LMFDB - Embedded newform 945.2.g.b.944.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(944,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("945.944");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.g (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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			944.17
Character	$\chi$	$=$	945.944
Dual form			945.2.g.b.944.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.631409 q^{2} -1.60132 q^{4} +(-2.21891 - 0.276494i) q^{5} +(2.40407 + 1.10473i) q^{7} -2.27391 q^{8} +O(q^{10})$	\(q+0.631409 q^{2} -1.60132 q^{4} +(-2.21891 - 0.276494i) q^{5} +(2.40407 + 1.10473i) q^{7} -2.27391 q^{8} +(-1.40104 - 0.174581i) q^{10} -4.53086i q^{11} +0.148283 q^{13} +(1.51795 + 0.697539i) q^{14} +1.76688 q^{16} +5.50137i q^{17} +4.84681i q^{19} +(3.55319 + 0.442757i) q^{20} -2.86082i q^{22} +5.63680 q^{23} +(4.84710 + 1.22703i) q^{25} +0.0936272 q^{26} +(-3.84969 - 1.76903i) q^{28} +5.60345i q^{29} +9.41406i q^{31} +5.66344 q^{32} +3.47362i q^{34} +(-5.02896 - 3.11601i) q^{35} +5.50294i q^{37} +3.06032i q^{38} +(5.04559 + 0.628723i) q^{40} -3.55319 q^{41} -11.3868i q^{43} +7.25536i q^{44} +3.55913 q^{46} -3.21633i q^{47} +(4.55913 + 5.31172i) q^{49} +(3.06051 + 0.774759i) q^{50} -0.237449 q^{52} -8.99969 q^{53} +(-1.25276 + 10.0535i) q^{55} +(-5.46664 - 2.51206i) q^{56} +3.53807i q^{58} +7.28647 q^{59} +8.15661i q^{61} +5.94412i q^{62} +0.0421952 q^{64} +(-0.329026 - 0.0409994i) q^{65} +10.3286i q^{67} -8.80946i q^{68} +(-3.17533 - 1.96748i) q^{70} -5.66910i q^{71} +13.0415 q^{73} +3.47461i q^{74} -7.76130i q^{76} +(5.00539 - 10.8925i) q^{77} +13.0624 q^{79} +(-3.92054 - 0.488532i) q^{80} -2.24351 q^{82} -0.0389759i q^{83} +(1.52110 - 12.2070i) q^{85} -7.18971i q^{86} +10.3028i q^{88} +8.78200 q^{89} +(0.356483 + 0.163813i) q^{91} -9.02633 q^{92} -2.03082i q^{94} +(1.34012 - 10.7546i) q^{95} +4.42241 q^{97} +(2.87868 + 3.35387i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4}+O(q^{10}) $ 32 * q + 32 * q^4	$ 32 q + 32 q^{4} + 32 q^{16} + 20 q^{25} - 24 q^{46} + 8 q^{49} + 56 q^{64} + 40 q^{79} + 76 q^{85} + 40 q^{91}+O(q^{100}) $ 32 * q + 32 * q^4 + 32 * q^16 + 20 * q^25 - 24 * q^46 + 8 * q^49 + 56 * q^64 + 40 * q^79 + 76 * q^85 + 40 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	0.631409			0.446474			0.223237	−	0.974764i	$-0.428338\pi$
$2$	0.631409			0.446474			0.223237	+	0.974764i	$0.428338\pi$
$3$		0			0
$3$		0			0
$4$	−1.60132			−0.800661
$5$	−2.21891	−	0.276494i	−0.992326	−	0.123652i
$5$	−2.21891	−	0.276494i	−0.992326	−	0.123652i
$6$		0			0
$7$	2.40407	+	1.10473i	0.908654	+	0.417550i
$7$	2.40407	+	1.10473i	0.908654	+	0.417550i
$8$	−2.27391			−0.803948
$9$		0			0
$10$	−1.40104	−	0.174581i	−0.443047	−	0.0552074i
$11$		−	4.53086i		−	1.36610i	−0.730370	−	0.683052i	$-0.760652\pi$
$11$		−	4.53086i		−	1.36610i	0.730370	−	0.683052i	$-0.239348\pi$
$12$		0			0
$13$	0.148283			0.0411263			0.0205631	−	0.999789i	$-0.493454\pi$
$13$	0.148283			0.0411263			0.0205631	+	0.999789i	$0.493454\pi$
$14$	1.51795	+	0.697539i	0.405690	+	0.186425i
$15$		0			0
$16$	1.76688			0.441719
$17$			5.50137i			1.33428i	0.744933	+	0.667139i	$0.232481\pi$
$17$			5.50137i			1.33428i	−0.744933	+	0.667139i	$0.767519\pi$
$18$		0			0
$19$			4.84681i			1.11193i	0.831204	+	0.555967i	$0.187652\pi$
$19$			4.84681i			1.11193i	−0.831204	+	0.555967i	$0.812348\pi$
$20$	3.55319	+	0.442757i	0.794517	+	0.0990034i
$21$		0			0
$22$		−	2.86082i		−	0.609930i
$23$	5.63680			1.17535			0.587677	−	0.809096i	$-0.300043\pi$
$23$	5.63680			1.17535			0.587677	+	0.809096i	$0.300043\pi$
$24$		0			0
$25$	4.84710	+	1.22703i	0.969420	+	0.245406i
$26$	0.0936272			0.0183618
$27$		0			0
$28$	−3.84969	−	1.76903i	−0.727524	−	0.334316i
$29$			5.60345i			1.04053i	0.854004	+	0.520267i	$0.174168\pi$
$29$			5.60345i			1.04053i	−0.854004	+	0.520267i	$0.825832\pi$
$30$		0			0
$31$			9.41406i			1.69081i	0.534122	+	0.845407i	$0.320642\pi$
$31$			9.41406i			1.69081i	−0.534122	+	0.845407i	$0.679358\pi$
$32$	5.66344			1.00116
$33$		0			0
$34$			3.47362i			0.595720i
$35$	−5.02896	−	3.11601i	−0.850050	−	0.526703i
$36$		0			0
$37$			5.50294i			0.904678i	0.891846	+	0.452339i	$0.149410\pi$
$37$			5.50294i			0.904678i	−0.891846	+	0.452339i	$0.850590\pi$
$38$			3.06032i			0.496450i
$39$		0			0
$40$	5.04559	+	0.628723i	0.797778	+	0.0994099i
$41$	−3.55319			−0.554914			−0.277457	−	0.960738i	$-0.589492\pi$
$41$	−3.55319			−0.554914			−0.277457	+	0.960738i	$0.589492\pi$
$42$		0			0
$43$		−	11.3868i		−	1.73646i	−0.496158	−	0.868232i	$-0.665256\pi$
$43$		−	11.3868i		−	1.73646i	0.496158	−	0.868232i	$-0.334744\pi$
$44$			7.25536i			1.09379i
$45$		0			0
$46$	3.55913			0.524765
$47$		−	3.21633i		−	0.469150i	−0.972098	−	0.234575i	$-0.924630\pi$
$47$		−	3.21633i		−	0.469150i	0.972098	−	0.234575i	$-0.0753698\pi$
$48$		0			0
$49$	4.55913	+	5.31172i	0.651304	+	0.758817i
$50$	3.06051	+	0.774759i	0.432821	+	0.109567i
$51$		0			0
$52$	−0.237449			−0.0329282
$53$	−8.99969			−1.23620			−0.618101	−	0.786099i	$-0.712098\pi$
$53$	−8.99969			−1.23620			−0.618101	+	0.786099i	$0.712098\pi$
$54$		0			0
$55$	−1.25276	+	10.0535i	−0.168922	+	1.35562i
$56$	−5.46664	−	2.51206i	−0.730511	−	0.335689i
$57$		0			0
$58$			3.53807i			0.464571i
$59$	7.28647			0.948617			0.474309	−	0.880359i	$-0.342698\pi$
$59$	7.28647			0.948617			0.474309	+	0.880359i	$0.342698\pi$
$60$		0			0
$61$			8.15661i			1.04435i	0.852839	+	0.522174i	$0.174879\pi$
$61$			8.15661i			1.04435i	−0.852839	+	0.522174i	$0.825121\pi$
$62$			5.94412i			0.754905i
$63$		0			0
$64$	0.0421952			0.00527440
$65$	−0.329026	−	0.0409994i	−0.0408106	−	0.00508535i
$66$		0			0
$67$			10.3286i			1.26184i	0.775846	+	0.630922i	$0.217323\pi$
$67$			10.3286i			1.26184i	−0.775846	+	0.630922i	$0.782677\pi$
$68$		−	8.80946i		−	1.06830i
$69$		0			0
$70$	−3.17533	−	1.96748i	−0.379525	−	0.235159i
$71$		−	5.66910i		−	0.672798i	−0.941719	−	0.336399i	$-0.890791\pi$
$71$		−	5.66910i		−	0.672798i	0.941719	−	0.336399i	$-0.109209\pi$
$72$		0			0
$73$	13.0415			1.52640			0.763199	−	0.646164i	$-0.223628\pi$
$73$	13.0415			1.52640			0.763199	+	0.646164i	$0.223628\pi$
$74$			3.47461i			0.403915i
$75$		0			0
$76$		−	7.76130i		−	0.890283i
