LMFDB - Embedded newform 3450.2.d.y.2899.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3450,2,Mod(2899,3450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3450, 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("3450.2899");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3450.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:	$27.5483886973$
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			2899.4
Root			$-1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	3450.2899
Dual form			3450.2.d.y.2899.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +1.44949i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +1.44949i q^{7} -1.00000i q^{8} -1.00000 q^{9} +2.00000 q^{11} +1.00000i q^{12} +2.89898i q^{13} -1.44949 q^{14} +1.00000 q^{16} -5.44949i q^{17} -1.00000i q^{18} -6.89898 q^{19} +1.44949 q^{21} +2.00000i q^{22} -1.00000i q^{23} -1.00000 q^{24} -2.89898 q^{26} +1.00000i q^{27} -1.44949i q^{28} -5.00000 q^{29} +2.00000 q^{31} +1.00000i q^{32} -2.00000i q^{33} +5.44949 q^{34} +1.00000 q^{36} +8.34847i q^{37} -6.89898i q^{38} +2.89898 q^{39} -4.89898 q^{41} +1.44949i q^{42} -10.8990i q^{43} -2.00000 q^{44} +1.00000 q^{46} -3.89898i q^{47} -1.00000i q^{48} +4.89898 q^{49} -5.44949 q^{51} -2.89898i q^{52} -0.898979i q^{53} -1.00000 q^{54} +1.44949 q^{56} +6.89898i q^{57} -5.00000i q^{58} -10.0000 q^{59} -4.89898 q^{61} +2.00000i q^{62} -1.44949i q^{63} -1.00000 q^{64} +2.00000 q^{66} -2.00000i q^{67} +5.44949i q^{68} -1.00000 q^{69} +10.7980 q^{71} +1.00000i q^{72} -2.10102i q^{73} -8.34847 q^{74} +6.89898 q^{76} +2.89898i q^{77} +2.89898i q^{78} -10.0000 q^{79} +1.00000 q^{81} -4.89898i q^{82} +2.55051i q^{83} -1.44949 q^{84} +10.8990 q^{86} +5.00000i q^{87} -2.00000i q^{88} +10.3485 q^{89} -4.20204 q^{91} +1.00000i q^{92} -2.00000i q^{93} +3.89898 q^{94} +1.00000 q^{96} -12.6969i q^{97} +4.89898i q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 8 q^{11} + 4 q^{14} + 4 q^{16} - 8 q^{19} - 4 q^{21} - 4 q^{24} + 8 q^{26} - 20 q^{29} + 8 q^{31} + 12 q^{34} + 4 q^{36} - 8 q^{39} - 8 q^{44} + 4 q^{46} - 12 q^{51} - 4 q^{54} - 4 q^{56} - 40 q^{59} - 4 q^{64} + 8 q^{66} - 4 q^{69} + 4 q^{71} - 4 q^{74} + 8 q^{76} - 40 q^{79} + 4 q^{81} + 4 q^{84} + 24 q^{86} + 12 q^{89} - 56 q^{91} - 4 q^{94} + 4 q^{96} - 8 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 8 * q^11 + 4 * q^14 + 4 * q^16 - 8 * q^19 - 4 * q^21 - 4 * q^24 + 8 * q^26 - 20 * q^29 + 8 * q^31 + 12 * q^34 + 4 * q^36 - 8 * q^39 - 8 * q^44 + 4 * q^46 - 12 * q^51 - 4 * q^54 - 4 * q^56 - 40 * q^59 - 4 * q^64 + 8 * q^66 - 4 * q^69 + 4 * q^71 - 4 * q^74 + 8 * q^76 - 40 * q^79 + 4 * q^81 + 4 * q^84 + 24 * q^86 + 12 * q^89 - 56 * q^91 - 4 * q^94 + 4 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3450\mathbb{Z}\right)^\times$.

$n$	$277$	$1151$	$1201$
$\chi(n)$	$-1$	$1$	$1$

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
$7$	1.44949i	0.547856i	0.961750	+	0.273928i	$0.0883229\pi$
$7$	1.44949i	0.547856i	−0.961750	+	0.273928i	$0.911677\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	1.00000i	0.288675i
$13$	2.89898i	0.804032i	0.915633	+	0.402016i	$0.131690\pi$
$13$	2.89898i	0.804032i	−0.915633	+	0.402016i	$0.868310\pi$
$14$	−1.44949	−0.387392
$15$	0	0
$16$	1.00000	0.250000
$17$	− 5.44949i	− 1.32170i	−0.750520	−	0.660848i	$-0.770197\pi$
$17$	− 5.44949i	− 1.32170i	0.750520	−	0.660848i	$-0.229803\pi$
$18$	− 1.00000i	− 0.235702i
$19$	−6.89898	−1.58273	−0.791367	−	0.611341i	$-0.790630\pi$
$19$	−6.89898	−1.58273	−0.791367	+	0.611341i	$0.790630\pi$
$20$	0	0
$21$	1.44949	0.316305
$22$	2.00000i	0.426401i
$23$	− 1.00000i	− 0.208514i
$23$	− 1.00000i	− 0.208514i
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−2.89898	−0.568537
$27$	1.00000i	0.192450i
$28$	− 1.44949i	− 0.273928i
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	1.00000i	0.176777i
$33$	− 2.00000i	− 0.348155i
$34$	5.44949	0.934580
$35$	0	0
$36$	1.00000	0.166667
$37$	8.34847i	1.37248i	0.727375	+	0.686240i	$0.240740\pi$
$37$	8.34847i	1.37248i	−0.727375	+	0.686240i	$0.759260\pi$
$38$	− 6.89898i	− 1.11916i
$39$	2.89898	0.464208
$40$	0	0
$41$	−4.89898	−0.765092	−0.382546	−	0.923936i	$-0.624953\pi$
$41$	−4.89898	−0.765092	−0.382546	+	0.923936i	$0.624953\pi$
$42$	1.44949i	0.223661i
$43$	− 10.8990i	− 1.66208i	−0.556214	−	0.831039i	$-0.687746\pi$
$43$	− 10.8990i	− 1.66208i	0.556214	−	0.831039i	$-0.312254\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	1.00000	0.147442
$47$	− 3.89898i	− 0.568725i	−0.958717	−	0.284362i	$-0.908218\pi$
$47$	− 3.89898i	− 0.568725i	0.958717	−	0.284362i	$-0.0917819\pi$
$48$	− 1.00000i	− 0.144338i
$49$	4.89898	0.699854
$50$	0	0
$51$	−5.44949	−0.763081
$52$	− 2.89898i	− 0.402016i
$53$	− 0.898979i	− 0.123484i	−0.998092	−	0.0617422i	$-0.980334\pi$
$53$	− 0.898979i	− 0.123484i	0.998092	−	0.0617422i	$-0.0196656\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	1.44949	0.193696
$57$	6.89898i	0.913792i
$58$	− 5.00000i	− 0.656532i
$59$	−10.0000	−1.30189	−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000	−1.30189	−0.650945	+	0.759125i	$0.725627\pi$
$60$	0	0
$61$	−4.89898	−0.627250	−0.313625	−	0.949547i	$-0.601543\pi$
$61$	−4.89898	−0.627250	−0.313625	+	0.949547i	$0.601543\pi$
$62$	2.00000i	0.254000i
$63$	− 1.44949i	− 0.182619i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	2.00000	0.246183
$67$	− 2.00000i	− 0.244339i	−0.992509	−	0.122169i	$-0.961015\pi$
$67$	− 2.00000i	− 0.244339i	0.992509	−	0.122169i	$-0.0389851\pi$
