LMFDB - Embedded newform 6025.2.a.e.1.5

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			1.5
Root			$2.03850$ 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)

$f(q)$	$=$	$q+2.54794 q^{2} -1.35541 q^{3} +4.49198 q^{4} -3.45349 q^{6} +1.88303 q^{7} +6.34942 q^{8} -1.16287 q^{9} +O(q^{10})$	\(q+2.54794 q^{2} -1.35541 q^{3} +4.49198 q^{4} -3.45349 q^{6} +1.88303 q^{7} +6.34942 q^{8} -1.16287 q^{9} +0.101859 q^{11} -6.08846 q^{12} +2.74788 q^{13} +4.79785 q^{14} +7.19396 q^{16} -2.79407 q^{17} -2.96293 q^{18} +3.13294 q^{19} -2.55227 q^{21} +0.259531 q^{22} +5.40901 q^{23} -8.60604 q^{24} +7.00143 q^{26} +5.64239 q^{27} +8.45855 q^{28} +0.973704 q^{29} -7.26952 q^{31} +5.63091 q^{32} -0.138061 q^{33} -7.11912 q^{34} -5.22362 q^{36} +4.56447 q^{37} +7.98254 q^{38} -3.72449 q^{39} +3.64602 q^{41} -6.50303 q^{42} +12.3719 q^{43} +0.457551 q^{44} +13.7818 q^{46} -4.76442 q^{47} -9.75073 q^{48} -3.45419 q^{49} +3.78710 q^{51} +12.3434 q^{52} +2.50802 q^{53} +14.3764 q^{54} +11.9562 q^{56} -4.24641 q^{57} +2.48094 q^{58} -1.73190 q^{59} +5.93152 q^{61} -18.5223 q^{62} -2.18973 q^{63} -0.0407041 q^{64} -0.351770 q^{66} +3.23509 q^{67} -12.5509 q^{68} -7.33140 q^{69} +0.488209 q^{71} -7.38358 q^{72} +6.00741 q^{73} +11.6300 q^{74} +14.0731 q^{76} +0.191804 q^{77} -9.48978 q^{78} -0.0506949 q^{79} -4.15910 q^{81} +9.28983 q^{82} +4.64675 q^{83} -11.4648 q^{84} +31.5229 q^{86} -1.31976 q^{87} +0.646748 q^{88} -1.98982 q^{89} +5.17435 q^{91} +24.2972 q^{92} +9.85315 q^{93} -12.1394 q^{94} -7.63217 q^{96} +3.09593 q^{97} -8.80106 q^{98} -0.118450 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.54794	1.80166	0.900832	−	0.434168i	$-0.142958\pi$
$2$	2.54794	1.80166	0.900832	+	0.434168i	$0.142958\pi$
$3$	−1.35541	−0.782544	−0.391272	−	0.920275i	$-0.627965\pi$
$3$	−1.35541	−0.782544	−0.391272	+	0.920275i	$0.627965\pi$
$4$	4.49198	2.24599
$5$	0	0
$5$	0	0
$6$	−3.45349	−1.40988
$7$	1.88303	0.711719	0.355860	−	0.934539i	$-0.384188\pi$
$7$	1.88303	0.711719	0.355860	+	0.934539i	$0.384188\pi$
$8$	6.34942	2.24486
$9$	−1.16287	−0.387625
$10$	0	0
$11$	0.101859	0.0307117	0.0153559	−	0.999882i	$-0.495112\pi$
$11$	0.101859	0.0307117	0.0153559	+	0.999882i	$0.495112\pi$
$12$	−6.08846	−1.75759
$13$	2.74788	0.762125	0.381062	−	0.924549i	$-0.375558\pi$
$13$	2.74788	0.762125	0.381062	+	0.924549i	$0.375558\pi$
$14$	4.79785	1.28228
$15$	0	0
$16$	7.19396	1.79849
$17$	−2.79407	−0.677662	−0.338831	−	0.940847i	$-0.610032\pi$
$17$	−2.79407	−0.677662	−0.338831	+	0.940847i	$0.610032\pi$
$18$	−2.96293	−0.698370
$19$	3.13294	0.718746	0.359373	−	0.933194i	$-0.382991\pi$
$19$	3.13294	0.718746	0.359373	+	0.933194i	$0.382991\pi$
$20$	0	0
$21$	−2.55227	−0.556952
$22$	0.259531	0.0553322
$23$	5.40901	1.12786	0.563928	−	0.825824i	$-0.309289\pi$
$23$	5.40901	1.12786	0.563928	+	0.825824i	$0.309289\pi$
$24$	−8.60604	−1.75670
$25$	0	0
$26$	7.00143	1.37309
$27$	5.64239	1.08588
$28$	8.45855	1.59852
$29$	0.973704	0.180812	0.0904062	−	0.995905i	$-0.471183\pi$
$29$	0.973704	0.180812	0.0904062	+	0.995905i	$0.471183\pi$
$30$	0	0
$31$	−7.26952	−1.30564	−0.652822	−	0.757511i	$-0.726415\pi$
$31$	−7.26952	−1.30564	−0.652822	+	0.757511i	$0.726415\pi$
$32$	5.63091	0.995414
$33$	−0.138061	−0.0240333
$34$	−7.11912	−1.22092
$35$	0	0
$36$	−5.22362	−0.870603
$37$	4.56447	0.750395	0.375197	−	0.926945i	$-0.377575\pi$
$37$	4.56447	0.750395	0.375197	+	0.926945i	$0.377575\pi$
$38$	7.98254	1.29494
$39$	−3.72449	−0.596396
$40$	0	0
$41$	3.64602	0.569413	0.284706	−	0.958615i	$-0.408104\pi$
$41$	3.64602	0.569413	0.284706	+	0.958615i	$0.408104\pi$
$42$	−6.50303	−1.00344
$43$	12.3719	1.88670	0.943352	−	0.331795i	$-0.107654\pi$
$43$	12.3719	1.88670	0.943352	+	0.331795i	$0.107654\pi$
$44$	0.457551	0.0689784
$45$	0	0
$46$	13.7818	2.03202
$47$	−4.76442	−0.694961	−0.347481	−	0.937687i	$-0.612963\pi$
$47$	−4.76442	−0.694961	−0.347481	+	0.937687i	$0.612963\pi$
$48$	−9.75073	−1.40740
$49$	−3.45419	−0.493456
$50$	0	0
$51$	3.78710	0.530300
$52$	12.3434	1.71173
$53$	2.50802	0.344502	0.172251	−	0.985053i	$-0.444896\pi$
$53$	2.50802	0.344502	0.172251	+	0.985053i	$0.444896\pi$
$54$	14.3764	1.95639
$55$	0	0
$56$	11.9562	1.59771
$57$	−4.24641	−0.562451
$58$	2.48094	0.325763
$59$	−1.73190	−0.225475	−0.112737	−	0.993625i	$-0.535962\pi$
$59$	−1.73190	−0.225475	−0.112737	+	0.993625i	$0.535962\pi$
$60$	0	0
$61$	5.93152	0.759453	0.379727	−	0.925099i	$-0.376018\pi$
$61$	5.93152	0.759453	0.379727	+	0.925099i	$0.376018\pi$
$62$	−18.5223	−2.35233
$63$	−2.18973	−0.275880
$64$	−0.0407041	−0.00508802
$65$	0	0
$66$	−0.351770	−0.0432999
$67$	3.23509	0.395229	0.197614	−	0.980280i	$-0.436681\pi$
$67$	3.23509	0.395229	0.197614	+	0.980280i	$0.436681\pi$
$68$	−12.5509	−1.52202
$69$	−7.33140	−0.882597
$70$	0	0
$71$	0.488209	0.0579398	0.0289699	−	0.999580i	$-0.490777\pi$
$71$	0.488209	0.0579398	0.0289699	+	0.999580i	$0.490777\pi$
$72$	−7.38358	−0.870163
$73$	6.00741	0.703114	0.351557	−	0.936166i	$-0.385652\pi$
$73$	6.00741	0.703114	0.351557	+	0.936166i	$0.385652\pi$
$74$	11.6300	1.35196
$75$	0	0
$76$	14.0731	1.61430
$77$	0.191804	0.0218581
$78$	−9.48978	−1.07451
