LMFDB - Embedded newform 6025.2.a.e.1.4

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:	$5$
Coefficient field:	5.5.38569.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 5x^{3} + 4x - 1 $ x^5 - 5x^3 + 4x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.15098$ of defining polynomial
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)

$f(q)$	$=$	$q+0.717838 q^{2} -0.928169 q^{3} -1.48471 q^{4} -0.666275 q^{6} +1.52425 q^{7} -2.50146 q^{8} -2.13850 q^{9} +O(q^{10})$	\(q+0.717838 q^{2} -0.928169 q^{3} -1.48471 q^{4} -0.666275 q^{6} +1.52425 q^{7} -2.50146 q^{8} -2.13850 q^{9} +4.86530 q^{11} +1.37806 q^{12} +3.32124 q^{13} +1.09416 q^{14} +1.17378 q^{16} +8.03303 q^{17} -1.53510 q^{18} +0.900578 q^{19} -1.41476 q^{21} +3.49249 q^{22} -2.61237 q^{23} +2.32177 q^{24} +2.38411 q^{26} +4.76940 q^{27} -2.26307 q^{28} -5.55138 q^{29} +0.512300 q^{31} +5.84549 q^{32} -4.51582 q^{33} +5.76641 q^{34} +3.17505 q^{36} -6.28760 q^{37} +0.646469 q^{38} -3.08268 q^{39} -0.544057 q^{41} -1.01557 q^{42} +2.92273 q^{43} -7.22356 q^{44} -1.87525 q^{46} +3.68420 q^{47} -1.08947 q^{48} -4.67666 q^{49} -7.45601 q^{51} -4.93108 q^{52} +8.48471 q^{53} +3.42365 q^{54} -3.81285 q^{56} -0.835889 q^{57} -3.98499 q^{58} -4.89641 q^{59} -8.63153 q^{61} +0.367748 q^{62} -3.25961 q^{63} +1.84855 q^{64} -3.24163 q^{66} -6.25115 q^{67} -11.9267 q^{68} +2.42472 q^{69} -12.6119 q^{71} +5.34937 q^{72} +9.81374 q^{73} -4.51348 q^{74} -1.33710 q^{76} +7.41594 q^{77} -2.21286 q^{78} +12.8533 q^{79} +1.98869 q^{81} -0.390545 q^{82} -8.17033 q^{83} +2.10051 q^{84} +2.09805 q^{86} +5.15262 q^{87} -12.1703 q^{88} -3.31410 q^{89} +5.06241 q^{91} +3.87860 q^{92} -0.475502 q^{93} +2.64465 q^{94} -5.42561 q^{96} +13.9803 q^{97} -3.35708 q^{98} -10.4045 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 5 q^{3} + 3 q^{4} - 8 q^{6} + 10 q^{7} + 6 q^{9}+O(q^{10}) $ 5 * q + q^2 + 5 * q^3 + 3 * q^4 - 8 * q^6 + 10 * q^7 + 6 * q^9	$ 5 q + q^{2} + 5 q^{3} + 3 q^{4} - 8 q^{6} + 10 q^{7} + 6 q^{9} - 3 q^{11} - 8 q^{12} + q^{13} - q^{14} + 15 q^{16} + 5 q^{17} - 4 q^{18} + 3 q^{19} + 11 q^{21} + 13 q^{22} + 8 q^{23} - 14 q^{24} + 14 q^{26} + 14 q^{27} + 17 q^{28} + 9 q^{29} - 16 q^{31} + 16 q^{32} - 23 q^{33} - 10 q^{34} - 17 q^{36} - 7 q^{37} + 22 q^{38} - 19 q^{39} + 9 q^{41} - 17 q^{42} + 32 q^{43} - 8 q^{44} + 5 q^{46} + 7 q^{47} + 6 q^{48} + 9 q^{49} - 8 q^{51} + 10 q^{52} + 32 q^{53} + 32 q^{54} - 18 q^{56} - 3 q^{57} - 11 q^{58} - 8 q^{59} - 12 q^{61} - 17 q^{62} + 11 q^{63} - 16 q^{64} + 15 q^{66} + 5 q^{67} + 2 q^{68} + 7 q^{69} - 11 q^{71} - 7 q^{72} + 29 q^{73} + 10 q^{74} - 8 q^{76} + 5 q^{77} - 2 q^{78} + 16 q^{79} - 15 q^{81} + 2 q^{82} + 10 q^{83} + 5 q^{84} + 14 q^{86} + 37 q^{87} - 10 q^{88} + 9 q^{89} + 12 q^{91} + 25 q^{92} - 15 q^{93} - 11 q^{94} - 3 q^{96} + 43 q^{97} - 30 q^{98} - 30 q^{99}+O(q^{100}) $ 5 * q + q^2 + 5 * q^3 + 3 * q^4 - 8 * q^6 + 10 * q^7 + 6 * q^9 - 3 * q^11 - 8 * q^12 + q^13 - q^14 + 15 * q^16 + 5 * q^17 - 4 * q^18 + 3 * q^19 + 11 * q^21 + 13 * q^22 + 8 * q^23 - 14 * q^24 + 14 * q^26 + 14 * q^27 + 17 * q^28 + 9 * q^29 - 16 * q^31 + 16 * q^32 - 23 * q^33 - 10 * q^34 - 17 * q^36 - 7 * q^37 + 22 * q^38 - 19 * q^39 + 9 * q^41 - 17 * q^42 + 32 * q^43 - 8 * q^44 + 5 * q^46 + 7 * q^47 + 6 * q^48 + 9 * q^49 - 8 * q^51 + 10 * q^52 + 32 * q^53 + 32 * q^54 - 18 * q^56 - 3 * q^57 - 11 * q^58 - 8 * q^59 - 12 * q^61 - 17 * q^62 + 11 * q^63 - 16 * q^64 + 15 * q^66 + 5 * q^67 + 2 * q^68 + 7 * q^69 - 11 * q^71 - 7 * q^72 + 29 * q^73 + 10 * q^74 - 8 * q^76 + 5 * q^77 - 2 * q^78 + 16 * q^79 - 15 * q^81 + 2 * q^82 + 10 * q^83 + 5 * q^84 + 14 * q^86 + 37 * q^87 - 10 * q^88 + 9 * q^89 + 12 * q^91 + 25 * q^92 - 15 * q^93 - 11 * q^94 - 3 * q^96 + 43 * q^97 - 30 * q^98 - 30 * 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 $

$2$	0.717838	0.507588	0.253794	−	0.967258i	$-0.418322\pi$
$2$	0.717838	0.507588	0.253794	+	0.967258i	$0.418322\pi$
$3$	−0.928169	−0.535879	−0.267939	−	0.963436i	$-0.586343\pi$
$3$	−0.928169	−0.535879	−0.267939	+	0.963436i	$0.586343\pi$
$4$	−1.48471	−0.742355
$5$	0	0
$5$	0	0
$6$	−0.666275	−0.272006
$7$	1.52425	0.576113	0.288056	−	0.957613i	$-0.406991\pi$
$7$	1.52425	0.576113	0.288056	+	0.957613i	$0.406991\pi$
$8$	−2.50146	−0.884398
$9$	−2.13850	−0.712834
$10$	0	0
$11$	4.86530	1.46694	0.733471	−	0.679720i	$-0.237899\pi$
$11$	4.86530	1.46694	0.733471	+	0.679720i	$0.237899\pi$
$12$	1.37806	0.397812
$13$	3.32124	0.921147	0.460573	−	0.887622i	$-0.347644\pi$
$13$	3.32124	0.921147	0.460573	+	0.887622i	$0.347644\pi$
$14$	1.09416	0.292428
$15$	0	0
$16$	1.17378	0.293445
$17$	8.03303	1.94830	0.974148	−	0.225911i	$-0.0725359\pi$
$17$	8.03303	1.94830	0.974148	+	0.225911i	$0.0725359\pi$
$18$	−1.53510	−0.361826
$19$	0.900578	0.206607	0.103303	−	0.994650i	$-0.467059\pi$
$19$	0.900578	0.206607	0.103303	+	0.994650i	$0.467059\pi$
$20$	0	0
$21$	−1.41476	−0.308727
$22$	3.49249	0.744602
$23$	−2.61237	−0.544716	−0.272358	−	0.962196i	$-0.587803\pi$
$23$	−2.61237	−0.544716	−0.272358	+	0.962196i	$0.587803\pi$
$24$	2.32177	0.473930
$25$	0	0
$26$	2.38411	0.467563
$27$	4.76940	0.917871
$28$	−2.26307	−0.427680
$29$	−5.55138	−1.03087	−0.515433	−	0.856930i	$-0.672369\pi$
$29$	−5.55138	−1.03087	−0.515433	+	0.856930i	$0.672369\pi$
$30$	0	0
$31$	0.512300	0.0920119	0.0460059	−	0.998941i	$-0.485351\pi$
$31$	0.512300	0.0920119	0.0460059	+	0.998941i	$0.485351\pi$
$32$	5.84549	1.03335
$33$	−4.51582	−0.786104
$34$	5.76641	0.988931
$35$	0	0
$36$	3.17505	0.529176
$37$	−6.28760	−1.03368	−0.516838	−	0.856083i	$-0.672891\pi$
$37$	−6.28760	−1.03368	−0.516838	+	0.856083i	$0.672891\pi$
$38$	0.646469	0.104871
