LMFDB - Embedded newform 25.10.a.d.1.2

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:	$0$
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			1.2
Root			$22.2334$ 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)

$f(q)$	$=$	$q+21.4187 q^{2} -210.171 q^{3} -53.2406 q^{4} -4501.59 q^{6} +9905.49 q^{7} -12106.7 q^{8} +24489.0 q^{9} +O(q^{10})$	\(q+21.4187 q^{2} -210.171 q^{3} -53.2406 q^{4} -4501.59 q^{6} +9905.49 q^{7} -12106.7 q^{8} +24489.0 q^{9} +36453.6 q^{11} +11189.6 q^{12} +164867. q^{13} +212162. q^{14} -232050. q^{16} +82357.1 q^{17} +524521. q^{18} -609617. q^{19} -2.08185e6 q^{21} +780787. q^{22} +1.88578e6 q^{23} +2.54448e6 q^{24} +3.53123e6 q^{26} -1.01008e6 q^{27} -527374. q^{28} +339235. q^{29} +547314. q^{31} +1.22842e6 q^{32} -7.66150e6 q^{33} +1.76398e6 q^{34} -1.30381e6 q^{36} +5.25687e6 q^{37} -1.30572e7 q^{38} -3.46503e7 q^{39} +2.05812e6 q^{41} -4.45904e7 q^{42} -6.76158e6 q^{43} -1.94081e6 q^{44} +4.03909e7 q^{46} +3.15241e7 q^{47} +4.87703e7 q^{48} +5.77651e7 q^{49} -1.73091e7 q^{51} -8.77761e6 q^{52} -4.89593e7 q^{53} -2.16345e7 q^{54} -1.19923e8 q^{56} +1.28124e8 q^{57} +7.26597e6 q^{58} +8.77960e7 q^{59} +3.84654e7 q^{61} +1.17227e7 q^{62} +2.42575e8 q^{63} +1.45121e8 q^{64} -1.64099e8 q^{66} -1.36116e8 q^{67} -4.38474e6 q^{68} -3.96337e8 q^{69} +3.49218e8 q^{71} -2.96481e8 q^{72} +1.61345e8 q^{73} +1.12595e8 q^{74} +3.24564e7 q^{76} +3.61091e8 q^{77} -7.42163e8 q^{78} -1.26975e8 q^{79} -2.69727e8 q^{81} +4.40822e7 q^{82} -2.87494e8 q^{83} +1.10839e8 q^{84} -1.44824e8 q^{86} -7.12976e7 q^{87} -4.41333e8 q^{88} -5.63133e8 q^{89} +1.63309e9 q^{91} -1.00400e8 q^{92} -1.15030e8 q^{93} +6.75205e8 q^{94} -2.58179e8 q^{96} -4.71704e8 q^{97} +1.23725e9 q^{98} +8.92711e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	21.4187	0.946580	0.473290	−	0.880907i	$-0.343066\pi$
$2$	21.4187	0.946580	0.473290	+	0.880907i	$0.343066\pi$
$3$	−210.171	−1.49805	−0.749027	−	0.662539i	$-0.769479\pi$
$3$	−210.171	−1.49805	−0.749027	+	0.662539i	$0.769479\pi$
$4$	−53.2406	−0.103986
$5$	0	0
$5$	0	0
$6$	−4501.59	−1.41803
$7$	9905.49	1.55932	0.779659	−	0.626204i	$-0.215392\pi$
$7$	9905.49	1.55932	0.779659	+	0.626204i	$0.215392\pi$
$8$	−12106.7	−1.04501
$9$	24489.0	1.24417
$10$	0	0
$11$	36453.6	0.750712	0.375356	−	0.926881i	$-0.377520\pi$
$11$	36453.6	0.750712	0.375356	+	0.926881i	$0.377520\pi$
$12$	11189.6	0.155776
$13$	164867.	1.60099	0.800494	−	0.599341i	$-0.204571\pi$
$13$	164867.	1.60099	0.800494	+	0.599341i	$0.204571\pi$
$14$	212162.	1.47602
$15$	0	0
$16$	−232050.	−0.885201
$17$	82357.1	0.239156	0.119578	−	0.992825i	$-0.461846\pi$
$17$	82357.1	0.239156	0.119578	+	0.992825i	$0.461846\pi$
$18$	524521.	1.17771
$19$	−609617.	−1.07316	−0.536582	−	0.843848i	$-0.680285\pi$
$19$	−609617.	−1.07316	−0.536582	+	0.843848i	$0.680285\pi$
$20$	0	0
$21$	−2.08185e6	−2.33594
$22$	780787.	0.710609
$23$	1.88578e6	1.40513	0.702564	−	0.711620i	$-0.252038\pi$
$23$	1.88578e6	1.40513	0.702564	+	0.711620i	$0.252038\pi$
$24$	2.54448e6	1.56548
$25$	0	0
$26$	3.53123e6	1.51546
$27$	−1.01008e6	−0.365778
$28$	−527374.	−0.162147
$29$	339235.	0.0890657	0.0445328	−	0.999008i	$-0.485820\pi$
$29$	339235.	0.0890657	0.0445328	+	0.999008i	$0.485820\pi$
$30$	0	0
$31$	547314.	0.106441	0.0532205	−	0.998583i	$-0.483051\pi$
$31$	547314.	0.106441	0.0532205	+	0.998583i	$0.483051\pi$
$32$	1.22842e6	0.207097
$33$	−7.66150e6	−1.12461
$34$	1.76398e6	0.226380
$35$	0	0
$36$	−1.30381e6	−0.129376
$37$	5.25687e6	0.461126	0.230563	−	0.973057i	$-0.425943\pi$
$37$	5.25687e6	0.461126	0.230563	+	0.973057i	$0.425943\pi$
$38$	−1.30572e7	−1.01584
$39$	−3.46503e7	−2.39837
$40$	0	0
$41$	2.05812e6	0.113748	0.0568739	−	0.998381i	$-0.481887\pi$
$41$	2.05812e6	0.113748	0.0568739	+	0.998381i	$0.481887\pi$
$42$	−4.45904e7	−2.21116
$43$	−6.76158e6	−0.301606	−0.150803	−	0.988564i	$-0.548186\pi$
$43$	−6.76158e6	−0.301606	−0.150803	+	0.988564i	$0.548186\pi$
$44$	−1.94081e6	−0.0780632
$45$	0	0
$46$	4.03909e7	1.33007
$47$	3.15241e7	0.942330	0.471165	−	0.882045i	$-0.343834\pi$
$47$	3.15241e7	0.942330	0.471165	+	0.882045i	$0.343834\pi$
$48$	4.87703e7	1.32608
$49$	5.77651e7	1.43147
$50$	0	0
$51$	−1.73091e7	−0.358268
$52$	−8.77761e6	−0.166480
$53$	−4.89593e7	−0.852303	−0.426151	−	0.904652i	$-0.640131\pi$
$53$	−4.89593e7	−0.852303	−0.426151	+	0.904652i	$0.640131\pi$
$54$	−2.16345e7	−0.346238
$55$	0	0
$56$	−1.19923e8	−1.62950
$57$	1.28124e8	1.60766
$58$	7.26597e6	0.0843078
$59$	8.77960e7	0.943281	0.471640	−	0.881791i	$-0.343662\pi$
$59$	8.77960e7	0.943281	0.471640	+	0.881791i	$0.343662\pi$
$60$	0	0
$61$	3.84654e7	0.355701	0.177851	−	0.984057i	$-0.443086\pi$
$61$	3.84654e7	0.355701	0.177851	+	0.984057i	$0.443086\pi$
$62$	1.17227e7	0.100755
$63$	2.42575e8	1.94005
$64$	1.45121e8	1.08124
$65$	0	0
$66$	−1.64099e8	−1.06453
$67$	−1.36116e8	−0.825227	−0.412613	−	0.910906i	$-0.635384\pi$
$67$	−1.36116e8	−0.825227	−0.412613	+	0.910906i	$0.635384\pi$
$68$	−4.38474e6	−0.0248687
$69$	−3.96337e8	−2.10496
$70$	0	0
$71$	3.49218e8	1.63092	0.815462	−	0.578810i	$-0.196483\pi$
$71$	3.49218e8	1.63092	0.815462	+	0.578810i	$0.196483\pi$
$72$	−2.96481e8	−1.30017
$73$	1.61345e8	0.664971	0.332486	−	0.943108i	$-0.392113\pi$
$73$	1.61345e8	0.664971	0.332486	+	0.943108i	$0.392113\pi$
$74$	1.12595e8	0.436492
$75$	0	0
$76$	3.24564e7	0.111594
$77$	3.61091e8	1.17060
$78$	−7.42163e8	−2.27025
$79$	−1.26975e8	−0.366772	−0.183386	−	0.983041i	$-0.558706\pi$
$79$	−1.26975e8	−0.366772	−0.183386	+	0.983041i	$0.558706\pi$
$80$	0	0
$81$	−2.69727e8	−0.696213
$82$	4.40822e7	0.107671
