LMFDB - Embedded newform 197.2.a.c.1.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [197,2,Mod(1,197)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("197.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(197, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	197.a (trivial)

Newform invariants

comment:select newform

sage:traces = [10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$1.57305291982$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 15x^{8} - x^{7} + 78x^{6} + 7x^{5} - 165x^{4} - 15x^{3} + 123x^{2} + 9x - 26 $ x^10 - 15x^8 - x^7 + 78x^6 + 7x^5 - 165x^4 - 15x^3 + 123x^2 + 9*x - 26
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.82964$ of defining polynomial
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)

$f(q)$	$=$	\(q+1.82964 q^{2} +0.661864 q^{3} +1.34760 q^{4} +2.39480 q^{5} +1.21098 q^{6} -2.47846 q^{7} -1.19366 q^{8} -2.56194 q^{9} +4.38163 q^{10} +2.44912 q^{11} +0.891928 q^{12} +0.427303 q^{13} -4.53471 q^{14} +1.58503 q^{15} -4.87917 q^{16} -3.61425 q^{17} -4.68743 q^{18} -0.675704 q^{19} +3.22723 q^{20} -1.64041 q^{21} +4.48103 q^{22} +8.55393 q^{23} -0.790040 q^{24} +0.735052 q^{25} +0.781813 q^{26} -3.68124 q^{27} -3.33998 q^{28} +4.41033 q^{29} +2.90004 q^{30} +0.899928 q^{31} -6.53984 q^{32} +1.62099 q^{33} -6.61279 q^{34} -5.93542 q^{35} -3.45247 q^{36} -9.25303 q^{37} -1.23630 q^{38} +0.282816 q^{39} -2.85857 q^{40} -3.48904 q^{41} -3.00136 q^{42} +4.73199 q^{43} +3.30044 q^{44} -6.13532 q^{45} +15.6507 q^{46} +9.87379 q^{47} -3.22935 q^{48} -0.857212 q^{49} +1.34488 q^{50} -2.39214 q^{51} +0.575834 q^{52} +0.432240 q^{53} -6.73537 q^{54} +5.86515 q^{55} +2.95844 q^{56} -0.447224 q^{57} +8.06933 q^{58} -0.232893 q^{59} +2.13599 q^{60} -8.06257 q^{61} +1.64655 q^{62} +6.34967 q^{63} -2.20723 q^{64} +1.02330 q^{65} +2.96583 q^{66} +12.2707 q^{67} -4.87056 q^{68} +5.66154 q^{69} -10.8597 q^{70} -14.4805 q^{71} +3.05808 q^{72} +10.8630 q^{73} -16.9298 q^{74} +0.486504 q^{75} -0.910579 q^{76} -6.07007 q^{77} +0.517454 q^{78} +8.35190 q^{79} -11.6846 q^{80} +5.24933 q^{81} -6.38370 q^{82} -0.446491 q^{83} -2.21061 q^{84} -8.65538 q^{85} +8.65785 q^{86} +2.91904 q^{87} -2.92342 q^{88} +16.9275 q^{89} -11.2255 q^{90} -1.05906 q^{91} +11.5273 q^{92} +0.595630 q^{93} +18.0655 q^{94} -1.61817 q^{95} -4.32848 q^{96} +6.50799 q^{97} -1.56839 q^{98} -6.27450 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{3} + 10 q^{4} + 2 q^{5} - 4 q^{6} + 11 q^{7} - 3 q^{8} + 12 q^{9} - 2 q^{10} + 2 q^{11} + 4 q^{12} + 8 q^{13} - 9 q^{14} - q^{15} - 2 q^{16} - 3 q^{17} - 9 q^{18} + 17 q^{19} - 2 q^{20} - 2 q^{21}+ \cdots - q^{99}+O(q^{100}) $ 10 * q + 10 * q^3 + 10 * q^4 + 2 * q^5 - 4 * q^6 + 11 * q^7 - 3 * q^8 + 12 * q^9 - 2 * q^10 + 2 * q^11 + 4 * q^12 + 8 * q^13 - 9 * q^14 - q^15 - 2 * q^16 - 3 * q^17 - 9 * q^18 + 17 * q^19 - 2 * q^20 - 2 * q^21 + 3 * q^22 - 4 * q^23 - 15 * q^24 + 6 * q^25 - 13 * q^26 + 19 * q^27 + 16 * q^28 - 9 * q^29 - 19 * q^30 + 20 * q^31 - 16 * q^32 - 2 * q^33 - 8 * q^34 - 12 * q^35 - 12 * q^36 + 12 * q^37 - 15 * q^38 - 9 * q^39 - 15 * q^40 - 18 * q^41 - 31 * q^42 + 11 * q^43 - 24 * q^44 - 15 * q^45 - 13 * q^46 + 5 * q^47 - 22 * q^48 + q^49 - 24 * q^50 - 13 * q^51 + 9 * q^52 - 6 * q^53 - 15 * q^54 - 17 * q^55 - 6 * q^56 + 3 * q^57 - 15 * q^58 - q^59 - 23 * q^60 + 4 * q^61 - 16 * q^62 - 11 * q^63 - 17 * q^64 - 17 * q^65 + 24 * q^66 + 46 * q^67 + 15 * q^68 - 21 * q^69 + 25 * q^70 - 5 * q^71 + 7 * q^72 + 25 * q^73 + 3 * q^74 + 46 * q^75 + 49 * q^76 - 14 * q^77 + 15 * q^78 - q^79 + 9 * q^80 + 22 * q^81 + 52 * q^82 + 28 * q^83 - 14 * q^84 - 30 * q^85 + 27 * q^86 - 7 * q^87 + 9 * q^88 - 6 * q^89 - 10 * q^90 + 51 * q^91 + 32 * q^92 + 15 * q^93 - 3 * q^94 - 13 * q^95 + 75 * q^96 + 2 * q^97 + 22 * q^98 - 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 $

$2$	1.82964	1.29375	0.646877	−	0.762594i	$-0.276075\pi$
$2$	1.82964	1.29375	0.646877	+	0.762594i	$0.276075\pi$
$3$	0.661864	0.382127	0.191064	−	0.981578i	$-0.438806\pi$
$3$	0.661864	0.382127	0.191064	+	0.981578i	$0.438806\pi$
$4$	1.34760	0.673800
$5$	2.39480	1.07099	0.535493	−	0.844540i	$-0.320126\pi$
$5$	2.39480	1.07099	0.535493	+	0.844540i	$0.320126\pi$
$6$	1.21098	0.494379
$7$	−2.47846	−0.936772	−0.468386	−	0.883524i	$-0.655164\pi$
$7$	−2.47846	−0.936772	−0.468386	+	0.883524i	$0.655164\pi$
$8$	−1.19366	−0.422022
$9$	−2.56194	−0.853979
$10$	4.38163	1.38559
$11$	2.44912	0.738438	0.369219	−	0.929342i	$-0.379625\pi$
$11$	2.44912	0.738438	0.369219	+	0.929342i	$0.379625\pi$
$12$	0.891928	0.257477
$13$	0.427303	0.118513	0.0592563	−	0.998243i	$-0.481127\pi$
$13$	0.427303	0.118513	0.0592563	+	0.998243i	$0.481127\pi$
$14$	−4.53471	−1.21195
$15$	1.58503	0.409253
$16$	−4.87917	−1.21979
$17$	−3.61425	−0.876583	−0.438292	−	0.898833i	$-0.644416\pi$
$17$	−3.61425	−0.876583	−0.438292	+	0.898833i	$0.644416\pi$
$18$	−4.68743	−1.10484
$19$	−0.675704	−0.155017	−0.0775085	−	0.996992i	$-0.524697\pi$
$19$	−0.675704	−0.155017	−0.0775085	+	0.996992i	$0.524697\pi$
$20$	3.22723	0.721630
$21$	−1.64041	−0.357966
$22$	4.48103	0.955358
$23$	8.55393	1.78362	0.891809	−	0.452412i	$-0.149436\pi$
$23$	8.55393	1.78362	0.891809	+	0.452412i	$0.149436\pi$
$24$	−0.790040	−0.161266
$25$	0.735052	0.147010
$26$	0.781813	0.153326
$27$	−3.68124	−0.708456
$28$	−3.33998	−0.631197
$29$	4.41033	0.818977	0.409489	−	0.912315i	$-0.365707\pi$
$29$	4.41033	0.818977	0.409489	+	0.912315i	$0.365707\pi$
$30$	2.90004	0.529473
$31$	0.899928	0.161632	0.0808159	−	0.996729i	$-0.474247\pi$
$31$	0.899928	0.161632	0.0808159	+	0.996729i	$0.474247\pi$
$32$	−6.53984	−1.15609
$33$	1.62099	0.282177
$34$	−6.61279	−1.13408
$35$	−5.93542	−1.00327
$36$	−3.45247	−0.575411
$37$	−9.25303	−1.52119	−0.760594	−	0.649227i	$-0.775092\pi$
$37$	−9.25303	−1.52119	−0.760594	+	0.649227i	$0.775092\pi$
$38$	−1.23630	−0.200554
$39$	0.282816	0.0452869
$40$	−2.85857	−0.451980
$41$	−3.48904	−0.544896	−0.272448	−	0.962171i	$-0.587833\pi$
