LMFDB - Embedded newform 585.2.i.h.196.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			196.9
Character	$\chi$	$=$	585.196
Dual form			585.2.i.h.391.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.300757 - 0.520926i) q^{2} +(1.48936 + 0.884196i) q^{3} +(0.819091 + 1.41871i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.908536 - 0.509919i) q^{6} +(1.29950 - 2.25080i) q^{7} +2.18842 q^{8} +(1.43640 + 2.63377i) q^{9} +O(q^{10})$	\(q+(0.300757 - 0.520926i) q^{2} +(1.48936 + 0.884196i) q^{3} +(0.819091 + 1.41871i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.908536 - 0.509919i) q^{6} +(1.29950 - 2.25080i) q^{7} +2.18842 q^{8} +(1.43640 + 2.63377i) q^{9} +0.601514 q^{10} +(2.56147 - 4.43660i) q^{11} +(-0.0344920 + 2.83720i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-0.781667 - 1.35389i) q^{14} +(-0.0210550 + 1.73192i) q^{15} +(-0.980001 + 1.69741i) q^{16} -5.36998 q^{17} +(1.80401 + 0.0438692i) q^{18} -4.53480 q^{19} +(-0.819091 + 1.41871i) q^{20} +(3.92557 - 2.20324i) q^{21} +(-1.54076 - 2.66868i) q^{22} +(-0.399834 - 0.692533i) q^{23} +(3.25934 + 1.93499i) q^{24} +(-0.500000 + 0.866025i) q^{25} -0.601514 q^{26} +(-0.189458 + 5.19270i) q^{27} +4.25763 q^{28} +(1.66550 - 2.88474i) q^{29} +(0.895871 + 0.531856i) q^{30} +(3.49199 + 6.04830i) q^{31} +(2.77790 + 4.81146i) q^{32} +(7.73779 - 4.34286i) q^{33} +(-1.61506 + 2.79736i) q^{34} +2.59900 q^{35} +(-2.56001 + 4.19512i) q^{36} -10.6386 q^{37} +(-1.36387 + 2.36229i) q^{38} +(0.0210550 - 1.73192i) q^{39} +(1.09421 + 1.89522i) q^{40} +(-2.26990 - 3.93158i) q^{41} +(0.0329160 - 2.70757i) q^{42} +(-3.32801 + 5.76428i) q^{43} +8.39232 q^{44} +(-1.56272 + 2.56084i) q^{45} -0.481011 q^{46} +(2.67547 - 4.63406i) q^{47} +(-2.96042 + 1.66155i) q^{48} +(0.122600 + 0.212349i) q^{49} +(0.300757 + 0.520926i) q^{50} +(-7.99784 - 4.74811i) q^{51} +(0.819091 - 1.41871i) q^{52} -9.68150 q^{53} +(2.64803 + 1.66043i) q^{54} +5.12295 q^{55} +(2.84385 - 4.92569i) q^{56} +(-6.75395 - 4.00965i) q^{57} +(-1.00182 - 1.73521i) q^{58} +(0.409124 + 0.708623i) q^{59} +(-2.47434 + 1.38873i) q^{60} +(2.12396 - 3.67881i) q^{61} +4.20095 q^{62} +(7.79470 + 0.189549i) q^{63} -0.578115 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.0648816 - 5.33696i) q^{66} +(4.82116 + 8.35049i) q^{67} +(-4.39850 - 7.61842i) q^{68} +(0.0168370 - 1.38496i) q^{69} +(0.781667 - 1.35389i) q^{70} -1.13844 q^{71} +(3.14343 + 5.76379i) q^{72} +1.97256 q^{73} +(-3.19962 + 5.54190i) q^{74} +(-1.51042 + 0.847727i) q^{75} +(-3.71441 - 6.43355i) q^{76} +(-6.65727 - 11.5307i) q^{77} +(-0.895871 - 0.531856i) q^{78} +(-3.63802 + 6.30124i) q^{79} -1.96000 