LMFDB - Embedded newform 2394.2.e.b.1063.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2394,2,Mod(1063,2394)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2394, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2394.1063");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2394.e (of order $2$, degree $1$, 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:	$19.1161862439$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} + 54x^{8} - 114x^{7} + 120x^{6} + 46x^{5} + 9x^{4} - 4x^{3} + 8x^{2} + 4x + 1 $ x^12 - 2x^11 + 2x^10 + 54x^8 - 114x^7 + 120x^6 + 46x^5 + 9x^4 - 4x^3 + 8x^2 + 4x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 798)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1063.3
Root			$-0.242887 + 0.242887i$ of defining polynomial
Character	$\chi$	$=$	2394.1063
Dual form			2394.2.e.b.1063.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} -0.485775i q^{5} +(2.59339 - 0.523742i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} -0.485775i q^{5} +(2.59339 - 0.523742i) q^{7} +1.00000i q^{8} -0.485775 q^{10} +0.891167 q^{11} +2.48577 q^{13} +(-0.523742 - 2.59339i) q^{14} +1.00000 q^{16} -5.60771i q^{17} +(-3.47504 - 2.63136i) q^{19} +0.485775i q^{20} -0.891167i q^{22} -7.41755 q^{23} +4.76402 q^{25} -2.48577i q^{26} +(-2.59339 + 0.523742i) q^{28} +2.73485i q^{29} +2.14079 q^{31} -1.00000i q^{32} -5.60771 q^{34} +(-0.254421 - 1.25980i) q^{35} +5.04600i q^{37} +(-2.63136 + 3.47504i) q^{38} +0.485775 q^{40} +7.37545 q^{41} +0.621571 q^{43} -0.891167 q^{44} +7.41755i q^{46} -1.33960i q^{47} +(6.45139 - 2.71654i) q^{49} -4.76402i q^{50} -2.48577 q^{52} -12.4495i q^{53} -0.432906i q^{55} +(0.523742 + 2.59339i) q^{56} +2.73485 q^{58} +11.1661 q^{59} -5.88429i q^{61} -2.14079i q^{62} -1.00000 q^{64} -1.20753i q^{65} +8.29320i q^{67} +5.60771i q^{68} +(-1.25980 + 0.254421i) q^{70} +5.99757i q^{71} -9.16848i q^{73} +5.04600 q^{74} +(3.47504 + 2.63136i) q^{76} +(2.31115 - 0.466741i) q^{77} -12.9087i q^{79} -0.485775i q^{80} -7.37545i q^{82} -17.4940i q^{83} -2.72408 q^{85} -0.621571i q^{86} +0.891167i q^{88} -9.70397 q^{89} +(6.44659 - 1.30190i) q^{91} +7.41755 q^{92} -1.33960 q^{94} +(-1.27825 + 1.68809i) q^{95} -2.53160 q^{97} +(-2.71654 - 6.45139i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4}+O(q^{10}) $ 12 * q - 12 * q^4	$ 12 q - 12 q^{4} + 4 q^{10} - 12 q^{11} + 20 q^{13} + 4 q^{14} + 12 q^{16} - 8 q^{19} + 12 q^{23} - 12 q^{25} + 24 q^{31} + 4 q^{34} - 4 q^{35} - 4 q^{40} + 16 q^{41} + 12 q^{44} + 4 q^{49} - 20 q^{52} - 4 q^{56} + 8 q^{58} - 40 q^{59} - 12 q^{64} - 24 q^{70} + 8 q^{76} - 8 q^{77} + 8 q^{85} + 16 q^{89} + 24 q^{91} - 12 q^{92} + 44 q^{95} - 60 q^{97} + 16 q^{98}+O(q^{100}) $ 12 * q - 12 * q^4 + 4 * q^10 - 12 * q^11 + 20 * q^13 + 4 * q^14 + 12 * q^16 - 8 * q^19 + 12 * q^23 - 12 * q^25 + 24 * q^31 + 4 * q^34 - 4 * q^35 - 4 * q^40 + 16 * q^41 + 12 * q^44 + 4 * q^49 - 20 * q^52 - 4 * q^56 + 8 * q^58 - 40 * q^59 - 12 * q^64 - 24 * q^70 + 8 * q^76 - 8 * q^77 + 8 * q^85 + 16 * q^89 + 24 * q^91 - 12 * q^92 + 44 * q^95 - 60 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times$.

$n$	$533$	$1009$	$1711$
$\chi(n)$	$1$	$-1$	$-1$

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
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$		−	0.485775i		−	0.217245i	−0.994083	−	0.108622i	$-0.965356\pi$
$5$		−	0.485775i		−	0.217245i	0.994083	−	0.108622i	$-0.0346440\pi$
$6$		0			0
$7$	2.59339	−	0.523742i	0.980211	−	0.197956i
$7$	2.59339	−	0.523742i	0.980211	−	0.197956i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.485775			−0.153615
$11$	0.891167			0.268697			0.134348	−	0.990934i	$-0.457106\pi$
$11$	0.891167			0.268697			0.134348	+	0.990934i	$0.457106\pi$
$12$		0			0
$13$	2.48577			0.689430			0.344715	−	0.938707i	$-0.387976\pi$
$13$	2.48577			0.689430			0.344715	+	0.938707i	$0.387976\pi$
$14$	−0.523742	−	2.59339i	−0.139976	−	0.693114i
$15$		0			0
$16$	1.00000			0.250000
$17$		−	5.60771i		−	1.36007i	−0.733180	−	0.680034i	$-0.761965\pi$
$17$		−	5.60771i		−	1.36007i	0.733180	−	0.680034i	$-0.238035\pi$
$18$		0			0
$19$	−3.47504	−	2.63136i	−0.797230	−	0.603676i
$19$	−3.47504	−	2.63136i	−0.797230	−	0.603676i
$20$			0.485775i			0.108622i
$21$		0			0
$22$		−	0.891167i		−	0.189997i
$23$	−7.41755			−1.54667			−0.773333	−	0.634000i	$-0.781412\pi$
$23$	−7.41755			−1.54667			−0.773333	+	0.634000i	$0.781412\pi$
$24$		0			0
$25$	4.76402			0.952805
$26$		−	2.48577i		−	0.487500i
$27$		0			0
$28$	−2.59339	+	0.523742i	−0.490105	+	0.0989779i
$29$			2.73485i			0.507849i	0.967224	+	0.253924i	$0.0817214\pi$
$29$			2.73485i			0.507849i	−0.967224	+	0.253924i	$0.918279\pi$
$30$		0			0
$31$	2.14079			0.384498			0.192249	−	0.981346i	$-0.438422\pi$
$31$	2.14079			0.384498			0.192249	+	0.981346i	$0.438422\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−5.60771			−0.961714
$35$	−0.254421	−	1.25980i	−0.0430049	−	0.212946i
$36$		0			0
$37$			5.04600i			0.829557i	0.909922	+	0.414778i	$0.136141\pi$
$37$			5.04600i			0.829557i	−0.909922	+	0.414778i	$0.863859\pi$
$38$	−2.63136	+	3.47504i	−0.426863	+	0.563727i
$39$		0			0
$40$	0.485775			0.0768077
$41$	7.37545			1.15185			0.575926	−	0.817502i	$-0.304642\pi$
$41$	7.37545			1.15185			0.575926	+	0.817502i	$0.304642\pi$
$42$		0			0
$43$	0.621571			0.0947887			0.0473944	−	0.998876i	$-0.484908\pi$
$43$	0.621571			0.0947887			0.0473944	+	0.998876i	$0.484908\pi$
$44$	−0.891167			−0.134348
$45$		0			0
$46$			7.41755i			1.09366i
$47$		−	1.33960i		−	0.195400i	−0.995216	−	0.0977002i	$-0.968851\pi$
$47$		−	1.33960i		−	0.195400i	0.995216	−	0.0977002i	$-0.0311486\pi$
$48$		0			0
$49$	6.45139	−	2.71654i	0.921627	−	0.388077i
$50$		−	4.76402i		−	0.673735i
$51$		0			0
$52$	−2.48577			−0.344715
$53$		−	12.4495i		−	1.71007i	−0.518569	−	0.855036i	$-0.673535\pi$
$53$		−	12.4495i		−	1.71007i	0.518569	−	0.855036i	$-0.326465\pi$
$54$		0			0
$55$		−	0.432906i		−	0.0583730i
$56$	0.523742	+	2.59339i	0.0699880	+	0.346557i
$57$		0			0
$58$	2.73485			0.359103
$59$	11.1661			1.45370			0.726848	−	0.686798i	$-0.240984\pi$
$59$	11.1661			1.45370			0.726848	+	0.686798i	$0.240984\pi$