$41$	−3.48904	−0.544896	−0.272448	+	0.962171i	$0.587833\pi$
$42$	−3.00136	−0.463120
$43$	4.73199	0.721621	0.360811	−	0.932639i	$-0.382500\pi$
$43$	4.73199	0.721621	0.360811	+	0.932639i	$0.382500\pi$
$44$	3.30044	0.497560
$45$	−6.13532	−0.914599
$46$	15.6507	2.30756
$47$	9.87379	1.44024	0.720120	−	0.693850i	$-0.244087\pi$
$47$	9.87379	1.44024	0.720120	+	0.693850i	$0.244087\pi$
$48$	−3.22935	−0.466116
$49$	−0.857212	−0.122459
$50$	1.34488	0.190195
$51$	−2.39214	−0.334966
$52$	0.575834	0.0798538
$53$	0.432240	0.0593728	0.0296864	−	0.999559i	$-0.490549\pi$
$53$	0.432240	0.0593728	0.0296864	+	0.999559i	$0.490549\pi$
$54$	−6.73537	−0.916568
$55$	5.86515	0.790857
$56$	2.95844	0.395339
$57$	−0.447224	−0.0592362
$58$	8.06933	1.05956
$59$	−0.232893	−0.0303201	−0.0151600	−	0.999885i	$-0.504826\pi$
$59$	−0.232893	−0.0303201	−0.0151600	+	0.999885i	$0.504826\pi$
$60$	2.13599	0.275755
$61$	−8.06257	−1.03231	−0.516153	−	0.856496i	$-0.672637\pi$
$61$	−8.06257	−1.03231	−0.516153	+	0.856496i	$0.672637\pi$
$62$	1.64655	0.209112
$63$	6.34967	0.799983
$64$	−2.20723	−0.275904
$65$	1.02330	0.126925
$66$	2.96583	0.365068
$67$	12.2707	1.49911	0.749554	−	0.661944i	$-0.230268\pi$
$67$	12.2707	1.49911	0.749554	+	0.661944i	$0.230268\pi$
$68$	−4.87056	−0.590642
$69$	5.66154	0.681569
$70$	−10.8597	−1.29798
$71$	−14.4805	−1.71852	−0.859259	−	0.511540i	$-0.829075\pi$
$71$	−14.4805	−1.71852	−0.859259	+	0.511540i	$0.829075\pi$
$72$	3.05808	0.360398
$73$	10.8630	1.27142	0.635708	−	0.771930i	$-0.280708\pi$
$73$	10.8630	1.27142	0.635708	+	0.771930i	$0.280708\pi$
$74$	−16.9298	−1.96804
$75$	0.486504	0.0561767
$76$	−0.910579	−0.104451
$77$	−6.07007	−0.691748
$78$	0.517454	0.0585901
$79$	8.35190	0.939663	0.469831	−	0.882756i	$-0.344315\pi$
$79$	8.35190	0.939663	0.469831	+	0.882756i	$0.344315\pi$
$80$	−11.6846	−1.30638
$81$	5.24933	0.583259
$82$	−6.38370	−0.704961
$83$	−0.446491	−0.0490087	−0.0245044	−	0.999700i	$-0.507801\pi$
$83$	−0.446491	−0.0490087	−0.0245044	+	0.999700i	$0.507801\pi$
$84$	−2.21061	−0.241198
$85$	−8.65538	−0.938808
$86$	8.65785	0.933600
$87$	2.91904	0.312954
$88$	−2.92342	−0.311637
$89$	16.9275	1.79431	0.897157	−	0.441711i	$-0.145628\pi$
$89$	16.9275	1.79431	0.897157	+	0.441711i	$0.145628\pi$
$90$	−11.2255	−1.18327
$91$	−1.05906	−0.111019
$92$	11.5273	1.20180
$93$	0.595630	0.0617639
$94$	18.0655	1.86332
$95$	−1.61817	−0.166021
$96$	−4.32848	−0.441774
$97$	6.50799	0.660786	0.330393	−	0.943843i	$-0.392819\pi$
$97$	6.50799	0.660786	0.330393	+	0.943843i	$0.392819\pi$
$98$	−1.56839	−0.158432
$99$	−6.27450	−0.630611
$100$	0.990556	0.0990556
$101$	7.81122	0.777245	0.388623	−	0.921397i	$-0.372951\pi$
$101$	7.81122	0.777245	0.388623	+	0.921397i	$0.372951\pi$
$102$	−4.37676	−0.433364
$103$	0.291943	0.0287660	0.0143830	−	0.999897i	$-0.495422\pi$
$103$	0.291943	0.0287660	0.0143830	+	0.999897i	$0.495422\pi$
$104$	−0.510054	−0.0500150
$105$	−3.92844	−0.383376
$106$	0.790846	0.0768138
$107$	−15.2591	−1.47515	−0.737574	−	0.675266i	$-0.764029\pi$
$107$	−15.2591	−1.47515	−0.737574	+	0.675266i	$0.764029\pi$
$108$	−4.96085	−0.477358
$109$	−4.64110	−0.444536	−0.222268	−	0.974986i	$-0.571346\pi$
$109$	−4.64110	−0.444536	−0.222268	+	0.974986i	$0.571346\pi$
$110$	10.7311	1.02317
$111$	−6.12425	−0.581288
$112$	12.0929	1.14267
$113$	3.00447	0.282637	0.141318	−	0.989964i	$-0.454866\pi$
$113$	3.00447	0.282637	0.141318	+	0.989964i	$0.454866\pi$
$114$	−0.818261	−0.0766371
$115$	20.4849	1.91023
$116$	5.94336	0.551827
$117$	−1.09472	−0.101207
$118$	−0.426111	−0.0392267
$119$	8.95778	0.821158
$120$	−1.89198	−0.172714
$121$	−5.00180	−0.454709
$122$	−14.7516	−1.33555
$123$	−2.30927	−0.208220
$124$	1.21274	0.108908
$125$	−10.2137	−0.913540
$126$	11.6176	1.03498
$127$	−5.47730	−0.486031	−0.243016	−	0.970022i	$-0.578137\pi$
$127$	−5.47730	−0.486031	−0.243016	+	0.970022i	$0.578137\pi$
$128$	9.04122	0.799139
$129$	3.13193	0.275751
$130$	1.87228	0.164210
$131$	−9.82962	−0.858818	−0.429409	−	0.903110i	$-0.641278\pi$
$131$	−9.82962	−0.858818	−0.429409	+	0.903110i	$0.641278\pi$
$132$	2.18444	0.190131
$133$	1.67471	0.145216
$134$	22.4511	1.93948
$135$	−8.81583	−0.758746
$136$	4.31418	0.369938
$137$	−5.13739	−0.438917	−0.219458	−	0.975622i	$-0.570429\pi$
$137$	−5.13739	−0.438917	−0.219458	+	0.975622i	$0.570429\pi$
$138$	10.3586	0.881783
$139$	12.0692	1.02369	0.511847	−	0.859076i	$-0.328961\pi$
$139$	12.0692	1.02369	0.511847	+	0.859076i	$0.328961\pi$
$140$	−7.99857	−0.676003
$141$	6.53510	0.550355
$142$	−26.4942	−2.22334
$143$	1.04652	0.0875142
$144$	12.5001	1.04168
$145$	10.5618	0.877113
$146$	19.8754	1.64490
$147$	−0.567358	−0.0467949
$148$	−12.4694	−1.02498
$149$	−21.8887	−1.79319	−0.896597	−	0.442847i	$-0.853968\pi$
$149$	−21.8887	−1.79319	−0.896597	+	0.442847i	$0.853968\pi$
$150$	0.890130	0.0726788
$151$	4.21008	0.342611	0.171306	−	0.985218i	$-0.445201\pi$
$151$	4.21008	0.342611	0.171306	+	0.985218i	$0.445201\pi$
$152$	0.806560	0.0654207
$153$	9.25947	0.748584
$154$	−11.1061	−0.894952
$155$	2.15514	0.173105
$156$	0.381124	0.0305143
$157$	−9.05645	−0.722783	−0.361392	−	0.932414i	$-0.617698\pi$
$157$	−9.05645	−0.722783	−0.361392	+	0.932414i	$0.617698\pi$
$158$	15.2810	1.21569
$159$	0.286084	0.0226879
$160$	−15.6616	−1.23816
$161$	−21.2006	−1.67084
$162$	9.60440	0.754593
$163$	7.80210	0.611108	0.305554	−	0.952175i	$-0.401158\pi$
$163$	7.80210	0.611108	0.305554	+	0.952175i	$0.401158\pi$
$164$	−4.70183	−0.367151
$165$	3.88193	0.302208
$166$	−0.816920	−0.0634053
$167$	2.46900	0.191057	0.0955286	−	0.995427i	$-0.469546\pi$
$167$	2.46900	0.191057	0.0955286	+	0.995427i	$0.469546\pi$
$168$	1.95809	0.151070
$169$	−12.8174	−0.985955
$170$	−15.8363	−1.21459
$171$	1.73111	0.132381
$172$	6.37683	0.486228
$173$	−14.5901	−1.10926	−0.554632	−	0.832096i	$-0.687141\pi$
$173$	−14.5901	−1.10926	−0.554632	+	0.832096i	$0.687141\pi$
$174$	5.34080	0.404885
$175$	−1.82180	−0.137715
$176$	−11.9497	−0.900742
$177$	−0.154143	−0.0115861
$178$	30.9714	2.32140
$179$	1.85653	0.138764	0.0693820	−	0.997590i	$-0.477897\pi$
