LMFDB - Embedded newform 325.10.a.k.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,10,Mod(1,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("325.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	325.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:	$167.386646753$
Analytic rank:	$1$
Dimension:	$27$
Twist minimal:	no (minimal twist has level 65)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-37.2225 q^{2} -132.249 q^{3} +873.511 q^{4} +4922.65 q^{6} -6816.48 q^{7} -13456.3 q^{8} -2193.09 q^{9} -40762.4 q^{11} -115521. q^{12} +28561.0 q^{13} +253726. q^{14} +53640.4 q^{16} -491145. q^{17} +81632.3 q^{18} +713534. q^{19} +901476. q^{21} +1.51728e6 q^{22} -1.62288e6 q^{23} +1.77959e6 q^{24} -1.06311e6 q^{26} +2.89310e6 q^{27} -5.95427e6 q^{28} -2.06761e6 q^{29} +7.21399e6 q^{31} +4.89302e6 q^{32} +5.39080e6 q^{33} +1.82816e7 q^{34} -1.91569e6 q^{36} -6.13511e6 q^{37} -2.65595e7 q^{38} -3.77718e6 q^{39} -532270. q^{41} -3.35551e7 q^{42} -2.95343e7 q^{43} -3.56064e7 q^{44} +6.04077e7 q^{46} -2.98650e7 q^{47} -7.09391e6 q^{48} +6.11080e6 q^{49} +6.49536e7 q^{51} +2.49484e7 q^{52} -1.01037e8 q^{53} -1.07688e8 q^{54} +9.17249e7 q^{56} -9.43645e7 q^{57} +7.69617e7 q^{58} +1.55968e8 q^{59} -1.25023e7 q^{61} -2.68522e8 q^{62} +1.49492e7 q^{63} -2.09594e8 q^{64} -2.00659e8 q^{66} +1.62345e8 q^{67} -4.29020e8 q^{68} +2.14625e8 q^{69} -2.03300e8 q^{71} +2.95110e7 q^{72} +1.19966e8 q^{73} +2.28364e8 q^{74} +6.23280e8 q^{76} +2.77856e8 q^{77} +1.40596e8 q^{78} +1.36039e8 q^{79} -3.39444e8 q^{81} +1.98124e7 q^{82} +6.00605e8 q^{83} +7.87449e8 q^{84} +1.09934e9 q^{86} +2.73441e8 q^{87} +5.48513e8 q^{88} -2.21485e7 q^{89} -1.94685e8 q^{91} -1.41761e9 q^{92} -9.54046e8 q^{93} +1.11165e9 q^{94} -6.47099e8 q^{96} +6.11371e8 q^{97} -2.27459e8 q^{98} +8.93957e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 48 q^{2} - 324 q^{3} + 6570 q^{4} - 1786 q^{6} - 3736 q^{7} - 36864 q^{8} + 214173 q^{9} - 66096 q^{11} - 114398 q^{12} + 771147 q^{13} - 359458 q^{14} + 998622 q^{16} - 779040 q^{17} - 1709648 q^{18}+ \cdots + 2142297632 q^{99}+O(q^{100}) $ 27 * q - 48 * q^2 - 324 * q^3 + 6570 * q^4 - 1786 * q^6 - 3736 * q^7 - 36864 * q^8 + 214173 * q^9 - 66096 * q^11 - 114398 * q^12 + 771147 * q^13 - 359458 * q^14 + 998622 * q^16 - 779040 * q^17 - 1709648 * q^18 - 761728 * q^19 - 2688628 * q^21 - 6061956 * q^22 - 4311518 * q^23 - 3567212 * q^24 - 1370928 * q^26 - 11899092 * q^27 - 137728 * q^28 + 4433670 * q^29 + 6106898 * q^31 - 32810006 * q^32 + 8840028 * q^33 + 18784070 * q^34 + 97588100 * q^36 - 29239496 * q^37 - 47346226 * q^38 - 9253764 * q^39 - 20531542 * q^41 - 106639738 * q^42 - 47500676 * q^43 + 43383046 * q^44 - 32105710 * q^46 - 134711080 * q^47 - 93484396 * q^48 + 146756645 * q^49 - 68396394 * q^51 + 187645770 * q^52 - 138404222 * q^53 + 1549570 * q^54 - 278046454 * q^56 - 103323872 * q^57 - 45680202 * q^58 - 495705656 * q^59 + 100256494 * q^61 - 380024874 * q^62 - 400619958 * q^63 + 554167194 * q^64 + 78712808 * q^66 - 805369894 * q^67 + 100947682 * q^68 - 659167072 * q^69 - 235437654 * q^71 - 1888149924 * q^72 - 251667626 * q^73 + 1855922170 * q^74 + 463619480 * q^76 - 1309691528 * q^77 - 51009946 * q^78 - 411718216 * q^79 + 1988439299 * q^81 - 2460333322 * q^82 - 2304849010 * q^83 - 476824718 * q^84 + 3316508396 * q^86 - 2481466544 * q^87 - 4501137582 * q^88 - 1619966906 * q^89 - 106703896 * q^91 - 2915597990 * q^92 - 3160578792 * q^93 + 4199181314 * q^94 + 2027406718 * q^96 + 861912866 * q^97 + 3534969754 * q^98 + 2142297632 * q^99

Coefficient data

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

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

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

$2$	−37.2225	−1.64502	−0.822508	−	0.568754i	$-0.807426\pi$
$2$	−37.2225	−1.64502	−0.822508	+	0.568754i	$0.807426\pi$
$3$	−132.249	−0.942645	−0.471322	−	0.881961i	$-0.656223\pi$
$3$	−132.249	−0.942645	−0.471322	+	0.881961i	$0.656223\pi$
$4$	873.511	1.70608
$5$	0	0
$5$	0	0
$6$	4922.65	1.55067
$7$	−6816.48	−1.07305	−0.536524	−	0.843885i	$-0.680263\pi$
$7$	−6816.48	−1.07305	−0.536524	+	0.843885i	$0.680263\pi$
$8$	−13456.3	−1.16151
$9$	−2193.09	−0.111421
$10$	0	0
$11$	−40762.4	−0.839446	−0.419723	−	0.907652i	$-0.637873\pi$
$11$	−40762.4	−0.839446	−0.419723	+	0.907652i	$0.637873\pi$
$12$	−115521.	−1.60822
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	253726.	1.76518
$15$	0	0
$16$	53640.4	0.204622
$17$	−491145.	−1.42623	−0.713114	−	0.701048i	$-0.752716\pi$
$17$	−491145.	−1.42623	−0.713114	+	0.701048i	$0.752716\pi$
$18$	81632.3	0.183289
$19$	713534.	1.25610	0.628049	−	0.778174i	$-0.283854\pi$
$19$	713534.	1.25610	0.628049	+	0.778174i	$0.283854\pi$
$20$	0	0
$21$	901476.	1.01150
$22$	1.51728e6	1.38090
$23$	−1.62288e6	−1.20924	−0.604620	−	0.796514i	$-0.706675\pi$
$23$	−1.62288e6	−1.20924	−0.604620	+	0.796514i	$0.706675\pi$
$24$	1.77959e6	1.09489
$25$	0	0
$26$	−1.06311e6	−0.456245
$27$	2.89310e6	1.04767
$28$	−5.95427e6	−1.83070
$29$	−2.06761e6	−0.542848	−0.271424	−	0.962460i	$-0.587495\pi$
$29$	−2.06761e6	−0.542848	−0.271424	+	0.962460i	$0.587495\pi$
$30$	0	0
$31$	7.21399e6	1.40297	0.701484	−	0.712685i	$-0.252521\pi$
$31$	7.21399e6	1.40297	0.701484	+	0.712685i	$0.252521\pi$
$32$	4.89302e6	0.824902
$33$	5.39080e6	0.791299
$34$	1.82816e7	2.34617
$35$	0	0
$36$	−1.91569e6	−0.190092
$37$	−6.13511e6	−0.538164	−0.269082	−	0.963117i	$-0.586720\pi$
$37$	−6.13511e6	−0.538164	−0.269082	+	0.963117i	$0.586720\pi$
$38$	−2.65595e7	−2.06630
$39$	−3.77718e6	−0.261443
$40$	0	0
$41$	−532270.	−0.0294174	−0.0147087	−	0.999892i	$-0.504682\pi$
$41$	−532270.	−0.0294174	−0.0147087	+	0.999892i	$0.504682\pi$
$42$	−3.35551e7	−1.66394
$43$	−2.95343e7	−1.31740	−0.658701	−	0.752405i	$-0.728894\pi$
$43$	−2.95343e7	−1.31740	−0.658701	+	0.752405i	$0.728894\pi$
$44$	−3.56064e7	−1.43216
$45$	0	0
$46$	6.04077e7	1.98922
$47$	−2.98650e7	−0.892735	−0.446368	−	0.894850i	$-0.647283\pi$
