LMFDB - Embedded newform 435.4.a.j.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [435,4,Mod(1,435)] 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("435.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(435, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	435.a (trivial)

Newform invariants

comment:select newform

sage:traces = [7,-1] 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:	$25.6658308525$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 35x^{5} + 18x^{4} + 329x^{3} - 167x^{2} - 767x + 638 $ x^7 - x^6 - 35x^5 + 18x^4 + 329x^3 - 167x^2 - 767*x + 638
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-3.52131$ of defining polynomial
Character	$\chi$	$=$	435.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.52131 q^{2} +3.00000 q^{3} +4.39964 q^{4} -5.00000 q^{5} +10.5639 q^{6} -8.86571 q^{7} -12.6780 q^{8} +9.00000 q^{9} -17.6066 q^{10} -61.9492 q^{11} +13.1989 q^{12} +31.6208 q^{13} -31.2189 q^{14} -15.0000 q^{15} -79.8403 q^{16} -48.6694 q^{17} +31.6918 q^{18} -127.727 q^{19} -21.9982 q^{20} -26.5971 q^{21} -218.143 q^{22} +184.026 q^{23} -38.0339 q^{24} +25.0000 q^{25} +111.347 q^{26} +27.0000 q^{27} -39.0059 q^{28} -29.0000 q^{29} -52.8197 q^{30} -251.985 q^{31} -179.719 q^{32} -185.848 q^{33} -171.380 q^{34} +44.3285 q^{35} +39.5968 q^{36} +197.740 q^{37} -449.765 q^{38} +94.8624 q^{39} +63.3899 q^{40} -163.446 q^{41} -93.6568 q^{42} -33.2231 q^{43} -272.555 q^{44} -45.0000 q^{45} +648.012 q^{46} +528.945 q^{47} -239.521 q^{48} -264.399 q^{49} +88.0328 q^{50} -146.008 q^{51} +139.120 q^{52} -240.256 q^{53} +95.0754 q^{54} +309.746 q^{55} +112.399 q^{56} -383.180 q^{57} -102.118 q^{58} -202.976 q^{59} -65.9947 q^{60} +492.192 q^{61} -887.318 q^{62} -79.7914 q^{63} +5.87624 q^{64} -158.104 q^{65} -654.428 q^{66} -229.556 q^{67} -214.128 q^{68} +552.077 q^{69} +156.095 q^{70} +21.2064 q^{71} -114.102 q^{72} -1145.48 q^{73} +696.303 q^{74} +75.0000 q^{75} -561.952 q^{76} +549.224 q^{77} +334.040 q^{78} +95.6307 q^{79} +399.201 q^{80} +81.0000 q^{81} -575.545 q^{82} +1239.97 q^{83} -117.018 q^{84} +243.347 q^{85} -116.989 q^{86} -87.0000 q^{87} +785.391 q^{88} +116.863 q^{89} -158.459 q^{90} -280.341 q^{91} +809.648 q^{92} -755.955 q^{93} +1862.58 q^{94} +638.633 q^{95} -539.156 q^{96} -275.722 q^{97} -931.032 q^{98} -557.543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 21 q^{3} + 15 q^{4} - 35 q^{5} - 3 q^{6} - 37 q^{7} - 36 q^{8} + 63 q^{9} + 5 q^{10} - 11 q^{11} + 45 q^{12} - 133 q^{13} - 75 q^{14} - 105 q^{15} - 53 q^{16} + 21 q^{17} - 9 q^{18} - 170 q^{19}+ \cdots - 99 q^{99}+O(q^{100}) $ 7 * q - q^2 + 21 * q^3 + 15 * q^4 - 35 * q^5 - 3 * q^6 - 37 * q^7 - 36 * q^8 + 63 * q^9 + 5 * q^10 - 11 * q^11 + 45 * q^12 - 133 * q^13 - 75 * q^14 - 105 * q^15 - 53 * q^16 + 21 * q^17 - 9 * q^18 - 170 * q^19 - 75 * q^20 - 111 * q^21 - 369 * q^22 - 68 * q^23 - 108 * q^24 + 175 * q^25 + 181 * q^26 + 189 * q^27 - 637 * q^28 - 203 * q^29 + 15 * q^30 - 480 * q^31 - 779 * q^32 - 33 * q^33 - 897 * q^34 + 185 * q^35 + 135 * q^36 - 1032 * q^37 - 194 * q^38 - 399 * q^39 + 180 * q^40 - 638 * q^41 - 225 * q^42 - 512 * q^43 + 625 * q^44 - 315 * q^45 + 16 * q^46 - 111 * q^47 - 159 * q^48 + 178 * q^49 - 25 * q^50 + 63 * q^51 - 1263 * q^52 + 410 * q^53 - 27 * q^54 + 55 * q^55 + 1174 * q^56 - 510 * q^57 + 29 * q^58 - 426 * q^59 - 225 * q^60 - 1192 * q^61 + 460 * q^62 - 333 * q^63 + 390 * q^64 + 665 * q^65 - 1107 * q^66 - 1671 * q^67 + 1509 * q^68 - 204 * q^69 + 375 * q^70 - 1324 * q^71 - 324 * q^72 - 852 * q^73 + 1780 * q^74 + 525 * q^75 - 564 * q^76 - 2107 * q^77 + 543 * q^78 + 366 * q^79 + 265 * q^80 + 567 * q^81 - 318 * q^82 + 470 * q^83 - 1911 * q^84 - 105 * q^85 - 2196 * q^86 - 609 * q^87 - 2518 * q^88 + 51 * q^89 + 45 * q^90 - 1297 * q^91 - 684 * q^92 - 1440 * q^93 - 1837 * q^94 + 850 * q^95 - 2337 * q^96 - 3322 * q^97 + 1068 * q^98 - 99 * 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 $

$2$	3.52131	1.24497	0.622486	−	0.782631i	$-0.286123\pi$
$2$	3.52131	1.24497	0.622486	+	0.782631i	$0.286123\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.39964	0.549955
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	10.5639	0.718785
$7$	−8.86571	−0.478703	−0.239352	−	0.970933i	$-0.576935\pi$
$7$	−8.86571	−0.478703	−0.239352	+	0.970933i	$0.576935\pi$
$8$	−12.6780	−0.560293
$9$	9.00000	0.333333
$10$	−17.6066	−0.556768
$11$	−61.9492	−1.69804	−0.849018	−	0.528364i	$-0.822806\pi$
$11$	−61.9492	−1.69804	−0.849018	+	0.528364i	$0.822806\pi$
$12$	13.1989	0.317517
$13$	31.6208	0.674618	0.337309	−	0.941394i	$-0.390483\pi$
$13$	31.6208	0.674618	0.337309	+	0.941394i	$0.390483\pi$
$14$	−31.2189	−0.595972
$15$	−15.0000	−0.258199
$16$	−79.8403	−1.24750
$17$	−48.6694	−0.694357	−0.347178	−	0.937799i	$-0.612860\pi$
$17$	−48.6694	−0.694357	−0.347178	+	0.937799i	$0.612860\pi$
$18$	31.6918	0.414991
$19$	−127.727	−1.54224	−0.771118	−	0.636692i	$-0.780302\pi$
$19$	−127.727	−1.54224	−0.771118	+	0.636692i	$0.780302\pi$
$20$	−21.9982	−0.245948
$21$	−26.5971	−0.276379
$22$	−218.143	−2.11401
$23$	184.026	1.66835	0.834175	−	0.551501i	$-0.185945\pi$
$23$	184.026	1.66835	0.834175	+	0.551501i	$0.185945\pi$
$24$	−38.0339	−0.323485
$25$	25.0000	0.200000
$26$	111.347	0.839881
$27$	27.0000	0.192450
$28$	−39.0059	−0.263265
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	−52.8197	−0.321450
$31$	−251.985	−1.45993	−0.729965	−	0.683484i	$-0.760464\pi$
$31$	−251.985	−1.45993	−0.729965	+	0.683484i	$0.760464\pi$
$32$	−179.719	−0.992815
$33$	−185.848	−0.980361
$34$	−171.380	−0.864455
$35$	44.3285	0.214083
$36$	39.5968	0.183318
$37$	197.740	0.878600	0.439300	−	0.898340i	$-0.355226\pi$
$37$	197.740	0.878600	0.439300	+	0.898340i	$0.355226\pi$
$38$	−449.765	−1.92004
$39$	94.8624	0.389491
$40$	63.3899	0.250571
$41$	−163.446	−0.622585	−0.311293	−	0.950314i	$-0.600762\pi$
$41$	−163.446	−0.622585	−0.311293	+	0.950314i	$0.600762\pi$
$42$	−93.6568	−0.344085
