LMFDB - Embedded newform 6025.2.a.j.1.15

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:	$1$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q+0.0694400 q^{2} +2.28670 q^{3} -1.99518 q^{4} +0.158789 q^{6} -0.976003 q^{7} -0.277425 q^{8} +2.22902 q^{9} +O(q^{10})$	\(q+0.0694400 q^{2} +2.28670 q^{3} -1.99518 q^{4} +0.158789 q^{6} -0.976003 q^{7} -0.277425 q^{8} +2.22902 q^{9} +0.634315 q^{11} -4.56238 q^{12} +1.72293 q^{13} -0.0677737 q^{14} +3.97109 q^{16} +3.57240 q^{17} +0.154783 q^{18} -8.41472 q^{19} -2.23183 q^{21} +0.0440468 q^{22} -3.47484 q^{23} -0.634389 q^{24} +0.119641 q^{26} -1.76301 q^{27} +1.94730 q^{28} -5.33815 q^{29} +2.47454 q^{31} +0.830603 q^{32} +1.45049 q^{33} +0.248067 q^{34} -4.44729 q^{36} +3.69225 q^{37} -0.584318 q^{38} +3.93984 q^{39} +8.97339 q^{41} -0.154978 q^{42} -9.17725 q^{43} -1.26557 q^{44} -0.241293 q^{46} +5.13597 q^{47} +9.08071 q^{48} -6.04742 q^{49} +8.16902 q^{51} -3.43756 q^{52} -7.54486 q^{53} -0.122423 q^{54} +0.270768 q^{56} -19.2420 q^{57} -0.370681 q^{58} +14.0018 q^{59} +8.35758 q^{61} +0.171832 q^{62} -2.17553 q^{63} -7.88451 q^{64} +0.100722 q^{66} -11.8979 q^{67} -7.12757 q^{68} -7.94594 q^{69} -6.10073 q^{71} -0.618386 q^{72} -9.09745 q^{73} +0.256390 q^{74} +16.7889 q^{76} -0.619094 q^{77} +0.273583 q^{78} -12.5062 q^{79} -10.7185 q^{81} +0.623112 q^{82} -14.3752 q^{83} +4.45290 q^{84} -0.637268 q^{86} -12.2068 q^{87} -0.175975 q^{88} +12.5612 q^{89} -1.68159 q^{91} +6.93293 q^{92} +5.65855 q^{93} +0.356642 q^{94} +1.89934 q^{96} -1.27290 q^{97} -0.419932 q^{98} +1.41390 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9}+O(q^{10}) $ 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9	$ 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9} + 2 q^{11} - 20 q^{12} - 14 q^{13} - 5 q^{14} + 38 q^{16} - 7 q^{17} - 9 q^{18} + 30 q^{19} + q^{21} - q^{22} - 43 q^{23} - 6 q^{24} - 22 q^{26} - 42 q^{27} - 32 q^{28} - 4 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} + 7 q^{34} + 15 q^{36} - 16 q^{37} - 14 q^{38} - 21 q^{39} - q^{41} + 25 q^{42} - 35 q^{43} - 52 q^{44} - 27 q^{46} - 50 q^{47} - 26 q^{48} + 46 q^{49} - 7 q^{51} - 3 q^{52} - 4 q^{53} - 31 q^{54} - 51 q^{56} - 2 q^{58} + 6 q^{59} + 19 q^{61} - 28 q^{63} + 49 q^{64} - 27 q^{66} - 65 q^{67} + 25 q^{68} + 2 q^{69} - 34 q^{71} + 10 q^{72} - 8 q^{73} - 42 q^{74} + 71 q^{76} - q^{77} + 59 q^{78} - 12 q^{79} + 29 q^{81} - 11 q^{82} - 41 q^{83} - 10 q^{84} - 13 q^{86} - 40 q^{87} + 52 q^{88} - 24 q^{89} + 46 q^{91} - 85 q^{92} + 30 q^{93} + 14 q^{94} - 30 q^{96} - 9 q^{97} + 64 q^{98} + 2 q^{99}+O(q^{100}) $ 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9 + 2 * q^11 - 20 * q^12 - 14 * q^13 - 5 * q^14 + 38 * q^16 - 7 * q^17 - 9 * q^18 + 30 * q^19 + q^21 - q^22 - 43 * q^23 - 6 * q^24 - 22 * q^26 - 42 * q^27 - 32 * q^28 - 4 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 + 7 * q^34 + 15 * q^36 - 16 * q^37 - 14 * q^38 - 21 * q^39 - q^41 + 25 * q^42 - 35 * q^43 - 52 * q^44 - 27 * q^46 - 50 * q^47 - 26 * q^48 + 46 * q^49 - 7 * q^51 - 3 * q^52 - 4 * q^53 - 31 * q^54 - 51 * q^56 - 2 * q^58 + 6 * q^59 + 19 * q^61 - 28 * q^63 + 49 * q^64 - 27 * q^66 - 65 * q^67 + 25 * q^68 + 2 * q^69 - 34 * q^71 + 10 * q^72 - 8 * q^73 - 42 * q^74 + 71 * q^76 - q^77 + 59 * q^78 - 12 * q^79 + 29 * q^81 - 11 * q^82 - 41 * q^83 - 10 * q^84 - 13 * q^86 - 40 * q^87 + 52 * q^88 - 24 * q^89 + 46 * q^91 - 85 * q^92 + 30 * q^93 + 14 * q^94 - 30 * q^96 - 9 * q^97 + 64 * q^98 + 2 * 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 $

$2$	0.0694400	0.0491015	0.0245507	−	0.999699i	$-0.492184\pi$
$2$	0.0694400	0.0491015	0.0245507	+	0.999699i	$0.492184\pi$
$3$	2.28670	1.32023	0.660115	−	0.751165i	$-0.270508\pi$
$3$	2.28670	1.32023	0.660115	+	0.751165i	$0.270508\pi$
$4$	−1.99518	−0.997589
$5$	0	0
$5$	0	0
$6$	0.158789	0.0648252
$7$	−0.976003	−0.368895	−0.184447	−	0.982842i	$-0.559050\pi$
$7$	−0.976003	−0.368895	−0.184447	+	0.982842i	$0.559050\pi$
$8$	−0.277425	−0.0980846
$9$	2.22902	0.743006
$10$	0	0
$11$	0.634315	0.191253	0.0956266	−	0.995417i	$-0.469515\pi$
$11$	0.634315	0.191253	0.0956266	+	0.995417i	$0.469515\pi$
$12$	−4.56238	−1.31705
$13$	1.72293	0.477856	0.238928	−	0.971037i	$-0.423204\pi$
$13$	1.72293	0.477856	0.238928	+	0.971037i	$0.423204\pi$
$14$	−0.0677737	−0.0181133
$15$	0	0
$16$	3.97109	0.992773
$17$	3.57240	0.866434	0.433217	−	0.901290i	$-0.357378\pi$
$17$	3.57240	0.866434	0.433217	+	0.901290i	$0.357378\pi$
$18$	0.154783	0.0364827
$19$	−8.41472	−1.93047	−0.965235	−	0.261385i	$-0.915821\pi$
$19$	−8.41472	−1.93047	−0.965235	+	0.261385i	$0.915821\pi$
$20$	0	0
$21$	−2.23183	−0.487026
$22$	0.0440468	0.00939081
$23$	−3.47484	−0.724555	−0.362277	−	0.932070i	$-0.618001\pi$
$23$	−3.47484	−0.724555	−0.362277	+	0.932070i	$0.618001\pi$
$24$	−0.634389	−0.129494
$25$	0	0
$26$	0.119641	0.0234634
$27$	−1.76301	−0.339291
$28$	1.94730	0.368005
$29$	−5.33815	−0.991269	−0.495635	−	0.868531i	$-0.665065\pi$
$29$	−5.33815	−0.991269	−0.495635	+	0.868531i	$0.665065\pi$
$30$	0	0
$31$	2.47454	0.444441	0.222221	−	0.974996i	$-0.428670\pi$
$31$	2.47454	0.444441	0.222221	+	0.974996i	$0.428670\pi$
$32$	0.830603	0.146831
$33$	1.45049	0.252498
$34$	0.248067	0.0425432
$35$	0	0
$36$	−4.44729	−0.741215
$37$	3.69225	0.607002	0.303501	−	0.952831i	$-0.401844\pi$
$37$	3.69225	0.607002	0.303501	+	0.952831i	$0.401844\pi$
$38$	−0.584318	−0.0947889
$39$	3.93984	0.630880
$40$	0	0
$41$	8.97339	1.40141	0.700704	−	0.713452i	$-0.252869\pi$
$41$	8.97339	1.40141	0.700704	+	0.713452i	$0.252869\pi$
$42$	−0.154978	−0.0239137
$43$	−9.17725	−1.39952	−0.699759	−	0.714379i	$-0.746709\pi$
