LMFDB - Embedded newform 245.10.a.m.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,10,Mod(1,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("245.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$N$	$=$	$245 = 5 \cdot 7^{2}$
Weight:	$k$	$=$	$10$
Character orbit:	$[\chi]$	$=$	245.a (trivial)

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:	yes
Analytic conductor:	$126.183779860$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{13} - x^{12} - 5109 x^{11} + 3203 x^{10} + 9635922 x^{9} + 242128 x^{8} - 8405086048 x^{7} + \cdots - 96\!\cdots\!52$ x^13 - x^12 - 5109x^11 + 3203x^10 + 9635922x^9 + 242128x^8 - 8405086048x^7 - 4775917264x^6 + 3475841466656x^5 + 1485626212224x^4 - 636895157285888x^3 + 323463590100992x^2 + 40992624146128896*x - 96856528223895552
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$2^{14}\cdot 3^{3}\cdot 5^{3}\cdot 7^{7}$
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.56137$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56137 q^{2} +177.556 q^{3} -505.439 q^{4} +625.000 q^{5} -454.786 q^{6} +2606.03 q^{8} +11843.1 q^{9} -1600.85 q^{10} +61420.1 q^{11} -89743.7 q^{12} -124067. q^{13} +110972. q^{15} +252110. q^{16} -378822. q^{17} -30334.5 q^{18} +723503. q^{19} -315900. q^{20} -157319. q^{22} +550898. q^{23} +462717. q^{24} +390625. q^{25} +317781. q^{26} -1.39202e6 q^{27} -3.62757e6 q^{29} -284241. q^{30} +9.99103e6 q^{31} -1.98004e6 q^{32} +1.09055e7 q^{33} +970303. q^{34} -5.98596e6 q^{36} +4.29506e6 q^{37} -1.85316e6 q^{38} -2.20288e7 q^{39} +1.62877e6 q^{40} -3.15614e7 q^{41} +2.85304e7 q^{43} -3.10441e7 q^{44} +7.40193e6 q^{45} -1.41105e6 q^{46} +253613. q^{47} +4.47636e7 q^{48} -1.00053e6 q^{50} -6.72621e7 q^{51} +6.27083e7 q^{52} -3.77798e7 q^{53} +3.56548e6 q^{54} +3.83876e7 q^{55} +1.28462e8 q^{57} +9.29154e6 q^{58} -5.52319e6 q^{59} -5.60898e7 q^{60} +1.08962e8 q^{61} -2.55907e7 q^{62} -1.24009e8 q^{64} -7.75418e7 q^{65} -2.79330e7 q^{66} +1.05611e8 q^{67} +1.91472e8 q^{68} +9.78153e7 q^{69} +3.77844e8 q^{71} +3.08635e7 q^{72} +3.95504e8 q^{73} -1.10012e7 q^{74} +6.93578e7 q^{75} -3.65687e8 q^{76} +5.64238e7 q^{78} -1.08755e8 q^{79} +1.57569e8 q^{80} -4.80269e8 q^{81} +8.08402e7 q^{82} -1.26402e8 q^{83} -2.36764e8 q^{85} -7.30768e7 q^{86} -6.44097e8 q^{87} +1.60063e8 q^{88} -2.22530e8 q^{89} -1.89591e7 q^{90} -2.78446e8 q^{92} +1.77397e9 q^{93} -649597. q^{94} +4.52189e8 q^{95} -3.51567e8 q^{96} +1.34841e9 q^{97} +7.27404e8 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$13 q - q^{2} + 268 q^{3} + 3563 q^{4} + 8125 q^{5} + 3040 q^{6} - 4695 q^{8} + 82107 q^{9} - 625 q^{10} + 129087 q^{11} + 356068 q^{12} + 35889 q^{13} + 167500 q^{15} + 1379187 q^{16} + 251650 q^{17} + 391089 q^{18}+ \cdots + 5266142099 q^{99}+O(q^{100})$ 13 * q - q^2 + 268 * q^3 + 3563 * q^4 + 8125 * q^5 + 3040 * q^6 - 4695 * q^8 + 82107 * q^9 - 625 * q^10 + 129087 * q^11 + 356068 * q^12 + 35889 * q^13 + 167500 * q^15 + 1379187 * q^16 + 251650 * q^17 + 391089 * q^18 - 22537 * q^19 + 2226875 * q^20 - 867693 * q^22 + 1640451 * q^23 + 3300104 * q^24 + 5078125 * q^25 - 215949 * q^26 + 4833346 * q^27 + 175192 * q^29 + 1900000 * q^30 + 3363236 * q^31 + 11618029 * q^32 + 1855346 * q^33 + 30084718 * q^34 + 2860133 * q^36 + 57134155 * q^37 + 28383363 * q^38 - 10216786 * q^39 - 2934375 * q^40 + 46043487 * q^41 - 23472776 * q^43 + 171806579 * q^44 + 51316875 * q^45 - 53075341 * q^46 - 1336787 * q^47 + 304545376 * q^48 - 390625 * q^50 + 234254040 * q^51 + 80069087 * q^52 + 122467755 * q^53 - 99983754 * q^54 + 80679375 * q^55 + 32652030 * q^57 + 37365152 * q^58 - 136056496 * q^59 + 222542500 * q^60 - 50448822 * q^61 - 109231036 * q^62 + 1109008839 * q^64 + 22430625 * q^65 - 500348610 * q^66 + 585418818 * q^67 + 480342846 * q^68 - 521416036 * q^69 + 497194080 * q^71 - 870751121 * q^72 - 346232592 * q^73 - 613439215 * q^74 + 104687500 * q^75 - 1436195213 * q^76 - 327612138 * q^78 + 136453862 * q^79 + 861991875 * q^80 - 344488883 * q^81 - 224863259 * q^82 - 523042314 * q^83 + 157281250 * q^85 - 2285275668 * q^86 + 2310323838 * q^87 - 1816859183 * q^88 - 843350780 * q^89 + 244430625 * q^90 - 172327913 * q^92 + 198172924 * q^93 + 2777934057 * q^94 - 14085625 * q^95 - 1583073484 * q^96 + 694973158 * q^97 + 5266142099 * q^99

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

)

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

$2$	−2.56137	−0.113197	−0.0565987	−	0.998397i	$-0.518026\pi$
$2$	−2.56137	−0.113197	−0.0565987	+	0.998397i	$0.518026\pi$
$3$	177.556	1.26558	0.632790	−	0.774324i	$-0.281910\pi$
$3$	177.556	1.26558	0.632790	+	0.774324i	$0.281910\pi$
$4$	−505.439	−0.987186
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	−454.786	−0.143260
$7$	0	0
$7$	0	0
$8$	2606.03	0.224944
$9$	11843.1	0.601691
$10$	−1600.85	−0.0506234
$11$	61420.1	1.26486	0.632431	−	0.774616i	$-0.282057\pi$
$11$	61420.1	1.26486	0.632431	+	0.774616i	$0.282057\pi$
$12$	−89743.7	−1.24936
$13$	−124067.	−1.20479	−0.602394	−	0.798199i	$-0.705786\pi$
$13$	−124067.	−1.20479	−0.602394	+	0.798199i	$0.705786\pi$
$14$	0	0
$15$	110972.	0.565984
$16$	252110.	0.961723
$17$	−378822.	−1.10006	−0.550029	−	0.835146i	$-0.685383\pi$
$17$	−378822.	−1.10006	−0.550029	+	0.835146i	$0.685383\pi$
$18$	−30334.5	−0.0681099
$19$	723503.	1.27365	0.636823	−	0.771010i	$-0.280248\pi$
$19$	723503.	1.27365	0.636823	+	0.771010i	$0.280248\pi$
$20$	−315900.	−0.441483
$21$	0	0
$22$	−157319.	−0.143179
$23$	550898.	0.410484	0.205242	−	0.978711i	$-0.434202\pi$
$23$	550898.	0.410484	0.205242	+	0.978711i	$0.434202\pi$
$24$	462717.	0.284685
$25$	390625.	0.200000
$26$	317781.	0.136379
$27$	−1.39202e6	−0.504091
$28$	0	0
$29$	−3.62757e6	−0.952413	−0.476207	−	0.879333i	$-0.657989\pi$
$29$	−3.62757e6	−0.952413	−0.476207	+	0.879333i	$0.657989\pi$