$179$	1.85653	0.138764	0.0693820	+	0.997590i	$0.477897\pi$
$180$	−8.26796	−0.616257
$181$	21.8401	1.62336	0.811680	−	0.584103i	$-0.198553\pi$
$181$	21.8401	1.62336	0.811680	+	0.584103i	$0.198553\pi$
$182$	−1.93770	−0.143632
$183$	−5.33633	−0.394473
$184$	−10.2105	−0.752727
$185$	−22.1591	−1.62917
$186$	1.08979	0.0799073
$187$	−8.85173	−0.647303
$188$	13.3059	0.970434
$189$	9.12383	0.663661
$190$	−2.96068	−0.214790
$191$	−6.86482	−0.496721	−0.248361	−	0.968668i	$-0.579892\pi$
$191$	−6.86482	−0.496721	−0.248361	+	0.968668i	$0.579892\pi$
$192$	−1.46089	−0.105430
$193$	−9.21587	−0.663373	−0.331687	−	0.943390i	$-0.607618\pi$
$193$	−9.21587	−0.663373	−0.331687	+	0.943390i	$0.607618\pi$
$194$	11.9073	0.854895
$195$	0.677288	0.0485016
$196$	−1.15518	−0.0825129
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	−11.4801	−0.815855
$199$	−20.7712	−1.47243	−0.736216	−	0.676746i	$-0.763389\pi$
$199$	−20.7712	−1.47243	−0.736216	+	0.676746i	$0.763389\pi$
$200$	−0.877402	−0.0620417
$201$	8.12155	0.572850
$202$	14.2918	1.00556
$203$	−10.9308	−0.767195
$204$	−3.22365	−0.225700
$205$	−8.35553	−0.583576
$206$	0.534151	0.0372161
$207$	−21.9146	−1.52317
$208$	−2.08489	−0.144561
$209$	−1.65488	−0.114471
$210$	−7.18765	−0.495995
$211$	7.15252	0.492400	0.246200	−	0.969219i	$-0.420818\pi$
$211$	7.15252	0.492400	0.246200	+	0.969219i	$0.420818\pi$
$212$	0.582487	0.0400054
$213$	−9.58411	−0.656693
$214$	−27.9187	−1.90848
$215$	11.3321	0.772846
$216$	4.39415	0.298984
$217$	−2.23044	−0.151412
$218$	−8.49156	−0.575121
$219$	7.18982	0.485843
$220$	7.90388	0.532880
$221$	−1.54438	−0.103886
$222$	−11.2052	−0.752043
$223$	15.1364	1.01361	0.506803	−	0.862062i	$-0.330827\pi$
$223$	15.1364	1.01361	0.506803	+	0.862062i	$0.330827\pi$
$224$	16.2088	1.08299
$225$	−1.88316	−0.125544
$226$	5.49711	0.365663
$227$	−23.7864	−1.57876	−0.789380	−	0.613905i	$-0.789598\pi$
$227$	−23.7864	−1.57876	−0.789380	+	0.613905i	$0.789598\pi$
$228$	−0.602679	−0.0399134
$229$	−19.8173	−1.30956	−0.654781	−	0.755819i	$-0.727239\pi$
$229$	−19.8173	−1.30956	−0.654781	+	0.755819i	$0.727239\pi$
$230$	37.4802	2.47137
$231$	−4.01756	−0.264336
$232$	−5.26443	−0.345627
$233$	−29.0910	−1.90581	−0.952907	−	0.303261i	$-0.901925\pi$
$233$	−29.0910	−1.90581	−0.952907	+	0.303261i	$0.901925\pi$
$234$	−2.00296	−0.130937
$235$	23.6457	1.54248
$236$	−0.313847	−0.0204297
$237$	5.52782	0.359071
$238$	16.3896	1.06238
$239$	−17.2766	−1.11753	−0.558765	−	0.829326i	$-0.688725\pi$
$239$	−17.2766	−1.11753	−0.558765	+	0.829326i	$0.688725\pi$
$240$	−7.73363	−0.499204
$241$	4.48258	0.288749	0.144374	−	0.989523i	$-0.453883\pi$
$241$	4.48258	0.288749	0.144374	+	0.989523i	$0.453883\pi$
$242$	−9.15151	−0.588281
$243$	14.5181	0.931335
$244$	−10.8651	−0.695569
$245$	−2.05285	−0.131152
$246$	−4.22514	−0.269385
$247$	−0.288730	−0.0183715
$248$	−1.07421	−0.0682122
$249$	−0.295516	−0.0187276
$250$	−18.6874	−1.18190
$251$	7.48094	0.472193	0.236097	−	0.971730i	$-0.424132\pi$
$251$	7.48094	0.472193	0.236097	+	0.971730i	$0.424132\pi$
$252$	8.55682	0.539029
$253$	20.9496	1.31709
$254$	−10.0215	−0.628805
$255$	−5.72869	−0.358744
$256$	20.9567	1.30979
$257$	26.1724	1.63259	0.816296	−	0.577634i	$-0.196024\pi$
$257$	26.1724	1.63259	0.816296	+	0.577634i	$0.196024\pi$
$258$	5.73032	0.356754
$259$	22.9333	1.42501
$260$	1.37901	0.0855223
$261$	−11.2990	−0.699389
$262$	−17.9847	−1.11110
$263$	−2.11510	−0.130422	−0.0652112	−	0.997871i	$-0.520772\pi$
$263$	−2.11510	−0.130422	−0.0652112	+	0.997871i	$0.520772\pi$
$264$	−1.93490	−0.119085
$265$	1.03513	0.0635874
$266$	3.06412	0.187873
$267$	11.2037	0.685656
$268$	16.5360	1.01010
$269$	5.43243	0.331221	0.165611	−	0.986191i	$-0.447041\pi$
$269$	5.43243	0.331221	0.165611	+	0.986191i	$0.447041\pi$
$270$	−16.1298	−0.981631
$271$	8.88131	0.539501	0.269751	−	0.962930i	$-0.413059\pi$
$271$	8.88131	0.539501	0.269751	+	0.962930i	$0.413059\pi$
$272$	17.6345	1.06925
$273$	−0.700951	−0.0424235
$274$	−9.39960	−0.567850
$275$	1.80023	0.108558
$276$	7.62949	0.459241
$277$	3.85160	0.231420	0.115710	−	0.993283i	$-0.463086\pi$
$277$	3.85160	0.231420	0.115710	+	0.993283i	$0.463086\pi$
$278$	22.0823	1.32441
$279$	−2.30556	−0.138030
$280$	7.08487	0.423402
$281$	−16.6051	−0.990575	−0.495288	−	0.868729i	$-0.664937\pi$
$281$	−16.6051	−0.990575	−0.495288	+	0.868729i	$0.664937\pi$
$282$	11.9569	0.712024
$283$	19.9449	1.18560	0.592801	−	0.805349i	$-0.298022\pi$
$283$	19.9449	1.18560	0.592801	+	0.805349i	$0.298022\pi$
$284$	−19.5139	−1.15794
$285$	−1.07101	−0.0634412
$286$	1.91476	0.113222
$287$	8.64745	0.510443
$288$	16.7546	0.987277
$289$	−3.93723	−0.231602
$290$	19.3244	1.13477
$291$	4.30740	0.252504
$292$	14.6390	0.856680
$293$	14.7094	0.859331	0.429665	−	0.902988i	$-0.358631\pi$
$293$	14.7094	0.859331	0.429665	+	0.902988i	$0.358631\pi$
$294$	−1.03806	−0.0605411
$295$	−0.557731	−0.0324724
$296$	11.0450	0.641976
$297$	−9.01582	−0.523151
$298$	−40.0486	−2.31995
$299$	3.65512	0.211381
$300$	0.655613	0.0378519
$301$	−11.7281	−0.675994
$302$	7.70295	0.443255
$303$	5.16996	0.297006
$304$	3.29688	0.189089
$305$	−19.3082	−1.10559
$306$	16.9415	0.968483
$307$	−4.72211	−0.269505	−0.134753	−	0.990879i	$-0.543024\pi$
$307$	−4.72211	−0.269505	−0.134753	+	0.990879i	$0.543024\pi$
$308$	−8.18002	−0.466100
$309$	0.193226	0.0109923
$310$	3.94315	0.223956
$311$	17.5323	0.994168	0.497084	−	0.867702i	$-0.334404\pi$
$311$	17.5323	0.994168	0.497084	+	0.867702i	$0.334404\pi$
$312$	−0.337587	−0.0191121
$313$	12.1697	0.687873	0.343937	−	0.938993i	$-0.388239\pi$
$313$	12.1697	0.687873	0.343937	+	0.938993i	$0.388239\pi$
$314$	−16.5701	−0.935104
$315$	15.2062	0.856770
$316$	11.2550	0.633145
$317$	−16.4965	−0.926535	−0.463268	−	0.886218i	$-0.653323\pi$
$317$	−16.4965	−0.926535	−0.463268	+	0.886218i	$0.653323\pi$
$318$	0.523432	0.0293526
$319$	10.8014	0.604764
$320$	−5.28587	−0.295489
$321$	−10.0994	−0.563695
$322$	−38.7896	−2.16166
$323$	2.44216	0.135885
$324$	7.07400	0.393000
