LMFDB - Embedded newform 3234.2.e.b.2155.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3234,2,Mod(2155,3234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3234, 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("3234.2155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3234.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:	$25.8236200137$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 $ x^16 - 8x^15 + 74x^14 - 378x^13 + 1878x^12 - 6718x^11 + 22086x^10 - 56904x^9 + 130215x^8 - 239606x^7 + 378750x^6 - 477124x^5 + 493030x^4 - 386266x^3 + 223844x^2 - 82874*x + 13417
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 462)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2155.4
Root			$0.500000 - 1.56688i$ of defining polynomial
Character	$\chi$	$=$	3234.2155
Dual form			3234.2.e.b.2155.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +0.700858i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +0.700858i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +0.700858 q^{10} +(0.176300 - 3.31194i) q^{11} -1.00000i q^{12} +7.03562 q^{13} -0.700858 q^{15} +1.00000 q^{16} -0.617785 q^{17} +1.00000i q^{18} +0.783393 q^{19} -0.700858i q^{20} +(-3.31194 - 0.176300i) q^{22} -5.27184 q^{23} -1.00000 q^{24} +4.50880 q^{25} -7.03562i q^{26} -1.00000i q^{27} +2.09176i q^{29} +0.700858i q^{30} -6.17793i q^{31} -1.00000i q^{32} +(3.31194 + 0.176300i) q^{33} +0.617785i q^{34} +1.00000 q^{36} -3.99419 q^{37} -0.783393i q^{38} +7.03562i q^{39} -0.700858 q^{40} -5.85343 q^{41} -3.62441i q^{43} +(-0.176300 + 3.31194i) q^{44} -0.700858i q^{45} +5.27184i q^{46} +2.34976i q^{47} +1.00000i q^{48} -4.50880i q^{50} -0.617785i q^{51} -7.03562 q^{52} +7.90136 q^{53} -1.00000 q^{54} +(2.32120 + 0.123562i) q^{55} +0.783393i q^{57} +2.09176 q^{58} -3.76387i q^{59} +0.700858 q^{60} +8.36572 q^{61} -6.17793 q^{62} -1.00000 q^{64} +4.93097i q^{65} +(0.176300 - 3.31194i) q^{66} +2.14081 q^{67} +0.617785 q^{68} -5.27184i q^{69} -4.48503 q^{71} -1.00000i q^{72} +5.28943 q^{73} +3.99419i q^{74} +4.50880i q^{75} -0.783393 q^{76} +7.03562 q^{78} +4.33957i q^{79} +0.700858i q^{80} +1.00000 q^{81} +5.85343i q^{82} -4.03988 q^{83} -0.432980i q^{85} -3.62441 q^{86} -2.09176 q^{87} +(3.31194 + 0.176300i) q^{88} -16.2115i q^{89} -0.700858 q^{90} +5.27184 q^{92} +6.17793 q^{93} +2.34976 q^{94} +0.549047i q^{95} +1.00000 q^{96} -10.4926i q^{97} +(-0.176300 + 3.31194i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 16 q^{6} - 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 + 16 * q^6 - 16 * q^9	$ 16 q - 16 q^{4} + 16 q^{6} - 16 q^{9} + 4 q^{10} + 8 q^{11} - 4 q^{15} + 16 q^{16} - 20 q^{19} + 2 q^{22} + 8 q^{23} - 16 q^{24} - 20 q^{25} - 2 q^{33} + 16 q^{36} - 28 q^{37} - 4 q^{40} - 32 q^{41} - 8 q^{44} - 16 q^{54} + 14 q^{55} + 4 q^{60} + 56 q^{61} + 8 q^{62} - 16 q^{64} + 8 q^{66} + 32 q^{67} - 56 q^{71} - 88 q^{73} + 20 q^{76} + 16 q^{81} - 8 q^{83} + 24 q^{86} - 2 q^{88} - 4 q^{90} - 8 q^{92} - 8 q^{93} + 28 q^{94} + 16 q^{96} - 8 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 + 16 * q^6 - 16 * q^9 + 4 * q^10 + 8 * q^11 - 4 * q^15 + 16 * q^16 - 20 * q^19 + 2 * q^22 + 8 * q^23 - 16 * q^24 - 20 * q^25 - 2 * q^33 + 16 * q^36 - 28 * q^37 - 4 * q^40 - 32 * q^41 - 8 * q^44 - 16 * q^54 + 14 * q^55 + 4 * q^60 + 56 * q^61 + 8 * q^62 - 16 * q^64 + 8 * q^66 + 32 * q^67 - 56 * q^71 - 88 * q^73 + 20 * q^76 + 16 * q^81 - 8 * q^83 + 24 * q^86 - 2 * q^88 - 4 * q^90 - 8 * q^92 - 8 * q^93 + 28 * q^94 + 16 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times$.

$n$	$199$	$1079$	$2059$
$\chi(n)$	$-1$	$1$	$-1$

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
$5$			0.700858i			0.313433i	0.987644	+	0.156717i	$0.0500909\pi$
$5$			0.700858i			0.313433i	−0.987644	+	0.156717i	$0.949909\pi$
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	0.700858			0.221631
$11$	0.176300	−	3.31194i	0.0531566	−	0.998586i
$11$	0.176300	−	3.31194i	0.0531566	−	0.998586i
$12$		−	1.00000i		−	0.288675i
$13$	7.03562			1.95133			0.975665	−	0.219267i	$-0.0703667\pi$
$13$	7.03562			1.95133			0.975665	+	0.219267i	$0.0703667\pi$
$14$		0			0
$15$	−0.700858			−0.180961
$16$	1.00000			0.250000
$17$	−0.617785			−0.149835			−0.0749175	−	0.997190i	$-0.523869\pi$
$17$	−0.617785			−0.149835			−0.0749175	+	0.997190i	$0.523869\pi$
$18$			1.00000i			0.235702i
$19$	0.783393			0.179723			0.0898613	−	0.995954i	$-0.471358\pi$
$19$	0.783393			0.179723			0.0898613	+	0.995954i	$0.471358\pi$
$20$		−	0.700858i		−	0.156717i
$21$		0			0
$22$	−3.31194	−	0.176300i	−0.706107	−	0.0375874i
$23$	−5.27184			−1.09925			−0.549627	−	0.835410i	$-0.685230\pi$
$23$	−5.27184			−1.09925			−0.549627	+	0.835410i	$0.685230\pi$
$24$	−1.00000			−0.204124
$25$	4.50880			0.901760
$26$		−	7.03562i		−	1.37980i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$			2.09176i			0.388431i	0.980959	+	0.194215i	$0.0622161\pi$
$29$			2.09176i			0.388431i	−0.980959	+	0.194215i	$0.937784\pi$
$30$			0.700858i			0.127959i
$31$		−	6.17793i		−	1.10959i	−0.831988	−	0.554794i	$-0.812797\pi$
$31$		−	6.17793i		−	1.10959i	0.831988	−	0.554794i	$-0.187203\pi$
$32$		−	1.00000i		−	0.176777i
$33$	3.31194	+	0.176300i	0.576534	+	0.0306900i
$34$			0.617785i			0.105949i
$35$		0			0
$36$	1.00000			0.166667
$37$	−3.99419			−0.656640			−0.328320	−	0.944567i	$-0.606482\pi$
$37$	−3.99419			−0.656640			−0.328320	+	0.944567i	$0.606482\pi$
$38$		−	0.783393i		−	0.127083i
$39$			7.03562i			1.12660i
$40$	−0.700858			−0.110815
$41$	−5.85343			−0.914152			−0.457076	−	0.889428i	$-0.651103\pi$
$41$	−5.85343			−0.914152			−0.457076	+	0.889428i	$0.651103\pi$
$42$		0			0
$43$		−	3.62441i		−	0.552717i	−0.961055	−	0.276359i	$-0.910872\pi$
$43$		−	3.62441i		−	0.552717i	0.961055	−	0.276359i	$-0.0891277\pi$
$44$	−0.176300	+	3.31194i	−0.0265783	+	0.499293i
$45$		−	0.700858i		−	0.104478i
$46$			5.27184i			0.777290i
$47$			2.34976i			0.342747i	0.985206	+	0.171374i	$0.0548205\pi$
$47$			2.34976i			0.342747i	−0.985206	+	0.171374i	$0.945179\pi$
$48$			1.00000i			0.144338i
$49$		0			0
$50$		−	4.50880i		−	0.637640i
$51$		−	0.617785i		−	0.0865072i
$52$	−7.03562			−0.975665
$53$	7.90136			1.08534			0.542668	−	0.839947i	$-0.317414\pi$
$53$	7.90136			1.08534			0.542668	+	0.839947i	$0.317414\pi$
$54$	−1.00000			−0.136083
$55$	2.32120	+	0.123562i	0.312990	+	0.0166610i
$56$		0			0
$57$			0.783393i			0.103763i
$58$	2.09176			0.274662
$59$		−	3.76387i		−	0.490014i	−0.969521	−	0.245007i	$-0.921210\pi$
$59$		−	3.76387i		−	0.490014i	0.969521	−	0.245007i	$-0.0787903\pi$
