LMFDB - Embedded newform 250.3.f.c.93.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,3,Mod(7,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([17]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("250.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	250.f (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.81200660901$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 30x^{14} + 351x^{12} + 2130x^{10} + 7341x^{8} + 14480x^{6} + 15196x^{4} + 6560x^{2} + 16 $ x^16 + 30x^14 + 351x^12 + 2130x^10 + 7341x^8 + 14480x^6 + 15196x^4 + 6560*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			93.1
Root			$3.40366i$ of defining polynomial
Character	$\chi$	$=$	250.93
Dual form			250.3.f.c.207.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.221232 - 1.39680i) q^{2} +(-2.25584 + 1.14941i) q^{3} +(-1.90211 - 0.618034i) q^{4} +(1.10643 + 3.40526i) q^{6} +(6.58346 - 6.58346i) q^{7} +(-1.28408 + 2.52015i) q^{8} +(-1.52238 + 2.09537i) q^{9} +O(q^{10})$	\(q+(0.221232 - 1.39680i) q^{2} +(-2.25584 + 1.14941i) q^{3} +(-1.90211 - 0.618034i) q^{4} +(1.10643 + 3.40526i) q^{6} +(6.58346 - 6.58346i) q^{7} +(-1.28408 + 2.52015i) q^{8} +(-1.52238 + 2.09537i) q^{9} +(-3.81477 + 2.77159i) q^{11} +(5.00125 - 0.792120i) q^{12} +(-2.77559 - 17.5244i) q^{13} +(-7.73932 - 10.6523i) q^{14} +(3.23607 + 2.35114i) q^{16} +(-14.6123 - 7.44532i) q^{17} +(2.59002 + 2.59002i) q^{18} +(-16.0908 + 5.22822i) q^{19} +(-7.28417 + 22.4184i) q^{21} +(3.02742 + 5.94165i) q^{22} +(-37.3144 - 5.91002i) q^{23} -7.16099i q^{24} -25.0922 q^{26} +(4.59034 - 28.9823i) q^{27} +(-16.5913 + 8.45369i) q^{28} +(1.46851 + 0.477149i) q^{29} +(-9.29144 - 28.5961i) q^{31} +(4.00000 - 4.00000i) q^{32} +(5.41983 - 10.6370i) q^{33} +(-13.6323 + 18.7633i) q^{34} +(4.19074 - 3.04475i) q^{36} +(-8.01234 + 1.26903i) q^{37} +(3.74300 + 23.6323i) q^{38} +(26.4040 + 36.3420i) q^{39} +(-30.0830 - 21.8566i) q^{41} +(29.7025 + 15.1342i) q^{42} +(25.9880 + 25.9880i) q^{43} +(8.96907 - 2.91423i) q^{44} +(-16.5103 + 50.8134i) q^{46} +(20.9883 + 41.1918i) q^{47} +(-10.0025 - 1.58424i) q^{48} -37.6840i q^{49} +41.5207 q^{51} +(-5.55119 + 35.0488i) q^{52} +(72.8025 - 37.0947i) q^{53} +(-39.4670 - 12.8236i) q^{54} +(8.13761 + 25.0450i) q^{56} +(30.2890 - 30.2890i) q^{57} +(0.991364 - 1.94566i) q^{58} +(-24.7807 + 34.1077i) q^{59} +(96.0793 - 69.8057i) q^{61} +(-41.9987 + 6.65194i) q^{62} +(3.77229 + 23.8173i) q^{63} +(-4.70228 - 6.47214i) q^{64} +(-13.6588 - 9.92368i) q^{66} +(-77.9450 - 39.7150i) q^{67} +(23.1927 + 23.1927i) q^{68} +(90.9685 - 29.5575i) q^{69} +(-5.14879 + 15.8463i) q^{71} +(-3.32579 - 6.52723i) q^{72} +(-62.5804 - 9.91177i) q^{73} +11.4724i q^{74} +33.8378 q^{76} +(-6.86772 + 43.3611i) q^{77} +(56.6041 - 28.8412i) q^{78} +(19.2036 + 6.23964i) q^{79} +(15.7542 + 48.4864i) q^{81} +(-37.1847 + 37.1847i) q^{82} +(11.2828 - 22.1438i) q^{83} +(27.7106 - 38.1404i) q^{84} +(42.0494 - 30.5507i) q^{86} +(-3.86118 + 0.611550i) q^{87} +(-2.08636 - 13.1727i) q^{88} +(39.7082 + 54.6536i) q^{89} +(-133.644 - 97.0982i) q^{91} +(67.3236 + 34.3031i) q^{92} +(53.8287 + 53.8287i) q^{93} +(62.1801 - 20.2035i) q^{94} +(-4.42574 + 13.6210i) q^{96} +(-13.3540 - 26.2088i) q^{97} +(-52.6370 - 8.33689i) q^{98} -12.2128i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 2 q^{3} + 4 q^{6} + 2 q^{7} - 8 q^{8} + 40 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 2 * q^3 + 4 * q^6 + 2 * q^7 - 8 * q^8 + 40 * q^9	$ 16 q + 4 q^{2} - 2 q^{3} + 4 q^{6} + 2 q^{7} - 8 q^{8} + 40 q^{9} + 32 q^{11} + 16 q^{12} + 8 q^{13} + 30 q^{14} + 16 q^{16} - 8 q^{17} + 16 q^{18} - 30 q^{19} - 68 q^{21} + 8 q^{22} - 42 q^{23} - 56 q^{26} + 40 q^{27} - 4 q^{28} - 100 q^{29} + 132 q^{31} + 64 q^{32} - 134 q^{33} - 100 q^{34} + 48 q^{36} + 82 q^{37} - 20 q^{38} + 320 q^{39} - 88 q^{41} + 128 q^{42} + 78 q^{43} - 40 q^{44} - 26 q^{46} - 168 q^{47} - 32 q^{48} - 168 q^{51} + 16 q^{52} + 518 q^{53} - 80 q^{54} + 48 q^{56} - 280 q^{57} - 80 q^{58} + 350 q^{59} + 372 q^{61} + 158 q^{62} - 142 q^{63} - 202 q^{66} - 158 q^{67} + 196 q^{68} + 30 q^{69} + 122 q^{71} - 68 q^{72} - 352 q^{73} + 40 q^{76} - 96 q^{77} - 158 q^{78} - 760 q^{79} - 144 q^{81} - 352 q^{82} - 32 q^{83} + 20 q^{84} + 264 q^{86} + 440 q^{87} + 244 q^{88} - 550 q^{89} - 798 q^{91} + 436 q^{92} - 54 q^{93} - 190 q^{94} - 16 q^{96} - 618 q^{97} - 336 q^{98}+O(q^{100}) $ 16 * q + 4 * q^2 - 2 * q^3 + 4 * q^6 + 2 * q^7 - 8 * q^8 + 40 * q^9 + 32 * q^11 + 16 * q^12 + 8 * q^13 + 30 * q^14 + 16 * q^16 - 8 * q^17 + 16 * q^18 - 30 * q^19 - 68 * q^21 + 8 * q^22 - 42 * q^23 - 56 * q^26 + 40 * q^27 - 4 * q^28 - 100 * q^29 + 132 * q^31 + 64 * q^32 - 134 * q^33 - 100 * q^34 + 48 * q^36 + 82 * q^37 - 20 * q^38 + 320 * q^39 - 88 * q^41 + 128 * q^42 + 78 * q^43 - 40 * q^44 - 26 * q^46 - 168 * q^47 - 32 * q^48 - 168 * q^51 + 16 * q^52 + 518 * q^53 - 80 * q^54 + 48 * q^56 - 280 * q^57 - 80 * q^58 + 350 * q^59 + 372 * q^61 + 158 * q^62 - 142 * q^63 - 202 * q^66 - 158 * q^67 + 196 * q^68 + 30 * q^69 + 122 * q^71 - 68 * q^72 - 352 * q^73 + 40 * q^76 - 96 * q^77 - 158 * q^78 - 760 * q^79 - 144 * q^81 - 352 * q^82 - 32 * q^83 + 20 * q^84 + 264 * q^86 + 440 * q^87 + 244 * q^88 - 550 * q^89 - 798 * q^91 + 436 * q^92 - 54 * q^93 - 190 * q^94 - 16 * q^96 - 618 * q^97 - 336 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{11}{20}\right)$

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 $

$2$	0.221232	−	1.39680i	0.110616	−	0.698401i
$2$	0.221232	−	1.39680i	0.110616	−	0.698401i
$3$	−2.25584	+	1.14941i	−0.751948	+	0.383137i	−0.787567	−	0.616229i	$-0.788660\pi$
$3$	−2.25584	+	1.14941i	−0.751948	+	0.383137i	0.0356190	+	0.999365i	$0.488660\pi$
$4$	−1.90211	−	0.618034i	−0.475528	−	0.154508i
$5$		0			0
$5$		0			0
$6$	1.10643	+	3.40526i	0.184406	+	0.567543i
$7$	6.58346	−	6.58346i	0.940495	−	0.940495i	−0.0578317	−	0.998326i	$-0.518419\pi$
$7$	6.58346	−	6.58346i	0.940495	−	0.940495i	0.998326	+	0.0578317i	$0.0184187\pi$
$8$	−1.28408	+	2.52015i	−0.160510	+	0.315018i
$9$	−1.52238	+	2.09537i	−0.169153	+	0.232819i
$10$		0			0
$11$	−3.81477	+	2.77159i	−0.346797	+	0.251963i	−0.747524	−	0.664235i	$-0.768758\pi$
$11$	−3.81477	+	2.77159i	−0.346797	+	0.251963i	0.400727	+	0.916198i	$0.368758\pi$
$12$	5.00125	−	0.792120i	0.416771	−	0.0660100i
$13$	−2.77559	−	17.5244i	−0.213507	−	1.34803i	−0.828717	−	0.559668i	$-0.810929\pi$
$13$	−2.77559	−	17.5244i	−0.213507	−	1.34803i	0.615210	−	0.788363i	$-0.289071\pi$
$14$	−7.73932	−	10.6523i	−0.552809	−	0.760876i
$15$		0			0
$16$	3.23607	+	2.35114i	0.202254	+	0.146946i
$17$	−14.6123	−	7.44532i	−0.859545	−	0.437960i	−0.0320852	−	0.999485i	$-0.510215\pi$
$17$	−14.6123	−	7.44532i	−0.859545	−	0.437960i	−0.827460	+	0.561525i	$0.810215\pi$
$18$	2.59002	+	2.59002i	0.143890	+	0.143890i
$19$	−16.0908	+	5.22822i	−0.846885	+	0.275170i	−0.700141	−	0.714005i	$-0.746879\pi$
$19$	−16.0908	+	5.22822i	−0.846885	+	0.275170i	−0.146744	+	0.989174i	$0.546879\pi$
$20$		0			0
$21$	−7.28417	+	22.4184i	−0.346865	+	1.06754i
$22$	3.02742	+	5.94165i	0.137610	+	0.270075i
$23$	−37.3144	−	5.91002i	−1.62237	−	0.256957i	−0.721936	−	0.691960i	$-0.756747\pi$
$23$	−37.3144	−	5.91002i	−1.62237	−	0.256957i	−0.900429	+	0.435003i	$0.856747\pi$
$24$		−	7.16099i		−	0.298375i
$25$		0			0
$26$	−25.0922			−0.965084
$27$	4.59034	−	28.9823i	0.170013	−	1.07342i
$28$	−16.5913	+	8.45369i	−0.592546	+	0.301917i
$29$	1.46851	+	0.477149i	0.0506384	+	0.0164534i	0.334227	−	0.942493i	$-0.391525\pi$
$29$	1.46851	+	0.477149i	0.0506384	+	0.0164534i	−0.283588	+	0.958946i	$0.591525\pi$
$30$		0			0
$31$	−9.29144	−	28.5961i	−0.299724	−	0.922456i	−0.981594	−	0.190982i	$-0.938833\pi$
$31$	−9.29144	−	28.5961i	−0.299724	−	0.922456i	0.681870	−	0.731474i	$-0.261167\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	5.41983	−	10.6370i	0.164237	−	0.322334i
$34$	−13.6323	+	18.7633i	−0.400951	+	0.551862i
$35$		0			0
$36$	4.19074	−	3.04475i	0.116409	−	0.0845764i
$37$	−8.01234	+	1.26903i	−0.216550	+	0.0342981i	−0.263766	−	0.964587i	$-0.584965\pi$
$37$	−8.01234	+	1.26903i	−0.216550	+	0.0342981i	0.0472168	+	0.998885i	$0.484965\pi$
$38$	3.74300	+	23.6323i	0.0984999	+	0.621904i
$39$	26.4040	+	36.3420i	0.677027	+	0.931847i
$40$		0			0
$41$	−30.0830	−	21.8566i	−0.733733	−	0.533088i	0.157009	−	0.987597i	$-0.449815\pi$
$41$	−30.0830	−	21.8566i	−0.733733	−	0.533088i	−0.890742	+	0.454509i	$0.849815\pi$
$42$	29.7025	+	15.1342i	0.707203	+	0.360338i
$43$	25.9880	+	25.9880i	0.604371	+	0.604371i	0.941470	−	0.337098i	$-0.109445\pi$
$43$	25.9880	+	25.9880i	0.604371	+	0.604371i	−0.337098	+	0.941470i	$0.609445\pi$
$44$	8.96907	−	2.91423i	0.203842	−	0.0662324i
$45$		0			0
$46$	−16.5103	+	50.8134i	−0.358919	+	1.10464i
$47$	20.9883	+	41.1918i	0.446559	+	0.876421i	0.999078	+	0.0429212i	$0.0136664\pi$
