LMFDB - Embedded newform 187.4.a.d.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [187,4,Mod(1,187)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("187.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(187, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	187.a (trivial)

Newform invariants

comment:select newform

sage:traces = [10,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$11.0333571711$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 55 x^{8} + 72 x^{7} + 1037 x^{6} - 812 x^{5} - 7851 x^{4} + 2526 x^{3} + 20108 x^{2} + \cdots - 5760 $ x^10 - 2x^9 - 55x^8 + 72x^7 + 1037x^6 - 812x^5 - 7851x^4 + 2526x^3 + 20108x^2 + 4072*x - 5760
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-3.27779$ of defining polynomial
Character	$\chi$	$=$	187.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.27779 q^{2} +2.36616 q^{3} +10.2995 q^{4} -19.2230 q^{5} -10.1219 q^{6} +31.3553 q^{7} -9.83664 q^{8} -21.4013 q^{9} +82.2318 q^{10} +11.0000 q^{11} +24.3701 q^{12} +9.57258 q^{13} -134.131 q^{14} -45.4846 q^{15} -40.3167 q^{16} -17.0000 q^{17} +91.5503 q^{18} +63.4395 q^{19} -197.986 q^{20} +74.1916 q^{21} -47.0557 q^{22} +54.7491 q^{23} -23.2750 q^{24} +244.523 q^{25} -40.9495 q^{26} -114.525 q^{27} +322.943 q^{28} -269.083 q^{29} +194.573 q^{30} -284.119 q^{31} +251.159 q^{32} +26.0277 q^{33} +72.7224 q^{34} -602.743 q^{35} -220.422 q^{36} -31.1211 q^{37} -271.381 q^{38} +22.6502 q^{39} +189.090 q^{40} -435.326 q^{41} -317.376 q^{42} -521.820 q^{43} +113.294 q^{44} +411.397 q^{45} -234.205 q^{46} +291.633 q^{47} -95.3956 q^{48} +640.156 q^{49} -1046.02 q^{50} -40.2246 q^{51} +98.5925 q^{52} -213.400 q^{53} +489.914 q^{54} -211.453 q^{55} -308.431 q^{56} +150.108 q^{57} +1151.08 q^{58} -662.285 q^{59} -468.467 q^{60} -280.731 q^{61} +1215.40 q^{62} -671.045 q^{63} -751.873 q^{64} -184.013 q^{65} -111.341 q^{66} -714.408 q^{67} -175.091 q^{68} +129.545 q^{69} +2578.41 q^{70} +535.414 q^{71} +210.517 q^{72} +1233.31 q^{73} +133.130 q^{74} +578.579 q^{75} +653.393 q^{76} +344.909 q^{77} -96.8928 q^{78} -366.474 q^{79} +775.007 q^{80} +306.851 q^{81} +1862.23 q^{82} +536.211 q^{83} +764.134 q^{84} +326.791 q^{85} +2232.24 q^{86} -636.693 q^{87} -108.203 q^{88} -159.938 q^{89} -1759.87 q^{90} +300.151 q^{91} +563.887 q^{92} -672.270 q^{93} -1247.54 q^{94} -1219.50 q^{95} +594.282 q^{96} -979.902 q^{97} -2738.45 q^{98} -235.414 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 8 q^{2} - 9 q^{3} + 40 q^{4} - 41 q^{5} + 31 q^{6} - 63 q^{7} - 96 q^{8} + 61 q^{9} - 47 q^{10} + 110 q^{11} - 171 q^{12} - 99 q^{13} - 95 q^{14} - 150 q^{15} + 180 q^{16} - 170 q^{17} - 207 q^{18}+ \cdots + 671 q^{99}+O(q^{100}) $ 10 * q - 8 * q^2 - 9 * q^3 + 40 * q^4 - 41 * q^5 + 31 * q^6 - 63 * q^7 - 96 * q^8 + 61 * q^9 - 47 * q^10 + 110 * q^11 - 171 * q^12 - 99 * q^13 - 95 * q^14 - 150 * q^15 + 180 * q^16 - 170 * q^17 - 207 * q^18 - 73 * q^19 - 343 * q^20 - 152 * q^21 - 88 * q^22 - 58 * q^23 + 157 * q^24 + 529 * q^25 - 285 * q^26 - 246 * q^27 - 1031 * q^28 - 754 * q^29 - 754 * q^30 - 228 * q^31 - 466 * q^32 - 99 * q^33 + 136 * q^34 + 20 * q^35 - 535 * q^36 - 1177 * q^37 - 747 * q^38 - 791 * q^39 + 537 * q^40 - 327 * q^41 - 632 * q^42 - 487 * q^43 + 440 * q^44 - 834 * q^45 - 854 * q^46 - 573 * q^47 - 1857 * q^48 + 2215 * q^49 - 855 * q^50 + 153 * q^51 + 1673 * q^52 - 2022 * q^53 + 3572 * q^54 - 451 * q^55 + 1997 * q^56 - 1310 * q^57 + 4514 * q^58 - 602 * q^59 + 4936 * q^60 - 570 * q^61 + 166 * q^62 - 1903 * q^63 + 968 * q^64 - 2018 * q^65 + 341 * q^66 - 12 * q^67 - 680 * q^68 - 1034 * q^69 + 5460 * q^70 + 636 * q^71 - 2989 * q^72 - 201 * q^73 + 959 * q^74 + 3213 * q^75 + 6999 * q^76 - 693 * q^77 + 3669 * q^78 - 1097 * q^79 - 1409 * q^80 + 3554 * q^81 + 2249 * q^82 - 477 * q^83 + 8476 * q^84 + 697 * q^85 - 1271 * q^86 + 1782 * q^87 - 1056 * q^88 - 195 * q^89 + 3292 * q^90 - 1128 * q^91 - 2064 * q^92 - 2632 * q^93 + 465 * q^94 - 1644 * q^95 + 8367 * q^96 - 994 * q^97 + 225 * q^98 + 671 * 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 $

$2$	−4.27779	−1.51243	−0.756213	−	0.654325i	$-0.772953\pi$
$2$	−4.27779	−1.51243	−0.756213	+	0.654325i	$0.772953\pi$
$3$	2.36616	0.455367	0.227683	−	0.973735i	$-0.426885\pi$
$3$	2.36616	0.455367	0.227683	+	0.973735i	$0.426885\pi$
$4$	10.2995	1.28743
$5$	−19.2230	−1.71936	−0.859678	−	0.510837i	$-0.829336\pi$
$5$	−19.2230	−1.71936	−0.859678	+	0.510837i	$0.829336\pi$
$6$	−10.1219	−0.688709
$7$	31.3553	1.69303	0.846514	−	0.532366i	$-0.178697\pi$
$7$	31.3553	1.69303	0.846514	+	0.532366i	$0.178697\pi$
$8$	−9.83664	−0.434722
$9$	−21.4013	−0.792641
$10$	82.2318	2.60040
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	24.3701	0.586255
$13$	9.57258	0.204227	0.102114	−	0.994773i	$-0.467439\pi$
$13$	9.57258	0.204227	0.102114	+	0.994773i	$0.467439\pi$
$14$	−134.131	−2.56058
$15$	−45.4846	−0.782937
$16$	−40.3167	−0.629948
$17$	−17.0000	−0.242536
$17$	−17.0000	−0.242536
$18$	91.5503	1.19881
$19$	63.4395	0.766001	0.383001	−	0.923748i	$-0.374891\pi$
$19$	63.4395	0.766001	0.383001	+	0.923748i	$0.374891\pi$
$20$	−197.986	−2.21356
$21$	74.1916	0.770949
$22$	−47.0557	−0.456014
$23$	54.7491	0.496347	0.248174	−	0.968716i	$-0.420170\pi$
$23$	54.7491	0.496347	0.248174	+	0.968716i	$0.420170\pi$
$24$	−23.2750	−0.197958
$25$	244.523	1.95618
$26$	−40.9495	−0.308879
$27$	−114.525	−0.816309
$28$	322.943	2.17966
$29$	−269.083	−1.72302	−0.861508	−	0.507743i	$-0.830480\pi$
$29$	−269.083	−1.72302	−0.861508	+	0.507743i	$0.830480\pi$
$30$	194.573	1.18414
$31$	−284.119	−1.64611	−0.823053	−	0.567964i	$-0.807731\pi$
$31$	−284.119	−1.64611	−0.823053	+	0.567964i	$0.807731\pi$
$32$	251.159	1.38747
$33$	26.0277	0.137298
$34$	72.7224	0.366817
$35$	−602.743	−2.91092
$36$	−220.422	−1.02047
$37$	−31.1211	−0.138278	−0.0691390	−	0.997607i	$-0.522025\pi$
$37$	−31.1211	−0.138278	−0.0691390	+	0.997607i	$0.522025\pi$
$38$	−271.381	−1.15852
$39$	22.6502	0.0929983
$40$	189.090	0.747442