$60$	0.700858			0.0904803
$61$	8.36572			1.07112			0.535560	−	0.844497i	$-0.320100\pi$
$61$	8.36572			1.07112			0.535560	+	0.844497i	$0.320100\pi$
$62$	−6.17793			−0.784597
$63$		0			0
$64$	−1.00000			−0.125000
$65$			4.93097i			0.611611i
$66$	0.176300	−	3.31194i	0.0217011	−	0.407671i
$67$	2.14081			0.261541			0.130771	−	0.991413i	$-0.458255\pi$
$67$	2.14081			0.261541			0.130771	+	0.991413i	$0.458255\pi$
$68$	0.617785			0.0749175
$69$		−	5.27184i		−	0.634655i
$70$		0			0
$71$	−4.48503			−0.532275			−0.266138	−	0.963935i	$-0.585748\pi$
$71$	−4.48503			−0.532275			−0.266138	+	0.963935i	$0.585748\pi$
$72$		−	1.00000i		−	0.117851i
$73$	5.28943			0.619081			0.309540	−	0.950886i	$-0.399825\pi$
$73$	5.28943			0.619081			0.309540	+	0.950886i	$0.399825\pi$
$74$			3.99419i			0.464315i
$75$			4.50880i			0.520631i
$76$	−0.783393			−0.0898613
$77$		0			0
$78$	7.03562			0.796627
$79$			4.33957i			0.488240i	0.969745	+	0.244120i	$0.0784991\pi$
$79$			4.33957i			0.488240i	−0.969745	+	0.244120i	$0.921501\pi$
$80$			0.700858i			0.0783583i
$81$	1.00000			0.111111
$82$			5.85343i			0.646403i
$83$	−4.03988			−0.443435			−0.221717	−	0.975111i	$-0.571166\pi$
$83$	−4.03988			−0.443435			−0.221717	+	0.975111i	$0.571166\pi$
$84$		0			0
$85$		−	0.432980i		−	0.0469632i
$86$	−3.62441			−0.390830
$87$	−2.09176			−0.224261
$88$	3.31194	+	0.176300i	0.353054	+	0.0187937i
$89$		−	16.2115i		−	1.71841i	−0.511628	−	0.859207i	$-0.670957\pi$
$89$		−	16.2115i		−	1.71841i	0.511628	−	0.859207i	$-0.329043\pi$
$90$	−0.700858			−0.0738769
$91$		0			0
$92$	5.27184			0.549627
$93$	6.17793			0.640621
$94$	2.34976			0.242359
$95$			0.549047i			0.0563310i
$96$	1.00000			0.102062
$97$		−	10.4926i		−	1.06536i	−0.846317	−	0.532680i	$-0.821185\pi$
$97$		−	10.4926i		−	1.06536i	0.846317	−	0.532680i	$-0.178815\pi$
$98$		0			0
$99$	−0.176300	+	3.31194i	−0.0177189	+	0.332862i
$100$	−4.50880			−0.450880
$101$	14.9947			1.49203			0.746016	−	0.665928i	$-0.231964\pi$
$101$	14.9947			1.49203			0.746016	+	0.665928i	$0.231964\pi$
$102$	−0.617785			−0.0611698
$103$		−	14.3517i		−	1.41411i	−0.707156	−	0.707057i	$-0.750022\pi$
$103$		−	14.3517i		−	1.41411i	0.707156	−	0.707057i	$-0.249978\pi$
$104$			7.03562i			0.689899i
$105$		0			0
$106$		−	7.90136i		−	0.767448i
$107$			11.4671i			1.10857i	0.832328	+	0.554284i	$0.187008\pi$
$107$			11.4671i			1.10857i	−0.832328	+	0.554284i	$0.812992\pi$
$108$			1.00000i			0.0962250i
$109$			1.45285i			0.139158i	0.997576	+	0.0695788i	$0.0221655\pi$
$109$			1.45285i			0.139158i	−0.997576	+	0.0695788i	$0.977834\pi$
$110$	0.123562	−	2.32120i	0.0117811	−	0.221317i
$111$		−	3.99419i		−	0.379111i
$112$		0			0
$113$	12.0074			1.12956			0.564781	−	0.825241i	$-0.308961\pi$
$113$	12.0074			1.12956			0.564781	+	0.825241i	$0.308961\pi$
$114$	0.783393			0.0733715
$115$		−	3.69481i		−	0.344543i
$116$		−	2.09176i		−	0.194215i
$117$	−7.03562			−0.650443
$118$	−3.76387			−0.346492
$119$		0			0
$120$		−	0.700858i		−	0.0639793i
$121$	−10.9378	−	1.16779i	−0.994349	−	0.106163i
$122$		−	8.36572i		−	0.757397i
$123$		−	5.85343i		−	0.527786i
$124$			6.17793i			0.554794i
$125$			6.66432i			0.596074i
$126$		0			0
$127$		−	3.43188i		−	0.304530i	−0.988340	−	0.152265i	$-0.951343\pi$
$127$		−	3.43188i		−	0.304530i	0.988340	−	0.152265i	$-0.0486568\pi$
$128$			1.00000i			0.0883883i
$129$	3.62441			0.319111
$130$	4.93097			0.432475
$131$	14.6058			1.27611			0.638056	−	0.769990i	$-0.279739\pi$
$131$	14.6058			1.27611			0.638056	+	0.769990i	$0.279739\pi$
$132$	−3.31194	−	0.176300i	−0.288267	−	0.0153450i
$133$		0			0
$134$		−	2.14081i		−	0.184938i
$135$	0.700858			0.0603202
$136$		−	0.617785i		−	0.0529746i
$137$	16.7161			1.42815			0.714075	−	0.700069i	$-0.246847\pi$
$137$	16.7161			1.42815			0.714075	+	0.700069i	$0.246847\pi$
$138$	−5.27184			−0.448769
$139$	12.9399			1.09755			0.548775	−	0.835970i	$-0.315094\pi$
$139$	12.9399			1.09755			0.548775	+	0.835970i	$0.315094\pi$
$140$		0			0
$141$	−2.34976			−0.197885
$142$			4.48503i			0.376375i
$143$	1.24038	−	23.3015i	0.103726	−	1.94857i
$144$	−1.00000			−0.0833333
$145$	−1.46603			−0.121747
$146$		−	5.28943i		−	0.437756i
$147$		0			0
$148$	3.99419			0.328320
$149$			9.72861i			0.796999i	0.917169	+	0.398500i	$0.130469\pi$
$149$			9.72861i			0.796999i	−0.917169	+	0.398500i	$0.869531\pi$
$150$	4.50880			0.368142
$151$		−	19.7877i		−	1.61030i	−0.593069	−	0.805151i	$-0.702084\pi$
$151$		−	19.7877i		−	1.61030i	0.593069	−	0.805151i	$-0.297916\pi$
$152$			0.783393i			0.0635416i
$153$	0.617785			0.0499450
$154$		0			0
$155$	4.32985			0.347782
$156$		−	7.03562i		−	0.563300i
$157$			12.0105i			0.958539i	0.877668	+	0.479269i	$0.159098\pi$
$157$			12.0105i			0.958539i	−0.877668	+	0.479269i	$0.840902\pi$
$158$	4.33957			0.345238
$159$			7.90136i			0.626619i
$160$	0.700858			0.0554077
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	22.3960			1.75419			0.877094	−	0.480319i	$-0.159479\pi$
$163$	22.3960			1.75419			0.877094	+	0.480319i	$0.159479\pi$
$164$	5.85343			0.457076
$165$	−0.123562	+	2.32120i	−0.00961926	+	0.180705i
$166$			4.03988i			0.313556i
$167$	17.9924			1.39229			0.696145	−	0.717901i	$-0.254897\pi$
$167$	17.9924			1.39229			0.696145	+	0.717901i	$0.254897\pi$
$168$		0			0
$169$	36.4999			2.80769
$170$	−0.432980			−0.0332080
$171$	−0.783393			−0.0599075
$172$			3.62441i			0.276359i
$173$	−0.378382			−0.0287679			−0.0143839	−	0.999897i	$-0.504579\pi$
$173$	−0.378382			−0.0287679			−0.0143839	+	0.999897i	$0.504579\pi$
$174$			2.09176i			0.158576i
$175$		0			0
$176$	0.176300	−	3.31194i	0.0132891	−	0.249647i
$177$	3.76387			0.282910
$178$	−16.2115			−1.21510
$179$	−4.31093			−0.322214			−0.161107	−	0.986937i	$-0.551506\pi$
$179$	−4.31093			−0.322214			−0.161107	+	0.986937i	$0.551506\pi$
$180$			0.700858i			0.0522389i
$181$		−	6.96276i		−	0.517538i	−0.965939	−	0.258769i	$-0.916683\pi$
$181$		−	6.96276i		−	0.517538i	0.965939	−	0.258769i	$-0.0833169\pi$
$182$		0			0
$183$			8.36572i			0.618412i
$184$		−	5.27184i		−	0.388645i
$185$		−	2.79936i		−	0.205813i
$186$		−	6.17793i		−	0.452987i
$187$	−0.108916	+	2.04606i	−0.00796471	+	0.149623i
$188$		−	2.34976i		−	0.171374i
$189$		0			0
$190$	0.549047			0.0398321
$191$	−18.5590			−1.34288			−0.671440	−	0.741059i	$-0.734324\pi$
$191$	−18.5590			−1.34288			−0.671440	+	0.741059i	$0.734324\pi$
$192$		−	1.00000i		−	0.0721688i
$193$			17.5212i			1.26120i	0.776107	+	0.630601i	$0.217192\pi$
$193$			17.5212i			1.26120i	−0.776107	+	0.630601i	$0.782808\pi$