$83$	−2.87494e8	−0.664931	−0.332466	−	0.943115i	$-0.607881\pi$
$83$	−2.87494e8	−0.664931	−0.332466	+	0.943115i	$0.607881\pi$
$84$	1.10839e8	0.242904
$85$	0	0
$86$	−1.44824e8	−0.285494
$87$	−7.12976e7	−0.133425
$88$	−4.41333e8	−0.784502
$89$	−5.63133e8	−0.951385	−0.475692	−	0.879612i	$-0.657802\pi$
$89$	−5.63133e8	−0.951385	−0.475692	+	0.879612i	$0.657802\pi$
$90$	0	0
$91$	1.63309e9	2.49645
$92$	−1.00400e8	−0.146113
$93$	−1.15030e8	−0.159454
$94$	6.75205e8	0.891991
$95$	0	0
$96$	−2.58179e8	−0.310242
$97$	−4.71704e8	−0.541000	−0.270500	−	0.962720i	$-0.587189\pi$
$97$	−4.71704e8	−0.541000	−0.270500	+	0.962720i	$0.587189\pi$
$98$	1.23725e9	1.35500
$99$	8.92711e8	0.934012
$100$	0	0
$101$	−1.25673e9	−1.20170	−0.600851	−	0.799361i	$-0.705172\pi$
$101$	−1.25673e9	−1.20170	−0.600851	+	0.799361i	$0.705172\pi$
$102$	−3.70738e8	−0.339130
$103$	1.95398e9	1.71062	0.855309	−	0.518119i	$-0.173367\pi$
$103$	1.95398e9	1.71062	0.855309	+	0.518119i	$0.173367\pi$
$104$	−1.99599e9	−1.67305
$105$	0	0
$106$	−1.04864e9	−0.806773
$107$	2.12306e9	1.56580	0.782899	−	0.622148i	$-0.213740\pi$
$107$	2.12306e9	1.56580	0.782899	+	0.622148i	$0.213740\pi$
$108$	5.37771e7	0.0380356
$109$	−1.18863e8	−0.0806544	−0.0403272	−	0.999187i	$-0.512840\pi$
$109$	−1.18863e8	−0.0806544	−0.0403272	+	0.999187i	$0.512840\pi$
$110$	0	0
$111$	−1.10484e9	−0.690791
$112$	−2.29857e9	−1.38031
$113$	−1.85455e9	−1.07001	−0.535003	−	0.844850i	$-0.679689\pi$
$113$	−1.85455e9	−1.07001	−0.535003	+	0.844850i	$0.679689\pi$
$114$	2.74425e9	1.52178
$115$	0	0
$116$	−1.80611e7	−0.00926154
$117$	4.03742e9	1.99190
$118$	1.88047e9	0.892891
$119$	8.15787e8	0.372920
$120$	0	0
$121$	−1.02908e9	−0.436432
$122$	8.23877e8	0.336700
$123$	−4.32557e8	−0.170400
$124$	−2.91393e7	−0.0110683
$125$	0	0
$126$	5.19564e9	1.83642
$127$	−5.39208e9	−1.83924	−0.919622	−	0.392805i	$-0.871505\pi$
$127$	−5.39208e9	−1.83924	−0.919622	+	0.392805i	$0.871505\pi$
$128$	2.47934e9	0.816379
$129$	1.42109e9	0.451823
$130$	0	0
$131$	3.83690e9	1.13831	0.569154	−	0.822231i	$-0.307271\pi$
$131$	3.83690e9	1.13831	0.569154	+	0.822231i	$0.307271\pi$
$132$	4.07903e8	0.116943
$133$	−6.03856e9	−1.67340
$134$	−2.91543e9	−0.781143
$135$	0	0
$136$	−9.97072e8	−0.249920
$137$	−2.55408e9	−0.619430	−0.309715	−	0.950829i	$-0.600234\pi$
$137$	−2.55408e9	−0.619430	−0.309715	+	0.950829i	$0.600234\pi$
$138$	−8.48901e9	−1.99251
$139$	−4.09121e9	−0.929577	−0.464789	−	0.885422i	$-0.653870\pi$
$139$	−4.09121e9	−0.929577	−0.464789	+	0.885422i	$0.653870\pi$
$140$	0	0
$141$	−6.62547e9	−1.41166
$142$	7.47978e9	1.54380
$143$	6.00999e9	1.20188
$144$	−5.68267e9	−1.10134
$145$	0	0
$146$	3.45580e9	0.629449
$147$	−1.21406e10	−2.14443
$148$	−2.79879e8	−0.0479504
$149$	−6.13643e9	−1.01995	−0.509974	−	0.860190i	$-0.670345\pi$
$149$	−6.13643e9	−1.01995	−0.509974	+	0.860190i	$0.670345\pi$
$150$	0	0
$151$	−5.83754e9	−0.913763	−0.456882	−	0.889528i	$-0.651034\pi$
$151$	−5.83754e9	−0.913763	−0.456882	+	0.889528i	$0.651034\pi$
$152$	7.38046e9	1.12147
$153$	2.01684e9	0.297550
$154$	7.73408e9	1.10807
$155$	0	0
$156$	1.84480e9	0.249396
$157$	−1.35031e9	−0.177371	−0.0886857	−	0.996060i	$-0.528267\pi$
$157$	−1.35031e9	−0.177371	−0.0886857	+	0.996060i	$0.528267\pi$
$158$	−2.71963e9	−0.347179
$159$	1.02898e10	1.27680
$160$	0	0
$161$	1.86796e10	2.19104
$162$	−5.77720e9	−0.659022
$163$	−4.50806e9	−0.500202	−0.250101	−	0.968220i	$-0.580464\pi$
$163$	−4.50806e9	−0.500202	−0.250101	+	0.968220i	$0.580464\pi$
$164$	−1.09575e8	−0.0118281
$165$	0	0
$166$	−6.15773e9	−0.629411
$167$	1.81836e10	1.80908	0.904538	−	0.426393i	$-0.140216\pi$
$167$	1.81836e10	1.80908	0.904538	+	0.426393i	$0.140216\pi$
$168$	2.52043e10	2.44109
$169$	1.65766e10	1.56316
$170$	0	0
$171$	−1.49289e10	−1.33520
$172$	3.59991e8	0.0313627
$173$	9.77143e9	0.829375	0.414687	−	0.909964i	$-0.363891\pi$
$173$	9.77143e9	0.829375	0.414687	+	0.909964i	$0.363891\pi$
$174$	−1.52710e9	−0.126298
$175$	0	0
$176$	−8.45906e9	−0.664531
$177$	−1.84522e10	−1.41309
$178$	−1.20616e10	−0.900562
$179$	6.65866e9	0.484784	0.242392	−	0.970178i	$-0.422068\pi$
$179$	6.65866e9	0.484784	0.242392	+	0.970178i	$0.422068\pi$
$180$	0	0
$181$	−7.32873e9	−0.507546	−0.253773	−	0.967264i	$-0.581672\pi$
$181$	−7.32873e9	−0.507546	−0.253773	+	0.967264i	$0.581672\pi$
$182$	3.49785e10	2.36309
$183$	−8.08432e9	−0.532860
$184$	−2.28306e10	−1.46837
$185$	0	0
$186$	−2.46378e9	−0.150936
$187$	3.00221e9	0.179537
$188$	−1.67836e9	−0.0979887
$189$	−1.00053e10	−0.570364
$190$	0	0
$191$	8.06956e9	0.438732	0.219366	−	0.975643i	$-0.429601\pi$
$191$	8.06956e9	0.438732	0.219366	+	0.975643i	$0.429601\pi$
$192$	−3.05003e10	−1.61975
$193$	3.12603e9	0.162176	0.0810878	−	0.996707i	$-0.474161\pi$
$193$	3.12603e9	0.162176	0.0810878	+	0.996707i	$0.474161\pi$
$194$	−1.01033e10	−0.512100
$195$	0	0
$196$	−3.07545e9	−0.148853
$197$	−2.40133e10	−1.13594	−0.567968	−	0.823051i	$-0.692270\pi$
$197$	−2.40133e10	−1.13594	−0.567968	+	0.823051i	$0.692270\pi$
$198$	1.91207e10	0.884117
$199$	9.73605e9	0.440093	0.220046	−	0.975489i	$-0.429379\pi$
$199$	9.73605e9	0.440093	0.220046	+	0.975489i	$0.429379\pi$
$200$	0	0
$201$	2.86077e10	1.23623
$202$	−2.69175e10	−1.13751
$203$	3.36029e9	0.138882
$204$	9.21546e8	0.0372547
$205$	0	0
$206$	4.18517e10	1.61924
$207$	4.61808e10	1.74822
$208$	−3.82574e10	−1.41720
$209$	−2.22227e10	−0.805637
$210$	0	0
$211$	−2.39305e10	−0.831151	−0.415576	−	0.909559i	$-0.636420\pi$
$211$	−2.39305e10	−0.831151	−0.415576	+	0.909559i	$0.636420\pi$
$212$	2.60662e9	0.0886272
$213$	−7.33956e10	−2.44321
$214$	4.54732e10	1.48215
$215$	0	0