$30$	−284241.	−0.0640680
$31$	9.99103e6	1.94304	0.971522	−	0.236948i	$-0.0761472\pi$
$31$	9.99103e6	1.94304	0.971522	+	0.236948i	$0.0761472\pi$
$32$	−1.98004e6	−0.333809
$33$	1.09055e7	1.60078
$34$	970303.	0.124524
$35$	0	0
$36$	−5.98596e6	−0.593981
$37$	4.29506e6	0.376757	0.188379	−	0.982096i	$-0.439677\pi$
$37$	4.29506e6	0.376757	0.188379	+	0.982096i	$0.439677\pi$
$38$	−1.85316e6	−0.144174
$39$	−2.20288e7	−1.52475
$40$	1.62877e6	0.100598
$41$	−3.15614e7	−1.74433	−0.872165	−	0.489212i	$-0.837285\pi$
$41$	−3.15614e7	−1.74433	−0.872165	+	0.489212i	$0.837285\pi$
$42$	0	0
$43$	2.85304e7	1.27262	0.636312	−	0.771432i	$-0.280459\pi$
$43$	2.85304e7	1.27262	0.636312	+	0.771432i	$0.280459\pi$
$44$	−3.10441e7	−1.24866
$45$	7.40193e6	0.269085
$46$	−1.41105e6	−0.0464657
$47$	253613.	0.00758109	0.00379055	−	0.999993i	$-0.498793\pi$
$47$	253613.	0.00758109	0.00379055	+	0.999993i	$0.498793\pi$
$48$	4.47636e7	1.21714
$49$	0	0
$50$	−1.00053e6	−0.0226395
$51$	−6.72621e7	−1.39221
$52$	6.27083e7	1.18935
$53$	−3.77798e7	−0.657686	−0.328843	−	0.944385i	$-0.606659\pi$
$53$	−3.77798e7	−0.657686	−0.328843	+	0.944385i	$0.606659\pi$
$54$	3.56548e6	0.0570618
$55$	3.83876e7	0.565664
$56$	0	0
$57$	1.28462e8	1.61190
$58$	9.29154e6	0.107811
$59$	−5.52319e6	−0.0593411	−0.0296705	−	0.999560i	$-0.509446\pi$
$59$	−5.52319e6	−0.0593411	−0.0296705	+	0.999560i	$0.509446\pi$
$60$	−5.60898e7	−0.558732
$61$	1.08962e8	1.00761	0.503805	−	0.863817i	$-0.331933\pi$
$61$	1.08962e8	1.00761	0.503805	+	0.863817i	$0.331933\pi$
$62$	−2.55907e7	−0.219948
$63$	0	0
$64$	−1.24009e8	−0.923937
$65$	−7.75418e7	−0.538798
$66$	−2.79330e7	−0.181205
$67$	1.05611e8	0.640284	0.320142	−	0.947370i	$-0.396269\pi$
$67$	1.05611e8	0.640284	0.320142	+	0.947370i	$0.396269\pi$
$68$	1.91472e8	1.08596
$69$	9.78153e7	0.519500
$70$	0	0
$71$	3.77844e8	1.76461	0.882307	−	0.470675i	$-0.155990\pi$
$71$	3.77844e8	1.76461	0.882307	+	0.470675i	$0.155990\pi$
$72$	3.08635e7	0.135347
$73$	3.95504e8	1.63004	0.815019	−	0.579435i	$-0.196727\pi$
$73$	3.95504e8	1.63004	0.815019	+	0.579435i	$0.196727\pi$
$74$	−1.10012e7	−0.0426480
$75$	6.93578e7	0.253116
$76$	−3.65687e8	−1.25733
$77$	0	0
$78$	5.64238e7	0.172598
$79$	−1.08755e8	−0.314144	−0.157072	−	0.987587i	$-0.550205\pi$
$79$	−1.08755e8	−0.314144	−0.157072	+	0.987587i	$0.550205\pi$
$80$	1.57569e8	0.430096
$81$	−4.80269e8	−1.23966
$82$	8.08402e7	0.197454
$83$	−1.26402e8	−0.292350	−0.146175	−	0.989259i	$-0.546696\pi$
$83$	−1.26402e8	−0.292350	−0.146175	+	0.989259i	$0.546696\pi$
$84$	0	0
$85$	−2.36764e8	−0.491961
$86$	−7.30768e7	−0.144058
$87$	−6.44097e8	−1.20535
$88$	1.60063e8	0.284524
$89$	−2.22530e8	−0.375953	−0.187977	−	0.982174i	$-0.560193\pi$
$89$	−2.22530e8	−0.375953	−0.187977	+	0.982174i	$0.560193\pi$
$90$	−1.89591e7	−0.0304597
$91$	0	0
$92$	−2.78446e8	−0.405224
$93$	1.77397e9	2.45908
$94$	−649597.	−0.000858160 0
$95$	4.52189e8	0.569592
$96$	−3.51567e8	−0.422462
$97$	1.34841e9	1.54650	0.773251	−	0.634100i	$-0.218629\pi$
$97$	1.34841e9	1.54650	0.773251	+	0.634100i	$0.218629\pi$
$98$	0	0
$99$	7.27404e8	0.761057
$100$	−1.97437e8	−0.197437
$101$	−2.82967e8	−0.270576	−0.135288	−	0.990806i	$-0.543196\pi$
$101$	−2.82967e8	−0.270576	−0.135288	+	0.990806i	$0.543196\pi$
$102$	1.72283e8	0.157595
$103$	−5.68288e8	−0.497509	−0.248755	−	0.968567i	$-0.580021\pi$
$103$	−5.68288e8	−0.497509	−0.248755	+	0.968567i	$0.580021\pi$
$104$	−3.23322e8	−0.271010
$105$	0	0
$106$	9.67680e7	0.0744484
$107$	−7.04831e7	−0.0519826	−0.0259913	−	0.999662i	$-0.508274\pi$
$107$	−7.04831e7	−0.0519826	−0.0259913	+	0.999662i	$0.508274\pi$
$108$	7.03583e8	0.497632
$109$	1.37924e9	0.935881	0.467941	−	0.883760i	$-0.344996\pi$
$109$	1.37924e9	0.935881	0.467941	+	0.883760i	$0.344996\pi$
$110$	−9.83246e7	−0.0640317
$111$	7.62614e8	0.476816
$112$	0	0
$113$	2.75046e8	0.158691	0.0793456	−	0.996847i	$-0.474717\pi$
$113$	2.75046e8	0.158691	0.0793456	+	0.996847i	$0.474717\pi$
$114$	−3.29039e8	−0.182463
$115$	3.44312e8	0.183574
$116$	1.83352e9	0.940209
$117$	−1.46933e9	−0.724910
$118$	1.41469e7	0.00671726
$119$	0	0
$120$	2.89198e8	0.127315
$121$	1.41448e9	0.599878
$122$	−2.79093e8	−0.114059
$123$	−5.60391e9	−2.20759
$124$	−5.04986e9	−1.91815
$125$	2.44141e8	0.0894427
$126$	0	0
$127$	3.10782e8	0.106008	0.0530041	−	0.998594i	$-0.483120\pi$
$127$	3.10782e8	0.106008	0.0530041	+	0.998594i	$0.483120\pi$
$128$	1.33141e9	0.438396
$129$	5.06574e9	1.61061
$130$	1.98613e8	0.0609905
$131$	1.82219e9	0.540595	0.270298	−	0.962777i	$-0.412878\pi$
$131$	1.82219e9	0.540595	0.270298	+	0.962777i	$0.412878\pi$
$132$	−5.51207e9	−1.58027
$133$	0	0
$134$	−2.70508e8	−0.0724785
$135$	−8.70014e8	−0.225436
$136$	−9.87224e8	−0.247452
$137$	2.98052e9	0.722851	0.361426	−	0.932401i	$-0.382290\pi$
$137$	2.98052e9	0.722851	0.361426	+	0.932401i	$0.382290\pi$
$138$	−2.50541e8	−0.0588061
$139$	−1.75415e9	−0.398566	−0.199283	−	0.979942i	$-0.563861\pi$
$139$	−1.75415e9	−0.398566	−0.199283	+	0.979942i	$0.563861\pi$
$140$	0	0
$141$	4.50305e7	0.00959447
$142$	−9.67796e8	−0.199750
$143$	−7.62020e9	−1.52389
$144$	2.98576e9	0.578660
$145$	−2.26723e9	−0.425932
$146$	−1.01303e9	−0.184516
$147$	0	0
$148$	−2.17089e9	−0.371930
$149$	−9.07770e8	−0.150882	−0.0754411	−	0.997150i	$-0.524036\pi$
$149$	−9.07770e8	−0.150882	−0.0754411	+	0.997150i	$0.524036\pi$
$150$	−1.77651e8	−0.0286521
$151$	8.00466e8	0.125299	0.0626494	−	0.998036i	$-0.480045\pi$
$151$	8.00466e8	0.125299	0.0626494	+	0.998036i	$0.480045\pi$
$152$	1.88547e9	0.286500
$153$	−4.48643e9	−0.661895
$154$	0	0
$155$	6.24440e9	0.868956
$156$	1.11342e10	1.50522
$157$	9.10237e9	1.19566	0.597828	−	0.801625i	$-0.296031\pi$
$157$	9.10237e9	1.19566	0.597828	+	0.801625i	$0.296031\pi$
$158$	2.78562e8	0.0355603
$159$	−6.70803e9	−0.832354
$160$	−1.23752e9	−0.149284
$161$	0	0
$162$	1.23015e9	0.140326
