LMFDB - Embedded newform 603.2.g.h.163.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(37,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("603.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.g (of order $3$, degree $2$, 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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 11x^{10} + 89x^{8} + 326x^{6} + 881x^{4} + 416x^{2} + 169 $ x^12 + 11x^10 + 89x^8 + 326x^6 + 881x^4 + 416*x^2 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.6
Root			$-1.23628 + 2.14130i$ of defining polynomial
Character	$\chi$	$=$	603.163
Dual form			603.2.g.h.37.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23628 - 2.14130i) q^{2} +(-2.05677 - 3.56243i) q^{4} +2.75329 q^{5} +(2.34706 + 4.06522i) q^{7} -5.22584 q^{8} +O(q^{10})$	\(q+(1.23628 - 2.14130i) q^{2} +(-2.05677 - 3.56243i) q^{4} +2.75329 q^{5} +(2.34706 + 4.06522i) q^{7} -5.22584 q^{8} +(3.40383 - 5.89560i) q^{10} +(-2.47256 - 4.28259i) q^{11} +(0.0567688 - 0.0983265i) q^{13} +11.6065 q^{14} +(-2.34706 + 4.06522i) q^{16} +(2.61292 - 4.52571i) q^{17} +(-0.209711 + 0.363229i) q^{19} +(-5.66287 - 9.80838i) q^{20} -12.2271 q^{22} +(-1.81367 + 3.14137i) q^{23} +2.58058 q^{25} +(-0.140364 - 0.243118i) q^{26} +(9.65471 - 16.7225i) q^{28} +(3.19031 + 5.52579i) q^{29} +(-3.69412 - 6.39840i) q^{31} +(0.577393 + 1.00007i) q^{32} +(-6.46060 - 11.1901i) q^{34} +(6.46212 + 11.1927i) q^{35} +(-5.63735 + 9.76417i) q^{37} +(0.518521 + 0.898105i) q^{38} -14.3882 q^{40} +(4.42659 + 7.66708i) q^{41} -1.11354 q^{43} +(-10.1710 + 17.6166i) q^{44} +(4.48441 + 7.76722i) q^{46} +(-1.67331 - 2.89825i) q^{47} +(-7.51736 + 13.0205i) q^{49} +(3.19031 - 5.52579i) q^{50} -0.467041 q^{52} +4.66439 q^{53} +(-6.80765 - 11.7912i) q^{55} +(-12.2654 - 21.2442i) q^{56} +15.7765 q^{58} -6.66136 q^{59} +(-0.347058 + 0.601122i) q^{61} -18.2678 q^{62} -6.53296 q^{64} +(0.156301 - 0.270721i) q^{65} +(-1.25089 - 8.08921i) q^{67} -21.4967 q^{68} +31.9559 q^{70} +(-1.81367 - 3.14137i) q^{71} +(-5.36442 + 9.29145i) q^{73} +(13.9387 + 24.1425i) q^{74} +1.72530 q^{76} +(11.6065 - 20.1030i) q^{77} +(7.17031 + 12.4193i) q^{79} +(-6.46212 + 11.1927i) q^{80} +21.8900 q^{82} +(-0.140364 + 0.243118i) q^{83} +(7.19412 - 12.4606i) q^{85} +(-1.37664 + 2.38441i) q^{86} +(12.9212 + 22.3802i) q^{88} +4.07106 q^{89} +0.532959 q^{91} +14.9212 q^{92} -8.27470 q^{94} +(-0.577393 + 1.00007i) q^{95} +(9.46060 - 16.3862i) q^{97} +(18.5871 + 32.1938i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{4} + 6 q^{7}+O(q^{10}) $ 12 * q - 10 * q^4 + 6 * q^7	$ 12 q - 10 q^{4} + 6 q^{7} + 4 q^{10} - 14 q^{13} - 6 q^{16} - 10 q^{19} - 88 q^{22} + 16 q^{25} + 20 q^{28} - 26 q^{34} - 38 q^{37} - 84 q^{40} + 16 q^{43} + 2 q^{46} - 24 q^{49} - 20 q^{52} - 8 q^{55} + 12 q^{58} + 18 q^{61} - 64 q^{64} + 44 q^{67} + 148 q^{70} + 24 q^{73} + 80 q^{76} + 42 q^{79} + 56 q^{82} + 42 q^{85} + 52 q^{88} - 8 q^{91} - 40 q^{94} + 62 q^{97}+O(q^{100}) $ 12 * q - 10 * q^4 + 6 * q^7 + 4 * q^10 - 14 * q^13 - 6 * q^16 - 10 * q^19 - 88 * q^22 + 16 * q^25 + 20 * q^28 - 26 * q^34 - 38 * q^37 - 84 * q^40 + 16 * q^43 + 2 * q^46 - 24 * q^49 - 20 * q^52 - 8 * q^55 + 12 * q^58 + 18 * q^61 - 64 * q^64 + 44 * q^67 + 148 * q^70 + 24 * q^73 + 80 * q^76 + 42 * q^79 + 56 * q^82 + 42 * q^85 + 52 * q^88 - 8 * q^91 - 40 * q^94 + 62 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.23628	−	2.14130i	0.874181	−	1.51413i	0.0165481	−	0.999863i	$-0.494732\pi$
$2$	1.23628	−	2.14130i	0.874181	−	1.51413i	0.857633	−	0.514263i	$-0.171934\pi$
$3$		0			0
$3$		0			0
$4$	−2.05677	−	3.56243i	−1.02838	−	1.78121i
$5$	2.75329			1.23131			0.615653	−	0.788017i	$-0.288892\pi$
$5$	2.75329			1.23131			0.615653	+	0.788017i	$0.288892\pi$
$6$		0			0
$7$	2.34706	+	4.06522i	0.887105	+	1.53651i	0.843282	+	0.537471i	$0.180620\pi$
$7$	2.34706	+	4.06522i	0.887105	+	1.53651i	0.0438224	+	0.999039i	$0.486046\pi$
$8$	−5.22584			−1.84761
$9$		0			0
$10$	3.40383	−	5.89560i	1.07638	−	1.86435i
$11$	−2.47256	−	4.28259i	−0.745504	−	1.29125i	−0.949959	−	0.312375i	$-0.898876\pi$
$11$	−2.47256	−	4.28259i	−0.745504	−	1.29125i	0.204455	−	0.978876i	$-0.434458\pi$
$12$		0			0
$13$	0.0567688	−	0.0983265i	0.0157448	−	0.0272709i	−0.858046	−	0.513573i	$-0.828321\pi$
$13$	0.0567688	−	0.0983265i	0.0157448	−	0.0272709i	0.873790	+	0.486303i	$0.161655\pi$
$14$	11.6065			3.10196
$15$		0			0
$16$	−2.34706	+	4.06522i	−0.586765	+	1.01631i
$17$	2.61292	−	4.52571i	0.633726	−	1.09765i	−0.353057	−	0.935602i	$-0.614858\pi$
$17$	2.61292	−	4.52571i	0.633726	−	1.09765i	0.986783	−	0.162045i	$-0.0518088\pi$
$18$		0			0
$19$	−0.209711	+	0.363229i	−0.0481109	+	0.0833305i	−0.889078	−	0.457756i	$-0.848653\pi$
$19$	−0.209711	+	0.363229i	−0.0481109	+	0.0833305i	0.840967	+	0.541086i	$0.181987\pi$
$20$	−5.66287	−	9.80838i	−1.26626	−	2.19322i
$21$		0			0
$22$	−12.2271			−2.60682
$23$	−1.81367	+	3.14137i	−0.378177	+	0.655021i	−0.990797	−	0.135356i	$-0.956782\pi$
$23$	−1.81367	+	3.14137i	−0.378177	+	0.655021i	0.612620	+	0.790377i	$0.290115\pi$
$24$		0			0
$25$	2.58058			0.516116
$26$	−0.140364	−	0.243118i	−0.0275277	−	0.0476793i
$27$		0			0
$28$	9.65471	−	16.7225i	1.82457	−	3.16025i
$29$	3.19031	+	5.52579i	0.592426	+	1.02611i	0.993905	+	0.110244i	$0.0351633\pi$
$29$	3.19031	+	5.52579i	0.592426	+	1.02611i	−0.401478	+	0.915869i	$0.631503\pi$
$30$		0			0
$31$	−3.69412	−	6.39840i	−0.663483	−	1.14919i	−0.979694	−	0.200497i	$-0.935744\pi$
$31$	−3.69412	−	6.39840i	−0.663483	−	1.14919i	0.316211	−	0.948689i	$-0.397589\pi$
$32$	0.577393	+	1.00007i	0.102070	+	0.176790i
$33$		0			0
$34$	−6.46060	−	11.1901i	−1.10798	−	1.91908i
$35$	6.46212	+	11.1927i	1.09230	+	1.89192i
$36$		0			0
$37$	−5.63735	+	9.76417i	−0.926774	+	1.60522i	−0.138092	+	0.990419i	$0.544097\pi$
$37$	−5.63735	+	9.76417i	−0.926774	+	1.60522i	−0.788683	+	0.614801i	$0.789236\pi$
$38$	0.518521	+	0.898105i	0.0841153	+	0.145692i
$39$		0			0
$40$	−14.3882			−2.27498
$41$	4.42659	+	7.66708i	0.691318	+	1.19740i	0.971406	+	0.237423i	$0.0763028\pi$
$41$	4.42659	+	7.66708i	0.691318	+	1.19740i	−0.280089	+	0.959974i	$0.590364\pi$
$42$		0			0
$43$	−1.11354			−0.169813			−0.0849064	−	0.996389i	$-0.527059\pi$
$43$	−1.11354			−0.169813			−0.0849064	+	0.996389i	$0.527059\pi$
$44$	−10.1710	+	17.6166i	−1.53333	+	2.65580i
$45$		0			0
$46$	4.48441	+	7.76722i	0.661190	+	1.14521i
$47$	−1.67331	−	2.89825i	−0.244077	−	0.422754i	0.717795	−	0.696255i	$-0.245152\pi$
$47$	−1.67331	−	2.89825i	−0.244077	−	0.422754i	−0.961872	+	0.273501i	$0.911818\pi$
$48$		0			0
$49$	−7.51736	+	13.0205i	−1.07391	+	1.86007i
$50$	3.19031	−	5.52579i	0.451179	−	0.781464i
$51$		0			0
$52$	−0.467041			−0.0647670
$53$	4.66439			0.640703			0.320351	−	0.947299i	$-0.396199\pi$
$53$	4.66439			0.640703			0.320351	+	0.947299i	$0.396199\pi$
$54$		0			0
$55$	−6.80765	−	11.7912i	−0.917944	−	1.58993i
$56$	−12.2654	−	21.2442i	−1.63903	−	2.83888i
$57$		0			0
$58$	15.7765			2.07155
$59$	−6.66136			−0.867235			−0.433617	−	0.901097i	$-0.642763\pi$
$59$	−6.66136			−0.867235			−0.433617	+	0.901097i	$0.642763\pi$
$60$		0			0
$61$	−0.347058	+	0.601122i	−0.0444363	+	0.0769658i	−0.887388	−	0.461023i	$-0.847482\pi$