$216$	1.22287e10	0.382242
$217$	5.42141e9	0.165975
$218$	−2.54589e9	−0.0763459
$219$	−3.39101e10	−0.996163
$220$	0	0
$221$	1.35779e10	0.382885
$222$	−2.36643e10	−0.653890
$223$	2.02289e10	0.547773	0.273886	−	0.961762i	$-0.411691\pi$
$223$	2.02289e10	0.547773	0.273886	+	0.961762i	$0.411691\pi$
$224$	1.21681e10	0.322930
$225$	0	0
$226$	−3.97220e10	−1.01285
$227$	4.42152e10	1.10524	0.552618	−	0.833434i	$-0.313629\pi$
$227$	4.42152e10	1.10524	0.552618	+	0.833434i	$0.313629\pi$
$228$	−6.82140e9	−0.167173
$229$	−4.89483e10	−1.17619	−0.588096	−	0.808791i	$-0.700122\pi$
$229$	−4.89483e10	−1.17619	−0.588096	+	0.808791i	$0.700122\pi$
$230$	0	0
$231$	−7.58909e10	−1.75362
$232$	−4.10702e9	−0.0930746
$233$	6.68132e10	1.48512	0.742559	−	0.669781i	$-0.233612\pi$
$233$	6.68132e10	1.48512	0.742559	+	0.669781i	$0.233612\pi$
$234$	8.64761e10	1.88549
$235$	0	0
$236$	−4.67431e9	−0.0980876
$237$	2.66865e10	0.549444
$238$	1.74731e10	0.352999
$239$	−2.21153e10	−0.438431	−0.219216	−	0.975676i	$-0.570350\pi$
$239$	−2.21153e10	−0.438431	−0.219216	+	0.975676i	$0.570350\pi$
$240$	0	0
$241$	9.97637e10	1.90500	0.952502	−	0.304532i	$-0.0985002\pi$
$241$	9.97637e10	1.90500	0.952502	+	0.304532i	$0.0985002\pi$
$242$	−2.20416e10	−0.413118
$243$	7.65703e10	1.40874
$244$	−2.04792e9	−0.0369878
$245$	0	0
$246$	−9.26480e9	−0.161298
$247$	−1.00506e11	−1.71812
$248$	−6.62616e9	−0.111232
$249$	6.04229e10	0.996104
$250$	0	0
$251$	−4.97276e10	−0.790799	−0.395399	−	0.918509i	$-0.629394\pi$
$251$	−4.97276e10	−0.790799	−0.395399	+	0.918509i	$0.629394\pi$
$252$	−1.29149e10	−0.201738
$253$	6.87435e10	1.05485
$254$	−1.15491e11	−1.74099
$255$	0	0
$256$	−2.11977e10	−0.308467
$257$	5.81308e10	0.831204	0.415602	−	0.909547i	$-0.363571\pi$
$257$	5.81308e10	0.831204	0.415602	+	0.909547i	$0.363571\pi$
$258$	3.04379e10	0.427686
$259$	5.20718e10	0.719041
$260$	0	0
$261$	8.30753e9	0.110813
$262$	8.21814e10	1.07750
$263$	−3.23476e10	−0.416909	−0.208454	−	0.978032i	$-0.566843\pi$
$263$	−3.23476e10	−0.416909	−0.208454	+	0.978032i	$0.566843\pi$
$264$	9.27555e10	1.17523
$265$	0	0
$266$	−1.29338e11	−1.58401
$267$	1.18354e11	1.42523
$268$	7.24691e9	0.0858116
$269$	6.24220e9	0.0726863	0.0363431	−	0.999339i	$-0.488429\pi$
$269$	6.24220e9	0.0726863	0.0363431	+	0.999339i	$0.488429\pi$
$270$	0	0
$271$	8.05816e10	0.907557	0.453779	−	0.891114i	$-0.350076\pi$
$271$	8.05816e10	0.907557	0.453779	+	0.891114i	$0.350076\pi$
$272$	−1.91110e10	−0.211701
$273$	−3.43228e11	−3.73982
$274$	−5.47050e10	−0.586340
$275$	0	0
$276$	2.11012e10	0.218885
$277$	−7.07976e10	−0.722536	−0.361268	−	0.932462i	$-0.617656\pi$
$277$	−7.07976e10	−0.722536	−0.361268	+	0.932462i	$0.617656\pi$
$278$	−8.76284e10	−0.879920
$279$	1.34031e10	0.132430
$280$	0	0
$281$	8.15619e10	0.780385	0.390193	−	0.920733i	$-0.372408\pi$
$281$	8.15619e10	0.780385	0.390193	+	0.920733i	$0.372408\pi$
$282$	−1.41909e11	−1.33625
$283$	1.89301e11	1.75434	0.877168	−	0.480184i	$-0.159430\pi$
$283$	1.89301e11	1.75434	0.877168	+	0.480184i	$0.159430\pi$
$284$	−1.85926e10	−0.169593
$285$	0	0
$286$	1.28726e11	1.13768
$287$	2.03867e10	0.177369
$288$	3.00828e10	0.257663
$289$	−1.11805e11	−0.942805
$290$	0	0
$291$	9.91387e10	0.810447
$292$	−8.59011e9	−0.0691474
$293$	−5.39489e10	−0.427640	−0.213820	−	0.976873i	$-0.568591\pi$
$293$	−5.39489e10	−0.427640	−0.213820	+	0.976873i	$0.568591\pi$
$294$	−2.60035e11	−2.02987
$295$	0	0
$296$	−6.36433e10	−0.481881
$297$	−3.68209e10	−0.274594
$298$	−1.31434e11	−0.965462
$299$	3.10903e11	2.24959
$300$	0	0
$301$	−6.69768e10	−0.470300
$302$	−1.25032e11	−0.864950
$303$	2.64129e11	1.80022
$304$	1.41462e11	0.949966
$305$	0	0
$306$	4.31980e10	0.281655
$307$	−1.30037e11	−0.835496	−0.417748	−	0.908563i	$-0.637181\pi$
$307$	−1.30037e11	−0.835496	−0.417748	+	0.908563i	$0.637181\pi$
$308$	−1.92247e10	−0.121725
$309$	−4.10671e11	−2.56260
$310$	0	0
$311$	2.09580e9	0.0127036	0.00635182	−	0.999980i	$-0.497978\pi$
$311$	2.09580e9	0.0127036	0.00635182	+	0.999980i	$0.497978\pi$
$312$	4.19500e11	2.50632
$313$	−2.43788e11	−1.43570	−0.717848	−	0.696200i	$-0.754873\pi$
$313$	−2.43788e11	−1.43570	−0.717848	+	0.696200i	$0.754873\pi$
$314$	−2.89217e10	−0.167896
$315$	0	0
$316$	6.76022e9	0.0381390
$317$	−3.46483e11	−1.92715	−0.963573	−	0.267445i	$-0.913821\pi$
$317$	−3.46483e11	−1.92715	−0.963573	+	0.267445i	$0.913821\pi$
$318$	2.20395e11	1.20859
$319$	1.23664e10	0.0668626
$320$	0	0
$321$	−4.46207e11	−2.34565
$322$	4.00092e11	2.07400
$323$	−5.02063e10	−0.256653
$324$	1.43604e10	0.0723961
$325$	0	0
$326$	−9.65566e10	−0.473481
$327$	2.49816e10	0.120825
$328$	−2.49170e10	−0.118868
$329$	3.12262e11	1.46939
$330$	0	0
$331$	−1.43303e11	−0.656189	−0.328094	−	0.944645i	$-0.606406\pi$
$331$	−1.43303e11	−0.656189	−0.328094	+	0.944645i	$0.606406\pi$
$332$	1.53063e10	0.0691433
$333$	1.28735e11	0.573718
$334$	3.89470e11	1.71244
$335$	0	0
$336$	4.83094e11	2.06778
$337$	3.34820e11	1.41409	0.707044	−	0.707170i	$-0.250028\pi$
$337$	3.34820e11	1.41409	0.707044	+	0.707170i	$0.250028\pi$
$338$	3.55048e11	1.47966
$339$	3.89773e11	1.60293
$340$	0	0
$341$	1.99515e10	0.0799064
$342$	−3.19757e11	−1.26387
$343$	1.72469e11	0.672804
$344$	8.18604e10	0.315182
$345$	0	0
$346$	2.09291e11	0.785070
$347$	−9.22101e10	−0.341425	−0.170713	−	0.985321i	$-0.554607\pi$
$347$	−9.22101e10	−0.341425	−0.170713	+	0.985321i	$0.554607\pi$
$348$	3.79592e9	0.0138743
$349$	−4.71738e11	−1.70211	−0.851053	−	0.525080i	$-0.824035\pi$
$349$	−4.71738e11	−1.70211	−0.851053	+	0.525080i	$0.824035\pi$
$350$	0	0
$351$	−1.66528e11	−0.585606
$352$	4.47805e10	0.155470
