LMFDB - Embedded newform 25.10.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,10,Mod(1,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	25.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:	$12.8758959041$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 652x + 4000 $ x^3 - x^2 - 652*x + 4000
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-27.7229$ of defining polynomial
Character	$\chi$	$=$	25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-31.7828 q^{2} -268.664 q^{3} +498.143 q^{4} +8538.88 q^{6} +637.237 q^{7} +440.406 q^{8} +52497.3 q^{9} +O(q^{10})$	\(q-31.7828 q^{2} -268.664 q^{3} +498.143 q^{4} +8538.88 q^{6} +637.237 q^{7} +440.406 q^{8} +52497.3 q^{9} -49042.6 q^{11} -133833. q^{12} +72726.2 q^{13} -20253.2 q^{14} -269047. q^{16} +67319.3 q^{17} -1.66851e6 q^{18} +341136. q^{19} -171203. q^{21} +1.55871e6 q^{22} -134355. q^{23} -118321. q^{24} -2.31144e6 q^{26} -8.81603e6 q^{27} +317435. q^{28} +4.45784e6 q^{29} +456520. q^{31} +8.32555e6 q^{32} +1.31760e7 q^{33} -2.13959e6 q^{34} +2.61512e7 q^{36} +1.30516e7 q^{37} -1.08422e7 q^{38} -1.95389e7 q^{39} -2.56667e7 q^{41} +5.44129e6 q^{42} +3.42710e6 q^{43} -2.44302e7 q^{44} +4.27016e6 q^{46} -3.39814e7 q^{47} +7.22831e7 q^{48} -3.99475e7 q^{49} -1.80863e7 q^{51} +3.62281e7 q^{52} -8.42456e7 q^{53} +2.80198e8 q^{54} +280643. q^{56} -9.16509e7 q^{57} -1.41682e8 q^{58} -7.46358e7 q^{59} +1.78017e8 q^{61} -1.45094e7 q^{62} +3.34533e7 q^{63} -1.26857e8 q^{64} -4.18769e8 q^{66} +6.94299e7 q^{67} +3.35347e7 q^{68} +3.60963e7 q^{69} -2.07860e8 q^{71} +2.31201e7 q^{72} -3.02516e8 q^{73} -4.14815e8 q^{74} +1.69935e8 q^{76} -3.12518e7 q^{77} +6.21000e8 q^{78} +3.72244e8 q^{79} +1.33524e9 q^{81} +8.15758e8 q^{82} +4.50079e8 q^{83} -8.52835e7 q^{84} -1.08923e8 q^{86} -1.19766e9 q^{87} -2.15987e7 q^{88} +5.82741e7 q^{89} +4.63438e7 q^{91} -6.69279e7 q^{92} -1.22650e8 q^{93} +1.08002e9 q^{94} -2.23678e9 q^{96} +7.85850e8 q^{97} +1.26964e9 q^{98} -2.57461e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 33 q^{2} - 89 q^{3} + 341 q^{4} + 3421 q^{6} - 5258 q^{7} + 105 q^{8} + 58234 q^{9}+O(q^{10}) $ 3 * q - 33 * q^2 - 89 * q^3 + 341 * q^4 + 3421 * q^6 - 5258 * q^7 + 105 * q^8 + 58234 * q^9	\( 3 q - 33 q^{2} - 89 q^{3} + 341 q^{4} + 3421 q^{6} - 5258 q^{7} + 105 q^{8} + 58234 q^{9} - 54699 q^{11} - 141853 q^{12} - 215884 q^{13} + 272922 q^{14} - 699247 q^{16} - 334983 q^{17} - 2571854 q^{18} + 818845 q^{19} - 2375394 q^{21} - 72761 q^{22} - 3526854 q^{23} + 2805735 q^{24} - 1280004 q^{26} - 6633395 q^{27} + 428134 q^{28} + 2175480 q^{29} + 4274066 q^{31} + 9464577 q^{32} + 22122137 q^{33} - 6838963 q^{34} + 26795798 q^{36} + 10305042 q^{37} + 24180495 q^{38} - 50414092 q^{39} + 5926311 q^{41} + 47560254 q^{42} + 24429956 q^{43} - 21995703 q^{44} + 14223246 q^{46} - 66858708 q^{47} + 29557871 q^{48} - 6453929 q^{49} - 25634699 q^{51} + 57862932 q^{52} - 132620514 q^{53} + 282250495 q^{54} - 169538130 q^{56} - 252946415 q^{57} - 201908320 q^{58} + 5670960 q^{59} + 125306926 q^{61} + 39831174 q^{62} - 284323404 q^{63} + 167542401 q^{64} - 556915843 q^{66} - 88829483 q^{67} + 71162559 q^{68} - 314274942 q^{69} + 297550596 q^{71} + 552918990 q^{72} - 181321729 q^{73} - 251507358 q^{74} + 89414865 q^{76} - 561214086 q^{77} + 1439424692 q^{78} - 310025170 q^{79} + 1398847363 q^{81} + 1368322979 q^{82} + 731088801 q^{83} + 38267082 q^{84} + 33947196 q^{86} - 1046385560 q^{87} + 943671285 q^{88} - 1103860035 q^{89} + 1183187656 q^{91} + 190024242 q^{92} - 107386758 q^{93} + 1727891132 q^{94} - 2567180449 q^{96} + 332236842 q^{97} - 457927581 q^{98} - 892234522 q^{99}+O(q^{100}) \) 3 * q - 33 * q^2 - 89 * q^3 + 341 * q^4 + 3421 * q^6 - 5258 * q^7 + 105 * q^8 + 58234 * q^9 - 54699 * q^11 - 141853 * q^12 - 215884 * q^13 + 272922 * q^14 - 699247 * q^16 - 334983 * q^17 - 2571854 * q^18 + 818845 * q^19 - 2375394 * q^21 - 72761 * q^22 - 3526854 * q^23 + 2805735 * q^24 - 1280004 * q^26 - 6633395 * q^27 + 428134 * q^28 + 2175480 * q^29 + 4274066 * q^31 + 9464577 * q^32 + 22122137 * q^33 - 6838963 * q^34 + 26795798 * q^36 + 10305042 * q^37 + 24180495 * q^38 - 50414092 * q^39 + 5926311 * q^41 + 47560254 * q^42 + 24429956 * q^43 - 21995703 * q^44 + 14223246 * q^46 - 66858708 * q^47 + 29557871 * q^48 - 6453929 * q^49 - 25634699 * q^51 + 57862932 * q^52 - 132620514 * q^53 + 282250495 * q^54 - 169538130 * q^56 - 252946415 * q^57 - 201908320 * q^58 + 5670960 * q^59 + 125306926 * q^61 + 39831174 * q^62 - 284323404 * q^63 + 167542401 * q^64 - 556915843 * q^66 - 88829483 * q^67 + 71162559 * q^68 - 314274942 * q^69 + 297550596 * q^71 + 552918990 * q^72 - 181321729 * q^73 - 251507358 * q^74 + 89414865 * q^76 - 561214086 * q^77 + 1439424692 * q^78 - 310025170 * q^79 + 1398847363 * q^81 + 1368322979 * q^82 + 731088801 * q^83 + 38267082 * q^84 + 33947196 * q^86 - 1046385560 * q^87 + 943671285 * q^88 - 1103860035 * q^89 + 1183187656 * q^91 + 190024242 * q^92 - 107386758 * q^93 + 1727891132 * q^94 - 2567180449 * q^96 + 332236842 * q^97 - 457927581 * q^98 - 892234522 * 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 $

$2$	−31.7828	−1.40461	−0.702306	−	0.711875i	$-0.747846\pi$
$2$	−31.7828	−1.40461	−0.702306	+	0.711875i	$0.747846\pi$
$3$	−268.664	−1.91498	−0.957489	−	0.288470i	$-0.906854\pi$
$3$	−268.664	−1.91498	−0.957489	+	0.288470i	$0.906854\pi$
$4$	498.143	0.972936
$5$	0	0
$5$	0	0
$6$	8538.88	2.68980
$7$	637.237	0.100314	0.0501568	−	0.998741i	$-0.484028\pi$
$7$	637.237	0.100314	0.0501568	+	0.998741i	$0.484028\pi$
$8$	440.406	0.0380144
$9$	52497.3	2.66714
$10$	0	0
$11$	−49042.6	−1.00996	−0.504982	−	0.863130i	$-0.668501\pi$
$11$	−49042.6	−1.00996	−0.504982	+	0.863130i	$0.668501\pi$
$12$	−133833.	−1.86315
$13$	72726.2	0.706229	0.353115	−	0.935580i	$-0.385123\pi$
$13$	72726.2	0.706229	0.353115	+	0.935580i	$0.385123\pi$
$14$	−20253.2	−0.140902
$15$	0	0
$16$	−269047.	−1.02633
$17$	67319.3	0.195488	0.0977439	−	0.995212i	$-0.468837\pi$
$17$	67319.3	0.195488	0.0977439	+	0.995212i	$0.468837\pi$
$18$	−1.66851e6	−3.74630
$19$	341136.	0.600532	0.300266	−	0.953855i	$-0.402925\pi$
$19$	341136.	0.600532	0.300266	+	0.953855i	$0.402925\pi$
$20$	0	0
$21$	−171203.	−0.192098
$22$	1.55871e6	1.41861
$23$	−134355.	−0.100110	−0.0500550	−	0.998746i	$-0.515940\pi$
$23$	−134355.	−0.100110	−0.0500550	+	0.998746i	$0.515940\pi$
