LMFDB - Embedded newform 275.8.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,8,Mod(1,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("275.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	275.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:	$85.9058820081$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 200x^{2} + 471x + 2765 $ x^4 - x^3 - 200x^2 + 471x + 2765
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$5.54688$ of defining polynomial
Character	$\chi$	$=$	275.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+20.3206 q^{2} -23.7588 q^{3} +284.925 q^{4} -482.793 q^{6} +57.2967 q^{7} +3188.81 q^{8} -1622.52 q^{9} +1331.00 q^{11} -6769.50 q^{12} -15352.8 q^{13} +1164.30 q^{14} +28328.0 q^{16} +19940.6 q^{17} -32970.5 q^{18} +3263.67 q^{19} -1361.30 q^{21} +27046.7 q^{22} -49400.9 q^{23} -75762.5 q^{24} -311978. q^{26} +90509.7 q^{27} +16325.3 q^{28} -177002. q^{29} -283819. q^{31} +167474. q^{32} -31623.0 q^{33} +405204. q^{34} -462296. q^{36} +29849.2 q^{37} +66319.6 q^{38} +364766. q^{39} -22206.2 q^{41} -27662.5 q^{42} -230466. q^{43} +379236. q^{44} -1.00385e6 q^{46} +660596. q^{47} -673041. q^{48} -820260. q^{49} -473766. q^{51} -4.37441e6 q^{52} +1.29865e6 q^{53} +1.83921e6 q^{54} +182709. q^{56} -77540.9 q^{57} -3.59679e6 q^{58} -1.46020e6 q^{59} +653316. q^{61} -5.76737e6 q^{62} -92965.0 q^{63} -222831. q^{64} -642598. q^{66} +2.93609e6 q^{67} +5.68159e6 q^{68} +1.17371e6 q^{69} -5.63522e6 q^{71} -5.17390e6 q^{72} -1.04096e6 q^{73} +606553. q^{74} +929902. q^{76} +76261.9 q^{77} +7.41225e6 q^{78} +1.40438e6 q^{79} +1.39804e6 q^{81} -451243. q^{82} +643837. q^{83} -387870. q^{84} -4.68320e6 q^{86} +4.20537e6 q^{87} +4.24431e6 q^{88} +4.81454e6 q^{89} -879668. q^{91} -1.40756e7 q^{92} +6.74322e6 q^{93} +1.34237e7 q^{94} -3.97898e6 q^{96} -1.35697e7 q^{97} -1.66681e7 q^{98} -2.15957e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 21 q^{2} + 189 q^{4} + 411 q^{6} - 1262 q^{7} + 2367 q^{8} - 2706 q^{9} + 5324 q^{11} - 4353 q^{12} - 2696 q^{13} - 16259 q^{14} + 7633 q^{16} + 24824 q^{17} + 13470 q^{18} - 22730 q^{19} + 5544 q^{21}+ \cdots - 3601686 q^{99}+O(q^{100}) $ 4 * q + 21 * q^2 + 189 * q^4 + 411 * q^6 - 1262 * q^7 + 2367 * q^8 - 2706 * q^9 + 5324 * q^11 - 4353 * q^12 - 2696 * q^13 - 16259 * q^14 + 7633 * q^16 + 24824 * q^17 + 13470 * q^18 - 22730 * q^19 + 5544 * q^21 + 27951 * q^22 + 160 * q^23 - 179787 * q^24 - 343346 * q^26 + 264060 * q^27 + 249037 * q^28 - 433924 * q^29 - 517576 * q^31 + 376727 * q^32 + 371131 * q^34 - 353298 * q^36 - 523762 * q^37 + 126695 * q^38 - 144696 * q^39 - 277004 * q^41 - 54717 * q^42 + 251596 * q^43 + 251559 * q^44 - 399654 * q^46 + 711180 * q^47 - 1790325 * q^48 + 241462 * q^49 - 2200542 * q^51 - 5757946 * q^52 + 940654 * q^53 + 1284201 * q^54 + 2594823 * q^56 - 551700 * q^57 - 5209629 * q^58 + 1014028 * q^59 + 3634268 * q^61 - 5520995 * q^62 + 87120 * q^63 + 1670385 * q^64 + 547041 * q^66 + 163644 * q^67 + 2116383 * q^68 + 602232 * q^69 - 5547896 * q^71 - 10064430 * q^72 + 3614404 * q^73 - 3922253 * q^74 + 599375 * q^76 - 1679722 * q^77 + 5685402 * q^78 - 8995368 * q^79 + 561564 * q^81 - 3995374 * q^82 + 5010356 * q^83 - 6175065 * q^84 - 9767128 * q^86 - 5173554 * q^87 + 3150477 * q^88 - 8759946 * q^89 - 18295460 * q^91 - 23023838 * q^92 + 17520930 * q^93 + 4317674 * q^94 - 7304979 * q^96 - 11731552 * q^97 - 16303462 * q^98 - 3601686 * 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 $

$2$	20.3206	1.79610	0.898051	−	0.439892i	$-0.144983\pi$
$2$	20.3206	1.79610	0.898051	+	0.439892i	$0.144983\pi$
$3$	−23.7588	−0.508043	−0.254022	−	0.967199i	$-0.581753\pi$
$3$	−23.7588	−0.508043	−0.254022	+	0.967199i	$0.581753\pi$
$4$	284.925	2.22598
$5$	0	0
$5$	0	0
$6$	−482.793	−0.912497
$7$	57.2967	0.0631374	0.0315687	−	0.999502i	$-0.489950\pi$
$7$	57.2967	0.0631374	0.0315687	+	0.999502i	$0.489950\pi$
$8$	3188.81	2.20198
$9$	−1622.52	−0.741892
$10$	0	0
$11$	1331.00	0.301511
$11$	1331.00	0.301511
$12$	−6769.50	−1.13089
$13$	−15352.8	−1.93815	−0.969074	−	0.246769i	$-0.920631\pi$
$13$	−15352.8	−1.93815	−0.969074	+	0.246769i	$0.920631\pi$
$14$	1164.30	0.113401
$15$	0	0
$16$	28328.0	1.72901
$17$	19940.6	0.984390	0.492195	−	0.870485i	$-0.336195\pi$
$17$	19940.6	0.984390	0.492195	+	0.870485i	$0.336195\pi$
$18$	−32970.5	−1.33251
$19$	3263.67	0.109161	0.0545806	−	0.998509i	$-0.482618\pi$
$19$	3263.67	0.109161	0.0545806	+	0.998509i	$0.482618\pi$
$20$	0	0
$21$	−1361.30	−0.0320765
$22$	27046.7	0.541545
$23$	−49400.9	−0.846618	−0.423309	−	0.905985i	$-0.639132\pi$
$23$	−49400.9	−0.846618	−0.423309	+	0.905985i	$0.639132\pi$
$24$	−75762.5	−1.11870
$25$	0	0
$26$	−311978.	−3.48111
$27$	90509.7	0.884957
$28$	16325.3	0.140543
$29$	−177002.	−1.34768	−0.673839	−	0.738879i	$-0.735356\pi$
$29$	−177002.	−1.34768	−0.673839	+	0.738879i	$0.735356\pi$
$30$	0	0
$31$	−283819.	−1.71110	−0.855551	−	0.517718i	$-0.826782\pi$
$31$	−283819.	−1.71110	−0.855551	+	0.517718i	$0.826782\pi$
$32$	167474.	0.903486
$33$	−31623.0	−0.153181
$34$	405204.	1.76806
$35$	0	0
$36$	−462296.	−1.65144
$37$	29849.2	0.0968784	0.0484392	−	0.998826i	$-0.484575\pi$
$37$	29849.2	0.0968784	0.0484392	+	0.998826i	$0.484575\pi$
$38$	66319.6	0.196065
$39$	364766.	0.984664
$40$	0	0
$41$	−22206.2	−0.0503189	−0.0251595	−	0.999683i	$-0.508009\pi$
$41$	−22206.2	−0.0503189	−0.0251595	+	0.999683i	$0.508009\pi$
$42$	−27662.5	−0.0576127
$43$	−230466.	−0.442046	−0.221023	−	0.975269i	$-0.570940\pi$
$43$	−230466.	−0.442046	−0.221023	+	0.975269i	$0.570940\pi$
$44$	379236.	0.671158
$45$	0	0
$46$	−1.00385e6	−1.52061
$47$	660596.	0.928097	0.464048	−	0.885810i	$-0.346396\pi$
$47$	660596.	0.928097	0.464048	+	0.885810i	$0.346396\pi$
$48$	−673041.	−0.878410
$49$	−820260.	−0.996014
$50$	0	0
$51$	−473766.	−0.500113
