LMFDB - Embedded newform 6025.2.a.n.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.35802 q^{2} +2.46294 q^{3} +3.56028 q^{4} -5.80768 q^{6} -4.19376 q^{7} -3.67917 q^{8} +3.06609 q^{9} +O(q^{10})$	\(q-2.35802 q^{2} +2.46294 q^{3} +3.56028 q^{4} -5.80768 q^{6} -4.19376 q^{7} -3.67917 q^{8} +3.06609 q^{9} -0.00154189 q^{11} +8.76876 q^{12} +3.62049 q^{13} +9.88899 q^{14} +1.55501 q^{16} +1.85005 q^{17} -7.22992 q^{18} -0.186852 q^{19} -10.3290 q^{21} +0.00363582 q^{22} +6.05012 q^{23} -9.06158 q^{24} -8.53720 q^{26} +0.162785 q^{27} -14.9309 q^{28} -10.2684 q^{29} -1.07383 q^{31} +3.69158 q^{32} -0.00379760 q^{33} -4.36246 q^{34} +10.9161 q^{36} +6.88655 q^{37} +0.440601 q^{38} +8.91707 q^{39} -7.15211 q^{41} +24.3560 q^{42} -7.53860 q^{43} -0.00548956 q^{44} -14.2663 q^{46} +11.2316 q^{47} +3.82990 q^{48} +10.5876 q^{49} +4.55657 q^{51} +12.8899 q^{52} -6.06845 q^{53} -0.383850 q^{54} +15.4295 q^{56} -0.460206 q^{57} +24.2132 q^{58} +11.2625 q^{59} +6.10819 q^{61} +2.53211 q^{62} -12.8585 q^{63} -11.8149 q^{64} +0.00895482 q^{66} +8.53974 q^{67} +6.58668 q^{68} +14.9011 q^{69} -11.9780 q^{71} -11.2807 q^{72} +7.27876 q^{73} -16.2386 q^{74} -0.665244 q^{76} +0.00646633 q^{77} -21.0267 q^{78} +14.7311 q^{79} -8.79735 q^{81} +16.8648 q^{82} +1.15932 q^{83} -36.7741 q^{84} +17.7762 q^{86} -25.2906 q^{87} +0.00567288 q^{88} +7.45253 q^{89} -15.1835 q^{91} +21.5401 q^{92} -2.64477 q^{93} -26.4844 q^{94} +9.09216 q^{96} -8.29265 q^{97} -24.9659 q^{98} -0.00472759 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9	$ 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9} + q^{11} + 26 q^{12} + 11 q^{13} - q^{14} + 43 q^{16} + 20 q^{17} + 18 q^{18} + 2 q^{21} + 23 q^{22} + 79 q^{23} - 2 q^{24} + 2 q^{26} + 26 q^{27} + 30 q^{28} + 2 q^{29} + q^{31} + 68 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 16 q^{37} + 45 q^{38} - 2 q^{39} - 2 q^{41} + 19 q^{42} + 25 q^{43} + 3 q^{44} + 14 q^{46} + 88 q^{47} + 75 q^{48} + 40 q^{49} - 10 q^{51} + 18 q^{52} + 34 q^{53} + 4 q^{54} - 15 q^{56} + 51 q^{57} + 53 q^{58} + q^{59} + 9 q^{61} + 39 q^{62} + 110 q^{63} + 17 q^{64} + 26 q^{66} + 30 q^{67} + 44 q^{68} - 7 q^{69} + 5 q^{71} + 18 q^{72} + 23 q^{73} - 18 q^{74} + 43 q^{76} + 30 q^{77} + 46 q^{78} + 5 q^{79} + 44 q^{81} + 5 q^{82} + 65 q^{83} - 65 q^{84} + 40 q^{86} + 33 q^{87} + 71 q^{88} - 9 q^{89} + q^{91} + 117 q^{92} + 68 q^{93} - 72 q^{94} + 83 q^{96} - 8 q^{97} + 76 q^{98} - 40 q^{99}+O(q^{100}) $ 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9 + q^11 + 26 * q^12 + 11 * q^13 - q^14 + 43 * q^16 + 20 * q^17 + 18 * q^18 + 2 * q^21 + 23 * q^22 + 79 * q^23 - 2 * q^24 + 2 * q^26 + 26 * q^27 + 30 * q^28 + 2 * q^29 + q^31 + 68 * q^32 + 20 * q^33 + 5 * q^34 + 32 * q^36 + 16 * q^37 + 45 * q^38 - 2 * q^39 - 2 * q^41 + 19 * q^42 + 25 * q^43 + 3 * q^44 + 14 * q^46 + 88 * q^47 + 75 * q^48 + 40 * q^49 - 10 * q^51 + 18 * q^52 + 34 * q^53 + 4 * q^54 - 15 * q^56 + 51 * q^57 + 53 * q^58 + q^59 + 9 * q^61 + 39 * q^62 + 110 * q^63 + 17 * q^64 + 26 * q^66 + 30 * q^67 + 44 * q^68 - 7 * q^69 + 5 * q^71 + 18 * q^72 + 23 * q^73 - 18 * q^74 + 43 * q^76 + 30 * q^77 + 46 * q^78 + 5 * q^79 + 44 * q^81 + 5 * q^82 + 65 * q^83 - 65 * q^84 + 40 * q^86 + 33 * q^87 + 71 * q^88 - 9 * q^89 + q^91 + 117 * q^92 + 68 * q^93 - 72 * q^94 + 83 * q^96 - 8 * q^97 + 76 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.35802	−1.66737	−0.833687	−	0.552237i	$-0.813774\pi$
$2$	−2.35802	−1.66737	−0.833687	+	0.552237i	$0.813774\pi$
$3$	2.46294	1.42198	0.710991	−	0.703201i	$-0.248247\pi$
$3$	2.46294	1.42198	0.710991	+	0.703201i	$0.248247\pi$
$4$	3.56028	1.78014
$5$	0	0
$5$	0	0
$6$	−5.80768	−2.37098
$7$	−4.19376	−1.58509	−0.792546	−	0.609812i	$-0.791245\pi$
$7$	−4.19376	−1.58509	−0.792546	+	0.609812i	$0.791245\pi$
$8$	−3.67917	−1.30078
$9$	3.06609	1.02203
$10$	0	0
$11$	−0.00154189	−0.000464898 0	−0.000232449	−	1.00000i	$-0.500074\pi$
$11$	−0.00154189	−0.000464898 0	−0.000232449		1.00000i	$0.500074\pi$
$12$	8.76876	2.53132
$13$	3.62049	1.00414	0.502072	−	0.864826i	$-0.332571\pi$
$13$	3.62049	1.00414	0.502072	+	0.864826i	$0.332571\pi$
$14$	9.88899	2.64294
$15$	0	0
$16$	1.55501	0.388752
$17$	1.85005	0.448703	0.224351	−	0.974508i	$-0.427974\pi$
$17$	1.85005	0.448703	0.224351	+	0.974508i	$0.427974\pi$
$18$	−7.22992	−1.70411
$19$	−0.186852	−0.0428668	−0.0214334	−	0.999770i	$-0.506823\pi$
$19$	−0.186852	−0.0428668	−0.0214334	+	0.999770i	$0.506823\pi$
$20$	0	0
$21$	−10.3290	−2.25397
$22$	0.00363582	0.000775159 0
$23$	6.05012	1.26154	0.630769	−	0.775971i	$-0.282740\pi$
$23$	6.05012	1.26154	0.630769	+	0.775971i	$0.282740\pi$
$24$	−9.06158	−1.84969
$25$	0	0
$26$	−8.53720	−1.67428
$27$	0.162785	0.0313279
$28$	−14.9309	−2.82168
$29$	−10.2684	−1.90680	−0.953400	−	0.301710i	$-0.902442\pi$
$29$	−10.2684	−1.90680	−0.953400	+	0.301710i	$0.902442\pi$
$30$	0	0
$31$	−1.07383	−0.192865	−0.0964325	−	0.995340i	$-0.530743\pi$
$31$	−1.07383	−0.192865	−0.0964325	+	0.995340i	$0.530743\pi$
$32$	3.69158	0.652586
$33$	−0.00379760	−0.000661077 0
$34$	−4.36246	−0.748155
$35$	0	0
$36$	10.9161	1.81936
$37$	6.88655	1.13214	0.566071	−	0.824357i	$-0.308463\pi$
$37$	6.88655	1.13214	0.566071	+	0.824357i	$0.308463\pi$
$38$	0.440601	0.0714750
$39$	8.91707	1.42787
$40$	0	0
$41$	−7.15211	−1.11697	−0.558486	−	0.829514i	$-0.688618\pi$
$41$	−7.15211	−1.11697	−0.558486	+	0.829514i	$0.688618\pi$
$42$	24.3560	3.75822
$43$	−7.53860	−1.14963	−0.574813	−	0.818285i	$-0.694925\pi$
$43$	−7.53860	−1.14963	−0.574813	+	0.818285i	$0.694925\pi$
$44$	−0.00548956	−0.000827583 0
$45$	0	0
$46$	−14.2663	−2.10346
