LMFDB - Embedded newform 77.4.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,4,Mod(1,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, 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("77.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	77.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:	$4.54314707044$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 42x^{3} + 18x^{2} + 368x + 352 $ x^5 - x^4 - 42x^3 + 18x^2 + 368*x + 352
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$4.44399$ of defining polynomial
Character	$\chi$	$=$	77.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.44399 q^{2} +8.26395 q^{3} +11.7491 q^{4} -22.0150 q^{5} +36.7249 q^{6} +7.00000 q^{7} +16.6609 q^{8} +41.2928 q^{9} -97.8345 q^{10} +11.0000 q^{11} +97.0937 q^{12} -51.5769 q^{13} +31.1080 q^{14} -181.931 q^{15} -19.9519 q^{16} -26.5590 q^{17} +183.505 q^{18} +99.6432 q^{19} -258.656 q^{20} +57.8476 q^{21} +48.8839 q^{22} +28.1455 q^{23} +137.684 q^{24} +359.660 q^{25} -229.207 q^{26} +118.115 q^{27} +82.2435 q^{28} -43.9369 q^{29} -808.499 q^{30} -83.8402 q^{31} -221.953 q^{32} +90.9034 q^{33} -118.028 q^{34} -154.105 q^{35} +485.152 q^{36} +306.353 q^{37} +442.814 q^{38} -426.228 q^{39} -366.789 q^{40} +200.991 q^{41} +257.074 q^{42} -13.7546 q^{43} +129.240 q^{44} -909.062 q^{45} +125.079 q^{46} -266.533 q^{47} -164.881 q^{48} +49.0000 q^{49} +1598.33 q^{50} -219.482 q^{51} -605.980 q^{52} +308.867 q^{53} +524.903 q^{54} -242.165 q^{55} +116.626 q^{56} +823.446 q^{57} -195.255 q^{58} -622.446 q^{59} -2137.52 q^{60} -87.3303 q^{61} -372.585 q^{62} +289.050 q^{63} -826.742 q^{64} +1135.46 q^{65} +403.974 q^{66} +608.395 q^{67} -312.044 q^{68} +232.593 q^{69} -684.842 q^{70} -464.926 q^{71} +687.974 q^{72} -255.407 q^{73} +1361.43 q^{74} +2972.21 q^{75} +1170.72 q^{76} +77.0000 q^{77} -1894.16 q^{78} +261.237 q^{79} +439.240 q^{80} -138.809 q^{81} +893.204 q^{82} +953.986 q^{83} +679.656 q^{84} +584.696 q^{85} -61.1255 q^{86} -363.092 q^{87} +183.269 q^{88} -839.910 q^{89} -4039.86 q^{90} -361.038 q^{91} +330.684 q^{92} -692.851 q^{93} -1184.47 q^{94} -2193.64 q^{95} -1834.21 q^{96} -349.146 q^{97} +217.756 q^{98} +454.221 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 2 q^{3} + 45 q^{4} - 24 q^{5} + 4 q^{6} + 35 q^{7} + 57 q^{8} + 63 q^{9} - 10 q^{10} + 55 q^{11} + 24 q^{12} - 50 q^{13} + 7 q^{14} - 146 q^{15} + 433 q^{16} + 222 q^{17} + 245 q^{18} + 160 q^{19}+ \cdots + 693 q^{99}+O(q^{100}) $ 5 * q + q^2 + 2 * q^3 + 45 * q^4 - 24 * q^5 + 4 * q^6 + 35 * q^7 + 57 * q^8 + 63 * q^9 - 10 * q^10 + 55 * q^11 + 24 * q^12 - 50 * q^13 + 7 * q^14 - 146 * q^15 + 433 * q^16 + 222 * q^17 + 245 * q^18 + 160 * q^19 - 430 * q^20 + 14 * q^21 + 11 * q^22 + 54 * q^23 - 220 * q^24 + 125 * q^25 - 1026 * q^26 + 110 * q^27 + 315 * q^28 + 14 * q^29 - 1080 * q^30 - 34 * q^31 - 583 * q^32 + 22 * q^33 - 750 * q^34 - 168 * q^35 - 411 * q^36 + 1044 * q^37 - 156 * q^38 - 124 * q^39 + 1158 * q^40 - 114 * q^41 + 28 * q^42 + 672 * q^43 + 495 * q^44 - 530 * q^45 - 1224 * q^46 - 292 * q^47 - 1652 * q^48 + 245 * q^49 + 1143 * q^50 + 768 * q^51 - 914 * q^52 - 710 * q^53 + 1608 * q^54 - 264 * q^55 + 399 * q^56 + 2012 * q^57 - 810 * q^58 + 270 * q^59 - 3068 * q^60 + 138 * q^61 - 480 * q^62 + 441 * q^63 + 3001 * q^64 - 196 * q^65 + 44 * q^66 + 1942 * q^67 + 3130 * q^68 - 1306 * q^69 - 70 * q^70 - 278 * q^71 + 3565 * q^72 - 338 * q^73 + 462 * q^74 + 3960 * q^75 - 1332 * q^76 + 385 * q^77 + 280 * q^78 + 576 * q^79 - 1602 * q^80 - 1439 * q^81 + 1386 * q^82 + 1644 * q^83 + 168 * q^84 + 360 * q^85 + 2020 * q^86 - 1956 * q^87 + 627 * q^88 - 3656 * q^89 - 6162 * q^90 - 350 * q^91 - 748 * q^92 - 1442 * q^93 + 976 * q^94 - 1276 * q^95 - 4508 * q^96 + 692 * q^97 + 49 * q^98 + 693 * 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 $

$2$	4.44399	1.57119	0.785594	−	0.618742i	$-0.212357\pi$
$2$	4.44399	1.57119	0.785594	+	0.618742i	$0.212357\pi$
$3$	8.26395	1.59040	0.795199	−	0.606349i	$-0.207367\pi$
$3$	8.26395	1.59040	0.795199	+	0.606349i	$0.207367\pi$
$4$	11.7491	1.46863
$5$	−22.0150	−1.96908	−0.984541	−	0.175155i	$-0.943957\pi$
$5$	−22.0150	−1.96908	−0.984541	+	0.175155i	$0.943957\pi$
$6$	36.7249	2.49881
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	16.6609	0.736313
$9$	41.2928	1.52936
$10$	−97.8345	−3.09380
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	97.0937	2.33571
$13$	−51.5769	−1.10037	−0.550186	−	0.835042i	$-0.685443\pi$
$13$	−51.5769	−1.10037	−0.550186	+	0.835042i	$0.685443\pi$
$14$	31.1080	0.593854
$15$	−181.931	−3.13162
$16$	−19.9519	−0.311748
$17$	−26.5590	−0.378912	−0.189456	−	0.981889i	$-0.560672\pi$
$17$	−26.5590	−0.378912	−0.189456	+	0.981889i	$0.560672\pi$
$18$	183.505	2.40292
$19$	99.6432	1.20314	0.601571	−	0.798819i	$-0.294542\pi$
$19$	99.6432	1.20314	0.601571	+	0.798819i	$0.294542\pi$
$20$	−258.656	−2.89186
$21$	57.8476	0.601114
$22$	48.8839	0.473731
$23$	28.1455	0.255163	0.127582	−	0.991828i	$-0.459279\pi$
$23$	28.1455	0.255163	0.127582	+	0.991828i	$0.459279\pi$
$24$	137.684	1.17103
$25$	359.660	2.87728
$26$	−229.207	−1.72889
$27$	118.115	0.841899
$28$	82.2435	0.555092
$29$	−43.9369	−0.281340	−0.140670	−	0.990057i	$-0.544926\pi$
$29$	−43.9369	−0.281340	−0.140670	+	0.990057i	$0.544926\pi$
$30$	−808.499	−4.92037
$31$	−83.8402	−0.485747	−0.242873	−	0.970058i	$-0.578090\pi$
$31$	−83.8402	−0.485747	−0.242873	+	0.970058i	$0.578090\pi$
$32$	−221.953	−1.22613
$33$	90.9034	0.479523
$34$	−118.028	−0.595342
$35$	−154.105	−0.744243
$36$	485.152	2.24608
$37$	306.353	1.36119	0.680596	−	0.732659i	$-0.261721\pi$
$37$	306.353	1.36119	0.680596	+	0.732659i	$0.261721\pi$
$38$	442.814	1.89036
$39$	−426.228	−1.75003
$40$	−366.789	−1.44986
$41$	200.991	0.765599	0.382800	−	0.923831i	$-0.374960\pi$
$41$	200.991	0.765599	0.382800	+	0.923831i	$0.374960\pi$
$42$	257.074	0.944463
$43$	−13.7546	−0.0487805	−0.0243903	−	0.999703i	$-0.507764\pi$
