LMFDB - Embedded newform 814.2.h.c.445.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [814,2,Mod(75,814)] 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("814.75"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(814, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([6, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 814 = 2 \cdot 11 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	814.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.49982272453$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			445.7
Character	$\chi$	$=$	814.445
Dual form			814.2.h.c.75.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.0995997 - 0.0723634i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.20393 + 3.70530i) q^{5} +(0.0380437 - 0.117086i) q^{6} +(-0.832227 + 0.604649i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.922367 - 2.83875i) q^{9} -3.89599 q^{10} +(2.06994 + 2.59140i) q^{11} +0.123112 q^{12} +(-0.00398386 - 0.0122611i) q^{13} +(-0.832227 - 0.604649i) q^{14} +(0.388039 - 0.281927i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.86476 + 5.73913i) q^{17} +(2.41479 - 1.75445i) q^{18} +(-3.89000 - 2.82625i) q^{19} +(-1.20393 - 3.70530i) q^{20} +0.126644 q^{21} +(-1.82492 + 2.76942i) q^{22} +1.10089 q^{23} +(0.0380437 + 0.117086i) q^{24} +(-8.23476 - 5.98290i) q^{25} +(0.0104299 - 0.00757775i) q^{26} +(-0.227686 + 0.700744i) q^{27} +(0.317883 - 0.978342i) q^{28} +(-2.15337 + 1.56451i) q^{29} +(0.388039 + 0.281927i) q^{30} +(-2.94841 - 9.07427i) q^{31} +1.00000 q^{32} +(-0.0186433 - 0.407891i) q^{33} -6.03448 q^{34} +(-1.23847 - 3.81161i) q^{35} +(2.41479 + 1.75445i) q^{36} +(0.809017 - 0.587785i) q^{37} +(1.48585 - 4.57297i) q^{38} +(-0.000490461 + 0.00150948i) q^{39} +(3.15192 - 2.29000i) q^{40} +(-1.44607 - 1.05063i) q^{41} +(0.0391352 + 0.120446i) q^{42} +0.161529 q^{43} +(-3.19780 - 0.879802i) q^{44} +11.6289 q^{45} +(0.340195 + 1.04701i) q^{46} +(4.39472 + 3.19295i) q^{47} +(-0.0995997 + 0.0723634i) q^{48} +(-1.83612 + 5.65099i) q^{49} +(3.14540 - 9.68054i) q^{50} +(0.601033 - 0.436676i) q^{51} +(0.0104299 + 0.00757775i) q^{52} +(-2.62892 - 8.09097i) q^{53} -0.736806 q^{54} +(-12.0940 + 4.54992i) q^{55} +1.02869 q^{56} +(0.182926 + 0.562988i) q^{57} +(-2.15337 - 1.56451i) q^{58} +(-6.54972 + 4.75865i) q^{59} +(-0.148218 + 0.456167i) q^{60} +(1.56913 - 4.82930i) q^{61} +(7.71904 - 5.60821i) q^{62} +(2.48407 + 1.80478i) q^{63} +(0.309017 + 0.951057i) q^{64} +0.0502272 q^{65} +(0.382166 - 0.143776i) q^{66} +5.89099 q^{67} +(-1.86476 - 5.73913i) q^{68} +(-0.109649 - 0.0796644i) q^{69} +(3.24235 - 2.35570i) q^{70} +(-3.63779 + 11.1960i) q^{71} +(-0.922367 + 2.83875i) q^{72} +(-0.439766 + 0.319509i) q^{73} +(0.809017 + 0.587785i) q^{74} +(0.387236 + 1.19179i) q^{75} +4.80831 q^{76} +(-3.28955 - 0.905044i) q^{77} -0.00158717 q^{78} +(4.39093 + 13.5139i) q^{79} +(3.15192 + 2.29000i) q^{80} +(-7.17098 + 5.21002i) q^{81} +(0.552350 - 1.69996i) q^{82} +(0.493688 - 1.51942i) q^{83} +(-0.102457 + 0.0744395i) q^{84} +(-19.0202 - 13.8190i) q^{85} +(0.0499151 + 0.153623i) q^{86} +0.327688 q^{87} +(-0.151434 - 3.31317i) q^{88} -18.5606 q^{89} +(3.59353 + 11.0598i) q^{90} +(0.0107291 + 0.00779515i) q^{91} +(-0.890642 + 0.647089i) q^{92} +(-0.362985 + 1.11715i) q^{93} +(-1.67864 + 5.16631i) q^{94} +(15.1554 - 11.0110i) q^{95} +(-0.0995997 - 0.0723634i) q^{96} +(3.79460 + 11.6786i) q^{97} -5.94180 q^{98} +(5.44709 - 8.26628i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 11 q^{2} - 11 q^{4} + q^{5} - 5 q^{6} - q^{7} - 11 q^{8} - 25 q^{9} + 16 q^{10} - 4 q^{11} + 10 q^{12} + 3 q^{13} - q^{14} - 18 q^{15} - 11 q^{16} - 7 q^{17} - 10 q^{18} + 15 q^{19} + q^{20}+ \cdots + 45 q^{99}+O(q^{100}) $ 44 * q - 11 * q^2 - 11 * q^4 + q^5 - 5 * q^6 - q^7 - 11 * q^8 - 25 * q^9 + 16 * q^10 - 4 * q^11 + 10 * q^12 + 3 * q^13 - q^14 - 18 * q^15 - 11 * q^16 - 7 * q^17 - 10 * q^18 + 15 * q^19 + q^20 + 30 * q^21 + 6 * q^22 + 36 * q^23 - 5 * q^24 - 48 * q^25 - 12 * q^26 - 36 * q^27 - 6 * q^28 - 3 * q^29 - 18 * q^30 - 46 * q^31 + 44 * q^32 - 49 * q^33 + 38 * q^34 - 22 * q^35 - 10 * q^36 + 11 * q^37 - 15 * q^38 + 46 * q^39 - 9 * q^40 + 10 * q^41 - 5 * q^42 - 4 * q^43 - 9 * q^44 + 166 * q^45 - 14 * q^46 - 17 * q^47 - 36 * q^49 + 22 * q^50 - 15 * q^51 - 12 * q^52 - 23 * q^53 + 34 * q^54 - 34 * q^55 + 14 * q^56 - 13 * q^57 - 3 * q^58 - 18 * q^59 + 2 * q^60 + 30 * q^61 + 14 * q^62 + 79 * q^63 - 11 * q^64 + 68 * q^65 - 9 * q^66 + 44 * q^67 - 7 * q^68 - 91 * q^69 + 8 * q^70 - 47 * q^71 - 25 * q^72 - 36 * q^73 + 11 * q^74 - 38 * q^75 - 2 * q^77 - 4 * q^78 + 13 * q^79 - 9 * q^80 - 38 * q^81 - 20 * q^82 + 44 * q^83 - 10 * q^84 + 23 * q^85 - 39 * q^86 - 20 * q^87 + 11 * q^88 + 90 * q^89 - 24 * q^90 - 54 * q^91 - 4 * q^92 - 69 * q^93 + 33 * q^94 + 47 * q^95 - 121 * q^97 + 114 * q^98 + 45 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/814\mathbb{Z}\right)^\times$.

$n$	$519$	$705$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−0.0995997	−	0.0723634i	−0.0575039	−	0.0417790i	0.558662	−	0.829395i	$-0.311315\pi$
$3$	−0.0995997	−	0.0723634i	−0.0575039	−	0.0417790i	−0.616166	+	0.787616i	$0.711315\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−1.20393	+	3.70530i	−0.538412	+	1.65706i	0.197746	+	0.980253i	$0.436638\pi$
$5$	−1.20393	+	3.70530i	−0.538412	+	1.65706i	−0.736159	+	0.676809i	$0.763362\pi$
$6$	0.0380437	−	0.117086i	0.0155313	−	0.0478004i
$7$	−0.832227	+	0.604649i	−0.314552	+	0.228536i	−0.733847	−	0.679314i	$-0.762277\pi$
$7$	−0.832227	+	0.604649i	−0.314552	+	0.228536i	0.419295	+	0.907850i	$0.362277\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−0.922367	−	2.83875i	−0.307456	−	0.946252i
$10$	−3.89599			−1.23202
$11$	2.06994	+	2.59140i	0.624111	+	0.781336i
$11$	2.06994	+	2.59140i	0.624111	+	0.781336i
$12$	0.123112			0.0355394
$13$	−0.00398386	−	0.0122611i	−0.00110492	−	0.00340061i	0.950503	−	0.310717i	$-0.100569\pi$
$13$	−0.00398386	−	0.0122611i	−0.00110492	−	0.00340061i	−0.951607	+	0.307316i	$0.900569\pi$
$14$	−0.832227	−	0.604649i	−0.222422	−	0.161599i
$15$	0.388039	−	0.281927i	0.100191	−	0.0727932i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−1.86476	+	5.73913i	−0.452270	+	1.39194i	0.422040	+	0.906577i	$0.361314\pi$
$17$	−1.86476	+	5.73913i	−0.452270	+	1.39194i	−0.874310	+	0.485367i	$0.838686\pi$
$18$	2.41479	−	1.75445i	0.569171	−	0.413527i
$19$	−3.89000	−	2.82625i	−0.892428	−	0.648387i	0.0440820	−	0.999028i	$-0.485964\pi$
$19$	−3.89000	−	2.82625i	−0.892428	−	0.648387i	−0.936510	+	0.350641i	$0.885964\pi$
$20$	−1.20393	−	3.70530i	−0.269206	−	0.828531i
$21$	0.126644			0.0276360
$22$	−1.82492	+	2.76942i	−0.389074	+	0.590442i
$23$	1.10089			0.229552			0.114776	−	0.993391i	$-0.463385\pi$
$23$	1.10089			0.229552			0.114776	+	0.993391i	$0.463385\pi$
$24$	0.0380437	+	0.117086i	0.00776564	+	0.0239002i
$25$	−8.23476	−	5.98290i	−1.64695	−	1.19658i
$26$	0.0104299	−	0.00757775i	0.00204547	−	0.00148612i
$27$	−0.227686	+	0.700744i	−0.0438181	+	0.134858i
$28$	0.317883	−	0.978342i	0.0600742	−	0.184889i
$29$	−2.15337	+	1.56451i	−0.399870	+	0.290523i	−0.769488	−	0.638661i	$-0.779489\pi$
$29$	−2.15337	+	1.56451i	−0.399870	+	0.290523i	0.369618	+	0.929184i	$0.379489\pi$
$30$	0.388039	+	0.281927i	0.0708459	+	0.0514726i
$31$	−2.94841	−	9.07427i	−0.529550	−	1.62979i	−0.755139	−	0.655565i	$-0.772431\pi$
$31$	−2.94841	−	9.07427i	−0.529550	−	1.62979i	0.225589	−	0.974223i	$-0.427569\pi$
$32$	1.00000			0.176777
$33$	−0.0186433	−	0.407891i	−0.00324539	−	0.0710046i
$34$	−6.03448			−1.03491
$35$	−1.23847	−	3.81161i	−0.209339	−	0.644279i
$36$	2.41479	+	1.75445i	0.402465	+	0.292408i
$37$	0.809017	−	0.587785i	0.133002	−	0.0966313i
$37$	0.809017	−	0.587785i	0.133002	−	0.0966313i
$38$	1.48585	−	4.57297i	0.241037	−	0.741834i
$39$	−0.000490461		0.00150948i	−7.85366e−5		0.000241711i
$40$	3.15192	−	2.29000i	0.498362	−	0.362081i
$41$	−1.44607	−	1.05063i	−0.225839	−	0.164081i	0.469112	−	0.883138i	$-0.344574\pi$
$41$	−1.44607	−	1.05063i	−0.225839	−	0.164081i	−0.694951	+	0.719057i	$0.744574\pi$
$42$	0.0391352	+	0.120446i	0.00603869	+	0.0185852i
$43$	0.161529			0.0246329			0.0123165	−	0.999924i	$-0.496079\pi$
$43$	0.161529			0.0246329			0.0123165	+	0.999924i	$0.496079\pi$
$44$	−3.19780	−	0.879802i	−0.482087	−	0.132635i
$45$	11.6289			1.73354
$46$	0.340195	+	1.04701i	0.0501590	+	0.154374i
$47$	4.39472	+	3.19295i	0.641036	+	0.465740i	0.860206	−	0.509947i	$-0.170335\pi$
$47$	4.39472	+	3.19295i	0.641036	+	0.465740i	−0.219170	+	0.975687i	$0.570335\pi$
$48$	−0.0995997	+	0.0723634i	−0.0143760	+	0.0104448i
$49$	−1.83612	+	5.65099i	−0.262302	+	0.807284i
$50$	3.14540	−	9.68054i	0.444826	−	1.36903i
$51$	0.601033	−	0.436676i	0.0841614	−	0.0611468i
$52$	0.0104299	+	0.00757775i	0.00144636	+	0.00105085i
$53$	−2.62892	−	8.09097i	−0.361109	−	1.11138i	−0.952382	−	0.304909i	$-0.901374\pi$
$53$	−2.62892	−	8.09097i	−0.361109	−	1.11138i	0.591272	−	0.806472i	$-0.298626\pi$
$54$	−0.736806			−0.100267
$55$	−12.0940	+	4.54992i	−1.63075	+	0.613511i
$56$	1.02869			0.137464
$57$	0.182926	+	0.562988i	0.0242291	+	0.0745696i
$58$	−2.15337	−	1.56451i	−0.282751	−	0.205431i
$59$	−6.54972	+	4.75865i	−0.852701	+	0.619524i	−0.925890	−	0.377794i	$-0.876683\pi$
$59$	−6.54972	+	4.75865i	−0.852701	+	0.619524i	0.0731881	+	0.997318i	$0.476683\pi$
$60$	−0.148218	+	0.456167i	−0.0191348	+	0.0588910i
