LMFDB - Embedded newform 1150.2.b.i.599.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(599,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("1150.599");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$9.18279623245$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			599.4
Root			$0.618034i$ of defining polynomial
Character	$\chi$	$=$	1150.599
Dual form			1150.2.b.i.599.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +0.618034i q^{3} -1.00000 q^{4} -0.618034 q^{6} +1.61803i q^{7} -1.00000i q^{8} +2.61803 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +0.618034i q^{3} -1.00000 q^{4} -0.618034 q^{6} +1.61803i q^{7} -1.00000i q^{8} +2.61803 q^{9} +3.85410 q^{11} -0.618034i q^{12} -4.09017i q^{13} -1.61803 q^{14} +1.00000 q^{16} -5.09017i q^{17} +2.61803i q^{18} +4.85410 q^{19} -1.00000 q^{21} +3.85410i q^{22} -1.00000i q^{23} +0.618034 q^{24} +4.09017 q^{26} +3.47214i q^{27} -1.61803i q^{28} +4.76393 q^{29} -2.09017 q^{31} +1.00000i q^{32} +2.38197i q^{33} +5.09017 q^{34} -2.61803 q^{36} -2.47214i q^{37} +4.85410i q^{38} +2.52786 q^{39} -12.3262 q^{41} -1.00000i q^{42} -3.85410 q^{44} +1.00000 q^{46} +9.70820i q^{47} +0.618034i q^{48} +4.38197 q^{49} +3.14590 q^{51} +4.09017i q^{52} +8.47214i q^{53} -3.47214 q^{54} +1.61803 q^{56} +3.00000i q^{57} +4.76393i q^{58} +11.7082 q^{59} +6.32624 q^{61} -2.09017i q^{62} +4.23607i q^{63} -1.00000 q^{64} -2.38197 q^{66} +5.52786i q^{67} +5.09017i q^{68} +0.618034 q^{69} +7.09017 q^{71} -2.61803i q^{72} +1.23607i q^{73} +2.47214 q^{74} -4.85410 q^{76} +6.23607i q^{77} +2.52786i q^{78} -10.4721 q^{79} +5.70820 q^{81} -12.3262i q^{82} -10.9443i q^{83} +1.00000 q^{84} +2.94427i q^{87} -3.85410i q^{88} +1.52786 q^{89} +6.61803 q^{91} +1.00000i q^{92} -1.29180i q^{93} -9.70820 q^{94} -0.618034 q^{96} +14.6180i q^{97} +4.38197i q^{98} +10.0902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 2 q^{6} + 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 2 * q^6 + 6 * q^9	$ 4 q - 4 q^{4} + 2 q^{6} + 6 q^{9} + 2 q^{11} - 2 q^{14} + 4 q^{16} + 6 q^{19} - 4 q^{21} - 2 q^{24} - 6 q^{26} + 28 q^{29} + 14 q^{31} - 2 q^{34} - 6 q^{36} + 28 q^{39} - 18 q^{41} - 2 q^{44} + 4 q^{46} + 22 q^{49} + 26 q^{51} + 4 q^{54} + 2 q^{56} + 20 q^{59} - 6 q^{61} - 4 q^{64} - 14 q^{66} - 2 q^{69} + 6 q^{71} - 8 q^{74} - 6 q^{76} - 24 q^{79} - 4 q^{81} + 4 q^{84} + 24 q^{89} + 22 q^{91} - 12 q^{94} + 2 q^{96} + 18 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 2 * q^6 + 6 * q^9 + 2 * q^11 - 2 * q^14 + 4 * q^16 + 6 * q^19 - 4 * q^21 - 2 * q^24 - 6 * q^26 + 28 * q^29 + 14 * q^31 - 2 * q^34 - 6 * q^36 + 28 * q^39 - 18 * q^41 - 2 * q^44 + 4 * q^46 + 22 * q^49 + 26 * q^51 + 4 * q^54 + 2 * q^56 + 20 * q^59 - 6 * q^61 - 4 * q^64 - 14 * q^66 - 2 * q^69 + 6 * q^71 - 8 * q^74 - 6 * q^76 - 24 * q^79 - 4 * q^81 + 4 * q^84 + 24 * q^89 + 22 * q^91 - 12 * q^94 + 2 * q^96 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	0.618034i	0.356822i	0.983956	+	0.178411i	$0.0570957\pi$
$3$	0.618034i	0.356822i	−0.983956	+	0.178411i	$0.942904\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−0.618034	−0.252311
$7$	1.61803i	0.611559i	0.952102	+	0.305780i	$0.0989171\pi$
$7$	1.61803i	0.611559i	−0.952102	+	0.305780i	$0.901083\pi$
$8$	− 1.00000i	− 0.353553i
$9$	2.61803	0.872678
$10$	0	0
$11$	3.85410	1.16206	0.581028	−	0.813884i	$-0.302651\pi$
$11$	3.85410	1.16206	0.581028	+	0.813884i	$0.302651\pi$
$12$	− 0.618034i	− 0.178411i
$13$	− 4.09017i	− 1.13441i	−0.823577	−	0.567205i	$-0.808025\pi$
$13$	− 4.09017i	− 1.13441i	0.823577	−	0.567205i	$-0.191975\pi$
$14$	−1.61803	−0.432438
$15$	0	0
$16$	1.00000	0.250000
$17$	− 5.09017i	− 1.23455i	−0.786748	−	0.617274i	$-0.788237\pi$
$17$	− 5.09017i	− 1.23455i	0.786748	−	0.617274i	$-0.211763\pi$
$18$	2.61803i	0.617077i
$19$	4.85410	1.11361	0.556804	−	0.830644i	$-0.312028\pi$
$19$	4.85410	1.11361	0.556804	+	0.830644i	$0.312028\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	3.85410i	0.821697i
$23$	− 1.00000i	− 0.208514i
$23$	− 1.00000i	− 0.208514i
$24$	0.618034	0.126156
$25$	0	0
$26$	4.09017	0.802148
$27$	3.47214i	0.668213i
$28$	− 1.61803i	− 0.305780i
$29$	4.76393	0.884640	0.442320	−	0.896857i	$-0.354156\pi$
$29$	4.76393	0.884640	0.442320	+	0.896857i	$0.354156\pi$
$30$	0	0
$31$	−2.09017	−0.375406	−0.187703	−	0.982226i	$-0.560104\pi$
$31$	−2.09017	−0.375406	−0.187703	+	0.982226i	$0.560104\pi$
$32$	1.00000i	0.176777i
$33$	2.38197i	0.414647i
$34$	5.09017	0.872957
$35$	0	0
$36$	−2.61803	−0.436339
$37$	− 2.47214i	− 0.406417i	−0.979136	−	0.203208i	$-0.934863\pi$
$37$	− 2.47214i	− 0.406417i	0.979136	−	0.203208i	$-0.0651369\pi$
$38$	4.85410i	0.787439i
$39$	2.52786	0.404782
$40$	0	0
$41$	−12.3262	−1.92503	−0.962517	−	0.271220i	$-0.912573\pi$
$41$	−12.3262	−1.92503	−0.962517	+	0.271220i	$0.912573\pi$
$42$	− 1.00000i	− 0.154303i
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	−3.85410	−0.581028
$45$	0	0
$46$	1.00000	0.147442
$47$	9.70820i	1.41609i	0.706169	+	0.708044i	$0.250422\pi$
$47$	9.70820i	1.41609i	−0.706169	+	0.708044i	$0.749578\pi$
$48$	0.618034i	0.0892055i
$49$	4.38197	0.625995
$50$	0	0
$51$	3.14590	0.440514
$52$	4.09017i	0.567205i
$53$	8.47214i	1.16374i	0.813283	+	0.581869i	$0.197678\pi$
$53$	8.47214i	1.16374i	−0.813283	+	0.581869i	$0.802322\pi$
$54$	−3.47214	−0.472498
$55$	0	0
$56$	1.61803	0.216219
$57$	3.00000i	0.397360i
$58$	4.76393i	0.625535i
$59$	11.7082	1.52428	0.762139	−	0.647413i	$-0.224149\pi$
$59$	11.7082	1.52428	0.762139	+	0.647413i	$0.224149\pi$
$60$	0	0
$61$	6.32624	0.809992	0.404996	−	0.914319i	$-0.367273\pi$