$68$	5.44949i	0.660848i
$69$	−1.00000	−0.120386
$70$	0	0
$71$	10.7980	1.28148	0.640741	−	0.767757i	$-0.278627\pi$
$71$	10.7980	1.28148	0.640741	+	0.767757i	$0.278627\pi$
$72$	1.00000i	0.117851i
$73$	− 2.10102i	− 0.245906i	−0.992413	−	0.122953i	$-0.960764\pi$
$73$	− 2.10102i	− 0.245906i	0.992413	−	0.122953i	$-0.0392364\pi$
$74$	−8.34847	−0.970490
$75$	0	0
$76$	6.89898	0.791367
$77$	2.89898i	0.330369i
$78$	2.89898i	0.328245i
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 4.89898i	− 0.541002i
$83$	2.55051i	0.279955i	0.990155	+	0.139977i	$0.0447030\pi$
$83$	2.55051i	0.279955i	−0.990155	+	0.139977i	$0.955297\pi$
$84$	−1.44949	−0.158152
$85$	0	0
$86$	10.8990	1.17527
$87$	5.00000i	0.536056i
$88$	− 2.00000i	− 0.213201i
$89$	10.3485	1.09694	0.548468	−	0.836172i	$-0.315211\pi$
$89$	10.3485	1.09694	0.548468	+	0.836172i	$0.315211\pi$
$90$	0	0
$91$	−4.20204	−0.440494
$92$	1.00000i	0.104257i
$93$	− 2.00000i	− 0.207390i
$94$	3.89898	0.402149
$95$	0	0
$96$	1.00000	0.102062
$97$	− 12.6969i	− 1.28918i	−0.764529	−	0.644589i	$-0.777028\pi$
$97$	− 12.6969i	− 1.28918i	0.764529	−	0.644589i	$-0.222972\pi$
$98$	4.89898i	0.494872i
$99$	−2.00000	−0.201008
$100$	0	0
$101$	−13.6969	−1.36290	−0.681448	−	0.731866i	$-0.738650\pi$
$101$	−13.6969	−1.36290	−0.681448	+	0.731866i	$0.738650\pi$
$102$	− 5.44949i	− 0.539580i
$103$	13.2474i	1.30531i	0.757655	+	0.652655i	$0.226345\pi$
$103$	13.2474i	1.30531i	−0.757655	+	0.652655i	$0.773655\pi$
$104$	2.89898	0.284268
$105$	0	0
$106$	0.898979	0.0873166
$107$	− 2.00000i	− 0.193347i	−0.995316	−	0.0966736i	$-0.969180\pi$
$107$	− 2.00000i	− 0.193347i	0.995316	−	0.0966736i	$-0.0308203\pi$
$108$	− 1.00000i	− 0.0962250i
$109$	−3.44949	−0.330401	−0.165201	−	0.986260i	$-0.552827\pi$
$109$	−3.44949	−0.330401	−0.165201	+	0.986260i	$0.552827\pi$
$110$	0	0
$111$	8.34847	0.792402
$112$	1.44949i	0.136964i
$113$	− 14.3485i	− 1.34979i	−0.737914	−	0.674895i	$-0.764189\pi$
$113$	− 14.3485i	− 1.34979i	0.737914	−	0.674895i	$-0.235811\pi$
$114$	−6.89898	−0.646149
$115$	0	0
$116$	5.00000	0.464238
$117$	− 2.89898i	− 0.268011i
$118$	− 10.0000i	− 0.920575i
$119$	7.89898	0.724098
$120$	0	0
$121$	−7.00000	−0.636364
$122$	− 4.89898i	− 0.443533i
$123$	4.89898i	0.441726i
$124$	−2.00000	−0.179605
$125$	0	0
$126$	1.44949	0.129131
$127$	1.79796i	0.159543i	0.996813	+	0.0797715i	$0.0254191\pi$
$127$	1.79796i	0.159543i	−0.996813	+	0.0797715i	$0.974581\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−10.8990	−0.959602
$130$	0	0
$131$	8.89898	0.777507	0.388754	−	0.921342i	$-0.372906\pi$
$131$	8.89898	0.777507	0.388754	+	0.921342i	$0.372906\pi$
$132$	2.00000i	0.174078i
$133$	− 10.0000i	− 0.867110i
$134$	2.00000	0.172774
$135$	0	0
$136$	−5.44949	−0.467290
$137$	− 22.3485i	− 1.90936i	−0.297636	−	0.954679i	$-0.596198\pi$
$137$	− 22.3485i	− 1.90936i	0.297636	−	0.954679i	$-0.403802\pi$
$138$	− 1.00000i	− 0.0851257i
$139$	−15.6969	−1.33140	−0.665698	−	0.746221i	$-0.731866\pi$
$139$	−15.6969	−1.33140	−0.665698	+	0.746221i	$0.731866\pi$
$140$	0	0
$141$	−3.89898	−0.328353
$142$	10.7980i	0.906145i
$143$	5.79796i	0.484850i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	2.10102	0.173882
$147$	− 4.89898i	− 0.404061i
$148$	− 8.34847i	− 0.686240i
$149$	−20.0000	−1.63846	−0.819232	−	0.573462i	$-0.805600\pi$
$149$	−20.0000	−1.63846	−0.819232	+	0.573462i	$0.805600\pi$
$150$	0	0
$151$	−18.6969	−1.52154	−0.760768	−	0.649024i	$-0.775177\pi$
$151$	−18.6969	−1.52154	−0.760768	+	0.649024i	$0.775177\pi$
$152$	6.89898i	0.559581i
$153$	5.44949i	0.440565i
$154$	−2.89898	−0.233606
$155$	0	0
$156$	−2.89898	−0.232104
$157$	− 8.89898i	− 0.710216i	−0.934825	−	0.355108i	$-0.884444\pi$
$157$	− 8.89898i	− 0.710216i	0.934825	−	0.355108i	$-0.115556\pi$
$158$	− 10.0000i	− 0.795557i
$159$	−0.898979	−0.0712937
$160$	0	0
$161$	1.44949	0.114236
$162$	1.00000i	0.0785674i
$163$	− 17.7980i	− 1.39404i	−0.717050	−	0.697022i	$-0.754508\pi$
$163$	− 17.7980i	− 1.39404i	0.717050	−	0.697022i	$-0.245492\pi$
$164$	4.89898	0.382546
$165$	0	0
$166$	−2.55051	−0.197958
$167$	− 7.00000i	− 0.541676i	−0.962625	−	0.270838i	$-0.912699\pi$
$167$	− 7.00000i	− 0.541676i	0.962625	−	0.270838i	$-0.0873008\pi$
$168$	− 1.44949i	− 0.111831i
$169$	4.59592	0.353532
$170$	0	0
$171$	6.89898	0.527578
$172$	10.8990i	0.831039i
$173$	19.7980i	1.50521i	0.658472	+	0.752605i	$0.271203\pi$
$173$	19.7980i	1.50521i	−0.658472	+	0.752605i	$0.728797\pi$
$174$	−5.00000	−0.379049
$175$	0	0
$176$	2.00000	0.150756
$177$	10.0000i	0.751646i
$178$	10.3485i	0.775651i
$179$	−3.10102	−0.231781	−0.115891	−	0.993262i	$-0.536972\pi$
$179$	−3.10102	−0.231781	−0.115891	+	0.993262i	$0.536972\pi$
$180$	0	0
$181$	−18.3485	−1.36383	−0.681915	−	0.731431i	$-0.738853\pi$
$181$	−18.3485	−1.36383	−0.681915	+	0.731431i	$0.738853\pi$
$182$	− 4.20204i	− 0.311476i
$183$	4.89898i	0.362143i
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	2.00000	0.146647
$187$	− 10.8990i	− 0.797012i
$188$	3.89898i	0.284362i
$189$	−1.44949	−0.105435
$190$	0	0
$191$	2.00000	0.144715	0.0723575	−	0.997379i	$-0.476948\pi$
$191$	2.00000	0.144715	0.0723575	+	0.997379i	$0.476948\pi$
$192$	1.00000i	0.0721688i
$193$	− 9.69694i	− 0.698001i	−0.937123	−	0.349000i	$-0.886521\pi$
$193$	− 9.69694i	− 0.698001i	0.937123	−	0.349000i	$-0.113479\pi$
$194$	12.6969	0.911587
$195$	0	0
$196$	−4.89898	−0.349927
$197$	− 3.89898i	− 0.277791i	−0.990307	−	0.138895i	$-0.955645\pi$
$197$	− 3.89898i	− 0.277791i	0.990307	−	0.138895i	$-0.0443552\pi$
$198$	− 2.00000i	− 0.142134i
