LMFDB - Embedded newform 1850.2.b.m.149.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1850,2,Mod(149,1850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1850, 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("1850.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1850 = 2 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1850.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:	$14.7723243739$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{33})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 17x^{2} + 64 $ x^4 + 17*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 370)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.3
Root			$-2.37228i$ of defining polynomial
Character	$\chi$	$=$	1850.149
Dual form			1850.2.b.m.149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -2.00000i q^{3} -1.00000 q^{4} +2.00000 q^{6} -4.37228i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -2.00000i q^{3} -1.00000 q^{4} +2.00000 q^{6} -4.37228i q^{7} -1.00000i q^{8} -1.00000 q^{9} +2.37228 q^{11} +2.00000i q^{12} -6.74456i q^{13} +4.37228 q^{14} +1.00000 q^{16} +0.372281i q^{17} -1.00000i q^{18} +2.00000 q^{19} -8.74456 q^{21} +2.37228i q^{22} +4.74456i q^{23} -2.00000 q^{24} +6.74456 q^{26} -4.00000i q^{27} +4.37228i q^{28} +9.11684 q^{29} -8.37228 q^{31} +1.00000i q^{32} -4.74456i q^{33} -0.372281 q^{34} +1.00000 q^{36} +1.00000i q^{37} +2.00000i q^{38} -13.4891 q^{39} -0.372281 q^{41} -8.74456i q^{42} -1.62772i q^{43} -2.37228 q^{44} -4.74456 q^{46} +2.74456i q^{47} -2.00000i q^{48} -12.1168 q^{49} +0.744563 q^{51} +6.74456i q^{52} +4.37228i q^{53} +4.00000 q^{54} -4.37228 q^{56} -4.00000i q^{57} +9.11684i q^{58} -1.25544 q^{59} +0.372281 q^{61} -8.37228i q^{62} +4.37228i q^{63} -1.00000 q^{64} +4.74456 q^{66} -6.74456i q^{67} -0.372281i q^{68} +9.48913 q^{69} +4.74456 q^{71} +1.00000i q^{72} +2.74456i q^{73} -1.00000 q^{74} -2.00000 q^{76} -10.3723i q^{77} -13.4891i q^{78} -6.74456 q^{79} -11.0000 q^{81} -0.372281i q^{82} -10.7446i q^{83} +8.74456 q^{84} +1.62772 q^{86} -18.2337i q^{87} -2.37228i q^{88} -10.0000 q^{89} -29.4891 q^{91} -4.74456i q^{92} +16.7446i q^{93} -2.74456 q^{94} +2.00000 q^{96} +17.1168i q^{97} -12.1168i q^{98} -2.37228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 8 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} + 8 q^{6} - 4 q^{9} - 2 q^{11} + 6 q^{14} + 4 q^{16} + 8 q^{19} - 12 q^{21} - 8 q^{24} + 4 q^{26} + 2 q^{29} - 22 q^{31} + 10 q^{34} + 4 q^{36} - 8 q^{39} + 10 q^{41} + 2 q^{44} + 4 q^{46} - 14 q^{49} - 20 q^{51} + 16 q^{54} - 6 q^{56} - 28 q^{59} - 10 q^{61} - 4 q^{64} - 4 q^{66} - 8 q^{69} - 4 q^{71} - 4 q^{74} - 8 q^{76} - 4 q^{79} - 44 q^{81} + 12 q^{84} + 18 q^{86} - 40 q^{89} - 72 q^{91} + 12 q^{94} + 8 q^{96} + 2 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 8 * q^6 - 4 * q^9 - 2 * q^11 + 6 * q^14 + 4 * q^16 + 8 * q^19 - 12 * q^21 - 8 * q^24 + 4 * q^26 + 2 * q^29 - 22 * q^31 + 10 * q^34 + 4 * q^36 - 8 * q^39 + 10 * q^41 + 2 * q^44 + 4 * q^46 - 14 * q^49 - 20 * q^51 + 16 * q^54 - 6 * q^56 - 28 * q^59 - 10 * q^61 - 4 * q^64 - 4 * q^66 - 8 * q^69 - 4 * q^71 - 4 * q^74 - 8 * q^76 - 4 * q^79 - 44 * q^81 + 12 * q^84 + 18 * q^86 - 40 * q^89 - 72 * q^91 + 12 * q^94 + 8 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times$.

$n$	$1001$	$1777$
$\chi(n)$	$1$	$-1$

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
$3$	− 2.00000i	− 1.15470i	−0.816497	−	0.577350i	$-0.804087\pi$
$3$	− 2.00000i	− 1.15470i	0.816497	−	0.577350i	$-0.195913\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	2.00000	0.816497
$7$	− 4.37228i	− 1.65257i	−0.563254	−	0.826284i	$-0.690451\pi$
$7$	− 4.37228i	− 1.65257i	0.563254	−	0.826284i	$-0.309549\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	2.37228	0.715270	0.357635	−	0.933862i	$-0.383583\pi$
$11$	2.37228	0.715270	0.357635	+	0.933862i	$0.383583\pi$
$12$	2.00000i	0.577350i
$13$	− 6.74456i	− 1.87061i	−0.353849	−	0.935303i	$-0.615127\pi$
$13$	− 6.74456i	− 1.87061i	0.353849	−	0.935303i	$-0.384873\pi$
$14$	4.37228	1.16854
$15$	0	0
$16$	1.00000	0.250000
$17$	0.372281i	0.0902915i	0.998980	+	0.0451457i	$0.0143752\pi$
$17$	0.372281i	0.0902915i	−0.998980	+	0.0451457i	$0.985625\pi$
$18$	− 1.00000i	− 0.235702i
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	0	0
$21$	−8.74456	−1.90822
$22$	2.37228i	0.505772i
$23$	4.74456i	0.989310i	0.869090	+	0.494655i	$0.164706\pi$
$23$	4.74456i	0.989310i	−0.869090	+	0.494655i	$0.835294\pi$
$24$	−2.00000	−0.408248
$25$	0	0
$26$	6.74456	1.32272
$27$	− 4.00000i	− 0.769800i
$28$	4.37228i	0.826284i
$29$	9.11684	1.69296	0.846478	−	0.532424i	$-0.178719\pi$
$29$	9.11684	1.69296	0.846478	+	0.532424i	$0.178719\pi$
$30$	0	0
$31$	−8.37228	−1.50371	−0.751853	−	0.659331i	$-0.770840\pi$
$31$	−8.37228	−1.50371	−0.751853	+	0.659331i	$0.770840\pi$
$32$	1.00000i	0.176777i
$33$	− 4.74456i	− 0.825922i
$34$	−0.372281	−0.0638457
$35$	0	0
$36$	1.00000	0.166667
$37$	1.00000i	0.164399i
$37$	1.00000i	0.164399i
$38$	2.00000i	0.324443i
$39$	−13.4891	−2.15999
$40$	0	0
$41$	−0.372281	−0.0581406	−0.0290703	−	0.999577i	$-0.509255\pi$
$41$	−0.372281	−0.0581406	−0.0290703	+	0.999577i	$0.509255\pi$
$42$	− 8.74456i	− 1.34932i
$43$	− 1.62772i	− 0.248225i	−0.992268	−	0.124112i	$-0.960392\pi$
$43$	− 1.62772i	− 0.248225i	0.992268	−	0.124112i	$-0.0396083\pi$
$44$	−2.37228	−0.357635
$45$	0	0
$46$	−4.74456	−0.699548
$47$	2.74456i	0.400336i	0.979762	+	0.200168i	$0.0641487\pi$
$47$	2.74456i	0.400336i	−0.979762	+	0.200168i	$0.935851\pi$
$48$	− 2.00000i	− 0.288675i
$49$	−12.1168	−1.73098
$50$	0	0
$51$	0.744563	0.104260
$52$	6.74456i	0.935303i