$194$	−10.4926			−0.753323
$195$	−4.93097			−0.353114
$196$		0			0
$197$			18.8663i			1.34417i	0.740474	+	0.672086i	$0.234601\pi$
$197$			18.8663i			1.34417i	−0.740474	+	0.672086i	$0.765399\pi$
$198$	3.31194	+	0.176300i	0.235369	+	0.0125291i
$199$		−	13.5324i		−	0.959283i	−0.877464	−	0.479642i	$-0.840767\pi$
$199$		−	13.5324i		−	0.959283i	0.877464	−	0.479642i	$-0.159233\pi$
$200$			4.50880i			0.318820i
$201$			2.14081i			0.151001i
$202$		−	14.9947i		−	1.05503i
$203$		0			0
$204$			0.617785i			0.0432536i
$205$		−	4.10242i		−	0.286525i
$206$	−14.3517			−0.999930
$207$	5.27184			0.366418
$208$	7.03562			0.487832
$209$	0.138113	−	2.59455i	0.00955344	−	0.179469i
$210$		0			0
$211$		−	4.94368i		−	0.340337i	−0.985415	−	0.170168i	$-0.945569\pi$
$211$		−	4.94368i		−	0.340337i	0.985415	−	0.170168i	$-0.0544312\pi$
$212$	−7.90136			−0.542668
$213$		−	4.48503i		−	0.307309i
$214$	11.4671			0.783876
$215$	2.54020			0.173240
$216$	1.00000			0.0680414
$217$		0			0
$218$	1.45285			0.0983993
$219$			5.28943i			0.357426i
$220$	−2.32120	−	0.123562i	−0.156495	−	0.00833052i
$221$	−4.34650			−0.292377
$222$	−3.99419			−0.268072
$223$			22.9194i			1.53480i	0.641169	+	0.767400i	$0.278450\pi$
$223$			22.9194i			1.53480i	−0.641169	+	0.767400i	$0.721550\pi$
$224$		0			0
$225$	−4.50880			−0.300587
$226$		−	12.0074i		−	0.798721i
$227$	−24.2282			−1.60808			−0.804042	−	0.594573i	$-0.797321\pi$
$227$	−24.2282			−1.60808			−0.804042	+	0.594573i	$0.797321\pi$
$228$		−	0.783393i		−	0.0518815i
$229$			13.3778i			0.884031i	0.897007	+	0.442016i	$0.145736\pi$
$229$			13.3778i			0.884031i	−0.897007	+	0.442016i	$0.854264\pi$
$230$	−3.69481			−0.243628
$231$		0			0
$232$	−2.09176			−0.137331
$233$		−	27.9050i		−	1.82811i	−0.405585	−	0.914057i	$-0.632932\pi$
$233$		−	27.9050i		−	1.82811i	0.405585	−	0.914057i	$-0.367068\pi$
$234$			7.03562i			0.459933i
$235$	−1.64685			−0.107428
$236$			3.76387i			0.245007i
$237$	−4.33957			−0.281886
$238$		0			0
$239$		−	9.27514i		−	0.599959i	−0.953946	−	0.299979i	$-0.903020\pi$
$239$		−	9.27514i		−	0.599959i	0.953946	−	0.299979i	$-0.0969798\pi$
$240$	−0.700858			−0.0452402
$241$	−19.0970			−1.23015			−0.615074	−	0.788470i	$-0.710874\pi$
$241$	−19.0970			−1.23015			−0.615074	+	0.788470i	$0.710874\pi$
$242$	−1.16779	+	10.9378i	−0.0750685	+	0.703111i
$243$			1.00000i			0.0641500i
$244$	−8.36572			−0.535560
$245$		0			0
$246$	−5.85343			−0.373201
$247$	5.51165			0.350698
$248$	6.17793			0.392299
$249$		−	4.03988i		−	0.256017i
$250$	6.66432			0.421488
$251$			12.1328i			0.765818i	0.923786	+	0.382909i	$0.125078\pi$
$251$			12.1328i			0.765818i	−0.923786	+	0.382909i	$0.874922\pi$
$252$		0			0
$253$	−0.929428	+	17.4600i	−0.0584326	+	1.09770i
$254$	−3.43188			−0.215335
$255$	0.432980			0.0271142
$256$	1.00000			0.0625000
$257$		−	19.9471i		−	1.24427i	−0.782912	−	0.622133i	$-0.786266\pi$
$257$		−	19.9471i		−	1.24427i	0.782912	−	0.622133i	$-0.213734\pi$
$258$		−	3.62441i		−	0.225646i
$259$		0			0
$260$		−	4.93097i		−	0.305806i
$261$		−	2.09176i		−	0.129477i
$262$		−	14.6058i		−	0.902347i
$263$			16.7867i			1.03511i	0.855649	+	0.517556i	$0.173158\pi$
$263$			16.7867i			1.03511i	−0.855649	+	0.517556i	$0.826842\pi$
$264$	−0.176300	+	3.31194i	−0.0108505	+	0.203836i
$265$			5.53773i			0.340180i
$266$		0			0
$267$	16.2115			0.992127
$268$	−2.14081			−0.130771
$269$		−	19.4953i		−	1.18865i	−0.804224	−	0.594326i	$-0.797419\pi$
$269$		−	19.4953i		−	1.18865i	0.804224	−	0.594326i	$-0.202581\pi$
$270$		−	0.700858i		−	0.0426528i
$271$	10.6826			0.648922			0.324461	−	0.945899i	$-0.394817\pi$
$271$	10.6826			0.648922			0.324461	+	0.945899i	$0.394817\pi$
$272$	−0.617785			−0.0374587
$273$		0			0
$274$		−	16.7161i		−	1.00986i
$275$	0.794903	−	14.9329i	0.0479345	−	0.900485i
$276$			5.27184i			0.317327i
$277$		−	30.7880i		−	1.84987i	−0.380127	−	0.924934i	$-0.624120\pi$
$277$		−	30.7880i		−	1.84987i	0.380127	−	0.924934i	$-0.375880\pi$
$278$		−	12.9399i		−	0.776086i
$279$			6.17793i			0.369863i
$280$		0			0
$281$			21.3381i			1.27292i	0.771308	+	0.636462i	$0.219603\pi$
$281$			21.3381i			1.27292i	−0.771308	+	0.636462i	$0.780397\pi$
$282$			2.34976i			0.139926i
$283$	2.52307			0.149981			0.0749905	−	0.997184i	$-0.476107\pi$
$283$	2.52307			0.149981			0.0749905	+	0.997184i	$0.476107\pi$
$284$	4.48503			0.266138
$285$	−0.549047			−0.0325227
$286$	−23.3015	−	1.24038i	−1.37785	−	0.0733454i
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	−16.6183			−0.977549
$290$			1.46603i			0.0860882i
$291$	10.4926			0.615086
$292$	−5.28943			−0.309540
$293$	5.71831			0.334067			0.167034	−	0.985951i	$-0.446581\pi$
$293$	5.71831			0.334067			0.167034	+	0.985951i	$0.446581\pi$
$294$		0			0
$295$	2.63794			0.153587
$296$		−	3.99419i		−	0.232157i
$297$	−3.31194	−	0.176300i	−0.192178	−	0.0102300i
$298$	9.72861			0.563563
$299$	−37.0906			−2.14501
$300$		−	4.50880i		−	0.260316i
$301$		0			0
$302$	−19.7877			−1.13866
$303$			14.9947i			0.861425i
$304$	0.783393			0.0449307
$305$			5.86318i			0.335725i
$306$		−	0.617785i		−	0.0353164i
$307$	20.7839			1.18620			0.593099	−	0.805130i	$-0.297904\pi$
$307$	20.7839			1.18620			0.593099	+	0.805130i	$0.297904\pi$
$308$		0			0
$309$	14.3517			0.816439
$310$		−	4.32985i		−	0.245919i
$311$		−	7.36751i		−	0.417773i	−0.977940	−	0.208887i	$-0.933016\pi$
$311$		−	7.36751i		−	0.417773i	0.977940	−	0.208887i	$-0.0669840\pi$
$312$	−7.03562			−0.398313
$313$			7.35395i			0.415670i	0.978164	+	0.207835i	$0.0666417\pi$
$313$			7.35395i			0.415670i	−0.978164	+	0.207835i	$0.933358\pi$
$314$	12.0105			0.677789
$315$		0			0
$316$		−	4.33957i		−	0.244120i
$317$	−14.7806			−0.830161			−0.415080	−	0.909785i	$-0.636247\pi$
$317$	−14.7806			−0.830161			−0.415080	+	0.909785i	$0.636247\pi$
$318$	7.90136			0.443087
$319$	6.92779	+	0.368779i	0.387882	+	0.0206477i
$320$		−	0.700858i		−	0.0391791i
$321$	−11.4671			−0.640032
$322$		0			0
$323$	−0.483969			−0.0269287
$324$	−1.00000			−0.0555556
$325$	31.7222			1.75963
$326$		−	22.3960i		−	1.24040i
$327$	−1.45285			−0.0803427
$328$		−	5.85343i		−	0.323202i
$329$		0			0
$330$	2.32120	+	0.123562i	0.127778	+	0.00680184i
$331$	27.2898			1.49998			0.749991	−	0.661448i	$-0.230058\pi$
$331$	27.2898			1.49998			0.749991	+	0.661448i	$0.230058\pi$
$332$	4.03988			0.221717
$333$	3.99419			0.218880
$334$		−	17.9924i		−	0.984498i
$335$			1.50040i			0.0819757i
$336$		0			0
$337$		−	13.0929i		−	0.713215i	−0.934254	−	0.356607i	$-0.883933\pi$
$337$		−	13.0929i		−	0.713215i	0.934254	−	0.356607i	$-0.116067\pi$
$338$		−	36.4999i		−	1.98533i
