LMFDB - Embedded newform 435.4.a.i.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,4,Mod(1,435)]

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

lf = mfeigenbasis(mf)

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")

//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);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	435.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:	$25.6658308525$
Analytic rank:	$0$
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} - 2x^{6} - 37x^{5} + 55x^{4} + 336x^{3} - 227x^{2} - 824x - 166 $ x^7 - 2x^6 - 37x^5 + 55x^4 + 336x^3 - 227x^2 - 824x - 166
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			1.4
Root			$-0.218728$ 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)

$f(q)$	$=$	\(q+0.218728 q^{2} -3.00000 q^{3} -7.95216 q^{4} +5.00000 q^{5} -0.656184 q^{6} -21.0000 q^{7} -3.48919 q^{8} +9.00000 q^{9} +1.09364 q^{10} -1.46553 q^{11} +23.8565 q^{12} -79.4367 q^{13} -4.59329 q^{14} -15.0000 q^{15} +62.8541 q^{16} -65.4406 q^{17} +1.96855 q^{18} +116.908 q^{19} -39.7608 q^{20} +63.0000 q^{21} -0.320553 q^{22} -177.448 q^{23} +10.4676 q^{24} +25.0000 q^{25} -17.3750 q^{26} -27.0000 q^{27} +166.995 q^{28} +29.0000 q^{29} -3.28092 q^{30} +77.7850 q^{31} +41.6614 q^{32} +4.39659 q^{33} -14.3137 q^{34} -105.000 q^{35} -71.5694 q^{36} +175.767 q^{37} +25.5710 q^{38} +238.310 q^{39} -17.4459 q^{40} +62.4580 q^{41} +13.7799 q^{42} +66.0473 q^{43} +11.6541 q^{44} +45.0000 q^{45} -38.8128 q^{46} +179.320 q^{47} -188.562 q^{48} +98.0000 q^{49} +5.46820 q^{50} +196.322 q^{51} +631.693 q^{52} +676.773 q^{53} -5.90566 q^{54} -7.32765 q^{55} +73.2729 q^{56} -350.723 q^{57} +6.34312 q^{58} +415.156 q^{59} +119.282 q^{60} -426.377 q^{61} +17.0138 q^{62} -189.000 q^{63} -493.720 q^{64} -397.183 q^{65} +0.961658 q^{66} +79.1909 q^{67} +520.394 q^{68} +532.343 q^{69} -22.9665 q^{70} +218.606 q^{71} -31.4027 q^{72} +1024.13 q^{73} +38.4453 q^{74} -75.0000 q^{75} -929.669 q^{76} +30.7761 q^{77} +52.1251 q^{78} +1053.21 q^{79} +314.270 q^{80} +81.0000 q^{81} +13.6613 q^{82} -1179.75 q^{83} -500.986 q^{84} -327.203 q^{85} +14.4464 q^{86} -87.0000 q^{87} +5.11351 q^{88} +1411.60 q^{89} +9.84277 q^{90} +1668.17 q^{91} +1411.09 q^{92} -233.355 q^{93} +39.2223 q^{94} +584.539 q^{95} -124.984 q^{96} +884.714 q^{97} +21.4353 q^{98} -13.1898 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} + 35 q^{5} + 6 q^{6} - 50 q^{7} - 33 q^{8} + 63 q^{9} - 10 q^{10} + 76 q^{11} - 66 q^{12} + 30 q^{13} + 89 q^{14} - 105 q^{15} + 138 q^{16} - 140 q^{17} - 18 q^{18} + 90 q^{19}+ \cdots + 684 q^{99}+O(q^{100}) $ 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 + 35 * q^5 + 6 * q^6 - 50 * q^7 - 33 * q^8 + 63 * q^9 - 10 * q^10 + 76 * q^11 - 66 * q^12 + 30 * q^13 + 89 * q^14 - 105 * q^15 + 138 * q^16 - 140 * q^17 - 18 * q^18 + 90 * q^19 + 110 * q^20 + 150 * q^21 + 61 * q^22 + 34 * q^23 + 99 * q^24 + 175 * q^25 - 241 * q^26 - 189 * q^27 - 57 * q^28 + 203 * q^29 + 30 * q^30 + 524 * q^31 - 6 * q^32 - 228 * q^33 + 255 * q^34 - 250 * q^35 + 198 * q^36 - 28 * q^37 + 222 * q^38 - 90 * q^39 - 165 * q^40 + 1532 * q^41 - 267 * q^42 - 464 * q^43 + 1475 * q^44 + 315 * q^45 + 72 * q^46 - 360 * q^47 - 414 * q^48 + 569 * q^49 - 50 * q^50 + 420 * q^51 - 205 * q^52 + 282 * q^53 + 54 * q^54 + 380 * q^55 + 1102 * q^56 - 270 * q^57 - 58 * q^58 + 766 * q^59 - 330 * q^60 + 1200 * q^61 + 2856 * q^62 - 450 * q^63 + 701 * q^64 + 150 * q^65 - 183 * q^66 + 1546 * q^67 + 1801 * q^68 - 102 * q^69 + 445 * q^70 + 1802 * q^71 - 297 * q^72 - 220 * q^73 + 1594 * q^74 - 525 * q^75 + 1960 * q^76 + 3222 * q^77 + 723 * q^78 + 1298 * q^79 + 690 * q^80 + 567 * q^81 + 856 * q^82 + 1652 * q^83 + 171 * q^84 - 700 * q^85 + 7628 * q^86 - 609 * q^87 + 550 * q^88 + 2846 * q^89 - 90 * q^90 - 816 * q^91 + 472 * q^92 - 1572 * q^93 + 745 * q^94 + 450 * q^95 + 18 * q^96 + 1110 * q^97 - 761 * q^98 + 684 * 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 $

$2$	0.218728	0.0773321	0.0386660	−	0.999252i	$-0.487689\pi$
$2$	0.218728	0.0773321	0.0386660	+	0.999252i	$0.487689\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.95216	−0.994020
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−0.656184	−0.0446477
$7$	−21.0000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−21.0000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	−3.48919	−0.154202
$9$	9.00000	0.333333
$10$	1.09364	0.0345840
$11$	−1.46553	−0.0401704	−0.0200852	−	0.999798i	$-0.506394\pi$
$11$	−1.46553	−0.0401704	−0.0200852	+	0.999798i	$0.506394\pi$
$12$	23.8565	0.573898
$13$	−79.4367	−1.69475	−0.847376	−	0.530994i	$-0.821819\pi$
$13$	−79.4367	−1.69475	−0.847376	+	0.530994i	$0.821819\pi$
$14$	−4.59329	−0.0876863
$15$	−15.0000	−0.258199
$16$	62.8541	0.982095
$17$	−65.4406	−0.933628	−0.466814	−	0.884355i	$-0.654598\pi$
$17$	−65.4406	−0.933628	−0.466814	+	0.884355i	$0.654598\pi$
$18$	1.96855	0.0257774
$19$	116.908	1.41160	0.705802	−	0.708409i	$-0.250587\pi$
$19$	116.908	1.41160	0.705802	+	0.708409i	$0.250587\pi$
$20$	−39.7608	−0.444539
$21$	63.0000	0.654654
$22$	−0.320553	−0.00310646
$23$	−177.448	−1.60871	−0.804356	−	0.594148i	$-0.797489\pi$
$23$	−177.448	−1.60871	−0.804356	+	0.594148i	$0.797489\pi$
$24$	10.4676	0.0890284
$25$	25.0000	0.200000
$26$	−17.3750	−0.131059
$27$	−27.0000	−0.192450
$28$	166.995	1.12711
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	−3.28092	−0.0199671
$31$	77.7850	0.450664	0.225332	−	0.974282i	$-0.427653\pi$
$31$	77.7850	0.450664	0.225332	+	0.974282i	$0.427653\pi$
$32$	41.6614	0.230149
$33$	4.39659	0.0231924
$34$	−14.3137	−0.0721994
$35$	−105.000	−0.507093
$36$	−71.5694	−0.331340
$37$	175.767	0.780973	0.390486	−	0.920609i	$-0.372307\pi$
$37$	175.767	0.780973	0.390486	+	0.920609i	$0.372307\pi$
$38$	25.5710	0.109162
$39$	238.310	0.978465
$40$	−17.4459	−0.0689611
$41$	62.4580	0.237910	0.118955	−	0.992900i	$-0.462046\pi$
$41$	62.4580	0.237910	0.118955	+	0.992900i	$0.462046\pi$
$42$	13.7799	0.0506257