$325$	0.314090	0.0174226
$326$	14.2751	0.790623
$327$	−3.07177	−0.169869
$328$	4.16472	0.229958
$329$	−24.4718	−1.34918
$330$	7.10256	0.390983
$331$	3.14512	0.172872	0.0864358	−	0.996257i	$-0.472452\pi$
$331$	3.14512	0.172872	0.0864358	+	0.996257i	$0.472452\pi$
$332$	−0.601691	−0.0330221
$333$	23.7057	1.29906
$334$	4.51740	0.247181
$335$	29.3859	1.60552
$336$	8.00383	0.436645
$337$	28.8759	1.57297	0.786486	−	0.617608i	$-0.211898\pi$
$337$	28.8759	1.57297	0.786486	+	0.617608i	$0.211898\pi$
$338$	−23.4513	−1.27558
$339$	1.98855	0.108003
$340$	−11.6640	−0.632569
$341$	2.20403	0.119355
$342$	3.16732	0.171269
$343$	19.4738	1.05149
$344$	−5.64838	−0.304540
$345$	13.5582	0.729951
$346$	−26.6947	−1.43511
$347$	31.5438	1.69336	0.846681	−	0.532101i	$-0.178597\pi$
$347$	31.5438	1.69336	0.846681	+	0.532101i	$0.178597\pi$
$348$	3.93369	0.210868
$349$	−6.54560	−0.350378	−0.175189	−	0.984535i	$-0.556054\pi$
$349$	−6.54560	−0.350378	−0.175189	+	0.984535i	$0.556054\pi$
$350$	−3.33325	−0.178170
$351$	−1.57301	−0.0839609
$352$	−16.0169	−0.853702
$353$	−2.38253	−0.126809	−0.0634047	−	0.997988i	$-0.520196\pi$
$353$	−2.38253	−0.126809	−0.0634047	+	0.997988i	$0.520196\pi$
$354$	−0.282028	−0.0149896
$355$	−34.6778	−1.84051
$356$	22.8115	1.20901
$357$	5.92883	0.313787
$358$	3.39680	0.179526
$359$	−15.0342	−0.793473	−0.396737	−	0.917932i	$-0.629857\pi$
$359$	−15.0342	−0.793473	−0.396737	+	0.917932i	$0.629857\pi$
$360$	7.32348	0.385981
$361$	−18.5434	−0.975970
$362$	39.9596	2.10023
$363$	−3.31051	−0.173757
$364$	−1.42718	−0.0748048
$365$	26.0146	1.36167
$366$	−9.76358	−0.510351
$367$	−29.0871	−1.51833	−0.759167	−	0.650896i	$-0.774393\pi$
$367$	−29.0871	−1.51833	−0.759167	+	0.650896i	$0.774393\pi$
$368$	−41.7361	−2.17565
$369$	8.93869	0.465330
$370$	−40.5433	−2.10775
$371$	−1.07129	−0.0556187
$372$	0.802671	0.0416165
$373$	−3.41639	−0.176894	−0.0884469	−	0.996081i	$-0.528190\pi$
$373$	−3.41639	−0.176894	−0.0884469	+	0.996081i	$0.528190\pi$
$374$	−16.1955	−0.837451
$375$	−6.76007	−0.349088
$376$	−11.7859	−0.607813
$377$	1.88455	0.0970591
$378$	16.6934	0.858615
$379$	−10.8111	−0.555331	−0.277666	−	0.960678i	$-0.589561\pi$
$379$	−10.8111	−0.555331	−0.277666	+	0.960678i	$0.589561\pi$
$380$	−2.18065	−0.111865
$381$	−3.62522	−0.185726
$382$	−12.5602	−0.642635
$383$	−20.0610	−1.02507	−0.512534	−	0.858667i	$-0.671293\pi$
$383$	−20.0610	−1.02507	−0.512534	+	0.858667i	$0.671293\pi$
$384$	5.98406	0.305373
$385$	−14.5366	−0.740852
$386$	−16.8618	−0.858242
$387$	−12.1230	−0.616249
$388$	8.77017	0.445238
$389$	15.1626	0.768773	0.384387	−	0.923172i	$-0.374413\pi$
$389$	15.1626	0.768773	0.384387	+	0.923172i	$0.374413\pi$
$390$	1.23920	0.0627492
$391$	−30.9160	−1.56349
$392$	1.02322	0.0516804
$393$	−6.50587	−0.328178
$394$	1.82964	0.0921762
$395$	20.0011	1.00637
$396$	−8.45552	−0.424906
$397$	33.7992	1.69633	0.848167	−	0.529729i	$-0.177706\pi$
$397$	33.7992	1.69633	0.848167	+	0.529729i	$0.177706\pi$
$398$	−38.0040	−1.90497
$399$	1.10843	0.0554908
$400$	−3.58645	−0.179322
$401$	18.8451	0.941080	0.470540	−	0.882379i	$-0.344059\pi$
$401$	18.8451	0.941080	0.470540	+	0.882379i	$0.344059\pi$
$402$	14.8595	0.741127
$403$	0.384542	0.0191554
$404$	10.5264	0.523708
$405$	12.5711	0.624662
$406$	−19.9996	−0.992561
$407$	−22.6618	−1.12330
$408$	2.85540	0.141363
$409$	−27.1293	−1.34146	−0.670728	−	0.741704i	$-0.734018\pi$
$409$	−27.1293	−1.34146	−0.670728	+	0.741704i	$0.734018\pi$
$410$	−15.2877	−0.755004
$411$	−3.40025	−0.167722
$412$	0.393422	0.0193825
$413$	0.577217	0.0284030
$414$	−40.0960	−1.97061
$415$	−1.06925	−0.0524876
$416$	−2.79449	−0.137011
$417$	7.98815	0.391182
$418$	−3.02785	−0.148097
$419$	18.7712	0.917035	0.458518	−	0.888685i	$-0.348381\pi$
$419$	18.7712	0.917035	0.458518	+	0.888685i	$0.348381\pi$
$420$	−5.29397	−0.258319
$421$	−30.2422	−1.47392	−0.736958	−	0.675938i	$-0.763739\pi$
$421$	−30.2422	−1.47392	−0.736958	+	0.675938i	$0.763739\pi$
$422$	13.0866	0.637045
$423$	−25.2960	−1.22993
$424$	−0.515948	−0.0250566
$425$	−2.65666	−0.128867
$426$	−17.5355	−0.849599
$427$	19.9828	0.967036
$428$	−20.5631	−0.993956
$429$	0.692652	0.0334416
$430$	20.7338	0.999873
$431$	39.4571	1.90058	0.950292	−	0.311361i	$-0.100785\pi$
$431$	39.4571	1.90058	0.950292	+	0.311361i	$0.100785\pi$
$432$	17.9614	0.864170
$433$	26.0606	1.25239	0.626197	−	0.779665i	$-0.284611\pi$
$433$	26.0606	1.25239	0.626197	+	0.779665i	$0.284611\pi$
$434$	−4.08091	−0.195890
$435$	6.99050	0.335169
$436$	−6.25434	−0.299529
$437$	−5.77992	−0.276491
$438$	13.1548	0.628561
$439$	−38.8850	−1.85588	−0.927940	−	0.372730i	$-0.878422\pi$
$439$	−38.8850	−1.85588	−0.927940	+	0.372730i	$0.878422\pi$
$440$	−7.00099	−0.333759
$441$	2.19612	0.104577
$442$	−2.82566	−0.134403
$443$	30.5988	1.45379	0.726896	−	0.686747i	$-0.240962\pi$
$443$	30.5988	1.45379	0.726896	+	0.686747i	$0.240962\pi$
$444$	−8.25304	−0.391672
$445$	40.5380	1.92169
$446$	27.6942	1.31136
$447$	−14.4874	−0.685228
$448$	5.47055	0.258459
$449$	34.6750	1.63641	0.818207	−	0.574924i	$-0.194968\pi$
$449$	34.6750	1.63641	0.818207	+	0.574924i	$0.194968\pi$
$450$	−3.44551	−0.162423
$451$	−8.54508	−0.402372
$452$	4.04883	0.190441
$453$	2.78650	0.130921
$454$	−43.5207	−2.04253
$455$	−2.53622	−0.118900
$456$	0.533833	0.0249990
$457$	−8.62517	−0.403468	−0.201734	−	0.979440i	$-0.564658\pi$
$457$	−8.62517	−0.403468	−0.201734	+	0.979440i	$0.564658\pi$
$458$	−36.2586	−1.69425
$459$	13.3049	0.621021
$460$	27.6055	1.28711
$461$	17.2908	0.805315	0.402657	−	0.915351i	$-0.368087\pi$
$461$	17.2908	0.805315	0.402657	+	0.915351i	$0.368087\pi$
$462$	−7.35070	−0.341986
$463$	17.1023	0.794814	0.397407	−	0.917643i	$-0.369910\pi$
$463$	17.1023	0.794814	0.397407	+	0.917643i	$0.369910\pi$
$464$	−21.5188	−0.998983
$465$	1.42641	0.0661483
$466$	−53.2262	−2.46566
$467$	20.0251	0.926650	0.463325	−	0.886188i	$-0.346656\pi$
$467$	20.0251	0.926650	0.463325	+	0.886188i	$0.346656\pi$
$468$	−1.47525	−0.0681935
$469$	−30.4125	−1.40432
$470$	43.2633	1.99559
$471$	−5.99413	−0.276195
