LMFDB - Embedded newform 35.6.a.d.1.2

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			1.2
Root			$4.73688$ 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)

$f(q)$	$=$	\(q-2.73688 q^{2} -28.3358 q^{3} -24.5095 q^{4} +25.0000 q^{5} +77.5516 q^{6} -49.0000 q^{7} +154.660 q^{8} +559.917 q^{9} -68.4220 q^{10} +63.4296 q^{11} +694.496 q^{12} -868.146 q^{13} +134.107 q^{14} -708.395 q^{15} +361.019 q^{16} +1189.74 q^{17} -1532.43 q^{18} +1532.71 q^{19} -612.737 q^{20} +1388.45 q^{21} -173.599 q^{22} -2337.74 q^{23} -4382.40 q^{24} +625.000 q^{25} +2376.01 q^{26} -8980.10 q^{27} +1200.97 q^{28} +8169.03 q^{29} +1938.79 q^{30} -2369.72 q^{31} -5937.17 q^{32} -1797.33 q^{33} -3256.18 q^{34} -1225.00 q^{35} -13723.3 q^{36} +12841.3 q^{37} -4194.85 q^{38} +24599.6 q^{39} +3866.49 q^{40} +1652.93 q^{41} -3800.03 q^{42} +12971.1 q^{43} -1554.63 q^{44} +13997.9 q^{45} +6398.11 q^{46} -6219.00 q^{47} -10229.8 q^{48} +2401.00 q^{49} -1710.55 q^{50} -33712.3 q^{51} +21277.8 q^{52} +19944.4 q^{53} +24577.5 q^{54} +1585.74 q^{55} -7578.32 q^{56} -43430.7 q^{57} -22357.7 q^{58} -30708.0 q^{59} +17362.4 q^{60} +19901.3 q^{61} +6485.64 q^{62} -27435.9 q^{63} +4696.70 q^{64} -21703.6 q^{65} +4919.07 q^{66} +31668.6 q^{67} -29160.0 q^{68} +66241.7 q^{69} +3352.68 q^{70} -32747.5 q^{71} +86596.6 q^{72} -54441.9 q^{73} -35145.0 q^{74} -17709.9 q^{75} -37566.1 q^{76} -3108.05 q^{77} -67326.1 q^{78} +47649.2 q^{79} +9025.48 q^{80} +118398. q^{81} -4523.87 q^{82} -56509.0 q^{83} -34030.3 q^{84} +29743.6 q^{85} -35500.2 q^{86} -231476. q^{87} +9810.00 q^{88} +2533.69 q^{89} -38310.6 q^{90} +42539.1 q^{91} +57296.8 q^{92} +67148.0 q^{93} +17020.7 q^{94} +38317.9 q^{95} +168235. q^{96} +58075.1 q^{97} -6571.25 q^{98} +35515.3 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.73688	−0.483816	−0.241908	−	0.970299i	$-0.577773\pi$
$2$	−2.73688	−0.483816	−0.241908	+	0.970299i	$0.577773\pi$
$3$	−28.3358	−1.81774	−0.908871	−	0.417077i	$-0.863054\pi$
$3$	−28.3358	−1.81774	−0.908871	+	0.417077i	$0.863054\pi$
$4$	−24.5095	−0.765922
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	77.5516	0.879453
$7$	−49.0000	−0.377964
$7$	−49.0000	−0.377964
$8$	154.660	0.854382
$9$	559.917	2.30419
$10$	−68.4220	−0.216369
$11$	63.4296	0.158056	0.0790279	−	0.996872i	$-0.474818\pi$
$11$	63.4296	0.158056	0.0790279	+	0.996872i	$0.474818\pi$
$12$	694.496	1.39225
$13$	−868.146	−1.42474	−0.712368	−	0.701806i	$-0.752377\pi$
$13$	−868.146	−1.42474	−0.712368	+	0.701806i	$0.752377\pi$
$14$	134.107	0.182865
$15$	−708.395	−0.812919
$16$	361.019	0.352558
$17$	1189.74	0.998460	0.499230	−	0.866469i	$-0.333616\pi$
$17$	1189.74	0.998460	0.499230	+	0.866469i	$0.333616\pi$
$18$	−1532.43	−1.11480
$19$	1532.71	0.974041	0.487020	−	0.873391i	$-0.338084\pi$
$19$	1532.71	0.974041	0.487020	+	0.873391i	$0.338084\pi$
$20$	−612.737	−0.342531
$21$	1388.45	0.687042
$22$	−173.599	−0.0764699
$23$	−2337.74	−0.921460	−0.460730	−	0.887540i	$-0.652412\pi$
$23$	−2337.74	−0.921460	−0.460730	+	0.887540i	$0.652412\pi$
$24$	−4382.40	−1.55305
$25$	625.000	0.200000
$26$	2376.01	0.689310
$27$	−8980.10	−2.37067
$28$	1200.97	0.289491
$29$	8169.03	1.80375	0.901874	−	0.432000i	$-0.142192\pi$
$29$	8169.03	1.80375	0.901874	+	0.432000i	$0.142192\pi$
$30$	1938.79	0.393303
$31$	−2369.72	−0.442887	−0.221444	−	0.975173i	$-0.571077\pi$
$31$	−2369.72	−0.442887	−0.221444	+	0.975173i	$0.571077\pi$
$32$	−5937.17	−1.02496
$33$	−1797.33	−0.287305
$34$	−3256.18	−0.483071
$35$	−1225.00	−0.169031
$36$	−13723.3	−1.76483
$37$	12841.3	1.54207	0.771035	−	0.636793i	$-0.219739\pi$
$37$	12841.3	1.54207	0.771035	+	0.636793i	$0.219739\pi$
$38$	−4194.85	−0.471257
$39$	24599.6	2.58980
$40$	3866.49	0.382091
$41$	1652.93	0.153566	0.0767830	−	0.997048i	$-0.475535\pi$
$41$	1652.93	0.153566	0.0767830	+	0.997048i	$0.475535\pi$
$42$	−3800.03	−0.332402
$43$	12971.1	1.06980	0.534902	−	0.844914i	$-0.320348\pi$
$43$	12971.1	1.06980	0.534902	+	0.844914i	$0.320348\pi$
$44$	−1554.63	−0.121058
$45$	13997.9	1.03046
$46$	6398.11	0.445817
$47$	−6219.00	−0.410654	−0.205327	−	0.978693i	$-0.565826\pi$
$47$	−6219.00	−0.410654	−0.205327	+	0.978693i	$0.565826\pi$
$48$	−10229.8	−0.640859
$49$	2401.00	0.142857
$50$	−1710.55	−0.0967633
$51$	−33712.3	−1.81494
$52$	21277.8	1.09124
$53$	19944.4	0.975283	0.487642	−	0.873044i	$-0.337857\pi$
$53$	19944.4	0.975283	0.487642	+	0.873044i	$0.337857\pi$
$54$	24577.5	1.14697
$55$	1585.74	0.0706847
$56$	−7578.32	−0.322926
$57$	−43430.7	−1.77056
$58$	−22357.7	−0.872682
$59$	−30708.0	−1.14847	−0.574237	−	0.818689i	$-0.694701\pi$
$59$	−30708.0	−1.14847	−0.574237	+	0.818689i	$0.694701\pi$
$60$	17362.4	0.622632
$61$	19901.3	0.684790	0.342395	−	0.939556i	$-0.388762\pi$
$61$	19901.3	0.684790	0.342395	+	0.939556i	$0.388762\pi$
$62$	6485.64	0.214276
$63$	−27435.9	−0.870901
$64$	4696.70	0.143332
$65$	−21703.6	−0.637161
$66$	4919.07	0.139003
$67$	31668.6	0.861869	0.430935	−	0.902383i	$-0.358184\pi$
$67$	31668.6	0.861869	0.430935	+	0.902383i	$0.358184\pi$
$68$	−29160.0	−0.764743
$69$	66241.7	1.67498
$70$	3352.68	0.0817799
$71$	−32747.5	−0.770960	−0.385480	−	0.922716i	$-0.625964\pi$
$71$	−32747.5	−0.770960	−0.385480	+	0.922716i	$0.625964\pi$
$72$	86596.6	1.96865
$73$	−54441.9	−1.19571	−0.597856	−	0.801604i	$-0.703980\pi$
$73$	−54441.9	−1.19571	−0.597856	+	0.801604i	$0.703980\pi$
$74$	−35145.0	−0.746078
$75$	−17709.9	−0.363548
$76$	−37566.1	−0.746039
$77$	−3108.05	−0.0597394
$78$	−67326.1	−1.25299
$79$	47649.2	0.858989	0.429495	−	0.903069i	$-0.358692\pi$
$79$	47649.2	0.858989	0.429495	+	0.903069i	$0.358692\pi$
$80$	9025.48	0.157669
$81$	118398.	2.00509
$82$	−4523.87	−0.0742977
$83$	−56509.0	−0.900372	−0.450186	−	0.892935i	$-0.648642\pi$
$83$	−56509.0	−0.900372	−0.450186	+	0.892935i	$0.648642\pi$
