LMFDB - Embedded newform 289.10.a.i.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.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:	$148.845356651$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-35.0759 q^{2} -118.571 q^{3} +718.321 q^{4} -1635.44 q^{5} +4158.98 q^{6} +10785.0 q^{7} -7236.92 q^{8} -5623.96 q^{9} +O(q^{10})$	\(q-35.0759 q^{2} -118.571 q^{3} +718.321 q^{4} -1635.44 q^{5} +4158.98 q^{6} +10785.0 q^{7} -7236.92 q^{8} -5623.96 q^{9} +57364.5 q^{10} -21197.3 q^{11} -85172.0 q^{12} -71034.1 q^{13} -378293. q^{14} +193915. q^{15} -113939. q^{16} +197266. q^{18} -239108. q^{19} -1.17477e6 q^{20} -1.27878e6 q^{21} +743516. q^{22} +2.36865e6 q^{23} +858087. q^{24} +721532. q^{25} +2.49159e6 q^{26} +3.00067e6 q^{27} +7.74707e6 q^{28} +1.37916e6 q^{29} -6.80176e6 q^{30} +4.72814e6 q^{31} +7.70182e6 q^{32} +2.51339e6 q^{33} -1.76381e7 q^{35} -4.03981e6 q^{36} -1.04815e7 q^{37} +8.38694e6 q^{38} +8.42257e6 q^{39} +1.18355e7 q^{40} +7.22217e6 q^{41} +4.48545e7 q^{42} -1.01797e7 q^{43} -1.52265e7 q^{44} +9.19763e6 q^{45} -8.30825e7 q^{46} +4.00577e7 q^{47} +1.35098e7 q^{48} +7.59618e7 q^{49} -2.53084e7 q^{50} -5.10253e7 q^{52} +2.21414e7 q^{53} -1.05251e8 q^{54} +3.46669e7 q^{55} -7.80499e7 q^{56} +2.83512e7 q^{57} -4.83753e7 q^{58} -9.89019e7 q^{59} +1.39293e8 q^{60} -2.14505e8 q^{61} -1.65844e8 q^{62} -6.06542e7 q^{63} -2.11812e8 q^{64} +1.16172e8 q^{65} -8.81594e7 q^{66} +1.65755e8 q^{67} -2.80852e8 q^{69} +6.18674e8 q^{70} +2.59100e7 q^{71} +4.07001e7 q^{72} +3.65612e8 q^{73} +3.67649e8 q^{74} -8.55527e7 q^{75} -1.71756e8 q^{76} -2.28612e8 q^{77} -2.95430e8 q^{78} -5.47273e8 q^{79} +1.86340e8 q^{80} -2.45095e8 q^{81} -2.53324e8 q^{82} +5.77055e8 q^{83} -9.18576e8 q^{84} +3.57064e8 q^{86} -1.63528e8 q^{87} +1.53403e8 q^{88} +3.72848e7 q^{89} -3.22616e8 q^{90} -7.66100e8 q^{91} +1.70145e9 q^{92} -5.60619e8 q^{93} -1.40506e9 q^{94} +3.91046e8 q^{95} -9.13211e8 q^{96} -8.89204e8 q^{97} -2.66443e9 q^{98} +1.19213e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) $ 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9	$ 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9} + 156200 q^{13} + 1207872 q^{15} + 3407880 q^{16} + 2193336 q^{18} + 1185568 q^{19} + 5198336 q^{21} + 13827692 q^{25} + 3618944 q^{26} - 9167544 q^{30} + 61884888 q^{32} + 1635208 q^{33} + 46992776 q^{35} + 156027320 q^{36} + 84813952 q^{38} - 4635776 q^{42} + 125448912 q^{43} + 164193176 q^{47} + 270850284 q^{49} - 226223888 q^{50} + 103553016 q^{52} + 426167208 q^{53} + 677761520 q^{55} + 375214512 q^{59} + 336918024 q^{60} + 190014416 q^{64} + 1377178928 q^{66} + 311910088 q^{67} + 533688136 q^{69} + 1477690280 q^{70} + 2757942680 q^{72} + 4047975520 q^{76} + 3440336432 q^{77} + 3266558756 q^{81} + 2072890608 q^{83} + 2630025952 q^{84} + 1538547296 q^{86} - 1010436256 q^{87} + 1873849184 q^{89} - 1998451624 q^{93} - 6880776704 q^{94} - 4667454128 q^{98}+O(q^{100}) $ 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9 + 156200 * q^13 + 1207872 * q^15 + 3407880 * q^16 + 2193336 * q^18 + 1185568 * q^19 + 5198336 * q^21 + 13827692 * q^25 + 3618944 * q^26 - 9167544 * q^30 + 61884888 * q^32 + 1635208 * q^33 + 46992776 * q^35 + 156027320 * q^36 + 84813952 * q^38 - 4635776 * q^42 + 125448912 * q^43 + 164193176 * q^47 + 270850284 * q^49 - 226223888 * q^50 + 103553016 * q^52 + 426167208 * q^53 + 677761520 * q^55 + 375214512 * q^59 + 336918024 * q^60 + 190014416 * q^64 + 1377178928 * q^66 + 311910088 * q^67 + 533688136 * q^69 + 1477690280 * q^70 + 2757942680 * q^72 + 4047975520 * q^76 + 3440336432 * q^77 + 3266558756 * q^81 + 2072890608 * q^83 + 2630025952 * q^84 + 1538547296 * q^86 - 1010436256 * q^87 + 1873849184 * q^89 - 1998451624 * q^93 - 6880776704 * q^94 - 4667454128 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−35.0759	−1.55015	−0.775076	−	0.631868i	$-0.782288\pi$
$2$	−35.0759	−1.55015	−0.775076	+	0.631868i	$0.782288\pi$
$3$	−118.571	−0.845147	−0.422573	−	0.906329i	$-0.638873\pi$
$3$	−118.571	−0.845147	−0.422573	+	0.906329i	$0.638873\pi$
$4$	718.321	1.40297
$5$	−1635.44	−1.17022	−0.585112	−	0.810952i	$-0.698949\pi$
$5$	−1635.44	−1.17022	−0.585112	+	0.810952i	$0.698949\pi$
$6$	4158.98	1.31011
$7$	10785.0	1.69776	0.848882	−	0.528582i	$-0.177276\pi$
$7$	10785.0	1.69776	0.848882	+	0.528582i	$0.177276\pi$
$8$	−7236.92	−0.624667
$9$	−5623.96	−0.285727
$10$	57364.5	1.81403
$11$	−21197.3	−0.436530	−0.218265	−	0.975890i	$-0.570040\pi$
$11$	−21197.3	−0.436530	−0.218265	+	0.975890i	$0.570040\pi$
$12$	−85172.0	−1.18572
$13$	−71034.1	−0.689798	−0.344899	−	0.938640i	$-0.612087\pi$
$13$	−71034.1	−0.689798	−0.344899	+	0.938640i	$0.612087\pi$
$14$	−378293.	−2.63179
$15$	193915.	0.989011
$16$	−113939.	−0.434642
$17$	0	0
$17$	0	0
$18$	197266.	0.442920
$19$	−239108.	−0.420923	−0.210462	−	0.977602i	$-0.567497\pi$
$19$	−239108.	−0.420923	−0.210462	+	0.977602i	$0.567497\pi$
$20$	−1.17477e6	−1.64179
$21$	−1.27878e6	−1.43486
$22$	743516.	0.676688
$23$	2.36865e6	1.76492	0.882460	−	0.470388i	$-0.155886\pi$
$23$	2.36865e6	1.76492	0.882460	+	0.470388i	$0.155886\pi$
$24$	858087.	0.527936
$25$	721532.	0.369424
$26$	2.49159e6	1.06929
$27$	3.00067e6	1.08663
$28$	7.74707e6	2.38192
$29$	1.37916e6	0.362096	0.181048	−	0.983474i	$-0.442051\pi$
$29$	1.37916e6	0.362096	0.181048	+	0.983474i	$0.442051\pi$
$30$	−6.80176e6	−1.53312
$31$	4.72814e6	0.919523	0.459761	−	0.888042i	$-0.347935\pi$
$31$	4.72814e6	0.919523	0.459761	+	0.888042i	$0.347935\pi$
$32$	7.70182e6	1.29843
$33$	2.51339e6	0.368932
$34$	0	0
$35$	−1.76381e7	−1.98676
$36$	−4.03981e6	−0.400866
$37$	−1.04815e7	−0.919424	−0.459712	−	0.888068i	$-0.652047\pi$
$37$	−1.04815e7	−0.919424	−0.459712	+	0.888068i	$0.652047\pi$
$38$	8.38694e6	0.652495
$39$	8.42257e6	0.582981
$40$	1.18355e7	0.731001
$41$	7.22217e6	0.399154	0.199577	−	0.979882i	$-0.436043\pi$
$41$	7.22217e6	0.399154	0.199577	+	0.979882i	$0.436043\pi$
$42$	4.48545e7	2.22425
$43$	−1.01797e7	−0.454076	−0.227038	−	0.973886i	$-0.572904\pi$
$43$	−1.01797e7	−0.454076	−0.227038	+	0.973886i	$0.572904\pi$
$44$	−1.52265e7	−0.612439
$45$	9.19763e6	0.334364
$46$	−8.30825e7	−2.73589
$47$	4.00577e7	1.19742	0.598709	−	0.800966i	$-0.295680\pi$
$47$	4.00577e7	1.19742	0.598709	+	0.800966i	$0.295680\pi$
