LMFDB - Embedded newform 2401.4.a.c.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2401,4,Mod(1,2401)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2401, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("2401.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2401 = 7^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2401.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:	$141.663585924$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	no (minimal twist has level 49)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	2401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.904464 q^{2} -9.08614 q^{3} -7.18194 q^{4} +3.14137 q^{5} +8.21809 q^{6} +13.7315 q^{8} +55.5579 q^{9} +O(q^{10})$	\(q-0.904464 q^{2} -9.08614 q^{3} -7.18194 q^{4} +3.14137 q^{5} +8.21809 q^{6} +13.7315 q^{8} +55.5579 q^{9} -2.84125 q^{10} +53.3996 q^{11} +65.2561 q^{12} +57.9905 q^{13} -28.5429 q^{15} +45.0359 q^{16} -76.7741 q^{17} -50.2501 q^{18} -20.7785 q^{19} -22.5611 q^{20} -48.2981 q^{22} +66.2950 q^{23} -124.767 q^{24} -115.132 q^{25} -52.4504 q^{26} -259.481 q^{27} +27.2983 q^{29} +25.8160 q^{30} -294.724 q^{31} -150.586 q^{32} -485.196 q^{33} +69.4394 q^{34} -399.014 q^{36} +33.3900 q^{37} +18.7934 q^{38} -526.910 q^{39} +43.1357 q^{40} +92.5468 q^{41} -321.813 q^{43} -383.513 q^{44} +174.528 q^{45} -59.9615 q^{46} +393.190 q^{47} -409.202 q^{48} +104.133 q^{50} +697.580 q^{51} -416.485 q^{52} +514.909 q^{53} +234.691 q^{54} +167.748 q^{55} +188.796 q^{57} -24.6904 q^{58} -113.337 q^{59} +204.993 q^{60} -258.048 q^{61} +266.567 q^{62} -224.088 q^{64} +182.169 q^{65} +438.843 q^{66} +49.2473 q^{67} +551.387 q^{68} -602.366 q^{69} +461.374 q^{71} +762.894 q^{72} +428.267 q^{73} -30.2001 q^{74} +1046.10 q^{75} +149.230 q^{76} +476.571 q^{78} +93.0732 q^{79} +141.474 q^{80} +857.615 q^{81} -83.7053 q^{82} -1154.75 q^{83} -241.175 q^{85} +291.068 q^{86} -248.036 q^{87} +733.258 q^{88} +581.259 q^{89} -157.854 q^{90} -476.127 q^{92} +2677.90 q^{93} -355.626 q^{94} -65.2729 q^{95} +1368.24 q^{96} -348.070 q^{97} +2966.77 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) $ 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9} - 78 q^{10} + q^{11} + 91 q^{12} - 77 q^{13} - 161 q^{15} + 461 q^{16} - 211 q^{17} + 8 q^{18} - 314 q^{19} - 476 q^{20} - 61 q^{22} - 69 q^{23} - 330 q^{24} + 606 q^{25} - 504 q^{26} + 50 q^{27} + 57 q^{29} + 42 q^{30} - 638 q^{31} - 1600 q^{32} - 1574 q^{33} - 1343 q^{34} + 782 q^{36} + 71 q^{37} - 1359 q^{38} - 84 q^{39} + 155 q^{40} - 1393 q^{41} - 125 q^{43} + 52 q^{44} - 1129 q^{45} - 1454 q^{46} - 1483 q^{47} + 974 q^{48} + 3074 q^{50} - 2044 q^{51} - 3899 q^{52} + 2213 q^{53} - 1142 q^{54} - 1604 q^{55} + 98 q^{57} + 2403 q^{58} - 2073 q^{59} - 1519 q^{60} - 2575 q^{61} - 1742 q^{62} + 1358 q^{64} + 1876 q^{65} + 48 q^{66} + 176 q^{67} - 3038 q^{68} + 638 q^{69} - 1259 q^{71} - 3799 q^{72} + 307 q^{73} + 3845 q^{74} - 131 q^{75} - 1974 q^{76} - 6041 q^{78} + 22 q^{79} + 804 q^{80} + 795 q^{81} - 8043 q^{82} - 6349 q^{83} + 3094 q^{85} + 1745 q^{86} - 9508 q^{87} + 1299 q^{88} - 2253 q^{89} - 11156 q^{90} + 1284 q^{92} - 3430 q^{93} - 2738 q^{94} - 3290 q^{95} - 3031 q^{96} + 770 q^{97} + 5384 q^{99}+O(q^{100}) \) 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9 - 78 * q^10 + q^11 + 91 * q^12 - 77 * q^13 - 161 * q^15 + 461 * q^16 - 211 * q^17 + 8 * q^18 - 314 * q^19 - 476 * q^20 - 61 * q^22 - 69 * q^23 - 330 * q^24 + 606 * q^25 - 504 * q^26 + 50 * q^27 + 57 * q^29 + 42 * q^30 - 638 * q^31 - 1600 * q^32 - 1574 * q^33 - 1343 * q^34 + 782 * q^36 + 71 * q^37 - 1359 * q^38 - 84 * q^39 + 155 * q^40 - 1393 * q^41 - 125 * q^43 + 52 * q^44 - 1129 * q^45 - 1454 * q^46 - 1483 * q^47 + 974 * q^48 + 3074 * q^50 - 2044 * q^51 - 3899 * q^52 + 2213 * q^53 - 1142 * q^54 - 1604 * q^55 + 98 * q^57 + 2403 * q^58 - 2073 * q^59 - 1519 * q^60 - 2575 * q^61 - 1742 * q^62 + 1358 * q^64 + 1876 * q^65 + 48 * q^66 + 176 * q^67 - 3038 * q^68 + 638 * q^69 - 1259 * q^71 - 3799 * q^72 + 307 * q^73 + 3845 * q^74 - 131 * q^75 - 1974 * q^76 - 6041 * q^78 + 22 * q^79 + 804 * q^80 + 795 * q^81 - 8043 * q^82 - 6349 * q^83 + 3094 * q^85 + 1745 * q^86 - 9508 * q^87 + 1299 * q^88 - 2253 * q^89 - 11156 * q^90 + 1284 * q^92 - 3430 * q^93 - 2738 * q^94 - 3290 * q^95 - 3031 * q^96 + 770 * q^97 + 5384 * q^99

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 $

$2$	−0.904464	−0.319776	−0.159888	−	0.987135i	$-0.551113\pi$
$2$	−0.904464	−0.319776	−0.159888	+	0.987135i	$0.551113\pi$
$3$	−9.08614	−1.74863	−0.874314	−	0.485361i	$-0.838688\pi$
$3$	−9.08614	−1.74863	−0.874314	+	0.485361i	$0.838688\pi$
$4$	−7.18194	−0.897743
$5$	3.14137	0.280972	0.140486	−	0.990083i	$-0.455133\pi$
$5$	3.14137	0.280972	0.140486	+	0.990083i	$0.455133\pi$
$6$	8.21809	0.559170
$7$	0	0
$7$	0	0
$8$	13.7315	0.606853
$9$	55.5579	2.05770
$10$	−2.84125	−0.0898483
$11$	53.3996	1.46369	0.731845	−	0.681471i	$-0.238659\pi$
$11$	53.3996	1.46369	0.731845	+	0.681471i	$0.238659\pi$
$12$	65.2561	1.56982
$13$	57.9905	1.23721	0.618603	−	0.785704i	$-0.287699\pi$
$13$	57.9905	1.23721	0.618603	+	0.785704i	$0.287699\pi$
$14$	0	0
$15$	−28.5429	−0.491316
$16$	45.0359	0.703686
$17$	−76.7741	−1.09532	−0.547660	−	0.836701i	$-0.684481\pi$
$17$	−76.7741	−1.09532	−0.547660	+	0.836701i	$0.684481\pi$
$18$	−50.2501	−0.658004
$19$	−20.7785	−0.250890	−0.125445	−	0.992101i	$-0.540036\pi$
$19$	−20.7785	−0.250890	−0.125445	+	0.992101i	$0.540036\pi$
$20$	−22.5611	−0.252241
$21$	0	0
$22$	−48.2981	−0.468054
$23$	66.2950	0.601020	0.300510	−	0.953779i	$-0.402843\pi$
$23$	66.2950	0.601020	0.300510	+	0.953779i	$0.402843\pi$
$24$	−124.767	−1.06116
$25$	−115.132	−0.921055
$26$	−52.4504	−0.395629
$27$	−259.481	−1.84952
$28$	0	0
$29$	27.2983	0.174799	0.0873996	−	0.996173i	$-0.472144\pi$
$29$	27.2983	0.174799	0.0873996	+	0.996173i	$0.472144\pi$
$30$	25.8160	0.157111