$43$	−9.17725	−1.39952	−0.699759	+	0.714379i	$0.746709\pi$
$44$	−1.26557	−0.190792
$45$	0	0
$46$	−0.241293	−0.0355767
$47$	5.13597	0.749159	0.374579	−	0.927195i	$-0.377787\pi$
$47$	5.13597	0.749159	0.374579	+	0.927195i	$0.377787\pi$
$48$	9.08071	1.31069
$49$	−6.04742	−0.863917
$50$	0	0
$51$	8.16902	1.14389
$52$	−3.43756	−0.476704
$53$	−7.54486	−1.03637	−0.518183	−	0.855270i	$-0.673392\pi$
$53$	−7.54486	−1.03637	−0.518183	+	0.855270i	$0.673392\pi$
$54$	−0.122423	−0.0166597
$55$	0	0
$56$	0.270768	0.0361829
$57$	−19.2420	−2.54866
$58$	−0.370681	−0.0486728
$59$	14.0018	1.82288	0.911440	−	0.411434i	$-0.134972\pi$
$59$	14.0018	1.82288	0.911440	+	0.411434i	$0.134972\pi$
$60$	0	0
$61$	8.35758	1.07008	0.535039	−	0.844827i	$-0.320297\pi$
$61$	8.35758	1.07008	0.535039	+	0.844827i	$0.320297\pi$
$62$	0.171832	0.0218227
$63$	−2.17553	−0.274091
$64$	−7.88451	−0.985563
$65$	0	0
$66$	0.100722	0.0123980
$67$	−11.8979	−1.45357	−0.726783	−	0.686867i	$-0.758985\pi$
$67$	−11.8979	−1.45357	−0.726783	+	0.686867i	$0.758985\pi$
$68$	−7.12757	−0.864345
$69$	−7.94594	−0.956579
$70$	0	0
$71$	−6.10073	−0.724023	−0.362012	−	0.932174i	$-0.617910\pi$
$71$	−6.10073	−0.724023	−0.362012	+	0.932174i	$0.617910\pi$
$72$	−0.618386	−0.0728774
$73$	−9.09745	−1.06478	−0.532388	−	0.846500i	$-0.678705\pi$
$73$	−9.09745	−1.06478	−0.532388	+	0.846500i	$0.678705\pi$
$74$	0.256390	0.0298047
$75$	0	0
$76$	16.7889	1.92581
$77$	−0.619094	−0.0705523
$78$	0.273583	0.0309771
$79$	−12.5062	−1.40706	−0.703529	−	0.710667i	$-0.748393\pi$
$79$	−12.5062	−1.40706	−0.703529	+	0.710667i	$0.748393\pi$
$80$	0	0
$81$	−10.7185	−1.19095
$82$	0.623112	0.0688112
$83$	−14.3752	−1.57788	−0.788941	−	0.614469i	$-0.789370\pi$
$83$	−14.3752	−1.57788	−0.788941	+	0.614469i	$0.789370\pi$
$84$	4.45290	0.485851
$85$	0	0
$86$	−0.637268	−0.0687184
$87$	−12.2068	−1.30870
$88$	−0.175975	−0.0187590
$89$	12.5612	1.33149	0.665744	−	0.746180i	$-0.268114\pi$
$89$	12.5612	1.33149	0.665744	+	0.746180i	$0.268114\pi$
$90$	0	0
$91$	−1.68159	−0.176279
$92$	6.93293	0.722808
$93$	5.65855	0.586764
$94$	0.356642	0.0367848
$95$	0	0
$96$	1.89934	0.193851
$97$	−1.27290	−0.129244	−0.0646218	−	0.997910i	$-0.520584\pi$
$97$	−1.27290	−0.129244	−0.0646218	+	0.997910i	$0.520584\pi$
$98$	−0.419932	−0.0424196
$99$	1.41390	0.142102
$100$	0	0
$101$	−10.0311	−0.998131	−0.499065	−	0.866564i	$-0.666323\pi$
$101$	−10.0311	−0.998131	−0.499065	+	0.866564i	$0.666323\pi$
$102$	0.567256	0.0561668
$103$	−2.83287	−0.279131	−0.139566	−	0.990213i	$-0.544571\pi$
$103$	−2.83287	−0.279131	−0.139566	+	0.990213i	$0.544571\pi$
$104$	−0.477985	−0.0468703
$105$	0	0
$106$	−0.523915	−0.0508871
$107$	−12.4734	−1.20585	−0.602926	−	0.797797i	$-0.705999\pi$
$107$	−12.4734	−1.20585	−0.602926	+	0.797797i	$0.705999\pi$
$108$	3.51751	0.338473
$109$	9.07891	0.869602	0.434801	−	0.900527i	$-0.356819\pi$
$109$	9.07891	0.869602	0.434801	+	0.900527i	$0.356819\pi$
$110$	0	0
$111$	8.44309	0.801383
$112$	−3.87580	−0.366229
$113$	10.5864	0.995888	0.497944	−	0.867209i	$-0.334088\pi$
$113$	10.5864	0.995888	0.497944	+	0.867209i	$0.334088\pi$
$114$	−1.33616	−0.125143
$115$	0	0
$116$	10.6506	0.988879
$117$	3.84045	0.355050
$118$	0.972285	0.0895061
$119$	−3.48667	−0.319623
$120$	0	0
$121$	−10.5976	−0.963422
$122$	0.580350	0.0525425
$123$	20.5195	1.85018
$124$	−4.93715	−0.443370
$125$	0	0
$126$	−0.151069	−0.0134583
$127$	1.90038	0.168631	0.0843157	−	0.996439i	$-0.473130\pi$
$127$	1.90038	0.168631	0.0843157	+	0.996439i	$0.473130\pi$
$128$	−2.20871	−0.195224
$129$	−20.9857	−1.84769
$130$	0	0
$131$	10.0276	0.876114	0.438057	−	0.898947i	$-0.355667\pi$
$131$	10.0276	0.876114	0.438057	+	0.898947i	$0.355667\pi$
$132$	−2.89399	−0.251889
$133$	8.21280	0.712140
$134$	−0.826193	−0.0713722
$135$	0	0
$136$	−0.991073	−0.0849838
$137$	−5.22389	−0.446307	−0.223153	−	0.974783i	$-0.571635\pi$
$137$	−5.22389	−0.446307	−0.223153	+	0.974783i	$0.571635\pi$
$138$	−0.551766	−0.0469694
$139$	11.9060	1.00985	0.504925	−	0.863163i	$-0.331520\pi$
$139$	11.9060	1.00985	0.504925	+	0.863163i	$0.331520\pi$
$140$	0	0
$141$	11.7445	0.989061
$142$	−0.423634	−0.0355506
$143$	1.09288	0.0913915
$144$	8.85164	0.737636
$145$	0	0
$146$	−0.631727	−0.0522821
$147$	−13.8287	−1.14057
$148$	−7.36670	−0.605539
$149$	−3.27249	−0.268092	−0.134046	−	0.990975i	$-0.542797\pi$
$149$	−3.27249	−0.268092	−0.134046	+	0.990975i	$0.542797\pi$
$150$	0	0
$151$	14.4560	1.17641	0.588206	−	0.808711i	$-0.299834\pi$
$151$	14.4560	1.17641	0.588206	+	0.808711i	$0.299834\pi$
$152$	2.33445	0.189349
$153$	7.96294	0.643766
$154$	−0.0429898	−0.00346422
$155$	0	0
$156$	−7.86069	−0.629359
$157$	−13.6715	−1.09111	−0.545554	−	0.838076i	$-0.683681\pi$
$157$	−13.6715	−1.09111	−0.545554	+	0.838076i	$0.683681\pi$
$158$	−0.868430	−0.0690886
$159$	−17.2529	−1.36824
$160$	0	0
$161$	3.39146	0.267284
$162$	−0.744295	−0.0584773
$163$	−8.90823	−0.697747	−0.348873	−	0.937170i	$-0.613436\pi$
$163$	−8.90823	−0.697747	−0.348873	+	0.937170i	$0.613436\pi$
$164$	−17.9035	−1.39803
$165$	0	0
$166$	−0.998213	−0.0774764
$167$	−20.3344	−1.57353	−0.786763	−	0.617255i	$-0.788245\pi$
$167$	−20.3344	−1.57353	−0.786763	+	0.617255i	$0.788245\pi$
$168$	0.619166	0.0477697
$169$	−10.0315	−0.771654
$170$	0	0
$171$	−18.7566	−1.43435
$172$	18.3103	1.39614
$173$	12.6065	0.958455	0.479228	−	0.877691i	$-0.340917\pi$
$173$	12.6065	0.958455	0.479228	+	0.877691i	$0.340917\pi$
$174$	−0.847638	−0.0642593
$175$	0	0
$176$	2.51892	0.189871
$177$	32.0180	2.40662
$178$	0.872252	0.0653780
$179$	−17.0714	−1.27598	−0.637988	−	0.770046i	$-0.720233\pi$
$179$	−17.0714	−1.27598	−0.637988	+	0.770046i	$0.720233\pi$
$180$	0	0
$181$	−16.7745	−1.24684	−0.623419	−	0.781888i	$-0.714257\pi$