$48$	1.35098e7	0.367337
$49$	7.59618e7	1.88240
$50$	−2.53084e7	−0.572664
$51$	0	0
$52$	−5.10253e7	−0.967767
$53$	2.21414e7	0.385447	0.192723	−	0.981253i	$-0.438268\pi$
$53$	2.21414e7	0.385447	0.192723	+	0.981253i	$0.438268\pi$
$54$	−1.05251e8	−1.68444
$55$	3.46669e7	0.510838
$56$	−7.80499e7	−1.06054
$57$	2.83512e7	0.355742
$58$	−4.83753e7	−0.561304
$59$	−9.89019e7	−1.06260	−0.531301	−	0.847183i	$-0.678297\pi$
$59$	−9.89019e7	−1.06260	−0.531301	+	0.847183i	$0.678297\pi$
$60$	1.39293e8	1.38755
$61$	−2.14505e8	−1.98360	−0.991798	−	0.127812i	$-0.959204\pi$
$61$	−2.14505e8	−1.98360	−0.991798	+	0.127812i	$0.959204\pi$
$62$	−1.65844e8	−1.42540
$63$	−6.06542e7	−0.485097
$64$	−2.11812e8	−1.57812
$65$	1.16172e8	0.807218
$66$	−8.81594e7	−0.571901
$67$	1.65755e8	1.00492	0.502458	−	0.864602i	$-0.332429\pi$
$67$	1.65755e8	1.00492	0.502458	+	0.864602i	$0.332429\pi$
$68$	0	0
$69$	−2.80852e8	−1.49162
$70$	6.18674e8	3.07979
$71$	2.59100e7	0.121005	0.0605027	−	0.998168i	$-0.480730\pi$
$71$	2.59100e7	0.121005	0.0605027	+	0.998168i	$0.480730\pi$
$72$	4.07001e7	0.178484
$73$	3.65612e8	1.50684	0.753421	−	0.657539i	$-0.228402\pi$
$73$	3.65612e8	1.50684	0.753421	+	0.657539i	$0.228402\pi$
$74$	3.67649e8	1.42525
$75$	−8.55527e7	−0.312218
$76$	−1.71756e8	−0.590544
$77$	−2.28612e8	−0.741125
$78$	−2.95430e8	−0.903709
$79$	−5.47273e8	−1.58082	−0.790409	−	0.612579i	$-0.790132\pi$
$79$	−5.47273e8	−1.58082	−0.790409	+	0.612579i	$0.790132\pi$
$80$	1.86340e8	0.508629
$81$	−2.45095e8	−0.632634
$82$	−2.53324e8	−0.618749
$83$	5.77055e8	1.33465	0.667323	−	0.744768i	$-0.267440\pi$
$83$	5.77055e8	1.33465	0.667323	+	0.744768i	$0.267440\pi$
$84$	−9.18576e8	−2.01307
$85$	0	0
$86$	3.57064e8	0.703887
$87$	−1.63528e8	−0.306024
$88$	1.53403e8	0.272686
$89$	3.72848e7	0.0629908	0.0314954	−	0.999504i	$-0.489973\pi$
$89$	3.72848e7	0.0629908	0.0314954	+	0.999504i	$0.489973\pi$
$90$	−3.22616e8	−0.518315
$91$	−7.66100e8	−1.17111
$92$	1.70145e9	2.47613
$93$	−5.60619e8	−0.777132
$94$	−1.40506e9	−1.85618
$95$	3.91046e8	0.492575
$96$	−9.13211e8	−1.09736
$97$	−8.89204e8	−1.01983	−0.509916	−	0.860224i	$-0.670324\pi$
$97$	−8.89204e8	−1.01983	−0.509916	+	0.860224i	$0.670324\pi$
$98$	−2.66443e9	−2.91801
$99$	1.19213e8	0.124728
$100$	5.18292e8	0.518292
$101$	−1.51590e9	−1.44952	−0.724760	−	0.689002i	$-0.758049\pi$
$101$	−1.51590e9	−1.44952	−0.724760	+	0.689002i	$0.758049\pi$
$102$	0	0
$103$	4.65778e8	0.407766	0.203883	−	0.978995i	$-0.434644\pi$
$103$	4.65778e8	0.407766	0.203883	+	0.978995i	$0.434644\pi$
$104$	5.14068e8	0.430894
$105$	2.09137e9	1.67911
$106$	−7.76632e8	−0.597501
$107$	−1.88637e9	−1.39124	−0.695618	−	0.718412i	$-0.744869\pi$
$107$	−1.88637e9	−1.39124	−0.695618	+	0.718412i	$0.744869\pi$
$108$	2.15544e9	1.52451
$109$	−5.88893e8	−0.399593	−0.199796	−	0.979837i	$-0.564028\pi$
$109$	−5.88893e8	−0.399593	−0.199796	+	0.979837i	$0.564028\pi$
$110$	−1.21598e9	−0.791877
$111$	1.24280e9	0.777049
$112$	−1.22883e9	−0.737920
$113$	1.46525e9	0.845393	0.422696	−	0.906271i	$-0.361084\pi$
$113$	1.46525e9	0.845393	0.422696	+	0.906271i	$0.361084\pi$
$114$	−9.94447e8	−0.551454
$115$	−3.87377e9	−2.06535
$116$	9.90680e8	0.508010
$117$	3.99493e8	0.197094
$118$	3.46908e9	1.64720
$119$	0	0
$120$	−1.40335e9	−0.617803
$121$	−1.90862e9	−0.809441
$122$	7.52397e9	3.07488
$123$	−8.56338e8	−0.337343
$124$	3.39632e9	1.29006
$125$	2.01419e9	0.737915
$126$	2.12750e9	0.751973
$127$	−2.87764e9	−0.981566	−0.490783	−	0.871282i	$-0.663289\pi$
$127$	−2.87764e9	−0.981566	−0.490783	+	0.871282i	$0.663289\pi$
$128$	3.48616e9	1.14790
$129$	1.20702e9	0.383761
$130$	−4.07484e9	−1.25131
$131$	−5.71635e9	−1.69589	−0.847946	−	0.530083i	$-0.822161\pi$
$131$	−5.71635e9	−1.69589	−0.847946	+	0.530083i	$0.822161\pi$
$132$	1.80542e9	0.517601
$133$	−2.57877e9	−0.714629
$134$	−5.81401e9	−1.55777
$135$	−4.90740e9	−1.27160
$136$	0	0
$137$	−2.50282e9	−0.606997	−0.303499	−	0.952832i	$-0.598155\pi$
$137$	−2.50282e9	−0.606997	−0.303499	+	0.952832i	$0.598155\pi$
$138$	9.85116e9	2.31223
$139$	−8.09336e8	−0.183892	−0.0919459	−	0.995764i	$-0.529309\pi$
$139$	−8.09336e8	−0.183892	−0.0919459	+	0.995764i	$0.529309\pi$
$140$	−1.26699e10	−2.78737
$141$	−4.74968e9	−1.01199
$142$	−9.08817e8	−0.187577
$143$	1.50573e9	0.301118
$144$	6.40787e8	0.124189
$145$	−2.25553e9	−0.423733
$146$	−1.28242e10	−2.33583
$147$	−9.00685e9	−1.59091
$148$	−7.52909e9	−1.28993
$149$	4.26492e9	0.708880	0.354440	−	0.935079i	$-0.384672\pi$
$149$	4.26492e9	0.708880	0.354440	+	0.935079i	$0.384672\pi$
$150$	3.00084e9	0.483985
$151$	8.41177e9	1.31671	0.658357	−	0.752706i	$-0.271252\pi$
$151$	8.41177e9	1.31671	0.658357	+	0.752706i	$0.271252\pi$
$152$	1.73041e9	0.262937
$153$	0	0
$154$	8.01880e9	1.14886
$155$	−7.73258e9	−1.07605
$156$	6.05012e9	0.817905
$157$	1.40154e9	0.184101	0.0920504	−	0.995754i	$-0.470658\pi$
$157$	1.40154e9	0.184101	0.0920504	+	0.995754i	$0.470658\pi$
$158$	1.91961e10	2.45051
$159$	−2.62533e9	−0.325759
$160$	−1.25958e10	−1.51945
$161$	2.55458e10	2.99642
$162$	8.59695e9	0.980678
$163$	−9.27080e9	−1.02866	−0.514331	−	0.857592i	$-0.671960\pi$
$163$	−9.27080e9	−1.02866	−0.514331	+	0.857592i	$0.671960\pi$
$164$	5.18784e9	0.560001
$165$	−4.11049e9	−0.431733
$166$	−2.02408e10	−2.06890
$167$	1.35795e10	1.35102	0.675509	−	0.737352i	$-0.263924\pi$
$167$	1.35795e10	1.35102	0.675509	+	0.737352i	$0.263924\pi$
$168$	9.25444e9	0.896310
$169$	−5.55865e9	−0.524179
$170$	0	0
$171$	1.34473e9	0.120269
$172$	−7.31232e9	−0.637055
$173$	6.63039e9	0.562771	0.281386	−	0.959595i	$-0.409206\pi$
$173$	6.63039e9	0.562771	0.281386	+	0.959595i	$0.409206\pi$
$174$	5.73590e9	0.474384
$175$	7.78170e9	0.627196
$176$	2.41520e9	0.189734
$177$	1.17269e10	0.898055
$178$	−1.30780e9	−0.0976453
$179$	−4.34584e9	−0.316399	−0.158200	−	0.987407i	$-0.550569\pi$
$179$	−4.34584e9	−0.316399	−0.158200	+	0.987407i	$0.550569\pi$
$180$	6.60686e9	0.469104
$181$	1.32517e10	0.917737	0.458869	−	0.888504i	$-0.348255\pi$
$181$	1.32517e10	0.917737	0.458869	+	0.888504i	$0.348255\pi$
$182$	2.68717e10	1.81541
$183$	2.54340e10	1.67643
$184$	−1.71417e10	−1.10249
$185$	1.71419e10	1.07593
$186$	1.96642e10	1.20467
$187$	0	0
$188$	2.87743e10	1.67994
$189$	3.23621e10	1.84484
$190$	−1.37163e10	−0.763566
$191$	4.77283e8	0.0259493	0.0129746	−	0.999916i	$-0.495870\pi$
