LMFDB - Embedded newform 35.6.a.d.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [35,6,Mod(1,35)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("35.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	35.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$5.61343369345$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 82x^{2} + 58x + 1168 $ x^4 - x^3 - 82x^2 + 58x + 1168
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-7.92431$ of defining polynomial
Character	$\chi$	$=$	35.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+9.92431 q^{2} +0.133419 q^{3} +66.4919 q^{4} +25.0000 q^{5} +1.32409 q^{6} -49.0000 q^{7} +342.308 q^{8} -242.982 q^{9} +248.108 q^{10} +674.476 q^{11} +8.87129 q^{12} -770.741 q^{13} -486.291 q^{14} +3.33548 q^{15} +1269.43 q^{16} -693.730 q^{17} -2411.43 q^{18} -1391.69 q^{19} +1662.30 q^{20} -6.53754 q^{21} +6693.71 q^{22} +1321.87 q^{23} +45.6704 q^{24} +625.000 q^{25} -7649.07 q^{26} -64.8394 q^{27} -3258.10 q^{28} +172.983 q^{29} +33.1023 q^{30} -4694.07 q^{31} +1644.34 q^{32} +89.9880 q^{33} -6884.79 q^{34} -1225.00 q^{35} -16156.3 q^{36} +13295.3 q^{37} -13811.6 q^{38} -102.832 q^{39} +8557.69 q^{40} +20700.2 q^{41} -64.8806 q^{42} -8548.62 q^{43} +44847.2 q^{44} -6074.55 q^{45} +13118.7 q^{46} +13781.0 q^{47} +169.366 q^{48} +2401.00 q^{49} +6202.69 q^{50} -92.5570 q^{51} -51248.0 q^{52} +6727.47 q^{53} -643.486 q^{54} +16861.9 q^{55} -16773.1 q^{56} -185.679 q^{57} +1716.74 q^{58} +38517.7 q^{59} +221.782 q^{60} +7676.86 q^{61} -46585.4 q^{62} +11906.1 q^{63} -24302.8 q^{64} -19268.5 q^{65} +893.069 q^{66} -49040.1 q^{67} -46127.4 q^{68} +176.363 q^{69} -12157.3 q^{70} +22757.6 q^{71} -83174.7 q^{72} -22821.6 q^{73} +131946. q^{74} +83.3870 q^{75} -92536.4 q^{76} -33049.3 q^{77} -1020.53 q^{78} +20160.9 q^{79} +31735.7 q^{80} +59036.0 q^{81} +205435. q^{82} -108242. q^{83} -434.693 q^{84} -17343.3 q^{85} -84839.2 q^{86} +23.0793 q^{87} +230878. q^{88} -36635.3 q^{89} -60285.7 q^{90} +37766.3 q^{91} +87893.9 q^{92} -626.280 q^{93} +136766. q^{94} -34792.4 q^{95} +219.386 q^{96} +147232. q^{97} +23828.3 q^{98} -163886. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 7 q^{2} + 14 q^{3} + 49 q^{4} + 100 q^{5} + 136 q^{6} - 196 q^{7} + 489 q^{8} + 774 q^{9} + 175 q^{10} + 770 q^{11} + 840 q^{12} + 58 q^{13} - 343 q^{14} + 350 q^{15} - 615 q^{16} + 2006 q^{17} - 1409 q^{18}+ \cdots - 420668 q^{99}+O(q^{100}) $ 4 * q + 7 * q^2 + 14 * q^3 + 49 * q^4 + 100 * q^5 + 136 * q^6 - 196 * q^7 + 489 * q^8 + 774 * q^9 + 175 * q^10 + 770 * q^11 + 840 * q^12 + 58 * q^13 - 343 * q^14 + 350 * q^15 - 615 * q^16 + 2006 * q^17 - 1409 * q^18 + 564 * q^19 + 1225 * q^20 - 686 * q^21 - 1736 * q^22 - 6340 * q^23 - 6244 * q^24 + 2500 * q^25 - 8730 * q^26 - 7438 * q^27 - 2401 * q^28 + 8066 * q^29 + 3400 * q^30 - 5856 * q^31 - 3495 * q^32 - 8130 * q^33 + 3402 * q^34 - 4900 * q^35 - 28759 * q^36 + 29544 * q^37 - 36860 * q^38 + 57466 * q^39 + 12225 * q^40 + 13156 * q^41 - 6664 * q^42 - 5692 * q^43 + 44952 * q^44 + 19350 * q^45 + 30928 * q^46 + 39926 * q^47 - 57156 * q^48 + 9604 * q^49 + 4375 * q^50 + 9830 * q^51 - 23398 * q^52 + 20300 * q^53 + 77292 * q^54 + 19250 * q^55 - 23961 * q^56 - 50876 * q^57 - 22234 * q^58 + 8432 * q^59 + 21000 * q^60 + 30540 * q^61 - 137568 * q^62 - 37926 * q^63 + 37121 * q^64 + 1450 * q^65 - 166756 * q^66 + 32792 * q^67 - 72554 * q^68 - 36540 * q^69 - 8575 * q^70 - 83920 * q^71 - 71795 * q^72 - 75424 * q^73 + 168762 * q^74 + 8750 * q^75 - 125092 * q^76 - 37730 * q^77 - 89204 * q^78 + 129486 * q^79 - 15375 * q^80 + 146308 * q^81 + 247230 * q^82 - 187520 * q^83 - 41160 * q^84 + 50150 * q^85 + 36156 * q^86 - 238670 * q^87 + 475556 * q^88 - 30324 * q^89 - 35225 * q^90 - 2842 * q^91 + 124464 * q^92 + 8256 * q^93 + 245756 * q^94 + 14100 * q^95 + 172340 * q^96 + 180270 * q^97 + 16807 * q^98 - 420668 * 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 $

$2$	9.92431	1.75439	0.877193	−	0.480138i	$-0.159413\pi$
$2$	9.92431	1.75439	0.877193	+	0.480138i	$0.159413\pi$
$3$	0.133419	0.00855885	0.00427942	−	0.999991i	$-0.498638\pi$
$3$	0.133419	0.00855885	0.00427942	+	0.999991i	$0.498638\pi$
$4$	66.4919	2.07787
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	1.32409	0.0150155
$7$	−49.0000	−0.377964
$7$	−49.0000	−0.377964
$8$	342.308	1.89100
$9$	−242.982	−0.999927
$10$	248.108	0.784585
$11$	674.476	1.68068	0.840339	−	0.542061i	$-0.182356\pi$
$11$	674.476	1.68068	0.840339	+	0.542061i	$0.182356\pi$
$12$	8.87129	0.0177842
$13$	−770.741	−1.26488	−0.632441	−	0.774608i	$-0.717947\pi$
$13$	−770.741	−1.26488	−0.632441	+	0.774608i	$0.717947\pi$
$14$	−486.291	−0.663096
$15$	3.33548	0.00382763
$16$	1269.43	1.23968
$17$	−693.730	−0.582195	−0.291097	−	0.956693i	$-0.594020\pi$
$17$	−693.730	−0.582195	−0.291097	+	0.956693i	$0.594020\pi$
$18$	−2411.43	−1.75426
$19$	−1391.69	−0.884423	−0.442211	−	0.896911i	$-0.645806\pi$
$19$	−1391.69	−0.884423	−0.442211	+	0.896911i	$0.645806\pi$
$20$	1662.30	0.929252
$21$	−6.53754	−0.00323494
$22$	6693.71	2.94856
$23$	1321.87	0.521039	0.260520	−	0.965469i	$-0.416106\pi$
$23$	1321.87	0.521039	0.260520	+	0.965469i	$0.416106\pi$
$24$	45.6704	0.0161848
$25$	625.000	0.200000
$26$	−7649.07	−2.21909
$27$	−64.8394	−0.0171171
$28$	−3258.10	−0.785361
$29$	172.983	0.0381952	0.0190976	−	0.999818i	$-0.493921\pi$
$29$	172.983	0.0381952	0.0190976	+	0.999818i	$0.493921\pi$
$30$	33.1023	0.00671515
$31$	−4694.07	−0.877295	−0.438648	−	0.898659i	$-0.644542\pi$
$31$	−4694.07	−0.877295	−0.438648	+	0.898659i	$0.644542\pi$
$32$	1644.34	0.283868
$33$	89.9880	0.0143847
$34$	−6884.79	−1.02139
$35$	−1225.00	−0.169031
$36$	−16156.3	−2.07772
$37$	13295.3	1.59659	0.798293	−	0.602269i	$-0.205737\pi$
$37$	13295.3	1.59659	0.798293	+	0.602269i	$0.205737\pi$
$38$	−13811.6	−1.55162
$39$	−102.832	−0.0108259
$40$	8557.69	0.845681
$41$	20700.2	1.92316	0.961578	−	0.274532i	$-0.0885229\pi$
$41$	20700.2	1.92316	0.961578	+	0.274532i	$0.0885229\pi$
$42$	−64.8806	−0.00567533
$43$	−8548.62	−0.705058	−0.352529	−	0.935801i	$-0.614678\pi$
$43$	−8548.62	−0.705058	−0.352529	+	0.935801i	$0.614678\pi$
$44$	44847.2	3.49223
$45$	−6074.55	−0.447181
$46$	13118.7	0.914104