$43$	−13.7546	−0.0487805	−0.0243903	+	0.999703i	$0.507764\pi$
$44$	129.240	0.442810
$45$	−909.062	−3.01144
$46$	125.079	0.400909
$47$	−266.533	−0.827189	−0.413594	−	0.910461i	$-0.635727\pi$
$47$	−266.533	−0.827189	−0.413594	+	0.910461i	$0.635727\pi$
$48$	−164.881	−0.495803
$49$	49.0000	0.142857
$50$	1598.33	4.52075
$51$	−219.482	−0.602621
$52$	−605.980	−1.61605
$53$	308.867	0.800493	0.400247	−	0.916407i	$-0.368924\pi$
$53$	308.867	0.800493	0.400247	+	0.916407i	$0.368924\pi$
$54$	524.903	1.32278
$55$	−242.165	−0.593700
$56$	116.626	0.278300
$57$	823.446	1.91348
$58$	−195.255	−0.442039
$59$	−622.446	−1.37348	−0.686742	−	0.726901i	$-0.740960\pi$
$59$	−622.446	−1.37348	−0.686742	+	0.726901i	$0.740960\pi$
$60$	−2137.52	−4.59921
$61$	−87.3303	−0.183303	−0.0916516	−	0.995791i	$-0.529215\pi$
$61$	−87.3303	−0.183303	−0.0916516	+	0.995791i	$0.529215\pi$
$62$	−372.585	−0.763200
$63$	289.050	0.578045
$64$	−826.742	−1.61473
$65$	1135.46	2.16672
$66$	403.974	0.753421
$67$	608.395	1.10936	0.554681	−	0.832063i	$-0.312840\pi$
$67$	608.395	1.10936	0.554681	+	0.832063i	$0.312840\pi$
$68$	−312.044	−0.556483
$69$	232.593	0.405811
$70$	−684.842	−1.16935
$71$	−464.926	−0.777135	−0.388567	−	0.921420i	$-0.627030\pi$
$71$	−464.926	−0.777135	−0.388567	+	0.921420i	$0.627030\pi$
$72$	687.974	1.12609
$73$	−255.407	−0.409495	−0.204747	−	0.978815i	$-0.565637\pi$
$73$	−255.407	−0.409495	−0.204747	+	0.978815i	$0.565637\pi$
$74$	1361.43	2.13869
$75$	2972.21	4.57602
$76$	1170.72	1.76698
$77$	77.0000	0.113961
$78$	−1894.16	−2.74963
$79$	261.237	0.372043	0.186022	−	0.982546i	$-0.440441\pi$
$79$	261.237	0.372043	0.186022	+	0.982546i	$0.440441\pi$
$80$	439.240	0.613857
$81$	−138.809	−0.190410
$82$	893.204	1.20290
$83$	953.986	1.26161	0.630804	−	0.775942i	$-0.282725\pi$
$83$	953.986	1.26161	0.630804	+	0.775942i	$0.282725\pi$
$84$	679.656	0.882816
$85$	584.696	0.746109
$86$	−61.1255	−0.0766434
$87$	−363.092	−0.447443
$88$	183.269	0.222007
$89$	−839.910	−1.00034	−0.500170	−	0.865927i	$-0.666729\pi$
$89$	−839.910	−1.00034	−0.500170	+	0.865927i	$0.666729\pi$
$90$	−4039.86	−4.73154
$91$	−361.038	−0.415902
$92$	330.684	0.374741
$93$	−692.851	−0.772530
$94$	−1184.47	−1.29967
$95$	−2193.64	−2.36909
$96$	−1834.21	−1.95003
$97$	−349.146	−0.365468	−0.182734	−	0.983162i	$-0.558495\pi$
$97$	−349.146	−0.365468	−0.182734	+	0.983162i	$0.558495\pi$
$98$	217.756	0.224456
$99$	454.221	0.461121
$100$	4225.68	4.22568
$101$	1492.44	1.47033	0.735163	−	0.677890i	$-0.237106\pi$
$101$	1492.44	1.47033	0.735163	+	0.677890i	$0.237106\pi$
$102$	−975.377	−0.946831
$103$	558.687	0.534457	0.267228	−	0.963633i	$-0.413892\pi$
$103$	558.687	0.534457	0.267228	+	0.963633i	$0.413892\pi$
$104$	−859.314	−0.810218
$105$	−1273.52	−1.18364
$106$	1372.60	1.25773
$107$	−694.047	−0.627066	−0.313533	−	0.949577i	$-0.601513\pi$
$107$	−694.047	−0.627066	−0.313533	+	0.949577i	$0.601513\pi$
$108$	1387.74	1.23644
$109$	−341.005	−0.299654	−0.149827	−	0.988712i	$-0.547872\pi$
$109$	−341.005	−0.299654	−0.149827	+	0.988712i	$0.547872\pi$
$110$	−1076.18	−0.932815
$111$	2531.68	2.16484
$112$	−139.663	−0.117830
$113$	−990.910	−0.824929	−0.412464	−	0.910974i	$-0.635332\pi$
$113$	−990.910	−0.824929	−0.412464	+	0.910974i	$0.635332\pi$
$114$	3659.39	3.00643
$115$	−619.624	−0.502437
$116$	−516.218	−0.413186
$117$	−2129.75	−1.68287
$118$	−2766.15	−2.15800
$119$	−185.913	−0.143215
$120$	−3031.12	−2.30585
$121$	121.000	0.0909091
$122$	−388.095	−0.288004
$123$	1660.98	1.21761
$124$	−985.045	−0.713384
$125$	−5166.05	−3.69652
$126$	1284.54	0.908218
$127$	−666.090	−0.465401	−0.232700	−	0.972548i	$-0.574756\pi$
$127$	−666.090	−0.465401	−0.232700	+	0.972548i	$0.574756\pi$
$128$	−1898.41	−1.31092
$129$	−113.668	−0.0775804
$130$	5046.00	3.40433
$131$	30.4356	0.0202990	0.0101495	−	0.999948i	$-0.496769\pi$
$131$	30.4356	0.0202990	0.0101495	+	0.999948i	$0.496769\pi$
$132$	1068.03	0.704244
$133$	697.502	0.454745
$134$	2703.70	1.74302
$135$	−2600.31	−1.65777
$136$	−442.496	−0.278998
$137$	−2810.25	−1.75252	−0.876262	−	0.481836i	$-0.839970\pi$
$137$	−2810.25	−1.75252	−0.876262	+	0.481836i	$0.839970\pi$
$138$	1033.64	0.637605
$139$	3110.49	1.89804	0.949021	−	0.315212i	$-0.102076\pi$
$139$	3110.49	1.89804	0.949021	+	0.315212i	$0.102076\pi$
$140$	−1810.59	−1.09302
$141$	−2202.62	−1.31556
$142$	−2066.13	−1.22103
$143$	−567.345	−0.331775
$144$	−823.869	−0.476776
$145$	967.270	0.553982
$146$	−1135.03	−0.643394
$147$	404.933	0.227200
$148$	3599.36	1.99909
$149$	1916.92	1.05396	0.526979	−	0.849878i	$-0.323325\pi$
$149$	1916.92	1.05396	0.526979	+	0.849878i	$0.323325\pi$
$150$	13208.5	7.18980
$151$	−2289.28	−1.23377	−0.616883	−	0.787055i	$-0.711605\pi$
$151$	−2289.28	−1.23377	−0.616883	+	0.787055i	$0.711605\pi$
$152$	1660.14	0.885889
$153$	−1096.70	−0.579494
$154$	342.187	0.179054
$155$	1845.74	0.956475
$156$	−5007.79	−2.57015
$157$	280.036	0.142352	0.0711762	−	0.997464i	$-0.477325\pi$
$157$	280.036	0.142352	0.0711762	+	0.997464i	$0.477325\pi$
$158$	1160.93	0.584550
$159$	2552.46	1.27310
$160$	4886.29	2.41435
$161$	197.019	0.0964426
$162$	−616.865	−0.299170
$163$	−866.571	−0.416411	−0.208206	−	0.978085i	$-0.566762\pi$
$163$	−866.571	−0.416411	−0.208206	+	0.978085i	$0.566762\pi$
$164$	2361.46	1.12439
$165$	−2001.24	−0.944220
$166$	4239.51	1.98223
$167$	−1965.18	−0.910600	−0.455300	−	0.890338i	$-0.650468\pi$
$167$	−1965.18	−0.910600	−0.455300	+	0.890338i	$0.650468\pi$
$168$	963.791	0.442608
$169$	463.173	0.210820
$170$	2598.39	1.17228
$171$	4114.55	1.84004
$172$	−161.604	−0.0716407
$173$	3956.88	1.73894	0.869469	−	0.493988i	$-0.164461\pi$
$173$	3956.88	1.73894	0.869469	+	0.493988i	$0.164461\pi$
$174$	−1613.58	−0.703018
$175$	2517.62	1.08751
$176$	−219.471	−0.0939956
$177$	−5143.86	−2.18439
$178$	−3732.55	−1.57172
$179$	−3143.58	−1.31264	−0.656318	−	0.754484i	$-0.727887\pi$
$179$	−3143.58	−1.31264	−0.656318	+	0.754484i	$0.727887\pi$
$180$	−10680.6	−4.42271
$181$	683.772	0.280798	0.140399	−	0.990095i	$-0.455162\pi$