$61$	1.56913	−	4.82930i	0.200907	−	0.618328i	−0.798950	−	0.601398i	$-0.794611\pi$
$61$	1.56913	−	4.82930i	0.200907	−	0.618328i	0.999857	−	0.0169303i	$-0.00538935\pi$
$62$	7.71904	−	5.60821i	0.980319	−	0.712243i
$63$	2.48407	+	1.80478i	0.312963	+	0.227381i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	0.0502272			0.00622992
$66$	0.382166	−	0.143776i	0.0470414	−	0.0176976i
$67$	5.89099			0.719699			0.359849	−	0.933010i	$-0.382828\pi$
$67$	5.89099			0.719699			0.359849	+	0.933010i	$0.382828\pi$
$68$	−1.86476	−	5.73913i	−0.226135	−	0.695972i
$69$	−0.109649	−	0.0796644i	−0.0132002	−	0.00959047i
$70$	3.24235	−	2.35570i	0.387535	−	0.281560i
$71$	−3.63779	+	11.1960i	−0.431727	+	1.32872i	0.464677	+	0.885480i	$0.346170\pi$
$71$	−3.63779	+	11.1960i	−0.431727	+	1.32872i	−0.896404	+	0.443238i	$0.853830\pi$
$72$	−0.922367	+	2.83875i	−0.108702	+	0.334550i
$73$	−0.439766	+	0.319509i	−0.0514707	+	0.0373957i	−0.613223	−	0.789910i	$-0.710127\pi$
$73$	−0.439766	+	0.319509i	−0.0514707	+	0.0373957i	0.561752	+	0.827305i	$0.310127\pi$
$74$	0.809017	+	0.587785i	0.0940463	+	0.0683286i
$75$	0.387236	+	1.19179i	0.0447142	+	0.137616i
$76$	4.80831			0.551551
$77$	−3.28955	−	0.905044i	−0.374879	−	0.103139i
$78$	−0.00158717			−0.000179711
$79$	4.39093	+	13.5139i	0.494018	+	1.52043i	0.818482	+	0.574533i	$0.194816\pi$
$79$	4.39093	+	13.5139i	0.494018	+	1.52043i	−0.324464	+	0.945898i	$0.605184\pi$
$80$	3.15192	+	2.29000i	0.352395	+	0.256030i
$81$	−7.17098	+	5.21002i	−0.796776	+	0.578891i
$82$	0.552350	−	1.69996i	0.0609969	−	0.187729i
$83$	0.493688	−	1.51942i	0.0541893	−	0.166778i	−0.920299	−	0.391216i	$-0.872055\pi$
$83$	0.493688	−	1.51942i	0.0541893	−	0.166778i	0.974488	+	0.224438i	$0.0720547\pi$
$84$	−0.102457	+	0.0744395i	−0.0111790	+	0.00812202i
$85$	−19.0202	−	13.8190i	−2.06303	−	1.49888i
$86$	0.0499151	+	0.153623i	0.00538249	+	0.0165656i
$87$	0.327688			0.0351319
$88$	−0.151434	−	3.31317i	−0.0161429	−	0.353185i
$89$	−18.5606			−1.96742			−0.983710	−	0.179761i	$-0.942467\pi$
$89$	−18.5606			−1.96742			−0.983710	+	0.179761i	$0.942467\pi$
$90$	3.59353	+	11.0598i	0.378791	+	1.16580i
$91$	0.0107291	+	0.00779515i	0.00112472	+	0.000817154i
$92$	−0.890642	+	0.647089i	−0.0928558	+	0.0674637i
$93$	−0.362985	+	1.11715i	−0.0376398	+	0.115843i
$94$	−1.67864	+	5.16631i	−0.173138	+	0.532864i
$95$	15.1554	−	11.0110i	1.55491	−	1.12971i
$96$	−0.0995997	−	0.0723634i	−0.0101654	−	0.00738556i
$97$	3.79460	+	11.6786i	0.385283	+	1.18578i	0.936275	+	0.351268i	$0.114249\pi$
$97$	3.79460	+	11.6786i	0.385283	+	1.18578i	−0.550992	+	0.834510i	$0.685751\pi$
$98$	−5.94180			−0.600212
$99$	5.44709	−	8.26628i	0.547453	−	0.830792i
$100$	10.1787			1.01787
$101$	3.50827	+	10.7973i	0.349086	+	1.07438i	0.959360	+	0.282185i	$0.0910593\pi$
$101$	3.50827	+	10.7973i	0.349086	+	1.07438i	−0.610274	+	0.792190i	$0.708941\pi$
$102$	0.601033	+	0.436676i	0.0595111	+	0.0432373i
$103$	−11.3386	+	8.23801i	−1.11723	+	0.811715i	−0.983787	−	0.179342i	$-0.942603\pi$
$103$	−11.3386	+	8.23801i	−1.11723	+	0.811715i	−0.133443	+	0.991057i	$0.542603\pi$
$104$	−0.00398386	+	0.0122611i	−0.000390650	+	0.00120230i
$105$	−0.152470	+	0.469255i	−0.0148796	+	0.0457946i
$106$	6.88259	−	5.00050i	0.668497	−	0.485691i
$107$	9.52691	+	6.92171i	0.921001	+	0.669147i	0.943773	−	0.330594i	$-0.107249\pi$
$107$	9.52691	+	6.92171i	0.921001	+	0.669147i	−0.0227719	+	0.999741i	$0.507249\pi$
$108$	−0.227686	−	0.700744i	−0.0219091	−	0.0674292i
$109$	3.66858			0.351386			0.175693	−	0.984445i	$-0.443783\pi$
$109$	3.66858			0.351386			0.175693	+	0.984445i	$0.443783\pi$
$110$	−8.06447	−	10.0960i	−0.768917	−	0.962621i
$111$	−0.123112			−0.0116853
$112$	0.317883	+	0.978342i	0.0300371	+	0.0924446i
$113$	10.8512	+	7.88387i	1.02080	+	0.741652i	0.966446	−	0.256870i	$-0.0826912\pi$
$113$	10.8512	+	7.88387i	1.02080	+	0.741652i	0.0543505	+	0.998522i	$0.482691\pi$
$114$	−0.478906	+	0.347946i	−0.0448537	+	0.0325881i
$115$	−1.32539	+	4.07915i	−0.123594	+	0.380382i
$116$	0.822513	−	2.53143i	0.0763684	−	0.235038i
$117$	−0.0311316	+	0.0226184i	−0.00287811	+	0.00209107i
$118$	−6.54972	−	4.75865i	−0.602951	−	0.438070i
$119$	−1.91826	−	5.90379i	−0.175846	−	0.541199i
$120$	−0.479643			−0.0437852
$121$	−2.43068	+	10.7281i	−0.220971	+	0.975280i
$122$	5.07782			0.459725
$123$	0.0680010	+	0.209285i	0.00613144	+	0.0188706i
$124$	7.71904	+	5.60821i	0.693190	+	0.503632i
$125$	16.3229	−	11.8593i	1.45996	−	1.06073i
$126$	−0.948830	+	2.92020i	−0.0845285	+	0.260152i
$127$	4.94355	−	15.2147i	0.438669	−	1.35009i	−0.450610	−	0.892721i	$-0.648793\pi$
$127$	4.94355	−	15.2147i	0.438669	−	1.35009i	0.889279	−	0.457364i	$-0.151207\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	−0.0160882	−	0.0116888i	−0.00141649	−	0.00102914i
$130$	0.0155211	+	0.0477689i	0.00136129	+	0.00418961i
$131$	13.2172			1.15479			0.577395	−	0.816465i	$-0.304069\pi$
$131$	13.2172			1.15479			0.577395	+	0.816465i	$0.304069\pi$
$132$	0.254835	+	0.319032i	0.0221805	+	0.0277682i
$133$	4.94626			0.428895
$134$	1.82042	+	5.60266i	0.157260	+	0.483996i
$135$	−2.32235	−	1.68729i	−0.199876	−	0.145219i
$136$	4.88200	−	3.54698i	0.418628	−	0.304151i
$137$	1.25288	−	3.85597i	0.107041	−	0.329438i	−0.883163	−	0.469066i	$-0.844591\pi$
$137$	1.25288	−	3.85597i	0.107041	−	0.329438i	0.990204	+	0.139628i	$0.0445907\pi$
$138$	0.0418821	−	0.128900i	0.00356524	−	0.0109727i
$139$	−10.5791	+	7.68614i	−0.897305	+	0.651930i	−0.937772	−	0.347251i	$-0.887115\pi$
$139$	−10.5791	+	7.68614i	−0.897305	+	0.651930i	0.0404674	+	0.999181i	$0.487115\pi$
$140$	3.24235	+	2.35570i	0.274028	+	0.199093i
$141$	−0.206660	−	0.636035i	−0.0174039	−	0.0535638i
$142$	−11.7721			−0.987896
$143$	0.0235269	−	0.0357035i	0.00196742	−	0.00298567i
$144$	−2.98484			−0.248737
$145$	−3.20450	−	9.86244i	−0.266119	−	0.819031i
$146$	−0.439766	−	0.319509i	−0.0363953	−	0.0264427i
$147$	0.591801	−	0.429969i	0.0488110	−	0.0354632i
$148$	−0.309017	+	0.951057i	−0.0254010	+	0.0781764i
$149$	2.11285	−	6.50268i	0.173091	−	0.532720i	−0.826450	−	0.563010i	$-0.809643\pi$
$149$	2.11285	−	6.50268i	0.173091	−	0.532720i	0.999541	+	0.0302902i	$0.00964314\pi$
$150$	−1.01380	+	0.736567i	−0.0827762	+	0.0601404i
$151$	11.9858	+	8.70818i	0.975389	+	0.708661i	0.956673	−	0.291164i	$-0.0940424\pi$
$151$	11.9858	+	8.70818i	0.975389	+	0.708661i	0.0187154	+	0.999825i	$0.494042\pi$
$152$	1.48585	+	4.57297i	0.120518	+	0.370917i
$153$	18.0120			1.45618
$154$	−0.155778	−	3.40822i	−0.0125530	−	0.274642i
$155$	37.1726			2.98578
$156$	−0.000490461	−	0.00150948i	−3.92683e−5	−	0.000120855i
$157$	−12.0427	−	8.74955i	−0.961114	−	0.698290i	−0.00770490	−	0.999970i	$-0.502453\pi$
$157$	−12.0427	−	8.74955i	−0.961114	−	0.698290i	−0.953409	+	0.301680i	$0.902453\pi$
$158$	−11.4956	+	8.35204i	−0.914541	+	0.664453i
$159$	−0.323651	+	0.996096i	−0.0256672	+	0.0789956i
$160$	−1.20393	+	3.70530i	−0.0951787	+	0.292930i
$161$	−0.916194	+	0.665654i	−0.0722062	+	0.0524609i
$162$	−7.17098	−	5.21002i	−0.563406	−	0.409338i
$163$	1.38011	+	4.24753i	0.108098	+	0.332692i	0.990445	−	0.137907i	$-0.0440377\pi$
$163$	1.38011	+	4.24753i	0.108098	+	0.332692i	−0.882347	+	0.470600i	$0.844038\pi$
$164$	1.78744			0.139576
$165$	1.53380	+	0.421991i	0.119406	+	0.0328520i
$166$	1.59761			0.123998
$167$	5.62762	+	17.3200i	0.435478	+	1.34026i	0.892596	+	0.450857i	$0.148882\pi$
$167$	5.62762	+	17.3200i	0.435478	+	1.34026i	−0.457118	+	0.889406i	$0.651118\pi$
$168$	−0.102457	−	0.0744395i	−0.00790474	−	0.00574313i
$169$	10.5171	−	7.64111i	0.809007	−	0.587778i
$170$	7.26507	−	22.3596i	0.557206	−	1.71490i
$171$	−4.43503	+	13.6496i	−0.339155	+	1.04381i
$172$	−0.130680	+	0.0949442i	−0.00996422	+	0.00723943i
$173$	−20.0836	−	14.5916i	−1.52693	−	1.10938i	−0.957915	−	0.287052i	$-0.907325\pi$
$173$	−20.0836	−	14.5916i	−1.52693	−	1.10938i	−0.569015	−	0.822327i	$-0.692675\pi$
$174$	0.101261	+	0.311650i	0.00767659	+	0.0236261i
$175$	10.4707			0.791514
$176$	3.10421	−	1.16785i	0.233989	−	0.0880298i
$177$	0.996703			0.0749168
$178$	−5.73554	−	17.6522i	−0.429897	−	1.32309i
$179$	−7.02708	−	5.10547i	−0.525229	−	0.381601i	0.293341	−	0.956008i	$-0.405233\pi$
$179$	−7.02708	−	5.10547i	−0.525229	−	0.381601i	−0.818570	+	0.574407i	$0.805233\pi$
$180$	−9.40799	+	6.83530i	−0.701230	+	0.509473i
$181$	−1.41165	+	4.34461i	−0.104927	+	0.322932i	−0.989713	−	0.143065i	$-0.954304\pi$
$181$	−1.41165	+	4.34461i	−0.104927	+	0.322932i	0.884786	+	0.465997i	$0.154304\pi$
$182$	−0.00409816	+	0.0126128i	−0.000303775	+	0.000934925i
$183$	−0.505750	+	0.367449i	−0.0373861	+	0.0271626i
$184$	−0.890642	−	0.647089i	−0.0656590	−	0.0477040i
$185$	1.20393	+	3.70530i	0.0885144	+	0.272419i
$186$	−1.17464			−0.0861290
$187$	−18.7323	+	7.04735i	−1.36984	+	0.515353i
$188$	−5.43218			−0.396182
$189$	−0.234218	−	0.720848i	−0.0170368	−	0.0524340i
$190$	15.1554	+	11.0110i	1.09949	+	0.798825i
$191$	−0.152068	+	0.110484i	−0.0110032	+	0.00799432i	−0.593273	−	0.805001i	$-0.702165\pi$
$191$	−0.152068	+	0.110484i	−0.0110032	+	0.00799432i	0.582270	+	0.812995i	$0.302165\pi$
$192$	0.0380437	−	0.117086i	0.00274557	−	0.00844999i
$193$	−5.93474	+	18.2653i	−0.427192	+	1.31476i	0.473688	+	0.880693i	$0.342923\pi$
$193$	−5.93474	+	18.2653i	−0.427192	+	1.31476i	−0.900880	+	0.434069i	$0.857077\pi$
$194$	−9.93438	+	7.21775i	−0.713247	+	0.518204i
$195$	−0.00500262	−	0.00363461i	−0.000358245	−	0.000260280i
