LMFDB - Embedded newform 35.6.a.d.1.3

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			1.3
Root			$-3.86448$ 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)

$f(q)$	$=$	\(q+5.86448 q^{2} +26.2268 q^{3} +2.39209 q^{4} +25.0000 q^{5} +153.807 q^{6} -49.0000 q^{7} -173.635 q^{8} +444.847 q^{9} +146.612 q^{10} -676.537 q^{11} +62.7370 q^{12} +571.689 q^{13} -287.359 q^{14} +655.671 q^{15} -1094.82 q^{16} +1903.37 q^{17} +2608.80 q^{18} -1367.34 q^{19} +59.8022 q^{20} -1285.12 q^{21} -3967.54 q^{22} -1746.33 q^{23} -4553.89 q^{24} +625.000 q^{25} +3352.65 q^{26} +5293.81 q^{27} -117.212 q^{28} -273.868 q^{29} +3845.17 q^{30} -7565.95 q^{31} -864.258 q^{32} -17743.4 q^{33} +11162.3 q^{34} -1225.00 q^{35} +1064.11 q^{36} +7769.34 q^{37} -8018.71 q^{38} +14993.6 q^{39} -4340.87 q^{40} -783.889 q^{41} -7536.53 q^{42} +7996.03 q^{43} -1618.34 q^{44} +11121.2 q^{45} -10241.3 q^{46} +24154.4 q^{47} -28713.8 q^{48} +2401.00 q^{49} +3665.30 q^{50} +49919.4 q^{51} +1367.53 q^{52} +7980.61 q^{53} +31045.4 q^{54} -16913.4 q^{55} +8508.11 q^{56} -35860.9 q^{57} -1606.09 q^{58} +10820.1 q^{59} +1568.42 q^{60} +5839.92 q^{61} -44370.3 q^{62} -21797.5 q^{63} +29966.0 q^{64} +14292.2 q^{65} -104056. q^{66} +12849.4 q^{67} +4553.03 q^{68} -45800.8 q^{69} -7183.98 q^{70} -70670.5 q^{71} -77241.0 q^{72} -4283.01 q^{73} +45563.1 q^{74} +16391.8 q^{75} -3270.79 q^{76} +33150.3 q^{77} +87929.5 q^{78} +54126.1 q^{79} -27370.6 q^{80} +30742.1 q^{81} -4597.10 q^{82} -24745.8 q^{83} -3074.11 q^{84} +47584.2 q^{85} +46892.5 q^{86} -7182.68 q^{87} +117470. q^{88} +50597.7 q^{89} +65219.9 q^{90} -28012.7 q^{91} -4177.38 q^{92} -198431. q^{93} +141653. q^{94} -34183.4 q^{95} -22666.7 q^{96} -44803.8 q^{97} +14080.6 q^{98} -300956. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.86448	1.03670	0.518351	−	0.855168i	$-0.326546\pi$
$2$	5.86448	1.03670	0.518351	+	0.855168i	$0.326546\pi$
$3$	26.2268	1.68245	0.841226	−	0.540683i	$-0.181834\pi$
$3$	26.2268	1.68245	0.841226	+	0.540683i	$0.181834\pi$
$4$	2.39209	0.0747528
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	153.807	1.74420
$7$	−49.0000	−0.377964
$7$	−49.0000	−0.377964
$8$	−173.635	−0.959206
$9$	444.847	1.83065
$10$	146.612	0.463628
$11$	−676.537	−1.68581	−0.842907	−	0.538059i	$-0.819158\pi$
$11$	−676.537	−1.68581	−0.842907	+	0.538059i	$0.819158\pi$
$12$	62.7370	0.125768
$13$	571.689	0.938212	0.469106	−	0.883142i	$-0.344576\pi$
$13$	571.689	0.938212	0.469106	+	0.883142i	$0.344576\pi$
$14$	−287.359	−0.391837
$15$	655.671	0.752416
$16$	−1094.82	−1.06916
$17$	1903.37	1.59735	0.798676	−	0.601761i	$-0.205534\pi$
$17$	1903.37	1.59735	0.798676	+	0.601761i	$0.205534\pi$
$18$	2608.80	1.89784
$19$	−1367.34	−0.868943	−0.434472	−	0.900685i	$-0.643065\pi$
$19$	−1367.34	−0.868943	−0.434472	+	0.900685i	$0.643065\pi$
$20$	59.8022	0.0334305
$21$	−1285.12	−0.635907
$22$	−3967.54	−1.74769
$23$	−1746.33	−0.688346	−0.344173	−	0.938906i	$-0.611841\pi$
$23$	−1746.33	−0.688346	−0.344173	+	0.938906i	$0.611841\pi$
$24$	−4553.89	−1.61382
$25$	625.000	0.200000
$26$	3352.65	0.972647
$27$	5293.81	1.39752
$28$	−117.212	−0.0282539
$29$	−273.868	−0.0604708	−0.0302354	−	0.999543i	$-0.509626\pi$
$29$	−273.868	−0.0604708	−0.0302354	+	0.999543i	$0.509626\pi$
$30$	3845.17	0.780031
$31$	−7565.95	−1.41403	−0.707016	−	0.707198i	$-0.749959\pi$
$31$	−7565.95	−1.41403	−0.707016	+	0.707198i	$0.749959\pi$
$32$	−864.258	−0.149200
$33$	−17743.4	−2.83630
$34$	11162.3	1.65598
$35$	−1225.00	−0.169031
$36$	1064.11	0.136846
$37$	7769.34	0.932996	0.466498	−	0.884522i	$-0.345515\pi$
$37$	7769.34	0.932996	0.466498	+	0.884522i	$0.345515\pi$
$38$	−8018.71	−0.900836
$39$	14993.6	1.57850
$40$	−4340.87	−0.428970
$41$	−783.889	−0.0728274	−0.0364137	−	0.999337i	$-0.511593\pi$
$41$	−783.889	−0.0728274	−0.0364137	+	0.999337i	$0.511593\pi$
$42$	−7536.53	−0.659247
$43$	7996.03	0.659483	0.329741	−	0.944071i	$-0.393038\pi$
$43$	7996.03	0.659483	0.329741	+	0.944071i	$0.393038\pi$
$44$	−1618.34	−0.126019
$45$	11121.2	0.818690
$46$	−10241.3	−0.713611
$47$	24154.4	1.59497	0.797483	−	0.603341i	$-0.206164\pi$
$47$	24154.4	1.59497	0.797483	+	0.603341i	$0.206164\pi$
$48$	−28713.8	−1.79882
$49$	2401.00	0.142857
$50$	3665.30	0.207341
$51$	49919.4	2.68747
$52$	1367.53	0.0701340
$53$	7980.61	0.390253	0.195127	−	0.980778i	$-0.437488\pi$
$53$	7980.61	0.390253	0.195127	+	0.980778i	$0.437488\pi$
$54$	31045.4	1.44882
$55$	−16913.4	−0.753919
$56$	8508.11	0.362546
$57$	−35860.9	−1.46196
$58$	−1606.09	−0.0626902
$59$	10820.1	0.404672	0.202336	−	0.979316i	$-0.435147\pi$
$59$	10820.1	0.404672	0.202336	+	0.979316i	$0.435147\pi$
$60$	1568.42	0.0562452
$61$	5839.92	0.200947	0.100474	−	0.994940i	$-0.467964\pi$
$61$	5839.92	0.200947	0.100474	+	0.994940i	$0.467964\pi$
$62$	−44370.3	−1.46593
$63$	−21797.5	−0.691919
$64$	29966.0	0.914489
$65$	14292.2	0.419581
$66$	−104056.	−2.94040
$67$	12849.4	0.349701	0.174851	−	0.984595i	$-0.444056\pi$
$67$	12849.4	0.349701	0.174851	+	0.984595i	$0.444056\pi$
$68$	4553.03	0.119407
$69$	−45800.8	−1.15811
$70$	−7183.98	−0.175235
$71$	−70670.5	−1.66377	−0.831883	−	0.554951i	$-0.812737\pi$
$71$	−70670.5	−1.66377	−0.831883	+	0.554951i	$0.812737\pi$
$72$	−77241.0	−1.75597
$73$	−4283.01	−0.0940679	−0.0470340	−	0.998893i	$-0.514977\pi$
$73$	−4283.01	−0.0940679	−0.0470340	+	0.998893i	$0.514977\pi$
$74$	45563.1	0.967240
$75$	16391.8	0.336491
$76$	−3270.79	−0.0649560
$77$	33150.3	0.637178
$78$	87929.5	1.63643
$79$	54126.1	0.975752	0.487876	−	0.872913i	$-0.337772\pi$
$79$	54126.1	0.975752	0.487876	+	0.872913i	$0.337772\pi$
$80$	−27370.6	−0.478145
$81$	30742.1	0.520621
$82$	−4597.10	−0.0755004
$83$	−24745.8	−0.394281	−0.197141	−	0.980375i	$-0.563166\pi$
$83$	−24745.8	−0.394281	−0.197141	+	0.980375i	$0.563166\pi$
