LMFDB - Embedded newform 154.4.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [154,4,Mod(1,154)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(154, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("154.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 154 = 2 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	154.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:	$9.08629414088$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{37}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 9 $ x^2 - x - 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.54138$ of defining polynomial
Character	$\chi$	$=$	154.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} +9.08276 q^{3} +4.00000 q^{4} +6.91724 q^{5} -18.1655 q^{6} +7.00000 q^{7} -8.00000 q^{8} +55.4966 q^{9} -13.8345 q^{10} +11.0000 q^{11} +36.3311 q^{12} +7.08276 q^{13} -14.0000 q^{14} +62.8276 q^{15} +16.0000 q^{16} -68.3311 q^{17} -110.993 q^{18} -94.5725 q^{19} +27.6689 q^{20} +63.5793 q^{21} -22.0000 q^{22} +104.331 q^{23} -72.6621 q^{24} -77.1518 q^{25} -14.1655 q^{26} +258.828 q^{27} +28.0000 q^{28} +48.4966 q^{29} -125.655 q^{30} +38.8413 q^{31} -32.0000 q^{32} +99.9104 q^{33} +136.662 q^{34} +48.4207 q^{35} +221.986 q^{36} +144.317 q^{37} +189.145 q^{38} +64.3311 q^{39} -55.3379 q^{40} +409.986 q^{41} -127.159 q^{42} -16.8413 q^{43} +44.0000 q^{44} +383.883 q^{45} -208.662 q^{46} -535.449 q^{47} +145.324 q^{48} +49.0000 q^{49} +154.304 q^{50} -620.635 q^{51} +28.3311 q^{52} -155.807 q^{53} -517.655 q^{54} +76.0896 q^{55} -56.0000 q^{56} -858.979 q^{57} -96.9932 q^{58} +449.235 q^{59} +251.311 q^{60} -529.096 q^{61} -77.6826 q^{62} +388.476 q^{63} +64.0000 q^{64} +48.9932 q^{65} -199.821 q^{66} -296.814 q^{67} -273.324 q^{68} +947.614 q^{69} -96.8413 q^{70} -942.414 q^{71} -443.973 q^{72} -87.1587 q^{73} -288.635 q^{74} -700.752 q^{75} -378.290 q^{76} +77.0000 q^{77} -128.662 q^{78} -1328.97 q^{79} +110.676 q^{80} +852.462 q^{81} -819.973 q^{82} +611.001 q^{83} +254.317 q^{84} -472.662 q^{85} +33.6826 q^{86} +440.483 q^{87} -88.0000 q^{88} +1195.21 q^{89} -767.766 q^{90} +49.5793 q^{91} +417.324 q^{92} +352.787 q^{93} +1070.90 q^{94} -654.180 q^{95} -290.648 q^{96} -1854.79 q^{97} -98.0000 q^{98} +610.462 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} + 6 q^{3} + 8 q^{4} + 26 q^{5} - 12 q^{6} + 14 q^{7} - 16 q^{8} + 38 q^{9} - 52 q^{10} + 22 q^{11} + 24 q^{12} + 2 q^{13} - 28 q^{14} + 4 q^{15} + 32 q^{16} - 88 q^{17} - 76 q^{18} + 42 q^{19}+ \cdots + 418 q^{99}+O(q^{100}) $ 2 * q - 4 * q^2 + 6 * q^3 + 8 * q^4 + 26 * q^5 - 12 * q^6 + 14 * q^7 - 16 * q^8 + 38 * q^9 - 52 * q^10 + 22 * q^11 + 24 * q^12 + 2 * q^13 - 28 * q^14 + 4 * q^15 + 32 * q^16 - 88 * q^17 - 76 * q^18 + 42 * q^19 + 104 * q^20 + 42 * q^21 - 44 * q^22 + 160 * q^23 - 48 * q^24 + 162 * q^25 - 4 * q^26 + 396 * q^27 + 56 * q^28 + 24 * q^29 - 8 * q^30 + 248 * q^31 - 64 * q^32 + 66 * q^33 + 176 * q^34 + 182 * q^35 + 152 * q^36 - 52 * q^37 - 84 * q^38 + 80 * q^39 - 208 * q^40 + 528 * q^41 - 84 * q^42 - 204 * q^43 + 88 * q^44 + 50 * q^45 - 320 * q^46 + 24 * q^47 + 96 * q^48 + 98 * q^49 - 324 * q^50 - 560 * q^51 + 8 * q^52 + 248 * q^53 - 792 * q^54 + 286 * q^55 - 112 * q^56 - 1280 * q^57 - 48 * q^58 + 570 * q^59 + 16 * q^60 - 1338 * q^61 - 496 * q^62 + 266 * q^63 + 128 * q^64 - 48 * q^65 - 132 * q^66 - 180 * q^67 - 352 * q^68 + 776 * q^69 - 364 * q^70 - 60 * q^71 - 304 * q^72 - 4 * q^73 + 104 * q^74 - 1438 * q^75 + 168 * q^76 + 154 * q^77 - 160 * q^78 - 1928 * q^79 + 416 * q^80 + 902 * q^81 - 1056 * q^82 - 542 * q^83 + 168 * q^84 - 848 * q^85 + 408 * q^86 + 516 * q^87 - 176 * q^88 - 140 * q^89 - 100 * q^90 + 14 * q^91 + 640 * q^92 - 292 * q^93 - 48 * q^94 + 1952 * q^95 - 192 * q^96 - 2712 * q^97 - 196 * q^98 + 418 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	9.08276	1.74798	0.873989	−	0.485945i	$-0.161525\pi$
$3$	9.08276	1.74798	0.873989	+	0.485945i	$0.161525\pi$
$4$	4.00000	0.500000
$5$	6.91724	0.618697	0.309348	−	0.950949i	$-0.399889\pi$
$5$	6.91724	0.618697	0.309348	+	0.950949i	$0.399889\pi$
$6$	−18.1655	−1.23601
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	55.4966	2.05543
$10$	−13.8345	−0.437485
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	36.3311	0.873989
$13$	7.08276	0.151108	0.0755540	−	0.997142i	$-0.475927\pi$
$13$	7.08276	0.151108	0.0755540	+	0.997142i	$0.475927\pi$
$14$	−14.0000	−0.267261
$15$	62.8276	1.08147
$16$	16.0000	0.250000
$17$	−68.3311	−0.974866	−0.487433	−	0.873161i	$-0.662067\pi$
$17$	−68.3311	−0.974866	−0.487433	+	0.873161i	$0.662067\pi$
$18$	−110.993	−1.45341
$19$	−94.5725	−1.14192	−0.570958	−	0.820979i	$-0.693428\pi$
$19$	−94.5725	−1.14192	−0.570958	+	0.820979i	$0.693428\pi$
$20$	27.6689	0.309348
$21$	63.5793	0.660674
$22$	−22.0000	−0.213201
$23$	104.331	0.945849	0.472925	−	0.881103i	$-0.343198\pi$
$23$	104.331	0.945849	0.472925	+	0.881103i	$0.343198\pi$
$24$	−72.6621	−0.618004
$25$	−77.1518	−0.617215
$26$	−14.1655	−0.106850
$27$	258.828	1.84487
$28$	28.0000	0.188982
$29$	48.4966	0.310538	0.155269	−	0.987872i	$-0.450376\pi$
$29$	48.4966	0.310538	0.155269	+	0.987872i	$0.450376\pi$
$30$	−125.655	−0.764714
$31$	38.8413	0.225036	0.112518	−	0.993650i	$-0.464108\pi$
$31$	38.8413	0.225036	0.112518	+	0.993650i	$0.464108\pi$
$32$	−32.0000	−0.176777
$33$	99.9104	0.527035
$34$	136.662	0.689334
$35$	48.4207	0.233845
$36$	221.986	1.02771
$37$	144.317	0.641233	0.320617	−	0.947209i	$-0.396110\pi$
$37$	144.317	0.641233	0.320617	+	0.947209i	$0.396110\pi$
$38$	189.145	0.807457
$39$	64.3311	0.264134
$40$	−55.3379	−0.218742
$41$	409.986	1.56169	0.780843	−	0.624728i	$-0.214790\pi$
$41$	409.986	1.56169	0.780843	+	0.624728i	$0.214790\pi$
$42$	−127.159	−0.467167
$43$	−16.8413	−0.0597274	−0.0298637	−	0.999554i	$-0.509507\pi$
$43$	−16.8413	−0.0597274	−0.0298637	+	0.999554i	$0.509507\pi$
$44$	44.0000	0.150756
$45$	383.883	1.27169
$46$	−208.662	−0.668816
$47$	−535.449	−1.66177	−0.830885	−	0.556444i	$-0.812165\pi$