$47$	11.2316	1.63830	0.819148	−	0.573582i	$-0.194446\pi$
$47$	11.2316	1.63830	0.819148	+	0.573582i	$0.194446\pi$
$48$	3.82990	0.552799
$49$	10.5876	1.51252
$50$	0	0
$51$	4.55657	0.638047
$52$	12.8899	1.78751
$53$	−6.06845	−0.833566	−0.416783	−	0.909006i	$-0.636843\pi$
$53$	−6.06845	−0.833566	−0.416783	+	0.909006i	$0.636843\pi$
$54$	−0.383850	−0.0522354
$55$	0	0
$56$	15.4295	2.06186
$57$	−0.460206	−0.0609558
$58$	24.2132	3.17935
$59$	11.2625	1.46625	0.733127	−	0.680092i	$-0.238060\pi$
$59$	11.2625	1.46625	0.733127	+	0.680092i	$0.238060\pi$
$60$	0	0
$61$	6.10819	0.782074	0.391037	−	0.920375i	$-0.372117\pi$
$61$	6.10819	0.782074	0.391037	+	0.920375i	$0.372117\pi$
$62$	2.53211	0.321578
$63$	−12.8585	−1.62001
$64$	−11.8149	−1.47686
$65$	0	0
$66$	0.00895482	0.00110226
$67$	8.53974	1.04330	0.521648	−	0.853161i	$-0.325318\pi$
$67$	8.53974	1.04330	0.521648	+	0.853161i	$0.325318\pi$
$68$	6.58668	0.798753
$69$	14.9011	1.79388
$70$	0	0
$71$	−11.9780	−1.42153	−0.710766	−	0.703428i	$-0.751652\pi$
$71$	−11.9780	−1.42153	−0.710766	+	0.703428i	$0.751652\pi$
$72$	−11.2807	−1.32944
$73$	7.27876	0.851914	0.425957	−	0.904743i	$-0.359937\pi$
$73$	7.27876	0.851914	0.425957	+	0.904743i	$0.359937\pi$
$74$	−16.2386	−1.88770
$75$	0	0
$76$	−0.665244	−0.0763088
$77$	0.00646633	0.000736906 0
$78$	−21.0267	−2.38080
$79$	14.7311	1.65738	0.828689	−	0.559710i	$-0.189087\pi$
$79$	14.7311	1.65738	0.828689	+	0.559710i	$0.189087\pi$
$80$	0	0
$81$	−8.79735	−0.977483
$82$	16.8648	1.86241
$83$	1.15932	0.127251	0.0636257	−	0.997974i	$-0.479734\pi$
$83$	1.15932	0.127251	0.0636257	+	0.997974i	$0.479734\pi$
$84$	−36.7741	−4.01238
$85$	0	0
$86$	17.7762	1.91686
$87$	−25.2906	−2.71143
$88$	0.00567288	0.000604731 0
$89$	7.45253	0.789967	0.394983	−	0.918688i	$-0.370750\pi$
$89$	7.45253	0.789967	0.394983	+	0.918688i	$0.370750\pi$
$90$	0	0
$91$	−15.1835	−1.59166
$92$	21.5401	2.24571
$93$	−2.64477	−0.274250
$94$	−26.4844	−2.73165
$95$	0	0
$96$	9.09216	0.927965
$97$	−8.29265	−0.841991	−0.420996	−	0.907063i	$-0.638319\pi$
$97$	−8.29265	−0.841991	−0.420996	+	0.907063i	$0.638319\pi$
$98$	−24.9659	−2.52193
$99$	−0.00472759	−0.000475140 0
$100$	0	0
$101$	4.27966	0.425842	0.212921	−	0.977069i	$-0.431702\pi$
$101$	4.27966	0.425842	0.212921	+	0.977069i	$0.431702\pi$
$102$	−10.7445	−1.06386
$103$	−0.547927	−0.0539888	−0.0269944	−	0.999636i	$-0.508594\pi$
$103$	−0.547927	−0.0539888	−0.0269944	+	0.999636i	$0.508594\pi$
$104$	−13.3204	−1.30617
$105$	0	0
$106$	14.3096	1.38987
$107$	3.62216	0.350167	0.175084	−	0.984554i	$-0.443980\pi$
$107$	3.62216	0.350167	0.175084	+	0.984554i	$0.443980\pi$
$108$	0.579558	0.0557680
$109$	−8.65638	−0.829131	−0.414565	−	0.910020i	$-0.636066\pi$
$109$	−8.65638	−0.829131	−0.414565	+	0.910020i	$0.636066\pi$
$110$	0	0
$111$	16.9612	1.60988
$112$	−6.52134	−0.616209
$113$	10.5694	0.994285	0.497143	−	0.867669i	$-0.334383\pi$
$113$	10.5694	0.994285	0.497143	+	0.867669i	$0.334383\pi$
$114$	1.08518	0.101636
$115$	0	0
$116$	−36.5584	−3.39437
$117$	11.1008	1.02627
$118$	−26.5573	−2.44479
$119$	−7.75866	−0.711235
$120$	0	0
$121$	−11.0000	−1.00000
$122$	−14.4033	−1.30401
$123$	−17.6152	−1.58831
$124$	−3.82312	−0.343326
$125$	0	0
$126$	30.3206	2.70117
$127$	−18.4273	−1.63516	−0.817581	−	0.575814i	$-0.804685\pi$
$127$	−18.4273	−1.63516	−0.817581	+	0.575814i	$0.804685\pi$
$128$	20.4765	1.80989
$129$	−18.5672	−1.63475
$130$	0	0
$131$	−0.664361	−0.0580455	−0.0290227	−	0.999579i	$-0.509240\pi$
$131$	−0.664361	−0.0580455	−0.0290227	+	0.999579i	$0.509240\pi$
$132$	−0.0135205	−0.00117681
$133$	0.783612	0.0679478
$134$	−20.1369	−1.73956
$135$	0	0
$136$	−6.80664	−0.583664
$137$	13.9003	1.18758	0.593791	−	0.804619i	$-0.297631\pi$
$137$	13.9003	1.18758	0.593791	+	0.804619i	$0.297631\pi$
$138$	−35.1372	−2.99108
$139$	−1.64233	−0.139301	−0.0696505	−	0.997571i	$-0.522188\pi$
$139$	−1.64233	−0.139301	−0.0696505	+	0.997571i	$0.522188\pi$
$140$	0	0
$141$	27.6628	2.32963
$142$	28.2445	2.37023
$143$	−0.00558241	−0.000466824 0
$144$	4.76781	0.397317
$145$	0	0
$146$	−17.1635	−1.42046
$147$	26.0767	2.15077
$148$	24.5180	2.01537
$149$	1.62890	0.133445	0.0667223	−	0.997772i	$-0.478746\pi$
$149$	1.62890	0.133445	0.0667223	+	0.997772i	$0.478746\pi$
$150$	0	0
$151$	20.2681	1.64940	0.824698	−	0.565573i	$-0.191345\pi$
$151$	20.2681	1.64940	0.824698	+	0.565573i	$0.191345\pi$
$152$	0.687459	0.0557603
$153$	5.67242	0.458588
$154$	−0.0152478	−0.00122870
$155$	0	0
$156$	31.7472	2.54181
$157$	−3.03276	−0.242040	−0.121020	−	0.992650i	$-0.538617\pi$
$157$	−3.03276	−0.242040	−0.121020	+	0.992650i	$0.538617\pi$
$158$	−34.7363	−2.76347
$159$	−14.9463	−1.18532
$160$	0	0
$161$	−25.3728	−1.99965
$162$	20.7444	1.62983
$163$	−0.309203	−0.0242187	−0.0121093	−	0.999927i	$-0.503855\pi$
$163$	−0.309203	−0.0242187	−0.0121093	+	0.999927i	$0.503855\pi$
$164$	−25.4635	−1.98836
$165$	0	0
$166$	−2.73369	−0.212176
$167$	−3.01179	−0.233060	−0.116530	−	0.993187i	$-0.537177\pi$
$167$	−3.01179	−0.233060	−0.116530	+	0.993187i	$0.537177\pi$
$168$	38.0021	2.93193
$169$	0.107956	0.00830434
$170$	0	0
$171$	−0.572906	−0.0438112
$172$	−26.8395	−2.04649
$173$	9.59450	0.729456	0.364728	−	0.931114i	$-0.381162\pi$
$173$	9.59450	0.729456	0.364728	+	0.931114i	$0.381162\pi$
$174$	59.6357	4.52097
$175$	0	0
$176$	−0.00239766	−0.000180730 0
$177$	27.7389	2.08499
$178$	−17.5732	−1.31717
$179$	15.7851	1.17984	0.589918	−	0.807463i	$-0.299160\pi$
$179$	15.7851	1.17984	0.589918	+	0.807463i	$0.299160\pi$
$180$	0	0
$181$	24.7451	1.83929	0.919643	−	0.392755i	$-0.128478\pi$
$181$	24.7451	1.83929	0.919643	+	0.392755i	$0.128478\pi$