$181$	−16.7745	−1.24684	−0.623419	+	0.781888i	$0.714257\pi$
$182$	−0.116770	−0.00865554
$183$	19.1113	1.41275
$184$	0.964008	0.0710676
$185$	0	0
$186$	0.392930	0.0288110
$187$	2.26603	0.165708
$188$	−10.2472	−0.747352
$189$	1.72070	0.125163
$190$	0	0
$191$	−22.0771	−1.59745	−0.798723	−	0.601699i	$-0.794491\pi$
$191$	−22.0771	−1.59745	−0.798723	+	0.601699i	$0.794491\pi$
$192$	−18.0295	−1.30117
$193$	21.0044	1.51193	0.755965	−	0.654612i	$-0.227168\pi$
$193$	21.0044	1.51193	0.755965	+	0.654612i	$0.227168\pi$
$194$	−0.0883902	−0.00634605
$195$	0	0
$196$	12.0657	0.861834
$197$	−8.88004	−0.632677	−0.316338	−	0.948646i	$-0.602453\pi$
$197$	−8.88004	−0.632677	−0.316338	+	0.948646i	$0.602453\pi$
$198$	0.0981812	0.00697743
$199$	10.2652	0.727684	0.363842	−	0.931461i	$-0.381465\pi$
$199$	10.2652	0.727684	0.363842	+	0.931461i	$0.381465\pi$
$200$	0	0
$201$	−27.2071	−1.91904
$202$	−0.696559	−0.0490097
$203$	5.21005	0.365674
$204$	−16.2986	−1.14113
$205$	0	0
$206$	−0.196714	−0.0137057
$207$	−7.74549	−0.538349
$208$	6.84193	0.474403
$209$	−5.33758	−0.369208
$210$	0	0
$211$	−1.64030	−0.112923	−0.0564613	−	0.998405i	$-0.517982\pi$
$211$	−1.64030	−0.112923	−0.0564613	+	0.998405i	$0.517982\pi$
$212$	15.0533	1.03387
$213$	−13.9506	−0.955877
$214$	−0.866155	−0.0592091
$215$	0	0
$216$	0.489102	0.0332792
$217$	−2.41516	−0.163952
$218$	0.630439	0.0426987
$219$	−20.8032	−1.40575
$220$	0	0
$221$	6.15501	0.414031
$222$	0.586288	0.0393491
$223$	−23.6879	−1.58626	−0.793129	−	0.609053i	$-0.791550\pi$
$223$	−23.6879	−1.58626	−0.793129	+	0.609053i	$0.791550\pi$
$224$	−0.810671	−0.0541652
$225$	0	0
$226$	0.735122	0.0488996
$227$	−8.68004	−0.576115	−0.288057	−	0.957613i	$-0.593009\pi$
$227$	−8.68004	−0.576115	−0.288057	+	0.957613i	$0.593009\pi$
$228$	38.3912	2.54252
$229$	10.4786	0.692443	0.346221	−	0.938153i	$-0.387465\pi$
$229$	10.4786	0.692443	0.346221	+	0.938153i	$0.387465\pi$
$230$	0	0
$231$	−1.41568	−0.0931452
$232$	1.48094	0.0972282
$233$	−10.7280	−0.702818	−0.351409	−	0.936222i	$-0.614297\pi$
$233$	−10.7280	−0.702818	−0.351409	+	0.936222i	$0.614297\pi$
$234$	0.266681	0.0174335
$235$	0	0
$236$	−27.9361	−1.81848
$237$	−28.5980	−1.85764
$238$	−0.242114	−0.0156939
$239$	27.6682	1.78971	0.894853	−	0.446360i	$-0.147280\pi$
$239$	27.6682	1.78971	0.894853	+	0.446360i	$0.147280\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−0.735900	−0.0473055
$243$	−19.2211	−1.23303
$244$	−16.6749	−1.06750
$245$	0	0
$246$	1.42487	0.0908466
$247$	−14.4980	−0.922486
$248$	−0.686500	−0.0435928
$249$	−32.8718	−2.08317
$250$	0	0
$251$	−2.36744	−0.149432	−0.0747158	−	0.997205i	$-0.523805\pi$
$251$	−2.36744	−0.149432	−0.0747158	+	0.997205i	$0.523805\pi$
$252$	4.34057	0.273430
$253$	−2.20414	−0.138573
$254$	0.131962	0.00828005
$255$	0	0
$256$	15.6156	0.975978
$257$	21.7229	1.35504	0.677518	−	0.735506i	$-0.263056\pi$
$257$	21.7229	1.35504	0.677518	+	0.735506i	$0.263056\pi$
$258$	−1.45724	−0.0907241
$259$	−3.60365	−0.223920
$260$	0	0
$261$	−11.8988	−0.736519
$262$	0.696315	0.0430185
$263$	16.3366	1.00736	0.503680	−	0.863890i	$-0.331979\pi$
$263$	16.3366	1.00736	0.503680	+	0.863890i	$0.331979\pi$
$264$	−0.402403	−0.0247662
$265$	0	0
$266$	0.570296	0.0349671
$267$	28.7238	1.75787
$268$	23.7385	1.45006
$269$	−1.70739	−0.104101	−0.0520506	−	0.998644i	$-0.516576\pi$
$269$	−1.70739	−0.104101	−0.0520506	+	0.998644i	$0.516576\pi$
$270$	0	0
$271$	−24.7442	−1.50310	−0.751551	−	0.659675i	$-0.770694\pi$
$271$	−24.7442	−1.50310	−0.751551	+	0.659675i	$0.770694\pi$
$272$	14.1863	0.860172
$273$	−3.84530	−0.232728
$274$	−0.362747	−0.0219143
$275$	0	0
$276$	15.8536	0.954272
$277$	−14.4691	−0.869365	−0.434682	−	0.900584i	$-0.643139\pi$
$277$	−14.4691	−0.869365	−0.434682	+	0.900584i	$0.643139\pi$
$278$	0.826750	0.0495852
$279$	5.51580	0.330222
$280$	0	0
$281$	22.9162	1.36706	0.683532	−	0.729921i	$-0.260443\pi$
$281$	22.9162	1.36706	0.683532	+	0.729921i	$0.260443\pi$
$282$	0.815535	0.0485644
$283$	−22.7218	−1.35067	−0.675336	−	0.737510i	$-0.736001\pi$
$283$	−22.7218	−1.35067	−0.675336	+	0.737510i	$0.736001\pi$
$284$	12.1720	0.722278
$285$	0	0
$286$	0.0758898	0.00448746
$287$	−8.75806	−0.516972
$288$	1.85143	0.109096
$289$	−4.23798	−0.249293
$290$	0	0
$291$	−2.91075	−0.170631
$292$	18.1510	1.06221
$293$	−9.96571	−0.582203	−0.291101	−	0.956692i	$-0.594022\pi$
$293$	−9.96571	−0.582203	−0.291101	+	0.956692i	$0.594022\pi$
$294$	−0.960262	−0.0560036
$295$	0	0
$296$	−1.02432	−0.0595376
$297$	−1.11830	−0.0648904
$298$	−0.227241	−0.0131637
$299$	−5.98693	−0.346233
$300$	0	0
$301$	8.95703	0.516275
$302$	1.00382	0.0577635
$303$	−22.9381	−1.31776
$304$	−33.4156	−1.91652
$305$	0	0
$306$	0.552946	0.0316098
$307$	−18.8590	−1.07634	−0.538171	−	0.842836i	$-0.680885\pi$
$307$	−18.8590	−1.07634	−0.538171	+	0.842836i	$0.680885\pi$
$308$	1.23520	0.0703822
$309$	−6.47794	−0.368517
$310$	0	0
$311$	−22.9234	−1.29987	−0.649933	−	0.759992i	$-0.725203\pi$
$311$	−22.9234	−1.29987	−0.649933	+	0.759992i	$0.725203\pi$
$312$	−1.09301	−0.0618796
$313$	−7.49903	−0.423870	−0.211935	−	0.977284i	$-0.567977\pi$
$313$	−7.49903	−0.423870	−0.211935	+	0.977284i	$0.567977\pi$
$314$	−0.949352	−0.0535750
$315$	0	0
$316$	24.9521	1.40367
$317$	22.0957	1.24102	0.620510	−	0.784198i	$-0.286926\pi$
$317$	22.0957	1.24102	0.620510	+	0.784198i	$0.286926\pi$
$318$	−1.19804	−0.0671827
$319$	−3.38607	−0.189583
$320$	0	0
$321$	−28.5231	−1.59200
$322$	0.235503	0.0131241
$323$	−30.0607	−1.67262
$324$	21.3854	1.18808
$325$	0	0
$326$	−0.618588	−0.0342604
$327$	20.7608	1.14807
$328$	−2.48944	−0.137457
$329$	−5.01273	−0.276361
$330$	0	0
$331$	−10.3654	−0.569732	−0.284866	−	0.958567i	$-0.591949\pi$
