LMFDB - Embedded newform 666.2.t.a.85.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(85,666)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("666.85"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.3
Character	$\chi$	$=$	666.85
Dual form			666.2.t.a.619.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.52427 - 0.822567i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.98479 + 1.72327i) q^{5} +(0.908769 + 1.47450i) q^{6} -0.480194 q^{7} -1.00000i q^{8} +(1.64677 + 2.50762i) q^{9} +3.44654 q^{10} +(1.57883 + 2.73461i) q^{11} +(-0.0497688 - 1.73134i) q^{12} +(1.16995 - 0.675468i) q^{13} +(0.415860 + 0.240097i) q^{14} +(5.96712 - 0.171530i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.944880 - 0.545527i) q^{17} +(-0.172333 - 2.99505i) q^{18} +(0.333391 + 0.192483i) q^{19} +(-2.98479 - 1.72327i) q^{20} +(0.731943 + 0.394992i) q^{21} -3.15766i q^{22} +(-6.91907 - 3.99473i) q^{23} +(-0.822567 + 1.52427i) q^{24} +(3.43932 - 5.95707i) q^{25} -1.35094 q^{26} +(-0.447426 - 5.17685i) q^{27} +(-0.240097 - 0.415860i) q^{28} +(-5.40267 + 3.11923i) q^{29} +(-5.25344 - 2.83501i) q^{30} +(-3.60235 - 2.07982i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.157153 - 5.46697i) q^{33} -1.09105 q^{34} +(1.43328 - 0.827504i) q^{35} +(-1.34828 + 2.67995i) q^{36} +(5.65702 - 2.23564i) q^{37} +(-0.192483 - 0.333391i) q^{38} +(-2.33892 + 0.0672344i) q^{39} +(1.72327 + 2.98479i) q^{40} +(1.65030 + 2.85840i) q^{41} +(-0.436386 - 0.708045i) q^{42} +(7.47606 - 4.31631i) q^{43} +(-1.57883 + 2.73461i) q^{44} +(-9.23656 - 4.64689i) q^{45} +(3.99473 + 6.91907i) q^{46} +(-5.93648 - 10.2823i) q^{47} +(1.47450 - 0.908769i) q^{48} -6.76941 q^{49} +(-5.95707 + 3.43932i) q^{50} +(-1.88898 + 0.0543004i) q^{51} +(1.16995 + 0.675468i) q^{52} +(1.47126 + 2.54830i) q^{53} +(-2.20094 + 4.70700i) q^{54} +(-9.42495 - 5.44150i) q^{55} +0.480194i q^{56} +(-0.349845 - 0.567632i) q^{57} +6.23847 q^{58} +0.340484i q^{59} +(3.13211 + 5.08191i) q^{60} -14.2169i q^{61} +(2.07982 + 3.60235i) q^{62} +(-0.790768 - 1.20414i) q^{63} -1.00000 q^{64} +(-2.32803 + 4.03226i) q^{65} +(-2.59739 + 4.81311i) q^{66} +(4.44667 + 7.70185i) q^{67} +(0.944880 + 0.545527i) q^{68} +(7.26057 + 11.7804i) q^{69} -1.65501 q^{70} +(1.04493 - 1.80988i) q^{71} +(2.50762 - 1.64677i) q^{72} -7.32053 q^{73} +(-6.01695 - 0.892387i) q^{74} +(-10.1425 + 6.25109i) q^{75} +0.384966i q^{76} +(-0.758145 - 1.31315i) q^{77} +(2.05918 + 1.11124i) q^{78} -16.2973i q^{79} -3.44654i q^{80} +(-3.57631 + 8.25893i) q^{81} -3.30060i q^{82} +(5.37919 - 9.31702i) q^{83} +(0.0238987 + 0.831377i) q^{84} +(-1.88018 + 3.25657i) q^{85} -8.63261 q^{86} +(10.8009 - 0.310481i) q^{87} +(2.73461 - 1.57883i) q^{88} +(2.15753 - 1.24565i) q^{89} +(5.67565 + 8.64261i) q^{90} +(-0.561801 + 0.324356i) q^{91} -7.98946i q^{92} +(3.78015 + 6.13337i) q^{93} +11.8730i q^{94} -1.32680 q^{95} +(-1.73134 + 0.0497688i) q^{96} +(-10.9363 + 6.31410i) q^{97} +(5.86248 + 3.38471i) q^{98} +(-4.25740 + 8.46238i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 2 q^{3} + 38 q^{4} + 4 q^{7} + 2 q^{9} - 4 q^{11} + 2 q^{12} + 6 q^{13} + 6 q^{15} - 38 q^{16} - 12 q^{21} - 12 q^{23} + 50 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} - 18 q^{29} - 12 q^{30} - 6 q^{31}+ \cdots - 10 q^{99}+O(q^{100}) $ 76 * q - 2 * q^3 + 38 * q^4 + 4 * q^7 + 2 * q^9 - 4 * q^11 + 2 * q^12 + 6 * q^13 + 6 * q^15 - 38 * q^16 - 12 * q^21 - 12 * q^23 + 50 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 - 18 * q^29 - 12 * q^30 - 6 * q^31 + 4 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 18 * q^39 - 36 * q^41 + 42 * q^42 - 6 * q^43 + 4 * q^44 - 12 * q^45 - 20 * q^47 + 4 * q^48 + 72 * q^49 + 18 * q^51 + 6 * q^52 + 14 * q^53 + 18 * q^54 + 36 * q^57 + 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 - 16 * q^65 - 20 * q^67 - 66 * q^69 + 2 * q^71 + 28 * q^73 - 20 * q^74 - 78 * q^75 + 12 * q^77 + 22 * q^78 + 26 * q^81 + 32 * q^83 - 6 * q^84 - 12 * q^85 - 8 * q^86 - 72 * q^87 + 60 * q^89 - 10 * q^90 + 42 * q^91 - 6 * q^93 + 28 * q^95 + 12 * q^97 - 24 * q^98 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.52427	−	0.822567i	−0.880035	−	0.474909i
$3$	−1.52427	−	0.822567i	−0.880035	−	0.474909i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.98479	+	1.72327i	−1.33484	+	0.770670i	−0.986037	−	0.166527i	$-0.946745\pi$
$5$	−2.98479	+	1.72327i	−1.33484	+	0.770670i	−0.348802	+	0.937196i	$0.613411\pi$
$6$	0.908769	+	1.47450i	0.371003	+	0.601961i
$7$	−0.480194			−0.181496			−0.0907482	−	0.995874i	$-0.528926\pi$
$7$	−0.480194			−0.181496			−0.0907482	+	0.995874i	$0.528926\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.64677	+	2.50762i	0.548923	+	0.835873i
$10$	3.44654			1.08989
$11$	1.57883	+	2.73461i	0.476035	+	0.824517i	0.999623	−	0.0274546i	$-0.00874017\pi$
$11$	1.57883	+	2.73461i	0.476035	+	0.824517i	−0.523588	+	0.851972i	$0.675407\pi$
$12$	−0.0497688	−	1.73134i	−0.0143670	−	0.499794i
$13$	1.16995	−	0.675468i	0.324484	−	0.187341i	−0.328905	−	0.944363i	$-0.606680\pi$
$13$	1.16995	−	0.675468i	0.324484	−	0.187341i	0.653390	+	0.757022i	$0.273346\pi$
$14$	0.415860	+	0.240097i	0.111143	+	0.0641687i
$15$	5.96712	−	0.171530i	1.54070	−	0.0442889i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.944880	−	0.545527i	0.229167	−	0.132310i	−0.381021	−	0.924567i	$-0.624427\pi$
$17$	0.944880	−	0.545527i	0.229167	−	0.132310i	0.610188	+	0.792257i	$0.291094\pi$
$18$	−0.172333	−	2.99505i	−0.0406192	−	0.705939i
$19$	0.333391	+	0.192483i	0.0764851	+	0.0441587i	0.537755	−	0.843101i	$-0.319273\pi$
$19$	0.333391	+	0.192483i	0.0764851	+	0.0441587i	−0.461270	+	0.887260i	$0.652606\pi$
$20$	−2.98479	−	1.72327i	−0.667419	−	0.385335i
$21$	0.731943	+	0.394992i	0.159723	+	0.0861943i
$22$		−	3.15766i		−	0.673215i
$23$	−6.91907	−	3.99473i	−1.44273	−	0.832958i	−0.444695	−	0.895682i	$-0.646688\pi$
$23$	−6.91907	−	3.99473i	−1.44273	−	0.832958i	−0.998031	+	0.0627234i	$0.980021\pi$
$24$	−0.822567	+	1.52427i	−0.167906	+	0.311139i
$25$	3.43932	−	5.95707i	0.687863	−	1.19141i
$26$	−1.35094			−0.264940
$27$	−0.447426	−	5.17685i	−0.0861071	−	0.996286i
$28$	−0.240097	−	0.415860i	−0.0453741	−	0.0785902i
$29$	−5.40267	+	3.11923i	−1.00325	+	0.579227i	−0.909209	−	0.416341i	$-0.863312\pi$
$29$	−5.40267	+	3.11923i	−1.00325	+	0.579227i	−0.0940423	+	0.995568i	$0.529979\pi$
$30$	−5.25344	−	2.83501i	−0.959142	−	0.517599i
$31$	−3.60235	−	2.07982i	−0.647001	−	0.373546i	0.140305	−	0.990108i	$-0.455192\pi$
$31$	−3.60235	−	2.07982i	−0.647001	−	0.373546i	−0.787306	+	0.616562i	$0.788525\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−0.157153	−	5.46697i	−0.0273568	−	0.951677i
$34$	−1.09105			−0.187114
$35$	1.43328	−	0.827504i	0.242268	−	0.139874i
$36$	−1.34828	+	2.67995i	−0.224713	+	0.446659i
$37$	5.65702	−	2.23564i	0.930009	−	0.367538i
$37$	5.65702	−	2.23564i	0.930009	−	0.367538i
$38$	−0.192483	−	0.333391i	−0.0312249	−	0.0540831i
$39$	−2.33892	+	0.0672344i	−0.374528	+	0.0107661i
$40$	1.72327	+	2.98479i	0.272473	+	0.471937i
$41$	1.65030	+	2.85840i	0.257733	+	0.446407i	0.965634	−	0.259905i	$-0.0836911\pi$
$41$	1.65030	+	2.85840i	0.257733	+	0.446407i	−0.707901	+	0.706312i	$0.750358\pi$
$42$	−0.436386	−	0.708045i	−0.0673358	−	0.109254i
$43$	7.47606	−	4.31631i	1.14009	−	0.658231i	0.193636	−	0.981073i	$-0.437972\pi$
$43$	7.47606	−	4.31631i	1.14009	−	0.658231i	0.946453	+	0.322843i	$0.104638\pi$
$44$	−1.57883	+	2.73461i	−0.238018	+	0.412259i
$45$	−9.23656	−	4.64689i	−1.37691	−	0.692718i
$46$	3.99473	+	6.91907i	0.588991	+	1.02016i
$47$	−5.93648	−	10.2823i	−0.865925	−	1.49983i	−0.866126	−	0.499826i	$-0.833397\pi$
$47$	−5.93648	−	10.2823i	−0.865925	−	1.49983i	0.000200737	−	1.00000i	$-0.499936\pi$
$48$	1.47450	−	0.908769i	0.212825	−	0.131169i
$49$	−6.76941			−0.967059
$50$	−5.95707	+	3.43932i	−0.842457	+	0.486393i
$51$	−1.88898	+	0.0543004i	−0.264510	+	0.00760358i
$52$	1.16995	+	0.675468i	0.162242	+	0.0936706i
$53$	1.47126	+	2.54830i	0.202094	+	0.350037i	0.949203	−	0.314665i	$-0.101892\pi$
$53$	1.47126	+	2.54830i	0.202094	+	0.350037i	−0.747109	+	0.664701i	$0.768559\pi$
$54$	−2.20094	+	4.70700i	−0.299511	+	0.640541i
$55$	−9.42495	−	5.44150i	−1.27086	−	0.733732i
$56$			0.480194i			0.0641687i
$57$	−0.349845	−	0.567632i	−0.0463382	−	0.0751846i
$58$	6.23847			0.819151
$59$			0.340484i			0.0443273i	0.999754	+	0.0221636i	$0.00705548\pi$
$59$			0.340484i			0.0443273i	−0.999754	+	0.0221636i	$0.992945\pi$
$60$	3.13211	+	5.08191i	0.404353	+	0.656072i
$61$		−	14.2169i		−	1.82029i	−0.414286	−	0.910147i	$-0.635969\pi$
$61$		−	14.2169i		−	1.82029i	0.414286	−	0.910147i	$-0.364031\pi$
$62$	2.07982	+	3.60235i	0.264137	+	0.457499i
$63$	−0.790768	−	1.20414i	−0.0996275	−	0.151708i
$64$	−1.00000			−0.125000
$65$	−2.32803	+	4.03226i	−0.288756	+	0.500140i
$66$	−2.59739	+	4.81311i	−0.319716	+	0.592453i
$67$	4.44667	+	7.70185i	0.543247	+	0.940931i	0.998715	+	0.0506791i	$0.0161386\pi$
$67$	4.44667	+	7.70185i	0.543247	+	0.940931i	−0.455468	+	0.890252i	$0.650528\pi$
