LMFDB - Embedded newform 315.2.l.c.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(121,315)]

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([2, 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("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.l (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			151.1
Character	$\chi$	$=$	315.151
Dual form			315.2.l.c.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69765 q^{2} +(-0.273945 + 1.71025i) q^{3} +5.27730 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.739006 - 4.61365i) q^{6} +(-0.230272 + 2.63571i) q^{7} -8.84100 q^{8} +(-2.84991 - 0.937027i) q^{9} +O(q^{10})$	\(q-2.69765 q^{2} +(-0.273945 + 1.71025i) q^{3} +5.27730 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.739006 - 4.61365i) q^{6} +(-0.230272 + 2.63571i) q^{7} -8.84100 q^{8} +(-2.84991 - 0.937027i) q^{9} +(1.34882 - 2.33623i) q^{10} +(1.96183 + 3.39799i) q^{11} +(-1.44569 + 9.02550i) q^{12} +(0.993996 + 1.72165i) q^{13} +(0.621192 - 7.11022i) q^{14} +(-1.34415 - 1.09237i) q^{15} +13.2953 q^{16} +(2.23716 - 3.87488i) q^{17} +(7.68805 + 2.52777i) q^{18} +(0.0804749 + 0.139387i) q^{19} +(-2.63865 + 4.57028i) q^{20} +(-4.44464 - 1.11586i) q^{21} +(-5.29232 - 9.16657i) q^{22} +(-3.11185 + 5.38989i) q^{23} +(2.42194 - 15.1203i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.68145 - 4.64441i) q^{26} +(2.38327 - 4.61736i) q^{27} +(-1.21521 + 13.9094i) q^{28} +(-0.384982 + 0.666809i) q^{29} +(3.62604 + 2.94682i) q^{30} -8.03014 q^{31} -18.1840 q^{32} +(-6.34884 + 2.42436i) q^{33} +(-6.03507 + 10.4530i) q^{34} +(-2.16746 - 1.51728i) q^{35} +(-15.0398 - 4.94497i) q^{36} +(-3.50272 - 6.06689i) q^{37} +(-0.217093 - 0.376016i) q^{38} +(-3.21675 + 1.22834i) q^{39} +(4.42050 - 7.65653i) q^{40} +(1.42108 + 2.46138i) q^{41} +(11.9901 + 3.01020i) q^{42} +(-1.53771 + 2.66340i) q^{43} +(10.3532 + 17.9322i) q^{44} +(2.23644 - 1.99958i) q^{45} +(8.39468 - 14.5400i) q^{46} -5.67661 q^{47} +(-3.64218 + 22.7383i) q^{48} +(-6.89395 - 1.21386i) q^{49} +(1.34882 + 2.33623i) q^{50} +(6.01415 + 4.88760i) q^{51} +(5.24562 + 9.08567i) q^{52} +(5.50814 - 9.54037i) q^{53} +(-6.42922 + 12.4560i) q^{54} -3.92366 q^{55} +(2.03583 - 23.3023i) q^{56} +(-0.260432 + 0.0994480i) q^{57} +(1.03855 - 1.79882i) q^{58} -3.36563 q^{59} +(-7.09347 - 5.76475i) q^{60} -6.89632 q^{61} +21.6625 q^{62} +(3.12599 - 7.29577i) q^{63} +22.4635 q^{64} -1.98799 q^{65} +(17.1269 - 6.54006i) q^{66} +10.0898 q^{67} +(11.8062 - 20.4489i) q^{68} +(-8.36558 - 6.79858i) q^{69} +(5.84704 + 4.09308i) q^{70} +6.78242 q^{71} +(25.1961 + 8.28426i) q^{72} +(-7.20971 + 12.4876i) q^{73} +(9.44910 + 16.3663i) q^{74} +(1.61809 - 0.617882i) q^{75} +(0.424690 + 0.735585i) q^{76} +(-9.40787 + 4.38835i) q^{77} +(8.67767 - 3.31364i) q^{78} +11.3183 q^{79} +(-6.64765 + 11.5141i) q^{80} +(7.24396 + 5.34088i) q^{81} +(-3.83357 - 6.63994i) q^{82} +(-2.40898 + 4.17248i) q^{83} +(-23.4557 - 5.88873i) q^{84} +(2.23716 + 3.87488i) q^{85} +(4.14821 - 7.18491i) q^{86} +(-1.03495 - 0.841085i) q^{87} +(-17.3445 - 30.0416i) q^{88} +(5.16019 + 8.93770i) q^{89} +(-6.03314 + 5.39416i) q^{90} +(-4.76667 + 2.22344i) q^{91} +(-16.4222 + 28.4441i) q^{92} +(2.19981 - 13.7335i) q^{93} +15.3135 q^{94} -0.160950 q^{95} +(4.98142 - 31.0993i) q^{96} +(6.51896 - 11.2912i) q^{97} +(18.5974 + 3.27456i) q^{98} +(-2.40703 - 11.5222i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) $ 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.69765			−1.90752			−0.953762	−	0.300562i	$-0.902826\pi$
$2$	−2.69765			−1.90752			−0.953762	+	0.300562i	$0.902826\pi$
$3$	−0.273945	+	1.71025i	−0.158162	+	0.987413i
$3$	−0.273945	+	1.71025i	−0.158162	+	0.987413i
$4$	5.27730			2.63865
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	0.739006	−	4.61365i	0.301698	−	1.88352i
$7$	−0.230272	+	2.63571i	−0.0870345	+	0.996205i
$7$	−0.230272	+	2.63571i	−0.0870345	+	0.996205i
$8$	−8.84100			−3.12577
$9$	−2.84991	−	0.937027i	−0.949970	−	0.312342i
$10$	1.34882	−	2.33623i	0.426536	−	0.738781i
$11$	1.96183	+	3.39799i	0.591514	+	1.02453i	0.994029	+	0.109118i	$0.0348027\pi$
$11$	1.96183	+	3.39799i	0.591514	+	1.02453i	−0.402515	+	0.915413i	$0.631864\pi$
$12$	−1.44569	+	9.02550i	−0.417334	+	2.60544i
$13$	0.993996	+	1.72165i	0.275685	+	0.477500i	0.970308	−	0.241874i	$-0.0777620\pi$
$13$	0.993996	+	1.72165i	0.275685	+	0.477500i	−0.694623	+	0.719374i	$0.744429\pi$
$14$	0.621192	−	7.11022i	0.166020	−	1.90029i
$15$	−1.34415	−	1.09237i	−0.347057	−	0.282048i
$16$	13.2953			3.32383
$17$	2.23716	−	3.87488i	0.542591	−	0.939795i	−0.456163	−	0.889896i	$-0.650777\pi$
$17$	2.23716	−	3.87488i	0.542591	−	0.939795i	0.998754	−	0.0498992i	$-0.0158900\pi$
$18$	7.68805	+	2.52777i	1.81209	+	0.595801i
$19$	0.0804749	+	0.139387i	0.0184622	+	0.0319775i	0.875109	−	0.483926i	$-0.160790\pi$
$19$	0.0804749	+	0.139387i	0.0184622	+	0.0319775i	−0.856647	+	0.515904i	$0.827456\pi$
$20$	−2.63865	+	4.57028i	−0.590020	+	1.02195i
$21$	−4.44464	−	1.11586i	−0.969901	−	0.243501i
$22$	−5.29232	−	9.16657i	−1.12833	−	1.95432i
$23$	−3.11185	+	5.38989i	−0.648866	+	1.12387i	0.334528	+	0.942386i	$0.391423\pi$
$23$	−3.11185	+	5.38989i	−0.648866	+	1.12387i	−0.983394	+	0.181483i	$0.941910\pi$
$24$	2.42194	−	15.1203i	0.494377	−	3.08642i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.68145	−	4.64441i	−0.525876	−	0.910843i
$27$	2.38327	−	4.61736i	0.458660	−	0.888612i
$28$	−1.21521	+	13.9094i	−0.229654	+	2.62864i
$29$	−0.384982	+	0.666809i	−0.0714894	+	0.123823i	−0.899554	−	0.436809i	$-0.856109\pi$
$29$	−0.384982	+	0.666809i	−0.0714894	+	0.123823i	0.828065	+	0.560632i	$0.189442\pi$
$30$	3.62604	+	2.94682i	0.662021	+	0.538014i
$31$	−8.03014			−1.44225			−0.721127	−	0.692802i	$-0.756376\pi$
$31$	−8.03014			−1.44225			−0.721127	+	0.692802i	$0.756376\pi$
$32$	−18.1840			−3.21452
$33$	−6.34884	+	2.42436i	−1.10519	+	0.422026i
$34$	−6.03507	+	10.4530i	−1.03501	+	1.79268i
$35$	−2.16746	−	1.51728i	−0.366367	−	0.256467i
$36$	−15.0398	−	4.94497i	−2.50664	−	0.824162i
$37$	−3.50272	−	6.06689i	−0.575843	−	0.997390i	−0.995949	−	0.0899150i	$-0.971340\pi$
$37$	−3.50272	−	6.06689i	−0.575843	−	0.997390i	0.420106	−	0.907475i	$-0.361993\pi$
$38$	−0.217093	−	0.376016i	−0.0352171	−	0.0609978i
$39$	−3.21675	+	1.22834i	−0.515093	+	0.196693i
$40$	4.42050	−	7.65653i	0.698943	−	1.21060i
$41$	1.42108	+	2.46138i	0.221935	+	0.384404i	0.955396	−	0.295329i	$-0.0954292\pi$
$41$	1.42108	+	2.46138i	0.221935	+	0.384404i	−0.733460	+	0.679732i	$0.762096\pi$
$42$	11.9901	+	3.01020i	1.85011	+	0.464484i
$43$	−1.53771	+	2.66340i	−0.234499	+	0.406165i	−0.959127	−	0.282976i	$-0.908678\pi$
$43$	−1.53771	+	2.66340i	−0.234499	+	0.406165i	0.724628	+	0.689140i	$0.242012\pi$
$44$	10.3532	+	17.9322i	1.56080	+	2.70338i
$45$	2.23644	−	1.99958i	0.333389	−	0.298080i
$46$	8.39468	−	14.5400i	1.23773	−	2.14381i
$47$	−5.67661			−0.828018			−0.414009	−	0.910273i	$-0.635872\pi$
$47$	−5.67661			−0.828018			−0.414009	+	0.910273i	$0.635872\pi$
$48$	−3.64218	+	22.7383i	−0.525703	+	3.28199i
$49$	−6.89395	−	1.21386i	−0.984850	−	0.173408i
$50$	1.34882	+	2.33623i	0.190752	+	0.330393i
$51$	6.01415	+	4.88760i	0.842149	+	0.684402i
$52$	5.24562	+	9.08567i	0.727436	+	1.25996i
$53$	5.50814	−	9.54037i	0.756601	−	1.31047i	−0.187974	−	0.982174i	$-0.560192\pi$
$53$	5.50814	−	9.54037i	0.756601	−	1.31047i	0.944575	−	0.328297i	$-0.106475\pi$
$54$	−6.42922	+	12.4560i	−0.874905	+	1.69505i
$55$	−3.92366			−0.529066
$56$	2.03583	−	23.3023i	0.272050	−	3.11391i
$57$	−0.260432	+	0.0994480i	−0.0344950	+	0.0131722i
$58$	1.03855	−	1.79882i	0.136368	−	0.236196i
$59$	−3.36563			−0.438167			−0.219084	−	0.975706i	$-0.570307\pi$
$59$	−3.36563			−0.438167			−0.219084	+	0.975706i	$0.570307\pi$
$60$	−7.09347	−	5.76475i	−0.915763	−	0.744227i
$61$	−6.89632			−0.882983			−0.441492	−	0.897265i	$-0.645550\pi$
$61$	−6.89632			−0.882983			−0.441492	+	0.897265i	$0.645550\pi$
$62$	21.6625			2.75114
$63$	3.12599	−	7.29577i	0.393837	−	0.919180i
$64$	22.4635			2.80794
$65$	−1.98799			−0.246580
$66$	17.1269	−	6.54006i	2.10818	−	0.805026i
$67$	10.0898			1.23266			0.616330	−	0.787488i	$-0.288619\pi$
$67$	10.0898			1.23266			0.616330	+	0.787488i	$0.288619\pi$
$68$	11.8062	−	20.4489i	1.43171	−	2.47979i
$69$	−8.36558	−	6.79858i	−1.00710	−	0.818452i
$70$	5.84704	+	4.09308i	0.698854	+	0.489216i
$71$	6.78242			0.804925			0.402463	−	0.915436i	$-0.368154\pi$
$71$	6.78242			0.804925			0.402463	+	0.915436i	$0.368154\pi$
$72$	25.1961	+	8.28426i	2.96938	+	0.976309i
$73$	−7.20971	+	12.4876i	−0.843833	+	1.46156i	0.0427985	+	0.999084i	$0.486373\pi$
$73$	−7.20971	+	12.4876i	−0.843833	+	1.46156i	−0.886631	+	0.462477i	$0.846961\pi$
$74$	9.44910	+	16.3663i	1.09844	+	1.90255i
