LMFDB - Embedded newform 945.2.bh.c.64.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(64,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("945.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bh (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			64.22
Character	$\chi$	$=$	945.64
Dual form			945.2.bh.c.694.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03279 - 0.596282i) q^{2} +(-0.288895 + 0.500381i) q^{4} +(-1.52125 - 1.63884i) q^{5} +(0.866025 - 0.500000i) q^{7} +3.07418i q^{8} +O(q^{10})$	\(q+(1.03279 - 0.596282i) q^{2} +(-0.288895 + 0.500381i) q^{4} +(-1.52125 - 1.63884i) q^{5} +(0.866025 - 0.500000i) q^{7} +3.07418i q^{8} +(-2.54835 - 0.785481i) q^{10} +(-2.02111 - 3.50067i) q^{11} +(-2.53546 - 1.46385i) q^{13} +(0.596282 - 1.03279i) q^{14} +(1.25529 + 2.17422i) q^{16} -3.25867i q^{17} +3.90229 q^{19} +(1.25953 - 0.287754i) q^{20} +(-4.17478 - 2.41031i) q^{22} +(-7.50189 - 4.33122i) q^{23} +(-0.371578 + 4.98617i) q^{25} -3.49147 q^{26} +0.577790i q^{28} +(-3.27941 - 5.68010i) q^{29} +(1.72072 - 2.98038i) q^{31} +(-2.73173 - 1.57717i) q^{32} +(-1.94309 - 3.36553i) q^{34} +(-2.13686 - 0.658649i) q^{35} -4.39850i q^{37} +(4.03025 - 2.32686i) q^{38} +(5.03808 - 4.67661i) q^{40} +(-3.10915 + 5.38521i) q^{41} +(-5.49353 + 3.17169i) q^{43} +2.33556 q^{44} -10.3305 q^{46} +(9.71907 - 5.61131i) q^{47} +(0.500000 - 0.866025i) q^{49} +(2.58940 + 5.37124i) q^{50} +(1.46496 - 0.845798i) q^{52} +2.38454i q^{53} +(-2.66241 + 8.63768i) q^{55} +(1.53709 + 2.66232i) q^{56} +(-6.77389 - 3.91091i) q^{58} +(-0.624888 + 1.08234i) q^{59} +(2.49109 + 4.31469i) q^{61} -4.10414i q^{62} -8.78290 q^{64} +(1.45807 + 6.38209i) q^{65} +(-8.47762 - 4.89455i) q^{67} +(1.63058 + 0.941415i) q^{68} +(-2.59967 + 0.593927i) q^{70} +9.24009 q^{71} -13.1780i q^{73} +(-2.62274 - 4.54273i) q^{74} +(-1.12735 + 1.95263i) q^{76} +(-3.50067 - 2.02111i) q^{77} +(2.12371 + 3.67837i) q^{79} +(1.65359 - 5.36476i) q^{80} +7.41572i q^{82} +(-10.5572 + 6.09519i) q^{83} +(-5.34044 + 4.95727i) q^{85} +(-3.78245 + 6.55139i) q^{86} +(10.7617 - 6.21327i) q^{88} -4.60378 q^{89} -2.92770 q^{91} +(4.33452 - 2.50253i) q^{92} +(6.69185 - 11.5906i) q^{94} +(-5.93637 - 6.39521i) q^{95} +(1.37170 - 0.791954i) q^{97} -1.19256i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 34 q^{4} + 10 q^{5}+O(q^{10}) $ 64 * q + 34 * q^4 + 10 * q^5	$ 64 q + 34 q^{4} + 10 q^{5} - 4 q^{10} - 18 q^{11} + 6 q^{14} - 46 q^{16} + 48 q^{19} + 2 q^{20} + 18 q^{25} + 12 q^{26} + 30 q^{29} - 4 q^{31} + 34 q^{34} - 8 q^{35} - 6 q^{40} - 28 q^{41} - 68 q^{44} - 24 q^{46} + 32 q^{49} + 58 q^{50} - 12 q^{55} - 18 q^{56} - 16 q^{59} + 40 q^{61} - 100 q^{64} + 18 q^{65} - 4 q^{70} + 176 q^{71} + 20 q^{74} - 22 q^{79} - 64 q^{80} - 14 q^{85} - 60 q^{86} + 200 q^{89} - 16 q^{91} - 42 q^{94} - 68 q^{95}+O(q^{100}) $ 64 * q + 34 * q^4 + 10 * q^5 - 4 * q^10 - 18 * q^11 + 6 * q^14 - 46 * q^16 + 48 * q^19 + 2 * q^20 + 18 * q^25 + 12 * q^26 + 30 * q^29 - 4 * q^31 + 34 * q^34 - 8 * q^35 - 6 * q^40 - 28 * q^41 - 68 * q^44 - 24 * q^46 + 32 * q^49 + 58 * q^50 - 12 * q^55 - 18 * q^56 - 16 * q^59 + 40 * q^61 - 100 * q^64 + 18 * q^65 - 4 * q^70 + 176 * q^71 + 20 * q^74 - 22 * q^79 - 64 * q^80 - 14 * q^85 - 60 * q^86 + 200 * q^89 - 16 * q^91 - 42 * q^94 - 68 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$136$	$596$	$757$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	1.03279	−	0.596282i	0.730294	−	0.421635i	−0.0882360	−	0.996100i	$-0.528123\pi$
$2$	1.03279	−	0.596282i	0.730294	−	0.421635i	0.818530	+	0.574464i	$0.194790\pi$
$3$		0			0
$3$		0			0
$4$	−0.288895	+	0.500381i	−0.144448	+	0.250191i
$5$	−1.52125	−	1.63884i	−0.680325	−	0.732911i
$5$	−1.52125	−	1.63884i	−0.680325	−	0.732911i
$6$		0			0
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$			3.07418i			1.08689i
$9$		0			0
$10$	−2.54835	−	0.785481i	−0.805858	−	0.248391i
$11$	−2.02111	−	3.50067i	−0.609389	−	1.05549i	−0.991341	−	0.131310i	$-0.958082\pi$
$11$	−2.02111	−	3.50067i	−0.609389	−	1.05549i	0.381953	−	0.924182i	$-0.375252\pi$
$12$		0			0
$13$	−2.53546	−	1.46385i	−0.703210	−	0.405999i	0.105332	−	0.994437i	$-0.466410\pi$
$13$	−2.53546	−	1.46385i	−0.703210	−	0.405999i	−0.808542	+	0.588438i	$0.799743\pi$
$14$	0.596282	−	1.03279i	0.159363	−	0.276025i
$15$		0			0
$16$	1.25529	+	2.17422i	0.313822	+	0.543556i
$17$		−	3.25867i		−	0.790345i	−0.918607	−	0.395172i	$-0.870685\pi$
$17$		−	3.25867i		−	0.790345i	0.918607	−	0.395172i	$-0.129315\pi$
$18$		0			0
$19$	3.90229			0.895246			0.447623	−	0.894222i	$-0.352271\pi$
$19$	3.90229			0.895246			0.447623	+	0.894222i	$0.352271\pi$
$20$	1.25953	−	0.287754i	0.281639	−	0.0643437i
$21$		0			0
$22$	−4.17478	−	2.41031i	−0.890065	−	0.513879i
$23$	−7.50189	−	4.33122i	−1.56425	−	0.903121i	−0.996819	−	0.0797013i	$-0.974603\pi$
$23$	−7.50189	−	4.33122i	−1.56425	−	0.903121i	−0.567433	−	0.823420i	$-0.692063\pi$
$24$		0			0
$25$	−0.371578	+	4.98617i	−0.0743156	+	0.997235i
$26$	−3.49147			−0.684733
$27$		0			0
$28$			0.577790i			0.109192i
$29$	−3.27941	−	5.68010i	−0.608971	−	1.05477i	−0.991410	−	0.130788i	$-0.958249\pi$
$29$	−3.27941	−	5.68010i	−0.608971	−	1.05477i	0.382439	−	0.923981i	$-0.375084\pi$
$30$		0			0
$31$	1.72072	−	2.98038i	0.309051	−	0.535291i	−0.669104	−	0.743169i	$-0.733322\pi$
$31$	1.72072	−	2.98038i	0.309051	−	0.535291i	0.978155	+	0.207877i	$0.0666554\pi$
$32$	−2.73173	−	1.57717i	−0.482907	−	0.278807i
$33$		0			0
$34$	−1.94309	−	3.36553i	−0.333237	−	0.577184i
$35$	−2.13686	−	0.658649i	−0.361196	−	0.111332i
$36$		0			0
$37$		−	4.39850i		−	0.723108i	−0.932351	−	0.361554i	$-0.882246\pi$
$37$		−	4.39850i		−	0.723108i	0.932351	−	0.361554i	$-0.117754\pi$
$38$	4.03025	−	2.32686i	0.653792	−	0.377467i
$39$		0			0
$40$	5.03808	−	4.67661i	0.796591	−	0.739436i
$41$	−3.10915	+	5.38521i	−0.485568	+	0.841028i	−0.999862	−	0.0165856i	$-0.994720\pi$
$41$	−3.10915	+	5.38521i	−0.485568	+	0.841028i	0.514295	+	0.857613i	$0.328054\pi$
$42$		0			0
$43$	−5.49353	+	3.17169i	−0.837756	+	0.483678i	−0.856501	−	0.516146i	$-0.827366\pi$
$43$	−5.49353	+	3.17169i	−0.837756	+	0.483678i	0.0187451	+	0.999824i	$0.494033\pi$
$44$	2.33556			0.352099
$45$		0			0
$46$	−10.3305			−1.52315
$47$	9.71907	−	5.61131i	1.41767	−	0.818493i	0.421578	−	0.906792i	$-0.361476\pi$
$47$	9.71907	−	5.61131i	1.41767	−	0.818493i	0.996094	+	0.0882989i	$0.0281431\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	2.58940	+	5.37124i	0.366197	+	0.759608i
$51$		0			0
$52$	1.46496	−	0.845798i	0.203154	−	0.117291i
$53$			2.38454i			0.327542i	0.986498	+	0.163771i	$0.0523659\pi$
$53$			2.38454i			0.327542i	−0.986498	+	0.163771i	$0.947634\pi$
$54$		0			0
$55$	−2.66241	+	8.63768i	−0.358999	+	1.16470i
$56$	1.53709	+	2.66232i	0.205402	+	0.355767i
$57$		0			0
$58$	−6.77389	−	3.91091i	−0.889455	−	0.513527i
$59$	−0.624888	+	1.08234i	−0.0813535	+	0.140908i	−0.903832	−	0.427888i	$-0.859258\pi$
$59$	−0.624888	+	1.08234i	−0.0813535	+	0.140908i	0.822478	+	0.568797i	$0.192591\pi$
$60$		0			0
$61$	2.49109	+	4.31469i	0.318951	+	0.552440i	0.980270	−	0.197666i	$-0.0633360\pi$
$61$	2.49109	+	4.31469i	0.318951	+	0.552440i	−0.661318	+	0.750105i	$0.730003\pi$
$62$		−	4.10414i		−	0.521227i
$63$		0			0
$64$	−8.78290			−1.09786
$65$	1.45807	+	6.38209i	0.180851	+	0.791601i
$66$		0			0
$67$	−8.47762	−	4.89455i	−1.03571	−	0.597965i	−0.117092	−	0.993121i	$-0.537357\pi$