$60$		0			0
$61$		−	5.88429i		−	0.753407i	−0.926334	−	0.376703i	$-0.877058\pi$
$61$		−	5.88429i		−	0.753407i	0.926334	−	0.376703i	$-0.122942\pi$
$62$		−	2.14079i		−	0.271881i
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	1.20753i		−	0.149775i
$66$		0			0
$67$			8.29320i			1.01318i	0.862189	+	0.506588i	$0.169093\pi$
$67$			8.29320i			1.01318i	−0.862189	+	0.506588i	$0.830907\pi$
$68$			5.60771i			0.680034i
$69$		0			0
$70$	−1.25980	+	0.254421i	−0.150575	+	0.0304091i
$71$			5.99757i			0.711781i	0.934528	+	0.355890i	$0.115822\pi$
$71$			5.99757i			0.711781i	−0.934528	+	0.355890i	$0.884178\pi$
$72$		0			0
$73$		−	9.16848i		−	1.07309i	−0.843872	−	0.536545i	$-0.819729\pi$
$73$		−	9.16848i		−	1.07309i	0.843872	−	0.536545i	$-0.180271\pi$
$74$	5.04600			0.586585
$75$		0			0
$76$	3.47504	+	2.63136i	0.398615	+	0.301838i
$77$	2.31115	−	0.466741i	0.263380	−	0.0531901i
$78$		0			0
$79$		−	12.9087i		−	1.45234i	−0.687513	−	0.726172i	$-0.741298\pi$
$79$		−	12.9087i		−	1.45234i	0.687513	−	0.726172i	$-0.258702\pi$
$80$		−	0.485775i		−	0.0543112i
$81$		0			0
$82$		−	7.37545i		−	0.814483i
$83$		−	17.4940i		−	1.92022i	−0.279626	−	0.960109i	$-0.590210\pi$
$83$		−	17.4940i		−	1.92022i	0.279626	−	0.960109i	$-0.409790\pi$
$84$		0			0
$85$	−2.72408			−0.295468
$86$		−	0.621571i		−	0.0670257i
$87$		0			0
$88$			0.891167i			0.0949987i
$89$	−9.70397			−1.02862			−0.514309	−	0.857605i	$-0.671952\pi$
$89$	−9.70397			−1.02862			−0.514309	+	0.857605i	$0.671952\pi$
$90$		0			0
$91$	6.44659	−	1.30190i	0.675787	−	0.136477i
$92$	7.41755			0.773333
$93$		0			0
$94$	−1.33960			−0.138169
$95$	−1.27825	+	1.68809i	−0.131146	+	0.173194i
$96$		0			0
$97$	−2.53160			−0.257045			−0.128522	−	0.991707i	$-0.541023\pi$
$97$	−2.53160			−0.257045			−0.128522	+	0.991707i	$0.541023\pi$
$98$	−2.71654	−	6.45139i	−0.274412	−	0.651689i
$99$		0			0
$100$	−4.76402			−0.476402
$101$			1.95547i			0.194577i	0.995256	+	0.0972884i	$0.0310169\pi$
$101$			1.95547i			0.194577i	−0.995256	+	0.0972884i	$0.968983\pi$
$102$		0			0
$103$	−14.8366			−1.46189			−0.730947	−	0.682435i	$-0.760921\pi$
$103$	−14.8366			−1.46189			−0.730947	+	0.682435i	$0.760921\pi$
$104$			2.48577i			0.243750i
$105$		0			0
$106$	−12.4495			−1.20920
$107$			9.12044i			0.881707i	0.897579	+	0.440853i	$0.145324\pi$
$107$			9.12044i			0.881707i	−0.897579	+	0.440853i	$0.854676\pi$
$108$		0			0
$109$		−	3.34904i		−	0.320780i	−0.987054	−	0.160390i	$-0.948725\pi$
$109$		−	3.34904i		−	0.320780i	0.987054	−	0.160390i	$-0.0512752\pi$
$110$	−0.432906			−0.0412760
$111$		0			0
$112$	2.59339	−	0.523742i	0.245053	−	0.0494890i
$113$			13.5907i			1.27850i	0.768997	+	0.639252i	$0.220756\pi$
$113$			13.5907i			1.27850i	−0.768997	+	0.639252i	$0.779244\pi$
$114$		0			0
$115$			3.60326i			0.336006i
$116$		−	2.73485i		−	0.253924i
$117$		0			0
$118$		−	11.1661i		−	1.02792i
$119$	−2.93699	−	14.5430i	−0.269234	−	1.33315i
$120$		0			0
$121$	−10.2058			−0.927802
$122$	−5.88429			−0.532739
$123$		0			0
$124$	−2.14079			−0.192249
$125$		−	4.74311i		−	0.424237i
$126$		0			0
$127$		−	14.2727i		−	1.26650i	−0.773949	−	0.633248i	$-0.781722\pi$
$127$		−	14.2727i		−	1.26650i	0.773949	−	0.633248i	$-0.218278\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−1.20753			−0.105907
$131$			7.35769i			0.642845i	0.946936	+	0.321422i	$0.104161\pi$
$131$			7.35769i			0.642845i	−0.946936	+	0.321422i	$0.895839\pi$
$132$		0			0
$133$	−10.3903	−	5.00413i	−0.900955	−	0.433913i
$134$	8.29320			0.716423
$135$		0			0
$136$	5.60771			0.480857
$137$	8.66850			0.740600			0.370300	−	0.928912i	$-0.379255\pi$
$137$	8.66850			0.740600			0.370300	+	0.928912i	$0.379255\pi$
$138$		0			0
$139$		−	20.6572i		−	1.75212i	−0.482201	−	0.876061i	$-0.660162\pi$
$139$		−	20.6572i		−	1.75212i	0.482201	−	0.876061i	$-0.339838\pi$
$140$	0.254421	+	1.25980i	0.0215025	+	0.106473i
$141$		0			0
$142$	5.99757			0.503305
$143$	2.21524			0.185248
$144$		0			0
$145$	1.32852			0.110328
$146$	−9.16848			−0.758789
$147$		0			0
$148$		−	5.04600i		−	0.414778i
$149$	10.0744			0.825331			0.412665	−	0.910883i	$-0.364598\pi$
$149$	10.0744			0.825331			0.412665	+	0.910883i	$0.364598\pi$
$150$		0			0
$151$			6.27565i			0.510705i	0.966848	+	0.255353i	$0.0821915\pi$
$151$			6.27565i			0.510705i	−0.966848	+	0.255353i	$0.917808\pi$
$152$	2.63136	−	3.47504i	0.213432	−	0.281863i
$153$		0			0
$154$	−0.466741	−	2.31115i	−0.0376111	−	0.186238i
$155$		−	1.03994i		−	0.0835302i
$156$		0			0
$157$			16.0116i			1.27786i	0.769263	+	0.638932i	$0.220623\pi$
$157$			16.0116i			1.27786i	−0.769263	+	0.638932i	$0.779377\pi$
$158$	−12.9087			−1.02696
$159$		0			0
$160$	−0.485775			−0.0384038
$161$	−19.2366	+	3.88488i	−1.51606	+	0.306172i
$162$		0			0
$163$	15.0635			1.17987			0.589934	−	0.807452i	$-0.299154\pi$
$163$	15.0635			1.17987			0.589934	+	0.807452i	$0.299154\pi$
$164$	−7.37545			−0.575926
$165$		0			0
$166$	−17.4940			−1.35780
$167$	−15.0611			−1.16546			−0.582732	−	0.812664i	$-0.698016\pi$
$167$	−15.0611			−1.16546			−0.582732	+	0.812664i	$0.698016\pi$
$168$		0			0
$169$	−6.82092			−0.524687
$170$			2.72408i			0.208927i
$171$		0			0
$172$	−0.621571			−0.0473944
$173$	−5.48926			−0.417341			−0.208670	−	0.977986i	$-0.566914\pi$
$173$	−5.48926			−0.417341			−0.208670	+	0.977986i	$0.566914\pi$
$174$		0			0
$175$	12.3550	−	2.49512i	0.933950	−	0.188613i
$176$	0.891167			0.0671742
$177$		0			0
$178$			9.70397i			0.727343i
$179$			0.275291i			0.0205762i	0.999947	+	0.0102881i	$0.00327486\pi$
$179$			0.275291i			0.0205762i	−0.999947	+	0.0102881i	$0.996725\pi$
$180$		0			0
$181$	−10.3631			−0.770281			−0.385141	−	0.922858i	$-0.625847\pi$
$181$	−10.3631			−0.770281			−0.385141	+	0.922858i	$0.625847\pi$
$182$	−1.30190	−	6.44659i	−0.0965036	−	0.477853i
$183$		0			0
$184$		−	7.41755i		−	0.546829i
$185$	2.45122			0.180217
$186$		0			0
$187$		−	4.99740i		−	0.365446i
$188$			1.33960i			0.0977002i
$189$		0			0
$190$	1.68809	+	1.27825i	0.122467	+	0.0927339i
$191$	2.13337			0.154365			0.0771826	−	0.997017i	$-0.475408\pi$
$191$	2.13337			0.154365			0.0771826	+	0.997017i	$0.475408\pi$
$192$		0			0
$193$			2.80119i			0.201634i	0.994905	+	0.100817i	$0.0321457\pi$