$39$	−3.08268	−0.493623
$40$	0	0
$41$	−0.544057	−0.0849674	−0.0424837	−	0.999097i	$-0.513527\pi$
$41$	−0.544057	−0.0849674	−0.0424837	+	0.999097i	$0.513527\pi$
$42$	−1.01557	−0.156706
$43$	2.92273	0.445712	0.222856	−	0.974851i	$-0.428462\pi$
$43$	2.92273	0.445712	0.222856	+	0.974851i	$0.428462\pi$
$44$	−7.22356	−1.08899
$45$	0	0
$46$	−1.87525	−0.276491
$47$	3.68420	0.537395	0.268698	−	0.963225i	$-0.413407\pi$
$47$	3.68420	0.537395	0.268698	+	0.963225i	$0.413407\pi$
$48$	−1.08947	−0.157251
$49$	−4.67666	−0.668094
$50$	0	0
$51$	−7.45601	−1.04405
$52$	−4.93108	−0.683818
$53$	8.48471	1.16546	0.582732	−	0.812664i	$-0.301984\pi$
$53$	8.48471	1.16546	0.582732	+	0.812664i	$0.301984\pi$
$54$	3.42365	0.465900
$55$	0	0
$56$	−3.81285	−0.509513
$57$	−0.835889	−0.110716
$58$	−3.98499	−0.523255
$59$	−4.89641	−0.637459	−0.318729	−	0.947846i	$-0.603256\pi$
$59$	−4.89641	−0.637459	−0.318729	+	0.947846i	$0.603256\pi$
$60$	0	0
$61$	−8.63153	−1.10515	−0.552577	−	0.833462i	$-0.686355\pi$
$61$	−8.63153	−1.10515	−0.552577	+	0.833462i	$0.686355\pi$
$62$	0.367748	0.0467041
$63$	−3.25961	−0.410673
$64$	1.84855	0.231069
$65$	0	0
$66$	−3.24163	−0.399017
$67$	−6.25115	−0.763699	−0.381850	−	0.924224i	$-0.624713\pi$
$67$	−6.25115	−0.763699	−0.381850	+	0.924224i	$0.624713\pi$
$68$	−11.9267	−1.44633
$69$	2.42472	0.291902
$70$	0	0
$71$	−12.6119	−1.49676	−0.748379	−	0.663272i	$-0.769167\pi$
$71$	−12.6119	−1.49676	−0.748379	+	0.663272i	$0.769167\pi$
$72$	5.34937	0.630429
$73$	9.81374	1.14861	0.574306	−	0.818641i	$-0.305272\pi$
$73$	9.81374	1.14861	0.574306	+	0.818641i	$0.305272\pi$
$74$	−4.51348	−0.524681
$75$	0	0
$76$	−1.33710	−0.153376
$77$	7.41594	0.845125
$78$	−2.21286	−0.250557
$79$	12.8533	1.44611	0.723057	−	0.690788i	$-0.242736\pi$
$79$	12.8533	1.44611	0.723057	+	0.690788i	$0.242736\pi$
$80$	0	0
$81$	1.98869	0.220966
$82$	−0.390545	−0.0431284
$83$	−8.17033	−0.896810	−0.448405	−	0.893830i	$-0.648008\pi$
$83$	−8.17033	−0.896810	−0.448405	+	0.893830i	$0.648008\pi$
$84$	2.10051	0.229185
$85$	0	0
$86$	2.09805	0.226238
$87$	5.15262	0.552419
$88$	−12.1703	−1.29736
$89$	−3.31410	−0.351294	−0.175647	−	0.984453i	$-0.556202\pi$
$89$	−3.31410	−0.351294	−0.175647	+	0.984453i	$0.556202\pi$
$90$	0	0
$91$	5.06241	0.530685
$92$	3.87860	0.404372
$93$	−0.475502	−0.0493072
$94$	2.64465	0.272775
$95$	0	0
$96$	−5.42561	−0.553749
$97$	13.9803	1.41948	0.709740	−	0.704463i	$-0.248812\pi$
$97$	13.9803	1.41948	0.709740	+	0.704463i	$0.248812\pi$
$98$	−3.35708	−0.339116
$99$	−10.4045	−1.04569
$100$	0	0
$101$	10.2388	1.01880	0.509400	−	0.860530i	$-0.329867\pi$
$101$	10.2388	1.01880	0.509400	+	0.860530i	$0.329867\pi$
$102$	−5.35221	−0.529947
$103$	16.1020	1.58657	0.793287	−	0.608848i	$-0.208368\pi$
$103$	16.1020	1.58657	0.793287	+	0.608848i	$0.208368\pi$
$104$	−8.30794	−0.814660
$105$	0	0
$106$	6.09064	0.591576
$107$	3.85560	0.372735	0.186367	−	0.982480i	$-0.440329\pi$
$107$	3.85560	0.372735	0.186367	+	0.982480i	$0.440329\pi$
$108$	−7.08117	−0.681386
$109$	−9.61567	−0.921014	−0.460507	−	0.887656i	$-0.652332\pi$
$109$	−9.61567	−0.921014	−0.460507	+	0.887656i	$0.652332\pi$
$110$	0	0
$111$	5.83596	0.553925
$112$	1.78914	0.169057
$113$	5.33091	0.501490	0.250745	−	0.968053i	$-0.419324\pi$
$113$	5.33091	0.501490	0.250745	+	0.968053i	$0.419324\pi$
$114$	−0.600033	−0.0561982
$115$	0	0
$116$	8.24219	0.765268
$117$	−7.10248	−0.656625
$118$	−3.51483	−0.323566
$119$	12.2444	1.12244
$120$	0	0
$121$	12.6711	1.15192
$122$	−6.19603	−0.560963
$123$	0.504977	0.0455323
$124$	−0.760617	−0.0683054
$125$	0	0
$126$	−2.33987	−0.208452
$127$	−10.3651	−0.919755	−0.459878	−	0.887982i	$-0.652107\pi$
$127$	−10.3651	−0.919755	−0.459878	+	0.887982i	$0.652107\pi$
$128$	−10.3640	−0.916059
$129$	−2.71279	−0.238848
$130$	0	0
$131$	11.1834	0.977096	0.488548	−	0.872537i	$-0.337527\pi$
$131$	11.1834	0.977096	0.488548	+	0.872537i	$0.337527\pi$
$132$	6.70468	0.583568
$133$	1.37271	0.119029
$134$	−4.48731	−0.387644
$135$	0	0
$136$	−20.0943	−1.72307
$137$	11.7078	1.00026	0.500131	−	0.865950i	$-0.333285\pi$
$137$	11.7078	1.00026	0.500131	+	0.865950i	$0.333285\pi$
$138$	1.74055	0.148166
$139$	−3.33109	−0.282540	−0.141270	−	0.989971i	$-0.545119\pi$
$139$	−3.33109	−0.282540	−0.141270	+	0.989971i	$0.545119\pi$
$140$	0	0
$141$	−3.41956	−0.287979
$142$	−9.05330	−0.759736
$143$	16.1588	1.35127
$144$	−2.51013	−0.209178
$145$	0	0
$146$	7.04467	0.583021
$147$	4.34073	0.358017
$148$	9.33526	0.767354
$149$	6.91612	0.566591	0.283295	−	0.959033i	$-0.408572\pi$
$149$	6.91612	0.566591	0.283295	+	0.959033i	$0.408572\pi$
$150$	0	0
$151$	7.97439	0.648947	0.324473	−	0.945895i	$-0.394813\pi$
$151$	7.97439	0.648947	0.324473	+	0.945895i	$0.394813\pi$
$152$	−2.25276	−0.182723
$153$	−17.1786	−1.38881
$154$	5.32344	0.428975
$155$	0	0
$156$	4.57688	0.366443
$157$	18.3891	1.46761	0.733805	−	0.679361i	$-0.237743\pi$
$157$	18.3891	1.46761	0.733805	+	0.679361i	$0.237743\pi$
$158$	9.22662	0.734030
$159$	−7.87525	−0.624548
$160$	0	0
$161$	−3.98190	−0.313818
$162$	1.42756	0.112160
$163$	1.69352	0.132646	0.0663232	−	0.997798i	$-0.478873\pi$
$163$	1.69352	0.132646	0.0663232	+	0.997798i	$0.478873\pi$
$164$	0.807767	0.0630760
$165$	0	0
$166$	−5.86497	−0.455210
$167$	−10.6749	−0.826050	−0.413025	−	0.910720i	$-0.635528\pi$
$167$	−10.6749	−0.826050	−0.413025	+	0.910720i	$0.635528\pi$
$168$	3.53897	0.273037
$169$	−1.96935	−0.151488
$170$	0	0
$171$	−1.92589	−0.147276
$172$	−4.33941	−0.330877
$173$	6.54164	0.497352	0.248676	−	0.968587i	$-0.420005\pi$
$173$	6.54164	0.497352	0.248676	+	0.968587i	$0.420005\pi$
$174$	3.69875	0.280401
$175$	0	0
$176$	5.71079	0.430467
$177$	4.54470	0.341601
$178$	−2.37899	−0.178313