$77$	5.00539	−	10.8925i	0.570417	−	1.24132i
$78$		0			0
$79$	13.0624			1.46964			0.734818	−	0.678265i	$-0.237268\pi$
$79$	13.0624			1.46964			0.734818	+	0.678265i	$0.237268\pi$
$80$	−3.92054	−	0.488532i	−0.438329	−	0.0546195i
$81$		0			0
$82$	−2.24351			−0.247755
$83$		−	0.0389759i		−	0.00427816i	−0.999998	−	0.00213908i	$-0.999319\pi$
$83$		−	0.0389759i		−	0.00427816i	0.999998	−	0.00213908i	$-0.000680891\pi$
$84$		0			0
$85$	1.52110	−	12.2070i	0.164986	−	1.32404i
$86$		−	7.18971i		−	0.775286i
$87$		0			0
$88$			10.3028i			1.09828i
$89$	8.78200			0.930890			0.465445	−	0.885077i	$-0.345894\pi$
$89$	8.78200			0.930890			0.465445	+	0.885077i	$0.345894\pi$
$90$		0			0
$91$	0.356483	+	0.163813i	0.0373695	+	0.0171723i
$92$	−9.02633			−0.941060
$93$		0			0
$94$		−	2.03082i		−	0.209463i
$95$	1.34012	−	10.7546i	0.137493	−	1.10340i
$96$		0			0
$97$	4.42241			0.449028			0.224514	−	0.974471i	$-0.427921\pi$
$97$	4.42241			0.449028			0.224514	+	0.974471i	$0.427921\pi$
$98$	2.87868	+	3.35387i	0.290790	+	0.338792i
$99$		0			0
$100$	−7.76177	−	1.96487i	−0.776177	−	0.196487i
$101$	−2.15128			−0.214060			−0.107030	−	0.994256i	$-0.534134\pi$
$101$	−2.15128			−0.214060			−0.107030	+	0.994256i	$0.534134\pi$
$102$		0			0
$103$	−13.3035			−1.31084			−0.655419	−	0.755266i	$-0.727508\pi$
$103$	−13.3035			−1.31084			−0.655419	+	0.755266i	$0.727508\pi$
$104$	−0.337182			−0.0330634
$105$		0			0
$106$	−5.68249			−0.551932
$107$	−11.3269			−1.09501			−0.547505	−	0.836802i	$-0.684422\pi$
$107$	−11.3269			−1.09501			−0.547505	+	0.836802i	$0.684422\pi$
$108$		0			0
$109$	−6.20264			−0.594106			−0.297053	−	0.954861i	$-0.596004\pi$
$109$	−6.20264			−0.594106			−0.297053	+	0.954861i	$0.596004\pi$
$110$	−0.791002	+	6.34791i	−0.0754191	+	0.605249i
$111$		0			0
$112$	4.24770	+	1.95193i	0.401370	+	0.184440i
$113$	11.8538			1.11511			0.557554	−	0.830141i	$-0.311740\pi$
$113$	11.8538			1.11511			0.557554	+	0.830141i	$0.311740\pi$
$114$		0			0
$115$	−12.5075	−	1.55854i	−1.16633	−	0.145335i
$116$		−	8.97292i		−	0.833115i
$117$		0			0
$118$	4.60074			0.423533
$119$	−6.07755	+	13.2257i	−0.557128	+	1.21240i
$120$		0			0
$121$	−9.52865			−0.866241
$122$			5.15016i			0.466274i
$123$		0			0
$124$		−	15.0749i		−	1.35377i
$125$	−10.4160	−	4.06287i	−0.931636	−	0.363394i
$126$		0			0
$127$		−	16.2690i		−	1.44364i	−0.692081	−	0.721820i	$-0.743306\pi$
$127$		−	16.2690i		−	1.44364i	0.692081	−	0.721820i	$-0.256694\pi$
$128$	−11.3002			−0.998809
$129$		0			0
$130$	−0.207750	−	0.0258874i	−0.0182209	−	0.00227047i
$131$	−8.08463			−0.706357			−0.353179	−	0.935556i	$-0.614899\pi$
$131$	−8.08463			−0.706357			−0.353179	+	0.935556i	$0.614899\pi$
$132$		0			0
$133$	−5.35443	+	11.6521i	−0.464288	+	1.01036i
$134$			6.52160i			0.563380i
$135$		0			0
$136$		−	12.5096i		−	1.07269i
$137$	−5.40431			−0.461722			−0.230861	−	0.972987i	$-0.574154\pi$
$137$	−5.40431			−0.461722			−0.230861	+	0.972987i	$0.574154\pi$
$138$		0			0
$139$		−	4.72369i		−	0.400659i	−0.979729	−	0.200329i	$-0.935799\pi$
$139$		−	4.72369i		−	0.400659i	0.979729	−	0.200329i	$-0.0642012\pi$
$140$	8.05299	+	4.98974i	0.680602	+	0.421710i
$141$		0			0
$142$		−	3.57952i		−	0.300387i
$143$		−	0.671848i		−	0.0561828i
$144$		0			0
$145$	1.54932	−	12.4335i	0.128664	−	1.03255i
$146$	8.23456			0.681497
$147$		0			0
$148$		−	8.81198i		−	0.724340i
$149$			22.2430i			1.82222i	0.412166	+	0.911109i	$0.364772\pi$
$149$			22.2430i			1.82222i	−0.412166	+	0.911109i	$0.635228\pi$
$150$		0			0
$151$	4.49156			0.365518			0.182759	−	0.983158i	$-0.441497\pi$
$151$	4.49156			0.365518			0.182759	+	0.983158i	$0.441497\pi$
$152$		−	11.0212i		−	0.893937i
$153$		0			0
$154$	3.16045	−	6.87763i	0.254676	−	0.554215i
$155$	2.60293	−	20.8889i	0.209073	−	1.67784i
$156$		0			0
$157$	−10.0020			−0.798248			−0.399124	−	0.916897i	$-0.630686\pi$
$157$	−10.0020			−0.798248			−0.399124	+	0.916897i	$0.630686\pi$
$158$	8.24772			0.656154
$159$		0			0
$160$	−12.5667	−	1.56591i	−0.993481	−	0.123796i
$161$	13.5513	+	6.22716i	1.06799	+	0.490769i
$162$		0			0
$163$		−	5.50294i		−	0.431024i	−0.976501	−	0.215512i	$-0.930858\pi$
$163$		−	5.50294i		−	0.431024i	0.976501	−	0.215512i	$-0.0691420\pi$
$164$	5.68980			0.444298
$165$		0			0
$166$		−	0.0246097i		−	0.00191009i
$167$		−	13.5355i		−	1.04741i	−0.851899	−	0.523706i	$-0.824549\pi$
$167$		−	13.5355i		−	1.04741i	0.851899	−	0.523706i	$-0.175451\pi$
$168$		0			0
$169$	−12.9780			−0.998309
$170$	0.960435	−	7.70763i	0.0736620	−	0.591148i
$171$		0			0
$172$			18.2339i			1.39032i
$173$			0.0116667i			0.000887005i	1.00000		0.000443502i	$0.000141171\pi$
$173$			0.0116667i			0.000887005i	−1.00000		0.000443502i	$0.999859\pi$
$174$		0			0
$175$	10.2972	+	8.30463i	0.778398	+	0.627771i
$176$		−	8.00546i		−	0.603435i
$177$		0			0
$178$	5.54504			0.415618
$179$			10.7300i			0.801995i	0.916079	+	0.400998i	$0.131336\pi$
$179$			10.7300i			0.801995i	−0.916079	+	0.400998i	$0.868664\pi$
$180$		0			0
$181$		−	5.62018i		−	0.417745i	−0.977943	−	0.208872i	$-0.933021\pi$
$181$		−	5.62018i		−	0.417745i	0.977943	−	0.208872i	$-0.0669793\pi$
$182$	0.225086	+	0.103433i	0.0166845	+	0.00766697i
$183$		0			0
$184$	−12.8176			−0.944923
$185$	1.52153	−	12.2105i	0.111865	−	0.897735i
$186$		0			0
$187$	24.9259			1.82276
$188$			5.15038i			0.375630i
$189$		0			0
$190$	0.846162	−	6.79057i	0.0613870	−	0.492640i
$191$			15.0533i			1.08922i	0.838690	+	0.544609i	$0.183322\pi$
$191$			15.0533i			1.08922i	−0.838690	+	0.544609i	$0.816678\pi$
$192$		0			0
$193$			5.96624i			0.429460i	0.976673	+	0.214730i	$0.0688871\pi$
$193$			5.96624i			0.429460i	−0.976673	+	0.214730i	$0.931113\pi$
$194$	2.79235			0.200479
$195$		0			0
$196$	−7.30063	−	8.50577i	−0.521474	−	0.607555i
$197$	2.93196			0.208894			0.104447	−	0.994530i	$-0.466693\pi$
$197$	2.93196			0.208894			0.104447	+	0.994530i	$0.466693\pi$
$198$		0			0
$199$			8.24346i			0.584363i	0.956363	+	0.292182i	$0.0943812\pi$
$199$			8.24346i			0.584363i	−0.956363	+	0.292182i	$0.905619\pi$
$200$	−11.0219	−	2.79016i	−0.779364	−	0.197294i
$201$		0			0
$202$	−1.35834			−0.0955723
$203$	−6.19032	+	13.4711i	−0.434475	+	0.945485i
$204$		0			0
$205$	7.88419	+	0.982436i	0.550656	+	0.0686163i