$67$	−8.47762	−	4.89455i	−1.03571	−	0.597965i	−0.918614	+	0.395156i	$0.870691\pi$
$68$	1.63058	+	0.941415i	0.197737	+	0.114163i
$69$		0			0
$70$	−2.59967	+	0.593927i	−0.310720	+	0.0709878i
$71$	9.24009			1.09660			0.548298	−	0.836283i	$-0.315276\pi$
$71$	9.24009			1.09660			0.548298	+	0.836283i	$0.315276\pi$
$72$		0			0
$73$		−	13.1780i		−	1.54237i	−0.636612	−	0.771184i	$-0.719665\pi$
$73$		−	13.1780i		−	1.54237i	0.636612	−	0.771184i	$-0.280335\pi$
$74$	−2.62274	−	4.54273i	−0.304888	−	0.528081i
$75$		0			0
$76$	−1.12735	+	1.95263i	−0.129316	+	0.223982i
$77$	−3.50067	−	2.02111i	−0.398938	−	0.230327i
$78$		0			0
$79$	2.12371	+	3.67837i	0.238936	+	0.413849i	0.960409	−	0.278593i	$-0.0898681\pi$
$79$	2.12371	+	3.67837i	0.238936	+	0.413849i	−0.721473	+	0.692442i	$0.756535\pi$
$80$	1.65359	−	5.36476i	0.184877	−	0.599798i
$81$		0			0
$82$			7.41572i			0.818930i
$83$	−10.5572	+	6.09519i	−1.15880	+	0.669034i	−0.951016	−	0.309140i	$-0.899959\pi$
$83$	−10.5572	+	6.09519i	−1.15880	+	0.669034i	−0.207785	+	0.978175i	$0.566625\pi$
$84$		0			0
$85$	−5.34044	+	4.95727i	−0.579252	+	0.537691i
$86$	−3.78245	+	6.55139i	−0.407872	+	0.706454i
$87$		0			0
$88$	10.7617	−	6.21327i	1.14720	−	0.662337i
$89$	−4.60378			−0.487999			−0.244000	−	0.969775i	$-0.578460\pi$
$89$	−4.60378			−0.487999			−0.244000	+	0.969775i	$0.578460\pi$
$90$		0			0
$91$	−2.92770			−0.306906
$92$	4.33452	−	2.50253i	0.451905	−	0.260907i
$93$		0			0
$94$	6.69185	−	11.5906i	0.690211	−	1.19548i
$95$	−5.93637	−	6.39521i	−0.609058	−	0.656135i
$96$		0			0
$97$	1.37170	−	0.791954i	0.139276	−	0.0804108i	−0.428743	−	0.903426i	$-0.641043\pi$
$97$	1.37170	−	0.791954i	0.139276	−	0.0804108i	0.568019	+	0.823016i	$0.307710\pi$
$98$		−	1.19256i		−	0.120467i
$99$		0			0
$100$	−2.38764	−	1.62641i	−0.238764	−	0.162641i
$101$	9.61034	+	16.6456i	0.956264	+	1.65630i	0.731448	+	0.681897i	$0.238845\pi$
$101$	9.61034	+	16.6456i	0.956264	+	1.65630i	0.224817	+	0.974401i	$0.427822\pi$
$102$		0			0
$103$	13.3744	+	7.72170i	1.31782	+	0.760842i	0.983377	−	0.181575i	$-0.0581196\pi$
$103$	13.3744	+	7.72170i	1.31782	+	0.760842i	0.334440	+	0.942417i	$0.391453\pi$
$104$	4.50014	−	7.79447i	0.441275	−	0.764310i
$105$		0			0
$106$	1.42186	+	2.46274i	0.138103	+	0.239202i
$107$		−	1.41993i		−	0.137270i	−0.997642	−	0.0686351i	$-0.978136\pi$
$107$		−	1.41993i		−	0.137270i	0.997642	−	0.0686351i	$-0.0218644\pi$
$108$		0			0
$109$	4.94762			0.473896			0.236948	−	0.971522i	$-0.423853\pi$
$109$	4.94762			0.473896			0.236948	+	0.971522i	$0.423853\pi$
$110$	2.40079	+	10.5085i	0.228906	+	1.00194i
$111$		0			0
$112$	2.17422	+	1.25529i	0.205445	+	0.118614i
$113$	10.7333	+	6.19686i	1.00970	+	0.582952i	0.911104	−	0.412176i	$-0.135231\pi$
$113$	10.7333	+	6.19686i	1.00970	+	0.582952i	0.0985975	+	0.995127i	$0.468564\pi$
$114$		0			0
$115$	4.31411	+	18.8833i	0.402293	+	1.76087i
$116$	3.78962			0.351857
$117$		0			0
$118$			1.49044i			0.137206i
$119$	−1.62934	−	2.82210i	−0.149361	−	0.258701i
$120$		0			0
$121$	−2.66980	+	4.62422i	−0.242709	+	0.420384i
$122$	5.14555	+	2.97078i	0.465856	+	0.268962i
$123$		0			0
$124$	0.994216	+	1.72203i	0.0892832	+	0.154643i
$125$	8.73679	−	6.97628i	0.781443	−	0.623977i
$126$		0			0
$127$		−	1.19904i		−	0.106398i	−0.998584	−	0.0531989i	$-0.983058\pi$
$127$		−	1.19904i		−	0.106398i	0.998584	−	0.0531989i	$-0.0169417\pi$
$128$	−3.60743	+	2.08275i	−0.318855	+	0.184091i
$129$		0			0
$130$	5.31141	+	5.72195i	0.465841	+	0.501848i
$131$	6.09913	−	10.5640i	0.532884	−	0.922981i	−0.466379	−	0.884585i	$-0.654442\pi$
$131$	6.09913	−	10.5640i	0.532884	−	0.922981i	0.999263	−	0.0383963i	$-0.0122249\pi$
$132$		0			0
$133$	3.37948	−	1.95114i	0.293038	−	0.169186i
$134$	−11.6741			−1.00849
$135$		0			0
$136$	10.0178			0.859015
$137$	8.99833	−	5.19519i	0.768779	−	0.443855i	−0.0636599	−	0.997972i	$-0.520277\pi$
$137$	8.99833	−	5.19519i	0.768779	−	0.443855i	0.832439	+	0.554117i	$0.186944\pi$
$138$		0			0
$139$	2.85630	−	4.94726i	0.242268	−	0.419621i	−0.719092	−	0.694915i	$-0.755442\pi$
$139$	2.85630	−	4.94726i	0.242268	−	0.419621i	0.961360	+	0.275294i	$0.0887752\pi$
$140$	0.946904	−	0.878965i	0.0800280	−	0.0742861i
$141$		0			0
$142$	9.54308	−	5.50970i	0.800837	−	0.462364i
$143$			11.8344i			0.989644i
$144$		0			0
$145$	−4.31996	+	14.0153i	−0.358753	+	1.16391i
$146$	−7.85781	−	13.6101i	−0.650317	−	1.12638i
$147$		0			0
$148$	2.20092	+	1.27070i	0.180915	+	0.104451i
$149$	−2.66565	+	4.61704i	−0.218378	+	0.378242i	−0.954312	−	0.298811i	$-0.903410\pi$
$149$	−2.66565	+	4.61704i	−0.218378	+	0.378242i	0.735934	+	0.677053i	$0.236743\pi$
$150$		0			0
$151$	−5.64321	−	9.77432i	−0.459238	−	0.795423i	0.539683	−	0.841868i	$-0.318544\pi$
$151$	−5.64321	−	9.77432i	−0.459238	−	0.795423i	−0.998921	+	0.0464453i	$0.985211\pi$
$152$			11.9963i			0.973031i
$153$		0			0
$154$	−4.82062			−0.388456
$155$	−7.50201	+	1.71392i	−0.602576	+	0.137666i
$156$		0			0
$157$	−4.10414	−	2.36953i	−0.327546	−	0.189109i	0.327205	−	0.944953i	$-0.393893\pi$
$157$	−4.10414	−	2.36953i	−0.327546	−	0.189109i	−0.654751	+	0.755845i	$0.727227\pi$
$158$	4.38670	+	2.53266i	0.348987	+	0.201488i
$159$		0			0
$160$	1.57094	+	6.87614i	0.124194	+	0.543607i
$161$	−8.66243			−0.682695
$162$		0			0
$163$			15.2832i			1.19707i	0.801097	+	0.598535i	$0.204250\pi$
$163$			15.2832i			1.19707i	−0.801097	+	0.598535i	$0.795750\pi$
$164$	−1.79644	−	3.11152i	−0.140278	−	0.242969i
$165$		0			0
$166$	−7.26891	+	12.5901i	−0.564177	+	0.977183i
$167$	−4.96139	−	2.86446i	−0.383924	−	0.221659i	0.295600	−	0.955312i	$-0.404480\pi$
$167$	−4.96139	−	2.86446i	−0.383924	−	0.221659i	−0.679524	+	0.733653i	$0.737814\pi$
$168$		0			0
$169$	−2.21429	−	3.83527i	−0.170330	−	0.295020i
$170$	−2.55963	+	8.30423i	−0.196314	+	0.636905i
$171$		0			0
$172$		−	3.66514i		−	0.279465i
$173$	4.68882	−	2.70709i	0.356484	−	0.205816i	−0.311053	−	0.950393i	$-0.600682\pi$
$173$	4.68882	−	2.70709i	0.356484	−	0.205816i	0.667538	+	0.744576i	$0.267348\pi$
$174$		0			0
$175$	2.17129	+	4.50394i	0.164134	+	0.340466i
$176$	5.07416	−	8.78871i	0.382479	−	0.662474i
$177$		0			0
$178$	−4.75474	+	2.74515i	−0.356383	+	0.205758i
$179$	−11.7867			−0.880981			−0.440491	−	0.897757i	$-0.645195\pi$
$179$	−11.7867			−0.880981			−0.440491	+	0.897757i	$0.645195\pi$
$180$		0			0
$181$	−9.83846			−0.731287			−0.365643	−	0.930755i	$-0.619151\pi$
$181$	−9.83846			−0.731287			−0.365643	+	0.930755i	$0.619151\pi$
$182$	−3.02370	+	1.74573i	−0.224132	+	0.129402i
$183$		0			0
$184$	13.3149	−	23.0622i	0.981591	−	1.70016i
$185$	−7.20842	+	6.69123i	−0.529974	+	0.491949i
$186$		0			0
$187$	−11.4075	+	6.58615i	−0.834202	+	0.481627i
$188$			6.48432i			0.472917i
$189$		0			0
$190$	−9.94438	−	3.06517i	−0.721441	−	0.222371i
$191$	6.60131	+	11.4338i	0.477654	+	0.827321i	0.999672	−	0.0256132i	$-0.00815383\pi$
$191$	6.60131	+	11.4338i	0.477654	+	0.827321i	−0.522018	+	0.852935i	$0.674821\pi$
$192$		0			0
$193$	−3.63667	−	2.09963i	−0.261773	−	0.151135i	0.363370	−	0.931645i	$-0.381626\pi$
$193$	−3.63667	−	2.09963i	−0.261773	−	0.151135i	−0.625143	+	0.780510i	$0.714959\pi$
$194$	0.944456	−	1.63585i	0.0678080	−	0.117447i
$195$		0			0
$196$	0.288895	+	0.500381i	0.0206354	+	0.0357415i
$197$			15.2029i			1.08316i	0.840648	+	0.541581i	$0.182174\pi$
$197$			15.2029i			1.08316i	−0.840648	+	0.541581i	$0.817826\pi$
$198$		0			0
$199$	12.6279			0.895166			0.447583	−	0.894242i	$-0.352285\pi$