$353$	−4.01029e11	−1.37464	−0.687322	−	0.726353i	$-0.741214\pi$
$353$	−4.01029e11	−1.37464	−0.687322	+	0.726353i	$0.741214\pi$
$354$	−3.95222e11	−1.33760
$355$	0	0
$356$	2.99816e10	0.0989303
$357$	−1.71455e11	−0.558654
$358$	1.42620e11	0.458887
$359$	−2.36110e10	−0.0750220	−0.0375110	−	0.999296i	$-0.511943\pi$
$359$	−2.36110e10	−0.0750220	−0.0375110	+	0.999296i	$0.511943\pi$
$360$	0	0
$361$	4.89457e10	0.151681
$362$	−1.56972e11	−0.480433
$363$	2.16284e11	0.653799
$364$	−8.69465e10	−0.259595
$365$	0	0
$366$	−1.73155e11	−0.504395
$367$	1.23035e11	0.354022	0.177011	−	0.984209i	$-0.443357\pi$
$367$	1.23035e11	0.354022	0.177011	+	0.984209i	$0.443357\pi$
$368$	−4.37596e11	−1.24382
$369$	5.04012e10	0.141521
$370$	0	0
$371$	−4.84966e11	−1.32901
$372$	6.12424e9	0.0165809
$373$	−2.39248e11	−0.639968	−0.319984	−	0.947423i	$-0.603678\pi$
$373$	−2.39248e11	−0.639968	−0.319984	+	0.947423i	$0.603678\pi$
$374$	6.43034e10	0.169946
$375$	0	0
$376$	−3.81653e11	−0.984745
$377$	5.59287e10	0.142593
$378$	−2.14300e11	−0.539896
$379$	−5.90629e11	−1.47041	−0.735205	−	0.677845i	$-0.762914\pi$
$379$	−5.90629e11	−1.47041	−0.735205	+	0.677845i	$0.762914\pi$
$380$	0	0
$381$	1.13326e12	2.75529
$382$	1.72839e11	0.415295
$383$	−5.30525e10	−0.125983	−0.0629914	−	0.998014i	$-0.520064\pi$
$383$	−5.30525e10	−0.125983	−0.0629914	+	0.998014i	$0.520064\pi$
$384$	−5.21087e11	−1.22298
$385$	0	0
$386$	6.69554e10	0.153512
$387$	−1.65584e11	−0.375249
$388$	2.51138e10	0.0562562
$389$	3.10395e11	0.687293	0.343646	−	0.939099i	$-0.388338\pi$
$389$	3.10395e11	0.687293	0.343646	+	0.939099i	$0.388338\pi$
$390$	0	0
$391$	1.55307e11	0.336045
$392$	−6.99345e11	−1.49591
$393$	−8.06407e11	−1.70525
$394$	−5.14333e11	−1.07525
$395$	0	0
$396$	−4.75285e10	−0.0971238
$397$	−2.09351e11	−0.422979	−0.211489	−	0.977380i	$-0.567831\pi$
$397$	−2.09351e11	−0.422979	−0.211489	+	0.977380i	$0.567831\pi$
$398$	2.08533e11	0.416583
$399$	1.26913e12	2.50685
$400$	0	0
$401$	4.43868e11	0.857244	0.428622	−	0.903484i	$-0.358999\pi$
$401$	4.43868e11	0.857244	0.428622	+	0.903484i	$0.358999\pi$
$402$	6.12739e11	1.17020
$403$	9.02338e10	0.170411
$404$	6.69092e10	0.124960
$405$	0	0
$406$	7.19730e10	0.131463
$407$	1.91632e11	0.346172
$408$	2.09556e11	0.374394
$409$	4.56031e11	0.805823	0.402912	−	0.915239i	$-0.367998\pi$
$409$	4.56031e11	0.805823	0.402912	+	0.915239i	$0.367998\pi$
$410$	0	0
$411$	5.36794e11	0.927940
$412$	−1.04031e11	−0.177880
$413$	8.69663e11	1.47087
$414$	9.89132e11	1.65483
$415$	0	0
$416$	2.02526e11	0.331559
$417$	8.59856e11	1.39256
$418$	−4.75982e11	−0.762600
$419$	−1.12392e12	−1.78144	−0.890720	−	0.454552i	$-0.849799\pi$
$419$	−1.12392e12	−1.78144	−0.890720	+	0.454552i	$0.849799\pi$
$420$	0	0
$421$	−1.02822e12	−1.59521	−0.797605	−	0.603180i	$-0.793900\pi$
$421$	−1.02822e12	−1.59521	−0.797605	+	0.603180i	$0.793900\pi$
$422$	−5.12559e11	−0.786751
$423$	7.71994e11	1.17242
$424$	5.92736e11	0.890666
$425$	0	0
$426$	−1.57204e12	−2.31270
$427$	3.81018e11	0.554652
$428$	−1.13033e11	−0.162820
$429$	−1.26313e12	−1.80048
$430$	0	0
$431$	−1.37714e12	−1.92234	−0.961171	−	0.275953i	$-0.911007\pi$
$431$	−1.37714e12	−1.92234	−0.961171	+	0.275953i	$0.911007\pi$
$432$	2.34389e11	0.323787
$433$	1.94790e11	0.266299	0.133150	−	0.991096i	$-0.457491\pi$
$433$	1.94790e11	0.266299	0.133150	+	0.991096i	$0.457491\pi$
$434$	1.16119e11	0.157109
$435$	0	0
$436$	6.32835e9	0.00838689
$437$	−1.14961e12	−1.50793
$438$	−7.26309e11	−0.942948
$439$	−5.32533e11	−0.684315	−0.342157	−	0.939643i	$-0.611158\pi$
$439$	−5.32533e11	−0.684315	−0.342157	+	0.939643i	$0.611158\pi$
$440$	0	0
$441$	1.41461e12	1.78099
$442$	2.90821e11	0.362432
$443$	7.26633e11	0.896393	0.448196	−	0.893935i	$-0.352067\pi$
$443$	7.26633e11	0.896393	0.448196	+	0.893935i	$0.352067\pi$
$444$	5.88225e10	0.0718323
$445$	0	0
$446$	4.33276e11	0.518511
$447$	1.28970e12	1.52794
$448$	1.43749e12	1.68599
$449$	9.34830e11	1.08549	0.542743	−	0.839899i	$-0.317386\pi$
$449$	9.34830e11	1.08549	0.542743	+	0.839899i	$0.317386\pi$
$450$	0	0
$451$	7.50258e10	0.0853918
$452$	9.87374e10	0.111265
$453$	1.22688e12	1.36887
$454$	9.47031e11	1.04620
$455$	0	0
$456$	−1.55116e12	−1.68002
$457$	−1.09190e12	−1.17101	−0.585503	−	0.810670i	$-0.699103\pi$
$457$	−1.09190e12	−1.17101	−0.585503	+	0.810670i	$0.699103\pi$
$458$	−1.04841e12	−1.11336
$459$	−8.31870e10	−0.0874779
$460$	0	0
$461$	9.93683e11	1.02469	0.512347	−	0.858779i	$-0.328776\pi$
$461$	9.93683e11	1.02469	0.512347	+	0.858779i	$0.328776\pi$
$462$	−1.62548e12	−1.65994
$463$	−6.95734e11	−0.703605	−0.351802	−	0.936074i	$-0.614431\pi$
$463$	−6.95734e11	−0.703605	−0.351802	+	0.936074i	$0.614431\pi$
$464$	−7.87197e10	−0.0788411
$465$	0	0
$466$	1.43105e12	1.40578
$467$	1.87957e12	1.82866	0.914328	−	0.404975i	$-0.132720\pi$
$467$	1.87957e12	1.82866	0.914328	+	0.404975i	$0.132720\pi$
$468$	−2.14955e11	−0.207129
$469$	−1.34830e12	−1.28679
$470$	0	0
$471$	2.83795e11	0.265712
$472$	−1.06292e12	−0.985739
$473$	−2.46484e11	−0.226419
$474$	5.71589e11	0.520093
$475$	0	0
$476$	−4.34330e10	−0.0387783
$477$	−1.19896e12	−1.06041
$478$	−4.73679e11	−0.415010
$479$	−2.29011e11	−0.198768	−0.0993838	−	0.995049i	$-0.531687\pi$
$479$	−2.29011e11	−0.198768	−0.0993838	+	0.995049i	$0.531687\pi$
$480$	0	0
$481$	8.66683e11	0.738256
$482$	2.13681e12	1.80324
$483$	−3.92591e12	−3.28230
$484$	5.47890e10	0.0453826
$485$	0	0
$486$	1.64003e12	1.33349
$487$	−4.81410e11	−0.387824	−0.193912	−	0.981019i	$-0.562118\pi$
$487$	−4.81410e11	−0.387824	−0.193912	+	0.981019i	$0.562118\pi$
$488$	−4.65689e11	−0.371712
$489$	9.47465e11	0.749330