$84$	−34030.3	−0.526220
$85$	29743.6	0.446525
$86$	−35500.2	−0.517589
$87$	−231476.	−3.27875
$88$	9810.00	0.135040
$89$	2533.69	0.0339061	0.0169531	−	0.999856i	$-0.494603\pi$
$89$	2533.69	0.0339061	0.0169531	+	0.999856i	$0.494603\pi$
$90$	−38310.6	−0.498555
$91$	42539.1	0.538499
$92$	57296.8	0.705766
$93$	67148.0	0.805055
$94$	17020.7	0.198681
$95$	38317.9	0.435604
$96$	168235.	1.86310
$97$	58075.1	0.626701	0.313350	−	0.949638i	$-0.398549\pi$
$97$	58075.1	0.626701	0.313350	+	0.949638i	$0.398549\pi$
$98$	−6571.25	−0.0691166
$99$	35515.3	0.364190
$100$	−15318.4	−0.153184
$101$	98422.7	0.960045	0.480023	−	0.877256i	$-0.340628\pi$
$101$	98422.7	0.960045	0.480023	+	0.877256i	$0.340628\pi$
$102$	92266.5	0.878099
$103$	179343.	1.66568	0.832840	−	0.553514i	$-0.186713\pi$
$103$	179343.	1.66568	0.832840	+	0.553514i	$0.186713\pi$
$104$	−134267.	−1.21727
$105$	34711.3	0.307254
$106$	−54585.3	−0.471858
$107$	159436.	1.34626	0.673128	−	0.739526i	$-0.264950\pi$
$107$	159436.	1.34626	0.673128	+	0.739526i	$0.264950\pi$
$108$	220098.	1.81575
$109$	−97547.7	−0.786413	−0.393207	−	0.919450i	$-0.628634\pi$
$109$	−97547.7	−0.786413	−0.393207	+	0.919450i	$0.628634\pi$
$110$	−4339.98	−0.0341984
$111$	−363868.	−2.80308
$112$	−17689.9	−0.133254
$113$	140601.	1.03584	0.517919	−	0.855430i	$-0.326707\pi$
$113$	140601.	1.03584	0.517919	+	0.855430i	$0.326707\pi$
$114$	118864.	0.856623
$115$	−58443.5	−0.412090
$116$	−200219.	−1.38153
$117$	−486090.	−3.28286
$118$	84044.0	0.555650
$119$	−58297.4	−0.377383
$120$	−109560.	−0.694543
$121$	−157028.	−0.975018
$122$	−54467.5	−0.331312
$123$	−46837.1	−0.279143
$124$	58080.7	0.339217
$125$	15625.0	0.0894427
$126$	75088.9	0.421356
$127$	233889.	1.28677	0.643385	−	0.765543i	$-0.277529\pi$
$127$	233889.	1.28677	0.643385	+	0.765543i	$0.277529\pi$
$128$	177135.	0.955609
$129$	−367546.	−1.94463
$130$	59400.2	0.308269
$131$	181216.	0.922610	0.461305	−	0.887242i	$-0.347381\pi$
$131$	181216.	0.922610	0.461305	+	0.887242i	$0.347381\pi$
$132$	44051.6	0.220053
$133$	−75103.0	−0.368153
$134$	−86673.0	−0.416986
$135$	−224503.	−1.06020
$136$	184005.	0.853066
$137$	−203830.	−0.927827	−0.463914	−	0.885880i	$-0.653555\pi$
$137$	−203830.	−0.927827	−0.463914	+	0.885880i	$0.653555\pi$
$138$	−181296.	−0.810381
$139$	51086.4	0.224269	0.112134	−	0.993693i	$-0.464231\pi$
$139$	51086.4	0.224269	0.112134	+	0.993693i	$0.464231\pi$
$140$	30024.1	0.129464
$141$	176220.	0.746463
$142$	89625.8	0.373003
$143$	−55066.1	−0.225188
$144$	202141.	0.812359
$145$	204226.	0.806660
$146$	149001.	0.578505
$147$	−68034.2	−0.259677
$148$	−314733.	−1.18110
$149$	−307059.	−1.13307	−0.566533	−	0.824039i	$-0.691716\pi$
$149$	−307059.	−1.13307	−0.566533	+	0.824039i	$0.691716\pi$
$150$	48469.8	0.175891
$151$	358221.	1.27852	0.639261	−	0.768990i	$-0.279240\pi$
$151$	358221.	1.27852	0.639261	+	0.768990i	$0.279240\pi$
$152$	237049.	0.832203
$153$	666158.	2.30064
$154$	8506.36	0.0289029
$155$	−59243.0	−0.198065
$156$	−602924.	−1.98359
$157$	437769.	1.41741	0.708705	−	0.705505i	$-0.249280\pi$
$157$	437769.	1.41741	0.708705	+	0.705505i	$0.249280\pi$
$158$	−130410.	−0.415593
$159$	−565140.	−1.77281
$160$	−148429.	−0.458374
$161$	114549.	0.348279
$162$	−324042.	−0.970095
$163$	−430265.	−1.26843	−0.634216	−	0.773156i	$-0.718677\pi$
$163$	−430265.	−1.26843	−0.634216	+	0.773156i	$0.718677\pi$
$164$	−40512.5	−0.117620
$165$	−44933.2	−0.128486
$166$	154658.	0.435615
$167$	229736.	0.637437	0.318718	−	0.947849i	$-0.396748\pi$
$167$	229736.	0.637437	0.318718	+	0.947849i	$0.396748\pi$
$168$	214738.	0.586996
$169$	382384.	1.02987
$170$	−81404.6	−0.216036
$171$	858193.	2.24437
$172$	−317914.	−0.819387
$173$	67029.4	0.170275	0.0851374	−	0.996369i	$-0.472867\pi$
$173$	67029.4	0.170275	0.0851374	+	0.996369i	$0.472867\pi$
$174$	633522.	1.58631
$175$	−30625.0	−0.0755929
$176$	22899.3	0.0557238
$177$	870135.	2.08763
$178$	−6934.39	−0.0164043
$179$	−234462.	−0.546940	−0.273470	−	0.961881i	$-0.588171\pi$
$179$	−234462.	−0.546940	−0.273470	+	0.961881i	$0.588171\pi$
$180$	−343082.	−0.789254
$181$	−199344.	−0.452278	−0.226139	−	0.974095i	$-0.572610\pi$
$181$	−199344.	−0.452278	−0.226139	+	0.974095i	$0.572610\pi$
$182$	−116424.	−0.260535
$183$	−563920.	−1.24477
$184$	−361554.	−0.787279
$185$	321032.	0.689634
$186$	−183776.	−0.389499
$187$	75464.9	0.157812
$188$	152425.	0.314529
$189$	440025.	0.896031
$190$	−104871.	−0.210752
$191$	300904.	0.596821	0.298410	−	0.954438i	$-0.403544\pi$
$191$	300904.	0.596821	0.298410	+	0.954438i	$0.403544\pi$
$192$	−133085.	−0.260541
$193$	−173138.	−0.334579	−0.167289	−	0.985908i	$-0.553501\pi$
$193$	−173138.	−0.334579	−0.167289	+	0.985908i	$0.553501\pi$
$194$	−158944.	−0.303208
$195$	614990.	1.15819
$196$	−58847.3	−0.109417
$197$	100950.	0.185329	0.0926644	−	0.995697i	$-0.470462\pi$
$197$	100950.	0.185329	0.0926644	+	0.995697i	$0.470462\pi$
$198$	−97201.1	−0.176201
$199$	−809079.	−1.44830	−0.724149	−	0.689643i	$-0.757767\pi$
$199$	−809079.	−1.44830	−0.724149	+	0.689643i	$0.757767\pi$
$200$	96662.3	0.170876
$201$	−897354.	−1.56666
$202$	−269371.	−0.464486
$203$	−400283.	−0.681752
$204$	826272.	1.39010
$205$	41323.3	0.0686768
$206$	−490840.	−0.805883
$207$	−1.30894e6	−2.12322
$208$	−313417.	−0.502302
$209$	97219.4	0.153953
$210$	−95000.7	−0.148655
$211$	183306.	0.283446	0.141723	−	0.989906i	$-0.454736\pi$
$211$	183306.	0.283446	0.141723	+	0.989906i	$0.454736\pi$
$212$	−488826.	−0.746991
$213$	927925.	1.40141
$214$	−436358.	−0.651340
$215$	324277.	0.478431
$216$	−1.38886e6	−2.02546
$217$	116116.	0.167396
$218$	266976.	0.380480
$219$	1.54266e6	2.17350
$220$	−38865.7	−0.0541389
$221$	−1.03287e6	−1.42254
$222$	995862.	1.35618
$223$	−678874.	−0.914171	−0.457085	−	0.889423i	$-0.651107\pi$