$47$	20.9883	+	41.1918i	0.446559	+	0.876421i	−0.552520	+	0.833500i	$0.686334\pi$
$48$	−10.0025	−	1.58424i	−0.208385	−	0.0330050i
$49$		−	37.6840i		−	0.769060i
$50$		0			0
$51$	41.5207			0.814132
$52$	−5.55119	+	35.0488i	−0.106754	+	0.674016i
$53$	72.8025	−	37.0947i	1.37363	−	0.699900i	0.397606	−	0.917556i	$-0.369841\pi$
$53$	72.8025	−	37.0947i	1.37363	−	0.699900i	0.976026	+	0.217656i	$0.0698411\pi$
$54$	−39.4670	−	12.8236i	−0.730870	−	0.237474i
$55$		0			0
$56$	8.13761	+	25.0450i	0.145314	+	0.447232i
$57$	30.2890	−	30.2890i	0.531386	−	0.531386i
$58$	0.991364	−	1.94566i	0.0170925	−	0.0335459i
$59$	−24.7807	+	34.1077i	−0.420012	+	0.578097i	−0.965625	−	0.259940i	$-0.916297\pi$
$59$	−24.7807	+	34.1077i	−0.420012	+	0.578097i	0.545612	+	0.838038i	$0.316297\pi$
$60$		0			0
$61$	96.0793	−	69.8057i	1.57507	−	1.14436i	0.652983	−	0.757372i	$-0.273517\pi$
$61$	96.0793	−	69.8057i	1.57507	−	1.14436i	0.922087	−	0.386983i	$-0.126483\pi$
$62$	−41.9987	+	6.65194i	−0.677398	+	0.107289i
$63$	3.77229	+	23.8173i	0.0598776	+	0.378052i
$64$	−4.70228	−	6.47214i	−0.0734732	−	0.101127i
$65$		0			0
$66$	−13.6588	−	9.92368i	−0.206951	−	0.150359i
$67$	−77.9450	−	39.7150i	−1.16336	−	0.592761i	−0.237781	−	0.971319i	$-0.576420\pi$
$67$	−77.9450	−	39.7150i	−1.16336	−	0.592761i	−0.925577	+	0.378558i	$0.876420\pi$
$68$	23.1927	+	23.1927i	0.341069	+	0.341069i
$69$	90.9685	−	29.5575i	1.31838	−	0.428369i
$70$		0			0
$71$	−5.14879	+	15.8463i	−0.0725181	+	0.223188i	−0.980746	−	0.195288i	$-0.937436\pi$
$71$	−5.14879	+	15.8463i	−0.0725181	+	0.223188i	0.908228	+	0.418476i	$0.137436\pi$
$72$	−3.32579	−	6.52723i	−0.0461915	−	0.0906560i
$73$	−62.5804	−	9.91177i	−0.857266	−	0.135778i	−0.287697	−	0.957721i	$-0.592890\pi$
$73$	−62.5804	−	9.91177i	−0.857266	−	0.135778i	−0.569569	+	0.821944i	$0.692890\pi$
$74$			11.4724i			0.155032i
$75$		0			0
$76$	33.8378			0.445234
$77$	−6.86772	+	43.3611i	−0.0891912	+	0.563131i
$78$	56.6041	−	28.8412i	0.725693	−	0.369759i
$79$	19.2036	+	6.23964i	0.243084	+	0.0789827i	0.428025	−	0.903767i	$-0.359209\pi$
$79$	19.2036	+	6.23964i	0.243084	+	0.0789827i	−0.184941	+	0.982750i	$0.559209\pi$
$80$		0			0
$81$	15.7542	+	48.4864i	0.194496	+	0.598598i
$82$	−37.1847	+	37.1847i	−0.453472	+	0.453472i
$83$	11.2828	−	22.1438i	0.135938	−	0.266793i	−0.812995	−	0.582270i	$-0.802165\pi$
$83$	11.2828	−	22.1438i	0.135938	−	0.266793i	0.948933	+	0.315477i	$0.102165\pi$
$84$	27.7106	−	38.1404i	0.329888	−	0.454052i
$85$		0			0
$86$	42.0494	−	30.5507i	0.488947	−	0.355241i
$87$	−3.86118	+	0.611550i	−0.0443813	+	0.00702931i
$88$	−2.08636	−	13.1727i	−0.0237086	−	0.149690i
$89$	39.7082	+	54.6536i	0.446159	+	0.614085i	0.971567	−	0.236765i	$-0.0760872\pi$
$89$	39.7082	+	54.6536i	0.446159	+	0.614085i	−0.525408	+	0.850851i	$0.676087\pi$
$90$		0			0
$91$	−133.644	−	97.0982i	−1.46862	−	1.06701i
$92$	67.3236	+	34.3031i	0.731778	+	0.372860i
$93$	53.8287	+	53.8287i	0.578804	+	0.578804i
$94$	62.1801	−	20.2035i	0.661490	−	0.214931i
$95$		0			0
$96$	−4.42574	+	13.6210i	−0.0461014	+	0.141886i
$97$	−13.3540	−	26.2088i	−0.137671	−	0.270194i	0.811870	−	0.583839i	$-0.198450\pi$
$97$	−13.3540	−	26.2088i	−0.137671	−	0.270194i	−0.949540	+	0.313645i	$0.898450\pi$
$98$	−52.6370	−	8.33689i	−0.537113	−	0.0850703i
$99$		−	12.2128i		−	0.123361i
$100$		0			0
$101$	140.710			1.39317			0.696586	−	0.717474i	$-0.254702\pi$
$101$	140.710			1.39317			0.696586	+	0.717474i	$0.254702\pi$
$102$	9.18570	−	57.9962i	0.0900559	−	0.568591i
$103$	−33.1201	+	16.8755i	−0.321554	+	0.163840i	−0.607316	−	0.794461i	$-0.707754\pi$
$103$	−33.1201	+	16.8755i	−0.321554	+	0.163840i	0.285761	+	0.958301i	$0.407754\pi$
$104$	47.7282	+	15.5078i	0.458925	+	0.149114i
$105$		0			0
$106$	−35.7078	−	109.897i	−0.336866	−	1.03677i
$107$	−93.0390	+	93.0390i	−0.869523	+	0.869523i	−0.992420	−	0.122896i	$-0.960782\pi$
$107$	−93.0390	+	93.0390i	−0.869523	+	0.869523i	0.122896	+	0.992420i	$0.460782\pi$
$108$	−26.6434	+	52.2906i	−0.246698	+	0.484172i
$109$	110.706	−	152.374i	1.01565	−	1.39793i	0.100448	−	0.994942i	$-0.467972\pi$
$109$	110.706	−	152.374i	1.01565	−	1.39793i	0.915206	−	0.402986i	$-0.132028\pi$
$110$		0			0
$111$	16.6160	−	12.0722i	0.149693	−	0.108759i
$112$	36.7832	−	5.82588i	0.328421	−	0.0520168i
$113$	−25.0599	−	158.222i	−0.221769	−	1.40020i	−0.807585	−	0.589752i	$-0.799226\pi$
$113$	−25.0599	−	158.222i	−0.221769	−	1.40020i	0.585815	−	0.810445i	$-0.300774\pi$
$114$	−35.6069	−	49.0087i	−0.312341	−	0.429901i
$115$		0			0
$116$	−2.49838	−	1.81518i	−0.0215378	−	0.0156481i
$117$	40.9456	+	20.8628i	0.349962	+	0.178315i
$118$	42.1595	+	42.1595i	0.357284	+	0.357284i
$119$	−145.215	+	47.1833i	−1.22030	+	0.396498i
$120$		0			0
$121$	−30.5203	+	93.9318i	−0.252234	+	0.776296i
$122$	−76.2489	−	149.647i	−0.624991	−	1.22661i
$123$	92.9849	+	14.7274i	0.755975	+	0.119735i
$124$			60.1355i			0.484964i
$125$		0			0
$126$	34.1026			0.270655
$127$	−18.3506	+	115.861i	−0.144493	+	0.912294i	0.803800	+	0.594899i	$0.202808\pi$
$127$	−18.3506	+	115.861i	−0.144493	+	0.912294i	−0.948293	+	0.317395i	$0.897192\pi$
$128$	−10.0806	+	5.13632i	−0.0787546	+	0.0401275i
$129$	−88.4957	−	28.7540i	−0.686013	−	0.222899i
$130$		0			0
$131$	54.0155	+	166.243i	0.412332	+	1.26903i	0.914615	+	0.404325i	$0.132494\pi$
$131$	54.0155	+	166.243i	0.412332	+	1.26903i	−0.502283	+	0.864703i	$0.667506\pi$
$132$	−16.8832	+	16.8832i	−0.127903	+	0.127903i
$133$	−71.5135	+	140.353i	−0.537695	+	1.05529i
$134$	−72.7178	+	100.088i	−0.542671	+	0.746922i
$135$		0			0
$136$	37.5266	−	27.2647i	0.275931	−	0.200476i
$137$	60.2465	−	9.54211i	0.439756	−	0.0696505i	0.0673690	−	0.997728i	$-0.478540\pi$
$137$	60.2465	−	9.54211i	0.439756	−	0.0696505i	0.372387	+	0.928078i	$0.378540\pi$
$138$	−21.1608	−	133.604i	−0.153339	−	0.968146i
$139$	−45.5691	−	62.7205i	−0.327835	−	0.451227i	0.613004	−	0.790080i	$-0.289961\pi$
$139$	−45.5691	−	62.7205i	−0.327835	−	0.451227i	−0.940839	+	0.338853i	$0.889961\pi$
$140$		0			0
$141$	−94.6925	−	68.7982i	−0.671578	−	0.487930i
$142$	20.9951	+	10.6976i	0.147853	+	0.0753349i
$143$	59.1588	+	59.1588i	0.413698	+	0.413698i
$144$	−9.85302	+	3.20144i	−0.0684237	+	0.0222322i
$145$		0			0
$146$	−27.6896	+	85.2197i	−0.189654	+	0.583697i
$147$	43.3143	+	85.0092i	0.294655	+	0.578294i
$148$	16.0247	+	2.53806i	0.108275	+	0.0171490i
$149$			146.792i			0.985181i	0.870261	+	0.492590i	$0.163950\pi$
$149$			146.792i			0.985181i	−0.870261	+	0.492590i	$0.836050\pi$
$150$		0			0
$151$	−81.4983			−0.539724			−0.269862	−	0.962899i	$-0.586978\pi$
$151$	−81.4983			−0.539724			−0.269862	+	0.962899i	$0.586978\pi$
$152$	7.48599	−	47.2647i	0.0492499	−	0.310952i
$153$	37.8460	−	19.2835i	0.247360	−	0.126036i
$154$	59.0475	+	19.1857i	0.383425	+	0.124582i
$155$		0			0
$156$	−27.7629	−	85.4453i	−0.177967	−	0.547726i
$157$	211.160	−	211.160i	1.34497	−	1.34497i	0.453938	−	0.891033i	$-0.350019\pi$
$157$	211.160	−	211.160i	1.34497	−	1.34497i	0.891033	−	0.453938i	$-0.149981\pi$
$158$	12.9640	−	25.4433i	0.0820506	−	0.161033i
$159$	−121.594	+	167.360i	−0.764742	+	1.05258i
$160$		0			0
$161$	−284.566	+	206.750i	−1.76749	+	1.28416i
$162$	71.2113	−	11.2788i	0.439576	−	0.0696219i
$163$	13.4333	+	84.8146i	0.0824129	+	0.520335i	0.994013	+	0.109258i	$0.0348473\pi$
$163$	13.4333	+	84.8146i	0.0824129	+	0.520335i	−0.911601	+	0.411077i	$0.865153\pi$
$164$	43.7132	+	60.1661i	0.266544	+	0.366866i
$165$		0			0
$166$	−28.4344	−	20.6588i	−0.171291	−	0.124451i
$167$	35.0337	+	17.8505i	0.209782	+	0.106889i	0.555725	−	0.831366i	$-0.312441\pi$
$167$	35.0337	+	17.8505i	0.209782	+	0.106889i	−0.345943	+	0.938256i	$0.612441\pi$
$168$	−47.1441	−	47.1441i	−0.280620	−	0.280620i
$169$	−138.672	+	45.0574i	−0.820546	+	0.266612i
$170$		0			0
$171$	13.5412	−	41.6755i	0.0791883	−	0.243717i
$172$	−33.3706	−	65.4935i	−0.194015	−	0.380776i
$173$	−224.889	−	35.6189i	−1.29993	−	0.205889i	−0.532179	−	0.846632i	$-0.678627\pi$
$173$	−224.889	−	35.6189i	−1.29993	−	0.205889i	−0.767756	+	0.640742i	$0.778627\pi$
$174$			5.52860i			0.0317735i
$175$		0			0
$176$	−18.8613			−0.107166
$177$	16.6977	−	105.425i	0.0943372	−	0.595622i
$178$	85.1250	−	43.3733i	0.478230	−	0.243670i
$179$	7.90838	+	2.56959i	0.0441809	+	0.0143552i	0.331024	−	0.943622i	$-0.392606\pi$
$179$	7.90838	+	2.56959i	0.0441809	+	0.0143552i	−0.286843	+	0.957978i	$0.592606\pi$
$180$		0			0
$181$	33.4318	+	102.892i	0.184706	+	0.568466i	0.999943	−	0.0106608i	$-0.00339351\pi$
$181$	33.4318	+	102.892i	0.184706	+	0.568466i	−0.815237	+	0.579127i	$0.803394\pi$
$182$	−165.193	+	165.193i	−0.907656	+	0.907656i
$183$	−136.505	+	267.905i	−0.745927	+	1.46396i
$184$	62.8088	−	86.4488i	0.341352	−	0.469831i
$185$		0			0
$186$	87.0967	−	63.2795i	0.468262	−	0.340212i
$187$	76.3778	−	12.0971i	0.408438	−	0.0646902i
$188$	−14.4641	−	91.3229i	−0.0769368	−	0.485760i
