LMFDB - Embedded newform 630.2.r.b.299.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(59,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3, 1]))

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

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

chi := DirichletCharacter("630.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.r (of order $6$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.7
Character	$\chi$	$=$	630.299
Dual form			630.2.r.b.59.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.13878 - 1.30506i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.21378 - 0.314891i) q^{5} +(0.560822 - 1.63874i) q^{6} +(2.52491 + 0.790468i) q^{7} -1.00000 q^{8} +(-0.406351 + 2.97235i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.13878 - 1.30506i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.21378 - 0.314891i) q^{5} +(0.560822 - 1.63874i) q^{6} +(2.52491 + 0.790468i) q^{7} -1.00000 q^{8} +(-0.406351 + 2.97235i) q^{9} +(-0.834189 - 2.07464i) q^{10} -4.56510i q^{11} +(1.69960 - 0.333685i) q^{12} +(0.341322 + 0.591187i) q^{13} +(0.577888 + 2.58187i) q^{14} +(2.11007 + 3.24771i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-5.72947 + 3.30791i) q^{17} +(-2.77731 + 1.13427i) q^{18} +(-6.76346 - 3.90489i) q^{19} +(1.37960 - 1.75975i) q^{20} +(-1.84371 - 4.19532i) q^{21} +(3.95349 - 2.28255i) q^{22} -3.50894 q^{23} +(1.13878 + 1.30506i) q^{24} +(4.80169 + 1.39420i) q^{25} +(-0.341322 + 0.591187i) q^{26} +(4.34184 - 2.85455i) q^{27} +(-1.94702 + 1.79140i) q^{28} +(-4.33820 - 2.50466i) q^{29} +(-1.75757 + 3.45123i) q^{30} +(-4.52018 - 2.60973i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-5.95771 + 5.19865i) q^{33} +(-5.72947 - 3.30791i) q^{34} +(-5.34069 - 2.54500i) q^{35} +(-2.37096 - 1.83809i) q^{36} +(1.37526 + 0.794006i) q^{37} -7.80978i q^{38} +(0.382842 - 1.11868i) q^{39} +(2.21378 + 0.314891i) q^{40} +(-3.41784 - 5.91987i) q^{41} +(2.71140 - 3.69436i) q^{42} +(-2.05488 - 1.18639i) q^{43} +(3.95349 + 2.28255i) q^{44} +(1.83554 - 6.45219i) q^{45} +(-1.75447 - 3.03883i) q^{46} +(-3.30466 + 1.90795i) q^{47} +(-0.560822 + 1.63874i) q^{48} +(5.75032 + 3.99172i) q^{49} +(1.19343 + 4.85548i) q^{50} +(10.8416 + 3.71030i) q^{51} -0.682644 q^{52} +(-0.983879 - 1.70413i) q^{53} +(4.64303 + 2.33287i) q^{54} +(-1.43751 + 10.1061i) q^{55} +(-2.52491 - 0.790468i) q^{56} +(2.60601 + 13.2735i) q^{57} -5.00932i q^{58} +(4.68295 - 8.11110i) q^{59} +(-3.86763 + 0.203517i) q^{60} +(-12.3974 + 7.15763i) q^{61} -5.21945i q^{62} +(-3.37555 + 7.18371i) q^{63} +1.00000 q^{64} +(-0.569454 - 1.41624i) q^{65} +(-7.48102 - 2.56021i) q^{66} +(6.28937 + 3.63117i) q^{67} -6.61583i q^{68} +(3.99592 + 4.57937i) q^{69} +(-0.466313 - 5.89767i) q^{70} +8.48088i q^{71} +(0.406351 - 2.97235i) q^{72} +(-0.735176 - 1.27336i) q^{73} +1.58801i q^{74} +(-3.64856 - 7.85417i) q^{75} +(6.76346 - 3.90489i) q^{76} +(3.60856 - 11.5264i) q^{77} +(1.16023 - 0.227788i) q^{78} +(-0.587811 - 1.01812i) q^{79} +(0.834189 + 2.07464i) q^{80} +(-8.66976 - 2.41564i) q^{81} +(3.41784 - 5.91987i) q^{82} +(9.77023 + 5.64084i) q^{83} +(4.55511 + 0.500958i) q^{84} +(13.7255 - 5.51885i) q^{85} -2.37277i q^{86} +(1.67154 + 8.51386i) q^{87} +4.56510i q^{88} +(0.739183 - 1.28030i) q^{89} +(6.50553 - 1.63647i) q^{90} +(0.394492 + 1.76250i) q^{91} +(1.75447 - 3.03883i) q^{92} +(1.74165 + 8.87100i) q^{93} +(-3.30466 - 1.90795i) q^{94} +(13.7432 + 10.7743i) q^{95} +(-1.69960 + 0.333685i) q^{96} +(4.40260 - 7.62553i) q^{97} +(-0.581771 + 6.97578i) q^{98} +(13.5691 + 1.85503i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9}+O(q^{10}) $ 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9	$ 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9} + 3 q^{12} + 3 q^{14} + 6 q^{15} - 24 q^{16} + 3 q^{18} + 5 q^{21} - 6 q^{22} + 6 q^{23} + 3 q^{24} + 3 q^{28} - 3 q^{29} - 3 q^{30} + 24 q^{32} - 24 q^{33} + 12 q^{35} + 3 q^{41} - 8 q^{42} - 6 q^{44} + 9 q^{45} + 3 q^{46} - 6 q^{49} - 18 q^{50} - 8 q^{51} - 42 q^{55} + 22 q^{57} - 9 q^{60} - 9 q^{61} + 10 q^{63} + 48 q^{64} - 21 q^{65} - 24 q^{66} + 33 q^{67} + 42 q^{69} + 12 q^{70} - 3 q^{72} - 18 q^{73} - 39 q^{75} - 6 q^{77} + 18 q^{78} - 37 q^{81} - 3 q^{82} + 9 q^{83} - 13 q^{84} + 33 q^{85} + 18 q^{87} + 33 q^{89} + 15 q^{90} - 3 q^{92} + 32 q^{93} + 33 q^{95} - 3 q^{96} - 24 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) $ 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9 + 3 * q^12 + 3 * q^14 + 6 * q^15 - 24 * q^16 + 3 * q^18 + 5 * q^21 - 6 * q^22 + 6 * q^23 + 3 * q^24 + 3 * q^28 - 3 * q^29 - 3 * q^30 + 24 * q^32 - 24 * q^33 + 12 * q^35 + 3 * q^41 - 8 * q^42 - 6 * q^44 + 9 * q^45 + 3 * q^46 - 6 * q^49 - 18 * q^50 - 8 * q^51 - 42 * q^55 + 22 * q^57 - 9 * q^60 - 9 * q^61 + 10 * q^63 + 48 * q^64 - 21 * q^65 - 24 * q^66 + 33 * q^67 + 42 * q^69 + 12 * q^70 - 3 * q^72 - 18 * q^73 - 39 * q^75 - 6 * q^77 + 18 * q^78 - 37 * q^81 - 3 * q^82 + 9 * q^83 - 13 * q^84 + 33 * q^85 + 18 * q^87 + 33 * q^89 + 15 * q^90 - 3 * q^92 + 32 * q^93 + 33 * q^95 - 3 * q^96 - 24 * q^97 - 3 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.13878	−	1.30506i	−0.657476	−	0.753475i
$3$	−1.13878	−	1.30506i	−0.657476	−	0.753475i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.21378	−	0.314891i	−0.990035	−	0.140824i
$5$	−2.21378	−	0.314891i	−0.990035	−	0.140824i
$6$	0.560822	−	1.63874i	0.228955	−	0.669014i
$7$	2.52491	+	0.790468i	0.954325	+	0.298769i
$7$	2.52491	+	0.790468i	0.954325	+	0.298769i
$8$	−1.00000			−0.353553
$9$	−0.406351	+	2.97235i	−0.135450	+	0.990784i
$10$	−0.834189	−	2.07464i	−0.263794	−	0.656059i
$11$		−	4.56510i		−	1.37643i	−0.725508	−	0.688214i	$-0.758395\pi$
$11$		−	4.56510i		−	1.37643i	0.725508	−	0.688214i	$-0.241605\pi$
$12$	1.69960	−	0.333685i	0.490633	−	0.0963267i
$13$	0.341322	+	0.591187i	0.0946657	+	0.163966i	0.909469	−	0.415772i	$-0.136488\pi$
$13$	0.341322	+	0.591187i	0.0946657	+	0.163966i	−0.814803	+	0.579737i	$0.803155\pi$
$14$	0.577888	+	2.58187i	0.154447	+	0.690033i
$15$	2.11007	+	3.24771i	0.544817	+	0.838555i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.72947	+	3.30791i	−1.38960	+	0.802287i	−0.993270	−	0.115821i	$-0.963050\pi$
$17$	−5.72947	+	3.30791i	−1.38960	+	0.802287i	−0.396332	+	0.918107i	$0.629717\pi$
$18$	−2.77731	+	1.13427i	−0.654618	+	0.267349i
$19$	−6.76346	−	3.90489i	−1.55165	−	0.895843i	−0.998008	−	0.0630848i	$-0.979906\pi$
$19$	−6.76346	−	3.90489i	−1.55165	−	0.895843i	−0.553637	−	0.832758i	$-0.686761\pi$
$20$	1.37960	−	1.75975i	0.308487	−	0.393492i
$21$	−1.84371	−	4.19532i	−0.402331	−	0.915494i
$22$	3.95349	−	2.28255i	0.842887	−	0.486641i
$23$	−3.50894			−0.731664			−0.365832	−	0.930681i	$-0.619216\pi$
$23$	−3.50894			−0.731664			−0.365832	+	0.930681i	$0.619216\pi$
$24$	1.13878	+	1.30506i	0.232453	+	0.266394i
$25$	4.80169	+	1.39420i	0.960337	+	0.278841i
$26$	−0.341322	+	0.591187i	−0.0669388	+	0.115941i
$27$	4.34184	−	2.85455i	0.835587	−	0.549358i
$28$	−1.94702	+	1.79140i	−0.367952	+	0.338543i
$29$	−4.33820	−	2.50466i	−0.805583	−	0.465104i	0.0398366	−	0.999206i	$-0.487316\pi$
$29$	−4.33820	−	2.50466i	−0.805583	−	0.465104i	−0.845420	+	0.534103i	$0.820650\pi$
$30$	−1.75757	+	3.45123i	−0.320886	+	0.630105i
$31$	−4.52018	−	2.60973i	−0.811848	−	0.468721i	0.0357493	−	0.999361i	$-0.488618\pi$
$31$	−4.52018	−	2.60973i	−0.811848	−	0.468721i	−0.847597	+	0.530640i	$0.821952\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−5.95771	+	5.19865i	−1.03710	+	0.904969i
$34$	−5.72947	−	3.30791i	−0.982597	−	0.567303i
$35$	−5.34069	−	2.54500i	−0.902742	−	0.430183i
$36$	−2.37096	−	1.83809i	−0.395160	−	0.306348i
$37$	1.37526	+	0.794006i	0.226091	+	0.130534i	0.608767	−	0.793349i	$-0.291664\pi$
$37$	1.37526	+	0.794006i	0.226091	+	0.130534i	−0.382676	+	0.923882i	$0.624998\pi$
$38$		−	7.80978i		−	1.26691i
$39$	0.382842	−	1.11868i	0.0613038	−	0.179132i
$40$	2.21378	+	0.314891i	0.350030	+	0.0497887i
$41$	−3.41784	−	5.91987i	−0.533777	−	0.924528i	−0.999221	−	0.0394513i	$-0.987439\pi$
$41$	−3.41784	−	5.91987i	−0.533777	−	0.924528i	0.465445	−	0.885077i	$-0.345894\pi$
$42$	2.71140	−	3.69436i	0.418378	−	0.570053i
$43$	−2.05488	−	1.18639i	−0.313366	−	0.180922i	0.335066	−	0.942195i	$-0.391242\pi$
$43$	−2.05488	−	1.18639i	−0.313366	−	0.180922i	−0.648432	+	0.761273i	$0.724575\pi$
$44$	3.95349	+	2.28255i	0.596011	+	0.344107i
$45$	1.83554	−	6.45219i	0.273626	−	0.961836i
$46$	−1.75447	−	3.03883i	−0.258682	−	0.448051i
$47$	−3.30466	+	1.90795i	−0.482034	+	0.278303i	−0.721264	−	0.692660i	$-0.756438\pi$
$47$	−3.30466	+	1.90795i	−0.482034	+	0.278303i	0.239230	+	0.970963i	$0.423105\pi$
$48$	−0.560822	+	1.63874i	−0.0809477	+	0.236532i
$49$	5.75032	+	3.99172i	0.821474	+	0.570246i
$50$	1.19343	+	4.85548i	0.168776	+	0.686669i
$51$	10.8416	+	3.71030i	1.51813	+	0.519546i
$52$	−0.682644			−0.0946657
$53$	−0.983879	−	1.70413i	−0.135146	−	0.234080i	0.790507	−	0.612453i	$-0.209817\pi$
$53$	−0.983879	−	1.70413i	−0.135146	−	0.234080i	−0.925653	+	0.378373i	$0.876484\pi$
$54$	4.64303	+	2.33287i	0.631837	+	0.317463i
$55$	−1.43751	+	10.1061i	−0.193834	+	1.36271i
$56$	−2.52491	−	0.790468i	−0.337405	−	0.105631i
$57$	2.60601	+	13.2735i	0.345174	+	1.75812i
$58$		−	5.00932i		−	0.657756i
$59$	4.68295	−	8.11110i	0.609668	−	1.05598i	−0.381627	−	0.924316i	$-0.624636\pi$
$59$	4.68295	−	8.11110i	0.609668	−	1.05598i	0.991295	−	0.131659i	$-0.0420304\pi$