$24$	−118321.	−0.0727968
$25$	0	0
$26$	−2.31144e6	−0.991978
$27$	−8.81603e6	−3.19254
$28$	317435.	0.0975988
$29$	4.45784e6	1.17040	0.585199	−	0.810890i	$-0.301016\pi$
$29$	4.45784e6	1.17040	0.585199	+	0.810890i	$0.301016\pi$
$30$	0	0
$31$	456520.	0.0887834	0.0443917	−	0.999014i	$-0.485865\pi$
$31$	456520.	0.0887834	0.0443917	+	0.999014i	$0.485865\pi$
$32$	8.32555e6	1.40358
$33$	1.31760e7	1.93406
$34$	−2.13959e6	−0.274585
$35$	0	0
$36$	2.61512e7	2.59496
$37$	1.30516e7	1.14487	0.572433	−	0.819951i	$-0.305999\pi$
$37$	1.30516e7	1.14487	0.572433	+	0.819951i	$0.305999\pi$
$38$	−1.08422e7	−0.843515
$39$	−1.95389e7	−1.35241
$40$	0	0
$41$	−2.56667e7	−1.41854	−0.709272	−	0.704935i	$-0.750976\pi$
$41$	−2.56667e7	−1.41854	−0.709272	+	0.704935i	$0.750976\pi$
$42$	5.44129e6	0.269824
$43$	3.42710e6	0.152869	0.0764344	−	0.997075i	$-0.475646\pi$
$43$	3.42710e6	0.152869	0.0764344	+	0.997075i	$0.475646\pi$
$44$	−2.44302e7	−0.982631
$45$	0	0
$46$	4.27016e6	0.140616
$47$	−3.39814e7	−1.01578	−0.507891	−	0.861421i	$-0.669575\pi$
$47$	−3.39814e7	−1.01578	−0.507891	+	0.861421i	$0.669575\pi$
$48$	7.22831e7	1.96540
$49$	−3.99475e7	−0.989937
$50$	0	0
$51$	−1.80863e7	−0.374355
$52$	3.62281e7	0.687116
$53$	−8.42456e7	−1.46658	−0.733290	−	0.679916i	$-0.762016\pi$
$53$	−8.42456e7	−1.46658	−0.733290	+	0.679916i	$0.762016\pi$
$54$	2.80198e8	4.48428
$55$	0	0
$56$	280643.	0.00381337
$57$	−9.16509e7	−1.15001
$58$	−1.41682e8	−1.64396
$59$	−7.46358e7	−0.801887	−0.400944	−	0.916103i	$-0.631318\pi$
$59$	−7.46358e7	−0.801887	−0.400944	+	0.916103i	$0.631318\pi$
$60$	0	0
$61$	1.78017e8	1.64618	0.823088	−	0.567913i	$-0.192249\pi$
$61$	1.78017e8	1.64618	0.823088	+	0.567913i	$0.192249\pi$
$62$	−1.45094e7	−0.124706
$63$	3.34533e7	0.267551
$64$	−1.26857e8	−0.945159
$65$	0	0
$66$	−4.18769e8	−2.71661
$67$	6.94299e7	0.420930	0.210465	−	0.977601i	$-0.432502\pi$
$67$	6.94299e7	0.420930	0.210465	+	0.977601i	$0.432502\pi$
$68$	3.35347e7	0.190197
$69$	3.60963e7	0.191708
$70$	0	0
$71$	−2.07860e8	−0.970753	−0.485376	−	0.874305i	$-0.661317\pi$
$71$	−2.07860e8	−0.970753	−0.485376	+	0.874305i	$0.661317\pi$
$72$	2.31201e7	0.101390
$73$	−3.02516e8	−1.24680	−0.623398	−	0.781905i	$-0.714248\pi$
$73$	−3.02516e8	−1.24680	−0.623398	+	0.781905i	$0.714248\pi$
$74$	−4.14815e8	−1.60809
$75$	0	0
$76$	1.69935e8	0.584279
$77$	−3.12518e7	−0.101313
$78$	6.21000e8	1.89962
$79$	3.72244e8	1.07524	0.537621	−	0.843187i	$-0.319323\pi$
$79$	3.72244e8	1.07524	0.537621	+	0.843187i	$0.319323\pi$
$80$	0	0
$81$	1.33524e9	3.44650
$82$	8.15758e8	1.99250
$83$	4.50079e8	1.04097	0.520484	−	0.853872i	$-0.325752\pi$
$83$	4.50079e8	1.04097	0.520484	+	0.853872i	$0.325752\pi$
$84$	−8.52835e7	−0.186899
$85$	0	0
$86$	−1.08923e8	−0.214721
$87$	−1.19766e9	−2.24129
$88$	−2.15987e7	−0.0383932
$89$	5.82741e7	0.0984511	0.0492255	−	0.998788i	$-0.484325\pi$
$89$	5.82741e7	0.0984511	0.0492255	+	0.998788i	$0.484325\pi$
$90$	0	0
$91$	4.63438e7	0.0708444
$92$	−6.69279e7	−0.0974006
$93$	−1.22650e8	−0.170018
$94$	1.08002e9	1.42678
$95$	0	0
$96$	−2.23678e9	−2.68783
$97$	7.85850e8	0.901295	0.450647	−	0.892702i	$-0.351193\pi$
$97$	7.85850e8	0.901295	0.450647	+	0.892702i	$0.351193\pi$
$98$	1.26964e9	1.39048
$99$	−2.57461e9	−2.69372
$100$	0	0
$101$	−1.60460e8	−0.153433	−0.0767167	−	0.997053i	$-0.524444\pi$
$101$	−1.60460e8	−0.153433	−0.0767167	+	0.997053i	$0.524444\pi$
$102$	5.74832e8	0.525823
$103$	−1.39454e9	−1.22085	−0.610425	−	0.792074i	$-0.709001\pi$
$103$	−1.39454e9	−1.22085	−0.610425	+	0.792074i	$0.709001\pi$
$104$	3.20291e7	0.0268469
$105$	0	0
$106$	2.67756e9	2.05998
$107$	−1.56463e9	−1.15394	−0.576972	−	0.816764i	$-0.695766\pi$
$107$	−1.56463e9	−1.15394	−0.576972	+	0.816764i	$0.695766\pi$
$108$	−4.39165e9	−3.10614
$109$	1.24703e9	0.846172	0.423086	−	0.906089i	$-0.360947\pi$
$109$	1.24703e9	0.846172	0.423086	+	0.906089i	$0.360947\pi$
$110$	0	0
$111$	−3.50649e9	−2.19240
$112$	−1.71447e8	−0.102955
$113$	−1.81056e9	−1.04463	−0.522313	−	0.852754i	$-0.674931\pi$
$113$	−1.81056e9	−1.04463	−0.522313	+	0.852754i	$0.674931\pi$
$114$	2.91292e9	1.61531
$115$	0	0
$116$	2.22064e9	1.13872
$117$	3.81793e9	1.88361
$118$	2.37213e9	1.12634
$119$	4.28984e7	0.0196101
$120$	0	0
$121$	4.72275e7	0.0200291
$122$	−5.65786e9	−2.31224
$123$	6.89572e9	2.71648
$124$	2.27412e8	0.0863806
$125$	0	0
$126$	−1.06324e9	−0.375805
$127$	−3.06491e9	−1.04545	−0.522723	−	0.852503i	$-0.675084\pi$
$127$	−3.06491e9	−1.04545	−0.522723	+	0.852503i	$0.675084\pi$
$128$	−2.30815e8	−0.0760010
$129$	−9.20739e8	−0.292740
$130$	0	0
$131$	−1.83508e9	−0.544421	−0.272211	−	0.962238i	$-0.587755\pi$
$131$	−1.83508e9	−0.544421	−0.272211	+	0.962238i	$0.587755\pi$
$132$	6.56352e9	1.88172
$133$	2.17385e8	0.0602416
$134$	−2.20667e9	−0.591243
$135$	0	0
$136$	2.96478e7	0.00743136
$137$	−4.62426e9	−1.12150	−0.560751	−	0.827984i	$-0.689488\pi$
$137$	−4.62426e9	−1.12150	−0.560751	+	0.827984i	$0.689488\pi$
$138$	−1.14724e9	−0.269276
$139$	2.57140e8	0.0584255	0.0292128	−	0.999573i	$-0.490700\pi$
$139$	2.57140e8	0.0584255	0.0292128	+	0.999573i	$0.490700\pi$
$140$	0	0
$141$	9.12958e9	1.94520
$142$	6.60637e9	1.36353
$143$	−3.56668e9	−0.713267
$144$	−1.41242e10	−2.73737
$145$	0	0
$146$	9.61479e9	1.75127
$147$	1.07325e10	1.89571
$148$	6.50155e9	1.11388
$149$	3.14809e9	0.523250	0.261625	−	0.965170i	$-0.415742\pi$
$149$	3.14809e9	0.523250	0.261625	+	0.965170i	$0.415742\pi$
$150$	0	0
$151$	−1.02772e10	−1.60871	−0.804356	−	0.594147i	$-0.797490\pi$
$151$	−1.02772e10	−1.60871	−0.804356	+	0.594147i	$0.797490\pi$
$152$	1.50238e8	0.0228289
$153$	3.53408e9	0.521393
$154$	9.93267e8	0.142306
$155$	0	0
$156$	−9.73317e9	−1.31581
$157$	3.25077e9	0.427009	0.213505	−	0.976942i	$-0.431512\pi$
$157$	3.25077e9	0.427009	0.213505	+	0.976942i	$0.431512\pi$
$158$	−1.18309e10	−1.51030
$159$	2.26338e10	2.80847
$160$	0	0
$161$	−8.56158e7	−0.0100424
$162$	−4.24377e10	−4.84100
$163$	3.40049e9	0.377309	0.188655	−	0.982043i	$-0.439587\pi$
$163$	3.40049e9	0.377309	0.188655	+	0.982043i	$0.439587\pi$
$164$	−1.27857e10	−1.38015
$165$	0	0
$166$	−1.43047e10	−1.46216
$167$	5.27785e9	0.525089	0.262544	−	0.964920i	$-0.415438\pi$
$167$	5.27785e9	0.525089	0.262544	+	0.964920i	$0.415438\pi$
$168$	−7.53987e7	−0.00730251
$169$	−5.31540e9	−0.501240
$170$	0	0
$171$	1.79087e10	1.60170
$172$	1.70719e9	0.148732
$173$	6.58861e9	0.559224	0.279612	−	0.960113i	$-0.409794\pi$