$47$	−535.449	−1.66177	−0.830885	+	0.556444i	$0.812165\pi$
$48$	145.324	0.436995
$49$	49.0000	0.142857
$50$	154.304	0.436437
$51$	−620.635	−1.70404
$52$	28.3311	0.0755540
$53$	−155.807	−0.403807	−0.201903	−	0.979405i	$-0.564713\pi$
$53$	−155.807	−0.403807	−0.201903	+	0.979405i	$0.564713\pi$
$54$	−517.655	−1.30452
$55$	76.0896	0.186544
$56$	−56.0000	−0.133631
$57$	−858.979	−1.99605
$58$	−96.9932	−0.219583
$59$	449.235	0.991277	0.495639	−	0.868529i	$-0.334934\pi$
$59$	449.235	0.991277	0.495639	+	0.868529i	$0.334934\pi$
$60$	251.311	0.540734
$61$	−529.096	−1.11056	−0.555278	−	0.831665i	$-0.687388\pi$
$61$	−529.096	−1.11056	−0.555278	+	0.831665i	$0.687388\pi$
$62$	−77.6826	−0.159124
$63$	388.476	0.776879
$64$	64.0000	0.125000
$65$	48.9932	0.0934900
$66$	−199.821	−0.372670
$67$	−296.814	−0.541218	−0.270609	−	0.962689i	$-0.587225\pi$
$67$	−296.814	−0.541218	−0.270609	+	0.962689i	$0.587225\pi$
$68$	−273.324	−0.487433
$69$	947.614	1.65332
$70$	−96.8413	−0.165354
$71$	−942.414	−1.57527	−0.787634	−	0.616144i	$-0.788694\pi$
$71$	−942.414	−1.57527	−0.787634	+	0.616144i	$0.788694\pi$
$72$	−443.973	−0.726704
$73$	−87.1587	−0.139742	−0.0698709	−	0.997556i	$-0.522259\pi$
$73$	−87.1587	−0.139742	−0.0698709	+	0.997556i	$0.522259\pi$
$74$	−288.635	−0.453420
$75$	−700.752	−1.07888
$76$	−378.290	−0.570958
$77$	77.0000	0.113961
$78$	−128.662	−0.186771
$79$	−1328.97	−1.89266	−0.946331	−	0.323198i	$-0.895242\pi$
$79$	−1328.97	−1.89266	−0.946331	+	0.323198i	$0.895242\pi$
$80$	110.676	0.154674
$81$	852.462	1.16936
$82$	−819.973	−1.10428
$83$	611.001	0.808024	0.404012	−	0.914754i	$-0.367615\pi$
$83$	611.001	0.808024	0.404012	+	0.914754i	$0.367615\pi$
$84$	254.317	0.330337
$85$	−472.662	−0.603146
$86$	33.6826	0.0422336
$87$	440.483	0.542813
$88$	−88.0000	−0.106600
$89$	1195.21	1.42351	0.711756	−	0.702427i	$-0.247900\pi$
$89$	1195.21	1.42351	0.711756	+	0.702427i	$0.247900\pi$
$90$	−767.766	−0.899218
$91$	49.5793	0.0571135
$92$	417.324	0.472925
$93$	352.787	0.393358
$94$	1070.90	1.17505
$95$	−654.180	−0.706500
$96$	−290.648	−0.309002
$97$	−1854.79	−1.94150	−0.970748	−	0.240102i	$-0.922819\pi$
$97$	−1854.79	−1.94150	−0.970748	+	0.240102i	$0.922819\pi$
$98$	−98.0000	−0.101015
$99$	610.462	0.619735
$100$	−308.607	−0.308607
$101$	−1434.95	−1.41369	−0.706844	−	0.707370i	$-0.749882\pi$
$101$	−1434.95	−1.41369	−0.706844	+	0.707370i	$0.749882\pi$
$102$	1241.27	1.20494
$103$	568.745	0.544079	0.272040	−	0.962286i	$-0.412302\pi$
$103$	568.745	0.544079	0.272040	+	0.962286i	$0.412302\pi$
$104$	−56.6621	−0.0534248
$105$	439.793	0.408757
$106$	311.614	0.285534
$107$	1783.71	1.61157	0.805784	−	0.592209i	$-0.201744\pi$
$107$	1783.71	1.61157	0.805784	+	0.592209i	$0.201744\pi$
$108$	1035.31	0.922433
$109$	−529.587	−0.465369	−0.232684	−	0.972552i	$-0.574751\pi$
$109$	−529.587	−0.465369	−0.232684	+	0.972552i	$0.574751\pi$
$110$	−152.179	−0.131907
$111$	1310.80	1.12086
$112$	112.000	0.0944911
$113$	1995.09	1.66091	0.830453	−	0.557089i	$-0.188082\pi$
$113$	1995.09	1.66091	0.830453	+	0.557089i	$0.188082\pi$
$114$	1717.96	1.41142
$115$	721.683	0.585194
$116$	193.986	0.155269
$117$	393.069	0.310592
$118$	−898.469	−0.700939
$119$	−478.317	−0.368465
$120$	−502.621	−0.382357
$121$	121.000	0.0909091
$122$	1058.19	0.785281
$123$	3723.81	2.72979
$124$	155.365	0.112518
$125$	−1398.33	−1.00057
$126$	−776.952	−0.549336
$127$	−1150.65	−0.803965	−0.401982	−	0.915647i	$-0.631679\pi$
$127$	−1150.65	−0.803965	−0.401982	+	0.915647i	$0.631679\pi$
$128$	−128.000	−0.0883883
$129$	−152.966	−0.104402
$130$	−97.9863	−0.0661074
$131$	−2230.85	−1.48786	−0.743932	−	0.668255i	$-0.767041\pi$
$131$	−2230.85	−1.48786	−0.743932	+	0.668255i	$0.767041\pi$
$132$	399.642	0.263518
$133$	−662.007	−0.431604
$134$	593.628	0.382699
$135$	1790.37	1.14141
$136$	546.648	0.344667
$137$	656.594	0.409464	0.204732	−	0.978818i	$-0.434368\pi$
$137$	656.594	0.409464	0.204732	+	0.978818i	$0.434368\pi$
$138$	−1895.23	−1.16908
$139$	1012.17	0.617636	0.308818	−	0.951121i	$-0.400067\pi$
$139$	1012.17	0.617636	0.308818	+	0.951121i	$0.400067\pi$
$140$	193.683	0.116923
$141$	−4863.35	−2.90474
$142$	1884.83	1.11388
$143$	77.9104	0.0455608
$144$	887.945	0.513857
$145$	335.462	0.192128
$146$	174.317	0.0988124
$147$	445.055	0.249711
$148$	577.269	0.320617
$149$	−786.677	−0.432531	−0.216265	−	0.976335i	$-0.569388\pi$
$149$	−786.677	−0.432531	−0.216265	+	0.976335i	$0.569388\pi$
$150$	1401.50	0.762882
$151$	205.573	0.110790	0.0553950	−	0.998465i	$-0.482358\pi$
$151$	205.573	0.110790	0.0553950	+	0.998465i	$0.482358\pi$
$152$	756.580	0.403729
$153$	−3792.14	−2.00377
$154$	−154.000	−0.0805823
$155$	268.675	0.139229
$156$	257.324	0.132067
$157$	−3284.08	−1.66941	−0.834707	−	0.550695i	$-0.814363\pi$
$157$	−3284.08	−1.66941	−0.834707	+	0.550695i	$0.814363\pi$
$158$	2657.93	1.33831
$159$	−1415.16	−0.705845
$160$	−221.352	−0.109371
$161$	730.317	0.357497
$162$	−1704.92	−0.826861
$163$	−1403.88	−0.674601	−0.337301	−	0.941397i	$-0.609514\pi$
$163$	−1403.88	−0.674601	−0.337301	+	0.941397i	$0.609514\pi$
$164$	1639.95	0.780843
$165$	691.104	0.326075
$166$	−1222.00	−0.571360
$167$	4161.31	1.92822	0.964108	−	0.265512i	$-0.0855409\pi$
$167$	4161.31	1.92822	0.964108	+	0.265512i	$0.0855409\pi$
$168$	−508.635	−0.233583
$169$	−2146.83	−0.977166
$170$	945.324	0.426489
$171$	−5248.45	−2.34713
$172$	−67.3653	−0.0298637
$173$	−2693.66	−1.18379	−0.591894	−	0.806016i	$-0.701620\pi$
$173$	−2693.66	−1.18379	−0.591894	+	0.806016i	$0.701620\pi$
$174$	−880.966	−0.383827
$175$	−540.063	−0.233285
$176$	176.000	0.0753778
$177$	4080.29	1.73273
$178$	−2390.43	−1.00657
$179$	1877.74	0.784071	0.392035	−	0.919950i	$-0.371771\pi$
$179$	1877.74	0.784071	0.392035	+	0.919950i	$0.371771\pi$
$180$	1535.53	0.635843
$181$	639.291	0.262531	0.131265	−	0.991347i	$-0.458096\pi$
$181$	639.291	0.262531	0.131265	+	0.991347i	$0.458096\pi$
$182$	−99.1587	−0.0403853
$183$	−4805.66	−1.94123
$184$	−834.648	−0.334408