$206$	−8.39998			−0.585255
$207$		0			0
$208$	0.261998			0.0181663
$209$	21.9602			1.51902
$210$		0			0
$211$	8.65523			0.595851			0.297925	−	0.954589i	$-0.403705\pi$
$211$	8.65523			0.595851			0.297925	+	0.954589i	$0.403705\pi$
$212$	14.4114			0.989779
$213$		0			0
$214$	−7.15190			−0.488894
$215$	−3.14838	+	25.2662i	−0.214717	+	1.72314i
$216$		0			0
$217$	−10.4000	+	22.6321i	−0.706000	+	1.53637i
$218$	−3.91641			−0.265253
$219$		0			0
$220$	2.00607	−	16.0990i	0.135249	−	1.08539i
$221$			0.815758i			0.0548738i
$222$		0			0
$223$	−4.12585			−0.276287			−0.138144	−	0.990412i	$-0.544114\pi$
$223$	−4.12585			−0.276287			−0.138144	+	0.990412i	$0.544114\pi$
$224$	13.6153	+	6.25659i	0.909712	+	0.418036i
$225$		0			0
$226$	7.48457			0.497866
$227$			12.0529i			0.799978i	0.916520	+	0.399989i	$0.130986\pi$
$227$			12.0529i			0.799978i	−0.916520	+	0.399989i	$0.869014\pi$
$228$		0			0
$229$		−	9.29639i		−	0.614323i	−0.951657	−	0.307161i	$-0.900621\pi$
$229$		−	9.29639i		−	0.614323i	0.951657	−	0.307161i	$-0.0993791\pi$
$230$	−7.89737	−	0.984079i	−0.520737	−	0.0648882i
$231$		0			0
$232$		−	12.7417i		−	0.836535i
$233$	5.23047			0.342660			0.171330	−	0.985214i	$-0.445194\pi$
$233$	5.23047			0.342660			0.171330	+	0.985214i	$0.445194\pi$
$234$		0			0
$235$	−0.889297	+	7.13673i	−0.0580113	+	0.465549i
$236$	−11.6680			−0.759521
$237$		0			0
$238$	−3.83742	+	8.35082i	−0.248743	+	0.541303i
$239$			0.0819988i			0.00530406i	0.999996	+	0.00265203i	$0.000844168\pi$
$239$			0.0819988i			0.00530406i	−0.999996	+	0.00265203i	$0.999156\pi$
$240$		0			0
$241$		−	9.41406i		−	0.606413i	−0.952925	−	0.303206i	$-0.901943\pi$
$241$		−	9.41406i		−	0.606413i	0.952925	−	0.303206i	$-0.0980572\pi$
$242$	−6.01648			−0.386754
$243$		0			0
$244$		−	13.0614i		−	0.836168i
$245$	−8.64762	−	13.0468i	−0.552476	−	0.833529i
$246$		0			0
$247$			0.718699i			0.0457297i
$248$		−	21.4067i		−	1.35933i
$249$		0			0
$250$	−6.57676	−	2.56533i	−0.415951	−	0.162246i
$251$	−6.26337			−0.395341			−0.197670	−	0.980269i	$-0.563338\pi$
$251$	−6.26337			−0.395341			−0.197670	+	0.980269i	$0.563338\pi$
$252$		0			0
$253$		−	25.5395i		−	1.60566i
$254$		−	10.2724i		−	0.644547i
$255$		0			0
$256$	−7.21947			−0.451217
$257$			20.4296i			1.27437i	0.770712	+	0.637183i	$0.219900\pi$
$257$			20.4296i			1.27437i	−0.770712	+	0.637183i	$0.780100\pi$
$258$		0			0
$259$	−6.07928	+	13.2295i	−0.377748	+	0.822039i
$260$	0.526876	+	0.0656532i	0.0326755	+	0.00407164i
$261$		0			0
$262$	−5.10471			−0.315370
$263$	17.7423			1.09404			0.547018	−	0.837121i	$-0.315763\pi$
$263$	17.7423			1.09404			0.547018	+	0.837121i	$0.315763\pi$
$264$		0			0
$265$	19.9695	+	2.48836i	1.22671	+	0.152859i
$266$	−3.38084	+	7.35723i	−0.207293	+	0.451101i
$267$		0			0
$268$		−	16.5395i		−	1.01031i
$269$	−21.2108			−1.29325			−0.646623	−	0.762810i	$-0.723819\pi$
$269$	−21.2108			−1.29325			−0.646623	+	0.762810i	$0.723819\pi$
$270$		0			0
$271$			11.6764i			0.709289i	0.935001	+	0.354645i	$0.115398\pi$
$271$			11.6764i			0.709289i	−0.935001	+	0.354645i	$0.884602\pi$
$272$			9.72024i			0.589376i
$273$		0			0
$274$	−3.41233			−0.206147
$275$	5.55950	−	21.9615i	0.335251	−	1.32433i
$276$		0			0
$277$		−	3.85001i		−	0.231324i	−0.993289	−	0.115662i	$-0.963101\pi$
$277$		−	3.85001i		−	0.231324i	0.993289	−	0.115662i	$-0.0368990\pi$
$278$		−	2.98259i		−	0.178884i
$279$		0			0
$280$	11.4354	+	7.08553i	0.683396	+	0.423442i
$281$			3.54026i			0.211194i	0.994409	+	0.105597i	$0.0336754\pi$
$281$			3.54026i			0.211194i	−0.994409	+	0.105597i	$0.966325\pi$
$282$		0			0
$283$	2.00607			0.119248			0.0596241	−	0.998221i	$-0.481010\pi$
$283$	2.00607			0.119248			0.0596241	+	0.998221i	$0.481010\pi$
$284$			9.07806i			0.538684i
$285$		0			0
$286$		−	0.424211i		−	0.0250841i
$287$	−8.54212	−	3.92532i	−0.504225	−	0.231705i
$288$		0			0
$289$	−13.2650			−0.780297
$290$	0.978256	−	7.85065i	0.0574452	−	0.461006i
$291$		0			0
$292$	−20.8837			−1.22213
$293$			15.6732i			0.915639i	0.889045	+	0.457819i	$0.151369\pi$
$293$			15.6732i			0.915639i	−0.889045	+	0.457819i	$0.848631\pi$
$294$		0			0
$295$	−16.1680	−	2.01467i	−0.941337	−	0.117299i
$296$		−	12.5132i		−	0.727314i
$297$		0			0
$298$			14.0444i			0.813573i
$299$	0.835840			0.0483379
$300$		0			0
$301$	12.5793	−	27.3746i	0.725061	−	1.57785i
$302$	2.83601			0.163194
$303$		0			0
$304$			8.56372i			0.491163i
$305$	2.25526	−	18.0988i	0.129136	−	1.03633i
$306$		0			0
$307$	−22.6233			−1.29118			−0.645589	−	0.763685i	$-0.723388\pi$
$307$	−22.6233			−1.29118			−0.645589	+	0.763685i	$0.723388\pi$
$308$	−8.01524	+	17.4424i	−0.456711	+	0.993873i
$309$		0			0
$310$	1.64352	−	13.1895i	0.0933455	−	0.749111i
$311$	16.5929			0.940897			0.470449	−	0.882427i	$-0.344092\pi$
$311$	16.5929			0.940897			0.470449	+	0.882427i	$0.344092\pi$
$312$		0			0
$313$	−11.4741			−0.648553			−0.324276	−	0.945962i	$-0.605121\pi$
$313$	−11.4741			−0.648553			−0.324276	+	0.945962i	$0.605121\pi$
$314$	−6.31537			−0.356397
$315$		0			0
$316$	−20.9171			−1.17668
$317$	18.5988			1.04461			0.522306	−	0.852758i	$-0.325072\pi$
$317$	18.5988			1.04461			0.522306	+	0.852758i	$0.325072\pi$
$318$		0			0
$319$	25.3884			1.42148
$320$	−0.0936272	−	0.0116667i	−0.00523392	−	0.000652190i
$321$		0			0
$322$	8.55640	+	3.93189i	0.476829	+	0.219116i
$323$	−26.6641			−1.48363
$324$		0			0
$325$	0.718742	+	0.181948i	0.0398686	+	0.0100926i
$326$		−	3.47461i		−	0.192441i
$327$		0			0
$328$	8.07962			0.446122
$329$	3.55319	−	7.73229i	0.195893	−	0.426295i
$330$		0			0
$331$	−8.18388			−0.449827			−0.224913	−	0.974379i	$-0.572210\pi$
$331$	−8.18388			−0.449827			−0.224913	+	0.974379i	$0.572210\pi$
$332$			0.0624130i			0.00342536i
$333$		0			0
$334$		−	8.54647i		−	0.467642i
$335$	2.85581	−	22.9183i	0.156030	−	1.25216i
$336$		0			0
$337$		−	10.7095i		−	0.583384i	−0.956512	−	0.291692i	$-0.905782\pi$
$337$		−	10.7095i		−	0.583384i	0.956512	−	0.291692i	$-0.0942183\pi$
$338$	−8.19444			−0.445719
$339$		0			0
$340$	−2.43577	+	19.5474i	−0.132098	+	1.06011i
$341$	42.6537			2.30983
$342$		0			0
$343$	5.09244	+	17.8064i	0.274966	+	0.961454i
$344$			25.8924i			1.39603i
$345$		0			0
$346$			0.00736648i			0.000396025i
$347$	3.47808			0.186713			0.0933566	−	0.995633i	$-0.470240\pi$