$199$	12.6279			0.895166			0.447583	+	0.894242i	$0.352285\pi$
$200$	−15.3284	−	1.14230i	−1.08388	−	0.0807727i
$201$		0			0
$202$	19.8509	+	11.4609i	1.39671	+	0.806389i
$203$	−5.68010	−	3.27941i	−0.398665	−	0.230169i
$204$		0			0
$205$	13.5553	−	3.09687i	0.946742	−	0.216295i
$206$	18.4173			1.28319
$207$		0			0
$208$		−	7.35021i		−	0.509646i
$209$	−7.88696	−	13.6606i	−0.545553	−	0.944925i
$210$		0			0
$211$	−1.77656	+	3.07710i	−0.122304	+	0.211836i	−0.920676	−	0.390328i	$-0.872362\pi$
$211$	−1.77656	+	3.07710i	−0.122304	+	0.211836i	0.798372	+	0.602164i	$0.205695\pi$
$212$	−1.19318	−	0.688883i	−0.0819480	−	0.0473127i
$213$		0			0
$214$	−0.846681	−	1.46649i	−0.0578779	−	0.100248i
$215$	13.5549	+	4.17806i	0.924439	+	0.284941i
$216$		0			0
$217$		−	3.44144i		−	0.233620i
$218$	5.10986	−	2.95018i	0.346083	−	0.199811i
$219$		0			0
$220$	−3.55298	−	3.82760i	−0.239542	−	0.258057i
$221$	−4.77021	+	8.26224i	−0.320879	+	0.555779i
$222$		0			0
$223$	8.89357	−	5.13470i	0.595557	−	0.343845i	−0.171735	−	0.985143i	$-0.554937\pi$
$223$	8.89357	−	5.13470i	0.595557	−	0.343845i	0.767292	+	0.641298i	$0.221604\pi$
$224$	−3.15434			−0.210758
$225$		0			0
$226$	14.7803			0.983172
$227$	−7.88525	+	4.55255i	−0.523362	+	0.302163i	−0.738309	−	0.674462i	$-0.764375\pi$
$227$	−7.88525	+	4.55255i	−0.523362	+	0.302163i	0.214947	+	0.976626i	$0.431042\pi$
$228$		0			0
$229$	14.6780	−	25.4231i	0.969951	−	1.68000i	0.274270	−	0.961653i	$-0.411564\pi$
$229$	14.6780	−	25.4231i	0.969951	−	1.68000i	0.695681	−	0.718351i	$-0.255103\pi$
$230$	15.7153	+	16.9300i	1.03624	+	1.11633i
$231$		0			0
$232$	17.4617	−	10.0815i	1.14641	−	0.661883i
$233$		−	16.2244i		−	1.06290i	−0.847091	−	0.531448i	$-0.821648\pi$
$233$		−	16.2244i		−	1.06290i	0.847091	−	0.531448i	$-0.178352\pi$
$234$		0			0
$235$	−23.9812	−	7.39176i	−1.56436	−	0.482185i
$236$	−0.361054	−	0.625364i	−0.0235026	−	0.0407077i
$237$		0			0
$238$	−3.36553	−	1.94309i	−0.218155	−	0.125952i
$239$	8.20101	−	14.2046i	0.530479	−	0.918817i	−0.468889	−	0.883257i	$-0.655345\pi$
$239$	8.20101	−	14.2046i	0.530479	−	0.918817i	0.999368	−	0.0355593i	$-0.0113213\pi$
$240$		0			0
$241$	−0.695013	−	1.20380i	−0.0447697	−	0.0775434i	0.842772	−	0.538270i	$-0.180922\pi$
$241$	−0.695013	−	1.20380i	−0.0447697	−	0.0775434i	−0.887542	+	0.460727i	$0.847589\pi$
$242$			6.36781i			0.409338i
$243$		0			0
$244$	−2.87865			−0.184287
$245$	−2.17990	+	0.498025i	−0.139269	+	0.0318176i
$246$		0			0
$247$	−9.89410	−	5.71236i	−0.629546	−	0.363469i
$248$	9.16222	+	5.28981i	0.581801	+	0.335903i
$249$		0			0
$250$	4.86345	−	12.4146i	0.307592	−	0.785170i
$251$	−13.0190			−0.821752			−0.410876	−	0.911691i	$-0.634777\pi$
$251$	−13.0190			−0.821752			−0.410876	+	0.911691i	$0.634777\pi$
$252$		0			0
$253$			35.0155i			2.20141i
$254$	−0.714967	−	1.23836i	−0.0448610	−	0.0777016i
$255$		0			0
$256$	6.29909	−	10.9103i	0.393693	−	0.681896i
$257$	5.25151	+	3.03196i	0.327580	+	0.189128i	0.654766	−	0.755831i	$-0.272767\pi$
$257$	5.25151	+	3.03196i	0.327580	+	0.189128i	−0.327186	+	0.944960i	$0.606100\pi$
$258$		0			0
$259$	−2.19925	−	3.80921i	−0.136655	−	0.236693i
$260$	−3.61471	−	1.11417i	−0.224175	−	0.0690977i
$261$		0			0
$262$		−	14.5472i		−	0.898730i
$263$	−23.6992	+	13.6827i	−1.46135	+	0.843713i	−0.999074	−	0.0430209i	$-0.986302\pi$
$263$	−23.6992	+	13.6827i	−1.46135	+	0.843713i	−0.462280	+	0.886734i	$0.652968\pi$
$264$		0			0
$265$	3.90788	−	3.62750i	0.240059	−	0.222835i
$266$	2.32686	−	4.03025i	0.142669	−	0.247110i
$267$		0			0
$268$	4.89828	−	2.82803i	0.299210	−	0.172749i
$269$	18.6269			1.13570			0.567850	−	0.823132i	$-0.307775\pi$
$269$	18.6269			1.13570			0.567850	+	0.823132i	$0.307775\pi$
$270$		0			0
$271$	16.8341			1.02260			0.511300	−	0.859402i	$-0.329164\pi$
$271$	16.8341			1.02260			0.511300	+	0.859402i	$0.329164\pi$
$272$	7.08509	−	4.09058i	0.429597	−	0.248028i
$273$		0			0
$274$	6.19559	−	10.7311i	0.374290	−	0.648288i
$275$	18.2060	−	8.77685i	1.09786	−	0.529264i
$276$		0			0
$277$	−15.3556	+	8.86557i	−0.922629	+	0.532680i	−0.884473	−	0.466592i	$-0.845482\pi$
$277$	−15.3556	+	8.86557i	−0.922629	+	0.532680i	−0.0381563	+	0.999272i	$0.512148\pi$
$278$		−	6.81265i		−	0.408595i
$279$		0			0
$280$	2.02480	−	6.56910i	0.121005	−	0.392579i
$281$	−14.6728	−	25.4141i	−0.875307	−	1.51608i	−0.856435	−	0.516255i	$-0.827326\pi$
$281$	−14.6728	−	25.4141i	−0.875307	−	1.51608i	−0.0188725	−	0.999822i	$-0.506008\pi$
$282$		0			0
$283$	15.0805	+	8.70671i	0.896440	+	0.517560i	0.876044	−	0.482232i	$-0.160174\pi$
$283$	15.0805	+	8.70671i	0.896440	+	0.517560i	0.0203967	+	0.999792i	$0.493507\pi$
$284$	−2.66942	+	4.62356i	−0.158401	+	0.274358i
$285$		0			0
$286$	7.05665	+	12.2225i	0.417269	+	0.722730i
$287$			6.21830i			0.367055i
$288$		0			0
$289$	6.38104			0.375355
$290$	3.89546	+	17.0508i	0.228749	+	1.00126i
$291$		0			0
$292$	6.59402	+	3.80706i	0.385886	+	0.222791i
$293$	−5.29842	−	3.05904i	−0.309537	−	0.178711i	0.337182	−	0.941439i	$-0.390526\pi$
$293$	−5.29842	−	3.05904i	−0.309537	−	0.178711i	−0.646719	+	0.762728i	$0.723859\pi$
$294$		0			0
$295$	2.72439	−	0.622420i	0.158620	−	0.0362387i
$296$	13.5218			0.785937
$297$		0			0
$298$			6.35791i			0.368304i
$299$	12.6805	+	21.9633i	0.733332	+	1.27017i
$300$		0			0
$301$	−3.17169	+	5.49353i	−0.182813	+	0.316642i
$302$	−11.6565	−	6.72989i	−0.670756	−	0.387261i
$303$		0			0
$304$	4.89850	+	8.48445i	0.280948	+	0.486616i
$305$	3.28150	−	10.6462i	0.187898	−	0.609601i
$306$		0			0
$307$			5.40835i			0.308671i	0.988019	+	0.154335i	$0.0493236\pi$
$307$			5.40835i			0.308671i	−0.988019	+	0.154335i	$0.950676\pi$
$308$	2.02265	−	1.16778i	0.115251	−	0.0665404i
$309$		0			0
$310$	−6.72602	+	6.24344i	−0.382012	+	0.354603i
$311$	−9.87784	+	17.1089i	−0.560121	+	0.970158i	0.437365	+	0.899284i	$0.355912\pi$
$311$	−9.87784	+	17.1089i	−0.560121	+	0.970158i	−0.997485	+	0.0708733i	$0.977421\pi$
$312$		0			0
$313$	−11.4466	+	6.60869i	−0.647000	+	0.373545i	−0.787306	−	0.616563i	$-0.788525\pi$
$313$	−11.4466	+	6.60869i	−0.647000	+	0.373545i	0.140306	+	0.990108i	$0.455191\pi$
$314$	−5.65163			−0.318940
$315$		0			0
$316$	−2.45412			−0.138055
$317$	16.6240	−	9.59784i	0.933694	−	0.539069i	0.0457161	−	0.998954i	$-0.485443\pi$
$317$	16.6240	−	9.59784i	0.933694	−	0.539069i	0.887978	+	0.459886i	$0.152110\pi$
$318$		0			0
$319$	−13.2561	+	22.9603i	−0.742200	+	1.28553i
$320$	13.3610	+	14.3938i	0.746904	+	0.804635i
$321$		0			0
$322$	−8.94648	+	5.16525i	−0.498568	+	0.287848i
$323$		−	12.7163i		−	0.707553i
$324$		0			0
$325$	8.24113	−	12.0983i	0.457136	−	0.671094i
$326$	9.11308	+	15.7843i	0.504727	+	0.874212i
$327$		0			0
$328$	−16.5551	−	9.55809i	−0.914102	−	0.527757i
$329$	5.61131	−	9.71907i	0.309361	−	0.535830i
$330$		0			0
$331$	−17.2640	−	29.9021i	−0.948915	−	1.64357i	−0.747716	−	0.664019i	$-0.768849\pi$
$331$	−17.2640	−	29.9021i	−0.948915	−	1.64357i	−0.201199	−	0.979550i	$-0.564484\pi$
$332$		−	7.04348i		−	0.386561i
$333$		0			0
$334$	−6.83210			−0.373836
$335$	4.87522	+	21.3393i	0.266362	+	1.16589i
$336$		0			0
$337$	8.37265	+	4.83395i	0.456087	+	0.263322i	0.710398	−	0.703800i	$-0.248515\pi$
$337$	8.37265	+	4.83395i	0.456087	+	0.263322i	−0.254310	+	0.967123i	$0.581848\pi$
$338$	−4.57380	−	2.64069i	−0.248782	−	0.143634i
$339$		0			0
$340$	−0.937697	−	4.10439i	−0.0508537	−	0.222592i
$341$	−13.9111			−0.753328