$223$	−678874.	−0.914171	−0.457085	+	0.889423i	$0.651107\pi$
$224$	290922.	0.387397
$225$	349948.	0.460837
$226$	−384808.	−0.501156
$227$	−256484.	−0.330366	−0.165183	−	0.986263i	$-0.552821\pi$
$227$	−256484.	−0.330366	−0.165183	+	0.986263i	$0.552821\pi$
$228$	1.06446e6	1.35611
$229$	321802.	0.405509	0.202754	−	0.979230i	$-0.435011\pi$
$229$	321802.	0.405509	0.202754	+	0.979230i	$0.435011\pi$
$230$	159953.	0.199376
$231$	88069.1	0.108591
$232$	1.26342e6	1.54109
$233$	193589.	0.233609	0.116805	−	0.993155i	$-0.462735\pi$
$233$	193589.	0.233609	0.116805	+	0.993155i	$0.462735\pi$
$234$	1.33037e6	1.58830
$235$	−155475.	−0.183650
$236$	752637.	0.879641
$237$	−1.35018e6	−1.56142
$238$	159553.	0.182584
$239$	−482857.	−0.546794	−0.273397	−	0.961901i	$-0.588147\pi$
$239$	−482857.	−0.546794	−0.273397	+	0.961901i	$0.588147\pi$
$240$	−255744.	−0.286601
$241$	−1.06213e6	−1.17797	−0.588984	−	0.808145i	$-0.700472\pi$
$241$	−1.06213e6	−1.17797	−0.588984	+	0.808145i	$0.700472\pi$
$242$	429766.	0.471730
$243$	−1.17275e6	−1.27406
$244$	−487771.	−0.524495
$245$	60025.0	0.0638877
$246$	128188.	0.135054
$247$	−1.33062e6	−1.38775
$248$	−366500.	−0.378395
$249$	1.60123e6	1.63664
$250$	−42763.7	−0.0432738
$251$	1.43228e6	1.43497	0.717484	−	0.696575i	$-0.245293\pi$
$251$	1.43228e6	1.43497	0.717484	+	0.696575i	$0.245293\pi$
$252$	672441.	0.667042
$253$	−148282.	−0.145642
$254$	−640126.	−0.622560
$255$	−842808.	−0.811667
$256$	−635092.	−0.605671
$257$	−491843.	−0.464508	−0.232254	−	0.972655i	$-0.574610\pi$
$257$	−491843.	−0.464508	−0.232254	+	0.972655i	$0.574610\pi$
$258$	1.00593e6	0.940844
$259$	−629223.	−0.582847
$260$	531945.	0.488016
$261$	4.57398e6	4.15617
$262$	−495966.	−0.446374
$263$	−1.41098e6	−1.25786	−0.628928	−	0.777464i	$-0.716506\pi$
$263$	−1.41098e6	−1.25786	−0.628928	+	0.777464i	$0.716506\pi$
$264$	−277974.	−0.245468
$265$	498609.	0.436160
$266$	205548.	0.178118
$267$	−71794.0	−0.0616325
$268$	−776181.	−0.660124
$269$	847237.	0.713878	0.356939	−	0.934128i	$-0.383820\pi$
$269$	847237.	0.713878	0.356939	+	0.934128i	$0.383820\pi$
$270$	614436.	0.512941
$271$	1.14845e6	0.949923	0.474961	−	0.880007i	$-0.342462\pi$
$271$	1.14845e6	0.949923	0.474961	+	0.880007i	$0.342462\pi$
$272$	429520.	0.352015
$273$	−1.20538e6	−0.978853
$274$	557859.	0.448898
$275$	39643.5	0.0316111
$276$	−1.62355e6	−1.28290
$277$	1.17885e6	0.923124	0.461562	−	0.887108i	$-0.347289\pi$
$277$	1.17885e6	0.923124	0.461562	+	0.887108i	$0.347289\pi$
$278$	−139817.	−0.108505
$279$	−1.32685e6	−1.02049
$280$	−189458.	−0.144417
$281$	112265.	0.0848164	0.0424082	−	0.999100i	$-0.486497\pi$
$281$	112265.	0.0848164	0.0424082	+	0.999100i	$0.486497\pi$
$282$	−482294.	−0.361151
$283$	1.67112e6	1.24034	0.620172	−	0.784466i	$-0.287063\pi$
$283$	1.67112e6	1.24034	0.620172	+	0.784466i	$0.287063\pi$
$284$	802624.	0.590495
$285$	−1.08577e6	−0.791816
$286$	150709.	0.108949
$287$	−80993.6	−0.0580425
$288$	−3.32433e6	−2.36169
$289$	−4368.41	−0.00307665
$290$	−558941.	−0.390275
$291$	−1.64560e6	−1.13918
$292$	1.33434e6	0.915822
$293$	2.28723e6	1.55647	0.778235	−	0.627973i	$-0.216115\pi$
$293$	2.28723e6	1.55647	0.778235	+	0.627973i	$0.216115\pi$
$294$	186201.	0.125636
$295$	−767699.	−0.513613
$296$	1.98603e6	1.31752
$297$	−569604.	−0.374699
$298$	840382.	0.548196
$299$	2.02950e6	1.31284
$300$	434060.	0.278450
$301$	−635582.	−0.404348
$302$	−980406.	−0.618570
$303$	−2.78888e6	−1.74511
$304$	553339.	0.343406
$305$	497533.	0.306247
$306$	−1.82319e6	−1.11309
$307$	449789.	0.272372	0.136186	−	0.990683i	$-0.456515\pi$
$307$	449789.	0.272372	0.136186	+	0.990683i	$0.456515\pi$
$308$	76176.7	0.0457557
$309$	−5.08183e6	−3.02778
$310$	162141.	0.0958272
$311$	−605586.	−0.355038	−0.177519	−	0.984117i	$-0.556807\pi$
$311$	−605586.	−0.355038	−0.177519	+	0.984117i	$0.556807\pi$
$312$	3.80456e6	2.21268
$313$	−2.03261e6	−1.17272	−0.586359	−	0.810052i	$-0.699439\pi$
$313$	−2.03261e6	−1.17272	−0.586359	+	0.810052i	$0.699439\pi$
$314$	−1.19812e6	−0.685766
$315$	−685899.	−0.389479
$316$	−1.16786e6	−0.657918
$317$	−2.61940e6	−1.46404	−0.732021	−	0.681282i	$-0.761423\pi$
$317$	−2.61940e6	−1.46404	−0.732021	+	0.681282i	$0.761423\pi$
$318$	1.54672e6	0.857716
$319$	518158.	0.285093
$320$	117418.	0.0641000
$321$	−4.51775e6	−2.44715
$322$	−313507.	−0.168503
$323$	1.82354e6	0.972541
$324$	−2.90189e6	−1.53574
$325$	−542591.	−0.284947
$326$	1.17758e6	0.613688
$327$	2.76409e6	1.42950
$328$	255642.	0.131204
$329$	304731.	0.155213
$330$	122977.	0.0621639
$331$	1.79427e6	0.900155	0.450078	−	0.892989i	$-0.351396\pi$
$331$	1.79427e6	0.900155	0.450078	+	0.892989i	$0.351396\pi$
$332$	1.38501e6	0.689615
$333$	7.19005e6	3.55322
$334$	−628758.	−0.308402
$335$	791714.	0.385440
$336$	501259.	0.242222
$337$	−1.10766e6	−0.531292	−0.265646	−	0.964071i	$-0.585585\pi$
$337$	−1.10766e6	−0.531292	−0.265646	+	0.964071i	$0.585585\pi$
$338$	−1.04654e6	−0.498269
$339$	−3.98404e6	−1.88289
$340$	−729000.	−0.342003
$341$	−150311.	−0.0700009
$342$	−2.34877e6	−1.08586
$343$	−117649.	−0.0539949
$344$	2.00610e6	0.914022
$345$	1.65604e6	0.749072
$346$	−183451.	−0.0823817
$347$	−2.46825e6	−1.10044	−0.550218	−	0.835021i	$-0.685455\pi$
$347$	−2.46825e6	−1.10044	−0.550218	+	0.835021i	$0.685455\pi$
$348$	5.67336e6	2.51126
$349$	2.41856e6	1.06290	0.531451	−	0.847089i	$-0.321647\pi$
$349$	2.41856e6	1.06290	0.531451	+	0.847089i	$0.321647\pi$
$350$	83816.9	0.0365731
$351$	7.79604e6	3.37758
$352$	−376593.	−0.162000
$353$	−1.84853e6	−0.789570	−0.394785	−	0.918774i	$-0.629181\pi$
$353$	−1.84853e6	−0.789570	−0.394785	+	0.918774i	$0.629181\pi$
$354$	−2.38145e6	−1.01003
$355$	−818687.	−0.344784
$356$	−62099.4	−0.0259694
$357$	1.65190e6	0.685984
$358$	641693.	0.264618
$359$	−552362.	−0.226197	−0.113099	−	0.993584i	$-0.536078\pi$