$173$	6.58861e9	0.559224	0.279612	+	0.960113i	$0.409794\pi$
$174$	3.80650e10	3.14814
$175$	0	0
$176$	1.31947e10	1.03656
$177$	2.00520e10	1.53560
$178$	−1.85211e9	−0.138286
$179$	−1.23663e10	−0.900326	−0.450163	−	0.892946i	$-0.648634\pi$
$179$	−1.23663e10	−0.900326	−0.450163	+	0.892946i	$0.648634\pi$
$180$	0	0
$181$	−2.59914e10	−1.80002	−0.900009	−	0.435872i	$-0.856440\pi$
$181$	−2.59914e10	−1.80002	−0.900009	+	0.435872i	$0.856440\pi$
$182$	−1.47293e9	−0.0995090
$183$	−4.78267e10	−3.15239
$184$	−5.91706e7	−0.00380562
$185$	0	0
$186$	3.89817e9	0.238810
$187$	−3.30151e9	−0.197436
$188$	−1.69276e10	−0.988292
$189$	−5.61790e9	−0.320255
$190$	0	0
$191$	1.50506e10	0.818284	0.409142	−	0.912471i	$-0.365828\pi$
$191$	1.50506e10	0.818284	0.409142	+	0.912471i	$0.365828\pi$
$192$	3.40819e10	1.80996
$193$	1.40329e10	0.728014	0.364007	−	0.931396i	$-0.381408\pi$
$193$	1.40329e10	0.728014	0.364007	+	0.931396i	$0.381408\pi$
$194$	−2.49765e10	−1.26597
$195$	0	0
$196$	−1.98996e10	−0.963146
$197$	−2.57285e10	−1.21707	−0.608536	−	0.793526i	$-0.708243\pi$
$197$	−2.57285e10	−1.21707	−0.608536	+	0.793526i	$0.708243\pi$
$198$	8.18280e10	3.78363
$199$	−2.94367e10	−1.33061	−0.665303	−	0.746573i	$-0.731698\pi$
$199$	−2.94367e10	−1.33061	−0.665303	+	0.746573i	$0.731698\pi$
$200$	0	0
$201$	−1.86533e10	−0.806072
$202$	5.09985e9	0.215515
$203$	2.84070e9	0.117407
$204$	−9.00956e9	−0.364223
$205$	0	0
$206$	4.43222e10	1.71482
$207$	−7.05326e9	−0.267007
$208$	−1.95667e10	−0.724825
$209$	−1.67302e10	−0.606516
$210$	0	0
$211$	1.17275e10	0.407319	0.203659	−	0.979042i	$-0.434716\pi$
$211$	1.17275e10	0.407319	0.203659	+	0.979042i	$0.434716\pi$
$212$	−4.19664e10	−1.42689
$213$	5.58445e10	1.85897
$214$	4.97283e10	1.62084
$215$	0	0
$216$	−3.88263e9	−0.121363
$217$	2.90911e8	0.00890619
$218$	−3.96341e10	−1.18854
$219$	8.12751e10	2.38759
$220$	0	0
$221$	4.89588e9	0.138059
$222$	1.11446e11	3.07947
$223$	2.58340e10	0.699550	0.349775	−	0.936834i	$-0.386258\pi$
$223$	2.58340e10	0.699550	0.349775	+	0.936834i	$0.386258\pi$
$224$	5.30535e9	0.140799
$225$	0	0
$226$	5.75447e10	1.46729
$227$	−2.50896e10	−0.627159	−0.313580	−	0.949562i	$-0.601528\pi$
$227$	−2.50896e10	−0.627159	−0.313580	+	0.949562i	$0.601528\pi$
$228$	−4.56553e10	−1.11888
$229$	−2.30463e10	−0.553785	−0.276892	−	0.960901i	$-0.589305\pi$
$229$	−2.30463e10	−0.553785	−0.276892	+	0.960901i	$0.589305\pi$
$230$	0	0
$231$	8.39622e9	0.194013
$232$	1.96326e9	0.0444920
$233$	3.17197e10	0.705062	0.352531	−	0.935800i	$-0.385321\pi$
$233$	3.17197e10	0.705062	0.352531	+	0.935800i	$0.385321\pi$
$234$	−1.21344e11	−2.64575
$235$	0	0
$236$	−3.71793e10	−0.780185
$237$	−1.00009e11	−2.05906
$238$	−1.36343e9	−0.0275446
$239$	2.23794e10	0.443668	0.221834	−	0.975084i	$-0.428796\pi$
$239$	2.23794e10	0.443668	0.221834	+	0.975084i	$0.428796\pi$
$240$	0	0
$241$	−2.10823e10	−0.402569	−0.201285	−	0.979533i	$-0.564512\pi$
$241$	−2.10823e10	−0.402569	−0.201285	+	0.979533i	$0.564512\pi$
$242$	−1.50102e9	−0.0281331
$243$	−1.85206e11	−3.40743
$244$	8.86778e10	1.60162
$245$	0	0
$246$	−2.19165e11	−3.81560
$247$	2.48095e10	0.424113
$248$	2.01054e8	0.00337505
$249$	−1.20920e11	−1.99343
$250$	0	0
$251$	−7.96509e10	−1.26666	−0.633329	−	0.773883i	$-0.718312\pi$
$251$	−7.96509e10	−1.26666	−0.633329	+	0.773883i	$0.718312\pi$
$252$	1.66645e10	0.260310
$253$	6.58910e9	0.101108
$254$	9.74114e10	1.46845
$255$	0	0
$256$	7.22868e10	1.05191
$257$	−3.30815e10	−0.473027	−0.236514	−	0.971628i	$-0.576005\pi$
$257$	−3.30815e10	−0.473027	−0.236514	+	0.971628i	$0.576005\pi$
$258$	2.92636e10	0.411187
$259$	8.31695e9	0.114846
$260$	0	0
$261$	2.34025e11	3.12162
$262$	5.83240e10	0.764701
$263$	6.05028e10	0.779784	0.389892	−	0.920861i	$-0.372512\pi$
$263$	6.05028e10	0.779784	0.389892	+	0.920861i	$0.372512\pi$
$264$	5.80278e9	0.0735222
$265$	0	0
$266$	−6.90908e9	−0.0846161
$267$	−1.56562e10	−0.188532
$268$	3.45860e10	0.409538
$269$	2.61933e10	0.305004	0.152502	−	0.988303i	$-0.451267\pi$
$269$	2.61933e10	0.305004	0.152502	+	0.988303i	$0.451267\pi$
$270$	0	0
$271$	5.42857e10	0.611398	0.305699	−	0.952128i	$-0.401110\pi$
$271$	5.42857e10	0.611398	0.305699	+	0.952128i	$0.401110\pi$
$272$	−1.81120e10	−0.200635
$273$	−1.24509e10	−0.135666
$274$	1.46972e11	1.57528
$275$	0	0
$276$	1.79811e10	0.186520
$277$	1.76561e11	1.80192	0.900961	−	0.433900i	$-0.142863\pi$
$277$	1.76561e11	1.80192	0.900961	+	0.433900i	$0.142863\pi$
$278$	−8.17261e9	−0.0820652
$279$	2.39661e10	0.236798
$280$	0	0
$281$	−7.91126e9	−0.0756950	−0.0378475	−	0.999284i	$-0.512050\pi$
$281$	−7.91126e9	−0.0756950	−0.0378475	+	0.999284i	$0.512050\pi$
$282$	−2.90163e11	−2.73225
$283$	−1.34806e11	−1.24931	−0.624657	−	0.780899i	$-0.714761\pi$
$283$	−1.34806e11	−1.24931	−0.624657	+	0.780899i	$0.714761\pi$
$284$	−1.03544e11	−0.944480
$285$	0	0
$286$	1.13359e11	1.00186
$287$	−1.63558e10	−0.142299
$288$	4.37069e11	3.74356
$289$	−1.14056e11	−0.961785
$290$	0	0
$291$	−2.11130e11	−1.72596
$292$	−1.50696e11	−1.21305
$293$	1.02784e11	0.814741	0.407370	−	0.913263i	$-0.366446\pi$
$293$	1.02784e11	0.814741	0.407370	+	0.913263i	$0.366446\pi$
$294$	−3.41107e11	−2.66273
$295$	0	0
$296$	5.74799e9	0.0435215
$297$	4.32361e11	3.22435
$298$	−1.00055e11	−0.734964
$299$	−9.77110e9	−0.0707006
$300$	0	0
$301$	2.18388e9	0.0153348
$302$	3.26638e11	2.25962
$303$	4.31098e10	0.293822
$304$	−9.17815e10	−0.616345
$305$	0	0
$306$	−1.12323e11	−0.732356
$307$	−2.61472e11	−1.67998	−0.839988	−	0.542606i	$-0.817438\pi$
$307$	−2.61472e11	−1.67998	−0.839988	+	0.542606i	$0.817438\pi$
$308$	−1.55679e10	−0.0985713
$309$	3.74662e11	2.33790
$310$	0	0
$311$	−8.24828e10	−0.499967	−0.249984	−	0.968250i	$-0.580425\pi$
$311$	−8.24828e10	−0.499967	−0.249984	+	0.968250i	$0.580425\pi$
$312$	−8.60505e9	−0.0514112
$313$	−1.35766e11	−0.799540	−0.399770	−	0.916615i	$-0.630910\pi$
$313$	−1.35766e11	−0.799540	−0.399770	+	0.916615i	$0.630910\pi$
$314$	−1.03318e11	−0.599783
$315$	0	0
$316$	1.85431e11	1.04614
$317$	−9.06853e10	−0.504394	−0.252197	−	0.967676i	$-0.581153\pi$
$317$	−9.06853e10	−0.504394	−0.252197	+	0.967676i	$0.581153\pi$
$318$	−7.19363e11	−3.94481
$319$	−2.18624e11	−1.18206
$320$	0	0
$321$	4.20360e11	2.20978
$322$	2.72111e9	0.0141057
$323$	2.29650e10	0.117397
$324$	6.65143e11	3.35322
$325$	0	0
$326$	−1.08077e11	−0.529973
$327$	−3.35033e11	−1.62040
$328$	−1.13038e10	−0.0539251