$181$	683.772	0.280798	0.140399	+	0.990095i	$0.455162\pi$
$182$	−1604.45	−0.653460
$183$	−721.693	−0.291525
$184$	468.929	0.187880
$185$	−6744.36	−2.68030
$186$	−3079.03	−1.21379
$187$	−292.149	−0.114246
$188$	−3131.52	−1.21484
$189$	826.806	0.318208
$190$	−9748.54	−3.72228
$191$	2739.68	1.03789	0.518944	−	0.854809i	$-0.326325\pi$
$191$	2739.68	1.03789	0.518944	+	0.854809i	$0.326325\pi$
$192$	−6832.15	−2.56806
$193$	2651.93	0.989067	0.494534	−	0.869159i	$-0.335339\pi$
$193$	2651.93	0.989067	0.494534	+	0.869159i	$0.335339\pi$
$194$	−1551.60	−0.574219
$195$	9383.42	3.44595
$196$	575.705	0.209805
$197$	−1879.52	−0.679749	−0.339874	−	0.940471i	$-0.610385\pi$
$197$	−1879.52	−0.679749	−0.339874	+	0.940471i	$0.610385\pi$
$198$	2018.56	0.724507
$199$	−3119.39	−1.11119	−0.555597	−	0.831452i	$-0.687510\pi$
$199$	−3119.39	−1.11119	−0.555597	+	0.831452i	$0.687510\pi$
$200$	5992.25	2.11858
$201$	5027.75	1.76433
$202$	6632.37	2.31016
$203$	−307.558	−0.106337
$204$	−2578.71	−0.885029
$205$	−4424.82	−1.50753
$206$	2482.80	0.839733
$207$	1162.21	0.390237
$208$	1029.05	0.343039
$209$	1096.08	0.362761
$210$	−5659.49	−1.85972
$211$	−520.718	−0.169894	−0.0849472	−	0.996385i	$-0.527072\pi$
$211$	−520.718	−0.169894	−0.0849472	+	0.996385i	$0.527072\pi$
$212$	3628.90	1.17563
$213$	−3842.12	−1.23595
$214$	−3084.34	−0.985238
$215$	302.808	0.0960528
$216$	1967.90	0.619901
$217$	−586.881	−0.183595
$218$	−1515.42	−0.470814
$219$	−2110.67	−0.651260
$220$	−2845.21	−0.871929
$221$	1369.83	0.416944
$222$	11250.8	3.40137
$223$	2101.08	0.630935	0.315467	−	0.948936i	$-0.397839\pi$
$223$	2101.08	0.630935	0.315467	+	0.948936i	$0.397839\pi$
$224$	−1553.67	−0.463433
$225$	14851.4	4.40041
$226$	−4403.60	−1.29612
$227$	−6051.96	−1.76953	−0.884764	−	0.466040i	$-0.845680\pi$
$227$	−6051.96	−1.76953	−0.884764	+	0.466040i	$0.845680\pi$
$228$	9674.73	2.81020
$229$	−2995.73	−0.864470	−0.432235	−	0.901761i	$-0.642275\pi$
$229$	−2995.73	−0.864470	−0.432235	+	0.901761i	$0.642275\pi$
$230$	−2753.61	−0.789424
$231$	636.324	0.181243
$232$	−732.026	−0.207155
$233$	−65.3656	−0.0183787	−0.00918936	−	0.999958i	$-0.502925\pi$
$233$	−65.3656	−0.0183787	−0.00918936	+	0.999958i	$0.502925\pi$
$234$	−9464.61	−2.64411
$235$	5867.73	1.62880
$236$	−7313.17	−2.01715
$237$	2158.85	0.591697
$238$	−826.196	−0.225018
$239$	−1102.33	−0.298343	−0.149171	−	0.988811i	$-0.547661\pi$
$239$	−1102.33	−0.298343	−0.149171	+	0.988811i	$0.547661\pi$
$240$	3629.86	0.976277
$241$	5297.43	1.41592	0.707962	−	0.706250i	$-0.249615\pi$
$241$	5297.43	1.41592	0.707962	+	0.706250i	$0.249615\pi$
$242$	537.723	0.142835
$243$	−4336.22	−1.14473
$244$	−1026.05	−0.269205
$245$	−1078.74	−0.281297
$246$	7381.39	1.91309
$247$	−5139.28	−1.32391
$248$	−1396.85	−0.357661
$249$	7883.69	2.00646
$250$	−22957.9	−5.80793
$251$	177.964	0.0447530	0.0223765	−	0.999750i	$-0.492877\pi$
$251$	177.964	0.0447530	0.0223765	+	0.999750i	$0.492877\pi$
$252$	3396.07	0.848937
$253$	309.601	0.0769346
$254$	−2960.10	−0.731232
$255$	4831.90	1.18661
$256$	−1822.59	−0.444969
$257$	3496.69	0.848707	0.424354	−	0.905497i	$-0.360501\pi$
$257$	3496.69	0.848707	0.424354	+	0.905497i	$0.360501\pi$
$258$	−505.138	−0.121893
$259$	2144.47	0.514482
$260$	13340.7	3.18212
$261$	−1814.28	−0.430272
$262$	135.256	0.0318936
$263$	5747.94	1.34766	0.673828	−	0.738889i	$-0.264649\pi$
$263$	5747.94	1.34766	0.673828	+	0.738889i	$0.264649\pi$
$264$	1514.53	0.353079
$265$	−6799.71	−1.57624
$266$	3099.70	0.714491
$267$	−6940.97	−1.59094
$268$	7148.08	1.62925
$269$	235.217	0.0533140	0.0266570	−	0.999645i	$-0.491514\pi$
$269$	235.217	0.0533140	0.0266570	+	0.999645i	$0.491514\pi$
$270$	−11555.7	−2.60467
$271$	−1179.58	−0.264406	−0.132203	−	0.991223i	$-0.542205\pi$
$271$	−1179.58	−0.264406	−0.132203	+	0.991223i	$0.542205\pi$
$272$	529.902	0.118125
$273$	−2983.60	−0.661449
$274$	−12488.7	−2.75354
$275$	3956.26	0.867533
$276$	2732.76	0.595988
$277$	−3638.98	−0.789331	−0.394666	−	0.918825i	$-0.629140\pi$
$277$	−3638.98	−0.789331	−0.394666	+	0.918825i	$0.629140\pi$
$278$	13823.0	2.98218
$279$	−3462.00	−0.742883
$280$	−2567.52	−0.547995
$281$	3236.81	0.687160	0.343580	−	0.939123i	$-0.388360\pi$
$281$	3236.81	0.687160	0.343580	+	0.939123i	$0.388360\pi$
$282$	−9788.42	−2.06699
$283$	8303.78	1.74420	0.872100	−	0.489328i	$-0.162758\pi$
$283$	8303.78	1.74420	0.872100	+	0.489328i	$0.162758\pi$
$284$	−5462.45	−1.14133
$285$	−18128.2	−3.76779
$286$	−2521.28	−0.521281
$287$	1406.94	0.289369
$288$	−9165.06	−1.87520
$289$	−4207.62	−0.856426
$290$	4298.54	0.870411
$291$	−2885.32	−0.581239
$292$	−3000.80	−0.601398
$293$	−1894.16	−0.377672	−0.188836	−	0.982009i	$-0.560471\pi$
$293$	−1894.16	−0.377672	−0.188836	+	0.982009i	$0.560471\pi$
$294$	1799.52	0.356974
$295$	13703.2	2.70450
$296$	5104.10	1.00226
$297$	1299.27	0.253842
$298$	8518.76	1.65597
$299$	−1451.66	−0.280775
$300$	34920.8	6.72050
$301$	−96.2825	−0.0184373
$302$	−10173.5	−1.93848
$303$	12333.4	2.33840
$304$	−1988.07	−0.375077
$305$	1922.58	0.360939
$306$	−4873.71	−0.910495
$307$	6596.30	1.22629	0.613144	−	0.789971i	$-0.289904\pi$
$307$	6596.30	1.22629	0.613144	+	0.789971i	$0.289904\pi$
$308$	904.679	0.167366
$309$	4616.96	0.849999
$310$	8202.47	1.50280
$311$	−5242.26	−0.955824	−0.477912	−	0.878408i	$-0.658606\pi$
$311$	−5242.26	−0.955824	−0.477912	+	0.878408i	$0.658606\pi$
$312$	−7101.33	−1.28857
$313$	5338.75	0.964103	0.482051	−	0.876143i	$-0.339892\pi$
$313$	5338.75	0.964103	0.482051	+	0.876143i	$0.339892\pi$
$314$	1244.48	0.223662
$315$	−6363.43	−1.13822
$316$	3069.29	0.546395
$317$	−5807.21	−1.02891	−0.514456	−	0.857517i	$-0.672006\pi$
$317$	−5807.21	−1.02891	−0.514456	+	0.857517i	$0.672006\pi$
$318$	11343.1	2.00028
$319$	−483.306	−0.0848273
$320$	18200.7	3.17953
$321$	−5735.56	−0.997283
$322$	875.550	0.151530
$323$	−2646.42	−0.455885
$324$	−1630.87	−0.279642
$325$	−18550.1	−3.16608
$326$	−3851.03	−0.654261
$327$	−2818.04	−0.476570
$328$	3348.69	0.563720
$329$	−1865.73	−0.312648