$182$	35.8030	2.65389
$183$	15.0441	1.11209
$184$	−22.2594	−1.64099
$185$	0	0
$186$	6.23644	0.457278
$187$	−0.00285258	−0.000208601 0
$188$	39.9876	2.91639
$189$	−0.682680	−0.0496577
$190$	0	0
$191$	−14.2705	−1.03258	−0.516288	−	0.856415i	$-0.672687\pi$
$191$	−14.2705	−1.03258	−0.516288	+	0.856415i	$0.672687\pi$
$192$	−29.0993	−2.10006
$193$	14.1174	1.01619	0.508097	−	0.861300i	$-0.330349\pi$
$193$	14.1174	1.01619	0.508097	+	0.861300i	$0.330349\pi$
$194$	19.5543	1.40391
$195$	0	0
$196$	37.6949	2.69249
$197$	5.62457	0.400734	0.200367	−	0.979721i	$-0.435787\pi$
$197$	5.62457	0.400734	0.200367	+	0.979721i	$0.435787\pi$
$198$	0.0111478	0.000792237 0
$199$	−0.712689	−0.0505212	−0.0252606	−	0.999681i	$-0.508042\pi$
$199$	−0.712689	−0.0505212	−0.0252606	+	0.999681i	$0.508042\pi$
$200$	0	0
$201$	21.0329	1.48355
$202$	−10.0915	−0.710038
$203$	43.0633	3.02245
$204$	16.2226	1.13581
$205$	0	0
$206$	1.29202	0.0900196
$207$	18.5502	1.28933
$208$	5.62990	0.390363
$209$	0.000288106 0	1.99287e−5 0
$210$	0	0
$211$	−24.7629	−1.70475	−0.852375	−	0.522931i	$-0.824839\pi$
$211$	−24.7629	−1.70475	−0.852375	+	0.522931i	$0.824839\pi$
$212$	−21.6054	−1.48386
$213$	−29.5013	−2.02139
$214$	−8.54113	−0.583860
$215$	0	0
$216$	−0.598912	−0.0407508
$217$	4.50337	0.305709
$218$	20.4119	1.38247
$219$	17.9272	1.21141
$220$	0	0
$221$	6.69808	0.450562
$222$	−39.9949	−2.68428
$223$	18.9744	1.27062	0.635309	−	0.772258i	$-0.280873\pi$
$223$	18.9744	1.27062	0.635309	+	0.772258i	$0.280873\pi$
$224$	−15.4816	−1.03441
$225$	0	0
$226$	−24.9229	−1.65785
$227$	2.41046	0.159988	0.0799939	−	0.996795i	$-0.474510\pi$
$227$	2.41046	0.159988	0.0799939	+	0.996795i	$0.474510\pi$
$228$	−1.63846	−0.108510
$229$	3.06568	0.202586	0.101293	−	0.994857i	$-0.467702\pi$
$229$	3.06568	0.202586	0.101293	+	0.994857i	$0.467702\pi$
$230$	0	0
$231$	0.0159262	0.00104787
$232$	37.7793	2.48033
$233$	16.8436	1.10346	0.551730	−	0.834023i	$-0.313968\pi$
$233$	16.8436	1.10346	0.551730	+	0.834023i	$0.313968\pi$
$234$	−26.1759	−1.71117
$235$	0	0
$236$	40.0976	2.61013
$237$	36.2818	2.35676
$238$	18.2951	1.18590
$239$	−5.03805	−0.325884	−0.162942	−	0.986636i	$-0.552098\pi$
$239$	−5.03805	−0.325884	−0.162942	+	0.986636i	$0.552098\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	25.9383	1.66737
$243$	−22.1557	−1.42129
$244$	21.7468	1.39220
$245$	0	0
$246$	41.5372	2.64831
$247$	−0.676496	−0.0430444
$248$	3.95079	0.250875
$249$	2.85533	0.180949
$250$	0	0
$251$	−6.29163	−0.397124	−0.198562	−	0.980088i	$-0.563627\pi$
$251$	−6.29163	−0.397124	−0.198562	+	0.980088i	$0.563627\pi$
$252$	−45.7797	−2.88385
$253$	−0.00932864	−0.000586487 0
$254$	43.4521	2.72643
$255$	0	0
$256$	−24.6545	−1.54090
$257$	10.0170	0.624840	0.312420	−	0.949944i	$-0.398860\pi$
$257$	10.0170	0.624840	0.312420	+	0.949944i	$0.398860\pi$
$258$	43.7818	2.72573
$259$	−28.8805	−1.79455
$260$	0	0
$261$	−31.4840	−1.94881
$262$	1.56658	0.0967836
$263$	26.4109	1.62856	0.814282	−	0.580470i	$-0.197131\pi$
$263$	26.4109	1.62856	0.814282	+	0.580470i	$0.197131\pi$
$264$	0.0139720	0.000859916 0
$265$	0	0
$266$	−1.84778	−0.113294
$267$	18.3552	1.12332
$268$	30.4038	1.85721
$269$	5.94871	0.362699	0.181350	−	0.983419i	$-0.441953\pi$
$269$	5.94871	0.362699	0.181350	+	0.983419i	$0.441953\pi$
$270$	0	0
$271$	7.35562	0.446822	0.223411	−	0.974724i	$-0.428281\pi$
$271$	7.35562	0.446822	0.223411	+	0.974724i	$0.428281\pi$
$272$	2.87684	0.174434
$273$	−37.3960	−2.26331
$274$	−32.7772	−1.98014
$275$	0	0
$276$	53.0521	3.19336
$277$	10.9353	0.657037	0.328519	−	0.944497i	$-0.393451\pi$
$277$	10.9353	0.657037	0.328519	+	0.944497i	$0.393451\pi$
$278$	3.87266	0.232267
$279$	−3.29245	−0.197114
$280$	0	0
$281$	22.3980	1.33615	0.668077	−	0.744092i	$-0.267118\pi$
$281$	22.3980	1.33615	0.668077	+	0.744092i	$0.267118\pi$
$282$	−65.2295	−3.88436
$283$	3.94081	0.234257	0.117129	−	0.993117i	$-0.462631\pi$
$283$	3.94081	0.234257	0.117129	+	0.993117i	$0.462631\pi$
$284$	−42.6451	−2.53052
$285$	0	0
$286$	0.0131635	0.000778371 0
$287$	29.9942	1.77050
$288$	11.3187	0.666963
$289$	−13.5773	−0.798666
$290$	0	0
$291$	−20.4243	−1.19730
$292$	25.9144	1.51652
$293$	−3.97082	−0.231978	−0.115989	−	0.993251i	$-0.537004\pi$
$293$	−3.97082	−0.231978	−0.115989	+	0.993251i	$0.537004\pi$
$294$	−61.4895	−3.58614
$295$	0	0
$296$	−25.3368	−1.47267
$297$	−0.000250997 0	−1.45643e−5 0
$298$	−3.84098	−0.222502
$299$	21.9044	1.26677
$300$	0	0
$301$	31.6151	1.82226
$302$	−47.7927	−2.75016
$303$	10.5406	0.605539
$304$	−0.290557	−0.0166646
$305$	0	0
$306$	−13.3757	−0.764638
$307$	−26.7995	−1.52953	−0.764764	−	0.644310i	$-0.777145\pi$
$307$	−26.7995	−1.52953	−0.764764	+	0.644310i	$0.777145\pi$
$308$	0.0230219	0.00131179
$309$	−1.34951	−0.0767711
$310$	0	0
$311$	12.9276	0.733056	0.366528	−	0.930407i	$-0.380546\pi$
$311$	12.9276	0.733056	0.366528	+	0.930407i	$0.380546\pi$
$312$	−32.8074	−1.85735
$313$	2.88291	0.162952	0.0814760	−	0.996675i	$-0.474037\pi$
$313$	2.88291	0.162952	0.0814760	+	0.996675i	$0.474037\pi$
$314$	7.15131	0.403572
$315$	0	0
$316$	52.4467	2.95036
$317$	22.9141	1.28699	0.643493	−	0.765452i	$-0.277484\pi$
$317$	22.9141	1.28699	0.643493	+	0.765452i	$0.277484\pi$
$318$	35.2436	1.97636
$319$	0.0158328	0.000886467 0
$320$	0	0
$321$	8.92117	0.497931
$322$	59.8296	3.33417
$323$	−0.345685	−0.0192344
$324$	−31.3210	−1.74006
$325$	0	0
$326$	0.729108	0.0403816
$327$	−21.3202	−1.17901
$328$	26.3138	1.45294
$329$	−47.1026	−2.59685
$330$	0	0
$331$	−11.4543	−0.629585	−0.314793	−	0.949160i	$-0.601935\pi$
$331$	−11.4543	−0.629585	−0.314793	+	0.949160i	$0.601935\pi$
$332$	4.12748	0.226525
$333$	21.1148	1.15708