$31$	−294.724	−1.70755	−0.853774	−	0.520643i	$-0.825692\pi$
$31$	−294.724	−1.70755	−0.853774	+	0.520643i	$0.825692\pi$
$32$	−150.586	−0.831875
$33$	−485.196	−2.55945
$34$	69.4394	0.350258
$35$	0	0
$36$	−399.014	−1.84729
$37$	33.3900	0.148359	0.0741795	−	0.997245i	$-0.476366\pi$
$37$	33.3900	0.148359	0.0741795	+	0.997245i	$0.476366\pi$
$38$	18.7934	0.0802288
$39$	−526.910	−2.16341
$40$	43.1357	0.170509
$41$	92.5468	0.352521	0.176261	−	0.984344i	$-0.443600\pi$
$41$	92.5468	0.352521	0.176261	+	0.984344i	$0.443600\pi$
$42$	0	0
$43$	−321.813	−1.14130	−0.570651	−	0.821193i	$-0.693309\pi$
$43$	−321.813	−1.14130	−0.570651	+	0.821193i	$0.693309\pi$
$44$	−383.513	−1.31402
$45$	174.528	0.578157
$46$	−59.9615	−0.192192
$47$	393.190	1.22027	0.610134	−	0.792298i	$-0.291116\pi$
$47$	393.190	1.22027	0.610134	+	0.792298i	$0.291116\pi$
$48$	−409.202	−1.23048
$49$	0	0
$50$	104.133	0.294532
$51$	697.580	1.91531
$52$	−416.485	−1.11069
$53$	514.909	1.33449	0.667247	−	0.744836i	$-0.267472\pi$
$53$	514.909	1.33449	0.667247	+	0.744836i	$0.267472\pi$
$54$	234.691	0.591434
$55$	167.748	0.411256
$56$	0	0
$57$	188.796	0.438714
$58$	−24.6904	−0.0558966
$59$	−113.337	−0.250088	−0.125044	−	0.992151i	$-0.539907\pi$
$59$	−113.337	−0.250088	−0.125044	+	0.992151i	$0.539907\pi$
$60$	204.993	0.441076
$61$	−258.048	−0.541634	−0.270817	−	0.962631i	$-0.587294\pi$
$61$	−258.048	−0.541634	−0.270817	+	0.962631i	$0.587294\pi$
$62$	266.567	0.546034
$63$	0	0
$64$	−224.088	−0.437672
$65$	182.169	0.347621
$66$	438.843	0.818452
$67$	49.2473	0.0897988	0.0448994	−	0.998992i	$-0.485703\pi$
$67$	49.2473	0.0897988	0.0448994	+	0.998992i	$0.485703\pi$
$68$	551.387	0.983316
$69$	−602.366	−1.05096
$70$	0	0
$71$	461.374	0.771198	0.385599	−	0.922666i	$-0.373995\pi$
$71$	461.374	0.771198	0.385599	+	0.922666i	$0.373995\pi$
$72$	762.894	1.24872
$73$	428.267	0.686642	0.343321	−	0.939218i	$-0.388448\pi$
$73$	428.267	0.686642	0.343321	+	0.939218i	$0.388448\pi$
$74$	−30.2001	−0.0474417
$75$	1046.10	1.61058
$76$	149.230	0.225235
$77$	0	0
$78$	476.571	0.691808
$79$	93.0732	0.132551	0.0662756	−	0.997801i	$-0.478888\pi$
$79$	93.0732	0.132551	0.0662756	+	0.997801i	$0.478888\pi$
$80$	141.474	0.197716
$81$	857.615	1.17643
$82$	−83.7053	−0.112728
$83$	−1154.75	−1.52711	−0.763556	−	0.645741i	$-0.776549\pi$
$83$	−1154.75	−1.52711	−0.763556	+	0.645741i	$0.776549\pi$
$84$	0	0
$85$	−241.175	−0.307755
$86$	291.068	0.364962
$87$	−248.036	−0.305659
$88$	733.258	0.888245
$89$	581.259	0.692285	0.346142	−	0.938182i	$-0.387491\pi$
$89$	581.259	0.692285	0.346142	+	0.938182i	$0.387491\pi$
$90$	−157.854	−0.184881
$91$	0	0
$92$	−476.127	−0.539562
$93$	2677.90	2.98587
$94$	−355.626	−0.390213
$95$	−65.2729	−0.0704932
$96$	1368.24	1.45464
$97$	−348.070	−0.364341	−0.182171	−	0.983267i	$-0.558312\pi$
$97$	−348.070	−0.364341	−0.182171	+	0.983267i	$0.558312\pi$
$98$	0	0
$99$	2966.77	3.01183
$100$	826.870	0.826870
$101$	693.964	0.683683	0.341842	−	0.939758i	$-0.388949\pi$
$101$	693.964	0.683683	0.341842	+	0.939758i	$0.388949\pi$
$102$	−630.936	−0.612470
$103$	−1967.75	−1.88241	−0.941206	−	0.337833i	$-0.890306\pi$
$103$	−1967.75	−1.88241	−0.941206	+	0.337833i	$0.890306\pi$
$104$	796.298	0.750803
$105$	0	0
$106$	−465.717	−0.426740
$107$	−663.690	−0.599638	−0.299819	−	0.953996i	$-0.596926\pi$
$107$	−663.690	−0.599638	−0.299819	+	0.953996i	$0.596926\pi$
$108$	1863.58	1.66040
$109$	−1310.25	−1.15136	−0.575682	−	0.817673i	$-0.695263\pi$
$109$	−1310.25	−1.15136	−0.575682	+	0.817673i	$0.695263\pi$
$110$	−151.722	−0.131510
$111$	−303.386	−0.259425
$112$	0	0
$113$	−2163.06	−1.80074	−0.900369	−	0.435128i	$-0.856703\pi$
$113$	−2163.06	−1.80074	−0.900369	+	0.435128i	$0.856703\pi$
$114$	−170.760	−0.140290
$115$	208.257	0.168870
$116$	−196.055	−0.156925
$117$	3221.83	2.54580
$118$	102.509	0.0799724
$119$	0	0
$120$	−391.937	−0.298157
$121$	1520.52	1.14239
$122$	233.395	0.173202
$123$	−840.893	−0.616429
$124$	2116.69	1.53294
$125$	−754.342	−0.539763
$126$	0	0
$127$	1606.07	1.12217	0.561084	−	0.827759i	$-0.310384\pi$
$127$	1606.07	1.12217	0.561084	+	0.827759i	$0.310384\pi$
$128$	1407.36	0.971833
$129$	2924.04	1.99571
$130$	−164.766	−0.111161
$131$	−109.787	−0.0732221	−0.0366111	−	0.999330i	$-0.511656\pi$
$131$	−109.787	−0.0732221	−0.0366111	+	0.999330i	$0.511656\pi$
$132$	3484.65	2.29773
$133$	0	0
$134$	−44.5425	−0.0287155
$135$	−815.124	−0.519665
$136$	−1054.23	−0.664699
$137$	2009.57	1.25321	0.626603	−	0.779339i	$-0.284445\pi$
$137$	2009.57	1.25321	0.626603	+	0.779339i	$0.284445\pi$
$138$	544.818	0.336073
$139$	313.953	0.191577	0.0957884	−	0.995402i	$-0.469463\pi$
$139$	313.953	0.191577	0.0957884	+	0.995402i	$0.469463\pi$
$140$	0	0
$141$	−3572.57	−2.13379
$142$	−417.297	−0.246611
$143$	3096.67	1.81089
$144$	2502.10	1.44797
$145$	85.7541	0.0491137
$146$	−387.352	−0.219572
$147$	0	0
$148$	−239.805	−0.133188
$149$	703.586	0.386845	0.193423	−	0.981116i	$-0.438041\pi$
$149$	703.586	0.386845	0.193423	+	0.981116i	$0.438041\pi$
$150$	−946.163	−0.515026
$151$	−689.283	−0.371477	−0.185739	−	0.982599i	$-0.559468\pi$
$151$	−689.283	−0.371477	−0.185739	+	0.982599i	$0.559468\pi$
$152$	−285.321	−0.152254
$153$	−4265.40	−2.25384
$154$	0	0
$155$	−925.836	−0.479774
$156$	3784.24	1.94219
$157$	−678.513	−0.344912	−0.172456	−	0.985017i	$-0.555170\pi$
$157$	−678.513	−0.344912	−0.172456	+	0.985017i	$0.555170\pi$
$158$	−84.1814	−0.0423868
$159$	−4678.54	−2.33353
$160$	−473.044	−0.233734
$161$	0	0
$162$	−775.682	−0.376194
$163$	3215.69	1.54523	0.772615	−	0.634875i	$-0.218948\pi$
$163$	3215.69	1.54523	0.772615	+	0.634875i	$0.218948\pi$
$164$	−664.666	−0.316474
$165$	−1524.18	−0.719134
$166$	1044.43	0.488335
$167$	279.523	0.129522	0.0647610	−	0.997901i	$-0.479372\pi$
$167$	279.523	0.129522	0.0647610	+	0.997901i	$0.479372\pi$
$168$	0	0
$169$	1165.90	0.530679
$170$	218.135	0.0984127
$171$	−1154.41	−0.516257
$172$	2311.24	1.02460
$173$	−2956.70	−1.29939	−0.649693	−	0.760197i	$-0.725103\pi$