$191$	4.77283e8	0.0259493	0.0129746	+	0.999916i	$0.495870\pi$
$192$	2.51147e10	1.33374
$193$	−1.38605e10	−0.719070	−0.359535	−	0.933132i	$-0.617065\pi$
$193$	−1.38605e10	−0.719070	−0.359535	+	0.933132i	$0.617065\pi$
$194$	3.11897e10	1.58090
$195$	−1.37746e10	−0.682218
$196$	5.45650e10	2.64096
$197$	2.83003e10	1.33873	0.669364	−	0.742934i	$-0.266567\pi$
$197$	2.83003e10	1.33873	0.669364	+	0.742934i	$0.266567\pi$
$198$	−4.18151e9	−0.193348
$199$	−2.49935e10	−1.12977	−0.564884	−	0.825171i	$-0.691079\pi$
$199$	−2.49935e10	−1.12977	−0.564884	+	0.825171i	$0.691079\pi$
$200$	−5.22167e9	−0.230767
$201$	−1.96537e10	−0.849302
$202$	5.31716e10	2.24698
$203$	1.48742e10	0.614753
$204$	0	0
$205$	−1.18114e10	−0.467099
$206$	−1.63376e10	−0.632100
$207$	−1.33212e10	−0.504284
$208$	8.09355e9	0.299815
$209$	5.06845e9	0.183746
$210$	−7.33567e10	−2.60287
$211$	1.80312e10	0.626260	0.313130	−	0.949710i	$-0.398623\pi$
$211$	1.80312e10	0.626260	0.313130	+	0.949710i	$0.398623\pi$
$212$	1.59047e10	0.540771
$213$	−3.07217e9	−0.102267
$214$	6.61663e10	2.15663
$215$	1.66483e10	0.531370
$216$	−2.17156e10	−0.678781
$217$	5.09928e10	1.56113
$218$	2.06560e10	0.619429
$219$	−4.33509e10	−1.27350
$220$	2.49020e10	0.716691
$221$	0	0
$222$	−4.35924e10	−1.20454
$223$	−3.30245e10	−0.894262	−0.447131	−	0.894468i	$-0.647554\pi$
$223$	−3.30245e10	−0.894262	−0.447131	+	0.894468i	$0.647554\pi$
$224$	8.30638e10	2.20443
$225$	−4.05787e9	−0.105554
$226$	−5.13950e10	−1.31049
$227$	−3.66514e10	−0.916166	−0.458083	−	0.888909i	$-0.651464\pi$
$227$	−3.66514e10	−0.916166	−0.458083	+	0.888909i	$0.651464\pi$
$228$	2.03653e10	0.499096
$229$	5.79474e9	0.139243	0.0696217	−	0.997573i	$-0.477821\pi$
$229$	5.79474e9	0.139243	0.0696217	+	0.997573i	$0.477821\pi$
$230$	1.35876e11	3.20161
$231$	2.71068e10	0.626360
$232$	−9.98087e9	−0.226189
$233$	7.30737e7	0.00162428	0.000812138	−	1.00000i	$-0.499741\pi$
$233$	7.30737e7	0.00162428	0.000812138		1.00000i	$0.499741\pi$
$234$	−1.40126e10	−0.305525
$235$	−6.55120e10	−1.40125
$236$	−7.10434e10	−1.49080
$237$	6.48906e10	1.33602
$238$	0	0
$239$	6.99325e10	1.38640	0.693200	−	0.720745i	$-0.256200\pi$
$239$	6.99325e10	1.38640	0.693200	+	0.720745i	$0.256200\pi$
$240$	−2.20945e10	−0.429866
$241$	−5.86797e10	−1.12050	−0.560250	−	0.828324i	$-0.689295\pi$
$241$	−5.86797e10	−1.12050	−0.560250	+	0.828324i	$0.689295\pi$
$242$	6.69467e10	1.25476
$243$	−3.00010e10	−0.551960
$244$	−1.54084e11	−2.78293
$245$	−1.24231e11	−2.20283
$246$	3.00369e10	0.522934
$247$	1.69848e10	0.290352
$248$	−3.42171e10	−0.574396
$249$	−6.84219e10	−1.12797
$250$	−7.06497e10	−1.14388
$251$	−3.69311e10	−0.587300	−0.293650	−	0.955913i	$-0.594870\pi$
$251$	−3.69311e10	−0.587300	−0.293650	+	0.955913i	$0.594870\pi$
$252$	−4.35692e10	−0.680577
$253$	−5.02090e10	−0.770440
$254$	1.00936e11	1.52158
$255$	0	0
$256$	−1.38329e10	−0.201295
$257$	3.07821e10	0.440149	0.220074	−	0.975483i	$-0.429370\pi$
$257$	3.07821e10	0.440149	0.220074	+	0.975483i	$0.429370\pi$
$258$	−4.23373e10	−0.594888
$259$	−1.13043e11	−1.56097
$260$	8.34488e10	1.13250
$261$	−7.75634e9	−0.103460
$262$	2.00506e11	2.62889
$263$	2.21843e10	0.285920	0.142960	−	0.989728i	$-0.454338\pi$
$263$	2.21843e10	0.285920	0.142960	+	0.989728i	$0.454338\pi$
$264$	−1.81892e10	−0.230460
$265$	−3.62110e10	−0.451059
$266$	9.04528e10	1.10778
$267$	−4.42089e9	−0.0532365
$268$	1.19065e11	1.40987
$269$	−5.70776e10	−0.664631	−0.332316	−	0.943168i	$-0.607830\pi$
$269$	−5.70776e10	−0.664631	−0.332316	+	0.943168i	$0.607830\pi$
$270$	1.72132e11	1.97117
$271$	−3.32663e10	−0.374664	−0.187332	−	0.982297i	$-0.559984\pi$
$271$	−3.32663e10	−0.374664	−0.187332	+	0.982297i	$0.559984\pi$
$272$	0	0
$273$	9.08371e10	0.989764
$274$	8.77887e10	0.940938
$275$	−1.52946e10	−0.161265
$276$	−2.01742e11	−2.09270
$277$	3.42210e10	0.349248	0.174624	−	0.984635i	$-0.444129\pi$
$277$	3.42210e10	0.349248	0.174624	+	0.984635i	$0.444129\pi$
$278$	2.83882e10	0.285060
$279$	−2.65908e10	−0.262732
$280$	1.27646e11	1.24107
$281$	6.69886e10	0.640947	0.320474	−	0.947257i	$-0.396158\pi$
$281$	6.69886e10	0.640947	0.320474	+	0.947257i	$0.396158\pi$
$282$	1.66599e11	1.56875
$283$	2.10268e10	0.194865	0.0974327	−	0.995242i	$-0.468937\pi$
$283$	2.10268e10	0.194865	0.0974327	+	0.995242i	$0.468937\pi$
$284$	1.86117e10	0.169767
$285$	−4.63667e10	−0.416298
$286$	−5.28150e10	−0.466778
$287$	7.78908e10	0.677669
$288$	−4.33147e10	−0.370996
$289$	0	0
$290$	7.91148e10	0.656851
$291$	1.05434e11	0.861908
$292$	2.62627e11	2.11406
$293$	−3.54172e10	−0.280743	−0.140372	−	0.990099i	$-0.544830\pi$
$293$	−3.54172e10	−0.280743	−0.140372	+	0.990099i	$0.544830\pi$
$294$	3.15924e11	2.46615
$295$	1.61748e11	1.24348
$296$	7.58538e10	0.574334
$297$	−6.36062e10	−0.474346
$298$	−1.49596e11	−1.09887
$299$	−1.68255e11	−1.21744
$300$	−6.14543e10	−0.438033
$301$	−1.09788e11	−0.770914
$302$	−2.95051e11	−2.04111
$303$	1.79741e11	1.22506
$304$	2.72437e10	0.182951
$305$	3.50810e11	2.32125
$306$	0	0
$307$	−9.48586e9	−0.0609472	−0.0304736	−	0.999536i	$-0.509702\pi$
$307$	−9.48586e9	−0.0609472	−0.0304736	+	0.999536i	$0.509702\pi$
$308$	−1.64217e11	−1.03978
$309$	−5.52277e10	−0.344622
$310$	2.71227e11	1.66804
$311$	−1.56456e11	−0.948354	−0.474177	−	0.880429i	$-0.657254\pi$
$311$	−1.56456e11	−0.948354	−0.474177	+	0.880429i	$0.657254\pi$
$312$	−6.09535e10	−0.364169
$313$	−7.93382e10	−0.467232	−0.233616	−	0.972329i	$-0.575056\pi$
$313$	−7.93382e10	−0.467232	−0.233616	+	0.972329i	$0.575056\pi$
$314$	−4.91602e10	−0.285384
$315$	9.91961e10	0.567672
$316$	−3.93118e11	−2.21784
$317$	1.26108e11	0.701417	0.350709	−	0.936485i	$-0.385941\pi$
$317$	1.26108e11	0.701417	0.350709	+	0.936485i	$0.385941\pi$
$318$	9.20859e10	0.504976
$319$	−2.92345e10	−0.158066
$320$	3.46405e11	1.84675
$321$	2.23669e11	1.17580
$322$	−8.96041e11	−4.64490
$323$	0	0
$324$	−1.76057e11	−0.887567
$325$	−5.12534e10	−0.254828
$326$	3.25182e11	1.59458
$327$	6.98256e10	0.337714
$328$	−5.22662e10	−0.249338
$329$	4.32021e11	2.03294
$330$	1.44179e11	0.669252
$331$	1.07985e11	0.494467	0.247234	−	0.968956i	$-0.420478\pi$
$331$	1.07985e11	0.494467	0.247234	+	0.968956i	$0.420478\pi$
$332$	4.14511e11	1.87247
$333$	5.89475e10	0.262704
$334$	−4.76315e11	−2.09428
$335$	−2.71082e11	−1.17598
$336$	1.45703e11	0.623651