$47$	13781.0	0.909986	0.454993	−	0.890495i	$-0.349642\pi$
$47$	13781.0	0.909986	0.454993	+	0.890495i	$0.349642\pi$
$48$	169.366	0.0106102
$49$	2401.00	0.142857
$50$	6202.69	0.350877
$51$	−92.5570	−0.00498292
$52$	−51248.0	−2.62826
$53$	6727.47	0.328975	0.164487	−	0.986379i	$-0.447403\pi$
$53$	6727.47	0.328975	0.164487	+	0.986379i	$0.447403\pi$
$54$	−643.486	−0.0300299
$55$	16861.9	0.751622
$56$	−16773.1	−0.714731
$57$	−185.679	−0.00756964
$58$	1716.74	0.0670091
$59$	38517.7	1.44056	0.720278	−	0.693686i	$-0.244014\pi$
$59$	38517.7	1.44056	0.720278	+	0.693686i	$0.244014\pi$
$60$	221.782	0.00795332
$61$	7676.86	0.264155	0.132078	−	0.991239i	$-0.457835\pi$
$61$	7676.86	0.264155	0.132078	+	0.991239i	$0.457835\pi$
$62$	−46585.4	−1.53911
$63$	11906.1	0.377937
$64$	−24302.8	−0.741661
$65$	−19268.5	−0.565673
$66$	893.069	0.0252363
$67$	−49040.1	−1.33464	−0.667320	−	0.744771i	$-0.732559\pi$
$67$	−49040.1	−1.33464	−0.667320	+	0.744771i	$0.732559\pi$
$68$	−46127.4	−1.20973
$69$	176.363	0.00445950
$70$	−12157.3	−0.296545
$71$	22757.6	0.535772	0.267886	−	0.963451i	$-0.413675\pi$
$71$	22757.6	0.535772	0.267886	+	0.963451i	$0.413675\pi$
$72$	−83174.7	−1.89086
$73$	−22821.6	−0.501232	−0.250616	−	0.968087i	$-0.580633\pi$
$73$	−22821.6	−0.501232	−0.250616	+	0.968087i	$0.580633\pi$
$74$	131946.	2.80103
$75$	83.3870	0.00171177
$76$	−92536.4	−1.83772
$77$	−33049.3	−0.635237
$78$	−1020.53	−0.0189929
$79$	20160.9	0.363448	0.181724	−	0.983350i	$-0.441832\pi$
$79$	20160.9	0.363448	0.181724	+	0.983350i	$0.441832\pi$
$80$	31735.7	0.554400
$81$	59036.0	0.999780
$82$	205435.	3.37396
$83$	−108242.	−1.72466	−0.862328	−	0.506350i	$-0.830994\pi$
$83$	−108242.	−1.72466	−0.862328	+	0.506350i	$0.830994\pi$
$84$	−434.693	−0.00672179
$85$	−17343.3	−0.260365
$86$	−84839.2	−1.23694
$87$	23.0793	0.000326907 0
$88$	230878.	3.17817
$89$	−36635.3	−0.490258	−0.245129	−	0.969490i	$-0.578830\pi$
$89$	−36635.3	−0.490258	−0.245129	+	0.969490i	$0.578830\pi$
$90$	−60285.7	−0.784528
$91$	37766.3	0.478081
$92$	87893.9	1.08265
$93$	−626.280	−0.00750863
$94$	136766.	1.59647
$95$	−34792.4	−0.395526
$96$	219.386	0.00242958
$97$	147232.	1.58881	0.794405	−	0.607388i	$-0.207783\pi$
$97$	147232.	1.58881	0.794405	+	0.607388i	$0.207783\pi$
$98$	23828.3	0.250627
$99$	−163886.	−1.68056
$100$	41557.4	0.415574
$101$	−106647.	−1.04026	−0.520132	−	0.854086i	$-0.674117\pi$
$101$	−106647.	−1.04026	−0.520132	+	0.854086i	$0.674117\pi$
$102$	−918.564	−0.00874196
$103$	−87459.8	−0.812298	−0.406149	−	0.913807i	$-0.633129\pi$
$103$	−87459.8	−0.812298	−0.406149	+	0.913807i	$0.633129\pi$
$104$	−263831.	−2.39189
$105$	−163.439	−0.00144671
$106$	66765.5	0.577148
$107$	−164801.	−1.39155	−0.695777	−	0.718258i	$-0.744940\pi$
$107$	−164801.	−1.39155	−0.695777	+	0.718258i	$0.744940\pi$
$108$	−4311.29	−0.0355670
$109$	−91743.7	−0.739622	−0.369811	−	0.929107i	$-0.620578\pi$
$109$	−91743.7	−0.739622	−0.369811	+	0.929107i	$0.620578\pi$
$110$	167343.	1.31864
$111$	1773.84	0.0136649
$112$	−62201.9	−0.468553
$113$	−147541.	−1.08696	−0.543482	−	0.839421i	$-0.682894\pi$
$113$	−147541.	−1.08696	−0.543482	+	0.839421i	$0.682894\pi$
$114$	−1842.73	−0.0132801
$115$	33046.9	0.233016
$116$	11502.0	0.0793646
$117$	187276.	1.26479
$118$	382261.	2.52729
$119$	33992.8	0.220049
$120$	1141.76	0.00723806
$121$	293867.	1.82468
$122$	76187.5	0.463430
$123$	2761.80	0.0164600
$124$	−312118.	−1.82291
$125$	15625.0	0.0894427
$126$	118160.	0.663047
$127$	−105224.	−0.578905	−0.289452	−	0.957192i	$-0.593473\pi$
$127$	−105224.	−0.578905	−0.289452	+	0.957192i	$0.593473\pi$
$128$	−293807.	−1.58503
$129$	−1140.55	−0.00603449
$130$	−191227.	−0.992408
$131$	327117.	1.66542	0.832711	−	0.553707i	$-0.186787\pi$
$131$	327117.	1.66542	0.832711	+	0.553707i	$0.186787\pi$
$132$	5983.47	0.0298895
$133$	68193.0	0.334280
$134$	−486689.	−2.34147
$135$	−1620.98	−0.00765498
$136$	−237469.	−1.10093
$137$	106825.	0.486264	0.243132	−	0.969993i	$-0.421825\pi$
$137$	106825.	0.486264	0.243132	+	0.969993i	$0.421825\pi$
$138$	1750.28	0.00782368
$139$	90143.0	0.395726	0.197863	−	0.980230i	$-0.436600\pi$
$139$	90143.0	0.395726	0.197863	+	0.980230i	$0.436600\pi$
$140$	−81452.5	−0.351224
$141$	1838.65	0.00778843
$142$	225853.	0.939950
$143$	−519846.	−2.12586
$144$	−308448.	−1.23958
$145$	4324.57	0.0170814
$146$	−226488.	−0.879354
$147$	320.340	0.00122269
$148$	884026.	3.31750
$149$	465454.	1.71756	0.858778	−	0.512348i	$-0.171224\pi$
$149$	465454.	1.71756	0.858778	+	0.512348i	$0.171224\pi$
$150$	827.558	0.00300310
$151$	−156745.	−0.559437	−0.279718	−	0.960082i	$-0.590241\pi$
$151$	−156745.	−0.559437	−0.279718	+	0.960082i	$0.590241\pi$
$152$	−476388.	−1.67244
$153$	168564.	0.582152
$154$	−327992.	−1.11445
$155$	−117352.	−0.392338
$156$	−6837.47	−0.0224949
$157$	−395491.	−1.28052	−0.640261	−	0.768157i	$-0.721174\pi$
$157$	−395491.	−1.28052	−0.640261	+	0.768157i	$0.721174\pi$
$158$	200083.	0.637628
$159$	897.574	0.00281564
$160$	41108.5	0.126950
$161$	−64771.8	−0.196934
$162$	585892.	1.75400
$163$	362186.	1.06773	0.533866	−	0.845569i	$-0.320739\pi$
$163$	362186.	1.06773	0.533866	+	0.845569i	$0.320739\pi$
$164$	1.37639e6	3.99607
$165$	2249.70	0.00643302
$166$	−1.07423e6	−3.02571
$167$	187502.	0.520254	0.260127	−	0.965574i	$-0.416236\pi$
$167$	187502.	0.520254	0.260127	+	0.965574i	$0.416236\pi$
$168$	−2237.85	−0.00611727
$169$	222749.	0.599928
$170$	−172120.	−0.456782
$171$	338157.	0.884358
$172$	−568414.	−1.46502
$173$	−81318.8	−0.206574	−0.103287	−	0.994652i	$-0.532936\pi$
$173$	−81318.8	−0.206574	−0.103287	+	0.994652i	$0.532936\pi$
$174$	229.046	0.000573520 0
$175$	−30625.0	−0.0755929
$176$	856198.	2.08350
$177$	5139.00	0.0123295
$178$	−363580.	−0.860102
$179$	−728608.	−1.69966	−0.849829	−	0.527059i	$-0.823295\pi$
$179$	−728608.	−1.69966	−0.849829	+	0.527059i	$0.823295\pi$
$180$	−403908.	−0.929184
$181$	727174.	1.64984	0.824920	−	0.565249i	$-0.191220\pi$
$181$	727174.	1.64984	0.824920	+	0.565249i	$0.191220\pi$
$182$	374804.	0.838738
$183$	1024.24	0.00226086
$184$	452488.	0.985286
$185$	332381.	0.714015
$186$	−6215.39	−0.0131730
$187$	−467904.	−0.978483
$188$	916322.	1.89083
$189$	3177.13	0.00646964
$190$	−345290.	−0.693905
$191$	−144726.	−0.287054	−0.143527	−	0.989646i	$-0.545844\pi$