$61$	−0.347058	+	0.601122i	−0.0444363	+	0.0769658i	0.842952	+	0.537989i	$0.180816\pi$
$62$	−18.2678			−2.32002
$63$		0			0
$64$	−6.53296			−0.816620
$65$	0.156301	−	0.270721i	0.0193867	−	0.0335788i
$66$		0			0
$67$	−1.25089	−	8.08921i	−0.152820	−	0.988254i
$67$	−1.25089	−	8.08921i	−0.152820	−	0.988254i
$68$	−21.4967			−2.60686
$69$		0			0
$70$	31.9559			3.81946
$71$	−1.81367	−	3.14137i	−0.215243	−	0.372812i	0.738105	−	0.674686i	$-0.235721\pi$
$71$	−1.81367	−	3.14137i	−0.215243	−	0.372812i	−0.953348	+	0.301874i	$0.902388\pi$
$72$		0			0
$73$	−5.36442	+	9.29145i	−0.627858	+	1.08748i	0.360122	+	0.932905i	$0.382735\pi$
$73$	−5.36442	+	9.29145i	−0.627858	+	1.08748i	−0.987981	+	0.154577i	$0.950598\pi$
$74$	13.9387	+	24.1425i	1.62034	+	2.80651i
$75$		0			0
$76$	1.72530			0.197906
$77$	11.6065	−	20.1030i	1.32268	−	2.29095i
$78$		0			0
$79$	7.17031	+	12.4193i	0.806722	+	1.39728i	0.915122	+	0.403177i	$0.132094\pi$
$79$	7.17031	+	12.4193i	0.806722	+	1.39728i	−0.108400	+	0.994107i	$0.534573\pi$
$80$	−6.46212	+	11.1927i	−0.722487	+	1.25138i
$81$		0			0
$82$	21.8900			2.41735
$83$	−0.140364	+	0.243118i	−0.0154070	+	0.0266856i	−0.873626	−	0.486598i	$-0.838238\pi$
$83$	−0.140364	+	0.243118i	−0.0154070	+	0.0266856i	0.858219	+	0.513283i	$0.171571\pi$
$84$		0			0
$85$	7.19412	−	12.4606i	0.780311	−	1.35154i
$86$	−1.37664	+	2.38441i	−0.148447	+	0.257118i
$87$		0			0
$88$	12.9212	+	22.3802i	1.37740	+	2.38573i
$89$	4.07106			0.431531			0.215766	−	0.976445i	$-0.430775\pi$
$89$	4.07106			0.431531			0.215766	+	0.976445i	$0.430775\pi$
$90$		0			0
$91$	0.532959			0.0558693
$92$	14.9212			1.55564
$93$		0			0
$94$	−8.27470			−0.853470
$95$	−0.577393	+	1.00007i	−0.0592393	+	0.102605i
$96$		0			0
$97$	9.46060	−	16.3862i	0.960578	−	1.66377i	0.239525	−	0.970890i	$-0.423008\pi$
$97$	9.46060	−	16.3862i	0.960578	−	1.66377i	0.721053	−	0.692880i	$-0.243658\pi$
$98$	18.5871	+	32.1938i	1.87758	+	3.25207i
$99$		0			0
$100$	−5.30765	−	9.19313i	−0.530765	−	0.919313i
$101$	5.95954	+	10.3222i	0.592996	+	1.02710i	0.993826	+	0.110947i	$0.0353883\pi$
$101$	5.95954	+	10.3222i	0.592996	+	1.02710i	−0.400830	+	0.916152i	$0.631278\pi$
$102$		0			0
$103$	5.32325	+	9.22014i	0.524515	+	0.908487i	0.999593	+	0.0285430i	$0.00908675\pi$
$103$	5.32325	+	9.22014i	0.524515	+	0.908487i	−0.475077	+	0.879944i	$0.657580\pi$
$104$	−0.296665	+	0.513839i	−0.0290904	+	0.0503860i
$105$		0			0
$106$	5.76648	−	9.98784i	0.560090	−	0.970104i
$107$	−0.443713			−0.0428954			−0.0214477	−	0.999770i	$-0.506828\pi$
$107$	−0.443713			−0.0428954			−0.0214477	+	0.999770i	$0.506828\pi$
$108$		0			0
$109$	−2.19235			−0.209989			−0.104994	−	0.994473i	$-0.533482\pi$
$109$	−2.19235			−0.209989			−0.104994	+	0.994473i	$0.533482\pi$
$110$	−33.6646			−3.20980
$111$		0			0
$112$	−22.0347			−2.08209
$113$	−9.35577	−	16.2047i	−0.880117	−	1.52441i	−0.851210	−	0.524825i	$-0.824131\pi$
$113$	−9.35577	−	16.2047i	−0.880117	−	1.52441i	−0.0289065	−	0.999582i	$-0.509203\pi$
$114$		0			0
$115$	−4.99355	+	8.64909i	−0.465651	+	0.806532i
$116$	13.1235	−	22.7305i	1.21848	−	2.11048i
$117$		0			0
$118$	−8.23529	+	14.2639i	−0.758120	+	1.31310i
$119$	24.5307			2.24873
$120$		0			0
$121$	−6.72708	+	11.6516i	−0.611552	+	1.05924i
$122$	0.858121	+	1.48631i	0.0776906	+	0.134564i
$123$		0			0
$124$	−15.1959	+	26.3200i	−1.36463	+	2.36361i
$125$	−6.66136			−0.595810
$126$		0			0
$127$	−2.90383	−	5.02958i	−0.257673	−	0.446303i	0.707945	−	0.706267i	$-0.249622\pi$
$127$	−2.90383	−	5.02958i	−0.257673	−	0.446303i	−0.965618	+	0.259965i	$0.916289\pi$
$128$	−9.23134	+	15.9892i	−0.815943	+	1.41325i
$129$		0			0
$130$	−0.386462	−	0.669372i	−0.0338950	−	0.0587079i
$131$	−6.57549			−0.574503			−0.287251	−	0.957855i	$-0.592742\pi$
$131$	−6.57549			−0.574503			−0.287251	+	0.957855i	$0.592742\pi$
$132$		0			0
$133$	−1.96881			−0.170718
$134$	−18.8678	−	7.32200i	−1.62993	−	0.632524i
$135$		0			0
$136$	−13.6547	+	23.6507i	−1.17088	+	2.02803i
$137$	1.59850			0.136569			0.0682845	−	0.997666i	$-0.478247\pi$
$137$	1.59850			0.136569			0.0682845	+	0.997666i	$0.478247\pi$
$138$		0			0
$139$	−19.1483			−1.62413			−0.812067	−	0.583564i	$-0.801658\pi$
$139$	−19.1483			−1.62413			−0.812067	+	0.583564i	$0.801658\pi$
$140$	26.5822	−	46.0417i	2.24660	−	3.89123i
$141$		0			0
$142$	−8.96881			−0.752646
$143$	−0.561456			−0.0469513
$144$		0			0
$145$	8.78384	+	15.2141i	0.729459	+	1.26346i
$146$	13.2638	+	22.9736i	1.09772	+	1.90131i
$147$		0			0
$148$	46.3789			3.81232
$149$	11.8872			0.973837			0.486919	−	0.873447i	$-0.338121\pi$
$149$	11.8872			0.973837			0.486919	+	0.873447i	$0.338121\pi$
$150$		0			0
$151$	1.75733	−	3.04379i	0.143010	−	0.247700i	−0.785619	−	0.618711i	$-0.787655\pi$
$151$	1.75733	−	3.04379i	0.143010	−	0.247700i	0.928629	+	0.371011i	$0.120989\pi$
$152$	1.09591	−	1.89818i	0.0888904	−	0.153963i
$153$		0			0
$154$	−28.6977	−	49.7058i	−2.31252	−	4.00541i
$155$	−10.1710	−	17.6166i	−0.816951	−	1.41500i
$156$		0			0
$157$	0.580579	−	1.00559i	0.0463352	−	0.0802550i	−0.841928	−	0.539590i	$-0.818579\pi$
$157$	0.580579	−	1.00559i	0.0463352	−	0.0802550i	0.888263	+	0.459335i	$0.151912\pi$
$158$	35.4580			2.82089
$159$		0			0
$160$	1.58973	+	2.75349i	0.125679	+	0.217682i
$161$	−17.0272			−1.34193
$162$		0			0
$163$	0.200562	+	0.347383i	0.0157092	+	0.0272092i	0.873773	−	0.486334i	$-0.161666\pi$
$163$	0.200562	+	0.347383i	0.0157092	+	0.0272092i	−0.858064	+	0.513543i	$0.828333\pi$
$164$	18.2090	−	31.5388i	1.42188	−	2.46277i
$165$		0			0
$166$	0.347058	+	0.601122i	0.0269369	+	0.0466562i
$167$	3.45511	+	5.98442i	0.267364	+	0.463088i	0.968180	−	0.250254i	$-0.0805140\pi$
$167$	3.45511	+	5.98442i	0.267364	+	0.463088i	−0.700816	+	0.713342i	$0.747181\pi$
$168$		0			0
$169$	6.49355	+	11.2472i	0.499504	+	0.865167i
$170$	−17.7879	−	30.8095i	−1.36427	−	2.36298i
$171$		0			0
$172$	2.29029	+	3.96690i	0.174633	+	0.302473i
$173$	0.0588717	−	0.101969i	0.00447593	−	0.00775254i	−0.863779	−	0.503871i	$-0.831909\pi$
$173$	0.0588717	−	0.101969i	0.00447593	−	0.00775254i	0.868255	+	0.496119i	$0.165242\pi$
$174$		0			0
$175$	6.05677	+	10.4906i	0.457849	+	0.793017i
$176$	23.2129			1.74974
$177$		0			0
$178$	5.03296	−	8.71734i	0.377236	−	0.653392i
$179$	−11.8872			−0.888491			−0.444245	−	0.895905i	$-0.646528\pi$
$179$	−11.8872			−0.888491			−0.444245	+	0.895905i	$0.646528\pi$
$180$		0			0
$181$	−2.30588	−	3.99391i	−0.171395	−	0.296865i	0.767513	−	0.641034i	$-0.221494\pi$
$181$	−2.30588	−	3.99391i	−0.171395	−	0.296865i	−0.938908	+	0.344169i	$0.888161\pi$
$182$	0.658885	−	1.14122i	0.0488398	−	0.0845931i
$183$		0			0
$184$	9.47796	−	16.4163i	0.698725	−	1.21023i
$185$	−15.5212	+	26.8836i	−1.14114	+	1.97652i
$186$		0			0
$187$	−25.8424			−1.88978
$188$	−6.88321	+	11.9221i	−0.502010	+	0.869507i
$189$		0			0
$190$	1.42764	+	2.47274i	0.103572	+	0.179391i
$191$	10.5332	−	18.2440i	0.762154	−	1.32009i	−0.179584	−	0.983743i	$-0.557475\pi$
$191$	10.5332	−	18.2440i	0.762154	−	1.32009i	0.941738	−	0.336347i	$-0.109191\pi$
$192$		0			0
$193$	8.53296			0.614216			0.307108	−	0.951675i	$-0.400639\pi$
$193$	8.53296			0.614216			0.307108	+	0.951675i	$0.400639\pi$
$194$	−23.3919	−	40.5159i	−1.67944	−	2.90887i
