LMFDB - Embedded newform 197.6.a.a.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,6,Mod(1,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("197.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	197.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:	$31.5956125032$
Analytic rank:	$1$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.78681 q^{2} -17.1157 q^{3} -28.8073 q^{4} -96.1357 q^{5} +30.5825 q^{6} +140.530 q^{7} +108.651 q^{8} +49.9467 q^{9} +171.776 q^{10} +176.222 q^{11} +493.057 q^{12} -348.520 q^{13} -251.100 q^{14} +1645.43 q^{15} +727.695 q^{16} +1642.29 q^{17} -89.2453 q^{18} -138.460 q^{19} +2769.41 q^{20} -2405.26 q^{21} -314.876 q^{22} -144.967 q^{23} -1859.64 q^{24} +6117.08 q^{25} +622.739 q^{26} +3304.24 q^{27} -4048.28 q^{28} -5102.87 q^{29} -2940.07 q^{30} -95.4999 q^{31} -4777.09 q^{32} -3016.16 q^{33} -2934.46 q^{34} -13509.9 q^{35} -1438.83 q^{36} -8813.51 q^{37} +247.402 q^{38} +5965.16 q^{39} -10445.3 q^{40} -1895.44 q^{41} +4297.74 q^{42} +14050.5 q^{43} -5076.49 q^{44} -4801.66 q^{45} +259.029 q^{46} +19049.3 q^{47} -12455.0 q^{48} +2941.56 q^{49} -10930.1 q^{50} -28108.9 q^{51} +10039.9 q^{52} +1415.63 q^{53} -5904.05 q^{54} -16941.2 q^{55} +15268.7 q^{56} +2369.84 q^{57} +9117.86 q^{58} +12357.5 q^{59} -47400.4 q^{60} -30196.6 q^{61} +170.640 q^{62} +7018.99 q^{63} -14750.5 q^{64} +33505.2 q^{65} +5389.31 q^{66} +30511.7 q^{67} -47310.0 q^{68} +2481.22 q^{69} +24139.7 q^{70} +67506.1 q^{71} +5426.77 q^{72} -76337.4 q^{73} +15748.1 q^{74} -104698. q^{75} +3988.67 q^{76} +24764.4 q^{77} -10658.6 q^{78} -52240.4 q^{79} -69957.5 q^{80} -68691.4 q^{81} +3386.79 q^{82} +39800.8 q^{83} +69289.1 q^{84} -157883. q^{85} -25105.6 q^{86} +87339.1 q^{87} +19146.7 q^{88} -11353.4 q^{89} +8579.66 q^{90} -48977.4 q^{91} +4176.12 q^{92} +1634.55 q^{93} -34037.5 q^{94} +13311.0 q^{95} +81763.2 q^{96} +103709. q^{97} -5256.00 q^{98} +8801.72 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 8 q^{2} - 100 q^{3} + 512 q^{4} - 154 q^{5} - 216 q^{6} - 737 q^{7} - 261 q^{8} + 2510 q^{9} - 1567 q^{10} - 808 q^{11} - 3200 q^{12} - 2460 q^{13} - 1423 q^{14} - 3541 q^{15} + 5120 q^{16} - 2501 q^{17}+ \cdots - 108889 q^{99}+O(q^{100}) $ 38 * q - 8 * q^2 - 100 * q^3 + 512 * q^4 - 154 * q^5 - 216 * q^6 - 737 * q^7 - 261 * q^8 + 2510 * q^9 - 1567 * q^10 - 808 * q^11 - 3200 * q^12 - 2460 * q^13 - 1423 * q^14 - 3541 * q^15 + 5120 * q^16 - 2501 * q^17 - 1343 * q^18 - 7983 * q^19 - 6981 * q^20 - 3382 * q^21 - 8023 * q^22 - 7132 * q^23 - 10467 * q^24 + 13564 * q^25 - 7886 * q^26 - 30397 * q^27 - 23730 * q^28 - 12497 * q^29 - 12917 * q^30 - 26380 * q^31 - 18140 * q^32 - 12946 * q^33 - 48406 * q^34 - 12864 * q^35 - 5030 * q^36 - 46630 * q^37 - 15482 * q^38 - 13541 * q^39 - 74754 * q^40 - 23754 * q^41 - 41309 * q^42 - 96541 * q^43 - 39950 * q^44 - 49281 * q^45 - 49587 * q^46 - 63551 * q^47 - 126814 * q^48 + 67147 * q^49 - 158667 * q^50 - 140697 * q^51 - 243408 * q^52 - 109108 * q^53 - 345313 * q^54 - 176321 * q^55 - 439504 * q^56 - 172501 * q^57 - 283105 * q^58 - 129225 * q^59 - 491987 * q^60 - 156006 * q^61 - 257561 * q^62 - 285435 * q^63 - 71443 * q^64 - 214451 * q^65 - 370574 * q^66 - 326834 * q^67 - 244233 * q^68 - 63505 * q^69 - 267713 * q^70 - 118805 * q^71 - 237565 * q^72 - 226965 * q^73 - 82169 * q^74 - 166814 * q^75 - 177290 * q^76 - 74218 * q^77 + 87061 * q^78 - 18825 * q^79 - 154730 * q^80 + 211130 * q^81 - 279743 * q^82 - 191524 * q^83 - 121632 * q^84 + 10830 * q^85 + 188032 * q^86 - 202673 * q^87 - 344937 * q^88 + 22634 * q^89 + 597315 * q^90 - 490747 * q^91 + 409454 * q^92 - 49403 * q^93 - 151313 * q^94 + 135623 * q^95 + 669377 * q^96 - 585150 * q^97 + 726482 * q^98 - 108889 * 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 $

$2$	−1.78681	−0.315866	−0.157933	−	0.987450i	$-0.550483\pi$
$2$	−1.78681	−0.315866	−0.157933	+	0.987450i	$0.550483\pi$
$3$	−17.1157	−1.09797	−0.548986	−	0.835832i	$-0.684986\pi$
$3$	−17.1157	−1.09797	−0.548986	+	0.835832i	$0.684986\pi$
$4$	−28.8073	−0.900228
$5$	−96.1357	−1.71973	−0.859864	−	0.510523i	$-0.829452\pi$
$5$	−96.1357	−1.71973	−0.859864	+	0.510523i	$0.829452\pi$
$6$	30.5825	0.346812
$7$	140.530	1.08398	0.541992	−	0.840384i	$-0.317670\pi$
$7$	140.530	1.08398	0.541992	+	0.840384i	$0.317670\pi$
$8$	108.651	0.600218
$9$	49.9467	0.205542
$10$	171.776	0.543204
$11$	176.222	0.439116	0.219558	−	0.975600i	$-0.429539\pi$
$11$	176.222	0.439116	0.219558	+	0.975600i	$0.429539\pi$
$12$	493.057	0.988425
$13$	−348.520	−0.571965	−0.285982	−	0.958235i	$-0.592320\pi$
$13$	−348.520	−0.571965	−0.285982	+	0.958235i	$0.592320\pi$
$14$	−251.100	−0.342394
$15$	1645.43	1.88821
$16$	727.695	0.710640
$17$	1642.29	1.37825	0.689124	−	0.724643i	$-0.257995\pi$
$17$	1642.29	1.37825	0.689124	+	0.724643i	$0.257995\pi$
$18$	−89.2453	−0.0649238
$19$	−138.460	−0.0879916	−0.0439958	−	0.999032i	$-0.514009\pi$
$19$	−138.460	−0.0879916	−0.0439958	+	0.999032i	$0.514009\pi$
$20$	2769.41	1.54815
$21$	−2405.26	−1.19018
$22$	−314.876	−0.138702
$23$	−144.967	−0.0571414	−0.0285707	−	0.999592i	$-0.509096\pi$
$23$	−144.967	−0.0571414	−0.0285707	+	0.999592i	$0.509096\pi$
$24$	−1859.64	−0.659023
$25$	6117.08	1.95746
$26$	622.739	0.180665
$27$	3304.24	0.872292
$28$	−4048.28	−0.975832
$29$	−5102.87	−1.12673	−0.563364	−	0.826208i	$-0.690493\pi$
$29$	−5102.87	−1.12673	−0.563364	+	0.826208i	$0.690493\pi$
$30$	−2940.07	−0.596423
$31$	−95.4999	−0.0178484	−0.00892419	−	0.999960i	$-0.502841\pi$
$31$	−95.4999	−0.0178484	−0.00892419	+	0.999960i	$0.502841\pi$
$32$	−4777.09	−0.824686
$33$	−3016.16	−0.482136
$34$	−2934.46	−0.435343
$35$	−13509.9	−1.86416
$36$	−1438.83	−0.185035
$37$	−8813.51	−1.05839	−0.529194	−	0.848501i	$-0.677505\pi$
$37$	−8813.51	−1.05839	−0.529194	+	0.848501i	$0.677505\pi$
$38$	247.402	0.0277936
$39$	5965.16	0.628001
$40$	−10445.3	−1.03221
$41$	−1895.44	−0.176096	−0.0880482	−	0.996116i	$-0.528063\pi$
$41$	−1895.44	−0.176096	−0.0880482	+	0.996116i	$0.528063\pi$
$42$	4297.74	0.375939
$43$	14050.5	1.15883	0.579417	−	0.815032i	$-0.303280\pi$
$43$	14050.5	1.15883	0.579417	+	0.815032i	$0.303280\pi$
$44$	−5076.49	−0.395304
