LMFDB - Embedded newform 65.6.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,6,Mod(1,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("65.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	65.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$10.4249482878$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 163x^{4} - 8x^{3} + 6120x^{2} + 6624x - 19440 $ x^6 - 163x^4 - 8x^3 + 6120x^2 + 6624x - 19440
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-10.7882$ of defining polynomial
Character	$\chi$	$=$	65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-10.7882 q^{2} +0.527294 q^{3} +84.3852 q^{4} -25.0000 q^{5} -5.68855 q^{6} +231.710 q^{7} -565.142 q^{8} -242.722 q^{9} +269.705 q^{10} -466.402 q^{11} +44.4958 q^{12} +169.000 q^{13} -2499.74 q^{14} -13.1824 q^{15} +3396.54 q^{16} +882.905 q^{17} +2618.53 q^{18} +167.308 q^{19} -2109.63 q^{20} +122.180 q^{21} +5031.63 q^{22} +3037.27 q^{23} -297.996 q^{24} +625.000 q^{25} -1823.21 q^{26} -256.118 q^{27} +19552.9 q^{28} +6278.22 q^{29} +142.214 q^{30} -4294.08 q^{31} -18558.0 q^{32} -245.931 q^{33} -9524.96 q^{34} -5792.76 q^{35} -20482.2 q^{36} -7285.93 q^{37} -1804.96 q^{38} +89.1127 q^{39} +14128.6 q^{40} +18984.4 q^{41} -1318.10 q^{42} +14295.7 q^{43} -39357.4 q^{44} +6068.05 q^{45} -32766.7 q^{46} +8375.45 q^{47} +1790.98 q^{48} +36882.8 q^{49} -6742.62 q^{50} +465.551 q^{51} +14261.1 q^{52} +20546.0 q^{53} +2763.06 q^{54} +11660.0 q^{55} -130949. q^{56} +88.2207 q^{57} -67730.7 q^{58} -118.006 q^{59} -1112.40 q^{60} +24590.5 q^{61} +46325.3 q^{62} -56241.2 q^{63} +91518.2 q^{64} -4225.00 q^{65} +2653.15 q^{66} -34789.8 q^{67} +74504.2 q^{68} +1601.54 q^{69} +62493.5 q^{70} +9033.72 q^{71} +137172. q^{72} +30590.1 q^{73} +78602.1 q^{74} +329.559 q^{75} +14118.4 q^{76} -108070. q^{77} -961.365 q^{78} -14290.7 q^{79} -84913.5 q^{80} +58846.4 q^{81} -204808. q^{82} +65535.3 q^{83} +10310.2 q^{84} -22072.6 q^{85} -154225. q^{86} +3310.47 q^{87} +263583. q^{88} -85188.3 q^{89} -65463.3 q^{90} +39159.1 q^{91} +256301. q^{92} -2264.24 q^{93} -90356.0 q^{94} -4182.71 q^{95} -9785.53 q^{96} +51071.6 q^{97} -397898. q^{98} +113206. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 38 q^{3} + 134 q^{4} - 150 q^{5} + 318 q^{6} + 220 q^{7} + 24 q^{8} + 518 q^{9} - 170 q^{11} + 2238 q^{12} + 1014 q^{13} - 1440 q^{14} - 950 q^{15} + 3506 q^{16} + 728 q^{17} + 7788 q^{18} + 1218 q^{19}+ \cdots - 32270 q^{99}+O(q^{100}) $ 6 * q + 38 * q^3 + 134 * q^4 - 150 * q^5 + 318 * q^6 + 220 * q^7 + 24 * q^8 + 518 * q^9 - 170 * q^11 + 2238 * q^12 + 1014 * q^13 - 1440 * q^14 - 950 * q^15 + 3506 * q^16 + 728 * q^17 + 7788 * q^18 + 1218 * q^19 - 3350 * q^20 - 396 * q^21 + 5154 * q^22 + 8954 * q^23 + 12618 * q^24 + 3750 * q^25 + 13112 * q^27 + 13212 * q^28 + 8364 * q^29 - 7950 * q^30 + 2862 * q^31 - 29672 * q^32 - 3772 * q^33 - 21484 * q^34 - 5500 * q^35 - 2138 * q^36 + 13840 * q^37 - 27706 * q^38 + 6422 * q^39 - 600 * q^40 + 2248 * q^41 - 47028 * q^42 + 3822 * q^43 - 73482 * q^44 - 12950 * q^45 - 39886 * q^46 - 10860 * q^47 + 13962 * q^48 + 85902 * q^49 - 55028 * q^51 + 22646 * q^52 + 6584 * q^53 + 45504 * q^54 + 4250 * q^55 - 188800 * q^56 + 11692 * q^57 - 88500 * q^58 - 28874 * q^59 - 55950 * q^60 + 972 * q^61 + 123466 * q^62 - 125236 * q^63 + 14022 * q^64 - 25350 * q^65 - 158040 * q^66 + 60040 * q^67 + 3504 * q^68 + 153088 * q^69 + 36000 * q^70 - 74174 * q^71 + 298668 * q^72 + 48960 * q^73 + 226112 * q^74 + 23750 * q^75 - 93422 * q^76 + 231588 * q^77 + 53742 * q^78 + 214508 * q^79 - 87650 * q^80 + 116006 * q^81 + 58732 * q^82 + 123260 * q^83 - 235268 * q^84 - 18200 * q^85 - 304666 * q^86 + 228144 * q^87 + 127622 * q^88 + 94028 * q^89 - 194700 * q^90 + 37180 * q^91 + 430298 * q^92 + 192892 * q^93 - 125920 * q^94 - 30450 * q^95 - 385858 * q^96 + 246284 * q^97 - 4736 * q^98 - 32270 * 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 $

$2$	−10.7882	−1.90710	−0.953551	−	0.301231i	$-0.902602\pi$
$2$	−10.7882	−1.90710	−0.953551	+	0.301231i	$0.902602\pi$
$3$	0.527294	0.0338259	0.0169130	−	0.999857i	$-0.494616\pi$
$3$	0.527294	0.0338259	0.0169130	+	0.999857i	$0.494616\pi$
$4$	84.3852	2.63704
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−5.68855	−0.0645095
$7$	231.710	1.78731	0.893656	−	0.448752i	$-0.148131\pi$
$7$	231.710	1.78731	0.893656	+	0.448752i	$0.148131\pi$
$8$	−565.142	−3.12200
$9$	−242.722	−0.998856
$10$	269.705	0.852882
$11$	−466.402	−1.16219	−0.581097	−	0.813835i	$-0.697376\pi$
$11$	−466.402	−1.16219	−0.581097	+	0.813835i	$0.697376\pi$
$12$	44.4958	0.0892003
$13$	169.000	0.277350
$13$	169.000	0.277350
$14$	−2499.74	−3.40859
$15$	−13.1824	−0.0151274
$16$	3396.54	3.31693
$17$	882.905	0.740955	0.370478	−	0.928841i	$-0.379194\pi$
$17$	882.905	0.740955	0.370478	+	0.928841i	$0.379194\pi$
$18$	2618.53	1.90492
$19$	167.308	0.106325	0.0531623	−	0.998586i	$-0.483070\pi$
$19$	167.308	0.106325	0.0531623	+	0.998586i	$0.483070\pi$
$20$	−2109.63	−1.17932
$21$	122.180	0.0604575
$22$	5031.63	2.21642
$23$	3037.27	1.19719	0.598597	−	0.801051i	$-0.295725\pi$
$23$	3037.27	1.19719	0.598597	+	0.801051i	$0.295725\pi$
$24$	−297.996	−0.105605
$25$	625.000	0.200000
$26$	−1823.21	−0.528935
$27$	−256.118	−0.0676132
$28$	19552.9	4.71321
$29$	6278.22	1.38625	0.693125	−	0.720818i	$-0.256233\pi$
$29$	6278.22	1.38625	0.693125	+	0.720818i	$0.256233\pi$
$30$	142.214	0.0288495
$31$	−4294.08	−0.802538	−0.401269	−	0.915960i	$-0.631431\pi$
$31$	−4294.08	−0.802538	−0.401269	+	0.915960i	$0.631431\pi$
$32$	−18558.0	−3.20373
$33$	−245.931	−0.0393123
$34$	−9524.96	−1.41308
$35$	−5792.76	−0.799311
$36$	−20482.2	−2.63402
$37$	−7285.93	−0.874945	−0.437472	−	0.899232i	$-0.644126\pi$
$37$	−7285.93	−0.874945	−0.437472	+	0.899232i	$0.644126\pi$
$38$	−1804.96	−0.202772
$39$	89.1127	0.00938162
$40$	14128.6	1.39620
$41$	18984.4	1.76375	0.881875	−	0.471482i	$-0.156281\pi$
$41$	18984.4	1.76375	0.881875	+	0.471482i	$0.156281\pi$
$42$	−1318.10	−0.115299
$43$	14295.7	1.17906	0.589528	−	0.807748i	$-0.299314\pi$
$43$	14295.7	1.17906	0.589528	+	0.807748i	$0.299314\pi$
$44$	−39357.4	−3.06475
$45$	6068.05	0.446702
$46$	−32766.7	−2.28317
$47$	8375.45	0.553049	0.276524	−	0.961007i	$-0.410817\pi$
