LMFDB - Embedded newform 945.2.bh.c.64.11

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			64.11
Character	$\chi$	$=$	945.64
Dual form			945.2.bh.c.694.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03279 + 0.596282i) q^{2} +(-0.288895 + 0.500381i) q^{4} +(2.17990 + 0.498025i) q^{5} +(-0.866025 + 0.500000i) q^{7} -3.07418i q^{8} +O(q^{10})$	\(q+(-1.03279 + 0.596282i) q^{2} +(-0.288895 + 0.500381i) q^{4} +(2.17990 + 0.498025i) q^{5} +(-0.866025 + 0.500000i) q^{7} -3.07418i q^{8} +(-2.54835 + 0.785481i) q^{10} +(-2.02111 - 3.50067i) q^{11} +(2.53546 + 1.46385i) q^{13} +(0.596282 - 1.03279i) q^{14} +(1.25529 + 2.17422i) q^{16} +3.25867i q^{17} +3.90229 q^{19} +(-0.878965 + 0.946904i) q^{20} +(4.17478 + 2.41031i) q^{22} +(7.50189 + 4.33122i) q^{23} +(4.50394 + 2.17129i) q^{25} -3.49147 q^{26} -0.577790i q^{28} +(-3.27941 - 5.68010i) q^{29} +(1.72072 - 2.98038i) q^{31} +(2.73173 + 1.57717i) q^{32} +(-1.94309 - 3.36553i) q^{34} +(-2.13686 + 0.658649i) q^{35} +4.39850i q^{37} +(-4.03025 + 2.32686i) q^{38} +(1.53102 - 6.70141i) q^{40} +(-3.10915 + 5.38521i) q^{41} +(5.49353 - 3.17169i) q^{43} +2.33556 q^{44} -10.3305 q^{46} +(-9.71907 + 5.61131i) q^{47} +(0.500000 - 0.866025i) q^{49} +(-5.94633 + 0.443131i) q^{50} +(-1.46496 + 0.845798i) q^{52} -2.38454i q^{53} +(-2.66241 - 8.63768i) q^{55} +(1.53709 + 2.66232i) q^{56} +(6.77389 + 3.91091i) q^{58} +(-0.624888 + 1.08234i) q^{59} +(2.49109 + 4.31469i) q^{61} +4.10414i q^{62} -8.78290 q^{64} +(4.79802 + 4.45377i) q^{65} +(8.47762 + 4.89455i) q^{67} +(-1.63058 - 0.941415i) q^{68} +(1.81419 - 1.95442i) q^{70} +9.24009 q^{71} +13.1780i q^{73} +(-2.62274 - 4.54273i) q^{74} +(-1.12735 + 1.95263i) q^{76} +(3.50067 + 2.02111i) q^{77} +(2.12371 + 3.67837i) q^{79} +(1.65359 + 5.36476i) q^{80} -7.41572i q^{82} +(10.5572 - 6.09519i) q^{83} +(-1.62290 + 7.10359i) q^{85} +(-3.78245 + 6.55139i) q^{86} +(-10.7617 + 6.21327i) q^{88} -4.60378 q^{89} -2.92770 q^{91} +(-4.33452 + 2.50253i) q^{92} +(6.69185 - 11.5906i) q^{94} +(8.50660 + 1.94344i) q^{95} +(-1.37170 + 0.791954i) q^{97} +1.19256i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.818530	−	0.574464i	$-0.805210\pi$
$2$	−1.03279	+	0.596282i	−0.730294	+	0.421635i	0.0882360	+	0.996100i	$0.471877\pi$
$3$		0			0
$3$		0			0
$4$	−0.288895	+	0.500381i	−0.144448	+	0.250191i
$5$	2.17990	+	0.498025i	0.974882	+	0.222724i
$5$	2.17990	+	0.498025i	0.974882	+	0.222724i
$6$		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	0.808542	−	0.588438i	$-0.200257\pi$
$13$	2.53546	+	1.46385i	0.703210	+	0.405999i	−0.105332	+	0.994437i	$0.533590\pi$
$14$	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	$0.129315\pi$
$17$			3.25867i			0.790345i	−0.918607	+	0.395172i	$0.870685\pi$
$18$		0			0
$19$	3.90229			0.895246			0.447623	−	0.894222i	$-0.352271\pi$
$19$	3.90229			0.895246			0.447623	+	0.894222i	$0.352271\pi$
$20$	−0.878965	+	0.946904i	−0.196543	+	0.211734i
$21$		0			0
$22$	4.17478	+	2.41031i	0.890065	+	0.513879i
$23$	7.50189	+	4.33122i	1.56425	+	0.903121i	0.996819	+	0.0797013i	$0.0253966\pi$
$23$	7.50189	+	4.33122i	1.56425	+	0.903121i	0.567433	+	0.823420i	$0.307937\pi$
$24$		0			0
$25$	4.50394	+	2.17129i	0.900788	+	0.434258i
$26$	−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	$0.117754\pi$
$37$			4.39850i			0.723108i	−0.932351	+	0.361554i	$0.882246\pi$
$38$	−4.03025	+	2.32686i	−0.653792	+	0.377467i
$39$		0			0
$40$	1.53102	−	6.70141i	0.242075	−	1.05959i
$41$	−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	−0.0187451	−	0.999824i	$-0.505967\pi$
$43$	5.49353	−	3.17169i	0.837756	−	0.483678i	0.856501	+	0.516146i	$0.172634\pi$
$44$	2.33556			0.352099
$45$		0			0
$46$	−10.3305			−1.52315
$47$	−9.71907	+	5.61131i	−1.41767	+	0.818493i	−0.996094	−	0.0882989i	$-0.971857\pi$