$347$	3.47808			0.186713			0.0933566	+	0.995633i	$0.470240\pi$
$348$		0			0
$349$		−	17.2548i		−	0.923630i	−0.886976	−	0.461815i	$-0.847198\pi$
$349$		−	17.2548i		−	0.923630i	0.886976	−	0.461815i	$-0.152802\pi$
$350$	6.50177	+	5.24362i	0.347534	+	0.280283i
$351$		0			0
$352$		−	25.6602i		−	1.36769i
$353$		−	31.4782i		−	1.67541i	−0.546121	−	0.837707i	$-0.683896\pi$
$353$		−	31.4782i		−	1.67541i	0.546121	−	0.837707i	$-0.316104\pi$
$354$		0			0
$355$	−1.56747	+	12.5792i	−0.0831929	+	0.667635i
$356$	−14.0628			−0.745328
$357$		0			0
$358$			6.77500i			0.358070i
$359$			21.9862i			1.16039i	0.814479	+	0.580193i	$0.197023\pi$
$359$			21.9862i			1.16039i	−0.814479	+	0.580193i	$0.802977\pi$
$360$		0			0
$361$	−4.49156			−0.236398
$362$		−	3.54864i		−	0.186512i
$363$		0			0
$364$	−0.570844	−	0.262317i	−0.0299203	−	0.0137492i
$365$	−28.9380	−	3.60592i	−1.51468	−	0.188742i
$366$		0			0
$367$	34.4285			1.79715			0.898576	−	0.438818i	$-0.144603\pi$
$367$	34.4285			1.79715			0.898576	+	0.438818i	$0.144603\pi$
$368$	9.95953			0.519176
$369$		0			0
$370$	0.960710	−	7.70984i	0.0499449	−	0.400815i
$371$	−21.6359	−	9.94226i	−1.12328	−	0.516176i
$372$		0			0
$373$		−	14.2735i		−	0.739052i	−0.929220	−	0.369526i	$-0.879520\pi$
$373$		−	14.2735i		−	0.739052i	0.929220	−	0.369526i	$-0.120480\pi$
$374$	15.7384			0.813816
$375$		0			0
$376$			7.31364i			0.377172i
$377$			0.830895i			0.0427933i
$378$		0			0
$379$	27.5521			1.41526			0.707628	−	0.706585i	$-0.249765\pi$
$379$	27.5521			1.41526			0.707628	+	0.706585i	$0.249765\pi$
$380$	−2.14596	+	17.2216i	−0.110085	+	0.883450i
$381$		0			0
$382$			9.50479i			0.486308i
$383$		−	14.4893i		−	0.740368i	−0.928959	−	0.370184i	$-0.879295\pi$
$383$		−	14.4893i		−	0.740368i	0.928959	−	0.370184i	$-0.120705\pi$
$384$		0			0
$385$	−14.1182	+	22.7855i	−0.719531	+	1.16126i
$386$			3.76714i			0.191743i
$387$		0			0
$388$	−7.08171			−0.359519
$389$		−	7.74863i		−	0.392871i	−0.980517	−	0.196436i	$-0.937063\pi$
$389$		−	7.74863i		−	0.392871i	0.980517	−	0.196436i	$-0.0629367\pi$
$390$		0			0
$391$			31.0101i			1.56825i
$392$	−10.3670	−	12.0784i	−0.523615	−	0.610050i
$393$		0			0
$394$	1.85127			0.0932655
$395$	−28.9843	−	3.61168i	−1.45836	−	0.181723i
$396$		0			0
$397$	9.26686			0.465091			0.232545	−	0.972586i	$-0.425295\pi$
$397$	9.26686			0.465091			0.232545	+	0.972586i	$0.425295\pi$
$398$			5.20500i			0.260903i
$399$		0			0
$400$	8.56423	+	2.16801i	0.428212	+	0.108401i
$401$			5.96267i			0.297762i	0.988855	+	0.148881i	$0.0475671\pi$
$401$			5.96267i			0.297762i	−0.988855	+	0.148881i	$0.952433\pi$
$402$		0			0
$403$			1.39594i			0.0695369i
$404$	3.44489			0.171390
$405$		0			0
$406$	−3.90862	+	8.50577i	−0.193982	+	0.422134i
$407$	24.9330			1.23588
$408$		0			0
$409$			3.18669i			0.157572i	0.996892	+	0.0787858i	$0.0251043\pi$
$409$			3.18669i			0.157572i	−0.996892	+	0.0787858i	$0.974896\pi$
$410$	4.97815	+	0.620319i	0.245853	+	0.0306354i
$411$		0			0
$412$	21.3033			1.04954
$413$	17.5172	+	8.04961i	0.861965	+	0.396095i
$414$		0			0
$415$	−0.0107766	+	0.0864839i	−0.000529003	+	0.00424533i
$416$	0.839791			0.0411741
$417$		0			0
$418$	13.8659			0.678202
$419$	−4.48265			−0.218992			−0.109496	−	0.993987i	$-0.534924\pi$
$419$	−4.48265			−0.218992			−0.109496	+	0.993987i	$0.534924\pi$
$420$		0			0
$421$	7.65013			0.372844			0.186422	−	0.982470i	$-0.440311\pi$
$421$	7.65013			0.372844			0.186422	+	0.982470i	$0.440311\pi$
$422$	5.46500			0.266032
$423$		0			0
$424$	20.4645			0.993842
$425$	−6.75035	+	26.6657i	−0.327440	+	1.29348i
$426$		0			0
$427$	−9.01088	+	19.6091i	−0.436067	+	0.948950i
$428$	18.1380			0.876733
$429$		0			0
$430$	−1.98791	+	15.9533i	−0.0958657	+	0.769336i
$431$			7.76903i			0.374221i	0.982339	+	0.187110i	$0.0599122\pi$
$431$			7.76903i			0.374221i	−0.982339	+	0.187110i	$0.940088\pi$
$432$		0			0
$433$	−4.42867			−0.212828			−0.106414	−	0.994322i	$-0.533937\pi$
$433$	−4.42867			−0.212828			−0.106414	+	0.994322i	$0.533937\pi$
$434$	−6.56667	+	14.2901i	−0.315210	+	0.685947i
$435$		0			0
$436$	9.93243			0.475677
$437$			27.3205i			1.30692i
$438$		0			0
$439$			22.6274i			1.07995i	0.841681	+	0.539974i	$0.181566\pi$
$439$			22.6274i			1.07995i	−0.841681	+	0.539974i	$0.818434\pi$
$440$	2.84865	−	22.8609i	0.135804	−	1.08985i
$441$		0			0
$442$			0.515078i			0.0244997i
$443$	7.96935			0.378635			0.189318	−	0.981916i	$-0.439372\pi$
$443$	7.96935			0.378635			0.189318	+	0.981916i	$0.439372\pi$
$444$		0			0
$445$	−19.4865	−	2.42818i	−0.923746	−	0.115107i
$446$	−2.60510			−0.123355
$447$		0			0
$448$	0.101440	+	0.0466144i	0.00479260	+	0.00220232i
$449$		−	4.63325i		−	0.218657i	−0.994006	−	0.109328i	$-0.965130\pi$
$449$		−	4.63325i		−	0.218657i	0.994006	−	0.109328i	$-0.0348700\pi$
$450$		0			0
$451$			16.0990i			0.758071i
$452$	−18.9817			−0.892823
$453$		0			0
$454$			7.61030i			0.357169i
$455$	−0.745709	−	0.462051i	−0.0349594	−	0.0216613i
$456$		0			0
$457$		−	28.6143i		−	1.33852i	−0.743028	−	0.669260i	$-0.766611\pi$
$457$		−	28.6143i		−	1.33852i	0.743028	−	0.669260i	$-0.233389\pi$
$458$		−	5.86983i		−	0.274279i
$459$		0			0
$460$	20.0286	+	2.49573i	0.933838	+	0.116364i
$461$	0.0864695			0.00402728			0.00201364	−	0.999998i	$-0.499359\pi$
$461$	0.0864695			0.00402728			0.00201364	+	0.999998i	$0.499359\pi$
$462$		0			0
$463$		−	24.5503i		−	1.14095i	−0.821315	−	0.570475i	$-0.806759\pi$
$463$		−	24.5503i		−	1.14095i	0.821315	−	0.570475i	$-0.193241\pi$
$464$			9.90060i			0.459624i
$465$		0			0
$466$	3.30257			0.152989
$467$		−	13.2264i		−	0.612043i	−0.952025	−	0.306021i	$-0.901002\pi$
$467$		−	13.2264i		−	0.612043i	0.952025	−	0.306021i	$-0.0989979\pi$
$468$		0			0
$469$	−11.4104	+	24.8308i	−0.526883	+	1.14658i
$470$	−0.561510	+	4.50620i	−0.0259005	+	0.207856i
$471$		0			0
$472$	−16.5688			−0.762639
$473$	−51.5917			−2.37219
$474$		0			0
$475$	−5.94719	+	23.4930i	−0.272876	+	1.07793i
$476$	9.73211	−	21.1786i	0.446071	−	0.970719i
$477$		0			0
$478$			0.0517748i			0.00236812i
$479$	31.1095			1.42143			0.710716	−	0.703479i	$-0.248371\pi$
$479$	31.1095			1.42143			0.710716	+	0.703479i	$0.248371\pi$
$480$		0			0
$481$			0.815992i			0.0372060i
$482$		−	5.94412i		−	0.270747i
$483$		0			0