$60$	−3.86763	+	0.203517i	−0.499309	+	0.0262740i
$61$	−12.3974	+	7.15763i	−1.58732	+	0.916440i	−0.593575	+	0.804779i	$0.702284\pi$
$61$	−12.3974	+	7.15763i	−1.58732	+	0.916440i	−0.993746	+	0.111661i	$0.964383\pi$
$62$		−	5.21945i		−	0.662871i
$63$	−3.37555	+	7.18371i	−0.425279	+	0.905062i
$64$	1.00000			0.125000
$65$	−0.569454	−	1.41624i	−0.0706321	−	0.175663i
$66$	−7.48102	−	2.56021i	−0.920850	−	0.315140i
$67$	6.28937	+	3.63117i	0.768369	+	0.443618i	0.832292	−	0.554337i	$-0.187028\pi$
$67$	6.28937	+	3.63117i	0.768369	+	0.443618i	−0.0639235	+	0.997955i	$0.520361\pi$
$68$		−	6.61583i		−	0.802287i
$69$	3.99592	+	4.57937i	0.481052	+	0.551291i
$70$	−0.466313	−	5.89767i	−0.0557350	−	0.704907i
$71$			8.48088i			1.00650i	0.864142	+	0.503248i	$0.167862\pi$
$71$			8.48088i			1.00650i	−0.864142	+	0.503248i	$0.832138\pi$
$72$	0.406351	−	2.97235i	0.0478889	−	0.350295i
$73$	−0.735176	−	1.27336i	−0.0860458	−	0.149036i	0.819791	−	0.572663i	$-0.194090\pi$
$73$	−0.735176	−	1.27336i	−0.0860458	−	0.149036i	−0.905836	+	0.423628i	$0.860756\pi$
$74$			1.58801i			0.184603i
$75$	−3.64856	−	7.85417i	−0.421299	−	0.906922i
$76$	6.76346	−	3.90489i	0.775823	−	0.447921i
$77$	3.60856	−	11.5264i	0.411234	−	1.31356i
$78$	1.16023	−	0.227788i	0.131370	−	0.0257920i
$79$	−0.587811	−	1.01812i	−0.0661339	−	0.114547i	0.831062	−	0.556179i	$-0.187733\pi$
$79$	−0.587811	−	1.01812i	−0.0661339	−	0.114547i	−0.897196	+	0.441632i	$0.854400\pi$
$80$	0.834189	+	2.07464i	0.0932651	+	0.231952i
$81$	−8.66976	−	2.41564i	−0.963306	−	0.268404i
$82$	3.41784	−	5.91987i	0.377437	−	0.653740i
$83$	9.77023	+	5.64084i	1.07242	+	0.619163i	0.928842	−	0.370476i	$-0.120805\pi$
$83$	9.77023	+	5.64084i	1.07242	+	0.619163i	0.143580	+	0.989639i	$0.454139\pi$
$84$	4.55511	+	0.500958i	0.497003	+	0.0546590i
$85$	13.7255	−	5.51885i	1.48873	−	0.598603i
$86$		−	2.37277i		−	0.255863i
$87$	1.67154	+	8.51386i	0.179208	+	0.912782i
$88$			4.56510i			0.486641i
$89$	0.739183	−	1.28030i	0.0783532	−	0.135712i	−0.824186	−	0.566319i	$-0.808367\pi$
$89$	0.739183	−	1.28030i	0.0783532	−	0.135712i	0.902540	+	0.430607i	$0.141700\pi$
$90$	6.50553	−	1.63647i	0.685743	−	0.172499i
$91$	0.394492	+	1.76250i	0.0413540	+	0.184760i
$92$	1.75447	−	3.03883i	0.182916	−	0.316820i
$93$	1.74165	+	8.87100i	0.180601	+	0.919880i
$94$	−3.30466	−	1.90795i	−0.340850	−	0.196790i
$95$	13.7432	+	10.7743i	1.41003	+	1.10542i
$96$	−1.69960	+	0.333685i	−0.173465	+	0.0340566i
$97$	4.40260	−	7.62553i	0.447017	−	0.774255i	−0.551174	−	0.834391i	$-0.685820\pi$
$97$	4.40260	−	7.62553i	0.447017	−	0.774255i	0.998190	+	0.0601352i	$0.0191532\pi$
$98$	−0.581771	+	6.97578i	−0.0587677	+	0.704660i
$99$	13.5691	+	1.85503i	1.36374	+	0.186438i
$100$	−3.60826	+	3.46128i	−0.360826	+	0.346128i
$101$	0.894182			0.0889745			0.0444872	−	0.999010i	$-0.485835\pi$
$101$	0.894182			0.0889745			0.0444872	+	0.999010i	$0.485835\pi$
$102$	2.20760	+	11.2443i	0.218585	+	1.11335i
$103$	13.5510			1.33522			0.667611	−	0.744510i	$-0.267317\pi$
$103$	13.5510			1.33522			0.667611	+	0.744510i	$0.267317\pi$
$104$	−0.341322	−	0.591187i	−0.0334694	−	0.0579707i
$105$	2.76051	+	9.86811i	0.269399	+	0.963029i
$106$	0.983879	−	1.70413i	0.0955628	−	0.165520i
$107$	2.12855	−	3.68676i	0.205775	−	0.356412i	−0.744605	−	0.667506i	$-0.767362\pi$
$107$	2.12855	−	3.68676i	0.205775	−	0.356412i	0.950379	+	0.311094i	$0.100695\pi$
$108$	0.301195	+	5.18742i	0.0289825	+	0.499159i
$109$	3.35599	+	5.81274i	0.321445	+	0.556760i	0.980786	−	0.195084i	$-0.0624980\pi$
$109$	3.35599	+	5.81274i	0.321445	+	0.556760i	−0.659341	+	0.751844i	$0.729165\pi$
$110$	−9.47093	+	3.80815i	−0.903018	+	0.363093i
$111$	−0.529896	−	2.69899i	−0.0502955	−	0.256177i
$112$	−0.577888	−	2.58187i	−0.0546053	−	0.243964i
$113$	−3.41846	−	5.92094i	−0.321581	−	0.556995i	0.659233	−	0.751939i	$-0.270881\pi$
$113$	−3.41846	−	5.92094i	−0.321581	−	0.556995i	−0.980814	+	0.194943i	$0.937548\pi$
$114$	−10.1922	+	8.89363i	−0.954588	+	0.832965i
$115$	7.76804	+	1.10493i	0.724373	+	0.103036i
$116$	4.33820	−	2.50466i	0.402792	−	0.232552i
$117$	−1.89591	+	0.774300i	−0.175277	+	0.0715841i
$118$	9.36589			0.862200
$119$	−17.0812	+	3.82321i	−1.56583	+	0.350473i
$120$	−2.11007	−	3.24771i	−0.192622	−	0.296474i
$121$	−9.84010			−0.894554
$122$	−12.3974	−	7.15763i	−1.12241	−	0.648021i
$123$	−3.83360	+	11.2019i	−0.345664	+	1.01004i
$124$	4.52018	−	2.60973i	0.405924	−	0.234360i
$125$	−10.1909	−	4.59847i	−0.911500	−	0.411300i
$126$	−7.90905	+	0.668543i	−0.704594	+	0.0595586i
$127$			11.2278i			0.996304i	0.867090	+	0.498152i	$0.165988\pi$
$127$			11.2278i			0.996304i	−0.867090	+	0.498152i	$0.834012\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	0.791759	+	4.03277i	0.0697105	+	0.355066i
$130$	0.941774	−	1.20128i	0.0825990	−	0.105359i
$131$	−2.26585			−0.197968			−0.0989842	−	0.995089i	$-0.531559\pi$
$131$	−2.26585			−0.197968			−0.0989842	+	0.995089i	$0.531559\pi$
$132$	−1.52331	−	7.75886i	−0.132587	−	0.675322i
$133$	−13.9904	−	15.2058i	−1.21312	−	1.31851i
$134$			7.26234i			0.627371i
$135$	−10.5108	+	4.95215i	−0.904623	+	0.426214i
$136$	5.72947	−	3.30791i	0.491298	−	0.283651i
$137$	−3.86237			−0.329985			−0.164992	−	0.986295i	$-0.552760\pi$
$137$	−3.86237			−0.329985			−0.164992	+	0.986295i	$0.552760\pi$
$138$	−1.96789	+	5.75025i	−0.167518	+	0.489494i
$139$	11.4418	−	6.60593i	0.970482	−	0.560308i	0.0710985	−	0.997469i	$-0.477350\pi$
$139$	11.4418	−	6.60593i	0.970482	−	0.560308i	0.899383	+	0.437161i	$0.144016\pi$
$140$	4.87438	−	3.35268i	0.411960	−	0.283353i
$141$	6.25327	+	2.14004i	0.526620	+	0.180224i
$142$	−7.34466	+	4.24044i	−0.616350	+	0.355850i
$143$	2.69883	−	1.55817i	0.225687	−	0.130301i
$144$	2.77731	−	1.13427i	0.231442	−	0.0945222i
$145$	8.81514	+	6.91084i	0.732058	+	0.573914i
$146$	0.735176	−	1.27336i	0.0608436	−	0.105384i
$147$	−1.33894	−	12.0502i	−0.110434	−	0.993883i
$148$	−1.37526	+	0.794006i	−0.113046	+	0.0652669i
$149$		−	4.30568i		−	0.352735i	−0.984324	−	0.176367i	$-0.943565\pi$
$149$		−	4.30568i		−	0.352735i	0.984324	−	0.176367i	$-0.0564347\pi$
$150$	4.97763	−	7.08683i	0.406422	−	0.578637i
$151$	16.0440			1.30565			0.652823	−	0.757511i	$-0.273585\pi$
$151$	16.0440			1.30565			0.652823	+	0.757511i	$0.273585\pi$
$152$	6.76346	+	3.90489i	0.548589	+	0.316728i
$153$	−7.50411	−	18.3742i	−0.606671	−	1.48547i
$154$	11.7865	−	2.63812i	0.949781	−	0.212585i
$155$	9.18492	+	7.20074i	0.737751	+	0.578377i
$156$	0.777383	+	0.890890i	0.0622405	+	0.0713283i
$157$	−5.05908	+	8.76259i	−0.403759	+	0.699330i	−0.994176	−	0.107768i	$-0.965630\pi$
$157$	−5.05908	+	8.76259i	−0.403759	+	0.699330i	0.590417	+	0.807098i	$0.298963\pi$
$158$	0.587811	−	1.01812i	0.0467637	−	0.0809972i
$159$	−1.10356	+	3.22465i	−0.0875182	+	0.255731i
$160$	−1.37960	+	1.75975i	−0.109067	+	0.139120i
$161$	−8.85975	−	2.77371i	−0.698246	−	0.218599i
$162$	−2.24288	−	8.71605i	−0.176217	−	0.684797i
$163$	−19.6914	−	11.3688i	−1.54235	−	0.890476i	−0.998690	−	0.0511701i	$-0.983705\pi$
$163$	−19.6914	−	11.3688i	−1.54235	−	0.890476i	−0.543660	−	0.839306i	$-0.682962\pi$
$164$	6.83568			0.533777
$165$	14.8261	−	9.63266i	1.15421	−	0.749901i
$166$			11.2817i			0.875629i
$167$	−11.3198	+	6.53552i	−0.875956	+	0.505733i	−0.869323	−	0.494245i	$-0.835445\pi$
$167$	−11.3198	+	6.53552i	−0.875956	+	0.505733i	−0.00663315	+	0.999978i	$0.502111\pi$
$168$	1.84371	+	4.19532i	0.142246	+	0.323676i
$169$	6.26700	−	10.8548i	0.482077	−	0.834982i
$170$	11.6422	+	9.12717i	0.892915	+	0.700022i
$171$	14.3550	−	18.5166i	1.09776	−	1.41600i
$172$	2.05488	−	1.18639i	0.156683	−	0.0904611i
$173$	−0.603730	+	0.348564i	−0.0459007	+	0.0265008i	−0.522775	−	0.852471i	$-0.675103\pi$
$173$	−0.603730	+	0.348564i	−0.0459007	+	0.0265008i	0.476874	+	0.878972i	$0.341770\pi$
$174$	−6.53745	+	5.70452i	−0.495603	+	0.432459i
$175$	11.0217	+	7.31582i	0.833166	+	0.553024i
$176$	−3.95349	+	2.28255i	−0.298005	+	0.172054i
$177$	−15.9183	+	3.12526i	−1.19649	+	0.234909i
$178$	1.47837			0.110808
$179$	−10.6754	+	6.16342i	−0.797913	+	0.460675i	−0.842741	−	0.538319i	$-0.819059\pi$
$179$	−10.6754	+	6.16342i	−0.797913	+	0.460675i	0.0448277	+	0.998995i	$0.485726\pi$
$180$	4.66999	+	4.81572i	0.348081	+	0.358943i
$181$		−	11.6266i		−	0.864199i	−0.901826	−	0.432100i	$-0.857773\pi$
$181$		−	11.6266i		−	0.864199i	0.901826	−	0.432100i	$-0.142227\pi$
$182$	−1.32912	+	1.22289i	−0.0985211	+	0.0906466i
$183$	23.4590	+	8.02831i	1.73414	+	0.593470i
$184$	3.50894			0.258682
$185$	−2.79450	−	2.19081i	−0.205456	−	0.161072i
$186$	−6.81169	+	5.94382i	−0.499457	+	0.435822i
$187$	15.1009	+	26.1556i	1.10429	+	1.91269i
$188$		−	3.81589i		−	0.278303i
$189$	13.2192	−	3.77539i	0.961553	−	0.274619i
$190$	−2.45923	+	17.2892i	−0.178411	+	1.25429i
$191$	−0.510138	+	0.294528i	−0.0369123	+	0.0213113i	−0.518343	−	0.855173i	$-0.673451\pi$
$191$	−0.510138	+	0.294528i	−0.0369123	+	0.0213113i	0.481430	+	0.876484i	$0.340117\pi$
$192$	−1.13878	−	1.30506i	−0.0821845	−	0.0941844i
$193$	−12.1383	−	7.00807i	−0.873736	−	0.504452i	−0.00514832	−	0.999987i	$-0.501639\pi$
$193$	−12.1383	−	7.00807i	−0.873736	−	0.504452i	−0.868588	+	0.495535i	$0.834972\pi$
$194$	8.80520			0.632177
$195$	−1.19979	+	2.35596i	−0.0859189	+	0.168714i
$196$	−6.33209	+	2.98406i	−0.452292	+	0.213147i
$197$	−10.4933			−0.747615			−0.373808	−	0.927506i	$-0.621948\pi$
$197$	−10.4933			−0.747615			−0.373808	+	0.927506i	$0.621948\pi$
$198$	5.17803	+	12.6787i	0.367987	+	0.901034i
