LMFDB - Embedded newform 2850.2.d.w.799.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2850,2,Mod(799,2850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2850, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2850.799");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2850.d (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:	$22.7573645761$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			799.1
Root			$-1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	2850.799
Dual form			2850.2.d.w.799.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -4.44949i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -4.44949i q^{7} +1.00000i q^{8} -1.00000 q^{9} +3.44949 q^{11} -1.00000i q^{12} -2.44949i q^{13} -4.44949 q^{14} +1.00000 q^{16} -4.44949i q^{17} +1.00000i q^{18} -1.00000 q^{19} +4.44949 q^{21} -3.44949i q^{22} -1.00000i q^{23} -1.00000 q^{24} -2.44949 q^{26} -1.00000i q^{27} +4.44949i q^{28} +4.34847 q^{29} -3.00000 q^{31} -1.00000i q^{32} +3.44949i q^{33} -4.44949 q^{34} +1.00000 q^{36} +7.79796i q^{37} +1.00000i q^{38} +2.44949 q^{39} -0.898979 q^{41} -4.44949i q^{42} -2.44949i q^{43} -3.44949 q^{44} -1.00000 q^{46} +7.79796i q^{47} +1.00000i q^{48} -12.7980 q^{49} +4.44949 q^{51} +2.44949i q^{52} -7.44949i q^{53} -1.00000 q^{54} +4.44949 q^{56} -1.00000i q^{57} -4.34847i q^{58} -6.44949 q^{59} -9.44949 q^{61} +3.00000i q^{62} +4.44949i q^{63} -1.00000 q^{64} +3.44949 q^{66} -15.2474i q^{67} +4.44949i q^{68} +1.00000 q^{69} -1.55051 q^{71} -1.00000i q^{72} -1.00000i q^{73} +7.79796 q^{74} +1.00000 q^{76} -15.3485i q^{77} -2.44949i q^{78} +5.00000 q^{79} +1.00000 q^{81} +0.898979i q^{82} +8.34847i q^{83} -4.44949 q^{84} -2.44949 q^{86} +4.34847i q^{87} +3.44949i q^{88} -2.10102 q^{89} -10.8990 q^{91} +1.00000i q^{92} -3.00000i q^{93} +7.79796 q^{94} +1.00000 q^{96} -1.55051i q^{97} +12.7980i q^{98} -3.44949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 4 q^{11} - 8 q^{14} + 4 q^{16} - 4 q^{19} + 8 q^{21} - 4 q^{24} - 12 q^{29} - 12 q^{31} - 8 q^{34} + 4 q^{36} + 16 q^{41} - 4 q^{44} - 4 q^{46} - 12 q^{49} + 8 q^{51} - 4 q^{54} + 8 q^{56} - 16 q^{59} - 28 q^{61} - 4 q^{64} + 4 q^{66} + 4 q^{69} - 16 q^{71} - 8 q^{74} + 4 q^{76} + 20 q^{79} + 4 q^{81} - 8 q^{84} - 28 q^{89} - 24 q^{91} - 8 q^{94} + 4 q^{96} - 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 4 * q^11 - 8 * q^14 + 4 * q^16 - 4 * q^19 + 8 * q^21 - 4 * q^24 - 12 * q^29 - 12 * q^31 - 8 * q^34 + 4 * q^36 + 16 * q^41 - 4 * q^44 - 4 * q^46 - 12 * q^49 + 8 * q^51 - 4 * q^54 + 8 * q^56 - 16 * q^59 - 28 * q^61 - 4 * q^64 + 4 * q^66 + 4 * q^69 - 16 * q^71 - 8 * q^74 + 4 * q^76 + 20 * q^79 + 4 * q^81 - 8 * q^84 - 28 * q^89 - 24 * q^91 - 8 * q^94 + 4 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2850\mathbb{Z}\right)^\times$.

$n$	$1027$	$1351$	$1901$
$\chi(n)$	$-1$	$1$	$1$

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
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	− 4.44949i	− 1.68175i	−0.541230	−	0.840875i	$-0.682041\pi$
$7$	− 4.44949i	− 1.68175i	0.541230	−	0.840875i	$-0.317959\pi$
$8$	1.00000i	0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	3.44949	1.04006	0.520030	−	0.854148i	$-0.325921\pi$
$11$	3.44949	1.04006	0.520030	+	0.854148i	$0.325921\pi$
$12$	− 1.00000i	− 0.288675i
$13$	− 2.44949i	− 0.679366i	−0.940540	−	0.339683i	$-0.889680\pi$
$13$	− 2.44949i	− 0.679366i	0.940540	−	0.339683i	$-0.110320\pi$
$14$	−4.44949	−1.18918
$15$	0	0
$16$	1.00000	0.250000
$17$	− 4.44949i	− 1.07916i	−0.841934	−	0.539580i	$-0.818583\pi$
$17$	− 4.44949i	− 1.07916i	0.841934	−	0.539580i	$-0.181417\pi$
$18$	1.00000i	0.235702i
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0	0
$21$	4.44949	0.970958
$22$	− 3.44949i	− 0.735434i
$23$	− 1.00000i	− 0.208514i	−0.994550	−	0.104257i	$-0.966753\pi$
$23$	− 1.00000i	− 0.208514i	0.994550	−	0.104257i	$-0.0332465\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−2.44949	−0.480384
$27$	− 1.00000i	− 0.192450i
$28$	4.44949i	0.840875i
$29$	4.34847	0.807490	0.403745	−	0.914871i	$-0.367708\pi$
$29$	4.34847	0.807490	0.403745	+	0.914871i	$0.367708\pi$
$30$	0	0
$31$	−3.00000	−0.538816	−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000	−0.538816	−0.269408	+	0.963026i	$0.586828\pi$
$32$	− 1.00000i	− 0.176777i
$33$	3.44949i	0.600479i
$34$	−4.44949	−0.763081
$35$	0	0
$36$	1.00000	0.166667
$37$	7.79796i	1.28198i	0.767551	+	0.640988i	$0.221475\pi$
$37$	7.79796i	1.28198i	−0.767551	+	0.640988i	$0.778525\pi$
$38$	1.00000i	0.162221i
$39$	2.44949	0.392232
$40$	0	0
$41$	−0.898979	−0.140397	−0.0701985	−	0.997533i	$-0.522363\pi$
$41$	−0.898979	−0.140397	−0.0701985	+	0.997533i	$0.522363\pi$
$42$	− 4.44949i	− 0.686571i
$43$	− 2.44949i	− 0.373544i	−0.982403	−	0.186772i	$-0.940197\pi$
$43$	− 2.44949i	− 0.373544i	0.982403	−	0.186772i	$-0.0598025\pi$
$44$	−3.44949	−0.520030
$45$	0	0
$46$	−1.00000	−0.147442
$47$	7.79796i	1.13745i	0.822528	+	0.568725i	$0.192563\pi$
$47$	7.79796i	1.13745i	−0.822528	+	0.568725i	$0.807437\pi$
$48$	1.00000i	0.144338i
$49$	−12.7980	−1.82828
$50$	0	0
$51$	4.44949	0.623053
$52$	2.44949i	0.339683i
$53$	− 7.44949i	− 1.02327i	−0.859204	−	0.511633i	$-0.829041\pi$
$53$	− 7.44949i	− 1.02327i	0.859204	−	0.511633i	$-0.170959\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	4.44949	0.594588
$57$	− 1.00000i	− 0.132453i
$58$	− 4.34847i	− 0.570982i
$59$	−6.44949	−0.839652	−0.419826	−	0.907605i	$-0.637909\pi$
$59$	−6.44949	−0.839652	−0.419826	+	0.907605i	$0.637909\pi$
$60$	0	0
$61$	−9.44949	−1.20988	−0.604942	−	0.796270i	$-0.706804\pi$