$339$			12.0074i			0.652153i
$340$			0.432980i			0.0234816i
$341$	−20.4609	−	1.08917i	−1.10802	−	0.0589819i
$342$			0.783393i			0.0423610i
$343$		0			0
$344$	3.62441			0.195415
$345$	3.69481			0.198922
$346$			0.378382i			0.0203420i
$347$		−	11.3473i		−	0.609157i	−0.952487	−	0.304578i	$-0.901484\pi$
$347$		−	11.3473i		−	0.609157i	0.952487	−	0.304578i	$-0.0985156\pi$
$348$	2.09176			0.112130
$349$	12.4060			0.664076			0.332038	−	0.943266i	$-0.392264\pi$
$349$	12.4060			0.664076			0.332038	+	0.943266i	$0.392264\pi$
$350$		0			0
$351$		−	7.03562i		−	0.375534i
$352$	−3.31194	−	0.176300i	−0.176527	−	0.00939685i
$353$			6.82398i			0.363204i	0.983372	+	0.181602i	$0.0581282\pi$
$353$			6.82398i			0.363204i	−0.983372	+	0.181602i	$0.941872\pi$
$354$		−	3.76387i		−	0.200047i
$355$		−	3.14337i		−	0.166833i
$356$			16.2115i			0.859207i
$357$		0			0
$358$			4.31093i			0.227840i
$359$			20.4315i			1.07833i	0.842200	+	0.539166i	$0.181260\pi$
$359$			20.4315i			1.07833i	−0.842200	+	0.539166i	$0.818740\pi$
$360$	0.700858			0.0369384
$361$	−18.3863			−0.967700
$362$	−6.96276			−0.365955
$363$	1.16779	−	10.9378i	0.0612932	−	0.574088i
$364$		0			0
$365$			3.70714i			0.194040i
$366$	8.36572			0.437283
$367$			20.1568i			1.05218i	0.850430	+	0.526088i	$0.176342\pi$
$367$			20.1568i			1.05218i	−0.850430	+	0.526088i	$0.823658\pi$
$368$	−5.27184			−0.274814
$369$	5.85343			0.304717
$370$	−2.79936			−0.145532
$371$		0			0
$372$	−6.17793			−0.320311
$373$			8.33854i			0.431753i	0.976421	+	0.215877i	$0.0692609\pi$
$373$			8.33854i			0.431753i	−0.976421	+	0.215877i	$0.930739\pi$
$374$	2.04606	+	0.108916i	0.105799	+	0.00563190i
$375$	−6.66432			−0.344144
$376$	−2.34976			−0.121179
$377$			14.7169i			0.757956i
$378$		0			0
$379$	−12.2093			−0.627151			−0.313575	−	0.949563i	$-0.601527\pi$
$379$	−12.2093			−0.627151			−0.313575	+	0.949563i	$0.601527\pi$
$380$		−	0.549047i		−	0.0281655i
$381$	3.43188			0.175821
$382$			18.5590i			0.949560i
$383$		−	18.6517i		−	0.953057i	−0.879159	−	0.476529i	$-0.841895\pi$
$383$		−	18.6517i		−	0.953057i	0.879159	−	0.476529i	$-0.158105\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	17.5212			0.891805
$387$			3.62441i			0.184239i
$388$			10.4926i			0.532680i
$389$	−9.51444			−0.482401			−0.241201	−	0.970475i	$-0.577541\pi$
$389$	−9.51444			−0.482401			−0.241201	+	0.970475i	$0.577541\pi$
$390$			4.93097i			0.249689i
$391$	3.25686			0.164707
$392$		0			0
$393$			14.6058i			0.736764i
$394$	18.8663			0.950472
$395$	−3.04142			−0.153031
$396$	0.176300	−	3.31194i	0.00885943	−	0.166431i
$397$			34.0696i			1.70990i	0.518707	+	0.854952i	$0.326414\pi$
$397$			34.0696i			1.70990i	−0.518707	+	0.854952i	$0.673586\pi$
$398$	−13.5324			−0.678316
$399$		0			0
$400$	4.50880			0.225440
$401$	−29.6358			−1.47994			−0.739969	−	0.672641i	$-0.765160\pi$
$401$	−29.6358			−1.47994			−0.739969	+	0.672641i	$0.765160\pi$
$402$	2.14081			0.106774
$403$		−	43.4655i		−	2.16517i
$404$	−14.9947			−0.746016
$405$			0.700858i			0.0348259i
$406$		0			0
$407$	−0.704177	+	13.2285i	−0.0349048	+	0.655712i
$408$	0.617785			0.0305849
$409$	27.3288			1.35132			0.675662	−	0.737212i	$-0.263858\pi$
$409$	27.3288			1.35132			0.675662	+	0.737212i	$0.263858\pi$
$410$	−4.10242			−0.202604
$411$			16.7161i			0.824543i
$412$			14.3517i			0.707057i
$413$		0			0
$414$		−	5.27184i		−	0.259097i
$415$		−	2.83138i		−	0.138987i
$416$		−	7.03562i		−	0.344950i
$417$			12.9399i			0.633671i
$418$	−2.59455	−	0.138113i	−0.126903	−	0.00675531i
$419$		−	25.6972i		−	1.25539i	−0.778459	−	0.627696i	$-0.783998\pi$
$419$		−	25.6972i		−	1.25539i	0.778459	−	0.627696i	$-0.216002\pi$
$420$		0			0
$421$	−36.9246			−1.79959			−0.899797	−	0.436309i	$-0.856285\pi$
$421$	−36.9246			−1.79959			−0.899797	+	0.436309i	$0.856285\pi$
$422$	−4.94368			−0.240654
$423$		−	2.34976i		−	0.114249i
$424$			7.90136i			0.383724i
$425$	−2.78547			−0.135115
$426$	−4.48503			−0.217300
$427$		0			0
$428$		−	11.4671i		−	0.554284i
$429$	23.3015	+	1.24038i	1.12501	+	0.0598863i
$430$		−	2.54020i		−	0.122499i
$431$		−	20.1287i		−	0.969566i	−0.874635	−	0.484783i	$-0.838899\pi$
$431$		−	20.1287i		−	0.969566i	0.874635	−	0.484783i	$-0.161101\pi$
$432$		−	1.00000i		−	0.0481125i
$433$		−	38.1992i		−	1.83574i	−0.396884	−	0.917869i	$-0.629908\pi$
$433$		−	38.1992i		−	1.83574i	0.396884	−	0.917869i	$-0.370092\pi$
$434$		0			0
$435$		−	1.46603i		−	0.0702907i
$436$		−	1.45285i		−	0.0695788i
$437$	−4.12992			−0.197561
$438$	5.28943			0.252739
$439$	7.32197			0.349459			0.174729	−	0.984616i	$-0.444095\pi$
$439$	7.32197			0.349459			0.174729	+	0.984616i	$0.444095\pi$
$440$	−0.123562	+	2.32120i	−0.00589057	+	0.110659i
$441$		0			0
$442$			4.34650i			0.206742i
$443$	−33.0248			−1.56905			−0.784527	−	0.620094i	$-0.787094\pi$
$443$	−33.0248			−1.56905			−0.784527	+	0.620094i	$0.787094\pi$
$444$			3.99419i			0.189556i
$445$	11.3619			0.538608
$446$	22.9194			1.08527
$447$	−9.72861			−0.460148
$448$		0			0
$449$	−22.5285			−1.06319			−0.531594	−	0.846999i	$-0.678407\pi$
$449$	−22.5285			−1.06319			−0.531594	+	0.846999i	$0.678407\pi$
$450$			4.50880i			0.212547i
$451$	−1.03196	+	19.3862i	−0.0485932	+	0.912859i
$452$	−12.0074			−0.564781
$453$	19.7877			0.929709
$454$			24.2282i			1.13709i
$455$		0			0
$456$	−0.783393			−0.0366857
$457$			33.1752i			1.55187i	0.630814	+	0.775934i	$0.282721\pi$
$457$			33.1752i			1.55187i	−0.630814	+	0.775934i	$0.717279\pi$
$458$	13.3778			0.625105
$459$			0.617785i			0.0288357i
$460$			3.69481i			0.172271i
$461$	7.42955			0.346029			0.173014	−	0.984919i	$-0.444649\pi$
$461$	7.42955			0.346029			0.173014	+	0.984919i	$0.444649\pi$
$462$		0			0
$463$	−15.7504			−0.731984			−0.365992	−	0.930618i	$-0.619270\pi$
$463$	−15.7504			−0.731984			−0.365992	+	0.930618i	$0.619270\pi$
$464$			2.09176i			0.0971077i
$465$			4.32985i			0.200792i
$466$	−27.9050			−1.29267
$467$		−	13.3731i		−	0.618835i	−0.950926	−	0.309418i	$-0.899866\pi$
$467$		−	13.3731i		−	0.618835i	0.950926	−	0.309418i	$-0.100134\pi$
$468$	7.03562			0.325222
$469$		0			0
$470$			1.64685i			0.0759633i
$471$	−12.0105			−0.553413
$472$	3.76387			0.173246
$473$	−12.0038	−	0.638985i	−0.551936	−	0.0293806i
$474$			4.33957i			0.199323i
$475$	3.53216			0.162067
$476$		0			0
$477$	−7.90136			−0.361779
$478$	−9.27514			−0.424235
$479$	−11.2610			−0.514528			−0.257264	−	0.966341i	$-0.582821\pi$
$479$	−11.2610			−0.514528			−0.257264	+	0.966341i	$0.582821\pi$
$480$			0.700858i			0.0319896i
$481$	−28.1016			−1.28132
$482$			19.0970i			0.869845i