$199$	−19.0237	+	10.9833i	−1.34855	+	0.778587i	−0.988045	−	0.154169i	$-0.950730\pi$
$199$	−19.0237	+	10.9833i	−1.34855	+	0.778587i	−0.360508	+	0.932756i	$0.617397\pi$
$200$	−4.80169	−	1.39420i	−0.339531	−	0.0985850i
$201$	−2.42334	−	12.3431i	−0.170929	−	0.870615i
$202$	0.447091	+	0.774384i	0.0314572	+	0.0544855i
$203$	−8.97370	−	9.75324i	−0.629830	−	0.684543i
$204$	−8.63404	+	7.53399i	−0.604503	+	0.527484i
$205$	5.70224	+	14.1816i	0.398262	+	0.990483i
$206$	6.77551	+	11.7355i	0.472072	+	0.817653i
$207$	1.42586	−	10.4298i	0.0991042	−	0.724922i
$208$	0.341322	−	0.591187i	0.0236664	−	0.0409915i
$209$	−17.8262	+	30.8759i	−1.23306	+	2.13573i
$210$	−7.16578	+	7.32473i	−0.494485	+	0.505454i
$211$	−6.82852	−	11.8273i	−0.470095	−	0.814228i	0.529320	−	0.848422i	$-0.322447\pi$
$211$	−6.82852	−	11.8273i	−0.470095	−	0.814228i	−0.999415	+	0.0341938i	$0.989114\pi$
$212$	1.96776			0.135146
$213$	11.0680	−	9.65787i	0.758369	−	0.661746i
$214$	4.25710			0.291009
$215$	4.17548	+	3.27347i	0.284765	+	0.223249i
$216$	−4.34184	+	2.85455i	−0.295425	+	0.194228i
$217$	−9.35013	−	10.1624i	−0.634728	−	0.689867i
$218$	−3.35599	+	5.81274i	−0.227296	+	0.393689i
$219$	−0.824606	+	2.40953i	−0.0557217	+	0.162821i
$220$	−8.03342	−	6.29799i	−0.541613	−	0.424610i
$221$	−3.91119	−	2.25813i	−0.263095	−	0.151898i
$222$	2.07245	−	1.80840i	0.139094	−	0.121372i
$223$	13.5359	−	23.4449i	0.906433	−	1.56999i	0.0874521	−	0.996169i	$-0.472128\pi$
$223$	13.5359	−	23.4449i	0.906433	−	1.56999i	0.818981	−	0.573820i	$-0.194539\pi$
$224$	1.94702	−	1.79140i	0.130091	−	0.119693i
$225$	−6.09523	+	13.7058i	−0.406349	+	0.913718i
$226$	3.41846	−	5.92094i	0.227392	−	0.393855i
$227$			7.76228i			0.515200i	0.966252	+	0.257600i	$0.0829317\pi$
$227$			7.76228i			0.515200i	−0.966252	+	0.257600i	$0.917068\pi$
$228$	−12.7982	−	4.37989i	−0.847583	−	0.290066i
$229$			0.498498i			0.0329417i	0.999864	+	0.0164708i	$0.00524307\pi$
$229$			0.498498i			0.0329417i	−0.999864	+	0.0164708i	$0.994757\pi$
$230$	2.92712	+	7.27978i	0.193008	+	0.480015i
$231$	−19.1520	+	8.41673i	−1.26011	+	0.553780i
$232$	4.33820	+	2.50466i	0.284817	+	0.164439i
$233$	−8.94844	+	15.4992i	−0.586232	+	1.01538i	0.408489	+	0.912763i	$0.366056\pi$
$233$	−8.94844	+	15.4992i	−0.586232	+	1.01538i	−0.994721	+	0.102620i	$0.967277\pi$
$234$	−1.61852	−	1.25476i	−0.105806	−	0.0820262i
$235$	7.91660	−	3.18317i	0.516422	−	0.207647i
$236$	4.68295	+	8.11110i	0.304834	+	0.527988i
$237$	−0.659315	+	1.92654i	−0.0428271	+	0.125142i
$238$	−11.8516	−	12.8811i	−0.768225	−	0.834961i
$239$	23.9059	−	13.8021i	1.54634	−	0.892781i	0.547925	−	0.836527i	$-0.315418\pi$
$239$	23.9059	−	13.8021i	1.54634	−	0.892781i	0.998417	−	0.0562537i	$-0.0179156\pi$
$240$	1.75757	−	3.45123i	0.113450	−	0.222776i
$241$			14.0418i			0.904514i	0.891888	+	0.452257i	$0.149381\pi$
$241$			14.0418i			0.904514i	−0.891888	+	0.452257i	$0.850619\pi$
$242$	−4.92005	−	8.52177i	−0.316273	−	0.547800i
$243$	6.72042	+	14.0654i	0.431115	+	0.902297i
$244$		−	14.3153i		−	0.916440i
$245$	−11.4730	−	10.6475i	−0.732984	−	0.680246i
$246$	−11.6179	+	2.28096i	−0.740733	+	0.145429i
$247$		−	5.33130i		−	0.339222i
$248$	4.52018	+	2.60973i	0.287032	+	0.165718i
$249$	−3.76453	−	19.1744i	−0.238568	−	1.21513i
$250$	−1.11304	−	11.1248i	−0.0703951	−	0.703594i
$251$	16.0764			1.01473			0.507367	−	0.861730i	$-0.330619\pi$
$251$	16.0764			1.01473			0.507367	+	0.861730i	$0.330619\pi$
$252$	−4.53350	−	6.51517i	−0.285584	−	0.410417i
$253$			16.0186i			1.00708i
$254$	−9.72354	+	5.61389i	−0.610109	+	0.352247i
$255$	−22.8327	−	11.6277i	−1.42984	−	0.728158i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$			25.4828i			1.58957i	0.606891	+	0.794785i	$0.292417\pi$
$257$			25.4828i			1.58957i	−0.606891	+	0.794785i	$0.707583\pi$
$258$	−3.09660	+	2.70207i	−0.192786	+	0.168224i
$259$	2.84476	+	3.09189i	0.176765	+	0.192121i
$260$	1.51123	+	0.214959i	0.0937224	+	0.0133312i
$261$	9.20756	−	11.8769i	0.569934	−	0.735161i
$262$	−1.13293	−	1.96229i	−0.0699924	−	0.121230i
$263$	25.4304			1.56811			0.784054	−	0.620693i	$-0.213149\pi$
$263$	25.4304			1.56811			0.784054	+	0.620693i	$0.213149\pi$
$264$	5.95771	−	5.19865i	0.366672	−	0.319955i
$265$	1.64148	+	4.08239i	0.100835	+	0.250779i
$266$	6.17338	−	19.7190i	0.378514	−	1.20905i
$267$	−2.51264	+	0.493309i	−0.153771	+	0.0301900i
$268$	−6.28937	+	3.63117i	−0.384185	+	0.221809i
$269$	12.2442	+	21.2076i	0.746544	+	1.29305i	0.949470	+	0.313858i	$0.101621\pi$
$269$	12.2442	+	21.2076i	0.746544	+	1.29305i	−0.202926	+	0.979194i	$0.565045\pi$
$270$	−9.54407	−	6.62651i	−0.580834	−	0.403277i
$271$	−17.8062	−	10.2804i	−1.08165	−	0.624492i	−0.150311	−	0.988639i	$-0.548027\pi$
$271$	−17.8062	−	10.2804i	−1.08165	−	0.624492i	−0.931342	+	0.364147i	$0.881361\pi$
$272$	5.72947	+	3.30791i	0.347400	+	0.200572i
$273$	1.85092	−	2.52194i	0.112023	−	0.152635i
$274$	−1.93119	−	3.34491i	−0.116667	−	0.202074i
$275$	6.36467	−	21.9202i	0.383804	−	1.32184i
$276$	−5.96381	+	1.17088i	−0.358979	+	0.0704788i
$277$		−	1.96358i		−	0.117980i	−0.998259	−	0.0589902i	$-0.981212\pi$
$277$		−	1.96358i		−	0.117980i	0.998259	−	0.0589902i	$-0.0187881\pi$
$278$	11.4418	+	6.60593i	0.686234	+	0.396197i
$279$	9.59380	−	12.3751i	0.574366	−	0.740878i
$280$	5.34069	+	2.54500i	0.319167	+	0.152093i
$281$	−25.5282	−	14.7387i	−1.52288	−	0.879237i	−0.999634	−	0.0270583i	$-0.991386\pi$
$281$	−25.5282	−	14.7387i	−1.52288	−	0.879237i	−0.523250	−	0.852179i	$-0.675281\pi$
$282$	1.27331	+	6.48551i	0.0758244	+	0.386206i
$283$	−12.5657	+	21.7644i	−0.746951	+	1.29376i	0.202326	+	0.979318i	$0.435150\pi$
$283$	−12.5657	+	21.7644i	−0.746951	+	1.29376i	−0.949278	+	0.314439i	$0.898183\pi$
$284$	−7.34466	−	4.24044i	−0.435825	−	0.251624i
$285$	−1.58942	−	30.2053i	−0.0941493	−	1.78921i
$286$	2.69883	+	1.55817i	0.159585	+	0.0921364i
$287$	−3.95026	−	17.6488i	−0.233176	−	1.04178i
$288$	2.37096	+	1.83809i	0.139710	+	0.108310i
$289$	13.3846	−	23.1828i	0.787329	−	1.36369i
$290$	−1.57739	+	11.0896i	−0.0926276	+	0.651201i
$291$	−14.9654	+	2.93817i	−0.877285	+	0.172238i
$292$	1.47035			0.0860458
$293$	26.8539	−	15.5041i	1.56882	−	0.905761i	0.572517	−	0.819893i	$-0.305967\pi$
$293$	26.8539	−	15.5041i	1.56882	−	0.905761i	0.996307	−	0.0858678i	$-0.0273663\pi$
$294$	9.76631	−	7.18465i	0.569583	−	0.419017i
$295$	−12.9211	+	16.4816i	−0.752298	+	0.959597i
$296$	−1.37526	−	0.794006i	−0.0799353	−	0.0461507i
$297$	−13.0313	−	19.8209i	−0.756152	−	1.15013i
$298$	3.72883	−	2.15284i	0.216005	−	0.124711i
$299$	−1.19768	−	2.07444i	−0.0692636	−	0.119968i
$300$	8.62619	+	0.767340i	0.498033	+	0.0443024i
$301$	−4.25058	−	4.61983i	−0.245000	−	0.266283i
$302$	8.02202	+	13.8945i	0.461615	+	0.799541i
$303$	−1.01828	−	1.16696i	−0.0584986	−	0.0670401i
$304$			7.80978i			0.447921i
$305$	29.6990	−	11.9416i	1.70056	−	0.683775i
$306$	12.1605	−	15.6858i	0.695167	−	0.896700i
$307$	−4.89776			−0.279530			−0.139765	−	0.990185i	$-0.544635\pi$
$307$	−4.89776			−0.279530			−0.139765	+	0.990185i	$0.544635\pi$
$308$	8.17791	+	8.88833i	0.465980	+	0.506460i
$309$	−15.4317	−	17.6849i	−0.877876	−	1.00606i
$310$	−1.64356	+	11.5547i	−0.0933479	+	0.656265i
$311$	4.53478	−	7.85447i	0.257144	−	0.445386i	−0.708332	−	0.705880i	$-0.750552\pi$
$311$	4.53478	−	7.85447i	0.257144	−	0.445386i	0.965476	+	0.260493i	$0.0838852\pi$
$312$	−0.382842	+	1.11868i	−0.0216742	+	0.0633327i
$313$	−15.0417	−	26.0531i	−0.850209	−	1.47261i	−0.881019	−	0.473081i	$-0.843142\pi$
$313$	−15.0417	−	26.0531i	−0.850209	−	1.47261i	0.0308097	−	0.999525i	$-0.490191\pi$
$314$	−10.1182			−0.571001
$315$	9.73483	−	14.8403i	0.548495	−	0.836154i
$316$	1.17562			0.0661339
$317$	−1.68610	−	2.92040i	−0.0947006	−	0.164026i	0.814783	−	0.579766i	$-0.196856\pi$
$317$	−1.68610	−	2.92040i	−0.0947006	−	0.164026i	−0.909484	+	0.415740i	$0.863523\pi$
$318$	−3.34441	+	0.656612i	−0.187545	+	0.0368210i
$319$	−11.4340	+	19.8043i	−0.640182	+	1.10883i
$320$	−2.21378	−	0.314891i	−0.123754	−	0.0176030i
$321$	−7.23539	+	1.42053i	−0.403840	+	0.0792864i
$322$	−2.02778	−	9.05962i	−0.113003	−	0.504873i
$323$	51.6681			2.87489
$324$	6.42688	−	6.30041i	0.357049	−	0.350023i
$325$	0.814687	+	3.31457i	0.0451907	+	0.183859i
$326$		−	22.7377i		−	1.25932i
$327$	3.76422	−	10.9992i	0.208162	−	0.608257i
$328$	3.41784	+	5.91987i	0.188719	+	0.326870i
$329$	−9.85213	+	2.20516i	−0.543166	+	0.121574i
$330$	15.7552	+	8.02345i	0.867294	+	0.441677i
$331$	−5.46742	−	9.46984i	−0.300516	−	0.520510i	0.675737	−	0.737143i	$-0.263826\pi$
$331$	−5.46742	−	9.46984i	−0.300516	−	0.520510i	−0.976253	+	0.216634i	$0.930492\pi$
$332$	−9.77023	+	5.64084i	−0.536211	+	0.309582i
$333$	−2.91890	+	3.76511i	−0.159955	+	0.206327i
$334$	−11.3198	−	6.53552i	−0.619394	−	0.357608i
$335$	−12.7799	−	10.0191i	−0.698240	−	0.547402i
$336$	−2.71140	+	3.69436i	−0.147919	+	0.201544i
$337$	1.26189	−	0.728550i	0.0687393	−	0.0396867i	−0.465236	−	0.885186i	$-0.654031\pi$
$337$	1.26189	−	0.728550i	0.0687393	−	0.0396867i	0.533976	+	0.845500i	$0.320697\pi$
$338$	12.5340			0.681760
$339$	−3.83429	+	11.2039i	−0.208250	+	0.608514i
$340$	−2.08327	+	14.6460i	−0.112981	+	0.794292i
$341$	−11.9136	+	20.6350i	−0.645160	+	1.11745i
$342$	23.2134	+	3.17351i	1.25524	+	0.171604i
$343$	11.3637	+	14.6242i	0.613582	+	0.789631i
$344$	2.05488	+	1.18639i	0.110792	+	0.0639656i
$345$	−7.40410	−	11.3960i	−0.398623	−	0.613541i
$346$	−0.603730	−	0.348564i	−0.0324567	−	0.0187389i