$173$	−2956.70	−1.29939	−0.649693	+	0.760197i	$0.725103\pi$
$174$	224.340	0.0977424
$175$	0	0
$176$	2404.90	1.02998
$177$	1029.80	0.437312
$178$	−525.728	−0.221376
$179$	−4007.68	−1.67345	−0.836726	−	0.547622i	$-0.815533\pi$
$179$	−4007.68	−1.67345	−0.836726	+	0.547622i	$0.815533\pi$
$180$	−1253.45	−0.519036
$181$	−1861.15	−0.764299	−0.382150	−	0.924100i	$-0.624816\pi$
$181$	−1861.15	−0.764299	−0.382150	+	0.924100i	$0.624816\pi$
$182$	0	0
$183$	2344.66	0.947116
$184$	910.332	0.364731
$185$	104.890	0.0416848
$186$	−2422.07	−0.954810
$187$	−4099.71	−1.60321
$188$	−2823.87	−1.09549
$189$	0	0
$190$	59.0370	0.0225421
$191$	−1099.71	−0.416607	−0.208304	−	0.978064i	$-0.566794\pi$
$191$	−1099.71	−0.416607	−0.208304	+	0.978064i	$0.566794\pi$
$192$	2036.09	0.765325
$193$	−1888.51	−0.704341	−0.352171	−	0.935936i	$-0.614556\pi$
$193$	−1888.51	−0.704341	−0.352171	+	0.935936i	$0.614556\pi$
$194$	314.817	0.116508
$195$	−1655.22	−0.607859
$196$	0	0
$197$	5265.05	1.90416	0.952080	−	0.305851i	$-0.0989408\pi$
$197$	5265.05	1.90416	0.952080	+	0.305851i	$0.0989408\pi$
$198$	−2683.34	−0.963113
$199$	−114.838	−0.0409077	−0.0204538	−	0.999791i	$-0.506511\pi$
$199$	−114.838	−0.0409077	−0.0204538	+	0.999791i	$0.506511\pi$
$200$	−1580.94	−0.558945
$201$	−447.468	−0.157025
$202$	−627.665	−0.218626
$203$	0	0
$204$	−5009.98	−1.71945
$205$	290.723	0.0990488
$206$	1779.76	0.601951
$207$	3683.21	1.23672
$208$	2611.65	0.870604
$209$	−1109.56	−0.367226
$210$	0	0
$211$	3695.54	1.20574	0.602871	−	0.797839i	$-0.294023\pi$
$211$	3695.54	1.20574	0.602871	+	0.797839i	$0.294023\pi$
$212$	−3698.05	−1.19803
$213$	−4192.11	−1.34854
$214$	600.284	0.191750
$215$	−1010.93	−0.320674
$216$	−3563.07	−1.12239
$217$	0	0
$218$	1185.07	0.368179
$219$	−3891.29	−1.20068
$220$	−1204.76	−0.369203
$221$	−4452.17	−1.35514
$222$	274.402	0.0829579
$223$	−2487.77	−0.747055	−0.373527	−	0.927619i	$-0.621852\pi$
$223$	−2487.77	−0.747055	−0.373527	+	0.927619i	$0.621852\pi$
$224$	0	0
$225$	−6396.48	−1.89525
$226$	1956.41	0.575833
$227$	856.423	0.250409	0.125204	−	0.992131i	$-0.460041\pi$
$227$	856.423	0.250409	0.125204	+	0.992131i	$0.460041\pi$
$228$	−1355.92	−0.393852
$229$	−3433.96	−0.990928	−0.495464	−	0.868628i	$-0.665002\pi$
$229$	−3433.96	−0.990928	−0.495464	+	0.868628i	$0.665002\pi$
$230$	−188.361	−0.0540007
$231$	0	0
$232$	374.848	0.106077
$233$	2244.94	0.631206	0.315603	−	0.948891i	$-0.397793\pi$
$233$	2244.94	0.631206	0.315603	+	0.948891i	$0.397793\pi$
$234$	−2914.03	−0.814086
$235$	1235.15	0.342862
$236$	813.980	0.224515
$237$	−845.676	−0.231783
$238$	0	0
$239$	2047.64	0.554189	0.277094	−	0.960843i	$-0.410629\pi$
$239$	2047.64	0.554189	0.277094	+	0.960843i	$0.410629\pi$
$240$	−1285.45	−0.345732
$241$	−719.345	−0.192270	−0.0961350	−	0.995368i	$-0.530648\pi$
$241$	−719.345	−0.192270	−0.0961350	+	0.995368i	$0.530648\pi$
$242$	−1375.26	−0.365309
$243$	−786.427	−0.207610
$244$	1853.29	0.486248
$245$	0	0
$246$	760.557	0.197119
$247$	−1204.96	−0.310403
$248$	−4047.01	−1.03623
$249$	10492.2	2.67035
$250$	682.275	0.172604
$251$	3348.08	0.841947	0.420973	−	0.907073i	$-0.361689\pi$
$251$	3348.08	0.841947	0.420973	+	0.907073i	$0.361689\pi$
$252$	0	0
$253$	3540.13	0.879708
$254$	−1452.63	−0.358843
$255$	2191.35	0.538148
$256$	519.792	0.126902
$257$	4011.43	0.973643	0.486822	−	0.873501i	$-0.338156\pi$
$257$	4011.43	0.973643	0.486822	+	0.873501i	$0.338156\pi$
$258$	−2644.69	−0.638182
$259$	0	0
$260$	−1308.33	−0.312074
$261$	1516.64	0.359684
$262$	99.2981	0.0234147
$263$	6062.30	1.42136	0.710680	−	0.703516i	$-0.248388\pi$
$263$	6062.30	1.42136	0.710680	+	0.703516i	$0.248388\pi$
$264$	−6662.49	−1.55321
$265$	1617.52	0.374956
$266$	0	0
$267$	−5281.40	−1.21055
$268$	−353.692	−0.0806163
$269$	1854.70	0.420384	0.210192	−	0.977660i	$-0.432591\pi$
$269$	1854.70	0.420384	0.210192	+	0.977660i	$0.432591\pi$
$270$	737.251	0.166176
$271$	−1616.24	−0.362287	−0.181143	−	0.983457i	$-0.557980\pi$
$271$	−1616.24	−0.362287	−0.181143	+	0.983457i	$0.557980\pi$
$272$	−3457.59	−0.770761
$273$	0	0
$274$	−1817.58	−0.400746
$275$	−6148.00	−1.34814
$276$	4326.16	0.943493
$277$	7395.03	1.60406	0.802029	−	0.597285i	$-0.203754\pi$
$277$	7395.03	1.60406	0.802029	+	0.597285i	$0.203754\pi$
$278$	−283.959	−0.0612617
$279$	−16374.2	−3.51362
$280$	0	0
$281$	5488.05	1.16509	0.582544	−	0.812799i	$-0.302057\pi$
$281$	5488.05	1.16509	0.582544	+	0.812799i	$0.302057\pi$
$282$	3231.27	0.682337
$283$	−7255.74	−1.52406	−0.762030	−	0.647542i	$-0.775797\pi$
$283$	−7255.74	−1.52406	−0.762030	+	0.647542i	$0.775797\pi$
$284$	−3313.57	−0.692338
$285$	593.078	0.123266
$286$	−2800.83	−0.579079
$287$	0	0
$288$	−8366.21	−1.71175
$289$	981.257	0.199727
$290$	−77.5615	−0.0157054
$291$	3162.61	0.637098
$292$	−3075.79	−0.616428
$293$	−1168.80	−0.233045	−0.116523	−	0.993188i	$-0.537175\pi$
$293$	−1168.80	−0.233045	−0.116523	+	0.993188i	$0.537175\pi$
$294$	0	0
$295$	−356.033	−0.0702679
$296$	458.496	0.0900322
$297$	−13856.2	−2.70713
$298$	−636.368	−0.123704
$299$	3844.48	0.743586
$300$	−7513.06	−1.44589
$301$	0	0
$302$	623.432	0.118790
$303$	−6305.45	−1.19551
$304$	−935.778	−0.176548
$305$	−810.624	−0.152184
$306$	3857.91	0.720725
$307$	−6628.11	−1.23220	−0.616101	−	0.787667i	$-0.711289\pi$
$307$	−6628.11	−1.23220	−0.616101	+	0.787667i	$0.711289\pi$
$308$	0	0
$309$	17879.3	3.29164
$310$	837.386	0.153420
$311$	6231.85	1.13626	0.568128	−	0.822940i	$-0.307668\pi$
$311$	6231.85	1.13626	0.568128	+	0.822940i	$0.307668\pi$
$312$	−7235.28	−1.31287
$313$	−1662.13	−0.300158	−0.150079	−	0.988674i	$-0.547953\pi$
$313$	−1662.13	−0.300158	−0.150079	+	0.988674i	$0.547953\pi$
$314$	613.691	0.110295
$315$	0	0
$316$	−668.446	−0.118997
$317$	−2588.65	−0.458653	−0.229326	−	0.973350i	$-0.573652\pi$
$317$	−2588.65	−0.458653	−0.229326	+	0.973350i	$0.573652\pi$
$318$	4231.57	0.746209
$319$	1457.72	0.255852
$320$	−703.942	−0.122974
$321$	6030.38	1.04854