$337$	2.39230e11	1.01037	0.505186	−	0.863011i	$-0.331424\pi$
$337$	2.39230e11	1.01037	0.505186	+	0.863011i	$0.331424\pi$
$338$	1.94975e11	0.812557
$339$	−1.73736e11	−0.714481
$340$	0	0
$341$	−1.00224e11	−0.401399
$342$	−4.71678e10	−0.186435
$343$	3.84033e11	1.49811
$344$	7.36699e10	0.283646
$345$	4.59317e11	1.74553
$346$	−2.32567e11	−0.872381
$347$	−1.33301e11	−0.493573	−0.246786	−	0.969070i	$-0.579375\pi$
$347$	−1.33301e11	−0.493573	−0.246786	+	0.969070i	$0.579375\pi$
$348$	−1.17466e11	−0.429343
$349$	−1.00639e11	−0.363120	−0.181560	−	0.983380i	$-0.558115\pi$
$349$	−1.00639e11	−0.363120	−0.181560	+	0.983380i	$0.558115\pi$
$350$	−2.72950e11	−0.972249
$351$	−2.13150e11	−0.749554
$352$	−1.63258e11	−0.566803
$353$	9.24641e10	0.316947	0.158474	−	0.987363i	$-0.449343\pi$
$353$	9.24641e10	0.316947	0.158474	+	0.987363i	$0.449343\pi$
$354$	−4.11331e11	−1.39212
$355$	−4.23742e10	−0.141603
$356$	2.67825e10	0.0883743
$357$	0	0
$358$	1.52435e11	0.490467
$359$	4.04248e11	1.28447	0.642234	−	0.766509i	$-0.278008\pi$
$359$	4.04248e11	1.28447	0.642234	+	0.766509i	$0.278008\pi$
$360$	−6.65625e10	−0.208866
$361$	−2.65515e11	−0.822824
$362$	−4.64816e11	−1.42263
$363$	2.26307e11	0.684097
$364$	−5.50306e11	−1.64304
$365$	−5.97936e11	−1.76334
$366$	−8.92123e11	−2.59872
$367$	5.43157e11	1.56289	0.781444	−	0.623975i	$-0.214483\pi$
$367$	5.43157e11	1.56289	0.781444	+	0.623975i	$0.214483\pi$
$368$	−2.69881e11	−0.767109
$369$	−4.06172e10	−0.114049
$370$	−6.01267e11	−1.66786
$371$	2.38795e11	0.654398
$372$	−4.02705e11	−1.09029
$373$	7.02135e10	0.187815	0.0939077	−	0.995581i	$-0.470064\pi$
$373$	7.02135e10	0.187815	0.0939077	+	0.995581i	$0.470064\pi$
$374$	0	0
$375$	−2.38825e11	−0.623646
$376$	−2.89895e11	−0.747988
$377$	−9.79674e10	−0.249773
$378$	−1.13513e12	−2.85978
$379$	−3.37065e11	−0.839146	−0.419573	−	0.907722i	$-0.637820\pi$
$379$	−3.37065e11	−0.839146	−0.419573	+	0.907722i	$0.637820\pi$
$380$	2.80897e11	0.691068
$381$	3.41204e11	0.829568
$382$	−1.67411e10	−0.0402253
$383$	−2.69746e11	−0.640562	−0.320281	−	0.947323i	$-0.603777\pi$
$383$	−2.69746e11	−0.640562	−0.320281	+	0.947323i	$0.603777\pi$
$384$	−4.13357e11	−0.970142
$385$	3.73881e11	0.867283
$386$	4.86170e11	1.11467
$387$	5.72504e10	0.129742
$388$	−6.38735e11	−1.43080
$389$	−6.98737e11	−1.54718	−0.773590	−	0.633687i	$-0.781541\pi$
$389$	−6.98737e11	−1.54718	−0.773590	+	0.633687i	$0.781541\pi$
$390$	4.83157e11	1.05754
$391$	0	0
$392$	−5.49729e11	−1.17588
$393$	6.77792e11	1.43328
$394$	−9.92658e11	−2.07523
$395$	8.95031e11	1.84991
$396$	8.56332e10	0.174990
$397$	5.38044e11	1.08708	0.543538	−	0.839384i	$-0.317084\pi$
$397$	5.38044e11	1.08708	0.543538	+	0.839384i	$0.317084\pi$
$398$	8.76672e11	1.75131
$399$	3.05767e11	0.603966
$400$	−8.22106e10	−0.160568
$401$	−9.77776e10	−0.188838	−0.0944190	−	0.995533i	$-0.530099\pi$
$401$	−9.77776e10	−0.188838	−0.0944190	+	0.995533i	$0.530099\pi$
$402$	6.89372e11	1.31655
$403$	−3.35859e11	−0.634285
$404$	−1.08890e12	−2.03363
$405$	4.00838e11	0.740323
$406$	−5.21726e11	−0.952961
$407$	2.22180e11	0.401356
$408$	0	0
$409$	8.67529e11	1.53295	0.766477	−	0.642271i	$-0.222008\pi$
$409$	8.67529e11	1.53295	0.766477	+	0.642271i	$0.222008\pi$
$410$	4.14296e11	0.724075
$411$	2.96761e11	0.513002
$412$	3.34578e11	0.572085
$413$	−1.06665e12	−1.80405
$414$	4.67252e11	0.781718
$415$	−9.43738e11	−1.56183
$416$	−5.47092e11	−0.895654
$417$	9.59637e10	0.155416
$418$	−1.77781e11	−0.284834
$419$	5.57776e11	0.884091	0.442045	−	0.896993i	$-0.354253\pi$
$419$	5.57776e11	0.884091	0.442045	+	0.896993i	$0.354253\pi$
$420$	1.50227e12	2.35574
$421$	2.55514e11	0.396411	0.198206	−	0.980160i	$-0.436489\pi$
$421$	2.55514e11	0.396411	0.198206	+	0.980160i	$0.436489\pi$
$422$	−6.32462e11	−0.970798
$423$	−2.25283e11	−0.342134
$424$	−1.60236e11	−0.240776
$425$	0	0
$426$	1.07759e11	0.158530
$427$	−2.31343e12	−3.36768
$428$	−1.35502e12	−1.95186
$429$	−1.78536e11	−0.254489
$430$	−5.83956e11	−0.823705
$431$	−8.68561e11	−1.21242	−0.606210	−	0.795305i	$-0.707311\pi$
$431$	−8.68561e11	−1.21242	−0.606210	+	0.795305i	$0.707311\pi$
$432$	−3.41893e11	−0.472294
$433$	4.20026e11	0.574223	0.287112	−	0.957897i	$-0.407305\pi$
$433$	4.20026e11	0.574223	0.287112	+	0.957897i	$0.407305\pi$
$434$	−1.78862e12	−2.41999
$435$	2.67440e11	0.358117
$436$	−4.23015e11	−0.560617
$437$	−5.66362e11	−0.742896
$438$	1.52057e12	1.97412
$439$	−2.86798e11	−0.368541	−0.184270	−	0.982876i	$-0.558992\pi$
$439$	−2.86798e11	−0.368541	−0.184270	+	0.982876i	$0.558992\pi$
$440$	−2.50882e11	−0.319104
$441$	−4.27206e11	−0.537853
$442$	0	0
$443$	2.71905e11	0.335428	0.167714	−	0.985836i	$-0.446361\pi$
$443$	2.71905e11	0.335428	0.167714	+	0.985836i	$0.446361\pi$
$444$	8.92731e11	1.09018
$445$	−6.09770e10	−0.0737133
$446$	1.15837e12	1.38624
$447$	−5.05695e11	−0.599107
$448$	−2.28438e12	−2.67928
$449$	2.15739e10	0.0250507	0.0125254	−	0.999922i	$-0.496013\pi$
$449$	2.15739e10	0.0250507	0.0125254	+	0.999922i	$0.496013\pi$
$450$	1.42333e11	0.163625
$451$	−1.53091e11	−0.174243
$452$	1.05252e12	1.18606
$453$	−9.97391e11	−1.11282
$454$	1.28558e12	1.42020
$455$	1.25291e12	1.37047
$456$	−2.05176e11	−0.222220
$457$	1.57168e12	1.68555	0.842775	−	0.538266i	$-0.180921\pi$
$457$	1.57168e12	1.68555	0.842775	+	0.538266i	$0.180921\pi$
$458$	−2.03256e11	−0.215848
$459$	0	0
$460$	−2.78261e12	−2.89763
$461$	9.53263e11	0.983012	0.491506	−	0.870874i	$-0.336447\pi$
$461$	9.53263e11	0.983012	0.491506	+	0.870874i	$0.336447\pi$
$462$	−9.50795e11	−0.970953
$463$	1.32544e12	1.34044	0.670219	−	0.742164i	$-0.266200\pi$
$463$	1.32544e12	1.34044	0.670219	+	0.742164i	$0.266200\pi$
$464$	−1.57140e11	−0.157382
$465$	9.16858e11	0.909418
$466$	−2.56313e9	−0.00251787
$467$	−2.18931e11	−0.213001	−0.106500	−	0.994313i	$-0.533965\pi$
$467$	−2.18931e11	−0.213001	−0.106500	+	0.994313i	$0.533965\pi$
$468$	2.86964e11	0.276517
$469$	1.78766e12	1.70611
$470$	2.29789e12	2.17215
$471$	−1.66181e11	−0.155592
$472$	7.15745e11	0.663773
$473$	2.15783e11	0.198218
$474$	−2.27610e12	−2.07104
$475$	−1.72524e11	−0.155499
$476$	0	0
$477$	−1.24523e11	−0.110132
$478$	−2.45295e12	−2.14913
$479$	−1.42034e12	−1.23277	−0.616387	−	0.787443i	$-0.711404\pi$
$479$	−1.42034e12	−1.23277	−0.616387	+	0.787443i	$0.711404\pi$
$480$	1.49350e12	1.28416
$481$	7.44544e11	0.634217
$482$	2.05825e12	1.73694