$347$	−17.9097	+	31.0205i	−0.961443	+	1.66527i	−0.242562	+	0.970136i	$0.577988\pi$
$347$	−17.9097	+	31.0205i	−0.961443	+	1.66527i	−0.718881	+	0.695133i	$0.755346\pi$
$348$	−8.20899	−	2.80934i	−0.440048	−	0.150596i
$349$	−2.63799	−	1.52304i	−0.141208	−	0.0815266i	0.427731	−	0.903906i	$-0.359313\pi$
$349$	−2.63799	−	1.52304i	−0.141208	−	0.0815266i	−0.568940	+	0.822379i	$0.692646\pi$
$350$	−0.824810	+	13.2030i	−0.0440879	+	0.705731i
$351$	3.16954	+	1.59252i	0.169177	+	0.0850023i
$352$	−3.95349	−	2.28255i	−0.210722	−	0.121660i
$353$		−	34.1324i		−	1.81668i	−0.418229	−	0.908342i	$-0.637349\pi$
$353$		−	34.1324i		−	1.81668i	0.418229	−	0.908342i	$-0.362651\pi$
$354$	−10.6657	−	12.2230i	−0.566876	−	0.649647i
$355$	2.67055	−	18.7748i	0.141738	−	0.996465i
$356$	0.739183	+	1.28030i	0.0391766	+	0.0678559i
$357$	24.4413	+	17.9381i	1.29357	+	0.949387i
$358$	−10.6754	−	6.16342i	−0.564210	−	0.325747i
$359$	−21.0726	−	12.1663i	−1.11217	−	0.642110i	−0.172778	−	0.984961i	$-0.555274\pi$
$359$	−21.0726	−	12.1663i	−1.11217	−	0.642110i	−0.939390	+	0.342851i	$0.888608\pi$
$360$	−1.83554	+	6.45219i	−0.0967415	+	0.340060i
$361$	20.9963	+	36.3667i	1.10507	+	1.91404i
$362$	10.0689	−	5.81331i	0.529212	−	0.305541i
$363$	11.2057	+	12.8419i	0.588148	+	0.674025i
$364$	−1.72361	−	0.539609i	−0.0903419	−	0.0282832i
$365$	1.22655	+	3.05045i	0.0642006	+	0.159668i
$366$	4.77679	+	24.3303i	0.249687	+	1.27176i
$367$	−13.4469			−0.701921			−0.350960	−	0.936390i	$-0.614145\pi$
$367$	−13.4469			−0.701921			−0.350960	+	0.936390i	$0.614145\pi$
$368$	1.75447	+	3.03883i	0.0914581	+	0.158410i
$369$	18.9848	−	7.75347i	0.988308	−	0.403630i
$370$	0.500051	−	3.51552i	0.0259964	−	0.182763i
$371$	−1.13714	−	5.08049i	−0.0590376	−	0.263766i
$372$	−8.55334	−	2.92718i	−0.443470	−	0.151767i
$373$		−	2.80160i		−	0.145061i	−0.997366	−	0.0725306i	$-0.976892\pi$
$373$		−	2.80160i		−	0.145061i	0.997366	−	0.0725306i	$-0.0231075\pi$
$374$	−15.1009	+	26.1556i	−0.780851	+	1.35247i
$375$	5.60392	+	18.5363i	0.289385	+	0.957213i
$376$	3.30466	−	1.90795i	0.170425	−	0.0983948i
$377$		−	3.41958i		−	0.176117i
$378$	9.87917	+	9.56044i	0.508130	+	0.491736i
$379$	−13.2036			−0.678225			−0.339112	−	0.940746i	$-0.610127\pi$
$379$	−13.2036			−0.678225			−0.339112	+	0.940746i	$0.610127\pi$
$380$	−16.2025	+	6.51483i	−0.831169	+	0.334204i
$381$	14.6529	−	12.7860i	0.750691	−	0.655046i
$382$	−0.510138	−	0.294528i	−0.0261009	−	0.0150694i
$383$		−	3.19887i		−	0.163454i	−0.996655	−	0.0817272i	$-0.973956\pi$
$383$		−	3.19887i		−	0.163454i	0.996655	−	0.0817272i	$-0.0260436\pi$
$384$	0.560822	−	1.63874i	0.0286193	−	0.0836268i
$385$	−11.6182	+	24.3808i	−0.592116	+	1.24256i
$386$		−	14.0161i		−	0.713403i
$387$	4.36136	−	5.62574i	0.221700	−	0.285972i
$388$	4.40260	+	7.62553i	0.223508	+	0.387128i
$389$		−	18.6567i		−	0.945932i	−0.881081	−	0.472966i	$-0.843183\pi$
$389$		−	18.6567i		−	0.945932i	0.881081	−	0.472966i	$-0.156817\pi$
$390$	−2.64022	+	0.138930i	−0.133693	+	0.00703499i
$391$	20.1044	−	11.6073i	1.01672	−	0.587005i
$392$	−5.75032	−	3.99172i	−0.290435	−	0.201612i
$393$	2.58031	+	2.95707i	0.130159	+	0.149164i
$394$	−5.24664	−	9.08745i	−0.264322	−	0.457819i
$395$	0.980691	+	2.43899i	0.0493439	+	0.122719i
$396$	−8.39104	+	10.8236i	−0.421666	+	0.543909i
$397$	5.38403	−	9.32542i	0.270217	−	0.468029i	−0.698700	−	0.715414i	$-0.746238\pi$
$397$	5.38403	−	9.32542i	0.270217	−	0.468029i	0.968917	+	0.247385i	$0.0795713\pi$
$398$	−19.0237	−	10.9833i	−0.953571	−	0.550544i
$399$	−3.91237	+	35.5744i	−0.195864	+	1.78095i
$400$	−1.19343	−	4.85548i	−0.0596714	−	0.242774i
$401$			3.28767i			0.164178i	0.996625	+	0.0820891i	$0.0261592\pi$
$401$			3.28767i			0.164178i	−0.996625	+	0.0820891i	$0.973841\pi$
$402$	9.47777	−	8.27022i	0.472708	−	0.412481i
$403$		−	3.56303i		−	0.177487i
$404$	−0.447091	+	0.774384i	−0.0222436	+	0.0385271i
$405$	18.4323	+	8.07773i	0.915909	+	0.401386i
$406$	3.95971	−	12.6481i	0.196517	−	0.627713i
$407$	3.62471	−	6.27819i	0.179670	−	0.311198i
$408$	−10.8416	−	3.71030i	−0.536741	−	0.183687i
$409$	25.1059	+	14.4949i	1.24140	+	0.716725i	0.969380	−	0.245565i	$-0.0789734\pi$
$409$	25.1059	+	14.4949i	1.24140	+	0.716725i	0.272025	+	0.962290i	$0.412307\pi$
$410$	−9.43047	+	12.0291i	−0.465738	+	0.594073i
$411$	4.39840	+	5.04062i	0.216957	+	0.248635i
$412$	−6.77551	+	11.7355i	−0.333805	+	0.578168i
$413$	18.2356	−	16.7781i	0.897314	−	0.825594i
$414$	9.74541	−	3.98007i	0.478961	−	0.195610i
$415$	−19.8529	−	15.5642i	−0.974542	−	0.764015i
$416$	0.682644			0.0334694
$417$	−21.6508	−	7.40950i	−1.06025	−	0.362845i
$418$	−35.6524			−1.74381
$419$	−15.2535	−	26.4199i	−0.745183	−	1.29069i	−0.950109	−	0.311917i	$-0.899029\pi$
$419$	−15.2535	−	26.4199i	−0.745183	−	1.29069i	0.204926	−	0.978777i	$-0.434305\pi$
$420$	−9.92629	−	2.54338i	−0.484353	−	0.124104i
$421$	3.34147	−	5.78760i	0.162853	−	0.282070i	−0.773038	−	0.634360i	$-0.781264\pi$
$421$	3.34147	−	5.78760i	0.162853	−	0.282070i	0.935891	+	0.352290i	$0.114597\pi$
$422$	6.82852	−	11.8273i	0.332407	−	0.575746i
$423$	−4.32824	−	10.5979i	−0.210446	−	0.515288i
$424$	0.983879	+	1.70413i	0.0477814	+	0.0827598i
$425$	−32.1230	+	7.89552i	−1.55820	+	0.382989i
$426$	13.8980	+	4.75626i	0.673359	+	0.230442i
$427$	−36.9601	+	8.27262i	−1.78862	+	0.400340i
$428$	2.12855	+	3.68676i	0.102887	+	0.178206i
$429$	−5.10687	−	1.74771i	−0.246562	−	0.0843802i
$430$	−0.747165	+	5.25281i	−0.0360315	+	0.253313i
$431$	16.7004	−	9.64197i	0.804429	−	0.464437i	−0.0405887	−	0.999176i	$-0.512923\pi$
$431$	16.7004	−	9.64197i	0.804429	−	0.464437i	0.845017	+	0.534739i	$0.179590\pi$
$432$	−4.64303	−	2.33287i	−0.223388	−	0.112240i
$433$	−12.0085			−0.577094			−0.288547	−	0.957466i	$-0.593172\pi$
$433$	−12.0085			−0.577094			−0.288547	+	0.957466i	$0.593172\pi$
$434$	4.12581	−	13.1786i	0.198045	−	0.632595i
$435$	−1.01948	−	19.3742i	−0.0488804	−	0.928922i
$436$	−6.71198			−0.321445
$437$	23.7326	+	13.7020i	1.13528	+	0.655456i
$438$	−2.49902	+	0.490635i	−0.119408	+	0.0234434i
$439$	11.6672	−	6.73606i	0.556845	−	0.321495i	−0.195033	−	0.980797i	$-0.562481\pi$
$439$	11.6672	−	6.73606i	0.556845	−	0.321495i	0.751878	+	0.659302i	$0.229148\pi$
$440$	1.43751	−	10.1061i	0.0685305	−	0.481791i
$441$	−14.2014	+	15.4699i	−0.676259	+	0.736664i
$442$		−	4.51626i		−	0.214816i
$443$	3.50536	+	6.07147i	0.166545	+	0.288464i	0.937203	−	0.348785i	$-0.113406\pi$
$443$	3.50536	+	6.07147i	0.166545	+	0.288464i	−0.770658	+	0.637249i	$0.780072\pi$
$444$	2.60234	+	0.890592i	0.123502	+	0.0422656i
$445$	−2.03955	+	2.60155i	−0.0966838	+	0.123325i
$446$	27.0719			1.28189
$447$	−5.61916	+	4.90323i	−0.265777	+	0.231915i
$448$	2.52491	+	0.790468i	0.119291	+	0.0373461i
$449$			12.1011i			0.571086i	0.958366	+	0.285543i	$0.0921740\pi$
$449$			12.1011i			0.571086i	−0.958366	+	0.285543i	$0.907826\pi$
$450$	−14.9172	+	1.57426i	−0.703202	+	0.0742113i
$451$	−27.0248	+	15.6028i	−1.27255	+	0.734705i
$452$	6.83691			0.321581
$453$	−18.2707	−	20.9384i	−0.858430	−	0.983771i
$454$	−6.72233	+	3.88114i	−0.315494	+	0.182151i
$455$	−0.318326	−	4.02601i	−0.0149233	−	0.188742i
$456$	−2.60601	−	13.2735i	−0.122038	−	0.621590i
$457$	16.4885	−	9.51961i	0.771297	−	0.445309i	−0.0620400	−	0.998074i	$-0.519761\pi$
$457$	16.4885	−	9.51961i	0.771297	−	0.445309i	0.833337	+	0.552765i	$0.186427\pi$
$458$	−0.431712	+	0.249249i	−0.0201726	+	0.0116466i
$459$	−15.4338	+	30.7175i	−0.720390	+	1.43377i
$460$	−4.84092	+	6.17485i	−0.225709	+	0.287904i
$461$	−6.78876	+	11.7585i	−0.316184	+	0.547647i	−0.979689	−	0.200525i	$-0.935735\pi$
$461$	−6.78876	+	11.7585i	−0.316184	+	0.547647i	0.663504	+	0.748172i	$0.269068\pi$
$462$	−16.8651	−	12.3778i	−0.784636	−	0.575867i
$463$	−29.4895	+	17.0258i	−1.37049	+	0.791254i	−0.990990	−	0.133937i	$-0.957238\pi$
$463$	−29.4895	+	17.0258i	−1.37049	+	0.791254i	−0.379502	+	0.925191i	$0.623905\pi$
$464$			5.00932i			0.232552i
$465$	−1.06225	−	20.1869i	−0.0492606	−	0.936146i
$466$	−17.8969			−0.829057
$467$	12.7222	+	7.34517i	0.588714	+	0.339894i	0.764589	−	0.644519i	$-0.222942\pi$
$467$	12.7222	+	7.34517i	0.588714	+	0.339894i	−0.175875	+	0.984412i	$0.556275\pi$
$468$	0.277393	−	2.02906i	0.0128225	−	0.0937933i
$469$	13.0098	+	14.1399i	0.600735	+	0.652921i
$470$	6.71501	+	5.26439i	0.309740	+	0.242828i
$471$	17.1969	−	3.37628i	0.792390	−	0.155571i
$472$	−4.68295	+	8.11110i	−0.215550	+	0.373344i
$473$	−5.41596	+	9.38073i	−0.249026	+	0.431326i
$474$	−1.99809	+	0.392288i	−0.0917754	+	0.0180184i
$475$	−27.0318	−	28.1797i	−1.24031	−	1.29297i
$476$	5.22960	−	16.7044i	0.239698	−	0.765643i
$477$	5.46507	−	2.23196i	0.250228	−	0.102195i
$478$	23.9059	+	13.8021i	1.09343	+	0.631291i
$479$	5.02408			0.229556			0.114778	−	0.993391i	$-0.463384\pi$
$479$	5.02408			0.229556			0.114778	+	0.993391i	$0.463384\pi$
$480$	3.86763	−	0.203517i	0.176532	−	0.00928925i
$481$			1.08405i			0.0494283i
$482$	−12.1606	+	7.02092i	−0.553899	+	0.319794i
$483$	6.46948	+	14.7211i	0.294371	+	0.669835i
$484$	4.92005	−	8.52177i	0.223639	−	0.387353i
$485$	−12.1476	+	15.4949i	−0.551595	+	0.703589i
$486$	−8.82080	+	12.8528i	−0.400120	+	0.583013i
$487$	−12.8332	+	7.40923i	−0.581526	+	0.335744i	−0.761740	−	0.647883i	$-0.775654\pi$
$487$	−12.8332	+	7.40923i	−0.581526	+	0.335744i	0.180213	+	0.983628i	$0.442321\pi$
$488$	12.3974	−	7.15763i	0.561203	−	0.324011i
$489$	7.58723	+	38.6450i	0.343106	+	1.74759i
$490$	3.48453	−	15.2597i	0.157415	−	0.689362i