$322$	0	0
$323$	1595.25	0.274805
$324$	−6159.34	−1.05613
$325$	−6676.55	−1.13953
$326$	−2908.48	−0.494128
$327$	11905.1	2.01331
$328$	1270.81	0.213929
$329$	0	0
$330$	1378.57	0.229962
$331$	−1315.48	−0.218445	−0.109223	−	0.994017i	$-0.534836\pi$
$331$	−1315.48	−0.218445	−0.109223	+	0.994017i	$0.534836\pi$
$332$	8293.36	1.37095
$333$	1855.08	0.305278
$334$	−252.819	−0.0414181
$335$	154.704	0.0252310
$336$	0	0
$337$	−3019.13	−0.488019	−0.244010	−	0.969773i	$-0.578463\pi$
$337$	−3019.13	−0.488019	−0.244010	+	0.969773i	$0.578463\pi$
$338$	−1054.52	−0.169699
$339$	19653.8	3.14882
$340$	1732.11	0.276285
$341$	−15738.2	−2.49932
$342$	1044.12	0.165087
$343$	0	0
$344$	−4418.98	−0.692603
$345$	−1892.25	−0.295291
$346$	2674.23	0.415513
$347$	−409.784	−0.0633958	−0.0316979	−	0.999497i	$-0.510091\pi$
$347$	−409.784	−0.0633958	−0.0316979	+	0.999497i	$0.510091\pi$
$348$	1781.38	0.274403
$349$	4353.76	0.667769	0.333884	−	0.942614i	$-0.391640\pi$
$349$	4353.76	0.667769	0.333884	+	0.942614i	$0.391640\pi$
$350$	0	0
$351$	−15047.4	−2.28824
$352$	−8041.21	−1.21761
$353$	11101.6	1.67388	0.836940	−	0.547295i	$-0.184342\pi$
$353$	11101.6	1.67388	0.836940	+	0.547295i	$0.184342\pi$
$354$	−931.413	−0.139842
$355$	1449.35	0.216685
$356$	−4174.57	−0.621494
$357$	0	0
$358$	3624.80	0.535130
$359$	−9976.84	−1.46673	−0.733367	−	0.679833i	$-0.762052\pi$
$359$	−9976.84	−1.46673	−0.733367	+	0.679833i	$0.762052\pi$
$360$	2396.53	0.350856
$361$	−6427.25	−0.937054
$362$	1683.34	0.244405
$363$	−13815.7	−1.99761
$364$	0	0
$365$	1345.34	0.192927
$366$	−2120.66	−0.302865
$367$	−6008.60	−0.854622	−0.427311	−	0.904105i	$-0.640539\pi$
$367$	−6008.60	−0.854622	−0.427311	+	0.904105i	$0.640539\pi$
$368$	2985.66	0.422929
$369$	5141.70	0.725383
$370$	−94.8695	−0.0133298
$371$	0	0
$372$	−19232.6	−2.68054
$373$	22.3692	0.00310518	0.00155259	−	0.999999i	$-0.499506\pi$
$373$	22.3692	0.00310518	0.00155259	+	0.999999i	$0.499506\pi$
$374$	3708.04	0.512669
$375$	6854.05	0.943845
$376$	5399.09	0.740524
$377$	1583.05	0.216263
$378$	0	0
$379$	6700.80	0.908172	0.454086	−	0.890958i	$-0.349966\pi$
$379$	6700.80	0.908172	0.454086	+	0.890958i	$0.349966\pi$
$380$	468.786	0.0632848
$381$	−14592.9	−1.96225
$382$	994.645	0.133221
$383$	7418.11	0.989681	0.494841	−	0.868984i	$-0.335226\pi$
$383$	7418.11	0.989681	0.494841	+	0.868984i	$0.335226\pi$
$384$	−12787.5	−1.69937
$385$	0	0
$386$	1708.09	0.225232
$387$	−17879.2	−2.34846
$388$	2499.82	0.327085
$389$	−4351.30	−0.567146	−0.283573	−	0.958951i	$-0.591520\pi$
$389$	−4351.30	−0.567146	−0.283573	+	0.958951i	$0.591520\pi$
$390$	1497.08	0.194379
$391$	−5089.74	−0.658310
$392$	0	0
$393$	997.536	0.128038
$394$	−4762.05	−0.608905
$395$	292.377	0.0372432
$396$	−21307.2	−2.70385
$397$	−7184.81	−0.908300	−0.454150	−	0.890925i	$-0.650057\pi$
$397$	−7184.81	−0.908300	−0.454150	+	0.890925i	$0.650057\pi$
$398$	103.867	0.0130813
$399$	0	0
$400$	−5185.06	−0.648133
$401$	11999.7	1.49436	0.747178	−	0.664624i	$-0.231408\pi$
$401$	11999.7	1.49436	0.747178	+	0.664624i	$0.231408\pi$
$402$	404.719	0.0502128
$403$	−17091.2	−2.11259
$404$	−4984.01	−0.613772
$405$	2694.08	0.330543
$406$	0	0
$407$	1783.01	0.217152
$408$	9578.83	1.16231
$409$	−12518.5	−1.51345	−0.756723	−	0.653735i	$-0.773201\pi$
$409$	−12518.5	−1.51345	−0.756723	+	0.653735i	$0.773201\pi$
$410$	−262.949	−0.0316735
$411$	−18259.2	−2.19139
$412$	14132.3	1.68992
$413$	0	0
$414$	−3331.33	−0.395474
$415$	−3627.49	−0.429076
$416$	−8732.54	−1.02920
$417$	−2852.62	−0.334996
$418$	1003.56	0.117430
$419$	−9523.60	−1.11040	−0.555201	−	0.831716i	$-0.687359\pi$
$419$	−9523.60	−1.11040	−0.555201	+	0.831716i	$0.687359\pi$
$420$	0	0
$421$	−11087.1	−1.28350	−0.641751	−	0.766913i	$-0.721792\pi$
$421$	−11087.1	−1.28350	−0.641751	+	0.766913i	$0.721792\pi$
$422$	−3342.48	−0.385568
$423$	21844.8	2.51094
$424$	7070.49	0.809843
$425$	8839.14	1.00885
$426$	3791.61	0.431231
$427$	0	0
$428$	4766.58	0.538321
$429$	−28136.8	−3.16657
$430$	914.352	0.102544
$431$	−1026.44	−0.114715	−0.0573573	−	0.998354i	$-0.518267\pi$
$431$	−1026.44	−0.114715	−0.0573573	+	0.998354i	$0.518267\pi$
$432$	−11685.9	−1.30148
$433$	13804.7	1.53212	0.766062	−	0.642767i	$-0.222214\pi$
$433$	13804.7	1.53212	0.766062	+	0.642767i	$0.222214\pi$
$434$	0	0
$435$	−779.173	−0.0858816
$436$	9410.11	1.03363
$437$	−1377.51	−0.150790
$438$	3519.53	0.383949
$439$	−1587.56	−0.172597	−0.0862984	−	0.996269i	$-0.527504\pi$
$439$	−1587.56	−0.172597	−0.0862984	+	0.996269i	$0.527504\pi$
$440$	2303.43	0.249572
$441$	0	0
$442$	4026.83	0.433341
$443$	−6213.84	−0.666430	−0.333215	−	0.942851i	$-0.608134\pi$
$443$	−6213.84	−0.666430	−0.333215	+	0.942851i	$0.608134\pi$
$444$	2178.90	0.232897
$445$	1825.95	0.194513
$446$	2250.10	0.238890
$447$	−6392.87	−0.676449
$448$	0	0
$449$	−5023.31	−0.527984	−0.263992	−	0.964525i	$-0.585039\pi$
$449$	−5023.31	−0.527984	−0.263992	+	0.964525i	$0.585039\pi$
$450$	5785.39	0.606057
$451$	4941.96	0.515982
$452$	15535.0	1.61660
$453$	6262.92	0.649575
$454$	−774.604	−0.0800748
$455$	0	0
$456$	2592.46	0.266235
$457$	−9345.09	−0.956553	−0.478277	−	0.878209i	$-0.658738\pi$
$457$	−9345.09	−0.956553	−0.478277	+	0.878209i	$0.658738\pi$
$458$	3105.89	0.316875
$459$	19921.4	2.02582
$460$	−1495.69	−0.151602
$461$	−10592.5	−1.07015	−0.535077	−	0.844803i	$-0.679717\pi$
$461$	−10592.5	−1.07015	−0.535077	+	0.844803i	$0.679717\pi$
$462$	0	0
$463$	−5186.28	−0.520576	−0.260288	−	0.965531i	$-0.583818\pi$
$463$	−5186.28	−0.520576	−0.260288	+	0.965531i	$0.583818\pi$
$464$	1229.40	0.123004
$465$	8412.28	0.838946
$466$	−2030.47	−0.201845
$467$	−5292.77	−0.524454	−0.262227	−	0.965006i	$-0.584457\pi$
$467$	−5292.77	−0.524454	−0.262227	+	0.965006i	$0.584457\pi$
$468$	−23139.0	−2.28547
$469$	0	0
$470$	−1117.15	−0.109639
$471$	6165.06	0.603123
$472$	−1556.29	−0.151767
$473$	−17184.7	−1.67051
$474$	764.883	0.0741187
$475$	2392.27	0.231084
$476$	0	0
$477$	28607.3	2.74599