$52$	−4.37441e6	−4.31428
$53$	1.29865e6	1.19819	0.599094	−	0.800678i	$-0.295527\pi$
$53$	1.29865e6	1.19819	0.599094	+	0.800678i	$0.295527\pi$
$54$	1.83921e6	1.58947
$55$	0	0
$56$	182709.	0.139028
$57$	−77540.9	−0.0554586
$58$	−3.59679e6	−2.42056
$59$	−1.46020e6	−0.925618	−0.462809	−	0.886458i	$-0.653158\pi$
$59$	−1.46020e6	−0.925618	−0.462809	+	0.886458i	$0.653158\pi$
$60$	0	0
$61$	653316.	0.368526	0.184263	−	0.982877i	$-0.441010\pi$
$61$	653316.	0.368526	0.184263	+	0.982877i	$0.441010\pi$
$62$	−5.76737e6	−3.07331
$63$	−92965.0	−0.0468411
$64$	−222831.	−0.106254
$65$	0	0
$66$	−642598.	−0.275128
$67$	2.93609e6	1.19263	0.596317	−	0.802749i	$-0.296630\pi$
$67$	2.93609e6	1.19263	0.596317	+	0.802749i	$0.296630\pi$
$68$	5.68159e6	2.19123
$69$	1.17371e6	0.430119
$70$	0	0
$71$	−5.63522e6	−1.86856	−0.934279	−	0.356543i	$-0.883955\pi$
$71$	−5.63522e6	−1.86856	−0.934279	+	0.356543i	$0.883955\pi$
$72$	−5.17390e6	−1.63363
$73$	−1.04096e6	−0.313186	−0.156593	−	0.987663i	$-0.550051\pi$
$73$	−1.04096e6	−0.313186	−0.156593	+	0.987663i	$0.550051\pi$
$74$	606553.	0.174003
$75$	0	0
$76$	929902.	0.242991
$77$	76261.9	0.0190366
$78$	7.41225e6	1.76856
$79$	1.40438e6	0.320472	0.160236	−	0.987079i	$-0.448774\pi$
$79$	1.40438e6	0.320472	0.160236	+	0.987079i	$0.448774\pi$
$80$	0	0
$81$	1.39804e6	0.292295
$82$	−451243.	−0.0903778
$83$	643837.	0.123596	0.0617978	−	0.998089i	$-0.480317\pi$
$83$	643837.	0.123596	0.0617978	+	0.998089i	$0.480317\pi$
$84$	−387870.	−0.0714017
$85$	0	0
$86$	−4.68320e6	−0.793959
$87$	4.20537e6	0.684679
$88$	4.24431e6	0.663923
$89$	4.81454e6	0.723919	0.361960	−	0.932194i	$-0.382108\pi$
$89$	4.81454e6	0.723919	0.361960	+	0.932194i	$0.382108\pi$
$90$	0	0
$91$	−879668.	−0.122370
$92$	−1.40756e7	−1.88455
$93$	6.74322e6	0.869314
$94$	1.34237e7	1.66696
$95$	0	0
$96$	−3.97898e6	−0.459010
$97$	−1.35697e7	−1.50963	−0.754814	−	0.655939i	$-0.772273\pi$
$97$	−1.35697e7	−1.50963	−0.754814	+	0.655939i	$0.772273\pi$
$98$	−1.66681e7	−1.78894
$99$	−2.15957e6	−0.223689
$100$	0	0
$101$	−1.47531e7	−1.42482	−0.712409	−	0.701765i	$-0.752396\pi$
$101$	−1.47531e7	−1.42482	−0.712409	+	0.701765i	$0.752396\pi$
$102$	−9.62719e6	−0.898253
$103$	−8.75997e6	−0.789900	−0.394950	−	0.918703i	$-0.629238\pi$
$103$	−8.75997e6	−0.789900	−0.394950	+	0.918703i	$0.629238\pi$
$104$	−4.89573e7	−4.26777
$105$	0	0
$106$	2.63892e7	2.15207
$107$	−1.48202e7	−1.16953	−0.584764	−	0.811204i	$-0.698813\pi$
$107$	−1.48202e7	−1.16953	−0.584764	+	0.811204i	$0.698813\pi$
$108$	2.57885e7	1.96990
$109$	−1.10204e6	−0.0815085	−0.0407542	−	0.999169i	$-0.512976\pi$
$109$	−1.10204e6	−0.0815085	−0.0407542	+	0.999169i	$0.512976\pi$
$110$	0	0
$111$	−709183.	−0.0492184
$112$	1.62310e6	0.109165
$113$	−418341.	−0.0272744	−0.0136372	−	0.999907i	$-0.504341\pi$
$113$	−418341.	−0.0272744	−0.0136372	+	0.999907i	$0.504341\pi$
$114$	−1.57568e6	−0.0996093
$115$	0	0
$116$	−5.04324e7	−2.99990
$117$	2.49103e7	1.43790
$118$	−2.96722e7	−1.66250
$119$	1.14253e6	0.0621518
$120$	0	0
$121$	1.77156e6	0.0909091
$122$	1.32757e7	0.661911
$123$	527594.	0.0255642
$124$	−8.08673e7	−3.80888
$125$	0	0
$126$	−1.88910e6	−0.0841314
$127$	2.80475e7	1.21501	0.607506	−	0.794315i	$-0.292170\pi$
$127$	2.80475e7	1.21501	0.607506	+	0.794315i	$0.292170\pi$
$128$	−2.59647e7	−1.09433
$129$	5.47560e6	0.224578
$130$	0	0
$131$	1.61684e7	0.628373	0.314187	−	0.949361i	$-0.398268\pi$
$131$	1.61684e7	0.628373	0.314187	+	0.949361i	$0.398268\pi$
$132$	−9.01020e6	−0.340977
$133$	186997.	0.00689215
$134$	5.96630e7	2.14209
$135$	0	0
$136$	6.35869e7	2.16761
$137$	−1.88648e7	−0.626803	−0.313402	−	0.949621i	$-0.601469\pi$
$137$	−1.88648e7	−0.626803	−0.313402	+	0.949621i	$0.601469\pi$
$138$	2.38504e7	0.772537
$139$	−3.61313e7	−1.14112	−0.570560	−	0.821256i	$-0.693274\pi$
$139$	−3.61313e7	−1.14112	−0.570560	+	0.821256i	$0.693274\pi$
$140$	0	0
$141$	−1.56950e7	−0.471513
$142$	−1.14511e8	−3.35612
$143$	−2.04346e7	−0.584374
$144$	−4.59627e7	−1.28274
$145$	0	0
$146$	−2.11528e7	−0.562515
$147$	1.94884e7	0.506018
$148$	8.50480e6	0.215649
$149$	−3.60326e6	−0.0892367	−0.0446183	−	0.999004i	$-0.514207\pi$
$149$	−3.60326e6	−0.0892367	−0.0446183	+	0.999004i	$0.514207\pi$
$150$	0	0
$151$	3.09419e7	0.731354	0.365677	−	0.930742i	$-0.380837\pi$
$151$	3.09419e7	0.731354	0.365677	+	0.930742i	$0.380837\pi$
$152$	1.04072e7	0.240371
$153$	−3.23540e7	−0.730311
$154$	1.54969e6	0.0341917
$155$	0	0
$156$	1.03931e8	2.19184
$157$	7.23162e7	1.49137	0.745687	−	0.666296i	$-0.232121\pi$
$157$	7.23162e7	1.49137	0.745687	+	0.666296i	$0.232121\pi$
$158$	2.85379e7	0.575601
$159$	−3.08543e7	−0.608732
$160$	0	0
$161$	−2.83051e6	−0.0534533
$162$	2.84090e7	0.524992
$163$	1.03076e8	1.86424	0.932118	−	0.362154i	$-0.117959\pi$
$163$	1.03076e8	1.86424	0.932118	+	0.362154i	$0.117959\pi$
$164$	−6.32712e6	−0.112009
$165$	0	0
$166$	1.30831e7	0.221990
$167$	−1.39849e7	−0.232355	−0.116177	−	0.993228i	$-0.537064\pi$
$167$	−1.39849e7	−0.232355	−0.116177	+	0.993228i	$0.537064\pi$
$168$	−4.34094e6	−0.0706320
$169$	1.72961e8	2.75642
$170$	0	0
$171$	−5.29536e6	−0.0809858
$172$	−6.56656e7	−0.983984
$173$	1.05233e8	1.54523	0.772614	−	0.634876i	$-0.218949\pi$
$173$	1.05233e8	1.54523	0.772614	+	0.634876i	$0.218949\pi$
$174$	8.54555e7	1.22975
$175$	0	0
$176$	3.77046e7	0.521315
$177$	3.46928e7	0.470254
$178$	9.78342e7	1.30023
$179$	−1.70572e7	−0.222291	−0.111146	−	0.993804i	$-0.535452\pi$
$179$	−1.70572e7	−0.222291	−0.111146	+	0.993804i	$0.535452\pi$
$180$	0	0
$181$	1.42099e8	1.78122	0.890609	−	0.454770i	$-0.150279\pi$
$181$	1.42099e8	1.78122	0.890609	+	0.454770i	$0.150279\pi$
$182$	−1.78753e7	−0.219788
$183$	−1.55220e7	−0.187227
$184$	−1.57530e8	−1.86424
$185$	0	0
$186$	1.37026e8	1.56138
$187$	2.65410e7	0.296805
$188$	1.88221e8	2.06592
$189$	5.18591e6	0.0558739
$190$	0	0