$484$	15.2584			0.693565
$485$	−9.81293	−	1.22277i	−0.445582	−	0.0555232i
$486$		0			0
$487$		−	0.975691i		−	0.0442128i	−0.999756	−	0.0221064i	$-0.992963\pi$
$487$		−	0.975691i		−	0.0442128i	0.999756	−	0.0221064i	$-0.00703726\pi$
$488$		−	18.5474i		−	0.839601i
$489$		0			0
$490$	−5.46019	−	8.23786i	−0.246666	−	0.372149i
$491$			20.8643i			0.941591i	0.882242	+	0.470796i	$0.156033\pi$
$491$			20.8643i			0.941591i	−0.882242	+	0.470796i	$0.843967\pi$
$492$		0			0
$493$	−30.8266			−1.38836
$494$			0.453793i			0.0204171i
$495$		0			0
$496$			16.6335i			0.746865i
$497$	6.26285	−	13.6289i	0.280927	−	0.611341i
$498$		0			0
$499$	5.91050			0.264590			0.132295	−	0.991210i	$-0.457765\pi$
$499$	5.91050			0.264590			0.132295	+	0.991210i	$0.457765\pi$
$500$	16.6794	+	6.50596i	0.745924	+	0.290955i
$501$		0			0
$502$	−3.95475			−0.176509
$503$			16.4740i			0.734538i	0.930115	+	0.367269i	$0.119707\pi$
$503$			16.4740i			0.734538i	−0.930115	+	0.367269i	$0.880293\pi$
$504$		0			0
$505$	4.77349	+	0.594817i	0.212417	+	0.0264690i
$506$		−	16.1259i		−	0.716883i
$507$		0			0
$508$			26.0519i			1.15587i
$509$	−27.0391			−1.19849			−0.599243	−	0.800567i	$-0.704532\pi$
$509$	−27.0391			−1.19849			−0.599243	+	0.800567i	$0.704532\pi$
$510$		0			0
$511$	31.3528	+	14.4074i	1.38697	+	0.637347i
$512$	18.0420			0.797353
$513$		0			0
$514$			12.8995i			0.568971i
$515$	29.5193	+	3.67836i	1.30078	+	0.162088i
$516$		0			0
$517$	−14.5727			−0.640907
$518$	−3.83852	+	8.35321i	−0.168655	+	0.367019i
$519$		0			0
$520$	0.748175	+	0.0932288i	0.0328096	+	0.00408836i
$521$	−31.6454			−1.38641			−0.693206	−	0.720740i	$-0.743802\pi$
$521$	−31.6454			−1.38641			−0.693206	+	0.720740i	$0.743802\pi$
$522$		0			0
$523$	35.3137			1.54416			0.772079	−	0.635526i	$-0.219217\pi$
$523$	35.3137			1.54416			0.772079	+	0.635526i	$0.219217\pi$
$524$	12.9461			0.565553
$525$		0			0
$526$	11.2026			0.488459
$527$	−51.7902			−2.25602
$528$		0			0
$529$	8.77349			0.381456
$530$	12.6089	+	1.57118i	0.547696	+	0.0682475i
$531$		0			0
$532$	8.57417	−	18.6587i	0.371738	−	0.808959i
$533$	−0.526876			−0.0228216
$534$		0			0
$535$	25.1333	+	3.13182i	1.08661	+	0.135400i
$536$		−	23.4864i		−	1.01446i
$537$		0			0
$538$	−13.3927			−0.577401
$539$	24.0666	−	20.6567i	1.03662	−	0.889749i
$540$		0			0
$541$	23.1178			0.993913			0.496956	−	0.867776i	$-0.334451\pi$
$541$	23.1178			0.993913			0.496956	+	0.867776i	$0.334451\pi$
$542$			7.37257i			0.316679i
$543$		0			0
$544$			31.1567i			1.33583i
$545$	13.7631	+	1.71500i	0.589546	+	0.0734624i
$546$		0			0
$547$		−	44.2319i		−	1.89122i	−0.325302	−	0.945610i	$-0.605466\pi$
$547$		−	44.2319i		−	1.89122i	0.325302	−	0.945610i	$-0.394534\pi$
$548$	8.65405			0.369683
$549$		0			0
$550$	3.51032	−	13.8667i	0.149681	−	0.591278i
$551$	−27.1588			−1.15701
$552$		0			0
$553$	31.4030	+	14.4305i	1.33539	+	0.613646i
$554$		−	2.43093i		−	0.103280i
$555$		0			0
$556$			7.56416i			0.320792i
$557$	21.7878			0.923180			0.461590	−	0.887093i	$-0.347279\pi$
$557$	21.7878			0.923180			0.461590	+	0.887093i	$0.347279\pi$
$558$		0			0
$559$		−	1.68846i		−	0.0714143i
$560$	−8.88556	−	5.50561i	−0.375483	−	0.232655i
$561$		0			0
$562$			2.23535i			0.0942927i
$563$			10.1104i			0.426104i	0.977041	+	0.213052i	$0.0683403\pi$
$563$			10.1104i			0.426104i	−0.977041	+	0.213052i	$0.931660\pi$
$564$		0			0
$565$	−26.3024	−	3.27750i	−1.10655	−	0.137885i
$566$	1.26665			0.0532412
$567$		0			0
$568$			12.8910i			0.540895i
$569$		−	43.6209i		−	1.82868i	−0.404942	−	0.914342i	$-0.632708\pi$
$569$		−	43.6209i		−	1.82868i	0.404942	−	0.914342i	$-0.367292\pi$
$570$		0			0
$571$	−5.99489			−0.250879			−0.125439	−	0.992101i	$-0.540034\pi$
$571$	−5.99489			−0.250879			−0.125439	+	0.992101i	$0.540034\pi$
$572$			1.07585i			0.0449833i
$573$		0			0
$574$	−5.39357	−	2.47849i	−0.225123	−	0.103450i
$575$	27.3221	+	6.91653i	1.13941	+	0.288439i
$576$		0			0
$577$	−18.3774			−0.765063			−0.382532	−	0.923942i	$-0.624948\pi$
$577$	−18.3774			−0.765063			−0.382532	+	0.923942i	$0.624948\pi$
$578$	−8.37568			−0.348382
$579$		0			0
$580$	−2.48096	+	19.9101i	−0.103016	+	0.826721i
$581$	0.0430580	−	0.0937009i	0.00178635	−	0.00388737i
$582$		0			0
$583$			40.7763i			1.68878i
$584$	−29.6553			−1.22714
$585$		0			0
$586$			9.89621i			0.408809i
$587$		−	28.8305i		−	1.18996i	−0.803740	−	0.594980i	$-0.797160\pi$
$587$		−	28.8305i		−	1.18996i	0.803740	−	0.594980i	$-0.202840\pi$
$588$		0			0
$589$	−45.6281			−1.88007
$590$	−10.2086	−	1.27208i	−0.420283	−	0.0523707i
$591$		0			0
$592$			9.72302i			0.399614i
$593$		−	45.2683i		−	1.85895i	−0.368891	−	0.929473i	$-0.620262\pi$
$593$		−	45.2683i		−	1.85895i	0.368891	−	0.929473i	$-0.379738\pi$
$594$		0			0
$595$	17.1423	−	27.6662i	0.702767	−	1.13420i
$596$		−	35.6182i		−	1.45898i
$597$		0			0
$598$	0.527757			0.0215816
$599$			19.0252i			0.777350i	0.921375	+	0.388675i	$0.127067\pi$
$599$			19.0252i			0.777350i	−0.921375	+	0.388675i	$0.872933\pi$
$600$		0			0
$601$		−	4.80803i		−	0.196124i	−0.995180	−	0.0980618i	$-0.968736\pi$
$601$		−	4.80803i		−	0.196124i	0.995180	−	0.0980618i	$-0.0312643\pi$
$602$	7.94271	−	17.2846i	0.323721	−	0.704467i
$603$		0			0
$604$	−7.19243			−0.292656
$605$	21.1432	+	2.63462i	0.859593	+	0.107112i
$606$		0			0
$607$	−47.2526			−1.91792			−0.958962	−	0.283535i	$-0.908493\pi$
$607$	−47.2526			−1.91792			−0.958962	+	0.283535i	$0.908493\pi$
$608$			27.4496i			1.11323i
$609$		0			0
$610$	1.42399	−	11.4277i	0.0576557	−	0.462695i
$611$		−	0.476926i		−	0.0192944i
$612$		0			0
$613$		−	15.4404i		−	0.623631i	−0.950143	−	0.311816i	$-0.899063\pi$
$613$		−	15.4404i		−	0.623631i	0.950143	−	0.311816i	$-0.100937\pi$
$614$	−14.2845			−0.576477
$615$		0			0
$616$	−11.3818	+	24.7686i	−0.458586	+	0.997954i
$617$	−30.2595			−1.21820			−0.609100	−	0.793094i	$-0.708469\pi$
$617$	−30.2595			−1.21820			−0.609100	+	0.793094i	$0.708469\pi$
$618$		0			0
$619$			6.77605i			0.272352i	0.990685	+	0.136176i	$0.0434813\pi$
$619$			6.77605i			0.272352i	−0.990685	+	0.136176i	$0.956519\pi$
$620$	−4.16814	+	33.4499i	−0.167396	+	1.34338i
$621$		0			0
$622$	10.4769			0.420086
$623$	21.1126	+	9.70177i	0.845857	+	0.388693i
$624$		0			0
$625$	21.9888	+	11.8951i	0.879552	+	0.475804i