$185$	998.277	0.396729
$186$	−705.573	−0.278146
$187$	−751.642	−0.293933
$188$	−2141.79	−0.830885
$189$	1811.79	0.697294
$190$	1308.36	0.499571
$191$	3705.56	1.40379	0.701897	−	0.712278i	$-0.252337\pi$
$191$	3705.56	1.40379	0.701897	+	0.712278i	$0.252337\pi$
$192$	581.297	0.218497
$193$	2147.38	0.800891	0.400445	−	0.916321i	$-0.368855\pi$
$193$	2147.38	0.800891	0.400445	+	0.916321i	$0.368855\pi$
$194$	3709.57	1.37284
$195$	444.993	0.163419
$196$	196.000	0.0714286
$197$	2356.98	0.852426	0.426213	−	0.904623i	$-0.359847\pi$
$197$	2356.98	0.852426	0.426213	+	0.904623i	$0.359847\pi$
$198$	−1220.92	−0.438219
$199$	5191.26	1.84924	0.924619	−	0.380893i	$-0.124383\pi$
$199$	5191.26	1.84924	0.924619	+	0.380893i	$0.124383\pi$
$200$	617.215	0.218218
$201$	−2695.89	−0.946037
$202$	2869.89	0.999628
$203$	339.476	0.117372
$204$	−2482.54	−0.852022
$205$	2835.97	0.966209
$206$	−1137.49	−0.384722
$207$	5790.02	1.94413
$208$	113.324	0.0377770
$209$	−1040.30	−0.344301
$210$	−879.587	−0.289035
$211$	4020.35	1.31172	0.655858	−	0.754884i	$-0.272307\pi$
$211$	4020.35	1.31172	0.655858	+	0.754884i	$0.272307\pi$
$212$	−623.228	−0.201903
$213$	−8559.73	−2.75353
$214$	−3567.42	−1.13955
$215$	−116.495	−0.0369531
$216$	−2070.62	−0.652259
$217$	271.889	0.0850555
$218$	1059.17	0.329066
$219$	−791.642	−0.244266
$220$	304.358	0.0932720
$221$	−483.973	−0.147310
$222$	−2621.60	−0.792569
$223$	−444.758	−0.133557	−0.0667785	−	0.997768i	$-0.521272\pi$
$223$	−444.758	−0.133557	−0.0667785	+	0.997768i	$0.521272\pi$
$224$	−224.000	−0.0668153
$225$	−4281.66	−1.26864
$226$	−3990.18	−1.17444
$227$	4757.40	1.39101	0.695506	−	0.718520i	$-0.255180\pi$
$227$	4757.40	1.39101	0.695506	+	0.718520i	$0.255180\pi$
$228$	−3435.92	−0.998023
$229$	1032.94	0.298073	0.149037	−	0.988832i	$-0.452383\pi$
$229$	1032.94	0.298073	0.149037	+	0.988832i	$0.452383\pi$
$230$	−1443.37	−0.413794
$231$	699.373	0.199201
$232$	−387.973	−0.109792
$233$	−2952.57	−0.830168	−0.415084	−	0.909783i	$-0.636248\pi$
$233$	−2952.57	−0.830168	−0.415084	+	0.909783i	$0.636248\pi$
$234$	−786.138	−0.219622
$235$	−3703.83	−1.02813
$236$	1796.94	0.495639
$237$	−12070.7	−3.30833
$238$	956.635	0.260544
$239$	5382.65	1.45680	0.728399	−	0.685154i	$-0.240265\pi$
$239$	5382.65	1.45680	0.728399	+	0.685154i	$0.240265\pi$
$240$	1005.24	0.270367
$241$	2758.35	0.737265	0.368632	−	0.929575i	$-0.379826\pi$
$241$	2758.35	0.737265	0.368632	+	0.929575i	$0.379826\pi$
$242$	−242.000	−0.0642824
$243$	754.367	0.199147
$244$	−2116.39	−0.555278
$245$	338.945	0.0883852
$246$	−7447.62	−1.93025
$247$	−669.834	−0.172553
$248$	−310.731	−0.0795621
$249$	5549.57	1.41241
$250$	2796.66	0.707506
$251$	−3814.42	−0.959220	−0.479610	−	0.877482i	$-0.659222\pi$
$251$	−3814.42	−0.959220	−0.479610	+	0.877482i	$0.659222\pi$
$252$	1553.90	0.388440
$253$	1147.64	0.285184
$254$	2301.30	0.568489
$255$	−4293.08	−1.05429
$256$	256.000	0.0625000
$257$	−6959.85	−1.68927	−0.844637	−	0.535339i	$-0.820184\pi$
$257$	−6959.85	−1.68927	−0.844637	+	0.535339i	$0.820184\pi$
$258$	305.932	0.0738235
$259$	1010.22	0.242363
$260$	195.973	0.0467450
$261$	2691.39	0.638288
$262$	4461.70	1.05208
$263$	956.774	0.224324	0.112162	−	0.993690i	$-0.464222\pi$
$263$	956.774	0.224324	0.112162	+	0.993690i	$0.464222\pi$
$264$	−799.283	−0.186335
$265$	−1077.75	−0.249834
$266$	1324.01	0.305190
$267$	10855.9	2.48827
$268$	−1187.26	−0.270609
$269$	−974.888	−0.220966	−0.110483	−	0.993878i	$-0.535240\pi$
$269$	−974.888	−0.220966	−0.110483	+	0.993878i	$0.535240\pi$
$270$	−3580.74	−0.807101
$271$	3520.03	0.789027	0.394514	−	0.918890i	$-0.370913\pi$
$271$	3520.03	0.789027	0.394514	+	0.918890i	$0.370913\pi$
$272$	−1093.30	−0.243716
$273$	450.317	0.0998331
$274$	−1313.19	−0.289535
$275$	−848.670	−0.186097
$276$	3790.46	0.826662
$277$	2310.59	0.501192	0.250596	−	0.968092i	$-0.419374\pi$
$277$	2310.59	0.501192	0.250596	+	0.968092i	$0.419374\pi$
$278$	−2024.35	−0.436735
$279$	2155.56	0.462545
$280$	−387.365	−0.0826768
$281$	5616.65	1.19239	0.596194	−	0.802840i	$-0.296679\pi$
$281$	5616.65	1.19239	0.596194	+	0.802840i	$0.296679\pi$
$282$	9726.71	2.05396
$283$	−1065.17	−0.223737	−0.111869	−	0.993723i	$-0.535684\pi$
$283$	−1065.17	−0.223737	−0.111869	+	0.993723i	$0.535684\pi$
$284$	−3769.66	−0.787634
$285$	−5941.76	−1.23495
$286$	−155.821	−0.0322163
$287$	2869.90	0.590262
$288$	−1775.89	−0.363352
$289$	−243.868	−0.0496372
$290$	−670.925	−0.135855
$291$	−16846.6	−3.39369
$292$	−348.635	−0.0698709
$293$	3453.14	0.688514	0.344257	−	0.938875i	$-0.388131\pi$
$293$	3453.14	0.688514	0.344257	+	0.938875i	$0.388131\pi$
$294$	−890.111	−0.176572
$295$	3107.46	0.613300
$296$	−1154.54	−0.226710
$297$	2847.10	0.556248
$298$	1573.35	0.305845
$299$	738.952	0.142925
$300$	−2803.01	−0.539439
$301$	−117.889	−0.0225748
$302$	−411.146	−0.0783404
$303$	−13033.3	−2.47110
$304$	−1513.16	−0.285479
$305$	−3659.89	−0.687097
$306$	7584.28	1.41688
$307$	4864.91	0.904413	0.452207	−	0.891913i	$-0.350637\pi$
$307$	4864.91	0.904413	0.452207	+	0.891913i	$0.350637\pi$
$308$	308.000	0.0569803
$309$	5165.78	0.951039
$310$	−537.349	−0.0984496
$311$	378.550	0.0690213	0.0345106	−	0.999404i	$-0.489013\pi$
$311$	378.550	0.0690213	0.0345106	+	0.999404i	$0.489013\pi$
$312$	−514.648	−0.0933853
$313$	1912.52	0.345375	0.172687	−	0.984977i	$-0.444755\pi$
$313$	1912.52	0.345375	0.172687	+	0.984977i	$0.444755\pi$
$314$	6568.15	1.18045
$315$	2687.18	0.480652
$316$	−5315.86	−0.946331
$317$	−6640.27	−1.17651	−0.588256	−	0.808674i	$-0.700185\pi$
$317$	−6640.27	−1.17651	−0.588256	+	0.808674i	$0.700185\pi$
$318$	2830.32	0.499108
$319$	533.462	0.0936306
$320$	442.703	0.0773371
$321$	16201.0	2.81699
$322$	−1460.63	−0.252789
$323$	6462.24	1.11322
$324$	3409.85	0.584679
$325$	−546.448	−0.0932661
$326$	2807.75	0.477015
$327$	−4810.11	−0.813455
$328$	−3279.89	−0.552139
$329$	−3748.14	−0.628090
$330$	−1382.21	−0.230570
$331$	−5342.84	−0.887218	−0.443609	−	0.896220i	$-0.646302\pi$