$189$	−160.583	−	221.024i	−0.849647	−	1.16944i
$190$		0			0
$191$	−185.233	−	134.580i	−0.969808	−	0.704607i	−0.0144000	−	0.999896i	$-0.504584\pi$
$191$	−185.233	−	134.580i	−0.969808	−	0.704607i	−0.955408	+	0.295290i	$0.904584\pi$
$192$	18.0468	+	9.19528i	0.0939935	+	0.0478921i
$193$	−176.707	−	176.707i	−0.915582	−	0.915582i	0.0811226	−	0.996704i	$-0.474149\pi$
$193$	−176.707	−	176.707i	−0.915582	−	0.915582i	−0.996704	+	0.0811226i	$0.974149\pi$
$194$	−39.5628	+	12.8547i	−0.203932	+	0.0662616i
$195$		0			0
$196$	−23.2900	+	71.6791i	−0.118826	+	0.365710i
$197$	−7.84117	−	15.3892i	−0.0398029	−	0.0781175i	0.870249	−	0.492613i	$-0.163958\pi$
$197$	−7.84117	−	15.3892i	−0.0398029	−	0.0781175i	−0.910051	+	0.414495i	$0.863958\pi$
$198$	−17.0588	−	2.70185i	−0.0861556	−	0.0136457i
$199$		−	266.747i		−	1.34044i	−0.742164	−	0.670218i	$-0.766200\pi$
$199$		−	266.747i		−	1.34044i	0.742164	−	0.670218i	$-0.233800\pi$
$200$		0			0
$201$	221.481			1.10189
$202$	31.1296	−	196.544i	0.154107	−	0.972992i
$203$	12.8092	−	6.52661i	0.0630995	−	0.0321508i
$204$	−78.9771	−	25.6612i	−0.387143	−	0.125790i
$205$		0			0
$206$	16.2446	+	49.9956i	0.0788571	+	0.242697i
$207$	69.1902	−	69.1902i	0.334252	−	0.334252i
$208$	32.2203	−	63.2360i	0.154905	−	0.304019i
$209$	46.8923	−	64.5417i	0.224365	−	0.308812i
$210$		0			0
$211$	200.960	−	146.006i	0.952419	−	0.691973i	0.00104087	−	0.999999i	$-0.499669\pi$
$211$	200.960	−	146.006i	0.952419	−	0.691973i	0.951378	+	0.308027i	$0.0996687\pi$
$212$	−161.404	+	25.5639i	−0.761341	+	0.120585i
$213$	−6.59908	−	41.6650i	−0.0309816	−	0.195610i
$214$	109.374	+	150.540i	0.511093	+	0.703459i
$215$		0			0
$216$	67.1452	+	48.7839i	0.310858	+	0.225851i
$217$	−249.431	−	127.092i	−1.14945	−	0.585676i
$218$	−188.345	−	188.345i	−0.863967	−	0.863967i
$219$	152.564	−	49.5712i	0.696641	−	0.226352i
$220$		0			0
$221$	−89.9171	+	276.736i	−0.406865	+	1.25220i
$222$	−13.1865	−	25.8800i	−0.0593986	−	0.116576i
$223$	55.9618	+	8.86348i	0.250950	+	0.0397466i	0.280642	−	0.959813i	$-0.409453\pi$
$223$	55.9618	+	8.86348i	0.250950	+	0.0397466i	−0.0296920	+	0.999559i	$0.509453\pi$
$224$		−	52.6677i		−	0.235124i
$225$		0			0
$226$	−226.549			−1.00243
$227$	−24.1307	+	152.356i	−0.106303	+	0.671170i	0.875779	+	0.482713i	$0.160349\pi$
$227$	−24.1307	+	152.356i	−0.106303	+	0.671170i	−0.982081	+	0.188457i	$0.939651\pi$
$228$	−76.3328	+	38.8935i	−0.334793	+	0.170586i
$229$	80.9675	+	26.3079i	0.353570	+	0.114882i	0.480416	−	0.877041i	$-0.340486\pi$
$229$	80.9675	+	26.3079i	0.353570	+	0.114882i	−0.126847	+	0.991922i	$0.540486\pi$
$230$		0			0
$231$	−34.3472	−	105.710i	−0.148689	−	0.457618i
$232$	−3.08817	+	3.08817i	−0.0133111	+	0.0133111i
$233$	24.9874	−	49.0406i	0.107242	−	0.210475i	−0.831149	−	0.556050i	$-0.812316\pi$
$233$	24.9874	−	49.0406i	0.107242	−	0.210475i	0.938391	+	0.345575i	$0.112316\pi$
$234$	38.1997	−	52.5774i	0.163247	−	0.224690i
$235$		0			0
$236$	68.2155	−	49.5615i	0.289049	−	0.210006i
$237$	−50.4923	+	7.99719i	−0.213048	+	0.0337434i
$238$	33.7795	+	213.275i	0.141931	+	0.896115i
$239$	8.97514	+	12.3532i	0.0375529	+	0.0516871i	0.827381	−	0.561642i	$-0.189830\pi$
$239$	8.97514	+	12.3532i	0.0375529	+	0.0516871i	−0.789828	+	0.613329i	$0.789830\pi$
$240$		0			0
$241$	191.342	+	139.018i	0.793950	+	0.576839i	0.909133	−	0.416506i	$-0.136745\pi$
$241$	191.342	+	139.018i	0.793950	+	0.576839i	−0.115183	+	0.993344i	$0.536745\pi$
$242$	124.452	+	63.4115i	0.514265	+	0.262031i
$243$	95.4714	+	95.4714i	0.392886	+	0.392886i
$244$	−225.896	+	73.3980i	−0.925803	+	0.300812i
$245$		0			0
$246$	41.1424	−	126.623i	0.167246	−	0.514729i
$247$	136.283	+	267.471i	0.551753	+	1.08288i
$248$	83.9974	+	13.3039i	0.338699	+	0.0536447i
$249$			62.9216i			0.252697i
$250$		0			0
$251$	−68.4984			−0.272902			−0.136451	−	0.990647i	$-0.543570\pi$
$251$	−68.4984			−0.272902			−0.136451	+	0.990647i	$0.543570\pi$
$252$	7.54458	−	47.6346i	0.0299388	−	0.189026i
$253$	158.726	−	80.8750i	0.627376	−	0.319664i
$254$	157.776	+	51.2644i	0.621164	+	0.201828i
$255$		0			0
$256$	4.94427	+	15.2169i	0.0193136	+	0.0594410i
$257$	−8.28497	+	8.28497i	−0.0322372	+	0.0322372i	−0.723042	−	0.690804i	$-0.757257\pi$
$257$	−8.28497	+	8.28497i	−0.0322372	+	0.0322372i	0.690804	+	0.723042i	$0.257257\pi$
$258$	−59.7417	+	117.250i	−0.231557	+	0.454456i
$259$	−44.3943	+	61.1035i	−0.171407	+	0.235921i
$260$		0			0
$261$	−3.23543	+	2.35068i	−0.0123963	+	0.00900643i
$262$	244.158	−	38.6708i	0.931901	−	0.147599i
$263$	−14.4577	−	91.2822i	−0.0549722	−	0.347081i	−0.999809	−	0.0195395i	$-0.993780\pi$
$263$	−14.4577	−	91.2822i	−0.0549722	−	0.347081i	0.944837	−	0.327541i	$-0.106220\pi$
$264$	19.8474	+	27.3176i	0.0751794	+	0.103476i
$265$		0			0
$266$	180.225	+	130.941i	0.677536	+	0.492259i
$267$	−152.395	−	77.6491i	−0.570767	−	0.290820i
$268$	123.715	+	123.715i	0.461623	+	0.461623i
$269$	203.293	−	66.0538i	0.755735	−	0.245553i	0.0942877	−	0.995545i	$-0.469943\pi$
$269$	203.293	−	66.0538i	0.755735	−	0.245553i	0.661447	+	0.749992i	$0.269943\pi$
$270$		0			0
$271$	119.535	−	367.892i	0.441090	−	1.35754i	−0.445625	−	0.895220i	$-0.647019\pi$
$271$	119.535	−	367.892i	0.441090	−	1.35754i	0.886715	−	0.462316i	$-0.152981\pi$
$272$	−29.7813	−	58.4490i	−0.109490	−	0.214886i
$273$	413.086	+	65.4265i	1.51314	+	0.239657i
$274$		−	86.2635i		−	0.314830i
$275$		0			0
$276$	−191.300			−0.693116
$277$	−5.68749	+	35.9094i	−0.0205324	+	0.129637i	−0.995825	−	0.0912789i	$-0.970905\pi$
$277$	−5.68749	+	35.9094i	−0.0205324	+	0.129637i	0.975293	+	0.220916i	$0.0709045\pi$
$278$	−97.6895	+	49.7753i	−0.351401	+	0.179048i
$279$	74.0645	+	24.0650i	0.265464	+	0.0862545i
$280$		0			0
$281$	−53.3063	−	164.060i	−0.189702	−	0.583843i	0.810295	−	0.586022i	$-0.199307\pi$
$281$	−53.3063	−	164.060i	−0.189702	−	0.583843i	−0.999998	+	0.00217821i	$0.999307\pi$
$282$	−117.046	+	117.046i	−0.415058	+	0.415058i
$283$	147.924	−	290.318i	0.522701	−	1.02586i	−0.467207	−	0.884148i	$-0.654740\pi$
$283$	147.924	−	290.318i	0.522701	−	1.02586i	0.989908	−	0.141710i	$-0.0452602\pi$
$284$	19.5872	−	26.9594i	0.0689688	−	0.0949275i
$285$		0			0
$286$	95.7209	−	69.5453i	0.334689	−	0.243165i
$287$	−341.943	+	54.1584i	−1.19144	+	0.188705i
$288$	2.29198	+	14.4710i	0.00795826	+	0.0502465i
$289$	−11.7845	−	16.2200i	−0.0407769	−	0.0561246i
$290$		0			0
$291$	60.2493	+	43.7737i	0.207042	+	0.150425i
$292$	112.909	+	57.5301i	0.386676	+	0.197021i
$293$	−68.8337	−	68.8337i	−0.234927	−	0.234927i	0.579818	−	0.814746i	$-0.303123\pi$
$293$	−68.8337	−	68.8337i	−0.234927	−	0.234927i	−0.814746	+	0.579818i	$0.803123\pi$
$294$	128.323	−	41.6948i	0.436474	−	0.141819i
$295$		0			0
$296$	7.09033	−	21.8218i	0.0239538	−	0.0737223i
$297$	62.8160	+	123.283i	0.211502	+	0.415095i
$298$	205.039	+	32.4750i	0.688051	+	0.108977i
$299$			670.316i			2.24186i
$300$		0			0
$301$	342.182			1.13682
$302$	−18.0300	+	113.837i	−0.0597021	+	0.376944i
$303$	−317.421	+	161.734i	−1.04759	+	0.533775i
$304$	−64.3633	−	20.9129i	−0.211721	−	0.0687924i
$305$		0			0
$306$	−18.5625	−	57.1296i	−0.0606618	−	0.186698i
$307$	196.445	−	196.445i	0.639887	−	0.639887i	−0.310641	−	0.950527i	$-0.600544\pi$
$307$	196.445	−	196.445i	0.639887	−	0.639887i	0.950527	+	0.310641i	$0.100544\pi$
$308$	39.8618	−	78.2332i	0.129421	−	0.254004i
$309$	55.3169	−	76.1372i	0.179019	−	0.246399i
$310$		0			0
$311$	−194.521	+	141.328i	−0.625470	+	0.454431i	−0.854828	−	0.518911i	$-0.826337\pi$
$311$	−194.521	+	141.328i	−0.625470	+	0.454431i	0.229358	+	0.973342i	$0.426337\pi$
$312$	−125.492	+	19.8760i	−0.402218	+	0.0637052i
$313$	32.2507	+	203.623i	0.103037	+	0.650552i	0.984108	+	0.177568i	$0.0568230\pi$
$313$	32.2507	+	203.623i	0.103037	+	0.650552i	−0.881071	+	0.472984i	$0.843177\pi$
$314$	−248.234	−	341.665i	−0.790554	−	1.08810i
$315$		0			0
$316$	−32.6712	−	23.7370i	−0.103390	−	0.0751170i
$317$	−30.8396	−	15.7136i	−0.0972858	−	0.0495696i	0.404671	−	0.914463i	$-0.367386\pi$
$317$	−30.8396	−	15.7136i	−0.0972858	−	0.0495696i	−0.501956	+	0.864893i	$0.667386\pi$
$318$	206.868	+	206.868i	0.650529	+	0.650529i
$319$	−6.92450	+	2.24991i	−0.0217069	+	0.00705300i
$320$		0			0
$321$	102.942	−	316.822i	0.320690	−	0.986983i
$322$	225.833	+	443.222i	0.701345	+	1.37647i
$323$	274.049	+	43.4051i	0.848449	+	0.134381i
$324$		−	101.963i		−	0.314701i
$325$		0			0
$326$	121.441			0.372519
$327$	−74.5958	+	470.979i	−0.228122	+	1.44030i
$328$	93.7109	−	47.7481i	0.285704	−	0.145573i
$329$	409.360	+	133.009i	1.24426	+	0.404283i
$330$		0			0
$331$	7.67891	+	23.6332i	0.0231991	+	0.0713995i	0.961986	−	0.273099i	$-0.0880488\pi$
$331$	7.67891	+	23.6332i	0.0231991	+	0.0713995i	−0.938787	+	0.344499i	$0.888049\pi$
$332$	−35.1468	+	35.1468i	−0.105864	+	0.105864i
$333$	9.53870	−	18.7207i	0.0286447	−	0.0562185i
$334$	32.6842	−	44.9860i	0.0978570	−	0.134689i
$335$		0			0