$199$	−24.1464	−1.71169	−0.855847	−	0.517228i	$-0.826964\pi$
$199$	−24.1464	−1.71169	−0.855847	+	0.517228i	$0.826964\pi$
$200$	0	0
$201$	−2.00000	−0.141069
$202$	− 13.6969i	− 0.963713i
$203$	− 7.24745i	− 0.508671i
$204$	5.44949	0.381541
$205$	0	0
$206$	−13.2474	−0.922993
$207$	1.00000i	0.0695048i
$208$	2.89898i	0.201008i
$209$	−13.7980	−0.954425
$210$	0	0
$211$	10.7980	0.743362	0.371681	−	0.928360i	$-0.378781\pi$
$211$	10.7980	0.743362	0.371681	+	0.928360i	$0.378781\pi$
$212$	0.898979i	0.0617422i
$213$	− 10.7980i	− 0.739864i
$214$	2.00000	0.136717
$215$	0	0
$216$	1.00000	0.0680414
$217$	2.89898i	0.196796i
$218$	− 3.44949i	− 0.233629i
$219$	−2.10102	−0.141974
$220$	0	0
$221$	15.7980	1.06269
$222$	8.34847i	0.560313i
$223$	− 24.6969i	− 1.65383i	−0.562327	−	0.826915i	$-0.690094\pi$
$223$	− 24.6969i	− 1.65383i	0.562327	−	0.826915i	$-0.309906\pi$
$224$	−1.44949	−0.0968481
$225$	0	0
$226$	14.3485	0.954446
$227$	− 4.75255i	− 0.315438i	−0.987484	−	0.157719i	$-0.949586\pi$
$227$	− 4.75255i	− 0.315438i	0.987484	−	0.157719i	$-0.0504140\pi$
$228$	− 6.89898i	− 0.456896i
$229$	−3.10102	−0.204921	−0.102461	−	0.994737i	$-0.532672\pi$
$229$	−3.10102	−0.204921	−0.102461	+	0.994737i	$0.532672\pi$
$230$	0	0
$231$	2.89898	0.190739
$232$	5.00000i	0.328266i
$233$	26.6969i	1.74897i	0.485048	+	0.874487i	$0.338802\pi$
$233$	26.6969i	1.74897i	−0.485048	+	0.874487i	$0.661198\pi$
$234$	2.89898	0.189512
$235$	0	0
$236$	10.0000	0.650945
$237$	10.0000i	0.649570i
$238$	7.89898i	0.512015i
$239$	8.10102	0.524011	0.262006	−	0.965066i	$-0.415616\pi$
$239$	8.10102	0.524011	0.262006	+	0.965066i	$0.415616\pi$
$240$	0	0
$241$	−8.00000	−0.515325	−0.257663	−	0.966235i	$-0.582952\pi$
$241$	−8.00000	−0.515325	−0.257663	+	0.966235i	$0.582952\pi$
$242$	− 7.00000i	− 0.449977i
$243$	− 1.00000i	− 0.0641500i
$244$	4.89898	0.313625
$245$	0	0
$246$	−4.89898	−0.312348
$247$	− 20.0000i	− 1.27257i
$248$	− 2.00000i	− 0.127000i
$249$	2.55051	0.161632
$250$	0	0
$251$	−5.24745	−0.331216	−0.165608	−	0.986192i	$-0.552959\pi$
$251$	−5.24745	−0.331216	−0.165608	+	0.986192i	$0.552959\pi$
$252$	1.44949i	0.0913093i
$253$	− 2.00000i	− 0.125739i
$254$	−1.79796	−0.112814
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 8.20204i	− 0.511629i	−0.966726	−	0.255815i	$-0.917656\pi$
$257$	− 8.20204i	− 0.511629i	0.966726	−	0.255815i	$-0.0823437\pi$
$258$	− 10.8990i	− 0.678541i
$259$	−12.1010	−0.751921
$260$	0	0
$261$	5.00000	0.309492
$262$	8.89898i	0.549781i
$263$	19.7980i	1.22079i	0.792095	+	0.610397i	$0.208990\pi$
$263$	19.7980i	1.22079i	−0.792095	+	0.610397i	$0.791010\pi$
$264$	−2.00000	−0.123091
$265$	0	0
$266$	10.0000	0.613139
$267$	− 10.3485i	− 0.633316i
$268$	2.00000i	0.122169i
$269$	−3.79796	−0.231566	−0.115783	−	0.993275i	$-0.536938\pi$
$269$	−3.79796	−0.231566	−0.115783	+	0.993275i	$0.536938\pi$
$270$	0	0
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	− 5.44949i	− 0.330424i
$273$	4.20204i	0.254319i
$274$	22.3485	1.35012
$275$	0	0
$276$	1.00000	0.0601929
$277$	25.5959i	1.53791i	0.639303	+	0.768955i	$0.279223\pi$
$277$	25.5959i	1.53791i	−0.639303	+	0.768955i	$0.720777\pi$
$278$	− 15.6969i	− 0.941440i
$279$	−2.00000	−0.119737
$280$	0	0
$281$	−0.752551	−0.0448934	−0.0224467	−	0.999748i	$-0.507146\pi$
$281$	−0.752551	−0.0448934	−0.0224467	+	0.999748i	$0.507146\pi$
$282$	− 3.89898i	− 0.232181i
$283$	− 11.5959i	− 0.689306i	−0.938730	−	0.344653i	$-0.887997\pi$
$283$	− 11.5959i	− 0.689306i	0.938730	−	0.344653i	$-0.112003\pi$
$284$	−10.7980	−0.640741
$285$	0	0
$286$	−5.79796	−0.342841
$287$	− 7.10102i	− 0.419160i
$288$	− 1.00000i	− 0.0589256i
$289$	−12.6969	−0.746879
$290$	0	0
$291$	−12.6969	−0.744308
$292$	2.10102i	0.122953i
$293$	− 7.79796i	− 0.455562i	−0.973712	−	0.227781i	$-0.926853\pi$
$293$	− 7.79796i	− 0.455562i	0.973712	−	0.227781i	$-0.0731470\pi$
$294$	4.89898	0.285714
$295$	0	0
$296$	8.34847	0.485245
$297$	2.00000i	0.116052i
$298$	− 20.0000i	− 1.15857i
$299$	2.89898	0.167652
$300$	0	0
$301$	15.7980	0.910579
$302$	− 18.6969i	− 1.07589i
$303$	13.6969i	0.786869i
$304$	−6.89898	−0.395684
$305$	0	0
$306$	−5.44949	−0.311527
$307$	− 20.1010i	− 1.14723i	−0.819126	−	0.573613i	$-0.805541\pi$
$307$	− 20.1010i	− 1.14723i	0.819126	−	0.573613i	$-0.194459\pi$
$308$	− 2.89898i	− 0.165185i
$309$	13.2474	0.753621
$310$	0	0
$311$	14.5959	0.827659	0.413829	−	0.910355i	$-0.364191\pi$
$311$	14.5959	0.827659	0.413829	+	0.910355i	$0.364191\pi$
$312$	− 2.89898i	− 0.164122i
$313$	12.8990i	0.729093i	0.931185	+	0.364547i	$0.118776\pi$
$313$	12.8990i	0.729093i	−0.931185	+	0.364547i	$0.881224\pi$
$314$	8.89898	0.502198
$315$	0	0
$316$	10.0000	0.562544
$317$	10.5959i	0.595126i	0.954702	+	0.297563i	$0.0961738\pi$
$317$	10.5959i	0.595126i	−0.954702	+	0.297563i	$0.903826\pi$
$318$	− 0.898979i	− 0.0504123i
$319$	−10.0000	−0.559893
$320$	0	0
$321$	−2.00000	−0.111629
$322$	1.44949i	0.0807769i
$323$	37.5959i	2.09189i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	17.7980	0.985738
$327$	3.44949i	0.190757i
$328$	4.89898i	0.270501i
$329$	5.65153	0.311579
$330$	0	0
$331$	−6.79796	−0.373650	−0.186825	−	0.982393i	$-0.559820\pi$
$331$	−6.79796	−0.373650	−0.186825	+	0.982393i	$0.559820\pi$
$332$	− 2.55051i	− 0.139977i
$333$	− 8.34847i	− 0.457493i
$334$	7.00000	0.383023
$335$	0	0
$336$	1.44949	0.0790761
$337$	− 16.4949i	− 0.898534i	−0.893397	−	0.449267i	$-0.851685\pi$
$337$	− 16.4949i	− 0.898534i	0.893397	−	0.449267i	$-0.148315\pi$
$338$	4.59592i	0.249985i
$339$	−14.3485	−0.779302
$340$	0	0
$341$	4.00000	0.216612