$179$	15.5321	1.16093	0.580463	−	0.814286i	$-0.302871\pi$
$179$	15.5321	1.16093	0.580463	+	0.814286i	$0.302871\pi$
$180$	0	0
$181$	7.45316	0.553989	0.276995	−	0.960871i	$-0.410662\pi$
$181$	7.45316	0.553989	0.276995	+	0.960871i	$0.410662\pi$
$182$	3.63399	0.269369
$183$	8.01152	0.592229
$184$	6.53471	0.481746
$185$	0	0
$186$	−0.341333	−0.0250277
$187$	39.0831	2.85804
$188$	−5.46996	−0.398938
$189$	7.26976	0.528798
$190$	0	0
$191$	−19.7989	−1.43260	−0.716299	−	0.697794i	$-0.754165\pi$
$191$	−19.7989	−1.43260	−0.716299	+	0.697794i	$0.754165\pi$
$192$	−1.71577	−0.123825
$193$	−13.9031	−1.00077	−0.500385	−	0.865803i	$-0.666808\pi$
$193$	−13.9031	−1.00077	−0.500385	+	0.865803i	$0.666808\pi$
$194$	10.0356	0.720511
$195$	0	0
$196$	6.94348	0.495963
$197$	−12.6289	−0.899772	−0.449886	−	0.893086i	$-0.648535\pi$
$197$	−12.6289	−0.899772	−0.449886	+	0.893086i	$0.648535\pi$
$198$	−7.46870	−0.530778
$199$	16.6713	1.18180	0.590899	−	0.806745i	$-0.298773\pi$
$199$	16.6713	1.18180	0.590899	+	0.806745i	$0.298773\pi$
$200$	0	0
$201$	5.80212	0.409250
$202$	7.34980	0.517130
$203$	−8.46170	−0.593895
$204$	11.0700	0.775056
$205$	0	0
$206$	11.5586	0.805326
$207$	5.58655	0.388292
$208$	3.89841	0.270306
$209$	4.38158	0.303081
$210$	0	0
$211$	7.35907	0.506619	0.253310	−	0.967385i	$-0.418481\pi$
$211$	7.35907	0.506619	0.253310	+	0.967385i	$0.418481\pi$
$212$	−12.5973	−0.865188
$213$	11.7060	0.802081
$214$	2.76769	0.189196
$215$	0	0
$216$	−11.9304	−0.811764
$217$	0.780874	0.0530092
$218$	−6.90249	−0.467496
$219$	−9.10881	−0.615516
$220$	0	0
$221$	26.6796	1.79467
$222$	4.18927	0.281165
$223$	20.3021	1.35953	0.679763	−	0.733431i	$-0.262082\pi$
$223$	20.3021	1.35953	0.679763	+	0.733431i	$0.262082\pi$
$224$	8.91000	0.595324
$225$	0	0
$226$	3.82673	0.254550
$227$	−5.93500	−0.393920	−0.196960	−	0.980412i	$-0.563107\pi$
$227$	−5.93500	−0.393920	−0.196960	+	0.980412i	$0.563107\pi$
$228$	1.24105	0.0821907
$229$	11.3079	0.747245	0.373623	−	0.927581i	$-0.378116\pi$
$229$	11.3079	0.747245	0.373623	+	0.927581i	$0.378116\pi$
$230$	0	0
$231$	−6.88325	−0.452884
$232$	13.8865	0.911695
$233$	4.19060	0.274535	0.137268	−	0.990534i	$-0.456168\pi$
$233$	4.19060	0.274535	0.137268	+	0.990534i	$0.456168\pi$
$234$	−5.09843	−0.333295
$235$	0	0
$236$	7.26975	0.473220
$237$	−11.9301	−0.774942
$238$	8.78946	0.569736
$239$	9.57349	0.619258	0.309629	−	0.950857i	$-0.399795\pi$
$239$	9.57349	0.619258	0.309629	+	0.950857i	$0.399795\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	9.09582	0.584701
$243$	−16.1540	−1.03628
$244$	12.8153	0.820416
$245$	0	0
$246$	0.362492	0.0231116
$247$	2.99104	0.190315
$248$	−1.28150	−0.0813751
$249$	7.58345	0.480582
$250$	0	0
$251$	−8.57172	−0.541042	−0.270521	−	0.962714i	$-0.587196\pi$
$251$	−8.57172	−0.541042	−0.270521	+	0.962714i	$0.587196\pi$
$252$	4.83958	0.304865
$253$	−12.7099	−0.799067
$254$	−7.44047	−0.466857
$255$	0	0
$256$	−11.1368	−0.696050
$257$	12.9406	0.807210	0.403605	−	0.914933i	$-0.367757\pi$
$257$	12.9406	0.807210	0.403605	+	0.914933i	$0.367757\pi$
$258$	−1.94734	−0.121236
$259$	−9.58388	−0.595514
$260$	0	0
$261$	11.8716	0.734836
$262$	8.02784	0.495962
$263$	−4.52659	−0.279121	−0.139561	−	0.990214i	$-0.544569\pi$
$263$	−4.52659	−0.279121	−0.139561	+	0.990214i	$0.544569\pi$
$264$	11.2961	0.695229
$265$	0	0
$266$	0.985381	0.0604176
$267$	3.07605	0.188251
$268$	9.28114	0.566936
$269$	12.1257	0.739317	0.369659	−	0.929168i	$-0.379475\pi$
$269$	12.1257	0.739317	0.369659	+	0.929168i	$0.379475\pi$
$270$	0	0
$271$	−28.2735	−1.71749	−0.858746	−	0.512402i	$-0.828756\pi$
$271$	−28.2735	−1.71749	−0.858746	+	0.512402i	$0.828756\pi$
$272$	9.42901	0.571718
$273$	−4.69877	−0.284383
$274$	8.40428	0.507721
$275$	0	0
$276$	−3.60000	−0.216695
$277$	−25.0944	−1.50777	−0.753887	−	0.657004i	$-0.771823\pi$
$277$	−25.0944	−1.50777	−0.753887	+	0.657004i	$0.771823\pi$
$278$	−2.39118	−0.143414
$279$	−1.09555	−0.0655892
$280$	0	0
$281$	24.5912	1.46699	0.733494	−	0.679696i	$-0.237888\pi$
$281$	24.5912	1.46699	0.733494	+	0.679696i	$0.237888\pi$
$282$	−2.45469	−0.146174
$283$	12.8894	0.766197	0.383098	−	0.923708i	$-0.374857\pi$
$283$	12.8894	0.766197	0.383098	+	0.923708i	$0.374857\pi$
$284$	18.7250	1.11112
$285$	0	0
$286$	11.5994	0.685888
$287$	−0.829280	−0.0489508
$288$	−12.5006	−0.736605
$289$	47.5296	2.79586
$290$	0	0
$291$	−12.9761	−0.760670
$292$	−14.5705	−0.852677
$293$	−23.8124	−1.39113	−0.695567	−	0.718461i	$-0.744847\pi$
$293$	−23.8124	−1.39113	−0.695567	+	0.718461i	$0.744847\pi$
$294$	3.11594	0.181725
$295$	0	0
$296$	15.7282	0.914180
$297$	23.2046	1.34647
$298$	4.96465	0.287595
$299$	−8.67630	−0.501763
$300$	0	0
$301$	4.45498	0.256781
$302$	5.72432	0.329397
$303$	−9.50335	−0.545953
$304$	1.05708	0.0606278
$305$	0	0
$306$	−12.3315	−0.704944
$307$	9.16919	0.523313	0.261657	−	0.965161i	$-0.415731\pi$
$307$	9.16919	0.523313	0.261657	+	0.965161i	$0.415731\pi$
$308$	−11.0105	−0.627382
$309$	−14.9454	−0.850211
$310$	0	0
$311$	27.8462	1.57901	0.789506	−	0.613742i	$-0.210337\pi$
$311$	27.8462	1.57901	0.789506	+	0.613742i	$0.210337\pi$
$312$	7.71117	0.436559
$313$	−5.87604	−0.332134	−0.166067	−	0.986115i	$-0.553107\pi$
$313$	−5.87604	−0.332134	−0.166067	+	0.986115i	$0.553107\pi$
$314$	13.2004	0.744940
$315$	0	0
$316$	−19.0835	−1.07353
$317$	−6.31512	−0.354693	−0.177346	−	0.984149i	$-0.556751\pi$
$317$	−6.31512	−0.354693	−0.177346	+	0.984149i	$0.556751\pi$
$318$	−5.65315	−0.317013
$319$	−27.0091	−1.51222
$320$	0	0
$321$	−3.57865	−0.199741
$322$	−2.85836	−0.159290
$323$	7.23437	0.402531
$324$	−2.95263	−0.164035
$325$	0	0
$326$	1.21567	0.0673297
$327$	8.92497	0.493552
$328$	1.36093	0.0751450