$47$	8375.45	0.553049	0.276524	+	0.961007i	$0.410817\pi$
$48$	1790.98	0.112198
$49$	36882.8	2.19449
$50$	−6742.62	−0.381420
$51$	465.551	0.0250635
$52$	14261.1	0.731383
$53$	20546.0	1.00470	0.502351	−	0.864664i	$-0.332468\pi$
$53$	20546.0	1.00470	0.502351	+	0.864664i	$0.332468\pi$
$54$	2763.06	0.128945
$55$	11660.0	0.519749
$56$	−130949.	−5.57999
$57$	88.2207	0.00359653
$58$	−67730.7	−2.64372
$59$	−118.006	−0.00441341	−0.00220670	−	0.999998i	$-0.500702\pi$
$59$	−118.006	−0.00441341	−0.00220670	+	0.999998i	$0.500702\pi$
$60$	−1112.40	−0.0398916
$61$	24590.5	0.846143	0.423071	−	0.906096i	$-0.360952\pi$
$61$	24590.5	0.846143	0.423071	+	0.906096i	$0.360952\pi$
$62$	46325.3	1.53052
$63$	−56241.2	−1.78527
$64$	91518.2	2.79291
$65$	−4225.00	−0.124035
$66$	2653.15	0.0749725
$67$	−34789.8	−0.946813	−0.473407	−	0.880844i	$-0.656976\pi$
$67$	−34789.8	−0.946813	−0.473407	+	0.880844i	$0.656976\pi$
$68$	74504.2	1.95393
$69$	1601.54	0.0404962
$70$	62493.5	1.52437
$71$	9033.72	0.212677	0.106339	−	0.994330i	$-0.466087\pi$
$71$	9033.72	0.212677	0.106339	+	0.994330i	$0.466087\pi$
$72$	137172.	3.11843
$73$	30590.1	0.671853	0.335926	−	0.941888i	$-0.390951\pi$
$73$	30590.1	0.671853	0.335926	+	0.941888i	$0.390951\pi$
$74$	78602.1	1.66861
$75$	329.559	0.00676519
$76$	14118.4	0.280382
$77$	−108070.	−2.07720
$78$	−961.365	−0.0178917
$79$	−14290.7	−0.257624	−0.128812	−	0.991669i	$-0.541116\pi$
$79$	−14290.7	−0.257624	−0.128812	+	0.991669i	$0.541116\pi$
$80$	−84913.5	−1.48338
$81$	58846.4	0.996569
$82$	−204808.	−3.36365
$83$	65535.3	1.04419	0.522096	−	0.852887i	$-0.325150\pi$
$83$	65535.3	1.04419	0.522096	+	0.852887i	$0.325150\pi$
$84$	10310.2	0.159429
$85$	−22072.6	−0.331365
$86$	−154225.	−2.24858
$87$	3310.47	0.0468912
$88$	263583.	3.62837
$89$	−85188.3	−1.14000	−0.570000	−	0.821644i	$-0.693057\pi$
$89$	−85188.3	−1.14000	−0.570000	+	0.821644i	$0.693057\pi$
$90$	−65463.3	−0.851906
$91$	39159.1	0.495711
$92$	256301.	3.15705
$93$	−2264.24	−0.0271466
$94$	−90356.0	−1.05472
$95$	−4182.71	−0.0475498
$96$	−9785.53	−0.108369
$97$	51071.6	0.551124	0.275562	−	0.961283i	$-0.411136\pi$
$97$	51071.6	0.551124	0.275562	+	0.961283i	$0.411136\pi$
$98$	−397898.	−4.18511
$99$	113206.	1.16086
$100$	52740.8	0.527408
$101$	−149777.	−1.46098	−0.730488	−	0.682926i	$-0.760707\pi$
$101$	−149777.	−1.46098	−0.730488	+	0.682926i	$0.760707\pi$
$102$	−5022.45	−0.0477986
$103$	79535.6	0.738700	0.369350	−	0.929290i	$-0.379580\pi$
$103$	79535.6	0.738700	0.369350	+	0.929290i	$0.379580\pi$
$104$	−95509.1	−0.865887
$105$	−3054.49	−0.0270374
$106$	−221654.	−1.91607
$107$	15175.1	0.128136	0.0640682	−	0.997946i	$-0.479592\pi$
$107$	15175.1	0.128136	0.0640682	+	0.997946i	$0.479592\pi$
$108$	−21612.6	−0.178299
$109$	−112925.	−0.910384	−0.455192	−	0.890393i	$-0.650429\pi$
$109$	−112925.	−0.910384	−0.455192	+	0.890393i	$0.650429\pi$
$110$	−125791.	−0.991214
$111$	−3841.83	−0.0295958
$112$	787014.	5.92840
$113$	−30361.7	−0.223682	−0.111841	−	0.993726i	$-0.535675\pi$
$113$	−30361.7	−0.223682	−0.111841	+	0.993726i	$0.535675\pi$
$114$	−951.743	−0.00685895
$115$	−75931.8	−0.535401
$116$	529789.	3.65559
$117$	−41020.0	−0.277033
$118$	1273.07	0.00841682
$119$	204578.	1.32432
$120$	7449.91	0.0472278
$121$	56479.5	0.350693
$122$	−265288.	−1.61368
$123$	10010.4	0.0596605
$124$	−362357.	−2.11632
$125$	−15625.0	−0.0894427
$126$	606742.	3.40469
$127$	4509.41	0.0248091	0.0124045	−	0.999923i	$-0.496051\pi$
$127$	4509.41	0.0248091	0.0124045	+	0.999923i	$0.496051\pi$
$128$	−393460.	−2.12264
$129$	7538.04	0.0398827
$130$	45580.1	0.236547
$131$	−149727.	−0.762292	−0.381146	−	0.924515i	$-0.624471\pi$
$131$	−149727.	−0.762292	−0.381146	+	0.924515i	$0.624471\pi$
$132$	−20752.9	−0.103668
$133$	38767.1	0.190035
$134$	375319.	1.80567
$135$	6402.96	0.0302375
$136$	−498967.	−2.31326
$137$	158516.	0.721558	0.360779	−	0.932651i	$-0.382511\pi$
$137$	158516.	0.721558	0.360779	+	0.932651i	$0.382511\pi$
$138$	−17277.7	−0.0772304
$139$	69849.6	0.306639	0.153319	−	0.988177i	$-0.451004\pi$
$139$	69849.6	0.306639	0.153319	+	0.988177i	$0.451004\pi$
$140$	−488824.	−2.10781
$141$	4416.33	0.0187074
$142$	−97457.6	−0.405597
$143$	−78821.9	−0.322334
$144$	−824415.	−3.31314
$145$	−156955.	−0.619950
$146$	−330012.	−1.28129
$147$	19448.1	0.0742306
$148$	−614825.	−2.30726
$149$	−56811.4	−0.209638	−0.104819	−	0.994491i	$-0.533426\pi$
$149$	−56811.4	−0.209638	−0.104819	+	0.994491i	$0.533426\pi$
$150$	−3555.35	−0.0129019
$151$	25593.3	0.0913447	0.0456724	−	0.998956i	$-0.485457\pi$
$151$	25593.3	0.0913447	0.0456724	+	0.998956i	$0.485457\pi$
$152$	−94553.1	−0.331945
$153$	−214301.	−0.740107
$154$	1.16588e6	3.96144
$155$	107352.	0.358906
$156$	7519.80	0.0247397
$157$	−464261.	−1.50319	−0.751593	−	0.659627i	$-0.770714\pi$
$157$	−464261.	−1.50319	−0.751593	+	0.659627i	$0.770714\pi$
$158$	154171.	0.491316
$159$	10833.8	0.0339850
$160$	463950.	1.43275
$161$	703768.	2.13976
$162$	−634847.	−1.90056
$163$	233236.	0.687584	0.343792	−	0.939046i	$-0.388288\pi$
$163$	233236.	0.687584	0.343792	+	0.939046i	$0.388288\pi$
$164$	1.60200e6	4.65108
$165$	6148.27	0.0175810
$166$	−707008.	−1.99138
$167$	−5473.80	−0.0151879	−0.00759395	−	0.999971i	$-0.502417\pi$
$167$	−5473.80	−0.0151879	−0.00759395	+	0.999971i	$0.502417\pi$
$168$	−69048.9	−0.188748
$169$	28561.0	0.0769231
$170$	238124.	0.631947
$171$	−40609.4	−0.106203
$172$	1.20635e6	3.10922
$173$	−583869.	−1.48320	−0.741601	−	0.670841i	$-0.765933\pi$
$173$	−583869.	−1.48320	−0.741601	+	0.670841i	$0.765933\pi$
$174$	−35714.0	−0.0894263
$175$	144819.	0.357463
$176$	−1.58415e6	−3.85492
$177$	−62.2238	−0.000149288 0
$178$	919029.	2.17410
$179$	495004.	1.15472	0.577359	−	0.816490i	$-0.304083\pi$
$179$	495004.	1.15472	0.577359	+	0.816490i	$0.304083\pi$
$180$	512054.	1.17797
$181$	648193.	1.47065	0.735323	−	0.677717i	$-0.237031\pi$
$181$	648193.	1.47065	0.735323	+	0.677717i	$0.237031\pi$
$182$	−422456.	−0.945372
$183$	12966.4	0.0286216
$184$	−1.71649e6	−3.73764
$185$	182148.	0.391287
$186$	24427.1	0.0517713
$187$	−411789.	−0.861133
$188$	706765.	1.45841
$189$	−59345.3	−0.120846
$190$	45123.9	0.0906824
$191$	−882509.	−1.75039	−0.875197	−	0.483767i	$-0.839268\pi$
