LMFDB - Embedded newform 483.2.u.a.218.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(113,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 13]))

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

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

chi := DirichletCharacter("483.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.u (of order $22$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			218.10
Character	$\chi$	$=$	483.218
Dual form			483.2.u.a.113.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.07128 - 1.66695i) q^{2} +(-1.25731 + 1.19129i) q^{3} +(-0.800245 + 1.75229i) q^{4} +(3.65018 - 1.07179i) q^{5} +(3.33276 + 0.819664i) q^{6} +(0.755750 - 0.654861i) q^{7} +(-0.144404 + 0.0207621i) q^{8} +(0.161658 - 2.99564i) q^{9} +(-5.69700 - 4.93648i) q^{10} +(3.83235 + 2.46290i) q^{11} +(-1.08133 - 3.15650i) q^{12} +(-2.85046 + 3.28961i) q^{13} +(-1.90124 - 0.558255i) q^{14} +(-3.31260 + 5.69600i) q^{15} +(2.71232 + 3.13019i) q^{16} +(-0.260828 - 0.571133i) q^{17} +(-5.16677 + 2.93971i) q^{18} +(6.25501 + 2.85657i) q^{19} +(-1.04295 + 7.25388i) q^{20} +(-0.170083 + 1.72368i) q^{21} -9.02680i q^{22} +(-0.441836 - 4.77544i) q^{23} +(0.156827 - 0.198131i) q^{24} +(7.96882 - 5.12125i) q^{25} +(8.53726 + 1.22747i) q^{26} +(3.36542 + 3.95903i) q^{27} +(0.542723 + 1.84834i) q^{28} +(-4.65769 + 2.12710i) q^{29} +(13.0437 - 0.580093i) q^{30} +(0.310518 + 2.15970i) q^{31} +(2.23000 - 7.59467i) q^{32} +(-7.75247 + 1.46881i) q^{33} +(-0.672631 + 1.04663i) q^{34} +(2.05675 - 3.20037i) q^{35} +(5.11987 + 2.68052i) q^{36} +(2.26731 - 7.72175i) q^{37} +(-1.93914 - 13.4870i) q^{38} +(-0.334962 - 7.53178i) q^{39} +(-0.504847 + 0.230556i) q^{40} +(-0.586531 - 1.99754i) q^{41} +(3.05550 - 1.56303i) q^{42} +(4.09328 + 0.588525i) q^{43} +(-7.38253 + 4.74447i) q^{44} +(-2.62062 - 11.1079i) q^{45} +(-7.48708 + 5.85237i) q^{46} -7.07894i q^{47} +(-7.13919 - 0.704454i) q^{48} +(0.142315 - 0.989821i) q^{49} +(-17.0737 - 7.79732i) q^{50} +(1.00833 + 0.407370i) q^{51} +(-3.48328 - 7.62733i) q^{52} +(0.460792 + 0.531783i) q^{53} +(2.99419 - 9.85124i) q^{54} +(16.6285 + 4.88256i) q^{55} +(-0.0955367 + 0.110255i) q^{56} +(-11.2675 + 3.85994i) q^{57} +(8.53548 + 5.48542i) q^{58} +(6.97879 + 6.04716i) q^{59} +(-7.33016 - 10.3628i) q^{60} +(4.85630 - 0.698230i) q^{61} +(3.26746 - 2.83127i) q^{62} +(-1.83956 - 2.36982i) q^{63} +(-7.10078 + 2.08498i) q^{64} +(-6.87893 + 15.0628i) q^{65} +(10.7535 + 11.3495i) q^{66} +(1.69159 + 2.63217i) q^{67} +1.20952 q^{68} +(6.24445 + 5.47785i) q^{69} -7.53821 q^{70} +(-3.37089 - 5.24521i) q^{71} +(0.0388519 + 0.435938i) q^{72} +(1.23299 - 2.69988i) q^{73} +(-15.3007 + 4.49269i) q^{74} +(-3.91839 + 15.9322i) q^{75} +(-10.0111 + 8.67465i) q^{76} +(4.50915 - 0.648318i) q^{77} +(-12.1963 + 8.62704i) q^{78} +(-6.32714 - 5.48250i) q^{79} +(13.2554 + 8.51871i) q^{80} +(-8.94773 - 0.968537i) q^{81} +(-2.70146 + 3.11765i) q^{82} +(-2.28750 - 0.671670i) q^{83} +(-2.88428 - 1.67740i) q^{84} +(-1.56420 - 1.80519i) q^{85} +(-3.40403 - 7.45378i) q^{86} +(3.32218 - 8.22308i) q^{87} +(-0.604540 - 0.276084i) q^{88} +(2.14317 - 14.9061i) q^{89} +(-15.7089 + 16.2682i) q^{90} +4.35277i q^{91} +(8.72154 + 3.04729i) q^{92} +(-2.96325 - 2.34550i) q^{93} +(-11.8002 + 7.58356i) q^{94} +(25.8936 + 3.72293i) q^{95} +(6.24365 + 12.2054i) q^{96} +(1.16478 + 3.96688i) q^{97} +(-1.80244 + 0.823148i) q^{98} +(7.99749 - 11.0822i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36}+ \cdots - 132 q^{97}+O(q^{100}) $ 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−1.07128	−	1.66695i	−0.757512	−	1.17871i	−0.979062	−	0.203563i	$-0.934748\pi$
$2$	−1.07128	−	1.66695i	−0.757512	−	1.17871i	0.221549	−	0.975149i	$-0.428889\pi$
$3$	−1.25731	+	1.19129i	−0.725908	+	0.687791i
$3$	−1.25731	+	1.19129i	−0.725908	+	0.687791i
$4$	−0.800245	+	1.75229i	−0.400123	+	0.876146i
$5$	3.65018	−	1.07179i	1.63241	−	0.479319i	0.668095	−	0.744076i	$-0.267110\pi$
$5$	3.65018	−	1.07179i	1.63241	−	0.479319i	0.964315	+	0.264757i	$0.0852916\pi$
$6$	3.33276	+	0.819664i	1.36059	+	0.334627i
$7$	0.755750	−	0.654861i	0.285646	−	0.247514i
$7$	0.755750	−	0.654861i	0.285646	−	0.247514i
$8$	−0.144404	+	0.0207621i	−0.0510544	+	0.00734052i
$9$	0.161658	−	2.99564i	0.0538859	−	0.998547i
$10$	−5.69700	−	4.93648i	−1.80155	−	1.56105i
$11$	3.83235	+	2.46290i	1.15550	+	0.742592i	0.970726	−	0.240190i	$-0.0772097\pi$
$11$	3.83235	+	2.46290i	1.15550	+	0.742592i	0.184770	+	0.982782i	$0.440846\pi$
$12$	−1.08133	−	3.15650i	−0.312154	−	0.911203i
$13$	−2.85046	+	3.28961i	−0.790575	+	0.912372i	−0.997825	−	0.0659155i	$-0.979003\pi$
$13$	−2.85046	+	3.28961i	−0.790575	+	0.912372i	0.207250	+	0.978288i	$0.433549\pi$
$14$	−1.90124	−	0.558255i	−0.508129	−	0.149200i
$15$	−3.31260	+	5.69600i	−0.855309	+	1.47070i
$16$	2.71232	+	3.13019i	0.678080	+	0.782546i
$17$	−0.260828	−	0.571133i	−0.0632601	−	0.138520i	0.875361	−	0.483469i	$-0.160623\pi$
$17$	−0.260828	−	0.571133i	−0.0632601	−	0.138520i	−0.938621	+	0.344949i	$0.887896\pi$
$18$	−5.16677	+	2.93971i	−1.21782	+	0.692896i
$19$	6.25501	+	2.85657i	1.43500	+	0.655342i	0.972845	−	0.231458i	$-0.0743497\pi$
$19$	6.25501	+	2.85657i	1.43500	+	0.655342i	0.462153	+	0.886800i	$0.347077\pi$
$20$	−1.04295	+	7.25388i	−0.233211	+	1.62202i
$21$	−0.170083	+	1.72368i	−0.0371151	+	0.376138i
$22$		−	9.02680i		−	1.92452i
$23$	−0.441836	−	4.77544i	−0.0921292	−	0.995747i
$23$	−0.441836	−	4.77544i	−0.0921292	−	0.995747i
$24$	0.156827	−	0.198131i	0.0320121	−	0.0404433i
$25$	7.96882	−	5.12125i	1.59376	−	1.02425i
$26$	8.53726	+	1.22747i	1.67430	+	0.240727i
$27$	3.36542	+	3.95903i	0.647676	+	0.761916i
$28$	0.542723	+	1.84834i	0.102565	+	0.349304i
$29$	−4.65769	+	2.12710i	−0.864912	+	0.394992i	−0.797921	−	0.602762i	$-0.794067\pi$
$29$	−4.65769	+	2.12710i	−0.864912	+	0.394992i	−0.0669905	+	0.997754i	$0.521340\pi$
$30$	13.0437	−	0.580093i	2.38144	−	0.105910i
$31$	0.310518	+	2.15970i	0.0557707	+	0.387894i	0.998520	+	0.0543908i	$0.0173217\pi$
$31$	0.310518	+	2.15970i	0.0557707	+	0.387894i	−0.942749	+	0.333503i	$0.891769\pi$
$32$	2.23000	−	7.59467i	0.394211	−	1.34256i
$33$	−7.75247	+	1.46881i	−1.34953	+	0.255686i
$34$	−0.672631	+	1.04663i	−0.115355	+	0.179496i
$35$	2.05675	−	3.20037i	0.347654	−	0.540960i
$36$	5.11987	+	2.68052i	0.853312	+	0.446753i
$37$	2.26731	−	7.72175i	0.372744	−	1.26945i	−0.533178	−	0.846003i	$-0.679003\pi$
$37$	2.26731	−	7.72175i	0.372744	−	1.26945i	0.905922	−	0.423445i	$-0.139179\pi$
$38$	−1.93914	−	13.4870i	−0.314570	−	2.18788i
$39$	−0.334962	−	7.53178i	−0.0536368	−	1.20605i
$40$	−0.504847	+	0.230556i	−0.0798233	+	0.0364541i
$41$	−0.586531	−	1.99754i	−0.0916008	−	0.311964i	0.900929	−	0.433967i	$-0.142886\pi$
$41$	−0.586531	−	1.99754i	−0.0916008	−	0.311964i	−0.992530	+	0.122003i	$0.961068\pi$
$42$	3.05550	−	1.56303i	0.471473	−	0.241181i
$43$	4.09328	+	0.588525i	0.624220	+	0.0897492i	0.447165	−	0.894452i	$-0.352434\pi$
$43$	4.09328	+	0.588525i	0.624220	+	0.0897492i	0.177055	+	0.984201i	$0.443343\pi$
$44$	−7.38253	+	4.74447i	−1.11296	+	0.715255i
$45$	−2.62062	−	11.1079i	−0.390659	−	1.65587i
$46$	−7.48708	+	5.85237i	−1.10391	+	0.862884i
$47$		−	7.07894i		−	1.03257i	−0.856417	−	0.516285i	$-0.827315\pi$
$47$		−	7.07894i		−	1.03257i	0.856417	−	0.516285i	$-0.172685\pi$
$48$	−7.13919	−	0.704454i	−1.03045	−	0.101679i
$49$	0.142315	−	0.989821i	0.0203307	−	0.141403i
$50$	−17.0737	−	7.79732i	−2.41459	−	1.10271i
$51$	1.00833	+	0.407370i	0.141194	+	0.0570432i
$52$	−3.48328	−	7.62733i	−0.483045	−	1.05772i
$53$	0.460792	+	0.531783i	0.0632947	+	0.0730460i	0.786514	−	0.617573i	$-0.211884\pi$
$53$	0.460792	+	0.531783i	0.0632947	+	0.0730460i	−0.723219	+	0.690619i	$0.757338\pi$
$54$	2.99419	−	9.85124i	0.407457	−	1.34058i
$55$	16.6285	+	4.88256i	2.24218	+	0.658364i
$56$	−0.0955367	+	0.110255i	−0.0127666	+	0.0147335i
$57$	−11.2675	+	3.85994i	−1.49242	+	0.511261i
$58$	8.53548	+	5.48542i	1.12076	+	0.720271i
$59$	6.97879	+	6.04716i	0.908561	+	0.787273i	0.977628	−	0.210339i	$-0.0674569\pi$
$59$	6.97879	+	6.04716i	0.908561	+	0.787273i	−0.0690674	+	0.997612i	$0.522002\pi$
$60$	−7.33016	−	10.3628i	−0.946319	−	1.33784i
$61$	4.85630	−	0.698230i	0.621785	−	0.0893992i	0.175780	−	0.984430i	$-0.443755\pi$
$61$	4.85630	−	0.698230i	0.621785	−	0.0893992i	0.446005	+	0.895030i	$0.352846\pi$
$62$	3.26746	−	2.83127i	0.414968	−	0.359572i
$63$	−1.83956	−	2.36982i	−0.231762	−	0.298569i
$64$	−7.10078	+	2.08498i	−0.887598	+	0.260622i
$65$	−6.87893	+	15.0628i	−0.853226	+	1.86830i
$66$	10.7535	+	11.3495i	1.32367	+	1.39702i
$67$	1.69159	+	2.63217i	0.206661	+	0.321571i	0.929076	−	0.369889i	$-0.120604\pi$
$67$	1.69159	+	2.63217i	0.206661	+	0.321571i	−0.722415	+	0.691460i	$0.756968\pi$
$68$	1.20952			0.146676
$69$	6.24445	+	5.47785i	0.751744	+	0.659455i
$70$	−7.53821			−0.900989
$71$	−3.37089	−	5.24521i	−0.400051	−	0.622492i	0.581533	−	0.813523i	$-0.302453\pi$
$71$	−3.37089	−	5.24521i	−0.400051	−	0.622492i	−0.981584	+	0.191031i	$0.938817\pi$
$72$	0.0388519	+	0.435938i	0.00457874	+	0.0513758i
$73$	1.23299	−	2.69988i	0.144311	−	0.315997i	−0.823650	−	0.567099i	$-0.808066\pi$
$73$	1.23299	−	2.69988i	0.144311	−	0.315997i	0.967961	+	0.251102i	$0.0807930\pi$
$74$	−15.3007	+	4.49269i	−1.77867	+	0.522265i