$491$	−7.03712	+	4.06288i	−0.317581	+	0.183355i	−0.650314	−	0.759666i	$-0.725363\pi$
$491$	−7.03712	+	4.06288i	−0.317581	+	0.183355i	0.332733	+	0.943021i	$0.392029\pi$
$492$	−7.78434	−	8.92095i	−0.350945	−	0.402188i
$493$	33.1408			1.49259
$494$	4.61704	−	2.66565i	0.207730	−	0.119933i
$495$	−29.4549	−	8.37942i	−1.32390	−	0.376627i
$496$			5.21945i			0.234360i
$497$	−6.70387	+	21.4134i	−0.300709	+	0.960524i
$498$	14.7233	−	12.8474i	0.659765	−	0.575705i
$499$	1.70496			0.0763243			0.0381622	−	0.999272i	$-0.487850\pi$
$499$	1.70496			0.0763243			0.0381622	+	0.999272i	$0.487850\pi$
$500$	9.07784	−	6.52632i	0.405973	−	0.291866i
$501$	21.4201	+	7.33052i	0.956978	+	0.327504i
$502$	8.03821	+	13.9226i	0.358763	+	0.621396i
$503$			33.2589i			1.48294i	0.670985	+	0.741471i	$0.265871\pi$
$503$			33.2589i			1.48294i	−0.670985	+	0.741471i	$0.734129\pi$
$504$	3.37555	−	7.18371i	0.150359	−	0.319988i
$505$	−1.97953	−	0.281570i	−0.0880878	−	0.0125297i
$506$	−13.8726	+	8.00932i	−0.616710	+	0.356058i
$507$	−21.3028	+	4.18241i	−0.946092	+	0.185747i
$508$	−9.72354	−	5.61389i	−0.431412	−	0.249076i
$509$	6.75948			0.299609			0.149804	−	0.988716i	$-0.452136\pi$
$509$	6.75948			0.299609			0.149804	+	0.988716i	$0.452136\pi$
$510$	−1.34643	−	25.5876i	−0.0596211	−	1.13304i
$511$	−0.849699	−	3.79625i	−0.0375885	−	0.167936i
$512$	−1.00000			−0.0441942
$513$	−40.5126	+	2.35226i	−1.78867	+	0.103855i
$514$	−22.0687	+	12.7414i	−0.973409	+	0.561998i
$515$	−29.9990	−	4.26710i	−1.32192	−	0.188031i
$516$	−3.88836	−	1.33070i	−0.171176	−	0.0585809i
$517$	8.70996	+	15.0861i	0.383063	+	0.663485i
$518$	−1.25527	+	4.00958i	−0.0551535	+	0.176171i
$519$	1.14241	+	0.390964i	0.0501463	+	0.0171614i
$520$	0.569454	+	1.41624i	0.0249722	+	0.0621063i
$521$	20.1496	+	34.9001i	0.882770	+	1.52900i	0.848249	+	0.529598i	$0.177657\pi$
$521$	20.1496	+	34.9001i	0.882770	+	1.52900i	0.0345209	+	0.999404i	$0.489009\pi$
$522$	14.8895	+	2.03554i	0.651694	+	0.0890932i
$523$	6.81446	−	11.8030i	0.297975	−	0.516109i	−0.677697	−	0.735341i	$-0.737022\pi$
$523$	6.81446	−	11.8030i	0.297975	−	0.516109i	0.975673	+	0.219233i	$0.0703553\pi$
$524$	1.13293	−	1.96229i	0.0494921	−	0.0857228i
$525$	−3.00380	−	22.7151i	−0.131097	−	0.991370i
$526$	12.7152	+	22.0234i	0.554410	+	0.960266i
$527$	34.5310			1.50419
$528$	7.48102	+	2.56021i	0.325570	+	0.111419i
$529$	−10.6873			−0.464667
$530$	−2.71471	+	3.46276i	−0.117920	+	0.150413i
$531$	22.2061	+	17.2153i	0.963664	+	0.747081i
$532$	20.1638	−	4.51318i	0.874212	−	0.195671i
$533$	2.33317	−	4.04116i	0.101061	−	0.175042i
$534$	−1.68354	−	1.92935i	−0.0728537	−	0.0834912i
$535$	−5.87308	+	7.49143i	−0.253915	+	0.323883i
$536$	−6.28937	−	3.63117i	−0.271659	−	0.156843i
$537$	20.2005	+	6.91316i	0.871717	+	0.298325i
$538$	−12.2442	+	21.2076i	−0.527886	+	0.914326i
$539$	18.2226	−	26.2508i	0.784902	−	1.13070i
$540$	0.966691	−	11.5787i	0.0415998	−	0.498266i
$541$	4.14554	−	7.18028i	0.178231	−	0.308704i	−0.763044	−	0.646347i	$-0.776296\pi$
$541$	4.14554	−	7.18028i	0.178231	−	0.308704i	0.941275	+	0.337642i	$0.109629\pi$
$542$		−	20.5609i		−	0.883165i
$543$	−15.1734	+	13.2402i	−0.651153	+	0.568190i
$544$			6.61583i			0.283651i
$545$	−5.59905	−	13.9249i	−0.239837	−	0.596478i
$546$	3.10952	+	0.341976i	0.133075	+	0.0146352i
$547$	−13.0289	−	7.52224i	−0.557076	−	0.321628i	0.194895	−	0.980824i	$-0.437563\pi$
$547$	−13.0289	−	7.52224i	−0.557076	−	0.321628i	−0.751971	+	0.659196i	$0.770897\pi$
$548$	1.93119	−	3.34491i	0.0824962	−	0.142888i
$549$	−16.2373	−	39.7579i	−0.692991	−	1.69682i
$550$	22.1658	−	5.44811i	0.945151	−	0.232308i
$551$	19.5608	+	33.8804i	0.833319	+	1.44335i
$552$	−3.99592	−	4.57937i	−0.170078	−	0.194911i
$553$	−0.679378	−	3.03530i	−0.0288901	−	0.129074i
$554$	1.70051	−	0.981792i	0.0722479	−	0.0417124i
$555$	0.323188	+	6.14185i	0.0137186	+	0.260707i
$556$			13.2119i			0.560308i
$557$	−6.05011	−	10.4791i	−0.256352	−	0.444014i	0.708910	−	0.705299i	$-0.249187\pi$
$557$	−6.05011	−	10.4791i	−0.256352	−	0.444014i	−0.965262	+	0.261285i	$0.915854\pi$
$558$	15.5140	+	2.12093i	0.656762	+	0.0897861i
$559$		−	1.61976i		−	0.0685085i
$560$	0.466313	+	5.89767i	0.0197053	+	0.249222i
$561$	16.9379	−	49.4931i	0.715118	−	2.08960i
$562$		−	29.4774i		−	1.24343i
$563$	−23.9538	−	13.8297i	−1.00953	−	0.582854i	−0.0984780	−	0.995139i	$-0.531397\pi$
$563$	−23.9538	−	13.8297i	−1.00953	−	0.582854i	−0.911055	+	0.412285i	$0.864731\pi$
$564$	−4.97996	+	4.34547i	−0.209694	+	0.182977i
$565$	5.70327	+	14.1841i	0.239939	+	0.596731i
$566$	−25.1313			−1.05635
$567$	−19.9809	−	12.9524i	−0.839117	−	0.543951i
$568$		−	8.48088i		−	0.355850i
$569$	20.6797	−	11.9394i	0.866938	−	0.500527i	0.000608821	−	1.00000i	$-0.499806\pi$
$569$	20.6797	−	11.9394i	0.866938	−	0.500527i	0.866330	+	0.499473i	$0.166473\pi$
$570$	25.3639	−	16.4792i	1.06238	−	0.690236i
$571$	−14.7569	+	25.5597i	−0.617556	+	1.06964i	0.372374	+	0.928083i	$0.378544\pi$
$571$	−14.7569	+	25.5597i	−0.617556	+	1.06964i	−0.989930	+	0.141556i	$0.954789\pi$
$572$			3.11634i			0.130301i
$573$	0.965312	+	0.330356i	0.0403265	+	0.0138008i
$574$	13.3092	−	12.2454i	0.555515	−	0.511114i
$575$	−16.8488	−	4.89217i	−0.702645	−	0.204018i
$576$	−0.406351	+	2.97235i	−0.0169313	+	0.123848i
$577$	10.1979	+	17.6634i	0.424546	+	0.735335i	0.996378	−	0.0850355i	$-0.0271004\pi$
$577$	10.1979	+	17.6634i	0.424546	+	0.735335i	−0.571832	+	0.820371i	$0.693767\pi$
$578$	26.7692			1.11345
$579$	4.67698	+	23.8219i	0.194369	+	0.990004i
$580$	−10.3925	+	4.17872i	−0.431526	+	0.173512i
$581$	20.2100	+	21.9657i	0.838453	+	0.911289i
$582$	−10.0272	−	11.4913i	−0.415641	−	0.476330i
$583$	−7.77951	+	4.49150i	−0.322194	+	0.186019i
$584$	0.735176	+	1.27336i	0.0304218	+	0.0526921i
$585$	4.44097	−	1.11713i	0.183611	−	0.0461875i
$586$	26.8539	+	15.5041i	1.10933	+	0.640470i
$587$	32.0984	+	18.5320i	1.32484	+	0.764899i	0.984497	−	0.175401i	$-0.0561223\pi$
$587$	32.0984	+	18.5320i	1.32484	+	0.764899i	0.340346	+	0.940300i	$0.389456\pi$
$588$	11.1052	+	4.86555i	0.457973	+	0.200652i
$589$	20.3814	+	35.3016i	0.839800	+	1.45458i
$590$	−20.7341	−	2.94924i	−0.853608	−	0.121418i
$591$	11.9496	+	13.6943i	0.491539	+	0.563310i
$592$		−	1.58801i		−	0.0652669i
$593$	9.28698	+	5.36184i	0.381371	+	0.220184i	0.678414	−	0.734679i	$-0.262667\pi$
$593$	9.28698	+	5.36184i	0.381371	+	0.220184i	−0.297044	+	0.954864i	$0.596001\pi$
$594$	10.6498	−	21.1959i	0.436965	−	0.869678i
$595$	39.0180	−	3.08504i	1.59958	−	0.126474i
$596$	3.72883	+	2.15284i	0.152739	+	0.0881837i
$597$	35.9977	+	12.3194i	1.47329	+	0.504199i
$598$	1.19768	−	2.07444i	0.0489767	−	0.0848302i
$599$	14.8121	+	8.55178i	0.605206	+	0.349416i	0.771087	−	0.636730i	$-0.219713\pi$
$599$	14.8121	+	8.55178i	0.605206	+	0.349416i	−0.165881	+	0.986146i	$0.553047\pi$
$600$	3.64856	+	7.85417i	0.148952	+	0.320645i
$601$	−20.0797	−	11.5930i	−0.819069	−	0.472890i	0.0310264	−	0.999519i	$-0.490122\pi$
$601$	−20.0797	−	11.5930i	−0.819069	−	0.472890i	−0.850095	+	0.526629i	$0.823456\pi$
$602$	1.87560	−	5.99103i	0.0764438	−	0.244176i
$603$	−13.3488	+	17.2187i	−0.543606	+	0.701200i
$604$	−8.02202	+	13.8945i	−0.326411	+	0.565361i
$605$	21.7839	+	3.09856i	0.885640	+	0.125974i
$606$	0.501477	−	1.46533i	0.0203711	−	0.0595252i
$607$	20.3434			0.825713			0.412857	−	0.910796i	$-0.364531\pi$
$607$	20.3434			0.825713			0.412857	+	0.910796i	$0.364531\pi$
$608$	−6.76346	+	3.90489i	−0.274295	+	0.158364i
$609$	−2.50946	+	22.8180i	−0.101688	+	0.924632i
$610$	25.1912	+	19.7493i	1.01996	+	0.799625i
$611$	−2.25591	−	1.30245i	−0.0912642	−	0.0526914i
$612$	19.6646	+	2.68835i	0.794893	+	0.108670i
$613$	−5.31424	+	3.06818i	−0.214640	+	0.123922i	−0.603466	−	0.797389i	$-0.706214\pi$
$613$	−5.31424	+	3.06818i	−0.214640	+	0.123922i	0.388826	+	0.921311i	$0.372881\pi$
$614$	−2.44888	−	4.24159i	−0.0988288	−	0.171177i
$615$	12.0141	−	23.5915i	0.484457	−	0.951300i
$616$	−3.60856	+	11.5264i	−0.145393	+	0.464414i
$617$	−10.4874	−	18.1648i	−0.422208	−	0.731286i	0.573947	−	0.818892i	$-0.305412\pi$
$617$	−10.4874	−	18.1648i	−0.422208	−	0.731286i	−0.996155	+	0.0876065i	$0.972078\pi$
$618$	7.59971	−	22.2066i	0.305705	−	0.893282i
$619$		−	22.5678i		−	0.907075i	−0.891237	−	0.453538i	$-0.850162\pi$
$619$		−	22.5678i		−	0.907075i	0.891237	−	0.453538i	$-0.149838\pi$
$620$	−10.8285	+	4.35401i	−0.434882	+	0.174861i
$621$	−15.2352	+	10.0164i	−0.611369	+	0.401946i
$622$	9.06956			0.363656
$623$	2.87841	−	2.64834i	0.115321	−	0.106104i
$624$	−1.16023	+	0.227788i	−0.0464462	+	0.00911883i
$625$	21.1124	+	13.3891i	0.844496	+	0.535562i
$626$	15.0417	−	26.0531i	0.601189	−	1.04129i
$627$	60.5949	−	11.8967i	2.41993	−	0.475107i
$628$	−5.05908	−	8.76259i	−0.201879	−	0.349665i
$629$	−10.5060			−0.418902
$630$	17.7195	+	1.01048i	0.705960	+	0.0402585i
$631$	15.1577			0.603418			0.301709	−	0.953400i	$-0.402443\pi$
$631$	15.1577			0.603418			0.301709	+	0.953400i	$0.402443\pi$
$632$	0.587811	+	1.01812i	0.0233819	+	0.0404986i
$633$	−7.65917	+	22.3804i	−0.304425	+	0.889541i
$634$	1.68610	−	2.92040i	0.0669634	−	0.115984i
$635$	3.53553	−	24.8559i	0.140303	−	0.986376i
$636$	−2.24085	−	2.56804i	−0.0888554	−	0.101829i
$637$	−0.397142	+	4.76198i	−0.0157354	+	0.188676i
$638$	−22.8680			−0.905354
$639$	−25.2082	−	3.44621i	−0.997219	−	0.136330i
$640$	−0.834189	−	2.07464i	−0.0329742	−	0.0820073i
$641$		−	15.6801i		−	0.619327i	−0.950846	−	0.309663i	$-0.899784\pi$
$641$		−	15.6801i		−	0.619327i	0.950846	−	0.309663i	$-0.100216\pi$