$191$	−882509.	−1.75039	−0.875197	+	0.483767i	$0.839268\pi$
$192$	48257.0	0.0944729
$193$	693680.	1.34050	0.670249	−	0.742137i	$-0.266187\pi$
$193$	693680.	1.34050	0.670249	+	0.742137i	$0.266187\pi$
$194$	−550970.	−1.05105
$195$	−2227.82	−0.00419559
$196$	3.11236e6	5.78695
$197$	−190019.	−0.348844	−0.174422	−	0.984671i	$-0.555806\pi$
$197$	−190019.	−0.348844	−0.174422	+	0.984671i	$0.555806\pi$
$198$	−1.22129e6	−2.21389
$199$	−141002.	−0.252403	−0.126201	−	0.992005i	$-0.540279\pi$
$199$	−141002.	−0.252403	−0.126201	+	0.992005i	$0.540279\pi$
$200$	−353214.	−0.624400
$201$	−18344.4	−0.0320268
$202$	1.61583e6	2.78623
$203$	1.45473e6	2.47766
$204$	39285.6	0.0660934
$205$	−474610.	−0.788773
$206$	−858045.	−1.40878
$207$	−737213.	−1.19582
$208$	574015.	0.919952
$209$	−78032.9	−0.123570
$210$	32952.4	0.0515631
$211$	−417539.	−0.645640	−0.322820	−	0.946460i	$-0.604631\pi$
$211$	−417539.	−0.645640	−0.322820	+	0.946460i	$0.604631\pi$
$212$	1.73378e6	2.64944
$213$	4763.43	0.00719400
$214$	−163712.	−0.244369
$215$	−357393.	−0.527290
$216$	144743.	0.211088
$217$	−994982.	−1.43439
$218$	1.21826e6	1.73620
$219$	16130.0	0.0227260
$220$	983935.	1.37060
$221$	149211.	0.205504
$222$	41446.4	0.0564422
$223$	289938.	0.390429	0.195215	−	0.980761i	$-0.437460\pi$
$223$	289938.	0.390429	0.195215	+	0.980761i	$0.437460\pi$
$224$	−4.30008e6	−5.72607
$225$	−151701.	−0.199771
$226$	327549.	0.426584
$227$	−1.05748e6	−1.36210	−0.681049	−	0.732238i	$-0.738476\pi$
$227$	−1.05748e6	−1.36210	−0.681049	+	0.732238i	$0.738476\pi$
$228$	7444.53	0.00948419
$229$	−827977.	−1.04335	−0.521674	−	0.853145i	$-0.674692\pi$
$229$	−827977.	−1.04335	−0.521674	+	0.853145i	$0.674692\pi$
$230$	819168.	1.02106
$231$	−56984.8	−0.0702633
$232$	−3.54809e6	−4.32787
$233$	339021.	0.409107	0.204554	−	0.978855i	$-0.434426\pi$
$233$	339021.	0.409107	0.204554	+	0.978855i	$0.434426\pi$
$234$	442532.	0.528330
$235$	−209386.	−0.247331
$236$	−9957.96	−0.0116383
$237$	−7535.42	−0.00871438
$238$	−2.20703e6	−2.52561
$239$	1.66517e6	1.88567	0.942833	−	0.333267i	$-0.108151\pi$
$239$	1.66517e6	1.88567	0.942833	+	0.333267i	$0.108151\pi$
$240$	−44774.4	−0.0501767
$241$	−9484.31	−0.0105187	−0.00525937	−	0.999986i	$-0.501674\pi$
$241$	−9484.31	−0.0105187	−0.00525937	+	0.999986i	$0.501674\pi$
$242$	−609312.	−0.668808
$243$	93266.1	0.101323
$244$	2.07508e6	2.23131
$245$	−922069.	−0.981405
$246$	−107994.	−0.113779
$247$	28275.1	0.0294891
$248$	2.42676e6	2.50552
$249$	34556.4	0.0353207
$250$	168566.	0.170576
$251$	872880.	0.874521	0.437261	−	0.899335i	$-0.355949\pi$
$251$	872880.	0.874521	0.437261	+	0.899335i	$0.355949\pi$
$252$	−4.74593e6	−4.70782
$253$	−1.41659e6	−1.39137
$254$	−48648.4	−0.0473135
$255$	−11638.8	−0.0112087
$256$	1.31614e6	1.25517
$257$	−207242.	−0.195724	−0.0978622	−	0.995200i	$-0.531200\pi$
$257$	−207242.	−0.195724	−0.0978622	+	0.995200i	$0.531200\pi$
$258$	−81321.9	−0.0760603
$259$	−1.68823e6	−1.56380
$260$	−356528.	−0.327084
$261$	−1.52386e6	−1.38466
$262$	1.61528e6	1.45377
$263$	2.22009e6	1.97916	0.989581	−	0.143976i	$-0.0459888\pi$
$263$	2.22009e6	1.97916	0.989581	+	0.143976i	$0.0459888\pi$
$264$	138986.	0.122733
$265$	−513650.	−0.449317
$266$	−418227.	−0.362417
$267$	−44919.3	−0.0385616
$268$	−2.93574e6	−2.49678
$269$	939034.	0.791226	0.395613	−	0.918417i	$-0.370532\pi$
$269$	939034.	0.791226	0.395613	+	0.918417i	$0.370532\pi$
$270$	−69076.4	−0.0576660
$271$	404835.	0.334853	0.167427	−	0.985885i	$-0.446454\pi$
$271$	404835.	0.334853	0.167427	+	0.985885i	$0.446454\pi$
$272$	2.99882e6	2.45770
$273$	20648.3	0.0167679
$274$	−1.71010e6	−1.37608
$275$	−291501.	−0.232439
$276$	135146.	0.106790
$277$	484637.	0.379505	0.189752	−	0.981832i	$-0.439231\pi$
$277$	484637.	0.379505	0.189752	+	0.981832i	$0.439231\pi$
$278$	−753552.	−0.584792
$279$	1.04227e6	0.801620
$280$	3.27374e6	2.49545
$281$	−2.25453e6	−1.70330	−0.851650	−	0.524111i	$-0.824398\pi$
$281$	−2.25453e6	−1.70330	−0.851650	+	0.524111i	$0.824398\pi$
$282$	−47644.2	−0.0356769
$283$	−271952.	−0.201849	−0.100924	−	0.994894i	$-0.532180\pi$
$283$	−271952.	−0.201849	−0.100924	+	0.994894i	$0.532180\pi$
$284$	762313.	0.560838
$285$	−2205.52	−0.00160842
$286$	850346.	0.614725
$287$	4.39889e6	3.15237
$288$	4.50444e6	3.20007
$289$	−640335.	−0.450986
$290$	1.69327e6	1.18231
$291$	26929.7	0.0186423
$292$	2.58136e6	1.77170
$293$	−1.81834e6	−1.23739	−0.618694	−	0.785632i	$-0.712338\pi$
$293$	−1.81834e6	−1.23739	−0.618694	+	0.785632i	$0.712338\pi$
$294$	−209809.	−0.141565
$295$	2950.15	0.00197374
$296$	4.11759e6	2.73158
$297$	119454.	0.0785796
$298$	612892.	0.399801
$299$	513299.	0.332042
$300$	27809.9	0.0178401
$301$	3.31247e6	2.10734
$302$	−276105.	−0.174204
$303$	−78976.7	−0.0494188
$304$	568270.	0.352672
$305$	−614764.	−0.378406
$306$	2.31192e6	1.41146
$307$	−2.29926e6	−1.39233	−0.696166	−	0.717881i	$-0.745112\pi$
$307$	−2.29926e6	−1.39233	−0.696166	+	0.717881i	$0.745112\pi$
$308$	−9.11953e6	−5.47767
$309$	41938.6	0.0249872
$310$	−1.15813e6	−0.684470
$311$	−1.59531e6	−0.935286	−0.467643	−	0.883917i	$-0.654897\pi$
$311$	−1.59531e6	−0.935286	−0.467643	+	0.883917i	$0.654897\pi$
$312$	−50361.4	−0.0292894
$313$	−985636.	−0.568664	−0.284332	−	0.958726i	$-0.591772\pi$
$313$	−985636.	−0.568664	−0.284332	+	0.958726i	$0.591772\pi$
$314$	5.00854e6	2.86673
$315$	1.40603e6	0.798396
$316$	−1.20593e6	−0.679365
$317$	−1.82666e6	−1.02096	−0.510480	−	0.859890i	$-0.670532\pi$
$317$	−1.82666e6	−1.02096	−0.510480	+	0.859890i	$0.670532\pi$
$318$	−116877.	−0.0648129
$319$	−2.92817e6	−1.61109
$320$	−2.28795e6	−1.24903
$321$	8001.74	0.00433433
$322$	−7.59239e6	−4.08074
$323$	147718.	0.0787818
$324$	4.96577e6	2.62799
$325$	105625.	0.0554700
$326$	−2.51619e6	−1.31129
$327$	−59544.8	−0.0307946
$328$	−1.07289e7	−5.50643
$329$	1.94068e6	0.988472
$330$	−66328.8	−0.0335287
$331$	2.10290e6	1.05499	0.527495	−	0.849558i	$-0.323131\pi$
$331$	2.10290e6	1.05499	0.527495	+	0.849558i	$0.323131\pi$
$332$	5.53021e6	2.75357
$333$	1.76846e6	0.873944
$334$	59052.4	0.0289649
$335$	869744.	0.423428
$336$	414988.	0.200534
$337$	−121239.	−0.0581526	−0.0290763	−	0.999577i	$-0.509257\pi$
$337$	−121239.	−0.0581526	−0.0290763	+	0.999577i	$0.509257\pi$
$338$	−308122.	−0.146700