$75$	−3.91839	+	15.9322i	−0.452456	+	1.83969i
$76$	−10.0111	+	8.67465i	−1.14835	+	0.995051i
$77$	4.50915	−	0.648318i	0.513865	−	0.0738827i
$78$	−12.1963	+	8.62704i	−1.38096	+	0.976820i
$79$	−6.32714	−	5.48250i	−0.711859	−	0.616830i	0.221758	−	0.975102i	$-0.428821\pi$
$79$	−6.32714	−	5.48250i	−0.711859	−	0.616830i	−0.933617	+	0.358272i	$0.883366\pi$
$80$	13.2554	+	8.51871i	1.48199	+	0.952420i
$81$	−8.94773	−	0.968537i	−0.994193	−	0.107615i
$82$	−2.70146	+	3.11765i	−0.298327	+	0.344287i
$83$	−2.28750	−	0.671670i	−0.251085	−	0.0737253i	0.153768	−	0.988107i	$-0.450859\pi$
$83$	−2.28750	−	0.671670i	−0.251085	−	0.0737253i	−0.404853	+	0.914382i	$0.632677\pi$
$84$	−2.88428	−	1.67740i	−0.314701	−	0.183019i
$85$	−1.56420	−	1.80519i	−0.169662	−	0.195800i
$86$	−3.40403	−	7.45378i	−0.367066	−	0.803761i
$87$	3.32218	−	8.22308i	0.356175	−	0.881607i
$88$	−0.604540	−	0.276084i	−0.0644442	−	0.0294307i
$89$	2.14317	−	14.9061i	0.227176	−	1.58004i	−0.482745	−	0.875761i	$-0.660360\pi$
$89$	2.14317	−	14.9061i	0.227176	−	1.58004i	0.709921	−	0.704282i	$-0.248731\pi$
$90$	−15.7089	+	16.2682i	−1.65586	+	1.71481i
$91$			4.35277i			0.456295i
$92$	8.72154	+	3.04729i	0.909283	+	0.317702i
$93$	−2.96325	−	2.34550i	−0.307274	−	0.243217i
$94$	−11.8002	+	7.58356i	−1.21710	+	0.782184i
$95$	25.8936	+	3.72293i	2.65662	+	0.381965i
$96$	6.24365	+	12.2054i	0.637240	+	1.24571i
$97$	1.16478	+	3.96688i	0.118266	+	0.402775i	0.997253	−	0.0740693i	$-0.0235986\pi$
$97$	1.16478	+	3.96688i	0.118266	+	0.402775i	−0.878988	+	0.476845i	$0.841780\pi$
$98$	−1.80244	+	0.823148i	−0.182074	+	0.0831505i
$99$	7.99749	−	11.0822i	0.803778	−	1.11380i
$100$	2.59692	+	18.0620i	0.259692	+	1.80620i
$101$	−2.44178	+	8.31594i	−0.242966	+	0.827467i	0.744226	+	0.667928i	$0.232819\pi$
$101$	−2.44178	+	8.31594i	−0.242966	+	0.827467i	−0.987192	+	0.159538i	$0.948999\pi$
$102$	−0.401139	−	2.11724i	−0.0397186	−	0.209638i
$103$	0.463751	−	0.721610i	0.0456947	−	0.0711024i	−0.817655	−	0.575709i	$-0.804726\pi$
$103$	0.463751	−	0.721610i	0.0456947	−	0.0711024i	0.863349	+	0.504607i	$0.168362\pi$
$104$	0.343318	−	0.534213i	0.0336651	−	0.0523839i
$105$	1.22659	+	6.47404i	0.119703	+	0.631801i
$106$	0.392816	−	1.33781i	0.0381537	−	0.129939i
$107$	2.57664	+	17.9209i	0.249093	+	1.73248i	0.603477	+	0.797381i	$0.293782\pi$
$107$	2.57664	+	17.9209i	0.249093	+	1.73248i	−0.354383	+	0.935100i	$0.615309\pi$
$108$	−9.63054	+	2.72901i	−0.926699	+	0.262599i
$109$	−16.8223	+	7.68250i	−1.61129	+	0.735850i	−0.998519	−	0.0544132i	$-0.982671\pi$
$109$	−16.8223	+	7.68250i	−1.61129	+	0.735850i	−0.612768	+	0.790263i	$0.709944\pi$
$110$	−9.67483	−	32.9494i	−0.922459	−	3.14161i
$111$	6.34813	+	12.4097i	0.602538	+	1.17787i
$112$	4.09967	+	0.589444i	0.387383	+	0.0556972i
$113$	−9.18297	+	5.90154i	−0.863861	+	0.555170i	−0.895869	−	0.444318i	$-0.853446\pi$
$113$	−9.18297	+	5.90154i	−0.863861	+	0.555170i	0.0320082	+	0.999488i	$0.489810\pi$
$114$	18.5050	+	14.6473i	1.73315	+	1.37184i
$115$	−6.73104	−	16.9576i	−0.627673	−	1.58131i
$116$		−	9.86384i		−	0.915834i
$117$	9.39368	+	9.07074i	0.868446	+	0.838591i
$118$	2.60404	−	18.1115i	0.239722	−	1.66730i
$119$	−0.571133	−	0.260828i	−0.0523557	−	0.0239101i
$120$	0.360090	−	0.891299i	0.0328716	−	0.0813641i
$121$	4.05143	+	8.87140i	0.368312	+	0.806491i
$122$	−6.36639	−	7.34720i	−0.576386	−	0.665184i
$123$	3.11710	+	1.81280i	0.281060	+	0.163455i
$124$	−4.03292	−	1.18417i	−0.362167	−	0.106342i
$125$	11.1424	−	12.8590i	0.996603	−	1.15014i
$126$	−1.97968	+	5.60520i	−0.176364	+	0.499351i
$127$	1.87386	+	1.20425i	0.166278	+	0.106860i	0.621133	−	0.783705i	$-0.286673\pi$
$127$	1.87386	+	1.20425i	0.166278	+	0.106860i	−0.454855	+	0.890565i	$0.650309\pi$
$128$	−0.881445	−	0.763776i	−0.0779094	−	0.0675089i
$129$	−5.84763	+	4.13633i	−0.514855	+	0.364183i
$130$	32.4782	−	4.66965i	2.84852	−	0.409556i
$131$	−7.94428	+	6.88376i	−0.694095	+	0.601437i	−0.928779	−	0.370635i	$-0.879140\pi$
$131$	−7.94428	+	6.88376i	−0.694095	+	0.601437i	0.234684	+	0.972072i	$0.424595\pi$
$132$	3.63010	−	14.7600i	0.315960	−	1.28469i
$133$	6.59788	−	1.93731i	0.572108	−	0.167986i
$134$	2.57552	−	5.63961i	0.222491	−	0.487188i
$135$	16.5277	+	10.8442i	1.42247	+	0.933316i
$136$	0.0495225	+	0.0770584i	0.00424652	+	0.00660771i
$137$	−22.2612			−1.90190			−0.950952	−	0.309337i	$-0.899893\pi$
$137$	−22.2612			−1.90190			−0.950952	+	0.309337i	$0.899893\pi$
$138$	2.44172	−	16.2775i	0.207853	−	1.38564i
$139$	19.0243			1.61362			0.806810	−	0.590811i	$-0.201192\pi$
$139$	19.0243			1.61362			0.806810	+	0.590811i	$0.201192\pi$
$140$	3.96207	+	6.16510i	0.334856	+	0.521046i
$141$	8.43307	+	8.90042i	0.710192	+	0.749551i
$142$	−5.13232	+	11.2382i	−0.430695	+	0.943090i
$143$	−19.0259	+	5.58651i	−1.59103	+	0.467168i
$144$	9.81538	−	7.61912i	0.817948	−	0.634927i
$145$	−14.7216	+	12.7564i	−1.22256	+	1.05936i
$146$	−5.82145	+	0.836998i	−0.481787	+	0.0692705i
$147$	1.00023	+	1.41405i	0.0824976	+	0.116629i
$148$	11.7164	+	10.1523i	0.963079	+	0.834513i
$149$	9.28232	+	5.96539i	0.760438	+	0.488704i	0.862489	−	0.506075i	$-0.168904\pi$
$149$	9.28232	+	5.96539i	0.760438	+	0.488704i	−0.102052	+	0.994779i	$0.532541\pi$
$150$	30.7559	−	10.5361i	2.51121	−	0.860271i
$151$	0.0110540	−	0.0127570i	0.000899565	−	0.00103815i	−0.755300	−	0.655380i	$-0.772509\pi$
$151$	0.0110540	−	0.0127570i	0.000899565	−	0.00103815i	0.756199	+	0.654342i	$0.227054\pi$
$152$	−0.962555	−	0.282632i	−0.0780735	−	0.0229245i
$153$	−1.75308	+	0.689019i	−0.141728	+	0.0557039i
$154$	−5.91129	−	6.82200i	−0.476346	−	0.549732i
$155$	3.44819	+	7.55049i	0.276966	+	0.606470i
$156$	13.4659	+	5.44032i	1.07814	+	0.435574i
$157$	−8.64765	−	3.94925i	−0.690158	−	0.315184i	0.0392834	−	0.999228i	$-0.487492\pi$
$157$	−8.64765	−	3.94925i	−0.690158	−	0.315184i	−0.729441	+	0.684044i	$0.760220\pi$
$158$	−2.36089	+	16.4204i	−0.187822	+	1.30633i
$159$	−1.21287	−	0.119679i	−0.0961865	−	0.00949113i
$160$		−	30.1120i		−	2.38056i
$161$	−3.46116	−	3.31969i	−0.272778	−	0.261628i
$162$	7.97106	+	15.9530i	0.626266	+	1.25339i
$163$	2.07098	−	1.33094i	0.162212	−	0.104247i	−0.457016	−	0.889458i	$-0.651082\pi$
$163$	2.07098	−	1.33094i	0.162212	−	0.104247i	0.619228	+	0.785211i	$0.287446\pi$
$164$	3.96964	+	0.570749i	0.309977	+	0.0445680i
$165$	−26.7237	+	13.6704i	−2.08044	+	1.06424i
$166$	1.33092	+	4.53269i	0.103299	+	0.351805i
$167$	10.8909	−	4.97371i	0.842764	−	0.384877i	0.0532283	−	0.998582i	$-0.483049\pi$
$167$	10.8909	−	4.97371i	0.842764	−	0.384877i	0.789535	+	0.613705i	$0.210322\pi$
$168$	−0.0112267	−	0.252437i	−0.000866156	−	0.0194759i
$169$	−0.846293	−	5.88610i	−0.0650995	−	0.452777i
$170$	−1.33345	+	4.54132i	−0.102271	+	0.348303i
$171$	9.56842	−	18.2760i	0.731716	−	1.39760i
$172$	−4.30690	+	6.70166i	−0.328398	+	0.510997i
$173$	−8.63719	+	13.4397i	−0.656673	+	1.02180i	0.340010	+	0.940422i	$0.389570\pi$
$173$	−8.63719	+	13.4397i	−0.656673	+	1.02180i	−0.996683	+	0.0813819i	$0.974067\pi$
$174$	−17.2665	+	3.27135i	−1.30897	+	0.248001i
$175$	2.66873	−	9.08885i	0.201737	−	0.687053i
$176$	2.68522	+	18.6761i	0.202406	+	1.40777i
$177$	−15.9784	+	0.710610i	−1.20101	+	0.0534127i
$178$	−27.1437	+	12.3961i	−2.03450	+	0.929127i
$179$	0.737009	+	2.51002i	0.0550867	+	0.187608i	0.982440	−	0.186579i	$-0.0597400\pi$
$179$	0.737009	+	2.51002i	0.0550867	+	0.187608i	−0.927353	+	0.374187i	$0.877922\pi$
$180$	21.5614	+	4.29695i	1.60709	+	0.320276i
$181$	−19.0914	−	2.74494i	−1.41906	−	0.204029i	−0.610298	−	0.792172i	$-0.708950\pi$
$181$	−19.0914	−	2.74494i	−1.41906	−	0.204029i	−0.808757	+	0.588142i	$0.799859\pi$
$182$	7.25586	−	4.66306i	0.537840	−	0.345649i
$183$	−5.27408	+	6.66315i	−0.389871	+	0.492554i
$184$	0.162951	+	0.680417i	0.0120129	+	0.0501610i
$185$		−	30.6159i		−	2.25092i
$186$	−0.735348	+	7.45228i	−0.0539183	+	0.546428i
$187$	0.407061	−	2.83117i	0.0297673	−	0.207036i
$188$	12.4044	+	5.66489i	0.904682	+	0.413154i
$189$	5.13603	+	0.788153i	0.373591	+	0.0573297i
$190$	−21.5334	−	47.1516i	−1.56220	−	3.42074i
$191$	−5.56407	−	6.42128i	−0.402602	−	0.464627i	0.517857	−	0.855467i	$-0.326730\pi$
$191$	−5.56407	−	6.42128i	−0.402602	−	0.464627i	−0.920459	+	0.390840i	$0.872185\pi$
$192$	6.44407	−	11.0806i	0.465061	−	0.799670i
$193$	14.5215	+	4.26391i	1.04528	+	0.306923i	0.758910	−	0.651195i	$-0.225732\pi$
$193$	14.5215	+	4.26391i	1.04528	+	0.306923i	0.286373	+	0.958118i	$0.407550\pi$
$194$	5.36478	−	6.19128i	0.385169	−	0.444508i
$195$	−9.29515	−	27.1333i	−0.665640	−	1.94306i
$196$	1.62057	+	1.04148i	0.115755	+	0.0743912i
$197$	−9.49076	−	8.22379i	−0.676189	−	0.585921i	0.247582	−	0.968867i	$-0.420364\pi$
$197$	−9.49076	−	8.22379i	−0.676189	−	0.585921i	−0.923771	+	0.382946i	$0.874909\pi$
$198$	−27.0410	−	1.45925i	−1.92172	−	0.103704i
$199$	−22.5859	+	3.24736i	−1.60107	+	0.230199i	−0.884235	−	0.467042i	$-0.845320\pi$
$199$	−22.5859	+	3.24736i	−1.60107	+	0.230199i	−0.716837	+	0.697241i	$0.754411\pi$
$200$	−1.04440	+	0.904977i	−0.0738502	+	0.0639915i
$201$	−5.26254	−	1.29428i	−0.371191	−	0.0912913i
$202$	16.4781	−	4.83841i	1.15940	−	0.340429i
$203$	−2.12710	+	4.65769i	−0.149293	+	0.326906i
$204$	−1.52074	+	1.44089i	−0.106473	+	0.100882i
$205$	−4.28189	−	6.66275i	−0.299060	−	0.465347i
$206$	−1.69970			−0.118424