$53$	4.37228i	0.600579i	0.953848	+	0.300290i	$0.0970833\pi$
$53$	4.37228i	0.600579i	−0.953848	+	0.300290i	$0.902917\pi$
$54$	4.00000	0.544331
$55$	0	0
$56$	−4.37228	−0.584271
$57$	− 4.00000i	− 0.529813i
$58$	9.11684i	1.19710i
$59$	−1.25544	−0.163444	−0.0817220	−	0.996655i	$-0.526042\pi$
$59$	−1.25544	−0.163444	−0.0817220	+	0.996655i	$0.526042\pi$
$60$	0	0
$61$	0.372281	0.0476657	0.0238329	−	0.999716i	$-0.492413\pi$
$61$	0.372281	0.0476657	0.0238329	+	0.999716i	$0.492413\pi$
$62$	− 8.37228i	− 1.06328i
$63$	4.37228i	0.550856i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	4.74456	0.584015
$67$	− 6.74456i	− 0.823979i	−0.911188	−	0.411990i	$-0.864834\pi$
$67$	− 6.74456i	− 0.823979i	0.911188	−	0.411990i	$-0.135166\pi$
$68$	− 0.372281i	− 0.0451457i
$69$	9.48913	1.14236
$70$	0	0
$71$	4.74456	0.563076	0.281538	−	0.959550i	$-0.409155\pi$
$71$	4.74456	0.563076	0.281538	+	0.959550i	$0.409155\pi$
$72$	1.00000i	0.117851i
$73$	2.74456i	0.321227i	0.987017	+	0.160613i	$0.0513472\pi$
$73$	2.74456i	0.321227i	−0.987017	+	0.160613i	$0.948653\pi$
$74$	−1.00000	−0.116248
$75$	0	0
$76$	−2.00000	−0.229416
$77$	− 10.3723i	− 1.18203i
$78$	− 13.4891i	− 1.52734i
$79$	−6.74456	−0.758823	−0.379411	−	0.925228i	$-0.623873\pi$
$79$	−6.74456	−0.758823	−0.379411	+	0.925228i	$0.623873\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	− 0.372281i	− 0.0411116i
$83$	− 10.7446i	− 1.17937i	−0.807634	−	0.589684i	$-0.799252\pi$
$83$	− 10.7446i	− 1.17937i	0.807634	−	0.589684i	$-0.200748\pi$
$84$	8.74456	0.954110
$85$	0	0
$86$	1.62772	0.175521
$87$	− 18.2337i	− 1.95486i
$88$	− 2.37228i	− 0.252886i
$89$	−10.0000	−1.06000	−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000	−1.06000	−0.529999	+	0.847998i	$0.677808\pi$
$90$	0	0
$91$	−29.4891	−3.09130
$92$	− 4.74456i	− 0.494655i
$93$	16.7446i	1.73633i
$94$	−2.74456	−0.283080
$95$	0	0
$96$	2.00000	0.204124
$97$	17.1168i	1.73795i	0.494854	+	0.868976i	$0.335222\pi$
$97$	17.1168i	1.73795i	−0.494854	+	0.868976i	$0.664778\pi$
$98$	− 12.1168i	− 1.22399i
$99$	−2.37228	−0.238423
$100$	0	0
$101$	11.4891	1.14321	0.571605	−	0.820529i	$-0.306321\pi$
$101$	11.4891	1.14321	0.571605	+	0.820529i	$0.306321\pi$
$102$	0.744563i	0.0737227i
$103$	− 13.4891i	− 1.32912i	−0.747234	−	0.664562i	$-0.768618\pi$
$103$	− 13.4891i	− 1.32912i	0.747234	−	0.664562i	$-0.231382\pi$
$104$	−6.74456	−0.661359
$105$	0	0
$106$	−4.37228	−0.424674
$107$	19.4891i	1.88408i	0.335494	+	0.942042i	$0.391097\pi$
$107$	19.4891i	1.88408i	−0.335494	+	0.942042i	$0.608903\pi$
$108$	4.00000i	0.384900i
$109$	17.1168	1.63950	0.819748	−	0.572724i	$-0.194113\pi$
$109$	17.1168	1.63950	0.819748	+	0.572724i	$0.194113\pi$
$110$	0	0
$111$	2.00000	0.189832
$112$	− 4.37228i	− 0.413142i
$113$	− 11.6277i	− 1.09384i	−0.837184	−	0.546922i	$-0.815799\pi$
$113$	− 11.6277i	− 1.09384i	0.837184	−	0.546922i	$-0.184201\pi$
$114$	4.00000	0.374634
$115$	0	0
$116$	−9.11684	−0.846478
$117$	6.74456i	0.623535i
$118$	− 1.25544i	− 0.115572i
$119$	1.62772	0.149213
$120$	0	0
$121$	−5.37228	−0.488389
$122$	0.372281i	0.0337048i
$123$	0.744563i	0.0671350i
$124$	8.37228	0.751853
$125$	0	0
$126$	−4.37228	−0.389514
$127$	− 5.25544i	− 0.466345i	−0.972435	−	0.233172i	$-0.925089\pi$
$127$	− 5.25544i	− 0.466345i	0.972435	−	0.233172i	$-0.0749106\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−3.25544	−0.286625
$130$	0	0
$131$	−14.7446	−1.28824	−0.644119	−	0.764925i	$-0.722776\pi$
$131$	−14.7446	−1.28824	−0.644119	+	0.764925i	$0.722776\pi$
$132$	4.74456i	0.412961i
$133$	− 8.74456i	− 0.758250i
$134$	6.74456	0.582641
$135$	0	0
$136$	0.372281	0.0319229
$137$	5.25544i	0.449002i	0.974474	+	0.224501i	$0.0720753\pi$
$137$	5.25544i	0.449002i	−0.974474	+	0.224501i	$0.927925\pi$
$138$	9.48913i	0.807768i
$139$	19.1168	1.62147	0.810735	−	0.585414i	$-0.199068\pi$
$139$	19.1168	1.62147	0.810735	+	0.585414i	$0.199068\pi$
$140$	0	0
$141$	5.48913	0.462268
$142$	4.74456i	0.398155i
$143$	− 16.0000i	− 1.33799i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	−2.74456	−0.227142
$147$	24.2337i	1.99876i
$148$	− 1.00000i	− 0.0821995i
$149$	−11.4891	−0.941226	−0.470613	−	0.882340i	$-0.655967\pi$
$149$	−11.4891	−0.941226	−0.470613	+	0.882340i	$0.655967\pi$
$150$	0	0
$151$	−20.0000	−1.62758	−0.813788	−	0.581161i	$-0.802599\pi$
$151$	−20.0000	−1.62758	−0.813788	+	0.581161i	$0.802599\pi$
$152$	− 2.00000i	− 0.162221i
$153$	− 0.372281i	− 0.0300972i
$154$	10.3723	0.835822
$155$	0	0
$156$	13.4891	1.07999
$157$	11.6277i	0.927993i	0.885837	+	0.463996i	$0.153585\pi$
$157$	11.6277i	0.927993i	−0.885837	+	0.463996i	$0.846415\pi$
$158$	− 6.74456i	− 0.536569i
$159$	8.74456	0.693489
$160$	0	0
$161$	20.7446	1.63490
$162$	− 11.0000i	− 0.864242i
$163$	− 13.6277i	− 1.06741i	−0.845672	−	0.533703i	$-0.820800\pi$
$163$	− 13.6277i	− 1.06741i	0.845672	−	0.533703i	$-0.179200\pi$
$164$	0.372281	0.0290703
$165$	0	0
$166$	10.7446	0.833940
$167$	− 21.4891i	− 1.66288i	−0.555616	−	0.831439i	$-0.687517\pi$
$167$	− 21.4891i	− 1.66288i	0.555616	−	0.831439i	$-0.312483\pi$
$168$	8.74456i	0.674658i
$169$	−32.4891	−2.49916
$170$	0	0
$171$	−2.00000	−0.152944
$172$	1.62772i	0.124112i
$173$	5.86141i	0.445634i	0.974860	+	0.222817i	$0.0715253\pi$
$173$	5.86141i	0.445634i	−0.974860	+	0.222817i	$0.928475\pi$
$174$	18.2337	1.38229
$175$	0	0
$176$	2.37228	0.178817
$177$	2.51087i	0.188729i
$178$	− 10.0000i	− 0.749532i
$179$	−8.23369	−0.615415	−0.307707	−	0.951481i	$-0.599562\pi$
$179$	−8.23369	−0.615415	−0.307707	+	0.951481i	$0.599562\pi$
$180$	0	0
$181$	−15.4891	−1.15130	−0.575649	−	0.817697i	$-0.695250\pi$
$181$	−15.4891	−1.15130	−0.575649	+	0.817697i	$0.695250\pi$
$182$	− 29.4891i	− 2.18588i
$183$	− 0.744563i	− 0.0550397i
$184$	4.74456	0.349774