$330$	−8893.49	−1.48355
$331$	−1366.51	−0.226919	−0.113460	−	0.993543i	$-0.536193\pi$
$331$	−1366.51	−0.226919	−0.113460	+	0.993543i	$0.536193\pi$
$332$	11208.4	1.85284
$333$	12650.2	2.08176
$334$	−8733.25	−1.43072
$335$	−13393.8	−2.18443
$336$	−1154.17	−0.187396
$337$	−3363.75	−0.543724	−0.271862	−	0.962336i	$-0.587639\pi$
$337$	−3363.75	−0.543724	−0.271862	+	0.962336i	$0.587639\pi$
$338$	2058.34	0.331239
$339$	−8188.83	−1.31196
$340$	6869.64	1.09576
$341$	−922.242	−0.146458
$342$	18285.0	2.89106
$343$	343.000	0.0539949
$344$	−229.164	−0.0359177
$345$	−5120.54	−0.799075
$346$	17584.4	2.73220
$347$	2984.97	0.461791	0.230896	−	0.972979i	$-0.425834\pi$
$347$	2984.97	0.461791	0.230896	+	0.972979i	$0.425834\pi$
$348$	−4265.99	−0.657130
$349$	1286.08	0.197255	0.0986276	−	0.995124i	$-0.468555\pi$
$349$	1286.08	0.197255	0.0986276	+	0.995124i	$0.468555\pi$
$350$	11188.3	1.70868
$351$	−6092.01	−0.926403
$352$	−2441.48	−0.369691
$353$	8417.60	1.26919	0.634594	−	0.772846i	$-0.281167\pi$
$353$	8417.60	1.26919	0.634594	+	0.772846i	$0.281167\pi$
$354$	−22859.3	−3.43208
$355$	10235.3	1.53024
$356$	−9868.16	−1.46913
$357$	−1536.38	−0.227769
$358$	−13970.0	−2.06240
$359$	7483.47	1.10017	0.550087	−	0.835108i	$-0.314595\pi$
$359$	7483.47	1.10017	0.550087	+	0.835108i	$0.314595\pi$
$360$	−15145.7	−2.21736
$361$	3069.76	0.447553
$362$	3038.68	0.441186
$363$	999.938	0.144582
$364$	−4241.86	−0.610808
$365$	5622.79	0.806329
$366$	−3207.20	−0.458041
$367$	8588.73	1.22160	0.610801	−	0.791784i	$-0.290847\pi$
$367$	8588.73	1.22160	0.610801	+	0.791784i	$0.290847\pi$
$368$	−561.556	−0.0795466
$369$	8299.50	1.17088
$370$	−29971.9	−4.21125
$371$	2162.07	0.302558
$372$	−8140.36	−1.13456
$373$	11833.0	1.64260	0.821298	−	0.570500i	$-0.193251\pi$
$373$	11833.0	1.64260	0.821298	+	0.570500i	$0.193251\pi$
$374$	−1298.31	−0.179502
$375$	−42691.9	−5.87894
$376$	−4440.67	−0.609070
$377$	2266.13	0.309579
$378$	3674.32	0.499965
$379$	5056.39	0.685301	0.342651	−	0.939463i	$-0.388675\pi$
$379$	5056.39	0.685301	0.342651	+	0.939463i	$0.388675\pi$
$380$	−25773.3	−3.47932
$381$	−5504.53	−0.740172
$382$	12175.1	1.63072
$383$	6457.09	0.861467	0.430733	−	0.902479i	$-0.358255\pi$
$383$	6457.09	0.861467	0.430733	+	0.902479i	$0.358255\pi$
$384$	−15688.4	−2.08488
$385$	−1695.16	−0.224398
$386$	11785.1	1.55401
$387$	−567.968	−0.0746032
$388$	−4102.14	−0.536739
$389$	12444.5	1.62201	0.811004	−	0.585040i	$-0.198921\pi$
$389$	12444.5	1.62201	0.811004	+	0.585040i	$0.198921\pi$
$390$	41699.9	5.41424
$391$	−747.518	−0.0966844
$392$	816.382	0.105188
$393$	251.518	0.0322835
$394$	−8352.59	−1.06801
$395$	−5751.12	−0.732584
$396$	5336.68	0.677217
$397$	−619.207	−0.0782799	−0.0391400	−	0.999234i	$-0.512462\pi$
$397$	−619.207	−0.0782799	−0.0391400	+	0.999234i	$0.512462\pi$
$398$	−13862.5	−1.74589
$399$	5764.12	0.723226
$400$	−7175.90	−0.896987
$401$	9731.89	1.21194	0.605969	−	0.795488i	$-0.292785\pi$
$401$	9731.89	1.21194	0.605969	+	0.795488i	$0.292785\pi$
$402$	22343.3	2.77209
$403$	4324.22	0.534502
$404$	17534.7	2.15937
$405$	3055.87	0.374932
$406$	−1366.79	−0.167075
$407$	3369.88	0.410415
$408$	−3656.76	−0.443717
$409$	4621.43	0.558717	0.279358	−	0.960187i	$-0.409878\pi$
$409$	4621.43	0.558717	0.279358	+	0.960187i	$0.409878\pi$
$410$	−19663.9	−2.36861
$411$	−23223.7	−2.78721
$412$	6564.05	0.784922
$413$	−4357.12	−0.519128
$414$	5164.85	0.613137
$415$	−21002.0	−2.48421
$416$	11447.6	1.34920
$417$	25704.9	3.01864
$418$	4870.95	0.569966
$419$	186.428	0.0217365	0.0108682	−	0.999941i	$-0.496540\pi$
$419$	186.428	0.0217365	0.0108682	+	0.999941i	$0.496540\pi$
$420$	−14962.6	−1.73834
$421$	2670.29	0.309126	0.154563	−	0.987983i	$-0.450603\pi$
$421$	2670.29	0.309126	0.154563	+	0.987983i	$0.450603\pi$
$422$	−2314.07	−0.266936
$423$	−11005.9	−1.26507
$424$	5145.99	0.589413
$425$	−9552.22	−1.09024
$426$	−17074.4	−1.94192
$427$	−611.312	−0.0692821
$428$	−8154.40	−0.920930
$429$	−4688.51	−0.527654
$430$	1345.68	0.150917
$431$	−12514.9	−1.39866	−0.699328	−	0.714801i	$-0.746517\pi$
$431$	−12514.9	−1.39866	−0.699328	+	0.714801i	$0.746517\pi$
$432$	−2356.62	−0.262460
$433$	−16651.2	−1.84805	−0.924025	−	0.382332i	$-0.875121\pi$
$433$	−16651.2	−1.84805	−0.924025	+	0.382332i	$0.875121\pi$
$434$	−2608.10	−0.288462
$435$	7993.47	0.881052
$436$	−4006.49	−0.440083
$437$	2804.51	0.306998
$438$	−9379.80	−1.02325
$439$	6033.38	0.655940	0.327970	−	0.944688i	$-0.393636\pi$
$439$	6033.38	0.655940	0.327970	+	0.944688i	$0.393636\pi$
$440$	−4034.68	−0.437149
$441$	2023.35	0.218481
$442$	6087.51	0.655098
$443$	6320.03	0.677819	0.338910	−	0.940819i	$-0.389942\pi$
$443$	6320.03	0.677819	0.338910	+	0.940819i	$0.389942\pi$
$444$	29744.9	3.17935
$445$	18490.6	1.96975
$446$	9337.17	0.991318
$447$	15841.3	1.67621
$448$	−5787.19	−0.610311
$449$	−17893.6	−1.88074	−0.940368	−	0.340159i	$-0.889519\pi$
$449$	−17893.6	−1.88074	−0.940368	+	0.340159i	$0.889519\pi$
$450$	65999.5	6.91388
$451$	2210.90	0.230837
$452$	−11642.3	−1.21152
$453$	−18918.5	−1.96218
$454$	−26894.9	−2.78026
$455$	7948.25	0.818945
$456$	13719.3	1.40892
$457$	6208.00	0.635444	0.317722	−	0.948184i	$-0.397082\pi$
$457$	6208.00	0.635444	0.317722	+	0.948184i	$0.397082\pi$
$458$	−13313.0	−1.35825
$459$	−3137.02	−0.319006
$460$	−7280.01	−0.737896
$461$	7981.28	0.806346	0.403173	−	0.915124i	$-0.367907\pi$
$461$	7981.28	0.806346	0.403173	+	0.915124i	$0.367907\pi$
$462$	2827.82	0.284766
$463$	−7495.19	−0.752334	−0.376167	−	0.926552i	$-0.622758\pi$
$463$	−7495.19	−0.752334	−0.376167	+	0.926552i	$0.622758\pi$
$464$	876.623	0.0877073
$465$	15253.1	1.52118
$466$	−290.484	−0.0288765
$467$	1519.39	0.150555	0.0752773	−	0.997163i	$-0.476016\pi$
$467$	1519.39	0.150555	0.0752773	+	0.997163i	$0.476016\pi$
$468$	−25022.6	−2.47152
$469$	4258.77	0.419300
$470$	26076.2	2.55916
$471$	2314.20	0.226397
$472$	−10370.5	−1.01131
$473$	−151.301	−0.0147079
$474$	9593.90	0.929667
$475$	35837.7	3.46178
$476$	−2184.31	−0.210331
