LMFDB - Embedded newform 5415.2.a.z.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5415,2,Mod(1,5415)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5415, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("5415.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5415 = 3 \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5415.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:	$43.2389926945$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.8797896.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 8x^{3} + 5x^{2} + 13x - 4 $ x^5 - x^4 - 8x^3 + 5x^2 + 13*x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 285)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.290697$ of defining polynomial
Character	$\chi$	$=$	5415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.290697 q^{2} +1.00000 q^{3} -1.91550 q^{4} +1.00000 q^{5} +0.290697 q^{6} -0.486575 q^{7} -1.13822 q^{8} +1.00000 q^{9} +0.290697 q^{10} +5.34764 q^{11} -1.91550 q^{12} +2.48657 q^{13} -0.141446 q^{14} +1.00000 q^{15} +3.50011 q^{16} -3.41561 q^{17} +0.290697 q^{18} -1.91550 q^{20} -0.486575 q^{21} +1.55454 q^{22} +6.41238 q^{23} -1.13822 q^{24} +1.00000 q^{25} +0.722840 q^{26} +1.00000 q^{27} +0.932031 q^{28} -2.76624 q^{29} +0.290697 q^{30} -4.83099 q^{31} +3.29392 q^{32} +5.34764 q^{33} -0.992907 q^{34} -0.486575 q^{35} -1.91550 q^{36} +6.31756 q^{37} +2.48657 q^{39} -1.13822 q^{40} -2.58139 q^{41} -0.141446 q^{42} -2.48657 q^{43} -10.2434 q^{44} +1.00000 q^{45} +1.86406 q^{46} +11.1107 q^{47} +3.50011 q^{48} -6.76325 q^{49} +0.290697 q^{50} -3.41561 q^{51} -4.76302 q^{52} -2.99678 q^{53} +0.290697 q^{54} +5.34764 q^{55} +0.553831 q^{56} -0.804139 q^{58} -12.7332 q^{59} -1.91550 q^{60} +11.8548 q^{61} -1.40436 q^{62} -0.486575 q^{63} -6.04269 q^{64} +2.48657 q^{65} +1.55454 q^{66} +15.1754 q^{67} +6.54258 q^{68} +6.41238 q^{69} -0.141446 q^{70} +9.92903 q^{71} -1.13822 q^{72} -11.0128 q^{73} +1.83650 q^{74} +1.00000 q^{75} -2.60202 q^{77} +0.722840 q^{78} -8.13272 q^{79} +3.50011 q^{80} +1.00000 q^{81} -0.750404 q^{82} -5.86106 q^{83} +0.932031 q^{84} -3.41561 q^{85} -0.722840 q^{86} -2.76624 q^{87} -6.08681 q^{88} +6.51043 q^{89} +0.290697 q^{90} -1.20990 q^{91} -12.2829 q^{92} -4.83099 q^{93} +3.22984 q^{94} +3.29392 q^{96} -2.00000 q^{97} -1.96606 q^{98} +5.34764 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 5 q^{3} + 7 q^{4} + 5 q^{5} + q^{6} + 2 q^{7} + 6 q^{8} + 5 q^{9} + q^{10} + 5 q^{11} + 7 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} + 7 q^{16} + 10 q^{17} + q^{18} + 7 q^{20} + 2 q^{21}+ \cdots + 5 q^{99}+O(q^{100}) $ 5 * q + q^2 + 5 * q^3 + 7 * q^4 + 5 * q^5 + q^6 + 2 * q^7 + 6 * q^8 + 5 * q^9 + q^10 + 5 * q^11 + 7 * q^12 + 8 * q^13 + 4 * q^14 + 5 * q^15 + 7 * q^16 + 10 * q^17 + q^18 + 7 * q^20 + 2 * q^21 - 2 * q^22 - 2 * q^23 + 6 * q^24 + 5 * q^25 - 2 * q^26 + 5 * q^27 + 10 * q^28 + 7 * q^29 + q^30 + 9 * q^31 + 23 * q^32 + 5 * q^33 - 25 * q^34 + 2 * q^35 + 7 * q^36 - 6 * q^37 + 8 * q^39 + 6 * q^40 - 12 * q^41 + 4 * q^42 - 8 * q^43 + 16 * q^44 + 5 * q^45 + 20 * q^46 + 6 * q^47 + 7 * q^48 + 15 * q^49 + q^50 + 10 * q^51 + 4 * q^52 - 8 * q^53 + q^54 + 5 * q^55 - 36 * q^56 + 38 * q^58 + q^59 + 7 * q^60 + 7 * q^61 + 15 * q^62 + 2 * q^63 + 14 * q^64 + 8 * q^65 - 2 * q^66 + 14 * q^67 - q^68 - 2 * q^69 + 4 * q^70 + 27 * q^71 + 6 * q^72 + 26 * q^73 - 18 * q^74 + 5 * q^75 + 14 * q^77 - 2 * q^78 - 23 * q^79 + 7 * q^80 + 5 * q^81 - 36 * q^82 - 12 * q^83 + 10 * q^84 + 10 * q^85 + 2 * q^86 + 7 * q^87 + 9 * q^89 + q^90 - 46 * q^91 - 52 * q^92 + 9 * q^93 - 45 * q^94 + 23 * q^96 - 10 * q^97 - 21 * q^98 + 5 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.290697	0.205554	0.102777	−	0.994704i	$-0.467227\pi$
$2$	0.290697	0.205554	0.102777	+	0.994704i	$0.467227\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.91550	−0.957748
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.290697	0.118677
$7$	−0.486575	−0.183908	−0.0919539	−	0.995763i	$-0.529311\pi$
$7$	−0.486575	−0.183908	−0.0919539	+	0.995763i	$0.529311\pi$
$8$	−1.13822	−0.402423
$9$	1.00000	0.333333
$10$	0.290697	0.0919265
$11$	5.34764	1.61237	0.806187	−	0.591661i	$-0.201528\pi$
$11$	5.34764	1.61237	0.806187	+	0.591661i	$0.201528\pi$
$12$	−1.91550	−0.552956
$13$	2.48657	0.689652	0.344826	−	0.938667i	$-0.387938\pi$
$13$	2.48657	0.689652	0.344826	+	0.938667i	$0.387938\pi$
$14$	−0.141446	−0.0378030
$15$	1.00000	0.258199
$16$	3.50011	0.875028
$17$	−3.41561	−0.828406	−0.414203	−	0.910184i	$-0.635940\pi$
$17$	−3.41561	−0.828406	−0.414203	+	0.910184i	$0.635940\pi$
$18$	0.290697	0.0685180
$19$	0	0
$19$	0	0
$20$	−1.91550	−0.428318
$21$	−0.486575	−0.106179
$22$	1.55454	0.331430
$23$	6.41238	1.33707	0.668537	−	0.743679i	$-0.266921\pi$
$23$	6.41238	1.33707	0.668537	+	0.743679i	$0.266921\pi$
$24$	−1.13822	−0.232339
$25$	1.00000	0.200000
$26$	0.722840	0.141761
$27$	1.00000	0.192450
$28$	0.932031	0.176137
$29$	−2.76624	−0.513679	−0.256839	−	0.966454i	$-0.582681\pi$
$29$	−2.76624	−0.513679	−0.256839	+	0.966454i	$0.582681\pi$
$30$	0.290697	0.0530738
$31$	−4.83099	−0.867671	−0.433836	−	0.900992i	$-0.642840\pi$
$31$	−4.83099	−0.867671	−0.433836	+	0.900992i	$0.642840\pi$
$32$	3.29392	0.582288
$33$	5.34764	0.930904
$34$	−0.992907	−0.170282
$35$	−0.486575	−0.0822461
$36$	−1.91550	−0.319249
$37$	6.31756	1.03860	0.519301	−	0.854592i	$-0.326192\pi$
$37$	6.31756	1.03860	0.519301	+	0.854592i	$0.326192\pi$
$38$	0	0
$39$	2.48657	0.398171
$40$	−1.13822	−0.179969
$41$	−2.58139	−0.403146	−0.201573	−	0.979473i	$-0.564605\pi$
$41$	−2.58139	−0.403146	−0.201573	+	0.979473i	$0.564605\pi$
$42$	−0.141446	−0.0218256
$43$	−2.48657	−0.379199	−0.189600	−	0.981862i	$-0.560719\pi$
$43$	−2.48657	−0.379199	−0.189600	+	0.981862i	$0.560719\pi$
$44$	−10.2434	−1.54425
$45$	1.00000	0.149071
$46$	1.86406	0.274841
$47$	11.1107	1.62066	0.810328	−	0.585976i	$-0.199289\pi$