$329$	5.61564	0.309600
$330$	0	0
$331$	7.33322	0.403070	0.201535	−	0.979481i	$-0.435407\pi$
$331$	7.33322	0.403070	0.201535	+	0.979481i	$0.435407\pi$
$332$	12.1306	0.665751
$333$	13.4460	0.736839
$334$	−7.66286	−0.419293
$335$	0	0
$336$	−1.66062	−0.0905943
$337$	−20.9593	−1.14172	−0.570862	−	0.821046i	$-0.693391\pi$
$337$	−20.9593	−1.14172	−0.570862	+	0.821046i	$0.693391\pi$
$338$	−1.41367	−0.0768936
$339$	−4.94799	−0.268738
$340$	0	0
$341$	2.49249	0.134976
$342$	−1.38247	−0.0747557
$343$	−17.7982	−0.961010
$344$	−7.31108	−0.394187
$345$	0	0
$346$	4.69583	0.252450
$347$	−26.1547	−1.40406	−0.702029	−	0.712148i	$-0.747722\pi$
$347$	−26.1547	−1.40406	−0.702029	+	0.712148i	$0.747722\pi$
$348$	−7.65015	−0.410091
$349$	20.5460	1.09980	0.549902	−	0.835229i	$-0.314665\pi$
$349$	20.5460	1.09980	0.549902	+	0.835229i	$0.314665\pi$
$350$	0	0
$351$	15.8403	0.845494
$352$	28.4401	1.51586
$353$	20.2567	1.07815	0.539077	−	0.842257i	$-0.318773\pi$
$353$	20.2567	1.07815	0.539077	+	0.842257i	$0.318773\pi$
$354$	3.26236	0.173392
$355$	0	0
$356$	4.92048	0.260785
$357$	−11.3648	−0.601491
$358$	11.1496	0.589272
$359$	−16.5290	−0.872368	−0.436184	−	0.899858i	$-0.643670\pi$
$359$	−16.5290	−0.872368	−0.436184	+	0.899858i	$0.643670\pi$
$360$	0	0
$361$	−18.1890	−0.957314
$362$	5.35016	0.281198
$363$	−11.7610	−0.617291
$364$	−7.51620	−0.393956
$365$	0	0
$366$	5.75097	0.300608
$367$	35.6165	1.85916	0.929582	−	0.368614i	$-0.120168\pi$
$367$	35.6165	1.85916	0.929582	+	0.368614i	$0.120168\pi$
$368$	−3.06634	−0.159844
$369$	1.16347	0.0605677
$370$	0	0
$371$	12.9328	0.671439
$372$	0.705982	0.0366034
$373$	−24.7825	−1.28319	−0.641594	−	0.767045i	$-0.721726\pi$
$373$	−24.7825	−1.28319	−0.641594	+	0.767045i	$0.721726\pi$
$374$	28.0553	1.45071
$375$	0	0
$376$	−9.21585	−0.475271
$377$	−18.4375	−0.949579
$378$	5.21851	0.268411
$379$	−0.476989	−0.0245013	−0.0122506	−	0.999925i	$-0.503900\pi$
$379$	−0.476989	−0.0245013	−0.0122506	+	0.999925i	$0.503900\pi$
$380$	0	0
$381$	9.62059	0.492878
$382$	−14.2124	−0.727169
$383$	23.4566	1.19858	0.599289	−	0.800533i	$-0.295450\pi$
$383$	23.4566	1.19858	0.599289	+	0.800533i	$0.295450\pi$
$384$	9.61957	0.490897
$385$	0	0
$386$	−9.98019	−0.507979
$387$	−6.25026	−0.317719
$388$	−20.7566	−1.05376
$389$	36.6562	1.85854	0.929271	−	0.369400i	$-0.120437\pi$
$389$	36.6562	1.85854	0.929271	+	0.369400i	$0.120437\pi$
$390$	0	0
$391$	−20.9852	−1.06127
$392$	11.6984	0.590861
$393$	−10.3801	−0.523605
$394$	−9.06550	−0.456713
$395$	0	0
$396$	15.4476	0.776270
$397$	30.8395	1.54779	0.773895	−	0.633314i	$-0.218306\pi$
$397$	30.8395	1.54779	0.773895	+	0.633314i	$0.218306\pi$
$398$	11.9673	0.599867
$399$	−1.27411	−0.0637851
$400$	0	0
$401$	−36.8823	−1.84181	−0.920907	−	0.389782i	$-0.872550\pi$
$401$	−36.8823	−1.84181	−0.920907	+	0.389782i	$0.872550\pi$
$402$	4.16498	0.207730
$403$	1.70147	0.0847564
$404$	−15.2017	−0.756311
$405$	0	0
$406$	−6.07412	−0.301454
$407$	−30.5911	−1.51634
$408$	18.6509	0.923356
$409$	−7.02816	−0.347520	−0.173760	−	0.984788i	$-0.555592\pi$
$409$	−7.02816	−0.347520	−0.173760	+	0.984788i	$0.555592\pi$
$410$	0	0
$411$	−10.8668	−0.536020
$412$	−23.9067	−1.17780
$413$	−7.46336	−0.367248
$414$	4.01023	0.197092
$415$	0	0
$416$	19.4143	0.951864
$417$	3.09182	0.151407
$418$	3.14527	0.153840
$419$	10.4901	0.512477	0.256238	−	0.966614i	$-0.417517\pi$
$419$	10.4901	0.512477	0.256238	+	0.966614i	$0.417517\pi$
$420$	0	0
$421$	0.737658	0.0359513	0.0179756	−	0.999838i	$-0.494278\pi$
$421$	0.737658	0.0359513	0.0179756	+	0.999838i	$0.494278\pi$
$422$	5.28261	0.257154
$423$	−7.87866	−0.383073
$424$	−21.2241	−1.03073
$425$	0	0
$426$	8.40299	0.407126
$427$	−13.1566	−0.636693
$428$	−5.72444	−0.276701
$429$	−14.9981	−0.724117
$430$	0	0
$431$	12.0457	0.580219	0.290109	−	0.956994i	$-0.406308\pi$
$431$	12.0457	0.580219	0.290109	+	0.956994i	$0.406308\pi$
$432$	5.59823	0.269345
$433$	−6.71138	−0.322528	−0.161264	−	0.986911i	$-0.551557\pi$
$433$	−6.71138	−0.322528	−0.161264	+	0.986911i	$0.551557\pi$
$434$	0.560541	0.0269068
$435$	0	0
$436$	14.2765	0.683719
$437$	−2.35264	−0.112542
$438$	−6.53865	−0.312429
$439$	2.10269	0.100356	0.0501780	−	0.998740i	$-0.484021\pi$
$439$	2.10269	0.100356	0.0501780	+	0.998740i	$0.484021\pi$
$440$	0	0
$441$	10.0010	0.476240
$442$	19.1516	0.910951
$443$	−27.2375	−1.29409	−0.647047	−	0.762450i	$-0.723996\pi$
$443$	−27.2375	−1.29409	−0.647047	+	0.762450i	$0.723996\pi$
$444$	−8.66470	−0.411209
$445$	0	0
$446$	14.5736	0.690079
$447$	−6.41933	−0.303624
$448$	2.81766	0.133122
$449$	−15.0683	−0.711116	−0.355558	−	0.934654i	$-0.615709\pi$
$449$	−15.0683	−0.711116	−0.355558	+	0.934654i	$0.615709\pi$
$450$	0	0
$451$	−2.64700	−0.124642
$452$	−7.91486	−0.372283
$453$	−7.40159	−0.347757
$454$	−4.26036	−0.199949
$455$	0	0
$456$	2.09094	0.0979172
$457$	0.141399	0.00661436	0.00330718	−	0.999995i	$-0.498947\pi$
$457$	0.141399	0.00661436	0.00330718	+	0.999995i	$0.498947\pi$
$458$	8.11721	0.379292
$459$	38.3127	1.78829
$460$	0	0
$461$	3.44939	0.160654	0.0803270	−	0.996769i	$-0.474404\pi$
$461$	3.44939	0.160654	0.0803270	+	0.996769i	$0.474404\pi$
$462$	−4.94105	−0.229879
$463$	16.3766	0.761087	0.380544	−	0.924763i	$-0.375737\pi$
$463$	16.3766	0.761087	0.380544	+	0.924763i	$0.375737\pi$
$464$	−6.51610	−0.302502
$465$	0	0
$466$	3.00817	0.139351
$467$	−3.07418	−0.142256	−0.0711281	−	0.997467i	$-0.522660\pi$
$467$	−3.07418	−0.142256	−0.0711281	+	0.997467i	$0.522660\pi$
$468$	10.5451	0.487448
$469$	−9.52832	−0.439977
$470$	0	0
$471$	−17.0682	−0.786461
$472$	12.2482	0.563767
$473$	14.2200	0.653835
$474$	−8.56386	−0.393351
$475$	0	0
$476$	−18.1793	−0.833247
$477$	−18.1446	−0.830782
