LMFDB - Embedded newform 230.2.l.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	230.17
Dual form			230.2.l.a.203.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.936950 + 0.349464i) q^{2} +(-0.565213 + 0.308630i) q^{3} +(0.755750 - 0.654861i) q^{4} +(-1.72918 - 1.41772i) q^{5} +(0.421721 - 0.486692i) q^{6} +(1.82117 + 2.43280i) q^{7} +(-0.479249 + 0.877679i) q^{8} +(-1.39771 + 2.17488i) q^{9} +(2.11560 + 0.724045i) q^{10} +(1.38662 - 0.633249i) q^{11} +(-0.225050 + 0.603382i) q^{12} +(3.84199 + 2.87608i) q^{13} +(-2.55652 - 1.64298i) q^{14} +(1.41491 + 0.267637i) q^{15} +(0.142315 - 0.989821i) q^{16} +(0.428269 + 5.98798i) q^{17} +(0.549541 - 2.52620i) q^{18} +(-0.682687 - 0.787863i) q^{19} +(-2.23524 + 0.0609327i) q^{20} +(-1.78018 - 0.812983i) q^{21} +(-1.07790 + 1.07790i) q^{22} +(-2.30796 + 4.20396i) q^{23} -0.643986i q^{24} +(0.980143 + 4.90299i) q^{25} +(-4.60484 - 1.35210i) q^{26} +(0.256596 - 3.58768i) q^{27} +(2.96950 + 0.645974i) q^{28} +(-0.893636 - 0.774340i) q^{29} +(-1.41923 + 0.243697i) q^{30} +(0.384033 - 0.112762i) q^{31} +(0.212565 + 0.977147i) q^{32} +(-0.588297 + 0.785873i) q^{33} +(-2.49385 - 5.46077i) q^{34} +(0.299891 - 6.78867i) q^{35} +(0.367924 + 2.55897i) q^{36} +(-1.28246 + 0.278981i) q^{37} +(0.914973 + 0.499613i) q^{38} +(-3.05919 - 0.439844i) q^{39} +(2.07301 - 0.838226i) q^{40} +(8.30875 - 5.33971i) q^{41} +(1.95205 + 0.139614i) q^{42} +(3.57839 + 6.55334i) q^{43} +(0.633249 - 1.38662i) q^{44} +(5.50026 - 1.77920i) q^{45} +(0.693312 - 4.74545i) q^{46} +(-8.35033 - 8.35033i) q^{47} +(0.225050 + 0.603382i) q^{48} +(-0.629726 + 2.14465i) q^{49} +(-2.63176 - 4.25133i) q^{50} +(-2.09013 - 3.25231i) q^{51} +(4.78701 - 0.342374i) q^{52} +(7.94381 - 5.94666i) q^{53} +(1.01335 + 3.45115i) q^{54} +(-3.29549 - 0.870837i) q^{55} +(-3.00801 + 0.432487i) q^{56} +(0.629021 + 0.234613i) q^{57} +(1.10790 + 0.413224i) q^{58} +(-7.59217 + 1.09159i) q^{59} +(1.24458 - 0.724300i) q^{60} +(0.961272 + 3.27379i) q^{61} +(-0.320413 + 0.239859i) q^{62} +(-7.83652 + 0.560479i) q^{63} +(-0.540641 - 0.841254i) q^{64} +(-2.56603 - 10.4201i) q^{65} +(0.276570 - 0.941912i) q^{66} +(-4.22193 - 11.3194i) q^{67} +(4.24495 + 4.24495i) q^{68} +(0.00702364 - 3.08844i) q^{69} +(2.09141 + 6.46544i) q^{70} +(-0.865969 + 1.89621i) q^{71} +(-1.23899 - 2.26905i) q^{72} +(0.260594 + 0.0186380i) q^{73} +(1.10410 - 0.709564i) q^{74} +(-2.06720 - 2.46873i) q^{75} +(-1.03188 - 0.148362i) q^{76} +(4.06584 + 2.22012i) q^{77} +(3.02001 - 0.656964i) q^{78} +(0.108205 + 0.752579i) q^{79} +(-1.64938 + 1.50982i) q^{80} +(-2.25966 - 4.94797i) q^{81} +(-5.91884 + 7.90665i) q^{82} +(1.22112 + 5.61340i) q^{83} +(-1.87776 + 0.551361i) q^{84} +(7.74872 - 10.9615i) q^{85} +(-5.64293 - 4.88963i) q^{86} +(0.744078 + 0.161864i) q^{87} +(-0.108748 + 1.52049i) q^{88} +(3.11654 + 0.915098i) q^{89} +(-4.53170 + 3.58917i) q^{90} +14.5846i q^{91} +(1.00877 + 4.68854i) q^{92} +(-0.182259 + 0.182259i) q^{93} +(10.7420 + 4.90570i) q^{94} +(0.0635218 + 2.33022i) q^{95} +(-0.421721 - 0.486692i) q^{96} +(-3.03964 + 13.9730i) q^{97} +(-0.159457 - 2.22950i) q^{98} +(-0.560854 + 3.90083i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{22}\right)$

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 $

$2$	−0.936950	+	0.349464i	−0.662524	+	0.247108i
$2$	−0.936950	+	0.349464i	−0.662524	+	0.247108i
$3$	−0.565213	+	0.308630i	−0.326326	+	0.178187i	−0.634058	−	0.773286i	$-0.718612\pi$
$3$	−0.565213	+	0.308630i	−0.326326	+	0.178187i	0.307732	+	0.951473i	$0.400430\pi$
$4$	0.755750	−	0.654861i	0.377875	−	0.327430i
$5$	−1.72918	−	1.41772i	−0.773314	−	0.634023i
$5$	−1.72918	−	1.41772i	−0.773314	−	0.634023i
$6$	0.421721	−	0.486692i	0.172167	−	0.198691i
$7$	1.82117	+	2.43280i	0.688338	+	0.919513i	0.999524	−	0.0308365i	$-0.00981712\pi$
$7$	1.82117	+	2.43280i	0.688338	+	0.919513i	−0.311186	+	0.950349i	$0.600726\pi$
$8$	−0.479249	+	0.877679i	−0.169440	+	0.310306i
$9$	−1.39771	+	2.17488i	−0.465903	+	0.724959i
$10$	2.11560	+	0.724045i	0.669011	+	0.228963i
$11$	1.38662	−	0.633249i	0.418082	−	0.190932i	−0.195256	−	0.980752i	$-0.562554\pi$
$11$	1.38662	−	0.633249i	0.418082	−	0.190932i	0.613338	+	0.789821i	$0.289826\pi$
$12$	−0.225050	+	0.603382i	−0.0649663	+	0.174181i
$13$	3.84199	+	2.87608i	1.06558	+	0.797680i	0.980069	−	0.198657i	$-0.0636580\pi$
$13$	3.84199	+	2.87608i	1.06558	+	0.797680i	0.0855073	+	0.996338i	$0.472749\pi$
$14$	−2.55652	−	1.64298i	−0.683260	−	0.439104i
$15$	1.41491	+	0.267637i	0.365327	+	0.0691035i
$16$	0.142315	−	0.989821i	0.0355787	−	0.247455i
$17$	0.428269	+	5.98798i	0.103870	+	1.45230i	0.735762	+	0.677241i	$0.236824\pi$
$17$	0.428269	+	5.98798i	0.103870	+	1.45230i	−0.631891	+	0.775057i	$0.717721\pi$
$18$	0.549541	−	2.52620i	0.129528	−	0.595431i
$19$	−0.682687	−	0.787863i	−0.156619	−	0.180748i	0.672017	−	0.740536i	$-0.265428\pi$
$19$	−0.682687	−	0.787863i	−0.156619	−	0.180748i	−0.828636	+	0.559788i	$0.810883\pi$
$20$	−2.23524	+	0.0609327i	−0.499814	+	0.0136250i
$21$	−1.78018	−	0.812983i	−0.388468	−	0.177407i
$22$	−1.07790	+	1.07790i	−0.229808	+	0.229808i
$23$	−2.30796	+	4.20396i	−0.481244	+	0.876587i
$23$	−2.30796	+	4.20396i	−0.481244	+	0.876587i
$24$		−	0.643986i		−	0.131453i
$25$	0.980143	+	4.90299i	0.196029	+	0.980598i
$26$	−4.60484	−	1.35210i	−0.903083	−	0.265169i
$27$	0.256596	−	3.58768i	0.0493819	−	0.690449i
$28$	2.96950	+	0.645974i	0.561182	+	0.122078i
$29$	−0.893636	−	0.774340i	−0.165944	−	0.143791i	0.567930	−	0.823077i	$-0.307744\pi$
$29$	−0.893636	−	0.774340i	−0.165944	−	0.143791i	−0.733874	+	0.679285i	$0.762290\pi$
$30$	−1.41923	+	0.243697i	−0.259114	+	0.0444928i
$31$	0.384033	−	0.112762i	0.0689744	−	0.0202527i	−0.247063	−	0.968999i	$-0.579466\pi$
$31$	0.384033	−	0.112762i	0.0689744	−	0.0202527i	0.316038	+	0.948747i	$0.397647\pi$
$32$	0.212565	+	0.977147i	0.0375766	+	0.172737i
$33$	−0.588297	+	0.785873i	−0.102409	+	0.136803i
$34$	−2.49385	−	5.46077i	−0.427692	−	0.936514i
$35$	0.299891	−	6.78867i	0.0506908	−	1.14749i
$36$	0.367924	+	2.55897i	0.0613207	+	0.426495i
$37$	−1.28246	+	0.278981i	−0.210834	+	0.0458642i	−0.316742	−	0.948512i	$-0.602589\pi$
$37$	−1.28246	+	0.278981i	−0.210834	+	0.0458642i	0.105907	+	0.994376i	$0.466225\pi$
$38$	0.914973	+	0.499613i	0.148428	+	0.0810480i
$39$	−3.05919	−	0.439844i	−0.489862	−	0.0704315i
$40$	2.07301	−	0.838226i	0.327772	−	0.132535i
$41$	8.30875	−	5.33971i	1.29761	−	0.833922i	0.304659	−	0.952461i	$-0.401458\pi$
$41$	8.30875	−	5.33971i	1.29761	−	0.833922i	0.992949	+	0.118539i	$0.0378211\pi$
$42$	1.95205	+	0.139614i	0.301208	+	0.0215428i
$43$	3.57839	+	6.55334i	0.545700	+	0.999375i	0.994399	+	0.105692i	$0.0337057\pi$
$43$	3.57839	+	6.55334i	0.545700	+	0.999375i	−0.448699	+	0.893683i	$0.648112\pi$
$44$	0.633249	−	1.38662i	0.0954658	−	0.209041i
$45$	5.50026	−	1.77920i	0.819930	−	0.265228i
$46$	0.693312	−	4.74545i	0.102223	−	0.699679i
$47$	−8.35033	−	8.35033i	−1.21802	−	1.21802i	−0.968324	−	0.249697i	$-0.919669\pi$
$47$	−8.35033	−	8.35033i	−1.21802	−	1.21802i	−0.249697	−	0.968324i	$-0.580331\pi$
$48$	0.225050	+	0.603382i	0.0324832	+	0.0870907i
$49$	−0.629726	+	2.14465i	−0.0899609	+	0.306379i
$50$	−2.63176	−	4.25133i	−0.372188	−	0.601229i
$51$	−2.09013	−	3.25231i	−0.292677	−	0.455414i
$52$	4.78701	−	0.342374i	0.663839	−	0.0474787i
$53$	7.94381	−	5.94666i	1.09117	−	0.816837i	0.107031	−	0.994256i	$-0.465866\pi$
$53$	7.94381	−	5.94666i	1.09117	−	0.816837i	0.984135	+	0.177419i	$0.0567748\pi$
$54$	1.01335	+	3.45115i	0.137899	+	0.469641i
$55$	−3.29549	−	0.870837i	−0.444364	−	0.117424i
$56$	−3.00801	+	0.432487i	−0.401963	+	0.0577935i
$57$	0.629021	+	0.234613i	0.0833159	+	0.0310752i
$58$	1.10790	+	0.413224i	0.145474	+	0.0542589i
$59$	−7.59217	+	1.09159i	−0.988416	+	0.142113i	−0.617515	−	0.786559i	$-0.711860\pi$
$59$	−7.59217	+	1.09159i	−0.988416	+	0.142113i	−0.370901	+	0.928672i	$0.620951\pi$
$60$	1.24458	−	0.724300i	0.160675	−	0.0935068i
$61$	0.961272	+	3.27379i	0.123078	+	0.419166i	0.997863	−	0.0653463i	$-0.0208152\pi$
$61$	0.961272	+	3.27379i	0.123078	+	0.419166i	−0.874784	+	0.484512i	$0.838997\pi$
$62$	−0.320413	+	0.239859i	−0.0406926	+	0.0304621i
$63$	−7.83652	+	0.560479i	−0.987308	+	0.0706137i
$64$	−0.540641	−	0.841254i	−0.0675801	−	0.105157i
$65$	−2.56603	−	10.4201i	−0.318277	−	1.29246i
$66$	0.276570	−	0.941912i	0.0340434	−	0.115941i
$67$	−4.22193	−	11.3194i	−0.515791	−	1.38289i	−0.890176	−	0.455616i	$-0.849419\pi$
$67$	−4.22193	−	11.3194i	−0.515791	−	1.38289i	0.374385	−	0.927273i	$-0.377854\pi$
$68$	4.24495	+	4.24495i	0.514776	+	0.514776i
$69$	0.00702364	−	3.08844i	0.000845547	−	0.371804i
$70$	2.09141	+	6.46544i	0.249972	+	0.772768i
$71$	−0.865969	+	1.89621i	−0.102772	+	0.225039i	−0.954032	−	0.299705i	$-0.903112\pi$
$71$	−0.865969	+	1.89621i	−0.102772	+	0.225039i	0.851260	+	0.524744i	$0.175839\pi$
$72$	−1.23899	−	2.26905i	−0.146017	−	0.267410i
$73$	0.260594	+	0.0186380i	0.0305002	+	0.00218142i	0.0865810	−	0.996245i	$-0.472406\pi$
$73$	0.260594	+	0.0186380i	0.0305002	+	0.00218142i	−0.0560807	+	0.998426i	$0.517860\pi$
$74$	1.10410	−	0.709564i	0.128349	−	0.0824851i
$75$	−2.06720	−	2.46873i	−0.238699	−	0.285065i
$76$	−1.03188	−	0.148362i	−0.118365	−	0.0170183i
$77$	4.06584	+	2.22012i	0.463346	+	0.253006i
$78$	3.02001	−	0.656964i	0.341949	−	0.0743865i
$79$	0.108205	+	0.752579i	0.0121740	+	0.0846718i	0.995003	−	0.0998487i	$-0.0318359\pi$