$483$	−3.02898e12	−2.53241
$484$	−1.37100e12	−1.13562
$485$	1.45424e12	1.19343
$486$	1.05231e12	0.855621
$487$	−7.40911e11	−0.596878	−0.298439	−	0.954429i	$-0.596466\pi$
$487$	−7.40911e11	−0.596878	−0.298439	+	0.954429i	$0.596466\pi$
$488$	1.55236e12	1.23909
$489$	1.09925e12	0.869371
$490$	4.35751e12	3.41473
$491$	2.27702e12	1.76807	0.884036	−	0.467418i	$-0.154816\pi$
$491$	2.27702e12	1.76807	0.884036	+	0.467418i	$0.154816\pi$
$492$	−6.15126e11	−0.473283
$493$	0	0
$494$	−5.95759e11	−0.450090
$495$	−1.94965e11	−0.145960
$496$	−5.38719e11	−0.399664
$497$	2.79438e11	0.205439
$498$	2.39996e12	1.74853
$499$	1.41291e11	0.102014	0.0510071	−	0.998698i	$-0.483757\pi$
$499$	1.41291e11	0.102014	0.0510071	+	0.998698i	$0.483757\pi$
$500$	1.44684e12	1.03527
$501$	−1.61014e12	−1.14181
$502$	1.29539e12	0.910405
$503$	−1.69321e12	−1.17938	−0.589692	−	0.807628i	$-0.700751\pi$
$503$	−1.69321e12	−1.17938	−0.589692	+	0.807628i	$0.700751\pi$
$504$	4.38949e11	0.303024
$505$	2.47916e12	1.69626
$506$	1.76113e12	1.19430
$507$	6.59094e11	0.443008
$508$	−2.06707e12	−1.37711
$509$	1.99900e12	1.32003	0.660015	−	0.751253i	$-0.270550\pi$
$509$	1.99900e12	1.32003	0.660015	+	0.751253i	$0.270550\pi$
$510$	0	0
$511$	3.94311e12	2.55826
$512$	−1.29971e12	−0.835859
$513$	−7.17484e11	−0.457387
$514$	−1.07971e12	−0.682297
$515$	−7.61751e11	−0.477178
$516$	8.67028e11	0.538405
$517$	−8.49117e11	−0.522709
$518$	3.96508e12	2.41973
$519$	−7.86171e11	−0.475624
$520$	−8.40726e11	−0.504243
$521$	2.07948e12	1.23648	0.618238	−	0.785991i	$-0.287847\pi$
$521$	2.07948e12	1.23648	0.618238	+	0.785991i	$0.287847\pi$
$522$	2.72061e11	0.160379
$523$	9.71740e11	0.567927	0.283963	−	0.958835i	$-0.408351\pi$
$523$	9.71740e11	0.567927	0.283963	+	0.958835i	$0.408351\pi$
$524$	−4.10618e12	−2.37929
$525$	−9.22682e11	−0.530073
$526$	−7.78134e11	−0.443219
$527$	0	0
$528$	−2.86372e11	−0.160353
$529$	3.80933e12	2.11494
$530$	1.27013e12	0.699210
$531$	5.56220e11	0.303614
$532$	−1.85239e12	−1.00260
$533$	−5.13020e11	−0.275335
$534$	1.55067e11	0.0825246
$535$	3.08505e12	1.62806
$536$	−1.19956e12	−0.627738
$537$	5.15290e11	0.267404
$538$	2.00205e12	1.03028
$539$	−1.61019e12	−0.821726
$540$	−3.52509e12	−1.78402
$541$	−2.59266e12	−1.30124	−0.650620	−	0.759403i	$-0.725491\pi$
$541$	−2.59266e12	−1.30124	−0.650620	+	0.759403i	$0.725491\pi$
$542$	1.16685e12	0.580787
$543$	−1.57127e12	−0.775623
$544$	0	0
$545$	9.63098e11	0.467613
$546$	−3.18620e12	−1.53428
$547$	−5.58809e11	−0.266883	−0.133441	−	0.991057i	$-0.542603\pi$
$547$	−5.58809e11	−0.266883	−0.133441	+	0.991057i	$0.542603\pi$
$548$	−1.79783e12	−0.851600
$549$	1.20637e12	0.566766
$550$	5.36471e11	0.249985
$551$	−3.29768e11	−0.152415
$552$	2.03251e12	0.931764
$553$	−5.90232e12	−2.68386
$554$	−1.20033e12	−0.541387
$555$	−2.03252e12	−0.909321
$556$	−5.81364e11	−0.257995
$557$	3.73545e12	1.64435	0.822175	−	0.569235i	$-0.192761\pi$
$557$	3.73545e12	1.64435	0.822175	+	0.569235i	$0.192761\pi$
$558$	9.32699e11	0.407275
$559$	7.23108e11	0.313221
$560$	2.00967e12	0.863532
$561$	0	0
$562$	−2.34969e12	−0.993566
$563$	4.79014e11	0.200937	0.100469	−	0.994940i	$-0.467966\pi$
$563$	4.79014e11	0.200937	0.100469	+	0.994940i	$0.467966\pi$
$564$	−3.41180e12	−1.41980
$565$	−2.39632e12	−0.989299
$566$	−7.37535e11	−0.302071
$567$	−2.64334e12	−1.07406
$568$	−1.87508e11	−0.0755881
$569$	−4.70752e12	−1.88273	−0.941363	−	0.337395i	$-0.890454\pi$
$569$	−4.70752e12	−1.88273	−0.941363	+	0.337395i	$0.890454\pi$
$570$	1.62636e12	0.645325
$571$	−4.64774e11	−0.182970	−0.0914848	−	0.995806i	$-0.529161\pi$
$571$	−4.64774e11	−0.182970	−0.0914848	+	0.995806i	$0.529161\pi$
$572$	1.08160e12	0.422459
$573$	−5.65918e10	−0.0219310
$574$	−2.73209e12	−1.05049
$575$	1.70905e12	0.652004
$576$	1.19122e12	0.450911
$577$	1.23582e11	0.0464158	0.0232079	−	0.999731i	$-0.492612\pi$
$577$	1.23582e11	0.0464158	0.0232079	+	0.999731i	$0.492612\pi$
$578$	0	0
$579$	1.64345e12	0.607719
$580$	−1.62020e12	−0.594486
$581$	6.22352e12	2.26591
$582$	−3.69819e12	−1.33609
$583$	−4.69340e11	−0.168259
$584$	−2.64590e12	−0.941274
$585$	−6.53346e11	−0.230644
$586$	1.24229e12	0.435195
$587$	−2.85606e12	−0.992878	−0.496439	−	0.868072i	$-0.665359\pi$
$587$	−2.85606e12	−0.992878	−0.496439	+	0.868072i	$0.665359\pi$
$588$	−6.46981e12	−2.23200
$589$	−1.13054e12	−0.387049
$590$	−5.67346e12	−1.92759
$591$	−3.35559e12	−1.13142
$592$	1.19425e12	0.399621
$593$	−6.66611e11	−0.221374	−0.110687	−	0.993855i	$-0.535305\pi$
$593$	−6.66611e11	−0.221374	−0.110687	+	0.993855i	$0.535305\pi$
$594$	2.23105e12	0.735308
$595$	0	0
$596$	3.06358e12	0.994538
$597$	2.96351e12	0.954819
$598$	5.90169e12	1.88721
$599$	−2.92151e11	−0.0927230	−0.0463615	−	0.998925i	$-0.514763\pi$
$599$	−2.92151e11	−0.0927230	−0.0463615	+	0.998925i	$0.514763\pi$
$600$	6.19138e11	0.195032
$601$	3.82913e12	1.19720	0.598598	−	0.801050i	$-0.295725\pi$
$601$	3.82913e12	1.19720	0.598598	+	0.801050i	$0.295725\pi$
$602$	3.85092e12	1.19503
$603$	−9.32199e11	−0.287131
$604$	6.04236e12	1.84731
$605$	3.12143e12	0.947228
$606$	−6.30460e12	−1.89902
$607$	1.66205e12	0.496928	0.248464	−	0.968641i	$-0.420074\pi$
$607$	1.66205e12	0.496928	0.248464	+	0.968641i	$0.420074\pi$
$608$	−1.84157e12	−0.546539
$609$	−1.76364e12	−0.519557
$610$	−1.23050e13	−3.59829
$611$	−2.84547e12	−0.825977
$612$	0	0
$613$	−3.34407e12	−0.956540	−0.478270	−	0.878213i	$-0.658736\pi$
$613$	−3.34407e12	−0.956540	−0.478270	+	0.878213i	$0.658736\pi$
$614$	3.32725e11	0.0944774
$615$	1.40049e12	0.394767
$616$	1.65445e12	0.462957
$617$	3.02182e12	0.839431	0.419716	−	0.907656i	$-0.362130\pi$
$617$	3.02182e12	0.839431	0.419716	+	0.907656i	$0.362130\pi$
$618$	1.93716e12	0.534217
$619$	4.41312e12	1.20820	0.604099	−	0.796909i	$-0.293533\pi$
$619$	4.41312e12	1.20820	0.604099	+	0.796909i	$0.293533\pi$
$620$	−5.55448e12	−1.50966
$621$	7.10752e12	1.91781
$622$	5.48784e12	1.47009
$623$	4.02115e11	0.106944
$624$	−9.59659e11	−0.253388
$625$	−4.70333e12	−1.23295
$626$	2.78286e12	0.724281
$627$	−6.00971e11	−0.155292
$628$	1.00675e12	0.258288
$629$	0	0
$630$	−3.47940e12	−0.879977
$631$	2.58843e12	0.649986	0.324993	−	0.945716i	$-0.394638\pi$
$631$	2.58843e12	0.649986	0.324993	+	0.945716i	$0.394638\pi$
$632$	3.96057e12	0.987486
$633$	−2.13798e12	−0.529281
$634$	−4.42336e12	−1.08730