$478$	6.87221	0.314328
$479$	6.97404	0.318652	0.159326	−	0.987226i	$-0.449068\pi$
$479$	6.97404	0.318652	0.159326	+	0.987226i	$0.449068\pi$
$480$	0	0
$481$	−20.8826	−0.952167
$482$	0.717838	0.0326966
$483$	3.69588	0.168168
$484$	−18.8130	−0.855134
$485$	0	0
$486$	−11.5960	−0.526004
$487$	−8.78335	−0.398011	−0.199006	−	0.979998i	$-0.563771\pi$
$487$	−8.78335	−0.398011	−0.199006	+	0.979998i	$0.563771\pi$
$488$	21.5914	0.977396
$489$	−1.57187	−0.0710824
$490$	0	0
$491$	−15.7914	−0.712655	−0.356327	−	0.934361i	$-0.615971\pi$
$491$	−15.7914	−0.712655	−0.356327	+	0.934361i	$0.615971\pi$
$492$	−0.749744	−0.0338011
$493$	−44.5944	−2.00843
$494$	2.14708	0.0966017
$495$	0	0
$496$	0.601328	0.0270004
$497$	−19.2237	−0.862301
$498$	5.44368	0.243937
$499$	−27.8404	−1.24631	−0.623153	−	0.782100i	$-0.714149\pi$
$499$	−27.8404	−1.24631	−0.623153	+	0.782100i	$0.714149\pi$
$500$	0	0
$501$	9.90814	0.442663
$502$	−6.15310	−0.274626
$503$	21.5171	0.959401	0.479701	−	0.877432i	$-0.340745\pi$
$503$	21.5171	0.959401	0.479701	+	0.877432i	$0.340745\pi$
$504$	8.15378	0.363198
$505$	0	0
$506$	−9.12367	−0.405597
$507$	1.82789	0.0811794
$508$	15.3892	0.682785
$509$	−8.85210	−0.392363	−0.196181	−	0.980568i	$-0.562854\pi$
$509$	−8.85210	−0.392363	−0.196181	+	0.980568i	$0.562854\pi$
$510$	0	0
$511$	14.9586	0.661730
$512$	12.7336	0.562753
$513$	4.29522	0.189639
$514$	9.28922	0.409730
$515$	0	0
$516$	4.02770	0.177310
$517$	17.9247	0.788328
$518$	−6.87967	−0.302275
$519$	−6.07175	−0.266520
$520$	0	0
$521$	11.2083	0.491045	0.245522	−	0.969391i	$-0.421040\pi$
$521$	11.2083	0.491045	0.245522	+	0.969391i	$0.421040\pi$
$522$	8.52190	0.372994
$523$	9.39942	0.411008	0.205504	−	0.978656i	$-0.434117\pi$
$523$	9.39942	0.411008	0.205504	+	0.978656i	$0.434117\pi$
$524$	−16.6041	−0.725351
$525$	0	0
$526$	−3.24935	−0.141679
$527$	4.11532	0.179266
$528$	−5.30058	−0.230678
$529$	−16.1755	−0.703285
$530$	0	0
$531$	10.4710	0.454402
$532$	−2.03807	−0.0883616
$533$	−1.80695	−0.0782675
$534$	2.20810	0.0955539
$535$	0	0
$536$	15.6370	0.675414
$537$	−14.4165	−0.622116
$538$	8.70429	0.375268
$539$	−22.7533	−0.980056
$540$	0	0
$541$	27.2887	1.17323	0.586615	−	0.809866i	$-0.300460\pi$
$541$	27.2887	1.17323	0.586615	+	0.809866i	$0.300460\pi$
$542$	−20.2958	−0.871778
$543$	−6.91780	−0.296871
$544$	46.9570	2.01327
$545$	0	0
$546$	−3.37296	−0.144349
$547$	32.7588	1.40066	0.700332	−	0.713817i	$-0.253035\pi$
$547$	32.7588	1.40066	0.700332	+	0.713817i	$0.253035\pi$
$548$	−17.3826	−0.742549
$549$	18.4585	0.787791
$550$	0	0
$551$	−4.99945	−0.212984
$552$	−6.06532	−0.258157
$553$	19.5917	0.833125
$554$	−18.0137	−0.765328
$555$	0	0
$556$	4.94571	0.209745
$557$	14.4303	0.611429	0.305715	−	0.952123i	$-0.401105\pi$
$557$	14.4303	0.611429	0.305715	+	0.952123i	$0.401105\pi$
$558$	−0.786430	−0.0332923
$559$	9.70710	0.410567
$560$	0	0
$561$	−36.2757	−1.53156
$562$	17.6525	0.744625
$563$	−23.9148	−1.00789	−0.503944	−	0.863736i	$-0.668118\pi$
$563$	−23.9148	−1.00789	−0.503944	+	0.863736i	$0.668118\pi$
$564$	5.07705	0.213782
$565$	0	0
$566$	9.25251	0.388912
$567$	3.03127	0.127301
$568$	31.5481	1.32373
$569$	−28.7548	−1.20546	−0.602731	−	0.797944i	$-0.705921\pi$
$569$	−28.7548	−1.20546	−0.602731	+	0.797944i	$0.705921\pi$
$570$	0	0
$571$	14.1677	0.592898	0.296449	−	0.955049i	$-0.404197\pi$
$571$	14.1677	0.592898	0.296449	+	0.955049i	$0.404197\pi$
$572$	−23.9912	−1.00312
$573$	18.3767	0.767699
$574$	−0.595288	−0.0248468
$575$	0	0
$576$	−3.95313	−0.164714
$577$	−3.66600	−0.152618	−0.0763089	−	0.997084i	$-0.524314\pi$
$577$	−3.66600	−0.152618	−0.0763089	+	0.997084i	$0.524314\pi$
$578$	34.1185	1.41914
$579$	12.9045	0.536291
$580$	0	0
$581$	−12.4536	−0.516664
$582$	−9.31470	−0.386107
$583$	41.2807	1.70967
$584$	−24.5486	−1.01583
$585$	0	0
$586$	−17.0934	−0.706123
$587$	34.0600	1.40581	0.702903	−	0.711286i	$-0.251887\pi$
$587$	34.0600	1.40581	0.702903	+	0.711286i	$0.251887\pi$
$588$	−6.44472	−0.265776
$589$	0.461367	0.0190103
$590$	0	0
$591$	11.7218	0.482169
$592$	−7.38026	−0.303327
$593$	37.3587	1.53414	0.767068	−	0.641565i	$-0.221715\pi$
$593$	37.3587	1.53414	0.767068	+	0.641565i	$0.221715\pi$
$594$	16.6571	0.683449
$595$	0	0
$596$	−10.2684	−0.420611
$597$	−15.4738	−0.633301
$598$	−6.22817	−0.254689
$599$	29.9607	1.22416	0.612080	−	0.790796i	$-0.290333\pi$
$599$	29.9607	1.22416	0.612080	+	0.790796i	$0.290333\pi$
$600$	0	0
$601$	−29.6156	−1.20805	−0.604023	−	0.796967i	$-0.706436\pi$
$601$	−29.6156	−1.20805	−0.604023	+	0.796967i	$0.706436\pi$
$602$	3.19795	0.130339
$603$	13.3681	0.544391
$604$	−11.8397	−0.481749
$605$	0	0
$606$	−6.82186	−0.277119
$607$	38.1377	1.54796	0.773981	−	0.633209i	$-0.218263\pi$
$607$	38.1377	1.54796	0.773981	+	0.633209i	$0.218263\pi$
$608$	5.26433	0.213497
$609$	7.85389	0.318256
$610$	0	0
$611$	12.2361	0.495020
$612$	25.5053	1.03099
$613$	11.2180	0.453093	0.226546	−	0.974000i	$-0.427257\pi$
$613$	11.2180	0.453093	0.226546	+	0.974000i	$0.427257\pi$
$614$	6.58199	0.265627
$615$	0	0
$616$	−18.5506	−0.747426
$617$	21.5056	0.865781	0.432891	−	0.901446i	$-0.357494\pi$
$617$	21.5056	0.865781	0.432891	+	0.901446i	$0.357494\pi$
$618$	−10.7283	−0.431557
$619$	20.6409	0.829628	0.414814	−	0.909906i	$-0.363847\pi$
$619$	20.6409	0.829628	0.414814	+	0.909906i	$0.363847\pi$
$620$	0	0
$621$	−12.4594	−0.499979
$622$	19.9890	0.801488
$623$	−5.05152	−0.202385
$624$	−3.61838	−0.144851
$625$	0	0
$626$	−4.21804	−0.168587
$627$	−4.06685	−0.162414
$628$	−27.3025	−1.08949
$629$	−50.5085	−2.01391
$630$	0	0
$631$	−42.5015	−1.69196	−0.845978	−	0.533217i	$-0.820983\pi$
$631$	−42.5015	−1.69196	−0.845978	+	0.533217i	$0.820983\pi$
$632$	−32.1521	−1.27894