$84$	−3074.11	−0.0475359
$85$	47584.2	0.714358
$86$	46892.5	0.683687
$87$	−7182.68	−0.101739
$88$	117470.	1.61704
$89$	50597.7	0.677105	0.338552	−	0.940948i	$-0.390063\pi$
$89$	50597.7	0.677105	0.338552	+	0.940948i	$0.390063\pi$
$90$	65219.9	0.848738
$91$	−28012.7	−0.354611
$92$	−4177.38	−0.0514558
$93$	−198431.	−2.37904
$94$	141653.	1.65351
$95$	−34183.4	−0.388603
$96$	−22666.7	−0.251022
$97$	−44803.8	−0.483488	−0.241744	−	0.970340i	$-0.577719\pi$
$97$	−44803.8	−0.483488	−0.241744	+	0.970340i	$0.577719\pi$
$98$	14080.6	0.148100
$99$	−300956.	−3.08613
$100$	1495.06	0.0149506
$101$	56542.4	0.551532	0.275766	−	0.961225i	$-0.411068\pi$
$101$	56542.4	0.551532	0.275766	+	0.961225i	$0.411068\pi$
$102$	292751.	2.78611
$103$	112268.	1.04270	0.521352	−	0.853342i	$-0.325428\pi$
$103$	112268.	1.04270	0.521352	+	0.853342i	$0.325428\pi$
$104$	−99265.1	−0.899939
$105$	−32127.9	−0.284386
$106$	46802.1	0.404577
$107$	−95494.2	−0.806338	−0.403169	−	0.915125i	$-0.632091\pi$
$107$	−95494.2	−0.806338	−0.403169	+	0.915125i	$0.632091\pi$
$108$	12663.3	0.104469
$109$	−61831.4	−0.498475	−0.249237	−	0.968442i	$-0.580180\pi$
$109$	−61831.4	−0.498475	−0.249237	+	0.968442i	$0.580180\pi$
$110$	−99188.4	−0.781590
$111$	203765.	1.56972
$112$	53646.4	0.404106
$113$	−191050.	−1.40751	−0.703754	−	0.710443i	$-0.748494\pi$
$113$	−191050.	−1.40751	−0.703754	+	0.710443i	$0.748494\pi$
$114$	−210306.	−1.51561
$115$	−43658.3	−0.307838
$116$	−655.116	−0.00452036
$117$	254314.	1.71754
$118$	63454.5	0.419525
$119$	−93265.1	−0.603742
$120$	−113847.	−0.721722
$121$	296651.	1.84197
$122$	34248.1	0.208323
$123$	−20558.9	−0.122529
$124$	−18098.4	−0.105703
$125$	15625.0	0.0894427
$126$	−127831.	−0.717315
$127$	122110.	0.671802	0.335901	−	0.941897i	$-0.390959\pi$
$127$	122110.	0.671802	0.335901	+	0.941897i	$0.390959\pi$
$128$	203391.	1.09725
$129$	209711.	1.10955
$130$	83816.4	0.434981
$131$	−384005.	−1.95505	−0.977527	−	0.210812i	$-0.932389\pi$
$131$	−384005.	−1.95505	−0.977527	+	0.210812i	$0.932389\pi$
$132$	−42443.9	−0.212022
$133$	66999.5	0.328430
$134$	75355.2	0.362536
$135$	132345.	0.624992
$136$	−330491.	−1.53219
$137$	−361164.	−1.64400	−0.822001	−	0.569485i	$-0.807142\pi$
$137$	−361164.	−1.64400	−0.822001	+	0.569485i	$0.807142\pi$
$138$	−268597.	−1.20062
$139$	−297689.	−1.30685	−0.653425	−	0.756991i	$-0.726668\pi$
$139$	−297689.	−1.30685	−0.653425	+	0.756991i	$0.726668\pi$
$140$	−2930.31	−0.0126355
$141$	633493.	2.68345
$142$	−414445.	−1.72483
$143$	−386769.	−1.58165
$144$	−487030.	−1.95726
$145$	−6846.69	−0.0270434
$146$	−25117.6	−0.0975205
$147$	62970.6	0.240350
$148$	18585.0	0.0697441
$149$	93592.3	0.345362	0.172681	−	0.984978i	$-0.444757\pi$
$149$	93592.3	0.345362	0.172681	+	0.984978i	$0.444757\pi$
$150$	96129.2	0.348841
$151$	−95862.0	−0.342140	−0.171070	−	0.985259i	$-0.554722\pi$
$151$	−95862.0	−0.342140	−0.171070	+	0.985259i	$0.554722\pi$
$152$	237417.	0.833496
$153$	846708.	2.92419
$154$	194409.	0.660564
$155$	−189149.	−0.632374
$156$	35866.0	0.117997
$157$	232416.	0.752517	0.376259	−	0.926515i	$-0.377210\pi$
$157$	232416.	0.752517	0.376259	+	0.926515i	$0.377210\pi$
$158$	317421.	1.01156
$159$	209306.	0.656583
$160$	−21606.4	−0.0667242
$161$	85570.2	0.260170
$162$	180287.	0.539729
$163$	343004.	1.01118	0.505592	−	0.862772i	$-0.331274\pi$
$163$	343004.	1.01118	0.505592	+	0.862772i	$0.331274\pi$
$164$	−1875.13	−0.00544405
$165$	−443586.	−1.26843
$166$	−145121.	−0.408752
$167$	−588919.	−1.63405	−0.817023	−	0.576605i	$-0.804377\pi$
$167$	−588919.	−1.63405	−0.817023	+	0.576605i	$0.804377\pi$
$168$	223141.	0.609966
$169$	−44465.1	−0.119757
$170$	279057.	0.740577
$171$	−608256.	−1.59073
$172$	19127.2	0.0492982
$173$	236377.	0.600468	0.300234	−	0.953866i	$-0.402935\pi$
$173$	236377.	0.600468	0.300234	+	0.953866i	$0.402935\pi$
$174$	−42122.7	−0.105473
$175$	−30625.0	−0.0755929
$176$	740689.	1.80241
$177$	283778.	0.680842
$178$	296729.	0.701957
$179$	316194.	0.737600	0.368800	−	0.929509i	$-0.379769\pi$
$179$	316194.	0.737600	0.368800	+	0.929509i	$0.379769\pi$
$180$	26602.9	0.0611994
$181$	−54339.9	−0.123288	−0.0616442	−	0.998098i	$-0.519634\pi$
$181$	−54339.9	−0.123288	−0.0616442	+	0.998098i	$0.519634\pi$
$182$	−164280.	−0.367626
$183$	153163.	0.338084
$184$	303224.	0.660266
$185$	194234.	0.417249
$186$	−1.16369e6	−2.46636
$187$	−1.28770e6	−2.69284
$188$	57779.5	0.119228
$189$	−259397.	−0.528214
$190$	−200468.	−0.402866
$191$	884422.	1.75419	0.877094	−	0.480318i	$-0.159479\pi$
$191$	884422.	1.75419	0.877094	+	0.480318i	$0.159479\pi$
$192$	785913.	1.53858
$193$	−123842.	−0.239318	−0.119659	−	0.992815i	$-0.538180\pi$
$193$	−123842.	−0.239318	−0.119659	+	0.992815i	$0.538180\pi$
$194$	−262751.	−0.501233
$195$	374840.	0.705926
$196$	5743.41	0.0106790
$197$	−437627.	−0.803412	−0.401706	−	0.915769i	$-0.631583\pi$
$197$	−437627.	−0.803412	−0.401706	+	0.915769i	$0.631583\pi$
$198$	−1.76495e6	−3.19940
$199$	915515.	1.63883	0.819413	−	0.573204i	$-0.194300\pi$
$199$	915515.	1.63883	0.819413	+	0.573204i	$0.194300\pi$
$200$	−108522.	−0.191841
$201$	337000.	0.588356
$202$	331592.	0.571775
$203$	13419.5	0.0228558
$204$	119412.	0.200896
$205$	−19597.2	−0.0325694
$206$	658390.	1.08097
$207$	−776851.	−1.26012
$208$	−625899.	−1.00310
$209$	925054.	1.46488
$210$	−188413.	−0.294824
$211$	−700562.	−1.08328	−0.541640	−	0.840611i	$-0.682196\pi$
$211$	−700562.	−1.08328	−0.541640	+	0.840611i	$0.682196\pi$
$212$	19090.3	0.0291725
$213$	−1.85346e6	−2.79921
$214$	−560023.	−0.835933
$215$	199901.	0.294930
$216$	−919191.	−1.34051
$217$	370732.	0.534454
$218$	−362609.	−0.516770
$219$	−112330.	−0.158265
$220$	−40458.4	−0.0563576
$221$	1.08813e6	1.49866
$222$	1.19498e6	1.62734
$223$	769708.	1.03649	0.518244	−	0.855233i	$-0.326586\pi$