$43$	−33.2231	−0.117825	−0.0589124	−	0.998263i	$-0.518763\pi$
$43$	−33.2231	−0.117825	−0.0589124	+	0.998263i	$0.518763\pi$
$44$	−272.555	−0.933844
$45$	−45.0000	−0.149071
$46$	648.012	2.07705
$47$	528.945	1.64159	0.820793	−	0.571226i	$-0.193532\pi$
$47$	528.945	1.64159	0.820793	+	0.571226i	$0.193532\pi$
$48$	−239.521	−0.720247
$49$	−264.399	−0.770843
$50$	88.0328	0.248994
$51$	−146.008	−0.400887
$52$	139.120	0.371010
$53$	−240.256	−0.622673	−0.311336	−	0.950300i	$-0.600777\pi$
$53$	−240.256	−0.622673	−0.311336	+	0.950300i	$0.600777\pi$
$54$	95.0754	0.239595
$55$	309.746	0.759385
$56$	112.399	0.268214
$57$	−383.180	−0.890411
$58$	−102.118	−0.231186
$59$	−202.976	−0.447885	−0.223942	−	0.974602i	$-0.571893\pi$
$59$	−202.976	−0.447885	−0.223942	+	0.974602i	$0.571893\pi$
$60$	−65.9947	−0.141998
$61$	492.192	1.03309	0.516547	−	0.856259i	$-0.327217\pi$
$61$	492.192	1.03309	0.516547	+	0.856259i	$0.327217\pi$
$62$	−887.318	−1.81757
$63$	−79.7914	−0.159568
$64$	5.87624	0.0114770
$65$	−158.104	−0.301698
$66$	−654.428	−1.22052
$67$	−229.556	−0.418577	−0.209289	−	0.977854i	$-0.567115\pi$
$67$	−229.556	−0.418577	−0.209289	+	0.977854i	$0.567115\pi$
$68$	−214.128	−0.381865
$69$	552.077	0.963222
$70$	156.095	0.266527
$71$	21.2064	0.0354471	0.0177235	−	0.999843i	$-0.494358\pi$
$71$	21.2064	0.0354471	0.0177235	+	0.999843i	$0.494358\pi$
$72$	−114.102	−0.186764
$73$	−1145.48	−1.83656	−0.918279	−	0.395934i	$-0.870421\pi$
$73$	−1145.48	−1.83656	−0.918279	+	0.395934i	$0.870421\pi$
$74$	696.303	1.09383
$75$	75.0000	0.115470
$76$	−561.952	−0.848161
$77$	549.224	0.812855
$78$	334.040	0.484905
$79$	95.6307	0.136194	0.0680968	−	0.997679i	$-0.478307\pi$
$79$	95.6307	0.136194	0.0680968	+	0.997679i	$0.478307\pi$
$80$	399.201	0.557901
$81$	81.0000	0.111111
$82$	−575.545	−0.775101
$83$	1239.97	1.63982	0.819908	−	0.572496i	$-0.194025\pi$
$83$	1239.97	1.63982	0.819908	+	0.572496i	$0.194025\pi$
$84$	−117.018	−0.151996
$85$	243.347	0.310526
$86$	−116.989	−0.146689
$87$	−87.0000	−0.107211
$88$	785.391	0.951397
$89$	116.863	0.139185	0.0695927	−	0.997575i	$-0.477830\pi$
$89$	116.863	0.139185	0.0695927	+	0.997575i	$0.477830\pi$
$90$	−158.459	−0.185589
$91$	−280.341	−0.322942
$92$	809.648	0.917518
$93$	−755.955	−0.842891
$94$	1862.58	2.04373
$95$	638.633	0.689709
$96$	−539.156	−0.573202
$97$	−275.722	−0.288611	−0.144306	−	0.989533i	$-0.546095\pi$
$97$	−275.722	−0.288611	−0.144306	+	0.989533i	$0.546095\pi$
$98$	−931.032	−0.959678
$99$	−557.543	−0.566012
$100$	109.991	0.109991
$101$	−1909.39	−1.88111	−0.940553	−	0.339648i	$-0.889692\pi$
$101$	−1909.39	−1.88111	−0.940553	+	0.339648i	$0.889692\pi$
$102$	−514.141	−0.499093
$103$	1501.97	1.43683	0.718415	−	0.695614i	$-0.244868\pi$
$103$	1501.97	1.43683	0.718415	+	0.695614i	$0.244868\pi$
$104$	−400.888	−0.377984
$105$	132.986	0.123601
$106$	−846.016	−0.775210
$107$	1434.61	1.29616	0.648080	−	0.761572i	$-0.275572\pi$
$107$	1434.61	1.29616	0.648080	+	0.761572i	$0.275572\pi$
$108$	118.790	0.105839
$109$	−347.951	−0.305758	−0.152879	−	0.988245i	$-0.548855\pi$
$109$	−347.951	−0.305758	−0.152879	+	0.988245i	$0.548855\pi$
$110$	1090.71	0.945413
$111$	593.219	0.507260
$112$	707.840	0.597184
$113$	−1812.68	−1.50905	−0.754524	−	0.656272i	$-0.772132\pi$
$113$	−1812.68	−1.50905	−0.754524	+	0.656272i	$0.772132\pi$
$114$	−1349.30	−1.10854
$115$	−920.129	−0.746108
$116$	−127.590	−0.102124
$117$	284.587	0.224873
$118$	−714.742	−0.557604
$119$	431.489	0.332391
$120$	190.170	0.144667
$121$	2506.71	1.88333
$122$	1733.16	1.28617
$123$	−490.338	−0.359450
$124$	−1108.64	−0.802897
$125$	−125.000	−0.0894427
$126$	−280.970	−0.198657
$127$	550.739	0.384804	0.192402	−	0.981316i	$-0.438372\pi$
$127$	550.739	0.384804	0.192402	+	0.981316i	$0.438372\pi$
$128$	1458.44	1.00710
$129$	−99.6692	−0.0680262
$130$	−556.734	−0.375606
$131$	−124.824	−0.0832515	−0.0416257	−	0.999133i	$-0.513254\pi$
$131$	−124.824	−0.0832515	−0.0416257	+	0.999133i	$0.513254\pi$
$132$	−817.664	−0.539155
$133$	1132.39	0.738273
$134$	−808.337	−0.521117
$135$	−135.000	−0.0860663
$136$	617.030	0.389043
$137$	−549.879	−0.342915	−0.171458	−	0.985192i	$-0.554848\pi$
$137$	−549.879	−0.342915	−0.171458	+	0.985192i	$0.554848\pi$
$138$	1944.04	1.19918
$139$	−2243.32	−1.36889	−0.684445	−	0.729065i	$-0.739955\pi$
$139$	−2243.32	−1.36889	−0.684445	+	0.729065i	$0.739955\pi$
$140$	195.030	0.117736
$141$	1586.83	0.947770
$142$	74.6745	0.0441306
$143$	−1958.88	−1.14553
$144$	−718.563	−0.415835
$145$	145.000	0.0830455
$146$	−4033.61	−2.28646
$147$	−793.198	−0.445047
$148$	869.984	0.483191
$149$	−614.305	−0.337757	−0.168879	−	0.985637i	$-0.554015\pi$
$149$	−614.305	−0.337757	−0.168879	+	0.985637i	$0.554015\pi$
$150$	264.098	0.143757
$151$	−1121.72	−0.604531	−0.302266	−	0.953224i	$-0.597743\pi$
$151$	−1121.72	−0.604531	−0.302266	+	0.953224i	$0.597743\pi$
$152$	1619.32	0.864104
$153$	−438.025	−0.231452
$154$	1933.99	1.01198
$155$	1259.92	0.652901
$156$	417.361	0.214203
$157$	3238.34	1.64616	0.823082	−	0.567923i	$-0.192253\pi$
$157$	3238.34	1.64616	0.823082	+	0.567923i	$0.192253\pi$
$158$	336.746	0.169557
$159$	−720.767	−0.359500
$160$	898.594	0.444001
$161$	−1631.52	−0.798644
$162$	285.226	0.138330
$163$	−2973.43	−1.42881	−0.714407	−	0.699730i	$-0.753303\pi$
$163$	−2973.43	−1.42881	−0.714407	+	0.699730i	$0.753303\pi$
$164$	−719.105	−0.342394
$165$	929.238	0.438431
$166$	4366.33	2.04152
$167$	4133.13	1.91515	0.957577	−	0.288176i	$-0.0930489\pi$
$167$	4133.13	1.91515	0.957577	+	0.288176i	$0.0930489\pi$
$168$	337.198	0.154853
$169$	−1197.12	−0.544890
$170$	856.901	0.386596
$171$	−1149.54	−0.514079
$172$	−146.170	−0.0647984
$173$	347.755	0.152829	0.0764143	−	0.997076i	$-0.475653\pi$
$173$	347.755	0.152829	0.0764143	+	0.997076i	$0.475653\pi$
$174$	−306.354	−0.133475
$175$	−221.643	−0.0957406
$176$	4946.04	2.11831
$177$	−608.928	−0.258587
$178$	411.513	0.173282
$179$	789.082	0.329490	0.164745	−	0.986336i	$-0.447320\pi$
$179$	789.082	0.329490	0.164745	+	0.986336i	$0.447320\pi$