$195$		0			0
$196$	61.8459			4.41757
$197$	4.58289	+	7.93780i	0.326518	+	0.565545i	0.981818	−	0.189823i	$-0.0607914\pi$
$197$	4.58289	+	7.93780i	0.326518	+	0.565545i	−0.655301	+	0.755368i	$0.727458\pi$
$198$		0			0
$199$	−5.15294	+	8.92516i	−0.365282	+	0.632688i	−0.988821	−	0.149105i	$-0.952361\pi$
$199$	−5.15294	+	8.92516i	−0.365282	+	0.632688i	0.623539	+	0.781792i	$0.285694\pi$
$200$	−13.4857			−0.953583
$201$		0			0
$202$	29.4706			2.07354
$203$	−14.9757	+	25.9387i	−1.05109	+	1.82054i
$204$		0			0
$205$	12.1877	+	21.1097i	0.851224	+	1.47436i
$206$	26.3241			1.83408
$207$		0			0
$208$	0.266479	+	0.461556i	0.0184770	+	0.0320031i
$209$	2.07409			0.143467
$210$		0			0
$211$	−7.50177	+	12.9934i	−0.516443	+	0.894506i	0.483375	+	0.875414i	$0.339411\pi$
$211$	−7.50177	+	12.9934i	−0.516443	+	0.894506i	−0.999818	+	0.0190922i	$0.993922\pi$
$212$	−9.59356	−	16.6165i	−0.658889	−	1.14123i
$213$		0			0
$214$	−0.548553	+	0.950121i	−0.0374983	+	0.0649490i
$215$	−3.06589			−0.209092
$216$		0			0
$217$	17.3406	−	30.0348i	1.17716	−	2.03890i
$218$	−2.71035	+	4.69446i	−0.183568	+	0.317949i
$219$		0			0
$220$	−28.0035	+	48.5036i	−1.88800	+	3.27011i
$221$	−0.296665	−	0.513839i	−0.0199558	−	0.0345645i
$222$		0			0
$223$	14.2435			0.953816			0.476908	−	0.878953i	$-0.341758\pi$
$223$	14.2435			0.953816			0.476908	+	0.878953i	$0.341758\pi$
$224$	−2.71035	+	4.69446i	−0.181093	+	0.313662i
$225$		0			0
$226$	−46.2653			−3.07753
$227$	−7.16394	−	12.4083i	−0.475487	−	0.823568i	0.524118	−	0.851645i	$-0.324395\pi$
$227$	−7.16394	−	12.4083i	−0.475487	−	0.823568i	−0.999606	+	0.0280770i	$0.991062\pi$
$228$		0			0
$229$	10.8168	−	18.7353i	0.714794	−	1.23806i	−0.248244	−	0.968697i	$-0.579854\pi$
$229$	10.8168	−	18.7353i	0.714794	−	1.23806i	0.963039	−	0.269363i	$-0.0868131\pi$
$230$	12.3468	+	21.3854i	0.814127	+	1.41011i
$231$		0			0
$232$	−16.6721	−	28.8769i	−1.09458	−	1.89586i
$233$	1.45813	+	2.52556i	0.0955256	+	0.165455i	0.909828	−	0.414986i	$-0.136213\pi$
$233$	1.45813	+	2.52556i	0.0955256	+	0.165455i	−0.814302	+	0.580441i	$0.802880\pi$
$234$		0			0
$235$	−4.60709	−	7.97972i	−0.300534	−	0.520539i
$236$	13.7009	+	23.7306i	0.891851	+	1.54473i
$237$		0			0
$238$	30.3268	−	52.5275i	1.96579	−	3.40485i
$239$	−2.07846	−	3.60000i	−0.134445	−	0.232865i	0.790941	−	0.611893i	$-0.209592\pi$
$239$	−2.07846	−	3.60000i	−0.134445	−	0.232865i	−0.925385	+	0.379028i	$0.876258\pi$
$240$		0			0
$241$	−15.3570			−0.989234			−0.494617	−	0.869111i	$-0.664692\pi$
$241$	−15.3570			−0.989234			−0.494617	+	0.869111i	$0.664692\pi$
$242$	16.6331	+	28.8093i	1.06921	+	1.85193i
$243$		0			0
$244$	2.85527			0.182790
$245$	−20.6974	+	35.8490i	−1.32231	+	2.29031i
$246$		0			0
$247$	0.0238100	+	0.0412402i	0.00151500	+	0.00262405i
$248$	19.3049	+	33.4370i	1.22586	+	2.12325i
$249$		0			0
$250$	−8.23529	+	14.2639i	−0.520846	+	0.902131i
$251$	3.98956	−	6.91013i	0.251819	−	0.436163i	−0.712208	−	0.701969i	$-0.752305\pi$
$251$	3.98956	−	6.91013i	0.251819	−	0.436163i	0.964027	+	0.265806i	$0.0856379\pi$
$252$		0			0
$253$	17.9376			1.12773
$254$	−14.3598			−0.901011
$255$		0			0
$256$	16.2921	+	28.2187i	1.01825	+	1.76367i
$257$	−14.4412	−	25.0130i	−0.900820	−	1.56027i	−0.826432	−	0.563037i	$-0.809633\pi$
$257$	−14.4412	−	25.0130i	−0.900820	−	1.56027i	−0.0743887	−	0.997229i	$-0.523701\pi$
$258$		0			0
$259$	−52.9247			−3.28858
$260$	−1.28590			−0.0797480
$261$		0			0
$262$	−8.12913	+	14.0801i	−0.502219	+	0.869870i
$263$	15.5464			0.958633			0.479316	−	0.877642i	$-0.340885\pi$
$263$	15.5464			0.958633			0.479316	+	0.877642i	$0.340885\pi$
$264$		0			0
$265$	12.8424			0.788901
$266$	−2.43400	+	4.21581i	−0.149238	+	0.258488i
$267$		0			0
$268$	−26.2444	+	21.0938i	−1.60313	+	1.28851i
$269$	−10.6465			−0.649131			−0.324566	−	0.945863i	$-0.605218\pi$
$269$	−10.6465			−0.649131			−0.324566	+	0.945863i	$0.605218\pi$
$270$		0			0
$271$	24.8424			1.50907			0.754534	−	0.656261i	$-0.227863\pi$
$271$	24.8424			1.50907			0.754534	+	0.656261i	$0.227863\pi$
$272$	12.2654	+	21.2442i	0.743696	+	1.28812i
$273$		0			0
$274$	1.97619	−	3.42286i	0.119386	−	0.206783i
$275$	−6.38063	−	11.0516i	−0.384766	−	0.666435i
$276$		0			0
$277$	−15.5018			−0.931411			−0.465706	−	0.884940i	$-0.654199\pi$
$277$	−15.5018			−0.931411			−0.465706	+	0.884940i	$0.654199\pi$
$278$	−23.6726	+	41.0021i	−1.41979	+	2.45914i
$279$		0			0
$280$	−33.7700	−	58.4914i	−2.01814	−	3.49553i
$281$	10.6669	−	18.4755i	0.636331	−	1.10216i	−0.349900	−	0.936787i	$-0.613784\pi$
$281$	10.6669	−	18.4755i	0.636331	−	1.10216i	0.986231	−	0.165371i	$-0.0528822\pi$
$282$		0			0
$283$	−14.4230			−0.857356			−0.428678	−	0.903457i	$-0.641021\pi$
$283$	−14.4230			−0.857356			−0.428678	+	0.903457i	$0.641021\pi$
$284$	−7.46061	+	12.9221i	−0.442706	+	0.766788i
$285$		0			0
$286$	−0.694116	+	1.20224i	−0.0410440	+	0.0710902i
$287$	−20.7789	+	35.9902i	−1.22654	+	2.12443i
$288$		0			0
$289$	−5.15471	−	8.92822i	−0.303218	−	0.525190i
$290$	43.4371			2.55071
$291$		0			0
$292$	44.1335			2.58272
$293$	−6.66136			−0.389161			−0.194580	−	0.980887i	$-0.562334\pi$
$293$	−6.66136			−0.389161			−0.194580	+	0.980887i	$0.562334\pi$
$294$		0			0
$295$	−18.3406			−1.06783
$296$	29.4599	−	51.0260i	1.71232	−	2.96583i
$297$		0			0
$298$	14.6959	−	25.4540i	0.851310	−	1.47451i
$299$	0.205920	+	0.356664i	0.0119087	+	0.0206264i
$300$		0			0
$301$	−2.61354	−	4.52678i	−0.150642	−	0.260919i
$302$	−4.34510	−	7.52593i	−0.250032	−	0.433069i
$303$		0			0
$304$	−0.984406	−	1.70504i	−0.0564595	−	0.0977908i
$305$	−0.955550	+	1.65506i	−0.0547146	+	0.0947686i
$306$		0			0
$307$	−0.402057	+	0.696382i	−0.0229466	+	0.0397446i	−0.877271	−	0.479996i	$-0.840638\pi$
$307$	−0.402057	+	0.696382i	−0.0229466	+	0.0397446i	0.854324	+	0.519741i	$0.173971\pi$
$308$	−95.4873			−5.44089
$309$		0			0
$310$	−50.2965			−2.85665
$311$	−11.4569			−0.649659			−0.324829	−	0.945773i	$-0.605307\pi$
$311$	−11.4569			−0.649659			−0.324829	+	0.945773i	$0.605307\pi$
$312$		0			0
$313$	26.1354			1.47726			0.738629	−	0.674112i	$-0.235473\pi$
$313$	26.1354			1.47726			0.738629	+	0.674112i	$0.235473\pi$
$314$	−1.43551	−	2.48638i	−0.0810108	−	0.140315i
$315$		0			0
$316$	29.4953	−	51.0874i	1.65924	−	2.87389i
$317$	2.73735	−	4.74123i	0.153745	−	0.266294i	−0.778856	−	0.627202i	$-0.784200\pi$
$317$	2.73735	−	4.74123i	0.153745	−	0.266294i	0.932601	+	0.360908i	$0.117533\pi$
$318$		0			0
$319$	15.7765	−	27.3256i	0.883313	−	1.52994i
$320$	−17.9871			−1.00551
$321$		0			0
$322$	−21.0503	+	36.4602i	−1.17309	+	2.03185i
$323$	1.09591	+	1.89818i	0.0609783	+	0.105618i
$324$		0			0
$325$	0.146496	−	0.253739i	0.00812616	−	0.0140749i
$326$	0.991801			0.0549308
$327$		0			0
$328$	−23.1327	−	40.0670i	−1.27729	−	2.21233i
$329$	7.85470	−	13.6047i	0.433044	−	0.750054i
$330$		0			0
$331$	13.5833	+	23.5269i	0.746605	+	1.29316i	0.949441	+	0.313945i	$0.101651\pi$
$331$	13.5833	+	23.5269i	0.746605	+	1.29316i	−0.202837	+	0.979213i	$0.565016\pi$
$332$	1.15479			0.0633771
$333$		0			0
$334$	17.0859			0.934898
$335$	−3.44404	−	22.2719i	−0.188168	−	1.21684i
$336$		0			0
$337$	0.129132	−	0.223663i	0.00703425	−	0.0121837i	−0.862487	−	0.506079i	$-0.831094\pi$