$43$	66.0473	0.234235	0.117118	−	0.993118i	$-0.462635\pi$
$43$	66.0473	0.234235	0.117118	+	0.993118i	$0.462635\pi$
$44$	11.6541	0.0399301
$45$	45.0000	0.149071
$46$	−38.8128	−0.124405
$47$	179.320	0.556521	0.278260	−	0.960506i	$-0.410242\pi$
$47$	179.320	0.556521	0.278260	+	0.960506i	$0.410242\pi$
$48$	−188.562	−0.567013
$49$	98.0000	0.285714
$50$	5.46820	0.0154664
$51$	196.322	0.539031
$52$	631.693	1.68462
$53$	676.773	1.75400	0.876999	−	0.480492i	$-0.159542\pi$
$53$	676.773	1.75400	0.876999	+	0.480492i	$0.159542\pi$
$54$	−5.90566	−0.0148826
$55$	−7.32765	−0.0179647
$56$	73.2729	0.174848
$57$	−350.723	−0.814990
$58$	6.34312	0.0143602
$59$	415.156	0.916080	0.458040	−	0.888932i	$-0.348552\pi$
$59$	415.156	0.916080	0.458040	+	0.888932i	$0.348552\pi$
$60$	119.282	0.256655
$61$	−426.377	−0.894951	−0.447475	−	0.894296i	$-0.647677\pi$
$61$	−426.377	−0.894951	−0.447475	+	0.894296i	$0.647677\pi$
$62$	17.0138	0.0348508
$63$	−189.000	−0.377964
$64$	−493.720	−0.964297
$65$	−397.183	−0.757916
$66$	0.961658	0.00179351
$67$	79.1909	0.144399	0.0721993	−	0.997390i	$-0.476998\pi$
$67$	79.1909	0.144399	0.0721993	+	0.997390i	$0.476998\pi$
$68$	520.394	0.928045
$69$	532.343	0.928790
$70$	−22.9665	−0.0392145
$71$	218.606	0.365404	0.182702	−	0.983168i	$-0.441516\pi$
$71$	218.606	0.365404	0.182702	+	0.983168i	$0.441516\pi$
$72$	−31.4027	−0.0514006
$73$	1024.13	1.64199	0.820996	−	0.570933i	$-0.193419\pi$
$73$	1024.13	1.64199	0.820996	+	0.570933i	$0.193419\pi$
$74$	38.4453	0.0603943
$75$	−75.0000	−0.115470
$76$	−929.669	−1.40316
$77$	30.7761	0.0455489
$78$	52.1251	0.0756667
$79$	1053.21	1.49994	0.749972	−	0.661470i	$-0.230067\pi$
$79$	1053.21	1.49994	0.749972	+	0.661470i	$0.230067\pi$
$80$	314.270	0.439206
$81$	81.0000	0.111111
$82$	13.6613	0.0183981
$83$	−1179.75	−1.56017	−0.780084	−	0.625675i	$-0.784824\pi$
$83$	−1179.75	−1.56017	−0.780084	+	0.625675i	$0.784824\pi$
$84$	−500.986	−0.650739
$85$	−327.203	−0.417531
$86$	14.4464	0.0181139
$87$	−87.0000	−0.107211
$88$	5.11351	0.00619434
$89$	1411.60	1.68123	0.840613	−	0.541637i	$-0.182195\pi$
$89$	1411.60	1.68123	0.840613	+	0.541637i	$0.182195\pi$
$90$	9.84277	0.0115280
$91$	1668.17	1.92167
$92$	1411.09	1.59909
$93$	−233.355	−0.260191
$94$	39.2223	0.0430369
$95$	584.539	0.631288
$96$	−124.984	−0.132877
$97$	884.714	0.926073	0.463037	−	0.886339i	$-0.346760\pi$
$97$	884.714	0.926073	0.463037	+	0.886339i	$0.346760\pi$
$98$	21.4353	0.0220949
$99$	−13.1898	−0.0133901
$100$	−198.804	−0.198804
$101$	−647.242	−0.637654	−0.318827	−	0.947813i	$-0.603289\pi$
$101$	−647.242	−0.637654	−0.318827	+	0.947813i	$0.603289\pi$
$102$	42.9411	0.0416844
$103$	−1550.51	−1.48326	−0.741631	−	0.670808i	$-0.765947\pi$
$103$	−1550.51	−1.48326	−0.741631	+	0.670808i	$0.765947\pi$
$104$	277.169	0.261334
$105$	315.000	0.292770
$106$	148.029	0.135640
$107$	−1212.45	−1.09544	−0.547718	−	0.836663i	$-0.684503\pi$
$107$	−1212.45	−1.09544	−0.547718	+	0.836663i	$0.684503\pi$
$108$	214.708	0.191299
$109$	−1128.35	−0.991528	−0.495764	−	0.868457i	$-0.665112\pi$
$109$	−1128.35	−0.991528	−0.495764	+	0.868457i	$0.665112\pi$
$110$	−1.60276	−0.00138925
$111$	−527.302	−0.450895
$112$	−1319.94	−1.11359
$113$	−825.104	−0.686896	−0.343448	−	0.939172i	$-0.611595\pi$
$113$	−825.104	−0.686896	−0.343448	+	0.939172i	$0.611595\pi$
$114$	−76.7130	−0.0630249
$115$	−887.238	−0.719438
$116$	−230.613	−0.184585
$117$	−714.930	−0.564917
$118$	90.8063	0.0708424
$119$	1374.25	1.05864
$120$	52.3378	0.0398147
$121$	−1328.85	−0.998386
$122$	−93.2607	−0.0692084
$123$	−187.374	−0.137357
$124$	−618.558	−0.447969
$125$	125.000	0.0894427
$126$	−41.3396	−0.0292288
$127$	2020.56	1.41178	0.705889	−	0.708322i	$-0.250548\pi$
$127$	2020.56	1.41178	0.705889	+	0.708322i	$0.250548\pi$
$128$	−441.282	−0.304720
$129$	−198.142	−0.135236
$130$	−86.8752	−0.0586112
$131$	286.621	0.191162	0.0955809	−	0.995422i	$-0.469529\pi$
$131$	286.621	0.191162	0.0955809	+	0.995422i	$0.469529\pi$
$132$	−34.9624	−0.0230537
$133$	−2455.06	−1.60061
$134$	17.3213	0.0111666
$135$	−135.000	−0.0860663
$136$	228.335	0.143967
$137$	1903.55	1.18709	0.593545	−	0.804801i	$-0.297728\pi$
$137$	1903.55	1.18709	0.593545	+	0.804801i	$0.297728\pi$
$138$	116.438	0.0718253
$139$	−1439.13	−0.878167	−0.439083	−	0.898446i	$-0.644697\pi$
$139$	−1439.13	−0.878167	−0.439083	+	0.898446i	$0.644697\pi$
$140$	834.977	0.504060
$141$	−537.959	−0.321307
$142$	47.8152	0.0282575
$143$	116.417	0.0680788
$144$	565.687	0.327365
$145$	145.000	0.0830455
$146$	224.006	0.126979
$147$	−294.000	−0.164957
$148$	−1397.73	−0.776302
$149$	1733.83	0.953295	0.476647	−	0.879095i	$-0.341852\pi$
$149$	1733.83	0.953295	0.476647	+	0.879095i	$0.341852\pi$
$150$	−16.4046	−0.00892954
$151$	−2585.20	−1.39325	−0.696623	−	0.717437i	$-0.745315\pi$
$151$	−2585.20	−1.39325	−0.696623	+	0.717437i	$0.745315\pi$
$152$	−407.913	−0.217672
$153$	−588.966	−0.311209
$154$	6.73161	0.00352239
$155$	388.925	0.201543
$156$	−1895.08	−0.972614
$157$	2911.36	1.47995	0.739975	−	0.672635i	$-0.234837\pi$
$157$	2911.36	1.47995	0.739975	+	0.672635i	$0.234837\pi$
$158$	230.367	0.115994
$159$	−2030.32	−1.01267
$160$	208.307	0.102926
$161$	3726.40	1.82411
$162$	17.7170	0.00859245
$163$	−2877.35	−1.38265	−0.691323	−	0.722546i	$-0.742972\pi$
$163$	−2877.35	−1.38265	−0.691323	+	0.722546i	$0.742972\pi$
$164$	−496.676	−0.236487
$165$	21.9830	0.0103719
$166$	−258.044	−0.120651
$167$	1135.80	0.526292	0.263146	−	0.964756i	$-0.415240\pi$
$167$	1135.80	0.526292	0.263146	+	0.964756i	$0.415240\pi$
$168$	−219.819	−0.100949
$169$	4113.18	1.87218
$170$	−71.5685	−0.0322886
$171$	1052.17	0.470535
$172$	−525.219	−0.232835
$173$	3337.04	1.46653	0.733267	−	0.679941i	$-0.237995\pi$
$173$	3337.04	1.46653	0.733267	+	0.679941i	$0.237995\pi$
$174$	−19.0294	−0.00829087
$175$	−525.000	−0.226779
$176$	−92.1145	−0.0394511
$177$	−1245.47	−0.528899
$178$	308.756	0.130013
$179$	−4693.70	−1.95991	−0.979955	−	0.199220i	$-0.936159\pi$
$179$	−4693.70	−1.95991	−0.979955	+	0.199220i	$0.936159\pi$
$180$	−357.847	−0.148180
