LMFDB - Embedded newform 2031.4.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2031,4,Mod(1,2031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2031, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2031.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2031 = 3 \cdot 677 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2031.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:	$119.832879222$
Analytic rank:	$0$
Dimension:	$94$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	2031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.02302 q^{2} +3.00000 q^{3} +17.2308 q^{4} -13.6796 q^{5} -15.0691 q^{6} -35.1340 q^{7} -46.3664 q^{8} +9.00000 q^{9} +68.7130 q^{10} +39.5183 q^{11} +51.6923 q^{12} +28.5863 q^{13} +176.479 q^{14} -41.0388 q^{15} +95.0532 q^{16} -121.549 q^{17} -45.2072 q^{18} +21.0701 q^{19} -235.710 q^{20} -105.402 q^{21} -198.501 q^{22} +179.013 q^{23} -139.099 q^{24} +62.1318 q^{25} -143.590 q^{26} +27.0000 q^{27} -605.386 q^{28} +128.363 q^{29} +206.139 q^{30} +146.982 q^{31} -106.523 q^{32} +118.555 q^{33} +610.542 q^{34} +480.620 q^{35} +155.077 q^{36} -227.825 q^{37} -105.836 q^{38} +85.7590 q^{39} +634.274 q^{40} -217.840 q^{41} +529.437 q^{42} -387.632 q^{43} +680.930 q^{44} -123.117 q^{45} -899.188 q^{46} -305.512 q^{47} +285.159 q^{48} +891.400 q^{49} -312.090 q^{50} -364.646 q^{51} +492.564 q^{52} -413.534 q^{53} -135.622 q^{54} -540.595 q^{55} +1629.04 q^{56} +63.2103 q^{57} -644.770 q^{58} +841.542 q^{59} -707.131 q^{60} -621.544 q^{61} -738.296 q^{62} -316.206 q^{63} -225.356 q^{64} -391.050 q^{65} -595.504 q^{66} -678.618 q^{67} -2094.38 q^{68} +537.040 q^{69} -2414.16 q^{70} +214.078 q^{71} -417.297 q^{72} -957.035 q^{73} +1144.37 q^{74} +186.395 q^{75} +363.054 q^{76} -1388.44 q^{77} -430.769 q^{78} -929.253 q^{79} -1300.29 q^{80} +81.0000 q^{81} +1094.21 q^{82} -512.188 q^{83} -1816.16 q^{84} +1662.74 q^{85} +1947.08 q^{86} +385.089 q^{87} -1832.32 q^{88} +1022.01 q^{89} +618.417 q^{90} -1004.35 q^{91} +3084.54 q^{92} +440.947 q^{93} +1534.59 q^{94} -288.231 q^{95} -319.570 q^{96} -843.203 q^{97} -4477.52 q^{98} +355.664 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 94 q + 19 q^{2} + 282 q^{3} + 409 q^{4} + 84 q^{5} + 57 q^{6} + 39 q^{7} + 228 q^{8} + 846 q^{9} + 145 q^{10} + 357 q^{11} + 1227 q^{12} + 271 q^{13} + 366 q^{14} + 252 q^{15} + 1865 q^{16} + 690 q^{17}+ \cdots + 3213 q^{99}+O(q^{100}) $ 94 * q + 19 * q^2 + 282 * q^3 + 409 * q^4 + 84 * q^5 + 57 * q^6 + 39 * q^7 + 228 * q^8 + 846 * q^9 + 145 * q^10 + 357 * q^11 + 1227 * q^12 + 271 * q^13 + 366 * q^14 + 252 * q^15 + 1865 * q^16 + 690 * q^17 + 171 * q^18 + 345 * q^19 + 939 * q^20 + 117 * q^21 + 148 * q^22 + 1135 * q^23 + 684 * q^24 + 3280 * q^25 + 1261 * q^26 + 2538 * q^27 + 214 * q^28 + 1396 * q^29 + 435 * q^30 + 889 * q^31 + 2048 * q^32 + 1071 * q^33 + 1590 * q^34 + 2104 * q^35 + 3681 * q^36 + 711 * q^37 + 2075 * q^38 + 813 * q^39 + 1675 * q^40 + 2931 * q^41 + 1098 * q^42 + 585 * q^43 + 4058 * q^44 + 756 * q^45 + 1148 * q^46 + 2733 * q^47 + 5595 * q^48 + 8415 * q^49 + 2640 * q^50 + 2070 * q^51 + 2174 * q^52 + 3430 * q^53 + 513 * q^54 + 2458 * q^55 + 4034 * q^56 + 1035 * q^57 + 259 * q^58 + 5376 * q^59 + 2817 * q^60 + 2064 * q^61 + 3610 * q^62 + 351 * q^63 + 10194 * q^64 + 5442 * q^65 + 444 * q^66 + 1429 * q^67 + 6932 * q^68 + 3405 * q^69 + 3888 * q^70 + 5336 * q^71 + 2052 * q^72 + 2412 * q^73 + 5911 * q^74 + 9840 * q^75 + 5988 * q^76 + 7100 * q^77 + 3783 * q^78 + 2018 * q^79 + 8054 * q^80 + 7614 * q^81 + 3546 * q^82 + 6229 * q^83 + 642 * q^84 + 2728 * q^85 + 6619 * q^86 + 4188 * q^87 + 3679 * q^88 + 11972 * q^89 + 1305 * q^90 + 5586 * q^91 + 15073 * q^92 + 2667 * q^93 + 3650 * q^94 + 8168 * q^95 + 6144 * q^96 + 5859 * q^97 + 8121 * q^98 + 3213 * 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 $

$2$	−5.02302	−1.77591	−0.887954	−	0.459933i	$-0.847873\pi$
$2$	−5.02302	−1.77591	−0.887954	+	0.459933i	$0.847873\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	17.2308	2.15385
$5$	−13.6796	−1.22354	−0.611771	−	0.791035i	$-0.709543\pi$
$5$	−13.6796	−1.22354	−0.611771	+	0.791035i	$0.709543\pi$
$6$	−15.0691	−1.02532
$7$	−35.1340	−1.89706	−0.948529	−	0.316689i	$-0.897429\pi$
$7$	−35.1340	−1.89706	−0.948529	+	0.316689i	$0.897429\pi$
$8$	−46.3664	−2.04912
$9$	9.00000	0.333333
$10$	68.7130	2.17290
$11$	39.5183	1.08320	0.541600	−	0.840636i	$-0.317819\pi$
$11$	39.5183	1.08320	0.541600	+	0.840636i	$0.317819\pi$
$12$	51.6923	1.24352
$13$	28.5863	0.609878	0.304939	−	0.952372i	$-0.401364\pi$
$13$	28.5863	0.609878	0.304939	+	0.952372i	$0.401364\pi$
$14$	176.479	3.36900
$15$	−41.0388	−0.706412
$16$	95.0532	1.48521
$17$	−121.549	−1.73411	−0.867056	−	0.498210i	$-0.833991\pi$
$17$	−121.549	−1.73411	−0.867056	+	0.498210i	$0.833991\pi$
$18$	−45.2072	−0.591969
$19$	21.0701	0.254411	0.127206	−	0.991876i	$-0.459399\pi$
$19$	21.0701	0.254411	0.127206	+	0.991876i	$0.459399\pi$
$20$	−235.710	−2.63532
$21$	−105.402	−1.09527
$22$	−198.501	−1.92366
$23$	179.013	1.62291	0.811453	−	0.584417i	$-0.198677\pi$
$23$	179.013	1.62291	0.811453	+	0.584417i	$0.198677\pi$
$24$	−139.099	−1.18306
$25$	62.1318	0.497055
$26$	−143.590	−1.08309
$27$	27.0000	0.192450
$28$	−605.386	−4.08597
$29$	128.363	0.821945	0.410972	−	0.911648i	$-0.365189\pi$
$29$	128.363	0.821945	0.410972	+	0.911648i	$0.365189\pi$
$30$	206.139	1.25452
$31$	146.982	0.851575	0.425787	−	0.904823i	$-0.359997\pi$
$31$	146.982	0.851575	0.425787	+	0.904823i	$0.359997\pi$
$32$	−106.523	−0.588464
$33$	118.555	0.625386
$34$	610.542	3.07962
$35$	480.620	2.32113
$36$	155.077	0.717949
$37$	−227.825	−1.01228	−0.506139	−	0.862452i	$-0.668928\pi$
$37$	−227.825	−1.01228	−0.506139	+	0.862452i	$0.668928\pi$
$38$	−105.836	−0.451810
$39$	85.7590	0.352113
$40$	634.274	2.50719
$41$	−217.840	−0.829777	−0.414888	−	0.909872i	$-0.636179\pi$
$41$	−217.840	−0.829777	−0.414888	+	0.909872i	$0.636179\pi$