$633$	−6.83046	−0.271486
$634$	−4.53323	−0.180038
$635$	0	0
$636$	11.6925	0.463636
$637$	−15.5323	−0.615413
$638$	−19.3882	−0.767585
$639$	26.9706	1.06694
$640$	0	0
$641$	−40.4487	−1.59763	−0.798814	−	0.601578i	$-0.794539\pi$
$641$	−40.4487	−1.59763	−0.798814	+	0.601578i	$0.794539\pi$
$642$	−2.56889	−0.101386
$643$	−0.980526	−0.0386682	−0.0193341	−	0.999813i	$-0.506155\pi$
$643$	−0.980526	−0.0386682	−0.0193341	+	0.999813i	$0.506155\pi$
$644$	5.91197	0.232964
$645$	0	0
$646$	5.19310	0.204320
$647$	−2.41644	−0.0950000	−0.0475000	−	0.998871i	$-0.515125\pi$
$647$	−2.41644	−0.0950000	−0.0475000	+	0.998871i	$0.515125\pi$
$648$	−4.97463	−0.195422
$649$	−23.8225	−0.935115
$650$	0	0
$651$	−0.724784	−0.0284065
$652$	−2.51438	−0.0984707
$653$	−14.8011	−0.579212	−0.289606	−	0.957146i	$-0.593524\pi$
$653$	−14.8011	−0.579212	−0.289606	+	0.957146i	$0.593524\pi$
$654$	6.40668	0.250521
$655$	0	0
$656$	−0.638604	−0.0249333
$657$	−20.9867	−0.818769
$658$	4.03112	0.157149
$659$	−43.0848	−1.67835	−0.839173	−	0.543864i	$-0.816961\pi$
$659$	−43.0848	−1.67835	−0.839173	+	0.543864i	$0.816961\pi$
$660$	0	0
$661$	43.0000	1.67251	0.836254	−	0.548343i	$-0.184741\pi$
$661$	43.0000	1.67251	0.836254	+	0.548343i	$0.184741\pi$
$662$	5.26406	0.204594
$663$	−24.7632	−0.961724
$664$	20.4377	0.793137
$665$	0	0
$666$	9.65207	0.374010
$667$	14.5022	0.561529
$668$	15.8492	0.613222
$669$	−18.8438	−0.728542
$670$	0	0
$671$	−41.9950	−1.62120
$672$	−8.26999	−0.319022
$673$	36.1609	1.39390	0.696949	−	0.717120i	$-0.254540\pi$
$673$	36.1609	1.39390	0.696949	+	0.717120i	$0.254540\pi$
$674$	−15.0453	−0.579525
$675$	0	0
$676$	2.92391	0.112458
$677$	44.3029	1.70270	0.851349	−	0.524600i	$-0.175785\pi$
$677$	44.3029	1.70270	0.851349	+	0.524600i	$0.175785\pi$
$678$	−3.55185	−0.136408
$679$	21.3094	0.817781
$680$	0	0
$681$	5.50868	0.211093
$682$	1.78921	0.0685122
$683$	30.6570	1.17306	0.586528	−	0.809929i	$-0.300494\pi$
$683$	30.6570	1.17306	0.586528	+	0.809929i	$0.300494\pi$
$684$	2.85938	0.109331
$685$	0	0
$686$	−12.7762	−0.487797
$687$	−10.4956	−0.400433
$688$	3.43064	0.130792
$689$	28.1798	1.07356
$690$	0	0
$691$	−46.1525	−1.75572	−0.877862	−	0.478914i	$-0.841031\pi$
$691$	−46.1525	−1.75572	−0.877862	+	0.478914i	$0.841031\pi$
$692$	−9.71243	−0.369211
$693$	−15.8590	−0.602433
$694$	−18.7748	−0.712683
$695$	0	0
$696$	−12.8891	−0.488558
$697$	−4.37043	−0.165542
$698$	14.7487	0.558247
$699$	−3.88958	−0.147118
$700$	0	0
$701$	22.7262	0.858355	0.429177	−	0.903220i	$-0.358803\pi$
$701$	22.7262	0.858355	0.429177	+	0.903220i	$0.358803\pi$
$702$	11.3708	0.429163
$703$	−5.66248	−0.213564
$704$	8.99377	0.338965
$705$	0	0
$706$	14.5410	0.547257
$707$	15.6065	0.586944
$708$	−6.74756	−0.253589
$709$	−20.4380	−0.767565	−0.383783	−	0.923423i	$-0.625379\pi$
$709$	−20.4380	−0.767565	−0.383783	+	0.923423i	$0.625379\pi$
$710$	0	0
$711$	−27.4869	−1.03084
$712$	8.29007	0.310684
$713$	−1.33832	−0.0501203
$714$	−8.15811	−0.305309
$715$	0	0
$716$	−23.0607	−0.861819
$717$	−8.88583	−0.331847
$718$	−11.8651	−0.442803
$719$	45.2265	1.68667	0.843333	−	0.537392i	$-0.180590\pi$
$719$	45.2265	1.68667	0.843333	+	0.537392i	$0.180590\pi$
$720$	0	0
$721$	24.5434	0.914046
$722$	−13.0567	−0.485921
$723$	−0.928169	−0.0345190
$724$	−11.0658	−0.411256
$725$	0	0
$726$	−8.44246	−0.313329
$727$	−18.5669	−0.688607	−0.344304	−	0.938858i	$-0.611885\pi$
$727$	−18.5669	−0.688607	−0.344304	+	0.938858i	$0.611885\pi$
$728$	−12.6634	−0.469336
$729$	9.02761	0.334356
$730$	0	0
$731$	23.4784	0.868379
$732$	−11.8948	−0.439644
$733$	−3.19633	−0.118059	−0.0590297	−	0.998256i	$-0.518801\pi$
$733$	−3.19633	−0.118059	−0.0590297	+	0.998256i	$0.518801\pi$
$734$	25.5668	0.943689
$735$	0	0
$736$	−15.2706	−0.562881
$737$	−30.4137	−1.12030
$738$	0.835180	0.0307434
$739$	12.6762	0.466303	0.233151	−	0.972440i	$-0.425096\pi$
$739$	12.6762	0.466303	0.233151	+	0.972440i	$0.425096\pi$
$740$	0	0
$741$	−2.77619	−0.101986
$742$	9.28367	0.340814
$743$	43.4469	1.59391	0.796955	−	0.604038i	$-0.206443\pi$
$743$	43.4469	1.59391	0.796955	+	0.604038i	$0.206443\pi$
$744$	1.18945	0.0436072
$745$	0	0
$746$	−17.7898	−0.651330
$747$	17.4723	0.639276
$748$	−58.0270	−2.12168
$749$	5.87690	0.214737
$750$	0	0
$751$	22.9677	0.838103	0.419052	−	0.907962i	$-0.362363\pi$
$751$	22.9677	0.838103	0.419052	+	0.907962i	$0.362363\pi$
$752$	4.32444	0.157696
$753$	7.95601	0.289933
$754$	−13.2351	−0.481994
$755$	0	0
$756$	−10.7935	−0.392555
$757$	1.54288	0.0560768	0.0280384	−	0.999607i	$-0.491074\pi$
$757$	1.54288	0.0560768	0.0280384	+	0.999607i	$0.491074\pi$
$758$	−0.342401	−0.0124365
$759$	11.7970	0.428203
$760$	0	0
$761$	−5.01867	−0.181927	−0.0909633	−	0.995854i	$-0.528995\pi$
$761$	−5.01867	−0.181927	−0.0909633	+	0.995854i	$0.528995\pi$
$762$	6.90602	0.250179
$763$	−14.6567	−0.530608
$764$	29.3956	1.06350
$765$	0	0
$766$	16.8381	0.608384
$767$	−16.2622	−0.587193
$768$	10.3368	0.372998
$769$	19.1860	0.691865	0.345933	−	0.938259i	$-0.387563\pi$
$769$	19.1860	0.691865	0.345933	+	0.938259i	$0.387563\pi$
$770$	0	0
$771$	−12.0110	−0.432567
$772$	20.6421	0.742926
$773$	17.6749	0.635722	0.317861	−	0.948137i	$-0.397036\pi$
$773$	17.6749	0.635722	0.317861	+	0.948137i	$0.397036\pi$
$774$	−4.48667	−0.161270
$775$	0	0
$776$	−34.9710	−1.25539
$777$	8.89547	0.319123
$778$	26.3132	0.943373
$779$	−0.489966	−0.0175549
$780$	0	0
$781$	−61.3607	−2.19566
$782$	−15.0640	−0.538686
$783$	−26.4768	−0.946202
$784$	−5.48937	−0.196049
$785$	0	0
$786$	−7.45120	−0.265775
$787$	−19.3853	−0.691011	−0.345506	−	0.938417i	$-0.612293\pi$
$787$	−19.3853	−0.691011	−0.345506	+	0.938417i	$0.612293\pi$
$788$	18.7502	0.667950
$789$	4.20144	0.149575
$790$	0	0