$193$			2.80119i			0.201634i	−0.994905	+	0.100817i	$0.967854\pi$
$194$			2.53160i			0.181758i
$195$		0			0
$196$	−6.45139	+	2.71654i	−0.460813	+	0.194039i
$197$	25.8438			1.84129			0.920647	−	0.390397i	$-0.127662\pi$
$197$	25.8438			1.84129			0.920647	+	0.390397i	$0.127662\pi$
$198$		0			0
$199$		−	10.9515i		−	0.776334i	−0.921589	−	0.388167i	$-0.873108\pi$
$199$		−	10.9515i		−	0.776334i	0.921589	−	0.388167i	$-0.126892\pi$
$200$			4.76402i			0.336867i
$201$		0			0
$202$	1.95547			0.137587
$203$	1.43236	+	7.09254i	0.100532	+	0.497799i
$204$		0			0
$205$		−	3.58281i		−	0.250234i
$206$			14.8366i			1.03371i
$207$		0			0
$208$	2.48577			0.172357
$209$	−3.09684	−	2.34498i	−0.214213	−	0.162206i
$210$		0			0
$211$		−	26.9244i		−	1.85355i	−0.375616	−	0.926775i	$-0.622569\pi$
$211$		−	26.9244i		−	1.85355i	0.375616	−	0.926775i	$-0.377431\pi$
$212$			12.4495i			0.855036i
$213$		0			0
$214$	9.12044			0.623461
$215$		−	0.301943i		−	0.0205924i
$216$		0			0
$217$	5.55192	−	1.12122i	0.376889	−	0.0761136i
$218$	−3.34904			−0.226826
$219$		0			0
$220$			0.432906i			0.0291865i
$221$		−	13.9395i		−	0.937672i
$222$		0			0
$223$	5.27498			0.353239			0.176619	−	0.984279i	$-0.443484\pi$
$223$	5.27498			0.353239			0.176619	+	0.984279i	$0.443484\pi$
$224$	−0.523742	−	2.59339i	−0.0349940	−	0.173278i
$225$		0			0
$226$	13.5907			0.904039
$227$	−1.65074			−0.109564			−0.0547819	−	0.998498i	$-0.517446\pi$
$227$	−1.65074			−0.109564			−0.0547819	+	0.998498i	$0.517446\pi$
$228$		0			0
$229$		−	24.5788i		−	1.62422i	−0.583507	−	0.812108i	$-0.698320\pi$
$229$		−	24.5788i		−	1.62422i	0.583507	−	0.812108i	$-0.301680\pi$
$230$	3.60326			0.237592
$231$		0			0
$232$	−2.73485			−0.179552
$233$	8.24684			0.540268			0.270134	−	0.962823i	$-0.412932\pi$
$233$	8.24684			0.540268			0.270134	+	0.962823i	$0.412932\pi$
$234$		0			0
$235$	−0.650742			−0.0424498
$236$	−11.1661			−0.726848
$237$		0			0
$238$	−14.5430	+	2.93699i	−0.942682	+	0.190377i
$239$	4.11049			0.265886			0.132943	−	0.991124i	$-0.457557\pi$
$239$	4.11049			0.265886			0.132943	+	0.991124i	$0.457557\pi$
$240$		0			0
$241$	12.0763			0.777900			0.388950	−	0.921259i	$-0.372838\pi$
$241$	12.0763			0.777900			0.388950	+	0.921259i	$0.372838\pi$
$242$			10.2058i			0.656055i
$243$		0			0
$244$			5.88429i			0.376703i
$245$	−1.31963	−	3.13392i	−0.0843078	−	0.200219i
$246$		0			0
$247$	−8.63818	−	6.54097i	−0.549634	−	0.416192i
$248$			2.14079i			0.135940i
$249$		0			0
$250$	−4.74311			−0.299981
$251$			14.9744i			0.945176i	0.881283	+	0.472588i	$0.156680\pi$
$251$			14.9744i			0.945176i	−0.881283	+	0.472588i	$0.843320\pi$
$252$		0			0
$253$	−6.61028			−0.415585
$254$	−14.2727			−0.895547
$255$		0			0
$256$	1.00000			0.0625000
$257$	6.10268			0.380675			0.190337	−	0.981719i	$-0.439042\pi$
$257$	6.10268			0.380675			0.190337	+	0.981719i	$0.439042\pi$
$258$		0			0
$259$	2.64280	+	13.0863i	0.164216	+	0.813141i
$260$			1.20753i			0.0748876i
$261$		0			0
$262$	7.35769			0.454560
$263$	−14.7967			−0.912404			−0.456202	−	0.889876i	$-0.650791\pi$
$263$	−14.7967			−0.912404			−0.456202	+	0.889876i	$0.650791\pi$
$264$		0			0
$265$	−6.04766			−0.371505
$266$	−5.00413	+	10.3903i	−0.306823	+	0.637071i
$267$		0			0
$268$		−	8.29320i		−	0.506588i
$269$	10.5582			0.643745			0.321872	−	0.946783i	$-0.395688\pi$
$269$	10.5582			0.643745			0.321872	+	0.946783i	$0.395688\pi$
$270$		0			0
$271$			13.1357i			0.797938i	0.916964	+	0.398969i	$0.130632\pi$
$271$			13.1357i			0.797938i	−0.916964	+	0.398969i	$0.869368\pi$
$272$		−	5.60771i		−	0.340017i
$273$		0			0
$274$		−	8.66850i		−	0.523684i
$275$	4.24554			0.256016
$276$		0			0
$277$	−23.6200			−1.41919			−0.709595	−	0.704609i	$-0.751122\pi$
$277$	−23.6200			−1.41919			−0.709595	+	0.704609i	$0.751122\pi$
$278$	−20.6572			−1.23894
$279$		0			0
$280$	1.25980	−	0.254421i	0.0752877	−	0.0152045i
$281$		−	8.15906i		−	0.486729i	−0.969935	−	0.243364i	$-0.921749\pi$
$281$		−	8.15906i		−	0.486729i	0.969935	−	0.243364i	$-0.0782511\pi$
$282$		0			0
$283$			32.6524i			1.94098i	0.241139	+	0.970491i	$0.422479\pi$
$283$			32.6524i			1.94098i	−0.241139	+	0.970491i	$0.577521\pi$
$284$		−	5.99757i		−	0.355890i
$285$		0			0
$286$		−	2.21524i		−	0.130990i
$287$	19.1275	−	3.86283i	1.12906	−	0.228016i
$288$		0			0
$289$	−14.4464			−0.849786
$290$		−	1.32852i		−	0.0780134i
$291$		0			0
$292$			9.16848i			0.536545i
$293$	26.4395			1.54461			0.772307	−	0.635249i	$-0.219103\pi$
$293$	26.4395			1.54461			0.772307	+	0.635249i	$0.219103\pi$
$294$		0			0
$295$		−	5.42418i		−	0.315808i
$296$	−5.04600			−0.293293
$297$		0			0
$298$		−	10.0744i		−	0.583597i
$299$	−18.4384			−1.06632
$300$		0			0
$301$	1.61198	−	0.325543i	0.0929129	−	0.0187640i
$302$	6.27565			0.361123
$303$		0			0
$304$	−3.47504	−	2.63136i	−0.199307	−	0.150919i
$305$	−2.85844			−0.163674
$306$		0			0
$307$	15.5724			0.888763			0.444381	−	0.895838i	$-0.353424\pi$
$307$	15.5724			0.888763			0.444381	+	0.895838i	$0.353424\pi$
$308$	−2.31115	+	0.466741i	−0.131690	+	0.0265951i
$309$		0			0
$310$	−1.03994			−0.0590648
$311$			12.3207i			0.698645i	0.937003	+	0.349322i	$0.113588\pi$
$311$			12.3207i			0.698645i	−0.937003	+	0.349322i	$0.886412\pi$
$312$		0			0
$313$		−	1.79634i		−	0.101535i	−0.998710	−	0.0507677i	$-0.983833\pi$
$313$		−	1.79634i		−	0.101535i	0.998710	−	0.0507677i	$-0.0161668\pi$
$314$	16.0116			0.903586
$315$		0			0
$316$			12.9087i			0.726172i
$317$			1.03249i			0.0579905i	0.999580	+	0.0289953i	$0.00923077\pi$
$317$			1.03249i			0.0579905i	−0.999580	+	0.0289953i	$0.990769\pi$
$318$		0			0
$319$			2.43721i			0.136457i
$320$			0.485775i			0.0271556i
$321$		0			0
$322$	3.88488	+	19.2366i	0.216496	+	1.07202i
$323$	−14.7559	+	19.4870i	−0.821040	+	1.08429i
$324$		0			0
$325$	11.8423			0.656892
$326$		−	15.0635i		−	0.834292i
$327$		0			0
$328$			7.37545i			0.407241i
$329$	−0.701604	−	3.47411i	−0.0386807	−	0.191534i
$330$		0			0
$331$			32.2163i			1.77077i	0.464862	+	0.885383i	$0.346104\pi$
$331$			32.2163i			1.77077i	−0.464862	+	0.885383i	$0.653896\pi$
$332$			17.4940i			0.960109i
$333$		0			0
$334$			15.0611i			0.824108i