$75$	1.61809	−	0.617882i	0.186841	−	0.0713469i
$76$	0.424690	+	0.735585i	0.0487153	+	0.0843774i
$77$	−9.40787	+	4.38835i	−1.07213	+	0.500099i
$78$	8.67767	−	3.31364i	0.982552	−	0.375196i
$79$	11.3183			1.27341			0.636703	−	0.771109i	$-0.280298\pi$
$79$	11.3183			1.27341			0.636703	+	0.771109i	$0.280298\pi$
$80$	−6.64765	+	11.5141i	−0.743230	+	1.28731i
$81$	7.24396	+	5.34088i	0.804884	+	0.593432i
$82$	−3.83357	−	6.63994i	−0.423347	−	0.733259i
$83$	−2.40898	+	4.17248i	−0.264420	+	0.457989i	−0.967412	−	0.253209i	$-0.918514\pi$
$83$	−2.40898	+	4.17248i	−0.264420	+	0.457989i	0.702991	+	0.711198i	$0.251847\pi$
$84$	−23.4557	−	5.88873i	−2.55923	−	0.642514i
$85$	2.23716	+	3.87488i	0.242654	+	0.420289i
$86$	4.14821	−	7.18491i	0.447313	−	0.774769i
$87$	−1.03495	−	0.841085i	−0.110958	−	0.0901737i
$88$	−17.3445	−	30.0416i	−1.84893	−	3.20245i
$89$	5.16019	+	8.93770i	0.546979	+	0.947395i	0.998480	+	0.0551241i	$0.0175554\pi$
$89$	5.16019	+	8.93770i	0.546979	+	0.947395i	−0.451501	+	0.892271i	$0.649111\pi$
$90$	−6.03314	+	5.39416i	−0.635948	+	0.568595i
$91$	−4.76667	+	2.22344i	−0.499682	+	0.233080i
$92$	−16.4222	+	28.4441i	−1.71213	+	2.96550i
$93$	2.19981	−	13.7335i	0.228110	−	1.42410i
$94$	15.3135			1.57947
$95$	−0.160950			−0.0165131
$96$	4.98142	−	31.0993i	0.508414	−	3.17405i
$97$	6.51896	−	11.2912i	0.661900	−	1.14644i	−0.318216	−	0.948018i	$-0.603084\pi$
$97$	6.51896	−	11.2912i	0.661900	−	1.14644i	0.980116	−	0.198426i	$-0.0635828\pi$
$98$	18.5974	+	3.27456i	1.87863	+	0.330781i
$99$	−2.40703	−	11.5222i	−0.241915	−	1.15803i
$100$	−2.63865	−	4.57028i	−0.263865	−	0.457028i
$101$	0.964868	+	1.67120i	0.0960079	+	0.166291i	0.910029	−	0.414545i	$-0.136059\pi$
$101$	0.964868	+	1.67120i	0.0960079	+	0.166291i	−0.814021	+	0.580836i	$0.802726\pi$
$102$	−16.2240	−	13.1850i	−1.60642	−	1.30551i
$103$	−0.772287	+	1.33764i	−0.0760957	+	0.131802i	−0.901562	−	0.432649i	$-0.857579\pi$
$103$	−0.772287	+	1.33764i	−0.0760957	+	0.131802i	0.825467	+	0.564451i	$0.190912\pi$
$104$	−8.78792	−	15.2211i	−0.861727	−	1.49255i
$105$	3.18869	−	3.29124i	0.311184	−	0.321192i
$106$	−14.8590	+	25.7366i	−1.44323	+	2.49976i
$107$	−0.350836	−	0.607665i	−0.0339166	−	0.0587452i	0.848569	−	0.529085i	$-0.177465\pi$
$107$	−0.350836	−	0.607665i	−0.0339166	−	0.0587452i	−0.882485	+	0.470340i	$0.844131\pi$
$108$	12.5772	−	24.3672i	1.21024	−	2.34474i
$109$	−6.34253	+	10.9856i	−0.607504	+	1.05223i	0.384146	+	0.923272i	$0.374496\pi$
$109$	−6.34253	+	10.9856i	−0.607504	+	1.05223i	−0.991650	+	0.128956i	$0.958837\pi$
$110$	10.5846			1.00921
$111$	11.3354	−	4.32853i	1.07591	−	0.410846i
$112$	−3.06153	+	35.0426i	−0.289288	+	3.31121i
$113$	3.27999	+	5.68110i	0.308555	+	0.534433i	0.978047	−	0.208387i	$-0.0668212\pi$
$113$	3.27999	+	5.68110i	0.308555	+	0.534433i	−0.669491	+	0.742820i	$0.733488\pi$
$114$	0.702553	−	0.268276i	0.0658001	−	0.0251263i
$115$	−3.11185	−	5.38989i	−0.290182	−	0.502610i
$116$	−2.03167	+	3.51895i	−0.188636	+	0.326726i
$117$	−1.21956	−	5.83795i	−0.112749	−	0.539719i
$118$	9.07927			0.835815
$119$	9.69790	+	6.78878i	0.889005	+	0.622327i
$120$	11.8836	+	9.65763i	1.08482	+	0.881617i
$121$	−2.19754	+	3.80626i	−0.199777	+	0.346023i
$122$	18.6038			1.68431
$123$	−4.59888	+	1.75612i	−0.414667	+	0.158344i
$124$	−42.3774			−3.80561
$125$	1.00000			0.0894427
$126$	−8.43281	+	19.6814i	−0.751254	+	1.75336i
$127$	6.28822			0.557989			0.278994	−	0.960293i	$-0.409999\pi$
$127$	6.28822			0.557989			0.278994	+	0.960293i	$0.409999\pi$
$128$	−24.2306			−2.14170
$129$	−4.13383	−	3.35950i	−0.363963	−	0.295787i
$130$	5.36290			0.470358
$131$	4.83369	−	8.37220i	0.422321	−	0.731482i	−0.573845	−	0.818964i	$-0.694549\pi$
$131$	4.83369	−	8.37220i	0.422321	−	0.731482i	0.996166	+	0.0874820i	$0.0278820\pi$
$132$	−33.5047	+	12.7941i	−2.91621	+	1.11358i
$133$	−0.385914	+	0.180012i	−0.0334630	+	0.0156090i
$134$	−27.2186			−2.35133
$135$	2.80712	+	4.37265i	0.241598	+	0.376338i
$136$	−19.7787	+	34.2578i	−1.69601	+	2.93758i
$137$	1.64582	+	2.85065i	0.140612	+	0.243547i	0.927727	−	0.373259i	$-0.121760\pi$
$137$	1.64582	+	2.85065i	0.140612	+	0.243547i	−0.787115	+	0.616806i	$0.788426\pi$
$138$	22.5674	+	18.3402i	1.92106	+	1.56122i
$139$	5.50800	+	9.54013i	0.467182	+	0.809183i	0.999297	−	0.0374890i	$-0.0119359\pi$
$139$	5.50800	+	9.54013i	0.467182	+	0.809183i	−0.532115	+	0.846672i	$0.678603\pi$
$140$	−11.4383	−	8.00713i	−0.966715	−	0.676726i
$141$	1.55508	−	9.70842i	0.130961	−	0.817596i
$142$	−18.2966			−1.53542
$143$	−3.90010	+	6.75517i	−0.326143	+	0.564896i
$144$	−37.8904	−	12.4581i	−3.15753	−	1.03817i
$145$	−0.384982	−	0.666809i	−0.0319710	−	0.0553755i
$146$	19.4493	−	33.6871i	1.60963	−	2.78796i
$147$	3.96456	−	11.4578i	0.326992	−	0.945027i
$148$	−18.4849	−	32.0168i	−1.51945	−	2.63176i
$149$	−8.10505	+	14.0384i	−0.663992	+	1.15007i	0.315566	+	0.948904i	$0.397806\pi$
$149$	−8.10505	+	14.0384i	−0.663992	+	1.15007i	−0.979558	+	0.201164i	$0.935528\pi$
$150$	−4.36504	+	1.66683i	−0.356404	+	0.136096i
$151$	9.58267	+	16.5977i	0.779827	+	1.35070i	0.932041	+	0.362352i	$0.118026\pi$
$151$	9.58267	+	16.5977i	0.779827	+	1.35070i	−0.152215	+	0.988347i	$0.548641\pi$
$152$	−0.711479	−	1.23232i	−0.0577086	−	0.0999542i
$153$	−10.0066	+	8.94676i	−0.808983	+	0.723303i
$154$	25.3791	−	11.8382i	2.04511	−	0.953952i
$155$	4.01507	−	6.95430i	0.322498	−	0.558583i
$156$	−16.9758	+	6.48234i	−1.35915	+	0.519003i
$157$	−7.21070			−0.575477			−0.287738	−	0.957709i	$-0.592903\pi$
$157$	−7.21070			−0.575477			−0.287738	+	0.957709i	$0.592903\pi$
$158$	−30.5327			−2.42905
$159$	14.8075	+	12.0338i	1.17431	+	0.954344i
$160$	9.09202	−	15.7478i	0.718787	−	1.24498i
$161$	−13.4896	−	9.44309i	−1.06313	−	0.744219i
$162$	−19.5417	−	14.4078i	−1.53534	−	1.13199i
$163$	4.40268	+	7.62567i	0.344845	+	0.597288i	0.985326	−	0.170686i	$-0.0545983\pi$
$163$	4.40268	+	7.62567i	0.344845	+	0.597288i	−0.640481	+	0.767974i	$0.721265\pi$
$164$	7.49947	+	12.9895i	0.585610	+	1.01431i
$165$	1.07486	−	6.71043i	0.0836781	−	0.522407i
$166$	6.49858	−	11.2559i	0.504388	−	0.873626i
$167$	0.470408	+	0.814771i	0.0364013	+	0.0630488i	0.883652	−	0.468144i	$-0.155077\pi$
$167$	0.470408	+	0.814771i	0.0364013	+	0.0630488i	−0.847251	+	0.531193i	$0.821744\pi$
$168$	39.2951	+	9.86533i	3.03168	+	0.761127i
$169$	4.52394	−	7.83570i	0.347996	−	0.602746i
$170$	−6.03507	−	10.4530i	−0.462869	−	0.801712i
$171$	−0.0987371	−	0.472646i	−0.00755061	−	0.0361442i
$172$	−8.11498	+	14.0556i	−0.618762	+	1.07173i
$173$	−9.52486			−0.724162			−0.362081	−	0.932147i	$-0.617934\pi$
$173$	−9.52486			−0.724162			−0.362081	+	0.932147i	$0.617934\pi$
$174$	2.79192	+	2.26895i	0.211655	+	0.172009i
$175$	2.39773	−	1.11843i	0.181251	−	0.0845457i
$176$	26.0831	+	45.1773i	1.96609	+	3.40537i
$177$	0.921995	−	5.75606i	0.0693014	−	0.432652i
$178$	−13.9204	−	24.1108i	−1.04338	−	1.80718i
$179$	11.9714	−	20.7351i	0.894784	−	1.54981i	0.0607130	−	0.998155i	$-0.480663\pi$
$179$	11.9714	−	20.7351i	0.894784	−	1.54981i	0.834071	−	0.551657i	$-0.186004\pi$
$180$	11.8024	−	10.5524i	0.879698	−	0.786528i
$181$	−2.51843			−0.187193			−0.0935967	−	0.995610i	$-0.529836\pi$
$181$	−2.51843			−0.187193			−0.0935967	+	0.995610i	$0.529836\pi$
$182$	12.8588	−	5.99805i	0.953156	−	0.444605i
$183$	1.88921	−	11.7944i	0.139654	−	0.871869i
$184$	27.5119	−	47.6520i	2.02820	−	3.51295i
$185$	7.00544			0.515050
$186$	−5.93432	+	37.0482i	−0.435125	+	2.71651i
$187$	17.5557			1.28380
$188$	−29.9572			−2.18485
$189$	11.6212	+	7.34485i	0.845321	+	0.534259i
$190$	0.434186			0.0314991
$191$	−9.41147			−0.680990			−0.340495	−	0.940246i	$-0.610595\pi$
$191$	−9.41147			−0.680990			−0.340495	+	0.940246i	$0.610595\pi$
$192$	−6.15376	+	38.4182i	−0.444109	+	2.77260i
$193$	7.55487			0.543811			0.271906	−	0.962324i	$-0.412346\pi$
$193$	7.55487			0.543811			0.271906	+	0.962324i	$0.412346\pi$
$194$	−17.5858	+	30.4596i	−1.26259	+	2.18687i
$195$	0.544599	−	3.39996i	0.0389996	−	0.243476i
$196$	−36.3815	−	6.40590i	−2.59868	−	0.457564i
$197$	21.1556			1.50727			0.753637	−	0.657291i	$-0.228298\pi$
$197$	21.1556			1.50727			0.753637	+	0.657291i	$0.228298\pi$
$198$	6.49331	+	31.0829i	0.461459	+	2.20897i
$199$	−0.0783738	+	0.135747i	−0.00555577	+	0.00962288i	−0.868790	−	0.495181i	$-0.835102\pi$
$199$	−0.0783738	+	0.135747i	−0.00555577	+	0.00962288i	0.863234	+	0.504804i	$0.168435\pi$
$200$	4.42050	+	7.65653i	0.312577	+	0.541399i
$201$	−2.76403	+	17.2560i	−0.194960	+	1.21715i
$202$	−2.60287	−	4.50831i	−0.183138	−	0.317203i
$203$	−1.66887	−	1.16825i	−0.117131	−	0.0819950i
$204$	31.7385	+	25.7934i	2.22214	+	1.80590i
$205$	−2.84216			−0.198505
$206$	2.08336	−	3.60848i	0.145154	−	0.251415i
$207$	13.9190	−	12.4448i	0.967435	−	0.864973i
$208$	13.2155	+	22.8899i	0.916329	+	1.58713i
$209$	−0.315756	+	0.546905i	−0.0218413	+	0.0378302i