$196$	−1.83612	−	5.65099i	−0.131151	−	0.403642i
$197$	−0.922455			−0.0657222			−0.0328611	−	0.999460i	$-0.510462\pi$
$197$	−0.922455			−0.0657222			−0.0328611	+	0.999460i	$0.510462\pi$
$198$	9.54494	+	2.62607i	0.678330	+	0.186627i
$199$	13.2663			0.940421			0.470210	−	0.882554i	$-0.344178\pi$
$199$	13.2663			0.940421			0.470210	+	0.882554i	$0.344178\pi$
$200$	3.14540	+	9.68054i	0.222413	+	0.684517i
$201$	−0.586741	−	0.426292i	−0.0413855	−	0.0300683i
$202$	−9.18477	+	6.67312i	−0.646238	+	0.469519i
$203$	0.846111	−	2.60406i	0.0593853	−	0.182769i
$204$	−0.229574	+	0.706556i	−0.0160734	+	0.0494688i
$205$	5.63388	−	4.09325i	0.393487	−	0.285885i
$206$	−11.3386	−	8.23801i	−0.790001	−	0.573969i
$207$	−1.01543	−	3.12517i	−0.0705772	−	0.217214i
$208$	−0.0128920			−0.000893902
$209$	−0.728141	−	15.9307i	−0.0503665	−	1.10195i
$210$	−0.493404			−0.0340481
$211$	5.04635	+	15.5311i	0.347405	+	1.06920i	0.960284	+	0.279026i	$0.0900114\pi$
$211$	5.04635	+	15.5311i	0.347405	+	1.06920i	−0.612879	+	0.790177i	$0.709989\pi$
$212$	6.88259	+	5.00050i	0.472698	+	0.343436i
$213$	1.17250	−	0.851873i	0.0803385	−	0.0583694i
$214$	−3.63896	+	11.1996i	−0.248754	+	0.765586i
$215$	−0.194469	+	0.598513i	−0.0132627	+	0.0408183i
$216$	0.596089	−	0.433084i	0.0405587	−	0.0294676i
$217$	7.94049	+	5.76911i	0.539036	+	0.391632i
$218$	1.13365	+	3.48902i	0.0767806	+	0.236306i
$219$	0.0669213			0.00452213
$220$	7.10986	−	10.7896i	0.479346	−	0.727436i
$221$	0.0777968			0.00523318
$222$	−0.0380437	−	0.117086i	−0.00255333	−	0.00785833i
$223$	−15.9151	−	11.5630i	−1.06575	−	0.774313i	−0.0906073	−	0.995887i	$-0.528881\pi$
$223$	−15.9151	−	11.5630i	−1.06575	−	0.774313i	−0.975144	+	0.221573i	$0.928881\pi$
$224$	−0.832227	+	0.604649i	−0.0556055	+	0.0403998i
$225$	−9.38852	+	28.8949i	−0.625901	+	1.92633i
$226$	−4.14480	+	12.7564i	−0.275708	+	0.848541i
$227$	−6.11633	+	4.44377i	−0.405955	+	0.294943i	−0.771962	−	0.635669i	$-0.780725\pi$
$227$	−6.11633	+	4.44377i	−0.405955	+	0.294943i	0.366007	+	0.930612i	$0.380725\pi$
$228$	−0.478906	−	0.347946i	−0.0317163	−	0.0230433i
$229$	−1.73258	−	5.33234i	−0.114492	−	0.352371i	0.877349	−	0.479854i	$-0.159310\pi$
$229$	−1.73258	−	5.33234i	−0.114492	−	0.352371i	−0.991841	+	0.127483i	$0.959310\pi$
$230$	−4.28907			−0.282813
$231$	0.262146	+	0.328185i	0.0172479	+	0.0215930i
$232$	2.66171			0.174750
$233$	2.34871	+	7.22858i	0.153869	+	0.473560i	0.998045	−	0.0625067i	$-0.0199095\pi$
$233$	2.34871	+	7.22858i	0.153869	+	0.473560i	−0.844176	+	0.536067i	$0.819909\pi$
$234$	−0.0311316	−	0.0226184i	−0.00203513	−	0.00147861i
$235$	−17.1218	+	12.4397i	−1.11690	+	0.811477i
$236$	2.50177	−	7.69966i	0.162851	−	0.501205i
$237$	0.540576	−	1.66372i	0.0351142	−	0.108070i
$238$	5.02206	−	3.64874i	0.325532	−	0.236513i
$239$	4.49499	+	3.26580i	0.290757	+	0.211247i	0.723596	−	0.690224i	$-0.242488\pi$
$239$	4.49499	+	3.26580i	0.290757	+	0.211247i	−0.432839	+	0.901471i	$0.642488\pi$
$240$	−0.148218	−	0.456167i	−0.00956742	−	0.0294455i
$241$	−10.5708			−0.680924			−0.340462	−	0.940258i	$-0.610583\pi$
$241$	−10.5708			−0.680924			−0.340462	+	0.940258i	$0.610583\pi$
$242$	−10.9541	+	1.00345i	−0.704159	+	0.0645043i
$243$	3.30166			0.211802
$244$	1.56913	+	4.82930i	0.100454	+	0.309164i
$245$	−18.7281	−	13.6067i	−1.19649	−	0.869303i
$246$	−0.178029	+	0.129346i	−0.0113507	+	0.00824677i
$247$	−0.0191556	+	0.0589550i	−0.00121884	+	0.00375121i
$248$	−2.94841	+	9.07427i	−0.187224	+	0.576217i
$249$	−0.159121	+	0.115608i	−0.0100839	+	0.00732639i
$250$	16.3229	+	11.8593i	1.03235	+	0.750047i
$251$	9.43708	+	29.0443i	0.595663	+	1.83326i	0.551397	+	0.834243i	$0.314095\pi$
$251$	9.43708	+	29.0443i	0.595663	+	1.83326i	0.0442659	+	0.999020i	$0.485905\pi$
$252$	−3.07048			−0.193422
$253$	2.27879	+	2.85285i	0.143266	+	0.179357i
$254$	15.9977			1.00378
$255$	0.894418	+	2.75273i	0.0560106	+	0.172383i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−4.89214	+	3.55435i	−0.305164	+	0.221714i	−0.729818	−	0.683641i	$-0.760395\pi$
$257$	−4.89214	+	3.55435i	−0.305164	+	0.221714i	0.424655	+	0.905355i	$0.360395\pi$
$258$	0.00614515	−	0.0189128i	0.000382580	−	0.00117746i
$259$	−0.317883	+	0.978342i	−0.0197523	+	0.0607912i
$260$	−0.0406347	+	0.0295228i	−0.00252006	+	0.00183093i
$261$	6.42746	+	4.66983i	0.397850	+	0.289055i
$262$	4.08433	+	12.5703i	0.252331	+	0.776594i
$263$	10.9524			0.675352			0.337676	−	0.941262i	$-0.390359\pi$
$263$	10.9524			0.675352			0.337676	+	0.941262i	$0.390359\pi$
$264$	−0.224669	+	0.340949i	−0.0138274	+	0.0209839i
$265$	33.1445			2.03605
$266$	1.52848	+	4.70417i	0.0937170	+	0.288431i
$267$	1.84863	+	1.34311i	0.113134	+	0.0821970i
$268$	−4.76591	+	3.46264i	−0.291124	+	0.211514i
$269$	6.75603	−	20.7929i	0.411923	−	1.26777i	−0.503052	−	0.864256i	$-0.667790\pi$
$269$	6.75603	−	20.7929i	0.411923	−	1.26777i	0.914975	−	0.403511i	$-0.132210\pi$
$270$	0.887060	−	2.73009i	0.0539848	−	0.166148i
$271$	−20.6161	+	14.9785i	−1.25234	+	0.909878i	−0.998355	−	0.0573300i	$-0.981741\pi$
$271$	−20.6161	+	14.9785i	−1.25234	+	0.909878i	−0.253985	+	0.967208i	$0.581741\pi$
$272$	4.88200	+	3.54698i	0.296015	+	0.215067i
$273$	−0.000504532	−	0.00155279i	−3.05357e−5	−	9.39792e-5i
$274$	4.05441			0.244936
$275$	−1.54140	−	33.7238i	−0.0929501	−	2.03362i
$276$	0.135533			0.00815814
$277$	−6.56012	−	20.1900i	−0.394159	−	1.21310i	−0.929614	−	0.368534i	$-0.879860\pi$
$277$	−6.56012	−	20.1900i	−0.394159	−	1.21310i	0.535455	−	0.844564i	$-0.320140\pi$
$278$	−10.5791	−	7.68614i	−0.634490	−	0.460984i
$279$	−23.0401	+	16.7396i	−1.37938	+	1.00218i
$280$	−1.23847	+	3.81161i	−0.0740125	+	0.227787i
$281$	4.59224	−	14.1335i	0.273950	−	0.843131i	−0.715545	−	0.698566i	$-0.753822\pi$
$281$	4.59224	−	14.1335i	0.273950	−	0.843131i	0.989495	−	0.144565i	$-0.0461783\pi$
$282$	0.541043	−	0.393091i	0.0322187	−	0.0234082i
$283$	17.4605	+	12.6858i	1.03792	+	0.754091i	0.969878	−	0.243591i	$-0.0783255\pi$
$283$	17.4605	+	12.6858i	1.03792	+	0.754091i	0.0680398	+	0.997683i	$0.478326\pi$
$284$	−3.63779	−	11.1960i	−0.215863	−	0.664359i
$285$	−2.30627			−0.136612
$286$	0.0412262	+	0.0113424i	0.00243776	+	0.000670693i
$287$	1.83872			0.108536
$288$	−0.922367	−	2.83875i	−0.0543510	−	0.167275i
$289$	−15.7070	−	11.4118i	−0.923944	−	0.671284i
$290$	8.38949	−	6.09532i	0.492648	−	0.357930i
$291$	0.467160	−	1.43777i	0.0273854	−	0.0842837i
$292$	0.167976	−	0.516976i	0.00983004	−	0.0302537i
$293$	10.6793	−	7.75894i	0.623889	−	0.453282i	−0.230389	−	0.973099i	$-0.574000\pi$
$293$	10.6793	−	7.75894i	0.623889	−	0.453282i	0.854278	+	0.519817i	$0.174000\pi$
$294$	0.591801	+	0.429969i	0.0345146	+	0.0250763i
$295$	−9.74687	−	29.9978i	−0.567485	−	1.74654i
$296$	−1.00000			−0.0581238
$297$	−2.28720	+	0.860477i	−0.132717	+	0.0499299i
$298$	6.83732			0.396075
$299$	−0.00438581	−	0.0134981i	−0.000253638	−	0.000780617i
$300$	−1.01380	−	0.736567i	−0.0585316	−	0.0425257i
$301$	−0.134429	+	0.0976681i	−0.00774834	+	0.00562950i
$302$	−4.57816	+	14.0901i	−0.263443	+	0.810796i
$303$	0.431910	−	1.32928i	0.0248126	−	0.0763653i
$304$	−3.89000	+	2.82625i	−0.223107	+	0.162097i
$305$	16.0049	+	11.6282i	0.916438	+	0.665831i
$306$	5.56601	+	17.1304i	0.318188	+	0.979281i
$307$	5.20755			0.297210			0.148605	−	0.988897i	$-0.452522\pi$
$307$	5.20755			0.297210			0.148605	+	0.988897i	$0.452522\pi$
$308$	3.19327	−	1.20135i	0.181954	−	0.0684534i
$309$	1.72546			0.0981578
$310$	11.4870	+	35.3532i	0.652416	+	2.00793i
$311$	−4.55430	−	3.30889i	−0.258251	−	0.187630i	0.451125	−	0.892461i	$-0.351023\pi$
$311$	−4.55430	−	3.30889i	−0.258251	−	0.187630i	−0.709375	+	0.704831i	$0.751023\pi$
$312$	0.00128404		0.000932912i	7.26947e−5		5.28158e-5i
$313$	7.69627	−	23.6867i	0.435019	−	1.33885i	−0.458049	−	0.888927i	$-0.651452\pi$
$313$	7.69627	−	23.6867i	0.435019	−	1.33885i	0.893067	−	0.449923i	$-0.148548\pi$
$314$	4.59991	−	14.1571i	0.259588	−	0.798930i
$315$	−9.67790	+	7.03141i	−0.545288	+	0.396175i
$316$	−11.4956	−	8.35204i	−0.646678	−	0.469839i
$317$	−8.14750	−	25.0754i	−0.457609	−	1.40838i	−0.868045	−	0.496486i	$-0.834623\pi$
$317$	−8.14750	−	25.0754i	−0.457609	−	1.40838i	0.410436	−	0.911890i	$-0.365377\pi$
$318$	−1.04736			−0.0587329
$319$	−8.51162	−	2.34178i	−0.476559	−	0.131114i
$320$	−3.89599			−0.217792
$321$	−0.447999	−	1.37880i	−0.0250049	−	0.0769571i
$322$	−0.916194	−	0.665654i	−0.0510575	−	0.0370954i
$323$	23.4742	−	17.0550i	1.30614	−	0.948964i
$324$	2.73907	−	8.42999i	0.152171	−	0.468333i
$325$	−0.0405506	+	0.124802i	−0.00224934	+	0.00692276i
$326$	−3.61316	+	2.62512i	−0.200115	+	0.145392i
$327$	−0.365389	−	0.265471i	−0.0202061	−	0.0146806i
$328$	0.552350	+	1.69996i	0.0304984	+	0.0938646i
$329$	−5.58803			−0.308078
$330$	0.0726342	+	1.58914i	0.00399838	+	0.0874791i
$331$	−21.3680			−1.17449			−0.587247	−	0.809408i	$-0.699788\pi$
$331$	−21.3680			−1.17449			−0.587247	+	0.809408i	$0.699788\pi$
$332$	0.493688	+	1.51942i	0.0270947	+	0.0833888i
$333$	−2.41479	−	1.75445i	−0.132330	−	0.0961431i
$334$	−14.7333	+	10.7044i	−0.806170	+	0.585717i
$335$	−7.09232	+	21.8279i	−0.387495	+	1.19259i
$336$	0.0391352	−	0.120446i	0.00213500	−	0.00657085i
$337$	9.36386	−	6.80324i	0.510082	−	0.370596i	−0.302773	−	0.953063i	$-0.597912\pi$
$337$	9.36386	−	6.80324i	0.510082	−	0.370596i	0.812855	+	0.582466i	$0.197912\pi$
$338$	10.5171	+	7.64111i	0.572054	+	0.415622i