$342$	6.89898i	0.373054i
$343$	17.2474i	0.931275i
$344$	−10.8990	−0.587634
$345$	0	0
$346$	−19.7980	−1.06434
$347$	− 32.6969i	− 1.75526i	−0.479335	−	0.877632i	$-0.659122\pi$
$347$	− 32.6969i	− 1.75526i	0.479335	−	0.877632i	$-0.340878\pi$
$348$	− 5.00000i	− 0.268028i
$349$	−13.1010	−0.701282	−0.350641	−	0.936510i	$-0.614036\pi$
$349$	−13.1010	−0.701282	−0.350641	+	0.936510i	$0.614036\pi$
$350$	0	0
$351$	−2.89898	−0.154736
$352$	2.00000i	0.106600i
$353$	26.0000i	1.38384i	0.721974	+	0.691920i	$0.243235\pi$
$353$	26.0000i	1.38384i	−0.721974	+	0.691920i	$0.756765\pi$
$354$	−10.0000	−0.531494
$355$	0	0
$356$	−10.3485	−0.548468
$357$	− 7.89898i	− 0.418058i
$358$	− 3.10102i	− 0.163894i
$359$	6.20204	0.327331	0.163666	−	0.986516i	$-0.447668\pi$
$359$	6.20204	0.327331	0.163666	+	0.986516i	$0.447668\pi$
$360$	0	0
$361$	28.5959	1.50505
$362$	− 18.3485i	− 0.964374i
$363$	7.00000i	0.367405i
$364$	4.20204	0.220247
$365$	0	0
$366$	−4.89898	−0.256074
$367$	− 8.20204i	− 0.428143i	−0.976818	−	0.214072i	$-0.931327\pi$
$367$	− 8.20204i	− 0.428143i	0.976818	−	0.214072i	$-0.0686726\pi$
$368$	− 1.00000i	− 0.0521286i
$369$	4.89898	0.255031
$370$	0	0
$371$	1.30306	0.0676516
$372$	2.00000i	0.103695i
$373$	3.24745i	0.168147i	0.996460	+	0.0840733i	$0.0267930\pi$
$373$	3.24745i	0.168147i	−0.996460	+	0.0840733i	$0.973207\pi$
$374$	10.8990	0.563573
$375$	0	0
$376$	−3.89898	−0.201075
$377$	− 14.4949i	− 0.746525i
$378$	− 1.44949i	− 0.0745537i
$379$	38.2929	1.96697	0.983486	−	0.180984i	$-0.0579284\pi$
$379$	38.2929	1.96697	0.983486	+	0.180984i	$0.0579284\pi$
$380$	0	0
$381$	1.79796	0.0921122
$382$	2.00000i	0.102329i
$383$	9.79796i	0.500652i	0.968162	+	0.250326i	$0.0805379\pi$
$383$	9.79796i	0.500652i	−0.968162	+	0.250326i	$0.919462\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	9.69694	0.493561
$387$	10.8990i	0.554026i
$388$	12.6969i	0.644589i
$389$	23.7980	1.20660	0.603302	−	0.797513i	$-0.293851\pi$
$389$	23.7980	1.20660	0.603302	+	0.797513i	$0.293851\pi$
$390$	0	0
$391$	−5.44949	−0.275593
$392$	− 4.89898i	− 0.247436i
$393$	− 8.89898i	− 0.448894i
$394$	3.89898	0.196428
$395$	0	0
$396$	2.00000	0.100504
$397$	28.0000i	1.40528i	0.711546	+	0.702640i	$0.247995\pi$
$397$	28.0000i	1.40528i	−0.711546	+	0.702640i	$0.752005\pi$
$398$	− 24.1464i	− 1.21035i
$399$	−10.0000	−0.500626
$400$	0	0
$401$	−18.6969	−0.933681	−0.466840	−	0.884342i	$-0.654608\pi$
$401$	−18.6969	−0.933681	−0.466840	+	0.884342i	$0.654608\pi$
$402$	− 2.00000i	− 0.0997509i
$403$	5.79796i	0.288817i
$404$	13.6969	0.681448
$405$	0	0
$406$	7.24745	0.359685
$407$	16.6969i	0.827637i
$408$	5.44949i	0.269790i
$409$	−25.6969	−1.27063	−0.635316	−	0.772252i	$-0.719130\pi$
$409$	−25.6969	−1.27063	−0.635316	+	0.772252i	$0.719130\pi$
$410$	0	0
$411$	−22.3485	−1.10237
$412$	− 13.2474i	− 0.652655i
$413$	− 14.4949i	− 0.713247i
$414$	−1.00000	−0.0491473
$415$	0	0
$416$	−2.89898	−0.142134
$417$	15.6969i	0.768682i
$418$	− 13.7980i	− 0.674880i
$419$	−14.1464	−0.691098	−0.345549	−	0.938401i	$-0.612307\pi$
$419$	−14.1464	−0.691098	−0.345549	+	0.938401i	$0.612307\pi$
$420$	0	0
$421$	−12.4949	−0.608964	−0.304482	−	0.952518i	$-0.598483\pi$
$421$	−12.4949	−0.608964	−0.304482	+	0.952518i	$0.598483\pi$
$422$	10.7980i	0.525636i
$423$	3.89898i	0.189575i
$424$	−0.898979	−0.0436583
$425$	0	0
$426$	10.7980	0.523163
$427$	− 7.10102i	− 0.343642i
$428$	2.00000i	0.0966736i
$429$	5.79796	0.279928
$430$	0	0
$431$	11.3031	0.544449	0.272225	−	0.962234i	$-0.412241\pi$
$431$	11.3031	0.544449	0.272225	+	0.962234i	$0.412241\pi$
$432$	1.00000i	0.0481125i
$433$	16.6969i	0.802404i	0.915990	+	0.401202i	$0.131407\pi$
$433$	16.6969i	0.802404i	−0.915990	+	0.401202i	$0.868593\pi$
$434$	−2.89898	−0.139155
$435$	0	0
$436$	3.44949	0.165201
$437$	6.89898i	0.330023i
$438$	− 2.10102i	− 0.100391i
$439$	10.6969	0.510537	0.255269	−	0.966870i	$-0.417836\pi$
$439$	10.6969	0.510537	0.255269	+	0.966870i	$0.417836\pi$
$440$	0	0
$441$	−4.89898	−0.233285
$442$	15.7980i	0.751432i
$443$	5.30306i	0.251956i	0.992033	+	0.125978i	$0.0402069\pi$
$443$	5.30306i	0.251956i	−0.992033	+	0.125978i	$0.959793\pi$
$444$	−8.34847	−0.396201
$445$	0	0
$446$	24.6969	1.16943
$447$	20.0000i	0.945968i
$448$	− 1.44949i	− 0.0684820i
$449$	−3.79796	−0.179237	−0.0896184	−	0.995976i	$-0.528565\pi$
$449$	−3.79796	−0.179237	−0.0896184	+	0.995976i	$0.528565\pi$
$450$	0	0
$451$	−9.79796	−0.461368
$452$	14.3485i	0.674895i
$453$	18.6969i	0.878459i
$454$	4.75255	0.223048
$455$	0	0
$456$	6.89898	0.323074
$457$	0.404082i	0.0189022i	0.999955	+	0.00945108i	$0.00300842\pi$
$457$	0.404082i	0.0189022i	−0.999955	+	0.00945108i	$0.996992\pi$
$458$	− 3.10102i	− 0.144901i
$459$	5.44949	0.254360
$460$	0	0
$461$	21.4949	1.00112	0.500559	−	0.865703i	$-0.333128\pi$
$461$	21.4949	1.00112	0.500559	+	0.865703i	$0.333128\pi$
$462$	2.89898i	0.134873i
$463$	− 4.00000i	− 0.185896i	−0.995671	−	0.0929479i	$-0.970371\pi$
$463$	− 4.00000i	− 0.185896i	0.995671	−	0.0929479i	$-0.0296290\pi$
$464$	−5.00000	−0.232119
$465$	0	0
$466$	−26.6969	−1.23671
$467$	− 29.9444i	− 1.38566i	−0.721100	−	0.692830i	$-0.756363\pi$
$467$	− 29.9444i	− 1.38566i	0.721100	−	0.692830i	$-0.243637\pi$
$468$	2.89898i	0.134005i
$469$	2.89898	0.133862
$470$	0	0
$471$	−8.89898	−0.410043
$472$	10.0000i	0.460287i
$473$	− 21.7980i	− 1.00227i
$474$	−10.0000	−0.459315
$475$	0	0
$476$	−7.89898	−0.362049
$477$	0.898979i	0.0411614i
$478$	8.10102i	0.370532i
$479$	30.0000	1.37073	0.685367	−	0.728197i	$-0.259642\pi$
$479$	30.0000	1.37073	0.685367	+	0.728197i	$0.259642\pi$