$223$	769708.	1.03649	0.518244	+	0.855233i	$0.326586\pi$
$224$	42348.6	0.0563922
$225$	278029.	0.366129
$226$	−1.12041e6	−1.45917
$227$	−254422.	−0.327710	−0.163855	−	0.986484i	$-0.552393\pi$
$227$	−254422.	−0.327710	−0.163855	+	0.986484i	$0.552393\pi$
$228$	−85782.5	−0.109285
$229$	−392135.	−0.494136	−0.247068	−	0.968998i	$-0.579467\pi$
$229$	−392135.	−0.494136	−0.247068	+	0.968998i	$0.579467\pi$
$230$	−256033.	−0.319136
$231$	869428.	1.07202
$232$	47553.0	0.0580040
$233$	−1.52018e6	−1.83444	−0.917222	−	0.398377i	$-0.869574\pi$
$233$	−1.52018e6	−1.83444	−0.917222	+	0.398377i	$0.869574\pi$
$234$	1.49142e6	1.78057
$235$	603860.	0.713291
$236$	25882.8	0.0302504
$237$	1.41956e6	1.64166
$238$	−546951.	−0.625902
$239$	−472223.	−0.534752	−0.267376	−	0.963592i	$-0.586157\pi$
$239$	−472223.	−0.534752	−0.267376	+	0.963592i	$0.586157\pi$
$240$	−717845.	−0.804456
$241$	−357240.	−0.396202	−0.198101	−	0.980182i	$-0.563477\pi$
$241$	−357240.	−0.396202	−0.198101	+	0.980182i	$0.563477\pi$
$242$	1.73970e6	1.90958
$243$	−480128.	−0.521604
$244$	13969.6	0.0150214
$245$	60025.0	0.0638877
$246$	−120567.	−0.127026
$247$	−781691.	−0.815253
$248$	1.31371e6	1.35635
$249$	−649004.	−0.663359
$250$	91632.5	0.0927255
$251$	−47641.6	−0.0477312	−0.0238656	−	0.999715i	$-0.507597\pi$
$251$	−47641.6	−0.0477312	−0.0238656	+	0.999715i	$0.507597\pi$
$252$	−52141.6	−0.0517229
$253$	1.18146e6	1.16042
$254$	716110.	0.696459
$255$	1.24798e6	1.20187
$256$	233871.	0.223037
$257$	−40866.7	−0.0385956	−0.0192978	−	0.999814i	$-0.506143\pi$
$257$	−40866.7	−0.0385956	−0.0192978	+	0.999814i	$0.506143\pi$
$258$	1.22984e6	1.15027
$259$	−380698.	−0.352639
$260$	34188.3	0.0313649
$261$	−121829.	−0.110701
$262$	−2.25199e6	−2.02681
$263$	1.66805e6	1.48703	0.743516	−	0.668718i	$-0.233157\pi$
$263$	1.66805e6	1.48703	0.743516	+	0.668718i	$0.233157\pi$
$264$	3.08088e6	2.72060
$265$	199515.	0.174527
$266$	392917.	0.340484
$267$	1.32702e6	1.13920
$268$	30737.0	0.0261412
$269$	−1.10986e6	−0.935163	−0.467581	−	0.883950i	$-0.654875\pi$
$269$	−1.10986e6	−0.935163	−0.467581	+	0.883950i	$0.654875\pi$
$270$	776136.	0.647931
$271$	63944.2	0.0528905	0.0264453	−	0.999650i	$-0.491581\pi$
$271$	63944.2	0.0528905	0.0264453	+	0.999650i	$0.491581\pi$
$272$	−2.08386e6	−1.70783
$273$	−734686.	−0.596616
$274$	−2.11804e6	−1.70434
$275$	−422836.	−0.337163
$276$	−109560.	−0.0865720
$277$	−1.03013e6	−0.806667	−0.403334	−	0.915053i	$-0.632149\pi$
$277$	−1.03013e6	−0.806667	−0.403334	+	0.915053i	$0.632149\pi$
$278$	−1.74579e6	−1.35482
$279$	−3.36569e6	−2.58859
$280$	212703.	0.162135
$281$	−849393.	−0.641716	−0.320858	−	0.947127i	$-0.603971\pi$
$281$	−849393.	−0.641716	−0.320858	+	0.947127i	$0.603971\pi$
$282$	3.71511e6	2.78195
$283$	1.36010e6	1.00949	0.504747	−	0.863268i	$-0.331586\pi$
$283$	1.36010e6	1.00949	0.504747	+	0.863268i	$0.331586\pi$
$284$	−169050.	−0.124371
$285$	−896523.	−0.653807
$286$	−2.26820e6	−1.63970
$287$	38410.5	0.0275262
$288$	−384463.	−0.273132
$289$	2.20296e6	1.55153
$290$	−40152.3	−0.0280359
$291$	−1.17506e6	−0.813446
$292$	−10245.3	−0.00703184
$293$	−1.07839e6	−0.733851	−0.366925	−	0.930250i	$-0.619590\pi$
$293$	−1.07839e6	−0.733851	−0.366925	+	0.930250i	$0.619590\pi$
$294$	369290.	0.249172
$295$	270504.	0.180975
$296$	−1.34903e6	−0.894936
$297$	−3.58146e6	−2.35597
$298$	548870.	0.358038
$299$	−998358.	−0.645815
$300$	39210.6	0.0251536
$301$	−391806.	−0.249261
$302$	−562180.	−0.354698
$303$	1.48293e6	0.927927
$304$	1.49699e6	0.929044
$305$	145998.	0.0898663
$306$	4.96550e6	3.03151
$307$	1.17194e6	0.709676	0.354838	−	0.934928i	$-0.384536\pi$
$307$	1.17194e6	0.709676	0.354838	+	0.934928i	$0.384536\pi$
$308$	79298.5	0.0476309
$309$	2.94442e6	1.75430
$310$	−1.10926e6	−0.655584
$311$	−798202.	−0.467963	−0.233982	−	0.972241i	$-0.575176\pi$
$311$	−798202.	−0.467963	−0.233982	+	0.972241i	$0.575176\pi$
$312$	−2.60341e6	−1.51411
$313$	−161807.	−0.0933546	−0.0466773	−	0.998910i	$-0.514863\pi$
$313$	−161807.	−0.0933546	−0.0466773	+	0.998910i	$0.514863\pi$
$314$	1.36300e6	0.780137
$315$	−544938.	−0.309436
$316$	129475.	0.0729402
$317$	2.61024e6	1.45892	0.729461	−	0.684022i	$-0.239771\pi$
$317$	2.61024e6	1.45892	0.729461	+	0.684022i	$0.239771\pi$
$318$	1.22747e6	0.680681
$319$	185282.	0.101943
$320$	749149.	0.408972
$321$	−2.50451e6	−1.35663
$322$	501825.	0.269719
$323$	−2.60255e6	−1.38801
$324$	73538.0	0.0389179
$325$	357305.	0.187642
$326$	2.01154e6	1.04830
$327$	−1.62164e6	−0.838660
$328$	136110.	0.0698565
$329$	−1.18357e6	−0.602841
$330$	−2.60140e6	−1.31499
$331$	−182935.	−0.0917754	−0.0458877	−	0.998947i	$-0.514612\pi$
$331$	−182935.	−0.0917754	−0.0458877	+	0.998947i	$0.514612\pi$
$332$	−59194.1	−0.0294736
$333$	3.45617e6	1.70799
$334$	−3.45370e6	−1.69402
$335$	321236.	0.156391
$336$	1.40698e6	0.679890
$337$	2.88308e6	1.38287	0.691436	−	0.722438i	$-0.256978\pi$
$337$	2.88308e6	1.38287	0.691436	+	0.722438i	$0.256978\pi$
$338$	−260765.	−0.124153
$339$	−5.01064e6	−2.36807
$340$	113826.	0.0534002
$341$	5.11865e6	2.38380
$342$	−3.56710e6	−1.64911
$343$	−117649.	−0.0539949
$344$	−1.38839e6	−0.632580
$345$	−1.14502e6	−0.517923
$346$	1.38623e6	0.622507
$347$	−217786.	−0.0970970	−0.0485485	−	0.998821i	$-0.515460\pi$
$347$	−217786.	−0.0970970	−0.0485485	+	0.998821i	$0.515460\pi$
$348$	−17181.6	−0.00760529
$349$	−486940.	−0.213999	−0.106999	−	0.994259i	$-0.534124\pi$
$349$	−486940.	−0.213999	−0.106999	+	0.994259i	$0.534124\pi$
$350$	−179600.	−0.0783674
$351$	3.02641e6	1.31117
$352$	584702.	0.251523
$353$	−3.86915e6	−1.65264	−0.826322	−	0.563198i	$-0.809571\pi$
$353$	−3.86915e6	−1.65264	−0.826322	+	0.563198i	$0.809571\pi$
$354$	1.66421e6	0.705830
$355$	−1.76676e6	−0.744059
$356$	121034.	0.0506155
$357$	−2.44605e6	−1.01577
$358$	1.85431e6	0.764672