$61$	6.32624	0.809992	0.404996	+	0.914319i	$0.367273\pi$
$62$	− 2.09017i	− 0.265452i
$63$	4.23607i	0.533694i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−2.38197	−0.293200
$67$	5.52786i	0.675336i	0.941265	+	0.337668i	$0.109638\pi$
$67$	5.52786i	0.675336i	−0.941265	+	0.337668i	$0.890362\pi$
$68$	5.09017i	0.617274i
$69$	0.618034	0.0744025
$70$	0	0
$71$	7.09017	0.841448	0.420724	−	0.907189i	$-0.361776\pi$
$71$	7.09017	0.841448	0.420724	+	0.907189i	$0.361776\pi$
$72$	− 2.61803i	− 0.308538i
$73$	1.23607i	0.144671i	0.997380	+	0.0723354i	$0.0230452\pi$
$73$	1.23607i	0.144671i	−0.997380	+	0.0723354i	$0.976955\pi$
$74$	2.47214	0.287380
$75$	0	0
$76$	−4.85410	−0.556804
$77$	6.23607i	0.710666i
$78$	2.52786i	0.286224i
$79$	−10.4721	−1.17821	−0.589104	−	0.808057i	$-0.700519\pi$
$79$	−10.4721	−1.17821	−0.589104	+	0.808057i	$0.700519\pi$
$80$	0	0
$81$	5.70820	0.634245
$82$	− 12.3262i	− 1.36121i
$83$	− 10.9443i	− 1.20129i	−0.799516	−	0.600645i	$-0.794911\pi$
$83$	− 10.9443i	− 1.20129i	0.799516	−	0.600645i	$-0.205089\pi$
$84$	1.00000	0.109109
$85$	0	0
$86$	0	0
$87$	2.94427i	0.315659i
$88$	− 3.85410i	− 0.410849i
$89$	1.52786	0.161953	0.0809766	−	0.996716i	$-0.474196\pi$
$89$	1.52786	0.161953	0.0809766	+	0.996716i	$0.474196\pi$
$90$	0	0
$91$	6.61803	0.693758
$92$	1.00000i	0.104257i
$93$	− 1.29180i	− 0.133953i
$94$	−9.70820	−1.00132
$95$	0	0
$96$	−0.618034	−0.0630778
$97$	14.6180i	1.48424i	0.670269	+	0.742118i	$0.266179\pi$
$97$	14.6180i	1.48424i	−0.670269	+	0.742118i	$0.733821\pi$
$98$	4.38197i	0.442645i
$99$	10.0902	1.01410
$100$	0	0
$101$	−13.7082	−1.36402	−0.682009	−	0.731344i	$-0.738893\pi$
$101$	−13.7082	−1.36402	−0.682009	+	0.731344i	$0.738893\pi$
$102$	3.14590i	0.311490i
$103$	3.56231i	0.351004i	0.984479	+	0.175502i	$0.0561549\pi$
$103$	3.56231i	0.351004i	−0.984479	+	0.175502i	$0.943845\pi$
$104$	−4.09017	−0.401074
$105$	0	0
$106$	−8.47214	−0.822887
$107$	− 4.18034i	− 0.404129i	−0.979372	−	0.202064i	$-0.935235\pi$
$107$	− 4.18034i	− 0.404129i	0.979372	−	0.202064i	$-0.0647650\pi$
$108$	− 3.47214i	− 0.334106i
$109$	−8.56231	−0.820120	−0.410060	−	0.912059i	$-0.634492\pi$
$109$	−8.56231	−0.820120	−0.410060	+	0.912059i	$0.634492\pi$
$110$	0	0
$111$	1.52786	0.145018
$112$	1.61803i	0.152890i
$113$	− 18.9443i	− 1.78213i	−0.453878	−	0.891064i	$-0.649960\pi$
$113$	− 18.9443i	− 1.78213i	0.453878	−	0.891064i	$-0.350040\pi$
$114$	−3.00000	−0.280976
$115$	0	0
$116$	−4.76393	−0.442320
$117$	− 10.7082i	− 0.989974i
$118$	11.7082i	1.07783i
$119$	8.23607	0.754999
$120$	0	0
$121$	3.85410	0.350373
$122$	6.32624i	0.572751i
$123$	− 7.61803i	− 0.686895i
$124$	2.09017	0.187703
$125$	0	0
$126$	−4.23607	−0.377379
$127$	− 6.18034i	− 0.548416i	−0.961670	−	0.274208i	$-0.911584\pi$
$127$	− 6.18034i	− 0.548416i	0.961670	−	0.274208i	$-0.0884158\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	0	0
$130$	0	0
$131$	−14.9443	−1.30569	−0.652844	−	0.757493i	$-0.726424\pi$
$131$	−14.9443	−1.30569	−0.652844	+	0.757493i	$0.726424\pi$
$132$	− 2.38197i	− 0.207324i
$133$	7.85410i	0.681037i
$134$	−5.52786	−0.477535
$135$	0	0
$136$	−5.09017	−0.436478
$137$	5.32624i	0.455051i	0.973772	+	0.227526i	$0.0730635\pi$
$137$	5.32624i	0.455051i	−0.973772	+	0.227526i	$0.926936\pi$
$138$	0.618034i	0.0526105i
$139$	−17.2361	−1.46194	−0.730972	−	0.682407i	$-0.760933\pi$
$139$	−17.2361	−1.46194	−0.730972	+	0.682407i	$0.760933\pi$
$140$	0	0
$141$	−6.00000	−0.505291
$142$	7.09017i	0.594994i
$143$	− 15.7639i	− 1.31825i
$144$	2.61803	0.218169
$145$	0	0
$146$	−1.23607	−0.102298
$147$	2.70820i	0.223369i
$148$	2.47214i	0.203208i
$149$	1.14590	0.0938756	0.0469378	−	0.998898i	$-0.485054\pi$
$149$	1.14590	0.0938756	0.0469378	+	0.998898i	$0.485054\pi$
$150$	0	0
$151$	17.5623	1.42920	0.714600	−	0.699533i	$-0.246609\pi$
$151$	17.5623	1.42920	0.714600	+	0.699533i	$0.246609\pi$
$152$	− 4.85410i	− 0.393720i
$153$	− 13.3262i	− 1.07736i
$154$	−6.23607	−0.502517
$155$	0	0
$156$	−2.52786	−0.202391
$157$	9.70820i	0.774799i	0.921912	+	0.387400i	$0.126627\pi$
$157$	9.70820i	0.774799i	−0.921912	+	0.387400i	$0.873373\pi$
$158$	− 10.4721i	− 0.833118i
$159$	−5.23607	−0.415247
$160$	0	0
$161$	1.61803	0.127519
$162$	5.70820i	0.448479i
$163$	− 3.61803i	− 0.283386i	−0.989911	−	0.141693i	$-0.954745\pi$
$163$	− 3.61803i	− 0.283386i	0.989911	−	0.141693i	$-0.0452546\pi$
$164$	12.3262	0.962517
$165$	0	0
$166$	10.9443	0.849440
$167$	− 8.00000i	− 0.619059i	−0.950890	−	0.309529i	$-0.899829\pi$
$167$	− 8.00000i	− 0.619059i	0.950890	−	0.309529i	$-0.100171\pi$
$168$	1.00000i	0.0771517i
$169$	−3.72949	−0.286884
$170$	0	0
$171$	12.7082	0.971821
$172$	0	0
$173$	21.5623i	1.63935i	0.572828	+	0.819676i	$0.305846\pi$
$173$	21.5623i	1.63935i	−0.572828	+	0.819676i	$0.694154\pi$
$174$	−2.94427	−0.223205
$175$	0	0
$176$	3.85410	0.290514
$177$	7.23607i	0.543896i
$178$	1.52786i	0.114518i
$179$	20.1803	1.50835	0.754175	−	0.656674i	$-0.228037\pi$
$179$	20.1803	1.50835	0.754175	+	0.656674i	$0.228037\pi$
$180$	0	0
$181$	−18.8541	−1.40141	−0.700707	−	0.713449i	$-0.747132\pi$
$181$	−18.8541	−1.40141	−0.700707	+	0.713449i	$0.747132\pi$
$182$	6.61803i	0.490561i
$183$	3.90983i	0.289023i
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	1.29180	0.0947191
$187$	− 19.6180i	− 1.43461i
$188$	− 9.70820i	− 0.708044i
$189$	−5.61803	−0.408652
$190$	0	0
$191$	−0.291796	−0.0211136	−0.0105568	−	0.999944i	$-0.503360\pi$
$191$	−0.291796	−0.0211136	−0.0105568	+	0.999944i	$0.503360\pi$
$192$	− 0.618034i	− 0.0446028i
$193$	− 5.23607i	− 0.376900i	−0.982083	−	0.188450i	$-0.939654\pi$
$193$	− 5.23607i	− 0.376900i	0.982083	−	0.188450i	$-0.0603464\pi$