$207$	−14.3769	+	0.551596i	−0.999265	+	0.0383386i
$208$	−18.0284			−1.25005
$209$	16.9359	+	26.3528i	1.17148	+	1.82286i
$210$	9.47787	−	8.98020i	0.654035	−	0.619693i
$211$	−4.23890	+	9.28190i	−0.291818	+	0.638992i	−0.997585	−	0.0694513i	$-0.977875\pi$
$211$	−4.23890	+	9.28190i	−0.291818	+	0.638992i	0.705767	+	0.708444i	$0.250602\pi$
$212$	−1.30059	+	0.381886i	−0.0893246	+	0.0262281i
$213$	10.4868	+	2.57915i	0.718545	+	0.176720i
$214$	27.1130	−	23.4935i	1.85341	−	1.60598i
$215$	15.5720	−	2.23891i	1.06200	−	0.152693i
$216$	−0.568177	−	0.501825i	−0.0386596	−	0.0341449i
$217$	1.64898	+	1.42885i	0.111940	+	0.0969965i
$218$	30.8278	+	19.8118i	2.08792	+	1.34183i
$219$	1.66608	+	4.86344i	0.112583	+	0.328641i
$220$	−21.8625	+	25.2307i	−1.47397	+	1.70105i
$221$	2.62228	+	0.769972i	0.176394	+	0.0517939i
$222$	13.8856	−	23.8763i	0.931943	−	1.60247i
$223$	−3.66342	−	4.22781i	−0.245321	−	0.283115i	0.619713	−	0.784828i	$-0.287249\pi$
$223$	−3.66342	−	4.22781i	−0.245321	−	0.283115i	−0.865034	+	0.501713i	$0.832703\pi$
$224$	−3.28813	−	7.20000i	−0.219698	−	0.481070i
$225$	−14.0532	−	24.6996i	−0.936881	−	1.64664i
$226$	19.6751	+	8.98533i	1.30877	+	0.597696i
$227$	−0.720764	+	5.01302i	−0.0478388	+	0.332726i	0.951821	+	0.306653i	$0.0992092\pi$
$227$	−0.720764	+	5.01302i	−0.0478388	+	0.332726i	−0.999660	+	0.0260727i	$0.991700\pi$
$228$	2.25301	−	22.8328i	0.149209	−	1.51214i
$229$			9.05477i			0.598356i	0.954197	+	0.299178i	$0.0967124\pi$
$229$			9.05477i			0.598356i	−0.954197	+	0.299178i	$0.903288\pi$
$230$	−21.0567	+	29.3868i	−1.38844	+	1.93771i
$231$	−4.89706	+	6.18684i	−0.322203	+	0.407064i
$232$	0.628425	−	0.403864i	0.0412581	−	0.0265150i
$233$	−22.6608	−	3.25813i	−1.48456	−	0.213447i	−0.648132	−	0.761528i	$-0.724450\pi$
$233$	−22.6608	−	3.25813i	−1.48456	−	0.213447i	−0.836426	+	0.548081i	$0.815359\pi$
$234$	5.05718	−	25.3761i	0.330598	−	1.65889i
$235$	−7.58713	−	25.8394i	−0.494930	−	1.68558i
$236$	−16.1811	+	7.38967i	−1.05330	+	0.481027i
$237$	14.4864	−	0.644257i	0.940995	−	0.0418490i
$238$	0.177059	+	1.23147i	0.0114770	+	0.0798245i
$239$	1.36427	−	4.64629i	0.0882475	−	0.300543i	−0.903529	−	0.428527i	$-0.859033\pi$
$239$	1.36427	−	4.64629i	0.0882475	−	0.300543i	0.991776	+	0.127984i	$0.0408507\pi$
$240$	−26.8144	+	5.08033i	−1.73086	+	0.327934i
$241$	15.1519	−	23.5769i	0.976022	−	1.51872i	0.125962	−	0.992035i	$-0.459798\pi$
$241$	15.1519	−	23.5769i	0.976022	−	1.51872i	0.850060	−	0.526685i	$-0.176565\pi$
$242$	10.4480	−	16.2573i	0.671620	−	1.04506i
$243$	12.4039	−	9.44159i	0.795710	−	0.605678i
$244$	−2.66272	+	9.06840i	−0.170463	+	0.580545i
$245$	−0.541406	−	3.76556i	−0.0345891	−	0.240573i
$246$	−0.317453	−	7.13808i	−0.0202400	−	0.455107i
$247$	−27.2266	+	12.4340i	−1.73239	+	0.791156i
$248$	−0.0896799	−	0.305422i	−0.00569468	−	0.0193943i
$249$	3.67625	−	1.88057i	0.232973	−	0.119177i
$250$	−33.3719	−	4.79816i	−2.11063	−	0.303462i
$251$	1.15916	−	0.744947i	0.0731656	−	0.0470207i	−0.503547	−	0.863968i	$-0.667972\pi$
$251$	1.15916	−	0.744947i	0.0731656	−	0.0470207i	0.576712	+	0.816947i	$0.304335\pi$
$252$	5.62471	−	1.32700i	0.354323	−	0.0835933i
$253$	10.0681	−	19.3893i	0.632979	−	1.21900i
$254$		−	4.41373i		−	0.276942i
$255$	4.11719	+	0.406261i	0.257829	+	0.0254410i
$256$	−2.43532	+	16.9380i	−0.152207	+	1.05863i
$257$	14.5273	+	6.63441i	0.906190	+	0.413843i	0.813308	−	0.581834i	$-0.197665\pi$
$257$	14.5273	+	6.63441i	0.906190	+	0.413843i	0.0928826	+	0.995677i	$0.470392\pi$
$258$	13.1595	+	5.31653i	0.819276	+	0.330993i
$259$	−3.34315	−	7.32048i	−0.207733	−	0.454873i
$260$	−20.8895	−	24.1078i	−1.29551	−	1.49510i
$261$	5.61907	+	14.2966i	0.347812	+	0.884940i
$262$	19.9855	+	5.86826i	1.23471	+	0.362542i
$263$	−11.9217	+	13.7583i	−0.735121	+	0.848375i	−0.993038	−	0.117792i	$-0.962418\pi$
$263$	−11.9217	+	13.7583i	−0.735121	+	0.848375i	0.257917	+	0.966167i	$0.416964\pi$
$264$	1.08899	−	0.373059i	0.0670227	−	0.0229602i
$265$	2.25193	+	1.44723i	0.138335	+	0.0889027i
$266$	−10.2976	−	8.92293i	−0.631387	−	0.547100i
$267$	15.0628	+	21.2947i	0.921831	+	1.30322i
$268$	−5.96602	+	0.857785i	−0.364433	+	0.0523975i
$269$	6.63437	−	5.74872i	0.404505	−	0.350505i	−0.428722	−	0.903436i	$-0.641036\pi$
$269$	6.63437	−	5.74872i	0.404505	−	0.350505i	0.833227	+	0.552931i	$0.186491\pi$
$270$	0.370859	−	39.1680i	0.0225698	−	2.38369i
$271$	21.5138	−	6.31704i	1.30687	−	0.383733i	0.447134	−	0.894467i	$-0.352445\pi$
$271$	21.5138	−	6.31704i	1.30687	−	0.383733i	0.859739	+	0.510734i	$0.170626\pi$
$272$	1.08030	−	2.36554i	0.0655031	−	0.143432i
$273$	−5.18541	−	5.47278i	−0.313835	−	0.331228i
$274$	23.8481	+	37.1084i	1.44072	+	2.24180i
$275$	43.1524			2.60219
$276$	−14.5959	+	6.55848i	−0.878569	+	0.394774i
$277$	−17.3824			−1.04441			−0.522205	−	0.852820i	$-0.674890\pi$
$277$	−17.3824			−1.04441			−0.522205	+	0.852820i	$0.674890\pi$
$278$	−20.3804	−	31.7126i	−1.22234	−	1.90199i
$279$	6.51989	−	0.581069i	0.390335	−	0.0347877i
$280$	−0.230556	+	0.504847i	−0.0137784	+	0.0301704i
$281$	17.7141	−	5.20132i	1.05673	−	0.310285i	0.293199	−	0.956052i	$-0.405280\pi$
$281$	17.7141	−	5.20132i	1.05673	−	0.310285i	0.763535	+	0.645767i	$0.223462\pi$
$282$	5.80235	−	23.5924i	0.345525	−	1.40491i
$283$	−1.85956	+	1.61131i	−0.110539	+	0.0957827i	−0.708377	−	0.705835i	$-0.750572\pi$
$283$	−1.85956	+	1.61131i	−0.110539	+	0.0957827i	0.597838	+	0.801617i	$0.296027\pi$
$284$	11.8887	−	1.70933i	0.705463	−	0.101430i
$285$	−36.9913	+	26.1659i	−2.19118	+	1.54993i
$286$	29.6946	+	25.7305i	1.75588	+	1.52148i
$287$	−1.75138	−	1.12554i	−0.103381	−	0.0664388i
$288$	−22.3904	−	7.90800i	−1.31937	−	0.465984i
$289$	10.8745	−	12.5498i	0.639675	−	0.738224i
$290$	37.0353	+	10.8745i	2.17479	+	0.638575i
$291$	−6.19019	−	3.60000i	−0.362875	−	0.211036i
$292$	3.74428	+	4.32113i	0.219117	+	0.252875i
$293$	−2.37252	−	5.19509i	−0.138604	−	0.303501i	0.827583	−	0.561344i	$-0.189715\pi$
$293$	−2.37252	−	5.19509i	−0.138604	−	0.303501i	−0.966187	+	0.257843i	$0.916988\pi$
$294$	1.28562	−	3.18218i	0.0749790	−	0.185589i
$295$	31.9551	+	14.5934i	1.86050	+	0.849662i
$296$	−0.167088	+	1.16212i	−0.00971180	+	0.0675471i
$297$	3.14677	+	23.4611i	0.182594	+	1.36135i
$298$		−	21.8638i		−	1.26654i
$299$	16.9687	+	12.1587i	0.981327	+	0.703157i
$300$	−24.7822	−	19.6158i	−1.43080	−	1.13252i
$301$	3.47890	−	2.23575i	0.200520	−	0.128867i
$302$	−0.0331074	−	0.00476012i	−0.00190512	−	0.000273914i
$303$	−6.83662	−	13.3646i	−0.392753	−	0.767775i
$304$	8.02401	+	27.3273i	0.460209	+	1.56733i
$305$	16.9780	−	7.75359i	0.972158	−	0.443969i
$306$	3.02660	+	2.18416i	0.173019	+	0.124860i
$307$	−3.04256	−	21.1615i	−0.173648	−	1.20775i	−0.871096	−	0.491113i	$-0.836590\pi$
$307$	−3.04256	−	21.1615i	−0.173648	−	1.20775i	0.697448	−	0.716636i	$-0.254319\pi$
$308$	−2.47238	+	8.42016i	−0.140877	+	0.479783i
$309$	0.276568	+	1.45975i	0.0157334	+	0.0830422i
$310$	8.89230	−	13.8367i	0.505049	−	0.785871i
$311$	−15.2334	+	23.7036i	−0.863806	+	1.34411i	0.0741119	+	0.997250i	$0.476388\pi$
$311$	−15.2334	+	23.7036i	−0.863806	+	1.34411i	−0.937918	+	0.346858i	$0.887249\pi$
$312$	0.204745	+	1.08066i	0.0115914	+	0.0611804i
$313$	2.95056	−	10.0487i	0.166776	−	0.567986i	−0.833114	−	0.553102i	$-0.813444\pi$
$313$	2.95056	−	10.0487i	0.166776	−	0.567986i	0.999889	−	0.0148837i	$-0.00473781\pi$
$314$	2.68089	+	18.6460i	0.151291	+	1.05225i
$315$	−9.25466	−	6.67865i	−0.521441	−	0.376299i
$316$	14.6702	−	6.69966i	0.825264	−	0.376885i
$317$	−6.89564	−	23.4844i	−0.387298	−	1.31902i	−0.890554	−	0.454878i	$-0.849683\pi$
$317$	−6.89564	−	23.4844i	−0.387298	−	1.31902i	0.503256	−	0.864138i	$-0.332135\pi$
$318$	1.09983	+	2.15000i	0.0616752	+	0.120566i
$319$	−23.0887	−	3.31966i	−1.29272	−	0.185865i
$320$	−23.6845	+	15.2211i	−1.32400	+	0.850885i
$321$	−24.5886	−	19.4626i	−1.37240	−	1.08630i
$322$	−1.82587	+	9.32592i	−0.101752	+	0.519713i
$323$		−	4.31752i		−	0.240233i
$324$	8.85754	−	14.9040i	0.492085	−	0.827999i
$325$	−5.86791	+	40.8122i	−0.325493	+	2.26385i
$326$	−4.43722	−	2.02641i	−0.245755	−	0.112232i
$327$	11.9988	−	29.6995i	0.663535	−	1.64239i
$328$	0.126170	+	0.276275i	0.00696660	+	0.0152547i
$329$	−4.63572	−	5.34990i	−0.255575	−	0.294950i
$330$	51.4166	+	29.9021i	2.83039	+	1.64606i
$331$	−27.5598	−	8.09227i	−1.51482	−	0.444792i	−0.584456	−	0.811426i	$-0.698692\pi$
$331$	−27.5598	−	8.09227i	−1.51482	−	0.444792i	−0.930365	+	0.366634i	$0.880510\pi$
$332$	3.00752	−	3.47086i	0.165059	−	0.190488i
$333$	−22.7651	−	8.04033i	−1.24752	−	0.440607i
$334$	−19.9582	−	12.8263i	−1.09206	−	0.701826i
$335$	8.99576	+	7.79487i	0.491491	+	0.425879i
$336$	−5.85676	+	4.14278i	−0.319512	+	0.226007i
$337$	13.1951	−	1.89716i	0.718781	−	0.103345i	0.226788	−	0.973944i	$-0.427178\pi$
$337$	13.1951	−	1.89716i	0.718781	−	0.103345i	0.491993	+	0.870599i	$0.336269\pi$
$338$	−8.90522	+	7.71641i	−0.484380	+	0.419718i
$339$	4.51540	−	18.3596i	0.245243	−	0.997159i
$340$	4.41496	−	1.29635i	0.239435	−	0.0703045i
$341$	−4.12911	+	9.04150i	−0.223604	+	0.489624i
$342$	−40.7157	+	3.62868i	−2.20165	+	0.196217i
$343$	−0.540641	−	0.841254i	−0.0291919	−	0.0454234i
$344$	−0.603304			−0.0325280
$345$	28.6645	+	13.3024i	1.54324	+	0.716177i
$346$	31.6563			1.70185
$347$	11.9476	+	18.5908i	0.641379	+	0.998005i	0.997966	+	0.0637432i	$0.0203039\pi$