$359$	−552362.	−0.226197	−0.113099	+	0.993584i	$0.536078\pi$
$360$	2.16491e6	0.880409
$361$	−126886.	−0.0512444
$362$	545579.	0.218820
$363$	4.44950e6	1.77233
$364$	−1.04261e6	−0.412448
$365$	−1.36105e6	−0.534739
$366$	1.54338e6	0.602241
$367$	4.18145e6	1.62055	0.810273	−	0.586053i	$-0.199319\pi$
$367$	4.18145e6	1.62055	0.810273	+	0.586053i	$0.199319\pi$
$368$	−843969.	−0.324868
$369$	925505.	0.353845
$370$	−878625.	−0.333656
$371$	−977274.	−0.368622
$372$	−1.64576e6	−0.616609
$373$	2.29821e6	0.855300	0.427650	−	0.903944i	$-0.359342\pi$
$373$	2.29821e6	0.855300	0.427650	+	0.903944i	$0.359342\pi$
$374$	−206538.	−0.0763522
$375$	−442747.	−0.162584
$376$	−961829.	−0.350855
$377$	−7.09191e6	−2.56986
$378$	−1.20430e6	−0.433514
$379$	3.55567e6	1.27152	0.635760	−	0.771886i	$-0.280687\pi$
$379$	3.55567e6	1.27152	0.635760	+	0.771886i	$0.280687\pi$
$380$	−939151.	−0.333639
$381$	−6.62744e6	−2.33902
$382$	−823536.	−0.288752
$383$	−1.57080e6	−0.547172	−0.273586	−	0.961848i	$-0.588210\pi$
$383$	−1.57080e6	−0.547172	−0.273586	+	0.961848i	$0.588210\pi$
$384$	−5.01927e6	−1.73705
$385$	−77701.3	−0.0267163
$386$	473857.	0.161875
$387$	7.26273e6	2.46503
$388$	−1.42339e6	−0.480004
$389$	−1.33556e6	−0.447495	−0.223747	−	0.974647i	$-0.571829\pi$
$389$	−1.33556e6	−0.447495	−0.223747	+	0.974647i	$0.571829\pi$
$390$	−1.68315e6	−0.560353
$391$	−2.78131e6	−0.920042
$392$	371338.	0.122055
$393$	−5.13490e6	−1.67707
$394$	−276289.	−0.0896651
$395$	1.19123e6	0.384152
$396$	−870463.	−0.278941
$397$	−1.47124e6	−0.468496	−0.234248	−	0.972177i	$-0.575263\pi$
$397$	−1.47124e6	−0.468496	−0.234248	+	0.972177i	$0.575263\pi$
$398$	2.21435e6	0.700710
$399$	2.12810e6	0.669207
$400$	225637.	0.0705116
$401$	994719.	0.308915	0.154458	−	0.987999i	$-0.450637\pi$
$401$	994719.	0.308915	0.154458	+	0.987999i	$0.450637\pi$
$402$	2.45595e6	0.757974
$403$	2.05726e6	0.630997
$404$	−2.41229e6	−0.735320
$405$	2.95996e6	0.896703
$406$	1.09552e6	0.329843
$407$	814517.	0.243733
$408$	−5.21393e6	−1.55065
$409$	−995359.	−0.294220	−0.147110	−	0.989120i	$-0.546997\pi$
$409$	−995359.	−0.294220	−0.147110	+	0.989120i	$0.546997\pi$
$410$	−113097.	−0.0332270
$411$	5.77569e6	1.68655
$412$	−4.39561e6	−1.27578
$413$	1.50469e6	0.434082
$414$	3.58241e6	1.02725
$415$	−1.41272e6	−0.402659
$416$	5.15433e6	1.46029
$417$	−1.44757e6	−0.407662
$418$	−266078.	−0.0744848
$419$	62520.7	0.0173976	0.00869879	−	0.999962i	$-0.497231\pi$
$419$	62520.7	0.0173976	0.00869879	+	0.999962i	$0.497231\pi$
$420$	−850758.	−0.235333
$421$	3.26482e6	0.897747	0.448874	−	0.893595i	$-0.351825\pi$
$421$	3.26482e6	0.897747	0.448874	+	0.893595i	$0.351825\pi$
$422$	−501686.	−0.137136
$423$	−3.48213e6	−0.946224
$424$	3.08459e6	0.833264
$425$	743589.	0.199692
$426$	−2.53962e6	−0.678023
$427$	−975165.	−0.258826
$428$	−3.90770e6	−1.03113
$429$	1.56034e6	0.409333
$430$	−887506.	−0.231473
$431$	−2.05017e6	−0.531615	−0.265807	−	0.964026i	$-0.585639\pi$
$431$	−2.05017e6	−0.531615	−0.265807	+	0.964026i	$0.585639\pi$
$432$	−3.24199e6	−0.835800
$433$	627607.	0.160867	0.0804337	−	0.996760i	$-0.474369\pi$
$433$	627607.	0.160867	0.0804337	+	0.996760i	$0.474369\pi$
$434$	−317796.	−0.0809887
$435$	−5.78690e6	−1.46630
$436$	2.39085e6	0.602331
$437$	−3.58309e6	−0.897540
$438$	−4.22206e6	−1.05157
$439$	6.13266e6	1.51876	0.759378	−	0.650650i	$-0.225504\pi$
$439$	6.13266e6	1.51876	0.759378	+	0.650650i	$0.225504\pi$
$440$	245250.	0.0603917
$441$	1.34436e6	0.329169
$442$	2.82684e6	0.688249
$443$	−2.08811e6	−0.505526	−0.252763	−	0.967528i	$-0.581339\pi$
$443$	−2.08811e6	−0.505526	−0.252763	+	0.967528i	$0.581339\pi$
$444$	8.91822e6	2.14694
$445$	63342.2	0.0151633
$446$	1.85800e6	0.442291
$447$	8.70075e6	2.05962
$448$	−230139.	−0.0541744
$449$	−6.77740e6	−1.58653	−0.793263	−	0.608880i	$-0.791619\pi$
$449$	−6.77740e6	−1.58653	−0.793263	+	0.608880i	$0.791619\pi$
$450$	−957766.	−0.222961
$451$	104845.	0.0242720
$452$	−3.44606e6	−0.793371
$453$	−1.01505e7	−2.32402
$454$	701965.	0.159836
$455$	1.06348e6	0.240824
$456$	−6.71697e6	−1.51273
$457$	3.89825e6	0.873131	0.436566	−	0.899672i	$-0.356195\pi$
$457$	3.89825e6	0.873131	0.436566	+	0.899672i	$0.356195\pi$
$458$	−880733.	−0.196192
$459$	−1.06840e7	−2.36702
$460$	1.43242e6	0.315628
$461$	4.27807e6	0.937552	0.468776	−	0.883317i	$-0.344695\pi$
$461$	4.27807e6	0.937552	0.468776	+	0.883317i	$0.344695\pi$
$462$	−241034.	−0.0525381
$463$	7.18974e6	1.55869	0.779347	−	0.626593i	$-0.215551\pi$
$463$	7.18974e6	1.55869	0.779347	+	0.626593i	$0.215551\pi$
$464$	2.94918e6	0.635925
$465$	1.67870e6	0.360031
$466$	−529829.	−0.113024
$467$	−5.72641e6	−1.21504	−0.607519	−	0.794305i	$-0.707835\pi$
$467$	−5.72641e6	−1.21504	−0.607519	+	0.794305i	$0.707835\pi$
$468$	1.19138e7	2.51441
$469$	−1.55176e6	−0.325756
$470$	425516.	0.0888529
$471$	−1.24045e7	−2.57649
$472$	−4.74928e6	−0.981235
$473$	822750.	0.169089
$474$	3.69527e6	0.755441
$475$	957946.	0.194808
$476$	1.42884e6	0.289046
$477$	1.11672e7	2.24723
$478$	1.32152e6	0.264548
$479$	−696853.	−0.138772	−0.0693861	−	0.997590i	$-0.522104\pi$
$479$	−696853.	−0.138772	−0.0693861	+	0.997590i	$0.522104\pi$
$480$	4.20586e6	0.833205
$481$	−1.11481e7	−2.19704
$482$	2.90691e6	0.569920
$483$	−3.24584e6	−0.633082
$484$	3.84867e6	0.746788
$485$	1.45188e6	0.280269
$486$	3.20967e6	0.616411
$487$	7.51712e6	1.43625	0.718123	−	0.695916i	$-0.245001\pi$
$487$	7.51712e6	1.43625	0.718123	+	0.695916i	$0.245001\pi$
$488$	3.07793e6	0.585072
$489$	1.21919e7	2.30568
$490$	−164281.	−0.0309099
$491$	−255540.	−0.0478360	−0.0239180	−	0.999714i	$-0.507614\pi$
$491$	−255540.	−0.0478360	−0.0239180	+	0.999714i	$0.507614\pi$
$492$	1.14795e6	0.213802
$493$	9.71905e6	1.80097
$494$	3.64174e6	0.671416
$495$	887883.	0.162871
$496$	−855515.	−0.156143