$335$	4.02862			0.220107
$336$		0			0
$337$			7.67408i			0.418034i	0.977912	+	0.209017i	$0.0670264\pi$
$337$			7.67408i			0.418034i	−0.977912	+	0.209017i	$0.932974\pi$
$338$			6.82092i			0.371009i
$339$		0			0
$340$	2.72408			0.147734
$341$	1.90780			0.103313
$342$		0			0
$343$	15.3082	−	10.4239i	0.826567	−	0.562839i
$344$			0.621571i			0.0335129i
$345$		0			0
$346$			5.48926i			0.295104i
$347$	−12.6598			−0.679611			−0.339806	−	0.940496i	$-0.610361\pi$
$347$	−12.6598			−0.679611			−0.339806	+	0.940496i	$0.610361\pi$
$348$		0			0
$349$			4.17532i			0.223500i	0.993736	+	0.111750i	$0.0356456\pi$
$349$			4.17532i			0.223500i	−0.993736	+	0.111750i	$0.964354\pi$
$350$	−2.49512	−	12.3550i	−0.133370	−	0.660402i
$351$		0			0
$352$		−	0.891167i		−	0.0474993i
$353$		−	9.19196i		−	0.489239i	−0.969619	−	0.244619i	$-0.921337\pi$
$353$		−	9.19196i		−	0.489239i	0.969619	−	0.244619i	$-0.0786630\pi$
$354$		0			0
$355$	2.91347			0.154631
$356$	9.70397			0.514309
$357$		0			0
$358$	0.275291			0.0145496
$359$	23.8550			1.25902			0.629511	−	0.776992i	$-0.283255\pi$
$359$	23.8550			1.25902			0.629511	+	0.776992i	$0.283255\pi$
$360$		0			0
$361$	5.15187	+	18.2882i	0.271151	+	0.962537i
$362$			10.3631i			0.544671i
$363$		0			0
$364$	−6.44659	+	1.30190i	−0.337893	+	0.0682383i
$365$	−4.45381			−0.233123
$366$		0			0
$367$			33.4750i			1.74738i	0.486483	+	0.873690i	$0.338280\pi$
$367$			33.4750i			1.74738i	−0.486483	+	0.873690i	$0.661720\pi$
$368$	−7.41755			−0.386667
$369$		0			0
$370$		−	2.45122i		−	0.127433i
$371$	−6.52033	−	32.2865i	−0.338519	−	1.67623i
$372$		0			0
$373$			28.1534i			1.45773i	0.684657	+	0.728865i	$0.259952\pi$
$373$			28.1534i			1.45773i	−0.684657	+	0.728865i	$0.740048\pi$
$374$	−4.99740			−0.258409
$375$		0			0
$376$	1.33960			0.0690845
$377$			6.79822i			0.350126i
$378$		0			0
$379$			4.63390i			0.238028i	0.992893	+	0.119014i	$0.0379733\pi$
$379$			4.63390i			0.238028i	−0.992893	+	0.119014i	$0.962027\pi$
$380$	1.27825	−	1.68809i	0.0655728	−	0.0865971i
$381$		0			0
$382$		−	2.13337i		−	0.109153i
$383$	−28.0882			−1.43524			−0.717621	−	0.696434i	$-0.754769\pi$
$383$	−28.0882			−1.43524			−0.717621	+	0.696434i	$0.754769\pi$
$384$		0			0
$385$	−0.226731	−	1.12270i	−0.0115553	−	0.0572179i
$386$	2.80119			0.142577
$387$		0			0
$388$	2.53160			0.128522
$389$	18.5829			0.942192			0.471096	−	0.882082i	$-0.343858\pi$
$389$	18.5829			0.942192			0.471096	+	0.882082i	$0.343858\pi$
$390$		0			0
$391$			41.5955i			2.10357i
$392$	2.71654	+	6.45139i	0.137206	+	0.325844i
$393$		0			0
$394$		−	25.8438i		−	1.30199i
$395$	−6.27072			−0.315514
$396$		0			0
$397$		−	2.48117i		−	0.124526i	−0.998060	−	0.0622631i	$-0.980168\pi$
$397$		−	2.48117i		−	0.124526i	0.998060	−	0.0622631i	$-0.0198318\pi$
$398$	−10.9515			−0.548951
$399$		0			0
$400$	4.76402			0.238201
$401$		−	15.8800i		−	0.793009i	−0.918033	−	0.396505i	$-0.870223\pi$
$401$		−	15.8800i		−	0.793009i	0.918033	−	0.396505i	$-0.129777\pi$
$402$		0			0
$403$	5.32153			0.265084
$404$		−	1.95547i		−	0.0972884i
$405$		0			0
$406$	7.09254	−	1.43236i	0.351997	−	0.0710866i
$407$			4.49682i			0.222899i
$408$		0			0
$409$	11.8039			0.583666			0.291833	−	0.956469i	$-0.405735\pi$
$409$	11.8039			0.583666			0.291833	+	0.956469i	$0.405735\pi$
$410$	−3.58281			−0.176942
$411$		0			0
$412$	14.8366			0.730947
$413$	28.9580	−	5.84813i	1.42493	−	0.287768i
$414$		0			0
$415$	−8.49815			−0.417158
$416$		−	2.48577i		−	0.121875i
$417$		0			0
$418$	−2.34498	+	3.09684i	−0.114697	+	0.151472i
$419$			28.1019i			1.37287i	0.727193	+	0.686433i	$0.240825\pi$
$419$			28.1019i			1.37287i	−0.727193	+	0.686433i	$0.759175\pi$
$420$		0			0
$421$			12.1232i			0.590849i	0.955366	+	0.295424i	$0.0954611\pi$
$421$			12.1232i			0.590849i	−0.955366	+	0.295424i	$0.904539\pi$
$422$	−26.9244			−1.31066
$423$		0			0
$424$	12.4495			0.604602
$425$		−	26.7152i		−	1.29588i
$426$		0			0
$427$	−3.08185	−	15.2603i	−0.149141	−	0.738498i
$428$		−	9.12044i		−	0.440853i
$429$		0			0
$430$	−0.301943			−0.0145610
$431$		−	28.7367i		−	1.38420i	−0.721802	−	0.692100i	$-0.756686\pi$
$431$		−	28.7367i		−	1.38420i	0.721802	−	0.692100i	$-0.243314\pi$
$432$		0			0
$433$	18.4055			0.884512			0.442256	−	0.896889i	$-0.354178\pi$
$433$	18.4055			0.884512			0.442256	+	0.896889i	$0.354178\pi$
$434$	−1.12122	−	5.55192i	−0.0538204	−	0.266501i
$435$		0			0
$436$			3.34904i			0.160390i
$437$	25.7763	+	19.5183i	1.23305	+	0.933685i
$438$		0			0
$439$	−24.8635			−1.18667			−0.593335	−	0.804955i	$-0.702189\pi$
$439$	−24.8635			−1.18667			−0.593335	+	0.804955i	$0.702189\pi$
$440$	0.432906			0.0206380
$441$		0			0
$442$	−13.9395			−0.663034
$443$	0.911526			0.0433079			0.0216539	−	0.999766i	$-0.493107\pi$
$443$	0.911526			0.0433079			0.0216539	+	0.999766i	$0.493107\pi$
$444$		0			0
$445$			4.71394i			0.223462i
$446$		−	5.27498i		−	0.249778i
$447$		0			0
$448$	−2.59339	+	0.523742i	−0.122526	+	0.0247445i
$449$			16.3156i			0.769980i	0.922921	+	0.384990i	$0.125795\pi$
$449$			16.3156i			0.769980i	−0.922921	+	0.384990i	$0.874205\pi$
$450$		0			0
$451$	6.57276			0.309499
$452$		−	13.5907i		−	0.639252i
$453$		0			0
$454$			1.65074i			0.0774733i
$455$	−0.632432	−	3.13159i	−0.0296489	−	0.146811i
$456$		0			0
$457$	5.83109			0.272767			0.136383	−	0.990656i	$-0.456452\pi$
$457$	5.83109			0.272767			0.136383	+	0.990656i	$0.456452\pi$
$458$	−24.5788			−1.14849
$459$		0			0
$460$		−	3.60326i		−	0.168003i
$461$		−	35.3279i		−	1.64538i	−0.568487	−	0.822692i	$-0.692471\pi$
$461$		−	35.3279i		−	1.64538i	0.568487	−	0.822692i	$-0.307529\pi$
$462$		0			0
$463$	15.5104			0.720831			0.360415	−	0.932792i	$-0.382635\pi$
$463$	15.5104			0.720831			0.360415	+	0.932792i	$0.382635\pi$
$464$			2.73485i			0.126962i
$465$		0			0
$466$		−	8.24684i		−	0.382027i
$467$		−	9.72058i		−	0.449815i	−0.974380	−	0.224907i	$-0.927792\pi$
$467$		−	9.72058i		−	0.449815i	0.974380	−	0.224907i	$-0.0722079\pi$
$468$		0			0
$469$	4.34349	+	21.5075i	0.200564	+	0.993125i
$470$			0.650742i			0.0300165i
$471$		0			0
$472$			11.1661i			0.513959i
$473$	0.553924			0.0254694
$474$		0			0
$475$	−16.5552	−	12.5359i	−0.759604	−	0.575185i