$339$	−0.510274	−	1.57046i	−0.0277143	−	0.0852958i
$340$	23.5103			1.27502
$341$	17.4120	−	26.4237i	0.942913	−	1.43092i
$342$	−14.3520			−0.776070
$343$	−4.11397	−	12.6615i	−0.222134	−	0.683657i
$344$	−0.130680	−	0.0949442i	−0.00704577	−	0.00511905i
$345$	0.427190	−	0.310372i	0.0229991	−	0.0167098i
$346$	7.67126	−	23.6097i	0.412410	−	1.26927i
$347$	−1.16607	+	3.58878i	−0.0625977	+	0.192656i	−0.977464	−	0.211100i	$-0.932295\pi$
$347$	−1.16607	+	3.58878i	−0.0625977	+	0.192656i	0.914867	+	0.403756i	$0.132295\pi$
$348$	−0.265105	+	0.192610i	−0.0142111	+	0.0103250i
$349$	25.6603	+	18.6433i	1.37357	+	0.997955i	0.997449	+	0.0713827i	$0.0227412\pi$
$349$	25.6603	+	18.6433i	1.37357	+	0.997955i	0.376118	+	0.926572i	$0.377259\pi$
$350$	3.23564	+	9.95827i	0.172952	+	0.532292i
$351$	0.00949894			0.000507016
$352$	2.06994	+	2.59140i	0.110328	+	0.138122i
$353$	−31.6492			−1.68452			−0.842258	−	0.539074i	$-0.818774\pi$
$353$	−31.6492			−1.68452			−0.842258	+	0.539074i	$0.818774\pi$
$354$	0.307998	+	0.947921i	0.0163699	+	0.0503814i
$355$	−37.1049	−	26.9583i	−1.96932	−	1.43080i
$356$	15.0158	−	10.9097i	0.795838	−	0.578210i
$357$	−0.236160	+	0.726827i	−0.0124989	+	0.0384678i
$358$	2.68411	−	8.26083i	0.141859	−	0.436599i
$359$	−6.70312	+	4.87010i	−0.353777	+	0.257034i	−0.750452	−	0.660925i	$-0.770164\pi$
$359$	−6.70312	+	4.87010i	−0.353777	+	0.257034i	0.396675	+	0.917959i	$0.370164\pi$
$360$	−9.40799	−	6.83530i	−0.495844	−	0.360252i
$361$	1.27310	+	3.91819i	0.0670051	+	0.206221i
$362$	−4.56819			−0.240099
$363$	1.01842	−	0.892622i	0.0534530	−	0.0468505i
$364$	−0.0132619			−0.000695113
$365$	−0.654431	−	2.01413i	−0.0342545	−	0.105425i
$366$	−0.505750	−	0.367449i	−0.0264360	−	0.0192069i
$367$	−11.3995	+	8.28225i	−0.595051	+	0.432330i	−0.844119	−	0.536156i	$-0.819876\pi$
$367$	−11.3995	+	8.28225i	−0.595051	+	0.432330i	0.249068	+	0.968486i	$0.419876\pi$
$368$	0.340195	−	1.04701i	0.0177339	−	0.0545793i
$369$	−1.64868	+	5.07411i	−0.0858268	+	0.264148i
$370$	−3.15192	+	2.29000i	−0.163861	+	0.119052i
$371$	7.08005	+	5.14396i	0.367578	+	0.267061i
$372$	−0.362985	−	1.11715i	−0.0188199	−	0.0579216i
$373$	6.02010			0.311709			0.155855	−	0.987780i	$-0.450187\pi$
$373$	6.02010			0.311709			0.155855	+	0.987780i	$0.450187\pi$
$374$	−12.4910	−	15.6377i	−0.645896	−	0.808608i
$375$	−2.48393			−0.128270
$376$	−1.67864	−	5.16631i	−0.0865690	−	0.266432i
$377$	0.0277613	+	0.0201698i	0.00142978	+	0.00103880i
$378$	0.613190	−	0.445509i	0.0315391	−	0.0229145i
$379$	7.27394	−	22.3869i	0.373637	−	1.14994i	−0.570756	−	0.821119i	$-0.693350\pi$
$379$	7.27394	−	22.3869i	0.373637	−	1.14994i	0.944394	−	0.328817i	$-0.106650\pi$
$380$	−5.78885	+	17.8162i	−0.296962	+	0.913954i
$381$	−1.59336	+	1.15765i	−0.0816305	+	0.0593080i
$382$	−0.152068	−	0.110484i	−0.00778046	−	0.00565284i
$383$	−0.346438	−	1.06623i	−0.0177022	−	0.0544817i	0.941815	−	0.336131i	$-0.109119\pi$
$383$	−0.346438	−	1.06623i	−0.0177022	−	0.0544817i	−0.959517	+	0.281649i	$0.909119\pi$
$384$	0.123112			0.00628253
$385$	7.31384	−	11.0992i	0.372748	−	0.565666i
$386$	−19.2052			−0.977520
$387$	−0.148989	−	0.458541i	−0.00757353	−	0.0233089i
$388$	−9.93438	−	7.21775i	−0.504342	−	0.366426i
$389$	9.27686	−	6.74003i	0.470356	−	0.341733i	−0.327224	−	0.944947i	$-0.606113\pi$
$389$	9.27686	−	6.74003i	0.470356	−	0.341733i	0.797580	+	0.603213i	$0.206113\pi$
$390$	0.00191083	−	0.00588093i	9.67586e−5	−	0.000297792i
$391$	−2.05290	+	6.31818i	−0.103820	+	0.319524i
$392$	4.80702	−	3.49250i	0.242791	−	0.176398i
$393$	−1.31643	−	0.956440i	−0.0664049	−	0.0482460i
$394$	−0.285054	−	0.877307i	−0.0143608	−	0.0441981i
$395$	−55.3594			−2.78543
$396$	0.452006	+	9.88928i	0.0227142	+	0.496955i
$397$	14.2583			0.715601			0.357801	−	0.933798i	$-0.383527\pi$
$397$	14.2583			0.715601			0.357801	+	0.933798i	$0.383527\pi$
$398$	4.09950	+	12.6170i	0.205489	+	0.632432i
$399$	−0.492646	−	0.357928i	−0.0246631	−	0.0179188i
$400$	−8.23476	+	5.98290i	−0.411738	+	0.299145i
$401$	−4.65774	+	14.3350i	−0.232596	+	0.715858i	0.764835	+	0.644226i	$0.222820\pi$
$401$	−4.65774	+	14.3350i	−0.232596	+	0.715858i	−0.997431	+	0.0716313i	$0.977180\pi$
$402$	0.224115	−	0.689755i	0.0111778	−	0.0344019i
$403$	−0.0995141	+	0.0723013i	−0.00495715	+	0.00360158i
$404$	−9.18477	−	6.67312i	−0.456959	−	0.332000i
$405$	−10.6714	−	32.8432i	−0.530265	−	1.63199i
$406$	2.73807			0.135888
$407$	3.19780	+	0.879802i	0.158509	+	0.0436102i
$408$	−0.742917			−0.0367799
$409$	4.69646	+	14.4542i	0.232225	+	0.714715i	0.997477	+	0.0709849i	$0.0226142\pi$
$409$	4.69646	+	14.4542i	0.232225	+	0.714715i	−0.765252	+	0.643730i	$0.777386\pi$
$410$	5.63388	+	4.09325i	0.278237	+	0.202151i
$411$	−0.403818	+	0.293391i	−0.0199189	+	0.0144719i
$412$	4.33098	−	13.3294i	0.213372	−	0.656691i
$413$	2.57355	−	7.92056i	0.126636	−	0.389745i
$414$	2.65843	−	1.93146i	0.130655	−	0.0949261i
$415$	5.03553	+	3.65853i	0.247185	+	0.179590i
$416$	−0.00398386	−	0.0122611i	−0.000195325	−	0.000601148i
$417$	1.60987			0.0788356
$418$	14.9260	−	5.61537i	0.730055	−	0.274657i
$419$	24.8206			1.21257			0.606283	−	0.795249i	$-0.292660\pi$
$419$	24.8206			1.21257			0.606283	+	0.795249i	$0.292660\pi$
$420$	−0.152470	−	0.469255i	−0.00743978	−	0.0228973i
$421$	0.0760425	+	0.0552481i	0.00370609	+	0.00269263i	0.589637	−	0.807669i	$-0.299271\pi$
$421$	0.0760425	+	0.0552481i	0.00370609	+	0.00269263i	−0.585931	+	0.810361i	$0.699271\pi$
$422$	−13.2115	+	9.59873i	−0.643126	+	0.467259i
$423$	5.01046	−	15.4206i	0.243617	−	0.749776i
$424$	−2.62892	+	8.09097i	−0.127671	+	0.392932i
$425$	49.6925	−	36.1037i	2.41044	−	1.75129i
$426$	1.17250	+	0.851873i	0.0568079	+	0.0412734i
$427$	1.61415	+	4.96785i	0.0781143	+	0.240411i
$428$	−11.7759			−0.569210
$429$	−0.00492690	+	0.00185357i	−0.000237873	+	8.94910e-5i
$430$	−0.629314			−0.0303482
$431$	−4.65385	−	14.3231i	−0.224168	−	0.689919i	−0.998375	−	0.0569859i	$-0.981851\pi$
$431$	−4.65385	−	14.3231i	−0.224168	−	0.689919i	0.774207	−	0.632933i	$-0.218149\pi$
$432$	0.596089	+	0.433084i	0.0286793	+	0.0208368i
$433$	18.2902	−	13.2886i	0.878972	−	0.638611i	−0.0540071	−	0.998541i	$-0.517199\pi$
$433$	18.2902	−	13.2886i	0.878972	−	0.638611i	0.932979	+	0.359930i	$0.117199\pi$
$434$	−3.03300	+	9.33461i	−0.145589	+	0.448076i
$435$	−0.394512	+	1.21418i	−0.0189154	+	0.0582157i
$436$	−2.96794	+	2.15633i	−0.142139	+	0.103270i
$437$	−4.28248	−	3.11140i	−0.204859	−	0.148839i
$438$	0.0206798	+	0.0636460i	0.000988121	+	0.00304112i
$439$	15.2327			0.727019			0.363510	−	0.931590i	$-0.381578\pi$
$439$	15.2327			0.727019			0.363510	+	0.931590i	$0.381578\pi$
$440$	12.4586	+	3.42770i	0.593941	+	0.163409i
$441$	17.7353			0.844540
$442$	0.0240405	+	0.0739891i	0.00114349	+	0.00351930i
$443$	3.92633	+	2.85265i	0.186546	+	0.135533i	0.677138	−	0.735856i	$-0.263220\pi$
$443$	3.92633	+	2.85265i	0.186546	+	0.135533i	−0.490593	+	0.871389i	$0.663220\pi$
$444$	0.0995997	−	0.0723634i	0.00472679	−	0.00343422i
$445$	22.3456	−	68.7727i	1.05928	−	3.26014i
$446$	6.07901	−	18.7093i	0.287850	−	0.885910i
$447$	−0.680995	+	0.494772i	−0.0322100	+	0.0234019i
$448$	−0.832227	−	0.604649i	−0.0393191	−	0.0285670i
$449$	8.93595	+	27.5020i	0.421713	+	1.29790i	0.906106	+	0.423050i	$0.139040\pi$
$449$	8.93595	+	27.5020i	0.421713	+	1.29790i	−0.484393	+	0.874850i	$0.660960\pi$
$450$	−30.3819			−1.43222
$451$	−0.270679	−	5.92210i	−0.0127458	−	0.278861i
$452$	−13.4128			−0.630887
$453$	−0.563626	−	1.73466i	−0.0264815	−	0.0815016i
$454$	−6.11633	−	4.44377i	−0.287053	−	0.208557i
$455$	−0.0418005	+	0.0303698i	−0.00195964	+	0.00142376i
$456$	0.182926	−	0.562988i	0.00856629	−	0.0263643i
$457$	−12.9387	+	39.8213i	−0.605248	+	1.86276i	−0.110169	+	0.993913i	$0.535139\pi$
$457$	−12.9387	+	39.8213i	−0.605248	+	1.86276i	−0.495079	+	0.868848i	$0.664861\pi$
$458$	4.53596	−	3.29557i	0.211951	−	0.153992i
$459$	−3.59709	−	2.61344i	−0.167898	−	0.121985i
$460$	−1.32539	−	4.07915i	−0.0617969	−	0.190191i
$461$	−17.2212			−0.802073			−0.401036	−	0.916062i	$-0.631350\pi$
$461$	−17.2212			−0.802073			−0.401036	+	0.916062i	$0.631350\pi$
$462$	−0.231115	+	0.350730i	−0.0107524	+	0.0163175i
$463$	14.3437			0.666610			0.333305	−	0.942819i	$-0.391836\pi$
$463$	14.3437			0.666610			0.333305	+	0.942819i	$0.391836\pi$
$464$	0.822513	+	2.53143i	0.0381842	+	0.117519i
$465$	−3.70238	−	2.68994i	−0.171694	−	0.124743i
$466$	−6.14900	+	4.46751i	−0.284847	+	0.206953i
$467$	0.274469	−	0.844728i	0.0127009	−	0.0390894i	−0.944505	−	0.328496i	$-0.893458\pi$
$467$	0.274469	−	0.844728i	0.0127009	−	0.0390894i	0.957206	+	0.289407i	$0.0934581\pi$
$468$	0.0118912	−	0.0365973i	0.000549671	−	0.00169171i
$469$	−4.90264	+	3.56198i	−0.226383	+	0.164477i
$470$	−17.1218	−	12.4397i	−0.789769	−	0.573801i
$471$	0.566304	+	1.74291i	0.0260939	+	0.0803089i
$472$	8.09590			0.372644
$473$	0.334355	+	0.418585i	0.0153737	+	0.0192466i
$474$	1.74934			0.0803499
$475$	15.1240	+	46.5470i	0.693938	+	2.13572i
$476$	5.02206	+	3.64874i	0.230186	+	0.167240i
$477$	−20.5435	+	14.9257i	−0.940621	+	0.683401i
$478$	−1.71694	+	5.28418i	−0.0785308	+	0.241693i
$479$	5.16083	−	15.8834i	0.235805	−	0.725732i	−0.761209	−	0.648506i	$-0.775394\pi$
$479$	5.16083	−	15.8834i	0.235805	−	0.725732i	0.997014	−	0.0772253i	$-0.0246061\pi$
$480$	0.388039	−	0.281927i	0.0177115	−	0.0128681i
$481$	−0.0104299	−	0.00757775i	−0.000475562	−	0.000345516i
