243e6i	0.0110598	−	0.0191561i	−0.860443	−	0.509547i	$-0.829813\pi$
$83$	4.78186e6	−	8.28243e6i	0.0110598	−	0.0191561i	0.871502	+	0.490391i	$0.163146\pi$
$84$		0			0
$85$	1.96801e8	+	3.40869e8i	0.408924	+	0.708276i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.11827e8			1.03365			0.516825	−	0.856091i	$-0.327114\pi$
$89$	6.11827e8			1.03365			0.516825	+	0.856091i	$0.327114\pi$
$90$		0			0
$91$	2.04635e8			0.312819
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.15471e7	+	2.00002e7i	0.0145451	+	0.0251929i
$96$		0			0
$97$	1.29656e8	−	2.24571e8i	0.148703	−	0.257562i	−0.782045	−	0.623222i	$-0.785823\pi$
$97$	1.29656e8	−	2.24571e8i	0.148703	−	0.257562i	0.930749	+	0.365660i	$0.119157\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.82775e8	+	1.35581e9i	−0.748498	+	1.29644i	0.200044	+	0.979787i	$0.435891\pi$
$101$	−7.82775e8	+	1.35581e9i	−0.748498	+	1.29644i	−0.948542	+	0.316650i	$0.897442\pi$
$102$		0			0
$103$	−1.88547e8	−	3.26574e8i	−0.165064	−	0.285900i	0.771614	−	0.636091i	$-0.219450\pi$
$103$	−1.88547e8	−	3.26574e8i	−0.165064	−	0.285900i	−0.936678	+	0.350192i	$0.886116\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.17717e9			−1.60570			−0.802852	−	0.596178i	$-0.796685\pi$
$107$	−2.17717e9			−1.60570			−0.802852	+	0.596178i	$0.796685\pi$
$108$		0			0
$109$	1.50811e9			1.02333			0.511664	−	0.859185i	$-0.329029\pi$
$109$	1.50811e9			1.02333			0.511664	+	0.859185i	$0.329029\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.26773e8	+	1.25881e9i	0.419320	+	0.726284i	0.995871	−	0.0907774i	$-0.0289352\pi$
$113$	7.26773e8	+	1.25881e9i	0.419320	+	0.726284i	−0.576551	+	0.817061i	$0.695602\pi$
$114$		0			0
$115$	3.49162e8	−	6.04767e8i	0.186160	−	0.322439i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.86991e9	−	3.23877e9i	0.854788	−	1.48054i
$120$		0			0
$121$	7.16286e8	+	1.24064e9i	0.303775	+	0.526154i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	2.30615e9			0.844877
$126$		0			0
$127$	2.43679e9			0.831193			0.415597	−	0.909549i	$-0.363573\pi$
$127$	2.43679e9			0.831193			0.415597	+	0.909549i	$0.363573\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.16789e8	+	1.24152e9i	0.212653	+	0.368325i	0.952544	−	0.304401i	$-0.0984564\pi$
$131$	7.16789e8	+	1.24152e9i	0.212653	+	0.368325i	−0.739891	+	0.672726i	$0.765123\pi$
$132$		0			0
$133$	1.09715e8	−	1.90032e8i	0.0304042	−	0.0526616i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.65452e8	+	8.06186e8i	−0.112884	+	0.195521i	−0.916932	−	0.399044i	$-0.869342\pi$
$137$	−4.65452e8	+	8.06186e8i	−0.112884	+	0.195521i	0.804048	+	0.594564i	$0.202675\pi$
$138$		0			0
$139$	−2.42158e9	−	4.19430e9i	−0.550215	−	0.953000i	−0.998259	−	0.0589882i	$-0.981213\pi$
$139$	−2.42158e9	−	4.19430e9i	−0.550215	−	0.953000i	0.448044	−	0.894011i	$-0.352121\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.83722e8			0.196725
$144$		0			0
$145$	−2.93666e9			−0.551694
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.26635e9	−	7.38953e9i	−0.709117	−	1.22823i	−0.965185	−	0.261568i	$-0.915760\pi$
$149$	−4.26635e9	−	7.38953e9i	−0.709117	−	1.22823i	0.256068	−	0.966659i	$-0.417573\pi$
$150$		0			0
$151$	3.57258e9	−	6.18788e9i	0.559223	−	0.968603i	−0.438338	−	0.898810i	$-0.644433\pi$
$151$	3.57258e9	−	6.18788e9i	0.559223	−	0.968603i	0.997562	−	0.0697929i	$-0.0222339\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.46459e9	+	4.26880e9i	−0.342967	+	0.594037i
$156$		0			0
$157$	1.69119e9	+	2.92923e9i	0.222149	+	0.384774i	0.955460	−	0.295119i	$-0.0953594\pi$
$157$	1.69119e9	+	2.92923e9i	0.222149	+	0.384774i	−0.733311	+	0.679893i	$0.762026\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−6.63514e9			−0.778276
$162$		0			0
$163$	−9.01515e8			−0.100030			−0.0500148	−	0.998748i	$-0.515927\pi$
$163$	−9.01515e8			−0.100030			−0.0500148	+	0.998748i	$0.515927\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.02803e9	−	3.51264e9i	−0.201767	−	0.349470i	0.747331	−	0.664452i	$-0.231335\pi$
$167$	−2.02803e9	−	3.51264e9i	−0.201767	−	0.349470i	−0.949098	+	0.314982i	$0.898002\pi$
$168$		0			0
$169$	4.77938e9	−	8.27812e9i	0.450693	−	0.780624i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.13801e8	−	8.89929e8i	0.0436101	−	0.0755349i	−0.843396	−	0.537292i	$-0.819447\pi$
$173$	5.13801e8	−	8.89929e8i	0.0436101	−	0.0755349i	0.887007	+	0.461757i	$0.152781\pi$
$174$		0			0
$175$	−4.77628e9	−	8.27275e9i	−0.384962	−	0.666774i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.48472e10			1.08095			0.540476	−	0.841360i	$-0.318244\pi$
$179$	1.48472e10			1.08095			0.540476	+	0.841360i	$0.318244\pi$
$180$		0			0
$181$	2.53270e10			1.75400			0.877001	−	0.480488i	$-0.159541\pi$
$181$	2.53270e10			1.75400			0.877001	+	0.480488i	$0.159541\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.40809e9	+	5.90298e9i	0.213913	+	0.370509i
$186$		0			0
$187$	8.98902e9	−	1.55694e10i	0.537558	−	0.931077i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.08280e9	−	1.39998e10i	0.439452	−	0.761154i	−0.558195	−	0.829710i	$-0.688506\pi$
$191$	8.08280e9	−	1.39998e10i	0.439452	−	0.761154i	0.997647	+	0.0685562i	$0.0218392\pi$
$192$		0			0
$193$	9.00943e8	+	1.56048e9i	0.0467401	+	0.0809562i	0.888449	−	0.458975i	$-0.151783\pi$
$193$	9.00943e8	+	1.56048e9i	0.0467401	+	0.0809562i	−0.841709	+	0.539932i	$0.818450\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.86979e10			−0.884495			−0.442247	−	0.896893i	$-0.645819\pi$
$197$	−1.86979e10			−0.884495			−0.442247	+	0.896893i	$0.645819\pi$
$198$		0			0