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−9.75035	−	16.8881i	−0.525704	−	0.910546i
$345$		0			0
$346$	3.22838	−	5.59172i	0.173559	−	0.300613i
$347$	0.805161	+	0.464860i	0.0432233	+	0.0249550i	0.521456	−	0.853278i	$-0.325389\pi$
$347$	0.805161	+	0.464860i	0.0432233	+	0.0249550i	−0.478233	+	0.878233i	$0.658722\pi$
$348$		0			0
$349$	−15.8412	−	27.4378i	−0.847961	−	1.46871i	−0.883024	−	0.469327i	$-0.844497\pi$
$349$	−15.8412	−	27.4378i	−0.847961	−	1.46871i	0.0350631	−	0.999385i	$-0.488837\pi$
$350$	4.92811	+	3.35693i	0.263419	+	0.179435i
$351$		0			0
$352$			12.7505i			0.679606i
$353$	7.15773	−	4.13252i	0.380967	−	0.219952i	−0.297272	−	0.954793i	$-0.596077\pi$
$353$	7.15773	−	4.13252i	0.380967	−	0.219952i	0.678239	+	0.734841i	$0.262743\pi$
$354$		0			0
$355$	−14.0565	−	15.1430i	−0.746042	−	0.803707i
$356$	1.33001	−	2.30364i	0.0704903	−	0.122093i
$357$		0			0
$358$	−12.1732	+	7.02821i	−0.643375	+	0.371453i
$359$	−16.7567			−0.884386			−0.442193	−	0.896920i	$-0.645799\pi$
$359$	−16.7567			−0.884386			−0.442193	+	0.896920i	$0.645799\pi$
$360$		0			0
$361$	−3.77216			−0.198535
$362$	−10.1611	+	5.86650i	−0.534054	+	0.308336i
$363$		0			0
$364$	0.845798	−	1.46496i	0.0443318	−	0.0767850i
$365$	−21.5966	+	20.0471i	−1.13042	+	1.04931i
$366$		0			0
$367$	3.47459	−	2.00605i	0.181372	−	0.104715i	−0.406565	−	0.913622i	$-0.633274\pi$
$367$	3.47459	−	2.00605i	0.181372	−	0.104715i	0.587937	+	0.808907i	$0.299940\pi$
$368$		−	21.7477i		−	1.13368i
$369$		0			0
$370$	−3.45493	+	11.2089i	−0.179613	+	0.582722i
$371$	1.19227	+	2.06508i	0.0618997	+	0.107213i
$372$		0			0
$373$	−5.76983	−	3.33121i	−0.298750	−	0.172484i	0.343131	−	0.939288i	$-0.388513\pi$
$373$	−5.76983	−	3.33121i	−0.298750	−	0.172484i	−0.641881	+	0.766804i	$0.721846\pi$
$374$	−7.85441	+	13.6042i	−0.406142	+	0.703458i
$375$		0			0
$376$	17.2502	+	29.8782i	0.889610	+	1.54085i
$377$			19.2022i			0.988966i
$378$		0			0
$379$	−16.9848			−0.872450			−0.436225	−	0.899838i	$-0.643685\pi$
$379$	−16.9848			−0.872450			−0.436225	+	0.899838i	$0.643685\pi$
$380$	4.91503	−	1.12290i	0.252136	−	0.0576035i
$381$		0			0
$382$	13.6356	+	7.87249i	0.697656	+	0.402792i
$383$	−7.54893	−	4.35838i	−0.385732	−	0.222703i	0.294577	−	0.955628i	$-0.404821\pi$
$383$	−7.54893	−	4.35838i	−0.385732	−	0.222703i	−0.680309	+	0.732925i	$0.738155\pi$
$384$		0			0
$385$	2.01313	+	8.81166i	0.102599	+	0.449084i
$386$	−5.00789			−0.254895
$387$		0			0
$388$			0.915167i			0.0464606i
$389$	−10.0602	−	17.4248i	−0.510074	−	0.883474i	−0.999932	−	0.0116719i	$-0.996285\pi$
$389$	−10.0602	−	17.4248i	−0.510074	−	0.883474i	0.489858	−	0.871802i	$-0.337049\pi$
$390$		0			0
$391$	−14.1140	+	24.4462i	−0.713777	+	1.23630i
$392$	2.66232	+	1.53709i	0.134467	+	0.0776348i
$393$		0			0
$394$	9.06522	+	15.7014i	0.456699	+	0.791026i
$395$	2.79756	−	9.07615i	0.140760	−	0.456671i
$396$		0			0
$397$		−	29.2717i		−	1.46911i	−0.678551	−	0.734553i	$-0.737392\pi$
$397$		−	29.2717i		−	1.46911i	0.678551	−	0.734553i	$-0.262608\pi$
$398$	13.0420	−	7.52978i	0.653734	−	0.377434i
$399$		0			0
$400$	−11.3075	+	5.45119i	−0.565375	+	0.272560i
$401$	2.19436	−	3.80075i	0.109581	−	0.189800i	−0.806019	−	0.591889i	$-0.798382\pi$
$401$	2.19436	−	3.80075i	0.109581	−	0.189800i	0.915601	+	0.402089i	$0.131716\pi$
$402$		0			0
$403$	−8.72564	+	5.03775i	−0.434655	+	0.250948i
$404$	−11.1055			−0.552520
$405$		0			0
$406$	−7.82181			−0.388190
$407$	−15.3977	+	8.88986i	−0.763235	+	0.440654i
$408$		0			0
$409$	1.93960	−	3.35948i	0.0959069	−	0.166116i	−0.814080	−	0.580753i	$-0.802758\pi$
$409$	1.93960	−	3.35948i	0.0959069	−	0.166116i	0.909987	+	0.414637i	$0.136092\pi$
$410$	12.1532	−	11.2812i	0.600202	−	0.557138i
$411$		0			0
$412$	−7.72759	+	4.46152i	−0.380711	+	0.219804i
$413$			1.24978i			0.0614974i
$414$		0			0
$415$	26.0492	+	8.02918i	1.27870	+	0.394137i
$416$	4.61747	+	7.99770i	0.226390	+	0.392119i
$417$		0			0
$418$	−16.2912	−	9.40571i	−0.796827	−	0.460048i
$419$	11.4391	−	19.8131i	0.558835	−	0.967931i	−0.438759	−	0.898605i	$-0.644582\pi$
$419$	11.4391	−	19.8131i	0.558835	−	0.967931i	0.997594	−	0.0693264i	$-0.0220850\pi$
$420$		0			0
$421$	−9.08277	−	15.7318i	−0.442667	−	0.766722i	0.555219	−	0.831704i	$-0.312634\pi$
$421$	−9.08277	−	15.7318i	−0.442667	−	0.766722i	−0.997886	+	0.0649822i	$0.979301\pi$
$422$			4.23733i			0.206270i
$423$		0			0
$424$	−7.33052			−0.356002
$425$	16.2483	+	1.21085i	0.788159	+	0.0587350i
$426$		0			0
$427$	4.31469	+	2.49109i	0.208803	+	0.120552i
$428$	0.710508	+	0.410212i	0.0343437	+	0.0198283i
$429$		0			0
$430$	16.4907	−	3.76750i	0.795253	−	0.181685i
$431$	11.0896			0.534165			0.267083	−	0.963674i	$-0.413940\pi$
$431$	11.0896			0.534165			0.267083	+	0.963674i	$0.413940\pi$
$432$		0			0
$433$		−	19.4639i		−	0.935376i	−0.883894	−	0.467688i	$-0.845087\pi$
$433$		−	19.4639i		−	0.935376i	0.883894	−	0.467688i	$-0.154913\pi$
$434$	−2.05207	−	3.55429i	−0.0985026	−	0.170611i
$435$		0			0
$436$	−1.42934	+	2.47570i	−0.0684531	+	0.118564i
$437$	−29.2745	−	16.9016i	−1.40039	−	0.808516i
$438$		0			0
$439$	1.31143	+	2.27146i	0.0625911	+	0.108411i	0.895623	−	0.444814i	$-0.146730\pi$
$439$	1.31143	+	2.27146i	0.0625911	+	0.108411i	−0.833032	+	0.553225i	$0.813397\pi$
$440$	−26.5538	−	8.18472i	−1.26590	−	0.390191i
$441$		0			0
$442$			11.3776i			0.541175i
$443$	10.2895	−	5.94064i	0.488868	−	0.282248i	−0.235236	−	0.971938i	$-0.575586\pi$
$443$	10.2895	−	5.94064i	0.488868	−	0.282248i	0.724105	+	0.689690i	$0.242253\pi$
$444$		0			0
$445$	7.00351	+	7.54484i	0.331998	+	0.357660i
$446$	6.12346	−	10.6062i	0.289954	−	0.502216i
$447$		0			0
$448$	−7.60622	+	4.39145i	−0.359360	+	0.207477i
$449$	20.2366			0.955022			0.477511	−	0.878626i	$-0.341539\pi$
$449$	20.2366			0.955022			0.477511	+	0.878626i	$0.341539\pi$
$450$		0			0
$451$	25.1358			1.18360
$452$	−6.20158	+	3.58049i	−0.291698	+	0.168412i
$453$		0			0
$454$	−5.42921	+	9.40367i	−0.254805	+	0.441336i
$455$	4.45377	+	4.79802i	0.208796	+	0.224935i
$456$		0			0
$457$	25.7674	−	14.8768i	1.20535	−	0.695908i	0.243609	−	0.969873i	$-0.421669\pi$
$457$	25.7674	−	14.8768i	1.20535	−	0.695908i	0.961740	+	0.273965i	$0.0883353\pi$
$458$		−	35.0090i		−	1.63586i
$459$		0			0
$460$	−10.6951	−	3.29658i	−0.498664	−	0.153704i
$461$	6.40055	+	11.0861i	0.298103	+	0.516330i	0.975702	−	0.219102i	$-0.0703127\pi$
$461$	6.40055	+	11.0861i	0.298103	+	0.516330i	−0.677599	+	0.735432i	$0.736979\pi$
$462$		0			0
$463$	21.6269	+	12.4863i	1.00509	+	0.580287i	0.909749	−	0.415158i	$-0.136274\pi$
$463$	21.6269	+	12.4863i	1.00509	+	0.580287i	0.0953374	+	0.995445i	$0.469607\pi$
$464$	8.23321	−	14.2603i	0.382217	−	0.662020i
$465$		0			0
$466$	−9.67433	−	16.7564i	−0.448155	−	0.776227i
$467$			1.50301i			0.0695509i	0.999395	+	0.0347754i	$0.0110716\pi$
$467$			1.50301i			0.0695509i	−0.999395	+	0.0347754i	$0.988928\pi$
$468$		0			0
$469$	−9.78911			−0.452019
$470$	−29.1751	+	6.66541i	−1.34575	+	0.307453i
$471$		0			0
$472$	−3.32730	−	1.92102i	−0.153151	−	0.0884220i
$473$	22.2061	+	12.8207i	1.02104	+	0.589496i
$474$		0			0
$475$	−1.45000	+	19.4575i	−0.0665308	+	0.892770i
$476$	1.88283			0.0862994
$477$		0			0
$478$		−	19.5605i		−	0.894674i
$479$	−6.43125	−	11.1393i	−0.293852	−	0.508966i	0.680866	−	0.732408i	$-0.261604\pi$
$479$	−6.43125	−	11.1393i	−0.293852	−	0.508966i	−0.974717	+	0.223443i	$0.928270\pi$
$480$		0			0