$490$	0	0
$491$	−1.70320e12	−1.32251	−0.661257	−	0.750160i	$-0.729977\pi$
$491$	−1.70320e12	−1.32251	−0.661257	+	0.750160i	$0.729977\pi$
$492$	2.30296e10	0.0177192
$493$	2.79384e10	0.0213006
$494$	−2.15270e12	−1.62634
$495$	0	0
$496$	−1.27004e11	−0.0942217
$497$	3.45917e12	2.54313
$498$	1.29418e12	0.942892
$499$	2.06075e12	1.48789	0.743947	−	0.668238i	$-0.232951\pi$
$499$	2.06075e12	1.48789	0.743947	+	0.668238i	$0.232951\pi$
$500$	0	0
$501$	−3.82168e12	−2.71010
$502$	−1.06510e12	−0.748555
$503$	−5.97493e11	−0.416176	−0.208088	−	0.978110i	$-0.566724\pi$
$503$	−5.97493e11	−0.416176	−0.208088	+	0.978110i	$0.566724\pi$
$504$	−2.93679e12	−2.02738
$505$	0	0
$506$	1.47239e12	0.998497
$507$	−3.48392e12	−2.34170
$508$	2.87077e11	0.191255
$509$	−8.46938e11	−0.559270	−0.279635	−	0.960106i	$-0.590213\pi$
$509$	−8.46938e11	−0.559270	−0.279635	+	0.960106i	$0.590213\pi$
$510$	0	0
$511$	1.59820e12	1.03690
$512$	−1.72345e12	−1.10837
$513$	6.15760e11	0.392540
$514$	1.24508e12	0.786801
$515$	0	0
$516$	−7.56597e10	−0.0469830
$517$	1.14917e12	0.707418
$518$	1.11531e12	0.680630
$519$	−2.05367e12	−1.24245
$520$	0	0
$521$	7.31013e11	0.434666	0.217333	−	0.976098i	$-0.430264\pi$
$521$	7.31013e11	0.434666	0.217333	+	0.976098i	$0.430264\pi$
$522$	1.77936e11	0.104893
$523$	1.04453e12	0.610467	0.305233	−	0.952278i	$-0.401266\pi$
$523$	1.04453e12	0.610467	0.305233	+	0.952278i	$0.401266\pi$
$524$	−2.04279e11	−0.118368
$525$	0	0
$526$	−6.92842e11	−0.394638
$527$	4.50751e10	0.0254559
$528$	1.77785e12	0.995504
$529$	1.75502e12	0.974386
$530$	0	0
$531$	2.15003e12	1.17360
$532$	3.21496e11	0.174010
$533$	3.39315e11	0.182109
$534$	2.53500e12	1.34909
$535$	0	0
$536$	1.64792e12	0.862371
$537$	−1.39946e12	−0.726233
$538$	1.33700e11	0.0688034
$539$	2.10575e12	1.07462
$540$	0	0
$541$	−1.88034e12	−0.943733	−0.471866	−	0.881670i	$-0.656420\pi$
$541$	−1.88034e12	−0.943733	−0.471866	+	0.881670i	$0.656420\pi$
$542$	1.72595e12	0.859076
$543$	1.54029e12	0.760331
$544$	1.01169e11	0.0495284
$545$	0	0
$546$	−7.35148e12	−3.54004
$547$	−1.08624e12	−0.518780	−0.259390	−	0.965773i	$-0.583521\pi$
$547$	−1.08624e12	−0.518780	−0.259390	+	0.965773i	$0.583521\pi$
$548$	1.35981e11	0.0644117
$549$	9.41977e11	0.442553
$550$	0	0
$551$	−2.06804e11	−0.0955821
$552$	4.79834e12	2.19971
$553$	−1.25775e12	−0.571914
$554$	−1.51639e12	−0.683938
$555$	0	0
$556$	2.17819e11	0.0966626
$557$	2.11965e12	0.933072	0.466536	−	0.884502i	$-0.345502\pi$
$557$	2.11965e12	0.933072	0.466536	+	0.884502i	$0.345502\pi$
$558$	2.87078e11	0.125356
$559$	−1.11476e12	−0.482868
$560$	0	0
$561$	−6.30978e11	−0.268956
$562$	1.74695e12	0.738697
$563$	3.04489e12	1.27727	0.638636	−	0.769509i	$-0.279499\pi$
$563$	3.04489e12	1.27727	0.638636	+	0.769509i	$0.279499\pi$
$564$	3.52744e11	0.146792
$565$	0	0
$566$	4.05456e12	1.66062
$567$	−2.67178e12	−1.08562
$568$	−4.22788e12	−1.70433
$569$	3.25275e12	1.30090	0.650452	−	0.759548i	$-0.274580\pi$
$569$	3.25275e12	1.30090	0.650452	+	0.759548i	$0.274580\pi$
$570$	0	0
$571$	−1.35916e12	−0.535066	−0.267533	−	0.963549i	$-0.586208\pi$
$571$	−1.35916e12	−0.535066	−0.267533	+	0.963549i	$0.586208\pi$
$572$	−3.19975e11	−0.124978
$573$	−1.69599e12	−0.657245
$574$	4.36655e11	0.167894
$575$	0	0
$576$	3.55386e12	1.34524
$577$	−2.35782e12	−0.885564	−0.442782	−	0.896629i	$-0.646008\pi$
$577$	−2.35782e12	−0.885564	−0.442782	+	0.896629i	$0.646008\pi$
$578$	−2.39472e12	−0.892440
$579$	−6.57002e11	−0.242948
$580$	0	0
$581$	−2.84777e12	−1.03684
$582$	2.12342e12	0.767154
$583$	−1.78474e12	−0.639834
$584$	−1.95336e12	−0.694902
$585$	0	0
$586$	−1.15551e12	−0.404796
$587$	−2.37065e12	−0.824130	−0.412065	−	0.911154i	$-0.635192\pi$
$587$	−2.37065e12	−0.824130	−0.412065	+	0.911154i	$0.635192\pi$
$588$	6.46371e11	0.222989
$589$	−3.33652e11	−0.114229
$590$	0	0
$591$	5.04690e12	1.70169
$592$	−1.21986e12	−0.408189
$593$	4.56707e12	1.51667	0.758336	−	0.651864i	$-0.226013\pi$
$593$	4.56707e12	1.51667	0.758336	+	0.651864i	$0.226013\pi$
$594$	−7.88655e11	−0.259925
$595$	0	0
$596$	3.26707e11	0.106060
$597$	−2.04624e12	−0.659283
$598$	6.65912e12	2.12942
$599$	−5.30493e12	−1.68368	−0.841839	−	0.539729i	$-0.818527\pi$
$599$	−5.30493e12	−1.68368	−0.841839	+	0.539729i	$0.818527\pi$
$600$	0	0
$601$	−2.71307e12	−0.848255	−0.424128	−	0.905602i	$-0.639419\pi$
$601$	−2.71307e12	−0.848255	−0.424128	+	0.905602i	$0.639419\pi$
$602$	−1.43455e12	−0.445177
$603$	−3.33335e12	−1.02672
$604$	3.10794e11	0.0950182
$605$	0	0
$606$	5.65730e12	1.70405
$607$	−4.00734e12	−1.19814	−0.599069	−	0.800698i	$-0.704462\pi$
$607$	−4.00734e12	−1.19814	−0.599069	+	0.800698i	$0.704462\pi$
$608$	−7.48868e11	−0.222249
$609$	−7.06237e11	−0.208052
$610$	0	0
$611$	5.19728e12	1.50866
$612$	−1.07378e11	−0.0309409
$613$	−2.24954e12	−0.643459	−0.321730	−	0.946832i	$-0.604264\pi$
$613$	−2.24954e12	−0.643459	−0.321730	+	0.946832i	$0.604264\pi$
$614$	−2.78522e12	−0.790864
$615$	0	0
$616$	−4.37162e12	−1.22329
$617$	1.19664e12	0.332414	0.166207	−	0.986091i	$-0.446848\pi$
$617$	1.19664e12	0.332414	0.166207	+	0.986091i	$0.446848\pi$
$618$	−8.79602e12	−2.42571
$619$	−4.36723e12	−1.19563	−0.597817	−	0.801633i	$-0.703965\pi$
$619$	−4.36723e12	−1.19563	−0.597817	+	0.801633i	$0.703965\pi$
$620$	0	0
$621$	−1.90478e12	−0.513965
$622$	4.48893e10	0.0120250
$623$	−5.57811e12	−1.48351
$624$	8.04060e12	2.12304
$625$	0	0
$626$	−5.22161e12	−1.35900
$627$	4.67058e12	1.20689
$628$	7.18911e10	0.0184441
$629$	4.32940e11	0.110281
$630$	0	0
$631$	2.78790e12	0.700077	0.350039	−	0.936735i	$-0.386168\pi$
$631$	2.78790e12	0.700077	0.350039	+	0.936735i	$0.386168\pi$