$191$	−144726.	−0.287054	−0.143527	+	0.989646i	$0.545844\pi$
$192$	−3242.45	−0.00634776
$193$	155707.	0.300895	0.150448	−	0.988618i	$-0.451929\pi$
$193$	155707.	0.300895	0.150448	+	0.988618i	$0.451929\pi$
$194$	1.46117e6	2.78739
$195$	−2570.79	−0.00484151
$196$	159647.	0.296839
$197$	−476409.	−0.874609	−0.437305	−	0.899313i	$-0.644067\pi$
$197$	−476409.	−0.874609	−0.437305	+	0.899313i	$0.644067\pi$
$198$	−1.62645e6	−2.94834
$199$	−162445.	−0.290786	−0.145393	−	0.989374i	$-0.546445\pi$
$199$	−162445.	−0.290786	−0.145393	+	0.989374i	$0.546445\pi$
$200$	213942.	0.378200
$201$	−6542.89	−0.0114230
$202$	−1.05839e6	−1.82502
$203$	−8476.17	−0.0144364
$204$	−6154.28	−0.0103539
$205$	517505.	0.860061
$206$	−867978.	−1.42508
$207$	−321192.	−0.521001
$208$	−978400.	−1.56804
$209$	−938664.	−1.48643
$210$	−1622.01	−0.00253809
$211$	−220597.	−0.341109	−0.170554	−	0.985348i	$-0.554556\pi$
$211$	−220597.	−0.341109	−0.170554	+	0.985348i	$0.554556\pi$
$212$	447322.	0.683567
$213$	3036.29	0.00458559
$214$	−1.63553e6	−2.44132
$215$	−213716.	−0.315312
$216$	−22195.0	−0.0323684
$217$	230010.	0.331586
$218$	−910492.	−1.29758
$219$	−3044.84	−0.00428997
$220$	1.12118e6	1.56177
$221$	534687.	0.736408
$222$	17604.2	0.0239736
$223$	744023.	1.00190	0.500950	−	0.865476i	$-0.332984\pi$
$223$	744023.	1.00190	0.500950	+	0.865476i	$0.332984\pi$
$224$	−80572.6	−0.107292
$225$	−151864.	−0.199985
$226$	−1.46424e6	−1.90696
$227$	−318343.	−0.410045	−0.205022	−	0.978757i	$-0.565727\pi$
$227$	−318343.	−0.410045	−0.205022	+	0.978757i	$0.565727\pi$
$228$	−12346.1	−0.0157287
$229$	1.43755e6	1.81148	0.905741	−	0.423832i	$-0.139315\pi$
$229$	1.43755e6	1.81148	0.905741	+	0.423832i	$0.139315\pi$
$230$	327967.	0.408800
$231$	−4409.41	−0.00543689
$232$	59213.4	0.0722271
$233$	−192194.	−0.231926	−0.115963	−	0.993254i	$-0.536995\pi$
$233$	−192194.	−0.231926	−0.115963	+	0.993254i	$0.536995\pi$
$234$	1.85859e6	2.21893
$235$	344524.	0.406958
$236$	2.56111e6	2.99329
$237$	2689.85	0.00311070
$238$	337355.	0.386051
$239$	−783481.	−0.887225	−0.443613	−	0.896219i	$-0.646303\pi$
$239$	−783481.	−0.887225	−0.443613	+	0.896219i	$0.646303\pi$
$240$	4234.15	0.00474502
$241$	−833352.	−0.924243	−0.462121	−	0.886817i	$-0.652912\pi$
$241$	−833352.	−0.924243	−0.462121	+	0.886817i	$0.652912\pi$
$242$	2.91642e6	3.20120
$243$	23632.5	0.0256740
$244$	510448.	0.548880
$245$	60025.0	0.0638877
$246$	27409.0	0.0288772
$247$	1.07264e6	1.11869
$248$	−1.60682e6	−1.65897
$249$	−14441.6	−0.0147611
$250$	155067.	0.156917
$251$	−310658.	−0.311242	−0.155621	−	0.987817i	$-0.549738\pi$
$251$	−310658.	−0.311242	−0.155621	+	0.987817i	$0.549738\pi$
$252$	791661.	0.785304
$253$	891572.	0.875700
$254$	−1.04428e6	−1.01562
$255$	−2313.92	−0.00222843
$256$	−2.13814e6	−2.03909
$257$	−698374.	−0.659561	−0.329781	−	0.944058i	$-0.606975\pi$
$257$	−698374.	−0.659561	−0.329781	+	0.944058i	$0.606975\pi$
$258$	−11319.2	−0.0105868
$259$	−651468.	−0.603453
$260$	−1.28120e6	−1.17539
$261$	−42031.8	−0.0381924
$262$	3.24641e6	2.92179
$263$	574995.	0.512595	0.256298	−	0.966598i	$-0.417497\pi$
$263$	574995.	0.512595	0.256298	+	0.966598i	$0.417497\pi$
$264$	30803.6	0.0272014
$265$	168187.	0.147122
$266$	676769.	0.586457
$267$	−4887.85	−0.00419604
$268$	−3.26077e6	−2.77321
$269$	−246902.	−0.208038	−0.104019	−	0.994575i	$-0.533170\pi$
$269$	−246902.	−0.208038	−0.104019	+	0.994575i	$0.533170\pi$
$270$	−16087.1	−0.0134298
$271$	−1.29025e6	−1.06721	−0.533607	−	0.845733i	$-0.679164\pi$
$271$	−1.29025e6	−1.06721	−0.533607	+	0.845733i	$0.679164\pi$
$272$	−880640.	−0.721733
$273$	5038.75	0.00409182
$274$	1.06016e6	0.853094
$275$	421547.	0.336136
$276$	11726.7	0.00926626
$277$	−968667.	−0.758534	−0.379267	−	0.925287i	$-0.623824\pi$
$277$	−968667.	−0.758534	−0.379267	+	0.925287i	$0.623824\pi$
$278$	894607.	0.694257
$279$	1.14058e6	0.877231
$280$	−419327.	−0.319637
$281$	1.37144e6	1.03612	0.518062	−	0.855343i	$-0.326654\pi$
$281$	1.37144e6	1.03612	0.518062	+	0.855343i	$0.326654\pi$
$282$	18247.3	0.0136639
$283$	−151658.	−0.112564	−0.0562818	−	0.998415i	$-0.517925\pi$
$283$	−151658.	−0.112564	−0.0562818	+	0.998415i	$0.517925\pi$
$284$	1.51319e6	1.11326
$285$	−4641.97	−0.00338525
$286$	−5.15911e6	−3.72958
$287$	−1.01431e6	−0.726885
$288$	−399545.	−0.283847
$289$	−938595.	−0.661049
$290$	42918.4	0.0299674
$291$	19643.5	0.0135984
$292$	−1.51745e6	−1.04149
$293$	566468.	0.385484	0.192742	−	0.981249i	$-0.438262\pi$
$293$	566468.	0.385484	0.192742	+	0.981249i	$0.438262\pi$
$294$	3179.15	0.00214507
$295$	962942.	0.644236
$296$	4.55107e6	3.01915
$297$	−43732.6	−0.0287683
$298$	4.61931e6	3.01326
$299$	−1.01882e6	−0.659054
$300$	5544.56	0.00355683
$301$	418883.	0.266487
$302$	−1.55558e6	−0.981468
$303$	−14228.7	−0.00890345
$304$	−1.76666e6	−1.09640
$305$	191921.	0.118134
$306$	1.67288e6	1.02132
$307$	−1.62246e6	−0.982492	−0.491246	−	0.871021i	$-0.663458\pi$
$307$	−1.62246e6	−0.982492	−0.491246	+	0.871021i	$0.663458\pi$
$308$	−2.19751e6	−1.31994
$309$	−11668.8	−0.00695234
$310$	−1.16464e6	−0.688313
$311$	−458811.	−0.268988	−0.134494	−	0.990914i	$-0.542941\pi$
$311$	−458811.	−0.268988	−0.134494	+	0.990914i	$0.542941\pi$
$312$	−35200.1	−0.0204719
$313$	−706205.	−0.407446	−0.203723	−	0.979029i	$-0.565304\pi$
$313$	−706205.	−0.407446	−0.203723	+	0.979029i	$0.565304\pi$
$314$	−3.92497e6	−2.24653
$315$	297653.	0.169018
$316$	1.34054e6	0.755198
$317$	−1.12397e6	−0.628213	−0.314106	−	0.949388i	$-0.601705\pi$
$317$	−1.12397e6	−0.628213	−0.314106	+	0.949388i	$0.601705\pi$
$318$	8907.80	0.00493972
$319$	116673.	0.0641938
$320$	−607569.	−0.331681
$321$	−21987.6	−0.0119101
$322$	−642816.	−0.345499
$323$	965461.	0.514906
$324$	3.92541e6	2.07741
$325$	−481713.	−0.252976
$326$	3.59444e6	1.87322
$327$	−12240.4	−0.00633031
$328$	7.08583e6	3.63669
$329$	−675267.	−0.343943
$330$	22326.7	0.0112860
$331$	2.85545e6	1.43253	0.716266	−	0.697827i	$-0.245850\pi$
$331$	2.85545e6	1.43253	0.716266	+	0.697827i	$0.245850\pi$
$332$	−7.19724e6	−3.58361
$333$	−3.23051e6	−1.59647
$334$	1.86083e6	0.912726
$335$	−1.22600e6	−0.596869
$336$	−8298.93	−0.00401027
$337$	816793.	0.391776	0.195888	−	0.980626i	$-0.437241\pi$
$337$	816793.	0.391776	0.195888	+	0.980626i	$0.437241\pi$