$626$	−7.24484			−0.289562
$627$		0			0
$628$	16.0165			0.639126
$629$	−30.2737			−1.20709
$630$		0			0
$631$	−22.3392			−0.889311			−0.444655	−	0.895702i	$-0.646674\pi$
$631$	−22.3392			−0.889311			−0.444655	+	0.895702i	$0.646674\pi$
$632$	−29.7027			−1.18151
$633$		0			0
$634$	11.7434			0.466392
$635$	−4.49829	+	36.0994i	−0.178509	+	1.43256i
$636$		0			0
$637$	0.676040	+	0.787637i	0.0267857	+	0.0312073i
$638$	16.0305			0.634653
$639$		0			0
$640$	25.0742	+	3.12445i	0.991144	+	0.123505i
$641$			39.7803i			1.57123i	0.618717	+	0.785614i	$0.287653\pi$
$641$			39.7803i			1.57123i	−0.618717	+	0.785614i	$0.712347\pi$
$642$		0			0
$643$	28.6778			1.13094			0.565470	−	0.824769i	$-0.308695\pi$
$643$	28.6778			1.13094			0.565470	+	0.824769i	$0.308695\pi$
$644$	−21.6999	−	9.97169i	−0.855098	−	0.392940i
$645$		0			0
$646$	−16.8360			−0.662402
$647$			37.8582i			1.48836i	0.667979	+	0.744180i	$0.267160\pi$
$647$			37.8582i			1.48836i	−0.667979	+	0.744180i	$0.732840\pi$
$648$		0			0
$649$		−	33.0139i		−	1.29591i
$650$	0.453820	+	0.114883i	0.0178003	+	0.00450610i
$651$		0			0
$652$			8.81198i			0.345104i
$653$	0.778605			0.0304692			0.0152346	−	0.999884i	$-0.495150\pi$
$653$	0.778605			0.0304692			0.0152346	+	0.999884i	$0.495150\pi$
$654$		0			0
$655$	17.9390	+	2.23535i	0.700936	+	0.0873425i
$656$	−6.27804			−0.245116
$657$		0			0
$658$	2.24351	−	4.88224i	0.0874613	−	0.190329i
$659$			0.220093i			0.00857360i	0.999991	+	0.00428680i	$0.00136453\pi$
$659$			0.220093i			0.00857360i	−0.999991	+	0.00428680i	$0.998635\pi$
$660$		0			0
$661$		−	23.2389i		−	0.903889i	−0.892046	−	0.451945i	$-0.850730\pi$
$661$		−	23.2389i		−	0.903889i	0.892046	−	0.451945i	$-0.149270\pi$
$662$	−5.16738			−0.200836
$663$		0			0
$664$			0.0886276i			0.00343942i
$665$	15.1027	−	24.3744i	0.585659	−	0.945199i
$666$		0			0
$667$			31.5855i			1.22300i
$668$			21.6748i			0.838622i
$669$		0			0
$670$	1.80319	−	14.4708i	0.0696631	−	0.559057i
$671$	36.9564			1.42669
$672$		0			0
$673$			4.88224i			0.188196i	0.995563	+	0.0940982i	$0.0299968\pi$
$673$			4.88224i			0.188196i	−0.995563	+	0.0940982i	$0.970003\pi$
$674$		−	6.76209i		−	0.260466i
$675$		0			0
$676$	20.7820			0.799307
$677$		−	7.31817i		−	0.281260i	−0.990062	−	0.140630i	$-0.955087\pi$
$677$		−	7.31817i		−	0.281260i	0.990062	−	0.140630i	$-0.0449128\pi$
$678$		0			0
$679$	10.6318	+	4.88559i	0.408011	+	0.187492i
$680$	−3.45884	+	27.7577i	−0.132640	+	1.06446i
$681$		0			0
$682$	26.9320			1.03128
$683$	33.3366			1.27559			0.637794	−	0.770207i	$-0.279847\pi$
$683$	33.3366			1.27559			0.637794	+	0.770207i	$0.279847\pi$
$684$		0			0
$685$	11.9917	+	1.49426i	0.458178	+	0.0570928i
$686$	3.21541	+	11.2431i	0.122765	+	0.429264i
$687$		0			0
$688$		−	20.1190i		−	0.767030i
$689$	−1.33450			−0.0508404
$690$		0			0
$691$		−	45.0610i		−	1.71420i	−0.515149	−	0.857101i	$-0.672263\pi$
$691$		−	45.0610i		−	1.71420i	0.515149	−	0.857101i	$-0.327737\pi$
$692$		−	0.0186822i		−	0.000710190i
$693$		0			0
$694$	2.19609			0.0833626
$695$	−1.30608	+	10.4814i	−0.0495423	+	0.397584i
$696$		0			0
$697$		−	19.5474i		−	0.740410i
$698$		−	10.8949i		−	0.412377i
$699$		0			0
$700$	−16.4892	−	13.2984i	−0.623233	−	0.502632i
$701$		−	3.53070i		−	0.133353i	−0.997775	−	0.0666764i	$-0.978760\pi$
$701$		−	3.53070i		−	0.133353i	0.997775	−	0.0666764i	$-0.0212395\pi$
$702$		0			0
$703$	−26.6717			−1.00594
$704$		−	0.191180i		−	0.00720537i
$705$		0			0
$706$		−	19.8756i		−	0.748028i
$707$	−5.17183	−	2.37659i	−0.194507	−	0.0893809i
$708$		0			0
$709$	−21.3513			−0.801866			−0.400933	−	0.916107i	$-0.631314\pi$
$709$	−21.3513			−0.801866			−0.400933	+	0.916107i	$0.631314\pi$
$710$	−0.989718	+	7.94263i	−0.0371435	+	0.298082i
$711$		0			0
$712$	−19.9695			−0.748388
$713$			53.0651i			1.98731i
$714$		0			0
$715$	−0.185762	+	1.49077i	−0.00694711	+	0.0557516i
$716$		−	17.1821i		−	0.642127i
$717$		0			0
$718$			13.8823i			0.518082i
$719$	52.7583			1.96755			0.983777	−	0.179396i	$-0.0574145\pi$
$719$	52.7583			1.96755			0.983777	+	0.179396i	$0.0574145\pi$
$720$		0			0
$721$	−31.9827	−	14.6969i	−1.19110	−	0.547340i
$722$	−2.83601			−0.105545
$723$		0			0
$724$			8.99972i			0.334472i
$725$	−6.87560	+	27.1605i	−0.255354	+	1.00871i
$726$		0			0
$727$	36.9585			1.37072			0.685358	−	0.728206i	$-0.259646\pi$
$727$	36.9585			1.37072			0.685358	+	0.728206i	$0.259646\pi$
$728$	−0.810609	−	0.372496i	−0.0300432	−	0.0138056i
$729$		0			0
$730$	−18.2717	−	2.27681i	−0.676267	−	0.0842685i
$731$	62.6427			2.31693
$732$		0			0
$733$	−0.355683			−0.0131374			−0.00656872	−	0.999978i	$-0.502091\pi$
$733$	−0.355683			−0.0131374			−0.00656872	+	0.999978i	$0.502091\pi$
$734$	21.7385			0.802381
$735$		0			0
$736$	31.9237			1.17672
$737$	46.7976			1.72381
$738$		0			0
$739$	−48.9931			−1.80224			−0.901120	−	0.433569i	$-0.857254\pi$
$739$	−48.9931			−1.80224			−0.901120	+	0.433569i	$0.857254\pi$
$740$	−2.43646	+	19.5530i	−0.0895662	+	0.718782i
$741$		0			0
$742$	−13.6611	−	6.27763i	−0.501515	−	0.230459i
$743$	−18.3097			−0.671720			−0.335860	−	0.941912i	$-0.609027\pi$
$743$	−18.3097			−0.671720			−0.335860	+	0.941912i	$0.609027\pi$
$744$		0			0
$745$	6.15007	−	49.3552i	0.225321	−	1.80823i
$746$		−	9.01240i		−	0.329968i
$747$		0			0
$748$	−39.9144			−1.45941
$749$	−27.2306	−	12.5132i	−0.994986	−	0.457222i
$750$		0			0
$751$	−15.0605			−0.549566			−0.274783	−	0.961506i	$-0.588606\pi$
$751$	−15.0605			−0.549566			−0.274783	+	0.961506i	$0.588606\pi$
$752$		−	5.68286i		−	0.207232i
$753$		0			0
$754$			0.524635i			0.0191061i
$755$	−9.96635	−	1.24189i	−0.362713	−	0.0451970i
$756$		0			0
$757$			12.0537i			0.438098i	0.975714	+	0.219049i	$0.0702955\pi$
$757$			12.0537i			0.438098i	−0.975714	+	0.219049i	$0.929704\pi$
$758$	17.3966			0.631875
$759$		0			0
$760$	−3.04730	+	24.4550i	−0.110537	+	0.887077i
$761$	−25.4685			−0.923234			−0.461617	−	0.887079i	$-0.652731\pi$
$761$	−25.4685			−0.923234			−0.461617	+	0.887079i	$0.652731\pi$
$762$		0			0
$763$	−14.9116	−	6.85227i	−0.539836	−	0.248069i
$764$		−	24.1052i		−	0.872095i
$765$		0			0
$766$		−	9.14867i		−	0.330555i
$767$	1.08046			0.0390131
$768$		0			0
$769$		−	53.3260i		−	1.92298i	−0.274832	−	0.961492i	$-0.588622\pi$