$347$	11.9476	+	18.5908i	0.641379	+	0.998005i	−0.356587	+	0.934262i	$0.616060\pi$
$348$	11.7507	+	12.4019i	0.629903	+	0.664812i
$349$	−7.35422	+	16.1035i	−0.393662	+	0.862000i	0.604211	+	0.796824i	$0.293488\pi$
$349$	−7.35422	+	16.1035i	−0.393662	+	0.862000i	−0.997874	+	0.0651763i	$0.979239\pi$
$350$	−18.0096	+	5.28811i	−0.962655	+	0.282661i
$351$	−22.6167	−	0.214144i	−1.20719	−	0.0114302i
$352$	27.2510	−	23.6131i	1.45248	−	1.25858i
$353$	16.0129	−	2.30231i	0.852282	−	0.122540i	0.297691	−	0.954662i	$-0.403784\pi$
$353$	16.0129	−	2.30231i	0.852282	−	0.122540i	0.554592	+	0.832123i	$0.312874\pi$
$354$	18.3020	+	25.8740i	0.972739	+	1.37519i
$355$	−17.9261	−	15.5331i	−0.951420	−	0.824410i
$356$	24.4048	+	15.6840i	1.29345	+	0.831250i
$357$	1.02881	−	0.352444i	0.0544506	−	0.0186533i
$358$	3.39454	−	3.91751i	0.179407	−	0.207047i
$359$	−25.9857	−	7.63008i	−1.37147	−	0.402700i	−0.488679	−	0.872464i	$-0.662521\pi$
$359$	−25.9857	−	7.63008i	−1.37147	−	0.402700i	−0.882792	+	0.469764i	$0.844339\pi$
$360$	0.609050	+	1.54961i	0.0320998	+	0.0816717i
$361$	18.5228	+	21.3765i	0.974886	+	1.12508i
$362$	15.8767	+	34.7651i	0.834460	+	1.82721i
$363$	−15.6623	−	6.32767i	−0.822059	−	0.332117i
$364$	−7.62733	−	3.48328i	−0.399781	−	0.182574i
$365$	1.60695	−	11.1766i	0.0841114	−	0.585007i
$366$	16.7572	+	1.65350i	0.875911	+	0.0864299i
$367$			20.1857i			1.05368i	0.849963	+	0.526842i	$0.176624\pi$
$367$			20.1857i			1.05368i	−0.849963	+	0.526842i	$0.823376\pi$
$368$	13.7496	−	14.3355i	0.716747	−	0.747292i
$369$	−6.07873	+	1.43412i	−0.316446	+	0.0746572i
$370$	−51.0351	+	32.7983i	−2.65319	+	1.70510i
$371$	0.696487	+	0.100140i	0.0361598	+	0.00519900i
$372$	6.48132	−	3.31550i	0.336041	−	0.171901i
$373$	5.88856	+	20.0546i	0.304898	+	1.03839i	0.959335	+	0.282271i	$0.0910878\pi$
$373$	5.88856	+	20.0546i	0.304898	+	1.03839i	−0.654436	+	0.756117i	$0.727094\pi$
$374$	−5.15550	+	2.35444i	−0.266585	+	0.121745i
$375$	1.30936	+	29.4415i	0.0676148	+	1.52035i
$376$	0.146974	+	1.02222i	0.00757959	+	0.0527172i
$377$	6.27925	−	21.3852i	0.323398	−	1.10139i
$378$	−4.18834	−	9.40585i	−0.215425	−	0.483785i
$379$	−11.8807	+	18.4868i	−0.610271	+	0.949601i	0.389322	+	0.921102i	$0.372709\pi$
$379$	−11.8807	+	18.4868i	−0.610271	+	0.949601i	−0.999594	+	0.0284993i	$0.990927\pi$
$380$	−27.2449	+	42.3938i	−1.39763	+	2.17476i
$381$	−3.79064	+	0.718185i	−0.194200	+	0.0367937i
$382$	−4.74325	+	16.1540i	−0.242686	+	0.826512i
$383$	0.853080	+	5.93330i	0.0435903	+	0.303177i	0.999940	+	0.0109527i	$0.00348643\pi$
$383$	0.853080	+	5.93330i	0.0435903	+	0.303177i	−0.956350	+	0.292225i	$0.905604\pi$
$384$	2.01813	−	0.0897524i	0.102987	−	0.00458016i
$385$	15.7644	−	7.19934i	0.803426	−	0.366912i
$386$	−8.44897	−	28.7746i	−0.430041	−	1.46459i
$387$	2.42472	−	12.1669i	0.123255	−	0.618476i
$388$	−7.88324	−	1.13344i	−0.400211	−	0.0575416i
$389$	5.52809	−	3.55269i	0.280285	−	0.180128i	−0.392944	−	0.919563i	$-0.628543\pi$
$389$	5.52809	−	3.55269i	0.280285	−	0.180128i	0.673229	+	0.739434i	$0.264907\pi$
$390$	−35.2722	+	44.5621i	−1.78608	+	2.25649i
$391$	−2.61217	+	1.49791i	−0.132103	+	0.0757528i
$392$			0.145889i			0.00736849i
$393$	1.78787	−	18.1190i	0.0901863	−	0.913981i
$394$	−3.54135	+	24.6306i	−0.178411	+	1.24087i
$395$	−28.9713	−	13.2308i	−1.45771	−	0.665712i
$396$	13.0193	+	22.8824i	0.654243	+	1.14988i
$397$	0.458667	+	1.00434i	0.0230199	+	0.0504064i	0.920793	−	0.390052i	$-0.127543\pi$
$397$	0.458667	+	1.00434i	0.0230199	+	0.0504064i	−0.897773	+	0.440459i	$0.854816\pi$
$398$	29.6091	+	34.1707i	1.48417	+	1.71282i
$399$	−5.98768	+	10.2958i	−0.299759	+	0.515434i
$400$	37.6445	+	11.0534i	1.88222	+	0.552671i
$401$	15.1721	−	17.5095i	0.757659	−	0.874385i	−0.237628	−	0.971356i	$-0.576370\pi$
$401$	15.1721	−	17.5095i	0.757659	−	0.874385i	0.995287	+	0.0969714i	$0.0309155\pi$
$402$	3.48018	+	10.1589i	0.173575	+	0.506681i
$403$	−7.98969	−	5.13466i	−0.397995	−	0.255776i
$404$	−12.6179	−	10.9335i	−0.627766	−	0.543962i
$405$	−33.6989	+	6.05476i	−1.67451	+	0.300863i
$406$	10.0429	−	1.44395i	0.498419	−	0.0716619i
$407$	27.7070	−	24.0083i	1.37339	−	1.19005i
$408$	−0.154064	−	0.0378908i	−0.00762731	−	0.00187587i
$409$	20.5806	−	6.04301i	1.01764	−	0.298808i	0.269967	−	0.962869i	$-0.412987\pi$
$409$	20.5806	−	6.04301i	1.01764	−	0.298808i	0.747678	+	0.664062i	$0.231169\pi$
$410$	−6.51936	+	14.2754i	−0.321968	+	0.705012i
$411$	27.9893	−	26.5196i	1.38061	−	1.30811i
$412$	0.893358	+	1.39009i	0.0440126	+	0.0684849i
$413$	9.23426			0.454388
$414$	16.3212	+	23.3747i	0.802146	+	1.14880i
$415$	−9.06967			−0.445212
$416$	18.6269	+	28.9841i	0.913261	+	1.42106i
$417$	−23.9194	+	22.6635i	−1.17134	+	1.10983i
$418$	25.7857	−	56.4627i	1.26122	−	2.76168i
$419$	3.59173	−	1.05463i	0.175467	−	0.0515219i	−0.192819	−	0.981234i	$-0.561763\pi$
$419$	3.59173	−	1.05463i	0.175467	−	0.0515219i	0.368286	+	0.929713i	$0.379945\pi$
$420$	−12.3260	−	3.03147i	−0.601446	−	0.147921i
$421$	−9.36821	+	8.11760i	−0.456579	+	0.395628i	−0.852559	−	0.522631i	$-0.824950\pi$
$421$	−9.36821	+	8.11760i	−0.456579	+	0.395628i	0.395980	+	0.918259i	$0.370405\pi$
$422$	20.0135	−	2.87751i	0.974244	−	0.140075i
$423$	−21.2060	−	1.14436i	−1.03107	−	0.0556409i
$424$	−0.0775811	−	0.0672244i	−0.00376767	−	0.00326470i
$425$	−5.00341	−	3.21550i	−0.242701	−	0.155974i
$426$	−6.93505	−	20.2440i	−0.336004	−	0.980825i
$427$	3.21290	−	3.70788i	0.155483	−	0.179437i
$428$	−33.4646	−	9.82610i	−1.61757	−	0.474963i
$429$	17.2663	−	29.6894i	0.833626	−	1.43342i
$430$	−20.4142	−	23.5592i	−0.984460	−	1.13613i
$431$	0.958870	+	2.09963i	0.0461871	+	0.101136i	0.931319	−	0.364205i	$-0.118659\pi$
$431$	0.958870	+	2.09963i	0.0461871	+	0.101136i	−0.885132	+	0.465340i	$0.845932\pi$
$432$	−3.26439	+	21.2726i	−0.157058	+	1.02348i
$433$	−0.00657273	−	0.00300166i	−0.000315865	−	0.000144251i	0.415257	−	0.909704i	$-0.363692\pi$
$433$	−0.00657273	−	0.00300166i	−0.000315865	−	0.000144251i	−0.415573	+	0.909560i	$0.636419\pi$
$434$	0.615294	−	4.27947i	0.0295351	−	0.205421i
$435$	3.31313	−	33.5764i	0.158852	−	1.60987i
$436$		−	35.6255i		−	1.70615i
$437$	10.8777	−	31.1325i	0.520349	−	1.48927i
$438$	6.32226	−	7.98740i	0.302089	−	0.381653i
$439$	−4.10571	+	2.63858i	−0.195955	+	0.125933i	−0.634939	−	0.772562i	$-0.718975\pi$
$439$	−4.10571	+	2.63858i	−0.195955	+	0.125933i	0.438984	+	0.898495i	$0.355338\pi$
$440$	−2.50258	−	0.359817i	−0.119306	−	0.0171536i
$441$	−2.94214	−	0.586336i	−0.140102	−	0.0279208i
$442$	−1.52571	−	5.19608i	−0.0725704	−	0.247152i
$443$	−29.3101	+	13.3855i	−1.39256	+	0.635962i	−0.963597	−	0.267359i	$-0.913849\pi$
$443$	−29.3101	+	13.3855i	−1.39256	+	0.635962i	−0.428966	+	0.903321i	$0.641122\pi$
$444$	−26.8254	+	1.19301i	−1.27308	+	0.0566177i
$445$	−8.15323	−	56.7070i	−0.386500	−	2.68817i
$446$	−3.12299	+	10.6359i	−0.147878	+	0.503626i
$447$	−18.7773	+	3.55760i	−0.888134	+	0.168268i
$448$	−4.00104	+	6.22575i	−0.189032	+	0.294139i
$449$	−11.3204	+	17.6149i	−0.534244	+	0.831300i	−0.998520	−	0.0543908i	$-0.982678\pi$
$449$	−11.3204	+	17.6149i	−0.534244	+	0.831300i	0.464276	+	0.885691i	$0.346315\pi$
$450$	−26.1181	+	49.8863i	−1.23122	+	2.35166i
$451$	2.67195	−	9.09983i	0.125817	−	0.428494i
$452$	−2.99259	−	20.8139i	−0.140760	−	0.979004i
$453$	0.00129898	+	0.0292081i	6.10313e−5	+	0.00137232i
$454$	9.12861	−	4.16889i	0.428427	−	0.195656i
$455$	4.66526	+	15.8884i	0.218711	+	0.744860i
$456$	1.54693	−	0.791326i	0.0724415	−	0.0370573i
$457$	−19.8380	−	2.85227i	−0.927983	−	0.133424i	−0.338281	−	0.941045i	$-0.609845\pi$
$457$	−19.8380	−	2.85227i	−0.927983	−	0.133424i	−0.589701	+	0.807621i	$0.700755\pi$
$458$	15.0939	−	9.70023i	0.705290	−	0.453262i
$459$	1.38334	−	2.95473i	0.0645687	−	0.137915i
$460$	35.1012	+	1.77552i	1.63660	+	0.0827839i
$461$		−	22.5325i		−	1.04944i	−0.851274	−	0.524722i	$-0.824169\pi$
$461$		−	22.5325i		−	1.04944i	0.851274	−	0.524722i	$-0.175831\pi$
$462$	15.5593	+	1.53530i	0.723884	+	0.0714287i
$463$	−4.20149	+	29.2220i	−0.195260	+	1.35806i	0.622554	+	0.782577i	$0.286095\pi$
$463$	−4.20149	+	29.2220i	−0.195260	+	1.35806i	−0.817813	+	0.575484i	$0.804814\pi$
$464$	−19.2914	−	8.81007i	−0.895579	−	0.408997i
$465$	−13.3303	−	5.38551i	−0.618177	−	0.249747i
$466$	18.8450	+	41.2648i	0.872978	+	1.91156i
$467$	5.04741	+	5.82502i	0.233566	+	0.269550i	0.860418	−	0.509589i	$-0.170202\pi$
$467$	5.04741	+	5.82502i	0.233566	+	0.269550i	−0.626852	+	0.779138i	$0.715657\pi$
$468$	−23.4118	+	9.20166i	−1.08221	+	0.425347i
$469$	3.00213	+	0.881504i	0.138625	+	0.0407041i
$470$	−34.9450	+	40.3287i	−1.61189	+	1.86023i
$471$	15.5775	−	5.33643i	0.717772	−	0.245889i
$472$	−1.13331	−	0.728337i	−0.0521650	−	0.0335244i
$473$	14.2374	+	12.3368i	0.654636	+	0.567245i
$474$	−16.5930	−	23.4580i	−0.762143	−	1.07746i
$475$	64.4743	−	9.27000i	2.95828	−	0.425337i
$476$	0.914093	−	0.792066i	0.0418974	−	0.0363043i
$477$	1.66752	−	1.29440i	0.0763505	−	0.0592666i
$478$	−9.20665	+	2.70332i	−0.421103	+	0.123647i
$479$	−0.130362	+	0.285454i	−0.00595641	+	0.0130427i	−0.912587	−	0.408883i	$-0.865918\pi$
$479$	−0.130362	+	0.285454i	−0.00595641	+	0.0130427i	0.906630	+	0.421926i	$0.138646\pi$
$480$	35.8721	+	37.8601i	1.63733	+	1.72807i
$481$	18.9386	+	29.4691i	0.863528	+	1.34368i
$482$	−55.5335			−2.52948