$331$	−10.3654	−0.569732	−0.284866	+	0.958567i	$0.591949\pi$
$332$	28.6811	1.57408
$333$	8.23010	0.451007
$334$	−1.41202	−0.0772625
$335$	0	0
$336$	−8.86281	−0.483506
$337$	−13.4934	−0.735034	−0.367517	−	0.930017i	$-0.619792\pi$
$337$	−13.4934	−0.735034	−0.367517	+	0.930017i	$0.619792\pi$
$338$	−0.696587	−0.0378893
$339$	24.2081	1.31480
$340$	0	0
$341$	1.56964	0.0850008
$342$	−1.30246	−0.0704287
$343$	12.7343	0.687589
$344$	2.54600	0.137271
$345$	0	0
$346$	0.875396	0.0470616
$347$	4.20460	0.225715	0.112857	−	0.993611i	$-0.464000\pi$
$347$	4.20460	0.225715	0.112857	+	0.993611i	$0.464000\pi$
$348$	24.3547	1.30555
$349$	−11.6192	−0.621964	−0.310982	−	0.950416i	$-0.600658\pi$
$349$	−11.6192	−0.621964	−0.310982	+	0.950416i	$0.600658\pi$
$350$	0	0
$351$	−3.03755	−0.162132
$352$	0.526864	0.0280819
$353$	10.5244	0.560155	0.280078	−	0.959977i	$-0.409640\pi$
$353$	10.5244	0.560155	0.280078	+	0.959977i	$0.409640\pi$
$354$	2.22333	0.118169
$355$	0	0
$356$	−25.0619	−1.32828
$357$	−7.97299	−0.421975
$358$	−1.18544	−0.0626523
$359$	−9.80351	−0.517410	−0.258705	−	0.965956i	$-0.583296\pi$
$359$	−9.80351	−0.517410	−0.258705	+	0.965956i	$0.583296\pi$
$360$	0	0
$361$	51.8075	2.72671
$362$	−1.16482	−0.0612216
$363$	−24.2337	−1.27194
$364$	3.35507	0.175854
$365$	0	0
$366$	1.32709	0.0693681
$367$	−24.3474	−1.27092	−0.635462	−	0.772132i	$-0.719190\pi$
$367$	−24.3474	−1.27092	−0.635462	+	0.772132i	$0.719190\pi$
$368$	−13.7989	−0.719318
$369$	20.0019	1.04126
$370$	0	0
$371$	7.36381	0.382310
$372$	−11.2898	−0.585350
$373$	29.4468	1.52470	0.762350	−	0.647165i	$-0.224046\pi$
$373$	29.4468	1.52470	0.762350	+	0.647165i	$0.224046\pi$
$374$	0.157353	0.00813652
$375$	0	0
$376$	−1.42485	−0.0734809
$377$	−9.19728	−0.473684
$378$	0.119485	0.00614567
$379$	24.6841	1.26794	0.633968	−	0.773359i	$-0.281425\pi$
$379$	24.6841	1.26794	0.633968	+	0.773359i	$0.281425\pi$
$380$	0	0
$381$	4.34560	0.222632
$382$	−1.53304	−0.0784370
$383$	1.20124	0.0613804	0.0306902	−	0.999529i	$-0.490229\pi$
$383$	1.20124	0.0613804	0.0306902	+	0.999529i	$0.490229\pi$
$384$	−5.05066	−0.257740
$385$	0	0
$386$	1.45855	0.0742380
$387$	−20.4563	−1.03985
$388$	2.53966	0.128932
$389$	23.3156	1.18215	0.591073	−	0.806618i	$-0.298704\pi$
$389$	23.3156	1.18215	0.591073	+	0.806618i	$0.298704\pi$
$390$	0	0
$391$	−12.4135	−0.627779
$392$	1.67771	0.0847369
$393$	22.9301	1.15667
$394$	−0.616630	−0.0310654
$395$	0	0
$396$	−2.82098	−0.141760
$397$	−28.2128	−1.41596	−0.707980	−	0.706233i	$-0.750393\pi$
$397$	−28.2128	−1.41596	−0.707980	+	0.706233i	$0.750393\pi$
$398$	0.712818	0.0357303
$399$	18.7802	0.940188
$400$	0	0
$401$	−11.4175	−0.570162	−0.285081	−	0.958503i	$-0.592021\pi$
$401$	−11.4175	−0.570162	−0.285081	+	0.958503i	$0.592021\pi$
$402$	−1.88926	−0.0942277
$403$	4.26348	0.212379
$404$	20.0138	0.995725
$405$	0	0
$406$	0.361786	0.0179551
$407$	2.34205	0.116091
$408$	−2.26629	−0.112198
$409$	−15.5135	−0.767092	−0.383546	−	0.923522i	$-0.625297\pi$
$409$	−15.5135	−0.767092	−0.383546	+	0.923522i	$0.625297\pi$
$410$	0	0
$411$	−11.9455	−0.589227
$412$	5.65208	0.278458
$413$	−13.6658	−0.672451
$414$	−0.537847	−0.0264337
$415$	0	0
$416$	1.43107	0.0701642
$417$	27.2254	1.33323
$418$	−0.370642	−0.0181287
$419$	−0.638641	−0.0311997	−0.0155998	−	0.999878i	$-0.504966\pi$
$419$	−0.638641	−0.0311997	−0.0155998	+	0.999878i	$0.504966\pi$
$420$	0	0
$421$	18.2881	0.891309	0.445655	−	0.895205i	$-0.352971\pi$
$421$	18.2881	0.891309	0.445655	+	0.895205i	$0.352971\pi$
$422$	−0.113902	−0.00554467
$423$	11.4482	0.556630
$424$	2.09313	0.101652
$425$	0	0
$426$	−0.968727	−0.0469350
$427$	−8.15703	−0.394746
$428$	24.8867	1.20294
$429$	2.49910	0.120658
$430$	0	0
$431$	−25.9278	−1.24890	−0.624449	−	0.781065i	$-0.714677\pi$
$431$	−25.9278	−1.24890	−0.624449	+	0.781065i	$0.714677\pi$
$432$	−7.00106	−0.336839
$433$	11.6930	0.561929	0.280964	−	0.959718i	$-0.409346\pi$
$433$	11.6930	0.561929	0.280964	+	0.959718i	$0.409346\pi$
$434$	−0.167709	−0.00805028
$435$	0	0
$436$	−18.1140	−0.867505
$437$	29.2398	1.39873
$438$	−1.44457	−0.0690243
$439$	23.6929	1.13080	0.565401	−	0.824816i	$-0.308721\pi$
$439$	23.6929	1.13080	0.565401	+	0.824816i	$0.308721\pi$
$440$	0	0
$441$	−13.4798	−0.641896
$442$	0.427404	0.0203295
$443$	−4.53912	−0.215660	−0.107830	−	0.994169i	$-0.534390\pi$
$443$	−4.53912	−0.215660	−0.107830	+	0.994169i	$0.534390\pi$
$444$	−16.8455	−0.799450
$445$	0	0
$446$	−1.64489	−0.0778877
$447$	−7.48321	−0.353944
$448$	7.69531	0.363569
$449$	16.3706	0.772576	0.386288	−	0.922378i	$-0.373757\pi$
$449$	16.3706	0.772576	0.386288	+	0.922378i	$0.373757\pi$
$450$	0	0
$451$	5.69196	0.268024
$452$	−21.1218	−0.993487
$453$	33.0566	1.55313
$454$	−0.602742	−0.0282881
$455$	0	0
$456$	5.33821	0.249984
$457$	18.8784	0.883095	0.441547	−	0.897238i	$-0.354430\pi$
$457$	18.8784	0.883095	0.441547	+	0.897238i	$0.354430\pi$
$458$	0.727631	0.0340000
$459$	−6.29816	−0.293973
$460$	0	0
$461$	−21.7096	−1.01112	−0.505559	−	0.862792i	$-0.668714\pi$
$461$	−21.7096	−1.01112	−0.505559	+	0.862792i	$0.668714\pi$
$462$	−0.0983051	−0.00457357
$463$	−19.2453	−0.894405	−0.447202	−	0.894433i	$-0.647580\pi$
$463$	−19.2453	−0.894405	−0.447202	+	0.894433i	$0.647580\pi$
$464$	−21.1983	−0.984105
$465$	0	0
$466$	−0.744955	−0.0345094
$467$	34.3210	1.58818	0.794092	−	0.607797i	$-0.207947\pi$
$467$	34.3210	1.58818	0.794092	+	0.607797i	$0.207947\pi$
$468$	−7.66239	−0.354194
$469$	11.6124	0.536213
$470$	0	0
$471$	−31.2628	−1.44051
$472$	−3.88445	−0.178796
$473$	−5.82127	−0.267662
$474$	−1.98584	−0.0912128
$475$	0	0
$476$	6.95653	0.318852
$477$	−16.8176	−0.770027
$478$	1.92128	0.0878772
$479$	17.1284	0.782616	0.391308	−	0.920260i	$-0.372023\pi$