$181$	1068.75	0.438892	0.219446	−	0.975625i	$-0.429575\pi$
$181$	1068.75	0.438892	0.219446	+	0.975625i	$0.429575\pi$
$182$	364.876	0.148607
$183$	1279.13	0.516700
$184$	619.147	0.248066
$185$	878.837	0.349262
$186$	−51.0413	−0.0201211
$187$	95.9052	0.0375042
$188$	−1425.98	−0.553192
$189$	567.000	0.218218
$190$	127.855	0.0488188
$191$	−1082.04	−0.409913	−0.204956	−	0.978771i	$-0.565705\pi$
$191$	−1082.04	−0.409913	−0.204956	+	0.978771i	$0.565705\pi$
$192$	1481.16	0.556737
$193$	−4044.87	−1.50858	−0.754290	−	0.656541i	$-0.772019\pi$
$193$	−4044.87	−1.50858	−0.754290	+	0.656541i	$0.772019\pi$
$194$	193.512	0.0716152
$195$	1191.55	0.437583
$196$	−779.311	−0.284006
$197$	1433.82	0.518556	0.259278	−	0.965803i	$-0.416515\pi$
$197$	1433.82	0.518556	0.259278	+	0.965803i	$0.416515\pi$
$198$	−2.88497	−0.00103549
$199$	3460.17	1.23259	0.616293	−	0.787517i	$-0.288634\pi$
$199$	3460.17	1.23259	0.616293	+	0.787517i	$0.288634\pi$
$200$	−87.2297	−0.0308403
$201$	−237.573	−0.0833686
$202$	−141.570	−0.0493111
$203$	−609.000	−0.210559
$204$	−1561.18	−0.535807
$205$	312.290	0.106397
$206$	−339.139	−0.114704
$207$	−1597.03	−0.536237
$208$	−4992.92	−1.66441
$209$	−171.332	−0.0567046
$210$	68.8994	0.0226405
$211$	2044.61	0.667093	0.333547	−	0.942734i	$-0.391755\pi$
$211$	2044.61	0.667093	0.333547	+	0.942734i	$0.391755\pi$
$212$	−5381.81	−1.74351
$213$	−655.817	−0.210966
$214$	−265.196	−0.0847123
$215$	330.237	0.104753
$216$	94.2080	0.0296761
$217$	−1633.48	−0.511005
$218$	−246.802	−0.0766769
$219$	−3072.39	−0.948005
$220$	58.2706	0.0178573
$221$	5198.39	1.58227
$222$	−115.336	−0.0348686
$223$	−2296.00	−0.689470	−0.344735	−	0.938700i	$-0.612031\pi$
$223$	−2296.00	−0.689470	−0.344735	+	0.938700i	$0.612031\pi$
$224$	−874.890	−0.260965
$225$	225.000	0.0666667
$226$	−180.473	−0.0531191
$227$	−5953.92	−1.74086	−0.870431	−	0.492290i	$-0.836160\pi$
$227$	−5953.92	−1.74086	−0.870431	+	0.492290i	$0.836160\pi$
$228$	2789.01	0.810116
$229$	1286.19	0.371151	0.185576	−	0.982630i	$-0.440585\pi$
$229$	1286.19	0.371151	0.185576	+	0.982630i	$0.440585\pi$
$230$	−194.064	−0.0556356
$231$	−92.3284	−0.0262977
$232$	−101.186	−0.0286345
$233$	203.636	0.0572559	0.0286280	−	0.999590i	$-0.490886\pi$
$233$	203.636	0.0572559	0.0286280	+	0.999590i	$0.490886\pi$
$234$	−156.375	−0.0436862
$235$	896.599	0.248884
$236$	−3301.39	−0.910601
$237$	−3159.63	−0.865993
$238$	300.588	0.0818665
$239$	2264.94	0.612998	0.306499	−	0.951871i	$-0.400842\pi$
$239$	2264.94	0.612998	0.306499	+	0.951871i	$0.400842\pi$
$240$	−942.811	−0.253576
$241$	−3584.42	−0.958060	−0.479030	−	0.877799i	$-0.659012\pi$
$241$	−3584.42	−0.958060	−0.479030	+	0.877799i	$0.659012\pi$
$242$	−290.657	−0.0772073
$243$	−243.000	−0.0641500
$244$	3390.62	0.889599
$245$	490.000	0.127775
$246$	−40.9840	−0.0106221
$247$	−9286.76	−2.39232
$248$	−271.406	−0.0694932
$249$	3539.24	0.900763
$250$	27.3410	0.00691679
$251$	−4549.43	−1.14405	−0.572027	−	0.820235i	$-0.693843\pi$
$251$	−4549.43	−1.14405	−0.572027	+	0.820235i	$0.693843\pi$
$252$	1502.96	0.375704
$253$	260.055	0.0646225
$254$	441.954	0.109176
$255$	981.609	0.241062
$256$	3853.24	0.940732
$257$	1342.72	0.325901	0.162951	−	0.986634i	$-0.447899\pi$
$257$	1342.72	0.325901	0.162951	+	0.986634i	$0.447899\pi$
$258$	−43.3392	−0.0104581
$259$	−3691.12	−0.885540
$260$	3158.46	0.753383
$261$	261.000	0.0618984
$262$	62.6921	0.0147829
$263$	6631.18	1.55474	0.777369	−	0.629045i	$-0.216554\pi$
$263$	6631.18	1.55474	0.777369	+	0.629045i	$0.216554\pi$
$264$	−15.3405	−0.00357630
$265$	3383.86	0.784412
$266$	−536.991	−0.123778
$267$	−4234.79	−0.970656
$268$	−629.739	−0.143535
$269$	5563.54	1.26102	0.630511	−	0.776180i	$-0.282845\pi$
$269$	5563.54	1.26102	0.630511	+	0.776180i	$0.282845\pi$
$270$	−29.5283	−0.00665569
$271$	−3556.15	−0.797125	−0.398562	−	0.917141i	$-0.630491\pi$
$271$	−3556.15	−0.797125	−0.398562	+	0.917141i	$0.630491\pi$
$272$	−4113.21	−0.916912
$273$	−5004.51	−1.10948
$274$	416.360	0.0918002
$275$	−36.6383	−0.00803407
$276$	−4233.27	−0.923236
$277$	7099.67	1.53999	0.769996	−	0.638049i	$-0.220258\pi$
$277$	7099.67	1.53999	0.769996	+	0.638049i	$0.220258\pi$
$278$	−314.778	−0.0679105
$279$	700.065	0.150221
$280$	366.365	0.0781945
$281$	1382.11	0.293415	0.146708	−	0.989180i	$-0.453132\pi$
$281$	1382.11	0.293415	0.146708	+	0.989180i	$0.453132\pi$
$282$	−117.667	−0.0248474
$283$	−1867.69	−0.392305	−0.196153	−	0.980573i	$-0.562845\pi$
$283$	−1867.69	−0.392305	−0.196153	+	0.980573i	$0.562845\pi$
$284$	−1738.39	−0.363219
$285$	−1753.62	−0.364475
$286$	25.4636	0.00526467
$287$	−1311.62	−0.269764
$288$	374.953	0.0767164
$289$	−630.524	−0.128338
$290$	31.7156	0.00642208
$291$	−2654.14	−0.534669
$292$	−8144.05	−1.63217
$293$	4914.25	0.979842	0.489921	−	0.871767i	$-0.337026\pi$
$293$	4914.25	0.979842	0.489921	+	0.871767i	$0.337026\pi$
$294$	−64.3060	−0.0127565
$295$	2075.78	0.409683
$296$	−613.285	−0.120427
$297$	39.5693	0.00773079
$298$	379.237	0.0737203
$299$	14095.8	2.72637
$300$	596.412	0.114780
$301$	−1386.99	−0.265598
$302$	−565.455	−0.107743
$303$	1941.73	0.368150
$304$	7348.13	1.38633
$305$	−2131.89	−0.400234
$306$	−128.823	−0.0240665
$307$	−2357.55	−0.438282	−0.219141	−	0.975693i	$-0.570326\pi$
$307$	−2357.55	−0.438282	−0.219141	+	0.975693i	$0.570326\pi$
$308$	−244.737	−0.0452765
$309$	4651.52	0.856361
$310$	85.0688	0.0155858
$311$	9821.76	1.79081	0.895404	−	0.445255i	$-0.146887\pi$
$311$	9821.76	1.79081	0.895404	+	0.445255i	$0.146887\pi$
$312$	−831.508	−0.150881
$313$	−823.712	−0.148751	−0.0743753	−	0.997230i	$-0.523696\pi$
$313$	−823.712	−0.148751	−0.0743753	+	0.997230i	$0.523696\pi$
$314$	636.797	0.114448
$315$	−945.000	−0.169031
$316$	−8375.30	−1.49097
$317$	−657.982	−0.116580	−0.0582901	−	0.998300i	$-0.518565\pi$
$317$	−657.982	−0.116580	−0.0582901	+	0.998300i	$0.518565\pi$
$318$	−444.088	−0.0783120
$319$	−42.5004	−0.00745945
$320$	−2468.60	−0.431247
$321$	3637.34	0.632450
$322$	815.068	0.141062
$323$	−7650.51	−1.31791
$324$	−644.125	−0.110447
$325$	−1985.92	−0.338950
$326$	−629.357	−0.106923