$359$	1.56454e6	0.640693	0.320346	−	0.947300i	$-0.396201\pi$
$359$	1.56454e6	0.640693	0.320346	+	0.947300i	$0.396201\pi$
$360$	−1.93102e6	−0.785293
$361$	−606489.	−0.244937
$362$	−318675.	−0.127813
$363$	7.78023e6	3.09903
$364$	−67009.0	−0.0265082
$365$	−107075.	−0.0420685
$366$	898218.	0.350493
$367$	3.59726e6	1.39414	0.697070	−	0.717003i	$-0.254487\pi$
$367$	3.59726e6	1.39414	0.697070	+	0.717003i	$0.254487\pi$
$368$	1.91193e6	0.735956
$369$	−348711.	−0.133321
$370$	1.13908e6	0.432563
$371$	−391050.	−0.147502
$372$	−474665.	−0.177840
$373$	235126.	0.0875042	0.0437521	−	0.999042i	$-0.486069\pi$
$373$	235126.	0.0875042	0.0437521	+	0.999042i	$0.486069\pi$
$374$	−7.55169e6	−2.79168
$375$	409794.	0.150483
$376$	−4.19405e6	−1.52990
$377$	−156567.	−0.0567344
$378$	−1.52123e6	−0.547601
$379$	5.00375e6	1.78936	0.894680	−	0.446708i	$-0.147404\pi$
$379$	5.00375e6	1.78936	0.894680	+	0.446708i	$0.147404\pi$
$380$	−81769.8	−0.0290492
$381$	3.20255e6	1.13027
$382$	5.18667e6	1.81857
$383$	95576.7	0.0332931	0.0166466	−	0.999861i	$-0.494701\pi$
$383$	95576.7	0.0332931	0.0166466	+	0.999861i	$0.494701\pi$
$384$	5.33430e6	1.84608
$385$	828758.	0.284955
$386$	−726270.	−0.248102
$387$	3.55701e6	1.20728
$388$	−107175.	−0.0361421
$389$	−202953.	−0.0680018	−0.0340009	−	0.999422i	$-0.510825\pi$
$389$	−202953.	−0.0680018	−0.0340009	+	0.999422i	$0.510825\pi$
$390$	2.19824e6	0.731835
$391$	−3.32391e6	−1.09953
$392$	−416897.	−0.137029
$393$	−1.00712e7	−3.28928
$394$	−2.56645e6	−0.832899
$395$	1.35315e6	0.436369
$396$	−719913.	−0.230697
$397$	5.10471e6	1.62553	0.812765	−	0.582592i	$-0.197961\pi$
$397$	5.10471e6	1.62553	0.812765	+	0.582592i	$0.197961\pi$
$398$	5.36902e6	1.69897
$399$	1.75719e6	0.552567
$400$	−684265.	−0.213833
$401$	3.55590e6	1.10430	0.552152	−	0.833744i	$-0.313807\pi$
$401$	3.55590e6	1.10430	0.552152	+	0.833744i	$0.313807\pi$
$402$	1.97633e6	0.609950
$403$	−4.32537e6	−1.32666
$404$	135255.	0.0412286
$405$	768553.	0.232829
$406$	78698.4	0.0236947
$407$	−5.25625e6	−1.57286
$408$	−8.66774e6	−2.57784
$409$	4.06243e6	1.20082	0.600409	−	0.799693i	$-0.295005\pi$
$409$	4.06243e6	1.20082	0.600409	+	0.799693i	$0.295005\pi$
$410$	−114927.	−0.0337648
$411$	−9.47218e6	−2.76596
$412$	268554.	0.0779451
$413$	−530187.	−0.152952
$414$	−4.55582e6	−1.30637
$415$	−618644.	−0.176328
$416$	−494086.	−0.139981
$417$	−7.80744e6	−2.19871
$418$	5.42496e6	1.51864
$419$	−5.00441e6	−1.39257	−0.696287	−	0.717764i	$-0.745166\pi$
$419$	−5.00441e6	−1.39257	−0.696287	+	0.717764i	$0.745166\pi$
$420$	−76852.8	−0.0212587
$421$	2.18001e6	0.599450	0.299725	−	0.954026i	$-0.403105\pi$
$421$	2.18001e6	0.599450	0.299725	+	0.954026i	$0.403105\pi$
$422$	−4.10843e6	−1.12304
$423$	1.07450e7	2.91982
$424$	−1.38571e6	−0.374333
$425$	1.18961e6	0.319470
$426$	−1.08696e7	−2.90195
$427$	−286156.	−0.0759509
$428$	−228431.	−0.0602761
$429$	−1.01437e7	−2.66106
$430$	1.17231e6	0.305754
$431$	1.89764e6	0.492064	0.246032	−	0.969262i	$-0.420873\pi$
$431$	1.89764e6	0.492064	0.246032	+	0.969262i	$0.420873\pi$
$432$	−5.79580e6	−1.49418
$433$	2.54804e6	0.653109	0.326555	−	0.945178i	$-0.394112\pi$
$433$	2.54804e6	0.653109	0.326555	+	0.945178i	$0.394112\pi$
$434$	2.17415e6	0.554070
$435$	−179567.	−0.0454992
$436$	−147906.	−0.0372624
$437$	2.38782e6	0.598134
$438$	−658755.	−0.164074
$439$	−3.49094e6	−0.864531	−0.432266	−	0.901746i	$-0.642286\pi$
$439$	−3.49094e6	−0.864531	−0.432266	+	0.901746i	$0.642286\pi$
$440$	2.93676e6	0.723164
$441$	1.06808e6	0.261521
$442$	6.38134e6	1.55366
$443$	7.44707e6	1.80292	0.901459	−	0.432865i	$-0.142497\pi$
$443$	7.44707e6	1.80292	0.901459	+	0.432865i	$0.142497\pi$
$444$	487425.	0.117341
$445$	1.26494e6	0.302811
$446$	4.51394e6	1.07453
$447$	2.45463e6	0.581055
$448$	−1.46833e6	−0.345644
$449$	6.53613e6	1.53005	0.765024	−	0.644002i	$-0.222727\pi$
$449$	6.53613e6	1.53005	0.765024	+	0.644002i	$0.222727\pi$
$450$	1.63050e6	0.379567
$451$	530330.	0.122773
$452$	−457009.	−0.105215
$453$	−2.51416e6	−0.575635
$454$	−1.49205e6	−0.339738
$455$	−700319.	−0.158587
$456$	6.22671e6	1.40232
$457$	−3.97253e6	−0.889769	−0.444884	−	0.895588i	$-0.646755\pi$
$457$	−3.97253e6	−0.889769	−0.444884	+	0.895588i	$0.646755\pi$
$458$	−2.29966e6	−0.512272
$459$	1.00761e7	2.23234
$460$	−104435.	−0.0230117
$461$	−3.06530e6	−0.671771	−0.335885	−	0.941903i	$-0.609035\pi$
$461$	−3.06530e6	−0.671771	−0.335885	+	0.941903i	$0.609035\pi$
$462$	5.09874e6	1.11137
$463$	−6.12862e6	−1.32865	−0.664324	−	0.747445i	$-0.731281\pi$
$463$	−6.12862e6	−1.32865	−0.664324	+	0.747445i	$0.731281\pi$
$464$	299837.	0.0646532
$465$	−4.96077e6	−1.06394
$466$	−8.91504e6	−1.90177
$467$	3.32929e6	0.706414	0.353207	−	0.935545i	$-0.385091\pi$
$467$	3.32929e6	0.706414	0.353207	+	0.935545i	$0.385091\pi$
$468$	608342.	0.128391
$469$	−629623.	−0.132175
$470$	3.54132e6	0.739470
$471$	6.09553e6	1.26607
$472$	−1.87876e6	−0.388164
$473$	−5.40961e6	−1.11177
$474$	8.32496e6	1.70191
$475$	−854585.	−0.173789
$476$	−223098.	−0.0451314
$477$	3.55015e6	0.714416
$478$	−2.76934e6	−0.554379
$479$	1.66554e6	0.331678	0.165839	−	0.986153i	$-0.446967\pi$
$479$	1.66554e6	0.331678	0.165839	+	0.986153i	$0.446967\pi$
$480$	−566669.	−0.112260
$481$	4.44164e6	0.875349
$482$	−2.09502e6	−0.410744
$483$	2.24424e6	0.437725
$484$	709617.	0.137693
$485$	−1.12010e6	−0.216222
$486$	−2.81570e6	−0.540748
$487$	6.07174e6	1.16009	0.580044	−	0.814585i	$-0.303035\pi$
$487$	6.07174e6	1.16009	0.580044	+	0.814585i	$0.303035\pi$
$488$	−1.01401e6	−0.192750
$489$	8.99592e6	1.70127
$490$	352015.	0.0662325
$491$	3.17811e6	0.594930	0.297465	−	0.954733i	$-0.403859\pi$
$491$	3.17811e6	0.594930	0.297465	+	0.954733i	$0.403859\pi$
$492$	−49178.8	−0.00915936
$493$	−521271.	−0.0965932
$494$	−4.58421e6	−0.845176
$495$	−7.52389e6	−1.38016