$635$	4.70620e12	1.14865
$636$	−1.88583e12	−0.457031
$637$	−5.39588e12	−1.29848
$638$	1.02543e12	0.245026
$639$	−1.45717e11	−0.0345745
$640$	−5.70141e12	−1.34330
$641$	−2.23675e12	−0.523307	−0.261653	−	0.965162i	$-0.584268\pi$
$641$	−2.23675e12	−0.523307	−0.261653	+	0.965162i	$0.584268\pi$
$642$	−7.84539e12	−1.82267
$643$	−4.25453e12	−0.981527	−0.490764	−	0.871293i	$-0.663282\pi$
$643$	−4.25453e12	−0.981527	−0.490764	+	0.871293i	$0.663282\pi$
$644$	1.83501e13	4.20389
$645$	−1.97401e12	−0.449086
$646$	0	0
$647$	3.30319e11	0.0741079	0.0370539	−	0.999313i	$-0.488203\pi$
$647$	3.30319e11	0.0741079	0.0370539	+	0.999313i	$0.488203\pi$
$648$	1.77373e12	0.395186
$649$	2.09646e12	0.463858
$650$	1.79776e12	0.395023
$651$	−6.04626e12	−1.31939
$652$	−6.65941e12	−1.44318
$653$	−1.35293e12	−0.291184	−0.145592	−	0.989345i	$-0.546509\pi$
$653$	−1.35293e12	−0.291184	−0.145592	+	0.989345i	$0.546509\pi$
$654$	−2.44920e12	−0.523509
$655$	9.34874e12	1.98457
$656$	−8.22885e11	−0.173489
$657$	−2.05619e12	−0.430545
$658$	−1.51535e13	−3.15136
$659$	3.08677e12	0.637558	0.318779	−	0.947829i	$-0.396727\pi$
$659$	3.08677e12	0.637558	0.318779	+	0.947829i	$0.396727\pi$
$660$	−2.95265e12	−0.605709
$661$	6.15803e12	1.25469	0.627343	−	0.778743i	$-0.284142\pi$
$661$	6.15803e12	1.25469	0.627343	+	0.778743i	$0.284142\pi$
$662$	−3.78768e12	−0.766500
$663$	0	0
$664$	−4.17610e12	−0.833710
$665$	4.21742e12	0.836276
$666$	−2.06764e12	−0.407231
$667$	3.26674e12	0.639070
$668$	9.75448e12	1.89544
$669$	3.91575e12	0.755783
$670$	9.50845e12	1.82294
$671$	4.54694e12	0.865900
$672$	−9.84894e12	−1.86306
$673$	7.92971e12	1.49001	0.745005	−	0.667058i	$-0.232447\pi$
$673$	7.92971e12	1.49001	0.745005	+	0.667058i	$0.232447\pi$
$674$	−8.39121e12	−1.56623
$675$	2.16508e12	0.401427
$676$	−3.99290e12	−0.735408
$677$	2.46341e12	0.450701	0.225350	−	0.974278i	$-0.427647\pi$
$677$	2.46341e12	0.450701	0.225350	+	0.974278i	$0.427647\pi$
$678$	6.09395e12	1.10755
$679$	−9.59003e12	−1.73143
$680$	0	0
$681$	4.34579e12	0.774295
$682$	3.51545e12	0.622230
$683$	5.68009e12	0.998763	0.499381	−	0.866382i	$-0.333561\pi$
$683$	5.68009e12	0.998763	0.499381	+	0.866382i	$0.333561\pi$
$684$	9.65951e11	0.168734
$685$	4.09320e12	0.710323
$686$	−1.34703e13	−2.32230
$687$	−6.87088e11	−0.117681
$688$	1.15987e12	0.197361
$689$	−1.57280e12	−0.265880
$690$	−1.61110e13	−2.70583
$691$	5.44139e12	0.907943	0.453971	−	0.891016i	$-0.350007\pi$
$691$	5.44139e12	0.907943	0.453971	+	0.891016i	$0.350007\pi$
$692$	4.76275e12	0.789552
$693$	1.28571e12	0.211759
$694$	4.67566e12	0.765112
$695$	1.32362e12	0.215195
$696$	1.18344e12	0.191163
$697$	0	0
$698$	3.53000e12	0.562892
$699$	−8.66441e9	−0.00137275
$700$	5.58976e12	0.879938
$701$	7.42727e11	0.116171	0.0580856	−	0.998312i	$-0.481500\pi$
$701$	7.42727e11	0.116171	0.0580856	+	0.998312i	$0.481500\pi$
$702$	7.47643e12	1.16192
$703$	2.50621e12	0.387007
$704$	4.48984e12	0.688897
$705$	7.76781e12	1.18426
$706$	−3.24326e12	−0.491316
$707$	−1.63489e13	−2.46094
$708$	8.42367e12	1.25995
$709$	5.72142e12	0.850347	0.425173	−	0.905112i	$-0.360213\pi$
$709$	5.72142e12	0.850347	0.425173	+	0.905112i	$0.360213\pi$
$710$	1.48631e12	0.219507
$711$	3.07784e12	0.451682
$712$	−2.69827e11	−0.0393483
$713$	1.11993e13	1.62288
$714$	0	0
$715$	−2.46253e12	−0.352375
$716$	−3.12171e12	−0.443899
$717$	−8.29196e12	−1.17171
$718$	−1.41794e13	−1.99112
$719$	−4.81513e12	−0.671936	−0.335968	−	0.941873i	$-0.609063\pi$
$719$	−4.81513e12	−0.671936	−0.335968	+	0.941873i	$0.609063\pi$
$720$	−1.04797e12	−0.145329
$721$	5.02340e12	0.692291
$722$	9.31319e12	1.27550
$723$	6.95771e12	0.946986
$724$	9.51899e12	1.28756
$725$	9.95108e11	0.133767
$726$	−7.93792e12	−1.06045
$727$	−1.09017e13	−1.44740	−0.723700	−	0.690114i	$-0.757560\pi$
$727$	−1.09017e13	−1.44740	−0.723700	+	0.690114i	$0.757560\pi$
$728$	5.54420e12	0.731557
$729$	8.38145e12	1.09912
$730$	2.09732e13	2.73345
$731$	0	0
$732$	1.82698e13	2.35198
$733$	−5.31441e12	−0.679966	−0.339983	−	0.940432i	$-0.610421\pi$
$733$	−5.31441e12	−0.679966	−0.339983	+	0.940432i	$0.610421\pi$
$734$	−1.90517e13	−2.42272
$735$	1.47301e13	1.86172
$736$	1.82429e13	2.29162
$737$	−3.51356e12	−0.438676
$738$	1.42468e12	0.176793
$739$	−9.75394e12	−1.20304	−0.601520	−	0.798857i	$-0.705438\pi$
$739$	−9.75394e12	−1.20304	−0.601520	+	0.798857i	$0.705438\pi$
$740$	1.23134e13	1.50950
$741$	−2.01391e12	−0.245390
$742$	−8.37594e12	−1.01442
$743$	−3.69441e12	−0.444729	−0.222365	−	0.974964i	$-0.571378\pi$
$743$	−3.69441e12	−0.444729	−0.222365	+	0.974964i	$0.571378\pi$
$744$	4.05716e12	0.485449
$745$	−6.97501e12	−0.829548
$746$	−2.46281e12	−0.291142
$747$	−3.24534e12	−0.381344
$748$	0	0
$749$	−2.03445e13	−2.36199
$750$	8.37700e12	0.966747
$751$	9.80164e12	1.12440	0.562198	−	0.827003i	$-0.309956\pi$
$751$	9.80164e12	1.12440	0.562198	+	0.827003i	$0.309956\pi$
$752$	−4.56413e12	−0.520449
$753$	4.37895e12	0.496355
$754$	3.43630e12	0.387186
$755$	−1.37569e13	−1.54085
$756$	2.32464e13	2.58826
$757$	3.18101e11	0.0352073	0.0176037	−	0.999845i	$-0.494396\pi$
$757$	3.18101e11	0.0352073	0.0176037	+	0.999845i	$0.494396\pi$
$758$	1.18229e13	1.30080
$759$	5.95332e12	0.651135
$760$	−2.82997e12	−0.307695
$761$	1.17912e13	1.27446	0.637230	−	0.770674i	$-0.280080\pi$
$761$	1.17912e13	1.27446	0.637230	+	0.770674i	$0.280080\pi$
$762$	−1.19681e13	−1.28596
$763$	−6.35119e12	−0.678414
$764$	3.42842e11	0.0364061
$765$	0	0
$766$	9.46161e12	0.992969
$767$	7.02541e12	0.732981
$768$	1.64018e12	0.170124
$769$	6.40708e11	0.0660681	0.0330341	−	0.999454i	$-0.489483\pi$
$769$	6.40708e11	0.0660681	0.0330341	+	0.999454i	$0.489483\pi$
$770$	−1.31142e13	−1.34442
$771$	−3.64986e12	−0.371990
$772$	−9.95629e12	−1.00883
$773$	1.64262e13	1.65474	0.827371	−	0.561656i	$-0.189835\pi$
$773$	1.64262e13	1.65474	0.827371	+	0.561656i	$0.189835\pi$
$774$	−2.00811e12	−0.201119
$775$	3.41150e12	0.339694
$776$	6.43510e12	0.637056
$777$	1.34036e13	1.31925
$778$	2.45089e13	2.39836
$779$	−1.72688e12	−0.168013
$780$	−9.89459e12	−0.957132
$781$	−5.49223e11	−0.0528225
$782$	0	0
$783$	4.13840e12	0.393464
$784$	−8.65500e12	−0.818172
$785$	−2.29213e12	−0.215439
$786$	−2.37742e13	−2.22180
$787$	−2.95065e12	−0.274177	−0.137089	−	0.990559i	$-0.543774\pi$
$787$	−2.95065e12	−0.274177	−0.137089	+	0.990559i	$0.543774\pi$