$479$	17.1284	0.782616	0.391308	+	0.920260i	$0.372023\pi$
$480$	0	0
$481$	6.36151	0.290060
$482$	−0.0694400	−0.00316290
$483$	7.75526	0.352877
$484$	21.1442	0.961099
$485$	0	0
$486$	−1.33471	−0.0605438
$487$	−2.60718	−0.118143	−0.0590714	−	0.998254i	$-0.518814\pi$
$487$	−2.60718	−0.118143	−0.0590714	+	0.998254i	$0.518814\pi$
$488$	−2.31860	−0.104958
$489$	−20.3705	−0.921186
$490$	0	0
$491$	−8.00612	−0.361311	−0.180656	−	0.983546i	$-0.557822\pi$
$491$	−8.00612	−0.361311	−0.180656	+	0.983546i	$0.557822\pi$
$492$	−40.9401	−1.84572
$493$	−19.0700	−0.858869
$494$	−1.00674	−0.0452954
$495$	0	0
$496$	9.82664	0.441229
$497$	5.95433	0.267088
$498$	−2.28262	−0.102287
$499$	17.3488	0.776640	0.388320	−	0.921525i	$-0.373056\pi$
$499$	17.3488	0.776640	0.388320	+	0.921525i	$0.373056\pi$
$500$	0	0
$501$	−46.4989	−2.07742
$502$	−0.164395	−0.00733732
$503$	17.8615	0.796405	0.398203	−	0.917297i	$-0.369634\pi$
$503$	17.8615	0.796405	0.398203	+	0.917297i	$0.369634\pi$
$504$	0.603547	0.0268841
$505$	0	0
$506$	−0.153056	−0.00680416
$507$	−22.9391	−1.01876
$508$	−3.79159	−0.168225
$509$	6.58215	0.291749	0.145874	−	0.989303i	$-0.453400\pi$
$509$	6.58215	0.291749	0.145874	+	0.989303i	$0.453400\pi$
$510$	0	0
$511$	8.87914	0.392790
$512$	5.50176	0.243146
$513$	14.8352	0.654990
$514$	1.50844	0.0665343
$515$	0	0
$516$	41.8702	1.84323
$517$	3.25782	0.143279
$518$	−0.250237	−0.0109948
$519$	28.8274	1.26538
$520$	0	0
$521$	−8.09318	−0.354569	−0.177284	−	0.984160i	$-0.556731\pi$
$521$	−8.09318	−0.354569	−0.177284	+	0.984160i	$0.556731\pi$
$522$	−0.826255	−0.0361642
$523$	−12.1368	−0.530706	−0.265353	−	0.964151i	$-0.585488\pi$
$523$	−12.1368	−0.530706	−0.265353	+	0.964151i	$0.585488\pi$
$524$	−20.0068	−0.874001
$525$	0	0
$526$	1.13442	0.0494629
$527$	8.84005	0.385079
$528$	5.76003	0.250673
$529$	−10.9255	−0.475020
$530$	0	0
$531$	31.2103	1.35441
$532$	−16.3860	−0.710423
$533$	15.4606	0.669672
$534$	1.99458	0.0863140
$535$	0	0
$536$	3.30079	0.142572
$537$	−39.0373	−1.68458
$538$	−0.118561	−0.00511152
$539$	−3.83597	−0.165227
$540$	0	0
$541$	30.5746	1.31450	0.657252	−	0.753671i	$-0.271719\pi$
$541$	30.5746	1.31450	0.657252	+	0.753671i	$0.271719\pi$
$542$	−1.71823	−0.0738045
$543$	−38.3583	−1.64611
$544$	2.96724	0.127219
$545$	0	0
$546$	−0.267018	−0.0114273
$547$	5.94759	0.254301	0.127150	−	0.991883i	$-0.459417\pi$
$547$	5.94759	0.254301	0.127150	+	0.991883i	$0.459417\pi$
$548$	10.4226	0.445231
$549$	18.6292	0.795075
$550$	0	0
$551$	44.9190	1.91361
$552$	2.20440	0.0938256
$553$	12.2061	0.519056
$554$	−1.00473	−0.0426871
$555$	0	0
$556$	−23.7545	−1.00742
$557$	41.3055	1.75017	0.875085	−	0.483970i	$-0.160806\pi$
$557$	41.3055	1.75017	0.875085	+	0.483970i	$0.160806\pi$
$558$	0.383017	0.0162144
$559$	−15.8118	−0.668768
$560$	0	0
$561$	5.18173	0.218773
$562$	1.59130	0.0671249
$563$	43.2213	1.82156	0.910779	−	0.412893i	$-0.135482\pi$
$563$	43.2213	1.82156	0.910779	+	0.412893i	$0.135482\pi$
$564$	−23.4323	−0.986677
$565$	0	0
$566$	−1.57780	−0.0663200
$567$	10.4613	0.439334
$568$	1.69250	0.0710155
$569$	−38.0917	−1.59689	−0.798444	−	0.602069i	$-0.794343\pi$
$569$	−38.0917	−1.59689	−0.798444	+	0.602069i	$0.794343\pi$
$570$	0	0
$571$	−33.7665	−1.41308	−0.706542	−	0.707671i	$-0.749746\pi$
$571$	−33.7665	−1.41308	−0.706542	+	0.707671i	$0.749746\pi$
$572$	−2.18050	−0.0911712
$573$	−50.4839	−2.10900
$574$	−0.608160	−0.0253841
$575$	0	0
$576$	−17.5747	−0.732280
$577$	−43.2951	−1.80240	−0.901199	−	0.433406i	$-0.857311\pi$
$577$	−43.2951	−1.80240	−0.901199	+	0.433406i	$0.857311\pi$
$578$	−0.294285	−0.0122406
$579$	48.0309	1.99610
$580$	0	0
$581$	14.0302	0.582072
$582$	−0.202122	−0.00837824
$583$	−4.78582	−0.198208
$584$	2.52386	0.104438
$585$	0	0
$586$	−0.692019	−0.0285870
$587$	−16.2999	−0.672768	−0.336384	−	0.941725i	$-0.609204\pi$
$587$	−16.2999	−0.672768	−0.336384	+	0.941725i	$0.609204\pi$
$588$	27.5906	1.13782
$589$	−20.8226	−0.857980
$590$	0	0
$591$	−20.3060	−0.835278
$592$	14.6623	0.602616
$593$	28.5022	1.17045	0.585223	−	0.810873i	$-0.301007\pi$
$593$	28.5022	1.17045	0.585223	+	0.810873i	$0.301007\pi$
$594$	−0.0776548	−0.00318622
$595$	0	0
$596$	6.52919	0.267446
$597$	23.4736	0.960710
$598$	−0.415732	−0.0170005
$599$	−32.5007	−1.32794	−0.663972	−	0.747757i	$-0.731131\pi$
$599$	−32.5007	−1.32794	−0.663972	+	0.747757i	$0.731131\pi$
$600$	0	0
$601$	−2.70728	−0.110432	−0.0552162	−	0.998474i	$-0.517585\pi$
$601$	−2.70728	−0.110432	−0.0552162	+	0.998474i	$0.517585\pi$
$602$	0.621976	0.0253499
$603$	−26.5207	−1.08001
$604$	−28.8423	−1.17358
$605$	0	0
$606$	−1.59282	−0.0647041
$607$	−17.6749	−0.717401	−0.358701	−	0.933453i	$-0.616780\pi$
$607$	−17.6749	−0.717401	−0.358701	+	0.933453i	$0.616780\pi$
$608$	−6.98929	−0.283453
$609$	11.9139	0.482774
$610$	0	0
$611$	8.84895	0.357990
$612$	−15.8875	−0.642213
$613$	18.1838	0.734436	0.367218	−	0.930135i	$-0.380310\pi$
$613$	18.1838	0.734436	0.367218	+	0.930135i	$0.380310\pi$
$614$	−1.30957	−0.0528500
$615$	0	0
$616$	0.171752	0.00692009
$617$	−33.6359	−1.35413	−0.677065	−	0.735923i	$-0.736748\pi$
$617$	−33.6359	−1.35413	−0.677065	+	0.735923i	$0.736748\pi$
$618$	−0.449828	−0.0180947
$619$	35.8335	1.44027	0.720135	−	0.693834i	$-0.244080\pi$
$619$	35.8335	1.44027	0.720135	+	0.693834i	$0.244080\pi$
$620$	0	0
$621$	6.12617	0.245835
$622$	−1.59180	−0.0638253
$623$	−12.2598	−0.491179
$624$	15.6455	0.626320
$625$	0	0
$626$	−0.520733	−0.0208127
$627$	−12.2055	−0.487440
$628$	27.2772	1.08848
$629$	13.1902	0.525927
$630$	0	0
$631$	−18.1164	−0.721202	−0.360601	−	0.932720i	$-0.617428\pi$
$631$	−18.1164	−0.721202	−0.360601	+	0.932720i	$0.617428\pi$
$632$	3.46953	0.138011