$79$	0.108205	+	0.752579i	0.0121740	+	0.0846718i	−0.982829	+	0.184521i	$0.940927\pi$
$80$	−1.64938	+	1.50982i	−0.184406	+	0.168803i
$81$	−2.25966	−	4.94797i	−0.251074	−	0.549775i
$82$	−5.91884	+	7.90665i	−0.653627	+	0.873143i
$83$	1.22112	+	5.61340i	0.134035	+	0.616151i	0.994329	+	0.106351i	$0.0339168\pi$
$83$	1.22112	+	5.61340i	0.134035	+	0.616151i	−0.860293	+	0.509800i	$0.829720\pi$
$84$	−1.87776	+	0.551361i	−0.204881	+	0.0601585i
$85$	7.74872	−	10.9615i	0.840466	−	1.18894i
$86$	−5.64293	−	4.88963i	−0.608493	−	0.527262i
$87$	0.744078	+	0.161864i	0.0797736	+	0.0173537i
$88$	−0.108748	+	1.52049i	−0.0115925	+	0.162085i
$89$	3.11654	+	0.915098i	0.330352	+	0.0970002i	0.442703	−	0.896668i	$-0.354020\pi$
$89$	3.11654	+	0.915098i	0.330352	+	0.0970002i	−0.112350	+	0.993669i	$0.535838\pi$
$90$	−4.53170	+	3.58917i	−0.477683	+	0.378331i
$91$			14.5846i			1.52888i
$92$	1.00877	+	4.68854i	0.105171	+	0.488814i
$93$	−0.182259	+	0.182259i	−0.0188994	+	0.0188994i
$94$	10.7420	+	4.90570i	1.10795	+	0.505984i
$95$	0.0635218	+	2.33022i	0.00651720	+	0.239075i
$96$	−0.421721	−	0.486692i	−0.0430417	−	0.0496728i
$97$	−3.03964	+	13.9730i	−0.308628	+	1.41874i	0.517705	+	0.855559i	$0.326787\pi$
$97$	−3.03964	+	13.9730i	−0.308628	+	1.41874i	−0.826333	+	0.563182i	$0.809577\pi$
$98$	−0.159457	−	2.22950i	−0.0161076	−	0.225213i
$99$	−0.560854	+	3.90083i	−0.0563680	+	0.392048i
$100$	3.95152	+	3.06358i	0.395152	+	0.306358i
$101$	16.3898	+	10.5331i	1.63085	+	1.04808i	0.948367	+	0.317175i	$0.102734\pi$
$101$	16.3898	+	10.5331i	1.63085	+	1.04808i	0.682478	+	0.730906i	$0.260902\pi$
$102$	3.09491	+	2.31682i	0.306442	+	0.229399i
$103$	4.55361	−	12.2087i	0.448681	−	1.20296i	−0.494058	−	0.869429i	$-0.664487\pi$
$103$	4.55361	−	12.2087i	0.448681	−	1.20296i	0.942739	−	0.333531i	$-0.108240\pi$
$104$	−4.36554	+	1.99368i	−0.428077	+	0.195496i
$105$	1.92568	+	3.92960i	0.187927	+	0.383490i
$106$	−5.36480	+	8.34780i	−0.521076	+	0.810810i
$107$	−3.68806	+	6.75418i	−0.356538	+	0.652951i	−0.992968	−	0.118383i	$-0.962229\pi$
$107$	−3.68806	+	6.75418i	−0.356538	+	0.652951i	0.636430	+	0.771335i	$0.280411\pi$
$108$	−2.15551	−	2.87942i	−0.207414	−	0.277072i
$109$	3.61973	−	4.17739i	0.346707	−	0.400122i	−0.555435	−	0.831560i	$-0.687448\pi$
$109$	3.61973	−	4.17739i	0.346707	−	0.400122i	0.902142	+	0.431438i	$0.141994\pi$
$110$	3.39203	−	0.335725i	0.323418	−	0.0320101i
$111$	0.638759	−	0.553487i	0.0606283	−	0.0525347i
$112$	2.66722	−	1.45641i	0.252029	−	0.137618i
$113$	−16.5955	+	6.18982i	−1.56118	+	0.582289i	−0.973876	−	0.227080i	$-0.927082\pi$
$113$	−16.5955	+	6.18982i	−1.56118	+	0.582289i	−0.587301	+	0.809369i	$0.699809\pi$
$114$	−0.671350			−0.0628777
$115$	9.95093	−	3.99737i	0.927929	−	0.372757i
$116$	−1.18245			−0.109788
$117$	−11.6251	+	4.33594i	−1.07474	+	0.400858i
$118$	6.73201	−	3.67595i	0.619732	−	0.338399i
$119$	−13.7876	+	11.9470i	−1.26391	+	1.09518i
$120$	−0.912991	+	1.11357i	−0.0833443	+	0.101654i
$121$	−5.68175	+	6.55709i	−0.516523	+	0.596099i
$122$	−2.04474	−	2.73145i	−0.185122	−	0.247294i
$123$	−3.04822	+	5.58240i	−0.274849	+	0.503348i
$124$	0.216389	−	0.336708i	0.0194323	−	0.0302373i
$125$	5.25622	−	9.86773i	0.470131	−	0.882597i
$126$	7.14655	−	3.26372i	0.636666	−	0.290755i
$127$	3.68774	−	9.88722i	0.327234	−	0.877349i	−0.664296	−	0.747470i	$-0.731268\pi$
$127$	3.68774	−	9.88722i	0.327234	−	0.877349i	0.991530	−	0.129879i	$-0.0414588\pi$
$128$	0.800541	+	0.599278i	0.0707585	+	0.0529692i
$129$	−4.04511	−	2.59963i	−0.356152	−	0.228885i
$130$	6.04570	+	8.86640i	0.530243	+	0.777635i
$131$	3.02120	−	21.0129i	0.263963	−	1.83591i	−0.238300	−	0.971191i	$-0.576590\pi$
$131$	3.02120	−	21.0129i	0.263963	−	1.83591i	0.502264	−	0.864714i	$-0.332501\pi$
$132$	0.0700320	+	0.979175i	0.00609550	+	0.0852263i
$133$	0.673423	−	3.09568i	0.0583932	−	0.268429i
$134$	7.91148	+	9.13033i	0.683448	+	0.788741i
$135$	−5.53002	+	5.83997i	−0.475949	+	0.502625i
$136$	−5.46077	−	2.49385i	−0.468257	−	0.213846i
$137$	−2.26877	+	2.26877i	−0.193834	+	0.193834i	−0.797351	−	0.603516i	$-0.793766\pi$
$137$	−2.26877	+	2.26877i	−0.193834	+	0.193834i	0.603516	+	0.797351i	$0.293766\pi$
$138$	1.07272	+	2.89617i	0.0913158	+	0.246538i
$139$		−	5.52306i		−	0.468460i	−0.972181	−	0.234230i	$-0.924743\pi$
$139$		−	5.52306i		−	0.468460i	0.972181	−	0.234230i	$-0.0752568\pi$
$140$	−4.21899	−	5.32692i	−0.356570	−	0.450207i
$141$	7.29687	+	2.14256i	0.614508	+	0.180436i
$142$	0.148713	−	2.07928i	0.0124797	−	0.174489i
$143$	7.14866	+	1.55510i	0.597801	+	0.130044i
$144$	1.95383	+	1.69300i	0.162819	+	0.141083i
$145$	0.447462	+	2.60590i	0.0371597	+	0.216408i
$146$	−0.250677	+	0.0736053i	−0.0207462	+	0.00609162i
$147$	−0.305973	−	1.40654i	−0.0252363	−	0.116009i
$148$	−0.786521	+	1.05067i	−0.0646517	+	0.0863645i
$149$	2.69261	+	5.89599i	0.220587	+	0.483018i	0.987279	−	0.158997i	$-0.0508259\pi$
$149$	2.69261	+	5.89599i	0.220587	+	0.483018i	−0.766692	+	0.642015i	$0.778099\pi$
$150$	2.79959	+	1.59067i	0.228586	+	0.129877i
$151$	0.437790	+	3.04490i	0.0356269	+	0.247790i	0.999850	−	0.0173004i	$-0.00550718\pi$
$151$	0.437790	+	3.04490i	0.0356269	+	0.247790i	−0.964223	+	0.265091i	$0.914598\pi$
$152$	1.01867	−	0.221598i	0.0826249	−	0.0179739i
$153$	−13.6217	−	7.43802i	−1.10125	−	0.601328i
$154$	−4.58534	−	0.659273i	−0.369498	−	0.0531257i
$155$	−0.823929	−	0.349465i	−0.0661796	−	0.0280697i
$156$	−2.60001	+	1.67093i	−0.208168	+	0.133781i
$157$	−6.52474	−	0.466659i	−0.520731	−	0.0372434i	−0.191500	−	0.981493i	$-0.561335\pi$
$157$	−6.52474	−	0.466659i	−0.520731	−	0.0372434i	−0.329231	+	0.944249i	$0.606790\pi$
$158$	−0.364382	−	0.667315i	−0.0289887	−	0.0530888i
$159$	−2.65463	+	5.81282i	−0.210526	+	0.460987i
$160$	1.01776	−	1.99102i	0.0804607	−	0.157404i
$161$	−14.4306	+	2.04132i	−1.13729	+	0.160879i
$162$	3.84633	+	3.84633i	0.302196	+	0.302196i
$163$	−2.44669	−	6.55983i	−0.191640	−	0.513806i	0.805222	−	0.592974i	$-0.202046\pi$
$163$	−2.44669	−	6.55983i	−0.191640	−	0.513806i	−0.996861	+	0.0791682i	$0.974774\pi$
$164$	2.78257	−	9.47655i	0.217282	−	0.739995i
$165$	2.13142	−	0.524877i	0.165931	−	0.0408616i
$166$	−3.10581	−	4.83274i	−0.241058	−	0.375093i
$167$	23.9870	−	1.71559i	1.85617	−	0.132756i	0.901948	−	0.431845i	$-0.142137\pi$
$167$	23.9870	−	1.71559i	1.85617	−	0.132756i	0.954225	+	0.299089i	$0.0966827\pi$
$168$	1.56669	−	1.17281i	0.120873	−	0.0904842i
$169$	2.82654	+	9.62632i	0.217426	+	0.740486i
$170$	−3.42952	+	12.9782i	−0.263032	+	0.995386i
$171$	2.66770	−	0.383558i	0.204004	−	0.0293314i
$172$	6.99589	+	2.60933i	0.533432	+	0.198960i
$173$	9.33157	+	3.48050i	0.709466	+	0.264617i	0.678183	−	0.734893i	$-0.262768\pi$
$173$	9.33157	+	3.48050i	0.709466	+	0.264617i	0.0312835	+	0.999511i	$0.490041\pi$
$174$	−0.753730	+	0.108370i	−0.0571401	+	0.00821551i
$175$	−10.1430	+	11.3137i	−0.766738	+	0.855234i
$176$	−0.429466	−	1.46263i	−0.0323722	−	0.110250i
$177$	3.95429	−	2.96015i	0.297223	−	0.222498i
$178$	−3.23983	+	0.231718i	−0.242836	+	0.0173680i
$179$	3.59318	+	5.59109i	0.268567	+	0.417898i	0.949175	−	0.314750i	$-0.101921\pi$
$179$	3.59318	+	5.59109i	0.268567	+	0.417898i	−0.680608	+	0.732648i	$0.738284\pi$
$180$	2.99169	−	4.94653i	0.222987	−	0.368693i
$181$	2.69144	−	9.16619i	0.200053	−	0.681317i	−0.796957	−	0.604037i	$-0.793558\pi$
$181$	2.69144	−	9.16619i	0.200053	−	0.681317i	0.997009	−	0.0772807i	$-0.0246238\pi$
$182$	−5.09681	−	13.6651i	−0.377800	−	1.01292i
$183$	−1.55371	−	1.55371i	−0.114854	−	0.114854i
$184$	−2.58364	−	4.04040i	−0.190468	−	0.297862i
$185$	2.61312	+	1.33575i	0.192120	+	0.0982065i
$186$	0.107074	−	0.234460i	0.00785108	−	0.0171915i
$187$	4.38572	+	8.03186i	0.320716	+	0.587347i
$188$	−11.7791	−	0.842455i	−0.859076	−	0.0614424i
$189$	9.19542	−	5.90953i	0.668868	−	0.429855i
$190$	−0.873844	−	2.16110i	−0.0633953	−	0.156782i
$191$	−16.7161	−	2.40341i	−1.20953	−	0.173905i	−0.492105	−	0.870536i	$-0.663772\pi$
$191$	−16.7161	−	2.40341i	−1.20953	−	0.173905i	−0.717429	+	0.696631i	$0.754681\pi$
$192$	0.565213	+	0.308630i	0.0407907	+	0.0222734i
$193$	6.69641	−	1.45671i	0.482018	−	0.104857i	0.0350108	−	0.999387i	$-0.488853\pi$
$193$	6.69641	−	1.45671i	0.482018	−	0.104857i	0.447007	+	0.894530i	$0.352490\pi$
$194$	−2.03507	−	14.1542i	−0.146110	−	1.01621i
$195$	4.66631	+	5.09764i	0.334162	+	0.365049i
$196$	0.928532	+	2.03320i	0.0663237	+	0.145229i
$197$	11.4538	−	15.3004i	0.816047	−	1.09011i	−0.178305	−	0.983975i	$-0.557061\pi$
$197$	11.4538	−	15.3004i	0.816047	−	1.09011i	0.994352	−	0.106136i	$-0.0338478\pi$
$198$	−0.837707	−	3.85088i	−0.0595333	−	0.273670i
$199$	26.1607	−	7.68147i	1.85448	−	0.544525i	0.854810	−	0.518941i	$-0.173674\pi$
$199$	26.1607	−	7.68147i	1.85448	−	0.544525i	0.999673	−	0.0255842i	$-0.00814458\pi$
$200$	−4.77298	−	1.48950i	−0.337501	−	0.105324i
$201$	5.87981	+	5.09488i	0.414729	+	0.359365i
$202$	−19.0373	−	4.14132i	−1.33946	−	0.291382i
$203$	0.256350	−	3.58424i	0.0179923	−	0.251565i
$204$	−3.70942	−	1.08918i	−0.259711	−	0.0762582i
$205$	−21.9375	−	2.54615i	−1.53218	−	0.177830i
$206$			13.0303i			0.907862i
$207$	−5.91724	−	10.8955i	−0.411277	−	0.757287i
$208$	3.39358	−	3.39358i	0.235302	−	0.235302i
$209$	−1.44554	−	0.660156i	−0.0999902	−	0.0456640i
$210$	−3.17752	−	3.00888i	−0.219270	−	0.207632i
$211$	−7.12686	−	8.22484i	−0.490633	−	0.566221i	0.455401	−	0.890286i	$-0.349496\pi$