$327$	3385.06	0.572459
$328$	−217.928	−0.0366861
$329$	−3765.71	−0.631035
$330$	4.80829	0.000802084 0
$331$	8443.16	1.40205	0.701024	−	0.713138i	$-0.252727\pi$
$331$	8443.16	1.40205	0.701024	+	0.713138i	$0.252727\pi$
$332$	9381.53	1.55084
$333$	1581.91	0.260324
$334$	248.431	0.0406993
$335$	395.955	0.0645770
$336$	3959.81	0.642932
$337$	6836.82	1.10512	0.552560	−	0.833473i	$-0.313651\pi$
$337$	6836.82	1.10512	0.552560	+	0.833473i	$0.313651\pi$
$338$	899.669	0.144780
$339$	2475.31	0.396580
$340$	2601.97	0.415034
$341$	−113.996	−0.0181033
$342$	230.139	0.0363874
$343$	5145.00	0.809924
$344$	−230.451	−0.0361195
$345$	2661.71	0.415368
$346$	729.904	0.113410
$347$	7797.57	1.20633	0.603164	−	0.797617i	$-0.293907\pi$
$347$	7797.57	1.20633	0.603164	+	0.797617i	$0.293907\pi$
$348$	691.838	0.106570
$349$	7869.23	1.20696	0.603482	−	0.797377i	$-0.293780\pi$
$349$	7869.23	1.20696	0.603482	+	0.797377i	$0.293780\pi$
$350$	−114.832	−0.0175373
$351$	2144.79	0.326155
$352$	−61.0561	−0.00924517
$353$	943.862	0.142314	0.0711568	−	0.997465i	$-0.477331\pi$
$353$	943.862	0.142314	0.0711568	+	0.997465i	$0.477331\pi$
$354$	−272.419	−0.0409009
$355$	1093.03	0.163414
$356$	−11225.2	−1.67117
$357$	−4122.76	−0.611203
$358$	−1026.64	−0.151564
$359$	5181.28	0.761720	0.380860	−	0.924633i	$-0.375628\pi$
$359$	5181.28	0.761720	0.380860	+	0.924633i	$0.375628\pi$
$360$	−157.013	−0.0229870
$361$	6808.42	0.992625
$362$	233.766	0.0339405
$363$	3986.56	0.576419
$364$	−13265.5	−1.91018
$365$	5120.66	0.734321
$366$	279.782	0.0399575
$367$	7016.17	0.997933	0.498966	−	0.866621i	$-0.333713\pi$
$367$	7016.17	0.997933	0.498966	+	0.866621i	$0.333713\pi$
$368$	−11153.3	−1.57991
$369$	562.122	0.0793033
$370$	192.226	0.0270091
$371$	−14212.2	−1.98885
$372$	1855.68	0.258635
$373$	−4322.19	−0.599985	−0.299993	−	0.953942i	$-0.596984\pi$
$373$	−4322.19	−0.599985	−0.299993	+	0.953942i	$0.596984\pi$
$374$	20.9772	0.00290028
$375$	−375.000	−0.0516398
$376$	−625.680	−0.0858164
$377$	−2303.66	−0.314707
$378$	124.019	0.0168752
$379$	−6955.45	−0.942684	−0.471342	−	0.881951i	$-0.656230\pi$
$379$	−6955.45	−0.942684	−0.471342	+	0.881951i	$0.656230\pi$
$380$	−4648.34	−0.627513
$381$	−6061.68	−0.815090
$382$	−236.672	−0.0316994
$383$	−8543.13	−1.13977	−0.569887	−	0.821723i	$-0.693013\pi$
$383$	−8543.13	−1.13977	−0.569887	+	0.821723i	$0.693013\pi$
$384$	1323.85	0.175930
$385$	153.881	0.0203701
$386$	−884.727	−0.116662
$387$	594.426	0.0780785
$388$	−7035.38	−0.920535
$389$	5928.65	0.772736	0.386368	−	0.922345i	$-0.373729\pi$
$389$	5928.65	0.772736	0.386368	+	0.922345i	$0.373729\pi$
$390$	260.626	0.0338392
$391$	11612.3	1.50194
$392$	−341.940	−0.0440576
$393$	−859.863	−0.110367
$394$	313.617	0.0401010
$395$	5266.06	0.670795
$396$	104.887	0.0133100
$397$	10989.4	1.38927	0.694637	−	0.719360i	$-0.255565\pi$
$397$	10989.4	1.38927	0.694637	+	0.719360i	$0.255565\pi$
$398$	756.836	0.0953185
$399$	7365.19	0.924112
$400$	1571.35	0.196419
$401$	797.168	0.0992735	0.0496368	−	0.998767i	$-0.484194\pi$
$401$	797.168	0.0992735	0.0496368	+	0.998767i	$0.484194\pi$
$402$	−51.9639	−0.00644707
$403$	−6178.98	−0.763764
$404$	5146.97	0.633840
$405$	405.000	0.0496904
$406$	−133.205	−0.0162829
$407$	−257.592	−0.0313720
$408$	−685.004	−0.0831194
$409$	−7879.82	−0.952645	−0.476323	−	0.879271i	$-0.658031\pi$
$409$	−7879.82	−0.952645	−0.476323	+	0.879271i	$0.658031\pi$
$410$	68.3067	0.00822787
$411$	−5710.66	−0.685367
$412$	12329.9	1.47439
$413$	−8718.27	−1.03874
$414$	−349.315	−0.0414683
$415$	−5898.73	−0.697728
$416$	−3309.45	−0.390046
$417$	4317.38	0.507010
$418$	−37.4751	−0.00438509
$419$	9358.61	1.09116	0.545582	−	0.838057i	$-0.316309\pi$
$419$	9358.61	1.09116	0.545582	+	0.838057i	$0.316309\pi$
$420$	−2504.93	−0.291019
$421$	−3252.50	−0.376525	−0.188263	−	0.982119i	$-0.560286\pi$
$421$	−3252.50	−0.376525	−0.188263	+	0.982119i	$0.560286\pi$
$422$	447.213	0.0515877
$423$	1613.88	0.185507
$424$	−2361.39	−0.270470
$425$	−1636.02	−0.186726
$426$	−143.446	−0.0163145
$427$	8953.92	1.01478
$428$	9641.57	1.08888
$429$	−349.250	−0.0393053
$430$	72.2321	0.00810079
$431$	4340.20	0.485058	0.242529	−	0.970144i	$-0.422023\pi$
$431$	4340.20	0.485058	0.242529	+	0.970144i	$0.422023\pi$
$432$	−1697.06	−0.189004
$433$	2983.79	0.331159	0.165579	−	0.986196i	$-0.447051\pi$
$433$	2983.79	0.331159	0.165579	+	0.986196i	$0.447051\pi$
$434$	−357.289	−0.0395171
$435$	−435.000	−0.0479463
$436$	8972.84	0.985598
$437$	−20745.0	−2.27086
$438$	−672.019	−0.0733112
$439$	−6943.69	−0.754907	−0.377454	−	0.926028i	$-0.623200\pi$
$439$	−6943.69	−0.754907	−0.377454	+	0.926028i	$0.623200\pi$
$440$	25.5675	0.00277019
$441$	882.000	0.0952380
$442$	1137.03	0.122360
$443$	13772.2	1.47706	0.738528	−	0.674223i	$-0.235521\pi$
$443$	13772.2	1.47706	0.738528	+	0.674223i	$0.235521\pi$
$444$	4193.19	0.448198
$445$	7057.99	0.751867
$446$	−502.201	−0.0533182
$447$	−5201.49	−0.550385
$448$	10368.1	1.09341
$449$	6057.15	0.636648	0.318324	−	0.947982i	$-0.396880\pi$
$449$	6057.15	0.636648	0.318324	+	0.947982i	$0.396880\pi$
$450$	49.2138	0.00515547
$451$	−91.5341	−0.00955693
$452$	6561.36	0.682788
$453$	7755.59	0.804391
$454$	−1302.29	−0.134624
$455$	8340.85	0.859396
$456$	1223.74	0.125673
$457$	−18653.8	−1.90938	−0.954690	−	0.297603i	$-0.903813\pi$
$457$	−18653.8	−1.90938	−0.954690	+	0.297603i	$0.903813\pi$
$458$	281.325	0.0287019
$459$	1766.90	0.179677
$460$	7055.45	0.715135
$461$	−2879.46	−0.290910	−0.145455	−	0.989365i	$-0.546465\pi$
$461$	−2879.46	−0.290910	−0.145455	+	0.989365i	$0.546465\pi$
$462$	−20.1948	−0.00203365
$463$	7645.28	0.767400	0.383700	−	0.923458i	$-0.374650\pi$
$463$	7645.28	0.767400	0.383700	+	0.923458i	$0.374650\pi$
$464$	1822.77	0.182370
$465$	−1166.77	−0.116361
$466$	44.5409	0.00442772
$467$	7486.58	0.741837	0.370918	−	0.928665i	$-0.379043\pi$
$467$	7486.58	0.741837	0.370918	+	0.928665i	$0.379043\pi$
$468$	5685.24	0.561539
$469$	−1663.01	−0.163733
$470$	196.111	0.0192467
$471$	−8734.09	−0.854449
$472$	−1448.56	−0.141261