$210$	−8.60195	+	8.87861i	−0.593591	+	0.612683i
$211$	2.20424	+	3.81786i	0.151746	+	0.262832i	0.931870	−	0.362794i	$-0.118177\pi$
$211$	2.20424	+	3.81786i	0.151746	+	0.262832i	−0.780123	+	0.625626i	$0.784844\pi$
$212$	29.0681	−	50.3474i	1.99640	−	3.45787i
$213$	−1.85801	+	11.5996i	−0.127309	+	0.794794i
$214$	0.946431	+	1.63927i	0.0646967	+	0.112058i
$215$	−1.53771	−	2.66340i	−0.104871	−	0.181642i
$216$	−21.0705	+	40.8221i	−1.43366	+	2.77759i
$217$	1.84911	−	21.1651i	0.125526	−	1.43678i
$218$	17.1099	−	29.6352i	1.15883	−	2.00715i
$219$	−19.3818	−	15.7513i	−1.30970	−	1.06437i
$220$	−20.7063			−1.39602
$221$	8.89491			0.598337
$222$	−30.5790	+	11.6769i	−2.05233	+	0.783699i
$223$	−2.93191	+	5.07822i	−0.196335	+	0.340063i	−0.947337	−	0.320237i	$-0.896237\pi$
$223$	−2.93191	+	5.07822i	−0.196335	+	0.340063i	0.751002	+	0.660300i	$0.229571\pi$
$224$	4.18727	−	47.9279i	0.279774	−	3.20232i
$225$	0.613465	+	2.93661i	0.0408977	+	0.195774i
$226$	−8.84825	−	15.3256i	−0.588577	−	1.01944i
$227$	5.83971	+	10.1147i	0.387595	+	0.671335i	0.992126	−	0.125248i	$-0.0399725\pi$
$227$	5.83971	+	10.1147i	0.387595	+	0.671335i	−0.604530	+	0.796582i	$0.706639\pi$
$228$	−1.37438	+	0.524817i	−0.0910203	+	0.0347569i
$229$	8.50142	−	14.7249i	0.561790	−	0.973049i	−0.435551	−	0.900164i	$-0.643446\pi$
$229$	8.50142	−	14.7249i	0.561790	−	0.973049i	0.997340	−	0.0728843i	$-0.0232204\pi$
$230$	8.39468	+	14.5400i	0.553529	+	0.958740i
$231$	−4.92795	−	17.2920i	−0.324235	−	1.13773i
$232$	3.40363	−	5.89526i	0.223459	−	0.387043i
$233$	0.351193	+	0.608285i	0.0230074	+	0.0398501i	0.877300	−	0.479943i	$-0.159343\pi$
$233$	0.351193	+	0.608285i	0.0230074	+	0.0398501i	−0.854292	+	0.519793i	$0.826009\pi$
$234$	3.28995	+	15.7487i	0.215071	+	1.02953i
$235$	2.83830	−	4.91609i	0.185150	−	0.320690i
$236$	−17.7614			−1.15617
$237$	−3.10058	+	19.3571i	−0.201404	+	1.25738i
$238$	−26.1615	−	18.3137i	−1.69580	−	1.18710i
$239$	−1.37629	−	2.38380i	−0.0890246	−	0.154195i	0.818074	−	0.575112i	$-0.195042\pi$
$239$	−1.37629	−	2.38380i	−0.0890246	−	0.154195i	−0.907099	+	0.420917i	$0.861708\pi$
$240$	−17.8709	−	14.5234i	−1.15356	−	0.937479i
$241$	−7.61650	−	13.1922i	−0.490622	−	0.849781i	0.509320	−	0.860577i	$-0.329897\pi$
$241$	−7.61650	−	13.1922i	−0.490622	−	0.849781i	−0.999942	+	0.0107956i	$0.996564\pi$
$242$	5.92820	−	10.2679i	0.381079	−	0.660048i
$243$	−11.1187	+	10.9259i	−0.713264	+	0.700895i
$244$	−36.3940			−2.32988
$245$	4.49821	−	5.36341i	0.287380	−	0.342655i
$246$	12.4062	−	4.73739i	0.790987	−	0.302045i
$247$	−0.159983	+	0.277099i	−0.0101795	+	0.0176314i
$248$	70.9945			4.50815
$249$	−6.47606	−	5.26299i	−0.410403	−	0.333528i
$250$	−2.69765			−0.170614
$251$	−15.2671			−0.963651			−0.481825	−	0.876267i	$-0.660026\pi$
$251$	−15.2671			−0.963651			−0.481825	+	0.876267i	$0.660026\pi$
$252$	16.4968	−	38.5020i	1.03920	−	2.42540i
$253$	−24.4197			−1.53525
$254$	−16.9634			−1.06438
$255$	−7.23986	+	2.76460i	−0.453378	+	0.173126i
$256$	20.4385			1.27741
$257$	−14.2786	+	24.7313i	−0.890678	+	1.54270i	−0.0516129	+	0.998667i	$0.516436\pi$
$257$	−14.2786	+	24.7313i	−0.890678	+	1.54270i	−0.839065	+	0.544032i	$0.816897\pi$
$258$	11.1516	+	9.06275i	0.694269	+	0.564222i
$259$	16.7971	−	7.83512i	1.04372	−	0.486851i
$260$	−10.4912			−0.650639
$261$	1.72198	−	1.53961i	0.106588	−	0.0952992i
$262$	−13.0396	+	22.5852i	−0.805589	+	1.39532i
$263$	6.85092	+	11.8661i	0.422446	+	0.731698i	0.996178	−	0.0873450i	$-0.0278383\pi$
$263$	6.85092	+	11.8661i	0.422446	+	0.731698i	−0.573732	+	0.819043i	$0.694505\pi$
$264$	56.1301	−	21.4338i	3.45457	−	1.31916i
$265$	5.50814	+	9.54037i	0.338362	+	0.586060i
$266$	1.04106	−	0.485608i	0.0638315	−	0.0297746i
$267$	−16.6993	+	6.37677i	−1.02198	+	0.390252i
$268$	53.2467			3.25256
$269$	−9.33523	+	16.1691i	−0.569179	+	0.985847i	0.427469	+	0.904030i	$0.359405\pi$
$269$	−9.33523	+	16.1691i	−0.569179	+	0.985847i	−0.996647	+	0.0818164i	$0.973928\pi$
$270$	−7.57262	−	11.7959i	−0.460855	−	0.717874i
$271$	12.3195	+	21.3380i	0.748356	+	1.29619i	0.948610	+	0.316447i	$0.102490\pi$
$271$	12.3195	+	21.3380i	0.748356	+	1.29619i	−0.200254	+	0.979744i	$0.564177\pi$
$272$	29.7437	−	51.5177i	1.80348	−	3.12372i
$273$	−2.49683	−	8.76129i	−0.151115	−	0.530257i
$274$	−4.43985	−	7.69004i	−0.268221	−	0.464573i
$275$	1.96183	−	3.39799i	0.118303	−	0.204906i
$276$	−44.1477	−	35.8781i	−2.65738	−	2.15961i
$277$	7.37884	+	12.7805i	0.443352	+	0.767908i	0.997936	−	0.0642201i	$-0.0204560\pi$
$277$	7.37884	+	12.7805i	0.443352	+	0.767908i	−0.554584	+	0.832128i	$0.687123\pi$
$278$	−14.8586	−	25.7359i	−0.891161	−	1.54354i
$279$	22.8852	+	7.52446i	1.37010	+	0.450477i
$280$	19.1625	+	13.4143i	1.14518	+	0.801655i
$281$	−6.43418	+	11.1443i	−0.383831	+	0.664815i	−0.991606	−	0.129294i	$-0.958729\pi$
$281$	−6.43418	+	11.1443i	−0.383831	+	0.664815i	0.607775	+	0.794109i	$0.292062\pi$
$282$	−4.19504	+	26.1899i	−0.249811	+	1.55958i
$283$	12.6352			0.751085			0.375543	−	0.926805i	$-0.377456\pi$
$283$	12.6352			0.751085			0.375543	+	0.926805i	$0.377456\pi$
$284$	35.7929			2.12392
$285$	0.0440913	−	0.275264i	0.00261174	−	0.0163053i
$286$	10.5211	−	18.2231i	0.622125	−	1.07755i
$287$	−6.81473	+	3.17877i	−0.402261	+	0.187637i
$288$	51.8229	+	17.0389i	3.05369	+	1.00403i
$289$	−1.50977	−	2.61501i	−0.0888103	−	0.153824i
$290$	1.03855	+	1.79882i	0.0609856	+	0.105630i
$291$	17.5249	+	14.2422i	1.02733	+	0.834892i
$292$	−38.0478	+	65.9007i	−2.22658	+	3.85655i
$293$	−5.42891	−	9.40315i	−0.317160	−	0.549338i	0.662734	−	0.748855i	$-0.269396\pi$
$293$	−5.42891	−	9.40315i	−0.317160	−	0.549338i	−0.979894	+	0.199517i	$0.936063\pi$
$294$	−10.6950	+	30.9092i	−0.623745	+	1.80266i
$295$	1.68281	−	2.91472i	0.0979772	−	0.169701i
$296$	30.9676	+	53.6374i	1.79995	+	3.11761i
$297$	20.3653	−	0.960162i	1.18171	−	0.0557143i
$298$	21.8646	−	37.8705i	1.26658	−	2.19378i
$299$	−12.3727			−0.715530
$300$	8.53916	−	3.26075i	0.493009	−	0.188259i
$301$	−6.66586	−	4.66628i	−0.384214	−	0.268960i
$302$	−25.8507	−	44.7747i	−1.48754	−	2.57649i
$303$	−3.12249	+	1.19235i	−0.179382	+	0.0684987i
$304$	1.06994	+	1.85319i	0.0613652	+	0.106288i
$305$	3.44816	−	5.97239i	0.197441	−	0.341978i
$306$	26.9942	−	24.1352i	1.54316	−	1.37972i
$307$	11.8223			0.674737			0.337368	−	0.941373i	$-0.390463\pi$
$307$	11.8223			0.674737			0.337368	+	0.941373i	$0.390463\pi$
$308$	−49.6481	+	23.1587i	−2.82897	+	1.31959i
$309$	−2.07613	−	1.68724i	−0.118107	−	0.0959839i
$310$	−10.8312	+	18.7603i	−0.615173	+	1.06551i
$311$	−19.4629			−1.10364			−0.551820	−	0.833963i	$-0.686066\pi$
$311$	−19.4629			−1.10364			−0.551820	+	0.833963i	$0.686066\pi$
$312$	28.4393	−	10.8598i	1.61006	−	0.614815i
$313$	14.1898			0.802055			0.401027	−	0.916066i	$-0.368653\pi$
$313$	14.1898			0.802055			0.401027	+	0.916066i	$0.368653\pi$
$314$	19.4519			1.09774
$315$	4.75533	+	6.35507i	0.267932	+	0.358067i
$316$	59.7300			3.36007
$317$	−7.74784			−0.435162			−0.217581	−	0.976042i	$-0.569817\pi$
$317$	−7.74784			−0.435162			−0.217581	+	0.976042i	$0.569817\pi$
$318$	−39.9454	−	32.4630i	−2.24003	−	1.82043i
$319$	−3.02108			−0.169148
$320$	−11.2318	+	19.4540i	−0.627875	+	1.08751i
$321$	1.13537	−	0.433550i	0.0633701	−	0.0241984i
$322$	36.3902	+	25.4741i	2.02795	+	1.41962i
$323$	0.720141			0.0400697
$324$	38.2286	+	28.1855i	2.12381	+	1.56586i
$325$	0.993996	−	1.72165i	0.0551370	−	0.0955000i
$326$	−11.8769	−	20.5714i	−0.657799	−	1.13934i
$327$	−17.0506	−	13.8568i	−0.942900	−	0.766280i
$328$	−12.5638	−	21.7611i	−0.693719	−	1.20156i
$329$	1.30716	−	14.9619i	0.0720662	−	0.824876i
$330$	−2.89961	+	18.1024i	−0.159618	+	0.996504i
$331$	−27.8055			−1.52833			−0.764164	−	0.645022i	$-0.776848\pi$
$331$	−27.8055			−1.52833			−0.764164	+	0.645022i	$0.776848\pi$
$332$	−12.7129	+	22.0194i	−0.697712	+	1.20847i
$333$	4.29759	+	20.5722i	0.235507	+	1.12735i
$334$	−1.26899	−	2.19796i	−0.0694363	−	0.120267i
$335$	−5.04488	+	8.73799i	−0.275631	+	0.477407i
$336$	−59.0929	−	14.8357i	−3.22378	−	0.809355i
$337$	1.53501	+	2.65871i	0.0836172	+	0.144829i	0.904801	−	0.425834i	$-0.140019\pi$
$337$	1.53501	+	2.65871i	0.0836172	+	0.144829i	−0.821184	+	0.570664i	$0.806686\pi$
$338$	−12.2040	+	21.1380i	−0.663810	+	1.14975i
$339$	−10.6146	+	4.05329i	−0.576508	+	0.220144i
$340$	11.8062	+	20.4489i	0.640279	+	1.10900i
$341$	−15.7538	−	27.2863i	−0.853113	−	1.47764i
$342$	0.266358	+	1.27503i	0.0144030	+	0.0689459i
$343$	4.78686	−	17.8909i	0.258466	−	0.966020i
$344$	13.5949	−	23.5471i	0.732990	−	1.26958i
$345$	10.0705	−	3.84552i	0.542179	−	0.207036i
$346$	25.6947			1.38136
$347$	−26.6099			−1.42849			−0.714247	−	0.699893i	$-0.753231\pi$
$347$	−26.6099			−1.42849			−0.714247	+	0.699893i	$0.753231\pi$
$348$	−5.46172	−	4.43866i	−0.292779	−	0.237937i