$633$	−3.75087	−0.149084
$634$	1.53433	0.0609359
$635$	0	0
$636$	34.4226	1.36494
$637$	−10.4193	−0.412828
$638$	−0.235128	−0.00930883
$639$	−13.5986	−0.537954
$640$	0	0
$641$	40.4201	1.59650	0.798249	−	0.602328i	$-0.205760\pi$
$641$	40.4201	1.59650	0.798249	+	0.602328i	$0.205760\pi$
$642$	−1.98064	−0.0781696
$643$	35.3985	1.39598	0.697990	−	0.716107i	$-0.254078\pi$
$643$	35.3985	1.39598	0.697990	+	0.716107i	$0.254078\pi$
$644$	−6.76656	−0.266640
$645$	0	0
$646$	−2.08742	−0.0821283
$647$	−35.7729	−1.40638	−0.703189	−	0.711003i	$-0.748241\pi$
$647$	−35.7729	−1.40638	−0.703189	+	0.711003i	$0.748241\pi$
$648$	2.97359	0.116814
$649$	8.88155	0.348631
$650$	0	0
$651$	−5.52276	−0.216454
$652$	17.7735	0.696065
$653$	22.7559	0.890507	0.445254	−	0.895405i	$-0.353114\pi$
$653$	22.7559	0.890507	0.445254	+	0.895405i	$0.353114\pi$
$654$	1.44163	0.0563721
$655$	0	0
$656$	35.6342	1.39128
$657$	−20.2784	−0.791135
$658$	−0.348084	−0.0135697
$659$	34.3151	1.33673	0.668364	−	0.743835i	$-0.266995\pi$
$659$	34.3151	1.33673	0.668364	+	0.743835i	$0.266995\pi$
$660$	0	0
$661$	16.3753	0.636925	0.318462	−	0.947935i	$-0.396834\pi$
$661$	16.3753	0.636925	0.318462	+	0.947935i	$0.396834\pi$
$662$	−0.719771	−0.0279747
$663$	14.0747	0.546615
$664$	3.98804	0.154766
$665$	0	0
$666$	0.571498	0.0221451
$667$	18.5492	0.718229
$668$	40.5708	1.56973
$669$	−54.1672	−2.09423
$670$	0	0
$671$	5.30134	0.204656
$672$	−1.85377	−0.0715106
$673$	−25.3140	−0.975783	−0.487891	−	0.872904i	$-0.662234\pi$
$673$	−25.3140	−0.975783	−0.487891	+	0.872904i	$0.662234\pi$
$674$	−0.936984	−0.0360913
$675$	0	0
$676$	20.0146	0.769793
$677$	34.6641	1.33225	0.666125	−	0.745840i	$-0.267952\pi$
$677$	34.6641	1.33225	0.666125	+	0.745840i	$0.267952\pi$
$678$	1.68101	0.0645587
$679$	1.24236	0.0476772
$680$	0	0
$681$	−19.8487	−0.760604
$682$	0.108996	0.00417366
$683$	−5.63531	−0.215629	−0.107815	−	0.994171i	$-0.534385\pi$
$683$	−5.63531	−0.215629	−0.107815	+	0.994171i	$0.534385\pi$
$684$	37.4227	1.43089
$685$	0	0
$686$	0.884271	0.0337616
$687$	23.9614	0.914183
$688$	−36.4437	−1.38940
$689$	−12.9993	−0.495234
$690$	0	0
$691$	21.6786	0.824695	0.412347	−	0.911027i	$-0.364709\pi$
$691$	21.6786	0.824695	0.412347	+	0.911027i	$0.364709\pi$
$692$	−25.1522	−0.956145
$693$	−1.37997	−0.0524208
$694$	0.291968	0.0110829
$695$	0	0
$696$	3.38646	0.128364
$697$	32.0565	1.21423
$698$	−0.806840	−0.0305393
$699$	−24.5319	−0.927881
$700$	0	0
$701$	3.59447	0.135761	0.0678807	−	0.997693i	$-0.478376\pi$
$701$	3.59447	0.135761	0.0678807	+	0.997693i	$0.478376\pi$
$702$	−0.210927	−0.00796093
$703$	−31.0693	−1.17180
$704$	−5.00126	−0.188492
$705$	0	0
$706$	0.730812	0.0275045
$707$	9.79038	0.368205
$708$	−63.8816	−2.40082
$709$	0.363596	0.0136551	0.00682757	−	0.999977i	$-0.497827\pi$
$709$	0.363596	0.0136551	0.00682757	+	0.999977i	$0.497827\pi$
$710$	0	0
$711$	−27.8766	−1.04545
$712$	−3.48480	−0.130598
$713$	−8.59865	−0.322022
$714$	−0.553644	−0.0207196
$715$	0	0
$716$	34.0605	1.27290
$717$	63.2690	2.36282
$718$	−0.680756	−0.0254056
$719$	−22.7117	−0.847003	−0.423501	−	0.905896i	$-0.639199\pi$
$719$	−22.7117	−0.847003	−0.423501	+	0.905896i	$0.639199\pi$
$720$	0	0
$721$	2.76489	0.102970
$722$	3.59751	0.133886
$723$	−2.28670	−0.0850435
$724$	33.4681	1.24383
$725$	0	0
$726$	−1.68279	−0.0624541
$727$	−3.87470	−0.143705	−0.0718524	−	0.997415i	$-0.522891\pi$
$727$	−3.87470	−0.143705	−0.0718524	+	0.997415i	$0.522891\pi$
$728$	0.466515	0.0172902
$729$	−11.7974	−0.436940
$730$	0	0
$731$	−32.7848	−1.21259
$732$	−38.1305	−1.40934
$733$	−30.8173	−1.13826	−0.569131	−	0.822247i	$-0.692720\pi$
$733$	−30.8173	−1.13826	−0.569131	+	0.822247i	$0.692720\pi$
$734$	−1.69068	−0.0624042
$735$	0	0
$736$	−2.88621	−0.106387
$737$	−7.54705	−0.277999
$738$	1.38893	0.0511272
$739$	28.7674	1.05823	0.529114	−	0.848551i	$-0.322524\pi$
$739$	28.7674	1.05823	0.529114	+	0.848551i	$0.322524\pi$
$740$	0	0
$741$	−33.1527	−1.21789
$742$	0.511343	0.0187720
$743$	7.60661	0.279059	0.139530	−	0.990218i	$-0.455441\pi$
$743$	7.60661	0.279059	0.139530	+	0.990218i	$0.455441\pi$
$744$	−1.56982	−0.0575525
$745$	0	0
$746$	2.04479	0.0748650
$747$	−32.0426	−1.17238
$748$	−4.52112	−0.165309
$749$	12.1741	0.444832
$750$	0	0
$751$	51.8155	1.89077	0.945387	−	0.325949i	$-0.105684\pi$
$751$	51.8155	1.89077	0.945387	+	0.325949i	$0.105684\pi$
$752$	20.3954	0.743744
$753$	−5.41364	−0.197284
$754$	−0.638659	−0.0232586
$755$	0	0
$756$	−3.43310	−0.124861
$757$	−2.43810	−0.0886142	−0.0443071	−	0.999018i	$-0.514108\pi$
$757$	−2.43810	−0.0886142	−0.0443071	+	0.999018i	$0.514108\pi$
$758$	1.71406	0.0622575
$759$	−5.04023	−0.182949
$760$	0	0
$761$	−8.94360	−0.324205	−0.162103	−	0.986774i	$-0.551828\pi$
$761$	−8.94360	−0.324205	−0.162103	+	0.986774i	$0.551828\pi$
$762$	0.301759	0.0109316
$763$	−8.86105	−0.320792
$764$	44.0478	1.59359
$765$	0	0
$766$	0.0834140	0.00301387
$767$	24.1242	0.871074
$768$	35.7084	1.28851
$769$	34.7603	1.25349	0.626743	−	0.779226i	$-0.284387\pi$
$769$	34.7603	1.25349	0.626743	+	0.779226i	$0.284387\pi$
$770$	0	0
$771$	49.6738	1.78896
$772$	−41.9075	−1.50829
$773$	−45.8252	−1.64822	−0.824109	−	0.566431i	$-0.808324\pi$
$773$	−45.8252	−1.64822	−0.824109	+	0.566431i	$0.808324\pi$
$774$	−1.42048	−0.0510582
$775$	0	0
$776$	0.353135	0.0126768
$777$	−8.24048	−0.295626
$778$	1.61903	0.0580451
$779$	−75.5086	−2.70538
$780$	0	0
$781$	−3.86978	−0.138472
$782$	−0.861994	−0.0308249
$783$	9.41119	0.336329
$784$	−24.0148	−0.857673
$785$	0	0
$786$	1.59227	0.0567943
$787$	22.4693	0.800944	0.400472	−	0.916309i	$-0.368846\pi$
$787$	22.4693	0.800944	0.400472	+	0.916309i	$0.368846\pi$
$788$	17.7173	0.631151
$789$	37.3571	1.32995