$61$	−9.44949	−1.20988	−0.604942	+	0.796270i	$0.706804\pi$
$62$	3.00000i	0.381000i
$63$	4.44949i	0.560583i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	3.44949	0.424603
$67$	− 15.2474i	− 1.86277i	−0.364033	−	0.931386i	$-0.618600\pi$
$67$	− 15.2474i	− 1.86277i	0.364033	−	0.931386i	$-0.381400\pi$
$68$	4.44949i	0.539580i
$69$	1.00000	0.120386
$70$	0	0
$71$	−1.55051	−0.184012	−0.0920059	−	0.995758i	$-0.529328\pi$
$71$	−1.55051	−0.184012	−0.0920059	+	0.995758i	$0.529328\pi$
$72$	− 1.00000i	− 0.117851i
$73$	− 1.00000i	− 0.117041i	−0.998286	−	0.0585206i	$-0.981362\pi$
$73$	− 1.00000i	− 0.117041i	0.998286	−	0.0585206i	$-0.0186383\pi$
$74$	7.79796	0.906494
$75$	0	0
$76$	1.00000	0.114708
$77$	− 15.3485i	− 1.74912i
$78$	− 2.44949i	− 0.277350i
$79$	5.00000	0.562544	0.281272	−	0.959628i	$-0.409244\pi$
$79$	5.00000	0.562544	0.281272	+	0.959628i	$0.409244\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0.898979i	0.0992757i
$83$	8.34847i	0.916364i	0.888859	+	0.458182i	$0.151499\pi$
$83$	8.34847i	0.916364i	−0.888859	+	0.458182i	$0.848501\pi$
$84$	−4.44949	−0.485479
$85$	0	0
$86$	−2.44949	−0.264135
$87$	4.34847i	0.466205i
$88$	3.44949i	0.367717i
$89$	−2.10102	−0.222708	−0.111354	−	0.993781i	$-0.535519\pi$
$89$	−2.10102	−0.222708	−0.111354	+	0.993781i	$0.535519\pi$
$90$	0	0
$91$	−10.8990	−1.14252
$92$	1.00000i	0.104257i
$93$	− 3.00000i	− 0.311086i
$94$	7.79796	0.804298
$95$	0	0
$96$	1.00000	0.102062
$97$	− 1.55051i	− 0.157430i	−0.996897	−	0.0787152i	$-0.974918\pi$
$97$	− 1.55051i	− 0.157430i	0.996897	−	0.0787152i	$-0.0250818\pi$
$98$	12.7980i	1.29279i
$99$	−3.44949	−0.346687
$100$	0	0
$101$	−1.55051	−0.154282	−0.0771408	−	0.997020i	$-0.524579\pi$
$101$	−1.55051	−0.154282	−0.0771408	+	0.997020i	$0.524579\pi$
$102$	− 4.44949i	− 0.440565i
$103$	1.89898i	0.187112i	0.995614	+	0.0935560i	$0.0298234\pi$
$103$	1.89898i	0.187112i	−0.995614	+	0.0935560i	$0.970177\pi$
$104$	2.44949	0.240192
$105$	0	0
$106$	−7.44949	−0.723558
$107$	− 17.3485i	− 1.67714i	−0.544794	−	0.838570i	$-0.683392\pi$
$107$	− 17.3485i	− 1.67714i	0.544794	−	0.838570i	$-0.316608\pi$
$108$	1.00000i	0.0962250i
$109$	2.89898	0.277672	0.138836	−	0.990315i	$-0.455664\pi$
$109$	2.89898	0.277672	0.138836	+	0.990315i	$0.455664\pi$
$110$	0	0
$111$	−7.79796	−0.740150
$112$	− 4.44949i	− 0.420437i
$113$	− 16.7980i	− 1.58022i	−0.612966	−	0.790110i	$-0.710024\pi$
$113$	− 16.7980i	− 1.58022i	0.612966	−	0.790110i	$-0.289976\pi$
$114$	−1.00000	−0.0936586
$115$	0	0
$116$	−4.34847	−0.403745
$117$	2.44949i	0.226455i
$118$	6.44949i	0.593724i
$119$	−19.7980	−1.81488
$120$	0	0
$121$	0.898979	0.0817254
$122$	9.44949i	0.855517i
$123$	− 0.898979i	− 0.0810583i
$124$	3.00000	0.269408
$125$	0	0
$126$	4.44949	0.396392
$127$	− 0.101021i	− 0.00896412i	−0.999990	−	0.00448206i	$-0.998573\pi$
$127$	− 0.101021i	− 0.00896412i	0.999990	−	0.00448206i	$-0.00142669\pi$
$128$	1.00000i	0.0883883i
$129$	2.44949	0.215666
$130$	0	0
$131$	9.24745	0.807953	0.403977	−	0.914769i	$-0.367628\pi$
$131$	9.24745	0.807953	0.403977	+	0.914769i	$0.367628\pi$
$132$	− 3.44949i	− 0.300240i
$133$	4.44949i	0.385820i
$134$	−15.2474	−1.31718
$135$	0	0
$136$	4.44949	0.381541
$137$	4.89898i	0.418548i	0.977857	+	0.209274i	$0.0671101\pi$
$137$	4.89898i	0.418548i	−0.977857	+	0.209274i	$0.932890\pi$
$138$	− 1.00000i	− 0.0851257i
$139$	22.2474	1.88700	0.943502	−	0.331367i	$-0.107510\pi$
$139$	22.2474	1.88700	0.943502	+	0.331367i	$0.107510\pi$
$140$	0	0
$141$	−7.79796	−0.656707
$142$	1.55051i	0.130116i
$143$	− 8.44949i	− 0.706582i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	−1.00000	−0.0827606
$147$	− 12.7980i	− 1.05556i
$148$	− 7.79796i	− 0.640988i
$149$	−5.79796	−0.474987	−0.237494	−	0.971389i	$-0.576326\pi$
$149$	−5.79796	−0.474987	−0.237494	+	0.971389i	$0.576326\pi$
$150$	0	0
$151$	−23.7980	−1.93665	−0.968325	−	0.249692i	$-0.919671\pi$
$151$	−23.7980	−1.93665	−0.968325	+	0.249692i	$0.919671\pi$
$152$	− 1.00000i	− 0.0811107i
$153$	4.44949i	0.359720i
$154$	−15.3485	−1.23681
$155$	0	0
$156$	−2.44949	−0.196116
$157$	4.89898i	0.390981i	0.980706	+	0.195491i	$0.0626299\pi$
$157$	4.89898i	0.390981i	−0.980706	+	0.195491i	$0.937370\pi$
$158$	− 5.00000i	− 0.397779i
$159$	7.44949	0.590783
$160$	0	0
$161$	−4.44949	−0.350669
$162$	− 1.00000i	− 0.0785674i
$163$	19.7980i	1.55070i	0.631534	+	0.775348i	$0.282425\pi$
$163$	19.7980i	1.55070i	−0.631534	+	0.775348i	$0.717575\pi$
$164$	0.898979	0.0701985
$165$	0	0
$166$	8.34847	0.647967
$167$	− 18.0000i	− 1.39288i	−0.717614	−	0.696441i	$-0.754766\pi$
$167$	− 18.0000i	− 1.39288i	0.717614	−	0.696441i	$-0.245234\pi$
$168$	4.44949i	0.343286i
$169$	7.00000	0.538462
$170$	0	0
$171$	1.00000	0.0764719
$172$	2.44949i	0.186772i
$173$	− 1.65153i	− 0.125564i	−0.998027	−	0.0627818i	$-0.980003\pi$
$173$	− 1.65153i	− 0.125564i	0.998027	−	0.0627818i	$-0.0199972\pi$
$174$	4.34847	0.329657
$175$	0	0
$176$	3.44949	0.260015
$177$	− 6.44949i	− 0.484773i
$178$	2.10102i	0.157478i
$179$	−25.7980	−1.92823	−0.964115	−	0.265485i	$-0.914468\pi$
$179$	−25.7980	−1.92823	−0.964115	+	0.265485i	$0.914468\pi$
$180$	0	0
$181$	−14.4495	−1.07402	−0.537011	−	0.843575i	$-0.680447\pi$
$181$	−14.4495	−1.07402	−0.537011	+	0.843575i	$0.680447\pi$
$182$	10.8990i	0.807886i
$183$	− 9.44949i	− 0.698526i
$184$	1.00000	0.0737210
$185$	0	0
$186$	−3.00000	−0.219971
$187$	− 15.3485i	− 1.12239i
$188$	− 7.79796i	− 0.568725i
$189$	−4.44949	−0.323653
$190$	0	0
$191$	−0.101021	−0.00730959	−0.00365479	−	0.999993i	$-0.501163\pi$
$191$	−0.101021	−0.00730959	−0.00365479	+	0.999993i	$0.501163\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	− 15.3485i	− 1.10481i	−0.833577	−	0.552403i	$-0.813711\pi$