$42$	529.437	1.94509
$43$	−387.632	−1.37473	−0.687364	−	0.726313i	$-0.741232\pi$
$43$	−387.632	−1.37473	−0.687364	+	0.726313i	$0.741232\pi$
$44$	680.930	2.33305
$45$	−123.117	−0.407847
$46$	−899.188	−2.88213
$47$	−305.512	−0.948160	−0.474080	−	0.880482i	$-0.657219\pi$
$47$	−305.512	−0.948160	−0.474080	+	0.880482i	$0.657219\pi$
$48$	285.159	0.857484
$49$	891.400	2.59883
$50$	−312.090	−0.882723
$51$	−364.646	−1.00119
$52$	492.564	1.31358
$53$	−413.534	−1.07176	−0.535880	−	0.844294i	$-0.680020\pi$
$53$	−413.534	−1.07176	−0.535880	+	0.844294i	$0.680020\pi$
$54$	−135.622	−0.341773
$55$	−540.595	−1.32534
$56$	1629.04	3.88731
$57$	63.2103	0.146884
$58$	−644.770	−1.45970
$59$	841.542	1.85694	0.928470	−	0.371408i	$-0.121125\pi$
$59$	841.542	1.85694	0.928470	+	0.371408i	$0.121125\pi$
$60$	−707.131	−1.52150
$61$	−621.544	−1.30460	−0.652300	−	0.757961i	$-0.726196\pi$
$61$	−621.544	−1.30460	−0.652300	+	0.757961i	$0.726196\pi$
$62$	−738.296	−1.51232
$63$	−316.206	−0.632353
$64$	−225.356	−0.440148
$65$	−391.050	−0.746212
$66$	−595.504	−1.11063
$67$	−678.618	−1.23741	−0.618704	−	0.785624i	$-0.712342\pi$
$67$	−678.618	−1.23741	−0.618704	+	0.785624i	$0.712342\pi$
$68$	−2094.38	−3.73501
$69$	537.040	0.936985
$70$	−2414.16	−4.12211
$71$	214.078	0.357836	0.178918	−	0.983864i	$-0.442740\pi$
$71$	214.078	0.357836	0.178918	+	0.983864i	$0.442740\pi$
$72$	−417.297	−0.683041
$73$	−957.035	−1.53442	−0.767209	−	0.641397i	$-0.778355\pi$
$73$	−957.035	−1.53442	−0.767209	+	0.641397i	$0.778355\pi$
$74$	1144.37	1.79771
$75$	186.395	0.286975
$76$	363.054	0.547962
$77$	−1388.44	−2.05490
$78$	−430.769	−0.625321
$79$	−929.253	−1.32341	−0.661703	−	0.749766i	$-0.730166\pi$
$79$	−929.253	−1.32341	−0.661703	+	0.749766i	$0.730166\pi$
$80$	−1300.29	−1.81721
$81$	81.0000	0.111111
$82$	1094.21	1.47361
$83$	−512.188	−0.677348	−0.338674	−	0.940904i	$-0.609978\pi$
$83$	−512.188	−0.677348	−0.338674	+	0.940904i	$0.609978\pi$
$84$	−1816.16	−2.35904
$85$	1662.74	2.12176
$86$	1947.08	2.44139
$87$	385.089	0.474550
$88$	−1832.32	−2.21961
$89$	1022.01	1.21722	0.608609	−	0.793470i	$-0.291728\pi$
$89$	1022.01	1.21722	0.608609	+	0.793470i	$0.291728\pi$
$90$	618.417	0.724299
$91$	−1004.35	−1.15698
$92$	3084.54	3.49549
$93$	440.947	0.491657
$94$	1534.59	1.68384
$95$	−288.231	−0.311283
$96$	−319.570	−0.339750
$97$	−843.203	−0.882622	−0.441311	−	0.897354i	$-0.645486\pi$
$97$	−843.203	−0.882622	−0.441311	+	0.897354i	$0.645486\pi$
$98$	−4477.52	−4.61529
$99$	355.664	0.361067
$100$	1070.58	1.07058
$101$	−1860.27	−1.83271	−0.916356	−	0.400363i	$-0.868884\pi$
$101$	−1860.27	−1.83271	−0.916356	+	0.400363i	$0.868884\pi$
$102$	1831.63	1.77802
$103$	856.183	0.819050	0.409525	−	0.912299i	$-0.365694\pi$
$103$	856.183	0.819050	0.409525	+	0.912299i	$0.365694\pi$
$104$	−1325.44	−1.24972
$105$	1441.86	1.34011
$106$	2077.19	1.90335
$107$	−717.404	−0.648169	−0.324084	−	0.946028i	$-0.605056\pi$
$107$	−717.404	−0.648169	−0.324084	+	0.946028i	$0.605056\pi$
$108$	465.231	0.414508
$109$	573.161	0.503659	0.251830	−	0.967772i	$-0.418968\pi$
$109$	573.161	0.503659	0.251830	+	0.967772i	$0.418968\pi$
$110$	2715.42	2.35368
$111$	−683.476	−0.584439
$112$	−3339.60	−2.81752
$113$	−147.383	−0.122696	−0.0613478	−	0.998116i	$-0.519540\pi$
$113$	−147.383	−0.122696	−0.0613478	+	0.998116i	$0.519540\pi$
$114$	−317.507	−0.260853
$115$	−2448.83	−1.98569
$116$	2211.79	1.77034
$117$	257.277	0.203293
$118$	−4227.09	−3.29775
$119$	4270.50	3.28971
$120$	1902.82	1.44753
$121$	230.693	0.173323
$122$	3122.03	2.31685
$123$	−653.519	−0.479072
$124$	2532.62	1.83416
$125$	860.012	0.615375
$126$	1588.31	1.12300
$127$	2010.20	1.40454	0.702268	−	0.711912i	$-0.252171\pi$
$127$	2010.20	1.40454	0.702268	+	0.711912i	$0.252171\pi$
$128$	1984.15	1.37013
$129$	−1162.90	−0.793700
$130$	1964.25	1.32520
$131$	1009.32	0.673164	0.336582	−	0.941654i	$-0.390729\pi$
$131$	1009.32	0.673164	0.336582	+	0.941654i	$0.390729\pi$
$132$	2042.79	1.34699
$133$	−740.277	−0.482633
$134$	3408.71	2.19752
$135$	−369.350	−0.235471
$136$	5635.77	3.55341
$137$	244.928	0.152742	0.0763708	−	0.997079i	$-0.475667\pi$
$137$	244.928	0.152742	0.0763708	+	0.997079i	$0.475667\pi$
$138$	−2697.56	−1.66400
$139$	2209.52	1.34826	0.674132	−	0.738611i	$-0.264518\pi$
$139$	2209.52	1.34826	0.674132	+	0.738611i	$0.264518\pi$
$140$	8281.45	4.99936
$141$	−916.537	−0.547421
$142$	−1075.32	−0.635483
$143$	1129.68	0.660621
$144$	855.478	0.495069
$145$	−1755.96	−1.00568
$146$	4807.21	2.72498
$147$	2674.20	1.50044
$148$	−3925.61	−2.18029
$149$	−2566.77	−1.41126	−0.705630	−	0.708580i	$-0.749336\pi$
$149$	−2566.77	−1.41126	−0.705630	+	0.708580i	$0.749336\pi$
$150$	−936.269	−0.509640
$151$	−1945.08	−1.04827	−0.524134	−	0.851636i	$-0.675611\pi$
$151$	−1945.08	−1.04827	−0.524134	+	0.851636i	$0.675611\pi$
$152$	−976.943	−0.521320
$153$	−1093.94	−0.578037
$154$	6974.14	3.64930
$155$	−2010.66	−1.04194
$156$	1477.69	0.758398
$157$	759.735	0.386200	0.193100	−	0.981179i	$-0.438146\pi$
$157$	759.735	0.386200	0.193100	+	0.981179i	$0.438146\pi$
$158$	4667.66	2.35025
$159$	−1240.60	−0.618781
$160$	1457.20	0.720011
$161$	−6289.46	−3.07875
$162$	−406.865	−0.197323
$163$	−420.898	−0.202253	−0.101127	−	0.994874i	$-0.532245\pi$
$163$	−420.898	−0.202253	−0.101127	+	0.994874i	$0.532245\pi$
$164$	−3753.55	−1.78721
$165$	−1621.78	−0.765186
$166$	2572.73	1.20291
$167$	3566.39	1.65255	0.826275	−	0.563268i	$-0.190456\pi$
$167$	3566.39	1.65255	0.826275	+	0.563268i	$0.190456\pi$
$168$	4887.11	2.24434
$169$	−1379.82	−0.628048
$170$	−8351.98	−3.76805
$171$	189.631	0.0848037
$172$	−6679.19	−2.96095
$173$	1557.93	0.684668	0.342334	−	0.939578i	$-0.388783\pi$
$173$	1557.93	0.684668	0.342334	+	0.939578i	$0.388783\pi$
$174$	−1934.31	−0.842757
$175$	−2182.94	−0.942942
$176$	3756.34	1.60878
$177$	2524.63	1.07210
$178$	−5133.56	−2.16167
$179$	1292.23	0.539586	0.269793	−	0.962918i	$-0.413045\pi$
$179$	1292.23	0.539586	0.269793	+	0.962918i	$0.413045\pi$