$337$	0.129132	−	0.223663i	0.00703425	−	0.0121837i	0.869521	+	0.493896i	$0.164428\pi$
$338$	32.1114			1.74663
$339$		0			0
$340$	−59.1865			−3.20984
$341$	−18.2678	+	31.6408i	−0.989258	+	1.71345i
$342$		0			0
$343$	−37.7160			−2.03647
$344$	5.81917			0.313749
$345$		0			0
$346$	−0.145564	−	0.252123i	−0.00782555	−	0.0135542i
$347$	−11.5090	−	19.9342i	−0.617838	−	1.07013i	−0.989880	−	0.141910i	$-0.954676\pi$
$347$	−11.5090	−	19.9342i	−0.617838	−	1.07013i	0.372042	−	0.928216i	$-0.378658\pi$
$348$		0			0
$349$	4.77647			0.255678			0.127839	−	0.991795i	$-0.459196\pi$
$349$	4.77647			0.255678			0.127839	+	0.991795i	$0.459196\pi$
$350$	29.9514			1.60097
$351$		0			0
$352$	2.85527	−	4.94548i	0.152187	−	0.263595i
$353$	6.11584	−	10.5929i	0.325513	−	0.563805i	−0.656103	−	0.754671i	$-0.727796\pi$
$353$	6.11584	−	10.5929i	0.325513	−	0.563805i	0.981616	+	0.190866i	$0.0611296\pi$
$354$		0			0
$355$	−4.99355	−	8.64909i	−0.265030	−	0.459046i
$356$	−8.37322	−	14.5028i	−0.443780	−	0.768649i
$357$		0			0
$358$	−14.6959	+	25.4540i	−0.776702	+	1.34529i
$359$	7.28656			0.384570			0.192285	−	0.981339i	$-0.438410\pi$
$359$	7.28656			0.384570			0.192285	+	0.981339i	$0.438410\pi$
$360$		0			0
$361$	9.41204	+	16.3021i	0.495371	+	0.858007i
$362$	−11.4029			−0.599321
$363$		0			0
$364$	−1.09617	−	1.89863i	−0.0574551	−	0.0995151i
$365$	−14.7698	+	25.5820i	−0.773086	+	1.33902i
$366$		0			0
$367$	6.52381	+	11.2996i	0.340540	+	0.589833i	0.984533	−	0.175199i	$-0.0560568\pi$
$367$	6.52381	+	11.2996i	0.340540	+	0.589833i	−0.643993	+	0.765031i	$0.722723\pi$
$368$	−8.51359	−	14.7460i	−0.443801	−	0.768686i
$369$		0			0
$370$	38.3771	+	66.4711i	1.99513	+	3.45567i
$371$	10.9476	+	18.9618i	0.568370	+	0.984446i
$372$		0			0
$373$	−7.50177	−	12.9934i	−0.388427	−	0.672775i	0.603811	−	0.797127i	$-0.293648\pi$
$373$	−7.50177	−	12.9934i	−0.388427	−	0.672775i	−0.992238	+	0.124352i	$0.960315\pi$
$374$	−31.9484	+	55.3362i	−1.65201	+	2.86137i
$375$		0			0
$376$	8.74444	+	15.1458i	0.450960	+	0.781086i
$377$	0.724441			0.0373106
$378$		0			0
$379$	5.89561	−	10.2115i	0.302837	−	0.524529i	−0.673940	−	0.738786i	$-0.735399\pi$
$379$	5.89561	−	10.2115i	0.302837	−	0.524529i	0.976777	+	0.214256i	$0.0687328\pi$
$380$	4.75026			0.243683
$381$		0			0
$382$	−26.0439	−	45.1093i	−1.33252	−	2.30799i
$383$	−9.93316	+	17.2047i	−0.507561	+	0.879121i	0.492401	+	0.870369i	$0.336119\pi$
$383$	−9.93316	+	17.2047i	−0.507561	+	0.879121i	−0.999962	+	0.00875269i	$0.997214\pi$
$384$		0			0
$385$	31.9559	−	55.3493i	1.62862	−	2.82086i
$386$	10.5491	−	18.2716i	0.536936	−	0.930000i
$387$		0			0
$388$	−77.8330			−3.95137
$389$	−1.12291	+	1.94494i	−0.0569339	+	0.0986125i	−0.893088	−	0.449883i	$-0.851466\pi$
$389$	−1.12291	+	1.94494i	−0.0569339	+	0.0986125i	0.836154	+	0.548495i	$0.184799\pi$
$390$		0			0
$391$	9.47796	+	16.4163i	0.479321	+	0.830208i
$392$	39.2846	−	68.0429i	1.98417	−	3.43668i
$393$		0			0
$394$	22.6629			1.14174
$395$	19.7419	+	34.1940i	0.993323	+	1.72049i
$396$		0			0
$397$	−14.3699			−0.721206			−0.360603	−	0.932719i	$-0.617429\pi$
$397$	−14.3699			−0.721206			−0.360603	+	0.932719i	$0.617429\pi$
$398$	12.7409	+	22.0680i	0.638646	+	1.10617i
$399$		0			0
$400$	−6.05677	+	10.4906i	−0.302838	+	0.524532i
$401$	−29.9833			−1.49729			−0.748647	−	0.662969i	$-0.769296\pi$
$401$	−29.9833			−1.49729			−0.748647	+	0.662969i	$0.769296\pi$
$402$		0			0
$403$	−0.838842			−0.0417857
$404$	24.5148	−	42.4608i	1.21966	−	2.11251i
$405$		0			0
$406$	37.0283	+	64.1349i	1.83768	+	3.18296i
$407$	55.7547			2.76366
$408$		0			0
$409$	9.89468	+	17.1381i	0.489260	+	0.847424i	0.999924	−	0.0123570i	$-0.00393345\pi$
$409$	9.89468	+	17.1381i	0.489260	+	0.847424i	−0.510663	+	0.859781i	$0.670600\pi$
$410$	60.2694			2.97649
$411$		0			0
$412$	21.8974	−	37.9274i	1.07881	−	1.86855i
$413$	−15.6346	−	27.0799i	−0.769328	−	1.33252i
$414$		0			0
$415$	−0.386462	+	0.669372i	−0.0189707	+	0.0328582i
$416$	0.131112			0.00642828
$417$		0			0
$418$	2.56415	−	4.44123i	0.125417	−	0.217228i
$419$	7.54210	−	13.0633i	0.368456	−	0.638184i	−0.620869	−	0.783915i	$-0.713220\pi$
$419$	7.54210	−	13.0633i	0.368456	−	0.638184i	0.989324	+	0.145731i	$0.0465533\pi$
$420$		0			0
$421$	9.46060	−	16.3862i	0.461081	−	0.798616i	−0.537934	−	0.842987i	$-0.680795\pi$
$421$	9.46060	−	16.3862i	0.461081	−	0.798616i	0.999015	+	0.0443709i	$0.0141283\pi$
$422$	18.5486	+	32.1270i	0.902930	+	1.56392i
$423$		0			0
$424$	−24.3753			−1.18377
$425$	6.74285	−	11.6790i	0.327076	−	0.566513i
$426$		0			0
$427$	−3.25826			−0.157678
$428$	0.912615	+	1.58070i	0.0441129	+	0.0764058i
$429$		0			0
$430$	−3.79029	+	6.56497i	−0.182784	+	0.316591i
$431$	−12.5191	−	21.6837i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960629\pi$
$431$	−12.5191	−	21.6837i	−0.603023	−	1.04447i	0.389337	−	0.921095i	$-0.372704\pi$
$432$		0			0
$433$	−6.03296	−	10.4494i	−0.289925	−	0.502166i	0.683866	−	0.729607i	$-0.260297\pi$
$433$	−6.03296	−	10.4494i	−0.289925	−	0.502166i	−0.973792	+	0.227442i	$0.926964\pi$
$434$	−42.8757	−	74.2628i	−2.05810	−	3.56473i
$435$		0			0
$436$	4.50915	+	7.81007i	0.215949	+	0.374035i
$437$	−0.760692	−	1.31756i	−0.0363888	−	0.0630273i
$438$		0			0
$439$	7.12913	−	12.3480i	0.340255	−	0.589339i	−0.644225	−	0.764836i	$-0.722820\pi$
$439$	7.12913	−	12.3480i	0.340255	−	0.589339i	0.984480	+	0.175497i	$0.0561533\pi$
$440$	35.5757	+	61.6190i	1.69601	+	2.93757i
$441$		0			0
$442$	−1.46704			−0.0697800
$443$	−16.8912	−	29.2564i	−0.802524	−	1.39001i	−0.917950	−	0.396697i	$-0.870156\pi$
$443$	−16.8912	−	29.2564i	−0.802524	−	1.39001i	0.115425	−	0.993316i	$-0.463177\pi$
$444$		0			0
$445$	11.2088			0.531347
$446$	17.6089	−	30.4996i	0.833808	−	1.44420i
$447$		0			0
$448$	−15.3332	−	26.5579i	−0.724427	−	1.25474i
$449$	−11.8013	−	20.4405i	−0.556939	−	0.964647i	−0.997750	−	0.0670468i	$-0.978642\pi$
$449$	−11.8013	−	20.4405i	−0.556939	−	0.964647i	0.440811	−	0.897600i	$-0.354691\pi$
$450$		0			0
$451$	21.8900	−	37.9146i	1.03076	−	1.78533i
$452$	−38.4853	+	66.6585i	−1.81020	+	3.13535i
$453$		0			0
$454$	−35.4265			−1.66265
$455$	1.46739			0.0687922
$456$		0			0
$457$	8.92119	+	15.4520i	0.417316	+	0.722812i	0.995668	−	0.0929747i	$-0.0296376\pi$
$457$	8.92119	+	15.4520i	0.417316	+	0.722812i	−0.578353	+	0.815787i	$0.696304\pi$
$458$	−26.7452	−	46.3240i	−1.24972	−	2.16458i
$459$		0			0
$460$	41.0823			1.91547
$461$	35.1773			1.63837			0.819184	−	0.573531i	$-0.194427\pi$
$461$	35.1773			1.63837			0.819184	+	0.573531i	$0.194427\pi$
$462$		0			0
$463$	−12.2444	+	21.2080i	−0.569047	+	0.985619i	0.427613	+	0.903962i	$0.359355\pi$
$463$	−12.2444	+	21.2080i	−0.569047	+	0.985619i	−0.996660	+	0.0816571i	$0.973979\pi$
$464$	−29.9514			−1.39046
$465$		0			0
$466$	7.21064			0.334027
$467$	5.60400	−	9.70641i	0.259322	−	0.449159i	−0.706738	−	0.707475i	$-0.749834\pi$
$467$	5.60400	−	9.70641i	0.259322	−	0.449159i	0.966061	+	0.258316i	$0.0831675\pi$
$468$		0			0
$469$	29.9485	−	24.0710i	1.38290	−	1.11149i
$470$	−22.7826			−1.05088
$471$		0			0
$472$	34.8112			1.60232
$473$	2.75329	+	4.76883i	0.126596	+	0.219271i
$474$		0			0
$475$	−0.541175	+	0.937342i	−0.0248308	+	0.0430082i