$191$	1.15805e7	0.120257	0.0601285	−	0.998191i	$-0.480849\pi$
$191$	1.15805e7	0.120257	0.0601285	+	0.998191i	$0.480849\pi$
$192$	5.29420e6	0.0539816
$193$	1.25212e8	1.25370	0.626851	−	0.779139i	$-0.284344\pi$
$193$	1.25212e8	1.25370	0.626851	+	0.779139i	$0.284344\pi$
$194$	−2.75744e8	−2.71144
$195$	0	0
$196$	−2.33713e8	−2.21711
$197$	−8.53930e7	−0.795775	−0.397888	−	0.917434i	$-0.630257\pi$
$197$	−8.53930e7	−0.795775	−0.397888	+	0.917434i	$0.630257\pi$
$198$	−4.38837e7	−0.401768
$199$	−7.61982e7	−0.685424	−0.342712	−	0.939441i	$-0.611345\pi$
$199$	−7.61982e7	−0.685424	−0.342712	+	0.939441i	$0.611345\pi$
$200$	0	0
$201$	−6.97580e7	−0.605910
$202$	−2.99792e8	−2.55912
$203$	−1.01417e7	−0.0850888
$204$	−1.34988e8	−1.11324
$205$	0	0
$206$	−1.78008e8	−1.41874
$207$	8.01538e7	0.628099
$208$	−4.34916e8	−3.35107
$209$	4.34394e6	0.0329133
$210$	0	0
$211$	2.37773e7	0.174251	0.0871253	−	0.996197i	$-0.472232\pi$
$211$	2.37773e7	0.174251	0.0871253	+	0.996197i	$0.472232\pi$
$212$	3.70017e8	2.66714
$213$	1.33886e8	0.949308
$214$	−3.01155e8	−2.10059
$215$	0	0
$216$	2.88619e8	1.94866
$217$	−1.62619e7	−0.108035
$218$	−2.23940e7	−0.146397
$219$	2.47319e7	0.159112
$220$	0	0
$221$	−3.06145e8	−1.90789
$222$	−1.44110e7	−0.0884013
$223$	−2.38876e8	−1.44247	−0.721233	−	0.692692i	$-0.756425\pi$
$223$	−2.38876e8	−1.44247	−0.721233	+	0.692692i	$0.756425\pi$
$224$	9.59569e6	0.0570437
$225$	0	0
$226$	−8.50093e6	−0.0489877
$227$	−1.74334e8	−0.989220	−0.494610	−	0.869115i	$-0.664689\pi$
$227$	−1.74334e8	−0.989220	−0.494610	+	0.869115i	$0.664689\pi$
$228$	−2.20934e7	−0.123450
$229$	3.22965e8	1.77718	0.888591	−	0.458700i	$-0.151685\pi$
$229$	3.22965e8	1.77718	0.888591	+	0.458700i	$0.151685\pi$
$230$	0	0
$231$	−1.81190e6	−0.00967144
$232$	−5.64427e8	−2.96756
$233$	1.81022e8	0.937529	0.468764	−	0.883323i	$-0.344699\pi$
$233$	1.81022e8	0.937529	0.468764	+	0.883323i	$0.344699\pi$
$234$	5.06191e8	2.58261
$235$	0	0
$236$	−4.16049e8	−2.06041
$237$	−3.33665e7	−0.162814
$238$	2.32169e7	0.111631
$239$	3.45882e8	1.63884	0.819419	−	0.573196i	$-0.194296\pi$
$239$	3.45882e8	1.63884	0.819419	+	0.573196i	$0.194296\pi$
$240$	0	0
$241$	−2.76641e8	−1.27308	−0.636541	−	0.771243i	$-0.719635\pi$
$241$	−2.76641e8	−1.27308	−0.636541	+	0.771243i	$0.719635\pi$
$242$	3.59991e7	0.163282
$243$	−2.31161e8	−1.03346
$244$	1.86146e8	0.820332
$245$	0	0
$246$	1.07210e7	0.0459159
$247$	−5.01066e7	−0.211571
$248$	−9.05047e8	−3.76782
$249$	−1.52968e7	−0.0627919
$250$	0	0
$251$	−7.09109e7	−0.283045	−0.141522	−	0.989935i	$-0.545200\pi$
$251$	−7.09109e7	−0.283045	−0.141522	+	0.989935i	$0.545200\pi$
$252$	−2.64881e7	−0.104267
$253$	−6.57526e7	−0.255265
$254$	5.69940e8	2.18228
$255$	0	0
$256$	−4.99094e8	−1.85927
$257$	2.56446e8	0.942390	0.471195	−	0.882029i	$-0.343823\pi$
$257$	2.56446e8	0.942390	0.471195	+	0.882029i	$0.343823\pi$
$258$	1.11267e8	0.403365
$259$	1.71026e6	0.00611665
$260$	0	0
$261$	2.87189e8	0.999831
$262$	3.28551e8	1.12862
$263$	−8.81699e7	−0.298865	−0.149433	−	0.988772i	$-0.547745\pi$
$263$	−8.81699e7	−0.298865	−0.149433	+	0.988772i	$0.547745\pi$
$264$	−1.00840e8	−0.337302
$265$	0	0
$266$	3.79989e6	0.0123790
$267$	−1.14388e8	−0.367782
$268$	8.36566e8	2.65478
$269$	−1.58440e8	−0.496287	−0.248143	−	0.968723i	$-0.579820\pi$
$269$	−1.58440e8	−0.496287	−0.248143	+	0.968723i	$0.579820\pi$
$270$	0	0
$271$	−4.31603e8	−1.31732	−0.658661	−	0.752440i	$-0.728877\pi$
$271$	−4.31603e8	−1.31732	−0.658661	+	0.752440i	$0.728877\pi$
$272$	5.64878e8	1.70202
$273$	2.08999e7	0.0621691
$274$	−3.83344e8	−1.12580
$275$	0	0
$276$	3.34419e8	0.957436
$277$	1.10453e8	0.312248	0.156124	−	0.987737i	$-0.450100\pi$
$277$	1.10453e8	0.312248	0.156124	+	0.987737i	$0.450100\pi$
$278$	−7.34208e8	−2.04957
$279$	4.60502e8	1.26945
$280$	0	0
$281$	6.00166e8	1.61361	0.806807	−	0.590815i	$-0.201194\pi$
$281$	6.00166e8	1.61361	0.806807	+	0.590815i	$0.201194\pi$
$282$	−3.18931e8	−0.846886
$283$	1.93403e8	0.507237	0.253619	−	0.967304i	$-0.418379\pi$
$283$	1.93403e8	0.507237	0.253619	+	0.967304i	$0.418379\pi$
$284$	−1.60562e9	−4.15937
$285$	0	0
$286$	−4.15243e8	−1.04959
$287$	−1.27234e6	−0.00317700
$288$	−2.71729e8	−0.670289
$289$	−1.27108e7	−0.0309764
$290$	0	0
$291$	3.22401e8	0.766956
$292$	−2.96595e8	−0.697147
$293$	1.38457e7	0.0321571	0.0160786	−	0.999871i	$-0.494882\pi$
$293$	1.38457e7	0.0321571	0.0160786	+	0.999871i	$0.494882\pi$
$294$	3.96016e8	0.908860
$295$	0	0
$296$	9.51836e7	0.213325
$297$	1.20468e8	0.266824
$298$	−7.32203e7	−0.160278
$299$	7.58444e8	1.64087
$300$	0	0
$301$	−1.32049e7	−0.0279096
$302$	6.28757e8	1.31359
$303$	3.50517e8	0.723869
$304$	9.24532e7	0.188740
$305$	0	0
$306$	−6.57451e8	−1.31171
$307$	−1.20833e8	−0.238343	−0.119172	−	0.992874i	$-0.538024\pi$
$307$	−1.20833e8	−0.238343	−0.119172	+	0.992874i	$0.538024\pi$
$308$	2.17290e7	0.0423752
$309$	2.08127e8	0.401304
$310$	0	0
$311$	4.07456e7	0.0768103	0.0384051	−	0.999262i	$-0.487772\pi$
$311$	4.07456e7	0.0768103	0.0384051	+	0.999262i	$0.487772\pi$
$312$	1.16317e9	2.16821
$313$	7.97906e8	1.47078	0.735388	−	0.677646i	$-0.237000\pi$
$313$	7.97906e8	1.47078	0.735388	+	0.677646i	$0.237000\pi$
$314$	1.46951e9	2.67866
$315$	0	0
$316$	4.00144e8	0.713365
$317$	−8.47170e8	−1.49370	−0.746850	−	0.664993i	$-0.768434\pi$
$317$	−8.47170e8	−1.49370	−0.746850	+	0.664993i	$0.768434\pi$
$318$	−6.26977e8	−1.09334
$319$	−2.35590e8	−0.406340
$320$	0	0
$321$	3.52110e8	0.594171
$322$	−5.75176e7	−0.0960075
$323$	6.50795e7	0.107457
$324$	3.98337e8	0.650644
$325$	0	0
$326$	2.09456e9	3.34836
$327$	2.61831e7	0.0414098
$328$	−7.08115e7	−0.110801
$329$	3.78500e7	0.0585976
$330$	0	0
$331$	−5.52693e8	−0.837695	−0.418847	−	0.908057i	$-0.637566\pi$
$331$	−5.52693e8	−0.837695	−0.418847	+	0.908057i	$0.637566\pi$
$332$	1.83446e8	0.275121
$333$	−4.84309e7	−0.0718733
$334$	−2.84181e8	−0.417333