$478$	−1852.02	−0.177216
$479$	−3971.90	−0.378874	−0.189437	−	0.981893i	$-0.560666\pi$
$479$	−3971.90	−0.378874	−0.189437	+	0.981893i	$0.560666\pi$
$480$	4298.15	0.408714
$481$	1936.30	0.183551
$482$	650.622	0.0614834
$483$	0	0
$484$	−10920.3	−1.02557
$485$	−1093.41	−0.102370
$486$	711.295	0.0663889
$487$	−11943.5	−1.11132	−0.555659	−	0.831410i	$-0.687534\pi$
$487$	−11943.5	−1.11132	−0.555659	+	0.831410i	$0.687534\pi$
$488$	−3543.39	−0.328693
$489$	−29218.2	−2.70203
$490$	0	0
$491$	9512.82	0.874353	0.437177	−	0.899376i	$-0.355978\pi$
$491$	9512.82	0.874353	0.437177	+	0.899376i	$0.355978\pi$
$492$	6039.24	0.553395
$493$	−2095.80	−0.191461
$494$	1089.84	0.0992596
$495$	9319.71	0.846242
$496$	−13273.2	−1.20158
$497$	0	0
$498$	−9489.84	−0.853916
$499$	−3780.91	−0.339192	−0.169596	−	0.985514i	$-0.554246\pi$
$499$	−3780.91	−0.339192	−0.169596	+	0.985514i	$0.554246\pi$
$500$	5417.64	0.484569
$501$	−2539.79	−0.226486
$502$	−3028.21	−0.269235
$503$	15560.0	1.37930	0.689648	−	0.724145i	$-0.257765\pi$
$503$	15560.0	1.37930	0.689648	+	0.724145i	$0.257765\pi$
$504$	0	0
$505$	2179.99	0.192096
$506$	−3201.92	−0.281310
$507$	−10593.5	−0.927960
$508$	−11534.7	−1.00742
$509$	16928.5	1.47415	0.737073	−	0.675813i	$-0.236207\pi$
$509$	16928.5	1.47415	0.737073	+	0.675813i	$0.236207\pi$
$510$	−1982.00	−0.172087
$511$	0	0
$512$	−11729.0	−1.01241
$513$	5391.62	0.464027
$514$	−3628.20	−0.311348
$515$	−6181.43	−0.528906
$516$	−21000.3	−1.79164
$517$	20996.2	1.78609
$518$	0	0
$519$	26865.0	2.27214
$520$	2501.46	0.210955
$521$	−14567.1	−1.22495	−0.612474	−	0.790491i	$-0.709825\pi$
$521$	−14567.1	−1.22495	−0.612474	+	0.790491i	$0.709825\pi$
$522$	−1371.74	−0.115018
$523$	1694.23	0.141651	0.0708254	−	0.997489i	$-0.477437\pi$
$523$	1694.23	0.141651	0.0708254	+	0.997489i	$0.477437\pi$
$524$	788.481	0.0657347
$525$	0	0
$526$	−5483.13	−0.454517
$527$	22627.2	1.87031
$528$	−21851.2	−1.80105
$529$	−7771.97	−0.638774
$530$	−1462.99	−0.119902
$531$	−6296.76	−0.514607
$532$	0	0
$533$	5366.84	0.436142
$534$	4776.84	0.387105
$535$	−2084.89	−0.168482
$536$	676.241	0.0544947
$537$	36414.3	2.92624
$538$	−1677.51	−0.134429
$539$	0	0
$540$	5854.18	0.466525
$541$	10056.5	0.799191	0.399596	−	0.916691i	$-0.369151\pi$
$541$	10056.5	0.799191	0.399596	+	0.916691i	$0.369151\pi$
$542$	1461.83	0.115851
$543$	16910.7	1.33647
$544$	11561.1	0.911170
$545$	−4115.96	−0.323502
$546$	0	0
$547$	13385.9	1.04633	0.523163	−	0.852233i	$-0.324752\pi$
$547$	13385.9	1.04633	0.523163	+	0.852233i	$0.324752\pi$
$548$	−14432.6	−1.12506
$549$	−14336.6	−1.11452
$550$	5560.64	0.431103
$551$	−567.219	−0.0438554
$552$	−8271.40	−0.637779
$553$	0	0
$554$	−6688.54	−0.512940
$555$	−953.047	−0.0728912
$556$	−2254.79	−0.171987
$557$	13511.5	1.02783	0.513914	−	0.857842i	$-0.328195\pi$
$557$	13511.5	1.02783	0.513914	+	0.857842i	$0.328195\pi$
$558$	14809.9	1.12357
$559$	−18662.1	−1.41203
$560$	0	0
$561$	37250.5	2.80342
$562$	−4963.74	−0.372567
$563$	−21009.0	−1.57269	−0.786344	−	0.617789i	$-0.788029\pi$
$563$	−21009.0	−1.57269	−0.786344	+	0.617789i	$0.788029\pi$
$564$	25658.0	1.91560
$565$	−6794.96	−0.505957
$566$	6562.56	0.487358
$567$	0	0
$568$	6335.37	0.468004
$569$	14913.0	1.09875	0.549373	−	0.835577i	$-0.314866\pi$
$569$	14913.0	1.09875	0.549373	+	0.835577i	$0.314866\pi$
$570$	−536.418	−0.0394177
$571$	−17668.8	−1.29495	−0.647474	−	0.762087i	$-0.724175\pi$
$571$	−17668.8	−1.29495	−0.647474	+	0.762087i	$0.724175\pi$
$572$	−22240.1	−1.62571
$573$	9992.08	0.728491
$574$	0	0
$575$	−7632.67	−0.553573
$576$	−12449.8	−0.900596
$577$	−6857.88	−0.494796	−0.247398	−	0.968914i	$-0.579576\pi$
$577$	−6857.88	−0.494796	−0.247398	+	0.968914i	$0.579576\pi$
$578$	−887.512	−0.0638679
$579$	17159.2	1.23163
$580$	−615.881	−0.0440915
$581$	0	0
$582$	−2860.47	−0.203729
$583$	27496.0	1.95329
$584$	5880.76	0.416691
$585$	10120.9	0.715299
$586$	1057.14	0.0745224
$587$	−5215.96	−0.366756	−0.183378	−	0.983042i	$-0.558703\pi$
$587$	−5215.96	−0.366756	−0.183378	+	0.983042i	$0.558703\pi$
$588$	0	0
$589$	6123.93	0.428407
$590$	322.019	0.0224700
$591$	−47839.0	−3.32967
$592$	1503.75	0.104398
$593$	11235.6	0.778065	0.389032	−	0.921224i	$-0.372809\pi$
$593$	11235.6	0.778065	0.389032	+	0.921224i	$0.372809\pi$
$594$	12532.4	0.865676
$595$	0	0
$596$	−5053.11	−0.347288
$597$	1043.43	0.0715323
$598$	−3477.20	−0.237781
$599$	2209.24	0.150696	0.0753482	−	0.997157i	$-0.475993\pi$
$599$	2209.24	0.150696	0.0753482	+	0.997157i	$0.475993\pi$
$600$	14364.6	0.977387
$601$	−11191.5	−0.759587	−0.379793	−	0.925071i	$-0.624005\pi$
$601$	−11191.5	−0.759587	−0.379793	+	0.925071i	$0.624005\pi$
$602$	0	0
$603$	2736.08	0.184779
$604$	4950.39	0.333491
$605$	4776.51	0.320980
$606$	5703.05	0.382295
$607$	−37.2973	−0.00249399	−0.00124699	−	0.999999i	$-0.500397\pi$
$607$	−37.2973	−0.00249399	−0.00124699	+	0.999999i	$0.500397\pi$
$608$	3128.94	0.208710
$609$	0	0
$610$	733.180	0.0486649
$611$	22801.3	1.50972
$612$	30633.9	2.02337
$613$	−8887.23	−0.585566	−0.292783	−	0.956179i	$-0.594581\pi$
$613$	−8887.23	−0.585566	−0.292783	+	0.956179i	$0.594581\pi$
$614$	5994.89	0.394029
$615$	−2641.55	−0.173199
$616$	0	0
$617$	2240.48	0.146189	0.0730944	−	0.997325i	$-0.476713\pi$
$617$	2240.48	0.146189	0.0730944	+	0.997325i	$0.476713\pi$
$618$	−16171.2	−1.05259
$619$	7839.71	0.509054	0.254527	−	0.967066i	$-0.418080\pi$
$619$	7839.71	0.509054	0.254527	+	0.967066i	$0.418080\pi$
$620$	6649.31	0.430714
$621$	−17202.3	−1.11160
$622$	−5636.48	−0.363348
$623$	0	0
$624$	−23729.8	−1.52236
$625$	12021.8	0.769396
$626$	1503.34	0.0959833
$627$	10081.7	0.642141
$628$	4873.04	0.309643
$629$	−2563.49	−0.162501
$630$	0	0
$631$	−5772.45	−0.364180	−0.182090	−	0.983282i	$-0.558286\pi$
$631$	−5772.45	−0.364180	−0.182090	+	0.983282i	$0.558286\pi$
$632$	1278.04	0.0804392
$633$	−33578.2	−2.10839
$634$	2341.34	0.146666
$635$	5045.24	0.315298
$636$	33601.0	2.09491
$637$	0	0
$638$	−1318.46	−0.0818154