$211$	−7.12686	−	8.22484i	−0.490633	−	0.566221i	−0.946035	+	0.324065i	$0.894950\pi$
$212$	2.10930	−	9.69627i	0.144867	−	0.665943i
$213$	−0.0957690	−	1.33903i	−0.00656198	−	0.0917485i
$214$	1.09518	−	7.61717i	0.0748653	−	0.520699i
$215$	3.10310	−	16.4051i	0.211630	−	1.11882i
$216$	3.02586	+	1.94460i	0.205883	+	0.132313i
$217$	0.973719	+	0.728917i	0.0661004	+	0.0494821i
$218$	−1.93166	+	5.17897i	−0.130828	+	0.350764i
$219$	−0.153043	+	0.0698925i	−0.0103417	+	0.00472290i
$220$	−3.06084	+	1.49995i	−0.206362	+	0.101127i
$221$	−15.5765	+	24.2375i	−1.04779	+	1.63039i
$222$	−0.405061	+	0.741813i	−0.0271859	+	0.0497872i
$223$	−14.9828	−	20.0147i	−1.00333	−	1.34029i	−0.939583	−	0.342320i	$-0.888787\pi$
$223$	−14.9828	−	20.0147i	−1.00333	−	1.34029i	−0.0637424	−	0.997966i	$-0.520304\pi$
$224$	−1.99009	+	2.29668i	−0.132968	+	0.153454i
$225$	−12.0334	−	4.72126i	−0.802224	−	0.314751i
$226$	13.3861	−	11.5991i	0.890428	−	0.771560i
$227$	−5.96840	+	3.25899i	−0.396136	+	0.216307i	−0.664954	−	0.746884i	$-0.731549\pi$
$227$	−5.96840	+	3.25899i	−0.396136	+	0.216307i	0.268818	+	0.963191i	$0.413367\pi$
$228$	0.629021	−	0.234613i	0.0416579	−	0.0155376i
$229$	17.9061			1.18327			0.591634	−	0.806207i	$-0.298483\pi$
$229$	17.9061			1.18327			0.591634	+	0.806207i	$0.298483\pi$
$230$	−7.92658	+	7.22283i	−0.522663	+	0.476259i
$231$	−2.98326			−0.196284
$232$	1.10790	−	0.413224i	0.0727369	−	0.0271295i
$233$	−7.93825	+	4.33462i	−0.520052	+	0.283970i	−0.717760	−	0.696291i	$-0.754832\pi$
$233$	−7.93825	+	4.33462i	−0.520052	+	0.283970i	0.197707	+	0.980261i	$0.436650\pi$
$234$	9.37688	−	8.12511i	0.612986	−	0.531155i
$235$	2.60082	+	26.2777i	0.169659	+	1.71417i
$236$	−5.02294	+	5.79678i	−0.326965	+	0.377338i
$237$	−0.293427	−	0.391972i	−0.0190601	−	0.0254613i
$238$	8.74324	−	16.0120i	0.566740	−	1.03791i
$239$	5.17370	−	8.05044i	0.334659	−	0.520740i	−0.632617	−	0.774464i	$-0.718019\pi$
$239$	5.17370	−	8.05044i	0.334659	−	0.520740i	0.967276	+	0.253725i	$0.0816558\pi$
$240$	0.466275	−	1.36242i	0.0300979	−	0.0879436i
$241$	20.7835	−	9.49149i	1.33878	−	0.611401i	0.388113	−	0.921612i	$-0.373127\pi$
$241$	20.7835	−	9.49149i	1.33878	−	0.611401i	0.950668	+	0.310211i	$0.100400\pi$
$242$	3.03205	−	8.12924i	0.194907	−	0.522567i
$243$	11.4425	+	8.56578i	0.734040	+	0.549495i
$244$	2.87036	+	1.84467i	0.183756	+	0.118093i
$245$	4.12943	−	2.81572i	0.263819	−	0.179890i
$246$	0.905181	−	6.29567i	0.0577122	−	0.401397i
$247$	−0.356922	−	4.99042i	−0.0227104	−	0.317533i
$248$	−0.0850784	+	0.391099i	−0.00540248	+	0.0248348i
$249$	−2.42265	−	2.79589i	−0.153530	−	0.177182i
$250$	−1.47640	+	11.0824i	−0.0933754	+	0.700914i
$251$	10.0860	+	4.60613i	0.636624	+	0.290736i	0.707462	−	0.706751i	$-0.249840\pi$
$251$	10.0860	+	4.60613i	0.636624	+	0.290736i	−0.0708381	+	0.997488i	$0.522567\pi$
$252$	−5.55541	+	5.55541i	−0.349958	+	0.349958i
$253$	−0.538118	+	7.29082i	−0.0338312	+	0.458370i
$254$			10.5526i			0.662126i
$255$	−0.996641	+	8.58705i	−0.0624121	+	0.537742i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	0.363054	−	5.07615i	0.0226467	−	0.316642i	−0.973484	−	0.228756i	$-0.926534\pi$
$257$	0.363054	−	5.07615i	0.0226467	−	0.316642i	0.996131	−	0.0878861i	$-0.0280112\pi$
$258$	4.69854	+	1.02211i	0.292518	+	0.0636335i
$259$	−3.01428	−	2.61189i	−0.187298	−	0.162295i
$260$	−8.76301	−	6.19461i	−0.543459	−	0.384174i
$261$	2.93314	−	0.861247i	0.181557	−	0.0533098i
$262$	4.51255	+	20.7438i	0.278786	+	1.28156i
$263$	−8.24542	+	11.0146i	−0.508435	+	0.679189i	−0.979160	−	0.203091i	$-0.934901\pi$
$263$	−8.24542	+	11.0146i	−0.508435	+	0.679189i	0.470725	+	0.882280i	$0.343992\pi$
$264$	−0.407803	−	0.892964i	−0.0250986	−	0.0549582i
$265$	−22.1670	−	0.979232i	−1.36171	−	0.0601537i
$266$	0.450864	+	3.13583i	0.0276443	+	0.192270i
$267$	−2.04393	+	0.444631i	−0.125087	+	0.0272110i
$268$	−10.6034	−	5.78988i	−0.647705	−	0.353673i
$269$	17.5624	+	2.52510i	1.07080	+	0.153958i	0.655099	−	0.755543i	$-0.272627\pi$
$269$	17.5624	+	2.52510i	1.07080	+	0.153958i	0.415702	+	0.909501i	$0.363536\pi$
$270$	3.14049	−	7.40430i	0.191124	−	0.450612i
$271$	2.36123	−	1.51747i	0.143435	−	0.0921798i	−0.466955	−	0.884281i	$-0.654649\pi$
$271$	2.36123	−	1.51747i	0.143435	−	0.0921798i	0.610390	+	0.792101i	$0.291013\pi$
$272$	5.98798	+	0.428269i	0.363074	+	0.0259676i
$273$	−4.50125	−	8.24342i	−0.272428	−	0.498915i
$274$	1.33287	−	2.91858i	0.0805217	−	0.176318i
$275$	4.46390	+	6.17792i	0.269183	+	0.372542i
$276$	−2.01719	−	2.33869i	−0.121421	−	0.140772i
$277$	−12.4874	−	12.4874i	−0.750293	−	0.750293i	0.224241	−	0.974534i	$-0.428010\pi$
$277$	−12.4874	−	12.4874i	−0.750293	−	0.750293i	−0.974534	+	0.224241i	$0.928010\pi$
$278$	1.93011	+	5.17483i	0.115760	+	0.310366i
$279$	−0.291522	+	0.992834i	−0.0174530	+	0.0594394i
$280$	5.81455	+	3.51667i	0.347486	+	0.210161i
$281$	8.74104	+	13.6013i	0.521447	+	0.811387i	0.997690	−	0.0679263i	$-0.0216383\pi$
$281$	8.74104	+	13.6013i	0.521447	+	0.811387i	−0.476244	+	0.879313i	$0.658002\pi$
$282$	−7.58555	+	0.542529i	−0.451713	+	0.0323071i
$283$	−13.4685	+	10.0824i	−0.800619	+	0.599336i	−0.919282	−	0.393599i	$-0.871230\pi$
$283$	−13.4685	+	10.0824i	−0.800619	+	0.599336i	0.118664	+	0.992935i	$0.462139\pi$
$284$	0.587296	+	2.00015i	0.0348496	+	0.118687i
$285$	−0.755077	−	1.29746i	−0.0447269	−	0.0768551i
$286$	−7.24138	+	1.04115i	−0.428192	+	0.0615647i
$287$	28.1221	+	10.4890i	1.66000	+	0.619146i
$288$	−2.42228	−	0.903464i	−0.142734	−	0.0532371i
$289$	−18.8455	+	2.70957i	−1.10856	+	0.159387i
$290$	−1.32992	−	2.28522i	−0.0780955	−	0.134193i
$291$	−2.59443	−	8.83583i	−0.152088	−	0.517966i
$292$	0.209149	−	0.156567i	0.0122395	−	0.00916239i
$293$	−9.52076	+	0.680938i	−0.556209	+	0.0397808i	−0.346615	−	0.938008i	$-0.612669\pi$
$293$	−9.52076	+	0.680938i	−0.556209	+	0.0397808i	−0.209594	+	0.977788i	$0.567214\pi$
$294$	0.778216	+	1.21093i	0.0453865	+	0.0706227i
$295$	14.6758	+	8.87601i	0.854459	+	0.516781i
$296$	0.369760	−	1.25929i	0.0214918	−	0.0731945i
$297$	−1.91609	−	5.13724i	−0.111183	−	0.298093i
$298$	−4.58328	−	4.58328i	−0.265502	−	0.265502i
$299$	−20.9581	+	9.51370i	−1.21204	+	0.550191i
$300$	−3.17896	−	0.512017i	−0.183537	−	0.0295613i
$301$	−9.42610	+	20.6403i	−0.543311	+	1.18969i
$302$	−1.47427	−	2.69992i	−0.0848347	−	0.155363i
$303$	−12.5145	−	0.895058i	−0.718942	−	0.0514197i
$304$	−0.877000	+	0.563614i	−0.0502994	+	0.0323255i
$305$	2.97910	−	7.02380i	0.170583	−	0.402182i
$306$	15.3622	+	2.20875i	0.878197	+	0.126266i
$307$	3.37802	+	1.84454i	0.192794	+	0.105273i	0.572746	−	0.819733i	$-0.305878\pi$
$307$	3.37802	+	1.84454i	0.192794	+	0.105273i	−0.379953	+	0.925006i	$0.624060\pi$
$308$	4.52663	−	0.984708i	0.257929	−	0.0561089i
$309$	1.19421	+	8.30590i	0.0679361	+	0.472506i
$310$	0.894105	+	0.0394973i	0.0507818	+	0.00224330i
$311$	5.64569	+	12.3623i	0.320137	+	0.701003i	0.999461	−	0.0328358i	$-0.0104539\pi$
$311$	5.64569	+	12.3623i	0.320137	+	0.701003i	−0.679323	+	0.733839i	$0.737727\pi$
$312$	1.85215	−	2.47419i	0.104858	−	0.140073i
$313$	0.401158	+	1.84410i	0.0226748	+	0.104234i	0.987093	−	0.160146i	$-0.0511963\pi$
$313$	0.401158	+	1.84410i	0.0226748	+	0.104234i	−0.964419	+	0.264380i	$0.914833\pi$
$314$	6.27643	−	1.84293i	0.354200	−	0.104002i
$315$	14.3454	+	10.1408i	0.808270	+	0.571370i
$316$	0.574610	+	0.497903i	0.0323244	+	0.0280092i
$317$	31.3998	+	6.83061i	1.76359	+	0.383645i	0.973381	−	0.229194i	$-0.0736089\pi$
$317$	31.3998	+	6.83061i	1.76359	+	0.383645i	0.790208	+	0.612839i	$0.209973\pi$
$318$	0.455879	−	6.37402i	0.0255644	−	0.357437i
$319$	−1.72948	−	0.507822i	−0.0968325	−	0.0284326i
$320$	−0.257795	+	2.22116i	−0.0144112	+	0.124166i
$321$		−	4.95580i		−	0.276606i
$322$	12.8074	−	6.95560i	0.713728	−	0.387620i
$323$	4.42533	−	4.42533i	0.246232	−	0.246232i
$324$	−4.94797	−	2.25966i	−0.274887	−	0.125537i
$325$	−10.3357	+	21.6562i	−0.573321	+	1.20127i
$326$	4.58485	+	5.29120i	0.253932	+	0.293053i
$327$	−0.756652	+	3.47827i	−0.0418429	+	0.192349i
$328$	0.704591	+	9.85146i	0.0389045	+	0.543956i
$329$	5.10731	−	35.5221i	0.281575	−	1.95840i
$330$	−1.81361	+	1.23664i	−0.0998358	+	0.0680747i
$331$	−8.46987	−	5.44325i	−0.465546	−	0.299188i	0.286760	−	0.958003i	$-0.407422\pi$
$331$	−8.46987	−	5.44325i	−0.465546	−	0.299188i	−0.752306	+	0.658814i	$0.771058\pi$
$332$	4.59886	+	3.44266i	0.252395	+	0.188941i
$333$	1.18575	−	3.17912i	0.0649787	−	0.174215i
$334$	−21.8751	+	9.99003i	−1.19695	+	0.546630i
$335$	−8.74730	+	25.5589i	−0.477916	+	1.39643i
$336$	−1.05805	+	1.64637i	−0.0577216	+	0.0898166i
$337$	−9.99784	+	18.3097i	−0.544617	+	0.997392i	0.449926	+	0.893066i	$0.351450\pi$
$337$	−9.99784	+	18.3097i	−0.544617	+	0.997392i	−0.994543	+	0.104326i	$0.966732\pi$
$338$	−6.01238	−	8.03160i	−0.327030	−	0.436861i
$339$	7.46965	−	8.62044i	0.405696	−	0.468198i
$340$	−1.32215	−	13.3585i	−0.0717034	−	0.724464i
$341$	0.461102	−	0.399547i	0.0249701	−	0.0216367i
$342$	−2.36546	+	1.29164i	−0.127910	+	0.0698439i
$343$	13.5670	−	5.06024i	0.732551	−	0.273227i
$344$	−7.46667			−0.402576
$345$	−4.39069	+	5.33052i	−0.236387	+	0.286985i
$346$	−9.95952			−0.535427
$347$	10.0188	−	3.73684i	0.537840	−	0.200604i	−0.0658407	−	0.997830i	$-0.520973\pi$
$347$	10.0188	−	3.73684i	0.537840	−	0.200604i	0.603681	+	0.797226i	$0.293700\pi$
$348$	0.668336	−	0.364939i	0.0358265	−	0.0195628i