$47$	−2.98650e7	−0.892735	−0.446368	+	0.894850i	$0.647283\pi$
$48$	−7.09391e6	−0.192886
$49$	6.11080e6	0.151431
$50$	0	0
$51$	6.49536e7	1.34443
$52$	2.49484e7	0.473181
$53$	−1.01037e8	−1.75890	−0.879449	−	0.475994i	$-0.842088\pi$
$53$	−1.01037e8	−1.75890	−0.879449	+	0.475994i	$0.842088\pi$
$54$	−1.07688e8	−1.72344
$55$	0	0
$56$	9.17249e7	1.24635
$57$	−9.43645e7	−1.18405
$58$	7.69617e7	0.892994
$59$	1.55968e8	1.67572	0.837860	−	0.545886i	$-0.183807\pi$
$59$	1.55968e8	1.67572	0.837860	+	0.545886i	$0.183807\pi$
$60$	0	0
$61$	−1.25023e7	−0.115612	−0.0578062	−	0.998328i	$-0.518411\pi$
$61$	−1.25023e7	−0.115612	−0.0578062	+	0.998328i	$0.518411\pi$
$62$	−2.68522e8	−2.30790
$63$	1.49492e7	0.119560
$64$	−2.09594e8	−1.56160
$65$	0	0
$66$	−2.00659e8	−1.30170
$67$	1.62345e8	0.984240	0.492120	−	0.870527i	$-0.336222\pi$
$67$	1.62345e8	0.984240	0.492120	+	0.870527i	$0.336222\pi$
$68$	−4.29020e8	−2.43326
$69$	2.14625e8	1.13988
$70$	0	0
$71$	−2.03300e8	−0.949457	−0.474728	−	0.880132i	$-0.657454\pi$
$71$	−2.03300e8	−0.949457	−0.474728	+	0.880132i	$0.657454\pi$
$72$	2.95110e7	0.129416
$73$	1.19966e8	0.494431	0.247215	−	0.968961i	$-0.420484\pi$
$73$	1.19966e8	0.494431	0.247215	+	0.968961i	$0.420484\pi$
$74$	2.28364e8	0.885289
$75$	0	0
$76$	6.23280e8	2.14300
$77$	2.77856e8	0.900766
$78$	1.40596e8	0.430077
$79$	1.36039e8	0.392953	0.196477	−	0.980509i	$-0.437050\pi$
$79$	1.36039e8	0.392953	0.196477	+	0.980509i	$0.437050\pi$
$80$	0	0
$81$	−3.39444e8	−0.876165
$82$	1.98124e7	0.0483921
$83$	6.00605e8	1.38911	0.694557	−	0.719438i	$-0.255601\pi$
$83$	6.00605e8	1.38911	0.694557	+	0.719438i	$0.255601\pi$
$84$	7.87449e8	1.72570
$85$	0	0
$86$	1.09934e9	2.16715
$87$	2.73441e8	0.511713
$88$	5.48513e8	0.975023
$89$	−2.21485e7	−0.0374188	−0.0187094	−	0.999825i	$-0.505956\pi$
$89$	−2.21485e7	−0.0374188	−0.0187094	+	0.999825i	$0.505956\pi$
$90$	0	0
$91$	−1.94685e8	−0.297610
$92$	−1.41761e9	−2.06306
$93$	−9.54046e8	−1.32250
$94$	1.11165e9	1.46856
$95$	0	0
$96$	−6.47099e8	−0.777589
$97$	6.11371e8	0.701185	0.350592	−	0.936528i	$-0.385980\pi$
$97$	6.11371e8	0.701185	0.350592	+	0.936528i	$0.385980\pi$
$98$	−2.27459e8	−0.249107
$99$	8.93957e7	0.0935316
$100$	0	0
$101$	1.26038e9	1.20519	0.602595	−	0.798047i	$-0.294133\pi$
$101$	1.26038e9	1.20519	0.602595	+	0.798047i	$0.294133\pi$
$102$	−2.41773e9	−2.21160
$103$	4.51112e8	0.394927	0.197463	−	0.980310i	$-0.436730\pi$
$103$	4.51112e8	0.394927	0.197463	+	0.980310i	$0.436730\pi$
$104$	−3.84327e8	−0.322144
$105$	0	0
$106$	3.76086e9	2.89341
$107$	1.12075e9	0.826571	0.413286	−	0.910601i	$-0.364381\pi$
$107$	1.12075e9	0.826571	0.413286	+	0.910601i	$0.364381\pi$
$108$	2.52716e9	1.78741
$109$	1.23127e9	0.835474	0.417737	−	0.908568i	$-0.362823\pi$
$109$	1.23127e9	0.835474	0.417737	+	0.908568i	$0.362823\pi$
$110$	0	0
$111$	8.11365e8	0.507298
$112$	−3.65639e8	−0.219569
$113$	2.16070e9	1.24664	0.623319	−	0.781967i	$-0.285784\pi$
$113$	2.16070e9	1.24664	0.623319	+	0.781967i	$0.285784\pi$
$114$	3.51248e9	1.94779
$115$	0	0
$116$	−1.80608e9	−0.926141
$117$	−6.26369e7	−0.0309025
$118$	−5.80551e9	−2.75658
$119$	3.34788e9	1.53041
$120$	0	0
$121$	−6.96374e8	−0.295330
$122$	4.65365e8	0.190184
$123$	7.03924e7	0.0277302
$124$	6.30150e9	2.39357
$125$	0	0
$126$	−5.56445e8	−0.196678
$127$	3.64303e9	1.24264	0.621321	−	0.783556i	$-0.286596\pi$
$127$	3.64303e9	1.24264	0.621321	+	0.783556i	$0.286596\pi$
$128$	5.29638e9	1.74395
$129$	3.90589e9	1.24184
$130$	0	0
$131$	−4.88121e9	−1.44813	−0.724064	−	0.689733i	$-0.757728\pi$
$131$	−4.88121e9	−1.44813	−0.724064	+	0.689733i	$0.757728\pi$
$132$	4.70893e9	1.35002
$133$	−4.86379e9	−1.34785
$134$	−6.04286e9	−1.61909
$135$	0	0
$136$	6.60901e9	1.65658
$137$	1.73487e9	0.420749	0.210375	−	0.977621i	$-0.432532\pi$
$137$	1.73487e9	0.420749	0.210375	+	0.977621i	$0.432532\pi$
$138$	−7.98889e9	−1.87513
$139$	6.60807e8	0.150144	0.0750720	−	0.997178i	$-0.476081\pi$
$139$	6.60807e8	0.150144	0.0750720	+	0.997178i	$0.476081\pi$
$140$	0	0
$141$	3.94963e9	0.841532
$142$	7.56733e9	1.56187
$143$	−1.16422e9	−0.232820
$144$	−1.17638e8	−0.0227991
$145$	0	0
$146$	−4.46543e9	−0.813346
$147$	−8.08150e8	−0.142746
$148$	−5.35909e9	−0.918150
$149$	−5.03914e9	−0.837565	−0.418782	−	0.908087i	$-0.637543\pi$
$149$	−5.03914e9	−0.837565	−0.418782	+	0.908087i	$0.637543\pi$
$150$	0	0
$151$	−3.22365e8	−0.0504606	−0.0252303	−	0.999682i	$-0.508032\pi$
$151$	−3.22365e8	−0.0504606	−0.0252303	+	0.999682i	$0.508032\pi$
$152$	−9.60156e9	−1.45897
$153$	1.07713e9	0.158911
$154$	−1.03425e10	−1.48177
$155$	0	0
$156$	−3.29941e9	−0.446041
$157$	2.20422e9	0.289539	0.144769	−	0.989465i	$-0.453756\pi$
$157$	2.20422e9	0.289539	0.144769	+	0.989465i	$0.453756\pi$
$158$	−5.06370e9	−0.646414
$159$	1.33621e10	1.65802
$160$	0	0
$161$	1.10624e10	1.29757
$162$	1.26349e10	1.44130
$163$	3.76557e9	0.417818	0.208909	−	0.977935i	$-0.433009\pi$
$163$	3.76557e9	0.417818	0.208909	+	0.977935i	$0.433009\pi$
$164$	−4.64944e8	−0.0501884
$165$	0	0
$166$	−2.23560e10	−2.28511
$167$	−1.63486e10	−1.62651	−0.813256	−	0.581906i	$-0.802307\pi$
$167$	−1.63486e10	−1.62651	−0.813256	+	0.581906i	$0.802307\pi$
$168$	−1.21306e10	−1.17487
$169$	8.15731e8	0.0769231
$170$	0	0
$171$	−1.56485e9	−0.139955
$172$	−2.57985e10	−2.24759
$173$	1.35401e10	1.14925	0.574624	−	0.818418i	$-0.305148\pi$
$173$	1.35401e10	1.14925	0.574624	+	0.818418i	$0.305148\pi$
$174$	−1.01781e10	−0.841776
$175$	0	0
$176$	−2.18651e9	−0.171769
$177$	−2.06267e10	−1.57961
$178$	8.24422e8	0.0615544
$179$	1.49939e10	1.09163	0.545817	−	0.837905i	$-0.316219\pi$
$179$	1.49939e10	1.09163	0.545817	+	0.837905i	$0.316219\pi$
$180$	0	0
$181$	1.82087e10	1.26103	0.630514	−	0.776178i	$-0.282844\pi$
$181$	1.82087e10	1.26103	0.630514	+	0.776178i	$0.282844\pi$
$182$	7.24667e9	0.489573
$183$	1.65342e9	0.108981
$184$	2.18381e10	1.40454
$185$	0	0
$186$	3.55119e10	2.17553
$187$	2.00202e10	1.19724
$188$	−2.60874e10	−1.52307
$189$	−1.97208e10	−1.12421