$477$	12754.0	1.22425
$478$	−4898.75	−0.468753
$479$	−16394.2	−1.56382	−0.781909	−	0.623393i	$-0.785754\pi$
$479$	−16394.2	−1.56382	−0.781909	+	0.623393i	$0.785754\pi$
$480$	40380.1	3.83977
$481$	−15800.7	−1.49782
$482$	23541.8	2.22468
$483$	1628.15	0.153382
$484$	1421.64	0.133512
$485$	7686.45	0.719636
$486$	−19270.1	−1.79858
$487$	2275.01	0.211685	0.105843	−	0.994383i	$-0.466246\pi$
$487$	2275.01	0.211685	0.105843	+	0.994383i	$0.466246\pi$
$488$	−1455.00	−0.134968
$489$	−7161.29	−0.662259
$490$	−4793.89	−0.441971
$491$	−14629.2	−1.34462	−0.672308	−	0.740272i	$-0.734697\pi$
$491$	−14629.2	−1.34462	−0.672308	+	0.740272i	$0.734697\pi$
$492$	19515.0	1.78822
$493$	1166.92	0.106603
$494$	−22838.9	−2.08011
$495$	−9999.68	−0.907984
$496$	1672.77	0.151431
$497$	−3254.48	−0.293729
$498$	35035.1	3.15253
$499$	3534.01	0.317042	0.158521	−	0.987356i	$-0.449327\pi$
$499$	3534.01	0.317042	0.158521	+	0.987356i	$0.449327\pi$
$500$	−60696.3	−5.42884
$501$	−16240.1	−1.44822
$502$	790.872	0.0703155
$503$	−9233.35	−0.818479	−0.409239	−	0.912427i	$-0.634206\pi$
$503$	−9233.35	−0.818479	−0.409239	+	0.912427i	$0.634206\pi$
$504$	4815.82	0.425622
$505$	−32856.0	−2.89519
$506$	1375.86	0.120879
$507$	3827.63	0.335288
$508$	−7825.93	−0.683503
$509$	11565.3	1.00712	0.503560	−	0.863960i	$-0.332023\pi$
$509$	11565.3	1.00712	0.503560	+	0.863960i	$0.332023\pi$
$510$	21472.9	1.86439
$511$	−1787.85	−0.154775
$512$	7087.70	0.611787
$513$	11769.4	1.01292
$514$	15539.3	1.33348
$515$	−12299.5	−1.05239
$516$	−1335.49	−0.113937
$517$	−2931.87	−0.249407
$518$	9530.01	0.808349
$519$	32699.5	2.76560
$520$	18917.8	1.59539
$521$	−2440.24	−0.205200	−0.102600	−	0.994723i	$-0.532716\pi$
$521$	−2440.24	−0.205200	−0.102600	+	0.994723i	$0.532716\pi$
$522$	−8062.64	−0.676038
$523$	−911.213	−0.0761847	−0.0380923	−	0.999274i	$-0.512128\pi$
$523$	−911.213	−0.0761847	−0.0380923	+	0.999274i	$0.512128\pi$
$524$	357.590	0.0298119
$525$	20805.5	1.72957
$526$	25543.8	2.11742
$527$	2226.71	0.184055
$528$	−1813.69	−0.149490
$529$	−11374.8	−0.934892
$530$	−30217.9	−2.47657
$531$	−25702.6	−2.10056
$532$	8195.01	0.667854
$533$	−10366.5	−0.842445
$534$	−30845.6	−2.49966
$535$	15279.4	1.23474
$536$	10136.4	0.816838
$537$	−25978.3	−2.08761
$538$	1045.30	0.0837663
$539$	539.000	0.0430730
$540$	−30551.2	−2.43465
$541$	12277.5	0.975692	0.487846	−	0.872930i	$-0.337783\pi$
$541$	12277.5	0.975692	0.487846	+	0.872930i	$0.337783\pi$
$542$	−5242.02	−0.415432
$543$	5650.65	0.446580
$544$	5894.84	0.464594
$545$	7507.22	0.590044
$546$	−13259.1	−1.03926
$547$	−12539.2	−0.980141	−0.490071	−	0.871683i	$-0.663029\pi$
$547$	−12539.2	−0.980141	−0.490071	+	0.871683i	$0.663029\pi$
$548$	−33017.8	−2.57382
$549$	−3606.11	−0.280337
$550$	17581.6	1.36306
$551$	−4378.01	−0.338493
$552$	3875.20	0.298804
$553$	1828.66	0.140619
$554$	−16171.6	−1.24019
$555$	−55735.0	−4.26274
$556$	36545.3	2.78753
$557$	−14212.8	−1.08118	−0.540588	−	0.841287i	$-0.681798\pi$
$557$	−14212.8	−1.08118	−0.540588	+	0.841287i	$0.681798\pi$
$558$	−15385.1	−1.16721
$559$	709.421	0.0536768
$560$	3074.68	0.232016
$561$	−2414.30	−0.181697
$562$	14384.4	1.07966
$563$	4446.83	0.332880	0.166440	−	0.986052i	$-0.446773\pi$
$563$	4446.83	0.332880	0.166440	+	0.986052i	$0.446773\pi$
$564$	−25878.7	−1.93207
$565$	21814.9	1.62435
$566$	36901.9	2.74047
$567$	−971.661	−0.0719681
$568$	−7746.07	−0.572214
$569$	11258.8	0.829511	0.414756	−	0.909933i	$-0.363867\pi$
$569$	11258.8	0.829511	0.414756	+	0.909933i	$0.363867\pi$
$570$	−80561.4	−5.91991
$571$	−16450.6	−1.20567	−0.602835	−	0.797866i	$-0.705962\pi$
$571$	−16450.6	−1.20567	−0.602835	+	0.797866i	$0.705962\pi$
$572$	−6665.78	−0.487256
$573$	22640.6	1.65065
$574$	6252.43	0.454654
$575$	10122.8	0.734176
$576$	−34138.5	−2.46951
$577$	10175.6	0.734173	0.367086	−	0.930187i	$-0.380355\pi$
$577$	10175.6	0.734173	0.367086	+	0.930187i	$0.380355\pi$
$578$	−18698.6	−1.34561
$579$	21915.4	1.57301
$580$	11364.5	0.813597
$581$	6677.90	0.476843
$582$	−12822.4	−0.913237
$583$	3397.54	0.241358
$584$	−4255.30	−0.301516
$585$	46886.5	3.31371
$586$	−8417.62	−0.593394
$587$	−5123.98	−0.360289	−0.180144	−	0.983640i	$-0.557656\pi$
$587$	−5123.98	−0.360289	−0.180144	+	0.983640i	$0.557656\pi$
$588$	4757.59	0.333673
$589$	−8354.11	−0.584423
$590$	60896.7	4.24929
$591$	−15532.3	−1.08107
$592$	−6112.31	−0.424349
$593$	−23816.7	−1.64930	−0.824650	−	0.565643i	$-0.808628\pi$
$593$	−23816.7	−1.64930	−0.824650	+	0.565643i	$0.808628\pi$
$594$	5773.93	0.398834
$595$	4092.88	0.282003
$596$	22522.0	1.54788
$597$	−25778.4	−1.76724
$598$	−6451.16	−0.441150
$599$	11801.0	0.804965	0.402482	−	0.915428i	$-0.368147\pi$
$599$	11801.0	0.804965	0.402482	+	0.915428i	$0.368147\pi$
$600$	49519.6	3.36938
$601$	−10944.5	−0.742820	−0.371410	−	0.928469i	$-0.621125\pi$
$601$	−10944.5	−0.742820	−0.371410	+	0.928469i	$0.621125\pi$
$602$	−427.879	−0.0289685
$603$	25122.4	1.69662
$604$	−26896.9	−1.81195
$605$	−2663.82	−0.179007
$606$	54809.6	3.67407
$607$	−1280.36	−0.0856150	−0.0428075	−	0.999083i	$-0.513630\pi$
$607$	−1280.36	−0.0856150	−0.0428075	+	0.999083i	$0.513630\pi$
$608$	−22116.1	−1.47521
$609$	−2541.64	−0.169118
$610$	8543.91	0.567103
$611$	13747.0	0.910216
$612$	−12885.2	−0.851065
$613$	−11029.9	−0.726744	−0.363372	−	0.931644i	$-0.618375\pi$
$613$	−11029.9	−0.726744	−0.363372	+	0.931644i	$0.618375\pi$
$614$	29313.9	1.92673
$615$	−36566.5	−2.39757
$616$	1282.89	0.0839106
$617$	−20861.3	−1.36117	−0.680586	−	0.732668i	$-0.738275\pi$
$617$	−20861.3	−1.36117	−0.680586	+	0.732668i	$0.738275\pi$
$618$	20517.7	1.33551
$619$	−16877.9	−1.09593	−0.547966	−	0.836501i	$-0.684598\pi$
$619$	−16877.9	−1.09593	−0.547966	+	0.836501i	$0.684598\pi$
$620$	21685.8	1.40471
$621$	3324.42	0.214822
$622$	−23296.6	−1.50178
$623$	−5879.37	−0.378093
$624$	8504.06	0.545568
$625$	68773.0	4.40147
$626$	23725.4	1.51479
$627$	9057.91	0.576935
$628$	3290.17	0.209064
$629$	−8136.43	−0.515772
$630$	−28279.0	−1.78836