$336$	−76.2808	+	55.4213i	−0.227026	+	0.164944i
$337$	−249.970	+	39.5913i	−0.741750	+	0.117482i	−0.515862	−	0.856672i	$-0.672528\pi$
$337$	−249.970	+	39.5913i	−0.741750	+	0.117482i	−0.225888	+	0.974153i	$0.572528\pi$
$338$	32.2575	+	203.666i	0.0954364	+	0.602562i
$339$	238.394	+	328.121i	0.703226	+	0.967907i
$340$		0			0
$341$	114.702	+	83.3356i	0.336368	+	0.244386i
$342$	−55.2167	−	28.1343i	−0.161452	−	0.0822641i
$343$	74.4988	+	74.4988i	0.217198	+	0.217198i
$344$	−98.8641	+	32.1229i	−0.287396	+	0.0933805i
$345$		0			0
$346$	−99.5050	+	306.245i	−0.287587	+	0.885101i
$347$	−94.7100	−	185.879i	−0.272939	−	0.535674i	0.713328	−	0.700830i	$-0.247187\pi$
$347$	−94.7100	−	185.879i	−0.272939	−	0.535674i	−0.986267	+	0.165157i	$0.947187\pi$
$348$	7.72235	+	1.22310i	0.0221907	+	0.00351466i
$349$		−	198.448i		−	0.568620i	−0.958732	−	0.284310i	$-0.908235\pi$
$349$		−	198.448i		−	0.568620i	0.958732	−	0.284310i	$-0.0917645\pi$
$350$		0			0
$351$	−520.638			−1.48330
$352$	−4.17271	+	26.3455i	−0.0118543	+	0.0748451i
$353$	162.747	−	82.9237i	0.461039	−	0.234911i	−0.208014	−	0.978126i	$-0.566700\pi$
$353$	162.747	−	82.9237i	0.461039	−	0.234911i	0.669053	+	0.743215i	$0.266700\pi$
$354$	−143.564	−	46.6467i	−0.405548	−	0.131770i
$355$		0			0
$356$	−41.7516	−	128.498i	−0.117280	−	0.360950i
$357$	273.350	−	273.350i	0.765687	−	0.765687i
$358$	5.33879	−	10.4780i	0.0149128	−	0.0292681i
$359$	114.552	−	157.667i	0.319086	−	0.439184i	−0.619102	−	0.785310i	$-0.712503\pi$
$359$	114.552	−	157.667i	0.319086	−	0.439184i	0.938188	+	0.346127i	$0.112503\pi$
$360$		0			0
$361$	−60.4750	+	43.9376i	−0.167521	+	0.121711i
$362$	151.116	−	23.9345i	0.417449	−	0.0661174i
$363$	−39.1172	−	246.976i	−0.107761	−	0.680375i
$364$	194.196	+	267.289i	0.533507	+	0.734309i
$365$		0			0
$366$	344.012	+	249.939i	0.939922	+	0.682894i
$367$	−122.499	−	62.4163i	−0.333785	−	0.170072i	0.279063	−	0.960273i	$-0.409976\pi$
$367$	−122.499	−	62.4163i	−0.333785	−	0.170072i	−0.612848	+	0.790201i	$0.709976\pi$
$368$	−106.857	−	106.857i	−0.290371	−	0.290371i
$369$	91.5954	−	29.7611i	0.248226	−	0.0806535i
$370$		0			0
$371$	235.081	−	723.504i	0.633641	−	1.95015i
$372$	−69.1204	−	135.656i	−0.185807	−	0.364668i
$373$	−396.832	−	62.8520i	−1.06389	−	0.168504i	−0.400139	−	0.916455i	$-0.631038\pi$
$373$	−396.832	−	62.8520i	−1.06389	−	0.168504i	−0.663754	+	0.747951i	$0.731038\pi$
$374$		−	109.361i		−	0.292409i
$375$		0			0
$376$	−130.760			−0.347766
$377$	4.28575	−	27.0592i	0.0113680	−	0.0717750i
$378$	−344.253	+	175.406i	−0.910722	+	0.464036i
$379$	−509.120	−	165.423i	−1.34332	−	0.436473i	−0.452883	−	0.891570i	$-0.649604\pi$
$379$	−509.120	−	165.423i	−1.34332	−	0.436473i	−0.890442	+	0.455097i	$0.849604\pi$
$380$		0			0
$381$	−91.7760	−	282.458i	−0.240882	−	0.741359i
$382$	−228.961	+	228.961i	−0.599374	+	0.599374i
$383$	210.372	−	412.878i	0.549274	−	1.07801i	−0.434846	−	0.900505i	$-0.643197\pi$
$383$	210.372	−	412.878i	0.549274	−	1.07801i	0.984120	−	0.177505i	$-0.0568027\pi$
$384$	16.8365	−	23.1735i	0.0438451	−	0.0603476i
$385$		0			0
$386$	−285.918	+	207.732i	−0.740721	+	0.538165i
$387$	−94.0178	+	14.8910i	−0.242940	+	0.0384779i
$388$	9.20298	+	58.1053i	0.0237190	+	0.149756i
$389$	19.0616	+	26.2360i	0.0490015	+	0.0674448i	0.832815	−	0.553552i	$-0.186728\pi$
$389$	19.0616	+	26.2360i	0.0490015	+	0.0674448i	−0.783813	+	0.620997i	$0.786728\pi$
$390$		0			0
$391$	501.246	+	364.176i	1.28196	+	0.931397i
$392$	94.9691	+	48.3892i	0.242268	+	0.123442i
$393$	−312.932	−	312.932i	−0.796264	−	0.796264i
$394$	−23.2303	+	7.54799i	−0.0589602	+	0.0191573i
$395$		0			0
$396$	−7.54790	+	23.2301i	−0.0190604	+	0.0586618i
$397$	−74.2593	−	145.742i	−0.187051	−	0.367109i	0.778369	−	0.627807i	$-0.216047\pi$
$397$	−74.2593	−	145.742i	−0.187051	−	0.367109i	−0.965420	+	0.260698i	$0.916047\pi$
$398$	−372.593	−	59.0129i	−0.936163	−	0.148274i
$399$		−	398.813i		−	0.999532i
$400$		0			0
$401$	−461.933			−1.15195			−0.575977	−	0.817466i	$-0.695378\pi$
$401$	−461.933			−1.15195			−0.575977	+	0.817466i	$0.695378\pi$
$402$	48.9985	−	309.365i	0.121887	−	0.769564i
$403$	−475.341	+	242.198i	−1.17951	+	0.600988i
$404$	−267.647	−	86.9637i	−0.662492	−	0.215257i
$405$		0			0
$406$	−6.28258	−	19.3358i	−0.0154743	−	0.0476251i
$407$	27.0480	−	27.0480i	0.0664570	−	0.0664570i
$408$	−53.3159	+	104.638i	−0.130676	+	0.256466i
$409$	−152.579	+	210.007i	−0.373054	+	0.513465i	−0.953728	−	0.300672i	$-0.902789\pi$
$409$	−152.579	+	210.007i	−0.373054	+	0.513465i	0.580674	+	0.814136i	$0.302789\pi$
$410$		0			0
$411$	−124.939	+	90.7735i	−0.303988	+	0.220860i
$412$	73.4278	−	11.6298i	0.178223	−	0.0282277i
$413$	61.4041	+	387.690i	0.148678	+	0.938717i
$414$	−81.3379	−	111.952i	−0.196468	−	0.270416i
$415$		0			0
$416$	−81.2000	−	58.9952i	−0.195192	−	0.141815i
$417$	174.888	+	89.1101i	0.419397	+	0.213693i
$418$	−79.7779	−	79.7779i	−0.190856	−	0.190856i
$419$	374.972	−	121.836i	0.894922	−	0.290778i	0.174782	−	0.984607i	$-0.444078\pi$
$419$	374.972	−	121.836i	0.894922	−	0.290778i	0.720139	+	0.693829i	$0.244078\pi$
$420$		0			0
$421$	96.2390	−	296.193i	0.228596	−	0.703547i	−0.769310	−	0.638875i	$-0.779400\pi$
$421$	96.2390	−	296.193i	0.228596	−	0.703547i	0.997907	−	0.0646716i	$-0.0206000\pi$
$422$	−159.483	−	313.003i	−0.377922	−	0.741713i
$423$	−118.264	−	18.7312i	−0.279584	−	0.0442818i
$424$			231.105i			0.545060i
$425$		0			0
$426$	−59.6576			−0.140041
$427$	172.971	−	1092.10i	0.405085	−	2.55760i
$428$	234.472	−	119.469i	0.547832	−	0.279134i
$429$	−201.451	−	65.4553i	−0.469582	−	0.152577i
$430$		0			0
$431$	223.411	+	687.587i	0.518354	+	1.59533i	0.777095	+	0.629383i	$0.216692\pi$
$431$	223.411	+	687.587i	0.518354	+	1.59533i	−0.258741	+	0.965947i	$0.583308\pi$
$432$	82.9961	−	82.9961i	0.192121	−	0.192121i
$433$	108.774	−	213.481i	0.251210	−	0.493027i	−0.730621	−	0.682783i	$-0.760770\pi$
$433$	108.774	−	213.481i	0.251210	−	0.493027i	0.981831	+	0.189755i	$0.0607695\pi$
$434$	−232.704	+	320.290i	−0.536184	+	0.737994i
$435$		0			0
$436$	−304.748	+	221.413i	−0.698964	+	0.507827i
$437$	631.318	−	99.9910i	1.44466	−	0.228812i
$438$	−35.4891	−	224.069i	−0.0810252	−	0.511573i
$439$	−43.7867	−	60.2673i	−0.0997420	−	0.137283i	0.756229	−	0.654307i	$-0.227040\pi$
$439$	−43.7867	−	60.2673i	−0.0997420	−	0.137283i	−0.855971	+	0.517024i	$0.827040\pi$
$440$		0			0
$441$	78.9618	+	57.3691i	0.179052	+	0.130089i
$442$	366.653	+	186.819i	0.829533	+	0.422668i
$443$	−144.493	−	144.493i	−0.326170	−	0.326170i	0.524958	−	0.851128i	$-0.324081\pi$
$443$	−144.493	−	144.493i	−0.326170	−	0.326170i	−0.851128	+	0.524958i	$0.824081\pi$
$444$	−39.0664	+	12.6935i	−0.0879875	+	0.0285889i
$445$		0			0
$446$	24.7611	−	76.2067i	0.0555181	−	0.170867i
$447$	−168.724	−	331.140i	−0.377459	−	0.740805i
$448$	−73.5664	−	11.6518i	−0.164211	−	0.0260084i
$449$		−	63.0893i		−	0.140511i	−0.997529	−	0.0702554i	$-0.977619\pi$
$449$		−	63.0893i		−	0.140511i	0.997529	−	0.0702554i	$-0.0223814\pi$
$450$		0			0
$451$	175.338			0.388775
$452$	−50.1199	+	316.444i	−0.110885	+	0.700098i
$453$	183.848	−	93.6750i	0.405845	−	0.206788i
$454$	207.472	+	67.4118i	0.456987	+	0.148484i
$455$		0			0
$456$	37.4393	+	115.226i	0.0821037	+	0.252689i
$457$	−456.270	+	456.270i	−0.998403	+	0.998403i	−0.999999	−	0.00159596i	$-0.999492\pi$
$457$	−456.270	+	456.270i	−0.998403	+	0.998403i	0.00159596	+	0.999999i	$0.499492\pi$
$458$	54.6596	−	107.275i	0.119344	−	0.234226i
$459$	−282.858	+	389.320i	−0.616247	+	0.848192i
$460$		0			0
$461$	−279.602	+	203.143i	−0.606512	+	0.440656i	−0.848184	−	0.529701i	$-0.822304\pi$
$461$	−279.602	+	203.143i	−0.606512	+	0.440656i	0.241673	+	0.970358i	$0.422304\pi$
$462$	−155.254	+	24.5899i	−0.336048	+	0.0532248i
$463$	111.539	+	704.232i	0.240906	+	1.52102i	0.750654	+	0.660696i	$0.229739\pi$
$463$	111.539	+	704.232i	0.240906	+	1.52102i	−0.509748	+	0.860324i	$0.670261\pi$
$464$	3.63036	+	4.99677i	0.00782406	+	0.0107689i
$465$		0			0
$466$	−62.9720	−	45.7518i	−0.135133	−	0.0981799i
$467$	88.9445	+	45.3195i	0.190459	+	0.0970438i	0.546620	−	0.837381i	$-0.315914\pi$
$467$	88.9445	+	45.3195i	0.190459	+	0.0970438i	−0.356160	+	0.934425i	$0.615914\pi$
$468$	−64.9892	−	64.9892i	−0.138866	−	0.138866i
$469$	−774.610	+	251.686i	−1.65162	+	0.536644i
$470$		0			0
$471$	−233.635	+	719.055i	−0.496041	+	1.52666i
$472$	−54.1361	−	106.248i	−0.114695	−	0.225102i
$473$	−171.166	−	27.1101i	−0.361874	−	0.0573152i
$474$			72.2970i			0.152525i
$475$		0			0
$476$	305.377			0.641548
$477$	−33.1055	+	209.020i	−0.0694037	+	0.438197i
$478$	19.2406	−	9.80358i	0.0402523	−	0.0205096i
$479$	−828.170	−	269.089i	−1.72896	−	0.561772i	−0.735658	−	0.677353i	$-0.763127\pi$
$479$	−828.170	−	269.089i	−1.72896	−	0.561772i	−0.993298	+	0.115581i	$0.963127\pi$
$480$		0			0
$481$	44.4780	+	136.889i	0.0924698	+	0.284593i