$45$	−4801.66	−0.353476
$46$	259.029	0.0180490
$47$	19049.3	1.25787	0.628933	−	0.777459i	$-0.283492\pi$
$47$	19049.3	1.25787	0.628933	+	0.777459i	$0.283492\pi$
$48$	−12455.0	−0.780262
$49$	2941.56	0.175020
$50$	−10930.1	−0.618298
$51$	−28108.9	−1.51328
$52$	10039.9	0.514899
$53$	1415.63	0.0692244	0.0346122	−	0.999401i	$-0.488980\pi$
$53$	1415.63	0.0692244	0.0346122	+	0.999401i	$0.488980\pi$
$54$	−5904.05	−0.275528
$55$	−16941.2	−0.755159
$56$	15268.7	0.650627
$57$	2369.84	0.0966122
$58$	9117.86	0.355896
$59$	12357.5	0.462168	0.231084	−	0.972934i	$-0.425773\pi$
$59$	12357.5	0.462168	0.231084	+	0.972934i	$0.425773\pi$
$60$	−47400.4	−1.69982
$61$	−30196.6	−1.03904	−0.519521	−	0.854458i	$-0.673890\pi$
$61$	−30196.6	−1.03904	−0.519521	+	0.854458i	$0.673890\pi$
$62$	170.640	0.00563771
$63$	7018.99	0.222804
$64$	−14750.5	−0.450149
$65$	33505.2	0.983624
$66$	5389.31	0.152291
$67$	30511.7	0.830386	0.415193	−	0.909733i	$-0.363714\pi$
$67$	30511.7	0.830386	0.415193	+	0.909733i	$0.363714\pi$
$68$	−47310.0	−1.24074
$69$	2481.22	0.0627396
$70$	24139.7	0.588825
$71$	67506.1	1.58927	0.794634	−	0.607089i	$-0.207663\pi$
$71$	67506.1	1.58927	0.794634	+	0.607089i	$0.207663\pi$
$72$	5426.77	0.123370
$73$	−76337.4	−1.67660	−0.838302	−	0.545206i	$-0.816451\pi$
$73$	−76337.4	−1.67660	−0.838302	+	0.545206i	$0.816451\pi$
$74$	15748.1	0.334309
$75$	−104698.	−2.14924
$76$	3988.67	0.0792125
$77$	24764.4	0.475994
$78$	−10658.6	−0.198365
$79$	−52240.4	−0.941756	−0.470878	−	0.882198i	$-0.656063\pi$
$79$	−52240.4	−0.941756	−0.470878	+	0.882198i	$0.656063\pi$
$80$	−69957.5	−1.22211
$81$	−68691.4	−1.16329
$82$	3386.79	0.0556230
$83$	39800.8	0.634157	0.317079	−	0.948399i	$-0.397298\pi$
$83$	39800.8	0.634157	0.317079	+	0.948399i	$0.397298\pi$
$84$	69289.1	1.07144
$85$	−157883.	−2.37021
$86$	−25105.6	−0.366037
$87$	87339.1	1.23712
$88$	19146.7	0.263565
$89$	−11353.4	−0.151933	−0.0759665	−	0.997110i	$-0.524204\pi$
$89$	−11353.4	−0.151933	−0.0759665	+	0.997110i	$0.524204\pi$
$90$	8579.66	0.111651
$91$	−48977.4	−0.620000
$92$	4176.12	0.0514403
$93$	1634.55	0.0195970
$94$	−34037.5	−0.397318
$95$	13311.0	0.151322
$96$	81763.2	0.905482
$97$	103709.	1.11914	0.559571	−	0.828782i	$-0.310966\pi$
$97$	103709.	1.11914	0.559571	+	0.828782i	$0.310966\pi$
$98$	−5256.00	−0.0552828
$99$	8801.72	0.0902567
$100$	−176217.	−1.76217
$101$	41723.2	0.406981	0.203490	−	0.979077i	$-0.434771\pi$
$101$	41723.2	0.406981	0.203490	+	0.979077i	$0.434771\pi$
$102$	50225.3	0.477994
$103$	116579.	1.08275	0.541374	−	0.840782i	$-0.317904\pi$
$103$	116579.	1.08275	0.541374	+	0.840782i	$0.317904\pi$
$104$	−37867.1	−0.343304
$105$	231231.	2.04679
$106$	−2529.46	−0.0218657
$107$	20396.3	0.172223	0.0861117	−	0.996285i	$-0.472556\pi$
$107$	20396.3	0.172223	0.0861117	+	0.996285i	$0.472556\pi$
$108$	−95186.2	−0.785262
$109$	−43938.3	−0.354224	−0.177112	−	0.984191i	$-0.556675\pi$
$109$	−43938.3	−0.354224	−0.177112	+	0.984191i	$0.556675\pi$
$110$	30270.8	0.238530
$111$	150849.	1.16208
$112$	102263.	0.770321
$113$	−210370.	−1.54985	−0.774923	−	0.632056i	$-0.782211\pi$
$113$	−210370.	−1.54985	−0.774923	+	0.632056i	$0.782211\pi$
$114$	−4234.46	−0.0305166
$115$	13936.5	0.0982677
$116$	147000.	1.01431
$117$	−17407.4	−0.117563
$118$	−22080.5	−0.145983
$119$	230790.	1.49400
$120$	178778.	1.13334
$121$	−129997.	−0.807178
$122$	53955.5	0.328198
$123$	32441.8	0.193349
$124$	2751.10	0.0160676
$125$	−287646.	−1.64658
$126$	−12541.6	−0.0703763
$127$	249916.	1.37495	0.687473	−	0.726210i	$-0.258720\pi$
$127$	249916.	1.37495	0.687473	+	0.726210i	$0.258720\pi$
$128$	179223.	0.966873
$129$	−240484.	−1.27237
$130$	−59867.5	−0.310694
$131$	−288544.	−1.46904	−0.734521	−	0.678586i	$-0.762593\pi$
$131$	−288544.	−1.46904	−0.734521	+	0.678586i	$0.762593\pi$
$132$	86887.5	0.434033
$133$	−19457.8	−0.0953814
$134$	−54518.7	−0.262291
$135$	−317655.	−1.50011
$136$	178437.	0.827250
$137$	−76717.7	−0.349216	−0.174608	−	0.984638i	$-0.555866\pi$
$137$	−76717.7	−0.349216	−0.174608	+	0.984638i	$0.555866\pi$
$138$	−4433.46	−0.0198173
$139$	−292888.	−1.28577	−0.642886	−	0.765962i	$-0.722263\pi$
$139$	−292888.	−1.28577	−0.642886	+	0.765962i	$0.722263\pi$
$140$	389184.	1.67817
$141$	−326042.	−1.38110
$142$	−120621.	−0.501996
$143$	−61417.0	−0.251159
$144$	36346.0	0.146066
$145$	490568.	1.93767
$146$	136401.	0.529583
$147$	−50346.7	−0.192167
$148$	253893.	0.952790
$149$	388410.	1.43326	0.716630	−	0.697453i	$-0.245684\pi$
$149$	388410.	1.43326	0.716630	+	0.697453i	$0.245684\pi$
$150$	187075.	0.678873
$151$	155035.	0.553333	0.276667	−	0.960966i	$-0.410770\pi$
$151$	155035.	0.553333	0.276667	+	0.960966i	$0.410770\pi$
$152$	−15043.9	−0.0528142
$153$	82027.0	0.283288
$154$	−44249.3	−0.150351
$155$	9180.96	0.0306944
$156$	−171840.	−0.565345
$157$	9382.95	0.0303802	0.0151901	−	0.999885i	$-0.495165\pi$
$157$	9382.95	0.0303802	0.0151901	+	0.999885i	$0.495165\pi$
$158$	93343.6	0.297469
$159$	−24229.4	−0.0760064
$160$	459249.	1.41824
$161$	−20372.2	−0.0619403
$162$	122738.	0.367446
$163$	−457950.	−1.35005	−0.675023	−	0.737797i	$-0.735866\pi$
$163$	−457950.	−1.35005	−0.675023	+	0.737797i	$0.735866\pi$
$164$	54602.5	0.158527
$165$	289961.	0.829144
$166$	−71116.5	−0.200309
$167$	−82704.6	−0.229477	−0.114738	−	0.993396i	$-0.536603\pi$
$167$	−82704.6	−0.229477	−0.114738	+	0.993396i	$0.536603\pi$
$168$	−261334.	−0.714370
$169$	−249827.	−0.672856
$170$	282107.	0.748671
$171$	−6915.63	−0.0180860
$172$	−404757.	−1.04321
$173$	−156470.	−0.397479	−0.198740	−	0.980052i	$-0.563685\pi$
$173$	−156470.	−0.397479	−0.198740	+	0.980052i	$0.563685\pi$
$174$	−156058.	−0.390764
$175$	859630.	2.12186
$176$	128236.	0.312053
$177$	−211507.	−0.507447
$178$	20286.4	0.0479905
$179$	−164148.	−0.382915	−0.191457	−	0.981501i	$-0.561321\pi$
$179$	−164148.	−0.382915	−0.191457	+	0.981501i	$0.561321\pi$
$180$	138323.	0.318209
$181$	−708785.	−1.60812	−0.804059	−	0.594549i	$-0.797330\pi$
$181$	−708785.	−1.60812	−0.804059	+	0.594549i	$0.797330\pi$
$182$	87513.3	0.195837
$183$	516835.	1.14084
$184$	−15750.9	−0.0342973
$185$	847293.	1.82014
$186$	−2920.63	−0.00619004
$187$	289408.	0.605210
$188$	−548759.	−1.13237
$189$	464343.	0.945550