q^{80} +(-4.87353 + 7.56629i) q^{81} -2.73075 q^{82} +(8.03275 - 13.9131i) q^{83} +(6.34116 + 3.76458i) q^{84} +(-2.68499 - 4.65054i) q^{85} +(2.00184 + 3.46729i) q^{86} +(5.03121 - 2.82379i) q^{87} +(5.60557 - 9.70913i) q^{88} +4.74177 q^{89} +(0.864012 + 1.58425i) q^{90} -2.59900 q^{91} +(0.655001 - 1.13449i) q^{92} +(-0.147048 + 12.0957i) q^{93} +(-1.60933 - 2.78745i) q^{94} +(-2.26740 - 3.92725i) q^{95} +(-0.116978 + 9.62221i) q^{96} +(3.48300 - 6.03274i) q^{97} +0.147491 q^{98} +(15.3643 + 0.373624i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) $ 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.300757	−	0.520926i	0.212667	−	0.368350i	−0.739881	−	0.672738i	$-0.765118\pi$
$2$	0.300757	−	0.520926i	0.212667	−	0.368350i	0.952548	+	0.304387i	$0.0984517\pi$
$3$	1.48936	+	0.884196i	0.859883	+	0.510491i
$3$	1.48936	+	0.884196i	0.859883	+	0.510491i
$4$	0.819091	+	1.41871i	0.409545	+	0.709353i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.908536	−	0.509919i	0.370908	−	0.208174i
$7$	1.29950	−	2.25080i	0.491165	−	0.850722i	−0.508783	−	0.860895i	$-0.669905\pi$
$7$	1.29950	−	2.25080i	0.491165	−	0.850722i	0.999948	+	0.0101721i	$0.00323794\pi$
$8$	2.18842			0.773722
$9$	1.43640	+	2.63377i	0.478799	+	0.877925i
$10$	0.601514			0.190215
$11$	2.56147	−	4.43660i	0.772313	−	1.33769i	−0.163979	−	0.986464i	$-0.552433\pi$
$11$	2.56147	−	4.43660i	0.772313	−	1.33769i	0.936292	−	0.351222i	$-0.114234\pi$
$12$	−0.0344920	+	2.83720i	−0.00995697	+	0.819030i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	−0.781667	−	1.35389i	−0.208909	−	0.361841i
$15$	−0.0210550	+	1.73192i	−0.00543639	+	0.447181i
$16$	−0.980001	+	1.69741i	−0.245000	+	0.424353i
$17$	−5.36998			−1.30241			−0.651206	−	0.758901i	$-0.725736\pi$
$17$	−5.36998			−1.30241			−0.651206	+	0.758901i	$0.725736\pi$
$18$	1.80401	+	0.0438692i	0.425209	+	0.0103401i
$19$	−4.53480			−1.04035			−0.520177	−	0.854059i	$-0.674134\pi$
$19$	−4.53480			−1.04035			−0.520177	+	0.854059i	$0.674134\pi$
$20$	−0.819091	+	1.41871i	−0.183154	+	0.317232i
$21$	3.92557	−	2.20324i	0.856630	−	0.480787i
$22$	−1.54076	−	2.66868i	−0.328491	−	0.568964i
$23$	−0.399834	−	0.692533i	−0.0833712	−	0.144403i	0.821325	−	0.570461i	$-0.193235\pi$
$23$	−0.399834	−	0.692533i	−0.0833712	−	0.144403i	−0.904696	+	0.426058i	$0.859902\pi$
$24$	3.25934	+	1.93499i	0.665310	+	0.394978i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.601514			−0.117967
$27$	−0.189458	+	5.19270i	−0.0364612	+	0.999335i
$28$	4.25763			0.804617
$29$	1.66550	−	2.88474i	0.309276	−	0.535682i	−0.668928	−	0.743327i	$-0.733247\pi$
$29$	1.66550	−	2.88474i	0.309276	−	0.535682i	0.978204	+	0.207645i	$0.0665798\pi$