$185$	0	0
$186$	−16.7446	−1.22777
$187$	0.883156i	0.0645828i
$188$	− 2.74456i	− 0.200168i
$189$	−17.4891	−1.27215
$190$	0	0
$191$	24.3723	1.76352	0.881758	−	0.471702i	$-0.156360\pi$
$191$	24.3723	1.76352	0.881758	+	0.471702i	$0.156360\pi$
$192$	2.00000i	0.144338i
$193$	− 2.00000i	− 0.143963i	−0.997406	−	0.0719816i	$-0.977068\pi$
$193$	− 2.00000i	− 0.143963i	0.997406	−	0.0719816i	$-0.0229323\pi$
$194$	−17.1168	−1.22892
$195$	0	0
$196$	12.1168	0.865489
$197$	4.51087i	0.321387i	0.987004	+	0.160693i	$0.0513730\pi$
$197$	4.51087i	0.321387i	−0.987004	+	0.160693i	$0.948627\pi$
$198$	− 2.37228i	− 0.168591i
$199$	22.7446	1.61232	0.806160	−	0.591698i	$-0.201542\pi$
$199$	22.7446	1.61232	0.806160	+	0.591698i	$0.201542\pi$
$200$	0	0
$201$	−13.4891	−0.951450
$202$	11.4891i	0.808372i
$203$	− 39.8614i	− 2.79772i
$204$	−0.744563	−0.0521298
$205$	0	0
$206$	13.4891	0.939832
$207$	− 4.74456i	− 0.329770i
$208$	− 6.74456i	− 0.467651i
$209$	4.74456	0.328188
$210$	0	0
$211$	3.11684	0.214572	0.107286	−	0.994228i	$-0.465784\pi$
$211$	3.11684	0.214572	0.107286	+	0.994228i	$0.465784\pi$
$212$	− 4.37228i	− 0.300290i
$213$	− 9.48913i	− 0.650184i
$214$	−19.4891	−1.33225
$215$	0	0
$216$	−4.00000	−0.272166
$217$	36.6060i	2.48498i
$218$	17.1168i	1.15930i
$219$	5.48913	0.370921
$220$	0	0
$221$	2.51087	0.168900
$222$	2.00000i	0.134231i
$223$	− 4.37228i	− 0.292790i	−0.989226	−	0.146395i	$-0.953233\pi$
$223$	− 4.37228i	− 0.292790i	0.989226	−	0.146395i	$-0.0467670\pi$
$224$	4.37228	0.292135
$225$	0	0
$226$	11.6277	0.773464
$227$	− 5.62772i	− 0.373525i	−0.982405	−	0.186762i	$-0.940201\pi$
$227$	− 5.62772i	− 0.373525i	0.982405	−	0.186762i	$-0.0597995\pi$
$228$	4.00000i	0.264906i
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	0	0
$231$	−20.7446	−1.36489
$232$	− 9.11684i	− 0.598550i
$233$	28.2337i	1.84965i	0.380392	+	0.924825i	$0.375789\pi$
$233$	28.2337i	1.84965i	−0.380392	+	0.924825i	$0.624211\pi$
$234$	−6.74456	−0.440906
$235$	0	0
$236$	1.25544	0.0817220
$237$	13.4891i	0.876213i
$238$	1.62772i	0.105509i
$239$	22.6060	1.46226	0.731129	−	0.682239i	$-0.238994\pi$
$239$	22.6060	1.46226	0.731129	+	0.682239i	$0.238994\pi$
$240$	0	0
$241$	24.2337	1.56103	0.780515	−	0.625138i	$-0.214957\pi$
$241$	24.2337	1.56103	0.780515	+	0.625138i	$0.214957\pi$
$242$	− 5.37228i	− 0.345343i
$243$	10.0000i	0.641500i
$244$	−0.372281	−0.0238329
$245$	0	0
$246$	−0.744563	−0.0474716
$247$	− 13.4891i	− 0.858292i
$248$	8.37228i	0.531640i
$249$	−21.4891	−1.36182
$250$	0	0
$251$	−11.4891	−0.725187	−0.362594	−	0.931947i	$-0.618109\pi$
$251$	−11.4891	−0.725187	−0.362594	+	0.931947i	$0.618109\pi$
$252$	− 4.37228i	− 0.275428i
$253$	11.2554i	0.707623i
$254$	5.25544	0.329755
$255$	0	0
$256$	1.00000	0.0625000
$257$	24.9783i	1.55810i	0.626962	+	0.779050i	$0.284298\pi$
$257$	24.9783i	1.55810i	−0.626962	+	0.779050i	$0.715702\pi$
$258$	− 3.25544i	− 0.202675i
$259$	4.37228	0.271680
$260$	0	0
$261$	−9.11684	−0.564318
$262$	− 14.7446i	− 0.910922i
$263$	17.1168i	1.05547i	0.849409	+	0.527735i	$0.176959\pi$
$263$	17.1168i	1.05547i	−0.849409	+	0.527735i	$0.823041\pi$
$264$	−4.74456	−0.292008
$265$	0	0
$266$	8.74456	0.536164
$267$	20.0000i	1.22398i
$268$	6.74456i	0.411990i
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	0	0
$271$	4.74456	0.288212	0.144106	−	0.989562i	$-0.453969\pi$
$271$	4.74456	0.288212	0.144106	+	0.989562i	$0.453969\pi$
$272$	0.372281i	0.0225729i
$273$	58.9783i	3.56953i
$274$	−5.25544	−0.317493
$275$	0	0
$276$	−9.48913	−0.571178
$277$	− 10.7446i	− 0.645578i	−0.946471	−	0.322789i	$-0.895380\pi$
$277$	− 10.7446i	− 0.645578i	0.946471	−	0.322789i	$-0.104620\pi$
$278$	19.1168i	1.14655i
$279$	8.37228	0.501235
$280$	0	0
$281$	13.2554	0.790753	0.395377	−	0.918519i	$-0.370614\pi$
$281$	13.2554	0.790753	0.395377	+	0.918519i	$0.370614\pi$
$282$	5.48913i	0.326873i
$283$	17.4891i	1.03962i	0.854282	+	0.519810i	$0.173997\pi$
$283$	17.4891i	1.03962i	−0.854282	+	0.519810i	$0.826003\pi$
$284$	−4.74456	−0.281538
$285$	0	0
$286$	16.0000	0.946100
$287$	1.62772i	0.0960812i
$288$	− 1.00000i	− 0.0589256i
$289$	16.8614	0.991847
$290$	0	0
$291$	34.2337	2.00681
$292$	− 2.74456i	− 0.160613i
$293$	− 9.86141i	− 0.576110i	−0.957614	−	0.288055i	$-0.906991\pi$
$293$	− 9.86141i	− 0.576110i	0.957614	−	0.288055i	$-0.0930085\pi$
$294$	−24.2337	−1.41334
$295$	0	0
$296$	1.00000	0.0581238
$297$	− 9.48913i	− 0.550615i
$298$	− 11.4891i	− 0.665547i
$299$	32.0000	1.85061
$300$	0	0
$301$	−7.11684	−0.410208
$302$	− 20.0000i	− 1.15087i
$303$	− 22.9783i	− 1.32007i
$304$	2.00000	0.114708
$305$	0	0
$306$	0.372281	0.0212819
$307$	− 0.510875i	− 0.0291572i	−0.999894	−	0.0145786i	$-0.995359\pi$
$307$	− 0.510875i	− 0.0291572i	0.999894	−	0.0145786i	$-0.00464067\pi$
$308$	10.3723i	0.591016i
$309$	−26.9783	−1.53474
$310$	0	0
$311$	4.37228	0.247929	0.123965	−	0.992287i	$-0.460439\pi$
$311$	4.37228	0.247929	0.123965	+	0.992287i	$0.460439\pi$
$312$	13.4891i	0.763671i
$313$	− 19.4891i	− 1.10159i	−0.834640	−	0.550795i	$-0.814325\pi$
$313$	− 19.4891i	− 1.10159i	0.834640	−	0.550795i	$-0.185675\pi$
$314$	−11.6277	−0.656190
$315$	0	0
$316$	6.74456	0.379411
$317$	19.6277i	1.10240i	0.834372	+	0.551201i	$0.185830\pi$
$317$	19.6277i	1.10240i	−0.834372	+	0.551201i	$0.814170\pi$
$318$	8.74456i	0.490371i
$319$	21.6277	1.21092
$320$	0	0
$321$	38.9783	2.17555
$322$	20.7446i	1.15605i
$323$	0.744563i	0.0414286i
$324$	11.0000	0.611111
$325$	0	0
$326$	13.6277	0.754770
$327$	− 34.2337i	− 1.89313i
$328$	0.372281i	0.0205558i
$329$	12.0000	0.661581
$330$	0	0
$331$	0.510875	0.0280802	0.0140401	−	0.999901i	$-0.495531\pi$
$331$	0.510875	0.0280802	0.0140401	+	0.999901i	$0.495531\pi$
$332$	10.7446i	0.589684i