$180$	−197.984	−0.0819825
$181$	−4547.86	−1.86762	−0.933812	−	0.357763i	$-0.883539\pi$
$181$	−4547.86	−1.86762	−0.933812	+	0.357763i	$0.883539\pi$
$182$	−987.168	−0.402054
$183$	1476.58	0.596458
$184$	−2333.08	−0.934764
$185$	−988.699	−0.392922
$186$	−2661.95	−1.04938
$187$	3015.03	1.17904
$188$	2327.17	0.902799
$189$	−239.374	−0.0921265
$190$	2248.83	0.858669
$191$	−1121.45	−0.424843	−0.212421	−	0.977178i	$-0.568135\pi$
$191$	−1121.45	−0.424843	−0.212421	+	0.977178i	$0.568135\pi$
$192$	17.6287	0.00662627
$193$	−3950.05	−1.47322	−0.736608	−	0.676320i	$-0.763574\pi$
$193$	−3950.05	−1.47322	−0.736608	+	0.676320i	$0.763574\pi$
$194$	−970.902	−0.359313
$195$	−474.312	−0.174186
$196$	−1163.26	−0.423930
$197$	−436.434	−0.157841	−0.0789205	−	0.996881i	$-0.525147\pi$
$197$	−436.434	−0.157841	−0.0789205	+	0.996881i	$0.525147\pi$
$198$	−1963.28	−0.704669
$199$	775.787	0.276352	0.138176	−	0.990408i	$-0.455876\pi$
$199$	775.787	0.276352	0.138176	+	0.990408i	$0.455876\pi$
$200$	−316.949	−0.112059
$201$	−688.667	−0.241666
$202$	−6723.57	−2.34192
$203$	257.105	0.0888929
$204$	−642.384	−0.220470
$205$	817.231	0.278429
$206$	5288.91	1.78881
$207$	1656.23	0.556116
$208$	−2524.61	−0.841589
$209$	7912.57	2.61877
$210$	468.284	0.153879
$211$	2474.44	0.807335	0.403667	−	0.914906i	$-0.367735\pi$
$211$	2474.44	0.807335	0.403667	+	0.914906i	$0.367735\pi$
$212$	−1057.04	−0.342442
$213$	63.6193	0.0204654
$214$	5051.71	1.61368
$215$	166.115	0.0526929
$216$	−342.305	−0.107828
$217$	2234.02	0.698873
$218$	−1225.24	−0.380660
$219$	−3436.45	−1.06034
$220$	1362.77	0.417628
$221$	−1538.97	−0.468426
$222$	2088.91	0.631525
$223$	−1035.62	−0.310987	−0.155494	−	0.987837i	$-0.549697\pi$
$223$	−1035.62	−0.310987	−0.155494	+	0.987837i	$0.549697\pi$
$224$	1593.33	0.475264
$225$	225.000	0.0666667
$226$	−6383.01	−1.87872
$227$	−1068.43	−0.312398	−0.156199	−	0.987726i	$-0.549924\pi$
$227$	−1068.43	−0.312398	−0.156199	+	0.987726i	$0.549924\pi$
$228$	−1685.85	−0.489686
$229$	−638.809	−0.184339	−0.0921696	−	0.995743i	$-0.529380\pi$
$229$	−638.809	−0.184339	−0.0921696	+	0.995743i	$0.529380\pi$
$230$	−3240.06	−0.928884
$231$	1647.67	0.469302
$232$	367.661	0.104044
$233$	4199.81	1.18085	0.590427	−	0.807091i	$-0.298959\pi$
$233$	4199.81	1.18085	0.590427	+	0.807091i	$0.298959\pi$
$234$	1002.12	0.279960
$235$	−2644.72	−0.734139
$236$	−893.022	−0.246317
$237$	286.892	0.0786314
$238$	1519.41	0.413817
$239$	1481.20	0.400882	0.200441	−	0.979706i	$-0.435763\pi$
$239$	1481.20	0.400882	0.200441	+	0.979706i	$0.435763\pi$
$240$	1197.60	0.322104
$241$	7144.57	1.90964	0.954818	−	0.297191i	$-0.0960498\pi$
$241$	7144.57	1.90964	0.954818	+	0.297191i	$0.0960498\pi$
$242$	8826.90	2.34469
$243$	243.000	0.0641500
$244$	2165.47	0.568156
$245$	1322.00	0.344732
$246$	−1726.64	−0.447505
$247$	−4038.82	−1.04042
$248$	3194.66	0.817988
$249$	3719.92	0.946748
$250$	−440.164	−0.111354
$251$	−5209.72	−1.31010	−0.655049	−	0.755587i	$-0.727352\pi$
$251$	−5209.72	−1.31010	−0.655049	+	0.755587i	$0.727352\pi$
$252$	−351.054	−0.0877551
$253$	−11400.3	−2.83292
$254$	1939.32	0.479071
$255$	730.041	0.179282
$256$	5088.62	1.24234
$257$	3431.65	0.832919	0.416460	−	0.909154i	$-0.363271\pi$
$257$	3431.65	0.832919	0.416460	+	0.909154i	$0.363271\pi$
$258$	−350.966	−0.0846907
$259$	−1753.10	−0.420589
$260$	−695.602	−0.165921
$261$	−261.000	−0.0618984
$262$	−439.545	−0.103646
$263$	−1738.29	−0.407558	−0.203779	−	0.979017i	$-0.565322\pi$
$263$	−1738.29	−0.407558	−0.203779	+	0.979017i	$0.565322\pi$
$264$	2356.17	0.549290
$265$	1201.28	0.278468
$266$	3987.49	0.919130
$267$	350.590	0.0803587
$268$	−1009.96	−0.230199
$269$	2829.31	0.641287	0.320643	−	0.947200i	$-0.396101\pi$
$269$	2829.31	0.641287	0.320643	+	0.947200i	$0.396101\pi$
$270$	−475.377	−0.107150
$271$	−1399.29	−0.313657	−0.156828	−	0.987626i	$-0.550127\pi$
$271$	−1399.29	−0.313657	−0.156828	+	0.987626i	$0.550127\pi$
$272$	3885.78	0.866213
$273$	−841.022	−0.186451
$274$	−1936.30	−0.426920
$275$	−1548.73	−0.339607
$276$	2428.94	0.529729
$277$	−3526.40	−0.764912	−0.382456	−	0.923974i	$-0.624922\pi$
$277$	−3526.40	−0.764912	−0.382456	+	0.923974i	$0.624922\pi$
$278$	−7899.42	−1.70423
$279$	−2267.86	−0.486643
$280$	−561.996	−0.119949
$281$	−857.124	−0.181963	−0.0909817	−	0.995853i	$-0.529000\pi$
$281$	−857.124	−0.181963	−0.0909817	+	0.995853i	$0.529000\pi$
$282$	5587.74	1.17995
$283$	−7197.47	−1.51182	−0.755910	−	0.654676i	$-0.772805\pi$
$283$	−7197.47	−1.51182	−0.755910	+	0.654676i	$0.772805\pi$
$284$	93.3008	0.0194943
$285$	1915.90	0.398204
$286$	−6897.85	−1.42615
$287$	1449.07	0.298034
$288$	−1617.47	−0.330938
$289$	−2544.29	−0.517869
$290$	510.590	0.103389
$291$	−827.165	−0.166630
$292$	−5039.72	−1.01003
$293$	2936.05	0.585412	0.292706	−	0.956202i	$-0.405444\pi$
$293$	2936.05	0.585412	0.292706	+	0.956202i	$0.405444\pi$
$294$	−2793.10	−0.554071
$295$	1014.88	0.200300
$296$	−2506.94	−0.492274
$297$	−1672.63	−0.326787
$298$	−2163.16	−0.420498
$299$	5819.04	1.12550
$300$	329.973	0.0635034
$301$	294.546	0.0564031
$302$	−3949.93	−0.752625
$303$	−5728.18	−1.08606
$304$	10197.7	1.92395
$305$	−2460.96	−0.462014
$306$	−1542.42	−0.288152
$307$	−3828.27	−0.711698	−0.355849	−	0.934544i	$-0.615808\pi$
$307$	−3828.27	−0.711698	−0.355849	+	0.934544i	$0.615808\pi$
$308$	2416.39	0.447034
$309$	4505.91	0.829555
$310$	4436.59	0.812843
$311$	−8035.81	−1.46517	−0.732587	−	0.680673i	$-0.761687\pi$
$311$	−8035.81	−1.46517	−0.732587	+	0.680673i	$0.761687\pi$
$312$	−1202.66	−0.218229
$313$	−1288.78	−0.232736	−0.116368	−	0.993206i	$-0.537125\pi$
$313$	−1288.78	−0.232736	−0.116368	+	0.993206i	$0.537125\pi$
$314$	11403.2	2.04943
$315$	398.957	0.0713608
$316$	420.741	0.0749004
$317$	8166.90	1.44700	0.723499	−	0.690325i	$-0.242532\pi$
$317$	8166.90	1.44700	0.723499	+	0.690325i	$0.242532\pi$
$318$	−2538.05	−0.447568
$319$	1796.53	0.315317
$320$	−29.3812	−0.00513269
$321$	4303.83	0.748338
$322$	−5745.09	−0.994289
$323$	6216.38	1.07086
$324$	356.371	0.0611062