$334$	7.10188	0.388598
$335$	0	0
$336$	−16.0617	−0.876237
$337$	−27.1623	−1.47963	−0.739814	−	0.672812i	$-0.765086\pi$
$337$	−27.1623	−1.47963	−0.739814	+	0.672812i	$0.765086\pi$
$338$	−0.254564	−0.0138464
$339$	26.0318	1.41385
$340$	0	0
$341$	0.00165573	8.96626e−5 0
$342$	1.35092	0.0730497
$343$	−15.0456	−0.812388
$344$	27.7358	1.49541
$345$	0	0
$346$	−22.6241	−1.21628
$347$	−33.7017	−1.80920	−0.904600	−	0.426262i	$-0.859830\pi$
$347$	−33.7017	−1.80920	−0.904600	+	0.426262i	$0.859830\pi$
$348$	−90.0414	−4.82672
$349$	20.4275	1.09346	0.546730	−	0.837309i	$-0.315872\pi$
$349$	20.4275	1.09346	0.546730	+	0.837309i	$0.315872\pi$
$350$	0	0
$351$	0.589361	0.0314577
$352$	−0.00569202	−0.000303386 0
$353$	33.3503	1.77506	0.887529	−	0.460753i	$-0.152420\pi$
$353$	33.3503	1.77506	0.887529	+	0.460753i	$0.152420\pi$
$354$	−65.4091	−3.47645
$355$	0	0
$356$	26.5331	1.40625
$357$	−19.1091	−1.01136
$358$	−37.2217	−1.96723
$359$	26.0067	1.37258	0.686290	−	0.727328i	$-0.259238\pi$
$359$	26.0067	1.37258	0.686290	+	0.727328i	$0.259238\pi$
$360$	0	0
$361$	−18.9651	−0.998162
$362$	−58.3495	−3.06678
$363$	−27.0924	−1.42198
$364$	−54.0573	−2.83337
$365$	0	0
$366$	−35.4744	−1.85428
$367$	12.8622	0.671400	0.335700	−	0.941969i	$-0.391027\pi$
$367$	12.8622	0.671400	0.335700	+	0.941969i	$0.391027\pi$
$368$	9.40800	0.490426
$369$	−21.9290	−1.14158
$370$	0	0
$371$	25.4496	1.32128
$372$	−9.41613	−0.488203
$373$	−4.28214	−0.221721	−0.110860	−	0.993836i	$-0.535361\pi$
$373$	−4.28214	−0.221721	−0.110860	+	0.993836i	$0.535361\pi$
$374$	0.00672644	0.000347816 0
$375$	0	0
$376$	−41.3229	−2.13107
$377$	−37.1768	−1.91470
$378$	1.60978	0.0827979
$379$	14.5535	0.747565	0.373782	−	0.927516i	$-0.378061\pi$
$379$	14.5535	0.747565	0.373782	+	0.927516i	$0.378061\pi$
$380$	0	0
$381$	−45.3855	−2.32517
$382$	33.6501	1.72169
$383$	−13.2341	−0.676230	−0.338115	−	0.941105i	$-0.609789\pi$
$383$	−13.2341	−0.676230	−0.338115	+	0.941105i	$0.609789\pi$
$384$	50.4326	2.57363
$385$	0	0
$386$	−33.2892	−1.69437
$387$	−23.1141	−1.17495
$388$	−29.5241	−1.49886
$389$	7.60226	0.385450	0.192725	−	0.981253i	$-0.438267\pi$
$389$	7.60226	0.385450	0.192725	+	0.981253i	$0.438267\pi$
$390$	0	0
$391$	11.1930	0.566055
$392$	−38.9536	−1.96746
$393$	−1.63628	−0.0825396
$394$	−13.2629	−0.668173
$395$	0	0
$396$	−0.0168315	−0.000845815 0
$397$	22.7794	1.14327	0.571633	−	0.820509i	$-0.306310\pi$
$397$	22.7794	1.14327	0.571633	+	0.820509i	$0.306310\pi$
$398$	1.68054	0.0842378
$399$	1.92999	0.0966205
$400$	0	0
$401$	2.58478	0.129078	0.0645388	−	0.997915i	$-0.479442\pi$
$401$	2.58478	0.129078	0.0645388	+	0.997915i	$0.479442\pi$
$402$	−49.5961	−2.47363
$403$	−3.88778	−0.193664
$404$	15.2368	0.758057
$405$	0	0
$406$	−101.544	−5.03956
$407$	−0.0106183	−0.000526330 0
$408$	−16.7644	−0.829960
$409$	−5.89731	−0.291603	−0.145802	−	0.989314i	$-0.546576\pi$
$409$	−5.89731	−0.291603	−0.145802	+	0.989314i	$0.546576\pi$
$410$	0	0
$411$	34.2356	1.68872
$412$	−1.95077	−0.0961076
$413$	−47.2323	−2.32415
$414$	−43.7419	−2.14980
$415$	0	0
$416$	13.3653	0.655290
$417$	−4.04498	−0.198083
$418$	−0.000679360 0	−3.32286e−5 0
$419$	12.8095	0.625785	0.312893	−	0.949788i	$-0.398702\pi$
$419$	12.8095	0.625785	0.312893	+	0.949788i	$0.398702\pi$
$420$	0	0
$421$	−12.3651	−0.602639	−0.301320	−	0.953523i	$-0.597427\pi$
$421$	−12.3651	−0.602639	−0.301320	+	0.953523i	$0.597427\pi$
$422$	58.3916	2.84246
$423$	34.4371	1.67439
$424$	22.3268	1.08429
$425$	0	0
$426$	69.5647	3.37042
$427$	−25.6163	−1.23966
$428$	12.8959	0.623346
$429$	−0.0137492	−0.000663816 0
$430$	0	0
$431$	−14.4278	−0.694962	−0.347481	−	0.937687i	$-0.612963\pi$
$431$	−14.4278	−0.694962	−0.347481	+	0.937687i	$0.612963\pi$
$432$	0.253132	0.0121788
$433$	−14.2643	−0.685498	−0.342749	−	0.939427i	$-0.611358\pi$
$433$	−14.2643	−0.685498	−0.342749	+	0.939427i	$0.611358\pi$
$434$	−10.6191	−0.509731
$435$	0	0
$436$	−30.8191	−1.47597
$437$	−1.13048	−0.0540781
$438$	−42.2727	−2.01987
$439$	3.79363	0.181060	0.0905299	−	0.995894i	$-0.471144\pi$
$439$	3.79363	0.181060	0.0905299	+	0.995894i	$0.471144\pi$
$440$	0	0
$441$	32.4626	1.54584
$442$	−15.7942	−0.751255
$443$	7.25201	0.344553	0.172277	−	0.985049i	$-0.444888\pi$
$443$	7.25201	0.344553	0.172277	+	0.985049i	$0.444888\pi$
$444$	60.3865	2.86582
$445$	0	0
$446$	−44.7420	−2.11860
$447$	4.01189	0.189756
$448$	49.5487	2.34096
$449$	26.1238	1.23286	0.616430	−	0.787410i	$-0.288578\pi$
$449$	26.1238	1.23286	0.616430	+	0.787410i	$0.288578\pi$
$450$	0	0
$451$	0.0110278	0.000519278 0
$452$	37.6300	1.76996
$453$	49.9193	2.34541
$454$	−5.68392	−0.266760
$455$	0	0
$456$	1.69317	0.0792901
$457$	−22.4610	−1.05068	−0.525340	−	0.850892i	$-0.676062\pi$
$457$	−22.4610	−1.05068	−0.525340	+	0.850892i	$0.676062\pi$
$458$	−7.22894	−0.337786
$459$	0.301160	0.0140569
$460$	0	0
$461$	−3.17158	−0.147715	−0.0738575	−	0.997269i	$-0.523531\pi$
$461$	−3.17158	−0.147715	−0.0738575	+	0.997269i	$0.523531\pi$
$462$	−0.0375544	−0.00174719
$463$	9.01797	0.419101	0.209550	−	0.977798i	$-0.432800\pi$
$463$	9.01797	0.419101	0.209550	+	0.977798i	$0.432800\pi$
$464$	−15.9675	−0.741273
$465$	0	0
$466$	−39.7175	−1.83988
$467$	−9.43147	−0.436436	−0.218218	−	0.975900i	$-0.570024\pi$
$467$	−9.43147	−0.436436	−0.218218	+	0.975900i	$0.570024\pi$
$468$	39.5218	1.82689
$469$	−35.8136	−1.65372
$470$	0	0
$471$	−7.46951	−0.344177
$472$	−41.4367	−1.90728
$473$	0.0116237	0.000534459 0
$474$	−85.5535	−3.92960
$475$	0	0
$476$	−27.6230	−1.26610
$477$	−18.6064	−0.851930
$478$	11.8798	0.543371
$479$	17.3967	0.794877	0.397439	−	0.917629i	$-0.369899\pi$