$333$	− 1.00000i	− 0.0547997i
$334$	21.4891	1.17583
$335$	0	0
$336$	−8.74456	−0.477055
$337$	− 18.7446i	− 1.02108i	−0.859854	−	0.510541i	$-0.829445\pi$
$337$	− 18.7446i	− 1.02108i	0.859854	−	0.510541i	$-0.170555\pi$
$338$	− 32.4891i	− 1.76718i
$339$	−23.2554	−1.26306
$340$	0	0
$341$	−19.8614	−1.07556
$342$	− 2.00000i	− 0.108148i
$343$	22.3723i	1.20799i
$344$	−1.62772	−0.0877607
$345$	0	0
$346$	−5.86141	−0.315111
$347$	22.9783i	1.23354i	0.787145	+	0.616769i	$0.211559\pi$
$347$	22.9783i	1.23354i	−0.787145	+	0.616769i	$0.788441\pi$
$348$	18.2337i	0.977428i
$349$	22.0000	1.17763	0.588817	−	0.808267i	$-0.299594\pi$
$349$	22.0000	1.17763	0.588817	+	0.808267i	$0.299594\pi$
$350$	0	0
$351$	−26.9783	−1.43999
$352$	2.37228i	0.126443i
$353$	− 5.86141i	− 0.311971i	−0.987759	−	0.155986i	$-0.950145\pi$
$353$	− 5.86141i	− 0.311971i	0.987759	−	0.155986i	$-0.0498553\pi$
$354$	−2.51087	−0.133451
$355$	0	0
$356$	10.0000	0.529999
$357$	− 3.25544i	− 0.172296i
$358$	− 8.23369i	− 0.435164i
$359$	−14.9783	−0.790522	−0.395261	−	0.918569i	$-0.629346\pi$
$359$	−14.9783	−0.790522	−0.395261	+	0.918569i	$0.629346\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	− 15.4891i	− 0.814090i
$363$	10.7446i	0.563943i
$364$	29.4891	1.54565
$365$	0	0
$366$	0.744563	0.0389189
$367$	21.1168i	1.10229i	0.834409	+	0.551145i	$0.185809\pi$
$367$	21.1168i	1.10229i	−0.834409	+	0.551145i	$0.814191\pi$
$368$	4.74456i	0.247327i
$369$	0.372281	0.0193802
$370$	0	0
$371$	19.1168	0.992497
$372$	− 16.7446i	− 0.868165i
$373$	8.51087i	0.440676i	0.975424	+	0.220338i	$0.0707161\pi$
$373$	8.51087i	0.440676i	−0.975424	+	0.220338i	$0.929284\pi$
$374$	−0.883156	−0.0456669
$375$	0	0
$376$	2.74456	0.141540
$377$	− 61.4891i	− 3.16685i
$378$	− 17.4891i	− 0.899544i
$379$	8.00000	0.410932	0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000	0.410932	0.205466	+	0.978664i	$0.434129\pi$
$380$	0	0
$381$	−10.5109	−0.538488
$382$	24.3723i	1.24699i
$383$	− 9.48913i	− 0.484872i	−0.970167	−	0.242436i	$-0.922054\pi$
$383$	− 9.48913i	− 0.484872i	0.970167	−	0.242436i	$-0.0779464\pi$
$384$	−2.00000	−0.102062
$385$	0	0
$386$	2.00000	0.101797
$387$	1.62772i	0.0827416i
$388$	− 17.1168i	− 0.868976i
$389$	13.8614	0.702801	0.351401	−	0.936225i	$-0.385706\pi$
$389$	13.8614	0.702801	0.351401	+	0.936225i	$0.385706\pi$
$390$	0	0
$391$	−1.76631	−0.0893262
$392$	12.1168i	0.611993i
$393$	29.4891i	1.48753i
$394$	−4.51087	−0.227255
$395$	0	0
$396$	2.37228	0.119212
$397$	− 20.9783i	− 1.05287i	−0.850216	−	0.526434i	$-0.823529\pi$
$397$	− 20.9783i	− 1.05287i	0.850216	−	0.526434i	$-0.176471\pi$
$398$	22.7446i	1.14008i
$399$	−17.4891	−0.875551
$400$	0	0
$401$	10.0000	0.499376	0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000	0.499376	0.249688	+	0.968326i	$0.419672\pi$
$402$	− 13.4891i	− 0.672776i
$403$	56.4674i	2.81284i
$404$	−11.4891	−0.571605
$405$	0	0
$406$	39.8614	1.97829
$407$	2.37228i	0.117590i
$408$	− 0.744563i	− 0.0368613i
$409$	28.2337	1.39607	0.698033	−	0.716066i	$-0.254059\pi$
$409$	28.2337	1.39607	0.698033	+	0.716066i	$0.254059\pi$
$410$	0	0
$411$	10.5109	0.518463
$412$	13.4891i	0.664562i
$413$	5.48913i	0.270102i
$414$	4.74456	0.233183
$415$	0	0
$416$	6.74456	0.330679
$417$	− 38.2337i	− 1.87231i
$418$	4.74456i	0.232064i
$419$	9.48913	0.463574	0.231787	−	0.972767i	$-0.425543\pi$
$419$	9.48913	0.463574	0.231787	+	0.972767i	$0.425543\pi$
$420$	0	0
$421$	15.4891	0.754894	0.377447	−	0.926031i	$-0.376802\pi$
$421$	15.4891	0.754894	0.377447	+	0.926031i	$0.376802\pi$
$422$	3.11684i	0.151726i
$423$	− 2.74456i	− 0.133445i
$424$	4.37228	0.212337
$425$	0	0
$426$	9.48913	0.459750
$427$	− 1.62772i	− 0.0787708i
$428$	− 19.4891i	− 0.942042i
$429$	−32.0000	−1.54497
$430$	0	0
$431$	4.37228	0.210605	0.105303	−	0.994440i	$-0.466419\pi$
$431$	4.37228	0.210605	0.105303	+	0.994440i	$0.466419\pi$
$432$	− 4.00000i	− 0.192450i
$433$	32.9783i	1.58483i	0.609980	+	0.792417i	$0.291177\pi$
$433$	32.9783i	1.58483i	−0.609980	+	0.792417i	$0.708823\pi$
$434$	−36.6060	−1.75714
$435$	0	0
$436$	−17.1168	−0.819748
$437$	9.48913i	0.453926i
$438$	5.48913i	0.262281i
$439$	7.62772	0.364051	0.182026	−	0.983294i	$-0.441735\pi$
$439$	7.62772	0.364051	0.182026	+	0.983294i	$0.441735\pi$
$440$	0	0
$441$	12.1168	0.576993
$442$	2.51087i	0.119430i
$443$	− 28.9783i	− 1.37680i	−0.725332	−	0.688399i	$-0.758314\pi$
$443$	− 28.9783i	− 1.37680i	0.725332	−	0.688399i	$-0.241686\pi$
$444$	−2.00000	−0.0949158
$445$	0	0
$446$	4.37228	0.207034
$447$	22.9783i	1.08683i
$448$	4.37228i	0.206571i
$449$	−18.0000	−0.849473	−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000	−0.849473	−0.424736	+	0.905317i	$0.639633\pi$
$450$	0	0
$451$	−0.883156	−0.0415862
$452$	11.6277i	0.546922i
$453$	40.0000i	1.87936i
$454$	5.62772	0.264122
$455$	0	0
$456$	−4.00000	−0.187317
$457$	− 9.86141i	− 0.461297i	−0.973037	−	0.230649i	$-0.925915\pi$
$457$	− 9.86141i	− 0.461297i	0.973037	−	0.230649i	$-0.0740848\pi$
$458$	10.0000i	0.467269i
$459$	1.48913	0.0695064
$460$	0	0
$461$	24.0951	1.12222	0.561110	−	0.827741i	$-0.310374\pi$
$461$	24.0951	1.12222	0.561110	+	0.827741i	$0.310374\pi$
$462$	− 20.7446i	− 0.965124i
$463$	− 17.4891i	− 0.812789i	−0.913698	−	0.406394i	$-0.866786\pi$
$463$	− 17.4891i	− 0.812789i	0.913698	−	0.406394i	$-0.133214\pi$
$464$	9.11684	0.423239
$465$	0	0
$466$	−28.2337	−1.30790
$467$	− 21.3505i	− 0.987985i	−0.869466	−	0.493992i	$-0.835537\pi$
$467$	− 21.3505i	− 0.987985i	0.869466	−	0.493992i	$-0.164463\pi$
$468$	− 6.74456i	− 0.311768i
$469$	−29.4891	−1.36168
$470$	0	0
$471$	23.2554	1.07155
$472$	1.25544i	0.0577862i
$473$	− 3.86141i	− 0.177548i
$474$	−13.4891	−0.619576
$475$	0	0
$476$	−1.62772	−0.0746064