$497$	1.60463e6	0.291395
$498$	−4.38236e6	−0.791835
$499$	8.14998e6	1.46523	0.732614	−	0.680645i	$-0.238300\pi$
$499$	8.14998e6	1.46523	0.732614	+	0.680645i	$0.238300\pi$
$500$	−382961.	−0.0685061
$501$	−6.50974e6	−1.15870
$502$	−3.91997e6	−0.694261
$503$	5.64001e6	0.993939	0.496969	−	0.867768i	$-0.334446\pi$
$503$	5.64001e6	0.993939	0.496969	+	0.867768i	$0.334446\pi$
$504$	−4.24323e6	−0.744082
$505$	2.46057e6	0.429345
$506$	405829.	0.0704640
$507$	−1.08352e7	−1.87204
$508$	−5.73251e6	−0.985565
$509$	−7.79954e6	−1.33436	−0.667182	−	0.744895i	$-0.732500\pi$
$509$	−7.79954e6	−1.33436	−0.667182	+	0.744895i	$0.732500\pi$
$510$	2.30666e6	0.392698
$511$	2.66766e6	0.451937
$512$	−3.93016e6	−0.662575
$513$	−1.37639e7	−2.30913
$514$	1.34611e6	0.224737
$515$	4.48358e6	0.744915
$516$	9.00836e6	1.48943
$517$	−394469.	−0.0649062
$518$	1.72211e6	0.281991
$519$	−1.89933e6	−0.309516
$520$	−3.35668e6	−0.544379
$521$	6.04835e6	0.976208	0.488104	−	0.872786i	$-0.337689\pi$
$521$	6.04835e6	0.976208	0.488104	+	0.872786i	$0.337689\pi$
$522$	−1.25184e7	−2.01082
$523$	−7.64614e6	−1.22233	−0.611165	−	0.791503i	$-0.709299\pi$
$523$	−7.64614e6	−1.22233	−0.611165	+	0.791503i	$0.709299\pi$
$524$	−4.44151e6	−0.706647
$525$	867784.	0.137408
$526$	3.86167e6	0.608571
$527$	−2.81936e6	−0.442205
$528$	−648870.	−0.101291
$529$	−971316.	−0.150911
$530$	−1.36463e6	−0.211021
$531$	−1.71939e7	−2.64630
$532$	1.84074e6	0.281976
$533$	−1.43499e6	−0.218791
$534$	196492.	0.0298188
$535$	3.98591e6	0.602064
$536$	4.89785e6	0.736365
$537$	6.64366e6	0.994195
$538$	−2.31878e6	−0.345386
$539$	152294.	0.0225794
$540$	5.50245e6	0.812029
$541$	−1.17724e7	−1.72930	−0.864651	−	0.502374i	$-0.832460\pi$
$541$	−1.17724e7	−1.72930	−0.864651	+	0.502374i	$0.832460\pi$
$542$	−3.14316e6	−0.459588
$543$	5.64856e6	0.822125
$544$	−7.06371e6	−1.02338
$545$	−2.43869e6	−0.351695
$546$	3.29898e6	0.473585
$547$	930880.	0.133023	0.0665113	−	0.997786i	$-0.478813\pi$
$547$	930880.	0.133023	0.0665113	+	0.997786i	$0.478813\pi$
$548$	4.99578e6	0.710643
$549$	1.11431e7	1.57788
$550$	−108499.	−0.0152940
$551$	1.25208e7	1.75692
$552$	1.02449e7	1.43107
$553$	−2.33481e6	−0.324667
$554$	−3.22638e6	−0.446622
$555$	−9.09670e6	−1.25358
$556$	−1.25210e6	−0.171772
$557$	−4.66844e6	−0.637579	−0.318790	−	0.947825i	$-0.603276\pi$
$557$	−4.66844e6	−0.637579	−0.318790	+	0.947825i	$0.603276\pi$
$558$	3.63142e6	0.493732
$559$	−1.12608e7	−1.52419
$560$	−442249.	−0.0595932
$561$	−2.13836e6	−0.286862
$562$	−307256.	−0.0410355
$563$	1.30772e6	0.173878	0.0869388	−	0.996214i	$-0.472292\pi$
$563$	1.30772e6	0.173878	0.0869388	+	0.996214i	$0.472292\pi$
$564$	−4.31907e6	−0.571732
$565$	3.51502e6	0.463241
$566$	−4.57366e6	−0.600099
$567$	−5.80153e6	−0.757852
$568$	−5.06471e6	−0.658694
$569$	1.46759e7	1.90031	0.950154	−	0.311779i	$-0.100925\pi$
$569$	1.46759e7	1.90031	0.950154	+	0.311779i	$0.100925\pi$
$570$	2.97161e6	0.383094
$571$	1.12905e6	0.144918	0.0724590	−	0.997371i	$-0.476915\pi$
$571$	1.12905e6	0.144918	0.0724590	+	0.997371i	$0.476915\pi$
$572$	1.34964e6	0.172476
$573$	−8.52634e6	−1.08487
$574$	221670.	0.0280819
$575$	−1.46109e6	−0.184292
$576$	2.62977e6	0.330264
$577$	8.94245e6	1.11819	0.559097	−	0.829102i	$-0.311148\pi$
$577$	8.94245e6	1.11819	0.559097	+	0.829102i	$0.311148\pi$
$578$	11955.8	0.00148854
$579$	4.90600e6	0.608178
$580$	−5.00547e6	−0.617839
$581$	2.76894e6	0.340309
$582$	4.50382e6	0.551154
$583$	1.26506e6	0.154149
$584$	−8.41997e6	−1.02159
$585$	−1.21522e7	−1.46814
$586$	−6.25987e6	−0.753046
$587$	3.97509e6	0.476158	0.238079	−	0.971246i	$-0.423482\pi$
$587$	3.97509e6	0.476158	0.238079	+	0.971246i	$0.423482\pi$
$588$	1.66749e6	0.198893
$589$	−3.63211e6	−0.431390
$590$	2.10110e6	0.248494
$591$	−2.86051e6	−0.336880
$592$	4.63595e6	0.543669
$593$	−3.27487e6	−0.382434	−0.191217	−	0.981548i	$-0.561243\pi$
$593$	−3.27487e6	−0.382434	−0.191217	+	0.981548i	$0.561243\pi$
$594$	1.55894e6	0.181285
$595$	−1.45744e6	−0.168771
$596$	7.52585e6	0.867841
$597$	2.29259e7	2.63263
$598$	−5.55449e6	−0.635172
$599$	−4.45624e6	−0.507460	−0.253730	−	0.967275i	$-0.581657\pi$
$599$	−4.45624e6	−0.507460	−0.253730	+	0.967275i	$0.581657\pi$
$600$	−2.73900e6	−0.310609
$601$	−8.18581e6	−0.924433	−0.462216	−	0.886767i	$-0.652946\pi$
$601$	−8.18581e6	−0.924433	−0.462216	+	0.886767i	$0.652946\pi$
$602$	1.73951e6	0.195630
$603$	1.77318e7	1.98591
$604$	−8.77981e6	−0.979248
$605$	−3.92569e6	−0.436041
$606$	7.63284e6	0.844315
$607$	−6.82736e6	−0.752109	−0.376055	−	0.926598i	$-0.622719\pi$
$607$	−6.82736e6	−0.752109	−0.376055	+	0.926598i	$0.622719\pi$
$608$	−9.09999e6	−0.998348
$609$	1.13423e7	1.23925
$610$	−1.36169e6	−0.148167
$611$	5.39900e6	0.585073
$612$	−1.63272e7	−1.76211
$613$	6.39746e6	0.687632	0.343816	−	0.939037i	$-0.388280\pi$
$613$	6.39746e6	0.687632	0.343816	+	0.939037i	$0.388280\pi$
$614$	−1.23102e6	−0.131778
$615$	−1.17093e6	−0.124837
$616$	−480690.	−0.0510403
$617$	−1.68341e7	−1.78024	−0.890118	−	0.455730i	$-0.849378\pi$
$617$	−1.68341e7	−1.78024	−0.890118	+	0.455730i	$0.849378\pi$
$618$	1.39083e7	1.46489
$619$	−8.82274e6	−0.925501	−0.462751	−	0.886488i	$-0.653137\pi$
$619$	−8.82274e6	−0.925501	−0.462751	+	0.886488i	$0.653137\pi$
$620$	1.45202e6	0.151702
$621$	2.09931e7	2.18448
$622$	1.65742e6	0.171773
$623$	−124151.	−0.0128153
$624$	8.88093e6	0.913055
$625$	390625.	0.0400000
$626$	5.56301e6	0.567380
$627$	−2.75479e6	−0.279846
$628$	−1.07295e7	−1.08563
$629$	1.52778e7	1.53970
$630$	1.87722e6	0.188436
$631$	−375030.	−0.0374966	−0.0187483	−	0.999824i	$-0.505968\pi$
$631$	−375030.	−0.0374966	−0.0187483	+	0.999824i	$0.505968\pi$
$632$	7.36940e6	0.733905
$633$	−5.19412e6	−0.515232
$634$	7.16898e6	0.708328
$635$	5.84723e6	0.575461
$636$	1.38513e7	1.35784
$637$	−2.08442e6	−0.203534