$496$	8.28339e6	1.51183
$497$	3.46285e6	0.628844
$498$	−3.80607e6	−0.687706
$499$	6.34535e6	1.14079	0.570393	−	0.821372i	$-0.306791\pi$
$499$	6.34535e6	1.14079	0.570393	+	0.821372i	$0.306791\pi$
$500$	37376.4	0.00668609
$501$	−1.54455e7	−2.74921
$502$	−279393.	−0.0494831
$503$	−1.02132e7	−1.79988	−0.899941	−	0.436012i	$-0.856391\pi$
$503$	−1.02132e7	−1.79988	−0.899941	+	0.436012i	$0.856391\pi$
$504$	3.78481e6	0.663694
$505$	1.41356e6	0.246653
$506$	6.92863e6	1.20302
$507$	−1.16618e6	−0.201486
$508$	292098.	0.0502191
$509$	365958.	0.0626090	0.0313045	−	0.999510i	$-0.490034\pi$
$509$	365958.	0.0626090	0.0313045	+	0.999510i	$0.490034\pi$
$510$	7.31877e6	1.24599
$511$	209867.	0.0355543
$512$	−5.13698e6	−0.866031
$513$	−7.23843e6	−1.21437
$514$	−239662.	−0.0400121
$515$	2.80669e6	0.466312
$516$	501647.	0.0829418
$517$	−1.63413e7	−2.68882
$518$	−2.23259e6	−0.365582
$519$	6.19942e6	1.01026
$520$	−2.48163e6	−0.402465
$521$	−4.87107e6	−0.786195	−0.393097	−	0.919497i	$-0.628596\pi$
$521$	−4.87107e6	−0.786195	−0.393097	+	0.919497i	$0.628596\pi$
$522$	−714465.	−0.114764
$523$	−5.97444e6	−0.955087	−0.477544	−	0.878608i	$-0.658473\pi$
$523$	−5.97444e6	−0.955087	−0.477544	+	0.878608i	$0.658473\pi$
$524$	−918574.	−0.146146
$525$	−803197.	−0.127181
$526$	9.78226e6	1.54161
$527$	−1.44008e7	−2.25871
$528$	1.94259e7	3.03248
$529$	−3.38667e6	−0.526179
$530$	1.17005e6	0.180932
$531$	4.81331e6	0.740812
$532$	160269.	0.0245510
$533$	−448140.	−0.0683276
$534$	7.78227e6	1.18101
$535$	−2.38735e6	−0.360606
$536$	−2.23111e6	−0.335436
$537$	8.29277e6	1.24098
$538$	−6.50874e6	−0.969486
$539$	−1.62437e6	−0.240831
$540$	316582.	0.0467199
$541$	2.15541e6	0.316619	0.158310	−	0.987390i	$-0.449396\pi$
$541$	2.15541e6	0.316619	0.158310	+	0.987390i	$0.449396\pi$
$542$	374999.	0.0548318
$543$	−1.42516e6	−0.207427
$544$	−1.64500e6	−0.238325
$545$	−1.54579e6	−0.222925
$546$	−4.30855e6	−0.618514
$547$	3.29386e6	0.470692	0.235346	−	0.971912i	$-0.424378\pi$
$547$	3.29386e6	0.470692	0.235346	+	0.971912i	$0.424378\pi$
$548$	−863936.	−0.122894
$549$	2.59787e6	0.367863
$550$	−2.47971e6	−0.349538
$551$	374469.	0.0525457
$552$	7.95261e6	1.11087
$553$	−2.65218e6	−0.368799
$554$	−6.04120e6	−0.836274
$555$	5.09413e6	0.702001
$556$	−712099.	−0.0976907
$557$	−7.08864e6	−0.968111	−0.484055	−	0.875037i	$-0.660837\pi$
$557$	−7.08864e6	−0.968111	−0.484055	+	0.875037i	$0.660837\pi$
$558$	−1.97380e7	−2.68360
$559$	4.57124e6	0.618735
$560$	1.34116e6	0.180722
$561$	−3.37723e7	−4.53058
$562$	−4.98124e6	−0.665269
$563$	5.57433e6	0.741177	0.370589	−	0.928797i	$-0.379156\pi$
$563$	5.57433e6	0.741177	0.370589	+	0.928797i	$0.379156\pi$
$564$	1.51537e6	0.200596
$565$	−4.77625e6	−0.629457
$566$	7.97625e6	1.04654
$567$	−1.50636e6	−0.196776
$568$	1.22709e7	1.59590
$569$	−1.22641e7	−1.58801	−0.794005	−	0.607911i	$-0.792008\pi$
$569$	−1.22641e7	−1.58801	−0.794005	+	0.607911i	$0.792008\pi$
$570$	−5.25764e6	−0.677803
$571$	2.14667e6	0.275533	0.137767	−	0.990465i	$-0.456008\pi$
$571$	2.14667e6	0.275533	0.137767	+	0.990465i	$0.456008\pi$
$572$	−925185.	−0.118233
$573$	2.31956e7	2.95134
$574$	225258.	0.0285365
$575$	−1.09146e6	−0.137669
$576$	1.33303e7	1.67411
$577$	4.63935e6	0.580120	0.290060	−	0.957008i	$-0.406325\pi$
$577$	4.63935e6	0.580120	0.290060	+	0.957008i	$0.406325\pi$
$578$	1.29192e7	1.60848
$579$	−3.24799e6	−0.402641
$580$	−16377.9	−0.00202157
$581$	1.21254e6	0.149024
$582$	−6.89113e6	−0.843301
$583$	−5.39918e6	−0.657895
$584$	743680.	0.0902306
$585$	6.35785e6	0.768105
$586$	−6.32421e6	−0.760785
$587$	3.95890e6	0.474219	0.237110	−	0.971483i	$-0.423800\pi$
$587$	3.95890e6	0.474219	0.237110	+	0.971483i	$0.423800\pi$
$588$	150631.	0.0179669
$589$	1.03452e7	1.22871
$590$	1.58636e6	0.187617
$591$	−1.14776e7	−1.35170
$592$	−8.50607e6	−0.997527
$593$	1.13423e7	1.32454	0.662271	−	0.749264i	$-0.269593\pi$
$593$	1.13423e7	1.32454	0.662271	+	0.749264i	$0.269593\pi$
$594$	−2.10034e7	−2.44244
$595$	−2.33163e6	−0.270002
$596$	223881.	0.0258168
$597$	2.40111e7	2.75725
$598$	−5.85485e6	−0.669518
$599$	−9.26926e6	−1.05555	−0.527774	−	0.849385i	$-0.676973\pi$
$599$	−9.26926e6	−1.05555	−0.527774	+	0.849385i	$0.676973\pi$
$600$	−2.84618e6	−0.322764
$601$	7.97681e6	0.900831	0.450415	−	0.892819i	$-0.351276\pi$
$601$	7.97681e6	0.900831	0.450415	+	0.892819i	$0.351276\pi$
$602$	−2.29773e6	−0.258410
$603$	5.71604e6	0.640179
$604$	−229310.	−0.0255759
$605$	7.41628e6	0.823755
$606$	8.69660e6	0.961984
$607$	1.10438e7	1.21660	0.608299	−	0.793708i	$-0.291852\pi$
$607$	1.10438e7	1.21660	0.608299	+	0.793708i	$0.291852\pi$
$608$	1.18173e6	0.129646
$609$	351951.	0.0384538
$610$	856201.	0.0931647
$611$	1.38088e7	1.49642
$612$	2.02540e6	0.218591
$613$	6.46147e6	0.694513	0.347256	−	0.937770i	$-0.387113\pi$
$613$	6.46147e6	0.694513	0.347256	+	0.937770i	$0.387113\pi$
$614$	6.87282e6	0.735723
$615$	−513973.	−0.0547965
$616$	−5.75605e6	−0.611185
$617$	−1.26159e6	−0.133415	−0.0667076	−	0.997773i	$-0.521249\pi$
$617$	−1.26159e6	−0.133415	−0.0667076	+	0.997773i	$0.521249\pi$
$618$	1.72675e7	1.81869
$619$	−1.50526e7	−1.57901	−0.789506	−	0.613743i	$-0.789663\pi$
$619$	−1.50526e7	−1.57901	−0.789506	+	0.613743i	$0.789663\pi$
$620$	−452461.	−0.0472718
$621$	−9.24475e6	−0.961980
$622$	−4.68104e6	−0.485139
$623$	−2.47929e6	−0.255922
$624$	−1.64153e7	−1.68767
$625$	390625.	0.0400000
$626$	−948912.	−0.0967810
$627$	2.42612e7	2.46459
$628$	555959.	0.0562528
$629$	1.47879e7	1.49032
$630$	−3.19578e6	−0.320793
$631$	2.35746e6	0.235706	0.117853	−	0.993031i	$-0.462399\pi$
$631$	2.35746e6	0.235706	0.117853	+	0.993031i	$0.462399\pi$
$632$	−9.39819e6	−0.935947
$633$	−1.83735e7	−1.82257
$634$	1.53077e7	1.51247
$635$	3.05274e6	0.300439
$636$	500679.	0.0490814
$637$	1.37262e6	0.134030