$483$		0			0
$484$	10.9378	+	1.16779i	0.497174	+	0.0530814i
$485$	7.35380			0.333919
$486$	1.00000			0.0453609
$487$	2.66963			0.120972			0.0604862	−	0.998169i	$-0.480735\pi$
$487$	2.66963			0.120972			0.0604862	+	0.998169i	$0.480735\pi$
$488$			8.36572i			0.378698i
$489$			22.3960i			1.01278i
$490$		0			0
$491$			11.3063i			0.510245i	0.966909	+	0.255123i	$0.0821158\pi$
$491$			11.3063i			0.510245i	−0.966909	+	0.255123i	$0.917884\pi$
$492$			5.85343i			0.263893i
$493$		−	1.29226i		−	0.0582005i
$494$		−	5.51165i		−	0.247981i
$495$	−2.32120	−	0.123562i	−0.104330	−	0.00555368i
$496$		−	6.17793i		−	0.277397i
$497$		0			0
$498$	−4.03988			−0.181032
$499$	21.4400			0.959787			0.479894	−	0.877327i	$-0.340675\pi$
$499$	21.4400			0.959787			0.479894	+	0.877327i	$0.340675\pi$
$500$		−	6.66432i		−	0.298037i
$501$			17.9924i			0.803839i
$502$	12.1328			0.541515
$503$	−30.0822			−1.34130			−0.670649	−	0.741775i	$-0.733984\pi$
$503$	−30.0822			−1.34130			−0.670649	+	0.741775i	$0.733984\pi$
$504$		0			0
$505$			10.5092i			0.467652i
$506$	17.4600	+	0.929428i	0.776191	+	0.0413181i
$507$			36.4999i			1.62102i
$508$			3.43188i			0.152265i
$509$		−	13.4813i		−	0.597548i	−0.954324	−	0.298774i	$-0.903422\pi$
$509$		−	13.4813i		−	0.597548i	0.954324	−	0.298774i	$-0.0965776\pi$
$510$		−	0.432980i		−	0.0191727i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		−	0.783393i		−	0.0345876i
$514$	−19.9471			−0.879829
$515$	10.0585			0.443230
$516$	−3.62441			−0.159556
$517$	7.78224	+	0.414263i	0.342263	+	0.0182193i
$518$		0			0
$519$		−	0.378382i		−	0.0166091i
$520$	−4.93097			−0.216237
$521$		−	11.1268i		−	0.487473i	−0.969841	−	0.243737i	$-0.921627\pi$
$521$		−	11.1268i		−	0.487473i	0.969841	−	0.243737i	$-0.0783733\pi$
$522$	−2.09176			−0.0915540
$523$	14.9088			0.651916			0.325958	−	0.945384i	$-0.394313\pi$
$523$	14.9088			0.651916			0.325958	+	0.945384i	$0.394313\pi$
$524$	−14.6058			−0.638056
$525$		0			0
$526$	16.7867			0.731935
$527$			3.81663i			0.166255i
$528$	3.31194	+	0.176300i	0.144134	+	0.00767249i
$529$	4.79227			0.208360
$530$	5.53773			0.240544
$531$			3.76387i			0.163338i
$532$		0			0
$533$	−41.1825			−1.78381
$534$		−	16.2115i		−	0.701540i
$535$	−8.03682			−0.347462
$536$			2.14081i			0.0924688i
$537$		−	4.31093i		−	0.186030i
$538$	−19.4953			−0.840504
$539$		0			0
$540$	−0.700858			−0.0301601
$541$		−	26.5815i		−	1.14283i	−0.820663	−	0.571413i	$-0.806395\pi$
$541$		−	26.5815i		−	1.14283i	0.820663	−	0.571413i	$-0.193605\pi$
$542$		−	10.6826i		−	0.458857i
$543$	6.96276			0.298801
$544$			0.617785i			0.0264873i
$545$	−1.01824			−0.0436166
$546$		0			0
$547$		−	18.2285i		−	0.779393i	−0.920943	−	0.389696i	$-0.872580\pi$
$547$		−	18.2285i		−	0.779393i	0.920943	−	0.389696i	$-0.127420\pi$
$548$	−16.7161			−0.714075
$549$	−8.36572			−0.357040
$550$	−14.9329	−	0.794903i	−0.636739	−	0.0338948i
$551$			1.63867i			0.0698098i
$552$	5.27184			0.224384
$553$		0			0
$554$	−30.7880			−1.30805
$555$	2.79936			0.118826
$556$	−12.9399			−0.548775
$557$			31.4847i			1.33405i	0.745035	+	0.667025i	$0.232433\pi$
$557$			31.4847i			1.33405i	−0.745035	+	0.667025i	$0.767567\pi$
$558$	6.17793			0.261532
$559$		−	25.5000i		−	1.07853i
$560$		0			0
$561$	−2.04606	−	0.108916i	−0.0863849	−	0.00459843i
$562$	21.3381			0.900094
$563$	−21.9402			−0.924669			−0.462335	−	0.886705i	$-0.652988\pi$
$563$	−21.9402			−0.924669			−0.462335	+	0.886705i	$0.652988\pi$
$564$	2.34976			0.0989426
$565$			8.41549i			0.354042i
$566$		−	2.52307i		−	0.106053i
$567$		0			0
$568$		−	4.48503i		−	0.188188i
$569$			31.0614i			1.30216i	0.759009	+	0.651080i	$0.225684\pi$
$569$			31.0614i			1.30216i	−0.759009	+	0.651080i	$0.774316\pi$
$570$			0.549047i			0.0229970i
$571$			9.76821i			0.408787i	0.978889	+	0.204393i	$0.0655222\pi$
$571$			9.76821i			0.408787i	−0.978889	+	0.204393i	$0.934478\pi$
$572$	−1.24038	+	23.3015i	−0.0518630	+	0.974285i
$573$		−	18.5590i		−	0.775313i
$574$		0			0
$575$	−23.7697			−0.991263
$576$	1.00000			0.0416667
$577$			19.3888i			0.807168i	0.914943	+	0.403584i	$0.132236\pi$
$577$			19.3888i			0.807168i	−0.914943	+	0.403584i	$0.867764\pi$
$578$			16.6183i			0.691232i
$579$	−17.5212			−0.728156
$580$	1.46603			0.0608735
$581$		0			0
$582$		−	10.4926i		−	0.434931i
$583$	1.39301	−	26.1688i	0.0576928	−	1.08380i
$584$			5.28943i			0.218878i
$585$		−	4.93097i		−	0.203870i
$586$		−	5.71831i		−	0.236221i
$587$			14.0625i			0.580421i	0.956963	+	0.290210i	$0.0937253\pi$
$587$			14.0625i			0.580421i	−0.956963	+	0.290210i	$0.906275\pi$
$588$		0			0
$589$		−	4.83974i		−	0.199418i
$590$		−	2.63794i		−	0.108602i
$591$	−18.8663			−0.776058
$592$	−3.99419			−0.164160
$593$	38.1093			1.56496			0.782480	−	0.622676i	$-0.213954\pi$
$593$	38.1093			1.56496			0.782480	+	0.622676i	$0.213954\pi$
$594$	−0.176300	+	3.31194i	−0.00723370	+	0.135890i
$595$		0			0
$596$		−	9.72861i		−	0.398500i
$597$	13.5324			0.553842
$598$			37.0906i			1.51675i
$599$	−24.5324			−1.00237			−0.501183	−	0.865342i	$-0.667101\pi$
$599$	−24.5324			−1.00237			−0.501183	+	0.865342i	$0.667101\pi$
$600$	−4.50880			−0.184071
$601$	3.08091			0.125673			0.0628365	−	0.998024i	$-0.479985\pi$
$601$	3.08091			0.125673			0.0628365	+	0.998024i	$0.479985\pi$
$602$		0			0
$603$	−2.14081			−0.0871804
$604$			19.7877i			0.805151i
$605$	0.818456	−	7.66587i	0.0332750	−	0.311662i
$606$	14.9947			0.609120
$607$	−40.7678			−1.65471			−0.827356	−	0.561677i	$-0.810156\pi$
$607$	−40.7678			−1.65471			−0.827356	+	0.561677i	$0.810156\pi$
$608$		−	0.783393i		−	0.0317708i
$609$		0			0
$610$	5.86318			0.237393
$611$			16.5320i			0.668813i
$612$	−0.617785			−0.0249725
$613$			8.95511i			0.361693i	0.983511	+	0.180847i	$0.0578838\pi$
$613$			8.95511i			0.361693i	−0.983511	+	0.180847i	$0.942116\pi$
$614$		−	20.7839i		−	0.838768i
$615$	4.10242			0.165426
$616$		0			0
$617$	19.1914			0.772618			0.386309	−	0.922369i	$-0.373750\pi$
$617$	19.1914			0.772618			0.386309	+	0.922369i	$0.373750\pi$
$618$		−	14.3517i		−	0.577310i
$619$			3.37081i			0.135484i	0.997703	+	0.0677422i	$0.0215795\pi$
$619$			3.37081i			0.135484i	−0.997703	+	0.0677422i	$0.978420\pi$
$620$	−4.32985			−0.173891
$621$			5.27184i			0.211552i
$622$	−7.36751			−0.295410
$623$		0			0
$624$			7.03562i			0.281650i
$625$	17.8733			0.714930
$626$	7.35395			0.293923
$627$	2.59455	+	0.138113i	0.103616	+	0.00551568i
$628$		−	12.0105i		−	0.479269i
$629$	2.46755			0.0983876
$630$		0			0
$631$	33.1910			1.32131			0.660657	−	0.750688i	$-0.270278\pi$