$68$	0.944880	+	0.545527i	0.114584	+	0.0661549i
$69$	7.26057	+	11.7804i	0.874070	+	1.41820i
$70$	−1.65501			−0.197811
$71$	1.04493	−	1.80988i	0.124011	−	0.214793i	−0.797335	−	0.603537i	$-0.793758\pi$
$71$	1.04493	−	1.80988i	0.124011	−	0.214793i	0.921346	+	0.388744i	$0.127091\pi$
$72$	2.50762	−	1.64677i	0.295526	−	0.194073i
$73$	−7.32053			−0.856803			−0.428402	−	0.903588i	$-0.640923\pi$
$73$	−7.32053			−0.856803			−0.428402	+	0.903588i	$0.640923\pi$
$74$	−6.01695	−	0.892387i	−0.699456	−	0.103738i
$75$	−10.1425	+	6.25109i	−1.17116	+	0.721813i
$76$			0.384966i			0.0441587i
$77$	−0.758145	−	1.31315i	−0.0863987	−	0.149647i
$78$	2.05918	+	1.11124i	0.233157	+	0.125823i
$79$		−	16.2973i		−	1.83359i	−0.399361	−	0.916794i	$-0.630768\pi$
$79$		−	16.2973i		−	1.83359i	0.399361	−	0.916794i	$-0.369232\pi$
$80$		−	3.44654i		−	0.385335i
$81$	−3.57631	+	8.25893i	−0.397368	+	0.917659i
$82$		−	3.30060i		−	0.364490i
$83$	5.37919	−	9.31702i	0.590442	−	1.02268i	−0.403730	−	0.914878i	$-0.632287\pi$
$83$	5.37919	−	9.31702i	0.590442	−	1.02268i	0.994173	−	0.107798i	$-0.0343801\pi$
$84$	0.0238987	+	0.831377i	0.00260756	+	0.0907107i
$85$	−1.88018	+	3.25657i	−0.203934	+	0.353224i
$86$	−8.63261			−0.930879
$87$	10.8009	−	0.310481i	1.15798	−	0.0332870i
$88$	2.73461	−	1.57883i	0.291511	−	0.168304i
$89$	2.15753	−	1.24565i	0.228697	−	0.132038i	−0.381274	−	0.924462i	$-0.624514\pi$
$89$	2.15753	−	1.24565i	0.228697	−	0.132038i	0.609971	+	0.792424i	$0.291181\pi$
$90$	5.67565	+	8.64261i	0.598266	+	0.911011i
$91$	−0.561801	+	0.324356i	−0.0588927	+	0.0340017i
$92$		−	7.98946i		−	0.832958i
$93$	3.78015	+	6.13337i	0.391983	+	0.636000i
$94$			11.8730i			1.22460i
$95$	−1.32680			−0.136127
$96$	−1.73134	+	0.0497688i	−0.176704	+	0.00507950i
$97$	−10.9363	+	6.31410i	−1.11042	+	0.641100i	−0.938938	−	0.344088i	$-0.888188\pi$
$97$	−10.9363	+	6.31410i	−1.11042	+	0.641100i	−0.171480	+	0.985188i	$0.554855\pi$
$98$	5.86248	+	3.38471i	0.592200	+	0.341907i
$99$	−4.25740	+	8.46238i	−0.427885	+	0.850501i
$100$	6.87863			0.687863
$101$	0.492396	+	0.852854i	0.0489952	+	0.0848622i	0.889483	−	0.456968i	$-0.151065\pi$
$101$	0.492396	+	0.852854i	0.0489952	+	0.0848622i	−0.840488	+	0.541831i	$0.817731\pi$
$102$	1.66306	+	0.897465i	0.164667	+	0.0888622i
$103$	−1.04404	−	0.602776i	−0.102872	−	0.0593933i	0.447681	−	0.894193i	$-0.352250\pi$
$103$	−1.04404	−	0.602776i	−0.102872	−	0.0593933i	−0.550553	+	0.834800i	$0.685583\pi$
$104$	−0.675468	−	1.16995i	−0.0662351	−	0.114723i
$105$	−2.86537	+	0.0823677i	−0.279632	+	0.00803827i
$106$		−	2.94253i		−	0.285804i
$107$	7.88782	−	13.6621i	0.762544	−	1.32077i	−0.178991	−	0.983851i	$-0.557283\pi$
$107$	7.88782	−	13.6621i	0.762544	−	1.32077i	0.941535	−	0.336915i	$-0.109383\pi$
$108$	4.25957	−	2.97591i	0.409878	−	0.286357i
$109$	4.39231	−	2.53590i	0.420707	−	0.242895i	−0.274673	−	0.961538i	$-0.588570\pi$
$109$	4.39231	−	2.53590i	0.420707	−	0.242895i	0.695380	+	0.718643i	$0.255236\pi$
$110$	5.44150	+	9.42495i	0.518827	+	0.898634i
$111$	−10.4618	−	1.24556i	−0.992987	−	0.118224i
$112$	0.240097	−	0.415860i	0.0226870	−	0.0392951i
$113$		−	0.595128i		−	0.0559850i	−0.999608	−	0.0279925i	$-0.991089\pi$
$113$		−	0.595128i		−	0.0559850i	0.999608	−	0.0279925i	$-0.00891145\pi$
$114$	0.0191593	+	0.666506i	0.00179443	+	0.0624240i
$115$	27.5360			2.56774
$116$	−5.40267	−	3.11923i	−0.501625	−	0.289614i
$117$	3.62044	+	1.82144i	0.334710	+	0.168392i
$118$	0.170242	−	0.294868i	0.0156721	−	0.0271448i
$119$	−0.453726	+	0.261959i	−0.0415930	+	0.0240137i
$120$	−0.171530	−	5.96712i	−0.0156585	−	0.544721i
$121$	0.514592	−	0.891300i	0.0467811	−	0.0810272i
$122$	−7.10847	+	12.3122i	−0.643571	+	1.11470i
$123$	−0.164267	−	5.71444i	−0.0148114	−	0.515254i
$124$		−	4.15963i		−	0.373546i
$125$			6.47477i			0.579121i
$126$	0.0827533	+	1.43820i	0.00737225	+	0.128125i
$127$	3.39075	+	5.87296i	0.300881	+	0.521141i	0.976336	−	0.216261i	$-0.0693861\pi$
$127$	3.39075	+	5.87296i	0.300881	+	0.521141i	−0.675455	+	0.737401i	$0.736053\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−14.9460	+	0.429635i	−1.31592	+	0.0378272i
$130$	4.03226	−	2.32803i	0.353653	−	0.204181i
$131$		−	8.07078i		−	0.705148i	−0.935784	−	0.352574i	$-0.885307\pi$
$131$		−	8.07078i		−	0.705148i	0.935784	−	0.352574i	$-0.114693\pi$
$132$	4.65596	−	2.86958i	0.405249	−	0.249765i
$133$	−0.160092	−	0.0924293i	−0.0138818	−	0.00801464i
$134$		−	8.89333i		−	0.768267i
$135$	10.2566	+	14.6808i	0.882746	+	1.26352i
$136$	−0.545527	−	0.944880i	−0.0467785	−	0.0810228i
$137$	0.0848084	+	0.146893i	0.00724567	+	0.0125499i	0.869626	−	0.493712i	$-0.164360\pi$
$137$	0.0848084	+	0.146893i	0.00724567	+	0.0125499i	−0.862380	+	0.506262i	$0.831027\pi$
$138$	−0.397625	−	13.8324i	−0.0338481	−	1.17749i
$139$	8.65398			0.734021			0.367011	−	0.930217i	$-0.380381\pi$
$139$	8.65398			0.734021			0.367011	+	0.930217i	$0.380381\pi$
$140$	1.43328	+	0.827504i	0.121134	+	0.0699369i
$141$	0.590903	+	20.5561i	0.0497630	+	1.73113i
$142$	−1.80988	+	1.04493i	−0.151881	+	0.0876888i
$143$	3.69429	+	2.13290i	0.308932	+	0.178362i
$144$	−2.99505	+	0.172333i	−0.249587	+	0.0143611i
$145$	10.7506	−	18.6205i	0.892785	−	1.54635i
$146$	6.33976	+	3.66026i	0.524683	+	0.302926i
$147$	10.3184	+	5.56829i	0.851046	+	0.459265i
$148$	4.76464	+	3.78130i	0.391651	+	0.310821i
$149$	−2.53720	+	4.39456i	−0.207855	+	0.360016i	−0.951039	−	0.309072i	$-0.899982\pi$
$149$	−2.53720	+	4.39456i	−0.207855	+	0.360016i	0.743183	+	0.669088i	$0.233315\pi$
$150$	11.9092	−	0.342341i	0.972384	−	0.0279520i
$151$	4.93152			0.401321			0.200661	−	0.979661i	$-0.435691\pi$
$151$	4.93152			0.401321			0.200661	+	0.979661i	$0.435691\pi$
$152$	0.192483	−	0.333391i	0.0156125	−	0.0270416i
$153$	2.92397	+	1.47104i	0.236389	+	0.118927i
$154$			1.51629i			0.122186i
$155$	14.3363			1.15152
$156$	−1.22769	−	1.99195i	−0.0982938	−	0.159484i
$157$	7.07318			0.564501			0.282251	−	0.959341i	$-0.408919\pi$
$157$	7.07318			0.564501			0.282251	+	0.959341i	$0.408919\pi$
$158$	−8.14864	+	14.1139i	−0.648271	+	1.12284i
$159$	−0.146446	−	5.09450i	−0.0116139	−	0.404020i
$160$	−1.72327	+	2.98479i	−0.136236	+	0.235968i
$161$	3.32250	+	1.91825i	0.261850	+	0.151179i
$162$	7.22664	−	5.36429i	0.567779	−	0.421458i
$163$	−16.5023	+	9.52761i	−1.29256	+	0.746260i	−0.979107	−	0.203344i	$-0.934819\pi$
$163$	−16.5023	+	9.52761i	−1.29256	+	0.746260i	−0.313452	+	0.949604i	$0.601486\pi$
$164$	−1.65030	+	2.85840i	−0.128867	+	0.223204i
$165$	9.89013	+	16.0469i	0.769946	+	1.24925i
$166$	−9.31702	+	5.37919i	−0.723141	+	0.417506i
$167$	8.96444	−	5.17562i	0.693689	−	0.400501i	−0.111304	−	0.993786i	$-0.535503\pi$
$167$	8.96444	−	5.17562i	0.693689	−	0.400501i	0.804993	+	0.593285i	$0.202169\pi$
$168$	0.394992	−	0.731943i	0.0304743	−	0.0564707i
$169$	−5.58749	+	9.67781i	−0.429807	+	0.744447i
$170$	3.25657	−	1.88018i	0.249767	−	0.144203i
$171$	0.0663424	+	1.15299i	0.00507333	+	0.0881715i
$172$	7.47606	+	4.31631i	0.570044	+	0.329115i
$173$	1.93394	−	3.34967i	0.147034	−	0.254671i	−0.783096	−	0.621901i	$-0.786361\pi$
$173$	1.93394	−	3.34967i	0.147034	−	0.254671i	0.930130	+	0.367230i	$0.119694\pi$
$174$	−9.50908	−	5.13156i	−0.720881	−	0.389022i
$175$	−1.65154	+	2.86055i	−0.124845	+	0.216237i
$176$	−3.15766			−0.238018
$177$	0.280071	−	0.518988i	0.0210514	−	0.0390096i
$178$	−2.49130			−0.186731
$179$			2.26842i			0.169550i	0.996400	+	0.0847748i	$0.0270171\pi$
$179$			2.26842i			0.169550i	−0.996400	+	0.0847748i	$0.972983\pi$
$180$	−0.593952	−	10.3225i	−0.0442706	−	0.769397i
$181$	−1.66515	+	2.88412i	−0.123769	+	0.214375i	−0.921251	−	0.388968i	$-0.872832\pi$
$181$	−1.66515	+	2.88412i	−0.123769	+	0.214375i	0.797482	+	0.603343i	$0.206165\pi$
$182$	0.648712			0.0480857
$183$	−11.6944	+	21.6704i	−0.864474	+	1.60192i
$184$	−3.99473	+	6.91907i	−0.294495	+	0.510081i
$185$	−13.0324	+	16.4215i	−0.958162	+	1.20733i
$186$	−0.207020	−	7.20172i	−0.0151794	−	0.528056i
$187$	2.98361	+	1.72259i	0.218183	+	0.125968i
$188$	5.93648	−	10.2823i	0.432963	−	0.749913i
$189$	0.214851	+	2.48590i	0.0156281	+	0.180822i
$190$	1.14904	+	0.663401i	0.0833604	+	0.0481282i
$191$	−4.54498	+	2.62405i	−0.328863	+	0.189869i	−0.655336	−	0.755337i	$-0.727473\pi$
$191$	−4.54498	+	2.62405i	−0.328863	+	0.189869i	0.326473	+	0.945207i	$0.394140\pi$
$192$	1.52427	+	0.822567i	0.110004	+	0.0593636i
$193$	−5.51469	−	3.18391i	−0.396956	−	0.229183i	0.288214	−	0.957566i	$-0.406939\pi$
$193$	−5.51469	−	3.18391i	−0.396956	−	0.229183i	−0.685170	+	0.728384i	$0.740272\pi$
$194$	12.6282			0.906652
$195$	6.86533	−	4.23128i	0.491637	−	0.303008i
$196$	−3.38471	−	5.86248i	−0.241765	−	0.418749i
$197$	−3.14271	−	5.44333i	−0.223909	−	0.387821i	0.732083	−	0.681216i	$-0.238548\pi$
$197$	−3.14271	−	5.44333i	−0.223909	−	0.387821i	−0.955991	+	0.293394i	$0.905215\pi$
$198$	7.91821	−	5.19993i	0.562723	−	0.369543i
$199$			13.2707i			0.940735i	0.882471	+	0.470368i	$0.155879\pi$
$199$			13.2707i			0.940735i	−0.882471	+	0.470368i	$0.844121\pi$
$200$	−5.95707	−	3.43932i	−0.421228	−	0.243196i