$190$	0	0
$191$	9.54730e9	0.519075	0.259538	−	0.965733i	$-0.416430\pi$
$191$	9.54730e9	0.519075	0.259538	+	0.965733i	$0.416430\pi$
$192$	2.77187e10	1.47203
$193$	−6.05753e8	−0.0314259	−0.0157129	−	0.999877i	$-0.505002\pi$
$193$	−6.05753e8	−0.0314259	−0.0157129	+	0.999877i	$0.505002\pi$
$194$	−2.27567e10	−1.15346
$195$	0	0
$196$	5.33785e9	0.258353
$197$	4.53488e9	0.214520	0.107260	−	0.994231i	$-0.465792\pi$
$197$	4.53488e9	0.214520	0.107260	+	0.994231i	$0.465792\pi$
$198$	−3.32753e9	−0.153861
$199$	2.63037e10	1.18899	0.594494	−	0.804100i	$-0.297352\pi$
$199$	2.63037e10	1.18899	0.594494	+	0.804100i	$0.297352\pi$
$200$	0	0
$201$	−2.14700e10	−0.927789
$202$	−4.69145e10	−1.98256
$203$	1.40938e10	0.582502
$204$	5.67377e10	2.29370
$205$	0	0
$206$	−1.67915e10	−0.649661
$207$	3.55913e9	0.134734
$208$	1.53202e9	0.0567519
$209$	−2.90854e10	−1.05443
$210$	0	0
$211$	−4.77575e10	−1.65871	−0.829355	−	0.558721i	$-0.811292\pi$
$211$	−4.77575e10	−1.65871	−0.829355	+	0.558721i	$0.811292\pi$
$212$	−8.82573e10	−3.00081
$213$	2.68863e10	0.895001
$214$	−4.17169e10	−1.35972
$215$	0	0
$216$	−3.89306e10	−1.21688
$217$	−4.91740e10	−1.50545
$218$	−4.58308e10	−1.37437
$219$	−1.58654e10	−0.466073
$220$	0	0
$221$	−1.40276e10	−0.395565
$222$	−3.02010e10	−0.834513
$223$	−6.38736e10	−1.72961	−0.864807	−	0.502104i	$-0.832559\pi$
$223$	−6.38736e10	−1.72961	−0.864807	+	0.502104i	$0.832559\pi$
$224$	−3.33532e10	−0.885159
$225$	0	0
$226$	−8.04264e10	−2.05074
$227$	4.22941e10	1.05722	0.528608	−	0.848866i	$-0.322714\pi$
$227$	4.22941e10	1.05722	0.528608	+	0.848866i	$0.322714\pi$
$228$	−8.24284e10	−2.02009
$229$	2.40369e10	0.577588	0.288794	−	0.957391i	$-0.406746\pi$
$229$	2.40369e10	0.577588	0.288794	+	0.957391i	$0.406746\pi$
$230$	0	0
$231$	−3.67463e10	−0.849102
$232$	2.78225e10	0.630522
$233$	6.02252e10	1.33868	0.669339	−	0.742957i	$-0.266577\pi$
$233$	6.02252e10	1.33868	0.669339	+	0.742957i	$0.266577\pi$
$234$	2.33150e9	0.0508351
$235$	0	0
$236$	1.36240e11	2.85891
$237$	−1.79911e10	−0.370415
$238$	−1.24616e11	−2.51755
$239$	−1.55942e9	−0.0309153	−0.0154577	−	0.999881i	$-0.504921\pi$
$239$	−1.55942e9	−0.0309153	−0.0154577	+	0.999881i	$0.504921\pi$
$240$	0	0
$241$	−3.22896e10	−0.616575	−0.308288	−	0.951293i	$-0.599756\pi$
$241$	−3.22896e10	−0.616575	−0.308288	+	0.951293i	$0.599756\pi$
$242$	2.59207e10	0.485823
$243$	−1.20536e10	−0.221763
$244$	−1.09209e10	−0.197244
$245$	0	0
$246$	−2.62018e9	−0.0456166
$247$	2.03792e10	0.348379
$248$	−9.70739e10	−1.62956
$249$	−7.94297e10	−1.30944
$250$	0	0
$251$	1.05445e11	1.67685	0.838424	−	0.545019i	$-0.183478\pi$
$251$	1.05445e11	1.67685	0.838424	+	0.545019i	$0.183478\pi$
$252$	1.30583e10	0.203978
$253$	6.61527e10	1.01509
$254$	−1.35602e11	−2.04416
$255$	0	0
$256$	−8.98322e10	−1.30723
$257$	−8.39088e10	−1.19980	−0.599900	−	0.800075i	$-0.704793\pi$
$257$	−8.39088e10	−1.19980	−0.599900	+	0.800075i	$0.704793\pi$
$258$	−1.45387e11	−2.04285
$259$	4.18199e10	0.577476
$260$	0	0
$261$	4.53447e9	0.0604845
$262$	1.81691e11	2.38219
$263$	7.08565e10	0.913227	0.456613	−	0.889665i	$-0.349062\pi$
$263$	7.08565e10	0.913227	0.456613	+	0.889665i	$0.349062\pi$
$264$	−7.25405e10	−0.919101
$265$	0	0
$266$	1.81042e11	2.21724
$267$	2.92913e9	0.0352726
$268$	1.41810e11	1.67919
$269$	9.05787e9	0.105473	0.0527364	−	0.998608i	$-0.483206\pi$
$269$	9.05787e9	0.105473	0.0527364	+	0.998608i	$0.483206\pi$
$270$	0	0
$271$	−9.36362e10	−1.05459	−0.527293	−	0.849683i	$-0.676793\pi$
$271$	−9.36362e10	−1.05459	−0.527293	+	0.849683i	$0.676793\pi$
$272$	−2.63452e10	−0.291837
$273$	2.57470e10	0.280540
$274$	−6.45760e10	−0.692139
$275$	0	0
$276$	1.87478e11	1.94473
$277$	1.77801e11	1.81458	0.907288	−	0.420511i	$-0.138149\pi$
$277$	1.77801e11	1.81458	0.907288	+	0.420511i	$0.138149\pi$
$278$	−2.45969e10	−0.246989
$279$	−1.58209e10	−0.156320
$280$	0	0
$281$	−5.62732e10	−0.538422	−0.269211	−	0.963081i	$-0.586763\pi$
$281$	−5.62732e10	−0.538422	−0.269211	+	0.963081i	$0.586763\pi$
$282$	−1.47015e11	−1.38433
$283$	−8.99873e10	−0.833955	−0.416977	−	0.908917i	$-0.636911\pi$
$283$	−8.99873e10	−0.833955	−0.416977	+	0.908917i	$0.636911\pi$
$284$	−1.77585e11	−1.61985
$285$	0	0
$286$	4.33350e10	0.382993
$287$	3.62821e9	0.0315663
$288$	−1.07308e10	−0.0919111
$289$	1.22635e11	1.03413
$290$	0	0
$291$	−8.08535e10	−0.660968
$292$	1.04792e11	0.843537
$293$	−9.29810e10	−0.737038	−0.368519	−	0.929620i	$-0.620135\pi$
$293$	−9.29810e10	−0.737038	−0.368519	+	0.929620i	$0.620135\pi$
$294$	3.00813e10	0.234819
$295$	0	0
$296$	8.25562e10	0.625082
$297$	−1.17930e11	−0.879467
$298$	1.87569e11	1.37781
$299$	−4.63512e10	−0.335383
$300$	0	0
$301$	2.01320e11	1.41363
$302$	1.19992e10	0.0830084
$303$	−1.66685e11	−1.13607
$304$	3.82742e10	0.257025
$305$	0	0
$306$	−4.00933e10	−0.261412
$307$	−2.69852e10	−0.173381	−0.0866907	−	0.996235i	$-0.527629\pi$
$307$	−2.69852e10	−0.173381	−0.0866907	+	0.996235i	$0.527629\pi$
$308$	2.42711e11	1.53678
$309$	−5.96592e10	−0.372276
$310$	0	0
$311$	−2.25101e11	−1.36445	−0.682223	−	0.731144i	$-0.738987\pi$
$311$	−2.25101e11	−1.36445	−0.682223	+	0.731144i	$0.738987\pi$
$312$	5.08270e10	0.303668
$313$	−4.35700e10	−0.256589	−0.128295	−	0.991736i	$-0.540950\pi$
$313$	−4.35700e10	−0.256589	−0.128295	+	0.991736i	$0.540950\pi$
$314$	−8.20466e10	−0.476296
$315$	0	0
$316$	1.18831e11	0.670408
$317$	2.47102e11	1.37439	0.687193	−	0.726475i	$-0.258843\pi$
$317$	2.47102e11	1.37439	0.687193	+	0.726475i	$0.258843\pi$
$318$	−4.97371e11	−2.72746
$319$	8.42809e10	0.455692
$320$	0	0
$321$	−1.48218e11	−0.779163
$322$	−4.11768e11	−2.13453
$323$	−3.50448e11	−1.79148
$324$	−2.96508e11	−1.49480
$325$	0	0
$326$	−1.40164e11	−0.687316
$327$	−1.62834e11	−0.787555
$328$	7.16241e9	0.0341686
$329$	2.03574e11	0.957947
$330$	0	0
$331$	−2.07256e11	−0.949032	−0.474516	−	0.880247i	$-0.657377\pi$
$331$	−2.07256e11	−0.949032	−0.474516	+	0.880247i	$0.657377\pi$
$332$	5.24635e11	2.36993
$333$	1.34549e10	0.0599626