$193$	− 15.3485i	− 1.10481i	0.833577	−	0.552403i	$-0.186289\pi$
$194$	−1.55051	−0.111320
$195$	0	0
$196$	12.7980	0.914140
$197$	− 27.3485i	− 1.94850i	−0.225475	−	0.974249i	$-0.572394\pi$
$197$	− 27.3485i	− 1.94850i	0.225475	−	0.974249i	$-0.427606\pi$
$198$	3.44949i	0.245145i
$199$	10.0000	0.708881	0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000	0.708881	0.354441	+	0.935079i	$0.384671\pi$
$200$	0	0
$201$	15.2474	1.07547
$202$	1.55051i	0.109094i
$203$	− 19.3485i	− 1.35800i
$204$	−4.44949	−0.311527
$205$	0	0
$206$	1.89898	0.132308
$207$	1.00000i	0.0695048i
$208$	− 2.44949i	− 0.169842i
$209$	−3.44949	−0.238606
$210$	0	0
$211$	−3.65153	−0.251382	−0.125691	−	0.992069i	$-0.540115\pi$
$211$	−3.65153	−0.251382	−0.125691	+	0.992069i	$0.540115\pi$
$212$	7.44949i	0.511633i
$213$	− 1.55051i	− 0.106239i
$214$	−17.3485	−1.18592
$215$	0	0
$216$	1.00000	0.0680414
$217$	13.3485i	0.906153i
$218$	− 2.89898i	− 0.196344i
$219$	1.00000	0.0675737
$220$	0	0
$221$	−10.8990	−0.733145
$222$	7.79796i	0.523365i
$223$	16.1010i	1.07820i	0.842240	+	0.539102i	$0.181236\pi$
$223$	16.1010i	1.07820i	−0.842240	+	0.539102i	$0.818764\pi$
$224$	−4.44949	−0.297294
$225$	0	0
$226$	−16.7980	−1.11738
$227$	− 29.5959i	− 1.96435i	−0.187969	−	0.982175i	$-0.560190\pi$
$227$	− 29.5959i	− 1.96435i	0.187969	−	0.982175i	$-0.439810\pi$
$228$	1.00000i	0.0662266i
$229$	−7.24745	−0.478925	−0.239462	−	0.970906i	$-0.576971\pi$
$229$	−7.24745	−0.478925	−0.239462	+	0.970906i	$0.576971\pi$
$230$	0	0
$231$	15.3485	1.00986
$232$	4.34847i	0.285491i
$233$	6.24745i	0.409284i	0.978837	+	0.204642i	$0.0656030\pi$
$233$	6.24745i	0.409284i	−0.978837	+	0.204642i	$0.934397\pi$
$234$	2.44949	0.160128
$235$	0	0
$236$	6.44949	0.419826
$237$	5.00000i	0.324785i
$238$	19.7980i	1.28331i
$239$	8.69694	0.562558	0.281279	−	0.959626i	$-0.409241\pi$
$239$	8.69694	0.562558	0.281279	+	0.959626i	$0.409241\pi$
$240$	0	0
$241$	−4.44949	−0.286617	−0.143308	−	0.989678i	$-0.545774\pi$
$241$	−4.44949	−0.286617	−0.143308	+	0.989678i	$0.545774\pi$
$242$	− 0.898979i	− 0.0577886i
$243$	1.00000i	0.0641500i
$244$	9.44949	0.604942
$245$	0	0
$246$	−0.898979	−0.0573168
$247$	2.44949i	0.155857i
$248$	− 3.00000i	− 0.190500i
$249$	−8.34847	−0.529063
$250$	0	0
$251$	−18.0000	−1.13615	−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000	−1.13615	−0.568075	+	0.822977i	$0.692312\pi$
$252$	− 4.44949i	− 0.280292i
$253$	− 3.44949i	− 0.216868i
$254$	−0.101021	−0.00633859
$255$	0	0
$256$	1.00000	0.0625000
$257$	21.4949i	1.34081i	0.741993	+	0.670407i	$0.233881\pi$
$257$	21.4949i	1.34081i	−0.741993	+	0.670407i	$0.766119\pi$
$258$	− 2.44949i	− 0.152499i
$259$	34.6969	2.15596
$260$	0	0
$261$	−4.34847	−0.269163
$262$	− 9.24745i	− 0.571309i
$263$	− 6.79796i	− 0.419180i	−0.977789	−	0.209590i	$-0.932787\pi$
$263$	− 6.79796i	− 0.419180i	0.977789	−	0.209590i	$-0.0672129\pi$
$264$	−3.44949	−0.212301
$265$	0	0
$266$	4.44949	0.272816
$267$	− 2.10102i	− 0.128580i
$268$	15.2474i	0.931386i
$269$	2.89898	0.176754	0.0883769	−	0.996087i	$-0.471832\pi$
$269$	2.89898	0.176754	0.0883769	+	0.996087i	$0.471832\pi$
$270$	0	0
$271$	22.9444	1.39377	0.696886	−	0.717182i	$-0.254568\pi$
$271$	22.9444	1.39377	0.696886	+	0.717182i	$0.254568\pi$
$272$	− 4.44949i	− 0.269790i
$273$	− 10.8990i	− 0.659636i
$274$	4.89898	0.295958
$275$	0	0
$276$	−1.00000	−0.0601929
$277$	− 21.0454i	− 1.26450i	−0.774766	−	0.632248i	$-0.782132\pi$
$277$	− 21.0454i	− 1.26450i	0.774766	−	0.632248i	$-0.217868\pi$
$278$	− 22.2474i	− 1.33431i
$279$	3.00000	0.179605
$280$	0	0
$281$	7.00000	0.417585	0.208792	−	0.977960i	$-0.433047\pi$
$281$	7.00000	0.417585	0.208792	+	0.977960i	$0.433047\pi$
$282$	7.79796i	0.464362i
$283$	29.7980i	1.77130i	0.464349	+	0.885652i	$0.346288\pi$
$283$	29.7980i	1.77130i	−0.464349	+	0.885652i	$0.653712\pi$
$284$	1.55051	0.0920059
$285$	0	0
$286$	−8.44949	−0.499629
$287$	4.00000i	0.236113i
$288$	1.00000i	0.0589256i
$289$	−2.79796	−0.164586
$290$	0	0
$291$	1.55051	0.0908925
$292$	1.00000i	0.0585206i
$293$	− 23.2474i	− 1.35813i	−0.734078	−	0.679065i	$-0.762385\pi$
$293$	− 23.2474i	− 1.35813i	0.734078	−	0.679065i	$-0.237615\pi$
$294$	−12.7980	−0.746392
$295$	0	0
$296$	−7.79796	−0.453247
$297$	− 3.44949i	− 0.200160i
$298$	5.79796i	0.335867i
$299$	−2.44949	−0.141658
$300$	0	0
$301$	−10.8990	−0.628207
$302$	23.7980i	1.36942i
$303$	− 1.55051i	− 0.0890745i
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	4.44949	0.254360
$307$	16.3485i	0.933056i	0.884506	+	0.466528i	$0.154495\pi$
$307$	16.3485i	0.933056i	−0.884506	+	0.466528i	$0.845505\pi$
$308$	15.3485i	0.874560i
$309$	−1.89898	−0.108029
$310$	0	0
$311$	−23.7980	−1.34946	−0.674729	−	0.738065i	$-0.735740\pi$
$311$	−23.7980	−1.34946	−0.674729	+	0.738065i	$0.735740\pi$
$312$	2.44949i	0.138675i
$313$	31.8990i	1.80304i	0.432741	+	0.901518i	$0.357547\pi$
$313$	31.8990i	1.80304i	−0.432741	+	0.901518i	$0.642453\pi$
$314$	4.89898	0.276465
$315$	0	0
$316$	−5.00000	−0.281272
$317$	− 15.2474i	− 0.856382i	−0.903688	−	0.428191i	$-0.859151\pi$
$317$	− 15.2474i	− 0.856382i	0.903688	−	0.428191i	$-0.140849\pi$
$318$	− 7.44949i	− 0.417747i
$319$	15.0000	0.839839
$320$	0	0
$321$	17.3485	0.968297
$322$	4.44949i	0.247960i
$323$	4.44949i	0.247576i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	19.7980	1.09651
$327$	2.89898i	0.160314i
$328$	− 0.898979i	− 0.0496378i
$329$	34.6969	1.91290
$330$	0	0
$331$	−22.3485	−1.22838	−0.614191	−	0.789157i	$-0.710518\pi$
$331$	−22.3485	−1.22838	−0.614191	+	0.789157i	$0.710518\pi$
$332$	− 8.34847i	− 0.458182i