$325$	790.520	0.134924
$326$	−10470.4	−1.77883
$327$	−1043.85	−0.176530
$328$	2072.17	0.348830
$329$	−4689.47	−0.785832
$330$	3272.14	0.545834
$331$	−5018.85	−0.833417	−0.416708	−	0.909040i	$-0.636816\pi$
$331$	−5018.85	−0.833417	−0.416708	+	0.909040i	$0.636816\pi$
$332$	5455.44	0.901825
$333$	1779.66	0.292867
$334$	14554.0	2.38431
$335$	1147.78	0.187194
$336$	2123.52	0.344785
$337$	−3702.30	−0.598448	−0.299224	−	0.954183i	$-0.596728\pi$
$337$	−3702.30	−0.598448	−0.299224	+	0.954183i	$0.596728\pi$
$338$	−4215.45	−0.678373
$339$	−5438.03	−0.871249
$340$	1070.64	0.170775
$341$	15610.3	2.47901
$342$	−4047.89	−0.640014
$343$	5385.02	0.847708
$344$	421.201	0.0660164
$345$	−2760.39	−0.430766
$346$	1224.56	0.190267
$347$	1084.12	0.167719	0.0838594	−	0.996478i	$-0.473275\pi$
$347$	1084.12	0.167719	0.0838594	+	0.996478i	$0.473275\pi$
$348$	−382.769	−0.0589614
$349$	−3145.52	−0.482453	−0.241226	−	0.970469i	$-0.577550\pi$
$349$	−3145.52	−0.482453	−0.241226	+	0.970469i	$0.577550\pi$
$350$	−780.473	−0.119194
$351$	853.762	0.129830
$352$	11133.4	1.68584
$353$	−7477.34	−1.12742	−0.563709	−	0.825974i	$-0.690626\pi$
$353$	−7477.34	−1.12742	−0.563709	+	0.825974i	$0.690626\pi$
$354$	−2144.23	−0.321933
$355$	−106.032	−0.0158524
$356$	514.157	0.0765458
$357$	1294.47	0.191906
$358$	2778.60	0.410206
$359$	3987.75	0.586255	0.293128	−	0.956073i	$-0.405304\pi$
$359$	3987.75	0.586255	0.293128	+	0.956073i	$0.405304\pi$
$360$	570.509	0.0835235
$361$	9455.09	1.37849
$362$	−16014.5	−2.32514
$363$	7520.12	1.08734
$364$	−1233.40	−0.177604
$365$	5727.42	0.821334
$366$	5199.49	0.742573
$367$	6261.36	0.890573	0.445286	−	0.895388i	$-0.353102\pi$
$367$	6261.36	0.890573	0.445286	+	0.895388i	$0.353102\pi$
$368$	−14692.7	−2.08127
$369$	−1471.02	−0.207528
$370$	−3481.52	−0.489177
$371$	2130.04	0.298075
$372$	−3325.93	−0.463553
$373$	−9332.46	−1.29549	−0.647743	−	0.761859i	$-0.724287\pi$
$373$	−9332.46	−1.29549	−0.647743	+	0.761859i	$0.724287\pi$
$374$	10616.9	1.46788
$375$	−375.000	−0.0516398
$376$	−6705.95	−0.919769
$377$	−917.004	−0.125273
$378$	−842.911	−0.114695
$379$	−4570.38	−0.619432	−0.309716	−	0.950829i	$-0.600234\pi$
$379$	−4570.38	−0.619432	−0.309716	+	0.950829i	$0.600234\pi$
$380$	2809.76	0.379309
$381$	1652.22	0.222167
$382$	−3948.96	−0.528918
$383$	2266.02	0.302320	0.151160	−	0.988509i	$-0.451699\pi$
$383$	2266.02	0.302320	0.151160	+	0.988509i	$0.451699\pi$
$384$	4375.33	0.581452
$385$	−2746.12	−0.363520
$386$	−13909.4	−1.83411
$387$	−299.008	−0.0392750
$388$	−1213.08	−0.158723
$389$	3874.40	0.504987	0.252494	−	0.967599i	$-0.418749\pi$
$389$	3874.40	0.504987	0.252494	+	0.967599i	$0.418749\pi$
$390$	−1670.20	−0.216856
$391$	−8956.43	−1.15843
$392$	3352.05	0.431898
$393$	−374.473	−0.0480653
$394$	−1536.82	−0.196508
$395$	−478.154	−0.0609076
$396$	−2452.99	−0.311281
$397$	−10370.5	−1.31104	−0.655519	−	0.755179i	$-0.727550\pi$
$397$	−10370.5	−1.31104	−0.655519	+	0.755179i	$0.727550\pi$
$398$	2731.79	0.344051
$399$	3397.16	0.426242
$400$	−1996.01	−0.249501
$401$	−10537.9	−1.31231	−0.656155	−	0.754626i	$-0.727818\pi$
$401$	−10537.9	−1.31231	−0.656155	+	0.754626i	$0.727818\pi$
$402$	−2425.01	−0.300867
$403$	−7967.97	−0.984895
$404$	−8400.65	−1.03452
$405$	−405.000	−0.0496904
$406$	905.349	0.110669
$407$	−12249.8	−1.49189
$408$	1851.09	0.224614
$409$	−4052.17	−0.489894	−0.244947	−	0.969536i	$-0.578771\pi$
$409$	−4052.17	−0.489894	−0.244947	+	0.969536i	$0.578771\pi$
$410$	2877.73	0.346636
$411$	−1649.64	−0.197982
$412$	6608.14	0.790193
$413$	1799.52	0.214404
$414$	5832.11	0.692349
$415$	−6199.86	−0.733348
$416$	−5682.85	−0.669771
$417$	−6729.95	−0.790329
$418$	27862.6	3.26030
$419$	−12386.0	−1.44414	−0.722071	−	0.691819i	$-0.756810\pi$
$419$	−12386.0	−1.44414	−0.722071	+	0.691819i	$0.756810\pi$
$420$	585.089	0.0679748
$421$	−16516.0	−1.91198	−0.955989	−	0.293402i	$-0.905213\pi$
$421$	−16516.0	−1.91198	−0.955989	+	0.293402i	$0.905213\pi$
$422$	8713.29	1.00511
$423$	4760.50	0.547195
$424$	3045.96	0.348879
$425$	−1216.74	−0.138871
$426$	224.024	0.0254788
$427$	−4363.63	−0.494546
$428$	6311.78	0.712830
$429$	−5876.65	−0.661370
$430$	584.944	0.0656012
$431$	11987.2	1.33969	0.669843	−	0.742503i	$-0.266361\pi$
$431$	11987.2	1.33969	0.669843	+	0.742503i	$0.266361\pi$
$432$	−2155.69	−0.240082
$433$	−14217.4	−1.57793	−0.788965	−	0.614439i	$-0.789383\pi$
$433$	−14217.4	−1.57793	−0.788965	+	0.614439i	$0.789383\pi$
$434$	7866.70	0.870078
$435$	435.000	0.0479463
$436$	−1530.86	−0.168153
$437$	−23505.0	−2.57299
$438$	−12100.8	−1.32009
$439$	685.738	0.0745524	0.0372762	−	0.999305i	$-0.488132\pi$
$439$	685.738	0.0745524	0.0372762	+	0.999305i	$0.488132\pi$
$440$	−3926.96	−0.425478
$441$	−2379.59	−0.256948
$442$	−5419.18	−0.583177
$443$	−13828.1	−1.48305	−0.741527	−	0.670923i	$-0.765898\pi$
$443$	−13828.1	−1.48305	−0.741527	+	0.670923i	$0.765898\pi$
$444$	2609.95	0.278971
$445$	−584.317	−0.0622456
$446$	−3646.74	−0.387170
$447$	−1842.92	−0.195004
$448$	−52.0970	−0.00549409
$449$	−4346.88	−0.456887	−0.228443	−	0.973557i	$-0.573364\pi$
$449$	−4346.88	−0.456887	−0.228443	+	0.973557i	$0.573364\pi$
$450$	792.295	0.0829981
$451$	10125.4	1.05717
$452$	−7975.14	−0.829909
$453$	−3365.16	−0.349026
$454$	−3762.29	−0.388927
$455$	1401.70	0.144424
$456$	4857.95	0.498891
$457$	2375.45	0.243149	0.121574	−	0.992582i	$-0.461206\pi$
$457$	2375.45	0.243149	0.121574	+	0.992582i	$0.461206\pi$
$458$	−2249.45	−0.229497
$459$	−1314.07	−0.133629
$460$	−4048.24	−0.410326
$461$	−5656.94	−0.571519	−0.285759	−	0.958301i	$-0.592246\pi$
$461$	−5656.94	−0.571519	−0.285759	+	0.958301i	$0.592246\pi$
$462$	5801.96	0.584268
$463$	−11017.3	−1.10587	−0.552935	−	0.833225i	$-0.686492\pi$
$463$	−11017.3	−1.10587	−0.552935	+	0.833225i	$0.686492\pi$
$464$	2315.37	0.231656
$465$	3779.77	0.376952
$466$	14788.9	1.47013
$467$	−4441.89	−0.440142	−0.220071	−	0.975484i	$-0.570629\pi$
$467$	−4441.89	−0.440142	−0.220071	+	0.975484i	$0.570629\pi$
$468$	1252.08	0.123670