$79$	−0.0506949	−0.00570362	−0.00285181	−	0.999996i	$-0.500908\pi$
$79$	−0.0506949	−0.00570362	−0.00285181	+	0.999996i	$0.500908\pi$
$80$	0	0
$81$	−4.15910	−0.462122
$82$	9.28983	1.02589
$83$	4.64675	0.510047	0.255023	−	0.966935i	$-0.417917\pi$
$83$	4.64675	0.510047	0.255023	+	0.966935i	$0.417917\pi$
$84$	−11.4648	−1.25091
$85$	0	0
$86$	31.5229	3.39921
$87$	−1.31976	−0.141494
$88$	0.646748	0.0689436
$89$	−1.98982	−0.210920	−0.105460	−	0.994424i	$-0.533632\pi$
$89$	−1.98982	−0.210920	−0.105460	+	0.994424i	$0.533632\pi$
$90$	0	0
$91$	5.17435	0.542419
$92$	24.2972	2.53316
$93$	9.85315	1.02172
$94$	−12.1394	−1.25209
$95$	0	0
$96$	−7.63217	−0.778955
$97$	3.09593	0.314344	0.157172	−	0.987571i	$-0.449762\pi$
$97$	3.09593	0.314344	0.157172	+	0.987571i	$0.449762\pi$
$98$	−8.80106	−0.889041
$99$	−0.118450	−0.0119046
$100$	0	0
$101$	18.9935	1.88992	0.944962	−	0.327179i	$-0.106098\pi$
$101$	18.9935	1.88992	0.944962	+	0.327179i	$0.106098\pi$
$102$	9.64930	0.955423
$103$	−14.9681	−1.47485	−0.737425	−	0.675429i	$-0.763958\pi$
$103$	−14.9681	−1.47485	−0.737425	+	0.675429i	$0.763958\pi$
$104$	17.4475	1.71086
$105$	0	0
$106$	6.39027	0.620677
$107$	8.77446	0.848259	0.424130	−	0.905602i	$-0.360580\pi$
$107$	8.77446	0.848259	0.424130	+	0.905602i	$0.360580\pi$
$108$	25.3455	2.43887
$109$	−9.88950	−0.947242	−0.473621	−	0.880729i	$-0.657053\pi$
$109$	−9.88950	−0.947242	−0.473621	+	0.880729i	$0.657053\pi$
$110$	0	0
$111$	−6.18671	−0.587217
$112$	13.5465	1.28002
$113$	14.1882	1.33472	0.667359	−	0.744736i	$-0.267425\pi$
$113$	14.1882	1.33472	0.667359	+	0.744736i	$0.267425\pi$
$114$	−10.8196	−1.01335
$115$	0	0
$116$	4.37386	0.406103
$117$	−3.19544	−0.295419
$118$	−4.41279	−0.406230
$119$	−5.26133	−0.482305
$120$	0	0
$121$	−10.9896	−0.999057
$122$	15.1131	1.36828
$123$	−4.94184	−0.445591
$124$	−32.6546	−2.93247
$125$	0	0
$126$	−5.57930	−0.497043
$127$	−0.0337073	−0.00299104	−0.00149552	−	0.999999i	$-0.500476\pi$
$127$	−0.0337073	−0.00299104	−0.00149552	+	0.999999i	$0.500476\pi$
$128$	−11.3655	−1.00458
$129$	−16.7690	−1.47643
$130$	0	0
$131$	−4.82602	−0.421652	−0.210826	−	0.977524i	$-0.567615\pi$
$131$	−4.82602	−0.421652	−0.210826	+	0.977524i	$0.567615\pi$
$132$	−0.620167	−0.0539786
$133$	5.89943	0.511546
$134$	8.24280	0.712070
$135$	0	0
$136$	−17.7407	−1.52126
$137$	12.0842	1.03243	0.516213	−	0.856460i	$-0.327341\pi$
$137$	12.0842	1.03243	0.516213	+	0.856460i	$0.327341\pi$
$138$	−18.6800	−1.59014
$139$	−9.10250	−0.772064	−0.386032	−	0.922485i	$-0.626155\pi$
$139$	−9.10250	−0.772064	−0.386032	+	0.922485i	$0.626155\pi$
$140$	0	0
$141$	6.45772	0.543838
$142$	1.24393	0.104388
$143$	0.279897	0.0234062
$144$	−8.36567	−0.697139
$145$	0	0
$146$	15.3065	1.26678
$147$	4.68183	0.386151
$148$	20.5035	1.68538
$149$	5.25996	0.430912	0.215456	−	0.976514i	$-0.430876\pi$
$149$	5.25996	0.430912	0.215456	+	0.976514i	$0.430876\pi$
$150$	0	0
$151$	10.4093	0.847096	0.423548	−	0.905874i	$-0.360785\pi$
$151$	10.4093	0.847096	0.423548	+	0.905874i	$0.360785\pi$
$152$	19.8924	1.61348
$153$	3.24916	0.262679
$154$	0.488706	0.0393810
$155$	0	0
$156$	−16.7304	−1.33950
$157$	8.90569	0.710752	0.355376	−	0.934724i	$-0.384353\pi$
$157$	8.90569	0.710752	0.355376	+	0.934724i	$0.384353\pi$
$158$	−0.129167	−0.0102760
$159$	−3.39938	−0.269588
$160$	0	0
$161$	10.1853	0.802717
$162$	−10.5971	−0.832589
$163$	9.94413	0.778885	0.389442	−	0.921051i	$-0.372668\pi$
$163$	9.94413	0.778885	0.389442	+	0.921051i	$0.372668\pi$
$164$	16.3779	1.27890
$165$	0	0
$166$	11.8396	0.918933
$167$	−18.7926	−1.45421	−0.727106	−	0.686525i	$-0.759135\pi$
$167$	−18.7926	−1.45421	−0.727106	+	0.686525i	$0.759135\pi$
$168$	−16.2055	−1.25028
$169$	−5.44915	−0.419166
$170$	0	0
$171$	−3.64322	−0.278604
$172$	55.5746	4.23752
$173$	6.01905	0.457620	0.228810	−	0.973471i	$-0.426517\pi$
$173$	6.01905	0.457620	0.228810	+	0.973471i	$0.426517\pi$
$174$	−3.36268	−0.254924
$175$	0	0
$176$	0.732772	0.0552348
$177$	2.34743	0.176444
$178$	−5.06994	−0.380008
$179$	−15.9115	−1.18928	−0.594642	−	0.803990i	$-0.702706\pi$
$179$	−15.9115	−1.18928	−0.594642	+	0.803990i	$0.702706\pi$
$180$	0	0
$181$	4.17479	0.310310	0.155155	−	0.987890i	$-0.450412\pi$
$181$	4.17479	0.310310	0.155155	+	0.987890i	$0.450412\pi$
$182$	13.1839	0.977257
$183$	−8.03962	−0.594305
$184$	34.3441	2.53188
$185$	0	0
$186$	25.1052	1.84080
$187$	−0.284602	−0.0208122
$188$	−21.4017	−1.56088
$189$	10.6248	0.772840
$190$	0	0
$191$	11.9638	0.865667	0.432833	−	0.901474i	$-0.357514\pi$
$191$	11.9638	0.865667	0.432833	+	0.901474i	$0.357514\pi$
$192$	0.0551706	0.00398160
$193$	−5.70228	−0.410459	−0.205230	−	0.978714i	$-0.565794\pi$
$193$	−5.70228	−0.410459	−0.205230	+	0.978714i	$0.565794\pi$
$194$	7.88823	0.566342
$195$	0	0
$196$	−15.5162	−1.10830
$197$	−6.62448	−0.471974	−0.235987	−	0.971756i	$-0.575832\pi$
$197$	−6.62448	−0.471974	−0.235987	+	0.971756i	$0.575832\pi$
$198$	−0.301802	−0.0214482
$199$	−10.0754	−0.714224	−0.357112	−	0.934062i	$-0.616239\pi$
$199$	−10.0754	−0.714224	−0.357112	+	0.934062i	$0.616239\pi$
$200$	0	0
$201$	−4.38486	−0.309284
$202$	48.3943	3.40501
$203$	1.83352	0.128688
$204$	17.0116	1.19105
$205$	0	0
$206$	−38.1378	−2.65718