$41$	−435.326	−1.65821	−0.829104	−	0.559095i	$-0.811149\pi$
$41$	−435.326	−1.65821	−0.829104	+	0.559095i	$0.811149\pi$
$42$	−317.376	−1.16600
$43$	−521.820	−1.85062	−0.925312	−	0.379206i	$-0.876197\pi$
$43$	−521.820	−1.85062	−0.925312	+	0.379206i	$0.876197\pi$
$44$	113.294	0.388176
$45$	411.397	1.36283
$46$	−234.205	−0.750689
$47$	291.633	0.905085	0.452542	−	0.891743i	$-0.350517\pi$
$47$	291.633	0.905085	0.452542	+	0.891743i	$0.350517\pi$
$48$	−95.3956	−0.286858
$49$	640.156	1.86634
$50$	−1046.02	−2.95858
$51$	−40.2246	−0.110443
$52$	98.5925	0.262929
$53$	−213.400	−0.553071	−0.276536	−	0.961004i	$-0.589186\pi$
$53$	−213.400	−0.553071	−0.276536	+	0.961004i	$0.589186\pi$
$54$	489.914	1.23461
$55$	−211.453	−0.518405
$56$	−308.431	−0.735997
$57$	150.108	0.348811
$58$	1151.08	2.60594
$59$	−662.285	−1.46139	−0.730696	−	0.682703i	$-0.760804\pi$
$59$	−662.285	−1.46139	−0.730696	+	0.682703i	$0.760804\pi$
$60$	−468.467	−1.00798
$61$	−280.731	−0.589244	−0.294622	−	0.955614i	$-0.595194\pi$
$61$	−280.731	−0.589244	−0.294622	+	0.955614i	$0.595194\pi$
$62$	1215.40	2.48961
$63$	−671.045	−1.34196
$64$	−751.873	−1.46850
$65$	−184.013	−0.351139
$66$	−111.341	−0.207654
$67$	−714.408	−1.30267	−0.651334	−	0.758791i	$-0.725790\pi$
$67$	−714.408	−1.30267	−0.651334	+	0.758791i	$0.725790\pi$
$68$	−175.091	−0.312249
$69$	129.545	0.226020
$70$	2578.41	4.40255
$71$	535.414	0.894957	0.447478	−	0.894295i	$-0.352322\pi$
$71$	535.414	0.894957	0.447478	+	0.894295i	$0.352322\pi$
$72$	210.517	0.344579
$73$	1233.31	1.97738	0.988688	−	0.149986i	$-0.0479229\pi$
$73$	1233.31	1.97738	0.988688	+	0.149986i	$0.0479229\pi$
$74$	133.130	0.209135
$75$	578.579	0.890781
$76$	653.393	0.986176
$77$	344.909	0.510467
$78$	−96.8928	−0.140653
$79$	−366.474	−0.521918	−0.260959	−	0.965350i	$-0.584039\pi$
$79$	−366.474	−0.521918	−0.260959	+	0.965350i	$0.584039\pi$
$80$	775.007	1.08310
$81$	306.851	0.420921
$82$	1862.23	2.50792
$83$	536.211	0.709118	0.354559	−	0.935034i	$-0.384631\pi$
$83$	536.211	0.709118	0.354559	+	0.935034i	$0.384631\pi$
$84$	764.134	0.992546
$85$	326.791	0.417005
$86$	2232.24	2.79893
$87$	−636.693	−0.784605
$88$	−108.203	−0.131074
$89$	−159.938	−0.190487	−0.0952436	−	0.995454i	$-0.530363\pi$
$89$	−159.938	−0.190487	−0.0952436	+	0.995454i	$0.530363\pi$
$90$	−1759.87	−2.06118
$91$	300.151	0.345763
$92$	563.887	0.639014
$93$	−672.270	−0.749582
$94$	−1247.54	−1.36887
$95$	−1219.50	−1.31703
$96$	594.282	0.631809
$97$	−979.902	−1.02571	−0.512855	−	0.858475i	$-0.671412\pi$
$97$	−979.902	−1.02571	−0.512855	+	0.858475i	$0.671412\pi$
$98$	−2738.45	−2.82271
$99$	−235.414	−0.238990
$100$	2518.46	2.51846
$101$	665.028	0.655176	0.327588	−	0.944821i	$-0.393764\pi$
$101$	665.028	0.655176	0.327588	+	0.944821i	$0.393764\pi$
$102$	172.072	0.167036
$103$	−1147.02	−1.09728	−0.548639	−	0.836059i	$-0.684854\pi$
$103$	−1147.02	−1.09728	−0.548639	+	0.836059i	$0.684854\pi$
$104$	−94.1620	−0.0887821
$105$	−1426.18	−1.32554
$106$	912.881	0.836479
$107$	82.4252	0.0744705	0.0372352	−	0.999307i	$-0.488145\pi$
$107$	82.4252	0.0744705	0.0372352	+	0.999307i	$0.488145\pi$
$108$	−1179.55	−1.05094
$109$	637.329	0.560047	0.280023	−	0.959993i	$-0.409658\pi$
$109$	637.329	0.560047	0.280023	+	0.959993i	$0.409658\pi$
$110$	904.550	0.784050
$111$	−73.6375	−0.0629672
$112$	−1264.14	−1.06652
$113$	602.312	0.501422	0.250711	−	0.968062i	$-0.419336\pi$
$113$	602.312	0.501422	0.250711	+	0.968062i	$0.419336\pi$
$114$	−642.129	−0.527552
$115$	−1052.44	−0.853397
$116$	−2771.41	−2.21827
$117$	−204.866	−0.161879
$118$	2833.11	2.21025
$119$	−533.040	−0.410620
$120$	447.415	0.340360
$121$	121.000	0.0909091
$122$	1200.91	0.891188
$123$	−1030.05	−0.755093
$124$	−2926.28	−2.11925
$125$	−2297.59	−1.64402
$126$	2870.59	2.02962
$127$	−375.777	−0.262557	−0.131279	−	0.991346i	$-0.541908\pi$
$127$	−375.777	−0.262557	−0.131279	+	0.991346i	$0.541908\pi$
$128$	1207.08	0.833529
$129$	−1234.71	−0.842713
$130$	787.170	0.531072
$131$	420.274	0.280302	0.140151	−	0.990130i	$-0.455241\pi$
$131$	420.274	0.280302	0.140151	+	0.990130i	$0.455241\pi$
$132$	268.072	0.176762
$133$	1989.17	1.29686
$134$	3056.08	1.97019
$135$	2201.51	1.40353
$136$	167.223	0.105436
$137$	−822.546	−0.512955	−0.256478	−	0.966550i	$-0.582562\pi$
$137$	−822.546	−0.512955	−0.256478	+	0.966550i	$0.582562\pi$
$138$	−554.166	−0.341839
$139$	709.771	0.433108	0.216554	−	0.976271i	$-0.430518\pi$
$139$	709.771	0.433108	0.216554	+	0.976271i	$0.430518\pi$
$140$	−6207.93	−3.74761
$141$	690.048	0.412146
$142$	−2290.39	−1.35356
$143$	105.298	0.0615768
$144$	862.830	0.499323
$145$	5172.58	2.96248
$146$	−5275.85	−2.99064
$147$	1514.71	0.849871
$148$	−320.531	−0.178024
$149$	917.357	0.504381	0.252191	−	0.967678i	$-0.418849\pi$
$149$	917.357	0.504381	0.252191	+	0.967678i	$0.418849\pi$
$150$	−2475.04	−1.34724
$151$	−1948.37	−1.05004	−0.525021	−	0.851090i	$-0.675942\pi$
$151$	−1948.37	−1.05004	−0.525021	+	0.851090i	$0.675942\pi$
$152$	−624.032	−0.332998
$153$	363.822	0.192244
$154$	−1475.45	−0.772044
$155$	5461.62	2.83024
$156$	233.285	0.119729
$157$	−1393.18	−0.708203	−0.354101	−	0.935207i	$-0.615213\pi$
$157$	−1393.18	−0.708203	−0.354101	+	0.935207i	$0.615213\pi$
$158$	1567.70	0.789362
$159$	−504.938	−0.251850
$160$	−4828.03	−2.38556
$161$	1716.68	0.840330
$162$	−1312.64	−0.636612
$163$	1559.08	0.749180	0.374590	−	0.927191i	$-0.377784\pi$
$163$	1559.08	0.749180	0.374590	+	0.927191i	$0.377784\pi$
$164$	−4483.63	−2.13483
$165$	−500.330	−0.236065
$166$	−2293.80	−1.07249
$167$	−3146.52	−1.45800	−0.728998	−	0.684516i	$-0.760014\pi$
$167$	−3146.52	−1.45800	−0.728998	+	0.684516i	$0.760014\pi$
$168$	−729.796	−0.335149
$169$	−2105.37	−0.958291
$170$	−1397.94	−0.630689
$171$	−1357.69	−0.607164
$172$	−5374.47	−2.38256
$173$	−3719.03	−1.63441	−0.817205	−	0.576347i	$-0.804478\pi$
$173$	−3719.03	−1.63441	−0.817205	+	0.576347i	$0.804478\pi$
$174$	2723.64	1.18666
$175$	7667.09	3.31187
$176$	−443.484	−0.189937
$177$	−1567.07	−0.665469
$178$	684.179	0.288098