$190$	−23784.2	−0.0477974
$191$	918508.	1.82179	0.910897	−	0.412633i	$-0.135391\pi$
$191$	918508.	1.82179	0.910897	+	0.412633i	$0.135391\pi$
$192$	252465.	0.494251
$193$	182636.	0.352935	0.176467	−	0.984306i	$-0.443533\pi$
$193$	182636.	0.352935	0.176467	+	0.984306i	$0.443533\pi$
$194$	−185308.	−0.353500
$195$	−573465.	−1.07999
$196$	−84738.3	−0.157558
$197$	−38809.0	−0.0712470
$197$	−38809.0	−0.0712470
$198$	−15727.0	−0.0285091
$199$	507573.	0.908586	0.454293	−	0.890852i	$-0.349892\pi$
$199$	507573.	0.908586	0.454293	+	0.890852i	$0.349892\pi$
$200$	664628.	1.17491
$201$	−522229.	−0.911740
$202$	−74551.4	−0.128552
$203$	−717104.	−1.22136
$204$	809742.	1.36230
$205$	182220.	0.302838
$206$	−208305.	−0.342004
$207$	−7240.64	−0.0117450
$208$	−253616.	−0.406461
$209$	−24399.8	−0.0386385
$210$	−413167.	−0.646513
$211$	−237438.	−0.367151	−0.183575	−	0.983006i	$-0.558767\pi$
$211$	−237438.	−0.367151	−0.183575	+	0.983006i	$0.558767\pi$
$212$	−40780.4	−0.0623178
$213$	−1.15541e6	−1.74497
$214$	−36444.3	−0.0543996
$215$	−1.35076e6	−1.99288
$216$	359009.	0.523566
$217$	−13420.6	−0.0193473
$218$	78509.5	0.111887
$219$	1.30657e6	1.84086
$220$	488032.	0.679816
$221$	−572371.	−0.788310
$222$	−269539.	−0.367062
$223$	−404970.	−0.545332	−0.272666	−	0.962109i	$-0.587905\pi$
$223$	−404970.	−0.545332	−0.272666	+	0.962109i	$0.587905\pi$
$224$	−671322.	−0.893945
$225$	305528.	0.402341
$226$	375892.	0.489544
$227$	−359358.	−0.462874	−0.231437	−	0.972850i	$-0.574343\pi$
$227$	−359358.	−0.462874	−0.231437	+	0.972850i	$0.574343\pi$
$228$	−68268.8	−0.0869731
$229$	−491606.	−0.619482	−0.309741	−	0.950821i	$-0.600242\pi$
$229$	−491606.	−0.619482	−0.309741	+	0.950821i	$0.600242\pi$
$230$	−24902.0	−0.0310395
$231$	−423860.	−0.522628
$232$	−554433.	−0.676283
$233$	180695.	0.218050	0.109025	−	0.994039i	$-0.465227\pi$
$233$	180695.	0.218050	0.109025	+	0.994039i	$0.465227\pi$
$234$	31103.8	0.0371342
$235$	−1.83132e6	−2.16319
$236$	−355985.	−0.416056
$237$	894130.	1.03402
$238$	−412379.	−0.471904
$239$	−1.65255e6	−1.87137	−0.935686	−	0.352833i	$-0.885218\pi$
$239$	−1.65255e6	−1.87137	−0.935686	+	0.352833i	$0.885218\pi$
$240$	1.19737e6	1.34184
$241$	−885940.	−0.982566	−0.491283	−	0.871000i	$-0.663472\pi$
$241$	−885940.	−0.982566	−0.491283	+	0.871000i	$0.663472\pi$
$242$	232280.	0.254960
$243$	372770.	0.404972
$244$	869882.	0.935375
$245$	−282789.	−0.300986
$246$	−57967.3	−0.0610724
$247$	48256.2	0.0503281
$248$	−10376.2	−0.0107129
$249$	−681218.	−0.696287
$250$	513968.	0.520099
$251$	−617027.	−0.618187	−0.309094	−	0.951032i	$-0.600026\pi$
$251$	−617027.	−0.618187	−0.309094	+	0.951032i	$0.600026\pi$
$252$	−202198.	−0.200575
$253$	−25546.5	−0.0250917
$254$	−446553.	−0.434299
$255$	2.70227e6	2.60243
$256$	151778.	0.144746
$257$	−1.49616e6	−1.41301	−0.706506	−	0.707707i	$-0.749730\pi$
$257$	−1.49616e6	−1.41301	−0.706506	+	0.707707i	$0.749730\pi$
$258$	429700.	0.401898
$259$	−1.23856e6	−1.14727
$260$	−965196.	−0.885486
$261$	−254872.	−0.231590
$262$	515574.	0.464021
$263$	1.17809e6	1.05024	0.525121	−	0.851028i	$-0.324020\pi$
$263$	1.17809e6	1.05024	0.525121	+	0.851028i	$0.324020\pi$
$264$	−327710.	−0.289387
$265$	−136092.	−0.119047
$266$	34767.3	0.0301278
$267$	194322.	0.166818
$268$	−878961.	−0.747537
$269$	−843390.	−0.710637	−0.355319	−	0.934745i	$-0.615628\pi$
$269$	−843390.	−0.710637	−0.355319	+	0.934745i	$0.615628\pi$
$270$	567590.	0.473833
$271$	−1.38882e6	−1.14874	−0.574370	−	0.818596i	$-0.694753\pi$
$271$	−1.38882e6	−1.14874	−0.574370	+	0.818596i	$0.694753\pi$
$272$	1.19509e6	0.979438
$273$	838281.	0.680743
$274$	137080.	0.110306
$275$	1.07796e6	0.859553
$276$	−71477.2	−0.0564800
$277$	22216.4	0.0173970	0.00869850	−	0.999962i	$-0.497231\pi$
$277$	22216.4	0.0173970	0.00869850	+	0.999962i	$0.497231\pi$
$278$	523335.	0.406133
$279$	−4769.91	−0.00366859
$280$	−1.46787e6	−1.11890
$281$	−84719.7	−0.0640057	−0.0320029	−	0.999488i	$-0.510189\pi$
$281$	−84719.7	−0.0640057	−0.0320029	+	0.999488i	$0.510189\pi$
$282$	582575.	0.436244
$283$	−684685.	−0.508188	−0.254094	−	0.967180i	$-0.581777\pi$
$283$	−684685.	−0.508188	−0.254094	+	0.967180i	$0.581777\pi$
$284$	−1.94467e6	−1.43070
$285$	−227826.	−0.166147
$286$	109740.	0.0793326
$287$	−266365.	−0.190886
$288$	−238600.	−0.169508
$289$	1.27726e6	0.899569
$290$	−876552.	−0.612044
$291$	−1.77504e6	−1.22879
$292$	2.19908e6	1.50933
$293$	1.50151e6	1.02178	0.510891	−	0.859646i	$-0.329316\pi$
$293$	1.50151e6	1.02178	0.510891	+	0.859646i	$0.329316\pi$
$294$	89960.1	0.0606990
$295$	−1.18799e6	−0.794802
$296$	−957598.	−0.635263
$297$	582280.	0.383037
$298$	−694016.	−0.452719
$299$	50524.1	0.0326829
$300$	3.01607e6	1.93481
$301$	1.97451e6	1.25616
$302$	−277018.	−0.174779
$303$	−714121.	−0.446853
$304$	−100757.	−0.0625303
$305$	2.90297e6	1.78687
$306$	−146567.	−0.0894812
$307$	−2.15201e6	−1.30316	−0.651582	−	0.758578i	$-0.725894\pi$
$307$	−2.15201e6	−1.30316	−0.651582	+	0.758578i	$0.725894\pi$
$308$	−713396.	−0.428503
$309$	−1.99533e6	−1.18883
$310$	−16404.6	−0.00969532
$311$	3.29274e6	1.93044	0.965219	−	0.261441i	$-0.0841978\pi$
$311$	3.29274e6	1.93044	0.965219	+	0.261441i	$0.0841978\pi$
$312$	648121.	0.376938
$313$	−1.95422e6	−1.12749	−0.563744	−	0.825949i	$-0.690640\pi$
$313$	−1.95422e6	−1.12749	−0.563744	+	0.825949i	$0.690640\pi$
$314$	−16765.5	−0.00959608
$315$	−674776.	−0.383162
$316$	1.50490e6	0.847796
$317$	−1.05820e6	−0.591454	−0.295727	−	0.955272i	$-0.595562\pi$
$317$	−1.05820e6	−0.591454	−0.295727	+	0.955272i	$0.595562\pi$
$318$	43293.4	0.0240079
$319$	−899239.	−0.494764
$320$	1.41805e6	0.774134
$321$	−349097.	−0.189096
$322$	36401.3	0.0195649
$323$	−227392.	−0.121274
$324$	1.97881e6	1.04723
$325$	−2.13192e6	−1.11960
$326$	818269.	0.426434
$327$	752035.	0.388927
$328$	−205942.	−0.105696
$329$	2.67699e6	1.36351
$330$	−518105.	−0.261899
$331$	292872.	0.146929	0.0734646	−	0.997298i	$-0.476594\pi$
$331$	292872.	0.146929	0.0734646	+	0.997298i	$0.476594\pi$
$332$	−1.14655e6	−0.570886
$333$	−440206.	−0.217543
$334$	147777.	0.0724840
$335$	−2.93327e6	−1.42804
$336$	−1.75030e6	−0.845791
$337$	2.74512e6	1.31670	0.658349	−	0.752713i	$-0.271255\pi$