$201$	−0.442610	−	15.3973i	−0.0312193	−	1.08605i
$202$		−	0.984791i		−	0.0692897i
$203$	2.59433	−	1.49784i	0.182086	−	0.105128i
$204$	−0.991516	−	1.60875i	−0.0694200	−	0.112635i
$205$	−9.85159	−	5.68782i	−0.688065	−	0.397254i
$206$	0.602776	+	1.04404i	0.0419974	+	0.0727417i
$207$	−1.37685	−	23.9288i	−0.0956974	−	1.66317i
$208$			1.35094i			0.0936706i
$209$			1.21559i			0.0840843i
$210$	2.52267	+	1.36135i	0.174081	+	0.0939424i
$211$	−8.29561	+	14.3684i	−0.571093	+	0.989163i	0.425361	+	0.905024i	$0.360147\pi$
$211$	−8.29561	+	14.3684i	−0.571093	+	0.989163i	−0.996454	+	0.0841389i	$0.973186\pi$
$212$	−1.47126	+	2.54830i	−0.101047	+	0.175018i
$213$	−3.08150	+	1.89920i	−0.211141	+	0.130131i
$214$	−13.6621	+	7.88782i	−0.933922	+	0.539200i
$215$	−14.8763	+	25.7665i	−1.01456	+	1.75726i
$216$	−5.17685	+	0.447426i	−0.352240	+	0.0304435i
$217$	1.72983	+	0.998716i	0.117428	+	0.0677973i
$218$	−5.07180			−0.343506
$219$	11.1584	+	6.02162i	0.754016	+	0.406904i
$220$		−	10.8830i		−	0.733732i
$221$	0.736972	−	1.27647i	0.0495741	−	0.0858649i
$222$	8.43737	+	6.30957i	0.566279	+	0.423471i
$223$	−9.16344	−	15.8715i	−0.613629	−	1.06284i	−0.990623	−	0.136621i	$-0.956376\pi$
$223$	−9.16344	−	15.8715i	−0.613629	−	1.06284i	0.376994	−	0.926216i	$-0.376958\pi$
$224$	−0.415860	+	0.240097i	−0.0277858	+	0.0160422i
$225$	20.6018	−	1.18541i	1.37345	−	0.0790276i
$226$	−0.297564	+	0.515396i	−0.0197937	+	0.0342837i
$227$		−	1.86789i		−	0.123977i	−0.998077	−	0.0619883i	$-0.980256\pi$
$227$		−	1.86789i		−	0.123977i	0.998077	−	0.0619883i	$-0.0197441\pi$
$228$	0.316661	−	0.586791i	0.0209714	−	0.0388612i
$229$	−3.40970	−	5.90577i	−0.225319	−	0.390264i	0.731096	−	0.682275i	$-0.239009\pi$
$229$	−3.40970	−	5.90577i	−0.225319	−	0.390264i	−0.956415	+	0.292011i	$0.905676\pi$
$230$	−23.8469	−	13.7680i	−1.57241	−	0.907834i
$231$	0.0754639	+	2.62521i	0.00496516	+	0.172726i
$232$	3.11923	+	5.40267i	0.204788	+	0.354703i
$233$	−28.3171			−1.85512			−0.927559	−	0.373678i	$-0.878097\pi$
$233$	−28.3171			−1.85512			−0.927559	+	0.373678i	$0.878097\pi$
$234$	−2.22468	−	3.38763i	−0.145432	−	0.221457i
$235$	35.4383	+	20.4603i	2.31174	+	1.33468i
$236$	−0.294868	+	0.170242i	−0.0191943	+	0.0110818i
$237$	−13.4056	+	24.8414i	−0.870788	+	1.61362i
$238$	0.523918			0.0339605
$239$		−	19.4823i		−	1.26021i	−0.776511	−	0.630104i	$-0.783012\pi$
$239$		−	19.4823i		−	1.26021i	0.776511	−	0.630104i	$-0.216988\pi$
$240$	−2.83501	+	5.25344i	−0.182999	+	0.339108i
$241$			23.8689i			1.53753i	0.639530	+	0.768766i	$0.279129\pi$
$241$			23.8689i			1.53753i	−0.639530	+	0.768766i	$0.720871\pi$
$242$	−0.891300	+	0.514592i	−0.0572949	+	0.0330792i
$243$	12.2448	−	9.64705i	0.785503	−	0.618858i
$244$	12.3122	−	7.10847i	0.788210	−	0.455073i
$245$	20.2053	−	11.6655i	1.29087	−	0.745283i
$246$	−2.71496	+	5.03098i	−0.173100	+	0.320764i
$247$	0.520065			0.0330909
$248$	−2.07982	+	3.60235i	−0.132069	+	0.228749i
$249$	−15.8632	+	9.77687i	−1.00529	+	0.619584i
$250$	3.23739	−	5.60732i	0.204750	−	0.354638i
$251$		−	15.8983i		−	1.00349i	−0.865016	−	0.501745i	$-0.832692\pi$
$251$		−	15.8983i		−	1.00349i	0.865016	−	0.501745i	$-0.167308\pi$
$252$	0.647436	−	1.28690i	0.0407846	−	0.0810669i
$253$		−	25.2280i		−	1.58607i
$254$		−	6.78151i		−	0.425510i
$255$	5.54464	−	3.41730i	0.347219	−	0.213999i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$		−	16.9104i		−	1.05484i	−0.849604	−	0.527421i	$-0.823159\pi$
$257$		−	16.9104i		−	1.05484i	0.849604	−	0.527421i	$-0.176841\pi$
$258$	13.1584	+	7.10090i	0.819206	+	0.442083i
$259$	−2.71647	+	1.07354i	−0.168793	+	0.0667067i
$260$	−4.65605			−0.288756
$261$	−16.7188	−	8.41119i	−1.03487	−	0.520640i
$262$	−4.03539	+	6.98950i	−0.249307	+	0.431813i
$263$	22.9136			1.41291			0.706455	−	0.707757i	$-0.250293\pi$
$263$	22.9136			1.41291			0.706455	+	0.707757i	$0.250293\pi$
$264$	−5.46697	+	0.157153i	−0.336469	+	0.00967209i
$265$	−8.78283	−	5.07077i	−0.539525	−	0.311495i
$266$	0.0924293	+	0.160092i	0.00566721	+	0.00981589i
$267$	−4.31327	+	0.123989i	−0.263968	+	0.00758799i
$268$	−4.44667	+	7.70185i	−0.271623	+	0.470466i
$269$	−18.9536			−1.15562			−0.577812	−	0.816170i	$-0.696093\pi$
$269$	−18.9536			−1.15562			−0.577812	+	0.816170i	$0.696093\pi$
$270$	−1.54207	−	17.8422i	−0.0938474	−	1.08584i
$271$	2.10857	+	3.65215i	0.128086	+	0.221852i	0.922935	−	0.384955i	$-0.125783\pi$
$271$	2.10857	+	3.65215i	0.128086	+	0.221852i	−0.794849	+	0.606808i	$0.792450\pi$
$272$			1.09105i			0.0661549i
$273$	1.12314	−	0.0322856i	0.0679754	−	0.00195401i
$274$		−	0.169617i		−	0.0102469i
$275$	21.7204			1.30979
$276$	−6.57186	+	12.1780i	−0.395580	+	0.733032i
$277$		−	30.8890i		−	1.85594i	−0.372654	−	0.927971i	$-0.621552\pi$
$277$		−	30.8890i		−	1.85594i	0.372654	−	0.927971i	$-0.378448\pi$
$278$	−7.49457	−	4.32699i	−0.449494	−	0.259516i
$279$	−0.716842	−	12.4583i	−0.0429162	−	0.745859i
$280$	−0.827504	−	1.43328i	−0.0494528	−	0.0856548i
$281$	28.0267	+	16.1812i	1.67193	+	0.965290i	0.966556	+	0.256456i	$0.0825549\pi$
$281$	28.0267	+	16.1812i	1.67193	+	0.965290i	0.705375	+	0.708834i	$0.250778\pi$
$282$	9.76631	−	18.0975i	0.581575	−	1.07769i
$283$	−14.1673	+	8.17949i	−0.842158	+	0.486220i	−0.857997	−	0.513655i	$-0.828291\pi$
$283$	−14.1673	+	8.17949i	−0.842158	+	0.486220i	0.0158393	+	0.999875i	$0.494958\pi$
$284$	2.08986			0.124011
$285$	2.02240	+	1.09138i	0.119796	+	0.0646480i
$286$	−2.13290	−	3.69429i	−0.126121	−	0.218448i
$287$	−0.792464	−	1.37259i	−0.0467776	−	0.0810213i
$288$	2.67995	+	1.34828i	0.157918	+	0.0794481i
$289$	−7.90480	+	13.6915i	−0.464988	+	0.805383i
$290$	−18.6205	+	10.7506i	−1.09343	+	0.631295i
$291$	21.8637	−	0.628490i	1.28167	−	0.0368427i
$292$	−3.66026	−	6.33976i	−0.214201	−	0.371007i
$293$	−8.99539	−	15.5805i	−0.525516	−	0.910221i	−0.999558	−	0.0297185i	$-0.990539\pi$
$293$	−8.99539	−	15.5805i	−0.525516	−	0.910221i	0.474042	−	0.880502i	$-0.342794\pi$
$294$	−6.15183	−	9.98147i	−0.358782	−	0.582131i
$295$	−0.586746	−	1.01627i	−0.0341617	−	0.0591698i
$296$	−2.23564	−	5.65702i	−0.129944	−	0.328808i
$297$	13.4503	−	9.39691i	0.780465	−	0.545264i
$298$	4.39456	−	2.53720i	0.254570	−	0.146976i
$299$	−10.7932			−0.624190
$300$	−10.4849	−	5.65813i	−0.605343	−	0.326672i
$301$	−3.58996	+	2.07267i	−0.206922	+	0.119466i
$302$	−4.27082	−	2.46576i	−0.245758	−	0.141889i
$303$	−0.0490118	−	1.70500i	−0.00281566	−	0.0979499i
$304$	−0.333391	+	0.192483i	−0.0191213	+	0.0110397i
$305$	24.4996	+	42.4346i	1.40285	+	2.42980i
$306$	−1.79671	−	2.73595i	−0.102711	−	0.156404i
$307$	−8.71513			−0.497399			−0.248699	−	0.968581i	$-0.580003\pi$
$307$	−8.71513			−0.497399			−0.248699	+	0.968581i	$0.580003\pi$
$308$	0.758145	−	1.31315i	0.0431993	−	0.0748234i
$309$	1.09557	+	1.77758i	0.0623247	+	0.101123i
$310$	−12.4156	−	7.16817i	−0.705161	−	0.407125i
$311$		−	24.5989i		−	1.39487i	−0.716646	−	0.697437i	$-0.754324\pi$
$311$		−	24.5989i		−	1.39487i	0.716646	−	0.697437i	$-0.245676\pi$
$312$	0.0672344	+	2.33892i	0.00380640	+	0.132415i
$313$	−8.97718	−	5.18298i	−0.507420	−	0.292959i	0.224352	−	0.974508i	$-0.427973\pi$
$313$	−8.97718	−	5.18298i	−0.507420	−	0.292959i	−0.731773	+	0.681549i	$0.761307\pi$
$314$	−6.12555	−	3.53659i	−0.345685	−	0.199581i
$315$	4.43534	+	2.23141i	0.249903	+	0.125726i
$316$	14.1139	−	8.14864i	0.793967	−	0.458397i
$317$	−14.9365	+	25.8708i	−0.838918	+	1.45305i	0.0518816	+	0.998653i	$0.483478\pi$
$317$	−14.9365	+	25.8708i	−0.838918	+	1.45305i	−0.890800	+	0.454396i	$0.849855\pi$
$318$	−2.42043	+	4.48519i	−0.135731	+	0.251517i
$319$	−17.0598	−	9.84948i	−0.955165	−	0.551465i
$320$	2.98479	−	1.72327i	0.166855	−	0.0963337i
$321$	−23.2611	+	14.3364i	−1.29831	+	0.800180i
$322$	−1.91825	−	3.32250i	−0.106900	−	0.185156i
$323$	0.420019			0.0233705
$324$	−8.94060	+	1.03229i	−0.496700	+	0.0573494i
$325$		−	9.29259i		−	0.515460i
$326$	19.0552			1.05537
$327$	−8.78098	+	0.252417i	−0.485590	+	0.0139587i
$328$	2.85840	−	1.65030i	0.157829	−	0.0911224i
$329$	2.85067	+	4.93750i	0.157162	+	0.272213i
$330$	−0.541633	−	18.8421i	−0.0298159	−	1.03722i
$331$	−20.3700	−	11.7606i	−1.11964	−	0.646423i	−0.178329	−	0.983971i	$-0.557069\pi$
$331$	−20.3700	−	11.7606i	−1.11964	−	0.646423i	−0.941308	+	0.337548i	$0.890403\pi$
$332$	10.7584			0.590442
$333$	14.9219	+	10.5041i	0.817718	+	0.575620i
$334$	−10.3512			−0.566395
$335$	−26.5447	−	15.3256i	−1.45029	−	0.837328i
$336$	−0.708045	+	0.436386i	−0.0386270	+	0.0238068i
$337$	2.11229	+	3.65859i	0.115064	+	0.199296i	0.917805	−	0.397031i	$-0.129959\pi$
$337$	2.11229	+	3.65859i	0.115064	+	0.199296i	−0.802741	+	0.596327i	$0.796626\pi$
$338$	9.67781	−	5.58749i	0.526403	−	0.303919i
$339$	−0.489533	+	0.907133i	−0.0265878	+	0.0492687i
$340$	−3.76036			−0.203934
$341$		−	13.1347i		−	0.711285i
$342$	0.519042	−	1.03169i	0.0280666	−	0.0557875i
$343$	6.61199			0.357014
$344$	−4.31631	−	7.47606i	−0.232720	−	0.403082i
$345$	−41.9721	−	22.6502i	−2.25970	−	1.21944i
$346$	−3.34967	+	1.93394i	−0.180080	+	0.103969i
$347$	22.1211	+	12.7716i	1.18752	+	0.685616i	0.957743	−	0.287627i	$-0.0928662\pi$