$476$	−50.4540	−	87.3889i	−2.31256	−	4.00546i
$477$		0			0
$478$	−10.2782			−0.470116
$479$	−15.9086	+	27.5546i	−0.726884	+	1.25900i	0.231310	+	0.972880i	$0.425699\pi$
$479$	−15.9086	+	27.5546i	−0.726884	+	1.25900i	−0.958194	+	0.286120i	$0.907634\pi$
$480$		0			0
$481$	0.640051	+	1.10860i	0.0291838	+	0.0505478i
$482$	−18.9856	+	32.8840i	−0.864770	+	1.49782i
$483$		0			0
$484$	55.3442			2.51564
$485$	26.0477	−	45.1160i	1.18277	−	2.04861i
$486$		0			0
$487$	5.92119	−	10.2558i	0.268315	−	0.464735i	−0.700112	−	0.714033i	$-0.746867\pi$
$487$	5.92119	−	10.2558i	0.268315	−	0.464735i	0.968427	+	0.249298i	$0.0801999\pi$
$488$	1.81367	−	3.14137i	0.0821010	−	0.142203i
$489$		0			0
$490$	51.1756	+	88.6388i	2.31188	+	4.00429i
$491$	39.8823			1.79986			0.899931	−	0.436033i	$-0.143617\pi$
$491$	39.8823			1.79986			0.899931	+	0.436033i	$0.143617\pi$
$492$		0			0
$493$	33.3442			1.50175
$494$	0.117743			0.00529752
$495$		0			0
$496$	34.6812			1.55723
$497$	8.51359	−	14.7460i	0.381886	−	0.661447i
$498$		0			0
$499$	−16.5365	+	28.6421i	−0.740275	+	1.28219i	0.212094	+	0.977249i	$0.431972\pi$
$499$	−16.5365	+	28.6421i	−0.740275	+	1.28219i	−0.952370	+	0.304945i	$0.901362\pi$
$500$	13.7009	+	23.7306i	0.612722	+	1.06126i
$501$		0			0
$502$	−9.86442	−	17.0857i	−0.440271	−	0.762571i
$503$	11.3643	+	19.6835i	0.506709	+	0.877646i	0.999970	+	0.00776435i	$0.00247150\pi$
$503$	11.3643	+	19.6835i	0.506709	+	0.877646i	−0.493261	+	0.869881i	$0.664195\pi$
$504$		0			0
$505$	16.4083	+	28.4200i	0.730160	+	1.26467i
$506$	22.1759	−	38.4098i	0.985839	−	1.70752i
$507$		0			0
$508$	−11.9450	+	20.6893i	−0.529974	+	0.917941i
$509$	17.5434			0.777597			0.388798	−	0.921323i	$-0.372890\pi$
$509$	17.5434			0.777597			0.388798	+	0.921323i	$0.372890\pi$
$510$		0			0
$511$	−50.3625			−2.22790
$512$	43.6407			1.92867
$513$		0			0
$514$	−71.4136			−3.14992
$515$	14.6564	+	25.3857i	0.645839	+	1.11863i
$516$		0			0
$517$	−8.27470	+	14.3322i	−0.363921	+	0.630329i
$518$	−65.4297	+	113.328i	−2.87482	+	4.97933i
$519$		0			0
$520$	−0.816803	+	1.41474i	−0.0358192	+	0.0620406i
$521$	25.1374			1.10129			0.550645	−	0.834740i	$-0.314382\pi$
$521$	25.1374			1.10129			0.550645	+	0.834740i	$0.314382\pi$
$522$		0			0
$523$	−16.6135	+	28.7755i	−0.726459	+	1.25826i	0.231911	+	0.972737i	$0.425502\pi$
$523$	−16.6135	+	28.7755i	−0.726459	+	1.25826i	−0.958371	+	0.285527i	$0.907831\pi$
$524$	13.5243	+	23.4247i	0.590810	+	1.02331i
$525$		0			0
$526$	19.2197	−	33.2895i	0.838019	−	1.45149i
$527$	−38.6097			−1.68187
$528$		0			0
$529$	4.92119	+	8.52375i	0.213965	+	0.370598i
$530$	15.8768	−	27.4994i	0.689642	−	1.19450i
$531$		0			0
$532$	4.04939	+	7.01375i	0.175563	+	0.304085i
$533$	1.00517			0.0435387
$534$		0			0
$535$	−1.22167			−0.0528173
$536$	6.53693	+	42.2729i	0.282352	+	1.82591i
$537$		0			0
$538$	−13.1621	+	22.7974i	−0.567458	+	0.982866i
$539$	74.3484			3.20241
$540$		0			0
$541$	7.79476			0.335123			0.167562	−	0.985862i	$-0.446411\pi$
$541$	7.79476			0.335123			0.167562	+	0.985862i	$0.446411\pi$
$542$	30.7121	−	53.1949i	1.31920	−	2.28492i
$543$		0			0
$544$	6.03473			0.258737
$545$	−6.03615			−0.258560
$546$		0			0
$547$	−10.0521	−	17.4107i	−0.429797	−	0.744429i	0.567058	−	0.823678i	$-0.308081\pi$
$547$	−10.0521	−	17.4107i	−0.429797	−	0.744429i	−0.996855	+	0.0792482i	$0.974748\pi$
$548$	−3.28774	−	5.69454i	−0.140445	−	0.243259i
$549$		0			0
$550$	−31.5529			−1.34542
$551$	−2.67617			−0.114009
$552$		0			0
$553$	−33.6583	+	58.2978i	−1.43129	+	2.47907i
$554$	−19.1645	+	33.1939i	−0.814222	+	1.41027i
$555$		0			0
$556$	39.3836	+	68.2143i	1.67023	+	2.89293i
$557$	−6.63436	−	11.4910i	−0.281107	−	0.486891i	0.690551	−	0.723284i	$-0.257368\pi$
$557$	−6.63436	−	11.4910i	−0.281107	−	0.486891i	−0.971658	+	0.236393i	$0.924035\pi$
$558$		0			0
$559$	−0.0632142	+	0.109490i	−0.00267368	+	0.00463094i
$560$	−60.6679			−2.56369
$561$		0			0
$562$	−26.3744	−	45.6818i	−1.11254	−	1.92697i
$563$	4.79550			0.202106			0.101053	−	0.994881i	$-0.467779\pi$
$563$	4.79550			0.202106			0.101053	+	0.994881i	$0.467779\pi$
$564$		0			0
$565$	−25.7591	−	44.6161i	−1.08369	−	1.87701i
$566$	−17.8308	+	30.8838i	−0.749484	+	1.29814i
$567$		0			0
$568$	9.47796	+	16.4163i	0.397686	+	0.688813i
$569$	8.59946	+	14.8947i	0.360508	+	0.624418i	0.988044	−	0.154169i	$-0.0492700\pi$
$569$	8.59946	+	14.8947i	0.360508	+	0.624418i	−0.627537	+	0.778587i	$0.715937\pi$
$570$		0			0
$571$	−18.1473	−	31.4321i	−0.759442	−	1.31539i	−0.943135	−	0.332409i	$-0.892139\pi$
$571$	−18.1473	−	31.4321i	−0.759442	−	1.31539i	0.183693	−	0.982984i	$-0.441195\pi$
$572$	1.15479	+	2.00015i	0.0482840	+	0.0836304i
$573$		0			0
$574$	51.3771	+	88.9878i	2.14444	+	3.71428i
$575$	−4.68032	+	8.10656i	−0.195183	+	0.338067i
$576$		0			0
$577$	−5.64556	−	9.77840i	−0.235028	−	0.407080i	0.724253	−	0.689534i	$-0.242185\pi$
$577$	−5.64556	−	9.77840i	−0.235028	−	0.407080i	−0.959281	+	0.282454i	$0.908851\pi$
$578$	−25.4906			−1.06027
$579$		0			0
$580$	36.1327	−	62.5836i	1.50033	−	2.59864i
$581$	−1.31777			−0.0546703
$582$		0			0
$583$	−11.5330	−	19.9757i	−0.477646	−	0.827308i
$584$	28.0336	−	48.5557i	1.16004	−	2.00925i
$585$		0			0
$586$	−8.23529	+	14.2639i	−0.340197	+	0.589238i
$587$	−11.3368	+	19.6359i	−0.467920	+	0.810461i	−0.999328	−	0.0366548i	$-0.988330\pi$
$587$	−11.3368	+	19.6359i	−0.467920	+	0.810461i	0.531408	+	0.847116i	$0.321663\pi$
$588$		0			0
$589$	3.09878			0.127683
$590$	−22.6741	+	39.2727i	−0.933478	+	1.61683i
$591$		0			0
$592$	−26.4624	−	45.8342i	−1.08760	−	1.88377i
$593$	23.6885	−	41.0297i	0.972771	−	1.68489i	0.285669	−	0.958328i	$-0.407784\pi$
$593$	23.6885	−	41.0297i	0.972771	−	1.68489i	0.687102	−	0.726561i	$-0.258882\pi$
$594$		0			0
$595$	67.5400			2.76887
$596$	−24.4492	−	42.3473i	−1.00148	−	1.73461i
$597$		0			0
$598$	1.01830			0.0416413
$599$	−21.1774	−	36.6804i	−0.865286	−	1.49872i	−0.866763	−	0.498720i	$-0.833804\pi$
$599$	−21.1774	−	36.6804i	−0.865286	−	1.49872i	0.00147772	−	0.999999i	$-0.499530\pi$
$600$		0			0
$601$	−4.88179	+	8.45550i	−0.199132	+	0.344907i	−0.948247	−	0.317533i	$-0.897146\pi$
$601$	−4.88179	+	8.45550i	−0.199132	+	0.344907i	0.749115	+	0.662440i	$0.230479\pi$
$602$	−12.9242			−0.526753
$603$		0			0
$604$	−14.4577			−0.588275
$605$	−18.5216	+	32.0803i	−0.753008	+	1.30425i
$606$		0			0
$607$	−10.4294	−	18.0643i	−0.423317	−	0.733206i	0.572945	−	0.819594i	$-0.305801\pi$
$607$	−10.4294	−	18.0643i	−0.423317	−	0.733206i	−0.996262	+	0.0863880i	$0.972468\pi$
$608$	−0.484342			−0.0196426
$609$		0			0
$610$	2.36265	+	4.09223i	0.0956610	+	0.165690i
$611$	−0.379967			−0.0153718
$612$		0			0
$613$	16.9276	−	29.3195i	0.683701	−	1.18420i	−0.290142	−	0.956983i	$-0.593703\pi$
$613$	16.9276	−	29.3195i	0.683701	−	1.18420i	0.973843	−	0.227221i	$-0.0729640\pi$
$614$	0.994108	+	1.72184i	0.0401189	+	0.0694880i
$615$		0			0
$616$	−60.6536	+	105.055i	−2.44380	+	4.23279i
$617$	−36.8616			−1.48399			−0.741997	−	0.670404i	$-0.766121\pi$
$617$	−36.8616			−1.48399			−0.741997	+	0.670404i	$0.766121\pi$
$618$		0			0
$619$	11.7682	−	20.3832i	0.473006	−	0.819270i	−0.526517	−	0.850165i	$-0.676502\pi$
$619$	11.7682	−	20.3832i	0.473006	−	0.819270i	0.999523	+	0.0308945i	$0.00983559\pi$