$473$	−96.7944	−0.00940932
$474$	−691.101	−0.0669690
$475$	2922.69	0.282321
$476$	−10928.3	−1.05230
$477$	6090.96	0.584666
$478$	495.405	0.0474044
$479$	13351.7	1.27361	0.636803	−	0.771027i	$-0.280257\pi$
$479$	13351.7	1.27361	0.636803	+	0.771027i	$0.280257\pi$
$480$	−624.922	−0.0594243
$481$	−13962.4	−1.32355
$482$	−784.013	−0.0740888
$483$	−11179.2	−1.05315
$484$	10567.2	0.992416
$485$	4423.57	0.414152
$486$	−53.1509	−0.00496086
$487$	−3228.98	−0.300450	−0.150225	−	0.988652i	$-0.548000\pi$
$487$	−3228.98	−0.300450	−0.150225	+	0.988652i	$0.548000\pi$
$488$	1487.71	0.138003
$489$	8632.05	0.798271
$490$	107.177	0.00988113
$491$	−7804.20	−0.717309	−0.358655	−	0.933470i	$-0.616764\pi$
$491$	−7804.20	−0.717309	−0.358655	+	0.933470i	$0.616764\pi$
$492$	1490.03	0.136536
$493$	−1897.78	−0.173370
$494$	−2031.28	−0.185003
$495$	−65.9489	−0.00598824
$496$	4889.10	0.442595
$497$	−4590.72	−0.414330
$498$	774.131	0.0696579
$499$	−3990.42	−0.357988	−0.178994	−	0.983850i	$-0.557284\pi$
$499$	−3990.42	−0.357988	−0.178994	+	0.983850i	$0.557284\pi$
$500$	−994.020	−0.0889078
$501$	−3407.40	−0.303855
$502$	−995.089	−0.0884721
$503$	6235.12	0.552704	0.276352	−	0.961056i	$-0.410874\pi$
$503$	6235.12	0.552704	0.276352	+	0.961056i	$0.410874\pi$
$504$	659.456	0.0582828
$505$	−3236.21	−0.285167
$506$	56.8813	0.00499739
$507$	−12339.6	−1.08090
$508$	−16067.8	−1.40334
$509$	−13441.4	−1.17049	−0.585246	−	0.810856i	$-0.699002\pi$
$509$	−13441.4	−1.17049	−0.585246	+	0.810856i	$0.699002\pi$
$510$	214.706	0.0186418
$511$	−21506.8	−1.86184
$512$	4373.07	0.377469
$513$	−3156.51	−0.271663
$514$	293.691	0.0252026
$515$	−7752.53	−0.663335
$516$	1575.66	0.134427
$517$	−262.798	−0.0223556
$518$	−807.351	−0.0684806
$519$	−10011.1	−0.846703
$520$	1385.85	0.116872
$521$	11314.2	0.951407	0.475703	−	0.879606i	$-0.342194\pi$
$521$	11314.2	0.951407	0.475703	+	0.879606i	$0.342194\pi$
$522$	57.0881	0.00478674
$523$	12003.7	1.00361	0.501804	−	0.864982i	$-0.332670\pi$
$523$	12003.7	1.00361	0.501804	+	0.864982i	$0.332670\pi$
$524$	−2279.26	−0.190019
$525$	1575.00	0.130931
$526$	1450.43	0.120231
$527$	−5090.30	−0.420753
$528$	276.344	0.0227771
$529$	19320.6	1.58795
$530$	740.146	0.0606602
$531$	3736.40	0.305360
$532$	19523.0	1.59104
$533$	−4961.46	−0.403198
$534$	−926.268	−0.0750628
$535$	−6062.23	−0.489894
$536$	−276.312	−0.0222665
$537$	14081.1	1.13155
$538$	1216.90	0.0975174
$539$	−143.622	−0.0114772
$540$	1073.54	0.0855516
$541$	2058.05	0.163553	0.0817767	−	0.996651i	$-0.473941\pi$
$541$	2058.05	0.163553	0.0817767	+	0.996651i	$0.473941\pi$
$542$	−777.830	−0.0616433
$543$	−3206.25	−0.253395
$544$	−2726.35	−0.214874
$545$	−5641.76	−0.443425
$546$	−1094.63	−0.0857980
$547$	−2919.73	−0.228224	−0.114112	−	0.993468i	$-0.536402\pi$
$547$	−2919.73	−0.228224	−0.114112	+	0.993468i	$0.536402\pi$
$548$	−15137.3	−1.17999
$549$	−3837.39	−0.298317
$550$	−8.01382	−0.000621292 0
$551$	3390.32	0.262128
$552$	−1857.44	−0.143221
$553$	−22117.4	−1.70078
$554$	1552.90	0.119091
$555$	−2636.51	−0.201646
$556$	11444.2	0.872915
$557$	3685.44	0.280354	0.140177	−	0.990126i	$-0.455233\pi$
$557$	3685.44	0.280354	0.140177	+	0.990126i	$0.455233\pi$
$558$	153.124	0.0116169
$559$	−5246.58	−0.396971
$560$	−6599.68	−0.498013
$561$	−287.716	−0.0216531
$562$	302.306	0.0226904
$563$	−9449.71	−0.707385	−0.353693	−	0.935362i	$-0.615074\pi$
$563$	−9449.71	−0.707385	−0.353693	+	0.935362i	$0.615074\pi$
$564$	4277.94	0.319386
$565$	−4125.52	−0.307189
$566$	−408.515	−0.0303378
$567$	−1701.00	−0.125988
$568$	−762.756	−0.0563460
$569$	2727.43	0.200949	0.100474	−	0.994940i	$-0.467964\pi$
$569$	2727.43	0.200949	0.100474	+	0.994940i	$0.467964\pi$
$570$	−383.565	−0.0281856
$571$	−9211.18	−0.675089	−0.337545	−	0.941310i	$-0.609596\pi$
$571$	−9211.18	−0.675089	−0.337545	+	0.941310i	$0.609596\pi$
$572$	−925.765	−0.0676716
$573$	3246.11	0.236663
$574$	−286.888	−0.0208614
$575$	−4436.19	−0.321742
$576$	−4443.48	−0.321432
$577$	18864.4	1.36107	0.680534	−	0.732717i	$-0.261748\pi$
$577$	18864.4	1.36107	0.680534	+	0.732717i	$0.261748\pi$
$578$	−137.913	−0.00992463
$579$	12134.6	0.870980
$580$	−1153.06	−0.0825488
$581$	24774.7	1.76906
$582$	−580.536	−0.0413470
$583$	−991.831	−0.0704587
$584$	−3573.38	−0.253198
$585$	−3574.65	−0.252639
$586$	1074.88	0.0757732
$587$	−14024.1	−0.986092	−0.493046	−	0.870003i	$-0.664117\pi$
$587$	−14024.1	−0.986092	−0.493046	+	0.870003i	$0.664117\pi$
$588$	2337.93	0.163971
$589$	9093.66	0.636159
$590$	454.032	0.0316817
$591$	−4301.46	−0.299388
$592$	11047.7	0.766989
$593$	−17324.6	−1.19973	−0.599863	−	0.800102i	$-0.704778\pi$
$593$	−17324.6	−1.19973	−0.599863	+	0.800102i	$0.704778\pi$
$594$	8.65492	0.000597838 0
$595$	6871.27	0.473436
$596$	−13787.7	−0.947594
$597$	−10380.5	−0.711634
$598$	3083.16	0.210836
$599$	−8141.83	−0.555369	−0.277685	−	0.960672i	$-0.589567\pi$
$599$	−8141.83	−0.555369	−0.277685	+	0.960672i	$0.589567\pi$
$600$	261.689	0.0178057
$601$	400.990	0.0272158	0.0136079	−	0.999907i	$-0.495668\pi$
$601$	400.990	0.0272158	0.0136079	+	0.999907i	$0.495668\pi$
$602$	−303.375	−0.0205393
$603$	712.718	0.0481329
$604$	20557.9	1.38491
$605$	−6644.26	−0.446492
$606$	424.710	0.0284698
$607$	−19203.1	−1.28407	−0.642034	−	0.766677i	$-0.721909\pi$
$607$	−19203.1	−1.28407	−0.642034	+	0.766677i	$0.721909\pi$
$608$	4870.54	0.324879
$609$	1827.00	0.121566
$610$	−466.303	−0.0309509
$611$	−14244.6	−0.943164
$612$	4683.55	0.309348
$613$	6903.39	0.454853	0.227427	−	0.973795i	$-0.426969\pi$
$613$	6903.39	0.454853	0.227427	+	0.973795i	$0.426969\pi$
$614$	−515.663	−0.0338933
$615$	−936.871	−0.0614281
$616$	−107.384	−0.00702372
$617$	−18090.6	−1.18039	−0.590193	−	0.807262i	$-0.700948\pi$
$617$	−18090.6	−1.18039	−0.590193	+	0.807262i	$0.700948\pi$
$618$	1017.42	0.0662242
$619$	−23420.2	−1.52074	−0.760369	−	0.649492i	$-0.774982\pi$
$619$	−23420.2	−1.52074	−0.760369	+	0.649492i	$0.774982\pi$
$620$	−3092.79	−0.200338
$621$	4791.08	0.309597
$622$	2148.30	0.138487
$623$	−29643.5	−1.90633
$624$	14978.8	0.960946