$163$	9.55974e8	0.106072	0.0530362	−	0.998593i	$-0.483110\pi$
$163$	9.55974e8	0.106072	0.0530362	+	0.998593i	$0.483110\pi$
$164$	1.59524e10	1.72198
$165$	6.81594e9	0.715892
$166$	3.23762e8	0.0330933
$167$	−1.37955e9	−0.137250	−0.0686251	−	0.997643i	$-0.521861\pi$
$167$	−1.37955e9	−0.137250	−0.0686251	+	0.997643i	$0.521861\pi$
$168$	0	0
$169$	4.78808e9	0.451514
$170$	6.06439e8	0.0556887
$171$	8.56851e9	0.766342
$172$	−1.44204e10	−1.25632
$173$	2.24196e10	1.90292	0.951460	−	0.307773i	$-0.0995836\pi$
$173$	2.24196e10	1.90292	0.951460	+	0.307773i	$0.0995836\pi$
$174$	1.64977e9	0.136443
$175$	0	0
$176$	1.54846e10	1.21645
$177$	−9.80674e8	−0.0751009
$178$	5.69981e8	0.0425569
$179$	−6.40788e9	−0.466526	−0.233263	−	0.972414i	$-0.574940\pi$
$179$	−6.40788e9	−0.466526	−0.233263	+	0.972414i	$0.574940\pi$
$180$	−3.74123e9	−0.265637
$181$	−9.27682e8	−0.0642459	−0.0321230	−	0.999484i	$-0.510227\pi$
$181$	−9.27682e8	−0.0642459	−0.0321230	+	0.999484i	$0.510227\pi$
$182$	0	0
$183$	1.93469e10	1.27521
$184$	1.43566e9	0.0923361
$185$	2.68441e9	0.168491
$186$	−4.54378e9	−0.278361
$187$	−2.32673e10	−1.39142
$188$	−1.28186e8	−0.00748395
$189$	0	0
$190$	−1.15822e9	−0.0644764
$191$	1.19777e10	0.651215	0.325608	−	0.945505i	$-0.394431\pi$
$191$	1.19777e10	0.651215	0.325608	+	0.945505i	$0.394431\pi$
$192$	−2.20185e10	−1.16932
$193$	2.81326e10	1.45949	0.729746	−	0.683718i	$-0.239638\pi$
$193$	2.81326e10	1.45949	0.729746	+	0.683718i	$0.239638\pi$
$194$	−3.45378e9	−0.175060
$195$	−1.37680e10	−0.681891
$196$	0	0
$197$	3.85039e10	1.82141	0.910703	−	0.413062i	$-0.135541\pi$
$197$	3.85039e10	1.82141	0.910703	+	0.413062i	$0.135541\pi$
$198$	−1.86315e9	−0.0861497
$199$	3.31316e10	1.49763	0.748813	−	0.662781i	$-0.230624\pi$
$199$	3.31316e10	1.49763	0.748813	+	0.662781i	$0.230624\pi$
$200$	1.01798e9	0.0449889
$201$	1.87519e10	0.810330
$202$	7.24782e8	0.0306285
$203$	0	0
$204$	3.39969e10	1.37437
$205$	−1.97259e10	−0.780088
$206$	1.45559e9	0.0563168
$207$	6.52434e9	0.246985
$208$	−3.12785e10	−1.15867
$209$	4.44376e10	1.61099
$210$	0	0
$211$	3.03122e10	1.05280	0.526401	−	0.850236i	$-0.323541\pi$
$211$	3.03122e10	1.05280	0.526401	+	0.850236i	$0.323541\pi$
$212$	1.90954e10	0.649259
$213$	6.70884e10	2.23326
$214$	1.80533e8	0.00588430
$215$	1.78315e10	0.569135
$216$	−3.62766e9	−0.113393
$217$	0	0
$218$	−3.53274e9	−0.105939
$219$	7.02240e10	2.06294
$220$	−1.94026e10	−0.558416
$221$	4.69993e10	1.32534
$222$	−1.95333e9	−0.0539744
$223$	1.91220e10	0.517798	0.258899	−	0.965904i	$-0.416640\pi$
$223$	1.91220e10	0.517798	0.258899	+	0.965904i	$0.416640\pi$
$224$	0	0
$225$	4.62621e9	0.120338
$226$	−7.04495e8	−0.0179634
$227$	7.97902e9	0.199450	0.0997249	−	0.995015i	$-0.468204\pi$
$227$	7.97902e9	0.199450	0.0997249	+	0.995015i	$0.468204\pi$
$228$	−6.49298e10	−1.59125
$229$	2.88522e10	0.693298	0.346649	−	0.937995i	$-0.387320\pi$
$229$	2.88522e10	0.693298	0.346649	+	0.937995i	$0.387320\pi$
$230$	−8.81908e8	−0.0207801
$231$	0	0
$232$	−9.45358e9	−0.214240
$233$	6.91973e10	1.53811	0.769055	−	0.639182i	$-0.220727\pi$
$233$	6.91973e10	1.53811	0.769055	+	0.639182i	$0.220727\pi$
$234$	3.76350e9	0.0820580
$235$	1.58508e8	0.00339037
$236$	2.79164e9	0.0585807
$237$	−1.93101e10	−0.397574
$238$	0	0
$239$	−9.68936e10	−1.92090	−0.960450	−	0.278454i	$-0.910178\pi$
$239$	−9.68936e10	−1.92090	−0.960450	+	0.278454i	$0.910178\pi$
$240$	2.79773e10	0.544320
$241$	3.79341e10	0.724357	0.362179	−	0.932109i	$-0.382033\pi$
$241$	3.79341e10	0.724357	0.362179	+	0.932109i	$0.382033\pi$
$242$	−3.62300e9	−0.0679046
$243$	−5.78755e10	−1.06480
$244$	−5.50739e10	−0.994699
$245$	0	0
$246$	1.43537e10	0.249893
$247$	−8.97627e10	−1.53447
$248$	2.60370e10	0.437077
$249$	−2.24435e10	−0.369993
$250$	−6.25333e8	−0.0101247
$251$	−1.01212e11	−1.60954	−0.804770	−	0.593587i	$-0.797711\pi$
$251$	−1.01212e11	−1.60954	−0.804770	+	0.593587i	$0.797711\pi$
$252$	0	0
$253$	3.38362e10	0.519206
$254$	−7.96027e8	−0.0119999
$255$	−4.20388e10	−0.622616
$256$	6.00822e10	0.874312
$257$	−8.96566e10	−1.28199	−0.640993	−	0.767547i	$-0.721477\pi$
$257$	−8.96566e10	−1.28199	−0.640993	+	0.767547i	$0.721477\pi$
$258$	−1.29752e10	−0.182317
$259$	0	0
$260$	3.91927e10	0.531894
$261$	−4.29617e10	−0.573059
$262$	−4.66729e9	−0.0611940
$263$	5.75178e10	0.741312	0.370656	−	0.928770i	$-0.379133\pi$
$263$	5.75178e10	0.741312	0.370656	+	0.928770i	$0.379133\pi$
$264$	2.84201e10	0.360087
$265$	−2.36124e10	−0.294126
$266$	0	0
$267$	−3.95115e10	−0.475798
$268$	−5.33800e10	−0.632079
$269$	−1.13252e11	−1.31875	−0.659373	−	0.751816i	$-0.729178\pi$
$269$	−1.13252e11	−1.31875	−0.659373	+	0.751816i	$0.729178\pi$
$270$	2.22842e9	0.0255188
$271$	−1.48390e10	−0.167126	−0.0835628	−	0.996503i	$-0.526630\pi$
$271$	−1.48390e10	−0.167126	−0.0835628	+	0.996503i	$0.526630\pi$
$272$	−9.55049e10	−1.05795
$273$	0	0
$274$	−7.63419e9	−0.0818249
$275$	2.39922e10	0.252973
$276$	−4.94397e10	−0.512843
$277$	−5.27359e10	−0.538205	−0.269102	−	0.963112i	$-0.586727\pi$
$277$	−5.27359e10	−0.538205	−0.269102	+	0.963112i	$0.586727\pi$
$278$	4.49302e9	0.0451166
$279$	1.18325e11	1.16911
$280$	0	0
$281$	4.52563e10	0.433013	0.216507	−	0.976281i	$-0.430534\pi$
$281$	4.52563e10	0.433013	0.216507	+	0.976281i	$0.430534\pi$
$282$	−1.15340e8	−0.00108607
$283$	9.89752e10	0.917249	0.458625	−	0.888630i	$-0.348342\pi$
$283$	9.89752e10	0.917249	0.458625	+	0.888630i	$0.348342\pi$
$284$	−1.90977e11	−1.74200
$285$	8.02889e10	0.720864
$286$	1.95181e10	0.172501
$287$	0	0
$288$	−2.34497e10	−0.200850
$289$	2.49186e10	0.210127
$290$	5.80722e9	0.0482144
$291$	2.39419e11	1.95722
$292$	−1.99903e11	−1.60915
$293$	1.17784e11	0.933648	0.466824	−	0.884350i	$-0.345398\pi$
$293$	1.17784e11	0.933648	0.466824	+	0.884350i	$0.345398\pi$
$294$	0	0
$295$	−3.45199e9	−0.0265381
$296$	1.11931e10	0.0847495
$297$	−8.54981e10	−0.637606
$298$	2.32513e9	0.0170795