$347$	22.1211	+	12.7716i	1.18752	+	0.685616i	0.229779	+	0.973243i	$0.426200\pi$
$348$	5.66932	+	9.19860i	0.303908	+	0.493097i
$349$	−12.8280	+	22.2188i	−0.686667	+	1.18934i	0.286243	+	0.958157i	$0.407594\pi$
$349$	−12.8280	+	22.2188i	−0.686667	+	1.18934i	−0.972910	+	0.231185i	$0.925740\pi$
$350$	2.86055	−	1.65154i	0.152903	−	0.0882785i
$351$	−4.02026	−	5.75441i	−0.214586	−	0.307148i
$352$	2.73461	+	1.57883i	0.145755	+	0.0841519i
$353$	−15.7201	−	9.07598i	−0.836695	−	0.483066i	0.0194447	−	0.999811i	$-0.493810\pi$
$353$	−15.7201	−	9.07598i	−0.836695	−	0.483066i	−0.856139	+	0.516745i	$0.827143\pi$
$354$	−0.502043	+	0.309422i	−0.0266833	+	0.0164456i
$355$			7.20280i			0.382285i
$356$	2.15753	+	1.24565i	0.114349	+	0.0660192i
$357$	0.907078	−	0.0260747i	0.0480076	−	0.00138002i
$358$	1.13421	−	1.96451i	0.0599449	−	0.103828i
$359$	3.62838			0.191499			0.0957493	−	0.995405i	$-0.469475\pi$
$359$	3.62838			0.191499			0.0957493	+	0.995405i	$0.469475\pi$
$360$	−4.64689	+	9.23656i	−0.244913	+	0.486809i
$361$	−9.42590	−	16.3261i	−0.496100	−	0.859270i
$362$	2.88412	−	1.66515i	0.151586	−	0.0875182i
$363$	−1.51753	+	0.935290i	−0.0796496	+	0.0490900i
$364$	−0.561801	−	0.324356i	−0.0294464	−	0.0170009i
$365$	21.8502	−	12.6152i	1.14369	−	0.660312i
$366$	20.9628	−	12.9199i	1.09575	−	0.675335i
$367$	−22.6758			−1.18367			−0.591835	−	0.806059i	$-0.701596\pi$
$367$	−22.6758			−1.18367			−0.591835	+	0.806059i	$0.701596\pi$
$368$	6.91907	−	3.99473i	0.360682	−	0.208240i
$369$	−4.45012	+	8.84544i	−0.231664	+	0.460475i
$370$	19.4971	−	7.70523i	1.01361	−	0.400576i
$371$	−0.706493	−	1.22368i	−0.0366793	−	0.0635304i
$372$	−3.42158	+	6.34039i	−0.177401	+	0.328734i
$373$	13.3477	+	23.1189i	0.691117	+	1.19705i	0.971472	+	0.237154i	$0.0762145\pi$
$373$	13.3477	+	23.1189i	0.691117	+	1.19705i	−0.280355	+	0.959896i	$0.590452\pi$
$374$	−1.72259	−	2.98361i	−0.0890729	−	0.154279i
$375$	5.32593	−	9.86927i	0.275030	−	0.509647i
$376$	−10.2823	+	5.93648i	−0.530269	+	0.306151i
$377$	−4.21389	+	7.29866i	−0.217026	+	0.375900i
$378$	1.05688	−	2.26027i	0.0543601	−	0.116256i
$379$	−11.6509	−	20.1799i	−0.598466	−	1.03657i	−0.993048	−	0.117712i	$-0.962444\pi$
$379$	−11.6509	−	20.1799i	−0.598466	−	1.03657i	0.394582	−	0.918861i	$-0.370889\pi$
$380$	−0.663401	−	1.14904i	−0.0340317	−	0.0589447i
$381$	−0.337507	−	11.7411i	−0.0172910	−	0.601513i
$382$	5.24809			0.268516
$383$	12.3960	−	7.15683i	0.633406	−	0.365697i	−0.148664	−	0.988888i	$-0.547497\pi$
$383$	12.3960	−	7.15683i	0.633406	−	0.365697i	0.782070	+	0.623191i	$0.214164\pi$
$384$	−0.908769	−	1.47450i	−0.0463754	−	0.0752451i
$385$	4.52581	+	2.61298i	0.230657	+	0.133170i
$386$	3.18391	+	5.51469i	0.162057	+	0.280690i
$387$	23.1350	+	11.6392i	1.17602	+	0.591652i
$388$	−10.9363	−	6.31410i	−0.555209	−	0.320550i
$389$			18.7709i			0.951722i	0.879520	+	0.475861i	$0.157864\pi$
$389$			18.7709i			0.951722i	−0.879520	+	0.475861i	$0.842136\pi$
$390$	−8.06119	+	0.231726i	−0.408194	+	0.0117339i
$391$	−8.71693			−0.440834
$392$			6.76941i			0.341907i
$393$	−6.63876	+	12.3020i	−0.334881	+	0.620554i
$394$			6.28542i			0.316655i
$395$	28.0846	+	48.6440i	1.41309	+	2.44754i
$396$	−9.45734	+	0.544169i	−0.475249	+	0.0273455i
$397$	39.5953			1.98723			0.993616	−	0.112812i	$-0.0359857\pi$
$397$	39.5953			1.98723			0.993616	+	0.112812i	$0.0359857\pi$
$398$	6.63535	−	11.4928i	0.332600	−	0.576080i
$399$	0.167994	+	0.272573i	0.00841021	+	0.0136457i
$400$	3.43932	+	5.95707i	0.171966	+	0.297853i
$401$	24.0748	+	13.8996i	1.20224	+	0.694111i	0.961052	−	0.276368i	$-0.0891309\pi$
$401$	24.0748	+	13.8996i	1.20224	+	0.694111i	0.241184	+	0.970479i	$0.422464\pi$
$402$	−7.31536	+	13.5558i	−0.364857	+	0.676102i
$403$	−5.61940			−0.279922
$404$	−0.492396	+	0.852854i	−0.0244976	+	0.0424311i
$405$	−3.55783	−	30.8141i	−0.176790	−	1.53117i
$406$	−2.99568			−0.148673
$407$	15.0451	+	11.9401i	0.745758	+	0.591847i
$408$	0.0543004	+	1.88898i	0.00268827	+	0.0935185i
$409$		−	14.7125i		−	0.727486i	−0.931499	−	0.363743i	$-0.881499\pi$
$409$		−	14.7125i		−	0.727486i	0.931499	−	0.363743i	$-0.118501\pi$
$410$	5.68782	+	9.85159i	0.280901	+	0.486535i
$411$	−0.00844162	−	0.293664i	−0.000416395	−	0.0144854i
$412$		−	1.20555i		−	0.0593933i
$413$		−	0.163499i		−	0.00804524i
$414$	−10.7720	+	21.4114i	−0.529416	+	1.05231i
$415$			37.0792i			1.82014i
$416$	0.675468	−	1.16995i	0.0331175	−	0.0573613i
$417$	−13.1910	−	7.11848i	−0.645964	−	0.348593i
$418$	0.607797	−	1.05273i	0.0297283	−	0.0514909i
$419$	−0.661695			−0.0323259			−0.0161630	−	0.999869i	$-0.505145\pi$
$419$	−0.661695			−0.0323259			−0.0161630	+	0.999869i	$0.505145\pi$
$420$	−1.50402	−	2.44030i	−0.0733887	−	0.119075i
$421$	−19.0635	+	11.0063i	−0.929098	+	0.536415i	−0.886526	−	0.462678i	$-0.846889\pi$
$421$	−19.0635	+	11.0063i	−0.929098	+	0.536415i	−0.0425721	+	0.999093i	$0.513555\pi$
$422$	14.3684	−	8.29561i	0.699444	−	0.403824i
$423$	16.0081	−	31.8190i	0.778339	−	1.54709i
$424$	2.54830	−	1.47126i	0.123757	−	0.0714509i
$425$		−	7.50496i		−	0.364044i
$426$	3.61826	−	0.104010i	0.175305	−	0.00503930i
$427$			6.82690i			0.330377i
$428$	15.7756			0.762544
$429$	−3.87662	−	6.28990i	−0.187165	−	0.303679i
$430$	25.7665	−	14.8763i	1.24257	−	0.717400i
$431$	−5.70464	−	3.29357i	−0.274783	−	0.158646i	0.356276	−	0.934381i	$-0.384046\pi$
$431$	−5.70464	−	3.29357i	−0.274783	−	0.158646i	−0.631059	+	0.775735i	$0.717379\pi$
$432$	4.70700	+	2.20094i	0.226466	+	0.105893i
$433$	−12.7700			−0.613686			−0.306843	−	0.951760i	$-0.599273\pi$
$433$	−12.7700			−0.613686			−0.306843	+	0.951760i	$0.599273\pi$
$434$	−0.998716	−	1.72983i	−0.0479399	−	0.0830344i
$435$	−31.7033	+	19.5395i	−1.52006	+	0.936850i
$436$	4.39231	+	2.53590i	0.210353	+	0.121448i
$437$	−1.53784	−	2.66361i	−0.0735647	−	0.127418i
$438$	−6.65267	−	10.7941i	−0.317877	−	0.515762i
$439$		−	35.9750i		−	1.71699i	−0.512819	−	0.858497i	$-0.671399\pi$
$439$		−	35.9750i		−	1.71699i	0.512819	−	0.858497i	$-0.328601\pi$
$440$	−5.44150	+	9.42495i	−0.259413	+	0.449317i
$441$	−11.1477	−	16.9751i	−0.530841	−	0.808339i
$442$	−1.27647	+	0.736972i	−0.0607156	+	0.0350542i
$443$	−7.80056	−	13.5110i	−0.370616	−	0.641925i	0.619045	−	0.785356i	$-0.287520\pi$
$443$	−7.80056	−	13.5110i	−0.370616	−	0.641925i	−0.989660	+	0.143430i	$0.954187\pi$
$444$	−4.15219	−	9.68294i	−0.197054	−	0.459532i
$445$	−4.29318	+	7.43600i	−0.203516	+	0.352500i
$446$			18.3269i			0.867803i
$447$	7.48218	−	4.61145i	0.353895	−	0.218114i
$448$	0.480194			0.0226870
$449$	−7.19308	−	4.15293i	−0.339462	−	0.195989i	0.320572	−	0.947224i	$-0.396125\pi$
$449$	−7.19308	−	4.15293i	−0.339462	−	0.195989i	−0.660034	+	0.751235i	$0.729458\pi$
$450$	−18.4344	−	9.27431i	−0.869006	−	0.437195i
$451$	−5.21108	+	9.02585i	−0.245380	+	0.425011i
$452$	0.515396	−	0.297564i	0.0242422	−	0.0139962i
$453$	−7.51694	−	4.05651i	−0.353177	−	0.190591i
$454$	−0.933947	+	1.61764i	−0.0438323	+	0.0759198i
$455$	1.11791	−	1.93627i	0.0524082	−	0.0907737i
$456$	−0.567632	+	0.349845i	−0.0265818	+	0.0163830i
$457$		−	3.28231i		−	0.153540i	−0.997049	−	0.0767700i	$-0.975539\pi$
$457$		−	3.28231i		−	0.153540i	0.997049	−	0.0767700i	$-0.0244607\pi$
$458$			6.81939i			0.318649i
$459$	−3.24688	−	4.64742i	−0.151551	−	0.216923i
$460$	13.7680	+	23.8469i	0.641936	+	1.11187i
$461$	27.7237	+	16.0063i	1.29122	+	0.745487i	0.978871	−	0.204480i	$-0.0655502\pi$
$461$	27.7237	+	16.0063i	1.29122	+	0.745487i	0.312351	+	0.949967i	$0.398884\pi$
$462$	1.24725	−	2.31123i	0.0580273	−	0.107528i
$463$	−18.2739	+	10.5505i	−0.849261	+	0.490321i	−0.860402	−	0.509617i	$-0.829787\pi$
$463$	−18.2739	+	10.5505i	−0.849261	+	0.490321i	0.0111402	+	0.999938i	$0.496454\pi$
$464$		−	6.23847i		−	0.289614i
$465$	−21.8524	−	11.7926i	−1.01338	−	0.546869i
$466$	24.5234	+	14.1586i	1.13602	+	0.655883i
$467$			26.7437i			1.23755i	0.785568	+	0.618776i	$0.212371\pi$
$467$			26.7437i			1.23755i	−0.785568	+	0.618776i	$0.787629\pi$
$468$	0.232811	+	4.04612i	0.0107617	+	0.187032i
$469$	−2.13526	−	3.69839i	−0.0985973	−	0.170776i
$470$	−20.4603	−	35.4383i	−0.943764	−	1.63465i
$471$	−10.7814	−	5.81816i	−0.496781	−	0.268087i
$472$	0.340484			0.0156721
$473$	23.6069	+	13.6294i	1.08544	+	0.626682i
$474$	24.0303	−	14.8105i	1.10375	−	0.680267i
$475$	2.29327	−	1.32402i	0.105223	−	0.0607502i
$476$	−0.453726	−	0.261959i	−0.0207965	−	0.0120069i
$477$	−3.96735	+	7.88584i	−0.181652	+	0.361068i
$478$	−9.74117	+	16.8722i	−0.445551	+	0.771716i
$479$	−6.20074	−	3.58000i	−0.283319	−	0.163574i	0.351606	−	0.936148i	$-0.385636\pi$
$479$	−6.20074	−	3.58000i	−0.283319	−	0.163574i	−0.634925	+	0.772574i	$0.718969\pi$
$480$	5.08191	−	3.13211i	0.231956	−	0.142960i
$481$	5.10830	−	6.43672i	0.232918	−	0.293489i
$482$	11.9345	−	20.6711i	0.543600	−	0.941542i
$483$	−3.48648	−	5.65689i	−0.158641	−	0.257398i
$484$	1.02918			0.0467811
$485$	21.7618	−	37.6925i	0.988153	−	1.71153i
$486$	−15.4278	+	2.23220i	−0.699820	+	0.101255i
$487$		−	24.2615i		−	1.09939i	−0.835364	−	0.549697i	$-0.814743\pi$
$487$		−	24.2615i		−	1.09939i	0.835364	−	0.549697i	$-0.185257\pi$