$47$	11.1107	1.62066	0.810328	+	0.585976i	$0.199289\pi$
$48$	3.50011	0.505198
$49$	−6.76325	−0.966178
$50$	0.290697	0.0411108
$51$	−3.41561	−0.478281
$52$	−4.76302	−0.660512
$53$	−2.99678	−0.411639	−0.205820	−	0.978590i	$-0.565986\pi$
$53$	−2.99678	−0.411639	−0.205820	+	0.978590i	$0.565986\pi$
$54$	0.290697	0.0395589
$55$	5.34764	0.721075
$56$	0.553831	0.0740087
$57$	0	0
$58$	−0.804139	−0.105589
$59$	−12.7332	−1.65772	−0.828859	−	0.559458i	$-0.811009\pi$
$59$	−12.7332	−1.65772	−0.828859	+	0.559458i	$0.811009\pi$
$60$	−1.91550	−0.247289
$61$	11.8548	1.51786	0.758929	−	0.651174i	$-0.225723\pi$
$61$	11.8548	1.51786	0.758929	+	0.651174i	$0.225723\pi$
$62$	−1.40436	−0.178353
$63$	−0.486575	−0.0613026
$64$	−6.04269	−0.755336
$65$	2.48657	0.308422
$66$	1.55454	0.191351
$67$	15.1754	1.85397	0.926985	−	0.375097i	$-0.122391\pi$
$67$	15.1754	1.85397	0.926985	+	0.375097i	$0.122391\pi$
$68$	6.54258	0.793404
$69$	6.41238	0.771960
$70$	−0.141446	−0.0169060
$71$	9.92903	1.17836	0.589180	−	0.808002i	$-0.299451\pi$
$71$	9.92903	1.17836	0.589180	+	0.808002i	$0.299451\pi$
$72$	−1.13822	−0.134141
$73$	−11.0128	−1.28896	−0.644478	−	0.764623i	$-0.722925\pi$
$73$	−11.0128	−1.28896	−0.644478	+	0.764623i	$0.722925\pi$
$74$	1.83650	0.213489
$75$	1.00000	0.115470
$76$	0	0
$77$	−2.60202	−0.296528
$78$	0.722840	0.0818455
$79$	−8.13272	−0.915002	−0.457501	−	0.889209i	$-0.651255\pi$
$79$	−8.13272	−0.915002	−0.457501	+	0.889209i	$0.651255\pi$
$80$	3.50011	0.391324
$81$	1.00000	0.111111
$82$	−0.750404	−0.0828683
$83$	−5.86106	−0.643335	−0.321668	−	0.946853i	$-0.604243\pi$
$83$	−5.86106	−0.643335	−0.321668	+	0.946853i	$0.604243\pi$
$84$	0.932031	0.101693
$85$	−3.41561	−0.370475
$86$	−0.722840	−0.0779459
$87$	−2.76624	−0.296572
$88$	−6.08681	−0.648856
$89$	6.51043	0.690104	0.345052	−	0.938584i	$-0.387861\pi$
$89$	6.51043	0.690104	0.345052	+	0.938584i	$0.387861\pi$
$90$	0.290697	0.0306422
$91$	−1.20990	−0.126832
$92$	−12.2829	−1.28058
$93$	−4.83099	−0.500950
$94$	3.22984	0.333132
$95$	0	0
$96$	3.29392	0.336184
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	−1.96606	−0.198602
$99$	5.34764	0.537458
$100$	−1.91550	−0.191550
$101$	1.51665	0.150912	0.0754561	−	0.997149i	$-0.475959\pi$
$101$	1.51665	0.150912	0.0754561	+	0.997149i	$0.475959\pi$
$102$	−0.992907	−0.0983125
$103$	9.15478	0.902047	0.451023	−	0.892512i	$-0.351059\pi$
$103$	9.15478	0.902047	0.451023	+	0.892512i	$0.351059\pi$
$104$	−2.83028	−0.277532
$105$	−0.486575	−0.0474848
$106$	−0.871155	−0.0846140
$107$	−0.138936	−0.0134315	−0.00671574	−	0.999977i	$-0.502138\pi$
$107$	−0.138936	−0.0134315	−0.00671574	+	0.999977i	$0.502138\pi$
$108$	−1.91550	−0.184319
$109$	15.7299	1.50666	0.753328	−	0.657645i	$-0.228447\pi$
$109$	15.7299	1.50666	0.753328	+	0.657645i	$0.228447\pi$
$110$	1.55454	0.148220
$111$	6.31756	0.599637
$112$	−1.70307	−0.160925
$113$	−14.8011	−1.39237	−0.696187	−	0.717860i	$-0.745122\pi$
$113$	−14.8011	−1.39237	−0.696187	+	0.717860i	$0.745122\pi$
$114$	0	0
$115$	6.41238	0.597958
$116$	5.29873	0.491974
$117$	2.48657	0.229884
$118$	−3.70150	−0.340750
$119$	1.66195	0.152350
$120$	−1.13822	−0.103905
$121$	17.5972	1.59975
$122$	3.44617	0.312002
$123$	−2.58139	−0.232756
$124$	9.25374	0.831010
$125$	1.00000	0.0894427
$126$	−0.141446	−0.0126010
$127$	9.83099	0.872359	0.436180	−	0.899860i	$-0.356331\pi$
$127$	9.83099	0.872359	0.436180	+	0.899860i	$0.356331\pi$
$128$	−8.34443	−0.737551
$129$	−2.48657	−0.218931
$130$	0.722840	0.0633973
$131$	14.2292	1.24321	0.621605	−	0.783331i	$-0.286481\pi$
$131$	14.2292	1.24321	0.621605	+	0.783331i	$0.286481\pi$
$132$	−10.2434	−0.891571
$133$	0	0
$134$	4.41145	0.381091
$135$	1.00000	0.0860663
$136$	3.88772	0.333370
$137$	6.58439	0.562543	0.281271	−	0.959628i	$-0.409244\pi$
$137$	6.58439	0.562543	0.281271	+	0.959628i	$0.409244\pi$
$138$	1.86406	0.158680
$139$	0.233756	0.0198269	0.00991347	−	0.999951i	$-0.496844\pi$
$139$	0.233756	0.0198269	0.00991347	+	0.999951i	$0.496844\pi$
$140$	0.932031	0.0787710
$141$	11.1107	0.935686
$142$	2.88634	0.242216
$143$	13.2973	1.11198
$144$	3.50011	0.291676
$145$	−2.76624	−0.229724
$146$	−3.20140	−0.264950
$147$	−6.76325	−0.557823
$148$	−12.1013	−0.994718
$149$	−2.67299	−0.218980	−0.109490	−	0.993988i	$-0.534922\pi$
$149$	−2.67299	−0.218980	−0.109490	+	0.993988i	$0.534922\pi$
$150$	0.290697	0.0237353
$151$	−5.95266	−0.484421	−0.242210	−	0.970224i	$-0.577872\pi$
$151$	−5.95266	−0.484421	−0.242210	+	0.970224i	$0.577872\pi$
$152$	0	0
$153$	−3.41561	−0.276135
$154$	−0.756401	−0.0609525
$155$	−4.83099	−0.388034
$156$	−4.76302	−0.381347
$157$	−7.20848	−0.575299	−0.287650	−	0.957736i	$-0.592874\pi$
$157$	−7.20848	−0.575299	−0.287650	+	0.957736i	$0.592874\pi$
$158$	−2.36416	−0.188082
$159$	−2.99678	−0.237660
$160$	3.29392	0.260407
$161$	−3.12010	−0.245899
$162$	0.290697	0.0228393
$163$	14.1756	1.11032	0.555161	−	0.831743i	$-0.312657\pi$
$163$	14.1756	1.11032	0.555161	+	0.831743i	$0.312657\pi$
$164$	4.94465	0.386112
$165$	5.34764	0.416313
$166$	−1.70379	−0.132240
$167$	−12.5563	−0.971639	−0.485819	−	0.874059i	$-0.661479\pi$
$167$	−12.5563	−0.971639	−0.485819	+	0.874059i	$0.661479\pi$
$168$	0.553831	0.0427290
$169$	−6.81695	−0.524381
$170$	−0.992907	−0.0761525
$171$	0	0
$172$	4.76302	0.363177
$173$	−2.18964	−0.166475	−0.0832376	−	0.996530i	$-0.526526\pi$
$173$	−2.18964	−0.166475	−0.0832376	+	0.996530i	$0.526526\pi$
$174$	−0.804139	−0.0609616
$175$	−0.486575	−0.0367816
$176$	18.7173	1.41087
$177$	−12.7332	−0.957084
$178$	1.89256	0.141854
$179$	−7.50421	−0.560891	−0.280445	−	0.959870i	$-0.590482\pi$
$179$	−7.50421	−0.560891	−0.280445	+	0.959870i	$0.590482\pi$
$180$	−1.91550	−0.142773
$181$	12.6652	0.941397	0.470699	−	0.882294i	$-0.344002\pi$
$181$	12.6652	0.941397	0.470699	+	0.882294i	$0.344002\pi$
$182$	−0.351716	−0.0260709
$183$	11.8548	0.876335
$184$	−7.29873	−0.538069
$185$	6.31756	0.464477