$199$	2.89890e10			1.31037			0.655186	−	0.755468i	$-0.272590\pi$
$199$	2.89890e10			1.31037			0.655186	+	0.755468i	$0.272590\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.39514e10	+	2.41645e10i	0.576613	+	0.998723i
$204$		0			0
$205$	6.11146e9	−	1.05854e10i	0.241687	−	0.418614i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	5.27422e8	−	9.13522e8i	0.0191205	−	0.0331177i
$210$		0			0
$211$	9.89949e9	+	1.71464e10i	0.343828	+	0.595528i	0.985140	−	0.171752i	$-0.0549428\pi$
$211$	9.89949e9	+	1.71464e10i	0.343828	+	0.595528i	−0.641312	+	0.767280i	$0.721610\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.68058e8			0.00536398
$216$		0			0
$217$	4.68347e10			1.43383
$218$		0			0
$219$		0			0
$220$		0			0
$221$	9.55578e9	+	1.65511e10i	0.269464	+	0.466726i
$222$		0			0
$223$	3.39384e10	−	5.87831e10i	0.919009	−	1.59177i	0.118085	−	0.993003i	$-0.462324\pi$
$223$	3.39384e10	−	5.87831e10i	0.919009	−	1.59177i	0.800924	−	0.598766i	$-0.204342\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.72803e10	+	4.72508e10i	−0.681919	+	1.18112i	0.292476	+	0.956273i	$0.405521\pi$
$227$	−2.72803e10	+	4.72508e10i	−0.681919	+	1.18112i	−0.974395	+	0.224845i	$0.927812\pi$
$228$		0			0
$229$	−2.31976e10	−	4.01794e10i	−0.557421	−	0.965481i	−0.997711	−	0.0676254i	$-0.978458\pi$
$229$	−2.31976e10	−	4.01794e10i	−0.557421	−	0.965481i	0.440290	−	0.897856i	$-0.354876\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.91389e8			−0.00869975			−0.00434988	−	0.999991i	$-0.501385\pi$
$233$	−3.91389e8			−0.00869975			−0.00434988	+	0.999991i	$0.501385\pi$
$234$		0			0
$235$	3.29784e10			0.705382
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4.53269e10	−	7.85085e10i	−0.898598	−	1.55642i	−0.829287	−	0.558823i	$-0.811253\pi$
$239$	−4.53269e10	−	7.85085e10i	−0.898598	−	1.55642i	−0.0693115	−	0.997595i	$-0.522080\pi$
$240$		0			0
$241$	3.38832e10	−	5.86874e10i	0.647004	−	1.12064i	−0.336830	−	0.941565i	$-0.609355\pi$
$241$	3.38832e10	−	5.86874e10i	0.647004	−	1.12064i	0.983835	−	0.179079i	$-0.0573118\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.03238e8	+	1.78813e8i	−0.00183059	+	0.00317067i
$246$		0			0
$247$	5.60676e8	+	9.71120e8i	0.00958464	+	0.0166011i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	5.47163e10			0.870131			0.435066	−	0.900399i	$-0.356725\pi$
$251$	5.47163e10			0.870131			0.435066	+	0.900399i	$0.356725\pi$
$252$		0			0
$253$	−3.18965e10			−0.489441
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.70450e10	+	2.95228e10i	0.243724	+	0.422142i	0.961772	−	0.273851i	$-0.0882977\pi$
$257$	1.70450e10	+	2.95228e10i	0.243724	+	0.422142i	−0.718048	+	0.695993i	$0.754964\pi$
$258$		0			0
$259$	3.23820e10	−	5.60872e10i	0.447151	−	0.774488i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.58680e10	−	6.21252e10i	0.462282	−	0.800695i	−0.536793	−	0.843714i	$-0.680364\pi$
$263$	3.58680e10	−	6.21252e10i	0.462282	−	0.800695i	0.999074	+	0.0430190i	$0.0136976\pi$
$264$		0			0
$265$	−2.21102e10	−	3.82959e10i	−0.275414	−	0.477031i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2.31610e9			0.0269695			0.0134847	−	0.999909i	$-0.495708\pi$
$269$	2.31610e9			0.0269695			0.0134847	+	0.999909i	$0.495708\pi$
$270$		0			0
$271$	8.04662e10			0.906258			0.453129	−	0.891445i	$-0.350308\pi$
$271$	8.04662e10			0.906258			0.453129	+	0.891445i	$0.350308\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.29605e10	−	3.97688e10i	−0.242095	−	0.419320i
$276$		0			0
$277$	8.28220e10	−	1.43452e11i	0.845253	−	1.46402i	−0.0401491	−	0.999194i	$-0.512783\pi$
$277$	8.28220e10	−	1.43452e11i	0.845253	−	1.46402i	0.885402	−	0.464827i	$-0.153883\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.28589e10	+	2.22722e10i	−0.123034	+	0.213101i	−0.920963	−	0.389651i	$-0.872596\pi$
$281$	−1.28589e10	+	2.22722e10i	−0.123034	+	0.213101i	0.797929	+	0.602752i	$0.205929\pi$
$282$		0			0
$283$	−2.16563e10	−	3.75098e10i	−0.200699	−	0.347621i	0.748055	−	0.663637i	$-0.230988\pi$
$283$	−2.16563e10	−	3.75098e10i	−0.200699	−	0.347621i	−0.948754	+	0.316016i	$0.897655\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.16136e11			−1.01041
$288$		0			0
$289$	2.30686e11			1.94528
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.41737e10	+	4.18700e10i	0.191619	+	0.331894i	0.945787	−	0.324788i	$-0.105293\pi$
$293$	2.41737e10	+	4.18700e10i	0.191619	+	0.331894i	−0.754168	+	0.656681i	$0.771960\pi$
$294$		0			0
$295$	−2.04874e10	+	3.54852e10i	−0.157503	+	0.272803i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.69538e10	−	2.93648e10i	0.122672	−	0.212474i
$300$		0			0
$301$	−7.98404e8	−	1.38288e9i	−0.00560626	−	0.00971033i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.37353e10			−0.157053
$306$		0			0
$307$	1.37971e11			0.886470			0.443235	−	0.896406i	$-0.353831\pi$
$307$	1.37971e11			0.886470			0.443235	+	0.896406i	$0.353831\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.02226e11	+	1.77060e11i	0.619638	+	1.07325i	0.989552	+	0.144179i	$0.0460540\pi$
$311$	1.02226e11	+	1.77060e11i	0.619638	+	1.07325i	−0.369913	+	0.929066i	$0.620613\pi$
$312$		0			0
$313$	8.70922e10	−	1.50848e11i	0.512897	−	0.888363i	−0.486992	−	0.873407i	$-0.661906\pi$
$313$	8.70922e10	−	1.50848e11i	0.512897	−	0.888363i	0.999888	−	0.0149562i	$-0.00476090\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.21234e10	−	7.29598e10i	0.234292	−	0.405805i	−0.724775	−	0.688986i	$-0.758056\pi$
$317$	4.21234e10	−	7.29598e10i	0.234292	−	0.405805i	0.959067	+	0.283181i	$0.0913896\pi$
$318$		0			0