$791$	8.12565	0.288915
$792$	26.0263	0.924803
$793$	−28.6674	−1.01801
$794$	22.1377	0.785639
$795$	0	0
$796$	−24.7521	−0.877314
$797$	−17.2108	−0.609637	−0.304818	−	0.952410i	$-0.598596\pi$
$797$	−17.2108	−0.609637	−0.304818	+	0.952410i	$0.598596\pi$
$798$	−0.914601	−0.0323765
$799$	29.5953	1.04700
$800$	0	0
$801$	7.08721	0.250414
$802$	−26.4755	−0.934882
$803$	47.7468	1.68495
$804$	−8.61447	−0.303809
$805$	0	0
$806$	1.22138	0.0430213
$807$	−11.2547	−0.396185
$808$	−25.6119	−0.901025
$809$	−24.5329	−0.862529	−0.431265	−	0.902226i	$-0.641932\pi$
$809$	−24.5329	−0.862529	−0.431265	+	0.902226i	$0.641932\pi$
$810$	0	0
$811$	−6.49622	−0.228113	−0.114057	−	0.993474i	$-0.536385\pi$
$811$	−6.49622	−0.228113	−0.114057	+	0.993474i	$0.536385\pi$
$812$	12.5632	0.440881
$813$	26.2426	0.920368
$814$	−21.9594	−0.769677
$815$	0	0
$816$	−8.75172	−0.306372
$817$	2.63215	0.0920872
$818$	−5.04508	−0.176397
$819$	−10.8260	−0.378290
$820$	0	0
$821$	7.98932	0.278829	0.139415	−	0.990234i	$-0.455478\pi$
$821$	7.98932	0.278829	0.139415	+	0.990234i	$0.455478\pi$
$822$	−7.80059	−0.272077
$823$	46.7786	1.63060	0.815300	−	0.579038i	$-0.196572\pi$
$823$	46.7786	1.63060	0.815300	+	0.579038i	$0.196572\pi$
$824$	−40.2783	−1.40316
$825$	0	0
$826$	−5.35748	−0.186411
$827$	−48.4168	−1.68362	−0.841809	−	0.539775i	$-0.818509\pi$
$827$	−48.4168	−1.68362	−0.841809	+	0.539775i	$0.818509\pi$
$828$	−8.29440	−0.288250
$829$	18.2855	0.635083	0.317541	−	0.948244i	$-0.397143\pi$
$829$	18.2855	0.635083	0.317541	+	0.948244i	$0.397143\pi$
$830$	0	0
$831$	23.2918	0.807984
$832$	6.13950	0.212849
$833$	−37.5677	−1.30164
$834$	2.21942	0.0768524
$835$	0	0
$836$	−6.50538	−0.224993
$837$	2.44337	0.0844551
$838$	7.53021	0.260127
$839$	43.9448	1.51714	0.758571	−	0.651591i	$-0.225898\pi$
$839$	43.9448	1.51714	0.758571	+	0.651591i	$0.225898\pi$
$840$	0	0
$841$	1.81782	0.0626835
$842$	0.529519	0.0182484
$843$	−22.8248	−0.786128
$844$	−10.9261	−0.376091
$845$	0	0
$846$	−5.65560	−0.194443
$847$	19.3140	0.663637
$848$	9.95919	0.342000
$849$	−11.9636	−0.410589
$850$	0	0
$851$	16.4255	0.563059
$852$	−17.3800	−0.595428
$853$	10.4853	0.359009	0.179504	−	0.983757i	$-0.442551\pi$
$853$	10.4853	0.359009	0.179504	+	0.983757i	$0.442551\pi$
$854$	−9.44431	−0.323178
$855$	0	0
$856$	−9.64461	−0.329646
$857$	11.7870	0.402637	0.201319	−	0.979526i	$-0.435477\pi$
$857$	11.7870	0.402637	0.201319	+	0.979526i	$0.435477\pi$
$858$	−10.7662	−0.367553
$859$	−36.0085	−1.22859	−0.614297	−	0.789075i	$-0.710560\pi$
$859$	−36.0085	−1.22859	−0.614297	+	0.789075i	$0.710560\pi$
$860$	0	0
$861$	0.769712	0.0262317
$862$	8.64682	0.294512
$863$	16.0397	0.545997	0.272999	−	0.962014i	$-0.411985\pi$
$863$	16.0397	0.545997	0.272999	+	0.962014i	$0.411985\pi$
$864$	27.8795	0.948480
$865$	0	0
$866$	−4.81768	−0.163711
$867$	−44.1155	−1.49824
$868$	−1.15937	−0.0393516
$869$	62.5354	2.12137
$870$	0	0
$871$	−20.7616	−0.703479
$872$	24.0532	0.814543
$873$	−29.8968	−1.01185
$874$	−1.68881	−0.0571250
$875$	0	0
$876$	13.5239	0.456931
$877$	−28.8674	−0.974784	−0.487392	−	0.873183i	$-0.662052\pi$
$877$	−28.8674	−0.974784	−0.487392	+	0.873183i	$0.662052\pi$
$878$	1.50939	0.0509395
$879$	22.1019	0.745479
$880$	0	0
$881$	47.7739	1.60954	0.804772	−	0.593583i	$-0.202287\pi$
$881$	47.7739	1.60954	0.804772	+	0.593583i	$0.202287\pi$
$882$	7.17912	0.241734
$883$	−6.62147	−0.222830	−0.111415	−	0.993774i	$-0.535538\pi$
$883$	−6.62147	−0.222830	−0.111415	+	0.993774i	$0.535538\pi$
$884$	−39.6115	−1.33228
$885$	0	0
$886$	−19.5521	−0.656867
$887$	−20.1721	−0.677312	−0.338656	−	0.940910i	$-0.609972\pi$
$887$	−20.1721	−0.677312	−0.338656	+	0.940910i	$0.609972\pi$
$888$	−14.5984	−0.489890
$889$	−15.7990	−0.529883
$890$	0	0
$891$	9.67559	0.324144
$892$	−30.1427	−1.00925
$893$	3.31791	0.111030
$894$	−4.60804	−0.154116
$895$	0	0
$896$	−15.7974	−0.527753
$897$	8.05308	0.268884
$898$	−10.8166	−0.360954
$899$	−2.84397	−0.0948518
$900$	0	0
$901$	68.1579	2.27067
$902$	−1.90012	−0.0632670
$903$	−4.13497	−0.137603
$904$	−13.3350	−0.443517
$905$	0	0
$906$	−5.31314	−0.176517
$907$	47.8707	1.58952	0.794761	−	0.606923i	$-0.207596\pi$
$907$	47.8707	1.58952	0.794761	+	0.606923i	$0.207596\pi$
$908$	8.81175	0.292428
$909$	−21.8957	−0.726235
$910$	0	0
$911$	26.7420	0.886000	0.443000	−	0.896522i	$-0.353914\pi$
$911$	26.7420	0.886000	0.443000	+	0.896522i	$0.353914\pi$
$912$	−0.981151	−0.0324891
$913$	−39.7511	−1.31557
$914$	0.101501	0.00335737
$915$	0	0
$916$	−16.7889	−0.554721
$917$	17.0463	0.562917
$918$	27.5023	0.907712
$919$	−34.8435	−1.14938	−0.574690	−	0.818371i	$-0.694878\pi$
$919$	−34.8435	−1.14938	−0.574690	+	0.818371i	$0.694878\pi$
$920$	0	0
$921$	−8.51056	−0.280433
$922$	2.47610	0.0815460
$923$	−41.8872	−1.37873
$924$	10.2196	0.336201
$925$	0	0
$926$	11.7558	0.386319
$927$	−34.4341	−1.13096
$928$	−32.4506	−1.06524
$929$	21.0556	0.690813	0.345407	−	0.938453i	$-0.387741\pi$
$929$	21.0556	0.690813	0.345407	+	0.938453i	$0.387741\pi$
$930$	0	0
$931$	−4.21170	−0.138033
$932$	−6.22182	−0.203802
$933$	−25.8460	−0.846160
$934$	−2.20676	−0.0722075
$935$	0	0
$936$	17.7665	0.580717
$937$	−21.9995	−0.718693	−0.359346	−	0.933204i	$-0.617000\pi$
$937$	−21.9995	−0.718693	−0.359346	+	0.933204i	$0.617000\pi$
$938$	−6.83978	−0.223327
$939$	5.45396	0.177983
$940$	0	0
$941$	55.2783	1.80202	0.901010	−	0.433798i	$-0.142827\pi$
$941$	55.2783	1.80202	0.901010	+	0.433798i	$0.142827\pi$
$942$	−12.2522	−0.399198
$943$	1.42128	0.0462831
$944$	−5.74731	−0.187059
$945$	0	0
$946$	10.2076	0.331878
$947$	−44.0780	−1.43234	−0.716170	−	0.697925i	$-0.754107\pi$
$947$	−44.0780	−1.43234	−0.716170	+	0.697925i	$0.754107\pi$
$948$	17.7127	0.575282