$186$	−1.40436	−0.102972
$187$	−18.2654	−1.33570
$188$	−21.2824	−1.55218
$189$	−0.486575	−0.0353931
$190$	0	0
$191$	8.15777	0.590276	0.295138	−	0.955455i	$-0.404634\pi$
$191$	8.15777	0.590276	0.295138	+	0.955455i	$0.404634\pi$
$192$	−6.04269	−0.436094
$193$	3.36505	0.242221	0.121111	−	0.992639i	$-0.461354\pi$
$193$	3.36505	0.242221	0.121111	+	0.992639i	$0.461354\pi$
$194$	−0.581394	−0.0417417
$195$	2.48657	0.178067
$196$	12.9550	0.925355
$197$	3.83399	0.273160	0.136580	−	0.990629i	$-0.456389\pi$
$197$	3.83399	0.273160	0.136580	+	0.990629i	$0.456389\pi$
$198$	1.55454	0.110477
$199$	12.6985	0.900173	0.450086	−	0.892985i	$-0.351393\pi$
$199$	12.6985	0.900173	0.450086	+	0.892985i	$0.351393\pi$
$200$	−1.13822	−0.0804846
$201$	15.1754	1.07039
$202$	0.440885	0.0310206
$203$	1.34598	0.0944695
$204$	6.54258	0.458072
$205$	−2.58139	−0.180292
$206$	2.66127	0.185419
$207$	6.41238	0.445692
$208$	8.70329	0.603465
$209$	0	0
$210$	−0.141446	−0.00976069
$211$	9.15657	0.630364	0.315182	−	0.949031i	$-0.397934\pi$
$211$	9.15657	0.630364	0.315182	+	0.949031i	$0.397934\pi$
$212$	5.74031	0.394246
$213$	9.92903	0.680326
$214$	−0.0403884	−0.00276089
$215$	−2.48657	−0.169583
$216$	−1.13822	−0.0774463
$217$	2.35064	0.159572
$218$	4.57265	0.309699
$219$	−11.0128	−0.744179
$220$	−10.2434	−0.690608
$221$	−8.49316	−0.571312
$222$	1.83650	0.123258
$223$	−10.8975	−0.729753	−0.364876	−	0.931056i	$-0.618889\pi$
$223$	−10.8975	−0.729753	−0.364876	+	0.931056i	$0.618889\pi$
$224$	−1.60274	−0.107087
$225$	1.00000	0.0666667
$226$	−4.30265	−0.286208
$227$	24.6351	1.63509	0.817545	−	0.575864i	$-0.195334\pi$
$227$	24.6351	1.63509	0.817545	+	0.575864i	$0.195334\pi$
$228$	0	0
$229$	17.1676	1.13447	0.567234	−	0.823557i	$-0.308013\pi$
$229$	17.1676	1.13447	0.567234	+	0.823557i	$0.308013\pi$
$230$	1.86406	0.122913
$231$	−2.60202	−0.171201
$232$	3.14860	0.206716
$233$	28.4631	1.86468	0.932341	−	0.361581i	$-0.117763\pi$
$233$	28.4631	1.86468	0.932341	+	0.361581i	$0.117763\pi$
$234$	0.722840	0.0472535
$235$	11.1107	0.724780
$236$	24.3903	1.58768
$237$	−8.13272	−0.528277
$238$	0.483123	0.0313162
$239$	4.07741	0.263746	0.131873	−	0.991267i	$-0.457901\pi$
$239$	4.07741	0.263746	0.131873	+	0.991267i	$0.457901\pi$
$240$	3.50011	0.225931
$241$	12.6684	0.816045	0.408023	−	0.912972i	$-0.366218\pi$
$241$	12.6684	0.816045	0.408023	+	0.912972i	$0.366218\pi$
$242$	5.11547	0.328835
$243$	1.00000	0.0641500
$244$	−22.7079	−1.45372
$245$	−6.76325	−0.432088
$246$	−0.750404	−0.0478440
$247$	0	0
$248$	5.49875	0.349171
$249$	−5.86106	−0.371430
$250$	0.290697	0.0183853
$251$	−11.6241	−0.733706	−0.366853	−	0.930279i	$-0.619565\pi$
$251$	−11.6241	−0.733706	−0.366853	+	0.930279i	$0.619565\pi$
$252$	0.932031	0.0587124
$253$	34.2911	2.15586
$254$	2.85784	0.179317
$255$	−3.41561	−0.213894
$256$	9.65968	0.603730
$257$	−10.5483	−0.657986	−0.328993	−	0.944332i	$-0.606709\pi$
$257$	−10.5483	−0.657986	−0.328993	+	0.944332i	$0.606709\pi$
$258$	−0.722840	−0.0450021
$259$	−3.07397	−0.191007
$260$	−4.76302	−0.295390
$261$	−2.76624	−0.171226
$262$	4.13639	0.255547
$263$	23.7935	1.46717	0.733585	−	0.679598i	$-0.237846\pi$
$263$	23.7935	1.46717	0.733585	+	0.679598i	$0.237846\pi$
$264$	−6.08681	−0.374617
$265$	−2.99678	−0.184091
$266$	0	0
$267$	6.51043	0.398432
$268$	−29.0684	−1.77564
$269$	4.22754	0.257757	0.128879	−	0.991660i	$-0.458862\pi$
$269$	4.22754	0.257757	0.128879	+	0.991660i	$0.458862\pi$
$270$	0.290697	0.0176913
$271$	31.1471	1.89205	0.946027	−	0.324089i	$-0.105058\pi$
$271$	31.1471	1.89205	0.946027	+	0.324089i	$0.105058\pi$
$272$	−11.9550	−0.724879
$273$	−1.20990	−0.0732267
$274$	1.91406	0.115633
$275$	5.34764	0.322475
$276$	−12.2829	−0.739343
$277$	1.05393	0.0633243	0.0316621	−	0.999499i	$-0.489920\pi$
$277$	1.05393	0.0633243	0.0316621	+	0.999499i	$0.489920\pi$
$278$	0.0679523	0.00407551
$279$	−4.83099	−0.289224
$280$	0.553831	0.0330977
$281$	−25.6354	−1.52928	−0.764638	−	0.644459i	$-0.777082\pi$
$281$	−25.6354	−1.52928	−0.764638	+	0.644459i	$0.777082\pi$
$282$	3.22984	0.192334
$283$	29.4112	1.74831	0.874157	−	0.485644i	$-0.161415\pi$
$283$	29.4112	1.74831	0.874157	+	0.485644i	$0.161415\pi$
$284$	−19.0190	−1.12857
$285$	0	0
$286$	3.86549	0.228571
$287$	1.25604	0.0741417
$288$	3.29392	0.194096
$289$	−5.33363	−0.313743
$290$	−0.804139	−0.0472207
$291$	−2.00000	−0.117242
$292$	21.0950	1.23449
$293$	10.8548	0.634147	0.317073	−	0.948401i	$-0.397300\pi$
$293$	10.8548	0.634147	0.317073	+	0.948401i	$0.397300\pi$
$294$	−1.96606	−0.114663
$295$	−12.7332	−0.741354
$296$	−7.19080	−0.417957
$297$	5.34764	0.310301
$298$	−0.777031	−0.0450122
$299$	15.9449	0.922116
$300$	−1.91550	−0.110591
$301$	1.20990	0.0697377
$302$	−1.73042	−0.0995746
$303$	1.51665	0.0871291
$304$	0	0
$305$	11.8548	0.678806
$306$	−0.992907	−0.0567607
$307$	−33.6891	−1.92274	−0.961368	−	0.275266i	$-0.911234\pi$
$307$	−33.6891	−1.92274	−0.961368	+	0.275266i	$0.911234\pi$
$308$	4.98417	0.283999
$309$	9.15478	0.520797
$310$	−1.40436	−0.0797620
$311$	−11.7221	−0.664701	−0.332350	−	0.943156i	$-0.607842\pi$
$311$	−11.7221	−0.664701	−0.332350	+	0.943156i	$0.607842\pi$
$312$	−2.83028	−0.160233
$313$	4.47856	0.253143	0.126572	−	0.991957i	$-0.459603\pi$
$313$	4.47856	0.253143	0.126572	+	0.991957i	$0.459603\pi$
$314$	−2.09548	−0.118255
$315$	−0.486575	−0.0274154
$316$	15.5782	0.876341
$317$	−12.3873	−0.695742	−0.347871	−	0.937542i	$-0.613095\pi$
$317$	−12.3873	−0.695742	−0.347871	+	0.937542i	$0.613095\pi$
$318$	−0.871155	−0.0488519
$319$	−14.7929	−0.828242
$320$	−6.04269	−0.337797
$321$	−0.138936	−0.00775467
$322$	−0.907005	−0.0505454
$323$	0	0
$324$	−1.91550	−0.106416
$325$	2.48657	0.137930
$326$	4.12082	0.228231
$327$	15.7299	0.869868
$328$	2.93820	0.162235
$329$	−5.40616	−0.298051
$330$	1.55454	0.0855748
$331$	−24.5058	−1.34696	−0.673480	−	0.739206i	$-0.735201\pi$
$331$	−24.5058	−1.34696	−0.673480	+	0.739206i	$0.735201\pi$