$179$	1495.57	0.624494	0.312247	−	0.950001i	$-0.398918\pi$
$179$	1495.57	0.624494	0.312247	+	0.950001i	$0.398918\pi$
$180$	4237.17	1.75456
$181$	492.669	0.202319	0.101160	−	0.994870i	$-0.467745\pi$
$181$	492.669	0.202319	0.101160	+	0.994870i	$0.467745\pi$
$182$	−1283.98	−0.522940
$183$	−664.253	−0.268322
$184$	−538.548	−0.215773
$185$	598.241	0.237749
$186$	2875.83	1.13369
$187$	−187.000	−0.0731272
$188$	3003.66	1.16524
$189$	−3590.97	−1.38203
$190$	5216.75	1.99191
$191$	1218.14	0.461473	0.230737	−	0.973016i	$-0.425886\pi$
$191$	1218.14	0.461473	0.230737	+	0.973016i	$0.425886\pi$
$192$	−1779.05	−0.668707
$193$	−639.615	−0.238552	−0.119276	−	0.992861i	$-0.538057\pi$
$193$	−639.615	−0.238552	−0.119276	+	0.992861i	$0.538057\pi$
$194$	4191.81	1.55131
$195$	−435.404	−0.159897
$196$	6593.27	2.40279
$197$	−2419.57	−0.875063	−0.437531	−	0.899203i	$-0.644147\pi$
$197$	−2419.57	−0.875063	−0.437531	+	0.899203i	$0.644147\pi$
$198$	1007.05	0.361455
$199$	2711.32	0.965830	0.482915	−	0.875667i	$-0.339578\pi$
$199$	2711.32	0.965830	0.482915	+	0.875667i	$0.339578\pi$
$200$	−2405.28	−0.850396
$201$	−1690.40	−0.593192
$202$	−2844.85	−0.990905
$203$	−8437.19	−2.91712
$204$	−414.292	−0.142188
$205$	8368.26	2.85105
$206$	4906.73	1.65955
$207$	−1171.70	−0.393425
$208$	−385.935	−0.128653
$209$	697.835	0.230958
$210$	6100.91	2.00477
$211$	824.475	0.269001	0.134500	−	0.990914i	$-0.457057\pi$
$211$	824.475	0.269001	0.134500	+	0.990914i	$0.457057\pi$
$212$	−2197.91	−0.712042
$213$	1266.87	0.407534
$214$	−352.597	−0.112631
$215$	10030.9	3.18188
$216$	1126.54	0.354868
$217$	−8908.65	−2.78690
$218$	−2726.36	−0.847029
$219$	2918.21	0.900432
$220$	−2177.85	−0.667412
$221$	−162.734	−0.0495324
$222$	315.005	0.0952333
$223$	2300.63	0.690859	0.345430	−	0.938445i	$-0.387733\pi$
$223$	2300.63	0.690859	0.345430	+	0.938445i	$0.387733\pi$
$224$	7875.18	2.34903
$225$	−5233.11	−1.55055
$226$	−2576.56	−0.758364
$227$	−4787.87	−1.39992	−0.699960	−	0.714182i	$-0.746799\pi$
$227$	−4787.87	−1.39992	−0.699960	+	0.714182i	$0.746799\pi$
$228$	1546.03	0.449072
$229$	−1918.32	−0.553564	−0.276782	−	0.960933i	$-0.589268\pi$
$229$	−1918.32	−0.553564	−0.276782	+	0.960933i	$0.589268\pi$
$230$	4502.12	1.29070
$231$	816.107	0.232450
$232$	2646.87	0.749034
$233$	−319.028	−0.0897006	−0.0448503	−	0.998994i	$-0.514281\pi$
$233$	−319.028	−0.0897006	−0.0448503	+	0.998994i	$0.514281\pi$
$234$	876.372	0.244830
$235$	−5606.05	−1.55616
$236$	−6821.18	−1.88145
$237$	−867.134	−0.237664
$238$	2280.23	0.621032
$239$	−813.866	−0.220270	−0.110135	−	0.993917i	$-0.535128\pi$
$239$	−813.866	−0.220270	−0.110135	+	0.993917i	$0.535128\pi$
$240$	1833.79	0.493210
$241$	−1970.26	−0.526620	−0.263310	−	0.964711i	$-0.584814\pi$
$241$	−1970.26	−0.526620	−0.263310	+	0.964711i	$0.584814\pi$
$242$	−517.612	−0.137493
$243$	3818.23	1.00798
$244$	−2891.38	−0.758613
$245$	−12305.7	−3.20891
$246$	4406.33	1.14202
$247$	607.279	0.156438
$248$	2794.78	0.715599
$249$	1268.76	0.322909
$250$	9828.58	2.48646
$251$	4130.76	1.03877	0.519386	−	0.854540i	$-0.326161\pi$
$251$	4130.76	1.03877	0.519386	+	0.854540i	$0.326161\pi$
$252$	−6911.41	−1.72769
$253$	602.241	0.149654
$254$	1607.49	0.397099
$255$	773.237	0.189890
$256$	851.359	0.207851
$257$	1742.43	0.422918	0.211459	−	0.977387i	$-0.432178\pi$
$257$	1742.43	0.422918	0.211459	+	0.977387i	$0.432178\pi$
$258$	5281.82	1.27454
$259$	−975.813	−0.234108
$260$	−1895.24	−0.452069
$261$	5758.73	1.36573
$262$	−1797.84	−0.423936
$263$	−2845.63	−0.667183	−0.333592	−	0.942718i	$-0.608261\pi$
$263$	−2845.63	−0.667183	−0.333592	+	0.942718i	$0.608261\pi$
$264$	−256.025	−0.0596866
$265$	4102.19	0.950926
$266$	−8509.23	−1.96141
$267$	−378.437	−0.0867415
$268$	−7358.02	−1.67710
$269$	1951.30	0.442277	0.221139	−	0.975242i	$-0.429023\pi$
$269$	1951.30	0.442277	0.221139	+	0.975242i	$0.429023\pi$
$270$	−9417.60	−2.12273
$271$	3004.76	0.673528	0.336764	−	0.941589i	$-0.390668\pi$
$271$	3004.76	0.673528	0.336764	+	0.941589i	$0.390668\pi$
$272$	685.384	0.152785
$273$	710.204	0.157449
$274$	3518.68	0.775807
$275$	2689.75	0.589811
$276$	1334.24	0.290986
$277$	2080.17	0.451211	0.225605	−	0.974219i	$-0.427564\pi$
$277$	2080.17	0.451211	0.225605	+	0.974219i	$0.427564\pi$
$278$	−3036.25	−0.655044
$279$	6080.52	1.30477
$280$	5928.96	1.26544
$281$	−1288.97	−0.273643	−0.136822	−	0.990596i	$-0.543689\pi$
$281$	−1288.97	−0.273643	−0.136822	+	0.990596i	$0.543689\pi$
$282$	−2951.88	−0.623340
$283$	3292.43	0.691571	0.345786	−	0.938314i	$-0.387612\pi$
$283$	3292.43	0.691571	0.345786	+	0.938314i	$0.387612\pi$
$284$	5514.48	1.15220
$285$	−2885.52	−0.599731
$286$	−450.444	−0.0931305
$287$	−13649.8	−2.80739
$288$	−5375.14	−1.09977
$289$	289.000	0.0588235
$290$	−22127.2	−4.48053
$291$	−2318.60	−0.467075
$292$	12702.5	2.54574
$293$	3409.31	0.679775	0.339887	−	0.940466i	$-0.389611\pi$
$293$	3409.31	0.679775	0.339887	+	0.940466i	$0.389611\pi$
$294$	−6479.60	−1.28537
$295$	12731.1	2.51265
$296$	306.128	0.0601125
$297$	−1259.78	−0.246127
$298$	−3924.26	−0.762840
$299$	524.090	0.101368
$300$	5959.06	1.14682
$301$	−16361.8	−3.13316
$302$	8334.72	1.58811
$303$	1573.56	0.298345
$304$	−2557.67	−0.482541
$305$	5396.48	1.01312
$306$	−1556.35	−0.290754
$307$	−6048.51	−1.12445	−0.562226	−	0.826984i	$-0.690055\pi$
$307$	−6048.51	−1.12445	−0.562226	+	0.826984i	$0.690055\pi$
$308$	3552.37	0.657193
$309$	−2714.04	−0.499664
$310$	−23363.6	−4.28053
$311$	−4320.03	−0.787673	−0.393837	−	0.919181i	$-0.628852\pi$
$311$	−4320.03	−0.787673	−0.393837	+	0.919181i	$0.628852\pi$
$312$	−222.802	−0.0404284
$313$	4330.89	0.782097	0.391049	−	0.920370i	$-0.372112\pi$
$313$	4330.89	0.782097	0.391049	+	0.920370i	$0.372112\pi$
$314$	5959.72	1.07110
$315$	12899.5	2.30731
$316$	−3774.48	−0.671935
$317$	2937.44	0.520452	0.260226	−	0.965548i	$-0.416203\pi$
$317$	2937.44	0.520452	0.260226	+	0.965548i	$0.416203\pi$
$318$	2160.02	0.380905
$319$	−2959.91	−0.519509
$320$	14453.2	2.52488
$321$	195.031	0.0339114
$322$	−7343.58	−1.27094