$337$	2.74512e6	1.31670	0.658349	+	0.752713i	$0.271255\pi$
$338$	446393.	0.212533
$339$	3.60063e6	1.70169
$340$	4.54818e6	2.13373
$341$	−16829.2	−0.00783750
$342$	12356.9	0.00571275
$343$	−1.94850e6	−0.894265
$344$	1.52660e6	0.695553
$345$	−238534.	−0.107895
$346$	279582.	0.125550
$347$	1.06559e6	0.475078	0.237539	−	0.971378i	$-0.423659\pi$
$347$	1.06559e6	0.475078	0.237539	+	0.971378i	$0.423659\pi$
$348$	−2.51600e6	−1.11369
$349$	−3.86363e6	−1.69798	−0.848988	−	0.528412i	$-0.822788\pi$
$349$	−3.86363e6	−1.69798	−0.848988	+	0.528412i	$0.822788\pi$
$350$	−1.53600e6	−0.670224
$351$	−1.15159e6	−0.498921
$352$	−841829.	−0.362132
$353$	2.21033e6	0.944105	0.472053	−	0.881570i	$-0.343513\pi$
$353$	2.21033e6	0.944105	0.472053	+	0.881570i	$0.343513\pi$
$354$	377922.	0.160285
$355$	−6.48974e6	−2.73311
$356$	327062.	0.136774
$357$	−3.95013e6	−1.64037
$358$	293301.	0.120950
$359$	3.82505e6	1.56639	0.783197	−	0.621773i	$-0.213588\pi$
$359$	3.82505e6	1.56639	0.783197	+	0.621773i	$0.213588\pi$
$360$	−521706.	−0.212163
$361$	−2.45693e6	−0.992257
$362$	1.26646e6	0.507951
$363$	2.22498e6	0.886258
$364$	1.41091e6	0.558142
$365$	7.33875e6	2.88330
$366$	−923486.	−0.360353
$367$	165142.	0.0640017	0.0320008	−	0.999488i	$-0.489812\pi$
$367$	165142.	0.0640017	0.0320008	+	0.999488i	$0.489812\pi$
$368$	−105492.	−0.0406069
$369$	−94671.0	−0.0361952
$370$	−1.51395e6	−0.574921
$371$	198937.	0.0750381
$372$	−47086.9	−0.0176418
$373$	4.17984e6	1.55556	0.777781	−	0.628536i	$-0.216345\pi$
$373$	4.17984e6	1.55556	0.777781	+	0.628536i	$0.216345\pi$
$374$	−517117.	−0.191166
$375$	4.92325e6	1.80790
$376$	2.06973e6	0.754995
$377$	1.77845e6	0.644449
$378$	−829694.	−0.298668
$379$	−2.63851e6	−0.943542	−0.471771	−	0.881721i	$-0.656385\pi$
$379$	−2.63851e6	−0.943542	−0.471771	+	0.881721i	$0.656385\pi$
$380$	−383453.	−0.136224
$381$	−4.27749e6	−1.50965
$382$	−1.64120e6	−0.575444
$383$	−4.25043e6	−1.48059	−0.740297	−	0.672280i	$-0.765315\pi$
$383$	−4.25043e6	−1.48059	−0.740297	+	0.672280i	$0.765315\pi$
$384$	−3.06753e6	−1.06160
$385$	−2.38075e6	−0.818580
$386$	−326337.	−0.111480
$387$	701777.	0.238189
$388$	−2.98756e6	−1.00748
$389$	1.99233e6	0.667556	0.333778	−	0.942652i	$-0.391676\pi$
$389$	1.99233e6	0.667556	0.333778	+	0.942652i	$0.391676\pi$
$390$	1.02467e6	0.341133
$391$	−238079.	−0.0787550
$392$	319603.	0.105050
$393$	4.93863e6	1.61297
$394$	69344.3	0.0225046
$395$	5.02217e6	1.61956
$396$	−253554.	−0.0812516
$397$	−318582.	−0.101448	−0.0507242	−	0.998713i	$-0.516153\pi$
$397$	−318582.	−0.101448	−0.0507242	+	0.998713i	$0.516153\pi$
$398$	−906937.	−0.286992
$399$	333033.	0.104726
$400$	4.45137e6	1.39105
$401$	787093.	0.244436	0.122218	−	0.992503i	$-0.460999\pi$
$401$	787093.	0.244436	0.122218	+	0.992503i	$0.460999\pi$
$402$	933125.	0.287988
$403$	33283.6	0.0102087
$404$	−1.20193e6	−0.366376
$405$	6.60370e6	2.00055
$406$	1.28133e6	0.385785
$407$	−1.55314e6	−0.464754
$408$	−3.05407e6	−0.908297
$409$	5.53933e6	1.63738	0.818689	−	0.574237i	$-0.194701\pi$
$409$	5.53933e6	1.63738	0.818689	+	0.574237i	$0.194701\pi$
$410$	−325592.	−0.0956564
$411$	1.31308e6	0.383429
$412$	−3.35833e6	−0.974721
$413$	1.73659e6	0.500982
$414$	12937.7	0.00370984
$415$	−3.82628e6	−1.09058
$416$	1.66491e6	0.471691
$417$	5.01298e6	1.41174
$418$	43597.7	0.0122046
$419$	−2.62212e6	−0.729654	−0.364827	−	0.931075i	$-0.618872\pi$
$419$	−2.62212e6	−0.729654	−0.364827	+	0.931075i	$0.618872\pi$
$420$	−6.66115e6	−1.84258
$421$	4.19009e6	1.15218	0.576088	−	0.817388i	$-0.304579\pi$
$421$	4.19009e6	1.15218	0.576088	+	0.817388i	$0.304579\pi$
$422$	424257.	0.115971
$423$	951450.	0.258544
$424$	153810.	0.0415498
$425$	1.00460e7	2.69787
$426$	2.06450e6	0.551178
$427$	−4.24351e6	−1.12630
$428$	−587562.	−0.155040
$429$	1.05119e6	0.275765
$430$	2.41355e6	0.629483
$431$	−5.97331e6	−1.54889	−0.774447	−	0.632639i	$-0.781972\pi$
$431$	−5.97331e6	−1.54889	−0.774447	+	0.632639i	$0.781972\pi$
$432$	2.40448e6	0.619885
$433$	−5.57568e6	−1.42915	−0.714575	−	0.699559i	$-0.753380\pi$
$433$	−5.57568e6	−1.42915	−0.714575	+	0.699559i	$0.753380\pi$
$434$	23980.0	0.00611118
$435$	−8.39641e6	−2.12750
$436$	1.26575e6	0.318882
$437$	20072.2	0.00502796
$438$	−2.33459e6	−0.581467
$439$	3.38123e6	0.837362	0.418681	−	0.908133i	$-0.362493\pi$
$439$	3.38123e6	0.837362	0.418681	+	0.908133i	$0.362493\pi$
$440$	−1.84069e6	−0.453261
$441$	146921.	0.0359739
$442$	1.02272e6	0.249001
$443$	−5.92927e6	−1.43546	−0.717732	−	0.696320i	$-0.754820\pi$
$443$	−5.92927e6	−1.43546	−0.717732	+	0.696320i	$0.754820\pi$
$444$	−4.34556e6	−1.04614
$445$	1.09147e6	0.261283
$446$	723605.	0.172252
$447$	−6.64791e6	−1.57368
$448$	−2.07288e6	−0.487954
$449$	4.08430e6	0.956096	0.478048	−	0.878334i	$-0.341345\pi$
$449$	4.08430e6	0.956096	0.478048	+	0.878334i	$0.341345\pi$
$450$	−545920.	−0.127086
$451$	−334019.	−0.0773267
$452$	6.06021e6	1.39522
$453$	−2.65353e6	−0.607544
$454$	642105.	0.146206
$455$	4.70848e6	1.06623
$456$	257486.	0.0579884
$457$	−1.62270e6	−0.363452	−0.181726	−	0.983349i	$-0.558168\pi$
$457$	−1.62270e6	−0.363452	−0.181726	+	0.983349i	$0.558168\pi$
$458$	878407.	0.195673
$459$	5.42652e6	1.20224
$460$	−401474.	−0.0884633
$461$	1.68060e6	0.368308	0.184154	−	0.982897i	$-0.441045\pi$
$461$	1.68060e6	0.368308	0.184154	+	0.982897i	$0.441045\pi$
$462$	757358.	0.165081
$463$	−5.92990e6	−1.28557	−0.642784	−	0.766048i	$-0.722221\pi$
$463$	−5.92990e6	−1.28557	−0.642784	+	0.766048i	$0.722221\pi$
$464$	−3.71333e6	−0.800698
$465$	−157138.	−0.0337015
$466$	−322867.	−0.0688745
$467$	8.68490e6	1.84278	0.921388	−	0.388644i	$-0.127057\pi$
$467$	8.68490e6	1.84278	0.921388	+	0.388644i	$0.127057\pi$
$468$	501461.	0.105833
$469$	4.28780e6	0.900124
$470$	3.27222e6	0.683279
$471$	−160596.	−0.0333566
$472$	1.34265e6	0.277401
$473$	2.47601e6	0.508862
$474$	−1.59764e6	−0.326613
$475$	−846972.	−0.172240
$476$	−6.64845e6	−1.34494
$477$	70705.9	0.0142285
$478$	2.95280e6	0.591104
$479$	−501591.	−0.0998875	−0.0499438	−	0.998752i	$-0.515904\pi$
$479$	−501591.	−0.0998875	−0.0499438	+	0.998752i	$0.515904\pi$
$480$	−7.86036e6	−1.55718
$481$	3.07168e6	0.605360
$482$	1.58301e6	0.310360
$483$	348684.	0.0680087