$194$	−14.6180	−1.04951
$195$	0	0
$196$	−4.38197	−0.312998
$197$	− 2.43769i	− 0.173679i	−0.996222	−	0.0868393i	$-0.972323\pi$
$197$	− 2.43769i	− 0.173679i	0.996222	−	0.0868393i	$-0.0276767\pi$
$198$	10.0902i	0.717077i
$199$	−2.00000	−0.141776	−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000	−0.141776	−0.0708881	+	0.997484i	$0.522583\pi$
$200$	0	0
$201$	−3.41641	−0.240975
$202$	− 13.7082i	− 0.964506i
$203$	7.70820i	0.541010i
$204$	−3.14590	−0.220257
$205$	0	0
$206$	−3.56231	−0.248198
$207$	− 2.61803i	− 0.181966i
$208$	− 4.09017i	− 0.283602i
$209$	18.7082	1.29407
$210$	0	0
$211$	14.0000	0.963800	0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000	0.963800	0.481900	+	0.876226i	$0.339947\pi$
$212$	− 8.47214i	− 0.581869i
$213$	4.38197i	0.300247i
$214$	4.18034	0.285762
$215$	0	0
$216$	3.47214	0.236249
$217$	− 3.38197i	− 0.229583i
$218$	− 8.56231i	− 0.579913i
$219$	−0.763932	−0.0516217
$220$	0	0
$221$	−20.8197	−1.40048
$222$	1.52786i	0.102544i
$223$	3.05573i	0.204627i	0.994752	+	0.102313i	$0.0326244\pi$
$223$	3.05573i	0.204627i	−0.994752	+	0.102313i	$0.967376\pi$
$224$	−1.61803	−0.108109
$225$	0	0
$226$	18.9443	1.26015
$227$	− 23.2361i	− 1.54223i	−0.636695	−	0.771116i	$-0.719699\pi$
$227$	− 23.2361i	− 1.54223i	0.636695	−	0.771116i	$-0.280301\pi$
$228$	− 3.00000i	− 0.198680i
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	0	0
$231$	−3.85410	−0.253581
$232$	− 4.76393i	− 0.312767i
$233$	− 19.7082i	− 1.29113i	−0.763706	−	0.645564i	$-0.776622\pi$
$233$	− 19.7082i	− 1.29113i	0.763706	−	0.645564i	$-0.223378\pi$
$234$	10.7082	0.700017
$235$	0	0
$236$	−11.7082	−0.762139
$237$	− 6.47214i	− 0.420410i
$238$	8.23607i	0.533865i
$239$	−24.3607	−1.57576	−0.787881	−	0.615828i	$-0.788822\pi$
$239$	−24.3607	−1.57576	−0.787881	+	0.615828i	$0.788822\pi$
$240$	0	0
$241$	0	0		−	1.00000i	$-0.5\pi$
$241$	0	0			1.00000i	$0.5\pi$
$242$	3.85410i	0.247751i
$243$	13.9443i	0.894525i
$244$	−6.32624	−0.404996
$245$	0	0
$246$	7.61803	0.485708
$247$	− 19.8541i	− 1.26329i
$248$	2.09017i	0.132726i
$249$	6.76393	0.428647
$250$	0	0
$251$	12.8541	0.811344	0.405672	−	0.914019i	$-0.367038\pi$
$251$	12.8541	0.811344	0.405672	+	0.914019i	$0.367038\pi$
$252$	− 4.23607i	− 0.266847i
$253$	− 3.85410i	− 0.242305i
$254$	6.18034	0.387789
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 30.1803i	− 1.88260i	−0.337574	−	0.941299i	$-0.609606\pi$
$257$	− 30.1803i	− 1.88260i	0.337574	−	0.941299i	$-0.390394\pi$
$258$	0	0
$259$	4.00000	0.248548
$260$	0	0
$261$	12.4721	0.772006
$262$	− 14.9443i	− 0.923260i
$263$	21.7426i	1.34071i	0.742041	+	0.670354i	$0.233858\pi$
$263$	21.7426i	1.34071i	−0.742041	+	0.670354i	$0.766142\pi$
$264$	2.38197	0.146600
$265$	0	0
$266$	−7.85410	−0.481566
$267$	0.944272i	0.0577885i
$268$	− 5.52786i	− 0.337668i
$269$	−8.18034	−0.498764	−0.249382	−	0.968405i	$-0.580227\pi$
$269$	−8.18034	−0.498764	−0.249382	+	0.968405i	$0.580227\pi$
$270$	0	0
$271$	−14.6738	−0.891368	−0.445684	−	0.895190i	$-0.647039\pi$
$271$	−14.6738	−0.891368	−0.445684	+	0.895190i	$0.647039\pi$
$272$	− 5.09017i	− 0.308637i
$273$	4.09017i	0.247548i
$274$	−5.32624	−0.321770
$275$	0	0
$276$	−0.618034	−0.0372013
$277$	2.58359i	0.155233i	0.996983	+	0.0776165i	$0.0247310\pi$
$277$	2.58359i	0.155233i	−0.996983	+	0.0776165i	$0.975269\pi$
$278$	− 17.2361i	− 1.03375i
$279$	−5.47214	−0.327608
$280$	0	0
$281$	27.2361	1.62477	0.812384	−	0.583123i	$-0.198169\pi$
$281$	27.2361	1.62477	0.812384	+	0.583123i	$0.198169\pi$
$282$	− 6.00000i	− 0.357295i
$283$	9.05573i	0.538307i	0.963097	+	0.269154i	$0.0867439\pi$
$283$	9.05573i	0.538307i	−0.963097	+	0.269154i	$0.913256\pi$
$284$	−7.09017	−0.420724
$285$	0	0
$286$	15.7639	0.932141
$287$	− 19.9443i	− 1.17727i
$288$	2.61803i	0.154269i
$289$	−8.90983	−0.524108
$290$	0	0
$291$	−9.03444	−0.529608
$292$	− 1.23607i	− 0.0723354i
$293$	− 15.8885i	− 0.928219i	−0.885778	−	0.464109i	$-0.846374\pi$
$293$	− 15.8885i	− 0.928219i	0.885778	−	0.464109i	$-0.153626\pi$
$294$	−2.70820	−0.157946
$295$	0	0
$296$	−2.47214	−0.143690
$297$	13.3820i	0.776500i
$298$	1.14590i	0.0663801i
$299$	−4.09017	−0.236541
$300$	0	0
$301$	0	0
$302$	17.5623i	1.01060i
$303$	− 8.47214i	− 0.486711i
$304$	4.85410	0.278402
$305$	0	0
$306$	13.3262	0.761810
$307$	27.4508i	1.56670i	0.621579	+	0.783351i	$0.286491\pi$
$307$	27.4508i	1.56670i	−0.621579	+	0.783351i	$0.713509\pi$
$308$	− 6.23607i	− 0.355333i
$309$	−2.20163	−0.125246
$310$	0	0
$311$	4.00000	0.226819	0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000	0.226819	0.113410	+	0.993548i	$0.463823\pi$
$312$	− 2.52786i	− 0.143112i
$313$	11.7984i	0.666884i	0.942771	+	0.333442i	$0.108210\pi$
$313$	11.7984i	0.666884i	−0.942771	+	0.333442i	$0.891790\pi$
$314$	−9.70820	−0.547866
$315$	0	0
$316$	10.4721	0.589104
$317$	0.0901699i	0.00506445i	0.999997	+	0.00253222i	$0.000806033\pi$
$317$	0.0901699i	0.00506445i	−0.999997	+	0.00253222i	$0.999194\pi$
$318$	− 5.23607i	− 0.293624i
$319$	18.3607	1.02800
$320$	0	0
$321$	2.58359	0.144202
$322$	1.61803i	0.0901695i
$323$	− 24.7082i	− 1.37480i
$324$	−5.70820	−0.317122
$325$	0	0
$326$	3.61803	0.200384
$327$	− 5.29180i	− 0.292637i
$328$	12.3262i	0.680603i
$329$	−15.7082	−0.866021
$330$	0	0
$331$	14.7639	0.811499	0.405750	−	0.913984i	$-0.367011\pi$
$331$	14.7639	0.811499	0.405750	+	0.913984i	$0.367011\pi$
$332$	10.9443i	0.600645i
$333$	− 6.47214i	− 0.354671i
$334$	8.00000	0.437741
$335$	0	0
$336$	−1.00000	−0.0545545
$337$	29.3262i	1.59750i	0.601662	+	0.798751i	$0.294506\pi$
$337$	29.3262i	1.59750i	−0.601662	+	0.798751i	$0.705494\pi$
$338$	− 3.72949i	− 0.202858i
$339$	11.7082	0.635902
$340$	0	0