$788$	2.03287e13	1.87820
$789$	−2.63041e12	−0.241644
$790$	−3.13940e13	−2.86764
$791$	1.58027e13	1.43528
$792$	−8.62734e11	−0.0779137
$793$	1.52372e13	1.36828
$794$	−1.88724e13	−1.68513
$795$	4.29356e12	0.381211
$796$	−1.79534e13	−1.58503
$797$	−1.14843e13	−1.00819	−0.504094	−	0.863649i	$-0.668173\pi$
$797$	−1.14843e13	−1.00819	−0.504094	+	0.863649i	$0.668173\pi$
$798$	−1.07251e13	−0.936240
$799$	0	0
$800$	5.55711e12	0.479671
$801$	−2.09688e11	−0.0179981
$802$	3.42964e12	0.292728
$803$	−7.75000e12	−0.657782
$804$	−1.41177e13	−1.19155
$805$	−4.17785e13	−3.50648
$806$	1.17806e13	0.983238
$807$	6.76774e12	0.561711
$808$	1.09704e13	0.905467
$809$	9.69132e12	0.795453	0.397727	−	0.917504i	$-0.369799\pi$
$809$	9.69132e12	0.795453	0.397727	+	0.917504i	$0.369799\pi$
$810$	−1.40598e13	−1.14761
$811$	1.92605e13	1.56341	0.781707	−	0.623646i	$-0.214349\pi$
$811$	1.92605e13	1.56341	0.781707	+	0.623646i	$0.214349\pi$
$812$	1.06844e13	0.862482
$813$	3.94441e12	0.316647
$814$	−7.79317e12	−0.622163
$815$	1.51618e13	1.20377
$816$	0	0
$817$	2.43406e12	0.191131
$818$	−3.04294e13	−2.37631
$819$	4.30851e12	0.334619
$820$	−8.48438e12	−0.655327
$821$	2.01071e13	1.54456	0.772279	−	0.635284i	$-0.219117\pi$
$821$	2.01071e13	1.54456	0.772279	+	0.635284i	$0.219117\pi$
$822$	−1.04092e13	−0.795231
$823$	−1.02420e13	−0.778188	−0.389094	−	0.921198i	$-0.627212\pi$
$823$	−1.02420e13	−0.778188	−0.389094	+	0.921198i	$0.627212\pi$
$824$	−3.37080e12	−0.254718
$825$	1.81349e12	0.136293
$826$	3.74139e13	2.79655
$827$	8.99775e12	0.668897	0.334448	−	0.942414i	$-0.391450\pi$
$827$	8.99775e12	0.668897	0.334448	+	0.942414i	$0.391450\pi$
$828$	−9.56888e12	−0.707497
$829$	8.74712e12	0.643235	0.321617	−	0.946870i	$-0.395774\pi$
$829$	8.74712e12	0.643235	0.321617	+	0.946870i	$0.395774\pi$
$830$	3.31025e13	2.42108
$831$	−4.05761e12	−0.295166
$832$	1.50459e13	1.08858
$833$	0	0
$834$	−3.36602e12	−0.240918
$835$	−2.22085e13	−1.58099
$836$	3.64078e12	0.257790
$837$	1.41876e13	0.999179
$838$	−1.95645e13	−1.37047
$839$	−1.38983e13	−0.968352	−0.484176	−	0.874971i	$-0.660880\pi$
$839$	−1.38983e13	−0.968352	−0.484176	+	0.874971i	$0.660880\pi$
$840$	−1.51351e13	−1.04888
$841$	−1.26051e13	−0.868887
$842$	−8.96241e12	−0.614498
$843$	−7.94289e12	−0.541695
$844$	1.29522e13	0.878624
$845$	9.09083e12	0.613407
$846$	7.90201e12	0.530361
$847$	−2.05844e13	−1.37424
$848$	−2.52277e12	−0.167532
$849$	−2.49317e12	−0.164690
$850$	0	0
$851$	−2.48270e13	−1.62271
$852$	−2.20680e12	−0.143478
$853$	1.12894e13	0.730127	0.365064	−	0.930983i	$-0.381047\pi$
$853$	1.12894e13	0.730127	0.365064	+	0.930983i	$0.381047\pi$
$854$	8.11457e13	5.22042
$855$	−2.19923e12	−0.140742
$856$	1.36515e13	0.869059
$857$	1.71291e13	1.08473	0.542365	−	0.840143i	$-0.317529\pi$
$857$	1.71291e13	1.08473	0.542365	+	0.840143i	$0.317529\pi$
$858$	6.26232e12	0.394496
$859$	−4.07005e12	−0.255053	−0.127527	−	0.991835i	$-0.540704\pi$
$859$	−4.07005e12	−0.255053	−0.127527	+	0.991835i	$0.540704\pi$
$860$	1.19588e13	0.745498
$861$	−9.23557e12	−0.572730
$862$	3.04656e13	1.87943
$863$	−2.43498e13	−1.49433	−0.747167	−	0.664637i	$-0.768586\pi$
$863$	−2.43498e13	−1.49433	−0.747167	+	0.664637i	$0.768586\pi$
$864$	2.31106e13	1.41091
$865$	−1.08436e13	−0.658568
$866$	−1.47328e13	−0.890134
$867$	0	0
$868$	3.66292e13	2.19023
$869$	1.16007e13	0.690075
$870$	−9.38071e12	−0.555136
$871$	−1.17743e13	−0.693189
$872$	4.26177e12	0.249612
$873$	5.00085e12	0.291393
$874$	1.98657e13	1.15160
$875$	2.17230e13	1.25281
$876$	−3.11399e13	−1.78669
$877$	−3.24681e13	−1.85336	−0.926679	−	0.375854i	$-0.877349\pi$
$877$	−3.24681e13	−1.85336	−0.926679	+	0.375854i	$0.877349\pi$
$878$	1.00597e13	0.571294
$879$	4.19944e12	0.237269
$880$	−3.94991e12	−0.222032
$881$	−5.75612e12	−0.321913	−0.160956	−	0.986962i	$-0.551458\pi$
$881$	−5.75612e12	−0.321913	−0.160956	+	0.986962i	$0.551458\pi$
$882$	1.49846e13	0.833754
$883$	1.16594e13	0.645438	0.322719	−	0.946495i	$-0.395403\pi$
$883$	1.16594e13	0.645438	0.322719	+	0.946495i	$0.395403\pi$
$884$	0	0
$885$	−1.91786e13	−1.05093
$886$	−9.53731e12	−0.519965
$887$	−1.26043e13	−0.683696	−0.341848	−	0.939755i	$-0.611053\pi$
$887$	−1.26043e13	−0.683696	−0.341848	+	0.939755i	$0.611053\pi$
$888$	−8.99405e12	−0.485397
$889$	−3.10352e13	−1.66647
$890$	2.13883e12	0.114267
$891$	5.19537e12	0.276164
$892$	−2.37222e13	−1.25462
$893$	−9.57813e12	−0.504022
$894$	1.77377e13	0.928708
$895$	7.10736e12	0.370258
$896$	3.75981e13	1.94886
$897$	1.99501e13	1.02891
$898$	−7.56726e11	−0.0388325
$899$	6.52086e12	0.332955
$900$	−2.91485e12	−0.148090
$901$	0	0
$902$	5.36980e12	0.270103
$903$	1.30177e13	0.651535
$904$	−1.06039e13	−0.528089
$905$	−2.16724e13	−1.07396
$906$	3.49844e13	1.72503
$907$	2.63722e13	1.29394	0.646969	−	0.762516i	$-0.276036\pi$
$907$	2.63722e13	1.29394	0.646969	+	0.762516i	$0.276036\pi$
$908$	−2.63275e13	−1.28536
$909$	8.52535e12	0.414166
$910$	−4.39470e13	−2.12443
$911$	−4.17031e12	−0.200602	−0.100301	−	0.994957i	$-0.531981\pi$
$911$	−4.17031e12	−0.200602	−0.100301	+	0.994957i	$0.531981\pi$
$912$	−3.23031e12	−0.154621
$913$	−1.22320e13	−0.582613
$914$	−5.51282e13	−2.61286
$915$	−4.15958e13	−1.96180
$916$	4.16249e12	0.195354
$917$	−6.16506e13	−2.87922
$918$	0	0
$919$	3.08220e13	1.42541	0.712706	−	0.701462i	$-0.247469\pi$
$919$	3.08220e13	1.42541	0.712706	+	0.701462i	$0.247469\pi$
$920$	2.80342e13	1.29016
$921$	1.12475e12	0.0515093
$922$	−3.34366e13	−1.52382
$923$	−1.84049e12	−0.0834692
$924$	1.94714e13	0.878765
$925$	−7.56274e12	−0.339658
$926$	−4.64912e13	−2.07788
$927$	−2.61951e12	−0.116510
$928$	1.06220e13	0.470156
$929$	−2.37926e12	−0.104802	−0.0524011	−	0.998626i	$-0.516687\pi$
$929$	−2.37926e12	−0.104802	−0.0524011	+	0.998626i	$0.516687\pi$
$930$	−3.21597e13	−1.40974
$931$	−1.81631e13	−0.792348
$932$	5.24904e10	0.00227881
$933$	1.85511e13	0.801499
$934$	7.67920e12	0.330183
$935$	0	0
$936$	−2.89110e12	−0.123118
$937$	3.37885e13	1.43199	0.715995	−	0.698105i	$-0.245973\pi$
$937$	3.37885e13	1.43199	0.715995	+	0.698105i	$0.245973\pi$
$938$	−6.27039e13	−2.64473
$939$	9.40719e12	0.394880
$940$	−4.70586e13	−1.96591
$941$	1.76401e13	0.733411	0.366705	−	0.930337i	$-0.380486\pi$
$941$	1.76401e13	0.733411	0.366705	+	0.930337i	$0.380486\pi$
$942$	5.82897e12	0.241192