$332$	11.2268	0.616153
$333$	6.31756	0.346200
$334$	−3.65009	−0.199724
$335$	15.1754	0.829121
$336$	−1.70307	−0.0929098
$337$	−10.5008	−0.572013	−0.286006	−	0.958228i	$-0.592328\pi$
$337$	−10.5008	−0.572013	−0.286006	+	0.958228i	$0.592328\pi$
$338$	−1.98167	−0.107788
$339$	−14.8011	−0.803888
$340$	6.54258	0.354821
$341$	−25.8344	−1.39901
$342$	0	0
$343$	6.69684	0.361596
$344$	2.83028	0.152598
$345$	6.41238	0.345231
$346$	−0.636522	−0.0342196
$347$	−1.45512	−0.0781151	−0.0390576	−	0.999237i	$-0.512436\pi$
$347$	−1.45512	−0.0781151	−0.0390576	+	0.999237i	$0.512436\pi$
$348$	5.29873	0.284042
$349$	23.7332	1.27041	0.635204	−	0.772345i	$-0.280916\pi$
$349$	23.7332	1.27041	0.635204	+	0.772345i	$0.280916\pi$
$350$	−0.141446	−0.00756060
$351$	2.48657	0.132724
$352$	17.6147	0.938866
$353$	−7.39055	−0.393359	−0.196680	−	0.980468i	$-0.563016\pi$
$353$	−7.39055	−0.393359	−0.196680	+	0.980468i	$0.563016\pi$
$354$	−3.70150	−0.196732
$355$	9.92903	0.526978
$356$	−12.4707	−0.660945
$357$	1.66195	0.0879596
$358$	−2.18145	−0.115293
$359$	2.35868	0.124487	0.0622433	−	0.998061i	$-0.480175\pi$
$359$	2.35868	0.124487	0.0622433	+	0.998061i	$0.480175\pi$
$360$	−1.13822	−0.0599896
$361$	0	0
$362$	3.68174	0.193508
$363$	17.5972	0.923615
$364$	2.31756	0.121473
$365$	−11.0128	−0.576438
$366$	3.44617	0.180134
$367$	−22.1486	−1.15615	−0.578073	−	0.815985i	$-0.696195\pi$
$367$	−22.1486	−1.15615	−0.578073	+	0.815985i	$0.696195\pi$
$368$	22.4441	1.16998
$369$	−2.58139	−0.134382
$370$	1.83650	0.0954750
$371$	1.45816	0.0757037
$372$	9.25374	0.479784
$373$	−31.1738	−1.61412	−0.807060	−	0.590469i	$-0.798943\pi$
$373$	−31.1738	−1.61412	−0.807060	+	0.590469i	$0.798943\pi$
$374$	−5.30971	−0.274559
$375$	1.00000	0.0516398
$376$	−12.6464	−0.652189
$377$	−6.87847	−0.354259
$378$	−0.141446	−0.00727519
$379$	26.0349	1.33732	0.668662	−	0.743567i	$-0.266868\pi$
$379$	26.0349	1.33732	0.668662	+	0.743567i	$0.266868\pi$
$380$	0	0
$381$	9.83099	0.503657
$382$	2.37144	0.121334
$383$	2.13294	0.108988	0.0544941	−	0.998514i	$-0.482645\pi$
$383$	2.13294	0.108988	0.0544941	+	0.998514i	$0.482645\pi$
$384$	−8.34443	−0.425825
$385$	−2.60202	−0.132611
$386$	0.978209	0.0497895
$387$	−2.48657	−0.126400
$388$	3.83099	0.194489
$389$	−13.0427	−0.661291	−0.330645	−	0.943755i	$-0.607266\pi$
$389$	−13.0427	−0.661291	−0.330645	+	0.943755i	$0.607266\pi$
$390$	0.722840	0.0366024
$391$	−21.9022	−1.10764
$392$	7.69808	0.388812
$393$	14.2292	0.717768
$394$	1.11453	0.0561492
$395$	−8.13272	−0.409201
$396$	−10.2434	−0.514749
$397$	0.0286428	0.00143754	0.000718770	−	1.00000i	$-0.499771\pi$
$397$	0.0286428	0.00143754	0.000718770		1.00000i	$0.499771\pi$
$398$	3.69142	0.185034
$399$	0	0
$400$	3.50011	0.175006
$401$	27.3191	1.36425	0.682126	−	0.731234i	$-0.261055\pi$
$401$	27.3191	1.36425	0.682126	+	0.731234i	$0.261055\pi$
$402$	4.41145	0.220023
$403$	−12.0126	−0.598391
$404$	−2.90513	−0.144536
$405$	1.00000	0.0496904
$406$	0.391274	0.0194186
$407$	33.7841	1.67461
$408$	3.88772	0.192471
$409$	6.73917	0.333230	0.166615	−	0.986022i	$-0.446716\pi$
$409$	6.73917	0.333230	0.166615	+	0.986022i	$0.446716\pi$
$410$	−0.750404	−0.0370598
$411$	6.58439	0.324784
$412$	−17.5359	−0.863933
$413$	6.19564	0.304867
$414$	1.86406	0.0916137
$415$	−5.86106	−0.287708
$416$	8.19058	0.401576
$417$	0.233756	0.0114471
$418$	0	0
$419$	26.4076	1.29010	0.645048	−	0.764142i	$-0.276837\pi$
$419$	26.4076	1.29010	0.645048	+	0.764142i	$0.276837\pi$
$420$	0.932031	0.0454785
$421$	−37.8895	−1.84662	−0.923311	−	0.384053i	$-0.874528\pi$
$421$	−37.8895	−1.84662	−0.923311	+	0.384053i	$0.874528\pi$
$422$	2.66179	0.129574
$423$	11.1107	0.540219
$424$	3.41100	0.165653
$425$	−3.41561	−0.165681
$426$	2.88634	0.139844
$427$	−5.76826	−0.279146
$428$	0.266132	0.0128640
$429$	13.2973	0.642000
$430$	−0.722840	−0.0348585
$431$	19.2057	0.925106	0.462553	−	0.886592i	$-0.346933\pi$
$431$	19.2057	0.925106	0.462553	+	0.886592i	$0.346933\pi$
$432$	3.50011	0.168399
$433$	−16.9512	−0.814624	−0.407312	−	0.913289i	$-0.633534\pi$
$433$	−16.9512	−0.814624	−0.407312	+	0.913289i	$0.633534\pi$
$434$	0.683323	0.0328006
$435$	−2.76624	−0.132631
$436$	−30.1306	−1.44300
$437$	0	0
$438$	−3.20140	−0.152969
$439$	−11.1029	−0.529911	−0.264955	−	0.964261i	$-0.585357\pi$
$439$	−11.1029	−0.529911	−0.264955	+	0.964261i	$0.585357\pi$
$440$	−6.08681	−0.290177
$441$	−6.76325	−0.322059
$442$	−2.46894	−0.117435
$443$	−13.8942	−0.660132	−0.330066	−	0.943958i	$-0.607071\pi$
$443$	−13.8942	−0.660132	−0.330066	+	0.943958i	$0.607071\pi$
$444$	−12.1013	−0.574301
$445$	6.51043	0.308624
$446$	−3.16788	−0.150004
$447$	−2.67299	−0.126428
$448$	2.94022	0.138912
$449$	−27.8675	−1.31515	−0.657573	−	0.753391i	$-0.728417\pi$
$449$	−27.8675	−1.31515	−0.657573	+	0.753391i	$0.728417\pi$
$450$	0.290697	0.0137036
$451$	−13.8044	−0.650022
$452$	28.3515	1.33354
$453$	−5.95266	−0.279680
$454$	7.16136	0.336099
$455$	−1.20990	−0.0567212
$456$	0	0
$457$	−36.5660	−1.71048	−0.855242	−	0.518229i	$-0.826591\pi$
$457$	−36.5660	−1.71048	−0.855242	+	0.518229i	$0.826591\pi$
$458$	4.99058	0.233194
$459$	−3.41561	−0.159427
$460$	−12.2829	−0.572693
$461$	21.9180	1.02082	0.510412	−	0.859930i	$-0.329493\pi$
$461$	21.9180	1.02082	0.510412	+	0.859930i	$0.329493\pi$
$462$	−0.756401	−0.0351910
$463$	−14.0255	−0.651821	−0.325910	−	0.945401i	$-0.605671\pi$
$463$	−14.0255	−0.651821	−0.325910	+	0.945401i	$0.605671\pi$
$464$	−9.68216	−0.449483
$465$	−4.83099	−0.224032
$466$	8.27415	0.383293
$467$	33.9294	1.57007	0.785033	−	0.619453i	$-0.212646\pi$
$467$	33.9294	1.57007	0.785033	+	0.619453i	$0.212646\pi$
$468$	−4.76302	−0.220171
$469$	−7.38397	−0.340960
$470$	3.22984	0.148981
$471$	−7.20848	−0.332149
$472$	14.4932	0.667103
$473$	−13.2973	−0.611411
$474$	−2.36416	−0.108589
$475$	0	0
$476$	−3.18345	−0.145913
$477$	−2.99678	−0.137213
$478$	1.18529	0.0542140