$469$	2035.17	0.200374
$470$	−9312.90	−0.913983
$471$	9715.02	0.950413
$472$	2573.32	0.250947
$473$	2058.14	0.200071
$474$	1010.24	0.0978939
$475$	−3193.17	−0.308447
$476$	1898.40	0.182800
$477$	−2162.30	−0.207558
$478$	5215.76	0.499087
$479$	−6919.43	−0.660035	−0.330017	−	0.943975i	$-0.607055\pi$
$479$	−6919.43	−0.660035	−0.330017	+	0.943975i	$0.607055\pi$
$480$	2695.78	0.256344
$481$	6252.69	0.592720
$482$	25158.3	2.37744
$483$	−4894.56	−0.461097
$484$	11028.6	1.03575
$485$	1378.61	0.129071
$486$	855.679	0.0798650
$487$	4439.83	0.413116	0.206558	−	0.978434i	$-0.433774\pi$
$487$	4439.83	0.413116	0.206558	+	0.978434i	$0.433774\pi$
$488$	−6240.01	−0.578836
$489$	−8920.28	−0.824926
$490$	4655.16	0.429181
$491$	12089.1	1.11115	0.555575	−	0.831466i	$-0.312498\pi$
$491$	12089.1	1.11115	0.555575	+	0.831466i	$0.312498\pi$
$492$	−2157.31	−0.197681
$493$	1411.41	0.128939
$494$	−14221.9	−1.29529
$495$	2787.72	0.253128
$496$	20118.6	1.82127
$497$	−188.010	−0.0169686
$498$	13099.0	1.17867
$499$	7312.25	0.655994	0.327997	−	0.944679i	$-0.393626\pi$
$499$	7312.25	0.655994	0.327997	+	0.944679i	$0.393626\pi$
$500$	−549.955	−0.0491895
$501$	12399.4	1.10572
$502$	−18345.0	−1.63103
$503$	7487.34	0.663706	0.331853	−	0.943331i	$-0.392326\pi$
$503$	7487.34	0.663706	0.331853	+	0.943331i	$0.392326\pi$
$504$	1011.59	0.0894046
$505$	9546.96	0.841256
$506$	−40143.9	−3.52690
$507$	−3591.37	−0.314593
$508$	2423.05	0.211625
$509$	−16901.9	−1.47184	−0.735919	−	0.677070i	$-0.763250\pi$
$509$	−16901.9	−1.47184	−0.735919	+	0.677070i	$0.763250\pi$
$510$	2570.70	0.223201
$511$	10155.5	0.879166
$512$	6251.09	0.539574
$513$	−3448.62	−0.296804
$514$	12083.9	1.03696
$515$	−7509.85	−0.642570
$516$	−438.509	−0.0374114
$517$	−32767.7	−2.78747
$518$	−6173.22	−0.523621
$519$	1043.27	0.0882356
$520$	2004.44	0.169039
$521$	−8351.65	−0.702289	−0.351144	−	0.936321i	$-0.614207\pi$
$521$	−8351.65	−0.702289	−0.351144	+	0.936321i	$0.614207\pi$
$522$	−919.063	−0.0770618
$523$	5420.89	0.453230	0.226615	−	0.973984i	$-0.427234\pi$
$523$	5420.89	0.453230	0.226615	+	0.973984i	$0.427234\pi$
$524$	−549.182	−0.0457846
$525$	−664.928	−0.0552759
$526$	−6121.07	−0.507398
$527$	12264.0	1.01371
$528$	14838.1	1.22301
$529$	21698.5	1.78339
$530$	4230.08	0.346685
$531$	−1826.78	−0.149295
$532$	4982.10	0.406018
$533$	−5168.30	−0.420007
$534$	1234.54	0.100044
$535$	−7173.05	−0.579660
$536$	2910.30	0.234526
$537$	2367.25	0.190231
$538$	9962.89	0.798384
$539$	16379.3	1.30892
$540$	−593.952	−0.0473326
$541$	14428.9	1.14667	0.573333	−	0.819323i	$-0.305650\pi$
$541$	14428.9	1.14667	0.573333	+	0.819323i	$0.305650\pi$
$542$	−4927.34	−0.390494
$543$	−13643.6	−1.07827
$544$	8746.81	0.689368
$545$	1739.75	0.136739
$546$	−2961.50	−0.232126
$547$	4990.35	0.390077	0.195038	−	0.980796i	$-0.437517\pi$
$547$	4990.35	0.390077	0.195038	+	0.980796i	$0.437517\pi$
$548$	−2419.27	−0.188588
$549$	4429.73	0.344365
$550$	−5453.57	−0.422801
$551$	3704.07	0.286386
$552$	−6999.23	−0.539686
$553$	−847.834	−0.0651963
$554$	−12417.5	−0.952294
$555$	−2966.10	−0.226854
$556$	−9869.80	−0.752828
$557$	23481.4	1.78625	0.893123	−	0.449812i	$-0.148509\pi$
$557$	23481.4	1.78625	0.893123	+	0.449812i	$0.148509\pi$
$558$	−7985.86	−0.605857
$559$	−1050.54	−0.0794868
$560$	−3539.20	−0.267069
$561$	9045.10	0.680721
$562$	−3018.20	−0.226539
$563$	8869.38	0.663943	0.331972	−	0.943289i	$-0.392286\pi$
$563$	8869.38	0.663943	0.331972	+	0.943289i	$0.392286\pi$
$564$	6981.51	0.521231
$565$	9063.39	0.674867
$566$	−25344.5	−1.88217
$567$	−718.122	−0.0531892
$568$	−268.855	−0.0198607
$569$	25722.7	1.89517	0.947585	−	0.319503i	$-0.103516\pi$
$569$	25722.7	1.89517	0.947585	+	0.319503i	$0.103516\pi$
$570$	6746.48	0.495753
$571$	26056.8	1.90971	0.954853	−	0.297078i	$-0.0960122\pi$
$571$	26056.8	1.90971	0.954853	+	0.297078i	$0.0960122\pi$
$572$	−8618.40	−0.629988
$573$	−3364.34	−0.245283
$574$	5102.61	0.371043
$575$	4600.64	0.333670
$576$	52.8862	0.00382568
$577$	−25737.2	−1.85694	−0.928471	−	0.371406i	$-0.878876\pi$
$577$	−25737.2	−1.85694	−0.928471	+	0.371406i	$0.878876\pi$
$578$	−8959.23	−0.644732
$579$	−11850.1	−0.850562
$580$	637.948	0.0456713
$581$	−10993.2	−0.784985
$582$	−2912.71	−0.207449
$583$	14883.7	1.05732
$584$	14522.4	1.02901
$585$	−1422.94	−0.100566
$586$	10338.7	0.728822
$587$	−6862.44	−0.482527	−0.241263	−	0.970460i	$-0.577562\pi$
$587$	−6862.44	−0.482527	−0.241263	+	0.970460i	$0.577562\pi$
$588$	−3489.79	−0.244756
$589$	32185.2	2.25156
$590$	3573.71	0.249368
$591$	−1309.30	−0.0911295
$592$	−15787.6	−1.09606
$593$	4016.32	0.278129	0.139065	−	0.990283i	$-0.455590\pi$
$593$	4016.32	0.278129	0.139065	+	0.990283i	$0.455590\pi$
$594$	−5889.85	−0.406841
$595$	−2157.44	−0.148650
$596$	−2702.72	−0.185751
$597$	2327.36	0.159552
$598$	20490.7	1.40121
$599$	−1729.64	−0.117982	−0.0589911	−	0.998259i	$-0.518788\pi$
$599$	−1729.64	−0.117982	−0.0589911	+	0.998259i	$0.518788\pi$
$600$	−950.848	−0.0646970
$601$	2597.41	0.176291	0.0881453	−	0.996108i	$-0.471906\pi$
$601$	2597.41	0.176291	0.0881453	+	0.996108i	$0.471906\pi$
$602$	1037.19	0.0702203
$603$	−2066.00	−0.139526
$604$	−4935.17	−0.332465
$605$	−12533.5	−0.842249
$606$	−20170.7	−1.35211
$607$	−13844.6	−0.925755	−0.462877	−	0.886422i	$-0.653183\pi$
$607$	−13844.6	−0.925755	−0.462877	+	0.886422i	$0.653183\pi$
$608$	22954.9	1.53116
$609$	771.316	0.0513224
$610$	−8665.82	−0.575195
$611$	16725.7	1.10744
$612$	−1927.15	−0.127288
$613$	1127.16	0.0742667	0.0371334	−	0.999310i	$-0.488177\pi$
$613$	1127.16	0.0742667	0.0371334	+	0.999310i	$0.488177\pi$
$614$	−13480.6	−0.886044
$615$	2451.69	0.160751
$616$	−6963.05	−0.455437
$617$	29575.8	1.92978	0.964892	−	0.262645i	$-0.0845949\pi$
$617$	29575.8	1.92978	0.964892	+	0.262645i	$0.0845949\pi$
$618$	15866.7	1.03277
$619$	12535.0	0.813935	0.406967	−	0.913443i	$-0.366586\pi$
$619$	12535.0	0.813935	0.406967	+	0.913443i	$0.366586\pi$
$620$	5543.22	0.359066
$621$	4968.70	0.321074
$622$	−28296.6	−1.82410
$623$	−1036.08	−0.0666285