$341$	−8.05573	−0.436242
$342$	12.7082i	0.687181i
$343$	18.4164i	0.994393i
$344$	0	0
$345$	0	0
$346$	−21.5623	−1.15920
$347$	− 8.61803i	− 0.462640i	−0.972878	−	0.231320i	$-0.925696\pi$
$347$	− 8.61803i	− 0.462640i	0.972878	−	0.231320i	$-0.0743045\pi$
$348$	− 2.94427i	− 0.157830i
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	0	0
$351$	14.2016	0.758027
$352$	3.85410i	0.205424i
$353$	− 24.0000i	− 1.27739i	−0.769460	−	0.638696i	$-0.779474\pi$
$353$	− 24.0000i	− 1.27739i	0.769460	−	0.638696i	$-0.220526\pi$
$354$	−7.23607	−0.384593
$355$	0	0
$356$	−1.52786	−0.0809766
$357$	5.09017i	0.269400i
$358$	20.1803i	1.06656i
$359$	18.3607	0.969040	0.484520	−	0.874780i	$-0.338994\pi$
$359$	18.3607	0.969040	0.484520	+	0.874780i	$0.338994\pi$
$360$	0	0
$361$	4.56231	0.240121
$362$	− 18.8541i	− 0.990950i
$363$	2.38197i	0.125021i
$364$	−6.61803	−0.346879
$365$	0	0
$366$	−3.90983	−0.204370
$367$	− 2.47214i	− 0.129044i	−0.997916	−	0.0645222i	$-0.979448\pi$
$367$	− 2.47214i	− 0.129044i	0.997916	−	0.0645222i	$-0.0205523\pi$
$368$	− 1.00000i	− 0.0521286i
$369$	−32.2705	−1.67994
$370$	0	0
$371$	−13.7082	−0.711694
$372$	1.29180i	0.0669765i
$373$	2.18034i	0.112894i	0.998406	+	0.0564469i	$0.0179771\pi$
$373$	2.18034i	0.112894i	−0.998406	+	0.0564469i	$0.982023\pi$
$374$	19.6180	1.01442
$375$	0	0
$376$	9.70820	0.500662
$377$	− 19.4853i	− 1.00354i
$378$	− 5.61803i	− 0.288960i
$379$	−33.4508	−1.71825	−0.859127	−	0.511762i	$-0.828993\pi$
$379$	−33.4508	−1.71825	−0.859127	+	0.511762i	$0.828993\pi$
$380$	0	0
$381$	3.81966	0.195687
$382$	− 0.291796i	− 0.0149296i
$383$	− 17.8885i	− 0.914062i	−0.889451	−	0.457031i	$-0.848913\pi$
$383$	− 17.8885i	− 0.914062i	0.889451	−	0.457031i	$-0.151087\pi$
$384$	0.618034	0.0315389
$385$	0	0
$386$	5.23607	0.266509
$387$	0	0
$388$	− 14.6180i	− 0.742118i
$389$	−5.67376	−0.287671	−0.143836	−	0.989602i	$-0.545944\pi$
$389$	−5.67376	−0.287671	−0.143836	+	0.989602i	$0.545944\pi$
$390$	0	0
$391$	−5.09017	−0.257421
$392$	− 4.38197i	− 0.221323i
$393$	− 9.23607i	− 0.465898i
$394$	2.43769	0.122809
$395$	0	0
$396$	−10.0902	−0.507050
$397$	− 8.32624i	− 0.417882i	−0.977928	−	0.208941i	$-0.932998\pi$
$397$	− 8.32624i	− 0.417882i	0.977928	−	0.208941i	$-0.0670016\pi$
$398$	− 2.00000i	− 0.100251i
$399$	−4.85410	−0.243009
$400$	0	0
$401$	11.7082	0.584680	0.292340	−	0.956314i	$-0.405566\pi$
$401$	11.7082	0.584680	0.292340	+	0.956314i	$0.405566\pi$
$402$	− 3.41641i	− 0.170395i
$403$	8.54915i	0.425864i
$404$	13.7082	0.682009
$405$	0	0
$406$	−7.70820	−0.382552
$407$	− 9.52786i	− 0.472279i
$408$	− 3.14590i	− 0.155745i
$409$	−21.2148	−1.04900	−0.524502	−	0.851409i	$-0.675748\pi$
$409$	−21.2148	−1.04900	−0.524502	+	0.851409i	$0.675748\pi$
$410$	0	0
$411$	−3.29180	−0.162372
$412$	− 3.56231i	− 0.175502i
$413$	18.9443i	0.932187i
$414$	2.61803	0.128669
$415$	0	0
$416$	4.09017	0.200537
$417$	− 10.6525i	− 0.521654i
$418$	18.7082i	0.915048i
$419$	−5.52786	−0.270054	−0.135027	−	0.990842i	$-0.543112\pi$
$419$	−5.52786	−0.270054	−0.135027	+	0.990842i	$0.543112\pi$
$420$	0	0
$421$	−28.7426	−1.40083	−0.700415	−	0.713735i	$-0.747002\pi$
$421$	−28.7426	−1.40083	−0.700415	+	0.713735i	$0.747002\pi$
$422$	14.0000i	0.681509i
$423$	25.4164i	1.23579i
$424$	8.47214	0.411443
$425$	0	0
$426$	−4.38197	−0.212307
$427$	10.2361i	0.495358i
$428$	4.18034i	0.202064i
$429$	9.74265	0.470379
$430$	0	0
$431$	34.6525	1.66915	0.834576	−	0.550894i	$-0.185713\pi$
$431$	34.6525	1.66915	0.834576	+	0.550894i	$0.185713\pi$
$432$	3.47214i	0.167053i
$433$	29.5066i	1.41800i	0.705211	+	0.708998i	$0.250852\pi$
$433$	29.5066i	1.41800i	−0.705211	+	0.708998i	$0.749148\pi$
$434$	3.38197	0.162340
$435$	0	0
$436$	8.56231	0.410060
$437$	− 4.85410i	− 0.232203i
$438$	− 0.763932i	− 0.0365021i
$439$	15.6180	0.745408	0.372704	−	0.927950i	$-0.378431\pi$
$439$	15.6180	0.745408	0.372704	+	0.927950i	$0.378431\pi$
$440$	0	0
$441$	11.4721	0.546292
$442$	− 20.8197i	− 0.990290i
$443$	− 13.9098i	− 0.660876i	−0.943828	−	0.330438i	$-0.892804\pi$
$443$	− 13.9098i	− 0.660876i	0.943828	−	0.330438i	$-0.107196\pi$
$444$	−1.52786	−0.0725092
$445$	0	0
$446$	−3.05573	−0.144693
$447$	0.708204i	0.0334969i
$448$	− 1.61803i	− 0.0764449i
$449$	−18.5623	−0.876009	−0.438005	−	0.898973i	$-0.644315\pi$
$449$	−18.5623	−0.876009	−0.438005	+	0.898973i	$0.644315\pi$
$450$	0	0
$451$	−47.5066	−2.23700
$452$	18.9443i	0.891064i
$453$	10.8541i	0.509970i
$454$	23.2361	1.09052
$455$	0	0
$456$	3.00000	0.140488
$457$	33.7771i	1.58003i	0.613090	+	0.790013i	$0.289926\pi$
$457$	33.7771i	1.58003i	−0.613090	+	0.790013i	$0.710074\pi$
$458$	− 10.0000i	− 0.467269i
$459$	17.6738	0.824941
$460$	0	0
$461$	−34.7639	−1.61912	−0.809559	−	0.587039i	$-0.800294\pi$
$461$	−34.7639	−1.61912	−0.809559	+	0.587039i	$0.800294\pi$
$462$	− 3.85410i	− 0.179309i
$463$	− 2.00000i	− 0.0929479i	−0.998920	−	0.0464739i	$-0.985202\pi$
$463$	− 2.00000i	− 0.0929479i	0.998920	−	0.0464739i	$-0.0147984\pi$
$464$	4.76393	0.221160
$465$	0	0
$466$	19.7082	0.912965
$467$	23.1246i	1.07008i	0.844827	+	0.535040i	$0.179703\pi$
$467$	23.1246i	1.07008i	−0.844827	+	0.535040i	$0.820297\pi$
$468$	10.7082i	0.494987i
$469$	−8.94427	−0.413008
$470$	0	0
$471$	−6.00000	−0.276465
$472$	− 11.7082i	− 0.538914i
$473$	0	0
$474$	6.47214	0.297275
$475$	0	0
$476$	−8.23607	−0.377500
$477$	22.1803i	1.01557i
$478$	− 24.3607i	− 1.11423i
$479$	−3.88854	−0.177672	−0.0888361	−	0.996046i	$-0.528315\pi$
$479$	−3.88854	−0.177672	−0.0888361	+	0.996046i	$0.528315\pi$
$480$	0	0
$481$	−10.1115	−0.461043
$482$	0	0
$483$	1.00000i	0.0455016i
$484$	−3.85410	−0.175186
$485$	0	0
$486$	−13.9443	−0.632525