$30$	0.895871	+	0.531856i	0.163563	+	0.0971031i
$31$	3.49199	+	6.04830i	0.627179	+	1.08631i	0.988115	+	0.153716i	$0.0491240\pi$
$31$	3.49199	+	6.04830i	0.627179	+	1.08631i	−0.360936	+	0.932591i	$0.617543\pi$
$32$	2.77790	+	4.81146i	0.491068	+	0.850554i
$33$	7.73779	−	4.34286i	1.34698	−	0.755995i
$34$	−1.61506	+	2.79736i	−0.276980	+	0.479744i
$35$	2.59900			0.439311
$36$	−2.56001	+	4.19512i	−0.426669	+	0.699187i
$37$	−10.6386			−1.74897			−0.874484	−	0.485054i	$-0.838800\pi$
$37$	−10.6386			−1.74897			−0.874484	+	0.485054i	$0.838800\pi$
$38$	−1.36387	+	2.36229i	−0.221249	+	0.383215i
$39$	0.0210550	−	1.73192i	0.00337150	−	0.277330i
$40$	1.09421	+	1.89522i	0.173009	+	0.299661i
$41$	−2.26990	−	3.93158i	−0.354499	−	0.614010i	0.632533	−	0.774533i	$-0.282015\pi$
$41$	−2.26990	−	3.93158i	−0.354499	−	0.614010i	−0.987032	+	0.160523i	$0.948682\pi$
$42$	0.0329160	−	2.70757i	0.00507906	−	0.417788i
$43$	−3.32801	+	5.76428i	−0.507517	+	0.879044i	0.492446	+	0.870343i	$0.336103\pi$
$43$	−3.32801	+	5.76428i	−0.507517	+	0.879044i	−0.999962	+	0.00870122i	$0.997230\pi$
$44$	8.39232			1.26519
$45$	−1.56272	+	2.56084i	−0.232956	+	0.381748i
$46$	−0.481011			−0.0709212
$47$	2.67547	−	4.63406i	0.390258	−	0.675946i	−0.602225	−	0.798326i	$-0.705719\pi$
$47$	2.67547	−	4.63406i	0.390258	−	0.675946i	0.992483	+	0.122380i	$0.0390525\pi$
$48$	−2.96042	+	1.66155i	−0.427300	+	0.239824i
$49$	0.122600	+	0.212349i	0.0175142	+	0.0303356i
$50$	0.300757	+	0.520926i	0.0425334	+	0.0736701i
$51$	−7.99784	−	4.74811i	−1.11992	−	0.664869i
$52$	0.819091	−	1.41871i	0.113587	−	0.196739i
$53$	−9.68150			−1.32986			−0.664928	−	0.746907i	$-0.731538\pi$
$53$	−9.68150			−1.32986			−0.664928	+	0.746907i	$0.731538\pi$
$54$	2.64803	+	1.66043i	0.360351	+	0.225956i
$55$	5.12295			0.690778
$56$	2.84385	−	4.92569i	0.380025	−	0.658222i
$57$	−6.75395	−	4.00965i	−0.894583	−	0.531091i
$58$	−1.00182	−	1.73521i	−0.131546	−	0.227844i
$59$	0.409124	+	0.708623i	0.0532634	+	0.0922549i	0.891428	−	0.453163i	$-0.149704\pi$
$59$	0.409124	+	0.708623i	0.0532634	+	0.0922549i	−0.838164	+	0.545418i	$0.816371\pi$
$60$	−2.47434	+	1.38873i	−0.319435	+	0.179284i
$61$	2.12396	−	3.67881i	0.271945	−	0.471023i	−0.697415	−	0.716668i	$-0.745666\pi$
$61$	2.12396	−	3.67881i	0.271945	−	0.471023i	0.969360	+	0.245645i	$0.0789997\pi$
$62$	4.20095			0.533522
$63$	7.79470	+	0.189549i	0.982039	+	0.0238809i
$64$	−0.578115			−0.0722644
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$	0.0648816	−	5.33696i	0.00798637	−	0.656934i
$67$	4.82116	+	8.35049i	0.588998	+	1.02018i	0.994364	+	0.106021i	$0.0338109\pi$
$67$	4.82116	+	8.35049i	0.588998	+	1.02018i	−0.405365	+	0.914155i	$0.632856\pi$