$47$	−9.71907	+	5.61131i	−1.41767	+	0.818493i	−0.421578	+	0.906792i	$0.638524\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	−5.94633	+	0.443131i	−0.840939	+	0.0626682i
$51$		0			0
$52$	−1.46496	+	0.845798i	−0.203154	+	0.117291i
$53$		−	2.38454i		−	0.327542i	−0.986498	−	0.163771i	$-0.947634\pi$
$53$		−	2.38454i		−	0.327542i	0.986498	−	0.163771i	$-0.0523659\pi$
$54$		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
$65$	4.79802	+	4.45377i	0.595121	+	0.552422i
$66$		0			0
$67$	8.47762	+	4.89455i	1.03571	+	0.597965i	0.918614	−	0.395156i	$-0.129309\pi$
$67$	8.47762	+	4.89455i	1.03571	+	0.597965i	0.117092	+	0.993121i	$0.462643\pi$
$68$	−1.63058	−	0.941415i	−0.197737	−	0.114163i
$69$		0			0
$70$	1.81419	−	1.95442i	0.216837	−	0.233598i
$71$	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	$0.280335\pi$
$73$			13.1780i			1.54237i	−0.636612	+	0.771184i	$0.719665\pi$
$74$	−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	0.207785	−	0.978175i	$-0.433375\pi$
$83$	10.5572	−	6.09519i	1.15880	−	0.669034i	0.951016	+	0.309140i	$0.100041\pi$
$84$		0			0
$85$	−1.62290	+	7.10359i	−0.176028	+	0.770493i
$86$	−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
$95$	8.50660	+	1.94344i	0.872759	+	0.199392i
$96$		0			0
$97$	−1.37170	+	0.791954i	−0.139276	+	0.0804108i	−0.568019	−	0.823016i	$-0.692290\pi$
$97$	−1.37170	+	0.791954i	−0.139276	+	0.0804108i	0.428743	+	0.903426i	$0.358957\pi$
$98$			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	−0.334440	−	0.942417i	$-0.608547\pi$
$103$	−13.3744	−	7.72170i	−1.31782	−	0.760842i	−0.983377	+	0.181575i	$0.941880\pi$
$104$	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	$0.0218644\pi$
$107$			1.41993i			0.137270i	−0.997642	+	0.0686351i	$0.978136\pi$
$108$		0			0
$109$	4.94762			0.473896			0.236948	−	0.971522i	$-0.423853\pi$
$109$	4.94762			0.473896			0.236948	+	0.971522i	$0.423853\pi$
$110$	7.90021	+	7.33338i	0.753255	+	0.699210i
$111$		0			0
$112$	−2.17422	−	1.25529i	−0.205445	−	0.118614i
$113$	−10.7333	−	6.19686i	−1.00970	−	0.582952i	−0.0985975	−	0.995127i	$-0.531436\pi$
$113$	−10.7333	−	6.19686i	−1.00970	−	0.582952i	−0.911104	+	0.412176i	$0.864769\pi$
$114$		0			0
$115$	14.1963	+	13.1778i	1.32381	+	1.22883i
$116$	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	$0.0169417\pi$
$127$			1.19904i			0.106398i	−0.998584	+	0.0531989i	$0.983058\pi$
$128$	3.60743	−	2.08275i	0.318855	−	0.184091i
$129$		0			0
$130$	−7.61106	−	1.73884i	−0.667534	−	0.152506i
$131$	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	−0.832439	−	0.554117i	$-0.813056\pi$
$137$	−8.99833	+	5.19519i	−0.768779	+	0.443855i	0.0636599	+	0.997972i	$0.479723\pi$
$138$		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	$0.0887752\pi$
$140$	0.287754	−	1.25953i	0.0243196	−	0.106449i
$141$		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
$155$	5.23531	−	5.63997i	0.420510	−	0.453013i
$156$		0			0
$157$	4.10414	+	2.36953i	0.327546	+	0.189109i	0.654751	−	0.755845i	$-0.272773\pi$
$157$	4.10414	+	2.36953i	0.327546	+	0.189109i	−0.327205	+	0.944953i	$0.606107\pi$
$158$	−4.38670	−	2.53266i	−0.348987	−	0.201488i
$159$		0			0
$160$	5.16944	+	4.79854i	0.408680	+	0.379358i
$161$	−8.66243			−0.682695
$162$		0			0
$163$		−	15.2832i		−	1.19707i	−0.801097	−	0.598535i	$-0.795750\pi$
$163$		−	15.2832i		−	1.19707i	0.801097	−	0.598535i	$-0.204250\pi$
$164$	−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	0.679524	−	0.733653i	$-0.262186\pi$
$167$	4.96139	+	2.86446i	0.383924	+	0.221659i	−0.295600	+	0.955312i	$0.595520\pi$
$168$		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	−0.667538	−	0.744576i	$-0.732652\pi$
$173$	−4.68882	+	2.70709i	−0.356484	+	0.205816i	0.311053	+	0.950393i	$0.399318\pi$
$174$		0			0
$175$	−4.98617	+	0.371578i	−0.376919	+	0.0280887i
$176$	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