$319$	6.70671e10	+	1.16164e11i	0.362620	+	0.628076i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.04933e10			0.104761
$324$		0			0
$325$	4.88164e10			0.242712
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.56672e11	−	2.71364e11i	−0.737243	−	1.27694i
$330$		0			0
$331$	1.44388e11	−	2.50088e11i	0.661160	−	1.14516i	−0.319152	−	0.947704i	$-0.603398\pi$
$331$	1.44388e11	−	2.50088e11i	0.661160	−	1.14516i	0.980311	−	0.197458i	$-0.0632688\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	6.05202e10	−	1.04824e11i	0.262542	−	0.454736i
$336$		0			0
$337$	−6.75149e10	−	1.16939e11i	−0.285144	−	0.493885i	0.687500	−	0.726185i	$-0.258708\pi$
$337$	−6.75149e10	−	1.16939e11i	−0.285144	−	0.493885i	−0.972644	+	0.232300i	$0.925375\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.25144e11			0.901708
$342$		0			0
$343$	2.57319e11			1.00380
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.95952e10	+	3.39398e10i	0.0725548	+	0.125669i	0.900020	−	0.435848i	$-0.143551\pi$
$347$	1.95952e10	+	3.39398e10i	0.0725548	+	0.125669i	−0.827466	+	0.561517i	$0.810218\pi$
$348$		0			0
$349$	2.29409e10	−	3.97348e10i	0.0827744	−	0.143369i	−0.821666	−	0.569969i	$-0.806955\pi$
$349$	2.29409e10	−	3.97348e10i	0.0827744	−	0.143369i	0.904441	+	0.426599i	$0.140289\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2.64795e11	+	4.58638e11i	−0.907660	+	1.57211i	−0.0903538	+	0.995910i	$0.528800\pi$
$353$	−2.64795e11	+	4.58638e11i	−0.907660	+	1.57211i	−0.817306	+	0.576204i	$0.804534\pi$
$354$		0			0
$355$	3.02714e10	+	5.24315e10i	0.101159	+	0.175212i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−4.54893e10			−0.144539			−0.0722693	−	0.997385i	$-0.523024\pi$
$359$	−4.54893e10			−0.144539			−0.0722693	+	0.997385i	$0.523024\pi$
$360$		0			0
$361$	−3.21485e11			−0.996274
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−8.75719e10	−	1.51679e11i	−0.258254	−	0.447309i
$366$		0			0
$367$	−1.22583e11	+	2.12321e11i	−0.352723	+	0.610935i	−0.986726	−	0.162396i	$-0.948078\pi$
$367$	−1.22583e11	+	2.12321e11i	−0.352723	+	0.610935i	0.634002	+	0.773331i	$0.281411\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−2.10080e11	+	3.63869e11i	−0.575707	+	0.997154i
$372$		0			0
$373$	8.01449e10	+	1.38815e11i	0.214381	+	0.371318i	0.953081	−	0.302716i	$-0.0978933\pi$
$373$	8.01449e10	+	1.38815e11i	0.214381	+	0.371318i	−0.738700	+	0.674034i	$0.764560\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.42591e11			−0.363544
$378$		0			0
$379$	−3.55772e11			−0.885719			−0.442859	−	0.896591i	$-0.646036\pi$
$379$	−3.55772e11			−0.885719			−0.442859	+	0.896591i	$0.646036\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.48504e11	+	4.30421e11i	0.590118	+	1.02211i	0.994216	+	0.107398i	$0.0342521\pi$
$383$	2.48504e11	+	4.30421e11i	0.590118	+	1.02211i	−0.404098	+	0.914716i	$0.632415\pi$
$384$		0			0
$385$	6.41018e10	−	1.11027e11i	0.148695	−	0.257547i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.97134e11	−	5.14651e11i	0.657929	−	1.13957i	−0.323221	−	0.946323i	$-0.604766\pi$
$389$	2.97134e11	−	5.14651e11i	0.657929	−	1.13957i	0.981151	−	0.193244i	$-0.0619009\pi$
$390$		0			0
$391$	−3.09839e11	−	5.36657e11i	−0.670411	−	1.16119i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	7.75909e10			0.160370
$396$		0			0
$397$	−1.18575e11			−0.239572			−0.119786	−	0.992800i	$-0.538221\pi$
$397$	−1.18575e11			−0.239572			−0.119786	+	0.992800i	$0.538221\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	2.63799e11	+	4.56913e11i	0.509475	+	0.882437i	0.999940	+	0.0109760i	$0.00349385\pi$
$401$	2.63799e11	+	4.56913e11i	0.509475	+	0.882437i	−0.490464	+	0.871461i	$0.663173\pi$
$402$		0			0
$403$	−1.19670e11	+	2.07274e11i	−0.226002	+	0.391446i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.55667e11	−	2.69623e11i	0.281204	−	0.487059i
$408$		0			0
$409$	4.48436e10	+	7.76714e10i	0.0792402	+	0.137248i	0.902922	−	0.429804i	$-0.141417\pi$
$409$	4.48436e10	+	7.76714e10i	0.0792402	+	0.137248i	−0.823682	+	0.567052i	$0.808084\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	3.89322e11			0.658467
$414$		0			0
$415$	6.36944e9			0.0105411
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−4.63269e11	−	8.02406e11i	−0.734294	−	1.27184i	−0.955032	−	0.296502i	$-0.904180\pi$
$419$	−4.63269e11	−	8.02406e11i	−0.734294	−	1.27184i	0.220738	−	0.975333i	$-0.429153\pi$
$420$		0			0
$421$	−6.13462e11	+	1.06255e12i	−0.951740	+	1.64846i	−0.210082	+	0.977684i	$0.567373\pi$
$421$	−6.13462e11	+	1.06255e12i	−0.951740	+	1.64846i	−0.741658	+	0.670779i	$0.765960\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	4.46073e11	−	7.72621e11i	0.663217	−	1.14873i
$426$		0			0
$427$	1.12761e11	+	1.95307e11i	0.164147	+	0.284310i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−9.56151e11			−1.33469			−0.667343	−	0.744751i	$-0.732568\pi$
$431$	−9.56151e11			−1.33469			−0.667343	+	0.744751i	$0.732568\pi$
$432$		0			0
$433$	7.42841e10			0.101555			0.0507774	−	0.998710i	$-0.483830\pi$
$433$	7.42841e10			0.101555			0.0507774	+	0.998710i	$0.483830\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.81795e10	−	3.14878e10i	−0.0238460	−	0.0413025i
$438$		0			0
$439$	8.32590e10	−	1.44209e11i	0.106989	−	0.185311i	−0.807560	−	0.589786i	$-0.799212\pi$
$439$	8.32590e10	−	1.44209e11i	0.106989	−	0.185311i	0.914549	+	0.404475i	$0.132546\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.20791e11	+	5.55626e11i	−0.395735	+	0.685434i	−0.993195	−	0.116465i	$-0.962844\pi$
$443$	−3.20791e11	+	5.55626e11i	−0.395735	+	0.685434i	0.597459	+	0.801899i	$0.296177\pi$
$444$		0			0