$329$	−2.16542e10	−0.101897
$330$	0	0
$331$	−3.45169e11	−1.58054	−0.790271	−	0.612758i	$-0.790060\pi$
$331$	−3.45169e11	−1.58054	−0.790271	+	0.612758i	$0.790060\pi$
$332$	2.24204e11	1.01279
$333$	6.85173e11	3.05352
$334$	−1.67745e11	−0.737546
$335$	0	0
$336$	4.60615e10	0.197157
$337$	8.39418e10	0.354523	0.177261	−	0.984164i	$-0.443276\pi$
$337$	8.39418e10	0.354523	0.177261	+	0.984164i	$0.443276\pi$
$338$	1.68938e11	0.704048
$339$	4.86433e11	2.00043
$340$	0	0
$341$	−2.23889e10	−0.0896681
$342$	−5.69189e11	−2.24977
$343$	−5.11709e10	−0.199618
$344$	1.50932e9	0.00581122
$345$	0	0
$346$	−2.09404e11	−0.785493
$347$	1.56153e11	0.578188	0.289094	−	0.957301i	$-0.406646\pi$
$347$	1.56153e11	0.578188	0.289094	+	0.957301i	$0.406646\pi$
$348$	−5.96607e11	−2.18063
$349$	6.31862e9	0.0227986	0.0113993	−	0.999935i	$-0.496371\pi$
$349$	6.31862e9	0.0227986	0.0113993	+	0.999935i	$0.496371\pi$
$350$	0	0
$351$	−6.41156e11	−2.25466
$352$	−4.08307e11	−1.41757
$353$	−2.83875e11	−0.973064	−0.486532	−	0.873663i	$-0.661738\pi$
$353$	−2.83875e11	−0.973064	−0.486532	+	0.873663i	$0.661738\pi$
$354$	−6.37307e11	−2.15692
$355$	0	0
$356$	2.90288e10	0.0957866
$357$	−1.15253e10	−0.0375529
$358$	3.93034e11	1.26461
$359$	6.00733e11	1.90878	0.954391	−	0.298558i	$-0.0965058\pi$
$359$	6.00733e11	1.90878	0.954391	+	0.298558i	$0.0965058\pi$
$360$	0	0
$361$	−2.06314e11	−0.639361
$362$	8.26079e11	2.52833
$363$	−1.26883e10	−0.0383552
$364$	2.30859e10	0.0689271
$365$	0	0
$366$	1.52006e12	4.42789
$367$	4.97260e11	1.43082	0.715412	−	0.698702i	$-0.246239\pi$
$367$	4.97260e11	1.43082	0.715412	+	0.698702i	$0.246239\pi$
$368$	3.61477e10	0.102746
$369$	−1.34743e12	−3.78346
$370$	0	0
$371$	−5.36845e10	−0.147118
$372$	−6.10974e10	−0.165417
$373$	1.39183e11	0.372303	0.186151	−	0.982521i	$-0.440398\pi$
$373$	1.39183e11	0.372303	0.186151	+	0.982521i	$0.440398\pi$
$374$	1.04931e11	0.277321
$375$	0	0
$376$	−1.49656e10	−0.0386144
$377$	3.24202e11	0.826569
$378$	1.78552e11	0.449834
$379$	−5.65247e11	−1.40722	−0.703610	−	0.710587i	$-0.748430\pi$
$379$	−5.65247e11	−1.40722	−0.703610	+	0.710587i	$0.748430\pi$
$380$	0	0
$381$	8.23432e11	2.00201
$382$	−4.78350e11	−1.14937
$383$	−5.38864e11	−1.27963	−0.639816	−	0.768528i	$-0.720989\pi$
$383$	−5.38864e11	−1.27963	−0.639816	+	0.768528i	$0.720989\pi$
$384$	6.20117e10	0.145540
$385$	0	0
$386$	−4.46004e11	−1.02258
$387$	1.79914e11	0.407723
$388$	3.91466e11	0.876902
$389$	7.67552e11	1.69955	0.849776	−	0.527144i	$-0.176737\pi$
$389$	7.67552e11	1.69955	0.849776	+	0.527144i	$0.176737\pi$
$390$	0	0
$391$	−9.04466e9	−0.0195703
$392$	−1.75931e10	−0.0376319
$393$	4.93021e11	1.04255
$394$	8.17722e11	1.70951
$395$	0	0
$396$	−1.28252e12	−2.62082
$397$	−6.25258e11	−1.26329	−0.631643	−	0.775259i	$-0.717619\pi$
$397$	−6.25258e11	−1.26329	−0.631643	+	0.775259i	$0.717619\pi$
$398$	9.35578e11	1.86899
$399$	−5.84034e10	−0.115361
$400$	0	0
$401$	−1.61329e11	−0.311574	−0.155787	−	0.987791i	$-0.549791\pi$
$401$	−1.61329e11	−0.311574	−0.155787	+	0.987791i	$0.549791\pi$
$402$	5.92853e11	1.13222
$403$	3.32009e10	0.0627014
$404$	−7.99320e10	−0.149281
$405$	0	0
$406$	−9.02853e10	−0.164911
$407$	−6.40083e11	−1.15628
$408$	−7.96531e9	−0.0142309
$409$	−7.24004e11	−1.27934	−0.639670	−	0.768649i	$-0.720929\pi$
$409$	−7.24004e11	−1.27934	−0.639670	+	0.768649i	$0.720929\pi$
$410$	0	0
$411$	1.24237e12	2.14765
$412$	−6.94679e11	−1.18781
$413$	−4.75607e10	−0.0804403
$414$	2.24172e11	0.375042
$415$	0	0
$416$	6.05486e11	0.991252
$417$	−6.90842e10	−0.111884
$418$	5.31731e11	0.851920
$419$	2.80040e11	0.443871	0.221936	−	0.975061i	$-0.428763\pi$
$419$	2.80040e11	0.443871	0.221936	+	0.975061i	$0.428763\pi$
$420$	0	0
$421$	−6.55915e10	−0.101760	−0.0508801	−	0.998705i	$-0.516203\pi$
$421$	−6.55915e10	−0.101760	−0.0508801	+	0.998705i	$0.516203\pi$
$422$	−3.72732e11	−0.572125
$423$	−1.78393e12	−2.70924
$424$	−3.71023e10	−0.0557512
$425$	0	0
$426$	−1.77489e12	−2.61113
$427$	1.13439e11	0.165134
$428$	−7.79410e11	−1.12271
$429$	9.58239e11	1.36589
$430$	0	0
$431$	1.00292e12	1.39997	0.699987	−	0.714156i	$-0.253189\pi$
$431$	1.00292e12	1.39997	0.699987	+	0.714156i	$0.253189\pi$
$432$	2.37192e12	3.27660
$433$	−7.98482e11	−1.09162	−0.545808	−	0.837910i	$-0.683777\pi$
$433$	−7.98482e11	−1.09162	−0.545808	+	0.837910i	$0.683777\pi$
$434$	−9.24596e9	−0.0125097
$435$	0	0
$436$	6.21201e11	0.823271
$437$	−4.58332e10	−0.0601193
$438$	−2.58315e12	−3.35363
$439$	7.98379e11	1.02593	0.512966	−	0.858409i	$-0.328547\pi$
$439$	7.98379e11	1.02593	0.512966	+	0.858409i	$0.328547\pi$
$440$	0	0
$441$	−2.09714e12	−2.64030
$442$	−1.55604e11	−0.193920
$443$	7.56642e11	0.933413	0.466707	−	0.884412i	$-0.345440\pi$
$443$	7.56642e11	0.933413	0.466707	+	0.884412i	$0.345440\pi$
$444$	−1.74673e12	−2.13306
$445$	0	0
$446$	−8.21074e11	−0.982597
$447$	−8.45779e11	−1.00201
$448$	−8.08381e10	−0.0948124
$449$	−6.39419e11	−0.742467	−0.371234	−	0.928540i	$-0.621065\pi$
$449$	−6.39419e11	−0.742467	−0.371234	+	0.928540i	$0.621065\pi$
$450$	0	0
$451$	1.25876e12	1.43268
$452$	−9.01919e11	−1.01635
$453$	2.76111e12	3.08065
$454$	7.97418e11	0.880916
$455$	0	0
$456$	−4.03636e10	−0.0437168
$457$	1.34276e12	1.44005	0.720024	−	0.693949i	$-0.244131\pi$
$457$	1.34276e12	1.44005	0.720024	+	0.693949i	$0.244131\pi$
$458$	7.32474e11	0.777853
$459$	−5.93489e11	−0.624102
$460$	0	0
$461$	3.47112e11	0.357945	0.178972	−	0.983854i	$-0.442723\pi$
$461$	3.47112e11	0.357945	0.178972	+	0.983854i	$0.442723\pi$
$462$	−2.66855e11	−0.272513
$463$	−7.20214e11	−0.728362	−0.364181	−	0.931328i	$-0.618651\pi$
$463$	−7.20214e11	−0.728362	−0.364181	+	0.931328i	$0.618651\pi$
$464$	−1.19937e12	−1.20122
$465$	0	0
$466$	−1.00814e12	−0.990339
$467$	7.31553e10	0.0711737	0.0355869	−	0.999367i	$-0.488670\pi$
$467$	7.31553e10	0.0711737	0.0355869	+	0.999367i	$0.488670\pi$
$468$	1.90188e12	1.83264
$469$	4.42433e10	0.0422250
$470$	0	0
$471$	−8.73364e11	−0.817713
$472$	−3.28701e10	−0.0304833
$473$	−1.68074e11	−0.154392
$474$	3.17855e12	2.89219
$475$	0	0
$476$	2.13695e10	0.0190794
$477$	−4.42267e12	−3.91158
$478$	−7.11279e11	−0.623181
$479$	−4.80307e10	−0.0416878	−0.0208439	−	0.999783i	$-0.506635\pi$
$479$	−4.80307e10	−0.0416878	−0.0208439	+	0.999783i	$0.506635\pi$
$480$	0	0
$481$	9.49191e11	0.808539
$482$	6.70052e11	0.565454
$483$	2.30019e10	0.0192310
$484$	2.35261e10	0.0194870
$485$	0	0