$482$	236.512	−	236.512i	0.490688	−	0.490688i
$483$	404.297	−	793.478i	0.837055	−	1.64281i
$484$	116.106	−	159.806i	0.239889	−	0.330179i
$485$		0			0
$486$	154.476	−	112.233i	0.317852	−	0.230933i
$487$	490.364	−	77.6661i	1.00691	−	0.159479i	0.368868	−	0.929482i	$-0.379745\pi$
$487$	490.364	−	77.6661i	1.00691	−	0.159479i	0.638040	+	0.770003i	$0.279745\pi$
$488$	52.5472	+	331.770i	0.107679	+	0.679856i
$489$	−127.790	−	175.888i	−0.261330	−	0.359689i
$490$		0			0
$491$	135.584	+	98.5073i	0.276138	+	0.200626i	0.717231	−	0.696835i	$-0.245409\pi$
$491$	135.584	+	98.5073i	0.276138	+	0.200626i	−0.441093	+	0.897461i	$0.645409\pi$
$492$	−167.766	−	85.4809i	−0.340987	−	0.173742i
$493$	−17.9058	−	17.9058i	−0.0363200	−	0.0363200i
$494$	403.754	−	131.188i	0.817315	−	0.265562i
$495$		0			0
$496$	37.1658	−	114.384i	0.0749310	−	0.230614i
$497$	70.4269	+	138.221i	0.141704	+	0.278110i
$498$	87.8890	+	13.9202i	0.176484	+	0.0279523i
$499$		−	199.265i		−	0.399328i	−0.979864	−	0.199664i	$-0.936015\pi$
$499$		−	199.265i		−	0.399328i	0.979864	−	0.199664i	$-0.0639851\pi$
$500$		0			0
$501$	−99.5481			−0.198699
$502$	−15.1540	+	95.6787i	−0.0301873	+	0.190595i
$503$	−709.290	+	361.401i	−1.41012	+	0.718492i	−0.982638	−	0.185532i	$-0.940599\pi$
$503$	−709.290	+	361.401i	−1.41012	+	0.718492i	−0.427481	+	0.904024i	$0.640599\pi$
$504$	−64.8670	−	21.0766i	−0.128704	−	0.0418186i
$505$		0			0
$506$	−77.8511	−	239.601i	−0.153856	−	0.473520i
$507$	261.034	−	261.034i	0.514860	−	0.514860i
$508$	106.511	−	209.040i	0.209668	−	0.411496i
$509$	−99.1120	+	136.416i	−0.194719	+	0.268008i	−0.895201	−	0.445662i	$-0.852968\pi$
$509$	−99.1120	+	136.416i	−0.194719	+	0.268008i	0.700482	+	0.713670i	$0.252968\pi$
$510$		0			0
$511$	−477.250	+	346.742i	−0.933952	+	0.678556i
$512$	22.3488	−	3.53971i	0.0436501	−	0.00691349i
$513$	77.6635	+	490.348i	0.151391	+	0.955844i
$514$	9.73956	+	13.4054i	0.0189486	+	0.0260805i
$515$		0			0
$516$	150.558	+	109.387i	0.291779	+	0.211990i
$517$	−194.232	−	98.9663i	−0.375691	−	0.191424i
$518$	75.5281	+	75.5281i	0.145807	+	0.145807i
$519$	548.255	−	178.139i	1.05637	−	0.343235i
$520$		0			0
$521$	279.151	−	859.137i	0.535798	−	1.64902i	−0.206121	−	0.978526i	$-0.566084\pi$
$521$	279.151	−	859.137i	0.535798	−	1.64902i	0.741919	−	0.670490i	$-0.233916\pi$
$522$	2.56765	+	5.03930i	0.00491887	+	0.00965383i
$523$	−5.64280	−	0.893732i	−0.0107893	−	0.00170886i	0.151037	−	0.988528i	$-0.451739\pi$
$523$	−5.64280	−	0.893732i	−0.0107893	−	0.00170886i	−0.161827	+	0.986819i	$0.551739\pi$
$524$		−	349.596i		−	0.667168i
$525$		0			0
$526$	−130.702			−0.248482
$527$	−77.1383	+	487.032i	−0.146372	+	0.924159i
$528$	42.5481	−	21.6793i	0.0805835	−	0.0410594i
$529$	854.327	+	277.588i	1.61499	+	0.524740i
$530$		0			0
$531$	−33.7428	−	103.850i	−0.0635457	−	0.195574i
$532$	222.770	−	222.770i	0.418740	−	0.418740i
$533$	−299.526	+	587.853i	−0.561962	+	1.10291i
$534$	−142.175	+	195.687i	−0.266245	+	0.366455i
$535$		0			0
$536$	200.175	−	145.436i	0.373461	−	0.271335i
$537$	−20.7936	+	3.29338i	−0.0387218	+	0.00613293i
$538$	−47.2893	−	298.573i	−0.0878983	−	0.554968i
$539$	104.445	+	143.756i	0.193775	+	0.266708i
$540$		0			0
$541$	−568.079	−	412.734i	−1.05005	−	0.762909i	−0.0778309	−	0.996967i	$-0.524799\pi$
$541$	−568.079	−	412.734i	−1.05005	−	0.762909i	−0.972223	+	0.234058i	$0.924799\pi$
$542$	−487.428	−	248.357i	−0.899313	−	0.458223i
$543$	−193.682	−	193.682i	−0.356690	−	0.356690i
$544$	−88.2303	+	28.6678i	−0.162188	+	0.0526981i
$545$		0			0
$546$	182.776	−	562.526i	0.334754	−	1.03027i
$547$	52.1216	+	102.294i	0.0952862	+	0.187010i	0.933730	−	0.357979i	$-0.116534\pi$
$547$	52.1216	+	102.294i	0.0952862	+	0.187010i	−0.838443	+	0.544989i	$0.816534\pi$
$548$	−120.493	−	19.0842i	−0.219878	−	0.0348252i
$549$			307.592i			0.560277i
$550$		0			0
$551$	−26.1242			−0.0474124
$552$	−42.3216	+	267.208i	−0.0766696	+	0.484073i
$553$	167.505	−	85.3479i	0.302902	−	0.154336i
$554$	48.9001	+	15.8886i	0.0882672	+	0.0286798i
$555$		0			0
$556$	47.9142	+	147.465i	0.0861766	+	0.265224i
$557$	−719.095	+	719.095i	−1.29101	+	1.29101i	−0.356853	+	0.934160i	$0.616150\pi$
$557$	−719.095	+	719.095i	−1.29101	+	1.29101i	−0.934160	+	0.356853i	$0.883850\pi$
$558$	49.9995	−	98.1295i	0.0896048	−	0.175859i
$559$	383.292	−	527.556i	0.685674	−	0.943749i
$560$		0			0
$561$	−158.392	+	115.079i	−0.282339	+	0.205131i
$562$	−240.952	+	38.1631i	−0.428741	+	0.0679059i
$563$	−58.6570	−	370.346i	−0.104187	−	0.657808i	−0.983410	−	0.181398i	$-0.941938\pi$
$563$	−58.6570	−	370.346i	−0.104187	−	0.657808i	0.879223	−	0.476410i	$-0.158062\pi$
$564$	137.596	+	189.385i	0.243965	+	0.335789i
$565$		0			0
$566$	−372.791	−	270.849i	−0.658641	−	0.478531i
$567$	422.926	+	215.491i	0.745900	+	0.380055i
$568$	−33.3237	−	33.3237i	−0.0586684	−	0.0586684i
$569$	−648.640	+	210.756i	−1.13997	+	0.370397i	−0.817355	−	0.576135i	$-0.804560\pi$
$569$	−648.640	+	210.756i	−1.13997	+	0.370397i	−0.322610	+	0.946532i	$0.604560\pi$
$570$		0			0
$571$	−42.9687	+	132.244i	−0.0752517	+	0.231601i	−0.981606	−	0.190917i	$-0.938854\pi$
$571$	−42.9687	+	132.244i	−0.0752517	+	0.231601i	0.906354	+	0.422518i	$0.138854\pi$
$572$	−75.9646	−	149.089i	−0.132805	−	0.260645i
$573$	572.545	+	90.6822i	0.999206	+	0.158259i
$574$			489.608i			0.852976i
$575$		0			0
$576$	20.7202			0.0359725
$577$	11.0095	−	69.5115i	0.0190807	−	0.120471i	−0.976310	−	0.216379i	$-0.930575\pi$
$577$	11.0095	−	69.5115i	0.0190807	−	0.120471i	0.995390	+	0.0959080i	$0.0305755\pi$
$578$	−25.2632	+	12.8723i	−0.0437080	+	0.0222704i
$579$	601.733	+	195.515i	1.03926	+	0.337677i
$580$		0			0
$581$	−71.5028	−	220.063i	−0.123068	−	0.378766i
$582$	74.4722	−	74.4722i	0.127959	−	0.127959i
$583$	−174.913	+	343.287i	−0.300023	+	0.588828i
$584$	105.337	−	144.984i	0.180372	−	0.248261i
$585$		0			0
$586$	−111.375	+	80.9189i	−0.190060	+	0.138087i
$587$	216.783	−	34.3351i	0.369307	−	0.0584924i	0.0309770	−	0.999520i	$-0.490138\pi$
$587$	216.783	−	34.3351i	0.369307	−	0.0584924i	0.338330	+	0.941028i	$0.390138\pi$
$588$	−29.8502	−	188.467i	−0.0507656	−	0.320522i
$589$	299.014	+	411.557i	0.507664	+	0.698739i
$590$		0			0
$591$	35.3769	+	25.7028i	0.0598594	+	0.0434904i
$592$	−28.9121	−	14.7315i	−0.0488381	−	0.0248842i
$593$	597.816	+	597.816i	1.00812	+	1.00812i	0.999967	+	0.00815551i	$0.00259601\pi$
$593$	597.816	+	597.816i	1.00812	+	1.00812i	0.00815551	+	0.999967i	$0.497404\pi$
$594$	186.099	−	60.4673i	0.313298	−	0.101797i
$595$		0			0
$596$	90.7224	−	279.215i	0.152219	−	0.468481i
$597$	306.602	+	601.740i	0.513571	+	1.00794i
$598$	936.299	+	148.295i	1.56572	+	0.247985i
$599$		−	658.191i		−	1.09882i	−0.835554	−	0.549408i	$-0.814853\pi$
$599$		−	658.191i		−	1.09882i	0.835554	−	0.549408i	$-0.185147\pi$
$600$		0			0
$601$	−350.388			−0.583009			−0.291504	−	0.956570i	$-0.594156\pi$
$601$	−350.388			−0.583009			−0.291504	+	0.956570i	$0.594156\pi$
$602$	75.7014	−	477.960i	0.125750	−	0.793954i
$603$	201.879	−	102.863i	0.334791	−	0.170585i
$604$	155.019	+	50.3687i	0.256654	+	0.0833920i
$605$		0			0
$606$	155.687	+	479.154i	0.256909	+	0.790684i
$607$	−814.998	+	814.998i	−1.34266	+	1.34266i	−0.449268	+	0.893397i	$0.648315\pi$
$607$	−814.998	+	814.998i	−1.34266	+	1.34266i	−0.893397	+	0.449268i	$0.851685\pi$
$608$	−43.4504	+	85.2762i	−0.0714644	+	0.140257i
$609$	−21.3938	+	29.4460i	−0.0351294	+	0.0483514i
$610$		0			0
$611$	663.607	−	482.139i	1.08610	−	0.789097i
$612$	−83.9053	+	13.2893i	−0.137100	+	0.0217145i
$613$	−100.273	−	633.098i	−0.163577	−	1.03279i	−0.923731	−	0.383043i	$-0.874876\pi$
$613$	−100.273	−	633.098i	−0.163577	−	1.03279i	0.760153	−	0.649744i	$-0.225124\pi$
$614$	−230.935	−	317.855i	−0.376116	−	0.517679i
$615$		0			0
$616$	−100.458	−	72.9867i	−0.163081	−	0.118485i
$617$	348.494	+	177.567i	0.564820	+	0.287790i	0.712993	−	0.701171i	$-0.247339\pi$
$617$	348.494	+	177.567i	0.564820	+	0.287790i	−0.148173	+	0.988962i	$0.547339\pi$
$618$	−94.1107	−	94.1107i	−0.152283	−	0.152283i
$619$	−506.694	+	164.635i	−0.818569	+	0.265969i	−0.688223	−	0.725499i	$-0.741609\pi$
$619$	−506.694	+	164.635i	−0.818569	+	0.265969i	−0.130346	+	0.991469i	$0.541609\pi$
$620$		0			0
$621$	−342.572	+	1054.33i	−0.551645	+	1.69779i
$622$	154.373	+	302.974i	0.248188	+	0.487097i
$623$	621.227	+	98.3927i	0.997154	+	0.157934i
$624$			179.685i			0.287957i
$625$		0			0
$626$	291.556			0.465744
$627$	−31.5968	+	199.495i	−0.0503937	+	0.318173i
$628$	−532.155	+	271.147i	−0.847381	+	0.431762i
$629$	126.527	+	41.1110i	0.201155	+	0.0653593i
$630$		0			0
$631$	−69.5221	−	213.967i	−0.110178	−	0.339092i	0.880733	−	0.473613i	$-0.157050\pi$
$631$	−69.5221	−	213.967i	−0.110178	−	0.339092i	−0.990911	+	0.134521i	$0.957050\pi$
$632$	−40.3838	+	40.3838i	−0.0638984	+	0.0638984i
$633$	−285.514	+	560.353i	−0.451049	+	0.885234i