$333$	− 7.79796i	− 0.427326i
$334$	−18.0000	−0.984916
$335$	0	0
$336$	4.44949	0.242740
$337$	24.8990i	1.35633i	0.734908	+	0.678167i	$0.237225\pi$
$337$	24.8990i	1.35633i	−0.734908	+	0.678167i	$0.762775\pi$
$338$	− 7.00000i	− 0.380750i
$339$	16.7980	0.912340
$340$	0	0
$341$	−10.3485	−0.560401
$342$	− 1.00000i	− 0.0540738i
$343$	25.7980i	1.39296i
$344$	2.44949	0.132068
$345$	0	0
$346$	−1.65153	−0.0887868
$347$	23.5959i	1.26670i	0.773867	+	0.633348i	$0.218320\pi$
$347$	23.5959i	1.26670i	−0.773867	+	0.633348i	$0.781680\pi$
$348$	− 4.34847i	− 0.233102i
$349$	25.9444	1.38877	0.694386	−	0.719603i	$-0.255676\pi$
$349$	25.9444	1.38877	0.694386	+	0.719603i	$0.255676\pi$
$350$	0	0
$351$	−2.44949	−0.130744
$352$	− 3.44949i	− 0.183858i
$353$	− 18.2474i	− 0.971214i	−0.874177	−	0.485607i	$-0.838599\pi$
$353$	− 18.2474i	− 0.971214i	0.874177	−	0.485607i	$-0.161401\pi$
$354$	−6.44949	−0.342787
$355$	0	0
$356$	2.10102	0.111354
$357$	− 19.7980i	− 1.04782i
$358$	25.7980i	1.36346i
$359$	22.8990	1.20856	0.604281	−	0.796771i	$-0.293460\pi$
$359$	22.8990	1.20856	0.604281	+	0.796771i	$0.293460\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	14.4495i	0.759448i
$363$	0.898979i	0.0471842i
$364$	10.8990	0.571262
$365$	0	0
$366$	−9.44949	−0.493933
$367$	5.55051i	0.289734i	0.989451	+	0.144867i	$0.0462755\pi$
$367$	5.55051i	0.289734i	−0.989451	+	0.144867i	$0.953725\pi$
$368$	− 1.00000i	− 0.0521286i
$369$	0.898979	0.0467990
$370$	0	0
$371$	−33.1464	−1.72088
$372$	3.00000i	0.155543i
$373$	− 22.4495i	− 1.16239i	−0.813764	−	0.581195i	$-0.802585\pi$
$373$	− 22.4495i	− 1.16239i	0.813764	−	0.581195i	$-0.197415\pi$
$374$	−15.3485	−0.793650
$375$	0	0
$376$	−7.79796	−0.402149
$377$	− 10.6515i	− 0.548582i
$378$	4.44949i	0.228857i
$379$	1.30306	0.0669338	0.0334669	−	0.999440i	$-0.489345\pi$
$379$	1.30306	0.0669338	0.0334669	+	0.999440i	$0.489345\pi$
$380$	0	0
$381$	0.101021	0.00517544
$382$	0.101021i	0.00516866i
$383$	16.2474i	0.830206i	0.909774	+	0.415103i	$0.136254\pi$
$383$	16.2474i	0.830206i	−0.909774	+	0.415103i	$0.863746\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−15.3485	−0.781217
$387$	2.44949i	0.124515i
$388$	1.55051i	0.0787152i
$389$	−21.5959	−1.09496	−0.547478	−	0.836820i	$-0.684412\pi$
$389$	−21.5959	−1.09496	−0.547478	+	0.836820i	$0.684412\pi$
$390$	0	0
$391$	−4.44949	−0.225020
$392$	− 12.7980i	− 0.646395i
$393$	9.24745i	0.466472i
$394$	−27.3485	−1.37780
$395$	0	0
$396$	3.44949	0.173343
$397$	− 23.9444i	− 1.20173i	−0.799349	−	0.600867i	$-0.794822\pi$
$397$	− 23.9444i	− 1.20173i	0.799349	−	0.600867i	$-0.205178\pi$
$398$	− 10.0000i	− 0.501255i
$399$	−4.44949	−0.222753
$400$	0	0
$401$	11.2020	0.559403	0.279702	−	0.960087i	$-0.409764\pi$
$401$	11.2020	0.559403	0.279702	+	0.960087i	$0.409764\pi$
$402$	− 15.2474i	− 0.760474i
$403$	7.34847i	0.366053i
$404$	1.55051	0.0771408
$405$	0	0
$406$	−19.3485	−0.960248
$407$	26.8990i	1.33333i
$408$	4.44949i	0.220283i
$409$	22.8990	1.13228	0.566141	−	0.824309i	$-0.308436\pi$
$409$	22.8990	1.13228	0.566141	+	0.824309i	$0.308436\pi$
$410$	0	0
$411$	−4.89898	−0.241649
$412$	− 1.89898i	− 0.0935560i
$413$	28.6969i	1.41208i
$414$	1.00000	0.0491473
$415$	0	0
$416$	−2.44949	−0.120096
$417$	22.2474i	1.08946i
$418$	3.44949i	0.168720i
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	3.65153i	0.177754i
$423$	− 7.79796i	− 0.379150i
$424$	7.44949	0.361779
$425$	0	0
$426$	−1.55051	−0.0751225
$427$	42.0454i	2.03472i
$428$	17.3485i	0.838570i
$429$	8.44949	0.407945
$430$	0	0
$431$	−5.10102	−0.245708	−0.122854	−	0.992425i	$-0.539205\pi$
$431$	−5.10102	−0.245708	−0.122854	+	0.992425i	$0.539205\pi$
$432$	− 1.00000i	− 0.0481125i
$433$	4.65153i	0.223538i	0.993734	+	0.111769i	$0.0356517\pi$
$433$	4.65153i	0.223538i	−0.993734	+	0.111769i	$0.964348\pi$
$434$	13.3485	0.640747
$435$	0	0
$436$	−2.89898	−0.138836
$437$	1.00000i	0.0478365i
$438$	− 1.00000i	− 0.0477818i
$439$	12.1010	0.577550	0.288775	−	0.957397i	$-0.406752\pi$
$439$	12.1010	0.577550	0.288775	+	0.957397i	$0.406752\pi$
$440$	0	0
$441$	12.7980	0.609427
$442$	10.8990i	0.518412i
$443$	21.2474i	1.00950i	0.863267	+	0.504748i	$0.168415\pi$
$443$	21.2474i	1.00950i	−0.863267	+	0.504748i	$0.831585\pi$
$444$	7.79796	0.370075
$445$	0	0
$446$	16.1010	0.762405
$447$	− 5.79796i	− 0.274234i
$448$	4.44949i	0.210219i
$449$	15.0000	0.707894	0.353947	−	0.935266i	$-0.384839\pi$
$449$	15.0000	0.707894	0.353947	+	0.935266i	$0.384839\pi$
$450$	0	0
$451$	−3.10102	−0.146021
$452$	16.7980i	0.790110i
$453$	− 23.7980i	− 1.11813i
$454$	−29.5959	−1.38901
$455$	0	0
$456$	1.00000	0.0468293
$457$	24.8990i	1.16473i	0.812929	+	0.582363i	$0.197872\pi$
$457$	24.8990i	1.16473i	−0.812929	+	0.582363i	$0.802128\pi$
$458$	7.24745i	0.338651i
$459$	−4.44949	−0.207684
$460$	0	0
$461$	12.0000	0.558896	0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000	0.558896	0.279448	+	0.960161i	$0.409849\pi$
$462$	− 15.3485i	− 0.714075i
$463$	− 14.6969i	− 0.683025i	−0.939877	−	0.341512i	$-0.889061\pi$
$463$	− 14.6969i	− 0.683025i	0.939877	−	0.341512i	$-0.110939\pi$
$464$	4.34847	0.201873
$465$	0	0
$466$	6.24745	0.289407
$467$	6.34847i	0.293772i	0.989153	+	0.146886i	$0.0469251\pi$
$467$	6.34847i	0.293772i	−0.989153	+	0.146886i	$0.953075\pi$
$468$	− 2.44949i	− 0.113228i
$469$	−67.8434	−3.13272
$470$	0	0
$471$	−4.89898	−0.225733
$472$	− 6.44949i	− 0.296862i
$473$	− 8.44949i	− 0.388508i
$474$	5.00000	0.229658
$475$	0	0
$476$	19.7980	0.907438
$477$	7.44949i	0.341089i
$478$	− 8.69694i	− 0.397789i
$479$	−16.5959	−0.758287	−0.379143	−	0.925338i	$-0.623781\pi$
$479$	−16.5959	−0.758287	−0.379143	+	0.925338i	$0.623781\pi$