$638$	1.08658e6	0.105684
$639$	−3.14376e7	−3.04577
$640$	5.08478e6	0.490707
$641$	3.11408e6	0.299354	0.149677	−	0.988735i	$-0.452177\pi$
$641$	3.11408e6	0.299354	0.149677	+	0.988735i	$0.452177\pi$
$642$	−1.46876e7	−1.40642
$643$	−5.53949e6	−0.528375	−0.264187	−	0.964471i	$-0.585104\pi$
$643$	−5.53949e6	−0.528375	−0.264187	+	0.964471i	$0.585104\pi$
$644$	204692.	0.0194485
$645$	5.24277e6	0.496205
$646$	−1.52626e7	−1.43895
$647$	−6.75129e6	−0.634054	−0.317027	−	0.948416i	$-0.602685\pi$
$647$	−6.75129e6	−0.634054	−0.317027	+	0.948416i	$0.602685\pi$
$648$	−5.33791e6	−0.499383
$649$	−7.32023e6	−0.682202
$650$	2.09541e6	0.194529
$651$	9.72312e6	0.899193
$652$	820497.	0.0755889
$653$	−1.18732e6	−0.108965	−0.0544824	−	0.998515i	$-0.517351\pi$
$653$	−1.18732e6	−0.108965	−0.0544824	+	0.998515i	$0.517351\pi$
$654$	−9.51009e6	−0.869441
$655$	−9.60012e6	−0.874326
$656$	858221.	0.0778645
$657$	−1.90528e6	−0.172205
$658$	−6.94099e6	−0.624967
$659$	−1.60043e6	−0.143556	−0.0717781	−	0.997421i	$-0.522867\pi$
$659$	−1.60043e6	−0.143556	−0.0717781	+	0.997421i	$0.522867\pi$
$660$	−1.06110e6	−0.0948190
$661$	2.18068e6	0.194128	0.0970641	−	0.995278i	$-0.469055\pi$
$661$	2.18068e6	0.194128	0.0970641	+	0.995278i	$0.469055\pi$
$662$	−1.07282e6	−0.0951439
$663$	2.85383e7	2.52142
$664$	4.29673e6	0.378197
$665$	1.67499e6	0.146878
$666$	2.02686e7	1.77067
$667$	478264.	0.0416248
$668$	−1.40875e6	−0.122150
$669$	2.01870e7	1.74384
$670$	1.88388e6	0.162131
$671$	−3.95092e6	−0.338760
$672$	1.11067e6	0.0948773
$673$	4.74231e6	0.403601	0.201800	−	0.979427i	$-0.435321\pi$
$673$	4.74231e6	0.403601	0.201800	+	0.979427i	$0.435321\pi$
$674$	1.69078e7	1.43363
$675$	3.30863e6	0.279505
$676$	−106365.	−0.00895221
$677$	1.62647e7	1.36388	0.681939	−	0.731409i	$-0.261137\pi$
$677$	1.62647e7	1.36388	0.681939	+	0.731409i	$0.261137\pi$
$678$	−2.93848e7	−2.45498
$679$	2.19539e6	0.182741
$680$	−8.26228e6	−0.685216
$681$	−6.67268e6	−0.551356
$682$	3.00182e7	2.47129
$683$	−6.37968e6	−0.523295	−0.261648	−	0.965163i	$-0.584266\pi$
$683$	−6.37968e6	−0.523295	−0.261648	+	0.965163i	$0.584266\pi$
$684$	−1.45500e6	−0.118911
$685$	−9.02909e6	−0.735220
$686$	−689950.	−0.0559767
$687$	−1.02845e7	−0.831361
$688$	−8.75425e6	−0.705096
$689$	4.56242e6	0.366140
$690$	−6.71494e6	−0.536932
$691$	−1.68738e6	−0.134436	−0.0672182	−	0.997738i	$-0.521412\pi$
$691$	−1.68738e6	−0.134436	−0.0672182	+	0.997738i	$0.521412\pi$
$692$	565435.	0.0448867
$693$	1.47468e7	1.16645
$694$	−1.27720e6	−0.100661
$695$	−7.44222e6	−0.584441
$696$	1.24716e6	0.0975889
$697$	−1.49203e6	−0.116331
$698$	−2.85565e6	−0.221853
$699$	−3.98694e7	−3.08636
$700$	−73257.8	−0.00565078
$701$	7.09402e6	0.545252	0.272626	−	0.962120i	$-0.412108\pi$
$701$	7.09402e6	0.545252	0.272626	+	0.962120i	$0.412108\pi$
$702$	1.77483e7	1.35930
$703$	−1.06233e7	−0.810721
$704$	−2.02731e7	−1.54166
$705$	1.58373e7	1.20008
$706$	−2.26906e7	−1.71330
$707$	−2.77058e6	−0.208460
$708$	678823.	0.0508948
$709$	1.59881e7	1.19448	0.597242	−	0.802061i	$-0.296263\pi$
$709$	1.59881e7	1.19448	0.597242	+	0.802061i	$0.296263\pi$
$710$	−1.03611e7	−0.771368
$711$	2.40779e7	1.78626
$712$	−8.78553e6	−0.649483
$713$	1.32127e7	0.973344
$714$	−1.43448e7	−1.05305
$715$	−9.66921e6	−0.707336
$716$	756364.	0.0551377
$717$	−1.23849e7	−0.899695
$718$	9.17519e6	0.664208
$719$	−1.71955e6	−0.124049	−0.0620244	−	0.998075i	$-0.519756\pi$
$719$	−1.71955e6	−0.124049	−0.0620244	+	0.998075i	$0.519756\pi$
$720$	−1.21757e7	−0.875315
$721$	−5.50111e6	−0.394105
$722$	−3.55674e6	−0.253927
$723$	−9.36927e6	−0.666592
$724$	−129986.	−0.00921616
$725$	−171167.	−0.0120942
$726$	4.56270e7	3.21277
$727$	−9.77842e6	−0.686172	−0.343086	−	0.939304i	$-0.611472\pi$
$727$	−9.77842e6	−0.686172	−0.343086	+	0.939304i	$0.611472\pi$
$728$	4.86399e6	0.340145
$729$	−2.00626e7	−1.39819
$730$	−627940.	−0.0436125
$731$	1.52194e7	1.05343
$732$	366379.	0.0252727
$733$	3.78427e6	0.260149	0.130074	−	0.991504i	$-0.458478\pi$
$733$	3.78427e6	0.260149	0.130074	+	0.991504i	$0.458478\pi$
$734$	2.10960e7	1.44531
$735$	1.57427e6	0.107488
$736$	1.50928e6	0.102701
$737$	−8.69312e6	−0.589531
$738$	−2.04501e6	−0.138214
$739$	−2.79115e7	−1.88006	−0.940032	−	0.341085i	$-0.889205\pi$
$739$	−2.79115e7	−1.88006	−0.940032	+	0.341085i	$0.889205\pi$
$740$	464624.	0.0311905
$741$	−2.05013e7	−1.37163
$742$	−2.29330e6	−0.152916
$743$	−1.29261e7	−0.859003	−0.429501	−	0.903066i	$-0.641311\pi$
$743$	−1.29261e7	−0.859003	−0.429501	+	0.903066i	$0.641311\pi$
$744$	3.44545e7	2.28199
$745$	2.33981e6	0.154450
$746$	1.37889e6	0.0907158
$747$	−1.10081e7	−0.721789
$748$	−3.08029e6	−0.201297
$749$	4.67921e6	0.304767
$750$	2.40323e6	0.156006
$751$	−2.29989e7	−1.48801	−0.744006	−	0.668173i	$-0.767077\pi$
$751$	−2.29989e7	−1.48801	−0.744006	+	0.668173i	$0.767077\pi$
$752$	−2.64448e7	−1.70528
$753$	−1.24949e6	−0.0803055
$754$	−918183.	−0.0588168
$755$	−2.39655e6	−0.153010
$756$	−620501.	−0.0394855
$757$	−1.28294e7	−0.813707	−0.406853	−	0.913493i	$-0.633374\pi$
$757$	−1.28294e7	−0.813707	−0.406853	+	0.913493i	$0.633374\pi$
$758$	2.93444e7	1.85503
$759$	3.09859e7	1.95236
$760$	5.93543e6	0.372751
$761$	−2.75191e7	−1.72256	−0.861278	−	0.508134i	$-0.830335\pi$
$761$	−2.75191e7	−1.72256	−0.861278	+	0.508134i	$0.830335\pi$
$762$	1.87813e7	1.17176
$763$	3.02974e6	0.188406
$764$	2.11562e6	0.131131
$765$	2.11677e7	1.30774
$766$	560507.	0.0345151
$767$	6.18576e6	0.379668
$768$	6.13369e6	0.375248
$769$	2.27228e6	0.138563	0.0692814	−	0.997597i	$-0.477929\pi$
$769$	2.27228e6	0.138563	0.0692814	+	0.997597i	$0.477929\pi$
$770$	4.86023e6	0.295413
$771$	−1.07181e6	−0.0649352
$772$	−296242.	−0.0178897
$773$	−1.49746e7	−0.901374	−0.450687	−	0.892682i	$-0.648821\pi$
$773$	−1.49746e7	−0.901374	−0.450687	+	0.892682i	$0.648821\pi$