$480$	0	0
$481$	−24.2020	−1.10352
$482$	− 8.00000i	− 0.364390i
$483$	− 1.44949i	− 0.0659541i
$484$	7.00000	0.318182
$485$	0	0
$486$	1.00000	0.0453609
$487$	− 15.1010i	− 0.684293i	−0.939647	−	0.342146i	$-0.888846\pi$
$487$	− 15.1010i	− 0.684293i	0.939647	−	0.342146i	$-0.111154\pi$
$488$	4.89898i	0.221766i
$489$	−17.7980	−0.804852
$490$	0	0
$491$	25.1010	1.13279	0.566397	−	0.824133i	$-0.308337\pi$
$491$	25.1010	1.13279	0.566397	+	0.824133i	$0.308337\pi$
$492$	− 4.89898i	− 0.220863i
$493$	27.2474i	1.22716i
$494$	20.0000	0.899843
$495$	0	0
$496$	2.00000	0.0898027
$497$	15.6515i	0.702067i
$498$	2.55051i	0.114291i
$499$	−21.8990	−0.980333	−0.490166	−	0.871629i	$-0.663064\pi$
$499$	−21.8990	−0.980333	−0.490166	+	0.871629i	$0.663064\pi$
$500$	0	0
$501$	−7.00000	−0.312737
$502$	− 5.24745i	− 0.234205i
$503$	− 14.6969i	− 0.655304i	−0.944798	−	0.327652i	$-0.893743\pi$
$503$	− 14.6969i	− 0.655304i	0.944798	−	0.327652i	$-0.106257\pi$
$504$	−1.44949	−0.0645654
$505$	0	0
$506$	2.00000	0.0889108
$507$	− 4.59592i	− 0.204112i
$508$	− 1.79796i	− 0.0797715i
$509$	15.0000	0.664863	0.332432	−	0.943127i	$-0.392131\pi$
$509$	15.0000	0.664863	0.332432	+	0.943127i	$0.392131\pi$
$510$	0	0
$511$	3.04541	0.134721
$512$	1.00000i	0.0441942i
$513$	− 6.89898i	− 0.304597i
$514$	8.20204	0.361777
$515$	0	0
$516$	10.8990	0.479801
$517$	− 7.79796i	− 0.342954i
$518$	− 12.1010i	− 0.531688i
$519$	19.7980	0.869034
$520$	0	0
$521$	26.1464	1.14550	0.572748	−	0.819732i	$-0.305877\pi$
$521$	26.1464	1.14550	0.572748	+	0.819732i	$0.305877\pi$
$522$	5.00000i	0.218844i
$523$	16.0000i	0.699631i	0.936819	+	0.349816i	$0.113756\pi$
$523$	16.0000i	0.699631i	−0.936819	+	0.349816i	$0.886244\pi$
$524$	−8.89898	−0.388754
$525$	0	0
$526$	−19.7980	−0.863232
$527$	− 10.8990i	− 0.474767i
$528$	− 2.00000i	− 0.0870388i
$529$	−1.00000	−0.0434783
$530$	0	0
$531$	10.0000	0.433963
$532$	10.0000i	0.433555i
$533$	− 14.2020i	− 0.615159i
$534$	10.3485	0.447822
$535$	0	0
$536$	−2.00000	−0.0863868
$537$	3.10102i	0.133819i
$538$	− 3.79796i	− 0.163742i
$539$	9.79796	0.422028
$540$	0	0
$541$	−15.5959	−0.670521	−0.335260	−	0.942125i	$-0.608824\pi$
$541$	−15.5959	−0.670521	−0.335260	+	0.942125i	$0.608824\pi$
$542$	− 8.00000i	− 0.343629i
$543$	18.3485i	0.787408i
$544$	5.44949	0.233645
$545$	0	0
$546$	−4.20204	−0.179831
$547$	− 10.7980i	− 0.461687i	−0.972991	−	0.230844i	$-0.925851\pi$
$547$	− 10.7980i	− 0.461687i	0.972991	−	0.230844i	$-0.0741486\pi$
$548$	22.3485i	0.954679i
$549$	4.89898	0.209083
$550$	0	0
$551$	34.4949	1.46953
$552$	1.00000i	0.0425628i
$553$	− 14.4949i	− 0.616386i
$554$	−25.5959	−1.08747
$555$	0	0
$556$	15.6969	0.665698
$557$	28.6969i	1.21593i	0.793964	+	0.607964i	$0.208014\pi$
$557$	28.6969i	1.21593i	−0.793964	+	0.607964i	$0.791986\pi$
$558$	− 2.00000i	− 0.0846668i
$559$	31.5959	1.33636
$560$	0	0
$561$	−10.8990	−0.460155
$562$	− 0.752551i	− 0.0317445i
$563$	6.00000i	0.252870i	0.991975	+	0.126435i	$0.0403535\pi$
$563$	6.00000i	0.252870i	−0.991975	+	0.126435i	$0.959647\pi$
$564$	3.89898	0.164177
$565$	0	0
$566$	11.5959	0.487413
$567$	1.44949i	0.0608728i
$568$	− 10.7980i	− 0.453072i
$569$	44.4949	1.86532	0.932662	−	0.360753i	$-0.117480\pi$
$569$	44.4949	1.86532	0.932662	+	0.360753i	$0.117480\pi$
$570$	0	0
$571$	32.6969	1.36832	0.684162	−	0.729330i	$-0.260168\pi$
$571$	32.6969	1.36832	0.684162	+	0.729330i	$0.260168\pi$
$572$	− 5.79796i	− 0.242425i
$573$	− 2.00000i	− 0.0835512i
$574$	7.10102	0.296391
$575$	0	0
$576$	1.00000	0.0416667
$577$	− 2.00000i	− 0.0832611i	−0.999133	−	0.0416305i	$-0.986745\pi$
$577$	− 2.00000i	− 0.0832611i	0.999133	−	0.0416305i	$-0.0132552\pi$
$578$	− 12.6969i	− 0.528123i
$579$	−9.69694	−0.402991
$580$	0	0
$581$	−3.69694	−0.153375
$582$	− 12.6969i	− 0.526305i
$583$	− 1.79796i	− 0.0744639i
$584$	−2.10102	−0.0869408
$585$	0	0
$586$	7.79796	0.322131
$587$	4.89898i	0.202203i	0.994876	+	0.101101i	$0.0322366\pi$
$587$	4.89898i	0.202203i	−0.994876	+	0.101101i	$0.967763\pi$
$588$	4.89898i	0.202031i
$589$	−13.7980	−0.568535
$590$	0	0
$591$	−3.89898	−0.160383
$592$	8.34847i	0.343120i
$593$	43.5959i	1.79027i	0.445795	+	0.895135i	$0.352921\pi$
$593$	43.5959i	1.79027i	−0.445795	+	0.895135i	$0.647079\pi$
$594$	−2.00000	−0.0820610
$595$	0	0
$596$	20.0000	0.819232
$597$	24.1464i	0.988248i
$598$	2.89898i	0.118548i
$599$	21.3939	0.874130	0.437065	−	0.899430i	$-0.356018\pi$
$599$	21.3939	0.874130	0.437065	+	0.899430i	$0.356018\pi$
$600$	0	0
$601$	37.0000	1.50926	0.754631	−	0.656150i	$-0.227816\pi$
$601$	37.0000	1.50926	0.754631	+	0.656150i	$0.227816\pi$
$602$	15.7980i	0.643877i
$603$	2.00000i	0.0814463i
$604$	18.6969	0.760768
$605$	0	0
$606$	−13.6969	−0.556400
$607$	18.0000i	0.730597i	0.930890	+	0.365299i	$0.119033\pi$
$607$	18.0000i	0.730597i	−0.930890	+	0.365299i	$0.880967\pi$
$608$	− 6.89898i	− 0.279791i
$609$	−7.24745	−0.293681
$610$	0	0
$611$	11.3031	0.457273
$612$	− 5.44949i	− 0.220283i
$613$	0.146428i	0.00591418i	0.999996	+	0.00295709i	$0.000941272\pi$
$613$	0.146428i	0.00591418i	−0.999996	+	0.00295709i	$0.999059\pi$
$614$	20.1010	0.811211
$615$	0	0
$616$	2.89898	0.116803
$617$	12.4949i	0.503026i	0.967854	+	0.251513i	$0.0809281\pi$
$617$	12.4949i	0.503026i	−0.967854	+	0.251513i	$0.919072\pi$
$618$	13.2474i	0.532891i
$619$	44.4949	1.78840	0.894200	−	0.447667i	$-0.147745\pi$
$619$	44.4949	1.78840	0.894200	+	0.447667i	$0.147745\pi$
$620$	0	0
$621$	1.00000	0.0401286
$622$	14.5959i	0.585243i
$623$	15.0000i	0.600962i
$624$	2.89898	0.116052
$625$	0	0