$207$	−6.29000	−0.437185
$208$	19.7681	1.37067
$209$	0.319120	0.0220740
$210$	0	0
$211$	−15.0562	−1.03651	−0.518255	−	0.855226i	$-0.673418\pi$
$211$	−15.0562	−1.03651	−0.518255	+	0.855226i	$0.673418\pi$
$212$	11.2660	0.773750
$213$	−0.661722	−0.0453404
$214$	22.3568	1.52828
$215$	0	0
$216$	35.8259	2.43764
$217$	−13.6887	−0.929253
$218$	−25.1978	−1.70661
$219$	−8.14248	−0.550218
$220$	0	0
$221$	−7.67778	−0.516463
$222$	−15.7634	−1.05797
$223$	7.86590	0.526740	0.263370	−	0.964695i	$-0.415166\pi$
$223$	7.86590	0.526740	0.263370	+	0.964695i	$0.415166\pi$
$224$	10.6032	0.708455
$225$	0	0
$226$	36.1508	2.40471
$227$	−18.0615	−1.19878	−0.599392	−	0.800456i	$-0.704591\pi$
$227$	−18.0615	−1.19878	−0.599392	+	0.800456i	$0.704591\pi$
$228$	−19.0748	−1.26326
$229$	0.985673	0.0651351	0.0325676	−	0.999470i	$-0.489632\pi$
$229$	0.985673	0.0651351	0.0325676	+	0.999470i	$0.489632\pi$
$230$	0	0
$231$	−0.259973	−0.0171050
$232$	6.18246	0.405898
$233$	−8.09660	−0.530426	−0.265213	−	0.964190i	$-0.585442\pi$
$233$	−8.09660	−0.530426	−0.265213	+	0.964190i	$0.585442\pi$
$234$	−8.14178	−0.532245
$235$	0	0
$236$	−7.77969	−0.506415
$237$	0.0687121	0.00446333
$238$	−13.4055	−0.868952
$239$	6.58545	0.425977	0.212989	−	0.977055i	$-0.431680\pi$
$239$	6.58545	0.425977	0.212989	+	0.977055i	$0.431680\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−28.0009	−1.79996
$243$	−11.2899	−0.724247
$244$	26.6443	1.70573
$245$	0	0
$246$	−12.5915	−0.802804
$247$	8.60895	0.547775
$248$	−46.1573	−2.93099
$249$	−6.29823	−0.399134
$250$	0	0
$251$	12.8567	0.811507	0.405753	−	0.913983i	$-0.367009\pi$
$251$	12.8567	0.811507	0.405753	+	0.913983i	$0.367009\pi$
$252$	−9.83624	−0.619625
$253$	0.550958	0.0346384
$254$	−0.0858840	−0.00538884
$255$	0	0
$256$	−28.8773	−1.80483
$257$	−9.12512	−0.569209	−0.284605	−	0.958645i	$-0.591862\pi$
$257$	−9.12512	−0.569209	−0.284605	+	0.958645i	$0.591862\pi$
$258$	−42.7264	−2.66003
$259$	8.59505	0.534070
$260$	0	0
$261$	−1.13230	−0.0700874
$262$	−12.2964	−0.759674
$263$	30.2424	1.86483	0.932413	−	0.361395i	$-0.117699\pi$
$263$	30.2424	1.86483	0.932413	+	0.361395i	$0.117699\pi$
$264$	−0.876606	−0.0539514
$265$	0	0
$266$	15.0314	0.921633
$267$	2.69701	0.165055
$268$	14.5320	0.887681
$269$	24.3123	1.48235	0.741173	−	0.671314i	$-0.234270\pi$
$269$	24.3123	1.48235	0.741173	+	0.671314i	$0.234270\pi$
$270$	0	0
$271$	5.57082	0.338403	0.169202	−	0.985581i	$-0.445881\pi$
$271$	5.57082	0.338403	0.169202	+	0.985581i	$0.445881\pi$
$272$	−20.1004	−1.21877
$273$	−7.01334	−0.424467
$274$	30.7899	1.86008
$275$	0	0
$276$	−32.9326	−1.98231
$277$	−16.6836	−1.00242	−0.501211	−	0.865325i	$-0.667112\pi$
$277$	−16.6836	−1.00242	−0.501211	+	0.865325i	$0.667112\pi$
$278$	−23.1926	−1.39100
$279$	8.45354	0.506100
$280$	0	0
$281$	15.2585	0.910244	0.455122	−	0.890429i	$-0.349596\pi$
$281$	15.2585	0.910244	0.455122	+	0.890429i	$0.349596\pi$
$282$	16.4539	0.979813
$283$	25.0011	1.48616	0.743080	−	0.669203i	$-0.233364\pi$
$283$	25.0011	1.48616	0.743080	+	0.669203i	$0.233364\pi$
$284$	2.19303	0.130132
$285$	0	0
$286$	0.713161	0.0421701
$287$	6.86558	0.405262
$288$	−6.54805	−0.385847
$289$	−9.19316	−0.540774
$290$	0	0
$291$	−4.19624	−0.245988
$292$	26.9852	1.57919
$293$	14.3432	0.837936	0.418968	−	0.908001i	$-0.362392\pi$
$293$	14.3432	0.837936	0.418968	+	0.908001i	$0.362392\pi$
$294$	11.9290	0.695714
$295$	0	0
$296$	28.9818	1.68453
$297$	0.574730	0.0333492
$298$	13.4020	0.776359
$299$	14.8633	0.859567
$300$	0	0
$301$	23.2968	1.34280
$302$	26.5222	1.52618
$303$	−25.7439	−1.47895
$304$	22.5383	1.29266
$305$	0	0
$306$	8.27865	0.473259
$307$	−25.5804	−1.45995	−0.729977	−	0.683472i	$-0.760469\pi$
$307$	−25.5804	−1.45995	−0.729977	+	0.683472i	$0.760469\pi$
$308$	0.861583	0.0490932
$309$	20.2878	1.15413
$310$	0	0
$311$	−32.7022	−1.85437	−0.927187	−	0.374600i	$-0.877780\pi$
$311$	−32.7022	−1.85437	−0.927187	+	0.374600i	$0.877780\pi$
$312$	−23.6484	−1.33883
$313$	−19.4201	−1.09769	−0.548843	−	0.835925i	$-0.684932\pi$
$313$	−19.4201	−1.09769	−0.548843	+	0.835925i	$0.684932\pi$
$314$	22.6911	1.28054
$315$	0	0
$316$	−0.227721	−0.0128103
$317$	−9.09111	−0.510608	−0.255304	−	0.966861i	$-0.582176\pi$
$317$	−9.09111	−0.510608	−0.255304	+	0.966861i	$0.582176\pi$
$318$	−8.66140	−0.485707
$319$	0.0991809	0.00555306
$320$	0	0
$321$	−11.8930	−0.663800
$322$	25.9516	1.44623
$323$	−8.75367	−0.487067
$324$	−18.6826	−1.03792
$325$	0	0
$326$	25.3370	1.40329
$327$	13.4043	0.741258
$328$	23.1501	1.27825
$329$	−8.97155	−0.494617
$330$	0	0
$331$	−28.3132	−1.55623	−0.778117	−	0.628120i	$-0.783825\pi$
$331$	−28.3132	−1.55623	−0.778117	+	0.628120i	$0.783825\pi$
$332$	20.8731	1.14556
$333$	−5.30791	−0.290872
$334$	−47.8823	−2.62000
$335$	0	0
$336$	−18.3609	−1.00167
$337$	−4.58097	−0.249541	−0.124771	−	0.992186i	$-0.539819\pi$
$337$	−4.58097	−0.249541	−0.124771	+	0.992186i	$0.539819\pi$
$338$	−13.8841	−0.755196
$339$	−19.2308	−1.04448
$340$	0	0
$341$	−0.740469	−0.0400986
$342$	−9.28270	−0.501951
$343$	−19.6856	−1.06292
$344$	78.5547	4.23538
$345$	0	0
$346$	15.3362	0.824477
$347$	14.2341	0.764127	0.382064	−	0.924136i	$-0.375214\pi$