$299$	−6.83482e10	−0.494546
$300$	−3.50561e10	−0.249873
$301$	0	0
$302$	−2.05029e9	−0.0141835
$303$	−5.02425e10	−0.342436
$304$	1.82402e11	1.22490
$305$	6.81015e10	0.450617
$306$	1.14914e10	0.0749248
$307$	1.98293e11	1.27404	0.637022	−	0.770846i	$-0.280166\pi$
$307$	1.98293e11	1.27404	0.637022	+	0.770846i	$0.280166\pi$
$308$	0	0
$309$	−1.00903e11	−0.629638
$310$	−1.59942e10	−0.0983636
$311$	−2.22587e11	−1.34921	−0.674603	−	0.738181i	$-0.735685\pi$
$311$	−2.22587e11	−1.34921	−0.674603	+	0.738181i	$0.735685\pi$
$312$	−5.74078e10	−0.342985
$313$	−9.30008e10	−0.547693	−0.273846	−	0.961773i	$-0.588296\pi$
$313$	−9.30008e10	−0.547693	−0.273846	+	0.961773i	$0.588296\pi$
$314$	−2.33145e10	−0.135345
$315$	0	0
$316$	5.49692e10	0.310118
$317$	−2.35019e11	−1.30718	−0.653592	−	0.756847i	$-0.726739\pi$
$317$	−2.35019e11	−1.30718	−0.653592	+	0.756847i	$0.726739\pi$
$318$	1.71817e10	0.0942203
$319$	−2.22806e11	−1.20467
$320$	−7.75054e10	−0.413197
$321$	−1.25147e10	−0.0657881
$322$	0	0
$323$	−2.74079e11	−1.40109
$324$	2.42747e11	1.22377
$325$	−4.84636e10	−0.240958
$326$	−2.44860e9	−0.0120071
$327$	2.44892e11	1.18443
$328$	−8.22501e10	−0.392377
$329$	0	0
$330$	−1.74581e10	−0.0810372
$331$	2.15343e11	0.986063	0.493032	−	0.870011i	$-0.335889\pi$
$331$	2.15343e11	0.986063	0.493032	+	0.870011i	$0.335889\pi$
$332$	6.38887e10	0.288604
$333$	5.08668e10	0.226692
$334$	3.53353e9	0.0155364
$335$	6.60069e10	0.286344
$336$	0	0
$337$	−1.40598e11	−0.593808	−0.296904	−	0.954907i	$-0.595954\pi$
$337$	−1.40598e11	−0.593808	−0.296904	+	0.954907i	$0.595954\pi$
$338$	−1.22640e10	−0.0511102
$339$	4.88361e10	0.200836
$340$	1.19670e11	0.485657
$341$	6.13650e11	2.45768
$342$	−2.19471e10	−0.0867480
$343$	0	0
$344$	7.43512e10	0.286270
$345$	6.11345e10	0.232328
$346$	−5.74248e10	−0.215406
$347$	−3.78195e11	−1.40034	−0.700169	−	0.713977i	$-0.746892\pi$
$347$	−3.78195e11	−1.40034	−0.700169	+	0.713977i	$0.746892\pi$
$348$	3.25552e11	1.18991
$349$	−1.14065e11	−0.411563	−0.205781	−	0.978598i	$-0.565974\pi$
$349$	−1.14065e11	−0.411563	−0.205781	+	0.978598i	$0.565974\pi$
$350$	0	0
$351$	1.72704e11	0.607323
$352$	−1.21614e11	−0.422223
$353$	−2.46679e11	−0.845562	−0.422781	−	0.906232i	$-0.638946\pi$
$353$	−2.46679e11	−0.845562	−0.422781	+	0.906232i	$0.638946\pi$
$354$	2.51186e9	0.00850123
$355$	2.36152e11	0.789159
$356$	1.12475e11	0.371136
$357$	0	0
$358$	1.64129e10	0.0528095
$359$	−3.46303e11	−1.10035	−0.550175	−	0.835049i	$-0.685439\pi$
$359$	−3.46303e11	−1.10035	−0.550175	+	0.835049i	$0.685439\pi$
$360$	1.92897e10	0.0605291
$361$	2.00769e11	0.622176
$362$	2.37613e9	0.00727248
$363$	2.51149e11	0.759193
$364$	0	0
$365$	2.47190e11	0.728975
$366$	−4.95545e10	−0.144351
$367$	3.46091e9	0.00995847	0.00497924	−	0.999988i	$-0.498415\pi$
$367$	3.46091e9	0.00995847	0.00497924	+	0.999988i	$0.498415\pi$
$368$	1.38887e11	0.394772
$369$	−3.73784e11	−1.04955
$370$	−6.87577e9	−0.0190728
$371$	0	0
$372$	−8.96633e11	−2.42757
$373$	−3.48180e11	−0.931354	−0.465677	−	0.884955i	$-0.654189\pi$
$373$	−3.48180e11	−0.931354	−0.465677	+	0.884955i	$0.654189\pi$
$374$	5.95961e10	0.157505
$375$	4.33486e10	0.113197
$376$	6.60925e8	0.00170532
$377$	4.50062e11	1.14746
$378$	0	0
$379$	−9.54829e10	−0.237711	−0.118856	−	0.992912i	$-0.537923\pi$
$379$	−9.54829e10	−0.237711	−0.118856	+	0.992912i	$0.537923\pi$
$380$	−2.28554e11	−0.562294
$381$	5.51812e10	0.134162
$382$	−3.06794e10	−0.0737159
$383$	3.75656e11	0.892063	0.446032	−	0.895017i	$-0.352837\pi$
$383$	3.75656e11	0.892063	0.446032	+	0.895017i	$0.352837\pi$
$384$	2.36400e11	0.554825
$385$	0	0
$386$	−7.20578e10	−0.165211
$387$	3.37888e11	0.765727
$388$	−6.81542e11	−1.52669
$389$	5.25576e11	1.16376	0.581878	−	0.813276i	$-0.302318\pi$
$389$	5.25576e11	1.16376	0.581878	+	0.813276i	$0.302318\pi$
$390$	3.52649e10	0.0771883
$391$	−2.08693e11	−0.451556
$392$	0	0
$393$	3.23540e11	0.684166
$394$	−9.86226e10	−0.206178
$395$	−6.79721e10	−0.140489
$396$	−3.67658e11	−0.751305
$397$	−5.30855e11	−1.07255	−0.536276	−	0.844042i	$-0.680170\pi$
$397$	−5.30855e11	−1.07255	−0.536276	+	0.844042i	$0.680170\pi$
$398$	−8.48621e10	−0.169527
$399$	0	0
$400$	9.84805e10	0.192345
$401$	−2.40177e11	−0.463855	−0.231928	−	0.972733i	$-0.574503\pi$
$401$	−2.40177e11	−0.463855	−0.231928	+	0.972733i	$0.574503\pi$
$402$	−4.80303e10	−0.0917273
$403$	−1.23956e12	−2.34096
$404$	1.43023e11	0.267109
$405$	−3.00168e11	−0.554392
$406$	0	0
$407$	2.63803e11	0.476546
$408$	−1.75287e11	−0.313170
$409$	−3.29172e11	−0.581659	−0.290830	−	0.956775i	$-0.593931\pi$
$409$	−3.29172e11	−0.581659	−0.290830	+	0.956775i	$0.593931\pi$
$410$	5.05252e10	0.0883040
$411$	5.29208e11	0.914826
$412$	2.87235e11	0.491134
$413$	0	0
$414$	−1.67112e10	−0.0279580
$415$	−7.90014e10	−0.130743
$416$	2.45657e11	0.402169
$417$	−3.11460e11	−0.504417
$418$	−1.13821e11	−0.182360
$419$	−9.28534e10	−0.147175	−0.0735876	−	0.997289i	$-0.523445\pi$
$419$	−9.28534e10	−0.147175	−0.0735876	+	0.997289i	$0.523445\pi$
$420$	0	0
$421$	−1.04637e12	−1.62336	−0.811681	−	0.584101i	$-0.801447\pi$
$421$	−1.04637e12	−1.62336	−0.811681	+	0.584101i	$0.801447\pi$
$422$	−7.76407e10	−0.119175
$423$	3.00357e9	0.00456148
$424$	−9.84555e10	−0.147943
$425$	−1.47978e11	−0.220012
$426$	−1.71838e11	−0.252799
$427$	0	0
$428$	3.56249e10	0.0513165
$429$	−1.35301e12	−1.92861
$430$	−4.56730e10	−0.0644246
$431$	1.19221e12	1.66420	0.832099	−	0.554628i	$-0.187139\pi$
$431$	1.19221e12	1.66420	0.832099	+	0.554628i	$0.187139\pi$
$432$	−3.50943e11	−0.484796
$433$	−4.53584e11	−0.620100	−0.310050	−	0.950720i	$-0.600346\pi$
$433$	−4.53584e11	−0.620100	−0.310050	+	0.950720i	$0.600346\pi$
$434$	0	0
$435$	−4.02561e11	−0.539051
$436$	−6.97123e11	−0.923889
$437$	3.98577e11	0.522812
$438$	−1.79869e11	−0.233520
$439$	−3.75167e11	−0.482097	−0.241049	−	0.970513i	$-0.577491\pi$