$479$	17.3967	0.794877	0.397439	+	0.917629i	$0.369899\pi$
$480$	0	0
$481$	24.9327	1.13683
$482$	−2.35802	−0.107405
$483$	−62.4917	−2.84347
$484$	−39.1630	−1.78014
$485$	0	0
$486$	52.2438	2.36982
$487$	24.7592	1.12195	0.560974	−	0.827833i	$-0.310427\pi$
$487$	24.7592	1.12195	0.560974	+	0.827833i	$0.310427\pi$
$488$	−22.4730	−1.01731
$489$	−0.761550	−0.0344385
$490$	0	0
$491$	12.9015	0.582237	0.291118	−	0.956687i	$-0.405973\pi$
$491$	12.9015	0.582237	0.291118	+	0.956687i	$0.405973\pi$
$492$	−62.7151	−2.82742
$493$	−18.9971	−0.855586
$494$	1.59519	0.0717711
$495$	0	0
$496$	−1.66981	−0.0749767
$497$	50.2331	2.25326
$498$	−6.73293	−0.301710
$499$	−3.00341	−0.134451	−0.0672256	−	0.997738i	$-0.521415\pi$
$499$	−3.00341	−0.134451	−0.0672256	+	0.997738i	$0.521415\pi$
$500$	0	0
$501$	−7.41788	−0.331406
$502$	14.8358	0.662155
$503$	40.7134	1.81532	0.907660	−	0.419706i	$-0.137867\pi$
$503$	40.7134	1.81532	0.907660	+	0.419706i	$0.137867\pi$
$504$	47.3084	2.10728
$505$	0	0
$506$	0.0219972	0.000977893 0
$507$	0.265891	0.0118086
$508$	−65.6064	−2.91081
$509$	−13.8707	−0.614808	−0.307404	−	0.951579i	$-0.599460\pi$
$509$	−13.8707	−0.614808	−0.307404	+	0.951579i	$0.599460\pi$
$510$	0	0
$511$	−30.5254	−1.35036
$512$	17.1827	0.759376
$513$	−0.0304166	−0.00134293
$514$	−23.6202	−1.04184
$515$	0	0
$516$	−66.1042	−2.91007
$517$	−0.0173179	−0.000761641 0
$518$	68.1010	2.99218
$519$	23.6307	1.03727
$520$	0	0
$521$	39.8224	1.74465	0.872325	−	0.488926i	$-0.162611\pi$
$521$	39.8224	1.74465	0.872325	+	0.488926i	$0.162611\pi$
$522$	74.2399	3.24939
$523$	13.1463	0.574846	0.287423	−	0.957804i	$-0.407201\pi$
$523$	13.1463	0.574846	0.287423	+	0.957804i	$0.407201\pi$
$524$	−2.36531	−0.103329
$525$	0	0
$526$	−62.2774	−2.71542
$527$	−1.98663	−0.0865390
$528$	−0.00590530	−0.000256995 0
$529$	13.6040	0.591478
$530$	0	0
$531$	34.5319	1.49856
$532$	2.78988	0.120956
$533$	−25.8942	−1.12160
$534$	−43.2819	−1.87299
$535$	0	0
$536$	−31.4191	−1.35710
$537$	38.8779	1.67770
$538$	−14.0272	−0.604755
$539$	−0.0163250	−0.000703167 0
$540$	0	0
$541$	24.2833	1.04402	0.522010	−	0.852940i	$-0.325182\pi$
$541$	24.2833	1.04402	0.522010	+	0.852940i	$0.325182\pi$
$542$	−17.3447	−0.745020
$543$	60.9457	2.61543
$544$	6.82961	0.292817
$545$	0	0
$546$	88.1807	3.77379
$547$	16.5651	0.708274	0.354137	−	0.935194i	$-0.384775\pi$
$547$	16.5651	0.708274	0.354137	+	0.935194i	$0.384775\pi$
$548$	49.4889	2.11406
$549$	18.7283	0.799304
$550$	0	0
$551$	1.91868	0.0817383
$552$	−54.8237	−2.33345
$553$	−61.7787	−2.62710
$554$	−25.7857	−1.09553
$555$	0	0
$556$	−5.84716	−0.247975
$557$	−32.4555	−1.37518	−0.687592	−	0.726098i	$-0.741332\pi$
$557$	−32.4555	−1.37518	−0.687592	+	0.726098i	$0.741332\pi$
$558$	7.76368	0.328663
$559$	−27.2934	−1.15439
$560$	0	0
$561$	−0.00702574	−0.000296627 0
$562$	−52.8150	−2.22787
$563$	46.5540	1.96202	0.981010	−	0.193959i	$-0.0621329\pi$
$563$	46.5540	1.96202	0.981010	+	0.193959i	$0.0621329\pi$
$564$	98.4872	4.14706
$565$	0	0
$566$	−9.29253	−0.390594
$567$	36.8940	1.54940
$568$	44.0692	1.84910
$569$	−16.0302	−0.672021	−0.336011	−	0.941858i	$-0.609078\pi$
$569$	−16.0302	−0.672021	−0.336011	+	0.941858i	$0.609078\pi$
$570$	0	0
$571$	−29.5009	−1.23457	−0.617286	−	0.786739i	$-0.711768\pi$
$571$	−29.5009	−1.23457	−0.617286	+	0.786739i	$0.711768\pi$
$572$	−0.0198749	−0.000831012 0
$573$	−35.1474	−1.46830
$574$	−70.7271	−2.95209
$575$	0	0
$576$	−36.2255	−1.50939
$577$	−42.8540	−1.78403	−0.892017	−	0.452001i	$-0.850710\pi$
$577$	−42.8540	−1.78403	−0.892017	+	0.452001i	$0.850710\pi$
$578$	32.0156	1.33168
$579$	34.7704	1.44501
$580$	0	0
$581$	−4.86189	−0.201705
$582$	48.1611	1.99634
$583$	0.00935690	0.000387523 0
$584$	−26.7798	−1.10815
$585$	0	0
$586$	9.36329	0.386794
$587$	38.4588	1.58736	0.793682	−	0.608333i	$-0.208162\pi$
$587$	38.4588	1.58736	0.793682	+	0.608333i	$0.208162\pi$
$588$	92.8403	3.82867
$589$	0.200647	0.00826750
$590$	0	0
$591$	13.8530	0.569836
$592$	10.7087	0.440123
$593$	−12.9213	−0.530613	−0.265306	−	0.964164i	$-0.585473\pi$
$593$	−12.9213	−0.530613	−0.265306	+	0.964164i	$0.585473\pi$
$594$	0.000591856 0	2.42841e−5 0
$595$	0	0
$596$	5.79933	0.237550
$597$	−1.75531	−0.0718402
$598$	−51.6511	−2.11217
$599$	30.2590	1.23635	0.618176	−	0.786040i	$-0.287872\pi$
$599$	30.2590	1.23635	0.618176	+	0.786040i	$0.287872\pi$
$600$	0	0
$601$	1.10382	0.0450259	0.0225129	−	0.999747i	$-0.492833\pi$
$601$	1.10382	0.0450259	0.0225129	+	0.999747i	$0.492833\pi$
$602$	−74.5491	−3.03840
$603$	26.1836	1.06628
$604$	72.1601	2.93615
$605$	0	0
$606$	−24.8549	−1.00966
$607$	23.1761	0.940688	0.470344	−	0.882483i	$-0.344130\pi$
$607$	23.1761	0.940688	0.470344	+	0.882483i	$0.344130\pi$
$608$	−0.689779	−0.0279742
$609$	106.063	4.29787
$610$	0	0
$611$	40.6639	1.64509
$612$	20.1954	0.816350
$613$	−20.8980	−0.844062	−0.422031	−	0.906581i	$-0.638683\pi$
$613$	−20.8980	−0.844062	−0.422031	+	0.906581i	$0.638683\pi$
$614$	63.1939	2.55030
$615$	0	0
$616$	−0.0237907	−0.000958554 0
$617$	13.7563	0.553807	0.276904	−	0.960898i	$-0.410692\pi$
$617$	13.7563	0.553807	0.276904	+	0.960898i	$0.410692\pi$
$618$	3.18218	0.128006
$619$	26.6845	1.07254	0.536271	−	0.844046i	$-0.319833\pi$
$619$	26.6845	1.07254	0.536271	+	0.844046i	$0.319833\pi$
$620$	0	0
$621$	0.984868	0.0395214
$622$	−30.4835	−1.22228
$623$	−31.2541	−1.25217
$624$	13.8661	0.555089
$625$	0	0
$626$	−6.79798	−0.271702
$627$	0.000709588 0	2.83382e−5 0
$628$	−10.7975	−0.430865
$629$	12.7404	0.507995
$630$	0	0
$631$	−41.1680	−1.63887	−0.819436	−	0.573170i	$-0.805713\pi$
$631$	−41.1680	−1.63887	−0.819436	+	0.573170i	$0.805713\pi$
$632$	−54.1981	−2.15589