$620$	−41.8386	+	72.4666i	−1.68028	+	2.91033i
$621$		0			0
$622$	−14.1639	+	24.5325i	−0.567919	+	0.983665i
$623$	9.55501	+	16.5498i	0.382813	+	0.663052i
$624$		0			0
$625$	−31.2435			−1.24974
$626$	32.3106	−	55.9636i	1.29139	−	2.23676i
$627$		0			0
$628$	−4.77647			−0.190602
$629$	29.4599	+	51.0260i	1.17464	+	2.03454i
$630$		0			0
$631$	16.6135	−	28.7755i	0.661374	−	1.14553i	−0.318880	−	0.947795i	$-0.603307\pi$
$631$	16.6135	−	28.7755i	0.661374	−	1.14553i	0.980255	−	0.197739i	$-0.0633599\pi$
$632$	−37.4709	−	64.9015i	−1.49051	−	2.58164i
$633$		0			0
$634$	−6.76825	−	11.7230i	−0.268802	−	0.465578i
$635$	−7.99506	−	13.8479i	−0.317274	−	0.549535i
$636$		0			0
$637$	0.853504	+	1.47831i	0.0338170	+	0.0585728i
$638$	−39.0082	−	67.5642i	−1.54435	−	2.67489i
$639$		0			0
$640$	−25.4165	+	44.0227i	−1.00468	+	1.74015i
$641$	0.896679	+	1.55309i	0.0354167	+	0.0613435i	0.883190	−	0.469015i	$-0.155391\pi$
$641$	0.896679	+	1.55309i	0.0354167	+	0.0613435i	−0.847774	+	0.530358i	$0.822057\pi$
$642$		0			0
$643$	−14.6941			−0.579479			−0.289740	−	0.957105i	$-0.593569\pi$
$643$	−14.6941			−0.579479			−0.289740	+	0.957105i	$0.593569\pi$
$644$	35.0210	+	60.6581i	1.38002	+	2.39026i
$645$		0			0
$646$	5.41942			0.213224
$647$	1.05736	−	1.83140i	0.0415690	−	0.0719996i	−0.844492	−	0.535568i	$-0.820098\pi$
$647$	1.05736	−	1.83140i	0.0415690	−	0.0719996i	0.886061	+	0.463568i	$0.153431\pi$
$648$		0			0
$649$	16.4706	+	28.5279i	0.646527	+	1.11982i
$650$	−0.362221	−	0.627385i	−0.0142075	−	0.0246080i
$651$		0			0
$652$	0.825019	−	1.42897i	0.0323102	−	0.0559630i
$653$	−16.1372	+	27.9504i	−0.631496	+	1.09378i	0.355749	+	0.934581i	$0.384226\pi$
$653$	−16.1372	+	27.9504i	−0.631496	+	1.09378i	−0.987246	+	0.159203i	$0.949108\pi$
$654$		0			0
$655$	−18.1042			−0.707389
$656$	−41.5579			−1.62256
$657$		0			0
$658$	−19.4212	−	33.6385i	−0.757117	−	1.31136i
$659$	15.2179	+	26.3581i	0.592804	+	1.02677i	0.993853	+	0.110710i	$0.0353126\pi$
$659$	15.2179	+	26.3581i	0.592804	+	1.02677i	−0.401048	+	0.916057i	$0.631354\pi$
$660$		0			0
$661$	−25.3277			−0.985134			−0.492567	−	0.870274i	$-0.663941\pi$
$661$	−25.3277			−0.985134			−0.492567	+	0.870274i	$0.663941\pi$
$662$	67.1709			2.61067
$663$		0			0
$664$	0.733521	−	1.27049i	0.0284661	−	0.0493048i
$665$	−5.42070			−0.210206
$666$		0			0
$667$	−23.1447			−0.896167
$668$	14.2127	−	24.6171i	0.549906	−	0.952465i
$669$		0			0
$670$	−51.9485	−	20.1595i	−2.00695	−	0.778831i
$671$	3.43248			0.132510
$672$		0			0
$673$	34.4413			1.32761			0.663806	−	0.747904i	$-0.268940\pi$
$673$	34.4413			1.32761			0.663806	+	0.747904i	$0.268940\pi$
$674$	−0.319286	−	0.553019i	−0.0122984	−	0.0213015i
$675$		0			0
$676$	26.7115	−	46.2656i	1.02736	−	1.77945i
$677$	−0.459650	−	0.796137i	−0.0176658	−	0.0305980i	0.857057	−	0.515221i	$-0.172290\pi$
$677$	−0.459650	−	0.796137i	−0.0176658	−	0.0305980i	−0.874723	+	0.484623i	$0.838957\pi$
$678$		0			0
$679$	88.8183			3.40853
$680$	−37.5953	+	65.1170i	−1.44171	+	2.49712i
$681$		0			0
$682$	45.1682	+	78.2337i	1.72958	+	2.99572i
$683$	11.2080	−	19.4128i	0.428862	−	0.742811i	−0.567910	−	0.823090i	$-0.692248\pi$
$683$	11.2080	−	19.4128i	0.428862	−	0.742811i	0.996772	+	0.0802795i	$0.0255813\pi$
$684$		0			0
$685$	4.40112			0.168158
$686$	−46.6274	+	80.7611i	−1.78024	+	3.08347i
$687$		0			0
$688$	2.61354	−	4.52678i	0.0996402	−	0.172582i
$689$	0.264792	−	0.458633i	0.0100878	−	0.0174725i
$690$		0			0
$691$	2.53940	+	4.39838i	0.0966035	+	0.167322i	0.910277	−	0.414000i	$-0.135869\pi$
$691$	2.53940	+	4.39838i	0.0966035	+	0.167322i	−0.813673	+	0.581323i	$0.802535\pi$
$692$	−0.484342			−0.0184119
$693$		0			0
$694$	−56.9135			−2.16041
$695$	−52.7206			−1.99981
$696$		0			0
$697$	46.2653			1.75242
$698$	5.90504	−	10.2278i	0.223509	−	0.387129i
$699$		0			0
$700$	24.9147	−	43.1536i	0.941689	−	1.63105i
$701$	−18.5282	−	32.0919i	−0.699802	−	1.21209i	−0.968535	−	0.248878i	$-0.919938\pi$
$701$	−18.5282	−	32.0919i	−0.699802	−	1.21209i	0.268733	−	0.963215i	$-0.413395\pi$
$702$		0			0
$703$	−2.36442	−	4.09530i	−0.0891759	−	0.154457i
$704$	16.1531	+	27.9780i	0.608793	+	1.05446i
$705$		0			0
$706$	−15.1218	−	26.1916i	−0.569115	−	0.985736i
$707$	−27.9748	+	48.4537i	−1.05210	+	1.82229i
$708$		0			0
$709$	6.59888	−	11.4296i	0.247826	−	0.429247i	−0.715096	−	0.699026i	$-0.753617\pi$
$709$	6.59888	−	11.4296i	0.247826	−	0.429247i	0.962922	+	0.269779i	$0.0869505\pi$
$710$	−24.6937			−0.926738
$711$		0			0
$712$	−21.2747			−0.797303
$713$	26.7997			1.00365
$714$		0			0
$715$	−1.54585			−0.0578115
$716$	24.4492	+	42.3473i	0.913710	+	1.58259i
$717$		0			0
$718$	9.00822	−	15.6027i	0.336184	−	0.582287i
$719$	1.45813	−	2.52556i	0.0543793	−	0.0941876i	−0.837554	−	0.546354i	$-0.816015\pi$
$719$	1.45813	−	2.52556i	0.0543793	−	0.0941876i	0.891934	+	0.452166i	$0.149349\pi$
$720$		0			0
$721$	−24.9879	+	43.2804i	−0.930600	+	1.61185i
$722$	46.5436			1.73217
$723$		0			0
$724$	−9.48534	+	16.4291i	−0.352520	+	0.610582i
$725$	8.23286	+	14.2597i	0.305761	+	0.529593i
$726$		0			0
$727$	−1.33614	+	2.31426i	−0.0495547	+	0.0858312i	−0.889739	−	0.456470i	$-0.849114\pi$
$727$	−1.33614	+	2.31426i	−0.0495547	+	0.0858312i	0.840184	+	0.542301i	$0.182447\pi$
$728$	−2.78516			−0.103225
$729$		0			0
$730$	36.5191	+	63.2530i	1.35163	+	2.34110i
$731$	−2.90959	+	5.03955i	−0.107615	+	0.186395i
$732$		0			0
$733$	−0.427637	−	0.740689i	−0.0157951	−	0.0273580i	0.858020	−	0.513617i	$-0.171695\pi$
$733$	−0.427637	−	0.740689i	−0.0157951	−	0.0273580i	−0.873815	+	0.486259i	$0.838361\pi$
$734$	32.2610			1.19077
$735$		0			0
$736$	−4.18880			−0.154401
$737$	−31.5499	+	25.3581i	−1.16216	+	0.934076i
$738$		0			0
$739$	19.9230	−	34.5076i	0.732878	−	1.26938i	−0.222770	−	0.974871i	$-0.571510\pi$
$739$	19.9230	−	34.5076i	0.732878	−	1.26938i	0.955648	−	0.294511i	$-0.0951567\pi$
$740$	127.694			4.69414
$741$		0			0
$742$	54.1371			1.98743
$743$	6.78141	−	11.7457i	0.248786	−	0.430909i	−0.714403	−	0.699734i	$-0.753302\pi$
$743$	6.78141	−	11.7457i	0.248786	−	0.430909i	0.963189	+	0.268825i	$0.0866352\pi$
$744$		0			0
$745$	32.7288			1.19909
$746$	−37.0971			−1.35822
$747$		0			0
$748$	53.1518	+	92.0616i	1.94342	+	3.36611i
$749$	−1.04142	−	1.80379i	−0.0380527	−	0.0659092i
$750$		0			0
$751$	9.12643			0.333028			0.166514	−	0.986039i	$-0.446749\pi$
$751$	9.12643			0.333028			0.166514	+	0.986039i	$0.446749\pi$
$752$	15.7094			0.572863
$753$		0			0
$754$	0.895611	−	1.55124i	0.0326162	−	0.0564930i
$755$	4.83843	−	8.38041i	0.176089	−	0.304994i
$756$		0			0
$757$	−4.77563	−	8.27163i	−0.173573	−	0.300638i	0.766093	−	0.642729i	$-0.222198\pi$
$757$	−4.77563	−	8.27163i	−0.173573	−	0.300638i	−0.939667	+	0.342092i	$0.888865\pi$
$758$	−14.5772	−	25.2485i	−0.529469	−	0.917067i
$759$		0			0
$760$	3.01736	−	5.22623i	0.109451	−	0.189575i
$761$	26.5189			0.961310			0.480655	−	0.876910i	$-0.340399\pi$
$761$	26.5189			0.961310			0.480655	+	0.876910i	$0.340399\pi$
$762$		0			0
$763$	−5.14556	−	8.91238i	−0.186282	−	0.322650i
$764$	−86.6572			−3.13515
$765$		0			0
$766$	24.5603	+	42.5397i	0.887400	+	1.53702i
$767$	−0.378157	+	0.654988i	−0.0136545	+	0.0236502i
$768$		0			0