$339$	−16009.6	−0.00756624
$340$	−1.86260e6	−0.873823
$341$	2.00276e6	0.932704
$342$	438103.	0.202540
$343$	4.65176e6	2.13492
$344$	−8.07911e6	−3.68101
$345$	−40038.4	−0.0181104
$346$	6.29890e6	2.82862
$347$	388296.	0.173117	0.0865584	−	0.996247i	$-0.472413\pi$
$347$	388296.	0.173117	0.0865584	+	0.996247i	$0.472413\pi$
$348$	279355.	0.123654
$349$	1.54959e6	0.681011	0.340506	−	0.940242i	$-0.389402\pi$
$349$	1.54959e6	0.681011	0.340506	+	0.940242i	$0.389402\pi$
$350$	−1.56234e6	−0.681718
$351$	−43284.0	−0.0187525
$352$	8.65549e6	3.72336
$353$	592554.	0.253100	0.126550	−	0.991960i	$-0.459610\pi$
$353$	592554.	0.253100	0.126550	+	0.991960i	$0.459610\pi$
$354$	671.283	0.000284707 0
$355$	−225843.	−0.0951121
$356$	−7.18864e6	−3.00623
$357$	107873.	0.0447963
$358$	−5.34020e6	−2.20217
$359$	589168.	0.241270	0.120635	−	0.992697i	$-0.461507\pi$
$359$	589168.	0.241270	0.120635	+	0.992697i	$0.461507\pi$
$360$	−3.42931e6	−1.39460
$361$	−2.44811e6	−0.988695
$362$	−6.99284e6	−2.80467
$363$	29781.3	0.0118625
$364$	3.30445e6	1.30721
$365$	−764753.	−0.300462
$366$	−139885.	−0.0545842
$367$	3.28606e6	1.27353	0.636766	−	0.771057i	$-0.280272\pi$
$367$	3.28606e6	1.27353	0.636766	+	0.771057i	$0.280272\pi$
$368$	1.03162e7	3.97101
$369$	−4.60793e6	−1.76173
$370$	−1.96505e6	−0.746225
$371$	4.76072e6	1.79572
$372$	−191068.	−0.0715866
$373$	4.94295e6	1.83956	0.919781	−	0.392432i	$-0.128366\pi$
$373$	4.94295e6	1.83956	0.919781	+	0.392432i	$0.128366\pi$
$374$	4.44246e6	1.64227
$375$	−8238.97	−0.00302548
$376$	−4.73332e6	−1.72662
$377$	1.06102e6	0.384476
$378$	640229.	0.230465
$379$	−588891.	−0.210590	−0.105295	−	0.994441i	$-0.533579\pi$
$379$	−588891.	−0.210590	−0.105295	+	0.994441i	$0.533579\pi$
$380$	−352959.	−0.125391
$381$	2377.79	0.000839190 0
$382$	9.52068e6	3.33818
$383$	−2.27183e6	−0.791370	−0.395685	−	0.918386i	$-0.629493\pi$
$383$	−2.27183e6	−0.791370	−0.395685	+	0.918386i	$0.629493\pi$
$384$	−207469.	−0.0718001
$385$	2.70175e6	0.928954
$386$	−7.48356e6	−2.55647
$387$	−3.46988e6	−1.17771
$388$	4.30969e6	1.45334
$389$	−5.34339e6	−1.79037	−0.895185	−	0.445694i	$-0.852957\pi$
$389$	−5.34339e6	−1.79037	−0.895185	+	0.445694i	$0.852957\pi$
$390$	24034.1	0.00800142
$391$	2.68163e6	0.887067
$392$	−2.08440e7	−6.85119
$393$	−78950.1	−0.0257852
$394$	2.04996e6	0.665282
$395$	357268.	0.115213
$396$	9.55291e6	3.06124
$397$	5.07081e6	1.61473	0.807367	−	0.590050i	$-0.200892\pi$
$397$	5.07081e6	1.61473	0.807367	+	0.590050i	$0.200892\pi$
$398$	1.52116e6	0.481357
$399$	20441.7	0.00642812
$400$	2.12284e6	0.663387
$401$	4.70142e6	1.46005	0.730026	−	0.683420i	$-0.239508\pi$
$401$	4.70142e6	1.46005	0.730026	+	0.683420i	$0.239508\pi$
$402$	197903.	0.0610785
$403$	−725699.	−0.222584
$404$	−1.26390e7	−3.85265
$405$	−1.47116e6	−0.445679
$406$	−1.56939e7	−4.72515
$407$	3.39817e6	1.01686
$408$	−263102.	−0.0782482
$409$	−3.15579e6	−0.932824	−0.466412	−	0.884568i	$-0.654454\pi$
$409$	−3.15579e6	−0.932824	−0.466412	+	0.884568i	$0.654454\pi$
$410$	5.12019e6	1.50427
$411$	83584.4	0.0244074
$412$	6.71163e6	1.94798
$413$	−27343.2	−0.00788814
$414$	7.95320e6	2.28056
$415$	−1.63838e6	−0.466977
$416$	−3.13630e6	−0.888556
$417$	36831.3	0.0103723
$418$	841835.	0.235660
$419$	−682165.	−0.189825	−0.0949127	−	0.995486i	$-0.530257\pi$
$419$	−682165.	−0.189825	−0.0949127	+	0.995486i	$0.530257\pi$
$420$	−257754.	−0.0712987
$421$	−706461.	−0.194260	−0.0971299	−	0.995272i	$-0.530966\pi$
$421$	−706461.	−0.194260	−0.0971299	+	0.995272i	$0.530966\pi$
$422$	4.50449e6	1.23130
$423$	−2.03291e6	−0.552416
$424$	−1.16114e7	−3.13668
$425$	551816.	0.148191
$426$	−51388.8	−0.0137197
$427$	5.69789e6	1.51232
$428$	1.28055e6	0.337900
$429$	−41562.3	−0.0109033
$430$	3.85562e6	1.00560
$431$	4.89113e6	1.26828	0.634142	−	0.773217i	$-0.281354\pi$
$431$	4.89113e6	1.26828	0.634142	+	0.773217i	$0.281354\pi$
$432$	−869916.	−0.224268
$433$	−4.98945e6	−1.27889	−0.639444	−	0.768837i	$-0.720836\pi$
$433$	−4.98945e6	−1.27889	−0.639444	+	0.768837i	$0.720836\pi$
$434$	1.07341e7	2.73552
$435$	−82761.7	−0.0209704
$436$	−9.52922e6	−2.40072
$437$	508162.	0.127291
$438$	−174014.	−0.0433409
$439$	−5.44947e6	−1.34956	−0.674782	−	0.738017i	$-0.735762\pi$
$439$	−5.44947e6	−1.34956	−0.674782	+	0.738017i	$0.735762\pi$
$440$	−6.58958e6	−1.62266
$441$	−8.95225e6	−2.19198
$442$	−1.60972e6	−0.391917
$443$	1.00675e6	0.243732	0.121866	−	0.992547i	$-0.461112\pi$
$443$	1.00675e6	0.243732	0.121866	+	0.992547i	$0.461112\pi$
$444$	−324193.	−0.0780453
$445$	2.12971e6	0.509824
$446$	−3.12791e6	−0.744589
$447$	−29956.3	−0.00709119
$448$	2.12057e7	4.99181
$449$	200413.	0.0469148	0.0234574	−	0.999725i	$-0.492533\pi$
$449$	200413.	0.0469148	0.0234574	+	0.999725i	$0.492533\pi$
$450$	1.63658e6	0.380984
$451$	−8.85436e6	−2.04982
$452$	−2.56208e6	−0.589858
$453$	13495.2	0.00308982
$454$	1.14083e7	2.59766
$455$	−978977.	−0.221689
$456$	−49857.3	−0.0112284
$457$	647622.	0.145054	0.0725272	−	0.997366i	$-0.476894\pi$
$457$	647622.	0.145054	0.0725272	+	0.997366i	$0.476894\pi$
$458$	8.93238e6	1.98977
$459$	−226128.	−0.0500983
$460$	−6.40753e6	−1.41187
$461$	−2.89528e6	−0.634509	−0.317254	−	0.948340i	$-0.602761\pi$
$461$	−2.89528e6	−0.634509	−0.317254	+	0.948340i	$0.602761\pi$
$462$	614763.	0.133999
$463$	6.96850e6	1.51073	0.755364	−	0.655305i	$-0.227460\pi$
$463$	6.96850e6	1.51073	0.755364	+	0.655305i	$0.227460\pi$
$464$	2.13242e7	4.59810
$465$	56606.0	0.0121403
$466$	−3.65743e6	−0.780209
$467$	1.46098e6	0.309994	0.154997	−	0.987915i	$-0.450463\pi$
$467$	1.46098e6	0.309994	0.154997	+	0.987915i	$0.450463\pi$
$468$	−3.46148e6	−0.730546
$469$	−8.06115e6	−1.69225
$470$	2.25890e6	0.471686
$471$	−244802.	−0.0508467
$472$	66690.2	0.0137787
$473$	−6.66754e6	−1.37029
$474$	81293.6	0.0166192
$475$	104568.	0.0212649
$476$	1.72634e7	3.49228
$477$	−4.98697e6	−1.00355
$478$	−1.79642e7	−3.59616
$479$	−6.63657e6	−1.32162	−0.660808	−	0.750555i	$-0.729786\pi$
$479$	−6.63657e6	−1.32162	−0.660808	+	0.750555i	$0.729786\pi$
$480$	244638.	0.0484642
$481$	−1.23132e6	−0.242666
$482$	102319.	0.0200603
$483$	371093.	0.0723793
$484$	4.76604e6	0.924792
$485$	−1.27679e6	−0.246470
$486$	−1.00617e6	−0.193233
$487$	−6.08683e6	−1.16297	−0.581486	−	0.813557i	$-0.697528\pi$