$481$	−6.43873	+	11.1522i	−0.293581	+	0.508497i
$482$	−1.43561	−	0.828848i	−0.0653901	−	0.0377530i
$483$		0			0
$484$	−1.54258	−	2.67183i	−0.0701174	−	0.121447i
$485$	−3.38459	−	1.04324i	−0.153687	−	0.0473710i
$486$		0			0
$487$			15.1180i			0.685063i	0.939506	+	0.342532i	$0.111284\pi$
$487$			15.1180i			0.685063i	−0.939506	+	0.342532i	$0.888716\pi$
$488$	−13.2641	+	7.65806i	−0.600440	+	0.346664i
$489$		0			0
$490$	−1.95442	+	1.81419i	−0.0882917	+	0.0819568i
$491$	−11.7851	+	20.4124i	−0.531853	+	0.921197i	0.467456	+	0.884017i	$0.345171\pi$
$491$	−11.7851	+	20.4124i	−0.531853	+	0.921197i	−0.999309	+	0.0371799i	$0.988163\pi$
$492$		0			0
$493$	−18.5096	+	10.6865i	−0.833631	+	0.481297i
$494$	−13.6247			−0.613005
$495$		0			0
$496$	8.64001			0.387948
$497$	8.00215	−	4.62004i	0.358945	−	0.207237i
$498$		0			0
$499$	−17.0342	+	29.5041i	−0.762554	+	1.32078i	0.178976	+	0.983854i	$0.442722\pi$
$499$	−17.0342	+	29.5041i	−0.762554	+	1.32078i	−0.941530	+	0.336929i	$0.890612\pi$
$500$	0.966779	+	6.38714i	0.0432357	+	0.285642i
$501$		0			0
$502$	−13.4459	+	7.76300i	−0.600120	+	0.346479i
$503$			5.01986i			0.223825i	0.993718	+	0.111912i	$0.0356976\pi$
$503$			5.01986i			0.223825i	−0.993718	+	0.111912i	$0.964302\pi$
$504$		0			0
$505$	12.6597	−	41.0719i	0.563348	−	1.82768i
$506$	20.8791	+	36.1637i	0.928190	+	1.60767i
$507$		0			0
$508$	0.599978	+	0.346397i	0.0266197	+	0.0153689i
$509$	−1.83554	+	3.17925i	−0.0813590	+	0.140918i	−0.903834	−	0.427883i	$-0.859259\pi$
$509$	−1.83554	+	3.17925i	−0.0813590	+	0.140918i	0.822475	+	0.568801i	$0.192593\pi$
$510$		0			0
$511$	−6.58900	−	11.4125i	−0.291480	−	0.504859i
$512$		−	23.3551i		−	1.03216i
$513$		0			0
$514$	7.23161			0.318973
$515$	−7.69120	−	33.6651i	−0.338915	−	1.48346i
$516$		0			0
$517$	−39.2867	−	22.6822i	−1.72783	−	0.997561i
$518$	−4.54273	−	2.62274i	−0.199596	−	0.115237i
$519$		0			0
$520$	−19.6197	+	4.48236i	−0.860381	+	0.196565i
$521$	−10.7339			−0.470261			−0.235131	−	0.971964i	$-0.575552\pi$
$521$	−10.7339			−0.470261			−0.235131	+	0.971964i	$0.575552\pi$
$522$		0			0
$523$		−	36.6402i		−	1.60216i	−0.598555	−	0.801081i	$-0.704258\pi$
$523$		−	36.6402i		−	1.60216i	0.598555	−	0.801081i	$-0.295742\pi$
$524$	3.52402	+	6.10378i	0.153947	+	0.266645i
$525$		0			0
$526$	−16.3175	+	28.2628i	−0.711478	+	1.23232i
$527$	−9.71208	−	5.60727i	−0.423065	−	0.244257i
$528$		0			0
$529$	26.0189	+	45.0660i	1.13126	+	1.95939i
$530$	1.87301	−	6.07665i	0.0813585	−	0.263953i
$531$		0			0
$532$			2.25470i			0.0977538i
$533$	15.7663	−	9.10265i	0.682912	−	0.394280i
$534$		0			0
$535$	−2.32704	+	2.16008i	−0.100607	+	0.0933884i
$536$	15.0467	−	26.0617i	0.649920	−	1.12570i
$537$		0			0
$538$	19.2377	−	11.1069i	0.829395	−	0.478851i
$539$	−4.04223			−0.174111
$540$		0			0
$541$	1.34533			0.0578401			0.0289201	−	0.999582i	$-0.490793\pi$
$541$	1.34533			0.0578401			0.0289201	+	0.999582i	$0.490793\pi$
$542$	17.3861	−	10.0379i	0.746798	−	0.431164i
$543$		0			0
$544$	−5.13948	+	8.90184i	−0.220353	+	0.381663i
$545$	−7.52658	−	8.10835i	−0.322403	−	0.347323i
$546$		0			0
$547$	−29.1966	+	16.8567i	−1.24836	+	0.720739i	−0.970781	−	0.239965i	$-0.922864\pi$
$547$	−29.1966	+	16.8567i	−1.24836	+	0.720739i	−0.277575	+	0.960704i	$0.589531\pi$
$548$			6.00346i			0.256455i
$549$		0			0
$550$	13.5695	−	19.9205i	0.578604	−	0.849415i
$551$	−12.7972	−	22.1654i	−0.545179	−	0.944277i
$552$		0			0
$553$	3.67837	+	2.12371i	0.156420	+	0.0903093i
$554$	−10.5728	+	18.3126i	−0.449193	+	0.778026i
$555$		0			0
$556$	1.65034	+	2.85848i	0.0699901	+	0.121226i
$557$			13.8322i			0.586090i	0.956099	+	0.293045i	$0.0946686\pi$
$557$			13.8322i			0.586090i	−0.956099	+	0.293045i	$0.905331\pi$
$558$		0			0
$559$	18.5715			0.785491
$560$	−1.25033	−	5.47281i	−0.0528361	−	0.231269i
$561$		0			0
$562$	−30.3079	−	17.4983i	−1.27846	−	0.738121i
$563$	10.6277	+	6.13592i	0.447906	+	0.258598i	0.706945	−	0.707268i	$-0.250073\pi$
$563$	10.6277	+	6.13592i	0.447906	+	0.258598i	−0.259040	+	0.965867i	$0.583406\pi$
$564$		0			0
$565$	−6.17238	−	27.0171i	−0.259674	−	1.13662i
$566$	20.7666			0.872886
$567$		0			0
$568$			28.4057i			1.19188i
$569$	5.61071	+	9.71803i	0.235213	+	0.407401i	0.959335	−	0.282271i	$-0.0910879\pi$
$569$	5.61071	+	9.71803i	0.235213	+	0.407401i	−0.724122	+	0.689672i	$0.757755\pi$
$570$		0			0
$571$	−10.0493	+	17.4060i	−0.420551	+	0.728416i	−0.995993	−	0.0894262i	$-0.971497\pi$
$571$	−10.0493	+	17.4060i	−0.420551	+	0.728416i	0.575442	+	0.817843i	$0.304830\pi$
$572$	−5.92172	−	3.41891i	−0.247600	−	0.142952i
$573$		0			0
$574$	3.70786	+	6.42221i	0.154763	+	0.268058i
$575$	24.3837	−	35.7963i	1.01687	−	1.49281i
$576$		0			0
$577$			13.8945i			0.578435i	0.957263	+	0.289218i	$0.0933951\pi$
$577$			13.8945i			0.578435i	−0.957263	+	0.289218i	$0.906605\pi$
$578$	6.59028	−	3.80490i	0.274120	−	0.158263i
$579$		0			0
$580$	−5.76497	−	6.21057i	−0.239377	−	0.257880i
$581$	−6.09519	+	10.5572i	−0.252871	+	0.437986i
$582$		0			0
$583$	8.34751	−	4.81943i	0.345718	−	0.199601i
$584$	40.5116			1.67638
$585$		0			0
$586$	−7.29621			−0.301404
$587$	6.48110	−	3.74186i	0.267504	−	0.154443i	−0.360249	−	0.932856i	$-0.617308\pi$
$587$	6.48110	−	3.74186i	0.267504	−	0.154443i	0.627753	+	0.778413i	$0.283975\pi$
$588$		0			0
$589$	6.71475	−	11.6303i	0.276676	−	0.479218i
$590$	2.44259	−	2.26733i	0.100560	−	0.0933446i
$591$		0			0
$592$	9.56332	−	5.52138i	0.393050	−	0.226927i
$593$		−	26.8374i		−	1.10208i	−0.834479	−	0.551040i	$-0.814231\pi$
$593$		−	26.8374i		−	1.10208i	0.834479	−	0.551040i	$-0.185769\pi$
$594$		0			0
$595$	−2.14632	+	6.96334i	−0.0879906	+	0.285469i
$596$	−1.54019	−	2.66768i	−0.0630884	−	0.109272i
$597$		0			0
$598$	26.1926	+	15.1223i	1.07110	+	0.618397i
$599$	−23.0585	+	39.9385i	−0.942144	+	1.63184i	−0.180774	+	0.983525i	$0.557860\pi$
$599$	−23.0585	+	39.9385i	−0.942144	+	1.63184i	−0.761370	+	0.648317i	$0.775473\pi$
$600$		0			0
$601$	−3.70152	−	6.41122i	−0.150988	−	0.261519i	0.780603	−	0.625027i	$-0.214912\pi$
$601$	−3.70152	−	6.41122i	−0.150988	−	0.261519i	−0.931591	+	0.363508i	$0.881579\pi$
$602$			7.56489i			0.308322i
$603$		0			0
$604$	6.52118			0.265343
$605$	11.6398	−	2.65925i	0.473225	−	0.108114i
$606$		0			0
$607$	29.0245	+	16.7573i	1.17807	+	0.680157i	0.955567	−	0.294775i	$-0.0952448\pi$
$607$	29.0245	+	16.7573i	1.17807	+	0.680157i	0.222500	+	0.974933i	$0.428578\pi$
$608$	−10.6600	−	6.15456i	−0.432321	−	0.249600i
$609$		0			0
$610$	−2.95905	−	12.9520i	−0.119808	−	0.524413i
$611$	−32.8564			−1.32923
$612$		0			0
$613$			2.95377i			0.119302i	0.998219	+	0.0596508i	$0.0189987\pi$
$613$			2.95377i			0.119302i	−0.998219	+	0.0596508i	$0.981001\pi$
$614$	3.22490	+	5.58569i	0.130146	+	0.225420i
$615$		0			0
$616$	6.21327	−	10.7617i	0.250340	−	0.433601i
$617$	−32.6188	−	18.8325i	−1.31318	−	0.758166i	−0.330560	−	0.943785i	$-0.607238\pi$
$617$	−32.6188	−	18.8325i	−1.31318	−	0.758166i	−0.982622	+	0.185619i	$0.940571\pi$
$618$		0			0
$619$	−17.9983	−	31.1739i	−0.723411	−	1.25298i	−0.959625	−	0.281283i	$-0.909240\pi$
$619$	−17.9983	−	31.1739i	−0.723411	−	1.25298i	0.236214	−	0.971701i	$-0.424093\pi$
$620$	1.30968	−	4.24901i	0.0525979	−	0.170644i
$621$		0			0
$622$			23.5599i			0.944666i
$623$	−3.98699	+	2.30189i	−0.159735	+	0.0922232i
$624$		0			0
$625$	−24.7239	−	3.70551i	−0.988954	−	0.148220i
$626$	−7.88129	+	13.6508i	−0.315000	+	0.545596i
$627$		0			0
