LMFDB - Embedded newform 315.2.k.c.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(16,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 2]))

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

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

chi := DirichletCharacter("315.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.k (of order $3$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.2
Character	$\chi$	$=$	315.16
Dual form			315.2.k.c.256.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29282 - 2.23923i) q^{2} +(1.72292 - 0.177629i) q^{3} +(-2.34278 + 4.05782i) q^{4} +1.00000 q^{5} +(-2.62518 - 3.62838i) q^{6} +(-2.13970 - 1.55618i) q^{7} +6.94392 q^{8} +(2.93690 - 0.612079i) q^{9} +O(q^{10})$	\(q+(-1.29282 - 2.23923i) q^{2} +(1.72292 - 0.177629i) q^{3} +(-2.34278 + 4.05782i) q^{4} +1.00000 q^{5} +(-2.62518 - 3.62838i) q^{6} +(-2.13970 - 1.55618i) q^{7} +6.94392 q^{8} +(2.93690 - 0.612079i) q^{9} +(-1.29282 - 2.23923i) q^{10} +2.47043 q^{11} +(-3.31564 + 7.40743i) q^{12} +(-3.19209 - 5.52887i) q^{13} +(-0.718397 + 6.80315i) q^{14} +(1.72292 - 0.177629i) q^{15} +(-4.29169 - 7.43343i) q^{16} +(-2.57232 - 4.45539i) q^{17} +(-5.16748 - 5.78509i) q^{18} +(0.825096 - 1.42911i) q^{19} +(-2.34278 + 4.05782i) q^{20} +(-3.96295 - 2.30110i) q^{21} +(-3.19382 - 5.53186i) q^{22} +4.85733 q^{23} +(11.9638 - 1.23344i) q^{24} +1.00000 q^{25} +(-8.25363 + 14.2957i) q^{26} +(4.95131 - 1.57624i) q^{27} +(11.3275 - 5.03672i) q^{28} +(0.321747 - 0.557282i) q^{29} +(-2.62518 - 3.62838i) q^{30} +(-0.273744 + 0.474138i) q^{31} +(-4.15288 + 7.19299i) q^{32} +(4.25634 - 0.438818i) q^{33} +(-6.65112 + 11.5201i) q^{34} +(-2.13970 - 1.55618i) q^{35} +(-4.39680 + 13.3514i) q^{36} +(-3.30325 + 5.72139i) q^{37} -4.26681 q^{38} +(-6.48180 - 8.95879i) q^{39} +6.94392 q^{40} +(4.42604 + 7.66613i) q^{41} +(-0.0293057 + 11.8489i) q^{42} +(-3.75461 + 6.50318i) q^{43} +(-5.78767 + 10.0245i) q^{44} +(2.93690 - 0.612079i) q^{45} +(-6.27966 - 10.8767i) q^{46} +(0.817715 + 1.41632i) q^{47} +(-8.71462 - 12.0449i) q^{48} +(2.15662 + 6.65950i) q^{49} +(-1.29282 - 2.23923i) q^{50} +(-5.22331 - 7.21936i) q^{51} +29.9135 q^{52} +(4.66364 + 8.07767i) q^{53} +(-9.93074 - 9.04935i) q^{54} +2.47043 q^{55} +(-14.8579 - 10.8060i) q^{56} +(1.16772 - 2.60880i) q^{57} -1.66385 q^{58} +(4.44642 - 7.70143i) q^{59} +(-3.31564 + 7.40743i) q^{60} +(0.157313 + 0.272474i) q^{61} +1.41561 q^{62} +(-7.23658 - 3.26067i) q^{63} +4.30897 q^{64} +(-3.19209 - 5.52887i) q^{65} +(-6.48531 - 8.96363i) q^{66} +(0.593254 - 1.02755i) q^{67} +24.1056 q^{68} +(8.36878 - 0.862800i) q^{69} +(-0.718397 + 6.80315i) q^{70} -1.21039 q^{71} +(20.3936 - 4.25023i) q^{72} +(6.30120 + 10.9140i) q^{73} +17.0821 q^{74} +(1.72292 - 0.177629i) q^{75} +(3.86604 + 6.69618i) q^{76} +(-5.28597 - 3.84442i) q^{77} +(-11.6810 + 26.0964i) q^{78} +(-6.14958 - 10.6514i) q^{79} +(-4.29169 - 7.43343i) q^{80} +(8.25072 - 3.59522i) q^{81} +(11.4442 - 19.8219i) q^{82} +(3.21667 - 5.57144i) q^{83} +(18.6218 - 10.6900i) q^{84} +(-2.57232 - 4.45539i) q^{85} +19.4162 q^{86} +(0.455355 - 1.01730i) q^{87} +17.1544 q^{88} +(-1.44436 + 2.50171i) q^{89} +(-5.16748 - 5.78509i) q^{90} +(-1.77379 + 16.7976i) q^{91} +(-11.3797 + 19.7101i) q^{92} +(-0.387418 + 0.865526i) q^{93} +(2.11432 - 3.66211i) q^{94} +(0.825096 - 1.42911i) q^{95} +(-5.87739 + 13.1306i) q^{96} +(5.53831 - 9.59263i) q^{97} +(12.1241 - 13.4387i) q^{98} +(7.25538 - 1.51210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) $ 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.29282	−	2.23923i	−0.914164	−	1.58338i	−0.808121	−	0.589017i	$-0.799515\pi$
$2$	−1.29282	−	2.23923i	−0.914164	−	1.58338i	−0.106043	−	0.994362i	$-0.533818\pi$
$3$	1.72292	−	0.177629i	0.994727	−	0.102554i
$3$	1.72292	−	0.177629i	0.994727	−	0.102554i
$4$	−2.34278	+	4.05782i	−1.17139	+	2.02891i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−2.62518	−	3.62838i	−1.07173	−	1.48128i
$7$	−2.13970	−	1.55618i	−0.808730	−	0.588180i
$7$	−2.13970	−	1.55618i	−0.808730	−	0.588180i
$8$	6.94392			2.45505
$9$	2.93690	−	0.612079i	0.978965	−	0.204026i
$10$	−1.29282	−	2.23923i	−0.408826	−	0.708108i
$11$	2.47043			0.744861			0.372431	−	0.928060i	$-0.378524\pi$
$11$	2.47043			0.744861			0.372431	+	0.928060i	$0.378524\pi$
$12$	−3.31564	+	7.40743i	−0.957142	+	2.13834i
$13$	−3.19209	−	5.52887i	−0.885328	−	1.53343i	−0.845338	−	0.534233i	$-0.820601\pi$
$13$	−3.19209	−	5.52887i	−0.885328	−	1.53343i	−0.0399902	−	0.999200i	$-0.512733\pi$
$14$	−0.718397	+	6.80315i	−0.192000	+	1.81822i
$15$	1.72292	−	0.177629i	0.444856	−	0.0458635i
$16$	−4.29169	−	7.43343i	−1.07292	−	1.85836i
$17$	−2.57232	−	4.45539i	−0.623880	−	1.08059i	−0.988756	−	0.149536i	$-0.952222\pi$
$17$	−2.57232	−	4.45539i	−0.623880	−	1.08059i	0.364876	−	0.931056i	$-0.381111\pi$
$18$	−5.16748	−	5.78509i	−1.21799	−	1.36356i
$19$	0.825096	−	1.42911i	0.189290	−	0.327860i	−0.755724	−	0.654891i	$-0.772715\pi$
$19$	0.825096	−	1.42911i	0.189290	−	0.327860i	0.945014	+	0.327031i	$0.106048\pi$
$20$	−2.34278	+	4.05782i	−0.523862	+	0.907356i
$21$	−3.96295	−	2.30110i	−0.864786	−	0.502140i
$22$	−3.19382	−	5.53186i	−0.680925	−	1.17940i
$23$	4.85733			1.01282			0.506411	−	0.862292i	$-0.330972\pi$
$23$	4.85733			1.01282			0.506411	+	0.862292i	$0.330972\pi$
$24$	11.9638	−	1.23344i	2.44210	−	0.251774i
$25$	1.00000			0.200000
$26$	−8.25363	+	14.2957i	−1.61867	+	2.80362i
$27$	4.95131	−	1.57624i	0.952880	−	0.303347i
$28$	11.3275	−	5.03672i	2.14070	−	0.951851i
$29$	0.321747	−	0.557282i	0.0597469	−	0.103485i	−0.834605	−	0.550849i	$-0.814304\pi$
$29$	0.321747	−	0.557282i	0.0597469	−	0.103485i	0.894352	+	0.447364i	$0.147637\pi$
$30$	−2.62518	−	3.62838i	−0.479290	−	0.662448i
$31$	−0.273744	+	0.474138i	−0.0491659	+	0.0851578i	−0.889561	−	0.456816i	$-0.848990\pi$
$31$	−0.273744	+	0.474138i	−0.0491659	+	0.0851578i	0.840395	+	0.541974i	$0.182323\pi$
$32$	−4.15288	+	7.19299i	−0.734132	+	1.27155i
$33$	4.25634	−	0.438818i	0.740934	−	0.0763884i
$34$	−6.65112	+	11.5201i	−1.14066	+	1.97568i
$35$	−2.13970	−	1.55618i	−0.361675	−	0.263042i
$36$	−4.39680	+	13.3514i	−0.732801	+	2.22523i
$37$	−3.30325	+	5.72139i	−0.543051	+	0.940591i	0.455676	+	0.890146i	$0.349398\pi$
$37$	−3.30325	+	5.72139i	−0.543051	+	0.940591i	−0.998727	+	0.0504457i	$0.983936\pi$
$38$	−4.26681			−0.692169
$39$	−6.48180	−	8.95879i	−1.03792	−	1.43455i
$40$	6.94392			1.09793
$41$	4.42604	+	7.66613i	0.691231	+	1.19725i	0.971435	+	0.237307i	$0.0762647\pi$
$41$	4.42604	+	7.66613i	0.691231	+	1.19725i	−0.280203	+	0.959941i	$0.590402\pi$
$42$	−0.0293057	+	11.8489i	−0.00452196	+	1.82832i
$43$	−3.75461	+	6.50318i	−0.572573	+	0.991726i	0.423728	+	0.905790i	$0.360721\pi$
$43$	−3.75461	+	6.50318i	−0.572573	+	0.991726i	−0.996301	+	0.0859360i	$0.972612\pi$
$44$	−5.78767	+	10.0245i	−0.872524	+	1.51126i
$45$	2.93690	−	0.612079i	0.437807	−	0.0912433i
$46$	−6.27966	−	10.8767i	−0.925886	−	1.60368i
$47$	0.817715	+	1.41632i	0.119276	+	0.206592i	0.919481	−	0.393134i	$-0.128609\pi$
$47$	0.817715	+	1.41632i	0.119276	+	0.206592i	−0.800205	+	0.599727i	$0.795276\pi$
$48$	−8.71462	−	12.0449i	−1.25785	−	1.73853i
$49$	2.15662	+	6.65950i	0.308089	+	0.951358i
$50$	−1.29282	−	2.23923i	−0.182833	−	0.316676i
$51$	−5.22331	−	7.21936i	−0.731409	−	1.01091i
$52$	29.9135			4.14826
$53$	4.66364	+	8.07767i	0.640601	+	1.10955i	0.985299	+	0.170840i	$0.0546480\pi$
$53$	4.66364	+	8.07767i	0.640601	+	1.10955i	−0.344698	+	0.938714i	$0.612019\pi$
$54$	−9.93074	−	9.04935i	−1.35140	−	1.23146i
$55$	2.47043			0.333112
$56$	−14.8579	−	10.8060i	−1.98547	−	1.44401i
$57$	1.16772	−	2.60880i	0.154669	−	0.345544i
$58$	−1.66385			−0.218474
$59$	4.44642	−	7.70143i	0.578875	−	1.00264i	−0.416734	−	0.909029i	$-0.636825\pi$
$59$	4.44642	−	7.70143i	0.578875	−	1.00264i	0.995609	−	0.0936122i	$-0.0298414\pi$
$60$	−3.31564	+	7.40743i	−0.428047	+	0.956296i
$61$	0.157313	+	0.272474i	0.0201418	+	0.0348867i	0.875921	−	0.482455i	$-0.160255\pi$
$61$	0.157313	+	0.272474i	0.0201418	+	0.0348867i	−0.855779	+	0.517342i	$0.826922\pi$
$62$	1.41561			0.179783
$63$	−7.23658	−	3.26067i	−0.911723	−	0.410806i
$64$	4.30897			0.538621
$65$	−3.19209	−	5.52887i	−0.395931	−	0.685772i
$66$	−6.48531	−	8.96363i	−0.798287	−	1.10335i
$67$	0.593254	−	1.02755i	0.0724775	−	0.125535i	−0.827509	−	0.561452i	$-0.810243\pi$
$67$	0.593254	−	1.02755i	0.0724775	−	0.125535i	0.899987	+	0.435918i	$0.143576\pi$
$68$	24.1056			2.92323
$69$	8.36878	−	0.862800i	1.00748	−	0.103869i
$70$	−0.718397	+	6.80315i	−0.0858648	+	0.813132i
$71$	−1.21039			−0.143647			−0.0718235	−	0.997417i	$-0.522882\pi$
$71$	−1.21039			−0.143647			−0.0718235	+	0.997417i	$0.522882\pi$
$72$	20.3936	−	4.25023i	2.40340	−	0.500894i
$73$	6.30120	+	10.9140i	0.737500	+	1.27739i	0.953618	+	0.301020i	$0.0973271\pi$