$639$	25633.0	1.58689
$640$	4421.04	0.273058
$641$	2309.83	0.142329	0.0711645	−	0.997465i	$-0.477328\pi$
$641$	2309.83	0.142329	0.0711645	+	0.997465i	$0.477328\pi$
$642$	−5454.26	−0.335300
$643$	−11706.6	−0.717982	−0.358991	−	0.933341i	$-0.616879\pi$
$643$	−11706.6	−0.717982	−0.358991	+	0.933341i	$0.616879\pi$
$644$	0	0
$645$	9185.47	0.560740
$646$	−1442.85	−0.0878762
$647$	9280.94	0.563944	0.281972	−	0.959423i	$-0.409012\pi$
$647$	9280.94	0.563944	0.281972	+	0.959423i	$0.409012\pi$
$648$	11776.4	0.713919
$649$	−6052.15	−0.366052
$650$	6038.70	0.364396
$651$	0	0
$652$	−23094.9	−1.38722
$653$	7650.07	0.458454	0.229227	−	0.973373i	$-0.426380\pi$
$653$	7650.07	0.458454	0.229227	+	0.973373i	$0.426380\pi$
$654$	−10767.7	−0.643808
$655$	−344.880	−0.0205734
$656$	4167.93	0.248064
$657$	23793.6	1.41290
$658$	0	0
$659$	−27325.1	−1.61523	−0.807615	−	0.589710i	$-0.799242\pi$
$659$	−27325.1	−1.61523	−0.807615	+	0.589710i	$0.799242\pi$
$660$	10946.6	0.645598
$661$	1197.16	0.0704448	0.0352224	−	0.999379i	$-0.488786\pi$
$661$	1197.16	0.0704448	0.0352224	+	0.999379i	$0.488786\pi$
$662$	1189.81	0.0698536
$663$	40453.0	2.36963
$664$	−15856.5	−0.926734
$665$	0	0
$666$	−1677.85	−0.0976208
$667$	1809.74	0.105058
$668$	−2007.52	−0.116277
$669$	22604.2	1.30632
$670$	−139.924	−0.00806827
$671$	−13779.7	−0.792785
$672$	0	0
$673$	−18550.7	−1.06252	−0.531262	−	0.847208i	$-0.678282\pi$
$673$	−18550.7	−1.06252	−0.531262	+	0.847208i	$0.678282\pi$
$674$	2730.69	0.156057
$675$	29874.5	1.70351
$676$	−8373.44	−0.476413
$677$	−20273.3	−1.15091	−0.575456	−	0.817833i	$-0.695175\pi$
$677$	−20273.3	−1.15091	−0.575456	+	0.817833i	$0.695175\pi$
$678$	−17776.2	−1.00692
$679$	0	0
$680$	−3311.71	−0.186762
$681$	−7781.57	−0.437872
$682$	14234.6	0.799224
$683$	−18260.7	−1.02302	−0.511511	−	0.859277i	$-0.670914\pi$
$683$	−18260.7	−1.02302	−0.511511	+	0.859277i	$0.670914\pi$
$684$	8290.91	0.463466
$685$	6312.80	0.352116
$686$	0	0
$687$	31201.4	1.73276
$688$	−14493.1	−0.803118
$689$	29859.9	1.65105
$690$	1711.47	0.0944271
$691$	−30343.2	−1.67049	−0.835247	−	0.549875i	$-0.814675\pi$
$691$	−30343.2	−1.67049	−0.835247	+	0.549875i	$0.814675\pi$
$692$	21234.9	1.16652
$693$	0	0
$694$	370.635	0.0202725
$695$	986.242	0.0538278
$696$	−3405.92	−0.185490
$697$	−7105.19	−0.386124
$698$	−3937.82	−0.213537
$699$	−20397.9	−1.10375
$700$	0	0
$701$	−9464.46	−0.509940	−0.254970	−	0.966949i	$-0.582066\pi$
$701$	−9464.46	−0.509940	−0.254970	+	0.966949i	$0.582066\pi$
$702$	13609.9	0.731725
$703$	−693.794	−0.0372218
$704$	−11966.2	−0.640616
$705$	−11222.8	−0.599537
$706$	−10041.0	−0.535267
$707$	0	0
$708$	−7395.93	−0.392593
$709$	10796.2	0.571878	0.285939	−	0.958248i	$-0.407695\pi$
$709$	10796.2	0.571878	0.285939	+	0.958248i	$0.407695\pi$
$710$	−1310.88	−0.0692909
$711$	5170.95	0.272751
$712$	7981.58	0.420115
$713$	−19538.7	−1.02627
$714$	0	0
$715$	9727.78	0.508809
$716$	28782.9	1.50233
$717$	−18605.2	−0.969070
$718$	9023.70	0.469027
$719$	−20577.7	−1.06734	−0.533672	−	0.845692i	$-0.679188\pi$
$719$	−20577.7	−1.06734	−0.533672	+	0.845692i	$0.679188\pi$
$720$	7860.01	0.406840
$721$	0	0
$722$	5813.22	0.299648
$723$	6536.07	0.336209
$724$	13366.7	0.686144
$725$	−3142.91	−0.161000
$726$	12495.8	0.638790
$727$	−877.412	−0.0447612	−0.0223806	−	0.999750i	$-0.507125\pi$
$727$	−877.412	−0.0447612	−0.0223806	+	0.999750i	$0.507125\pi$
$728$	0	0
$729$	−16010.0	−0.813394
$730$	−1216.81	−0.0616936
$731$	24706.9	1.25009
$732$	−16839.2	−0.850267
$733$	29385.1	1.48071	0.740356	−	0.672215i	$-0.234657\pi$
$733$	29385.1	1.48071	0.740356	+	0.672215i	$0.234657\pi$
$734$	5434.56	0.273288
$735$	0	0
$736$	−9983.07	−0.499974
$737$	2629.79	0.131438
$738$	−4650.49	−0.231960
$739$	−33547.4	−1.66991	−0.834954	−	0.550320i	$-0.814506\pi$
$739$	−33547.4	−1.66991	−0.834954	+	0.550320i	$0.814506\pi$
$740$	−753.316	−0.0374222
$741$	10948.4	0.542779
$742$	0	0
$743$	6519.35	0.321900	0.160950	−	0.986963i	$-0.448544\pi$
$743$	6519.35	0.321900	0.160950	+	0.986963i	$0.448544\pi$
$744$	36771.7	1.81198
$745$	2210.22	0.108693
$746$	−20.2321	−0.000992965 0
$747$	−64155.5	−3.14234
$748$	29443.9	1.43927
$749$	0	0
$750$	−6199.25	−0.301819
$751$	−19844.3	−0.964219	−0.482109	−	0.876111i	$-0.660129\pi$
$751$	−19844.3	−0.964219	−0.482109	+	0.876111i	$0.660129\pi$
$752$	17707.6	0.858685
$753$	−30421.1	−1.47225
$754$	−1431.81	−0.0691557
$755$	−2165.29	−0.104375
$756$	0	0
$757$	35038.1	1.68228	0.841138	−	0.540821i	$-0.181886\pi$
$757$	35038.1	1.68228	0.841138	+	0.540821i	$0.181886\pi$
$758$	−6060.64	−0.290412
$759$	−32166.1	−1.53828
$760$	−896.296	−0.0427791
$761$	14439.0	0.687798	0.343899	−	0.939007i	$-0.388252\pi$
$761$	14439.0	0.687798	0.343899	+	0.939007i	$0.388252\pi$
$762$	13198.8	0.627482
$763$	0	0
$764$	7898.03	0.374006
$765$	−13399.2	−0.633267
$766$	−6709.42	−0.316477
$767$	−6572.47	−0.309411
$768$	−4722.90	−0.221905
$769$	−19397.3	−0.909603	−0.454802	−	0.890593i	$-0.650290\pi$
$769$	−19397.3	−0.909603	−0.454802	+	0.890593i	$0.650290\pi$
$770$	0	0
$771$	−36448.4	−1.70254
$772$	13563.2	0.632317
$773$	6769.59	0.314987	0.157494	−	0.987520i	$-0.449659\pi$
$773$	6769.59	0.314987	0.157494	+	0.987520i	$0.449659\pi$
$774$	16171.1	0.750981
$775$	33932.1	1.57275
$776$	−4779.53	−0.221102
$777$	0	0
$778$	3935.60	0.181360
$779$	−1922.98	−0.0884442
$780$	11887.7	0.545701
$781$	24637.2	1.12880
$782$	4603.49	0.210512
$783$	−7083.40	−0.323295
$784$	0	0
$785$	−2131.46	−0.0969108
$786$	−902.236	−0.0409436
$787$	33135.5	1.50083	0.750415	−	0.660967i	$-0.229854\pi$
$787$	33135.5	1.50083	0.750415	+	0.660967i	$0.229854\pi$
$788$	−37813.3	−1.70945
$789$	−55082.9	−2.48543
$790$	−264.444	−0.0119095
$791$	0	0
$792$	40738.3	1.82774
$793$	−14964.3	−0.670113
$794$	6498.40	0.290453
$795$	−14697.0	−0.655659
$796$	824.758	0.0367246
$797$	25165.0	1.11843	0.559216	−	0.829022i	$-0.311102\pi$
$797$	25165.0	1.11843	0.559216	+	0.829022i	$0.311102\pi$
$798$	0	0