$349$	4.70583	−	4.07762i	0.251897	−	0.218270i	−0.519754	−	0.854316i	$-0.673976\pi$
$349$	4.70583	−	4.07762i	0.251897	−	0.218270i	0.771651	+	0.636046i	$0.219431\pi$
$350$	5.54975	−	14.1450i	0.296647	−	0.756080i
$351$	11.3043	−	13.0458i	0.603378	−	0.696335i
$352$	0.913524	+	1.22033i	0.0486910	+	0.0650436i
$353$	11.0724	−	20.2775i	0.589322	−	1.07926i	−0.397523	−	0.917592i	$-0.630130\pi$
$353$	11.0724	−	20.2775i	0.589322	−	1.07926i	0.986845	−	0.161670i	$-0.0516880\pi$
$354$	−2.67051	+	4.15539i	−0.141936	+	0.220857i
$355$	4.18571	−	2.05119i	0.222154	−	0.108866i
$356$	2.95459	−	1.34931i	0.156593	−	0.0715135i
$357$	4.10573	−	11.0079i	0.217298	−	0.582599i
$358$	−5.32051	−	3.98289i	−0.281198	−	0.210502i
$359$	−12.8585	−	8.26364i	−0.678644	−	0.436138i	0.155388	−	0.987853i	$-0.450337\pi$
$359$	−12.8585	−	8.26364i	−0.678644	−	0.436138i	−0.834032	+	0.551715i	$0.813973\pi$
$360$	−1.07443	+	5.68014i	−0.0566273	+	0.299370i
$361$	2.54932	−	17.7309i	0.134175	−	0.933204i
$362$	0.681514	+	9.52882i	0.0358196	+	0.500823i
$363$	1.18769	−	5.45971i	0.0623374	−	0.286561i
$364$	9.55090	+	11.0223i	0.500603	+	0.577727i
$365$	−0.424191	−	0.401678i	−0.0222032	−	0.0210248i
$366$	1.99872	+	0.912784i	0.104475	+	0.0477120i
$367$	−5.72849	+	5.72849i	−0.299025	+	0.299025i	−0.840632	−	0.541607i	$-0.817816\pi$
$367$	−5.72849	+	5.72849i	−0.299025	+	0.299025i	0.541607	+	0.840632i	$0.317816\pi$
$368$	3.83271	+	2.88276i	0.199794	+	0.150274i
$369$			25.5339i			1.32924i
$370$	−2.91516	−	0.338343i	−0.151552	−	0.0175896i
$371$	28.9341	+	8.49581i	1.50218	+	0.441081i
$372$	−0.0183879	+	0.257096i	−0.000953367	+	0.0133298i
$373$	−23.0945	−	5.02389i	−1.19579	−	0.260127i	−0.429764	−	0.902941i	$-0.641403\pi$
$373$	−23.0945	−	5.02389i	−1.19579	−	0.260127i	−0.766022	+	0.642814i	$0.777767\pi$
$374$	−6.91605	−	5.99279i	−0.357620	−	0.309880i
$375$	0.0745908	+	7.19959i	0.00385185	+	0.371785i
$376$	11.3308	−	3.32702i	0.584341	−	0.171578i
$377$	−1.20628	−	5.54517i	−0.0621265	−	0.285591i
$378$	−6.55047	+	8.75041i	−0.336920	+	0.450072i
$379$	−8.35689	−	18.2990i	−0.429264	−	0.939958i	−0.993445	−	0.114307i	$-0.963535\pi$
$379$	−8.35689	−	18.2990i	−0.429264	−	0.939958i	0.564181	−	0.825651i	$-0.309192\pi$
$380$	1.57397	+	1.71946i	0.0807432	+	0.0882066i
$381$	0.967129	+	6.72653i	0.0495475	+	0.344610i
$382$	16.5020	−	3.58980i	0.844318	−	0.183670i
$383$	26.2316	+	14.3236i	1.34037	+	0.731899i	0.979639	−	0.200769i	$-0.0643440\pi$
$383$	26.2316	+	14.3236i	1.34037	+	0.731899i	0.360735	+	0.932668i	$0.382526\pi$
$384$	−0.637431	−	0.0916487i	−0.0325288	−	0.00467693i
$385$	−3.88308	−	9.60322i	−0.197900	−	0.489425i
$386$	−5.76513	+	3.70502i	−0.293437	+	0.188581i
$387$	−19.2543	−	1.37709i	−0.978749	−	0.0700015i
$388$	6.85315	+	12.5506i	0.347916	+	0.637161i
$389$	3.71981	−	8.14525i	0.188602	−	0.412981i	−0.791584	−	0.611060i	$-0.790743\pi$
$389$	3.71981	−	8.14525i	0.188602	−	0.412981i	0.980186	+	0.198080i	$0.0634705\pi$
$390$	−6.15354	−	3.14552i	−0.311597	−	0.159280i
$391$	−26.1617	−	12.0196i	−1.32305	−	0.607858i
$392$	−1.58052	−	1.58052i	−0.0798283	−	0.0798283i
$393$	4.77758	+	12.8092i	0.240997	+	0.646138i
$394$	−5.38465	+	18.3384i	−0.271275	+	0.923876i
$395$	0.879841	−	1.45475i	0.0442696	−	0.0731965i
$396$	2.13063	+	3.31533i	0.107068	+	0.166602i
$397$	4.44299	−	0.317769i	0.222987	−	0.0159484i	0.0406016	−	0.999175i	$-0.487073\pi$
$397$	4.44299	−	0.317769i	0.222987	−	0.0159484i	0.182386	+	0.983227i	$0.441618\pi$
$398$	−21.8269	+	16.3394i	−1.09408	+	0.819019i
$399$	0.574790	+	1.95755i	0.0287755	+	0.0980003i
$400$	4.99257	−	0.272398i	0.249629	−	0.0136199i
$401$	−11.4987	+	1.65326i	−0.574216	+	0.0825599i	−0.423305	−	0.905987i	$-0.639130\pi$
$401$	−11.4987	+	1.65326i	−0.574216	+	0.0825599i	−0.150912	+	0.988547i	$0.548221\pi$
$402$	−7.28956	−	2.71887i	−0.363570	−	0.135605i
$403$	1.79977	+	0.671278i	0.0896527	+	0.0334387i
$404$	19.2843	−	2.77266i	0.959429	−	0.137945i
$405$	−3.10747	+	11.7595i	−0.154411	+	0.584335i
$406$	1.01238	+	3.44784i	0.0502435	+	0.171114i
$407$	−1.60162	+	1.19895i	−0.0793891	+	0.0594300i
$408$	3.85617	−	0.275799i	0.190909	−	0.0136541i
$409$	13.8718	+	21.5849i	0.685914	+	1.06730i	0.993283	+	0.115713i	$0.0369152\pi$
$409$	13.8718	+	21.5849i	0.685914	+	1.06730i	−0.307369	+	0.951591i	$0.599448\pi$
$410$	21.4442	−	5.28078i	1.05905	−	0.260799i
$411$	0.582129	−	1.98255i	0.0287143	−	0.0977919i
$412$	−4.55361	−	12.2087i	−0.224340	−	0.601480i
$413$	−16.4823	−	16.4823i	−0.811039	−	0.811039i
$414$	9.35173	+	8.14063i	0.459612	+	0.400090i
$415$	5.84669	−	11.4378i	0.287003	−	0.561460i
$416$	−1.99368	+	4.36554i	−0.0977480	+	0.214038i
$417$	1.70458	+	3.12170i	0.0834736	+	0.152871i
$418$	1.58510	+	0.113369i	0.0775298	+	0.00554504i
$419$	−27.1520	+	17.4495i	−1.32646	+	0.852464i	−0.995824	−	0.0912943i	$-0.970900\pi$
$419$	−27.1520	+	17.4495i	−1.32646	+	0.852464i	−0.330636	+	0.943758i	$0.607263\pi$
$420$	4.02867	+	1.70874i	0.196579	+	0.0833779i
$421$	−11.8754	−	1.70742i	−0.578770	−	0.0832146i	−0.153288	−	0.988182i	$-0.548986\pi$
$421$	−11.8754	−	1.70742i	−0.578770	−	0.0832146i	−0.425482	+	0.904967i	$0.639895\pi$
$422$	9.55180	+	5.21568i	0.464974	+	0.253895i
$423$	29.8323	−	6.48962i	1.45050	−	0.315536i
$424$	1.41220	+	9.82204i	0.0685823	+	0.477001i
$425$	−28.9392	+	7.96887i	−1.40376	+	0.386547i
$426$	0.557672	+	1.22113i	0.0270193	+	0.0591640i
$427$	−6.21385	+	8.30073i	−0.300709	+	0.401700i
$428$	1.63580	+	7.51964i	0.0790692	+	0.363475i
$429$	−4.52046	+	1.32733i	−0.218250	+	0.0640840i
$430$	2.82554	+	16.4552i	0.136259	+	0.793538i
$431$	12.5264	+	10.8542i	0.603375	+	0.522827i	0.902109	−	0.431509i	$-0.142019\pi$
$431$	12.5264	+	10.8542i	0.603375	+	0.522827i	−0.298734	+	0.954337i	$0.596564\pi$
$432$	−3.51464	−	0.764564i	−0.169098	−	0.0367851i
$433$	−0.233422	+	3.26367i	−0.0112176	+	0.156842i	0.988756	+	0.149539i	$0.0477791\pi$
$433$	−0.233422	+	3.26367i	−0.0112176	+	0.156842i	−0.999973	+	0.00730269i	$0.997675\pi$
$434$	−1.16706	−	0.342679i	−0.0560205	−	0.0164491i
$435$	−1.05717	−	1.33479i	−0.0506874	−	0.0639982i
$436$		−	5.52748i		−	0.264718i
$437$	4.88776	−	1.05163i	0.233813	−	0.0503064i
$438$	0.118969	−	0.118969i	0.00568456	−	0.00568456i
$439$	−24.8489	−	11.3481i	−1.18597	−	0.541615i	−0.277973	−	0.960589i	$-0.589663\pi$
$439$	−24.8489	−	11.3481i	−1.18597	−	0.541615i	−0.907998	+	0.418974i	$0.862390\pi$
$440$	2.34368	−	2.47503i	0.111730	−	0.117993i
$441$	−3.78418	−	4.36718i	−0.180199	−	0.207961i
$442$	6.12425	−	28.1527i	0.291301	−	1.33909i
$443$	−1.86904	−	26.1325i	−0.0888006	−	1.24159i	−0.825119	−	0.564959i	$-0.808892\pi$
$443$	−1.86904	−	26.1325i	−0.0888006	−	1.24159i	0.736318	−	0.676635i	$-0.236563\pi$
$444$	0.120284	−	0.836596i	0.00570844	−	0.0397031i
$445$	−4.09171	−	6.00075i	−0.193966	−	0.284463i
$446$	21.0326	+	13.5168i	0.995923	+	0.640041i
$447$	−3.34157	−	2.50147i	−0.158051	−	0.118316i
$448$	1.06200	−	2.84734i	0.0501749	−	0.134524i
$449$	4.57010	−	2.08709i	0.215676	−	0.0984960i	−0.304647	−	0.952465i	$-0.598539\pi$
$449$	4.57010	−	2.08709i	0.215676	−	0.0984960i	0.520324	+	0.853969i	$0.325811\pi$
$450$	12.9246	+	0.218359i	0.609270	+	0.0102935i
$451$	8.13972	−	12.6657i	0.383285	−	0.596402i
$452$	−8.48860	+	15.5457i	−0.399270	+	0.731209i
$453$	−1.18719	−	1.58590i	−0.0557791	−	0.0745121i
$454$	4.45319	−	5.13925i	0.208998	−	0.241197i
$455$	20.6769	−	25.2195i	0.969349	−	1.18231i
$456$	−0.507372	+	0.439641i	−0.0237599	+	0.0205881i
$457$	−33.3638	+	18.2180i	−1.56069	+	0.852202i	−0.560988	+	0.827824i	$0.689579\pi$
$457$	−33.3638	+	18.2180i	−1.56069	+	0.852202i	−0.999703	+	0.0243781i	$0.992239\pi$
$458$	−16.7771	+	6.25753i	−0.783942	+	0.292395i
$459$	21.5928			1.00787
$460$	4.90269	−	9.53749i	0.228589	−	0.444688i
$461$	−35.7801			−1.66644			−0.833222	−	0.552938i	$-0.813506\pi$
$461$	−35.7801			−1.66644			−0.833222	+	0.552938i	$0.813506\pi$
$462$	2.79517	−	1.04254i	0.130043	−	0.0485035i
$463$	−5.12210	+	2.79688i	−0.238044	+	0.129982i	−0.593844	−	0.804580i	$-0.702390\pi$
$463$	−5.12210	+	2.79688i	−0.238044	+	0.129982i	0.355800	+	0.934562i	$0.384209\pi$
$464$	−0.893636	+	0.774340i	−0.0414860	+	0.0359478i
$465$	0.573550	−	0.0567668i	0.0265978	−	0.00263250i
$466$	5.92295	−	6.83545i	0.274376	−	0.316646i
$467$	−10.6426	−	14.2169i	−0.492482	−	0.657878i	0.483598	−	0.875290i	$-0.339330\pi$
$467$	−10.6426	−	14.2169i	−0.492482	−	0.657878i	−0.976080	+	0.217412i	$0.930239\pi$
$468$	−5.94623	+	10.8897i	−0.274865	+	0.503377i
$469$	19.8491	−	30.8858i	0.916546	−	1.42617i
$470$	−11.6199	−	23.7120i	−0.535988	−	1.09375i
$471$	3.83189	−	1.74997i	0.176564	−	0.0806342i
$472$	2.68047	−	7.18663i	0.123379	−	0.330791i
$473$	9.11177	+	6.82098i	0.418960	+	0.313629i
$474$	0.411907	+	0.264716i	0.0189195	+	0.0121588i
$475$	3.19375	−	4.11943i	0.146539	−	0.189012i
$476$	−2.59634	+	18.0579i	−0.119003	+	0.827684i
$477$	1.83013	+	25.5885i	0.0837957	+	1.17162i
$478$	−2.03416	+	9.35088i	−0.0930403	+	0.427699i
$479$	−1.63529	−	1.88723i	−0.0747185	−	0.0862297i	0.717160	−	0.696909i	$-0.245442\pi$
$479$	−1.63529	−	1.88723i	−0.0747185	−	0.0862297i	−0.791878	+	0.610679i	$0.790896\pi$
$480$	0.0392398	+	1.43946i	0.00179104	+	0.0657021i
$481$	−5.72955	−	2.61660i	−0.261245	−	0.119307i
$482$	−16.1561	+	16.1561i	−0.735891	+	0.735891i
$483$	7.52635	−	5.60749i	0.342461	−	0.255150i
$484$			8.67628i			0.394376i
$485$	25.0659	−	19.8525i	1.13818	−	0.901455i
$486$	−13.7145	−	4.02695i	−0.622103	−	0.182666i