$335$	0	0
$336$	−3.85631e7	−0.0554605
$337$	6.07500e8	0.864653	0.432326	−	0.901717i	$-0.357693\pi$
$337$	6.07500e8	0.864653	0.432326	+	0.901717i	$0.357693\pi$
$338$	3.51467e9	4.95081
$339$	9.93930e6	0.0138566
$340$	0	0
$341$	−3.77764e8	−0.515917
$342$	−1.07605e8	−0.145459
$343$	−9.41845e7	−0.126023
$344$	−7.34913e8	−0.973377
$345$	0	0
$346$	2.13840e9	2.77539
$347$	5.55344e8	0.713524	0.356762	−	0.934195i	$-0.383881\pi$
$347$	5.55344e8	0.713524	0.356762	+	0.934195i	$0.383881\pi$
$348$	1.19822e9	1.52408
$349$	−1.06059e9	−1.33554	−0.667770	−	0.744367i	$-0.732751\pi$
$349$	−1.06059e9	−1.33554	−0.667770	+	0.744367i	$0.732751\pi$
$350$	0	0
$351$	−1.38958e9	−1.71518
$352$	2.22907e8	0.272411
$353$	−7.87057e8	−0.952346	−0.476173	−	0.879351i	$-0.657976\pi$
$353$	−7.87057e8	−0.952346	−0.476173	+	0.879351i	$0.657976\pi$
$354$	7.04977e8	0.844624
$355$	0	0
$356$	1.37179e9	1.61143
$357$	−2.71452e7	−0.0315758
$358$	−3.46612e8	−0.399258
$359$	7.81980e8	0.892001	0.446000	−	0.895033i	$-0.352848\pi$
$359$	7.81980e8	0.892001	0.446000	+	0.895033i	$0.352848\pi$
$360$	0	0
$361$	−8.83220e8	−0.988084
$362$	2.88754e9	3.19925
$363$	−4.20902e7	−0.0461858
$364$	−2.50640e8	−0.272392
$365$	0	0
$366$	−3.15416e8	−0.336279
$367$	−1.34965e9	−1.42525	−0.712623	−	0.701547i	$-0.752493\pi$
$367$	−1.34965e9	−1.42525	−0.712623	+	0.701547i	$0.752493\pi$
$368$	−1.39943e9	−1.46381
$369$	3.60300e7	0.0373312
$370$	0	0
$371$	7.44082e7	0.0756505
$372$	1.92131e9	1.93508
$373$	−4.42171e8	−0.441173	−0.220587	−	0.975367i	$-0.570797\pi$
$373$	−4.42171e8	−0.441173	−0.220587	+	0.975367i	$0.570797\pi$
$374$	5.39327e8	0.533091
$375$	0	0
$376$	2.10652e9	2.04365
$377$	2.71749e9	2.61200
$378$	1.05381e8	0.100355
$379$	1.77496e9	1.67475	0.837377	−	0.546626i	$-0.184088\pi$
$379$	1.77496e9	1.67475	0.837377	+	0.546626i	$0.184088\pi$
$380$	0	0
$381$	−6.66375e8	−0.617279
$382$	2.35322e8	0.215994
$383$	−1.97521e9	−1.79646	−0.898229	−	0.439528i	$-0.855146\pi$
$383$	−1.97521e9	−1.79646	−0.898229	+	0.439528i	$0.855146\pi$
$384$	6.16890e8	0.555966
$385$	0	0
$386$	2.54437e9	2.25177
$387$	3.73935e8	0.327950
$388$	−3.86636e9	−3.36040
$389$	−1.62341e9	−1.39832	−0.699158	−	0.714967i	$-0.746442\pi$
$389$	−1.62341e9	−1.39832	−0.699158	+	0.714967i	$0.746442\pi$
$390$	0	0
$391$	−9.85084e8	−0.833402
$392$	−2.61566e9	−2.19321
$393$	−3.84143e8	−0.319241
$394$	−1.73523e9	−1.42929
$395$	0	0
$396$	−6.15317e8	−0.497927
$397$	−7.31101e6	−0.00586422	−0.00293211	−	0.999996i	$-0.500933\pi$
$397$	−7.31101e6	−0.00586422	−0.00293211	+	0.999996i	$0.500933\pi$
$398$	−1.54839e9	−1.23109
$399$	−4.44284e6	−0.00350151
$400$	0	0
$401$	−2.16086e9	−1.67348	−0.836742	−	0.547597i	$-0.815543\pi$
$401$	−2.16086e9	−1.67348	−0.836742	+	0.547597i	$0.815543\pi$
$402$	−1.41752e9	−1.08828
$403$	4.35743e9	3.31637
$404$	−4.20354e9	−3.17161
$405$	0	0
$406$	−2.06084e8	−0.152828
$407$	3.97293e7	0.0292099
$408$	−1.51075e9	−1.10124
$409$	−1.38777e9	−1.00297	−0.501483	−	0.865168i	$-0.667212\pi$
$409$	−1.38777e9	−1.00297	−0.501483	+	0.865168i	$0.667212\pi$
$410$	0	0
$411$	4.48207e8	0.318443
$412$	−2.49594e9	−1.75830
$413$	−8.36650e7	−0.0584411
$414$	1.62877e9	1.12813
$415$	0	0
$416$	−2.57119e9	−1.75109
$417$	8.58437e8	0.579739
$418$	8.82713e7	0.0591157
$419$	−8.21601e8	−0.545647	−0.272824	−	0.962064i	$-0.587958\pi$
$419$	−8.21601e8	−0.545647	−0.272824	+	0.962064i	$0.587958\pi$
$420$	0	0
$421$	−1.37924e9	−0.900850	−0.450425	−	0.892814i	$-0.648727\pi$
$421$	−1.37924e9	−0.900850	−0.450425	+	0.892814i	$0.648727\pi$
$422$	4.83168e8	0.312972
$423$	−1.07183e9	−0.688548
$424$	4.14114e9	2.63839
$425$	0	0
$426$	2.72064e9	1.70505
$427$	3.74329e7	0.0232678
$428$	−4.22265e9	−2.60334
$429$	4.85503e8	0.296887
$430$	0	0
$431$	3.10998e9	1.87106	0.935528	−	0.353253i	$-0.114925\pi$
$431$	3.10998e9	1.87106	0.935528	+	0.353253i	$0.114925\pi$
$432$	2.56396e9	1.53010
$433$	1.87998e9	1.11287	0.556436	−	0.830891i	$-0.312169\pi$
$433$	1.87998e9	1.11287	0.556436	+	0.830891i	$0.312169\pi$
$434$	−3.30451e8	−0.194041
$435$	0	0
$436$	−3.13998e8	−0.181436
$437$	−1.61228e8	−0.0924178
$438$	5.02567e8	0.285782
$439$	3.55542e8	0.200570	0.100285	−	0.994959i	$-0.468025\pi$
$439$	3.55542e8	0.200570	0.100285	+	0.994959i	$0.468025\pi$
$440$	0	0
$441$	1.33089e9	0.738934
$442$	−6.22104e9	−3.42677
$443$	−1.10119e9	−0.601795	−0.300897	−	0.953657i	$-0.597286\pi$
$443$	−1.10119e9	−0.601795	−0.300897	+	0.953657i	$0.597286\pi$
$444$	−2.02064e8	−0.109559
$445$	0	0
$446$	−4.85410e9	−2.59082
$447$	8.56092e7	0.0453361
$448$	−1.27675e7	−0.00670860
$449$	1.58190e9	0.824737	0.412369	−	0.911017i	$-0.364702\pi$
$449$	1.58190e9	0.824737	0.412369	+	0.911017i	$0.364702\pi$
$450$	0	0
$451$	−2.95565e7	−0.0151717
$452$	−1.19196e8	−0.0607124
$453$	−7.35144e8	−0.371560
$454$	−3.54258e9	−1.77674
$455$	0	0
$456$	−2.47264e8	−0.122119
$457$	−2.03131e9	−0.995562	−0.497781	−	0.867303i	$-0.665852\pi$
$457$	−2.03131e9	−0.995562	−0.497781	+	0.867303i	$0.665852\pi$
$458$	6.56284e9	3.19200
$459$	1.80482e9	0.871143
$460$	0	0
$461$	−3.41126e9	−1.62167	−0.810834	−	0.585276i	$-0.800986\pi$
$461$	−3.41126e9	−1.62167	−0.810834	+	0.585276i	$0.800986\pi$
$462$	−3.68187e7	−0.0173709
$463$	8.70628e8	0.407661	0.203830	−	0.979006i	$-0.434661\pi$
$463$	8.70628e8	0.407661	0.203830	+	0.979006i	$0.434661\pi$
$464$	−5.01413e9	−2.33014
$465$	0	0
$466$	3.67846e9	1.68390
$467$	3.03420e9	1.37859	0.689294	−	0.724482i	$-0.257921\pi$
$467$	3.03420e9	1.37859	0.689294	+	0.724482i	$0.257921\pi$
$468$	7.09756e9	3.20073
$469$	1.68228e8	0.0752998
$470$	0	0
$471$	−1.71815e9	−0.757683
$472$	−4.65632e9	−2.03820
$473$	−3.06750e8	−0.133282
$474$	−6.78026e8	−0.292430
$475$	0	0
$476$	3.25536e8	0.138349
$477$	−2.10708e9	−0.888927
$478$	7.02853e9	2.94352
$479$	2.57353e8	0.106993	0.0534964	−	0.998568i	$-0.482963\pi$