$632$	1.53725e12	0.383281
$633$	5.02950e12	1.24511
$634$	−7.42120e12	−1.82420
$635$	0	0
$636$	−5.47837e11	−0.132768
$637$	9.52355e12	2.29177
$638$	2.64871e11	0.0632909
$639$	8.55199e12	2.02915
$640$	0	0
$641$	−2.28295e12	−0.534115	−0.267058	−	0.963681i	$-0.586051\pi$
$641$	−2.28295e12	−0.534115	−0.267058	+	0.963681i	$0.586051\pi$
$642$	−9.55716e12	−2.22035
$643$	−2.29995e12	−0.530603	−0.265301	−	0.964166i	$-0.585471\pi$
$643$	−2.29995e12	−0.530603	−0.265301	+	0.964166i	$0.585471\pi$
$644$	−9.94512e11	−0.227837
$645$	0	0
$646$	−1.07535e12	−0.242943
$647$	1.85647e12	0.416503	0.208251	−	0.978075i	$-0.433223\pi$
$647$	1.85647e12	0.416503	0.208251	+	0.978075i	$0.433223\pi$
$648$	3.26551e12	0.727550
$649$	3.20048e12	0.708132
$650$	0	0
$651$	−1.13942e12	−0.248640
$652$	2.40012e11	0.0520138
$653$	7.75397e12	1.66884	0.834420	−	0.551129i	$-0.185803\pi$
$653$	7.75397e12	1.66884	0.834420	+	0.551129i	$0.185803\pi$
$654$	5.35073e11	0.114370
$655$	0	0
$656$	−4.77587e11	−0.100690
$657$	3.95117e12	0.827336
$658$	6.68824e12	1.39090
$659$	7.42166e12	1.53291	0.766455	−	0.642298i	$-0.222019\pi$
$659$	7.42166e12	1.53291	0.766455	+	0.642298i	$0.222019\pi$
$660$	0	0
$661$	5.79783e12	1.18130	0.590648	−	0.806929i	$-0.298872\pi$
$661$	5.79783e12	1.18130	0.590648	+	0.806929i	$0.298872\pi$
$662$	−3.06936e12	−0.621135
$663$	−2.85369e12	−0.573583
$664$	3.48060e12	0.694861
$665$	0	0
$666$	2.75734e12	0.543070
$667$	6.39724e11	0.125149
$668$	−9.68108e11	−0.188118
$669$	−4.25153e12	−0.820593
$670$	0	0
$671$	1.40220e12	0.267029
$672$	−2.55739e12	−0.483766
$673$	−6.32456e12	−1.18840	−0.594200	−	0.804318i	$-0.702531\pi$
$673$	−6.32456e12	−1.18840	−0.594200	+	0.804318i	$0.702531\pi$
$674$	7.17139e12	1.33855
$675$	0	0
$676$	−8.82546e11	−0.162546
$677$	−4.95066e12	−0.905762	−0.452881	−	0.891571i	$-0.649604\pi$
$677$	−4.95066e12	−0.905762	−0.452881	+	0.891571i	$0.649604\pi$
$678$	8.34843e12	1.51730
$679$	−4.67246e12	−0.843591
$680$	0	0
$681$	−9.29277e12	−1.65571
$682$	4.27336e11	0.0756379
$683$	7.32611e12	1.28819	0.644095	−	0.764945i	$-0.277234\pi$
$683$	7.32611e12	1.28819	0.644095	+	0.764945i	$0.277234\pi$
$684$	7.94824e11	0.138841
$685$	0	0
$686$	3.69406e12	0.636863
$687$	1.02875e13	1.76200
$688$	1.56903e12	0.266982
$689$	−8.07176e12	−1.36453
$690$	0	0
$691$	−5.66806e12	−0.945765	−0.472882	−	0.881126i	$-0.656786\pi$
$691$	−5.66806e12	−0.945765	−0.472882	+	0.881126i	$0.656786\pi$
$692$	−5.20237e11	−0.0862430
$693$	8.84274e12	1.45642
$694$	−1.97502e12	−0.323187
$695$	0	0
$696$	8.63178e11	0.139431
$697$	1.69501e11	0.0272034
$698$	−1.01040e13	−1.61118
$699$	−1.40422e13	−2.22479
$700$	0	0
$701$	−4.20985e12	−0.658470	−0.329235	−	0.944248i	$-0.606791\pi$
$701$	−4.20985e12	−0.658470	−0.329235	+	0.944248i	$0.606791\pi$
$702$	−3.56681e12	−0.554323
$703$	−3.20468e12	−0.494863
$704$	5.29018e12	0.811696
$705$	0	0
$706$	−8.58952e12	−1.30121
$707$	−1.24486e13	−1.87384
$708$	9.82407e11	0.146941
$709$	1.19654e13	1.77835	0.889176	−	0.457566i	$-0.151279\pi$
$709$	1.19654e13	1.77835	0.889176	+	0.457566i	$0.151279\pi$
$710$	0	0
$711$	−3.10949e12	−0.456326
$712$	6.81769e12	0.994208
$713$	1.03211e12	0.149563
$714$	−3.67234e12	−0.528811
$715$	0	0
$716$	−3.54511e11	−0.0504105
$717$	4.64799e12	0.656794
$718$	−5.05715e11	−0.0710143
$719$	−4.07118e11	−0.0568120	−0.0284060	−	0.999596i	$-0.509043\pi$
$719$	−4.07118e11	−0.0568120	−0.0284060	+	0.999596i	$0.509043\pi$
$720$	0	0
$721$	1.93551e13	2.66740
$722$	1.04835e12	0.143579
$723$	−2.09675e13	−2.85380
$724$	3.90186e11	0.0527774
$725$	0	0
$726$	4.63251e12	0.618873
$727$	6.44424e12	0.855592	0.427796	−	0.903875i	$-0.359290\pi$
$727$	6.44424e12	0.855592	0.427796	+	0.903875i	$0.359290\pi$
$728$	−1.97713e13	−2.60882
$729$	−1.07838e13	−1.41416
$730$	0	0
$731$	−5.56864e11	−0.0721308
$732$	4.30414e11	0.0554098
$733$	5.46122e12	0.698749	0.349375	−	0.936983i	$-0.386394\pi$
$733$	5.46122e12	0.698749	0.349375	+	0.936983i	$0.386394\pi$
$734$	2.63524e12	0.335110
$735$	0	0
$736$	2.31654e12	0.290998
$737$	−4.96192e12	−0.619507
$738$	1.07953e12	0.133961
$739$	−1.88201e12	−0.232125	−0.116062	−	0.993242i	$-0.537027\pi$
$739$	−1.88201e12	−0.232125	−0.116062	+	0.993242i	$0.537027\pi$
$740$	0	0
$741$	2.11234e13	2.57384
$742$	−1.03873e13	−1.25802
$743$	1.36704e13	1.64563	0.822813	−	0.568312i	$-0.192403\pi$
$743$	1.36704e13	1.64563	0.822813	+	0.568312i	$0.192403\pi$
$744$	1.39263e12	0.166632
$745$	0	0
$746$	−5.12437e12	−0.605781
$747$	−7.04042e12	−0.827287
$748$	−1.59840e11	−0.0186693
$749$	2.10300e13	2.44158
$750$	0	0
$751$	8.52585e12	0.978043	0.489021	−	0.872272i	$-0.337354\pi$
$751$	8.52585e12	0.978043	0.489021	+	0.872272i	$0.337354\pi$
$752$	−7.31518e12	−0.834152
$753$	1.04513e13	1.18466
$754$	1.19792e12	0.134976
$755$	0	0
$756$	5.32688e11	0.0593096
$757$	−7.50792e12	−0.830975	−0.415487	−	0.909599i	$-0.636389\pi$
$757$	−7.50792e12	−0.830975	−0.415487	+	0.909599i	$0.636389\pi$
$758$	−1.26505e13	−1.39186
$759$	−1.44479e13	−1.58022
$760$	0	0
$761$	−1.61560e13	−1.74624	−0.873118	−	0.487509i	$-0.837906\pi$
$761$	−1.61560e13	−1.74624	−0.873118	+	0.487509i	$0.837906\pi$
$762$	2.42729e13	2.60810
$763$	−1.17740e12	−0.125766
$764$	−4.29628e11	−0.0456218
$765$	0	0
$766$	−1.13631e12	−0.119253
$767$	1.44747e13	1.51018
$768$	4.45514e12	0.462100
$769$	1.11830e12	0.115317	0.0576583	−	0.998336i	$-0.481637\pi$
$769$	1.11830e12	0.115317	0.0576583	+	0.998336i	$0.481637\pi$
$770$	0	0
$771$	−1.22174e13	−1.24519
$772$	−1.66432e11	−0.0168639
$773$	−1.73165e13	−1.74442	−0.872212	−	0.489129i	$-0.837315\pi$