$949$	32.5938	1.05804
$950$	0	0
$951$	5.86150	0.190072
$952$	−30.6287	−0.992682
$953$	−53.6371	−1.73748	−0.868738	−	0.495273i	$-0.835068\pi$
$953$	−53.6371	−1.73748	−0.868738	+	0.495273i	$0.835068\pi$
$954$	−13.0248	−0.421695
$955$	0	0
$956$	−14.2139	−0.459709
$957$	25.0690	0.810367
$958$	5.00623	0.161744
$959$	17.8456	0.576264
$960$	0	0
$961$	−30.7375	−0.991534
$962$	−14.9903	−0.483308
$963$	−8.24520	−0.265698
$964$	−1.48471	−0.0478193
$965$	0	0
$966$	2.65304	0.0853602
$967$	−15.3819	−0.494648	−0.247324	−	0.968933i	$-0.579551\pi$
$967$	−15.3819	−0.494648	−0.247324	+	0.968933i	$0.579551\pi$
$968$	−31.6963	−1.01876
$969$	−6.71472	−0.215708
$970$	0	0
$971$	55.9223	1.79463	0.897316	−	0.441388i	$-0.145514\pi$
$971$	55.9223	1.79463	0.897316	+	0.441388i	$0.145514\pi$
$972$	23.9841	0.769289
$973$	−5.07742	−0.162775
$974$	−6.30502	−0.202026
$975$	0	0
$976$	−10.1315	−0.324302
$977$	−42.0109	−1.34405	−0.672024	−	0.740529i	$-0.734575\pi$
$977$	−42.0109	−1.34405	−0.672024	+	0.740529i	$0.734575\pi$
$978$	−1.12835	−0.0360806
$979$	−16.1241	−0.515328
$980$	0	0
$981$	20.5631	0.656530
$982$	−11.3356	−0.361735
$983$	−47.9608	−1.52971	−0.764856	−	0.644201i	$-0.777190\pi$
$983$	−47.9608	−1.52971	−0.764856	+	0.644201i	$0.777190\pi$
$984$	−1.26318	−0.0402686
$985$	0	0
$986$	−32.0115	−1.01945
$987$	−5.21227	−0.165908
$988$	−4.44082	−0.141281
$989$	−7.63524	−0.242787
$990$	0	0
$991$	−30.0197	−0.953607	−0.476803	−	0.879010i	$-0.658205\pi$
$991$	−30.0197	−0.953607	−0.476803	+	0.879010i	$0.658205\pi$
$992$	2.99465	0.0950802
$993$	−6.80647	−0.215997
$994$	−13.7995	−0.437694
$995$	0	0
$996$	−11.2592	−0.356762
$997$	−23.9634	−0.758930	−0.379465	−	0.925206i	$-0.623892\pi$
$997$	−23.9634	−0.758930	−0.379465	+	0.925206i	$0.623892\pi$
$998$	−19.9849	−0.632610
$999$	−29.9881	−0.948781

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.e.1.4		5
5.4	even	2		1205.2.a.a.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.a.1.2	✓	5	5.4	even	2
6025.2.a.e.1.4		5	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)

\(f(q)\)	\(=\)	\(q+0.717838 q^{2} -0.928169 q^{3} -1.48471 q^{4} -0.666275 q^{6} +1.52425 q^{7} -2.50146 q^{8} -2.13850 q^{9} +O(q^{10})\)	\(q+0.717838 q^{2} -0.928169 q^{3} -1.48471 q^{4} -0.666275 q^{6} +1.52425 q^{7} -2.50146 q^{8} -2.13850 q^{9} +4.86530 q^{11} +1.37806 q^{12} +3.32124 q^{13} +1.09416 q^{14} +1.17378 q^{16} +8.03303 q^{17} -1.53510 q^{18} +0.900578 q^{19} -1.41476 q^{21} +3.49249 q^{22} -2.61237 q^{23} +2.32177 q^{24} +2.38411 q^{26} +4.76940 q^{27} -2.26307 q^{28} -5.55138 q^{29} +0.512300 q^{31} +5.84549 q^{32} -4.51582 q^{33} +5.76641 q^{34} +3.17505 q^{36} -6.28760 q^{37} +0.646469 q^{38} -3.08268 q^{39} -0.544057 q^{41} -1.01557 q^{42} +2.92273 q^{43} -7.22356 q^{44} -1.87525 q^{46} +3.68420 q^{47} -1.08947 q^{48} -4.67666 q^{49} -7.45601 q^{51} -4.93108 q^{52} +8.48471 q^{53} +3.42365 q^{54} -3.81285 q^{56} -0.835889 q^{57} -3.98499 q^{58} -4.89641 q^{59} -8.63153 q^{61} +0.367748 q^{62} -3.25961 q^{63} +1.84855 q^{64} -3.24163 q^{66} -6.25115 q^{67} -11.9267 q^{68} +2.42472 q^{69} -12.6119 q^{71} +5.34937 q^{72} +9.81374 q^{73} -4.51348 q^{74} -1.33710 q^{76} +7.41594 q^{77} -2.21286 q^{78} +12.8533 q^{79} +1.98869 q^{81} -0.390545 q^{82} -8.17033 q^{83} +2.10051 q^{84} +2.09805 q^{86} +5.15262 q^{87} -12.1703 q^{88} -3.31410 q^{89} +5.06241 q^{91} +3.87860 q^{92} -0.475502 q^{93} +2.64465 q^{94} -5.42561 q^{96} +13.9803 q^{97} -3.35708 q^{98} -10.4045 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 5 q^{3} + 3 q^{4} - 8 q^{6} + 10 q^{7} + 6 q^{9}+O(q^{10}) \) 5 * q + q^2 + 5 * q^3 + 3 * q^4 - 8 * q^6 + 10 * q^7 + 6 * q^9	\( 5 q + q^{2} + 5 q^{3} + 3 q^{4} - 8 q^{6} + 10 q^{7} + 6 q^{9} - 3 q^{11} - 8 q^{12} + q^{13} - q^{14} + 15 q^{16} + 5 q^{17} - 4 q^{18} + 3 q^{19} + 11 q^{21} + 13 q^{22} + 8 q^{23} - 14 q^{24} + 14 q^{26} + 14 q^{27} + 17 q^{28} + 9 q^{29} - 16 q^{31} + 16 q^{32} - 23 q^{33} - 10 q^{34} - 17 q^{36} - 7 q^{37} + 22 q^{38} - 19 q^{39} + 9 q^{41} - 17 q^{42} + 32 q^{43} - 8 q^{44} + 5 q^{46} + 7 q^{47} + 6 q^{48} + 9 q^{49} - 8 q^{51} + 10 q^{52} + 32 q^{53} + 32 q^{54} - 18 q^{56} - 3 q^{57} - 11 q^{58} - 8 q^{59} - 12 q^{61} - 17 q^{62} + 11 q^{63} - 16 q^{64} + 15 q^{66} + 5 q^{67} + 2 q^{68} + 7 q^{69} - 11 q^{71} - 7 q^{72} + 29 q^{73} + 10 q^{74} - 8 q^{76} + 5 q^{77} - 2 q^{78} + 16 q^{79} - 15 q^{81} + 2 q^{82} + 10 q^{83} + 5 q^{84} + 14 q^{86} + 37 q^{87} - 10 q^{88} + 9 q^{89} + 12 q^{91} + 25 q^{92} - 15 q^{93} - 11 q^{94} - 3 q^{96} + 43 q^{97} - 30 q^{98} - 30 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 3 * q^4 - 8 * q^6 + 10 * q^7 + 6 * q^9 - 3 * q^11 - 8 * q^12 + q^13 - q^14 + 15 * q^16 + 5 * q^17 - 4 * q^18 + 3 * q^19 + 11 * q^21 + 13 * q^22 + 8 * q^23 - 14 * q^24 + 14 * q^26 + 14 * q^27 + 17 * q^28 + 9 * q^29 - 16 * q^31 + 16 * q^32 - 23 * q^33 - 10 * q^34 - 17 * q^36 - 7 * q^37 + 22 * q^38 - 19 * q^39 + 9 * q^41 - 17 * q^42 + 32 * q^43 - 8 * q^44 + 5 * q^46 + 7 * q^47 + 6 * q^48 + 9 * q^49 - 8 * q^51 + 10 * q^52 + 32 * q^53 + 32 * q^54 - 18 * q^56 - 3 * q^57 - 11 * q^58 - 8 * q^59 - 12 * q^61 - 17 * q^62 + 11 * q^63 - 16 * q^64 + 15 * q^66 + 5 * q^67 + 2 * q^68 + 7 * q^69 - 11 * q^71 - 7 * q^72 + 29 * q^73 + 10 * q^74 - 8 * q^76 + 5 * q^77 - 2 * q^78 + 16 * q^79 - 15 * q^81 + 2 * q^82 + 10 * q^83 + 5 * q^84 + 14 * q^86 + 37 * q^87 - 10 * q^88 + 9 * q^89 + 12 * q^91 + 25 * q^92 - 15 * q^93 - 11 * q^94 - 3 * q^96 + 43 * q^97 - 30 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

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Database

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