$625$	625.000	0.0400000
$626$	−180.169	−0.0115032
$627$	513.995	0.0327384
$628$	−23151.6	−1.47110
$629$	−11502.3	−0.729138
$630$	−206.698	−0.0130715
$631$	10835.5	0.683607	0.341803	−	0.939771i	$-0.388962\pi$
$631$	10835.5	0.683607	0.341803	+	0.939771i	$0.388962\pi$
$632$	−3674.85	−0.231294
$633$	−6133.83	−0.385146
$634$	−143.919	−0.00901539
$635$	10102.8	0.631366
$636$	16145.4	1.00662
$637$	−7784.79	−0.484214
$638$	−9.29603	−0.000576855 0
$639$	1967.45	0.121801
$640$	−2206.41	−0.136275
$641$	−910.547	−0.0561068	−0.0280534	−	0.999606i	$-0.508931\pi$
$641$	−910.547	−0.0561068	−0.0280534	+	0.999606i	$0.508931\pi$
$642$	795.589	0.0489087
$643$	−81.2497	−0.00498316	−0.00249158	−	0.999997i	$-0.500793\pi$
$643$	−81.2497	−0.00498316	−0.00249158	+	0.999997i	$0.500793\pi$
$644$	−29632.9	−1.81320
$645$	−990.710	−0.0604793
$646$	−1673.38	−0.101917
$647$	−29487.9	−1.79179	−0.895895	−	0.444266i	$-0.853465\pi$
$647$	−29487.9	−1.79179	−0.895895	+	0.444266i	$0.853465\pi$
$648$	−282.624	−0.0171335
$649$	−608.424	−0.0367993
$650$	−434.376	−0.0262117
$651$	4900.45	0.295029
$652$	22881.1	1.37438
$653$	28469.2	1.70610	0.853051	−	0.521827i	$-0.174749\pi$
$653$	28469.2	1.70610	0.853051	+	0.521827i	$0.174749\pi$
$654$	740.407	0.0442694
$655$	1433.11	0.0854902
$656$	3925.74	0.233650
$657$	9217.18	0.547331
$658$	−823.668	−0.0487993
$659$	1953.52	0.115476	0.0577378	−	0.998332i	$-0.481611\pi$
$659$	1953.52	0.115476	0.0577378	+	0.998332i	$0.481611\pi$
$660$	−174.812	−0.0103099
$661$	−16092.8	−0.946956	−0.473478	−	0.880806i	$-0.657002\pi$
$661$	−16092.8	−0.946956	−0.473478	+	0.880806i	$0.657002\pi$
$662$	1846.76	0.108423
$663$	−15595.2	−0.913523
$664$	4116.35	0.240581
$665$	−12275.3	−0.715814
$666$	346.008	0.0201314
$667$	−5145.98	−0.298730
$668$	−9032.06	−0.523145
$669$	6888.01	0.398066
$670$	86.6064	0.00499388
$671$	624.868	0.0359505
$672$	2624.67	0.150668
$673$	−843.429	−0.0483088	−0.0241544	−	0.999708i	$-0.507689\pi$
$673$	−843.429	−0.0483088	−0.0241544	+	0.999708i	$0.507689\pi$
$674$	1495.40	0.0854612
$675$	−675.000	−0.0384900
$676$	−32708.7	−1.86099
$677$	11706.7	0.664588	0.332294	−	0.943176i	$-0.392177\pi$
$677$	11706.7	0.664588	0.332294	+	0.943176i	$0.392177\pi$
$678$	541.420	0.0306683
$679$	−18579.0	−1.05007
$680$	1141.67	0.0643840
$681$	17861.8	1.00509
$682$	−24.9342	−0.00139997
$683$	5775.22	0.323547	0.161774	−	0.986828i	$-0.448279\pi$
$683$	5775.22	0.323547	0.161774	+	0.986828i	$0.448279\pi$
$684$	−8367.02	−0.467721
$685$	9517.76	0.530883
$686$	1125.36	0.0626331
$687$	−3858.56	−0.214284
$688$	4151.35	0.230042
$689$	−53760.6	−2.97259
$690$	582.192	0.0321212
$691$	20629.4	1.13571	0.567857	−	0.823127i	$-0.307773\pi$
$691$	20629.4	1.13571	0.567857	+	0.823127i	$0.307773\pi$
$692$	−26536.6	−1.45776
$693$	276.985	0.0151830
$694$	1705.55	0.0932878
$695$	−7195.64	−0.392728
$696$	303.559	0.0165322
$697$	−4087.29	−0.222119
$698$	1721.22	0.0933370
$699$	−610.908	−0.0330567
$700$	4174.88	0.225422
$701$	−5797.19	−0.312350	−0.156175	−	0.987729i	$-0.549916\pi$
$701$	−5797.19	−0.312350	−0.156175	+	0.987729i	$0.549916\pi$
$702$	469.126	0.0252222
$703$	20548.6	1.10242
$704$	723.562	0.0387362
$705$	−2689.80	−0.143693
$706$	206.449	0.0110054
$707$	13592.1	0.723031
$708$	9904.16	0.525736
$709$	−4622.24	−0.244841	−0.122420	−	0.992478i	$-0.539066\pi$
$709$	−4622.24	−0.244841	−0.122420	+	0.992478i	$0.539066\pi$
$710$	239.076	0.0126371
$711$	9478.90	0.499981
$712$	−4925.33	−0.259248
$713$	−13802.8	−0.724989
$714$	−901.764	−0.0472656
$715$	582.084	0.0304457
$716$	37325.1	1.94819
$717$	−6794.81	−0.353915
$718$	1133.29	0.0589054
$719$	20648.1	1.07099	0.535497	−	0.844537i	$-0.320124\pi$
$719$	20648.1	1.07099	0.535497	+	0.844537i	$0.320124\pi$
$720$	2828.43	0.146402
$721$	32560.6	1.68186
$722$	1489.19	0.0767618
$723$	10753.2	0.553136
$724$	−8498.87	−0.436268
$725$	725.000	0.0371391
$726$	871.972	0.0445757
$727$	−17177.6	−0.876314	−0.438157	−	0.898898i	$-0.644369\pi$
$727$	−17177.6	−0.876314	−0.438157	+	0.898898i	$0.644369\pi$
$728$	−5820.56	−0.296324
$729$	729.000	0.0370370
$730$	1120.03	0.0567866
$731$	−4322.18	−0.218689
$732$	−10171.9	−0.513610
$733$	23803.4	1.19945	0.599725	−	0.800206i	$-0.295277\pi$
$733$	23803.4	1.19945	0.599725	+	0.800206i	$0.295277\pi$
$734$	1534.63	0.0771722
$735$	−1470.00	−0.0737711
$736$	−7392.72	−0.370244
$737$	−116.057	−0.00580055
$738$	122.952	0.00613269
$739$	−16294.6	−0.811106	−0.405553	−	0.914072i	$-0.632921\pi$
$739$	−16294.6	−0.811106	−0.405553	+	0.914072i	$0.632921\pi$
$740$	−6988.65	−0.347173
$741$	27860.3	1.38120
$742$	−3108.62	−0.153802
$743$	25122.4	1.24045	0.620223	−	0.784426i	$-0.287042\pi$
$743$	25122.4	1.24045	0.620223	+	0.784426i	$0.287042\pi$
$744$	814.219	0.0401219
$745$	8669.15	0.426326
$746$	−945.385	−0.0463981
$747$	−10617.7	−0.520056
$748$	−762.653	−0.0372799
$749$	25461.4	1.24211
$750$	−82.0231	−0.00399341
$751$	−29871.6	−1.45144	−0.725719	−	0.687991i	$-0.758493\pi$
$751$	−29871.6	−1.45144	−0.725719	+	0.687991i	$0.758493\pi$
$752$	11271.0	0.546556
$753$	13648.3	0.660520
$754$	−503.876	−0.0243370
$755$	−12926.0	−0.623079
$756$	−4508.87	−0.216913
$757$	17699.3	0.849791	0.424896	−	0.905242i	$-0.360311\pi$
$757$	17699.3	0.849791	0.424896	+	0.905242i	$0.360311\pi$
$758$	−1521.35	−0.0728997
$759$	−780.164	−0.0373098
$760$	−2039.56	−0.0973457
$761$	10189.2	0.485360	0.242680	−	0.970106i	$-0.421973\pi$
$761$	10189.2	0.485360	0.242680	+	0.970106i	$0.421973\pi$
$762$	−1325.86	−0.0630326
$763$	23695.4	1.12429
$764$	8604.52	0.407462
$765$	−2944.83	−0.139177
$766$	−1868.62	−0.0881412
$767$	−32978.6	−1.55253
$768$	−11559.7	−0.543132
$769$	−17537.6	−0.822395	−0.411197	−	0.911546i	$-0.634889\pi$
$769$	−17537.6	−0.822395	−0.411197	+	0.911546i	$0.634889\pi$
$770$	33.6580	0.00157526
$771$	−4028.16	−0.188159
$772$	32165.4	1.49956
$773$	−18819.3	−0.875659	−0.437830	−	0.899058i	$-0.644253\pi$
$773$	−18819.3	−0.875659	−0.437830	+	0.899058i	$0.644253\pi$
$774$	130.018	0.00603797
$775$	1944.62	0.0901329
$776$	−3086.93	−0.142802
$777$	11073.3	0.511267