$338$	2.21063e6	1.05250
$339$	−19684.7	−0.00930316
$340$	−1.15319e6	−0.541006
$341$	−3.16604e6	−1.47445
$342$	3.35597e6	1.55151
$343$	−117649.	−0.0539949
$344$	−2.92626e6	−1.33327
$345$	4409.09	0.00199435
$346$	−807033.	−0.362411
$347$	−1.66997e6	−0.744537	−0.372268	−	0.928125i	$-0.621420\pi$
$347$	−1.66997e6	−0.744537	−0.372268	+	0.928125i	$0.621420\pi$
$348$	1534.58	0.000679269 0
$349$	2.32623e6	1.02233	0.511163	−	0.859484i	$-0.329215\pi$
$349$	2.32623e6	1.02233	0.511163	+	0.859484i	$0.329215\pi$
$350$	−303932.	−0.132619
$351$	49974.4	0.0216511
$352$	1.10907e6	0.477091
$353$	1.91401e6	0.817537	0.408768	−	0.912638i	$-0.365958\pi$
$353$	1.91401e6	0.817537	0.408768	+	0.912638i	$0.365958\pi$
$354$	51001.0	0.0216307
$355$	568939.	0.239604
$356$	−2.43595e6	−1.01869
$357$	4535.29	0.00188337
$358$	−7.23093e6	−2.98186
$359$	1.43287e6	0.586774	0.293387	−	0.955994i	$-0.405218\pi$
$359$	1.43287e6	0.586774	0.293387	+	0.955994i	$0.405218\pi$
$360$	−2.07937e6	−0.845619
$361$	−539285.	−0.217796
$362$	7.21670e6	2.89446
$363$	39207.5	0.0156172
$364$	2.51115e6	0.993390
$365$	−570540.	−0.224158
$366$	10164.9	0.00396643
$367$	306282.	0.118701	0.0593507	−	0.998237i	$-0.481097\pi$
$367$	306282.	0.118701	0.0593507	+	0.998237i	$0.481097\pi$
$368$	1.67802e6	0.645920
$369$	−5.02978e6	−1.92302
$370$	3.29866e6	1.25266
$371$	−329646.	−0.124341
$372$	−41642.5	−0.0156020
$373$	3.01040e6	1.12035	0.560174	−	0.828375i	$-0.310734\pi$
$373$	3.01040e6	1.12035	0.560174	+	0.828375i	$0.310734\pi$
$374$	−4.64363e6	−1.71664
$375$	2084.68	0.000765526 0
$376$	4.71733e6	1.72079
$377$	−133325.	−0.0483124
$378$	31530.8	0.0113503
$379$	2.60610e6	0.931952	0.465976	−	0.884797i	$-0.345703\pi$
$379$	2.60610e6	0.931952	0.465976	+	0.884797i	$0.345703\pi$
$380$	−2.31341e6	−0.821852
$381$	−14039.0	−0.00495476
$382$	−1.43631e6	−0.503604
$383$	239580.	0.0834552	0.0417276	−	0.999129i	$-0.486714\pi$
$383$	239580.	0.0834552	0.0417276	+	0.999129i	$0.486714\pi$
$384$	−39199.5	−0.0135660
$385$	−826233.	−0.284087
$386$	1.54529e6	0.527886
$387$	2.07716e6	0.705007
$388$	9.78971e6	3.30134
$389$	3.83014e6	1.28334	0.641669	−	0.766982i	$-0.278242\pi$
$389$	3.83014e6	1.28334	0.641669	+	0.766982i	$0.278242\pi$
$390$	−25513.3	−0.00849387
$391$	−917024.	−0.303346
$392$	821881.	0.270143
$393$	43643.6	0.0142541
$394$	−4.72802e6	−1.53440
$395$	504023.	0.162539
$396$	−1.08971e7	−3.49198
$397$	4.87686e6	1.55297	0.776487	−	0.630134i	$-0.217000\pi$
$397$	4.87686e6	1.55297	0.776487	+	0.630134i	$0.217000\pi$
$398$	−1.61215e6	−0.510150
$399$	9098.26	0.00286105
$400$	793392.	0.247935
$401$	1.76120e6	0.546951	0.273475	−	0.961879i	$-0.411827\pi$
$401$	1.76120e6	0.546951	0.273475	+	0.961879i	$0.411827\pi$
$402$	−64933.6	−0.0200403
$403$	3.61792e6	1.10968
$404$	−7.09113e6	−2.16153
$405$	1.47590e6	0.447115
$406$	−84120.1	−0.0253270
$407$	8.96733e6	2.68335
$408$	−31683.0	−0.00942270
$409$	−1.04639e6	−0.309304	−0.154652	−	0.987969i	$-0.549426\pi$
$409$	−1.04639e6	−0.309304	−0.154652	+	0.987969i	$0.549426\pi$
$410$	5.13587e6	1.50888
$411$	14252.5	0.00416186
$412$	−5.81537e6	−1.68785
$413$	−1.88737e6	−0.544479
$414$	−3.18761e6	−0.914037
$415$	−2.70606e6	−0.771289
$416$	−1.26736e6	−0.359060
$417$	12026.8	0.00338696
$418$	−9.31559e6	−2.60777
$419$	−960422.	−0.267256	−0.133628	−	0.991032i	$-0.542663\pi$
$419$	−960422.	−0.267256	−0.133628	+	0.991032i	$0.542663\pi$
$420$	−10867.3	−0.00300607
$421$	−2.31530e6	−0.636651	−0.318326	−	0.947981i	$-0.603121\pi$
$421$	−2.31530e6	−0.636651	−0.318326	+	0.947981i	$0.603121\pi$
$422$	−2.18927e6	−0.598436
$423$	−3.34853e6	−0.909920
$424$	2.30287e6	0.622091
$425$	−433581.	−0.116439
$426$	30133.1	0.00804489
$427$	−376166.	−0.0998412
$428$	−1.09579e7	−2.89147
$429$	−69357.5	−0.0181949
$430$	−2.12098e6	−0.553178
$431$	5.32857e6	1.38171	0.690856	−	0.722992i	$-0.257234\pi$
$431$	5.32857e6	1.38171	0.690856	+	0.722992i	$0.257234\pi$
$432$	−82308.9	−0.0212196
$433$	−7.30765e6	−1.87309	−0.936544	−	0.350550i	$-0.885995\pi$
$433$	−7.30765e6	−1.87309	−0.936544	+	0.350550i	$0.885995\pi$
$434$	2.28269e6	0.581730
$435$	576.981	0.000146197 0
$436$	−6.10021e6	−1.53684
$437$	−1.83965e6	−0.460819
$438$	−30217.9	−0.00752626
$439$	−1.22233e6	−0.302711	−0.151355	−	0.988479i	$-0.548364\pi$
$439$	−1.22233e6	−0.302711	−0.151355	+	0.988479i	$0.548364\pi$
$440$	5.77196e6	1.42132
$441$	−583400.	−0.142847
$442$	5.30639e6	1.29194
$443$	−4.69869e6	−1.13754	−0.568771	−	0.822496i	$-0.692581\pi$
$443$	−4.69869e6	−1.13754	−0.568771	+	0.822496i	$0.692581\pi$
$444$	117946.	0.0283940
$445$	−915882.	−0.219250
$446$	7.38391e6	1.75772
$447$	62100.5	0.0147003
$448$	1.19083e6	0.280322
$449$	4.75176e6	1.11234	0.556171	−	0.831068i	$-0.312270\pi$
$449$	4.75176e6	1.11234	0.556171	+	0.831068i	$0.312270\pi$
$450$	−1.50714e6	−0.350852
$451$	1.39618e7	3.23221
$452$	−9.81024e6	−2.25857
$453$	−20912.8	−0.00478813
$454$	−3.15934e6	−0.719377
$455$	944158.	0.213804
$456$	−63559.3	−0.0143142
$457$	−5.17959e6	−1.16012	−0.580062	−	0.814572i	$-0.696972\pi$
$457$	−5.17959e6	−1.16012	−0.580062	+	0.814572i	$0.696972\pi$
$458$	1.42667e7	3.17804
$459$	44981.0	0.00996547
$460$	2.19735e6	0.484177
$461$	685554.	0.150241	0.0751206	−	0.997174i	$-0.476066\pi$
$461$	685554.	0.150241	0.0751206	+	0.997174i	$0.476066\pi$
$462$	−43760.4	−0.00953841
$463$	3.43842e6	0.745429	0.372714	−	0.927946i	$-0.378427\pi$
$463$	3.43842e6	0.745429	0.372714	+	0.927946i	$0.378427\pi$
$464$	219589.	0.0473496
$465$	−15657.0	−0.00335796
$466$	−1.90739e6	−0.406888
$467$	4.97787e6	1.05621	0.528107	−	0.849178i	$-0.322902\pi$
$467$	4.97787e6	1.05621	0.528107	+	0.849178i	$0.322902\pi$
$468$	1.24524e7	2.62807
$469$	2.40296e6	0.504447
$470$	3.41916e6	0.713962
$471$	−52766.1	−0.0109598
$472$	1.31849e7	2.72409
$473$	−5.76584e6	−1.18498
$474$	26694.9	0.00545736
$475$	−869809.	−0.176885
$476$	2.26024e6	0.457233
$477$	−1.63466e6	−0.328950
$478$	−7.77551e6	−1.55654
$479$	−4.65268e6	−0.926540	−0.463270	−	0.886217i	$-0.653324\pi$
$479$	−4.65268e6	−0.926540	−0.463270	+	0.886217i	$0.653324\pi$
$480$	5484.66	0.00108654
$481$	−1.02472e7	−2.01949
$482$	−8.27044e6	−1.62148
$483$	−8641.81	−0.00168553
$484$	1.95397e7	3.79145
$485$	3.68079e6	0.710538
$486$	234536.	0.0450422