$487$	−0.613154	+	8.57302i	−0.0277847	+	0.388480i	0.964464	+	0.264214i	$0.0851124\pi$
$487$	−0.613154	+	8.57302i	−0.0277847	+	0.388480i	−0.992249	+	0.124267i	$0.960342\pi$
$488$	−3.33403	−	0.725273i	−0.150924	−	0.0328316i
$489$	3.40746	+	2.95258i	0.154091	+	0.133520i
$490$	−2.88507	+	4.08127i	−0.130334	+	0.184373i
$491$	−23.1819	+	6.80682i	−1.04619	+	0.307188i	−0.759275	−	0.650770i	$-0.774446\pi$
$491$	−23.1819	+	6.80682i	−1.04619	+	0.307188i	−0.286910	+	0.957958i	$0.592628\pi$
$492$	1.35200	+	6.21505i	0.0609530	+	0.280196i
$493$	4.25401	−	5.68269i	0.191591	−	0.255936i
$494$	2.07839	+	4.55104i	0.0935113	+	0.204761i
$495$	6.50010	−	5.95011i	0.292158	−	0.267438i
$496$	−0.0569610	−	0.396172i	−0.00255762	−	0.0177887i
$497$	−6.19018	+	1.34659i	−0.277667	+	0.0604029i
$498$	3.24697	+	1.77298i	0.145500	+	0.0794491i
$499$	20.5566	+	2.95559i	0.920238	+	0.132310i	0.586123	−	0.810222i	$-0.300653\pi$
$499$	20.5566	+	2.95559i	0.920238	+	0.132310i	0.334115	+	0.942532i	$0.391563\pi$
$500$	−2.48960	−	10.8996i	−0.111338	−	0.487446i
$501$	−13.0283	+	8.37278i	−0.582062	+	0.374068i
$502$	−11.0598	−	0.791010i	−0.493622	−	0.0353045i
$503$	13.6885	+	25.0687i	0.610341	+	1.11776i	0.981909	+	0.189351i	$0.0606384\pi$
$503$	13.6885	+	25.0687i	0.610341	+	1.11776i	−0.371568	+	0.928406i	$0.621180\pi$
$504$	3.26372	−	7.14655i	0.145378	−	0.318333i
$505$	−13.4080	−	41.4497i	−0.596648	−	1.84449i
$506$	−2.04369	−	7.01918i	−0.0908531	−	0.312041i
$507$	−4.56856	−	4.56856i	−0.202897	−	0.202897i
$508$	−3.68774	−	9.88722i	−0.163617	−	0.438674i
$509$	10.7070	−	36.4647i	0.474580	−	1.61627i	−0.279958	−	0.960012i	$-0.590320\pi$
$509$	10.7070	−	36.4647i	0.474580	−	1.61627i	0.754537	−	0.656257i	$-0.227861\pi$
$510$	−2.06706	−	8.39392i	−0.0915311	−	0.371689i
$511$	0.429244	+	0.667916i	0.0189886	+	0.0295469i
$512$	0.997452	−	0.0713392i	0.0440816	−	0.00315278i
$513$	−3.00177	+	2.24710i	−0.132532	+	0.0992118i
$514$	1.43377	+	4.88298i	0.0632409	+	0.215379i
$515$	−25.1825	+	14.6553i	−1.10968	+	0.645791i
$516$	−4.75949	+	0.684311i	−0.209525	+	0.0301251i
$517$	−16.8666	−	6.29091i	−0.741791	−	0.276674i
$518$	3.73699	+	1.39382i	0.164194	+	0.0612411i
$519$	−6.34851	+	0.912778i	−0.278669	+	0.0400665i
$520$	10.3753	+	2.74169i	0.454987	+	0.120231i
$521$	−6.04557	−	20.5893i	−0.264861	−	0.902035i	−0.979313	−	0.202350i	$-0.935142\pi$
$521$	−6.04557	−	20.5893i	−0.264861	−	0.902035i	0.714452	−	0.699685i	$-0.246676\pi$
$522$	−2.44723	+	1.83197i	−0.107112	+	0.0801832i
$523$	5.31316	−	0.380005i	0.232328	−	0.0166164i	0.0453104	−	0.998973i	$-0.485572\pi$
$523$	5.31316	−	0.380005i	0.232328	−	0.0166164i	0.187018	+	0.982357i	$0.440118\pi$
$524$	−11.4773	−	17.8590i	−0.501386	−	0.780172i
$525$	2.24121	−	9.52507i	0.0978146	−	0.415708i
$526$	3.87634	−	13.2016i	0.169016	−	0.575617i
$527$	0.839688	+	2.25129i	0.0365774	+	0.0980677i
$528$	0.694150	+	0.694150i	0.0302090	+	0.0302090i
$529$	−12.3466	−	19.4052i	−0.536809	−	0.843704i
$530$	21.1116	−	6.82908i	0.917028	−	0.296636i
$531$	8.23757	−	18.0378i	0.357480	−	0.782772i
$532$	−1.51830	−	2.78055i	−0.0658265	−	0.120552i
$533$	47.2795	+	3.38150i	2.04790	+	0.146469i
$534$	1.75968	−	1.13088i	0.0761489	−	0.0489379i
$535$	15.9529	−	6.45057i	0.689703	−	0.278883i
$536$	11.9582	+	1.71933i	0.516515	+	0.0742637i
$537$	−3.75649	−	2.05120i	−0.162104	−	0.0885157i
$538$	−17.3376	+	3.77155i	−0.747475	+	0.162603i
$539$	0.484906	+	3.37259i	0.0208864	+	0.145268i
$540$	−0.354946	+	8.03495i	−0.0152744	+	0.345769i
$541$	−14.9034	−	32.6339i	−0.640748	−	1.40304i	−0.899424	−	0.437078i	$-0.856013\pi$
$541$	−14.9034	−	32.6339i	−0.640748	−	1.40304i	0.258676	−	0.965964i	$-0.416714\pi$
$542$	−1.68205	+	2.24696i	−0.0722504	+	0.0965152i
$543$	1.30772	+	6.01150i	0.0561197	+	0.257978i
$544$	−5.76010	+	1.69132i	−0.246962	+	0.0725146i
$545$	−12.1815	+	2.09171i	−0.521800	+	0.0895990i
$546$	7.09823	+	6.15065i	0.303776	+	0.263223i
$547$	29.3994	+	6.39545i	1.25703	+	0.273450i	0.791272	−	0.611464i	$-0.209419\pi$
$547$	29.3994	+	6.39545i	1.25703	+	0.273450i	0.465755	+	0.884914i	$0.345783\pi$
$548$	−0.228894	+	3.20035i	−0.00977786	+	0.136712i
$549$	−8.46368	−	2.48516i	−0.361221	−	0.106064i
$550$	−6.34141	−	4.22842i	−0.270399	−	0.180301i
$551$			1.23269i			0.0525145i
$552$	2.70729	+	1.48630i	0.115230	+	0.0632610i
$553$	−1.63382	+	1.63382i	−0.0694770	+	0.0694770i
$554$	16.0639	+	7.33614i	0.682490	+	0.311683i
$555$	−1.88922	+	0.0515002i	−0.0801929	+	0.00218606i
$556$	−3.61683	−	4.17405i	−0.153388	−	0.177019i
$557$	3.06539	−	14.0914i	0.129885	−	0.597070i	−0.865484	−	0.500937i	$-0.832989\pi$
$557$	3.06539	−	14.0914i	0.129885	−	0.597070i	0.995368	−	0.0961331i	$-0.0306475\pi$
$558$	−0.0738181	−	1.03211i	−0.00312497	−	0.0436928i
$559$	−5.09976	+	35.4696i	−0.215697	+	1.50020i
$560$	−6.67689	−	1.26297i	−0.282150	−	0.0533701i
$561$	−4.95774	−	3.18614i	−0.209316	−	0.134519i
$562$	−12.9431	−	9.68908i	−0.545971	−	0.408709i
$563$	−1.80810	+	4.84770i	−0.0762023	+	0.204306i	−0.969465	−	0.245228i	$-0.921137\pi$
$563$	−1.80810	+	4.84770i	−0.0762023	+	0.204306i	0.893263	+	0.449534i	$0.148410\pi$
$564$	6.91768	−	3.15920i	0.291287	−	0.133026i
$565$	37.4721	+	12.8245i	1.57646	+	0.539531i
$566$	9.09587	−	14.1534i	0.382328	−	0.594914i
$567$	7.92220	−	14.5084i	0.332701	−	0.609296i
$568$	−1.24925	−	1.66880i	−0.0524173	−	0.0700212i
$569$	−13.4623	+	15.5364i	−0.564370	+	0.651318i	−0.964170	−	0.265285i	$-0.914534\pi$
$569$	−13.4623	+	15.5364i	−0.564370	+	0.651318i	0.399800	+	0.916602i	$0.369080\pi$
$570$	1.16089	+	0.951786i	0.0486242	+	0.0398659i
$571$	−21.4332	+	18.5719i	−0.896950	+	0.777212i	−0.975569	−	0.219693i	$-0.929494\pi$
$571$	−21.4332	+	18.5719i	−0.896950	+	0.777212i	0.0786191	+	0.996905i	$0.474949\pi$
$572$	6.42097	−	3.50611i	0.268474	−	0.146598i
$573$	10.1899	−	3.80064i	0.425690	−	0.158774i
$574$	−30.0145			−1.25278
$575$	−22.8741	−	7.19544i	−0.953917	−	0.300071i
$576$	2.58528			0.107720
$577$	−18.6624	+	6.96070i	−0.776924	+	0.289778i	−0.706475	−	0.707738i	$-0.749716\pi$
$577$	−18.6624	+	6.96070i	−0.776924	+	0.289778i	−0.0704488	+	0.997515i	$0.522443\pi$
$578$	16.7104	−	9.12456i	0.695060	−	0.379532i
$579$	−3.33531	+	2.89006i	−0.138611	+	0.120107i
$580$	2.04467	+	1.67638i	0.0849003	+	0.0696080i
$581$	−11.4324	+	13.1937i	−0.474297	+	0.547368i
$582$	5.51866	+	7.37207i	0.228756	+	0.305582i
$583$	7.24934	−	13.2762i	0.300237	−	0.549843i
$584$	−0.141248	+	0.219786i	−0.00584487	+	0.00909479i
$585$	26.2491	+	8.98351i	1.08527	+	0.371422i
$586$	8.68251	−	3.96517i	0.358671	−	0.163800i
$587$	7.82857	−	20.9892i	0.323120	−	0.866317i	−0.669252	−	0.743035i	$-0.733385\pi$
$587$	7.82857	−	20.9892i	0.323120	−	0.866317i	0.992372	−	0.123282i	$-0.0393419\pi$
$588$	−1.15232	−	0.862620i	−0.0475211	−	0.0355738i
$589$	−0.351016	−	0.225584i	−0.0144634	−	0.00929503i
$590$	−16.8523	−	3.18770i	−0.693800	−	0.131236i
$591$	−1.75165	+	12.1830i	−0.0720532	+	0.501141i
$592$	0.0936290	+	1.30911i	0.00384813	+	0.0538039i
$593$	−7.68184	+	35.3128i	−0.315455	+	1.45012i	0.497330	+	0.867561i	$0.334314\pi$
$593$	−7.68184	+	35.3128i	−0.315455	+	1.45012i	−0.812785	+	0.582563i	$0.802050\pi$
$594$	3.59056	+	4.14373i	0.147323	+	0.170019i
$595$	40.7788	−	1.11163i	1.67177	−	0.0455725i
$596$	5.89599	+	2.69261i	0.241509	+	0.110294i
$597$	−12.4156	+	12.4156i	−0.508138	+	0.508138i
$598$	16.3120	−	16.2380i	0.667047	−	0.664020i
$599$			32.2679i			1.31843i	0.751954	+	0.659215i	$0.229111\pi$
$599$			32.2679i			1.31843i	−0.751954	+	0.659215i	$0.770889\pi$
$600$	3.15746	−	0.631198i	0.128903	−	0.0257686i
$601$	11.9329	+	3.50381i	0.486753	+	0.142924i	0.515895	−	0.856652i	$-0.327459\pi$
$601$	11.9329	+	3.50381i	0.486753	+	0.142924i	−0.0291423	+	0.999575i	$0.509278\pi$
$602$	1.61874	−	22.6330i	0.0659751	−	0.922452i
$603$	30.5194	+	6.63910i	1.24285	+	0.270365i
$604$	2.32484	+	2.01449i	0.0945966	+	0.0819684i
$605$	19.1209	−	3.28328i	0.777375	−	0.133484i
$606$	12.0383	−	3.53476i	0.489022	−	0.143590i
$607$	1.51600	+	6.96893i	0.0615325	+	0.282860i	0.997624	−	0.0688969i	$-0.0219480\pi$
$607$	1.51600	+	6.96893i	0.0615325	+	0.282860i	−0.936091	+	0.351757i	$0.885584\pi$
$608$	0.624742	−	0.834558i	0.0253366	−	0.0338458i
$609$	0.961311	+	2.10498i	0.0389543	+	0.0852980i
$610$	−0.336705	+	7.62204i	−0.0136328	+	0.308607i
$611$	−8.06569	−	56.0981i	−0.326303	−	2.26949i
$612$	−15.1655	+	3.29905i	−0.613028	+	0.133356i
$613$	−11.5562	−	6.31019i	−0.466752	−	0.254866i	0.228620	−	0.973516i	$-0.426579\pi$
$613$	−11.5562	−	6.31019i	−0.466752	−	0.254866i	−0.695372	+	0.718650i	$0.744761\pi$
$614$	−3.80963	−	0.547743i	−0.153744	−	0.0221051i
$615$	13.1852	−	5.33146i	0.531679	−	0.214985i
$616$	−3.89710	+	2.50452i	−0.157019	+	0.100910i
$617$	−10.2915	−	0.736065i	−0.414322	−	0.0296329i	−0.137377	−	0.990519i	$-0.543867\pi$
$617$	−10.2915	−	0.736065i	−0.414322	−	0.0296329i	−0.276944	+	0.960886i	$0.589322\pi$
$618$	−4.02153	−	7.36488i	−0.161770	−	0.296259i
$619$	−3.41915	+	7.48689i	−0.137427	+	0.300923i	−0.965815	−	0.259231i	$-0.916531\pi$
$619$	−3.41915	+	7.48689i	−0.137427	+	0.300923i	0.828388	+	0.560154i	$0.189258\pi$
$620$	−0.851535	+	0.275451i	−0.0341985	+	0.0110624i
$621$	14.4903	+	9.35895i	0.581474	+	0.375562i
$622$	−9.60991	−	9.60991i	−0.385322	−	0.385322i
$623$	3.44950	+	9.24847i	0.138201	+	0.370532i
$624$	−0.870735	+	2.96545i	−0.0348573	+	0.118713i
$625$	−23.0786	+	9.61126i	−0.923146	+	0.384451i