$778$	1296.76	0.0597573
$779$	7301.83	0.335835
$780$	−9475.39	−0.434966
$781$	−320.373	−0.0146784
$782$	2539.93	0.116148
$783$	−783.000	−0.0357371
$784$	6159.70	0.280598
$785$	14556.8	0.661854
$786$	−188.076	−0.00853494
$787$	−11434.2	−0.517900	−0.258950	−	0.965891i	$-0.583376\pi$
$787$	−11434.2	−0.517900	−0.258950	+	0.965891i	$0.583376\pi$
$788$	−11402.0	−0.515455
$789$	−19893.5	−0.897628
$790$	1151.84	0.0518740
$791$	17327.2	0.778867
$792$	46.0216	0.00206478
$793$	33870.0	1.51672
$794$	2403.69	0.107435
$795$	−10151.6	−0.452880
$796$	−27515.8	−1.22522
$797$	−14273.6	−0.634375	−0.317187	−	0.948363i	$-0.602738\pi$
$797$	−14273.6	−0.634375	−0.317187	+	0.948363i	$0.602738\pi$
$798$	1610.97	0.0714635
$799$	−11734.8	−0.519583
$800$	1041.54	0.0460298
$801$	12704.4	0.560408
$802$	174.363	0.00767703
$803$	−1500.89	−0.0659594
$804$	1889.22	0.0828700
$805$	18632.0	0.815766
$806$	−1351.52	−0.0590635
$807$	−16690.6	−0.728051
$808$	2258.35	0.0983273
$809$	−92.7049	−0.00402884	−0.00201442	−	0.999998i	$-0.500641\pi$
$809$	−92.7049	−0.00402884	−0.00201442	+	0.999998i	$0.500641\pi$
$810$	88.5849	0.00384266
$811$	20484.6	0.886946	0.443473	−	0.896288i	$-0.353746\pi$
$811$	20484.6	0.886946	0.443473	+	0.896288i	$0.353746\pi$
$812$	4842.86	0.209300
$813$	10668.5	0.460220
$814$	−56.3427	−0.00242606
$815$	−14386.7	−0.618338
$816$	12339.6	0.529379
$817$	7721.45	0.330648
$818$	−1723.54	−0.0736700
$819$	15013.5	0.640556
$820$	−2483.38	−0.105760
$821$	12828.4	0.545328	0.272664	−	0.962109i	$-0.412095\pi$
$821$	12828.4	0.545328	0.272664	+	0.962109i	$0.412095\pi$
$822$	−1249.08	−0.0530009
$823$	−7959.43	−0.337118	−0.168559	−	0.985692i	$-0.553911\pi$
$823$	−7959.43	−0.337118	−0.168559	+	0.985692i	$0.553911\pi$
$824$	5410.00	0.228721
$825$	109.915	0.00463847
$826$	−1906.93	−0.0803277
$827$	15961.5	0.671144	0.335572	−	0.942015i	$-0.391070\pi$
$827$	15961.5	0.671144	0.335572	+	0.942015i	$0.391070\pi$
$828$	12699.8	0.533030
$829$	−6830.19	−0.286155	−0.143077	−	0.989712i	$-0.545700\pi$
$829$	−6830.19	−0.286155	−0.143077	+	0.989712i	$0.545700\pi$
$830$	−1290.22	−0.0539568
$831$	−21299.0	−0.889115
$832$	39219.5	1.63424
$833$	−6413.18	−0.266751
$834$	944.333	0.0392081
$835$	5679.00	0.235365
$836$	1362.46	0.0563655
$837$	−2100.19	−0.0867304
$838$	2046.99	0.0843820
$839$	14841.7	0.610720	0.305360	−	0.952237i	$-0.401223\pi$
$839$	14841.7	0.610720	0.305360	+	0.952237i	$0.401223\pi$
$840$	−1099.09	−0.0451456
$841$	841.000	0.0344828
$842$	−711.413	−0.0291175
$843$	−4146.33	−0.169404
$844$	−16259.0	−0.663104
$845$	20565.9	0.837265
$846$	353.000	0.0143456
$847$	27905.9	1.13206
$848$	42537.9	1.72259
$849$	5603.06	0.226498
$850$	−357.843	−0.0144399
$851$	−31189.5	−1.25636
$852$	5215.16	0.209705
$853$	−46778.2	−1.87767	−0.938836	−	0.344365i	$-0.888094\pi$
$853$	−46778.2	−1.87767	−0.938836	+	0.344365i	$0.888094\pi$
$854$	1958.47	0.0784749
$855$	5260.85	0.210429
$856$	4230.45	0.168918
$857$	14402.4	0.574070	0.287035	−	0.957920i	$-0.407330\pi$
$857$	14402.4	0.574070	0.287035	+	0.957920i	$0.407330\pi$
$858$	−76.3909	−0.00303956
$859$	23353.0	0.927584	0.463792	−	0.885944i	$-0.346488\pi$
$859$	23353.0	0.927584	0.463792	+	0.885944i	$0.346488\pi$
$860$	−2626.09	−0.104127
$861$	3934.86	0.155749
$862$	949.324	0.0375106
$863$	27267.6	1.07555	0.537776	−	0.843088i	$-0.319265\pi$
$863$	27267.6	1.07555	0.537776	+	0.843088i	$0.319265\pi$
$864$	−1124.86	−0.0442922
$865$	16685.2	0.655854
$866$	652.639	0.0256092
$867$	1891.57	0.0740959
$868$	12989.7	0.507949
$869$	−1543.51	−0.0602533
$870$	−95.1468	−0.00370779
$871$	−6290.66	−0.244720
$872$	3937.03	0.152895
$873$	7962.43	0.308691
$874$	−4537.51	−0.175611
$875$	−2625.00	−0.101419
$876$	24432.2	0.942336
$877$	−10549.3	−0.406185	−0.203092	−	0.979160i	$-0.565099\pi$
$877$	−10549.3	−0.406185	−0.203092	+	0.979160i	$0.565099\pi$
$878$	−1518.78	−0.0583786
$879$	−14742.8	−0.565712
$880$	−460.573	−0.0176431
$881$	25397.8	0.971251	0.485625	−	0.874167i	$-0.338592\pi$
$881$	25397.8	0.971251	0.485625	+	0.874167i	$0.338592\pi$
$882$	192.918	0.00736496
$883$	−33416.7	−1.27357	−0.636785	−	0.771041i	$-0.719736\pi$
$883$	−33416.7	−1.27357	−0.636785	+	0.771041i	$0.719736\pi$
$884$	−41338.4	−1.57281
$885$	−6227.34	−0.236531
$886$	3012.36	0.114224
$887$	−33336.9	−1.26194	−0.630971	−	0.775806i	$-0.717343\pi$
$887$	−33336.9	−1.26194	−0.630971	+	0.775806i	$0.717343\pi$
$888$	1839.86	0.0695288
$889$	−42431.8	−1.60081
$890$	1543.78	0.0581434
$891$	−118.708	−0.00446337
$892$	18258.2	0.685347
$893$	20963.9	0.785587
$894$	−1137.71	−0.0425624
$895$	−23468.5	−0.876498
$896$	9266.92	0.345520
$897$	−42287.5	−1.57407
$898$	1324.87	0.0492333
$899$	2255.76	0.0836863
$900$	−1789.24	−0.0662680
$901$	−44288.4	−1.63758
$902$	−20.0211	−0.000739057 0
$903$	4160.98	0.153343
$904$	2878.94	0.105921
$905$	5343.75	0.196279
$906$	1696.36	0.0622052
$907$	48386.2	1.77138	0.885688	−	0.464280i	$-0.153687\pi$
$907$	48386.2	1.77138	0.885688	+	0.464280i	$0.153687\pi$
$908$	47346.5	1.73045
$909$	−5825.18	−0.212551
$910$	1824.38	0.0664589
$911$	44095.4	1.60367	0.801836	−	0.597545i	$-0.203857\pi$
$911$	44095.4	1.60367	0.801836	+	0.597545i	$0.203857\pi$
$912$	−22044.4	−0.800397
$913$	1728.95	0.0626725
$914$	−4080.10	−0.147656
$915$	6395.66	0.231075
$916$	−10228.0	−0.368932
$917$	−6019.04	−0.216757
$918$	386.470	0.0138948
$919$	−27520.1	−0.987816	−0.493908	−	0.869514i	$-0.664432\pi$
$919$	−27520.1	−0.987816	−0.493908	+	0.869514i	$0.664432\pi$
$920$	3095.74	0.110939
$921$	7072.66	0.253043
$922$	−629.818	−0.0224967
$923$	−17365.3	−0.619270
$924$	734.210	0.0261404
$925$	4394.19	0.156195
$926$	1672.24	0.0593447
$927$	−13954.6	−0.494420
$928$	1208.18	0.0427376
$929$	13243.5	0.467712	0.233856	−	0.972271i	$-0.424866\pi$
$929$	13243.5	0.467712	0.233856	+	0.972271i	$0.424866\pi$
$930$	−255.206	−0.00899844
$931$	11457.0	0.403315
$932$	−1619.34	−0.0569135
$933$	−29465.3	−1.03392
$934$	1637.53	0.0573678
$935$	479.526	0.0167724
$936$	2494.52	0.0871112
$937$	48606.1	1.69466	0.847329	−	0.531069i	$-0.178210\pi$