$769$		−	53.3260i		−	1.92298i	0.274832	−	0.961492i	$-0.411378\pi$
$770$	−8.91437	+	14.3870i	−0.321252	+	0.518471i
$771$		0			0
$772$		−	9.55388i		−	0.343852i
$773$		−	17.5125i		−	0.629879i	−0.949112	−	0.314940i	$-0.898016\pi$
$773$		−	17.5125i		−	0.629879i	0.949112	−	0.314940i	$-0.101984\pi$
$774$		0			0
$775$	−11.5513	+	45.6309i	−0.414936	+	1.63911i
$776$	−10.0562			−0.360995
$777$		0			0
$778$		−	4.89256i		−	0.175407i
$779$		−	17.2216i		−	0.617028i
$780$		0			0
$781$	−25.6859			−0.919113
$782$			19.5801i			0.700182i
$783$		0			0
$784$	8.05542	+	9.38515i	0.287693	+	0.335184i
$785$	22.1936	+	2.76550i	0.792122	+	0.0987050i
$786$		0			0
$787$	−7.31818			−0.260865			−0.130432	−	0.991457i	$-0.541637\pi$
$787$	−7.31818			−0.260865			−0.130432	+	0.991457i	$0.541637\pi$
$788$	−4.69501			−0.167253
$789$		0			0
$790$	−18.3009	−	2.28045i	−0.651118	−	0.0811348i
$791$	28.4973	+	13.0952i	1.01325	+	0.465613i
$792$		0			0
$793$			1.20949i			0.0429501i
$794$	5.85118			0.207651
$795$		0			0
$796$		−	13.2004i		−	0.467877i
$797$			18.2410i			0.646130i	0.946377	+	0.323065i	$0.104713\pi$
$797$			18.2410i			0.646130i	−0.946377	+	0.323065i	$0.895287\pi$
$798$		0			0
$799$	17.6942			0.625976
$800$	27.4513	+	6.94922i	0.970549	+	0.245692i
$801$		0			0
$802$			3.76489i			0.132943i
$803$		−	59.0894i		−	2.08522i
$804$		0			0
$805$	−28.3472	−	17.5643i	−0.999109	−	0.619062i
$806$			0.881412i			0.0310464i
$807$		0			0
$808$	4.89181			0.172093
$809$		−	11.7958i		−	0.414717i	−0.978265	−	0.207359i	$-0.933513\pi$
$809$		−	11.7958i		−	0.414717i	0.978265	−	0.207359i	$-0.0664867\pi$
$810$		0			0
$811$		−	2.21924i		−	0.0779281i	−0.999241	−	0.0389641i	$-0.987594\pi$
$811$		−	2.21924i		−	0.0779281i	0.999241	−	0.0389641i	$-0.0124058\pi$
$812$	9.91269	−	21.5716i	0.347867	−	0.757013i
$813$		0			0
$814$	15.7429			0.551790
$815$	−1.52153	+	12.2105i	−0.0532970	+	0.427716i
$816$		0			0
$817$	55.1894			1.93083
$818$			2.01210i			0.0703516i
$819$		0			0
$820$	−12.6251	−	1.57320i	−0.440889	−	0.0549384i
$821$			26.2313i			0.915478i	0.889087	+	0.457739i	$0.151341\pi$
$821$			26.2313i			0.915478i	−0.889087	+	0.457739i	$0.848659\pi$
$822$		0			0
$823$		−	41.8603i		−	1.45916i	−0.683897	−	0.729579i	$-0.739716\pi$
$823$		−	41.8603i		−	1.45916i	0.683897	−	0.729579i	$-0.260284\pi$
$824$	30.2510			1.05385
$825$		0			0
$826$	11.0605	+	5.08260i	0.384845	+	0.176846i
$827$	−21.7686			−0.756968			−0.378484	−	0.925608i	$-0.623554\pi$
$827$	−21.7686			−0.756968			−0.378484	+	0.925608i	$0.623554\pi$
$828$		0			0
$829$		−	23.5665i		−	0.818500i	−0.912422	−	0.409250i	$-0.865790\pi$
$829$		−	23.5665i		−	0.818500i	0.912422	−	0.409250i	$-0.134210\pi$
$830$	−0.00680446	+	0.0546068i	−0.000236186	+	0.00189543i
$831$		0			0
$832$	0.00625682			0.000216916
$833$	−29.2217	+	25.0814i	−1.01247	+	0.869020i
$834$		0			0
$835$	−3.74250	+	30.0341i	−0.129515	+	1.03937i
$836$	−35.1653			−1.21622
$837$		0			0
$838$	−2.83039			−0.0977742
$839$	−51.4056			−1.77472			−0.887359	−	0.461080i	$-0.847462\pi$
$839$	−51.4056			−1.77472			−0.887359	+	0.461080i	$0.847462\pi$
$840$		0			0
$841$	−2.39862			−0.0827110
$842$	4.83036			0.166465
$843$		0			0
$844$	−13.8598			−0.477075
$845$	28.7970	+	3.58835i	0.990647	+	0.123443i
$846$		0			0
$847$	−22.9076	−	10.5266i	−0.787113	−	0.361699i
$848$	−15.9013			−0.546054
$849$		0			0
$850$	−4.26223	+	16.8370i	−0.146193	+	0.577503i
$851$			31.0190i			1.06332i
$852$		0			0
$853$	−33.6325			−1.15155			−0.575777	−	0.817607i	$-0.695300\pi$
$853$	−33.6325			−1.15155			−0.575777	+	0.817607i	$0.695300\pi$
$854$	−5.68956	+	12.3814i	−0.194693	+	0.423681i
$855$		0			0
$856$	25.7563			0.880332
$857$		−	1.52812i		−	0.0521996i	−0.999659	−	0.0260998i	$-0.991691\pi$
$857$		−	1.52812i		−	0.0521996i	0.999659	−	0.0260998i	$-0.00830877\pi$
$858$		0			0
$859$		−	22.6274i		−	0.772038i	−0.922491	−	0.386019i	$-0.873850\pi$
$859$		−	22.6274i		−	0.772038i	0.922491	−	0.386019i	$-0.126150\pi$
$860$	5.04156	−	40.4593i	0.171916	−	1.37965i
$861$		0			0
$862$			4.90544i			0.167080i
$863$	−38.6597			−1.31599			−0.657996	−	0.753021i	$-0.728596\pi$
$863$	−38.6597			−1.31599			−0.657996	+	0.753021i	$0.728596\pi$
$864$		0			0
$865$	0.00322579	−	0.0258874i	0.000109680	−	0.000880198i
$866$	−2.79630			−0.0950223
$867$		0			0
$868$	16.6538	−	36.2412i	0.565267	−	1.23011i
$869$		−	59.1839i		−	2.00767i
$870$		0			0
$871$			1.53156i			0.0518949i
$872$	14.1042			0.477630
$873$		0			0
$874$			17.2504i			0.583504i
$875$	−20.5524	−	21.2743i	−0.694799	−	0.719204i
$876$		0			0
$877$			42.7945i			1.44507i	0.691335	+	0.722534i	$0.257023\pi$
$877$			42.7945i			1.44507i	−0.691335	+	0.722534i	$0.742977\pi$
$878$			14.2872i			0.482169i
$879$		0			0
$880$	−2.21347	+	17.7634i	−0.0746159	+	0.598804i
$881$	−2.86297			−0.0964559			−0.0482279	−	0.998836i	$-0.515357\pi$
$881$	−2.86297			−0.0964559			−0.0482279	+	0.998836i	$0.515357\pi$
$882$		0			0
$883$		−	0.311937i		−	0.0104975i	−0.999986	−	0.00524875i	$-0.998329\pi$
$883$		−	0.311937i		−	0.0104975i	0.999986	−	0.00524875i	$-0.00167074\pi$
$884$		−	1.30629i		−	0.0439354i
$885$		0			0
$886$	5.03192			0.169051
$887$		−	5.36565i		−	0.180161i	−0.995934	−	0.0900805i	$-0.971288\pi$
$887$		−	5.36565i		−	0.180161i	0.995934	−	0.0900805i	$-0.0287124\pi$
$888$		0			0
$889$	17.9729	−	39.1118i	0.602792	−	1.31177i
$890$	−12.3039	−	1.53317i	−0.412429	−	0.0513921i
$891$		0			0
$892$	6.60681			0.221212
$893$	15.5889			0.521664
$894$		0			0
$895$	2.96678	−	23.8088i	0.0991684	−	0.795841i
$896$	−27.1666	−	12.4838i	−0.907572	−	0.417053i
$897$		0			0
$898$		−	2.92548i		−	0.0976244i
$899$	−52.7512			−1.75935
$900$		0			0
$901$		−	49.5106i		−	1.64944i
$902$			10.1650i			0.338459i
$903$		0			0
$904$	−26.9544			−0.896489
$905$	−1.55395	+	12.4707i	−0.0516550	+	0.414539i
$906$		0			0
$907$		−	33.4555i		−	1.11087i	−0.831559	−	0.555437i	$-0.812551\pi$
$907$		−	33.4555i		−	1.11087i	0.831559	−	0.555437i	$-0.187449\pi$
$908$		−	19.3005i		−	0.640511i
$909$		0			0
$910$	−0.470847	−	0.291744i	−0.0156084	−	0.00967121i
$911$			22.6543i			0.750570i	0.926910	+	0.375285i	$0.122455\pi$
$911$			22.6543i			0.750570i	−0.926910	+	0.375285i	$0.877545\pi$
$912$		0			0
$913$	−0.176594			−0.00584441
$914$		−	18.0673i		−	0.597614i