$479$	2.57353e8	0.106993	0.0534964	+	0.998568i	$0.482963\pi$
$480$	0	0
$481$	−4.58270e8	−0.187765
$482$	−5.62149e9	−2.28658
$483$	6.72496e7	0.0271566
$484$	5.04763e8	0.202362
$485$	0	0
$486$	−4.69731e9	−1.85619
$487$	2.20542e9	0.865246	0.432623	−	0.901575i	$-0.357588\pi$
$487$	2.20542e9	0.865246	0.432623	+	0.901575i	$0.357588\pi$
$488$	2.08330e9	0.811489
$489$	−2.44897e9	−0.947113
$490$	0	0
$491$	2.54808e9	0.971467	0.485734	−	0.874107i	$-0.338552\pi$
$491$	2.54808e9	0.971467	0.485734	+	0.874107i	$0.338552\pi$
$492$	1.50325e8	0.0569054
$493$	−3.52953e9	−1.32664
$494$	−1.01819e9	−0.380002
$495$	0	0
$496$	−8.04004e9	−2.95851
$497$	−3.22880e8	−0.117976
$498$	−3.10840e8	−0.112781
$499$	2.57194e9	0.926636	0.463318	−	0.886192i	$-0.346659\pi$
$499$	2.57194e9	0.926636	0.463318	+	0.886192i	$0.346659\pi$
$500$	0	0
$501$	3.32265e8	0.118046
$502$	−1.44095e9	−0.508377
$503$	−3.82351e9	−1.33960	−0.669798	−	0.742543i	$-0.733619\pi$
$503$	−3.82351e9	−1.33960	−0.669798	+	0.742543i	$0.733619\pi$
$504$	−2.96448e8	−0.103143
$505$	0	0
$506$	−1.33613e9	−0.458482
$507$	−4.10936e9	−1.40038
$508$	7.99143e9	2.70459
$509$	−1.06710e9	−0.358668	−0.179334	−	0.983788i	$-0.557394\pi$
$509$	−1.06710e9	−0.358668	−0.179334	+	0.983788i	$0.557394\pi$
$510$	0	0
$511$	−5.96435e7	−0.0197738
$512$	−6.81840e9	−2.24511
$513$	2.95394e8	0.0966029
$514$	5.21113e9	1.69263
$515$	0	0
$516$	1.56014e9	0.499907
$517$	8.79253e8	0.279832
$518$	3.47535e7	0.0109861
$519$	−2.50023e9	−0.785043
$520$	0	0
$521$	1.83762e9	0.569277	0.284638	−	0.958635i	$-0.408126\pi$
$521$	1.83762e9	0.569277	0.284638	+	0.958635i	$0.408126\pi$
$522$	5.83585e9	1.79580
$523$	−6.20406e9	−1.89636	−0.948179	−	0.317737i	$-0.897077\pi$
$523$	−6.20406e9	−1.89636	−0.948179	+	0.317737i	$0.897077\pi$
$524$	4.60679e9	1.39875
$525$	0	0
$526$	−1.79166e9	−0.536792
$527$	−5.65953e9	−1.68439
$528$	−8.95818e8	−0.264851
$529$	−9.64375e8	−0.283238
$530$	0	0
$531$	2.36921e9	0.686708
$532$	5.32803e7	0.0153418
$533$	3.40929e8	0.0975255
$534$	−2.32443e9	−0.660574
$535$	0	0
$536$	9.36264e9	2.62616
$537$	4.05260e8	0.112934
$538$	−3.21960e9	−0.891381
$539$	−1.09177e9	−0.300309
$540$	0	0
$541$	1.26501e9	0.343481	0.171740	−	0.985142i	$-0.445061\pi$
$541$	1.26501e9	0.343481	0.171740	+	0.985142i	$0.445061\pi$
$542$	−8.77042e9	−2.36604
$543$	−3.37611e9	−0.904936
$544$	3.33952e9	0.889382
$545$	0	0
$546$	4.24697e8	0.111662
$547$	8.11886e8	0.212099	0.106050	−	0.994361i	$-0.466180\pi$
$547$	8.11886e8	0.212099	0.106050	+	0.994361i	$0.466180\pi$
$548$	−5.37507e9	−1.39525
$549$	−1.06002e9	−0.273407
$550$	0	0
$551$	−5.77676e8	−0.147114
$552$	3.74274e9	0.947114
$553$	8.04665e7	0.0202338
$554$	2.24448e9	0.560829
$555$	0	0
$556$	−1.02947e10	−2.54011
$557$	−3.31656e9	−0.813194	−0.406597	−	0.913608i	$-0.633285\pi$
$557$	−3.31656e9	−0.813194	−0.406597	+	0.913608i	$0.633285\pi$
$558$	9.35766e9	2.28007
$559$	3.53831e9	0.856750
$560$	0	0
$561$	−6.30582e8	−0.150790
$562$	1.21957e10	2.89821
$563$	−1.83459e9	−0.433272	−0.216636	−	0.976252i	$-0.569508\pi$
$563$	−1.83459e9	−0.433272	−0.216636	+	0.976252i	$0.569508\pi$
$564$	−4.47190e9	−1.04958
$565$	0	0
$566$	3.93006e9	0.911049
$567$	8.01031e7	0.0184548
$568$	−1.79697e10	−4.11453
$569$	−2.66945e9	−0.607475	−0.303738	−	0.952756i	$-0.598235\pi$
$569$	−2.66945e9	−0.607475	−0.303738	+	0.952756i	$0.598235\pi$
$570$	0	0
$571$	−2.52473e9	−0.567530	−0.283765	−	0.958894i	$-0.591584\pi$
$571$	−2.52473e9	−0.567530	−0.283765	+	0.958894i	$0.591584\pi$
$572$	−5.82235e9	−1.30080
$573$	−2.75139e8	−0.0610958
$574$	−2.58547e7	−0.00570622
$575$	0	0
$576$	3.61547e8	0.0788289
$577$	6.76103e9	1.46520	0.732601	−	0.680658i	$-0.238306\pi$
$577$	6.76103e9	1.46520	0.732601	+	0.680658i	$0.238306\pi$
$578$	−2.58291e8	−0.0556367
$579$	−2.97488e9	−0.636935
$580$	0	0
$581$	3.68898e7	0.00780350
$582$	6.55137e9	1.37753
$583$	1.72850e9	0.361268
$584$	−3.31942e9	−0.689631
$585$	0	0
$586$	2.81352e8	0.0577574
$587$	3.20998e9	0.655041	0.327520	−	0.944844i	$-0.393787\pi$
$587$	3.20998e9	0.655041	0.327520	+	0.944844i	$0.393787\pi$
$588$	5.55275e9	1.12639
$589$	−9.26292e8	−0.186786
$590$	0	0
$591$	2.02884e9	0.404288
$592$	8.45569e8	0.167503
$593$	−5.05111e9	−0.994707	−0.497354	−	0.867548i	$-0.665695\pi$
$593$	−5.05111e9	−0.994707	−0.497354	+	0.867548i	$0.665695\pi$
$594$	2.44799e9	0.479244
$595$	0	0
$596$	−1.02666e9	−0.198639
$597$	1.81038e9	0.348225
$598$	1.54120e10	2.94717
$599$	−6.69582e9	−1.27295	−0.636473	−	0.771299i	$-0.719607\pi$
$599$	−6.69582e9	−1.27295	−0.636473	+	0.771299i	$0.719607\pi$
$600$	0	0
$601$	−5.51275e9	−1.03587	−0.517937	−	0.855418i	$-0.673300\pi$
$601$	−5.51275e9	−1.03587	−0.517937	+	0.855418i	$0.673300\pi$
$602$	−2.68332e8	−0.0501285
$603$	−4.76385e9	−0.884806
$604$	8.81614e9	1.62798
$605$	0	0
$606$	7.12270e9	1.30014
$607$	7.73610e8	0.140398	0.0701992	−	0.997533i	$-0.477637\pi$
$607$	7.73610e8	0.140398	0.0701992	+	0.997533i	$0.477637\pi$
$608$	5.46578e8	0.0986256
$609$	2.40954e8	0.0432288
$610$	0	0
$611$	−1.01420e10	−1.79879
$612$	−9.21847e9	−1.62566
$613$	−6.16150e9	−1.08038	−0.540188	−	0.841544i	$-0.681647\pi$
$613$	−6.16150e9	−1.08038	−0.540188	+	0.841544i	$0.681647\pi$
$614$	−2.45540e9	−0.428088
$615$	0	0
$616$	2.43185e8	0.0419184
$617$	−3.20717e9	−0.549698	−0.274849	−	0.961487i	$-0.588628\pi$
$617$	−3.20717e9	−0.549698	−0.274849	+	0.961487i	$0.588628\pi$
$618$	4.22925e9	0.720782
$619$	−7.43852e9	−1.26058	−0.630288	−	0.776361i	$-0.717063\pi$
$619$	−7.43852e9	−1.26058	−0.630288	+	0.776361i	$0.717063\pi$
$620$	0	0
$621$	−4.47126e9	−0.749220
$622$	8.27974e8	0.137959
$623$	2.75858e8	0.0457064
$624$	1.03331e10	1.70249
$625$	0	0
$626$	1.62139e10	2.64166
$627$	−1.03207e8	−0.0167214
$628$	2.06047e10	3.31977
$629$	5.95211e8	0.0953661
$630$	0	0
$631$	8.48900e9	1.34510	0.672549	−	0.740053i	$-0.265200\pi$
$631$	8.48900e9	1.34510	0.672549	+	0.740053i	$0.265200\pi$