$482$	−3.26655	−	10.0534i	−0.148787	−	0.457921i
$483$	0.139422			0.00634391
$484$	−4.33935	−	10.1079i	−0.197243	−	0.459451i
$485$	−47.8410			−2.17235
$486$	1.02027	+	3.14007i	0.0462804	+	0.142436i
$487$	−0.483104	−	0.350996i	−0.0218915	−	0.0159051i	0.576786	−	0.816896i	$-0.304307\pi$
$487$	−0.483104	−	0.350996i	−0.0218915	−	0.0159051i	−0.598677	+	0.800990i	$0.704307\pi$
$488$	−4.10805	+	2.98467i	−0.185963	+	0.135110i
$489$	0.169908	−	0.522922i	0.00768349	−	0.0236473i
$490$	7.15349	−	22.0162i	0.323162	−	0.994589i
$491$	−1.92270	+	1.39692i	−0.0867701	+	0.0630421i	−0.630324	−	0.776332i	$-0.717078\pi$
$491$	−1.92270	+	1.39692i	−0.0867701	+	0.0630421i	0.543554	+	0.839374i	$0.317078\pi$
$492$	−0.178029	−	0.129346i	−0.00802616	−	0.00583135i
$493$	−4.96344	−	15.2759i	−0.223542	−	0.687992i
$494$	−0.0619889			−0.00278901
$495$	24.0712	+	30.1351i	1.08192	+	1.35447i
$496$	−9.54125			−0.428415
$497$	−3.74216	−	11.5172i	−0.167859	−	0.516616i
$498$	−0.159121	−	0.115608i	−0.00713040	−	0.00518054i
$499$	−8.55432	+	6.21507i	−0.382944	+	0.278225i	−0.762558	−	0.646920i	$-0.776057\pi$
$499$	−8.55432	+	6.21507i	−0.382944	+	0.278225i	0.379614	+	0.925145i	$0.376057\pi$
$500$	−6.23479	+	19.1887i	−0.278828	+	0.858146i
$501$	0.692827	−	2.13230i	0.0309532	−	0.0952643i
$502$	−24.7066	+	17.9504i	−1.10271	+	0.801165i
$503$	−7.58774	−	5.51282i	−0.338321	−	0.245804i	0.405632	−	0.914036i	$-0.367051\pi$
$503$	−7.58774	−	5.51282i	−0.338321	−	0.245804i	−0.743953	+	0.668232i	$0.767051\pi$
$504$	−0.948830	−	2.92020i	−0.0422642	−	0.130076i
$505$	−44.2311			−1.96826
$506$	−2.00904	+	3.04884i	−0.0893127	+	0.135537i
$507$	−1.60044			−0.0710778
$508$	4.94355	+	15.2147i	0.219335	+	0.675043i
$509$	−17.6067	−	12.7920i	−0.780401	−	0.566995i	0.124698	−	0.992195i	$-0.460204\pi$
$509$	−17.6067	−	12.7920i	−0.780401	−	0.566995i	−0.905099	+	0.425200i	$0.860204\pi$
$510$	−2.34162	+	1.70128i	−0.103688	+	0.0753341i
$511$	0.172795	−	0.531808i	0.00764400	−	0.0235258i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	2.86618	−	2.08240i	0.126545	−	0.0919402i
$514$	−4.89214	−	3.55435i	−0.215783	−	0.156776i
$515$	−16.8734	−	51.9311i	−0.743532	−	2.28836i
$516$	0.0198861			0.000875438
$517$	0.822616	+	17.9977i	0.0361786	+	0.791538i
$518$	−1.02869			−0.0451980
$519$	0.944424	+	2.90664i	0.0414556	+	0.127587i
$520$	−0.0406347	−	0.0295228i	−0.00178195	−	0.00129466i
$521$	−25.2814	+	18.3680i	−1.10760	+	0.804718i	−0.982284	−	0.187399i	$-0.939994\pi$
$521$	−25.2814	+	18.3680i	−1.10760	+	0.804718i	−0.125315	+	0.992117i	$0.539994\pi$
$522$	−2.45507	+	7.55594i	−0.107456	+	0.330714i
$523$	−8.66414	+	26.6655i	−0.378856	+	1.16600i	0.561983	+	0.827149i	$0.310038\pi$
$523$	−8.66414	+	26.6655i	−0.378856	+	1.16600i	−0.940840	+	0.338852i	$0.889962\pi$
$524$	−10.6929	+	7.76886i	−0.467122	+	0.339384i
$525$	−1.04288	−	0.757699i	−0.0455151	−	0.0330687i
$526$	3.38447	+	10.4163i	0.147570	+	0.454173i
$527$	57.5765			2.50807
$528$	−0.393688	−	0.108314i	−0.0171331	−	0.00471377i
$529$	−21.7880			−0.947306
$530$	10.2422	+	31.5223i	0.444894	+	1.36924i
$531$	19.5499	+	14.2038i	0.848393	+	0.616394i
$532$	−4.00161	+	2.90734i	−0.173492	+	0.126049i
$533$	−0.00712092	+	0.0219160i	−0.000308441	+	0.000949285i
$534$	−0.706114	+	2.17320i	−0.0305566	+	0.0940434i
$535$	−37.1167	+	26.9669i	−1.60470	+	1.16588i
$536$	−4.76591	−	3.46264i	−0.205856	−	0.149563i
$537$	0.330446	+	1.01701i	0.0142598	+	0.0438871i
$538$	21.8630			0.942580
$539$	−18.4446	+	6.93911i	−0.794465	+	0.298889i
$540$	2.87059			0.123530
$541$	5.62645	+	17.3164i	0.241900	+	0.744491i	0.996131	+	0.0878822i	$0.0280099\pi$
$541$	5.62645	+	17.3164i	0.241900	+	0.744491i	−0.754231	+	0.656609i	$0.771990\pi$
$542$	−20.6161	−	14.9785i	−0.885538	−	0.643381i
$543$	0.454991	−	0.330570i	0.0195255	−	0.0141861i
$544$	−1.86476	+	5.73913i	−0.0799508	+	0.246063i
$545$	−4.41670	+	13.5932i	−0.189190	+	0.582268i
$546$	0.00132088		0.000959677i	5.65286e−5		4.10704e-5i
$547$	−4.01279	−	2.91546i	−0.171575	−	0.124656i	0.498684	−	0.866784i	$-0.333817\pi$
$547$	−4.01279	−	2.91546i	−0.171575	−	0.124656i	−0.670259	+	0.742128i	$0.733817\pi$
$548$	1.25288	+	3.85597i	0.0535204	+	0.164719i
$549$	−15.1565			−0.646864
$550$	31.5969	−	11.8872i	1.34730	−	0.506871i
$551$	12.7983			0.545226
$552$	0.0418821	+	0.128900i	0.00178262	+	0.00548634i
$553$	−11.8254	−	8.59166i	−0.502867	−	0.365354i
$554$	17.1746	−	12.4781i	0.729680	−	0.530143i
$555$	0.148218	−	0.456167i	0.00629150	−	0.0193632i
$556$	4.04085	−	12.4364i	0.171370	−	0.527423i
$557$	30.7938	−	22.3730i	1.30477	−	0.947973i	0.304783	−	0.952422i	$-0.401416\pi$
$557$	30.7938	−	22.3730i	1.30477	−	0.947973i	0.999990	+	0.00444866i	$0.00141606\pi$
$558$	−23.0401	−	16.7396i	−0.975366	−	0.708645i
$559$	−0.000643508	−	0.00198051i	−2.72175e−5	−	8.37668e-5i
$560$	−4.00776			−0.169359
$561$	2.37570	+	0.653620i	0.100302	+	0.0275959i
$562$	14.8608			0.626865
$563$	3.56130	+	10.9606i	0.150091	+	0.461933i	0.997631	−	0.0687996i	$-0.0219169\pi$
$563$	3.56130	+	10.9606i	0.150091	+	0.461933i	−0.847539	+	0.530732i	$0.821917\pi$
$564$	0.541043	+	0.393091i	0.0227820	+	0.0165521i
$565$	−42.2762	+	30.7155i	−1.77857	+	1.29221i
$566$	−6.66931	+	20.5260i	−0.280332	+	0.862773i
$567$	2.81765	−	8.67185i	0.118330	−	0.364183i
$568$	9.52387	−	6.91949i	0.399613	−	0.290335i
$569$	−8.46272	−	6.14852i	−0.354776	−	0.257760i	0.396094	−	0.918210i	$-0.370365\pi$
$569$	−8.46272	−	6.14852i	−0.354776	−	0.257760i	−0.750870	+	0.660450i	$0.770365\pi$
$570$	−0.712677	−	2.19339i	−0.0298507	−	0.0918712i
$571$	20.2874			0.849003			0.424501	−	0.905427i	$-0.360449\pi$
$571$	20.2874			0.849003			0.424501	+	0.905427i	$0.360449\pi$
$572$	0.00195229	+	0.0427135i	8.16294e−5	+	0.00178594i
$573$	0.0231409			0.000966724
$574$	0.568197	+	1.74873i	0.0237161	+	0.0729906i
$575$	−9.06559	−	6.58654i	−0.378061	−	0.274678i
$576$	2.41479	−	1.75445i	0.100616	−	0.0731020i
$577$	0.778795	−	2.39689i	0.0324217	−	0.0997837i	−0.933536	−	0.358483i	$-0.883294\pi$
$577$	0.778795	−	2.39689i	0.0324217	−	0.0997837i	0.965958	+	0.258700i	$0.0832940\pi$
$578$	5.99956	−	18.4647i	0.249549	−	0.768032i
$579$	1.91284	−	1.38976i	0.0794947	−	0.0577563i
$580$	8.38949	+	6.09532i	0.348355	+	0.253094i
$581$	0.507852	+	1.56301i	0.0210693	+	0.0648445i
$582$	1.51176			0.0626646
$583$	15.5252	−	23.5604i	0.642989	−	0.975773i
$584$	0.543581			0.0224935
$585$	−0.0463280	−	0.142583i	−0.00191543	−	0.00589507i
$586$	10.6793	+	7.75894i	0.441156	+	0.320519i
$587$	28.8328	−	20.9483i	1.19006	−	0.864627i	0.196787	−	0.980446i	$-0.436949\pi$
$587$	28.8328	−	20.9483i	1.19006	−	0.864627i	0.993270	+	0.115819i	$0.0369492\pi$
$588$	−0.226048	+	0.695704i	−0.00932206	+	0.0286904i
$589$	−14.1769	+	43.6319i	−0.584147	+	1.79782i
$590$	25.5176	−	18.5397i	1.05054	−	0.763265i
$591$	0.0918763	+	0.0667520i	0.00377928	+	0.00274581i
$592$	−0.309017	−	0.951057i	−0.0127005	−	0.0390882i
$593$	33.5776			1.37887			0.689433	−	0.724350i	$-0.257860\pi$
$593$	33.5776			1.37887			0.689433	+	0.724350i	$0.257860\pi$
$594$	−1.52515	−	1.90936i	−0.0625775	−	0.0783419i
$595$	24.1848			0.991479
$596$	2.11285	+	6.50268i	0.0865456	+	0.266360i
$597$	−1.32132	−	0.959993i	−0.0540779	−	0.0392899i
$598$	0.0114822	−	0.00834230i	0.000469542	−	0.000341142i
$599$	−2.70676	+	8.33056i	−0.110595	+	0.340377i	−0.991003	−	0.133840i	$-0.957269\pi$
$599$	−2.70676	+	8.33056i	−0.110595	+	0.340377i	0.880408	+	0.474218i	$0.157269\pi$
$600$	0.387236	−	1.19179i	0.0158088	−	0.0486546i
$601$	32.2557	−	23.4351i	1.31574	−	0.955938i	0.315761	−	0.948839i	$-0.397740\pi$
$601$	32.2557	−	23.4351i	1.31574	−	0.955938i	0.999975	−	0.00709960i	$-0.00225989\pi$
$602$	−0.134429	−	0.0976681i	−0.00547890	−	0.00398066i
$603$	−5.43366	−	16.7231i	−0.221276	−	0.681016i
$604$	−14.8152			−0.602823
$605$	−36.8245	−	21.9222i	−1.49713	−	0.891265i
$606$	1.39769			0.0567773
$607$	5.76277	+	17.7360i	0.233904	+	0.719882i	0.997265	+	0.0739097i	$0.0235477\pi$
$607$	5.76277	+	17.7360i	0.233904	+	0.719882i	−0.763361	+	0.645972i	$0.776452\pi$
$608$	−3.89000	−	2.82625i	−0.157760	−	0.114620i
$609$	−0.272711	+	0.198136i	−0.0110508	+	0.00802889i
$610$	−6.11333	+	18.8149i	−0.247521	+	0.761792i
$611$	0.0216410	−	0.0666043i	0.000875503	−	0.00269452i
$612$	−14.5720	+	10.5872i	−0.589038	+	0.427961i
$613$	−12.6095	−	9.16134i	−0.509293	−	0.370023i	0.303262	−	0.952907i	$-0.401924\pi$
$613$	−12.6095	−	9.16134i	−0.509293	−	0.370023i	−0.812555	+	0.582884i	$0.801924\pi$
$614$	1.60922	+	4.95267i	0.0649429	+	0.199874i
$615$	−0.857335			−0.0345711
$616$	2.12933	+	2.66574i	0.0857931	+	0.107406i
$617$	−17.2046			−0.692630			−0.346315	−	0.938118i	$-0.612567\pi$
$617$	−17.2046			−0.692630			−0.346315	+	0.938118i	$0.612567\pi$
$618$	0.533195	+	1.64101i	0.0214483	+	0.0660110i
$619$	−15.8991	−	11.5513i	−0.639037	−	0.464288i	0.220482	−	0.975391i	$-0.429237\pi$
$619$	−15.8991	−	11.5513i	−0.639037	−	0.464288i	−0.859519	+	0.511103i	$0.829237\pi$
$620$	−30.0733	+	21.8495i	−1.20777	+	0.877497i
$621$	−0.250658	+	0.771445i	−0.0100585	+	0.0309570i
$622$	1.73959	−	5.35390i	0.0697511	−	0.214672i
$623$	15.4466	−	11.2226i	0.618857	−	0.449626i
$624$	0.00128404		0.000932912i	5.14029e−5		3.73464e-5i
$625$	8.56370	+	26.3563i	0.342548	+	1.05425i
$626$	24.9056			0.995430
$627$	−1.08028	+	1.63939i	−0.0431422	+	0.0654708i
$628$	14.8856			0.594001
$629$	1.86476	+	5.73913i	0.0743528	+	0.228834i