$185$	−2.19056	+	9.58829i	−0.161053	+	0.704945i
$186$		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	0.625143	−	0.780510i	$-0.285041\pi$
$193$	3.63667	+	2.09963i	0.261773	+	0.151135i	−0.363370	+	0.931645i	$0.618374\pi$
$194$	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	$-0.817826\pi$
$197$		−	15.2029i		−	1.08316i	0.840648	−	0.541581i	$-0.182174\pi$
$198$		0			0
$199$	12.6279			0.895166			0.447583	−	0.894242i	$-0.352285\pi$
$199$	12.6279			0.895166			0.447583	+	0.894242i	$0.352285\pi$
$200$	6.67494	−	13.8459i	0.471990	−	0.979055i
$201$		0			0
$202$	−19.8509	−	11.4609i	−1.39671	−	0.806389i
$203$	5.68010	+	3.27941i	0.398665	+	0.230169i
$204$		0			0
$205$	−9.45961	+	10.1908i	−0.660688	+	0.711755i
$206$	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
$220$	5.09129	+	1.16317i	0.343255	+	0.0784207i
$221$	−4.77021	+	8.26224i	−0.320879	+	0.555779i
$222$		0			0
$223$	−8.89357	+	5.13470i	−0.595557	+	0.343845i	−0.767292	−	0.641298i	$-0.778396\pi$
$223$	−8.89357	+	5.13470i	−0.595557	+	0.343845i	0.171735	+	0.985143i	$0.445063\pi$
$224$	−3.15434			−0.210758
$225$		0			0
$226$	14.7803			0.983172
$227$	7.88525	−	4.55255i	0.523362	−	0.302163i	−0.214947	−	0.976626i	$-0.568958\pi$
$227$	7.88525	−	4.55255i	0.523362	−	0.302163i	0.738309	+	0.674462i	$0.235625\pi$
$228$		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	$-0.255103\pi$
$230$	−22.5195	−	5.14485i	−1.48489	−	0.339241i
$231$		0			0
$232$	−17.4617	+	10.0815i	−1.14641	+	0.661883i
$233$			16.2244i			1.06290i	0.847091	+	0.531448i	$0.178352\pi$
$233$			16.2244i			1.06290i	−0.847091	+	0.531448i	$0.821648\pi$
$234$		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
$245$	1.52125	−	1.63884i	0.0971893	−	0.104702i
$246$		0			0
$247$	9.89410	+	5.71236i	0.629546	+	0.363469i
$248$	−9.16222	−	5.28981i	−0.581801	−	0.335903i
$249$		0			0
$250$	−13.1831	−	1.99544i	−0.833773	−	0.126203i
$251$	−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	0.327186	−	0.944960i	$-0.393900\pi$
$257$	−5.25151	−	3.03196i	−0.327580	−	0.189128i	−0.654766	+	0.755831i	$0.727233\pi$
$258$		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	0.462280	−	0.886734i	$-0.347032\pi$
$263$	23.6992	−	13.6827i	1.46135	−	0.843713i	0.999074	+	0.0430209i	$0.0136982\pi$
$264$		0			0
$265$	1.18756	−	5.19807i	0.0729514	−	0.319315i
$266$	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
$275$	−1.50200	−	20.1552i	−0.0905742	−	1.21541i
$276$		0			0
$277$	15.3556	−	8.86557i	0.922629	−	0.532680i	0.0381563	−	0.999272i	$-0.487852\pi$
$277$	15.3556	−	8.86557i	0.922629	−	0.532680i	0.884473	+	0.466592i	$0.154518\pi$
$278$			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	−0.0203967	−	0.999792i	$-0.506493\pi$
$283$	−15.0805	−	8.70671i	−0.896440	−	0.517560i	−0.876044	+	0.482232i	$0.839826\pi$
$284$	−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
$290$	12.8187	+	11.8990i	0.752739	+	0.698731i
$291$		0			0
$292$	−6.59402	−	3.80706i	−0.385886	−	0.222791i
$293$	5.29842	+	3.05904i	0.309537	+	0.178711i	0.646719	−	0.762728i	$-0.276141\pi$
$293$	5.29842	+	3.05904i	0.309537	+	0.178711i	−0.337182	+	0.941439i	$0.609474\pi$
$294$		0			0
$295$	−1.90123	+	2.04818i	−0.110694	+	0.119250i
$296$	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	$-0.950676\pi$
$307$		−	5.40835i		−	0.308671i	0.988019	−	0.154335i	$-0.0493236\pi$
$308$	−2.02265	+	1.16778i	−0.115251	+	0.0665404i
$309$		0			0
$310$	−2.04396	+	8.94663i	−0.116089	+	0.508134i
$311$	−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	−0.140306	−	0.990108i	$-0.544809\pi$
$313$	11.4466	−	6.60869i	0.647000	−	0.373545i	0.787306	+	0.616563i	$0.211475\pi$
$314$	−5.65163			−0.318940
$315$		0			0
$316$	−2.45412			−0.138055
$317$	−16.6240	+	9.59784i	−0.933694	+	0.539069i	−0.887978	−	0.459886i	$-0.847890\pi$