$631$	−1332.58	−0.0840719	−0.0420359	−	0.999116i	$-0.513384\pi$
$631$	−1332.58	−0.0840719	−0.0420359	+	0.999116i	$0.513384\pi$
$632$	4352.42	0.273940
$633$	−4303.19	−0.270200
$634$	−25807.2	−1.61662
$635$	14664.0	0.916412
$636$	29989.0	1.86972
$637$	−2527.27	−0.157196
$638$	−2147.81	−0.133280
$639$	−19198.1	−1.18852
$640$	41793.5	2.58130
$641$	20472.2	1.26147	0.630736	−	0.775998i	$-0.282753\pi$
$641$	20472.2	1.26147	0.630736	+	0.775998i	$0.282753\pi$
$642$	−25488.8	−1.56692
$643$	27140.3	1.66455	0.832276	−	0.554361i	$-0.187037\pi$
$643$	27140.3	1.66455	0.832276	+	0.554361i	$0.187037\pi$
$644$	2314.79	0.141639
$645$	2502.39	0.152762
$646$	−11760.7	−0.716282
$647$	13662.1	0.830159	0.415079	−	0.909785i	$-0.363754\pi$
$647$	13662.1	0.830159	0.415079	+	0.909785i	$0.363754\pi$
$648$	−2312.67	−0.140201
$649$	−6846.91	−0.414121
$650$	−82436.7	−4.97451
$651$	−4849.96	−0.291989
$652$	−10181.4	−0.611556
$653$	1607.56	0.0963379	0.0481689	−	0.998839i	$-0.484661\pi$
$653$	1607.56	0.0963379	0.0481689	+	0.998839i	$0.484661\pi$
$654$	−12523.4	−0.748781
$655$	−670.040	−0.0399705
$656$	−4010.15	−0.238674
$657$	−10546.5	−0.626267
$658$	−8291.30	−0.491229
$659$	27361.6	1.61738	0.808692	−	0.588233i	$-0.200176\pi$
$659$	27361.6	1.61738	0.808692	+	0.588233i	$0.200176\pi$
$660$	−23512.7	−1.38671
$661$	−5117.29	−0.301119	−0.150559	−	0.988601i	$-0.548107\pi$
$661$	−5117.29	−0.301119	−0.150559	+	0.988601i	$0.548107\pi$
$662$	−6072.76	−0.356533
$663$	11320.2	0.663107
$664$	15894.2	0.928939
$665$	−15355.5	−0.895431
$666$	56217.3	3.27083
$667$	−1236.63	−0.0717877
$668$	−23089.0	−1.33734
$669$	17363.2	1.00344
$670$	−59522.1	−3.43215
$671$	−960.633	−0.0552680
$672$	−12839.4	−0.737042
$673$	11605.6	0.664729	0.332365	−	0.943151i	$-0.392154\pi$
$673$	11605.6	0.664729	0.332365	+	0.943151i	$0.392154\pi$
$674$	−14948.5	−0.854292
$675$	42481.3	2.42238
$676$	5441.85	0.309618
$677$	32514.6	1.84584	0.922922	−	0.384986i	$-0.125794\pi$
$677$	32514.6	1.84584	0.922922	+	0.384986i	$0.125794\pi$
$678$	−36391.1	−2.06134
$679$	−2444.02	−0.138134
$680$	9741.54	0.549369
$681$	−50013.1	−2.81425
$682$	−4098.44	−0.230113
$683$	7201.06	0.403427	0.201714	−	0.979445i	$-0.435349\pi$
$683$	7201.06	0.403427	0.201714	+	0.979445i	$0.435349\pi$
$684$	48342.1	2.70235
$685$	61867.6	3.45086
$686$	1524.29	0.0848362
$687$	−24756.6	−1.37485
$688$	274.431	0.0152072
$689$	−15930.4	−0.880841
$690$	−22755.7	−1.25550
$691$	−32357.7	−1.78140	−0.890698	−	0.454596i	$-0.849784\pi$
$691$	−32357.7	−1.78140	−0.890698	+	0.454596i	$0.849784\pi$
$692$	46489.7	2.55386
$693$	3179.55	0.174287
$694$	13265.2	0.725562
$695$	−68477.3	−3.73740
$696$	−6049.42	−0.329458
$697$	−5338.13	−0.290095
$698$	5715.31	0.309925
$699$	−540.178	−0.0292295
$700$	29579.7	1.59716
$701$	11077.3	0.596838	0.298419	−	0.954435i	$-0.403541\pi$
$701$	11077.3	0.596838	0.298419	+	0.954435i	$0.403541\pi$
$702$	−27072.8	−1.45555
$703$	30526.0	1.63771
$704$	−9094.16	−0.486859
$705$	48490.6	2.59044
$706$	37407.7	1.99413
$707$	10447.1	0.555731
$708$	−60435.6	−3.20806
$709$	−28594.0	−1.51463	−0.757314	−	0.653051i	$-0.773489\pi$
$709$	−28594.0	−1.51463	−0.757314	+	0.653051i	$0.773489\pi$
$710$	45485.8	2.40430
$711$	10787.2	0.568990
$712$	−13993.6	−0.736563
$713$	−2359.73	−0.123945
$714$	−6827.64	−0.357868
$715$	12490.1	0.653292
$716$	−36934.1	−1.92778
$717$	−9109.61	−0.474483
$718$	33256.5	1.72858
$719$	18240.5	0.946114	0.473057	−	0.881032i	$-0.343150\pi$
$719$	18240.5	0.946114	0.473057	+	0.881032i	$0.343150\pi$
$720$	18137.5	0.938811
$721$	3910.81	0.202006
$722$	13642.0	0.703190
$723$	43777.7	2.25188
$724$	8033.68	0.412389
$725$	−15802.4	−0.809496
$726$	4443.72	0.227165
$727$	−9792.53	−0.499566	−0.249783	−	0.968302i	$-0.580359\pi$
$727$	−9792.53	−0.499566	−0.249783	+	0.968302i	$0.580359\pi$
$728$	−6015.20	−0.306234
$729$	−32086.4	−1.63016
$730$	24987.6	1.26690
$731$	365.309	0.0184835
$732$	−8479.22	−0.428143
$733$	−22723.8	−1.14505	−0.572525	−	0.819887i	$-0.694036\pi$
$733$	−22723.8	−1.14505	−0.572525	+	0.819887i	$0.694036\pi$
$734$	38168.3	1.91937
$735$	−8914.61	−0.447375
$736$	−6246.98	−0.312863
$737$	6692.35	0.334485
$738$	36882.9	1.83967
$739$	−24063.6	−1.19783	−0.598913	−	0.800814i	$-0.704401\pi$
$739$	−24063.6	−1.19783	−0.598913	+	0.800814i	$0.704401\pi$
$740$	−79240.0	−3.93638
$741$	−42470.8	−2.10554
$742$	9608.22	0.475376
$743$	−29211.6	−1.44235	−0.721177	−	0.692751i	$-0.756399\pi$
$743$	−29211.6	−1.44235	−0.721177	+	0.692751i	$0.756399\pi$
$744$	−11543.5	−0.568824
$745$	−42200.9	−2.07533
$746$	52585.6	2.58083
$747$	39392.8	1.92946
$748$	−3432.48	−0.167786
$749$	−4858.33	−0.237008
$750$	−189723.	−9.23692
$751$	1880.93	0.0913931	0.0456965	−	0.998955i	$-0.485449\pi$
$751$	1880.93	0.0913931	0.0456965	+	0.998955i	$0.485449\pi$
$752$	5317.84	0.257874
$753$	1470.69	0.0711751
$754$	10070.6	0.486408
$755$	50398.4	2.42939
$756$	9714.21	0.467331
$757$	−36218.7	−1.73896	−0.869480	−	0.493968i	$-0.835546\pi$
$757$	−36218.7	−1.73896	−0.869480	+	0.493968i	$0.835546\pi$
$758$	22470.5	1.07674
$759$	2558.53	0.122357
$760$	−36548.0	−1.74439
$761$	36966.4	1.76088	0.880441	−	0.474156i	$-0.157247\pi$
$761$	36966.4	1.76088	0.880441	+	0.474156i	$0.157247\pi$
$762$	−24462.1	−1.16295
$763$	−2387.03	−0.113259
$764$	32188.7	1.52428
$765$	24143.8	1.14107
$766$	28695.2	1.35353
$767$	32103.8	1.51135
$768$	−15061.8	−0.707678
$769$	−38975.5	−1.82769	−0.913845	−	0.406062i	$-0.866902\pi$
$769$	−38975.5	−1.82769	−0.913845	+	0.406062i	$0.866902\pi$
$770$	−7533.26	−0.352571
$771$	28896.5	1.34978
$772$	31157.7	1.45258
$773$	27341.9	1.27221	0.636105	−	0.771603i	$-0.280545\pi$
$773$	27341.9	1.27221	0.636105	+	0.771603i	$0.280545\pi$
$774$	−2524.05	−0.117216
$775$	−30154.0	−1.39763
$776$	−5817.07	−0.269099
$777$	17721.8	0.818231
$778$	55303.3	2.54848
$779$	20027.4	0.921125
$780$	110246.	5.06084
$781$	−5114.19	−0.234315
$782$	−3321.96	−0.151909
$783$	−5189.61	−0.236860
$784$	−977.642	−0.0445354
$785$	−6165.00	−0.280303