$476$	2.93699	+	14.5430i	0.134617	+	0.666577i
$477$		0			0
$478$		−	4.11049i		−	0.188010i
$479$			9.76640i			0.446238i	0.974791	+	0.223119i	$0.0716239\pi$
$479$			9.76640i			0.446238i	−0.974791	+	0.223119i	$0.928376\pi$
$480$		0			0
$481$			12.5432i			0.571921i
$482$		−	12.0763i		−	0.550058i
$483$		0			0
$484$	10.2058			0.463901
$485$			1.22979i			0.0558417i
$486$		0			0
$487$			2.38139i			0.107911i	0.998543	+	0.0539555i	$0.0171829\pi$
$487$			2.38139i			0.107911i	−0.998543	+	0.0539555i	$0.982817\pi$
$488$	5.88429			0.266370
$489$		0			0
$490$	−3.13392	+	1.31963i	−0.141576	+	0.0596146i
$491$	−16.6491			−0.751362			−0.375681	−	0.926749i	$-0.622591\pi$
$491$	−16.6491			−0.751362			−0.375681	+	0.926749i	$0.622591\pi$
$492$		0			0
$493$	15.3362			0.690709
$494$	−6.54097	+	8.63818i	−0.294292	+	0.388650i
$495$		0			0
$496$	2.14079			0.0961244
$497$	3.14118	+	15.5541i	0.140901	+	0.697696i
$498$		0			0
$499$	−35.8702			−1.60577			−0.802885	−	0.596134i	$-0.796703\pi$
$499$	−35.8702			−1.60577			−0.802885	+	0.596134i	$0.796703\pi$
$500$			4.74311i			0.212118i
$501$		0			0
$502$	14.9744			0.668341
$503$			30.0897i			1.34163i	0.741623	+	0.670817i	$0.234057\pi$
$503$			30.0897i			1.34163i	−0.741623	+	0.670817i	$0.765943\pi$
$504$		0			0
$505$	0.949919			0.0422709
$506$			6.61028i			0.293863i
$507$		0			0
$508$			14.2727i			0.633248i
$509$	27.0959			1.20100			0.600501	−	0.799624i	$-0.294968\pi$
$509$	27.0959			1.20100			0.600501	+	0.799624i	$0.294968\pi$
$510$		0			0
$511$	−4.80192	−	23.7775i	−0.212424	−	1.05185i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$		−	6.10268i		−	0.269178i
$515$			7.20724i			0.317589i
$516$		0			0
$517$		−	1.19381i		−	0.0525035i
$518$	13.0863	−	2.64280i	0.574977	−	0.116118i
$519$		0			0
$520$	1.20753			0.0529535
$521$	25.5195			1.11803			0.559015	−	0.829157i	$-0.311179\pi$
$521$	25.5195			1.11803			0.559015	+	0.829157i	$0.311179\pi$
$522$		0			0
$523$	−9.85584			−0.430966			−0.215483	−	0.976508i	$-0.569133\pi$
$523$	−9.85584			−0.430966			−0.215483	+	0.976508i	$0.569133\pi$
$524$		−	7.35769i		−	0.321422i
$525$		0			0
$526$			14.7967i			0.645167i
$527$		−	12.0049i		−	0.522943i
$528$		0			0
$529$	32.0201			1.39218
$530$			6.04766i			0.262693i
$531$		0			0
$532$	10.3903	+	5.00413i	0.450477	+	0.216957i
$533$	18.3337			0.794121
$534$		0			0
$535$	4.43048			0.191546
$536$	−8.29320			−0.358211
$537$		0			0
$538$		−	10.5582i		−	0.455196i
$539$	5.74926	−	2.42089i	0.247638	−	0.104275i
$540$		0			0
$541$	−10.3841			−0.446449			−0.223225	−	0.974767i	$-0.571658\pi$
$541$	−10.3841			−0.446449			−0.223225	+	0.974767i	$0.571658\pi$
$542$	13.1357			0.564228
$543$		0			0
$544$	−5.60771			−0.240428
$545$	−1.62688			−0.0696878
$546$		0			0
$547$		−	28.8873i		−	1.23513i	−0.786519	−	0.617566i	$-0.788119\pi$
$547$		−	28.8873i		−	1.23513i	0.786519	−	0.617566i	$-0.211881\pi$
$548$	−8.66850			−0.370300
$549$		0			0
$550$		−	4.24554i		−	0.181030i
$551$	7.19638	−	9.50372i	0.306576	−	0.404872i
$552$		0			0
$553$	−6.76083	−	33.4774i	−0.287500	−	1.42360i
$554$			23.6200i			1.00352i
$555$		0			0
$556$			20.6572i			0.876061i
$557$	−20.1424			−0.853461			−0.426731	−	0.904379i	$-0.640335\pi$
$557$	−20.1424			−0.853461			−0.426731	+	0.904379i	$0.640335\pi$
$558$		0			0
$559$	1.54509			0.0653502
$560$	−0.254421	−	1.25980i	−0.0107512	−	0.0532365i
$561$		0			0
$562$	−8.15906			−0.344169
$563$	−20.2433			−0.853155			−0.426577	−	0.904451i	$-0.640281\pi$
$563$	−20.2433			−0.853155			−0.426577	+	0.904451i	$0.640281\pi$
$564$		0			0
$565$	6.60201			0.277749
$566$	32.6524			1.37248
$567$		0			0
$568$	−5.99757			−0.251653
$569$		−	15.8019i		−	0.662451i	−0.943552	−	0.331225i	$-0.892538\pi$
$569$		−	15.8019i		−	0.662451i	0.943552	−	0.331225i	$-0.107462\pi$
$570$		0			0
$571$	24.2408			1.01445			0.507224	−	0.861814i	$-0.330672\pi$
$571$	24.2408			1.01445			0.507224	+	0.861814i	$0.330672\pi$
$572$	−2.21524			−0.0926238
$573$		0			0
$574$	−3.86283	−	19.1275i	−0.161232	−	0.798365i
$575$	−35.3374			−1.47367
$576$		0			0
$577$			35.2958i			1.46938i	0.678401	+	0.734692i	$0.262673\pi$
$577$			35.2958i			1.46938i	−0.678401	+	0.734692i	$0.737327\pi$
$578$			14.4464i			0.600890i
$579$		0			0
$580$	−1.32852			−0.0551638
$581$	−9.16235	−	45.3689i	−0.380118	−	1.88222i
$582$		0			0
$583$		−	11.0946i		−	0.459491i
$584$	9.16848			0.379394
$585$		0			0
$586$		−	26.4395i		−	1.09221i
$587$		−	2.02100i		−	0.0834157i	−0.999130	−	0.0417079i	$-0.986720\pi$
$587$		−	2.02100i		−	0.0834157i	0.999130	−	0.0417079i	$-0.0132799\pi$
$588$		0			0
$589$	−7.43935	−	5.63320i	−0.306533	−	0.232112i
$590$	−5.42418			−0.223310
$591$		0			0
$592$			5.04600i			0.207389i
$593$			30.6794i			1.25985i	0.776656	+	0.629925i	$0.216914\pi$
$593$			30.6794i			1.25985i	−0.776656	+	0.629925i	$0.783086\pi$
$594$		0			0
$595$	−7.06462	+	1.42672i	−0.289621	+	0.0584896i
$596$	−10.0744			−0.412665
$597$		0			0
$598$			18.4384i			0.754001i
$599$			34.1802i			1.39657i	0.715822	+	0.698283i	$0.246052\pi$
$599$			34.1802i			1.39657i	−0.715822	+	0.698283i	$0.753948\pi$
$600$		0			0
$601$	1.95391			0.0797016			0.0398508	−	0.999206i	$-0.487312\pi$
$601$	1.95391			0.0797016			0.0398508	+	0.999206i	$0.487312\pi$
$602$	−0.325543	−	1.61198i	−0.0132681	−	0.0656994i
$603$		0			0
$604$		−	6.27565i		−	0.255353i
$605$			4.95773i			0.201560i
$606$		0			0
$607$	2.97381			0.120703			0.0603517	−	0.998177i	$-0.480778\pi$
$607$	2.97381			0.120703			0.0603517	+	0.998177i	$0.480778\pi$
$608$	−2.63136	+	3.47504i	−0.106716	+	0.140932i
$609$		0			0
$610$			2.85844i			0.115735i
$611$		−	3.32994i		−	0.134715i
$612$		0			0
$613$	−7.32225			−0.295743			−0.147871	−	0.989007i	$-0.547242\pi$
$613$	−7.32225			−0.295743			−0.147871	+	0.989007i	$0.547242\pi$
$614$		−	15.5724i		−	0.628450i
$615$		0			0
$616$	0.466741	+	2.31115i	0.0188055	+	0.0931188i
$617$	−1.84958			−0.0744611			−0.0372306	−	0.999307i	$-0.511854\pi$
$617$	−1.84958			−0.0744611			−0.0372306	+	0.999307i	$0.511854\pi$
$618$		0			0
$619$			13.4415i			0.540260i	0.962824	+	0.270130i	$0.0870667\pi$
$619$			13.4415i			0.540260i	−0.962824	+	0.270130i	$0.912933\pi$
$620$			1.03994i			0.0417651i