$317$	−16.6240	+	9.59784i	−0.933694	+	0.539069i	−0.0457161	+	0.998954i	$0.514557\pi$
$318$		0			0
$319$	−13.2561	+	22.9603i	−0.742200	+	1.28553i
$320$	−19.1459	−	4.37411i	−1.07029	−	0.244520i
$321$		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
$335$	16.0428	+	14.8917i	0.876510	+	0.813621i
$336$		0			0
$337$	−8.37265	−	4.83395i	−0.456087	−	0.263322i	0.254310	−	0.967123i	$-0.418152\pi$
$337$	−8.37265	−	4.83395i	−0.456087	−	0.263322i	−0.710398	+	0.703800i	$0.751485\pi$
$338$	4.57380	+	2.64069i	0.248782	+	0.143634i
$339$		0			0
$340$	−3.08565	−	2.86426i	−0.167343	−	0.155336i
$341$	−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	0.478233	−	0.878233i	$-0.341278\pi$
$347$	−0.805161	−	0.464860i	−0.0432233	−	0.0249550i	−0.521456	+	0.853278i	$0.674611\pi$
$348$		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	−0.678239	−	0.734841i	$-0.737257\pi$
$353$	−7.15773	+	4.13252i	−0.380967	+	0.219952i	0.297272	+	0.954793i	$0.403923\pi$
$354$		0			0
$355$	20.1425	+	4.60179i	1.06905	+	0.244238i
$356$	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
$365$	−6.56297	+	28.7267i	−0.343522	+	1.50363i
$366$		0			0
$367$	−3.47459	+	2.00605i	−0.181372	+	0.104715i	−0.587937	−	0.808907i	$-0.700060\pi$
$367$	−3.47459	+	2.00605i	−0.181372	+	0.104715i	0.406565	+	0.913622i	$0.366726\pi$
$368$			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	0.641881	−	0.766804i	$-0.278154\pi$
$373$	5.76983	+	3.33121i	0.298750	+	0.172484i	−0.343131	+	0.939288i	$0.611487\pi$
$374$	−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	$0.643685\pi$
$380$	−3.42997	+	3.69509i	−0.175954	+	0.189554i
$381$		0			0
$382$	−13.6356	−	7.87249i	−0.697656	−	0.402792i
$383$	7.54893	+	4.35838i	0.385732	+	0.222703i	0.680309	−	0.732925i	$-0.261845\pi$
$383$	7.54893	+	4.35838i	0.385732	+	0.222703i	−0.294577	+	0.955628i	$0.595179\pi$
$384$		0			0
$385$	6.62455	+	6.14925i	0.337618	+	0.313395i
$386$	−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	$0.262608\pi$
$397$			29.2717i			1.46911i	−0.678551	+	0.734553i	$0.737392\pi$
$398$	−13.0420	+	7.52978i	−0.653734	+	0.377434i
$399$		0			0
$400$	0.932876	+	12.5182i	0.0466438	+	0.625909i
$401$	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	$0.136092\pi$
$410$	3.69322	−	16.1655i	0.182395	−	0.798360i
$411$		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
$425$	−7.07553	+	14.6769i	−0.343214	+	0.711933i
$426$		0			0
$427$	−4.31469	−	2.49109i	−0.208803	−	0.120552i
$428$	−0.710508	−	0.410212i	−0.0343437	−	0.0198283i
$429$		0			0
$430$	−11.5081	+	12.3976i	−0.554971	+	0.597867i
$431$	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	$0.154913\pi$
$433$			19.4639i			0.935376i	−0.883894	+	0.467688i	$0.845087\pi$
$434$	−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	−0.724105	−	0.689690i	$-0.757747\pi$
$443$	−10.2895	+	5.94064i	−0.488868	+	0.282248i	0.235236	+	0.971938i	$0.424414\pi$
$444$		0			0
$445$	−10.0358	−	2.29280i	−0.475742	−	0.108689i
$446$	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
$455$	−6.38209	−	1.45807i	−0.299197	−	0.0683552i
$456$		0			0
$457$	−25.7674	+	14.8768i	−1.20535	+	0.695908i	−0.961740	−	0.273965i	$-0.911665\pi$
$457$	−25.7674	+	14.8768i	−1.20535	+	0.695908i	−0.243609	+	0.969873i	$0.578331\pi$
$458$			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	−0.0953374	−	0.995445i	$-0.530393\pi$
$463$	−21.6269	−	12.4863i	−1.00509	−	0.580287i	−0.909749	+	0.415158i	$0.863726\pi$
$464$	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	$-0.988928\pi$
$467$		−	1.50301i		−	0.0695509i	0.999395	−	0.0347754i	$-0.0110716\pi$
$468$		0			0
$469$	−9.78911			−0.452019
$470$	20.3600	−	21.9337i	0.939136	−	1.01173i
$471$		0			0
$472$	3.32730	+	1.92102i	0.153151	+	0.0884220i
$473$	−22.2061	−	12.8207i	−1.02104	−	0.589496i
$474$		0			0
$475$	17.5757	+	8.47300i	0.806427	+	0.388768i