$68$	−4.39850	−	7.61842i	−0.533396	−	0.923870i
$69$	0.0168370	−	1.38496i	0.00202694	−	0.166730i
$70$	0.781667	−	1.35389i	0.0934271	−	0.161820i
$71$	−1.13844			−0.135108			−0.0675539	−	0.997716i	$-0.521519\pi$
$71$	−1.13844			−0.135108			−0.0675539	+	0.997716i	$0.521519\pi$
$72$	3.14343	+	5.76379i	0.370457	+	0.679269i
$73$	1.97256			0.230871			0.115435	−	0.993315i	$-0.463174\pi$
$73$	1.97256			0.230871			0.115435	+	0.993315i	$0.463174\pi$
$74$	−3.19962	+	5.54190i	−0.371948	+	0.644233i
$75$	−1.51042	+	0.847727i	−0.174408	+	0.0978871i
$76$	−3.71441	−	6.43355i	−0.426072	−	0.737978i
$77$	−6.65727	−	11.5307i	−0.758666	−	1.31405i
$78$	−0.895871	−	0.531856i	−0.101437	−	0.0602208i
$79$	−3.63802	+	6.30124i	−0.409309	+	0.708944i	−0.994812	−	0.101726i	$-0.967564\pi$
$79$	−3.63802	+	6.30124i	−0.409309	+	0.708944i	0.585503	+	0.810670i	$0.300897\pi$
$80$	−1.96000			−0.219135
$81$	−4.87353	+	7.56629i	−0.541504	+	0.840698i
$82$	−2.73075			−0.301561
$83$	8.03275	−	13.9131i	0.881709	−	1.52716i	0.0322692	−	0.999479i	$-0.489727\pi$
$83$	8.03275	−	13.9131i	0.881709	−	1.52716i	0.849440	−	0.527686i	$-0.176940\pi$
$84$	6.34116	+	3.76458i	0.691877	+	0.410749i
$85$	−2.68499	−	4.65054i	−0.291228	−	0.504422i
$86$	2.00184	+	3.46729i	0.215864	+	0.373888i
$87$	5.03121	−	2.82379i	0.539402	−	0.302742i
$88$	5.60557	−	9.70913i	0.597556	−	1.03500i
$89$	4.74177			0.502626			0.251313	−	0.967906i	$-0.419138\pi$
$89$	4.74177			0.502626			0.251313	+	0.967906i	$0.419138\pi$
$90$	0.864012	+	1.58425i	0.0910748	+	0.166995i
$91$	−2.59900			−0.272449
$92$	0.655001	−	1.13449i	0.0682886	−	0.118279i
$93$	−0.147048	+	12.0957i	−0.0152481	+	1.25427i
$94$	−1.60933	−	2.78745i	−0.165990	−	0.287503i
$95$	−2.26740	−	3.92725i	−0.232630	−	0.402927i
$96$	−0.116978	+	9.62221i	−0.0119390	+	0.982063i
$97$	3.48300	−	6.03274i	0.353645	−	0.612532i	−0.633240	−	0.773956i	$-0.718275\pi$
$97$	3.48300	−	6.03274i	0.353645	−	0.612532i	0.986885	+	0.161424i	$0.0516086\pi$
$98$	0.147491			0.0148988
$99$	15.3643	+	0.373624i	1.54417	+	0.0375506i
$100$	−1.63818			−0.163818
$101$	6.12399	−	10.6071i	0.609360	−	1.05544i	−0.381986	−	0.924168i	$-0.624760\pi$
$101$	6.12399	−	10.6071i	0.609360	−	1.05544i	0.991346	−	0.131275i	$-0.0419070\pi$
$102$	−4.87882	+	2.73826i	−0.483075	+	0.271128i
$103$	−8.40857	−	14.5641i	−0.828521	−	1.43504i	−0.899198	−	0.437542i	$-0.855849\pi$
$103$	−8.40857	−	14.5641i	−0.828521	−	1.43504i	0.0706769	−	0.997499i	$-0.477484\pi$
$104$	−1.09421	−	1.89522i	−0.107296	−	0.185842i
$105$	3.87085	+	2.29802i	0.377756	+	0.224264i
$106$	−2.91178	+	5.04335i	−0.282817	+	0.489853i
$107$	−5.10514			−0.493532			−0.246766	−	0.969075i	$-0.579368\pi$