$479$	31.9497	1.45982	0.729909	−	0.683544i	$-0.239562\pi$
$479$	31.9497	1.45982	0.729909	+	0.683544i	$0.239562\pi$
$480$	3.29392	0.150346
$481$	15.7091	0.716273
$482$	3.68268	0.167741
$483$	−3.12010	−0.141970
$484$	−33.7074	−1.53216
$485$	−2.00000	−0.0908153
$486$	0.290697	0.0131863
$487$	−37.6229	−1.70486	−0.852428	−	0.522844i	$-0.824871\pi$
$487$	−37.6229	−1.70486	−0.852428	+	0.522844i	$0.824871\pi$
$488$	−13.4935	−0.610820
$489$	14.1756	0.641044
$490$	−1.96606	−0.0888174
$491$	−40.0842	−1.80897	−0.904487	−	0.426500i	$-0.859746\pi$
$491$	−40.0842	−1.80897	−0.904487	+	0.426500i	$0.859746\pi$
$492$	4.94465	0.222922
$493$	9.44840	0.425535
$494$	0	0
$495$	5.34764	0.240358
$496$	−16.9090	−0.759237
$497$	−4.83121	−0.216710
$498$	−1.70379	−0.0763489
$499$	−30.3067	−1.35671	−0.678357	−	0.734732i	$-0.737308\pi$
$499$	−30.3067	−1.35671	−0.678357	+	0.734732i	$0.737308\pi$
$500$	−1.91550	−0.0856635
$501$	−12.5563	−0.560976
$502$	−3.37909	−0.150816
$503$	−17.2879	−0.770827	−0.385414	−	0.922744i	$-0.625941\pi$
$503$	−17.2879	−0.770827	−0.385414	+	0.922744i	$0.625941\pi$
$504$	0.553831	0.0246696
$505$	1.51665	0.0674899
$506$	9.96833	0.443146
$507$	−6.81695	−0.302751
$508$	−18.8312	−0.835500
$509$	−5.60825	−0.248581	−0.124291	−	0.992246i	$-0.539665\pi$
$509$	−5.60825	−0.248581	−0.124291	+	0.992246i	$0.539665\pi$
$510$	−0.992907	−0.0439667
$511$	5.35857	0.237049
$512$	19.4969	0.861650
$513$	0	0
$514$	−3.06637	−0.135252
$515$	9.15478	0.403408
$516$	4.76302	0.209680
$517$	59.4158	2.61310
$518$	−0.893593	−0.0392622
$519$	−2.18964	−0.0961145
$520$	−2.83028	−0.124116
$521$	−13.7128	−0.600767	−0.300384	−	0.953818i	$-0.597115\pi$
$521$	−13.7128	−0.600767	−0.300384	+	0.953818i	$0.597115\pi$
$522$	−0.804139	−0.0351962
$523$	35.2342	1.54068	0.770341	−	0.637632i	$-0.220086\pi$
$523$	35.2342	1.54068	0.770341	+	0.637632i	$0.220086\pi$
$524$	−27.2559	−1.19068
$525$	−0.486575	−0.0212359
$526$	6.91670	0.301583
$527$	16.5008	0.718785
$528$	18.7173	0.814567
$529$	18.1187	0.787769
$530$	−0.871155	−0.0378405
$531$	−12.7332	−0.552573
$532$	0	0
$533$	−6.41883	−0.278030
$534$	1.89256	0.0818992
$535$	−0.138936	−0.00600674
$536$	−17.2730	−0.746080
$537$	−7.50421	−0.323830
$538$	1.22893	0.0529830
$539$	−36.1674	−1.55784
$540$	−1.91550	−0.0824298
$541$	30.2357	1.29994	0.649968	−	0.759962i	$-0.274782\pi$
$541$	30.2357	1.29994	0.649968	+	0.759962i	$0.274782\pi$
$542$	9.05438	0.388919
$543$	12.6652	0.543516
$544$	−11.2507	−0.482371
$545$	15.7299	0.673797
$546$	−0.351716	−0.0150520
$547$	−34.9531	−1.49449	−0.747244	−	0.664550i	$-0.768623\pi$
$547$	−34.9531	−1.49449	−0.747244	+	0.664550i	$0.768623\pi$
$548$	−12.6124	−0.538774
$549$	11.8548	0.505952
$550$	1.55454	0.0662860
$551$	0	0
$552$	−7.29873	−0.310654
$553$	3.95717	0.168276
$554$	0.306373	0.0130166
$555$	6.31756	0.268166
$556$	−0.447759	−0.0189892
$557$	3.16279	0.134012	0.0670058	−	0.997753i	$-0.478655\pi$
$557$	3.16279	0.134012	0.0670058	+	0.997753i	$0.478655\pi$
$558$	−1.40436	−0.0594511
$559$	−6.18305	−0.261515
$560$	−1.70307	−0.0719676
$561$	−18.2654	−0.771167
$562$	−7.45213	−0.314349
$563$	29.0570	1.22460	0.612302	−	0.790624i	$-0.290244\pi$
$563$	29.0570	1.22460	0.612302	+	0.790624i	$0.290244\pi$
$564$	−21.2824	−0.896151
$565$	−14.8011	−0.622689
$566$	8.54975	0.359373
$567$	−0.486575	−0.0204342
$568$	−11.3015	−0.474199
$569$	31.3398	1.31383	0.656916	−	0.753964i	$-0.271861\pi$
$569$	31.3398	1.31383	0.656916	+	0.753964i	$0.271861\pi$
$570$	0	0
$571$	2.56556	0.107365	0.0536827	−	0.998558i	$-0.482904\pi$
$571$	2.56556	0.107365	0.0536827	+	0.998558i	$0.482904\pi$
$572$	−25.4709	−1.06499
$573$	8.15777	0.340796
$574$	0.365128	0.0152401
$575$	6.41238	0.267415
$576$	−6.04269	−0.251779
$577$	3.12153	0.129951	0.0649755	−	0.997887i	$-0.479303\pi$
$577$	3.12153	0.129951	0.0649755	+	0.997887i	$0.479303\pi$
$578$	−1.55047	−0.0644911
$579$	3.36505	0.139847
$580$	5.29873	0.220018
$581$	2.85184	0.118314
$582$	−0.581394	−0.0240996
$583$	−16.0257	−0.663716
$584$	12.5351	0.518705
$585$	2.48657	0.102807
$586$	3.15547	0.130351
$587$	−9.27970	−0.383014	−0.191507	−	0.981491i	$-0.561338\pi$
$587$	−9.27970	−0.383014	−0.191507	+	0.981491i	$0.561338\pi$
$588$	12.9550	0.534254
$589$	0	0
$590$	−3.70150	−0.152388
$591$	3.83399	0.157709
$592$	22.1122	0.908805
$593$	34.0447	1.39805	0.699025	−	0.715097i	$-0.253618\pi$
$593$	34.0447	1.39805	0.699025	+	0.715097i	$0.253618\pi$
$594$	1.55454	0.0637837
$595$	1.66195	0.0681332
$596$	5.12010	0.209728
$597$	12.6985	0.519715
$598$	4.63513	0.189545
$599$	−25.0732	−1.02446	−0.512231	−	0.858848i	$-0.671181\pi$
$599$	−25.0732	−1.02446	−0.512231	+	0.858848i	$0.671181\pi$
$600$	−1.13822	−0.0464678
$601$	26.0225	1.06148	0.530739	−	0.847535i	$-0.321914\pi$
$601$	26.0225	1.06148	0.530739	+	0.847535i	$0.321914\pi$
$602$	0.351716	0.0143349
$603$	15.1754	0.617990
$604$	11.4023	0.463953
$605$	17.5972	0.715429
$606$	0.440885	0.0179097
$607$	7.54650	0.306303	0.153151	−	0.988203i	$-0.451058\pi$
$607$	7.54650	0.306303	0.153151	+	0.988203i	$0.451058\pi$
$608$	0	0
$609$	1.34598	0.0545420
$610$	3.44617	0.139531
$611$	27.6275	1.11769
$612$	6.54258	0.264468
$613$	−38.2690	−1.54567	−0.772836	−	0.634606i	$-0.781162\pi$
$613$	−38.2690	−1.54567	−0.772836	+	0.634606i	$0.781162\pi$
$614$	−9.79331	−0.395226
$615$	−2.58139	−0.104092
$616$	2.96169	0.119330
$617$	−11.6508	−0.469043	−0.234522	−	0.972111i	$-0.575352\pi$
$617$	−11.6508	−0.469043	−0.234522	+	0.972111i	$0.575352\pi$
$618$	2.66127	0.107052
$619$	−2.47710	−0.0995630	−0.0497815	−	0.998760i	$-0.515852\pi$
$619$	−2.47710	−0.0995630	−0.0497815	+	0.998760i	$0.515852\pi$
$620$	9.25374	0.371639
$621$	6.41238	0.257320
$622$	−3.40759	−0.136632
$623$	−3.16781	−0.126916
$624$	8.70329	0.348410
$625$	1.00000	0.0400000
$626$	1.30191	0.0520346
$627$	0	0
$628$	13.8078	0.550991
$629$	−21.5783	−0.860384
$630$	−0.141446	−0.00563534
$631$	−43.6558	−1.73791	−0.868954	−	0.494893i	$-0.835207\pi$