$773$	−1.73165e13	−1.74442	−0.872212	+	0.489129i	$0.837315\pi$
$774$	−3.54659e12	−0.355203
$775$	0	0
$776$	5.71078e12	0.565351
$777$	−1.09440e13	−1.07716
$778$	6.64825e12	0.650578
$779$	−1.25466e12	−0.122070
$780$	0	0
$781$	1.27302e13	1.22435
$782$	3.32648e12	0.318093
$783$	−3.42654e11	−0.0325783
$784$	−1.34044e13	−1.26714
$785$	0	0
$786$	−1.72722e13	−1.61416
$787$	−3.88515e11	−0.0361012	−0.0180506	−	0.999837i	$-0.505746\pi$
$787$	−3.88515e11	−0.0361012	−0.0180506	+	0.999837i	$0.505746\pi$
$788$	1.27848e12	0.118121
$789$	6.79853e12	0.624552
$790$	0	0
$791$	−1.83702e13	−1.66848
$792$	−1.08078e13	−0.976053
$793$	6.34166e12	0.569474
$794$	−4.48403e12	−0.400383
$795$	0	0
$796$	−5.18353e11	−0.0457633
$797$	−1.08432e12	−0.0951910	−0.0475955	−	0.998867i	$-0.515156\pi$
$797$	−1.08432e12	−0.0951910	−0.0475955	+	0.998867i	$0.515156\pi$
$798$	2.71831e13	2.37294
$799$	2.59624e12	0.225363
$800$	0	0
$801$	−1.37906e13	−1.18368
$802$	9.50706e12	0.811450
$803$	5.88161e12	0.499202
$804$	−1.52309e12	−0.128551
$805$	0	0
$806$	1.93269e12	0.161307
$807$	−1.31193e12	−0.108888
$808$	1.52149e13	1.25579
$809$	4.06803e12	0.333900	0.166950	−	0.985965i	$-0.446608\pi$
$809$	4.06803e12	0.333900	0.166950	+	0.985965i	$0.446608\pi$
$810$	0	0
$811$	4.87468e12	0.395688	0.197844	−	0.980234i	$-0.436606\pi$
$811$	4.87468e12	0.395688	0.197844	+	0.980234i	$0.436606\pi$
$812$	−1.78904e11	−0.0144417
$813$	−1.69359e13	−1.35957
$814$	4.10449e12	0.327680
$815$	0	0
$816$	4.01658e12	0.317140
$817$	4.12198e12	0.323673
$818$	9.76758e12	0.762777
$819$	3.99926e13	3.10600
$820$	0	0
$821$	−1.03829e12	−0.0797582	−0.0398791	−	0.999205i	$-0.512697\pi$
$821$	−1.03829e12	−0.0797582	−0.0398791	+	0.999205i	$0.512697\pi$
$822$	1.14974e13	0.878370
$823$	1.10923e13	0.842794	0.421397	−	0.906876i	$-0.361540\pi$
$823$	1.10923e13	0.842794	0.421397	+	0.906876i	$0.361540\pi$
$824$	−2.36563e13	−1.78761
$825$	0	0
$826$	1.86270e13	1.39230
$827$	−1.45526e13	−1.08184	−0.540922	−	0.841073i	$-0.681925\pi$
$827$	−1.45526e13	−1.08184	−0.540922	+	0.841073i	$0.681925\pi$
$828$	−2.45870e12	−0.181789
$829$	1.37985e13	1.01470	0.507348	−	0.861741i	$-0.330626\pi$
$829$	1.37985e13	1.01470	0.507348	+	0.861741i	$0.330626\pi$
$830$	0	0
$831$	1.48796e13	1.08240
$832$	2.39256e13	1.73104
$833$	4.75736e12	0.342345
$834$	1.84170e13	1.31817
$835$	0	0
$836$	1.18315e12	0.0837746
$837$	−5.52829e11	−0.0389337
$838$	−2.40728e13	−1.68628
$839$	9.20234e11	0.0641165	0.0320582	−	0.999486i	$-0.489794\pi$
$839$	9.20234e11	0.0641165	0.0320582	+	0.999486i	$0.489794\pi$
$840$	0	0
$841$	−1.43921e13	−0.992067
$842$	−2.20232e13	−1.50999
$843$	−1.71420e13	−1.16906
$844$	1.27407e12	0.0864277
$845$	0	0
$846$	1.65351e13	1.10979
$847$	−1.01936e13	−0.680536
$848$	1.13610e13	0.754460
$849$	−3.97855e13	−2.62809
$850$	0	0
$851$	9.91330e12	0.647941
$852$	3.90762e12	0.254059
$853$	−7.46964e12	−0.483091	−0.241545	−	0.970390i	$-0.577654\pi$
$853$	−7.46964e12	−0.483091	−0.241545	+	0.970390i	$0.577654\pi$
$854$	8.16090e12	0.525022
$855$	0	0
$856$	−2.57033e13	−1.63628
$857$	2.05568e13	1.30179	0.650897	−	0.759166i	$-0.274393\pi$
$857$	2.05568e13	1.30179	0.650897	+	0.759166i	$0.274393\pi$
$858$	−2.70545e13	−1.70430
$859$	−1.05923e12	−0.0663775	−0.0331888	−	0.999449i	$-0.510566\pi$
$859$	−1.05923e12	−0.0663775	−0.0331888	+	0.999449i	$0.510566\pi$
$860$	0	0
$861$	−4.28469e12	−0.265709
$862$	−2.94965e13	−1.81965
$863$	1.53023e13	0.939092	0.469546	−	0.882908i	$-0.344418\pi$
$863$	1.53023e13	0.939092	0.469546	+	0.882908i	$0.344418\pi$
$864$	−1.24080e12	−0.0757514
$865$	0	0
$866$	4.17213e12	0.252074
$867$	2.34982e13	1.41237
$868$	−2.88639e11	−0.0172590
$869$	−4.62869e12	−0.275340
$870$	0	0
$871$	−2.24410e13	−1.32118
$872$	1.43904e12	0.0842847
$873$	−1.15516e13	−0.673095
$874$	−2.46230e13	−1.42738
$875$	0	0
$876$	1.80539e12	0.103587
$877$	−1.74558e11	−0.00996416	−0.00498208	−	0.999988i	$-0.501586\pi$
$877$	−1.74558e11	−0.00996416	−0.00498208	+	0.999988i	$0.501586\pi$
$878$	−1.14061e13	−0.647759
$879$	1.13385e13	0.640629
$880$	0	0
$881$	8.59039e12	0.480420	0.240210	−	0.970721i	$-0.422784\pi$
$881$	8.59039e12	0.480420	0.240210	+	0.970721i	$0.422784\pi$
$882$	3.02990e13	1.68585
$883$	−1.70227e13	−0.942336	−0.471168	−	0.882043i	$-0.656167\pi$
$883$	−1.70227e13	−0.942336	−0.471168	+	0.882043i	$0.656167\pi$
$884$	−7.22898e11	−0.0398145
$885$	0	0
$886$	1.55635e13	0.848508
$887$	−2.01246e13	−1.09162	−0.545810	−	0.837909i	$-0.683778\pi$
$887$	−2.01246e13	−1.09162	−0.545810	+	0.837909i	$0.683778\pi$
$888$	1.33760e13	0.721885
$889$	−5.34112e13	−2.86797
$890$	0	0
$891$	−9.83253e12	−0.522655
$892$	−1.07700e12	−0.0569604
$893$	−1.92177e13	−1.01127
$894$	2.76237e13	1.44632
$895$	0	0
$896$	2.45591e13	1.27299
$897$	−6.53428e13	−3.37002
$898$	2.00228e13	1.02750
$899$	1.85668e11	0.00948023
$900$	0	0
$901$	−4.03214e12	−0.203833
$902$	1.60695e12	0.0808302
$903$	1.40766e13	0.704535
$904$	2.24525e13	1.11817
$905$	0	0
$906$	2.62782e13	1.29574
$907$	−2.10130e13	−1.03099	−0.515495	−	0.856893i	$-0.672392\pi$
$907$	−2.10130e13	−1.03099	−0.515495	+	0.856893i	$0.672392\pi$
$908$	−2.35404e12	−0.114929
$909$	−3.07761e13	−1.49512
$910$	0	0
$911$	1.95345e12	0.0939656	0.0469828	−	0.998896i	$-0.485039\pi$
$911$	1.95345e12	0.0939656	0.0469828	+	0.998896i	$0.485039\pi$
$912$	−2.97312e13	−1.42310
$913$	−1.04802e13	−0.499172
$914$	−2.33870e13	−1.10845
$915$	0	0
$916$	2.60604e12	0.122307
$917$	3.80064e13	1.77499
$918$	−1.78175e12	−0.0828048
$919$	−2.47656e12	−0.114533	−0.0572663	−	0.998359i	$-0.518238\pi$
$919$	−2.47656e12	−0.114533	−0.0572663	+	0.998359i	$0.518238\pi$
$920$	0	0