$484$	3.74486e6	0.726644
$485$	−9.97010e6	−1.92462
$486$	−666069.	−0.127917
$487$	5.53404e6	1.05735	0.528676	−	0.848823i	$-0.322688\pi$
$487$	5.53404e6	1.05735	0.528676	+	0.848823i	$0.322688\pi$
$488$	−3.28089e6	−0.623652
$489$	7.83812e6	1.48231
$490$	505290.	0.0950715
$491$	7.97234e6	1.49239	0.746194	−	0.665728i	$-0.231879\pi$
$491$	7.97234e6	1.49239	0.746194	+	0.665728i	$0.231879\pi$
$492$	−934560.	−0.174058
$493$	−8.38039e6	−1.55291
$494$	−86224.6	−0.0158970
$495$	−846159.	−0.155217
$496$	−69494.8	−0.0126838
$497$	9.48660e6	1.72274
$498$	1.21721e6	0.219934
$499$	1.23157e6	0.221416	0.110708	−	0.993853i	$-0.464688\pi$
$499$	1.23157e6	0.221416	0.110708	+	0.993853i	$0.464688\pi$
$500$	8.28630e6	1.48230
$501$	1.41555e6	0.251959
$502$	1.10251e6	0.195265
$503$	−3.37222e6	−0.594286	−0.297143	−	0.954833i	$-0.596034\pi$
$503$	−3.37222e6	−0.594286	−0.297143	+	0.954833i	$0.596034\pi$
$504$	762621.	0.133731
$505$	−4.01109e6	−0.699896
$506$	45646.7	0.00792562
$507$	4.27596e6	0.738777
$508$	−7.19942e6	−1.23776
$509$	2.06141e6	0.352671	0.176336	−	0.984330i	$-0.443576\pi$
$509$	2.06141e6	0.352671	0.176336	+	0.984330i	$0.443576\pi$
$510$	−4.82845e6	−0.822019
$511$	−1.07277e7	−1.81741
$512$	−6.00634e6	−1.01259
$513$	−457506.	−0.0767544
$514$	2.67336e6	0.446323
$515$	−1.12074e7	−1.86203
$516$	6.92770e6	1.14542
$517$	3.35691e6	0.552349
$518$	2.21307e6	0.362385
$519$	2.67808e6	0.436421
$520$	3.64038e6	0.590389
$521$	−4.49375e6	−0.725295	−0.362647	−	0.931926i	$-0.618127\pi$
$521$	−4.49375e6	−0.725295	−0.362647	+	0.931926i	$0.618127\pi$
$522$	455407.	0.0731516
$523$	−1.00504e7	−1.60668	−0.803342	−	0.595518i	$-0.796947\pi$
$523$	−1.00504e7	−1.60668	−0.803342	+	0.595518i	$0.796947\pi$
$524$	8.31218e6	1.32247
$525$	−1.47132e7	−2.32974
$526$	−2.10502e6	−0.331736
$527$	−156839.	−0.0245995
$528$	−2.19485e6	−0.342625
$529$	−6.41533e6	−0.996735
$530$	243171.	0.0376030
$531$	617215.	0.0949948
$532$	560525.	0.0858650
$533$	660599.	0.100721
$534$	−347216.	−0.0526922
$535$	−1.96081e6	−0.296177
$536$	3.31513e6	0.498413
$537$	2.80950e6	0.420430
$538$	1.50698e6	0.224466
$539$	518367.	0.0768539
$540$	9.15080e6	1.35044
$541$	1.43714e6	0.211109	0.105555	−	0.994414i	$-0.466338\pi$
$541$	1.43714e6	0.211109	0.105555	+	0.994414i	$0.466338\pi$
$542$	2.48155e6	0.362848
$543$	1.21313e7	1.76567
$544$	−7.84537e6	−1.13662
$545$	4.22404e6	0.609168
$546$	−1.49785e6	−0.215024
$547$	−6.80536e6	−0.972485	−0.486243	−	0.873824i	$-0.661633\pi$
$547$	−6.80536e6	−0.972485	−0.486243	+	0.873824i	$0.661633\pi$
$548$	2.21003e6	0.314374
$549$	−1.50822e6	−0.213567
$550$	−1.92612e6	−0.271504
$551$	706544.	0.0991426
$552$	269587.	0.0376575
$553$	−7.34132e6	−1.02085
$554$	−39696.5	−0.00549513
$555$	−1.45020e7	−1.99846
$556$	8.43731e6	1.15749
$557$	3.61967e6	0.494346	0.247173	−	0.968971i	$-0.420498\pi$
$557$	3.61967e6	0.494346	0.247173	+	0.968971i	$0.420498\pi$
$558$	8522.92	0.00115879
$559$	−4.89688e6	−0.662812
$560$	−9.83109e6	−1.32474
$561$	−4.95342e6	−0.664504
$562$	151378.	0.0202173
$563$	4.30849e6	0.572867	0.286433	−	0.958100i	$-0.407530\pi$
$563$	4.30849e6	0.572867	0.286433	+	0.958100i	$0.407530\pi$
$564$	9.39239e6	1.24331
$565$	2.02241e7	2.66531
$566$	1.22340e6	0.160520
$567$	−9.65317e6	−1.26099
$568$	7.33461e6	0.953907
$569$	−8.38186e6	−1.08532	−0.542662	−	0.839951i	$-0.682584\pi$
$569$	−8.38186e6	−1.08532	−0.542662	+	0.839951i	$0.682584\pi$
$570$	407083.	0.0524802
$571$	9.08840e6	1.16653	0.583267	−	0.812281i	$-0.301774\pi$
$571$	9.08840e6	1.16653	0.583267	+	0.812281i	$0.301774\pi$
$572$	1.76926e6	0.226100
$573$	−1.57209e7	−2.00028
$574$	475945.	0.0602944
$575$	−886777.	−0.111852
$576$	−736738.	−0.0925245
$577$	−5.90935e6	−0.738924	−0.369462	−	0.929246i	$-0.620458\pi$
$577$	−5.90935e6	−0.738924	−0.369462	+	0.929246i	$0.620458\pi$
$578$	−2.28222e6	−0.284144
$579$	−3.12595e6	−0.387512
$580$	−1.41319e7	−1.74434
$581$	5.59319e6	0.687416
$582$	3.17167e6	0.388133
$583$	249465.	0.0303975
$584$	−8.29415e6	−1.00633
$585$	1.67348e6	0.202176
$586$	−2.68291e6	−0.322747
$587$	−1.25855e7	−1.50757	−0.753783	−	0.657123i	$-0.771773\pi$
$587$	−1.25855e7	−1.50757	−0.753783	+	0.657123i	$0.771773\pi$
$588$	1.45035e6	0.172994
$589$	13222.9	0.00157051
$590$	2.12272e6	0.251051
$591$	664243.	0.0782272
$592$	−6.41355e6	−0.752132
$593$	−3.45677e6	−0.403677	−0.201838	−	0.979419i	$-0.564692\pi$
$593$	−3.45677e6	−0.403677	−0.201838	+	0.979419i	$0.564692\pi$
$594$	−1.04042e6	−0.120989
$595$	−2.21872e7	−2.56927
$596$	−1.11891e7	−1.29026
$597$	−8.68747e6	−0.997602
$598$	−90276.9	−0.0103234
$599$	8.73104e6	0.994257	0.497129	−	0.867677i	$-0.334388\pi$
$599$	8.73104e6	0.994257	0.497129	+	0.867677i	$0.334388\pi$
$600$	−1.13756e7	−1.29001
$601$	−1.68595e7	−1.90396	−0.951981	−	0.306156i	$-0.900957\pi$
$601$	−1.68595e7	−1.90396	−0.951981	+	0.306156i	$0.900957\pi$
$602$	−3.52808e6	−0.396777
$603$	1.52396e6	0.170679
$604$	−4.46613e6	−0.498126
$605$	1.24973e7	1.38813
$606$	1.27600e6	0.141146
$607$	−3.10155e6	−0.341670	−0.170835	−	0.985300i	$-0.554647\pi$
$607$	−3.10155e6	−0.341670	−0.170835	+	0.985300i	$0.554647\pi$
$608$	661437.	0.0725654
$609$	1.22737e7	1.34101
$610$	−5.18706e6	−0.564412
$611$	−6.63907e6	−0.719456
$612$	−2.36298e6	−0.255024
$613$	1.54366e7	1.65921	0.829605	−	0.558351i	$-0.188566\pi$
$613$	1.54366e7	1.65921	0.829605	+	0.558351i	$0.188566\pi$
$614$	3.84524e6	0.411626
$615$	−3.11881e6	−0.332508
$616$	2.69068e6	0.285700
$617$	−1.46018e7	−1.54417	−0.772083	−	0.635522i	$-0.780785\pi$
$617$	−1.46018e7	−1.54417	−0.772083	+	0.635522i	$0.780785\pi$
$618$	3.56528e6	0.375511
$619$	1.01174e7	1.06131	0.530655	−	0.847588i	$-0.321946\pi$
$619$	1.01174e7	1.06131	0.530655	+	0.847588i	$0.321946\pi$
$620$	−264479.	−0.0276319
$621$	−479007.	−0.0498440
$622$	−5.88350e6	−0.609761
$623$	−1.59549e6	−0.164693
$624$	4.34082e6	0.446283
$625$	8.53715e6	0.874204
$626$	3.49182e6	0.356136
$627$	417619.	0.0424239
$628$	−270297.	−0.0273491
$629$	−1.44743e7	−1.45872
$630$	1.20570e6	0.121028
$631$	1.83340e7	1.83309	0.916544	−	0.399933i	$-0.130967\pi$
$631$	1.83340e7	1.83309	0.916544	+	0.399933i	$0.130967\pi$
$632$	−5.67598e6	−0.565259
$633$	4.06392e6	0.403121
$634$	1.89081e6	0.186821