$487$	−3.55267e6	−0.678786	−0.339393	−	0.940645i	$-0.610222\pi$
$487$	−3.55267e6	−0.678786	−0.339393	+	0.940645i	$0.610222\pi$
$488$	2.62785e6	0.499517
$489$	48322.6	0.00913856
$490$	595706.	0.112084
$491$	−7.33350e6	−1.37280	−0.686401	−	0.727224i	$-0.740810\pi$
$491$	−7.33350e6	−1.37280	−0.686401	+	0.727224i	$0.740810\pi$
$492$	183637.	0.0342017
$493$	−120004.	−0.0222370
$494$	1.06452e7	1.96262
$495$	−4.09714e6	−0.751567
$496$	−5.95879e6	−1.08756
$497$	−1.11512e6	−0.202503
$498$	−143323.	−0.0258966
$499$	−6.53921e6	−1.17564	−0.587819	−	0.808992i	$-0.700013\pi$
$499$	−6.53921e6	−1.17564	−0.587819	+	0.808992i	$0.700013\pi$
$500$	1.03894e6	0.185850
$501$	25016.4	0.00445277
$502$	−3.08306e6	−0.546039
$503$	6.11279e6	1.07726	0.538629	−	0.842543i	$-0.318943\pi$
$503$	6.11279e6	1.07726	0.538629	+	0.842543i	$0.318943\pi$
$504$	4.07556e6	0.714679
$505$	−2.66616e6	−0.465220
$506$	8.84824e6	1.53632
$507$	29719.0	0.00513469
$508$	−6.99657e6	−1.20289
$509$	1.07468e7	1.83859	0.919295	−	0.393569i	$-0.128760\pi$
$509$	1.07468e7	1.83859	0.919295	+	0.393569i	$0.128760\pi$
$510$	−22964.1	−0.00390952
$511$	1.11826e6	0.189448
$512$	−1.18177e7	−1.99232
$513$	90236.6	0.0151387
$514$	−6.93088e6	−1.15713
$515$	−2.18650e6	−0.363271
$516$	−75837.3	−0.0125389
$517$	9.29493e6	1.52939
$518$	−6.46536e6	−1.05869
$519$	−10849.5	−0.00176804
$520$	−6.59577e6	−1.06969
$521$	−1.11135e7	−1.79373	−0.896866	−	0.442302i	$-0.854162\pi$
$521$	−1.11135e7	−1.79373	−0.896866	+	0.442302i	$0.854162\pi$
$522$	−417136.	−0.0670042
$523$	−277156.	−0.0443067	−0.0221534	−	0.999755i	$-0.507052\pi$
$523$	−277156.	−0.0443067	−0.0221534	+	0.999755i	$0.507052\pi$
$524$	2.17506e7	3.46053
$525$	−4085.96	−0.000646988 0
$526$	5.70643e6	0.899290
$527$	3.25642e6	0.510757
$528$	114233.	0.0178323
$529$	−4.68899e6	−0.728518
$530$	1.66914e6	0.258109
$531$	−9.35911e6	−1.44045
$532$	4.53428e6	0.694591
$533$	−1.59545e7	−2.43257
$534$	−48508.5	−0.00736148
$535$	−4.12002e6	−0.622322
$536$	−1.67868e7	−2.52381
$537$	−97210.3	−0.0145471
$538$	−2.45033e6	−0.364980
$539$	1.61942e6	0.240097
$540$	−107782.	−0.0159061
$541$	7.89961e6	1.16041	0.580207	−	0.814469i	$-0.302972\pi$
$541$	7.89961e6	1.16041	0.580207	+	0.814469i	$0.302972\pi$
$542$	−1.28049e7	−1.87231
$543$	97019.0	0.0141207
$544$	−1.14073e6	−0.165266
$545$	−2.29359e6	−0.330769
$546$	50006.1	0.00717863
$547$	−7.01645e6	−1.00265	−0.501325	−	0.865259i	$-0.667154\pi$
$547$	−7.01645e6	−1.00265	−0.501325	+	0.865259i	$0.667154\pi$
$548$	7.10300e6	1.01039
$549$	−1.86534e6	−0.264136
$550$	4.18357e6	0.589712
$551$	−240739.	−0.0337807
$552$	60370.6	0.00843291
$553$	−987885.	−0.137371
$554$	−9.61335e6	−1.33076
$555$	44346.1	0.00611115
$556$	5.99378e6	0.822268
$557$	5.34027e6	0.729332	0.364666	−	0.931138i	$-0.381183\pi$
$557$	5.34027e6	0.729332	0.364666	+	0.931138i	$0.381183\pi$
$558$	1.13194e7	1.53900
$559$	6.58878e6	0.891816
$560$	−1.55505e6	−0.209543
$561$	−62427.4	−0.00837468
$562$	1.36106e7	1.81776
$563$	3.95451e6	0.525801	0.262901	−	0.964823i	$-0.415321\pi$
$563$	3.95451e6	0.525801	0.262901	+	0.964823i	$0.415321\pi$
$564$	122255.	0.0161834
$565$	−3.68851e6	−0.486105
$566$	−1.50510e6	−0.197480
$567$	−2.89277e6	−0.377881
$568$	7.79009e6	1.01314
$569$	2.06862e6	0.267856	0.133928	−	0.990991i	$-0.457241\pi$
$569$	2.06862e6	0.267856	0.133928	+	0.990991i	$0.457241\pi$
$570$	−46068.3	−0.00593903
$571$	2.62182e6	0.336522	0.168261	−	0.985742i	$-0.446185\pi$
$571$	2.62182e6	0.336522	0.168261	+	0.985742i	$0.446185\pi$
$572$	−3.45655e7	−4.41726
$573$	−19309.3	−0.00245685
$574$	−1.00663e7	−1.27524
$575$	826171.	0.104208
$576$	5.90514e6	0.741607
$577$	4.89383e6	0.611940	0.305970	−	0.952041i	$-0.401019\pi$
$577$	4.89383e6	0.611940	0.305970	+	0.952041i	$0.401019\pi$
$578$	−9.31491e6	−1.15974
$579$	20774.3	0.00257532
$580$	287549.	0.0354929
$581$	5.30388e6	0.651859
$582$	194949.	0.0238568
$583$	4.53752e6	0.552901
$584$	−7.81200e6	−0.947830
$585$	4.68191e6	0.565631
$586$	5.62180e6	0.676288
$587$	3.88480e6	0.465343	0.232672	−	0.972555i	$-0.425253\pi$
$587$	3.88480e6	0.465343	0.232672	+	0.972555i	$0.425253\pi$
$588$	21300.0	0.00254060
$589$	6.53272e6	0.775900
$590$	9.55653e6	1.13024
$591$	−63562.1	−0.00748565
$592$	1.68774e7	1.97925
$593$	9.98996e6	1.16661	0.583307	−	0.812252i	$-0.301759\pi$
$593$	9.98996e6	1.16661	0.583307	+	0.812252i	$0.301759\pi$
$594$	−434016.	−0.0504707
$595$	849820.	0.0984089
$596$	3.09489e7	3.56886
$597$	−21673.2	−0.00248879
$598$	−1.01111e7	−1.15623
$599$	−9.87104e6	−1.12408	−0.562038	−	0.827111i	$-0.689983\pi$
$599$	−9.87104e6	−1.12408	−0.562038	+	0.827111i	$0.689983\pi$
$600$	28544.0	0.00323696
$601$	−320717.	−0.0362190	−0.0181095	−	0.999836i	$-0.505765\pi$
$601$	−320717.	−0.0362190	−0.0181095	+	0.999836i	$0.505765\pi$
$602$	4.15712e6	0.467521
$603$	1.19159e7	1.33454
$604$	−1.04223e7	−1.16244
$605$	7.34667e6	0.816022
$606$	−141210.	−0.0156201
$607$	963709.	0.106163	0.0530816	−	0.998590i	$-0.483096\pi$
$607$	963709.	0.106163	0.0530816	+	0.998590i	$0.483096\pi$
$608$	−2.28842e6	−0.251059
$609$	−1130.88	−0.000123559 0
$610$	1.90469e6	0.207252
$611$	−1.06216e7	−1.15103
$612$	1.12081e7	1.20964
$613$	1.31019e6	0.140826	0.0704129	−	0.997518i	$-0.477568\pi$
$613$	1.31019e6	0.140826	0.0704129	+	0.997518i	$0.477568\pi$
$614$	−1.61018e7	−1.72367
$615$	69045.0	0.00736113
$616$	−1.13130e7	−1.20123
$617$	−1.01289e7	−1.07115	−0.535575	−	0.844488i	$-0.679905\pi$
$617$	−1.01289e7	−1.07115	−0.535575	+	0.844488i	$0.679905\pi$
$618$	−115805.	−0.0121971
$619$	−2.79242e6	−0.292923	−0.146462	−	0.989216i	$-0.546789\pi$
$619$	−2.79242e6	−0.292923	−0.146462	+	0.989216i	$0.546789\pi$
$620$	−7.80294e6	−0.815228
$621$	−85709.5	−0.00891867
$622$	−4.55338e6	−0.471909
$623$	1.79513e6	0.185300
$624$	−130537.	−0.0134206
$625$	390625.	0.0400000
$626$	−7.00859e6	−0.714817
$627$	−125236.	−0.0127221
$628$	−2.62969e7	−2.66076
$629$	−9.22332e6	−0.929525
$630$	2.95400e6	0.296524
$631$	−4.46346e6	−0.446271	−0.223135	−	0.974787i	$-0.571629\pi$
$631$	−4.46346e6	−0.446271	−0.223135	+	0.974787i	$0.571629\pi$
$632$	6.90124e6	0.687281
$633$	−29431.8	−0.00291950
$634$	−1.11546e7	−1.10213
$635$	−2.63061e6	−0.258894
$636$	59681.4	0.00585054
$637$	−1.85055e6	−0.180697
$638$	1.15790e6	0.112621