$790$	0	0
$791$	−10.3324	−0.367378
$792$	−0.392251	−0.0139380
$793$	14.3996	0.511344
$794$	−1.95910	−0.0695257
$795$	0	0
$796$	−20.4810	−0.725929
$797$	32.4964	1.15108	0.575540	−	0.817774i	$-0.304792\pi$
$797$	32.4964	1.15108	0.575540	+	0.817774i	$0.304792\pi$
$798$	1.30410	0.0461646
$799$	18.3477	0.649096
$800$	0	0
$801$	27.9992	0.989304
$802$	−0.792830	−0.0279958
$803$	−5.77065	−0.203642
$804$	54.2830	1.91441
$805$	0	0
$806$	0.296056	0.0104281
$807$	−3.90429	−0.137437
$808$	2.78288	0.0979012
$809$	17.5672	0.617629	0.308814	−	0.951122i	$-0.400068\pi$
$809$	17.5672	0.617629	0.308814	+	0.951122i	$0.400068\pi$
$810$	0	0
$811$	36.9756	1.29839	0.649194	−	0.760623i	$-0.275106\pi$
$811$	36.9756	1.29839	0.649194	+	0.760623i	$0.275106\pi$
$812$	−10.3950	−0.364792
$813$	−56.5826	−1.98444
$814$	0.162632	0.00570025
$815$	0	0
$816$	32.4399	1.13562
$817$	77.2240	2.70173
$818$	−1.07726	−0.0376654
$819$	−3.74830	−0.130976
$820$	0	0
$821$	33.2217	1.15944	0.579722	−	0.814814i	$-0.303161\pi$
$821$	33.2217	1.15944	0.579722	+	0.814814i	$0.303161\pi$
$822$	−0.829494	−0.0289319
$823$	−4.23199	−0.147518	−0.0737590	−	0.997276i	$-0.523500\pi$
$823$	−4.23199	−0.147518	−0.0737590	+	0.997276i	$0.523500\pi$
$824$	0.785909	0.0273785
$825$	0	0
$826$	−0.948953	−0.0330183
$827$	44.7720	1.55687	0.778437	−	0.627722i	$-0.216013\pi$
$827$	44.7720	1.55687	0.778437	+	0.627722i	$0.216013\pi$
$828$	15.4536	0.537051
$829$	0.129251	0.00448908	0.00224454	−	0.999997i	$-0.499286\pi$
$829$	0.129251	0.00448908	0.00224454	+	0.999997i	$0.499286\pi$
$830$	0	0
$831$	−33.0866	−1.14776
$832$	−13.5845	−0.470957
$833$	−21.6038	−0.748526
$834$	1.89053	0.0654638
$835$	0	0
$836$	10.6494	0.368318
$837$	−4.36264	−0.150795
$838$	−0.0443472	−0.00153195
$839$	−29.8867	−1.03180	−0.515902	−	0.856647i	$-0.672543\pi$
$839$	−29.8867	−1.03180	−0.515902	+	0.856647i	$0.672543\pi$
$840$	0	0
$841$	−0.504166	−0.0173850
$842$	1.26993	0.0437646
$843$	52.4025	1.80484
$844$	3.27268	0.112650
$845$	0	0
$846$	0.794961	0.0273313
$847$	10.3433	0.355401
$848$	−29.9613	−1.02888
$849$	−51.9581	−1.78320
$850$	0	0
$851$	−12.8300	−0.439806
$852$	27.8339	0.953572
$853$	32.0133	1.09611	0.548057	−	0.836441i	$-0.315368\pi$
$853$	32.0133	1.09611	0.548057	+	0.836441i	$0.315368\pi$
$854$	−0.566424	−0.0193826
$855$	0	0
$856$	3.46044	0.118275
$857$	−27.6869	−0.945766	−0.472883	−	0.881125i	$-0.656787\pi$
$857$	−27.6869	−0.945766	−0.472883	+	0.881125i	$0.656787\pi$
$858$	0.173538	0.00592447
$859$	50.1431	1.71086	0.855431	−	0.517917i	$-0.173292\pi$
$859$	50.1431	1.71086	0.855431	+	0.517917i	$0.173292\pi$
$860$	0	0
$861$	−20.0271	−0.682522
$862$	−1.80043	−0.0613228
$863$	−2.80427	−0.0954585	−0.0477293	−	0.998860i	$-0.515198\pi$
$863$	−2.80427	−0.0954585	−0.0477293	+	0.998860i	$0.515198\pi$
$864$	−1.46436	−0.0498185
$865$	0	0
$866$	0.811960	0.0275915
$867$	−9.69100	−0.329124
$868$	4.81868	0.163557
$869$	−7.93287	−0.269104
$870$	0	0
$871$	−20.4994	−0.694595
$872$	−2.51872	−0.0852945
$873$	−2.83732	−0.0960287
$874$	2.03041	0.0686797
$875$	0	0
$876$	41.5061	1.40236
$877$	28.0756	0.948046	0.474023	−	0.880513i	$-0.342801\pi$
$877$	28.0756	0.948046	0.474023	+	0.880513i	$0.342801\pi$
$878$	1.64524	0.0555241
$879$	−22.7886	−0.768641
$880$	0	0
$881$	11.9769	0.403511	0.201756	−	0.979436i	$-0.435335\pi$
$881$	11.9769	0.403511	0.201756	+	0.979436i	$0.435335\pi$
$882$	−0.936037	−0.0315180
$883$	52.5540	1.76858	0.884292	−	0.466934i	$-0.154641\pi$
$883$	52.5540	1.76858	0.884292	+	0.466934i	$0.154641\pi$
$884$	−12.2803	−0.413032
$885$	0	0
$886$	−0.315196	−0.0105892
$887$	−25.1933	−0.845908	−0.422954	−	0.906151i	$-0.639007\pi$
$887$	−25.1933	−0.845908	−0.422954	+	0.906151i	$0.639007\pi$
$888$	−2.34232	−0.0786033
$889$	−1.85478	−0.0622072
$890$	0	0
$891$	−6.79893	−0.227773
$892$	47.2616	1.58243
$893$	−43.2178	−1.44623
$894$	−0.519634	−0.0173792
$895$	0	0
$896$	2.15570	0.0720170
$897$	−13.6903	−0.457107
$898$	1.13677	0.0379346
$899$	−13.2095	−0.440561
$900$	0	0
$901$	−26.9533	−0.897943
$902$	0.395249	0.0131604
$903$	20.4821	0.681601
$904$	−2.93694	−0.0976813
$905$	0	0
$906$	2.29545	0.0762611
$907$	20.4959	0.680556	0.340278	−	0.940325i	$-0.389479\pi$
$907$	20.4959	0.680556	0.340278	+	0.940325i	$0.389479\pi$
$908$	17.3182	0.574726
$909$	−22.3595	−0.741618
$910$	0	0
$911$	17.4653	0.578650	0.289325	−	0.957231i	$-0.406569\pi$
$911$	17.4653	0.578650	0.289325	+	0.957231i	$0.406569\pi$
$912$	−76.4117	−2.53024
$913$	−9.11840	−0.301775
$914$	1.31092	0.0433612
$915$	0	0
$916$	−20.9066	−0.690773
$917$	−9.78695	−0.323194
$918$	−0.437344	−0.0144345
$919$	11.6377	0.383891	0.191946	−	0.981406i	$-0.438520\pi$
$919$	11.6377	0.383891	0.191946	+	0.981406i	$0.438520\pi$
$920$	0	0
$921$	−43.1251	−1.42102
$922$	−1.50752	−0.0496474
$923$	−10.5112	−0.345979
$924$	2.82454	0.0929206
$925$	0	0
$926$	−1.33639	−0.0439166
$927$	−6.31452	−0.207396
$928$	−4.43388	−0.145549
$929$	15.1572	0.497293	0.248646	−	0.968594i	$-0.420014\pi$
$929$	15.1572	0.497293	0.248646	+	0.968594i	$0.420014\pi$
$930$	0	0
$931$	50.8873	1.66776
$932$	21.4044	0.701123
$933$	−52.4190	−1.71612
$934$	2.38325	0.0779822
$935$	0	0
$936$	−1.06544	−0.0348249
$937$	−9.27609	−0.303037	−0.151518	−	0.988454i	$-0.548416\pi$
$937$	−9.27609	−0.303037	−0.151518	+	0.988454i	$0.548416\pi$
$938$	0.806367	0.0263288
$939$	−17.1481	−0.559606
$940$	0	0
$941$	−9.73294	−0.317285	−0.158642	−	0.987336i	$-0.550712\pi$
$941$	−9.73294	−0.317285	−0.158642	+	0.987336i	$0.550712\pi$
$942$	−2.17089	−0.0707313
$943$	−31.1811	−1.01540
$944$	55.6024	1.80971
$945$	0	0
$946$	−0.404229	−0.0131426
$947$	−12.5577	−0.408072	−0.204036	−	0.978963i	$-0.565406\pi$