$445$	2.03738e11	+	3.52885e11i	0.246293	+	0.426593i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−2.77233e11			−0.321911			−0.160956	−	0.986962i	$-0.551458\pi$
$449$	−2.77233e11			−0.321911			−0.160956	+	0.986962i	$0.551458\pi$
$450$		0			0
$451$	−5.58291e11			−0.635427
$452$		0			0
$453$		0			0
$454$		0			0
$455$	6.81434e10	+	1.18028e11i	0.0745371	+	0.129102i
$456$		0			0
$457$	−3.77614e11	+	6.54047e11i	−0.404972	+	0.701432i	−0.994318	−	0.106448i	$-0.966052\pi$
$457$	−3.77614e11	+	6.54047e11i	−0.404972	+	0.701432i	0.589346	+	0.807881i	$0.299385\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−4.57870e11	+	7.93054e11i	−0.472159	+	0.817803i	−0.999492	−	0.0318552i	$-0.989858\pi$
$461$	−4.57870e11	+	7.93054e11i	−0.472159	+	0.817803i	0.527334	+	0.849658i	$0.323192\pi$
$462$		0			0
$463$	3.17947e11	+	5.50701e11i	0.321544	+	0.556931i	0.980807	−	0.194982i	$-0.0624648\pi$
$463$	3.17947e11	+	5.50701e11i	0.321544	+	0.556931i	−0.659263	+	0.751913i	$0.729131\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.17286e11			0.600566			0.300283	−	0.953850i	$-0.402919\pi$
$467$	6.17286e11			0.600566			0.300283	+	0.953850i	$0.402919\pi$
$468$		0			0
$469$	−1.15007e12			−1.09760
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.83809e9	−	6.64777e9i	−0.00352566	−	0.00610662i
$474$		0			0
$475$	2.61729e10	−	4.53328e10i	0.0235902	−	0.0408593i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−1.38971e11	+	2.40705e11i	−0.120619	+	0.208918i	−0.920012	−	0.391891i	$-0.871821\pi$
$479$	−1.38971e11	+	2.40705e11i	−0.120619	+	0.208918i	0.799393	+	0.600808i	$0.205155\pi$
$480$		0			0
$481$	1.65482e11	+	2.86623e11i	0.140960	+	0.244151i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.72702e11			0.141730
$486$		0			0
$487$	−4.99400e11			−0.402317			−0.201158	−	0.979559i	$-0.564471\pi$
$487$	−4.99400e11			−0.402317			−0.201158	+	0.979559i	$0.564471\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.03120e12	−	1.78610e12i	−0.800715	−	1.38688i	−0.919146	−	0.393917i	$-0.871120\pi$
$491$	−1.03120e12	−	1.78610e12i	−0.800715	−	1.38688i	0.118431	−	0.992962i	$-0.462213\pi$
$492$		0			0
$493$	−1.30297e12	+	2.25680e12i	−0.993395	+	1.72061i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.87623e11	−	4.98178e11i	0.211456	−	0.366253i
$498$		0			0
$499$	6.09561e11	+	1.05579e12i	0.440113	+	0.762299i	0.997697	−	0.0678218i	$-0.0216049\pi$
$499$	6.09561e11	+	1.05579e12i	0.440113	+	0.762299i	−0.557584	+	0.830120i	$0.688272\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.80430e12			1.25676			0.628380	−	0.777906i	$-0.283718\pi$
$503$	1.80430e12			1.25676			0.628380	+	0.777906i	$0.283718\pi$
$504$		0			0
$505$	−1.04266e12			−0.713395
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.01620e11	+	1.76010e11i	0.0671039	+	0.116227i	0.897625	−	0.440759i	$-0.145291\pi$
$509$	1.01620e11	+	1.76010e11i	0.0671039	+	0.116227i	−0.830521	+	0.556987i	$0.811957\pi$
$510$		0			0
$511$	−8.32065e11	+	1.44118e12i	−0.539837	+	0.935026i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.25573e11	−	2.17498e11i	0.0786615	−	0.136246i
$516$		0			0
$517$	−7.53156e11	−	1.30450e12i	−0.463636	−	0.803041i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.93093e11			−0.412118			−0.206059	−	0.978540i	$-0.566064\pi$
$521$	−6.93093e11			−0.412118			−0.206059	+	0.978540i	$0.566064\pi$
$522$		0			0
$523$	−1.97956e12			−1.15694			−0.578470	−	0.815704i	$-0.696350\pi$
$523$	−1.97956e12			−1.15694			−0.578470	+	0.815704i	$0.696350\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.18703e12	+	3.78804e12i	1.23511	+	2.13928i
$528$		0			0
$529$	3.50862e11	−	6.07712e11i	0.194799	−	0.337401i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2.96746e11	−	5.13978e11i	0.159262	−	0.275850i
$534$		0			0
$535$	−7.24998e11	−	1.25573e12i	−0.382600	−	0.662682i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	9.43090e9			0.00481287
$540$		0			0
$541$	−2.95899e12			−1.48510			−0.742551	−	0.669790i	$-0.766384\pi$
$541$	−2.95899e12			−1.48510			−0.742551	+	0.669790i	$0.766384\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	5.02202e11	+	8.69840e11i	0.243834	+	0.422333i
$546$		0			0
$547$	−1.63763e12	+	2.83645e12i	−0.782118	+	1.35467i	0.148588	+	0.988899i	$0.452527\pi$
$547$	−1.63763e12	+	2.83645e12i	−0.782118	+	1.35467i	−0.930706	+	0.365769i	$0.880806\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−7.64503e10	+	1.32416e11i	−0.0353343	+	0.0612009i
$552$		0			0
$553$	−3.68615e11	−	6.38460e11i	−0.167614	−	0.290316i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−3.76405e12			−1.65694			−0.828470	−	0.560034i	$-0.810788\pi$
$557$	−3.76405e12			−1.65694			−0.828470	+	0.560034i	$0.810788\pi$
$558$		0			0
$559$	8.16017e9			0.00353465
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.17493e12	−	2.03505e12i	−0.492863	−	0.853663i	0.507104	−	0.861885i	$-0.330716\pi$
$563$	−1.17493e12	−	2.03505e12i	−0.492863	−	0.853663i	−0.999966	+	0.00822214i	$0.997383\pi$
$564$		0			0
$565$	−4.84031e11	+	8.38366e11i	−0.199827	+	0.346111i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.33351e12	+	2.30970e12i	−0.533322	+	0.923742i	0.465920	+	0.884827i	$0.345723\pi$
$569$	−1.33351e12	+	2.30970e12i	−0.533322	+	0.923742i	−0.999243	+	0.0389148i	$0.987610\pi$
$570$		0			0
$571$	8.61712e11	+	1.49253e12i	0.339234	+	0.587571i	0.984289	−	0.176565i	$-0.0564987\pi$
$571$	8.61712e11	+	1.49253e12i	0.339234	+	0.587571i	−0.645055	+	0.764137i	$0.723165\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.58284e12			−0.603853
$576$		0			0