$73$	6.30120	+	10.9140i	0.737500	+	1.27739i	−0.216118	+	0.976367i	$0.569340\pi$
$74$	17.0821			1.98575
$75$	1.72292	−	0.177629i	0.198945	−	0.0205108i
$76$	3.86604	+	6.69618i	0.443465	+	0.768105i
$77$	−5.28597	−	3.84442i	−0.602392	−	0.438112i
$78$	−11.6810	+	26.0964i	−1.32261	+	2.95484i
$79$	−6.14958	−	10.6514i	−0.691882	−	1.19837i	−0.971221	−	0.238182i	$-0.923449\pi$
$79$	−6.14958	−	10.6514i	−0.691882	−	1.19837i	0.279339	−	0.960193i	$-0.409885\pi$
$80$	−4.29169	−	7.43343i	−0.479826	−	0.831083i
$81$	8.25072	−	3.59522i	0.916747	−	0.399469i
$82$	11.4442	−	19.8219i	1.26380	−	2.18896i
$83$	3.21667	−	5.57144i	0.353076	−	0.611545i	−0.633711	−	0.773570i	$-0.718469\pi$
$83$	3.21667	−	5.57144i	0.353076	−	0.611545i	0.986787	+	0.162025i	$0.0518025\pi$
$84$	18.6218	−	10.6900i	2.03180	−	1.16637i
$85$	−2.57232	−	4.45539i	−0.279008	−	0.483255i
$86$	19.4162			2.09370
$87$	0.455355	−	1.01730i	0.0488192	−	0.109066i
$88$	17.1544			1.82867
$89$	−1.44436	+	2.50171i	−0.153102	+	0.265181i	−0.932366	−	0.361515i	$-0.882260\pi$
$89$	−1.44436	+	2.50171i	−0.153102	+	0.265181i	0.779264	+	0.626696i	$0.215593\pi$
$90$	−5.16748	−	5.78509i	−0.544700	−	0.609802i
$91$	−1.77379	+	16.7976i	−0.185943	+	1.76087i
$92$	−11.3797	+	19.7101i	−1.18641	+	2.05493i
$93$	−0.387418	+	0.865526i	−0.0401734	+	0.0897509i
$94$	2.11432	−	3.66211i	0.218076	−	0.377718i
$95$	0.825096	−	1.42911i	0.0846531	−	0.146623i
$96$	−5.87739	+	13.1306i	−0.599858	+	1.34014i
$97$	5.53831	−	9.59263i	0.562330	−	0.973984i	−0.434963	−	0.900449i	$-0.643238\pi$
$97$	5.53831	−	9.59263i	0.562330	−	0.973984i	0.997293	−	0.0735357i	$-0.0234283\pi$
$98$	12.1241	−	13.4387i	1.22472	−	1.35752i
$99$	7.25538	−	1.51210i	0.729193	−	0.151971i
$100$	−2.34278	+	4.05782i	−0.234278	+	0.405782i
$101$	−15.3178			−1.52418			−0.762091	−	0.647470i	$-0.775827\pi$
$101$	−15.3178			−1.52418			−0.762091	+	0.647470i	$0.775827\pi$
$102$	−9.41304	+	21.0296i	−0.932030	+	2.08224i
$103$	−8.87687			−0.874664			−0.437332	−	0.899300i	$-0.644076\pi$
$103$	−8.87687			−0.874664			−0.437332	+	0.899300i	$0.644076\pi$
$104$	−22.1656	−	38.3920i	−2.17352	−	3.76465i
$105$	−3.96295	−	2.30110i	−0.386744	−	0.224564i
$106$	12.0585	−	20.8860i	1.17123	−	2.02863i
$107$	−0.437949	+	0.758550i	−0.0423381	+	0.0733317i	−0.886418	−	0.462886i	$-0.846814\pi$
$107$	−0.437949	+	0.758550i	−0.0423381	+	0.0733317i	0.844080	+	0.536218i	$0.180147\pi$
$108$	−5.20375	+	23.7843i	−0.500731	+	2.28865i
$109$	6.95218	+	12.0415i	0.665898	+	1.15337i	0.979041	+	0.203663i	$0.0652848\pi$
$109$	6.95218	+	12.0415i	0.665898	+	1.15337i	−0.313143	+	0.949706i	$0.601382\pi$
$110$	−3.19382	−	5.53186i	−0.304519	−	0.527442i
$111$	−4.67494	+	10.4442i	−0.443726	+	0.991324i
$112$	−2.38481	+	22.5839i	−0.225343	+	2.13398i
$113$	3.30719	+	5.72822i	0.311114	+	0.538866i	0.978604	−	0.205753i	$-0.0659644\pi$
$113$	3.30719	+	5.72822i	0.311114	+	0.538866i	−0.667489	+	0.744619i	$0.732631\pi$
$114$	−7.35137	+	0.757908i	−0.688519	+	0.0709846i
$115$	4.85733			0.452948
$116$	1.50757	+	2.61118i	0.139974	+	0.242442i
$117$	−12.7590	−	14.2839i	−1.17957	−	1.32055i
$118$	−22.9937			−2.11675
$119$	−1.42939	+	13.5362i	−0.131032	+	1.24086i
$120$	11.9638	−	1.23344i	1.09214	−	0.112597i
$121$	−4.89700			−0.445182
$122$	0.406755	−	0.704521i	0.0368259	−	0.0637843i
$123$	8.98743	+	12.4219i	0.810369	+	1.12005i
$124$	−1.28264	−	2.22161i	−0.115185	−	0.199506i
$125$	1.00000			0.0894427
$126$	2.05421	+	20.4199i	0.183003	+	1.81915i
$127$	−13.0086			−1.15432			−0.577162	−	0.816630i	$-0.695840\pi$
$127$	−13.0086			−1.15432			−0.577162	+	0.816630i	$0.695840\pi$
$128$	2.73502	+	4.73719i	0.241744	+	0.418712i
$129$	−5.31374	+	11.8714i	−0.467849	+	1.04522i
$130$	−8.25363	+	14.2957i	−0.723891	+	1.25382i
$131$	2.25010			0.196592			0.0982960	−	0.995157i	$-0.468661\pi$
$131$	2.25010			0.196592			0.0982960	+	0.995157i	$0.468661\pi$
$132$	−8.19104	+	18.2995i	−0.712938	+	1.59277i
$133$	−3.98941	+	1.77387i	−0.345925	+	0.153814i
$134$	−3.06789			−0.265025
$135$	4.95131	−	1.57624i	0.426141	−	0.135661i
$136$	−17.8620	−	30.9379i	−1.53165	−	2.65290i
$137$	16.6485			1.42237			0.711187	−	0.703003i	$-0.248158\pi$
$137$	16.6485			1.42237			0.711187	+	0.703003i	$0.248158\pi$
$138$	−12.7514	−	17.6242i	−1.08547	−	1.50027i
$139$	8.78569	+	15.2173i	0.745193	+	1.29071i	0.950105	+	0.311931i	$0.100976\pi$
$139$	8.78569	+	15.2173i	0.745193	+	1.29071i	−0.204912	+	0.978780i	$0.565691\pi$
$140$	11.3275	−	5.03672i	0.957351	−	0.425681i
$141$	1.66044	+	2.29496i	0.139834	+	0.193271i
$142$	1.56482	+	2.71035i	0.131317	+	0.227447i
$143$	−7.88583	−	13.6587i	−0.659446	−	1.14219i
$144$	−17.1541	−	19.2044i	−1.42951	−	1.60036i
$145$	0.321747	−	0.557282i	0.0267196	−	0.0462798i
$146$	16.2927	−	28.2197i	1.34839	−	2.33548i
$147$	4.89860	+	11.0907i	0.404030	+	0.914746i
$148$	−15.4776	−	26.8080i	−1.27225	−	2.20360i
$149$	8.04259			0.658875			0.329437	−	0.944177i	$-0.393141\pi$
$149$	8.04259			0.658875			0.329437	+	0.944177i	$0.393141\pi$
$150$	−2.62518	−	3.62838i	−0.214345	−	0.296256i
$151$	12.0429			0.980037			0.490018	−	0.871712i	$-0.336990\pi$
$151$	12.0429			0.980037			0.490018	+	0.871712i	$0.336990\pi$
$152$	5.72940	−	9.92361i	0.464716	−	0.804911i
$153$	−10.2817	−	11.5106i	−0.831226	−	0.930574i
$154$	−1.77475	+	16.8067i	−0.143013	+	1.35432i
$155$	−0.273744	+	0.474138i	−0.0219876	+	0.0380837i
$156$	51.5386	−	5.31350i	4.12639	−	0.425420i
$157$	−1.76403	+	3.05538i	−0.140785	+	0.243846i	−0.927792	−	0.373097i	$-0.878296\pi$
$157$	−1.76403	+	3.05538i	−0.140785	+	0.243846i	0.787008	+	0.616943i	$0.211629\pi$
$158$	−15.9006	+	27.5407i	−1.26499	+	2.19102i
$159$	9.46990	+	13.0888i	0.751012	+	1.03801i
$160$	−4.15288	+	7.19299i	−0.328314	+	0.568656i
$161$	−10.3932	−	7.55887i	−0.819100	−	0.595722i
$162$	−18.7173	−	13.8273i	−1.47057	−	1.08638i
$163$	1.15690	−	2.00380i	0.0906150	−	0.156950i	−0.817155	−	0.576418i	$-0.804450\pi$
$163$	1.15690	−	2.00380i	0.0906150	−	0.156950i	0.907770	+	0.419468i	$0.137783\pi$
$164$	−41.4770			−3.23881
$165$	4.25634	−	0.438818i	0.331356	−	0.0341619i
$166$	−16.6344			−1.29108
$167$	6.15059	+	10.6531i	0.475947	+	0.824365i	0.999620	−	0.0275545i	$-0.00877197\pi$
$167$	6.15059	+	10.6531i	0.475947	+	0.824365i	−0.523673	+	0.851919i	$0.675439\pi$
$168$	−27.5184	−	15.9786i	−2.12309	−	1.23278i
$169$	−13.8789	+	24.0390i	−1.06761	+	1.84916i
$170$	−6.65112	+	11.5201i	−0.510117	+	0.883549i
$171$	1.54849	−	4.70217i	0.118416	−	0.359584i
$172$	−17.5925	−	30.4711i	−1.34141	−	2.32340i
$173$	1.56719	+	2.71446i	0.119151	+	0.206376i	0.919432	−	0.393250i	$-0.128649\pi$
$173$	1.56719	+	2.71446i	0.119151	+	0.206376i	−0.800280	+	0.599626i	$0.795316\pi$
$174$	−2.86667	+	0.295547i	−0.217322	+	0.0224054i
$175$	−2.13970	−	1.55618i	−0.161746	−	0.117636i
$176$	−10.6023	−	18.3637i	−0.799179	−	1.38422i
$177$	6.29283	−	14.0587i	0.472998	−	1.05672i
$178$	7.46922			0.559842
$179$	−7.24402	−	12.5470i	−0.541443	−	0.937808i	−0.998821	−	0.0485352i	$-0.984545\pi$
$179$	−7.24402	−	12.5470i	−0.541443	−	0.937808i	0.457378	−	0.889272i	$-0.348789\pi$
$180$	−4.39680	+	13.3514i	−0.327718	+	0.995151i
$181$	10.6671			0.792880			0.396440	−	0.918061i	$-0.370245\pi$
$181$	10.6671			0.792880			0.396440	+	0.918061i	$0.370245\pi$
$182$	39.9069	−	17.7444i	2.95810	−	1.31530i
$183$	0.319436	+	0.441507i	0.0236134	+	0.0326371i
$184$	33.7289			2.48653
$185$	−3.30325	+	5.72139i	−0.242860	+	0.420645i
$186$	2.43898	−	0.251453i	0.178835	−	0.0184374i
$187$	−6.35473	−	11.0067i	−0.464704	−	0.804891i
$188$	−7.66292			−0.558876
$189$	−13.0472	−	4.33244i	−0.949046	−	0.315139i
$190$	−4.26681			−0.309547
$191$	−6.69720	−	11.5999i	−0.484592	−	0.839339i	0.515251	−	0.857039i	$-0.327699\pi$
$191$	−6.69720	−	11.5999i	−0.484592	−	0.839339i	−0.999843	+	0.0177007i	$0.994365\pi$
$192$	7.42400	−	0.765396i	0.535781	−	0.0552377i
$193$	−2.26582	+	3.92451i	−0.163097	+	0.282492i	−0.935978	−	0.352059i	$-0.885482\pi$
$193$	−2.26582	+	3.92451i	−0.163097	+	0.282492i	0.772881	+	0.634551i	$0.218815\pi$
$194$	−28.6402			−2.05625
$195$	−6.48180	−	8.95879i	−0.464172	−	0.641552i
$196$	−32.0755	−	6.85060i	−2.29111	−	0.489328i
$197$	1.62983			0.116121			0.0580603	−	0.998313i	$-0.481508\pi$
$197$	1.62983			0.116121			0.0580603	+	0.998313i	$0.481508\pi$
$198$	−12.7659	−	14.2916i	−0.907230	−	1.01566i
$199$	−11.4805	−	19.8849i	−0.813833	−	1.40960i	−0.910163	−	0.414250i	$-0.864044\pi$
$199$	−11.4805	−	19.8849i	−0.813833	−	1.40960i	0.0963300	−	0.995349i	$-0.469290\pi$
$200$	6.94392			0.491009
$201$	0.839607	−	1.87576i	0.0592213	−	0.132306i
$202$	19.8032	+	34.3002i	1.39335	+	2.41336i
$203$	−1.55567	+	0.691720i	−0.109187	+	0.0485493i
$204$	41.5319	−	4.28184i	2.90782	−	0.299789i
$205$	4.42604	+	7.66613i	0.309128	+	0.535425i