$476$	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	$-0.888716\pi$
$487$		−	15.1180i		−	0.685063i	0.939506	−	0.342532i	$-0.111284\pi$
$488$	13.2641	−	7.65806i	0.600440	−	0.346664i
$489$		0			0
$490$	−0.593927	+	2.59967i	−0.0268309	+	0.117441i
$491$	−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	$0.890612\pi$
$500$	−6.01481	+	2.35631i	−0.268991	+	0.105378i
$501$		0			0
$502$	13.4459	−	7.76300i	0.600120	−	0.346479i
$503$		−	5.01986i		−	0.223825i	−0.993718	−	0.111912i	$-0.964302\pi$
$503$		−	5.01986i		−	0.223825i	0.993718	−	0.111912i	$-0.0356976\pi$
$504$		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
$515$	−25.3092	−	23.4933i	−1.11526	−	1.03524i
$516$		0			0
$517$	39.2867	+	22.6822i	1.72783	+	0.997561i
$518$	4.54273	+	2.62274i	0.199596	+	0.115237i
$519$		0			0
$520$	13.6917	−	14.7500i	0.600420	−	0.646830i
$521$	−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	$0.295742\pi$
$523$			36.6402i			1.60216i	−0.598555	+	0.801081i	$0.704258\pi$
$524$	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
$535$	−0.707163	+	3.09532i	−0.0305733	+	0.133822i
$536$	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
$545$	10.7853	+	2.46404i	0.461993	+	0.105548i
$546$		0			0
$547$	29.1966	−	16.8567i	1.24836	−	0.720739i	0.277575	−	0.960704i	$-0.410469\pi$
$547$	29.1966	−	16.8567i	1.24836	−	0.720739i	0.970781	+	0.239965i	$0.0771361\pi$
$548$		−	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	$-0.905331\pi$
$557$		−	13.8322i		−	0.586090i	0.956099	−	0.293045i	$-0.0946686\pi$
$558$		0			0
$559$	18.5715			0.785491
$560$	−4.11443	−	3.81922i	−0.173866	−	0.161392i
$561$		0			0
$562$	30.3079	+	17.4983i	1.27846	+	0.738121i
$563$	−10.6277	−	6.13592i	−0.447906	−	0.258598i	0.259040	−	0.965867i	$-0.416594\pi$
$563$	−10.6277	−	6.13592i	−0.447906	−	0.258598i	−0.706945	+	0.707268i	$0.749927\pi$
$564$		0			0
$565$	−20.3113	−	18.8540i	−0.854503	−	0.793193i
$566$	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	$-0.906605\pi$
$577$		−	13.8945i		−	0.578435i	0.957263	−	0.289218i	$-0.0933951\pi$
$578$	−6.59028	+	3.80490i	−0.274120	+	0.158263i
$579$		0			0
$580$	8.26100	+	1.88733i	0.343019	+	0.0783669i
$581$	−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	−0.627753	−	0.778413i	$-0.716025\pi$
$587$	−6.48110	+	3.74186i	−0.267504	+	0.154443i	0.360249	+	0.932856i	$0.382692\pi$
$588$		0			0
$589$	6.71475	−	11.6303i	0.276676	−	0.479218i
$590$	0.742275	−	3.24901i	0.0305590	−	0.133760i
$591$		0			0
$592$	−9.56332	+	5.52138i	−0.393050	+	0.226927i
$593$			26.8374i			1.10208i	0.834479	+	0.551040i	$0.185769\pi$
$593$			26.8374i			1.10208i	−0.834479	+	0.551040i	$0.814231\pi$
$594$		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
$605$	−8.12287	+	8.75073i	−0.330242	+	0.355768i
$606$		0			0
$607$	−29.0245	−	16.7573i	−1.17807	−	0.680157i	−0.222500	−	0.974933i	$-0.571422\pi$
$607$	−29.0245	−	16.7573i	−1.17807	−	0.680157i	−0.955567	+	0.294775i	$0.904755\pi$
$608$	10.6600	+	6.15456i	0.432321	+	0.249600i
$609$		0			0
$610$	−9.73727	−	9.03863i	−0.394250	−	0.365963i
$611$	−32.8564			−1.32923
$612$		0			0
$613$		−	2.95377i		−	0.119302i	−0.998219	−	0.0596508i	$-0.981001\pi$
$613$		−	2.95377i		−	0.119302i	0.998219	−	0.0596508i	$-0.0189987\pi$
$614$	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	0.982622	−	0.185619i	$-0.0594289\pi$
$617$	32.6188	+	18.8325i	1.31318	+	0.758166i	0.330560	+	0.943785i	$0.392762\pi$
$618$		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
$625$	15.5710	+	19.5587i	0.622840	+	0.782349i
$626$	−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
$635$	−0.597153	+	2.61379i	−0.0236973	+	0.103725i
$636$		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	0.687520	−	0.726165i	$-0.258699\pi$
$643$	10.2039	+	5.89122i	0.402402	+	0.232327i	−0.285118	+	0.958493i	$0.592033\pi$