$331$	−5342.84	−0.887218	−0.443609	+	0.896220i	$0.646302\pi$
$332$	2444.00	0.404012
$333$	8009.12	1.31801
$334$	−8322.62	−1.36345
$335$	−2053.13	−0.334850
$336$	1017.27	0.165168
$337$	4264.37	0.689303	0.344652	−	0.938731i	$-0.387997\pi$
$337$	4264.37	0.689303	0.344652	+	0.938731i	$0.387997\pi$
$338$	4293.67	0.690961
$339$	18120.9	2.90323
$340$	−1890.65	−0.301573
$341$	427.255	0.0678508
$342$	10496.9	1.65967
$343$	343.000	0.0539949
$344$	134.731	0.0211168
$345$	6554.87	1.02291
$346$	5387.32	0.837064
$347$	−3767.11	−0.582792	−0.291396	−	0.956602i	$-0.594120\pi$
$347$	−3767.11	−0.582792	−0.291396	+	0.956602i	$0.594120\pi$
$348$	1761.93	0.271406
$349$	5616.88	0.861503	0.430752	−	0.902471i	$-0.358249\pi$
$349$	5616.88	0.861503	0.430752	+	0.902471i	$0.358249\pi$
$350$	1080.13	0.164958
$351$	1833.21	0.278774
$352$	−352.000	−0.0533002
$353$	−1338.83	−0.201866	−0.100933	−	0.994893i	$-0.532183\pi$
$353$	−1338.83	−0.201866	−0.100933	+	0.994893i	$0.532183\pi$
$354$	−8160.58	−1.22523
$355$	−6518.90	−0.974613
$356$	4780.86	0.711756
$357$	−4344.44	−0.644068
$358$	−3755.47	−0.554422
$359$	−3323.84	−0.488650	−0.244325	−	0.969693i	$-0.578566\pi$
$359$	−3323.84	−0.488650	−0.244325	+	0.969693i	$0.578566\pi$
$360$	−3071.06	−0.449609
$361$	2084.96	0.303974
$362$	−1278.58	−0.185637
$363$	1099.01	0.158907
$364$	198.317	0.0285567
$365$	−602.897	−0.0864578
$366$	9611.32	1.37265
$367$	612.596	0.0871315	0.0435657	−	0.999051i	$-0.486128\pi$
$367$	612.596	0.0871315	0.0435657	+	0.999051i	$0.486128\pi$
$368$	1669.30	0.236462
$369$	22752.8	3.20993
$370$	−1996.55	−0.280530
$371$	−1090.65	−0.152625
$372$	1411.15	0.196679
$373$	−11858.9	−1.64619	−0.823094	−	0.567905i	$-0.807754\pi$
$373$	−11858.9	−1.64619	−0.823094	+	0.567905i	$0.807754\pi$
$374$	1503.28	0.207842
$375$	−12700.7	−1.74897
$376$	4283.59	0.587525
$377$	343.490	0.0469247
$378$	−3623.59	−0.493061
$379$	6906.97	0.936114	0.468057	−	0.883698i	$-0.344954\pi$
$379$	6906.97	0.936114	0.468057	+	0.883698i	$0.344954\pi$
$380$	−2616.72	−0.353250
$381$	−10451.1	−1.40531
$382$	−7411.12	−0.992633
$383$	−5189.68	−0.692377	−0.346189	−	0.938165i	$-0.612524\pi$
$383$	−5189.68	−0.692377	−0.346189	+	0.938165i	$0.612524\pi$
$384$	−1162.59	−0.154501
$385$	532.627	0.0705070
$386$	−4294.76	−0.566315
$387$	−934.636	−0.122765
$388$	−7419.15	−0.970748
$389$	4600.72	0.599654	0.299827	−	0.953994i	$-0.403071\pi$
$389$	4600.72	0.599654	0.299827	+	0.953994i	$0.403071\pi$
$390$	−889.986	−0.115554
$391$	−7129.05	−0.922076
$392$	−392.000	−0.0505076
$393$	−20262.3	−2.60075
$394$	−4713.96	−0.602756
$395$	−9192.77	−1.17098
$396$	2441.85	0.309868
$397$	−5313.96	−0.671788	−0.335894	−	0.941900i	$-0.609038\pi$
$397$	−5313.96	−0.671788	−0.335894	+	0.941900i	$0.609038\pi$
$398$	−10382.5	−1.30761
$399$	−6012.86	−0.754434
$400$	−1234.43	−0.154304
$401$	15051.5	1.87440	0.937199	−	0.348794i	$-0.113409\pi$
$401$	15051.5	1.87440	0.937199	+	0.348794i	$0.113409\pi$
$402$	5391.78	0.668949
$403$	275.104	0.0340047
$404$	−5739.78	−0.706844
$405$	5896.68	0.723478
$406$	−678.952	−0.0829946
$407$	1587.49	0.193339
$408$	4965.08	0.602471
$409$	9547.20	1.15423	0.577113	−	0.816664i	$-0.304179\pi$
$409$	9547.20	1.15423	0.577113	+	0.816664i	$0.304179\pi$
$410$	−5671.95	−0.683213
$411$	5963.68	0.715734
$412$	2274.98	0.272040
$413$	3144.64	0.374668
$414$	−11580.0	−1.37470
$415$	4226.44	0.499922
$416$	−226.648	−0.0267124
$417$	9193.33	1.07961
$418$	2080.59	0.243457
$419$	−643.721	−0.0750545	−0.0375272	−	0.999296i	$-0.511948\pi$
$419$	−643.721	−0.0750545	−0.0375272	+	0.999296i	$0.511948\pi$
$420$	1759.17	0.204378
$421$	12480.4	1.44479	0.722396	−	0.691480i	$-0.243041\pi$
$421$	12480.4	1.44479	0.722396	+	0.691480i	$0.243041\pi$
$422$	−8040.69	−0.927523
$423$	−29715.6	−3.41565
$424$	1246.46	0.142767
$425$	5271.87	0.601701
$426$	17119.5	1.94704
$427$	−3703.68	−0.419750
$428$	7134.84	0.805784
$429$	707.642	0.0796393
$430$	232.991	0.0261298
$431$	−5652.33	−0.631701	−0.315850	−	0.948809i	$-0.602290\pi$
$431$	−5652.33	−0.631701	−0.315850	+	0.948809i	$0.602290\pi$
$432$	4141.24	0.461217
$433$	−2179.80	−0.241928	−0.120964	−	0.992657i	$-0.538599\pi$
$433$	−2179.80	−0.241928	−0.120964	+	0.992657i	$0.538599\pi$
$434$	−543.779	−0.0601433
$435$	3046.92	0.335836
$436$	−2118.35	−0.232684
$437$	−9866.85	−1.08008
$438$	1583.28	0.172722
$439$	−3515.01	−0.382146	−0.191073	−	0.981576i	$-0.561197\pi$
$439$	−3515.01	−0.382146	−0.191073	+	0.981576i	$0.561197\pi$
$440$	−608.717	−0.0659533
$441$	2719.33	0.293633
$442$	967.945	0.104164
$443$	6329.77	0.678863	0.339432	−	0.940631i	$-0.389765\pi$
$443$	6329.77	0.678863	0.339432	+	0.940631i	$0.389765\pi$
$444$	5243.20	0.560431
$445$	8267.58	0.880721
$446$	889.516	0.0944390
$447$	−7145.20	−0.756054
$448$	448.000	0.0472456
$449$	−10624.6	−1.11672	−0.558361	−	0.829598i	$-0.688570\pi$
$449$	−10624.6	−1.11672	−0.558361	+	0.829598i	$0.688570\pi$
$450$	8563.32	0.897064
$451$	4509.85	0.470866
$452$	7980.36	0.830453
$453$	1867.17	0.193659
$454$	−9514.80	−0.983595
$455$	342.952	0.0353359
$456$	6871.84	0.705709
$457$	−11373.9	−1.16422	−0.582110	−	0.813110i	$-0.697773\pi$
$457$	−11373.9	−1.16422	−0.582110	+	0.813110i	$0.697773\pi$
$458$	−2065.89	−0.210770
$459$	−17686.0	−1.79850
$460$	2886.73	0.292597
$461$	−8473.86	−0.856111	−0.428055	−	0.903753i	$-0.640801\pi$
$461$	−8473.86	−0.856111	−0.428055	+	0.903753i	$0.640801\pi$
$462$	−1398.75	−0.140856
$463$	9796.71	0.983352	0.491676	−	0.870778i	$-0.336385\pi$
$463$	9796.71	0.983352	0.491676	+	0.870778i	$0.336385\pi$
$464$	775.945	0.0776344
$465$	2440.31	0.243369
$466$	5905.13	0.587017
$467$	−3000.81	−0.297347	−0.148674	−	0.988886i	$-0.547500\pi$
$467$	−3000.81	−0.297347	−0.148674	+	0.988886i	$0.547500\pi$
$468$	1572.28	0.155296
$469$	−2077.70	−0.204561
$470$	7407.65	0.726999
$471$	−29828.5	−2.91810
$472$	−3593.88	−0.350469
$473$	−185.255	−0.0180085
$474$	24141.4	2.33934
$475$	7296.44	0.704808
$476$	−1913.27	−0.184232
$477$	−8646.76	−0.829996
$478$	−10765.3	−1.03011