$480$	0	0
$481$	19.1010	0.870932
$482$	4.44949i	0.202669i
$483$	− 4.44949i	− 0.202459i
$484$	−0.898979	−0.0408627
$485$	0	0
$486$	1.00000	0.0453609
$487$	32.0000i	1.45006i	0.688718	+	0.725029i	$0.258174\pi$
$487$	32.0000i	1.45006i	−0.688718	+	0.725029i	$0.741826\pi$
$488$	− 9.44949i	− 0.427758i
$489$	−19.7980	−0.895295
$490$	0	0
$491$	43.5959	1.96746	0.983728	−	0.179664i	$-0.0575009\pi$
$491$	43.5959	1.96746	0.983728	+	0.179664i	$0.0575009\pi$
$492$	0.898979i	0.0405291i
$493$	− 19.3485i	− 0.871411i
$494$	2.44949	0.110208
$495$	0	0
$496$	−3.00000	−0.134704
$497$	6.89898i	0.309462i
$498$	8.34847i	0.374104i
$499$	23.8434	1.06738	0.533688	−	0.845682i	$-0.320806\pi$
$499$	23.8434	1.06738	0.533688	+	0.845682i	$0.320806\pi$
$500$	0	0
$501$	18.0000	0.804181
$502$	18.0000i	0.803379i
$503$	29.7980i	1.32863i	0.747455	+	0.664313i	$0.231276\pi$
$503$	29.7980i	1.32863i	−0.747455	+	0.664313i	$0.768724\pi$
$504$	−4.44949	−0.198196
$505$	0	0
$506$	−3.44949	−0.153349
$507$	7.00000i	0.310881i
$508$	0.101021i	0.00448206i
$509$	30.1464	1.33622	0.668108	−	0.744064i	$-0.267104\pi$
$509$	30.1464	1.33622	0.668108	+	0.744064i	$0.267104\pi$
$510$	0	0
$511$	−4.44949	−0.196834
$512$	− 1.00000i	− 0.0441942i
$513$	1.00000i	0.0441511i
$514$	21.4949	0.948099
$515$	0	0
$516$	−2.44949	−0.107833
$517$	26.8990i	1.18302i
$518$	− 34.6969i	− 1.52450i
$519$	1.65153	0.0724942
$520$	0	0
$521$	15.6969	0.687695	0.343848	−	0.939025i	$-0.388270\pi$
$521$	15.6969	0.687695	0.343848	+	0.939025i	$0.388270\pi$
$522$	4.34847i	0.190327i
$523$	− 33.3939i	− 1.46021i	−0.683334	−	0.730106i	$-0.739471\pi$
$523$	− 33.3939i	− 1.46021i	0.683334	−	0.730106i	$-0.260529\pi$
$524$	−9.24745	−0.403977
$525$	0	0
$526$	−6.79796	−0.296405
$527$	13.3485i	0.581468i
$528$	3.44949i	0.150120i
$529$	22.0000	0.956522
$530$	0	0
$531$	6.44949	0.279884
$532$	− 4.44949i	− 0.192910i
$533$	2.20204i	0.0953810i
$534$	−2.10102	−0.0909200
$535$	0	0
$536$	15.2474	0.658589
$537$	− 25.7980i	− 1.11326i
$538$	− 2.89898i	− 0.124984i
$539$	−44.1464	−1.90152
$540$	0	0
$541$	22.1464	0.952149	0.476075	−	0.879405i	$-0.342059\pi$
$541$	22.1464	0.952149	0.476075	+	0.879405i	$0.342059\pi$
$542$	− 22.9444i	− 0.985546i
$543$	− 14.4495i	− 0.620087i
$544$	−4.44949	−0.190770
$545$	0	0
$546$	−10.8990	−0.466433
$547$	46.6413i	1.99424i	0.0758461	+	0.997120i	$0.475834\pi$
$547$	46.6413i	1.99424i	−0.0758461	+	0.997120i	$0.524166\pi$
$548$	− 4.89898i	− 0.209274i
$549$	9.44949	0.403294
$550$	0	0
$551$	−4.34847	−0.185251
$552$	1.00000i	0.0425628i
$553$	− 22.2474i	− 0.946058i
$554$	−21.0454	−0.894134
$555$	0	0
$556$	−22.2474	−0.943502
$557$	− 27.3485i	− 1.15879i	−0.815046	−	0.579396i	$-0.803289\pi$
$557$	− 27.3485i	− 1.15879i	0.815046	−	0.579396i	$-0.196711\pi$
$558$	− 3.00000i	− 0.127000i
$559$	−6.00000	−0.253773
$560$	0	0
$561$	15.3485	0.648013
$562$	− 7.00000i	− 0.295277i
$563$	6.24745i	0.263299i	0.991296	+	0.131649i	$0.0420273\pi$
$563$	6.24745i	0.263299i	−0.991296	+	0.131649i	$0.957973\pi$
$564$	7.79796	0.328353
$565$	0	0
$566$	29.7980	1.25250
$567$	− 4.44949i	− 0.186861i
$568$	− 1.55051i	− 0.0650580i
$569$	33.1918	1.39147	0.695737	−	0.718297i	$-0.255078\pi$
$569$	33.1918	1.39147	0.695737	+	0.718297i	$0.255078\pi$
$570$	0	0
$571$	−10.2474	−0.428842	−0.214421	−	0.976741i	$-0.568787\pi$
$571$	−10.2474	−0.428842	−0.214421	+	0.976741i	$0.568787\pi$
$572$	8.44949i	0.353291i
$573$	− 0.101021i	− 0.00422019i
$574$	4.00000	0.166957
$575$	0	0
$576$	1.00000	0.0416667
$577$	− 0.101021i	− 0.00420554i	−0.999998	−	0.00210277i	$-0.999331\pi$
$577$	− 0.101021i	− 0.00420554i	0.999998	−	0.00210277i	$-0.000669333\pi$
$578$	2.79796i	0.116380i
$579$	15.3485	0.637861
$580$	0	0
$581$	37.1464	1.54109
$582$	− 1.55051i	− 0.0642707i
$583$	− 25.6969i	− 1.06426i
$584$	1.00000	0.0413803
$585$	0	0
$586$	−23.2474	−0.960343
$587$	33.4495i	1.38061i	0.723519	+	0.690304i	$0.242523\pi$
$587$	33.4495i	1.38061i	−0.723519	+	0.690304i	$0.757477\pi$
$588$	12.7980i	0.527779i
$589$	3.00000	0.123613
$590$	0	0
$591$	27.3485	1.12497
$592$	7.79796i	0.320494i
$593$	8.49490i	0.348844i	0.984671	+	0.174422i	$0.0558056\pi$
$593$	8.49490i	0.348844i	−0.984671	+	0.174422i	$0.944194\pi$
$594$	−3.44949	−0.141534
$595$	0	0
$596$	5.79796	0.237494
$597$	10.0000i	0.409273i
$598$	2.44949i	0.100167i
$599$	−16.4495	−0.672108	−0.336054	−	0.941843i	$-0.609092\pi$
$599$	−16.4495	−0.672108	−0.336054	+	0.941843i	$0.609092\pi$
$600$	0	0
$601$	17.1464	0.699417	0.349709	−	0.936858i	$-0.386281\pi$
$601$	17.1464	0.699417	0.349709	+	0.936858i	$0.386281\pi$
$602$	10.8990i	0.444209i
$603$	15.2474i	0.620924i
$604$	23.7980	0.968325
$605$	0	0
$606$	−1.55051	−0.0629852
$607$	− 46.1918i	− 1.87487i	−0.348162	−	0.937434i	$-0.613194\pi$
$607$	− 46.1918i	− 1.87487i	0.348162	−	0.937434i	$-0.386806\pi$
$608$	1.00000i	0.0405554i
$609$	19.3485	0.784040
$610$	0	0
$611$	19.1010	0.772745
$612$	− 4.44949i	− 0.179860i
$613$	37.1918i	1.50216i	0.660209	+	0.751082i	$0.270468\pi$
$613$	37.1918i	1.50216i	−0.660209	+	0.751082i	$0.729532\pi$
$614$	16.3485	0.659771
$615$	0	0
$616$	15.3485	0.618407
$617$	− 28.2929i	− 1.13903i	−0.821982	−	0.569514i	$-0.807132\pi$
$617$	− 28.2929i	− 1.13903i	0.821982	−	0.569514i	$-0.192868\pi$
$618$	1.89898i	0.0763882i
$619$	−45.1464	−1.81459	−0.907294	−	0.420497i	$-0.861856\pi$
$619$	−45.1464	−1.81459	−0.907294	+	0.420497i	$0.861856\pi$
$620$	0	0
$621$	−1.00000	−0.0401286
$622$	23.7980i	0.954211i
$623$	9.34847i	0.374539i
$624$	2.44949	0.0980581
$625$	0	0
$626$	31.8990	1.27494
$627$	− 3.44949i	− 0.137759i
$628$	− 4.89898i	− 0.195491i
$629$	34.6969	1.38346
$630$	0	0