$477$	− 4.37228i	− 0.200193i
$478$	22.6060i	1.03397i
$479$	−14.7446	−0.673696	−0.336848	−	0.941559i	$-0.609361\pi$
$479$	−14.7446	−0.673696	−0.336848	+	0.941559i	$0.609361\pi$
$480$	0	0
$481$	6.74456	0.307526
$482$	24.2337i	1.10381i
$483$	− 41.4891i	− 1.88782i
$484$	5.37228	0.244195
$485$	0	0
$486$	−10.0000	−0.453609
$487$	19.7228i	0.893726i	0.894602	+	0.446863i	$0.147459\pi$
$487$	19.7228i	0.893726i	−0.894602	+	0.446863i	$0.852541\pi$
$488$	− 0.372281i	− 0.0168524i
$489$	−27.2554	−1.23253
$490$	0	0
$491$	−30.9783	−1.39803	−0.699014	−	0.715108i	$-0.746378\pi$
$491$	−30.9783	−1.39803	−0.699014	+	0.715108i	$0.746378\pi$
$492$	− 0.744563i	− 0.0335675i
$493$	3.39403i	0.152859i
$494$	13.4891	0.606904
$495$	0	0
$496$	−8.37228	−0.375927
$497$	− 20.7446i	− 0.930521i
$498$	− 21.4891i	− 0.962951i
$499$	−20.9783	−0.939115	−0.469558	−	0.882902i	$-0.655587\pi$
$499$	−20.9783	−0.939115	−0.469558	+	0.882902i	$0.655587\pi$
$500$	0	0
$501$	−42.9783	−1.92013
$502$	− 11.4891i	− 0.512785i
$503$	− 6.51087i	− 0.290306i	−0.989409	−	0.145153i	$-0.953633\pi$
$503$	− 6.51087i	− 0.290306i	0.989409	−	0.145153i	$-0.0463674\pi$
$504$	4.37228	0.194757
$505$	0	0
$506$	−11.2554	−0.500365
$507$	64.9783i	2.88579i
$508$	5.25544i	0.233172i
$509$	22.7446	1.00814	0.504068	−	0.863664i	$-0.331836\pi$
$509$	22.7446	1.00814	0.504068	+	0.863664i	$0.331836\pi$
$510$	0	0
$511$	12.0000	0.530849
$512$	1.00000i	0.0441942i
$513$	− 8.00000i	− 0.353209i
$514$	−24.9783	−1.10174
$515$	0	0
$516$	3.25544	0.143313
$517$	6.51087i	0.286348i
$518$	4.37228i	0.192107i
$519$	11.7228	0.514574
$520$	0	0
$521$	−36.0951	−1.58135	−0.790677	−	0.612233i	$-0.790271\pi$
$521$	−36.0951	−1.58135	−0.790677	+	0.612233i	$0.790271\pi$
$522$	− 9.11684i	− 0.399033i
$523$	− 28.0000i	− 1.22435i	−0.790721	−	0.612177i	$-0.790294\pi$
$523$	− 28.0000i	− 1.22435i	0.790721	−	0.612177i	$-0.209706\pi$
$524$	14.7446	0.644119
$525$	0	0
$526$	−17.1168	−0.746330
$527$	− 3.11684i	− 0.135772i
$528$	− 4.74456i	− 0.206481i
$529$	0.489125	0.0212663
$530$	0	0
$531$	1.25544	0.0544813
$532$	8.74456i	0.379125i
$533$	2.51087i	0.108758i
$534$	−20.0000	−0.865485
$535$	0	0
$536$	−6.74456	−0.291321
$537$	16.4674i	0.710620i
$538$	− 10.0000i	− 0.431131i
$539$	−28.7446	−1.23812
$540$	0	0
$541$	30.0000	1.28980	0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000	1.28980	0.644900	+	0.764267i	$0.276899\pi$
$542$	4.74456i	0.203796i
$543$	30.9783i	1.32940i
$544$	−0.372281	−0.0159614
$545$	0	0
$546$	−58.9783	−2.52404
$547$	33.6277i	1.43782i	0.695104	+	0.718909i	$0.255358\pi$
$547$	33.6277i	1.43782i	−0.695104	+	0.718909i	$0.744642\pi$
$548$	− 5.25544i	− 0.224501i
$549$	−0.372281	−0.0158886
$550$	0	0
$551$	18.2337	0.776781
$552$	− 9.48913i	− 0.403884i
$553$	29.4891i	1.25401i
$554$	10.7446	0.456493
$555$	0	0
$556$	−19.1168	−0.810735
$557$	− 2.74456i	− 0.116291i	−0.998308	−	0.0581454i	$-0.981481\pi$
$557$	− 2.74456i	− 0.116291i	0.998308	−	0.0581454i	$-0.0185187\pi$
$558$	8.37228i	0.354427i
$559$	−10.9783	−0.464331
$560$	0	0
$561$	1.76631	0.0745738
$562$	13.2554i	0.559147i
$563$	30.0951i	1.26836i	0.773187	+	0.634179i	$0.218662\pi$
$563$	30.0951i	1.26836i	−0.773187	+	0.634179i	$0.781338\pi$
$564$	−5.48913	−0.231134
$565$	0	0
$566$	−17.4891	−0.735123
$567$	48.0951i	2.01980i
$568$	− 4.74456i	− 0.199077i
$569$	−12.9783	−0.544077	−0.272038	−	0.962286i	$-0.587698\pi$
$569$	−12.9783	−0.544077	−0.272038	+	0.962286i	$0.587698\pi$
$570$	0	0
$571$	12.6060	0.527543	0.263772	−	0.964585i	$-0.415033\pi$
$571$	12.6060	0.527543	0.263772	+	0.964585i	$0.415033\pi$
$572$	16.0000i	0.668994i
$573$	− 48.7446i	− 2.03633i
$574$	−1.62772	−0.0679397
$575$	0	0
$576$	1.00000	0.0416667
$577$	15.4891i	0.644821i	0.946600	+	0.322410i	$0.104493\pi$
$577$	15.4891i	0.644821i	−0.946600	+	0.322410i	$0.895507\pi$
$578$	16.8614i	0.701342i
$579$	−4.00000	−0.166234
$580$	0	0
$581$	−46.9783	−1.94899
$582$	34.2337i	1.41903i
$583$	10.3723i	0.429576i
$584$	2.74456	0.113571
$585$	0	0
$586$	9.86141	0.407371
$587$	− 26.8397i	− 1.10779i	−0.832586	−	0.553896i	$-0.813141\pi$
$587$	− 26.8397i	− 1.10779i	0.832586	−	0.553896i	$-0.186859\pi$
$588$	− 24.2337i	− 0.999380i
$589$	−16.7446	−0.689948
$590$	0	0
$591$	9.02175	0.371105
$592$	1.00000i	0.0410997i
$593$	− 24.2337i	− 0.995158i	−0.867419	−	0.497579i	$-0.834222\pi$
$593$	− 24.2337i	− 0.995158i	0.867419	−	0.497579i	$-0.165778\pi$
$594$	9.48913	0.389344
$595$	0	0
$596$	11.4891	0.470613
$597$	− 45.4891i	− 1.86175i
$598$	32.0000i	1.30858i
$599$	5.48913	0.224280	0.112140	−	0.993692i	$-0.464230\pi$
$599$	5.48913	0.224280	0.112140	+	0.993692i	$0.464230\pi$
$600$	0	0
$601$	0.372281	0.0151857	0.00759284	−	0.999971i	$-0.497583\pi$
$601$	0.372281	0.0151857	0.00759284	+	0.999971i	$0.497583\pi$
$602$	− 7.11684i	− 0.290061i
$603$	6.74456i	0.274660i
$604$	20.0000	0.813788
$605$	0	0
$606$	22.9783	0.933428
$607$	− 39.7228i	− 1.61230i	−0.591712	−	0.806150i	$-0.701548\pi$
$607$	− 39.7228i	− 1.61230i	0.591712	−	0.806150i	$-0.298452\pi$
$608$	2.00000i	0.0811107i
$609$	−79.7228	−3.23053
$610$	0	0
$611$	18.5109	0.748870
$612$	0.372281i	0.0150486i
$613$	20.0951i	0.811633i	0.913955	+	0.405817i	$0.133013\pi$
$613$	20.0951i	0.811633i	−0.913955	+	0.405817i	$0.866987\pi$
$614$	0.510875	0.0206172
$615$	0	0
$616$	−10.3723	−0.417911
$617$	25.7228i	1.03556i	0.855513	+	0.517781i	$0.173242\pi$
$617$	25.7228i	1.03556i	−0.855513	+	0.517781i	$0.826758\pi$
$618$	− 26.9783i	− 1.08522i
$619$	−12.8832	−0.517818	−0.258909	−	0.965902i	$-0.583363\pi$
$619$	−12.8832	−0.517818	−0.258909	+	0.965902i	$0.583363\pi$
$620$	0	0
$621$	18.9783	0.761571
$622$	4.37228i	0.175313i
$623$	43.7228i	1.75172i
$624$	−13.4891	−0.539997
$625$	0	0