$107$	−5.10514			−0.493532			−0.246766	+	0.969075i	$0.579368\pi$
$108$	−7.52210	+	3.98450i	−0.723814	+	0.383409i
$109$	−6.15946			−0.589969			−0.294985	−	0.955502i	$-0.595315\pi$
$109$	−6.15946			−0.589969			−0.294985	+	0.955502i	$0.595315\pi$
$110$	1.54076	−	2.66868i	0.146906	−	0.254448i
$111$	−15.8447	−	9.40656i	−1.50391	−	0.892832i
$112$	2.54702	+	4.41157i	0.240671	+	0.416854i
$113$	1.58696	+	2.74870i	0.149289	+	0.258576i	0.930965	−	0.365109i	$-0.118968\pi$
$113$	1.58696	+	2.74870i	0.149289	+	0.258576i	−0.781676	+	0.623685i	$0.785635\pi$
$114$	−4.12003	+	2.31238i	−0.385876	+	0.216574i
$115$	0.399834	−	0.692533i	0.0372847	−	0.0645790i
$116$	5.45680			0.506651
$117$	1.56272	−	2.56084i	0.144473	−	0.236750i
$118$	0.492187			0.0453095
$119$	−6.97829	+	12.0867i	−0.639698	+	1.10799i
$120$	−0.0460772	+	3.79017i	−0.00420625	+	0.345993i
$121$	−7.62230	−	13.2022i	−0.692936	−	1.20020i
$122$	−1.27759	−	2.21285i	−0.115668	−	0.200342i
$123$	0.0955857	−	7.86259i	0.00861867	−	0.708945i
$124$	−5.72051	+	9.90821i	−0.513717	+	0.889783i
$125$	−1.00000			−0.0894427
$126$	2.44305	−	4.00345i	0.217644	−	0.356656i
$127$	14.2855			1.26763			0.633817	−	0.773483i	$-0.281487\pi$
$127$	14.2855			1.26763			0.633817	+	0.773483i	$0.281487\pi$
$128$	−5.72967	+	9.92408i	−0.506436	+	0.877173i
$129$	−10.0534	+	5.64249i	−0.885149	+	0.496793i
$130$	−0.300757	−	0.520926i	−0.0263781	−	0.0456882i
$131$	8.56471	+	14.8345i	0.748302	+	1.29610i	0.948636	+	0.316369i	$0.102464\pi$
$131$	8.56471	+	14.8345i	0.748302	+	1.29610i	−0.200334	+	0.979728i	$0.564203\pi$
$132$	12.4992	+	7.42045i	1.08792	+	0.645867i
$133$	−5.89297	+	10.2069i	−0.510985	+	0.885052i
$134$	5.79999			0.501043
$135$	−4.59174	+	2.43227i	−0.395194	+	0.209337i
$136$	−11.7517			−1.00770
$137$	0.122140	−	0.211552i	0.0104351	−	0.0180741i	−0.860761	−	0.509010i	$-0.830012\pi$
$137$	0.122140	−	0.211552i	0.0104351	−	0.0180741i	0.871196	+	0.490936i	$0.163345\pi$
$138$	−0.716400	−	0.425308i	−0.0609840	−	0.0362046i
$139$	−1.47612	−	2.55672i	−0.125203	−	0.216858i	0.796609	−	0.604495i	$-0.206625\pi$
$139$	−1.47612	−	2.55672i	−0.125203	−	0.216858i	−0.921812	+	0.387637i	$0.873292\pi$
$140$	2.12882	+	3.68722i	0.179918	+	0.311627i
$141$	8.08216	−	4.53614i	0.680641	−	0.382012i
$142$	−0.342393	+	0.593042i	−0.0287330	+	0.0497670i
$143$	−5.12295			−0.428402
$144$	−5.87827	−	0.142946i	−0.489856	−	0.0119121i
$145$	3.33101			0.276625
$146$	0.593261	−	1.02756i	0.0490986	−	0.0850413i
$147$	−0.00516268	+	0.424667i	−0.000425811	+	0.0350259i
$148$	−8.71394	−	15.0930i	−0.716282	−	1.24064i
$149$	11.0576	+	19.1524i	0.905878	+	1.56903i	0.819735	+	0.572744i	$0.194121\pi$