$769$	−9.00177	−	15.5915i	−0.324612	−	0.562245i	0.656822	−	0.754046i	$-0.271900\pi$
$769$	−9.00177	−	15.5915i	−0.324612	−	0.562245i	−0.981434	+	0.191801i	$0.938567\pi$
$770$	−79.0128	−	136.854i	−2.84742	−	4.93188i
$771$		0			0
$772$	−17.5503	−	30.3981i	−0.631650	−	1.09405i
$773$	14.2849	+	24.7423i	0.513794	+	0.889917i	0.999872	+	0.0160017i	$0.00509370\pi$
$773$	14.2849	+	24.7423i	0.513794	+	0.889917i	−0.486078	+	0.873915i	$0.661573\pi$
$774$		0			0
$775$	−9.53296	−	16.5116i	−0.342434	−	0.593113i
$776$	−49.4396	+	85.6319i	−1.77478	+	3.07400i
$777$		0			0
$778$	2.77647	+	4.80898i	0.0995411	+	0.172410i
$779$	−3.71321			−0.133040
$780$		0			0
$781$	−8.96881	+	15.5344i	−0.320929	+	0.555866i
$782$	46.8696			1.67605
$783$		0			0
$784$	−35.2874	−	61.1195i	−1.26026	−	2.18284i
$785$	1.59850	−	2.76868i	0.0570529	−	0.0988185i
$786$		0			0
$787$	7.47796	−	12.9522i	0.266561	−	0.461696i	−0.701411	−	0.712757i	$-0.747446\pi$
$787$	7.47796	−	12.9522i	0.266561	−	0.461696i	0.967971	+	0.251061i	$0.0807795\pi$
$788$	18.8519	−	32.6525i	0.671571	−	1.16320i
$789$		0			0
$790$	97.6259			3.47337
$791$	43.9171	−	76.0666i	1.56151	−	2.70462i
$792$		0			0
$793$	0.0394042	+	0.0682500i	0.00139928	+	0.00242363i
$794$	−17.7652	+	30.7703i	−0.630465	+	1.09200i
$795$		0			0
$796$	42.3936			1.50260
$797$	8.97761	+	15.5497i	0.318003	+	0.550798i	0.980071	−	0.198646i	$-0.0636543\pi$
$797$	8.97761	+	15.5497i	0.318003	+	0.550798i	−0.662068	+	0.749444i	$0.730321\pi$
$798$		0			0
$799$	−17.4889			−0.618712
$800$	1.49001	+	2.58077i	0.0526797	+	0.0912440i
$801$		0			0
$802$	−37.0677	+	64.2031i	−1.30891	+	2.26709i
$803$	53.0554			1.87228
$804$		0			0
$805$	−46.8807			−1.65233
$806$	−1.03704	+	1.79621i	−0.0365283	+	0.0632688i
$807$		0			0
$808$	−31.1436	−	53.9423i	−1.09563	−	1.89768i
$809$	−23.1811			−0.815003			−0.407501	−	0.913205i	$-0.633600\pi$
$809$	−23.1811			−0.815003			−0.407501	+	0.913205i	$0.633600\pi$
$810$		0			0
$811$	−5.17675	−	8.96640i	−0.181780	−	0.314853i	0.760707	−	0.649096i	$-0.224853\pi$
$811$	−5.17675	−	8.96640i	−0.181780	−	0.314853i	−0.942487	+	0.334243i	$0.891519\pi$
$812$	123.206			4.32369
$813$		0			0
$814$	68.9283	−	119.387i	2.41593	−	4.18452i
$815$	0.552204	+	0.956445i	0.0193429	+	0.0335028i
$816$		0			0
$817$	0.233521	−	0.404470i	0.00816985	−	0.0141506i
$818$	48.9303			1.71081
$819$		0			0
$820$	50.1344	−	86.8354i	1.75077	−	3.03242i
$821$	−6.13846	+	10.6321i	−0.214234	+	0.371064i	−0.953035	−	0.302859i	$-0.902059\pi$
$821$	−6.13846	+	10.6321i	−0.214234	+	0.371064i	0.738802	+	0.673923i	$0.235392\pi$
$822$		0			0
$823$	−5.33240	+	9.23598i	−0.185876	+	0.321946i	−0.943871	−	0.330314i	$-0.892846\pi$
$823$	−5.33240	+	9.23598i	−0.185876	+	0.321946i	0.757996	+	0.652260i	$0.226179\pi$
$824$	−27.8185	−	48.1830i	−0.969102	−	1.67853i
$825$		0			0
$826$	−77.3148			−2.69013
$827$	4.13918	−	7.16927i	0.143933	−	0.249300i	−0.785041	−	0.619444i	$-0.787358\pi$
$827$	4.13918	−	7.16927i	0.143933	−	0.249300i	0.928975	+	0.370144i	$0.120692\pi$
$828$		0			0
$829$	6.26180			0.217481			0.108741	−	0.994070i	$-0.465318\pi$
$829$	6.26180			0.217481			0.108741	+	0.994070i	$0.465318\pi$
$830$	0.955550	+	1.65506i	0.0331676	+	0.0574480i
$831$		0			0
$832$	−0.370868	+	0.642363i	−0.0128575	+	0.0222699i
$833$	39.2846	+	68.0429i	1.36113	+	2.35755i
$834$		0			0
$835$	9.51289	+	16.4768i	0.329207	+	0.570204i
$836$	−4.26591	−	7.38878i	−0.147540	−	0.255546i
$837$		0			0
$838$	−18.6483	−	32.2997i	−0.644194	−	1.11578i
$839$	2.81216	+	4.87080i	0.0970864	+	0.168159i	0.910477	−	0.413559i	$-0.135714\pi$
$839$	2.81216	+	4.87080i	0.0970864	+	0.168159i	−0.813391	+	0.581717i	$0.802381\pi$
$840$		0			0
$841$	−5.85621	+	10.1432i	−0.201938	+	0.349767i
$842$	−23.3919	−	40.5159i	−0.806137	−	1.39627i
$843$		0			0
$844$	61.7176			2.12441
$845$	17.8786	+	30.9667i	0.615043	+	1.06529i
$846$		0			0
$847$	−63.1553			−2.17004
$848$	−10.9476	+	18.9618i	−0.375942	+	0.651150i
$849$		0			0
$850$	−16.6721	−	28.8769i	−0.571848	−	0.990469i
$851$	−20.4486	−	35.4180i	−0.700969	−	1.21411i
$852$		0			0
$853$	8.92296	−	15.4550i	0.305516	−	0.529170i	−0.671860	−	0.740678i	$-0.734504\pi$
$853$	8.92296	−	15.4550i	0.305516	−	0.529170i	0.977376	+	0.211508i	$0.0678376\pi$
$854$	−4.02812	+	6.97691i	−0.137839	+	0.238745i
$855$		0			0
$856$	2.31877			0.0792541
$857$	−52.7659			−1.80245			−0.901224	−	0.433353i	$-0.857330\pi$
$857$	−52.7659			−1.80245			−0.901224	+	0.433353i	$0.857330\pi$
$858$		0			0
$859$	13.8012	+	23.9044i	0.470891	+	0.815607i	0.999446	−	0.0332919i	$-0.0105991\pi$
$859$	13.8012	+	23.9044i	0.470891	+	0.815607i	−0.528555	+	0.848899i	$0.677266\pi$
$860$	6.30582	+	10.9220i	0.215027	+	0.372437i
$861$		0			0
$862$	−61.9083			−2.10861
$863$	−0.131112			−0.00446309			−0.00223155	−	0.999998i	$-0.500710\pi$
$863$	−0.131112			−0.00446309			−0.00223155	+	0.999998i	$0.500710\pi$
$864$		0			0
$865$	0.162091	−	0.280749i	0.00551124	−	0.00954575i
$866$	−29.8337			−1.01379
$867$		0			0
$868$	−142.663			−4.84228
$869$	35.4580	−	61.4150i	1.20283	−	2.08336i
$870$		0			0
$871$	−0.866394	−	0.336220i	−0.0293567	−	0.0113924i
$872$	11.4569			0.387978
$873$		0			0
$874$	−3.76171			−0.127242
$875$	−15.6346	−	27.0799i	−0.528546	−	0.915468i
$876$		0			0
$877$	−18.0283	+	31.2259i	−0.608772	+	1.05442i	0.382671	+	0.923885i	$0.375004\pi$
$877$	−18.0283	+	31.2259i	−0.608772	+	1.05442i	−0.991443	+	0.130539i	$0.958329\pi$
$878$	−17.6272	−	30.5312i	−0.594889	−	1.03038i
$879$		0			0
$880$	63.9118			2.15447
$881$	−1.30183	+	2.25484i	−0.0438599	+	0.0759676i	−0.887122	−	0.461535i	$-0.847299\pi$
$881$	−1.30183	+	2.25484i	−0.0438599	+	0.0759676i	0.843262	+	0.537503i	$0.180632\pi$
$882$		0			0
$883$	10.8186	+	18.7383i	0.364074	+	0.630595i	0.988627	−	0.150388i	$-0.0480522\pi$
$883$	10.8186	+	18.7383i	0.364074	+	0.630595i	−0.624553	+	0.780982i	$0.714719\pi$
$884$	−1.22034	+	2.11369i	−0.0410445	+	0.0710912i
$885$		0			0
$886$	−83.5288			−2.80621
$887$	−0.319286	+	0.553019i	−0.0107206	+	0.0185686i	−0.871336	−	0.490687i	$-0.836746\pi$
$887$	−0.319286	+	0.553019i	−0.0107206	+	0.0185686i	0.860615	+	0.509256i	$0.170079\pi$
$888$		0			0
$889$	13.6309	−	23.6094i	0.457166	−	0.791834i
$890$	13.8572	−	24.0013i	0.464493	−	0.804526i
$891$		0			0
$892$	−29.2956	−	50.7415i	−0.980889	−	1.69895i
$893$	1.40364			0.0469711
$894$		0			0
$895$	−32.7288			−1.09400
$896$	−86.6660			−2.89531
$897$		0			0
$898$	−58.3589			−1.94746
$899$	23.5708	−	40.8258i	0.786130	−	1.36162i
$900$		0			0
$901$	12.1877	−	21.1097i	0.406030	−	0.703265i
$902$	−54.1243	−	93.7460i	−1.80214	−	3.12140i
$903$		0			0
$904$	48.8918	+	84.6830i	1.62612	+	2.81652i
$905$	−6.34875	−	10.9964i	−0.211040	−	0.365532i
$906$		0			0
$907$	29.0750	+	50.3593i	0.965419	+	1.67215i	0.708486	+	0.705725i	$0.249378\pi$
$907$	29.0750	+	50.3593i	0.965419	+	1.67215i	0.256932	+	0.966429i	$0.417288\pi$
$908$	−29.4691	+	51.0420i	−0.977968	+	1.69389i
$909$		0			0
$910$	1.81410	−	3.14211i	0.0601368	−	0.104160i
$911$	34.6379			1.14761			0.573803	−	0.818994i	$-0.305468\pi$
$911$	34.6379			1.14761			0.573803	+	0.818994i	$0.305468\pi$
$912$		0			0
$913$	1.38823			0.0459438
$914$	44.1163			1.45924
$915$		0			0
$916$	−88.9907			−2.94033