$799$	−30186.8	−1.33658
$800$	17337.2	0.766203
$801$	32293.5	1.42451
$802$	−10853.3	−0.477860
$803$	22869.3	1.00503
$804$	3213.69	0.140968
$805$	0	0
$806$	15458.4	0.675556
$807$	−16852.1	−0.735094
$808$	9529.18	0.414895
$809$	−2860.50	−0.124314	−0.0621570	−	0.998066i	$-0.519798\pi$
$809$	−2860.50	−0.124314	−0.0621570	+	0.998066i	$0.519798\pi$
$810$	−2436.70	−0.105700
$811$	24431.2	1.05782	0.528911	−	0.848677i	$-0.322600\pi$
$811$	24431.2	1.05782	0.528911	+	0.848677i	$0.322600\pi$
$812$	0	0
$813$	14685.4	0.633505
$814$	−1612.67	−0.0694400
$815$	10101.7	0.434167
$816$	31416.1	1.34777
$817$	6686.79	0.286342
$818$	11322.5	0.483965
$819$	0	0
$820$	−2087.96	−0.0889203
$821$	28644.4	1.21766	0.608830	−	0.793301i	$-0.291639\pi$
$821$	28644.4	1.21766	0.608830	+	0.793301i	$0.291639\pi$
$822$	16514.8	0.700755
$823$	−22649.4	−0.959307	−0.479654	−	0.877458i	$-0.659238\pi$
$823$	−22649.4	−0.959307	−0.479654	+	0.877458i	$0.659238\pi$
$824$	−27020.2	−1.14235
$825$	55861.5	2.35739
$826$	0	0
$827$	−11914.8	−0.500991	−0.250495	−	0.968118i	$-0.580594\pi$
$827$	−11914.8	−0.500991	−0.250495	+	0.968118i	$0.580594\pi$
$828$	−26452.6	−1.11026
$829$	−414.521	−0.0173666	−0.00868329	−	0.999962i	$-0.502764\pi$
$829$	−414.521	−0.0173666	−0.00868329	+	0.999962i	$0.502764\pi$
$830$	3280.94	0.137209
$831$	−67192.2	−2.80490
$832$	−12995.0	−0.541490
$833$	0	0
$834$	2580.09	0.107124
$835$	878.085	0.0363921
$836$	7968.83	0.329674
$837$	76475.2	3.15815
$838$	8613.76	0.355080
$839$	−10486.6	−0.431512	−0.215756	−	0.976447i	$-0.569222\pi$
$839$	−10486.6	−0.431512	−0.215756	+	0.976447i	$0.569222\pi$
$840$	0	0
$841$	−23643.8	−0.969445
$842$	10027.9	0.410434
$843$	−49865.2	−2.03730
$844$	−26541.2	−1.08245
$845$	3662.52	0.149106
$846$	−19757.8	−0.802941
$847$	0	0
$848$	23189.4	0.939065
$849$	65926.6	2.66501
$850$	−7994.68	−0.322606
$851$	2213.59	0.0891668
$852$	30107.5	1.21064
$853$	32314.7	1.29711	0.648554	−	0.761169i	$-0.275374\pi$
$853$	32314.7	1.29711	0.648554	+	0.761169i	$0.275374\pi$
$854$	0	0
$855$	−3626.42	−0.145054
$856$	−9113.47	−0.363893
$857$	33881.2	1.35048	0.675239	−	0.737599i	$-0.264040\pi$
$857$	33881.2	1.35048	0.675239	+	0.737599i	$0.264040\pi$
$858$	25448.7	1.01259
$859$	−34132.6	−1.35575	−0.677876	−	0.735176i	$-0.737099\pi$
$859$	−34132.6	−1.35575	−0.677876	+	0.735176i	$0.737099\pi$
$860$	7260.46	0.287883
$861$	0	0
$862$	928.381	0.0366830
$863$	−10222.3	−0.403212	−0.201606	−	0.979467i	$-0.564616\pi$
$863$	−10222.3	−0.403212	−0.201606	+	0.979467i	$0.564616\pi$
$864$	39074.1	1.53857
$865$	−9288.08	−0.365092
$866$	−12485.8	−0.489937
$867$	−8915.83	−0.349248
$868$	0	0
$869$	4970.07	0.194014
$870$	704.734	0.0274629
$871$	2855.88	0.111100
$872$	−17991.7	−0.698710
$873$	−19338.0	−0.749705
$874$	1245.91	0.0482192
$875$	0	0
$876$	27947.0	1.07790
$877$	−12326.7	−0.474623	−0.237311	−	0.971434i	$-0.576266\pi$
$877$	−12326.7	−0.474623	−0.237311	+	0.971434i	$0.576266\pi$
$878$	1435.89	0.0551924
$879$	10619.9	0.407510
$880$	7554.67	0.289395
$881$	25636.2	0.980370	0.490185	−	0.871618i	$-0.336929\pi$
$881$	25636.2	0.980370	0.490185	+	0.871618i	$0.336929\pi$
$882$	0	0
$883$	−8508.94	−0.324291	−0.162145	−	0.986767i	$-0.551841\pi$
$883$	−8508.94	−0.324291	−0.162145	+	0.986767i	$0.551841\pi$
$884$	31975.2	1.21656
$885$	3234.96	0.122872
$886$	5620.20	0.213109
$887$	−12446.3	−0.471144	−0.235572	−	0.971857i	$-0.575696\pi$
$887$	−12446.3	−0.471144	−0.235572	+	0.971857i	$0.575696\pi$
$888$	−4165.96	−0.157433
$889$	0	0
$890$	−1651.50	−0.0622006
$891$	45796.3	1.72192
$892$	17867.0	0.670663
$893$	−8169.89	−0.306153
$894$	5782.13	0.216312
$895$	−12589.6	−0.470194
$896$	0	0
$897$	−34931.5	−1.30026
$898$	4543.40	0.168837
$899$	−8045.48	−0.298478
$900$	45939.2	1.70145
$901$	−39531.7	−1.46170
$902$	−4469.83	−0.164999
$903$	0	0
$904$	−29702.1	−1.09278
$905$	−5846.55	−0.214747
$906$	−5664.59	−0.207719
$907$	−51327.1	−1.87904	−0.939519	−	0.342496i	$-0.888728\pi$
$907$	−51327.1	−1.87904	−0.939519	+	0.342496i	$0.888728\pi$
$908$	−6150.78	−0.224803
$909$	38555.2	1.40681
$910$	0	0
$911$	−5816.49	−0.211536	−0.105768	−	0.994391i	$-0.533730\pi$
$911$	−5816.49	−0.211536	−0.105768	+	0.994391i	$0.533730\pi$
$912$	8502.61	0.308717
$913$	−61663.3	−2.23522
$914$	8452.30	0.305883
$915$	7365.44	0.266114
$916$	24662.5	0.889599
$917$	0	0
$918$	−18018.2	−0.647809
$919$	15116.7	0.542605	0.271303	−	0.962494i	$-0.412546\pi$
$919$	15116.7	0.542605	0.271303	+	0.962494i	$0.412546\pi$
$920$	2859.69	0.102479
$921$	60223.9	2.15466
$922$	9580.52	0.342210
$923$	26755.3	0.954131
$924$	0	0
$925$	−3844.25	−0.136647
$926$	4690.80	0.166468
$927$	−109324.	−3.87344
$928$	−4110.74	−0.145411
$929$	−18602.8	−0.656982	−0.328491	−	0.944507i	$-0.606540\pi$
$929$	−18602.8	−0.656982	−0.328491	+	0.944507i	$0.606540\pi$
$930$	−7608.60	−0.268275
$931$	0	0
$932$	−16123.1	−0.566661
$933$	−56623.4	−1.98689
$934$	4787.12	0.167708
$935$	−12878.7	−0.450458
$936$	44240.6	1.54493
$937$	38612.0	1.34621	0.673106	−	0.739546i	$-0.264960\pi$
$937$	38612.0	1.34621	0.673106	+	0.739546i	$0.264960\pi$
$938$	0	0
$939$	15102.4	0.524864
$940$	−8870.80	−0.307802
$941$	−13430.2	−0.465263	−0.232632	−	0.972565i	$-0.574734\pi$
$941$	−13430.2	−0.465263	−0.232632	+	0.972565i	$0.574734\pi$
$942$	−5576.08	−0.192865
$943$	6135.39	0.211873
$944$	−5104.23	−0.175984
$945$	0	0
$946$	15542.9	0.534191
$947$	−55421.6	−1.90175	−0.950876	−	0.309573i	$-0.899814\pi$
$947$	−55421.6	−1.90175	−0.950876	+	0.309573i	$0.899814\pi$
$948$	6073.60	0.208081
$949$	24835.4	0.849517
$950$	−2163.72	−0.0738951
$951$	23520.8	0.802013
$952$	0	0
$953$	−4133.93	−0.140515	−0.0702577	−	0.997529i	$-0.522382\pi$
$953$	−4133.93	−0.140515	−0.0702577	+	0.997529i	$0.522382\pi$
$954$	−25874.2	−0.878102
$955$	−3454.58	−0.117055
$956$	−14706.1	−0.497519
$957$	−13245.1	−0.447390
$958$	3592.44	0.121155
$959$	0	0
$960$	6396.11	0.215035
$961$	57071.3	1.91572
$962$	−1751.32	−0.0586952
$963$	−36873.2	−1.23388