$915$		0			0
$916$			14.8865i			0.491864i
$917$	−19.4360	−	8.93136i	−0.641834	−	0.294940i
$918$		0			0
$919$	34.9138			1.15170			0.575850	−	0.817555i	$-0.304671\pi$
$919$	34.9138			1.15170			0.575850	+	0.817555i	$0.304671\pi$
$920$	28.4410	+	3.54398i	0.937672	+	0.116842i
$921$		0			0
$922$	0.0545976			0.00179808
$923$		−	0.840630i		−	0.0276697i
$924$		0			0
$925$	−6.75228	+	26.6733i	−0.222014	+	0.877013i
$926$		−	15.5013i		−	0.509405i
$927$		0			0
$928$			31.7348i			1.04175i
$929$	−54.1491			−1.77658			−0.888288	−	0.459288i	$-0.848105\pi$
$929$	−54.1491			−1.77658			−0.888288	+	0.459288i	$0.848105\pi$
$930$		0			0
$931$	−25.7449	+	22.0972i	−0.843755	+	0.724207i
$932$	−8.37568			−0.274354
$933$		0			0
$934$		−	8.35125i		−	0.273261i
$935$	−55.3083	−	6.89187i	−1.80877	−	0.225388i
$936$		0			0
$937$	−25.2570			−0.825111			−0.412556	−	0.910932i	$-0.635364\pi$
$937$	−25.2570			−0.825111			−0.412556	+	0.910932i	$0.635364\pi$
$938$	−7.20463	+	15.6784i	−0.235240	+	0.511918i
$939$		0			0
$940$	1.42405	−	11.4282i	0.0464474	−	0.372747i
$941$	21.7095			0.707709			0.353854	−	0.935301i	$-0.384871\pi$
$941$	21.7095			0.707709			0.353854	+	0.935301i	$0.384871\pi$
$942$		0			0
$943$	−20.0286			−0.652221
$944$	12.8743			0.419023
$945$		0			0
$946$	−32.5755			−1.05912
$947$	51.0148			1.65776			0.828880	−	0.559427i	$-0.188979\pi$
$947$	51.0148			1.65776			0.828880	+	0.559427i	$0.188979\pi$
$948$		0			0
$949$	1.93384			0.0627750
$950$	−3.75511	+	14.8337i	−0.121832	+	0.481268i
$951$		0			0
$952$	13.8198	−	30.0740i	0.447902	−	0.974704i
$953$	27.2123			0.881493			0.440746	−	0.897632i	$-0.354714\pi$
$953$	27.2123			0.881493			0.440746	+	0.897632i	$0.354714\pi$
$954$		0			0
$955$	4.16215	−	33.4019i	0.134684	−	1.08086i
$956$		−	0.131306i		−	0.00424675i
$957$		0			0
$958$	19.6429			0.634632
$959$	−12.9924	−	5.97033i	−0.419545	−	0.192792i
$960$		0			0
$961$	−57.6245			−1.85885
$962$			0.515225i			0.0166115i
$963$		0			0
$964$			15.0749i			0.485531i
$965$	1.64963	−	13.2385i	0.0531036	−	0.426164i
$966$		0			0
$967$			22.7046i			0.730130i	0.930982	+	0.365065i	$0.118953\pi$
$967$			22.7046i			0.730130i	−0.930982	+	0.365065i	$0.881047\pi$
$968$	21.6673			0.696413
$969$		0			0
$970$	−6.19597	−	0.772070i	−0.198941	−	0.0247897i
$971$	34.9031			1.12009			0.560047	−	0.828461i	$-0.310783\pi$
$971$	34.9031			1.12009			0.560047	+	0.828461i	$0.310783\pi$
$972$		0			0
$973$	5.21842	−	11.3561i	0.167295	−	0.364060i
$974$		−	0.616061i		−	0.0197399i
$975$		0			0
$976$			14.4117i			0.461308i
$977$	27.1089			0.867290			0.433645	−	0.901084i	$-0.357227\pi$
$977$	27.1089			0.867290			0.433645	+	0.901084i	$0.357227\pi$
$978$		0			0
$979$		−	39.7900i		−	1.27169i
$980$	13.8476	+	20.8921i	0.442346	+	0.667374i
$981$		0			0
$982$			13.1739i			0.420396i
$983$		−	28.5213i		−	0.909687i	−0.890571	−	0.454844i	$-0.849695\pi$
$983$		−	28.5213i		−	0.909687i	0.890571	−	0.454844i	$-0.150305\pi$
$984$		0			0
$985$	−6.50575	−	0.810671i	−0.207290	−	0.0258301i
$986$	−19.4642			−0.619867
$987$		0			0
$988$		−	1.15087i		−	0.0366140i
$989$		−	64.1848i		−	2.04096i
$990$		0			0
$991$	24.1027			0.765648			0.382824	−	0.923821i	$-0.374952\pi$
$991$	24.1027			0.765648			0.382824	+	0.923821i	$0.374952\pi$
$992$			53.3160i			1.69278i
$993$		0			0
$994$	3.95442	−	8.60543i	0.125427	−	0.272948i
$995$	2.27927	−	18.2915i	0.0722577	−	0.579879i
$996$		0			0
$997$	16.9299			0.536177			0.268088	−	0.963394i	$-0.413608\pi$
$997$	16.9299			0.536177			0.268088	+	0.963394i	$0.413608\pi$
$998$	3.73195			0.118133
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.g.b.944.17	yes	32
3.2	odd	2	inner	945.2.g.b.944.16	yes	32
5.4	even	2	inner	945.2.g.b.944.14	yes	32
7.6	odd	2	inner	945.2.g.b.944.20	yes	32
15.14	odd	2	inner	945.2.g.b.944.19	yes	32
21.20	even	2	inner	945.2.g.b.944.13	✓	32
35.34	odd	2	inner	945.2.g.b.944.15	yes	32
105.104	even	2	inner	945.2.g.b.944.18	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.g.b.944.13	✓	32	21.20	even	2	inner
945.2.g.b.944.14	yes	32	5.4	even	2	inner
945.2.g.b.944.15	yes	32	35.34	odd	2	inner
945.2.g.b.944.16	yes	32	3.2	odd	2	inner
945.2.g.b.944.17	yes	32	1.1	even	1	trivial
945.2.g.b.944.18	yes	32	105.104	even	2	inner
945.2.g.b.944.19	yes	32	15.14	odd	2	inner
945.2.g.b.944.20	yes	32	7.6	odd	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.631409 q^{2} -1.60132 q^{4} +(-2.21891 - 0.276494i) q^{5} +(2.40407 + 1.10473i) q^{7} -2.27391 q^{8} +O(q^{10})\)	\(q+0.631409 q^{2} -1.60132 q^{4} +(-2.21891 - 0.276494i) q^{5} +(2.40407 + 1.10473i) q^{7} -2.27391 q^{8} +(-1.40104 - 0.174581i) q^{10} -4.53086i q^{11} +0.148283 q^{13} +(1.51795 + 0.697539i) q^{14} +1.76688 q^{16} +5.50137i q^{17} +4.84681i q^{19} +(3.55319 + 0.442757i) q^{20} -2.86082i q^{22} +5.63680 q^{23} +(4.84710 + 1.22703i) q^{25} +0.0936272 q^{26} +(-3.84969 - 1.76903i) q^{28} +5.60345i q^{29} +9.41406i q^{31} +5.66344 q^{32} +3.47362i q^{34} +(-5.02896 - 3.11601i) q^{35} +5.50294i q^{37} +3.06032i q^{38} +(5.04559 + 0.628723i) q^{40} -3.55319 q^{41} -11.3868i q^{43} +7.25536i q^{44} +3.55913 q^{46} -3.21633i q^{47} +(4.55913 + 5.31172i) q^{49} +(3.06051 + 0.774759i) q^{50} -0.237449 q^{52} -8.99969 q^{53} +(-1.25276 + 10.0535i) q^{55} +(-5.46664 - 2.51206i) q^{56} +3.53807i q^{58} +7.28647 q^{59} +8.15661i q^{61} +5.94412i q^{62} +0.0421952 q^{64} +(-0.329026 - 0.0409994i) q^{65} +10.3286i q^{67} -8.80946i q^{68} +(-3.17533 - 1.96748i) q^{70} -5.66910i q^{71} +13.0415 q^{73} +3.47461i q^{74} -7.76130i q^{76} +(5.00539 - 10.8925i) q^{77} +13.0624 q^{79} +(-3.92054 - 0.488532i) q^{80} -2.24351 q^{82} -0.0389759i q^{83} +(1.52110 - 12.2070i) q^{85} -7.18971i q^{86} +10.3028i q^{88} +8.78200 q^{89} +(0.356483 + 0.163813i) q^{91} -9.02633 q^{92} -2.03082i q^{94} +(1.34012 - 10.7546i) q^{95} +4.42241 q^{97} +(2.87868 + 3.35387i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4}+O(q^{10}) \) 32 * q + 32 * q^4	\( 32 q + 32 q^{4} + 32 q^{16} + 20 q^{25} - 24 q^{46} + 8 q^{49} + 56 q^{64} + 40 q^{79} + 76 q^{85} + 40 q^{91}+O(q^{100}) \) 32 * q + 32 * q^4 + 32 * q^16 + 20 * q^25 - 24 * q^46 + 8 * q^49 + 56 * q^64 + 40 * q^79 + 76 * q^85 + 40 * q^91

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