$347$	14.2341	0.764127	0.382064	+	0.924136i	$0.375214\pi$
$348$	−5.92836	−0.317794
$349$	−0.322066	−0.0172398	−0.00861990	−	0.999963i	$-0.502744\pi$
$349$	−0.322066	−0.0172398	−0.00861990	+	0.999963i	$0.502744\pi$
$350$	0	0
$351$	15.5046	0.827574
$352$	0.573561	0.0305709
$353$	−24.8659	−1.32348	−0.661740	−	0.749733i	$-0.730182\pi$
$353$	−24.8659	−1.32348	−0.661740	+	0.749733i	$0.730182\pi$
$354$	5.98112	0.317893
$355$	0	0
$356$	−8.93824	−0.473726
$357$	7.13124	0.377425
$358$	−40.5416	−2.14269
$359$	−7.67822	−0.405241	−0.202620	−	0.979257i	$-0.564946\pi$
$359$	−7.67822	−0.405241	−0.202620	+	0.979257i	$0.564946\pi$
$360$	0	0
$361$	−9.18467	−0.483404
$362$	10.6371	0.559074
$363$	14.8954	0.781806
$364$	23.2431	1.21827
$365$	0	0
$366$	−20.4844	−1.07074
$367$	22.0889	1.15303	0.576515	−	0.817086i	$-0.304412\pi$
$367$	22.0889	1.15303	0.576515	+	0.817086i	$0.304412\pi$
$368$	38.9122	2.02844
$369$	−4.23987	−0.220719
$370$	0	0
$371$	4.72267	0.245189
$372$	44.2602	2.29479
$373$	−14.5313	−0.752404	−0.376202	−	0.926538i	$-0.622770\pi$
$373$	−14.5313	−0.752404	−0.376202	+	0.926538i	$0.622770\pi$
$374$	−0.725149	−0.0374966
$375$	0	0
$376$	−30.2513	−1.56009
$377$	2.67562	0.137802
$378$	27.0713	1.39240
$379$	29.1616	1.49793	0.748967	−	0.662608i	$-0.230550\pi$
$379$	29.1616	1.49793	0.748967	+	0.662608i	$0.230550\pi$
$380$	0	0
$381$	0.0456870	0.00234062
$382$	30.4829	1.55964
$383$	−4.19813	−0.214514	−0.107257	−	0.994231i	$-0.534207\pi$
$383$	−4.19813	−0.214514	−0.107257	+	0.994231i	$0.534207\pi$
$384$	15.4049	0.786129
$385$	0	0
$386$	−14.5291	−0.739509
$387$	−14.3870	−0.731333
$388$	13.9069	0.706014
$389$	−7.09851	−0.359909	−0.179954	−	0.983675i	$-0.557595\pi$
$389$	−7.09851	−0.359909	−0.179954	+	0.983675i	$0.557595\pi$
$390$	0	0
$391$	−15.1132	−0.764306
$392$	−21.9321	−1.10774
$393$	6.54122	0.329961
$394$	−16.8787	−0.850339
$395$	0	0
$396$	−0.532074	−0.0267377
$397$	−15.2966	−0.767714	−0.383857	−	0.923393i	$-0.625404\pi$
$397$	−15.2966	−0.767714	−0.383857	+	0.923393i	$0.625404\pi$
$398$	−25.6714	−1.28679
$399$	−7.99613	−0.400307
$400$	0	0
$401$	−10.7256	−0.535609	−0.267804	−	0.963473i	$-0.586298\pi$
$401$	−10.7256	−0.535609	−0.267804	+	0.963473i	$0.586298\pi$
$402$	−11.1723	−0.557226
$403$	−19.9758	−0.995064
$404$	85.3186	4.24476
$405$	0	0
$406$	4.67169	0.231852
$407$	0.464934	0.0230459
$408$	24.0459	1.19045
$409$	−22.6490	−1.11992	−0.559962	−	0.828519i	$-0.689184\pi$
$409$	−22.6490	−1.11992	−0.559962	+	0.828519i	$0.689184\pi$
$410$	0	0
$411$	−16.3790	−0.807919
$412$	−67.2364	−3.31250
$413$	−3.26123	−0.160475
$414$	−16.0265	−0.787661
$415$	0	0
$416$	15.4731	0.758630
$417$	12.3376	0.604174
$418$	0.813097	0.0397699
$419$	35.1617	1.71776	0.858880	−	0.512177i	$-0.171161\pi$
$419$	35.1617	1.71776	0.858880	+	0.512177i	$0.171161\pi$
$420$	0	0
$421$	16.4234	0.800426	0.400213	−	0.916422i	$-0.368936\pi$
$421$	16.4234	0.800426	0.400213	+	0.916422i	$0.368936\pi$
$422$	−38.3622	−1.86744
$423$	5.54042	0.269384
$424$	15.9244	0.773359
$425$	0	0
$426$	−1.68603	−0.0816882
$427$	11.1692	0.540517
$428$	39.4147	1.90518
$429$	−0.379374	−0.0183164
$430$	0	0
$431$	−31.8617	−1.53472	−0.767362	−	0.641214i	$-0.778431\pi$
$431$	−31.8617	−1.53472	−0.767362	+	0.641214i	$0.778431\pi$
$432$	40.5911	1.95294
$433$	−13.4632	−0.646999	−0.323500	−	0.946228i	$-0.604859\pi$
$433$	−13.4632	−0.646999	−0.323500	+	0.946228i	$0.604859\pi$
$434$	−34.8781	−1.67420
$435$	0	0
$436$	−44.4235	−2.12750
$437$	16.9461	0.810643
$438$	−20.7465	−0.991308
$439$	4.48571	0.214091	0.107046	−	0.994254i	$-0.465861\pi$
$439$	4.48571	0.214091	0.107046	+	0.994254i	$0.465861\pi$
$440$	0	0
$441$	4.01679	0.191276
$442$	−19.5625	−0.930493
$443$	33.9998	1.61538	0.807691	−	0.589606i	$-0.200717\pi$
$443$	33.9998	1.61538	0.807691	+	0.589606i	$0.200717\pi$
$444$	−27.7906	−1.31888
$445$	0	0
$446$	20.0418	0.949008
$447$	−7.12938	−0.337208
$448$	−0.0766472	−0.00362124
$449$	−13.0422	−0.615499	−0.307749	−	0.951467i	$-0.599576\pi$
$449$	−13.0422	−0.615499	−0.307749	+	0.951467i	$0.599576\pi$
$450$	0	0
$451$	0.371381	0.0174877
$452$	63.7334	2.99777
$453$	−14.1088	−0.662890
$454$	−46.0196	−2.15980
$455$	0	0
$456$	−26.9622	−1.26262
$457$	−9.50750	−0.444742	−0.222371	−	0.974962i	$-0.571380\pi$
$457$	−9.50750	−0.444742	−0.222371	+	0.974962i	$0.571380\pi$
$458$	2.51143	0.117352
$459$	−15.7652	−0.735858
$460$	0	0
$461$	18.6184	0.867144	0.433572	−	0.901119i	$-0.357253\pi$
$461$	18.6184	0.867144	0.433572	+	0.901119i	$0.357253\pi$
$462$	−0.662395	−0.0308174
$463$	12.7869	0.594258	0.297129	−	0.954837i	$-0.403971\pi$
$463$	12.7869	0.594258	0.297129	+	0.954837i	$0.403971\pi$
$464$	7.00479	0.325189
$465$	0	0
$466$	−20.6296	−0.955649
$467$	14.0763	0.651375	0.325688	−	0.945477i	$-0.394404\pi$
$467$	14.0763	0.651375	0.325688	+	0.945477i	$0.394404\pi$
$468$	−14.3539	−0.663508
$469$	6.09177	0.281292
$470$	0	0
$471$	−12.0708	−0.556194
$472$	−10.9966	−0.506159
$473$	1.26020	0.0579440
$474$	0.175074	0.00804142
$475$	0	0
$476$	−23.6338	−1.08325
$477$	−2.91651	−0.133538
$478$	16.7793	0.767468
$479$	16.6775	0.762013	0.381006	−	0.924572i	$-0.375578\pi$
$479$	16.6775	0.762013	0.381006	+	0.924572i	$0.375578\pi$