$917$	−15.4330	−	26.7308i	−0.509644	−	0.882730i
$918$		0			0
$919$	13.7380	−	23.7949i	0.453175	−	0.784921i	−0.545407	−	0.838172i	$-0.683625\pi$
$919$	13.7380	−	23.7949i	0.453175	−	0.784921i	0.998581	+	0.0532501i	$0.0169581\pi$
$920$	26.0955	−	45.1988i	0.860344	−	1.49016i
$921$		0			0
$922$	43.4889	−	75.3249i	1.43223	−	2.48070i
$923$	−0.411840			−0.0135559
$924$		0			0
$925$	−14.5476	+	25.1972i	−0.478323	+	0.828479i
$926$	30.2751	+	52.4380i	0.994901	+	1.72322i
$927$		0			0
$928$	−3.68413	+	6.38110i	−0.120937	+	0.209470i
$929$	38.1660			1.25219			0.626093	−	0.779748i	$-0.284653\pi$
$929$	38.1660			1.25219			0.626093	+	0.779748i	$0.284653\pi$
$930$		0			0
$931$	−3.15294	−	5.46106i	−0.103333	−	0.178979i
$932$	5.99809	−	10.3890i	0.196474	−	0.340303i
$933$		0			0
$934$	−13.8562	−	23.9997i	−0.453389	−	0.785293i
$935$	−71.1514			−2.32690
$936$		0			0
$937$	−25.9193			−0.846747			−0.423374	−	0.905955i	$-0.639154\pi$
$937$	−25.9193			−0.846747			−0.423374	+	0.905955i	$0.639154\pi$
$938$	−14.5184	−	93.8872i	−0.474041	−	3.06552i
$939$		0			0
$940$	−18.9514	+	32.8249i	−0.618128	+	1.07063i
$941$	−5.67831			−0.185108			−0.0925538	−	0.995708i	$-0.529503\pi$
$941$	−5.67831			−0.185108			−0.0925538	+	0.995708i	$0.529503\pi$
$942$		0			0
$943$	−32.1135			−1.04576
$944$	15.6346	−	27.0799i	0.508863	−	0.881376i
$945$		0			0
$946$	13.6153			0.442672
$947$	−45.5297			−1.47952			−0.739758	−	0.672873i	$-0.765060\pi$
$947$	−45.5297			−1.47952			−0.739758	+	0.672873i	$0.765060\pi$
$948$		0			0
$949$	0.609064	+	1.05493i	0.0197710	+	0.0342445i
$950$	1.33809	+	2.31763i	0.0434132	+	0.0751939i
$951$		0			0
$952$	−128.194			−4.15478
$953$	11.6065			0.375970			0.187985	−	0.982172i	$-0.439804\pi$
$953$	11.6065			0.375970			0.187985	+	0.982172i	$0.439804\pi$
$954$		0			0
$955$	29.0008	−	50.2309i	0.938445	−	1.62543i
$956$	−8.54984	+	14.8088i	−0.276521	+	0.478949i
$957$		0			0
$958$	39.3350	+	68.1302i	1.27086	+	2.20119i
$959$	3.75177	+	6.49826i	0.121151	+	0.209840i
$960$		0			0
$961$	−11.7930	+	20.4261i	−0.380419	+	0.658905i
$962$	3.16512			0.102048
$963$		0			0
$964$	31.5859	+	54.7084i	1.01731	+	1.76204i
$965$	23.4937			0.756288
$966$		0			0
$967$	8.55677	+	14.8208i	0.275167	+	0.476603i	0.970177	−	0.242396i	$-0.0779335\pi$
$967$	8.55677	+	14.8208i	0.275167	+	0.476603i	−0.695010	+	0.719000i	$0.744600\pi$
$968$	35.1546	−	60.8896i	1.12991	−	1.95707i
$969$		0			0
$970$	−64.4045	−	111.552i	−2.06790	−	3.58171i
$971$	−16.3953	−	28.3975i	−0.526150	−	0.911318i	−0.999536	−	0.0304630i	$-0.990302\pi$
$971$	−16.3953	−	28.3975i	−0.526150	−	0.911318i	0.473386	−	0.880855i	$-0.343032\pi$
$972$		0			0
$973$	−44.9421	−	77.8420i	−1.44078	−	2.49550i
$974$	−14.6405	−	25.3581i	−0.469111	−	0.812525i
$975$		0			0
$976$	−1.62913	−	2.82174i	−0.0521472	−	0.0903217i
$977$	11.0946	−	19.2165i	0.354949	−	0.614789i	−0.632160	−	0.774838i	$-0.717832\pi$
$977$	11.0946	−	19.2165i	0.354949	−	0.614789i	0.987109	+	0.160048i	$0.0511650\pi$
$978$		0			0
$979$	−10.0659	−	17.4347i	−0.321708	−	0.557215i
$980$	170.279			5.43938
$981$		0			0
$982$	49.3056	−	85.3998i	1.57340	−	2.72522i
$983$	−33.4379			−1.06650			−0.533252	−	0.845957i	$-0.679030\pi$
$983$	−33.4379			−1.06650			−0.533252	+	0.845957i	$0.679030\pi$
$984$		0			0
$985$	12.6180	+	21.8550i	0.402043	+	0.696359i
$986$	41.2227	−	71.3997i	1.31280	−	2.27383i
$987$		0			0
$988$	0.0979435	−	0.169643i	0.00311600	−	0.00539707i
$989$	2.01959	−	3.49803i	0.0642193	−	0.111231i
$990$		0			0
$991$	−28.7929			−0.914637			−0.457318	−	0.889303i	$-0.651190\pi$
$991$	−28.7929			−0.914637			−0.457318	+	0.889303i	$0.651190\pi$
$992$	4.26591	−	7.38878i	0.135443	−	0.234594i
$993$		0			0
$994$	−21.0503	−	36.4602i	−0.667676	−	1.15645i
$995$	−14.1875	+	24.5735i	−0.449775	+	0.779032i
$996$		0			0
$997$	−0.503636			−0.0159503			−0.00797516	−	0.999968i	$-0.502539\pi$
$997$	−0.503636			−0.0159503			−0.00797516	+	0.999968i	$0.502539\pi$
$998$	40.8874	+	70.8191i	1.29427	+	2.24174i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.g.h.163.6	yes	12
3.2	odd	2	inner	603.2.g.h.163.1	yes	12
67.37	even	3	inner	603.2.g.h.37.6	yes	12
201.104	odd	6	inner	603.2.g.h.37.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.g.h.37.1	✓	12	201.104	odd	6	inner
603.2.g.h.37.6	yes	12	67.37	even	3	inner
603.2.g.h.163.1	yes	12	3.2	odd	2	inner
603.2.g.h.163.6	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23628 - 2.14130i) q^{2} +(-2.05677 - 3.56243i) q^{4} +2.75329 q^{5} +(2.34706 + 4.06522i) q^{7} -5.22584 q^{8} +O(q^{10})\)	\(q+(1.23628 - 2.14130i) q^{2} +(-2.05677 - 3.56243i) q^{4} +2.75329 q^{5} +(2.34706 + 4.06522i) q^{7} -5.22584 q^{8} +(3.40383 - 5.89560i) q^{10} +(-2.47256 - 4.28259i) q^{11} +(0.0567688 - 0.0983265i) q^{13} +11.6065 q^{14} +(-2.34706 + 4.06522i) q^{16} +(2.61292 - 4.52571i) q^{17} +(-0.209711 + 0.363229i) q^{19} +(-5.66287 - 9.80838i) q^{20} -12.2271 q^{22} +(-1.81367 + 3.14137i) q^{23} +2.58058 q^{25} +(-0.140364 - 0.243118i) q^{26} +(9.65471 - 16.7225i) q^{28} +(3.19031 + 5.52579i) q^{29} +(-3.69412 - 6.39840i) q^{31} +(0.577393 + 1.00007i) q^{32} +(-6.46060 - 11.1901i) q^{34} +(6.46212 + 11.1927i) q^{35} +(-5.63735 + 9.76417i) q^{37} +(0.518521 + 0.898105i) q^{38} -14.3882 q^{40} +(4.42659 + 7.66708i) q^{41} -1.11354 q^{43} +(-10.1710 + 17.6166i) q^{44} +(4.48441 + 7.76722i) q^{46} +(-1.67331 - 2.89825i) q^{47} +(-7.51736 + 13.0205i) q^{49} +(3.19031 - 5.52579i) q^{50} -0.467041 q^{52} +4.66439 q^{53} +(-6.80765 - 11.7912i) q^{55} +(-12.2654 - 21.2442i) q^{56} +15.7765 q^{58} -6.66136 q^{59} +(-0.347058 + 0.601122i) q^{61} -18.2678 q^{62} -6.53296 q^{64} +(0.156301 - 0.270721i) q^{65} +(-1.25089 - 8.08921i) q^{67} -21.4967 q^{68} +31.9559 q^{70} +(-1.81367 - 3.14137i) q^{71} +(-5.36442 + 9.29145i) q^{73} +(13.9387 + 24.1425i) q^{74} +1.72530 q^{76} +(11.6065 - 20.1030i) q^{77} +(7.17031 + 12.4193i) q^{79} +(-6.46212 + 11.1927i) q^{80} +21.8900 q^{82} +(-0.140364 + 0.243118i) q^{83} +(7.19412 - 12.4606i) q^{85} +(-1.37664 + 2.38441i) q^{86} +(12.9212 + 22.3802i) q^{88} +4.07106 q^{89} +0.532959 q^{91} +14.9212 q^{92} -8.27470 q^{94} +(-0.577393 + 1.00007i) q^{95} +(9.46060 - 16.3862i) q^{97} +(18.5871 + 32.1938i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{4} + 6 q^{7}+O(q^{10}) \) 12 * q - 10 * q^4 + 6 * q^7	\( 12 q - 10 q^{4} + 6 q^{7} + 4 q^{10} - 14 q^{13} - 6 q^{16} - 10 q^{19} - 88 q^{22} + 16 q^{25} + 20 q^{28} - 26 q^{34} - 38 q^{37} - 84 q^{40} + 16 q^{43} + 2 q^{46} - 24 q^{49} - 20 q^{52} - 8 q^{55} + 12 q^{58} + 18 q^{61} - 64 q^{64} + 44 q^{67} + 148 q^{70} + 24 q^{73} + 80 q^{76} + 42 q^{79} + 56 q^{82} + 42 q^{85} + 52 q^{88} - 8 q^{91} - 40 q^{94} + 62 q^{97}+O(q^{100}) \) 12 * q - 10 * q^4 + 6 * q^7 + 4 * q^10 - 14 * q^13 - 6 * q^16 - 10 * q^19 - 88 * q^22 + 16 * q^25 + 20 * q^28 - 26 * q^34 - 38 * q^37 - 84 * q^40 + 16 * q^43 + 2 * q^46 - 24 * q^49 - 20 * q^52 - 8 * q^55 + 12 * q^58 + 18 * q^61 - 64 * q^64 + 44 * q^67 + 148 * q^70 + 24 * q^73 + 80 * q^76 + 42 * q^79 + 56 * q^82 + 42 * q^85 + 52 * q^88 - 8 * q^91 - 40 * q^94 + 62 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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