$639$	−5.52968e6	−0.535732
$640$	−7.34517e6	−0.708846
$641$	5.63340e6	0.541534	0.270767	−	0.962645i	$-0.412723\pi$
$641$	5.63340e6	0.541534	0.270767	+	0.962645i	$0.412723\pi$
$642$	−218212.	−0.0208949
$643$	6.56955e6	0.626626	0.313313	−	0.949650i	$-0.398561\pi$
$643$	6.56955e6	0.626626	0.313313	+	0.949650i	$0.398561\pi$
$644$	−4.30680e6	−0.409204
$645$	−28513.8	−0.00269870
$646$	9.58153e6	0.903345
$647$	1.26415e7	1.18724	0.593621	−	0.804745i	$-0.297698\pi$
$647$	1.26415e7	1.18724	0.593621	+	0.804745i	$0.297698\pi$
$648$	2.02085e7	1.89059
$649$	2.59792e7	2.42111
$650$	−4.78067e6	−0.443818
$651$	30687.7	0.00283800
$652$	2.40824e7	2.21861
$653$	−3.52591e6	−0.323585	−0.161792	−	0.986825i	$-0.551727\pi$
$653$	−3.52591e6	−0.323585	−0.161792	+	0.986825i	$0.551727\pi$
$654$	−121477.	−0.0111058
$655$	8.17792e6	0.744800
$656$	2.62774e7	2.38409
$657$	5.54524e6	0.501195
$658$	−6.70156e6	−0.603408
$659$	228429.	0.0204898	0.0102449	−	0.999948i	$-0.496739\pi$
$659$	228429.	0.0204898	0.0102449	+	0.999948i	$0.496739\pi$
$660$	149587.	0.0133670
$661$	−5.75333e6	−0.512172	−0.256086	−	0.966654i	$-0.582433\pi$
$661$	−5.75333e6	−0.512172	−0.256086	+	0.966654i	$0.582433\pi$
$662$	2.83383e7	2.51321
$663$	71337.5	0.00630280
$664$	−3.70522e7	−3.26133
$665$	1.70483e6	0.149495
$666$	−3.20606e7	−2.80082
$667$	228662.	0.0199012
$668$	1.24674e7	1.08102
$669$	99267.0	0.00857511
$670$	−1.21672e7	−1.04714
$671$	5.17786e6	0.443960
$672$	−10749.9	−0.000918296 0
$673$	−2.78862e6	−0.237330	−0.118665	−	0.992934i	$-0.537861\pi$
$673$	−2.78862e6	−0.237330	−0.118665	+	0.992934i	$0.537861\pi$
$674$	8.10611e6	0.687326
$675$	−40524.6	−0.00342341
$676$	1.48110e7	1.24657
$677$	1.80943e7	1.51729	0.758647	−	0.651502i	$-0.225861\pi$
$677$	1.80943e7	1.51729	0.758647	+	0.651502i	$0.225861\pi$
$678$	−195357.	−0.0163213
$679$	−7.21436e6	−0.600514
$680$	−5.93673e6	−0.492351
$681$	−42473.1	−0.00350951
$682$	−3.14207e7	−2.58676
$683$	9.00064e6	0.738281	0.369141	−	0.929374i	$-0.379652\pi$
$683$	9.00064e6	0.738281	0.369141	+	0.929374i	$0.379652\pi$
$684$	2.24847e7	1.83758
$685$	2.67063e6	0.217464
$686$	−1.16758e6	−0.0947279
$687$	191797.	0.0155042
$688$	−1.08519e7	−0.874043
$689$	−5.18514e6	−0.416114
$690$	43757.1	0.00349886
$691$	−2.07405e7	−1.65243	−0.826216	−	0.563353i	$-0.809511\pi$
$691$	−2.07405e7	−1.65243	−0.826216	+	0.563353i	$0.809511\pi$
$692$	−5.40704e6	−0.429234
$693$	8.03040e6	0.635190
$694$	−1.65733e7	−1.30620
$695$	2.25358e6	0.176974
$696$	7900.21	0.000618181 0
$697$	−1.43603e7	−1.11965
$698$	2.30862e7	1.79355
$699$	−25642.3	−0.00198502
$700$	−2.03631e6	−0.157072
$701$	−1.30675e7	−1.00438	−0.502188	−	0.864758i	$-0.667472\pi$
$701$	−1.30675e7	−1.00438	−0.502188	+	0.864758i	$0.667472\pi$
$702$	495961.	0.0379843
$703$	−1.85029e7	−1.41206
$704$	−1.63916e7	−1.24649
$705$	45966.1	0.00348309
$706$	1.89952e7	1.43427
$707$	5.22568e6	0.393183
$708$	341701.	0.0256191
$709$	1.04313e7	0.779334	0.389667	−	0.920956i	$-0.372590\pi$
$709$	1.04313e7	0.779334	0.389667	+	0.920956i	$0.372590\pi$
$710$	5.64632e6	0.420359
$711$	−4.89874e6	−0.363422
$712$	−1.25405e7	−0.927078
$713$	−6.20498e6	−0.457105
$714$	45009.6	0.00330415
$715$	−1.29962e7	−0.950714
$716$	−4.84465e7	−3.53167
$717$	−104531.	−0.00759363
$718$	1.42202e7	1.02943
$719$	−2.21542e6	−0.159821	−0.0799104	−	0.996802i	$-0.525463\pi$
$719$	−2.21542e6	−0.159821	−0.0799104	+	0.996802i	$0.525463\pi$
$720$	−7.71121e6	−0.554359
$721$	4.28553e6	0.307020
$722$	−5.35203e6	−0.382099
$723$	−111185.	−0.00791045
$724$	4.83512e7	3.42815
$725$	108114.	0.00763903
$726$	389107.	0.0273985
$727$	−2.78699e7	−1.95569	−0.977844	−	0.209335i	$-0.932870\pi$
$727$	−2.78699e7	−1.95569	−0.977844	+	0.209335i	$0.932870\pi$
$728$	1.29277e7	0.904051
$729$	−1.43426e7	−0.999561
$730$	−5.66221e6	−0.393259
$731$	5.93044e6	0.410481
$732$	68103.6	0.00469778
$733$	1.39510e7	0.959059	0.479530	−	0.877526i	$-0.340807\pi$
$733$	1.39510e7	0.959059	0.479530	+	0.877526i	$0.340807\pi$
$734$	3.03963e6	0.208248
$735$	8008.49	0.000546805 0
$736$	2.17361e6	0.147906
$737$	−3.30764e7	−2.24310
$738$	−4.99170e7	−3.37371
$739$	1.31926e7	0.888624	0.444312	−	0.895872i	$-0.353448\pi$
$739$	1.31926e7	0.888624	0.444312	+	0.895872i	$0.353448\pi$
$740$	2.21007e7	1.48363
$741$	143110.	0.00957470
$742$	−3.27151e6	−0.218142
$743$	8.04528e6	0.534650	0.267325	−	0.963606i	$-0.413860\pi$
$743$	8.04528e6	0.534650	0.267325	+	0.963606i	$0.413860\pi$
$744$	−214380.	−0.0141988
$745$	1.16363e7	0.768114
$746$	2.98762e7	1.96552
$747$	2.63010e7	1.72453
$748$	−3.11118e7	−2.03316
$749$	8.07524e6	0.525958
$750$	20689.0	0.00134303
$751$	7.74693e6	0.501221	0.250611	−	0.968088i	$-0.419369\pi$
$751$	7.74693e6	0.501221	0.250611	+	0.968088i	$0.419369\pi$
$752$	1.74939e7	1.12809
$753$	−41447.7	−0.00266387
$754$	−1.32316e6	−0.0847586
$755$	−3.91862e6	−0.250188
$756$	211253.	0.0134431
$757$	4.44611e6	0.281994	0.140997	−	0.990010i	$-0.454969\pi$
$757$	4.44611e6	0.281994	0.140997	+	0.990010i	$0.454969\pi$
$758$	2.58638e7	1.63500
$759$	118953.	0.00749498
$760$	−1.19097e7	−0.747940
$761$	−7.94660e6	−0.497416	−0.248708	−	0.968579i	$-0.580006\pi$
$761$	−7.94660e6	−0.497416	−0.248708	+	0.968579i	$0.580006\pi$
$762$	−139327.	−0.00869256
$763$	4.49544e6	0.279551
$764$	−9.62313e6	−0.596462
$765$	4.21410e6	0.260346
$766$	2.37767e6	0.146413
$767$	−2.96872e7	−1.82213
$768$	−285269.	−0.0174523
$769$	1.94209e7	1.18428	0.592139	−	0.805836i	$-0.298284\pi$
$769$	1.94209e7	1.18428	0.592139	+	0.805836i	$0.298284\pi$
$770$	−8.19979e6	−0.498398
$771$	−93176.5	−0.00564508
$772$	1.03533e7	0.625221
$773$	2.88010e7	1.73364	0.866821	−	0.498620i	$-0.166160\pi$
$773$	2.88010e7	1.73364	0.866821	+	0.498620i	$0.166160\pi$
$774$	2.06144e7	1.23685
$775$	−2.93380e6	−0.175459
$776$	5.03986e7	3.00444
$777$	−86918.3	−0.00516486
$778$	3.80115e7	2.25147
$779$	−2.88083e7	−1.70088
$780$	−170937.	−0.0100600
$781$	1.53494e7	0.900460
$782$	−9.10083e6	−0.532187
$783$	−11216.1	−0.000653789 0
$784$	3.04790e6	0.177096
$785$	−9.88727e6	−0.572667
$786$	433133.	0.0250072
$787$	−2.83115e7	−1.62939	−0.814695	−	0.579889i	$-0.803096\pi$
$787$	−2.83115e7	−1.62939	−0.814695	+	0.579889i	$0.803096\pi$
$788$	−3.16773e7	−1.81732
$789$	76715.4	0.00438722