$323$	−1078.47	−0.185783
$324$	3160.41	0.541908
$325$	2340.71	0.399506
$326$	−6669.40	−1.13308
$327$	1508.02	0.255027
$328$	4282.15	0.720860
$329$	9144.23	1.53233
$330$	2140.31	0.357030
$331$	361.577	0.0600425	0.0300213	−	0.999549i	$-0.490443\pi$
$331$	361.577	0.0600425	0.0300213	+	0.999549i	$0.490443\pi$
$332$	5522.69	0.912943
$333$	666.033	0.109605
$334$	13460.2	2.20511
$335$	13733.0	2.23975
$336$	−2991.16	−0.485658
$337$	−104.623	−0.0169115	−0.00845576	−	0.999964i	$-0.502692\pi$
$337$	−104.623	−0.0169115	−0.00845576	+	0.999964i	$0.502692\pi$
$338$	9006.31	1.44934
$339$	1425.16	0.228331
$340$	3365.77	0.536866
$341$	−3125.31	−0.496320
$342$	5807.90	0.918291
$343$	9317.43	1.46675
$344$	5132.96	0.804508
$345$	−2490.24	−0.388609
$346$	15909.2	2.47192
$347$	−4014.72	−0.621099	−0.310550	−	0.950557i	$-0.600513\pi$
$347$	−4014.72	−0.621099	−0.310550	+	0.950557i	$0.600513\pi$
$348$	−6557.60	−1.01013
$349$	6529.95	1.00155	0.500774	−	0.865578i	$-0.333049\pi$
$349$	6529.95	1.00155	0.500774	+	0.865578i	$0.333049\pi$
$350$	−32798.2	−5.00896
$351$	−1096.30	−0.166713
$352$	2762.75	0.418339
$353$	11703.9	1.76469	0.882347	−	0.470599i	$-0.155962\pi$
$353$	11703.9	1.76469	0.882347	+	0.470599i	$0.155962\pi$
$354$	6703.59	1.00647
$355$	−10292.2	−1.53875
$356$	−1647.27	−0.245240
$357$	−1261.26	−0.186983
$358$	−6397.75	−0.944501
$359$	−1225.85	−0.180217	−0.0901084	−	0.995932i	$-0.528721\pi$
$359$	−1225.85	−0.180217	−0.0901084	+	0.995932i	$0.528721\pi$
$360$	−4046.76	−0.592453
$361$	−2834.43	−0.413242
$362$	−2107.53	−0.305993
$363$	286.305	0.0413970
$364$	3091.40	0.445146
$365$	−23708.0	−3.39981
$366$	2841.53	0.405818
$367$	6298.77	0.895894	0.447947	−	0.894060i	$-0.352155\pi$
$367$	6298.77	0.895894	0.447947	+	0.894060i	$0.352155\pi$
$368$	−2207.30	−0.312673
$369$	9316.55	1.31436
$370$	−2559.15	−0.359578
$371$	−6691.23	−0.936365
$372$	−6924.02	−0.965038
$373$	−302.467	−0.0419870	−0.0209935	−	0.999780i	$-0.506683\pi$
$373$	−302.467	−0.0419870	−0.0209935	+	0.999780i	$0.506683\pi$
$374$	799.946	0.110600
$375$	−5436.44	−0.748631
$376$	−2868.68	−0.393460
$377$	−2575.82	−0.351887
$378$	15361.4	2.09023
$379$	−10438.7	−1.41477	−0.707387	−	0.706826i	$-0.750126\pi$
$379$	−10438.7	−1.41477	−0.707387	+	0.706826i	$0.750126\pi$
$380$	−12560.2	−1.69559
$381$	−889.146	−0.119560
$382$	−5210.94	−0.697944
$383$	6429.05	0.857726	0.428863	−	0.903370i	$-0.358914\pi$
$383$	6429.05	0.857726	0.428863	+	0.903370i	$0.358914\pi$
$384$	2856.13	0.379561
$385$	−6630.17	−0.877675
$386$	2736.14	0.360792
$387$	11167.6	1.46688
$388$	−10092.5	−1.32053
$389$	8007.61	1.04371	0.521853	−	0.853035i	$-0.325241\pi$
$389$	8007.61	1.04371	0.521853	+	0.853035i	$0.325241\pi$
$390$	1862.57	0.241833
$391$	−930.735	−0.120382
$392$	−6296.99	−0.811341
$393$	994.435	0.127640
$394$	10350.4	1.32347
$395$	7044.72	0.897362
$396$	−2424.64	−0.307684
$397$	−13505.0	−1.70730	−0.853648	−	0.520851i	$-0.825615\pi$
$397$	−13505.0	−1.70730	−0.853648	+	0.520851i	$0.825615\pi$
$398$	−11598.4	−1.46075
$399$	4706.68	0.590548
$400$	−9858.35	−1.23229
$401$	11304.3	1.40775	0.703877	−	0.710322i	$-0.251451\pi$
$401$	11304.3	1.40775	0.703877	+	0.710322i	$0.251451\pi$
$402$	7231.17	0.897159
$403$	−2719.75	−0.336180
$404$	6849.43	0.843495
$405$	−5898.60	−0.723713
$406$	36092.5	4.41192
$407$	−342.333	−0.0416924
$408$	395.675	0.0480119
$409$	13859.0	1.67551	0.837757	−	0.546043i	$-0.183867\pi$
$409$	13859.0	1.67551	0.837757	+	0.546043i	$0.183867\pi$
$410$	−35797.6	−4.31200
$411$	−1946.27	−0.233583
$412$	−11813.7	−1.41267
$413$	−20766.2	−2.47418
$414$	5012.30	0.595027
$415$	−10307.6	−1.21923
$416$	2404.24	0.283360
$417$	1679.43	0.197223
$418$	−2985.19	−0.349307
$419$	−4739.28	−0.552575	−0.276287	−	0.961075i	$-0.589104\pi$
$419$	−4739.28	−0.552575	−0.276287	+	0.961075i	$0.589104\pi$
$420$	−14688.9	−1.70654
$421$	−10855.0	−1.25663	−0.628316	−	0.777958i	$-0.716256\pi$
$421$	−10855.0	−1.25663	−0.628316	+	0.777958i	$0.716256\pi$
$422$	−3526.93	−0.406844
$423$	−6241.32	−0.717407
$424$	2099.14	0.240432
$425$	−4156.89	−0.474444
$426$	−5419.41	−0.616365
$427$	−8802.40	−0.997607
$428$	848.935	0.0958758
$429$	249.152	0.0280401
$430$	−42910.2	−4.81236
$431$	7947.95	0.888259	0.444129	−	0.895963i	$-0.353513\pi$
$431$	7947.95	0.888259	0.444129	+	0.895963i	$0.353513\pi$
$432$	4617.27	0.514233
$433$	10532.1	1.16892	0.584459	−	0.811423i	$-0.301307\pi$
$433$	10532.1	1.16892	0.584459	+	0.811423i	$0.301307\pi$
$434$	38109.3	4.21499
$435$	12239.1	1.34901
$436$	6564.15	0.721023
$437$	3473.26	0.380202
$438$	−12483.5	−1.36184
$439$	−7274.01	−0.790819	−0.395409	−	0.918505i	$-0.629397\pi$
$439$	−7274.01	−0.790819	−0.395409	+	0.918505i	$0.629397\pi$
$440$	2079.98	0.225362
$441$	−13700.2	−1.47934
$442$	696.141	0.0749141
$443$	15150.8	1.62492	0.812458	−	0.583019i	$-0.198129\pi$
$443$	15150.8	1.62492	0.812458	+	0.583019i	$0.198129\pi$
$444$	−758.427	−0.0810661
$445$	3074.48	0.327515
$446$	−9841.61	−1.04487
$447$	2170.61	0.229678
$448$	−23575.2	−2.48622
$449$	1323.63	0.139122	0.0695612	−	0.997578i	$-0.477840\pi$
$449$	1323.63	0.139122	0.0695612	+	0.997578i	$0.477840\pi$
$450$	22386.1	2.34509
$451$	−4788.59	−0.499968
$452$	6203.49	0.645548
$453$	−4610.15	−0.478154
$454$	20481.5	2.11728
$455$	−5769.80	−0.594489
$456$	−1476.56	−0.151636
$457$	−2436.93	−0.249442	−0.124721	−	0.992192i	$-0.539804\pi$
$457$	−2436.93	−0.249442	−0.124721	+	0.992192i	$0.539804\pi$
$458$	8206.17	0.837225
$459$	1946.93	0.197984
$460$	−10839.6	−1.09869
$461$	−8748.14	−0.883821	−0.441911	−	0.897059i	$-0.645699\pi$
$461$	−8748.14	−0.883821	−0.441911	+	0.897059i	$0.645699\pi$
$462$	−3491.13	−0.351563
$463$	−7776.39	−0.780560	−0.390280	−	0.920696i	$-0.627622\pi$
$463$	−7776.39	−0.780560	−0.390280	+	0.920696i	$0.627622\pi$
$464$	10848.5	1.08541
$465$	12923.0	1.28880
$466$	1364.73	0.135665
$467$	4940.70	0.489568	0.244784	−	0.969578i	$-0.421283\pi$
$467$	4940.70	0.489568	0.244784	+	0.969578i	$0.421283\pi$
$468$	−2110.01	−0.208408
$469$	−22400.5	−2.20545