$644$	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	$-0.760748\pi$
$647$		−	34.7373i		−	1.36566i	0.730575	−	0.682832i	$-0.239252\pi$
$648$		0			0
$649$	5.05188			0.198303
$650$	−15.7254	−	7.58099i	−0.616800	−	0.297351i
$651$		0			0
$652$	7.64741	+	4.41523i	0.299496	+	0.172914i
$653$	−36.5637	−	21.1100i	−1.43085	−	0.826100i	−0.433661	−	0.901076i	$-0.642779\pi$
$653$	−36.5637	−	21.1100i	−1.43085	−	0.826100i	−0.997185	+	0.0749764i	$0.976112\pi$
$654$		0			0
$655$	18.5566	−	19.9910i	0.725068	−	0.781112i
$656$	−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
$670$	−25.4485	−	5.81401i	−0.983161	−	0.224615i
$671$	10.0695	−	17.4410i	0.388731	−	0.673301i
$672$		0			0
$673$	−39.0265	+	22.5320i	−1.50436	+	0.868544i	−0.504375	+	0.863485i	$0.668277\pi$
$673$	−39.0265	+	22.5320i	−1.50436	+	0.868544i	−0.999987	+	0.00505962i	$0.998389\pi$
$674$	11.5296			0.444104
$675$		0			0
$676$	2.55879			0.0984151
$677$	−30.0957	+	17.3758i	−1.15667	+	0.667805i	−0.950504	−	0.310712i	$-0.899433\pi$
$677$	−30.0957	+	17.3758i	−1.15667	+	0.667805i	−0.206168	+	0.978517i	$0.566099\pi$
$678$		0			0
$679$	0.791954	−	1.37170i	0.0303924	−	0.0526412i
$680$	21.8377	+	4.98909i	0.837438	+	0.191323i
$681$		0			0
$682$	14.3672	−	8.29493i	0.550150	−	0.317629i
$683$		−	13.7295i		−	0.525344i	−0.964885	−	0.262672i	$-0.915396\pi$
$683$		−	13.7295i		−	0.525344i	0.964885	−	0.262672i	$-0.0846038\pi$
$684$		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
$695$	8.69031	−	9.36203i	0.329642	−	0.355122i
$696$		0			0
$697$	−17.5486	−	10.1317i	−0.664702	−	0.383766i
$698$	32.7213	+	18.8917i	1.23852	+	0.715061i
$699$		0			0
$700$	1.25455	−	2.60233i	0.0474176	−	0.0983590i
$701$	−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
$715$	5.89384	−	25.7979i	0.220417	−	0.964786i
$716$	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
$725$	−2.43711	−	32.7034i	−0.0905121	−	1.21457i
$726$		0			0
$727$	−9.44506	+	5.45311i	−0.350298	+	0.202245i	−0.664817	−	0.747007i	$-0.731490\pi$
$727$	−9.44506	+	5.45311i	−0.350298	+	0.202245i	0.314519	+	0.949251i	$0.398157\pi$
$728$			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	0.946041	−	0.324048i	$-0.105044\pi$
$733$	30.8217	+	17.7949i	1.13843	+	0.657271i	0.192386	+	0.981319i	$0.438377\pi$
$734$	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	$0.191372\pi$
$740$	−4.16496	−	3.86612i	−0.153107	−	0.142122i
$741$		0			0
$742$	−2.46274	−	1.42186i	−0.0904099	−	0.0521982i
$743$	−40.8171	−	23.5658i	−1.49743	−	0.864544i	−0.497438	−	0.867499i	$-0.665726\pi$
$743$	−40.8171	−	23.5658i	−1.49743	−	0.864544i	−0.999996	+	0.00295558i	$0.999059\pi$
$744$		0			0
$745$	−8.11025	+	8.73713i	−0.297137	+	0.320104i
$746$	−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	$0.467414\pi$
$757$			54.7392i			1.98953i	−0.102192	+	0.994765i	$0.532586\pi$
$758$	17.5417	−	10.1277i	0.637145	−	0.367856i
$759$		0			0
$760$	5.97447	−	26.1508i	0.216717	−	0.948590i
$761$	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	$0.291147\pi$
$770$	−10.5085	−	2.40079i	−0.378699	−	0.0865183i
$771$		0			0
$772$	−2.10123	+	1.21315i	−0.0756249	+	0.0436621i
$773$		−	28.7144i		−	1.03278i	−0.856352	−	0.516392i	$-0.827275\pi$
$773$		−	28.7144i		−	1.03278i	0.856352	−	0.516392i	$-0.172725\pi$
$774$		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
$785$	7.76654	+	7.20930i	0.277200	+	0.257311i
$786$		0			0
$787$	−17.0525	−	9.84527i	−0.607856	−	0.350946i	0.164270	−	0.986415i	$-0.447473\pi$
$787$	−17.0525	−	9.84527i	−0.607856	−	0.350946i	−0.772126	+	0.635469i	$0.780807\pi$
$788$	7.60725	+	4.39205i	0.270997	+	0.156460i
$789$		0			0
$790$	−8.30124	−	7.70563i	−0.295345	−	0.274154i
$791$	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	0.605713	−	0.795683i	$-0.292888\pi$
$797$	6.19641	+	3.57750i	0.219488	+	0.126721i	−0.386225	+	0.922405i	$0.626221\pi$