$626$	−1.02031	−	1.58763i	−0.0407798	−	0.0634546i
$627$	1.02078	−	0.0730078i	0.0407661	−	0.00291565i
$628$	−5.23667	+	3.92012i	−0.208966	+	0.156430i
$629$	−2.21977	−	7.55984i	−0.0885079	−	0.301430i
$630$	−16.9847	−	4.48824i	−0.676688	−	0.178816i
$631$	17.6540	−	2.53826i	0.702793	−	0.101046i	0.218352	−	0.975870i	$-0.429932\pi$
$631$	17.6540	−	2.53826i	0.702793	−	0.101046i	0.484441	+	0.874824i	$0.339023\pi$
$632$	−0.712380	−	0.265704i	−0.0283370	−	0.0105691i
$633$	6.56662	+	2.44922i	0.261000	+	0.0973479i
$634$	−31.8071	+	4.57317i	−1.26322	+	0.181624i
$635$	−20.3941	+	11.8686i	−0.809314	+	0.470992i
$636$	1.80036	+	6.13145i	0.0713888	+	0.243128i
$637$	−8.58759	+	6.42859i	−0.340253	+	0.254710i
$638$	1.79790	−	0.128589i	0.0711797	−	0.00509087i
$639$	−2.91365	−	4.53372i	−0.115262	−	0.179351i
$640$	−0.534674	−	2.17120i	−0.0211348	−	0.0858243i
$641$	−6.59443	+	22.4586i	−0.260464	+	0.887060i	0.720596	+	0.693356i	$0.243869\pi$
$641$	−6.59443	+	22.4586i	−0.260464	+	0.887060i	−0.981060	+	0.193705i	$0.937950\pi$
$642$	1.73187	+	4.64333i	0.0683516	+	0.183258i
$643$	−0.434144	−	0.434144i	−0.0171210	−	0.0171210i	0.698494	−	0.715615i	$-0.253854\pi$
$643$	−0.434144	−	0.434144i	−0.0171210	−	0.0171210i	−0.715615	+	0.698494i	$0.753854\pi$
$644$	−9.56914	+	10.9928i	−0.377077	+	0.433176i
$645$	3.30918	+	10.2301i	0.130299	+	0.402809i
$646$	−2.59982	+	5.69281i	−0.102288	+	0.223980i
$647$	−2.00015	−	3.66301i	−0.0786342	−	0.144008i	0.835403	−	0.549637i	$-0.185234\pi$
$647$	−2.00015	−	3.66301i	−0.0786342	−	0.144008i	−0.914038	+	0.405630i	$0.867052\pi$
$648$	5.42567	+	0.388052i	0.213140	+	0.0152441i
$649$	−9.83621	+	6.32135i	−0.386105	+	0.248135i
$650$	2.11595	−	23.9027i	0.0829943	−	0.937542i
$651$	−0.775324	−	0.111475i	−0.0303873	−	0.00436904i
$652$	−6.14486	−	3.35535i	−0.240651	−	0.131406i
$653$	−11.2747	+	2.45265i	−0.441211	+	0.0959796i	−0.427683	−	0.903929i	$-0.640670\pi$
$653$	−11.2747	+	2.45265i	−0.441211	+	0.0959796i	−0.0135284	+	0.999908i	$0.504306\pi$
$654$	−0.506587	−	3.52339i	−0.0198091	−	0.137775i
$655$	−35.0146	+	32.0519i	−1.36813	+	1.25237i
$656$	−4.10290	−	8.98410i	−0.160191	−	0.350770i
$657$	−0.404770	+	0.540709i	−0.0157916	+	0.0210951i
$658$	7.62841	+	35.0672i	0.297386	+	1.36706i
$659$	−40.2541	+	11.8197i	−1.56808	+	0.460429i	−0.946441	−	0.322878i	$-0.895350\pi$
$659$	−40.2541	+	11.8197i	−1.56808	+	0.460429i	−0.621635	+	0.783307i	$0.713531\pi$
$660$	1.26710	−	1.79246i	0.0493217	−	0.0697714i
$661$	−2.35141	−	2.03751i	−0.0914592	−	0.0792498i	0.607931	−	0.793990i	$-0.292000\pi$
$661$	−2.35141	−	2.03751i	−0.0914592	−	0.0792498i	−0.699390	+	0.714740i	$0.746545\pi$
$662$	9.83806	+	2.14014i	0.382367	+	0.0831789i
$663$	1.32363	−	18.5067i	0.0514054	−	0.718741i
$664$	−5.51198	−	1.61846i	−0.213906	−	0.0628086i
$665$	−5.55327	+	4.39826i	−0.215347	+	0.170557i
$666$			3.39305i			0.131478i
$667$	5.31777	−	1.96966i	0.205905	−	0.0762656i
$668$	17.0047	−	17.0047i	0.657933	−	0.657933i
$669$	14.6456	+	6.68844i	0.566233	+	0.258590i
$670$	−0.736137	−	27.0043i	−0.0284395	−	1.04327i
$671$	3.40605	+	3.93079i	0.131489	+	0.151746i
$672$	0.415998	−	1.91231i	0.0160475	−	0.0737691i
$673$	1.25616	+	17.5634i	0.0484213	+	0.677018i	0.962466	+	0.271404i	$0.0874878\pi$
$673$	1.25616	+	17.5634i	0.0484213	+	0.677018i	−0.914044	+	0.405614i	$0.867058\pi$
$674$	2.96890	−	20.6491i	0.114358	−	0.795375i
$675$	17.8419	−	2.25835i	0.686733	−	0.0869239i
$676$	8.44005	+	5.42409i	0.324617	+	0.208619i
$677$	−3.17017	−	2.37316i	−0.121839	−	0.0912079i	0.536620	−	0.843824i	$-0.319701\pi$
$677$	−3.17017	−	2.37316i	−0.121839	−	0.0912079i	−0.658460	+	0.752616i	$0.728792\pi$
$678$	−3.98615	+	10.6873i	−0.153087	+	0.410443i
$679$	−39.5292	+	18.0524i	−1.51699	+	0.692787i
$680$	5.90709	+	12.0542i	0.226526	+	0.462256i
$681$	2.36759	−	3.68405i	0.0907264	−	0.141173i
$682$	−0.292402	+	0.535494i	−0.0111967	+	0.0205051i
$683$	18.7189	+	25.0055i	0.716258	+	0.956809i	0.999998	−	0.00209242i	$-0.000666039\pi$
$683$	18.7189	+	25.0055i	0.716258	+	0.956809i	−0.283740	+	0.958901i	$0.591575\pi$
$684$	1.76494	−	2.03685i	0.0674841	−	0.0778808i
$685$	7.13960	−	0.706638i	0.272790	−	0.0269993i
$686$	−10.9432	+	9.48238i	−0.417815	+	0.362039i
$687$	−10.1207	+	5.52635i	−0.386131	+	0.210843i
$688$	6.99589	−	2.60933i	0.266716	−	0.0994799i
$689$	47.6231			1.81430
$690$	2.25103	−	6.52882i	0.0856952	−	0.248548i
$691$	26.1551			0.994988			0.497494	−	0.867467i	$-0.334254\pi$
$691$	26.1551			0.994988			0.497494	+	0.867467i	$0.334254\pi$
$692$	9.33157	−	3.48050i	0.354733	−	0.132309i
$693$	−10.5114	+	5.73963i	−0.399293	+	0.218031i
$694$	−8.08127	+	7.00246i	−0.306761	+	0.265810i
$695$	−7.83015	+	9.55038i	−0.297014	+	0.362266i
$696$	−0.498664	+	0.575489i	−0.0189018	+	0.0218138i
$697$	35.5324	+	47.4658i	1.34589	+	1.79789i
$698$	−2.98414	+	5.46505i	−0.112951	+	0.206855i
$699$	3.14901	−	4.89996i	0.119107	−	0.185334i
$700$	−0.256676	+	15.1926i	−0.00970144	+	0.574225i
$701$	28.2179	−	12.8867i	1.06577	−	0.486722i	0.196219	−	0.980560i	$-0.437134\pi$
$701$	28.2179	−	12.8867i	1.06577	−	0.486722i	0.869554	+	0.493838i	$0.164406\pi$
$702$	−6.03249	+	16.1737i	−0.227682	+	0.610438i
$703$	1.09531	+	0.819942i	0.0413106	+	0.0309247i
$704$	−1.28239	−	0.824140i	−0.0483318	−	0.0310609i
$705$	−9.58008	−	14.0498i	−0.360807	−	0.529146i
$706$	−3.28798	+	22.8684i	−0.123745	+	0.860663i
$707$	4.22374	+	59.0557i	0.158850	+	2.22102i
$708$	1.04997	−	4.82664i	0.0394604	−	0.181396i
$709$	4.44607	+	5.13104i	0.166976	+	0.192700i	0.833070	−	0.553167i	$-0.186581\pi$
$709$	4.44607	+	5.13104i	0.166976	+	0.192700i	−0.666095	+	0.745867i	$0.732035\pi$
$710$	−3.20498	+	3.38462i	−0.120281	+	0.127022i
$711$	−1.78801	−	0.816555i	−0.0670555	−	0.0306232i
$712$	−2.29676	+	2.29676i	−0.0860748	+	0.0860748i
$713$	−0.412286	+	1.87471i	−0.0154402	+	0.0702086i
$714$			11.7486i			0.439682i
$715$	−10.1566	−	12.8238i	−0.379837	−	0.479584i
$716$	6.37693	+	1.87244i	0.238317	+	0.0699762i
$717$	−0.439640	+	6.14697i	−0.0164187	+	0.229563i
$718$	14.9356	+	3.24904i	0.557391	+	0.121253i
$719$	3.77983	+	3.27524i	0.140964	+	0.122146i	0.722489	−	0.691383i	$-0.242998\pi$
$719$	3.77983	+	3.27524i	0.140964	+	0.122146i	−0.581525	+	0.813529i	$0.697544\pi$
$720$	−0.978322	−	5.69748i	−0.0364599	−	0.212333i
$721$	37.9943	−	11.1561i	1.41498	−	0.415476i
$722$	3.80773	+	17.5038i	0.141709	+	0.651425i
$723$	−8.81773	+	11.7791i	−0.327935	+	0.438070i
$724$	−3.96852	−	8.68986i	−0.147489	−	0.322956i
$725$	2.92069	−	5.14045i	0.108472	−	0.190912i
$726$	0.795170	+	5.53053i	0.0295115	+	0.205257i
$727$	49.3607	−	10.7378i	1.83069	−	0.398241i	0.840946	−	0.541119i	$-0.181999\pi$
$727$	49.3607	−	10.7378i	1.83069	−	0.398241i	0.989740	+	0.142877i	$0.0456354\pi$
$728$	−12.8006	−	6.98967i	−0.474423	−	0.259054i
$729$	7.04136	+	1.01240i	0.260791	+	0.0374961i
$730$	0.537818	+	0.228112i	0.0199055	+	0.00844281i
$731$	−37.7087	+	24.2339i	−1.39471	+	0.896324i
$732$	−2.19168	−	0.156752i	−0.0810069	−	0.00579373i
$733$	−8.99307	−	16.4696i	−0.332167	−	0.608318i	0.657207	−	0.753710i	$-0.271738\pi$
$733$	−8.99307	−	16.4696i	−0.332167	−	0.608318i	−0.989374	+	0.145392i	$0.953556\pi$
$734$	3.36541	−	7.36921i	0.124219	−	0.272003i
$735$	−1.46499	+	2.86594i	−0.0540370	+	0.105712i
$736$	−4.59848	−	1.36160i	−0.169502	−	0.0501894i
$737$	−13.0222	−	13.0222i	−0.479680	−	0.479680i
$738$	−8.92317	−	23.9240i	−0.328467	−	0.880653i
$739$	11.0149	−	37.5133i	0.405190	−	1.37995i	−0.464160	−	0.885751i	$-0.653644\pi$
$739$	11.0149	−	37.5133i	0.405190	−	1.37995i	0.869350	−	0.494198i	$-0.164538\pi$
$740$	2.84959	−	0.701733i	0.104753	−	0.0257962i
$741$	1.74193	+	2.71049i	0.0639913	+	0.0995725i
$742$	−30.0788	+	2.15128i	−1.10423	+	0.0789758i
$743$	−23.7459	+	17.7760i	−0.871153	+	0.652137i	−0.938382	−	0.345600i	$-0.887675\pi$
$743$	−23.7459	+	17.7760i	−0.871153	+	0.652137i	0.0672284	+	0.997738i	$0.478584\pi$
$744$	−0.0726174	−	0.247312i	−0.00266228	−	0.00906690i
$745$	3.70285	−	14.0126i	0.135662	−	0.513382i
$746$	23.3940	−	3.36355i	0.856516	−	0.123148i
$747$	−13.9152	−	5.19011i	−0.509132	−	0.189896i
$748$	8.57426	+	3.19803i	0.313506	+	0.116932i
$749$	−23.1482	+	3.32821i	−0.845816	+	0.121610i
$750$	−2.58589	−	6.71959i	−0.0944233	−	0.245365i
$751$	6.11225	+	20.8164i	0.223039	+	0.759601i	0.992643	+	0.121080i	$0.0386356\pi$
$751$	6.11225	+	20.8164i	0.223039	+	0.759601i	−0.769604	+	0.638522i	$0.779546\pi$
$752$	−9.45371	+	7.07696i	−0.344741	+	0.258070i
$753$	−7.12234	+	0.509400i	−0.259552	+	0.0185636i
$754$	3.06806	+	4.77400i	0.111732	+	0.173859i
$755$	3.55979	−	5.88585i	0.129554	−	0.214208i
$756$	3.07951	−	10.4878i	0.112001	−	0.381439i
$757$	15.2526	+	40.8938i	0.554365	+	1.48631i	0.847792	+	0.530329i	$0.177932\pi$
$757$	15.2526	+	40.8938i	0.554365	+	1.48631i	−0.293426	+	0.955982i	$0.594796\pi$
$758$	14.2248	+	14.2248i	0.516669	+	0.516669i
$759$	−1.94601	−	4.28694i	−0.0706357	−	0.155606i
$760$	−2.07563	−	1.06100i	−0.0752908	−	0.0384866i
$761$	5.37924	−	11.7789i	0.194997	−	0.426985i	−0.786725	−	0.617304i	$-0.788225\pi$
$761$	5.37924	−	11.7789i	0.194997	−	0.426985i	0.981722	+	0.190319i	$0.0609522\pi$
$762$	−3.25683	−	5.96444i	−0.117983	−	0.216069i
$763$	16.7549	+	1.19834i	0.606569	+	0.0433827i
$764$	−14.2071	+	9.13034i	−0.513994	+	0.330324i
$765$	13.0094	+	32.1735i	0.470356	+	1.16323i
$766$	−29.5833	−	4.25344i	−1.06889	−	0.153683i