$483$	8.30647	+	0.0506355i	0.377957	+	0.00230400i
$484$	−18.7874			−0.853974
$485$	8.50332	+	13.2314i	0.386116	+	0.600808i
$486$	−29.0268	−	10.5620i	−1.31668	−	0.479104i
$487$	−2.63898	+	5.77856i	−0.119584	+	0.261851i	−0.959952	−	0.280164i	$-0.909611\pi$
$487$	−2.63898	+	5.77856i	−0.119584	+	0.261851i	0.840369	+	0.542015i	$0.182338\pi$
$488$	−0.686770	+	0.201654i	−0.0310886	+	0.00912845i
$489$	−1.01833	+	4.14054i	−0.0460505	+	0.187242i
$490$	−5.69700	+	4.93648i	−0.257364	+	0.223007i
$491$	−19.1239	+	2.74960i	−0.863049	+	0.124088i	−0.559603	−	0.828761i	$-0.689046\pi$
$491$	−19.1239	+	2.74960i	−0.863049	+	0.124088i	−0.303446	+	0.952849i	$0.598137\pi$
$492$	−5.67100	+	4.01139i	−0.255668	+	0.180847i
$493$	2.42971	+	2.10536i	0.109429	+	0.0948205i
$494$	49.8943	+	32.0651i	2.24485	+	1.44268i
$495$	17.3145	−	49.0236i	0.778229	−	2.20345i
$496$	−5.91804	+	6.82978i	−0.265728	+	0.306666i
$497$	−5.98243	−	1.75660i	−0.268349	−	0.0787943i
$498$	−7.07313	−	4.11349i	−0.316954	−	0.184330i
$499$	−13.6612	−	15.7659i	−0.611561	−	0.705779i	0.362521	−	0.931976i	$-0.381916\pi$
$499$	−13.6612	−	15.7659i	−0.611561	−	0.705779i	−0.974082	+	0.226197i	$0.927371\pi$
$500$	13.6161	+	29.8150i	0.608929	+	1.33337i
$501$	−7.76812	+	19.2277i	−0.347054	+	0.859031i
$502$	−2.48358	−	1.13421i	−0.110848	−	0.0506224i
$503$	−3.28896	+	22.8752i	−0.146648	+	1.01996i	0.775009	+	0.631950i	$0.217745\pi$
$503$	−3.28896	+	22.8752i	−0.146648	+	1.01996i	−0.921657	+	0.388006i	$0.873164\pi$
$504$	0.314841	+	0.304017i	0.0140241	+	0.0135420i
$505$			32.9718i			1.46722i
$506$	−43.1069	+	3.98836i	−1.91633	+	0.177304i
$507$	8.07610	+	6.39247i	0.358672	+	0.283900i
$508$	−3.60975	+	2.31985i	−0.160157	+	0.102927i
$509$	−11.9807	−	1.72257i	−0.531036	−	0.0763515i	−0.128419	−	0.991720i	$-0.540990\pi$
$509$	−11.9807	−	1.72257i	−0.531036	−	0.0763515i	−0.402617	+	0.915368i	$0.631899\pi$
$510$	−3.73347	−	7.29838i	−0.165321	−	0.323178i
$511$	−0.836210	−	2.84787i	−0.0369918	−	0.125982i
$512$	28.7219	−	13.1169i	1.26934	−	0.579688i
$513$	9.74152	+	34.3773i	0.430098	+	1.51780i
$514$	−4.50367	−	31.3237i	−0.198648	−	1.38163i
$515$	0.919360	−	3.13105i	0.0405118	−	0.137971i
$516$	−2.56852	−	13.5568i	−0.113073	−	0.596806i
$517$	17.4347	−	27.1289i	0.766778	−	1.19313i
$518$	−8.62142	+	13.4152i	−0.378803	+	0.589429i
$519$	−5.15099	−	27.1873i	−0.226103	−	1.19339i
$520$	0.680608	−	2.31794i	0.0298466	−	0.101648i
$521$	−2.76437	−	19.2266i	−0.121109	−	0.842335i	−0.956303	−	0.292378i	$-0.905553\pi$
$521$	−2.76437	−	19.2266i	−0.121109	−	0.842335i	0.835193	−	0.549957i	$-0.185356\pi$
$522$	17.8122	−	24.6825i	0.779618	−	1.08032i
$523$	28.7283	−	13.1198i	1.25620	−	0.573687i	0.327616	−	0.944811i	$-0.393755\pi$
$523$	28.7283	−	13.1198i	1.25620	−	0.573687i	0.928584	+	0.371123i	$0.121027\pi$
$524$	−5.70498	−	19.4294i	−0.249223	−	0.848777i
$525$	7.47204	+	14.6067i	0.326106	+	0.637490i
$526$	35.7059	+	5.13374i	1.55685	+	0.223842i
$527$	1.15249	−	0.740658i	0.0502031	−	0.0322636i
$528$	−25.6248	−	20.2828i	−1.11518	−	0.882696i
$529$	−22.6096	+	4.21992i	−0.983024	+	0.183475i
$530$		−	5.30426i		−	0.230402i
$531$	19.2433	−	19.9284i	0.835087	−	0.864818i
$532$	−1.88518	+	13.1117i	−0.0817330	+	0.568466i
$533$	8.24301	+	3.76445i	0.357044	+	0.163057i
$534$	19.3607	−	47.9217i	0.837818	−	2.07378i
$535$	28.6127	+	62.6530i	1.23703	+	2.70873i
$536$	−0.298922	−	0.344974i	−0.0129115	−	0.0149006i
$537$	−3.91681	−	2.27789i	−0.169023	−	0.0982980i
$538$	−16.6901	−	4.90066i	−0.719562	−	0.211283i
$539$	2.98323	−	3.44283i	0.128497	−	0.148293i
$540$	−32.2283	+	20.2833i	−1.38689	+	0.872854i
$541$	−5.07084	−	3.25883i	−0.218012	−	0.140108i	0.427077	−	0.904215i	$-0.359543\pi$
$541$	−5.07084	−	3.25883i	−0.218012	−	0.140108i	−0.645089	+	0.764107i	$0.723180\pi$
$542$	−33.5776	−	29.0952i	−1.44228	−	1.24975i
$543$	27.2739	−	19.2922i	1.17043	−	0.827908i
$544$	−4.91921	+	0.707276i	−0.210910	+	0.0303242i
$545$	−53.1705	+	46.0725i	−2.27757	+	1.97353i
$546$	−3.56781	+	14.5067i	−0.152688	+	0.620831i
$547$	−13.4145	+	3.93886i	−0.573564	+	0.168414i	−0.555636	−	0.831426i	$-0.687525\pi$
$547$	−13.4145	+	3.93886i	−0.573564	+	0.168414i	−0.0179282	+	0.999839i	$0.505707\pi$
$548$	17.8144	−	39.0082i	0.760995	−	1.66635i
$549$	−1.30659	−	14.6606i	−0.0557639	−	0.625699i
$550$	−46.2285	−	71.9329i	−1.97119	−	3.06723i
$551$	−35.2101			−1.50000
$552$	−1.01545	−	0.661374i	−0.0432206	−	0.0281499i
$553$	−8.37201			−0.356014
$554$	18.6215	+	28.9757i	0.791154	+	1.23106i
$555$	36.4724	+	38.4936i	1.54817	+	1.63396i
$556$	−15.2241	+	33.3361i	−0.645646	+	1.41377i
$557$	−8.37176	+	2.45817i	−0.354723	+	0.104156i	−0.454239	−	0.890880i	$-0.650089\pi$
$557$	−8.37176	+	2.45817i	−0.354723	+	0.104156i	0.0995160	+	0.995036i	$0.468271\pi$
$558$	−7.95327	−	10.2458i	−0.336689	−	0.433741i
$559$	−13.6037	+	11.7877i	−0.575377	+	0.498567i
$560$	15.5963	−	2.24241i	0.659064	−	0.0947591i
$561$	2.86095	+	4.04459i	0.120789	+	0.170763i
$562$	−27.6472	−	23.9564i	−1.16623	−	1.01054i
$563$	2.35054	+	1.51060i	0.0990636	+	0.0636643i	0.589235	−	0.807962i	$-0.299429\pi$
$563$	2.35054	+	1.51060i	0.0990636	+	0.0636643i	−0.490171	+	0.871626i	$0.663066\pi$
$564$	−22.3447	+	7.65468i	−0.940880	+	0.322320i
$565$	−27.1943	+	31.3839i	−1.14407	+	1.32033i
$566$	4.67809	+	1.37361i	0.196635	+	0.0577372i
$567$	−7.39650	+	5.12755i	−0.310624	+	0.215337i
$568$	0.595671	+	0.687441i	0.0249938	+	0.0288444i
$569$	−12.0910	−	26.4755i	−0.506880	−	1.10991i	−0.974172	−	0.225809i	$-0.927497\pi$
$569$	−12.0910	−	26.4755i	−0.506880	−	1.10991i	0.467292	−	0.884103i	$-0.345230\pi$
$570$	83.2454	+	33.6317i	3.48677	+	1.40868i
$571$	30.7143	+	14.0268i	1.28536	+	0.587002i	0.936662	−	0.350235i	$-0.113898\pi$
$571$	30.7143	+	14.0268i	1.28536	+	0.587002i	0.348693	+	0.937237i	$0.386625\pi$
$572$	5.43619	−	37.8095i	0.227299	−	1.58090i
$573$	14.6454	+	1.44512i	0.611819	+	0.0603707i
$574$			4.12525i			0.172184i
$575$	−27.9771	−	35.7918i	−1.16673	−	1.49262i
$576$	5.09795	+	21.6085i	0.212415	+	0.900352i
$577$	−12.5995	+	8.09720i	−0.524524	+	0.337091i	−0.775959	−	0.630783i	$-0.782734\pi$
$577$	−12.5995	+	8.09720i	−0.524524	+	0.337091i	0.251435	+	0.967874i	$0.419097\pi$
$578$	−32.5696	−	4.68280i	−1.35472	−	0.194779i
$579$	−23.3376	+	11.9383i	−0.969879	+	0.496139i
$580$	−10.5720	−	36.0048i	−0.438977	−	1.49502i
$581$	−2.16862	+	0.990378i	−0.0899697	+	0.0410878i
$582$	0.630423	+	14.1754i	0.0261319	+	0.587588i
$583$	0.456188	+	3.17286i	0.0188934	+	0.131406i
$584$	−0.121994	+	0.415472i	−0.00504813	+	0.0171923i
$585$	44.0106	+	23.0418i	1.81961	+	0.952662i
$586$	−6.11832	+	9.52030i	−0.252746	+	0.393280i
$587$	−4.70097	+	7.31485i	−0.194030	+	0.301916i	−0.924613	−	0.380907i	$-0.875612\pi$
$587$	−4.70097	+	7.31485i	−0.194030	+	0.301916i	0.730584	+	0.682823i	$0.239248\pi$
$588$	−3.27826	+	0.621109i	−0.135193	+	0.0256141i
$589$	−4.22704	+	14.3960i	−0.174172	+	0.593176i
$590$	−9.90651	−	68.9013i	−0.407845	−	2.83662i
$591$	21.7297	−	0.966389i	0.893842	−	0.0397520i
$592$	30.3202	−	13.8468i	1.24615	−	0.569099i
$593$	4.31881	+	14.7085i	0.177352	+	0.604006i	0.999402	+	0.0345901i	$0.0110126\pi$
$593$	4.31881	+	14.7085i	0.177352	+	0.604006i	−0.822049	+	0.569416i	$0.807169\pi$
$594$	35.7374	−	30.3790i	1.46632	−	1.24646i
$595$	−2.36429	−	0.339934i	−0.0969266	−	0.0139359i
$596$	−17.8812	+	11.4916i	−0.732444	+	0.470713i
$597$	24.5289	−	30.9893i	1.00390	−	1.26831i
$598$	2.08965	−	41.3115i	0.0854521	−	1.68935i
$599$		−	25.3794i		−	1.03698i	−0.855085	−	0.518488i	$-0.826495\pi$
$599$		−	25.3794i		−	1.03698i	0.855085	−	0.518488i	$-0.173505\pi$
$600$	0.235044	−	2.38202i	0.00959563	−	0.0972455i
$601$	−1.07589	+	7.48298i	−0.0438865	+	0.305237i	0.956041	+	0.293232i	$0.0947307\pi$
$601$	−1.07589	+	7.48298i	−0.0438865	+	0.305237i	−0.999928	+	0.0120056i	$0.996178\pi$
$602$	−7.45378	−	3.40403i	−0.303793	−	0.138738i
$603$	8.15850	−	4.64190i	0.332240	−	0.189033i
$604$	0.0135081	+	0.0295787i	0.000549638	+	0.00120354i
$605$	24.2968	+	28.0399i	0.987803	+	1.13999i
$606$	−14.9541	+	25.7136i	−0.607470	+	1.04454i
$607$	−41.2783	−	12.1204i	−1.67543	−	0.491952i	−0.700352	−	0.713798i	$-0.746974\pi$
$607$	−41.2783	−	12.1204i	−1.67543	−	0.491952i	−0.975082	+	0.221846i	$0.928792\pi$
$608$	35.6433	−	41.1346i	1.44553	−	1.66823i
$609$	−2.87424	−	8.39015i	−0.116470	−	0.339986i
$610$	−31.1131	−	19.9952i	−1.25973	−	0.809582i
$611$	23.2869	+	20.1782i	0.942088	+	0.816324i
$612$	0.195528	−	3.62328i	0.00790375	−	0.146463i
$613$	20.5721	−	2.95782i	0.830899	−	0.119465i	0.286277	−	0.958147i	$-0.407582\pi$
$613$	20.5721	−	2.95782i	0.830899	−	0.119465i	0.544622	+	0.838682i	$0.316673\pi$
$614$	−32.0157	+	27.7418i	−1.29205	+	1.11957i
$615$	13.3209	+	3.27617i	0.537152	+	0.132108i
$616$	−0.637677	+	0.187239i	−0.0256928	+	0.00754407i
$617$	3.48843	−	7.63859i	0.140439	−	0.307518i	−0.826323	−	0.563196i	$-0.809571\pi$
$617$	3.48843	−	7.63859i	0.140439	−	0.307518i	0.966762	+	0.255678i	$0.0822987\pi$
$618$	2.13705	−	2.02483i	0.0859646	−	0.0814507i
$619$	−22.9935	−	35.7786i	−0.924186	−	1.43806i	−0.898788	−	0.438384i	$-0.855551\pi$
$619$	−22.9935	−	35.7786i	−0.924186	−	1.43806i	−0.0253984	−	0.999677i	$-0.508085\pi$
$620$	−15.9901			−0.642177
$621$	17.4191	−	17.8206i	0.699006	−	0.715116i
$622$	55.8320			2.23866
$623$	−8.14171	−	12.6688i	−0.326191	−	0.507563i