$628$	2.37133	−	1.36909i	0.0946265	−	0.0546326i
$629$	−14.3333			−0.571505
$630$		0			0
$631$	6.29101			0.250441			0.125221	−	0.992129i	$-0.460036\pi$
$631$	6.29101			0.250441			0.125221	+	0.992129i	$0.460036\pi$
$632$	−11.3080	+	6.52867i	−0.449807	+	0.259696i
$633$		0			0
$634$	11.4460	−	19.8251i	0.454580	−	0.787357i
$635$	−1.96504	+	1.82405i	−0.0779800	+	0.0723851i
$636$		0			0
$637$	−2.53546	+	1.46385i	−0.100459	+	0.0579998i
$638$			31.6175i			1.25175i
$639$		0			0
$640$	8.90112	+	2.74361i	0.351848	+	0.108451i
$641$	−18.9637	−	32.8460i	−0.749020	−	1.29734i	−0.948293	−	0.317397i	$-0.897191\pi$
$641$	−18.9637	−	32.8460i	−0.749020	−	1.29734i	0.199273	−	0.979944i	$-0.436142\pi$
$642$		0			0
$643$	−10.2039	−	5.89122i	−0.402402	−	0.232327i	0.285118	−	0.958493i	$-0.407967\pi$
$643$	−10.2039	−	5.89122i	−0.402402	−	0.232327i	−0.687520	+	0.726165i	$0.741301\pi$
$644$	2.50253	−	4.33452i	0.0986137	−	0.170804i
$645$		0			0
$646$	−7.58249	−	13.1333i	−0.298329	−	0.516721i
$647$			34.7373i			1.36566i	0.730575	+	0.682832i	$0.239252\pi$
$647$			34.7373i			1.36566i	−0.730575	+	0.682832i	$0.760748\pi$
$648$		0			0
$649$	5.05188			0.198303
$650$	1.29735	−	17.4091i	0.0508864	−	0.682840i
$651$		0			0
$652$	−7.64741	−	4.41523i	−0.299496	−	0.172914i
$653$	36.5637	+	21.1100i	1.43085	+	0.826100i	0.997185	−	0.0749764i	$-0.0238882\pi$
$653$	36.5637	+	21.1100i	1.43085	+	0.826100i	0.433661	+	0.901076i	$0.357221\pi$
$654$		0			0
$655$	−26.5910	+	6.07504i	−1.03900	+	0.237371i
$656$	−15.6115			−0.609528
$657$		0			0
$658$		−	13.3837i		−	0.521751i
$659$	5.03664	+	8.72372i	0.196200	+	0.339828i	0.947293	−	0.320368i	$-0.103807\pi$
$659$	5.03664	+	8.72372i	0.196200	+	0.339828i	−0.751093	+	0.660196i	$0.770473\pi$
$660$		0			0
$661$	8.24919	−	14.2880i	0.320856	−	0.555740i	−0.659809	−	0.751434i	$-0.729363\pi$
$661$	8.24919	−	14.2880i	0.320856	−	0.555740i	0.980665	+	0.195694i	$0.0626960\pi$
$662$	−35.6602	−	20.5884i	−1.38597	−	0.800192i
$663$		0			0
$664$	−18.7377	−	32.4547i	−0.727165	−	1.25949i
$665$	−8.33865	−	2.57024i	−0.323359	−	0.0996695i
$666$		0			0
$667$			56.8153i			2.19990i
$668$	2.86664	−	1.65506i	0.110914	−	0.0640361i
$669$		0			0
$670$	17.7593	+	19.1320i	0.686103	+	0.739135i
$671$	10.0695	−	17.4410i	0.388731	−	0.673301i
$672$		0			0
$673$	39.0265	−	22.5320i	1.50436	−	0.868544i	0.504375	−	0.863485i	$-0.331723\pi$
$673$	39.0265	−	22.5320i	1.50436	−	0.868544i	0.999987	−	0.00505962i	$-0.00161053\pi$
$674$	11.5296			0.444104
$675$		0			0
$676$	2.55879			0.0984151
$677$	30.0957	−	17.3758i	1.15667	−	0.667805i	0.206168	−	0.978517i	$-0.433901\pi$
$677$	30.0957	−	17.3758i	1.15667	−	0.667805i	0.950504	+	0.310712i	$0.100567\pi$
$678$		0			0
$679$	0.791954	−	1.37170i	0.0303924	−	0.0526412i
$680$	−15.2395	−	16.4175i	−0.584410	−	0.629581i
$681$		0			0
$682$	−14.3672	+	8.29493i	−0.550150	+	0.317629i
$683$			13.7295i			0.525344i	0.964885	+	0.262672i	$0.0846038\pi$
$683$			13.7295i			0.525344i	−0.964885	+	0.262672i	$0.915396\pi$
$684$		0			0
$685$	−22.2028	−	6.84360i	−0.848325	−	0.261481i
$686$	−0.596282	−	1.03279i	−0.0227662	−	0.0394321i
$687$		0			0
$688$	−13.7919	−	7.96278i	−0.525813	−	0.303578i
$689$	3.49061	−	6.04592i	0.132982	−	0.230331i
$690$		0			0
$691$	−19.4006	−	33.6028i	−0.738033	−	1.27831i	−0.953380	−	0.301774i	$-0.902421\pi$
$691$	−19.4006	−	33.6028i	−0.738033	−	1.27831i	0.215346	−	0.976538i	$-0.430912\pi$
$692$			3.12826i			0.118919i
$693$		0			0
$694$	1.10875			0.0420876
$695$	−12.4529	+	2.84502i	−0.472366	+	0.107918i
$696$		0			0
$697$	17.5486	+	10.1317i	0.664702	+	0.383766i
$698$	−32.7213	−	18.8917i	−1.23852	−	0.715061i
$699$		0			0
$700$	−2.88096	−	0.214694i	−0.108890	−	0.00811468i
$701$	−11.4854			−0.433798			−0.216899	−	0.976194i	$-0.569594\pi$
$701$	−11.4854			−0.433798			−0.216899	+	0.976194i	$0.569594\pi$
$702$		0			0
$703$		−	17.1642i		−	0.647360i
$704$	17.7512	+	30.7461i	0.669025	+	1.15879i
$705$		0			0
$706$	4.92829	−	8.53605i	0.185479	−	0.321258i
$707$	16.6456	+	9.61034i	0.626022	+	0.361434i
$708$		0			0
$709$	1.31096	+	2.27065i	0.0492341	+	0.0852759i	0.889592	−	0.456756i	$-0.150989\pi$
$709$	1.31096	+	2.27065i	0.0492341	+	0.0852759i	−0.840358	+	0.542032i	$0.817655\pi$
$710$	−23.5469	−	7.25791i	−0.883701	−	0.272385i
$711$		0			0
$712$		−	14.1528i		−	0.530400i
$713$	−25.8173	+	14.9056i	−0.966866	+	0.558220i
$714$		0			0
$715$	19.3947	−	18.0031i	0.725320	−	0.673280i
$716$	3.40513	−	5.89785i	0.127256	−	0.220413i
$717$		0			0
$718$	−17.3062	+	9.99174i	−0.645862	+	0.372888i
$719$	36.5399			1.36271			0.681353	−	0.731955i	$-0.261392\pi$
$719$	36.5399			1.36271			0.681353	+	0.731955i	$0.261392\pi$
$720$		0			0
$721$	15.4434			0.575142
$722$	−3.89585	+	2.24927i	−0.144989	+	0.0837092i
$723$		0			0
$724$	2.84228	−	4.92298i	0.105633	−	0.182961i
$725$	29.5405	−	14.2411i	1.09711	−	0.528901i
$726$		0			0
$727$	9.44506	−	5.45311i	0.350298	−	0.202245i	−0.314519	−	0.949251i	$-0.601843\pi$
$727$	9.44506	−	5.45311i	0.350298	−	0.202245i	0.664817	+	0.747007i	$0.268510\pi$
$728$		−	9.00027i		−	0.333572i
$729$		0			0
$730$	−10.3511	+	33.5821i	−0.383110	+	1.24293i
$731$	10.3355	+	17.9016i	0.382273	+	0.662116i
$732$		0			0
$733$	−30.8217	−	17.7949i	−1.13843	−	0.657271i	−0.192386	−	0.981319i	$-0.561623\pi$
$733$	−30.8217	−	17.7949i	−1.13843	−	0.657271i	−0.946041	+	0.324048i	$0.894956\pi$
$734$	2.39235	−	4.14367i	0.0883031	−	0.152946i
$735$		0			0
$736$	13.6621	+	23.6635i	0.503592	+	0.872247i
$737$			39.5698i			1.45757i
$738$		0			0
$739$	44.8355			1.64930			0.824651	−	0.565642i	$-0.191372\pi$
$739$	44.8355			1.64930			0.824651	+	0.565642i	$0.191372\pi$
$740$	−1.26568	−	5.54002i	−0.0465275	−	0.203655i
$741$		0			0
$742$	2.46274	+	1.42186i	0.0904099	+	0.0521982i
$743$	40.8171	+	23.5658i	1.49743	+	0.864544i	0.999996	−	0.00295558i	$-0.000940791\pi$
$743$	40.8171	+	23.5658i	1.49743	+	0.864544i	0.497438	+	0.867499i	$0.334274\pi$
$744$		0			0
$745$	11.6217	−	2.65512i	0.425786	−	0.0972760i
$746$	−7.94537			−0.290901
$747$		0			0
$748$		−	7.61083i		−	0.278279i
$749$	−0.709967	−	1.22970i	−0.0259416	−	0.0449322i
$750$		0			0
$751$	8.89808	−	15.4119i	0.324695	−	0.562389i	−0.656755	−	0.754104i	$-0.728072\pi$
$751$	8.89808	−	15.4119i	0.324695	−	0.562389i	0.981451	+	0.191715i	$0.0614048\pi$
$752$	24.4005	+	14.0876i	0.889794	+	0.513723i
$753$		0			0
$754$	11.4500	+	19.8319i	0.416983	+	0.722235i
$755$	−7.43378	+	24.1175i	−0.270543	+	0.877726i
$756$		0			0
$757$		−	54.7392i		−	1.98953i	−0.102192	−	0.994765i	$-0.532586\pi$
$757$		−	54.7392i		−	1.98953i	0.102192	−	0.994765i	$-0.467414\pi$
$758$	−17.5417	+	10.1277i	−0.637145	+	0.367856i
$759$		0			0
$760$	19.6600	−	18.2495i	0.713145	−	0.661978i
$761$	16.4392	−	28.4735i	0.595921	−	1.03217i	−0.397495	−	0.917604i	$-0.630120\pi$
$761$	16.4392	−	28.4735i	0.595921	−	1.03217i	0.993416	−	0.114561i	$-0.0365462\pi$
$762$		0			0
$763$	4.28476	−	2.47381i	0.155119	−	0.0895579i
$764$	−7.62835			−0.275984
$765$		0			0
$766$	−10.3953			−0.375597
$767$	3.16876	−	1.82948i	0.114417	−	0.0660588i
$768$		0			0
$769$	−10.5703	+	18.3083i	−0.381175	+	0.660215i	−0.991231	−	0.132144i	$-0.957814\pi$
$769$	−10.5703	+	18.3083i	−0.381175	+	0.660215i	0.610055	+	0.792359i	$0.291147\pi$
$770$	7.33338	+	7.90021i	0.264277	+	0.284704i
$771$		0			0
$772$	2.10123	−	1.21315i	0.0756249	−	0.0436621i
$773$			28.7144i			1.03278i	0.856352	+	0.516392i	$0.172725\pi$