$349$	−9.78331	+	16.9452i	−0.523688	+	0.907055i	0.475931	+	0.879482i	$0.342111\pi$
$349$	−9.78331	+	16.9452i	−0.523688	+	0.907055i	−0.999620	+	0.0275725i	$0.991222\pi$
$350$	−6.46823	+	3.01714i	−0.345741	+	0.161273i
$351$	10.3184	−	0.486484i	0.550758	−	0.0259666i
$352$	−35.6740	−	61.7891i	−1.90143	−	3.29337i
$353$	3.74250	+	6.48220i	0.199193	+	0.345013i	0.948267	−	0.317474i	$-0.102835\pi$
$353$	3.74250	+	6.48220i	0.199193	+	0.345013i	−0.749074	+	0.662486i	$0.769501\pi$
$354$	−2.48722	+	15.5278i	−0.132194	+	0.825295i
$355$	−3.39121	+	5.87375i	−0.179987	+	0.311746i
$356$	27.2319	+	47.1670i	1.44329	+	2.49984i
$357$	−14.2672	+	14.7261i	−0.755100	+	0.779387i
$358$	−32.2946	+	55.9359i	−1.70682	+	2.95630i
$359$	−1.89571	−	3.28347i	−0.100052	−	0.173295i	0.811654	−	0.584139i	$-0.198568\pi$
$359$	−1.89571	−	3.28347i	−0.100052	−	0.173295i	−0.911706	+	0.410844i	$0.865234\pi$
$360$	−19.7724	+	17.6783i	−1.04210	+	0.931728i
$361$	9.48705	−	16.4320i	0.499318	−	0.864845i
$362$	6.79384			0.357076
$363$	−5.90765	−	4.80105i	−0.310071	−	0.251990i
$364$	−25.1551	+	11.7338i	−1.31849	+	0.615016i
$365$	−7.20971	−	12.4876i	−0.377373	−	0.653630i
$366$	−5.09642	+	31.8172i	−0.266394	+	1.66311i
$367$	−16.2192	−	28.0924i	−0.846634	−	1.46641i	−0.884194	−	0.467119i	$-0.845292\pi$
$367$	−16.2192	−	28.0924i	−0.846634	−	1.46641i	0.0375599	−	0.999294i	$-0.488041\pi$
$368$	−41.3730	+	71.6602i	−2.15672	+	3.73555i
$369$	−1.74357	−	8.34631i	−0.0907664	−	0.434492i
$370$	−18.8982			−0.982471
$371$	23.8773	+	16.7147i	1.23965	+	0.867786i
$372$	11.6091	−	72.4760i	0.601902	−	3.75771i
$373$	−4.05975	+	7.03169i	−0.210206	+	0.364087i	−0.951779	−	0.306785i	$-0.900747\pi$
$373$	−4.05975	+	7.03169i	−0.210206	+	0.364087i	0.741573	+	0.670872i	$0.234080\pi$
$374$	−47.3591			−2.44888
$375$	−0.273945	+	1.71025i	−0.0141464	+	0.0883169i
$376$	50.1869			2.58819
$377$	−1.53068			−0.0788342
$378$	−31.3500	−	19.8138i	−1.61247	−	1.01911i
$379$	22.3585			1.14848			0.574240	−	0.818687i	$-0.305298\pi$
$379$	22.3585			1.14848			0.574240	+	0.818687i	$0.305298\pi$
$380$	−0.849381			−0.0435723
$381$	−1.72262	+	10.7544i	−0.0882526	+	0.550966i
$382$	25.3888			1.29901
$383$	−0.965199	+	1.67177i	−0.0493194	+	0.0854236i	−0.889631	−	0.456680i	$-0.849039\pi$
$383$	−0.965199	+	1.67177i	−0.0493194	+	0.0854236i	0.840312	+	0.542103i	$0.182372\pi$
$384$	6.63784	−	41.4403i	0.338736	−	2.11474i
$385$	0.903507	−	10.3416i	0.0460470	−	0.527058i
$386$	−20.3804			−1.03733
$387$	6.87802	−	6.14957i	0.349630	−	0.312600i
$388$	34.4025	−	59.5869i	1.74652	−	3.02506i
$389$	−15.4949	−	26.8380i	−0.785625	−	1.36074i	−0.928625	−	0.371019i	$-0.879008\pi$
$389$	−15.4949	−	26.8380i	−0.785625	−	1.36074i	0.143001	−	0.989723i	$-0.454325\pi$
$390$	−1.46914	+	9.17190i	−0.0743927	+	0.464437i
$391$	13.9234	+	24.1161i	0.704138	+	1.21960i
$392$	60.9494	+	10.7317i	3.07841	+	0.542035i
$393$	12.9944	+	10.5603i	0.655480	+	0.532698i
$394$	−57.0704			−2.87516
$395$	−5.65914	+	9.80192i	−0.284742	+	0.493188i
$396$	−12.7026	−	60.8063i	−0.638330	−	3.05563i
$397$	8.46510	+	14.6620i	0.424851	+	0.735864i	0.996407	−	0.0846997i	$-0.0269931\pi$
$397$	8.46510	+	14.6620i	0.424851	+	0.735864i	−0.571555	+	0.820563i	$0.693660\pi$
$398$	0.211425	−	0.366199i	0.0105978	−	0.0183559i
$399$	−0.202146	−	0.709323i	−0.0101200	−	0.0355105i
$400$	−6.64765	−	11.5141i	−0.332383	−	0.575704i
$401$	8.41715	−	14.5789i	0.420332	−	0.728037i	−0.575639	−	0.817704i	$-0.695247\pi$
$401$	8.41715	−	14.5789i	0.420332	−	0.728037i	0.995972	+	0.0896665i	$0.0285801\pi$
$402$	7.45639	−	46.5506i	0.371891	−	2.32173i
$403$	−7.98192	−	13.8251i	−0.397608	−	0.688677i
$404$	5.09190	+	8.81943i	0.253331	+	0.438783i
$405$	−8.24732	+	3.60301i	−0.409813	+	0.179035i
$406$	4.50201	+	3.15153i	0.223431	+	0.156408i
$407$	13.7435	−	23.8044i	0.681238	−	1.17994i
$408$	−53.1711	−	43.2113i	−2.63236	−	2.13928i
$409$	−11.9182			−0.589318			−0.294659	−	0.955603i	$-0.595206\pi$
$409$	−11.9182			−0.589318			−0.294659	+	0.955603i	$0.595206\pi$
$410$	7.66715			0.378653
$411$	−5.32618	+	2.03385i	−0.262721	+	0.100322i
$412$	−4.07559	+	7.05913i	−0.200790	+	0.347778i
$413$	0.775008	−	8.87082i	0.0381357	−	0.436505i
$414$	−37.5485	+	33.5717i	−1.84541	+	1.64996i
$415$	−2.40898	−	4.17248i	−0.118252	−	0.204819i
$416$	−18.0749	−	31.3066i	−0.886193	−	1.53493i
$417$	−17.8249	+	6.80658i	−0.872888	+	0.333320i
$418$	0.851798	−	1.47536i	0.0416628	−	0.0721621i
$419$	5.83768	+	10.1112i	0.285189	+	0.493962i	0.972655	−	0.232254i	$-0.0746102\pi$
$419$	5.83768	+	10.1112i	0.285189	+	0.493962i	−0.687466	+	0.726217i	$0.741277\pi$
$420$	16.8277	−	17.3689i	0.821105	−	0.847515i
$421$	−2.08963	+	3.61935i	−0.101843	+	0.176396i	−0.912444	−	0.409202i	$-0.865807\pi$
$421$	−2.08963	+	3.61935i	−0.101843	+	0.176396i	0.810601	+	0.585599i	$0.199140\pi$
$422$	−5.94627	−	10.2992i	−0.289460	−	0.501359i
$423$	16.1778	+	5.31913i	0.786592	+	0.258625i
$424$	−48.6974	+	84.3464i	−2.36496	+	4.09623i
$425$	−4.47432			−0.217036
$426$	5.01225	−	31.2917i	0.242844	−	1.51609i
$427$	1.58803	−	18.1767i	0.0768500	−	0.879633i
$428$	−1.85147	−	3.20683i	−0.0894940	−	0.155008i
$429$	−10.4846	−	8.52069i	−0.506202	−	0.411383i
$430$	4.14821	+	7.18491i	0.200045	+	0.346487i
$431$	−4.48625	+	7.77041i	−0.216095	+	0.374288i	−0.953611	−	0.301042i	$-0.902665\pi$
$431$	−4.48625	+	7.77041i	−0.216095	+	0.374288i	0.737516	+	0.675330i	$0.235999\pi$
$432$	31.6863	−	61.3893i	1.52451	−	2.95359i
$433$	9.18475			0.441391			0.220696	−	0.975343i	$-0.429167\pi$
$433$	9.18475			0.441391			0.220696	+	0.975343i	$0.429167\pi$
$434$	−4.98825	+	57.0960i	−0.239444	+	2.74070i
$435$	1.24587	−	0.475747i	0.0597351	−	0.0228103i
$436$	−33.4714	+	57.9742i	−1.60299	+	2.77646i
$437$	−1.00170			−0.0479180
$438$	52.2853	+	42.4915i	2.49829	+	2.03032i
$439$	32.1691			1.53535			0.767674	−	0.640841i	$-0.221414\pi$
$439$	32.1691			1.53535			0.767674	+	0.640841i	$0.221414\pi$
$440$	34.6891			1.65374
$441$	18.5097	+	9.91921i	0.881415	+	0.472343i
$442$	−23.9953			−1.14134
$443$	23.0771			1.09643			0.548214	−	0.836338i	$-0.315308\pi$
$443$	23.0771			1.09643			0.548214	+	0.836338i	$0.315308\pi$
$444$	59.8205	−	22.8430i	2.83896	−	1.08408i
$445$	−10.3204			−0.489233
$446$	7.90927	−	13.6993i	0.374515	−	0.648679i
$447$	−21.7888	−	17.7074i	−1.03057	−	0.837531i
$448$	−5.17271	+	59.2074i	−0.244388	+	2.79729i
$449$	25.7100			1.21333			0.606664	−	0.794958i	$-0.292507\pi$
$449$	25.7100			1.21333			0.606664	+	0.794958i	$0.292507\pi$
$450$	−1.65491	−	7.92193i	−0.0780133	−	0.373443i
$451$	−5.57583	+	9.65763i	−0.262556	+	0.454760i
$452$	17.3095	+	29.9809i	0.814170	+	1.41018i
$453$	−31.0113	+	11.8419i	−1.45704	+	0.556382i
$454$	−15.7535	−	27.2858i	−0.739347	−	1.28059i
$455$	0.457778	−	5.23977i	0.0214610	−	0.245644i
$456$	2.30248	−	0.879220i	0.107823	−	0.0411732i
$457$	17.5324			0.820130			0.410065	−	0.912056i	$-0.365506\pi$
$457$	17.5324			0.820130			0.410065	+	0.912056i	$0.365506\pi$
$458$	−22.9338	+	39.7226i	−1.07163	+	1.85611i
$459$	−12.5600	−	19.5646i	−0.586248	−	0.913199i
$460$	−16.4222	−	28.4441i	−0.765688	−	1.32621i
$461$	13.7588	−	23.8310i	0.640811	−	1.10992i	−0.344440	−	0.938808i	$-0.611931\pi$
$461$	13.7588	−	23.8310i	0.640811	−	1.10992i	0.985252	−	0.171110i	$-0.0547353\pi$
$462$	13.2939	+	46.6476i	0.618487	+	2.17024i
$463$	9.93332	+	17.2050i	0.461641	+	0.799585i	0.999043	−	0.0437411i	$-0.0139277\pi$
$463$	9.93332	+	17.2050i	0.461641	+	0.799585i	−0.537402	+	0.843326i	$0.680594\pi$
$464$	−5.11846	+	8.86543i	−0.237618	+	0.411567i
$465$	10.7937	+	8.77186i	0.500545	+	0.406785i
$466$	−0.947396	−	1.64094i	−0.0438873	−	0.0760150i
$467$	−12.7739	−	22.1250i	−0.591106	−	1.02382i	−0.994084	−	0.108615i	$-0.965358\pi$
$467$	−12.7739	−	22.1250i	−0.591106	−	1.02382i	0.402978	−	0.915210i	$-0.367975\pi$
$468$	−6.43600	−	30.8086i	−0.297504	−	1.42413i
$469$	−2.32339	+	26.5937i	−0.107284	+	1.22798i
$470$	−7.65674	+	13.2619i	−0.353179	+	0.611724i
$471$	1.97533	−	12.3321i	0.0910185	−	0.568233i
$472$	29.7555			1.36961
$473$	−12.0669			−0.554838
$474$	8.36427	−	52.2186i	0.384184	−	2.39848i
$475$	0.0804749	−	0.139387i	0.00369244	−	0.00639550i
$476$	51.1787	+	35.8265i	2.34577	+	1.64210i
$477$	−24.6373	+	22.0279i	−1.12806	+	1.00859i
$478$	3.71274	+	6.43065i	0.169817	+	0.294131i
$479$	0.0951153	+	0.164744i	0.00434593	+	0.00752737i	0.868190	−	0.496232i	$-0.165283\pi$
$479$	0.0951153	+	0.164744i	0.00434593	+	0.00752737i	−0.863844	+	0.503759i	$0.831950\pi$
$480$	24.4420	+	19.8637i	1.11562	+	0.906648i
$481$	6.96338	−	12.0609i	0.317503	−	0.549931i
$482$	20.5466	+	35.5878i	0.935873	+	1.62098i
$483$	19.8454	−	20.4837i	0.902999	−	0.932042i
$484$	−11.5971	+	20.0868i	−0.527141	+	0.913035i
$485$	6.51896	+	11.2912i	0.296011	+	0.512705i
$486$	29.9943	−	29.4742i	1.36057	−	1.33698i