$486$	5.88636e12	4.78612
$487$	1.24384e12	1.00204	0.501021	−	0.865435i	$-0.332958\pi$
$487$	1.24384e12	1.00204	0.501021	+	0.865435i	$0.332958\pi$
$488$	7.83997e10	0.0625785
$489$	−9.13590e11	−0.722539
$490$	0	0
$491$	−2.63145e11	−0.204328	−0.102164	−	0.994768i	$-0.532577\pi$
$491$	−2.63145e11	−0.204328	−0.102164	+	0.994768i	$0.532577\pi$
$492$	3.43506e12	2.64296
$493$	3.00099e11	0.228798
$494$	−7.88515e11	−0.595715
$495$	0	0
$496$	−1.22825e11	−0.0911212
$497$	−1.32456e11	−0.0973798
$498$	3.84317e12	2.80000
$499$	3.75452e10	0.0271083	0.0135542	−	0.999908i	$-0.495685\pi$
$499$	3.75452e10	0.0271083	0.0135542	+	0.999908i	$0.495685\pi$
$500$	0	0
$501$	−1.41797e12	−1.00553
$502$	2.53153e12	1.77916
$503$	2.86189e11	0.199341	0.0996707	−	0.995020i	$-0.468221\pi$
$503$	2.86189e11	0.199341	0.0996707	+	0.995020i	$0.468221\pi$
$504$	1.47330e10	0.0101708
$505$	0	0
$506$	−2.09420e11	−0.142017
$507$	1.42806e12	0.959864
$508$	−1.52677e12	−1.01715
$509$	−1.48505e12	−0.980646	−0.490323	−	0.871541i	$-0.663121\pi$
$509$	−1.48505e12	−0.980646	−0.490323	+	0.871541i	$0.663121\pi$
$510$	0	0
$511$	−1.92774e11	−0.125071
$512$	−2.17930e12	−1.40153
$513$	−3.00746e12	−1.91722
$514$	1.05142e12	0.664420
$515$	0	0
$516$	−4.58660e11	−0.284818
$517$	1.66654e12	1.02590
$518$	−2.64336e11	−0.161314
$519$	−1.77012e12	−1.07090
$520$	0	0
$521$	−1.77521e12	−1.05556	−0.527778	−	0.849383i	$-0.676975\pi$
$521$	−1.77521e12	−1.05556	−0.527778	+	0.849383i	$0.676975\pi$
$522$	−7.43795e12	−4.38466
$523$	1.20614e12	0.704922	0.352461	−	0.935826i	$-0.385345\pi$
$523$	1.20614e12	0.704922	0.352461	+	0.935826i	$0.385345\pi$
$524$	−9.14135e11	−0.529687
$525$	0	0
$526$	−1.92294e12	−1.09529
$527$	3.07326e10	0.0173561
$528$	−3.54495e12	−1.98499
$529$	−1.78310e12	−0.989978
$530$	0	0
$531$	−3.91818e12	−2.13875
$532$	1.08289e11	0.0586112
$533$	−1.86664e12	−1.00182
$534$	4.97596e11	0.264814
$535$	0	0
$536$	3.05773e10	0.0160014
$537$	3.32237e12	1.72410
$538$	−8.32495e11	−0.428412
$539$	1.95913e12	0.999802
$540$	0	0
$541$	3.24195e12	1.62711	0.813557	−	0.581485i	$-0.197528\pi$
$541$	3.24195e12	1.62711	0.813557	+	0.581485i	$0.197528\pi$
$542$	−1.72535e12	−0.858777
$543$	6.98296e12	3.44699
$544$	5.60471e11	0.274383
$545$	0	0
$546$	3.95725e11	0.190558
$547$	9.33463e11	0.445814	0.222907	−	0.974840i	$-0.428445\pi$
$547$	9.33463e11	0.445814	0.222907	+	0.974840i	$0.428445\pi$
$548$	−2.30355e12	−1.09115
$549$	9.34540e12	4.39059
$550$	0	0
$551$	1.52073e12	0.702861
$552$	1.58970e10	0.00728769
$553$	2.37208e11	0.107861
$554$	−5.61160e12	−2.53100
$555$	0	0
$556$	1.28092e11	0.0568443
$557$	−1.31760e12	−0.580012	−0.290006	−	0.957025i	$-0.593657\pi$
$557$	−1.31760e12	−0.580012	−0.290006	+	0.957025i	$0.593657\pi$
$558$	−7.61707e11	−0.332609
$559$	2.49240e11	0.107960
$560$	0	0
$561$	8.86998e11	0.378085
$562$	2.51442e11	0.106322
$563$	−4.33363e12	−1.81788	−0.908938	−	0.416931i	$-0.863106\pi$
$563$	−4.33363e12	−1.81788	−0.908938	+	0.416931i	$0.863106\pi$
$564$	4.54784e12	1.89256
$565$	0	0
$566$	4.28452e12	1.75480
$567$	8.50868e11	0.345731
$568$	−9.15429e10	−0.0369026
$569$	3.08940e12	1.23558	0.617788	−	0.786345i	$-0.288029\pi$
$569$	3.08940e12	1.23558	0.617788	+	0.786345i	$0.288029\pi$
$570$	0	0
$571$	−7.43095e11	−0.292538	−0.146269	−	0.989245i	$-0.546726\pi$
$571$	−7.43095e11	−0.292538	−0.146269	+	0.989245i	$0.546726\pi$
$572$	−1.77672e12	−0.693963
$573$	−4.04356e12	−1.56700
$574$	5.19832e11	0.199875
$575$	0	0
$576$	−6.65966e12	−2.52087
$577$	−2.25852e12	−0.848269	−0.424134	−	0.905599i	$-0.639422\pi$
$577$	−2.25852e12	−0.848269	−0.424134	+	0.905599i	$0.639422\pi$
$578$	3.62501e12	1.35093
$579$	−3.77013e12	−1.39413
$580$	0	0
$581$	2.86807e11	0.104423
$582$	6.71028e12	2.42430
$583$	4.13162e12	1.48119
$584$	−1.33230e11	−0.0473962
$585$	0	0
$586$	−3.26674e12	−1.14440
$587$	−4.75794e12	−1.65405	−0.827023	−	0.562169i	$-0.809967\pi$
$587$	−4.75794e12	−1.65405	−0.827023	+	0.562169i	$0.809967\pi$
$588$	5.34630e12	1.84440
$589$	1.55735e11	0.0533173
$590$	0	0
$591$	6.91232e12	2.33067
$592$	−3.51148e12	−1.17501
$593$	−2.01077e12	−0.667755	−0.333878	−	0.942616i	$-0.608357\pi$
$593$	−2.01077e12	−0.667755	−0.333878	+	0.942616i	$0.608357\pi$
$594$	−1.37416e13	−4.52896
$595$	0	0
$596$	1.56820e12	0.509089
$597$	7.90857e12	2.54808
$598$	3.10552e11	0.0993070
$599$	−3.29427e12	−1.04554	−0.522768	−	0.852475i	$-0.675101\pi$
$599$	−3.29427e12	−1.04554	−0.522768	+	0.852475i	$0.675101\pi$
$600$	0	0
$601$	−1.98887e12	−0.621830	−0.310915	−	0.950438i	$-0.600635\pi$
$601$	−1.98887e12	−0.621830	−0.310915	+	0.950438i	$0.600635\pi$
$602$	−6.94096e10	−0.0215395
$603$	3.64488e12	1.12268
$604$	−5.11952e12	−1.56517
$605$	0	0
$606$	−1.37015e12	−0.412706
$607$	−4.11631e12	−1.23072	−0.615360	−	0.788246i	$-0.710989\pi$
$607$	−4.11631e12	−1.23072	−0.615360	+	0.788246i	$0.710989\pi$
$608$	2.84015e12	0.842897
$609$	−7.63194e11	−0.224832
$610$	0	0
$611$	−2.47134e12	−0.717376
$612$	1.76048e12	0.507282
$613$	2.06864e12	0.591715	0.295858	−	0.955232i	$-0.404395\pi$
$613$	2.06864e12	0.591715	0.295858	+	0.955232i	$0.404395\pi$
$614$	8.31031e12	2.35971
$615$	0	0
$616$	−1.37635e10	−0.00385137
$617$	5.42058e12	1.50578	0.752891	−	0.658145i	$-0.228659\pi$
$617$	5.42058e12	1.50578	0.752891	+	0.658145i	$0.228659\pi$
$618$	−1.19078e13	−3.28385
$619$	3.87240e12	1.06016	0.530081	−	0.847947i	$-0.322162\pi$
$619$	3.87240e12	1.06016	0.530081	+	0.847947i	$0.322162\pi$
$620$	0	0
$621$	1.18447e12	0.319605
$622$	2.62153e12	0.702260
$623$	3.71344e10	0.00987599
$624$	5.25688e12	1.38802
$625$	0	0
$626$	4.31500e12	1.12304
$627$	4.49480e12	1.16147
$628$	1.61935e12	0.415453
$629$	8.78623e11	0.223807
$630$	0	0
$631$	−3.22937e12	−0.810933	−0.405467	−	0.914110i	$-0.632891\pi$
$631$	−3.22937e12	−0.810933	−0.405467	+	0.914110i	$0.632891\pi$
$632$	1.63939e11	0.0408747
$633$	−3.15076e12	−0.780006
$634$	2.88223e12	0.708478
$635$	0	0
$636$	1.12749e13	2.73246
$637$	−2.90523e12	−0.699123
$638$	6.94847e12	1.66034
$639$	−1.09121e13	−2.58913
$640$	0	0
$641$	1.10935e12	0.259543	0.129771	−	0.991544i	$-0.458576\pi$
$641$	1.10935e12	0.259543	0.129771	+	0.991544i	$0.458576\pi$
$642$	−1.33602e13	−3.10388
$643$	2.83993e12	0.655177	0.327588	−	0.944821i	$-0.393764\pi$
$643$	2.83993e12	0.655177	0.327588	+	0.944821i	$0.393764\pi$
$644$	−4.26489e10	−0.00977061
$645$	0	0
$646$	−7.29892e11	−0.164897