$638$	−1.41814e6	−0.137932
$639$	−1.83359e7	−1.77644
$640$	4.42838e6	0.427361
$641$	3.25010e6	0.312430	0.156215	−	0.987723i	$-0.450071\pi$
$641$	3.25010e6	0.312430	0.156215	+	0.987723i	$0.450071\pi$
$642$	1.23645e7	1.18397
$643$	2.71365e6	0.258837	0.129418	−	0.991590i	$-0.458689\pi$
$643$	2.71365e6	0.258837	0.129418	+	0.991590i	$0.458689\pi$
$644$	−2.80754e6	−0.266755
$645$	−9.18864e6	−0.869665
$646$	−4.99080e6	−0.470531
$647$	1.67261e7	1.57085	0.785426	−	0.618956i	$-0.212444\pi$
$647$	1.67261e7	1.57085	0.785426	+	0.618956i	$0.212444\pi$
$648$	1.83115e7	1.71311
$649$	−1.94779e6	−0.181523
$650$	1.48501e6	0.137862
$651$	−3.29025e6	−0.304282
$652$	1.05456e7	0.971519
$653$	−1.17470e7	−1.07806	−0.539031	−	0.842286i	$-0.681209\pi$
$653$	−1.17470e7	−1.07806	−0.539031	+	0.842286i	$0.681209\pi$
$654$	−7.56499e6	−0.691614
$655$	4.53040e6	0.412604
$656$	596740.	0.0541409
$657$	−3.04830e7	−2.75514
$658$	−834012.	−0.0750944
$659$	−9.16720e6	−0.822286	−0.411143	−	0.911571i	$-0.634870\pi$
$659$	−9.16720e6	−0.822286	−0.411143	+	0.911571i	$0.634870\pi$
$660$	1.10129e6	0.0984106
$661$	9.54925e6	0.850092	0.425046	−	0.905172i	$-0.360258\pi$
$661$	9.54925e6	0.850092	0.425046	+	0.905172i	$0.360258\pi$
$662$	−4.91069e6	−0.435510
$663$	2.92672e7	2.58581
$664$	−8.73965e6	−0.769262
$665$	−1.87757e6	−0.164643
$666$	−1.96783e7	−1.71910
$667$	−1.90971e7	−1.66208
$668$	−5.63070e6	−0.488227
$669$	1.92364e7	1.66173
$670$	−2.16683e6	−0.186482
$671$	1.26233e6	0.108235
$672$	−8.24349e6	−0.704187
$673$	3.70373e6	0.315211	0.157606	−	0.987502i	$-0.449623\pi$
$673$	3.70373e6	0.315211	0.157606	+	0.987502i	$0.449623\pi$
$674$	3.03154e6	0.257048
$675$	−5.61256e6	−0.474135
$676$	−9.37204e6	−0.788801
$677$	1.93998e7	1.62677	0.813386	−	0.581724i	$-0.197622\pi$
$677$	1.93998e7	1.62677	0.813386	+	0.581724i	$0.197622\pi$
$678$	1.09038e7	0.910972
$679$	−2.84568e6	−0.236871
$680$	4.60013e6	0.381503
$681$	7.26767e6	0.600520
$682$	411382.	0.0338676
$683$	290718.	0.0238463	0.0119231	−	0.999929i	$-0.496205\pi$
$683$	290718.	0.0238463	0.0119231	+	0.999929i	$0.496205\pi$
$684$	−2.10339e7	−1.71901
$685$	−5.09576e6	−0.414937
$686$	321991.	0.0261236
$687$	−9.11852e6	−0.737110
$688$	4.68281e6	0.377168
$689$	−1.73146e7	−1.38952
$690$	−4.53239e6	−0.362413
$691$	−2.05452e7	−1.63688	−0.818438	−	0.574594i	$-0.805160\pi$
$691$	−2.05452e7	−1.63688	−0.818438	+	0.574594i	$0.805160\pi$
$692$	−1.64286e6	−0.130417
$693$	−1.74025e6	−0.137651
$694$	6.75529e6	0.532409
$695$	1.27716e6	0.100296
$696$	−3.58000e7	−2.80130
$697$	1.96656e6	0.153330
$698$	−6.61930e6	−0.514249
$699$	−5.48549e6	−0.424642
$700$	750603.	0.0578982
$701$	−1.57106e7	−1.20753	−0.603764	−	0.797163i	$-0.706333\pi$
$701$	−1.57106e7	−1.20753	−0.603764	+	0.797163i	$0.706333\pi$
$702$	−2.13368e7	−1.63413
$703$	1.96820e7	1.50204
$704$	297910.	0.0226545
$705$	4.40551e6	0.333829
$706$	5.05921e6	0.382007
$707$	−4.82271e6	−0.362863
$708$	−2.13266e7	−1.59896
$709$	−6.48343e6	−0.484383	−0.242192	−	0.970228i	$-0.577866\pi$
$709$	−6.48343e6	−0.484383	−0.242192	+	0.970228i	$0.577866\pi$
$710$	2.24065e6	0.166812
$711$	2.66796e7	1.97927
$712$	391859.	0.0289688
$713$	5.53979e6	0.408103
$714$	−4.52106e6	−0.331890
$715$	−1.37665e6	−0.100707
$716$	5.74654e6	0.418913
$717$	1.36821e7	0.993930
$718$	1.51175e6	0.109438
$719$	−4.83478e6	−0.348782	−0.174391	−	0.984676i	$-0.555796\pi$
$719$	−4.83478e6	−0.348782	−0.174391	+	0.984676i	$0.555796\pi$
$720$	5.05352e6	0.363298
$721$	−8.78781e6	−0.629568
$722$	347272.	0.0247929
$723$	3.00962e7	2.14124
$724$	4.88581e6	0.346410
$725$	5.10565e6	0.360749
$726$	−1.21778e7	−0.857483
$727$	8.57824e6	0.601953	0.300976	−	0.953632i	$-0.402687\pi$
$727$	8.57824e6	0.601953	0.300976	+	0.953632i	$0.402687\pi$
$728$	6.57909e6	0.460084
$729$	4.45997e6	0.310823
$730$	3.72502e6	0.258715
$731$	1.54322e7	1.06816
$732$	1.38214e7	0.953397
$733$	863417.	0.0593555	0.0296777	−	0.999560i	$-0.490552\pi$
$733$	863417.	0.0593555	0.0296777	+	0.999560i	$0.490552\pi$
$734$	−1.14441e7	−0.784047
$735$	−1.70086e6	−0.116131
$736$	1.38796e7	0.944455
$737$	2.00872e6	0.136223
$738$	−2.53299e6	−0.171196
$739$	1.26850e7	0.854436	0.427218	−	0.904149i	$-0.359494\pi$
$739$	1.26850e7	0.854436	0.427218	+	0.904149i	$0.359494\pi$
$740$	−7.86833e6	−0.528206
$741$	3.77042e7	2.52257
$742$	2.67468e6	0.178346
$743$	1.16786e7	0.776104	0.388052	−	0.921637i	$-0.373148\pi$
$743$	1.16786e7	0.776104	0.388052	+	0.921637i	$0.373148\pi$
$744$	1.03851e7	0.687824
$745$	−7.67646e6	−0.506723
$746$	−6.28993e6	−0.413808
$747$	−3.16403e7	−2.07463
$748$	−1.84961e6	−0.120872
$749$	−7.81237e6	−0.508837
$750$	1.21174e6	0.0786607
$751$	−6.46655e6	−0.418382	−0.209191	−	0.977875i	$-0.567083\pi$
$751$	−6.46655e6	−0.418382	−0.209191	+	0.977875i	$0.567083\pi$
$752$	−2.24518e6	−0.144779
$753$	−4.05847e7	−2.60840
$754$	1.94097e7	1.24334
$755$	8.95551e6	0.571772
$756$	−1.07848e7	−0.686289
$757$	3.00203e6	0.190404	0.0952018	−	0.995458i	$-0.469650\pi$
$757$	3.00203e6	0.190404	0.0952018	+	0.995458i	$0.469650\pi$
$758$	−9.73144e6	−0.615183
$759$	4.20169e6	0.264740
$760$	5.92622e6	0.372172
$761$	−2.83373e7	−1.77377	−0.886885	−	0.461989i	$-0.847136\pi$
$761$	−2.83373e7	−1.77377	−0.886885	+	0.461989i	$0.847136\pi$
$762$	1.81385e7	1.13165
$763$	4.77984e6	0.297236
$764$	−7.37499e6	−0.457118
$765$	1.66539e7	1.02888
$766$	4.29909e6	0.264731
$767$	2.66590e7	1.63627
$768$	1.79958e7	1.10095
$769$	−4.74192e6	−0.289160	−0.144580	−	0.989493i	$-0.546183\pi$
$769$	−4.74192e6	−0.289160	−0.144580	+	0.989493i	$0.546183\pi$
$770$	212659.	0.0129258
$771$	1.39368e7	0.844356
$772$	4.24352e6	0.256261
$773$	−1.37810e7	−0.829530	−0.414765	−	0.909928i	$-0.636136\pi$
$773$	−1.37810e7	−0.829530	−0.414765	+	0.909928i	$0.636136\pi$
$774$	−1.98772e7	−1.19262
$775$	−1.48108e6	−0.0885774