$577$	1.55856e12			0.585374			0.292687	−	0.956208i	$-0.405451\pi$
$577$	1.55856e12			0.585374			0.292687	+	0.956208i	$0.405451\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.02596e10	−	5.24112e10i	−0.0110172	−	0.0190823i
$582$		0			0
$583$	−1.00990e12	+	1.74919e12i	−0.362050	+	0.627089i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.08311e12	−	1.87601e12i	0.376533	−	0.652173i	−0.614023	−	0.789288i	$-0.710450\pi$
$587$	1.08311e12	−	1.87601e12i	0.376533	−	0.652173i	0.990555	+	0.137115i	$0.0437830\pi$
$588$		0			0
$589$	1.28322e11	+	2.22260e11i	0.0439320	+	0.0760925i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	3.56244e12			1.18304			0.591522	−	0.806289i	$-0.298527\pi$
$593$	3.56244e12			1.18304			0.591522	+	0.806289i	$0.298527\pi$
$594$		0			0
$595$	2.49071e12			0.814699
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−7.72034e11	−	1.33720e12i	−0.245028	−	0.424401i	0.717111	−	0.696959i	$-0.245464\pi$
$599$	−7.72034e11	−	1.33720e12i	−0.245028	−	0.424401i	−0.962140	+	0.272557i	$0.912131\pi$
$600$		0			0
$601$	5.26387e11	−	9.11729e11i	0.164577	−	0.285056i	−0.771928	−	0.635710i	$-0.780707\pi$
$601$	5.26387e11	−	9.11729e11i	0.164577	−	0.285056i	0.936505	+	0.350654i	$0.114041\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.77046e11	+	8.26268e11i	−0.144764	+	0.250739i
$606$		0			0
$607$	2.23735e12	+	3.87521e12i	0.668937	+	1.15863i	0.978202	+	0.207657i	$0.0665839\pi$
$607$	2.23735e12	+	3.87521e12i	0.668937	+	1.15863i	−0.309264	+	0.950976i	$0.600083\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.60129e12			0.464818
$612$		0			0
$613$	−6.01862e12			−1.72157			−0.860785	−	0.508969i	$-0.830027\pi$
$613$	−6.01862e12			−1.72157			−0.860785	+	0.508969i	$0.830027\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.08095e12	−	1.87227e12i	−0.300278	−	0.520097i	0.675921	−	0.736974i	$-0.263746\pi$
$617$	−1.08095e12	−	1.87227e12i	−0.300278	−	0.520097i	−0.976199	+	0.216877i	$0.930413\pi$
$618$		0			0
$619$	2.08462e12	−	3.61066e12i	0.570714	−	0.988506i	−0.425779	−	0.904827i	$-0.640000\pi$
$619$	2.08462e12	−	3.61066e12i	0.570714	−	0.988506i	0.996493	−	0.0836784i	$-0.0266668\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.93582e12	−	3.35294e12i	0.514836	−	0.891722i
$624$		0			0
$625$	−7.06239e11	−	1.22324e12i	−0.185136	−	0.320666i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	6.04853e12			1.54071
$630$		0			0
$631$	4.10037e12			1.02965			0.514826	−	0.857295i	$-0.327857\pi$
$631$	4.10037e12			1.02965			0.514826	+	0.857295i	$0.327857\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	8.11452e11	+	1.40548e12i	0.198053	+	0.343038i
$636$		0			0
$637$	−5.01276e9	+	8.68236e9i	−0.00120628	+	0.00208935i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.35938e11	+	1.62109e12i	−0.218971	+	0.379268i	−0.954494	−	0.298231i	$-0.903603\pi$
$641$	−9.35938e11	+	1.62109e12i	−0.218971	+	0.379268i	0.735523	+	0.677500i	$0.236937\pi$
$642$		0			0
$643$	6.70831e11	+	1.16191e12i	0.154762	+	0.268055i	0.932972	−	0.359948i	$-0.117206\pi$
$643$	6.70831e11	+	1.16191e12i	0.154762	+	0.268055i	−0.778210	+	0.628004i	$0.783872\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.94367e12			−1.10912			−0.554562	−	0.832142i	$-0.687114\pi$
$647$	−4.94367e12			−1.10912			−0.554562	+	0.832142i	$0.687114\pi$
$648$		0			0
$649$	1.87155e12			0.414096
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.33570e12	−	2.31349e12i	−0.287474	−	0.497919i	0.685732	−	0.727854i	$-0.259482\pi$
$653$	−1.33570e12	−	2.31349e12i	−0.287474	−	0.497919i	−0.973206	+	0.229935i	$0.926149\pi$
$654$		0			0
$655$	−4.77382e11	+	8.26849e11i	−0.101340	+	0.175526i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−2.75044e12	+	4.76391e12i	−0.568092	+	0.983964i	0.428663	+	0.903465i	$0.358985\pi$
$659$	−2.75044e12	+	4.76391e12i	−0.568092	+	0.983964i	−0.996755	+	0.0804993i	$0.974349\pi$
$660$		0			0
$661$	−5.34684e11	−	9.26099e11i	−0.108941	−	0.188691i	0.806401	−	0.591370i	$-0.201413\pi$
$661$	−5.34684e11	−	9.26099e11i	−0.108941	−	0.188691i	−0.915341	+	0.402679i	$0.868079\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.46140e11			0.0289783
$666$		0			0
$667$	4.62342e12			0.904476
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.42063e11	+	9.38881e11i	0.103228	+	0.178797i
$672$		0			0
$673$	2.48284e12	−	4.30040e12i	0.466531	−	0.808055i	−0.532738	−	0.846280i	$-0.678837\pi$
$673$	2.48284e12	−	4.30040e12i	0.466531	−	0.808055i	0.999269	+	0.0382249i	$0.0121703\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.37870e12	−	2.38797e12i	0.252243	−	0.436898i	−0.711900	−	0.702281i	$-0.752165\pi$
$677$	1.37870e12	−	2.38797e12i	0.252243	−	0.436898i	0.964143	+	0.265383i	$0.0854984\pi$
$678$		0			0
$679$	−8.20466e11	−	1.42109e12i	−0.148131	−	0.256571i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−5.05528e12			−0.888898			−0.444449	−	0.895804i	$-0.646601\pi$
$683$	−5.05528e12			−0.888898			−0.444449	+	0.895804i	$0.646601\pi$
$684$		0			0
$685$	−6.19982e11			−0.107590
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.07357e12	−	1.85948e12i	−0.181487	−	0.314344i
$690$		0			0
$691$	1.27707e12	−	2.21195e12i	0.213090	−	0.369083i	−0.739590	−	0.673058i	$-0.764980\pi$
$691$	1.27707e12	−	2.21195e12i	0.213090	−	0.369083i	0.952680	+	0.303975i	$0.0983138\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.61277e12	−	2.79340e12i	0.262205	−	0.454153i
$696$		0			0
$697$	−5.42318e12	−	9.39323e12i	−0.870375	−	1.50753i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−8.11552e12			−1.26936			−0.634681	−	0.772774i	$-0.718868\pi$