$947$	−12.5577	−0.408072	−0.204036	+	0.978963i	$0.565406\pi$
$948$	57.0581	1.85316
$949$	−15.6743	−0.508810
$950$	0	0
$951$	50.5264	1.63843
$952$	0.967290	0.0313501
$953$	13.2448	0.429043	0.214521	−	0.976719i	$-0.431181\pi$
$953$	13.2448	0.429043	0.214521	+	0.976719i	$0.431181\pi$
$954$	−1.16782	−0.0378095
$955$	0	0
$956$	−55.2030	−1.78539
$957$	−7.74294	−0.250294
$958$	1.18940	0.0384276
$959$	5.09853	0.164640
$960$	0	0
$961$	−24.8766	−0.802472
$962$	0.441743	0.0142424
$963$	−27.8035	−0.895956
$964$	1.99518	0.0642604
$965$	0	0
$966$	0.538525	0.0173268
$967$	−7.05150	−0.226761	−0.113380	−	0.993552i	$-0.536168\pi$
$967$	−7.05150	−0.226761	−0.113380	+	0.993552i	$0.536168\pi$
$968$	2.94005	0.0944969
$969$	−68.7400	−2.20825
$970$	0	0
$971$	−48.6735	−1.56201	−0.781004	−	0.624526i	$-0.785292\pi$
$971$	−48.6735	−1.56201	−0.781004	+	0.624526i	$0.785292\pi$
$972$	38.3495	1.23006
$973$	−11.6203	−0.372529
$974$	−0.181043	−0.00580098
$975$	0	0
$976$	33.1887	1.06235
$977$	35.8543	1.14708	0.573541	−	0.819177i	$-0.305569\pi$
$977$	35.8543	1.14708	0.573541	+	0.819177i	$0.305569\pi$
$978$	−1.41453	−0.0452316
$979$	7.96778	0.254651
$980$	0	0
$981$	20.2371	0.646120
$982$	−0.555945	−0.0177409
$983$	8.67572	0.276713	0.138356	−	0.990383i	$-0.455818\pi$
$983$	8.67572	0.276713	0.138356	+	0.990383i	$0.455818\pi$
$984$	−5.69262	−0.181474
$985$	0	0
$986$	−1.32422	−0.0421717
$987$	−11.4626	−0.364859
$988$	28.9261	0.920262
$989$	31.8895	1.01403
$990$	0	0
$991$	−26.0844	−0.828599	−0.414300	−	0.910141i	$-0.635973\pi$
$991$	−26.0844	−0.828599	−0.414300	+	0.910141i	$0.635973\pi$
$992$	2.05536	0.0652578
$993$	−23.7025	−0.752177
$994$	0.413469	0.0131144
$995$	0	0
$996$	65.5851	2.07814
$997$	−43.1929	−1.36793	−0.683966	−	0.729514i	$-0.739747\pi$
$997$	−43.1929	−1.36793	−0.683966	+	0.729514i	$0.739747\pi$
$998$	1.20470	0.0381342
$999$	−6.50946	−0.205950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.j.1.15		25
5.4	even	2		1205.2.a.e.1.11	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.e.1.11	✓	25	5.4	even	2
6025.2.a.j.1.15		25	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)

\(f(q)\)	\(=\)	\(q+0.0694400 q^{2} +2.28670 q^{3} -1.99518 q^{4} +0.158789 q^{6} -0.976003 q^{7} -0.277425 q^{8} +2.22902 q^{9} +O(q^{10})\)	\(q+0.0694400 q^{2} +2.28670 q^{3} -1.99518 q^{4} +0.158789 q^{6} -0.976003 q^{7} -0.277425 q^{8} +2.22902 q^{9} +0.634315 q^{11} -4.56238 q^{12} +1.72293 q^{13} -0.0677737 q^{14} +3.97109 q^{16} +3.57240 q^{17} +0.154783 q^{18} -8.41472 q^{19} -2.23183 q^{21} +0.0440468 q^{22} -3.47484 q^{23} -0.634389 q^{24} +0.119641 q^{26} -1.76301 q^{27} +1.94730 q^{28} -5.33815 q^{29} +2.47454 q^{31} +0.830603 q^{32} +1.45049 q^{33} +0.248067 q^{34} -4.44729 q^{36} +3.69225 q^{37} -0.584318 q^{38} +3.93984 q^{39} +8.97339 q^{41} -0.154978 q^{42} -9.17725 q^{43} -1.26557 q^{44} -0.241293 q^{46} +5.13597 q^{47} +9.08071 q^{48} -6.04742 q^{49} +8.16902 q^{51} -3.43756 q^{52} -7.54486 q^{53} -0.122423 q^{54} +0.270768 q^{56} -19.2420 q^{57} -0.370681 q^{58} +14.0018 q^{59} +8.35758 q^{61} +0.171832 q^{62} -2.17553 q^{63} -7.88451 q^{64} +0.100722 q^{66} -11.8979 q^{67} -7.12757 q^{68} -7.94594 q^{69} -6.10073 q^{71} -0.618386 q^{72} -9.09745 q^{73} +0.256390 q^{74} +16.7889 q^{76} -0.619094 q^{77} +0.273583 q^{78} -12.5062 q^{79} -10.7185 q^{81} +0.623112 q^{82} -14.3752 q^{83} +4.45290 q^{84} -0.637268 q^{86} -12.2068 q^{87} -0.175975 q^{88} +12.5612 q^{89} -1.68159 q^{91} +6.93293 q^{92} +5.65855 q^{93} +0.356642 q^{94} +1.89934 q^{96} -1.27290 q^{97} -0.419932 q^{98} +1.41390 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9}+O(q^{10}) \) 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9	\( 25 q - 6 q^{2} - 15 q^{3} + 32 q^{4} - q^{6} - 19 q^{7} - 15 q^{8} + 32 q^{9} + 2 q^{11} - 20 q^{12} - 14 q^{13} - 5 q^{14} + 38 q^{16} - 7 q^{17} - 9 q^{18} + 30 q^{19} + q^{21} - q^{22} - 43 q^{23} - 6 q^{24} - 22 q^{26} - 42 q^{27} - 32 q^{28} - 4 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} + 7 q^{34} + 15 q^{36} - 16 q^{37} - 14 q^{38} - 21 q^{39} - q^{41} + 25 q^{42} - 35 q^{43} - 52 q^{44} - 27 q^{46} - 50 q^{47} - 26 q^{48} + 46 q^{49} - 7 q^{51} - 3 q^{52} - 4 q^{53} - 31 q^{54} - 51 q^{56} - 2 q^{58} + 6 q^{59} + 19 q^{61} - 28 q^{63} + 49 q^{64} - 27 q^{66} - 65 q^{67} + 25 q^{68} + 2 q^{69} - 34 q^{71} + 10 q^{72} - 8 q^{73} - 42 q^{74} + 71 q^{76} - q^{77} + 59 q^{78} - 12 q^{79} + 29 q^{81} - 11 q^{82} - 41 q^{83} - 10 q^{84} - 13 q^{86} - 40 q^{87} + 52 q^{88} - 24 q^{89} + 46 q^{91} - 85 q^{92} + 30 q^{93} + 14 q^{94} - 30 q^{96} - 9 q^{97} + 64 q^{98} + 2 q^{99}+O(q^{100}) \) 25 * q - 6 * q^2 - 15 * q^3 + 32 * q^4 - q^6 - 19 * q^7 - 15 * q^8 + 32 * q^9 + 2 * q^11 - 20 * q^12 - 14 * q^13 - 5 * q^14 + 38 * q^16 - 7 * q^17 - 9 * q^18 + 30 * q^19 + q^21 - q^22 - 43 * q^23 - 6 * q^24 - 22 * q^26 - 42 * q^27 - 32 * q^28 - 4 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 + 7 * q^34 + 15 * q^36 - 16 * q^37 - 14 * q^38 - 21 * q^39 - q^41 + 25 * q^42 - 35 * q^43 - 52 * q^44 - 27 * q^46 - 50 * q^47 - 26 * q^48 + 46 * q^49 - 7 * q^51 - 3 * q^52 - 4 * q^53 - 31 * q^54 - 51 * q^56 - 2 * q^58 + 6 * q^59 + 19 * q^61 - 28 * q^63 + 49 * q^64 - 27 * q^66 - 65 * q^67 + 25 * q^68 + 2 * q^69 - 34 * q^71 + 10 * q^72 - 8 * q^73 - 42 * q^74 + 71 * q^76 - q^77 + 59 * q^78 - 12 * q^79 + 29 * q^81 - 11 * q^82 - 41 * q^83 - 10 * q^84 - 13 * q^86 - 40 * q^87 + 52 * q^88 - 24 * q^89 + 46 * q^91 - 85 * q^92 + 30 * q^93 + 14 * q^94 - 30 * q^96 - 9 * q^97 + 64 * q^98 + 2 * q^99

Introduction

L-functions

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Database

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