$470$	23981.5	2.35358
$471$	−3296.48	−0.322492
$472$	6514.66	0.635300
$473$	−5740.02	−0.557984
$474$	3709.41	0.359449
$475$	15512.4	1.49844
$476$	−5490.03	−0.528646
$477$	4567.04	0.438387
$478$	3481.54	0.333143
$479$	−14961.9	−1.42720	−0.713599	−	0.700554i	$-0.752936\pi$
$479$	−14961.9	−1.42720	−0.713599	+	0.700554i	$0.752936\pi$
$480$	−11423.9	−1.08630
$481$	−297.910	−0.0282401
$482$	8428.34	0.796473
$483$	4061.92	0.382658
$484$	1246.24	0.117039
$485$	18836.6	1.76356
$486$	−16333.6	−1.52450
$487$	1391.71	0.129495	0.0647477	−	0.997902i	$-0.479376\pi$
$487$	1391.71	0.129495	0.0647477	+	0.997902i	$0.479376\pi$
$488$	2761.45	0.256158
$489$	3689.02	0.341152
$490$	52641.2	4.85324
$491$	11733.9	1.07850	0.539249	−	0.842146i	$-0.318708\pi$
$491$	11733.9	1.07850	0.539249	+	0.842146i	$0.318708\pi$
$492$	−10609.0	−0.972132
$493$	4574.41	0.417893
$494$	−2597.81	−0.236601
$495$	4525.37	0.410909
$496$	11454.7	1.03696
$497$	16788.1	1.51519
$498$	−5427.48	−0.488376
$499$	−19284.7	−1.73007	−0.865034	−	0.501713i	$-0.832703\pi$
$499$	−19284.7	−1.73007	−0.865034	+	0.501713i	$0.832703\pi$
$500$	−23663.9	−2.11656
$501$	−7445.17	−0.663923
$502$	−17670.5	−1.57106
$503$	5487.36	0.486420	0.243210	−	0.969974i	$-0.421800\pi$
$503$	5487.36	0.486420	0.243210	+	0.969974i	$0.421800\pi$
$504$	6600.83	0.583381
$505$	−12783.8	−1.12648
$506$	−2576.26	−0.226341
$507$	−4981.62	−0.436374
$508$	−3870.30	−0.338025
$509$	−368.970	−0.0321303	−0.0160651	−	0.999871i	$-0.505114\pi$
$509$	−368.970	−0.0321303	−0.0160651	+	0.999871i	$0.505114\pi$
$510$	−3307.75	−0.287195
$511$	38671.0	3.34775
$512$	−13298.6	−1.14789
$513$	−7265.41	−0.625294
$514$	−7453.76	−0.639633
$515$	22049.2	1.88661
$516$	−12716.8	−1.08494
$517$	3207.96	0.272893
$518$	4174.32	0.354072
$519$	−8799.81	−0.744256
$520$	1810.07	0.152648
$521$	5539.84	0.465844	0.232922	−	0.972495i	$-0.425171\pi$
$521$	5539.84	0.465844	0.232922	+	0.972495i	$0.425171\pi$
$522$	−24634.6	−2.06557
$523$	13532.6	1.13143	0.565717	−	0.824600i	$-0.308600\pi$
$523$	13532.6	1.13143	0.565717	+	0.824600i	$0.308600\pi$
$524$	4328.60	0.360870
$525$	18141.5	1.50812
$526$	12173.0	1.00907
$527$	4830.03	0.399239
$528$	−1049.35	−0.0864908
$529$	−9169.53	−0.753639
$530$	−17548.3	−1.43821
$531$	14173.8	1.15836
$532$	20487.4	1.66962
$533$	−4167.19	−0.338651
$534$	1618.87	0.131190
$535$	−1584.46	−0.128041
$536$	7027.37	0.566299
$537$	3538.76	0.284374
$538$	−8347.23	−0.668912
$539$	7041.72	0.562724
$540$	22674.4	1.80695
$541$	−22756.5	−1.80846	−0.904231	−	0.427045i	$-0.859555\pi$
$541$	−22756.5	−1.80846	−0.904231	+	0.427045i	$0.859555\pi$
$542$	−12853.7	−1.01866
$543$	1165.73	0.0921295
$544$	−4269.71	−0.336512
$545$	−12251.4	−0.962919
$546$	−3038.10	−0.238130
$547$	−9579.40	−0.748785	−0.374393	−	0.927270i	$-0.622149\pi$
$547$	−9579.40	−0.748785	−0.374393	+	0.927270i	$0.622149\pi$
$548$	−8471.79	−0.660396
$549$	6008.01	0.467059
$550$	−11506.2	−0.892046
$551$	−17070.5	−1.31983
$552$	−1274.29	−0.0982559
$553$	−11490.9	−0.883622
$554$	−8898.53	−0.682423
$555$	1415.53	0.108263
$556$	7310.26	0.557598
$557$	7566.06	0.575555	0.287778	−	0.957697i	$-0.407084\pi$
$557$	7566.06	0.575555	0.287778	+	0.957697i	$0.407084\pi$
$558$	−26011.2	−1.97337
$559$	−4995.16	−0.377948
$560$	24300.6	1.83373
$561$	−442.471	−0.0332997
$562$	5513.96	0.413865
$563$	−448.746	−0.0335922	−0.0167961	−	0.999859i	$-0.505347\pi$
$563$	−448.746	−0.0335922	−0.0167961	+	0.999859i	$0.505347\pi$
$564$	7107.13	0.530610
$565$	−11578.2	−0.862123
$566$	−14084.3	−1.04595
$567$	9621.42	0.712631
$568$	−5266.67	−0.389058
$569$	20307.4	1.49619	0.748095	−	0.663592i	$-0.230969\pi$
$569$	20307.4	1.49619	0.748095	+	0.663592i	$0.230969\pi$
$570$	12343.6	0.907049
$571$	−20122.7	−1.47479	−0.737397	−	0.675460i	$-0.763945\pi$
$571$	−20122.7	−1.47479	−0.737397	+	0.675460i	$0.763945\pi$
$572$	1084.52	0.0792761
$573$	2882.30	0.210140
$574$	58390.9	4.24597
$575$	13387.4	0.970946
$576$	16091.1	1.16399
$577$	4031.89	0.290901	0.145450	−	0.989366i	$-0.453537\pi$
$577$	4031.89	0.290901	0.145450	+	0.989366i	$0.453537\pi$
$578$	−1236.28	−0.0889663
$579$	−1513.43	−0.108628
$580$	53274.8	3.81399
$581$	16813.1	1.20056
$582$	9918.48	0.706416
$583$	−2347.40	−0.166757
$584$	−12131.7	−0.859609
$585$	3938.13	0.278327
$586$	−14584.3	−1.02811
$587$	−11047.0	−0.776758	−0.388379	−	0.921500i	$-0.626965\pi$
$587$	−11047.0	−0.776758	−0.388379	+	0.921500i	$0.626965\pi$
$588$	15600.7	1.09415
$589$	−18024.4	−1.26092
$590$	−54460.9	−3.80020
$591$	−5725.08	−0.398475
$592$	1254.70	0.0871080
$593$	22153.4	1.53412	0.767058	−	0.641578i	$-0.221720\pi$
$593$	22153.4	1.53412	0.767058	+	0.641578i	$0.221720\pi$
$594$	5389.05	0.372248
$595$	10246.6	0.706001
$596$	9448.29	0.649357
$597$	6415.40	0.439807
$598$	−2241.95	−0.153311
$599$	2802.41	0.191158	0.0955789	−	0.995422i	$-0.469530\pi$
$599$	2802.41	0.191158	0.0955789	+	0.995422i	$0.469530\pi$
$600$	−5691.28	−0.387242
$601$	5827.74	0.395538	0.197769	−	0.980249i	$-0.436630\pi$
$601$	5827.74	0.395538	0.197769	+	0.980249i	$0.436630\pi$
$602$	69992.5	4.73867
$603$	15289.3	1.03255
$604$	−20067.2	−1.35186
$605$	−2325.98	−0.156305
$606$	−6731.35	−0.451225
$607$	−8011.25	−0.535694	−0.267847	−	0.963461i	$-0.586312\pi$
$607$	−8011.25	−0.535694	−0.267847	+	0.963461i	$0.586312\pi$
$608$	15933.4	1.06281
$609$	−19963.7	−1.32836
$610$	−23085.0	−1.53227
$611$	2791.67	0.184843
$612$	3747.18	0.247501
$613$	−3144.06	−0.207158	−0.103579	−	0.994621i	$-0.533029\pi$
$613$	−3144.06	−0.207158	−0.103579	+	0.994621i	$0.533029\pi$
$614$	25874.2	1.70065
$615$	19800.6	1.29827
$616$	−3392.74	−0.221911
$617$	−10624.4	−0.693229	−0.346614	−	0.938008i	$-0.612669\pi$
$617$	−10624.4	−0.693229	−0.346614	+	0.938008i	$0.612669\pi$
$618$	11610.1	0.755706
$619$	7215.39	0.468516	0.234258	−	0.972175i	$-0.424734\pi$
$619$	7215.39	0.468516	0.234258	+	0.972175i	$0.424734\pi$
$620$	56251.7	3.64375
$621$	−6270.15	−0.405173
$622$	18480.2	1.19130
$623$	−5014.90	−0.322500
$624$	−913.181	−0.0585841