$943$	1.71068e13	0.704474
$944$	1.12688e13	0.461852
$945$	−5.29262e13	−2.15887
$946$	−7.56880e12	−0.307268
$947$	3.73290e13	1.50824	0.754121	−	0.656736i	$-0.228063\pi$
$947$	3.73290e13	1.50824	0.754121	+	0.656736i	$0.228063\pi$
$948$	4.66123e13	1.87440
$949$	−2.59709e13	−1.03942
$950$	6.05145e12	0.241048
$951$	−1.49528e13	−0.592801
$952$	0	0
$953$	−4.03536e13	−1.58476	−0.792381	−	0.610026i	$-0.791159\pi$
$953$	−4.03536e13	−1.58476	−0.792381	+	0.610026i	$0.791159\pi$
$954$	4.36774e12	0.170722
$955$	−7.80566e11	−0.0303665
$956$	5.02340e13	1.94508
$957$	3.46636e12	0.133589
$958$	4.98199e13	1.91099
$959$	−2.69928e13	−1.03054
$960$	−4.10735e13	−1.56078
$961$	−4.08433e12	−0.154478
$962$	−2.61156e13	−0.983133
$963$	1.06089e13	0.397513
$964$	−4.21509e13	−1.57203
$965$	2.26680e13	0.841472
$966$	1.06244e14	3.92562
$967$	−4.76728e13	−1.75328	−0.876641	−	0.481145i	$-0.840221\pi$
$967$	−4.76728e13	−1.75328	−0.876641	+	0.481145i	$0.840221\pi$
$968$	1.38125e13	0.505632
$969$	0	0
$970$	−5.10088e13	−1.85000
$971$	1.28032e13	0.462204	0.231102	−	0.972930i	$-0.425767\pi$
$971$	1.28032e13	0.462204	0.231102	+	0.972930i	$0.425767\pi$
$972$	−2.15504e13	−0.774384
$973$	−8.72866e12	−0.312205
$974$	2.59882e13	0.925252
$975$	6.07716e12	0.215367
$976$	2.44405e13	0.862155
$977$	4.43718e13	1.55805	0.779026	−	0.626992i	$-0.215714\pi$
$977$	4.43718e13	1.55805	0.779026	+	0.626992i	$0.215714\pi$
$978$	−3.85571e13	−1.34766
$979$	−7.90339e11	−0.0274974
$980$	−8.92376e13	−3.09051
$981$	3.31191e12	0.114174
$982$	−7.98686e13	−2.74078
$983$	3.07326e13	1.04981	0.524903	−	0.851162i	$-0.324102\pi$
$983$	3.07326e13	1.04981	0.524903	+	0.851162i	$0.324102\pi$
$984$	6.19725e12	0.210727
$985$	−4.62833e13	−1.56661
$986$	0	0
$987$	−5.12251e13	−1.71813
$988$	1.22006e13	0.407356
$989$	−2.41122e13	−0.801407
$990$	6.83859e12	0.226260
$991$	−1.60170e13	−0.527533	−0.263766	−	0.964587i	$-0.584965\pi$
$991$	−1.60170e13	−0.527533	−0.263766	+	0.964587i	$0.584965\pi$
$992$	3.64152e13	1.19394
$993$	−1.28039e13	−0.417898
$994$	−9.80156e12	−0.318461
$995$	4.08754e13	1.32208
$996$	−4.91489e13	−1.58251
$997$	−1.27762e13	−0.409518	−0.204759	−	0.978812i	$-0.565641\pi$
$997$	−1.27762e13	−0.409518	−0.204759	+	0.978812i	$0.565641\pi$
$998$	−4.95590e12	−0.158138
$999$	−3.14515e13	−0.999072

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.i.1.7		52
17.11	odd	16		17.10.d.a.2.2	✓	52
17.14	odd	16		17.10.d.a.9.2	yes	52
17.16	even	2	inner	289.10.a.i.1.8		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.d.a.2.2	✓	52	17.11	odd	16
17.10.d.a.9.2	yes	52	17.14	odd	16
289.10.a.i.1.7		52	1.1	even	1	trivial
289.10.a.i.1.8		52	17.16	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-35.0759 q^{2} -118.571 q^{3} +718.321 q^{4} -1635.44 q^{5} +4158.98 q^{6} +10785.0 q^{7} -7236.92 q^{8} -5623.96 q^{9} +O(q^{10})\)	\(q-35.0759 q^{2} -118.571 q^{3} +718.321 q^{4} -1635.44 q^{5} +4158.98 q^{6} +10785.0 q^{7} -7236.92 q^{8} -5623.96 q^{9} +57364.5 q^{10} -21197.3 q^{11} -85172.0 q^{12} -71034.1 q^{13} -378293. q^{14} +193915. q^{15} -113939. q^{16} +197266. q^{18} -239108. q^{19} -1.17477e6 q^{20} -1.27878e6 q^{21} +743516. q^{22} +2.36865e6 q^{23} +858087. q^{24} +721532. q^{25} +2.49159e6 q^{26} +3.00067e6 q^{27} +7.74707e6 q^{28} +1.37916e6 q^{29} -6.80176e6 q^{30} +4.72814e6 q^{31} +7.70182e6 q^{32} +2.51339e6 q^{33} -1.76381e7 q^{35} -4.03981e6 q^{36} -1.04815e7 q^{37} +8.38694e6 q^{38} +8.42257e6 q^{39} +1.18355e7 q^{40} +7.22217e6 q^{41} +4.48545e7 q^{42} -1.01797e7 q^{43} -1.52265e7 q^{44} +9.19763e6 q^{45} -8.30825e7 q^{46} +4.00577e7 q^{47} +1.35098e7 q^{48} +7.59618e7 q^{49} -2.53084e7 q^{50} -5.10253e7 q^{52} +2.21414e7 q^{53} -1.05251e8 q^{54} +3.46669e7 q^{55} -7.80499e7 q^{56} +2.83512e7 q^{57} -4.83753e7 q^{58} -9.89019e7 q^{59} +1.39293e8 q^{60} -2.14505e8 q^{61} -1.65844e8 q^{62} -6.06542e7 q^{63} -2.11812e8 q^{64} +1.16172e8 q^{65} -8.81594e7 q^{66} +1.65755e8 q^{67} -2.80852e8 q^{69} +6.18674e8 q^{70} +2.59100e7 q^{71} +4.07001e7 q^{72} +3.65612e8 q^{73} +3.67649e8 q^{74} -8.55527e7 q^{75} -1.71756e8 q^{76} -2.28612e8 q^{77} -2.95430e8 q^{78} -5.47273e8 q^{79} +1.86340e8 q^{80} -2.45095e8 q^{81} -2.53324e8 q^{82} +5.77055e8 q^{83} -9.18576e8 q^{84} +3.57064e8 q^{86} -1.63528e8 q^{87} +1.53403e8 q^{88} +3.72848e7 q^{89} -3.22616e8 q^{90} -7.66100e8 q^{91} +1.70145e9 q^{92} -5.60619e8 q^{93} -1.40506e9 q^{94} +3.91046e8 q^{95} -9.13211e8 q^{96} -8.89204e8 q^{97} -2.66443e9 q^{98} +1.19213e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) \) 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9} + 156200 q^{13} + 1207872 q^{15} + 3407880 q^{16} + 2193336 q^{18} + 1185568 q^{19} + 5198336 q^{21} + 13827692 q^{25} + 3618944 q^{26} - 9167544 q^{30} + 61884888 q^{32} + 1635208 q^{33} + 46992776 q^{35} + 156027320 q^{36} + 84813952 q^{38} - 4635776 q^{42} + 125448912 q^{43} + 164193176 q^{47} + 270850284 q^{49} - 226223888 q^{50} + 103553016 q^{52} + 426167208 q^{53} + 677761520 q^{55} + 375214512 q^{59} + 336918024 q^{60} + 190014416 q^{64} + 1377178928 q^{66} + 311910088 q^{67} + 533688136 q^{69} + 1477690280 q^{70} + 2757942680 q^{72} + 4047975520 q^{76} + 3440336432 q^{77} + 3266558756 q^{81} + 2072890608 q^{83} + 2630025952 q^{84} + 1538547296 q^{86} - 1010436256 q^{87} + 1873849184 q^{89} - 1998451624 q^{93} - 6880776704 q^{94} - 4667454128 q^{98}+O(q^{100}) \) 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9 + 156200 * q^13 + 1207872 * q^15 + 3407880 * q^16 + 2193336 * q^18 + 1185568 * q^19 + 5198336 * q^21 + 13827692 * q^25 + 3618944 * q^26 - 9167544 * q^30 + 61884888 * q^32 + 1635208 * q^33 + 46992776 * q^35 + 156027320 * q^36 + 84813952 * q^38 - 4635776 * q^42 + 125448912 * q^43 + 164193176 * q^47 + 270850284 * q^49 - 226223888 * q^50 + 103553016 * q^52 + 426167208 * q^53 + 677761520 * q^55 + 375214512 * q^59 + 336918024 * q^60 + 190014416 * q^64 + 1377178928 * q^66 + 311910088 * q^67 + 533688136 * q^69 + 1477690280 * q^70 + 2757942680 * q^72 + 4047975520 * q^76 + 3440336432 * q^77 + 3266558756 * q^81 + 2072890608 * q^83 + 2630025952 * q^84 + 1538547296 * q^86 - 1010436256 * q^87 + 1873849184 * q^89 - 1998451624 * q^93 - 6880776704 * q^94 - 4667454128 * q^98

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