$487$	− 42.1803i	− 1.91137i	−0.294385	−	0.955687i	$-0.595115\pi$
$487$	− 42.1803i	− 1.91137i	0.294385	−	0.955687i	$-0.404885\pi$
$488$	− 6.32624i	− 0.286375i
$489$	2.23607	0.101118
$490$	0	0
$491$	−16.1803	−0.730209	−0.365104	−	0.930967i	$-0.618967\pi$
$491$	−16.1803	−0.730209	−0.365104	+	0.930967i	$0.618967\pi$
$492$	7.61803i	0.343447i
$493$	− 24.2492i	− 1.09213i
$494$	19.8541	0.893278
$495$	0	0
$496$	−2.09017	−0.0938514
$497$	11.4721i	0.514596i
$498$	6.76393i	0.303099i
$499$	32.3607	1.44866	0.724331	−	0.689452i	$-0.242149\pi$
$499$	32.3607	1.44866	0.724331	+	0.689452i	$0.242149\pi$
$500$	0	0
$501$	4.94427	0.220894
$502$	12.8541i	0.573707i
$503$	− 20.6738i	− 0.921797i	−0.887453	−	0.460899i	$-0.847527\pi$
$503$	− 20.6738i	− 0.921797i	0.887453	−	0.460899i	$-0.152473\pi$
$504$	4.23607	0.188689
$505$	0	0
$506$	3.85410	0.171336
$507$	− 2.30495i	− 0.102366i
$508$	6.18034i	0.274208i
$509$	−5.34752	−0.237025	−0.118512	−	0.992953i	$-0.537813\pi$
$509$	−5.34752	−0.237025	−0.118512	+	0.992953i	$0.537813\pi$
$510$	0	0
$511$	−2.00000	−0.0884748
$512$	1.00000i	0.0441942i
$513$	16.8541i	0.744127i
$514$	30.1803	1.33120
$515$	0	0
$516$	0	0
$517$	37.4164i	1.64557i
$518$	4.00000i	0.175750i
$519$	−13.3262	−0.584957
$520$	0	0
$521$	−24.4721	−1.07214	−0.536072	−	0.844172i	$-0.680092\pi$
$521$	−24.4721	−1.07214	−0.536072	+	0.844172i	$0.680092\pi$
$522$	12.4721i	0.545891i
$523$	26.0000i	1.13690i	0.822718	+	0.568450i	$0.192457\pi$
$523$	26.0000i	1.13690i	−0.822718	+	0.568450i	$0.807543\pi$
$524$	14.9443	0.652844
$525$	0	0
$526$	−21.7426	−0.948024
$527$	10.6393i	0.463456i
$528$	2.38197i	0.103662i
$529$	−1.00000	−0.0434783
$530$	0	0
$531$	30.6525	1.33020
$532$	− 7.85410i	− 0.340519i
$533$	50.4164i	2.18378i
$534$	−0.944272	−0.0408626
$535$	0	0
$536$	5.52786	0.238767
$537$	12.4721i	0.538212i
$538$	− 8.18034i	− 0.352679i
$539$	16.8885	0.727441
$540$	0	0
$541$	−30.8328	−1.32561	−0.662803	−	0.748794i	$-0.730633\pi$
$541$	−30.8328	−1.32561	−0.662803	+	0.748794i	$0.730633\pi$
$542$	− 14.6738i	− 0.630292i
$543$	− 11.6525i	− 0.500056i
$544$	5.09017	0.218239
$545$	0	0
$546$	−4.09017	−0.175043
$547$	− 36.9230i	− 1.57871i	−0.613935	−	0.789356i	$-0.710414\pi$
$547$	− 36.9230i	− 1.57871i	0.613935	−	0.789356i	$-0.289586\pi$
$548$	− 5.32624i	− 0.227526i
$549$	16.5623	0.706862
$550$	0	0
$551$	23.1246	0.985142
$552$	− 0.618034i	− 0.0263053i
$553$	− 16.9443i	− 0.720544i
$554$	−2.58359	−0.109766
$555$	0	0
$556$	17.2361	0.730972
$557$	30.8328i	1.30643i	0.757173	+	0.653214i	$0.226580\pi$
$557$	30.8328i	1.30643i	−0.757173	+	0.653214i	$0.773420\pi$
$558$	− 5.47214i	− 0.231654i
$559$	0	0
$560$	0	0
$561$	12.1246	0.511902
$562$	27.2361i	1.14888i
$563$	− 21.8885i	− 0.922492i	−0.887272	−	0.461246i	$-0.847403\pi$
$563$	− 21.8885i	− 0.922492i	0.887272	−	0.461246i	$-0.152597\pi$
$564$	6.00000	0.252646
$565$	0	0
$566$	−9.05573	−0.380641
$567$	9.23607i	0.387878i
$568$	− 7.09017i	− 0.297497i
$569$	2.00000	0.0838444	0.0419222	−	0.999121i	$-0.486652\pi$
$569$	2.00000	0.0838444	0.0419222	+	0.999121i	$0.486652\pi$
$570$	0	0
$571$	−30.9787	−1.29642	−0.648209	−	0.761462i	$-0.724482\pi$
$571$	−30.9787	−1.29642	−0.648209	+	0.761462i	$0.724482\pi$
$572$	15.7639i	0.659123i
$573$	− 0.180340i	− 0.00753381i
$574$	19.9443	0.832458
$575$	0	0
$576$	−2.61803	−0.109085
$577$	− 12.4721i	− 0.519222i	−0.965713	−	0.259611i	$-0.916406\pi$
$577$	− 12.4721i	− 0.519222i	0.965713	−	0.259611i	$-0.0835943\pi$
$578$	− 8.90983i	− 0.370600i
$579$	3.23607	0.134486
$580$	0	0
$581$	17.7082	0.734660
$582$	− 9.03444i	− 0.374490i
$583$	32.6525i	1.35233i
$584$	1.23607	0.0511489
$585$	0	0
$586$	15.8885	0.656350
$587$	11.3820i	0.469784i	0.972021	+	0.234892i	$0.0754737\pi$
$587$	11.3820i	0.469784i	−0.972021	+	0.234892i	$0.924526\pi$
$588$	− 2.70820i	− 0.111684i
$589$	−10.1459	−0.418054
$590$	0	0
$591$	1.50658	0.0619723
$592$	− 2.47214i	− 0.101604i
$593$	− 34.7639i	− 1.42758i	−0.700358	−	0.713792i	$-0.746976\pi$
$593$	− 34.7639i	− 1.42758i	0.700358	−	0.713792i	$-0.253024\pi$
$594$	−13.3820	−0.549069
$595$	0	0
$596$	−1.14590	−0.0469378
$597$	− 1.23607i	− 0.0505889i
$598$	− 4.09017i	− 0.167259i
$599$	20.6180	0.842430	0.421215	−	0.906961i	$-0.361604\pi$
$599$	20.6180	0.842430	0.421215	+	0.906961i	$0.361604\pi$
$600$	0	0
$601$	0.270510	0.0110343	0.00551716	−	0.999985i	$-0.498244\pi$
$601$	0.270510	0.0110343	0.00551716	+	0.999985i	$0.498244\pi$
$602$	0	0
$603$	14.4721i	0.589351i
$604$	−17.5623	−0.714600
$605$	0	0
$606$	8.47214	0.344157
$607$	17.5279i	0.711434i	0.934594	+	0.355717i	$0.115763\pi$
$607$	17.5279i	0.711434i	−0.934594	+	0.355717i	$0.884237\pi$
$608$	4.85410i	0.196860i
$609$	−4.76393	−0.193044
$610$	0	0
$611$	39.7082	1.60642
$612$	13.3262i	0.538681i
$613$	43.3050i	1.74907i	0.484962	+	0.874535i	$0.338833\pi$
$613$	43.3050i	1.74907i	−0.484962	+	0.874535i	$0.661167\pi$
$614$	−27.4508	−1.10783
$615$	0	0
$616$	6.23607	0.251258
$617$	22.9098i	0.922315i	0.887318	+	0.461158i	$0.152566\pi$
$617$	22.9098i	0.922315i	−0.887318	+	0.461158i	$0.847434\pi$
$618$	− 2.20163i	− 0.0885624i
$619$	−21.7984	−0.876151	−0.438075	−	0.898938i	$-0.644340\pi$
$619$	−21.7984	−0.876151	−0.438075	+	0.898938i	$0.644340\pi$
$620$	0	0
$621$	3.47214	0.139332
$622$	4.00000i	0.160385i
$623$	2.47214i	0.0990440i
$624$	2.52786	0.101196
$625$	0	0
$626$	−11.7984	−0.471558
$627$	11.5623i	0.461754i
$628$	− 9.70820i	− 0.387400i
$629$	−12.5836	−0.501741
$630$	0	0
$631$	−16.0689	−0.639692	−0.319846	−	0.947470i	$-0.603631\pi$
$631$	−16.0689	−0.639692	−0.319846	+	0.947470i	$0.603631\pi$
$632$	10.4721i	0.416559i
$633$	8.65248i	0.343905i
$634$	−0.0901699	−0.00358111