$630$	−9.67790	−	7.03141i	−0.385577	−	0.280138i
$631$	−13.3737	+	9.71656i	−0.532399	+	0.386810i	−0.821254	−	0.570562i	$-0.806725\pi$
$631$	−13.3737	+	9.71656i	−0.532399	+	0.386810i	0.288856	+	0.957373i	$0.406725\pi$
$632$	4.39093	−	13.5139i	0.174662	−	0.537553i
$633$	0.621266	−	1.91206i	0.0246931	−	0.0759976i
$634$	21.3304	−	15.4975i	0.847139	−	0.615483i
$635$	50.4234	+	36.6347i	2.00099	+	1.45380i
$636$	−0.323651	−	0.996096i	−0.0128336	−	0.0394978i
$637$	0.0766019			0.00303508
$638$	−0.403073	−	8.81868i	−0.0159578	−	0.349135i
$639$	35.1380			1.39004
$640$	−1.20393	−	3.70530i	−0.0475894	−	0.146465i
$641$	−9.30043	−	6.75716i	−0.367345	−	0.266892i	0.388764	−	0.921337i	$-0.372902\pi$
$641$	−9.30043	−	6.75716i	−0.367345	−	0.266892i	−0.756109	+	0.654446i	$0.772902\pi$
$642$	1.17288	−	0.852145i	0.0462898	−	0.0336315i
$643$	6.41549	−	19.7449i	0.253002	−	0.778661i	−0.741214	−	0.671268i	$-0.765750\pi$
$643$	6.41549	−	19.7449i	0.253002	−	0.778661i	0.994217	−	0.107393i	$-0.0342502\pi$
$644$	0.349955	−	1.07705i	0.0137902	−	0.0424417i
$645$	0.0626795	−	0.0455393i	0.00246800	−	0.00179311i
$646$	23.4742	+	17.0550i	0.923578	+	0.671019i
$647$	7.49898	+	23.0795i	0.294815	+	0.907348i	0.983283	+	0.182082i	$0.0582835\pi$
$647$	7.49898	+	23.0795i	0.294815	+	0.907348i	−0.688468	+	0.725267i	$0.741717\pi$
$648$	8.86382			0.348204
$649$	−25.8891	−	7.12280i	−1.01624	−	0.279594i
$650$	−0.131224			−0.00514705
$651$	−0.373399	−	1.14920i	−0.0146346	−	0.0450408i
$652$	−3.61316	−	2.62512i	−0.141502	−	0.102807i
$653$	−0.967374	+	0.702838i	−0.0378563	+	0.0275042i	−0.606552	−	0.795043i	$-0.707448\pi$
$653$	−0.967374	+	0.702838i	−0.0378563	+	0.0275042i	0.568696	+	0.822548i	$0.307448\pi$
$654$	0.139566	−	0.429541i	0.00545747	−	0.0167964i
$655$	−15.9125	+	48.9736i	−0.621753	+	1.91356i
$656$	−1.44607	+	1.05063i	−0.0564596	+	0.0410203i
$657$	1.31263	+	0.953684i	0.0512107	+	0.0372068i
$658$	−1.72679	−	5.31453i	−0.0673175	−	0.207182i
$659$	−12.4217			−0.483881			−0.241940	−	0.970291i	$-0.577784\pi$
$659$	−12.4217			−0.483881			−0.241940	+	0.970291i	$0.577784\pi$
$660$	−1.48891	+	0.560149i	−0.0579559	+	0.0218038i
$661$	−30.0096			−1.16724			−0.583620	−	0.812027i	$-0.698364\pi$
$661$	−30.0096			−1.16724			−0.583620	+	0.812027i	$0.698364\pi$
$662$	−6.60309	−	20.3222i	−0.256636	−	0.789845i
$663$	−0.00774854	−	0.00562964i	−0.000300928	−	0.000218637i
$664$	−1.29249	+	0.939051i	−0.0501584	+	0.0364422i
$665$	−5.95493	+	18.3274i	−0.230922	+	0.710706i
$666$	0.922367	−	2.83875i	0.0357410	−	0.110000i
$667$	−2.37063	+	1.72236i	−0.0917911	+	0.0666901i
$668$	−14.7333	−	10.7044i	−0.570048	−	0.414164i
$669$	0.748399	+	2.30334i	0.0289348	+	0.0890521i
$670$	−22.9512			−0.886683
$671$	15.7626	−	5.93012i	0.608510	−	0.228930i
$672$	0.126644			0.00488540
$673$	−7.03743	−	21.6590i	−0.271273	−	0.834893i	−0.990181	−	0.139788i	$-0.955358\pi$
$673$	−7.03743	−	21.6590i	−0.271273	−	0.834893i	0.718908	−	0.695105i	$-0.244642\pi$
$674$	9.36386	+	6.80324i	0.360683	+	0.262051i
$675$	6.06742	−	4.40824i	0.233535	−	0.169673i
$676$	−4.01717	+	12.3636i	−0.154507	+	0.475522i
$677$	−12.0843	+	37.1917i	−0.464438	+	1.42939i	0.395250	+	0.918573i	$0.370658\pi$
$677$	−12.0843	+	37.1917i	−0.464438	+	1.42939i	−0.859688	+	0.510819i	$0.829342\pi$
$678$	1.33592	−	0.970599i	0.0513055	−	0.0372756i
$679$	−10.2194	−	7.42483i	−0.392184	−	0.284939i
$680$	7.26507	+	22.3596i	0.278603	+	0.857451i
$681$	0.930751			0.0356664
$682$	30.5111	+	8.39442i	1.16833	+	0.321439i
$683$	−10.5213			−0.402587			−0.201293	−	0.979531i	$-0.564514\pi$
$683$	−10.5213			−0.402587			−0.201293	+	0.979531i	$0.564514\pi$
$684$	−4.43503	−	13.6496i	−0.169577	−	0.521906i
$685$	12.7792	+	9.28460i	0.488267	+	0.354746i
$686$	10.7705	−	7.82524i	0.411220	−	0.298769i
$687$	−0.213302	+	0.656475i	−0.00813797	+	0.0250461i
$688$	0.0499151	−	0.153623i	0.00190300	−	0.00585682i
$689$	−0.0887307	+	0.0644666i	−0.00338037	+	0.00245598i
$690$	0.427190	+	0.310372i	0.0162628	+	0.0118156i
$691$	−6.59865	−	20.3086i	−0.251024	−	0.772574i	−0.994587	−	0.103907i	$-0.966865\pi$
$691$	−6.59865	−	20.3086i	−0.251024	−	0.772574i	0.743562	−	0.668666i	$-0.233135\pi$
$692$	24.8247			0.943694
$693$	0.464974	+	10.1730i	0.0176629	+	0.386440i
$694$	−3.77347			−0.143239
$695$	−15.7431	−	48.4522i	−0.597169	−	1.83790i
$696$	−0.265105	−	0.192610i	−0.0100488	−	0.00730088i
$697$	8.72630	−	6.34003i	0.330532	−	0.240146i
$698$	−9.80138	+	30.1655i	−0.370988	+	1.14178i
$699$	0.289154	−	0.889925i	0.0109368	−	0.0336601i
$700$	−8.47101	+	6.15455i	−0.320174	+	0.232620i
$701$	11.4675	+	8.33161i	0.433120	+	0.314680i	0.782895	−	0.622153i	$-0.213742\pi$
$701$	11.4675	+	8.33161i	0.433120	+	0.314680i	−0.349775	+	0.936834i	$0.613742\pi$
$702$	0.00293533	+	0.00903402i	0.000110787	+	0.000340967i
$703$	−4.80831			−0.181349
$704$	−1.82492	+	2.76942i	−0.0687792	+	0.104376i
$705$	2.60551			0.0981290
$706$	−9.78014	−	30.1002i	−0.368080	−	1.13284i
$707$	−9.44828	−	6.86457i	−0.355339	−	0.258169i
$708$	−0.806350	+	0.585847i	−0.0303045	+	0.0220175i
$709$	−5.21820	+	16.0600i	−0.195974	+	0.603145i	0.803990	+	0.594642i	$0.202706\pi$
$709$	−5.21820	+	16.0600i	−0.195974	+	0.603145i	−0.999964	+	0.00850215i	$0.997294\pi$
$710$	14.1728	−	43.6194i	0.531896	−	1.63701i
$711$	34.3126	−	24.9295i	1.28682	−	0.934930i
$712$	15.0158	+	10.9097i	0.562743	+	0.408856i
$713$	−3.24589	−	9.98981i	−0.121559	−	0.374121i
$714$	−0.764231			−0.0286006
$715$	0.103967	+	0.130159i	0.00388816	+	0.00486766i
$716$	8.68595			0.324609
$717$	−0.211375	−	0.650546i	−0.00789396	−	0.0242951i
$718$	−6.70312	−	4.87010i	−0.250158	−	0.181750i
$719$	33.9447	−	24.6622i	1.26592	−	0.919747i	0.266890	−	0.963727i	$-0.414004\pi$
$719$	33.9447	−	24.6622i	1.26592	−	0.919747i	0.999032	+	0.0439804i	$0.0140039\pi$
$720$	3.59353	−	11.0598i	0.133923	−	0.412173i
$721$	4.45523	−	13.7118i	0.165921	−	0.510654i
$722$	−3.33301	+	2.42157i	−0.124042	+	0.0901217i
$723$	1.05285	+	0.764938i	0.0391558	+	0.0284484i
$724$	−1.41165	−	4.34461i	−0.0524635	−	0.161466i
$725$	27.0928			1.00620
$726$	1.16364	+	0.692735i	0.0431868	+	0.0257098i
$727$	27.4101			1.01658			0.508291	−	0.861185i	$-0.330277\pi$
$727$	27.4101			1.01658			0.508291	+	0.861185i	$0.330277\pi$
$728$	−0.00409816	−	0.0126128i	−0.000151888	−	0.000467462i
$729$	21.1841	+	15.3911i	0.784596	+	0.570043i
$730$	1.71332	−	1.24480i	0.0634130	−	0.0460722i
$731$	−0.301212	+	0.927035i	−0.0111407	+	0.0342876i
$732$	0.193179	−	0.594545i	0.00714011	−	0.0219750i
$733$	−29.4923	+	21.4274i	−1.08932	+	0.791440i	−0.979285	−	0.202488i	$-0.935097\pi$
$733$	−29.4923	+	21.4274i	−1.08932	+	0.791440i	−0.110038	+	0.993927i	$0.535097\pi$
$734$	−11.3995	−	8.28225i	−0.420765	−	0.305703i
$735$	0.880680	+	2.71045i	0.0324844	+	0.0999766i
$736$	1.10089			0.0405795
$737$	12.1940	+	15.2659i	0.449172	+	0.562326i
$738$	−5.33524			−0.196393
$739$	1.04155	+	3.20557i	0.0383141	+	0.117919i	0.968384	−	0.249463i	$-0.0802542\pi$
$739$	1.04155	+	3.20557i	0.0383141	+	0.117919i	−0.930070	+	0.367382i	$0.880254\pi$
$740$	−3.15192	−	2.29000i	−0.115867	−	0.0841822i
$741$	0.00617408	−	0.00448573i	0.000226810	−	0.000164787i
$742$	−2.70434	+	8.32310i	−0.0992794	+	0.305551i
$743$	15.8675	−	48.8353i	0.582124	−	1.79159i	−0.0284035	−	0.999597i	$-0.509042\pi$
$743$	15.8675	−	48.8353i	0.582124	−	1.79159i	0.610527	−	0.791995i	$-0.290958\pi$
$744$	0.950306	−	0.690438i	0.0348399	−	0.0253127i
$745$	21.5507	+	15.6575i	0.789556	+	0.573646i
$746$	1.86031	+	5.72546i	0.0681109	+	0.209624i
$747$	−4.76861			−0.174474
$748$	11.0124	−	16.7120i	0.402654	−	0.611051i
$749$	−12.1138			−0.442627
$750$	−0.767578	−	2.36236i	−0.0280280	−	0.0862613i
$751$	−5.47558	−	3.97824i	−0.199807	−	0.145168i	0.483383	−	0.875409i	$-0.339408\pi$
$751$	−5.47558	−	3.97824i	−0.199807	−	0.145168i	−0.683190	+	0.730241i	$0.739408\pi$
$752$	4.39472	−	3.19295i	0.160259	−	0.116435i
$753$	1.16182	−	3.57571i	0.0423390	−	0.130306i
$754$	−0.0106039	+	0.0326354i	−0.000386170	+	0.00118851i
$755$	−46.6964	+	33.9269i	−1.69946	+	1.23473i
$756$	0.613190	+	0.445509i	0.0223015	+	0.0162030i
$757$	6.88647	+	21.1944i	0.250293	+	0.770323i	0.994721	+	0.102620i	$0.0327224\pi$
$757$	6.88647	+	21.1944i	0.250293	+	0.770323i	−0.744428	+	0.667703i	$0.767278\pi$
$758$	23.5390			0.854974
$759$	−0.0205243	−	0.449044i	−0.000744986	−	0.0162993i
$760$	−18.7331			−0.679521
$761$	14.3001	+	44.0111i	0.518378	+	1.59540i	0.777051	+	0.629438i	$0.216715\pi$
$761$	14.3001	+	44.0111i	0.518378	+	1.59540i	−0.258673	+	0.965965i	$0.583285\pi$
$762$	−1.59336	−	1.15765i	−0.0577215	−	0.0419371i
$763$	−3.05309	+	2.21820i	−0.110529	+	0.0803042i
$764$	0.0580847	−	0.178766i	0.00210143	−	0.00646754i
$765$	−21.6851	+	66.7399i	−0.784027	+	2.41299i
$766$	0.906987	−	0.658965i	0.0327708	−	0.0238094i
$767$	0.0844393	+	0.0613487i	0.00304893	+	0.00221517i
$768$	0.0380437	+	0.117086i	0.00137278	+	0.00422499i
$769$	43.1253			1.55514			0.777569	−	0.628798i	$-0.216453\pi$
$769$	43.1253			1.55514			0.777569	+	0.628798i	$0.216453\pi$
$770$	12.8160	+	3.52604i	0.461858	+	0.127070i
$771$	0.744461			0.0268111
$772$	−5.93474	−	18.2653i	−0.213596	−	0.657381i
$773$	−13.3419	−	9.69346i	−0.479875	−	0.348650i	0.321402	−	0.946943i	$-0.395846\pi$
$773$	−13.3419	−	9.69346i	−0.479875	−	0.348650i	−0.801277	+	0.598293i	$0.795846\pi$
$774$	0.390058	−	0.283394i	0.0140203	−	0.0101864i
$775$	−30.0110	+	92.3644i	−1.07803	+	3.31783i