$479$	14384.2	1.37209	0.686047	−	0.727557i	$-0.259345\pi$
$479$	14384.2	1.37209	0.686047	+	0.727557i	$0.259345\pi$
$480$	−2010.48	−0.191178
$481$	1022.17	0.0968955
$482$	−5516.69	−0.521325
$483$	6633.30	0.624898
$484$	484.000	0.0454545
$485$	−12830.0	−1.20120
$486$	−1508.73	−0.140818
$487$	−19562.5	−1.82025	−0.910126	−	0.414332i	$-0.864015\pi$
$487$	−19562.5	−1.82025	−0.910126	+	0.414332i	$0.864015\pi$
$488$	4232.77	0.392641
$489$	−12751.1	−1.17919
$490$	−677.889	−0.0624978
$491$	1724.88	0.158539	0.0792697	−	0.996853i	$-0.474741\pi$
$491$	1724.88	0.158539	0.0792697	+	0.996853i	$0.474741\pi$
$492$	14895.2	1.36490
$493$	−3313.82	−0.302732
$494$	1339.67	0.122013
$495$	4222.71	0.383428
$496$	621.461	0.0562589
$497$	−6596.90	−0.595395
$498$	−11099.1	−0.998724
$499$	20898.7	1.87486	0.937430	−	0.348173i	$-0.113198\pi$
$499$	20898.7	1.87486	0.937430	+	0.348173i	$0.113198\pi$
$500$	−5593.33	−0.500283
$501$	37796.2	3.37048
$502$	7628.84	0.678271
$503$	−6062.13	−0.537369	−0.268685	−	0.963228i	$-0.586589\pi$
$503$	−6062.13	−0.537369	−0.268685	+	0.963228i	$0.586589\pi$
$504$	−3107.81	−0.274668
$505$	−9925.86	−0.874644
$506$	−2295.28	−0.201656
$507$	−19499.2	−1.70807
$508$	−4602.59	−0.401982
$509$	310.270	0.0270186	0.0135093	−	0.999909i	$-0.495700\pi$
$509$	310.270	0.0270186	0.0135093	+	0.999909i	$0.495700\pi$
$510$	8586.16	0.745493
$511$	−610.111	−0.0528174
$512$	−512.000	−0.0441942
$513$	−24478.0	−2.10668
$514$	13919.7	1.19450
$515$	3934.15	0.336620
$516$	−611.863	−0.0522011
$517$	−5889.93	−0.501043
$518$	−2020.44	−0.171377
$519$	−24465.9	−2.06924
$520$	−391.945	−0.0330537
$521$	−6406.10	−0.538688	−0.269344	−	0.963044i	$-0.586807\pi$
$521$	−6406.10	−0.538688	−0.269344	+	0.963044i	$0.586807\pi$
$522$	−5382.79	−0.451338
$523$	21061.8	1.76094	0.880468	−	0.474106i	$-0.157229\pi$
$523$	21061.8	1.76094	0.880468	+	0.474106i	$0.157229\pi$
$524$	−8923.39	−0.743932
$525$	−4905.26	−0.407777
$526$	−1913.55	−0.158621
$527$	−2654.07	−0.219380
$528$	1598.57	0.131759
$529$	−1282.03	−0.105370
$530$	2155.51	0.176659
$531$	24931.0	2.03750
$532$	−2648.03	−0.215802
$533$	2903.84	0.235983
$534$	−21711.7	−1.75947
$535$	12338.4	0.997072
$536$	2374.51	0.191349
$537$	17055.0	1.37054
$538$	1949.78	0.156247
$539$	539.000	0.0430730
$540$	7161.49	0.570706
$541$	−6597.32	−0.524290	−0.262145	−	0.965029i	$-0.584430\pi$
$541$	−6597.32	−0.524290	−0.262145	+	0.965029i	$0.584430\pi$
$542$	−7040.05	−0.557927
$543$	5806.52	0.458898
$544$	2186.59	0.172334
$545$	−3663.28	−0.287922
$546$	−900.635	−0.0705927
$547$	13719.3	1.07238	0.536192	−	0.844096i	$-0.319862\pi$
$547$	13719.3	1.07238	0.536192	+	0.844096i	$0.319862\pi$
$548$	2626.37	0.204732
$549$	−29363.0	−2.28267
$550$	1697.34	0.131591
$551$	−4586.44	−0.354608
$552$	−7580.91	−0.584538
$553$	−9302.76	−0.715359
$554$	−4621.18	−0.354396
$555$	9067.12	0.693473
$556$	4048.69	0.308818
$557$	9528.54	0.724842	0.362421	−	0.932014i	$-0.381950\pi$
$557$	9528.54	0.724842	0.362421	+	0.932014i	$0.381950\pi$
$558$	−4311.12	−0.327069
$559$	−119.283	−0.00902529
$560$	774.731	0.0584613
$561$	−6826.98	−0.513789
$562$	−11233.3	−0.843146
$563$	−12164.1	−0.910576	−0.455288	−	0.890344i	$-0.650464\pi$
$563$	−12164.1	−0.910576	−0.455288	+	0.890344i	$0.650464\pi$
$564$	−19453.4	−1.45237
$565$	13800.5	1.02760
$566$	2130.34	0.158206
$567$	5967.24	0.441976
$568$	7539.32	0.556941
$569$	7553.23	0.556499	0.278249	−	0.960509i	$-0.410246\pi$
$569$	7553.23	0.556499	0.278249	+	0.960509i	$0.410246\pi$
$570$	11883.5	0.873239
$571$	18632.0	1.36555	0.682773	−	0.730631i	$-0.260774\pi$
$571$	18632.0	1.36555	0.682773	+	0.730631i	$0.260774\pi$
$572$	311.642	0.0227804
$573$	33656.7	2.45380
$574$	−5739.81	−0.417378
$575$	−8049.33	−0.583792
$576$	3551.78	0.256929
$577$	−8150.64	−0.588069	−0.294034	−	0.955795i	$-0.594998\pi$
$577$	−8150.64	−0.588069	−0.294034	+	0.955795i	$0.594998\pi$
$578$	487.735	0.0350988
$579$	19504.2	1.39994
$580$	1341.85	0.0960642
$581$	4277.00	0.305405
$582$	33693.2	2.39970
$583$	−1713.88	−0.121752
$584$	697.269	0.0494062
$585$	2718.95	0.192162
$586$	−6906.28	−0.486853
$587$	14337.5	1.00813	0.504065	−	0.863666i	$-0.331837\pi$
$587$	14337.5	1.00813	0.504065	+	0.863666i	$0.331837\pi$
$588$	1780.22	0.124856
$589$	−3673.32	−0.256972
$590$	−6214.92	−0.433668
$591$	21407.9	1.49002
$592$	2309.08	0.160308
$593$	−27017.3	−1.87094	−0.935471	−	0.353402i	$-0.885025\pi$
$593$	−27017.3	−1.87094	−0.935471	+	0.353402i	$0.885025\pi$
$594$	−5694.21	−0.393327
$595$	−3308.63	−0.227968
$596$	−3146.71	−0.216265
$597$	47151.0	3.23243
$598$	−1477.90	−0.101064
$599$	18429.3	1.25710	0.628549	−	0.777770i	$-0.283649\pi$
$599$	18429.3	1.25710	0.628549	+	0.777770i	$0.283649\pi$
$600$	5606.01	0.381441
$601$	−4515.02	−0.306442	−0.153221	−	0.988192i	$-0.548965\pi$
$601$	−4515.02	−0.306442	−0.153221	+	0.988192i	$0.548965\pi$
$602$	235.779	0.0159628
$603$	−16472.2	−1.11243
$604$	822.292	0.0553950
$605$	836.986	0.0562451
$606$	26066.5	1.74733
$607$	9714.87	0.649612	0.324806	−	0.945781i	$-0.394701\pi$
$607$	9714.87	0.649612	0.324806	+	0.945781i	$0.394701\pi$
$608$	3026.32	0.201864
$609$	3083.38	0.205164
$610$	7319.77	0.485851
$611$	−3792.46	−0.251107
$612$	−15168.6	−1.00188
$613$	10724.5	0.706618	0.353309	−	0.935507i	$-0.385056\pi$
$613$	10724.5	0.706618	0.353309	+	0.935507i	$0.385056\pi$
$614$	−9729.81	−0.639517
$615$	25758.5	1.68891
$616$	−616.000	−0.0402911
$617$	28206.5	1.84044	0.920219	−	0.391404i	$-0.128010\pi$
$617$	28206.5	1.84044	0.920219	+	0.391404i	$0.128010\pi$
$618$	−10331.6	−0.672486
$619$	156.324	0.0101505	0.00507526	−	0.999987i	$-0.498384\pi$
$619$	156.324	0.0101505	0.00507526	+	0.999987i	$0.498384\pi$
$620$	1074.70	0.0696144
$621$	27003.8	1.74497
$622$	−757.100	−0.0488054
$623$	8366.50	0.538037
$624$	1029.30	0.0660334
$625$	−28.6176	−0.00183152
$626$	−3825.05	−0.244217
$627$	−9448.77	−0.601830
$628$	−13136.3	−0.834707
$629$	−9861.36	−0.625116
$630$	−5374.36	−0.339873
$631$	16349.5	1.03148	0.515740	−	0.856745i	$-0.327517\pi$