$487$	−6.08683e6	−1.16297	−0.581486	+	0.813557i	$0.697528\pi$
$488$	−1.38972e7	−2.64166
$489$	122984.	0.0232582
$490$	9.94746e6	1.87164
$491$	1.91765e6	0.358976	0.179488	−	0.983760i	$-0.442556\pi$
$491$	1.91765e6	0.358976	0.179488	+	0.983760i	$0.442556\pi$
$492$	844727.	0.157327
$493$	5.54307e6	1.02715
$494$	−305038.	−0.0562388
$495$	−2.83015e6	−0.519154
$496$	−1.45850e7	−2.66197
$497$	2.09321e6	0.380121
$498$	−372801.	−0.0673603
$499$	4.96658e6	0.892907	0.446453	−	0.894807i	$-0.352687\pi$
$499$	4.96658e6	0.892907	0.446453	+	0.894807i	$0.352687\pi$
$500$	−1.31852e6	−0.235864
$501$	−2886.30	−0.000513745 0
$502$	−9.41680e6	−1.66780
$503$	−2.49704e6	−0.440054	−0.220027	−	0.975494i	$-0.570615\pi$
$503$	−2.49704e6	−0.440054	−0.220027	+	0.975494i	$0.570615\pi$
$504$	3.17843e7	5.57361
$505$	3.74444e6	0.653368
$506$	1.52825e7	2.65349
$507$	15060.0	0.00260199
$508$	380528.	0.0654225
$509$	8.69294e6	1.48721	0.743605	−	0.668619i	$-0.233114\pi$
$509$	8.69294e6	1.48721	0.743605	+	0.668619i	$0.233114\pi$
$510$	125561.	0.0213762
$511$	7.08805e6	1.20081
$512$	−1.60809e6	−0.271104
$513$	−42850.7	−0.00718894
$514$	2.23577e6	0.373266
$515$	−1.98839e6	−0.330357
$516$	636099.	0.105172
$517$	−3.90632e6	−0.642750
$518$	1.82129e7	2.98233
$519$	−307871.	−0.0501707
$520$	2.38773e6	0.387236
$521$	−1.81970e6	−0.293702	−0.146851	−	0.989159i	$-0.546914\pi$
$521$	−1.81970e6	−0.293702	−0.146851	+	0.989159i	$0.546914\pi$
$522$	1.64397e7	2.64069
$523$	−187933.	−0.0300435	−0.0150217	−	0.999887i	$-0.504782\pi$
$523$	−187933.	−0.0300435	−0.0150217	+	0.999887i	$0.504782\pi$
$524$	−1.26347e7	−2.01019
$525$	76362.2	0.0120915
$526$	−2.39508e7	−3.77446
$527$	−3.79126e6	−0.594644
$528$	−835314.	−0.130396
$529$	2.78869e6	0.433272
$530$	5.54136e6	0.856893
$531$	28642.6	0.00440836
$532$	3.27137e6	0.501131
$533$	3.20836e6	0.489177
$534$	484598.	0.0735409
$535$	−379378.	−0.0573043
$536$	1.96612e7	2.95595
$537$	261013.	0.0390594
$538$	−1.01305e7	−1.50895
$539$	−1.72022e7	−2.55042
$540$	540315.	0.0797375
$541$	−7.97826e6	−1.17197	−0.585983	−	0.810324i	$-0.699291\pi$
$541$	−7.97826e6	−1.17197	−0.585983	+	0.810324i	$0.699291\pi$
$542$	−4.36744e6	−0.638599
$543$	341788.	0.0497460
$544$	−1.63850e7	−2.37382
$545$	2.82313e6	0.407136
$546$	−222758.	−0.0319781
$547$	4.31881e6	0.617157	0.308579	−	0.951199i	$-0.400147\pi$
$547$	4.31881e6	0.617157	0.308579	+	0.951199i	$0.400147\pi$
$548$	1.33764e7	1.90278
$549$	−5.96866e6	−0.845174
$550$	3.14477e6	0.443284
$551$	1.05040e6	0.147392
$552$	−905096.	−0.126429
$553$	−3.31131e6	−0.460455
$554$	−5.22836e6	−0.723754
$555$	96045.7	0.0132357
$556$	5.89428e6	0.808618
$557$	−9.23520e6	−1.26127	−0.630636	−	0.776079i	$-0.717206\pi$
$557$	−9.23520e6	−1.26127	−0.630636	+	0.776079i	$0.717206\pi$
$558$	−1.12442e7	−1.52877
$559$	2.41597e6	0.327011
$560$	−1.96754e7	−2.65126
$561$	−217134.	−0.0291286
$562$	2.43224e7	3.24837
$563$	−8.89163e6	−1.18225	−0.591126	−	0.806579i	$-0.701317\pi$
$563$	−8.89163e6	−1.18225	−0.591126	+	0.806579i	$0.701317\pi$
$564$	372673.	0.0493321
$565$	759044.	0.100034
$566$	2.93387e6	0.384946
$567$	1.36353e7	1.78118
$568$	−5.10534e6	−0.663978
$569$	−7.25901e6	−0.939932	−0.469966	−	0.882684i	$-0.655734\pi$
$569$	−7.25901e6	−0.939932	−0.469966	+	0.882684i	$0.655734\pi$
$570$	23793.6	0.00306741
$571$	−3.72513e6	−0.478136	−0.239068	−	0.971003i	$-0.576842\pi$
$571$	−3.72513e6	−0.478136	−0.239068	+	0.971003i	$0.576842\pi$
$572$	−6.65140e6	−0.850008
$573$	−465342.	−0.0592087
$574$	−4.74560e7	−6.01190
$575$	1.89830e6	0.239439
$576$	−2.22135e7	−2.78972
$577$	1.17093e6	0.146417	0.0732086	−	0.997317i	$-0.476676\pi$
$577$	1.17093e6	0.146417	0.0732086	+	0.997317i	$0.476676\pi$
$578$	6.90806e6	0.860075
$579$	365773.	0.0453436
$580$	−1.32447e7	−1.63483
$581$	1.51852e7	1.86630
$582$	−290523.	−0.0355528
$583$	−9.58269e6	−1.16766
$584$	−1.72878e7	−2.09752
$585$	1.02550e6	0.123893
$586$	1.96166e7	2.35982
$587$	8.45511e6	1.01280	0.506400	−	0.862298i	$-0.330976\pi$
$587$	8.45511e6	1.01280	0.506400	+	0.862298i	$0.330976\pi$
$588$	1.64113e6	0.195749
$589$	−718435.	−0.0853295
$590$	−31826.8	−0.00376411
$591$	−100196.	−0.0118000
$592$	−2.47470e7	−2.90213
$593$	1.34570e7	1.57149	0.785746	−	0.618550i	$-0.212279\pi$
$593$	1.34570e7	1.57149	0.785746	+	0.618550i	$0.212279\pi$
$594$	−1.28869e6	−0.149859
$595$	−5.11446e6	−0.592253
$596$	−4.79404e6	−0.552823
$597$	−74349.7	−0.00853775
$598$	−5.53757e6	−0.633238
$599$	9.72026e6	1.10691	0.553453	−	0.832880i	$-0.313310\pi$
$599$	9.72026e6	1.10691	0.553453	+	0.832880i	$0.313310\pi$
$600$	−186248.	−0.0211209
$601$	1.52752e7	1.72505	0.862525	−	0.506014i	$-0.168882\pi$
$601$	1.52752e7	1.72505	0.862525	+	0.506014i	$0.168882\pi$
$602$	−3.57355e7	−4.01892
$603$	8.44424e6	0.945730
$604$	2.15969e6	0.240880
$605$	−1.41199e6	−0.156835
$606$	852017.	0.0942468
$607$	−3.44708e6	−0.379735	−0.189867	−	0.981810i	$-0.560806\pi$
$607$	−3.44708e6	−0.379735	−0.189867	+	0.981810i	$0.560806\pi$
$608$	−3.10491e6	−0.340636
$609$	767070.	0.0838092
$610$	6.63219e6	0.721660
$611$	1.41545e6	0.153388
$612$	−1.80838e7	−1.95169
$613$	5.45977e6	0.586844	0.293422	−	0.955983i	$-0.405206\pi$
$613$	5.45977e6	0.586844	0.293422	+	0.955983i	$0.405206\pi$
$614$	2.48049e7	2.65532
$615$	−250259.	−0.0266810
$616$	6.10750e7	6.48503
$617$	8.48025e6	0.896801	0.448400	−	0.893833i	$-0.351994\pi$
$617$	8.48025e6	0.896801	0.448400	+	0.893833i	$0.351994\pi$
$618$	−452442.	−0.0476532
$619$	8.43977e6	0.885328	0.442664	−	0.896688i	$-0.354034\pi$
$619$	8.43977e6	0.885328	0.442664	+	0.896688i	$0.354034\pi$
$620$	9.05892e6	0.946449
$621$	−777901.	−0.0809460
$622$	1.72105e7	1.78369
$623$	−1.97390e7	−2.03754
$624$	302675.	0.0311182
$625$	390625.	0.0400000
$626$	1.06332e7	1.08450
$627$	−41146.3	−0.00417986
$628$	−3.91768e7	−3.96396
$629$	−6.43279e6	−0.648295
$630$	−1.51685e7	−1.52262
$631$	−1.46417e7	−1.46392	−0.731962	−	0.681346i	$-0.761395\pi$
$631$	−1.46417e7	−1.46392	−0.731962	+	0.681346i	$0.761395\pi$
$632$	8.07630e6	0.804303
$633$	−220166.	−0.0218394
$634$	1.97063e7	1.94707
$635$	−112735.	−0.0110950
$636$	914211.	0.0896198
$637$	6.23319e6	0.608641
$638$	3.15897e7	3.07251
$639$	−2.19268e6	−0.212434