$642$	−4.84791	−	5.55576i	−0.191332	−	0.219268i
$643$	−9.19102	−	15.9193i	−0.362458	−	0.627796i	0.625906	−	0.779898i	$-0.284729\pi$
$643$	−9.19102	−	15.9193i	−0.362458	−	0.627796i	−0.988365	+	0.152102i	$0.951396\pi$
$644$	6.83197	−	6.28591i	0.269217	−	0.247700i
$645$	−0.482900	−	9.17701i	−0.0190142	−	0.361344i
$646$	25.8341	+	44.7459i	1.01643	+	1.76050i
$647$	−2.50834	+	1.44819i	−0.0986129	+	0.0569342i	−0.548495	−	0.836154i	$-0.684799\pi$
$647$	−2.50834	+	1.44819i	−0.0986129	+	0.0569342i	0.449883	+	0.893088i	$0.351466\pi$
$648$	8.66976	+	2.41564i	0.340580	+	0.0948951i
$649$	−37.0279	−	21.3781i	−1.45347	−	0.839164i
$650$	−2.46316	+	2.36282i	−0.0966130	+	0.0926776i
$651$	−2.61473	+	23.7752i	−0.102479	+	0.931823i
$652$	19.6914	−	11.3688i	0.771175	−	0.445238i
$653$	25.8701			1.01238			0.506189	−	0.862423i	$-0.331054\pi$
$653$	25.8701			1.01238			0.506189	+	0.862423i	$0.331054\pi$
$654$	11.4077	−	2.23969i	0.446076	−	0.0875787i
$655$	5.01611	+	0.713497i	0.195996	+	0.0278786i
$656$	−3.41784	+	5.91987i	−0.133444	+	0.231132i
$657$	4.08362	−	1.66777i	0.159317	−	0.0650659i
$658$	−6.83579	−	7.42962i	−0.266487	−	0.289637i
$659$	3.49291	+	2.01663i	0.136064	+	0.0785568i	0.566487	−	0.824071i	$-0.308302\pi$
$659$	3.49291	+	2.01663i	0.136064	+	0.0785568i	−0.430423	+	0.902627i	$0.641635\pi$
$660$	0.929075	+	17.6561i	0.0361642	+	0.687263i
$661$	−42.2828	−	24.4120i	−1.64461	−	0.949516i	−0.979164	−	0.203070i	$-0.934908\pi$
$661$	−42.2828	−	24.4120i	−1.64461	−	0.949516i	−0.665446	−	0.746446i	$-0.731758\pi$
$662$	5.46742	−	9.46984i	0.212497	−	0.368056i
$663$	1.50701	+	7.67585i	0.0585274	+	0.298105i
$664$	−9.77023	−	5.64084i	−0.379158	−	0.218907i
$665$	26.1836	+	38.0678i	1.01536	+	1.47621i
$666$	−4.72013	−	0.645290i	−0.182901	−	0.0250045i
$667$	15.2225	+	8.78870i	0.589417	+	0.340300i
$668$		−	13.0710i		−	0.505733i
$669$	−46.0115	+	9.03349i	−1.77891	+	0.349255i
$670$	2.28685	−	16.0773i	0.0883486	−	0.621119i
$671$	32.6753	+	56.5952i	1.26141	+	2.18483i
$672$	−4.55511	−	0.500958i	−0.175717	−	0.0193249i
$673$	−26.8527	−	15.5034i	−1.03509	−	0.597612i	−0.116655	−	0.993173i	$-0.537217\pi$
$673$	−26.8527	−	15.5034i	−1.03509	−	0.597612i	−0.918440	+	0.395560i	$0.870550\pi$
$674$	1.26189	+	0.728550i	0.0486060	+	0.0280627i
$675$	24.8280	−	7.65326i	0.955629	−	0.294574i
$676$	6.26700	+	10.8548i	0.241038	+	0.417491i
$677$	−30.6370	+	17.6883i	−1.17748	+	0.679816i	−0.955429	−	0.295220i	$-0.904607\pi$
$677$	−30.6370	+	17.6883i	−1.17748	+	0.679816i	−0.222046	+	0.975036i	$0.571274\pi$
$678$	−11.6200	+	2.28138i	−0.446265	+	0.0876158i
$679$	17.1439	−	15.7736i	0.657923	−	0.605337i
$680$	−13.7255	+	5.51885i	−0.526347	+	0.211638i
$681$	10.1302	−	8.83954i	0.388191	−	0.338732i
$682$	−23.8273			−0.912394
$683$	−16.9554	−	29.3676i	−0.648780	−	1.12372i	−0.983415	−	0.181371i	$-0.941946\pi$
$683$	−16.9554	−	29.3676i	−0.648780	−	1.12372i	0.334635	−	0.942348i	$-0.391387\pi$
$684$	8.85836	+	21.6902i	0.338708	+	0.829344i
$685$	8.55046	+	1.21623i	0.326696	+	0.0464697i
$686$	−6.98305	+	17.1533i	−0.266614	+	0.654917i
$687$	0.650569	−	0.567681i	0.0248207	−	0.0216584i
$688$			2.37277i			0.0904611i
$689$	0.671640	−	1.16331i	0.0255874	−	0.0443187i
$690$	6.16719	−	12.1101i	0.234781	−	0.461025i
$691$	10.6484	−	6.14785i	0.405084	−	0.233875i	−0.283591	−	0.958945i	$-0.591526\pi$
$691$	10.6484	−	6.14785i	0.405084	−	0.233875i	0.688675	+	0.725070i	$0.258193\pi$
$692$		−	0.697127i		−	0.0265008i
$693$	32.7943	+	15.4097i	1.24575	+	0.585366i
$694$	−35.8194			−1.35969
$695$	−27.4099	+	11.0212i	−1.03972	+	0.418057i
$696$	−1.67154	−	8.51386i	−0.0633594	−	0.322717i
$697$	39.1648	+	22.6118i	1.48347	+	0.856484i
$698$		−	3.04609i		−	0.115296i
$699$	30.4176	−	5.97193i	1.15050	−	0.225879i
$700$	−11.8466	+	5.88720i	−0.447758	+	0.222515i
$701$			15.9333i			0.601791i	0.953657	+	0.300895i	$0.0972855\pi$
$701$			15.9333i			0.601791i	−0.953657	+	0.300895i	$0.902714\pi$
$702$	0.205609	+	3.54116i	0.00776021	+	0.133652i
$703$	−6.20101	−	10.7405i	−0.233875	−	0.405084i
$704$		−	4.56510i		−	0.172054i
$705$	−13.1695	−	6.70668i	−0.495992	−	0.252588i
$706$	29.5595	−	17.0662i	1.11249	−	0.642295i
$707$	2.25773	+	0.706823i	0.0849106	+	0.0265828i
$708$	5.25260	−	15.3483i	0.197405	−	0.576824i
$709$	−4.90106	−	8.48889i	−0.184063	−	0.318807i	0.759197	−	0.650861i	$-0.225592\pi$
$709$	−4.90106	−	8.48889i	−0.184063	−	0.318807i	−0.943260	+	0.332054i	$0.892258\pi$
$710$	17.5948	−	7.07465i	0.660320	−	0.265507i
$711$	3.26507	−	1.33347i	0.122450	−	0.0500090i
$712$	−0.739183	+	1.28030i	−0.0277020	+	0.0479814i
$713$	15.8610	+	9.15737i	0.594000	+	0.342946i
$714$	−3.31425	+	30.1358i	−0.124033	+	1.12781i
$715$	−6.46527	+	2.59961i	−0.241788	+	0.0972200i
$716$		−	12.3268i		−	0.460675i
$717$	−45.2361	−	15.4810i	−1.68937	−	0.578148i
$718$		−	24.3325i		−	0.908081i
$719$	10.7248	−	18.5760i	0.399969	−	0.692767i	−0.593752	−	0.804648i	$-0.702354\pi$
$719$	10.7248	−	18.5760i	0.399969	−	0.692767i	0.993722	+	0.111881i	$0.0356874\pi$
$720$	−6.50553	+	1.63647i	−0.242447	+	0.0609877i
$721$	34.2151	+	10.7117i	1.27424	+	0.398923i
$722$	−20.9963	+	36.3667i	−0.781402	+	1.35343i
$723$	18.3254	−	15.9906i	0.681529	−	0.594696i
$724$	10.0689	+	5.81331i	0.374209	+	0.216050i
$725$	−17.3387	−	18.0749i	−0.643942	−	0.671286i
$726$	−5.51854	+	16.1254i	−0.204812	+	0.598469i
$727$	1.49310	−	2.58612i	0.0553760	−	0.0959140i	−0.837009	−	0.547190i	$-0.815698\pi$
$727$	1.49310	−	2.58612i	0.0553760	−	0.0959140i	0.892385	+	0.451276i	$0.149031\pi$
$728$	−0.394492	−	1.76250i	−0.0146209	−	0.0653225i
$729$	10.7031	−	24.7880i	0.396411	−	0.918073i
$730$	−2.02849	+	2.58745i	−0.0750778	+	0.0957658i
$731$	15.6978			0.580606
$732$	−18.6822	+	16.3020i	−0.690515	+	0.602538i
$733$	−46.7197			−1.72563			−0.862816	−	0.505519i	$-0.831301\pi$
$733$	−46.7197			−1.72563			−0.862816	+	0.505519i	$0.831301\pi$
$734$	−6.72343	−	11.6453i	−0.248166	−	0.429837i
$735$	−0.830383	+	27.0982i	−0.0306291	+	0.999531i
$736$	−1.75447	+	3.03883i	−0.0646706	+	0.112013i
$737$	16.5766	−	28.7116i	0.610608	−	1.05760i
$738$	16.2071	+	12.5646i	0.596591	+	0.462508i
$739$	−3.52514	−	6.10572i	−0.129674	−	0.224603i	0.793876	−	0.608080i	$-0.208060\pi$
$739$	−3.52514	−	6.10572i	−0.129674	−	0.224603i	−0.923550	+	0.383477i	$0.874727\pi$
$740$	3.29455	−	1.32470i	0.121110	−	0.0486970i
$741$	−6.95765	+	6.07119i	−0.255596	+	0.223031i
$742$	3.83126	−	3.52504i	0.140650	−	0.129408i
$743$	−7.76460	−	13.4487i	−0.284856	−	0.493384i	0.687719	−	0.725977i	$-0.258612\pi$
$743$	−7.76460	−	13.4487i	−0.284856	−	0.493384i	−0.972574	+	0.232593i	$0.925279\pi$
$744$	−1.74165	−	8.87100i	−0.0638522	−	0.325227i
$745$	−1.35582	+	9.53184i	−0.0496734	+	0.349220i
$746$	2.42626	−	1.40080i	0.0888315	−	0.0512869i
$747$	−20.7367	+	26.7484i	−0.758717	+	0.978673i
$748$	−30.2019			−1.10429
$749$	8.28866	−	7.62617i	0.302861	−	0.278654i
$750$	−13.2510	+	14.1213i	−0.483858	+	0.515637i
$751$	−20.2123			−0.737558			−0.368779	−	0.929517i	$-0.620224\pi$
$751$	−20.2123			−0.737558			−0.368779	+	0.929517i	$0.620224\pi$
$752$	3.30466	+	1.90795i	0.120509	+	0.0695756i
$753$	−18.3075	−	20.9807i	−0.667164	−	0.764578i
$754$	2.96145	−	1.70979i	0.107849	−	0.0622669i
$755$	−35.5180	−	5.05213i	−1.29263	−	0.183866i
$756$	−3.34000	+	13.3358i	−0.121475	+	0.485020i
$757$		−	6.00333i		−	0.218195i	−0.994031	−	0.109097i	$-0.965204\pi$
$757$		−	6.00333i		−	0.218195i	0.994031	−	0.109097i	$-0.0347960\pi$
$758$	−6.60181	−	11.4347i	−0.239789	−	0.415326i
$759$	20.9053	−	18.2417i	0.758813	−	0.662133i
$760$	−13.7432	−	10.7743i	−0.498520	−	0.390826i
$761$	−42.3917			−1.53670			−0.768349	−	0.640031i	$-0.778921\pi$
$761$	−42.3917			−1.53670			−0.768349	+	0.640031i	$0.778921\pi$
$762$	18.3994	+	6.29678i	0.666541	+	0.228108i
$763$	3.87877	+	17.3294i	0.140421	+	0.627368i
$764$		−	0.589056i		−	0.0213113i
$765$	10.8266	+	43.0395i	0.391437	+	1.55610i
$766$	2.77030	−	1.59943i	0.100095	−	0.0577899i
$767$	6.39357			0.230859
$768$	1.69960	−	0.333685i	0.0613292	−	0.0120408i
$769$	−33.6414	+	19.4229i	−1.21314	+	0.700406i	−0.963442	−	0.267918i	$-0.913664\pi$
$769$	−33.6414	+	19.4229i	−1.21314	+	0.700406i	−0.249697	+	0.968324i	$0.580331\pi$
$770$	−26.9234	+	2.12876i	−0.970254	+	0.0767152i
$771$	33.2565	−	29.0193i	1.19770	−	1.04510i
$772$	12.1383	−	7.00807i	0.436868	−	0.252226i
$773$	−16.6613	+	9.61939i	−0.599265	+	0.345986i	−0.768752	−	0.639547i	$-0.779122\pi$
$773$	−16.6613	+	9.61939i	−0.599265	+	0.345986i	0.169488	+	0.985532i	$0.445789\pi$
$774$	7.05271	+	0.964178i	0.253505	+	0.0346567i
$775$	−18.0660	−	18.8331i	−0.648950	−	0.676506i
$776$	−4.40260	+	7.62553i	−0.158044	+	0.273741i
$777$	0.795528	−	7.23357i	0.0285394	−	0.259503i
$778$	16.1572	−	9.32835i	0.579263	−	0.334437i
$779$			53.3851i			1.91272i
$780$	−1.44043	−	2.21703i	−0.0515755	−	0.0793824i
$781$	38.7160			1.38537
$782$	20.1044	+	11.6073i	0.718931	+	0.415075i
$783$	−25.9854	+	1.50878i	−0.928643	+	0.0539194i
$784$	0.581771	−	6.97578i	0.0207775	−	0.249135i
$785$	13.9590	−	17.8054i	0.498217	−	0.635503i
$786$	−1.27074	+	3.71315i	−0.0453258	+	0.132444i
$787$	16.0429	−	27.7872i	0.571869	−	0.990506i	−0.424505	−	0.905425i	$-0.639552\pi$
$787$	16.0429	−	27.7872i	0.571869	−	0.990506i	0.996374	−	0.0850802i	$-0.0271146\pi$
$788$	5.24664	−	9.08745i	0.186904	−	0.323727i
$789$	−28.9597	−	33.1882i	−1.03099	−	1.18153i
$790$	−1.62188	+	2.06880i	−0.0577041	+	0.0736046i