$635$	0	0
$636$	5.23607	0.207624
$637$	− 17.9230i	− 0.710135i
$638$	18.3607i	0.726906i
$639$	18.5623	0.734313
$640$	0	0
$641$	−44.3607	−1.75214	−0.876071	−	0.482183i	$-0.839844\pi$
$641$	−44.3607	−1.75214	−0.876071	+	0.482183i	$0.839844\pi$
$642$	2.58359i	0.101966i
$643$	21.7082i	0.856088i	0.903758	+	0.428044i	$0.140797\pi$
$643$	21.7082i	0.856088i	−0.903758	+	0.428044i	$0.859203\pi$
$644$	−1.61803	−0.0637595
$645$	0	0
$646$	24.7082	0.972131
$647$	44.2492i	1.73962i	0.493390	+	0.869808i	$0.335758\pi$
$647$	44.2492i	1.73962i	−0.493390	+	0.869808i	$0.664242\pi$
$648$	− 5.70820i	− 0.224239i
$649$	45.1246	1.77130
$650$	0	0
$651$	2.09017	0.0819202
$652$	3.61803i	0.141693i
$653$	− 21.0344i	− 0.823141i	−0.911378	−	0.411571i	$-0.864980\pi$
$653$	− 21.0344i	− 0.823141i	0.911378	−	0.411571i	$-0.135020\pi$
$654$	5.29180	0.206926
$655$	0	0
$656$	−12.3262	−0.481259
$657$	3.23607i	0.126251i
$658$	− 15.7082i	− 0.612370i
$659$	−34.2492	−1.33416	−0.667080	−	0.744986i	$-0.732456\pi$
$659$	−34.2492	−1.33416	−0.667080	+	0.744986i	$0.732456\pi$
$660$	0	0
$661$	34.3262	1.33514	0.667568	−	0.744549i	$-0.267335\pi$
$661$	34.3262	1.33514	0.667568	+	0.744549i	$0.267335\pi$
$662$	14.7639i	0.573817i
$663$	− 12.8673i	− 0.499723i
$664$	−10.9443	−0.424720
$665$	0	0
$666$	6.47214	0.250790
$667$	− 4.76393i	− 0.184460i
$668$	8.00000i	0.309529i
$669$	−1.88854	−0.0730153
$670$	0	0
$671$	24.3820	0.941255
$672$	− 1.00000i	− 0.0385758i
$673$	− 6.94427i	− 0.267682i	−0.991003	−	0.133841i	$-0.957269\pi$
$673$	− 6.94427i	− 0.267682i	0.991003	−	0.133841i	$-0.0427311\pi$
$674$	−29.3262	−1.12960
$675$	0	0
$676$	3.72949	0.143442
$677$	− 33.0557i	− 1.27043i	−0.772333	−	0.635217i	$-0.780910\pi$
$677$	− 33.0557i	− 1.27043i	0.772333	−	0.635217i	$-0.219090\pi$
$678$	11.7082i	0.449651i
$679$	−23.6525	−0.907699
$680$	0	0
$681$	14.3607	0.550302
$682$	− 8.05573i	− 0.308470i
$683$	11.4377i	0.437651i	0.975764	+	0.218826i	$0.0702226\pi$
$683$	11.4377i	0.437651i	−0.975764	+	0.218826i	$0.929777\pi$
$684$	−12.7082	−0.485910
$685$	0	0
$686$	−18.4164	−0.703142
$687$	− 6.18034i	− 0.235795i
$688$	0	0
$689$	34.6525	1.32015
$690$	0	0
$691$	−24.7639	−0.942064	−0.471032	−	0.882116i	$-0.656118\pi$
$691$	−24.7639	−0.942064	−0.471032	+	0.882116i	$0.656118\pi$
$692$	− 21.5623i	− 0.819676i
$693$	16.3262i	0.620182i
$694$	8.61803	0.327136
$695$	0	0
$696$	2.94427	0.111602
$697$	62.7426i	2.37655i
$698$	2.00000i	0.0757011i
$699$	12.1803	0.460703
$700$	0	0
$701$	−48.3394	−1.82575	−0.912877	−	0.408235i	$-0.866144\pi$
$701$	−48.3394	−1.82575	−0.912877	+	0.408235i	$0.866144\pi$
$702$	14.2016i	0.536006i
$703$	− 12.0000i	− 0.452589i
$704$	−3.85410	−0.145257
$705$	0	0
$706$	24.0000	0.903252
$707$	− 22.1803i	− 0.834178i
$708$	− 7.23607i	− 0.271948i
$709$	14.9098	0.559950	0.279975	−	0.960007i	$-0.409674\pi$
$709$	14.9098	0.559950	0.279975	+	0.960007i	$0.409674\pi$
$710$	0	0
$711$	−27.4164	−1.02820
$712$	− 1.52786i	− 0.0572591i
$713$	2.09017i	0.0782775i
$714$	−5.09017	−0.190495
$715$	0	0
$716$	−20.1803	−0.754175
$717$	− 15.0557i	− 0.562266i
$718$	18.3607i	0.685214i
$719$	−1.72949	−0.0644991	−0.0322495	−	0.999480i	$-0.510267\pi$
$719$	−1.72949	−0.0644991	−0.0322495	+	0.999480i	$0.510267\pi$
$720$	0	0
$721$	−5.76393	−0.214660
$722$	4.56231i	0.169791i
$723$	0	0
$724$	18.8541	0.700707
$725$	0	0
$726$	−2.38197	−0.0884031
$727$	52.7984i	1.95818i	0.203420	+	0.979092i	$0.434794\pi$
$727$	52.7984i	1.95818i	−0.203420	+	0.979092i	$0.565206\pi$
$728$	− 6.61803i	− 0.245281i
$729$	8.50658	0.315058
$730$	0	0
$731$	0	0
$732$	− 3.90983i	− 0.144511i
$733$	2.58359i	0.0954272i	0.998861	+	0.0477136i	$0.0151935\pi$
$733$	2.58359i	0.0954272i	−0.998861	+	0.0477136i	$0.984807\pi$
$734$	2.47214	0.0912482
$735$	0	0
$736$	1.00000	0.0368605
$737$	21.3050i	0.784778i
$738$	− 32.2705i	− 1.18789i
$739$	−21.8885	−0.805183	−0.402592	−	0.915380i	$-0.631890\pi$
$739$	−21.8885	−0.805183	−0.402592	+	0.915380i	$0.631890\pi$
$740$	0	0
$741$	12.2705	0.450768
$742$	− 13.7082i	− 0.503244i
$743$	44.6312i	1.63736i	0.574250	+	0.818680i	$0.305294\pi$
$743$	44.6312i	1.63736i	−0.574250	+	0.818680i	$0.694706\pi$
$744$	−1.29180	−0.0473595
$745$	0	0
$746$	−2.18034	−0.0798279
$747$	− 28.6525i	− 1.04834i
$748$	19.6180i	0.717306i
$749$	6.76393	0.247149
$750$	0	0
$751$	29.0132	1.05871	0.529353	−	0.848402i	$-0.322435\pi$
$751$	29.0132	1.05871	0.529353	+	0.848402i	$0.322435\pi$
$752$	9.70820i	0.354022i
$753$	7.94427i	0.289505i
$754$	19.4853	0.709612
$755$	0	0
$756$	5.61803	0.204326
$757$	17.8885i	0.650170i	0.945685	+	0.325085i	$0.105393\pi$
$757$	17.8885i	0.650170i	−0.945685	+	0.325085i	$0.894607\pi$
$758$	− 33.4508i	− 1.21499i
$759$	2.38197	0.0864599
$760$	0	0
$761$	−35.8673	−1.30019	−0.650094	−	0.759854i	$-0.725270\pi$
$761$	−35.8673	−1.30019	−0.650094	+	0.759854i	$0.725270\pi$
$762$	3.81966i	0.138372i
$763$	− 13.8541i	− 0.501552i
$764$	0.291796	0.0105568
$765$	0	0
$766$	17.8885	0.646339
$767$	− 47.8885i	− 1.72916i
$768$	0.618034i	0.0223014i
$769$	33.4164	1.20503	0.602513	−	0.798109i	$-0.294166\pi$
$769$	33.4164	1.20503	0.602513	+	0.798109i	$0.294166\pi$
$770$	0	0
$771$	18.6525	0.671753
$772$	5.23607i	0.188450i
$773$	− 11.0557i	− 0.397647i	−0.980035	−	0.198823i	$-0.936288\pi$
$773$	− 11.0557i	− 0.397647i	0.980035	−	0.198823i	$-0.0637120\pi$
$774$	0	0
$775$	0	0
$776$	14.6180	0.524757
$777$	2.47214i	0.0886874i
$778$	− 5.67376i	− 0.203414i
$779$	−59.8328	−2.14373
$780$	0	0
$781$	27.3262	0.977810
$782$	− 5.09017i	− 0.182024i
$783$	16.5410i	0.591128i
$784$	4.38197	0.156499
$785$	0	0
$786$	9.23607	0.329440
$787$	− 43.1246i	− 1.53723i	−0.639714	−	0.768613i	$-0.720947\pi$