$624$	22.6673	−	21.4771i	0.907420	−	0.859772i
$625$	7.21432	−	15.7972i	0.288573	−	0.631886i
$626$	−19.9116	+	5.84656i	−0.795826	+	0.233676i
$627$	−52.6876	−	12.9581i	−2.10414	−	0.517495i
$628$	13.8405	−	11.9928i	0.552295	−	0.478567i
$629$	−5.00153	+	0.719111i	−0.199424	+	0.0286728i
$630$	−1.21861	+	22.5818i	−0.0485506	+	0.899680i
$631$	−12.4154	−	10.7580i	−0.494247	−	0.428268i	0.371738	−	0.928338i	$-0.378762\pi$
$631$	−12.4154	−	10.7580i	−0.494247	−	0.428268i	−0.865985	+	0.500070i	$0.833308\pi$
$632$	1.02749	+	0.660329i	0.0408714	+	0.0262665i
$633$	−5.72782	−	16.7200i	−0.227660	−	0.664560i
$634$	−31.7602	+	36.6532i	−1.26136	+	1.45568i
$635$	8.13063	+	2.38737i	0.322654	+	0.0947398i
$636$	1.18030	−	2.02952i	0.0468020	−	0.0804759i
$637$	2.85046	+	3.28961i	0.112939	+	0.130339i
$638$	19.2009	+	42.0440i	0.760170	+	1.66454i
$639$	−16.2577	+	9.25005i	−0.643144	+	0.365926i
$640$	−4.03604	−	1.84320i	−0.159538	−	0.0728588i
$641$	6.09148	−	42.3672i	0.240599	−	1.67340i	−0.408545	−	0.912738i	$-0.633964\pi$
$641$	6.09148	−	42.3672i	0.240599	−	1.67340i	0.649144	−	0.760665i	$-0.275127\pi$
$642$	−6.10182	+	61.8381i	−0.240820	+	2.44055i
$643$			1.26017i			0.0496961i	0.999691	+	0.0248480i	$0.00791019\pi$
$643$			1.26017i			0.0496961i	−0.999691	+	0.0248480i	$0.992090\pi$
$644$	8.58685	−	3.40840i	0.338369	−	0.134310i
$645$	−16.9116	+	21.3658i	−0.665895	+	0.841276i
$646$	−7.19709	+	4.62529i	−0.283166	+	0.181980i
$647$	15.1066	+	2.17200i	0.593902	+	0.0853903i	0.432711	−	0.901533i	$-0.357557\pi$
$647$	15.1066	+	2.17200i	0.593902	+	0.0853903i	0.161192	+	0.986923i	$0.448466\pi$
$648$	1.31219	−	0.0459136i	0.0515479	−	0.00180366i
$649$	11.8516	+	40.3628i	0.465216	+	1.58438i
$650$	74.3181	−	33.9400i	2.91500	−	1.33123i
$651$	−3.77545	+	0.167906i	−0.147971	+	0.00658075i
$652$	0.674901	+	4.69404i	0.0264312	+	0.183833i
$653$	−0.955589	+	3.25444i	−0.0373951	+	0.127356i	−0.976075	−	0.217433i	$-0.930231\pi$
$653$	−0.955589	+	3.25444i	−0.0373951	+	0.127356i	0.938680	+	0.344789i	$0.112050\pi$
$654$	−62.3618	+	11.8152i	−2.43854	+	0.462013i
$655$	−21.6201	+	33.6416i	−0.844768	+	1.31448i
$656$	4.66181	−	7.25393i	0.182013	−	0.283218i
$657$	−7.88854	−	4.13006i	−0.307761	−	0.161129i
$658$	−3.95186	+	13.4588i	−0.154059	+	0.524678i
$659$	−3.28655	−	22.8585i	−0.128026	−	0.890439i	−0.948052	−	0.318114i	$-0.896951\pi$
$659$	−3.28655	−	22.8585i	−0.128026	−	0.890439i	0.820027	−	0.572325i	$-0.193959\pi$
$660$	−2.56910	−	57.7674i	−0.100002	−	2.24859i
$661$	8.49330	−	3.87876i	0.330351	−	0.150866i	−0.243333	−	0.969943i	$-0.578241\pi$
$661$	8.49330	−	3.87876i	0.330351	−	0.150866i	0.573684	+	0.819076i	$0.305514\pi$
$662$	16.0349	+	54.6099i	0.623214	+	2.12247i
$663$	−4.21428	+	2.15581i	−0.163669	+	0.0837246i
$664$	0.344268	+	0.0494983i	0.0133602	+	0.00192091i
$665$	22.0071	−	14.1431i	0.853397	−	0.548445i
$666$	10.9850	+	46.5617i	0.425661	+	1.80423i
$667$	12.2157	+	21.3027i	0.472996	+	0.824843i
$668$			23.0642i			0.892382i
$669$	9.64260	+	0.951476i	0.372805	+	0.0367862i
$670$	3.35665	−	23.3460i	0.129679	−	0.901935i
$671$	20.3307	+	9.28471i	0.784857	+	0.358432i
$672$	12.7115	+	5.13552i	0.490356	+	0.198107i
$673$	−14.7983	−	32.4038i	−0.570433	−	1.24907i	−0.946567	−	0.322508i	$-0.895474\pi$
$673$	−14.7983	−	32.4038i	−0.570433	−	1.24907i	0.376134	−	0.926565i	$-0.377253\pi$
$674$	−17.2981	−	19.9631i	−0.666299	−	0.768950i
$675$	47.0936	+	14.3136i	1.81264	+	0.550932i
$676$	10.9914	+	3.22737i	0.422746	+	0.124130i
$677$	−10.5764	+	12.2058i	−0.406485	+	0.469108i	−0.921672	−	0.387969i	$-0.873177\pi$
$677$	−10.5764	+	12.2058i	−0.406485	+	0.469108i	0.515188	+	0.857077i	$0.327722\pi$
$678$	−35.4419	+	12.1414i	−1.36114	+	0.466289i
$679$	3.47803	+	2.23520i	0.133475	+	0.0857790i
$680$	0.263356	+	0.228200i	0.0100993	+	0.00875106i
$681$	−5.06574	−	7.16156i	−0.194120	−	0.274432i
$682$	19.4952	−	2.80298i	0.746509	−	0.107332i
$683$	9.32854	−	8.08322i	0.356947	−	0.309296i	−0.457865	−	0.889022i	$-0.651386\pi$
$683$	9.32854	−	8.08322i	0.356947	−	0.309296i	0.814812	+	0.579726i	$0.196840\pi$
$684$	24.3678	+	31.3919i	0.931726	+	1.20030i
$685$	−81.2575	+	23.8594i	−3.10469	+	0.911619i
$686$	−0.823148	+	1.80244i	−0.0314279	+	0.0688176i
$687$	−10.7869	−	11.3847i	−0.411544	−	0.434352i
$688$	9.26010	+	14.4090i	0.353038	+	0.549338i
$689$	−3.06283			−0.116684
$690$	−8.53336	−	62.0329i	−0.324860	−	2.36155i
$691$	39.9363			1.51925			0.759624	−	0.650362i	$-0.225383\pi$
$691$	39.9363			1.51925			0.759624	+	0.650362i	$0.225383\pi$
$692$	−16.6385	−	25.8900i	−0.632500	−	0.984189i
$693$	−1.21319	−	13.6126i	−0.0460852	−	0.517100i
$694$	18.1907	−	39.8320i	0.690508	−	1.51200i
$695$	69.4421	−	20.3901i	2.63409	−	0.773439i
$696$	−0.309006	+	1.25642i	−0.0117128	+	0.0476244i
$697$	−0.987879	+	0.856002i	−0.0374186	+	0.0324234i
$698$	34.7222	−	4.99230i	1.31425	−	0.188961i
$699$	32.3730	−	22.8991i	1.22446	−	0.866123i
$700$	13.7907	+	11.9497i	0.521239	+	0.451656i
$701$	26.7185	+	17.1709i	1.00914	+	0.648538i	0.937172	−	0.348869i	$-0.113434\pi$
$701$	26.7185	+	17.1709i	1.00914	+	0.648538i	0.0719730	+	0.997407i	$0.477070\pi$
$702$	23.8719	+	37.9303i	0.900987	+	1.43159i
$703$	36.2398	−	41.8229i	1.36681	−	1.57738i
$704$	−32.3477	−	9.49815i	−1.21915	−	0.357975i
$705$	40.3216	+	23.4497i	1.51860	+	0.883166i
$706$	−20.9922	−	24.2263i	−0.790054	−	0.911770i
$707$	3.60041	+	7.88379i	0.135407	+	0.296501i
$708$	11.5415	−	28.5675i	0.433754	−	1.07363i
$709$	9.19529	+	4.19935i	0.345336	+	0.157710i	0.580530	−	0.814239i	$-0.302845\pi$
$709$	9.19529	+	4.19935i	0.345336	+	0.157710i	−0.235194	+	0.971948i	$0.575573\pi$
$710$	−6.68890	+	46.5223i	−0.251030	+	1.74595i
$711$	−17.4464	+	18.0676i	−0.654293	+	0.677587i
$712$			2.19699i			0.0823358i
$713$	10.1763	−	2.43709i	0.381106	−	0.0912699i
$714$	−1.68966	−	1.33741i	−0.0632339	−	0.0500515i
$715$	−63.4605	+	40.7836i	−2.37329	+	1.52522i
$716$	−4.98808	−	0.717178i	−0.186413	−	0.0268022i
$717$	3.81976	+	7.46707i	0.142651	+	0.278863i
$718$	15.1191	+	51.4908i	0.564238	+	1.92162i
$719$	−5.68409	+	2.59584i	−0.211981	+	0.0968084i	−0.518576	−	0.855032i	$-0.673538\pi$
$719$	−5.68409	+	2.59584i	−0.211981	+	0.0968084i	0.306595	+	0.951840i	$0.400810\pi$
$720$	27.6618	−	38.3312i	1.03090	−	1.42852i
$721$	−0.122075	−	0.849049i	−0.00454630	−	0.0316202i
$722$	15.7903	−	53.7770i	0.587656	−	2.00137i
$723$	9.03621	+	47.6938i	0.336060	+	1.77375i
$724$	20.0878	−	31.2572i	0.746556	−	1.16166i
$725$	−26.2229	+	40.8037i	−0.973895	+	1.51541i
$726$	6.23088	+	32.8871i	0.231250	+	1.22055i
$727$	−6.03047	+	20.5379i	−0.223658	+	0.761708i	0.768840	+	0.639442i	$0.220834\pi$
$727$	−6.03047	+	20.5379i	−0.223658	+	0.761708i	−0.992497	+	0.122266i	$0.960984\pi$
$728$	−0.0903728	−	0.628556i	−0.00334944	−	0.0232959i
$729$	−4.34786	+	26.6476i	−0.161032	+	0.986949i
$730$	−20.3523	+	9.29456i	−0.753271	+	0.344007i
$731$	−0.731516	−	2.49131i	−0.0270561	−	0.0921446i
$732$	−7.45523	−	14.5739i	−0.275553	−	0.538666i
$733$	−21.8132	−	3.13627i	−0.805690	−	0.115841i	−0.272850	−	0.962057i	$-0.587966\pi$
$733$	−21.8132	−	3.13627i	−0.805690	−	0.115841i	−0.532840	+	0.846216i	$0.678875\pi$
$734$	33.6485	−	21.6246i	1.24199	−	0.798179i
$735$	5.16659	+	4.08950i	0.190572	+	0.150844i
$736$	−37.2531	−	7.29360i	−1.37317	−	0.268846i
$737$			14.2536i			0.525039i
$738$	8.90266	+	8.59660i	0.327711	+	0.316445i
$739$	5.13306	−	35.7012i	0.188823	−	1.31329i	−0.646239	−	0.763135i	$-0.723659\pi$
$739$	5.13306	−	35.7012i	0.188823	−	1.31329i	0.835062	−	0.550156i	$-0.185432\pi$
$740$	53.6479	+	24.5002i	1.97214	+	0.900645i
$741$	19.4198	−	48.0682i	0.713406	−	1.76583i
$742$	−0.579208	−	1.26829i	−0.0212634	−	0.0465603i
$743$	−9.73610	−	11.2361i	−0.357183	−	0.412211i	0.548511	−	0.836143i	$-0.315195\pi$
$743$	−9.73610	−	11.2361i	−0.357183	−	0.412211i	−0.905694	+	0.423932i	$0.860649\pi$
$744$	0.476601	+	0.277175i	0.0174731	+	0.0101617i
$745$	40.2758	+	11.8260i	1.47559	+	0.433273i
$746$	27.1217	−	31.3001i	0.992997	−	1.14598i
$747$	−2.38187	+	6.74394i	−0.0871482	+	0.246748i
$748$	4.63529	+	2.97892i	0.169483	+	0.108920i
$749$	13.6830	+	11.8564i	0.499966	+	0.433223i
$750$	47.6748	−	33.7228i	1.74084	−	1.23138i
$751$	−0.499671	+	0.0718418i	−0.0182332	+	0.00262154i	−0.151425	−	0.988469i	$-0.548386\pi$
$751$	−0.499671	+	0.0718418i	−0.0182332	+	0.00262154i	0.133192	+	0.991090i	$0.457477\pi$
$752$	22.1584	−	19.2004i	0.808033	−	0.700165i
$753$	−0.569977	+	2.31753i	−0.0207711	+	0.0844554i
$754$	−42.3749	+	12.4424i	−1.54320	+	0.453125i
$755$	0.0266764	−	0.0584131i	0.000970853	−	0.00212587i
$756$	−5.49116	+	8.36911i	−0.199711	+	0.304382i
$757$	−23.5327	−	36.6177i	−0.855312	−	1.33089i	−0.942330	−	0.334685i	$-0.891370\pi$
$757$	−23.5327	−	36.6177i	−0.855312	−	1.33089i	0.0870181	−	0.996207i	$-0.472266\pi$
$758$	43.5441			1.58159
$759$	10.4395	+	36.3725i	0.378930	+	1.32024i
$760$	−3.81642			−0.138436
$761$	6.64224	+	10.3355i	0.240781	+	0.374663i	0.940521	−	0.339735i	$-0.110337\pi$
$761$	6.64224	+	10.3355i	0.240781	+	0.374663i	−0.699740	+	0.714397i	$0.746701\pi$
$762$	5.25803	+	5.54942i	0.190478	+	0.201034i
$763$	−7.68250	+	16.8223i	−0.278125	+	0.609009i
$764$	15.7046	−	4.61128i	0.568171	−	0.166830i
$765$	−5.66056	+	4.39397i	−0.204658	+	0.158864i
$766$	8.97663	−	7.77829i	0.324339	−	0.281041i