$701$	−8.11552e12			−1.26936			−0.634681	+	0.772774i	$0.718868\pi$
$702$		0			0
$703$	3.54892e11			0.0548020
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.95340e12	+	8.57954e12i	0.745617	+	1.29145i
$708$		0			0
$709$	1.02197e12	−	1.77010e12i	0.151890	−	0.263082i	−0.780032	−	0.625740i	$-0.784797\pi$
$709$	1.02197e12	−	1.77010e12i	0.151890	−	0.263082i	0.931922	+	0.362658i	$0.118131\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	3.88020e12	−	6.72071e12i	0.562279	−	0.973895i
$714$		0			0
$715$	3.27579e11	+	5.67384e11i	0.0468748	+	0.0811895i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.24231e13			1.73361			0.866804	−	0.498648i	$-0.166170\pi$
$719$	1.24231e13			1.73361			0.866804	+	0.498648i	$0.166170\pi$
$720$		0			0
$721$	−2.38626e12			−0.328858
$722$		0			0
$723$		0			0
$724$		0			0
$725$	3.32815e12	+	5.76453e12i	0.447386	+	0.774895i
$726$		0			0
$727$	2.68717e12	−	4.65431e12i	0.356771	−	0.617946i	−0.630648	−	0.776069i	$-0.717211\pi$
$727$	2.68717e12	−	4.65431e12i	0.356771	−	0.617946i	0.987419	+	0.158123i	$0.0505442\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	7.45657e10	−	1.29152e11i	0.00965853	−	0.0167291i
$732$		0			0
$733$	−6.43088e10	−	1.11386e11i	−0.00822815	−	0.0142516i	0.861882	−	0.507109i	$-0.169286\pi$
$733$	−6.43088e10	−	1.11386e11i	−0.00822815	−	0.0142516i	−0.870110	+	0.492857i	$0.835952\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.52860e12			−0.690258
$738$		0			0
$739$	1.36726e13			1.68636			0.843181	−	0.537630i	$-0.180680\pi$
$739$	1.36726e13			1.68636			0.843181	+	0.537630i	$0.180680\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−6.57907e12	−	1.13953e13i	−0.791981	−	1.37175i	−0.924739	−	0.380603i	$-0.875717\pi$
$743$	−6.57907e12	−	1.13953e13i	−0.791981	−	1.37175i	0.132758	−	0.991149i	$-0.457617\pi$
$744$		0			0
$745$	2.84139e12	−	4.92143e12i	0.337930	−	0.585313i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−6.88857e12	+	1.19314e13i	−0.799762	+	1.38523i
$750$		0			0
$751$	1.04341e12	+	1.80724e12i	0.119695	+	0.207317i	0.919647	−	0.392747i	$-0.128475\pi$
$751$	1.04341e12	+	1.80724e12i	0.119695	+	0.207317i	−0.799952	+	0.600064i	$0.795142\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	4.75867e12			0.532997
$756$		0			0
$757$	5.54660e12			0.613897			0.306948	−	0.951726i	$-0.400692\pi$
$757$	5.54660e12			0.613897			0.306948	+	0.951726i	$0.400692\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	5.67255e11	+	9.82514e11i	0.0613123	+	0.106196i	0.895052	−	0.445961i	$-0.147138\pi$
$761$	5.67255e11	+	9.82514e11i	0.0613123	+	0.106196i	−0.833740	+	0.552157i	$0.813805\pi$
$762$		0			0
$763$	4.77167e12	−	8.26478e12i	0.509695	−	0.882818i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−9.94777e11	+	1.72301e12i	−0.103788	+	0.179766i
$768$		0			0
$769$	1.30801e12	+	2.26554e12i	0.134878	+	0.233616i	0.925551	−	0.378623i	$-0.123602\pi$
$769$	1.30801e12	+	2.26554e12i	0.134878	+	0.233616i	−0.790673	+	0.612239i	$0.790269\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−5.33154e10			−0.00537088			−0.00268544	−	0.999996i	$-0.500855\pi$
$773$	−5.33154e10			−0.00537088			−0.00268544	+	0.999996i	$0.500855\pi$
$774$		0			0
$775$	1.11726e13			1.11249
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.18200e11	−	5.51138e11i	−0.0309586	−	0.0536219i
$780$		0			0
$781$	1.38266e12	−	2.39485e12i	0.132980	−	0.230329i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.12634e12	+	1.95087e12i	−0.105865	+	0.183364i
$786$		0			0
$787$	1.65392e12	+	2.86467e12i	0.153683	+	0.266187i	0.932579	−	0.360966i	$-0.117553\pi$
$787$	1.65392e12	+	2.86467e12i	0.153683	+	0.266187i	−0.778895	+	0.627154i	$0.784220\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	9.19804e12			0.835412
$792$		0			0
$793$	−1.15248e12			−0.103492
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.93437e12	+	3.35042e12i	0.169815	+	0.294128i	0.938355	−	0.345674i	$-0.112350\pi$
$797$	1.93437e12	+	3.35042e12i	0.169815	+	0.294128i	−0.768540	+	0.639802i	$0.779016\pi$
$798$		0			0
$799$	1.46322e13	−	2.53437e13i	1.27013	−	2.19993i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.99991e12	+	6.92804e12i	−0.339492	+	0.588018i
$804$		0			0
$805$	−2.20950e12	−	3.82697e12i	−0.185444	−	0.321198i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	7.39526e12			0.606995			0.303497	−	0.952832i	$-0.401846\pi$
$809$	7.39526e12			0.606995			0.303497	+	0.952832i	$0.401846\pi$
$810$		0			0
$811$	8.92803e12			0.724706			0.362353	−	0.932041i	$-0.381974\pi$
$811$	8.92803e12			0.724706			0.362353	+	0.932041i	$0.381974\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−3.00204e11	−	5.19969e11i	−0.0238346	−	0.0412827i
$816$		0			0
$817$	4.37507e9	−	7.57785e9i	0.000343547	−	0.000595040i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	5.27668e12	−	9.13947e12i	0.405337	−	0.702065i	−0.589024	−	0.808116i	$-0.700487\pi$
$821$	5.27668e12	−	9.13947e12i	0.405337	−	0.702065i	0.994361	+	0.106051i	$0.0338208\pi$
$822$		0			0
$823$	4.58015e12	+	7.93306e12i	0.348001	+	0.602756i	0.985894	−	0.167369i	$-0.0535272\pi$
$823$	4.58015e12	+	7.93306e12i	0.348001	+	0.602756i	−0.637893	+	0.770125i	$0.720194\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−2.44096e13			−1.81462			−0.907310	−	0.420462i	$-0.861868\pi$
$827$	−2.44096e13			−1.81462			−0.907310	+	0.420462i	$0.861868\pi$
$828$		0			0
$829$	9.12051e12			0.670693			0.335346	−	0.942095i	$-0.391147\pi$