$206$	11.4762	+	19.8774i	0.799586	+	1.38492i
$207$	14.2655	−	2.97307i	0.991519	−	0.206643i
$208$	−27.3990	+	47.4564i	−1.89978	+	3.29051i
$209$	2.03834	−	3.53051i	0.140995	−	0.244210i
$210$	−0.0293057	+	11.8489i	−0.00202228	+	0.817650i
$211$	4.10543	+	7.11081i	0.282629	+	0.489528i	0.972032	−	0.234850i	$-0.0754600\pi$
$211$	4.10543	+	7.11081i	0.282629	+	0.489528i	−0.689402	+	0.724379i	$0.742127\pi$
$212$	−43.7036			−3.00158
$213$	−2.08540	+	0.215000i	−0.142890	+	0.0147316i
$214$	2.26476			0.154816
$215$	−3.75461	+	6.50318i	−0.256062	+	0.443513i
$216$	34.3815	−	10.9453i	2.33936	−	0.744731i
$217$	1.32357	−	0.588519i	0.0898500	−	0.0399513i
$218$	17.9759	−	31.1351i	1.21748	−	2.10874i
$219$	12.7951	+	17.6847i	0.864612	+	1.19502i
$220$	−5.78767	+	10.0245i	−0.390205	+	0.675854i
$221$	−16.4222	+	28.4441i	−1.10468	+	1.91336i
$222$	29.4310	−	3.03426i	1.97528	−	0.203646i
$223$	1.75774	−	3.04449i	0.117707	−	0.203874i	−0.801152	−	0.598461i	$-0.795779\pi$
$223$	1.75774	−	3.04449i	0.117707	−	0.203874i	0.918859	+	0.394587i	$0.129112\pi$
$224$	20.0795	−	8.92822i	1.34162	−	0.596542i
$225$	2.93690	−	0.612079i	0.195793	−	0.0408053i
$226$	8.55123	−	14.8112i	0.568819	−	0.985224i
$227$	13.8018			0.916058			0.458029	−	0.888937i	$-0.348556\pi$
$227$	13.8018			0.916058			0.458029	+	0.888937i	$0.348556\pi$
$228$	7.85031	+	10.8503i	0.519899	+	0.718576i
$229$	11.0517			0.730319			0.365159	−	0.930945i	$-0.381015\pi$
$229$	11.0517			0.730319			0.365159	+	0.930945i	$0.381015\pi$
$230$	−6.27966	−	10.8767i	−0.414069	−	0.717188i
$231$	−9.79017	−	5.68469i	−0.644146	−	0.374025i
$232$	2.23419	−	3.86972i	0.146681	−	0.254060i
$233$	−10.9712	+	19.0026i	−0.718744	+	1.24490i	0.242753	+	0.970088i	$0.421949\pi$
$233$	−10.9712	+	19.0026i	−0.718744	+	1.24490i	−0.961498	+	0.274814i	$0.911384\pi$
$234$	−15.4899	+	47.0369i	−1.01261	+	3.07490i
$235$	0.817715	+	1.41632i	0.0533419	+	0.0923908i
$236$	20.8340	+	36.0855i	1.35618	+	2.34897i
$237$	−12.4872	−	17.2591i	−0.811132	−	1.12110i
$238$	32.1587	−	14.2992i	2.08454	−	0.926877i
$239$	5.46109	+	9.45889i	0.353249	+	0.611844i	0.986817	−	0.161843i	$-0.0517437\pi$
$239$	5.46109	+	9.45889i	0.353249	+	0.611844i	−0.633568	+	0.773687i	$0.718410\pi$
$240$	−8.71462	−	12.0449i	−0.562527	−	0.777493i
$241$	11.6949			0.753333			0.376666	−	0.926349i	$-0.377070\pi$
$241$	11.6949			0.753333			0.376666	+	0.926349i	$0.377070\pi$
$242$	6.33095	+	10.9655i	0.406969	+	0.704891i
$243$	13.5767	−	7.65984i	0.870946	−	0.491379i
$244$	−1.47420			−0.0943759
$245$	2.15662	+	6.65950i	0.137781	+	0.425460i
$246$	16.1964	−	36.1843i	1.03265	−	2.30703i
$247$	−10.5351			−0.670335
$248$	−1.90086	+	3.29238i	−0.120704	+	0.209066i
$249$	4.55242	−	10.1705i	0.288498	−	0.644530i
$250$	−1.29282	−	2.23923i	−0.0817653	−	0.141622i
$251$	−1.99070			−0.125652			−0.0628261	−	0.998024i	$-0.520011\pi$
$251$	−1.99070			−0.125652			−0.0628261	+	0.998024i	$0.520011\pi$
$252$	30.1849	−	21.7257i	1.90147	−	1.36859i
$253$	11.9997			0.754412
$254$	16.8178	+	29.1292i	1.05524	+	1.82773i
$255$	−5.22331	−	7.21936i	−0.327096	−	0.452094i
$256$	11.3808	−	19.7121i	0.711297	−	1.23200i
$257$	−1.68925			−0.105372			−0.0526862	−	0.998611i	$-0.516778\pi$
$257$	−1.68925			−0.105372			−0.0526862	+	0.998611i	$0.516778\pi$
$258$	33.4525	−	3.44887i	2.08266	−	0.214717i
$259$	15.9715	−	7.10162i	0.992418	−	0.441273i
$260$	29.9135			1.85516
$261$	0.603837	−	1.83361i	0.0373766	−	0.113498i
$262$	−2.90898	−	5.03850i	−0.179717	−	0.311279i
$263$	−22.8153			−1.40685			−0.703426	−	0.710769i	$-0.748347\pi$
$263$	−22.8153			−1.40685			−0.703426	+	0.710769i	$0.748347\pi$
$264$	29.5557	−	3.04712i	1.81903	−	0.187537i
$265$	4.66364	+	8.07767i	0.286485	+	0.496207i
$266$	9.12970	+	6.63992i	0.559778	+	0.407120i
$267$	−2.04414	+	4.56680i	−0.125100	+	0.279484i
$268$	2.77973	+	4.81463i	0.169799	+	0.294101i
$269$	2.76740	+	4.79328i	0.168732	+	0.292252i	0.937974	−	0.346705i	$-0.112700\pi$
$269$	2.76740	+	4.79328i	0.168732	+	0.292252i	−0.769243	+	0.638957i	$0.779366\pi$
$270$	−9.93074	−	9.04935i	−0.604365	−	0.550726i
$271$	−4.37567	+	7.57888i	−0.265803	+	0.460384i	−0.967774	−	0.251821i	$-0.918970\pi$
$271$	−4.37567	+	7.57888i	−0.265803	+	0.460384i	0.701971	+	0.712206i	$0.252304\pi$
$272$	−22.0792	+	38.2424i	−1.33875	+	2.31878i
$273$	−0.0723583	+	29.2559i	−0.00437932	+	1.77065i
$274$	−21.5235	−	37.2798i	−1.30028	−	2.25216i
$275$	2.47043			0.148972
$276$	−16.1051	+	35.9803i	−0.969416	+	2.16576i
$277$	−27.9996			−1.68233			−0.841167	−	0.540775i	$-0.818131\pi$
$277$	−27.9996			−1.68233			−0.841167	+	0.540775i	$0.818131\pi$
$278$	22.7167	−	39.3465i	1.36246	−	2.35984i
$279$	−0.513747	+	1.56005i	−0.0307572	+	0.0933976i
$280$	−14.8579	−	10.8060i	−0.887929	−	0.645780i
$281$	−6.08424	+	10.5382i	−0.362955	+	0.628657i	−0.988446	−	0.151575i	$-0.951566\pi$
$281$	−6.08424	+	10.5382i	−0.362955	+	0.628657i	0.625490	+	0.780232i	$0.284899\pi$
$282$	2.99231	−	6.68509i	0.178189	−	0.398091i
$283$	−0.526203	+	0.911410i	−0.0312795	+	0.0541777i	−0.881241	−	0.472666i	$-0.843292\pi$
$283$	−0.526203	+	0.911410i	−0.0312795	+	0.0541777i	0.849962	+	0.526844i	$0.176625\pi$
$284$	2.83568	−	4.91155i	0.168267	−	0.291447i
$285$	1.16772	−	2.60880i	0.0691700	−	0.154532i
$286$	−20.3900	+	35.3165i	−1.20568	+	2.08831i
$287$	2.45947	−	23.2909i	0.145178	−	1.37482i
$288$	−7.79389	+	23.6670i	−0.459259	+	1.39459i
$289$	−4.73369	+	8.19899i	−0.278452	+	0.482294i
$290$	−1.66385			−0.0977045
$291$	7.83813	−	17.5111i	0.459479	−	1.02652i
$292$	−59.0494			−3.45560
$293$	−9.43289	−	16.3382i	−0.551075	−	0.954490i	−0.998197	−	0.0600173i	$-0.980884\pi$
$293$	−9.43289	−	16.3382i	−0.551075	−	0.954490i	0.447122	−	0.894473i	$-0.352449\pi$
$294$	18.5017	−	25.3074i	1.07904	−	1.47596i
$295$	4.44642	−	7.70143i	0.258881	−	0.448395i
$296$	−22.9375	+	39.7289i	−1.33321	+	2.30919i
$297$	12.2318	−	3.89398i	0.709763	−	0.225952i
$298$	−10.3976	−	18.0093i	−0.602319	−	1.04325i
$299$	−15.5050	−	26.8555i	−0.896680	−	1.55310i
$300$	−3.31564	+	7.40743i	−0.191428	+	0.427668i
$301$	18.1538	−	8.07200i	1.04637	−	0.465262i
$302$	−15.5693	−	26.9669i	−0.895914	−	1.55177i
$303$	−26.3914	+	2.72088i	−1.51614	+	0.156311i
$304$	−14.1642			−0.812375
$305$	0.157313	+	0.272474i	0.00900771	+	0.0156018i
$306$	−12.4824	+	37.9043i	−0.713574	+	2.16684i
$307$	−31.4153			−1.79296			−0.896482	−	0.443080i	$-0.853886\pi$
$307$	−31.4153			−1.79296			−0.896482	+	0.443080i	$0.853886\pi$
$308$	27.9838	−	12.4428i	1.59453	−	0.708997i
$309$	−15.2941	+	1.57678i	−0.870052	+	0.0897002i
$310$	1.41561			0.0804012
$311$	9.15720	−	15.8607i	0.519257	−	0.899380i	−0.480492	−	0.876999i	$-0.659542\pi$
$311$	9.15720	−	15.8607i	0.519257	−	0.899380i	0.999750	−	0.0223811i	$-0.00712473\pi$
$312$	−45.0091	−	62.2091i	−2.54814	−	3.52189i
$313$	−3.20703	−	5.55473i	−0.181272	−	0.313972i	0.761042	−	0.648703i	$-0.224688\pi$
$313$	−3.20703	−	5.55473i	−0.181272	−	0.313972i	−0.942314	+	0.334731i	$0.891355\pi$
$314$	9.12229			0.514801
$315$	−7.23658	−	3.26067i	−0.407735	−	0.183718i
$316$	57.6285			3.24186
$317$	−4.74118	−	8.21197i	−0.266291	−	0.461230i	0.701610	−	0.712561i	$-0.252465\pi$
$317$	−4.74118	−	8.21197i	−0.266291	−	0.461230i	−0.967901	+	0.251331i	$0.919132\pi$
$318$	17.0659	−	38.1268i	0.957009	−	2.13804i
$319$	0.794852	−	1.37672i	0.0445032	−	0.0770818i
$320$	4.30897			0.240879
$321$	−0.619810	+	1.38471i	−0.0345944	+	0.0772870i
$322$	−3.48949	+	33.0451i	−0.194462	+	1.84153i
$323$	−8.48966			−0.472377
$324$	−4.74087	+	41.9027i	−0.263382	+	2.32793i
$325$	−3.19209	−	5.52887i	−0.177066	−	0.306687i
$326$	−5.98264			−0.331348
$327$	14.1170	+	19.5117i	0.780670	+	1.07900i
$328$	30.7341	+	53.2329i	1.69700	+	2.93930i
$329$	0.454389	−	4.30302i	0.0250513	−	0.237233i
$330$	−6.48531	−	8.96363i	−0.357005	−	0.493432i
$331$	−6.50291	−	11.2634i	−0.357432	−	0.619091i	0.630099	−	0.776515i	$-0.283014\pi$
$331$	−6.50291	−	11.2634i	−0.357432	−	0.619091i	−0.987531	+	0.157424i	$0.949681\pi$
$332$	15.0719	+	26.1053i	0.827179	+	1.43272i
$333$	−6.19935	+	18.8250i	−0.339722	+	1.03160i
$334$	15.9033	−	27.5453i	0.870188	−	1.50721i
$335$	0.593254	−	1.02755i	0.0324129	−	0.0561409i
$336$	−0.0972839	+	39.3339i	−0.00530727	+	2.14584i
$337$	−0.631277	−	1.09340i	−0.0343879	−	0.0595615i	0.848319	−	0.529485i	$-0.177615\pi$
$337$	−0.631277	−	1.09340i	−0.0343879	−	0.0595615i	−0.882707	+	0.469924i	$0.844281\pi$
$338$	71.7720			3.90388
$339$	6.71552	+	9.28181i	0.364737	+	0.504119i
$340$	24.1056			1.30731
$341$	−0.676264	+	1.17132i	−0.0366217	+	0.0634307i
$342$	−12.5312	+	2.61163i	−0.677609	+	0.141221i
$343$	5.74886	−	17.6054i	0.310409	−	0.950603i
$344$	−26.0717	+	45.1575i	−1.40569	+	2.43473i
$345$	8.36878	−	0.862800i	0.450560	−	0.0464516i
$346$	4.05220	−	7.01862i	0.217848	−	0.377324i
$347$	11.7238	−	20.3063i	0.629368	−	1.09010i	−0.358310	−	0.933603i	$-0.616647\pi$