$776$	8.98187e6	0.535442
$777$	1.78295e7	1.05947
$778$	3.65525e6	0.216505
$779$	2.53347e6	0.149580
$780$	−1.50731e7	−0.887086
$781$	−2.07716e6	−0.121855
$782$	7.61211e6	0.445131
$783$	−7.33588e7	−4.27610
$784$	866807.	0.0503654
$785$	1.09442e7	0.633885
$786$	1.40536e7	0.811392
$787$	1.22505e7	0.705046	0.352523	−	0.935803i	$-0.385324\pi$
$787$	1.22505e7	0.705046	0.352523	+	0.935803i	$0.385324\pi$
$788$	−2.47424e6	−0.141947
$789$	3.99812e7	2.28646
$790$	−3.26025e6	−0.185859
$791$	−6.88944e6	−0.391510
$792$	5.49279e6	0.311157
$793$	−1.72772e7	−0.975644
$794$	4.02659e6	0.226666
$795$	−1.41285e7	−0.792826
$796$	1.98301e7	1.10928
$797$	−1.42979e7	−0.797310	−0.398655	−	0.917101i	$-0.630523\pi$
$797$	−1.42979e7	−0.797310	−0.398655	+	0.917101i	$0.630523\pi$
$798$	−5.82436e6	−0.323773
$799$	−7.39902e6	−0.410022
$800$	−3.71073e6	−0.204991
$801$	1.41865e6	0.0781260
$802$	−2.72242e6	−0.149458
$803$	−3.45323e6	−0.188989
$804$	2.19937e7	1.19994
$805$	2.86373e6	0.155755
$806$	−5.63048e6	−0.305287
$807$	−2.40071e7	−1.29765
$808$	1.52220e7	0.820245
$809$	3.38944e7	1.82078	0.910389	−	0.413753i	$-0.135782\pi$
$809$	3.38944e7	1.82078	0.910389	+	0.413753i	$0.135782\pi$
$810$	−8.10106e6	−0.433839
$811$	−1.94505e7	−1.03843	−0.519216	−	0.854643i	$-0.673776\pi$
$811$	−1.94505e7	−1.03843	−0.519216	+	0.854643i	$0.673776\pi$
$812$	9.81073e6	0.522169
$813$	−3.25422e7	−1.72671
$814$	−2.22923e6	−0.117922
$815$	−1.07566e7	−0.567260
$816$	−1.21708e7	−0.639873
$817$	1.98809e7	1.04203
$818$	2.72418e6	0.142348
$819$	2.38184e7	1.24080
$820$	−1.01281e6	−0.0526011
$821$	5.51562e6	0.285586	0.142793	−	0.989753i	$-0.454392\pi$
$821$	5.51562e6	0.285586	0.142793	+	0.989753i	$0.454392\pi$
$822$	−1.58074e7	−0.815981
$823$	−2.72639e7	−1.40310	−0.701549	−	0.712621i	$-0.747508\pi$
$823$	−2.72639e7	−1.40310	−0.701549	+	0.712621i	$0.747508\pi$
$824$	2.77371e7	1.42313
$825$	−1.12333e6	−0.0574609
$826$	−4.11815e6	−0.210016
$827$	−5.97531e6	−0.303806	−0.151903	−	0.988395i	$-0.548540\pi$
$827$	−5.97531e6	−0.303806	−0.151903	+	0.988395i	$0.548540\pi$
$828$	3.20815e7	1.62622
$829$	6.28083e6	0.317418	0.158709	−	0.987325i	$-0.449267\pi$
$829$	6.28083e6	0.317418	0.158709	+	0.987325i	$0.449267\pi$
$830$	3.86645e6	0.194813
$831$	−3.34037e7	−1.67800
$832$	−4.07742e6	−0.204210
$833$	2.85657e6	0.142637
$834$	3.96183e6	0.197234
$835$	5.74339e6	0.285070
$836$	−2.38280e6	−0.117916
$837$	2.12803e7	1.04994
$838$	−171112.	−0.00841724
$839$	−1.22748e7	−0.602019	−0.301010	−	0.953621i	$-0.597324\pi$
$839$	−1.22748e7	−0.602019	−0.301010	+	0.953621i	$0.597324\pi$
$840$	5.36844e6	0.262513
$841$	4.62220e7	2.25350
$842$	−8.93542e6	−0.434345
$843$	−3.18113e6	−0.154174
$844$	−4.49274e6	−0.217098
$845$	9.55960e6	0.460572
$846$	9.53016e6	0.457798
$847$	7.69436e6	0.368522
$848$	7.20030e6	0.343844
$849$	−4.73526e7	−2.25463
$850$	−2.03511e6	−0.0966143
$851$	−3.00196e7	−1.42096
$852$	−2.27430e7	−1.07337
$853$	6.63619e6	0.312281	0.156141	−	0.987735i	$-0.450095\pi$
$853$	6.63619e6	0.312281	0.156141	+	0.987735i	$0.450095\pi$
$854$	2.66891e6	0.125224
$855$	2.14548e7	1.00371
$856$	2.46583e7	1.15022
$857$	−3.01234e7	−1.40105	−0.700523	−	0.713630i	$-0.747050\pi$
$857$	−3.01234e7	−1.40105	−0.700523	+	0.713630i	$0.747050\pi$
$858$	−4.27047e6	−0.198042
$859$	−4.11124e7	−1.90103	−0.950517	−	0.310672i	$-0.899446\pi$
$859$	−4.11124e7	−1.90103	−0.950517	+	0.310672i	$0.899446\pi$
$860$	−7.94786e6	−0.366441
$861$	2.29502e6	0.105506
$862$	5.61107e6	0.257204
$863$	−3.41903e6	−0.156270	−0.0781351	−	0.996943i	$-0.524897\pi$
$863$	−3.41903e6	−0.156270	−0.0781351	+	0.996943i	$0.524897\pi$
$864$	5.33164e7	2.42983
$865$	1.67574e6	0.0761492
$866$	−1.71768e6	−0.0778303
$867$	123782.	0.00559256
$868$	−2.84595e6	−0.128212
$869$	3.02237e6	0.135768
$870$	1.58380e7	0.709420
$871$	−2.74929e7	−1.22794
$872$	−1.50867e7	−0.671897
$873$	3.25172e7	1.44404
$874$	9.80647e6	0.434244
$875$	−765625.	−0.0338062
$876$	−3.78097e7	−1.66473
$877$	−2.94070e7	−1.29108	−0.645538	−	0.763728i	$-0.723367\pi$
$877$	−2.94070e7	−1.29108	−0.645538	+	0.763728i	$0.723367\pi$
$878$	−1.67844e7	−0.734798
$879$	−6.48105e7	−2.82926
$880$	572483.	0.0249204
$881$	3.32494e7	1.44326	0.721628	−	0.692281i	$-0.243394\pi$
$881$	3.32494e7	1.44326	0.721628	+	0.692281i	$0.243394\pi$
$882$	−3.67935e6	−0.159258
$883$	2.53523e7	1.09425	0.547124	−	0.837051i	$-0.315722\pi$
$883$	2.53523e7	1.09425	0.547124	+	0.837051i	$0.315722\pi$
$884$	2.53151e7	1.08956
$885$	2.17534e7	0.933616
$886$	5.71490e6	0.244582
$887$	1.95997e6	0.0836450	0.0418225	−	0.999125i	$-0.486684\pi$
$887$	1.95997e6	0.0836450	0.0418225	+	0.999125i	$0.486684\pi$
$888$	−5.62757e7	−2.39490
$889$	−1.14606e7	−0.486353
$890$	−173360.	−0.00733624
$891$	7.50997e6	0.316916
$892$	1.66389e7	0.700183
$893$	−9.53196e6	−0.399994
$894$	−2.38129e7	−0.996480
$895$	−5.86154e6	−0.244599
$896$	−8.67963e6	−0.361186
$897$	−5.75075e7	−2.38640
$898$	1.85489e7	0.767587
$899$	−1.93583e7	−0.798857
$900$	−8.57706e6	−0.352965
$901$	2.37287e7	0.973782
$902$	−286947.	−0.0117432
$903$	1.80097e7	0.735001
$904$	2.17453e7	0.885002
$905$	−4.98359e6	−0.202265
$906$	2.77806e7	1.12440
$907$	−8.69678e6	−0.351027	−0.175513	−	0.984477i	$-0.556159\pi$
$907$	−8.69678e6	−0.351027	−0.175513	+	0.984477i	$0.556159\pi$
$908$	6.28629e6	0.253034
$909$	5.51086e7	2.21212
$910$	−2.91061e6	−0.116515
$911$	−3.87563e7	−1.54720	−0.773600	−	0.633674i	$-0.781546\pi$
$911$	−3.87563e7	−1.54720	−0.773600	+	0.633674i	$0.781546\pi$
$912$	−1.56793e7	−0.624223
$913$	−3.58434e6	−0.142309
$914$	−1.06690e7	−0.422435
$915$	−1.40980e7	−0.556679
$916$	−7.88721e6	−0.310588
$917$	−8.87958e6	−0.348714
$918$	2.92409e7	1.14521
$919$	−1.97989e7	−0.773309	−0.386655	−	0.922225i	$-0.626369\pi$
$919$	−1.97989e7	−0.773309	−0.386655	+	0.922225i	$0.626369\pi$