$180$	−2121.39	−0.878440
$181$	−1086.68	−0.446257	−0.223128	−	0.974789i	$-0.571627\pi$
$181$	−1086.68	−0.446257	−0.223128	+	0.974789i	$0.571627\pi$
$182$	5044.89	2.05468
$183$	−1864.63	−0.753211
$184$	−8300.19	−3.32553
$185$	3116.56	1.23856
$186$	−2214.89	−0.873137
$187$	−4803.40	−1.87839
$188$	−5264.21	−2.04219
$189$	−948.619	−0.365089
$190$	1447.79	0.552809
$191$	1060.79	0.401863	0.200931	−	0.979605i	$-0.435603\pi$
$191$	1060.79	0.401863	0.200931	+	0.979605i	$0.435603\pi$
$192$	−676.067	−0.254119
$193$	−1048.70	−0.391125	−0.195563	−	0.980691i	$-0.562653\pi$
$193$	−1048.70	−0.391125	−0.195563	+	0.980691i	$0.562653\pi$
$194$	4235.43	1.56745
$195$	−1173.15	−0.430826
$196$	15359.5	5.59748
$197$	−3991.44	−1.44354	−0.721772	−	0.692131i	$-0.756672\pi$
$197$	−3991.44	−1.44354	−0.721772	+	0.692131i	$0.756672\pi$
$198$	−1786.51	−0.641221
$199$	−468.207	−0.166786	−0.0833928	−	0.996517i	$-0.526576\pi$
$199$	−468.207	−0.166786	−0.0833928	+	0.996517i	$0.526576\pi$
$200$	−2880.83	−1.01853
$201$	−2035.85	−0.714418
$202$	9344.19	3.25473
$203$	−4509.91	−1.55928
$204$	−6283.14	−2.15641
$205$	2979.96	1.01527
$206$	−4300.63	−1.45456
$207$	1611.12	0.540969
$208$	2717.22	0.905795
$209$	832.653	0.275578
$210$	−7242.49	−2.37990
$211$	840.716	0.274300	0.137150	−	0.990550i	$-0.456206\pi$
$211$	840.716	0.274300	0.137150	+	0.990550i	$0.456206\pi$
$212$	−7125.51	−2.30840
$213$	642.233	0.206597
$214$	3603.54	1.15109
$215$	5302.65	1.68204
$216$	−1251.89	−0.394354
$217$	−5164.08	−1.61549
$218$	−2879.00	−0.894452
$219$	−2871.11	−0.885897
$220$	−9314.86	−2.85458
$221$	−3474.63	−1.05760
$222$	3433.12	1.03791
$223$	525.454	0.157789	0.0788946	−	0.996883i	$-0.474861\pi$
$223$	525.454	0.157789	0.0788946	+	0.996883i	$0.474861\pi$
$224$	3742.60	1.11635
$225$	559.186	0.165685
$226$	740.307	0.217896
$227$	−1168.28	−0.341592	−0.170796	−	0.985306i	$-0.554634\pi$
$227$	−1168.28	−0.341592	−0.170796	+	0.985306i	$0.554634\pi$
$228$	1089.16	0.316366
$229$	−3670.58	−1.05921	−0.529604	−	0.848245i	$-0.677660\pi$
$229$	−3670.58	−1.05921	−0.529604	+	0.848245i	$0.677660\pi$
$230$	12300.5	3.52641
$231$	−4165.31	−1.18639
$232$	−5951.72	−1.68427
$233$	5409.09	1.52086	0.760432	−	0.649417i	$-0.224987\pi$
$233$	5409.09	1.52086	0.760432	+	0.649417i	$0.224987\pi$
$234$	−1292.31	−0.361029
$235$	4179.29	1.16011
$236$	14500.4	3.99956
$237$	−2787.76	−0.764069
$238$	−21450.8	−5.84222
$239$	4157.55	1.12523	0.562615	−	0.826719i	$-0.309796\pi$
$239$	4157.55	1.12523	0.562615	+	0.826719i	$0.309796\pi$
$240$	−3900.87	−1.04917
$241$	−1184.55	−0.316613	−0.158306	−	0.987390i	$-0.550603\pi$
$241$	−1184.55	−0.316613	−0.158306	+	0.987390i	$0.550603\pi$
$242$	−1158.78	−0.307806
$243$	243.000	0.0641500
$244$	−10709.7	−2.80991
$245$	−12194.0	−3.17978
$246$	3282.64	0.850787
$247$	602.316	0.155160
$248$	−6815.04	−1.74498
$249$	−1536.56	−0.391067
$250$	−4319.86	−1.09285
$251$	4252.19	1.06930	0.534652	−	0.845072i	$-0.320443\pi$
$251$	4252.19	1.06930	0.534652	+	0.845072i	$0.320443\pi$
$252$	−5448.48	−1.36199
$253$	7074.29	1.75793
$254$	−10097.3	−2.49433
$255$	4988.22	1.22500
$256$	−8163.61	−1.99307
$257$	5913.74	1.43537	0.717683	−	0.696370i	$-0.245203\pi$
$257$	5913.74	1.43537	0.717683	+	0.696370i	$0.245203\pi$
$258$	5841.25	1.40954
$259$	8004.42	1.92035
$260$	−6738.09	−1.60722
$261$	1155.27	0.273982
$262$	−5069.83	−1.19548
$263$	7182.35	1.68396	0.841982	−	0.539506i	$-0.181389\pi$
$263$	7182.35	1.68396	0.841982	+	0.539506i	$0.181389\pi$
$264$	−5496.95	−1.28149
$265$	5656.98	1.31134
$266$	3718.43	0.857111
$267$	3066.02	0.702761
$268$	−11693.1	−2.66519
$269$	−5560.07	−1.26023	−0.630117	−	0.776500i	$-0.716993\pi$
$269$	−5560.07	−1.26023	−0.630117	+	0.776500i	$0.716993\pi$
$270$	1855.25	0.418174
$271$	−8386.94	−1.87996	−0.939982	−	0.341224i	$-0.889159\pi$
$271$	−8386.94	−1.87996	−0.939982	+	0.341224i	$0.889159\pi$
$272$	−11553.6	−2.57551
$273$	−3013.06	−0.667980
$274$	−1230.28	−0.271255
$275$	2455.34	0.538410
$276$	9253.61	2.01812
$277$	697.310	0.151254	0.0756269	−	0.997136i	$-0.475904\pi$
$277$	697.310	0.151254	0.0756269	+	0.997136i	$0.475904\pi$
$278$	−11098.4	−2.39439
$279$	1322.84	0.283858
$280$	−22284.6	−4.75628
$281$	−6862.24	−1.45682	−0.728411	−	0.685141i	$-0.759741\pi$
$281$	−6862.24	−1.45682	−0.728411	+	0.685141i	$0.759741\pi$
$282$	4603.78	0.972168
$283$	5711.51	1.19970	0.599848	−	0.800114i	$-0.295228\pi$
$283$	5711.51	1.19970	0.599848	+	0.800114i	$0.295228\pi$
$284$	3688.72	0.770724
$285$	−864.692	−0.179719
$286$	−5674.42	−1.17320
$287$	7653.59	1.57414
$288$	−958.711	−0.196155
$289$	9861.11	2.00715
$290$	8820.21	1.78600
$291$	−2529.61	−0.509582
$292$	−16490.4	−3.30490
$293$	3196.02	0.637248	0.318624	−	0.947881i	$-0.396779\pi$
$293$	3196.02	0.637248	0.318624	+	0.947881i	$0.396779\pi$
$294$	−13432.6	−2.66464
$295$	−11512.0	−2.27204
$296$	10563.4	2.07428
$297$	1066.99	0.208462
$298$	12892.9	2.50627
$299$	5117.33	0.989775
$300$	3211.74	0.618099
$301$	13619.1	2.60794
$302$	9770.19	1.86163
$303$	−5580.82	−1.05812
$304$	2002.78	0.377853
$305$	8502.48	1.59623
$306$	5494.88	1.02654
$307$	−670.861	−0.124717	−0.0623584	−	0.998054i	$-0.519862\pi$
$307$	−670.861	−0.124717	−0.0623584	+	0.998054i	$0.519862\pi$
$308$	−23923.8	−4.42593
$309$	2568.55	0.472879
$310$	10099.6	1.85038
$311$	5484.95	1.00007	0.500037	−	0.866004i	$-0.333320\pi$
$311$	5484.95	1.00007	0.500037	+	0.866004i	$0.333320\pi$
$312$	−3976.33	−0.721524
$313$	1932.50	0.348982	0.174491	−	0.984659i	$-0.444172\pi$
$313$	1932.50	0.348982	0.174491	+	0.984659i	$0.444172\pi$
$314$	−3816.17	−0.685856
$315$	4325.58	0.773710
$316$	−16011.7	−2.85041
$317$	−3839.23	−0.680229	−0.340115	−	0.940384i	$-0.610466\pi$
$317$	−3839.23	−0.680229	−0.340115	+	0.940384i	$0.610466\pi$
$318$	6231.57	1.09890
$319$	5072.68	0.890331
$320$	3082.78	0.538539
$321$	−2152.21	−0.374220
$322$	31592.1	5.46757
$323$	−2561.04	−0.441177
$324$	1395.69	0.239316
$325$	1776.12	0.303143