$631$	−28.0000	−1.11466	−0.557331	−	0.830290i	$-0.688175\pi$
$631$	−28.0000	−1.11466	−0.557331	+	0.830290i	$0.688175\pi$
$632$	5.00000i	0.198889i
$633$	− 3.65153i	− 0.145135i
$634$	−15.2474	−0.605554
$635$	0	0
$636$	−7.44949	−0.295391
$637$	31.3485i	1.24207i
$638$	− 15.0000i	− 0.593856i
$639$	1.55051	0.0613372
$640$	0	0
$641$	37.7980	1.49293	0.746465	−	0.665425i	$-0.231750\pi$
$641$	37.7980	1.49293	0.746465	+	0.665425i	$0.231750\pi$
$642$	− 17.3485i	− 0.684689i
$643$	− 0.202041i	− 0.00796772i	−0.999992	−	0.00398386i	$-0.998732\pi$
$643$	− 0.202041i	− 0.00796772i	0.999992	−	0.00398386i	$-0.00126811\pi$
$644$	4.44949	0.175334
$645$	0	0
$646$	4.44949	0.175063
$647$	− 25.8990i	− 1.01819i	−0.860709	−	0.509097i	$-0.829979\pi$
$647$	− 25.8990i	− 1.01819i	0.860709	−	0.509097i	$-0.170021\pi$
$648$	1.00000i	0.0392837i
$649$	−22.2474	−0.873289
$650$	0	0
$651$	−13.3485	−0.523168
$652$	− 19.7980i	− 0.775348i
$653$	− 14.6969i	− 0.575136i	−0.957760	−	0.287568i	$-0.907153\pi$
$653$	− 14.6969i	− 0.575136i	0.957760	−	0.287568i	$-0.0928467\pi$
$654$	2.89898	0.113359
$655$	0	0
$656$	−0.898979	−0.0350993
$657$	1.00000i	0.0390137i
$658$	− 34.6969i	− 1.35263i
$659$	18.0454	0.702949	0.351475	−	0.936197i	$-0.385680\pi$
$659$	18.0454	0.702949	0.351475	+	0.936197i	$0.385680\pi$
$660$	0	0
$661$	23.5959	0.917775	0.458887	−	0.888494i	$-0.348248\pi$
$661$	23.5959	0.917775	0.458887	+	0.888494i	$0.348248\pi$
$662$	22.3485i	0.868598i
$663$	− 10.8990i	− 0.423281i
$664$	−8.34847	−0.323983
$665$	0	0
$666$	−7.79796	−0.302165
$667$	− 4.34847i	− 0.168373i
$668$	18.0000i	0.696441i
$669$	−16.1010	−0.622501
$670$	0	0
$671$	−32.5959	−1.25835
$672$	− 4.44949i	− 0.171643i
$673$	− 45.3485i	− 1.74806i	−0.485876	−	0.874028i	$-0.661499\pi$
$673$	− 45.3485i	− 1.74806i	0.485876	−	0.874028i	$-0.338501\pi$
$674$	24.8990	0.959073
$675$	0	0
$676$	−7.00000	−0.269231
$677$	− 22.3485i	− 0.858921i	−0.903086	−	0.429461i	$-0.858704\pi$
$677$	− 22.3485i	− 0.858921i	0.903086	−	0.429461i	$-0.141296\pi$
$678$	− 16.7980i	− 0.645122i
$679$	−6.89898	−0.264759
$680$	0	0
$681$	29.5959	1.13412
$682$	10.3485i	0.396263i
$683$	− 35.6413i	− 1.36378i	−0.731456	−	0.681889i	$-0.761159\pi$
$683$	− 35.6413i	− 1.36378i	0.731456	−	0.681889i	$-0.238841\pi$
$684$	−1.00000	−0.0382360
$685$	0	0
$686$	25.7980	0.984971
$687$	− 7.24745i	− 0.276507i
$688$	− 2.44949i	− 0.0933859i
$689$	−18.2474	−0.695172
$690$	0	0
$691$	9.75255	0.371005	0.185502	−	0.982644i	$-0.440609\pi$
$691$	9.75255	0.371005	0.185502	+	0.982644i	$0.440609\pi$
$692$	1.65153i	0.0627818i
$693$	15.3485i	0.583040i
$694$	23.5959	0.895689
$695$	0	0
$696$	−4.34847	−0.164828
$697$	4.00000i	0.151511i
$698$	− 25.9444i	− 0.982010i
$699$	−6.24745	−0.236300
$700$	0	0
$701$	−32.4949	−1.22732	−0.613658	−	0.789572i	$-0.710302\pi$
$701$	−32.4949	−1.22732	−0.613658	+	0.789572i	$0.710302\pi$
$702$	2.44949i	0.0924500i
$703$	− 7.79796i	− 0.294106i
$704$	−3.44949	−0.130008
$705$	0	0
$706$	−18.2474	−0.686752
$707$	6.89898i	0.259463i
$708$	6.44949i	0.242387i
$709$	12.7526	0.478932	0.239466	−	0.970905i	$-0.423028\pi$
$709$	12.7526	0.478932	0.239466	+	0.970905i	$0.423028\pi$
$710$	0	0
$711$	−5.00000	−0.187515
$712$	− 2.10102i	− 0.0787391i
$713$	3.00000i	0.112351i
$714$	−19.7980	−0.740920
$715$	0	0
$716$	25.7980	0.964115
$717$	8.69694i	0.324793i
$718$	− 22.8990i	− 0.854582i
$719$	19.2020	0.716115	0.358058	−	0.933699i	$-0.383439\pi$
$719$	19.2020	0.716115	0.358058	+	0.933699i	$0.383439\pi$
$720$	0	0
$721$	8.44949	0.314675
$722$	− 1.00000i	− 0.0372161i
$723$	− 4.44949i	− 0.165478i
$724$	14.4495	0.537011
$725$	0	0
$726$	0.898979	0.0333643
$727$	− 22.4949i	− 0.834290i	−0.908840	−	0.417145i	$-0.863031\pi$
$727$	− 22.4949i	− 0.834290i	0.908840	−	0.417145i	$-0.136969\pi$
$728$	− 10.8990i	− 0.403943i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−10.8990	−0.403113
$732$	9.44949i	0.349263i
$733$	4.14643i	0.153152i	0.997064	+	0.0765759i	$0.0243988\pi$
$733$	4.14643i	0.153152i	−0.997064	+	0.0765759i	$0.975601\pi$
$734$	5.55051	0.204873
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	− 52.5959i	− 1.93740i
$738$	− 0.898979i	− 0.0330919i
$739$	−32.8990	−1.21021	−0.605104	−	0.796146i	$-0.706869\pi$
$739$	−32.8990	−1.21021	−0.605104	+	0.796146i	$0.706869\pi$
$740$	0	0
$741$	−2.44949	−0.0899843
$742$	33.1464i	1.21684i
$743$	− 53.3939i	− 1.95883i	−0.201854	−	0.979416i	$-0.564697\pi$
$743$	− 53.3939i	− 1.95883i	0.201854	−	0.979416i	$-0.435303\pi$
$744$	3.00000	0.109985
$745$	0	0
$746$	−22.4495	−0.821934
$747$	− 8.34847i	− 0.305455i
$748$	15.3485i	0.561196i
$749$	−77.1918	−2.82053
$750$	0	0
$751$	−23.7980	−0.868400	−0.434200	−	0.900817i	$-0.642969\pi$
$751$	−23.7980	−0.868400	−0.434200	+	0.900817i	$0.642969\pi$
$752$	7.79796i	0.284362i
$753$	− 18.0000i	− 0.655956i
$754$	−10.6515	−0.387906
$755$	0	0
$756$	4.44949	0.161826
$757$	− 48.1464i	− 1.74991i	−0.484203	−	0.874956i	$-0.660890\pi$
$757$	− 48.1464i	− 1.74991i	0.484203	−	0.874956i	$-0.339110\pi$
$758$	− 1.30306i	− 0.0473293i
$759$	3.44949	0.125209
$760$	0	0
$761$	51.3485	1.86138	0.930690	−	0.365808i	$-0.119207\pi$
$761$	51.3485	1.86138	0.930690	+	0.365808i	$0.119207\pi$
$762$	− 0.101021i	− 0.00365959i
$763$	− 12.8990i	− 0.466974i
$764$	0.101021	0.00365479
$765$	0	0
$766$	16.2474	0.587044
$767$	15.7980i	0.570431i
$768$	1.00000i	0.0360844i
$769$	7.89898	0.284844	0.142422	−	0.989806i	$-0.454511\pi$
$769$	7.89898	0.284844	0.142422	+	0.989806i	$0.454511\pi$
$770$	0	0
$771$	−21.4949	−0.774120
$772$	15.3485i	0.552403i
$773$	18.4949i	0.665215i	0.943065	+	0.332608i	$0.107928\pi$
$773$	18.4949i	0.665215i	−0.943065	+	0.332608i	$0.892072\pi$