$334$	6.08536e11	2.67564
$335$	0	0
$336$	4.83555e10	0.206976
$337$	−7.53957e10	−0.318429	−0.159214	−	0.987244i	$-0.550896\pi$
$337$	−7.53957e10	−0.318429	−0.159214	+	0.987244i	$0.550896\pi$
$338$	−3.03635e10	−0.126540
$339$	−2.85751e11	−1.17514
$340$	0	0
$341$	−2.94060e11	−1.17772
$342$	5.82474e10	0.230229
$343$	2.33415e11	0.910555
$344$	3.97423e11	1.53017
$345$	0	0
$346$	−5.03995e11	−1.89053
$347$	−3.72852e11	−1.38056	−0.690278	−	0.723545i	$-0.742512\pi$
$347$	−3.72852e11	−1.38056	−0.690278	+	0.723545i	$0.742512\pi$
$348$	2.38854e11	0.873022
$349$	1.75594e11	0.633570	0.316785	−	0.948497i	$-0.397397\pi$
$349$	1.75594e11	0.633570	0.316785	+	0.948497i	$0.397397\pi$
$350$	0	0
$351$	8.26298e10	0.290573
$352$	−1.99451e11	−0.692460
$353$	−4.04373e11	−1.38610	−0.693052	−	0.720887i	$-0.743735\pi$
$353$	−4.04373e11	−1.38610	−0.693052	+	0.720887i	$0.743735\pi$
$354$	7.67775e11	2.59848
$355$	0	0
$356$	−1.93470e10	−0.0638393
$357$	−4.42755e11	−1.44263
$358$	−5.58111e11	−1.79575
$359$	1.84093e11	0.584941	0.292471	−	0.956275i	$-0.405523\pi$
$359$	1.84093e11	0.584941	0.292471	+	0.956275i	$0.405523\pi$
$360$	0	0
$361$	1.86443e11	0.577782
$362$	−6.77771e11	−2.07441
$363$	9.20950e10	0.278392
$364$	−1.70060e11	−0.507745
$365$	0	0
$366$	−6.15442e10	−0.179276
$367$	2.79309e11	0.803689	0.401845	−	0.915708i	$-0.368369\pi$
$367$	2.79309e11	0.803689	0.401845	+	0.915708i	$0.368369\pi$
$368$	−8.70521e10	−0.247437
$369$	1.16732e9	0.00327771
$370$	0	0
$371$	6.88719e11	1.88738
$372$	−8.33370e11	−2.25629
$373$	5.69504e11	1.52338	0.761688	−	0.647944i	$-0.224371\pi$
$373$	5.69504e11	1.52338	0.761688	+	0.647944i	$0.224371\pi$
$374$	−7.45202e11	−1.96948
$375$	0	0
$376$	4.01874e11	1.03692
$377$	−5.90531e10	−0.150559
$378$	7.34055e11	1.84934
$379$	5.46281e10	0.136000	0.0680001	−	0.997685i	$-0.478338\pi$
$379$	5.46281e10	0.136000	0.0680001	+	0.997685i	$0.478338\pi$
$380$	0	0
$381$	−4.81788e11	−1.17137
$382$	−3.55374e11	−0.853887
$383$	−5.83372e11	−1.38532	−0.692661	−	0.721263i	$-0.743562\pi$
$383$	−5.83372e11	−1.38532	−0.692661	+	0.721263i	$0.743562\pi$
$384$	−7.00444e11	−1.64393
$385$	0	0
$386$	2.25476e10	0.0516961
$387$	6.47714e10	0.146786
$388$	5.34040e11	1.19627
$389$	4.24751e11	0.940506	0.470253	−	0.882532i	$-0.344163\pi$
$389$	4.24751e11	0.940506	0.470253	+	0.882532i	$0.344163\pi$
$390$	0	0
$391$	7.97071e11	1.72465
$392$	−8.22290e10	−0.175889
$393$	6.45538e11	1.36507
$394$	−1.68799e11	−0.352889
$395$	0	0
$396$	7.80882e10	0.159572
$397$	1.61966e11	0.327241	0.163620	−	0.986523i	$-0.447683\pi$
$397$	1.61966e11	0.327241	0.163620	+	0.986523i	$0.447683\pi$
$398$	−9.79088e11	−1.95590
$399$	6.43233e11	1.27055
$400$	0	0
$401$	1.70193e11	0.328695	0.164347	−	0.986403i	$-0.447448\pi$
$401$	1.70193e11	0.328695	0.164347	+	0.986403i	$0.447448\pi$
$402$	7.99165e11	1.52623
$403$	2.06039e11	0.389113
$404$	1.10096e12	2.05615
$405$	0	0
$406$	−5.24608e11	−0.958225
$407$	2.50082e11	0.451760
$408$	−8.74038e11	−1.56156
$409$	−4.66309e11	−0.823985	−0.411992	−	0.911187i	$-0.635167\pi$
$409$	−4.66309e11	−0.823985	−0.411992	+	0.911187i	$0.635167\pi$
$410$	0	0
$411$	−2.29435e11	−0.396617
$412$	3.94051e11	0.673775
$413$	−1.06315e12	−1.79813
$414$	−1.32480e11	−0.221640
$415$	0	0
$416$	1.39750e11	0.228787
$417$	−8.73913e10	−0.141532
$418$	1.08263e12	1.73455
$419$	−1.12343e12	−1.78066	−0.890331	−	0.455313i	$-0.849527\pi$
$419$	−1.12343e12	−1.78066	−0.890331	+	0.455313i	$0.849527\pi$
$420$	0	0
$421$	1.85868e11	0.288361	0.144180	−	0.989551i	$-0.453945\pi$
$421$	1.85868e11	0.288361	0.144180	+	0.989551i	$0.453945\pi$
$422$	1.77765e12	2.72861
$423$	6.54968e10	0.0994691
$424$	1.35959e12	2.04297
$425$	0	0
$426$	−1.00078e12	−1.47229
$427$	8.52214e10	0.124058
$428$	9.78984e11	1.41019
$429$	1.53967e11	0.219467
$430$	0	0
$431$	−9.96119e11	−1.39048	−0.695238	−	0.718780i	$-0.744701\pi$
$431$	−9.96119e11	−1.39048	−0.695238	+	0.718780i	$0.744701\pi$
$432$	1.55187e11	0.214377
$433$	−7.07735e11	−0.967554	−0.483777	−	0.875191i	$-0.660735\pi$
$433$	−7.07735e11	−0.967554	−0.483777	+	0.875191i	$0.660735\pi$
$434$	1.83038e12	2.47649
$435$	0	0
$436$	1.07553e12	1.42538
$437$	−1.15798e12	−1.51892
$438$	5.90551e11	0.766697
$439$	5.59583e11	0.719075	0.359537	−	0.933131i	$-0.382934\pi$
$439$	5.59583e11	0.719075	0.359537	+	0.933131i	$0.382934\pi$
$440$	0	0
$441$	−1.34015e10	−0.0168726
$442$	5.22141e11	0.650710
$443$	9.38157e11	1.15733	0.578667	−	0.815564i	$-0.303573\pi$
$443$	9.38157e11	1.15733	0.578667	+	0.815564i	$0.303573\pi$
$444$	7.08737e11	0.865489
$445$	0	0
$446$	2.37753e12	2.84524
$447$	6.66424e11	0.789526
$448$	1.42869e12	1.67567
$449$	9.59461e11	1.11409	0.557043	−	0.830484i	$-0.311936\pi$
$449$	9.59461e11	1.11409	0.557043	+	0.830484i	$0.311936\pi$
$450$	0	0
$451$	2.16966e10	0.0246943
$452$	1.88739e12	2.12686
$453$	4.26326e10	0.0475664
$454$	−1.57429e12	−1.73914
$455$	0	0
$456$	1.26980e12	1.37529
$457$	1.57983e12	1.69429	0.847144	−	0.531364i	$-0.178320\pi$
$457$	1.57983e12	1.69429	0.847144	+	0.531364i	$0.178320\pi$
$458$	−8.94711e11	−0.950141
$459$	−1.42093e12	−1.49422
$460$	0	0
$461$	−8.03099e10	−0.0828161	−0.0414080	−	0.999142i	$-0.513184\pi$
$461$	−8.03099e10	−0.0828161	−0.0414080	+	0.999142i	$0.513184\pi$
$462$	1.36779e12	1.39679
$463$	1.49606e12	1.51299	0.756494	−	0.654001i	$-0.226911\pi$
$463$	1.49606e12	1.51299	0.756494	+	0.654001i	$0.226911\pi$
$464$	−1.10908e11	−0.111079
$465$	0	0
$466$	−2.24173e12	−2.20215
$467$	5.13408e11	0.499501	0.249750	−	0.968310i	$-0.419651\pi$
$467$	5.13408e11	0.499501	0.249750	+	0.968310i	$0.419651\pi$
$468$	−5.47141e10	−0.0527221
$469$	−1.10662e12	−1.05614
$470$	0	0
$471$	−2.91507e11	−0.272932
$472$	−2.09876e12	−1.94636
$473$	1.20389e12	1.10589
$474$	6.69671e11	0.609339
$475$	0	0
$476$	2.92441e12	2.61100
$477$	2.21584e11	0.195977
$478$	5.80456e10	0.0508562
$479$	−2.14608e12	−1.86267	−0.931335	−	0.364163i	$-0.881355\pi$
$479$	−2.14608e12	−1.86267	−0.931335	+	0.364163i	$0.881355\pi$
$480$	0	0