$149$	11.0576	+	19.1524i	0.905878	+	1.56903i	0.0861433	+	0.996283i	$0.472546\pi$
$150$	−0.0126649	+	1.04178i	−0.00103408	+	0.0850606i
$151$	−10.8347	+	18.7663i	−0.881718	+	1.52718i	−0.0322876	+	0.999479i	$0.510279\pi$
$151$	−10.8347	+	18.7663i	−0.881718	+	1.52718i	−0.849430	+	0.527701i	$0.823054\pi$
$152$	−9.92402			−0.804944
$153$	−7.71342	−	14.1433i	−0.623593	−	1.14342i
$154$	−8.00888			−0.645374
$155$	−3.49199	+	6.04830i	−0.280483	+	0.485811i
$156$	2.47434	−	1.38873i	0.198105	−	0.111187i
$157$	5.31055	+	9.19815i	0.423828	+	0.734092i	0.996310	−	0.0858253i	$-0.0273527\pi$
$157$	5.31055	+	9.19815i	0.423828	+	0.734092i	−0.572482	+	0.819917i	$0.694019\pi$
$158$	2.18832	+	3.79028i	0.174093	+	0.301538i
$159$	−14.4193	−	8.56034i	−1.14352	−	0.678879i
$160$	−2.77790	+	4.81146i	−0.219612	+	0.380380i
$161$	−2.07834			−0.163796
$162$	2.47573	+	4.81436i	0.194512	+	0.378252i
$163$	−15.6209			−1.22352			−0.611761	−	0.791042i	$-0.709539\pi$
$163$	−15.6209			−1.22352			−0.611761	+	0.791042i	$0.709539\pi$
$164$	3.71851	−	6.44065i	0.290367	−	0.502930i
$165$	7.62992	+	4.52969i	0.593989	+	0.352636i
$166$	−4.83181	−	8.36894i	−0.375021	−	0.649556i
$167$	−12.1521	−	21.0480i	−0.940355	−	1.62874i	−0.764795	−	0.644274i	$-0.777160\pi$
$167$	−12.1521	−	21.0480i	−0.940355	−	1.62874i	−0.175560	−	0.984469i	$-0.556173\pi$
$168$	8.59078	−	4.82161i	0.662793	−	0.371995i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−3.23011			−0.247738
$171$	−6.51376	−	11.9436i	−0.498120	−	0.913352i
$172$	−10.9038			−0.831404
$173$	6.84676	−	11.8589i	0.520549	−	0.901618i	−0.479165	−	0.877725i	$-0.659061\pi$
$173$	6.84676	−	11.8589i	0.520549	−	0.901618i	0.999715	−	0.0238931i	$-0.00760615\pi$
$174$	0.0421869	−	3.47016i	0.00319818	−	0.263072i
$175$	1.29950	+	2.25080i	0.0982330	+	0.170144i
$176$	5.02049	+	8.69575i	0.378434	+	0.655467i
$177$	−0.0172282	+	1.41714i	−0.00129495	+	0.106519i
$178$	1.42612	−	2.47011i	0.106892	−	0.185143i
$179$	−4.97769			−0.372050			−0.186025	−	0.982545i	$-0.559561\pi$
$179$	−4.97769			−0.372050			−0.186025	+	0.982545i	$0.559561\pi$
$180$	−4.91309	−	0.119475i	−0.366200	−	0.00890513i
$181$	24.4686			1.81874			0.909370	−	0.415989i	$-0.136565\pi$
$181$	24.4686			1.81874			0.909370	+	0.415989i	$0.136565\pi$
$182$	−0.781667	+	1.35389i	−0.0579410	+	0.100357i
$183$	6.41613	−	3.60108i	0.474294	−	0.266199i
$184$	−0.875003	−	1.51555i	−0.0645061	−	0.111728i
$185$	−5.31928	−	9.21326i	−0.391081	−	0.677372i
$186$	6.25674	+	3.71447i	0.458766	+	0.272358i
$187$	−13.7551	+	23.8245i	−1.00587	+	1.74222i
$188$	8.76582			0.639313
$189$	11.4415	+	7.17434i	0.832248	+	0.521857i
$190$	−2.72774			−0.197891