$640$	9.83650e6	0.949272
$641$	−8.49886e6	−0.816988	−0.408494	−	0.912761i	$-0.633946\pi$
$641$	−8.49886e6	−0.816988	−0.408494	+	0.912761i	$0.633946\pi$
$642$	−86324.4	−0.00826601
$643$	1.07051e7	1.02108	0.510542	−	0.859853i	$-0.329445\pi$
$643$	1.07051e7	1.02108	0.510542	+	0.859853i	$0.329445\pi$
$644$	5.93877e7	5.64263
$645$	−188451.	−0.0178361
$646$	−1.59361e6	−0.150245
$647$	1.94772e7	1.82922	0.914609	−	0.404340i	$-0.132499\pi$
$647$	1.94772e7	1.82922	0.914609	+	0.404340i	$0.132499\pi$
$648$	−3.32566e7	−3.11129
$649$	55038.2	0.00512923
$650$	−1.13950e6	−0.105787
$651$	−524648.	−0.0485194
$652$	1.96816e7	1.81319
$653$	1.36819e7	1.25563	0.627817	−	0.778361i	$-0.283949\pi$
$653$	1.36819e7	1.25563	0.627817	+	0.778361i	$0.283949\pi$
$654$	642381.	0.0587284
$655$	3.74317e6	0.340908
$656$	6.44813e7	5.85025
$657$	−7.42490e6	−0.671084
$658$	−2.09364e7	−1.88512
$659$	−7.40016e6	−0.663785	−0.331893	−	0.943317i	$-0.607687\pi$
$659$	−7.40016e6	−0.663785	−0.331893	+	0.943317i	$0.607687\pi$
$660$	518823.	0.0463617
$661$	1.88654e7	1.67943	0.839715	−	0.543028i	$-0.182722\pi$
$661$	1.88654e7	1.67943	0.839715	+	0.543028i	$0.182722\pi$
$662$	−2.26865e7	−2.01197
$663$	78678.1	0.00695136
$664$	−3.70368e7	−3.25997
$665$	−969178.	−0.0849864
$666$	−1.90784e7	−1.66670
$667$	1.90687e7	1.65961
$668$	−461908.	−0.0400511
$669$	152882.	0.0132066
$670$	−9.38297e6	−0.807520
$671$	−1.14691e7	−0.983381
$672$	−2.26741e6	−0.193690
$673$	−1.68803e7	−1.43662	−0.718311	−	0.695722i	$-0.755085\pi$
$673$	−1.68803e7	−1.43662	−0.718311	+	0.695722i	$0.755085\pi$
$674$	1.30795e6	0.110903
$675$	−160074.	−0.0135226
$676$	2.41013e6	0.202849
$677$	−1.07388e7	−0.900504	−0.450252	−	0.892902i	$-0.648666\pi$
$677$	−1.07388e7	−0.900504	−0.450252	+	0.892902i	$0.648666\pi$
$678$	172714.	0.0144296
$679$	1.18338e7	0.985032
$680$	1.24742e7	1.03452
$681$	−557604.	−0.0460742
$682$	−2.16062e7	−1.77876
$683$	−3.08525e6	−0.253069	−0.126535	−	0.991962i	$-0.540385\pi$
$683$	−3.08525e6	−0.253069	−0.126535	+	0.991962i	$0.540385\pi$
$684$	−3.42684e6	−0.280061
$685$	−3.96290e6	−0.322690
$686$	−5.01841e7	−4.07152
$687$	−436587.	−0.0352922
$688$	4.85560e7	3.91085
$689$	3.47227e6	0.278654
$690$	431942.	0.0345385
$691$	−1.14232e7	−0.910110	−0.455055	−	0.890463i	$-0.650380\pi$
$691$	−1.14232e7	−0.910110	−0.455055	+	0.890463i	$0.650380\pi$
$692$	−4.92700e7	−3.91126
$693$	2.62310e7	2.07483
$694$	−4.18902e6	−0.330152
$695$	−1.74624e6	−0.137133
$696$	−1.87089e6	−0.146394
$697$	1.67614e7	1.30686
$698$	−1.67173e7	−1.29876
$699$	178764.	0.0138384
$700$	1.22206e7	0.942643
$701$	−1.28448e7	−0.987264	−0.493632	−	0.869671i	$-0.664331\pi$
$701$	−1.28448e7	−0.987264	−0.493632	+	0.869671i	$0.664331\pi$
$702$	466956.	0.0357630
$703$	−1.21900e6	−0.0930282
$704$	−4.26842e7	−3.24590
$705$	−110408.	−0.00836620
$706$	−6.39259e6	−0.482687
$707$	−3.47050e7	−2.61122
$708$	−5250.77	−0.000393677 0
$709$	1.28235e7	0.958055	0.479028	−	0.877800i	$-0.340989\pi$
$709$	1.28235e7	0.958055	0.479028	+	0.877800i	$0.340989\pi$
$710$	2.43644e6	0.181388
$711$	3.46867e6	0.257329
$712$	4.81435e7	3.55908
$713$	−1.30423e7	−0.960793
$714$	−1.16376e6	−0.0854311
$715$	1.97055e6	0.144152
$716$	4.17710e7	3.04504
$717$	878036.	0.0637844
$718$	−6.35607e6	−0.460127
$719$	7.59185e6	0.547678	0.273839	−	0.961776i	$-0.411706\pi$
$719$	7.59185e6	0.547678	0.273839	+	0.961776i	$0.411706\pi$
$720$	2.06104e7	1.48168
$721$	1.84292e7	1.32029
$722$	2.64107e7	1.88554
$723$	−5001.02	−0.000355806 0
$724$	5.46979e7	3.87815
$725$	3.92389e6	0.277250
$726$	−321287.	−0.0226231
$727$	2.64094e6	0.185320	0.0926600	−	0.995698i	$-0.470463\pi$
$727$	2.64094e6	0.185320	0.0926600	+	0.995698i	$0.470463\pi$
$728$	−2.21305e7	−1.54761
$729$	−1.42505e7	−0.993141
$730$	8.25031e6	0.573011
$731$	1.26218e7	0.873628
$732$	1.09418e6	0.0754762
$733$	−2.36492e6	−0.162576	−0.0812881	−	0.996691i	$-0.525903\pi$
$733$	−2.36492e6	−0.162576	−0.0812881	+	0.996691i	$0.525903\pi$
$734$	−3.54506e7	−2.42876
$735$	−486201.	−0.0331969
$736$	−5.63657e7	−3.83549
$737$	1.62260e7	1.10038
$738$	4.97113e7	3.35980
$739$	−6.44734e6	−0.434280	−0.217140	−	0.976140i	$-0.569673\pi$
$739$	−6.44734e6	−0.434280	−0.217140	+	0.976140i	$0.569673\pi$
$740$	1.53706e7	1.03184
$741$	14909.3	0.000997498 0
$742$	−5.13596e7	−3.42462
$743$	7.54303e6	0.501273	0.250636	−	0.968081i	$-0.419360\pi$
$743$	7.54303e6	0.501273	0.250636	+	0.968081i	$0.419360\pi$
$744$	1.27962e6	0.0847516
$745$	1.42028e6	0.0937529
$746$	−5.33256e7	−3.50823
$747$	−1.59069e7	−1.04300
$748$	−3.47489e7	−2.27084
$749$	3.51623e6	0.229020
$750$	88883.6	0.00576991
$751$	−2.33272e7	−1.50925	−0.754627	−	0.656154i	$-0.772182\pi$
$751$	−2.33272e7	−1.50925	−0.754627	+	0.656154i	$0.772182\pi$
$752$	2.84476e7	1.83443
$753$	460264.	0.0295815
$754$	−1.14465e7	−0.733236
$755$	−639832.	−0.0408506
$756$	−5.00787e6	−0.318675
$757$	−2.12561e7	−1.34817	−0.674085	−	0.738654i	$-0.735462\pi$
$757$	−2.12561e7	−1.34817	−0.674085	+	0.738654i	$0.735462\pi$
$758$	6.35307e6	0.401616
$759$	−746959.	−0.0470644
$760$	2.36383e6	0.148451
$761$	−5.46782e6	−0.342257	−0.171129	−	0.985249i	$-0.554741\pi$
$761$	−5.46782e6	−0.342257	−0.171129	+	0.985249i	$0.554741\pi$
$762$	−25652.0	−0.00160042
$763$	−2.61660e7	−1.62714
$764$	−7.44707e7	−4.61585
$765$	5.35751e6	0.330986
$766$	2.45090e7	1.50922
$767$	−19943.0	−0.00122406
$768$	693994.	0.0424573
$769$	1.12535e7	0.686234	0.343117	−	0.939293i	$-0.388517\pi$
$769$	1.12535e7	0.686234	0.343117	+	0.939293i	$0.388517\pi$
$770$	−2.91471e7	−1.77161
$771$	−109277.	−0.00662056
$772$	5.85364e7	3.53494
$773$	1.16249e7	0.699747	0.349873	−	0.936797i	$-0.386225\pi$
$773$	1.16249e7	0.699747	0.349873	+	0.936797i	$0.386225\pi$
$774$	3.74338e7	2.24601
$775$	−2.68380e6	−0.160508
$776$	−2.88627e7	−1.72061
$777$	−890192.	−0.0528970
$778$	5.76456e7	3.41442
$779$	3.17625e6	0.187530
$780$	−187995.	−0.0110639
$781$	−4.21334e6	−0.247172
$782$	−2.89299e7	−1.69173
$783$	−1.60797e6	−0.0937287
$784$	1.25274e8	7.27897
$785$	1.16065e7	0.672245
$786$	851729.	0.0491751
$787$	−2.48768e7	−1.43172	−0.715859	−	0.698245i	$-0.753965\pi$
$787$	−2.48768e7	−1.43172	−0.715859	+	0.698245i	$0.753965\pi$
$788$	−1.60348e7	−0.919916
$789$	1.17064e6	0.0669470