$774$	2.08600e7	1.25159
$775$	−4.72872e6	−0.282806
$776$	7.77951e6	0.463765
$777$	−9.98450e6	−0.593299
$778$	−1.19021e6	−0.0704977
$779$	1.07184e6	0.0632829
$780$	896650.	0.0527699
$781$	4.78112e7	2.80480
$782$	−1.94930e7	−1.13989
$783$	−1.44980e6	−0.0845094
$784$	−2.62867e6	−0.152738
$785$	5.81039e6	0.336536
$786$	−5.90625e7	−3.41001
$787$	1.87087e6	0.107673	0.0538365	−	0.998550i	$-0.482855\pi$
$787$	1.87087e6	0.107673	0.0538365	+	0.998550i	$0.482855\pi$
$788$	−1.04684e6	−0.0600573
$789$	4.37477e7	2.50186
$790$	7.93554e6	0.452385
$791$	9.36145e6	0.531988
$792$	5.22564e7	2.96024
$793$	3.33861e6	0.188531
$794$	2.99365e7	1.68519
$795$	5.23266e6	0.293633
$796$	2.18999e6	0.122507
$797$	9.47450e6	0.528336	0.264168	−	0.964477i	$-0.414903\pi$
$797$	9.47450e6	0.528336	0.264168	+	0.964477i	$0.414903\pi$
$798$	1.03050e7	0.572848
$799$	4.59747e7	2.54772
$800$	−540161.	−0.0298400
$801$	2.25083e7	1.23954
$802$	2.08535e7	1.14483
$803$	2.89761e6	0.158581
$804$	806135.	0.0439812
$805$	2.13926e6	0.116352
$806$	−2.53660e7	−1.37535
$807$	−2.91081e7	−1.57337
$808$	−9.81774e6	−0.529033
$809$	−4.29215e6	−0.230570	−0.115285	−	0.993332i	$-0.536778\pi$
$809$	−4.29215e6	−0.230570	−0.115285	+	0.993332i	$0.536778\pi$
$810$	4.50716e6	0.241374
$811$	5.54068e6	0.295809	0.147904	−	0.989002i	$-0.452747\pi$
$811$	5.54068e6	0.295809	0.147904	+	0.989002i	$0.452747\pi$
$812$	32100.7	0.00170854
$813$	1.67705e6	0.0889858
$814$	−3.08251e7	−1.63059
$815$	8.57511e6	0.452216
$816$	−5.46530e7	−2.87335
$817$	−1.09333e7	−0.573053
$818$	2.38240e7	1.24489
$819$	−1.24614e7	−0.649167
$820$	−46878.3	−0.00243465
$821$	−2.40253e7	−1.24397	−0.621987	−	0.783028i	$-0.713674\pi$
$821$	−2.40253e7	−1.24397	−0.621987	+	0.783028i	$0.713674\pi$
$822$	−5.55494e7	−2.86748
$823$	3.21565e7	1.65489	0.827446	−	0.561545i	$-0.189793\pi$
$823$	3.21565e7	1.65489	0.827446	+	0.561545i	$0.189793\pi$
$824$	−1.94936e7	−1.00017
$825$	−1.10896e7	−0.567261
$826$	−3.10927e6	−0.158565
$827$	9.33348e6	0.474548	0.237274	−	0.971443i	$-0.423746\pi$
$827$	9.33348e6	0.474548	0.237274	+	0.971443i	$0.423746\pi$
$828$	−1.85830e6	−0.0941974
$829$	2.08810e7	1.05527	0.527636	−	0.849470i	$-0.323078\pi$
$829$	2.08810e7	1.05527	0.527636	+	0.849470i	$0.323078\pi$
$830$	−3.62803e6	−0.182800
$831$	−2.70172e7	−1.35718
$832$	1.71312e7	0.857985
$833$	4.56999e6	0.228193
$834$	−4.57866e7	−2.27941
$835$	−1.47230e7	−0.730768
$836$	2.21281e6	0.109504
$837$	−4.00527e7	−1.97614
$838$	−2.93483e7	−1.44368
$839$	5.98049e6	0.293313	0.146657	−	0.989187i	$-0.453149\pi$
$839$	5.98049e6	0.293313	0.146657	+	0.989187i	$0.453149\pi$
$840$	5.57852e6	0.272785
$841$	−2.04361e7	−0.996343
$842$	1.27846e7	0.621452
$843$	−2.22769e7	−1.07966
$844$	−1.67581e6	−0.0809782
$845$	−1.11163e6	−0.0535572
$846$	6.30139e7	3.02699
$847$	−1.45359e7	−0.696200
$848$	−8.73737e6	−0.417245
$849$	3.56710e7	1.69842
$850$	6.97642e6	0.331196
$851$	−1.35678e7	−0.642225
$852$	−4.43365e6	−0.209249
$853$	−3.33915e7	−1.57132	−0.785659	−	0.618660i	$-0.787676\pi$
$853$	−3.33915e7	−1.57132	−0.785659	+	0.618660i	$0.787676\pi$
$854$	−1.67815e6	−0.0787385
$855$	−1.52064e7	−0.711395
$856$	1.65811e7	0.773445
$857$	9.92905e6	0.461802	0.230901	−	0.972977i	$-0.425833\pi$
$857$	9.92905e6	0.461802	0.230901	+	0.972977i	$0.425833\pi$
$858$	−5.94876e7	−2.75872
$859$	−2.98210e7	−1.37892	−0.689461	−	0.724323i	$-0.742153\pi$
$859$	−2.98210e7	−1.37892	−0.689461	+	0.724323i	$0.742153\pi$
$860$	478181.	0.0220468
$861$	1.00739e6	0.0463115
$862$	1.11287e7	0.510124
$863$	1.31237e7	0.599830	0.299915	−	0.953966i	$-0.403042\pi$
$863$	1.31237e7	0.599830	0.299915	+	0.953966i	$0.403042\pi$
$864$	−4.57522e6	−0.208510
$865$	5.90943e6	0.268538
$866$	1.49429e7	0.677080
$867$	5.77766e7	2.61038
$868$	886823.	0.0399519
$869$	−3.66183e7	−1.64494
$870$	−1.05307e6	−0.0471691
$871$	7.34588e6	0.328094
$872$	1.07361e7	0.478140
$873$	−1.99309e7	−0.885096
$874$	1.40033e7	0.620087
$875$	−765625.	−0.0338062
$876$	−268703.	−0.0118307
$877$	2.20940e7	0.970008	0.485004	−	0.874512i	$-0.338818\pi$
$877$	2.20940e7	0.970008	0.485004	+	0.874512i	$0.338818\pi$
$878$	−2.04725e7	−0.896262
$879$	−2.82828e7	−1.23467
$880$	1.85172e7	0.806064
$881$	1.84644e6	0.0801483	0.0400742	−	0.999197i	$-0.487241\pi$
$881$	1.84644e6	0.0801483	0.0400742	+	0.999197i	$0.487241\pi$
$882$	6.26372e6	0.271120
$883$	4.08005e7	1.76102	0.880509	−	0.474030i	$-0.157201\pi$
$883$	4.08005e7	1.76102	0.880509	+	0.474030i	$0.157201\pi$
$884$	2.60292e6	0.112029
$885$	7.09446e6	0.304482
$886$	4.36732e7	1.86909
$887$	2.73192e6	0.116589	0.0582946	−	0.998299i	$-0.481434\pi$
$887$	2.73192e6	0.116589	0.0582946	+	0.998299i	$0.481434\pi$
$888$	−3.53808e7	−1.50569
$889$	−5.98338e6	−0.253917
$890$	7.41823e6	0.313925
$891$	−2.07982e7	−0.877670
$892$	1.84121e6	0.0774804
$893$	−3.30272e7	−1.38594
$894$	1.43951e7	0.602381
$895$	7.90485e6	0.329865
$896$	−9.96616e6	−0.414723
$897$	−2.61838e7	−1.08655
$898$	3.83310e7	1.58620
$899$	2.07207e6	0.0855076
$900$	665072.	0.0273692
$901$	1.51901e7	0.623372
$902$	3.11011e6	0.127280
$903$	−1.02758e7	−0.419370
$904$	3.31730e7	1.35009
$905$	−1.35850e6	−0.0551363
$906$	−1.47442e7	−0.596762
$907$	−4.64835e7	−1.87621	−0.938104	−	0.346354i	$-0.887419\pi$
$907$	−4.64835e7	−1.87621	−0.938104	+	0.346354i	$0.887419\pi$
$908$	−608600.	−0.0244972
$909$	2.51527e7	1.00966
$910$	−4.10700e6	−0.164407
$911$	2.51979e7	1.00593	0.502966	−	0.864306i	$-0.332242\pi$
$911$	2.51979e7	1.00593	0.502966	+	0.864306i	$0.332242\pi$
$912$	3.92614e7	1.56307
$913$	1.67414e7	0.664685
$914$	−2.32968e7	−0.922426
$915$	3.82906e6	0.151196
$916$	−938021.	−0.0369381
$917$	1.88162e7	0.738941
$918$	5.90909e7	2.31427
$919$	1.83012e7	0.714810	0.357405	−	0.933949i	$-0.383662\pi$
$919$	1.83012e7	0.714810	0.357405	+	0.933949i	$0.383662\pi$