$472$	0.277995	0.0127958
$473$	11.5892	0.532873
$474$	10.1140	0.464549
$475$	−0.496677	−0.0227891
$476$	12.0715	0.553297
$477$	−1.10737	−0.0507031
$478$	−31.6101	−1.44581
$479$	−27.6009	−1.26112	−0.630559	−	0.776141i	$-0.717175\pi$
$479$	−27.6009	−1.26112	−0.630559	+	0.776141i	$0.717175\pi$
$480$	−10.3658	−0.473133
$481$	−3.95385	−0.180280
$482$	8.20154	0.373570
$483$	−14.0319	−0.638475
$484$	−6.74042	−0.306383
$485$	15.5853	0.707693
$486$	26.5629	1.20492
$487$	10.3523	0.469109	0.234554	−	0.972103i	$-0.424637\pi$
$487$	10.3523	0.469109	0.234554	+	0.972103i	$0.424637\pi$
$488$	9.62397	0.435657
$489$	5.16393	0.233521
$490$	−3.75599	−0.169678
$491$	−36.6785	−1.65528	−0.827638	−	0.561262i	$-0.810316\pi$
$491$	−36.6785	−1.65528	−0.827638	+	0.561262i	$0.810316\pi$
$492$	−3.11197	−0.140298
$493$	−15.9400	−0.717902
$494$	−0.528274	−0.0237682
$495$	−15.0261	−0.675375
$496$	−4.39091	−0.197157
$497$	35.8894	1.60986
$498$	−0.540689	−0.0242289
$499$	14.0562	0.629243	0.314622	−	0.949217i	$-0.398122\pi$
$499$	14.0562	0.629243	0.314622	+	0.949217i	$0.398122\pi$
$500$	−13.7640	−0.615543
$501$	1.63414	0.0730082
$502$	13.6875	0.610902
$503$	25.4260	1.13369	0.566844	−	0.823825i	$-0.308164\pi$
$503$	25.4260	1.13369	0.566844	+	0.823825i	$0.308164\pi$
$504$	−7.57934	−0.337611
$505$	18.7063	0.832418
$506$	38.3304	1.70399
$507$	−8.48338	−0.376760
$508$	−7.38121	−0.327488
$509$	−15.1509	−0.671551	−0.335775	−	0.941942i	$-0.608998\pi$
$509$	−15.1509	−0.671551	−0.335775	+	0.941942i	$0.608998\pi$
$510$	−10.4815	−0.464127
$511$	−26.9235	−1.19103
$512$	20.2609	0.895412
$513$	2.48743	0.109823
$514$	47.8863	2.11217
$515$	0.699143	0.0308079
$516$	4.22059	0.185801
$517$	24.1821	1.06353
$518$	41.9598	1.84361
$519$	−9.65664	−0.423880
$520$	−1.22148	−0.0535653
$521$	23.8145	1.04333	0.521666	−	0.853150i	$-0.325311\pi$
$521$	23.8145	1.04333	0.521666	+	0.853150i	$0.325311\pi$
$522$	−20.6731	−0.904838
$523$	38.0421	1.66346	0.831732	−	0.555177i	$-0.187350\pi$
$523$	38.0421	1.66346	0.831732	+	0.555177i	$0.187350\pi$
$524$	−13.2464	−0.578672
$525$	−1.20578	−0.0526247
$526$	−3.86988	−0.168735
$527$	−3.25256	−0.141684
$528$	−7.90907	−0.344198
$529$	50.1698	2.18129
$530$	1.89392	0.0822664
$531$	0.596657	0.0258927
$532$	2.25684	0.0978463
$533$	−1.49088	−0.0645770
$534$	20.4988	0.887071
$535$	−36.5423	−1.57986
$536$	−14.6471	−0.632657
$537$	1.22877	0.0530255
$538$	9.93942	0.428519
$539$	−2.09942	−0.0904284
$540$	−11.8802	−0.511243
$541$	−23.8834	−1.02683	−0.513413	−	0.858141i	$-0.671619\pi$
$541$	−23.8834	−1.02683	−0.513413	+	0.858141i	$0.671619\pi$
$542$	16.2496	0.697982
$543$	14.4552	0.620330
$544$	23.6366	1.01341
$545$	−11.1145	−0.476092
$546$	−1.28249	−0.0548855
$547$	−10.8990	−0.466006	−0.233003	−	0.972476i	$-0.574855\pi$
$547$	−10.8990	−0.466006	−0.233003	+	0.972476i	$0.574855\pi$
$548$	−6.92315	−0.295742
$549$	20.6558	0.881568
$550$	3.29379	0.140448
$551$	−2.98007	−0.126955
$552$	−6.75795	−0.287637
$553$	−20.6999	−0.880249
$554$	7.04707	0.299401
$555$	−14.6663	−0.622551
$556$	16.2644	0.689766
$557$	−13.5365	−0.573559	−0.286779	−	0.957997i	$-0.592585\pi$
$557$	−13.5365	−0.573559	−0.286779	+	0.957997i	$0.592585\pi$
$558$	−4.21835	−0.178577
$559$	2.02199	0.0855212
$560$	28.9599	1.22378
$561$	−5.85864	−0.247352
$562$	−30.3814	−1.28156
$563$	−43.2131	−1.82121	−0.910607	−	0.413274i	$-0.864385\pi$
$563$	−43.2131	−1.82121	−0.910607	+	0.413274i	$0.864385\pi$
$564$	8.80671	0.370829
$565$	7.19510	0.302700
$566$	36.4921	1.53388
$567$	−13.0103	−0.546380
$568$	17.2848	0.725253
$569$	−19.9320	−0.835594	−0.417797	−	0.908540i	$-0.637198\pi$
$569$	−19.9320	−0.835594	−0.417797	+	0.908540i	$0.637198\pi$
$570$	−1.95957	−0.0820773
$571$	−24.7452	−1.03556	−0.517778	−	0.855515i	$-0.673241\pi$
$571$	−24.7452	−1.03556	−0.517778	+	0.855515i	$0.673241\pi$
$572$	1.41029	0.0589671
$573$	−4.54358	−0.189811
$574$	15.8218	0.660388
$575$	6.28758	0.262210
$576$	5.65479	0.235616
$577$	33.3646	1.38899	0.694493	−	0.719499i	$-0.255629\pi$
$577$	33.3646	1.38899	0.694493	+	0.719499i	$0.255629\pi$
$578$	−7.20373	−0.299636
$579$	−6.09965	−0.253493
$580$	14.2331	0.590999
$581$	1.10661	0.0459100
$582$	7.88102	0.326679
$583$	1.05861	0.0438431
$584$	−12.9667	−0.536566
$585$	−2.62164	−0.108391
$586$	26.9129	1.11176
$587$	39.7834	1.64204	0.821019	−	0.570901i	$-0.193406\pi$
$587$	39.7834	1.64204	0.821019	+	0.570901i	$0.193406\pi$
$588$	−0.764572	−0.0315304
$589$	−0.608085	−0.0250557
$590$	−1.02045	−0.0420113
$591$	0.661864	0.0272254
$592$	45.1471	1.85554
$593$	−3.83642	−0.157543	−0.0787715	−	0.996893i	$-0.525100\pi$
$593$	−3.83642	−0.157543	−0.0787715	+	0.996893i	$0.525100\pi$
$594$	−16.4957	−0.676829
$595$	21.4521	0.879449
$596$	−29.4973	−1.20825
$597$	−13.7477	−0.562657
$598$	6.68758	0.273475
$599$	−41.3503	−1.68953	−0.844763	−	0.535140i	$-0.820259\pi$
$599$	−41.3503	−1.68953	−0.844763	+	0.535140i	$0.820259\pi$
$600$	−0.580720	−0.0237078
$601$	−39.5659	−1.61393	−0.806963	−	0.590602i	$-0.798890\pi$
$601$	−39.5659	−1.61393	−0.806963	+	0.590602i	$0.798890\pi$
$602$	−21.4582	−0.874570
$603$	−31.4368	−1.28021
$604$	5.67351	0.230852
$605$	−11.9783	−0.486987
$606$	9.45919	0.384253
$607$	−20.6997	−0.840174	−0.420087	−	0.907484i	$-0.638000\pi$
$607$	−20.6997	−0.840174	−0.420087	+	0.907484i	$0.638000\pi$
$608$	4.41899	0.179214
$609$	−7.23473	−0.293166
$610$	−35.3272	−1.43036
$611$	4.21910	0.170687
$612$	12.4781	0.504396
$613$	−1.30007	−0.0525092	−0.0262546	−	0.999655i	$-0.508358\pi$
$613$	−1.30007	−0.0525092	−0.0262546	+	0.999655i	$0.508358\pi$
$614$	−8.63979	−0.348674
$615$	−5.53022	−0.223000
$616$	7.24559	0.291933
$617$	3.57289	0.143839	0.0719196	−	0.997410i	$-0.477087\pi$
$617$	3.57289	0.143839	0.0719196	+	0.997410i	$0.477087\pi$
$618$	0.353535	0.0142213
$619$	−9.76477	−0.392479	−0.196240	−	0.980556i	$-0.562873\pi$
$619$	−9.76477	−0.392479	−0.196240	+	0.980556i	$0.562873\pi$
$620$	2.90427	0.116638
$621$	−31.4891	−1.26361
$622$	32.0780	1.28621
$623$	−41.9543	−1.68086