$787$	− 43.1246i	− 1.53723i	0.639714	−	0.768613i	$-0.279053\pi$
$788$	2.43769i	0.0868393i
$789$	−13.4377	−0.478395
$790$	0	0
$791$	30.6525	1.08988
$792$	− 10.0902i	− 0.358539i
$793$	− 25.8754i	− 0.918862i
$794$	8.32624	0.295487
$795$	0	0
$796$	2.00000	0.0708881
$797$	0.291796i	0.0103359i	0.999987	+	0.00516797i	$0.00164502\pi$
$797$	0.291796i	0.0103359i	−0.999987	+	0.00516797i	$0.998355\pi$
$798$	− 4.85410i	− 0.171833i
$799$	49.4164	1.74823
$800$	0	0
$801$	4.00000	0.141333
$802$	11.7082i	0.413431i
$803$	4.76393i	0.168116i
$804$	3.41641	0.120487
$805$	0	0
$806$	−8.54915	−0.301131
$807$	− 5.05573i	− 0.177970i
$808$	13.7082i	0.482253i
$809$	4.25735	0.149681	0.0748403	−	0.997196i	$-0.476155\pi$
$809$	4.25735	0.149681	0.0748403	+	0.997196i	$0.476155\pi$
$810$	0	0
$811$	44.1803	1.55138	0.775691	−	0.631113i	$-0.217402\pi$
$811$	44.1803	1.55138	0.775691	+	0.631113i	$0.217402\pi$
$812$	− 7.70820i	− 0.270505i
$813$	− 9.06888i	− 0.318060i
$814$	9.52786	0.333951
$815$	0	0
$816$	3.14590	0.110128
$817$	0	0
$818$	− 21.2148i	− 0.741757i
$819$	17.3262	0.605428
$820$	0	0
$821$	−50.9443	−1.77797	−0.888984	−	0.457939i	$-0.848588\pi$
$821$	−50.9443	−1.77797	−0.888984	+	0.457939i	$0.848588\pi$
$822$	− 3.29180i	− 0.114815i
$823$	1.41641i	0.0493729i	0.999695	+	0.0246864i	$0.00785874\pi$
$823$	1.41641i	0.0493729i	−0.999695	+	0.0246864i	$0.992141\pi$
$824$	3.56231	0.124099
$825$	0	0
$826$	−18.9443	−0.659156
$827$	8.29180i	0.288334i	0.989553	+	0.144167i	$0.0460502\pi$
$827$	8.29180i	0.288334i	−0.989553	+	0.144167i	$0.953950\pi$
$828$	2.61803i	0.0909830i
$829$	−1.05573	−0.0366670	−0.0183335	−	0.999832i	$-0.505836\pi$
$829$	−1.05573	−0.0366670	−0.0183335	+	0.999832i	$0.505836\pi$
$830$	0	0
$831$	−1.59675	−0.0553906
$832$	4.09017i	0.141801i
$833$	− 22.3050i	− 0.772821i
$834$	10.6525	0.368865
$835$	0	0
$836$	−18.7082	−0.647037
$837$	− 7.25735i	− 0.250851i
$838$	− 5.52786i	− 0.190957i
$839$	43.0132	1.48498	0.742490	−	0.669858i	$-0.233645\pi$
$839$	43.0132	1.48498	0.742490	+	0.669858i	$0.233645\pi$
$840$	0	0
$841$	−6.30495	−0.217412
$842$	− 28.7426i	− 0.990537i
$843$	16.8328i	0.579753i
$844$	−14.0000	−0.481900
$845$	0	0
$846$	−25.4164	−0.873834
$847$	6.23607i	0.214274i
$848$	8.47214i	0.290934i
$849$	−5.59675	−0.192080
$850$	0	0
$851$	−2.47214	−0.0847437
$852$	− 4.38197i	− 0.150124i
$853$	− 13.7984i	− 0.472447i	−0.971699	−	0.236224i	$-0.924090\pi$
$853$	− 13.7984i	− 0.472447i	0.971699	−	0.236224i	$-0.0759098\pi$
$854$	−10.2361	−0.350271
$855$	0	0
$856$	−4.18034	−0.142881
$857$	− 33.4164i	− 1.14148i	−0.821130	−	0.570741i	$-0.806656\pi$
$857$	− 33.4164i	− 1.14148i	0.821130	−	0.570741i	$-0.193344\pi$
$858$	9.74265i	0.332608i
$859$	−34.0689	−1.16242	−0.581208	−	0.813755i	$-0.697420\pi$
$859$	−34.0689	−1.16242	−0.581208	+	0.813755i	$0.697420\pi$
$860$	0	0
$861$	12.3262	0.420077
$862$	34.6525i	1.18027i
$863$	− 37.2361i	− 1.26753i	−0.773525	−	0.633765i	$-0.781509\pi$
$863$	− 37.2361i	− 1.26753i	0.773525	−	0.633765i	$-0.218491\pi$
$864$	−3.47214	−0.118124
$865$	0	0
$866$	−29.5066	−1.00267
$867$	− 5.50658i	− 0.187013i
$868$	3.38197i	0.114791i
$869$	−40.3607	−1.36914
$870$	0	0
$871$	22.6099	0.766107
$872$	8.56231i	0.289956i
$873$	38.2705i	1.29526i
$874$	4.85410	0.164192
$875$	0	0
$876$	0.763932	0.0258109
$877$	− 23.7426i	− 0.801732i	−0.916137	−	0.400866i	$-0.868709\pi$
$877$	− 23.7426i	− 0.801732i	0.916137	−	0.400866i	$-0.131291\pi$
$878$	15.6180i	0.527083i
$879$	9.81966	0.331209
$880$	0	0
$881$	35.4164	1.19321	0.596605	−	0.802535i	$-0.296516\pi$
$881$	35.4164	1.19321	0.596605	+	0.802535i	$0.296516\pi$
$882$	11.4721i	0.386287i
$883$	4.56231i	0.153534i	0.997049	+	0.0767669i	$0.0244597\pi$
$883$	4.56231i	0.153534i	−0.997049	+	0.0767669i	$0.975540\pi$
$884$	20.8197	0.700241
$885$	0	0
$886$	13.9098	0.467310
$887$	− 58.8328i	− 1.97541i	−0.156321	−	0.987706i	$-0.549963\pi$
$887$	− 58.8328i	− 1.97541i	0.156321	−	0.987706i	$-0.450037\pi$
$888$	− 1.52786i	− 0.0512718i
$889$	10.0000	0.335389
$890$	0	0
$891$	22.0000	0.737028
$892$	− 3.05573i	− 0.102313i
$893$	47.1246i	1.57697i
$894$	−0.708204	−0.0236859
$895$	0	0
$896$	1.61803	0.0540547
$897$	− 2.52786i	− 0.0844029i
$898$	− 18.5623i	− 0.619432i
$899$	−9.95743	−0.332099
$900$	0	0
$901$	43.1246	1.43669
$902$	− 47.5066i	− 1.58180i
$903$	0	0
$904$	−18.9443	−0.630077
$905$	0	0
$906$	−10.8541	−0.360603
$907$	− 33.1246i	− 1.09988i	−0.835203	−	0.549942i	$-0.814650\pi$
$907$	− 33.1246i	− 1.09988i	0.835203	−	0.549942i	$-0.185350\pi$
$908$	23.2361i	0.771116i
$909$	−35.8885	−1.19035
$910$	0	0
$911$	−22.0689	−0.731175	−0.365587	−	0.930777i	$-0.619132\pi$
$911$	−22.0689	−0.731175	−0.365587	+	0.930777i	$0.619132\pi$
$912$	3.00000i	0.0993399i
$913$	− 42.1803i	− 1.39597i
$914$	−33.7771	−1.11725
$915$	0	0
$916$	10.0000	0.330409
$917$	− 24.1803i	− 0.798505i
$918$	17.6738i	0.583321i
$919$	−40.0000	−1.31948	−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000	−1.31948	−0.659739	+	0.751495i	$0.729333\pi$
$920$	0	0
$921$	−16.9656	−0.559034
$922$	− 34.7639i	− 1.14489i
$923$	− 29.0000i	− 0.954547i
$924$	3.85410	0.126791
$925$	0	0
$926$	2.00000	0.0657241
$927$	9.32624i	0.306314i
$928$	4.76393i	0.156384i
$929$	12.4721	0.409198	0.204599	−	0.978846i	$-0.434411\pi$
$929$	12.4721	0.409198	0.204599	+	0.978846i	$0.434411\pi$
$930$	0	0
$931$	21.2705	0.697113
$932$	19.7082i	0.645564i
$933$	2.47214i	0.0809341i
$934$	−23.1246	−0.756660
$935$	0	0
$936$	−10.7082	−0.350009
$937$	− 12.2016i	− 0.398610i	−0.979938	−	0.199305i	$-0.936132\pi$
$937$	− 12.2016i	− 0.398610i	0.979938	−	0.199305i	$-0.0638684\pi$
$938$	− 8.94427i	− 0.292041i