$488$	−14.2169			−0.643571
$489$	32.9910	−	0.948354i	1.49190	−	0.0428861i
$490$	−23.3310			−1.05399
$491$	−16.1023	+	27.8901i	−0.726688	+	1.25866i	0.231587	+	0.972814i	$0.425608\pi$
$491$	−16.1023	+	27.8901i	−0.726688	+	1.25866i	−0.958275	+	0.285847i	$0.907725\pi$
$492$	4.86672	−	2.99948i	0.219408	−	0.135227i
$493$	−3.40325	+	5.89460i	−0.153275	+	0.265480i
$494$	−0.450390	−	0.260033i	−0.0202640	−	0.0116994i
$495$	−1.87550	−	32.5951i	−0.0842974	−	1.46504i
$496$	3.60235	−	2.07982i	0.161750	−	0.0933866i
$497$	−0.501770	+	0.869092i	−0.0225075	+	0.0389841i
$498$	18.6264	−	0.535431i	0.834667	−	0.0239932i
$499$	−15.9643	+	9.21700i	−0.714661	+	0.412610i	−0.812784	−	0.582565i	$-0.802049\pi$
$499$	−15.9643	+	9.21700i	−0.714661	+	0.412610i	0.0981237	+	0.995174i	$0.468716\pi$
$500$	−5.60732	+	3.23739i	−0.250767	+	0.144780i
$501$	−17.9215	+	0.515168i	−0.800672	+	0.0230160i
$502$	−7.94913	+	13.7683i	−0.354787	+	0.614509i
$503$	−28.9751	+	16.7288i	−1.29193	+	0.745898i	−0.978997	−	0.203876i	$-0.934646\pi$
$503$	−28.9751	+	16.7288i	−1.29193	+	0.745898i	−0.312937	+	0.949774i	$0.601313\pi$
$504$	−1.20414	+	0.790768i	−0.0536369	+	0.0352236i
$505$	−2.93940	−	1.69706i	−0.130801	−	0.0755182i
$506$	−12.6140	+	21.8481i	−0.560760	+	0.971266i
$507$	16.4775	−	10.1555i	0.731789	−	0.451020i
$508$	−3.39075	+	5.87296i	−0.150440	+	0.260570i
$509$	−19.1727			−0.849817			−0.424908	−	0.905236i	$-0.639694\pi$
$509$	−19.1727			−0.849817			−0.424908	+	0.905236i	$0.639694\pi$
$510$	−6.51044	+	0.187148i	−0.288287	+	0.00828707i
$511$	3.51528			0.155507
$512$			1.00000i			0.0441942i
$513$	0.847290	−	1.81204i	0.0374088	−	0.0800034i
$514$	−8.45521	+	14.6449i	−0.372943	+	0.645957i
$515$	4.15498			0.183091
$516$	−7.84505	−	12.7288i	−0.345359	−	0.560352i
$517$	18.7454	−	32.4680i	0.824421	−	1.42794i
$518$	2.88930	+	0.428519i	0.126949	+	0.0188280i
$519$	−5.70316	+	3.51500i	−0.250341	+	0.154291i
$520$	4.03226	+	2.32803i	0.176826	+	0.102091i
$521$	18.7964	−	32.5563i	0.823485	−	1.42632i	−0.0795871	−	0.996828i	$-0.525360\pi$
$521$	18.7964	−	32.5563i	0.823485	−	1.42632i	0.903072	−	0.429489i	$-0.141306\pi$
$522$	10.2733	+	15.6437i	0.449650	+	0.684706i
$523$	−5.51977	−	3.18684i	−0.241363	−	0.139351i	0.374440	−	0.927251i	$-0.377835\pi$
$523$	−5.51977	−	3.18684i	−0.241363	−	0.139351i	−0.615803	+	0.787900i	$0.711168\pi$
$524$	6.98950	−	4.03539i	0.305338	−	0.176287i
$525$	4.87038	−	3.00174i	0.212561	−	0.131006i
$526$	−19.8437	−	11.4568i	−0.865228	−	0.499539i
$527$	−4.53839			−0.197695
$528$	4.81311	+	2.59739i	0.209464	+	0.113037i
$529$	20.4157	+	35.3610i	0.887640	+	1.53744i
$530$	5.07077	+	8.78283i	0.220260	+	0.381502i
$531$	−0.853805	+	0.560699i	−0.0370520	+	0.0243322i
$532$		−	0.184859i		−	0.00801464i
$533$	3.86152	+	2.22945i	0.167261	+	0.0965681i
$534$	3.79740	+	2.04926i	0.164329	+	0.0886801i
$535$			54.3713i			2.35068i
$536$	7.70185	−	4.44667i	0.332669	−	0.192067i
$537$	1.86593	−	3.45767i	0.0805207	−	0.149210i
$538$	16.4143	+	9.47682i	0.707672	+	0.408575i
$539$	−10.6878	−	18.5117i	−0.460354	−	0.797357i
$540$	−7.58564	+	16.2229i	−0.326434	+	0.698121i
$541$			8.62312i			0.370737i	0.982669	+	0.185369i	$0.0593479\pi$
$541$			8.62312i			0.370737i	−0.982669	+	0.185369i	$0.940652\pi$
$542$		−	4.21714i		−	0.181142i
$543$	4.91051	−	3.02647i	0.210730	−	0.129878i
$544$	0.545527	−	0.944880i	0.0233893	−	0.0405114i
$545$	−8.74007	+	15.1383i	−0.374384	+	0.648452i
$546$	−0.988809	−	0.533609i	−0.0423171	−	0.0228364i
$547$	7.56083	−	4.36525i	0.323278	−	0.186644i	−0.329575	−	0.944129i	$-0.606905\pi$
$547$	7.56083	−	4.36525i	0.323278	−	0.186644i	0.652853	+	0.757485i	$0.273572\pi$
$548$	−0.0848084	+	0.146893i	−0.00362284	+	0.00627494i
$549$	35.6507	−	23.4120i	1.52153	−	0.999200i
$550$	−18.8104	−	10.8602i	−0.802078	−	0.463080i
$551$	−2.40160			−0.102312
$552$	11.7804	−	7.26057i	0.501408	−	0.309030i
$553$			7.82586i			0.332790i
$554$	−15.4445	+	26.7507i	−0.656174	+	1.13653i
$555$	33.3726	−	14.3107i	1.41659	−	0.607455i
$556$	4.32699	+	7.49457i	0.183505	+	0.317841i
$557$	24.9911	−	14.4286i	1.05891	−	0.611361i	0.133778	−	0.991011i	$-0.457289\pi$
$557$	24.9911	−	14.4286i	1.05891	−	0.611361i	0.925130	+	0.379651i	$0.123956\pi$
$558$	−5.60835	+	11.1476i	−0.237420	+	0.471917i
$559$	5.83106	−	10.0997i	0.246627	−	0.427171i
$560$			1.65501i			0.0699369i
$561$	−3.13087	−	5.07990i	−0.132185	−	0.214474i
$562$	−16.1812	−	28.0267i	−0.682563	−	1.18223i
$563$	−39.2375	−	22.6538i	−1.65366	−	0.954742i	−0.975548	−	0.219785i	$-0.929464\pi$
$563$	−39.2375	−	22.6538i	−1.65366	−	0.954742i	−0.678114	−	0.734957i	$-0.737202\pi$
$564$	−17.5066	+	10.7898i	−0.737163	+	0.454332i
$565$	1.02557	+	1.77633i	0.0431459	+	0.0747309i
$566$	16.3590			0.687619
$567$	1.71732	−	3.96589i	0.0721209	−	0.166552i
$568$	−1.80988	−	1.04493i	−0.0759407	−	0.0438444i
$569$	7.70454	−	4.44822i	0.322991	−	0.186479i	−0.329734	−	0.944074i	$-0.606959\pi$
$569$	7.70454	−	4.44822i	0.322991	−	0.186479i	0.652725	+	0.757595i	$0.273626\pi$
$570$	−1.20576	−	1.95636i	−0.0505036	−	0.0819431i
$571$	32.1759			1.34652			0.673259	−	0.739406i	$-0.264894\pi$
$571$	32.1759			1.34652			0.673259	+	0.739406i	$0.264894\pi$
$572$			4.26580i			0.178362i
$573$	9.08621	−	0.261191i	0.379582	−	0.0109114i
$574$			1.58493i			0.0661536i
$575$	−47.5937	+	27.4783i	−1.98480	+	1.14592i
$576$	−1.64677	−	2.50762i	−0.0686153	−	0.104484i
$577$	25.1077	−	14.4959i	1.04525	−	0.603474i	0.123933	−	0.992291i	$-0.460449\pi$
$577$	25.1077	−	14.4959i	1.04525	−	0.603474i	0.921315	+	0.388817i	$0.127116\pi$
$578$	13.6915	−	7.90480i	0.569492	−	0.328796i
$579$	5.78687	+	9.38931i	0.240494	+	0.390207i
$580$	21.5011			0.892785
$581$	−2.58305	+	4.47398i	−0.107163	+	0.185612i
$582$	−19.2487	−	10.3875i	−0.797886	−	0.430577i
$583$	−4.64575	+	8.04668i	−0.192407	+	0.333259i
$584$			7.32053i			0.302926i
$585$	−13.9451	+	0.802391i	−0.576559	+	0.0331748i
$586$			17.9908i			0.743192i
$587$			5.24695i			0.216565i	0.994120	+	0.108282i	$0.0345351\pi$
$587$			5.24695i			0.216565i	−0.994120	+	0.108282i	$0.965465\pi$
$588$	0.336905	+	11.7201i	0.0138937	+	0.483330i
$589$	−0.800660	−	1.38678i	−0.0329906	−	0.0571414i
$590$			1.17349i			0.0483119i
$591$	0.312817	+	10.8822i	0.0128676	+	0.447633i
$592$	−0.892387	+	6.01695i	−0.0366769	+	0.247295i
$593$	−8.42504			−0.345975			−0.172987	−	0.984924i	$-0.555342\pi$
$593$	−8.42504			−0.345975			−0.172987	+	0.984924i	$0.555342\pi$
$594$	−16.3467	+	1.41282i	−0.670715	+	0.0579686i
$595$	0.902852	−	1.56378i	0.0370133	−	0.0641089i
$596$	−5.07440			−0.207855
$597$	10.9160	−	20.2281i	0.446764	−	0.827880i
$598$	9.34723	+	5.39662i	0.382236	+	0.220684i
$599$	16.0499	+	27.7993i	0.655781	+	1.13585i	0.981697	+	0.190448i	$0.0609940\pi$
$599$	16.0499	+	27.7993i	0.655781	+	1.13585i	−0.325916	+	0.945399i	$0.605673\pi$
$600$	6.25109	+	10.1425i	0.255199	+	0.414066i
$601$	1.21888	−	2.11117i	0.0497193	−	0.0861163i	−0.840095	−	0.542440i	$-0.817501\pi$
$601$	1.21888	−	2.11117i	0.0497193	−	0.0861163i	0.889814	+	0.456323i	$0.150834\pi$
$602$	4.14533			0.168951
$603$	−11.9907	+	23.8337i	−0.488299	+	0.970584i
$604$	2.46576	+	4.27082i	0.100330	+	0.173777i
$605$			3.54712i			0.144211i
$606$	−0.810057	+	1.50108i	−0.0329063	+	0.0609773i
$607$		−	1.71604i		−	0.0696518i	−0.999393	−	0.0348259i	$-0.988912\pi$
$607$		−	1.71604i		−	0.0696518i	0.999393	−	0.0348259i	$-0.0110877\pi$
$608$	0.384966			0.0156125
$609$	−5.18652	+	0.149091i	−0.210168	+	0.00604148i
$610$		−	48.9993i		−	1.98392i
$611$	−13.8907	−	8.01981i	−0.561958	−	0.324447i
$612$	0.188024	+	3.26776i	0.00760044	+	0.132091i
$613$	17.8592	+	30.9331i	0.721327	+	1.24938i	0.960468	+	0.278390i	$0.0898009\pi$
$613$	17.8592	+	30.9331i	0.721327	+	1.24938i	−0.239141	+	0.970985i	$0.576866\pi$
$614$	7.54752	+	4.35756i	0.304593	+	0.175857i
$615$	10.3378	+	16.7733i	0.416861	+	0.676366i
$616$	−1.31315	+	0.758145i	−0.0529082	+	0.0305465i
$617$	47.0472			1.89405			0.947025	−	0.321159i	$-0.104072\pi$
$617$	47.0472			1.89405			0.947025	+	0.321159i	$0.104072\pi$
$618$	−0.0599989	−	2.08722i	−0.00241351	−	0.0839602i
$619$	17.1311	+	29.6720i	0.688558	+	1.19262i	0.972304	+	0.233718i	$0.0750892\pi$
$619$	17.1311	+	29.6720i	0.688558	+	1.19262i	−0.283747	+	0.958899i	$0.591578\pi$
$620$	7.16817	+	12.4156i	0.287881	+	0.498624i
$621$	−17.5844	+	37.6064i	−0.705636	+	1.50909i
$622$	−12.2994	+	21.3032i	−0.493162	+	0.854182i
$623$	−1.03603	+	0.598153i	−0.0415077	+	0.0239645i
$624$	1.11124	−	2.05918i	0.0444850	−	0.0824334i
$625$	6.03880	+	10.4595i	0.241552	+	0.418380i
$626$	5.18298	+	8.97718i	0.207153	+	0.358800i
$627$	0.999906	−	1.85289i	0.0399324	−	0.0739971i
$628$	3.53659	+	6.12555i	0.141125	+	0.244436i
$629$	4.12560	−	5.19847i	0.164499	−	0.207277i
$630$	−2.72541	−	4.15013i	−0.108583	−	0.165345i
$631$	8.67244	−	5.00704i	0.345244	−	0.199327i	−0.317344	−	0.948310i	$-0.602791\pi$
$631$	8.67244	−	5.00704i	0.345244	−	0.199327i	0.662589	+	0.748983i	$0.269458\pi$
$632$	−16.2973			−0.648271
$633$	24.4637	−	15.0776i	0.972345	−	0.599280i