$635$	−2.40259e7	−2.36453
$636$	697985.	0.0684232
$637$	−1.02519e6	−0.100105
$638$	1.60677e6	0.156279
$639$	3.37171e6	0.326661
$640$	−1.72298e7	−1.66276
$641$	1.79215e7	1.72278	0.861391	−	0.507942i	$-0.169594\pi$
$641$	1.79215e7	1.72278	0.861391	+	0.507942i	$0.169594\pi$
$642$	623770.	0.0597292
$643$	1.36938e7	1.30616	0.653082	−	0.757287i	$-0.273475\pi$
$643$	1.36938e7	1.30616	0.653082	+	0.757287i	$0.273475\pi$
$644$	586868.	0.0557604
$645$	2.31191e7	2.18812
$646$	406306.	0.0383065
$647$	9.84305e6	0.924419	0.462210	−	0.886771i	$-0.347057\pi$
$647$	9.84305e6	0.924419	0.462210	+	0.886771i	$0.347057\pi$
$648$	−7.46340e6	−0.698231
$649$	2.17766e6	0.202945
$650$	3.80935e6	0.353645
$651$	229702.	0.0212428
$652$	1.31923e7	1.21535
$653$	−1.17007e7	−1.07381	−0.536906	−	0.843642i	$-0.680407\pi$
$653$	−1.17007e7	−1.07381	−0.536906	+	0.843642i	$0.680407\pi$
$654$	−1.34374e6	−0.122849
$655$	2.77394e7	2.52635
$656$	−1.37930e6	−0.125141
$657$	−3.81280e6	−0.344612
$658$	−4.78328e6	−0.430686
$659$	−7.01446e6	−0.629189	−0.314594	−	0.949226i	$-0.601868\pi$
$659$	−7.01446e6	−0.629189	−0.314594	+	0.949226i	$0.601868\pi$
$660$	−8.35300e6	−0.746419
$661$	−894132.	−0.0795972	−0.0397986	−	0.999208i	$-0.512672\pi$
$661$	−894132.	−0.0795972	−0.0397986	+	0.999208i	$0.512672\pi$
$662$	−523307.	−0.0464100
$663$	9.79652e6	0.865542
$664$	4.32440e6	0.380633
$665$	1.87059e6	0.164030
$666$	786564.	0.0687145
$667$	739750.	0.0643829
$668$	2.38250e6	0.206581
$669$	6.93134e6	0.598759
$670$	5.24119e6	0.451069
$671$	−5.32130e6	−0.456259
$672$	1.14901e7	0.981527
$673$	−6.63660e6	−0.564817	−0.282409	−	0.959294i	$-0.591133\pi$
$673$	−6.63660e6	−0.564817	−0.282409	+	0.959294i	$0.591133\pi$
$674$	−4.90501e6	−0.415901
$675$	2.02123e7	1.70748
$676$	7.19684e6	0.605724
$677$	−1.90982e7	−1.60148	−0.800739	−	0.599013i	$-0.795560\pi$
$677$	−1.90982e7	−1.60148	−0.800739	+	0.599013i	$0.795560\pi$
$678$	−6.43365e6	−0.537506
$679$	1.45741e7	1.21313
$680$	−1.71541e7	−1.42265
$681$	6.15066e6	0.508223
$682$	30070.6	0.00247560
$683$	1.10399e7	0.905551	0.452776	−	0.891625i	$-0.350434\pi$
$683$	1.10399e7	0.905551	0.452776	+	0.891625i	$0.350434\pi$
$684$	199221.	0.0162815
$685$	7.37531e6	0.600556
$686$	3.48161e6	0.282468
$687$	8.41417e6	0.680173
$688$	1.02245e7	0.823513
$689$	−493375.	−0.0395939
$690$	426214.	0.0340804
$691$	−1.10019e7	−0.876540	−0.438270	−	0.898843i	$-0.644409\pi$
$691$	−1.10019e7	−0.876540	−0.438270	+	0.898843i	$0.644409\pi$
$692$	4.50747e6	0.357822
$693$	1.23690e6	0.0978367
$694$	−1.90400e6	−0.150061
$695$	2.81570e7	2.21118
$696$	9.48949e6	0.742540
$697$	−3.11286e6	−0.242705
$698$	6.90357e6	0.536334
$699$	−3.09271e6	−0.239412
$700$	−2.47636e7	−1.91016
$701$	2.09298e7	1.60868	0.804341	−	0.594169i	$-0.202519\pi$
$701$	2.09298e7	1.60868	0.804341	+	0.594169i	$0.202519\pi$
$702$	2.05768e6	0.157592
$703$	1.22032e6	0.0931291
$704$	−2.59936e6	−0.197667
$705$	3.13443e7	2.37512
$706$	−3.94944e6	−0.298211
$707$	5.86334e6	0.441160
$708$	6.09293e6	0.456818
$709$	8.93459e6	0.667512	0.333756	−	0.942659i	$-0.391684\pi$
$709$	8.93459e6	0.667512	0.333756	+	0.942659i	$0.391684\pi$
$710$	1.15959e7	0.863297
$711$	−2.60923e6	−0.193570
$712$	−1.23356e6	−0.0911929
$713$	13844.4	0.00101988
$714$	7.05814e6	0.518137
$715$	5.90436e6	0.431925
$716$	4.72865e6	0.344711
$717$	2.82846e7	2.05471
$718$	−6.83464e6	−0.494771
$719$	2.40596e7	1.73566	0.867831	−	0.496859i	$-0.165513\pi$
$719$	2.40596e7	1.73566	0.867831	+	0.496859i	$0.165513\pi$
$720$	−3.49415e6	−0.251194
$721$	1.63828e7	1.17368
$722$	4.39006e6	0.313421
$723$	1.51635e7	1.07883
$724$	2.04182e7	1.44767
$725$	−3.12146e7	−2.20553
$726$	−3.97562e6	−0.279939
$727$	−2.08801e7	−1.46520	−0.732601	−	0.680658i	$-0.761694\pi$
$727$	−2.08801e7	−1.46520	−0.732601	+	0.680658i	$0.761694\pi$
$728$	−5.32145e6	−0.372136
$729$	1.03118e7	0.718647
$730$	−1.31130e7	−0.910739
$731$	2.30750e7	1.59716
$732$	−1.48886e7	−1.02702
$733$	−2.01592e7	−1.38584	−0.692919	−	0.721016i	$-0.743676\pi$
$733$	−2.01592e7	−1.38584	−0.692919	+	0.721016i	$0.743676\pi$
$734$	−295077.	−0.0202160
$735$	4.84012e6	0.330474
$736$	692522.	0.0471237
$737$	5.37684e6	0.364635
$738$	169159.	0.0114329
$739$	−7.43158e6	−0.500576	−0.250288	−	0.968171i	$-0.580525\pi$
$739$	−7.43158e6	−0.500576	−0.250288	+	0.968171i	$0.580525\pi$
$740$	−2.44082e7	−1.63854
$741$	−825937.	−0.0552588
$742$	−355464.	−0.0237020
$743$	−1.43501e7	−0.953634	−0.476817	−	0.879003i	$-0.658210\pi$
$743$	−1.43501e7	−0.953634	−0.476817	+	0.879003i	$0.658210\pi$
$744$	177595.	0.0117625
$745$	−3.73401e7	−2.46482
$746$	−7.46858e6	−0.491350
$747$	1.98792e6	0.130346
$748$	−8.33706e6	−0.544828
$749$	2.86628e6	0.186687
$750$	−8.79692e6	−0.571054
$751$	1.16954e7	0.756684	0.378342	−	0.925666i	$-0.376494\pi$
$751$	1.16954e7	0.756684	0.378342	+	0.925666i	$0.376494\pi$
$752$	1.38621e7	0.893890
$753$	1.05608e7	0.678752
$754$	−3.17776e6	−0.203560
$755$	−1.49044e7	−0.951583
$756$	−1.33765e7	−0.851211
$757$	−3.13800e7	−1.99028	−0.995139	−	0.0984786i	$-0.968602\pi$
$757$	−3.13800e7	−1.99028	−0.995139	+	0.0984786i	$0.968602\pi$
$758$	4.71453e6	0.298033
$759$	437245.	0.0275499
$760$	1.44625e6	0.0908260
$761$	−1.55647e7	−0.974268	−0.487134	−	0.873327i	$-0.661958\pi$
$761$	−1.55647e7	−0.974268	−0.487134	+	0.873327i	$0.661958\pi$
$762$	7.64307e6	0.476848
$763$	−6.17464e6	−0.383972
$764$	−2.64597e7	−1.64003
$765$	−7.88572e6	−0.487178
$766$	7.59472e6	0.467670
$767$	−4.30683e6	−0.264344
$768$	−2.59778e6	−0.158927
$769$	−2.03316e7	−1.23981	−0.619906	−	0.784676i	$-0.712829\pi$
$769$	−2.03316e7	−1.23981	−0.619906	+	0.784676i	$0.712829\pi$
$770$	4.25394e6	0.258562
$771$	2.56078e7	1.55145
$772$	−5.26127e6	−0.317722
$773$	4.36982e6	0.263035	0.131518	−	0.991314i	$-0.458015\pi$
$773$	4.36982e6	0.263035	0.131518	+	0.991314i	$0.458015\pi$
$774$	−1.25394e6	−0.0752359
$775$	−584181.	−0.0349376
$776$	1.12681e7	0.671730
$777$	2.11988e7	1.25967
$778$	−3.55992e6	−0.210859
$779$	262443.	0.0154950
$780$	1.65200e7	0.972239
$781$	1.18961e7	0.697872
$782$	425401.	0.0248761
$783$	−1.68611e7	−0.982837
$784$	2.14055e6	0.124376
$785$	−902036.	−0.0522456
$786$	−8.82440e6	−0.509482