$624$	−1.37991	−0.0552406
$625$	−28.1350	−1.12540
$626$	22.2663	0.889939
$627$	−1.09531	−0.0437423
$628$	−12.2045	−0.487012
$629$	33.4427	1.33345
$630$	27.8219	1.10845
$631$	13.9942	0.557102	0.278551	−	0.960421i	$-0.410146\pi$
$631$	13.9942	0.557102	0.278551	+	0.960421i	$0.410146\pi$
$632$	−9.96933	−0.396559
$633$	4.73400	0.188159
$634$	−30.1827	−1.19871
$635$	−13.1170	−0.520533
$636$	0.385527	0.0152871
$637$	−0.366290	−0.0145129
$638$	19.7628	0.782416
$639$	37.0981	1.46758
$640$	21.6519	0.855866
$641$	9.77562	0.386114	0.193057	−	0.981188i	$-0.438160\pi$
$641$	9.77562	0.386114	0.193057	+	0.981188i	$0.438160\pi$
$642$	−18.4783	−0.729282
$643$	−7.28129	−0.287146	−0.143573	−	0.989640i	$-0.545859\pi$
$643$	−7.28129	−0.287146	−0.143573	+	0.989640i	$0.545859\pi$
$644$	−28.5700	−1.12581
$645$	7.50034	0.295325
$646$	4.46828	0.175802
$647$	−23.9804	−0.942767	−0.471384	−	0.881928i	$-0.656245\pi$
$647$	−23.9804	−0.942767	−0.471384	+	0.881928i	$0.656245\pi$
$648$	−6.26591	−0.246148
$649$	−0.570384	−0.0223895
$650$	0.574673	0.0225405
$651$	−1.47625	−0.0578587
$652$	10.5141	0.411765
$653$	−38.0906	−1.49060	−0.745299	−	0.666730i	$-0.767693\pi$
$653$	−38.0906	−1.49060	−0.745299	+	0.666730i	$0.767693\pi$
$654$	−5.62025	−0.219769
$655$	−23.5399	−0.919782
$656$	17.0236	0.664660
$657$	−27.8303	−1.08576
$658$	−44.7748	−1.74550
$659$	14.7028	0.572739	0.286370	−	0.958119i	$-0.407551\pi$
$659$	14.7028	0.572739	0.286370	+	0.958119i	$0.407551\pi$
$660$	5.23129	0.203628
$661$	25.4067	0.988208	0.494104	−	0.869403i	$-0.335496\pi$
$661$	25.4067	0.988208	0.494104	+	0.869403i	$0.335496\pi$
$662$	5.75446	0.223653
$663$	−1.02217	−0.0396977
$664$	0.532958	0.0206828
$665$	4.01059	0.155524
$666$	43.3730	1.68067
$667$	37.7256	1.46074
$668$	3.32723	0.128734
$669$	10.0182	0.387327
$670$	53.7657	2.07715
$671$	−19.7462	−0.762295
$672$	10.7280	0.413841
$673$	30.5437	1.17737	0.588687	−	0.808361i	$-0.299645\pi$
$673$	30.5437	1.17737	0.588687	+	0.808361i	$0.299645\pi$
$674$	52.8327	2.03504
$675$	−2.70591	−0.104150
$676$	−17.2728	−0.664337
$677$	14.2822	0.548908	0.274454	−	0.961600i	$-0.411503\pi$
$677$	14.2822	0.548908	0.274454	+	0.961600i	$0.411503\pi$
$678$	3.63834	0.139730
$679$	−16.1298	−0.619006
$680$	10.3316	0.396198
$681$	−15.7434	−0.603287
$682$	4.03260	0.154416
$683$	−25.9111	−0.991461	−0.495731	−	0.868476i	$-0.665100\pi$
$683$	−25.9111	−0.991461	−0.495731	+	0.868476i	$0.665100\pi$
$684$	2.33284	0.0891985
$685$	−12.3030	−0.470074
$686$	35.6302	1.36037
$687$	−13.1163	−0.500419
$688$	−23.0882	−0.880229
$689$	0.184698	0.00703642
$690$	24.8068	0.944377
$691$	24.8832	0.946603	0.473302	−	0.880900i	$-0.343062\pi$
$691$	24.8832	0.946603	0.473302	+	0.880900i	$0.343062\pi$
$692$	−19.6616	−0.747422
$693$	15.5511	0.590738
$694$	57.7140	2.19079
$695$	28.9032	1.09636
$696$	−3.48433	−0.132073
$697$	12.6102	0.477647
$698$	−11.9761	−0.453303
$699$	−19.2543	−0.728264
$700$	−2.45506	−0.0927925
$701$	21.1982	0.800644	0.400322	−	0.916375i	$-0.368898\pi$
$701$	21.1982	0.800644	0.400322	+	0.916375i	$0.368898\pi$
$702$	−2.87804	−0.108625
$703$	6.25231	0.235810
$704$	−5.40578	−0.203738
$705$	15.6502	0.589422
$706$	−4.35919	−0.164060
$707$	−19.3598	−0.728101
$708$	−0.207724	−0.00780674
$709$	25.8806	0.971964	0.485982	−	0.873969i	$-0.338462\pi$
$709$	25.8806	0.971964	0.485982	+	0.873969i	$0.338462\pi$
$710$	−63.4481	−2.38117
$711$	−21.3970	−0.802452
$712$	−20.2057	−0.757241
$713$	7.69792	0.288290
$714$	10.8477	0.405963
$715$	2.50620	0.0937265
$716$	2.50187	0.0934992
$717$	−11.4348	−0.427039
$718$	−27.5072	−1.02656
$719$	−33.5697	−1.25194	−0.625968	−	0.779848i	$-0.715296\pi$
$719$	−33.5697	−1.25194	−0.625968	+	0.779848i	$0.715296\pi$
$720$	29.9353	1.11562
$721$	−0.723570	−0.0269471
$722$	−33.9279	−1.26267
$723$	2.96686	0.110339
$724$	29.4317	1.09382
$725$	3.24182	0.120398
$726$	−6.05705	−0.224798
$727$	48.7995	1.80987	0.904937	−	0.425545i	$-0.139918\pi$
$727$	48.7995	1.80987	0.904937	+	0.425545i	$0.139918\pi$
$728$	1.26415	0.0468526
$729$	−6.13900	−0.227370
$730$	47.5976	1.76166
$731$	−17.1026	−0.632561
$732$	−7.19124	−0.265796
$733$	26.7007	0.986214	0.493107	−	0.869969i	$-0.335861\pi$
$733$	26.7007	0.986214	0.493107	+	0.869969i	$0.335861\pi$
$734$	−53.2191	−1.96435
$735$	−1.35871	−0.0501167
$736$	−55.9413	−2.06202
$737$	30.0525	1.10700
$738$	16.3546	0.602022
$739$	17.3969	0.639954	0.319977	−	0.947425i	$-0.396325\pi$
$739$	17.3969	0.639954	0.319977	+	0.947425i	$0.396325\pi$
$740$	−29.8617	−1.09774
$741$	−0.191100	−0.00702024
$742$	−1.96008	−0.0719569
$743$	50.6579	1.85846	0.929229	−	0.369505i	$-0.120473\pi$
$743$	50.6579	1.85846	0.929229	+	0.369505i	$0.120473\pi$
$744$	−0.710979	−0.0260658
$745$	−52.4190	−1.92049
$746$	−6.25077	−0.228857
$747$	1.14388	0.0418524
$748$	−11.9286	−0.436153
$749$	37.8190	1.38188
$750$	−12.3685	−0.451635
$751$	6.22588	0.227186	0.113593	−	0.993527i	$-0.463764\pi$
$751$	6.22588	0.227186	0.113593	+	0.993527i	$0.463764\pi$
$752$	−48.1759	−1.75679
$753$	4.95137	0.180438
$754$	3.44805	0.125571
$755$	10.0823	0.366932
$756$	12.2953	0.447175
$757$	−1.43773	−0.0522550	−0.0261275	−	0.999659i	$-0.508318\pi$
$757$	−1.43773	−0.0522550	−0.0261275	+	0.999659i	$0.508318\pi$
$758$	−19.7806	−0.718462
$759$	13.8658	0.503297
$760$	1.93155	0.0700646
$761$	9.52056	0.345120	0.172560	−	0.984999i	$-0.444796\pi$
$761$	9.52056	0.345120	0.172560	+	0.984999i	$0.444796\pi$
$762$	−6.63287	−0.240284
$763$	11.5028	0.416429
$764$	−9.25104	−0.334691
$765$	22.1745	0.801722
$766$	−36.7044	−1.32619
$767$	−0.0995159	−0.00359331
$768$	13.8705	0.500508
$769$	−0.107823	−0.00388818	−0.00194409	−	0.999998i	$-0.500619\pi$
$769$	−0.107823	−0.00388818	−0.00194409	+	0.999998i	$0.500619\pi$
$770$	−26.5968	−0.958481
$771$	17.3226	0.623858
$772$	−12.4193	−0.446981
$773$	−18.3261	−0.659145	−0.329573	−	0.944130i	$-0.606905\pi$
$773$	−18.3261	−0.659145	−0.329573	+	0.944130i	$0.606905\pi$
$774$	−22.1809	−0.797275
$775$	0.661494	0.0237616
$776$	−7.76832	−0.278867
$777$	15.1787	0.544534