$634$	25.8708	−	14.9365i	1.02746	−	0.593205i
$635$	−20.2414	−	11.6864i	−0.803254	−	0.463759i
$636$	4.33875	−	2.67408i	0.172043	−	0.106034i
$637$	−7.91984	+	4.57252i	−0.313796	+	0.181170i
$638$	9.84948	+	17.0598i	0.389945	+	0.675404i
$639$	6.25924	−	0.360152i	0.247612	−	0.0142474i
$640$	−3.44654			−0.136236
$641$	−2.64011	+	4.57281i	−0.104278	+	0.180615i	−0.913443	−	0.406967i	$-0.866587\pi$
$641$	−2.64011	+	4.57281i	−0.104278	+	0.180615i	0.809165	+	0.587582i	$0.199920\pi$
$642$	27.3129	−	0.785134i	1.07796	−	0.0309868i
$643$	−2.93253	−	1.69309i	−0.115648	−	0.0667691i	0.441060	−	0.897477i	$-0.354602\pi$
$643$	−2.93253	−	1.69309i	−0.115648	−	0.0667691i	−0.556708	+	0.830708i	$0.687936\pi$
$644$			3.83649i			0.151179i
$645$	43.8702	−	27.0383i	1.72739	−	1.06463i
$646$	−0.363747	−	0.210010i	−0.0143114	−	0.00826271i
$647$	15.0995	+	8.71769i	0.593622	+	0.342728i	0.766528	−	0.642211i	$-0.221983\pi$
$647$	15.0995	+	8.71769i	0.593622	+	0.342728i	−0.172907	+	0.984938i	$0.555316\pi$
$648$	8.25893	+	3.57631i	0.324442	+	0.140491i
$649$	−0.931093	+	0.537567i	−0.0365486	+	0.0211013i
$650$	−4.64630	+	8.04762i	−0.182243	+	0.315654i
$651$	−1.81520	−	2.94521i	−0.0711435	−	0.115432i
$652$	−16.5023	−	9.52761i	−0.646280	−	0.373130i
$653$	−41.2587	+	23.8207i	−1.61458	+	0.932178i	−0.626289	+	0.779591i	$0.715427\pi$
$653$	−41.2587	+	23.8207i	−1.61458	+	0.932178i	−0.988290	+	0.152587i	$0.951240\pi$
$654$	7.73076	+	4.17189i	0.302297	+	0.163134i
$655$	13.9081	+	24.0896i	0.543436	+	0.941258i
$656$	−3.30060			−0.128867
$657$	−12.0552	−	18.3571i	−0.470319	−	0.716179i
$658$		−	5.70133i		−	0.222261i
$659$	−3.97201			−0.154728			−0.0773638	−	0.997003i	$-0.524650\pi$
$659$	−3.97201			−0.154728			−0.0773638	+	0.997003i	$0.524650\pi$
$660$	−8.95199	+	16.5886i	−0.348456	+	0.645709i
$661$	18.4962	−	10.6788i	0.719420	−	0.415357i	−0.0951192	−	0.995466i	$-0.530323\pi$
$661$	18.4962	−	10.6788i	0.719420	−	0.415357i	0.814539	+	0.580109i	$0.196990\pi$
$662$	11.7606	+	20.3700i	0.457090	+	0.791704i
$663$	−2.17332	+	1.33947i	−0.0844049	+	0.0520209i
$664$	−9.31702	−	5.37919i	−0.361571	−	0.208753i
$665$	0.637123			0.0247066
$666$	−7.67075	−	16.5578i	−0.297235	−	0.641600i
$667$	49.8420			1.92989
$668$	8.96444	+	5.17562i	0.346844	+	0.200251i
$669$	0.912106	+	31.7300i	0.0352641	+	1.22675i
$670$	15.3256	+	26.5447i	0.592080	+	1.02551i
$671$	38.8779	−	22.4461i	1.50086	−	0.866524i
$672$	0.831377	−	0.0238987i	0.0320711	−	0.000921911i
$673$	−22.8244			−0.879816			−0.439908	−	0.898043i	$-0.644989\pi$
$673$	−22.8244			−0.879816			−0.439908	+	0.898043i	$0.644989\pi$
$674$		−	4.22458i		−	0.162725i
$675$	−32.3777	−	15.1395i	−1.24622	−	0.582719i
$676$	−11.1750			−0.429807
$677$	−6.16271	−	10.6741i	−0.236852	−	0.410240i	0.722957	−	0.690893i	$-0.242782\pi$
$677$	−6.16271	−	10.6741i	−0.236852	−	0.410240i	−0.959809	+	0.280653i	$0.909449\pi$
$678$	0.877515	−	0.540834i	0.0337007	−	0.0207706i
$679$	5.25157	−	3.03200i	0.201537	−	0.116357i
$680$	3.25657	+	1.88018i	0.124884	+	0.0721016i
$681$	−1.53647	+	2.84717i	−0.0588776	+	0.109104i
$682$	−6.56736	+	11.3750i	−0.251477	+	0.435571i
$683$	2.66192	−	1.53686i	0.101855	−	0.0588063i	−0.448207	−	0.893930i	$-0.647937\pi$
$683$	2.66192	−	1.53686i	0.101855	−	0.0588063i	0.550062	+	0.835124i	$0.314604\pi$
$684$	−0.965349	+	0.633950i	−0.0369111	+	0.0242397i
$685$	−0.506271	−	0.292296i	−0.0193436	−	0.0111680i
$686$	−5.72615	−	3.30600i	−0.218626	−	0.126224i
$687$	0.339393	+	11.8067i	0.0129486	+	0.450452i
$688$			8.63261i			0.329115i
$689$	3.44260	+	1.98758i	0.131152	+	0.0757209i
$690$	25.0238	+	40.6017i	0.952641	+	1.54568i
$691$	8.09830	−	14.0267i	0.308074	−	0.533600i	−0.669867	−	0.742481i	$-0.733649\pi$
$691$	8.09830	−	14.0267i	0.308074	−	0.533600i	0.977941	+	0.208881i	$0.0669822\pi$
$692$	3.86787			0.147034
$693$	2.04438	−	4.06359i	0.0776596	−	0.154363i
$694$	−12.7716	−	22.1211i	−0.484804	−	0.839705i
$695$	−25.8303	+	14.9131i	−0.979800	+	0.565688i
$696$	−0.310481	−	10.8009i	−0.0117687	−	0.409406i
$697$	3.11867	+	1.80056i	0.118128	+	0.0682012i
$698$	22.2188	−	12.8280i	0.840992	−	0.485547i
$699$	43.1628	+	23.2927i	1.63257	+	0.881012i
$700$	−3.30308			−0.124845
$701$	−3.84777	+	2.22151i	−0.145328	+	0.0839052i	−0.570901	−	0.821019i	$-0.693406\pi$
$701$	−3.84777	+	2.22151i	−0.145328	+	0.0839052i	0.425573	+	0.904924i	$0.360073\pi$
$702$	0.604444	+	6.99360i	0.0228133	+	0.263956i
$703$	2.31632	+	0.343539i	0.0873618	+	0.0129568i
$704$	−1.57883	−	2.73461i	−0.0595044	−	0.103065i
$705$	−37.1874	−	60.3373i	−1.40056	−	2.27244i
$706$	9.07598	+	15.7201i	0.341579	+	0.591632i
$707$	−0.236446	−	0.409536i	−0.00889245	−	0.0154022i
$708$	0.589493	−	0.0169455i	0.0221545	−	0.000636850i
$709$	26.3142	−	15.1925i	0.988252	−	0.570567i	0.0835004	−	0.996508i	$-0.473390\pi$
$709$	26.3142	−	15.1925i	0.988252	−	0.570567i	0.904751	+	0.425940i	$0.140057\pi$
$710$	3.60140	−	6.23781i	0.135158	−	0.234101i
$711$	40.8674	−	26.8378i	1.53265	−	1.00650i
$712$	−1.24565	−	2.15753i	−0.0466826	−	0.0808567i
$713$	16.6166	+	28.7808i	0.622297	+	1.07785i
$714$	−0.798590	−	0.430957i	−0.0298865	−	0.0161282i
$715$	−14.7022			−0.549832
$716$	−1.96451	+	1.13421i	−0.0734172	+	0.0423874i
$717$	−16.0255	+	29.6962i	−0.598484	+	1.10903i
$718$	−3.14227	−	1.81419i	−0.117268	−	0.0677050i
$719$	−20.5554	−	35.6030i	−0.766588	−	1.32777i	−0.939403	−	0.342814i	$-0.888620\pi$
$719$	−20.5554	−	35.6030i	−0.766588	−	1.32777i	0.172816	−	0.984954i	$-0.444714\pi$
$720$	8.64261	−	5.67565i	0.322091	−	0.211519i
$721$	0.501342	+	0.289450i	0.0186709	+	0.0107797i
$722$			18.8518i			0.701591i
$723$	19.6338	−	36.3825i	0.730188	−	1.35308i
$724$	−3.33029			−0.123769
$725$			42.9121i			1.59372i
$726$	1.78186	−	0.0512212i	0.0661311	−	0.00190100i
$727$			7.32555i			0.271689i	0.990730	+	0.135845i	$0.0433748\pi$
$727$			7.32555i			0.271689i	−0.990730	+	0.135845i	$0.956625\pi$
$728$	0.324356	+	0.561801i	0.0120214	+	0.0208217i
$729$	−26.5996	+	4.63252i	−0.985171	+	0.171575i
$730$	−25.2305			−0.933822
$731$	4.70932	−	8.15679i	0.174181	−	0.301690i
$732$	−24.6143	+	0.707560i	−0.909771	+	0.0261522i
$733$	6.48200	+	11.2272i	0.239418	+	0.414685i	0.960548	−	0.278116i	$-0.0897099\pi$
$733$	6.48200	+	11.2272i	0.239418	+	0.414685i	−0.721129	+	0.692801i	$0.756377\pi$
$734$	19.6379	+	11.3379i	0.724846	+	0.418490i
$735$	−40.3939	+	1.16116i	−1.48995	+	0.0428299i
$736$	−7.98946			−0.294495
$737$	−14.0411	+	24.3198i	−0.517209	+	0.895833i
$738$	8.27664	−	5.43531i	0.304667	−	0.200077i
$739$	23.1115			0.850172			0.425086	−	0.905153i	$-0.360244\pi$
$739$	23.1115			0.850172			0.425086	+	0.905153i	$0.360244\pi$
$740$	−20.7376	−	3.07565i	−0.762331	−	0.113063i
$741$	−0.792717	−	0.427788i	−0.0291212	−	0.0157152i
$742$			1.41299i			0.0518723i
$743$	−19.9229	−	34.5075i	−0.730901	−	1.26596i	−0.956499	−	0.291736i	$-0.905767\pi$
$743$	−19.9229	−	34.5075i	−0.730901	−	1.26596i	0.225598	−	0.974220i	$-0.427566\pi$
$744$	6.13337	−	3.78015i	0.224860	−	0.138587i
$745$		−	17.4891i		−	0.640751i
$746$		−	26.6954i		−	0.977387i
$747$	32.2218	−	1.85402i	1.17893	−	0.0678351i
$748$			3.44518i			0.125968i
$749$	−3.78769	+	6.56046i	−0.138399	+	0.239714i
$750$	−9.54703	+	5.88407i	−0.348608	+	0.214856i
$751$	−0.276749	+	0.479344i	−0.0100987	+	0.0174915i	−0.871031	−	0.491229i	$-0.836548\pi$
$751$	−0.276749	+	0.479344i	−0.0100987	+	0.0174915i	0.860932	+	0.508720i	$0.169881\pi$
$752$	11.8730			0.432963
$753$	−13.0774	+	24.2332i	−0.476566	+	0.883105i
$754$	7.29866	−	4.21389i	0.265802	−	0.153461i
$755$	−14.7196	+	8.49834i	−0.535699	+	0.309286i
$756$	−2.04542	+	1.42901i	−0.0743913	+	0.0519728i
$757$	−4.11305	+	2.37467i	−0.149491	+	0.0863088i	−0.572880	−	0.819639i	$-0.694174\pi$
$757$	−4.11305	+	2.37467i	−0.149491	+	0.0863088i	0.423389	+	0.905948i	$0.360841\pi$
$758$			23.3018i			0.846358i
$759$	−20.7517	+	38.4541i	−0.753239	+	1.39580i
$760$			1.32680i			0.0481282i
$761$	7.11945			0.258080			0.129040	−	0.991639i	$-0.458810\pi$
$761$	7.11945			0.258080			0.129040	+	0.991639i	$0.458810\pi$
$762$	−5.57824	+	10.3368i	−0.202078	+	0.374463i
$763$	−2.10916	+	1.21772i	−0.0763567	+	0.0440846i
$764$	−4.54498	−	2.62405i	−0.164432	−	0.0949347i
$765$	−11.2624	+	0.648034i	−0.407195	+	0.0234297i
$766$	−14.3137			−0.517174
$767$	0.229986	+	0.398348i	0.00830432	+	0.0143835i
$768$	0.0497688	+	1.73134i	0.00179588	+	0.0624742i
$769$	−31.9973	−	18.4736i	−1.15385	−	0.666177i	−0.204029	−	0.978965i	$-0.565404\pi$
$769$	−31.9973	−	18.4736i	−1.15385	−	0.666177i	−0.949823	+	0.312788i	$0.898737\pi$
$770$	−2.61298	−	4.52581i	−0.0941651	−	0.163099i
$771$	−13.9099	+	25.7760i	−0.500955	+	0.928298i
$772$		−	6.36781i		−	0.229183i
$773$	9.49564	−	16.4469i	0.341534	−	0.591555i	−0.643184	−	0.765712i	$-0.722387\pi$
$773$	9.49564	−	16.4469i	0.341534	−	0.591555i	0.984718	+	0.174157i	$0.0557201\pi$
$774$	−14.2159	−	21.6473i	−0.510980	−	0.778097i
$775$	−24.7792	+	14.3063i	−0.890096	+	0.513897i
$776$	6.31410	+	10.9363i	0.226663	+	0.392592i
$777$	5.02368	+	0.598113i	0.180224	+	0.0214572i
$778$	9.38545	−	16.2561i	0.336485	−	0.582808i