$787$	−410710.	−0.0236373	−0.0118187	−	0.999930i	$-0.503762\pi$
$787$	−410710.	−0.0236373	−0.0118187	+	0.999930i	$0.503762\pi$
$788$	1.11798e6	0.0641386
$789$	−2.01638e7	−1.15314
$790$	−8.97366e6	−0.511566
$791$	−2.95633e7	−1.68001
$792$	956317.	0.0541737
$793$	1.05241e7	0.594295
$794$	569246.	0.0320442
$795$	2.32931e6	0.130710
$796$	−1.46218e7	−0.817935
$797$	−5.53609e6	−0.308715	−0.154357	−	0.988015i	$-0.549331\pi$
$797$	−5.53609e6	−0.308715	−0.154357	+	0.988015i	$0.549331\pi$
$798$	−595066.	−0.0330794
$799$	3.12845e7	1.73365
$800$	−2.92218e7	−1.61429
$801$	−567066.	−0.0312286
$802$	−1.40639e6	−0.0772091
$803$	−1.34523e7	−0.736223
$804$	1.50440e7	0.820774
$805$	1.95850e6	0.106520
$806$	−59471.6	−0.00322457
$807$	1.44352e7	0.780260
$808$	4.53327e6	0.244277
$809$	−1.66332e6	−0.0893522	−0.0446761	−	0.999002i	$-0.514226\pi$
$809$	−1.66332e6	−0.0893522	−0.0446761	+	0.999002i	$0.514226\pi$
$810$	−1.17996e7	−0.631907
$811$	−8.09719e6	−0.432297	−0.216149	−	0.976360i	$-0.569350\pi$
$811$	−8.09719e6	−0.432297	−0.216149	+	0.976360i	$0.569350\pi$
$812$	2.06578e7	1.09950
$813$	2.37705e7	1.26128
$814$	2.77516e6	0.146800
$815$	4.40253e7	2.32171
$816$	−2.04547e7	−1.07540
$817$	−1.94544e6	−0.101968
$818$	−9.89774e6	−0.517193
$819$	−2.44626e6	−0.127436
$820$	−5.24926e6	−0.272623
$821$	−1.10714e7	−0.573251	−0.286625	−	0.958043i	$-0.592533\pi$
$821$	−1.10714e7	−0.573251	−0.286625	+	0.958043i	$0.592533\pi$
$822$	−2.34622e6	−0.121112
$823$	−1.41131e7	−0.726309	−0.363155	−	0.931729i	$-0.618300\pi$
$823$	−1.41131e7	−0.726309	−0.363155	+	0.931729i	$0.618300\pi$
$824$	1.26664e7	0.649885
$825$	−1.84501e7	−0.943765
$826$	−3.10296e6	−0.158243
$827$	−1.83779e7	−0.934401	−0.467200	−	0.884151i	$-0.654737\pi$
$827$	−1.83779e7	−0.934401	−0.467200	+	0.884151i	$0.654737\pi$
$828$	208583.	0.0105731
$829$	−3.12197e7	−1.57777	−0.788883	−	0.614543i	$-0.789340\pi$
$829$	−3.12197e7	−1.57777	−0.788883	+	0.614543i	$0.789340\pi$
$830$	6.83684e6	0.344477
$831$	−380249.	−0.0191014
$832$	5.14084e6	0.257469
$833$	4.83089e6	0.241221
$834$	−8.95724e6	−0.445922
$835$	7.95087e6	0.394638
$836$	702891.	0.0347834
$837$	−315555.	−0.0155690
$838$	4.68522e6	0.230473
$839$	1.44949e7	0.710901	0.355450	−	0.934695i	$-0.384328\pi$
$839$	1.44949e7	0.710901	0.355450	+	0.934695i	$0.384328\pi$
$840$	2.51236e7	1.22852
$841$	5.52813e6	0.269518
$842$	−7.48691e6	−0.363934
$843$	1.45004e6	0.0702765
$844$	6.83996e6	0.330520
$845$	2.40173e7	1.15713
$846$	−1.70006e6	−0.0816655
$847$	−1.82684e7	−0.874967
$848$	1.03014e6	0.0491936
$849$	1.17188e7	0.557976
$850$	−1.79503e7	−0.852168
$851$	1.27767e6	0.0604777
$852$	3.32843e7	1.57087
$853$	2.52668e7	1.18899	0.594494	−	0.804100i	$-0.297352\pi$
$853$	2.52668e7	1.18899	0.594494	+	0.804100i	$0.297352\pi$
$854$	7.58235e6	0.355762
$855$	664839.	0.0311029
$856$	2.21608e6	0.103372
$857$	2.26423e7	1.05310	0.526550	−	0.850144i	$-0.323485\pi$
$857$	2.26423e7	1.05310	0.526550	+	0.850144i	$0.323485\pi$
$858$	−1.87828e6	−0.0871050
$859$	8.22381e6	0.380269	0.190134	−	0.981758i	$-0.439108\pi$
$859$	8.22381e6	0.380269	0.190134	+	0.981758i	$0.439108\pi$
$860$	3.89116e7	1.79405
$861$	4.55903e6	0.209587
$862$	1.06732e7	0.489244
$863$	−195571.	−0.00893876	−0.00446938	−	0.999990i	$-0.501423\pi$
$863$	−195571.	−0.00893876	−0.00446938	+	0.999990i	$0.501423\pi$
$864$	−1.57846e7	−0.719367
$865$	1.50423e7	0.683557
$866$	9.96268e6	0.451421
$867$	−2.18612e7	−0.987702
$868$	386610.	0.0174170
$869$	−9.20591e6	−0.413540
$870$	1.50028e7	0.672007
$871$	−1.06339e7	−0.474951
$872$	−4.77395e6	−0.212611
$873$	5.17990e6	0.230031
$874$	−35865.3	−0.00158816
$875$	−4.04227e7	−1.78486
$876$	−3.76387e7	−1.65720
$877$	−1.52626e7	−0.670084	−0.335042	−	0.942203i	$-0.608750\pi$
$877$	−1.52626e7	−0.670084	−0.335042	+	0.942203i	$0.608750\pi$
$878$	−6.04162e6	−0.264495
$879$	−2.56993e7	−1.12189
$880$	−1.23281e7	−0.536646
$881$	−8.85117e6	−0.384203	−0.192102	−	0.981375i	$-0.561530\pi$
$881$	−8.85117e6	−0.384203	−0.192102	+	0.981375i	$0.561530\pi$
$882$	−262520.	−0.0113629
$883$	2.59722e6	0.112100	0.0560502	−	0.998428i	$-0.482149\pi$
$883$	2.59722e6	0.112100	0.0560502	+	0.998428i	$0.482149\pi$
$884$	1.64885e7	0.709659
$885$	2.03333e7	0.872671
$886$	1.05945e7	0.453415
$887$	4.75701e6	0.203014	0.101507	−	0.994835i	$-0.467634\pi$
$887$	4.75701e6	0.203014	0.101507	+	0.994835i	$0.467634\pi$
$888$	1.63899e7	0.697501
$889$	3.51206e7	1.49042
$890$	−1.95025e6	−0.0825306
$891$	−1.21049e7	−0.510821
$892$	1.16661e7	0.490923
$893$	−2.63757e6	−0.110682
$894$	1.18786e7	0.497073
$895$	1.57805e7	0.658509
$896$	2.51862e7	1.04807
$897$	−864754.	−0.0358849
$898$	−7.29786e6	−0.301999
$899$	487324.	0.0201103
$900$	−8.80144e6	−0.362199
$901$	2.32487e6	0.0954084
$902$	596828.	0.0244249
$903$	−3.37951e7	−1.37922
$904$	−2.28570e7	−0.930246
$905$	6.81395e7	2.76553
$906$	4.74135e6	0.191903
$907$	−4.19917e7	−1.69491	−0.847453	−	0.530870i	$-0.821865\pi$
$907$	−4.19917e7	−1.69491	−0.847453	+	0.530870i	$0.821865\pi$
$908$	1.03521e7	0.416693
$909$	2.08393e6	0.0836516
$910$	−8.41315e6	−0.336787
$911$	−1.86284e7	−0.743668	−0.371834	−	0.928299i	$-0.621271\pi$
$911$	−1.86284e7	−0.743668	−0.371834	+	0.928299i	$0.621271\pi$
$912$	1.72452e6	0.0686565
$913$	7.01379e6	0.278468
$914$	2.89945e6	0.114802
$915$	−4.96863e7	−1.96193
$916$	1.41618e7	0.557675
$917$	−4.05490e7	−1.59242
$918$	−9.69616e6	−0.379746
$919$	−6.84631e6	−0.267404	−0.133702	−	0.991022i	$-0.542686\pi$
$919$	−6.84631e6	−0.267404	−0.133702	+	0.991022i	$0.542686\pi$
$920$	1.51422e6	0.0589821
$921$	3.68332e7	1.43084
$922$	−3.00291e6	−0.116336
$923$	−2.35272e7	−0.909005
$924$	1.22103e7	0.470484
$925$	−5.39129e7	−2.07176
$926$	1.05956e7	0.406068
$927$	5.82274e6	0.222550
$928$	2.43769e7	0.929197
$929$	3.48541e7	1.32500	0.662499	−	0.749063i	$-0.269496\pi$
$929$	3.48541e7	1.32500	0.662499	+	0.749063i	$0.269496\pi$
$930$	280777.	0.0106452
$931$	−407288.	−0.0154003
$932$	−5.20532e6	−0.196294
$933$	−5.63574e7	−2.11957
$934$	−1.55183e7	−0.582071
$935$	−2.78224e7	−1.04080
$936$	−1.89134e6	−0.0705634
$937$	−4.40806e7	−1.64021	−0.820104	−	0.572215i	$-0.806084\pi$
$937$	−4.40806e7	−1.64021	−0.820104	+	0.572215i	$0.806084\pi$
$938$	−7.66149e6	−0.284319