$631$	33.1910			1.32131			0.660657	+	0.750688i	$0.270278\pi$
$632$	−4.33957			−0.172619
$633$	4.94368			0.196494
$634$			14.7806i			0.587012i
$635$	2.40526			0.0954499
$636$		−	7.90136i		−	0.313309i
$637$		0			0
$638$	0.368779	−	6.92779i	0.0146001	−	0.274274i
$639$	4.48503			0.177425
$640$	−0.700858			−0.0277038
$641$	−34.4611			−1.36113			−0.680566	−	0.732686i	$-0.738266\pi$
$641$	−34.4611			−1.36113			−0.680566	+	0.732686i	$0.738266\pi$
$642$			11.4671i			0.452571i
$643$			2.69205i			0.106164i	0.998590	+	0.0530821i	$0.0169045\pi$
$643$			2.69205i			0.106164i	−0.998590	+	0.0530821i	$0.983095\pi$
$644$		0			0
$645$			2.54020i			0.100020i
$646$			0.483969i			0.0190415i
$647$			46.6810i			1.83522i	0.397480	+	0.917611i	$0.369885\pi$
$647$			46.6810i			1.83522i	−0.397480	+	0.917611i	$0.630115\pi$
$648$			1.00000i			0.0392837i
$649$	−12.4657	−	0.663572i	−0.489321	−	0.0260475i
$650$		−	31.7222i		−	1.24425i
$651$		0			0
$652$	−22.3960			−0.877094
$653$	39.9858			1.56477			0.782383	−	0.622798i	$-0.214004\pi$
$653$	39.9858			1.56477			0.782383	+	0.622798i	$0.214004\pi$
$654$			1.45285i			0.0568109i
$655$			10.2366i			0.399976i
$656$	−5.85343			−0.228538
$657$	−5.28943			−0.206360
$658$		0			0
$659$		−	24.9930i		−	0.973590i	−0.873516	−	0.486795i	$-0.838166\pi$
$659$		−	24.9930i		−	0.973590i	0.873516	−	0.486795i	$-0.161834\pi$
$660$	0.123562	−	2.32120i	0.00480963	−	0.0903524i
$661$			14.6955i			0.571588i	0.958291	+	0.285794i	$0.0922573\pi$
$661$			14.6955i			0.571588i	−0.958291	+	0.285794i	$0.907743\pi$
$662$		−	27.2898i		−	1.06065i
$663$		−	4.34650i		−	0.168804i
$664$		−	4.03988i		−	0.156778i
$665$		0			0
$666$		−	3.99419i		−	0.154772i
$667$		−	11.0274i		−	0.426984i
$668$	−17.9924			−0.696145
$669$	−22.9194			−0.886117
$670$	1.50040			0.0579655
$671$	1.47488	−	27.7067i	0.0569371	−	1.06961i
$672$		0			0
$673$			51.7415i			1.99449i	0.0741830	+	0.997245i	$0.476365\pi$
$673$			51.7415i			1.99449i	−0.0741830	+	0.997245i	$0.523635\pi$
$674$	−13.0929			−0.504319
$675$		−	4.50880i		−	0.173544i
$676$	−36.4999			−1.40384
$677$	37.4530			1.43944			0.719718	−	0.694266i	$-0.244271\pi$
$677$	37.4530			1.43944			0.719718	+	0.694266i	$0.244271\pi$
$678$	12.0074			0.461142
$679$		0			0
$680$	0.432980			0.0166040
$681$		−	24.2282i		−	0.928427i
$682$	−1.08917	+	20.4609i	−0.0417065	+	0.783488i
$683$	−42.0158			−1.60769			−0.803845	−	0.594839i	$-0.797216\pi$
$683$	−42.0158			−1.60769			−0.803845	+	0.594839i	$0.797216\pi$
$684$	0.783393			0.0299538
$685$			11.7156i			0.447630i
$686$		0			0
$687$	−13.3778			−0.510396
$688$		−	3.62441i		−	0.138179i
$689$	55.5910			2.11785
$690$		−	3.69481i		−	0.140659i
$691$			27.6503i			1.05187i	0.850525	+	0.525934i	$0.176284\pi$
$691$			27.6503i			1.05187i	−0.850525	+	0.525934i	$0.823716\pi$
$692$	0.378382			0.0143839
$693$		0			0
$694$	−11.3473			−0.430739
$695$			9.06905i			0.344009i
$696$		−	2.09176i		−	0.0792881i
$697$	3.61616			0.136972
$698$		−	12.4060i		−	0.469573i
$699$	27.9050			1.05546
$700$		0			0
$701$			8.73779i			0.330022i	0.986292	+	0.165011i	$0.0527659\pi$
$701$			8.73779i			0.330022i	−0.986292	+	0.165011i	$0.947234\pi$
$702$	−7.03562			−0.265542
$703$	−3.12902			−0.118013
$704$	−0.176300	+	3.31194i	−0.00664457	+	0.124823i
$705$		−	1.64685i		−	0.0620238i
$706$	6.82398			0.256824
$707$		0			0
$708$	−3.76387			−0.141455
$709$	−33.3365			−1.25198			−0.625990	−	0.779831i	$-0.715305\pi$
$709$	−33.3365			−1.25198			−0.625990	+	0.779831i	$0.715305\pi$
$710$	−3.14337			−0.117969
$711$		−	4.33957i		−	0.162747i
$712$	16.2115			0.607551
$713$			32.5690i			1.21972i
$714$		0			0
$715$	16.3310	+	0.869332i	0.610747	+	0.0325112i
$716$	4.31093			0.161107
$717$	9.27514			0.346386
$718$	20.4315			0.762495
$719$			10.4879i			0.391132i	0.980691	+	0.195566i	$0.0626544\pi$
$719$			10.4879i			0.391132i	−0.980691	+	0.195566i	$0.937346\pi$
$720$		−	0.700858i		−	0.0261194i
$721$		0			0
$722$			18.3863i			0.684267i
$723$		−	19.0970i		−	0.710226i
$724$			6.96276i			0.258769i
$725$			9.43134i			0.350271i
$726$	−10.9378	−	1.16779i	−0.405941	−	0.0433408i
$727$			9.73041i			0.360881i	0.983586	+	0.180440i	$0.0577523\pi$
$727$			9.73041i			0.360881i	−0.983586	+	0.180440i	$0.942248\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	3.70714			0.137207
$731$			2.23911i			0.0828163i
$732$		−	8.36572i		−	0.309206i
$733$	−1.60100			−0.0591342			−0.0295671	−	0.999563i	$-0.509413\pi$
$733$	−1.60100			−0.0591342			−0.0295671	+	0.999563i	$0.509413\pi$
$734$	20.1568			0.744001
$735$		0			0
$736$			5.27184i			0.194323i
$737$	0.377425	−	7.09021i	0.0139026	−	0.261171i
$738$		−	5.85343i		−	0.215468i
$739$		−	27.3381i		−	1.00565i	−0.864388	−	0.502825i	$-0.832294\pi$
$739$		−	27.3381i		−	1.00565i	0.864388	−	0.502825i	$-0.167706\pi$
$740$			2.79936i			0.102906i
$741$			5.51165i			0.202476i
$742$		0			0
$743$		−	49.7705i		−	1.82590i	−0.408067	−	0.912952i	$-0.633797\pi$
$743$		−	49.7705i		−	1.82590i	0.408067	−	0.912952i	$-0.366203\pi$
$744$			6.17793i			0.226494i
$745$	−6.81837			−0.249806
$746$	8.33854			0.305296
$747$	4.03988			0.147812
$748$	0.108916	−	2.04606i	0.00398236	−	0.0748115i
$749$		0			0
$750$			6.66432i			0.243346i
$751$	−23.0637			−0.841606			−0.420803	−	0.907152i	$-0.638252\pi$
$751$	−23.0637			−0.841606			−0.420803	+	0.907152i	$0.638252\pi$
$752$			2.34976i			0.0856868i
$753$	−12.1328			−0.442145
$754$	14.7169			0.535956
$755$	13.8684			0.504722
$756$		0			0
$757$	−35.4691			−1.28915			−0.644574	−	0.764542i	$-0.722965\pi$
$757$	−35.4691			−1.28915			−0.644574	+	0.764542i	$0.722965\pi$
$758$			12.2093i			0.443463i
$759$	−17.4600	−	0.929428i	−0.633757	−	0.0337361i
$760$	−0.549047			−0.0199160
$761$	16.2697			0.589776			0.294888	−	0.955532i	$-0.404718\pi$
$761$	16.2697			0.589776			0.294888	+	0.955532i	$0.404718\pi$
$762$		−	3.43188i		−	0.124324i
$763$		0			0
$764$	18.5590			0.671440
$765$			0.432980i			0.0156544i
$766$	−18.6517			−0.673913
$767$		−	26.4811i		−	0.956179i
$768$			1.00000i			0.0360844i
$769$	31.2492			1.12687			0.563437	−	0.826159i	$-0.309479\pi$
$769$	31.2492			1.12687			0.563437	+	0.826159i	$0.309479\pi$
$770$		0			0
$771$	19.9471			0.718377
$772$		−	17.5212i		−	0.630601i
$773$		−	16.5216i		−	0.594240i	−0.954840	−	0.297120i	$-0.903974\pi$
$773$		−	16.5216i		−	0.594240i	0.954840	−	0.297120i	$-0.0960261\pi$
$774$	3.62441			0.130277
$775$		−	27.8550i		−	1.00058i
$776$	10.4926			0.376662
$777$		0			0
$778$			9.51444i			0.341109i
$779$	−4.58553			−0.164294
$780$	4.93097			0.176557
$781$	−0.790713	+	14.8541i	−0.0282939	+	0.531523i