$634$	−28.7714	+	39.6005i	−0.0453808	+	0.0624613i
$635$		0			0
$636$	334.720	−	243.188i	0.526289	−	0.382371i
$637$	−660.389	+	104.595i	−1.03672	+	0.164200i
$638$	1.61076	+	10.1699i	0.00252470	+	0.0159403i
$639$	−25.3656	−	34.9127i	−0.0396957	−	0.0546364i
$640$		0			0
$641$	635.805	+	461.939i	0.991896	+	0.720654i	0.960335	−	0.278848i	$-0.0899524\pi$
$641$	635.805	+	461.939i	0.991896	+	0.720654i	0.0315601	+	0.999502i	$0.489952\pi$
$642$	−419.763	−	213.880i	−0.653837	−	0.333146i
$643$	408.621	+	408.621i	0.635491	+	0.635491i	0.949440	−	0.313949i	$-0.101652\pi$
$643$	408.621	+	408.621i	0.635491	+	0.635491i	−0.313949	+	0.949440i	$0.601652\pi$
$644$	669.056	−	217.389i	1.03891	−	0.337561i
$645$		0			0
$646$	121.257	−	373.190i	0.187704	−	0.577693i
$647$	−371.987	−	730.065i	−0.574941	−	1.12839i	−0.977093	−	0.212812i	$-0.931738\pi$
$647$	−371.987	−	730.065i	−0.574941	−	1.12839i	0.402152	−	0.915573i	$-0.368262\pi$
$648$	−142.423	−	22.5575i	−0.219788	−	0.0348110i
$649$		−	198.795i		−	0.306310i
$650$		0			0
$651$	708.759			1.08872
$652$	26.8666	−	169.629i	0.0412065	−	0.260167i
$653$	485.310	−	247.278i	0.743200	−	0.378679i	−0.0410232	−	0.999158i	$-0.513062\pi$
$653$	485.310	−	247.278i	0.743200	−	0.378679i	0.784223	+	0.620479i	$0.213062\pi$
$654$	641.362	+	208.391i	0.980676	+	0.318641i
$655$		0			0
$656$	−45.9628	−	141.459i	−0.0700653	−	0.215639i
$657$	116.040	−	116.040i	0.176621	−	0.176621i
$658$	276.351	−	542.369i	0.419986	−	0.824269i
$659$	223.989	−	308.295i	0.339893	−	0.467822i	−0.604517	−	0.796592i	$-0.706634\pi$
$659$	223.989	−	308.295i	0.339893	−	0.467822i	0.944410	+	0.328770i	$0.106634\pi$
$660$		0			0
$661$	807.083	−	586.380i	1.22100	−	0.887110i	0.224820	−	0.974400i	$-0.427821\pi$
$661$	807.083	−	586.380i	1.22100	−	0.887110i	0.996183	+	0.0872901i	$0.0278207\pi$
$662$	34.7098	−	5.49749i	0.0524317	−	0.00830437i
$663$	−115.245	−	727.626i	−0.173823	−	1.09748i
$664$	41.3176	+	56.8688i	0.0622253	+	0.0856457i
$665$		0			0
$666$	−24.0389	−	17.4653i	−0.0360945	−	0.0262242i
$667$	−51.9767	−	26.4835i	−0.0779261	−	0.0397053i
$668$	−55.6057	−	55.6057i	−0.0832421	−	0.0832421i
$669$	−136.429	+	44.3285i	−0.203930	+	0.0662608i
$670$		0			0
$671$	−173.047	+	532.585i	−0.257895	+	0.793719i
$672$	60.5368	+	118.810i	0.0900845	+	0.176801i
$673$	−327.061	−	51.8013i	−0.485974	−	0.0769708i	−0.0913606	−	0.995818i	$-0.529122\pi$
$673$	−327.061	−	51.8013i	−0.485974	−	0.0769708i	−0.394614	+	0.918847i	$0.629122\pi$
$674$			357.917i			0.531035i
$675$		0			0
$676$	291.617			0.431387
$677$	15.0662	−	95.1245i	0.0222544	−	0.140509i	−0.974059	−	0.226293i	$-0.927339\pi$
$677$	15.0662	−	95.1245i	0.0222544	−	0.140509i	0.996314	+	0.0857838i	$0.0273394\pi$
$678$	511.060	−	260.398i	0.753776	−	0.384068i
$679$	−260.460	−	84.6287i	−0.383594	−	0.124637i
$680$		0			0
$681$	−120.684	−	371.427i	−0.177216	−	0.545414i
$682$	141.779	−	141.779i	0.207887	−	0.207887i
$683$	−27.4839	+	53.9401i	−0.0402399	+	0.0789753i	−0.910251	−	0.414057i	$-0.864111\pi$
$683$	−27.4839	+	53.9401i	−0.0402399	+	0.0789753i	0.870011	+	0.493032i	$0.164111\pi$
$684$	−51.5138	+	70.9027i	−0.0753126	+	0.103659i
$685$		0			0
$686$	120.542	−	87.5786i	0.175717	−	0.127666i
$687$	−212.889	+	33.7183i	−0.309882	+	0.0490804i
$688$	22.9975	+	145.200i	0.0334265	+	0.211047i
$689$	−852.133	−	1172.86i	−1.23677	−	1.70226i
$690$		0			0
$691$	816.866	+	593.488i	1.18215	+	0.858883i	0.992413	−	0.122952i	$-0.0392362\pi$
$691$	816.866	+	593.488i	1.18215	+	0.858883i	0.189738	+	0.981835i	$0.439236\pi$
$692$	405.750	+	206.740i	0.586344	+	0.298757i
$693$	−80.4023	−	80.4023i	−0.116021	−	0.116021i
$694$	−280.589	+	91.1688i	−0.404307	+	0.131367i
$695$		0			0
$696$	3.41686	−	10.5160i	0.00490928	−	0.0151092i
$697$	276.852	+	543.352i	0.397205	+	0.779559i
$698$	−277.193	−	43.9031i	−0.397125	−	0.0628984i
$699$			139.349i			0.199354i
$700$		0			0
$701$	290.914			0.414998			0.207499	−	0.978235i	$-0.433468\pi$
$701$	290.914			0.414998			0.207499	+	0.978235i	$0.433468\pi$
$702$	−115.182	+	727.228i	−0.164076	+	1.03594i
$703$	122.290	−	62.3100i	0.173955	−	0.0886345i
$704$	35.8763	+	11.6569i	0.0509606	+	0.0165581i
$705$		0			0
$706$	−79.8232	−	245.671i	−0.113064	−	0.347975i
$707$	926.361	−	926.361i	1.31027	−	1.31027i
$708$	−96.9171	+	190.211i	−0.136889	+	0.268659i
$709$	710.682	−	978.170i	1.00237	−	1.37965i	0.0785145	−	0.996913i	$-0.474982\pi$
$709$	710.682	−	978.170i	1.00237	−	1.37965i	0.923858	−	0.382735i	$-0.125018\pi$
$710$		0			0
$711$	−42.3095	+	30.7396i	−0.0595070	+	0.0432343i
$712$	−188.724	+	29.8909i	−0.265061	+	0.0419816i
$713$	177.701	+	1121.96i	0.249230	+	1.57358i
$714$	−321.342	−	442.290i	−0.450059	−	0.619453i
$715$		0			0
$716$	−13.4545	−	9.77530i	−0.0187913	−	0.0136527i
$717$	−34.4455	−	17.5508i	−0.0480411	−	0.0244782i
$718$	−194.887	−	194.887i	−0.271430	−	0.271430i
$719$	746.586	−	242.581i	1.03837	−	0.337386i	0.260274	−	0.965535i	$-0.416187\pi$
$719$	746.586	−	242.581i	1.03837	−	0.337386i	0.778093	+	0.628149i	$0.216187\pi$
$720$		0			0
$721$	−106.946	+	329.144i	−0.148329	+	0.456511i
$722$	47.9932	+	94.1920i	0.0664726	+	0.130460i
$723$	−591.427	−	93.6728i	−0.818017	−	0.129561i
$724$		−	216.375i		−	0.298860i
$725$		0			0
$726$	−353.631			−0.487095
$727$	87.7449	−	554.000i	0.120695	−	0.762035i	−0.850890	−	0.525344i	$-0.823937\pi$
$727$	87.7449	−	554.000i	0.120695	−	0.762035i	0.971585	−	0.236692i	$-0.0760632\pi$
$728$	416.312	−	212.121i	0.571857	−	0.291376i
$729$	−761.482	−	247.421i	−1.04456	−	0.339397i
$730$		0			0
$731$	−186.254	−	573.232i	−0.254794	−	0.784175i
$732$	425.222	−	425.222i	0.580904	−	0.580904i
$733$	−418.560	+	821.470i	−0.571023	+	1.12070i	0.407238	+	0.913322i	$0.366492\pi$
$733$	−418.560	+	821.470i	−0.571023	+	1.12070i	−0.978262	+	0.207374i	$0.933508\pi$
$734$	−114.284	+	157.298i	−0.155700	+	0.214303i
$735$		0			0
$736$	−172.898	+	125.618i	−0.234915	+	0.170676i
$737$	407.416	−	64.5284i	0.552803	−	0.0875554i
$738$	−21.3066	−	134.525i	−0.0288708	−	0.182283i
$739$	767.079	+	1055.79i	1.03800	+	1.42868i	0.898771	+	0.438418i	$0.144461\pi$
$739$	767.079	+	1055.79i	1.03800	+	1.42868i	0.139225	+	0.990261i	$0.455539\pi$
$740$		0			0
$741$	−614.867	−	446.727i	−0.829780	−	0.602871i
$742$	−958.585	−	488.423i	−1.29189	−	0.658252i
$743$	519.059	+	519.059i	0.698599	+	0.698599i	0.964108	−	0.265510i	$-0.0855402\pi$
$743$	519.059	+	519.059i	0.698599	+	0.698599i	−0.265510	+	0.964108i	$0.585540\pi$
$744$	−204.777	+	66.5360i	−0.275237	+	0.0894301i
$745$		0			0
$746$	−175.584	+	540.391i	−0.235367	+	0.724385i
$747$	29.2227	+	57.3528i	0.0391201	+	0.0767776i
$748$	−152.756	−	24.1941i	−0.204219	−	0.0323451i
$749$			1225.04i			1.63556i
$750$		0			0
$751$	−404.740			−0.538934			−0.269467	−	0.963010i	$-0.586848\pi$
$751$	−404.740			−0.538934			−0.269467	+	0.963010i	$0.586848\pi$
$752$	−28.9283	+	182.646i	−0.0384684	+	0.242880i
$753$	154.522	−	78.7327i	0.205208	−	0.104559i
$754$	−36.8482	−	11.9727i	−0.0488703	−	0.0158789i
$755$		0			0
$756$	168.847	+	519.659i	0.223343	+	0.687379i
$757$	−167.278	+	167.278i	−0.220975	+	0.220975i	−0.808909	−	0.587934i	$-0.799941\pi$
$757$	−167.278	+	167.278i	−0.220975	+	0.220975i	0.587934	+	0.808909i	$0.299941\pi$
$758$	−343.697	+	674.543i	−0.453426	+	0.889899i
$759$	−265.103	+	364.883i	−0.349279	+	0.480742i
$760$		0			0
$761$	278.142	−	202.082i	0.365496	−	0.265548i	−0.389845	−	0.920881i	$-0.627471\pi$
$761$	278.142	−	202.082i	0.365496	−	0.265548i	0.755341	+	0.655332i	$0.227471\pi$
$762$	−414.841	+	65.7044i	−0.544411	+	0.0862262i
$763$	−274.319	−	1731.98i	−0.359526	−	2.26996i
$764$	269.160	+	370.467i	0.352303	+	0.484904i
$765$		0			0
$766$	−530.168	−	385.189i	−0.692125	−	0.502858i
$767$	666.499	+	339.598i	0.868969	+	0.442762i
$768$	−28.6440	−	28.6440i	−0.0372968	−	0.0372968i
$769$	−162.525	+	52.8077i	−0.211346	+	0.0686706i	−0.412777	−	0.910832i	$-0.635441\pi$
$769$	−162.525	+	52.8077i	−0.211346	+	0.0686706i	0.201430	+	0.979503i	$0.435441\pi$
$770$		0			0
$771$	9.16678	−	28.2124i	0.0118895	−	0.0365920i
$772$	226.906	+	445.328i	0.293920	+	0.576850i
$773$	525.026	+	83.1560i	0.679206	+	0.107576i	0.486500	−	0.873681i	$-0.338273\pi$
$773$	525.026	+	83.1560i	0.679206	+	0.107576i	0.192706	+	0.981256i	$0.438273\pi$
$774$			134.619i			0.173926i
$775$		0			0
$776$	83.1976			0.107213
$777$	29.9136	−	188.867i	0.0384989	−	0.243073i
$778$	40.8635	−	20.8210i	0.0525238	−	0.0267622i
$779$	598.332	+	194.410i	0.768077	+	0.249563i
$780$		0			0
$781$	−24.2782	−	74.7205i	−0.0310860	−	0.0956729i
$782$	619.574	−	619.574i	0.792294	−	0.792294i
$783$	20.5698	−	40.3706i	0.0262705	−	0.0515588i
$784$	88.6003	−	121.948i	0.113011	−	0.155546i
$785$		0			0
$786$	−506.334	+	367.873i	−0.644191	+	0.468032i
$787$	−373.957	+	59.2289i	−0.475167	+	0.0752591i	−0.389425	−	0.921058i	$-0.627326\pi$
$787$	−373.957	+	59.2289i	−0.475167	+	0.0752591i	−0.0857424	+	0.996317i	$0.527326\pi$