$790$	5.00208e6	0.285156
$791$	7.22949e6	0.410834
$792$	−5.60993e7	−3.17793
$793$	−5.91687e6	−0.334125
$794$	4.83995e7	2.72452
$795$	22439.4	0.00125919
$796$	−1.08012e7	−0.604215
$797$	1.04940e7	0.585187	0.292594	−	0.956237i	$-0.405482\pi$
$797$	1.04940e7	0.585187	0.292594	+	0.956237i	$0.405482\pi$
$798$	90293.9	0.00501939
$799$	−9.56027e6	−0.529789
$800$	1.02771e6	0.0567736
$801$	8.90172e6	0.490222
$802$	1.74787e7	0.959563
$803$	−1.53926e7	−0.842410
$804$	−435049.	−0.0237355
$805$	−1.61930e6	−0.0880717
$806$	3.59053e7	1.94680
$807$	−32941.4	−0.00178057
$808$	−3.65059e7	−1.96714
$809$	2.52546e6	0.135665	0.0678326	−	0.997697i	$-0.478392\pi$
$809$	2.52546e6	0.135665	0.0678326	+	0.997697i	$0.478392\pi$
$810$	1.46473e7	0.784413
$811$	−1.20569e7	−0.643698	−0.321849	−	0.946791i	$-0.604304\pi$
$811$	−1.20569e7	−0.643698	−0.321849	+	0.946791i	$0.604304\pi$
$812$	−563596.	−0.0299970
$813$	−172145.	−0.00913412
$814$	8.89945e7	4.70763
$815$	9.05465e6	0.477505
$816$	−117494.	−0.00617720
$817$	1.18971e7	0.623570
$818$	−1.03847e7	−0.542639
$819$	−9.17654e6	−0.478046
$820$	3.44098e7	1.78710
$821$	−602636.	−0.0312031	−0.0156015	−	0.999878i	$-0.504966\pi$
$821$	−602636.	−0.0312031	−0.0156015	+	0.999878i	$0.504966\pi$
$822$	141446.	0.00730150
$823$	1.05065e7	0.540702	0.270351	−	0.962762i	$-0.412860\pi$
$823$	1.05065e7	0.540702	0.270351	+	0.962762i	$0.412860\pi$
$824$	−2.99382e7	−1.53606
$825$	56242.5	0.00287693
$826$	−1.87308e7	−0.955226
$827$	3.20441e7	1.62924	0.814619	−	0.579997i	$-0.196946\pi$
$827$	3.20441e7	1.62924	0.814619	+	0.579997i	$0.196946\pi$
$828$	−2.13566e7	−1.08257
$829$	1.14547e7	0.578892	0.289446	−	0.957194i	$-0.406529\pi$
$829$	1.14547e7	0.578892	0.289446	+	0.957194i	$0.406529\pi$
$830$	−2.68558e7	−1.35314
$831$	−129239.	−0.00649218
$832$	1.87311e7	0.938114
$833$	−1.66565e6	−0.0831707
$834$	119358.	0.00594204
$835$	4.68755e6	0.232664
$836$	−6.24135e7	−3.08861
$837$	304361.	0.0150167
$838$	−9.53152e6	−0.468870
$839$	−2.57923e7	−1.26499	−0.632493	−	0.774566i	$-0.717968\pi$
$839$	−2.57923e7	−1.26499	−0.632493	+	0.774566i	$0.717968\pi$
$840$	−55946.3	−0.00273573
$841$	−2.04812e7	−0.998541
$842$	−2.29777e7	−1.11693
$843$	182977.	0.00886803
$844$	−1.46679e7	−0.708780
$845$	5.56872e6	0.268296
$846$	−3.32318e7	−1.59635
$847$	−1.43995e7	−0.689665
$848$	8.54004e6	0.407822
$849$	−20234.0	−0.000963415 0
$850$	−4.30300e6	−0.204279
$851$	1.75747e7	0.831884
$852$	201889.	0.00952826
$853$	1.61523e7	0.760082	0.380041	−	0.924970i	$-0.375910\pi$
$853$	1.61523e7	0.760082	0.380041	+	0.924970i	$0.375910\pi$
$854$	−3.73319e6	−0.175160
$855$	8.45393e6	0.395497
$856$	−5.64126e7	−2.63143
$857$	−6.83810e6	−0.318041	−0.159021	−	0.987275i	$-0.550834\pi$
$857$	−6.83810e6	−0.318041	−0.159021	+	0.987275i	$0.550834\pi$
$858$	−688325.	−0.0319209
$859$	−3.00489e7	−1.38946	−0.694729	−	0.719272i	$-0.744476\pi$
$859$	−3.00489e7	−1.38946	−0.694729	+	0.719272i	$0.744476\pi$
$860$	−1.42103e7	−0.655177
$861$	−135328.	−0.00622129
$862$	5.28824e7	2.42406
$863$	−2.77866e7	−1.27001	−0.635007	−	0.772506i	$-0.719003\pi$
$863$	−2.77866e7	−1.27001	−0.635007	+	0.772506i	$0.719003\pi$
$864$	−106618.	−0.00485899
$865$	−2.03297e6	−0.0923828
$866$	−7.25234e7	−3.28612
$867$	−125227.	−0.00565782
$868$	1.52938e7	0.688994
$869$	1.35981e7	0.610840
$870$	5726.14	0.000256486 0
$871$	3.77972e7	1.68816
$872$	−3.14046e7	−1.39863
$873$	−3.57747e7	−1.58869
$874$	−1.82572e7	−0.808455
$875$	−765625.	−0.0338062
$876$	−202457.	−0.00891399
$877$	7.87461e6	0.345724	0.172862	−	0.984946i	$-0.444698\pi$
$877$	7.87461e6	0.345724	0.172862	+	0.984946i	$0.444698\pi$
$878$	−1.21308e7	−0.531072
$879$	75577.7	0.00329930
$880$	2.14050e7	0.931768
$881$	−1.03666e7	−0.449983	−0.224991	−	0.974361i	$-0.572235\pi$
$881$	−1.03666e7	−0.449983	−0.224991	+	0.974361i	$0.572235\pi$
$882$	−5.78984e6	−0.250608
$883$	2.77598e7	1.19816	0.599080	−	0.800689i	$-0.295533\pi$
$883$	2.77598e7	1.19816	0.599080	+	0.800689i	$0.295533\pi$
$884$	3.55523e7	1.53016
$885$	128475.	0.00551392
$886$	−4.66312e7	−1.99569
$887$	2.05935e7	0.878863	0.439432	−	0.898276i	$-0.355180\pi$
$887$	2.05935e7	0.878863	0.439432	+	0.898276i	$0.355180\pi$
$888$	607200.	0.0258404
$889$	5.15600e6	0.218805
$890$	−9.08949e6	−0.384649
$891$	3.98184e7	1.68031
$892$	4.94715e7	2.08182
$893$	−1.91789e7	−0.804813
$894$	616304.	0.0257900
$895$	−1.82152e7	−0.760110
$896$	1.43965e7	0.599084
$897$	−135931.	−0.00564074
$898$	4.71579e7	1.95148
$899$	−811995.	−0.0335084
$900$	−1.00977e7	−0.415544
$901$	−4.66705e6	−0.191527
$902$	1.38561e8	5.67054
$903$	55887.0	0.00228082
$904$	−5.05043e7	−2.05545
$905$	1.81794e7	0.737831
$906$	−207545.	−0.00840023
$907$	−1.66276e7	−0.671136	−0.335568	−	0.942016i	$-0.608928\pi$
$907$	−1.66276e7	−0.671136	−0.335568	+	0.942016i	$0.608928\pi$
$908$	−2.11672e7	−0.852020
$909$	2.59132e7	1.04019
$910$	9.37011e6	0.375095
$911$	2.47318e7	0.987323	0.493662	−	0.869654i	$-0.335658\pi$
$911$	2.47318e7	0.987323	0.493662	+	0.869654i	$0.335658\pi$
$912$	−235706.	−0.00938389
$913$	−7.30069e7	−2.89859
$914$	−5.14038e7	−2.03531
$915$	25606.0	0.00101109
$916$	9.55853e7	3.76402
$917$	−1.60287e7	−0.629471
$918$	446406.	0.0174833
$919$	−2.32360e7	−0.907555	−0.453777	−	0.891115i	$-0.649924\pi$
$919$	−2.32360e7	−0.907555	−0.453777	+	0.891115i	$0.649924\pi$
$920$	1.13122e7	0.440633
$921$	−216468.	−0.00840900
$922$	6.80365e6	0.263581
$923$	−1.75402e7	−0.677688
$924$	−293190.	−0.0112972
$925$	8.30954e6	0.319317
$926$	3.41239e7	1.30777
$927$	2.12512e7	0.812239
$928$	284443.	0.0108424
$929$	1.23886e7	0.470960	0.235480	−	0.971879i	$-0.424334\pi$
$929$	1.23886e7	0.470960	0.235480	+	0.971879i	$0.424334\pi$
$930$	−155385.	−0.00589116
$931$	−3.34146e6	−0.126346
$932$	−1.27793e7	−0.481912
$933$	−61214.2	−0.00230223
$934$	4.94019e7	1.85301
$935$	−1.16976e7	−0.437591
$936$	6.41062e7	2.39172
$937$	−1.87333e7	−0.697050	−0.348525	−	0.937299i	$-0.613317\pi$
$937$	−1.87333e7	−0.697050	−0.348525	+	0.937299i	$0.613317\pi$
$938$	2.38478e7	0.884994
$939$	−94221.2	−0.00348726
$940$	2.29080e7	0.845607
$941$	−1.50137e6	−0.0552730	−0.0276365	−	0.999618i	$-0.508798\pi$
$941$	−1.50137e6	−0.0552730	−0.0276365	+	0.999618i	$0.508798\pi$
$942$	−523667.	−0.0192277
$943$	2.73630e7	1.00204