$778$	27.7421	0.994604
$779$	2.35755	0.0844682
$780$	0.912714	0.0326804
$781$	−35.4645	−1.26902
$782$	−56.5653	−2.02277
$783$	−16.2355	−0.580209
$784$	4.18249	0.149375
$785$	−21.6884	−0.774091
$786$	−11.9034	−0.424581
$787$	−12.3630	−0.440694	−0.220347	−	0.975422i	$-0.570719\pi$
$787$	−12.3630	−0.440694	−0.220347	+	0.975422i	$0.570719\pi$
$788$	1.34760	0.0480063
$789$	−1.39991	−0.0498380
$790$	36.5949	1.30199
$791$	−7.44648	−0.264766
$792$	7.48961	0.266132
$793$	−3.44516	−0.122341
$794$	61.8406	2.19464
$795$	0.685113	0.0242985
$796$	−27.9913	−0.992125
$797$	4.56337	0.161643	0.0808213	−	0.996729i	$-0.474246\pi$
$797$	4.56337	0.161643	0.0808213	+	0.996729i	$0.474246\pi$
$798$	2.02803	0.0717915
$799$	−35.6863	−1.26249
$800$	−4.80712	−0.169957
$801$	−43.3673	−1.53231
$802$	34.4799	1.21753
$803$	26.6048	0.938862
$804$	10.9446	0.385986
$805$	−50.7712	−1.78945
$806$	0.703575	0.0247824
$807$	3.59553	0.126569
$808$	−9.32393	−0.328015
$809$	−27.7914	−0.977095	−0.488547	−	0.872537i	$-0.662473\pi$
$809$	−27.7914	−0.977095	−0.488547	+	0.872537i	$0.662473\pi$
$810$	23.0006	0.808159
$811$	25.2664	0.887225	0.443612	−	0.896219i	$-0.353697\pi$
$811$	25.2664	0.887225	0.443612	+	0.896219i	$0.353697\pi$
$812$	−14.7304	−0.516936
$813$	5.87822	0.206158
$814$	−41.4631	−1.45328
$815$	18.6844	0.654488
$816$	11.6717	0.408590
$817$	−3.19742	−0.111864
$818$	−49.6369	−1.73551
$819$	2.71323	0.0948081
$820$	−11.2599	−0.393213
$821$	−41.2375	−1.43920	−0.719599	−	0.694390i	$-0.755674\pi$
$821$	−41.2375	−1.43920	−0.719599	+	0.694390i	$0.755674\pi$
$822$	−6.22125	−0.216991
$823$	−17.9367	−0.625234	−0.312617	−	0.949879i	$-0.601206\pi$
$823$	−17.9367	−0.625234	−0.312617	+	0.949879i	$0.601206\pi$
$824$	−0.348480	−0.0121399
$825$	1.19151	0.0414830
$826$	1.05610	0.0367465
$827$	44.4745	1.54653	0.773265	−	0.634083i	$-0.218622\pi$
$827$	44.4745	1.54653	0.773265	+	0.634083i	$0.218622\pi$
$828$	−29.5322	−1.02631
$829$	1.60966	0.0559059	0.0279529	−	0.999609i	$-0.491101\pi$
$829$	1.60966	0.0559059	0.0279529	+	0.999609i	$0.491101\pi$
$830$	−1.95636	−0.0679061
$831$	2.54924	0.0884321
$832$	−0.943157	−0.0326981
$833$	3.09818	0.107345
$834$	14.6155	0.506093
$835$	5.91276	0.204620
$836$	−2.23012	−0.0771303
$837$	−3.31285	−0.114509
$838$	34.3447	1.18642
$839$	−47.6291	−1.64434	−0.822169	−	0.569243i	$-0.807236\pi$
$839$	−47.6291	−1.64434	−0.822169	+	0.569243i	$0.807236\pi$
$840$	4.68922	0.161793
$841$	−9.54901	−0.329276
$842$	−55.3326	−1.90689
$843$	−10.9903	−0.378526
$844$	9.63874	0.331779
$845$	−30.6951	−1.05594
$846$	−46.2827	−1.59123
$847$	12.3968	0.425958
$848$	−2.10897	−0.0724225
$849$	13.2008	0.453051
$850$	−4.86074	−0.166722
$851$	−79.1498	−2.71322
$852$	−12.9156	−0.442480
$853$	41.7275	1.42872	0.714361	−	0.699778i	$-0.246718\pi$
$853$	41.7275	1.42872	0.714361	+	0.699778i	$0.246718\pi$
$854$	36.5614	1.25111
$855$	4.14566	0.141778
$856$	18.2141	0.622546
$857$	55.8573	1.90805	0.954024	−	0.299729i	$-0.0968963\pi$
$857$	55.8573	1.90805	0.954024	+	0.299729i	$0.0968963\pi$
$858$	1.26731	0.0432652
$859$	−13.5803	−0.463355	−0.231677	−	0.972793i	$-0.574421\pi$
$859$	−13.5803	−0.463355	−0.231677	+	0.972793i	$0.574421\pi$
$860$	15.2712	0.520744
$861$	5.72344	0.195054
$862$	72.1926	2.45889
$863$	−47.5067	−1.61715	−0.808574	−	0.588395i	$-0.799760\pi$
$863$	−47.5067	−1.61715	−0.808574	+	0.588395i	$0.799760\pi$
$864$	24.0747	0.819039
$865$	−34.9403	−1.18800
$866$	47.6817	1.62029
$867$	−2.60591	−0.0885013
$868$	−3.00574	−0.102022
$869$	20.4548	0.693883
$870$	12.7901	0.433626
$871$	5.24332	0.177663
$872$	5.53989	0.187604
$873$	−16.6731	−0.564297
$874$	−10.5752	−0.357712
$875$	25.3143	0.855778
$876$	9.68900	0.327361
$877$	−8.06528	−0.272345	−0.136173	−	0.990685i	$-0.543480\pi$
$877$	−8.06528	−0.272345	−0.136173	+	0.990685i	$0.543480\pi$
$878$	−71.1457	−2.40105
$879$	9.73560	0.328374
$880$	−28.6171	−0.964682
$881$	38.7817	1.30659	0.653294	−	0.757104i	$-0.273387\pi$
$881$	38.7817	1.30659	0.653294	+	0.757104i	$0.273387\pi$
$882$	4.01813	0.135297
$883$	13.6849	0.460535	0.230268	−	0.973127i	$-0.426040\pi$
$883$	13.6849	0.460535	0.230268	+	0.973127i	$0.426040\pi$
$884$	−2.08121	−0.0699985
$885$	−0.369142	−0.0124086
$886$	55.9849	1.88085
$887$	−4.89122	−0.164231	−0.0821156	−	0.996623i	$-0.526168\pi$
$887$	−4.89122	−0.164231	−0.0821156	+	0.996623i	$0.526168\pi$
$888$	7.31026	0.245316
$889$	13.5753	0.455300
$890$	74.1701	2.48619
$891$	12.8562	0.430701
$892$	20.3978	0.682969
$893$	−6.67175	−0.223262
$894$	−26.5067	−0.886517
$895$	4.44602	0.148614
$896$	−22.4084	−0.748611
$897$	2.41919	0.0807745
$898$	63.4429	2.11712
$899$	3.96898	0.132373
$900$	−2.53774	−0.0845914
$901$	−1.56222	−0.0520452
$902$	−15.6345	−0.520571
$903$	−7.76238	−0.258316
$904$	−3.58631	−0.119279
$905$	52.3025	1.73860
$906$	5.09830	0.169380
$907$	−4.79442	−0.159196	−0.0795981	−	0.996827i	$-0.525364\pi$
$907$	−4.79442	−0.159196	−0.0795981	+	0.996827i	$0.525364\pi$
$908$	−32.0546	−1.06377
$909$	−20.0118	−0.663751
$910$	−4.64039	−0.153827
$911$	27.3364	0.905694	0.452847	−	0.891588i	$-0.350408\pi$
$911$	27.3364	0.905694	0.452847	+	0.891588i	$0.350408\pi$
$912$	2.18208	0.0722560
$913$	−1.09351	−0.0361899
$914$	−15.7810	−0.521989
$915$	−12.7794	−0.422474
$916$	−26.7058	−0.882383
$917$	24.3624	0.804516
$918$	24.3433	0.803448
$919$	54.3152	1.79169	0.895846	−	0.444365i	$-0.146571\pi$
$919$	54.3152	1.79169	0.895846	+	0.444365i	$0.146571\pi$
$920$	−24.4520	−0.806160
$921$	−3.12540	−0.102985
$922$	31.6361	1.04188
$923$	−6.18756	−0.203666
$924$	−5.41406	−0.178110
$925$	−6.80146	−0.223631
$926$	31.2912	1.02829
$927$	−0.747938	−0.0245655
$928$	−28.8428	−0.946812
$929$	21.7090	0.712249	0.356124	−	0.934439i	$-0.384098\pi$
$929$	21.7090	0.712249	0.356124	+	0.934439i	$0.384098\pi$
$930$	2.60983	0.0855796
$931$	0.579222	0.0189832
$932$	−39.2031	−1.28414
$933$	11.6040	0.379899
$934$	36.6388	1.19886
$935$	−21.1981	−0.693252
$936$	1.30673	0.0427117
$937$	−14.5142	−0.474158	−0.237079	−	0.971490i	$-0.576190\pi$