$191$	6.12634	−	10.6111i	0.443287	−	0.767795i	−0.554644	−	0.832087i	$-0.687146\pi$
$191$	6.12634	−	10.6111i	0.443287	−	0.767795i	0.997931	+	0.0642925i	$0.0204791\pi$
$192$	−0.861022	−	0.511167i	−0.0621389	−	0.0368903i
$193$	−2.81469	−	4.87519i	−0.202606	−	0.350924i	0.746761	−	0.665092i	$-0.231608\pi$
$193$	−2.81469	−	4.87519i	−0.202606	−	0.350924i	−0.949367	+	0.314168i	$0.898274\pi$
$194$	−2.09507	−	3.62877i	−0.150418	−	0.260531i
$195$	1.51042	−	0.847727i	0.108163	−	0.0607070i
$196$	−0.200841	+	0.347866i	−0.0143458	+	0.0248476i
$197$	8.58427			0.611604			0.305802	−	0.952095i	$-0.401075\pi$
$197$	8.58427			0.611604			0.305802	+	0.952095i	$0.401075\pi$
$198$	4.81555	−	7.89129i	0.342226	−	0.560810i
$199$	14.3987			1.02069			0.510347	−	0.859969i	$-0.329517\pi$
$199$	14.3987			1.02069			0.510347	+	0.859969i	$0.329517\pi$
$200$	−1.09421	+	1.89522i	−0.0773722	+	0.134013i
$201$	−0.203019	+	16.6998i	−0.0143199	+	1.17791i
$202$	−3.68367	−	6.38030i	−0.259182	−	0.448916i
$203$	−4.32865	−	7.49743i	−0.303811	−	0.526217i
$204$	0.185221	−	15.2357i	0.0129681	−	1.06671i
$205$	2.26990	−	3.93158i	0.158537	−	0.274594i
$206$	−10.1157			−0.704797
$207$	1.24966	−	2.04782i	0.0868570	−	0.142334i
$208$	1.96000			0.135902
$209$	−11.6158	+	20.1191i	−0.803479	+	1.39167i
$210$	2.36129	−	1.32528i	0.162944	−	0.0914530i
$211$	−7.54047	−	13.0605i	−0.519107	−	0.899120i	−0.999753	−	0.0222054i	$-0.992931\pi$
$211$	−7.54047	−	13.0605i	−0.519107	−	0.899120i	0.480646	−	0.876915i	$-0.340402\pi$
$212$	−7.93003	−	13.7352i	−0.544637	−	0.943338i
$213$	−1.69555	−	1.00660i	−0.116177	−	0.0689712i
$214$	−1.53541	+	2.65940i	−0.104958	+	0.181793i
$215$	−6.65602			−0.453937
$216$	−0.414613	+	11.3638i	−0.0282108	+	0.773207i
$217$	18.1513			1.23219
$218$	−1.85250	+	3.20862i	−0.125467	+	0.217315i
$219$	2.93786	+	1.74413i	0.198522	+	0.117857i
$220$	4.19616	+	7.26796i	0.282905	+	0.490006i
$221$	2.68499	+	4.65054i	0.180612	+	0.312829i
$222$	−9.66551	+	5.42481i	−0.648707	+	0.364089i
$223$	2.50094	−	4.33175i	0.167475	−	0.290075i	−0.770056	−	0.637976i	$-0.779772\pi$
$223$	2.50094	−	4.33175i	0.167475	−	0.290075i	0.937531	+	0.347900i	$0.113105\pi$
$224$	14.4395			0.964781
$225$	−2.99911	−	0.0729314i	−0.199941	−	0.00486209i
$226$	1.90916			0.126995
$227$	1.87440	−	3.24655i	0.124408	−	0.215481i	−0.797093	−	0.603856i	$-0.793630\pi$
$227$	1.87440	−	3.24655i	0.124408	−	0.215481i	0.921501	+	0.388375i	$0.126964\pi$
$228$	0.156414	−	12.8661i	0.0103588	−	0.852081i
$229$	7.51441	+	13.0153i	0.496566	+	0.860078i	0.999992	−	0.00396049i	$-0.00126067\pi$
$229$	7.51441	+	13.0153i	0.496566	+	0.860078i	−0.503426	+	0.864038i	$0.667927\pi$
$230$	−0.240506	−	0.416568i	−0.0158585	−	0.0274677i