$631$	−43.6558	−1.73791	−0.868954	+	0.494893i	$0.835207\pi$
$632$	9.25685	0.368218
$633$	9.15657	0.363941
$634$	−3.60096	−0.143012
$635$	9.83099	0.390131
$636$	5.74031	0.227618
$637$	−16.8173	−0.666326
$638$	−4.30025	−0.170248
$639$	9.92903	0.392786
$640$	−8.34443	−0.329843
$641$	−24.2326	−0.957128	−0.478564	−	0.878053i	$-0.658843\pi$
$641$	−24.2326	−0.957128	−0.478564	+	0.878053i	$0.658843\pi$
$642$	−0.0403884	−0.00159400
$643$	8.31756	0.328013	0.164006	−	0.986459i	$-0.447558\pi$
$643$	8.31756	0.328013	0.164006	+	0.986459i	$0.447558\pi$
$644$	5.97654	0.235509
$645$	−2.48657	−0.0979088
$646$	0	0
$647$	−10.9164	−0.429170	−0.214585	−	0.976705i	$-0.568840\pi$
$647$	−10.9164	−0.429170	−0.214585	+	0.976705i	$0.568840\pi$
$648$	−1.13822	−0.0447136
$649$	−68.0924	−2.67286
$650$	0.722840	0.0283521
$651$	2.35064	0.0921287
$652$	−27.1534	−1.06341
$653$	−21.8452	−0.854868	−0.427434	−	0.904047i	$-0.640582\pi$
$653$	−21.8452	−0.854868	−0.427434	+	0.904047i	$0.640582\pi$
$654$	4.57265	0.178805
$655$	14.2292	0.555980
$656$	−9.03517	−0.352764
$657$	−11.0128	−0.429652
$658$	−1.57156	−0.0612657
$659$	26.4188	1.02913	0.514566	−	0.857451i	$-0.327953\pi$
$659$	26.4188	1.02913	0.514566	+	0.857451i	$0.327953\pi$
$660$	−10.2434	−0.398723
$661$	−18.6144	−0.724017	−0.362008	−	0.932175i	$-0.617909\pi$
$661$	−18.6144	−0.724017	−0.362008	+	0.932175i	$0.617909\pi$
$662$	−7.12376	−0.276873
$663$	−8.49316	−0.329847
$664$	6.67120	0.258893
$665$	0	0
$666$	1.83650	0.0711629
$667$	−17.7382	−0.686827
$668$	24.0516	0.930585
$669$	−10.8975	−0.421323
$670$	4.41145	0.170429
$671$	63.3954	2.44735
$672$	−1.60274	−0.0618269
$673$	−5.98693	−0.230779	−0.115390	−	0.993320i	$-0.536812\pi$
$673$	−5.98693	−0.230779	−0.115390	+	0.993320i	$0.536812\pi$
$674$	−3.05254	−0.117580
$675$	1.00000	0.0384900
$676$	13.0578	0.502224
$677$	−33.7287	−1.29630	−0.648150	−	0.761512i	$-0.724457\pi$
$677$	−33.7287	−1.29630	−0.648150	+	0.761512i	$0.724457\pi$
$678$	−4.30265	−0.165242
$679$	0.973149	0.0373460
$680$	3.88772	0.149087
$681$	24.6351	0.944020
$682$	−7.50998	−0.287572
$683$	−11.4959	−0.439880	−0.219940	−	0.975513i	$-0.570586\pi$
$683$	−11.4959	−0.439880	−0.219940	+	0.975513i	$0.570586\pi$
$684$	0	0
$685$	6.58439	0.251577
$686$	1.94675	0.0743274
$687$	17.1676	0.654985
$688$	−8.70329	−0.331810
$689$	−7.45171	−0.283888
$690$	1.86406	0.0709636
$691$	36.3039	1.38107	0.690533	−	0.723301i	$-0.257376\pi$
$691$	36.3039	1.38107	0.690533	+	0.723301i	$0.257376\pi$
$692$	4.19424	0.159441
$693$	−2.60202	−0.0988427
$694$	−0.423000	−0.0160569
$695$	0.233756	0.00886688
$696$	3.14860	0.119348
$697$	8.81703	0.333969
$698$	6.89917	0.261137
$699$	28.4631	1.07657
$700$	0.932031	0.0352275
$701$	13.5275	0.510925	0.255463	−	0.966819i	$-0.417772\pi$
$701$	13.5275	0.510925	0.255463	+	0.966819i	$0.417772\pi$
$702$	0.722840	0.0272818
$703$	0	0
$704$	−32.3141	−1.21788
$705$	11.1107	0.418452
$706$	−2.14841	−0.0808566
$707$	−0.737962	−0.0277539
$708$	24.3903	0.916645
$709$	−0.993555	−0.0373137	−0.0186569	−	0.999826i	$-0.505939\pi$
$709$	−0.993555	−0.0373137	−0.0186569	+	0.999826i	$0.505939\pi$
$710$	2.88634	0.108322
$711$	−8.13272	−0.305001
$712$	−7.41032	−0.277714
$713$	−30.9782	−1.16014
$714$	0.483123	0.0180804
$715$	13.2973	0.497291
$716$	14.3743	0.537192
$717$	4.07741	0.152274
$718$	0.685662	0.0255887
$719$	−1.40134	−0.0522612	−0.0261306	−	0.999659i	$-0.508319\pi$
$719$	−1.40134	−0.0522612	−0.0261306	+	0.999659i	$0.508319\pi$
$720$	3.50011	0.130441
$721$	−4.45448	−0.165894
$722$	0	0
$723$	12.6684	0.471144
$724$	−24.2601	−0.901621
$725$	−2.76624	−0.102736
$726$	5.11547	0.189853
$727$	−46.9669	−1.74191	−0.870953	−	0.491367i	$-0.836497\pi$
$727$	−46.9669	−1.74191	−0.870953	+	0.491367i	$0.836497\pi$
$728$	1.37714	0.0510402
$729$	1.00000	0.0370370
$730$	−3.20140	−0.118489
$731$	8.49316	0.314131
$732$	−22.7079	−0.839308
$733$	−21.6068	−0.798066	−0.399033	−	0.916937i	$-0.630654\pi$
$733$	−21.6068	−0.798066	−0.399033	+	0.916937i	$0.630654\pi$
$734$	−6.43852	−0.237650
$735$	−6.76325	−0.249466
$736$	21.1219	0.778563
$737$	81.1526	2.98929
$738$	−0.750404	−0.0276228
$739$	−30.8126	−1.13346	−0.566729	−	0.823904i	$-0.691791\pi$
$739$	−30.8126	−1.13346	−0.566729	+	0.823904i	$0.691791\pi$
$740$	−12.1013	−0.444851
$741$	0	0
$742$	0.423882	0.0155612
$743$	−44.4286	−1.62993	−0.814964	−	0.579512i	$-0.803243\pi$
$743$	−44.4286	−1.62993	−0.814964	+	0.579512i	$0.803243\pi$
$744$	5.49875	0.201594
$745$	−2.67299	−0.0979308
$746$	−9.06215	−0.331789
$747$	−5.86106	−0.214445
$748$	34.9873	1.27926
$749$	0.0676029	0.00247016
$750$	0.290697	0.0106148
$751$	−14.8787	−0.542931	−0.271466	−	0.962448i	$-0.587508\pi$
$751$	−14.8787	−0.542931	−0.271466	+	0.962448i	$0.587508\pi$
$752$	38.8886	1.41812
$753$	−11.6241	−0.423605
$754$	−1.99955	−0.0728194
$755$	−5.95266	−0.216640
$756$	0.932031	0.0338976
$757$	23.4408	0.851972	0.425986	−	0.904730i	$-0.359927\pi$
$757$	23.4408	0.851972	0.425986	+	0.904730i	$0.359927\pi$
$758$	7.56827	0.274892
$759$	34.2911	1.24469
$760$	0	0
$761$	36.3224	1.31669	0.658344	−	0.752717i	$-0.271257\pi$
$761$	36.3224	1.31669	0.658344	+	0.752717i	$0.271257\pi$
$762$	2.85784	0.103529
$763$	−7.65379	−0.277086
$764$	−15.6262	−0.565335
$765$	−3.41561	−0.123492
$766$	0.620039	0.0224029
$767$	−31.6620	−1.14325
$768$	9.65968	0.348564
$769$	20.8104	0.750441	0.375220	−	0.926936i	$-0.377567\pi$
$769$	20.8104	0.750441	0.375220	+	0.926936i	$0.377567\pi$
$770$	−0.756401	−0.0272588
$771$	−10.5483	−0.379889
$772$	−6.44573	−0.231987
$773$	−3.56702	−0.128297	−0.0641484	−	0.997940i	$-0.520433\pi$
$773$	−3.56702	−0.128297	−0.0641484	+	0.997940i	$0.520433\pi$
$774$	−0.722840	−0.0259820
$775$	−4.83099	−0.173534
$776$	2.27645	0.0817197
$777$	−3.07397	−0.110278
$778$	−3.79147	−0.135931
$779$	0	0
$780$	−4.76302	−0.170544
$781$	53.0969	1.89996
$782$	−6.36690	−0.227680
$783$	−2.76624	−0.0988575