$480$	0	0
$481$	12.5426	0.571894
$482$	2.54794	0.116055
$483$	−13.8053	−0.628162
$484$	−49.3652	−2.24387
$485$	0	0
$486$	−28.7659	−1.30485
$487$	−36.8312	−1.66898	−0.834490	−	0.551023i	$-0.814238\pi$
$487$	−36.8312	−1.66898	−0.834490	+	0.551023i	$0.814238\pi$
$488$	37.6617	1.70487
$489$	−13.4783	−0.609511
$490$	0	0
$491$	−9.65934	−0.435920	−0.217960	−	0.975958i	$-0.569940\pi$
$491$	−9.65934	−0.435920	−0.217960	+	0.975958i	$0.569940\pi$
$492$	−22.1987	−1.00079
$493$	−2.72060	−0.122530
$494$	21.9351	0.986906
$495$	0	0
$496$	−52.2966	−2.34819
$497$	0.919314	0.0412368
$498$	−16.0475	−0.719105
$499$	29.1258	1.30385	0.651926	−	0.758283i	$-0.273961\pi$
$499$	29.1258	1.30385	0.651926	+	0.758283i	$0.273961\pi$
$500$	0	0
$501$	25.4716	1.13799
$502$	32.7580	1.46206
$503$	−10.9075	−0.486340	−0.243170	−	0.969984i	$-0.578187\pi$
$503$	−10.9075	−0.486340	−0.243170	+	0.969984i	$0.578187\pi$
$504$	−13.9035	−0.619312
$505$	0	0
$506$	1.40381	0.0624068
$507$	7.38582	0.328016
$508$	−0.151413	−0.00671785
$509$	−19.7429	−0.875089	−0.437544	−	0.899197i	$-0.644152\pi$
$509$	−19.7429	−0.875089	−0.437544	+	0.899197i	$0.644152\pi$
$510$	0	0
$511$	11.3121	0.500420
$512$	−50.8464	−2.24711
$513$	17.6773	0.780471
$514$	−23.2502	−1.02552
$515$	0	0
$516$	−75.3261	−3.31605
$517$	−0.485300	−0.0213435
$518$	21.8996	0.962215
$519$	−8.15826	−0.358108
$520$	0	0
$521$	−18.6048	−0.815090	−0.407545	−	0.913185i	$-0.633615\pi$
$521$	−18.6048	−0.815090	−0.407545	+	0.913185i	$0.633615\pi$
$522$	−2.88502	−0.126274
$523$	−8.87015	−0.387864	−0.193932	−	0.981015i	$-0.562124\pi$
$523$	−8.87015	−0.387864	−0.193932	+	0.981015i	$0.562124\pi$
$524$	−21.6784	−0.947026
$525$	0	0
$526$	77.0557	3.35979
$527$	20.3116	0.884786
$528$	−0.993203	−0.0432236
$529$	6.25739	0.272060
$530$	0	0
$531$	2.01399	0.0873996
$532$	26.5002	1.14893
$533$	10.0188	0.433964
$534$	6.87182	0.297373
$535$	0	0
$536$	20.5409	0.887233
$537$	21.5666	0.930668
$538$	61.9461	2.67069
$539$	−0.351841	−0.0151549
$540$	0	0
$541$	35.3979	1.52187	0.760937	−	0.648826i	$-0.224740\pi$
$541$	35.3979	1.52187	0.760937	+	0.648826i	$0.224740\pi$
$542$	14.1941	0.609689
$543$	−5.65853	−0.242831
$544$	−15.7332	−0.674554
$545$	0	0
$546$	−17.8696	−0.764746
$547$	−17.0692	−0.729825	−0.364913	−	0.931042i	$-0.618901\pi$
$547$	−17.0692	−0.729825	−0.364913	+	0.931042i	$0.618901\pi$
$548$	54.2822	2.31882
$549$	−6.89761	−0.294383
$550$	0	0
$551$	3.05056	0.129958
$552$	−46.5502	−1.98131
$553$	−0.0954601	−0.00405937
$554$	−42.5089	−1.80603
$555$	0	0
$556$	−40.8883	−1.73405
$557$	−10.4050	−0.440876	−0.220438	−	0.975401i	$-0.570749\pi$
$557$	−10.4050	−0.440876	−0.220438	+	0.975401i	$0.570749\pi$
$558$	21.5391	0.911823
$559$	33.9966	1.43790
$560$	0	0
$561$	0.385752	0.0162865
$562$	38.8776	1.63995
$563$	−7.36991	−0.310605	−0.155302	−	0.987867i	$-0.549635\pi$
$563$	−7.36991	−0.310605	−0.155302	+	0.987867i	$0.549635\pi$
$564$	29.0080	1.22146
$565$	0	0
$566$	63.7012	2.67756
$567$	−7.83172	−0.328901
$568$	3.09985	0.130067
$569$	−16.9900	−0.712256	−0.356128	−	0.934437i	$-0.615903\pi$
$569$	−16.9900	−0.712256	−0.356128	+	0.934437i	$0.615903\pi$
$570$	0	0
$571$	−4.95180	−0.207226	−0.103613	−	0.994618i	$-0.533040\pi$
$571$	−4.95180	−0.207226	−0.103613	+	0.994618i	$0.533040\pi$
$572$	1.25729	0.0525701
$573$	−16.2157	−0.677422
$574$	17.4931	0.730146
$575$	0	0
$576$	0.0473338	0.00197224
$577$	−45.1820	−1.88095	−0.940476	−	0.339860i	$-0.889620\pi$
$577$	−45.1820	−1.88095	−0.940476	+	0.339860i	$0.889620\pi$
$578$	−23.4236	−0.974293
$579$	7.72890	0.321202
$580$	0	0
$581$	8.74998	0.363010
$582$	−10.6918	−0.443188
$583$	0.255465	0.0105803
$584$	38.1436	1.57839
$585$	0	0
$586$	36.5455	1.50968
$587$	2.12714	0.0877966	0.0438983	−	0.999036i	$-0.486022\pi$
$587$	2.12714	0.0877966	0.0438983	+	0.999036i	$0.486022\pi$
$588$	21.0307	0.867292
$589$	−22.7750	−0.938427
$590$	0	0
$591$	8.97885	0.369341
$592$	32.8366	1.34958
$593$	−28.3613	−1.16466	−0.582330	−	0.812953i	$-0.697859\pi$
$593$	−28.3613	−1.16466	−0.582330	+	0.812953i	$0.697859\pi$
$594$	1.46438	0.0600840
$595$	0	0
$596$	23.6276	0.967826
$597$	13.6562	0.558912
$598$	37.8708	1.54865
$599$	−13.2984	−0.543357	−0.271678	−	0.962388i	$-0.587579\pi$
$599$	−13.2984	−0.543357	−0.271678	+	0.962388i	$0.587579\pi$
$600$	0	0
$601$	11.6554	0.475432	0.237716	−	0.971335i	$-0.423601\pi$
$601$	11.6554	0.475432	0.237716	+	0.971335i	$0.423601\pi$
$602$	59.3587	2.41928
$603$	−3.76200	−0.153201
$604$	46.7583	1.90257
$605$	0	0
$606$	−65.5939	−2.66457
$607$	−26.6546	−1.08188	−0.540938	−	0.841062i	$-0.681931\pi$
$607$	−26.6546	−1.08188	−0.540938	+	0.841062i	$0.681931\pi$
$608$	17.6413	0.715450
$609$	−2.48516	−0.100704
$610$	0	0
$611$	−13.0920	−0.529647
$612$	14.5952	0.589974
$613$	−24.5975	−0.993485	−0.496743	−	0.867898i	$-0.665471\pi$
$613$	−24.5975	−0.993485	−0.496743	+	0.867898i	$0.665471\pi$
$614$	−65.1774	−2.63034
$615$	0	0
$616$	1.21785	0.0490685
$617$	7.14848	0.287787	0.143894	−	0.989593i	$-0.454038\pi$
$617$	7.14848	0.287787	0.143894	+	0.989593i	$0.454038\pi$
$618$	51.6921	2.07936
$619$	−39.5496	−1.58963	−0.794816	−	0.606851i	$-0.792432\pi$
$619$	−39.5496	−1.58963	−0.794816	+	0.606851i	$0.792432\pi$