$626$	−12.8990	−0.515547
$627$	13.7980i	0.551037i
$628$	8.89898i	0.355108i
$629$	45.4949	1.81400
$630$	0	0
$631$	15.4495	0.615034	0.307517	−	0.951543i	$-0.400502\pi$
$631$	15.4495	0.615034	0.307517	+	0.951543i	$0.400502\pi$
$632$	10.0000i	0.397779i
$633$	− 10.7980i	− 0.429180i
$634$	−10.5959	−0.420818
$635$	0	0
$636$	0.898979	0.0356469
$637$	14.2020i	0.562705i
$638$	− 10.0000i	− 0.395904i
$639$	−10.7980	−0.427161
$640$	0	0
$641$	−24.5505	−0.969687	−0.484843	−	0.874601i	$-0.661123\pi$
$641$	−24.5505	−0.969687	−0.484843	+	0.874601i	$0.661123\pi$
$642$	− 2.00000i	− 0.0789337i
$643$	19.7980i	0.780755i	0.920655	+	0.390378i	$0.127656\pi$
$643$	19.7980i	0.780755i	−0.920655	+	0.390378i	$0.872344\pi$
$644$	−1.44949	−0.0571179
$645$	0	0
$646$	−37.5959	−1.47919
$647$	20.5959i	0.809709i	0.914381	+	0.404855i	$0.132678\pi$
$647$	20.5959i	0.809709i	−0.914381	+	0.404855i	$0.867322\pi$
$648$	− 1.00000i	− 0.0392837i
$649$	−20.0000	−0.785069
$650$	0	0
$651$	2.89898	0.113620
$652$	17.7980i	0.697022i
$653$	0.303062i	0.0118597i	0.999982	+	0.00592986i	$0.00188754\pi$
$653$	0.303062i	0.0118597i	−0.999982	+	0.00592986i	$0.998112\pi$
$654$	−3.44949	−0.134886
$655$	0	0
$656$	−4.89898	−0.191273
$657$	2.10102i	0.0819686i
$658$	5.65153i	0.220320i
$659$	23.4495	0.913462	0.456731	−	0.889605i	$-0.349020\pi$
$659$	23.4495	0.913462	0.456731	+	0.889605i	$0.349020\pi$
$660$	0	0
$661$	−21.4495	−0.834288	−0.417144	−	0.908840i	$-0.636969\pi$
$661$	−21.4495	−0.834288	−0.417144	+	0.908840i	$0.636969\pi$
$662$	− 6.79796i	− 0.264210i
$663$	− 15.7980i	− 0.613542i
$664$	2.55051	0.0989790
$665$	0	0
$666$	8.34847	0.323497
$667$	5.00000i	0.193601i
$668$	7.00000i	0.270838i
$669$	−24.6969	−0.954839
$670$	0	0
$671$	−9.79796	−0.378246
$672$	1.44949i	0.0559153i
$673$	− 26.5959i	− 1.02520i	−0.858628	−	0.512599i	$-0.828683\pi$
$673$	− 26.5959i	− 1.02520i	0.858628	−	0.512599i	$-0.171317\pi$
$674$	16.4949	0.635360
$675$	0	0
$676$	−4.59592	−0.176766
$677$	− 33.3939i	− 1.28343i	−0.766943	−	0.641715i	$-0.778223\pi$
$677$	− 33.3939i	− 1.28343i	0.766943	−	0.641715i	$-0.221777\pi$
$678$	− 14.3485i	− 0.551050i
$679$	18.4041	0.706284
$680$	0	0
$681$	−4.75255	−0.182118
$682$	4.00000i	0.153168i
$683$	− 7.10102i	− 0.271713i	−0.990729	−	0.135856i	$-0.956621\pi$
$683$	− 7.10102i	− 0.271713i	0.990729	−	0.135856i	$-0.0433786\pi$
$684$	−6.89898	−0.263789
$685$	0	0
$686$	−17.2474	−0.658511
$687$	3.10102i	0.118311i
$688$	− 10.8990i	− 0.415520i
$689$	2.60612	0.0992854
$690$	0	0
$691$	−9.20204	−0.350062	−0.175031	−	0.984563i	$-0.556003\pi$
$691$	−9.20204	−0.350062	−0.175031	+	0.984563i	$0.556003\pi$
$692$	− 19.7980i	− 0.752605i
$693$	− 2.89898i	− 0.110123i
$694$	32.6969	1.24116
$695$	0	0
$696$	5.00000	0.189525
$697$	26.6969i	1.01122i
$698$	− 13.1010i	− 0.495881i
$699$	26.6969	1.00977
$700$	0	0
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	− 2.89898i	− 0.109415i
$703$	− 57.5959i	− 2.17227i
$704$	−2.00000	−0.0753778
$705$	0	0
$706$	−26.0000	−0.978523
$707$	− 19.8536i	− 0.746670i
$708$	− 10.0000i	− 0.375823i
$709$	−27.9444	−1.04947	−0.524737	−	0.851265i	$-0.675836\pi$
$709$	−27.9444	−1.04947	−0.524737	+	0.851265i	$0.675836\pi$
$710$	0	0
$711$	10.0000	0.375029
$712$	− 10.3485i	− 0.387825i
$713$	− 2.00000i	− 0.0749006i
$714$	7.89898	0.295612
$715$	0	0
$716$	3.10102	0.115891
$717$	− 8.10102i	− 0.302538i
$718$	6.20204i	0.231458i
$719$	−28.7980	−1.07398	−0.536991	−	0.843588i	$-0.680439\pi$
$719$	−28.7980	−1.07398	−0.536991	+	0.843588i	$0.680439\pi$
$720$	0	0
$721$	−19.2020	−0.715121
$722$	28.5959i	1.06423i
$723$	8.00000i	0.297523i
$724$	18.3485	0.681915
$725$	0	0
$726$	−7.00000	−0.259794
$727$	39.3939i	1.46104i	0.682892	+	0.730519i	$0.260722\pi$
$727$	39.3939i	1.46104i	−0.682892	+	0.730519i	$0.739278\pi$
$728$	4.20204i	0.155738i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−59.3939	−2.19676
$732$	− 4.89898i	− 0.181071i
$733$	40.1464i	1.48284i	0.671040	+	0.741421i	$0.265848\pi$
$733$	40.1464i	1.48284i	−0.671040	+	0.741421i	$0.734152\pi$
$734$	8.20204	0.302743
$735$	0	0
$736$	1.00000	0.0368605
$737$	− 4.00000i	− 0.147342i
$738$	4.89898i	0.180334i
$739$	−12.5959	−0.463348	−0.231674	−	0.972793i	$-0.574420\pi$
$739$	−12.5959	−0.463348	−0.231674	+	0.972793i	$0.574420\pi$
$740$	0	0
$741$	−20.0000	−0.734718
$742$	1.30306i	0.0478369i
$743$	24.2929i	0.891218i	0.895228	+	0.445609i	$0.147013\pi$
$743$	24.2929i	0.891218i	−0.895228	+	0.445609i	$0.852987\pi$
$744$	−2.00000	−0.0733236
$745$	0	0
$746$	−3.24745	−0.118898
$747$	− 2.55051i	− 0.0933183i
$748$	10.8990i	0.398506i
$749$	2.89898	0.105926
$750$	0	0
$751$	−25.2474	−0.921292	−0.460646	−	0.887584i	$-0.652382\pi$
$751$	−25.2474	−0.921292	−0.460646	+	0.887584i	$0.652382\pi$
$752$	− 3.89898i	− 0.142181i
$753$	5.24745i	0.191228i
$754$	14.4949	0.527873
$755$	0	0
$756$	1.44949	0.0527174
$757$	10.7526i	0.390808i	0.980723	+	0.195404i	$0.0626018\pi$
$757$	10.7526i	0.390808i	−0.980723	+	0.195404i	$0.937398\pi$
$758$	38.2929i	1.39086i
$759$	−2.00000	−0.0725954
$760$	0	0
$761$	−50.0908	−1.81579	−0.907895	−	0.419197i	$-0.862312\pi$
$761$	−50.0908	−1.81579	−0.907895	+	0.419197i	$0.862312\pi$
$762$	1.79796i	0.0651332i
$763$	− 5.00000i	− 0.181012i
$764$	−2.00000	−0.0723575
$765$	0	0
$766$	−9.79796	−0.354015
$767$	− 28.9898i	− 1.04676i
$768$	− 1.00000i	− 0.0360844i
$769$	−48.2929	−1.74148	−0.870742	−	0.491739i	$-0.836361\pi$
$769$	−48.2929	−1.74148	−0.870742	+	0.491739i	$0.836361\pi$
$770$	0	0
$771$	−8.20204	−0.295389
$772$	9.69694i	0.349000i