$773$			28.7144i			1.03278i	−0.856352	+	0.516392i	$0.827275\pi$
$774$		0			0
$775$	14.2213	+	9.68726i	0.510844	+	0.347977i
$776$	2.43461	+	4.21687i	0.0873974	+	0.151377i
$777$		0			0
$778$	−20.7802	−	11.9975i	−0.745008	−	0.430130i
$779$	−12.1328	+	21.0146i	−0.434703	+	0.752927i
$780$		0			0
$781$	−18.6753	−	32.3465i	−0.668253	−	1.15745i
$782$			33.6638i			1.20381i
$783$		0			0
$784$	2.51058			0.0896635
$785$	2.36017	+	10.3307i	0.0842380	+	0.368717i
$786$		0			0
$787$	17.0525	+	9.84527i	0.607856	+	0.350946i	0.772126	−	0.635469i	$-0.219193\pi$
$787$	17.0525	+	9.84527i	0.607856	+	0.350946i	−0.164270	+	0.986415i	$0.552527\pi$
$788$	−7.60725	−	4.39205i	−0.270997	−	0.156460i
$789$		0			0
$790$	−2.52266	−	11.0419i	−0.0897521	−	0.392853i
$791$	12.3937			0.440670
$792$		0			0
$793$		−	14.5863i		−	0.517975i
$794$	−17.4542	−	30.2316i	−0.619427	−	1.07288i
$795$		0			0
$796$	−3.64813	+	6.31875i	−0.129305	+	0.223962i
$797$	−6.19641	−	3.57750i	−0.219488	−	0.126721i	0.386225	−	0.922405i	$-0.373779\pi$
$797$	−6.19641	−	3.57750i	−0.219488	−	0.126721i	−0.605713	+	0.795683i	$0.707112\pi$
$798$		0			0
$799$	−18.2854	−	31.6713i	−0.646892	−	1.12045i
$800$	8.87909	−	13.0349i	0.313923	−	0.460852i
$801$		0			0
$802$		−	5.23384i		−	0.184813i
$803$	−46.1318	+	26.6342i	−1.62796	+	0.939902i
$804$		0			0
$805$	13.1778	+	14.1963i	0.464455	+	0.500355i
$806$	−6.00784	+	10.4059i	−0.211617	+	0.366532i
$807$		0			0
$808$	−51.1716	+	29.5439i	−1.80021	+	1.03935i
$809$	−8.45266			−0.297180			−0.148590	−	0.988899i	$-0.547473\pi$
$809$	−8.45266			−0.297180			−0.148590	+	0.988899i	$0.547473\pi$
$810$		0			0
$811$	32.5014			1.14128			0.570640	−	0.821201i	$-0.306695\pi$
$811$	32.5014			1.14128			0.570640	+	0.821201i	$0.306695\pi$
$812$	3.28191	−	1.89481i	0.115172	−	0.0664948i
$813$		0			0
$814$	−10.6017	+	18.3627i	−0.371590	+	0.643613i
$815$	25.0466	−	23.2496i	0.877345	−	0.814397i
$816$		0			0
$817$	−21.4373	+	12.3768i	−0.749997	+	0.433011i
$818$		−	4.62619i		−	0.161751i
$819$		0			0
$820$	−2.36644	+	7.67748i	−0.0826397	+	0.268109i
$821$	−18.6761	−	32.3479i	−0.651799	−	1.12895i	−0.982686	−	0.185278i	$-0.940681\pi$
$821$	−18.6761	−	32.3479i	−0.651799	−	1.12895i	0.330887	−	0.943670i	$-0.392652\pi$
$822$		0			0
$823$	32.7571	+	18.9123i	1.14184	+	0.659243i	0.946886	−	0.321569i	$-0.104210\pi$
$823$	32.7571	+	18.9123i	1.14184	+	0.659243i	0.194956	+	0.980812i	$0.437544\pi$
$824$	−23.7379	+	41.1153i	−0.826949	+	1.43232i
$825$		0			0
$826$	0.745219	+	1.29076i	0.0259295	+	0.0449112i
$827$		−	9.34608i		−	0.324995i	−0.986709	−	0.162498i	$-0.948045\pi$
$827$		−	9.34608i		−	0.324995i	0.986709	−	0.162498i	$-0.0519549\pi$
$828$		0			0
$829$	−22.4253			−0.778862			−0.389431	−	0.921056i	$-0.627328\pi$
$829$	−22.4253			−0.778862			−0.389431	+	0.921056i	$0.627328\pi$
$830$	31.6910	−	7.24020i	1.10001	−	0.251311i
$831$		0			0
$832$	22.2687	+	12.8568i	0.772029	+	0.445731i
$833$	−2.82210	−	1.62934i	−0.0977798	−	0.0564532i
$834$		0			0
$835$	2.85314	+	12.4885i	0.0987371	+	0.432182i
$836$	9.11402			0.315215
$837$		0			0
$838$		−	27.2837i		−	0.942499i
$839$	22.9325	+	39.7203i	0.791718	+	1.37130i	0.924902	+	0.380205i	$0.124147\pi$
$839$	22.9325	+	39.7203i	0.791718	+	1.37130i	−0.133184	+	0.991091i	$0.542520\pi$
$840$		0			0
$841$	−7.00904	+	12.1400i	−0.241691	+	0.418621i
$842$	−18.7612	−	10.8318i	−0.646554	−	0.373288i
$843$		0			0
$844$	−1.02648	−	1.77792i	−0.0353330	−	0.0611985i
$845$	−2.91688	+	9.46327i	−0.100344	+	0.325547i
$846$		0			0
$847$			5.33959i			0.183471i
$848$	−5.18453	+	2.99329i	−0.178038	+	0.102790i
$849$		0			0
$850$	17.5031	−	8.43803i	0.600352	−	0.289422i
$851$	−19.0508	+	32.9970i	−0.653054	+	1.13112i
$852$		0			0
$853$	16.9551	−	9.78905i	0.580533	−	0.335171i	−0.180812	−	0.983518i	$-0.557873\pi$
$853$	16.9551	−	9.78905i	0.580533	−	0.335171i	0.761345	+	0.648347i	$0.224539\pi$
$854$	5.94157			0.203316
$855$		0			0
$856$	4.36513			0.149197
$857$	21.1551	−	12.2139i	0.722646	−	0.417220i	−0.0930797	−	0.995659i	$-0.529671\pi$
$857$	21.1551	−	12.2139i	0.722646	−	0.417220i	0.815726	+	0.578439i	$0.196338\pi$
$858$		0			0
$859$	−20.8624	+	36.1348i	−0.711817	+	1.23290i	0.252357	+	0.967634i	$0.418794\pi$
$859$	−20.8624	+	36.1348i	−0.711817	+	1.23290i	−0.964174	+	0.265270i	$0.914539\pi$
$860$	−6.00658	+	5.57561i	−0.204823	+	0.190127i
$861$		0			0
$862$	11.4532	−	6.61251i	0.390098	−	0.225223i
$863$			14.4518i			0.491946i	0.969277	+	0.245973i	$0.0791075\pi$
$863$			14.4518i			0.491946i	−0.969277	+	0.245973i	$0.920892\pi$
$864$		0			0
$865$	−11.5694	−	3.56604i	−0.393370	−	0.121249i
$866$	−11.6060	−	20.1021i	−0.394387	−	0.683099i
$867$		0			0
$868$	1.72203	+	0.994216i	0.0584496	+	0.0337459i
$869$	8.58452	−	14.8688i	0.291210	−	0.504390i
$870$		0			0
$871$	14.3298	+	24.8199i	0.485546	+	0.840990i
$872$			15.2099i			0.515071i
$873$		0			0
$874$	−40.3126			−1.36359
$875$	4.07815	−	10.4100i	0.137867	−	0.351923i
$876$		0			0
$877$	12.3359	+	7.12212i	0.416553	+	0.240497i	0.693601	−	0.720359i	$-0.256023\pi$
$877$	12.3359	+	7.12212i	0.416553	+	0.240497i	−0.277049	+	0.960856i	$0.589356\pi$
$878$	2.70886	+	1.56396i	0.0914197	+	0.0527812i
$879$		0			0
$880$	−22.1223	+	5.05412i	−0.745744	+	0.170374i
$881$	−6.84632			−0.230658			−0.115329	−	0.993327i	$-0.536792\pi$
$881$	−6.84632			−0.230658			−0.115329	+	0.993327i	$0.536792\pi$
$882$		0			0
$883$			34.7167i			1.16831i	0.811642	+	0.584155i	$0.198574\pi$
$883$			34.7167i			1.16831i	−0.811642	+	0.584155i	$0.801426\pi$
$884$	−2.75618	−	4.77384i	−0.0927004	−	0.160562i
$885$		0			0
$886$	7.08460	−	12.2709i	0.238012	−	0.412248i
$887$	−23.0060	−	13.2825i	−0.772466	−	0.445984i	0.0612873	−	0.998120i	$-0.480479\pi$
$887$	−23.0060	−	13.2825i	−0.772466	−	0.445984i	−0.833754	+	0.552136i	$0.813813\pi$
$888$		0			0
$889$	−0.599521	−	1.03840i	−0.0201073	−	0.0348268i
$890$	11.7320	+	3.61618i	0.393258	+	0.121215i
$891$		0			0
$892$			5.93356i			0.198670i
$893$	37.9266	−	21.8969i	1.26917	−	0.732753i
$894$		0			0
$895$	17.9306	+	19.3165i	0.599354	+	0.645680i
$896$	−2.08275	+	3.60743i	−0.0695799	+	0.120516i
$897$		0			0
$898$	20.9001	−	12.0667i	0.697446	−	0.402671i
$899$	−22.5718			−0.752811
$900$		0			0
$901$	7.77045			0.258871
$902$	25.9600	−	14.9880i	0.864374	−	0.499046i
$903$		0			0
$904$	−19.0503	+	32.9960i	−0.633603	+	1.09743i
$905$	14.9668	+	16.1236i	0.497513	+	0.535968i
$906$		0			0
$907$	44.7576	−	25.8408i	1.48615	−	0.858029i	0.486275	−	0.873806i	$-0.338355\pi$
$907$	44.7576	−	25.8408i	1.48615	−	0.858029i	0.999876	+	0.0157765i	$0.00502202\pi$
$908$		−	5.26084i		−	0.174587i
$909$		0			0
$910$	7.46079	+	2.29965i	0.247323	+	0.0762327i
$911$	−12.5192	−	21.6839i	−0.414779	−	0.718419i	0.580626	−	0.814170i	$-0.302808\pi$
$911$	−12.5192	−	21.6839i	−0.414779	−	0.718419i	−0.995405	+	0.0957518i	$0.969474\pi$
$912$		0			0
$913$	42.6745	+	24.6381i	1.41232	+	0.815404i
$914$	17.7416	−	30.7293i	0.586839	−	1.01643i
$915$		0			0
$916$	8.48081	+	14.6892i	0.280214	+	0.485345i
$917$		−	12.1983i		−	0.402822i
$918$		0			0
$919$	32.0840			1.05836			0.529178	−	0.848511i	$-0.322501\pi$
$919$	32.0840			1.05836			0.529178	+	0.848511i	$0.322501\pi$
$920$	−58.0505	+	13.2623i	−1.91387	+	0.437247i
$921$		0			0
$922$	13.2209	+	7.63307i	0.435406	+	0.251382i
$923$	−23.4279	−	13.5261i	−0.771138	−	0.445217i
$924$		0			0
$925$	21.9317	+	1.63438i	0.721109	+	0.0537382i
$926$	29.7814			0.978678
$927$		0			0