$788$	5.40376	+	34.1180i	0.00685757	+	0.0432970i
$789$	137.535	+	189.301i	0.174316	+	0.239925i
$790$		0			0
$791$	−1206.63	−	876.669i	−1.52545	−	1.10830i
$792$	30.7780	+	15.6822i	0.0388611	+	0.0198007i
$793$	−1489.98	−	1489.98i	−1.87892	−	1.87892i
$794$	−220.001	+	71.4828i	−0.277080	+	0.0900287i
$795$		0			0
$796$	−164.859	+	507.383i	−0.207109	+	0.637416i
$797$	−432.478	−	848.786i	−0.542633	−	1.06498i	−0.985703	−	0.168490i	$-0.946111\pi$
$797$	−432.478	−	848.786i	−0.542633	−	1.06498i	0.443071	−	0.896487i	$-0.353889\pi$
$798$	−557.063	−	88.2301i	−0.698074	−	0.110564i
$799$		−	758.170i		−	0.948898i
$800$		0			0
$801$	−174.970			−0.218440
$802$	−102.194	+	645.229i	−0.127424	+	0.804525i
$803$	266.201	−	135.636i	0.331509	−	0.168912i
$804$	−421.281	−	136.883i	−0.523982	−	0.170252i
$805$		0			0
$806$	233.143	+	717.539i	0.289259	+	0.890247i
$807$	−382.674	+	382.674i	−0.474193	+	0.474193i
$808$	−180.683	+	354.611i	−0.223618	+	0.438874i
$809$	−427.150	+	587.922i	−0.527998	+	0.726727i	−0.986824	−	0.161799i	$-0.948270\pi$
$809$	−427.150	+	587.922i	−0.527998	+	0.726727i	0.458826	+	0.888526i	$0.348270\pi$
$810$		0			0
$811$	−121.097	+	87.9821i	−0.149318	+	0.108486i	−0.659936	−	0.751322i	$-0.729417\pi$
$811$	−121.097	+	87.9821i	−0.149318	+	0.108486i	0.510618	+	0.859808i	$0.329417\pi$
$812$	−28.3982	+	4.49783i	−0.0349731	+	0.00553920i
$813$	153.206	+	967.303i	0.188445	+	1.18979i
$814$	−31.7968	−	43.7646i	−0.0390624	−	0.0537648i
$815$		0			0
$816$	134.364	+	97.6211i	0.164662	+	0.119634i
$817$	−554.039	−	282.297i	−0.678138	−	0.345529i
$818$	259.583	+	259.583i	0.317339	+	0.317339i
$819$	406.913	−	132.214i	0.496842	−	0.161434i
$820$		0			0
$821$	−197.621	+	608.214i	−0.240707	+	0.740821i	0.755605	+	0.655027i	$0.227343\pi$
$821$	−197.621	+	608.214i	−0.240707	+	0.740821i	−0.996313	+	0.0857943i	$0.972657\pi$
$822$	99.1522	+	194.597i	0.120623	+	0.236736i
$823$	−1227.58	−	194.429i	−1.49159	−	0.236245i	−0.643234	−	0.765670i	$-0.722408\pi$
$823$	−1227.58	−	194.429i	−1.49159	−	0.236245i	−0.848357	+	0.529425i	$0.822408\pi$
$824$		−	105.137i		−	0.127594i
$825$		0			0
$826$	555.111			0.672047
$827$	176.628	−	1115.18i	0.213576	−	1.34847i	−0.614971	−	0.788549i	$-0.710832\pi$
$827$	176.628	−	1115.18i	0.213576	−	1.34847i	0.828548	−	0.559918i	$-0.189168\pi$
$828$	−174.369	+	88.8457i	−0.210591	+	0.107302i
$829$	−655.807	−	213.085i	−0.791082	−	0.257038i	−0.114517	−	0.993421i	$-0.536532\pi$
$829$	−655.807	−	213.085i	−0.791082	−	0.257038i	−0.676565	+	0.736383i	$0.736532\pi$
$830$		0			0
$831$	−28.4445	−	87.5433i	−0.0342293	−	0.105347i
$832$	−100.369	+	100.369i	−0.120635	+	0.120635i
$833$	−280.569	+	550.648i	−0.336818	+	0.661042i
$834$	163.160	−	224.571i	0.195636	−	0.269269i
$835$		0			0
$836$	−129.083	+	93.7846i	−0.154406	+	0.112183i
$837$	−871.432	+	138.021i	−1.04114	+	0.164900i
$838$	−87.2248	−	550.716i	−0.104087	−	0.657179i
$839$	−896.187	−	1233.50i	−1.06816	−	1.47020i	−0.871924	−	0.489642i	$-0.837128\pi$
$839$	−896.187	−	1233.50i	−1.06816	−	1.47020i	−0.196238	−	0.980556i	$-0.562872\pi$
$840$		0			0
$841$	−678.454	−	492.926i	−0.806723	−	0.586119i
$842$	−392.432	−	199.954i	−0.466072	−	0.237475i
$843$	308.823	+	308.823i	0.366338	+	0.366338i
$844$	−472.486	+	153.520i	−0.559818	+	0.181896i
$845$		0			0
$846$	−52.3275	+	161.048i	−0.0618529	+	0.190364i
$847$	417.467	+	819.326i	0.492878	+	0.967327i
$848$	322.809	+	51.1279i	0.380671	+	0.0602923i
$849$			824.938i			0.971658i
$850$		0			0
$851$	306.476			0.360136
$852$	−13.1982	+	83.3299i	−0.0154908	+	0.0978051i
$853$	796.644	−	405.910i	0.933932	−	0.475862i	0.0803183	−	0.996769i	$-0.474406\pi$
$853$	796.644	−	405.910i	0.933932	−	0.475862i	0.853613	+	0.520907i	$0.174406\pi$
$854$	−1487.18	−	483.213i	−1.74143	−	0.565823i
$855$		0			0
$856$	−115.003	−	353.941i	−0.134349	−	0.413483i
$857$	302.090	−	302.090i	0.352497	−	0.352497i	−0.508541	−	0.861038i	$-0.669815\pi$
$857$	302.090	−	302.090i	0.352497	−	0.352497i	0.861038	+	0.508541i	$0.169815\pi$
$858$	−135.995	+	266.906i	−0.158503	+	0.311079i
$859$	−623.184	+	857.740i	−0.725477	+	0.998533i	0.273847	+	0.961773i	$0.411704\pi$
$859$	−623.184	+	857.740i	−0.725477	+	0.998533i	−0.999324	+	0.0367598i	$0.988296\pi$
$860$		0			0
$861$	709.120	−	515.206i	0.823600	−	0.598380i
$862$	1009.85	−	159.944i	1.17152	−	0.185550i
$863$	−174.542	−	1102.02i	−0.202251	−	1.27696i	−0.854698	−	0.519126i	$-0.826258\pi$
$863$	−174.542	−	1102.02i	−0.202251	−	1.27696i	0.652447	−	0.757834i	$-0.273742\pi$
$864$	−97.5677	−	134.290i	−0.112926	−	0.155429i
$865$		0			0
$866$	−274.126	−	199.164i	−0.316543	−	0.229982i
$867$	45.2275	+	23.0446i	0.0521655	+	0.0265796i
$868$	395.900	+	395.900i	0.456106	+	0.456106i
$869$	−90.5512	+	29.4219i	−0.104202	+	0.0338571i
$870$		0			0
$871$	−479.637	+	1476.17i	−0.550674	+	1.69480i
$872$	241.850	+	474.657i	0.277350	+	0.544331i
$873$	75.2470	+	11.9179i	0.0861935	+	0.0136517i
$874$		−	903.948i		−	1.03427i
$875$		0			0
$876$	−320.831			−0.366246
$877$	−81.1642	+	512.451i	−0.0925476	+	0.584322i	0.897214	+	0.441595i	$0.145587\pi$
$877$	−81.1642	+	512.451i	−0.0925476	+	0.584322i	−0.989762	+	0.142727i	$0.954413\pi$
$878$	−93.8685	+	47.8284i	−0.106912	+	0.0544742i
$879$	234.396	+	76.1600i	0.266663	+	0.0866439i
$880$		0			0
$881$	116.262	+	357.816i	0.131965	+	0.406148i	0.995106	−	0.0988164i	$-0.0315056\pi$
$881$	116.262	+	357.816i	0.131965	+	0.406148i	−0.863140	+	0.504964i	$0.831506\pi$
$882$	97.6022	−	97.6022i	0.110660	−	0.110660i
$883$	185.934	−	364.916i	0.210571	−	0.413268i	−0.761430	−	0.648247i	$-0.775502\pi$
$883$	185.934	−	364.916i	0.210571	−	0.413268i	0.972000	+	0.234979i	$0.0755023\pi$
$884$	342.065	−	470.812i	0.386951	−	0.532593i
$885$		0			0
$886$	−233.795	+	169.862i	−0.263877	+	0.191718i
$887$	1009.72	−	159.924i	1.13835	−	0.180298i	0.441330	−	0.897345i	$-0.354507\pi$
$887$	1009.72	−	159.924i	1.13835	−	0.180298i	0.697025	+	0.717047i	$0.254507\pi$
$888$	9.08751	+	57.3763i	0.0102337	+	0.0646129i
$889$	641.958	+	883.579i	0.722113	+	0.993903i
$890$		0			0
$891$	−194.483	−	141.300i	−0.218275	−	0.158586i
$892$	−100.968	−	51.4457i	−0.113193	−	0.0576745i
$893$	−553.078	−	553.078i	−0.619349	−	0.619349i
$894$	−499.864	+	162.416i	−0.559132	+	0.181673i
$895$		0			0
$896$	−32.5504	+	100.180i	−0.0363286	+	0.111808i
$897$	−770.469	−	1512.13i	−0.858939	−	1.68576i
$898$	−88.1233	−	13.9574i	−0.0981328	−	0.0155427i
$899$		−	46.4272i		−	0.0516431i
$900$		0			0
$901$	−1339.99			−1.48723
$902$	38.7902	−	244.912i	0.0430047	−	0.271521i
$903$	−771.909	+	393.307i	−0.854827	+	0.435556i
$904$	430.922	+	140.015i	0.476684	+	0.154884i
$905$		0			0
$906$	−90.1726	−	277.523i	−0.0995282	−	0.306316i
$907$	−113.458	+	113.458i	−0.125092	+	0.125092i	−0.766881	−	0.641789i	$-0.778192\pi$
$907$	−113.458	+	113.458i	−0.125092	+	0.125092i	0.641789	+	0.766881i	$0.278192\pi$
$908$	140.060	−	274.884i	0.154251	−	0.302736i
$909$	−214.214	+	294.840i	−0.235659	+	0.324356i
$910$		0			0
$911$	1420.57	−	1032.11i	1.55936	−	1.13294i	0.622820	−	0.782365i	$-0.285987\pi$
$911$	1420.57	−	1032.11i	1.55936	−	1.13294i	0.936535	−	0.350573i	$-0.114013\pi$
$912$	169.231	−	26.8036i	0.185560	−	0.0293899i
$913$	18.3322	+	115.745i	0.0200791	+	0.126774i
$914$	536.378	+	738.260i	0.586846	+	0.807725i
$915$		0			0
$916$	−137.750	−	100.081i	−0.150382	−	0.109259i
$917$	1450.06	+	738.843i	1.58131	+	0.805718i
$918$	481.226	+	481.226i	0.524211	+	0.524211i
$919$	−416.300	+	135.264i	−0.452993	+	0.147186i	−0.526622	−	0.850099i	$-0.676542\pi$
$919$	−416.300	+	135.264i	−0.452993	+	0.147186i	0.0736296	+	0.997286i	$0.476542\pi$
$920$		0			0
$921$	−217.354	+	668.946i	−0.235998	+	0.726326i
$922$	221.893	+	435.490i	0.240665	+	0.472332i
$923$	291.989	+	46.2464i	0.316347	+	0.0501045i
$924$			222.300i			0.240584i
$925$		0			0
$926$	1008.35			1.08893
$927$	15.0607	−	95.0898i	0.0162468	−	0.102578i
$928$	7.78265	−	3.96546i	0.00838647	−	0.00427312i
$929$	1302.45	+	423.191i	1.40199	+	0.455534i	0.909833	−	0.414974i	$-0.136209\pi$
$929$	1302.45	+	423.191i	1.40199	+	0.455534i	0.492155	+	0.870507i	$0.336209\pi$
$930$		0			0
$931$	197.020	+	606.366i	0.211622	+	0.651306i
$932$	−77.8377	+	77.8377i	−0.0835168	+	0.0835168i
$933$	276.366	−	542.399i	0.296212	−	0.581349i
$934$	82.9797	−	114.212i	0.0888433	−	0.122282i
$935$		0			0
$936$	−105.155	+	76.3994i	−0.112345	+	0.0816233i
$937$	1246.16	−	197.372i	1.32994	−	0.210642i	0.549303	−	0.835623i	$-0.314893\pi$
$937$	1246.16	−	197.372i	1.32994	−	0.210642i	0.780640	+	0.624981i	$0.214893\pi$
$938$	180.187	+	1137.66i	0.192097	+	1.21285i
$939$	−306.799	−	422.272i	−0.326729	−	0.449704i
$940$		0			0
$941$	37.6478	+	27.3527i	0.0400083	+	0.0290677i	0.607610	−	0.794236i	$-0.292129\pi$
$941$	37.6478	+	27.3527i	0.0400083	+	0.0290677i	−0.567601	+	0.823303i	$0.692129\pi$