$633$	−60.9897	−2.42412
$634$	−54.0321	−2.14589
$635$	0	0
$636$	−53.2128	−2.11002
$637$	38.3324	1.51878
$638$	−0.0373342	−0.00147807
$639$	−36.7258	−1.45285
$640$	0	0
$641$	4.46482	0.176350	0.0881750	−	0.996105i	$-0.471897\pi$
$641$	4.46482	0.176350	0.0881750	+	0.996105i	$0.471897\pi$
$642$	−21.0363	−0.830238
$643$	−31.5481	−1.24414	−0.622068	−	0.782963i	$-0.713707\pi$
$643$	−31.5481	−1.24414	−0.622068	+	0.782963i	$0.713707\pi$
$644$	−90.3340	−3.55966
$645$	0	0
$646$	0.815134	0.0320710
$647$	34.2342	1.34588	0.672942	−	0.739695i	$-0.265030\pi$
$647$	34.2342	1.34588	0.672942	+	0.739695i	$0.265030\pi$
$648$	32.3669	1.27149
$649$	−0.0173656	−0.000681659 0
$650$	0	0
$651$	11.0916	0.434712
$652$	−1.10085	−0.0431125
$653$	−33.2389	−1.30074	−0.650369	−	0.759618i	$-0.725386\pi$
$653$	−33.2389	−1.30074	−0.650369	+	0.759618i	$0.725386\pi$
$654$	50.2735	1.96585
$655$	0	0
$656$	−11.1216	−0.434226
$657$	22.3174	0.870683
$658$	111.069	4.32992
$659$	−12.3196	−0.479903	−0.239951	−	0.970785i	$-0.577131\pi$
$659$	−12.3196	−0.479903	−0.239951	+	0.970785i	$0.577131\pi$
$660$	0	0
$661$	−26.6911	−1.03816	−0.519081	−	0.854725i	$-0.673726\pi$
$661$	−26.6911	−1.03816	−0.519081	+	0.854725i	$0.673726\pi$
$662$	27.0095	1.04975
$663$	16.4970	0.640691
$664$	−4.26531	−0.165526
$665$	0	0
$666$	−49.7892	−1.92929
$667$	−62.1253	−2.40550
$668$	−10.7228	−0.414878
$669$	46.7328	1.80680
$670$	0	0
$671$	−0.00941817	−0.000363585 0
$672$	−38.1303	−1.47091
$673$	11.4384	0.440917	0.220458	−	0.975396i	$-0.429245\pi$
$673$	11.4384	0.440917	0.220458	+	0.975396i	$0.429245\pi$
$674$	64.0494	2.46709
$675$	0	0
$676$	0.384355	0.0147829
$677$	−37.4103	−1.43780	−0.718898	−	0.695116i	$-0.755353\pi$
$677$	−37.4103	−1.43780	−0.718898	+	0.695116i	$0.755353\pi$
$678$	−61.3837	−2.35743
$679$	34.7774	1.33463
$680$	0	0
$681$	5.93683	0.227500
$682$	−0.00390424	−0.000149501 0
$683$	−27.7116	−1.06036	−0.530178	−	0.847886i	$-0.677875\pi$
$683$	−27.7116	−1.06036	−0.530178	+	0.847886i	$0.677875\pi$
$684$	−2.03970	−0.0779899
$685$	0	0
$686$	35.4780	1.35455
$687$	7.55059	0.288073
$688$	−11.7226	−0.446920
$689$	−21.9708	−0.837020
$690$	0	0
$691$	35.3711	1.34558	0.672790	−	0.739833i	$-0.265096\pi$
$691$	35.3711	1.34558	0.672790	+	0.739833i	$0.265096\pi$
$692$	34.1591	1.29853
$693$	0.0198264	0.000753141 0
$694$	79.4693	3.01661
$695$	0	0
$696$	93.0482	3.52698
$697$	−13.2318	−0.501188
$698$	−48.1686	−1.82321
$699$	41.4848	1.56910
$700$	0	0
$701$	8.60136	0.324869	0.162434	−	0.986719i	$-0.448065\pi$
$701$	8.60136	0.324869	0.162434	+	0.986719i	$0.448065\pi$
$702$	−1.38973	−0.0524518
$703$	−1.28676	−0.0485313
$704$	0.0182172	0.000686588 0
$705$	0	0
$706$	−78.6408	−2.95969
$707$	−17.9479	−0.674999
$708$	98.7583	3.71156
$709$	29.9089	1.12325	0.561626	−	0.827391i	$-0.310176\pi$
$709$	29.9089	1.12325	0.561626	+	0.827391i	$0.310176\pi$
$710$	0	0
$711$	45.1669	1.69389
$712$	−27.4191	−1.02757
$713$	−6.49678	−0.243306
$714$	45.0598	1.68632
$715$	0	0
$716$	56.1994	2.10027
$717$	−12.4084	−0.463402
$718$	−61.3244	−2.28861
$719$	40.9172	1.52595	0.762976	−	0.646426i	$-0.223737\pi$
$719$	40.9172	1.52595	0.762976	+	0.646426i	$0.223737\pi$
$720$	0	0
$721$	2.29787	0.0855773
$722$	44.7201	1.66431
$723$	2.46294	0.0915979
$724$	88.0993	3.27418
$725$	0	0
$726$	63.8845	2.37098
$727$	−16.6451	−0.617332	−0.308666	−	0.951170i	$-0.599883\pi$
$727$	−16.6451	−0.617332	−0.308666	+	0.951170i	$0.599883\pi$
$728$	55.8625	2.07040
$729$	−28.1763	−1.04357
$730$	0	0
$731$	−13.9468	−0.515840
$732$	53.5612	1.97968
$733$	42.4805	1.56905	0.784526	−	0.620096i	$-0.212906\pi$
$733$	42.4805	1.56905	0.784526	+	0.620096i	$0.212906\pi$
$734$	−30.3293	−1.11947
$735$	0	0
$736$	22.3345	0.823262
$737$	−0.0131674	−0.000485026 0
$738$	51.7092	1.90344
$739$	14.8301	0.545535	0.272767	−	0.962080i	$-0.412061\pi$
$739$	14.8301	0.545535	0.272767	+	0.962080i	$0.412061\pi$
$740$	0	0
$741$	−1.66617	−0.0612083
$742$	−60.0108	−2.20307
$743$	19.6188	0.719745	0.359872	−	0.933002i	$-0.382820\pi$
$743$	19.6188	0.719745	0.359872	+	0.933002i	$0.382820\pi$
$744$	9.73057	0.356740
$745$	0	0
$746$	10.0974	0.369691
$747$	3.55457	0.130055
$748$	−0.0101560	−0.000371339 0
$749$	−15.1905	−0.555047
$750$	0	0
$751$	−31.1590	−1.13701	−0.568504	−	0.822681i	$-0.692477\pi$
$751$	−31.1590	−1.13701	−0.568504	+	0.822681i	$0.692477\pi$
$752$	17.4652	0.636892
$753$	−15.4959	−0.564704
$754$	87.6637	3.19252
$755$	0	0
$756$	−2.43053	−0.0883975
$757$	9.09230	0.330465	0.165233	−	0.986255i	$-0.447163\pi$
$757$	9.09230	0.330465	0.165233	+	0.986255i	$0.447163\pi$
$758$	−34.3176	−1.24647
$759$	−0.0229759	−0.000833973 0
$760$	0	0
$761$	40.7603	1.47756	0.738780	−	0.673947i	$-0.235402\pi$
$761$	40.7603	1.47756	0.738780	+	0.673947i	$0.235402\pi$
$762$	107.020	3.87693
$763$	36.3028	1.31425
$764$	−50.8068	−1.83813
$765$	0	0
$766$	31.2063	1.12753
$767$	40.7758	1.47233
$768$	−60.7226	−2.19114
$769$	37.9586	1.36882	0.684410	−	0.729097i	$-0.260060\pi$
$769$	37.9586	1.36882	0.684410	+	0.729097i	$0.260060\pi$
$770$	0	0
$771$	24.6712	0.888511
$772$	50.2619	1.80896
$773$	−24.6640	−0.887102	−0.443551	−	0.896249i	$-0.646281\pi$
$773$	−24.6640	−0.887102	−0.443551	+	0.896249i	$0.646281\pi$
$774$	54.5035	1.95909
$775$	0	0
$776$	30.5100	1.09525
$777$	−71.1311	−2.55181
$778$	−17.9263	−0.642690
$779$	1.33639	0.0478810
$780$	0	0
$781$	0.0184689	0.000660868 0
$782$	−26.3934	−0.943826
$783$	−1.67154	−0.0597361
$784$	16.4639	0.587995
$785$	0	0
$786$	3.85840	0.137624
$787$	−1.46627	−0.0522669	−0.0261334	−	0.999658i	$-0.508319\pi$
$787$	−1.46627	−0.0522669	−0.0261334	+	0.999658i	$0.508319\pi$
$788$	20.0250	0.713361