$326$	2114.18	0.359183
$327$	1719.48	0.290788
$328$	10100.4	1.70031
$329$	10733.9	1.79872
$330$	8146.26	1.35890
$331$	−2303.25	−0.382471	−0.191235	−	0.981544i	$-0.561249\pi$
$331$	−2303.25	−0.382471	−0.191235	+	0.981544i	$0.561249\pi$
$332$	−8825.39	−1.45890
$333$	−2050.43	−0.337426
$334$	−17914.1	−2.93477
$335$	9283.23	1.51402
$336$	−10018.8	−1.62670
$337$	−6869.41	−1.11039	−0.555194	−	0.831721i	$-0.687356\pi$
$337$	−6869.41	−1.11039	−0.555194	+	0.831721i	$0.687356\pi$
$338$	6930.88	1.11536
$339$	−442.148	−0.0708383
$340$	28650.3	4.56994
$341$	5808.49	0.922426
$342$	−952.520	−0.150603
$343$	−19267.5	−3.03308
$344$	17973.1	2.81699
$345$	−7346.50	−1.14644
$346$	−7825.54	−1.21591
$347$	1038.15	0.160608	0.0803040	−	0.996770i	$-0.474411\pi$
$347$	1038.15	0.160608	0.0803040	+	0.996770i	$0.474411\pi$
$348$	6635.38	1.02211
$349$	41.3402	0.00634065	0.00317033	−	0.999995i	$-0.498991\pi$
$349$	41.3402	0.00634065	0.00317033	+	0.999995i	$0.498991\pi$
$350$	10965.0	1.67458
$351$	771.831	0.117371
$352$	−4209.62	−0.637425
$353$	−1492.44	−0.225027	−0.112513	−	0.993650i	$-0.535890\pi$
$353$	−1492.44	−0.225027	−0.112513	+	0.993650i	$0.535890\pi$
$354$	−12681.3	−1.90396
$355$	−2928.50	−0.437827
$356$	17609.9	2.62170
$357$	12811.5	1.89932
$358$	−6490.91	−0.958254
$359$	−8053.14	−1.18392	−0.591962	−	0.805966i	$-0.701646\pi$
$359$	−8053.14	−1.18392	−0.591962	+	0.805966i	$0.701646\pi$
$360$	5708.46	0.835729
$361$	−6415.05	−0.935275
$362$	5458.43	0.792511
$363$	692.079	0.100068
$364$	−17305.8	−2.49195
$365$	13091.9	1.87742
$366$	9366.09	1.33763
$367$	1698.14	0.241531	0.120766	−	0.992681i	$-0.461465\pi$
$367$	1698.14	0.241531	0.120766	+	0.992681i	$0.461465\pi$
$368$	17015.8	2.41035
$369$	−1960.56	−0.276592
$370$	−15654.6	−2.19957
$371$	14529.1	2.03319
$372$	7597.86	1.05895
$373$	374.355	0.0519662	0.0259831	−	0.999662i	$-0.491728\pi$
$373$	374.355	0.0519662	0.0259831	+	0.999662i	$0.491728\pi$
$374$	24127.6	3.33585
$375$	2580.04	0.355287
$376$	14165.5	1.94290
$377$	3669.43	0.501286
$378$	4764.93	0.648364
$379$	11871.4	1.60896	0.804478	−	0.593982i	$-0.202445\pi$
$379$	11871.4	1.60896	0.804478	+	0.593982i	$0.202445\pi$
$380$	−4966.44	−0.670455
$381$	6030.59	0.810910
$382$	−5328.35	−0.713671
$383$	−10227.5	−1.36449	−0.682246	−	0.731123i	$-0.738997\pi$
$383$	−10227.5	−1.36449	−0.682246	+	0.731123i	$0.738997\pi$
$384$	5952.46	0.791042
$385$	18993.3	2.51425
$386$	5267.65	0.694602
$387$	−3488.69	−0.458243
$388$	−14529.0	−1.90103
$389$	265.791	0.0346431	0.0173215	−	0.999850i	$-0.494486\pi$
$389$	265.791	0.0346431	0.0173215	+	0.999850i	$0.494486\pi$
$390$	5892.76	0.765106
$391$	−21758.8	−2.81430
$392$	−41330.9	−5.32533
$393$	3027.95	0.388652
$394$	20049.1	2.56360
$395$	12711.8	1.61924
$396$	6128.37	0.777682
$397$	−8625.59	−1.09044	−0.545222	−	0.838292i	$-0.683554\pi$
$397$	−8625.59	−1.09044	−0.545222	+	0.838292i	$0.683554\pi$
$398$	2351.82	0.296196
$399$	−2220.83	−0.278648
$400$	5905.83	0.738228
$401$	5980.54	0.744772	0.372386	−	0.928078i	$-0.378540\pi$
$401$	5980.54	0.744772	0.372386	+	0.928078i	$0.378540\pi$
$402$	10226.1	1.26874
$403$	4201.69	0.519357
$404$	−32053.9	−3.94738
$405$	−1108.05	−0.135949
$406$	22653.4	2.76913
$407$	−9003.26	−1.09650
$408$	16907.3	2.05156
$409$	−2777.63	−0.335807	−0.167904	−	0.985803i	$-0.553700\pi$
$409$	−2777.63	−0.335807	−0.167904	+	0.985803i	$0.553700\pi$
$410$	−14968.4	−1.80302
$411$	734.783	0.0881854
$412$	14752.7	1.76411
$413$	−29566.8	−3.52272
$414$	−8092.69	−0.960710
$415$	7006.53	0.828764
$416$	−3045.11	−0.358892
$417$	6628.55	0.778420
$418$	−4182.44	−0.489401
$419$	1036.64	0.120867	0.0604335	−	0.998172i	$-0.480752\pi$
$419$	1036.64	0.120867	0.0604335	+	0.998172i	$0.480752\pi$
$420$	24844.3	2.88638
$421$	−2048.46	−0.237140	−0.118570	−	0.992946i	$-0.537831\pi$
$421$	−2048.46	−0.237140	−0.118570	+	0.992946i	$0.537831\pi$
$422$	−4222.93	−0.487131
$423$	−2749.61	−0.316053
$424$	19174.1	2.19617
$425$	−7552.05	−0.861948
$426$	−3225.95	−0.366897
$427$	21837.3	2.47490
$428$	−12361.4	−1.39606
$429$	3389.05	0.381409
$430$	−26635.4	−2.98714
$431$	9103.53	1.01741	0.508703	−	0.860942i	$-0.330125\pi$
$431$	9103.53	1.01741	0.508703	+	0.860942i	$0.330125\pi$
$432$	2566.44	0.285828
$433$	16112.2	1.78823	0.894117	−	0.447834i	$-0.147804\pi$
$433$	16112.2	1.78823	0.894117	+	0.447834i	$0.147804\pi$
$434$	25939.3	2.86896
$435$	−5267.87	−0.580632
$436$	9876.00	1.08480
$437$	3771.83	0.412885
$438$	14421.6	1.57327
$439$	−430.018	−0.0467509	−0.0233754	−	0.999727i	$-0.507441\pi$
$439$	−430.018	−0.0467509	−0.0233754	+	0.999727i	$0.507441\pi$
$440$	25065.4	2.71579
$441$	8022.60	0.866278
$442$	17453.2	1.87820
$443$	5492.74	0.589092	0.294546	−	0.955637i	$-0.404832\pi$
$443$	5492.74	0.589092	0.294546	+	0.955637i	$0.404832\pi$
$444$	−11776.8	−1.25879
$445$	−13980.6	−1.48932
$446$	−2639.37	−0.280219
$447$	−7700.31	−0.814792
$448$	7917.65	0.834986
$449$	3121.35	0.328075	0.164038	−	0.986454i	$-0.447548\pi$
$449$	3121.35	0.328075	0.164038	+	0.986454i	$0.447548\pi$
$450$	−2808.81	−0.294241
$451$	−8608.65	−0.898815
$452$	−2539.52	−0.264267
$453$	−5835.24	−0.605218
$454$	5868.28	0.606635
$455$	13739.2	1.41561
$456$	−2930.83	−0.300984
$457$	9882.44	1.01156	0.505778	−	0.862664i	$-0.331206\pi$
$457$	9882.44	1.01156	0.505778	+	0.862664i	$0.331206\pi$
$458$	18437.4	1.88106
$459$	−3281.82	−0.333730
$460$	−42195.3	−4.27688
$461$	−1333.73	−0.134747	−0.0673734	−	0.997728i	$-0.521462\pi$
$461$	−1333.73	−0.134747	−0.0673734	+	0.997728i	$0.521462\pi$
$462$	20922.4	2.10693
$463$	17592.2	1.76583	0.882917	−	0.469530i	$-0.155577\pi$
$463$	17592.2	1.76583	0.882917	+	0.469530i	$0.155577\pi$
$464$	12201.3	1.22076
$465$	−6031.99	−0.601563
$466$	−27170.0	−2.70091
$467$	−16369.2	−1.62201	−0.811004	−	0.585040i	$-0.801079\pi$
$467$	−16369.2	−1.62201	−0.811004	+	0.585040i	$0.801079\pi$
$468$	4433.08	0.437861
$469$	23842.6	2.34744
$470$	−20992.7	−2.06025
$471$	2279.20	0.222973