$942$	952.691	+	485.420i	1.01135	+	0.515308i
$943$	993.358	+	993.358i	1.05340	+	1.05340i
$944$	−160.384	+	52.1120i	−0.169899	+	0.0552034i
$945$		0			0
$946$	−75.7348	+	233.088i	−0.0800580	+	0.246393i
$947$	−582.931	−	1144.07i	−0.615555	−	1.20809i	−0.962773	−	0.270310i	$-0.912874\pi$
$947$	−582.931	−	1144.07i	−0.615555	−	1.20809i	0.347218	−	0.937784i	$-0.387126\pi$
$948$	100.985	+	15.9944i	0.106524	+	0.0168717i
$949$			1124.20i			1.18461i
$950$		0			0
$951$	87.6306			0.0921458
$952$	67.5590	−	426.551i	0.0709654	−	0.448058i
$953$	−412.296	+	210.075i	−0.432630	+	0.220436i	−0.656723	−	0.754132i	$-0.728058\pi$
$953$	−412.296	+	210.075i	−0.432630	+	0.220436i	0.224093	+	0.974568i	$0.428058\pi$
$954$	284.636	+	92.4838i	0.298360	+	0.0969432i
$955$		0			0
$956$	−9.43702	−	29.0442i	−0.00987136	−	0.0303809i
$957$	13.0345	−	13.0345i	0.0136202	−	0.0136202i
$958$	−559.081	+	1097.26i	−0.583592	+	1.14536i
$959$	333.811	−	459.451i	0.348082	−	0.479094i
$960$		0			0
$961$	46.0580	−	33.4631i	0.0479272	−	0.0348211i
$962$	201.047	−	31.8427i	0.208989	−	0.0331005i
$963$	−53.3108	−	336.591i	−0.0553591	−	0.349524i
$964$	−278.036	−	382.684i	−0.288419	−	0.396975i
$965$		0			0
$966$	−1018.89	−	740.266i	−1.05475	−	0.766321i
$967$	−650.934	−	331.668i	−0.673148	−	0.342986i	0.0837799	−	0.996484i	$-0.473301\pi$
$967$	−650.934	−	331.668i	−0.673148	−	0.342986i	−0.756928	+	0.653498i	$0.773301\pi$
$968$	−197.532	−	197.532i	−0.204062	−	0.204062i
$969$	−668.103	+	217.080i	−0.689476	+	0.224024i
$970$		0			0
$971$	48.6355	−	149.685i	0.0500880	−	0.154155i	−0.922884	−	0.385078i	$-0.874175\pi$
$971$	48.6355	−	149.685i	0.0500880	−	0.154155i	0.972972	+	0.230923i	$0.0741745\pi$
$972$	−122.593	−	240.602i	−0.126124	−	0.247533i
$973$	−712.921	−	112.916i	−0.732704	−	0.116049i
$974$		−	702.124i		−	0.720867i
$975$		0			0
$976$	475.042			0.486723
$977$	−13.0640	+	82.4828i	−0.0133715	+	0.0844245i	−0.993472	−	0.114079i	$-0.963608\pi$
$977$	−13.0640	+	82.4828i	−0.0133715	+	0.0844245i	0.980100	+	0.198504i	$0.0636082\pi$
$978$	−273.952	+	139.586i	−0.280115	+	0.142726i
$979$	−302.955	−	98.4361i	−0.309454	−	0.100548i
$980$		0			0
$981$	150.744	+	463.941i	0.153663	+	0.472927i
$982$	167.591	−	167.591i	0.170663	−	0.170663i
$983$	−76.5307	+	150.200i	−0.0778543	+	0.152798i	−0.926652	−	0.375920i	$-0.877327\pi$
$983$	−76.5307	+	150.200i	−0.0778543	+	0.152798i	0.848798	+	0.528717i	$0.177327\pi$
$984$	−156.515	+	215.425i	−0.159060	+	0.218927i
$985$		0			0
$986$	−28.9721	+	21.0495i	−0.0293835	+	0.0213484i
$987$	−1076.33	+	170.475i	−1.09051	+	0.172720i
$988$	−93.9199	−	592.987i	−0.0950606	−	0.600189i
$989$	−816.136	−	1123.31i	−0.825213	−	1.13581i
$990$		0			0
$991$	269.381	+	195.717i	0.271827	+	0.197494i	0.715345	−	0.698772i	$-0.246270\pi$
$991$	269.381	+	195.717i	0.271827	+	0.197494i	−0.443517	+	0.896266i	$0.646270\pi$
$992$	−151.550	−	77.2187i	−0.152772	−	0.0778414i
$993$	−44.4867	−	44.4867i	−0.0448003	−	0.0448003i
$994$	208.648	−	67.7937i	0.209907	−	0.0682029i
$995$		0			0
$996$	38.8877	−	119.684i	0.0390438	−	0.120165i
$997$	−416.752	−	817.923i	−0.418006	−	0.820384i	−0.999974	−	0.00717202i	$-0.997717\pi$
$997$	−416.752	−	817.923i	−0.418006	−	0.820384i	0.581968	−	0.813212i	$-0.302283\pi$
$998$	−278.333	−	44.0837i	−0.278891	−	0.0441720i
$999$			238.041i			0.238279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.3.f.c.93.1		16
5.2	odd	4		250.3.f.b.157.2		16
5.3	odd	4		50.3.f.a.27.1	yes	16
5.4	even	2		250.3.f.a.93.2		16
20.3	even	4		400.3.bg.a.177.2		16
25.9	even	10		50.3.f.a.13.1	✓	16
25.12	odd	20	inner	250.3.f.c.207.1		16
25.13	odd	20		250.3.f.a.207.2		16
25.16	even	5		250.3.f.b.43.2		16
100.59	odd	10		400.3.bg.a.113.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.a.13.1	✓	16	25.9	even	10
50.3.f.a.27.1	yes	16	5.3	odd	4
250.3.f.a.93.2		16	5.4	even	2
250.3.f.a.207.2		16	25.13	odd	20
250.3.f.b.43.2		16	25.16	even	5
250.3.f.b.157.2		16	5.2	odd	4
250.3.f.c.93.1		16	1.1	even	1	trivial
250.3.f.c.207.1		16	25.12	odd	20	inner
400.3.bg.a.113.2		16	100.59	odd	10
400.3.bg.a.177.2		16	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	250.f (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.221232 - 1.39680i) q^{2} +(-2.25584 + 1.14941i) q^{3} +(-1.90211 - 0.618034i) q^{4} +(1.10643 + 3.40526i) q^{6} +(6.58346 - 6.58346i) q^{7} +(-1.28408 + 2.52015i) q^{8} +(-1.52238 + 2.09537i) q^{9} +O(q^{10})\)	\(q+(0.221232 - 1.39680i) q^{2} +(-2.25584 + 1.14941i) q^{3} +(-1.90211 - 0.618034i) q^{4} +(1.10643 + 3.40526i) q^{6} +(6.58346 - 6.58346i) q^{7} +(-1.28408 + 2.52015i) q^{8} +(-1.52238 + 2.09537i) q^{9} +(-3.81477 + 2.77159i) q^{11} +(5.00125 - 0.792120i) q^{12} +(-2.77559 - 17.5244i) q^{13} +(-7.73932 - 10.6523i) q^{14} +(3.23607 + 2.35114i) q^{16} +(-14.6123 - 7.44532i) q^{17} +(2.59002 + 2.59002i) q^{18} +(-16.0908 + 5.22822i) q^{19} +(-7.28417 + 22.4184i) q^{21} +(3.02742 + 5.94165i) q^{22} +(-37.3144 - 5.91002i) q^{23} -7.16099i q^{24} -25.0922 q^{26} +(4.59034 - 28.9823i) q^{27} +(-16.5913 + 8.45369i) q^{28} +(1.46851 + 0.477149i) q^{29} +(-9.29144 - 28.5961i) q^{31} +(4.00000 - 4.00000i) q^{32} +(5.41983 - 10.6370i) q^{33} +(-13.6323 + 18.7633i) q^{34} +(4.19074 - 3.04475i) q^{36} +(-8.01234 + 1.26903i) q^{37} +(3.74300 + 23.6323i) q^{38} +(26.4040 + 36.3420i) q^{39} +(-30.0830 - 21.8566i) q^{41} +(29.7025 + 15.1342i) q^{42} +(25.9880 + 25.9880i) q^{43} +(8.96907 - 2.91423i) q^{44} +(-16.5103 + 50.8134i) q^{46} +(20.9883 + 41.1918i) q^{47} +(-10.0025 - 1.58424i) q^{48} -37.6840i q^{49} +41.5207 q^{51} +(-5.55119 + 35.0488i) q^{52} +(72.8025 - 37.0947i) q^{53} +(-39.4670 - 12.8236i) q^{54} +(8.13761 + 25.0450i) q^{56} +(30.2890 - 30.2890i) q^{57} +(0.991364 - 1.94566i) q^{58} +(-24.7807 + 34.1077i) q^{59} +(96.0793 - 69.8057i) q^{61} +(-41.9987 + 6.65194i) q^{62} +(3.77229 + 23.8173i) q^{63} +(-4.70228 - 6.47214i) q^{64} +(-13.6588 - 9.92368i) q^{66} +(-77.9450 - 39.7150i) q^{67} +(23.1927 + 23.1927i) q^{68} +(90.9685 - 29.5575i) q^{69} +(-5.14879 + 15.8463i) q^{71} +(-3.32579 - 6.52723i) q^{72} +(-62.5804 - 9.91177i) q^{73} +11.4724i q^{74} +33.8378 q^{76} +(-6.86772 + 43.3611i) q^{77} +(56.6041 - 28.8412i) q^{78} +(19.2036 + 6.23964i) q^{79} +(15.7542 + 48.4864i) q^{81} +(-37.1847 + 37.1847i) q^{82} +(11.2828 - 22.1438i) q^{83} +(27.7106 - 38.1404i) q^{84} +(42.0494 - 30.5507i) q^{86} +(-3.86118 + 0.611550i) q^{87} +(-2.08636 - 13.1727i) q^{88} +(39.7082 + 54.6536i) q^{89} +(-133.644 - 97.0982i) q^{91} +(67.3236 + 34.3031i) q^{92} +(53.8287 + 53.8287i) q^{93} +(62.1801 - 20.2035i) q^{94} +(-4.42574 + 13.6210i) q^{96} +(-13.3540 - 26.2088i) q^{97} +(-52.6370 - 8.33689i) q^{98} -12.2128i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 2 q^{3} + 4 q^{6} + 2 q^{7} - 8 q^{8} + 40 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 2 * q^3 + 4 * q^6 + 2 * q^7 - 8 * q^8 + 40 * q^9	\( 16 q + 4 q^{2} - 2 q^{3} + 4 q^{6} + 2 q^{7} - 8 q^{8} + 40 q^{9} + 32 q^{11} + 16 q^{12} + 8 q^{13} + 30 q^{14} + 16 q^{16} - 8 q^{17} + 16 q^{18} - 30 q^{19} - 68 q^{21} + 8 q^{22} - 42 q^{23} - 56 q^{26} + 40 q^{27} - 4 q^{28} - 100 q^{29} + 132 q^{31} + 64 q^{32} - 134 q^{33} - 100 q^{34} + 48 q^{36} + 82 q^{37} - 20 q^{38} + 320 q^{39} - 88 q^{41} + 128 q^{42} + 78 q^{43} - 40 q^{44} - 26 q^{46} - 168 q^{47} - 32 q^{48} - 168 q^{51} + 16 q^{52} + 518 q^{53} - 80 q^{54} + 48 q^{56} - 280 q^{57} - 80 q^{58} + 350 q^{59} + 372 q^{61} + 158 q^{62} - 142 q^{63} - 202 q^{66} - 158 q^{67} + 196 q^{68} + 30 q^{69} + 122 q^{71} - 68 q^{72} - 352 q^{73} + 40 q^{76} - 96 q^{77} - 158 q^{78} - 760 q^{79} - 144 q^{81} - 352 q^{82} - 32 q^{83} + 20 q^{84} + 264 q^{86} + 440 q^{87} + 244 q^{88} - 550 q^{89} - 798 q^{91} + 436 q^{92} - 54 q^{93} - 190 q^{94} - 16 q^{96} - 618 q^{97} - 336 q^{98}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 + 4 * q^6 + 2 * q^7 - 8 * q^8 + 40 * q^9 + 32 * q^11 + 16 * q^12 + 8 * q^13 + 30 * q^14 + 16 * q^16 - 8 * q^17 + 16 * q^18 - 30 * q^19 - 68 * q^21 + 8 * q^22 - 42 * q^23 - 56 * q^26 + 40 * q^27 - 4 * q^28 - 100 * q^29 + 132 * q^31 + 64 * q^32 - 134 * q^33 - 100 * q^34 + 48 * q^36 + 82 * q^37 - 20 * q^38 + 320 * q^39 - 88 * q^41 + 128 * q^42 + 78 * q^43 - 40 * q^44 - 26 * q^46 - 168 * q^47 - 32 * q^48 - 168 * q^51 + 16 * q^52 + 518 * q^53 - 80 * q^54 + 48 * q^56 - 280 * q^57 - 80 * q^58 + 350 * q^59 + 372 * q^61 + 158 * q^62 - 142 * q^63 - 202 * q^66 - 158 * q^67 + 196 * q^68 + 30 * q^69 + 122 * q^71 - 68 * q^72 - 352 * q^73 + 40 * q^76 - 96 * q^77 - 158 * q^78 - 760 * q^79 - 144 * q^81 - 352 * q^82 - 32 * q^83 + 20 * q^84 + 264 * q^86 + 440 * q^87 + 244 * q^88 - 550 * q^89 - 798 * q^91 + 436 * q^92 - 54 * q^93 - 190 * q^94 - 16 * q^96 - 618 * q^97 - 336 * q^98

Introduction

L-functions

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