$790$	−3.85428e6	−0.219723
$791$	−7.03514e6	−0.399789
$792$	−6.39775e7	−3.62422
$793$	4.15580e6	0.234678
$794$	−5.47049e7	−3.07946
$795$	−270845.	−0.0151986
$796$	−1.18985e7	−0.665595
$797$	−1.88084e7	−1.04883	−0.524416	−	0.851462i	$-0.675716\pi$
$797$	−1.88084e7	−1.04883	−0.524416	+	0.851462i	$0.675716\pi$
$798$	−220529.	−0.0122591
$799$	7.39473e6	0.409784
$800$	−1.15988e7	−0.640747
$801$	2.06771e7	1.13870
$802$	−5.07199e7	−2.78447
$803$	−1.42673e7	−0.780823
$804$	−1.54800e6	−0.0844560
$805$	−1.75942e7	−0.956930
$806$	7.82898e6	0.424490
$807$	495147.	0.0267640
$808$	8.46456e7	4.56117
$809$	1.38160e7	0.742184	0.371092	−	0.928596i	$-0.378983\pi$
$809$	1.38160e7	0.742184	0.371092	+	0.928596i	$0.378983\pi$
$810$	1.58712e7	0.849956
$811$	3.04514e7	1.62575	0.812877	−	0.582435i	$-0.197900\pi$
$811$	3.04514e7	1.62575	0.812877	+	0.582435i	$0.197900\pi$
$812$	1.22758e8	6.53369
$813$	213467.	0.0113267
$814$	−3.66601e7	−1.93925
$815$	−5.83089e6	−0.307497
$816$	1.58126e6	0.0831340
$817$	2.39179e6	0.125363
$818$	3.40453e7	1.77899
$819$	−9.50477e6	−0.495144
$820$	−4.00501e7	−2.08003
$821$	−5.01920e6	−0.259882	−0.129941	−	0.991522i	$-0.541479\pi$
$821$	−5.01920e6	−0.259882	−0.129941	+	0.991522i	$0.541479\pi$
$822$	−901726.	−0.0465473
$823$	3.70421e7	1.90632	0.953162	−	0.302462i	$-0.0978085\pi$
$823$	3.70421e7	1.90632	0.953162	+	0.302462i	$0.0978085\pi$
$824$	−4.49489e7	−2.30622
$825$	−153707.	−0.00786245
$826$	294984.	0.0150435
$827$	−1.52758e7	−0.776674	−0.388337	−	0.921517i	$-0.626950\pi$
$827$	−1.52758e7	−0.776674	−0.388337	+	0.921517i	$0.626950\pi$
$828$	−6.22099e7	−3.15343
$829$	1.13644e7	0.574327	0.287163	−	0.957882i	$-0.407288\pi$
$829$	1.13644e7	0.574327	0.287163	+	0.957882i	$0.407288\pi$
$830$	1.76752e7	0.890572
$831$	255546.	0.0128371
$832$	1.54666e7	0.774615
$833$	3.25640e7	1.62602
$834$	−397343.	−0.0197811
$835$	136845.	0.00679223
$836$	−6.58483e6	−0.325858
$837$	1.09979e6	0.0542621
$838$	7.35933e6	0.362016
$839$	2.16145e7	1.06008	0.530042	−	0.847971i	$-0.322176\pi$
$839$	2.16145e7	1.06008	0.530042	+	0.847971i	$0.322176\pi$
$840$	1.72622e6	0.0844108
$841$	1.89049e7	0.921688
$842$	7.62144e6	0.370473
$843$	−1.18880e6	−0.0576157
$844$	−3.52341e7	−1.70258
$845$	−714025.	−0.0344010
$846$	2.19314e7	1.05351
$847$	1.30869e7	0.626799
$848$	6.97853e7	3.33253
$849$	−143399.	−0.00682772
$850$	−5.95310e6	−0.282615
$851$	−2.21294e7	−1.04748
$852$	401963.	0.0189709
$853$	−3.22268e7	−1.51651	−0.758253	−	0.651960i	$-0.773947\pi$
$853$	−3.22268e7	−1.51651	−0.758253	+	0.651960i	$0.773947\pi$
$854$	−6.14699e7	−2.88415
$855$	1.01524e6	0.0474954
$856$	−8.57609e6	−0.400042
$857$	−2.07998e7	−0.967404	−0.483702	−	0.875233i	$-0.660708\pi$
$857$	−2.07998e7	−0.967404	−0.483702	+	0.875233i	$0.660708\pi$
$858$	448382.	0.0207936
$859$	2.66909e7	1.23418	0.617092	−	0.786891i	$-0.288311\pi$
$859$	2.66909e7	1.23418	0.617092	+	0.786891i	$0.288311\pi$
$860$	−3.01587e7	−1.39048
$861$	2.31951e6	0.106632
$862$	−5.27665e7	−2.41875
$863$	−6.44627e6	−0.294633	−0.147316	−	0.989089i	$-0.547064\pi$
$863$	−6.44627e6	−0.294633	−0.147316	+	0.989089i	$0.547064\pi$
$864$	4.75305e6	0.216615
$865$	1.45967e7	0.663308
$866$	5.38272e7	2.43897
$867$	−337645.	−0.0152550
$868$	−8.39618e7	−3.78253
$869$	6.66522e6	0.299409
$870$	892849.	0.0399926
$871$	−5.87947e6	−0.262599
$872$	6.38188e7	2.84222
$873$	−1.23962e7	−0.550494
$874$	−5.48215e6	−0.242757
$875$	−3.62048e6	−0.159862
$876$	1.36113e6	0.0599295
$877$	−2.93830e7	−1.29002	−0.645012	−	0.764173i	$-0.723148\pi$
$877$	−2.93830e7	−1.29002	−0.645012	+	0.764173i	$0.723148\pi$
$878$	5.87900e7	2.57376
$879$	−958799.	−0.0418558
$880$	3.96038e7	1.72397
$881$	6.33454e6	0.274964	0.137482	−	0.990504i	$-0.456099\pi$
$881$	6.33454e6	0.274964	0.137482	+	0.990504i	$0.456099\pi$
$882$	9.65787e7	4.18032
$883$	−1.53999e7	−0.664686	−0.332343	−	0.943159i	$-0.607839\pi$
$883$	−1.53999e7	−0.664686	−0.332343	+	0.943159i	$0.607839\pi$
$884$	1.25912e7	0.541922
$885$	1555.60	6.67634e−5 0
$886$	−1.08610e7	−0.464822
$887$	−823263.	−0.0351342	−0.0175671	−	0.999846i	$-0.505592\pi$
$887$	−823263.	−0.0351342	−0.0175671	+	0.999846i	$0.505592\pi$
$888$	2.17118e6	0.0923982
$889$	1.04488e6	0.0443416
$890$	−2.29757e7	−0.972286
$891$	−2.74461e7	−1.15821
$892$	2.44665e7	1.02958
$893$	1.40128e6	0.0588027
$894$	323174.	0.0135236
$895$	−1.23751e7	−0.516406
$896$	−9.11688e7	−3.79381
$897$	270660.	0.0112316
$898$	−2.16209e6	−0.0894713
$899$	−2.69591e7	−1.11252
$900$	−1.28013e7	−0.526804
$901$	1.81402e7	0.744440
$902$	9.55226e7	3.90922
$903$	1.74664e6	0.0712828
$904$	1.71587e7	0.698335
$905$	−1.62048e7	−0.657693
$906$	−145589.	−0.00589260
$907$	−3.29987e6	−0.133192	−0.0665961	−	0.997780i	$-0.521214\pi$
$907$	−3.29987e6	−0.133192	−0.0665961	+	0.997780i	$0.521214\pi$
$908$	−8.92359e7	−3.59191
$909$	3.63543e7	1.45930
$910$	1.05614e7	0.422783
$911$	−3.58804e7	−1.43239	−0.716196	−	0.697900i	$-0.754118\pi$
$911$	−3.58804e7	−1.43239	−0.716196	+	0.697900i	$0.754118\pi$
$912$	299645.	0.0119295
$913$	−3.05658e7	−1.21355
$914$	−6.98667e6	−0.276633
$915$	−324161.	−0.0127999
$916$	−6.98690e7	−2.75135
$917$	−3.46933e7	−1.36246
$918$	2.43952e6	0.0955426
$919$	4.29501e7	1.67755	0.838776	−	0.544477i	$-0.183272\pi$
$919$	4.29501e7	1.67755	0.838776	+	0.544477i	$0.183272\pi$
$920$	4.29123e7	1.67152
$921$	−1.21239e6	−0.0470969
$922$	3.12348e7	1.21007
$923$	1.52670e6	0.0589860
$924$	−4.80867e6	−0.185287
$925$	−4.55371e6	−0.174989
$926$	−7.51775e7	−2.88111
$927$	−1.93050e7	−0.737855
$928$	−1.16511e8	−4.44117
$929$	−4.75514e6	−0.180769	−0.0903845	−	0.995907i	$-0.528810\pi$
$929$	−4.75514e6	−0.180769	−0.0903845	+	0.995907i	$0.528810\pi$
$930$	−610677.	−0.0231528
$931$	6.17080e6	0.233328
$932$	2.86084e7	1.07883
$933$	−841198.	−0.0316369
$934$	−1.57614e7	−0.591190
$935$	1.02947e7	0.385110
$936$	2.31821e7	0.864896
$937$	4.86133e7	1.80886	0.904432	−	0.426617i	$-0.140295\pi$
$937$	4.86133e7	1.80886	0.904432	+	0.426617i	$0.140295\pi$
$938$	8.69653e7	3.22730
$939$	−519720.	−0.0192356
$940$	−1.76691e7	−0.652222
$941$	825014.	0.0303730	0.0151865	−	0.999885i	$-0.495166\pi$
$941$	825014.	0.0303730	0.0151865	+	0.999885i	$0.495166\pi$
$942$	2.64097e6	0.0969698
$943$	5.76608e7	2.11155