$626$	19.4891	0.778942
$627$	− 9.48913i	− 0.378959i
$628$	− 11.6277i	− 0.463996i
$629$	−0.372281	−0.0148438
$630$	0	0
$631$	44.0951	1.75540	0.877699	−	0.479212i	$-0.159078\pi$
$631$	44.0951	1.75540	0.877699	+	0.479212i	$0.159078\pi$
$632$	6.74456i	0.268284i
$633$	− 6.23369i	− 0.247767i
$634$	−19.6277	−0.779516
$635$	0	0
$636$	−8.74456	−0.346744
$637$	81.7228i	3.23798i
$638$	21.6277i	0.856250i
$639$	−4.74456	−0.187692
$640$	0	0
$641$	−9.39403	−0.371042	−0.185521	−	0.982640i	$-0.559397\pi$
$641$	−9.39403	−0.371042	−0.185521	+	0.982640i	$0.559397\pi$
$642$	38.9783i	1.53835i
$643$	2.37228i	0.0935536i	0.998905	+	0.0467768i	$0.0148950\pi$
$643$	2.37228i	0.0935536i	−0.998905	+	0.0467768i	$0.985105\pi$
$644$	−20.7446	−0.817450
$645$	0	0
$646$	−0.744563	−0.0292944
$647$	9.48913i	0.373056i	0.982450	+	0.186528i	$0.0597235\pi$
$647$	9.48913i	0.373056i	−0.982450	+	0.186528i	$0.940276\pi$
$648$	11.0000i	0.432121i
$649$	−2.97825	−0.116907
$650$	0	0
$651$	73.2119	2.86940
$652$	13.6277i	0.533703i
$653$	− 23.4891i	− 0.919201i	−0.888126	−	0.459600i	$-0.847993\pi$
$653$	− 23.4891i	− 0.919201i	0.888126	−	0.459600i	$-0.152007\pi$
$654$	34.2337	1.33864
$655$	0	0
$656$	−0.372281	−0.0145351
$657$	− 2.74456i	− 0.107076i
$658$	12.0000i	0.467809i
$659$	−12.0000	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	0	0
$661$	−47.3505	−1.84172	−0.920861	−	0.389891i	$-0.872513\pi$
$661$	−47.3505	−1.84172	−0.920861	+	0.389891i	$0.872513\pi$
$662$	0.510875i	0.0198557i
$663$	− 5.02175i	− 0.195029i
$664$	−10.7446	−0.416970
$665$	0	0
$666$	1.00000	0.0387492
$667$	43.2554i	1.67486i
$668$	21.4891i	0.831439i
$669$	−8.74456	−0.338084
$670$	0	0
$671$	0.883156	0.0340939
$672$	− 8.74456i	− 0.337329i
$673$	31.4891i	1.21382i	0.794772	+	0.606908i	$0.207590\pi$
$673$	31.4891i	1.21382i	−0.794772	+	0.606908i	$0.792410\pi$
$674$	18.7446	0.722014
$675$	0	0
$676$	32.4891	1.24958
$677$	− 42.0000i	− 1.61419i	−0.590421	−	0.807096i	$-0.701038\pi$
$677$	− 42.0000i	− 1.61419i	0.590421	−	0.807096i	$-0.298962\pi$
$678$	− 23.2554i	− 0.893120i
$679$	74.8397	2.87208
$680$	0	0
$681$	−11.2554	−0.431309
$682$	− 19.8614i	− 0.760533i
$683$	− 14.3723i	− 0.549940i	−0.961453	−	0.274970i	$-0.911332\pi$
$683$	− 14.3723i	− 0.549940i	0.961453	−	0.274970i	$-0.0886679\pi$
$684$	2.00000	0.0764719
$685$	0	0
$686$	−22.3723	−0.854178
$687$	− 20.0000i	− 0.763048i
$688$	− 1.62772i	− 0.0620562i
$689$	29.4891	1.12345
$690$	0	0
$691$	−29.3505	−1.11655	−0.558273	−	0.829657i	$-0.688536\pi$
$691$	−29.3505	−1.11655	−0.558273	+	0.829657i	$0.688536\pi$
$692$	− 5.86141i	− 0.222817i
$693$	10.3723i	0.394010i
$694$	−22.9783	−0.872242
$695$	0	0
$696$	−18.2337	−0.691146
$697$	− 0.138593i	− 0.00524960i
$698$	22.0000i	0.832712i
$699$	56.4674	2.13579
$700$	0	0
$701$	42.4674	1.60397	0.801985	−	0.597344i	$-0.203777\pi$
$701$	42.4674	1.60397	0.801985	+	0.597344i	$0.203777\pi$
$702$	− 26.9783i	− 1.01823i
$703$	2.00000i	0.0754314i
$704$	−2.37228	−0.0894087
$705$	0	0
$706$	5.86141	0.220597
$707$	− 50.2337i	− 1.88923i
$708$	− 2.51087i	− 0.0943645i
$709$	−22.8832	−0.859395	−0.429697	−	0.902973i	$-0.641380\pi$
$709$	−22.8832	−0.859395	−0.429697	+	0.902973i	$0.641380\pi$
$710$	0	0
$711$	6.74456	0.252941
$712$	10.0000i	0.374766i
$713$	− 39.7228i	− 1.48763i
$714$	3.25544	0.121832
$715$	0	0
$716$	8.23369	0.307707
$717$	− 45.2119i	− 1.68847i
$718$	− 14.9783i	− 0.558983i
$719$	23.2554	0.867281	0.433641	−	0.901086i	$-0.357229\pi$
$719$	23.2554	0.867281	0.433641	+	0.901086i	$0.357229\pi$
$720$	0	0
$721$	−58.9783	−2.19646
$722$	− 15.0000i	− 0.558242i
$723$	− 48.4674i	− 1.80252i
$724$	15.4891	0.575649
$725$	0	0
$726$	−10.7446	−0.398768
$727$	− 48.0000i	− 1.78022i	−0.455744	−	0.890111i	$-0.650627\pi$
$727$	− 48.0000i	− 1.78022i	0.455744	−	0.890111i	$-0.349373\pi$
$728$	29.4891i	1.09294i
$729$	−13.0000	−0.481481
$730$	0	0
$731$	0.605969	0.0224126
$732$	0.744563i	0.0275198i
$733$	23.6277i	0.872710i	0.899775	+	0.436355i	$0.143731\pi$
$733$	23.6277i	0.872710i	−0.899775	+	0.436355i	$0.856269\pi$
$734$	−21.1168	−0.779437
$735$	0	0
$736$	−4.74456	−0.174887
$737$	− 16.0000i	− 0.589368i
$738$	0.372281i	0.0137039i
$739$	8.13859	0.299383	0.149691	−	0.988733i	$-0.452172\pi$
$739$	8.13859	0.299383	0.149691	+	0.988733i	$0.452172\pi$
$740$	0	0
$741$	−26.9783	−0.991071
$742$	19.1168i	0.701801i
$743$	− 0.372281i	− 0.0136577i	−0.999977	−	0.00682884i	$-0.997826\pi$
$743$	− 0.372281i	− 0.0136577i	0.999977	−	0.00682884i	$-0.00217370\pi$
$744$	16.7446	0.613885
$745$	0	0
$746$	−8.51087	−0.311605
$747$	10.7446i	0.393123i
$748$	− 0.883156i	− 0.0322914i
$749$	85.2119	3.11358
$750$	0	0
$751$	−0.744563	−0.0271695	−0.0135847	−	0.999908i	$-0.504324\pi$
$751$	−0.744563	−0.0271695	−0.0135847	+	0.999908i	$0.504324\pi$
$752$	2.74456i	0.100084i
$753$	22.9783i	0.837374i
$754$	61.4891	2.23930
$755$	0	0
$756$	17.4891	0.636073
$757$	− 47.9565i	− 1.74301i	−0.490388	−	0.871504i	$-0.663145\pi$
$757$	− 47.9565i	− 1.74301i	0.490388	−	0.871504i	$-0.336855\pi$
$758$	8.00000i	0.290573i
$759$	22.5109	0.817093
$760$	0	0
$761$	−0.372281	−0.0134952	−0.00674759	−	0.999977i	$-0.502148\pi$
$761$	−0.372281	−0.0134952	−0.00674759	+	0.999977i	$0.502148\pi$
$762$	− 10.5109i	− 0.380769i
$763$	− 74.8397i	− 2.70938i
$764$	−24.3723	−0.881758
$765$	0	0
$766$	9.48913	0.342856
$767$	8.46738i	0.305739i
$768$	− 2.00000i	− 0.0721688i
$769$	−11.7663	−0.424304	−0.212152	−	0.977237i	$-0.568047\pi$
$769$	−11.7663	−0.424304	−0.212152	+	0.977237i	$0.568047\pi$
$770$	0	0
$771$	49.9565	1.79914
$772$	2.00000i	0.0719816i
$773$	− 27.3505i	− 0.983730i	−0.870671	−	0.491865i	$-0.836315\pi$
$773$	− 27.3505i	− 0.983730i	0.870671	−	0.491865i	$-0.163685\pi$
$774$	−1.62772	−0.0585071