$439$	−3.75167e11	−0.482097	−0.241049	+	0.970513i	$0.577491\pi$
$440$	1.00039e11	0.127243
$441$	0	0
$442$	−1.20382e11	−0.150025
$443$	9.01687e11	1.11234	0.556172	−	0.831067i	$-0.312270\pi$
$443$	9.01687e11	1.11234	0.556172	+	0.831067i	$0.312270\pi$
$444$	−3.85455e11	−0.470707
$445$	−1.39081e11	−0.168131
$446$	−4.89783e10	−0.0586134
$447$	−1.61180e11	−0.190953
$448$	0	0
$449$	−1.14634e12	−1.33108	−0.665542	−	0.746361i	$-0.731799\pi$
$449$	−1.14634e12	−1.33108	−0.665542	+	0.746361i	$0.731799\pi$
$450$	−1.18494e10	−0.0136220
$451$	−1.93850e12	−2.20634
$452$	−1.39019e11	−0.156658
$453$	1.42127e11	0.158576
$454$	−2.04372e10	−0.0225772
$455$	0	0
$456$	3.34777e11	0.362588
$457$	5.27249e11	0.565448	0.282724	−	0.959201i	$-0.408762\pi$
$457$	5.27249e11	0.565448	0.282724	+	0.959201i	$0.408762\pi$
$458$	−7.39011e10	−0.0784795
$459$	5.27329e11	0.554530
$460$	−1.74029e11	−0.181222
$461$	−1.34068e12	−1.38252	−0.691262	−	0.722605i	$-0.742945\pi$
$461$	−1.34068e12	−1.38252	−0.691262	+	0.722605i	$0.742945\pi$
$462$	0	0
$463$	−9.25590e11	−0.936061	−0.468031	−	0.883712i	$-0.655036\pi$
$463$	−9.25590e11	−0.936061	−0.468031	+	0.883712i	$0.655036\pi$
$464$	−9.14548e11	−0.915958
$465$	1.10873e12	1.09973
$466$	−1.77240e11	−0.174110
$467$	5.16869e11	0.502869	0.251434	−	0.967874i	$-0.419098\pi$
$467$	5.16869e11	0.502869	0.251434	+	0.967874i	$0.419098\pi$
$468$	7.42660e11	0.715622
$469$	0	0
$470$	−4.05998e8	−0.000383781 0
$471$	1.61618e12	1.51320
$472$	−1.43936e10	−0.0133484
$473$	1.75234e12	1.60969
$474$	4.94603e10	0.0450043
$475$	2.82618e11	0.254729
$476$	0	0
$477$	−4.47430e11	−0.395724
$478$	2.48180e11	0.217441
$479$	−1.18715e12	−1.03038	−0.515189	−	0.857077i	$-0.672278\pi$
$479$	−1.18715e12	−1.03038	−0.515189	+	0.857077i	$0.672278\pi$
$480$	−2.19729e11	−0.188931
$481$	−5.32875e11	−0.453913
$482$	−9.71630e10	−0.0819954
$483$	0	0
$484$	−7.14934e11	−0.592191
$485$	8.42759e11	0.691617
$486$	1.48240e11	0.120532
$487$	−9.13222e10	−0.0735692	−0.0367846	−	0.999323i	$-0.511712\pi$
$487$	−9.13222e10	−0.0735692	−0.0367846	+	0.999323i	$0.511712\pi$
$488$	2.83960e11	0.226656
$489$	1.69739e11	0.134243
$490$	0	0
$491$	1.56534e12	1.21547	0.607733	−	0.794141i	$-0.292079\pi$
$491$	1.56534e12	1.21547	0.607733	+	0.794141i	$0.292079\pi$
$492$	2.83244e12	2.17930
$493$	1.37421e12	1.04771
$494$	2.29915e11	0.173699
$495$	4.54627e11	0.340355
$496$	2.51884e12	1.86867
$497$	0	0
$498$	5.74859e10	0.0418822
$499$	1.38428e12	0.999471	0.499735	−	0.866178i	$-0.333431\pi$
$499$	1.38428e12	0.999471	0.499735	+	0.866178i	$0.333431\pi$
$500$	−1.23398e11	−0.0882966
$501$	−2.44947e11	−0.173701
$502$	2.59242e11	0.182196
$503$	−4.84565e11	−0.337517	−0.168759	−	0.985657i	$-0.553976\pi$
$503$	−4.84565e11	−0.337517	−0.168759	+	0.985657i	$0.553976\pi$
$504$	0	0
$505$	−1.76854e11	−0.121005
$506$	−8.66670e10	−0.0587728
$507$	8.50152e11	0.571427
$508$	−1.57082e11	−0.104650
$509$	−1.74471e12	−1.15211	−0.576055	−	0.817411i	$-0.695409\pi$
$509$	−1.74471e12	−1.15211	−0.576055	+	0.817411i	$0.695409\pi$
$510$	1.07677e11	0.0704785
$511$	0	0
$512$	−8.35574e11	−0.537366
$513$	−1.00713e12	−0.642034
$514$	2.29643e11	0.145118
$515$	−3.55180e11	−0.222493
$516$	−2.56043e12	−1.58997
$517$	1.55770e10	0.00958904
$518$	0	0
$519$	3.98073e12	2.40830
$520$	−2.02077e11	−0.121199
$521$	−7.49241e11	−0.445504	−0.222752	−	0.974875i	$-0.571504\pi$
$521$	−7.49241e11	−0.445504	−0.222752	+	0.974875i	$0.571504\pi$
$522$	1.10041e11	0.0648688
$523$	1.88714e12	1.10292	0.551462	−	0.834200i	$-0.314070\pi$
$523$	1.88714e12	1.10292	0.551462	+	0.834200i	$0.314070\pi$
$524$	−9.21005e11	−0.533668
$525$	0	0
$526$	−1.47324e11	−0.0839146
$527$	−3.78483e12	−2.13746
$528$	2.74938e12	1.53951
$529$	−1.49766e12	−0.831503
$530$	6.04800e10	0.0332943
$531$	−6.54116e10	−0.0357050
$532$	0	0
$533$	3.91572e12	2.10155
$534$	1.01203e11	0.0538592
$535$	−4.40519e10	−0.0232473
$536$	2.75226e11	0.144028
$537$	−1.13776e12	−0.590425
$538$	2.90080e11	0.149279
$539$	0	0
$540$	4.39739e11	0.222548
$541$	6.00505e11	0.301390	0.150695	−	0.988580i	$-0.451849\pi$
$541$	6.00505e11	0.301390	0.150695	+	0.988580i	$0.451849\pi$
$542$	3.80081e10	0.0189182
$543$	−1.64715e11	−0.0813083
$544$	7.50082e11	0.367209
$545$	8.62025e11	0.418539
$546$	0	0
$547$	3.39461e12	1.62124	0.810619	−	0.585573i	$-0.199131\pi$
$547$	3.39461e12	1.62124	0.810619	+	0.585573i	$0.199131\pi$
$548$	−1.50647e12	−0.713589
$549$	1.29045e12	0.606270
$550$	−6.14529e10	−0.0286358
$551$	−2.62456e12	−1.21304
$552$	2.54910e11	0.116859
$553$	0	0
$554$	1.35076e11	0.0609234
$555$	4.76634e11	0.213239
$556$	8.86617e11	0.393459
$557$	1.30071e12	0.572572	0.286286	−	0.958144i	$-0.407579\pi$
$557$	1.30071e12	0.572572	0.286286	+	0.958144i	$0.407579\pi$
$558$	−3.03073e11	−0.132341
$559$	−3.53968e12	−1.53324
$560$	0	0
$561$	−4.13125e12	−1.76096
$562$	−1.15918e11	−0.0490160
$563$	−1.91933e12	−0.805123	−0.402562	−	0.915393i	$-0.631880\pi$
$563$	−1.91933e12	−0.805123	−0.402562	+	0.915393i	$0.631880\pi$
$564$	−2.27602e10	−0.00947153
$565$	1.71904e11	0.0709689
$566$	−2.53512e11	−0.103830
$567$	0	0
$568$	9.84673e11	0.396940
$569$	4.27941e12	1.71151	0.855754	−	0.517383i	$-0.173094\pi$
$569$	4.27941e12	1.71151	0.855754	+	0.517383i	$0.173094\pi$
$570$	−2.05649e11	−0.0816000
$571$	−9.47095e11	−0.372847	−0.186424	−	0.982469i	$-0.559690\pi$
$571$	−9.47095e11	−0.372847	−0.186424	+	0.982469i	$0.559690\pi$
$572$	3.85155e12	1.50436
$573$	2.12672e12	0.824165
$574$	0	0
$575$	2.15195e11	0.0820968
$576$	−1.46865e12	−0.555925
$577$	1.12407e12	0.422183	0.211091	−	0.977466i	$-0.432298\pi$
$577$	1.12407e12	0.422183	0.211091	+	0.977466i	$0.432298\pi$
$578$	−6.38255e10	−0.0237859
$579$	4.99511e12	1.84710
$580$	1.14595e12	0.420474
$581$	0	0
$582$	−6.13239e11	−0.221552
$583$	−2.32044e12	−0.831883
$584$	1.03070e12	0.366668
$585$	−9.18334e11	−0.324190
$586$	−3.01689e11	−0.105687