$829$	9.12051e12			0.670693			0.335346	+	0.942095i	$0.391147\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	9.16109e10	+	1.58675e11i	0.00659241	+	0.0114184i
$834$		0			0
$835$	1.35067e12	−	2.33942e12i	0.0961521	−	0.166540i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−3.03787e12	+	5.26175e12i	−0.211661	+	0.366608i	−0.952234	−	0.305368i	$-0.901221\pi$
$839$	−3.03787e12	+	5.26175e12i	−0.211661	+	0.366608i	0.740573	+	0.671975i	$0.234554\pi$
$840$		0			0
$841$	−2.46786e12	−	4.27445e12i	−0.170113	−	0.294645i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	6.36613e12			0.429556
$846$		0			0
$847$	9.06531e12			0.605212
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−5.36562e12	−	9.29353e12i	−0.350701	−	0.607432i
$852$		0			0
$853$	−8.39586e12	+	1.45421e13i	−0.542993	+	0.940492i	0.455737	+	0.890114i	$0.349376\pi$
$853$	−8.39586e12	+	1.45421e13i	−0.542993	+	0.940492i	−0.998730	+	0.0503774i	$0.983958\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.38853e13	−	2.40501e13i	0.879312	−	1.52301i	0.0272152	−	0.999630i	$-0.491336\pi$
$857$	1.38853e13	−	2.40501e13i	0.879312	−	1.52301i	0.852097	−	0.523384i	$-0.175331\pi$
$858$		0			0
$859$	−9.27026e11	−	1.60566e12i	−0.0580928	−	0.100620i	0.835516	−	0.549465i	$-0.185169\pi$
$859$	−9.27026e11	−	1.60566e12i	−0.0580928	−	0.100620i	−0.893609	+	0.448846i	$0.851835\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	8.72142e12			0.535228			0.267614	−	0.963526i	$-0.413765\pi$
$863$	8.72142e12			0.535228			0.267614	+	0.963526i	$0.413765\pi$
$864$		0			0
$865$	6.84383e11			0.0415649
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.77201e12	−	3.06921e12i	−0.105409	−	0.182573i
$870$		0			0
$871$	2.93859e12	−	5.08979e12i	0.173005	−	0.299653i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	7.29667e12	−	1.26382e13i	0.420812	−	0.728869i
$876$		0			0
$877$	−1.38111e13	−	2.39215e13i	−0.788369	−	1.36550i	−0.926966	−	0.375146i	$-0.877592\pi$
$877$	−1.38111e13	−	2.39215e13i	−0.788369	−	1.36550i	0.138596	−	0.990349i	$-0.455741\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.00186e13			−0.560295			−0.280147	−	0.959957i	$-0.590383\pi$
$881$	−1.00186e13			−0.560295			−0.280147	+	0.959957i	$0.590383\pi$
$882$		0			0
$883$	9.43702e12			0.522410			0.261205	−	0.965283i	$-0.415880\pi$
$883$	9.43702e12			0.522410			0.261205	+	0.965283i	$0.415880\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.87818e12	+	3.25310e12i	0.101878	+	0.176458i	0.912458	−	0.409170i	$-0.134182\pi$
$887$	1.87818e12	+	3.25310e12i	0.101878	+	0.176458i	−0.810580	+	0.585627i	$0.800848\pi$
$888$		0			0
$889$	7.71001e12	−	1.33541e13i	0.413997	−	0.717064i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	8.58528e11	−	1.48701e12i	0.0451776	−	0.0782499i
$894$		0			0
$895$	4.94412e12	+	8.56347e12i	0.257564	+	0.446114i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.26348e13			−1.66634
$900$		0			0
$901$	−3.92402e13			−1.98367
$902$		0			0
$903$		0			0
$904$		0			0
$905$	8.43389e12	+	1.46079e13i	0.417936	+	0.723886i
$906$		0			0
$907$	−1.18398e13	+	2.05070e13i	−0.580911	+	1.00617i	0.414460	+	0.910067i	$0.363970\pi$
$907$	−1.18398e13	+	2.05070e13i	−0.580911	+	1.00617i	−0.995372	+	0.0961004i	$0.969363\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−9.50149e12	+	1.64571e13i	−0.457045	+	0.791626i	−0.998803	−	0.0489090i	$-0.984426\pi$
$911$	−9.50149e12	+	1.64571e13i	−0.457045	+	0.791626i	0.541758	+	0.840535i	$0.317759\pi$
$912$		0			0
$913$	−1.45464e11	−	2.51951e11i	−0.00692848	−	0.0120005i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	9.07168e12			0.423668
$918$		0			0
$919$	5.56992e12			0.257590			0.128795	−	0.991671i	$-0.458889\pi$
$919$	5.56992e12			0.257590			0.128795	+	0.991671i	$0.458889\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.46984e12	+	2.54584e12i	0.0666597	+	0.115458i
$924$		0			0
$925$	7.72484e12	−	1.33798e13i	0.346938	−	0.600914i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.77147e13	+	3.06827e13i	−0.780301	+	1.35152i	0.151465	+	0.988463i	$0.451601\pi$
$929$	−1.77147e13	+	3.06827e13i	−0.780301	+	1.35152i	−0.931766	+	0.363059i	$0.881732\pi$
$930$		0			0
$931$	5.37518e9	+	9.31008e9i	0.000234487	+	0.000406144i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.19734e13			0.512347
$936$		0			0
$937$	−2.45592e13			−1.04084			−0.520422	−	0.853909i	$-0.674225\pi$
$937$	−2.45592e13			−1.04084			−0.520422	+	0.853909i	$0.674225\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.00258e13	−	1.73652e13i	−0.416838	−	0.721984i	0.578782	−	0.815482i	$-0.303528\pi$
$941$	−1.00258e13	−	1.73652e13i	−0.416838	−	0.721984i	−0.995619	+	0.0934986i	$0.970195\pi$
$942$		0			0
$943$	−9.62176e12	+	1.66654e13i	−0.396234	+	0.686297i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.56476e12	−	1.31025e13i	0.305647	−	0.529396i	−0.671758	−	0.740770i	$-0.734461\pi$
$947$	7.56476e12	−	1.31025e13i	0.305647	−	0.529396i	0.977405	+	0.211374i	$0.0677939\pi$
$948$		0			0
$949$	−4.25210e12	−	7.36486e12i	−0.170179	−	0.294759i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	2.18751e13			0.859075			0.429538	−	0.903049i	$-0.358677\pi$
$953$	2.18751e13			0.859075			0.429538	+	0.903049i	$0.358677\pi$
$954$		0			0
$955$	1.07663e13			0.418843
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.94538e12	+	5.10155e12i	0.112449	+	0.194768i
$960$		0			0
$961$	−1.41690e13	+	2.45413e13i	−0.535898	+	0.928203i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−6.00028e11	+	1.03928e12i	−0.0222740	+	0.0385797i
$966$		0			0
$967$	1.66120e13	+	2.87728e13i	0.610945	+	1.05819i	0.991082	+	0.133257i	$0.0425435\pi$