$625$	13601.1	0.870469
$626$	−18526.6	−1.18286
$627$	1651.19	0.105171
$628$	−14349.0	−0.911764
$629$	529.059	0.0335373
$630$	−55181.2	−3.48964
$631$	−8366.27	−0.527823	−0.263911	−	0.964547i	$-0.585013\pi$
$631$	−8366.27	−0.527823	−0.263911	+	0.964547i	$0.585013\pi$
$632$	3604.87	0.226889
$633$	1950.84	0.122494
$634$	−12565.8	−0.787145
$635$	7223.55	0.451429
$636$	−5200.59	−0.324240
$637$	6127.94	0.381159
$638$	12661.9	0.785719
$639$	−11458.6	−0.709379
$640$	−23203.6	−1.43313
$641$	2949.21	0.181727	0.0908633	−	0.995863i	$-0.471037\pi$
$641$	2949.21	0.181727	0.0908633	+	0.995863i	$0.471037\pi$
$642$	−834.300	−0.0512885
$643$	2173.33	0.133294	0.0666469	−	0.997777i	$-0.478770\pi$
$643$	2173.33	0.133294	0.0666469	+	0.997777i	$0.478770\pi$
$644$	17680.9	1.08187
$645$	23734.8	1.44892
$646$	4613.47	0.280982
$647$	−7493.45	−0.455329	−0.227664	−	0.973740i	$-0.573109\pi$
$647$	−7493.45	−0.455329	−0.227664	+	0.973740i	$0.573109\pi$
$648$	−3018.39	−0.182984
$649$	−7285.13	−0.440626
$650$	−10013.1	−0.604223
$651$	−21079.2	−1.26906
$652$	16057.7	0.964519
$653$	12606.2	0.755464	0.377732	−	0.925915i	$-0.376704\pi$
$653$	12606.2	0.755464	0.377732	+	0.925915i	$0.376704\pi$
$654$	−6450.99	−0.385709
$655$	−8078.93	−0.481939
$656$	17550.9	1.04458
$657$	−26394.5	−1.56735
$658$	−39117.1	−2.31754
$659$	−1850.16	−0.109366	−0.0546829	−	0.998504i	$-0.517415\pi$
$659$	−1850.16	−0.109366	−0.0546829	+	0.998504i	$0.517415\pi$
$660$	−5153.13	−0.303917
$661$	1824.25	0.107345	0.0536725	−	0.998559i	$-0.482907\pi$
$661$	1824.25	0.107345	0.0536725	+	0.998559i	$0.482907\pi$
$662$	−1546.75	−0.0908099
$663$	−385.053	−0.0225554
$664$	−5274.52	−0.308269
$665$	−38237.7	−2.22977
$666$	−2849.15	−0.165769
$667$	−14732.1	−0.855214
$668$	−32407.5	−1.87707
$669$	5443.65	0.314594
$670$	−58747.0	−3.38746
$671$	−3088.04	−0.177664
$672$	18633.9	1.06967
$673$	24526.8	1.40481	0.702407	−	0.711775i	$-0.252109\pi$
$673$	24526.8	1.40481	0.702407	+	0.711775i	$0.252109\pi$
$674$	447.556	0.0255774
$675$	−28004.0	−1.59685
$676$	−21684.1	−1.23374
$677$	−1416.13	−0.0803933	−0.0401966	−	0.999192i	$-0.512798\pi$
$677$	−1416.13	−0.0803933	−0.0401966	+	0.999192i	$0.512798\pi$
$678$	−6096.55	−0.345334
$679$	−30725.1	−1.73656
$680$	−3214.52	−0.181281
$681$	−11328.8	−0.637478
$682$	13369.4	0.750647
$683$	−7548.58	−0.422896	−0.211448	−	0.977389i	$-0.567818\pi$
$683$	−7548.58	−0.422896	−0.211448	+	0.977389i	$0.567818\pi$
$684$	−13983.5	−0.781683
$685$	15811.8	0.881952
$686$	−39858.0	−2.21834
$687$	−4539.04	−0.252075
$688$	21038.1	1.16580
$689$	−2042.79	−0.112952
$690$	10652.7	0.587742
$691$	31187.4	1.71697	0.858484	−	0.512840i	$-0.171407\pi$
$691$	31187.4	1.71697	0.858484	+	0.512840i	$0.171407\pi$
$692$	−38304.1	−2.10419
$693$	−7381.49	−0.404617
$694$	17174.1	0.939367
$695$	−13643.9	−0.744666
$696$	6262.92	0.341085
$697$	7400.54	0.402174
$698$	−27933.8	−1.51477
$699$	−754.870	−0.0408467
$700$	78967.0	4.26382
$701$	−29758.7	−1.60338	−0.801691	−	0.597739i	$-0.796066\pi$
$701$	−29758.7	−1.60338	−0.801691	+	0.597739i	$0.796066\pi$
$702$	4689.74	0.252141
$703$	−1974.31	−0.105921
$704$	−8270.60	−0.442770
$705$	−13264.8	−0.708625
$706$	−50066.9	−2.66897
$707$	20852.2	1.10923
$708$	−16140.0	−0.856748
$709$	31626.1	1.67524	0.837618	−	0.546257i	$-0.183948\pi$
$709$	31626.1	1.67524	0.837618	+	0.546257i	$0.183948\pi$
$710$	44028.1	2.32724
$711$	7843.02	0.413693
$712$	1573.25	0.0828090
$713$	−15555.3	−0.817040
$714$	5395.39	0.282797
$715$	−2024.15	−0.105872
$716$	15403.6	0.803995
$717$	−1925.73	−0.100304
$718$	5243.92	0.272565
$719$	−10826.3	−0.561550	−0.280775	−	0.959774i	$-0.590592\pi$
$719$	−10826.3	−0.561550	−0.280775	+	0.959774i	$0.590592\pi$
$720$	−16586.2	−0.858513
$721$	−35965.3	−1.85772
$722$	12125.1	0.624999
$723$	−4661.93	−0.239805
$724$	5074.23	0.260473
$725$	−65797.0	−3.37054
$726$	−1224.75	−0.0626099
$727$	9452.05	0.482197	0.241098	−	0.970501i	$-0.422492\pi$
$727$	9452.05	0.482197	0.241098	+	0.970501i	$0.422492\pi$
$728$	−2952.48	−0.150311
$729$	749.549	0.0380810
$730$	101418.	5.14197
$731$	8870.94	0.448842
$732$	−6841.45	−0.345447
$733$	−24006.9	−1.20971	−0.604854	−	0.796337i	$-0.706768\pi$
$733$	−24006.9	−1.20971	−0.604854	+	0.796337i	$0.706768\pi$
$734$	−26944.8	−1.35497
$735$	−29117.2	−1.46123
$736$	13750.8	0.688668
$737$	−7858.48	−0.392769
$738$	−39854.2	−1.98788
$739$	26667.0	1.32742	0.663709	−	0.747990i	$-0.268981\pi$
$739$	26667.0	1.32742	0.663709	+	0.747990i	$0.268981\pi$
$740$	6161.57	0.306086
$741$	1436.92	0.0712368
$742$	28623.7	1.41618
$743$	2551.64	0.125990	0.0629950	−	0.998014i	$-0.479935\pi$
$743$	2551.64	0.125990	0.0629950	+	0.998014i	$0.479935\pi$
$744$	6612.88	0.325860
$745$	−17634.3	−0.867211
$746$	1293.89	0.0635023
$747$	−11475.6	−0.562076
$748$	−1926.00	−0.0941465
$749$	2584.47	0.126081
$750$	23256.0	1.13225
$751$	30066.8	1.46092	0.730462	−	0.682953i	$-0.239305\pi$
$751$	30066.8	1.46092	0.730462	+	0.682953i	$0.239305\pi$
$752$	−11757.7	−0.570157
$753$	9774.03	0.473022
$754$	11018.8	0.532203
$755$	37453.5	1.80539
$756$	−36985.1	−1.77928
$757$	5853.78	0.281056	0.140528	−	0.990077i	$-0.455120\pi$
$757$	5853.78	0.281056	0.140528	+	0.990077i	$0.455120\pi$
$758$	44654.5	2.13974
$759$	1424.99	0.0681476
$760$	11995.7	0.572541
$761$	−2342.76	−0.111596	−0.0557982	−	0.998442i	$-0.517770\pi$
$761$	−2342.76	−0.111596	−0.0557982	+	0.998442i	$0.517770\pi$
$762$	3803.58	0.180826
$763$	19983.7	0.948175
$764$	12546.2	0.594116
$765$	−6993.75	−0.330535
$766$	−27502.1	−1.29725
$767$	−6339.77	−0.298456
$768$	2014.45	0.0946486
$769$	40493.5	1.89887	0.949437	−	0.313957i	$-0.101655\pi$
$769$	40493.5	1.89887	0.949437	+	0.313957i	$0.101655\pi$
$770$	28362.5	1.32742
$771$	4122.87	0.192583
$772$	−6587.69	−0.307119
$773$	−35472.5	−1.65053	−0.825264	−	0.564747i	$-0.808974\pi$
$773$	−35472.5	−1.65053	−0.825264	+	0.564747i	$0.808974\pi$
$774$	−47772.8	−2.21855
$775$	−69473.6	−3.22009
$776$	9638.94	0.445899
$777$	−2308.93	−0.106605
$778$	−34254.8	−1.57853