$647$	2.66962e12	0.598935	0.299467	−	0.954107i	$-0.403191\pi$
$647$	2.66962e12	0.598935	0.299467	+	0.954107i	$0.403191\pi$
$648$	5.88050e11	0.131017
$649$	3.66033e12	0.809878
$650$	0	0
$651$	−7.81574e10	−0.0170552
$652$	1.69393e12	0.367098
$653$	−4.72156e12	−1.01619	−0.508097	−	0.861300i	$-0.669651\pi$
$653$	−4.72156e12	−1.01619	−0.508097	+	0.861300i	$0.669651\pi$
$654$	1.06483e13	2.27604
$655$	0	0
$656$	6.90554e12	1.45590
$657$	−1.58813e13	−3.32538
$658$	6.88231e11	0.143126
$659$	4.01448e12	0.829173	0.414586	−	0.910010i	$-0.363926\pi$
$659$	4.01448e12	0.829173	0.414586	+	0.910010i	$0.363926\pi$
$660$	0	0
$661$	−8.01591e12	−1.63323	−0.816613	−	0.577186i	$-0.804151\pi$
$661$	−8.01591e12	−1.63323	−0.816613	+	0.577186i	$0.804151\pi$
$662$	1.09704e13	2.22005
$663$	−1.31535e12	−0.264380
$664$	1.98218e11	0.0395718
$665$	0	0
$666$	−2.17767e13	−4.28901
$667$	−5.98931e11	−0.117168
$668$	2.62912e12	0.510878
$669$	−6.94065e12	−1.33962
$670$	0	0
$671$	−8.73040e12	−1.66258
$672$	−1.42536e12	−0.269626
$673$	−3.55147e12	−0.667330	−0.333665	−	0.942692i	$-0.608286\pi$
$673$	−3.55147e12	−0.667330	−0.333665	+	0.942692i	$0.608286\pi$
$674$	−2.66790e12	−0.497967
$675$	0	0
$676$	−2.64783e12	−0.487675
$677$	−6.06872e12	−1.11032	−0.555160	−	0.831744i	$-0.687343\pi$
$677$	−6.06872e12	−1.11032	−0.555160	+	0.831744i	$0.687343\pi$
$678$	−1.54602e13	−2.80983
$679$	5.00773e11	0.0904122
$680$	0	0
$681$	6.74068e12	1.20100
$682$	7.11581e11	0.125949
$683$	9.96514e11	0.175223	0.0876113	−	0.996155i	$-0.472077\pi$
$683$	9.96514e11	0.175223	0.0876113	+	0.996155i	$0.472077\pi$
$684$	8.92111e12	1.55836
$685$	0	0
$686$	1.62635e12	0.280386
$687$	6.19170e12	1.06049
$688$	−9.22050e11	−0.156894
$689$	−6.12686e12	−1.03574
$690$	0	0
$691$	1.02702e13	1.71367	0.856835	−	0.515591i	$-0.172428\pi$
$691$	1.02702e13	1.71367	0.856835	+	0.515591i	$0.172428\pi$
$692$	3.28207e12	0.544090
$693$	−1.64063e12	−0.270217
$694$	−4.96299e12	−0.812130
$695$	0	0
$696$	−5.27457e11	−0.0852012
$697$	−1.72786e12	−0.277308
$698$	−2.00823e11	−0.0320232
$699$	−8.52194e12	−1.35018
$700$	0	0
$701$	−8.26127e12	−1.29216	−0.646079	−	0.763270i	$-0.723592\pi$
$701$	−8.26127e12	−1.29216	−0.646079	+	0.763270i	$0.723592\pi$
$702$	2.03777e13	3.16693
$703$	4.45236e12	0.687529
$704$	6.22140e12	0.954578
$705$	0	0
$706$	9.02234e12	1.36678
$707$	−1.02251e11	−0.0153915
$708$	9.98875e12	1.49404
$709$	−8.11428e12	−1.20598	−0.602992	−	0.797747i	$-0.706025\pi$
$709$	−8.11428e12	−1.20598	−0.602992	+	0.797747i	$0.706025\pi$
$710$	0	0
$711$	1.95418e13	2.86782
$712$	2.56643e10	0.00374256
$713$	−6.13355e10	−0.00888810
$714$	3.66304e11	0.0527473
$715$	0	0
$716$	−6.16017e12	−0.875960
$717$	−6.01254e12	−0.849614
$718$	−1.90929e13	−2.68110
$719$	1.06399e13	1.48476	0.742380	−	0.669979i	$-0.233697\pi$
$719$	1.06399e13	1.48476	0.742380	+	0.669979i	$0.233697\pi$
$720$	0	0
$721$	−8.88651e11	−0.122468
$722$	6.55723e12	0.898055
$723$	5.66405e12	0.770911
$724$	−1.29475e13	−1.75130
$725$	0	0
$726$	4.03270e11	0.0538742
$727$	−1.35040e13	−1.79290	−0.896450	−	0.443145i	$-0.853863\pi$
$727$	−1.35040e13	−1.79290	−0.896450	+	0.443145i	$0.853863\pi$
$728$	2.04101e10	0.00269311
$729$	2.34766e13	3.07866
$730$	0	0
$731$	2.30710e11	0.0298840
$732$	−2.38245e13	−3.06708
$733$	3.03764e12	0.388659	0.194329	−	0.980936i	$-0.437747\pi$
$733$	3.03764e12	0.388659	0.194329	+	0.980936i	$0.437747\pi$
$734$	−1.58043e13	−2.00975
$735$	0	0
$736$	−1.11858e12	−0.140513
$737$	−3.40502e12	−0.425124
$738$	4.28251e13	5.31429
$739$	7.29483e12	0.899736	0.449868	−	0.893095i	$-0.351471\pi$
$739$	7.29483e12	0.899736	0.449868	+	0.893095i	$0.351471\pi$
$740$	0	0
$741$	−6.66542e12	−0.812168
$742$	1.70624e12	0.206644
$743$	−1.18034e13	−1.42088	−0.710442	−	0.703756i	$-0.751505\pi$
$743$	−1.18034e13	−1.42088	−0.710442	+	0.703756i	$0.751505\pi$
$744$	−5.40160e10	−0.00646315
$745$	0	0
$746$	−4.42362e12	−0.522941
$747$	2.36279e13	2.77641
$748$	−1.64463e12	−0.192092
$749$	−9.97041e11	−0.115756
$750$	0	0
$751$	1.20855e13	1.38639	0.693197	−	0.720748i	$-0.256202\pi$
$751$	1.20855e13	1.38639	0.693197	+	0.720748i	$0.256202\pi$
$752$	9.14258e12	1.04253
$753$	2.13993e13	2.42562
$754$	−1.03040e13	−1.16101
$755$	0	0
$756$	−2.79852e12	−0.311588
$757$	1.48077e13	1.63891	0.819455	−	0.573144i	$-0.194276\pi$
$757$	1.48077e13	1.63891	0.819455	+	0.573144i	$0.194276\pi$
$758$	1.79651e13	1.97660
$759$	−1.77025e12	−0.193619
$760$	0	0
$761$	−1.75185e13	−1.89350	−0.946749	−	0.321972i	$-0.895654\pi$
$761$	−1.75185e13	−1.89350	−0.946749	+	0.321972i	$0.895654\pi$
$762$	−2.61709e13	−2.81204
$763$	7.94656e11	0.0848826
$764$	7.49736e12	0.796138
$765$	0	0
$766$	1.71266e13	1.79739
$767$	−5.42798e12	−0.566316
$768$	−1.94209e13	−2.01439
$769$	4.16729e12	0.429720	0.214860	−	0.976645i	$-0.431070\pi$
$769$	4.16729e12	0.429720	0.214860	+	0.976645i	$0.431070\pi$
$770$	0	0
$771$	8.88781e12	0.905837
$772$	6.99039e12	0.708311
$773$	−1.05896e13	−1.06677	−0.533386	−	0.845872i	$-0.679081\pi$
$773$	−1.05896e13	−1.06677	−0.533386	+	0.845872i	$0.679081\pi$
$774$	−5.71815e12	−0.572692
$775$	0	0
$776$	3.46093e11	0.0342622
$777$	−2.23446e12	−0.219927
$778$	−2.43949e13	−2.38721
$779$	−8.75583e12	−0.851881
$780$	0	0
$781$	1.01940e13	0.980426
$782$	2.87464e11	0.0274887
$783$	−3.93004e13	−3.73654
$784$	1.07478e13	1.01600
$785$	0	0
$786$	−1.56696e13	−1.46439
$787$	2.50861e12	0.233102	0.116551	−	0.993185i	$-0.462816\pi$
$787$	2.50861e12	0.233102	0.116551	+	0.993185i	$0.462816\pi$
$788$	−1.28165e13	−1.18413
$789$	−1.62549e13	−1.49327
$790$	0	0
$791$	−1.15376e12	−0.104790
$792$	−1.13387e12	−0.102400
$793$	1.29465e13	1.16258
$794$	1.98724e13	1.77443
$795$	0	0
$796$	−1.46637e13	−1.29460
$797$	1.85822e13	1.63131	0.815653	−	0.578541i	$-0.196378\pi$
$797$	1.85822e13	1.63131	0.815653	+	0.578541i	$0.196378\pi$
$798$	1.85622e12	0.162038
$799$	−2.28760e12	−0.198573
$800$	0	0
$801$	3.05923e12	0.262583
$802$	5.12746e12	0.437641
$803$	1.48362e13	1.25922
$804$	−9.29202e12	−0.784256
$805$	0	0
$806$	−1.05522e12	−0.0880712
$807$	−7.03720e12	−0.584075
$808$	−7.06675e10	−0.00583268
$809$	−4.47333e12	−0.367166	−0.183583	−	0.983004i	$-0.558770\pi$
$809$	−4.47333e12	−0.367166	−0.183583	+	0.983004i	$0.558770\pi$
$810$	0	0
$811$	−3.49582e12	−0.283763	−0.141881	−	0.989884i	$-0.545315\pi$
$811$	−3.49582e12	−0.283763	−0.141881	+	0.989884i	$0.545315\pi$
$812$	1.41508e12	0.114229
$813$	−1.45846e13	−1.17081