$782$		−	3.25686i		−	0.116465i
$783$	2.09176			0.0747535
$784$		0			0
$785$	−8.41762			−0.300438
$786$	14.6058			0.520970
$787$	22.0831			0.787177			0.393589	−	0.919287i	$-0.371233\pi$
$787$	22.0831			0.787177			0.393589	+	0.919287i	$0.371233\pi$
$788$		−	18.8663i		−	0.672086i
$789$	−16.7867			−0.597622
$790$			3.04142i			0.108209i
$791$		0			0
$792$	−3.31194	−	0.176300i	−0.117685	−	0.00626457i
$793$	58.8580			2.09011
$794$	34.0696			1.20909
$795$	−5.53773			−0.196403
$796$			13.5324i			0.479642i
$797$			25.7347i			0.911571i	0.890090	+	0.455785i	$0.150642\pi$
$797$			25.7347i			0.911571i	−0.890090	+	0.455785i	$0.849358\pi$
$798$		0			0
$799$		−	1.45165i		−	0.0513555i
$800$		−	4.50880i		−	0.159410i
$801$			16.2115i			0.572805i
$802$			29.6358i			1.04647i
$803$	0.932528	−	17.5182i	0.0329082	−	0.618205i
$804$		−	2.14081i		−	0.0755004i
$805$		0			0
$806$	−43.4655			−1.53101
$807$	19.4953			0.686268
$808$			14.9947i			0.527513i
$809$			28.9768i			1.01877i	0.860539	+	0.509385i	$0.170127\pi$
$809$			28.9768i			1.01877i	−0.860539	+	0.509385i	$0.829873\pi$
$810$	0.700858			0.0246256
$811$	−1.48290			−0.0520715			−0.0260358	−	0.999661i	$-0.508288\pi$
$811$	−1.48290			−0.0520715			−0.0260358	+	0.999661i	$0.508288\pi$
$812$		0			0
$813$			10.6826i			0.374655i
$814$	13.2285	+	0.704177i	0.463658	+	0.0246814i
$815$			15.6964i			0.549821i
$816$		−	0.617785i		−	0.0216268i
$817$		−	2.83934i		−	0.0993358i
$818$		−	27.3288i		−	0.955530i
$819$		0			0
$820$			4.10242i			0.143263i
$821$			5.52513i			0.192828i	0.995341	+	0.0964142i	$0.0307373\pi$
$821$			5.52513i			0.192828i	−0.995341	+	0.0964142i	$0.969263\pi$
$822$	16.7161			0.583040
$823$	−16.2218			−0.565455			−0.282728	−	0.959200i	$-0.591239\pi$
$823$	−16.2218			−0.565455			−0.282728	+	0.959200i	$0.591239\pi$
$824$	14.3517			0.499965
$825$	14.9329	+	0.794903i	0.519895	+	0.0276750i
$826$		0			0
$827$			5.86195i			0.203840i	0.994793	+	0.101920i	$0.0324986\pi$
$827$			5.86195i			0.203840i	−0.994793	+	0.101920i	$0.967501\pi$
$828$	−5.27184			−0.183209
$829$		−	19.4082i		−	0.674074i	−0.941491	−	0.337037i	$-0.890575\pi$
$829$		−	19.4082i		−	0.674074i	0.941491	−	0.337037i	$-0.109425\pi$
$830$	−2.83138			−0.0982788
$831$	30.7880			1.06802
$832$	−7.03562			−0.243916
$833$		0			0
$834$	12.9399			0.448073
$835$			12.6101i			0.436390i
$836$	−0.138113	+	2.59455i	−0.00477672	+	0.0897343i
$837$	−6.17793			−0.213540
$838$	−25.6972			−0.887696
$839$			17.8302i			0.615565i	0.951457	+	0.307783i	$0.0995870\pi$
$839$			17.8302i			0.615565i	−0.951457	+	0.307783i	$0.900413\pi$
$840$		0			0
$841$	24.6245			0.849122
$842$			36.9246i			1.27250i
$843$	−21.3381			−0.734924
$844$			4.94368i			0.170168i
$845$			25.5813i			0.880022i
$846$	−2.34976			−0.0807863
$847$		0			0
$848$	7.90136			0.271334
$849$			2.52307i			0.0865916i
$850$			2.78547i			0.0955408i
$851$	21.0567			0.721814
$852$			4.48503i			0.153655i
$853$	2.57158			0.0880491			0.0440246	−	0.999030i	$-0.485982\pi$
$853$	2.57158			0.0880491			0.0440246	+	0.999030i	$0.485982\pi$
$854$		0			0
$855$		−	0.549047i		−	0.0187770i
$856$	−11.4671			−0.391938
$857$	−16.3283			−0.557763			−0.278881	−	0.960326i	$-0.589964\pi$
$857$	−16.3283			−0.557763			−0.278881	+	0.960326i	$0.589964\pi$
$858$	1.24038	−	23.3015i	0.0423460	−	0.795501i
$859$			25.8385i			0.881598i	0.897606	+	0.440799i	$0.145305\pi$
$859$			25.8385i			0.881598i	−0.897606	+	0.440799i	$0.854695\pi$
$860$	−2.54020			−0.0866199
$861$		0			0
$862$	−20.1287			−0.685586
$863$	17.7945			0.605732			0.302866	−	0.953033i	$-0.402056\pi$
$863$	17.7945			0.605732			0.302866	+	0.953033i	$0.402056\pi$
$864$	−1.00000			−0.0340207
$865$		−	0.265192i		−	0.00901680i
$866$	−38.1992			−1.29806
$867$		−	16.6183i		−	0.564388i
$868$		0			0
$869$	14.3724	+	0.765069i	0.487550	+	0.0259532i
$870$	−1.46603			−0.0497030
$871$	15.0619			0.510353
$872$	−1.45285			−0.0491997
$873$			10.4926i			0.355120i
$874$			4.12992i			0.139697i
$875$		0			0
$876$		−	5.28943i		−	0.178713i
$877$			1.51986i			0.0513221i	0.999671	+	0.0256611i	$0.00816907\pi$
$877$			1.51986i			0.0513221i	−0.999671	+	0.0256611i	$0.991831\pi$
$878$		−	7.32197i		−	0.247105i
$879$			5.71831i			0.192874i
$880$	2.32120	+	0.123562i	0.0782475	+	0.00416526i
$881$			2.61558i			0.0881210i	0.999029	+	0.0440605i	$0.0140294\pi$
$881$			2.61558i			0.0881210i	−0.999029	+	0.0440605i	$0.985971\pi$
$882$		0			0
$883$	−32.7433			−1.10190			−0.550950	−	0.834538i	$-0.685735\pi$
$883$	−32.7433			−1.10190			−0.550950	+	0.834538i	$0.685735\pi$
$884$	4.34650			0.146189
$885$			2.63794i			0.0886733i
$886$			33.0248i			1.10949i
$887$	23.2200			0.779650			0.389825	−	0.920889i	$-0.372535\pi$
$887$	23.2200			0.779650			0.389825	+	0.920889i	$0.372535\pi$
$888$	3.99419			0.134036
$889$		0			0
$890$		−	11.3619i		−	0.380853i
$891$	0.176300	−	3.31194i	0.00590629	−	0.110954i
$892$		−	22.9194i		−	0.767400i
$893$			1.84078i			0.0615994i
$894$			9.72861i			0.325374i
$895$		−	3.02135i		−	0.100993i
$896$		0			0
$897$		−	37.0906i		−	1.23842i
$898$			22.5285i			0.751787i
$899$	12.9228			0.430998
$900$	4.50880			0.150293
$901$	−4.88135			−0.162621
$902$	19.3862	+	1.03196i	0.645489	+	0.0343606i
$903$		0			0
$904$			12.0074i			0.399361i
$905$	4.87991			0.162214
$906$		−	19.7877i		−	0.657403i
$907$	−14.9307			−0.495766			−0.247883	−	0.968790i	$-0.579735\pi$
$907$	−14.9307			−0.495766			−0.247883	+	0.968790i	$0.579735\pi$
$908$	24.2282			0.804042
$909$	−14.9947			−0.497344
$910$		0			0
$911$	33.6372			1.11445			0.557225	−	0.830362i	$-0.311866\pi$
$911$	33.6372			1.11445			0.557225	+	0.830362i	$0.311866\pi$
$912$			0.783393i			0.0259407i
$913$	−0.712234	+	13.3798i	−0.0235715	+	0.442808i
$914$	33.1752			1.09734
$915$	−5.86318			−0.193831
$916$		−	13.3778i		−	0.442016i
$917$		0			0
$918$	0.617785			0.0203899
$919$			27.0021i			0.890718i	0.895352	+	0.445359i	$0.146924\pi$
$919$			27.0021i			0.890718i	−0.895352	+	0.445359i	$0.853076\pi$
$920$	3.69481			0.121814
$921$			20.7839i			0.684851i
$922$		−	7.42955i		−	0.244679i
$923$	−31.5550			−1.03864
$924$		0			0
$925$	−18.0090			−0.592131
$926$			15.7504i			0.517591i
$927$			14.3517i			0.471372i
$928$	2.09176			0.0686655
$929$		−	37.7631i		−	1.23897i	−0.785010	−	0.619483i	$-0.787342\pi$
$929$		−	37.7631i		−	1.23897i	0.785010	−	0.619483i	$-0.212658\pi$
$930$	4.32985			0.141981
$931$		0			0
$932$			27.9050i			0.914057i
$933$	7.36751			0.241202
$934$	−13.3731			−0.437583
$935$	−1.43400	−	0.0763345i	−0.0468968	−	0.00249641i
$936$		−	7.03562i		−	0.229966i