$920$	7.58060e6	0.295280
$921$	3.07363e7	1.19400
$922$	−1.79764e7	−0.696426
$923$	−4.04015e7	−1.56097
$924$	2.07975e6	0.0801367
$925$	4.85584e6	0.186599
$926$	−3.59411e7	−1.37741
$927$	4.99419e7	1.90882
$928$	236692.	0.00902223
$929$	−1.99283e7	−0.757583	−0.378791	−	0.925482i	$-0.623660\pi$
$929$	−1.99283e7	−0.757583	−0.378791	+	0.925482i	$0.623660\pi$
$930$	−2.90923e7	−1.10299
$931$	−3.28298e6	−0.124135
$932$	−3.63640e6	−0.137130
$933$	−2.09343e7	−0.787326
$934$	1.95245e7	0.732341
$935$	−3.21925e7	−1.20427
$936$	−4.41578e7	−1.64747
$937$	−3.42218e7	−1.27337	−0.636684	−	0.771125i	$-0.719694\pi$
$937$	−3.42218e7	−1.27337	−0.636684	+	0.771125i	$0.719694\pi$
$938$	−3.69241e6	−0.137026
$939$	−4.24368e6	−0.157065
$940$	1.44449e6	0.0533205
$941$	−1.20137e7	−0.442286	−0.221143	−	0.975241i	$-0.570979\pi$
$941$	−1.20137e7	−0.442286	−0.221143	+	0.975241i	$0.570979\pi$
$942$	3.57471e7	1.31254
$943$	1.36893e6	0.0501305
$944$	−1.18462e7	−0.432661
$945$	−6.48492e6	−0.236225
$946$	−3.17245e7	−1.15257
$947$	8.21067e6	0.297511	0.148756	−	0.988874i	$-0.452473\pi$
$947$	8.21067e6	0.297511	0.148756	+	0.988874i	$0.452473\pi$
$948$	3.39571e6	0.122718
$949$	−2.44855e6	−0.0882557
$950$	−5.01170e6	−0.180167
$951$	6.84583e7	2.45457
$952$	1.61941e7	0.579114
$953$	5.17724e6	0.184657	0.0923285	−	0.995729i	$-0.470569\pi$
$953$	5.17724e6	0.184657	0.0923285	+	0.995729i	$0.470569\pi$
$954$	2.08198e7	0.740637
$955$	2.21106e7	0.784497
$956$	−1.12960e6	−0.0399742
$957$	4.85935e6	0.171513
$958$	9.76754e6	0.343852
$959$	1.76970e7	0.621375
$960$	1.96478e7	0.688076
$961$	2.86144e7	0.999486
$962$	2.60479e7	0.907477
$963$	−4.24803e7	−1.47612
$964$	−854550.	−0.0296173
$965$	−3.09606e6	−0.107026
$966$	1.31613e7	0.453790
$967$	2.72831e6	0.0938270	0.0469135	−	0.998899i	$-0.485061\pi$
$967$	2.72831e6	0.0938270	0.0469135	+	0.998899i	$0.485061\pi$
$968$	−5.15090e7	−1.76683
$969$	−6.82566e7	−2.33526
$970$	−6.56877e6	−0.224158
$971$	4.81341e7	1.63834	0.819171	−	0.573549i	$-0.194434\pi$
$971$	4.81341e7	1.63834	0.819171	+	0.573549i	$0.194434\pi$
$972$	−1.14851e6	−0.0389914
$973$	1.45868e7	0.493943
$974$	3.56076e7	1.20267
$975$	9.37099e6	0.315700
$976$	−6.39369e6	−0.214846
$977$	−1.54803e7	−0.518851	−0.259425	−	0.965763i	$-0.583533\pi$
$977$	−1.54803e7	−0.518851	−0.259425	+	0.965763i	$0.583533\pi$
$978$	5.27564e7	1.76371
$979$	−3.42312e7	−1.14147
$980$	143585.	0.00477578
$981$	−2.75055e7	−0.912531
$982$	1.86380e7	0.616766
$983$	562513.	0.0185673	0.00928364	−	0.999957i	$-0.497045\pi$
$983$	562513.	0.0185673	0.00928364	+	0.999957i	$0.497045\pi$
$984$	3.56975e6	0.117530
$985$	−1.09407e7	−0.359297
$986$	−3.05698e6	−0.100138
$987$	−3.10412e7	−1.01425
$988$	−1.86987e6	−0.0609425
$989$	−1.39637e7	−0.453952
$990$	−4.41237e7	−1.43082
$991$	−2.10005e7	−0.679274	−0.339637	−	0.940557i	$-0.610304\pi$
$991$	−2.10005e7	−0.679274	−0.339637	+	0.940557i	$0.610304\pi$
$992$	6.53893e6	0.210973
$993$	−4.79780e6	−0.154408
$994$	2.03078e7	0.651925
$995$	2.28879e7	0.732905
$996$	−1.55247e6	−0.0495880
$997$	−5.49674e6	−0.175133	−0.0875664	−	0.996159i	$-0.527909\pi$
$997$	−5.49674e6	−0.175133	−0.0875664	+	0.996159i	$0.527909\pi$
$998$	3.72122e7	1.18266
$999$	4.11294e7	1.30388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.6.a.d.1.3	✓	4
3.2	odd	2		315.6.a.l.1.2		4
4.3	odd	2		560.6.a.v.1.1		4
5.2	odd	4		175.6.b.f.99.6		8
5.3	odd	4		175.6.b.f.99.3		8
5.4	even	2		175.6.a.f.1.2		4
7.6	odd	2		245.6.a.e.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.6.a.d.1.3	✓	4	1.1	even	1	trivial
175.6.a.f.1.2		4	5.4	even	2
175.6.b.f.99.3		8	5.3	odd	4
175.6.b.f.99.6		8	5.2	odd	4
245.6.a.e.1.3		4	7.6	odd	2
315.6.a.l.1.2		4	3.2	odd	2
560.6.a.v.1.1		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)

\(f(q)\)	\(=\)	\(q+5.86448 q^{2} +26.2268 q^{3} +2.39209 q^{4} +25.0000 q^{5} +153.807 q^{6} -49.0000 q^{7} -173.635 q^{8} +444.847 q^{9} +146.612 q^{10} -676.537 q^{11} +62.7370 q^{12} +571.689 q^{13} -287.359 q^{14} +655.671 q^{15} -1094.82 q^{16} +1903.37 q^{17} +2608.80 q^{18} -1367.34 q^{19} +59.8022 q^{20} -1285.12 q^{21} -3967.54 q^{22} -1746.33 q^{23} -4553.89 q^{24} +625.000 q^{25} +3352.65 q^{26} +5293.81 q^{27} -117.212 q^{28} -273.868 q^{29} +3845.17 q^{30} -7565.95 q^{31} -864.258 q^{32} -17743.4 q^{33} +11162.3 q^{34} -1225.00 q^{35} +1064.11 q^{36} +7769.34 q^{37} -8018.71 q^{38} +14993.6 q^{39} -4340.87 q^{40} -783.889 q^{41} -7536.53 q^{42} +7996.03 q^{43} -1618.34 q^{44} +11121.2 q^{45} -10241.3 q^{46} +24154.4 q^{47} -28713.8 q^{48} +2401.00 q^{49} +3665.30 q^{50} +49919.4 q^{51} +1367.53 q^{52} +7980.61 q^{53} +31045.4 q^{54} -16913.4 q^{55} +8508.11 q^{56} -35860.9 q^{57} -1606.09 q^{58} +10820.1 q^{59} +1568.42 q^{60} +5839.92 q^{61} -44370.3 q^{62} -21797.5 q^{63} +29966.0 q^{64} +14292.2 q^{65} -104056. q^{66} +12849.4 q^{67} +4553.03 q^{68} -45800.8 q^{69} -7183.98 q^{70} -70670.5 q^{71} -77241.0 q^{72} -4283.01 q^{73} +45563.1 q^{74} +16391.8 q^{75} -3270.79 q^{76} +33150.3 q^{77} +87929.5 q^{78} +54126.1 q^{79} -27370.6 q^{80} +30742.1 q^{81} -4597.10 q^{82} -24745.8 q^{83} -3074.11 q^{84} +47584.2 q^{85} +46892.5 q^{86} -7182.68 q^{87} +117470. q^{88} +50597.7 q^{89} +65219.9 q^{90} -28012.7 q^{91} -4177.38 q^{92} -198431. q^{93} +141653. q^{94} -34183.4 q^{95} -22666.7 q^{96} -44803.8 q^{97} +14080.6 q^{98} -300956. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 7 q^{2} + 14 q^{3} + 49 q^{4} + 100 q^{5} + 136 q^{6} - 196 q^{7} + 489 q^{8} + 774 q^{9} + 175 q^{10} + 770 q^{11} + 840 q^{12} + 58 q^{13} - 343 q^{14} + 350 q^{15} - 615 q^{16} + 2006 q^{17} - 1409 q^{18}+ \cdots - 420668 q^{99}+O(q^{100}) \) 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

Introduction

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