$767$	−39.7855	+	5.72029i	−1.43657	+	0.206548i
$768$	−17.1161	−	24.1975i	−0.617625	−	0.873152i
$769$	4.14723	+	3.59359i	0.149553	+	0.129588i	0.726424	−	0.687247i	$-0.241181\pi$
$769$	4.14723	+	3.59359i	0.149553	+	0.129588i	−0.576871	+	0.816835i	$0.695726\pi$
$770$	−28.8890	−	18.5659i	−1.04109	−	0.669067i
$771$	−26.1689	+	8.96475i	−0.942449	+	0.322858i
$772$	−19.0924	+	22.0338i	−0.687151	+	0.793014i
$773$	11.9071	+	3.49625i	0.428270	+	0.125751i	0.488762	−	0.872417i	$-0.337449\pi$
$773$	11.9071	+	3.49625i	0.428270	+	0.125751i	−0.0604920	+	0.998169i	$0.519267\pi$
$774$	−22.8791	+	8.99228i	−0.822373	+	0.323221i
$775$	13.5348	+	15.6200i	0.486186	+	0.561088i
$776$	−0.250559	−	0.548648i	−0.00899456	−	0.0196953i
$777$	12.9242	+	5.22145i	0.463653	+	0.187319i
$778$	−11.8443	−	5.40911i	−0.424639	−	0.193926i
$779$	2.03735	−	14.1701i	0.0729958	−	0.507697i
$780$	54.9840	+	5.42550i	1.96874	+	0.194264i
$781$		−	28.4036i		−	1.01636i
$782$	5.29532	+	2.74966i	0.189360	+	0.0983278i
$783$	−24.0963	−	11.2814i	−0.861133	−	0.403163i
$784$	3.48433	−	2.23924i	0.124440	−	0.0799729i
$785$	−35.7983	−	5.14701i	−1.27769	−	0.183705i
$786$	−32.1187	+	16.4303i	−1.14564	+	0.586048i
$787$	−4.12841	−	14.0601i	−0.147162	−	0.501188i	0.852610	−	0.522548i	$-0.175018\pi$
$787$	−4.12841	−	14.0601i	−0.147162	−	0.501188i	−0.999772	+	0.0213604i	$0.993200\pi$
$788$	22.0054	−	10.0495i	0.783910	−	0.358000i
$789$	−1.40093	−	31.5006i	−0.0498745	−	1.12145i
$790$	8.98149	+	62.4677i	0.319547	+	2.22250i
$791$	−3.07534	+	10.4736i	−0.109347	+	0.372400i
$792$	−0.924777	+	1.76635i	−0.0328605	+	0.0627646i
$793$	−11.5458	+	17.9656i	−0.410002	+	0.637976i
$794$	1.18282	−	1.84051i	0.0419769	−	0.0653173i
$795$	−4.55545	+	0.863089i	−0.161565	+	0.0306106i
$796$	12.3839	−	42.1758i	0.438937	−	1.49488i
$797$	−6.24577	−	43.4403i	−0.221237	−	1.53873i	−0.733371	−	0.679829i	$-0.762054\pi$
$797$	−6.24577	−	43.4403i	−0.221237	−	1.53873i	0.512134	−	0.858906i	$-0.328855\pi$
$798$	23.5771	−	1.04855i	0.834619	−	0.0371181i
$799$	−4.04302	+	1.84638i	−0.143032	+	0.0653204i
$800$	−21.1238	−	71.9409i	−0.746838	−	2.54350i
$801$	−44.3069	−	8.82986i	−1.56551	−	0.311988i
$802$	−45.4412	−	6.53346i	−1.60458	−	0.230704i
$803$	11.3748	−	7.31013i	0.401407	−	0.257969i
$804$	6.47927	−	8.18576i	0.228506	−	0.288690i
$805$	−16.1919	−	8.40784i	−0.570689	−	0.296337i
$806$			18.8191i			0.662874i
$807$	−1.49308	+	15.1314i	−0.0525588	+	0.532650i
$808$	0.179946	−	1.25155i	0.00633046	−	0.0440293i
$809$	−23.3591	−	10.6678i	−0.821264	−	0.375059i	−0.0399535	−	0.999202i	$-0.512721\pi$
$809$	−23.3591	−	10.6678i	−0.821264	−	0.375059i	−0.781310	+	0.624143i	$0.785448\pi$
$810$	46.1941	+	49.6881i	1.62310	+	1.74586i
$811$	−16.4241	−	35.9637i	−0.576727	−	1.26286i	−0.943138	−	0.332402i	$-0.892141\pi$
$811$	−16.4241	−	35.9637i	−0.576727	−	1.26286i	0.366411	−	0.930453i	$-0.380586\pi$
$812$	−6.45944	−	7.45459i	−0.226682	−	0.261605i
$813$	−19.5242	+	33.5717i	−0.684742	+	1.17741i
$814$	−69.7027	−	20.4665i	−2.44308	−	0.717352i
$815$	6.13297	−	7.07782i	0.214828	−	0.247925i
$816$	1.45976	+	4.26117i	0.0511019	+	0.149171i
$817$	23.9224	+	15.3740i	0.836938	+	0.537867i
$818$	−32.1211	−	27.8331i	−1.12309	−	0.973160i
$819$	13.0393	+	0.703659i	0.455632	+	0.0245878i
$820$	15.1016	−	2.17129i	0.527372	−	0.0758247i
$821$	19.7832	−	17.1422i	0.690439	−	0.598268i	−0.237328	−	0.971430i	$-0.576272\pi$
$821$	19.7832	−	17.1422i	0.690439	−	0.598268i	0.927767	+	0.373161i	$0.121726\pi$
$822$	−74.1913	−	18.2467i	−2.58772	−	0.636428i
$823$	36.4077	−	10.6903i	1.26909	−	0.372639i	0.423222	−	0.906026i	$-0.360899\pi$
$823$	36.4077	−	10.6903i	1.26909	−	0.372639i	0.845872	+	0.533387i	$0.179081\pi$
$824$	−0.0519852	+	0.113832i	−0.00181099	+	0.00396551i
$825$	−54.2559	+	51.4070i	−1.88895	+	1.78976i
$826$	−9.89252	−	15.3931i	−0.344205	−	0.535593i
$827$	6.16871			0.214507			0.107253	−	0.994232i	$-0.465794\pi$
$827$	6.16871			0.214507			0.107253	+	0.994232i	$0.465794\pi$
$828$	10.5385	−	25.6340i	0.366238	−	0.890842i
$829$	31.7471			1.10262			0.551312	−	0.834299i	$-0.314127\pi$
$829$	31.7471			1.10262			0.551312	+	0.834299i	$0.314127\pi$
$830$	9.71619	+	15.1187i	0.337254	+	0.524777i
$831$	21.8551	−	20.7075i	0.758146	−	0.718336i
$832$	13.3817	−	29.3019i	0.463928	−	1.01586i
$833$	−0.602440	+	0.176892i	−0.0208733	+	0.00612895i
$834$	63.4034	+	15.5935i	2.19548	+	0.539960i
$835$	34.4230	−	29.8277i	1.19126	−	1.03223i
$836$	−59.7307	+	8.58798i	−2.06583	+	0.297022i
$837$	−7.50530	+	8.49766i	−0.259421	+	0.293722i
$838$	−5.60577	−	4.85743i	−0.193648	−	0.167797i
$839$	29.5217	+	18.9725i	1.01920	+	0.655002i	0.939759	−	0.341837i	$-0.111049\pi$
$839$	29.5217	+	18.9725i	1.01920	+	0.655002i	0.0794438	+	0.996839i	$0.474686\pi$
$840$	−0.311539	−	0.909408i	−0.0107491	−	0.0313776i
$841$	−1.82140	+	2.10201i	−0.0628069	+	0.0724831i
$842$	23.5677	+	6.92009i	0.812195	+	0.238482i
$843$	−16.0758	+	27.6423i	−0.553680	+	0.952051i
$844$	−12.8724	−	14.8556i	−0.443088	−	0.511351i
$845$	−9.39778	−	20.5783i	−0.323294	−	0.707914i
$846$	20.8100	+	36.5752i	0.715463	+	1.25748i
$847$	8.87140	+	4.05143i	0.304825	+	0.139209i
$848$	−0.414762	+	2.88473i	−0.0142430	+	0.0990621i
$849$	0.418496	−	4.24119i	0.0143627	−	0.145557i
$850$			11.7851i			0.404227i
$851$	−37.8765	−	7.41565i	−1.29839	−	0.254205i
$852$	−12.9114	+	16.3120i	−0.442339	+	0.558841i
$853$	25.6851	−	16.5068i	0.879442	−	0.565183i	−0.0211854	−	0.999776i	$-0.506744\pi$
$853$	25.6851	−	16.5068i	0.879442	−	0.565183i	0.900627	+	0.434593i	$0.143108\pi$
$854$	−9.62279	−	1.38355i	−0.329285	−	0.0473440i
$855$	15.3385	−	76.9660i	0.524564	−	2.63218i
$856$	−0.744153	−	2.53435i	−0.0254346	−	0.0866223i
$857$	−45.5872	+	20.8190i	−1.55723	+	0.711163i	−0.993397	−	0.114726i	$-0.963401\pi$
$857$	−45.5872	+	20.8190i	−1.55723	+	0.711163i	−0.563833	+	0.825889i	$0.690674\pi$
$858$	−67.9878	+	3.02363i	−2.32107	+	0.103225i
$859$	0.657330	+	4.57183i	0.0224278	+	0.155989i	0.997958	−	0.0638779i	$-0.0203468\pi$
$859$	0.657330	+	4.57183i	0.0224278	+	0.155989i	−0.975530	+	0.219867i	$0.929438\pi$
$860$	−8.53818	+	29.0784i	−0.291149	+	0.991564i
$861$	3.54288	−	0.671244i	0.120741	−	0.0228759i
$862$	2.47276	−	3.84769i	0.0842226	−	0.131053i
$863$	−16.4507	+	25.5977i	−0.559987	+	0.871357i	−0.999641	−	0.0268103i	$-0.991465\pi$
$863$	−16.4507	+	25.5977i	−0.559987	+	0.871357i	0.439653	+	0.898168i	$0.355101\pi$
$864$	37.5724	−	16.7306i	1.27824	−	0.569188i
$865$	−17.1227	+	58.3147i	−0.582191	+	1.98276i
$866$	0.00203763	+	0.0141721i	6.92416e−5	+	0.000481586i
$867$	1.27787	+	28.7336i	0.0433989	+	0.975846i
$868$	−3.82334	+	1.74606i	−0.129773	+	0.0592652i
$869$	−10.7450	−	36.5940i	−0.364498	−	1.24137i
$870$	−59.5195	+	30.4471i	−2.01790	+	1.03225i
$871$	−13.4806	−	1.93822i	−0.456774	−	0.0656741i
$872$	2.26970	−	1.45865i	0.0768618	−	0.0493961i
$873$	12.0716	−	2.84799i	0.408563	−	0.0963898i
$874$	−63.5495	+	15.2193i	−2.14959	+	0.514799i
$875$		−	17.0149i		−	0.575207i
$876$	−9.85543	−	0.972477i	−0.332984	−	0.0328570i
$877$	1.49500	−	10.3980i	0.0504826	−	0.351114i	−0.948887	−	0.315616i	$-0.897789\pi$
$877$	1.49500	−	10.3980i	0.0504826	−	0.351114i	0.999370	−	0.0354987i	$-0.0113020\pi$
$878$	8.79677	+	4.01735i	0.296877	+	0.135579i
$879$	9.17185	+	3.70549i	0.309359	+	0.124983i
$880$	29.8184	+	65.2932i	1.00518	+	2.20104i
$881$	13.7036	+	15.8147i	0.461684	+	0.532812i	0.938080	−	0.346419i	$-0.112602\pi$
$881$	13.7036	+	15.8147i	0.461684	+	0.532812i	−0.476395	+	0.879231i	$0.658057\pi$
$882$	2.17448	+	5.53254i	0.0732185	+	0.186290i
$883$	31.8310	+	9.34641i	1.07120	+	0.314532i	0.769352	−	0.638825i	$-0.220579\pi$
$883$	31.8310	+	9.34641i	1.07120	+	0.314532i	0.301845	+	0.953357i	$0.402397\pi$
$884$	−3.44768	+	3.97884i	−0.115958	+	0.133823i
$885$	−57.5625	+	19.7194i	−1.93494	+	0.662859i
$886$	53.7123	+	34.5188i	1.80450	+	1.15968i
$887$	19.0321	+	16.4914i	0.639036	+	0.553728i	0.912973	−	0.408020i	$-0.133781\pi$
$887$	19.0321	+	16.4914i	0.639036	+	0.553728i	−0.273937	+	0.961748i	$0.588326\pi$
$888$	−1.17434	−	1.66020i	−0.0394084	−	0.0557127i
$889$	2.20479	−	0.317000i	0.0739461	−	0.0106319i
$890$	−85.7933	+	74.3403i	−2.87580	+	2.49189i
$891$	−31.9054	−	25.7491i	−1.06887	−	0.862628i
$892$	10.3400	−	3.03610i	0.346209	−	0.101656i
$893$	20.2215	−	44.2788i	0.676686	−	1.48174i
$894$	26.0461	+	27.4896i	0.871113	+	0.919389i
$895$	5.38043	+	8.37212i	0.179848	+	0.279849i
$896$	−1.16632			−0.0389640
$897$	−35.8195	+	4.92740i	−1.19598	+	0.164521i
$898$	41.4906			1.38456
$899$	−6.04019	−	9.39872i	−0.201452	−	0.313465i
$900$	54.5270	−	4.85958i	1.81757	−	0.161986i
$901$	0.183531	−	0.401878i	0.00611432	−	0.0133885i
$902$	−18.0314	+	5.29450i	−0.600380	+	0.176287i
$903$	−1.71063	+	6.95541i	−0.0569260	+	0.231461i
$904$	1.20353	−	1.04286i	0.0400287	−	0.0346851i
$905$	−72.6292	+	10.4425i	−2.41428	+	0.347121i
$906$	0.0472969	−	0.0334555i	0.00157134	−	0.00111149i
$907$	−42.6864	−	36.9879i	−1.41738	−	1.22816i	−0.936165	−	0.351560i	$-0.885651\pi$
$907$	−42.6864	−	36.9879i	−1.41738	−	1.22816i	−0.481212	−	0.876604i	$-0.659803\pi$
$908$	−8.20749	−	5.27464i	−0.272375	−	0.175045i
$909$	24.5168	+	8.65903i	0.813172	+	0.287202i
$910$	21.4874	−	24.7978i	0.712300	−	0.822038i
$911$	10.2793	+	3.01827i	0.340568	+	0.0999998i	0.447544	−	0.894262i	$-0.352299\pi$