$767$	−32.3085	−	17.6418i	−1.16659	−	0.637008i
$768$	0.629269	−	0.136889i	0.0227068	−	0.00493956i
$769$	3.68508	+	25.6303i	0.132887	+	0.924252i	0.941764	+	0.336274i	$0.109167\pi$
$769$	3.68508	+	25.6303i	0.132887	+	0.924252i	−0.808877	+	0.587978i	$0.799924\pi$
$770$	6.99423	+	7.64073i	0.252055	+	0.275353i
$771$	1.36145	+	2.98116i	0.0490314	+	0.107364i
$772$	4.10686	−	5.48613i	0.147809	−	0.197450i
$773$	−0.656492	−	3.01784i	−0.0236124	−	0.108544i	0.963832	−	0.266509i	$-0.0858703\pi$
$773$	−0.656492	−	3.01784i	−0.0236124	−	0.108544i	−0.987445	+	0.157965i	$0.949507\pi$
$774$	18.5215	−	5.43841i	0.665742	−	0.195480i
$775$	0.929280	+	1.77239i	0.0333807	+	0.0636661i
$776$	−10.8070	−	9.36436i	−0.387950	−	0.336161i
$777$	2.50981	+	0.545977i	0.0900391	+	0.0195868i
$778$	−0.638803	+	8.93163i	−0.0229022	+	0.320215i
$779$	−9.87923	−	2.90080i	−0.353960	−	0.103932i
$780$	6.86481	+	0.796752i	0.245800	+	0.0285283i
$781$			3.17770i			0.113707i
$782$	28.7126	+	2.11921i	1.02676	+	0.0757827i
$783$	−3.00738	+	3.00738i	−0.107475	+	0.107475i
$784$	2.03320	+	0.928532i	0.0726144	+	0.0331619i
$785$	10.6209	+	10.0572i	0.379075	+	0.358957i
$786$	−8.95271	−	10.3320i	−0.319333	−	0.368529i
$787$	1.04159	−	4.78809i	0.0371285	−	0.170677i	−0.954849	−	0.297092i	$-0.903983\pi$
$787$	1.04159	−	4.78809i	0.0371285	−	0.170677i	0.991977	+	0.126415i	$0.0403470\pi$
$788$	−1.36348	−	19.0639i	−0.0485719	−	0.679124i
$789$	1.26099	−	8.77037i	0.0448924	−	0.312234i
$790$	−0.315984	+	1.67050i	−0.0112422	+	0.0594338i
$791$	−45.2819	−	29.1009i	−1.61004	−	1.03471i
$792$	−3.15489	−	2.36172i	−0.112104	−	0.0839200i
$793$	−5.72248	+	15.3426i	−0.203211	+	0.544831i
$794$	−4.05181	+	1.85040i	−0.143793	+	0.0656683i
$795$	12.8313	−	6.28791i	0.455079	−	0.223009i
$796$	14.7406	−	22.9369i	0.522468	−	0.812976i
$797$	13.5210	−	24.7618i	0.478937	−	0.877108i	−0.520789	−	0.853686i	$-0.674362\pi$
$797$	13.5210	−	24.7618i	0.478937	−	0.877108i	0.999726	−	0.0234220i	$-0.00745612\pi$
$798$	−1.22264	−	1.63326i	−0.0432811	−	0.0578168i
$799$	46.4254	−	53.5778i	1.64241	−	1.89545i
$800$	−4.58260	+	1.99995i	−0.162019	+	0.0707089i
$801$	−6.34624	+	5.49905i	−0.224233	+	0.194299i
$802$	10.1959	−	5.56740i	0.360031	−	0.196592i
$803$	0.373148	−	0.139177i	0.0131681	−	0.00491144i
$804$	7.78010			0.274383
$805$	27.8472	+	16.9287i	0.981484	+	0.596659i
$806$	−1.92088			−0.0676600
$807$	−10.7058	+	3.99307i	−0.376863	+	0.140563i
$808$	−17.0995	+	9.33701i	−0.601557	+	0.328475i
$809$	5.17685	−	4.48577i	0.182008	−	0.157711i	−0.559091	−	0.829106i	$-0.688850\pi$
$809$	5.17685	−	4.48577i	0.182008	−	0.157711i	0.741100	+	0.671395i	$0.234304\pi$
$810$	−1.19799	−	12.1040i	−0.0420930	−	0.425292i
$811$	−23.9634	+	27.6553i	−0.841469	+	0.971107i	−0.999868	−	0.0162679i	$-0.994822\pi$
$811$	−23.9634	+	27.6553i	−0.841469	+	0.971107i	0.158398	+	0.987375i	$0.449367\pi$
$812$	−2.15344	−	2.87666i	−0.0755711	−	0.100951i
$813$	−0.866262	+	1.58644i	−0.0303811	+	0.0556389i
$814$	1.08164	−	1.68307i	0.0379115	−	0.0589915i
$815$	−5.06923	+	14.8119i	−0.177567	+	0.518837i
$816$	−3.51666	+	1.60600i	−0.123108	+	0.0562214i
$817$	2.72021	−	7.29316i	0.0951681	−	0.255155i
$818$	−20.5403	−	15.3763i	−0.718174	−	0.537618i
$819$	−31.7198	−	20.3851i	−1.10838	−	0.712312i
$820$	−18.2467	+	12.4418i	−0.637201	+	0.434486i
$821$	−1.74414	+	12.1308i	−0.0608709	+	0.423366i	0.936486	+	0.350705i	$0.114058\pi$
$821$	−1.74414	+	12.1308i	−0.0608709	+	0.423366i	−0.997357	+	0.0726609i	$0.976851\pi$
$822$	0.147404	+	2.06098i	0.00514132	+	0.0718850i
$823$	4.15036	−	19.0789i	0.144673	−	0.665049i	−0.846491	−	0.532403i	$-0.821289\pi$
$823$	4.15036	−	19.0789i	0.144673	−	0.665049i	0.991164	−	0.132646i	$-0.0423473\pi$
$824$	8.53301	+	9.84762i	0.297262	+	0.343058i
$825$	−4.42974	−	2.11415i	−0.154224	−	0.0736051i
$826$	21.2030	+	9.68309i	0.737747	+	0.336918i
$827$	20.4404	−	20.4404i	0.710781	−	0.710781i	−0.255918	−	0.966699i	$-0.582378\pi$
$827$	20.4404	−	20.4404i	0.710781	−	0.710781i	0.966699	+	0.255918i	$0.0823776\pi$
$828$	−11.6070	−	4.35927i	−0.403370	−	0.151495i
$829$		−	27.7357i		−	0.963301i	−0.876363	−	0.481651i	$-0.840037\pi$
$829$		−	27.7357i		−	0.963301i	0.876363	−	0.481651i	$-0.159963\pi$
$830$	−1.48095	+	12.7599i	−0.0514046	+	0.442901i
$831$	10.9120	+	3.20405i	0.378533	+	0.111147i
$832$	0.342374	−	4.78701i	0.0118697	−	0.165960i
$833$	−13.1118	−	2.85230i	−0.454297	−	0.0988264i
$834$	−2.68803	−	2.32919i	−0.0930788	−	0.0806533i
$835$	−43.9102	−	31.0403i	−1.51957	−	1.07420i
$836$	−1.52478	+	0.447715i	−0.0527355	+	0.0154846i
$837$	−0.306014	−	1.40672i	−0.0105774	−	0.0486234i
$838$	19.3420	−	25.8379i	0.668160	−	0.892557i
$839$	−13.5691	−	29.7123i	−0.468459	−	1.02578i	−0.985477	−	0.169808i	$-0.945685\pi$
$839$	−13.5691	−	29.7123i	−0.468459	−	1.02578i	0.517018	−	0.855974i	$-0.327042\pi$
$840$	−4.37181	−	0.193126i	−0.150842	−	0.00666347i
$841$	−3.92815	−	27.3209i	−0.135453	−	0.942099i
$842$	11.7233	−	2.55025i	0.404012	−	0.0878874i
$843$	−9.13832	−	4.98990i	−0.314741	−	0.171861i
$844$	−10.7722	−	1.54882i	−0.370796	−	0.0533124i
$845$	8.75981	−	20.6529i	0.301347	−	0.710481i
$846$	−25.6835	+	16.5058i	−0.883016	+	0.567480i
$847$	−26.2996	−	1.88098i	−0.903664	−	0.0646313i
$848$	−4.75561	−	8.70925i	−0.163308	−	0.299077i
$849$	4.50084	−	9.85547i	0.154468	−	0.338239i
$850$	24.3298	−	17.5797i	0.834504	−	0.602977i
$851$	1.78703	−	6.03527i	0.0612588	−	0.206887i
$852$	−0.949252	−	0.949252i	−0.0325208	−	0.0325208i
$853$	−8.75498	−	23.4730i	−0.299765	−	0.803700i	−0.996281	−	0.0861598i	$-0.972540\pi$
$853$	−8.75498	−	23.4730i	−0.299765	−	0.803700i	0.696517	−	0.717541i	$-0.254732\pi$
$854$	2.92125	−	9.94888i	0.0999633	−	0.340444i
$855$	−5.15672	−	3.11881i	−0.176356	−	0.106661i
$856$	−4.16050	−	6.47387i	−0.142203	−	0.221272i
$857$	−25.7479	+	1.84153i	−0.879531	+	0.0629053i	−0.503797	−	0.863822i	$-0.668064\pi$
$857$	−25.7479	+	1.84153i	−0.879531	+	0.0629053i	−0.375734	+	0.926727i	$0.622610\pi$
$858$	3.77159	−	2.82338i	0.128760	−	0.0963885i
$859$	15.6516	+	53.3045i	0.534026	+	1.81872i	0.573096	+	0.819488i	$0.305742\pi$
$859$	15.6516	+	53.3045i	0.534026	+	1.81872i	−0.0390698	+	0.999236i	$0.512439\pi$
$860$	−8.39787	−	14.4302i	−0.286365	−	0.492067i
$861$	−19.1322	+	2.75079i	−0.652024	+	0.0937468i
$862$	−15.5297	−	5.79229i	−0.528945	−	0.197286i
$863$	29.5368	+	11.0167i	1.00544	+	0.375011i	0.797624	−	0.603155i	$-0.206090\pi$
$863$	29.5368	+	11.0167i	1.00544	+	0.375011i	0.207821	+	0.978167i	$0.433363\pi$
$864$	3.56023	−	0.511884i	0.121122	−	0.0174147i
$865$	−11.2016	−	19.2480i	−0.380866	−	0.654450i
$866$	−0.921832	−	3.13947i	−0.0313251	−	0.106684i
$867$	9.81546	−	7.34776i	0.333351	−	0.249543i
$868$	1.21323	−	0.0867717i	0.0411796	−	0.00294522i
$869$	0.626609	+	0.975022i	0.0212562	+	0.0330754i
$870$	1.45697	+	0.881186i	0.0493961	+	0.0298750i
$871$	16.3350	−	55.6318i	0.553489	−	1.88501i
$872$	1.93166	+	5.17897i	0.0654141	+	0.175382i
$873$	−26.1410	−	26.1410i	−0.884739	−	0.884739i
$874$	−4.21208	+	2.69342i	−0.142476	+	0.0911064i
$875$	33.5787	−	5.18350i	1.13517	−	0.175234i
$876$	−0.0698925	+	0.153043i	−0.00236145	+	0.00517085i
$877$	21.6111	+	39.5778i	0.729755	+	1.33645i	0.933910	+	0.357508i	$0.116373\pi$
$877$	21.6111	+	39.5778i	0.729755	+	1.33645i	−0.204155	+	0.978939i	$0.565445\pi$
$878$	27.2479	+	1.94881i	0.919572	+	0.0657691i
$879$	5.17110	−	3.32326i	0.174417	−	0.112091i
$880$	−1.33097	+	3.13801i	−0.0448670	+	0.105782i
$881$	45.4931	+	6.54091i	1.53270	+	0.220369i	0.856422	−	0.516277i	$-0.172682\pi$
$881$	45.4931	+	6.54091i	1.53270	+	0.220369i	0.676279	+	0.736646i	$0.263592\pi$
$882$	5.07176	+	2.76939i	0.170775	+	0.0932502i
$883$	−43.3689	+	9.43432i	−1.45948	+	0.317490i	−0.871104	−	0.491099i	$-0.836595\pi$
$883$	−43.3689	+	9.43432i	−1.45948	+	0.317490i	−0.588374	+	0.808589i	$0.700232\pi$
$884$	4.10025	+	28.5179i	0.137906	+	0.959161i
$885$	−11.0344	−	0.487445i	−0.370916	−	0.0163853i
$886$	10.8836	+	23.8317i	0.365641	+	0.800642i
$887$	16.9673	−	22.6657i	0.569707	−	0.761039i	−0.419470	−	0.907769i	$-0.637784\pi$
$887$	16.9673	−	22.6657i	0.569707	−	0.761039i	0.989177	+	0.146730i	$0.0468749\pi$
$888$	0.179660	+	0.825883i	0.00602899	+	0.0277148i
$889$	30.7696	−	9.03478i	1.03198	−	0.303017i
$890$	5.93078	+	4.19249i	0.198800	+	0.140533i
$891$	−6.26659	−	5.43003i	−0.209939	−	0.181913i
$892$	−24.4302	−	5.31445i	−0.817982	−	0.177941i
$893$	−0.878253	+	12.2796i	−0.0293896	+	0.410920i
$894$	4.00506	+	1.17599i	0.133949	+	0.0393311i
$895$	1.71334	−	14.7621i	0.0572707	−	0.493444i
$896$			3.03895i			0.101524i
$897$	8.90958	−	11.8456i	0.297482	−	0.395512i
$898$	−3.55259	+	3.55259i	−0.118551	+	0.118551i
$899$	−0.430502	−	0.196604i	−0.0143581	−	0.00655710i
$900$	−12.1860	+	4.31208i	−0.406199	+	0.143736i
$901$	39.0105	+	45.0206i	1.29963	+	1.49985i
$902$	−3.20032	+	14.7116i	−0.106559	+	0.489843i
$903$	−1.04245	−	14.5753i	−0.0346905	−	0.485037i
$904$	2.52072	−	17.5320i	0.0838380	−	0.583106i
$905$	−17.6491	+	12.0343i	−0.586675	+	0.400034i
$906$	1.66655	+	1.07103i	0.0553675	+	0.0355825i
$907$	−30.5252	−	22.8508i	−1.01357	−	0.758750i	−0.0428799	−	0.999080i	$-0.513653\pi$
$907$	−30.5252	−	22.8508i	−1.01357	−	0.758750i	−0.970691	+	0.240331i	$0.922744\pi$
$908$	−2.37643	+	6.37145i	−0.0788645	+	0.211444i
$909$	−45.8163	+	20.9236i	−1.51963	+	0.693992i
$910$	−10.5599	+	30.8552i	−0.350058	+	1.02284i