$773$	− 10.8990i	− 0.392009i	−0.980603	−	0.196005i	$-0.937203\pi$
$773$	− 10.8990i	− 0.392009i	0.980603	−	0.196005i	$-0.0627967\pi$
$774$	−10.8990	−0.391756
$775$	0	0
$776$	−12.6969	−0.455794
$777$	12.1010i	0.434122i
$778$	23.7980i	0.853198i
$779$	33.7980	1.21094
$780$	0	0
$781$	21.5959	0.772763
$782$	− 5.44949i	− 0.194873i
$783$	− 5.00000i	− 0.178685i
$784$	4.89898	0.174964
$785$	0	0
$786$	8.89898	0.317416
$787$	28.0000i	0.998092i	0.866575	+	0.499046i	$0.166316\pi$
$787$	28.0000i	0.998092i	−0.866575	+	0.499046i	$0.833684\pi$
$788$	3.89898i	0.138895i
$789$	19.7980	0.704826
$790$	0	0
$791$	20.7980	0.739490
$792$	2.00000i	0.0710669i
$793$	− 14.2020i	− 0.504329i
$794$	−28.0000	−0.993683
$795$	0	0
$796$	24.1464	0.855847
$797$	34.8990i	1.23619i	0.786105	+	0.618093i	$0.212094\pi$
$797$	34.8990i	1.23619i	−0.786105	+	0.618093i	$0.787906\pi$
$798$	− 10.0000i	− 0.353996i
$799$	−21.2474	−0.751681
$800$	0	0
$801$	−10.3485	−0.365645
$802$	− 18.6969i	− 0.660212i
$803$	− 4.20204i	− 0.148287i
$804$	2.00000	0.0705346
$805$	0	0
$806$	−5.79796	−0.204224
$807$	3.79796i	0.133694i
$808$	13.6969i	0.481857i
$809$	−11.3939	−0.400587	−0.200294	−	0.979736i	$-0.564190\pi$
$809$	−11.3939	−0.400587	−0.200294	+	0.979736i	$0.564190\pi$
$810$	0	0
$811$	45.7980	1.60818	0.804092	−	0.594505i	$-0.202652\pi$
$811$	45.7980	1.60818	0.804092	+	0.594505i	$0.202652\pi$
$812$	7.24745i	0.254336i
$813$	8.00000i	0.280572i
$814$	−16.6969	−0.585227
$815$	0	0
$816$	−5.44949	−0.190770
$817$	75.1918i	2.63063i
$818$	− 25.6969i	− 0.898472i
$819$	4.20204	0.146831
$820$	0	0
$821$	−51.7980	−1.80776	−0.903881	−	0.427785i	$-0.859294\pi$
$821$	−51.7980	−1.80776	−0.903881	+	0.427785i	$0.859294\pi$
$822$	− 22.3485i	− 0.779492i
$823$	− 56.0908i	− 1.95520i	−0.210465	−	0.977601i	$-0.567498\pi$
$823$	− 56.0908i	− 1.95520i	0.210465	−	0.977601i	$-0.432502\pi$
$824$	13.2474	0.461497
$825$	0	0
$826$	14.4949	0.504342
$827$	− 14.7526i	− 0.512996i	−0.966545	−	0.256498i	$-0.917431\pi$
$827$	− 14.7526i	− 0.512996i	0.966545	−	0.256498i	$-0.0825688\pi$
$828$	− 1.00000i	− 0.0347524i
$829$	33.1010	1.14965	0.574823	−	0.818278i	$-0.305071\pi$
$829$	33.1010	1.14965	0.574823	+	0.818278i	$0.305071\pi$
$830$	0	0
$831$	25.5959	0.887913
$832$	− 2.89898i	− 0.100504i
$833$	− 26.6969i	− 0.924994i
$834$	−15.6969	−0.543541
$835$	0	0
$836$	13.7980	0.477212
$837$	2.00000i	0.0691301i
$838$	− 14.1464i	− 0.488680i
$839$	9.30306	0.321177	0.160589	−	0.987021i	$-0.448661\pi$
$839$	9.30306	0.321177	0.160589	+	0.987021i	$0.448661\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	− 12.4949i	− 0.430603i
$843$	0.752551i	0.0259192i
$844$	−10.7980	−0.371681
$845$	0	0
$846$	−3.89898	−0.134050
$847$	− 10.1464i	− 0.348635i
$848$	− 0.898979i	− 0.0308711i
$849$	−11.5959	−0.397971
$850$	0	0
$851$	8.34847	0.286182
$852$	10.7980i	0.369932i
$853$	44.9898i	1.54042i	0.637790	+	0.770211i	$0.279849\pi$
$853$	44.9898i	1.54042i	−0.637790	+	0.770211i	$0.720151\pi$
$854$	7.10102	0.242992
$855$	0	0
$856$	−2.00000	−0.0683586
$857$	42.4949i	1.45160i	0.687907	+	0.725799i	$0.258530\pi$
$857$	42.4949i	1.45160i	−0.687907	+	0.725799i	$0.741470\pi$
$858$	5.79796i	0.197939i
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	0	0
$861$	−7.10102	−0.242002
$862$	11.3031i	0.384984i
$863$	− 20.3939i	− 0.694216i	−0.937825	−	0.347108i	$-0.887164\pi$
$863$	− 20.3939i	− 0.694216i	0.937825	−	0.347108i	$-0.112836\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−16.6969	−0.567385
$867$	12.6969i	0.431211i
$868$	− 2.89898i	− 0.0983978i
$869$	−20.0000	−0.678454
$870$	0	0
$871$	5.79796	0.196456
$872$	3.44949i	0.116814i
$873$	12.6969i	0.429726i
$874$	−6.89898	−0.233361
$875$	0	0
$876$	2.10102	0.0709869
$877$	− 9.59592i	− 0.324031i	−0.986788	−	0.162016i	$-0.948201\pi$
$877$	− 9.59592i	− 0.324031i	0.986788	−	0.162016i	$-0.0517995\pi$
$878$	10.6969i	0.361004i
$879$	−7.79796	−0.263019
$880$	0	0
$881$	−31.1010	−1.04782	−0.523910	−	0.851774i	$-0.675527\pi$
$881$	−31.1010	−1.04782	−0.523910	+	0.851774i	$0.675527\pi$
$882$	− 4.89898i	− 0.164957i
$883$	48.5959i	1.63538i	0.575657	+	0.817691i	$0.304746\pi$
$883$	48.5959i	1.63538i	−0.575657	+	0.817691i	$0.695254\pi$
$884$	−15.7980	−0.531343
$885$	0	0
$886$	−5.30306	−0.178160
$887$	− 10.1010i	− 0.339159i	−0.985517	−	0.169580i	$-0.945759\pi$
$887$	− 10.1010i	− 0.339159i	0.985517	−	0.169580i	$-0.0542410\pi$
$888$	− 8.34847i	− 0.280156i
$889$	−2.60612	−0.0874066
$890$	0	0
$891$	2.00000	0.0670025
$892$	24.6969i	0.826915i
$893$	26.8990i	0.900140i
$894$	−20.0000	−0.668900
$895$	0	0
$896$	1.44949	0.0484241
$897$	− 2.89898i	− 0.0967941i
$898$	− 3.79796i	− 0.126740i
$899$	−10.0000	−0.333519
$900$	0	0
$901$	−4.89898	−0.163209
$902$	− 9.79796i	− 0.326236i
$903$	− 15.7980i	− 0.525723i
$904$	−14.3485	−0.477223
$905$	0	0
$906$	−18.6969	−0.621164
$907$	2.49490i	0.0828417i	0.999142	+	0.0414209i	$0.0131884\pi$
$907$	2.49490i	0.0828417i	−0.999142	+	0.0414209i	$0.986812\pi$
$908$	4.75255i	0.157719i
$909$	13.6969	0.454299
$910$	0	0
$911$	21.3031	0.705802	0.352901	−	0.935661i	$-0.385195\pi$
$911$	21.3031	0.705802	0.352901	+	0.935661i	$0.385195\pi$
$912$	6.89898i	0.228448i
$913$	5.10102i	0.168819i
$914$	−0.404082	−0.0133658
$915$	0	0
$916$	3.10102	0.102461
$917$	12.8990i	0.425962i
$918$	5.44949i	0.179860i
$919$	27.9444	0.921800	0.460900	−	0.887452i	$-0.347527\pi$
$919$	27.9444	0.921800	0.460900	+	0.887452i	$0.347527\pi$
$920$	0	0
$921$	−20.1010	−0.662351
$922$	21.4949i	0.707897i
$923$	31.3031i	1.03035i
$924$	−2.89898	−0.0953694
$925$	0	0