$937$	−14.5142	−0.474158	−0.237079	+	0.971490i	$0.576190\pi$
$938$	−55.6442	−1.81685
$939$	8.05469	0.262855
$940$	31.8650	1.03932
$941$	−44.5490	−1.45226	−0.726128	−	0.687560i	$-0.758682\pi$
$941$	−44.5490	−1.45226	−0.726128	+	0.687560i	$0.758682\pi$
$942$	−10.9671	−0.357329
$943$	−29.8450	−0.971886
$944$	1.13633	0.0369842
$945$	21.8497	0.710772
$946$	21.2042	0.689406
$947$	−40.2068	−1.30655	−0.653274	−	0.757122i	$-0.726605\pi$
$947$	−40.2068	−1.30655	−0.653274	+	0.757122i	$0.726605\pi$
$948$	7.44930	0.241942
$949$	4.64179	0.150679
$950$	−0.908743	−0.0294835
$951$	−10.9184	−0.354054
$952$	−10.6925	−0.346547
$953$	25.6261	0.830109	0.415055	−	0.909797i	$-0.363762\pi$
$953$	25.6261	0.830109	0.415055	+	0.909797i	$0.363762\pi$
$954$	−2.02610	−0.0655973
$955$	−16.4399	−0.531981
$956$	−23.2820	−0.752993
$957$	7.14908	0.231097
$958$	−50.4999	−1.63158
$959$	12.7328	0.411165
$960$	−3.49853	−0.112914
$961$	−30.1901	−0.973875
$962$	−7.23414	−0.233238
$963$	39.0927	1.25975
$964$	6.04073	0.194559
$965$	−22.0701	−0.710463
$966$	−25.6734	−0.826029
$967$	30.8216	0.991156	0.495578	−	0.868563i	$-0.334956\pi$
$967$	30.8216	0.991156	0.495578	+	0.868563i	$0.334956\pi$
$968$	5.97044	0.191897
$969$	1.61638	0.0519255
$970$	28.5156	0.915580
$971$	5.70753	0.183163	0.0915817	−	0.995798i	$-0.470808\pi$
$971$	5.70753	0.183163	0.0915817	+	0.995798i	$0.470808\pi$
$972$	19.5646	0.627534
$973$	−29.9130	−0.958968
$974$	18.9411	0.606912
$975$	0.207885	0.00665764
$976$	39.3387	1.25920
$977$	−4.69258	−0.150129	−0.0750644	−	0.997179i	$-0.523916\pi$
$977$	−4.69258	−0.150129	−0.0750644	+	0.997179i	$0.523916\pi$
$978$	9.44816	0.302119
$979$	41.4576	1.32499
$980$	−2.76642	−0.0883701
$981$	11.8902	0.379625
$982$	−67.1086	−2.14152
$983$	10.5465	0.336381	0.168190	−	0.985755i	$-0.446208\pi$
$983$	10.5465	0.336381	0.168190	+	0.985755i	$0.446208\pi$
$984$	2.75648	0.0878733
$985$	2.39480	0.0763046
$986$	−29.1646	−0.928789
$987$	−16.1970	−0.515557
$988$	−0.389093	−0.0123787
$989$	40.4771	1.28710
$990$	−27.4925	−0.873769
$991$	−30.6070	−0.972265	−0.486132	−	0.873885i	$-0.661593\pi$
$991$	−30.6070	−0.972265	−0.486132	+	0.873885i	$0.661593\pi$
$992$	−5.88538	−0.186861
$993$	2.08164	0.0660589
$994$	65.6648	2.08276
$995$	−49.7428	−1.57695
$996$	−0.398238	−0.0126186
$997$	56.0308	1.77451	0.887257	−	0.461275i	$-0.152608\pi$
$997$	56.0308	1.77451	0.887257	+	0.461275i	$0.152608\pi$
$998$	25.7179	0.814086
$999$	34.0627	1.07769

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.2.a.c.1.8	✓	10
3.2	odd	2		1773.2.a.f.1.3		10
4.3	odd	2		3152.2.a.m.1.7		10
5.4	even	2		4925.2.a.i.1.3		10
7.6	odd	2		9653.2.a.j.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.2.a.c.1.8	✓	10	1.1	even	1	trivial
1773.2.a.f.1.3		10	3.2	odd	2
3152.2.a.m.1.7		10	4.3	odd	2
4925.2.a.i.1.3		10	5.4	even	2
9653.2.a.j.1.8		10	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q+1.82964 q^{2} +0.661864 q^{3} +1.34760 q^{4} +2.39480 q^{5} +1.21098 q^{6} -2.47846 q^{7} -1.19366 q^{8} -2.56194 q^{9} +4.38163 q^{10} +2.44912 q^{11} +0.891928 q^{12} +0.427303 q^{13} -4.53471 q^{14} +1.58503 q^{15} -4.87917 q^{16} -3.61425 q^{17} -4.68743 q^{18} -0.675704 q^{19} +3.22723 q^{20} -1.64041 q^{21} +4.48103 q^{22} +8.55393 q^{23} -0.790040 q^{24} +0.735052 q^{25} +0.781813 q^{26} -3.68124 q^{27} -3.33998 q^{28} +4.41033 q^{29} +2.90004 q^{30} +0.899928 q^{31} -6.53984 q^{32} +1.62099 q^{33} -6.61279 q^{34} -5.93542 q^{35} -3.45247 q^{36} -9.25303 q^{37} -1.23630 q^{38} +0.282816 q^{39} -2.85857 q^{40} -3.48904 q^{41} -3.00136 q^{42} +4.73199 q^{43} +3.30044 q^{44} -6.13532 q^{45} +15.6507 q^{46} +9.87379 q^{47} -3.22935 q^{48} -0.857212 q^{49} +1.34488 q^{50} -2.39214 q^{51} +0.575834 q^{52} +0.432240 q^{53} -6.73537 q^{54} +5.86515 q^{55} +2.95844 q^{56} -0.447224 q^{57} +8.06933 q^{58} -0.232893 q^{59} +2.13599 q^{60} -8.06257 q^{61} +1.64655 q^{62} +6.34967 q^{63} -2.20723 q^{64} +1.02330 q^{65} +2.96583 q^{66} +12.2707 q^{67} -4.87056 q^{68} +5.66154 q^{69} -10.8597 q^{70} -14.4805 q^{71} +3.05808 q^{72} +10.8630 q^{73} -16.9298 q^{74} +0.486504 q^{75} -0.910579 q^{76} -6.07007 q^{77} +0.517454 q^{78} +8.35190 q^{79} -11.6846 q^{80} +5.24933 q^{81} -6.38370 q^{82} -0.446491 q^{83} -2.21061 q^{84} -8.65538 q^{85} +8.65785 q^{86} +2.91904 q^{87} -2.92342 q^{88} +16.9275 q^{89} -11.2255 q^{90} -1.05906 q^{91} +11.5273 q^{92} +0.595630 q^{93} +18.0655 q^{94} -1.61817 q^{95} -4.32848 q^{96} +6.50799 q^{97} -1.56839 q^{98} -6.27450 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{3} + 10 q^{4} + 2 q^{5} - 4 q^{6} + 11 q^{7} - 3 q^{8} + 12 q^{9} - 2 q^{10} + 2 q^{11} + 4 q^{12} + 8 q^{13} - 9 q^{14} - q^{15} - 2 q^{16} - 3 q^{17} - 9 q^{18} + 17 q^{19} - 2 q^{20} - 2 q^{21}+ \cdots - q^{99}+O(q^{100}) \) 10 * q + 10 * q^3 + 10 * q^4 + 2 * q^5 - 4 * q^6 + 11 * q^7 - 3 * q^8 + 12 * q^9 - 2 * q^10 + 2 * q^11 + 4 * q^12 + 8 * q^13 - 9 * q^14 - q^15 - 2 * q^16 - 3 * q^17 - 9 * q^18 + 17 * q^19 - 2 * q^20 - 2 * q^21 + 3 * q^22 - 4 * q^23 - 15 * q^24 + 6 * q^25 - 13 * q^26 + 19 * q^27 + 16 * q^28 - 9 * q^29 - 19 * q^30 + 20 * q^31 - 16 * q^32 - 2 * q^33 - 8 * q^34 - 12 * q^35 - 12 * q^36 + 12 * q^37 - 15 * q^38 - 9 * q^39 - 15 * q^40 - 18 * q^41 - 31 * q^42 + 11 * q^43 - 24 * q^44 - 15 * q^45 - 13 * q^46 + 5 * q^47 - 22 * q^48 + q^49 - 24 * q^50 - 13 * q^51 + 9 * q^52 - 6 * q^53 - 15 * q^54 - 17 * q^55 - 6 * q^56 + 3 * q^57 - 15 * q^58 - q^59 - 23 * q^60 + 4 * q^61 - 16 * q^62 - 11 * q^63 - 17 * q^64 - 17 * q^65 + 24 * q^66 + 46 * q^67 + 15 * q^68 - 21 * q^69 + 25 * q^70 - 5 * q^71 + 7 * q^72 + 25 * q^73 + 3 * q^74 + 46 * q^75 + 49 * q^76 - 14 * q^77 + 15 * q^78 - q^79 + 9 * q^80 + 22 * q^81 + 52 * q^82 + 28 * q^83 - 14 * q^84 - 30 * q^85 + 27 * q^86 - 7 * q^87 + 9 * q^88 - 6 * q^89 - 10 * q^90 + 51 * q^91 + 32 * q^92 + 15 * q^93 - 3 * q^94 - 13 * q^95 + 75 * q^96 + 2 * q^97 + 22 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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