$347$	11.7238	−	20.3063i	0.629368	−	1.09010i	0.987679	−	0.156496i	$-0.0500197\pi$
$348$	3.06123	+	4.23107i	0.164099	+	0.226809i
$349$	1.25503	−	2.17378i	0.0671804	−	0.116360i	−0.830479	−	0.557050i	$-0.811933\pi$
$349$	1.25503	−	2.17378i	0.0671804	−	0.116360i	0.897659	+	0.440690i	$0.145266\pi$
$350$	−0.718397	+	6.80315i	−0.0383999	+	0.363644i
$351$	−24.5199	−	22.3436i	−1.30877	−	1.19262i
$352$	−10.2594	+	17.7698i	−0.546826	+	0.947131i
$353$	0.724165			0.0385434			0.0192717	−	0.999814i	$-0.493865\pi$
$353$	0.724165			0.0385434			0.0192717	+	0.999814i	$0.493865\pi$
$354$	−39.6164	+	4.08435i	−2.10559	+	0.217081i
$355$	−1.21039			−0.0642409
$356$	−6.76766	−	11.7219i	−0.358685	−	0.621261i
$357$	−0.0583093	+	23.5757i	−0.00308606	+	1.24776i
$358$	−18.7305	+	32.4421i	−0.989936	+	1.71462i
$359$	11.5624	−	20.0267i	0.610241	−	1.05697i	−0.380958	−	0.924592i	$-0.624406\pi$
$359$	11.5624	−	20.0267i	0.610241	−	1.05697i	0.991199	−	0.132377i	$-0.0422609\pi$
$360$	20.3936	−	4.25023i	1.07484	−	0.224007i
$361$	8.13843	+	14.0962i	0.428339	+	0.741904i
$362$	−13.7907	−	23.8862i	−0.724823	−	1.25543i
$363$	−8.43713	+	0.869847i	−0.442834	+	0.0456551i
$364$	−64.0059	−	46.5508i	−3.35482	−	2.43992i
$365$	6.30120	+	10.9140i	0.329820	+	0.571265i
$366$	0.575663	−	1.28608i	0.0300904	−	0.0672246i
$367$	−0.530037			−0.0276677			−0.0138339	−	0.999904i	$-0.504404\pi$
$367$	−0.530037			−0.0276677			−0.0138339	+	0.999904i	$0.504404\pi$
$368$	−20.8462	−	36.1066i	−1.08668	−	1.88219i
$369$	17.6911	+	19.8055i	0.920962	+	1.03103i
$370$	17.0821			0.888054
$371$	2.59150	−	24.5412i	0.134544	−	1.27412i
$372$	−2.60451	−	3.59981i	−0.135038	−	0.186642i
$373$	16.4305			0.850737			0.425369	−	0.905020i	$-0.360144\pi$
$373$	16.4305			0.850737			0.425369	+	0.905020i	$0.360144\pi$
$374$	−16.4311	+	28.4595i	−0.849631	+	1.47160i
$375$	1.72292	−	0.177629i	0.0889711	−	0.00917270i
$376$	5.67815	+	9.83484i	0.292828	+	0.507193i
$377$	−4.10819			−0.211582
$378$	7.16638	+	34.8169i	0.368599	+	1.79079i
$379$	3.76572			0.193432			0.0967160	−	0.995312i	$-0.469166\pi$
$379$	3.76572			0.193432			0.0967160	+	0.995312i	$0.469166\pi$
$380$	3.86604	+	6.69618i	0.198324	+	0.343507i
$381$	−22.4127	+	2.31069i	−1.14824	+	0.118380i
$382$	−17.3166	+	29.9932i	−0.885994	+	1.53459i
$383$	−7.91395			−0.404384			−0.202192	−	0.979346i	$-0.564807\pi$
$383$	−7.91395			−0.404384			−0.202192	+	0.979346i	$0.564807\pi$
$384$	5.55367	+	7.67598i	0.283410	+	0.391713i
$385$	−5.28597	−	3.84442i	−0.269398	−	0.195930i
$386$	11.7172			0.596390
$387$	−7.04645	+	21.3973i	−0.358191	+	1.08769i
$388$	25.9501	+	44.9469i	1.31742	+	2.28183i
$389$	30.9240			1.56791			0.783953	−	0.620820i	$-0.213200\pi$
$389$	30.9240			1.56791			0.783953	+	0.620820i	$0.213200\pi$
$390$	−11.6810	+	26.0964i	−0.591490	+	1.32144i
$391$	−12.4946	−	21.6413i	−0.631880	−	1.09445i
$392$	14.9754	+	46.2430i	0.756372	+	2.33563i
$393$	3.87674	−	0.399682i	0.195555	−	0.0201613i
$394$	−2.10708	−	3.64957i	−0.106153	−	0.183863i
$395$	−6.14958	−	10.6514i	−0.309419	−	0.535929i
$396$	−10.8620	+	32.9835i	−0.545835	+	1.65748i
$397$	12.1376	−	21.0230i	0.609171	−	1.05512i	−0.382206	−	0.924077i	$-0.624836\pi$
$397$	12.1376	−	21.0230i	0.609171	−	1.05512i	0.991377	−	0.131038i	$-0.0418311\pi$
$398$	−29.6846	+	51.4152i	−1.48795	+	2.57721i
$399$	−6.55833	+	3.76486i	−0.328327	+	0.188479i
$400$	−4.29169	−	7.43343i	−0.214585	−	0.371671i
$401$	−35.4068			−1.76813			−0.884065	−	0.467365i	$-0.845203\pi$
$401$	−35.4068			−1.76813			−0.884065	+	0.467365i	$0.845203\pi$
$402$	−5.28573	+	0.544945i	−0.263628	+	0.0271794i
$403$	3.49527			0.174112
$404$	35.8863	−	62.1570i	1.78541	−	3.09242i
$405$	8.25072	−	3.59522i	0.409982	−	0.178648i
$406$	3.56013	+	2.58924i	0.176686	+	0.128502i
$407$	−8.16043	+	14.1343i	−0.404497	+	0.700610i
$408$	−36.2702	−	50.1307i	−1.79564	−	2.48184i
$409$	10.8919	−	18.8653i	0.538568	−	0.932827i	−0.460413	−	0.887705i	$-0.652299\pi$
$409$	10.8919	−	18.8653i	0.538568	−	0.932827i	0.998981	−	0.0451225i	$-0.0143678\pi$
$410$	11.4442	−	19.8219i	0.565187	−	0.978933i
$411$	28.6840	−	2.95724i	1.41488	−	0.145870i
$412$	20.7966	−	36.0207i	1.02457	−	1.77461i
$413$	−21.4988	+	9.55931i	−1.05789	+	0.470383i
$414$	−25.1001	−	28.1001i	−1.23360	−	1.38104i
$415$	3.21667	−	5.57144i	0.157900	−	0.273491i
$416$	53.0255			2.59979
$417$	17.8401	+	24.6575i	0.873631	+	1.20748i
$418$	−10.5408			−0.515570
$419$	−1.62516	−	2.81486i	−0.0793943	−	0.137515i	0.823594	−	0.567179i	$-0.191965\pi$
$419$	−1.62516	−	2.81486i	−0.0793943	−	0.137515i	−0.902989	+	0.429664i	$0.858632\pi$
$420$	18.6218	−	10.6900i	0.908648	−	0.521616i
$421$	−11.3571	+	19.6710i	−0.553510	+	0.958707i	0.444508	+	0.895775i	$0.353379\pi$
$421$	−11.3571	+	19.6710i	−0.553510	+	0.958707i	−0.998018	+	0.0629324i	$0.979955\pi$
$422$	10.6152	−	18.3860i	0.516739	−	0.895018i
$423$	3.26845	+	3.65909i	0.158917	+	0.177911i
$424$	32.3840	+	56.0907i	1.57270	+	2.72400i
$425$	−2.57232	−	4.45539i	−0.124776	−	0.216118i
$426$	3.17749	+	4.39175i	0.153950	+	0.212781i
$427$	0.0874157	−	0.827819i	0.00423034	−	0.0400610i
$428$	−2.05204	−	3.55423i	−0.0991890	−	0.171800i
$429$	−16.0128	−	22.1320i	−0.773106	−	1.06854i
$430$	19.4162			0.936332
$431$	6.07416	+	10.5208i	0.292582	+	0.506767i	0.974420	−	0.224737i	$-0.0721522\pi$
$431$	6.07416	+	10.5208i	0.292582	+	0.506767i	−0.681837	+	0.731504i	$0.738819\pi$
$432$	−32.9664	−	30.0405i	−1.58609	−	1.44532i
$433$	−11.8389			−0.568941			−0.284471	−	0.958685i	$-0.591818\pi$
$433$	−11.8389			−0.568941			−0.284471	+	0.958685i	$0.591818\pi$
$434$	−3.02898	−	2.20294i	−0.145396	−	0.105745i
$435$	0.455355	−	1.01730i	0.0218326	−	0.0487760i
$436$	−65.1498			−3.12011
$437$	4.00776	−	6.94165i	0.191717	−	0.332064i
$438$	23.0583	−	51.5144i	1.10177	−	2.46145i
$439$	−14.9274	−	25.8550i	−0.712445	−	1.23399i	−0.963937	−	0.266131i	$-0.914255\pi$
$439$	−14.9274	−	25.8550i	−0.712445	−	1.23399i	0.251492	−	0.967859i	$-0.419079\pi$
$440$	17.1544			0.817805
$441$	10.4099	+	18.2382i	0.495710	+	0.868488i
$442$	84.9240			4.03942
$443$	−0.566390	−	0.981015i	−0.0269100	−	0.0466095i	0.852257	−	0.523124i	$-0.175233\pi$
$443$	−0.566390	−	0.981015i	−0.0269100	−	0.0466095i	−0.879167	+	0.476514i	$0.841900\pi$
$444$	−31.4285	−	43.4387i	−1.49153	−	2.06151i
$445$	−1.44436	+	2.50171i	−0.0684694	+	0.118592i
$446$	−9.08977			−0.430413
$447$	13.8567	−	1.42859i	0.655401	−	0.0675702i
$448$	−9.21990	−	6.70552i	−0.435599	−	0.316806i
$449$	−23.0291			−1.08681			−0.543406	−	0.839470i	$-0.682866\pi$
$449$	−23.0291			−1.08681			−0.543406	+	0.839470i	$0.682866\pi$
$450$	−5.16748	−	5.78509i	−0.243597	−	0.272712i
$451$	10.9342	+	18.9386i	0.514871	+	0.891783i
$452$	−30.9921			−1.45775
$453$	20.7489	−	2.13916i	0.974870	−	0.100507i
$454$	−17.8433	−	30.9055i	−0.837427	−	1.45047i
$455$	−1.77379	+	16.7976i	−0.0831564	+	0.787483i
$456$	8.10857	−	18.1153i	0.379719	−	0.848326i
$457$	11.8422	+	20.5113i	0.553955	+	0.959478i	0.997984	+	0.0634658i	$0.0202154\pi$
$457$	11.8422	+	20.5113i	0.553955	+	0.959478i	−0.444029	+	0.896012i	$0.646451\pi$
$458$	−14.2879	−	24.7474i	−0.667631	−	1.15637i
$459$	−19.7591	−	18.0054i	−0.922277	−	0.840422i
$460$	−11.3797	+	19.7101i	−0.530579	+	0.918990i
$461$	−12.4889	+	21.6313i	−0.581664	+	1.00747i	0.413618	+	0.910451i	$0.364265\pi$
$461$	−12.4889	+	21.6313i	−0.581664	+	1.00747i	−0.995282	+	0.0970216i	$0.969068\pi$
$462$	−0.0723974	+	29.2718i	−0.00336823	+	1.36185i
$463$	3.19536	+	5.53453i	0.148501	+	0.257212i	0.930674	−	0.365850i	$-0.119222\pi$
$463$	3.19536	+	5.53453i	0.148501	+	0.257212i	−0.782173	+	0.623062i	$0.785888\pi$
$464$	−5.52336			−0.256415
$465$	−0.387418	+	0.865526i	−0.0179661	+	0.0401378i
$466$	56.7350			2.62820
$467$	−18.1461	+	31.4300i	−0.839702	+	1.45441i	0.0504425	+	0.998727i	$0.483937\pi$
$467$	−18.1461	+	31.4300i	−0.839702	+	1.45441i	−0.890144	+	0.455679i	$0.849396\pi$
$468$	87.8529	−	18.3094i	4.06100	−	0.846354i
$469$	−2.86843	+	1.27543i	−0.132452	+	0.0588939i
$470$	2.11432	−	3.66211i	0.0975264	−	0.168921i
$471$	−2.49655	+	5.57751i	−0.115035	+	0.256998i
$472$	30.8756	−	53.4781i	1.42116	−	2.46153i
$473$	−9.27549	+	16.0656i	−0.426488	+	0.738698i
$474$	−22.5035	+	50.2748i	−1.03362	+	2.30920i
$475$	0.825096	−	1.42911i	0.0378580	−	0.0655720i
$476$	−51.5786	−	37.5126i	−2.36410	−	1.71939i
$477$	18.6408	+	20.8688i	0.853504	+	0.955515i
$478$	14.1204	−	24.4573i	0.645854	−	1.11865i
$479$	20.6282			0.942526			0.471263	−	0.881993i	$-0.343798\pi$
$479$	20.6282			0.942526			0.471263	+	0.881993i	$0.343798\pi$
$480$	−5.87739	+	13.1306i	−0.268265	+	0.599328i
$481$	42.1771			1.92311
$482$	−15.1194	−	26.1876i	−0.688670	−	1.19281i
$483$	−19.2493	−	11.1772i	−0.875875	−	0.508579i
$484$	11.4726	−	19.8711i	0.521482	−	0.903233i
$485$	5.53831	−	9.59263i	0.251482	−	0.435579i