$587$	−2.55175e12	−0.887089	−0.443545	−	0.896252i	$-0.646279\pi$
$587$	−2.55175e12	−0.887089	−0.443545	+	0.896252i	$0.646279\pi$
$588$	0	0
$589$	7.22854e12	2.47475
$590$	8.84181e9	0.00300405
$591$	6.83659e12	2.30513
$592$	1.08283e12	0.362336
$593$	1.17380e11	0.0389804	0.0194902	−	0.999810i	$-0.493796\pi$
$593$	1.17380e11	0.0389804	0.0194902	+	0.999810i	$0.493796\pi$
$594$	2.18992e11	0.0721754
$595$	0	0
$596$	4.58823e11	0.148949
$597$	5.88271e12	1.89537
$598$	1.75065e11	0.0559814
$599$	4.62131e11	0.146671	0.0733355	−	0.997307i	$-0.476636\pi$
$599$	4.62131e11	0.146671	0.0733355	+	0.997307i	$0.476636\pi$
$600$	1.80749e11	0.0569370
$601$	−3.15713e12	−0.987091	−0.493545	−	0.869720i	$-0.664299\pi$
$601$	−3.15713e12	−0.987091	−0.493545	+	0.869720i	$0.664299\pi$
$602$	0	0
$603$	1.25076e12	0.385253
$604$	−4.04587e11	−0.123693
$605$	8.84050e11	0.268273
$606$	1.28689e11	0.0387628
$607$	−1.20538e12	−0.360391	−0.180195	−	0.983631i	$-0.557673\pi$
$607$	−1.20538e12	−0.360391	−0.180195	+	0.983631i	$0.557673\pi$
$608$	−1.43256e12	−0.425155
$609$	0	0
$610$	−1.74433e11	−0.0510087
$611$	−3.14650e10	−0.00913361
$612$	2.26762e12	0.653414
$613$	−1.77289e12	−0.507118	−0.253559	−	0.967320i	$-0.581601\pi$
$613$	−1.77289e12	−0.507118	−0.253559	+	0.967320i	$0.581601\pi$
$614$	−5.07901e11	−0.144219
$615$	−3.50244e12	−0.987264
$616$	0	0
$617$	2.48233e12	0.689568	0.344784	−	0.938682i	$-0.387952\pi$
$617$	2.48233e12	0.689568	0.344784	+	0.938682i	$0.387952\pi$
$618$	2.58449e11	0.0712734
$619$	−4.73625e12	−1.29666	−0.648331	−	0.761359i	$-0.724533\pi$
$619$	−4.73625e12	−1.29666	−0.648331	+	0.761359i	$0.724533\pi$
$620$	−3.15616e12	−0.857821
$621$	−7.66863e11	−0.206921
$622$	5.70127e11	0.152727
$623$	0	0
$624$	−5.55368e12	−1.46639
$625$	1.52588e11	0.0400000
$626$	2.38209e11	0.0619974
$627$	7.89016e12	2.03883
$628$	−4.60070e12	−1.18033
$629$	−1.62707e12	−0.414455
$630$	0	0
$631$	−4.14529e12	−1.04093	−0.520467	−	0.853882i	$-0.674242\pi$
$631$	−4.14529e12	−1.04093	−0.520467	+	0.853882i	$0.674242\pi$
$632$	−2.83420e11	−0.0706649
$633$	5.38212e12	1.33241
$634$	6.01970e11	0.147970
$635$	1.94239e11	0.0474083
$636$	3.39050e12	0.821688
$637$	0	0
$638$	5.70688e11	0.136366
$639$	4.47484e12	1.06175
$640$	8.32131e11	0.196057
$641$	−5.77430e12	−1.35095	−0.675473	−	0.737384i	$-0.736061\pi$
$641$	−5.77430e12	−1.35095	−0.675473	+	0.737384i	$0.736061\pi$
$642$	3.20547e10	0.00744705
$643$	−5.07338e12	−1.17044	−0.585219	−	0.810875i	$-0.698991\pi$
$643$	−5.07338e12	−1.17044	−0.585219	+	0.810875i	$0.698991\pi$
$644$	0	0
$645$	3.16609e12	0.720285
$646$	7.02017e11	0.158599
$647$	−5.75157e12	−1.29038	−0.645189	−	0.764023i	$-0.723221\pi$
$647$	−5.75157e12	−1.29038	−0.645189	+	0.764023i	$0.723221\pi$
$648$	−1.25160e12	−0.278854
$649$	−3.39235e11	−0.0750583
$650$	1.24133e11	0.0272758
$651$	0	0
$652$	−4.83187e11	−0.104713
$653$	−2.83020e12	−0.609127	−0.304564	−	0.952492i	$-0.598511\pi$
$653$	−2.83020e12	−0.609127	−0.304564	+	0.952492i	$0.598511\pi$
$654$	−6.27259e11	−0.134075
$655$	1.13887e12	0.241762
$656$	−7.95694e12	−1.67756
$657$	4.68398e12	0.980779
$658$	0	0
$659$	−5.37338e12	−1.10985	−0.554923	−	0.831902i	$-0.687252\pi$
$659$	−5.37338e12	−1.10985	−0.554923	+	0.831902i	$0.687252\pi$
$660$	−3.44504e12	−0.706719
$661$	−2.32341e12	−0.473389	−0.236695	−	0.971584i	$-0.576064\pi$
$661$	−2.32341e12	−0.473389	−0.236695	+	0.971584i	$0.576064\pi$
$662$	−5.51572e11	−0.111620
$663$	8.34500e12	1.67732
$664$	−3.29409e11	−0.0657626
$665$	0	0
$666$	−1.30289e11	−0.0256609
$667$	−1.99843e12	−0.390950
$668$	6.97278e11	0.135492
$669$	3.39522e12	0.655315
$670$	−1.69068e11	−0.0324134
$671$	6.69248e12	1.27449
$672$	0	0
$673$	5.66684e12	1.06481	0.532406	−	0.846489i	$-0.321288\pi$
$673$	5.66684e12	1.06481	0.532406	+	0.846489i	$0.321288\pi$
$674$	3.60124e11	0.0672175
$675$	−5.43759e11	−0.100818
$676$	−2.42009e12	−0.445729
$677$	−3.78584e12	−0.692649	−0.346324	−	0.938115i	$-0.612570\pi$
$677$	−3.78584e12	−0.692649	−0.346324	+	0.938115i	$0.612570\pi$
$678$	−1.25087e11	−0.0227342
$679$	0	0
$680$	−6.17015e11	−0.110664
$681$	1.41672e12	0.252419
$682$	−1.57178e12	−0.278204
$683$	9.08477e12	1.59743	0.798713	−	0.601712i	$-0.205515\pi$
$683$	9.08477e12	1.59743	0.798713	+	0.601712i	$0.205515\pi$
$684$	−4.33086e12	−0.756523
$685$	1.86282e12	0.323269
$686$	0	0
$687$	5.12288e12	0.877423
$688$	7.19280e12	1.22391
$689$	4.68722e12	0.792372
$690$	−1.56588e11	−0.0262989
$691$	−9.23118e12	−1.54030	−0.770151	−	0.637862i	$-0.779819\pi$
$691$	−9.23118e12	−1.54030	−0.770151	+	0.637862i	$0.779819\pi$
$692$	−1.13318e13	−1.87854
$693$	0	0
$694$	9.68695e11	0.158515
$695$	−1.09634e12	−0.178244
$696$	−1.67854e12	−0.271138
$697$	1.19562e13	1.91886
$698$	2.92161e11	0.0465879
$699$	1.22864e13	1.94660
$700$	0	0
$701$	−5.84730e12	−0.914586	−0.457293	−	0.889316i	$-0.651181\pi$
$701$	−5.84730e12	−0.914586	−0.457293	+	0.889316i	$0.651181\pi$
$702$	−4.42358e11	−0.0687474
$703$	3.10749e12	0.479856
$704$	−7.61663e12	−1.16865
$705$	2.81441e10	0.00429078
$706$	6.31834e11	0.0957154
$707$	0	0
$708$	4.95671e11	0.0741385
$709$	−3.81574e12	−0.567114	−0.283557	−	0.958955i	$-0.591515\pi$
$709$	−3.81574e12	−0.567114	−0.283557	+	0.958955i	$0.591515\pi$
$710$	−6.04872e11	−0.0893308
$711$	−1.28800e12	−0.189018
$712$	−5.79921e11	−0.0845685
$713$	5.50404e12	0.797589
$714$	0	0
$715$	−4.76262e12	−0.681505
$716$	3.23879e12	0.460548
$717$	−1.72040e13	−2.43105
$718$	8.87008e11	0.124557
$719$	−1.82131e12	−0.254158	−0.127079	−	0.991893i	$-0.540560\pi$
$719$	−1.82131e12	−0.254158	−0.127079	+	0.991893i	$0.540560\pi$
$720$	1.86610e12	0.258785
$721$	0	0
$722$	−5.14242e11	−0.0704288
$723$	6.73542e12	0.916732
$724$	4.68887e11	0.0634227
$725$	−1.41702e12	−0.190483
$726$	−6.43285e11	−0.0859387
$727$	−6.45622e12	−0.857183	−0.428592	−	0.903498i	$-0.640990\pi$