$937$	−33.9310			−1.10848			−0.554239	−	0.832357i	$-0.686991\pi$
$937$	−33.9310			−1.10848			−0.554239	+	0.832357i	$0.686991\pi$
$938$		0			0
$939$	−7.35395			−0.239987
$940$	1.64685			0.0537142
$941$	26.8943			0.876729			0.438364	−	0.898797i	$-0.355558\pi$
$941$	26.8943			0.876729			0.438364	+	0.898797i	$0.355558\pi$
$942$			12.0105i			0.391322i
$943$	30.8583			1.00489
$944$		−	3.76387i		−	0.122503i
$945$		0			0
$946$	−0.638985	+	12.0038i	−0.0207752	+	0.390278i
$947$	−22.7254			−0.738477			−0.369239	−	0.929335i	$-0.620381\pi$
$947$	−22.7254			−0.738477			−0.369239	+	0.929335i	$0.620381\pi$
$948$	4.33957			0.140943
$949$	37.2144			1.20803
$950$		−	3.53216i		−	0.114598i
$951$		−	14.7806i		−	0.479294i
$952$		0			0
$953$		−	15.8105i		−	0.512152i	−0.966657	−	0.256076i	$-0.917570\pi$
$953$		−	15.8105i		−	0.512152i	0.966657	−	0.256076i	$-0.0824298\pi$
$954$			7.90136i			0.255816i
$955$		−	13.0072i		−	0.420903i
$956$			9.27514i			0.299979i
$957$	−0.368779	+	6.92779i	−0.0119209	+	0.223944i
$958$			11.2610i			0.363826i
$959$		0			0
$960$	0.700858			0.0226201
$961$	−7.16676			−0.231186
$962$			28.1016i			0.906031i
$963$		−	11.4671i		−	0.369523i
$964$	19.0970			0.615074
$965$	−12.2799			−0.395303
$966$		0			0
$967$		−	50.1237i		−	1.61187i	−0.592005	−	0.805934i	$-0.701663\pi$
$967$		−	50.1237i		−	1.61187i	0.592005	−	0.805934i	$-0.298337\pi$
$968$	1.16779	−	10.9378i	0.0375343	−	0.351555i
$969$		−	0.483969i		−	0.0155473i
$970$		−	7.35380i		−	0.236116i
$971$			33.3796i			1.07120i	0.844471	+	0.535602i	$0.179915\pi$
$971$			33.3796i			1.07120i	−0.844471	+	0.535602i	$0.820085\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$		−	2.66963i		−	0.0855405i
$975$			31.7222i			1.01592i
$976$	8.36572			0.267780
$977$	−30.8183			−0.985965			−0.492983	−	0.870039i	$-0.664093\pi$
$977$	−30.8183			−0.985965			−0.492983	+	0.870039i	$0.664093\pi$
$978$	22.3960			0.716144
$979$	−53.6914	−	2.85809i	−1.71598	−	0.0913450i
$980$		0			0
$981$		−	1.45285i		−	0.0463859i
$982$	11.3063			0.360798
$983$		−	33.3378i		−	1.06331i	−0.846961	−	0.531656i	$-0.821570\pi$
$983$		−	33.3378i		−	1.06331i	0.846961	−	0.531656i	$-0.178430\pi$
$984$	5.85343			0.186600
$985$	−13.2226			−0.421308
$986$	−1.29226			−0.0411540
$987$		0			0
$988$	−5.51165			−0.175349
$989$			19.1073i			0.607577i
$990$	−0.123562	+	2.32120i	−0.00392704	+	0.0737724i
$991$	−58.0685			−1.84461			−0.922303	−	0.386467i	$-0.873695\pi$
$991$	−58.0685			−1.84461			−0.922303	+	0.386467i	$0.873695\pi$
$992$	−6.17793			−0.196149
$993$			27.2898i			0.866015i
$994$		0			0
$995$	9.48426			0.300671
$996$			4.03988i			0.128009i
$997$	36.6484			1.16067			0.580334	−	0.814379i	$-0.302922\pi$
$997$	36.6484			1.16067			0.580334	+	0.814379i	$0.302922\pi$
$998$		−	21.4400i		−	0.678672i
$999$			3.99419i			0.126370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3234.2.e.b.2155.4		16
7.4	even	3		462.2.p.b.439.6	yes	16
7.5	odd	6		462.2.p.a.241.2	✓	16
7.6	odd	2		3234.2.e.a.2155.5		16
11.10	odd	2		3234.2.e.a.2155.12		16
21.5	even	6		1386.2.bk.a.703.7		16
21.11	odd	6		1386.2.bk.b.901.3		16
77.32	odd	6		462.2.p.a.439.2	yes	16
77.54	even	6		462.2.p.b.241.6	yes	16
77.76	even	2	inner	3234.2.e.b.2155.13		16
231.32	even	6		1386.2.bk.a.901.7		16
231.131	odd	6		1386.2.bk.b.703.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.2	✓	16	7.5	odd	6
462.2.p.a.439.2	yes	16	77.32	odd	6
462.2.p.b.241.6	yes	16	77.54	even	6
462.2.p.b.439.6	yes	16	7.4	even	3
1386.2.bk.a.703.7		16	21.5	even	6
1386.2.bk.a.901.7		16	231.32	even	6
1386.2.bk.b.703.3		16	231.131	odd	6
1386.2.bk.b.901.3		16	21.11	odd	6
3234.2.e.a.2155.5		16	7.6	odd	2
3234.2.e.a.2155.12		16	11.10	odd	2
3234.2.e.b.2155.4		16	1.1	even	1	trivial
3234.2.e.b.2155.13		16	77.76	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:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +0.700858i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +0.700858i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +0.700858 q^{10} +(0.176300 - 3.31194i) q^{11} -1.00000i q^{12} +7.03562 q^{13} -0.700858 q^{15} +1.00000 q^{16} -0.617785 q^{17} +1.00000i q^{18} +0.783393 q^{19} -0.700858i q^{20} +(-3.31194 - 0.176300i) q^{22} -5.27184 q^{23} -1.00000 q^{24} +4.50880 q^{25} -7.03562i q^{26} -1.00000i q^{27} +2.09176i q^{29} +0.700858i q^{30} -6.17793i q^{31} -1.00000i q^{32} +(3.31194 + 0.176300i) q^{33} +0.617785i q^{34} +1.00000 q^{36} -3.99419 q^{37} -0.783393i q^{38} +7.03562i q^{39} -0.700858 q^{40} -5.85343 q^{41} -3.62441i q^{43} +(-0.176300 + 3.31194i) q^{44} -0.700858i q^{45} +5.27184i q^{46} +2.34976i q^{47} +1.00000i q^{48} -4.50880i q^{50} -0.617785i q^{51} -7.03562 q^{52} +7.90136 q^{53} -1.00000 q^{54} +(2.32120 + 0.123562i) q^{55} +0.783393i q^{57} +2.09176 q^{58} -3.76387i q^{59} +0.700858 q^{60} +8.36572 q^{61} -6.17793 q^{62} -1.00000 q^{64} +4.93097i q^{65} +(0.176300 - 3.31194i) q^{66} +2.14081 q^{67} +0.617785 q^{68} -5.27184i q^{69} -4.48503 q^{71} -1.00000i q^{72} +5.28943 q^{73} +3.99419i q^{74} +4.50880i q^{75} -0.783393 q^{76} +7.03562 q^{78} +4.33957i q^{79} +0.700858i q^{80} +1.00000 q^{81} +5.85343i q^{82} -4.03988 q^{83} -0.432980i q^{85} -3.62441 q^{86} -2.09176 q^{87} +(3.31194 + 0.176300i) q^{88} -16.2115i q^{89} -0.700858 q^{90} +5.27184 q^{92} +6.17793 q^{93} +2.34976 q^{94} +0.549047i q^{95} +1.00000 q^{96} -10.4926i q^{97} +(-0.176300 + 3.31194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 16 q^{6} - 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 + 16 * q^6 - 16 * q^9	\( 16 q - 16 q^{4} + 16 q^{6} - 16 q^{9} + 4 q^{10} + 8 q^{11} - 4 q^{15} + 16 q^{16} - 20 q^{19} + 2 q^{22} + 8 q^{23} - 16 q^{24} - 20 q^{25} - 2 q^{33} + 16 q^{36} - 28 q^{37} - 4 q^{40} - 32 q^{41} - 8 q^{44} - 16 q^{54} + 14 q^{55} + 4 q^{60} + 56 q^{61} + 8 q^{62} - 16 q^{64} + 8 q^{66} + 32 q^{67} - 56 q^{71} - 88 q^{73} + 20 q^{76} + 16 q^{81} - 8 q^{83} + 24 q^{86} - 2 q^{88} - 4 q^{90} - 8 q^{92} - 8 q^{93} + 28 q^{94} + 16 q^{96} - 8 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 + 16 * q^6 - 16 * q^9 + 4 * q^10 + 8 * q^11 - 4 * q^15 + 16 * q^16 - 20 * q^19 + 2 * q^22 + 8 * q^23 - 16 * q^24 - 20 * q^25 - 2 * q^33 + 16 * q^36 - 28 * q^37 - 4 * q^40 - 32 * q^41 - 8 * q^44 - 16 * q^54 + 14 * q^55 + 4 * q^60 + 56 * q^61 + 8 * q^62 - 16 * q^64 + 8 * q^66 + 32 * q^67 - 56 * q^71 - 88 * q^73 + 20 * q^76 + 16 * q^81 - 8 * q^83 + 24 * q^86 - 2 * q^88 - 4 * q^90 - 8 * q^92 - 8 * q^93 + 28 * q^94 + 16 * q^96 - 8 * q^99

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