$928$			20.6887i			0.679140i
$929$	5.41000	+	9.37039i	0.177496	+	0.307433i	0.941022	−	0.338344i	$-0.109867\pi$
$929$	5.41000	+	9.37039i	0.177496	+	0.307433i	−0.763526	+	0.645777i	$0.776534\pi$
$930$		0			0
$931$	1.95114	−	3.37948i	0.0639461	−	0.110758i
$932$	8.11839	+	4.68715i	0.265927	+	0.153533i
$933$		0			0
$934$	0.896217	+	1.55229i	0.0293251	+	0.0507926i
$935$	28.1474	+	8.67592i	0.920518	+	0.283733i
$936$		0			0
$937$		−	12.4877i		−	0.407956i	−0.978975	−	0.203978i	$-0.934613\pi$
$937$		−	12.4877i		−	0.407956i	0.978975	−	0.203978i	$-0.0653871\pi$
$938$	−10.1101	+	5.83707i	−0.330107	+	0.190587i
$939$		0			0
$940$	10.6267	−	9.86429i	0.346606	−	0.321738i
$941$	10.6230	−	18.3995i	0.346299	−	0.599807i	−0.639290	−	0.768966i	$-0.720772\pi$
$941$	10.6230	−	18.3995i	0.346299	−	0.599807i	0.985589	+	0.169159i	$0.0541050\pi$
$942$		0			0
$943$	46.6490	−	26.9328i	1.51910	−	0.877053i
$944$	−3.13766			−0.102122
$945$		0			0
$946$	30.5790			0.994209
$947$	33.7201	−	19.4683i	1.09576	−	0.632636i	0.160654	−	0.987011i	$-0.448640\pi$
$947$	33.7201	−	19.4683i	1.09576	−	0.632636i	0.935103	+	0.354375i	$0.115306\pi$
$948$		0			0
$949$	−19.2906	+	33.4123i	−0.626200	+	1.08461i
$950$	10.1046	+	20.9601i	0.327836	+	0.680036i
$951$		0			0
$952$	8.67563	−	5.00888i	0.281179	−	0.162339i
$953$			9.56336i			0.309788i	0.987931	+	0.154894i	$0.0495036\pi$
$953$			9.56336i			0.309788i	−0.987931	+	0.154894i	$0.950496\pi$
$954$		0			0
$955$	8.69589	−	28.2122i	0.281392	−	0.912925i
$956$	4.73846	+	8.20726i	0.153253	+	0.265442i
$957$		0			0
$958$	−13.2843	−	7.66969i	−0.429196	−	0.247796i
$959$	5.19519	−	8.99833i	0.167761	−	0.290571i
$960$		0			0
$961$	9.57824	+	16.5900i	0.308975	+	0.535161i
$962$			15.3572i			0.495136i
$963$		0			0
$964$	0.803143			0.0258675
$965$	2.09134	+	9.15397i	0.0673225	+	0.294677i
$966$		0			0
$967$	3.17303	+	1.83195i	0.102038	+	0.0589116i	0.550151	−	0.835066i	$-0.314570\pi$
$967$	3.17303	+	1.83195i	0.102038	+	0.0589116i	−0.448113	+	0.893977i	$0.647904\pi$
$968$	−14.2157	−	8.20744i	−0.456910	−	0.263797i
$969$		0			0
$970$	−4.11764	+	0.940726i	−0.132210	+	0.0302049i
$971$	42.0771			1.35032			0.675159	−	0.737672i	$-0.264075\pi$
$971$	42.0771			1.35032			0.675159	+	0.737672i	$0.264075\pi$
$972$		0			0
$973$		−	5.71260i		−	0.183138i
$974$	9.01461	+	15.6138i	0.288847	+	0.500297i
$975$		0			0
$976$	−6.25407	+	10.8324i	−0.200188	+	0.346736i
$977$	11.5743	+	6.68243i	0.370295	+	0.213790i	0.673587	−	0.739108i	$-0.264753\pi$
$977$	11.5743	+	6.68243i	0.370295	+	0.213790i	−0.303292	+	0.952898i	$0.598086\pi$
$978$		0			0
$979$	9.30475	+	16.1163i	0.297381	+	0.515079i
$980$	0.380561	−	1.23466i	0.0121566	−	0.0394397i
$981$		0			0
$982$			28.1089i			0.896992i
$983$	−18.7616	+	10.8320i	−0.598401	+	0.345487i	−0.768412	−	0.639955i	$-0.778953\pi$
$983$	−18.7616	+	10.8320i	−0.598401	+	0.345487i	0.170011	+	0.985442i	$0.445620\pi$
$984$		0			0
$985$	24.9151	−	23.1275i	0.793861	−	0.736903i
$986$	−12.7444	+	22.0739i	−0.405863	+	0.702976i
$987$		0			0
$988$	5.71671	−	3.30055i	0.181873	−	0.105004i
$989$	54.9491			1.74728
$990$		0			0
$991$	−34.3470			−1.09107			−0.545534	−	0.838089i	$-0.683673\pi$
$991$	−34.3470			−1.09107			−0.545534	+	0.838089i	$0.683673\pi$
$992$	−9.40111	+	5.42773i	−0.298486	+	0.172331i
$993$		0			0
$994$	5.50970	−	9.54308i	0.174757	−	0.302688i
$995$	−19.2102	−	20.6950i	−0.609004	−	0.656077i
$996$		0			0
$997$	2.76981	−	1.59915i	0.0877208	−	0.0506456i	−0.455498	−	0.890237i	$-0.650539\pi$
$997$	2.76981	−	1.59915i	0.0877208	−	0.0506456i	0.543219	+	0.839591i	$0.317205\pi$
$998$			40.6287i			1.28608i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bh.c.64.22		64
3.2	odd	2		315.2.bh.c.274.11	yes	64
5.4	even	2	inner	945.2.bh.c.64.11		64
9.2	odd	6		315.2.bh.c.169.22	yes	64
9.7	even	3	inner	945.2.bh.c.694.11		64
15.14	odd	2		315.2.bh.c.274.22	yes	64
45.29	odd	6		315.2.bh.c.169.11	✓	64
45.34	even	6	inner	945.2.bh.c.694.22		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bh.c.169.11	✓	64	45.29	odd	6
315.2.bh.c.169.22	yes	64	9.2	odd	6
315.2.bh.c.274.11	yes	64	3.2	odd	2
315.2.bh.c.274.22	yes	64	15.14	odd	2
945.2.bh.c.64.11		64	5.4	even	2	inner
945.2.bh.c.64.22		64	1.1	even	1	trivial
945.2.bh.c.694.11		64	9.7	even	3	inner
945.2.bh.c.694.22		64	45.34	even	6	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.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.03279 - 0.596282i) q^{2} +(-0.288895 + 0.500381i) q^{4} +(-1.52125 - 1.63884i) q^{5} +(0.866025 - 0.500000i) q^{7} +3.07418i q^{8} +O(q^{10})\)	\(q+(1.03279 - 0.596282i) q^{2} +(-0.288895 + 0.500381i) q^{4} +(-1.52125 - 1.63884i) q^{5} +(0.866025 - 0.500000i) q^{7} +3.07418i q^{8} +(-2.54835 - 0.785481i) q^{10} +(-2.02111 - 3.50067i) q^{11} +(-2.53546 - 1.46385i) q^{13} +(0.596282 - 1.03279i) q^{14} +(1.25529 + 2.17422i) q^{16} -3.25867i q^{17} +3.90229 q^{19} +(1.25953 - 0.287754i) q^{20} +(-4.17478 - 2.41031i) q^{22} +(-7.50189 - 4.33122i) q^{23} +(-0.371578 + 4.98617i) q^{25} -3.49147 q^{26} +0.577790i q^{28} +(-3.27941 - 5.68010i) q^{29} +(1.72072 - 2.98038i) q^{31} +(-2.73173 - 1.57717i) q^{32} +(-1.94309 - 3.36553i) q^{34} +(-2.13686 - 0.658649i) q^{35} -4.39850i q^{37} +(4.03025 - 2.32686i) q^{38} +(5.03808 - 4.67661i) q^{40} +(-3.10915 + 5.38521i) q^{41} +(-5.49353 + 3.17169i) q^{43} +2.33556 q^{44} -10.3305 q^{46} +(9.71907 - 5.61131i) q^{47} +(0.500000 - 0.866025i) q^{49} +(2.58940 + 5.37124i) q^{50} +(1.46496 - 0.845798i) q^{52} +2.38454i q^{53} +(-2.66241 + 8.63768i) q^{55} +(1.53709 + 2.66232i) q^{56} +(-6.77389 - 3.91091i) q^{58} +(-0.624888 + 1.08234i) q^{59} +(2.49109 + 4.31469i) q^{61} -4.10414i q^{62} -8.78290 q^{64} +(1.45807 + 6.38209i) q^{65} +(-8.47762 - 4.89455i) q^{67} +(1.63058 + 0.941415i) q^{68} +(-2.59967 + 0.593927i) q^{70} +9.24009 q^{71} -13.1780i q^{73} +(-2.62274 - 4.54273i) q^{74} +(-1.12735 + 1.95263i) q^{76} +(-3.50067 - 2.02111i) q^{77} +(2.12371 + 3.67837i) q^{79} +(1.65359 - 5.36476i) q^{80} +7.41572i q^{82} +(-10.5572 + 6.09519i) q^{83} +(-5.34044 + 4.95727i) q^{85} +(-3.78245 + 6.55139i) q^{86} +(10.7617 - 6.21327i) q^{88} -4.60378 q^{89} -2.92770 q^{91} +(4.33452 - 2.50253i) q^{92} +(6.69185 - 11.5906i) q^{94} +(-5.93637 - 6.39521i) q^{95} +(1.37170 - 0.791954i) q^{97} -1.19256i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 34 q^{4} + 10 q^{5}+O(q^{10}) \) 64 * q + 34 * q^4 + 10 * q^5	\( 64 q + 34 q^{4} + 10 q^{5} - 4 q^{10} - 18 q^{11} + 6 q^{14} - 46 q^{16} + 48 q^{19} + 2 q^{20} + 18 q^{25} + 12 q^{26} + 30 q^{29} - 4 q^{31} + 34 q^{34} - 8 q^{35} - 6 q^{40} - 28 q^{41} - 68 q^{44} - 24 q^{46} + 32 q^{49} + 58 q^{50} - 12 q^{55} - 18 q^{56} - 16 q^{59} + 40 q^{61} - 100 q^{64} + 18 q^{65} - 4 q^{70} + 176 q^{71} + 20 q^{74} - 22 q^{79} - 64 q^{80} - 14 q^{85} - 60 q^{86} + 200 q^{89} - 16 q^{91} - 42 q^{94} - 68 q^{95}+O(q^{100}) \) 64 * q + 34 * q^4 + 10 * q^5 - 4 * q^10 - 18 * q^11 + 6 * q^14 - 46 * q^16 + 48 * q^19 + 2 * q^20 + 18 * q^25 + 12 * q^26 + 30 * q^29 - 4 * q^31 + 34 * q^34 - 8 * q^35 - 6 * q^40 - 28 * q^41 - 68 * q^44 - 24 * q^46 + 32 * q^49 + 58 * q^50 - 12 * q^55 - 18 * q^56 - 16 * q^59 + 40 * q^61 - 100 * q^64 + 18 * q^65 - 4 * q^70 + 176 * q^71 + 20 * q^74 - 22 * q^79 - 64 * q^80 - 14 * q^85 - 60 * q^86 + 200 * q^89 - 16 * q^91 - 42 * q^94 - 68 * q^95

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