$631$	16349.5	1.03148	0.515740	+	0.856745i	$0.327517\pi$
$632$	10631.7	0.669157
$633$	36515.8	2.29285
$634$	13280.5	0.831920
$635$	−7959.31	−0.497410
$636$	−5660.63	−0.352923
$637$	347.055	0.0215869
$638$	−1066.92	−0.0662068
$639$	−52300.8	−3.23785
$640$	−885.406	−0.0546856
$641$	−16933.8	−1.04344	−0.521721	−	0.853116i	$-0.674710\pi$
$641$	−16933.8	−1.04344	−0.521721	+	0.853116i	$0.674710\pi$
$642$	−32402.1	−1.99191
$643$	14717.7	0.902657	0.451328	−	0.892358i	$-0.350950\pi$
$643$	14717.7	0.902657	0.451328	+	0.892358i	$0.350950\pi$
$644$	2921.27	0.178749
$645$	−1058.10	−0.0645933
$646$	−12924.5	−0.787162
$647$	−4572.55	−0.277845	−0.138922	−	0.990303i	$-0.544364\pi$
$647$	−4572.55	−0.277845	−0.138922	+	0.990303i	$0.544364\pi$
$648$	−6819.70	−0.413431
$649$	4941.58	0.298881
$650$	1092.90	0.0659491
$651$	2469.51	0.148675
$652$	−5615.50	−0.337301
$653$	400.476	0.0239997	0.0119999	−	0.999928i	$-0.496180\pi$
$653$	400.476	0.0239997	0.0119999	+	0.999928i	$0.496180\pi$
$654$	9620.22	0.575199
$655$	−15431.3	−0.920536
$656$	6559.78	0.390421
$657$	−4837.01	−0.287229
$658$	7496.28	0.444127
$659$	1761.23	0.104109	0.0520544	−	0.998644i	$-0.483423\pi$
$659$	1761.23	0.104109	0.0520544	+	0.998644i	$0.483423\pi$
$660$	2764.42	0.163037
$661$	−20410.8	−1.20104	−0.600520	−	0.799610i	$-0.705040\pi$
$661$	−20410.8	−1.20104	−0.600520	+	0.799610i	$0.705040\pi$
$662$	10685.7	0.627358
$663$	−4395.81	−0.257495
$664$	−4888.00	−0.285680
$665$	−4579.26	−0.267032
$666$	−16018.2	−0.931973
$667$	5059.70	0.293722
$668$	16645.2	0.964108
$669$	−4039.63	−0.233455
$670$	4106.26	0.236774
$671$	−5820.06	−0.334845
$672$	−2034.54	−0.116792
$673$	4578.55	0.262244	0.131122	−	0.991366i	$-0.458142\pi$
$673$	4578.55	0.262244	0.131122	+	0.991366i	$0.458142\pi$
$674$	−8528.74	−0.487411
$675$	−19969.0	−1.13868
$676$	−8587.34	−0.488583
$677$	−16330.1	−0.927057	−0.463528	−	0.886082i	$-0.653417\pi$
$677$	−16330.1	−0.927057	−0.463528	+	0.886082i	$0.653417\pi$
$678$	−36241.9	−2.05289
$679$	−12983.5	−0.733816
$680$	3781.30	0.213244
$681$	43210.4	2.43146
$682$	−854.509	−0.0479778
$683$	−25379.8	−1.42186	−0.710929	−	0.703263i	$-0.751725\pi$
$683$	−25379.8	−1.42186	−0.710929	+	0.703263i	$0.751725\pi$
$684$	−20993.8	−1.17356
$685$	4541.81	0.253334
$686$	−686.000	−0.0381802
$687$	9381.98	0.521026
$688$	−269.461	−0.0149318
$689$	−1103.54	−0.0610184
$690$	−13109.7	−0.723304
$691$	18557.9	1.02167	0.510837	−	0.859678i	$-0.329336\pi$
$691$	18557.9	1.02167	0.510837	+	0.859678i	$0.329336\pi$
$692$	−10774.6	−0.591894
$693$	4273.24	0.234238
$694$	7534.22	0.412096
$695$	7001.44	0.382129
$696$	−3523.86	−0.191913
$697$	−28014.8	−1.52243
$698$	−11233.8	−0.609175
$699$	−26817.5	−1.45112
$700$	−2160.25	−0.116643
$701$	25115.0	1.35318	0.676590	−	0.736360i	$-0.263457\pi$
$701$	25115.0	1.35318	0.676590	+	0.736360i	$0.263457\pi$
$702$	−3666.43	−0.197123
$703$	−13648.5	−0.732235
$704$	704.000	0.0376889
$705$	−33641.0	−1.79715
$706$	2677.66	0.142741
$707$	−10044.6	−0.534324
$708$	16321.2	0.866366
$709$	36408.7	1.92857	0.964286	−	0.264864i	$-0.0853272\pi$
$709$	36408.7	1.92857	0.964286	+	0.264864i	$0.0853272\pi$
$710$	13037.8	0.689155
$711$	−73753.0	−3.89023
$712$	−9561.72	−0.503287
$713$	4052.36	0.212850
$714$	8688.89	0.455425
$715$	538.925	0.0281883
$716$	7510.95	0.392035
$717$	48889.3	2.54645
$718$	6647.67	0.345528
$719$	3503.59	0.181727	0.0908637	−	0.995863i	$-0.471037\pi$
$719$	3503.59	0.181727	0.0908637	+	0.995863i	$0.471037\pi$
$720$	6142.13	0.317922
$721$	3981.22	0.205643
$722$	−4169.91	−0.214942
$723$	25053.4	1.28872
$724$	2557.16	0.131265
$725$	−3741.60	−0.191668
$726$	−2198.03	−0.112364
$727$	−18869.2	−0.962613	−0.481306	−	0.876552i	$-0.659838\pi$
$727$	−18869.2	−0.962613	−0.481306	+	0.876552i	$0.659838\pi$
$728$	−396.635	−0.0201927
$729$	−16164.7	−0.821254
$730$	1205.79	0.0611349
$731$	1150.79	0.0582262
$732$	−19222.6	−0.970613
$733$	−26123.3	−1.31635	−0.658176	−	0.752864i	$-0.728672\pi$
$733$	−26123.3	−1.31635	−0.658176	+	0.752864i	$0.728672\pi$
$734$	−1225.19	−0.0616112
$735$	3078.55	0.154495
$736$	−3338.59	−0.167204
$737$	−3264.95	−0.163183
$738$	−45505.7	−2.26977
$739$	−1259.95	−0.0627170	−0.0313585	−	0.999508i	$-0.509983\pi$
$739$	−1259.95	−0.0627170	−0.0313585	+	0.999508i	$0.509983\pi$
$740$	3993.11	0.198364
$741$	−6083.95	−0.301619
$742$	2181.30	0.107922
$743$	−6987.68	−0.345024	−0.172512	−	0.985007i	$-0.555188\pi$
$743$	−6987.68	−0.345024	−0.172512	+	0.985007i	$0.555188\pi$
$744$	−2822.29	−0.139073
$745$	−5441.63	−0.267605
$746$	23717.7	1.16403
$747$	33908.4	1.66084
$748$	−3006.57	−0.146967
$749$	12486.0	0.609116
$750$	25401.4	1.23671
$751$	26501.3	1.28768	0.643838	−	0.765162i	$-0.277341\pi$
$751$	26501.3	1.28768	0.643838	+	0.765162i	$0.277341\pi$
$752$	−8567.18	−0.415443
$753$	−34645.5	−1.67670
$754$	−686.979	−0.0331808
$755$	1422.00	0.0685454
$756$	7247.17	0.348647
$757$	−18638.9	−0.894905	−0.447453	−	0.894308i	$-0.647669\pi$
$757$	−18638.9	−0.894905	−0.447453	+	0.894308i	$0.647669\pi$
$758$	−13813.9	−0.661932
$759$	10423.8	0.498496
$760$	5233.44	0.249785
$761$	10502.8	0.500298	0.250149	−	0.968207i	$-0.419520\pi$
$761$	10502.8	0.500298	0.250149	+	0.968207i	$0.419520\pi$
$762$	20902.1	0.993707
$763$	−3707.11	−0.175893
$764$	14822.2	0.701897
$765$	−26231.1	−1.23972
$766$	10379.4	0.489585
$767$	3181.82	0.149790
$768$	2325.19	0.109249
$769$	−31451.8	−1.47488	−0.737440	−	0.675413i	$-0.763965\pi$
$769$	−31451.8	−1.47488	−0.737440	+	0.675413i	$0.763965\pi$
$770$	−1065.25	−0.0498560
$771$	−63214.7	−2.95282
$772$	8589.53	0.400445
$773$	−12785.3	−0.594897	−0.297448	−	0.954738i	$-0.596136\pi$
$773$	−12785.3	−0.594897	−0.297448	+	0.954738i	$0.596136\pi$
$774$	1869.27	0.0868082
$775$	−2996.68	−0.138895
$776$	14838.3	0.686422
$777$	9175.60	0.423646
$778$	−9201.43	−0.424020
$779$	−38773.4	−1.78331
$780$	1779.97	0.0817093
$781$	−10366.6	−0.474961
$782$	14258.1	0.652006
$783$	12552.3	0.572900
$784$	784.000	0.0357143
$785$	−22716.7	−1.03286