$786$	1117.75	0.0507235
$787$	−18268.5	−0.827446	−0.413723	−	0.910403i	$-0.635772\pi$
$787$	−18268.5	−0.827446	−0.413723	+	0.910403i	$0.635772\pi$
$788$	−22082.7	−0.998302
$789$	47500.7	2.14331
$790$	−25558.0	−1.15103
$791$	−6936.37	−0.311794
$792$	7567.71	0.339529
$793$	4504.22	0.201702
$794$	−2751.75	−0.122993
$795$	−56192.4	−2.50684
$796$	−36649.9	−1.63194
$797$	12717.6	0.565219	0.282610	−	0.959235i	$-0.408800\pi$
$797$	12717.6	0.565219	0.282610	+	0.959235i	$0.408800\pi$
$798$	25615.7	1.13632
$799$	7078.86	0.313432
$800$	−79827.6	−3.52792
$801$	−34682.2	−1.52988
$802$	43248.4	1.90418
$803$	−2809.48	−0.123467
$804$	59071.4	2.59115
$805$	−4337.37	−0.189903
$806$	19216.8	0.839804
$807$	1943.82	0.0847904
$808$	24865.3	1.08262
$809$	12502.0	0.543322	0.271661	−	0.962393i	$-0.412427\pi$
$809$	12502.0	0.543322	0.271661	+	0.962393i	$0.412427\pi$
$810$	13580.3	0.589090
$811$	−23431.3	−1.01453	−0.507264	−	0.861791i	$-0.669343\pi$
$811$	−23431.3	−1.01453	−0.507264	+	0.861791i	$0.669343\pi$
$812$	−3613.52	−0.156170
$813$	−9747.95	−0.420511
$814$	14975.7	0.644839
$815$	19077.6	0.819948
$816$	4379.08	0.187866
$817$	−1370.56	−0.0586899
$818$	20537.6	0.877850
$819$	−14908.3	−0.636065
$820$	−51987.6	−2.21401
$821$	33116.5	1.40776	0.703881	−	0.710317i	$-0.251449\pi$
$821$	33116.5	1.40776	0.703881	+	0.710317i	$0.251449\pi$
$822$	−103206.	−4.37923
$823$	−6383.39	−0.270366	−0.135183	−	0.990821i	$-0.543162\pi$
$823$	−6383.39	−0.270366	−0.135183	+	0.990821i	$0.543162\pi$
$824$	9308.20	0.393527
$825$	32694.4	1.37972
$826$	−19363.0	−0.815649
$827$	−27701.3	−1.16477	−0.582386	−	0.812912i	$-0.697881\pi$
$827$	−27701.3	−1.16477	−0.582386	+	0.812912i	$0.697881\pi$
$828$	13654.9	0.573116
$829$	−13160.2	−0.551353	−0.275676	−	0.961251i	$-0.588902\pi$
$829$	−13160.2	−0.551353	−0.275676	+	0.961251i	$0.588902\pi$
$830$	−93332.7	−3.90316
$831$	−30072.3	−1.25535
$832$	42640.7	1.77680
$833$	−1301.39	−0.0541303
$834$	114232.	4.74286
$835$	43263.4	1.79305
$836$	12877.9	0.532763
$837$	−9902.80	−0.408950
$838$	828.483	0.0341521
$839$	−24842.9	−1.02226	−0.511128	−	0.859505i	$-0.670772\pi$
$839$	−24842.9	−1.02226	−0.511128	+	0.859505i	$0.670772\pi$
$840$	−21217.9	−0.871531
$841$	−22458.6	−0.920848
$842$	11866.8	0.485696
$843$	26748.8	1.09286
$844$	−6117.95	−0.249513
$845$	−10196.7	−0.415123
$846$	−48910.2	−1.98767
$847$	847.000	0.0343604
$848$	−6162.48	−0.249552
$849$	68622.0	2.77397
$850$	−42450.0	−1.71297
$851$	8622.47	0.347326
$852$	−45141.4	−1.81516
$853$	−10131.6	−0.406681	−0.203340	−	0.979108i	$-0.565180\pi$
$853$	−10131.6	−0.406681	−0.203340	+	0.979108i	$0.565180\pi$
$854$	−2716.67	−0.108855
$855$	−90581.8	−3.62320
$856$	−11563.4	−0.461716
$857$	10115.6	0.403199	0.201599	−	0.979468i	$-0.435386\pi$
$857$	10115.6	0.403199	0.201599	+	0.979468i	$0.435386\pi$
$858$	−20835.7	−0.829044
$859$	−27491.4	−1.09196	−0.545980	−	0.837798i	$-0.683843\pi$
$859$	−27491.4	−1.09196	−0.545980	+	0.837798i	$0.683843\pi$
$860$	3557.72	0.141066
$861$	11626.9	0.460212
$862$	−55616.1	−2.19755
$863$	−117.276	−0.00462588	−0.00231294	−	0.999997i	$-0.500736\pi$
$863$	−117.276	−0.00462588	−0.00231294	+	0.999997i	$0.500736\pi$
$864$	−26216.0	−1.03228
$865$	−87110.8	−3.42411
$866$	−73997.8	−2.90364
$867$	−34771.5	−1.36206
$868$	−6895.31	−0.269634
$869$	2873.60	0.112175
$870$	35522.9	1.38430
$871$	−31379.1	−1.22071
$872$	−5681.43	−0.220639
$873$	−14417.2	−0.558933
$874$	12463.2	0.482351
$875$	−36162.3	−1.39715
$876$	−24798.4	−0.956462
$877$	11597.4	0.446543	0.223271	−	0.974756i	$-0.428326\pi$
$877$	11597.4	0.446543	0.223271	+	0.974756i	$0.428326\pi$
$878$	26812.3	1.03061
$879$	−15653.2	−0.600648
$880$	4831.65	0.185085
$881$	7524.18	0.287737	0.143868	−	0.989597i	$-0.454046\pi$
$881$	7524.18	0.287737	0.143868	+	0.989597i	$0.454046\pi$
$882$	8991.75	0.343274
$883$	13467.4	0.513266	0.256633	−	0.966509i	$-0.417387\pi$
$883$	13467.4	0.513266	0.256633	+	0.966509i	$0.417387\pi$
$884$	16094.2	0.612339
$885$	113242.	4.30124
$886$	28086.2	1.06498
$887$	−12955.7	−0.490427	−0.245214	−	0.969469i	$-0.578858\pi$
$887$	−12955.7	−0.490427	−0.245214	+	0.969469i	$0.578858\pi$
$888$	42180.0	1.59400
$889$	−4662.63	−0.175905
$890$	82172.1	3.09485
$891$	−1526.90	−0.0574107
$892$	24685.7	0.926612
$893$	−26558.2	−0.995226
$894$	70398.6	2.63365
$895$	69205.8	2.58469
$896$	−13288.9	−0.495480
$897$	−11996.4	−0.446543
$898$	−79518.9	−2.95499
$899$	3683.68	0.136660
$900$	174490.	6.46260
$901$	−8203.20	−0.303317
$902$	9825.25	0.362688
$903$	−795.673	−0.0293226
$904$	−16509.4	−0.607405
$905$	−15053.2	−0.552913
$906$	−84073.5	−3.08295
$907$	47843.5	1.75151	0.875753	−	0.482759i	$-0.160365\pi$
$907$	47843.5	1.75151	0.875753	+	0.482759i	$0.160365\pi$
$908$	−71104.9	−2.59879
$909$	61626.9	2.24866
$910$	35322.0	1.28672
$911$	16969.8	0.617162	0.308581	−	0.951198i	$-0.400146\pi$
$911$	16969.8	0.617162	0.308581	+	0.951198i	$0.400146\pi$
$912$	−16429.3	−0.596522
$913$	10493.8	0.380389
$914$	27588.3	0.998402
$915$	15888.1	0.574036
$916$	−35197.1	−1.26959
$917$	213.049	0.00767231
$918$	−13940.9	−0.501218
$919$	12095.2	0.434149	0.217075	−	0.976155i	$-0.430348\pi$
$919$	12095.2	0.434149	0.217075	+	0.976155i	$0.430348\pi$
$920$	−10323.5	−0.369951
$921$	54511.4	1.95029
$922$	35468.8	1.26692
$923$	23979.4	0.855138
$924$	7476.22	0.266179
$925$	110183.	3.91653
$926$	−33308.6	−1.18206
$927$	23069.8	0.817379
$928$	9751.91	0.344959
$929$	−44544.3	−1.57314	−0.786571	−	0.617499i	$-0.788146\pi$
$929$	−44544.3	−1.57314	−0.786571	+	0.617499i	$0.788146\pi$
$930$	67784.8	2.39005
$931$	4882.52	0.171878
$932$	−767.985	−0.0269916
$933$	−43321.8	−1.52014
$934$	6752.16	0.236550
$935$	6431.66	0.224960
$936$	−35483.5	−1.23912
$937$	−49265.8	−1.71766	−0.858828	−	0.512264i	$-0.828807\pi$
$937$	−49265.8	−1.71766	−0.858828	+	0.512264i	$0.828807\pi$
$938$	18925.9	0.658799
$939$	44119.2	1.53331
$940$	68940.4	2.39211
$941$	−18403.1	−0.637538	−0.318769	−	0.947832i	$-0.603269\pi$