$486$	−34.7045	−	20.4986i	−1.57423	−	0.929836i
$487$	−4.41678	−	7.65008i	−0.200143	−	0.346658i	0.748431	−	0.663212i	$-0.230807\pi$
$487$	−4.41678	−	7.65008i	−0.200143	−	0.346658i	−0.948574	+	0.316554i	$0.897474\pi$
$488$	1.09237	+	1.89204i	0.0494491	+	0.0856484i
$489$	1.63730	−	3.65788i	0.0740415	−	0.165415i
$490$	12.1241	−	13.4387i	0.547709	−	0.607100i
$491$	8.71841	+	15.1007i	0.393456	+	0.681486i	0.992903	−	0.118929i	$-0.0379459\pi$
$491$	8.71841	+	15.1007i	0.393456	+	0.681486i	−0.599447	+	0.800415i	$0.704613\pi$
$492$	−71.4615	+	7.36750i	−3.22173	+	0.332152i
$493$	−3.31055			−0.149100
$494$	13.6201	+	23.5907i	0.612796	+	1.06139i
$495$	7.25538	−	1.51210i	0.326105	−	0.0679636i
$496$	4.69930			0.211005
$497$	2.58987	+	1.88358i	0.116172	+	0.0844903i
$498$	−28.6596	+	2.95474i	−1.28427	+	0.132405i
$499$	30.8164			1.37953			0.689767	−	0.724032i	$-0.257713\pi$
$499$	30.8164			1.37953			0.689767	+	0.724032i	$0.257713\pi$
$500$	−2.34278	+	4.05782i	−0.104772	+	0.181471i
$501$	12.4893	+	17.2620i	0.557980	+	0.771208i
$502$	2.57363	+	4.45765i	0.114867	+	0.198955i
$503$	23.0337			1.02702			0.513512	−	0.858083i	$-0.328344\pi$
$503$	23.0337			1.02702			0.513512	+	0.858083i	$0.328344\pi$
$504$	−50.2502	−	22.6418i	−2.23832	−	1.00855i
$505$	−15.3178			−0.681635
$506$	−15.5134	−	26.8701i	−0.689657	−	1.19452i
$507$	−19.6423	+	43.8826i	−0.872343	+	1.94889i
$508$	30.4762	−	52.7864i	1.35216	−	2.34202i
$509$	−23.9878			−1.06324			−0.531620	−	0.846983i	$-0.678416\pi$
$509$	−23.9878			−1.06324			−0.531620	+	0.846983i	$0.678416\pi$
$510$	−9.41304	+	21.0296i	−0.416816	+	0.931205i
$511$	3.50146	−	33.1585i	0.154895	−	1.46684i
$512$	−47.9131			−2.11748
$513$	1.83269	−	8.37651i	0.0809153	−	0.369832i
$514$	2.18390	+	3.78262i	0.0963276	+	0.166844i
$515$	−8.87687			−0.391161
$516$	−35.7229	−	49.3742i	−1.57261	−	2.17358i
$517$	2.02010	+	3.49892i	0.0888441	+	0.153882i
$518$	−36.5505	−	26.5827i	−1.60594	−	1.16798i
$519$	3.18231	+	4.39841i	0.139688	+	0.193069i
$520$	−22.1656	−	38.3920i	−0.972028	−	1.68360i
$521$	2.82741	+	4.89722i	0.123871	+	0.214551i	0.921291	−	0.388874i	$-0.127136\pi$
$521$	2.82741	+	4.89722i	0.123871	+	0.214551i	−0.797420	+	0.603425i	$0.793802\pi$
$522$	−4.88655	+	1.01841i	−0.213878	+	0.0445744i
$523$	−2.01049	+	3.48227i	−0.0879126	+	0.152269i	−0.906629	−	0.421930i	$-0.861353\pi$
$523$	−2.01049	+	3.48227i	−0.0879126	+	0.152269i	0.818716	+	0.574199i	$0.194686\pi$
$524$	−5.27149	+	9.13049i	−0.230286	+	0.398867i
$525$	−3.96295	−	2.30110i	−0.172957	−	0.100428i
$526$	29.4961	+	51.0888i	1.28609	+	2.22758i
$527$	2.81663			0.122694
$528$	−21.5288	−	29.7559i	−0.936922	−	1.29496i
$529$	0.593633			0.0258101
$530$	12.0585	−	20.8860i	0.523789	−	0.907229i
$531$	8.34480	−	25.3399i	0.362133	−	1.09966i
$532$	2.14829	−	20.3441i	0.0931400	−	0.882027i
$533$	28.2567	−	48.9420i	1.22393	−	2.11991i
$534$	12.8689	−	1.32675i	0.556890	−	0.0574140i
$535$	−0.437949	+	0.758550i	−0.0189342	+	0.0327950i
$536$	4.11951	−	7.13520i	0.177936	−	0.308194i
$537$	−14.7096	−	20.3307i	−0.634764	−	0.877336i
$538$	7.15553	−	12.3937i	0.308497	−	0.534332i
$539$	5.32777	+	16.4518i	0.229483	+	0.708629i
$540$	−5.20375	+	23.7843i	−0.223934	+	1.02351i
$541$	−20.6577	+	35.7801i	−0.888142	+	1.53831i	−0.0460730	+	0.998938i	$0.514671\pi$
$541$	−20.6577	+	35.7801i	−0.888142	+	1.53831i	−0.842069	+	0.539369i	$0.818663\pi$
$542$	22.6279			0.971950
$543$	18.3786	−	1.89478i	0.788700	−	0.0813130i
$544$	42.7302			1.83204
$545$	6.95218	+	12.0415i	0.297799	+	0.515803i
$546$	65.6045	−	37.6607i	2.80761	−	1.61173i
$547$	−9.86882	+	17.0933i	−0.421960	+	0.730857i	−0.996131	−	0.0878787i	$-0.971991\pi$
$547$	−9.86882	+	17.0933i	−0.421960	+	0.730857i	0.574171	+	0.818736i	$0.305325\pi$
$548$	−39.0037	+	67.5564i	−1.66616	+	2.88587i
$549$	0.628787	+	0.703939i	0.0268360	+	0.0300434i
$550$	−3.19382	−	5.53186i	−0.136185	−	0.235879i
$551$	−0.530945	−	0.919623i	−0.0226190	−	0.0391773i
$552$	58.1121	−	5.99121i	2.47342	−	0.255003i
$553$	−3.41720	+	32.3606i	−0.145314	+	1.37611i
$554$	36.1986	+	62.6977i	1.53793	+	2.66377i
$555$	−4.67494	+	10.4442i	−0.198440	+	0.443334i
$556$	−82.3318			−3.49165
$557$	−3.38731	−	5.86700i	−0.143525	−	0.248593i	0.785297	−	0.619120i	$-0.212510\pi$
$557$	−3.38731	−	5.86700i	−0.143525	−	0.248593i	−0.928822	+	0.370527i	$0.879177\pi$
$558$	4.15750	−	0.866465i	0.176001	−	0.0366804i
$559$	47.9403			2.02766
$560$	−2.38481	+	22.5839i	−0.100777	+	0.954345i
$561$	−12.9038	−	17.8349i	−0.544798	−	0.752990i
$562$	31.4634			1.32720
$563$	14.1126	−	24.4437i	0.594773	−	1.03018i	−0.398806	−	0.917035i	$-0.630575\pi$
$563$	14.1126	−	24.4437i	0.594773	−	1.03018i	0.993579	−	0.113142i	$-0.0360915\pi$
$564$	−13.2026	+	1.36115i	−0.555929	+	0.0573149i
$565$	3.30719	+	5.72822i	0.139135	+	0.240988i
$566$	2.72115			0.114378
$567$	−23.2489	−	5.14689i	−0.976360	−	0.216149i
$568$	−8.40485			−0.352660
$569$	−19.8886	−	34.4480i	−0.833773	−	1.44414i	−0.895026	−	0.446015i	$-0.852843\pi$
$569$	−19.8886	−	34.4480i	−0.833773	−	1.44414i	0.0612526	−	0.998122i	$-0.480490\pi$
$570$	−7.35137	+	0.757908i	−0.307915	+	0.0317453i
$571$	−16.4549	+	28.5007i	−0.688615	+	1.19272i	0.283671	+	0.958922i	$0.408448\pi$
$571$	−16.4549	+	28.5007i	−0.688615	+	1.19272i	−0.972286	+	0.233794i	$0.924886\pi$
$572$	73.8991			3.08988
$573$	−13.5992	−	18.7961i	−0.568115	−	0.785216i
$574$	−55.3335	+	24.6037i	−2.30957	+	1.02694i
$575$	4.85733			0.202565
$576$	12.6550	−	2.63743i	0.527292	−	0.109893i
$577$	−9.93085	−	17.2007i	−0.413427	−	0.716076i	0.581835	−	0.813307i	$-0.302335\pi$
$577$	−9.93085	−	17.2007i	−0.413427	−	0.716076i	−0.995262	+	0.0972307i	$0.969002\pi$
$578$	24.4793			1.01820
$579$	−3.20671	+	7.16409i	−0.133266	+	0.297729i
$580$	1.50757	+	2.61118i	0.0625983	+	0.108423i
$581$	−15.5529	+	6.91549i	−0.645242	+	0.286903i
$582$	−49.3447	+	5.08732i	−2.04541	+	0.210876i
$583$	11.5212	+	19.9553i	0.477159	+	0.826463i
$584$	43.7550	+	75.7859i	1.81060	+	3.13604i
$585$	−12.7590	−	14.2839i	−0.527518	−	0.590567i
$586$	−24.3901	+	42.2449i	−1.00755	+	1.74512i
$587$	−12.3770	+	21.4375i	−0.510852	+	0.884822i	0.489068	+	0.872245i	$0.337337\pi$
$587$	−12.3770	+	21.4375i	−0.510852	+	0.884822i	−0.999921	+	0.0125770i	$0.995997\pi$
$588$	−56.4804	−	6.10549i	−2.32921	−	0.251786i
$589$	0.451730	+	0.782420i	0.0186132	+	0.0322390i
$590$	−22.9937			−0.946638
$591$	2.80806	−	0.289504i	0.115508	−	0.0119086i
$592$	56.7061			2.33061
$593$	−2.69526	+	4.66833i	−0.110681	+	0.191706i	−0.916045	−	0.401075i	$-0.868637\pi$
$593$	−2.69526	+	4.66833i	−0.110681	+	0.191706i	0.805364	+	0.592781i	$0.201970\pi$
$594$	−24.5331	−	22.3557i	−1.00661	−	0.917267i
$595$	−1.42939	+	13.5362i	−0.0585993	+	0.554930i
$596$	−18.8420	+	32.6354i	−0.771800	+	1.33680i
$597$	−23.3121	−	32.2207i	−0.954102	−	1.31871i
$598$	−40.0906	+	69.4389i	−1.63943	+	2.83957i
$599$	2.54350	−	4.40548i	0.103925	−	0.180003i	−0.809374	−	0.587294i	$-0.800193\pi$
$599$	2.54350	−	4.40548i	0.103925	−	0.180003i	0.913298	+	0.407291i	$0.133527\pi$
$600$	11.9638	−	1.23344i	0.488420	−	0.0503549i
$601$	9.14504	−	15.8397i	0.373034	−	0.646114i	−0.616997	−	0.786966i	$-0.711651\pi$
$601$	9.14504	−	15.8397i	0.373034	−	0.646114i	0.990031	+	0.140852i	$0.0449842\pi$
$602$	−41.5448	−	30.2151i	−1.69324	−	1.23147i
$603$	1.11339	−	3.38092i	0.0453406	−	0.137682i
$604$	−28.2139	+	48.8679i	−1.14801	+	1.98841i
$605$	−4.89700			−0.199091
$606$	40.2121	+	55.5789i	1.63350	+	2.25774i
$607$	28.0586			1.13886			0.569431	−	0.822039i	$-0.307164\pi$
$607$	28.0586			1.13886			0.569431	+	0.822039i	$0.307164\pi$
$608$	6.85305	+	11.8698i	0.277928	+	0.481385i
$609$	−2.55743	+	1.46811i	−0.103632	+	0.0594908i
$610$	0.406755	−	0.704521i	0.0164690	−	0.0285252i
$611$	5.22045	−	9.04208i	0.211197	−	0.365804i
$612$	70.7956	−	14.7545i	2.86174	−	0.596416i
$613$	−6.77692	−	11.7380i	−0.273717	−	0.474092i	0.696094	−	0.717951i	$-0.254920\pi$
$613$	−6.77692	−	11.7380i	−0.273717	−	0.474092i	−0.969811	+	0.243859i	$0.921587\pi$
$614$	40.6144	+	70.3462i	1.63906	+	2.83894i
$615$	8.98743	+	12.4219i	0.362408	+	0.500900i
$616$	−36.7053	−	26.6953i	−1.47890	−	1.07559i
$617$	20.9055	+	36.2094i	0.841624	+	1.45774i	0.888521	+	0.458836i	$0.151734\pi$
$617$	20.9055	+	36.2094i	0.841624	+	1.45774i	−0.0468963	+	0.998900i	$0.514933\pi$
$618$	23.3034	+	32.2086i	0.937399	+	1.29562i
$619$	−17.1479			−0.689230			−0.344615	−	0.938744i	$-0.611991\pi$
$619$	−17.1479			−0.689230			−0.344615	+	0.938744i	$0.611991\pi$
$620$	−1.28264	−	2.22161i	−0.0515122	−	0.0892218i
$621$	24.0501	−	7.65631i	0.965099	−	0.307237i
$622$	−47.3546			−1.89875
$623$	6.98361	−	3.10522i	0.279792	−	0.124408i
$624$	−38.7766	+	86.6304i	−1.55231	+	3.46799i
$625$	1.00000			0.0400000
$626$	−8.29223	+	14.3626i	−0.331424	+	0.574044i