$472$	−39019.2	−3.80510
$473$	−15318.5	−1.48911
$474$	14003.0	1.35692
$475$	1309.12	0.126456
$476$	73583.9	7.08553
$477$	−3721.81	−0.357253
$478$	−20883.5	−1.99830
$479$	−308.753	−0.0294515	−0.0147258	−	0.999892i	$-0.504688\pi$
$479$	−308.753	−0.0294515	−0.0147258	+	0.999892i	$0.504688\pi$
$480$	4371.60	0.415698
$481$	−6512.69	−0.617366
$482$	5950.03	0.562274
$483$	−18868.4	−1.77752
$484$	3975.02	0.373311
$485$	11534.7	1.07992
$486$	−1220.59	−0.113924
$487$	−3782.62	−0.351965	−0.175983	−	0.984393i	$-0.556310\pi$
$487$	−3782.62	−0.351965	−0.175983	+	0.984393i	$0.556310\pi$
$488$	28818.7	2.67328
$489$	−1262.69	−0.116771
$490$	61250.8	5.64699
$491$	−15470.1	−1.42190	−0.710951	−	0.703242i	$-0.751735\pi$
$491$	−15470.1	−1.42190	−0.710951	+	0.703242i	$0.751735\pi$
$492$	−11260.6	−1.03185
$493$	−15602.4	−1.42534
$494$	−3025.45	−0.275549
$495$	−4865.35	−0.441780
$496$	13971.1	1.26476
$497$	−7521.41	−0.678836
$498$	7718.19	0.694499
$499$	21633.4	1.94077	0.970384	−	0.241567i	$-0.0776614\pi$
$499$	21633.4	1.94077	0.970384	+	0.241567i	$0.0776614\pi$
$500$	14818.7	1.32542
$501$	10699.2	0.954100
$502$	−21358.8	−1.89899
$503$	12611.3	1.11791	0.558957	−	0.829197i	$-0.311202\pi$
$503$	12611.3	1.11791	0.558957	+	0.829197i	$0.311202\pi$
$504$	14661.3	1.29577
$505$	25447.8	2.24240
$506$	−35534.3	−3.12193
$507$	−4139.47	−0.362604
$508$	34637.2	3.02516
$509$	−19163.1	−1.66874	−0.834372	−	0.551202i	$-0.814169\pi$
$509$	−19163.1	−1.66874	−0.834372	+	0.551202i	$0.814169\pi$
$510$	−25056.0	−2.17548
$511$	33624.5	2.91088
$512$	25132.8	2.16938
$513$	568.892	0.0489614
$514$	−29704.9	−2.54908
$515$	−11712.2	−1.00214
$516$	−20037.6	−1.70951
$517$	−12073.3	−1.02705
$518$	−40206.4	−3.41036
$519$	4673.80	0.395293
$520$	18131.6	1.52908
$521$	5977.48	0.502646	0.251323	−	0.967903i	$-0.419134\pi$
$521$	5977.48	0.502646	0.251323	+	0.967903i	$0.419134\pi$
$522$	−5802.93	−0.486566
$523$	7631.42	0.638047	0.319024	−	0.947747i	$-0.396645\pi$
$523$	7631.42	0.638047	0.319024	+	0.947747i	$0.396645\pi$
$524$	17391.3	1.44989
$525$	−6548.82	−0.544408
$526$	−36077.1	−2.99056
$527$	−17865.5	−1.47673
$528$	11269.0	0.928827
$529$	19878.7	1.63382
$530$	−28415.2	−2.32882
$531$	7573.88	0.618980
$532$	−12755.5	−1.03952
$533$	−6227.24	−0.506063
$534$	−15400.7	−1.24804
$535$	9813.81	0.793061
$536$	31465.0	2.53560
$537$	3876.69	0.311530
$538$	27928.3	2.23806
$539$	35226.6	2.81506
$540$	−6364.18	−0.507168
$541$	−23027.9	−1.83003	−0.915017	−	0.403415i	$-0.867823\pi$
$541$	−23027.9	−1.83003	−0.915017	+	0.403415i	$0.867823\pi$
$542$	42127.8	3.33864
$543$	−3260.05	−0.257646
$544$	12947.8	1.02046
$545$	−7840.62	−0.616248
$546$	15134.7	1.18627
$547$	2685.90	0.209947	0.104973	−	0.994475i	$-0.466524\pi$
$547$	2685.90	0.209947	0.104973	+	0.994475i	$0.466524\pi$
$548$	4220.29	0.328982
$549$	−5593.90	−0.434866
$550$	−12333.2	−0.956166
$551$	2704.62	0.209112
$552$	−24900.6	−1.92000
$553$	32648.4	2.51058
$554$	−3502.61	−0.268613
$555$	9349.69	0.715085
$556$	38071.6	2.90395
$557$	20746.5	1.57820	0.789098	−	0.614267i	$-0.210548\pi$
$557$	20746.5	1.57820	0.789098	+	0.614267i	$0.210548\pi$
$558$	−6644.67	−0.504106
$559$	−11081.0	−0.838417
$560$	45684.4	3.44736
$561$	−14410.2	−1.08449
$562$	34469.2	2.58718
$563$	17635.0	1.32012	0.660058	−	0.751215i	$-0.270532\pi$
$563$	17635.0	1.32012	0.660058	+	0.751215i	$0.270532\pi$
$564$	−15792.6	−1.17906
$565$	2016.14	0.150123
$566$	−28689.0	−2.13055
$567$	−2845.86	−0.210784
$568$	−9926.01	−0.733250
$569$	3218.21	0.237108	0.118554	−	0.992948i	$-0.462174\pi$
$569$	3218.21	0.237108	0.118554	+	0.992948i	$0.462174\pi$
$570$	4343.37	0.319164
$571$	11028.2	0.808258	0.404129	−	0.914702i	$-0.367575\pi$
$571$	11028.2	0.808258	0.404129	+	0.914702i	$0.367575\pi$
$572$	19465.3	1.42287
$573$	3182.36	0.232016
$574$	−38444.1	−2.79552
$575$	11122.4	0.806673
$576$	−2028.20	−0.146716
$577$	12569.6	0.906896	0.453448	−	0.891283i	$-0.350194\pi$
$577$	12569.6	0.906896	0.453448	+	0.891283i	$0.350194\pi$
$578$	−49532.6	−3.56450
$579$	−3146.10	−0.225816
$580$	−30256.5	−2.16609
$581$	17995.2	1.28497
$582$	12706.3	0.904970
$583$	−16342.1	−1.16093
$584$	44374.2	3.14421
$585$	−3519.45	−0.248737
$586$	−16053.7	−1.13169
$587$	−17324.0	−1.21813	−0.609063	−	0.793122i	$-0.708454\pi$
$587$	−17324.0	−1.21813	−0.609063	+	0.793122i	$0.708454\pi$
$588$	46078.5	3.23171
$589$	3096.93	0.216650
$590$	57824.9	4.03494
$591$	−11974.3	−0.833431
$592$	−21655.5	−1.50344
$593$	23303.3	1.61375	0.806873	−	0.590725i	$-0.201158\pi$
$593$	23303.3	1.61375	0.806873	+	0.590725i	$0.201158\pi$
$594$	−5359.53	−0.370209
$595$	−58418.8	−4.02510
$596$	−44227.4	−3.03964
$597$	−1404.62	−0.0962937
$598$	−25704.5	−1.75775
$599$	20359.4	1.38876	0.694378	−	0.719611i	$-0.255680\pi$
$599$	20359.4	1.38876	0.694378	+	0.719611i	$0.255680\pi$
$600$	−8642.48	−0.588046
$601$	18186.7	1.23436	0.617180	−	0.786822i	$-0.288275\pi$
$601$	18186.7	1.23436	0.617180	+	0.786822i	$0.288275\pi$
$602$	−68408.9	−4.63146
$603$	−6107.56	−0.412469
$604$	−33515.2	−2.25781
$605$	−3155.79	−0.212068
$606$	28032.6	1.87912
$607$	−12618.8	−0.843794	−0.421897	−	0.906644i	$-0.638636\pi$
$607$	−12618.8	−0.843794	−0.421897	+	0.906644i	$0.638636\pi$
$608$	−2244.46	−0.149712
$609$	−13529.7	−0.900250
$610$	−42708.2	−2.83476
$611$	−8733.47	−0.578262
$612$	−18849.4	−1.24500
$613$	15966.7	1.05202	0.526011	−	0.850477i	$-0.323687\pi$
$613$	15966.7	1.05202	0.526011	+	0.850477i	$0.323687\pi$
$614$	3369.75	0.221485
$615$	8939.89	0.586164
$616$	64376.7	4.21073
$617$	−27282.4	−1.78015	−0.890073	−	0.455818i	$-0.849347\pi$
$617$	−27282.4	−1.78015	−0.890073	+	0.455818i	$0.849347\pi$
$618$	−12901.9	−0.839789
$619$	−2040.53	−0.132497	−0.0662486	−	0.997803i	$-0.521103\pi$
$619$	−2040.53	−0.132497	−0.0662486	+	0.997803i	$0.521103\pi$
$620$	−34645.3	−2.24417
$621$	4833.36	0.312328
$622$	−27551.0	−1.77604
$623$	−35907.2	−2.30913
$624$	8151.66	0.522961
$625$	−19531.1	−1.24999