$941$	−18403.1	−0.637538	−0.318769	+	0.947832i	$0.603269\pi$
$942$	10284.3	0.355712
$943$	5657.01	0.195353
$944$	12419.0	0.428181
$945$	−18202.1	−0.626577
$946$	−672.381	−0.0231089
$947$	17689.3	0.606996	0.303498	−	0.952832i	$-0.401845\pi$
$947$	17689.3	0.606996	0.303498	+	0.952832i	$0.401845\pi$
$948$	25364.4	0.868986
$949$	13173.1	0.450597
$950$	159262.	5.43911
$951$	−47990.5	−1.63638
$952$	−3097.47	−0.105451
$953$	−5298.19	−0.180090	−0.0900448	−	0.995938i	$-0.528701\pi$
$953$	−5298.19	−0.180090	−0.0900448	+	0.995938i	$0.528701\pi$
$954$	56678.7	1.92352
$955$	−60314.1	−2.04368
$956$	−12951.4	−0.438156
$957$	−3994.01	−0.134909
$958$	−72855.6	−2.45705
$959$	−19671.7	−0.662392
$960$	150410.	5.05672
$961$	−22761.8	−0.764050
$962$	−70218.3	−2.35336
$963$	−28659.1	−0.959011
$964$	62239.9	2.07947
$965$	−58382.2	−1.94755
$966$	7235.50	0.240992
$967$	33990.6	1.13037	0.565184	−	0.824965i	$-0.308805\pi$
$967$	33990.6	1.13037	0.565184	+	0.824965i	$0.308805\pi$
$968$	2015.96	0.0669375
$969$	−21869.9	−0.725039
$970$	34158.5	1.13068
$971$	41991.0	1.38780	0.693900	−	0.720071i	$-0.255891\pi$
$971$	41991.0	1.38780	0.693900	+	0.720071i	$0.255891\pi$
$972$	−50946.5	−1.68118
$973$	21773.4	0.717393
$974$	10110.1	0.332597
$975$	−153297.	−5.03533
$976$	1742.40	0.0571444
$977$	−31233.4	−1.02277	−0.511384	−	0.859352i	$-0.670867\pi$
$977$	−31233.4	−1.02277	−0.511384	+	0.859352i	$0.670867\pi$
$978$	−31824.7	−1.04053
$979$	−9239.00	−0.301614
$980$	−12674.1	−0.413123
$981$	−14081.0	−0.458281
$982$	−65012.0	−2.11264
$983$	−45702.5	−1.48289	−0.741447	−	0.671012i	$-0.765860\pi$
$983$	−45702.5	−1.48289	−0.741447	+	0.671012i	$0.765860\pi$
$984$	27673.4	0.896540
$985$	41377.7	1.33848
$986$	5185.78	0.167494
$987$	−15418.3	−0.497235
$988$	−60381.8	−1.94433
$989$	−387.132	−0.0124470
$990$	−44438.5	−1.42661
$991$	−4310.72	−0.138178	−0.0690890	−	0.997611i	$-0.522009\pi$
$991$	−4310.72	−0.138178	−0.0690890	+	0.997611i	$0.522009\pi$
$992$	18608.6	0.595587
$993$	−11292.8	−0.360892
$994$	−14462.9	−0.461504
$995$	68673.3	2.18803
$996$	92626.0	2.94675
$997$	−6103.28	−0.193875	−0.0969373	−	0.995290i	$-0.530905\pi$
$997$	−6103.28	−0.193875	−0.0969373	+	0.995290i	$0.530905\pi$
$998$	15705.1	0.498133
$999$	36184.9	1.14599

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.4.a.e.1.4	✓	5
3.2	odd	2		693.4.a.o.1.2		5
4.3	odd	2		1232.4.a.y.1.1		5
5.4	even	2		1925.4.a.r.1.2		5
7.6	odd	2		539.4.a.h.1.4		5
11.10	odd	2		847.4.a.f.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.4.a.e.1.4	✓	5	1.1	even	1	trivial
539.4.a.h.1.4		5	7.6	odd	2
693.4.a.o.1.2		5	3.2	odd	2
847.4.a.f.1.2		5	11.10	odd	2
1232.4.a.y.1.1		5	4.3	odd	2
1925.4.a.r.1.2		5	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	77.a (trivial)

\(f(q)\)	\(=\)	\(q+4.44399 q^{2} +8.26395 q^{3} +11.7491 q^{4} -22.0150 q^{5} +36.7249 q^{6} +7.00000 q^{7} +16.6609 q^{8} +41.2928 q^{9} -97.8345 q^{10} +11.0000 q^{11} +97.0937 q^{12} -51.5769 q^{13} +31.1080 q^{14} -181.931 q^{15} -19.9519 q^{16} -26.5590 q^{17} +183.505 q^{18} +99.6432 q^{19} -258.656 q^{20} +57.8476 q^{21} +48.8839 q^{22} +28.1455 q^{23} +137.684 q^{24} +359.660 q^{25} -229.207 q^{26} +118.115 q^{27} +82.2435 q^{28} -43.9369 q^{29} -808.499 q^{30} -83.8402 q^{31} -221.953 q^{32} +90.9034 q^{33} -118.028 q^{34} -154.105 q^{35} +485.152 q^{36} +306.353 q^{37} +442.814 q^{38} -426.228 q^{39} -366.789 q^{40} +200.991 q^{41} +257.074 q^{42} -13.7546 q^{43} +129.240 q^{44} -909.062 q^{45} +125.079 q^{46} -266.533 q^{47} -164.881 q^{48} +49.0000 q^{49} +1598.33 q^{50} -219.482 q^{51} -605.980 q^{52} +308.867 q^{53} +524.903 q^{54} -242.165 q^{55} +116.626 q^{56} +823.446 q^{57} -195.255 q^{58} -622.446 q^{59} -2137.52 q^{60} -87.3303 q^{61} -372.585 q^{62} +289.050 q^{63} -826.742 q^{64} +1135.46 q^{65} +403.974 q^{66} +608.395 q^{67} -312.044 q^{68} +232.593 q^{69} -684.842 q^{70} -464.926 q^{71} +687.974 q^{72} -255.407 q^{73} +1361.43 q^{74} +2972.21 q^{75} +1170.72 q^{76} +77.0000 q^{77} -1894.16 q^{78} +261.237 q^{79} +439.240 q^{80} -138.809 q^{81} +893.204 q^{82} +953.986 q^{83} +679.656 q^{84} +584.696 q^{85} -61.1255 q^{86} -363.092 q^{87} +183.269 q^{88} -839.910 q^{89} -4039.86 q^{90} -361.038 q^{91} +330.684 q^{92} -692.851 q^{93} -1184.47 q^{94} -2193.64 q^{95} -1834.21 q^{96} -349.146 q^{97} +217.756 q^{98} +454.221 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 2 q^{3} + 45 q^{4} - 24 q^{5} + 4 q^{6} + 35 q^{7} + 57 q^{8} + 63 q^{9} - 10 q^{10} + 55 q^{11} + 24 q^{12} - 50 q^{13} + 7 q^{14} - 146 q^{15} + 433 q^{16} + 222 q^{17} + 245 q^{18} + 160 q^{19}+ \cdots + 693 q^{99}+O(q^{100}) \) 5 * q + q^2 + 2 * q^3 + 45 * q^4 - 24 * q^5 + 4 * q^6 + 35 * q^7 + 57 * q^8 + 63 * q^9 - 10 * q^10 + 55 * q^11 + 24 * q^12 - 50 * q^13 + 7 * q^14 - 146 * q^15 + 433 * q^16 + 222 * q^17 + 245 * q^18 + 160 * q^19 - 430 * q^20 + 14 * q^21 + 11 * q^22 + 54 * q^23 - 220 * q^24 + 125 * q^25 - 1026 * q^26 + 110 * q^27 + 315 * q^28 + 14 * q^29 - 1080 * q^30 - 34 * q^31 - 583 * q^32 + 22 * q^33 - 750 * q^34 - 168 * q^35 - 411 * q^36 + 1044 * q^37 - 156 * q^38 - 124 * q^39 + 1158 * q^40 - 114 * q^41 + 28 * q^42 + 672 * q^43 + 495 * q^44 - 530 * q^45 - 1224 * q^46 - 292 * q^47 - 1652 * q^48 + 245 * q^49 + 1143 * q^50 + 768 * q^51 - 914 * q^52 - 710 * q^53 + 1608 * q^54 - 264 * q^55 + 399 * q^56 + 2012 * q^57 - 810 * q^58 + 270 * q^59 - 3068 * q^60 + 138 * q^61 - 480 * q^62 + 441 * q^63 + 3001 * q^64 - 196 * q^65 + 44 * q^66 + 1942 * q^67 + 3130 * q^68 - 1306 * q^69 - 70 * q^70 - 278 * q^71 + 3565 * q^72 - 338 * q^73 + 462 * q^74 + 3960 * q^75 - 1332 * q^76 + 385 * q^77 + 280 * q^78 + 576 * q^79 - 1602 * q^80 - 1439 * q^81 + 1386 * q^82 + 1644 * q^83 + 168 * q^84 + 360 * q^85 + 2020 * q^86 - 1956 * q^87 + 627 * q^88 - 3656 * q^89 - 6162 * q^90 - 350 * q^91 - 748 * q^92 - 1442 * q^93 + 976 * q^94 - 1276 * q^95 - 4508 * q^96 + 692 * q^97 + 49 * q^98 + 693 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more