$627$	2.88477	−	6.44484i	0.115207	−	0.257382i
$628$	−8.26545	−	14.3162i	−0.329827	−	0.571278i
$629$	33.9881			1.35519
$630$	2.05421	+	20.4199i	0.0818416	+	0.813547i
$631$	−2.79587			−0.111302			−0.0556508	−	0.998450i	$-0.517723\pi$
$631$	−2.79587			−0.111302			−0.0556508	+	0.998450i	$0.517723\pi$
$632$	−42.7022	−	73.9623i	−1.69860	−	2.94206i
$633$	8.33640	+	11.5221i	0.331342	+	0.457963i
$634$	−12.2590	+	21.2333i	−0.486868	+	0.843280i
$635$	−13.0086			−0.516229
$636$	−75.2978	+	7.76301i	−2.98575	+	0.307823i
$637$	29.9354	−	33.1814i	1.18608	−	1.31470i
$638$	−4.11041			−0.162733
$639$	−3.55479	+	0.740855i	−0.140625	+	0.0293078i
$640$	2.73502	+	4.73719i	0.108111	+	0.187254i
$641$	13.7919			0.544746			0.272373	−	0.962192i	$-0.412191\pi$
$641$	13.7919			0.544746			0.272373	+	0.962192i	$0.412191\pi$
$642$	3.90200	−	0.402286i	0.154000	−	0.0158770i
$643$	−6.91039	−	11.9691i	−0.272519	−	0.472017i	0.696987	−	0.717084i	$-0.254523\pi$
$643$	−6.91039	−	11.9691i	−0.272519	−	0.472017i	−0.969506	+	0.245067i	$0.921190\pi$
$644$	55.0215	−	24.4650i	2.16815	−	0.964056i
$645$	−5.31374	+	11.8714i	−0.209228	+	0.467435i
$646$	10.9756	+	19.0103i	0.431830	+	0.747952i
$647$	14.5042	+	25.1221i	0.570220	+	0.987650i	0.996543	+	0.0830790i	$0.0264754\pi$
$647$	14.5042	+	25.1221i	0.570220	+	0.987650i	−0.426323	+	0.904571i	$0.640191\pi$
$648$	57.2923	−	24.9649i	2.25065	−	0.980716i
$649$	10.9846	−	19.0258i	0.431181	−	0.746828i
$650$	−8.25363	+	14.2957i	−0.323734	+	0.560723i
$651$	2.17587	−	1.24907i	0.0852791	−	0.0489551i
$652$	5.42071	+	9.38894i	0.212291	+	0.367699i
$653$	−34.9087			−1.36608			−0.683042	−	0.730379i	$-0.739343\pi$
$653$	−34.9087			−1.36608			−0.683042	+	0.730379i	$0.739343\pi$
$654$	25.4405	−	56.8363i	0.994802	−	2.22248i
$655$	2.25010			0.0879186
$656$	37.9904	−	65.8013i	1.48328	−	2.56911i
$657$	25.1862	+	28.1965i	0.982607	+	1.10005i
$658$	−10.2229	+	4.54556i	−0.398531	+	0.177204i
$659$	16.9405	−	29.3418i	0.659908	−	1.14299i	−0.320731	−	0.947170i	$-0.603928\pi$
$659$	16.9405	−	29.3418i	0.659908	−	1.14299i	0.980639	−	0.195824i	$-0.0627382\pi$
$660$	−8.19104	+	18.2995i	−0.318836	+	0.712308i
$661$	10.6327	−	18.4164i	0.413566	−	0.716317i	−0.581711	−	0.813395i	$-0.697617\pi$
$661$	10.6327	−	18.4164i	0.413566	−	0.716317i	0.995277	+	0.0970789i	$0.0309499\pi$
$662$	−16.8142	+	29.1231i	−0.653504	+	1.13190i
$663$	−23.2416	+	51.9239i	−0.902630	+	2.01656i
$664$	22.3363	−	38.6876i	0.866817	−	1.50137i
$665$	−3.98941	+	1.77387i	−0.154702	+	0.0687875i
$666$	50.1682	−	10.4556i	1.94398	−	0.405145i
$667$	1.56283	−	2.70690i	0.0605131	−	0.104812i
$668$	−57.6380			−2.23008
$669$	2.48765	−	5.55763i	0.0961781	−	0.214870i
$670$	−3.06789			−0.118523
$671$	0.388630	+	0.673126i	0.0150029	+	0.0259858i
$672$	33.0094	−	18.9493i	1.27337	−	0.730985i
$673$	−6.96999	+	12.0724i	−0.268673	+	0.465356i	−0.968520	−	0.248938i	$-0.919919\pi$
$673$	−6.96999	+	12.0724i	−0.268673	+	0.465356i	0.699846	+	0.714294i	$0.253252\pi$
$674$	−1.63226	+	2.82716i	−0.0628723	+	0.108898i
$675$	4.95131	−	1.57624i	0.190576	−	0.0606695i
$676$	−65.0306	−	112.636i	−2.50118	−	4.33217i
$677$	−0.108664	−	0.188212i	−0.00417630	−	0.00723356i	0.863930	−	0.503612i	$-0.167996\pi$
$677$	−0.108664	−	0.188212i	−0.00417630	−	0.00723356i	−0.868106	+	0.496379i	$0.834663\pi$
$678$	12.1022	−	27.0374i	0.464782	−	1.03836i
$679$	−26.7782	+	11.9067i	−1.02765	+	0.456939i
$680$	−17.8620	−	30.9379i	−0.684976	−	1.18641i
$681$	23.7794	−	2.45160i	0.911228	−	0.0939453i
$682$	3.49716			0.133913
$683$	−1.92685	−	3.33741i	−0.0737290	−	0.127702i	0.826804	−	0.562490i	$-0.190157\pi$
$683$	−1.92685	−	3.33741i	−0.0737290	−	0.127702i	−0.900533	+	0.434788i	$0.856823\pi$
$684$	15.4528	+	17.2997i	0.590851	+	0.661469i
$685$	16.6485			0.636105
$686$	−46.8549	+	9.88764i	−1.78893	+	0.377512i
$687$	19.0412	−	1.96310i	0.726468	−	0.0748970i
$688$	64.4546			2.45731
$689$	29.7736	−	51.5694i	1.13428	−	1.96464i
$690$	−12.7514	−	17.6242i	−0.485436	−	0.670942i
$691$	−15.7278	−	27.2414i	−0.598314	−	1.03631i	−0.993070	−	0.117524i	$-0.962504\pi$
$691$	−15.7278	−	27.2414i	−0.598314	−	1.03631i	0.394756	−	0.918786i	$-0.370829\pi$
$692$	−14.6864			−0.558292
$693$	−17.8774	−	8.05524i	−0.679107	−	0.305993i
$694$	−60.6274			−2.30138
$695$	8.78569	+	15.2173i	0.333260	+	0.577224i
$696$	3.16195	−	7.06407i	0.119853	−	0.267763i
$697$	22.7704	−	39.4395i	0.862491	−	1.49388i
$698$	−6.49015			−0.245656
$699$	−15.5270	+	34.6887i	−0.587285	+	1.31205i
$700$	11.3275	−	5.03672i	0.428141	−	0.190370i
$701$	−1.08645			−0.0410348			−0.0205174	−	0.999789i	$-0.506531\pi$
$701$	−1.08645			−0.0410348			−0.0205174	+	0.999789i	$0.506531\pi$
$702$	−18.3328	+	83.7921i	−0.691928	+	3.16253i
$703$	5.45100	+	9.44140i	0.205588	+	0.356089i
$704$	10.6450			0.401198
$705$	1.66044	+	2.29496i	0.0625357	+	0.0864333i
$706$	−0.936217	−	1.62158i	−0.0352350	−	0.0610288i
$707$	32.7755	+	23.8373i	1.23265	+	0.896493i
$708$	42.3051	+	58.4717i	1.58992	+	2.19750i
$709$	−14.3400	−	24.8376i	−0.538549	−	0.932795i	−0.998982	−	0.0451005i	$-0.985639\pi$
$709$	−14.3400	−	24.8376i	−0.538549	−	0.932795i	0.460433	−	0.887694i	$-0.347694\pi$
$710$	1.56482	+	2.71035i	0.0587267	+	0.101718i
$711$	−24.5802	−	27.5180i	−0.921828	−	1.03200i
$712$	−10.0295	+	17.3717i	−0.375873	+	0.651031i
$713$	−1.32966	+	2.30305i	−0.0497963	+	0.0862497i
$714$	52.8668	−	30.3486i	1.97849	−	1.13577i
$715$	−7.88583	−	13.6587i	−0.294913	−	0.510805i
$716$	67.8846			2.53697
$717$	11.0892	+	15.3268i	0.414133	+	0.572391i
$718$	−59.7927			−2.23144
$719$	−11.6921	+	20.2512i	−0.436040	+	0.755244i	−0.997380	−	0.0723419i	$-0.976953\pi$
$719$	−11.6921	+	20.2512i	−0.436040	+	0.755244i	0.561340	+	0.827585i	$0.310286\pi$
$720$	−17.1541	−	19.2044i	−0.639295	−	0.715704i
$721$	18.9938	+	13.8140i	0.707367	+	0.514460i
$722$	21.0431	−	36.4477i	0.783143	−	1.35644i
$723$	20.1493	−	2.07734i	0.749361	−	0.0772572i
$724$	−24.9907	+	43.2852i	−0.928773	+	1.60868i
$725$	0.321747	−	0.557282i	0.0119494	−	0.0206969i
$726$	12.8555	+	17.7682i	0.477113	+	0.659438i
$727$	−13.5709	+	23.5056i	−0.503318	+	0.871773i	0.496674	+	0.867937i	$0.334554\pi$
$727$	−13.5709	+	23.5056i	−0.503318	+	0.871773i	−0.999993	+	0.00383592i	$0.998779\pi$
$728$	−12.3170	+	116.641i	−0.456499	+	4.32300i
$729$	22.0309	−	15.6089i	0.815961	−	0.578107i
$730$	16.2927	−	28.2197i	0.603019	−	1.04446i
$731$	38.6323			1.42887
$732$	−2.53992	+	0.261860i	−0.0938783	+	0.00967862i
$733$	−36.2657			−1.33951			−0.669753	−	0.742584i	$-0.733600\pi$
$733$	−36.2657			−1.33951			−0.669753	+	0.742584i	$0.733600\pi$
$734$	0.685244	+	1.18688i	0.0252928	+	0.0438084i
$735$	4.89860	+	11.0907i	0.180688	+	0.409087i
$736$	−20.1719	+	34.9387i	−0.743545	+	1.28786i
$737$	1.46559	−	2.53848i	0.0539857	−	0.0935060i
$738$	21.4778	−	65.2196i	0.790608	−	2.40076i
$739$	−24.8169	−	42.9841i	−0.912903	−	1.58119i	−0.809942	−	0.586510i	$-0.800502\pi$
$739$	−24.8169	−	42.9841i	−0.912903	−	1.58119i	−0.102961	−	0.994685i	$-0.532832\pi$
$740$	−15.4776	−	26.8080i	−0.568967	−	0.985480i
$741$	−18.1512	+	1.87134i	−0.666801	+	0.0687455i
$742$	−58.3039	+	25.9245i	−2.14041	+	0.951718i
$743$	16.3452	+	28.3107i	0.599647	+	1.03862i	0.992873	+	0.119177i	$0.0380257\pi$
$743$	16.3452	+	28.3107i	0.599647	+	1.03862i	−0.393226	+	0.919442i	$0.628641\pi$
$744$	−2.69020	+	6.01014i	−0.0986275	+	0.220343i
$745$	8.04259			0.294658
$746$	−21.2417	−	36.7917i	−0.777713	−	1.34704i
$747$	6.03687	−	18.3316i	0.220878	−	0.670718i
$748$	59.5510			2.17740
$749$	2.11752	−	0.941541i	0.0773724	−	0.0344032i
$750$	−2.62518	−	3.62838i	−0.0958580	−	0.132490i
$751$	25.7330			0.939011			0.469505	−	0.882930i	$-0.344432\pi$
$751$	25.7330			0.939011			0.469505	+	0.882930i	$0.344432\pi$
$752$	7.01876	−	12.1569i	0.255948	−	0.443315i
$753$	−3.42982	+	0.353606i	−0.124990	+	0.0128861i
$754$	5.31116	+	9.19920i	0.193421	+	0.335015i
$755$	12.0429			0.438286
$756$	48.1471	−	42.7933i	1.75109	−	1.55638i
$757$	−43.8620			−1.59419			−0.797096	−	0.603852i	$-0.793632\pi$
$757$	−43.8620			−1.59419			−0.797096	+	0.603852i	$0.793632\pi$
$758$	−4.86841	−	8.43233i	−0.176829	−	0.306276i
$759$	20.6744	−	2.13148i	0.750435	−	0.0773679i
$760$	5.72940	−	9.92361i	0.207827	−	0.359967i
$761$	−2.38547			−0.0864730			−0.0432365	−	0.999065i	$-0.513767\pi$
$761$	−2.38547			−0.0864730			−0.0432365	+	0.999065i	$0.513767\pi$
$762$	34.1498	+	47.2000i	1.23712	+	1.70987i
$763$	3.86319	−	36.5841i	0.139857	−	1.32443i
$764$	62.7603			2.27059
$765$	−10.2817	−	11.5106i	−0.371736	−	0.416165i
$766$	10.2313	+	17.7212i	0.369673	+	0.640293i
$767$	−56.7736			−2.04998
$768$	16.1067	−	35.9838i	0.581200	−	1.29845i
$769$	−3.73404	−	6.46755i	−0.134653	−	0.233226i	0.790812	−	0.612059i	$-0.209659\pi$
$769$	−3.73404	−	6.46755i	−0.134653	−	0.233226i	−0.925465	+	0.378833i	$0.876325\pi$