$964$	5166.30	0.172609
$965$	−5932.50	−0.197900
$966$	0	0
$967$	34755.2	1.15579	0.577897	−	0.816110i	$-0.303874\pi$
$967$	34755.2	1.15579	0.577897	+	0.816110i	$0.303874\pi$
$968$	20879.1	0.693263
$969$	−14494.7	−0.480532
$970$	988.954	0.0327355
$971$	−44827.8	−1.48156	−0.740780	−	0.671748i	$-0.765544\pi$
$971$	−44827.8	−1.48156	−0.740780	+	0.671748i	$0.765544\pi$
$972$	5648.07	0.186381
$973$	0	0
$974$	10802.5	0.355373
$975$	60664.1	1.99262
$976$	−11621.4	−0.381140
$977$	7189.43	0.235425	0.117712	−	0.993048i	$-0.462444\pi$
$977$	7189.43	0.235425	0.117712	+	0.993048i	$0.462444\pi$
$978$	26426.8	0.864046
$979$	31039.0	1.01329
$980$	0	0
$981$	−72794.4	−2.36916
$982$	−8604.00	−0.279597
$983$	4290.04	0.139197	0.0695987	−	0.997575i	$-0.477828\pi$
$983$	4290.04	0.139197	0.0695987	+	0.997575i	$0.477828\pi$
$984$	−11546.7	−0.374082
$985$	16539.5	0.535016
$986$	1895.58	0.0612247
$987$	0	0
$988$	8653.93	0.278662
$989$	−21334.6	−0.685946
$990$	−8429.34	−0.270608
$991$	55039.0	1.76425	0.882125	−	0.471015i	$-0.156112\pi$
$991$	55039.0	1.76425	0.882125	+	0.471015i	$0.156112\pi$
$992$	44381.2	1.42047
$993$	11952.6	0.381980
$994$	0	0
$995$	−360.747	−0.0114939
$996$	−75354.6	−2.39729
$997$	−8768.33	−0.278531	−0.139266	−	0.990255i	$-0.544474\pi$
$997$	−8768.33	−0.278531	−0.139266	+	0.990255i	$0.544474\pi$
$998$	3419.70	0.108466
$999$	−8664.07	−0.274393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2401.4.a.c.1.18		39
7.6	odd	2		2401.4.a.d.1.18		39
49.6	odd	14		49.4.e.a.36.8	yes	78
49.41	odd	14		49.4.e.a.15.8	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.15.8	✓	78	49.41	odd	14
49.4.e.a.36.8	yes	78	49.6	odd	14
2401.4.a.c.1.18		39	1.1	even	1	trivial
2401.4.a.d.1.18		39	7.6	odd	2

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:	\( N \)	\(=\)	\( 2401 = 7^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2401.a (trivial)

\(f(q)\)	\(=\)	\(q-0.904464 q^{2} -9.08614 q^{3} -7.18194 q^{4} +3.14137 q^{5} +8.21809 q^{6} +13.7315 q^{8} +55.5579 q^{9} +O(q^{10})\)	\(q-0.904464 q^{2} -9.08614 q^{3} -7.18194 q^{4} +3.14137 q^{5} +8.21809 q^{6} +13.7315 q^{8} +55.5579 q^{9} -2.84125 q^{10} +53.3996 q^{11} +65.2561 q^{12} +57.9905 q^{13} -28.5429 q^{15} +45.0359 q^{16} -76.7741 q^{17} -50.2501 q^{18} -20.7785 q^{19} -22.5611 q^{20} -48.2981 q^{22} +66.2950 q^{23} -124.767 q^{24} -115.132 q^{25} -52.4504 q^{26} -259.481 q^{27} +27.2983 q^{29} +25.8160 q^{30} -294.724 q^{31} -150.586 q^{32} -485.196 q^{33} +69.4394 q^{34} -399.014 q^{36} +33.3900 q^{37} +18.7934 q^{38} -526.910 q^{39} +43.1357 q^{40} +92.5468 q^{41} -321.813 q^{43} -383.513 q^{44} +174.528 q^{45} -59.9615 q^{46} +393.190 q^{47} -409.202 q^{48} +104.133 q^{50} +697.580 q^{51} -416.485 q^{52} +514.909 q^{53} +234.691 q^{54} +167.748 q^{55} +188.796 q^{57} -24.6904 q^{58} -113.337 q^{59} +204.993 q^{60} -258.048 q^{61} +266.567 q^{62} -224.088 q^{64} +182.169 q^{65} +438.843 q^{66} +49.2473 q^{67} +551.387 q^{68} -602.366 q^{69} +461.374 q^{71} +762.894 q^{72} +428.267 q^{73} -30.2001 q^{74} +1046.10 q^{75} +149.230 q^{76} +476.571 q^{78} +93.0732 q^{79} +141.474 q^{80} +857.615 q^{81} -83.7053 q^{82} -1154.75 q^{83} -241.175 q^{85} +291.068 q^{86} -248.036 q^{87} +733.258 q^{88} +581.259 q^{89} -157.854 q^{90} -476.127 q^{92} +2677.90 q^{93} -355.626 q^{94} -65.2729 q^{95} +1368.24 q^{96} -348.070 q^{97} +2966.77 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) \) 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9	\( 39 q + q^{2} - q^{3} + 145 q^{4} - 27 q^{5} - 41 q^{6} - 12 q^{8} + 312 q^{9} - 78 q^{10} + q^{11} + 91 q^{12} - 77 q^{13} - 161 q^{15} + 461 q^{16} - 211 q^{17} + 8 q^{18} - 314 q^{19} - 476 q^{20} - 61 q^{22} - 69 q^{23} - 330 q^{24} + 606 q^{25} - 504 q^{26} + 50 q^{27} + 57 q^{29} + 42 q^{30} - 638 q^{31} - 1600 q^{32} - 1574 q^{33} - 1343 q^{34} + 782 q^{36} + 71 q^{37} - 1359 q^{38} - 84 q^{39} + 155 q^{40} - 1393 q^{41} - 125 q^{43} + 52 q^{44} - 1129 q^{45} - 1454 q^{46} - 1483 q^{47} + 974 q^{48} + 3074 q^{50} - 2044 q^{51} - 3899 q^{52} + 2213 q^{53} - 1142 q^{54} - 1604 q^{55} + 98 q^{57} + 2403 q^{58} - 2073 q^{59} - 1519 q^{60} - 2575 q^{61} - 1742 q^{62} + 1358 q^{64} + 1876 q^{65} + 48 q^{66} + 176 q^{67} - 3038 q^{68} + 638 q^{69} - 1259 q^{71} - 3799 q^{72} + 307 q^{73} + 3845 q^{74} - 131 q^{75} - 1974 q^{76} - 6041 q^{78} + 22 q^{79} + 804 q^{80} + 795 q^{81} - 8043 q^{82} - 6349 q^{83} + 3094 q^{85} + 1745 q^{86} - 9508 q^{87} + 1299 q^{88} - 2253 q^{89} - 11156 q^{90} + 1284 q^{92} - 3430 q^{93} - 2738 q^{94} - 3290 q^{95} - 3031 q^{96} + 770 q^{97} + 5384 q^{99}+O(q^{100}) \) 39 * q + q^2 - q^3 + 145 * q^4 - 27 * q^5 - 41 * q^6 - 12 * q^8 + 312 * q^9 - 78 * q^10 + q^11 + 91 * q^12 - 77 * q^13 - 161 * q^15 + 461 * q^16 - 211 * q^17 + 8 * q^18 - 314 * q^19 - 476 * q^20 - 61 * q^22 - 69 * q^23 - 330 * q^24 + 606 * q^25 - 504 * q^26 + 50 * q^27 + 57 * q^29 + 42 * q^30 - 638 * q^31 - 1600 * q^32 - 1574 * q^33 - 1343 * q^34 + 782 * q^36 + 71 * q^37 - 1359 * q^38 - 84 * q^39 + 155 * q^40 - 1393 * q^41 - 125 * q^43 + 52 * q^44 - 1129 * q^45 - 1454 * q^46 - 1483 * q^47 + 974 * q^48 + 3074 * q^50 - 2044 * q^51 - 3899 * q^52 + 2213 * q^53 - 1142 * q^54 - 1604 * q^55 + 98 * q^57 + 2403 * q^58 - 2073 * q^59 - 1519 * q^60 - 2575 * q^61 - 1742 * q^62 + 1358 * q^64 + 1876 * q^65 + 48 * q^66 + 176 * q^67 - 3038 * q^68 + 638 * q^69 - 1259 * q^71 - 3799 * q^72 + 307 * q^73 + 3845 * q^74 - 131 * q^75 - 1974 * q^76 - 6041 * q^78 + 22 * q^79 + 804 * q^80 + 795 * q^81 - 8043 * q^82 - 6349 * q^83 + 3094 * q^85 + 1745 * q^86 - 9508 * q^87 + 1299 * q^88 - 2253 * q^89 - 11156 * q^90 + 1284 * q^92 - 3430 * q^93 - 2738 * q^94 - 3290 * q^95 - 3031 * q^96 + 770 * q^97 + 5384 * q^99

Introduction

L-functions

Modular forms

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Database

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