$798$		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
$805$	−18.8833	−	4.31411i	−0.665547	−	0.152052i
$806$	−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
$815$	7.61140	−	33.3158i	0.266616	−	1.16700i
$816$		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	−0.194956	−	0.980812i	$-0.562456\pi$
$823$	−32.7571	−	18.9123i	−1.14184	−	0.659243i	−0.946886	+	0.321569i	$0.895790\pi$
$824$	−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	$0.0519549\pi$
$827$			9.34608i			0.324995i	−0.986709	+	0.162498i	$0.948045\pi$
$828$		0			0
$829$	−22.4253			−0.778862			−0.389431	−	0.921056i	$-0.627328\pi$
$829$	−22.4253			−0.778862			−0.389431	+	0.921056i	$0.627328\pi$
$830$	−22.1157	+	23.8251i	−0.767647	+	0.826982i
$831$		0			0
$832$	−22.2687	−	12.8568i	−0.772029	−	0.445731i
$833$	2.82210	+	1.62934i	0.0977798	+	0.0564532i
$834$		0			0
$835$	9.38877	+	8.71514i	0.324912	+	0.301600i
$836$	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
$850$	−1.44402	−	19.3772i	−0.0495294	−	0.664631i
$851$	−19.0508	+	32.9970i	−0.653054	+	1.13112i
$852$		0			0
$853$	−16.9551	+	9.78905i	−0.580533	+	0.335171i	−0.761345	−	0.648347i	$-0.775461\pi$
$853$	−16.9551	+	9.78905i	−0.580533	+	0.335171i	0.180812	+	0.983518i	$0.442127\pi$
$854$	5.94157			0.203316
$855$		0			0
$856$	4.36513			0.149197
$857$	−21.1551	+	12.2139i	−0.722646	+	0.417220i	−0.815726	−	0.578439i	$-0.803662\pi$
$857$	−21.1551	+	12.2139i	−0.722646	+	0.417220i	0.0930797	+	0.995659i	$0.470329\pi$
$858$		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	$0.914539\pi$
$860$	−1.82533	+	7.98965i	−0.0622434	+	0.272445i
$861$		0			0
$862$	−11.4532	+	6.61251i	−0.390098	+	0.225223i
$863$		−	14.4518i		−	0.491946i	−0.969277	−	0.245973i	$-0.920892\pi$
$863$		−	14.4518i		−	0.491946i	0.969277	−	0.245973i	$-0.0791075\pi$
$864$		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
$875$	−11.0544	−	1.67324i	−0.373708	−	0.0565657i
$876$		0			0
$877$	−12.3359	−	7.12212i	−0.416553	−	0.240497i	0.277049	−	0.960856i	$-0.410644\pi$
$877$	−12.3359	−	7.12212i	−0.416553	−	0.240497i	−0.693601	+	0.720359i	$0.743977\pi$
$878$	−2.70886	−	1.56396i	−0.0914197	−	0.0527812i
$879$		0			0
$880$	15.4382	−	16.6315i	0.520421	−	0.560646i
$881$	−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	$-0.801426\pi$
$883$		−	34.7167i		−	1.16831i	0.811642	−	0.584155i	$-0.198574\pi$
$884$	−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	0.833754	−	0.552136i	$-0.186187\pi$
$887$	23.0060	+	13.2825i	0.772466	+	0.445984i	−0.0612873	+	0.998120i	$0.519521\pi$
$888$		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
$895$	−25.6939	−	5.87008i	−0.858852	−	0.196215i
$896$	−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
$905$	−21.4469	−	4.89980i	−0.712918	−	0.162875i
$906$		0			0
$907$	−44.7576	+	25.8408i	−1.48615	+	0.858029i	−0.999876	−	0.0157765i	$-0.994978\pi$
$907$	−44.7576	+	25.8408i	−1.48615	+	0.858029i	−0.486275	+	0.873806i	$0.661645\pi$
$908$			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	$0.322501\pi$
$920$	40.5108	−	43.6421i	1.33560	−	1.43884i
$921$		0			0
$922$	−13.2209	−	7.63307i	−0.435406	−	0.251382i
$923$	23.4279	+	13.5261i	0.771138	+	0.445217i
$924$		0			0
$925$	−9.55041	+	19.8106i	−0.314016	+	0.651368i
$926$	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	$0.0653871\pi$
$937$			12.4877i			0.407956i	−0.978975	+	0.203978i	$0.934613\pi$
$938$	10.1101	−	5.83707i	0.330107	−	0.190587i
$939$		0			0
$940$	3.22935	−	14.1352i	0.105330	−	0.461039i
$941$	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	−0.935103	−	0.354375i	$-0.884694\pi$
$947$	−33.7201	+	19.4683i	−1.09576	+	0.632636i	−0.160654	+	0.987011i	$0.551360\pi$
$948$		0			0
$949$	−19.2906	+	33.4123i	−0.626200	+	1.08461i
$950$	−23.2043	+	1.72922i	−0.752847	+	0.0561034i