$784$	−23.6721	−0.845433
$785$	−7.20848	−0.257282
$786$	4.13639	0.147540
$787$	−44.5660	−1.58860	−0.794302	−	0.607523i	$-0.792163\pi$
$787$	−44.5660	−1.58860	−0.794302	+	0.607523i	$0.792163\pi$
$788$	−7.34399	−0.261619
$789$	23.7935	0.847071
$790$	−2.36416	−0.0841129
$791$	7.20186	0.256069
$792$	−6.08681	−0.216285
$793$	29.4779	1.04679
$794$	0.00832637	0.000295492 0
$795$	−2.99678	−0.106285
$796$	−24.3239	−0.862138
$797$	44.7396	1.58476	0.792378	−	0.610030i	$-0.208843\pi$
$797$	44.7396	1.58476	0.792378	+	0.610030i	$0.208843\pi$
$798$	0	0
$799$	−37.9496	−1.34256
$800$	3.29392	0.116458
$801$	6.51043	0.230035
$802$	7.94160	0.280428
$803$	−58.8927	−2.07828
$804$	−29.0684	−1.02516
$805$	−3.12010	−0.109969
$806$	−3.49203	−0.123002
$807$	4.22754	0.148816
$808$	−1.72628	−0.0607305
$809$	8.67442	0.304976	0.152488	−	0.988305i	$-0.451271\pi$
$809$	8.67442	0.304976	0.152488	+	0.988305i	$0.451271\pi$
$810$	0.290697	0.0102141
$811$	−26.7302	−0.938623	−0.469312	−	0.883033i	$-0.655498\pi$
$811$	−26.7302	−0.938623	−0.469312	+	0.883033i	$0.655498\pi$
$812$	−2.57823	−0.0904780
$813$	31.1471	1.09238
$814$	9.82093	0.344223
$815$	14.1756	0.496551
$816$	−11.9550	−0.418509
$817$	0	0
$818$	1.95906	0.0684968
$819$	−1.20990	−0.0422775
$820$	4.94465	0.172675
$821$	−9.44863	−0.329759	−0.164880	−	0.986314i	$-0.552724\pi$
$821$	−9.44863	−0.329759	−0.164880	+	0.986314i	$0.552724\pi$
$822$	1.91406	0.0667607
$823$	−19.4668	−0.678570	−0.339285	−	0.940684i	$-0.610185\pi$
$823$	−19.4668	−0.678570	−0.339285	+	0.940684i	$0.610185\pi$
$824$	−10.4202	−0.363004
$825$	5.34764	0.186181
$826$	1.80105	0.0626667
$827$	37.0018	1.28668	0.643340	−	0.765581i	$-0.277548\pi$
$827$	37.0018	1.28668	0.643340	+	0.765581i	$0.277548\pi$
$828$	−12.2829	−0.426860
$829$	−20.5418	−0.713448	−0.356724	−	0.934210i	$-0.616106\pi$
$829$	−20.5418	−0.713448	−0.356724	+	0.934210i	$0.616106\pi$
$830$	−1.70379	−0.0591396
$831$	1.05393	0.0365603
$832$	−15.0256	−0.520919
$833$	23.1006	0.800388
$834$	0.0679523	0.00235299
$835$	−12.5563	−0.434530
$836$	0	0
$837$	−4.83099	−0.166983
$838$	7.67661	0.265184
$839$	47.7891	1.64986	0.824932	−	0.565233i	$-0.191214\pi$
$839$	47.7891	1.64986	0.824932	+	0.565233i	$0.191214\pi$
$840$	0.553831	0.0191090
$841$	−21.3479	−0.736134
$842$	−11.0144	−0.379580
$843$	−25.6354	−0.882928
$844$	−17.5394	−0.603730
$845$	−6.81695	−0.234510
$846$	3.22984	0.111044
$847$	−8.56237	−0.294206
$848$	−10.4891	−0.360196
$849$	29.4112	1.00939
$850$	−0.992907	−0.0340564
$851$	40.5107	1.38869
$852$	−19.0190	−0.651581
$853$	11.4326	0.391446	0.195723	−	0.980659i	$-0.437295\pi$
$853$	11.4326	0.391446	0.195723	+	0.980659i	$0.437295\pi$
$854$	−1.67682	−0.0573795
$855$	0	0
$856$	0.158141	0.00540513
$857$	−5.57043	−0.190282	−0.0951412	−	0.995464i	$-0.530330\pi$
$857$	−5.57043	−0.190282	−0.0951412	+	0.995464i	$0.530330\pi$
$858$	3.86549	0.131966
$859$	−17.0142	−0.580517	−0.290258	−	0.956948i	$-0.593741\pi$
$859$	−17.0142	−0.580517	−0.290258	+	0.956948i	$0.593741\pi$
$860$	4.76302	0.162418
$861$	1.25604	0.0428058
$862$	5.58304	0.190159
$863$	−46.8850	−1.59598	−0.797992	−	0.602668i	$-0.794104\pi$
$863$	−46.8850	−1.59598	−0.797992	+	0.602668i	$0.794104\pi$
$864$	3.29392	0.112061
$865$	−2.18964	−0.0744500
$866$	−4.92768	−0.167449
$867$	−5.33363	−0.181140
$868$	−4.50263	−0.152829
$869$	−43.4908	−1.47532
$870$	−0.804139	−0.0272629
$871$	37.7348	1.27859
$872$	−17.9042	−0.606313
$873$	−2.00000	−0.0676897
$874$	0	0
$875$	−0.486575	−0.0164492
$876$	21.0950	0.712735
$877$	29.7844	1.00575	0.502873	−	0.864360i	$-0.332276\pi$
$877$	29.7844	1.00575	0.502873	+	0.864360i	$0.332276\pi$
$878$	−3.22757	−0.108925
$879$	10.8548	0.366125
$880$	18.7173	0.630961
$881$	−20.4884	−0.690271	−0.345135	−	0.938553i	$-0.612167\pi$
$881$	−20.4884	−0.690271	−0.345135	+	0.938553i	$0.612167\pi$
$882$	−1.96606	−0.0662006
$883$	31.4804	1.05940	0.529699	−	0.848186i	$-0.322305\pi$
$883$	31.4804	1.05940	0.529699	+	0.848186i	$0.322305\pi$
$884$	16.2686	0.547173
$885$	−12.7332	−0.428021
$886$	−4.03900	−0.135693
$887$	33.6103	1.12852	0.564262	−	0.825596i	$-0.309161\pi$
$887$	33.6103	1.12852	0.564262	+	0.825596i	$0.309161\pi$
$888$	−7.19080	−0.241307
$889$	−4.78351	−0.160434
$890$	1.89256	0.0634389
$891$	5.34764	0.179153
$892$	20.8742	0.698919
$893$	0	0
$894$	−0.777031	−0.0259878
$895$	−7.50421	−0.250838
$896$	4.06019	0.135641
$897$	15.9449	0.532384
$898$	−8.10099	−0.270334
$899$	13.3637	0.445704
$900$	−1.91550	−0.0638498
$901$	10.2358	0.341004
$902$	−4.01289	−0.133615
$903$	1.20990	0.0402631
$904$	16.8470	0.560323
$905$	12.6652	0.421006
$906$	−1.73042	−0.0574894
$907$	−21.9494	−0.728819	−0.364410	−	0.931239i	$-0.618729\pi$
$907$	−21.9494	−0.728819	−0.364410	+	0.931239i	$0.618729\pi$
$908$	−47.1885	−1.56600
$909$	1.51665	0.0503040
$910$	−0.351716	−0.0116593
$911$	−21.2865	−0.705253	−0.352626	−	0.935764i	$-0.614711\pi$
$911$	−21.2865	−0.705253	−0.352626	+	0.935764i	$0.614711\pi$
$912$	0	0
$913$	−31.3428	−1.03730
$914$	−10.6296	−0.351597
$915$	11.8548	0.391909
$916$	−32.8845	−1.08653
$917$	−6.92356	−0.228636
$918$	−0.992907	−0.0327708
$919$	−2.61948	−0.0864087	−0.0432043	−	0.999066i	$-0.513757\pi$
$919$	−2.61948	−0.0864087	−0.0432043	+	0.999066i	$0.513757\pi$
$920$	−7.29873	−0.240632
$921$	−33.6891	−1.11009
$922$	6.37151	0.209834
$923$	24.6893	0.812658
$924$	4.98417	0.163967
$925$	6.31756	0.207720
$926$	−4.07718	−0.133984
$927$	9.15478	0.300682
$928$	−9.11178	−0.299109
$929$	3.82474	0.125486	0.0627428	−	0.998030i	$-0.480015\pi$
$929$	3.82474	0.125486	0.0627428	+	0.998030i	$0.480015\pi$
$930$	−1.40436	−0.0460506
$931$	0	0
$932$	−54.5210	−1.78589
$933$	−11.7221	−0.383765
$934$	9.86319	0.322733
$935$	−18.2654	−0.597343
$936$	−2.83028	−0.0925105
$937$	−7.39167	−0.241475	−0.120738	−	0.992684i	$-0.538526\pi$
$937$	−7.39167	−0.241475	−0.120738	+	0.992684i	$0.538526\pi$
$938$	−2.14650	−0.0700856
$939$	4.47856	0.146152