$624$	−7573.84	−0.485892
$625$	625.000	0.0400000
$626$	−4538.20	−0.289749
$627$	23737.7	1.51195
$628$	14247.5	0.905316
$629$	−9623.88	−0.610062
$630$	1404.85	0.0888423
$631$	15162.1	0.956569	0.478284	−	0.878205i	$-0.341259\pi$
$631$	15162.1	0.956569	0.478284	+	0.878205i	$0.341259\pi$
$632$	−1212.40	−0.0763083
$633$	7423.33	0.466115
$634$	28758.2	1.80147
$635$	−2753.69	−0.172090
$636$	−3171.12	−0.197709
$637$	−8360.52	−0.520025
$638$	6326.14	0.392561
$639$	190.858	0.0118157
$640$	−7292.21	−0.450391
$641$	−10138.5	−0.624722	−0.312361	−	0.949964i	$-0.601120\pi$
$641$	−10138.5	−0.624722	−0.312361	+	0.949964i	$0.601120\pi$
$642$	15155.1	0.931660
$643$	29580.6	1.81423	0.907113	−	0.420888i	$-0.138282\pi$
$643$	29580.6	1.81423	0.907113	+	0.420888i	$0.138282\pi$
$644$	−7178.10	−0.439219
$645$	498.346	0.0304223
$646$	21889.8	1.33319
$647$	30140.7	1.83146	0.915728	−	0.401798i	$-0.131615\pi$
$647$	30140.7	1.83146	0.915728	+	0.401798i	$0.131615\pi$
$648$	−1026.92	−0.0622548
$649$	12574.2	0.760525
$650$	2783.67	0.167976
$651$	6702.07	0.403495
$652$	−13082.0	−0.785784
$653$	−10094.0	−0.604911	−0.302456	−	0.953163i	$-0.597806\pi$
$653$	−10094.0	−0.604911	−0.302456	+	0.953163i	$0.597806\pi$
$654$	−3675.73	−0.219774
$655$	624.121	0.0372312
$656$	13049.6	0.776678
$657$	−10309.4	−0.612186
$658$	−16513.1	−0.978339
$659$	16019.7	0.946947	0.473473	−	0.880808i	$-0.343000\pi$
$659$	16019.7	0.946947	0.473473	+	0.880808i	$0.343000\pi$
$660$	4088.32	0.241118
$661$	−26006.5	−1.53031	−0.765157	−	0.643844i	$-0.777338\pi$
$661$	−26006.5	−1.53031	−0.765157	+	0.643844i	$0.777338\pi$
$662$	−17672.9	−1.03758
$663$	−4616.90	−0.270446
$664$	−15720.3	−0.918777
$665$	−5661.93	−0.330166
$666$	6266.73	0.364611
$667$	−5336.75	−0.309805
$668$	18184.3	1.05325
$669$	−3106.85	−0.179549
$670$	4041.69	0.233051
$671$	−30490.9	−1.75423
$672$	4780.00	0.274394
$673$	30662.4	1.75624	0.878119	−	0.478443i	$-0.158799\pi$
$673$	30662.4	1.75624	0.878119	+	0.478443i	$0.158799\pi$
$674$	−13036.9	−0.745051
$675$	675.000	0.0384900
$676$	−5266.92	−0.299665
$677$	−4128.37	−0.234366	−0.117183	−	0.993110i	$-0.537386\pi$
$677$	−4128.37	−0.234366	−0.117183	+	0.993110i	$0.537386\pi$
$678$	−19149.0	−1.08468
$679$	2444.47	0.138159
$680$	−3085.15	−0.173985
$681$	−3205.30	−0.180363
$682$	54968.7	3.08630
$683$	−19130.6	−1.07176	−0.535881	−	0.844294i	$-0.680020\pi$
$683$	−19130.6	−1.07176	−0.535881	+	0.844294i	$0.680020\pi$
$684$	−5057.56	−0.282720
$685$	2749.40	0.153356
$686$	18962.4	1.05537
$687$	−1916.43	−0.106428
$688$	2652.54	0.146987
$689$	−7597.08	−0.420066
$690$	−9720.19	−0.536292
$691$	27493.6	1.51361	0.756807	−	0.653638i	$-0.226758\pi$
$691$	27493.6	1.51361	0.756807	+	0.653638i	$0.226758\pi$
$692$	1530.00	0.0840489
$693$	4943.01	0.270952
$694$	3817.51	0.208805
$695$	11216.6	0.612186
$696$	1102.98	0.0600697
$697$	7954.83	0.432296
$698$	−11076.4	−0.600640
$699$	12599.4	0.681766
$700$	−975.149	−0.0526531
$701$	13029.3	0.702010	0.351005	−	0.936374i	$-0.385840\pi$
$701$	13029.3	0.702010	0.351005	+	0.936374i	$0.385840\pi$
$702$	3006.36	0.161635
$703$	−25256.6	−1.35501
$704$	−364.029	−0.0194884
$705$	−7934.17	−0.423856
$706$	−26330.0	−1.40360
$707$	16928.1	0.900491
$708$	−2679.07	−0.142211
$709$	−33140.8	−1.75547	−0.877735	−	0.479146i	$-0.840946\pi$
$709$	−33140.8	−1.75547	−0.877735	+	0.479146i	$0.840946\pi$
$710$	−373.373	−0.0197358
$711$	860.676	0.0453979
$712$	−1481.59	−0.0779846
$713$	−46371.7	−2.43567
$714$	4558.22	0.238918
$715$	9794.42	0.512295
$716$	3471.68	0.181205
$717$	4443.59	0.231449
$718$	14042.1	0.729871
$719$	23672.8	1.22788	0.613940	−	0.789353i	$-0.289584\pi$
$719$	23672.8	1.22788	0.613940	+	0.789353i	$0.289584\pi$
$720$	3592.81	0.185967
$721$	−13316.0	−0.687815
$722$	33294.3	1.71619
$723$	21433.7	1.10253
$724$	−20009.0	−1.02711
$725$	−725.000	−0.0371391
$726$	26480.7	1.35371
$727$	16424.5	0.837895	0.418947	−	0.908010i	$-0.362399\pi$
$727$	16424.5	0.837895	0.418947	+	0.908010i	$0.362399\pi$
$728$	3554.16	0.180942
$729$	729.000	0.0370370
$730$	20168.0	1.02254
$731$	1616.95	0.0818125
$732$	6496.41	0.328025
$733$	19399.9	0.977559	0.488780	−	0.872407i	$-0.337442\pi$
$733$	19399.9	0.977559	0.488780	+	0.872407i	$0.337442\pi$
$734$	22048.2	1.10874
$735$	3965.99	0.199031
$736$	−33072.9	−1.65636
$737$	14220.8	0.710759
$738$	−5179.91	−0.258367
$739$	−5065.65	−0.252156	−0.126078	−	0.992020i	$-0.540239\pi$
$739$	−5065.65	−0.252156	−0.126078	+	0.992020i	$0.540239\pi$
$740$	−4349.92	−0.216090
$741$	−12116.5	−0.600687
$742$	7500.53	0.371096
$743$	−15186.2	−0.749833	−0.374917	−	0.927059i	$-0.622329\pi$
$743$	−15186.2	−0.749833	−0.374917	+	0.927059i	$0.622329\pi$
$744$	9583.98	0.472266
$745$	3071.53	0.151050
$746$	−32862.5	−1.61284
$747$	11159.8	0.546605
$748$	13265.1	0.648421
$749$	−12718.8	−0.620476
$750$	−1320.49	−0.0642901
$751$	−25919.9	−1.25943	−0.629713	−	0.776828i	$-0.716828\pi$
$751$	−25919.9	−1.25943	−0.629713	+	0.776828i	$0.716828\pi$
$752$	−42231.1	−2.04789
$753$	−15629.2	−0.756385
$754$	−3229.06	−0.155962
$755$	5608.60	0.270355
$756$	−1053.16	−0.0506655
$757$	25691.7	1.23353	0.616765	−	0.787148i	$-0.288443\pi$
$757$	25691.7	1.23353	0.616765	+	0.787148i	$0.288443\pi$
$758$	−16093.7	−0.771175
$759$	−34200.8	−1.63559
$760$	−8096.58	−0.386439
$761$	3453.84	0.164523	0.0822613	−	0.996611i	$-0.473786\pi$
$761$	3453.84	0.164523	0.0822613	+	0.996611i	$0.473786\pi$
$762$	5817.97	0.276592
$763$	3084.83	0.146367
$764$	−4933.96	−0.233645
$765$	2190.12	0.103509
$766$	7979.38	0.376379
$767$	−6418.26	−0.302151
$768$	15265.9	0.717265
$769$	24995.5	1.17212	0.586060	−	0.810268i	$-0.300678\pi$
$769$	24995.5	1.17212	0.586060	+	0.810268i	$0.300678\pi$
$770$	−9669.94	−0.452572
$771$	10294.9	0.480886
$772$	−17378.8	−0.810203
$773$	15444.9	0.718648	0.359324	−	0.933213i	$-0.383007\pi$
$773$	15444.9	0.718648	0.359324	+	0.933213i	$0.383007\pi$
$774$	−1052.90	−0.0488962
$775$	−6299.62	−0.291986
$776$	3495.59	0.161707
$777$	−5259.31	−0.242827
$778$	13643.0	0.628695