$967$	1.66120e13	+	2.87728e13i	0.610945	+	1.05819i	−0.380137	+	0.924930i	$0.624123\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	3.71430e13			1.34088			0.670441	−	0.741963i	$-0.266105\pi$
$971$	3.71430e13			1.34088			0.670441	+	0.741963i	$0.266105\pi$
$972$		0			0
$973$	−3.06475e13			−1.09619
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.34360e12	−	1.27195e13i	−0.257860	−	0.446626i	0.707809	−	0.706404i	$-0.249684\pi$
$977$	−7.34360e12	−	1.27195e13i	−0.257860	−	0.446626i	−0.965668	+	0.259778i	$0.916351\pi$
$978$		0			0
$979$	9.30588e12	−	1.61183e13i	0.323769	−	0.560785i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.09373e13	+	1.89439e13i	−0.373610	+	0.647112i	−0.990118	−	0.140237i	$-0.955214\pi$
$983$	−1.09373e13	+	1.89439e13i	−0.373610	+	0.647112i	0.616508	+	0.787349i	$0.288547\pi$
$984$		0			0
$985$	−6.22641e12	−	1.07845e13i	−0.210753	−	0.365035i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.64588e11			−0.00879399
$990$		0			0
$991$	4.20089e13			1.38360			0.691799	−	0.722091i	$-0.256819\pi$
$991$	4.20089e13			1.38360			0.691799	+	0.722091i	$0.256819\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	9.65334e12	+	1.67201e13i	0.312229	+	0.540797i
$996$		0			0
$997$	−1.34852e12	+	2.33571e12i	−0.0432245	+	0.0748670i	−0.886828	−	0.462099i	$-0.847096\pi$
$997$	−1.34852e12	+	2.33571e12i	−0.0432245	+	0.0748670i	0.843604	+	0.536966i	$0.180430\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.10.e.e.217.1		2
3.2	odd	2		324.10.e.b.217.1		2
9.2	odd	6		36.10.a.b.1.1		1
9.4	even	3	inner	324.10.e.e.109.1		2
9.5	odd	6		324.10.e.b.109.1		2
9.7	even	3		4.10.a.a.1.1	✓	1
36.7	odd	6		16.10.a.a.1.1		1
36.11	even	6		144.10.a.j.1.1		1
45.7	odd	12		100.10.c.a.49.1		2
45.34	even	6		100.10.a.a.1.1		1
45.43	odd	12		100.10.c.a.49.2		2
63.16	even	3		196.10.e.a.165.1		2
63.25	even	3		196.10.e.a.177.1		2
63.34	odd	6		196.10.a.a.1.1		1
63.52	odd	6		196.10.e.b.177.1		2
63.61	odd	6		196.10.e.b.165.1		2
72.43	odd	6		64.10.a.i.1.1		1
72.61	even	6		64.10.a.a.1.1		1
144.43	odd	12		256.10.b.b.129.2		2
144.61	even	12		256.10.b.j.129.2		2
144.115	odd	12		256.10.b.b.129.1		2
144.133	even	12		256.10.b.j.129.1		2
180.7	even	12		400.10.c.a.49.2		2
180.43	even	12		400.10.c.a.49.1		2
180.79	odd	6		400.10.a.k.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.10.a.a.1.1	✓	1	9.7	even	3
16.10.a.a.1.1		1	36.7	odd	6
36.10.a.b.1.1		1	9.2	odd	6
64.10.a.a.1.1		1	72.61	even	6
64.10.a.i.1.1		1	72.43	odd	6
100.10.a.a.1.1		1	45.34	even	6
100.10.c.a.49.1		2	45.7	odd	12
100.10.c.a.49.2		2	45.43	odd	12
144.10.a.j.1.1		1	36.11	even	6
196.10.a.a.1.1		1	63.34	odd	6
196.10.e.a.165.1		2	63.16	even	3
196.10.e.a.177.1		2	63.25	even	3
196.10.e.b.165.1		2	63.61	odd	6
196.10.e.b.177.1		2	63.52	odd	6
256.10.b.b.129.1		2	144.115	odd	12
256.10.b.b.129.2		2	144.43	odd	12
256.10.b.j.129.1		2	144.133	even	12
256.10.b.j.129.2		2	144.61	even	12
324.10.e.b.109.1		2	9.5	odd	6
324.10.e.b.217.1		2	3.2	odd	2
324.10.e.e.109.1		2	9.4	even	3	inner
324.10.e.e.217.1		2	1.1	even	1	trivial
400.10.a.k.1.1		1	180.79	odd	6
400.10.c.a.49.1		2	180.43	even	12
400.10.c.a.49.2		2	180.7	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	324.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(333.000 + 576.773i) q^{5} +(3164.00 - 5480.21i) q^{7} +O(q^{10})\)	\(q+(333.000 + 576.773i) q^{5} +(3164.00 - 5480.21i) q^{7} +(15210.0 - 26344.5i) q^{11} +(16169.0 + 28005.5i) q^{13} +590994. q^{17} +34676.0 q^{19} +(-524268. - 908059. i) q^{23} +(754784. - 1.30733e6i) q^{25} +(-2.20470e6 + 3.81866e6i) q^{29} +(3.70059e6 + 6.40961e6i) q^{31} +4.21445e6 q^{35} +1.02345e7 q^{37} +(-9.17637e6 - 1.58939e7i) q^{41} +(126170. - 218533. i) q^{43} +(2.47586e7 - 4.28831e7i) q^{47} +(155012. + 268488. i) q^{49} -6.63969e7 q^{53} +2.02597e7 q^{55} +(3.07619e7 + 5.32811e7i) q^{59} +(-1.78193e7 + 3.08640e7i) q^{61} +(-1.07686e7 + 1.86517e7i) q^{65} +(-9.08712e7 - 1.57394e8i) q^{67} +9.09050e7 q^{71} -2.62979e8 q^{73} +(-9.62489e7 - 1.66708e8i) q^{77} +(5.82514e7 - 1.00894e8i) q^{79} +(4.78186e6 - 8.28243e6i) q^{83} +(1.96801e8 + 3.40869e8i) q^{85} +6.11827e8 q^{89} +2.04635e8 q^{91} +(1.15471e7 + 2.00002e7i) q^{95} +(1.29656e8 - 2.24571e8i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 666 q^{5} + 6328 q^{7}+O(q^{10}) \) 2 * q + 666 * q^5 + 6328 * q^7	\( 2 q + 666 q^{5} + 6328 q^{7} + 30420 q^{11} + 32338 q^{13} + 1181988 q^{17} + 69352 q^{19} - 1048536 q^{23} + 1509569 q^{25} - 4409406 q^{29} + 7401184 q^{31} + 8428896 q^{35} + 20469004 q^{37} - 18352746 q^{41} + 252340 q^{43} + 49517136 q^{47} + 310023 q^{49} - 132793812 q^{53} + 40519440 q^{55} + 61523748 q^{59} - 35638622 q^{61} - 21537108 q^{65} - 181742372 q^{67} + 181809936 q^{71} - 525957356 q^{73} - 192497760 q^{77} + 116502832 q^{79} + 9563724 q^{83} + 393602004 q^{85} + 1223653428 q^{89} + 409269728 q^{91} + 23094216 q^{95} + 259312798 q^{97}+O(q^{100}) \) 2 * q + 666 * q^5 + 6328 * q^7 + 30420 * q^11 + 32338 * q^13 + 1181988 * q^17 + 69352 * q^19 - 1048536 * q^23 + 1509569 * q^25 - 4409406 * q^29 + 7401184 * q^31 + 8428896 * q^35 + 20469004 * q^37 - 18352746 * q^41 + 252340 * q^43 + 49517136 * q^47 + 310023 * q^49 - 132793812 * q^53 + 40519440 * q^55 + 61523748 * q^59 - 35638622 * q^61 - 21537108 * q^65 - 181742372 * q^67 + 181809936 * q^71 - 525957356 * q^73 - 192497760 * q^77 + 116502832 * q^79 + 9563724 * q^83 + 393602004 * q^85 + 1223653428 * q^89 + 409269728 * q^91 + 23094216 * q^95 + 259312798 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more