$940$	−21.2824	−0.694156
$941$	−48.6115	−1.58469	−0.792344	−	0.610075i	$-0.791139\pi$
$941$	−48.6115	−1.58469	−0.792344	+	0.610075i	$0.791139\pi$
$942$	−2.09548	−0.0682746
$943$	−16.5529	−0.539036
$944$	−44.5675	−1.45055
$945$	−0.486575	−0.0158283
$946$	−3.86549	−0.125678
$947$	−36.0207	−1.17051	−0.585257	−	0.810848i	$-0.699006\pi$
$947$	−36.0207	−1.17051	−0.585257	+	0.810848i	$0.699006\pi$
$948$	15.5782	0.505956
$949$	−27.3843	−0.888930
$950$	0	0
$951$	−12.3873	−0.401687
$952$	−1.89167	−0.0613093
$953$	−11.2121	−0.363196	−0.181598	−	0.983373i	$-0.558127\pi$
$953$	−11.2121	−0.363196	−0.181598	+	0.983373i	$0.558127\pi$
$954$	−0.871155	−0.0282047
$955$	8.15777	0.263979
$956$	−7.81026	−0.252602
$957$	−14.7929	−0.478186
$958$	9.28769	0.300072
$959$	−3.20380	−0.103456
$960$	−6.04269	−0.195027
$961$	−7.66153	−0.247146
$962$	4.56659	0.147233
$963$	−0.138936	−0.00447716
$964$	−24.2663	−0.781565
$965$	3.36505	0.108325
$966$	−0.907005	−0.0291824
$967$	−10.0461	−0.323062	−0.161531	−	0.986868i	$-0.551643\pi$
$967$	−10.0461	−0.323062	−0.161531	+	0.986868i	$0.551643\pi$
$968$	−20.0296	−0.643775
$969$	0	0
$970$	−0.581394	−0.0186674
$971$	37.8989	1.21623	0.608117	−	0.793847i	$-0.291925\pi$
$971$	37.8989	1.21623	0.608117	+	0.793847i	$0.291925\pi$
$972$	−1.91550	−0.0614395
$973$	−0.113740	−0.00364633
$974$	−10.9369	−0.350440
$975$	2.48657	0.0796341
$976$	41.4933	1.32817
$977$	−44.6435	−1.42827	−0.714135	−	0.700008i	$-0.753180\pi$
$977$	−44.6435	−1.42827	−0.714135	+	0.700008i	$0.753180\pi$
$978$	4.12082	0.131769
$979$	34.8154	1.11271
$980$	12.9550	0.413831
$981$	15.7299	0.502219
$982$	−11.6524	−0.371842
$983$	12.5091	0.398978	0.199489	−	0.979900i	$-0.436072\pi$
$983$	12.5091	0.398978	0.199489	+	0.979900i	$0.436072\pi$
$984$	2.93820	0.0936665
$985$	3.83399	0.122161
$986$	2.74662	0.0874703
$987$	−5.40616	−0.172080
$988$	0	0
$989$	−15.9449	−0.507017
$990$	1.55454	0.0494066
$991$	−50.3007	−1.59785	−0.798927	−	0.601428i	$-0.794599\pi$
$991$	−50.3007	−1.59785	−0.798927	+	0.601428i	$0.794599\pi$
$992$	−15.9129	−0.505235
$993$	−24.5058	−0.777667
$994$	−1.40442	−0.0445455
$995$	12.6985	0.402569
$996$	11.2268	0.355736
$997$	12.9375	0.409735	0.204867	−	0.978790i	$-0.434324\pi$
$997$	12.9375	0.409735	0.204867	+	0.978790i	$0.434324\pi$
$998$	−8.81007	−0.278878
$999$	6.31756	0.199879

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5415.2.a.z.1.3		5
19.8	odd	6		285.2.i.f.121.3	yes	10
19.12	odd	6		285.2.i.f.106.3	✓	10
19.18	odd	2		5415.2.a.y.1.3		5
57.8	even	6		855.2.k.i.406.3		10
57.50	even	6		855.2.k.i.676.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.f.106.3	✓	10	19.12	odd	6
285.2.i.f.121.3	yes	10	19.8	odd	6
855.2.k.i.406.3		10	57.8	even	6
855.2.k.i.676.3		10	57.50	even	6
5415.2.a.y.1.3		5	19.18	odd	2
5415.2.a.z.1.3		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5415 = 3 \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5415.a (trivial)

\(f(q)\)	\(=\)	\(q+0.290697 q^{2} +1.00000 q^{3} -1.91550 q^{4} +1.00000 q^{5} +0.290697 q^{6} -0.486575 q^{7} -1.13822 q^{8} +1.00000 q^{9} +0.290697 q^{10} +5.34764 q^{11} -1.91550 q^{12} +2.48657 q^{13} -0.141446 q^{14} +1.00000 q^{15} +3.50011 q^{16} -3.41561 q^{17} +0.290697 q^{18} -1.91550 q^{20} -0.486575 q^{21} +1.55454 q^{22} +6.41238 q^{23} -1.13822 q^{24} +1.00000 q^{25} +0.722840 q^{26} +1.00000 q^{27} +0.932031 q^{28} -2.76624 q^{29} +0.290697 q^{30} -4.83099 q^{31} +3.29392 q^{32} +5.34764 q^{33} -0.992907 q^{34} -0.486575 q^{35} -1.91550 q^{36} +6.31756 q^{37} +2.48657 q^{39} -1.13822 q^{40} -2.58139 q^{41} -0.141446 q^{42} -2.48657 q^{43} -10.2434 q^{44} +1.00000 q^{45} +1.86406 q^{46} +11.1107 q^{47} +3.50011 q^{48} -6.76325 q^{49} +0.290697 q^{50} -3.41561 q^{51} -4.76302 q^{52} -2.99678 q^{53} +0.290697 q^{54} +5.34764 q^{55} +0.553831 q^{56} -0.804139 q^{58} -12.7332 q^{59} -1.91550 q^{60} +11.8548 q^{61} -1.40436 q^{62} -0.486575 q^{63} -6.04269 q^{64} +2.48657 q^{65} +1.55454 q^{66} +15.1754 q^{67} +6.54258 q^{68} +6.41238 q^{69} -0.141446 q^{70} +9.92903 q^{71} -1.13822 q^{72} -11.0128 q^{73} +1.83650 q^{74} +1.00000 q^{75} -2.60202 q^{77} +0.722840 q^{78} -8.13272 q^{79} +3.50011 q^{80} +1.00000 q^{81} -0.750404 q^{82} -5.86106 q^{83} +0.932031 q^{84} -3.41561 q^{85} -0.722840 q^{86} -2.76624 q^{87} -6.08681 q^{88} +6.51043 q^{89} +0.290697 q^{90} -1.20990 q^{91} -12.2829 q^{92} -4.83099 q^{93} +3.22984 q^{94} +3.29392 q^{96} -2.00000 q^{97} -1.96606 q^{98} +5.34764 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 5 q^{3} + 7 q^{4} + 5 q^{5} + q^{6} + 2 q^{7} + 6 q^{8} + 5 q^{9} + q^{10} + 5 q^{11} + 7 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} + 7 q^{16} + 10 q^{17} + q^{18} + 7 q^{20} + 2 q^{21}+ \cdots + 5 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 7 * q^4 + 5 * q^5 + q^6 + 2 * q^7 + 6 * q^8 + 5 * q^9 + q^10 + 5 * q^11 + 7 * q^12 + 8 * q^13 + 4 * q^14 + 5 * q^15 + 7 * q^16 + 10 * q^17 + q^18 + 7 * q^20 + 2 * q^21 - 2 * q^22 - 2 * q^23 + 6 * q^24 + 5 * q^25 - 2 * q^26 + 5 * q^27 + 10 * q^28 + 7 * q^29 + q^30 + 9 * q^31 + 23 * q^32 + 5 * q^33 - 25 * q^34 + 2 * q^35 + 7 * q^36 - 6 * q^37 + 8 * q^39 + 6 * q^40 - 12 * q^41 + 4 * q^42 - 8 * q^43 + 16 * q^44 + 5 * q^45 + 20 * q^46 + 6 * q^47 + 7 * q^48 + 15 * q^49 + q^50 + 10 * q^51 + 4 * q^52 - 8 * q^53 + q^54 + 5 * q^55 - 36 * q^56 + 38 * q^58 + q^59 + 7 * q^60 + 7 * q^61 + 15 * q^62 + 2 * q^63 + 14 * q^64 + 8 * q^65 - 2 * q^66 + 14 * q^67 - q^68 - 2 * q^69 + 4 * q^70 + 27 * q^71 + 6 * q^72 + 26 * q^73 - 18 * q^74 + 5 * q^75 + 14 * q^77 - 2 * q^78 - 23 * q^79 + 7 * q^80 + 5 * q^81 - 36 * q^82 - 12 * q^83 + 10 * q^84 + 10 * q^85 + 2 * q^86 + 7 * q^87 + 9 * q^89 + q^90 - 46 * q^91 - 52 * q^92 + 9 * q^93 - 45 * q^94 + 23 * q^96 - 10 * q^97 - 21 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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