$939$	−7.29180	−0.237959
$940$	0	0
$941$	−60.5066	−1.97246	−0.986229	−	0.165385i	$-0.947113\pi$
$941$	−60.5066	−1.97246	−0.986229	+	0.165385i	$0.947113\pi$
$942$	− 6.00000i	− 0.195491i
$943$	12.3262i	0.401398i
$944$	11.7082	0.381070
$945$	0	0
$946$	0	0
$947$	5.68692i	0.184800i	0.995722	+	0.0924000i	$0.0294538\pi$
$947$	5.68692i	0.184800i	−0.995722	+	0.0924000i	$0.970546\pi$
$948$	6.47214i	0.210205i
$949$	5.05573	0.164116
$950$	0	0
$951$	−0.0557281	−0.00180711
$952$	− 8.23607i	− 0.266932i
$953$	20.7984i	0.673725i	0.941554	+	0.336863i	$0.109366\pi$
$953$	20.7984i	0.673725i	−0.941554	+	0.336863i	$0.890634\pi$
$954$	−22.1803	−0.718115
$955$	0	0
$956$	24.3607	0.787881
$957$	11.3475i	0.366813i
$958$	− 3.88854i	− 0.125633i
$959$	−8.61803	−0.278291
$960$	0	0
$961$	−26.6312	−0.859071
$962$	− 10.1115i	− 0.326006i
$963$	− 10.9443i	− 0.352674i
$964$	0	0
$965$	0	0
$966$	−1.00000	−0.0321745
$967$	50.5410i	1.62529i	0.582759	+	0.812645i	$0.301973\pi$
$967$	50.5410i	1.62529i	−0.582759	+	0.812645i	$0.698027\pi$
$968$	− 3.85410i	− 0.123876i
$969$	15.2705	0.490559
$970$	0	0
$971$	0.729490	0.0234105	0.0117052	−	0.999931i	$-0.496274\pi$
$971$	0.729490	0.0234105	0.0117052	+	0.999931i	$0.496274\pi$
$972$	− 13.9443i	− 0.447263i
$973$	− 27.8885i	− 0.894066i
$974$	42.1803	1.35155
$975$	0	0
$976$	6.32624	0.202498
$977$	− 3.43769i	− 0.109982i	−0.998487	−	0.0549908i	$-0.982487\pi$
$977$	− 3.43769i	− 0.109982i	0.998487	−	0.0549908i	$-0.0175129\pi$
$978$	2.23607i	0.0715016i
$979$	5.88854	0.188199
$980$	0	0
$981$	−22.4164	−0.715701
$982$	− 16.1803i	− 0.516335i
$983$	− 19.2705i	− 0.614634i	−0.951607	−	0.307317i	$-0.900569\pi$
$983$	− 19.2705i	− 0.614634i	0.951607	−	0.307317i	$-0.0994312\pi$
$984$	−7.61803	−0.242854
$985$	0	0
$986$	24.2492	0.772253
$987$	− 9.70820i	− 0.309016i
$988$	19.8541i	0.631643i
$989$	0	0
$990$	0	0
$991$	−10.5066	−0.333752	−0.166876	−	0.985978i	$-0.553368\pi$
$991$	−10.5066	−0.333752	−0.166876	+	0.985978i	$0.553368\pi$
$992$	− 2.09017i	− 0.0663630i
$993$	9.12461i	0.289561i
$994$	−11.4721	−0.363874
$995$	0	0
$996$	−6.76393	−0.214323
$997$	− 41.1935i	− 1.30461i	−0.757956	−	0.652306i	$-0.773802\pi$
$997$	− 41.1935i	− 1.30461i	0.757956	−	0.652306i	$-0.226198\pi$
$998$	32.3607i	1.02436i
$999$	8.58359	0.271573

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.b.i.599.4		4
5.2	odd	4		1150.2.a.j.1.2		2
5.3	odd	4		230.2.a.c.1.1	✓	2
5.4	even	2	inner	1150.2.b.i.599.1		4
15.8	even	4		2070.2.a.u.1.2		2
20.3	even	4		1840.2.a.l.1.2		2
20.7	even	4		9200.2.a.bu.1.1		2
40.3	even	4		7360.2.a.bn.1.1		2
40.13	odd	4		7360.2.a.bh.1.2		2
115.68	even	4		5290.2.a.o.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.c.1.1	✓	2	5.3	odd	4
1150.2.a.j.1.2		2	5.2	odd	4
1150.2.b.i.599.1		4	5.4	even	2	inner
1150.2.b.i.599.4		4	1.1	even	1	trivial
1840.2.a.l.1.2		2	20.3	even	4
2070.2.a.u.1.2		2	15.8	even	4
5290.2.a.o.1.1		2	115.68	even	4
7360.2.a.bh.1.2		2	40.13	odd	4
7360.2.a.bn.1.1		2	40.3	even	4
9200.2.a.bu.1.1		2	20.7	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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +0.618034i q^{3} -1.00000 q^{4} -0.618034 q^{6} +1.61803i q^{7} -1.00000i q^{8} +2.61803 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +0.618034i q^{3} -1.00000 q^{4} -0.618034 q^{6} +1.61803i q^{7} -1.00000i q^{8} +2.61803 q^{9} +3.85410 q^{11} -0.618034i q^{12} -4.09017i q^{13} -1.61803 q^{14} +1.00000 q^{16} -5.09017i q^{17} +2.61803i q^{18} +4.85410 q^{19} -1.00000 q^{21} +3.85410i q^{22} -1.00000i q^{23} +0.618034 q^{24} +4.09017 q^{26} +3.47214i q^{27} -1.61803i q^{28} +4.76393 q^{29} -2.09017 q^{31} +1.00000i q^{32} +2.38197i q^{33} +5.09017 q^{34} -2.61803 q^{36} -2.47214i q^{37} +4.85410i q^{38} +2.52786 q^{39} -12.3262 q^{41} -1.00000i q^{42} -3.85410 q^{44} +1.00000 q^{46} +9.70820i q^{47} +0.618034i q^{48} +4.38197 q^{49} +3.14590 q^{51} +4.09017i q^{52} +8.47214i q^{53} -3.47214 q^{54} +1.61803 q^{56} +3.00000i q^{57} +4.76393i q^{58} +11.7082 q^{59} +6.32624 q^{61} -2.09017i q^{62} +4.23607i q^{63} -1.00000 q^{64} -2.38197 q^{66} +5.52786i q^{67} +5.09017i q^{68} +0.618034 q^{69} +7.09017 q^{71} -2.61803i q^{72} +1.23607i q^{73} +2.47214 q^{74} -4.85410 q^{76} +6.23607i q^{77} +2.52786i q^{78} -10.4721 q^{79} +5.70820 q^{81} -12.3262i q^{82} -10.9443i q^{83} +1.00000 q^{84} +2.94427i q^{87} -3.85410i q^{88} +1.52786 q^{89} +6.61803 q^{91} +1.00000i q^{92} -1.29180i q^{93} -9.70820 q^{94} -0.618034 q^{96} +14.6180i q^{97} +4.38197i q^{98} +10.0902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 2 q^{6} + 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 2 * q^6 + 6 * q^9	\( 4 q - 4 q^{4} + 2 q^{6} + 6 q^{9} + 2 q^{11} - 2 q^{14} + 4 q^{16} + 6 q^{19} - 4 q^{21} - 2 q^{24} - 6 q^{26} + 28 q^{29} + 14 q^{31} - 2 q^{34} - 6 q^{36} + 28 q^{39} - 18 q^{41} - 2 q^{44} + 4 q^{46} + 22 q^{49} + 26 q^{51} + 4 q^{54} + 2 q^{56} + 20 q^{59} - 6 q^{61} - 4 q^{64} - 14 q^{66} - 2 q^{69} + 6 q^{71} - 8 q^{74} - 6 q^{76} - 24 q^{79} - 4 q^{81} + 4 q^{84} + 24 q^{89} + 22 q^{91} - 12 q^{94} + 2 q^{96} + 18 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 2 * q^6 + 6 * q^9 + 2 * q^11 - 2 * q^14 + 4 * q^16 + 6 * q^19 - 4 * q^21 - 2 * q^24 - 6 * q^26 + 28 * q^29 + 14 * q^31 - 2 * q^34 - 6 * q^36 + 28 * q^39 - 18 * q^41 - 2 * q^44 + 4 * q^46 + 22 * q^49 + 26 * q^51 + 4 * q^54 + 2 * q^56 + 20 * q^59 - 6 * q^61 - 4 * q^64 - 14 * q^66 - 2 * q^69 + 6 * q^71 - 8 * q^74 - 6 * q^76 - 24 * q^79 - 4 * q^81 + 4 * q^84 + 24 * q^89 + 22 * q^91 - 12 * q^94 + 2 * q^96 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more