$786$	40524.5	1.83901
$787$	−26171.7	−1.18542	−0.592708	−	0.805418i	$-0.701941\pi$
$787$	−26171.7	−1.18542	−0.592708	+	0.805418i	$0.701941\pi$
$788$	9427.93	0.426213
$789$	8690.15	0.392114
$790$	18385.5	0.828010
$791$	13965.6	0.627763
$792$	−4883.70	−0.219109
$793$	−3747.46	−0.167814
$794$	10627.9	0.475026
$795$	−9788.99	−0.436704
$796$	20765.0	0.924619
$797$	−9956.37	−0.442500	−0.221250	−	0.975217i	$-0.571014\pi$
$797$	−9956.37	−0.442500	−0.221250	+	0.975217i	$0.571014\pi$
$798$	12025.7	0.533466
$799$	36587.8	1.62000
$800$	2468.86	0.109109
$801$	66330.3	2.92593
$802$	−30102.9	−1.32540
$803$	−958.745	−0.0421337
$804$	−10783.6	−0.473019
$805$	5051.78	0.221182
$806$	−550.208	−0.0240450
$807$	−8854.67	−0.386244
$808$	11479.6	0.499814
$809$	27460.5	1.19340	0.596699	−	0.802465i	$-0.296478\pi$
$809$	27460.5	1.19340	0.596699	+	0.802465i	$0.296478\pi$
$810$	−11793.4	−0.511576
$811$	13721.5	0.594116	0.297058	−	0.954859i	$-0.403994\pi$
$811$	13721.5	0.594116	0.297058	+	0.954859i	$0.403994\pi$
$812$	1357.90	0.0586861
$813$	31971.6	1.37920
$814$	−3174.98	−0.136711
$815$	−9710.94	−0.417374
$816$	−9930.16	−0.426011
$817$	1592.73	0.0682037
$818$	−19094.4	−0.816162
$819$	2751.48	0.117393
$820$	11343.9	0.483105
$821$	−7959.34	−0.338347	−0.169173	−	0.985586i	$-0.554110\pi$
$821$	−7959.34	−0.338347	−0.169173	+	0.985586i	$0.554110\pi$
$822$	−11927.4	−0.506101
$823$	15031.6	0.636659	0.318329	−	0.947980i	$-0.396878\pi$
$823$	15031.6	0.636659	0.318329	+	0.947980i	$0.396878\pi$
$824$	−4549.96	−0.192361
$825$	−7708.27	−0.325294
$826$	−6289.28	−0.264930
$827$	34367.2	1.44506	0.722531	−	0.691339i	$-0.242979\pi$
$827$	34367.2	1.44506	0.722531	+	0.691339i	$0.242979\pi$
$828$	23160.1	0.972063
$829$	34355.0	1.43932	0.719662	−	0.694324i	$-0.244297\pi$
$829$	34355.0	1.43932	0.719662	+	0.694324i	$0.244297\pi$
$830$	−8452.87	−0.353498
$831$	20986.6	0.876072
$832$	453.297	0.0188885
$833$	−3348.22	−0.139267
$834$	−18386.7	−0.763403
$835$	28784.8	1.19298
$836$	−4161.19	−0.172150
$837$	10053.2	0.415161
$838$	1287.44	0.0530715
$839$	25095.0	1.03263	0.516314	−	0.856399i	$-0.327304\pi$
$839$	25095.0	1.03263	0.516314	+	0.856399i	$0.327304\pi$
$840$	−3518.35	−0.144517
$841$	−22037.1	−0.903566
$842$	−24960.8	−1.02162
$843$	51014.7	2.08427
$844$	16081.4	0.655858
$845$	−14850.2	−0.604569
$846$	59431.1	2.41523
$847$	847.000	0.0343604
$848$	−2492.91	−0.100952
$849$	−9674.67	−0.391088
$850$	−10543.7	−0.425467
$851$	15056.8	0.606510
$852$	−34238.9	−1.37677
$853$	−8877.88	−0.356357	−0.178179	−	0.983998i	$-0.557020\pi$
$853$	−8877.88	−0.356357	−0.178179	+	0.983998i	$0.557020\pi$
$854$	7407.35	0.296808
$855$	−36304.8	−1.45216
$856$	−14269.7	−0.569776
$857$	−28281.8	−1.12729	−0.563646	−	0.826016i	$-0.690602\pi$
$857$	−28281.8	−1.12729	−0.563646	+	0.826016i	$0.690602\pi$
$858$	−1415.28	−0.0563135
$859$	−25282.1	−1.00421	−0.502104	−	0.864807i	$-0.667441\pi$
$859$	−25282.1	−1.00421	−0.502104	+	0.864807i	$0.667441\pi$
$860$	−465.982	−0.0184766
$861$	26066.7	1.03176
$862$	11304.7	0.446680
$863$	−38721.6	−1.52735	−0.763673	−	0.645603i	$-0.776606\pi$
$863$	−38721.6	−1.52735	−0.763673	+	0.645603i	$0.776606\pi$
$864$	−8282.48	−0.326129
$865$	−18632.7	−0.732405
$866$	4359.61	0.171069
$867$	−2214.99	−0.0867648
$868$	1087.56	0.0425278
$869$	−14618.6	−0.570659
$870$	−6093.85	−0.237472
$871$	−2102.26	−0.0817824
$872$	4236.69	0.164533
$873$	−102934.	−3.99061
$874$	19733.7	0.763732
$875$	−9788.33	−0.378178
$876$	−3166.57	−0.122133
$877$	47198.6	1.81731	0.908656	−	0.417546i	$-0.137110\pi$
$877$	47198.6	1.81731	0.908656	+	0.417546i	$0.137110\pi$
$878$	7030.02	0.270218
$879$	31364.1	1.20351
$880$	1217.43	0.0466360
$881$	12794.1	0.489266	0.244633	−	0.969616i	$-0.421333\pi$
$881$	12794.1	0.489266	0.244633	+	0.969616i	$0.421333\pi$
$882$	−5438.66	−0.207630
$883$	−22310.6	−0.850295	−0.425148	−	0.905124i	$-0.639778\pi$
$883$	−22310.6	−0.850295	−0.425148	+	0.905124i	$0.639778\pi$
$884$	−1935.89	−0.0736550
$885$	28224.3	1.07203
$886$	−12659.5	−0.480029
$887$	−31281.7	−1.18415	−0.592073	−	0.805884i	$-0.701690\pi$
$887$	−31281.7	−1.18415	−0.592073	+	0.805884i	$0.701690\pi$
$888$	−10486.4	−0.396284
$889$	−8054.54	−0.303870
$890$	−16535.2	−0.622764
$891$	9377.09	0.352575
$892$	−1779.03	−0.0667785
$893$	50638.7	1.89760
$894$	14290.4	0.534611
$895$	12988.8	0.485102
$896$	−896.000	−0.0334077
$897$	6711.73	0.249831
$898$	21249.3	0.789642
$899$	1883.67	0.0698820
$900$	−17126.6	−0.634320
$901$	10646.5	0.393657
$902$	−9019.70	−0.332952
$903$	−1070.76	−0.0394603
$904$	−15960.7	−0.587219
$905$	4422.12	0.162427
$906$	−3734.34	−0.136937
$907$	−31863.9	−1.16651	−0.583255	−	0.812289i	$-0.698221\pi$
$907$	−31863.9	−1.16651	−0.583255	+	0.812289i	$0.698221\pi$
$908$	19029.6	0.695506
$909$	−79634.6	−2.90573
$910$	−685.904	−0.0249863
$911$	−38643.5	−1.40540	−0.702698	−	0.711488i	$-0.748022\pi$
$911$	−38643.5	−1.40540	−0.702698	+	0.711488i	$0.748022\pi$
$912$	−13743.7	−0.499011
$913$	6721.01	0.243629
$914$	22747.8	0.823227
$915$	−33241.9	−1.20103
$916$	4131.77	0.149037
$917$	−15615.9	−0.562360
$918$	35371.9	1.27173
$919$	−22868.7	−0.820857	−0.410428	−	0.911893i	$-0.634621\pi$
$919$	−22868.7	−0.820857	−0.410428	+	0.911893i	$0.634621\pi$
$920$	−5773.46	−0.206897
$921$	44186.8	1.58090
$922$	16947.7	0.605362
$923$	−6674.90	−0.238036
$924$	2797.49	0.0996003
$925$	−11134.3	−0.395778
$926$	−19593.4	−0.695335
$927$	31563.4	1.11832
$928$	−1551.89	−0.0548958
$929$	9352.39	0.330293	0.165146	−	0.986269i	$-0.447190\pi$
$929$	9352.39	0.330293	0.165146	+	0.986269i	$0.447190\pi$
$930$	−4880.62	−0.172088
$931$	−4634.05	−0.163131
$932$	−11810.3	−0.415084
$933$	3438.28	0.120648
$934$	6001.63	0.210256
$935$	−5199.28	−0.181855
$936$	−3144.55	−0.109811
$937$	6943.74	0.242094	0.121047	−	0.992647i	$-0.461375\pi$
$937$	6943.74	0.242094	0.121047	+	0.992647i	$0.461375\pi$
$938$	4155.39	0.144647
$939$	17371.0	0.603707
$940$	−14815.3	−0.514066
$941$	−17294.1	−0.599120	−0.299560	−	0.954077i	$-0.596840\pi$