$791$	−3.95097	−	17.6520i	−0.140480	−	0.627633i
$792$	−13.5691	−	1.85503i	−0.482156	−	0.0659156i
$793$	−8.46300	−	4.88611i	−0.300530	−	0.173511i
$794$	10.7681			0.382144
$795$	3.45846	−	6.79118i	0.122659	−	0.240858i
$796$		−	21.9666i		−	0.778587i
$797$	−39.6425	+	22.8876i	−1.40421	+	0.810721i	−0.994821	−	0.101639i	$-0.967591\pi$
$797$	−39.6425	+	22.8876i	−1.40421	+	0.810721i	−0.409389	+	0.912360i	$0.634258\pi$
$798$	−32.7645	+	14.3990i	−1.15985	+	0.509719i
$799$	12.6226	−	21.8631i	0.446557	−	0.773459i
$800$	3.60826	−	3.46128i	0.127571	−	0.122375i
$801$	3.50514	+	2.71736i	0.123848	+	0.0960133i
$802$	−2.84720	+	1.64383i	−0.100538	+	0.0580458i
$803$	−5.81302	+	3.35615i	−0.205137	+	0.118436i
$804$	11.9011	+	4.07288i	0.419720	+	0.143639i
$805$	18.7402	+	8.93024i	0.660504	+	0.314750i
$806$	3.08567	−	1.78151i	0.108688	−	0.0627512i
$807$	13.7337	−	40.1303i	0.483448	−	1.41265i
$808$	−0.894182			−0.0314572
$809$	15.0301	−	8.67763i	0.528430	−	0.305089i	−0.211947	−	0.977281i	$-0.567980\pi$
$809$	15.0301	−	8.67763i	0.528430	−	0.305089i	0.740377	+	0.672192i	$0.234647\pi$
$810$	2.22064	+	20.0017i	0.0780253	+	0.702789i
$811$		−	42.8371i		−	1.50421i	−0.659041	−	0.752107i	$-0.729038\pi$
$811$		−	42.8371i		−	1.50421i	0.659041	−	0.752107i	$-0.270962\pi$
$812$	12.9334	−	2.89483i	0.453873	−	0.101589i
$813$	6.86086	+	34.9453i	0.240621	+	1.22559i
$814$	7.24942			0.254092
$815$	40.0126	+	31.3688i	1.40158	+	1.09880i
$816$	−2.20760	−	11.2443i	−0.0772816	−	0.393629i
$817$	9.26541	+	16.0482i	0.324156	+	0.561454i
$818$			28.9897i			1.01360i
$819$	−5.39907	+	0.456377i	−0.188659	+	0.0159471i
$820$	−15.1327	−	2.15249i	−0.528457	−	0.0751684i
$821$	−7.17318	+	4.14144i	−0.250346	+	0.144537i	−0.619923	−	0.784663i	$-0.712836\pi$
$821$	−7.17318	+	4.14144i	−0.250346	+	0.144537i	0.369577	+	0.929200i	$0.379503\pi$
$822$	−2.16610	+	6.32944i	−0.0755515	+	0.220764i
$823$	23.4420	+	13.5343i	0.817138	+	0.471775i	0.849428	−	0.527704i	$-0.176947\pi$
$823$	23.4420	+	13.5343i	0.817138	+	0.471775i	−0.0322908	+	0.999479i	$0.510280\pi$
$824$	−13.5510			−0.472072
$825$	−35.8550	+	16.6560i	−1.24831	+	0.579888i
$826$	23.6480	+	7.40344i	0.822820	+	0.257599i
$827$	−35.7680			−1.24377			−0.621887	−	0.783107i	$-0.713634\pi$
$827$	−35.7680			−1.24377			−0.621887	+	0.783107i	$0.713634\pi$
$828$	8.31955	+	6.44973i	0.289124	+	0.224144i
$829$	2.71605	−	1.56811i	0.0943322	−	0.0544627i	−0.452092	−	0.891971i	$-0.649322\pi$
$829$	2.71605	−	1.56811i	0.0943322	−	0.0544627i	0.546424	+	0.837509i	$0.315989\pi$
$830$	3.55250	−	24.9752i	0.123309	−	0.866903i
$831$	−2.56259	+	2.23610i	−0.0888953	+	0.0775693i
$832$	0.341322	+	0.591187i	0.0118332	+	0.0204957i
$833$	−46.1506	−	3.84889i	−1.59902	−	0.133356i
$834$	−4.40861	−	22.4549i	−0.152658	−	0.777551i
$835$	27.1177	−	10.9037i	0.938446	−	0.377338i
$836$	−17.8262	−	30.8759i	−0.616532	−	1.06786i
$837$	−27.0755	+	1.57207i	−0.935865	+	0.0543388i
$838$	15.2535	−	26.4199i	0.526924	−	0.912659i
$839$	10.4737	−	18.1410i	0.361593	−	0.626298i	−0.626630	−	0.779317i	$-0.715566\pi$
$839$	10.4737	−	18.1410i	0.361593	−	0.626298i	0.988223	+	0.153019i	$0.0488996\pi$
$840$	−2.76051	−	9.86811i	−0.0952468	−	0.340482i
$841$	−1.95336	−	3.38332i	−0.0673573	−	0.116666i
$842$	6.68294			0.230309
$843$	9.83618	+	50.0999i	0.338776	+	1.72553i
$844$	13.6570			0.470095
$845$	−17.2919	+	22.0567i	−0.594858	+	0.758773i
$846$	7.01394	−	9.04732i	0.241144	−	0.311053i
$847$	−24.8453	−	7.77829i	−0.853696	−	0.267265i
$848$	−0.983879	+	1.70413i	−0.0337866	+	0.0585200i
$849$	42.7133	−	8.38596i	1.46592	−	0.287805i
$850$	−22.8992	−	23.8716i	−0.785437	−	0.818790i
$851$	−4.82570	−	2.78612i	−0.165423	−	0.0955069i
$852$	2.82994	+	14.4141i	0.0969523	+	0.493820i
$853$	−5.19207	+	8.99293i	−0.177773	+	0.307912i	−0.941117	−	0.338080i	$-0.890223\pi$
$853$	−5.19207	+	8.99293i	−0.177773	+	0.307912i	0.763344	+	0.645992i	$0.223556\pi$
$854$	−25.6444	−	27.8721i	−0.877532	−	0.953763i
$855$	−37.6097	+	36.4716i	−1.28622	+	1.24730i
$856$	−2.12855	+	3.68676i	−0.0727524	+	0.126011i
$857$			12.3219i			0.420909i	0.977604	+	0.210455i	$0.0674945\pi$
$857$			12.3219i			0.420909i	−0.977604	+	0.210455i	$0.932506\pi$
$858$	−1.03988	−	5.29654i	−0.0355008	−	0.180821i
$859$		−	3.27697i		−	0.111809i	−0.998436	−	0.0559043i	$-0.982196\pi$
$859$		−	3.27697i		−	0.111809i	0.998436	−	0.0559043i	$-0.0178042\pi$
$860$	−4.92265	+	1.97934i	−0.167861	+	0.0674949i
$861$	−18.5342	+	25.2535i	−0.631645	+	0.860636i
$862$	16.7004	+	9.64197i	0.568817	+	0.328407i
$863$	−13.9352	+	24.1365i	−0.474361	+	0.821617i	−0.999569	−	0.0293570i	$-0.990654\pi$
$863$	−13.9352	+	24.1365i	−0.474361	+	0.821617i	0.525208	+	0.850974i	$0.323987\pi$
$864$	−0.301195	−	5.18742i	−0.0102469	−	0.176479i
$865$	1.44629	−	0.581536i	0.0491753	−	0.0197728i
$866$	−6.00427	−	10.3997i	−0.204033	−	0.353396i
$867$	−45.4970	+	8.93248i	−1.54516	+	0.303363i
$868$	13.4759	−	3.01626i	0.457403	−	0.102379i
$869$	−4.64781	+	2.68341i	−0.157666	+	0.0910286i
$870$	16.2688	−	10.5700i	0.551564	−	0.358357i
$871$			4.95760i			0.167982i
$872$	−3.35599	−	5.81274i	−0.113648	−	0.196844i
$873$	20.8768	+	16.1847i	0.706571	+	0.547770i
$874$			27.4040i			0.926955i
$875$	−22.0961	−	19.6663i	−0.746984	−	0.664842i
$876$	−1.67441	−	1.91889i	−0.0565731	−	0.0648334i
$877$		−	33.1177i		−	1.11831i	−0.829065	−	0.559153i	$-0.811127\pi$
$877$		−	33.1177i		−	1.11831i	0.829065	−	0.559153i	$-0.188873\pi$
$878$	11.6672	+	6.73606i	0.393749	+	0.227331i
$879$	−50.8146	−	17.3901i	−1.71393	−	0.586554i
$880$	9.47093	−	3.80815i	0.319265	−	0.128373i
$881$	5.13912			0.173141			0.0865707	−	0.996246i	$-0.472409\pi$
$881$	5.13912			0.173141			0.0865707	+	0.996246i	$0.472409\pi$
$882$	−20.4981	−	4.56384i	−0.690206	−	0.153673i
$883$		−	54.5450i		−	1.83559i	−0.397060	−	0.917793i	$-0.629969\pi$
$883$		−	54.5450i		−	1.83559i	0.397060	−	0.917793i	$-0.370031\pi$
$884$	3.91119	−	2.25813i	0.131548	−	0.0759491i
$885$	36.2238	−	1.90612i	1.21765	−	0.0640735i
$886$	−3.50536	+	6.07147i	−0.117765	+	0.203975i
$887$		−	47.0422i		−	1.57952i	−0.613414	−	0.789762i	$-0.710204\pi$
$887$		−	47.0422i		−	1.57952i	0.613414	−	0.789762i	$-0.289796\pi$
$888$	0.529896	+	2.69899i	0.0177822	+	0.0905722i
$889$	−8.87520	+	28.3491i	−0.297665	+	0.950798i
$890$	−3.27278	−	0.465524i	−0.109704	−	0.0156044i
$891$	−11.0276	+	39.5783i	−0.369439	+	1.32592i
$892$	13.5359	+	23.4449i	0.453217	+	0.784994i
$893$	29.8013			0.997261
$894$	−7.05590	−	2.41472i	−0.235985	−	0.0807603i
$895$	25.5737	−	10.2829i	0.854836	−	0.343720i
$896$	0.577888	+	2.58187i	0.0193059	+	0.0862542i
$897$	−1.34337	+	3.92538i	−0.0448538	+	0.131064i
$898$	−10.4799	+	6.05055i	−0.349718	+	0.201910i
$899$	13.0729	+	22.6430i	0.436007	+	0.755187i
$900$	−8.82193	−	12.1315i	−0.294064	−	0.404384i
$901$	11.2742	+	6.50918i	0.375599	+	0.216852i
$902$	−27.0248	−	15.6028i	−0.899826	−	0.519515i
$903$	−1.18866	+	10.8082i	−0.0395561	+	0.359676i
$904$	3.41846	+	5.92094i	0.113696	+	0.196927i
$905$	−3.66112	+	25.7388i	−0.121700	+	0.855587i
$906$	8.99785	−	26.2921i	0.298934	−	0.873495i
$907$		−	11.8660i		−	0.394004i	−0.980403	−	0.197002i	$-0.936880\pi$
$907$		−	11.8660i		−	0.394004i	0.980403	−	0.197002i	$-0.0631205\pi$
$908$	−6.72233	−	3.88114i	−0.223088	−	0.128800i
$909$	−0.363352	+	2.65782i	−0.0120516	+	0.0881545i
$910$	3.32747	−	2.28868i	0.110304	−	0.0758692i
$911$	28.3773	+	16.3837i	0.940182	+	0.542815i	0.890017	−	0.455926i	$-0.150692\pi$
$911$	28.3773	+	16.3837i	0.940182	+	0.542815i	0.0501649	+	0.998741i	$0.484025\pi$
$912$	10.1922	−	8.89363i	0.337498	−	0.294498i
$913$	25.7510	−	44.6020i	0.852233	−	1.47611i
$914$	16.4885	+	9.51961i	0.545389	+	0.314881i
$915$	−49.4052	−	25.1600i	−1.63329	−	0.831764i
$916$	−0.431712	−	0.249249i	−0.0142642	−	0.00823542i
$917$	−5.72107	−	1.79108i	−0.188926	−	0.0591468i
$918$	−34.3190	+	1.99265i	−1.13270	+	0.0657674i
$919$	10.3565	−	17.9380i	0.341630	−	0.591720i	−0.643106	−	0.765777i	$-0.722354\pi$
$919$	10.3565	−	17.9380i	0.341630	−	0.591720i	0.984736	+	0.174057i	$0.0556878\pi$
$920$	−7.76804	−	1.10493i	−0.256105	−	0.0364286i
$921$	5.57749	+	6.39187i	0.183784	+	0.210619i
$922$	−13.5775			−0.447152
$923$	−5.01379	+	2.89471i	−0.165031	+	0.0952806i
$924$	2.28692	−	20.7945i	0.0752342	−	0.684089i
$925$	5.49656	+	5.72996i	0.180726	+	0.188400i
$926$	−29.4895	−	17.0258i	−0.969084	−	0.559501i
$927$	−5.50647	+	40.2784i	−0.180856	+	1.32292i
$928$	−4.33820	+	2.50466i	−0.142408	+	0.0822195i
$929$	13.9282	+	24.1243i	0.456969	+	0.791493i	0.998799	−	0.0489946i	$-0.0156017\pi$
$929$	13.9282	+	24.1243i	0.456969	+	0.791493i	−0.541830	+	0.840488i	$0.682268\pi$
$930$	16.9513	−	11.0134i	0.555854	−	0.361143i
$931$	−23.3049	−	49.4522i	−0.763786	−	1.62073i
$932$	−8.94844	−	15.4992i	−0.293116	−	0.507692i
$933$	−15.4147	+	3.02638i	−0.504654	+	0.0990792i
$934$			14.6903i			0.480683i
$935$	−25.1941	−	62.6580i	−0.823934	−	2.04914i
$936$	1.89591	−	0.774300i	0.0619699	−	0.0253088i
$937$	−47.7529			−1.56002			−0.780009	−	0.625768i	$-0.784785\pi$
$937$	−47.7529			−1.56002			−0.780009	+	0.625768i	$0.784785\pi$
$938$	−5.74065	+	18.3367i	−0.187439	+	0.598716i
$939$	−16.8715	+	49.2991i	−0.550580	+	1.60882i
$940$	−1.20159	+	8.44756i	−0.0391916	+	0.275529i
$941$	−12.0659	+	20.8988i	−0.393338	+	0.681282i	−0.992888	−	0.119056i	$-0.962013\pi$
$941$	−12.0659	+	20.8988i	−0.393338	+	0.681282i	0.599549	+	0.800338i	$0.295347\pi$
$942$	11.5224	+	13.2048i	0.375419	+	0.430235i