$621$		0			0
$622$	12.3207			0.494017
$623$	−25.1662	+	5.08238i	−1.00826	+	0.203621i
$624$		0			0
$625$	21.5160			0.860641
$626$	−1.79634			−0.0717963
$627$		0			0
$628$		−	16.0116i		−	0.638932i
$629$	28.2965			1.12825
$630$		0			0
$631$	−4.41110			−0.175603			−0.0878015	−	0.996138i	$-0.527984\pi$
$631$	−4.41110			−0.175603			−0.0878015	+	0.996138i	$0.527984\pi$
$632$	12.9087			0.513481
$633$		0			0
$634$	1.03249			0.0410055
$635$	−6.93330			−0.275140
$636$		0			0
$637$	16.0367	−	6.75270i	0.635397	−	0.267552i
$638$	2.43721			0.0964899
$639$		0			0
$640$	0.485775			0.0192019
$641$			10.7712i			0.425436i	0.977114	+	0.212718i	$0.0682316\pi$
$641$			10.7712i			0.425436i	−0.977114	+	0.212718i	$0.931768\pi$
$642$		0			0
$643$			1.99983i			0.0788654i	0.999222	+	0.0394327i	$0.0125551\pi$
$643$			1.99983i			0.0788654i	−0.999222	+	0.0394327i	$0.987445\pi$
$644$	19.2366	−	3.88488i	0.758030	−	0.153086i
$645$		0			0
$646$	19.4870	+	14.7559i	0.766707	+	0.580563i
$647$			40.3103i			1.58476i	0.610028	+	0.792380i	$0.291158\pi$
$647$			40.3103i			1.58476i	−0.610028	+	0.792380i	$0.708842\pi$
$648$		0			0
$649$	9.95081			0.390604
$650$		−	11.8423i		−	0.464493i
$651$		0			0
$652$	−15.0635			−0.589934
$653$	41.4971			1.62391			0.811954	−	0.583721i	$-0.198404\pi$
$653$	41.4971			1.62391			0.811954	+	0.583721i	$0.198404\pi$
$654$		0			0
$655$	3.57418			0.139655
$656$	7.37545			0.287963
$657$		0			0
$658$	−3.47411	+	0.701604i	−0.135435	+	0.0273514i
$659$			6.05762i			0.235972i	0.993015	+	0.117986i	$0.0376437\pi$
$659$			6.05762i			0.235972i	−0.993015	+	0.117986i	$0.962356\pi$
$660$		0			0
$661$	25.2012			0.980211			0.490106	−	0.871663i	$-0.336958\pi$
$661$	25.2012			0.980211			0.490106	+	0.871663i	$0.336958\pi$
$662$	32.2163			1.25212
$663$		0			0
$664$	17.4940			0.678900
$665$	−2.43088	+	5.04735i	−0.0942655	+	0.195728i
$666$		0			0
$667$		−	20.2859i		−	0.785473i
$668$	15.0611			0.582732
$669$		0			0
$670$		−	4.02862i		−	0.155639i
$671$		−	5.24389i		−	0.202438i
$672$		0			0
$673$			0.511437i			0.0197144i	0.999951	+	0.00985722i	$0.00313770\pi$
$673$			0.511437i			0.0197144i	−0.999951	+	0.00985722i	$0.996862\pi$
$674$	7.67408			0.295594
$675$		0			0
$676$	6.82092			0.262343
$677$	−43.9533			−1.68926			−0.844631	−	0.535349i	$-0.820180\pi$
$677$	−43.9533			−1.68926			−0.844631	+	0.535349i	$0.820180\pi$
$678$		0			0
$679$	−6.56543	+	1.32590i	−0.251958	+	0.0508836i
$680$		−	2.72408i		−	0.104464i
$681$		0			0
$682$		−	1.90780i		−	0.0730536i
$683$			21.6031i			0.826620i	0.910590	+	0.413310i	$0.135627\pi$
$683$			21.6031i			0.826620i	−0.910590	+	0.413310i	$0.864373\pi$
$684$		0			0
$685$		−	4.21094i		−	0.160892i
$686$	−10.4239	−	15.3082i	−0.397987	−	0.584471i
$687$		0			0
$688$	0.621571			0.0236972
$689$		−	30.9467i		−	1.17897i
$690$		0			0
$691$			35.0173i			1.33212i	0.745897	+	0.666061i	$0.232021\pi$
$691$			35.0173i			1.33212i	−0.745897	+	0.666061i	$0.767979\pi$
$692$	5.48926			0.208670
$693$		0			0
$694$			12.6598i			0.480558i
$695$	−10.0347			−0.380640
$696$		0			0
$697$		−	41.3594i		−	1.56660i
$698$	4.17532			0.158038
$699$		0			0
$700$	−12.3550	+	2.49512i	−0.466975	+	0.0943066i
$701$	10.9432			0.413320			0.206660	−	0.978413i	$-0.433741\pi$
$701$	10.9432			0.413320			0.206660	+	0.978413i	$0.433741\pi$
$702$		0			0
$703$	13.2778	−	17.5351i	0.500783	−	0.661347i
$704$	−0.891167			−0.0335871
$705$		0			0
$706$	−9.19196			−0.345944
$707$	1.02416	+	5.07131i	0.0385176	+	0.190726i
$708$		0			0
$709$	−11.3792			−0.427356			−0.213678	−	0.976904i	$-0.568544\pi$
$709$	−11.3792			−0.427356			−0.213678	+	0.976904i	$0.568544\pi$
$710$		−	2.91347i		−	0.109341i
$711$		0			0
$712$		−	9.70397i		−	0.363672i
$713$	−15.8794			−0.594690
$714$		0			0
$715$		−	1.07611i		−	0.0402441i
$716$		−	0.275291i		−	0.0102881i
$717$		0			0
$718$		−	23.8550i		−	0.890263i
$719$			27.7716i			1.03571i	0.855470	+	0.517853i	$0.173269\pi$
$719$			27.7716i			1.03571i	−0.855470	+	0.517853i	$0.826731\pi$
$720$		0			0
$721$	−38.4771	+	7.77055i	−1.43296	+	0.289390i
$722$	18.2882	−	5.15187i	0.680616	−	0.191733i
$723$		0			0
$724$	10.3631			0.385141
$725$			13.0289i			0.483881i
$726$		0			0
$727$			34.3359i			1.27345i	0.771091	+	0.636725i	$0.219711\pi$
$727$			34.3359i			1.27345i	−0.771091	+	0.636725i	$0.780289\pi$
$728$	1.30190	+	6.44659i	0.0482518	+	0.238927i
$729$		0			0
$730$			4.45381i			0.164843i
$731$		−	3.48559i		−	0.128919i
$732$		0			0
$733$		−	23.1388i		−	0.854649i	−0.904098	−	0.427325i	$-0.859456\pi$
$733$		−	23.1388i		−	0.854649i	0.904098	−	0.427325i	$-0.140544\pi$
$734$	33.4750			1.23558
$735$		0			0
$736$			7.41755i			0.273415i
$737$			7.39062i			0.272237i
$738$		0			0
$739$	−7.02692			−0.258489			−0.129245	−	0.991613i	$-0.541255\pi$
$739$	−7.02692			−0.258489			−0.129245	+	0.991613i	$0.541255\pi$
$740$	−2.45122			−0.0901085
$741$		0			0
$742$	−32.2865	+	6.52033i	−1.18527	+	0.239369i
$743$		−	16.2489i		−	0.596114i	−0.954548	−	0.298057i	$-0.903661\pi$
$743$		−	16.2489i		−	0.596114i	0.954548	−	0.298057i	$-0.0963385\pi$
$744$		0			0
$745$		−	4.89391i		−	0.179299i
$746$	28.1534			1.03077
$747$		0			0
$748$			4.99740i			0.182723i
$749$	4.77676	+	23.6529i	0.174539	+	0.864258i
$750$		0			0
$751$			40.7094i			1.48551i	0.669564	+	0.742754i	$0.266481\pi$
$751$			40.7094i			1.48551i	−0.669564	+	0.742754i	$0.733519\pi$
$752$		−	1.33960i		−	0.0488501i
$753$		0			0
$754$	6.79822			0.247577
$755$	3.04855			0.110948
$756$		0			0
$757$	−0.674342			−0.0245094			−0.0122547	−	0.999925i	$-0.503901\pi$
$757$	−0.674342			−0.0245094			−0.0122547	+	0.999925i	$0.503901\pi$
$758$	4.63390			0.168311
$759$		0			0
$760$	−1.68809	−	1.27825i	−0.0612334	−	0.0463669i
$761$			48.1903i			1.74690i	0.486915	+	0.873449i	$0.338122\pi$
$761$			48.1903i			1.74690i	−0.486915	+	0.873449i	$0.661878\pi$
$762$		0			0
$763$	−1.75403	−	8.68538i	−0.0635003	−	0.314432i
$764$	−2.13337			−0.0771826
$765$		0			0
$766$			28.0882i			1.01487i
$767$	27.7563			1.00222
$768$		0			0
$769$			1.93313i			0.0697104i	0.999392	+	0.0348552i	$0.0110970\pi$
$769$			1.93313i			0.0697104i	−0.999392	+	0.0348552i	$0.988903\pi$