$937$	48606.1	1.69466	0.847329	+	0.531069i	$0.178210\pi$
$938$	−363.747	−0.0126618
$939$	2471.13	0.0858812
$940$	−7129.89	−0.247395
$941$	38178.2	1.32261	0.661303	−	0.750118i	$-0.270004\pi$
$941$	38178.2	1.32261	0.661303	+	0.750118i	$0.270004\pi$
$942$	−1910.39	−0.0660763
$943$	−11083.0	−0.382728
$944$	26094.2	0.899677
$945$	2835.00	0.0975900
$946$	−21.1717	−0.000727643 0
$947$	−21472.2	−0.736803	−0.368402	−	0.929667i	$-0.620095\pi$
$947$	−21472.2	−0.736803	−0.368402	+	0.929667i	$0.620095\pi$
$948$	25125.9	0.860814
$949$	−81353.6	−2.78277
$950$	639.275	0.0218325
$951$	1973.95	0.0673076
$952$	−4795.03	−0.163243
$953$	5335.21	0.181348	0.0906739	−	0.995881i	$-0.471098\pi$
$953$	5335.21	0.181348	0.0906739	+	0.995881i	$0.471098\pi$
$954$	1332.26	0.0452134
$955$	−5410.18	−0.183319
$956$	−18011.1	−0.609332
$957$	127.501	0.00430671
$958$	2920.40	0.0984906
$959$	−39974.6	−1.34603
$960$	7405.80	0.248980
$961$	−23740.5	−0.796902
$962$	−3053.97	−0.102353
$963$	−10912.0	−0.365145
$964$	28503.8	0.952331
$965$	−20224.3	−0.674658
$966$	−2445.20	−0.0814422
$967$	−4578.60	−0.152263	−0.0761313	−	0.997098i	$-0.524257\pi$
$967$	−4578.60	−0.152263	−0.0761313	+	0.997098i	$0.524257\pi$
$968$	4636.61	0.153953
$969$	22951.5	0.760898
$970$	967.559	0.0320273
$971$	−13641.3	−0.450846	−0.225423	−	0.974261i	$-0.572376\pi$
$971$	−13641.3	−0.450846	−0.225423	+	0.974261i	$0.572376\pi$
$972$	1932.37	0.0637664
$973$	30221.7	0.995748
$974$	−706.269	−0.0232344
$975$	5957.75	0.195693
$976$	−26799.5	−0.878926
$977$	51144.7	1.67478	0.837391	−	0.546604i	$-0.184080\pi$
$977$	51144.7	1.67478	0.837391	+	0.546604i	$0.184080\pi$
$978$	1888.07	0.0617320
$979$	−2068.74	−0.0675354
$980$	−3896.56	−0.127011
$981$	−10155.2	−0.330509
$982$	−1707.00	−0.0554710
$983$	56699.8	1.83972	0.919859	−	0.392249i	$-0.128303\pi$
$983$	56699.8	1.83972	0.919859	+	0.392249i	$0.128303\pi$
$984$	653.783	0.0211807
$985$	7169.10	0.231905
$986$	−415.098	−0.0134071
$987$	11297.1	0.364328
$988$	73849.8	2.37801
$989$	−11719.9	−0.376817
$990$	−14.4249	−0.000463083 0
$991$	52946.3	1.69717	0.848585	−	0.529059i	$-0.177455\pi$
$991$	52946.3	1.69717	0.848585	+	0.529059i	$0.177455\pi$
$992$	3240.63	0.103720
$993$	−25329.5	−0.809473
$994$	−1004.12	−0.0320410
$995$	17300.8	0.551229
$996$	−28144.6	−0.895377
$997$	−2112.74	−0.0671126	−0.0335563	−	0.999437i	$-0.510683\pi$
$997$	−2112.74	−0.0671126	−0.0335563	+	0.999437i	$0.510683\pi$
$998$	−872.818	−0.0276839
$999$	−4745.72	−0.150298

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.4.a.i.1.4	✓	7
3.2	odd	2		1305.4.a.n.1.4		7
5.4	even	2		2175.4.a.n.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.i.1.4	✓	7	1.1	even	1	trivial
1305.4.a.n.1.4		7	3.2	odd	2
2175.4.a.n.1.4		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+0.218728 q^{2} -3.00000 q^{3} -7.95216 q^{4} +5.00000 q^{5} -0.656184 q^{6} -21.0000 q^{7} -3.48919 q^{8} +9.00000 q^{9} +1.09364 q^{10} -1.46553 q^{11} +23.8565 q^{12} -79.4367 q^{13} -4.59329 q^{14} -15.0000 q^{15} +62.8541 q^{16} -65.4406 q^{17} +1.96855 q^{18} +116.908 q^{19} -39.7608 q^{20} +63.0000 q^{21} -0.320553 q^{22} -177.448 q^{23} +10.4676 q^{24} +25.0000 q^{25} -17.3750 q^{26} -27.0000 q^{27} +166.995 q^{28} +29.0000 q^{29} -3.28092 q^{30} +77.7850 q^{31} +41.6614 q^{32} +4.39659 q^{33} -14.3137 q^{34} -105.000 q^{35} -71.5694 q^{36} +175.767 q^{37} +25.5710 q^{38} +238.310 q^{39} -17.4459 q^{40} +62.4580 q^{41} +13.7799 q^{42} +66.0473 q^{43} +11.6541 q^{44} +45.0000 q^{45} -38.8128 q^{46} +179.320 q^{47} -188.562 q^{48} +98.0000 q^{49} +5.46820 q^{50} +196.322 q^{51} +631.693 q^{52} +676.773 q^{53} -5.90566 q^{54} -7.32765 q^{55} +73.2729 q^{56} -350.723 q^{57} +6.34312 q^{58} +415.156 q^{59} +119.282 q^{60} -426.377 q^{61} +17.0138 q^{62} -189.000 q^{63} -493.720 q^{64} -397.183 q^{65} +0.961658 q^{66} +79.1909 q^{67} +520.394 q^{68} +532.343 q^{69} -22.9665 q^{70} +218.606 q^{71} -31.4027 q^{72} +1024.13 q^{73} +38.4453 q^{74} -75.0000 q^{75} -929.669 q^{76} +30.7761 q^{77} +52.1251 q^{78} +1053.21 q^{79} +314.270 q^{80} +81.0000 q^{81} +13.6613 q^{82} -1179.75 q^{83} -500.986 q^{84} -327.203 q^{85} +14.4464 q^{86} -87.0000 q^{87} +5.11351 q^{88} +1411.60 q^{89} +9.84277 q^{90} +1668.17 q^{91} +1411.09 q^{92} -233.355 q^{93} +39.2223 q^{94} +584.539 q^{95} -124.984 q^{96} +884.714 q^{97} +21.4353 q^{98} -13.1898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} + 35 q^{5} + 6 q^{6} - 50 q^{7} - 33 q^{8} + 63 q^{9} - 10 q^{10} + 76 q^{11} - 66 q^{12} + 30 q^{13} + 89 q^{14} - 105 q^{15} + 138 q^{16} - 140 q^{17} - 18 q^{18} + 90 q^{19}+ \cdots + 684 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 + 35 * q^5 + 6 * q^6 - 50 * q^7 - 33 * q^8 + 63 * q^9 - 10 * q^10 + 76 * q^11 - 66 * q^12 + 30 * q^13 + 89 * q^14 - 105 * q^15 + 138 * q^16 - 140 * q^17 - 18 * q^18 + 90 * q^19 + 110 * q^20 + 150 * q^21 + 61 * q^22 + 34 * q^23 + 99 * q^24 + 175 * q^25 - 241 * q^26 - 189 * q^27 - 57 * q^28 + 203 * q^29 + 30 * q^30 + 524 * q^31 - 6 * q^32 - 228 * q^33 + 255 * q^34 - 250 * q^35 + 198 * q^36 - 28 * q^37 + 222 * q^38 - 90 * q^39 - 165 * q^40 + 1532 * q^41 - 267 * q^42 - 464 * q^43 + 1475 * q^44 + 315 * q^45 + 72 * q^46 - 360 * q^47 - 414 * q^48 + 569 * q^49 - 50 * q^50 + 420 * q^51 - 205 * q^52 + 282 * q^53 + 54 * q^54 + 380 * q^55 + 1102 * q^56 - 270 * q^57 - 58 * q^58 + 766 * q^59 - 330 * q^60 + 1200 * q^61 + 2856 * q^62 - 450 * q^63 + 701 * q^64 + 150 * q^65 - 183 * q^66 + 1546 * q^67 + 1801 * q^68 - 102 * q^69 + 445 * q^70 + 1802 * q^71 - 297 * q^72 - 220 * q^73 + 1594 * q^74 - 525 * q^75 + 1960 * q^76 + 3222 * q^77 + 723 * q^78 + 1298 * q^79 + 690 * q^80 + 567 * q^81 + 856 * q^82 + 1652 * q^83 + 171 * q^84 - 700 * q^85 + 7628 * q^86 - 609 * q^87 + 550 * q^88 + 2846 * q^89 - 90 * q^90 - 816 * q^91 + 472 * q^92 - 1572 * q^93 + 745 * q^94 + 450 * q^95 + 18 * q^96 + 1110 * q^97 - 761 * q^98 + 684 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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