$481$	−1.75225e11	−0.149260
$482$	1.20190e12	1.01428
$483$	−1.46299e12	−1.22315
$484$	−6.08290e11	−0.503857
$485$	0	0
$486$	4.48665e11	0.364803
$487$	−1.20344e12	−0.969489	−0.484745	−	0.874656i	$-0.661087\pi$
$487$	−1.20344e12	−0.969489	−0.484745	+	0.874656i	$0.661087\pi$
$488$	1.68235e11	0.134285
$489$	−4.97995e11	−0.393854
$490$	0	0
$491$	−1.67385e12	−1.29972	−0.649858	−	0.760055i	$-0.725172\pi$
$491$	−1.67385e12	−1.29972	−0.649858	+	0.760055i	$0.725172\pi$
$492$	6.14886e10	0.0473098
$493$	1.01550e12	0.774226
$494$	−7.58566e11	−0.573089
$495$	0	0
$496$	3.86961e11	0.287078
$497$	1.38579e12	1.01881
$498$	2.95657e12	2.15405
$499$	−5.48884e11	−0.396304	−0.198152	−	0.980171i	$-0.563494\pi$
$499$	−5.48884e11	−0.396304	−0.198152	+	0.980171i	$0.563494\pi$
$500$	0	0
$501$	2.16210e12	1.53322
$502$	−3.92492e12	−2.75844
$503$	−1.49726e12	−1.04289	−0.521447	−	0.853283i	$-0.674608\pi$
$503$	−1.49726e12	−1.04289	−0.521447	+	0.853283i	$0.674608\pi$
$504$	−2.01161e11	−0.138869
$505$	0	0
$506$	−2.46236e12	−1.66984
$507$	−1.07880e11	−0.0725111
$508$	3.18223e12	2.12004
$509$	3.00504e12	1.98436	0.992179	−	0.124822i	$-0.0398359\pi$
$509$	3.00504e12	1.98436	0.992179	+	0.124822i	$0.0398359\pi$
$510$	0	0
$511$	−8.17746e11	−0.530548
$512$	6.32027e11	0.406463
$513$	2.06433e12	1.31598
$514$	3.12329e12	1.97369
$515$	0	0
$516$	3.41184e12	2.11868
$517$	1.21737e12	0.749403
$518$	−1.55664e12	−0.949957
$519$	−1.79067e12	−1.08333
$520$	0	0
$521$	−1.15582e12	−0.687258	−0.343629	−	0.939105i	$-0.611656\pi$
$521$	−1.15582e12	−0.687258	−0.343629	+	0.939105i	$0.611656\pi$
$522$	−1.68784e11	−0.0994979
$523$	−1.64038e12	−0.958710	−0.479355	−	0.877621i	$-0.659129\pi$
$523$	−1.64038e12	−0.958710	−0.479355	+	0.877621i	$0.659129\pi$
$524$	−4.26380e12	−2.47062
$525$	0	0
$526$	−2.63745e12	−1.50227
$527$	−3.54311e12	−2.00095
$528$	2.89165e11	0.161917
$529$	8.32600e11	0.462260
$530$	0	0
$531$	−3.42052e11	−0.186710
$532$	−4.24858e12	−2.29954
$533$	−1.52022e10	−0.00815893
$534$	−1.09029e11	−0.0580240
$535$	0	0
$536$	−2.18456e12	−1.14320
$537$	−1.98294e12	−1.02902
$538$	−3.37156e11	−0.173504
$539$	−2.49091e11	−0.127118
$540$	0	0
$541$	−6.56694e11	−0.329591	−0.164796	−	0.986328i	$-0.552696\pi$
$541$	−6.56694e11	−0.329591	−0.164796	+	0.986328i	$0.552696\pi$
$542$	3.48537e12	1.73481
$543$	−2.40809e12	−1.18870
$544$	−2.40318e12	−1.17650
$545$	0	0
$546$	−9.58368e11	−0.461493
$547$	1.75594e12	0.838621	0.419311	−	0.907843i	$-0.362272\pi$
$547$	1.75594e12	0.838621	0.419311	+	0.907843i	$0.362272\pi$
$548$	1.51543e12	0.717831
$549$	2.74186e10	0.0128816
$550$	0	0
$551$	−1.47531e12	−0.681870
$552$	−2.88807e12	−1.32398
$553$	−9.27306e11	−0.421658
$554$	−6.61819e12	−2.98500
$555$	0	0
$556$	5.77222e11	0.256157
$557$	7.12754e11	0.313755	0.156878	−	0.987618i	$-0.449857\pi$
$557$	7.12754e11	0.313755	0.156878	+	0.987618i	$0.449857\pi$
$558$	5.88894e11	0.257148
$559$	−8.43528e11	−0.365381
$560$	0	0
$561$	−2.64766e12	−1.12857
$562$	2.09463e12	0.885713
$563$	−1.27950e12	−0.536725	−0.268362	−	0.963318i	$-0.586482\pi$
$563$	−1.27950e12	−0.536725	−0.268362	+	0.963318i	$0.586482\pi$
$564$	3.45005e12	1.43572
$565$	0	0
$566$	3.34955e12	1.37187
$567$	2.31381e12	0.940167
$568$	2.73568e12	1.10280
$569$	−1.72251e12	−0.688901	−0.344450	−	0.938804i	$-0.611935\pi$
$569$	−1.72251e12	−0.688901	−0.344450	+	0.938804i	$0.611935\pi$
$570$	0	0
$571$	−3.40060e12	−1.33873	−0.669366	−	0.742933i	$-0.733434\pi$
$571$	−3.40060e12	−1.33873	−0.669366	+	0.742933i	$0.733434\pi$
$572$	−1.01696e12	−0.397210
$573$	−1.26262e12	−0.489304
$574$	−1.35051e11	−0.0519271
$575$	0	0
$576$	4.59659e11	0.173994
$577$	1.32866e11	0.0499027	0.0249513	−	0.999689i	$-0.492057\pi$
$577$	1.32866e11	0.0499027	0.0249513	+	0.999689i	$0.492057\pi$
$578$	−4.56478e12	−1.70116
$579$	8.01104e10	0.0296234
$580$	0	0
$581$	−4.09401e12	−1.49058
$582$	3.00957e12	1.08730
$583$	4.11853e12	1.47650
$584$	−1.61430e12	−0.574285
$585$	0	0
$586$	3.46098e12	1.21244
$587$	−1.22335e12	−0.425284	−0.212642	−	0.977130i	$-0.568207\pi$
$587$	−1.22335e12	−0.425284	−0.212642	+	0.977130i	$0.568207\pi$
$588$	−7.05928e11	−0.243536
$589$	5.14743e12	1.76227
$590$	0	0
$591$	−5.99736e11	−0.202216
$592$	−3.29090e11	−0.110120
$593$	−3.47329e11	−0.115344	−0.0576720	−	0.998336i	$-0.518368\pi$
$593$	−3.47329e11	−0.115344	−0.0576720	+	0.998336i	$0.518368\pi$
$594$	4.38963e12	1.44674
$595$	0	0
$596$	−4.40175e12	−1.42895
$597$	−3.47865e12	−1.12079
$598$	1.72531e12	0.551710
$599$	−1.75228e12	−0.556137	−0.278069	−	0.960561i	$-0.589694\pi$
$599$	−1.75228e12	−0.556137	−0.278069	+	0.960561i	$0.589694\pi$
$600$	0	0
$601$	2.93977e12	0.919133	0.459567	−	0.888143i	$-0.348005\pi$
$601$	2.93977e12	0.919133	0.459567	+	0.888143i	$0.348005\pi$
$602$	−7.49362e12	−2.32545
$603$	−3.56036e11	−0.109665
$604$	−2.81590e11	−0.0860896
$605$	0	0
$606$	6.20441e12	1.86885
$607$	2.63365e12	0.787425	0.393712	−	0.919234i	$-0.371191\pi$
$607$	2.63365e12	0.787425	0.393712	+	0.919234i	$0.371191\pi$
$608$	3.49134e12	1.03616
$609$	−1.86390e12	−0.549092
$610$	0	0
$611$	−8.52975e11	−0.247600
$612$	9.40881e11	0.271115
$613$	1.15480e11	0.0330321	0.0165160	−	0.999864i	$-0.494743\pi$
$613$	1.15480e11	0.0330321	0.0165160	+	0.999864i	$0.494743\pi$
$614$	1.00445e12	0.285215
$615$	0	0
$616$	−3.73893e12	−1.04625
$617$	−3.75780e12	−1.04388	−0.521939	−	0.852983i	$-0.674791\pi$
$617$	−3.75780e12	−1.04388	−0.521939	+	0.852983i	$0.674791\pi$
$618$	2.22066e12	0.612399
$619$	−2.17044e12	−0.594210	−0.297105	−	0.954845i	$-0.596021\pi$
$619$	−2.17044e12	−0.594210	−0.297105	+	0.954845i	$0.596021\pi$
$620$	0	0
$621$	−4.69517e12	−1.26689
$622$	8.37883e12	2.24454
$623$	1.50975e11	0.0401521
$624$	−2.02609e11	−0.0534969
$625$	0	0
$626$	1.62178e12	0.422093
$627$	3.84652e12	0.993950
$628$	1.92541e12	0.493976
$629$	3.01323e12	0.767545
$630$	0	0
$631$	−5.99337e12	−1.50501	−0.752505	−	0.658587i	$-0.771154\pi$
$631$	−5.99337e12	−1.50501	−0.752505	+	0.658587i	$0.771154\pi$