$727$	−6.45622e12	−0.857183	−0.428592	+	0.903498i	$0.640990\pi$
$728$	0	0
$729$	−8.22987e11	−0.107924
$730$	−6.33143e11	−0.0825181
$731$	−1.08080e13	−1.39996
$732$	−9.77870e12	−1.25887
$733$	1.37462e13	1.75879	0.879394	−	0.476096i	$-0.157948\pi$
$733$	1.37462e13	1.75879	0.879394	+	0.476096i	$0.157948\pi$
$734$	−8.86465e9	−0.00112727
$735$	0	0
$736$	−1.09080e12	−0.137023
$737$	6.48664e12	0.809871
$738$	9.57398e11	0.118806
$739$	1.53823e13	1.89724	0.948619	−	0.316420i	$-0.102481\pi$
$739$	1.53823e13	1.89724	0.948619	+	0.316420i	$0.102481\pi$
$740$	−1.35681e12	−0.166332
$741$	−1.59379e13	−1.94200
$742$	0	0
$743$	6.44915e12	0.776342	0.388171	−	0.921587i	$-0.373107\pi$
$743$	6.44915e12	0.776342	0.388171	+	0.921587i	$0.373107\pi$
$744$	4.62302e12	0.553156
$745$	−5.67357e11	−0.0674765
$746$	8.91817e11	0.105427
$747$	−1.49699e12	−0.175905
$748$	1.17602e13	1.37359
$749$	0	0
$750$	−1.11032e11	−0.0128136
$751$	−2.74018e12	−0.314340	−0.157170	−	0.987572i	$-0.550237\pi$
$751$	−2.74018e12	−0.314340	−0.157170	+	0.987572i	$0.550237\pi$
$752$	6.39385e10	0.00729091
$753$	−1.79708e13	−2.03700
$754$	−1.15277e12	−0.129889
$755$	5.00291e11	0.0560353
$756$	0	0
$757$	−1.18565e13	−1.31227	−0.656136	−	0.754643i	$-0.727810\pi$
$757$	−1.18565e13	−1.31227	−0.656136	+	0.754643i	$0.727810\pi$
$758$	2.44567e11	0.0269083
$759$	6.00782e12	0.657096
$760$	1.17842e12	0.128127
$761$	1.18396e13	1.27969	0.639847	−	0.768502i	$-0.278998\pi$
$761$	1.18396e13	1.27969	0.639847	+	0.768502i	$0.278998\pi$
$762$	−1.41339e11	−0.0151868
$763$	0	0
$764$	−6.05402e12	−0.642871
$765$	−2.80402e12	−0.296009
$766$	−9.62192e11	−0.100979
$767$	6.85244e11	0.0714934
$768$	1.06680e13	1.10651
$769$	−2.48568e12	−0.256316	−0.128158	−	0.991754i	$-0.540907\pi$
$769$	−2.48568e12	−0.256316	−0.128158	+	0.991754i	$0.540907\pi$
$770$	0	0
$771$	−1.59191e13	−1.62246
$772$	−1.42193e13	−1.44079
$773$	5.46173e12	0.550202	0.275101	−	0.961415i	$-0.411289\pi$
$773$	5.46173e12	0.550202	0.275101	+	0.961415i	$0.411289\pi$
$774$	−8.65455e11	−0.0866783
$775$	3.90275e12	0.388609
$776$	3.51401e12	0.347877
$777$	0	0
$778$	−1.34619e12	−0.131734
$779$	−2.28348e13	−2.22166
$780$	6.95889e12	0.673154
$781$	2.32072e13	2.23199
$782$	5.34538e11	0.0511150
$783$	5.04966e12	0.480103
$784$	0	0
$785$	5.68898e12	0.534713
$786$	−8.28704e11	−0.0774459
$787$	−1.01285e13	−0.941153	−0.470577	−	0.882359i	$-0.655954\pi$
$787$	−1.01285e13	−0.941153	−0.470577	+	0.882359i	$0.655954\pi$
$788$	−1.94614e13	−1.79807
$789$	1.02126e13	0.938189
$790$	1.74101e11	0.0159030
$791$	0	0
$792$	1.89564e12	0.171195
$793$	−1.35186e13	−1.21396
$794$	1.35971e12	0.121410
$795$	−4.19252e12	−0.372240
$796$	−1.67460e13	−1.47844
$797$	−1.18226e13	−1.03789	−0.518943	−	0.854809i	$-0.673674\pi$
$797$	−1.18226e13	−1.03789	−0.518943	+	0.854809i	$0.673674\pi$
$798$	0	0
$799$	−9.60744e10	−0.00833964
$800$	−7.73451e11	−0.0667618
$801$	−2.63544e12	−0.226208
$802$	6.15182e11	0.0525072
$803$	2.42919e13	2.06177
$804$	−9.47792e12	−0.799947
$805$	0	0
$806$	3.17496e12	0.264990
$807$	−2.01086e13	−1.66898
$808$	−7.37422e11	−0.0608646
$809$	3.50219e11	0.0287456	0.0143728	−	0.999897i	$-0.495425\pi$
$809$	3.50219e11	0.0287456	0.0143728	+	0.999897i	$0.495425\pi$
$810$	7.68841e11	0.0627558
$811$	3.99021e12	0.323893	0.161946	−	0.986800i	$-0.448223\pi$
$811$	3.99021e12	0.323893	0.161946	+	0.986800i	$0.448223\pi$
$812$	0	0
$813$	−2.63475e12	−0.211511
$814$	−6.75696e11	−0.0539438
$815$	5.97484e11	0.0474370
$816$	−1.69575e13	−1.33892
$817$	2.06418e13	1.62087
$818$	8.43131e11	0.0658423
$819$	0	0
$820$	9.97023e12	0.770092
$821$	1.67758e13	1.28867	0.644333	−	0.764745i	$-0.277135\pi$
$821$	1.67758e13	1.28867	0.644333	+	0.764745i	$0.277135\pi$
$822$	−1.35550e12	−0.103556
$823$	−8.57343e12	−0.651411	−0.325706	−	0.945471i	$-0.605602\pi$
$823$	−8.57343e12	−0.651411	−0.325706	+	0.945471i	$0.605602\pi$
$824$	−1.48098e12	−0.111912
$825$	4.25996e12	0.320157
$826$	0	0
$827$	−4.63367e12	−0.344469	−0.172235	−	0.985056i	$-0.555099\pi$
$827$	−4.63367e12	−0.344469	−0.172235	+	0.985056i	$0.555099\pi$
$828$	−3.29766e12	−0.243820
$829$	1.07635e13	0.791516	0.395758	−	0.918355i	$-0.370482\pi$
$829$	1.07635e13	0.791516	0.395758	+	0.918355i	$0.370482\pi$
$830$	2.02352e11	0.0147998
$831$	−9.36357e12	−0.681141
$832$	1.53854e13	1.11315
$833$	0	0
$834$	7.97762e11	0.0570987
$835$	−8.62218e11	−0.0613802
$836$	−2.24605e13	−1.59035
$837$	−1.39077e13	−0.979472
$838$	2.37832e11	0.0166599
$839$	1.96594e13	1.36975	0.684876	−	0.728659i	$-0.259856\pi$
$839$	1.96594e13	1.36975	0.684876	+	0.728659i	$0.259856\pi$
$840$	0	0
$841$	−1.34785e12	−0.0929093
$842$	2.68013e12	0.183760
$843$	8.03553e12	0.548012
$844$	−1.53210e13	−1.03931
$845$	2.99255e12	0.201923
$846$	−7.69323e9	−0.000516348 0
$847$	0	0
$848$	−9.52467e12	−0.632512
$849$	1.75736e13	1.16085
$850$	3.79025e11	0.0249047
$851$	2.36614e12	0.154653
$852$	−3.39091e13	−2.20464
$853$	1.38848e12	0.0897984	0.0448992	−	0.998992i	$-0.485703\pi$
$853$	1.38848e12	0.0897984	0.0448992	+	0.998992i	$0.485703\pi$
$854$	0	0
$855$	5.35532e12	0.342719
$856$	−1.83681e11	−0.0116932
$857$	2.05314e13	1.30019	0.650093	−	0.759854i	$-0.274730\pi$
$857$	2.05314e13	1.30019	0.650093	+	0.759854i	$0.274730\pi$
$858$	3.46556e12	0.218313
$859$	−9.16692e12	−0.574453	−0.287226	−	0.957863i	$-0.592733\pi$
$859$	−9.16692e12	−0.574453	−0.287226	+	0.957863i	$0.592733\pi$
$860$	−9.01275e12	−0.561842
$861$	0	0
$862$	−3.05368e12	−0.188383
$863$	−1.47606e13	−0.905849	−0.452925	−	0.891549i	$-0.649619\pi$
$863$	−1.47606e13	−0.905849	−0.452925	+	0.891549i	$0.649619\pi$
$864$	2.75625e12	0.168270
$865$	1.40123e13	0.851012
$866$	1.16179e12	0.0701938
$867$	4.42444e12	0.265933
$868$	0	0
$869$	−6.67976e12	−0.397349
$870$	1.03111e12	0.0610192
$871$	−1.31028e13	−0.771406
$872$	3.59435e12	0.210521
$873$	1.59694e13	0.930517