$789$	65.0485	2.31579
$790$	0	0
$791$	−44.3255	−1.57603
$792$	0.0173936	0.000618054 0
$793$	22.1146	0.785314
$794$	−53.7144	−1.90625
$795$	0	0
$796$	−2.53737	−0.0899347
$797$	4.18600	0.148276	0.0741379	−	0.997248i	$-0.476379\pi$
$797$	4.18600	0.148276	0.0741379	+	0.997248i	$0.476379\pi$
$798$	−4.55097	−0.161103
$799$	20.7790	0.735108
$800$	0	0
$801$	22.8502	0.807371
$802$	−6.09497	−0.215221
$803$	−0.0112231	−0.000396053 0
$804$	74.8829	2.64092
$805$	0	0
$806$	9.16748	0.322911
$807$	14.6513	0.515751
$808$	−15.7456	−0.553927
$809$	−35.8943	−1.26197	−0.630987	−	0.775793i	$-0.717350\pi$
$809$	−35.8943	−1.26197	−0.630987	+	0.775793i	$0.717350\pi$
$810$	0	0
$811$	−5.70034	−0.200166	−0.100083	−	0.994979i	$-0.531911\pi$
$811$	−5.70034	−0.200166	−0.100083	+	0.994979i	$0.531911\pi$
$812$	153.317	5.38038
$813$	18.1165	0.635373
$814$	0.0250382	0.000877590 0
$815$	0	0
$816$	7.08551	0.248042
$817$	1.40860	0.0492808
$818$	13.9060	0.486212
$819$	−46.5539	−1.62673
$820$	0	0
$821$	−16.8466	−0.587949	−0.293975	−	0.955813i	$-0.594978\pi$
$821$	−16.8466	−0.587949	−0.293975	+	0.955813i	$0.594978\pi$
$822$	−80.7284	−2.81573
$823$	50.2558	1.75181	0.875904	−	0.482486i	$-0.160266\pi$
$823$	50.2558	1.75181	0.875904	+	0.482486i	$0.160266\pi$
$824$	2.01591	0.0702277
$825$	0	0
$826$	111.375	3.87523
$827$	43.8440	1.52460	0.762302	−	0.647221i	$-0.224069\pi$
$827$	43.8440	1.52460	0.762302	+	0.647221i	$0.224069\pi$
$828$	66.0440	2.29519
$829$	−41.3116	−1.43481	−0.717406	−	0.696655i	$-0.754671\pi$
$829$	−41.3116	−1.43481	−0.717406	+	0.696655i	$0.754671\pi$
$830$	0	0
$831$	26.9330	0.934295
$832$	−42.7756	−1.48298
$833$	19.5876	0.678671
$834$	9.53815	0.330279
$835$	0	0
$836$	0.00102574	3.54758e−5 0
$837$	−0.174803	−0.00604206
$838$	−30.2051	−1.04342
$839$	−21.2296	−0.732926	−0.366463	−	0.930433i	$-0.619431\pi$
$839$	−21.2296	−0.732926	−0.366463	+	0.930433i	$0.619431\pi$
$840$	0	0
$841$	76.4406	2.63588
$842$	29.1573	1.00483
$843$	55.1651	1.89999
$844$	−88.1629	−3.03469
$845$	0	0
$846$	−81.2036	−2.79184
$847$	46.1314	1.58509
$848$	−9.43650	−0.324051
$849$	9.70600	0.333109
$850$	0	0
$851$	41.6645	1.42824
$852$	−105.033	−3.59836
$853$	−33.2081	−1.13702	−0.568512	−	0.822675i	$-0.692481\pi$
$853$	−33.2081	−1.13702	−0.568512	+	0.822675i	$0.692481\pi$
$854$	60.4038	2.06698
$855$	0	0
$856$	−13.3265	−0.455491
$857$	32.7448	1.11854	0.559270	−	0.828985i	$-0.311081\pi$
$857$	32.7448	1.11854	0.559270	+	0.828985i	$0.311081\pi$
$858$	0.0324208	0.00110683
$859$	−38.4663	−1.31245	−0.656226	−	0.754564i	$-0.727848\pi$
$859$	−38.4663	−1.31245	−0.656226	+	0.754564i	$0.727848\pi$
$860$	0	0
$861$	73.8741	2.51762
$862$	34.0211	1.15876
$863$	−7.69517	−0.261946	−0.130973	−	0.991386i	$-0.541810\pi$
$863$	−7.69517	−0.261946	−0.130973	+	0.991386i	$0.541810\pi$
$864$	0.600933	0.0204442
$865$	0	0
$866$	33.6355	1.14298
$867$	−33.4402	−1.13569
$868$	16.0332	0.544204
$869$	−0.0227138	−0.000770512 0
$870$	0	0
$871$	30.9181	1.04762
$872$	31.8483	1.07852
$873$	−25.4261	−0.860541
$874$	2.66569	0.0901684
$875$	0	0
$876$	63.8257	2.15647
$877$	−39.4975	−1.33374	−0.666868	−	0.745176i	$-0.732365\pi$
$877$	−39.4975	−1.33374	−0.666868	+	0.745176i	$0.732365\pi$
$878$	−8.94546	−0.301895
$879$	−9.77991	−0.329868
$880$	0	0
$881$	−46.9657	−1.58232	−0.791158	−	0.611612i	$-0.790522\pi$
$881$	−46.9657	−1.58232	−0.791158	+	0.611612i	$0.790522\pi$
$882$	−76.5477	−2.57749
$883$	−39.3728	−1.32500	−0.662500	−	0.749062i	$-0.730505\pi$
$883$	−39.3728	−1.32500	−0.662500	+	0.749062i	$0.730505\pi$
$884$	23.8470	0.802062
$885$	0	0
$886$	−17.1004	−0.574499
$887$	14.3545	0.481977	0.240989	−	0.970528i	$-0.422528\pi$
$887$	14.3545	0.481977	0.240989	+	0.970528i	$0.422528\pi$
$888$	−62.4030	−2.09411
$889$	77.2798	2.59188
$890$	0	0
$891$	0.0135646	0.000454430 0
$892$	67.5540	2.26188
$893$	−2.09865	−0.0702285
$894$	−9.46012	−0.316394
$895$	0	0
$896$	−85.8737	−2.86884
$897$	53.9494	1.80132
$898$	−61.6006	−2.05564
$899$	11.0265	0.367755
$900$	0	0
$901$	−11.2269	−0.374023
$902$	−0.0260038	−0.000865831 0
$903$	77.8662	2.59122
$904$	−38.8866	−1.29335
$905$	0	0
$906$	−117.711	−3.91068
$907$	−47.8647	−1.58932	−0.794660	−	0.607054i	$-0.792351\pi$
$907$	−47.8647	−1.58932	−0.794660	+	0.607054i	$0.792351\pi$
$908$	8.58190	0.284800
$909$	13.1218	0.435224
$910$	0	0
$911$	−16.5237	−0.547454	−0.273727	−	0.961807i	$-0.588257\pi$
$911$	−16.5237	−0.547454	−0.273727	+	0.961807i	$0.588257\pi$
$912$	−0.715625	−0.0236967
$913$	−0.00178754	−5.91589e−5 0
$914$	52.9635	1.75188
$915$	0	0
$916$	10.9147	0.360630
$917$	2.78617	0.0920075
$918$	−0.710141	−0.0234382
$919$	−0.344362	−0.0113595	−0.00567973	−	0.999984i	$-0.501808\pi$
$919$	−0.344362	−0.0113595	−0.00567973	+	0.999984i	$0.501808\pi$
$920$	0	0
$921$	−66.0057	−2.17496
$922$	7.47865	0.246296
$923$	−43.3664	−1.42742
$924$	0.0567017	0.00186535
$925$	0	0
$926$	−21.2646	−0.698798
$927$	−1.67999	−0.0551783
$928$	−37.9067	−1.24435
$929$	24.3956	0.800393	0.400196	−	0.916429i	$-0.368942\pi$
$929$	24.3956	0.800393	0.400196	+	0.916429i	$0.368942\pi$
$930$	0	0
$931$	−1.97832	−0.0648368
$932$	59.9678	1.96431
$933$	31.8399	1.04239
$934$	22.2396	0.727703
$935$	0	0
$936$	−40.8416	−1.33495
$937$	−49.5373	−1.61831	−0.809157	−	0.587593i	$-0.800076\pi$
$937$	−49.5373	−1.61831	−0.809157	+	0.587593i	$0.800076\pi$
$938$	84.4494	2.75737
$939$	7.10045	0.231715
$940$	0	0
$941$	−16.5851	−0.540658	−0.270329	−	0.962768i	$-0.587132\pi$
$941$	−16.5851	−0.540658	−0.270329	+	0.962768i	$0.587132\pi$
$942$	17.6133	0.573872
$943$	−43.2712	−1.40910
$944$	17.5133	0.570010
$945$	0	0
$946$	−0.0274090	−0.000891143 0