$770$	−1.77475	+	16.8067i	−0.0639574	+	0.605671i
$771$	−2.91044	+	0.300058i	−0.104817	+	0.0108063i
$772$	−10.6166	−	18.3885i	−0.382101	−	0.661818i
$773$	3.01784	+	5.22705i	0.108544	+	0.188004i	0.915181	−	0.403044i	$-0.132048\pi$
$773$	3.01784	+	5.22705i	0.108544	+	0.188004i	−0.806637	+	0.591048i	$0.798714\pi$
$774$	57.0234	−	11.8842i	2.04966	−	0.427170i
$775$	−0.273744	+	0.474138i	−0.00983317	+	0.0170316i
$776$	38.4576	−	66.6105i	1.38055	−	2.39118i
$777$	26.2561	−	15.0725i	0.941932	−	0.540723i
$778$	−39.9792	−	69.2460i	−1.43332	−	2.48259i
$779$	14.6076			0.523373
$780$	51.5386	−	5.31350i	1.84538	−	0.190254i
$781$	−2.99018			−0.106997
$782$	−32.3066	+	55.9568i	−1.15528	+	2.00101i
$783$	0.714660	−	3.26643i	0.0255399	−	0.116733i
$784$	40.2474	−	44.6116i	1.43741	−	1.59327i
$785$	−1.76403	+	3.05538i	−0.0629608	+	0.109051i
$786$	−5.90691	−	8.16421i	−0.210693	−	0.291208i
$787$	−0.777771	+	1.34714i	−0.0277245	+	0.0480203i	−0.879555	−	0.475798i	$-0.842159\pi$
$787$	−0.777771	+	1.34714i	−0.0277245	+	0.0480203i	0.851830	+	0.523818i	$0.175493\pi$
$788$	−3.81834	+	6.61355i	−0.136023	+	0.235598i
$789$	−39.3089	+	4.05265i	−1.39943	+	0.144278i
$790$	−15.9006	+	27.5407i	−0.565719	+	0.979854i
$791$	1.83774	−	17.4033i	0.0653426	−	0.618788i
$792$	50.3808	−	10.4999i	1.79020	−	0.373096i
$793$	1.00431	−	1.73952i	0.0356643	−	0.0617723i
$794$	−62.7673			−2.22753
$795$	9.46990	+	13.0888i	0.335863	+	0.464211i
$796$	107.585			3.81327
$797$	−25.6596	−	44.4438i	−0.908911	−	1.57428i	−0.815580	−	0.578645i	$-0.803582\pi$
$797$	−25.6596	−	44.4438i	−0.908911	−	1.57428i	−0.0933310	−	0.995635i	$-0.529751\pi$
$798$	16.9092	+	9.81835i	0.598578	+	0.347566i
$799$	4.20686	−	7.28649i	0.148828	−	0.257777i
$800$	−4.15288	+	7.19299i	−0.146826	+	0.254311i
$801$	−2.71070	+	8.23133i	−0.0957779	+	0.290840i
$802$	45.7747	+	79.2840i	1.61636	+	2.79962i
$803$	15.5666	+	26.9622i	0.549335	+	0.951476i
$804$	5.64447	+	7.80146i	0.199065	+	0.275136i
$805$	−10.3932	−	7.55887i	−0.366313	−	0.266415i
$806$	−4.51876	−	7.82672i	−0.159167	−	0.275684i
$807$	5.61943	+	7.76687i	0.197813	+	0.273407i
$808$	−106.366			−3.74193
$809$	3.47119	+	6.01228i	0.122041	+	0.211381i	0.920572	−	0.390572i	$-0.127723\pi$
$809$	3.47119	+	6.01228i	0.122041	+	0.211381i	−0.798532	+	0.601953i	$0.794389\pi$
$810$	−18.7173	−	13.8273i	−0.657658	−	0.485842i
$811$	−24.8086			−0.871147			−0.435573	−	0.900153i	$-0.643454\pi$
$811$	−24.8086			−0.871147			−0.435573	+	0.900153i	$0.643454\pi$
$812$	0.837726	−	7.93318i	0.0293984	−	0.278400i
$813$	−6.19270	+	13.8350i	−0.217187	+	0.485216i
$814$	42.2000			1.47911
$815$	1.15690	−	2.00380i	0.0405243	−	0.0701901i
$816$	−31.2478	+	69.8104i	−1.09389	+	2.44385i
$817$	6.19583	+	10.7315i	0.216765	+	0.375448i
$818$	−56.3250			−1.96936
$819$	5.07202	+	50.4185i	0.177231	+	1.76176i
$820$	−41.4770			−1.44844
$821$	20.1841	+	34.9598i	0.704429	+	1.22011i	0.966897	+	0.255166i	$0.0821301\pi$
$821$	20.1841	+	34.9598i	0.704429	+	1.22011i	−0.262469	+	0.964941i	$0.584537\pi$
$822$	−43.7052	−	60.4069i	−1.52440	−	2.10693i
$823$	0.713665	−	1.23610i	0.0248768	−	0.0430879i	−0.853319	−	0.521389i	$-0.825414\pi$
$823$	0.713665	−	1.23610i	0.0248768	−	0.0430879i	0.878196	+	0.478301i	$0.158747\pi$
$824$	−61.6402			−2.14734
$825$	4.25634	−	0.438818i	0.148187	−	0.0152777i
$826$	49.1997	+	35.7824i	1.71188	+	1.24503i
$827$	55.1650			1.91827			0.959137	−	0.282941i	$-0.0913101\pi$
$827$	55.1650			1.91827			0.959137	+	0.282941i	$0.0913101\pi$
$828$	−21.3567	+	64.8519i	−0.742197	+	2.25376i
$829$	25.1626	+	43.5829i	0.873933	+	1.51370i	0.857896	+	0.513824i	$0.171772\pi$
$829$	25.1626	+	43.5829i	0.873933	+	1.51370i	0.0160370	+	0.999871i	$0.494895\pi$
$830$	−16.6344			−0.577387
$831$	−48.2411	+	4.97353i	−1.67346	+	0.172530i
$832$	−13.7546	−	23.8237i	−0.476856	−	0.825939i
$833$	24.1232	−	26.7390i	0.835819	−	0.926451i
$834$	32.1499	−	71.8259i	1.11326	−	2.48713i
$835$	6.15059	+	10.6531i	0.212850	+	0.368667i
$836$	9.55077	+	16.5424i	0.330320	+	0.572131i
$837$	−0.608036	+	2.77909i	−0.0210168	+	0.0960595i
$838$	−4.20209	+	7.27823i	−0.145159	+	0.251422i
$839$	−6.27310	+	10.8653i	−0.216572	+	0.375113i	−0.953758	−	0.300577i	$-0.902821\pi$
$839$	−6.27310	+	10.8653i	−0.216572	+	0.375113i	0.737186	+	0.675690i	$0.236154\pi$
$840$	−27.5184	−	15.9786i	−0.949474	−	0.551315i
$841$	14.2930	+	24.7561i	0.492861	+	0.853660i
$842$	58.7307			2.02400
$843$	−8.61076	+	19.2372i	−0.296570	+	0.662565i
$844$	−38.4725			−1.32428
$845$	−13.8789	+	24.0390i	−0.477450	+	0.826967i
$846$	3.96804	−	12.0494i	0.136424	−	0.414266i
$847$	10.4781	+	7.62060i	0.360032	+	0.261847i
$848$	40.0298	−	69.3337i	1.37463	−	2.38093i
$849$	−0.744712	+	1.66375i	−0.0255585	+	0.0570999i
$850$	−6.65112	+	11.5201i	−0.228131	+	0.395135i
$851$	−16.0450	+	27.7907i	−0.550014	+	0.952652i
$852$	4.01322	−	8.96589i	0.137491	−	0.307166i
$853$	−6.22697	+	10.7854i	−0.213207	+	0.369286i	−0.952717	−	0.303860i	$-0.901724\pi$
$853$	−6.22697	+	10.7854i	−0.213207	+	0.369286i	0.739509	+	0.673147i	$0.235058\pi$
$854$	−1.96669	+	0.874479i	−0.0672989	+	0.0299240i
$855$	1.54849	−	4.70217i	0.0529574	−	0.160811i
$856$	−3.04108	+	5.26731i	−0.103942	+	0.180033i
$857$	−1.91756			−0.0655027			−0.0327514	−	0.999464i	$-0.510427\pi$
$857$	−1.91756			−0.0655027			−0.0327514	+	0.999464i	$0.510427\pi$
$858$	−28.8570	+	64.4692i	−0.985163	+	2.20094i
$859$	−35.0395			−1.19553			−0.597766	−	0.801671i	$-0.703945\pi$
$859$	−35.0395			−1.19553			−0.597766	+	0.801671i	$0.703945\pi$
$860$	−17.5925	−	30.4711i	−0.599899	−	1.03905i
$861$	0.100329	−	40.5652i	0.00341921	−	1.38246i
$862$	15.7056	−	27.2030i	0.534936	−	0.926536i
$863$	22.3784	−	38.7606i	0.761771	−	1.31943i	−0.180166	−	0.983636i	$-0.557664\pi$
$863$	22.3784	−	38.7606i	0.761771	−	1.31943i	0.941937	−	0.335789i	$-0.109003\pi$
$864$	−9.22431	+	42.1607i	−0.313817	+	1.43434i
$865$	1.56719	+	2.71446i	0.0532861	+	0.0922943i
$866$	15.3056	+	26.5101i	0.520106	+	0.900849i
$867$	−6.69939	+	14.9670i	−0.227523	+	0.508307i
$868$	−0.712741	+	6.74959i	−0.0241920	+	0.229096i
$869$	−15.1921	−	26.3134i	−0.515356	−	0.892622i
$870$	−2.86667	+	0.295547i	−0.0971894	+	0.0100200i
$871$	−7.57489			−0.256665
$872$	48.2754	+	83.6154i	1.63481	+	2.83157i
$873$	10.3940	−	31.5624i	0.351783	−	1.06823i
$874$	−20.7253			−0.701044
$875$	−2.13970	−	1.55618i	−0.0723350	−	0.0526084i
$876$	−101.737	+	10.4889i	−3.43738	+	0.354385i
$877$	−25.4155			−0.858220			−0.429110	−	0.903252i	$-0.641173\pi$
$877$	−25.4155			−0.858220			−0.429110	+	0.903252i	$0.641173\pi$
$878$	−38.5969	+	66.8518i	−1.30258	+	2.25614i
$879$	−19.1542	−	26.4739i	−0.646056	−	0.892943i
$880$	−10.6023	−	18.3637i	−0.357404	−	0.619041i
$881$	−7.62133			−0.256769			−0.128385	−	0.991724i	$-0.540979\pi$
$881$	−7.62133			−0.256769			−0.128385	+	0.991724i	$0.540979\pi$
$882$	27.3816	−	46.8891i	0.921985	−	1.57884i
$883$	−37.5533			−1.26377			−0.631884	−	0.775063i	$-0.717718\pi$
$883$	−37.5533			−1.26377			−0.631884	+	0.775063i	$0.717718\pi$
$884$	−76.9473	−	133.277i	−2.58802	−	4.48258i
$885$	6.29283	−	14.0587i	0.211531	−	0.472580i
$886$	−1.46448	+	2.53656i	−0.0492003	+	0.0852173i
$887$	33.8614			1.13695			0.568477	−	0.822699i	$-0.307533\pi$
$887$	33.8614			1.13695			0.568477	+	0.822699i	$0.307533\pi$
$888$	−32.4624	+	72.5240i	−1.08937	+	2.43375i
$889$	27.8344	+	20.2436i	0.933536	+	0.678950i
$890$	7.46922			0.250369
$891$	20.3828	−	8.88173i	0.682849	−	0.297549i
$892$	8.23599	+	14.2651i	0.275761	+	0.477632i
$893$	2.69878			0.0903111
$894$	−21.1133	−	29.1816i	−0.706133	−	0.975977i
$895$	−7.24402	−	12.5470i	−0.242141	−	0.419400i
$896$	1.51980	−	14.3923i	0.0507729	−	0.480814i
$897$	−31.4842	−	43.5158i	−1.05123	−	1.45295i
$898$	29.7726	+	51.5677i	0.993525	+	1.72084i
$899$	0.176153	+	0.305105i	0.00587502	+	0.0101758i
$900$	−4.39680	+	13.3514i	−0.146560	+	0.445045i
$901$	23.9928	−	41.5567i	0.799316	−	1.38446i
$902$	28.2720	−	48.9685i	0.941354	−	1.63047i
$903$	29.8438	−	17.1320i	0.993139	−	0.570119i
$904$	22.9649	+	39.7763i	0.763800	+	1.32294i
$905$	10.6671			0.354587
$906$	−31.6148	−	43.6962i	−1.05033	−	1.45171i
$907$	−43.3282			−1.43869			−0.719345	−	0.694653i	$-0.755558\pi$
$907$	−43.3282			−1.43869			−0.719345	+	0.694653i	$0.755558\pi$
$908$	−32.3346	+	56.0052i	−1.07306	+	1.85860i
$909$	−44.9869	+	9.37572i	−1.49212	+	0.310973i
$910$	39.9069	−	17.7444i	1.32290	−	0.588220i
$911$	6.17647	−	10.6980i	0.204636	−	0.354439i	−0.745381	−	0.666639i	$-0.767732\pi$
$911$	6.17647	−	10.6980i	0.204636	−	0.354439i	0.950017	+	0.312199i	$0.101066\pi$
$912$	−24.4038	+	2.51597i	−0.808091	+	0.0833122i
$913$	7.94655	−	13.7638i	0.262992	−	0.455516i
$914$	30.6197	−	53.0350i	1.01281	−	1.75424i
$915$	0.319436	+	0.441507i	0.0105602	+	0.0145958i
$916$	−25.8918	+	44.8459i	−0.855489	+	1.48175i