$775$	0	0
$776$	17.1168	0.614459
$777$	− 8.74456i	− 0.313709i
$778$	13.8614i	0.496956i
$779$	−0.744563	−0.0266767
$780$	0	0
$781$	11.2554	0.402751
$782$	− 1.76631i	− 0.0631632i
$783$	− 36.4674i	− 1.30324i
$784$	−12.1168	−0.432744
$785$	0	0
$786$	−29.4891	−1.05184
$787$	− 22.0000i	− 0.784215i	−0.919919	−	0.392108i	$-0.871746\pi$
$787$	− 22.0000i	− 0.784215i	0.919919	−	0.392108i	$-0.128254\pi$
$788$	− 4.51087i	− 0.160693i
$789$	34.2337	1.21875
$790$	0	0
$791$	−50.8397	−1.80765
$792$	2.37228i	0.0842953i
$793$	− 2.51087i	− 0.0891638i
$794$	20.9783	0.744490
$795$	0	0
$796$	−22.7446	−0.806160
$797$	− 4.51087i	− 0.159783i	−0.996804	−	0.0798917i	$-0.974543\pi$
$797$	− 4.51087i	− 0.159783i	0.996804	−	0.0798917i	$-0.0254574\pi$
$798$	− 17.4891i	− 0.619108i
$799$	−1.02175	−0.0361469
$800$	0	0
$801$	10.0000	0.353333
$802$	10.0000i	0.353112i
$803$	6.51087i	0.229764i
$804$	13.4891	0.475725
$805$	0	0
$806$	−56.4674	−1.98898
$807$	20.0000i	0.704033i
$808$	− 11.4891i	− 0.404186i
$809$	28.5109	1.00239	0.501194	−	0.865335i	$-0.332894\pi$
$809$	28.5109	1.00239	0.501194	+	0.865335i	$0.332894\pi$
$810$	0	0
$811$	26.5109	0.930923	0.465461	−	0.885068i	$-0.345888\pi$
$811$	26.5109	0.930923	0.465461	+	0.885068i	$0.345888\pi$
$812$	39.8614i	1.39886i
$813$	− 9.48913i	− 0.332798i
$814$	−2.37228	−0.0831484
$815$	0	0
$816$	0.744563	0.0260649
$817$	− 3.25544i	− 0.113893i
$818$	28.2337i	0.987168i
$819$	29.4891	1.03043
$820$	0	0
$821$	−21.2554	−0.741820	−0.370910	−	0.928669i	$-0.620954\pi$
$821$	−21.2554	−0.741820	−0.370910	+	0.928669i	$0.620954\pi$
$822$	10.5109i	0.366609i
$823$	− 17.7228i	− 0.617778i	−0.951098	−	0.308889i	$-0.900043\pi$
$823$	− 17.7228i	− 0.617778i	0.951098	−	0.308889i	$-0.0999572\pi$
$824$	−13.4891	−0.469916
$825$	0	0
$826$	−5.48913	−0.190991
$827$	− 2.64947i	− 0.0921310i	−0.998938	−	0.0460655i	$-0.985332\pi$
$827$	− 2.64947i	− 0.0921310i	0.998938	−	0.0460655i	$-0.0146683\pi$
$828$	4.74456i	0.164885i
$829$	−11.3505	−0.394220	−0.197110	−	0.980381i	$-0.563156\pi$
$829$	−11.3505	−0.394220	−0.197110	+	0.980381i	$0.563156\pi$
$830$	0	0
$831$	−21.4891	−0.745449
$832$	6.74456i	0.233826i
$833$	− 4.51087i	− 0.156293i
$834$	38.2337	1.32392
$835$	0	0
$836$	−4.74456	−0.164094
$837$	33.4891i	1.15755i
$838$	9.48913i	0.327796i
$839$	6.51087	0.224780	0.112390	−	0.993664i	$-0.464149\pi$
$839$	6.51087	0.224780	0.112390	+	0.993664i	$0.464149\pi$
$840$	0	0
$841$	54.1168	1.86610
$842$	15.4891i	0.533791i
$843$	− 26.5109i	− 0.913083i
$844$	−3.11684	−0.107286
$845$	0	0
$846$	2.74456	0.0943600
$847$	23.4891i	0.807096i
$848$	4.37228i	0.150145i
$849$	34.9783	1.20045
$850$	0	0
$851$	−4.74456	−0.162642
$852$	9.48913i	0.325092i
$853$	− 12.5109i	− 0.428364i	−0.976794	−	0.214182i	$-0.931291\pi$
$853$	− 12.5109i	− 0.428364i	0.976794	−	0.214182i	$-0.0687086\pi$
$854$	1.62772	0.0556994
$855$	0	0
$856$	19.4891	0.666125
$857$	− 57.8614i	− 1.97651i	−0.152820	−	0.988254i	$-0.548836\pi$
$857$	− 57.8614i	− 1.97651i	0.152820	−	0.988254i	$-0.451164\pi$
$858$	− 32.0000i	− 1.09246i
$859$	−37.7228	−1.28709	−0.643543	−	0.765410i	$-0.722536\pi$
$859$	−37.7228	−1.28709	−0.643543	+	0.765410i	$0.722536\pi$
$860$	0	0
$861$	3.25544	0.110945
$862$	4.37228i	0.148920i
$863$	20.8397i	0.709390i	0.934982	+	0.354695i	$0.115415\pi$
$863$	20.8397i	0.709390i	−0.934982	+	0.354695i	$0.884585\pi$
$864$	4.00000	0.136083
$865$	0	0
$866$	−32.9783	−1.12065
$867$	− 33.7228i	− 1.14529i
$868$	− 36.6060i	− 1.24249i
$869$	−16.0000	−0.542763
$870$	0	0
$871$	−45.4891	−1.54134
$872$	− 17.1168i	− 0.579649i
$873$	− 17.1168i	− 0.579317i
$874$	−9.48913	−0.320974
$875$	0	0
$876$	−5.48913	−0.185460
$877$	43.6277i	1.47320i	0.676327	+	0.736602i	$0.263571\pi$
$877$	43.6277i	1.47320i	−0.676327	+	0.736602i	$0.736429\pi$
$878$	7.62772i	0.257423i
$879$	−19.7228	−0.665234
$880$	0	0
$881$	−4.37228	−0.147306	−0.0736530	−	0.997284i	$-0.523466\pi$
$881$	−4.37228	−0.147306	−0.0736530	+	0.997284i	$0.523466\pi$
$882$	12.1168i	0.407995i
$883$	5.62772i	0.189388i	0.995506	+	0.0946939i	$0.0301872\pi$
$883$	5.62772i	0.189388i	−0.995506	+	0.0946939i	$0.969813\pi$
$884$	−2.51087	−0.0844499
$885$	0	0
$886$	28.9783	0.973543
$887$	− 19.6277i	− 0.659034i	−0.944150	−	0.329517i	$-0.893114\pi$
$887$	− 19.6277i	− 0.659034i	0.944150	−	0.329517i	$-0.106886\pi$
$888$	− 2.00000i	− 0.0671156i
$889$	−22.9783	−0.770666
$890$	0	0
$891$	−26.0951	−0.874219
$892$	4.37228i	0.146395i
$893$	5.48913i	0.183687i
$894$	−22.9783	−0.768508
$895$	0	0
$896$	−4.37228	−0.146068
$897$	− 64.0000i	− 2.13690i
$898$	− 18.0000i	− 0.600668i
$899$	−76.3288	−2.54571
$900$	0	0
$901$	−1.62772	−0.0542272
$902$	− 0.883156i	− 0.0294059i
$903$	14.2337i	0.473667i
$904$	−11.6277	−0.386732
$905$	0	0
$906$	−40.0000	−1.32891
$907$	− 28.4674i	− 0.945244i	−0.881265	−	0.472622i	$-0.843308\pi$
$907$	− 28.4674i	− 0.945244i	0.881265	−	0.472622i	$-0.156692\pi$
$908$	5.62772i	0.186762i
$909$	−11.4891	−0.381070
$910$	0	0
$911$	52.2337	1.73058	0.865290	−	0.501272i	$-0.167134\pi$
$911$	52.2337	1.73058	0.865290	+	0.501272i	$0.167134\pi$
$912$	− 4.00000i	− 0.132453i
$913$	− 25.4891i	− 0.843567i
$914$	9.86141	0.326186
$915$	0	0
$916$	−10.0000	−0.330409
$917$	64.4674i	2.12890i
$918$	1.48913i	0.0491485i
$919$	49.7228	1.64020	0.820102	−	0.572217i	$-0.193917\pi$
$919$	49.7228	1.64020	0.820102	+	0.572217i	$0.193917\pi$
$920$	0	0
$921$	−1.02175	−0.0336678
$922$	24.0951i	0.793530i
$923$	− 32.0000i	− 1.05329i
$924$	20.7446	0.682446
$925$	0	0
$926$	17.4891	0.574728
$927$	13.4891i	0.443041i
$928$	9.11684i	0.299275i
$929$	32.0951	1.05301	0.526503	−	0.850173i	$-0.323503\pi$
$929$	32.0951	1.05301	0.526503	+	0.850173i	$0.323503\pi$
$930$	0	0
$931$	−24.2337	−0.794227