$944$	4.88954e7	1.78582
$945$	79428.2	0.00289331
$946$	−5.72220e7	−2.07891
$947$	−3.39097e7	−1.22871	−0.614354	−	0.789030i	$-0.710583\pi$
$947$	−3.39097e7	−1.22871	−0.614354	+	0.789030i	$0.710583\pi$
$948$	178853.	0.00646363
$949$	1.75895e7	0.633999
$950$	−8.63225e6	−0.310324
$951$	−149959.	−0.00537678
$952$	1.16360e7	0.416113
$953$	−3.76399e7	−1.34251	−0.671253	−	0.741228i	$-0.734244\pi$
$953$	−3.76399e7	−1.34251	−0.671253	+	0.741228i	$0.734244\pi$
$954$	−1.62228e7	−0.577106
$955$	−3.61816e6	−0.128375
$956$	−5.20951e7	−1.84354
$957$	15566.4	0.000549425 0
$958$	−4.61746e7	−1.62551
$959$	−5.23443e6	−0.183790
$960$	−81061.4	−0.00283881
$961$	−6.59482e6	−0.230353
$962$	−1.01696e8	−3.54297
$963$	4.00437e7	1.39145
$964$	−5.54111e7	−1.92046
$965$	3.89268e6	0.134564
$966$	−85763.9	−0.00295707
$967$	−2.61787e6	−0.0900291	−0.0450145	−	0.998986i	$-0.514333\pi$
$967$	−2.61787e6	−0.0900291	−0.0450145	+	0.998986i	$0.514333\pi$
$968$	1.00593e8	3.45047
$969$	128811.	0.00440701
$970$	3.65293e7	1.24656
$971$	−2.74511e7	−0.934353	−0.467177	−	0.884164i	$-0.654729\pi$
$971$	−2.74511e7	−0.934353	−0.467177	+	0.884164i	$0.654729\pi$
$972$	1.57137e6	0.0533473
$973$	−4.41701e6	−0.149571
$974$	−3.52578e7	−1.19085
$975$	−64269.8	−0.00216519
$976$	9.74521e6	0.327466
$977$	−8.94121e6	−0.299681	−0.149841	−	0.988710i	$-0.547876\pi$
$977$	−8.94121e6	−0.299681	−0.149841	+	0.988710i	$0.547876\pi$
$978$	479568.	0.0160326
$979$	−2.47096e7	−0.823966
$980$	3.99117e6	0.132750
$981$	2.22921e7	0.739568
$982$	−7.27799e7	−2.40842
$983$	5.16638e7	1.70531	0.852653	−	0.522478i	$-0.174992\pi$
$983$	5.16638e7	1.70531	0.852653	+	0.522478i	$0.174992\pi$
$984$	945386.	0.0311259
$985$	−1.19102e7	−0.391137
$986$	−1.19095e6	−0.0390123
$987$	−90093.6	−0.00294375
$988$	7.13216e7	2.32449
$989$	−1.13002e7	−0.367363
$990$	−4.06613e7	−1.31854
$991$	5.83498e7	1.88736	0.943682	−	0.330855i	$-0.107337\pi$
$991$	5.83498e7	1.88736	0.943682	+	0.330855i	$0.107337\pi$
$992$	−7.71865e6	−0.249036
$993$	380972.	0.0122608
$994$	−1.10668e7	−0.355268
$995$	−4.06112e6	−0.130043
$996$	−960250.	−0.0306716
$997$	3.90170e6	0.124313	0.0621565	−	0.998066i	$-0.480202\pi$
$997$	3.90170e6	0.124313	0.0621565	+	0.998066i	$0.480202\pi$
$998$	−6.48971e7	−2.06252
$999$	−862056.	−0.0273289

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.6.a.d.1.4	✓	4
3.2	odd	2		315.6.a.l.1.1		4
4.3	odd	2		560.6.a.v.1.3		4
5.2	odd	4		175.6.b.f.99.8		8
5.3	odd	4		175.6.b.f.99.1		8
5.4	even	2		175.6.a.f.1.1		4
7.6	odd	2		245.6.a.e.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.6.a.d.1.4	✓	4	1.1	even	1	trivial
175.6.a.f.1.1		4	5.4	even	2
175.6.b.f.99.1		8	5.3	odd	4
175.6.b.f.99.8		8	5.2	odd	4
245.6.a.e.1.4		4	7.6	odd	2
315.6.a.l.1.1		4	3.2	odd	2
560.6.a.v.1.3		4	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	35.a (trivial)

\(f(q)\)	\(=\)	\(q+9.92431 q^{2} +0.133419 q^{3} +66.4919 q^{4} +25.0000 q^{5} +1.32409 q^{6} -49.0000 q^{7} +342.308 q^{8} -242.982 q^{9} +248.108 q^{10} +674.476 q^{11} +8.87129 q^{12} -770.741 q^{13} -486.291 q^{14} +3.33548 q^{15} +1269.43 q^{16} -693.730 q^{17} -2411.43 q^{18} -1391.69 q^{19} +1662.30 q^{20} -6.53754 q^{21} +6693.71 q^{22} +1321.87 q^{23} +45.6704 q^{24} +625.000 q^{25} -7649.07 q^{26} -64.8394 q^{27} -3258.10 q^{28} +172.983 q^{29} +33.1023 q^{30} -4694.07 q^{31} +1644.34 q^{32} +89.9880 q^{33} -6884.79 q^{34} -1225.00 q^{35} -16156.3 q^{36} +13295.3 q^{37} -13811.6 q^{38} -102.832 q^{39} +8557.69 q^{40} +20700.2 q^{41} -64.8806 q^{42} -8548.62 q^{43} +44847.2 q^{44} -6074.55 q^{45} +13118.7 q^{46} +13781.0 q^{47} +169.366 q^{48} +2401.00 q^{49} +6202.69 q^{50} -92.5570 q^{51} -51248.0 q^{52} +6727.47 q^{53} -643.486 q^{54} +16861.9 q^{55} -16773.1 q^{56} -185.679 q^{57} +1716.74 q^{58} +38517.7 q^{59} +221.782 q^{60} +7676.86 q^{61} -46585.4 q^{62} +11906.1 q^{63} -24302.8 q^{64} -19268.5 q^{65} +893.069 q^{66} -49040.1 q^{67} -46127.4 q^{68} +176.363 q^{69} -12157.3 q^{70} +22757.6 q^{71} -83174.7 q^{72} -22821.6 q^{73} +131946. q^{74} +83.3870 q^{75} -92536.4 q^{76} -33049.3 q^{77} -1020.53 q^{78} +20160.9 q^{79} +31735.7 q^{80} +59036.0 q^{81} +205435. q^{82} -108242. q^{83} -434.693 q^{84} -17343.3 q^{85} -84839.2 q^{86} +23.0793 q^{87} +230878. q^{88} -36635.3 q^{89} -60285.7 q^{90} +37766.3 q^{91} +87893.9 q^{92} -626.280 q^{93} +136766. q^{94} -34792.4 q^{95} +219.386 q^{96} +147232. q^{97} +23828.3 q^{98} -163886. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 7 q^{2} + 14 q^{3} + 49 q^{4} + 100 q^{5} + 136 q^{6} - 196 q^{7} + 489 q^{8} + 774 q^{9} + 175 q^{10} + 770 q^{11} + 840 q^{12} + 58 q^{13} - 343 q^{14} + 350 q^{15} - 615 q^{16} + 2006 q^{17} - 1409 q^{18}+ \cdots - 420668 q^{99}+O(q^{100}) \) 4 * q + 7 * q^2 + 14 * q^3 + 49 * q^4 + 100 * q^5 + 136 * q^6 - 196 * q^7 + 489 * q^8 + 774 * q^9 + 175 * q^10 + 770 * q^11 + 840 * q^12 + 58 * q^13 - 343 * q^14 + 350 * q^15 - 615 * q^16 + 2006 * q^17 - 1409 * q^18 + 564 * q^19 + 1225 * q^20 - 686 * q^21 - 1736 * q^22 - 6340 * q^23 - 6244 * q^24 + 2500 * q^25 - 8730 * q^26 - 7438 * q^27 - 2401 * q^28 + 8066 * q^29 + 3400 * q^30 - 5856 * q^31 - 3495 * q^32 - 8130 * q^33 + 3402 * q^34 - 4900 * q^35 - 28759 * q^36 + 29544 * q^37 - 36860 * q^38 + 57466 * q^39 + 12225 * q^40 + 13156 * q^41 - 6664 * q^42 - 5692 * q^43 + 44952 * q^44 + 19350 * q^45 + 30928 * q^46 + 39926 * q^47 - 57156 * q^48 + 9604 * q^49 + 4375 * q^50 + 9830 * q^51 - 23398 * q^52 + 20300 * q^53 + 77292 * q^54 + 19250 * q^55 - 23961 * q^56 - 50876 * q^57 - 22234 * q^58 + 8432 * q^59 + 21000 * q^60 + 30540 * q^61 - 137568 * q^62 - 37926 * q^63 + 37121 * q^64 + 1450 * q^65 - 166756 * q^66 + 32792 * q^67 - 72554 * q^68 - 36540 * q^69 - 8575 * q^70 - 83920 * q^71 - 71795 * q^72 - 75424 * q^73 + 168762 * q^74 + 8750 * q^75 - 125092 * q^76 - 37730 * q^77 - 89204 * q^78 + 129486 * q^79 - 15375 * q^80 + 146308 * q^81 + 247230 * q^82 - 187520 * q^83 - 41160 * q^84 + 50150 * q^85 + 36156 * q^86 - 238670 * q^87 + 475556 * q^88 - 30324 * q^89 - 35225 * q^90 - 2842 * q^91 + 124464 * q^92 + 8256 * q^93 + 245756 * q^94 + 14100 * q^95 + 172340 * q^96 + 180270 * q^97 + 16807 * q^98 - 420668 * q^99

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