$620$	0	0
$621$	30.5197	1.22471
$622$	−83.3232	−3.34096
$623$	−3.74689	−0.150116
$624$	−26.7939	−1.07261
$625$	0	0
$626$	−49.4811	−1.97766
$627$	−0.432537	−0.0172738
$628$	40.0042	1.59634
$629$	−12.7535	−0.508514
$630$	0	0
$631$	21.1747	0.842950	0.421475	−	0.906840i	$-0.361512\pi$
$631$	21.1747	0.842950	0.421475	+	0.906840i	$0.361512\pi$
$632$	−0.321883	−0.0128038
$633$	20.4072	0.811115
$634$	−23.1636	−0.919944
$635$	0	0
$636$	−15.2700	−0.605493
$637$	−9.49170	−0.376075
$638$	0.252707	0.0100048
$639$	−0.567726	−0.0224589
$640$	0	0
$641$	28.7697	1.13633	0.568167	−	0.822913i	$-0.307653\pi$
$641$	28.7697	1.13633	0.568167	+	0.822913i	$0.307653\pi$
$642$	−30.3025	−1.19594
$643$	−18.4705	−0.728407	−0.364203	−	0.931319i	$-0.618659\pi$
$643$	−18.4705	−0.728407	−0.364203	+	0.931319i	$0.618659\pi$
$644$	45.7524	1.80290
$645$	0	0
$646$	−22.3038	−0.877531
$647$	−39.2327	−1.54240	−0.771198	−	0.636595i	$-0.780342\pi$
$647$	−39.2327	−1.54240	−0.771198	+	0.636595i	$0.780342\pi$
$648$	−26.4079	−1.03740
$649$	−0.176411	−0.00692473
$650$	0	0
$651$	18.5538	0.727181
$652$	44.6689	1.74937
$653$	26.9191	1.05343	0.526713	−	0.850043i	$-0.323424\pi$
$653$	26.9191	1.05343	0.526713	+	0.850043i	$0.323424\pi$
$654$	34.1533	1.33550
$655$	0	0
$656$	26.2293	1.02408
$657$	−6.98587	−0.272545
$658$	−22.8589	−0.891134
$659$	−3.40549	−0.132659	−0.0663295	−	0.997798i	$-0.521129\pi$
$659$	−3.40549	−0.132659	−0.0663295	+	0.997798i	$0.521129\pi$
$660$	0	0
$661$	−49.3427	−1.91921	−0.959604	−	0.281353i	$-0.909217\pi$
$661$	−49.3427	−1.91921	−0.959604	+	0.281353i	$0.909217\pi$
$662$	−72.1402	−2.80381
$663$	10.4065	0.404155
$664$	29.5042	1.14498
$665$	0	0
$666$	−13.5242	−0.524053
$667$	5.26678	0.203930
$668$	−84.4159	−3.26615
$669$	−10.6615	−0.412197
$670$	0	0
$671$	0.604181	0.0233241
$672$	−14.3716	−0.554398
$673$	20.2032	0.778775	0.389387	−	0.921074i	$-0.372687\pi$
$673$	20.2032	0.778775	0.389387	+	0.921074i	$0.372687\pi$
$674$	−11.6720	−0.449589
$675$	0	0
$676$	−24.4775	−0.941443
$677$	−16.1199	−0.619536	−0.309768	−	0.950812i	$-0.600251\pi$
$677$	−16.1199	−0.619536	−0.309768	+	0.950812i	$0.600251\pi$
$678$	−48.9990	−1.88179
$679$	5.82974	0.223725
$680$	0	0
$681$	24.4807	0.938101
$682$	−1.88667	−0.0722443
$683$	−15.2875	−0.584959	−0.292480	−	0.956272i	$-0.594480\pi$
$683$	−15.2875	−0.584959	−0.292480	+	0.956272i	$0.594480\pi$
$684$	−16.3653	−0.625742
$685$	0	0
$686$	−50.1576	−1.91503
$687$	−1.33599	−0.0509711
$688$	89.0032	3.39322
$689$	6.89173	0.262554
$690$	0	0
$691$	36.8684	1.40254	0.701270	−	0.712896i	$-0.252617\pi$
$691$	36.8684	1.40254	0.701270	+	0.712896i	$0.252617\pi$
$692$	27.0375	1.02781
$693$	−0.223045	−0.00847276
$694$	36.2676	1.37670
$695$	0	0
$696$	−8.37974	−0.317633
$697$	−10.1872	−0.385869
$698$	−0.820604	−0.0310603
$699$	10.9742	0.415082
$700$	0	0
$701$	−0.362263	−0.0136825	−0.00684124	−	0.999977i	$-0.502178\pi$
$701$	−0.362263	−0.0136825	−0.00684124	+	0.999977i	$0.502178\pi$
$702$	39.5047	1.49101
$703$	14.3002	0.539344
$704$	−0.00414610	−0.000156262 0
$705$	0	0
$706$	−63.3569	−2.38447
$707$	35.7654	1.34510
$708$	10.5446	0.396292
$709$	−0.151650	−0.00569533	−0.00284766	−	0.999996i	$-0.500906\pi$
$709$	−0.151650	−0.00569533	−0.00284766	+	0.999996i	$0.500906\pi$
$710$	0	0
$711$	0.0589518	0.00221086
$712$	−12.6342	−0.473487
$713$	−39.3209	−1.47258
$714$	18.1699	0.679993
$715$	0	0
$716$	−71.4744	−2.67112
$717$	−8.92595	−0.333346
$718$	−19.5636	−0.730108
$719$	−51.5115	−1.92105	−0.960527	−	0.278188i	$-0.910266\pi$
$719$	−51.5115	−1.92105	−0.960527	+	0.278188i	$0.910266\pi$
$720$	0	0
$721$	−28.1854	−1.04968
$722$	−23.4020	−0.870931
$723$	−1.35541	−0.0504081
$724$	18.7531	0.696953
$725$	0	0
$726$	37.9526	1.40855
$727$	−32.9625	−1.22251	−0.611255	−	0.791434i	$-0.709335\pi$
$727$	−32.9625	−1.22251	−0.611255	+	0.791434i	$0.709335\pi$
$728$	32.8541	1.21765
$729$	27.7797	1.02888
$730$	0	0
$731$	−34.5681	−1.27855
$732$	−36.1138	−1.33481
$733$	−13.9413	−0.514934	−0.257467	−	0.966287i	$-0.582888\pi$
$733$	−13.9413	−0.514934	−0.257467	+	0.966287i	$0.582888\pi$
$734$	56.2811	2.07737
$735$	0	0
$736$	30.4577	1.12268
$737$	0.329524	0.0121382
$738$	−10.8029	−0.397661
$739$	34.1555	1.25643	0.628215	−	0.778040i	$-0.283786\pi$
$739$	34.1555	1.25643	0.628215	+	0.778040i	$0.283786\pi$
$740$	0	0
$741$	−11.6686	−0.428658
$742$	12.0331	0.441748
$743$	34.7810	1.27599	0.637996	−	0.770040i	$-0.279764\pi$
$743$	34.7810	1.27599	0.637996	+	0.770040i	$0.279764\pi$
$744$	62.5618	2.29363
$745$	0	0
$746$	−37.0249	−1.35558
$747$	−5.40359	−0.197707
$748$	−1.27843	−0.0467440
$749$	16.5226	0.603722
$750$	0	0
$751$	−17.1631	−0.626289	−0.313144	−	0.949706i	$-0.601382\pi$
$751$	−17.1631	−0.626289	−0.313144	+	0.949706i	$0.601382\pi$
$752$	−34.2750	−1.24988
$753$	−17.4260	−0.635040
$754$	6.81732	0.248272
$755$	0	0
$756$	47.7264	1.73579
$757$	34.2034	1.24315	0.621573	−	0.783357i	$-0.286494\pi$
$757$	34.2034	1.24315	0.621573	+	0.783357i	$0.286494\pi$
$758$	74.3021	2.69877
$759$	−0.746772	−0.0271061
$760$	0	0
$761$	38.7705	1.40543	0.702716	−	0.711471i	$-0.251971\pi$
$761$	38.7705	1.40543	0.702716	+	0.711471i	$0.251971\pi$