$626$	−9707.01	−0.619760
$627$	2497.96	0.159105
$628$	13090.8	0.831816
$629$	27691.9	1.75540
$630$	−21727.5	−1.37404
$631$	−654.545	−0.0412948	−0.0206474	−	0.999787i	$-0.506573\pi$
$631$	−654.545	−0.0412948	−0.0206474	+	0.999787i	$0.506573\pi$
$632$	43086.1	2.71182
$633$	2522.15	0.158367
$634$	19284.5	1.20802
$635$	−27498.7	−1.71851
$636$	−21376.5	−1.33276
$637$	25481.8	1.58497
$638$	−25480.2	−1.58115
$639$	1926.70	0.119279
$640$	−27142.5	−1.67641
$641$	20801.9	1.28179	0.640895	−	0.767629i	$-0.278563\pi$
$641$	20801.9	1.28179	0.640895	+	0.767629i	$0.278563\pi$
$642$	10810.6	0.664581
$643$	−5244.72	−0.321667	−0.160833	−	0.986982i	$-0.551418\pi$
$643$	−5244.72	−0.321667	−0.160833	+	0.986982i	$0.551418\pi$
$644$	−108372.	−6.63115
$645$	15908.0	0.971125
$646$	12864.2	0.783490
$647$	−452.603	−0.0275018	−0.0137509	−	0.999905i	$-0.504377\pi$
$647$	−452.603	−0.0275018	−0.0137509	+	0.999905i	$0.504377\pi$
$648$	−3755.67	−0.227680
$649$	33256.3	2.01144
$650$	−8921.49	−0.538353
$651$	−15492.3	−0.932702
$652$	−7252.39	−0.435622
$653$	−14789.8	−0.886326	−0.443163	−	0.896441i	$-0.646144\pi$
$653$	−14789.8	−0.886326	−0.443163	+	0.896441i	$0.646144\pi$
$654$	−8637.00	−0.516412
$655$	−13807.1	−0.823645
$656$	−20706.4	−1.23239
$657$	−8613.32	−0.511473
$658$	−53916.5	−3.19435
$659$	−2318.07	−0.137025	−0.0685123	−	0.997650i	$-0.521825\pi$
$659$	−2318.07	−0.137025	−0.0685123	+	0.997650i	$0.521825\pi$
$660$	−27944.6	−1.64809
$661$	22809.4	1.34218	0.671092	−	0.741374i	$-0.265826\pi$
$661$	22809.4	1.34218	0.671092	+	0.741374i	$0.265826\pi$
$662$	11569.3	0.679232
$663$	−10423.9	−0.610604
$664$	23748.3	1.38797
$665$	10126.7	0.590521
$666$	10299.3	0.599237
$667$	22978.7	1.33394
$668$	61451.7	3.55934
$669$	1576.36	0.0910996
$670$	−46629.9	−2.68876
$671$	−24562.3	−1.41314
$672$	11227.8	0.644526
$673$	10705.5	0.613175	0.306587	−	0.951843i	$-0.400813\pi$
$673$	10705.5	0.613175	0.306587	+	0.951843i	$0.400813\pi$
$674$	34505.2	1.97195
$675$	1677.56	0.0956582
$676$	−23775.4	−1.35272
$677$	677.000	0.0384331
$677$	677.000	0.0384331
$678$	2220.92	0.125802
$679$	29625.1	1.67439
$680$	−77095.2	−4.34774
$681$	−3504.83	−0.197218
$682$	−29176.2	−1.63814
$683$	30935.1	1.73309	0.866544	−	0.499101i	$-0.166336\pi$
$683$	30935.1	1.73309	0.866544	+	0.499101i	$0.166336\pi$
$684$	3267.48	0.182654
$685$	−3350.52	−0.186886
$686$	96781.0	5.38647
$687$	−11011.7	−0.611534
$688$	−36845.6	−2.04175
$689$	−11821.4	−0.653643
$690$	36901.6	2.03597
$691$	−3543.13	−0.195061	−0.0975303	−	0.995233i	$-0.531094\pi$
$691$	−3543.13	−0.195061	−0.0975303	+	0.995233i	$0.531094\pi$
$692$	26844.4	1.47467
$693$	−12495.9	−0.684965
$694$	−5214.66	−0.285225
$695$	−30225.3	−1.64966
$696$	−17855.2	−0.972411
$697$	26478.2	1.43893
$698$	−207.653	−0.0112604
$699$	16227.3	0.878072
$700$	−37613.7	−2.03095
$701$	4513.23	0.243170	0.121585	−	0.992581i	$-0.461202\pi$
$701$	4513.23	0.243170	0.121585	+	0.992581i	$0.461202\pi$
$702$	−3876.92	−0.208440
$703$	−4800.30	−0.257535
$704$	−8905.66	−0.476768
$705$	12537.9	0.669792
$706$	7496.56	0.399627
$707$	65358.8	3.47676
$708$	43501.2	2.30915
$709$	−3464.08	−0.183493	−0.0917463	−	0.995782i	$-0.529245\pi$
$709$	−3464.08	−0.183493	−0.0917463	+	0.995782i	$0.529245\pi$
$710$	14709.9	0.777541
$711$	−8363.28	−0.441136
$712$	−47386.7	−2.49423
$713$	26311.8	1.38203
$714$	−64352.4	−3.37301
$715$	−15453.6	−0.808297
$716$	22266.1	1.16218
$717$	12472.7	0.649651
$718$	40451.1	2.10254
$719$	12405.5	0.643458	0.321729	−	0.946832i	$-0.395736\pi$
$719$	12405.5	0.643458	0.321729	+	0.946832i	$0.395736\pi$
$720$	−11702.6	−0.605737
$721$	−30081.1	−1.55379
$722$	32223.0	1.66096
$723$	−3553.65	−0.182796
$724$	−18724.4	−0.961168
$725$	7975.42	0.408551
$726$	−3476.33	−0.177712
$727$	21499.3	1.09679	0.548393	−	0.836220i	$-0.315240\pi$
$727$	21499.3	1.09679	0.548393	+	0.836220i	$0.315240\pi$
$728$	46568.2	2.37078
$729$	729.000	0.0370370
$730$	−65760.8	−3.33413
$731$	47116.2	2.38393
$732$	−32129.0	−1.62230
$733$	−673.432	−0.0339342	−0.0169671	−	0.999856i	$-0.505401\pi$
$733$	−673.432	−0.0339342	−0.0169671	+	0.999856i	$0.505401\pi$
$734$	−8529.77	−0.428937
$735$	−36582.0	−1.83585
$736$	−19069.1	−0.955022
$737$	−26817.8	−1.34036
$738$	9847.93	0.491202
$739$	4945.31	0.246166	0.123083	−	0.992396i	$-0.460722\pi$
$739$	4945.31	0.246166	0.123083	+	0.992396i	$0.460722\pi$
$740$	53700.8	2.66767
$741$	1806.95	0.0895816
$742$	−72980.1	−3.61076
$743$	−34567.8	−1.70682	−0.853412	−	0.521236i	$-0.825471\pi$
$743$	−34567.8	−1.70682	−0.853412	+	0.521236i	$0.825471\pi$
$744$	−20445.1	−1.00747
$745$	35112.4	1.72674
$746$	−1880.39	−0.0922871
$747$	−4609.69	−0.225783
$748$	−82766.2	−4.04576
$749$	25205.3	1.22961
$750$	−12959.6	−0.630956
$751$	23901.2	1.16134	0.580670	−	0.814139i	$-0.302791\pi$
$751$	23901.2	1.16134	0.580670	+	0.814139i	$0.302791\pi$
$752$	−29039.9	−1.40821
$753$	12756.6	0.617363
$754$	−18431.6	−0.890238
$755$	26608.0	1.28260
$756$	−16345.4	−0.786346
$757$	−23421.3	−1.12452	−0.562260	−	0.826960i	$-0.690068\pi$
$757$	−23421.3	−1.12452	−0.562260	+	0.826960i	$0.690068\pi$
$758$	−59630.5	−2.85736
$759$	21222.9	1.01494
$760$	13364.2	0.637856
$761$	−5472.56	−0.260683	−0.130342	−	0.991469i	$-0.541607\pi$
$761$	−5472.56	−0.260683	−0.130342	+	0.991469i	$0.541607\pi$
$762$	−30291.8	−1.44010
$763$	−20137.4	−0.955471
$764$	18278.2	0.865550
$765$	14964.7	0.707253
$766$	51372.9	2.42321
$767$	24056.6	1.13251
$768$	−24490.8	−1.15070
$769$	25775.3	1.20869	0.604343	−	0.796724i	$-0.293436\pi$
$769$	25775.3	1.20869	0.604343	+	0.796724i	$0.293436\pi$
$770$	−95403.6	−4.46507
$771$	17741.2	0.828709
$772$	−18069.9	−0.842423
$773$	11151.9	0.518895	0.259447	−	0.965757i	$-0.416460\pi$
$773$	11151.9	0.518895	0.259447	+	0.965757i	$0.416460\pi$
$774$	17523.8	0.813796
$775$	9132.29	0.423279
$776$	39096.2	1.80860
$777$	24013.3	1.10871
$778$	−1335.08	−0.0615228
$779$	−4589.90	−0.211104
$780$	−20214.3	−0.927932
$781$	8459.98	0.387608