$487$	2.65585	−	4.60007i	0.120348	−	0.208449i	−0.799557	−	0.600590i	$-0.794932\pi$
$487$	2.65585	−	4.60007i	0.120348	−	0.208449i	0.919905	+	0.392141i	$0.128266\pi$
$488$	60.9704			2.76000
$489$	−14.2479	+	5.44067i	−0.644312	+	0.246036i
$490$	−12.1346	+	14.4686i	−0.548184	+	0.653624i
$491$	−10.1203	−	17.5288i	−0.456721	−	0.791065i	0.542064	−	0.840337i	$-0.317643\pi$
$491$	−10.1203	−	17.5288i	−0.456721	−	0.791065i	−0.998785	+	0.0492725i	$0.984310\pi$
$492$	−24.2697	+	9.26757i	−1.09416	+	0.417815i
$493$	1.72253	+	2.98352i	0.0775790	+	0.134371i
$494$	0.431579	−	0.747517i	0.0194177	−	0.0336324i
$495$	11.1821	+	3.67657i	0.502596	+	0.165250i
$496$	−106.763			−4.79381
$497$	−1.56180	+	17.8765i	−0.0700563	+	0.801871i
$498$	17.4701	+	14.1977i	0.782855	+	0.636214i
$499$	1.21499	−	2.10442i	0.0543902	−	0.0942066i	−0.837548	−	0.546363i	$-0.816012\pi$
$499$	1.21499	−	2.10442i	0.0543902	−	0.0942066i	0.891939	+	0.452157i	$0.149345\pi$
$500$	5.27730			0.236008
$501$	−1.52233	+	0.581313i	−0.0680125	+	0.0259712i
$502$	41.1852			1.83819
$503$	11.8338			0.527644			0.263822	−	0.964571i	$-0.415017\pi$
$503$	11.8338			0.527644			0.263822	+	0.964571i	$0.415017\pi$
$504$	−27.6369	+	64.5019i	−1.23104	+	2.87314i
$505$	−1.92974			−0.0858721
$506$	65.8757			2.92853
$507$	12.1617	+	9.88362i	0.540120	+	0.438947i
$508$	33.1848			1.47234
$509$	8.05825	−	13.9573i	0.357176	−	0.618646i	−0.630312	−	0.776342i	$-0.717073\pi$
$509$	8.05825	−	13.9573i	0.357176	−	0.618646i	0.987488	+	0.157695i	$0.0504064\pi$
$510$	19.5306	−	7.45792i	0.864829	−	0.330242i
$511$	−31.2535	−	21.8782i	−1.38257	−	0.967837i
$512$	−6.67474			−0.294985
$513$	0.835392	−	0.0393862i	0.0368834	−	0.00173894i
$514$	38.5188	−	66.7164i	1.69899	−	2.94274i
$515$	−0.772287	−	1.33764i	−0.0340310	−	0.0589435i
$516$	−21.8155	−	17.7291i	−0.960372	−	0.780480i
$517$	−11.1365	−	19.2890i	−0.489784	−	0.848331i
$518$	−45.3128	+	21.1364i	−1.99093	+	0.928680i
$519$	2.60928	−	16.2899i	0.114535	−	0.715047i
$520$	17.5758			0.770752
$521$	14.6673	−	25.4044i	0.642584	−	1.11299i	−0.342270	−	0.939602i	$-0.611196\pi$
$521$	14.6673	−	25.4044i	0.642584	−	1.11299i	0.984854	−	0.173386i	$-0.0554710\pi$
$522$	−4.64530	+	4.15331i	−0.203319	+	0.181786i
$523$	−2.13586	−	3.69941i	−0.0933945	−	0.161764i	0.815543	−	0.578697i	$-0.196438\pi$
$523$	−2.13586	−	3.69941i	−0.0933945	−	0.161764i	−0.908937	+	0.416933i	$0.863105\pi$
$524$	25.5088	−	44.1826i	1.11436	−	1.93013i
$525$	1.25596	+	4.40710i	0.0548145	+	0.192342i
$526$	−18.4814	−	32.0107i	−0.805826	−	1.39573i
$527$	−17.9647	+	31.1158i	−0.782555	+	1.35542i
$528$	−84.4098	+	32.2326i	−3.67346	+	1.40274i
$529$	−7.86726	−	13.6265i	−0.342055	−	0.592456i
$530$	−14.8590	−	25.7366i	−0.645434	−	1.11792i
$531$	9.59173	+	3.15368i	0.416246	+	0.136858i
$532$	−2.03658	+	0.949977i	−0.0882971	+	0.0411867i
$533$	−2.82510	+	4.89321i	−0.122369	+	0.211948i
$534$	45.0489	−	17.2023i	1.94945	−	0.744416i
$535$	0.701671			0.0303359
$536$	−89.2036			−3.85301
$537$	32.1827	+	26.1543i	1.38878	+	1.12864i
$538$	25.1831	−	43.6185i	1.08572	−	1.88053i
$539$	−9.40007	−	25.8069i	−0.404890	−	1.11158i
$540$	14.8140	+	23.0758i	0.637494	+	0.993024i
$541$	−13.6460	−	23.6356i	−0.586688	−	1.01617i	−0.994663	−	0.103180i	$-0.967098\pi$
$541$	−13.6460	−	23.6356i	−0.586688	−	1.01617i	0.407975	−	0.912993i	$-0.366235\pi$
$542$	−33.2337	−	57.5624i	−1.42751	−	2.47252i
$543$	0.689910	−	4.30714i	0.0296069	−	0.184837i
$544$	−40.6806	+	70.4609i	−1.74417	+	3.02099i
$545$	−6.34253	−	10.9856i	−0.271684	−	0.470571i
$546$	6.73558	+	23.6349i	0.288256	+	1.01148i
$547$	4.33062	−	7.50086i	0.185164	−	0.320713i	−0.758468	−	0.651711i	$-0.774052\pi$
$547$	4.33062	−	7.50086i	0.185164	−	0.320713i	0.943632	+	0.330997i	$0.107385\pi$
$548$	8.68550	+	15.0437i	0.371026	+	0.642636i
$549$	19.6539	+	6.46204i	0.838807	+	0.275793i
$550$	−5.29232	+	9.16657i	−0.225665	+	0.390864i
$551$	−0.123926			−0.00527941
$552$	73.9601	+	60.1062i	3.14795	+	2.55829i
$553$	−2.60628	+	29.8317i	−0.110830	+	1.26857i
$554$	−19.9055	−	34.4774i	−0.845704	−	1.46480i
$555$	−1.91910	+	11.9810i	−0.0814613	+	0.508567i
$556$	29.0674	+	50.3461i	1.23273	+	2.13515i
$557$	−21.6429	+	37.4865i	−0.917037	+	1.58835i	−0.113146	+	0.993578i	$0.536093\pi$
$557$	−21.6429	+	37.4865i	−0.917037	+	1.58835i	−0.803891	+	0.594777i	$0.797241\pi$
$558$	−61.7361	−	20.2983i	−2.61350	−	0.859297i
$559$	−6.11393			−0.258592
$560$	−28.8170	−	20.1727i	−1.21774	−	0.852451i
$561$	−4.80929	+	30.0246i	−0.203048	+	1.26764i
$562$	17.3572	−	30.0635i	0.732167	−	1.26815i
$563$	33.8772			1.42775			0.713876	−	0.700272i	$-0.246938\pi$
$563$	33.8772			1.42775			0.713876	+	0.700272i	$0.246938\pi$
$564$	8.20660	−	51.2342i	0.345560	−	2.15735i
$565$	−6.55997			−0.275980
$566$	−34.0853			−1.43271
$567$	−15.7451	+	17.8631i	−0.661232	+	0.750181i
$568$	−59.9634			−2.51601
$569$	32.6498			1.36875			0.684374	−	0.729131i	$-0.260075\pi$
$569$	32.6498			1.36875			0.684374	+	0.729131i	$0.260075\pi$
$570$	−0.118943	+	0.742566i	−0.00498197	+	0.0311027i
$571$	1.17120			0.0490131			0.0245065	−	0.999700i	$-0.492199\pi$
$571$	1.17120			0.0490131			0.0245065	+	0.999700i	$0.492199\pi$
$572$	−20.5820	+	35.6491i	−0.860577	+	1.49056i
$573$	2.57822	−	16.0960i	0.107707	−	0.672418i
$574$	18.3837	−	8.57520i	0.767323	−	0.357922i
$575$	6.22371			0.259546
$576$	−64.0190	−	21.0489i	−2.66746	−	0.877039i
$577$	0.527159	−	0.913066i	0.0219459	−	0.0380114i	−0.854844	−	0.518885i	$-0.826347\pi$
$577$	0.527159	−	0.913066i	0.0219459	−	0.0380114i	0.876790	+	0.480874i	$0.159681\pi$
$578$	4.07284	+	7.05436i	0.169408	+	0.293423i
$579$	−2.06961	+	12.9207i	−0.0860102	+	0.536966i
$580$	−2.03167	−	3.51895i	−0.0843604	−	0.146117i
$581$	−10.4427	−	7.31019i	−0.433238	−	0.303278i
$582$	−47.2759	−	38.4204i	−1.95965	−	1.59258i
$583$	43.2241			1.79016
$584$	63.7411	−	110.403i	2.63762	−	4.56850i
$585$	5.66560	+	1.86280i	0.234244	+	0.0770174i
$586$	14.6453	+	25.3664i	0.604991	+	1.04788i
$587$	−11.9179	+	20.6425i	−0.491906	+	0.852006i	−0.999957	−	0.00932152i	$-0.997033\pi$
$587$	−11.9179	+	20.6425i	−0.491906	+	0.852006i	0.508051	+	0.861327i	$0.330366\pi$
$588$	20.9222	−	60.4665i	0.862817	−	2.49360i
$589$	−0.646224	−	1.11929i	−0.0266272	−	0.0461197i
$590$	−4.53964	+	7.86288i	−0.186894	+	0.323710i
$591$	−5.79546	+	36.1814i	−0.238393	+	1.48830i
$592$	−46.5697	−	80.6611i	−1.91400	−	3.31515i
$593$	3.25508	+	5.63796i	0.133670	+	0.231523i	0.925089	−	0.379751i	$-0.123990\pi$
$593$	3.25508	+	5.63796i	0.133670	+	0.231523i	−0.791419	+	0.611275i	$0.790657\pi$
$594$	−54.9384	+	2.59018i	−2.25415	+	0.106276i
$595$	−10.7282	+	5.00424i	−0.439814	+	0.205154i
$596$	−42.7728	+	74.0847i	−1.75204	+	3.03463i
$597$	−0.210692	−	0.171226i	−0.00862304	−	0.00700781i
$598$	33.3771			1.36489
$599$	16.9829			0.693902			0.346951	−	0.937883i	$-0.387217\pi$
$599$	16.9829			0.693902			0.346951	+	0.937883i	$0.387217\pi$
$600$	−14.3056	+	5.46270i	−0.584022	+	0.223014i
$601$	−13.0322	+	22.5724i	−0.531594	+	0.920748i	0.467726	+	0.883874i	$0.345073\pi$
$601$	−13.0322	+	22.5724i	−0.531594	+	0.920748i	−0.999320	+	0.0368744i	$0.988260\pi$
$602$	17.9821	+	12.5880i	0.732897	+	0.513047i
$603$	−28.7549	−	9.45438i	−1.17099	−	0.385012i
$604$	50.5706	+	87.5909i	2.05769	+	3.56402i
$605$	−2.19754	−	3.80626i	−0.0893429	−	0.154746i
$606$	8.42338	−	3.21654i	0.342176	−	0.130663i
$607$	9.78930	−	16.9556i	0.397335	−	0.688205i	−0.596061	−	0.802939i	$-0.703268\pi$
$607$	9.78930	−	16.9556i	0.397335	−	0.688205i	0.993396	+	0.114734i	$0.0366017\pi$
$608$	−1.46336	−	2.53461i	−0.0593471	−	0.102792i
$609$	2.45518	−	2.53414i	0.0994887	−	0.102689i
$610$	−9.30192	+	16.1114i	−0.376624	+	0.652331i
$611$	−5.64252	−	9.77314i	−0.228272	−	0.395379i
$612$	−52.8077	+	47.2148i	−2.13462	+	1.90854i
$613$	−19.4227	+	33.6411i	−0.784475	+	1.35875i	0.144837	+	0.989456i	$0.453734\pi$
$613$	−19.4227	+	33.6411i	−0.784475	+	1.35875i	−0.929312	+	0.369295i	$0.879599\pi$
$614$	−31.8925			−1.28708
$615$	0.778594	−	4.86081i	0.0313960	−	0.196007i
$616$	83.1750	−	38.7975i	3.35122	−	1.56319i
$617$	16.5821	+	28.7211i	0.667571	+	1.15627i	0.978581	+	0.205861i	$0.0659994\pi$
$617$	16.5821	+	28.7211i	0.667571	+	1.15627i	−0.311010	+	0.950407i	$0.600667\pi$
$618$	5.60068	+	4.55158i	0.225292	+	0.183092i
$619$	−14.9067	−	25.8192i	−0.599152	−	1.03776i	−0.992946	−	0.118564i	$-0.962171\pi$
$619$	−14.9067	−	25.8192i	−0.599152	−	1.03776i	0.393794	−	0.919199i	$-0.371162\pi$
$620$	21.1887	−	36.6999i	0.850960	−	1.47391i
$621$	17.4707	+	27.2141i	0.701075	+	1.09206i
$622$	52.5040			2.10522
$623$	−24.7455	+	11.5427i	−0.991406	+	0.462447i
$624$	−42.7677	+	16.3312i	−1.71208	+	0.653772i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−38.2791			−1.52994
$627$	−0.848845	−	0.689843i	−0.0338996	−	0.0275497i
$628$	−38.0530			−1.51848