$932$	− 28.2337i	− 0.924825i
$933$	− 8.74456i	− 0.286284i
$934$	21.3505	0.698611
$935$	0	0
$936$	6.74456	0.220453
$937$	− 8.97825i	− 0.293307i	−0.989188	−	0.146653i	$-0.953150\pi$
$937$	− 8.97825i	− 0.293307i	0.989188	−	0.146653i	$-0.0468502\pi$
$938$	− 29.4891i	− 0.962854i
$939$	−38.9783	−1.27201
$940$	0	0
$941$	18.0000	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$942$	23.2554i	0.757703i
$943$	− 1.76631i	− 0.0575190i
$944$	−1.25544	−0.0408610
$945$	0	0
$946$	3.86141	0.125545
$947$	− 26.0951i	− 0.847977i	−0.905668	−	0.423988i	$-0.860630\pi$
$947$	− 26.0951i	− 0.847977i	0.905668	−	0.423988i	$-0.139370\pi$
$948$	− 13.4891i	− 0.438106i
$949$	18.5109	0.600888
$950$	0	0
$951$	39.2554	1.27294
$952$	− 1.62772i	− 0.0527547i
$953$	− 11.7663i	− 0.381148i	−0.981673	−	0.190574i	$-0.938965\pi$
$953$	− 11.7663i	− 0.381148i	0.981673	−	0.190574i	$-0.0610349\pi$
$954$	4.37228	0.141558
$955$	0	0
$956$	−22.6060	−0.731129
$957$	− 43.2554i	− 1.39825i
$958$	− 14.7446i	− 0.476375i
$959$	22.9783	0.742006
$960$	0	0
$961$	39.0951	1.26113
$962$	6.74456i	0.217453i
$963$	− 19.4891i	− 0.628028i
$964$	−24.2337	−0.780515
$965$	0	0
$966$	41.4891	1.33489
$967$	− 28.0000i	− 0.900419i	−0.892923	−	0.450210i	$-0.851349\pi$
$967$	− 28.0000i	− 0.900419i	0.892923	−	0.450210i	$-0.148651\pi$
$968$	5.37228i	0.172672i
$969$	1.48913	0.0478376
$970$	0	0
$971$	20.6060	0.661277	0.330639	−	0.943757i	$-0.392736\pi$
$971$	20.6060	0.661277	0.330639	+	0.943757i	$0.392736\pi$
$972$	− 10.0000i	− 0.320750i
$973$	− 83.5842i	− 2.67959i
$974$	−19.7228	−0.631960
$975$	0	0
$976$	0.372281	0.0119164
$977$	− 29.1168i	− 0.931530i	−0.884908	−	0.465765i	$-0.845779\pi$
$977$	− 29.1168i	− 0.931530i	0.884908	−	0.465765i	$-0.154221\pi$
$978$	− 27.2554i	− 0.871533i
$979$	−23.7228	−0.758184
$980$	0	0
$981$	−17.1168	−0.546499
$982$	− 30.9783i	− 0.988556i
$983$	− 2.13859i	− 0.0682105i	−0.999418	−	0.0341053i	$-0.989142\pi$
$983$	− 2.13859i	− 0.0682105i	0.999418	−	0.0341053i	$-0.0108581\pi$
$984$	0.744563	0.0237358
$985$	0	0
$986$	−3.39403	−0.108088
$987$	− 24.0000i	− 0.763928i
$988$	13.4891i	0.429146i
$989$	7.72281	0.245571
$990$	0	0
$991$	−14.6060	−0.463974	−0.231987	−	0.972719i	$-0.574523\pi$
$991$	−14.6060	−0.463974	−0.231987	+	0.972719i	$0.574523\pi$
$992$	− 8.37228i	− 0.265820i
$993$	− 1.02175i	− 0.0324242i
$994$	20.7446	0.657978
$995$	0	0
$996$	21.4891	0.680909
$997$	− 8.23369i	− 0.260764i	−0.991464	−	0.130382i	$-0.958380\pi$
$997$	− 8.23369i	− 0.260764i	0.991464	−	0.130382i	$-0.0416203\pi$
$998$	− 20.9783i	− 0.664055i
$999$	4.00000	0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.b.m.149.3		4
5.2	odd	4		1850.2.a.q.1.2		2
5.3	odd	4		370.2.a.f.1.1	✓	2
5.4	even	2	inner	1850.2.b.m.149.2		4
15.8	even	4		3330.2.a.bb.1.1		2
20.3	even	4		2960.2.a.o.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.a.f.1.1	✓	2	5.3	odd	4
1850.2.a.q.1.2		2	5.2	odd	4
1850.2.b.m.149.2		4	5.4	even	2	inner
1850.2.b.m.149.3		4	1.1	even	1	trivial
2960.2.a.o.1.2		2	20.3	even	4
3330.2.a.bb.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:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -2.00000i q^{3} -1.00000 q^{4} +2.00000 q^{6} -4.37228i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -2.00000i q^{3} -1.00000 q^{4} +2.00000 q^{6} -4.37228i q^{7} -1.00000i q^{8} -1.00000 q^{9} +2.37228 q^{11} +2.00000i q^{12} -6.74456i q^{13} +4.37228 q^{14} +1.00000 q^{16} +0.372281i q^{17} -1.00000i q^{18} +2.00000 q^{19} -8.74456 q^{21} +2.37228i q^{22} +4.74456i q^{23} -2.00000 q^{24} +6.74456 q^{26} -4.00000i q^{27} +4.37228i q^{28} +9.11684 q^{29} -8.37228 q^{31} +1.00000i q^{32} -4.74456i q^{33} -0.372281 q^{34} +1.00000 q^{36} +1.00000i q^{37} +2.00000i q^{38} -13.4891 q^{39} -0.372281 q^{41} -8.74456i q^{42} -1.62772i q^{43} -2.37228 q^{44} -4.74456 q^{46} +2.74456i q^{47} -2.00000i q^{48} -12.1168 q^{49} +0.744563 q^{51} +6.74456i q^{52} +4.37228i q^{53} +4.00000 q^{54} -4.37228 q^{56} -4.00000i q^{57} +9.11684i q^{58} -1.25544 q^{59} +0.372281 q^{61} -8.37228i q^{62} +4.37228i q^{63} -1.00000 q^{64} +4.74456 q^{66} -6.74456i q^{67} -0.372281i q^{68} +9.48913 q^{69} +4.74456 q^{71} +1.00000i q^{72} +2.74456i q^{73} -1.00000 q^{74} -2.00000 q^{76} -10.3723i q^{77} -13.4891i q^{78} -6.74456 q^{79} -11.0000 q^{81} -0.372281i q^{82} -10.7446i q^{83} +8.74456 q^{84} +1.62772 q^{86} -18.2337i q^{87} -2.37228i q^{88} -10.0000 q^{89} -29.4891 q^{91} -4.74456i q^{92} +16.7446i q^{93} -2.74456 q^{94} +2.00000 q^{96} +17.1168i q^{97} -12.1168i q^{98} -2.37228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 8 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} + 8 q^{6} - 4 q^{9} - 2 q^{11} + 6 q^{14} + 4 q^{16} + 8 q^{19} - 12 q^{21} - 8 q^{24} + 4 q^{26} + 2 q^{29} - 22 q^{31} + 10 q^{34} + 4 q^{36} - 8 q^{39} + 10 q^{41} + 2 q^{44} + 4 q^{46} - 14 q^{49} - 20 q^{51} + 16 q^{54} - 6 q^{56} - 28 q^{59} - 10 q^{61} - 4 q^{64} - 4 q^{66} - 8 q^{69} - 4 q^{71} - 4 q^{74} - 8 q^{76} - 4 q^{79} - 44 q^{81} + 12 q^{84} + 18 q^{86} - 40 q^{89} - 72 q^{91} + 12 q^{94} + 8 q^{96} + 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 8 * q^6 - 4 * q^9 - 2 * q^11 + 6 * q^14 + 4 * q^16 + 8 * q^19 - 12 * q^21 - 8 * q^24 + 4 * q^26 + 2 * q^29 - 22 * q^31 + 10 * q^34 + 4 * q^36 - 8 * q^39 + 10 * q^41 + 2 * q^44 + 4 * q^46 - 14 * q^49 - 20 * q^51 + 16 * q^54 - 6 * q^56 - 28 * q^59 - 10 * q^61 - 4 * q^64 - 4 * q^66 - 8 * q^69 - 4 * q^71 - 4 * q^74 - 8 * q^76 - 4 * q^79 - 44 * q^81 + 12 * q^84 + 18 * q^86 - 40 * q^89 - 72 * q^91 + 12 * q^94 + 8 * q^96 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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