$770$	−1.12270	+	0.226731i	−0.0404592	+	0.00817082i
$771$		0			0
$772$		−	2.80119i		−	0.100817i
$773$	34.5412			1.24236			0.621180	−	0.783668i	$-0.286654\pi$
$773$	34.5412			1.24236			0.621180	+	0.783668i	$0.286654\pi$
$774$		0			0
$775$	10.1988			0.366351
$776$		−	2.53160i		−	0.0908791i
$777$		0			0
$778$		−	18.5829i		−	0.666231i
$779$	−25.6300	−	19.4075i	−0.918291	−	0.695345i
$780$		0			0
$781$			5.34484i			0.191253i
$782$	41.5955			1.48745
$783$		0			0
$784$	6.45139	−	2.71654i	0.230407	−	0.0970193i
$785$	7.77802			0.277609
$786$		0			0
$787$	24.8459			0.885660			0.442830	−	0.896606i	$-0.353975\pi$
$787$	24.8459			0.885660			0.442830	+	0.896606i	$0.353975\pi$
$788$	−25.8438			−0.920647
$789$		0			0
$790$			6.27072i			0.223102i
$791$	7.11802	+	35.2460i	0.253088	+	1.25320i
$792$		0			0
$793$		−	14.6270i		−	0.519421i
$794$	−2.48117			−0.0880533
$795$		0			0
$796$			10.9515i			0.388167i
$797$	−24.7778			−0.877676			−0.438838	−	0.898566i	$-0.644610\pi$
$797$	−24.7778			−0.877676			−0.438838	+	0.898566i	$0.644610\pi$
$798$		0			0
$799$	−7.51207			−0.265758
$800$		−	4.76402i		−	0.168434i
$801$		0			0
$802$	−15.8800			−0.560742
$803$		−	8.17064i		−	0.288336i
$804$		0			0
$805$	1.88718	+	9.34467i	0.0665143	+	0.329356i
$806$		−	5.32153i		−	0.187443i
$807$		0			0
$808$	−1.95547			−0.0687933
$809$	−41.3361			−1.45330			−0.726650	−	0.687008i	$-0.758924\pi$
$809$	−41.3361			−1.45330			−0.726650	+	0.687008i	$0.758924\pi$
$810$		0			0
$811$	35.1844			1.23549			0.617745	−	0.786378i	$-0.288046\pi$
$811$	35.1844			1.23549			0.617745	+	0.786378i	$0.288046\pi$
$812$	−1.43236	−	7.09254i	−0.0502658	−	0.248899i
$813$		0			0
$814$	4.49682			0.157614
$815$		−	7.31749i		−	0.256320i
$816$		0			0
$817$	−2.15999	−	1.63558i	−0.0755684	−	0.0572216i
$818$		−	11.8039i		−	0.412714i
$819$		0			0
$820$			3.58281i			0.125117i
$821$	21.0286			0.733902			0.366951	−	0.930240i	$-0.380402\pi$
$821$	21.0286			0.733902			0.366951	+	0.930240i	$0.380402\pi$
$822$		0			0
$823$	−48.0745			−1.67577			−0.837886	−	0.545846i	$-0.816208\pi$
$823$	−48.0745			−1.67577			−0.837886	+	0.545846i	$0.816208\pi$
$824$		−	14.8366i		−	0.516857i
$825$		0			0
$826$	−5.84813	−	28.9580i	−0.203482	−	1.00758i
$827$			33.7556i			1.17380i	0.809661	+	0.586898i	$0.199651\pi$
$827$			33.7556i			1.17380i	−0.809661	+	0.586898i	$0.800349\pi$
$828$		0			0
$829$	39.5293			1.37291			0.686454	−	0.727173i	$-0.259166\pi$
$829$	39.5293			1.37291			0.686454	+	0.727173i	$0.259166\pi$
$830$			8.49815i			0.294975i
$831$		0			0
$832$	−2.48577			−0.0861787
$833$	−15.2336	−	36.1775i	−0.527811	−	1.25348i
$834$		0			0
$835$			7.31631i			0.253191i
$836$	3.09684	+	2.34498i	0.107107	+	0.0811029i
$837$		0			0
$838$	28.1019			0.970763
$839$	−45.9394			−1.58600			−0.793002	−	0.609219i	$-0.791483\pi$
$839$	−45.9394			−1.58600			−0.793002	+	0.609219i	$0.791483\pi$
$840$		0			0
$841$	21.5206			0.742090
$842$	12.1232			0.417793
$843$		0			0
$844$			26.9244i			0.926775i
$845$			3.31343i			0.113986i
$846$		0			0
$847$	−26.4677	+	5.34522i	−0.909442	+	0.183664i
$848$		−	12.4495i		−	0.427518i
$849$		0			0
$850$	−26.7152			−0.916325
$851$		−	37.4289i		−	1.28305i
$852$		0			0
$853$			38.3361i			1.31260i	0.754498	+	0.656302i	$0.227880\pi$
$853$			38.3361i			1.31260i	−0.754498	+	0.656302i	$0.772120\pi$
$854$	−15.2603	+	3.08185i	−0.522197	+	0.105459i
$855$		0			0
$856$	−9.12044			−0.311730
$857$	7.06201			0.241234			0.120617	−	0.992699i	$-0.461513\pi$
$857$	7.06201			0.241234			0.120617	+	0.992699i	$0.461513\pi$
$858$		0			0
$859$		−	26.0122i		−	0.887524i	−0.896145	−	0.443762i	$-0.853644\pi$
$859$		−	26.0122i		−	0.887524i	0.896145	−	0.443762i	$-0.146356\pi$
$860$			0.301943i			0.0102962i
$861$		0			0
$862$	−28.7367			−0.978777
$863$			0.119494i			0.00406763i	0.999998	+	0.00203382i	$0.000647385\pi$
$863$			0.119494i			0.00406763i	−0.999998	+	0.00203382i	$0.999353\pi$
$864$		0			0
$865$			2.66654i			0.0906651i
$866$		−	18.4055i		−	0.625444i
$867$		0			0
$868$	−5.55192	+	1.12122i	−0.188444	+	0.0380568i
$869$		−	11.5038i		−	0.390240i
$870$		0			0
$871$			20.6150i			0.698513i
$872$	3.34904			0.113413
$873$		0			0
$874$	19.5183	−	25.7763i	0.660215	−	0.871897i
$875$	−2.48417	−	12.3008i	−0.0839802	−	0.415842i
$876$		0			0
$877$			37.3530i			1.26132i	0.776059	+	0.630660i	$0.217216\pi$
$877$			37.3530i			1.26132i	−0.776059	+	0.630660i	$0.782784\pi$
$878$			24.8635i			0.839103i
$879$		0			0
$880$		−	0.432906i		−	0.0145933i
$881$			49.1797i			1.65690i	0.560060	+	0.828452i	$0.310778\pi$
$881$			49.1797i			1.65690i	−0.560060	+	0.828452i	$0.689222\pi$
$882$		0			0
$883$	31.5676			1.06233			0.531166	−	0.847268i	$-0.321754\pi$
$883$	31.5676			1.06233			0.531166	+	0.847268i	$0.321754\pi$
$884$			13.9395i			0.468836i
$885$		0			0
$886$		−	0.911526i		−	0.0306233i
$887$	−8.95891			−0.300811			−0.150405	−	0.988624i	$-0.548058\pi$
$887$	−8.95891			−0.300811			−0.150405	+	0.988624i	$0.548058\pi$
$888$		0			0
$889$	−7.47520	−	37.0147i	−0.250710	−	1.24143i
$890$	4.71394			0.158012
$891$		0			0
$892$	−5.27498			−0.176619
$893$	−3.52497	+	4.65516i	−0.117959	+	0.155779i
$894$		0			0
$895$	0.133729			0.00447008
$896$	0.523742	+	2.59339i	0.0174970	+	0.0866392i
$897$		0			0
$898$	16.3156			0.544458
$899$			5.85474i			0.195267i
$900$		0			0
$901$	−69.8132			−2.32582
$902$		−	6.57276i		−	0.218849i
$903$		0			0
$904$	−13.5907			−0.452020
$905$			5.03412i			0.167340i
$906$		0			0
$907$		−	47.4166i		−	1.57444i	−0.616671	−	0.787221i	$-0.711519\pi$
$907$		−	47.4166i		−	1.57444i	0.616671	−	0.787221i	$-0.288481\pi$
$908$	1.65074			0.0547819
$909$		0			0
$910$	−3.13159	+	0.632432i	−0.103811	+	0.0209649i
$911$		−	4.93940i		−	0.163650i	−0.996647	−	0.0818249i	$-0.973925\pi$
$911$		−	4.93940i		−	0.163650i	0.996647	−	0.0818249i	$-0.0260748\pi$
$912$		0			0
$913$		−	15.5901i		−	0.515957i
$914$		−	5.83109i		−	0.192875i
$915$		0			0
$916$			24.5788i			0.812108i
$917$	3.85353	+	19.0814i	0.127255	+	0.630123i
$918$		0			0
$919$	32.4315			1.06982			0.534909	−	0.844910i	$-0.320346\pi$
$919$	32.4315			1.06982			0.534909	+	0.844910i	$0.320346\pi$
$920$	−3.60326			−0.118796
$921$		0			0
$922$	−35.3279			−1.16346