$774$	2.44949	0.0880451
$775$	0	0
$776$	1.55051	0.0556601
$777$	34.6969i	1.24475i
$778$	21.5959i	0.774251i
$779$	0.898979	0.0322093
$780$	0	0
$781$	−5.34847	−0.191383
$782$	4.44949i	0.159113i
$783$	− 4.34847i	− 0.155402i
$784$	−12.7980	−0.457070
$785$	0	0
$786$	9.24745	0.329846
$787$	33.4495i	1.19235i	0.802856	+	0.596173i	$0.203313\pi$
$787$	33.4495i	1.19235i	−0.802856	+	0.596173i	$0.796687\pi$
$788$	27.3485i	0.974249i
$789$	6.79796	0.242014
$790$	0	0
$791$	−74.7423	−2.65753
$792$	− 3.44949i	− 0.122572i
$793$	23.1464i	0.821954i
$794$	−23.9444	−0.849755
$795$	0	0
$796$	−10.0000	−0.354441
$797$	− 3.50510i	− 0.124157i	−0.998071	−	0.0620786i	$-0.980227\pi$
$797$	− 3.50510i	− 0.124157i	0.998071	−	0.0620786i	$-0.0197729\pi$
$798$	4.44949i	0.157510i
$799$	34.6969	1.22749
$800$	0	0
$801$	2.10102	0.0742359
$802$	− 11.2020i	− 0.395558i
$803$	− 3.44949i	− 0.121730i
$804$	−15.2474	−0.537736
$805$	0	0
$806$	7.34847	0.258839
$807$	2.89898i	0.102049i
$808$	− 1.55051i	− 0.0545468i
$809$	3.55051	0.124829	0.0624146	−	0.998050i	$-0.480120\pi$
$809$	3.55051	0.124829	0.0624146	+	0.998050i	$0.480120\pi$
$810$	0	0
$811$	−19.4495	−0.682964	−0.341482	−	0.939888i	$-0.610929\pi$
$811$	−19.4495	−0.682964	−0.341482	+	0.939888i	$0.610929\pi$
$812$	19.3485i	0.678998i
$813$	22.9444i	0.804695i
$814$	26.8990	0.942809
$815$	0	0
$816$	4.44949	0.155763
$817$	2.44949i	0.0856968i
$818$	− 22.8990i	− 0.800644i
$819$	10.8990	0.380841
$820$	0	0
$821$	−23.1464	−0.807816	−0.403908	−	0.914800i	$-0.632348\pi$
$821$	−23.1464	−0.807816	−0.403908	+	0.914800i	$0.632348\pi$
$822$	4.89898i	0.170872i
$823$	− 31.7980i	− 1.10841i	−0.832381	−	0.554204i	$-0.813023\pi$
$823$	− 31.7980i	− 1.10841i	0.832381	−	0.554204i	$-0.186977\pi$
$824$	−1.89898	−0.0661541
$825$	0	0
$826$	28.6969	0.998494
$827$	− 0.247449i	− 0.00860463i	−0.999991	−	0.00430232i	$-0.998631\pi$
$827$	− 0.247449i	− 0.00860463i	0.999991	−	0.00430232i	$-0.00136947\pi$
$828$	− 1.00000i	− 0.0347524i
$829$	39.6413	1.37680	0.688400	−	0.725331i	$-0.258313\pi$
$829$	39.6413	1.37680	0.688400	+	0.725331i	$0.258313\pi$
$830$	0	0
$831$	21.0454	0.730057
$832$	2.44949i	0.0849208i
$833$	56.9444i	1.97301i
$834$	22.2474	0.770366
$835$	0	0
$836$	3.44949	0.119303
$837$	3.00000i	0.103695i
$838$	0	0
$839$	−10.6515	−0.367732	−0.183866	−	0.982951i	$-0.558861\pi$
$839$	−10.6515	−0.367732	−0.183866	+	0.982951i	$0.558861\pi$
$840$	0	0
$841$	−10.0908	−0.347959
$842$	− 22.0000i	− 0.758170i
$843$	7.00000i	0.241093i
$844$	3.65153	0.125691
$845$	0	0
$846$	−7.79796	−0.268099
$847$	− 4.00000i	− 0.137442i
$848$	− 7.44949i	− 0.255817i
$849$	−29.7980	−1.02266
$850$	0	0
$851$	7.79796	0.267311
$852$	1.55051i	0.0531196i
$853$	1.10102i	0.0376982i	0.999822	+	0.0188491i	$0.00600021\pi$
$853$	1.10102i	0.0376982i	−0.999822	+	0.0188491i	$0.994000\pi$
$854$	42.0454	1.43876
$855$	0	0
$856$	17.3485	0.592958
$857$	36.4949i	1.24664i	0.781966	+	0.623321i	$0.214217\pi$
$857$	36.4949i	1.24664i	−0.781966	+	0.623321i	$0.785783\pi$
$858$	− 8.44949i	− 0.288461i
$859$	4.20204	0.143372	0.0716859	−	0.997427i	$-0.477162\pi$
$859$	4.20204	0.143372	0.0716859	+	0.997427i	$0.477162\pi$
$860$	0	0
$861$	−4.00000	−0.136320
$862$	5.10102i	0.173741i
$863$	− 17.3031i	− 0.589003i	−0.955651	−	0.294502i	$-0.904846\pi$
$863$	− 17.3031i	− 0.589003i	0.955651	−	0.294502i	$-0.0951536\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	4.65153	0.158065
$867$	− 2.79796i	− 0.0950237i
$868$	− 13.3485i	− 0.453077i
$869$	17.2474	0.585080
$870$	0	0
$871$	−37.3485	−1.26550
$872$	2.89898i	0.0981718i
$873$	1.55051i	0.0524768i
$874$	1.00000	0.0338255
$875$	0	0
$876$	−1.00000	−0.0337869
$877$	9.10102i	0.307320i	0.988124	+	0.153660i	$0.0491060\pi$
$877$	9.10102i	0.307320i	−0.988124	+	0.153660i	$0.950894\pi$
$878$	− 12.1010i	− 0.408390i
$879$	23.2474	0.784117
$880$	0	0
$881$	50.6969	1.70802	0.854012	−	0.520254i	$-0.174163\pi$
$881$	50.6969	1.70802	0.854012	+	0.520254i	$0.174163\pi$
$882$	− 12.7980i	− 0.430930i
$883$	34.6515i	1.16612i	0.812430	+	0.583058i	$0.198144\pi$
$883$	34.6515i	1.16612i	−0.812430	+	0.583058i	$0.801856\pi$
$884$	10.8990	0.366572
$885$	0	0
$886$	21.2474	0.713822
$887$	4.89898i	0.164492i	0.996612	+	0.0822458i	$0.0262093\pi$
$887$	4.89898i	0.164492i	−0.996612	+	0.0822458i	$0.973791\pi$
$888$	− 7.79796i	− 0.261682i
$889$	−0.449490	−0.0150754
$890$	0	0
$891$	3.44949	0.115562
$892$	− 16.1010i	− 0.539102i
$893$	− 7.79796i	− 0.260949i
$894$	−5.79796	−0.193913
$895$	0	0
$896$	4.44949	0.148647
$897$	− 2.44949i	− 0.0817861i
$898$	− 15.0000i	− 0.500556i
$899$	−13.0454	−0.435089
$900$	0	0
$901$	−33.1464	−1.10427
$902$	3.10102i	0.103253i
$903$	− 10.8990i	− 0.362695i
$904$	16.7980	0.558692
$905$	0	0
$906$	−23.7980	−0.790634
$907$	22.0000i	0.730498i	0.930910	+	0.365249i	$0.119016\pi$
$907$	22.0000i	0.730498i	−0.930910	+	0.365249i	$0.880984\pi$
$908$	29.5959i	0.982175i
$909$	1.55051	0.0514272
$910$	0	0
$911$	6.49490	0.215186	0.107593	−	0.994195i	$-0.465686\pi$
$911$	6.49490	0.215186	0.107593	+	0.994195i	$0.465686\pi$
$912$	− 1.00000i	− 0.0331133i
$913$	28.7980i	0.953073i
$914$	24.8990	0.823585
$915$	0	0
$916$	7.24745	0.239462
$917$	− 41.1464i	− 1.35877i
$918$	4.44949i	0.146855i
$919$	−23.8434	−0.786520	−0.393260	−	0.919427i	$-0.628653\pi$
$919$	−23.8434	−0.786520	−0.393260	+	0.919427i	$0.628653\pi$
$920$	0	0
$921$	−16.3485	−0.538700
$922$	− 12.0000i	− 0.395199i
$923$	3.79796i	0.125011i
$924$	−15.3485	−0.504928
$925$	0	0
$926$	−14.6969	−0.482971
$927$	− 1.89898i	− 0.0623707i
$928$	− 4.34847i	− 0.142745i
$929$	31.5959	1.03663	0.518314	−	0.855190i	$-0.326560\pi$