$921$	2.73301e13	1.25162
$922$	2.12834e13	0.969954
$923$	5.75744e13	2.61109
$924$	4.04048e12	0.182351
$925$	0	0
$926$	−1.49017e13	−0.666018
$927$	4.78510e13	2.12830
$928$	4.16725e11	0.0184452
$929$	4.40844e13	1.94184	0.970922	−	0.239395i	$-0.0769490\pi$
$929$	4.40844e13	1.94184	0.970922	+	0.239395i	$0.0769490\pi$
$930$	0	0
$931$	−3.52146e13	−1.53621
$932$	−3.55718e12	−0.154431
$933$	−4.40477e11	−0.0190308
$934$	4.02578e13	1.73097
$935$	0	0
$936$	−4.88798e13	−2.08156
$937$	4.92250e12	0.208621	0.104310	−	0.994545i	$-0.466736\pi$
$937$	4.92250e12	0.208621	0.104310	+	0.994545i	$0.466736\pi$
$938$	−2.88787e13	−1.21805
$939$	5.12372e13	2.15075
$940$	0	0
$941$	−1.54680e13	−0.643103	−0.321552	−	0.946892i	$-0.604204\pi$
$941$	−1.54680e13	−0.643103	−0.321552	+	0.946892i	$0.604204\pi$
$942$	6.07852e12	0.251518
$943$	3.88116e12	0.159830
$944$	−2.03731e13	−0.834993
$945$	0	0
$946$	−5.27936e12	−0.214324
$947$	5.49107e12	0.221862	0.110931	−	0.993828i	$-0.464617\pi$
$947$	5.49107e12	0.221862	0.110931	+	0.993828i	$0.464617\pi$
$948$	−1.42080e12	−0.0571343
$949$	2.66004e13	1.06461
$950$	0	0
$951$	7.28207e13	2.88697
$952$	−9.87649e12	−0.389705
$953$	−1.76932e13	−0.694845	−0.347422	−	0.937709i	$-0.612943\pi$
$953$	−1.76932e13	−0.694845	−0.347422	+	0.937709i	$0.612943\pi$
$954$	−2.56802e13	−1.00376
$955$	0	0
$956$	1.17743e12	0.0455905
$957$	−2.59905e12	−0.100164
$958$	−4.90510e12	−0.188150
$959$	−2.52994e13	−0.965888
$960$	0	0
$961$	−2.61401e13	−0.988670
$962$	1.85632e13	0.698819
$963$	5.19916e13	1.94812
$964$	−5.31148e12	−0.198093
$965$	0	0
$966$	−8.40878e13	−3.10696
$967$	2.89231e13	1.06372	0.531858	−	0.846834i	$-0.321494\pi$
$967$	2.89231e13	1.06372	0.531858	+	0.846834i	$0.321494\pi$
$968$	1.24588e13	0.456076
$969$	1.05519e13	0.384481
$970$	0	0
$971$	2.69482e13	0.972843	0.486422	−	0.873724i	$-0.338302\pi$
$971$	2.69482e13	0.972843	0.486422	+	0.873724i	$0.338302\pi$
$972$	−4.07665e12	−0.146489
$973$	−4.05255e13	−1.44951
$974$	−1.03112e13	−0.367107
$975$	0	0
$976$	−8.92590e12	−0.314867
$977$	3.90598e13	1.37153	0.685764	−	0.727824i	$-0.259468\pi$
$977$	3.90598e13	1.37153	0.685764	+	0.727824i	$0.259468\pi$
$978$	2.02934e13	0.709301
$979$	−2.05282e13	−0.714216
$980$	0	0
$981$	−2.91084e12	−0.100348
$982$	−3.64804e13	−1.25187
$983$	9.03830e12	0.308742	0.154371	−	0.988013i	$-0.450665\pi$
$983$	9.03830e12	0.308742	0.154371	+	0.988013i	$0.450665\pi$
$984$	5.23684e12	0.178070
$985$	0	0
$986$	5.98404e11	0.0201627
$987$	−6.56285e13	−2.20123
$988$	5.35098e12	0.178660
$989$	−1.27509e13	−0.423795
$990$	0	0
$991$	4.89096e13	1.61088	0.805439	−	0.592678i	$-0.201929\pi$
$991$	4.89096e13	1.61088	0.805439	+	0.592678i	$0.201929\pi$
$992$	6.72333e11	0.0220436
$993$	3.01181e13	0.983007
$994$	7.40909e13	2.40728
$995$	0	0
$996$	−3.21695e12	−0.103580
$997$	4.01445e13	1.28676	0.643380	−	0.765547i	$-0.277532\pi$
$997$	4.01445e13	1.28676	0.643380	+	0.765547i	$0.277532\pi$
$998$	4.41384e13	1.40841
$999$	−5.30984e12	−0.168670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.10.a.d.1.2	yes	3
3.2	odd	2		225.10.a.m.1.2		3
4.3	odd	2		400.10.a.u.1.3		3
5.2	odd	4		25.10.b.c.24.5		6
5.3	odd	4		25.10.b.c.24.2		6
5.4	even	2		25.10.a.c.1.2	✓	3
15.2	even	4		225.10.b.m.199.2		6
15.8	even	4		225.10.b.m.199.5		6
15.14	odd	2		225.10.a.p.1.2		3
20.3	even	4		400.10.c.q.49.5		6
20.7	even	4		400.10.c.q.49.2		6
20.19	odd	2		400.10.a.y.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.10.a.c.1.2	✓	3	5.4	even	2
25.10.a.d.1.2	yes	3	1.1	even	1	trivial
25.10.b.c.24.2		6	5.3	odd	4
25.10.b.c.24.5		6	5.2	odd	4
225.10.a.m.1.2		3	3.2	odd	2
225.10.a.p.1.2		3	15.14	odd	2
225.10.b.m.199.2		6	15.2	even	4
225.10.b.m.199.5		6	15.8	even	4
400.10.a.u.1.3		3	4.3	odd	2
400.10.a.y.1.1		3	20.19	odd	2
400.10.c.q.49.2		6	20.7	even	4
400.10.c.q.49.5		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)

\(f(q)\)	\(=\)	\(q+21.4187 q^{2} -210.171 q^{3} -53.2406 q^{4} -4501.59 q^{6} +9905.49 q^{7} -12106.7 q^{8} +24489.0 q^{9} +O(q^{10})\)	\(q+21.4187 q^{2} -210.171 q^{3} -53.2406 q^{4} -4501.59 q^{6} +9905.49 q^{7} -12106.7 q^{8} +24489.0 q^{9} +36453.6 q^{11} +11189.6 q^{12} +164867. q^{13} +212162. q^{14} -232050. q^{16} +82357.1 q^{17} +524521. q^{18} -609617. q^{19} -2.08185e6 q^{21} +780787. q^{22} +1.88578e6 q^{23} +2.54448e6 q^{24} +3.53123e6 q^{26} -1.01008e6 q^{27} -527374. q^{28} +339235. q^{29} +547314. q^{31} +1.22842e6 q^{32} -7.66150e6 q^{33} +1.76398e6 q^{34} -1.30381e6 q^{36} +5.25687e6 q^{37} -1.30572e7 q^{38} -3.46503e7 q^{39} +2.05812e6 q^{41} -4.45904e7 q^{42} -6.76158e6 q^{43} -1.94081e6 q^{44} +4.03909e7 q^{46} +3.15241e7 q^{47} +4.87703e7 q^{48} +5.77651e7 q^{49} -1.73091e7 q^{51} -8.77761e6 q^{52} -4.89593e7 q^{53} -2.16345e7 q^{54} -1.19923e8 q^{56} +1.28124e8 q^{57} +7.26597e6 q^{58} +8.77960e7 q^{59} +3.84654e7 q^{61} +1.17227e7 q^{62} +2.42575e8 q^{63} +1.45121e8 q^{64} -1.64099e8 q^{66} -1.36116e8 q^{67} -4.38474e6 q^{68} -3.96337e8 q^{69} +3.49218e8 q^{71} -2.96481e8 q^{72} +1.61345e8 q^{73} +1.12595e8 q^{74} +3.24564e7 q^{76} +3.61091e8 q^{77} -7.42163e8 q^{78} -1.26975e8 q^{79} -2.69727e8 q^{81} +4.40822e7 q^{82} -2.87494e8 q^{83} +1.10839e8 q^{84} -1.44824e8 q^{86} -7.12976e7 q^{87} -4.41333e8 q^{88} -5.63133e8 q^{89} +1.63309e9 q^{91} -1.00400e8 q^{92} -1.15030e8 q^{93} +6.75205e8 q^{94} -2.58179e8 q^{96} -4.71704e8 q^{97} +1.23725e9 q^{98} +8.92711e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 33 q^{2} + 89 q^{3} + 341 q^{4} + 3421 q^{6} + 5258 q^{7} - 105 q^{8} + 58234 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more