$779$			1.27062i			0.0455246i
$780$	7.09706	+	3.82992i	0.254116	+	0.137133i
$781$	6.59908			0.236134
$782$	7.54908	+	4.35846i	0.269955	+	0.155858i
$783$	18.5651	+	26.5732i	0.663463	+	0.949649i
$784$	3.38471	−	5.86248i	0.120882	−	0.209374i
$785$	−21.1120	+	12.1890i	−0.753518	+	0.435044i
$786$	11.9003	−	7.33448i	0.424471	−	0.261612i
$787$	26.4114	−	45.7459i	0.941465	−	1.63067i	0.178787	−	0.983888i	$-0.442783\pi$
$787$	26.4114	−	45.7459i	0.941465	−	1.63067i	0.762678	−	0.646778i	$-0.223884\pi$
$788$	3.14271	−	5.44333i	0.111954	−	0.193911i
$789$	−34.9263	−	18.8479i	−1.24341	−	0.671004i
$790$		−	56.1692i		−	1.99841i
$791$			0.285777i			0.0101611i
$792$	8.46238	+	4.25740i	0.300698	+	0.151280i
$793$	−9.60310	−	16.6331i	−0.341016	−	0.590657i
$794$	−34.2906	−	19.7977i	−1.21693	−	0.702593i
$795$	9.21631	+	14.9537i	0.326869	+	0.530352i
$796$	−11.4928	+	6.63535i	−0.407350	+	0.235184i
$797$		−	0.582881i		−	0.0206467i	−0.999947	−	0.0103233i	$-0.996714\pi$
$797$		−	0.582881i		−	0.0206467i	0.999947	−	0.0103233i	$-0.00328608\pi$
$798$	−0.00920019	−	0.320052i	−0.000325683	−	0.0113297i
$799$	−11.2185	−	6.47702i	−0.396883	−	0.229141i
$800$		−	6.87863i		−	0.243196i
$801$	6.67656	+	3.35896i	0.235905	+	0.118683i
$802$	−13.8996	−	24.0748i	−0.490811	−	0.850109i
$803$	−11.5579	−	20.0188i	−0.407868	−	0.706449i
$804$	13.1132	−	8.08198i	0.462466	−	0.285030i
$805$	−13.2226			−0.466036
$806$	4.86654	+	2.80970i	0.171417	+	0.0989675i
$807$	28.8904	+	15.5906i	1.01699	+	0.548816i
$808$	0.852854	−	0.492396i	0.0300033	−	0.0173224i
$809$	−0.932228	−	0.538222i	−0.0327754	−	0.0189229i	0.483523	−	0.875332i	$-0.339357\pi$
$809$	−0.932228	−	0.538222i	−0.0327754	−	0.0189229i	−0.516298	+	0.856409i	$0.672690\pi$
$810$	−12.3259	+	28.4647i	−0.433088	+	1.00015i
$811$	−9.15259	+	15.8527i	−0.321391	+	0.556665i	−0.980775	−	0.195141i	$-0.937484\pi$
$811$	−9.15259	+	15.8527i	−0.321391	+	0.556665i	0.659384	+	0.751806i	$0.270817\pi$
$812$	2.59433	+	1.49784i	0.0910432	+	0.0525638i
$813$	−0.209882	−	7.30128i	−0.00736087	−	0.256067i
$814$	−7.05940	−	17.8630i	−0.247432	−	0.626096i
$815$	32.8373	−	56.8758i	1.15024	−	1.99227i
$816$	0.897465	−	1.66306i	0.0314175	−	0.0582186i
$817$	3.32327			0.116266
$818$	−7.35625	+	12.7414i	−0.257205	+	0.445492i
$819$	−1.73852	−	0.874644i	−0.0607487	−	0.0305625i
$820$		−	11.3756i		−	0.397254i
$821$	36.4894			1.27349			0.636744	−	0.771075i	$-0.280281\pi$
$821$	36.4894			1.27349			0.636744	+	0.771075i	$0.280281\pi$
$822$	−0.139521	+	0.258541i	−0.00486636	+	0.00901766i
$823$	−48.4327			−1.68826			−0.844130	−	0.536139i	$-0.819882\pi$
$823$	−48.4327			−1.68826			−0.844130	+	0.536139i	$0.819882\pi$
$824$	−0.602776	+	1.04404i	−0.0209987	+	0.0363708i
$825$	−33.1076	−	17.8665i	−1.15266	−	0.622030i
$826$	−0.0817493	+	0.141594i	−0.00284442	+	0.00492668i
$827$	−41.2844	−	23.8356i	−1.43560	−	0.828845i	−0.438061	−	0.898945i	$-0.644335\pi$
$827$	−41.2844	−	23.8356i	−1.43560	−	0.828845i	−0.997540	+	0.0701008i	$0.977668\pi$
$828$	20.0345	−	13.1568i	0.696248	−	0.457230i
$829$	−2.70886	+	1.56396i	−0.0940825	+	0.0543186i	−0.546303	−	0.837588i	$-0.683965\pi$
$829$	−2.70886	+	1.56396i	−0.0940825	+	0.0543186i	0.452221	+	0.891906i	$0.350632\pi$
$830$	18.5396	−	32.1115i	0.643518	−	1.11461i
$831$	−25.4083	+	47.0830i	−0.881403	+	1.63329i
$832$	−1.16995	+	0.675468i	−0.0405605	+	0.0234176i
$833$	−6.39629	+	3.69290i	−0.221618	+	0.127951i
$834$	7.86447	+	12.7603i	0.272324	+	0.441852i
$835$	−17.8380	+	30.8963i	−0.617309	+	1.06921i
$836$	−1.05273	+	0.607797i	−0.0364096	+	0.0210211i
$837$	−9.15513	+	19.5794i	−0.316447	+	0.676763i
$838$	0.573045	+	0.330848i	0.0197955	+	0.0114289i
$839$	24.9335	−	43.1861i	0.860800	−	1.49095i	−0.0103583	−	0.999946i	$-0.503297\pi$
$839$	24.9335	−	43.1861i	0.860800	−	1.49095i	0.871158	−	0.491003i	$-0.163369\pi$
$840$	0.0823677	+	2.86537i	0.00284196	+	0.0988648i
$841$	4.95924	−	8.58965i	0.171008	−	0.296195i
$842$	22.0126			0.758606
$843$	−29.4100	−	47.7183i	−1.01293	−	1.64350i
$844$	−16.5912			−0.571093
$845$		−	38.5150i		−	1.32496i
$846$	−29.7729	+	19.5520i	−1.02361	+	0.672212i
$847$	−0.247104	+	0.427997i	−0.00849060	+	0.0147061i
$848$	−2.94253			−0.101047
$849$	28.3229	−	0.814166i	0.972039	−	0.0279421i
$850$	−3.75248	+	6.49948i	−0.128709	+	0.222930i
$851$	−48.0721	−	7.12968i	−1.64789	−	0.244402i
$852$	−3.18551	−	1.71905i	−0.109134	−	0.0588938i
$853$	−2.06294	−	1.19104i	−0.0706337	−	0.0407804i	0.464267	−	0.885695i	$-0.346318\pi$
$853$	−2.06294	−	1.19104i	−0.0706337	−	0.0407804i	−0.534901	+	0.844915i	$0.679651\pi$
$854$	3.41345	−	5.91227i	0.116806	−	0.202314i
$855$	−2.18493	−	3.32711i	−0.0747232	−	0.113785i
$856$	−13.6621	−	7.88782i	−0.466961	−	0.269600i
$857$	−36.0471	+	20.8118i	−1.23135	+	0.710918i	−0.967311	−	0.253595i	$-0.918387\pi$
$857$	−36.0471	+	20.8118i	−1.23135	+	0.710918i	−0.264036	+	0.964513i	$0.585054\pi$
$858$	0.212303	+	7.38553i	0.00724792	+	0.252138i
$859$	−18.8119	−	10.8611i	−0.641854	−	0.370574i	0.143475	−	0.989654i	$-0.454172\pi$
$859$	−18.8119	−	10.8611i	−0.641854	−	0.370574i	−0.785328	+	0.619080i	$0.787506\pi$
$860$	−29.7526			−1.01456
$861$	0.0788799	+	2.74404i	0.00268822	+	0.0935167i
$862$	3.29357	+	5.70464i	0.112180	+	0.194301i
$863$	−7.13935	−	12.3657i	−0.243026	−	0.420934i	0.718549	−	0.695477i	$-0.244807\pi$
$863$	−7.13935	−	12.3657i	−0.243026	−	0.420934i	−0.961575	+	0.274543i	$0.911473\pi$
$864$	−2.97591	−	4.25957i	−0.101242	−	0.144914i
$865$			13.3308i			0.453260i
$866$	11.0591	+	6.38499i	0.375804	+	0.216971i
$867$	23.3112	−	14.3673i	0.791690	−	0.487938i
$868$			1.99743i			0.0677973i
$869$	44.5668	−	25.7306i	1.51182	−	0.872852i
$870$	37.2257	−	1.07008i	1.26207	−	0.0362793i
$871$	10.4047	+	6.00716i	0.352550	+	0.203545i
$872$	−2.53590	−	4.39231i	−0.0858764	−	0.148742i
$873$	−33.8430	−	17.0263i	−1.14541	−	0.576254i
$874$			3.07567i			0.104036i
$875$		−	3.10915i		−	0.105108i
$876$	0.364334	+	12.6743i	0.0123097	+	0.428225i
$877$	8.18576	−	14.1781i	0.276413	−	0.478762i	−0.694077	−	0.719900i	$-0.744187\pi$
$877$	8.18576	−	14.1781i	0.276413	−	0.478762i	0.970491	+	0.241138i	$0.0775208\pi$
$878$	−17.9875	+	31.1553i	−0.607049	+	1.05144i
$879$	0.895379	+	31.1481i	0.0302004	+	1.05060i
$880$	9.42495	−	5.44150i	0.317715	−	0.183433i
$881$	12.4391	−	21.5451i	0.419082	−	0.725872i	−0.576765	−	0.816910i	$-0.695685\pi$
$881$	12.4391	−	21.5451i	0.419082	−	0.725872i	0.995847	+	0.0910380i	$0.0290185\pi$
$882$	1.16659	+	20.2747i	0.0392812	+	0.682685i
$883$	−38.8179	−	22.4115i	−1.30633	−	0.754208i	−0.324845	−	0.945767i	$-0.605312\pi$
$883$	−38.8179	−	22.4115i	−1.30633	−	0.754208i	−0.981481	+	0.191559i	$0.938646\pi$
$884$	1.47394			0.0495741
$885$	0.0584033	+	2.03171i	0.00196320	+	0.0682952i
$886$			15.6011i			0.524130i
$887$	−16.8558	+	29.1951i	−0.565962	+	0.980275i	0.430997	+	0.902353i	$0.358162\pi$
$887$	−16.8558	+	29.1951i	−0.565962	+	0.980275i	−0.996959	+	0.0779220i	$0.975172\pi$
$888$	−1.24556	+	10.4618i	−0.0417984	+	0.351074i
$889$	−1.62822	−	2.82016i	−0.0546088	−	0.0945851i
$890$	7.43600	−	4.29318i	0.249255	−	0.143908i
$891$	−28.2314	+	3.25962i	−0.945787	+	0.109201i
$892$	9.16344	−	15.8715i	0.306815	−	0.531419i
$893$		−	4.57069i		−	0.152952i
$894$	−8.78548	+	0.252546i	−0.293830	+	0.00844641i
$895$	−3.90910	−	6.77076i	−0.130667	−	0.226321i
$896$	−0.415860	−	0.240097i	−0.0138929	−	0.00802108i
$897$	16.4518	+	8.87817i	0.549309	+	0.296433i
$898$	4.15293	+	7.19308i	0.138585	+	0.240036i
$899$	25.9497			0.865472
$900$	11.3275	+	17.2490i	0.377584	+	0.574966i
$901$	2.78034	+	1.60523i	0.0926265	+	0.0534779i
$902$	9.02585	−	5.21108i	0.300528	−	0.173510i
$903$	7.17696	−	0.206308i	0.238834	−	0.00686550i
$904$	−0.595128			−0.0197937
$905$		−	11.4780i		−	0.381541i
$906$	4.48161	+	7.27151i	0.148892	+	0.241580i
$907$			25.7604i			0.855360i	0.903930	+	0.427680i	$0.140669\pi$
$907$			25.7604i			0.855360i	−0.903930	+	0.427680i	$0.859331\pi$
$908$	1.61764	−	0.933947i	0.0536834	−	0.0309941i
$909$	−1.32777	+	2.63919i	−0.0440394	+	0.0875365i
$910$	−1.93627	+	1.11791i	−0.0641867	+	0.0370582i
$911$	−45.3764	+	26.1981i	−1.50339	+	0.867982i	−0.503396	+	0.864056i	$0.667916\pi$
$911$	−45.3764	+	26.1981i	−1.50339	+	0.867982i	−0.999992	+	0.00392616i	$0.998750\pi$
$912$	0.666506	−	0.0191593i	0.0220702	−	0.000634428i
$913$	33.9713			1.12429
$914$	−1.64116	+	2.84257i	−0.0542846	+	0.0940237i
$915$	−2.43863	−	84.8342i	−0.0806187	−	2.80453i
$916$	3.40970	−	5.90577i	0.112660	−	0.195132i
$917$			3.87554i			0.127982i
$918$	0.488166	+	5.64823i	0.0161119	+	0.186419i
$919$			20.5345i			0.677371i	0.940900	+	0.338686i	$0.109982\pi$
$919$			20.5345i			0.677371i	−0.940900	+	0.338686i	$0.890018\pi$
$920$		−	27.5360i		−	0.907834i
$921$	13.2842	+	7.16878i	0.437728	+	0.236219i
$922$	−16.0063	−	27.7237i	−0.527139	−	0.913032i
$923$		−	2.82327i		−	0.0929292i
$924$	−2.23576	+	1.37796i	−0.0735512	+	0.0453315i
$925$	6.13840	−	41.3884i	0.201829	−	1.36084i
$926$	21.1009			0.693419
$927$	−0.207756	−	3.61069i	−0.00682361	−	0.118590i
$928$	−3.11923	+	5.40267i	−0.102394	+	0.177351i