$632$	−1.83058e12	−0.456418
$633$	6.31590e12	1.56358
$634$	−9.19773e12	−2.26089
$635$	0	0
$636$	1.16720e13	2.82870
$637$	1.74531e11	0.0419995
$638$	−3.13714e12	−0.749620
$639$	4.45856e11	0.105789
$640$	0	0
$641$	−6.26847e12	−1.46656	−0.733281	−	0.679926i	$-0.762012\pi$
$641$	−6.26847e12	−1.46656	−0.733281	+	0.679926i	$0.762012\pi$
$642$	5.51704e12	1.28174
$643$	9.05874e11	0.208987	0.104493	−	0.994526i	$-0.466678\pi$
$643$	9.05874e11	0.208987	0.104493	+	0.994526i	$0.466678\pi$
$644$	9.66310e12	2.21376
$645$	0	0
$646$	1.30445e13	2.94702
$647$	−5.25490e12	−1.17895	−0.589474	−	0.807787i	$-0.700665\pi$
$647$	−5.25490e12	−1.17895	−0.589474	+	0.807787i	$0.700665\pi$
$648$	4.56768e12	1.01767
$649$	−6.35763e12	−1.40668
$650$	0	0
$651$	6.50323e12	1.41911
$652$	3.28927e12	0.712829
$653$	−4.71722e12	−1.01526	−0.507630	−	0.861575i	$-0.669478\pi$
$653$	−4.71722e12	−1.01526	−0.507630	+	0.861575i	$0.669478\pi$
$654$	6.06109e12	1.29554
$655$	0	0
$656$	−2.85512e10	−0.00601945
$657$	−2.63097e11	−0.0550898
$658$	−7.57754e12	−1.57584
$659$	−8.11959e12	−1.67707	−0.838533	−	0.544852i	$-0.816586\pi$
$659$	−8.11959e12	−1.67707	−0.838533	+	0.544852i	$0.816586\pi$
$660$	0	0
$661$	−9.75841e12	−1.98826	−0.994128	−	0.108211i	$-0.965488\pi$
$661$	−9.75841e12	−1.98826	−0.994128	+	0.108211i	$0.965488\pi$
$662$	7.71457e12	1.56117
$663$	1.85514e12	0.372877
$664$	−8.08195e12	−1.61347
$665$	0	0
$666$	−5.00823e11	−0.0986394
$667$	3.35550e12	0.656433
$668$	−1.42807e13	−2.77495
$669$	8.44724e12	1.63041
$670$	0	0
$671$	5.09622e11	0.0970503
$672$	4.41094e12	0.834391
$673$	6.37456e12	1.19779	0.598897	−	0.800826i	$-0.295606\pi$
$673$	6.37456e12	1.19779	0.598897	+	0.800826i	$0.295606\pi$
$674$	2.80641e12	0.523820
$675$	0	0
$676$	7.12550e11	0.131237
$677$	−9.25132e12	−1.69260	−0.846301	−	0.532706i	$-0.821175\pi$
$677$	−9.25132e12	−1.69260	−0.846301	+	0.532706i	$0.821175\pi$
$678$	1.06363e13	1.93312
$679$	−4.16740e12	−0.752404
$680$	0	0
$681$	−5.59337e12	−0.996579
$682$	1.09456e13	1.93736
$683$	4.14563e12	0.728949	0.364474	−	0.931213i	$-0.381249\pi$
$683$	4.14563e12	0.728949	0.364474	+	0.931213i	$0.381249\pi$
$684$	−1.36691e12	−0.238774
$685$	0	0
$686$	−8.68830e12	−1.49788
$687$	−3.17886e12	−0.544460
$688$	−1.58423e12	−0.269569
$689$	−2.88573e12	−0.487830
$690$	0	0
$691$	7.23801e12	1.20772	0.603862	−	0.797089i	$-0.293628\pi$
$691$	7.23801e12	1.20772	0.603862	+	0.797089i	$0.293628\pi$
$692$	1.18274e13	1.96071
$693$	−6.09364e11	−0.100364
$694$	1.38785e13	2.27104
$695$	0	0
$696$	−3.67951e12	−0.594359
$697$	2.61422e11	0.0419560
$698$	−6.53603e12	−1.04223
$699$	−7.96474e12	−1.26190
$700$	0	0
$701$	1.11053e13	1.73700	0.868502	−	0.495685i	$-0.165083\pi$
$701$	1.11053e13	1.73700	0.868502	+	0.495685i	$0.165083\pi$
$702$	−3.07569e12	−0.477997
$703$	−4.37761e12	−0.675987
$704$	8.54356e12	1.31088
$705$	0	0
$706$	1.50518e13	2.28016
$707$	−8.59137e12	−1.29323
$708$	−1.80176e13	−2.69493
$709$	1.24916e13	1.85656	0.928280	−	0.371882i	$-0.121288\pi$
$709$	1.24916e13	1.85656	0.928280	+	0.371882i	$0.121288\pi$
$710$	0	0
$711$	−2.98346e11	−0.0437831
$712$	2.98038e11	0.0434622
$713$	−1.17075e13	−1.69652
$714$	1.64804e13	2.37316
$715$	0	0
$716$	1.30974e13	1.86241
$717$	2.06233e11	0.0291422
$718$	−6.85239e12	−0.962238
$719$	1.65992e12	0.231636	0.115818	−	0.993270i	$-0.463051\pi$
$719$	1.65992e12	0.231636	0.115818	+	0.993270i	$0.463051\pi$
$720$	0	0
$721$	−3.07499e12	−0.423775
$722$	−6.93987e12	−0.950460
$723$	4.27028e12	0.581211
$724$	1.59055e13	2.15141
$725$	0	0
$726$	−3.42800e12	−0.457959
$727$	−5.15944e11	−0.0685011	−0.0342506	−	0.999413i	$-0.510904\pi$
$727$	−5.15944e11	−0.0685011	−0.0342506	+	0.999413i	$0.510904\pi$
$728$	2.61976e12	0.345676
$729$	8.27536e12	1.08521
$730$	0	0
$731$	1.45056e13	1.87892
$732$	1.44428e12	0.185931
$733$	−1.45685e12	−0.186400	−0.0932000	−	0.995647i	$-0.529710\pi$
$733$	−1.45685e12	−0.186400	−0.0932000	+	0.995647i	$0.529710\pi$
$734$	−1.03966e13	−1.32208
$735$	0	0
$736$	−7.94081e12	−0.997504
$737$	−6.61755e12	−0.826216
$738$	−4.34504e10	−0.00539188
$739$	8.71221e12	1.07455	0.537277	−	0.843406i	$-0.319453\pi$
$739$	8.71221e12	1.07455	0.537277	+	0.843406i	$0.319453\pi$
$740$	0	0
$741$	−2.69514e12	−0.328398
$742$	−2.56358e13	−3.10477
$743$	−3.64808e12	−0.439152	−0.219576	−	0.975595i	$-0.570467\pi$
$743$	−3.64808e12	−0.439152	−0.219576	+	0.975595i	$0.570467\pi$
$744$	1.28380e13	1.53610
$745$	0	0
$746$	−2.11983e13	−2.50598
$747$	−1.31718e12	−0.154776
$748$	1.74879e13	2.04259
$749$	−7.63954e12	−0.886950
$750$	0	0
$751$	−1.41139e12	−0.161908	−0.0809538	−	0.996718i	$-0.525797\pi$
$751$	−1.41139e12	−0.161908	−0.0809538	+	0.996718i	$0.525797\pi$
$752$	−1.60197e12	−0.182673
$753$	−1.39450e13	−1.58067
$754$	2.19810e12	0.247672
$755$	0	0
$756$	−1.72263e13	−1.91798
$757$	−1.11659e13	−1.23584	−0.617918	−	0.786243i	$-0.712024\pi$
$757$	−1.11659e13	−1.23584	−0.617918	+	0.786243i	$0.712024\pi$
$758$	−2.03339e12	−0.223722
$759$	−8.74865e12	−0.956870
$760$	0	0
$761$	1.74660e13	1.88783	0.943916	−	0.330185i	$-0.107111\pi$
$761$	1.74660e13	1.88783	0.943916	+	0.330185i	$0.107111\pi$
$762$	1.79333e13	1.92692
$763$	−8.39291e12	−0.896503
$764$	8.33968e12	0.885583
$765$	0	0
$766$	2.17145e13	2.27888
$767$	4.45460e12	0.464761
$768$	1.18803e13	1.23225
$769$	−6.53695e12	−0.674073	−0.337036	−	0.941492i	$-0.609425\pi$
$769$	−6.53695e12	−0.674073	−0.337036	+	0.941492i	$0.609425\pi$
$770$	0	0
$771$	1.10969e13	1.13098
$772$	−5.29132e11	−0.0536150
$773$	1.43446e13	1.44504	0.722522	−	0.691348i	$-0.242983\pi$
$773$	1.43446e13	1.44504	0.722522	+	0.691348i	$0.242983\pi$
$774$	−2.41095e12	−0.241465
$775$	0	0
$776$	−8.22682e12	−0.814431
$777$	−5.53066e12	−0.544355
$778$	−1.58103e13	−1.54715
$779$	−3.79793e11	−0.0369512
$780$	0	0
$781$	8.28700e12	0.797018
$782$	−2.96689e13	−2.83708
$783$	−5.98181e12	−0.568728
$784$	3.27786e11	0.0309861
$785$	0	0
$786$	−2.40285e13	−2.24556
$787$	1.15418e13	1.07248	0.536239	−	0.844066i	$-0.319845\pi$