$814$	2.03436e13	1.62412
$815$	0	0
$816$	4.86605e12	0.384212
$817$	1.16911e12	0.0918026
$818$	2.30108e13	1.79698
$819$	2.43293e12	0.188952
$820$	0	0
$821$	−6.84197e12	−0.525578	−0.262789	−	0.964853i	$-0.584642\pi$
$821$	−6.84197e12	−0.525578	−0.262789	+	0.964853i	$0.584642\pi$
$822$	−3.94860e13	−3.01662
$823$	8.11058e12	0.616244	0.308122	−	0.951347i	$-0.400300\pi$
$823$	8.11058e12	0.616244	0.308122	+	0.951347i	$0.400300\pi$
$824$	−6.14163e11	−0.0464099
$825$	0	0
$826$	1.51161e12	0.112987
$827$	−5.06349e10	−0.00376422	−0.00188211	−	0.999998i	$-0.500599\pi$
$827$	−5.06349e10	−0.00376422	−0.00188211	+	0.999998i	$0.500599\pi$
$828$	−3.51353e12	−0.259781
$829$	−1.50474e13	−1.10654	−0.553269	−	0.833002i	$-0.686620\pi$
$829$	−1.50474e13	−1.10654	−0.553269	+	0.833002i	$0.686620\pi$
$830$	0	0
$831$	−4.74356e13	−3.45064
$832$	−9.22584e12	−0.667499
$833$	−2.68924e12	−0.193521
$834$	2.19569e12	0.157153
$835$	0	0
$836$	−8.33403e12	−0.590102
$837$	−4.02469e12	−0.283444
$838$	−8.90044e12	−0.623467
$839$	2.68352e13	1.86972	0.934859	−	0.355020i	$-0.115526\pi$
$839$	2.68352e13	1.86972	0.934859	+	0.355020i	$0.115526\pi$
$840$	0	0
$841$	5.36519e12	0.369831
$842$	2.08468e12	0.142934
$843$	2.12547e12	0.144954
$844$	5.84197e12	0.396295
$845$	0	0
$846$	5.66983e13	3.80543
$847$	3.00951e10	0.00200919
$848$	2.26660e13	1.50520
$849$	3.62176e13	2.39241
$850$	0	0
$851$	−1.75354e12	−0.114613
$852$	2.78186e13	1.80866
$853$	4.22107e12	0.272993	0.136497	−	0.990641i	$-0.456416\pi$
$853$	4.22107e12	0.272993	0.136497	+	0.990641i	$0.456416\pi$
$854$	−3.60540e12	−0.231949
$855$	0	0
$856$	−6.89073e11	−0.0438665
$857$	−7.57740e12	−0.479851	−0.239926	−	0.970791i	$-0.577123\pi$
$857$	−7.57740e12	−0.479851	−0.239926	+	0.970791i	$0.577123\pi$
$858$	−3.04555e13	−1.91855
$859$	1.41463e13	0.886486	0.443243	−	0.896401i	$-0.353828\pi$
$859$	1.41463e13	0.886486	0.443243	+	0.896401i	$0.353828\pi$
$860$	0	0
$861$	4.39421e12	0.272500
$862$	−3.18757e13	−1.96642
$863$	1.52498e13	0.935868	0.467934	−	0.883763i	$-0.344998\pi$
$863$	1.52498e13	0.935868	0.467934	+	0.883763i	$0.344998\pi$
$864$	−7.33983e13	−4.48099
$865$	0	0
$866$	2.53780e13	1.53330
$867$	3.06427e13	1.84180
$868$	1.44915e11	0.00866515
$869$	−1.82558e13	−1.08596
$870$	0	0
$871$	5.04937e12	0.297273
$872$	5.49201e11	0.0321668
$873$	4.12550e13	2.40388
$874$	1.45671e12	0.0844443
$875$	0	0
$876$	4.04867e13	2.32297
$877$	3.30350e12	0.188572	0.0942858	−	0.995545i	$-0.469943\pi$
$877$	3.30350e12	0.188572	0.0942858	+	0.995545i	$0.469943\pi$
$878$	−2.53747e13	−1.44104
$879$	−2.76142e13	−1.56021
$880$	0	0
$881$	3.14728e13	1.76013	0.880063	−	0.474856i	$-0.157500\pi$
$881$	3.14728e13	1.76013	0.880063	+	0.474856i	$0.157500\pi$
$882$	6.66528e13	3.70860
$883$	1.10669e13	0.612637	0.306318	−	0.951929i	$-0.400903\pi$
$883$	1.10669e13	0.612637	0.306318	+	0.951929i	$0.400903\pi$
$884$	2.43885e12	0.134323
$885$	0	0
$886$	−2.40482e13	−1.31108
$887$	−6.92035e12	−0.375381	−0.187690	−	0.982228i	$-0.560100\pi$
$887$	−6.92035e12	−0.375381	−0.187690	+	0.982228i	$0.560100\pi$
$888$	−1.54428e12	−0.0833426
$889$	−1.95308e12	−0.104872
$890$	0	0
$891$	−6.54838e13	−3.48084
$892$	1.28690e13	0.680618
$893$	−1.15923e13	−0.610010
$894$	2.68812e13	1.40744
$895$	0	0
$896$	−1.47084e11	−0.00762394
$897$	2.62514e12	0.135390
$898$	2.03225e13	1.04288
$899$	2.03509e12	0.103912
$900$	0	0
$901$	−5.67136e12	−0.286699
$902$	−4.00069e13	−2.01236
$903$	−5.86729e11	−0.0293659
$904$	−7.97383e11	−0.0397108
$905$	0	0
$906$	−8.77557e13	−4.32712
$907$	−2.00486e13	−0.983676	−0.491838	−	0.870687i	$-0.663675\pi$
$907$	−2.00486e13	−0.983676	−0.491838	+	0.870687i	$0.663675\pi$
$908$	−1.24982e13	−0.610186
$909$	−8.42371e12	−0.409229
$910$	0	0
$911$	2.53798e13	1.22083	0.610416	−	0.792081i	$-0.291002\pi$
$911$	2.53798e13	1.22083	0.610416	+	0.792081i	$0.291002\pi$
$912$	2.46584e13	1.18029
$913$	−2.20730e13	−1.05134
$914$	−4.26768e13	−2.02271
$915$	0	0
$916$	−1.14803e13	−0.538797
$917$	−1.16938e12	−0.0546129
$918$	1.88627e13	0.876622
$919$	−6.15926e12	−0.284845	−0.142423	−	0.989806i	$-0.545489\pi$
$919$	−6.15926e12	−0.284845	−0.142423	+	0.989806i	$0.545489\pi$
$920$	0	0
$921$	7.02482e13	3.21712
$922$	−1.10322e13	−0.502774
$923$	−1.51169e13	−0.685574
$924$	4.18252e12	0.188762
$925$	0	0
$926$	2.28904e13	1.02307
$927$	−7.32095e13	−3.25618
$928$	3.71140e13	1.64275
$929$	2.20000e13	0.969061	0.484531	−	0.874774i	$-0.338990\pi$
$929$	2.20000e13	0.969061	0.484531	+	0.874774i	$0.338990\pi$
$930$	0	0
$931$	−1.36275e13	−0.594489
$932$	1.58010e13	0.685980
$933$	2.21601e13	0.957426
$934$	−2.32508e12	−0.0999715
$935$	0	0
$936$	1.68144e12	0.0716045
$937$	2.49274e12	0.105645	0.0528225	−	0.998604i	$-0.483178\pi$
$937$	2.49274e12	0.105645	0.0528225	+	0.998604i	$0.483178\pi$
$938$	−1.40617e12	−0.0593098
$939$	3.64753e13	1.53110
$940$	0	0
$941$	−1.26366e13	−0.525382	−0.262691	−	0.964880i	$-0.584610\pi$
$941$	−1.26366e13	−0.525382	−0.262691	+	0.964880i	$0.584610\pi$
$942$	2.77579e13	1.14857
$943$	3.44844e12	0.142010
$944$	2.00805e13	0.823002
$945$	0	0
$946$	5.34185e12	0.216861
$947$	−2.05809e13	−0.831551	−0.415775	−	0.909467i	$-0.636490\pi$
$947$	−2.05809e13	−0.831551	−0.415775	+	0.909467i	$0.636490\pi$
$948$	−4.98186e13	−2.00334
$949$	−2.20008e13	−0.880524
$950$	0	0
$951$	2.43639e13	0.965904
$952$	1.88927e10	0.000745466 0
$953$	−2.97887e13	−1.16986	−0.584929	−	0.811084i	$-0.698878\pi$
$953$	−2.97887e13	−1.16986	−0.584929	+	0.811084i	$0.698878\pi$
$954$	1.40565e14	5.49425
$955$	0	0
$956$	1.11481e13	0.431660
$957$	5.87364e13	2.26362
$958$	1.52655e12	0.0585553
$959$	−2.94675e12	−0.112502
$960$	0	0
$961$	−2.62312e13	−0.992118
$962$	−3.01679e13	−1.13568
$963$	−8.21389e13	−3.07773
$964$	−1.05020e13	−0.391674
$965$	0	0
$966$	−7.31063e11	−0.0270121
$967$	1.74473e13	0.641664	0.320832	−	0.947136i	$-0.396037\pi$
$967$	1.74473e13	0.641664	0.320832	+	0.947136i	$0.396037\pi$
$968$	2.07993e10	0.000761394 0
$969$	−6.16988e12	−0.224812
$970$	0	0
$971$	−2.53844e13	−0.916390	−0.458195	−	0.888852i	$-0.651504\pi$
$971$	−2.53844e13	−0.916390	−0.458195	+	0.888852i	$0.651504\pi$
$972$	−9.22592e13	−3.31521
$973$	1.63859e11	0.00586088
$974$	−3.95328e13	−1.40748
$975$	0	0
$976$	−4.78948e13	−1.68952
$977$	3.23029e13	1.13427	0.567135	−	0.823625i	$-0.308052\pi$
$977$	3.23029e13	1.13427	0.567135	+	0.823625i	$0.308052\pi$
$978$	2.90364e13	1.01489