$762$	0.116408	0.00421701
$763$	−18.6222	−0.674170
$764$	53.7410	1.94428
$765$	0	0
$766$	−10.6966	−0.386483
$767$	−4.75907	−0.171840
$768$	39.1404	1.41236
$769$	−33.8710	−1.22142	−0.610710	−	0.791854i	$-0.709116\pi$
$769$	−33.8710	−1.22142	−0.610710	+	0.791854i	$0.709116\pi$
$770$	0	0
$771$	12.3682	0.445431
$772$	−25.6146	−0.921888
$773$	−33.8092	−1.21603	−0.608017	−	0.793924i	$-0.708035\pi$
$773$	−33.8092	−1.21603	−0.608017	+	0.793924i	$0.708035\pi$
$774$	−36.6572	−1.31762
$775$	0	0
$776$	19.6574	0.705658
$777$	−11.6498	−0.417934
$778$	−18.0866	−0.648434
$779$	11.4228	0.409263
$780$	0	0
$781$	0.0497287	0.00177943
$782$	−38.5074	−1.37702
$783$	5.49401	0.196340
$784$	−24.8493	−0.887475
$785$	0	0
$786$	16.6666	0.594479
$787$	12.8480	0.457983	0.228991	−	0.973428i	$-0.426457\pi$
$787$	12.8480	0.457983	0.228991	+	0.973428i	$0.426457\pi$
$788$	−29.7570	−1.06005
$789$	−40.9907	−1.45931
$790$	0	0
$791$	26.7169	0.949945
$792$	−0.752087	−0.0267242
$793$	16.2991	0.578798
$794$	−38.9747	−1.38316
$795$	0	0
$796$	−45.2584	−1.60414
$797$	−13.6634	−0.483982	−0.241991	−	0.970279i	$-0.577800\pi$
$797$	−13.6634	−0.483982	−0.241991	+	0.970279i	$0.577800\pi$
$798$	−20.3736	−0.721219
$799$	13.3121	0.470949
$800$	0	0
$801$	2.31391	0.0817580
$802$	−27.3280	−0.964987
$803$	0.611911	0.0215939
$804$	−19.6967	−0.694649
$805$	0	0
$806$	−50.8970	−1.79277
$807$	−32.9530	−1.16000
$808$	120.598	4.24262
$809$	−13.6228	−0.478952	−0.239476	−	0.970902i	$-0.576976\pi$
$809$	−13.6228	−0.478952	−0.239476	+	0.970902i	$0.576976\pi$
$810$	0	0
$811$	−24.1386	−0.847620	−0.423810	−	0.905751i	$-0.639308\pi$
$811$	−24.1386	−0.847620	−0.423810	+	0.905751i	$0.639308\pi$
$812$	8.23613	0.289031
$813$	−7.55073	−0.264816
$814$	1.18462	0.0415210
$815$	0	0
$816$	27.2443	0.953740
$817$	38.7606	1.35606
$818$	−57.7083	−2.01772
$819$	−6.01712	−0.210255
$820$	0	0
$821$	2.73766	0.0955452	0.0477726	−	0.998858i	$-0.484788\pi$
$821$	2.73766	0.0955452	0.0477726	+	0.998858i	$0.484788\pi$
$822$	−41.7328	−1.45560
$823$	19.9711	0.696150	0.348075	−	0.937467i	$-0.386836\pi$
$823$	19.9711	0.696150	0.348075	+	0.937467i	$0.386836\pi$
$824$	−95.0387	−3.31083
$825$	0	0
$826$	−8.30942	−0.289122
$827$	7.15489	0.248800	0.124400	−	0.992232i	$-0.460299\pi$
$827$	7.15489	0.248800	0.124400	+	0.992232i	$0.460299\pi$
$828$	−28.2546	−0.981915
$829$	15.0136	0.521444	0.260722	−	0.965414i	$-0.416039\pi$
$829$	15.0136	0.521444	0.260722	+	0.965414i	$0.416039\pi$
$830$	0	0
$831$	22.6131	0.784440
$832$	−0.111850	−0.00387770
$833$	9.65126	0.334396
$834$	31.4354	1.08852
$835$	0	0
$836$	1.43348	0.0495779
$837$	−41.0174	−1.41777
$838$	89.5897	3.09483
$839$	−21.4227	−0.739595	−0.369797	−	0.929112i	$-0.620573\pi$
$839$	−21.4227	−0.739595	−0.369797	+	0.929112i	$0.620573\pi$
$840$	0	0
$841$	−28.0519	−0.967307
$842$	41.8457	1.44210
$843$	−20.6814	−0.712306
$844$	−67.6321	−2.32799
$845$	0	0
$846$	14.1166	0.485340
$847$	−20.6938	−0.711048
$848$	18.0426	0.619584
$849$	−33.8866	−1.16299
$850$	0	0
$851$	24.6893	0.846338
$852$	−2.97244	−0.101834
$853$	−13.7777	−0.471739	−0.235869	−	0.971785i	$-0.575794\pi$
$853$	−13.7777	−0.471739	−0.235869	+	0.971785i	$0.575794\pi$
$854$	28.4585	0.973831
$855$	0	0
$856$	55.7128	1.90422
$857$	3.34404	0.114230	0.0571151	−	0.998368i	$-0.481810\pi$
$857$	3.34404	0.114230	0.0571151	+	0.998368i	$0.481810\pi$
$858$	−0.966622	−0.0329999
$859$	−45.5215	−1.55317	−0.776587	−	0.630010i	$-0.783051\pi$
$859$	−45.5215	−1.55317	−0.776587	+	0.630010i	$0.783051\pi$
$860$	0	0
$861$	−9.30564	−0.317135
$862$	−81.1816	−2.76506
$863$	−8.49123	−0.289045	−0.144522	−	0.989502i	$-0.546165\pi$
$863$	−8.49123	−0.289045	−0.144522	+	0.989502i	$0.546165\pi$
$864$	31.7718	1.08090
$865$	0	0
$866$	−34.3033	−1.16567
$867$	12.4605	0.423180
$868$	−61.4896	−2.08709
$869$	−0.00516375	−0.000175168 0
$870$	0	0
$871$	8.88963	0.301214
$872$	−62.7926	−2.12642
$873$	−3.60018	−0.121848
$874$	43.1777	1.46051
$875$	0	0
$876$	−36.5759	−1.23579
$877$	−40.7608	−1.37640	−0.688198	−	0.725523i	$-0.741598\pi$
$877$	−40.7608	−1.37640	−0.688198	+	0.725523i	$0.741598\pi$
$878$	11.4293	0.385721
$879$	−19.4408	−0.655722
$880$	0	0
$881$	38.8435	1.30867	0.654335	−	0.756205i	$-0.272949\pi$
$881$	38.8435	1.30867	0.654335	+	0.756205i	$0.272949\pi$
$882$	10.2345	0.344614
$883$	37.8842	1.27491	0.637453	−	0.770490i	$-0.279988\pi$
$883$	37.8842	1.27491	0.637453	+	0.770490i	$0.279988\pi$
$884$	−34.4885	−1.15997
$885$	0	0
$886$	86.6295	2.91037
$887$	35.9591	1.20739	0.603695	−	0.797216i	$-0.293695\pi$
$887$	35.9591	1.20739	0.603695	+	0.797216i	$0.293695\pi$
$888$	−39.2821	−1.31822
$889$	−0.0634719	−0.00212878
$890$	0	0
$891$	−0.423643	−0.0141926
$892$	35.3335	1.18305
$893$	−14.9266	−0.499501
$894$	−18.1652	−0.607535
$895$	0	0
$896$	−21.4017	−0.714980
$897$	−20.1458	−0.672649
$898$	−33.2307	−1.10892
$899$	−7.07836	−0.236077
$900$	0	0
$901$	−7.00758	−0.233456
$902$	0.946256	0.0315069
$903$	−31.5766	−1.05080
$904$	90.0872	2.99625
$905$	0	0
$906$	−35.9484	−1.19430
$907$	−1.62695	−0.0540221	−0.0270110	−	0.999635i	$-0.508599\pi$
$907$	−1.62695	−0.0540221	−0.0270110	+	0.999635i	$0.508599\pi$
$908$	−81.1320	−2.69246