$911$	3.02224	−	4.70270i	0.100131	−	0.155807i	−0.787573	−	0.616221i	$-0.788663\pi$
$911$	3.02224	−	4.70270i	0.100131	−	0.155807i	0.887704	+	0.460414i	$0.152299\pi$
$912$	0.321744	−	0.589230i	0.0106540	−	0.0195113i
$913$	5.24791	+	7.01039i	0.173680	+	0.232010i
$914$	24.8936	−	28.7288i	0.823408	−	0.950264i
$915$	0.483924	+	4.88938i	0.0159980	+	0.161638i
$916$	13.5325	−	11.7260i	0.447127	−	0.387438i
$917$	56.6223	−	30.9181i	1.86983	−	1.02101i
$918$	−20.2314	+	7.54592i	−0.667736	+	0.249052i
$919$	19.2679			0.635589			0.317795	−	0.948160i	$-0.397058\pi$
$919$	19.2679			0.635589			0.317795	+	0.948160i	$0.397058\pi$
$920$	−1.26056	+	10.6495i	−0.0415595	+	0.351102i
$921$	−2.47858			−0.0816720
$922$	33.5241	−	12.5039i	1.10406	−	0.411793i
$923$	−8.78069	+	4.79462i	−0.289020	+	0.157817i
$924$	−2.25460	+	1.95362i	−0.0741709	+	0.0642694i
$925$	−2.62483	−	6.01443i	−0.0863039	−	0.197753i
$926$	3.82174	−	4.41052i	0.125590	−	0.144939i
$927$	20.1878	+	26.9678i	0.663055	+	0.885738i
$928$	0.566688	−	1.03781i	0.0186024	−	0.0340678i
$929$	7.57936	−	11.7937i	0.248671	−	0.386939i	−0.694369	−	0.719619i	$-0.744316\pi$
$929$	7.57936	−	11.7937i	0.248671	−	0.386939i	0.943040	+	0.332680i	$0.107953\pi$
$930$	−0.517550	+	0.253623i	−0.0169711	+	0.00831663i
$931$	2.11960	−	0.967987i	0.0694670	−	0.0317245i
$932$	−3.16076	+	8.47433i	−0.103534	+	0.277586i
$933$	−7.00639	−	5.24492i	−0.229379	−	0.171711i
$934$	14.9399	+	9.60128i	0.488848	+	0.314163i
$935$	3.80320	−	20.1063i	0.124378	−	0.657545i
$936$	1.76576	−	12.2811i	0.0577155	−	0.401420i
$937$	−1.73243	−	24.2225i	−0.0565959	−	0.791314i	−0.943921	−	0.330170i	$-0.892894\pi$
$937$	−1.73243	−	24.2225i	−0.0565959	−	0.791314i	0.887326	−	0.461144i	$-0.152561\pi$
$938$	−7.80412	+	35.8750i	−0.254814	+	1.17136i
$939$	−0.795882	−	0.918497i	−0.0259726	−	0.0299740i
$940$	19.1738	+	18.1562i	0.625380	+	0.592189i
$941$	10.1383	+	4.63000i	0.330498	+	0.150934i	0.573752	−	0.819029i	$-0.305487\pi$
$941$	10.1383	+	4.63000i	0.330498	+	0.150934i	−0.243253	+	0.969963i	$0.578215\pi$
$942$	−2.97874	+	2.97874i	−0.0970526	+	0.0970526i
$943$	3.27164	+	47.2535i	0.106539	+	1.53879i
$944$			7.67024i			0.249645i
$945$	−24.2786	−	2.81786i	−0.789783	−	0.0916649i
$946$	−10.9210	−	3.20668i	−0.355071	−	0.104258i
$947$	0.528326	−	7.38697i	0.0171683	−	0.240044i	−0.981621	−	0.190843i	$-0.938878\pi$
$947$	0.528326	−	7.38697i	0.0171683	−	0.240044i	0.998789	−	0.0492012i	$-0.0156676\pi$
$948$	−0.478445	−	0.104079i	−0.0155392	−	0.00338034i
$949$	0.947595	+	0.821096i	0.0307602	+	0.0266539i
$950$	−1.55279	+	4.97580i	−0.0503793	+	0.161436i
$951$	−19.8557	+	5.83016i	−0.643865	+	0.189056i
$952$	−3.87796	−	17.8267i	−0.125685	−	0.577767i
$953$	31.6808	−	42.3205i	1.02624	−	1.37090i	0.0995663	−	0.995031i	$-0.468254\pi$
$953$	31.6808	−	42.3205i	1.02624	−	1.37090i	0.926674	−	0.375866i	$-0.122655\pi$
$954$	−10.6570	−	23.3356i	−0.345033	−	0.755517i
$955$	25.4978	+	27.8547i	0.825090	+	0.901356i
$956$	−1.36189	−	9.47217i	−0.0440468	−	0.306352i
$957$	1.13426	−	0.246742i	0.0366653	−	0.00797604i
$958$	2.19171	+	1.19676i	0.0708108	+	0.0386656i
$959$	−9.65130	−	1.38765i	−0.311657	−	0.0448095i
$960$	−0.539806	−	1.33499i	−0.0174222	−	0.0430866i
$961$	−25.9441	+	16.6733i	−0.836906	+	0.537847i
$962$	6.28271	+	0.449348i	0.202563	+	0.0144876i
$963$	−9.53468	−	17.4615i	−0.307251	−	0.562688i
$964$	9.49149	−	20.7835i	0.305700	−	0.669390i
$965$	−13.6445	−	6.97471i	−0.439233	−	0.224524i
$966$	−5.09220	+	7.88413i	−0.163839	+	0.253668i
$967$	−36.7509	−	36.7509i	−1.18183	−	1.18183i	−0.979270	−	0.202558i	$-0.935075\pi$
$967$	−36.7509	−	36.7509i	−1.18183	−	1.18183i	−0.202558	−	0.979270i	$-0.564925\pi$
$968$	−3.03205	−	8.12924i	−0.0974537	−	0.261284i
$969$	−1.13547	+	3.86704i	−0.0364764	+	0.124227i
$970$	−16.5477	+	27.3604i	−0.531315	+	0.878489i
$971$	−7.17033	−	11.1573i	−0.230107	−	0.358053i	0.706930	−	0.707283i	$-0.250080\pi$
$971$	−7.17033	−	11.1573i	−0.230107	−	0.358053i	−0.937037	+	0.349230i	$0.886443\pi$
$972$	14.2571	−	1.01969i	0.457296	−	0.0327065i
$973$	13.4365	−	10.0584i	0.430755	−	0.322459i
$974$	−2.42147	−	8.24676i	−0.0775888	−	0.264243i
$975$	−0.841885	−	15.4303i	−0.0269619	−	0.494164i
$976$	3.37727	−	0.485579i	0.108104	−	0.0155430i
$977$	29.2937	+	10.9260i	0.937189	+	0.349554i	0.771214	−	0.636576i	$-0.219650\pi$
$977$	29.2937	+	10.9260i	0.937189	+	0.349554i	0.165976	+	0.986130i	$0.446923\pi$
$978$	−4.22444	−	1.57563i	−0.135083	−	0.0503832i
$979$	4.90094	−	0.704649i	0.156635	−	0.0225207i
$980$	1.27691	−	4.83218i	0.0407894	−	0.154358i
$981$	4.02599	+	13.7112i	0.128540	+	0.437766i
$982$	19.3415	−	14.4789i	0.617214	−	0.462040i
$983$	−58.7158	+	4.19944i	−1.87274	+	0.133941i	−0.960953	−	0.276713i	$-0.910755\pi$
$983$	−58.7158	+	4.19944i	−1.87274	+	0.133941i	−0.911791	+	0.410654i	$0.865300\pi$
$984$	−3.43870	−	5.35072i	−0.109622	−	0.170575i
$985$	−41.4974	+	10.2190i	−1.32222	+	0.325605i
$986$	−1.99990	+	6.81102i	−0.0636897	+	0.216907i
$987$	8.07645	+	21.6538i	0.257076	+	0.689248i
$988$	−3.53777	−	3.53777i	−0.112552	−	0.112552i
$989$	−35.8088	−	0.0814353i	−1.13865	−	0.00258949i
$990$	−4.01092	+	7.84651i	−0.127475	+	0.249378i
$991$	−15.1192	+	33.1064i	−0.480277	+	1.05166i	0.502111	+	0.864803i	$0.332557\pi$
$991$	−15.1192	+	33.1064i	−0.480277	+	1.05166i	−0.982387	+	0.186856i	$0.940170\pi$
$992$	0.191818	+	0.351288i	0.00609021	+	0.0111534i
$993$	6.46723	+	0.462545i	0.205231	+	0.0146784i
$994$	5.32930	−	3.42493i	0.169035	−	0.108632i
$995$	−56.1268	−	23.8059i	−1.77934	−	0.754697i
$996$	−3.66184	−	0.526493i	−0.116030	−	0.0166826i
$997$	−40.8367	−	22.2985i	−1.29331	−	0.706202i	−0.322620	−	0.946529i	$-0.604564\pi$
$997$	−40.8367	−	22.2985i	−1.29331	−	0.706202i	−0.970692	+	0.240327i	$0.922745\pi$
$998$	−20.2933	+	4.41455i	−0.642374	+	0.139740i
$999$	0.671822	+	4.67262i	0.0212555	+	0.147835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.17.3	✓	240
5.3	odd	4	inner	230.2.l.a.63.9	yes	240
23.19	odd	22	inner	230.2.l.a.157.9	yes	240
115.88	even	44	inner	230.2.l.a.203.3	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.17.3	✓	240	1.1	even	1	trivial
230.2.l.a.63.9	yes	240	5.3	odd	4	inner
230.2.l.a.157.9	yes	240	23.19	odd	22	inner
230.2.l.a.203.3	yes	240	115.88	even	44	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.936950 + 0.349464i) q^{2} +(-0.565213 + 0.308630i) q^{3} +(0.755750 - 0.654861i) q^{4} +(-1.72918 - 1.41772i) q^{5} +(0.421721 - 0.486692i) q^{6} +(1.82117 + 2.43280i) q^{7} +(-0.479249 + 0.877679i) q^{8} +(-1.39771 + 2.17488i) q^{9} +(2.11560 + 0.724045i) q^{10} +(1.38662 - 0.633249i) q^{11} +(-0.225050 + 0.603382i) q^{12} +(3.84199 + 2.87608i) q^{13} +(-2.55652 - 1.64298i) q^{14} +(1.41491 + 0.267637i) q^{15} +(0.142315 - 0.989821i) q^{16} +(0.428269 + 5.98798i) q^{17} +(0.549541 - 2.52620i) q^{18} +(-0.682687 - 0.787863i) q^{19} +(-2.23524 + 0.0609327i) q^{20} +(-1.78018 - 0.812983i) q^{21} +(-1.07790 + 1.07790i) q^{22} +(-2.30796 + 4.20396i) q^{23} -0.643986i q^{24} +(0.980143 + 4.90299i) q^{25} +(-4.60484 - 1.35210i) q^{26} +(0.256596 - 3.58768i) q^{27} +(2.96950 + 0.645974i) q^{28} +(-0.893636 - 0.774340i) q^{29} +(-1.41923 + 0.243697i) q^{30} +(0.384033 - 0.112762i) q^{31} +(0.212565 + 0.977147i) q^{32} +(-0.588297 + 0.785873i) q^{33} +(-2.49385 - 5.46077i) q^{34} +(0.299891 - 6.78867i) q^{35} +(0.367924 + 2.55897i) q^{36} +(-1.28246 + 0.278981i) q^{37} +(0.914973 + 0.499613i) q^{38} +(-3.05919 - 0.439844i) q^{39} +(2.07301 - 0.838226i) q^{40} +(8.30875 - 5.33971i) q^{41} +(1.95205 + 0.139614i) q^{42} +(3.57839 + 6.55334i) q^{43} +(0.633249 - 1.38662i) q^{44} +(5.50026 - 1.77920i) q^{45} +(0.693312 - 4.74545i) q^{46} +(-8.35033 - 8.35033i) q^{47} +(0.225050 + 0.603382i) q^{48} +(-0.629726 + 2.14465i) q^{49} +(-2.63176 - 4.25133i) q^{50} +(-2.09013 - 3.25231i) q^{51} +(4.78701 - 0.342374i) q^{52} +(7.94381 - 5.94666i) q^{53} +(1.01335 + 3.45115i) q^{54} +(-3.29549 - 0.870837i) q^{55} +(-3.00801 + 0.432487i) q^{56} +(0.629021 + 0.234613i) q^{57} +(1.10790 + 0.413224i) q^{58} +(-7.59217 + 1.09159i) q^{59} +(1.24458 - 0.724300i) q^{60} +(0.961272 + 3.27379i) q^{61} +(-0.320413 + 0.239859i) q^{62} +(-7.83652 + 0.560479i) q^{63} +(-0.540641 - 0.841254i) q^{64} +(-2.56603 - 10.4201i) q^{65} +(0.276570 - 0.941912i) q^{66} +(-4.22193 - 11.3194i) q^{67} +(4.24495 + 4.24495i) q^{68} +(0.00702364 - 3.08844i) q^{69} +(2.09141 + 6.46544i) q^{70} +(-0.865969 + 1.89621i) q^{71} +(-1.23899 - 2.26905i) q^{72} +(0.260594 + 0.0186380i) q^{73} +(1.10410 - 0.709564i) q^{74} +(-2.06720 - 2.46873i) q^{75} +(-1.03188 - 0.148362i) q^{76} +(4.06584 + 2.22012i) q^{77} +(3.02001 - 0.656964i) q^{78} +(0.108205 + 0.752579i) q^{79} +(-1.64938 + 1.50982i) q^{80} +(-2.25966 - 4.94797i) q^{81} +(-5.91884 + 7.90665i) q^{82} +(1.22112 + 5.61340i) q^{83} +(-1.87776 + 0.551361i) q^{84} +(7.74872 - 10.9615i) q^{85} +(-5.64293 - 4.88963i) q^{86} +(0.744078 + 0.161864i) q^{87} +(-0.108748 + 1.52049i) q^{88} +(3.11654 + 0.915098i) q^{89} +(-4.53170 + 3.58917i) q^{90} +14.5846i q^{91} +(1.00877 + 4.68854i) q^{92} +(-0.182259 + 0.182259i) q^{93} +(10.7420 + 4.90570i) q^{94} +(0.0635218 + 2.33022i) q^{95} +(-0.421721 - 0.486692i) q^{96} +(-3.03964 + 13.9730i) q^{97} +(-0.159457 - 2.22950i) q^{98} +(-0.560854 + 3.90083i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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