$929$	42.6476			1.39922			0.699610	−	0.714525i	$-0.253357\pi$
$929$	42.6476			1.39922			0.699610	+	0.714525i	$0.253357\pi$
$930$	13.0284	+	21.1389i	0.427219	+	0.693171i
$931$	−2.25686	−	1.30300i	−0.0739656	−	0.0427040i
$932$	−14.1586	−	24.5234i	−0.463779	−	0.803289i
$933$	−20.2342	+	37.4952i	−0.662438	+	1.22754i
$934$	13.3719	−	23.1607i	0.437541	−	0.757842i
$935$	−11.8739			−0.388319
$936$	1.82144	−	3.62044i	0.0595356	−	0.118338i
$937$	4.08392	+	7.07356i	0.133416	+	0.231083i	0.924991	−	0.379989i	$-0.124072\pi$
$937$	4.08392	+	7.07356i	0.133416	+	0.231083i	−0.791575	+	0.611072i	$0.790739\pi$
$938$			4.27053i			0.139438i
$939$	9.42026	+	15.2846i	0.307418	+	0.498793i
$940$			40.9206i			1.33468i
$941$	−54.7952			−1.78627			−0.893136	−	0.449787i	$-0.851500\pi$
$941$	−54.7952			−1.78627			−0.893136	+	0.449787i	$0.851500\pi$
$942$	6.42788	+	10.4294i	0.209432	+	0.339807i
$943$		−	26.3700i		−	0.858724i
$944$	−0.294868	−	0.170242i	−0.00959714	−	0.00554091i
$945$	−4.92515	−	7.04963i	−0.160215	−	0.229324i
$946$	−13.6294	−	23.6069i	−0.443131	−	0.767525i
$947$	35.7426	+	20.6360i	1.16148	+	0.670580i	0.951658	−	0.307159i	$-0.0993785\pi$
$947$	35.7426	+	20.6360i	1.16148	+	0.670580i	0.209821	+	0.977740i	$0.432712\pi$
$948$	−28.2161	+	0.811096i	−0.916415	+	0.0263432i
$949$	−8.56462	+	4.94478i	−0.278019	+	0.160514i
$950$	−2.64804			−0.0859138
$951$	44.0477	−	27.1477i	1.42834	−	0.880324i
$952$	0.261959	+	0.453726i	0.00849014	+	0.0147053i
$953$	−0.885286	−	1.53336i	−0.0286772	−	0.0496704i	0.851331	−	0.524630i	$-0.175796\pi$
$953$	−0.885286	−	1.53336i	−0.0286772	−	0.0496704i	−0.880008	+	0.474959i	$0.842463\pi$
$954$	7.37874	−	4.84566i	0.238896	−	0.156884i
$955$	9.04388	−	15.6645i	0.292653	−	0.506890i
$956$	16.8722	−	9.74117i	0.545686	−	0.315052i
$957$	17.9018	+	29.0460i	0.578683	+	0.938925i
$958$	3.58000	+	6.20074i	0.115665	+	0.200337i
$959$	−0.0407245	−	0.0705370i	−0.00131506	−	0.00227776i
$960$	−5.96712	+	0.171530i	−0.192588	+	0.00553611i
$961$	−6.84872	−	11.8623i	−0.220926	−	0.382656i
$962$	−7.64228	+	3.02021i	−0.246397	+	0.0973756i
$963$	47.2488	−	2.71866i	1.52257	−	0.0876076i
$964$	−20.6711	+	11.9345i	−0.665771	+	0.384383i
$965$	21.9469			0.706496
$966$	0.190937	+	6.64225i	0.00614331	+	0.213711i
$967$	50.7037	−	29.2738i	1.63052	−	0.941382i	0.646589	−	0.762839i	$-0.276195\pi$
$967$	50.7037	−	29.2738i	1.63052	−	0.941382i	0.983932	−	0.178543i	$-0.0571383\pi$
$968$	−0.891300	−	0.514592i	−0.0286475	−	0.0165396i
$969$	−0.640220	−	0.345494i	−0.0205668	−	0.0110989i
$970$	−37.6925	+	21.7618i	−1.21023	+	0.698729i
$971$	−0.0438050	−	0.0758725i	−0.00140577	−	0.00243486i	0.865322	−	0.501217i	$-0.167114\pi$
$971$	−0.0438050	−	0.0758725i	−0.00140577	−	0.00243486i	−0.866727	+	0.498782i	$0.833781\pi$
$972$	14.4770	+	5.78076i	0.464349	+	0.185418i
$973$	−4.15559			−0.133222
$974$	−12.1307	+	21.0111i	−0.388694	+	0.673238i
$975$	−7.64378	+	14.1644i	−0.244797	+	0.453623i
$976$	12.3122	+	7.10847i	0.394105	+	0.227537i
$977$		−	57.6325i		−	1.84383i	−0.387396	−	0.921913i	$-0.626625\pi$
$977$		−	57.6325i		−	1.84383i	0.387396	−	0.921913i	$-0.373375\pi$
$978$	−29.0452	−	15.6742i	−0.928763	−	0.501205i
$979$	6.81273	+	3.93333i	0.217736	+	0.125710i
$980$	20.2053	+	11.6655i	0.645434	+	0.372641i
$981$	13.5922	+	6.83820i	0.433965	+	0.218327i
$982$	27.8901	−	16.1023i	0.890008	−	0.513846i
$983$	−19.8239	+	34.3361i	−0.632286	+	1.09515i	0.354798	+	0.934943i	$0.384550\pi$
$983$	−19.8239	+	34.3361i	−0.632286	+	1.09515i	−0.987083	+	0.160208i	$0.948784\pi$
$984$	−5.71444	+	0.164267i	−0.182170	+	0.00523663i
$985$	18.7607	+	10.8315i	0.597764	+	0.345119i
$986$	5.89460	−	3.40325i	0.187722	−	0.108382i
$987$	−0.283748	−	9.87092i	−0.00903180	−	0.314195i
$988$	0.260033	+	0.450390i	0.00827274	+	0.0143288i
$989$	−68.9699			−2.19312
$990$	−14.6733	+	29.1659i	−0.466348	+	0.926954i
$991$		−	18.8014i		−	0.597247i	−0.954371	−	0.298624i	$-0.903472\pi$
$991$		−	18.8014i		−	0.597247i	0.954371	−	0.298624i	$-0.0965275\pi$
$992$	−4.15963			−0.132069
$993$	21.3754	+	34.6820i	0.678328	+	1.10060i
$994$	0.869092	−	0.501770i	0.0275659	−	0.0159152i
$995$	−22.8690	−	39.6103i	−0.724996	−	1.25573i
$996$	−16.3986	−	8.84948i	−0.519610	−	0.280407i
$997$	−27.1011	−	15.6468i	−0.858300	−	0.495540i	0.00514262	−	0.999987i	$-0.498363\pi$
$997$	−27.1011	−	15.6468i	−0.858300	−	0.495540i	−0.863443	+	0.504447i	$0.831696\pi$
$998$	18.4340			0.583518
$999$	−14.1047	−	28.2853i	−0.446253	−	0.894907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.t.a.85.3	yes	76
3.2	odd	2		1998.2.t.a.307.37		76
9.2	odd	6		1998.2.k.a.1639.2		76
9.7	even	3		666.2.k.a.529.35	yes	76
37.27	even	6		666.2.k.a.175.16	✓	76
111.101	odd	6		1998.2.k.a.1063.37		76
333.101	odd	6		1998.2.t.a.397.37		76
333.286	even	6	inner	666.2.t.a.619.3	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.16	✓	76	37.27	even	6
666.2.k.a.529.35	yes	76	9.7	even	3
666.2.t.a.85.3	yes	76	1.1	even	1	trivial
666.2.t.a.619.3	yes	76	333.286	even	6	inner
1998.2.k.a.1063.37		76	111.101	odd	6
1998.2.k.a.1639.2		76	9.2	odd	6
1998.2.t.a.307.37		76	3.2	odd	2
1998.2.t.a.397.37		76	333.101	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.52427 - 0.822567i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.98479 + 1.72327i) q^{5} +(0.908769 + 1.47450i) q^{6} -0.480194 q^{7} -1.00000i q^{8} +(1.64677 + 2.50762i) q^{9} +3.44654 q^{10} +(1.57883 + 2.73461i) q^{11} +(-0.0497688 - 1.73134i) q^{12} +(1.16995 - 0.675468i) q^{13} +(0.415860 + 0.240097i) q^{14} +(5.96712 - 0.171530i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.944880 - 0.545527i) q^{17} +(-0.172333 - 2.99505i) q^{18} +(0.333391 + 0.192483i) q^{19} +(-2.98479 - 1.72327i) q^{20} +(0.731943 + 0.394992i) q^{21} -3.15766i q^{22} +(-6.91907 - 3.99473i) q^{23} +(-0.822567 + 1.52427i) q^{24} +(3.43932 - 5.95707i) q^{25} -1.35094 q^{26} +(-0.447426 - 5.17685i) q^{27} +(-0.240097 - 0.415860i) q^{28} +(-5.40267 + 3.11923i) q^{29} +(-5.25344 - 2.83501i) q^{30} +(-3.60235 - 2.07982i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.157153 - 5.46697i) q^{33} -1.09105 q^{34} +(1.43328 - 0.827504i) q^{35} +(-1.34828 + 2.67995i) q^{36} +(5.65702 - 2.23564i) q^{37} +(-0.192483 - 0.333391i) q^{38} +(-2.33892 + 0.0672344i) q^{39} +(1.72327 + 2.98479i) q^{40} +(1.65030 + 2.85840i) q^{41} +(-0.436386 - 0.708045i) q^{42} +(7.47606 - 4.31631i) q^{43} +(-1.57883 + 2.73461i) q^{44} +(-9.23656 - 4.64689i) q^{45} +(3.99473 + 6.91907i) q^{46} +(-5.93648 - 10.2823i) q^{47} +(1.47450 - 0.908769i) q^{48} -6.76941 q^{49} +(-5.95707 + 3.43932i) q^{50} +(-1.88898 + 0.0543004i) q^{51} +(1.16995 + 0.675468i) q^{52} +(1.47126 + 2.54830i) q^{53} +(-2.20094 + 4.70700i) q^{54} +(-9.42495 - 5.44150i) q^{55} +0.480194i q^{56} +(-0.349845 - 0.567632i) q^{57} +6.23847 q^{58} +0.340484i q^{59} +(3.13211 + 5.08191i) q^{60} -14.2169i q^{61} +(2.07982 + 3.60235i) q^{62} +(-0.790768 - 1.20414i) q^{63} -1.00000 q^{64} +(-2.32803 + 4.03226i) q^{65} +(-2.59739 + 4.81311i) q^{66} +(4.44667 + 7.70185i) q^{67} +(0.944880 + 0.545527i) q^{68} +(7.26057 + 11.7804i) q^{69} -1.65501 q^{70} +(1.04493 - 1.80988i) q^{71} +(2.50762 - 1.64677i) q^{72} -7.32053 q^{73} +(-6.01695 - 0.892387i) q^{74} +(-10.1425 + 6.25109i) q^{75} +0.384966i q^{76} +(-0.758145 - 1.31315i) q^{77} +(2.05918 + 1.11124i) q^{78} -16.2973i q^{79} -3.44654i q^{80} +(-3.57631 + 8.25893i) q^{81} -3.30060i q^{82} +(5.37919 - 9.31702i) q^{83} +(0.0238987 + 0.831377i) q^{84} +(-1.88018 + 3.25657i) q^{85} -8.63261 q^{86} +(10.8009 - 0.310481i) q^{87} +(2.73461 - 1.57883i) q^{88} +(2.15753 - 1.24565i) q^{89} +(5.67565 + 8.64261i) q^{90} +(-0.561801 + 0.324356i) q^{91} -7.98946i q^{92} +(3.78015 + 6.13337i) q^{93} +11.8730i q^{94} -1.32680 q^{95} +(-1.73134 + 0.0497688i) q^{96} +(-10.9363 + 6.31410i) q^{97} +(5.86248 + 3.38471i) q^{98} +(-4.25740 + 8.46238i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 2 q^{3} + 38 q^{4} + 4 q^{7} + 2 q^{9} - 4 q^{11} + 2 q^{12} + 6 q^{13} + 6 q^{15} - 38 q^{16} - 12 q^{21} - 12 q^{23} + 50 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} - 18 q^{29} - 12 q^{30} - 6 q^{31}+ \cdots - 10 q^{99}+O(q^{100}) \) 76 * q - 2 * q^3 + 38 * q^4 + 4 * q^7 + 2 * q^9 - 4 * q^11 + 2 * q^12 + 6 * q^13 + 6 * q^15 - 38 * q^16 - 12 * q^21 - 12 * q^23 + 50 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 - 18 * q^29 - 12 * q^30 - 6 * q^31 + 4 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 18 * q^39 - 36 * q^41 + 42 * q^42 - 6 * q^43 + 4 * q^44 - 12 * q^45 - 20 * q^47 + 4 * q^48 + 72 * q^49 + 18 * q^51 + 6 * q^52 + 14 * q^53 + 18 * q^54 + 36 * q^57 + 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 - 16 * q^65 - 20 * q^67 - 66 * q^69 + 2 * q^71 + 28 * q^73 - 20 * q^74 - 78 * q^75 + 12 * q^77 + 22 * q^78 + 26 * q^81 + 32 * q^83 - 6 * q^84 - 12 * q^85 - 8 * q^86 - 72 * q^87 + 60 * q^89 - 10 * q^90 + 42 * q^91 - 6 * q^93 + 28 * q^95 + 12 * q^97 - 24 * q^98 - 10 * q^99

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