$629$	−31.3446			−1.24979
$630$	−12.8282	−	17.1437i	−0.511087	−	0.683023i
$631$	8.52204			0.339257			0.169629	−	0.985508i	$-0.445743\pi$
$631$	8.52204			0.339257			0.169629	+	0.985508i	$0.445743\pi$
$632$	−100.065			−3.98037
$633$	−7.13334	+	2.72392i	−0.283525	+	0.108266i
$634$	20.9009			0.830082
$635$	−3.14411	+	5.44575i	−0.124770	+	0.216108i
$636$	78.1436	+	63.5061i	3.09860	+	2.51818i
$637$	−4.76271	−	13.0755i	−0.188706	−	0.518072i
$638$	8.14980			0.322654
$639$	−19.3293	−	6.35531i	−0.764655	−	0.251412i
$640$	12.1153	−	20.9843i	0.478899	−	0.829477i
$641$	−0.773350	−	1.33948i	−0.0305455	−	0.0529063i	0.850349	−	0.526220i	$-0.176391\pi$
$641$	−0.773350	−	1.33948i	−0.0305455	−	0.0529063i	−0.880894	+	0.473314i	$0.843058\pi$
$642$	−3.06283	+	1.16957i	−0.120880	+	0.0461591i
$643$	−3.48336	−	6.03336i	−0.137370	−	0.237933i	0.789130	−	0.614226i	$-0.210532\pi$
$643$	−3.48336	−	6.03336i	−0.137370	−	0.237933i	−0.926500	+	0.376294i	$0.877198\pi$
$644$	−71.1888	−	49.8340i	−2.80523	−	1.96374i
$645$	4.97633	−	1.90025i	0.195943	−	0.0748224i
$646$	−1.94269			−0.0764340
$647$	−23.3064	+	40.3678i	−0.916268	+	1.58702i	−0.111234	+	0.993794i	$0.535480\pi$
$647$	−23.3064	+	40.3678i	−0.916268	+	1.58702i	−0.805034	+	0.593229i	$0.797853\pi$
$648$	−64.0439	−	47.2188i	−2.51588	−	1.85493i
$649$	−6.60278	−	11.4364i	−0.259182	−	0.448916i
$650$	−2.68145	+	4.64441i	−0.105175	+	0.182169i
$651$	35.6911	+	8.96051i	1.39884	+	0.351190i
$652$	23.2343	+	40.2429i	0.909924	+	1.57603i
$653$	11.1238	−	19.2669i	0.435307	−	0.753974i	−0.562014	−	0.827128i	$-0.689973\pi$
$653$	11.1238	−	19.2669i	0.435307	−	0.753974i	0.997321	+	0.0731543i	$0.0233066\pi$
$654$	45.9965	+	37.3806i	1.79860	+	1.46170i
$655$	4.83369	+	8.37220i	0.188868	+	0.327129i
$656$	18.8937	+	32.7249i	0.737675	+	1.27769i
$657$	32.2482	−	28.8328i	1.25812	−	1.12487i
$658$	−3.52626	+	40.3619i	−0.137468	+	1.57347i
$659$	4.70312	−	8.14605i	0.183208	−	0.317325i	−0.759763	−	0.650200i	$-0.774685\pi$
$659$	4.70312	−	8.14605i	0.183208	−	0.317325i	0.942971	+	0.332875i	$0.108019\pi$
$660$	5.67238	−	35.4130i	0.220797	−	1.37845i
$661$	−16.9883			−0.660767			−0.330384	−	0.943847i	$-0.607178\pi$
$661$	−16.9883			−0.660767			−0.330384	+	0.943847i	$0.607178\pi$
$662$	75.0094			2.91532
$663$	−2.43671	+	15.2125i	−0.0946341	+	0.590805i
$664$	21.2978	−	36.8889i	0.826516	−	1.43157i
$665$	0.0370622	−	0.424217i	0.00143721	−	0.0164504i
$666$	−11.5934	−	55.4966i	−0.449235	−	2.15045i
$667$	−2.39602	−	4.15002i	−0.0927741	−	0.160690i
$668$	2.48248	+	4.29979i	0.0960502	+	0.166364i
$669$	−7.88185	−	6.40546i	−0.304730	−	0.247649i
$670$	13.6093	−	23.5720i	0.525773	−	0.910666i
$671$	−13.5294	−	23.4336i	−0.522297	−	0.904644i
$672$	80.8216	+	20.2909i	3.11776	+	0.782737i
$673$	9.96125	−	17.2534i	0.383978	−	0.665069i	−0.607649	−	0.794206i	$-0.707887\pi$
$673$	9.96125	−	17.2534i	0.383978	−	0.665069i	0.991627	+	0.129136i	$0.0412205\pi$
$674$	−4.14091	−	7.17227i	−0.159502	−	0.276265i
$675$	−5.19039	+	0.244711i	−0.199778	+	0.00941893i
$676$	23.8742	−	41.3514i	0.918239	−	1.59044i
$677$	33.4042			1.28383			0.641914	−	0.766776i	$-0.278141\pi$
$677$	33.4042			1.28383			0.641914	+	0.766776i	$0.278141\pi$
$678$	28.6346	−	10.9343i	1.09970	−	0.419931i
$679$	28.2591	+	19.7821i	1.08449	+	0.759168i
$680$	−19.7787	−	34.2578i	−0.758480	−	1.31373i
$681$	−18.8984	+	7.21650i	−0.724187	+	0.276537i
$682$	42.4981	+	73.6088i	1.62733	+	2.81863i
$683$	−7.65577	+	13.2602i	−0.292940	+	0.507387i	−0.974504	−	0.224372i	$-0.927967\pi$
$683$	−7.65577	+	13.2602i	−0.292940	+	0.507387i	0.681564	+	0.731759i	$0.261300\pi$
$684$	−0.521065	−	2.49430i	−0.0199234	−	0.0953718i
$685$	−3.29165			−0.125767
$686$	−12.9133	+	48.2635i	−0.493031	+	1.84271i
$687$	22.8543	+	18.5734i	0.871947	+	0.708618i
$688$	−20.4444	+	35.4107i	−0.779435	+	1.35002i
$689$	21.9003			0.834333
$690$	−27.1667	+	10.3738i	−1.03422	+	0.394926i
$691$	−9.55329			−0.363424			−0.181712	−	0.983352i	$-0.558164\pi$
$691$	−9.55329			−0.363424			−0.181712	+	0.983352i	$0.558164\pi$
$692$	−50.2656			−1.91081
$693$	30.9236	−	3.69098i	1.17469	−	0.140209i
$694$	71.7842			2.72489
$695$	−11.0160			−0.417860
$696$	9.14996	+	7.43603i	0.346828	+	0.281862i
$697$	12.7167			0.481681
$698$	26.3919	−	45.7121i	0.998949	−	1.73023i
$699$	−1.13653	+	0.433992i	−0.0429874	+	0.0164151i
$700$	12.6535	−	5.90232i	0.478259	−	0.223087i
$701$	39.6830			1.49881			0.749403	−	0.662114i	$-0.230340\pi$
$701$	39.6830			1.49881			0.749403	+	0.662114i	$0.230340\pi$
$702$	−27.8355	+	1.31236i	−1.05058	+	0.0495319i
$703$	0.563762	−	0.976464i	0.0212627	−	0.0368280i
$704$	44.0696	+	76.3308i	1.66094	+	2.87682i
$705$	7.63020	+	6.20094i	0.287370	+	0.233541i
$706$	−10.0959	−	17.4867i	−0.379966	−	0.658120i
$707$	−4.62698	+	2.15828i	−0.174016	+	0.0811706i
$708$	4.86565	−	30.3765i	0.182862	−	1.14162i
$709$	−16.4886			−0.619241			−0.309620	−	0.950860i	$-0.600202\pi$
$709$	−16.4886			−0.619241			−0.309620	+	0.950860i	$0.600202\pi$
$710$	9.14829	−	15.8453i	0.343329	−	0.594664i
$711$	−32.2561	−	10.6055i	−1.20970	−	0.397739i
$712$	−45.6212	−	79.0183i	−1.70973	−	2.96134i
$713$	24.9886	−	43.2815i	0.935831	−	1.62091i
$714$	38.4879	−	39.7258i	1.44037	−	1.48670i
$715$	−3.90010	−	6.75517i	−0.145855	−	0.252629i
$716$	63.1767	−	109.425i	2.36102	−	4.08941i
$717$	4.45392	−	1.70077i	0.166335	−	0.0635163i
$718$	5.11396	+	8.85764i	0.190851	+	0.330564i
$719$	13.3872	+	23.1873i	0.499259	+	0.864742i	1.00000		0.000855526i	$-0.000272322\pi$
$719$	13.3872	+	23.1873i	0.499259	+	0.864742i	−0.500741	+	0.865597i	$0.666939\pi$
$720$	29.7342	−	26.5850i	1.10813	−	0.990766i
$721$	−3.34780	−	2.34355i	−0.124678	−	0.0872782i
$722$	−25.5927	+	44.3279i	−0.952462	+	1.64971i
$723$	24.6484	−	9.41219i	0.916683	−	0.350043i
$724$	−13.2905			−0.493938
$725$	0.769965			0.0285958
$726$	15.9367	+	12.9515i	0.591468	+	0.480677i
$727$	−21.6715	+	37.5362i	−0.803752	+	1.39214i	0.113378	+	0.993552i	$0.463833\pi$
$727$	−21.6715	+	37.5362i	−0.803752	+	1.39214i	−0.917130	+	0.398587i	$0.869501\pi$
$728$	42.1421	−	19.6574i	1.56189	−	0.728553i
$729$	−15.6401	−	22.0088i	−0.579262	−	0.815141i
$730$	19.4493	+	33.6871i	0.719849	+	1.24682i
$731$	6.88023	+	11.9169i	0.254474	+	0.440763i
$732$	9.96992	−	62.2428i	0.368499	−	2.30056i
$733$	9.18357	−	15.9064i	0.339203	−	0.587516i	−0.645080	−	0.764115i	$-0.723176\pi$
$733$	9.18357	−	15.9064i	0.339203	−	0.587516i	0.984283	+	0.176598i	$0.0565094\pi$
$734$	43.7536	+	75.7835i	1.61498	+	2.79722i
$735$	7.94050	+	9.16234i	0.292890	+	0.337958i
$736$	56.5861	−	98.0100i	2.08579	−	3.61270i
$737$	19.7944	+	34.2849i	0.729135	+	1.26290i
$738$	4.70353	+	22.5154i	0.173139	+	0.828803i
$739$	−15.5586	+	26.9484i	−0.572334	+	0.991312i	0.423992	+	0.905666i	$0.360629\pi$
$739$	−15.5586	+	26.9484i	−0.572334	+	0.991312i	−0.996326	+	0.0856457i	$0.972705\pi$
$740$	36.9698			1.35904
$741$	−0.430083	−	0.349522i	−0.0157995	−	0.0128400i
$742$	−64.4125	−	45.0905i	−2.36466	−	1.65532i
$743$	−2.83876	−	4.91687i	−0.104144	−	0.180382i	0.809244	−	0.587472i	$-0.199877\pi$
$743$	−2.83876	−	4.91687i	−0.104144	−	0.180382i	−0.913388	+	0.407090i	$0.866544\pi$
$744$	−19.4485	+	121.418i	−0.713018	+	4.45141i
$745$	−8.10505	−	14.0384i	−0.296946	−	0.514326i
$746$	10.9518	−	18.9690i	0.400973	−	0.694506i
$747$	10.7751	−	9.63391i	0.394241	−	0.352486i
$748$	92.6467			3.38750
$749$	1.68242	−	0.784774i	0.0614742	−	0.0286750i
$750$	0.739006	−	4.61365i	0.0269847	−	0.168467i
$751$	−9.83779	+	17.0396i	−0.358986	+	0.621782i	−0.987792	−	0.155780i	$-0.950211\pi$
$751$	−9.83779	+	17.0396i	−0.358986	+	0.621782i	0.628806	+	0.777562i	$0.283544\pi$
$752$	−75.4722			−2.75219
$753$	4.18234	−	26.1105i	0.152413	−	0.951521i
$754$	4.12924			0.150378
$755$	−19.1653			−0.697498
$756$	61.3288	+	38.7610i	2.23051	+	1.40972i
$757$	−15.9595			−0.580056			−0.290028	−	0.957018i	$-0.593665\pi$
$757$	−15.9595			−0.580056			−0.290028	+	0.957018i	$0.593665\pi$
$758$	−60.3154			−2.19075
$759$	6.68964	−	41.7638i	0.242819	−	1.51593i
$760$	1.42296			0.0516161
$761$	5.51055	−	9.54456i	0.199757	−	0.345990i	−0.748692	−	0.662918i	$-0.769318\pi$
$761$	5.51055	−	9.54456i	0.199757	−	0.345990i	0.948450	+	0.316928i	$0.102651\pi$
$762$	4.64703	−	29.0116i	0.168344	−	1.05098i
$763$	−27.4943	−	19.2467i	−0.995361	−	0.696779i
$764$	−49.6672			−1.79689
$765$	−2.74484	−	13.1393i	−0.0992399	−	0.475053i
$766$	2.60377	−	4.50985i	0.0940779	−	0.162948i
$767$	−3.34542	−	5.79444i	−0.120796	−	0.209225i
$768$	−5.59902	+	34.9550i	−0.202037	+	1.26133i
$769$	−18.7097	−	32.4061i	−0.674688	−	1.16859i	−0.976560	−	0.215245i	$-0.930945\pi$
$769$	−18.7097	−	32.4061i	−0.674688	−	1.16859i	0.301873	−	0.953348i	$-0.402388\pi$
$770$	−2.43734	+	27.8981i	−0.0878358	+	1.00538i
$771$	−38.3852	−	31.1951i	−1.38241	−	1.12346i