$632$	4.47831e9	0.705675
$633$	−5.64921e8	−0.0885268
$634$	−1.72150e10	−2.68283
$635$	0	0
$636$	−8.79118e9	−1.35502
$637$	1.25933e10	1.93042
$638$	−4.78732e9	−0.729828
$639$	9.14324e9	1.38627
$640$	0	0
$641$	8.52855e9	1.27900	0.639502	−	0.768789i	$-0.279140\pi$
$641$	8.52855e9	1.27900	0.639502	+	0.768789i	$0.279140\pi$
$642$	7.15508e9	1.06719
$643$	−3.63341e9	−0.538985	−0.269492	−	0.963003i	$-0.586856\pi$
$643$	−3.63341e9	−0.538985	−0.269492	+	0.963003i	$0.586856\pi$
$644$	−8.06484e8	−0.118986
$645$	0	0
$646$	1.32245e9	0.193004
$647$	−7.40964e9	−1.07555	−0.537777	−	0.843087i	$-0.680736\pi$
$647$	−7.40964e9	−1.07555	−0.537777	+	0.843087i	$0.680736\pi$
$648$	4.45809e9	0.643630
$649$	−1.94353e9	−0.279084
$650$	0	0
$651$	3.86364e8	0.0548863
$652$	2.93690e10	4.14975
$653$	−1.05796e10	−1.48687	−0.743434	−	0.668809i	$-0.766804\pi$
$653$	−1.05796e10	−1.48687	−0.743434	+	0.668809i	$0.766804\pi$
$654$	5.32055e8	0.0743763
$655$	0	0
$656$	−6.29058e8	−0.0870017
$657$	1.68897e9	0.232350
$658$	7.69133e8	0.105247
$659$	−1.32221e10	−1.79971	−0.899855	−	0.436190i	$-0.856328\pi$
$659$	−1.32221e10	−1.79971	−0.899855	+	0.436190i	$0.856328\pi$
$660$	0	0
$661$	−1.00271e10	−1.35043	−0.675215	−	0.737621i	$-0.735949\pi$
$661$	−1.00271e10	−1.35043	−0.675215	+	0.737621i	$0.735949\pi$
$662$	−1.12310e10	−1.50458
$663$	7.27365e9	0.969293
$664$	2.05308e9	0.272155
$665$	0	0
$666$	−9.84143e8	−0.129092
$667$	8.74407e9	1.14097
$668$	−3.98465e9	−0.517217
$669$	5.67542e9	0.732836
$670$	0	0
$671$	8.69563e8	0.111115
$672$	−2.27982e8	−0.0289807
$673$	−1.32089e9	−0.167037	−0.0835186	−	0.996506i	$-0.526616\pi$
$673$	−1.32089e9	−0.167037	−0.0835186	+	0.996506i	$0.526616\pi$
$674$	1.23447e10	1.55300
$675$	0	0
$676$	4.92811e10	6.13573
$677$	4.98616e9	0.617598	0.308799	−	0.951127i	$-0.400073\pi$
$677$	4.98616e9	0.617598	0.308799	+	0.951127i	$0.400073\pi$
$678$	2.01972e8	0.0248879
$679$	−7.77500e8	−0.0953139
$680$	0	0
$681$	4.14199e9	0.502567
$682$	−7.67637e9	−0.926639
$683$	−1.20350e10	−1.44535	−0.722674	−	0.691189i	$-0.757087\pi$
$683$	−1.20350e10	−1.44535	−0.722674	+	0.691189i	$0.757087\pi$
$684$	−1.50878e9	−0.180273
$685$	0	0
$686$	−1.91388e9	−0.226350
$687$	−7.67329e9	−0.902886
$688$	−6.52864e9	−0.764299
$689$	−1.99379e10	−2.32227
$690$	0	0
$691$	5.99590e9	0.691324	0.345662	−	0.938359i	$-0.387654\pi$
$691$	5.99590e9	0.691324	0.345662	+	0.938359i	$0.387654\pi$
$692$	2.99837e10	3.43965
$693$	−1.23736e8	−0.0141231
$694$	1.12849e10	1.28156
$695$	0	0
$696$	1.34101e10	1.50765
$697$	−4.42806e8	−0.0495334
$698$	−2.15517e10	−2.39877
$699$	−4.30086e9	−0.476305
$700$	0	0
$701$	6.71224e9	0.735961	0.367980	−	0.929834i	$-0.380049\pi$
$701$	6.71224e9	0.735961	0.367980	+	0.929834i	$0.380049\pi$
$702$	−2.82371e10	−3.08063
$703$	9.74179e7	0.0105754
$704$	−2.96588e8	−0.0320368
$705$	0	0
$706$	−1.59935e10	−1.71051
$707$	−8.45306e8	−0.0899592
$708$	9.88485e9	1.04678
$709$	−2.95266e9	−0.311137	−0.155569	−	0.987825i	$-0.549721\pi$
$709$	−2.95266e9	−0.311137	−0.155569	+	0.987825i	$0.549721\pi$
$710$	0	0
$711$	−2.27864e9	−0.237756
$712$	1.53527e10	1.59406
$713$	1.40209e10	1.44865
$714$	−5.51606e8	−0.0567134
$715$	0	0
$716$	−4.86004e9	−0.494816
$717$	−8.21776e9	−0.832600
$718$	1.58903e10	1.60212
$719$	5.39647e9	0.541451	0.270725	−	0.962657i	$-0.412737\pi$
$719$	5.39647e9	0.541451	0.270725	+	0.962657i	$0.412737\pi$
$720$	0	0
$721$	−5.01918e8	−0.0498722
$722$	−1.79475e10	−1.77470
$723$	6.57266e9	0.646781
$724$	4.04877e10	3.96495
$725$	0	0
$726$	−8.55297e8	−0.0829543
$727$	9.97938e9	0.963237	0.481618	−	0.876381i	$-0.340049\pi$
$727$	9.97938e9	0.963237	0.481618	+	0.876381i	$0.340049\pi$
$728$	−2.80510e9	−0.269456
$729$	2.43459e9	0.232745
$730$	0	0
$731$	−4.59563e9	−0.435145
$732$	−4.42262e9	−0.416764
$733$	−1.31032e10	−1.22889	−0.614444	−	0.788960i	$-0.710620\pi$
$733$	−1.31032e10	−1.22889	−0.614444	+	0.788960i	$0.710620\pi$
$734$	−2.74257e10	−2.55989
$735$	0	0
$736$	−8.27335e9	−0.764907
$737$	3.90793e9	0.359593
$738$	7.32150e8	0.0670506
$739$	1.61664e10	1.47352	0.736762	−	0.676152i	$-0.236354\pi$
$739$	1.61664e10	1.47352	0.736762	+	0.676152i	$0.236354\pi$
$740$	0	0
$741$	1.19047e9	0.107487
$742$	1.51202e9	0.135876
$743$	8.25837e9	0.738641	0.369321	−	0.929302i	$-0.379590\pi$
$743$	8.25837e9	0.738641	0.369321	+	0.929302i	$0.379590\pi$
$744$	2.15029e10	1.91422
$745$	0	0
$746$	−8.98516e9	−0.792392
$747$	−1.04464e9	−0.0916946
$748$	7.56219e9	0.660681
$749$	−8.49148e8	−0.0738409
$750$	0	0
$751$	3.14594e9	0.271026	0.135513	−	0.990776i	$-0.456732\pi$
$751$	3.14594e9	0.271026	0.135513	+	0.990776i	$0.456732\pi$
$752$	1.87134e10	1.60468
$753$	1.68476e9	0.143799
$754$	5.52209e10	4.69141
$755$	0	0
$756$	1.47760e9	0.124374
$757$	−5.42952e9	−0.454911	−0.227455	−	0.973789i	$-0.573041\pi$
$757$	−5.42952e9	−0.454911	−0.227455	+	0.973789i	$0.573041\pi$
$758$	3.60681e10	3.00803
$759$	1.56221e9	0.129686
$760$	0	0
$761$	7.44500e9	0.612377	0.306188	−	0.951971i	$-0.400946\pi$
$761$	7.44500e9	0.612377	0.306188	+	0.951971i	$0.400946\pi$
$762$	−1.35411e10	−1.10869
$763$	−6.31430e7	−0.00514623
$764$	3.29958e9	0.267690
$765$	0	0
$766$	−4.01373e10	−3.22662
$767$	2.24183e10	1.79398
$768$	1.18579e10	0.944590
$769$	−8.46082e9	−0.670919	−0.335460	−	0.942055i	$-0.608892\pi$
$769$	−8.46082e9	−0.670919	−0.335460	+	0.942055i	$0.608892\pi$
$770$	0	0
$771$	−6.09287e9	−0.478775
$772$	3.56760e10	2.79071
$773$	−4.75174e9	−0.370020	−0.185010	−	0.982737i	$-0.559232\pi$
$773$	−4.75174e9	−0.370020	−0.185010	+	0.982737i	$0.559232\pi$
$774$	7.59857e9	0.589031
$775$	0	0
$776$	−4.32713e10	−3.32417
$777$	−4.06338e7	−0.00310752
$778$	−3.29887e10	−2.51152
$779$	−7.24737e7	−0.00549287
$780$	0	0
$781$	−7.50048e9	−0.563391
$782$	−2.00175e10	−1.49688
$783$	−1.60204e10	−1.19264
$784$	−2.32364e10	−1.72211