$776$	3.79460	−	11.6786i	0.136218	−	0.419236i
$777$	0.102457	−	0.0744395i	0.00367563	−	0.00267050i
$778$	9.27686	+	6.74003i	0.332592	+	0.241642i
$779$	2.65587	+	8.17393i	0.0951565	+	0.292861i
$780$	0.00618358			0.000221408
$781$	−36.5432	+	13.7481i	−1.30762	+	0.491944i
$782$	−6.64332			−0.237565
$783$	−0.606033	−	1.86518i	−0.0216578	−	0.0666560i
$784$	4.80702	+	3.49250i	0.171679	+	0.124732i
$785$	46.9183	−	34.0881i	1.67459	−	1.21666i
$786$	0.502830	−	1.54755i	0.0179354	−	0.0551994i
$787$	4.49924	−	13.8472i	0.160380	−	0.493600i	−0.838286	−	0.545231i	$-0.816442\pi$
$787$	4.49924	−	13.8472i	0.160380	−	0.493600i	0.998666	+	0.0516309i	$0.0164419\pi$
$788$	0.746282	−	0.542206i	0.0265852	−	0.0193153i
$789$	−1.09085	−	0.792551i	−0.0388354	−	0.0282156i
$790$	−17.1070	−	52.6499i	−0.608640	−	1.87320i
$791$	−13.7977			−0.490588
$792$	−9.26559	+	3.48584i	−0.329238	+	0.123864i
$793$	−0.0654635			−0.00232468
$794$	4.40604	+	13.5604i	0.156365	+	0.481241i
$795$	−3.30119	−	2.39845i	−0.117081	−	0.0850643i
$796$	−10.7326	+	7.79772i	−0.380408	+	0.276383i
$797$	−2.71208	+	8.34693i	−0.0960668	+	0.295663i	−0.987530	−	0.157429i	$-0.949679\pi$
$797$	−2.71208	+	8.34693i	−0.0960668	+	0.295663i	0.891463	+	0.453093i	$0.149679\pi$
$798$	0.188174	−	0.579140i	0.00666129	−	0.0205013i
$799$	−26.5199	+	19.2678i	−0.938206	+	0.681647i
$800$	−8.23476	−	5.98290i	−0.291143	−	0.211527i
$801$	17.1197	+	52.6890i	0.604895	+	1.86167i
$802$	−15.0727			−0.532237
$803$	−1.73827	−	0.478244i	−0.0613420	−	0.0168769i
$804$	0.725252			0.0255776
$805$	−1.36342	−	4.19618i	−0.0480542	−	0.147896i
$806$	−0.0995141	−	0.0723013i	−0.00350524	−	0.00254670i
$807$	−2.17755	+	1.58208i	−0.0766533	+	0.0556919i
$808$	3.50827	−	10.7973i	0.123420	−	0.379849i
$809$	3.59350	−	11.0597i	0.126341	−	0.388837i	−0.867802	−	0.496910i	$-0.834468\pi$
$809$	3.59350	−	11.0597i	0.126341	−	0.388837i	0.994143	+	0.108073i	$0.0344680\pi$
$810$	27.9381	−	20.2982i	0.981643	−	0.713205i
$811$	10.1502	+	7.37453i	0.356421	+	0.258955i	0.751558	−	0.659667i	$-0.229303\pi$
$811$	10.1502	+	7.37453i	0.356421	+	0.258955i	−0.395137	+	0.918622i	$0.629303\pi$
$812$	0.846111	+	2.60406i	0.0296927	+	0.0913846i
$813$	3.13725			0.110028
$814$	0.151434	+	3.31317i	0.00530775	+	0.116126i
$815$	−17.3999			−0.609493
$816$	−0.229574	−	0.706556i	−0.00803670	−	0.0247344i
$817$	−0.628347	−	0.456521i	−0.0219831	−	0.0159717i
$818$	−12.2955	+	8.93320i	−0.429902	+	0.312342i
$819$	0.0122324	−	0.0376473i	0.000427433	−	0.00131550i
$820$	−2.15195	+	6.62302i	−0.0751494	+	0.231286i
$821$	25.5269	−	18.5464i	0.890894	−	0.647273i	−0.0452166	−	0.998977i	$-0.514398\pi$
$821$	25.5269	−	18.5464i	0.890894	−	0.647273i	0.936111	+	0.351705i	$0.114398\pi$
$822$	−0.403818	−	0.293391i	−0.0140848	−	0.0102332i
$823$	4.83276	+	14.8737i	0.168459	+	0.518464i	0.999275	−	0.0380839i	$-0.0121254\pi$
$823$	4.83276	+	14.8737i	0.168459	+	0.518464i	−0.830815	+	0.556548i	$0.812125\pi$
$824$	14.0153			0.488247
$825$	−2.28685	+	3.47042i	−0.0796177	+	0.120825i
$826$	8.32817			0.289774
$827$	2.09880	+	6.45945i	0.0729826	+	0.224617i	0.980893	−	0.194546i	$-0.0623234\pi$
$827$	2.09880	+	6.45945i	0.0729826	+	0.224617i	−0.907911	+	0.419163i	$0.862323\pi$
$828$	2.65843	+	1.93146i	0.0923867	+	0.0671229i
$829$	29.7860	−	21.6408i	1.03451	−	0.751616i	0.0653044	−	0.997865i	$-0.479198\pi$
$829$	29.7860	−	21.6408i	1.03451	−	0.751616i	0.969207	+	0.246249i	$0.0791982\pi$
$830$	−1.92340	+	5.91963i	−0.0667623	+	0.205473i
$831$	−0.807630	+	2.48563i	−0.0280164	+	0.0862255i
$832$	0.0104299	−	0.00757775i	0.000361591	−	0.000262711i
$833$	−29.0078	−	21.0754i	−1.00506	−	0.730221i
$834$	0.497477	+	1.53108i	0.0172262	+	0.0530168i
$835$	−70.9512			−2.45537
$836$	9.95292	+	12.4602i	0.344229	+	0.430946i
$837$	7.03005			0.242994
$838$	7.66998	+	23.6058i	0.264955	+	0.815448i
$839$	30.2815	+	22.0008i	1.04543	+	0.759552i	0.971339	−	0.237700i	$-0.0763934\pi$
$839$	30.2815	+	22.0008i	1.04543	+	0.759552i	0.0740943	+	0.997251i	$0.476393\pi$
$840$	0.399172	−	0.290015i	0.0137727	−	0.0100065i
$841$	−6.77220	+	20.8427i	−0.233524	+	0.718714i
$842$	−0.0290457	+	0.0893933i	−0.00100098	+	0.00308070i
$843$	−1.48013	+	1.07538i	−0.0509784	+	0.0370380i
$844$	−13.2115	−	9.59873i	−0.454759	−	0.330402i
$845$	15.6508	+	48.1683i	0.538405	+	1.65704i
$846$	16.2142			0.557456
$847$	−4.46385	−	10.3979i	−0.153380	−	0.357276i
$848$	−8.50735			−0.292144
$849$	−0.821072	−	2.52700i	−0.0281791	−	0.0867264i
$850$	49.6925	+	36.1037i	1.70444	+	1.23835i
$851$	0.890642	−	0.647089i	0.0305308	−	0.0221819i
$852$	−0.447856	+	1.37836i	−0.0153433	+	0.0472218i
$853$	−11.2210	+	34.5348i	−0.384201	+	1.18245i	0.552857	+	0.833276i	$0.313538\pi$
$853$	−11.2210	+	34.5348i	−0.384201	+	1.18245i	−0.937058	+	0.349173i	$0.886462\pi$
$854$	−4.22591	+	3.07030i	−0.144607	+	0.105063i
$855$	−45.2365	−	32.8662i	−1.54706	−	1.12400i
$856$	−3.63896	−	11.1996i	−0.124377	−	0.382793i
$857$	1.90793			0.0651737			0.0325869	−	0.999469i	$-0.489625\pi$
$857$	1.90793			0.0651737			0.0325869	+	0.999469i	$0.489625\pi$
$858$	−0.00328534	−	0.00411297i	−0.000112160	−	0.000140415i
$859$	3.72968			0.127255			0.0636275	−	0.997974i	$-0.479733\pi$
$859$	3.72968			0.127255			0.0636275	+	0.997974i	$0.479733\pi$
$860$	−0.194469	−	0.598513i	−0.00663133	−	0.0204091i
$861$	−0.183136	−	0.133056i	−0.00624127	−	0.00453455i
$862$	12.1839	−	8.85215i	0.414987	−	0.301505i
$863$	−10.8214	+	33.3048i	−0.368364	+	1.13371i	0.579483	+	0.814984i	$0.303255\pi$
$863$	−10.8214	+	33.3048i	−0.368364	+	1.13371i	−0.947847	+	0.318725i	$0.896745\pi$
$864$	−0.227686	+	0.700744i	−0.00774602	+	0.0238398i
$865$	78.2455	−	56.8487i	2.66043	−	1.93291i
$866$	18.2902	+	13.2886i	0.621527	+	0.451566i
$867$	0.738618	+	2.27323i	0.0250848	+	0.0772030i
$868$	−9.81499			−0.333142
$869$	−25.9309	+	39.3516i	−0.879645	+	1.33491i
$870$	−1.27667			−0.0432831
$871$	−0.0234689	−	0.0722298i	−0.000795212	−	0.00244741i
$872$	−2.96794	−	2.15633i	−0.100507	−	0.0730227i
$873$	29.6526	−	21.5439i	1.00359	−	0.729149i
$874$	1.63576	−	5.03436i	0.0553305	−	0.170290i
$875$	−6.41367	+	19.7392i	−0.216822	+	0.667308i
$876$	−0.0541405	+	0.0393354i	−0.00182924	+	0.00132902i
$877$	−15.1104	−	10.9783i	−0.510241	−	0.370712i	0.302674	−	0.953094i	$-0.402121\pi$
$877$	−15.1104	−	10.9783i	−0.510241	−	0.370712i	−0.812915	+	0.582382i	$0.802121\pi$
$878$	4.70718	+	14.4872i	0.158860	+	0.488919i
$879$	−1.62512			−0.0548138
$880$	0.589984	+	12.9081i	0.0198884	+	0.435130i
$881$	11.2289			0.378310			0.189155	−	0.981947i	$-0.439425\pi$
$881$	11.2289			0.378310			0.189155	+	0.981947i	$0.439425\pi$
$882$	5.48052	+	16.8673i	0.184539	+	0.567952i
$883$	7.27099	+	5.28269i	0.244688	+	0.177777i	0.703369	−	0.710824i	$-0.251678\pi$
$883$	7.27099	+	5.28269i	0.244688	+	0.177777i	−0.458681	+	0.888601i	$0.651678\pi$
$884$	−0.0629389	+	0.0457278i	−0.00211687	+	0.00153799i
$885$	−1.19996	+	3.69309i	−0.0403361	+	0.124142i
$886$	−1.49972	+	4.61568i	−0.0503842	+	0.155067i
$887$	27.1277	−	19.7094i	0.910858	−	0.661777i	−0.0303740	−	0.999539i	$-0.509670\pi$
$887$	27.1277	−	19.7094i	0.910858	−	0.661777i	0.941232	+	0.337762i	$0.109670\pi$
$888$	0.0995997	+	0.0723634i	0.00334235	+	0.00242836i
$889$	5.08538	+	15.6512i	0.170558	+	0.524924i
$890$	72.3119			2.42390
$891$	−28.3448	−	7.79841i	−0.949585	−	0.261257i
$892$	19.6721			0.658670
$893$	−8.07140	−	24.8412i	−0.270099	−	0.831279i
$894$	−0.680995	−	0.494772i	−0.0227759	−	0.0165476i
$895$	27.3774	−	19.8909i	0.915126	−	0.664878i
$896$	0.317883	−	0.978342i	0.0106197	−	0.0326841i
$897$	−0.000539945		0.00166178i	−1.80283e−5		5.54853e-5i
$898$	−23.3946	+	16.9972i	−0.780688	+	0.567203i
$899$	20.5458	+	14.9274i	0.685241	+	0.497857i
$900$	−9.38852	−	28.8949i	−0.312951	−	0.963163i
$901$	51.3375			1.71030
$902$	5.54860	−	2.08746i	0.184748	−	0.0695048i
$903$	0.0204567			0.000680755
$904$	−4.14480	−	12.7564i	−0.137854	−	0.424271i
$905$	−14.3986	−	10.4612i	−0.478625	−	0.347741i
$906$	1.47559	−	1.07208i	0.0490233	−	0.0356175i
$907$	9.06568	−	27.9013i	0.301021	−	0.926447i	−0.680111	−	0.733109i	$-0.738068\pi$
$907$	9.06568	−	27.9013i	0.301021	−	0.926447i	0.981132	−	0.193338i	$-0.0619315\pi$
$908$	2.33623	−	7.19017i	0.0775305	−	0.238614i
$909$	27.4151	−	19.9182i	0.909301	−	0.660646i
$910$	−0.0418005	−	0.0303698i	−0.00138567	−	0.00100675i
$911$	3.39763	+	10.4568i	0.112568	+	0.346450i	0.991432	−	0.130623i	$-0.0416977\pi$
$911$	3.39763	+	10.4568i	0.112568	+	0.346450i	−0.878864	+	0.477073i	$0.841698\pi$
$912$	0.591961			0.0196018
$913$	4.95932	−	1.86576i	0.164129	−	0.0617477i
$914$	−41.8706			−1.38496
$915$	−0.752624	−	2.31634i	−0.0248810	−	0.0765758i
$916$	4.53596	+	3.29557i	0.149872	+	0.108889i
$917$	−10.9997	+	7.99174i	−0.363242	+	0.263911i
$918$	1.37396	−	4.22863i	0.0453476	−	0.139566i
$919$	4.83111	−	14.8686i	0.159364	−	0.490471i	−0.839213	−	0.543802i	$-0.816984\pi$
$919$	4.83111	−	14.8686i	0.159364	−	0.490471i	0.998577	+	0.0533317i	$0.0169841\pi$
$920$	3.46993	−	2.52105i	0.114400	−	0.0831166i
$921$	−0.518670	−	0.376836i	−0.0170908	−	0.0124172i
$922$	−5.32165	−	16.3784i	−0.175259	−	0.539393i
$923$	0.151767			0.00499547
$924$	−0.404983	−	0.111422i	−0.0133230	−	0.00366551i
$925$	−10.1787			−0.334674
$926$	4.43246	+	13.6417i	0.145660	+	0.448294i
$927$	33.8441	+	24.5892i	1.11159	+	0.807614i
$928$	−2.15337	+	1.56451i	−0.0706877	+	0.0513576i