$772$	39.8693			1.43493
$773$	3.56136	−	6.16845i	0.128093	−	0.221864i	−0.794845	−	0.606813i	$-0.792448\pi$
$773$	3.56136	−	6.16845i	0.128093	−	0.221864i	0.922938	+	0.384949i	$0.125781\pi$
$774$	−18.5545	+	16.5894i	−0.666927	+	0.596292i
$775$	4.01507	+	6.95430i	0.144225	+	0.249806i
$776$	−57.6341	+	99.8252i	−2.06894	+	3.58352i
$777$	8.79853	+	30.8737i	0.315646	+	1.10759i
$778$	41.7999	+	72.3995i	1.49860	+	2.59565i
$779$	−0.228723	+	0.396159i	−0.00819484	+	0.0141939i
$780$	2.87402	−	17.9426i	0.102906	−	0.642449i
$781$	13.3059	+	23.0466i	0.476124	+	0.824671i
$782$	−37.5605	−	65.0567i	−1.34316	−	2.32642i
$783$	2.16138	+	3.36679i	0.0772415	+	0.120319i
$784$	−91.6572	−	16.1386i	−3.27347	−	0.576380i
$785$	3.60535	−	6.24465i	0.128680	−	0.222881i
$786$	−35.0543	−	28.4881i	−1.25034	−	1.01614i
$787$	−9.15600			−0.326376			−0.163188	−	0.986595i	$-0.552178\pi$
$787$	−9.15600			−0.326376			−0.163188	+	0.986595i	$0.552178\pi$
$788$	111.644			3.97717
$789$	−22.1709	+	8.46612i	−0.789303	+	0.301402i
$790$	15.2664	−	26.4421i	0.543153	−	0.940768i
$791$	−15.7290	+	7.33690i	−0.559260	+	0.260870i
$792$	21.2805	+	101.868i	0.756171	+	3.61973i
$793$	−6.85491	−	11.8731i	−0.243425	−	0.421625i
$794$	−22.8359	−	39.5529i	−0.810414	−	1.40368i
$795$	−17.8253	+	6.80676i	−0.632200	+	0.241411i
$796$	−0.413602	+	0.716380i	−0.0146597	+	0.0253914i
$797$	−21.7602	−	37.6897i	−0.770785	−	1.33504i	−0.937133	−	0.348972i	$-0.886531\pi$
$797$	−21.7602	−	37.6897i	−0.770785	−	1.33504i	0.166348	−	0.986067i	$-0.446802\pi$
$798$	0.545319	+	1.91350i	0.0193041	+	0.0677372i
$799$	−12.6995	+	21.9961i	−0.449275	+	0.778168i
$800$	9.09202	+	15.7478i	0.321452	+	0.556770i
$801$	−6.33119	−	30.3069i	−0.223702	−	1.07084i
$802$	−22.7065	+	39.3288i	−0.801795	+	1.38875i
$803$	−56.5769			−1.99655
$804$	−14.5866	+	91.0652i	−0.514431	+	3.21162i
$805$	14.9228	−	6.96081i	0.525958	−	0.245336i
$806$	21.5324	+	37.2952i	0.758447	+	1.31367i
$807$	−25.0958	−	20.3950i	−0.883415	−	0.717938i
$808$	−8.53040	−	14.7751i	−0.300098	−	0.519786i
$809$	17.9148	−	31.0293i	0.629850	−	1.09093i	−0.357731	−	0.933825i	$-0.616450\pi$
$809$	17.9148	−	31.0293i	0.629850	−	1.09093i	0.987581	−	0.157108i	$-0.0502171\pi$
$810$	22.2484	−	9.71965i	0.781728	−	0.341514i
$811$	21.5972			0.758379			0.379190	−	0.925319i	$-0.376203\pi$
$811$	21.5972			0.758379			0.379190	+	0.925319i	$0.376203\pi$
$812$	−8.80711	−	6.16520i	−0.309069	−	0.216356i
$813$	−39.8682	+	15.2240i	−1.39824	+	0.533929i
$814$	−37.0750	+	64.2158i	−1.29948	+	2.25076i
$815$	−8.80536			−0.308438
$816$	79.9599	+	64.9822i	2.79916	+	2.27483i
$817$	−0.494990			−0.0173175
$818$	32.1511			1.12414
$819$	15.6680	−	1.87010i	0.547484	−	0.0653467i
$820$	−14.9989			−0.523786
$821$	−25.5473			−0.891607			−0.445803	−	0.895131i	$-0.647082\pi$
$821$	−25.5473			−0.891607			−0.445803	+	0.895131i	$0.647082\pi$
$822$	14.3682	−	5.48661i	0.501147	−	0.191367i
$823$	40.8240			1.42304			0.711518	−	0.702668i	$-0.248008\pi$
$823$	40.8240			1.42304			0.711518	+	0.702668i	$0.248008\pi$
$824$	6.82779	−	11.8261i	0.237857	−	0.411981i
$825$	5.27397	+	4.28608i	0.183616	+	0.149222i
$826$	−2.09070	+	23.9303i	−0.0727447	+	0.832643i
$827$	−2.26313			−0.0786968			−0.0393484	−	0.999226i	$-0.512528\pi$
$827$	−2.26313			−0.0786968			−0.0393484	+	0.999226i	$0.512528\pi$
$828$	73.4546	−	65.6749i	2.55272	−	2.28236i
$829$	−0.766415	+	1.32747i	−0.0266187	+	0.0461049i	−0.879028	−	0.476770i	$-0.841807\pi$
$829$	−0.766415	+	1.32747i	−0.0266187	+	0.0461049i	0.852409	+	0.522875i	$0.175141\pi$
$830$	6.49858	+	11.2559i	0.225569	+	0.390697i
$831$	−23.8793	+	9.11851i	−0.828363	+	0.316318i
$832$	22.3287	+	38.6744i	0.774107	+	1.34079i
$833$	−20.1264	+	23.9976i	−0.697339	+	0.831468i
$834$	48.0853	−	18.3618i	1.66506	−	0.635816i
$835$	−0.940816			−0.0325583
$836$	−1.66634	+	2.88618i	−0.0576315	+	0.0998208i
$837$	−19.1380	+	37.0780i	−0.661505	+	1.28160i
$838$	−15.7480	−	27.2763i	−0.544006	−	0.942245i
$839$	−10.1354	+	17.5550i	−0.349911	+	0.606064i	−0.986233	−	0.165359i	$-0.947122\pi$
$839$	−10.1354	+	17.5550i	−0.349911	+	0.606064i	0.636322	+	0.771424i	$0.280455\pi$
$840$	−28.1912	+	29.0979i	−0.972688	+	1.00397i
$841$	14.2036	+	24.6013i	0.489779	+	0.848321i
$842$	5.63710	−	9.76374i	0.194267	−	0.336481i
$843$	−17.2970	−	14.0570i	−0.595739	−	0.484148i
$844$	11.6325	+	20.1480i	0.400406	+	0.693523i
$845$	4.52394	+	7.83570i	0.155628	+	0.269556i
$846$	−43.6420	−	14.3491i	−1.50044	−	0.493334i
$847$	−9.52616	−	6.66856i	−0.327323	−	0.229135i
$848$	73.2324	−	126.842i	2.51481	−	4.35578i
$849$	−3.46135	+	21.6094i	−0.118793	+	0.741632i
$850$	12.0701			0.414002
$851$	43.5998			1.49458
$852$	−9.80526	+	61.2148i	−0.335923	+	2.09718i
$853$	21.0061	−	36.3836i	0.719234	−	1.24575i	−0.242070	−	0.970259i	$-0.577826\pi$
$853$	21.0061	−	36.3836i	0.719234	−	1.24575i	0.961304	−	0.275490i	$-0.0888402\pi$
$854$	−4.28394	+	49.0343i	−0.146593	+	1.67792i
$855$	0.458692	+	0.150814i	0.0156869	+	0.00515774i
$856$	3.10174	+	5.37237i	0.106015	+	0.183624i
$857$	−25.7529	−	44.6054i	−0.879703	−	1.52369i	−0.851667	−	0.524084i	$-0.824408\pi$
$857$	−25.7529	−	44.6054i	−0.879703	−	1.52369i	−0.0280369	−	0.999607i	$-0.508926\pi$
$858$	28.2838	+	22.9858i	0.965593	+	0.784722i
$859$	10.4661	−	18.1278i	0.357099	−	0.618514i	−0.630376	−	0.776290i	$-0.717099\pi$
$859$	10.4661	−	18.1278i	0.357099	−	0.618514i	0.987475	+	0.157777i	$0.0504326\pi$
$860$	−8.11498	−	14.0556i	−0.276719	−	0.479291i
$861$	−3.56963	−	12.5257i	−0.121653	−	0.426875i
$862$	12.1023	−	20.9618i	0.412207	−	0.713963i
$863$	−2.54430	−	4.40686i	−0.0866090	−	0.150011i	0.819467	−	0.573127i	$-0.194270\pi$
$863$	−2.54430	−	4.40686i	−0.0866090	−	0.150011i	−0.906076	+	0.423116i	$0.860936\pi$
$864$	−43.3374	+	83.9623i	−1.47437	+	2.85646i
$865$	4.76243	−	8.24877i	0.161927	−	0.280467i
$866$	−24.7772			−0.841964
$867$	4.88591	−	1.86572i	0.165934	−	0.0633633i
$868$	9.75833	−	111.695i	0.331219	−	3.79117i
$869$	22.2045	+	38.4594i	0.753237	+	1.30464i
$870$	−3.36093	+	1.28340i	−0.113946	+	0.0435113i
$871$	10.0292	+	17.3711i	0.339826	+	0.588596i
$872$	56.0743	−	97.1236i	1.89892	−	3.28902i
$873$	−29.1586	+	26.0703i	−0.986868	+	0.882347i
$874$	2.70224			0.0914048
$875$	−0.230272	+	2.63571i	−0.00778460	+	0.0891033i
$876$	−102.284	−	83.1244i	−3.45585	−	2.80851i
$877$	−2.87582	+	4.98106i	−0.0971094	+	0.168198i	−0.910487	−	0.413538i	$-0.864293\pi$
$877$	−2.87582	+	4.98106i	−0.0971094	+	0.168198i	0.813378	+	0.581736i	$0.197626\pi$
$878$	−86.7809			−2.92871
$879$	17.5689	−	6.70885i	0.592586	−	0.226284i
$880$	−52.1662			−1.75852
$881$	38.0306			1.28129			0.640643	−	0.767839i	$-0.278668\pi$
$881$	38.0306			1.28129			0.640643	+	0.767839i	$0.278668\pi$
$882$	−49.9327	−	26.7585i	−1.68132	−	0.901006i
$883$	−43.8909			−1.47705			−0.738523	−	0.674228i	$-0.764476\pi$
$883$	−43.8909			−1.47705			−0.738523	+	0.674228i	$0.764476\pi$
$884$	46.9411			1.57880
$885$	4.52390	+	3.67650i	0.152069	+	0.123584i
$886$	−62.2540			−2.09146
$887$	−1.83177	+	3.17272i	−0.0615049	+	0.106530i	−0.895138	−	0.445789i	$-0.852923\pi$
$887$	−1.83177	+	3.17272i	−0.0615049	+	0.106530i	0.833633	+	0.552318i	$0.186257\pi$
$888$	−100.217	+	38.2686i	−3.36305	+	1.28421i
$889$	−1.44800	+	16.5739i	−0.0485643	+	0.555872i
$890$	27.8407			0.933223
$891$	−3.93685	+	35.0928i	−0.131889	+	1.17565i
$892$	−15.4726	+	26.7993i	−0.518061	+	0.897307i
$893$	−0.456824	−	0.791243i	−0.0152870	−	0.0264779i
$894$	58.7784	+	47.7683i	1.96584	+	1.59761i
$895$	11.9714	+	20.7351i	0.400160	+	0.693097i
$896$	5.57962	−	63.8648i	0.186402	−	2.13357i
$897$	3.38943	−	21.1604i	0.113170	−	0.706524i
$898$	−69.3565			−2.31445
$899$	3.09146	−	5.35457i	0.103106	−	0.178585i
$900$	3.23744	+	15.4974i	0.107915	+	0.516579i
$901$	−24.6452	−	42.6867i	−0.821050	−	1.42210i
$902$	15.0416	−	26.0529i	0.500832	−	0.867466i
$903$	9.80658	−	10.1220i	0.326342	−	0.336839i
$904$	−28.9984	−	50.2267i	−0.964472	−	1.67051i
$905$	1.25921	−	2.18102i	0.0418577	−	0.0724997i
$906$	83.6575	−	31.9453i	2.77933	−	1.06131i
$907$	−17.4694	−	30.2580i	−0.580063	−	1.00470i	−0.995471	−	0.0950640i	$-0.969694\pi$
$907$	−17.4694	−	30.2580i	−0.580063	−	1.00470i	0.415408	−	0.909635i	$-0.363639\pi$
$908$	30.8179	+	53.3782i	1.02273	+	1.77142i
$909$	−1.18383	−	5.66688i	−0.0392650	−	0.187958i
$910$	−1.23492	+	14.1351i	−0.0409373	+	0.468573i
$911$	−5.69235	+	9.85944i	−0.188596	+	0.326658i	−0.944782	−	0.327699i	$-0.893727\pi$
$911$	−5.69235	+	9.85944i	−0.188596	+	0.326658i	0.756186	+	0.654356i	$0.227060\pi$
$912$	−3.46252	+	1.32219i	−0.114655	+	0.0437821i
$913$	−18.9040			−0.625633
$914$	−47.2962			−1.56442
$915$	9.26967	+	7.53332i	0.306446	+	0.249044i
$916$	44.8646	−	77.7077i	1.48237	−	2.56754i
$917$	20.9536	+	14.6681i	0.691950	+	0.484383i
$918$	33.8823	+	52.7785i	1.11828	+	1.74195i