$926$	4.00000	0.131448
$927$	− 13.2474i	− 0.435103i
$928$	− 5.00000i	− 0.164133i
$929$	3.79796	0.124607	0.0623035	−	0.998057i	$-0.480155\pi$
$929$	3.79796	0.124607	0.0623035	+	0.998057i	$0.480155\pi$
$930$	0	0
$931$	−33.7980	−1.10768
$932$	− 26.6969i	− 0.874487i
$933$	− 14.5959i	− 0.477849i
$934$	29.9444	0.979810
$935$	0	0
$936$	−2.89898	−0.0947561
$937$	− 15.7980i	− 0.516097i	−0.966132	−	0.258048i	$-0.916921\pi$
$937$	− 15.7980i	− 0.516097i	0.966132	−	0.258048i	$-0.0830794\pi$
$938$	2.89898i	0.0946550i
$939$	12.8990	0.420942
$940$	0	0
$941$	2.00000	0.0651981	0.0325991	−	0.999469i	$-0.489622\pi$
$941$	2.00000	0.0651981	0.0325991	+	0.999469i	$0.489622\pi$
$942$	− 8.89898i	− 0.289944i
$943$	4.89898i	0.159533i
$944$	−10.0000	−0.325472
$945$	0	0
$946$	21.7980	0.708713
$947$	0.404082i	0.0131309i	0.999978	+	0.00656545i	$0.00208986\pi$
$947$	0.404082i	0.0131309i	−0.999978	+	0.00656545i	$0.997910\pi$
$948$	− 10.0000i	− 0.324785i
$949$	6.09082	0.197716
$950$	0	0
$951$	10.5959	0.343596
$952$	− 7.89898i	− 0.256007i
$953$	30.8434i	0.999115i	0.866281	+	0.499557i	$0.166504\pi$
$953$	30.8434i	0.999115i	−0.866281	+	0.499557i	$0.833496\pi$
$954$	−0.898979	−0.0291055
$955$	0	0
$956$	−8.10102	−0.262006
$957$	10.0000i	0.323254i
$958$	30.0000i	0.969256i
$959$	32.3939	1.04605
$960$	0	0
$961$	−27.0000	−0.870968
$962$	− 24.2020i	− 0.780305i
$963$	2.00000i	0.0644491i
$964$	8.00000	0.257663
$965$	0	0
$966$	1.44949	0.0466366
$967$	− 29.5959i	− 0.951741i	−0.879515	−	0.475870i	$-0.842133\pi$
$967$	− 29.5959i	− 0.951741i	0.879515	−	0.475870i	$-0.157867\pi$
$968$	7.00000i	0.224989i
$969$	37.5959	1.20775
$970$	0	0
$971$	26.1464	0.839079	0.419539	−	0.907737i	$-0.362192\pi$
$971$	26.1464	0.839079	0.419539	+	0.907737i	$0.362192\pi$
$972$	1.00000i	0.0320750i
$973$	− 22.7526i	− 0.729413i
$974$	15.1010	0.483868
$975$	0	0
$976$	−4.89898	−0.156813
$977$	− 24.7526i	− 0.791904i	−0.918271	−	0.395952i	$-0.870415\pi$
$977$	− 24.7526i	− 0.791904i	0.918271	−	0.395952i	$-0.129585\pi$
$978$	− 17.7980i	− 0.569116i
$979$	20.6969	0.661477
$980$	0	0
$981$	3.44949	0.110134
$982$	25.1010i	0.801006i
$983$	− 24.0000i	− 0.765481i	−0.923856	−	0.382741i	$-0.874980\pi$
$983$	− 24.0000i	− 0.765481i	0.923856	−	0.382741i	$-0.125020\pi$
$984$	4.89898	0.156174
$985$	0	0
$986$	−27.2474	−0.867736
$987$	− 5.65153i	− 0.179890i
$988$	20.0000i	0.636285i
$989$	−10.8990	−0.346567
$990$	0	0
$991$	18.2020	0.578207	0.289103	−	0.957298i	$-0.406643\pi$
$991$	18.2020	0.578207	0.289103	+	0.957298i	$0.406643\pi$
$992$	2.00000i	0.0635001i
$993$	6.79796i	0.215727i
$994$	−15.6515	−0.496436
$995$	0	0
$996$	−2.55051	−0.0808160
$997$	21.1010i	0.668276i	0.942524	+	0.334138i	$0.108445\pi$
$997$	21.1010i	0.668276i	−0.942524	+	0.334138i	$0.891555\pi$
$998$	− 21.8990i	− 0.693200i
$999$	−8.34847	−0.264134

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3450.2.d.y.2899.4		4
5.2	odd	4		3450.2.a.bf.1.1	✓	2
5.3	odd	4		3450.2.a.bl.1.2	yes	2
5.4	even	2	inner	3450.2.d.y.2899.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3450.2.a.bf.1.1	✓	2	5.2	odd	4
3450.2.a.bl.1.2	yes	2	5.3	odd	4
3450.2.d.y.2899.1		4	5.4	even	2	inner
3450.2.d.y.2899.4		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3450.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +1.44949i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +1.44949i q^{7} -1.00000i q^{8} -1.00000 q^{9} +2.00000 q^{11} +1.00000i q^{12} +2.89898i q^{13} -1.44949 q^{14} +1.00000 q^{16} -5.44949i q^{17} -1.00000i q^{18} -6.89898 q^{19} +1.44949 q^{21} +2.00000i q^{22} -1.00000i q^{23} -1.00000 q^{24} -2.89898 q^{26} +1.00000i q^{27} -1.44949i q^{28} -5.00000 q^{29} +2.00000 q^{31} +1.00000i q^{32} -2.00000i q^{33} +5.44949 q^{34} +1.00000 q^{36} +8.34847i q^{37} -6.89898i q^{38} +2.89898 q^{39} -4.89898 q^{41} +1.44949i q^{42} -10.8990i q^{43} -2.00000 q^{44} +1.00000 q^{46} -3.89898i q^{47} -1.00000i q^{48} +4.89898 q^{49} -5.44949 q^{51} -2.89898i q^{52} -0.898979i q^{53} -1.00000 q^{54} +1.44949 q^{56} +6.89898i q^{57} -5.00000i q^{58} -10.0000 q^{59} -4.89898 q^{61} +2.00000i q^{62} -1.44949i q^{63} -1.00000 q^{64} +2.00000 q^{66} -2.00000i q^{67} +5.44949i q^{68} -1.00000 q^{69} +10.7980 q^{71} +1.00000i q^{72} -2.10102i q^{73} -8.34847 q^{74} +6.89898 q^{76} +2.89898i q^{77} +2.89898i q^{78} -10.0000 q^{79} +1.00000 q^{81} -4.89898i q^{82} +2.55051i q^{83} -1.44949 q^{84} +10.8990 q^{86} +5.00000i q^{87} -2.00000i q^{88} +10.3485 q^{89} -4.20204 q^{91} +1.00000i q^{92} -2.00000i q^{93} +3.89898 q^{94} +1.00000 q^{96} -12.6969i q^{97} +4.89898i q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 8 q^{11} + 4 q^{14} + 4 q^{16} - 8 q^{19} - 4 q^{21} - 4 q^{24} + 8 q^{26} - 20 q^{29} + 8 q^{31} + 12 q^{34} + 4 q^{36} - 8 q^{39} - 8 q^{44} + 4 q^{46} - 12 q^{51} - 4 q^{54} - 4 q^{56} - 40 q^{59} - 4 q^{64} + 8 q^{66} - 4 q^{69} + 4 q^{71} - 4 q^{74} + 8 q^{76} - 40 q^{79} + 4 q^{81} + 4 q^{84} + 24 q^{86} + 12 q^{89} - 56 q^{91} - 4 q^{94} + 4 q^{96} - 8 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 8 * q^11 + 4 * q^14 + 4 * q^16 - 8 * q^19 - 4 * q^21 - 4 * q^24 + 8 * q^26 - 20 * q^29 + 8 * q^31 + 12 * q^34 + 4 * q^36 - 8 * q^39 - 8 * q^44 + 4 * q^46 - 12 * q^51 - 4 * q^54 - 4 * q^56 - 40 * q^59 - 4 * q^64 + 8 * q^66 - 4 * q^69 + 4 * q^71 - 4 * q^74 + 8 * q^76 - 40 * q^79 + 4 * q^81 + 4 * q^84 + 24 * q^86 + 12 * q^89 - 56 * q^91 - 4 * q^94 + 4 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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