$779$	−27616.9	−1.27019
$780$	−4484.43	−0.205857
$781$	5889.55	0.269840
$782$	3981.49	0.182069
$783$	30816.8	1.40651
$784$	−25809.0	−1.17570
$785$	26781.1	1.21765
$786$	−4253.98	−0.193046
$787$	43218.2	1.95751	0.978757	−	0.205025i	$-0.0657277\pi$
$787$	43218.2	1.95751	0.978757	+	0.205025i	$0.0657277\pi$
$788$	−24920.3	−1.12659
$789$	−6733.21	−0.303813
$790$	−30135.8	−1.35719
$791$	18885.7	0.848922
$792$	2315.69	0.103894
$793$	−2687.32	−0.120340
$794$	57771.5	2.58216
$795$	9706.41	0.433020
$796$	27925.1	1.24344
$797$	−36326.6	−1.61450	−0.807249	−	0.590211i	$-0.799044\pi$
$797$	−36326.6	−1.61450	−0.807249	+	0.590211i	$0.799044\pi$
$798$	−20134.2	−0.893160
$799$	−4957.75	−0.219515
$800$	61414.2	2.71415
$801$	3422.87	0.150988
$802$	−48357.4	−2.12912
$803$	13566.5	0.596201
$804$	−17410.2	−0.763695
$805$	−32999.6	−1.44483
$806$	11634.5	0.508447
$807$	4617.07	0.201398
$808$	−6541.64	−0.284819
$809$	−30002.5	−1.30387	−0.651935	−	0.758275i	$-0.726042\pi$
$809$	−30002.5	−1.30387	−0.651935	+	0.758275i	$0.726042\pi$
$810$	25232.9	1.09456
$811$	−44880.2	−1.94323	−0.971613	−	0.236575i	$-0.923975\pi$
$811$	−44880.2	−1.94323	−0.971613	+	0.236575i	$0.923975\pi$
$812$	−86898.6	−3.75559
$813$	7109.73	0.306702
$814$	1464.43	0.0630566
$815$	−29970.1	−1.28811
$816$	1621.72	0.0695732
$817$	−33104.0	−1.41758
$818$	−59286.0	−2.53409
$819$	−6423.63	−0.274066
$820$	86188.7	3.67053
$821$	3476.58	0.147788	0.0738938	−	0.997266i	$-0.476457\pi$
$821$	3476.58	0.147788	0.0738938	+	0.997266i	$0.476457\pi$
$822$	8325.74	0.353277
$823$	−19017.8	−0.805489	−0.402745	−	0.915312i	$-0.631944\pi$
$823$	−19017.8	−0.805489	−0.402745	+	0.915312i	$0.631944\pi$
$824$	11282.9	0.477011
$825$	6364.37	0.268581
$826$	88833.2	3.74201
$827$	4177.49	0.175654	0.0878269	−	0.996136i	$-0.472008\pi$
$827$	4177.49	0.175654	0.0878269	+	0.996136i	$0.472008\pi$
$828$	−12067.9	−0.506509
$829$	3643.41	0.152643	0.0763215	−	0.997083i	$-0.475682\pi$
$829$	3643.41	0.152643	0.0763215	+	0.997083i	$0.475682\pi$
$830$	44093.6	1.84399
$831$	4922.01	0.205466
$832$	−7197.36	−0.299908
$833$	−10882.7	−0.452655
$834$	−7184.24	−0.298285
$835$	60485.6	2.50681
$836$	7187.33	0.297343
$837$	32538.7	1.34373
$838$	20273.6	0.835729
$839$	25975.8	1.06887	0.534437	−	0.845208i	$-0.320524\pi$
$839$	25975.8	1.06887	0.534437	+	0.845208i	$0.320524\pi$
$840$	14028.8	0.576240
$841$	48016.7	1.96879
$842$	46435.5	1.90056
$843$	−3049.91	−0.124608
$844$	8491.66	0.346321
$845$	40471.4	1.64764
$846$	26699.0	1.08503
$847$	3793.99	0.153912
$848$	8603.59	0.348406
$849$	7790.40	0.314919
$850$	17782.3	0.717562
$851$	−1703.86	−0.0686339
$852$	13048.1	0.524672
$853$	−14464.1	−0.580586	−0.290293	−	0.956938i	$-0.593753\pi$
$853$	−14464.1	−0.580586	−0.290293	+	0.956938i	$0.593753\pi$
$854$	37654.8	1.50881
$855$	26098.8	1.04393
$856$	−810.787	−0.0323740
$857$	24320.5	0.969395	0.484697	−	0.874682i	$-0.338930\pi$
$857$	24320.5	0.969395	0.484697	+	0.874682i	$0.338930\pi$
$858$	−1065.82	−0.0424085
$859$	−17007.9	−0.675553	−0.337777	−	0.941226i	$-0.609675\pi$
$859$	−17007.9	−0.675553	−0.337777	+	0.941226i	$0.609675\pi$
$860$	103313.	4.09646
$861$	−32297.5	−1.27839
$862$	−33999.7	−1.34343
$863$	5113.63	0.201703	0.100852	−	0.994901i	$-0.467843\pi$
$863$	5113.63	0.201703	0.100852	+	0.994901i	$0.467843\pi$
$864$	−28764.0	−1.13261
$865$	71490.9	2.81013
$866$	−45054.2	−1.76790
$867$	683.819	0.0267863
$868$	−91754.3	−3.58795
$869$	−4031.21	−0.157364
$870$	−52356.4	−2.04028
$871$	−6838.72	−0.266040
$872$	−6269.18	−0.243465
$873$	20971.2	0.813020
$874$	−14857.9	−0.575028
$875$	−72041.5	−2.78337
$876$	30056.0	1.15925
$877$	−6992.34	−0.269230	−0.134615	−	0.990898i	$-0.542980\pi$
$877$	−6992.34	−0.269230	−0.134615	+	0.990898i	$0.542980\pi$
$878$	31116.7	1.19605
$879$	8066.96	0.309547
$880$	8525.07	0.326568
$881$	15036.1	0.575006	0.287503	−	0.957780i	$-0.407175\pi$
$881$	15036.1	0.575006	0.287503	+	0.957780i	$0.407175\pi$
$882$	58606.5	2.23739
$883$	19340.5	0.737102	0.368551	−	0.929608i	$-0.379854\pi$
$883$	19340.5	0.737102	0.368551	+	0.929608i	$0.379854\pi$
$884$	−1676.07	−0.0637697
$885$	30123.7	1.14418
$886$	−64812.1	−2.45757
$887$	−52364.7	−1.98223	−0.991113	−	0.133021i	$-0.957532\pi$
$887$	−52364.7	−1.98223	−0.991113	+	0.133021i	$0.957532\pi$
$888$	724.345	0.0273732
$889$	−11782.6	−0.444517
$890$	−13152.0	−0.495343
$891$	3375.36	0.126912
$892$	23695.3	0.889436
$893$	18501.0	0.693296
$894$	−9285.41	−0.347372
$895$	−28749.4	−1.07373
$896$	37848.3	1.41119
$897$	1240.08	0.0461595
$898$	−5662.21	−0.210413
$899$	76451.7	2.83627
$900$	−53898.2	−1.99623
$901$	3627.80	0.134139
$902$	20484.6	0.756165
$903$	−38714.7	−1.42674
$904$	−5924.72	−0.217979
$905$	−9470.57	−0.347859
$906$	19721.2	0.723173
$907$	−29867.5	−1.09342	−0.546712	−	0.837321i	$-0.684121\pi$
$907$	−29867.5	−1.09342	−0.546712	+	0.837321i	$0.684121\pi$
$908$	−49312.5	−1.80231
$909$	−14232.5	−0.519319
$910$	24682.0	0.899121
$911$	−36681.6	−1.33405	−0.667023	−	0.745037i	$-0.732432\pi$
$911$	−36681.6	−1.33405	−0.667023	+	0.745037i	$0.732432\pi$
$912$	−6051.85	−0.219733
$913$	5898.32	0.213807
$914$	10424.7	0.377262
$915$	12768.9	0.461341
$916$	−19757.7	−0.712677
$917$	13177.8	0.474559
$918$	−8328.53	−0.299436
$919$	−676.538	−0.0242839	−0.0121420	−	0.999926i	$-0.503865\pi$
$919$	−676.538	−0.0242839	−0.0121420	+	0.999926i	$0.503865\pi$
$920$	10352.5	0.370991
$921$	−14311.7	−0.512038
$922$	37422.7	1.33671
$923$	5125.29	0.182775
$924$	8405.47	0.299264
$925$	−7609.83	−0.270497
$926$	33265.7	1.18054
$927$	24547.8	0.869748
$928$	−67582.7	−2.39064
$929$	−38793.7	−1.37005	−0.685027	−	0.728518i	$-0.740210\pi$
$929$	−38793.7	−1.37005	−0.685027	+	0.728518i	$0.740210\pi$
$930$	−55282.0	−1.94921
$931$	40611.2	1.42962
$932$	−3285.82	−0.115484
$933$	−10221.9	−0.358680
$934$	−21135.3	−0.740436
$935$	3594.70	0.125732
$936$	2015.19	0.0703724
$937$	13087.1	0.456281	0.228141	−	0.973628i	$-0.426735\pi$
$937$	13087.1	0.456281	0.228141	+	0.973628i	$0.426735\pi$
$938$	95824.5	3.33559