$874$	−1.02090e12	−0.0591809
$875$	0	0
$876$	−3.54940e13	−2.03651
$877$	1.13101e13	0.645607	0.322804	−	0.946466i	$-0.395375\pi$
$877$	1.13101e13	0.645607	0.322804	+	0.946466i	$0.395375\pi$
$878$	9.60941e11	0.0545722
$879$	2.09133e13	1.18161
$880$	9.67789e12	0.544012
$881$	1.76889e13	0.989255	0.494628	−	0.869105i	$-0.335304\pi$
$881$	1.76889e13	0.989255	0.494628	+	0.869105i	$0.335304\pi$
$882$	0	0
$883$	2.94773e13	1.63179	0.815894	−	0.578201i	$-0.196245\pi$
$883$	2.94773e13	1.63179	0.815894	+	0.578201i	$0.196245\pi$
$884$	−2.37553e13	−1.30835
$885$	−6.12921e11	−0.0335861
$886$	−2.30955e12	−0.125914
$887$	−1.21733e13	−0.660316	−0.330158	−	0.943926i	$-0.607102\pi$
$887$	−1.21733e13	−0.660316	−0.330158	+	0.943926i	$0.607102\pi$
$888$	1.98740e12	0.107257
$889$	0	0
$890$	3.56238e11	0.0190320
$891$	−2.94982e13	−1.56800
$892$	−9.66500e12	−0.511163
$893$	1.83490e11	0.00965563
$894$	4.12841e11	0.0216154
$895$	−4.00492e12	−0.208637
$896$	0	0
$897$	−1.21356e13	−0.625888
$898$	2.93620e12	0.150675
$899$	−3.62432e13	−1.85058
$900$	−2.33827e12	−0.118796
$901$	1.43118e13	0.723493
$902$	4.96522e12	0.249752
$903$	0	0
$904$	7.16780e11	0.0356967
$905$	−5.79801e11	−0.0287317
$906$	−3.64040e11	−0.0179503
$907$	5.65317e12	0.277370	0.138685	−	0.990337i	$-0.455712\pi$
$907$	5.65317e12	0.277370	0.138685	+	0.990337i	$0.455712\pi$
$908$	−4.03291e12	−0.196894
$909$	−3.35120e12	−0.162803
$910$	0	0
$911$	9.15118e12	0.440194	0.220097	−	0.975478i	$-0.429363\pi$
$911$	9.15118e12	0.440194	0.220097	+	0.975478i	$0.429363\pi$
$912$	3.23866e13	1.55020
$913$	−7.76364e12	−0.369783
$914$	−1.35048e12	−0.0640073
$915$	1.20918e13	0.570292
$916$	−1.45831e13	−0.684414
$917$	0	0
$918$	−1.35068e12	−0.0627713
$919$	3.96150e13	1.83206	0.916030	−	0.401110i	$-0.131376\pi$
$919$	3.96150e13	1.83206	0.916030	+	0.401110i	$0.131376\pi$
$920$	8.97288e11	0.0412940
$921$	3.52081e13	1.61240
$922$	3.43398e12	0.156498
$923$	−4.68779e13	−2.12598
$924$	0	0
$925$	1.67776e12	0.0753515
$926$	2.37077e12	0.105960
$927$	−6.73029e12	−0.299347
$928$	7.18273e12	0.317924
$929$	−3.57785e11	−0.0157598	−0.00787991	−	0.999969i	$-0.502508\pi$
$929$	−3.57785e11	−0.0157598	−0.00787991	+	0.999969i	$0.502508\pi$
$930$	−2.83986e12	−0.124487
$931$	0	0
$932$	−3.49750e13	−1.51840
$933$	−3.95216e13	−1.70753
$934$	−1.32389e12	−0.0569235
$935$	−1.45421e13	−0.622263
$936$	−3.82914e12	−0.163065
$937$	3.35453e13	1.42169	0.710843	−	0.703350i	$-0.248313\pi$
$937$	3.35453e13	1.42169	0.710843	+	0.703350i	$0.248313\pi$
$938$	0	0
$939$	−1.65128e13	−0.693149
$940$	−8.01164e10	−0.00334692
$941$	−1.55016e13	−0.644502	−0.322251	−	0.946654i	$-0.604440\pi$
$941$	−1.55016e13	−0.644502	−0.322251	+	0.946654i	$0.604440\pi$
$942$	−4.13963e12	−0.171290
$943$	−1.73871e13	−0.716020
$944$	−1.39245e12	−0.0570697
$945$	0	0
$946$	−4.48839e12	−0.182213
$947$	1.07939e13	0.436119	0.218059	−	0.975935i	$-0.430027\pi$
$947$	1.07939e13	0.436119	0.218059	+	0.975935i	$0.430027\pi$
$948$	9.76011e12	0.392480
$949$	−4.90689e13	−1.96385
$950$	−7.23889e11	−0.0288347
$951$	−4.17290e13	−1.65434
$952$	0	0
$953$	1.09164e13	0.428708	0.214354	−	0.976756i	$-0.431235\pi$
$953$	1.09164e13	0.428708	0.214354	+	0.976756i	$0.431235\pi$
$954$	1.14603e12	0.0447949
$955$	7.48609e12	0.291232
$956$	4.89739e13	1.89629
$957$	−3.95605e13	−1.52461
$958$	3.04073e12	0.116636
$959$	0	0
$960$	−1.37615e13	−0.522934
$961$	7.33811e13	2.77542
$962$	1.36489e12	0.0513818
$963$	−8.34738e11	−0.0312775
$964$	−1.91734e13	−0.715076
$965$	1.75829e13	0.652705
$966$	0	0
$967$	−1.61178e13	−0.592769	−0.296385	−	0.955069i	$-0.595781\pi$
$967$	−1.61178e13	−0.592769	−0.296385	+	0.955069i	$0.595781\pi$
$968$	3.68618e12	0.134939
$969$	−4.86644e13	−1.77318
$970$	−2.15861e12	−0.0782892
$971$	−4.36523e13	−1.57587	−0.787936	−	0.615757i	$-0.788850\pi$
$971$	−4.36523e13	−1.57587	−0.787936	+	0.615757i	$0.788850\pi$
$972$	2.92525e13	1.05115
$973$	0	0
$974$	2.33910e11	0.00832785
$975$	−8.60500e12	−0.304951
$976$	2.74705e13	0.969042
$977$	−2.71335e12	−0.0952751	−0.0476376	−	0.998865i	$-0.515169\pi$
$977$	−2.71335e12	−0.0952751	−0.0476376	+	0.998865i	$0.515169\pi$
$978$	−4.34763e11	−0.0151960
$979$	−1.36678e13	−0.475529
$980$	0	0
$981$	1.63345e13	0.563112
$982$	−4.00942e12	−0.137588
$983$	4.23770e13	1.44757	0.723785	−	0.690026i	$-0.242401\pi$
$983$	4.23770e13	1.44757	0.723785	+	0.690026i	$0.242401\pi$
$984$	−1.46040e13	−0.496585
$985$	2.40649e13	0.814557
$986$	−3.51985e12	−0.118598
$987$	0	0
$988$	4.53696e13	1.51481
$989$	1.57174e13	0.522392
$990$	−1.16447e12	−0.0385273
$991$	5.03010e13	1.65670	0.828352	−	0.560207i	$-0.189279\pi$
$991$	5.03010e13	1.65670	0.828352	+	0.560207i	$0.189279\pi$
$992$	−1.97826e13	−0.648606
$993$	3.82354e13	1.24794
$994$	0	0
$995$	2.07072e13	0.669759
$996$	1.13438e13	0.365252
$997$	2.15692e13	0.691361	0.345681	−	0.938352i	$-0.387648\pi$
$997$	2.15692e13	0.691361	0.345681	+	0.938352i	$0.387648\pi$
$998$	−3.54564e12	−0.113138
$999$	−5.97882e12	−0.189920

Display

a_p

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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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.10.a.m.1.7		13
7.2	even	3		35.10.e.b.11.7	✓	26
7.4	even	3		35.10.e.b.16.7	yes	26
7.6	odd	2		245.10.a.l.1.7		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.e.b.11.7	✓	26	7.2	even	3
35.10.e.b.16.7	yes	26	7.4	even	3
245.10.a.l.1.7		13	7.6	odd	2
245.10.a.m.1.7		13	1.1	even	1	trivial

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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 $\F_{q}$

Introduction

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Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	245.10.a.m.1.7

Level	$245$
Weight	$10$
Character	245.1
Self dual	yes
Analytic conductor	$126.184$
Analytic rank	$0$
Dimension	$13$
CM	no
Inner twists	$1$