$787$	1.15418e13	1.07248	0.536239	+	0.844066i	$0.319845\pi$
$788$	3.96127e12	0.365988
$789$	−9.37073e12	−0.860849
$790$	0	0
$791$	−1.47283e13	−1.33770
$792$	−1.20294e12	−0.108638
$793$	−3.57077e11	−0.0320651
$794$	−6.02878e12	−0.538316
$795$	0	0
$796$	2.29766e13	2.02851
$797$	−2.04626e13	−1.79638	−0.898189	−	0.439609i	$-0.855117\pi$
$797$	−2.04626e13	−1.79638	−0.898189	+	0.439609i	$0.855117\pi$
$798$	−2.39427e13	−2.09007
$799$	1.46680e13	1.27324
$800$	0	0
$801$	4.85737e10	0.00416922
$802$	−6.33502e12	−0.540708
$803$	−4.89010e12	−0.415048
$804$	−1.87543e13	−1.58288
$805$	0	0
$806$	−7.66927e12	−0.640098
$807$	−1.19790e12	−0.0994234
$808$	−1.69601e13	−1.39984
$809$	−9.11347e12	−0.748024	−0.374012	−	0.927424i	$-0.622018\pi$
$809$	−9.11347e12	−0.748024	−0.374012	+	0.927424i	$0.622018\pi$
$810$	0	0
$811$	−6.43474e12	−0.522321	−0.261160	−	0.965295i	$-0.584105\pi$
$811$	−6.43474e12	−0.522321	−0.261160	+	0.965295i	$0.584105\pi$
$812$	1.23111e13	0.993793
$813$	1.23833e13	0.994100
$814$	−9.30867e12	−0.743152
$815$	0	0
$816$	3.48413e12	0.275099
$817$	−2.10737e13	−1.65479
$818$	1.73572e13	1.35547
$819$	4.26963e11	0.0331599
$820$	0	0
$821$	1.49394e13	1.14759	0.573796	−	0.818998i	$-0.305470\pi$
$821$	1.49394e13	1.14759	0.573796	+	0.818998i	$0.305470\pi$
$822$	8.54014e12	0.652442
$823$	−6.42394e11	−0.0488093	−0.0244046	−	0.999702i	$-0.507769\pi$
$823$	−6.42394e11	−0.0488093	−0.0244046	+	0.999702i	$0.507769\pi$
$824$	−6.07031e12	−0.458710
$825$	0	0
$826$	3.95731e13	2.95795
$827$	1.16049e13	0.862715	0.431358	−	0.902181i	$-0.358035\pi$
$827$	1.16049e13	0.862715	0.431358	+	0.902181i	$0.358035\pi$
$828$	3.10894e12	0.229867
$829$	1.57628e13	1.15914	0.579572	−	0.814921i	$-0.303220\pi$
$829$	1.57628e13	1.15914	0.579572	+	0.814921i	$0.303220\pi$
$830$	0	0
$831$	−2.35141e13	−1.71050
$832$	−5.98622e12	−0.433109
$833$	−3.00129e12	−0.215976
$834$	3.25292e12	0.232823
$835$	0	0
$836$	−2.54064e13	−1.79893
$837$	2.08708e13	1.46985
$838$	4.18167e13	2.92922
$839$	−6.01495e12	−0.419086	−0.209543	−	0.977799i	$-0.567198\pi$
$839$	−6.01495e12	−0.419086	−0.209543	+	0.977799i	$0.567198\pi$
$840$	0	0
$841$	−1.02321e13	−0.705316
$842$	−6.91848e12	−0.474358
$843$	7.44209e12	0.507541
$844$	−4.17167e13	−2.82989
$845$	0	0
$846$	−2.43795e12	−0.163628
$847$	4.74682e12	0.316904
$848$	−5.41968e12	−0.359909
$849$	1.19008e13	0.786123
$850$	0	0
$851$	9.95658e12	0.650769
$852$	2.34855e13	1.52694
$853$	7.80932e12	0.505059	0.252530	−	0.967589i	$-0.418737\pi$
$853$	7.80932e12	0.505059	0.252530	+	0.967589i	$0.418737\pi$
$854$	−3.17215e12	−0.204077
$855$	0	0
$856$	−1.50811e13	−0.960069
$857$	−7.77957e12	−0.492654	−0.246327	−	0.969187i	$-0.579224\pi$
$857$	−7.77957e12	−0.492654	−0.246327	+	0.969187i	$0.579224\pi$
$858$	−5.73102e12	−0.361027
$859$	7.85737e12	0.492389	0.246194	−	0.969220i	$-0.420820\pi$
$859$	7.85737e12	0.492389	0.246194	+	0.969220i	$0.420820\pi$
$860$	0	0
$861$	−4.79829e11	−0.0297558
$862$	3.70780e13	2.28736
$863$	−2.65186e13	−1.62743	−0.813713	−	0.581266i	$-0.802557\pi$
$863$	−2.65186e13	−1.62743	−0.813713	+	0.581266i	$0.802557\pi$
$864$	1.41560e13	0.864229
$865$	0	0
$866$	2.63436e13	1.59164
$867$	−1.62184e13	−0.974816
$868$	−4.29541e13	−2.56842
$869$	−5.54527e12	−0.329863
$870$	0	0
$871$	4.63672e12	0.272979
$872$	−1.65684e13	−0.970410
$873$	−1.34079e12	−0.0781264
$874$	4.31030e13	2.49865
$875$	0	0
$876$	−1.38586e13	−0.795156
$877$	6.14488e12	0.350764	0.175382	−	0.984500i	$-0.443884\pi$
$877$	6.14488e12	0.350764	0.175382	+	0.984500i	$0.443884\pi$
$878$	−2.08291e13	−1.18289
$879$	1.22967e13	0.694765
$880$	0	0
$881$	−2.66681e13	−1.49142	−0.745711	−	0.666269i	$-0.767890\pi$
$881$	−2.66681e13	−1.49142	−0.745711	+	0.666269i	$0.767890\pi$
$882$	4.98838e11	0.0277556
$883$	−4.25527e12	−0.235561	−0.117781	−	0.993040i	$-0.537578\pi$
$883$	−4.25527e12	−0.235561	−0.117781	+	0.993040i	$0.537578\pi$
$884$	−1.22533e13	−0.674864
$885$	0	0
$886$	−3.49205e13	−1.90383
$887$	1.61561e13	0.876355	0.438177	−	0.898889i	$-0.355624\pi$
$887$	1.61561e13	0.876355	0.438177	+	0.898889i	$0.355624\pi$
$888$	−1.09180e13	−0.589230
$889$	−2.48326e13	−1.33341
$890$	0	0
$891$	1.38366e13	0.735493
$892$	−5.57943e13	−2.95086
$893$	−2.13097e13	−1.12136
$894$	−2.48059e13	−1.29878
$895$	0	0
$896$	−3.61027e13	−1.87134
$897$	6.12992e12	0.316147
$898$	−3.57135e13	−1.83269
$899$	−1.49157e13	−0.761599
$900$	0	0
$901$	4.96239e13	2.50859
$902$	−8.07601e11	−0.0406226
$903$	−2.66244e13	−1.33256
$904$	−2.90751e13	−1.44798
$905$	0	0
$906$	−1.58689e12	−0.0782475
$907$	1.61349e13	0.791651	0.395826	−	0.918326i	$-0.370458\pi$
$907$	1.61349e13	0.791651	0.395826	+	0.918326i	$0.370458\pi$
$908$	3.69444e13	1.80369
$909$	−2.76413e12	−0.134283
$910$	0	0
$911$	1.70662e13	0.820924	0.410462	−	0.911878i	$-0.365367\pi$
$911$	1.70662e13	0.820924	0.410462	+	0.911878i	$0.365367\pi$
$912$	−5.06175e12	−0.242283
$913$	−2.44821e13	−1.16609
$914$	−5.88051e13	−2.78713
$915$	0	0
$916$	2.09965e13	0.985410
$917$	3.32727e13	1.55391
$918$	5.28905e13	2.45802
$919$	−2.39159e13	−1.10603	−0.553015	−	0.833171i	$-0.686523\pi$
$919$	−2.39159e13	−1.10603	−0.553015	+	0.833171i	$0.686523\pi$
$920$	0	0
$921$	3.56877e12	0.163437
$922$	2.98933e12	0.136234
$923$	−5.80646e12	−0.263332
$924$	−3.20983e13	−1.44863
$925$	0	0
$926$	−5.56871e13	−2.48889
$927$	−9.89329e11	−0.0440030
$928$	−1.01169e13	−0.447796
$929$	3.53859e12	0.155869	0.0779345	−	0.996958i	$-0.475168\pi$
$929$	3.53859e12	0.155869	0.0779345	+	0.996958i	$0.475168\pi$
$930$	0	0
$931$	4.36026e12	0.190213
$932$	5.26074e13	2.28389
$933$	2.97695e13	1.28619
$934$	−1.91103e13	−0.821687
$935$	0	0
$936$	8.42864e11	0.0358935
$937$	6.50586e12	0.275725	0.137863	−	0.990451i	$-0.455977\pi$
$937$	6.50586e12	0.275725	0.137863	+	0.990451i	$0.455977\pi$
$938$	4.11910e13	1.73736
$939$	5.76211e12	0.241873
$940$	0	0
$941$	−2.57328e13	−1.06988	−0.534939	−	0.844891i	$-0.679665\pi$
$941$	−2.57328e13	−1.06988	−0.534939	+	0.844891i	$0.679665\pi$