$947$	32.9410	1.07044	0.535220	−	0.844713i	$-0.320229\pi$
$947$	32.9410	1.07044	0.535220	+	0.844713i	$0.320229\pi$
$948$	129.173	4.19536
$949$	26.3527	0.855444
$950$	0	0
$951$	56.4362	1.83007
$952$	28.5454	0.925162
$953$	−32.0378	−1.03781	−0.518903	−	0.854833i	$-0.673660\pi$
$953$	−32.0378	−1.03781	−0.518903	+	0.854833i	$0.673660\pi$
$954$	43.8744	1.42049
$955$	0	0
$956$	−17.9369	−0.580119
$957$	0.0389953	0.00126054
$958$	−41.0219	−1.32536
$959$	−58.2945	−1.88243
$960$	0	0
$961$	−29.8469	−0.962803
$962$	−58.7919	−1.89553
$963$	11.1059	0.357882
$964$	3.56028	0.114669
$965$	0	0
$966$	147.357	4.74113
$967$	−12.8127	−0.412029	−0.206015	−	0.978549i	$-0.566049\pi$
$967$	−12.8127	−0.412029	−0.206015	+	0.978549i	$0.566049\pi$
$968$	40.4708	1.30078
$969$	−0.851403	−0.0273510
$970$	0	0
$971$	34.3395	1.10201	0.551003	−	0.834503i	$-0.314245\pi$
$971$	34.3395	1.10201	0.551003	+	0.834503i	$0.314245\pi$
$972$	−78.8805	−2.53009
$973$	6.88756	0.220805
$974$	−58.3829	−1.87071
$975$	0	0
$976$	9.49830	0.304033
$977$	−24.3574	−0.779261	−0.389631	−	0.920971i	$-0.627397\pi$
$977$	−24.3574	−0.779261	−0.389631	+	0.920971i	$0.627397\pi$
$978$	1.79575	0.0574219
$979$	−0.0114910	−0.000367254 0
$980$	0	0
$981$	−26.5413	−0.847398
$982$	−30.4220	−0.970807
$983$	−11.9684	−0.381732	−0.190866	−	0.981616i	$-0.561130\pi$
$983$	−11.9684	−0.381732	−0.190866	+	0.981616i	$0.561130\pi$
$984$	64.8094	2.06605
$985$	0	0
$986$	44.7956	1.42658
$987$	−116.011	−3.69267
$988$	−2.40851	−0.0766250
$989$	−45.6095	−1.45030
$990$	0	0
$991$	−7.24060	−0.230005	−0.115003	−	0.993365i	$-0.536688\pi$
$991$	−7.24060	−0.230005	−0.115003	+	0.993365i	$0.536688\pi$
$992$	−3.96412	−0.125861
$993$	−28.2113	−0.895258
$994$	−118.451	−3.75703
$995$	0	0
$996$	10.1658	0.322114
$997$	−45.8570	−1.45230	−0.726152	−	0.687534i	$-0.758693\pi$
$997$	−45.8570	−1.45230	−0.726152	+	0.687534i	$0.758693\pi$
$998$	7.08212	0.224181
$999$	1.12102	0.0354676

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.n.1.3	yes	40
5.4	even	2		6025.2.a.m.1.38	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.m.1.38	✓	40	5.4	even	2
6025.2.a.n.1.3	yes	40	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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.35802 q^{2} +2.46294 q^{3} +3.56028 q^{4} -5.80768 q^{6} -4.19376 q^{7} -3.67917 q^{8} +3.06609 q^{9} +O(q^{10})\)	\(q-2.35802 q^{2} +2.46294 q^{3} +3.56028 q^{4} -5.80768 q^{6} -4.19376 q^{7} -3.67917 q^{8} +3.06609 q^{9} -0.00154189 q^{11} +8.76876 q^{12} +3.62049 q^{13} +9.88899 q^{14} +1.55501 q^{16} +1.85005 q^{17} -7.22992 q^{18} -0.186852 q^{19} -10.3290 q^{21} +0.00363582 q^{22} +6.05012 q^{23} -9.06158 q^{24} -8.53720 q^{26} +0.162785 q^{27} -14.9309 q^{28} -10.2684 q^{29} -1.07383 q^{31} +3.69158 q^{32} -0.00379760 q^{33} -4.36246 q^{34} +10.9161 q^{36} +6.88655 q^{37} +0.440601 q^{38} +8.91707 q^{39} -7.15211 q^{41} +24.3560 q^{42} -7.53860 q^{43} -0.00548956 q^{44} -14.2663 q^{46} +11.2316 q^{47} +3.82990 q^{48} +10.5876 q^{49} +4.55657 q^{51} +12.8899 q^{52} -6.06845 q^{53} -0.383850 q^{54} +15.4295 q^{56} -0.460206 q^{57} +24.2132 q^{58} +11.2625 q^{59} +6.10819 q^{61} +2.53211 q^{62} -12.8585 q^{63} -11.8149 q^{64} +0.00895482 q^{66} +8.53974 q^{67} +6.58668 q^{68} +14.9011 q^{69} -11.9780 q^{71} -11.2807 q^{72} +7.27876 q^{73} -16.2386 q^{74} -0.665244 q^{76} +0.00646633 q^{77} -21.0267 q^{78} +14.7311 q^{79} -8.79735 q^{81} +16.8648 q^{82} +1.15932 q^{83} -36.7741 q^{84} +17.7762 q^{86} -25.2906 q^{87} +0.00567288 q^{88} +7.45253 q^{89} -15.1835 q^{91} +21.5401 q^{92} -2.64477 q^{93} -26.4844 q^{94} +9.09216 q^{96} -8.29265 q^{97} -24.9659 q^{98} -0.00472759 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9	\( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9} + q^{11} + 26 q^{12} + 11 q^{13} - q^{14} + 43 q^{16} + 20 q^{17} + 18 q^{18} + 2 q^{21} + 23 q^{22} + 79 q^{23} - 2 q^{24} + 2 q^{26} + 26 q^{27} + 30 q^{28} + 2 q^{29} + q^{31} + 68 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 16 q^{37} + 45 q^{38} - 2 q^{39} - 2 q^{41} + 19 q^{42} + 25 q^{43} + 3 q^{44} + 14 q^{46} + 88 q^{47} + 75 q^{48} + 40 q^{49} - 10 q^{51} + 18 q^{52} + 34 q^{53} + 4 q^{54} - 15 q^{56} + 51 q^{57} + 53 q^{58} + q^{59} + 9 q^{61} + 39 q^{62} + 110 q^{63} + 17 q^{64} + 26 q^{66} + 30 q^{67} + 44 q^{68} - 7 q^{69} + 5 q^{71} + 18 q^{72} + 23 q^{73} - 18 q^{74} + 43 q^{76} + 30 q^{77} + 46 q^{78} + 5 q^{79} + 44 q^{81} + 5 q^{82} + 65 q^{83} - 65 q^{84} + 40 q^{86} + 33 q^{87} + 71 q^{88} - 9 q^{89} + q^{91} + 117 q^{92} + 68 q^{93} - 72 q^{94} + 83 q^{96} - 8 q^{97} + 76 q^{98} - 40 q^{99}+O(q^{100}) \) 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9 + q^11 + 26 * q^12 + 11 * q^13 - q^14 + 43 * q^16 + 20 * q^17 + 18 * q^18 + 2 * q^21 + 23 * q^22 + 79 * q^23 - 2 * q^24 + 2 * q^26 + 26 * q^27 + 30 * q^28 + 2 * q^29 + q^31 + 68 * q^32 + 20 * q^33 + 5 * q^34 + 32 * q^36 + 16 * q^37 + 45 * q^38 - 2 * q^39 - 2 * q^41 + 19 * q^42 + 25 * q^43 + 3 * q^44 + 14 * q^46 + 88 * q^47 + 75 * q^48 + 40 * q^49 - 10 * q^51 + 18 * q^52 + 34 * q^53 + 4 * q^54 - 15 * q^56 + 51 * q^57 + 53 * q^58 + q^59 + 9 * q^61 + 39 * q^62 + 110 * q^63 + 17 * q^64 + 26 * q^66 + 30 * q^67 + 44 * q^68 - 7 * q^69 + 5 * q^71 + 18 * q^72 + 23 * q^73 - 18 * q^74 + 43 * q^76 + 30 * q^77 + 46 * q^78 + 5 * q^79 + 44 * q^81 + 5 * q^82 + 65 * q^83 - 65 * q^84 + 40 * q^86 + 33 * q^87 + 71 * q^88 - 9 * q^89 + q^91 + 117 * q^92 + 68 * q^93 - 72 * q^94 + 83 * q^96 - 8 * q^97 + 76 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

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