$951$		0			0
$952$	−8.67563	+	5.00888i	−0.281179	+	0.162339i
$953$		−	9.56336i		−	0.309788i	−0.987931	−	0.154894i	$-0.950496\pi$
$953$		−	9.56336i		−	0.309788i	0.987931	−	0.154894i	$-0.0495036\pi$
$954$		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
$965$	6.88190	+	6.38814i	0.221536	+	0.205641i
$966$		0			0
$967$	−3.17303	−	1.83195i	−0.102038	−	0.0589116i	0.448113	−	0.893977i	$-0.352096\pi$
$967$	−3.17303	−	1.83195i	−0.102038	−	0.0589116i	−0.550151	+	0.835066i	$0.685430\pi$
$968$	14.2157	+	8.20744i	0.456910	+	0.263797i
$969$		0			0
$970$	2.87351	−	3.09562i	0.0922630	−	0.0993944i
$971$	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	0.303292	−	0.952898i	$-0.401914\pi$
$977$	−11.5743	−	6.68243i	−0.370295	−	0.213790i	−0.673587	+	0.739108i	$0.735247\pi$
$978$		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	−0.170011	−	0.985442i	$-0.554380\pi$
$983$	18.7616	−	10.8320i	0.598401	−	0.345487i	0.768412	+	0.639955i	$0.221047\pi$
$984$		0			0
$985$	7.57143	−	33.1408i	0.241246	−	1.05596i
$986$	−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
$995$	27.5275	+	6.28900i	0.872681	+	0.199375i
$996$		0			0
$997$	−2.76981	+	1.59915i	−0.0877208	+	0.0506456i	−0.543219	−	0.839591i	$-0.682795\pi$
$997$	−2.76981	+	1.59915i	−0.0877208	+	0.0506456i	0.455498	+	0.890237i	$0.349461\pi$
$998$		−	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.64.11		64
3.2	odd	2		315.2.bh.c.274.22	yes	64
5.4	even	2	inner	945.2.bh.c.64.22		64
9.2	odd	6		315.2.bh.c.169.11	✓	64
9.7	even	3	inner	945.2.bh.c.694.22		64
15.14	odd	2		315.2.bh.c.274.11	yes	64
45.29	odd	6		315.2.bh.c.169.22	yes	64
45.34	even	6	inner	945.2.bh.c.694.11		64

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

\(f(q)\)	\(=\)	\(q+(-1.03279 + 0.596282i) q^{2} +(-0.288895 + 0.500381i) q^{4} +(2.17990 + 0.498025i) q^{5} +(-0.866025 + 0.500000i) q^{7} -3.07418i q^{8} +O(q^{10})\)	\(q+(-1.03279 + 0.596282i) q^{2} +(-0.288895 + 0.500381i) q^{4} +(2.17990 + 0.498025i) q^{5} +(-0.866025 + 0.500000i) q^{7} -3.07418i q^{8} +(-2.54835 + 0.785481i) q^{10} +(-2.02111 - 3.50067i) q^{11} +(2.53546 + 1.46385i) q^{13} +(0.596282 - 1.03279i) q^{14} +(1.25529 + 2.17422i) q^{16} +3.25867i q^{17} +3.90229 q^{19} +(-0.878965 + 0.946904i) q^{20} +(4.17478 + 2.41031i) q^{22} +(7.50189 + 4.33122i) q^{23} +(4.50394 + 2.17129i) q^{25} -3.49147 q^{26} -0.577790i q^{28} +(-3.27941 - 5.68010i) q^{29} +(1.72072 - 2.98038i) q^{31} +(2.73173 + 1.57717i) q^{32} +(-1.94309 - 3.36553i) q^{34} +(-2.13686 + 0.658649i) q^{35} +4.39850i q^{37} +(-4.03025 + 2.32686i) q^{38} +(1.53102 - 6.70141i) q^{40} +(-3.10915 + 5.38521i) q^{41} +(5.49353 - 3.17169i) q^{43} +2.33556 q^{44} -10.3305 q^{46} +(-9.71907 + 5.61131i) q^{47} +(0.500000 - 0.866025i) q^{49} +(-5.94633 + 0.443131i) q^{50} +(-1.46496 + 0.845798i) q^{52} -2.38454i q^{53} +(-2.66241 - 8.63768i) q^{55} +(1.53709 + 2.66232i) q^{56} +(6.77389 + 3.91091i) q^{58} +(-0.624888 + 1.08234i) q^{59} +(2.49109 + 4.31469i) q^{61} +4.10414i q^{62} -8.78290 q^{64} +(4.79802 + 4.45377i) q^{65} +(8.47762 + 4.89455i) q^{67} +(-1.63058 - 0.941415i) q^{68} +(1.81419 - 1.95442i) q^{70} +9.24009 q^{71} +13.1780i q^{73} +(-2.62274 - 4.54273i) q^{74} +(-1.12735 + 1.95263i) q^{76} +(3.50067 + 2.02111i) q^{77} +(2.12371 + 3.67837i) q^{79} +(1.65359 + 5.36476i) q^{80} -7.41572i q^{82} +(10.5572 - 6.09519i) q^{83} +(-1.62290 + 7.10359i) q^{85} +(-3.78245 + 6.55139i) q^{86} +(-10.7617 + 6.21327i) q^{88} -4.60378 q^{89} -2.92770 q^{91} +(-4.33452 + 2.50253i) q^{92} +(6.69185 - 11.5906i) q^{94} +(8.50660 + 1.94344i) q^{95} +(-1.37170 + 0.791954i) q^{97} +1.19256i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 34 q^{4} + 10 q^{5}+O(q^{10}) \) 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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