$785$	0	0
$786$	−7.80600e9	−0.573389
$787$	−2.48057e10	−1.81401	−0.907005	−	0.421120i	$-0.861637\pi$
$787$	−2.48057e10	−1.81401	−0.907005	+	0.421120i	$0.861637\pi$
$788$	−2.43306e10	−1.77138
$789$	2.09482e9	0.151837
$790$	0	0
$791$	−2.39696e7	−0.00172204
$792$	−6.88647e9	−0.492559
$793$	−1.00303e10	−0.714259
$794$	−1.48564e8	−0.0105327
$795$	0	0
$796$	−2.17108e10	−1.52574
$797$	1.77931e9	0.124494	0.0622469	−	0.998061i	$-0.480173\pi$
$797$	1.77931e9	0.124494	0.0622469	+	0.998061i	$0.480173\pi$
$798$	−9.02811e7	−0.00628907
$799$	1.31727e10	0.913609
$800$	0	0
$801$	−7.81168e9	−0.537070
$802$	−4.39099e10	−3.00575
$803$	−1.38551e9	−0.0944293
$804$	−1.98758e10	−1.34874
$805$	0	0
$806$	8.85455e10	5.95654
$807$	3.76436e9	0.252135
$808$	−4.70449e10	−3.13742
$809$	−3.20050e9	−0.212519	−0.106259	−	0.994338i	$-0.533887\pi$
$809$	−3.20050e9	−0.212519	−0.106259	+	0.994338i	$0.533887\pi$
$810$	0	0
$811$	−1.04039e10	−0.684896	−0.342448	−	0.939537i	$-0.611256\pi$
$811$	−1.04039e10	−0.684896	−0.342448	+	0.939537i	$0.611256\pi$
$812$	−2.88961e9	−0.189406
$813$	1.02544e10	0.669257
$814$	8.07322e8	0.0524640
$815$	0	0
$816$	−1.34208e10	−0.864698
$817$	−7.52164e8	−0.0482542
$818$	−2.82003e10	−1.80143
$819$	1.42728e9	0.0907851
$820$	0	0
$821$	−2.10942e10	−1.33034	−0.665168	−	0.746694i	$-0.731640\pi$
$821$	−2.10942e10	−1.33034	−0.665168	+	0.746694i	$0.731640\pi$
$822$	9.10781e9	0.571956
$823$	−6.82999e9	−0.427091	−0.213546	−	0.976933i	$-0.568501\pi$
$823$	−6.82999e9	−0.427091	−0.213546	+	0.976933i	$0.568501\pi$
$824$	−2.79339e10	−1.73935
$825$	0	0
$826$	−1.70012e9	−0.104966
$827$	4.91661e8	0.0302271	0.0151135	−	0.999886i	$-0.495189\pi$
$827$	4.91661e8	0.0302271	0.0151135	+	0.999886i	$0.495189\pi$
$828$	2.28379e10	1.39814
$829$	−7.00436e9	−0.427000	−0.213500	−	0.976943i	$-0.568486\pi$
$829$	−7.00436e9	−0.427000	−0.213500	+	0.976943i	$0.568486\pi$
$830$	0	0
$831$	−2.62424e9	−0.158636
$832$	3.42108e9	0.205936
$833$	−1.63565e10	−0.980466
$834$	1.74439e10	1.04127
$835$	0	0
$836$	1.23770e9	0.0732644
$837$	−2.56884e10	−1.51425
$838$	−1.66954e10	−0.980038
$839$	−1.25484e10	−0.733534	−0.366767	−	0.930313i	$-0.619535\pi$
$839$	−1.25484e10	−0.733534	−0.366767	+	0.930313i	$0.619535\pi$
$840$	0	0
$841$	1.40799e10	0.816234
$842$	−2.80269e10	−1.61802
$843$	−1.42593e10	−0.819786
$844$	6.77476e9	0.387878
$845$	0	0
$846$	−2.17802e10	−1.23670
$847$	1.01505e8	0.00573976
$848$	3.67881e10	2.07168
$849$	−4.59503e9	−0.257698
$850$	0	0
$851$	−1.47458e9	−0.0820190
$852$	3.81476e10	2.11314
$853$	7.63040e9	0.420945	0.210473	−	0.977600i	$-0.432500\pi$
$853$	7.63040e9	0.420945	0.210473	+	0.977600i	$0.432500\pi$
$854$	7.60657e8	0.0417913
$855$	0	0
$856$	−4.72588e10	−2.57528
$857$	4.02621e9	0.218506	0.109253	−	0.994014i	$-0.465154\pi$
$857$	4.02621e9	0.218506	0.109253	+	0.994014i	$0.465154\pi$
$858$	9.86570e9	0.533240
$859$	−8.90118e9	−0.479150	−0.239575	−	0.970878i	$-0.577008\pi$
$859$	−8.90118e9	−0.479150	−0.239575	+	0.970878i	$0.577008\pi$
$860$	0	0
$861$	3.02294e7	0.00161406
$862$	6.31965e10	3.36061
$863$	1.83195e10	0.970234	0.485117	−	0.874449i	$-0.338777\pi$
$863$	1.83195e10	0.970234	0.485117	+	0.874449i	$0.338777\pi$
$864$	1.51580e10	0.799546
$865$	0	0
$866$	3.82022e10	1.99883
$867$	3.01994e8	0.0157373
$868$	−4.63343e9	−0.240483
$869$	1.86923e9	0.0966261
$870$	0	0
$871$	−4.50773e10	−2.31150
$872$	−3.51418e9	−0.179480
$873$	2.20171e10	1.11998
$874$	−3.27625e9	−0.165992
$875$	0	0
$876$	7.04676e9	0.354181
$877$	−1.13275e10	−0.567068	−0.283534	−	0.958962i	$-0.591507\pi$
$877$	−1.13275e10	−0.567068	−0.283534	+	0.958962i	$0.591507\pi$
$878$	7.22482e9	0.360244
$879$	−3.28957e8	−0.0163372
$880$	0	0
$881$	9.78821e9	0.482267	0.241134	−	0.970492i	$-0.422481\pi$
$881$	9.78821e9	0.482267	0.241134	+	0.970492i	$0.422481\pi$
$882$	2.70444e10	1.32720
$883$	2.76210e10	1.35013	0.675067	−	0.737757i	$-0.264115\pi$
$883$	2.76210e10	1.35013	0.675067	+	0.737757i	$0.264115\pi$
$884$	−8.72285e10	−4.24693
$885$	0	0
$886$	−2.23768e10	−1.08088
$887$	1.15423e10	0.555343	0.277671	−	0.960676i	$-0.410437\pi$
$887$	1.15423e10	0.555343	0.277671	+	0.960676i	$0.410437\pi$
$888$	−2.26145e9	−0.108378
$889$	1.60703e9	0.0767127
$890$	0	0
$891$	1.86079e9	0.0881304
$892$	−6.80619e10	−3.21090
$893$	2.15596e9	0.101312
$894$	1.73963e9	0.0814283
$895$	0	0
$896$	−1.48769e9	−0.0690931
$897$	−1.80198e10	−0.833634
$898$	3.21450e10	1.48131
$899$	5.02367e10	2.30601
$900$	0	0
$901$	2.58958e10	1.17949
$902$	−6.00604e8	−0.0272499
$903$	3.13734e8	0.0141793
$904$	−1.33401e9	−0.0600579
$905$	0	0
$906$	−1.49385e10	−0.667359
$907$	1.95036e10	0.867939	0.433970	−	0.900928i	$-0.357113\pi$
$907$	1.95036e10	0.867939	0.433970	+	0.900928i	$0.357113\pi$
$908$	−4.96723e10	−2.20198
$909$	2.39372e10	1.05706
$910$	0	0
$911$	−1.90061e9	−0.0832874	−0.0416437	−	0.999133i	$-0.513259\pi$
$911$	−1.90061e9	−0.0832874	−0.0416437	+	0.999133i	$0.513259\pi$
$912$	−2.19658e9	−0.0958883
$913$	8.56948e8	0.0372655
$914$	−4.12773e10	−1.78813
$915$	0	0
$916$	9.20211e10	3.95597
$917$	9.26397e8	0.0396739
$918$	3.66749e10	1.56466
$919$	2.07615e10	0.882379	0.441189	−	0.897414i	$-0.354557\pi$
$919$	2.07615e10	0.882379	0.441189	+	0.897414i	$0.354557\pi$
$920$	0	0
$921$	2.87086e9	0.121089
$922$	−6.93188e10	−2.91268
$923$	8.65166e10	3.62154
$924$	−5.16255e8	−0.0215284
$925$	0	0
$926$	1.76916e10	0.732200
$927$	1.42132e10	0.586021
$928$	−2.96432e10	−1.21761
$929$	1.59072e9	0.0650939	0.0325469	−	0.999470i	$-0.489638\pi$
$929$	1.59072e9	0.0650939	0.0325469	+	0.999470i	$0.489638\pi$
$930$	0	0
$931$	−2.67706e9	−0.108726
$932$	5.15776e10	2.08692
$933$	−9.68068e8	−0.0390230
$934$	6.16566e10	2.47608
$935$	0	0
$936$	7.94341e10	3.16622
$937$	−1.79557e10	−0.713039	−0.356519	−	0.934288i	$-0.616037\pi$
$937$	−1.79557e10	−0.713039	−0.356519	+	0.934288i	$0.616037\pi$