$939$	3.34478e7	1.23795
$940$	5.27554e7	1.94736
$941$	−2.15485e7	−0.793309	−0.396654	−	0.917968i	$-0.629829\pi$
$941$	−2.15485e7	−0.793309	−0.396654	+	0.917968i	$0.629829\pi$
$942$	286954.	0.0105362
$943$	274777.	0.0100624
$944$	8.99246e6	0.328434
$945$	−4.46400e7	−1.62609
$946$	−4.42416e6	−0.160732
$947$	4.46945e7	1.61949	0.809746	−	0.586780i	$-0.199605\pi$
$947$	4.46945e7	1.61949	0.809746	+	0.586780i	$0.199605\pi$
$948$	−2.57575e7	−0.930856
$949$	2.66051e7	0.958959
$950$	1.51338e6	0.0544050
$951$	1.81119e7	0.649400
$952$	2.50756e7	0.896725
$953$	−9.80512e6	−0.349720	−0.174860	−	0.984593i	$-0.555947\pi$
$953$	−9.80512e6	−0.349720	−0.174860	+	0.984593i	$0.555947\pi$
$954$	−126338.	−0.00449431
$955$	−8.83014e7	−3.13299
$956$	4.76056e7	1.68466
$957$	1.53911e7	0.543237
$958$	896249.	0.0315511
$959$	−1.07811e7	−0.378544
$960$	−2.42709e7	−0.849977
$961$	−2.86200e7	−0.999681
$962$	−5.48852e6	−0.191213
$963$	1.01873e6	0.0353991
$964$	2.55215e7	0.884534
$965$	−1.75579e7	−0.606952
$966$	−623033.	−0.0214817
$967$	1.94270e7	0.668097	0.334048	−	0.942556i	$-0.391585\pi$
$967$	1.94270e7	0.668097	0.334048	+	0.942556i	$0.391585\pi$
$968$	−1.41243e7	−0.484483
$969$	3.89197e6	0.133156
$970$	1.78147e7	0.607923
$971$	−4.95650e7	−1.68705	−0.843524	−	0.537092i	$-0.819523\pi$
$971$	−4.95650e7	−1.68705	−0.843524	+	0.537092i	$0.819523\pi$
$972$	−1.07385e7	−0.364567
$973$	−4.11594e7	−1.39376
$974$	−9.88828e6	−0.333982
$975$	3.64894e7	1.22929
$976$	−2.19739e7	−0.738384
$977$	−6.61054e6	−0.221565	−0.110782	−	0.993845i	$-0.535336\pi$
$977$	−6.61054e6	−0.221565	−0.110782	+	0.993845i	$0.535336\pi$
$978$	−1.40052e7	−0.468213
$979$	−2.00072e6	−0.0667161
$980$	8.14638e6	0.270956
$981$	−2.19458e6	−0.0728078
$982$	−1.42451e7	−0.471396
$983$	−1.39873e7	−0.461690	−0.230845	−	0.972991i	$-0.574149\pi$
$983$	−1.39873e7	−0.461690	−0.230845	+	0.972991i	$0.574149\pi$
$984$	3.52484e6	0.116052
$985$	3.73093e6	0.122526
$986$	1.49742e7	0.490513
$987$	−4.58185e7	−1.49709
$988$	−1.39013e6	−0.0453068
$989$	−2.03687e6	−0.0662173
$990$	1.51193e6	0.0490278
$991$	2.21421e6	0.0716202	0.0358101	−	0.999359i	$-0.488599\pi$
$991$	2.21421e6	0.0716202	0.0358101	+	0.999359i	$0.488599\pi$
$992$	456212.	0.0147193
$993$	−5.01271e6	−0.161324
$994$	−1.69508e7	−0.544155
$995$	−4.87959e7	−1.56252
$996$	1.96241e7	0.626817
$997$	6.77351e6	0.215812	0.107906	−	0.994161i	$-0.465585\pi$
$997$	6.77351e6	0.215812	0.107906	+	0.994161i	$0.465585\pi$
$998$	−2.20059e6	−0.0699379
$999$	−2.91219e7	−0.923223

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.6.a.a.1.18	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.6.a.a.1.18	✓	38	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q-1.78681 q^{2} -17.1157 q^{3} -28.8073 q^{4} -96.1357 q^{5} +30.5825 q^{6} +140.530 q^{7} +108.651 q^{8} +49.9467 q^{9} +171.776 q^{10} +176.222 q^{11} +493.057 q^{12} -348.520 q^{13} -251.100 q^{14} +1645.43 q^{15} +727.695 q^{16} +1642.29 q^{17} -89.2453 q^{18} -138.460 q^{19} +2769.41 q^{20} -2405.26 q^{21} -314.876 q^{22} -144.967 q^{23} -1859.64 q^{24} +6117.08 q^{25} +622.739 q^{26} +3304.24 q^{27} -4048.28 q^{28} -5102.87 q^{29} -2940.07 q^{30} -95.4999 q^{31} -4777.09 q^{32} -3016.16 q^{33} -2934.46 q^{34} -13509.9 q^{35} -1438.83 q^{36} -8813.51 q^{37} +247.402 q^{38} +5965.16 q^{39} -10445.3 q^{40} -1895.44 q^{41} +4297.74 q^{42} +14050.5 q^{43} -5076.49 q^{44} -4801.66 q^{45} +259.029 q^{46} +19049.3 q^{47} -12455.0 q^{48} +2941.56 q^{49} -10930.1 q^{50} -28108.9 q^{51} +10039.9 q^{52} +1415.63 q^{53} -5904.05 q^{54} -16941.2 q^{55} +15268.7 q^{56} +2369.84 q^{57} +9117.86 q^{58} +12357.5 q^{59} -47400.4 q^{60} -30196.6 q^{61} +170.640 q^{62} +7018.99 q^{63} -14750.5 q^{64} +33505.2 q^{65} +5389.31 q^{66} +30511.7 q^{67} -47310.0 q^{68} +2481.22 q^{69} +24139.7 q^{70} +67506.1 q^{71} +5426.77 q^{72} -76337.4 q^{73} +15748.1 q^{74} -104698. q^{75} +3988.67 q^{76} +24764.4 q^{77} -10658.6 q^{78} -52240.4 q^{79} -69957.5 q^{80} -68691.4 q^{81} +3386.79 q^{82} +39800.8 q^{83} +69289.1 q^{84} -157883. q^{85} -25105.6 q^{86} +87339.1 q^{87} +19146.7 q^{88} -11353.4 q^{89} +8579.66 q^{90} -48977.4 q^{91} +4176.12 q^{92} +1634.55 q^{93} -34037.5 q^{94} +13311.0 q^{95} +81763.2 q^{96} +103709. q^{97} -5256.00 q^{98} +8801.72 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 8 q^{2} - 100 q^{3} + 512 q^{4} - 154 q^{5} - 216 q^{6} - 737 q^{7} - 261 q^{8} + 2510 q^{9} - 1567 q^{10} - 808 q^{11} - 3200 q^{12} - 2460 q^{13} - 1423 q^{14} - 3541 q^{15} + 5120 q^{16} - 2501 q^{17}+ \cdots - 108889 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 100 * q^3 + 512 * q^4 - 154 * q^5 - 216 * q^6 - 737 * q^7 - 261 * q^8 + 2510 * q^9 - 1567 * q^10 - 808 * q^11 - 3200 * q^12 - 2460 * q^13 - 1423 * q^14 - 3541 * q^15 + 5120 * q^16 - 2501 * q^17 - 1343 * q^18 - 7983 * q^19 - 6981 * q^20 - 3382 * q^21 - 8023 * q^22 - 7132 * q^23 - 10467 * q^24 + 13564 * q^25 - 7886 * q^26 - 30397 * q^27 - 23730 * q^28 - 12497 * q^29 - 12917 * q^30 - 26380 * q^31 - 18140 * q^32 - 12946 * q^33 - 48406 * q^34 - 12864 * q^35 - 5030 * q^36 - 46630 * q^37 - 15482 * q^38 - 13541 * q^39 - 74754 * q^40 - 23754 * q^41 - 41309 * q^42 - 96541 * q^43 - 39950 * q^44 - 49281 * q^45 - 49587 * q^46 - 63551 * q^47 - 126814 * q^48 + 67147 * q^49 - 158667 * q^50 - 140697 * q^51 - 243408 * q^52 - 109108 * q^53 - 345313 * q^54 - 176321 * q^55 - 439504 * q^56 - 172501 * q^57 - 283105 * q^58 - 129225 * q^59 - 491987 * q^60 - 156006 * q^61 - 257561 * q^62 - 285435 * q^63 - 71443 * q^64 - 214451 * q^65 - 370574 * q^66 - 326834 * q^67 - 244233 * q^68 - 63505 * q^69 - 267713 * q^70 - 118805 * q^71 - 237565 * q^72 - 226965 * q^73 - 82169 * q^74 - 166814 * q^75 - 177290 * q^76 - 74218 * q^77 + 87061 * q^78 - 18825 * q^79 - 154730 * q^80 + 211130 * q^81 - 279743 * q^82 - 191524 * q^83 - 121632 * q^84 + 10830 * q^85 + 188032 * q^86 - 202673 * q^87 - 344937 * q^88 + 22634 * q^89 + 597315 * q^90 - 490747 * q^91 + 409454 * q^92 - 49403 * q^93 - 151313 * q^94 + 135623 * q^95 + 669377 * q^96 - 585150 * q^97 + 726482 * q^98 - 108889 * q^99

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