$943$	11.9930	+	20.7725i	0.390545	+	0.676444i
$944$	−9.36589			−0.304834
$945$	−30.4532	+	4.19531i	−0.990644	+	0.136473i
$946$	−10.8319			−0.352176
$947$	−18.5909	−	32.2003i	−0.604122	−	1.04637i	−0.992190	−	0.124739i	$-0.960191\pi$
$947$	−18.5909	−	32.2003i	−0.604122	−	1.04637i	0.388067	−	0.921631i	$-0.373143\pi$
$948$	−1.33878	−	1.53426i	−0.0434815	−	0.0498303i
$949$	0.501864	−	0.869253i	0.0162912	−	0.0282172i
$950$	10.8884	−	37.5001i	0.353267	−	1.21666i
$951$	−1.89120	+	5.52615i	−0.0613263	+	0.179198i
$952$	17.0812	−	3.82321i	0.553605	−	0.123911i
$953$	−20.4203			−0.661478			−0.330739	−	0.943722i	$-0.607298\pi$
$953$	−20.4203			−0.661478			−0.330739	+	0.943722i	$0.607298\pi$
$954$	4.66547	+	3.61691i	0.151050	+	0.117102i
$955$	1.22208	−	0.491384i	0.0395456	−	0.0159008i
$956$			27.6041i			0.892781i
$957$	38.8666	−	7.63072i	1.25638	−	0.246666i
$958$	2.51204	+	4.35098i	0.0811604	+	0.140574i
$959$	−9.75214	−	3.05308i	−0.314913	−	0.0985892i
$960$	2.11007	+	3.24771i	0.0681021	+	0.104819i
$961$	−1.87866	−	3.25394i	−0.0606020	−	0.104966i
$962$	−0.938812	+	0.542024i	−0.0302685	+	0.0174755i
$963$	10.0934	+	7.82492i	0.325255	+	0.252155i
$964$	−12.1606	−	7.02092i	−0.391666	−	0.226129i
$965$	24.6649	+	19.3366i	0.793991	+	0.622468i
$966$	−9.51413	+	12.9633i	−0.306112	+	0.417087i
$967$	−26.8470	+	15.5001i	−0.863341	+	0.498450i	−0.865130	−	0.501548i	$-0.832764\pi$
$967$	−26.8470	+	15.5001i	−0.863341	+	0.498450i	0.00178853	+	0.999998i	$0.499431\pi$
$968$	9.84010			0.316273
$969$	−58.8387	−	67.4299i	−1.89017	−	2.16616i
$970$	−19.4928	−	2.77268i	−0.625877	−	0.0890254i
$971$	2.43683	−	4.22071i	0.0782015	−	0.135449i	−0.824273	−	0.566193i	$-0.808416\pi$
$971$	2.43683	−	4.22071i	0.0782015	−	0.135449i	0.902474	+	0.430744i	$0.141749\pi$
$972$	−15.5412	−	1.21265i	−0.498485	−	0.0388959i
$973$	34.1113	−	7.63498i	1.09356	−	0.244766i
$974$	−12.8332	−	7.40923i	−0.411201	−	0.237407i
$975$	3.39795	−	4.83779i	0.108822	−	0.154933i
$976$	12.3974	+	7.15763i	0.396830	+	0.229110i
$977$	−8.71518	+	15.0951i	−0.278823	+	0.482936i	−0.971093	−	0.238703i	$-0.923278\pi$
$977$	−8.71518	+	15.0951i	−0.278823	+	0.482936i	0.692269	+	0.721639i	$0.256611\pi$
$978$	−29.6740	+	25.8933i	−0.948869	+	0.827975i
$979$	−5.84470	−	3.37444i	−0.186797	−	0.107848i
$980$	14.9575	−	4.61215i	0.477801	−	0.147330i
$981$	−18.6412	+	7.61317i	−0.595169	+	0.243070i
$982$	−7.03712	−	4.06288i	−0.224563	−	0.129652i
$983$			12.6384i			0.403101i	0.979478	+	0.201551i	$0.0645980\pi$
$983$			12.6384i			0.403101i	−0.979478	+	0.201551i	$0.935402\pi$
$984$	3.83360	−	11.2019i	0.122211	−	0.357104i
$985$	23.2299	+	3.30424i	0.740165	+	0.105282i
$986$	16.5704	+	28.7008i	0.527709	+	0.914019i
$987$	14.0973	+	10.3464i	0.448722	+	0.329330i
$988$	4.61704	+	2.66565i	0.146888	+	0.0848056i
$989$	7.21045	+	4.16296i	0.229279	+	0.132374i
$990$	−7.47065	−	29.6984i	−0.237433	−	0.943877i
$991$	−5.82563	−	10.0903i	−0.185057	−	0.320529i	0.758538	−	0.651628i	$-0.225914\pi$
$991$	−5.82563	−	10.0903i	−0.185057	−	0.320529i	−0.943596	+	0.331099i	$0.892580\pi$
$992$	−4.52018	+	2.60973i	−0.143516	+	0.0828589i
$993$	−6.13250	+	17.9194i	−0.194609	+	0.568654i
$994$	−21.8965	+	4.90100i	−0.694515	+	0.155450i
$995$	45.5729	−	18.3243i	1.44476	−	0.580920i
$996$	18.4878	+	6.32702i	0.585808	+	0.200479i
$997$	−24.3985			−0.772710			−0.386355	−	0.922350i	$-0.626266\pi$
$997$	−24.3985			−0.772710			−0.386355	+	0.922350i	$0.626266\pi$
$998$	0.852478	+	1.47654i	0.0269847	+	0.0467389i
$999$	8.23768	−	0.478301i	0.260629	−	0.0151328i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.r.b.299.7	yes	48
3.2	odd	2		1890.2.r.a.89.24		48
5.4	even	2		630.2.r.a.299.18	yes	48
7.3	odd	6		630.2.bi.a.479.15	yes	48
9.4	even	3		1890.2.bi.a.719.16		48
9.5	odd	6		630.2.bi.b.509.10	yes	48
15.14	odd	2		1890.2.r.b.89.24		48
21.17	even	6		1890.2.bi.b.899.16		48
35.24	odd	6		630.2.bi.b.479.10	yes	48
45.4	even	6		1890.2.bi.b.719.16		48
45.14	odd	6		630.2.bi.a.509.15	yes	48
63.31	odd	6		1890.2.r.b.1529.24		48
63.59	even	6		630.2.r.a.59.18	✓	48
105.59	even	6		1890.2.bi.a.899.16		48
315.59	even	6	inner	630.2.r.b.59.7	yes	48
315.94	odd	6		1890.2.r.a.1529.24		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.18	✓	48	63.59	even	6
630.2.r.a.299.18	yes	48	5.4	even	2
630.2.r.b.59.7	yes	48	315.59	even	6	inner
630.2.r.b.299.7	yes	48	1.1	even	1	trivial
630.2.bi.a.479.15	yes	48	7.3	odd	6
630.2.bi.a.509.15	yes	48	45.14	odd	6
630.2.bi.b.479.10	yes	48	35.24	odd	6
630.2.bi.b.509.10	yes	48	9.5	odd	6
1890.2.r.a.89.24		48	3.2	odd	2
1890.2.r.a.1529.24		48	315.94	odd	6
1890.2.r.b.89.24		48	15.14	odd	2
1890.2.r.b.1529.24		48	63.31	odd	6
1890.2.bi.a.719.16		48	9.4	even	3
1890.2.bi.a.899.16		48	105.59	even	6
1890.2.bi.b.719.16		48	45.4	even	6
1890.2.bi.b.899.16		48	21.17	even	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.13878 - 1.30506i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.21378 - 0.314891i) q^{5} +(0.560822 - 1.63874i) q^{6} +(2.52491 + 0.790468i) q^{7} -1.00000 q^{8} +(-0.406351 + 2.97235i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.13878 - 1.30506i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.21378 - 0.314891i) q^{5} +(0.560822 - 1.63874i) q^{6} +(2.52491 + 0.790468i) q^{7} -1.00000 q^{8} +(-0.406351 + 2.97235i) q^{9} +(-0.834189 - 2.07464i) q^{10} -4.56510i q^{11} +(1.69960 - 0.333685i) q^{12} +(0.341322 + 0.591187i) q^{13} +(0.577888 + 2.58187i) q^{14} +(2.11007 + 3.24771i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-5.72947 + 3.30791i) q^{17} +(-2.77731 + 1.13427i) q^{18} +(-6.76346 - 3.90489i) q^{19} +(1.37960 - 1.75975i) q^{20} +(-1.84371 - 4.19532i) q^{21} +(3.95349 - 2.28255i) q^{22} -3.50894 q^{23} +(1.13878 + 1.30506i) q^{24} +(4.80169 + 1.39420i) q^{25} +(-0.341322 + 0.591187i) q^{26} +(4.34184 - 2.85455i) q^{27} +(-1.94702 + 1.79140i) q^{28} +(-4.33820 - 2.50466i) q^{29} +(-1.75757 + 3.45123i) q^{30} +(-4.52018 - 2.60973i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-5.95771 + 5.19865i) q^{33} +(-5.72947 - 3.30791i) q^{34} +(-5.34069 - 2.54500i) q^{35} +(-2.37096 - 1.83809i) q^{36} +(1.37526 + 0.794006i) q^{37} -7.80978i q^{38} +(0.382842 - 1.11868i) q^{39} +(2.21378 + 0.314891i) q^{40} +(-3.41784 - 5.91987i) q^{41} +(2.71140 - 3.69436i) q^{42} +(-2.05488 - 1.18639i) q^{43} +(3.95349 + 2.28255i) q^{44} +(1.83554 - 6.45219i) q^{45} +(-1.75447 - 3.03883i) q^{46} +(-3.30466 + 1.90795i) q^{47} +(-0.560822 + 1.63874i) q^{48} +(5.75032 + 3.99172i) q^{49} +(1.19343 + 4.85548i) q^{50} +(10.8416 + 3.71030i) q^{51} -0.682644 q^{52} +(-0.983879 - 1.70413i) q^{53} +(4.64303 + 2.33287i) q^{54} +(-1.43751 + 10.1061i) q^{55} +(-2.52491 - 0.790468i) q^{56} +(2.60601 + 13.2735i) q^{57} -5.00932i q^{58} +(4.68295 - 8.11110i) q^{59} +(-3.86763 + 0.203517i) q^{60} +(-12.3974 + 7.15763i) q^{61} -5.21945i q^{62} +(-3.37555 + 7.18371i) q^{63} +1.00000 q^{64} +(-0.569454 - 1.41624i) q^{65} +(-7.48102 - 2.56021i) q^{66} +(6.28937 + 3.63117i) q^{67} -6.61583i q^{68} +(3.99592 + 4.57937i) q^{69} +(-0.466313 - 5.89767i) q^{70} +8.48088i q^{71} +(0.406351 - 2.97235i) q^{72} +(-0.735176 - 1.27336i) q^{73} +1.58801i q^{74} +(-3.64856 - 7.85417i) q^{75} +(6.76346 - 3.90489i) q^{76} +(3.60856 - 11.5264i) q^{77} +(1.16023 - 0.227788i) q^{78} +(-0.587811 - 1.01812i) q^{79} +(0.834189 + 2.07464i) q^{80} +(-8.66976 - 2.41564i) q^{81} +(3.41784 - 5.91987i) q^{82} +(9.77023 + 5.64084i) q^{83} +(4.55511 + 0.500958i) q^{84} +(13.7255 - 5.51885i) q^{85} -2.37277i q^{86} +(1.67154 + 8.51386i) q^{87} +4.56510i q^{88} +(0.739183 - 1.28030i) q^{89} +(6.50553 - 1.63647i) q^{90} +(0.394492 + 1.76250i) q^{91} +(1.75447 - 3.03883i) q^{92} +(1.74165 + 8.87100i) q^{93} +(-3.30466 - 1.90795i) q^{94} +(13.7432 + 10.7743i) q^{95} +(-1.69960 + 0.333685i) q^{96} +(4.40260 - 7.62553i) q^{97} +(-0.581771 + 6.97578i) q^{98} +(13.5691 + 1.85503i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9}+O(q^{10}) \) 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9	\( 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9} + 3 q^{12} + 3 q^{14} + 6 q^{15} - 24 q^{16} + 3 q^{18} + 5 q^{21} - 6 q^{22} + 6 q^{23} + 3 q^{24} + 3 q^{28} - 3 q^{29} - 3 q^{30} + 24 q^{32} - 24 q^{33} + 12 q^{35} + 3 q^{41} - 8 q^{42} - 6 q^{44} + 9 q^{45} + 3 q^{46} - 6 q^{49} - 18 q^{50} - 8 q^{51} - 42 q^{55} + 22 q^{57} - 9 q^{60} - 9 q^{61} + 10 q^{63} + 48 q^{64} - 21 q^{65} - 24 q^{66} + 33 q^{67} + 42 q^{69} + 12 q^{70} - 3 q^{72} - 18 q^{73} - 39 q^{75} - 6 q^{77} + 18 q^{78} - 37 q^{81} - 3 q^{82} + 9 q^{83} - 13 q^{84} + 33 q^{85} + 18 q^{87} + 33 q^{89} + 15 q^{90} - 3 q^{92} + 32 q^{93} + 33 q^{95} - 3 q^{96} - 24 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9 + 3 * q^12 + 3 * q^14 + 6 * q^15 - 24 * q^16 + 3 * q^18 + 5 * q^21 - 6 * q^22 + 6 * q^23 + 3 * q^24 + 3 * q^28 - 3 * q^29 - 3 * q^30 + 24 * q^32 - 24 * q^33 + 12 * q^35 + 3 * q^41 - 8 * q^42 - 6 * q^44 + 9 * q^45 + 3 * q^46 - 6 * q^49 - 18 * q^50 - 8 * q^51 - 42 * q^55 + 22 * q^57 - 9 * q^60 - 9 * q^61 + 10 * q^63 + 48 * q^64 - 21 * q^65 - 24 * q^66 + 33 * q^67 + 42 * q^69 + 12 * q^70 - 3 * q^72 - 18 * q^73 - 39 * q^75 - 6 * q^77 + 18 * q^78 - 37 * q^81 - 3 * q^82 + 9 * q^83 - 13 * q^84 + 33 * q^85 + 18 * q^87 + 33 * q^89 + 15 * q^90 - 3 * q^92 + 32 * q^93 + 33 * q^95 - 3 * q^96 - 24 * q^97 - 3 * q^98 - 26 * q^99

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