$944$	−400812.	−0.0146390
$945$	1.48363e6	0.0540439
$946$	7.19308e7	2.61329
$947$	−2.90200e7	−1.05153	−0.525766	−	0.850630i	$-0.676221\pi$
$947$	−2.90200e7	−1.05153	−0.525766	+	0.850630i	$0.676221\pi$
$948$	−635878.	−0.0229802
$949$	5.16973e6	0.186338
$950$	−1.12810e6	−0.0405544
$951$	−963185.	−0.0345349
$952$	−1.15616e8	−4.13452
$953$	−1.85279e7	−0.660838	−0.330419	−	0.943834i	$-0.607190\pi$
$953$	−1.85279e7	−0.660838	−0.330419	+	0.943834i	$0.607190\pi$
$954$	5.38004e7	1.91388
$955$	2.20627e7	0.782800
$956$	1.40516e8	4.97257
$957$	−1.54401e6	−0.0544966
$958$	7.15967e7	2.52046
$959$	3.67298e7	1.28965
$960$	−1.20642e6	−0.0422495
$961$	−1.01901e7	−0.355933
$962$	1.32837e7	0.462789
$963$	−3.68333e6	−0.127990
$964$	−800336.	−0.0277383
$965$	−1.73420e7	−0.599489
$966$	−4.00342e6	−0.138035
$967$	1.43655e7	0.494032	0.247016	−	0.969011i	$-0.420550\pi$
$967$	1.43655e7	0.494032	0.247016	+	0.969011i	$0.420550\pi$
$968$	−3.19190e7	−1.09487
$969$	77890.6	0.00266487
$970$	1.37743e7	0.470044
$971$	−2.66582e7	−0.907368	−0.453684	−	0.891163i	$-0.649890\pi$
$971$	−2.66582e7	−0.907368	−0.453684	+	0.891163i	$0.649890\pi$
$972$	7.87028e6	0.267193
$973$	1.61849e7	0.548059
$974$	6.56660e7	2.21791
$975$	55695.4	0.00187632
$976$	8.35228e7	2.80660
$977$	−1.84613e6	−0.0618767	−0.0309383	−	0.999521i	$-0.509850\pi$
$977$	−1.84613e6	−0.0618767	−0.0309383	+	0.999521i	$0.509850\pi$
$978$	−1.32677e6	−0.0443557
$979$	3.97320e7	1.32490
$980$	−7.78090e7	−2.58800
$981$	2.74094e7	0.909342
$982$	−2.06880e7	−0.684604
$983$	−3.85226e7	−1.27154	−0.635772	−	0.771877i	$-0.719318\pi$
$983$	−3.85226e7	−1.27154	−0.635772	+	0.771877i	$0.719318\pi$
$984$	−5.65728e6	−0.186260
$985$	4.75048e6	0.156008
$986$	−5.97998e7	−1.95888
$987$	1.02331e6	0.0334360
$988$	2.38600e6	0.0777640
$989$	4.34200e7	1.41156
$990$	3.05322e7	0.990080
$991$	4.70175e7	1.52081	0.760406	−	0.649448i	$-0.225000\pi$
$991$	4.70175e7	1.52081	0.760406	+	0.649448i	$0.225000\pi$
$992$	7.96895e7	2.57112
$993$	1.10885e6	0.0356860
$994$	−2.25819e7	−0.724929
$995$	3.52506e6	0.112878
$996$	2.91605e6	0.0931422
$997$	1.02621e6	0.0326961	0.0163481	−	0.999866i	$-0.494796\pi$
$997$	1.02621e6	0.0326961	0.0163481	+	0.999866i	$0.494796\pi$
$998$	−5.35805e7	−1.70286
$999$	1.86606e6	0.0591578

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.6.a.d.1.1	✓	6
3.2	odd	2		585.6.a.m.1.6		6
4.3	odd	2		1040.6.a.q.1.4		6
5.2	odd	4		325.6.b.g.274.1		12
5.3	odd	4		325.6.b.g.274.12		12
5.4	even	2		325.6.a.g.1.6		6
13.12	even	2		845.6.a.h.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.6.a.d.1.1	✓	6	1.1	even	1	trivial
325.6.a.g.1.6		6	5.4	even	2
325.6.b.g.274.1		12	5.2	odd	4
325.6.b.g.274.12		12	5.3	odd	4
585.6.a.m.1.6		6	3.2	odd	2
845.6.a.h.1.6		6	13.12	even	2
1040.6.a.q.1.4		6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	65.a (trivial)

\(f(q)\)	\(=\)	\(q-10.7882 q^{2} +0.527294 q^{3} +84.3852 q^{4} -25.0000 q^{5} -5.68855 q^{6} +231.710 q^{7} -565.142 q^{8} -242.722 q^{9} +269.705 q^{10} -466.402 q^{11} +44.4958 q^{12} +169.000 q^{13} -2499.74 q^{14} -13.1824 q^{15} +3396.54 q^{16} +882.905 q^{17} +2618.53 q^{18} +167.308 q^{19} -2109.63 q^{20} +122.180 q^{21} +5031.63 q^{22} +3037.27 q^{23} -297.996 q^{24} +625.000 q^{25} -1823.21 q^{26} -256.118 q^{27} +19552.9 q^{28} +6278.22 q^{29} +142.214 q^{30} -4294.08 q^{31} -18558.0 q^{32} -245.931 q^{33} -9524.96 q^{34} -5792.76 q^{35} -20482.2 q^{36} -7285.93 q^{37} -1804.96 q^{38} +89.1127 q^{39} +14128.6 q^{40} +18984.4 q^{41} -1318.10 q^{42} +14295.7 q^{43} -39357.4 q^{44} +6068.05 q^{45} -32766.7 q^{46} +8375.45 q^{47} +1790.98 q^{48} +36882.8 q^{49} -6742.62 q^{50} +465.551 q^{51} +14261.1 q^{52} +20546.0 q^{53} +2763.06 q^{54} +11660.0 q^{55} -130949. q^{56} +88.2207 q^{57} -67730.7 q^{58} -118.006 q^{59} -1112.40 q^{60} +24590.5 q^{61} +46325.3 q^{62} -56241.2 q^{63} +91518.2 q^{64} -4225.00 q^{65} +2653.15 q^{66} -34789.8 q^{67} +74504.2 q^{68} +1601.54 q^{69} +62493.5 q^{70} +9033.72 q^{71} +137172. q^{72} +30590.1 q^{73} +78602.1 q^{74} +329.559 q^{75} +14118.4 q^{76} -108070. q^{77} -961.365 q^{78} -14290.7 q^{79} -84913.5 q^{80} +58846.4 q^{81} -204808. q^{82} +65535.3 q^{83} +10310.2 q^{84} -22072.6 q^{85} -154225. q^{86} +3310.47 q^{87} +263583. q^{88} -85188.3 q^{89} -65463.3 q^{90} +39159.1 q^{91} +256301. q^{92} -2264.24 q^{93} -90356.0 q^{94} -4182.71 q^{95} -9785.53 q^{96} +51071.6 q^{97} -397898. q^{98} +113206. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 38 q^{3} + 134 q^{4} - 150 q^{5} + 318 q^{6} + 220 q^{7} + 24 q^{8} + 518 q^{9} - 170 q^{11} + 2238 q^{12} + 1014 q^{13} - 1440 q^{14} - 950 q^{15} + 3506 q^{16} + 728 q^{17} + 7788 q^{18} + 1218 q^{19}+ \cdots - 32270 q^{99}+O(q^{100}) \) 6 * q + 38 * q^3 + 134 * q^4 - 150 * q^5 + 318 * q^6 + 220 * q^7 + 24 * q^8 + 518 * q^9 - 170 * q^11 + 2238 * q^12 + 1014 * q^13 - 1440 * q^14 - 950 * q^15 + 3506 * q^16 + 728 * q^17 + 7788 * q^18 + 1218 * q^19 - 3350 * q^20 - 396 * q^21 + 5154 * q^22 + 8954 * q^23 + 12618 * q^24 + 3750 * q^25 + 13112 * q^27 + 13212 * q^28 + 8364 * q^29 - 7950 * q^30 + 2862 * q^31 - 29672 * q^32 - 3772 * q^33 - 21484 * q^34 - 5500 * q^35 - 2138 * q^36 + 13840 * q^37 - 27706 * q^38 + 6422 * q^39 - 600 * q^40 + 2248 * q^41 - 47028 * q^42 + 3822 * q^43 - 73482 * q^44 - 12950 * q^45 - 39886 * q^46 - 10860 * q^47 + 13962 * q^48 + 85902 * q^49 - 55028 * q^51 + 22646 * q^52 + 6584 * q^53 + 45504 * q^54 + 4250 * q^55 - 188800 * q^56 + 11692 * q^57 - 88500 * q^58 - 28874 * q^59 - 55950 * q^60 + 972 * q^61 + 123466 * q^62 - 125236 * q^63 + 14022 * q^64 - 25350 * q^65 - 158040 * q^66 + 60040 * q^67 + 3504 * q^68 + 153088 * q^69 + 36000 * q^70 - 74174 * q^71 + 298668 * q^72 + 48960 * q^73 + 226112 * q^74 + 23750 * q^75 - 93422 * q^76 + 231588 * q^77 + 53742 * q^78 + 214508 * q^79 - 87650 * q^80 + 116006 * q^81 + 58732 * q^82 + 123260 * q^83 - 235268 * q^84 - 18200 * q^85 - 304666 * q^86 + 228144 * q^87 + 127622 * q^88 + 94028 * q^89 - 194700 * q^90 + 37180 * q^91 + 430298 * q^92 + 192892 * q^93 - 125920 * q^94 - 30450 * q^95 - 385858 * q^96 + 246284 * q^97 - 4736 * q^98 - 32270 * q^99

Introduction

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