$920$	−9.03885e6	−0.352082
$921$	−1.27451e7	−0.495103
$922$	−1.17085e7	−0.453603
$923$	2.84296e7	1.09841
$924$	−2.15853e6	−0.0831721
$925$	8.02580e6	0.308414
$926$	−1.96774e7	−0.754121
$927$	1.00417e8	3.83804
$928$	−4.85010e7	−1.84876
$929$	4.20864e7	1.59993	0.799967	−	0.600044i	$-0.204850\pi$
$929$	4.20864e7	1.59993	0.799967	+	0.600044i	$0.204850\pi$
$930$	−4.59439e6	−0.174189
$931$	3.68005e6	0.139149
$932$	−4.74476e6	−0.178927
$933$	1.71598e7	0.645368
$934$	1.56725e7	0.587856
$935$	1.88662e6	0.0705758
$936$	−7.51785e7	−2.80481
$937$	2.14089e7	0.796608	0.398304	−	0.917254i	$-0.369599\pi$
$937$	2.14089e7	0.796608	0.398304	+	0.917254i	$0.369599\pi$
$938$	4.24698e6	0.157606
$939$	5.75956e7	2.13170
$940$	3.81062e6	0.140662
$941$	−2.30140e7	−0.847264	−0.423632	−	0.905834i	$-0.639245\pi$
$941$	−2.30140e7	−0.847264	−0.423632	+	0.905834i	$0.639245\pi$
$942$	3.39497e7	1.24655
$943$	−3.86412e6	−0.141505
$944$	−1.10862e7	−0.404904
$945$	1.10006e7	0.400717
$946$	−2.25177e6	−0.0818079
$947$	−1.69350e7	−0.613636	−0.306818	−	0.951768i	$-0.599264\pi$
$947$	−1.69350e7	−0.613636	−0.306818	+	0.951768i	$0.599264\pi$
$948$	3.30922e7	1.19593
$949$	4.72635e7	1.70357
$950$	−2.62178e6	−0.0942514
$951$	7.42228e7	2.66125
$952$	−9.01626e6	−0.322429
$953$	2.73067e7	0.973952	0.486976	−	0.873415i	$-0.338100\pi$
$953$	2.73067e7	0.973952	0.486976	+	0.873415i	$0.338100\pi$
$954$	−3.05633e7	−1.08725
$955$	7.52259e6	0.266906
$956$	1.18346e7	0.418801
$957$	−1.46824e7	−0.518225
$958$	1.90720e6	0.0671402
$959$	9.98768e6	0.350686
$960$	−3.32712e6	−0.116517
$961$	−2.30136e7	−0.803851
$962$	3.05110e7	1.06296
$963$	8.92711e7	3.10202
$964$	2.60322e7	0.902232
$965$	−4.32844e6	−0.149628
$966$	8.88348e6	0.306295
$967$	−1.08494e7	−0.373111	−0.186555	−	0.982444i	$-0.559732\pi$
$967$	−1.08494e7	−0.373111	−0.186555	+	0.982444i	$0.559732\pi$
$968$	−2.42858e7	−0.833038
$969$	−5.16713e7	−1.76783
$970$	−3.97361e6	−0.135599
$971$	5.42053e7	1.84499	0.922495	−	0.386010i	$-0.126147\pi$
$971$	5.42053e7	1.84499	0.922495	+	0.386010i	$0.126147\pi$
$972$	2.87435e7	0.975830
$973$	−2.50323e6	−0.0847656
$974$	−2.05734e7	−0.694879
$975$	1.53748e7	0.517960
$976$	7.18476e6	0.241428
$977$	−4.07229e7	−1.36490	−0.682452	−	0.730930i	$-0.739086\pi$
$977$	−4.07229e7	−1.36490	−0.682452	+	0.730930i	$0.739086\pi$
$978$	−3.33678e7	−1.11553
$979$	160711.	0.00535905
$980$	−1.47118e6	−0.0489329
$981$	−5.46187e7	−1.81204
$982$	699382.	0.0231438
$983$	1.40230e7	0.462869	0.231434	−	0.972851i	$-0.425658\pi$
$983$	1.40230e7	0.462869	0.231434	+	0.972851i	$0.425658\pi$
$984$	−7.24381e6	−0.238495
$985$	2.52376e6	0.0828815
$986$	−2.65999e7	−0.871339
$987$	−8.63480e6	−0.282137
$988$	3.26128e7	1.06291
$989$	−3.03230e7	−0.985783
$990$	−2.43003e6	−0.0787995
$991$	3.52354e7	1.13971	0.569855	−	0.821745i	$-0.306999\pi$
$991$	3.52354e7	1.13971	0.569855	+	0.821745i	$0.306999\pi$
$992$	1.40695e7	0.453939
$993$	−5.08420e7	−1.63625
$994$	−4.39167e6	−0.140982
$995$	−2.02270e7	−0.647699
$996$	−3.92453e7	−1.25354
$997$	−1.29377e7	−0.412210	−0.206105	−	0.978530i	$-0.566079\pi$
$997$	−1.29377e7	−0.412210	−0.206105	+	0.978530i	$0.566079\pi$
$998$	−2.23055e7	−0.708901
$999$	−1.15316e8	−3.65574

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.6.a.d.1.2	✓	4
3.2	odd	2		315.6.a.l.1.3		4
4.3	odd	2		560.6.a.v.1.4		4
5.2	odd	4		175.6.b.f.99.4		8
5.3	odd	4		175.6.b.f.99.5		8
5.4	even	2		175.6.a.f.1.3		4
7.6	odd	2		245.6.a.e.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.6.a.d.1.2	✓	4	1.1	even	1	trivial
175.6.a.f.1.3		4	5.4	even	2
175.6.b.f.99.4		8	5.2	odd	4
175.6.b.f.99.5		8	5.3	odd	4
245.6.a.e.1.2		4	7.6	odd	2
315.6.a.l.1.3		4	3.2	odd	2
560.6.a.v.1.4		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)

\(f(q)\)	\(=\)	\(q-2.73688 q^{2} -28.3358 q^{3} -24.5095 q^{4} +25.0000 q^{5} +77.5516 q^{6} -49.0000 q^{7} +154.660 q^{8} +559.917 q^{9} -68.4220 q^{10} +63.4296 q^{11} +694.496 q^{12} -868.146 q^{13} +134.107 q^{14} -708.395 q^{15} +361.019 q^{16} +1189.74 q^{17} -1532.43 q^{18} +1532.71 q^{19} -612.737 q^{20} +1388.45 q^{21} -173.599 q^{22} -2337.74 q^{23} -4382.40 q^{24} +625.000 q^{25} +2376.01 q^{26} -8980.10 q^{27} +1200.97 q^{28} +8169.03 q^{29} +1938.79 q^{30} -2369.72 q^{31} -5937.17 q^{32} -1797.33 q^{33} -3256.18 q^{34} -1225.00 q^{35} -13723.3 q^{36} +12841.3 q^{37} -4194.85 q^{38} +24599.6 q^{39} +3866.49 q^{40} +1652.93 q^{41} -3800.03 q^{42} +12971.1 q^{43} -1554.63 q^{44} +13997.9 q^{45} +6398.11 q^{46} -6219.00 q^{47} -10229.8 q^{48} +2401.00 q^{49} -1710.55 q^{50} -33712.3 q^{51} +21277.8 q^{52} +19944.4 q^{53} +24577.5 q^{54} +1585.74 q^{55} -7578.32 q^{56} -43430.7 q^{57} -22357.7 q^{58} -30708.0 q^{59} +17362.4 q^{60} +19901.3 q^{61} +6485.64 q^{62} -27435.9 q^{63} +4696.70 q^{64} -21703.6 q^{65} +4919.07 q^{66} +31668.6 q^{67} -29160.0 q^{68} +66241.7 q^{69} +3352.68 q^{70} -32747.5 q^{71} +86596.6 q^{72} -54441.9 q^{73} -35145.0 q^{74} -17709.9 q^{75} -37566.1 q^{76} -3108.05 q^{77} -67326.1 q^{78} +47649.2 q^{79} +9025.48 q^{80} +118398. q^{81} -4523.87 q^{82} -56509.0 q^{83} -34030.3 q^{84} +29743.6 q^{85} -35500.2 q^{86} -231476. q^{87} +9810.00 q^{88} +2533.69 q^{89} -38310.6 q^{90} +42539.1 q^{91} +57296.8 q^{92} +67148.0 q^{93} +17020.7 q^{94} +38317.9 q^{95} +168235. q^{96} +58075.1 q^{97} -6571.25 q^{98} +35515.3 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 7 q^{2} + 14 q^{3} + 49 q^{4} + 100 q^{5} + 136 q^{6} - 196 q^{7} + 489 q^{8} + 774 q^{9} + 175 q^{10} + 770 q^{11} + 840 q^{12} + 58 q^{13} - 343 q^{14} + 350 q^{15} - 615 q^{16} + 2006 q^{17} - 1409 q^{18}+ \cdots - 420668 q^{99}+O(q^{100}) \) 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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