$929$	9.88662	−	30.4279i	0.324370	−	0.998307i	−0.647355	−	0.762189i	$-0.724125\pi$
$929$	9.88662	−	30.4279i	0.324370	−	0.998307i	0.971724	−	0.236118i	$-0.0758752\pi$
$930$	1.41418	−	4.35241i	0.0463729	−	0.142721i
$931$	23.1136	−	16.7930i	0.757518	−	0.550369i
$932$	−6.14900	−	4.46751i	−0.201417	−	0.146338i
$933$	0.214164	+	0.659129i	0.00701142	+	0.0215789i
$934$	0.888200			0.0290628
$935$	−3.56025	−	77.8934i	−0.116433	−	2.54739i
$936$	0.0384807			0.00125778
$937$	−6.06705	−	18.6724i	−0.198202	−	0.610002i	−0.999924	−	0.0123059i	$-0.996083\pi$
$937$	−6.06705	−	18.6724i	−0.198202	−	0.610002i	0.801723	−	0.597696i	$-0.203917\pi$
$938$	−4.90264	−	3.56198i	−0.160077	−	0.116303i
$939$	−2.48059	+	1.80226i	−0.0809511	+	0.0588145i
$940$	6.53994	−	20.1279i	0.213309	−	0.656499i
$941$	−15.1632	+	46.6676i	−0.494307	+	1.52132i	0.323726	+	0.946151i	$0.395064\pi$
$941$	−15.1632	+	46.6676i	−0.494307	+	1.52132i	−0.818034	+	0.575170i	$0.804936\pi$
$942$	−1.48260	+	1.07718i	−0.0483059	+	0.0350963i
$943$	−1.59197	−	1.15664i	−0.0518417	−	0.0376652i
$944$	2.50177	+	7.69966i	0.0814257	+	0.250603i
$945$	2.95294			0.0960593
$946$	−0.294777	+	0.447341i	−0.00958402	+	0.0145443i
$947$	57.7198			1.87564			0.937821	−	0.347120i	$-0.112840\pi$
$947$	57.7198			1.87564			0.937821	+	0.347120i	$0.112840\pi$
$948$	0.540576	+	1.66372i	0.0175571	+	0.0540352i
$949$	0.00566948	+	0.00411912i	0.000184039	+	0.000133712i
$950$	−39.5952	+	28.7676i	−1.28464	+	0.933345i
$951$	−1.00305	+	3.08708i	−0.0325263	+	0.100106i
$952$	−1.91826	+	5.90379i	−0.0621711	+	0.191343i
$953$	−1.07572	+	0.781554i	−0.0348459	+	0.0253170i	−0.605072	−	0.796171i	$-0.706856\pi$
$953$	−1.07572	+	0.781554i	−0.0348459	+	0.0253170i	0.570226	+	0.821488i	$0.306856\pi$
$954$	−20.5435	−	14.9257i	−0.665119	−	0.483237i
$955$	−0.226297	−	0.696471i	−0.00732281	−	0.0225373i
$956$	−5.55612			−0.179698
$957$	0.678296	+	0.849170i	0.0219262	+	0.0274498i
$958$	16.7008			0.539579
$959$	1.28882	+	3.96660i	0.0416183	+	0.128088i
$960$	0.388039	+	0.281927i	0.0125239	+	0.00909916i
$961$	−48.5698	+	35.2880i	−1.56677	+	1.13832i
$962$	0.00398386	−	0.0122611i	0.000128445	−	0.000395312i
$963$	10.8617	−	33.4289i	0.350014	−	1.07723i
$964$	8.55195	−	6.21335i	0.275440	−	0.200119i
$965$	−60.5333	−	43.9800i	−1.94864	−	1.41577i
$966$	0.0430837	+	0.132598i	0.00138619	+	0.00426627i
$967$	45.3576			1.45860			0.729301	−	0.684193i	$-0.239846\pi$
$967$	45.3576			1.45860			0.729301	+	0.684193i	$0.239846\pi$
$968$	8.27227	−	7.25049i	0.265881	−	0.233040i
$969$	−3.57218			−0.114755
$970$	−14.7837	−	45.4995i	−0.474676	−	1.46090i
$971$	13.4293	+	9.75699i	0.430968	+	0.313117i	0.782036	−	0.623233i	$-0.214181\pi$
$971$	13.4293	+	9.75699i	0.430968	+	0.313117i	−0.351068	+	0.936350i	$0.614181\pi$
$972$	−2.67110	+	1.94067i	−0.0856756	+	0.0622470i
$973$	4.15678	−	12.7932i	0.133260	−	0.410132i
$974$	0.184529	−	0.567923i	0.00591270	−	0.0181974i
$975$	0.0130699	−	0.00949585i	0.000418572	−	0.000304111i
$976$	−4.10805	−	2.98467i	−0.131495	−	0.0955370i
$977$	−11.2891	−	34.7444i	−0.361171	−	1.11157i	−0.952344	−	0.305026i	$-0.901335\pi$
$977$	−11.2891	−	34.7444i	−0.361171	−	1.11157i	0.591173	−	0.806545i	$-0.298665\pi$
$978$	0.549832			0.0175817
$979$	−38.4194	−	48.0979i	−1.22789	−	1.53722i
$980$	23.1492			0.739473
$981$	−3.38377	−	10.4142i	−0.108036	−	0.332499i
$982$	−1.92270	−	1.39692i	−0.0613557	−	0.0445775i
$983$	−19.1895	+	13.9420i	−0.612051	+	0.444681i	−0.850136	−	0.526564i	$-0.823480\pi$
$983$	−19.1895	+	13.9420i	−0.612051	+	0.444681i	0.238085	+	0.971244i	$0.423480\pi$
$984$	0.0680010	−	0.209285i	0.00216779	−	0.00667178i
$985$	1.11057	−	3.41798i	0.0353856	−	0.108906i
$986$	12.9945	−	9.44102i	0.413828	−	0.300663i
$987$	0.556566	+	0.404369i	0.0177157	+	0.0128712i
$988$	−0.0191556	−	0.0589550i	−0.000609422	−	0.00187561i
$989$	0.177826			0.00565454
$990$	−21.2218	+	32.2053i	−0.674473	+	1.02355i
$991$	3.64787			0.115878			0.0579392	−	0.998320i	$-0.481547\pi$
$991$	3.64787			0.115878			0.0579392	+	0.998320i	$0.481547\pi$
$992$	−2.94841	−	9.07427i	−0.0936121	−	0.288108i
$993$	2.12825	+	1.54627i	0.0675380	+	0.0490692i
$994$	9.79710	−	7.11801i	0.310745	−	0.225770i
$995$	−15.9716	+	49.1556i	−0.506334	+	1.55834i
$996$	0.0607790	−	0.187058i	0.00192585	−	0.00592717i
$997$	−12.7558	+	9.26761i	−0.403979	+	0.293508i	−0.771160	−	0.636642i	$-0.780323\pi$
$997$	−12.7558	+	9.26761i	−0.403979	+	0.293508i	0.367181	+	0.930150i	$0.380323\pi$
$998$	−8.55432	−	6.21507i	−0.270782	−	0.196735i
$999$	0.227686	+	0.700744i	0.00720365	+	0.0221706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	814.2.h.c.445.7	yes	44
11.3	even	5		8954.2.a.bt.1.10		22
11.8	odd	10		8954.2.a.bs.1.10		22
11.9	even	5	inner	814.2.h.c.75.7	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
814.2.h.c.75.7	✓	44	11.9	even	5	inner
814.2.h.c.445.7	yes	44	1.1	even	1	trivial
8954.2.a.bs.1.10		22	11.8	odd	10
8954.2.a.bt.1.10		22	11.3	even	5

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:	\( N \)	\(=\)	\( 814 = 2 \cdot 11 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	814.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.0995997 - 0.0723634i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.20393 + 3.70530i) q^{5} +(0.0380437 - 0.117086i) q^{6} +(-0.832227 + 0.604649i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.922367 - 2.83875i) q^{9} -3.89599 q^{10} +(2.06994 + 2.59140i) q^{11} +0.123112 q^{12} +(-0.00398386 - 0.0122611i) q^{13} +(-0.832227 - 0.604649i) q^{14} +(0.388039 - 0.281927i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.86476 + 5.73913i) q^{17} +(2.41479 - 1.75445i) q^{18} +(-3.89000 - 2.82625i) q^{19} +(-1.20393 - 3.70530i) q^{20} +0.126644 q^{21} +(-1.82492 + 2.76942i) q^{22} +1.10089 q^{23} +(0.0380437 + 0.117086i) q^{24} +(-8.23476 - 5.98290i) q^{25} +(0.0104299 - 0.00757775i) q^{26} +(-0.227686 + 0.700744i) q^{27} +(0.317883 - 0.978342i) q^{28} +(-2.15337 + 1.56451i) q^{29} +(0.388039 + 0.281927i) q^{30} +(-2.94841 - 9.07427i) q^{31} +1.00000 q^{32} +(-0.0186433 - 0.407891i) q^{33} -6.03448 q^{34} +(-1.23847 - 3.81161i) q^{35} +(2.41479 + 1.75445i) q^{36} +(0.809017 - 0.587785i) q^{37} +(1.48585 - 4.57297i) q^{38} +(-0.000490461 + 0.00150948i) q^{39} +(3.15192 - 2.29000i) q^{40} +(-1.44607 - 1.05063i) q^{41} +(0.0391352 + 0.120446i) q^{42} +0.161529 q^{43} +(-3.19780 - 0.879802i) q^{44} +11.6289 q^{45} +(0.340195 + 1.04701i) q^{46} +(4.39472 + 3.19295i) q^{47} +(-0.0995997 + 0.0723634i) q^{48} +(-1.83612 + 5.65099i) q^{49} +(3.14540 - 9.68054i) q^{50} +(0.601033 - 0.436676i) q^{51} +(0.0104299 + 0.00757775i) q^{52} +(-2.62892 - 8.09097i) q^{53} -0.736806 q^{54} +(-12.0940 + 4.54992i) q^{55} +1.02869 q^{56} +(0.182926 + 0.562988i) q^{57} +(-2.15337 - 1.56451i) q^{58} +(-6.54972 + 4.75865i) q^{59} +(-0.148218 + 0.456167i) q^{60} +(1.56913 - 4.82930i) q^{61} +(7.71904 - 5.60821i) q^{62} +(2.48407 + 1.80478i) q^{63} +(0.309017 + 0.951057i) q^{64} +0.0502272 q^{65} +(0.382166 - 0.143776i) q^{66} +5.89099 q^{67} +(-1.86476 - 5.73913i) q^{68} +(-0.109649 - 0.0796644i) q^{69} +(3.24235 - 2.35570i) q^{70} +(-3.63779 + 11.1960i) q^{71} +(-0.922367 + 2.83875i) q^{72} +(-0.439766 + 0.319509i) q^{73} +(0.809017 + 0.587785i) q^{74} +(0.387236 + 1.19179i) q^{75} +4.80831 q^{76} +(-3.28955 - 0.905044i) q^{77} -0.00158717 q^{78} +(4.39093 + 13.5139i) q^{79} +(3.15192 + 2.29000i) q^{80} +(-7.17098 + 5.21002i) q^{81} +(0.552350 - 1.69996i) q^{82} +(0.493688 - 1.51942i) q^{83} +(-0.102457 + 0.0744395i) q^{84} +(-19.0202 - 13.8190i) q^{85} +(0.0499151 + 0.153623i) q^{86} +0.327688 q^{87} +(-0.151434 - 3.31317i) q^{88} -18.5606 q^{89} +(3.59353 + 11.0598i) q^{90} +(0.0107291 + 0.00779515i) q^{91} +(-0.890642 + 0.647089i) q^{92} +(-0.362985 + 1.11715i) q^{93} +(-1.67864 + 5.16631i) q^{94} +(15.1554 - 11.0110i) q^{95} +(-0.0995997 - 0.0723634i) q^{96} +(3.79460 + 11.6786i) q^{97} -5.94180 q^{98} +(5.44709 - 8.26628i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 11 q^{2} - 11 q^{4} + q^{5} - 5 q^{6} - q^{7} - 11 q^{8} - 25 q^{9} + 16 q^{10} - 4 q^{11} + 10 q^{12} + 3 q^{13} - q^{14} - 18 q^{15} - 11 q^{16} - 7 q^{17} - 10 q^{18} + 15 q^{19} + q^{20}+ \cdots + 45 q^{99}+O(q^{100}) \) 44 * q - 11 * q^2 - 11 * q^4 + q^5 - 5 * q^6 - q^7 - 11 * q^8 - 25 * q^9 + 16 * q^10 - 4 * q^11 + 10 * q^12 + 3 * q^13 - q^14 - 18 * q^15 - 11 * q^16 - 7 * q^17 - 10 * q^18 + 15 * q^19 + q^20 + 30 * q^21 + 6 * q^22 + 36 * q^23 - 5 * q^24 - 48 * q^25 - 12 * q^26 - 36 * q^27 - 6 * q^28 - 3 * q^29 - 18 * q^30 - 46 * q^31 + 44 * q^32 - 49 * q^33 + 38 * q^34 - 22 * q^35 - 10 * q^36 + 11 * q^37 - 15 * q^38 + 46 * q^39 - 9 * q^40 + 10 * q^41 - 5 * q^42 - 4 * q^43 - 9 * q^44 + 166 * q^45 - 14 * q^46 - 17 * q^47 - 36 * q^49 + 22 * q^50 - 15 * q^51 - 12 * q^52 - 23 * q^53 + 34 * q^54 - 34 * q^55 + 14 * q^56 - 13 * q^57 - 3 * q^58 - 18 * q^59 + 2 * q^60 + 30 * q^61 + 14 * q^62 + 79 * q^63 - 11 * q^64 + 68 * q^65 - 9 * q^66 + 44 * q^67 - 7 * q^68 - 91 * q^69 + 8 * q^70 - 47 * q^71 - 25 * q^72 - 36 * q^73 + 11 * q^74 - 38 * q^75 - 2 * q^77 - 4 * q^78 + 13 * q^79 - 9 * q^80 - 38 * q^81 - 20 * q^82 + 44 * q^83 - 10 * q^84 + 23 * q^85 - 39 * q^86 - 20 * q^87 + 11 * q^88 + 90 * q^89 - 24 * q^90 - 54 * q^91 - 4 * q^92 - 69 * q^93 + 33 * q^94 + 47 * q^95 - 121 * q^97 + 114 * q^98 + 45 * q^99

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