$979$	−2.85791e12	−0.0994321
$980$	0	0
$981$	6.54659e13	2.25686
$982$	8.36348e12	0.287002
$983$	−1.78014e13	−0.608083	−0.304041	−	0.952659i	$-0.598336\pi$
$983$	−1.78014e13	−0.608083	−0.304041	+	0.952659i	$0.598336\pi$
$984$	3.03692e12	0.103265
$985$	0	0
$986$	−9.53796e12	−0.321373
$987$	5.81771e12	0.195130
$988$	1.23587e13	0.412635
$989$	−4.60447e11	−0.0153037
$990$	0	0
$991$	−3.38638e12	−0.111533	−0.0557666	−	0.998444i	$-0.517760\pi$
$991$	−3.38638e12	−0.111533	−0.0557666	+	0.998444i	$0.517760\pi$
$992$	3.80078e12	0.124615
$993$	9.27345e13	3.02670
$994$	4.20982e12	0.136781
$995$	0	0
$996$	−6.02355e13	−1.93948
$997$	4.17766e13	1.33908	0.669538	−	0.742778i	$-0.266492\pi$
$997$	4.17766e13	1.33908	0.669538	+	0.742778i	$0.266492\pi$
$998$	−1.19329e12	−0.0380767
$999$	−1.15063e14	−3.65503

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.10.a.c.1.1	✓	3
3.2	odd	2		225.10.a.p.1.3		3
4.3	odd	2		400.10.a.y.1.3		3
5.2	odd	4		25.10.b.c.24.1		6
5.3	odd	4		25.10.b.c.24.6		6
5.4	even	2		25.10.a.d.1.3	yes	3
15.2	even	4		225.10.b.m.199.6		6
15.8	even	4		225.10.b.m.199.1		6
15.14	odd	2		225.10.a.m.1.1		3
20.3	even	4		400.10.c.q.49.6		6
20.7	even	4		400.10.c.q.49.1		6
20.19	odd	2		400.10.a.u.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.10.a.c.1.1	✓	3	1.1	even	1	trivial
25.10.a.d.1.3	yes	3	5.4	even	2
25.10.b.c.24.1		6	5.2	odd	4
25.10.b.c.24.6		6	5.3	odd	4
225.10.a.m.1.1		3	15.14	odd	2
225.10.a.p.1.3		3	3.2	odd	2
225.10.b.m.199.1		6	15.8	even	4
225.10.b.m.199.6		6	15.2	even	4
400.10.a.u.1.1		3	20.19	odd	2
400.10.a.y.1.3		3	4.3	odd	2
400.10.c.q.49.1		6	20.7	even	4
400.10.c.q.49.6		6	20.3	even	4

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q-31.7828 q^{2} -268.664 q^{3} +498.143 q^{4} +8538.88 q^{6} +637.237 q^{7} +440.406 q^{8} +52497.3 q^{9} +O(q^{10})\)	\(q-31.7828 q^{2} -268.664 q^{3} +498.143 q^{4} +8538.88 q^{6} +637.237 q^{7} +440.406 q^{8} +52497.3 q^{9} -49042.6 q^{11} -133833. q^{12} +72726.2 q^{13} -20253.2 q^{14} -269047. q^{16} +67319.3 q^{17} -1.66851e6 q^{18} +341136. q^{19} -171203. q^{21} +1.55871e6 q^{22} -134355. q^{23} -118321. q^{24} -2.31144e6 q^{26} -8.81603e6 q^{27} +317435. q^{28} +4.45784e6 q^{29} +456520. q^{31} +8.32555e6 q^{32} +1.31760e7 q^{33} -2.13959e6 q^{34} +2.61512e7 q^{36} +1.30516e7 q^{37} -1.08422e7 q^{38} -1.95389e7 q^{39} -2.56667e7 q^{41} +5.44129e6 q^{42} +3.42710e6 q^{43} -2.44302e7 q^{44} +4.27016e6 q^{46} -3.39814e7 q^{47} +7.22831e7 q^{48} -3.99475e7 q^{49} -1.80863e7 q^{51} +3.62281e7 q^{52} -8.42456e7 q^{53} +2.80198e8 q^{54} +280643. q^{56} -9.16509e7 q^{57} -1.41682e8 q^{58} -7.46358e7 q^{59} +1.78017e8 q^{61} -1.45094e7 q^{62} +3.34533e7 q^{63} -1.26857e8 q^{64} -4.18769e8 q^{66} +6.94299e7 q^{67} +3.35347e7 q^{68} +3.60963e7 q^{69} -2.07860e8 q^{71} +2.31201e7 q^{72} -3.02516e8 q^{73} -4.14815e8 q^{74} +1.69935e8 q^{76} -3.12518e7 q^{77} +6.21000e8 q^{78} +3.72244e8 q^{79} +1.33524e9 q^{81} +8.15758e8 q^{82} +4.50079e8 q^{83} -8.52835e7 q^{84} -1.08923e8 q^{86} -1.19766e9 q^{87} -2.15987e7 q^{88} +5.82741e7 q^{89} +4.63438e7 q^{91} -6.69279e7 q^{92} -1.22650e8 q^{93} +1.08002e9 q^{94} -2.23678e9 q^{96} +7.85850e8 q^{97} +1.26964e9 q^{98} -2.57461e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 33 q^{2} - 89 q^{3} + 341 q^{4} + 3421 q^{6} - 5258 q^{7} + 105 q^{8} + 58234 q^{9}+O(q^{10}) \) 3 * q - 33 * q^2 - 89 * q^3 + 341 * q^4 + 3421 * q^6 - 5258 * q^7 + 105 * q^8 + 58234 * q^9	\( 3 q - 33 q^{2} - 89 q^{3} + 341 q^{4} + 3421 q^{6} - 5258 q^{7} + 105 q^{8} + 58234 q^{9} - 54699 q^{11} - 141853 q^{12} - 215884 q^{13} + 272922 q^{14} - 699247 q^{16} - 334983 q^{17} - 2571854 q^{18} + 818845 q^{19} - 2375394 q^{21} - 72761 q^{22} - 3526854 q^{23} + 2805735 q^{24} - 1280004 q^{26} - 6633395 q^{27} + 428134 q^{28} + 2175480 q^{29} + 4274066 q^{31} + 9464577 q^{32} + 22122137 q^{33} - 6838963 q^{34} + 26795798 q^{36} + 10305042 q^{37} + 24180495 q^{38} - 50414092 q^{39} + 5926311 q^{41} + 47560254 q^{42} + 24429956 q^{43} - 21995703 q^{44} + 14223246 q^{46} - 66858708 q^{47} + 29557871 q^{48} - 6453929 q^{49} - 25634699 q^{51} + 57862932 q^{52} - 132620514 q^{53} + 282250495 q^{54} - 169538130 q^{56} - 252946415 q^{57} - 201908320 q^{58} + 5670960 q^{59} + 125306926 q^{61} + 39831174 q^{62} - 284323404 q^{63} + 167542401 q^{64} - 556915843 q^{66} - 88829483 q^{67} + 71162559 q^{68} - 314274942 q^{69} + 297550596 q^{71} + 552918990 q^{72} - 181321729 q^{73} - 251507358 q^{74} + 89414865 q^{76} - 561214086 q^{77} + 1439424692 q^{78} - 310025170 q^{79} + 1398847363 q^{81} + 1368322979 q^{82} + 731088801 q^{83} + 38267082 q^{84} + 33947196 q^{86} - 1046385560 q^{87} + 943671285 q^{88} - 1103860035 q^{89} + 1183187656 q^{91} + 190024242 q^{92} - 107386758 q^{93} + 1727891132 q^{94} - 2567180449 q^{96} + 332236842 q^{97} - 457927581 q^{98} - 892234522 q^{99}+O(q^{100}) \) 3 * q - 33 * q^2 - 89 * q^3 + 341 * q^4 + 3421 * q^6 - 5258 * q^7 + 105 * q^8 + 58234 * q^9 - 54699 * q^11 - 141853 * q^12 - 215884 * q^13 + 272922 * q^14 - 699247 * q^16 - 334983 * q^17 - 2571854 * q^18 + 818845 * q^19 - 2375394 * q^21 - 72761 * q^22 - 3526854 * q^23 + 2805735 * q^24 - 1280004 * q^26 - 6633395 * q^27 + 428134 * q^28 + 2175480 * q^29 + 4274066 * q^31 + 9464577 * q^32 + 22122137 * q^33 - 6838963 * q^34 + 26795798 * q^36 + 10305042 * q^37 + 24180495 * q^38 - 50414092 * q^39 + 5926311 * q^41 + 47560254 * q^42 + 24429956 * q^43 - 21995703 * q^44 + 14223246 * q^46 - 66858708 * q^47 + 29557871 * q^48 - 6453929 * q^49 - 25634699 * q^51 + 57862932 * q^52 - 132620514 * q^53 + 282250495 * q^54 - 169538130 * q^56 - 252946415 * q^57 - 201908320 * q^58 + 5670960 * q^59 + 125306926 * q^61 + 39831174 * q^62 - 284323404 * q^63 + 167542401 * q^64 - 556915843 * q^66 - 88829483 * q^67 + 71162559 * q^68 - 314274942 * q^69 + 297550596 * q^71 + 552918990 * q^72 - 181321729 * q^73 - 251507358 * q^74 + 89414865 * q^76 - 561214086 * q^77 + 1439424692 * q^78 - 310025170 * q^79 + 1398847363 * q^81 + 1368322979 * q^82 + 731088801 * q^83 + 38267082 * q^84 + 33947196 * q^86 - 1046385560 * q^87 + 943671285 * q^88 - 1103860035 * q^89 + 1183187656 * q^91 + 190024242 * q^92 - 107386758 * q^93 + 1727891132 * q^94 - 2567180449 * q^96 + 332236842 * q^97 - 457927581 * q^98 - 892234522 * q^99

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