$939$	10247.6	0.356141
$940$	−57739.3	−2.00346
$941$	−24931.5	−0.863703	−0.431852	−	0.901945i	$-0.642140\pi$
$941$	−24931.5	−0.863703	−0.431852	+	0.901945i	$0.642140\pi$
$942$	14101.6	0.487745
$943$	−23833.7	−0.823046
$944$	26701.1	0.920601
$945$	69029.1	2.37621
$946$	24554.6	0.843910
$947$	18201.9	0.624587	0.312293	−	0.949986i	$-0.398903\pi$
$947$	18201.9	0.624587	0.312293	+	0.949986i	$0.398903\pi$
$948$	−8931.02	−0.305977
$949$	11806.0	0.403834
$950$	−66358.8	−2.26628
$951$	6950.45	0.236997
$952$	5243.33	0.178505
$953$	23365.4	0.794208	0.397104	−	0.917774i	$-0.370015\pi$
$953$	23365.4	0.794208	0.397104	+	0.917774i	$0.370015\pi$
$954$	−19536.8	−0.663028
$955$	−23416.2	−0.793436
$956$	−8382.38	−0.283583
$957$	−7003.62	−0.236567
$958$	64004.0	2.15853
$959$	−25791.2	−0.868447
$960$	34198.6	1.14975
$961$	50932.7	1.70967
$962$	1274.39	0.0427111
$963$	−1764.01	−0.0590284
$964$	−20292.6	−0.677988
$965$	12295.3	0.410155
$966$	−17376.1	−0.578743
$967$	−54197.2	−1.80234	−0.901170	−	0.433465i	$-0.857291\pi$
$967$	−54197.2	−1.80234	−0.901170	+	0.433465i	$0.857291\pi$
$968$	−1190.23	−0.0395202
$969$	−2551.83	−0.0845992
$970$	−80579.1	−2.66726
$971$	−52126.5	−1.72278	−0.861391	−	0.507943i	$-0.830406\pi$
$971$	−52126.5	−1.72278	−0.861391	+	0.507943i	$0.830406\pi$
$972$	39325.8	1.29771
$973$	22255.1	0.733264
$974$	−5953.43	−0.195852
$975$	5538.49	0.181922
$976$	11318.1	0.371193
$977$	−8648.15	−0.283192	−0.141596	−	0.989925i	$-0.545223\pi$
$977$	−8648.15	−0.283192	−0.141596	+	0.989925i	$0.545223\pi$
$978$	−15780.8	−0.515967
$979$	−1759.31	−0.0574340
$980$	−126742.	−4.13126
$981$	−13639.7	−0.443916
$982$	−50195.1	−1.63115
$983$	7430.21	0.241085	0.120543	−	0.992708i	$-0.461537\pi$
$983$	7430.21	0.241085	0.120543	+	0.992708i	$0.461537\pi$
$984$	10132.2	0.328256
$985$	46511.4	1.50454
$986$	−19568.4	−0.632032
$987$	21636.7	0.697774
$988$	6254.66	0.201404
$989$	−28569.2	−0.918552
$990$	−19358.6	−0.621470
$991$	19080.2	0.611608	0.305804	−	0.952094i	$-0.401075\pi$
$991$	19080.2	0.611608	0.305804	+	0.952094i	$0.401075\pi$
$992$	−71359.2	−2.28393
$993$	855.547	0.0273414
$994$	−71815.8	−2.29161
$995$	−52119.6	−1.66061
$996$	13067.5	0.415724
$997$	16879.5	0.536189	0.268095	−	0.963393i	$-0.413606\pi$
$997$	16879.5	0.536189	0.268095	+	0.963393i	$0.413606\pi$
$998$	82496.1	2.61660
$999$	3564.15	0.112878

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.4.a.d.1.3	✓	10
3.2	odd	2		1683.4.a.m.1.8		10
11.10	odd	2		2057.4.a.i.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.4.a.d.1.3	✓	10	1.1	even	1	trivial
1683.4.a.m.1.8		10	3.2	odd	2
2057.4.a.i.1.8		10	11.10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	187.a (trivial)

\(f(q)\)	\(=\)	\(q-4.27779 q^{2} +2.36616 q^{3} +10.2995 q^{4} -19.2230 q^{5} -10.1219 q^{6} +31.3553 q^{7} -9.83664 q^{8} -21.4013 q^{9} +82.2318 q^{10} +11.0000 q^{11} +24.3701 q^{12} +9.57258 q^{13} -134.131 q^{14} -45.4846 q^{15} -40.3167 q^{16} -17.0000 q^{17} +91.5503 q^{18} +63.4395 q^{19} -197.986 q^{20} +74.1916 q^{21} -47.0557 q^{22} +54.7491 q^{23} -23.2750 q^{24} +244.523 q^{25} -40.9495 q^{26} -114.525 q^{27} +322.943 q^{28} -269.083 q^{29} +194.573 q^{30} -284.119 q^{31} +251.159 q^{32} +26.0277 q^{33} +72.7224 q^{34} -602.743 q^{35} -220.422 q^{36} -31.1211 q^{37} -271.381 q^{38} +22.6502 q^{39} +189.090 q^{40} -435.326 q^{41} -317.376 q^{42} -521.820 q^{43} +113.294 q^{44} +411.397 q^{45} -234.205 q^{46} +291.633 q^{47} -95.3956 q^{48} +640.156 q^{49} -1046.02 q^{50} -40.2246 q^{51} +98.5925 q^{52} -213.400 q^{53} +489.914 q^{54} -211.453 q^{55} -308.431 q^{56} +150.108 q^{57} +1151.08 q^{58} -662.285 q^{59} -468.467 q^{60} -280.731 q^{61} +1215.40 q^{62} -671.045 q^{63} -751.873 q^{64} -184.013 q^{65} -111.341 q^{66} -714.408 q^{67} -175.091 q^{68} +129.545 q^{69} +2578.41 q^{70} +535.414 q^{71} +210.517 q^{72} +1233.31 q^{73} +133.130 q^{74} +578.579 q^{75} +653.393 q^{76} +344.909 q^{77} -96.8928 q^{78} -366.474 q^{79} +775.007 q^{80} +306.851 q^{81} +1862.23 q^{82} +536.211 q^{83} +764.134 q^{84} +326.791 q^{85} +2232.24 q^{86} -636.693 q^{87} -108.203 q^{88} -159.938 q^{89} -1759.87 q^{90} +300.151 q^{91} +563.887 q^{92} -672.270 q^{93} -1247.54 q^{94} -1219.50 q^{95} +594.282 q^{96} -979.902 q^{97} -2738.45 q^{98} -235.414 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 8 q^{2} - 9 q^{3} + 40 q^{4} - 41 q^{5} + 31 q^{6} - 63 q^{7} - 96 q^{8} + 61 q^{9} - 47 q^{10} + 110 q^{11} - 171 q^{12} - 99 q^{13} - 95 q^{14} - 150 q^{15} + 180 q^{16} - 170 q^{17} - 207 q^{18}+ \cdots + 671 q^{99}+O(q^{100}) \) 10 * q - 8 * q^2 - 9 * q^3 + 40 * q^4 - 41 * q^5 + 31 * q^6 - 63 * q^7 - 96 * q^8 + 61 * q^9 - 47 * q^10 + 110 * q^11 - 171 * q^12 - 99 * q^13 - 95 * q^14 - 150 * q^15 + 180 * q^16 - 170 * q^17 - 207 * q^18 - 73 * q^19 - 343 * q^20 - 152 * q^21 - 88 * q^22 - 58 * q^23 + 157 * q^24 + 529 * q^25 - 285 * q^26 - 246 * q^27 - 1031 * q^28 - 754 * q^29 - 754 * q^30 - 228 * q^31 - 466 * q^32 - 99 * q^33 + 136 * q^34 + 20 * q^35 - 535 * q^36 - 1177 * q^37 - 747 * q^38 - 791 * q^39 + 537 * q^40 - 327 * q^41 - 632 * q^42 - 487 * q^43 + 440 * q^44 - 834 * q^45 - 854 * q^46 - 573 * q^47 - 1857 * q^48 + 2215 * q^49 - 855 * q^50 + 153 * q^51 + 1673 * q^52 - 2022 * q^53 + 3572 * q^54 - 451 * q^55 + 1997 * q^56 - 1310 * q^57 + 4514 * q^58 - 602 * q^59 + 4936 * q^60 - 570 * q^61 + 166 * q^62 - 1903 * q^63 + 968 * q^64 - 2018 * q^65 + 341 * q^66 - 12 * q^67 - 680 * q^68 - 1034 * q^69 + 5460 * q^70 + 636 * q^71 - 2989 * q^72 - 201 * q^73 + 959 * q^74 + 3213 * q^75 + 6999 * q^76 - 693 * q^77 + 3669 * q^78 - 1097 * q^79 - 1409 * q^80 + 3554 * q^81 + 2249 * q^82 - 477 * q^83 + 8476 * q^84 + 697 * q^85 - 1271 * q^86 + 1782 * q^87 - 1056 * q^88 - 195 * q^89 + 3292 * q^90 - 1128 * q^91 - 2064 * q^92 - 2632 * q^93 + 465 * q^94 - 1644 * q^95 + 8367 * q^96 - 994 * q^97 + 225 * q^98 + 671 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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