$923$			14.9086i			0.490723i
$924$		0			0
$925$			24.0392i			0.790405i
$926$		−	15.5104i		−	0.509704i
$927$		0			0
$928$	2.73485			0.0897758
$929$		−	34.2591i		−	1.12400i	−0.827136	−	0.562002i	$-0.810031\pi$
$929$		−	34.2591i		−	1.12400i	0.827136	−	0.562002i	$-0.189969\pi$
$930$		0			0
$931$	−29.5671	−	7.53584i	−0.969021	−	0.246977i
$932$	−8.24684			−0.270134
$933$		0			0
$934$	−9.72058			−0.318067
$935$	−2.42761			−0.0793913
$936$		0			0
$937$			13.7815i			0.450222i	0.974333	+	0.225111i	$0.0722745\pi$
$937$			13.7815i			0.450222i	−0.974333	+	0.225111i	$0.927726\pi$
$938$	21.5075	−	4.34349i	0.702246	−	0.141820i
$939$		0			0
$940$	0.650742			0.0212249
$941$	−31.7858			−1.03619			−0.518093	−	0.855324i	$-0.673358\pi$
$941$	−31.7858			−1.03619			−0.518093	+	0.855324i	$0.673358\pi$
$942$		0			0
$943$	−54.7078			−1.78153
$944$	11.1661			0.363424
$945$		0			0
$946$		−	0.553924i		−	0.0180096i
$947$	14.1047			0.458341			0.229171	−	0.973386i	$-0.426399\pi$
$947$	14.1047			0.458341			0.229171	+	0.973386i	$0.426399\pi$
$948$		0			0
$949$		−	22.7908i		−	0.739820i
$950$	−12.5359	+	16.5552i	−0.406717	+	0.537121i
$951$		0			0
$952$	14.5430	−	2.93699i	0.471341	−	0.0951884i
$953$		−	31.6228i		−	1.02436i	−0.858877	−	0.512182i	$-0.828837\pi$
$953$		−	31.6228i		−	1.02436i	0.858877	−	0.512182i	$-0.171163\pi$
$954$		0			0
$955$		−	1.03634i		−	0.0335351i
$956$	−4.11049			−0.132943
$957$		0			0
$958$	9.76640			0.315538
$959$	22.4809	−	4.54006i	0.725945	−	0.146606i
$960$		0			0
$961$	−26.4170			−0.852162
$962$	12.5432			0.404409
$963$		0			0
$964$	−12.0763			−0.388950
$965$	1.36075			0.0438041
$966$		0			0
$967$	30.5646			0.982891			0.491445	−	0.870908i	$-0.336469\pi$
$967$	30.5646			0.982891			0.491445	+	0.870908i	$0.336469\pi$
$968$		−	10.2058i		−	0.328028i
$969$		0			0
$970$	1.22979			0.0394861
$971$	−6.99370			−0.224439			−0.112219	−	0.993683i	$-0.535796\pi$
$971$	−6.99370			−0.224439			−0.112219	+	0.993683i	$0.535796\pi$
$972$		0			0
$973$	−10.8190	−	53.5723i	−0.346843	−	1.71745i
$974$	2.38139			0.0763045
$975$		0			0
$976$		−	5.88429i		−	0.188352i
$977$			46.2954i			1.48112i	0.671990	+	0.740560i	$0.265440\pi$
$977$			46.2954i			1.48112i	−0.671990	+	0.740560i	$0.734560\pi$
$978$		0			0
$979$	−8.64786			−0.276387
$980$	1.31963	+	3.13392i	0.0421539	+	0.100109i
$981$		0			0
$982$			16.6491i			0.531293i
$983$	−22.1124			−0.705278			−0.352639	−	0.935760i	$-0.614716\pi$
$983$	−22.1124			−0.705278			−0.352639	+	0.935760i	$0.614716\pi$
$984$		0			0
$985$		−	12.5543i		−	0.400012i
$986$		−	15.3362i		−	0.488405i
$987$		0			0
$988$	8.63818	+	6.54097i	0.274817	+	0.208096i
$989$	−4.61054			−0.146607
$990$		0			0
$991$			50.2105i			1.59499i	0.603326	+	0.797494i	$0.293842\pi$
$991$			50.2105i			1.59499i	−0.603326	+	0.797494i	$0.706158\pi$
$992$		−	2.14079i		−	0.0679702i
$993$		0			0
$994$	15.5541	−	3.14118i	0.493345	−	0.0996322i
$995$	−5.31998			−0.168655
$996$		0			0
$997$		−	10.4887i		−	0.332182i	−0.986110	−	0.166091i	$-0.946886\pi$
$997$		−	10.4887i		−	0.332182i	0.986110	−	0.166091i	$-0.0531145\pi$
$998$			35.8702i			1.13545i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2394.2.e.b.1063.3		12
3.2	odd	2		798.2.e.b.265.10	yes	12
7.6	odd	2		2394.2.e.a.1063.4		12
19.18	odd	2		2394.2.e.a.1063.9		12
21.20	even	2		798.2.e.a.265.9	yes	12
57.56	even	2		798.2.e.a.265.4	✓	12
133.132	even	2	inner	2394.2.e.b.1063.10		12
399.398	odd	2		798.2.e.b.265.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.e.a.265.4	✓	12	57.56	even	2
798.2.e.a.265.9	yes	12	21.20	even	2
798.2.e.b.265.3	yes	12	399.398	odd	2
798.2.e.b.265.10	yes	12	3.2	odd	2
2394.2.e.a.1063.4		12	7.6	odd	2
2394.2.e.a.1063.9		12	19.18	odd	2
2394.2.e.b.1063.3		12	1.1	even	1	trivial
2394.2.e.b.1063.10		12	133.132	even	2	inner

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:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} -0.485775i q^{5} +(2.59339 - 0.523742i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} -0.485775i q^{5} +(2.59339 - 0.523742i) q^{7} +1.00000i q^{8} -0.485775 q^{10} +0.891167 q^{11} +2.48577 q^{13} +(-0.523742 - 2.59339i) q^{14} +1.00000 q^{16} -5.60771i q^{17} +(-3.47504 - 2.63136i) q^{19} +0.485775i q^{20} -0.891167i q^{22} -7.41755 q^{23} +4.76402 q^{25} -2.48577i q^{26} +(-2.59339 + 0.523742i) q^{28} +2.73485i q^{29} +2.14079 q^{31} -1.00000i q^{32} -5.60771 q^{34} +(-0.254421 - 1.25980i) q^{35} +5.04600i q^{37} +(-2.63136 + 3.47504i) q^{38} +0.485775 q^{40} +7.37545 q^{41} +0.621571 q^{43} -0.891167 q^{44} +7.41755i q^{46} -1.33960i q^{47} +(6.45139 - 2.71654i) q^{49} -4.76402i q^{50} -2.48577 q^{52} -12.4495i q^{53} -0.432906i q^{55} +(0.523742 + 2.59339i) q^{56} +2.73485 q^{58} +11.1661 q^{59} -5.88429i q^{61} -2.14079i q^{62} -1.00000 q^{64} -1.20753i q^{65} +8.29320i q^{67} +5.60771i q^{68} +(-1.25980 + 0.254421i) q^{70} +5.99757i q^{71} -9.16848i q^{73} +5.04600 q^{74} +(3.47504 + 2.63136i) q^{76} +(2.31115 - 0.466741i) q^{77} -12.9087i q^{79} -0.485775i q^{80} -7.37545i q^{82} -17.4940i q^{83} -2.72408 q^{85} -0.621571i q^{86} +0.891167i q^{88} -9.70397 q^{89} +(6.44659 - 1.30190i) q^{91} +7.41755 q^{92} -1.33960 q^{94} +(-1.27825 + 1.68809i) q^{95} -2.53160 q^{97} +(-2.71654 - 6.45139i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4}+O(q^{10}) \) 12 * q - 12 * q^4	\( 12 q - 12 q^{4} + 4 q^{10} - 12 q^{11} + 20 q^{13} + 4 q^{14} + 12 q^{16} - 8 q^{19} + 12 q^{23} - 12 q^{25} + 24 q^{31} + 4 q^{34} - 4 q^{35} - 4 q^{40} + 16 q^{41} + 12 q^{44} + 4 q^{49} - 20 q^{52} - 4 q^{56} + 8 q^{58} - 40 q^{59} - 12 q^{64} - 24 q^{70} + 8 q^{76} - 8 q^{77} + 8 q^{85} + 16 q^{89} + 24 q^{91} - 12 q^{92} + 44 q^{95} - 60 q^{97} + 16 q^{98}+O(q^{100}) \) 12 * q - 12 * q^4 + 4 * q^10 - 12 * q^11 + 20 * q^13 + 4 * q^14 + 12 * q^16 - 8 * q^19 + 12 * q^23 - 12 * q^25 + 24 * q^31 + 4 * q^34 - 4 * q^35 - 4 * q^40 + 16 * q^41 + 12 * q^44 + 4 * q^49 - 20 * q^52 - 4 * q^56 + 8 * q^58 - 40 * q^59 - 12 * q^64 - 24 * q^70 + 8 * q^76 - 8 * q^77 + 8 * q^85 + 16 * q^89 + 24 * q^91 - 12 * q^92 + 44 * q^95 - 60 * q^97 + 16 * q^98

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