$782$	109295.	4.99794
$783$	3465.80	0.158183
$784$	84730.3	3.85980
$785$	−10392.9	−0.472532
$786$	−15209.5	−0.690209
$787$	8228.09	0.372681	0.186340	−	0.982485i	$-0.440337\pi$
$787$	8228.09	0.372681	0.186340	+	0.982485i	$0.440337\pi$
$788$	−68775.5	−3.10917
$789$	21547.0	0.972237
$790$	−63851.8	−2.87563
$791$	5178.15	0.232761
$792$	−16490.9	−0.739870
$793$	−17767.7	−0.795647
$794$	43326.5	1.93653
$795$	16971.0	0.757104
$796$	−8067.57	−0.359230
$797$	−20295.2	−0.901998	−0.450999	−	0.892524i	$-0.648932\pi$
$797$	−20295.2	−0.901998	−0.450999	+	0.892524i	$0.648932\pi$
$798$	11155.3	0.494853
$799$	37134.6	1.64422
$800$	−6618.49	−0.292499
$801$	9198.05	0.405739
$802$	−30040.4	−1.32265
$803$	−37820.4	−1.66208
$804$	−35079.3	−1.53875
$805$	86037.3	3.76698
$806$	−21105.2	−0.922330
$807$	−16680.2	−0.727597
$808$	86254.0	3.75545
$809$	−44551.5	−1.93615	−0.968076	−	0.250656i	$-0.919354\pi$
$809$	−44551.5	−1.93615	−0.968076	+	0.250656i	$0.919354\pi$
$810$	5565.75	0.241433
$811$	27550.4	1.19288	0.596439	−	0.802659i	$-0.296582\pi$
$811$	27550.4	1.19288	0.596439	+	0.802659i	$0.296582\pi$
$812$	−77709.2	−3.35844
$813$	−25160.8	−1.08540
$814$	45223.6	1.94728
$815$	5757.72	0.247465
$816$	−34660.8	−1.48697
$817$	−8167.44	−0.349746
$818$	13952.1	0.596362
$819$	−9039.17	−0.385658
$820$	51347.0	2.18673
$821$	9610.08	0.408519	0.204260	−	0.978917i	$-0.434521\pi$
$821$	9610.08	0.408519	0.204260	+	0.978917i	$0.434521\pi$
$822$	−3690.83	−0.156609
$823$	9433.23	0.399540	0.199770	−	0.979843i	$-0.435980\pi$
$823$	9433.23	0.399540	0.199770	+	0.979843i	$0.435980\pi$
$824$	−39698.1	−1.67833
$825$	7366.02	0.310851
$826$	148515.	6.25603
$827$	22962.6	0.965524	0.482762	−	0.875752i	$-0.339634\pi$
$827$	22962.6	0.965524	0.482762	+	0.875752i	$0.339634\pi$
$828$	27760.8	1.16516
$829$	−18119.5	−0.759126	−0.379563	−	0.925166i	$-0.623926\pi$
$829$	−18119.5	−0.759126	−0.379563	+	0.925166i	$0.623926\pi$
$830$	−35194.0	−1.47181
$831$	2091.93	0.0873264
$832$	−6442.09	−0.268437
$833$	−108349.	−4.50667
$834$	−33295.3	−1.38240
$835$	−48786.9	−2.02196
$836$	14347.3	0.593553
$837$	3968.53	0.163886
$838$	−5207.08	−0.214649
$839$	−15737.0	−0.647557	−0.323778	−	0.946133i	$-0.604953\pi$
$839$	−15737.0	−0.647557	−0.323778	+	0.946133i	$0.604953\pi$
$840$	−66853.8	−2.74604
$841$	−7911.95	−0.324406
$842$	10289.5	0.421138
$843$	−20586.7	−0.841096
$844$	14486.2	0.590799
$845$	18875.4	0.768443
$846$	13811.4	0.561282
$847$	−8105.18	−0.328804
$848$	−39307.7	−1.59178
$849$	17134.5	0.692644
$850$	37934.1	1.53074
$851$	−40783.8	−1.64283
$852$	11066.2	0.444977
$853$	7583.87	0.304416	0.152208	−	0.988348i	$-0.451362\pi$
$853$	7583.87	0.304416	0.152208	+	0.988348i	$0.451362\pi$
$854$	−109689.	−4.39520
$855$	−2594.08	−0.103761
$856$	33263.4	1.32818
$857$	3578.03	0.142618	0.0713088	−	0.997454i	$-0.477282\pi$
$857$	3578.03	0.142618	0.0713088	+	0.997454i	$0.477282\pi$
$858$	−17023.3	−0.677348
$859$	5155.20	0.204765	0.102383	−	0.994745i	$-0.467353\pi$
$859$	5155.20	0.204765	0.102383	+	0.994745i	$0.467353\pi$
$860$	91368.8	3.62285
$861$	22960.8	0.908828
$862$	−45727.2	−1.80682
$863$	−25022.0	−0.986974	−0.493487	−	0.869753i	$-0.664278\pi$
$863$	−25022.0	−0.986974	−0.493487	+	0.869753i	$0.664278\pi$
$864$	−2876.13	−0.113250
$865$	−21311.9	−0.837720
$866$	−80932.2	−3.17574
$867$	29583.3	1.15883
$868$	−88981.1	−3.47951
$869$	−36722.5	−1.43351
$870$	26460.6	1.03115
$871$	−19399.2	−0.754668
$872$	−26575.4	−1.03206
$873$	−7588.83	−0.294207
$874$	−18946.0	−0.733246
$875$	−30215.7	−1.16740
$876$	−49471.3	−1.90808
$877$	−17056.2	−0.656724	−0.328362	−	0.944552i	$-0.606497\pi$
$877$	−17056.2	−0.656724	−0.328362	+	0.944552i	$0.606497\pi$
$878$	2159.99	0.0830252
$879$	9588.07	0.367915
$880$	−51385.2	−1.96840
$881$	−36423.2	−1.39288	−0.696441	−	0.717614i	$-0.745234\pi$
$881$	−36423.2	−1.39288	−0.696441	+	0.717614i	$0.745234\pi$
$882$	−40297.7	−1.53843
$883$	21918.4	0.835348	0.417674	−	0.908597i	$-0.362846\pi$
$883$	21918.4	0.835348	0.417674	+	0.908597i	$0.362846\pi$
$884$	−59870.6	−2.27790
$885$	−34535.9	−1.31176
$886$	−27590.1	−1.04617
$887$	27382.8	1.03656	0.518278	−	0.855212i	$-0.326573\pi$
$887$	27382.8	1.03656	0.518278	+	0.855212i	$0.326573\pi$
$888$	31690.3	1.19759
$889$	−70626.3	−2.66449
$890$	70225.1	2.64489
$891$	3200.98	0.120356
$892$	9053.97	0.339853
$893$	−6437.17	−0.241222
$894$	38678.8	1.44699
$895$	−17677.2	−0.660206
$896$	−69711.3	−2.59921
$897$	15352.0	0.571447
$898$	−15678.6	−0.582631
$899$	18867.1	0.699948
$900$	9635.21	0.356860
$901$	50264.6	1.85855
$902$	43241.4	1.59621
$903$	40857.2	1.50569
$904$	6833.60	0.251418
$905$	14865.4	0.546014
$906$	29310.6	1.07481
$907$	45169.3	1.65361	0.826805	−	0.562489i	$-0.190156\pi$
$907$	45169.3	1.65361	0.826805	+	0.562489i	$0.190156\pi$
$908$	−20130.3	−0.735735
$909$	−16742.4	−0.610904
$910$	−69012.1	−2.51399
$911$	−21554.8	−0.783912	−0.391956	−	0.919984i	$-0.628201\pi$
$911$	−21554.8	−0.783912	−0.391956	+	0.919984i	$0.628201\pi$
$912$	6008.34	0.218153
$913$	−20240.8	−0.733704
$914$	−49639.7	−1.79643
$915$	25507.4	0.921585
$916$	−63246.9	−2.28137
$917$	−35461.4	−1.27703
$918$	16484.6	0.592674
$919$	18824.7	0.675702	0.337851	−	0.941200i	$-0.390300\pi$
$919$	18824.7	0.675702	0.337851	+	0.941200i	$0.390300\pi$
$920$	113543.	4.06893
$921$	−2012.58	−0.0720052
$922$	6699.38	0.239298
$923$	6119.70	0.218236
$924$	−71771.4	−2.55531
$925$	−14155.2	−0.503157
$926$	−88366.2	−3.13596
$927$	7705.65	0.273017
$928$	−13673.7	−0.483685
$929$	11117.2	0.392621	0.196310	−	0.980542i	$-0.437104\pi$
$929$	11117.2	0.392621	0.196310	+	0.980542i	$0.437104\pi$
$930$	30298.8	1.06832
$931$	18781.9	0.661172
$932$	93202.8	3.27571
$933$	16454.8	0.577393
$934$	82223.1	2.88054
$935$	65708.6	2.29829
$936$	−11929.0	−0.416572
$937$	17424.4	0.607504	0.303752	−	0.952751i	$-0.401761\pi$
$937$	17424.4	0.607504	0.303752	+	0.952751i	$0.401761\pi$
$938$	−119762.	−4.16883
$939$	5797.51	0.201485
$940$	72012.3	2.49871