$779$	20876.4	0.960174
$780$	−2086.80	−0.0957943
$781$	−1313.72	−0.0601904
$782$	−31538.4	−1.44221
$783$	−783.000	−0.0357371
$784$	21109.7	0.961630
$785$	−16191.7	−0.736187
$786$	−1318.64	−0.0598399
$787$	−30204.3	−1.36807	−0.684033	−	0.729451i	$-0.739776\pi$
$787$	−30204.3	−1.36807	−0.684033	+	0.729451i	$0.739776\pi$
$788$	−1920.16	−0.0868055
$789$	−5214.88	−0.235304
$790$	−1683.73	−0.0758283
$791$	16070.7	0.722386
$792$	7068.52	0.317132
$793$	15563.5	0.696944
$794$	−36517.9	−1.63220
$795$	3603.84	0.160773
$796$	3413.19	0.151981
$797$	44520.9	1.97869	0.989343	−	0.145606i	$-0.0465131\pi$
$797$	44520.9	1.97869	0.989343	+	0.145606i	$0.0465131\pi$
$798$	11962.5	0.530660
$799$	−25743.4	−1.13985
$800$	−4492.97	−0.198563
$801$	1051.77	0.0463951
$802$	−37107.1	−1.63379
$803$	70961.8	3.11854
$804$	−3029.89	−0.132905
$805$	8157.59	0.357164
$806$	−28057.7	−1.22617
$807$	8487.93	0.370247
$808$	24207.2	1.05397
$809$	−10369.6	−0.450651	−0.225326	−	0.974284i	$-0.572345\pi$
$809$	−10369.6	−0.450651	−0.225326	+	0.974284i	$0.572345\pi$
$810$	−1426.13	−0.0618632
$811$	24341.6	1.05394	0.526972	−	0.849883i	$-0.323327\pi$
$811$	24341.6	1.05394	0.526972	+	0.849883i	$0.323327\pi$
$812$	1131.17	0.0488872
$813$	−4197.88	−0.181090
$814$	−43135.5	−1.85737
$815$	14867.1	0.638985
$816$	11657.3	0.500108
$817$	4243.47	0.181714
$818$	−14268.9	−0.609905
$819$	−2523.07	−0.107647
$820$	3595.52	0.153123
$821$	−17287.1	−0.734864	−0.367432	−	0.930050i	$-0.619763\pi$
$821$	−17287.1	−0.734864	−0.367432	+	0.930050i	$0.619763\pi$
$822$	−5808.89	−0.246482
$823$	5724.85	0.242474	0.121237	−	0.992624i	$-0.461314\pi$
$823$	5724.85	0.242474	0.121237	+	0.992624i	$0.461314\pi$
$824$	−19042.0	−0.805046
$825$	−4646.19	−0.196072
$826$	6336.69	0.266927
$827$	25964.5	1.09175	0.545874	−	0.837867i	$-0.316198\pi$
$827$	25964.5	1.09175	0.545874	+	0.837867i	$0.316198\pi$
$828$	7286.83	0.305839
$829$	−13876.2	−0.581349	−0.290675	−	0.956822i	$-0.593880\pi$
$829$	−13876.2	−0.581349	−0.290675	+	0.956822i	$0.593880\pi$
$830$	−21831.7	−0.912997
$831$	−10579.2	−0.441622
$832$	185.812	0.00774262
$833$	12868.2	0.535240
$834$	−23698.3	−0.983937
$835$	−20665.6	−0.856483
$836$	34812.5	1.44021
$837$	−6803.59	−0.280964
$838$	−43615.0	−1.79792
$839$	−20190.6	−0.830818	−0.415409	−	0.909635i	$-0.636362\pi$
$839$	−20190.6	−0.830818	−0.415409	+	0.909635i	$0.636362\pi$
$840$	−1685.99	−0.0692525
$841$	841.000	0.0344828
$842$	−58158.2	−2.38036
$843$	−2571.37	−0.105057
$844$	10886.7	0.443998
$845$	5985.62	0.243682
$846$	16763.2	0.681243
$847$	−22223.7	−0.901554
$848$	19182.1	0.776787
$849$	−21592.4	−0.872849
$850$	−4284.51	−0.172891
$851$	36389.2	1.46581
$852$	279.902	0.0112550
$853$	−14388.2	−0.577542	−0.288771	−	0.957398i	$-0.593247\pi$
$853$	−14388.2	−0.577542	−0.288771	+	0.957398i	$0.593247\pi$
$854$	−15365.7	−0.615696
$855$	5747.70	0.229903
$856$	−18188.0	−0.726229
$857$	−12095.7	−0.482125	−0.241063	−	0.970510i	$-0.577496\pi$
$857$	−12095.7	−0.482125	−0.241063	+	0.970510i	$0.577496\pi$
$858$	−20693.5	−0.823387
$859$	−16863.4	−0.669815	−0.334907	−	0.942251i	$-0.608705\pi$
$859$	−16863.4	−0.669815	−0.334907	+	0.942251i	$0.608705\pi$
$860$	730.848	0.0289787
$861$	4347.20	0.172070
$862$	42210.8	1.66787
$863$	6575.91	0.259382	0.129691	−	0.991554i	$-0.458601\pi$
$863$	6575.91	0.259382	0.129691	+	0.991554i	$0.458601\pi$
$864$	−4852.41	−0.191067
$865$	−1738.78	−0.0683470
$866$	−50063.8	−1.96448
$867$	−7632.86	−0.298992
$868$	9828.91	0.384349
$869$	−5924.25	−0.231262
$870$	1531.77	0.0596918
$871$	−7258.74	−0.282380
$872$	4411.31	0.171314
$873$	−2481.50	−0.0962038
$874$	−82768.4	−3.20330
$875$	1108.21	0.0428165
$876$	−15119.2	−0.583138
$877$	−2474.27	−0.0952683	−0.0476341	−	0.998865i	$-0.515168\pi$
$877$	−2474.27	−0.0952683	−0.0476341	+	0.998865i	$0.515168\pi$
$878$	2414.70	0.0928157
$879$	8808.15	0.337988
$880$	−24730.2	−0.947336
$881$	39922.4	1.52670	0.763349	−	0.645987i	$-0.223554\pi$
$881$	39922.4	1.52670	0.763349	+	0.645987i	$0.223554\pi$
$882$	−8379.29	−0.319893
$883$	15872.9	0.604944	0.302472	−	0.953158i	$-0.402188\pi$
$883$	15872.9	0.604944	0.302472	+	0.953158i	$0.402188\pi$
$884$	−6770.90	−0.257613
$885$	3044.64	0.115643
$886$	−48693.0	−1.84636
$887$	−48655.2	−1.84181	−0.920903	−	0.389792i	$-0.872547\pi$
$887$	−48655.2	−1.84181	−0.920903	+	0.389792i	$0.872547\pi$
$888$	−7520.82	−0.284214
$889$	−4882.69	−0.184207
$890$	−2057.56	−0.0774940
$891$	−5017.89	−0.188671
$892$	−4556.35	−0.171029
$893$	−67560.3	−2.53171
$894$	−6489.48	−0.242775
$895$	−3945.41	−0.147352
$896$	−12930.1	−0.482104
$897$	17457.1	0.649807
$898$	−15306.7	−0.568811
$899$	7307.56	0.271102
$900$	989.920	0.0366637
$901$	11693.1	0.432357
$902$	35654.6	1.31615
$903$	883.638	0.0325644
$904$	22981.1	0.845509
$905$	22739.3	0.835227
$906$	−11849.8	−0.434528
$907$	−26851.3	−0.983001	−0.491501	−	0.870877i	$-0.663551\pi$
$907$	−26851.3	−0.983001	−0.491501	+	0.870877i	$0.663551\pi$
$908$	−4700.73	−0.171805
$909$	−17184.5	−0.627035
$910$	4935.84	0.179804
$911$	29057.6	1.05677	0.528387	−	0.849003i	$-0.322797\pi$
$911$	29057.6	1.05677	0.528387	+	0.849003i	$0.322797\pi$
$912$	30593.2	1.11079
$913$	−76815.3	−2.78447
$914$	8364.72	0.302714
$915$	−7382.89	−0.266744
$916$	−2810.53	−0.101378
$917$	1106.65	0.0398527
$918$	−4627.27	−0.166364
$919$	24093.6	0.864825	0.432413	−	0.901676i	$-0.357662\pi$
$919$	24093.6	0.864825	0.432413	+	0.901676i	$0.357662\pi$
$920$	11665.4	0.418039
$921$	−11484.8	−0.410899
$922$	−19919.9	−0.711525
$923$	670.565	0.0239132
$924$	7249.17	0.258095
$925$	4943.49	0.175720
$926$	−38795.4	−1.37678
$927$	13517.7	0.478944
$928$	5211.84	0.184361
$929$	−53631.6	−1.89408	−0.947038	−	0.321123i	$-0.895940\pi$
$929$	−53631.6	−1.89408	−0.947038	+	0.321123i	$0.895940\pi$
$930$	13309.8	0.469295
$931$	33770.8	1.18882
$932$	18477.7	0.649417
$933$	−24107.4	−0.845919
$934$	−15641.3	−0.547964
$935$	−15075.2	−0.527284
$936$	−3607.99	−0.125995
$937$	26075.5	0.909125	0.454562	−	0.890715i	$-0.349796\pi$