$942$	1.08506e13	0.448978
$943$	8.63813e11	0.0355727
$944$	8.36618e12	0.342889
$945$	0	0
$946$	−4.48117e13	−1.81920
$947$	1.90853e13	0.771123	0.385562	−	0.922682i	$-0.374008\pi$
$947$	1.90853e13	0.771123	0.385562	+	0.922682i	$0.374008\pi$
$948$	−1.57154e13	−0.631957
$949$	3.42635e12	0.137130
$950$	0	0
$951$	−3.26790e13	−1.29556
$952$	−4.50502e13	−1.77758
$953$	3.48712e13	1.36946	0.684729	−	0.728798i	$-0.259921\pi$
$953$	3.48712e13	1.36946	0.684729	+	0.728798i	$0.259921\pi$
$954$	−8.24791e12	−0.322386
$955$	0	0
$956$	−1.36217e12	−0.0527439
$957$	−1.11461e13	−0.429555
$958$	7.98823e13	3.06412
$959$	−1.18257e13	−0.451484
$960$	0	0
$961$	2.56020e13	0.968320
$962$	6.52231e12	0.245535
$963$	−2.45790e12	−0.0920971
$964$	−2.82053e13	−1.05192
$965$	0	0
$966$	5.44561e13	2.01210
$967$	−9.08047e12	−0.333956	−0.166978	−	0.985961i	$-0.553401\pi$
$967$	−9.08047e12	−0.333956	−0.166978	+	0.985961i	$0.553401\pi$
$968$	9.37065e12	0.343029
$969$	4.63466e13	1.68873
$970$	0	0
$971$	−4.96409e12	−0.179206	−0.0896032	−	0.995978i	$-0.528560\pi$
$971$	−4.96409e12	−0.179206	−0.0896032	+	0.995978i	$0.528560\pi$
$972$	−1.05290e13	−0.378344
$973$	−4.50438e12	−0.161112
$974$	4.47949e13	1.59483
$975$	0	0
$976$	−6.70626e11	−0.0236568
$977$	−3.59885e13	−1.26368	−0.631842	−	0.775098i	$-0.717701\pi$
$977$	−3.59885e13	−1.26368	−0.631842	+	0.775098i	$0.717701\pi$
$978$	1.85366e13	0.647895
$979$	9.02826e11	0.0314110
$980$	0	0
$981$	−2.70028e12	−0.0930890
$982$	6.23046e13	2.13805
$983$	3.04093e13	1.03876	0.519381	−	0.854543i	$-0.326163\pi$
$983$	3.04093e13	1.03876	0.519381	+	0.854543i	$0.326163\pi$
$984$	−9.47225e11	−0.0322088
$985$	0	0
$986$	−3.77993e13	−1.27361
$987$	−2.69226e13	−0.903004
$988$	1.78015e13	0.594361
$989$	4.79307e13	1.59305
$990$	0	0
$991$	5.24412e13	1.72719	0.863597	−	0.504182i	$-0.168206\pi$
$991$	5.24412e13	1.72719	0.863597	+	0.504182i	$0.168206\pi$
$992$	3.52982e13	1.15731
$993$	2.74095e13	0.894600
$994$	−5.15826e13	−1.67596
$995$	0	0
$996$	−6.93827e13	−2.23401
$997$	2.53718e13	0.813248	0.406624	−	0.913596i	$-0.366706\pi$
$997$	2.53718e13	0.813248	0.406624	+	0.913596i	$0.366706\pi$
$998$	2.04308e13	0.651926
$999$	−1.77495e13	−0.563821

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.10.a.k.1.4		27
5.2	odd	4		65.10.b.a.14.6	✓	54
5.3	odd	4		65.10.b.a.14.49	yes	54
5.4	even	2		325.10.a.l.1.24		27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.10.b.a.14.6	✓	54	5.2	odd	4
65.10.b.a.14.49	yes	54	5.3	odd	4
325.10.a.k.1.4		27	1.1	even	1	trivial
325.10.a.l.1.24		27	5.4	even	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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	325.a (trivial)

\(f(q)\)	\(=\)	\(q-37.2225 q^{2} -132.249 q^{3} +873.511 q^{4} +4922.65 q^{6} -6816.48 q^{7} -13456.3 q^{8} -2193.09 q^{9} -40762.4 q^{11} -115521. q^{12} +28561.0 q^{13} +253726. q^{14} +53640.4 q^{16} -491145. q^{17} +81632.3 q^{18} +713534. q^{19} +901476. q^{21} +1.51728e6 q^{22} -1.62288e6 q^{23} +1.77959e6 q^{24} -1.06311e6 q^{26} +2.89310e6 q^{27} -5.95427e6 q^{28} -2.06761e6 q^{29} +7.21399e6 q^{31} +4.89302e6 q^{32} +5.39080e6 q^{33} +1.82816e7 q^{34} -1.91569e6 q^{36} -6.13511e6 q^{37} -2.65595e7 q^{38} -3.77718e6 q^{39} -532270. q^{41} -3.35551e7 q^{42} -2.95343e7 q^{43} -3.56064e7 q^{44} +6.04077e7 q^{46} -2.98650e7 q^{47} -7.09391e6 q^{48} +6.11080e6 q^{49} +6.49536e7 q^{51} +2.49484e7 q^{52} -1.01037e8 q^{53} -1.07688e8 q^{54} +9.17249e7 q^{56} -9.43645e7 q^{57} +7.69617e7 q^{58} +1.55968e8 q^{59} -1.25023e7 q^{61} -2.68522e8 q^{62} +1.49492e7 q^{63} -2.09594e8 q^{64} -2.00659e8 q^{66} +1.62345e8 q^{67} -4.29020e8 q^{68} +2.14625e8 q^{69} -2.03300e8 q^{71} +2.95110e7 q^{72} +1.19966e8 q^{73} +2.28364e8 q^{74} +6.23280e8 q^{76} +2.77856e8 q^{77} +1.40596e8 q^{78} +1.36039e8 q^{79} -3.39444e8 q^{81} +1.98124e7 q^{82} +6.00605e8 q^{83} +7.87449e8 q^{84} +1.09934e9 q^{86} +2.73441e8 q^{87} +5.48513e8 q^{88} -2.21485e7 q^{89} -1.94685e8 q^{91} -1.41761e9 q^{92} -9.54046e8 q^{93} +1.11165e9 q^{94} -6.47099e8 q^{96} +6.11371e8 q^{97} -2.27459e8 q^{98} +8.93957e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 48 q^{2} - 324 q^{3} + 6570 q^{4} - 1786 q^{6} - 3736 q^{7} - 36864 q^{8} + 214173 q^{9} - 66096 q^{11} - 114398 q^{12} + 771147 q^{13} - 359458 q^{14} + 998622 q^{16} - 779040 q^{17} - 1709648 q^{18}+ \cdots + 2142297632 q^{99}+O(q^{100}) \) 27 * q - 48 * q^2 - 324 * q^3 + 6570 * q^4 - 1786 * q^6 - 3736 * q^7 - 36864 * q^8 + 214173 * q^9 - 66096 * q^11 - 114398 * q^12 + 771147 * q^13 - 359458 * q^14 + 998622 * q^16 - 779040 * q^17 - 1709648 * q^18 - 761728 * q^19 - 2688628 * q^21 - 6061956 * q^22 - 4311518 * q^23 - 3567212 * q^24 - 1370928 * q^26 - 11899092 * q^27 - 137728 * q^28 + 4433670 * q^29 + 6106898 * q^31 - 32810006 * q^32 + 8840028 * q^33 + 18784070 * q^34 + 97588100 * q^36 - 29239496 * q^37 - 47346226 * q^38 - 9253764 * q^39 - 20531542 * q^41 - 106639738 * q^42 - 47500676 * q^43 + 43383046 * q^44 - 32105710 * q^46 - 134711080 * q^47 - 93484396 * q^48 + 146756645 * q^49 - 68396394 * q^51 + 187645770 * q^52 - 138404222 * q^53 + 1549570 * q^54 - 278046454 * q^56 - 103323872 * q^57 - 45680202 * q^58 - 495705656 * q^59 + 100256494 * q^61 - 380024874 * q^62 - 400619958 * q^63 + 554167194 * q^64 + 78712808 * q^66 - 805369894 * q^67 + 100947682 * q^68 - 659167072 * q^69 - 235437654 * q^71 - 1888149924 * q^72 - 251667626 * q^73 + 1855922170 * q^74 + 463619480 * q^76 - 1309691528 * q^77 - 51009946 * q^78 - 411718216 * q^79 + 1988439299 * q^81 - 2460333322 * q^82 - 2304849010 * q^83 - 476824718 * q^84 + 3316508396 * q^86 - 2481466544 * q^87 - 4501137582 * q^88 - 1619966906 * q^89 - 106703896 * q^91 - 2915597990 * q^92 - 3160578792 * q^93 + 4199181314 * q^94 + 2027406718 * q^96 + 861912866 * q^97 + 3534969754 * q^98 + 2142297632 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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