$941$	54044.8	1.87228	0.936138	−	0.351633i	$-0.114374\pi$
$941$	54044.8	1.87228	0.936138	+	0.351633i	$0.114374\pi$
$942$	−11448.5	−0.395979
$943$	−38996.2	−1.34665
$944$	79991.2	2.75794
$945$	12976.7	0.446702
$946$	76945.4	2.64451
$947$	−34259.8	−1.17560	−0.587800	−	0.809007i	$-0.700006\pi$
$947$	−34259.8	−1.17560	−0.587800	+	0.809007i	$0.700006\pi$
$948$	−48035.2	−1.64569
$949$	−27358.1	−0.935808
$950$	−6575.76	−0.224574
$951$	−11517.7	−0.392731
$952$	−198007.	−6.74103
$953$	40244.0	1.36792	0.683961	−	0.729518i	$-0.260256\pi$
$953$	40244.0	1.36792	0.683961	+	0.729518i	$0.260256\pi$
$954$	18694.7	0.634448
$955$	−14511.1	−0.491696
$956$	71637.8	2.42357
$957$	15218.0	0.514033
$958$	1550.87	0.0523031
$959$	−8605.30	−0.289760
$960$	9248.33	0.310926
$961$	−8187.17	−0.274820
$962$	32713.4	1.09638
$963$	−6456.63	−0.216056
$964$	−20410.7	−0.681935
$965$	14345.8	0.478558
$966$	94776.3	3.15670
$967$	6724.96	0.223640	0.111820	−	0.993728i	$-0.464332\pi$
$967$	6724.96	0.223640	0.111820	+	0.993728i	$0.464332\pi$
$968$	−10696.4	−0.355160
$969$	−7683.13	−0.254714
$970$	−57939.0	−1.91785
$971$	−17155.5	−0.566989	−0.283494	−	0.958974i	$-0.591494\pi$
$971$	−17155.5	−0.566989	−0.283494	+	0.958974i	$0.591494\pi$
$972$	4187.08	0.138169
$973$	−77629.2	−2.55774
$974$	19000.2	0.625058
$975$	5328.36	0.175020
$976$	−59079.7	−1.93760
$977$	9557.99	0.312986	0.156493	−	0.987679i	$-0.449981\pi$
$977$	9557.99	0.312986	0.156493	+	0.987679i	$0.449981\pi$
$978$	6342.54	0.207374
$979$	40387.9	1.31849
$980$	−210112.	−6.84876
$981$	5158.45	0.167886
$982$	77706.5	2.52517
$983$	2714.06	0.0880622	0.0440311	−	0.999030i	$-0.485980\pi$
$983$	2714.06	0.0880622	0.0440311	+	0.999030i	$0.485980\pi$
$984$	30301.3	0.981677
$985$	54601.3	1.76624
$986$	78371.0	2.53128
$987$	32201.6	1.03849
$988$	10378.4	0.334190
$989$	−69391.2	−2.23105
$990$	24438.8	0.784561
$991$	55187.0	1.76899	0.884496	−	0.466547i	$-0.154502\pi$
$991$	55187.0	1.76899	0.884496	+	0.466547i	$0.154502\pi$
$992$	−15657.1	−0.501121
$993$	−6909.74	−0.220820
$994$	37780.2	1.20555
$995$	6404.89	0.204069
$996$	−26476.2	−0.842298
$997$	34573.5	1.09825	0.549124	−	0.835741i	$-0.314962\pi$
$997$	34573.5	1.09825	0.549124	+	0.835741i	$0.314962\pi$
$998$	−108665.	−3.44662
$999$	−6151.28	−0.194813

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2031.4.a.d.1.7	✓	94

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2031.4.a.d.1.7	✓	94	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2031 = 3 \cdot 677 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2031.a (trivial)

\(f(q)\)	\(=\)	\(q-5.02302 q^{2} +3.00000 q^{3} +17.2308 q^{4} -13.6796 q^{5} -15.0691 q^{6} -35.1340 q^{7} -46.3664 q^{8} +9.00000 q^{9} +68.7130 q^{10} +39.5183 q^{11} +51.6923 q^{12} +28.5863 q^{13} +176.479 q^{14} -41.0388 q^{15} +95.0532 q^{16} -121.549 q^{17} -45.2072 q^{18} +21.0701 q^{19} -235.710 q^{20} -105.402 q^{21} -198.501 q^{22} +179.013 q^{23} -139.099 q^{24} +62.1318 q^{25} -143.590 q^{26} +27.0000 q^{27} -605.386 q^{28} +128.363 q^{29} +206.139 q^{30} +146.982 q^{31} -106.523 q^{32} +118.555 q^{33} +610.542 q^{34} +480.620 q^{35} +155.077 q^{36} -227.825 q^{37} -105.836 q^{38} +85.7590 q^{39} +634.274 q^{40} -217.840 q^{41} +529.437 q^{42} -387.632 q^{43} +680.930 q^{44} -123.117 q^{45} -899.188 q^{46} -305.512 q^{47} +285.159 q^{48} +891.400 q^{49} -312.090 q^{50} -364.646 q^{51} +492.564 q^{52} -413.534 q^{53} -135.622 q^{54} -540.595 q^{55} +1629.04 q^{56} +63.2103 q^{57} -644.770 q^{58} +841.542 q^{59} -707.131 q^{60} -621.544 q^{61} -738.296 q^{62} -316.206 q^{63} -225.356 q^{64} -391.050 q^{65} -595.504 q^{66} -678.618 q^{67} -2094.38 q^{68} +537.040 q^{69} -2414.16 q^{70} +214.078 q^{71} -417.297 q^{72} -957.035 q^{73} +1144.37 q^{74} +186.395 q^{75} +363.054 q^{76} -1388.44 q^{77} -430.769 q^{78} -929.253 q^{79} -1300.29 q^{80} +81.0000 q^{81} +1094.21 q^{82} -512.188 q^{83} -1816.16 q^{84} +1662.74 q^{85} +1947.08 q^{86} +385.089 q^{87} -1832.32 q^{88} +1022.01 q^{89} +618.417 q^{90} -1004.35 q^{91} +3084.54 q^{92} +440.947 q^{93} +1534.59 q^{94} -288.231 q^{95} -319.570 q^{96} -843.203 q^{97} -4477.52 q^{98} +355.664 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 94 q + 19 q^{2} + 282 q^{3} + 409 q^{4} + 84 q^{5} + 57 q^{6} + 39 q^{7} + 228 q^{8} + 846 q^{9} + 145 q^{10} + 357 q^{11} + 1227 q^{12} + 271 q^{13} + 366 q^{14} + 252 q^{15} + 1865 q^{16} + 690 q^{17}+ \cdots + 3213 q^{99}+O(q^{100}) \) 94 * q + 19 * q^2 + 282 * q^3 + 409 * q^4 + 84 * q^5 + 57 * q^6 + 39 * q^7 + 228 * q^8 + 846 * q^9 + 145 * q^10 + 357 * q^11 + 1227 * q^12 + 271 * q^13 + 366 * q^14 + 252 * q^15 + 1865 * q^16 + 690 * q^17 + 171 * q^18 + 345 * q^19 + 939 * q^20 + 117 * q^21 + 148 * q^22 + 1135 * q^23 + 684 * q^24 + 3280 * q^25 + 1261 * q^26 + 2538 * q^27 + 214 * q^28 + 1396 * q^29 + 435 * q^30 + 889 * q^31 + 2048 * q^32 + 1071 * q^33 + 1590 * q^34 + 2104 * q^35 + 3681 * q^36 + 711 * q^37 + 2075 * q^38 + 813 * q^39 + 1675 * q^40 + 2931 * q^41 + 1098 * q^42 + 585 * q^43 + 4058 * q^44 + 756 * q^45 + 1148 * q^46 + 2733 * q^47 + 5595 * q^48 + 8415 * q^49 + 2640 * q^50 + 2070 * q^51 + 2174 * q^52 + 3430 * q^53 + 513 * q^54 + 2458 * q^55 + 4034 * q^56 + 1035 * q^57 + 259 * q^58 + 5376 * q^59 + 2817 * q^60 + 2064 * q^61 + 3610 * q^62 + 351 * q^63 + 10194 * q^64 + 5442 * q^65 + 444 * q^66 + 1429 * q^67 + 6932 * q^68 + 3405 * q^69 + 3888 * q^70 + 5336 * q^71 + 2052 * q^72 + 2412 * q^73 + 5911 * q^74 + 9840 * q^75 + 5988 * q^76 + 7100 * q^77 + 3783 * q^78 + 2018 * q^79 + 8054 * q^80 + 7614 * q^81 + 3546 * q^82 + 6229 * q^83 + 642 * q^84 + 2728 * q^85 + 6619 * q^86 + 4188 * q^87 + 3679 * q^88 + 11972 * q^89 + 1305 * q^90 + 5586 * q^91 + 15073 * q^92 + 2667 * q^93 + 3650 * q^94 + 8168 * q^95 + 6144 * q^96 + 5859 * q^97 + 8121 * q^98 + 3213 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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