$917$	−4.81453	−	3.50155i	−0.158990	−	0.115631i
$918$	−14.7734	+	67.5232i	−0.487593	+	2.22860i
$919$	−24.8285	+	43.0042i	−0.819017	+	1.41858i	0.0873901	+	0.996174i	$0.472147\pi$
$919$	−24.8285	+	43.0042i	−0.819017	+	1.41858i	−0.906407	+	0.422405i	$0.861186\pi$
$920$	33.7289			1.11201
$921$	−54.1259	+	5.58025i	−1.78351	+	0.183875i
$922$	64.5836			2.12695
$923$	3.86368	+	6.69209i	0.127175	+	0.220273i
$924$	46.0036	−	26.4087i	1.51341	−	0.868783i
$925$	−3.30325	+	5.72139i	−0.108610	+	0.188118i
$926$	8.26208	−	14.3103i	0.271509	−	0.470267i
$927$	−26.0704	+	5.43334i	−0.856265	+	0.178454i
$928$	2.67235	+	4.62865i	0.0877243	+	0.151943i
$929$	16.7303	+	28.9778i	0.548905	+	0.950731i	0.998350	+	0.0574232i	$0.0182884\pi$
$929$	16.7303	+	28.9778i	0.548905	+	0.950731i	−0.449445	+	0.893308i	$0.648378\pi$
$930$	2.43898	−	0.251453i	0.0799773	−	0.00824546i
$931$	11.2966	+	2.41269i	0.370230	+	0.0790726i
$932$	−51.4061	−	89.0379i	−1.68386	−	2.91653i
$933$	12.9598	−	28.9533i	0.424285	−	0.947890i
$934$	93.8388			3.07050
$935$	−6.35473	−	11.0067i	−0.207822	−	0.359958i
$936$	−88.5971	−	99.1862i	−2.89589	−	3.24200i
$937$	−17.1934			−0.561685			−0.280842	−	0.959754i	$-0.590614\pi$
$937$	−17.1934			−0.561685			−0.280842	+	0.959754i	$0.590614\pi$
$938$	6.56436	+	4.77418i	0.214334	+	0.155883i
$939$	−6.51212	−	9.00069i	−0.212515	−	0.293726i
$940$	−7.66292			−0.249937
$941$	1.34774	−	2.33435i	0.0439349	−	0.0760976i	−0.843222	−	0.537566i	$-0.819344\pi$
$941$	1.34774	−	2.33435i	0.0439349	−	0.0760976i	0.887157	+	0.461468i	$0.152677\pi$
$942$	15.7170	−	1.62038i	0.512086	−	0.0527948i
$943$	21.4987	+	37.2369i	0.700095	+	1.21260i
$944$	−76.3307			−2.48435
$945$	−13.0472	−	4.33244i	−0.424426	−	0.140934i
$946$	47.9663			1.55952
$947$	15.6590	+	27.1222i	0.508849	+	0.881352i	0.999947	+	0.0102481i	$0.00326213\pi$
$947$	15.6590	+	27.1222i	0.508849	+	0.881352i	−0.491099	+	0.871104i	$0.663405\pi$
$948$	99.2892	−	10.2365i	3.22476	−	0.332465i
$949$	40.2281	−	69.6770i	1.30586	−	2.26181i
$950$	−4.26681			−0.138434
$951$	−9.62735	−	13.3064i	−0.312188	−	0.431489i
$952$	−9.92557	+	93.9942i	−0.321690	+	3.04637i
$953$	35.9575			1.16478			0.582389	−	0.812910i	$-0.302118\pi$
$953$	35.9575			1.16478			0.582389	+	0.812910i	$0.302118\pi$
$954$	22.6308	−	68.7208i	0.732699	−	2.22492i
$955$	−6.69720	−	11.5999i	−0.216716	−	0.375364i
$956$	−51.1766			−1.65517
$957$	1.12492	−	2.51317i	0.0363635	−	0.0812393i
$958$	−26.6686	−	46.1914i	−0.861624	−	1.49238i
$959$	−35.6227	−	25.9080i	−1.15032	−	0.836612i
$960$	7.42400	−	0.765396i	0.239609	−	0.0247031i
$961$	15.3501	+	26.5872i	0.495165	+	0.857652i
$962$	−54.5276	−	94.4445i	−1.75804	−	3.04501i
$963$	−0.821918	+	2.49584i	−0.0264859	+	0.0804273i
$964$	−27.3985	+	47.4557i	−0.882447	+	1.52844i
$965$	−2.26582	+	3.92451i	−0.0729392	+	0.126334i
$966$	−0.142347	+	57.5539i	−0.00457995	+	1.85177i
$967$	4.02540	+	6.97220i	0.129448	+	0.224211i	0.923463	−	0.383688i	$-0.125346\pi$
$967$	4.02540	+	6.97220i	0.129448	+	0.224211i	−0.794015	+	0.607898i	$0.792013\pi$
$968$	−34.0044			−1.09294
$969$	−14.6270	+	1.50801i	−0.469887	+	0.0484441i
$970$	−28.6402			−0.919582
$971$	11.8256	−	20.4825i	0.379501	−	0.657316i	−0.611488	−	0.791253i	$-0.709429\pi$
$971$	11.8256	−	20.4825i	0.379501	−	0.657316i	0.990990	+	0.133938i	$0.0427622\pi$
$972$	−0.725011	+	73.0371i	−0.0232547	+	2.34267i
$973$	4.88204	−	46.2325i	0.156511	−	1.48214i
$974$	−11.4202	+	19.7804i	−0.365928	+	0.633805i
$975$	−6.48180	−	8.95879i	−0.207584	−	0.286911i
$976$	1.35028	−	2.33875i	0.0432213	−	0.0748615i
$977$	5.63008	−	9.75159i	0.180122	−	0.311981i	−0.761800	−	0.647813i	$-0.775684\pi$
$977$	5.63008	−	9.75159i	0.180122	−	0.311981i	0.941922	+	0.335832i	$0.109017\pi$
$978$	−10.3076	+	1.06269i	−0.329601	+	0.0339810i
$979$	−3.56819	+	6.18029i	−0.114040	+	0.197523i
$980$	−32.0755	−	6.85060i	−1.02462	−	0.218834i
$981$	27.7882	+	31.1094i	0.887209	+	0.993248i
$982$	22.5427	−	39.0451i	0.719367	−	1.24598i
$983$	−2.37956			−0.0758962			−0.0379481	−	0.999280i	$-0.512082\pi$
$983$	−2.37956			−0.0758962			−0.0379481	+	0.999280i	$0.512082\pi$
$984$	62.4080	+	86.2568i	1.98949	+	2.74977i
$985$	1.62983			0.0519307
$986$	4.27995	+	7.41310i	0.136302	+	0.236081i
$987$	0.0185359	−	7.49446i	0.000590005	−	0.238551i
$988$	24.6815	−	42.7497i	0.785224	−	1.36005i
$989$	−18.2374	+	31.5881i	−0.579915	+	1.00444i
$990$	−12.7659	−	14.2916i	−0.405726	−	0.454218i
$991$	−17.5174	−	30.3409i	−0.556457	−	0.963812i	−0.997789	−	0.0664679i	$-0.978827\pi$
$991$	−17.5174	−	30.3409i	−0.556457	−	0.963812i	0.441331	−	0.897344i	$-0.354506\pi$
$992$	−2.27365	−	3.93808i	−0.0721884	−	0.125034i
$993$	−13.2047	−	18.2508i	−0.419038	−	0.579171i
$994$	0.869541	−	8.23447i	0.0275802	−	0.261182i
$995$	−11.4805	−	19.8849i	−0.363957	−	0.630392i
$996$	30.6048	+	42.3002i	0.969749	+	1.34033i
$997$	−31.3795			−0.993797			−0.496899	−	0.867809i	$-0.665528\pi$
$997$	−31.3795			−0.993797			−0.496899	+	0.867809i	$0.665528\pi$
$998$	−39.8402	−	69.0053i	−1.26112	−	2.18432i
$999$	−7.33712	+	33.5351i	−0.232136	+	1.06100i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.c.16.2	✓	36
3.2	odd	2		945.2.k.c.856.17		36
7.4	even	3		315.2.l.c.151.17	yes	36
9.4	even	3		315.2.l.c.121.17	yes	36
9.5	odd	6		945.2.l.c.226.2		36
21.11	odd	6		945.2.l.c.46.2		36
63.4	even	3	inner	315.2.k.c.256.2	yes	36
63.32	odd	6		945.2.k.c.361.17		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.2	✓	36	1.1	even	1	trivial
315.2.k.c.256.2	yes	36	63.4	even	3	inner
315.2.l.c.121.17	yes	36	9.4	even	3
315.2.l.c.151.17	yes	36	7.4	even	3
945.2.k.c.361.17		36	63.32	odd	6
945.2.k.c.856.17		36	3.2	odd	2
945.2.l.c.46.2		36	21.11	odd	6
945.2.l.c.226.2		36	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29282 - 2.23923i) q^{2} +(1.72292 - 0.177629i) q^{3} +(-2.34278 + 4.05782i) q^{4} +1.00000 q^{5} +(-2.62518 - 3.62838i) q^{6} +(-2.13970 - 1.55618i) q^{7} +6.94392 q^{8} +(2.93690 - 0.612079i) q^{9} +O(q^{10})\)	\(q+(-1.29282 - 2.23923i) q^{2} +(1.72292 - 0.177629i) q^{3} +(-2.34278 + 4.05782i) q^{4} +1.00000 q^{5} +(-2.62518 - 3.62838i) q^{6} +(-2.13970 - 1.55618i) q^{7} +6.94392 q^{8} +(2.93690 - 0.612079i) q^{9} +(-1.29282 - 2.23923i) q^{10} +2.47043 q^{11} +(-3.31564 + 7.40743i) q^{12} +(-3.19209 - 5.52887i) q^{13} +(-0.718397 + 6.80315i) q^{14} +(1.72292 - 0.177629i) q^{15} +(-4.29169 - 7.43343i) q^{16} +(-2.57232 - 4.45539i) q^{17} +(-5.16748 - 5.78509i) q^{18} +(0.825096 - 1.42911i) q^{19} +(-2.34278 + 4.05782i) q^{20} +(-3.96295 - 2.30110i) q^{21} +(-3.19382 - 5.53186i) q^{22} +4.85733 q^{23} +(11.9638 - 1.23344i) q^{24} +1.00000 q^{25} +(-8.25363 + 14.2957i) q^{26} +(4.95131 - 1.57624i) q^{27} +(11.3275 - 5.03672i) q^{28} +(0.321747 - 0.557282i) q^{29} +(-2.62518 - 3.62838i) q^{30} +(-0.273744 + 0.474138i) q^{31} +(-4.15288 + 7.19299i) q^{32} +(4.25634 - 0.438818i) q^{33} +(-6.65112 + 11.5201i) q^{34} +(-2.13970 - 1.55618i) q^{35} +(-4.39680 + 13.3514i) q^{36} +(-3.30325 + 5.72139i) q^{37} -4.26681 q^{38} +(-6.48180 - 8.95879i) q^{39} +6.94392 q^{40} +(4.42604 + 7.66613i) q^{41} +(-0.0293057 + 11.8489i) q^{42} +(-3.75461 + 6.50318i) q^{43} +(-5.78767 + 10.0245i) q^{44} +(2.93690 - 0.612079i) q^{45} +(-6.27966 - 10.8767i) q^{46} +(0.817715 + 1.41632i) q^{47} +(-8.71462 - 12.0449i) q^{48} +(2.15662 + 6.65950i) q^{49} +(-1.29282 - 2.23923i) q^{50} +(-5.22331 - 7.21936i) q^{51} +29.9135 q^{52} +(4.66364 + 8.07767i) q^{53} +(-9.93074 - 9.04935i) q^{54} +2.47043 q^{55} +(-14.8579 - 10.8060i) q^{56} +(1.16772 - 2.60880i) q^{57} -1.66385 q^{58} +(4.44642 - 7.70143i) q^{59} +(-3.31564 + 7.40743i) q^{60} +(0.157313 + 0.272474i) q^{61} +1.41561 q^{62} +(-7.23658 - 3.26067i) q^{63} +4.30897 q^{64} +(-3.19209 - 5.52887i) q^{65} +(-6.48531 - 8.96363i) q^{66} +(0.593254 - 1.02755i) q^{67} +24.1056 q^{68} +(8.36878 - 0.862800i) q^{69} +(-0.718397 + 6.80315i) q^{70} -1.21039 q^{71} +(20.3936 - 4.25023i) q^{72} +(6.30120 + 10.9140i) q^{73} +17.0821 q^{74} +(1.72292 - 0.177629i) q^{75} +(3.86604 + 6.69618i) q^{76} +(-5.28597 - 3.84442i) q^{77} +(-11.6810 + 26.0964i) q^{78} +(-6.14958 - 10.6514i) q^{79} +(-4.29169 - 7.43343i) q^{80} +(8.25072 - 3.59522i) q^{81} +(11.4442 - 19.8219i) q^{82} +(3.21667 - 5.57144i) q^{83} +(18.6218 - 10.6900i) q^{84} +(-2.57232 - 4.45539i) q^{85} +19.4162 q^{86} +(0.455355 - 1.01730i) q^{87} +17.1544 q^{88} +(-1.44436 + 2.50171i) q^{89} +(-5.16748 - 5.78509i) q^{90} +(-1.77379 + 16.7976i) q^{91} +(-11.3797 + 19.7101i) q^{92} +(-0.387418 + 0.865526i) q^{93} +(2.11432 - 3.66211i) q^{94} +(0.825096 - 1.42911i) q^{95} +(-5.87739 + 13.1306i) q^{96} +(5.53831 - 9.59263i) q^{97} +(12.1241 - 13.4387i) q^{98} +(7.25538 - 1.51210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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