$941$	−17294.1	−0.599120	−0.299560	+	0.954077i	$0.596840\pi$
$942$	59657.0	2.06341
$943$	42774.3	1.47712
$944$	7187.75	0.247819
$945$	12532.6	0.431413
$946$	370.509	0.0127339
$947$	52139.8	1.78914	0.894570	−	0.446928i	$-0.147482\pi$
$947$	52139.8	1.78914	0.894570	+	0.446928i	$0.147482\pi$
$948$	−48282.7	−1.65417
$949$	−617.324	−0.0211161
$950$	−14592.9	−0.498374
$951$	−60312.0	−2.05652
$952$	3826.54	0.130272
$953$	13921.4	0.473197	0.236599	−	0.971607i	$-0.423967\pi$
$953$	13921.4	0.473197	0.236599	+	0.971607i	$0.423967\pi$
$954$	17293.5	0.586896
$955$	25632.2	0.868523
$956$	21530.6	0.728399
$957$	4845.31	0.163664
$958$	−28768.5	−0.970217
$959$	4596.16	0.154763
$960$	4020.97	0.135184
$961$	−28282.4	−0.949359
$962$	−2044.33	−0.0685155
$963$	98989.9	3.31246
$964$	11033.4	0.368632
$965$	14853.9	0.495508
$966$	−13266.6	−0.441869
$967$	−18698.2	−0.621812	−0.310906	−	0.950441i	$-0.600632\pi$
$967$	−18698.2	−0.621812	−0.310906	+	0.950441i	$0.600632\pi$
$968$	−968.000	−0.0321412
$969$	58695.0	1.94588
$970$	25660.0	0.849374
$971$	−46060.5	−1.52230	−0.761149	−	0.648578i	$-0.775364\pi$
$971$	−46060.5	−1.52230	−0.761149	+	0.648578i	$0.775364\pi$
$972$	3017.47	0.0995734
$973$	7085.21	0.233444
$974$	39125.0	1.28711
$975$	−4963.26	−0.163027
$976$	−8465.54	−0.277639
$977$	−2625.78	−0.0859839	−0.0429919	−	0.999075i	$-0.513689\pi$
$977$	−2625.78	−0.0859839	−0.0429919	+	0.999075i	$0.513689\pi$
$978$	25502.1	0.833812
$979$	13147.4	0.429205
$980$	1355.78	0.0441926
$981$	−29390.3	−0.956533
$982$	−3449.76	−0.112104
$983$	−21740.7	−0.705412	−0.352706	−	0.935734i	$-0.614739\pi$
$983$	−21740.7	−0.705412	−0.352706	+	0.935734i	$0.614739\pi$
$984$	−29790.5	−0.965127
$985$	16303.8	0.527393
$986$	6627.64	0.214064
$987$	−34043.5	−1.09789
$988$	−2679.34	−0.0862764
$989$	−1757.07	−0.0564931
$990$	−8445.43	−0.271124
$991$	8494.35	0.272282	0.136141	−	0.990689i	$-0.456530\pi$
$991$	8494.35	0.272282	0.136141	+	0.990689i	$0.456530\pi$
$992$	−1242.92	−0.0397811
$993$	−48527.8	−1.55084
$994$	13193.8	0.421008
$995$	35909.2	1.14412
$996$	22198.3	0.706205
$997$	−9802.62	−0.311386	−0.155693	−	0.987805i	$-0.549761\pi$
$997$	−9802.62	−0.311386	−0.155693	+	0.987805i	$0.549761\pi$
$998$	−41797.5	−1.32573
$999$	37353.3	1.18299

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	154.4.a.g.1.2	✓	2
3.2	odd	2		1386.4.a.u.1.2		2
4.3	odd	2		1232.4.a.j.1.1		2
7.6	odd	2		1078.4.a.i.1.1		2
11.10	odd	2		1694.4.a.p.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.4.a.g.1.2	✓	2	1.1	even	1	trivial
1078.4.a.i.1.1		2	7.6	odd	2
1232.4.a.j.1.1		2	4.3	odd	2
1386.4.a.u.1.2		2	3.2	odd	2
1694.4.a.p.1.2		2	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	154.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +9.08276 q^{3} +4.00000 q^{4} +6.91724 q^{5} -18.1655 q^{6} +7.00000 q^{7} -8.00000 q^{8} +55.4966 q^{9} -13.8345 q^{10} +11.0000 q^{11} +36.3311 q^{12} +7.08276 q^{13} -14.0000 q^{14} +62.8276 q^{15} +16.0000 q^{16} -68.3311 q^{17} -110.993 q^{18} -94.5725 q^{19} +27.6689 q^{20} +63.5793 q^{21} -22.0000 q^{22} +104.331 q^{23} -72.6621 q^{24} -77.1518 q^{25} -14.1655 q^{26} +258.828 q^{27} +28.0000 q^{28} +48.4966 q^{29} -125.655 q^{30} +38.8413 q^{31} -32.0000 q^{32} +99.9104 q^{33} +136.662 q^{34} +48.4207 q^{35} +221.986 q^{36} +144.317 q^{37} +189.145 q^{38} +64.3311 q^{39} -55.3379 q^{40} +409.986 q^{41} -127.159 q^{42} -16.8413 q^{43} +44.0000 q^{44} +383.883 q^{45} -208.662 q^{46} -535.449 q^{47} +145.324 q^{48} +49.0000 q^{49} +154.304 q^{50} -620.635 q^{51} +28.3311 q^{52} -155.807 q^{53} -517.655 q^{54} +76.0896 q^{55} -56.0000 q^{56} -858.979 q^{57} -96.9932 q^{58} +449.235 q^{59} +251.311 q^{60} -529.096 q^{61} -77.6826 q^{62} +388.476 q^{63} +64.0000 q^{64} +48.9932 q^{65} -199.821 q^{66} -296.814 q^{67} -273.324 q^{68} +947.614 q^{69} -96.8413 q^{70} -942.414 q^{71} -443.973 q^{72} -87.1587 q^{73} -288.635 q^{74} -700.752 q^{75} -378.290 q^{76} +77.0000 q^{77} -128.662 q^{78} -1328.97 q^{79} +110.676 q^{80} +852.462 q^{81} -819.973 q^{82} +611.001 q^{83} +254.317 q^{84} -472.662 q^{85} +33.6826 q^{86} +440.483 q^{87} -88.0000 q^{88} +1195.21 q^{89} -767.766 q^{90} +49.5793 q^{91} +417.324 q^{92} +352.787 q^{93} +1070.90 q^{94} -654.180 q^{95} -290.648 q^{96} -1854.79 q^{97} -98.0000 q^{98} +610.462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} + 6 q^{3} + 8 q^{4} + 26 q^{5} - 12 q^{6} + 14 q^{7} - 16 q^{8} + 38 q^{9} - 52 q^{10} + 22 q^{11} + 24 q^{12} + 2 q^{13} - 28 q^{14} + 4 q^{15} + 32 q^{16} - 88 q^{17} - 76 q^{18} + 42 q^{19}+ \cdots + 418 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 + 6 * q^3 + 8 * q^4 + 26 * q^5 - 12 * q^6 + 14 * q^7 - 16 * q^8 + 38 * q^9 - 52 * q^10 + 22 * q^11 + 24 * q^12 + 2 * q^13 - 28 * q^14 + 4 * q^15 + 32 * q^16 - 88 * q^17 - 76 * q^18 + 42 * q^19 + 104 * q^20 + 42 * q^21 - 44 * q^22 + 160 * q^23 - 48 * q^24 + 162 * q^25 - 4 * q^26 + 396 * q^27 + 56 * q^28 + 24 * q^29 - 8 * q^30 + 248 * q^31 - 64 * q^32 + 66 * q^33 + 176 * q^34 + 182 * q^35 + 152 * q^36 - 52 * q^37 - 84 * q^38 + 80 * q^39 - 208 * q^40 + 528 * q^41 - 84 * q^42 - 204 * q^43 + 88 * q^44 + 50 * q^45 - 320 * q^46 + 24 * q^47 + 96 * q^48 + 98 * q^49 - 324 * q^50 - 560 * q^51 + 8 * q^52 + 248 * q^53 - 792 * q^54 + 286 * q^55 - 112 * q^56 - 1280 * q^57 - 48 * q^58 + 570 * q^59 + 16 * q^60 - 1338 * q^61 - 496 * q^62 + 266 * q^63 + 128 * q^64 - 48 * q^65 - 132 * q^66 - 180 * q^67 - 352 * q^68 + 776 * q^69 - 364 * q^70 - 60 * q^71 - 304 * q^72 - 4 * q^73 + 104 * q^74 - 1438 * q^75 + 168 * q^76 + 154 * q^77 - 160 * q^78 - 1928 * q^79 + 416 * q^80 + 902 * q^81 - 1056 * q^82 - 542 * q^83 + 168 * q^84 - 848 * q^85 + 408 * q^86 + 516 * q^87 - 176 * q^88 - 140 * q^89 - 100 * q^90 + 14 * q^91 + 640 * q^92 - 292 * q^93 - 48 * q^94 + 1952 * q^95 - 192 * q^96 - 2712 * q^97 - 196 * q^98 + 418 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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