$929$	31.5959	1.03663	0.518314	+	0.855190i	$0.326560\pi$
$930$	0	0
$931$	12.7980	0.419436
$932$	− 6.24745i	− 0.204642i
$933$	− 23.7980i	− 0.779110i
$934$	6.34847	0.207728
$935$	0	0
$936$	−2.44949	−0.0800641
$937$	19.3939i	0.633570i	0.948497	+	0.316785i	$0.102603\pi$
$937$	19.3939i	0.633570i	−0.948497	+	0.316785i	$0.897397\pi$
$938$	67.8434i	2.21516i
$939$	−31.8990	−1.04098
$940$	0	0
$941$	36.6413	1.19447	0.597237	−	0.802065i	$-0.296265\pi$
$941$	36.6413	1.19447	0.597237	+	0.802065i	$0.296265\pi$
$942$	4.89898i	0.159617i
$943$	0.898979i	0.0292748i
$944$	−6.44949	−0.209913
$945$	0	0
$946$	−8.44949	−0.274717
$947$	− 8.00000i	− 0.259965i	−0.991516	−	0.129983i	$-0.958508\pi$
$947$	− 8.00000i	− 0.259965i	0.991516	−	0.129983i	$-0.0414921\pi$
$948$	− 5.00000i	− 0.162392i
$949$	−2.44949	−0.0795138
$950$	0	0
$951$	15.2474	0.494432
$952$	− 19.7980i	− 0.641656i
$953$	− 15.4949i	− 0.501929i	−0.967996	−	0.250964i	$-0.919252\pi$
$953$	− 15.4949i	− 0.501929i	0.967996	−	0.250964i	$-0.0807477\pi$
$954$	7.44949	0.241186
$955$	0	0
$956$	−8.69694	−0.281279
$957$	15.0000i	0.484881i
$958$	16.5959i	0.536190i
$959$	21.7980	0.703893
$960$	0	0
$961$	−22.0000	−0.709677
$962$	− 19.1010i	− 0.615842i
$963$	17.3485i	0.559047i
$964$	4.44949	0.143308
$965$	0	0
$966$	−4.44949	−0.143160
$967$	34.8990i	1.12228i	0.827722	+	0.561138i	$0.189636\pi$
$967$	34.8990i	1.12228i	−0.827722	+	0.561138i	$0.810364\pi$
$968$	0.898979i	0.0288943i
$969$	−4.44949	−0.142938
$970$	0	0
$971$	41.6413	1.33633	0.668167	−	0.744011i	$-0.267079\pi$
$971$	41.6413	1.33633	0.668167	+	0.744011i	$0.267079\pi$
$972$	− 1.00000i	− 0.0320750i
$973$	− 98.9898i	− 3.17347i
$974$	32.0000	1.02535
$975$	0	0
$976$	−9.44949	−0.302471
$977$	− 19.5959i	− 0.626929i	−0.949600	−	0.313464i	$-0.898510\pi$
$977$	− 19.5959i	− 0.626929i	0.949600	−	0.313464i	$-0.101490\pi$
$978$	19.7980i	0.633069i
$979$	−7.24745	−0.231629
$980$	0	0
$981$	−2.89898	−0.0925573
$982$	− 43.5959i	− 1.39120i
$983$	50.4495i	1.60909i	0.593892	+	0.804544i	$0.297590\pi$
$983$	50.4495i	1.60909i	−0.593892	+	0.804544i	$0.702410\pi$
$984$	0.898979	0.0286584
$985$	0	0
$986$	−19.3485	−0.616181
$987$	34.6969i	1.10442i
$988$	− 2.44949i	− 0.0779287i
$989$	−2.44949	−0.0778892
$990$	0	0
$991$	44.1010	1.40092	0.700458	−	0.713694i	$-0.252979\pi$
$991$	44.1010	1.40092	0.700458	+	0.713694i	$0.252979\pi$
$992$	3.00000i	0.0952501i
$993$	− 22.3485i	− 0.709207i
$994$	6.89898	0.218822
$995$	0	0
$996$	8.34847	0.264531
$997$	− 39.4495i	− 1.24938i	−0.780874	−	0.624689i	$-0.785226\pi$
$997$	− 39.4495i	− 1.24938i	0.780874	−	0.624689i	$-0.214774\pi$
$998$	− 23.8434i	− 0.754749i
$999$	7.79796	0.246717

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2850.2.d.w.799.1		4
5.2	odd	4		2850.2.a.bj.1.2	yes	2
5.3	odd	4		2850.2.a.bc.1.1	✓	2
5.4	even	2	inner	2850.2.d.w.799.4		4
15.2	even	4		8550.2.a.bu.1.2		2
15.8	even	4		8550.2.a.bv.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2850.2.a.bc.1.1	✓	2	5.3	odd	4
2850.2.a.bj.1.2	yes	2	5.2	odd	4
2850.2.d.w.799.1		4	1.1	even	1	trivial
2850.2.d.w.799.4		4	5.4	even	2	inner
8550.2.a.bu.1.2		2	15.2	even	4
8550.2.a.bv.1.1		2	15.8	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:	\( N \)	\(=\)	\( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2850.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -4.44949i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -4.44949i q^{7} +1.00000i q^{8} -1.00000 q^{9} +3.44949 q^{11} -1.00000i q^{12} -2.44949i q^{13} -4.44949 q^{14} +1.00000 q^{16} -4.44949i q^{17} +1.00000i q^{18} -1.00000 q^{19} +4.44949 q^{21} -3.44949i q^{22} -1.00000i q^{23} -1.00000 q^{24} -2.44949 q^{26} -1.00000i q^{27} +4.44949i q^{28} +4.34847 q^{29} -3.00000 q^{31} -1.00000i q^{32} +3.44949i q^{33} -4.44949 q^{34} +1.00000 q^{36} +7.79796i q^{37} +1.00000i q^{38} +2.44949 q^{39} -0.898979 q^{41} -4.44949i q^{42} -2.44949i q^{43} -3.44949 q^{44} -1.00000 q^{46} +7.79796i q^{47} +1.00000i q^{48} -12.7980 q^{49} +4.44949 q^{51} +2.44949i q^{52} -7.44949i q^{53} -1.00000 q^{54} +4.44949 q^{56} -1.00000i q^{57} -4.34847i q^{58} -6.44949 q^{59} -9.44949 q^{61} +3.00000i q^{62} +4.44949i q^{63} -1.00000 q^{64} +3.44949 q^{66} -15.2474i q^{67} +4.44949i q^{68} +1.00000 q^{69} -1.55051 q^{71} -1.00000i q^{72} -1.00000i q^{73} +7.79796 q^{74} +1.00000 q^{76} -15.3485i q^{77} -2.44949i q^{78} +5.00000 q^{79} +1.00000 q^{81} +0.898979i q^{82} +8.34847i q^{83} -4.44949 q^{84} -2.44949 q^{86} +4.34847i q^{87} +3.44949i q^{88} -2.10102 q^{89} -10.8990 q^{91} +1.00000i q^{92} -3.00000i q^{93} +7.79796 q^{94} +1.00000 q^{96} -1.55051i q^{97} +12.7980i q^{98} -3.44949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 4 q^{11} - 8 q^{14} + 4 q^{16} - 4 q^{19} + 8 q^{21} - 4 q^{24} - 12 q^{29} - 12 q^{31} - 8 q^{34} + 4 q^{36} + 16 q^{41} - 4 q^{44} - 4 q^{46} - 12 q^{49} + 8 q^{51} - 4 q^{54} + 8 q^{56} - 16 q^{59} - 28 q^{61} - 4 q^{64} + 4 q^{66} + 4 q^{69} - 16 q^{71} - 8 q^{74} + 4 q^{76} + 20 q^{79} + 4 q^{81} - 8 q^{84} - 28 q^{89} - 24 q^{91} - 8 q^{94} + 4 q^{96} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 4 * q^11 - 8 * q^14 + 4 * q^16 - 4 * q^19 + 8 * q^21 - 4 * q^24 - 12 * q^29 - 12 * q^31 - 8 * q^34 + 4 * q^36 + 16 * q^41 - 4 * q^44 - 4 * q^46 - 12 * q^49 + 8 * q^51 - 4 * q^54 + 8 * q^56 - 16 * q^59 - 28 * q^61 - 4 * q^64 + 4 * q^66 + 4 * q^69 - 16 * q^71 - 8 * q^74 + 4 * q^76 + 20 * q^79 + 4 * q^81 - 8 * q^84 - 28 * q^89 - 24 * q^91 - 8 * q^94 + 4 * q^96 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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