$937$	26075.5	0.909125	0.454562	+	0.890715i	$0.349796\pi$
$938$	7166.48	0.249460
$939$	−3866.34	−0.134370
$940$	−11635.8	−0.403744
$941$	−18872.4	−0.653796	−0.326898	−	0.945060i	$-0.606003\pi$
$941$	−18872.4	−0.653796	−0.326898	+	0.945060i	$0.606003\pi$
$942$	34209.6	1.18324
$943$	−30078.3	−1.03869
$944$	16205.7	0.558739
$945$	1196.87	0.0412002
$946$	7247.37	0.249083
$947$	−9904.80	−0.339876	−0.169938	−	0.985455i	$-0.554357\pi$
$947$	−9904.80	−0.339876	−0.169938	+	0.985455i	$0.554357\pi$
$948$	1262.22	0.0432438
$949$	−36221.1	−1.23898
$950$	−11244.1	−0.384008
$951$	24500.7	0.835425
$952$	−5470.41	−0.186236
$953$	11915.9	0.405029	0.202514	−	0.979279i	$-0.435089\pi$
$953$	11915.9	0.405029	0.202514	+	0.979279i	$0.435089\pi$
$954$	−7614.14	−0.258403
$955$	5607.23	0.189996
$956$	6516.74	0.220467
$957$	5389.58	0.182049
$958$	−24365.5	−0.821725
$959$	4875.07	0.164155
$960$	−88.1436	−0.00296336
$961$	33705.4	1.13140
$962$	22017.7	0.737919
$963$	12911.5	0.432053
$964$	31433.6	1.05021
$965$	19750.2	0.658842
$966$	−17235.3	−0.574053
$967$	38119.9	1.26769	0.633843	−	0.773462i	$-0.281477\pi$
$967$	38119.9	1.26769	0.633843	+	0.773462i	$0.281477\pi$
$968$	−31780.0	−1.05521
$969$	18649.1	0.618263
$970$	4854.51	0.160690
$971$	−12393.2	−0.409593	−0.204797	−	0.978805i	$-0.565653\pi$
$971$	−12393.2	−0.409593	−0.204797	+	0.978805i	$0.565653\pi$
$972$	1069.11	0.0352797
$973$	19888.6	0.655292
$974$	15634.0	0.514318
$975$	2371.56	0.0778982
$976$	−39296.8	−1.28879
$977$	36796.8	1.20495	0.602474	−	0.798138i	$-0.294182\pi$
$977$	36796.8	1.20495	0.602474	+	0.798138i	$0.294182\pi$
$978$	−31411.1	−1.02701
$979$	−7239.60	−0.236342
$980$	5816.31	0.189587
$981$	−3131.56	−0.101919
$982$	42569.6	1.38335
$983$	17819.2	0.578174	0.289087	−	0.957303i	$-0.406648\pi$
$983$	17819.2	0.578174	0.289087	+	0.957303i	$0.406648\pi$
$984$	6216.50	0.201397
$985$	2182.17	0.0705886
$986$	4970.03	0.160525
$987$	−14068.4	−0.453700
$988$	−17769.4	−0.572185
$989$	−6113.90	−0.196573
$990$	9816.42	0.315138
$991$	−832.856	−0.0266968	−0.0133484	−	0.999911i	$-0.504249\pi$
$991$	−832.856	−0.0266968	−0.0133484	+	0.999911i	$0.504249\pi$
$992$	45286.4	1.44944
$993$	−15056.5	−0.481173
$994$	−662.042	−0.0211255
$995$	−3878.94	−0.123589
$996$	16366.3	0.520669
$997$	−5156.04	−0.163785	−0.0818923	−	0.996641i	$-0.526096\pi$
$997$	−5156.04	−0.163785	−0.0818923	+	0.996641i	$0.526096\pi$
$998$	25748.7	0.816694
$999$	5338.97	0.169087

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.4.a.j.1.6	✓	7
3.2	odd	2		1305.4.a.m.1.2		7
5.4	even	2		2175.4.a.m.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.j.1.6	✓	7	1.1	even	1	trivial
1305.4.a.m.1.2		7	3.2	odd	2
2175.4.a.m.1.2		7	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	435.a (trivial)

\(f(q)\)	\(=\)	\(q+3.52131 q^{2} +3.00000 q^{3} +4.39964 q^{4} -5.00000 q^{5} +10.5639 q^{6} -8.86571 q^{7} -12.6780 q^{8} +9.00000 q^{9} -17.6066 q^{10} -61.9492 q^{11} +13.1989 q^{12} +31.6208 q^{13} -31.2189 q^{14} -15.0000 q^{15} -79.8403 q^{16} -48.6694 q^{17} +31.6918 q^{18} -127.727 q^{19} -21.9982 q^{20} -26.5971 q^{21} -218.143 q^{22} +184.026 q^{23} -38.0339 q^{24} +25.0000 q^{25} +111.347 q^{26} +27.0000 q^{27} -39.0059 q^{28} -29.0000 q^{29} -52.8197 q^{30} -251.985 q^{31} -179.719 q^{32} -185.848 q^{33} -171.380 q^{34} +44.3285 q^{35} +39.5968 q^{36} +197.740 q^{37} -449.765 q^{38} +94.8624 q^{39} +63.3899 q^{40} -163.446 q^{41} -93.6568 q^{42} -33.2231 q^{43} -272.555 q^{44} -45.0000 q^{45} +648.012 q^{46} +528.945 q^{47} -239.521 q^{48} -264.399 q^{49} +88.0328 q^{50} -146.008 q^{51} +139.120 q^{52} -240.256 q^{53} +95.0754 q^{54} +309.746 q^{55} +112.399 q^{56} -383.180 q^{57} -102.118 q^{58} -202.976 q^{59} -65.9947 q^{60} +492.192 q^{61} -887.318 q^{62} -79.7914 q^{63} +5.87624 q^{64} -158.104 q^{65} -654.428 q^{66} -229.556 q^{67} -214.128 q^{68} +552.077 q^{69} +156.095 q^{70} +21.2064 q^{71} -114.102 q^{72} -1145.48 q^{73} +696.303 q^{74} +75.0000 q^{75} -561.952 q^{76} +549.224 q^{77} +334.040 q^{78} +95.6307 q^{79} +399.201 q^{80} +81.0000 q^{81} -575.545 q^{82} +1239.97 q^{83} -117.018 q^{84} +243.347 q^{85} -116.989 q^{86} -87.0000 q^{87} +785.391 q^{88} +116.863 q^{89} -158.459 q^{90} -280.341 q^{91} +809.648 q^{92} -755.955 q^{93} +1862.58 q^{94} +638.633 q^{95} -539.156 q^{96} -275.722 q^{97} -931.032 q^{98} -557.543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 21 q^{3} + 15 q^{4} - 35 q^{5} - 3 q^{6} - 37 q^{7} - 36 q^{8} + 63 q^{9} + 5 q^{10} - 11 q^{11} + 45 q^{12} - 133 q^{13} - 75 q^{14} - 105 q^{15} - 53 q^{16} + 21 q^{17} - 9 q^{18} - 170 q^{19}+ \cdots - 99 q^{99}+O(q^{100}) \) 7 * q - q^2 + 21 * q^3 + 15 * q^4 - 35 * q^5 - 3 * q^6 - 37 * q^7 - 36 * q^8 + 63 * q^9 + 5 * q^10 - 11 * q^11 + 45 * q^12 - 133 * q^13 - 75 * q^14 - 105 * q^15 - 53 * q^16 + 21 * q^17 - 9 * q^18 - 170 * q^19 - 75 * q^20 - 111 * q^21 - 369 * q^22 - 68 * q^23 - 108 * q^24 + 175 * q^25 + 181 * q^26 + 189 * q^27 - 637 * q^28 - 203 * q^29 + 15 * q^30 - 480 * q^31 - 779 * q^32 - 33 * q^33 - 897 * q^34 + 185 * q^35 + 135 * q^36 - 1032 * q^37 - 194 * q^38 - 399 * q^39 + 180 * q^40 - 638 * q^41 - 225 * q^42 - 512 * q^43 + 625 * q^44 - 315 * q^45 + 16 * q^46 - 111 * q^47 - 159 * q^48 + 178 * q^49 - 25 * q^50 + 63 * q^51 - 1263 * q^52 + 410 * q^53 - 27 * q^54 + 55 * q^55 + 1174 * q^56 - 510 * q^57 + 29 * q^58 - 426 * q^59 - 225 * q^60 - 1192 * q^61 + 460 * q^62 - 333 * q^63 + 390 * q^64 + 665 * q^65 - 1107 * q^66 - 1671 * q^67 + 1509 * q^68 - 204 * q^69 + 375 * q^70 - 1324 * q^71 - 324 * q^72 - 852 * q^73 + 1780 * q^74 + 525 * q^75 - 564 * q^76 - 2107 * q^77 + 543 * q^78 + 366 * q^79 + 265 * q^80 + 567 * q^81 - 318 * q^82 + 470 * q^83 - 1911 * q^84 - 105 * q^85 - 2196 * q^86 - 609 * q^87 - 2518 * q^88 + 51 * q^89 + 45 * q^90 - 1297 * q^91 - 684 * q^92 - 1440 * q^93 - 1837 * q^94 + 850 * q^95 - 2337 * q^96 - 3322 * q^97 + 1068 * q^98 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more