$911$	10.2793	+	3.01827i	0.340568	+	0.0999998i	−0.106976	+	0.994262i	$0.534117\pi$
$912$	−42.6434	−	24.7999i	−1.41206	−	0.821208i
$913$	−7.11222	−	8.20794i	−0.235380	−	0.271643i
$914$	16.4975	+	36.1246i	0.545690	+	1.19489i
$915$	−12.1098	+	29.9744i	−0.400339	+	0.990923i
$916$	−15.8666	−	7.24603i	−0.524247	−	0.239416i
$917$	−1.49598	+	10.4048i	−0.0494017	+	0.343597i
$918$	−6.40734	+	0.859399i	−0.211474	+	0.0283644i
$919$		−	44.0113i		−	1.45180i	−0.687800	−	0.725900i	$-0.741424\pi$
$919$		−	44.0113i		−	1.45180i	0.687800	−	0.725900i	$-0.258576\pi$
$920$	1.32406	+	2.30900i	0.0436531	+	0.0761254i
$921$	29.0349	+	22.9820i	0.956732	+	0.757281i
$922$	−37.5606	+	24.1387i	−1.23699	+	0.794966i
$923$	26.8633	+	3.86235i	0.884215	+	0.127131i
$924$	−6.92230	−	13.5321i	−0.227727	−	0.445173i
$925$	−21.4772	−	73.1447i	−0.706167	−	2.40498i
$926$	53.2126	−	24.3014i	1.74867	−	0.798593i
$927$	−2.08672	−	1.50588i	−0.0685368	−	0.0494597i
$928$	5.76796	+	40.1170i	0.189343	+	1.31691i
$929$	0.111363	−	0.379269i	0.00365372	−	0.0124434i	−0.957646	−	0.287948i	$-0.907027\pi$
$929$	0.111363	−	0.379269i	0.00365372	−	0.0124434i	0.961300	+	0.275505i	$0.0888450\pi$
$930$	5.30313	+	27.9903i	0.173896	+	0.917839i
$931$	3.71767	−	5.78481i	0.121842	−	0.189590i
$932$	23.8434	−	37.1010i	0.781016	−	1.21528i
$933$	−9.08477	−	47.9502i	−0.297422	−	1.56982i
$934$	4.30281	−	14.6540i	0.140792	−	0.479494i
$935$	−1.54858	−	10.7706i	−0.0506438	−	0.352236i
$936$	−1.54481	−	1.11482i	−0.0504937	−	0.0364389i
$937$	−20.8107	+	9.50392i	−0.679856	+	0.310480i	−0.725246	−	0.688490i	$-0.758274\pi$
$937$	−20.8107	+	9.50392i	−0.679856	+	0.310480i	0.0453905	+	0.998969i	$0.485547\pi$
$938$	−1.74671	−	5.94874i	−0.0570320	−	0.194233i
$939$	8.26113	+	16.1493i	0.269592	+	0.527012i
$940$	51.3498	+	7.38298i	1.67484	+	0.240806i
$941$	−43.4086	+	27.8970i	−1.41508	+	0.909416i	−1.00000		0.000369498i	$-0.999882\pi$
$941$	−43.4086	+	27.8970i	−1.41508	+	0.909416i	−0.415079	+	0.909785i	$0.636246\pi$
$942$	−25.5835	−	20.2501i	−0.833554	−	0.659783i
$943$	−9.27998	+	3.68353i	−0.302198	+	0.119952i
$944$			38.2467i			1.24483i
$945$	19.5922	−	2.62785i	0.637334	−	0.0854838i
$946$	5.31250	−	36.9492i	0.172724	−	1.20132i
$947$	−1.85203	−	0.845794i	−0.0601829	−	0.0274846i	0.385096	−	0.922876i	$-0.374168\pi$
$947$	−1.85203	−	0.845794i	−0.0601829	−	0.0274846i	−0.445279	+	0.895392i	$0.646896\pi$
$948$	−10.4638	+	25.9000i	−0.339847	+	0.841194i
$949$	5.36694	+	11.7520i	0.174218	+	0.381485i
$950$	−84.5229	−	97.5446i	−2.74229	−	3.16477i
$951$	36.6467	+	21.3125i	1.18835	+	0.691104i
$952$	0.0878891	+	0.0258066i	0.00284850	+	0.000836396i
$953$	16.6115	−	19.1707i	0.538100	−	0.621000i	−0.419969	−	0.907538i	$-0.637959\pi$
$953$	16.6115	−	19.1707i	0.538100	−	0.621000i	0.958069	+	0.286538i	$0.0925045\pi$
$954$	−3.94409	−	1.39300i	−0.127695	−	0.0451001i
$955$	−27.1921	−	17.4753i	−0.879916	−	0.565488i
$956$	7.04990	+	6.10877i	0.228010	+	0.197572i
$957$	32.9843	−	23.3315i	1.06623	−	0.754201i
$958$	0.615493	−	0.0884945i	0.0198857	−	0.00285913i
$959$	−16.8239	+	14.5780i	−0.543272	+	0.470748i
$960$	11.6460	−	47.3527i	0.375873	−	1.52830i
$961$	25.1764	−	7.39246i	0.812142	−	0.238466i
$962$	28.8349	−	63.1396i	0.929673	−	2.03570i
$963$	54.1012	−	4.82163i	1.74339	−	0.155375i
$964$	29.1883	+	45.4179i	0.940092	+	1.46281i
$965$	57.5763			1.85345
$966$	−8.81418	−	13.9007i	−0.283592	−	0.447248i
$967$	−29.5986			−0.951828			−0.475914	−	0.879492i	$-0.657883\pi$
$967$	−29.5986			−0.951828			−0.475914	+	0.879492i	$0.657883\pi$
$968$	−0.769231	−	1.19695i	−0.0247240	−	0.0384713i
$969$	5.14342	+	5.42846i	0.165230	+	0.174387i
$970$	12.9467	−	28.3492i	0.415692	−	0.910239i
$971$	−23.1376	+	6.79380i	−0.742520	+	0.218023i	−0.631048	−	0.775744i	$-0.717375\pi$
$971$	−23.1376	+	6.79380i	−0.742520	+	0.218023i	−0.111472	+	0.993768i	$0.535557\pi$
$972$	6.61828	+	29.2908i	0.212281	+	0.939503i
$973$	14.3776	−	12.4583i	0.460925	−	0.399394i
$974$	12.4597	−	1.79143i	0.399233	−	0.0574011i
$975$	−41.2414	−	58.3040i	−1.32078	−	1.86722i
$976$	15.3574	+	13.3073i	0.491579	+	0.425956i
$977$	2.48887	+	1.59950i	0.0796261	+	0.0511726i	0.579848	−	0.814725i	$-0.303112\pi$
$977$	2.48887	+	1.59950i	0.0796261	+	0.0511726i	−0.500222	+	0.865897i	$0.666748\pi$
$978$	7.99300	−	2.73819i	0.255588	−	0.0875575i
$979$	44.9256	−	51.8469i	1.43583	−	1.65703i
$980$	7.03162	+	2.06467i	0.224617	+	0.0659534i
$981$	20.2946	+	51.6356i	0.647955	+	1.64860i
$982$	25.0706	+	28.9330i	0.800034	+	0.923288i
$983$	0.0463535	+	0.101500i	0.00147845	+	0.00323734i	0.910370	−	0.413796i	$-0.135797\pi$
$983$	0.0463535	+	0.101500i	0.00147845	+	0.00323734i	−0.908891	+	0.417033i	$0.863070\pi$
$984$	−0.487759	−	0.197057i	−0.0155492	−	0.00628196i
$985$	−43.4572	−	19.8462i	−1.38466	−	0.632353i
$986$	0.906615	−	6.30565i	0.0288725	−	0.200813i
$987$	12.2018	+	1.20401i	0.388388	+	0.0383239i
$988$		−	57.6593i		−	1.83439i
$989$	1.00190	−	19.8072i	0.0318587	−	0.629833i
$990$	−100.269	+	23.6558i	−3.18675	+	0.751830i
$991$	18.3273	−	11.7783i	0.582187	−	0.374149i	−0.216150	−	0.976360i	$-0.569350\pi$
$991$	18.3273	−	11.7783i	0.582187	−	0.374149i	0.798337	+	0.602211i	$0.205714\pi$
$992$	17.0947	+	2.45784i	0.542756	+	0.0780366i
$993$	44.2914	−	22.6572i	1.40554	−	0.719003i
$994$	3.48072	+	11.8542i	0.110402	+	0.375993i
$995$	−78.9621	+	36.0608i	−2.50327	+	1.14320i
$996$	0.353418	+	7.94678i	0.0111985	+	0.251803i
$997$	−2.57245	−	17.8918i	−0.0814702	−	0.566637i	−0.989143	−	0.146958i	$-0.953052\pi$
$997$	−2.57245	−	17.8918i	−0.0814702	−	0.566637i	0.907673	−	0.419679i	$-0.137857\pi$
$998$	−11.6459	+	39.6624i	−0.368645	+	1.25549i
$999$	38.2011	−	17.0106i	1.20863	−	0.538192i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.u.a.218.10	yes	480
3.2	odd	2	inner	483.2.u.a.218.39	yes	480
23.21	odd	22	inner	483.2.u.a.113.39	yes	480
69.44	even	22	inner	483.2.u.a.113.10	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.u.a.113.10	✓	480	69.44	even	22	inner
483.2.u.a.113.39	yes	480	23.21	odd	22	inner
483.2.u.a.218.10	yes	480	1.1	even	1	trivial
483.2.u.a.218.39	yes	480	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07128 - 1.66695i) q^{2} +(-1.25731 + 1.19129i) q^{3} +(-0.800245 + 1.75229i) q^{4} +(3.65018 - 1.07179i) q^{5} +(3.33276 + 0.819664i) q^{6} +(0.755750 - 0.654861i) q^{7} +(-0.144404 + 0.0207621i) q^{8} +(0.161658 - 2.99564i) q^{9} +(-5.69700 - 4.93648i) q^{10} +(3.83235 + 2.46290i) q^{11} +(-1.08133 - 3.15650i) q^{12} +(-2.85046 + 3.28961i) q^{13} +(-1.90124 - 0.558255i) q^{14} +(-3.31260 + 5.69600i) q^{15} +(2.71232 + 3.13019i) q^{16} +(-0.260828 - 0.571133i) q^{17} +(-5.16677 + 2.93971i) q^{18} +(6.25501 + 2.85657i) q^{19} +(-1.04295 + 7.25388i) q^{20} +(-0.170083 + 1.72368i) q^{21} -9.02680i q^{22} +(-0.441836 - 4.77544i) q^{23} +(0.156827 - 0.198131i) q^{24} +(7.96882 - 5.12125i) q^{25} +(8.53726 + 1.22747i) q^{26} +(3.36542 + 3.95903i) q^{27} +(0.542723 + 1.84834i) q^{28} +(-4.65769 + 2.12710i) q^{29} +(13.0437 - 0.580093i) q^{30} +(0.310518 + 2.15970i) q^{31} +(2.23000 - 7.59467i) q^{32} +(-7.75247 + 1.46881i) q^{33} +(-0.672631 + 1.04663i) q^{34} +(2.05675 - 3.20037i) q^{35} +(5.11987 + 2.68052i) q^{36} +(2.26731 - 7.72175i) q^{37} +(-1.93914 - 13.4870i) q^{38} +(-0.334962 - 7.53178i) q^{39} +(-0.504847 + 0.230556i) q^{40} +(-0.586531 - 1.99754i) q^{41} +(3.05550 - 1.56303i) q^{42} +(4.09328 + 0.588525i) q^{43} +(-7.38253 + 4.74447i) q^{44} +(-2.62062 - 11.1079i) q^{45} +(-7.48708 + 5.85237i) q^{46} -7.07894i q^{47} +(-7.13919 - 0.704454i) q^{48} +(0.142315 - 0.989821i) q^{49} +(-17.0737 - 7.79732i) q^{50} +(1.00833 + 0.407370i) q^{51} +(-3.48328 - 7.62733i) q^{52} +(0.460792 + 0.531783i) q^{53} +(2.99419 - 9.85124i) q^{54} +(16.6285 + 4.88256i) q^{55} +(-0.0955367 + 0.110255i) q^{56} +(-11.2675 + 3.85994i) q^{57} +(8.53548 + 5.48542i) q^{58} +(6.97879 + 6.04716i) q^{59} +(-7.33016 - 10.3628i) q^{60} +(4.85630 - 0.698230i) q^{61} +(3.26746 - 2.83127i) q^{62} +(-1.83956 - 2.36982i) q^{63} +(-7.10078 + 2.08498i) q^{64} +(-6.87893 + 15.0628i) q^{65} +(10.7535 + 11.3495i) q^{66} +(1.69159 + 2.63217i) q^{67} +1.20952 q^{68} +(6.24445 + 5.47785i) q^{69} -7.53821 q^{70} +(-3.37089 - 5.24521i) q^{71} +(0.0388519 + 0.435938i) q^{72} +(1.23299 - 2.69988i) q^{73} +(-15.3007 + 4.49269i) q^{74} +(-3.91839 + 15.9322i) q^{75} +(-10.0111 + 8.67465i) q^{76} +(4.50915 - 0.648318i) q^{77} +(-12.1963 + 8.62704i) q^{78} +(-6.32714 - 5.48250i) q^{79} +(13.2554 + 8.51871i) q^{80} +(-8.94773 - 0.968537i) q^{81} +(-2.70146 + 3.11765i) q^{82} +(-2.28750 - 0.671670i) q^{83} +(-2.88428 - 1.67740i) q^{84} +(-1.56420 - 1.80519i) q^{85} +(-3.40403 - 7.45378i) q^{86} +(3.32218 - 8.22308i) q^{87} +(-0.604540 - 0.276084i) q^{88} +(2.14317 - 14.9061i) q^{89} +(-15.7089 + 16.2682i) q^{90} +4.35277i q^{91} +(8.72154 + 3.04729i) q^{92} +(-2.96325 - 2.34550i) q^{93} +(-11.8002 + 7.58356i) q^{94} +(25.8936 + 3.72293i) q^{95} +(6.24365 + 12.2054i) q^{96} +(1.16478 + 3.96688i) q^{97} +(-1.80244 + 0.823148i) q^{98} +(7.99749 - 11.0822i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36}+ \cdots - 132 q^{97}+O(q^{100}) \) 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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