$938$	3.41849e9	0.135246
$939$	−1.89573e10	−0.747218
$940$	0	0
$941$	−3.41831e10	−1.33736	−0.668680	−	0.743550i	$-0.733140\pi$
$941$	−3.41831e10	−1.33736	−0.668680	+	0.743550i	$0.733140\pi$
$942$	−3.49138e10	−1.36088
$943$	1.09701e9	0.0426009
$944$	−4.13647e10	−1.60040
$945$	0	0
$946$	−6.23334e9	−0.239388
$947$	3.28823e10	1.25817	0.629083	−	0.777338i	$-0.283431\pi$
$947$	3.28823e10	1.25817	0.629083	+	0.777338i	$0.283431\pi$
$948$	−9.50696e9	−0.362420
$949$	1.59817e10	0.607002
$950$	0	0
$951$	2.01278e10	0.758864
$952$	3.64332e9	0.136857
$953$	4.90002e9	0.183389	0.0916943	−	0.995787i	$-0.470772\pi$
$953$	4.90002e9	0.183389	0.0916943	+	0.995787i	$0.470772\pi$
$954$	−4.28170e10	−1.59660
$955$	0	0
$956$	9.85507e10	3.64802
$957$	5.59735e9	0.206438
$958$	5.22956e9	0.192170
$959$	−1.08089e9	−0.0395747
$960$	0	0
$961$	5.30408e10	1.92787
$962$	−9.31231e9	−0.337244
$963$	2.40460e10	0.867663
$964$	−7.88219e10	−2.83385
$965$	0	0
$966$	1.36655e9	0.0487760
$967$	4.47636e9	0.159196	0.0795981	−	0.996827i	$-0.474636\pi$
$967$	4.47636e9	0.159196	0.0795981	+	0.996827i	$0.474636\pi$
$968$	5.64918e9	0.200180
$969$	−1.54621e9	−0.0545929
$970$	0	0
$971$	−1.90189e9	−0.0666679	−0.0333340	−	0.999444i	$-0.510612\pi$
$971$	−1.90189e9	−0.0666679	−0.0333340	+	0.999444i	$0.510612\pi$
$972$	−6.58635e10	−2.30045
$973$	−2.07020e9	−0.0720474
$974$	4.48154e10	1.55407
$975$	0	0
$976$	1.85071e10	0.637184
$977$	1.69401e10	0.581146	0.290573	−	0.956853i	$-0.406154\pi$
$977$	1.69401e10	0.581146	0.290573	+	0.956853i	$0.406154\pi$
$978$	−4.97644e10	−1.70111
$979$	6.40816e9	0.218270
$980$	0	0
$981$	1.78807e9	0.0604705
$982$	5.17785e10	1.74485
$983$	−4.84911e10	−1.62827	−0.814133	−	0.580679i	$-0.802787\pi$
$983$	−4.84911e10	−1.62827	−0.814133	+	0.580679i	$0.802787\pi$
$984$	1.68240e9	0.0562919
$985$	0	0
$986$	−7.17221e10	−2.38278
$987$	−8.99272e8	−0.0297701
$988$	−1.42766e10	−0.470952
$989$	1.13852e10	0.374244
$990$	0	0
$991$	6.50917e9	0.212455	0.106228	−	0.994342i	$-0.466123\pi$
$991$	6.50917e9	0.212455	0.106228	+	0.994342i	$0.466123\pi$
$992$	−4.75322e10	−1.54596
$993$	1.31313e10	0.425585
$994$	−6.56110e9	−0.211897
$995$	0	0
$996$	−4.35846e9	−0.139774
$997$	−4.00286e10	−1.27920	−0.639598	−	0.768709i	$-0.720899\pi$
$997$	−4.00286e10	−1.27920	−0.639598	+	0.768709i	$0.720899\pi$
$998$	5.22633e10	1.66433
$999$	2.70164e9	0.0857332

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.8.a.c.1.4		4
5.4	even	2		55.8.a.a.1.1	✓	4
15.14	odd	2		495.8.a.c.1.4		4
55.54	odd	2		605.8.a.e.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.8.a.a.1.1	✓	4	5.4	even	2
275.8.a.c.1.4		4	1.1	even	1	trivial
495.8.a.c.1.4		4	15.14	odd	2
605.8.a.e.1.4		4	55.54	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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	275.a (trivial)

\(f(q)\)	\(=\)	\(q+20.3206 q^{2} -23.7588 q^{3} +284.925 q^{4} -482.793 q^{6} +57.2967 q^{7} +3188.81 q^{8} -1622.52 q^{9} +1331.00 q^{11} -6769.50 q^{12} -15352.8 q^{13} +1164.30 q^{14} +28328.0 q^{16} +19940.6 q^{17} -32970.5 q^{18} +3263.67 q^{19} -1361.30 q^{21} +27046.7 q^{22} -49400.9 q^{23} -75762.5 q^{24} -311978. q^{26} +90509.7 q^{27} +16325.3 q^{28} -177002. q^{29} -283819. q^{31} +167474. q^{32} -31623.0 q^{33} +405204. q^{34} -462296. q^{36} +29849.2 q^{37} +66319.6 q^{38} +364766. q^{39} -22206.2 q^{41} -27662.5 q^{42} -230466. q^{43} +379236. q^{44} -1.00385e6 q^{46} +660596. q^{47} -673041. q^{48} -820260. q^{49} -473766. q^{51} -4.37441e6 q^{52} +1.29865e6 q^{53} +1.83921e6 q^{54} +182709. q^{56} -77540.9 q^{57} -3.59679e6 q^{58} -1.46020e6 q^{59} +653316. q^{61} -5.76737e6 q^{62} -92965.0 q^{63} -222831. q^{64} -642598. q^{66} +2.93609e6 q^{67} +5.68159e6 q^{68} +1.17371e6 q^{69} -5.63522e6 q^{71} -5.17390e6 q^{72} -1.04096e6 q^{73} +606553. q^{74} +929902. q^{76} +76261.9 q^{77} +7.41225e6 q^{78} +1.40438e6 q^{79} +1.39804e6 q^{81} -451243. q^{82} +643837. q^{83} -387870. q^{84} -4.68320e6 q^{86} +4.20537e6 q^{87} +4.24431e6 q^{88} +4.81454e6 q^{89} -879668. q^{91} -1.40756e7 q^{92} +6.74322e6 q^{93} +1.34237e7 q^{94} -3.97898e6 q^{96} -1.35697e7 q^{97} -1.66681e7 q^{98} -2.15957e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 21 q^{2} + 189 q^{4} + 411 q^{6} - 1262 q^{7} + 2367 q^{8} - 2706 q^{9} + 5324 q^{11} - 4353 q^{12} - 2696 q^{13} - 16259 q^{14} + 7633 q^{16} + 24824 q^{17} + 13470 q^{18} - 22730 q^{19} + 5544 q^{21}+ \cdots - 3601686 q^{99}+O(q^{100}) \) 4 * q + 21 * q^2 + 189 * q^4 + 411 * q^6 - 1262 * q^7 + 2367 * q^8 - 2706 * q^9 + 5324 * q^11 - 4353 * q^12 - 2696 * q^13 - 16259 * q^14 + 7633 * q^16 + 24824 * q^17 + 13470 * q^18 - 22730 * q^19 + 5544 * q^21 + 27951 * q^22 + 160 * q^23 - 179787 * q^24 - 343346 * q^26 + 264060 * q^27 + 249037 * q^28 - 433924 * q^29 - 517576 * q^31 + 376727 * q^32 + 371131 * q^34 - 353298 * q^36 - 523762 * q^37 + 126695 * q^38 - 144696 * q^39 - 277004 * q^41 - 54717 * q^42 + 251596 * q^43 + 251559 * q^44 - 399654 * q^46 + 711180 * q^47 - 1790325 * q^48 + 241462 * q^49 - 2200542 * q^51 - 5757946 * q^52 + 940654 * q^53 + 1284201 * q^54 + 2594823 * q^56 - 551700 * q^57 - 5209629 * q^58 + 1014028 * q^59 + 3634268 * q^61 - 5520995 * q^62 + 87120 * q^63 + 1670385 * q^64 + 547041 * q^66 + 163644 * q^67 + 2116383 * q^68 + 602232 * q^69 - 5547896 * q^71 - 10064430 * q^72 + 3614404 * q^73 - 3922253 * q^74 + 599375 * q^76 - 1679722 * q^77 + 5685402 * q^78 - 8995368 * q^79 + 561564 * q^81 - 3995374 * q^82 + 5010356 * q^83 - 6175065 * q^84 - 9767128 * q^86 - 5173554 * q^87 + 3150477 * q^88 - 8759946 * q^89 - 18295460 * q^91 - 23023838 * q^92 + 17520930 * q^93 + 4317674 * q^94 - 7304979 * q^96 - 11731552 * q^97 - 16303462 * q^98 - 3601686 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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