$919$	−17.6042	−	30.4913i	−0.580708	−	1.00582i	−0.995396	−	0.0958515i	$-0.969443\pi$
$919$	−17.6042	−	30.4913i	−0.580708	−	1.00582i	0.414688	−	0.909964i	$-0.363891\pi$
$920$	27.5119	+	47.6520i	0.907041	+	1.57104i
$921$	−3.23867	+	20.2192i	−0.106718	+	0.666244i
$922$	−37.1164	+	64.2875i	−1.22236	+	2.11720i
$923$	6.74170	+	11.6770i	0.221906	+	0.384352i
$924$	−26.0063	−	91.2549i	−0.855543	−	3.00207i
$925$	−3.50272	+	6.06689i	−0.115169	+	0.199478i
$926$	−26.7966	−	46.4131i	−0.880591	−	1.52523i
$927$	3.45435	−	3.08850i	0.113456	−	0.101440i
$928$	7.00054	−	12.1253i	0.229804	−	0.398032i
$929$	41.3178			1.35559			0.677797	−	0.735249i	$-0.262935\pi$
$929$	41.3178			1.35559			0.677797	+	0.735249i	$0.262935\pi$
$930$	−29.1176	−	23.6634i	−0.954802	−	0.775953i
$931$	−0.385594	−	1.05861i	−0.0126373	−	0.0346945i
$932$	1.85335	+	3.21010i	0.0607086	+	0.105150i
$933$	5.33175	−	33.2864i	0.174554	−	1.08975i
$934$	34.4595	+	59.6856i	1.12755	+	1.95297i
$935$	−8.77785	+	15.2037i	−0.287066	+	0.497214i
$936$	10.7822	+	51.6133i	0.352426	+	1.68703i
$937$	−37.0566			−1.21059			−0.605293	−	0.796003i	$-0.706944\pi$
$937$	−37.0566			−1.21059			−0.605293	+	0.796003i	$0.706944\pi$
$938$	6.26768	−	71.7404i	0.204647	−	2.34241i
$939$	−3.88722	+	24.2681i	−0.126855	+	0.791960i
$940$	14.9786	−	25.9437i	0.488547	−	0.846189i
$941$	30.0963			0.981112			0.490556	−	0.871410i	$-0.336794\pi$
$941$	30.0963			0.981112			0.490556	+	0.871410i	$0.336794\pi$
$942$	−5.32875	+	33.2677i	−0.173620	+	1.08392i
$943$	−17.6888			−0.576026
$944$	−44.7470			−1.45639
$945$	−12.1714	+	6.39186i	−0.395937	+	0.207927i
$946$	32.5523			1.05837
$947$	58.5758			1.90346			0.951730	−	0.306938i	$-0.0993044\pi$
$947$	58.5758			1.90346			0.951730	+	0.306938i	$0.0993044\pi$
$948$	−16.3627	+	102.153i	−0.531436	+	3.31778i
$949$	−28.6657			−0.930527
$950$	−0.217093	+	0.376016i	−0.00704342	+	0.0121996i
$951$	2.12248	−	13.2507i	0.0688260	−	0.429685i
$952$	−85.7392	−	60.0197i	−2.77882	−	1.94525i
$953$	33.7935			1.09468			0.547340	−	0.836910i	$-0.315641\pi$
$953$	33.7935			1.09468			0.547340	+	0.836910i	$0.315641\pi$
$954$	66.4627	−	59.4235i	2.15181	−	1.92391i
$955$	4.70573	−	8.15057i	0.152274	−	0.263746i
$956$	−7.26308	−	12.5800i	−0.234905	−	0.406867i
$957$	0.827608	−	5.16680i	0.0267528	−	0.167019i
$958$	−0.256587	−	0.444422i	−0.00828996	−	0.0143586i
$959$	−7.89247	+	3.68149i	−0.254861	+	0.118882i
$960$	−30.1943	−	24.5384i	−0.974517	−	0.791974i
$961$	33.4831			1.08010
$962$	−18.7847	+	32.5361i	−0.605644	+	1.04901i
$963$	0.430451	+	2.06053i	0.0138711	+	0.0663998i
$964$	−40.1945	−	69.6190i	−1.29458	−	2.24228i
$965$	−3.77743	+	6.54271i	−0.121600	+	0.210617i
$966$	−53.5360	+	55.2579i	−1.72249	+	1.77789i
$967$	3.11625	+	5.39750i	0.100212	+	0.173572i	0.911772	−	0.410697i	$-0.134715\pi$
$967$	3.11625	+	5.39750i	0.100212	+	0.173572i	−0.811560	+	0.584269i	$0.801381\pi$
$968$	19.4285	−	33.6511i	0.624455	−	1.08159i
$969$	−0.197279	+	1.23162i	−0.00633751	+	0.0395654i
$970$	−17.5858	−	30.4596i	−0.564647	−	0.977998i
$971$	14.8809	+	25.7744i	0.477550	+	0.827141i	0.999669	−	0.0257316i	$-0.00819152\pi$
$971$	14.8809	+	25.7744i	0.477550	+	0.827141i	−0.522119	+	0.852873i	$0.674858\pi$
$972$	−58.6767	+	57.6591i	−1.88206	+	1.84942i
$973$	−26.4134	+	12.3207i	−0.846773	+	0.394982i
$974$	−7.16455	+	12.4094i	−0.229567	+	0.397621i
$975$	2.67215	+	2.17162i	0.0855774	+	0.0695474i
$976$	−91.6887			−2.93488
$977$	−37.3516			−1.19498			−0.597492	−	0.801875i	$-0.703836\pi$
$977$	−37.3516			−1.19498			−0.597492	+	0.801875i	$0.703836\pi$
$978$	38.4358	−	14.6770i	1.22904	−	0.469319i
$979$	−20.2468	+	35.0685i	−0.647091	+	1.12079i
$980$	23.7384	−	28.3043i	0.758295	−	0.904148i
$981$	28.3694	−	25.3648i	0.905766	−	0.809835i
$982$	27.3009	+	47.2866i	0.871208	+	1.50898i
$983$	8.92469	+	15.4580i	0.284653	+	0.493034i	0.972525	−	0.232798i	$-0.0747882\pi$
$983$	8.92469	+	15.4580i	0.284653	+	0.493034i	−0.687872	+	0.725832i	$0.741455\pi$
$984$	40.6587	−	15.5259i	1.29615	−	0.494946i
$985$	−10.5778	+	18.3213i	−0.337037	+	0.583765i
$986$	−4.64679	−	8.04848i	−0.147984	−	0.256316i
$987$	25.2305	+	6.33430i	0.803095	+	0.201623i
$988$	−0.844281	+	1.46234i	−0.0268602	+	0.0465231i
$989$	−9.57028	−	16.5762i	−0.304317	−	0.527093i
$990$	−30.1653	−	9.91810i	−0.958715	−	0.315218i
$991$	−13.4638	+	23.3199i	−0.427691	+	0.740782i	−0.996667	−	0.0815716i	$-0.974006\pi$
$991$	−13.4638	+	23.3199i	−0.427691	+	0.740782i	0.568977	+	0.822354i	$0.307339\pi$
$992$	146.020			4.63615
$993$	7.61716	−	47.5543i	0.241723	−	1.50909i
$994$	4.21318	−	48.2245i	0.133634	−	1.52959i
$995$	−0.0783738	−	0.135747i	−0.00248462	−	0.00430348i
$996$	−34.1761	−	27.7744i	−1.08291	−	0.880065i
$997$	19.3599	+	33.5324i	0.613135	+	1.06198i	0.990709	+	0.136001i	$0.0434251\pi$
$997$	19.3599	+	33.5324i	0.613135	+	1.06198i	−0.377574	+	0.925979i	$0.623242\pi$
$998$	−3.27760	+	5.67697i	−0.103751	+	0.179701i
$999$	−36.3609	+	1.71431i	−1.15041	+	0.0542383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.c.151.1	yes	36
3.2	odd	2		945.2.l.c.46.18		36
7.2	even	3		315.2.k.c.16.18	✓	36
9.4	even	3		315.2.k.c.256.18	yes	36
9.5	odd	6		945.2.k.c.361.1		36
21.2	odd	6		945.2.k.c.856.1		36
63.23	odd	6		945.2.l.c.226.18		36
63.58	even	3	inner	315.2.l.c.121.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.18	✓	36	7.2	even	3
315.2.k.c.256.18	yes	36	9.4	even	3
315.2.l.c.121.1	yes	36	63.58	even	3	inner
315.2.l.c.151.1	yes	36	1.1	even	1	trivial
945.2.k.c.361.1		36	9.5	odd	6
945.2.k.c.856.1		36	21.2	odd	6
945.2.l.c.46.18		36	3.2	odd	2
945.2.l.c.226.18		36	63.23	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.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.69765 q^{2} +(-0.273945 + 1.71025i) q^{3} +5.27730 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.739006 - 4.61365i) q^{6} +(-0.230272 + 2.63571i) q^{7} -8.84100 q^{8} +(-2.84991 - 0.937027i) q^{9} +O(q^{10})\)	\(q-2.69765 q^{2} +(-0.273945 + 1.71025i) q^{3} +5.27730 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.739006 - 4.61365i) q^{6} +(-0.230272 + 2.63571i) q^{7} -8.84100 q^{8} +(-2.84991 - 0.937027i) q^{9} +(1.34882 - 2.33623i) q^{10} +(1.96183 + 3.39799i) q^{11} +(-1.44569 + 9.02550i) q^{12} +(0.993996 + 1.72165i) q^{13} +(0.621192 - 7.11022i) q^{14} +(-1.34415 - 1.09237i) q^{15} +13.2953 q^{16} +(2.23716 - 3.87488i) q^{17} +(7.68805 + 2.52777i) q^{18} +(0.0804749 + 0.139387i) q^{19} +(-2.63865 + 4.57028i) q^{20} +(-4.44464 - 1.11586i) q^{21} +(-5.29232 - 9.16657i) q^{22} +(-3.11185 + 5.38989i) q^{23} +(2.42194 - 15.1203i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.68145 - 4.64441i) q^{26} +(2.38327 - 4.61736i) q^{27} +(-1.21521 + 13.9094i) q^{28} +(-0.384982 + 0.666809i) q^{29} +(3.62604 + 2.94682i) q^{30} -8.03014 q^{31} -18.1840 q^{32} +(-6.34884 + 2.42436i) q^{33} +(-6.03507 + 10.4530i) q^{34} +(-2.16746 - 1.51728i) q^{35} +(-15.0398 - 4.94497i) q^{36} +(-3.50272 - 6.06689i) q^{37} +(-0.217093 - 0.376016i) q^{38} +(-3.21675 + 1.22834i) q^{39} +(4.42050 - 7.65653i) q^{40} +(1.42108 + 2.46138i) q^{41} +(11.9901 + 3.01020i) q^{42} +(-1.53771 + 2.66340i) q^{43} +(10.3532 + 17.9322i) q^{44} +(2.23644 - 1.99958i) q^{45} +(8.39468 - 14.5400i) q^{46} -5.67661 q^{47} +(-3.64218 + 22.7383i) q^{48} +(-6.89395 - 1.21386i) q^{49} +(1.34882 + 2.33623i) q^{50} +(6.01415 + 4.88760i) q^{51} +(5.24562 + 9.08567i) q^{52} +(5.50814 - 9.54037i) q^{53} +(-6.42922 + 12.4560i) q^{54} -3.92366 q^{55} +(2.03583 - 23.3023i) q^{56} +(-0.260432 + 0.0994480i) q^{57} +(1.03855 - 1.79882i) q^{58} -3.36563 q^{59} +(-7.09347 - 5.76475i) q^{60} -6.89632 q^{61} +21.6625 q^{62} +(3.12599 - 7.29577i) q^{63} +22.4635 q^{64} -1.98799 q^{65} +(17.1269 - 6.54006i) q^{66} +10.0898 q^{67} +(11.8062 - 20.4489i) q^{68} +(-8.36558 - 6.79858i) q^{69} +(5.84704 + 4.09308i) q^{70} +6.78242 q^{71} +(25.1961 + 8.28426i) q^{72} +(-7.20971 + 12.4876i) q^{73} +(9.44910 + 16.3663i) q^{74} +(1.61809 - 0.617882i) q^{75} +(0.424690 + 0.735585i) q^{76} +(-9.40787 + 4.38835i) q^{77} +(8.67767 - 3.31364i) q^{78} +11.3183 q^{79} +(-6.64765 + 11.5141i) q^{80} +(7.24396 + 5.34088i) q^{81} +(-3.83357 - 6.63994i) q^{82} +(-2.40898 + 4.17248i) q^{83} +(-23.4557 - 5.88873i) q^{84} +(2.23716 + 3.87488i) q^{85} +(4.14821 - 7.18491i) q^{86} +(-1.03495 - 0.841085i) q^{87} +(-17.3445 - 30.0416i) q^{88} +(5.16019 + 8.93770i) q^{89} +(-6.03314 + 5.39416i) q^{90} +(-4.76667 + 2.22344i) q^{91} +(-16.4222 + 28.4441i) q^{92} +(2.19981 - 13.7335i) q^{93} +15.3135 q^{94} -0.160950 q^{95} +(4.98142 - 31.0993i) q^{96} +(6.51896 - 11.2912i) q^{97} +(18.5974 + 3.27456i) q^{98} +(-2.40703 - 11.5222i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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