$909$	−22.0871	−0.732582
$910$	0	0
$911$	56.6283	1.87618	0.938090	−	0.346391i	$-0.112593\pi$
$911$	56.6283	1.87618	0.938090	+	0.346391i	$0.112593\pi$
$912$	−30.5485	−1.01156
$913$	0.473315	0.0156644
$914$	−24.2245	−0.801276
$915$	0	0
$916$	4.42763	0.146293
$917$	−9.08756	−0.300098
$918$	−40.1688	−1.32577
$919$	−32.2609	−1.06419	−0.532094	−	0.846685i	$-0.678595\pi$
$919$	−32.2609	−1.06419	−0.532094	+	0.846685i	$0.678595\pi$
$920$	0	0
$921$	34.6719	1.14248
$922$	47.4384	1.56230
$923$	1.34154	0.0441573
$924$	−1.16779	−0.0384176
$925$	0	0
$926$	32.5802	1.07065
$927$	17.4060	0.571688
$928$	5.48284	0.179983
$929$	−35.5505	−1.16638	−0.583188	−	0.812337i	$-0.698195\pi$
$929$	−35.5505	−1.16638	−0.583188	+	0.812337i	$0.698195\pi$
$930$	0	0
$931$	−10.8218	−0.354669
$932$	−36.3698	−1.19133
$933$	44.3248	1.45113
$934$	35.8656	1.17356
$935$	0	0
$936$	−20.2892	−0.663173
$937$	−36.0338	−1.17717	−0.588586	−	0.808435i	$-0.700315\pi$
$937$	−36.0338	−1.17717	−0.588586	+	0.808435i	$0.700315\pi$
$938$	15.5215	0.506794
$939$	26.3221	0.858988
$940$	0	0
$941$	−15.9171	−0.518882	−0.259441	−	0.965759i	$-0.583538\pi$
$941$	−15.9171	−0.518882	−0.259441	+	0.965759i	$0.583538\pi$
$942$	−30.7557	−1.00208
$943$	19.7214	0.642216
$944$	−12.4593	−0.405514
$945$	0	0
$946$	3.21091	0.104396
$947$	32.9284	1.07003	0.535014	−	0.844843i	$-0.320306\pi$
$947$	32.9284	1.07003	0.535014	+	0.844843i	$0.320306\pi$
$948$	0.308654	0.0100246
$949$	16.5076	0.535861
$950$	0	0
$951$	12.3221	0.399573
$952$	−33.4064	−1.08271
$953$	−53.5805	−1.73564	−0.867822	−	0.496876i	$-0.834480\pi$
$953$	−53.5805	−1.73564	−0.867822	+	0.496876i	$0.834480\pi$
$954$	−7.43108	−0.240590
$955$	0	0
$956$	29.5817	0.956742
$957$	−0.134430	−0.00434552
$958$	42.4931	1.37289
$959$	22.7550	0.734797
$960$	0	0
$961$	21.8459	0.704708
$962$	31.9578	1.03036
$963$	−10.2036	−0.328806
$964$	4.49198	0.144677
$965$	0	0
$966$	−35.1750	−1.13174
$967$	35.3412	1.13650	0.568248	−	0.822857i	$-0.307621\pi$
$967$	35.3412	1.13650	0.568248	+	0.822857i	$0.307621\pi$
$968$	−69.7778	−2.24274
$969$	11.8648	0.381152
$970$	0	0
$971$	14.8435	0.476351	0.238176	−	0.971222i	$-0.423451\pi$
$971$	14.8435	0.476351	0.238176	+	0.971222i	$0.423451\pi$
$972$	−50.7140	−1.62665
$973$	−17.1403	−0.549493
$974$	−93.8435	−3.00694
$975$	0	0
$976$	42.6711	1.36587
$977$	47.7357	1.52720	0.763600	−	0.645690i	$-0.223430\pi$
$977$	47.7357	1.52720	0.763600	+	0.645690i	$0.223430\pi$
$978$	−34.3420	−1.09813
$979$	−0.202682	−0.00647774
$980$	0	0
$981$	11.5002	0.367174
$982$	−24.6114	−0.785381
$983$	33.1768	1.05817	0.529087	−	0.848568i	$-0.322534\pi$
$983$	33.1768	1.05817	0.529087	+	0.848568i	$0.322534\pi$
$984$	−31.3778	−1.00029
$985$	0	0
$986$	−6.93192	−0.220757
$987$	12.1601	0.387060
$988$	38.6713	1.23030
$989$	66.9200	2.12793
$990$	0	0
$991$	−48.4054	−1.53765	−0.768824	−	0.639460i	$-0.779158\pi$
$991$	−48.4054	−1.53765	−0.768824	+	0.639460i	$0.779158\pi$
$992$	−40.9340	−1.29966
$993$	38.3759	1.21782
$994$	2.34235	0.0742949
$995$	0	0
$996$	−28.2916	−0.896452
$997$	−53.7489	−1.70224	−0.851122	−	0.524968i	$-0.824077\pi$
$997$	−53.7489	−1.70224	−0.851122	+	0.524968i	$0.824077\pi$
$998$	74.2108	2.34910
$999$	25.7545	0.814837

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.e.1.5		5
5.4	even	2		1205.2.a.a.1.1	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.a.1.1	✓	5	5.4	even	2
6025.2.a.e.1.5		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)

\(f(q)\)	\(=\)	\(q+2.54794 q^{2} -1.35541 q^{3} +4.49198 q^{4} -3.45349 q^{6} +1.88303 q^{7} +6.34942 q^{8} -1.16287 q^{9} +O(q^{10})\)	\(q+2.54794 q^{2} -1.35541 q^{3} +4.49198 q^{4} -3.45349 q^{6} +1.88303 q^{7} +6.34942 q^{8} -1.16287 q^{9} +0.101859 q^{11} -6.08846 q^{12} +2.74788 q^{13} +4.79785 q^{14} +7.19396 q^{16} -2.79407 q^{17} -2.96293 q^{18} +3.13294 q^{19} -2.55227 q^{21} +0.259531 q^{22} +5.40901 q^{23} -8.60604 q^{24} +7.00143 q^{26} +5.64239 q^{27} +8.45855 q^{28} +0.973704 q^{29} -7.26952 q^{31} +5.63091 q^{32} -0.138061 q^{33} -7.11912 q^{34} -5.22362 q^{36} +4.56447 q^{37} +7.98254 q^{38} -3.72449 q^{39} +3.64602 q^{41} -6.50303 q^{42} +12.3719 q^{43} +0.457551 q^{44} +13.7818 q^{46} -4.76442 q^{47} -9.75073 q^{48} -3.45419 q^{49} +3.78710 q^{51} +12.3434 q^{52} +2.50802 q^{53} +14.3764 q^{54} +11.9562 q^{56} -4.24641 q^{57} +2.48094 q^{58} -1.73190 q^{59} +5.93152 q^{61} -18.5223 q^{62} -2.18973 q^{63} -0.0407041 q^{64} -0.351770 q^{66} +3.23509 q^{67} -12.5509 q^{68} -7.33140 q^{69} +0.488209 q^{71} -7.38358 q^{72} +6.00741 q^{73} +11.6300 q^{74} +14.0731 q^{76} +0.191804 q^{77} -9.48978 q^{78} -0.0506949 q^{79} -4.15910 q^{81} +9.28983 q^{82} +4.64675 q^{83} -11.4648 q^{84} +31.5229 q^{86} -1.31976 q^{87} +0.646748 q^{88} -1.98982 q^{89} +5.17435 q^{91} +24.2972 q^{92} +9.85315 q^{93} -12.1394 q^{94} -7.63217 q^{96} +3.09593 q^{97} -8.80106 q^{98} -0.118450 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 5 q^{3} + 3 q^{4} - 8 q^{6} + 10 q^{7} + 6 q^{9}+O(q^{10}) \) 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

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Database

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