$231$	0.280338	−	23.0598i	0.0184449	−	1.51722i
$232$	3.64482	−	6.31301i	0.239294	−	0.414469i
$233$	4.28953			0.281016			0.140508	−	0.990080i	$-0.455126\pi$
$233$	4.28953			0.281016			0.140508	+	0.990080i	$0.455126\pi$
$234$	−0.864012	−	1.58425i	−0.0564822	−	0.103566i
$235$	5.35095			0.349057
$236$	−0.670219	+	1.16085i	−0.0436275	+	0.0755651i
$237$	−10.9899	+	6.16810i	−0.713868	+	0.400661i
$238$	4.19753	+	7.27034i	0.272086	+	0.471266i
$239$	8.90599	+	15.4256i	0.576080	+	0.997801i	0.995923	+	0.0902038i	$0.0287518\pi$
$239$	8.90599	+	15.4256i	0.576080	+	0.997801i	−0.419843	+	0.907597i	$0.637915\pi$
$240$	−2.91915	−	1.73302i	−0.188430	−	0.111866i
$241$	8.04652	−	13.9370i	0.518322	−	0.897760i	−0.481452	−	0.876473i	$-0.659890\pi$
$241$	8.04652	−	13.9370i	0.518322	−	0.897760i	0.999773	−	0.0212871i	$-0.00677640\pi$
$242$	−9.16983			−0.589459
$243$	−13.9485	+	6.95978i	−0.894799	+	0.446470i
$244$	6.95887			0.445496
$245$	−0.122600	+	0.212349i	−0.00783261	+	0.0135665i
$246$	−4.06708	−	2.41452i	−0.259307	−	0.153944i
$247$	2.26740	+	3.92725i	0.144271	+	0.249885i
$248$	7.64192	+	13.2362i	0.485262	+	0.840499i
$249$	24.2656	−	13.6192i	1.53777	−	0.863079i
$250$	−0.300757	+	0.520926i	−0.0190215	+	0.0329463i
$251$	−13.8501			−0.874210			−0.437105	−	0.899411i	$-0.643996\pi$
$251$	−13.8501			−0.874210			−0.437105	+	0.899411i	$0.643996\pi$
$252$	6.11565	+	11.2136i	0.385250	+	0.706393i
$253$	−4.09666			−0.257555
$254$	4.29647	−	7.44170i	0.269584	−	0.466934i
$255$	0.113065	−	9.30039i	0.00708041	−	0.582413i
$256$	2.86836	+	4.96814i	0.179272	+	0.310509i
$257$	2.24959	+	3.89641i	0.140326	+	0.243051i	0.927619	−	0.373527i	$-0.121852\pi$
$257$	2.24959	+	3.89641i	0.140326	+	0.243051i	−0.787294	+	0.616578i	$0.788518\pi$
$258$	−0.0842977	+	6.93407i	−0.00524815	+	0.431696i
$259$	−13.8248	+	23.9453i	−0.859031	+	1.48789i
$260$	1.63818			0.101596
$261$	9.99007	+	0.242935i	0.618370	+	0.0150373i
$262$	10.3036			0.636557
$263$	−8.57024	+	14.8441i	−0.528464	+	0.915326i	0.470986	+	0.882141i	$0.343898\pi$
$263$	−8.57024	+	14.8441i	−0.528464	+	0.915326i	−0.999449	+	0.0331848i	$0.989435\pi$
$264$	16.9335	−	9.50399i	1.04218	−	0.584930i
$265$	−4.84075	−	8.38443i	−0.297365	−	0.515051i
$266$	3.54470	+	6.13960i	0.217339	+	0.376443i
$267$	7.06220	+	4.19265i	0.432200	+	0.256586i
$268$	−7.89794	+	13.6796i	−0.482443	+	0.835616i
$269$	1.81067			0.110398			0.0551992	−	0.998475i	$-0.482421\pi$
$269$	1.81067			0.110398			0.0551992	+	0.998475i	$0.482421\pi$
$270$	−0.113962	+	3.12348i	−0.00693548	+	0.190089i
$271$	19.6697			1.19485			0.597424	−	0.801926i	$-0.296191\pi$
$271$	19.6697			1.19485			0.597424	+	0.801926i	$0.296191\pi$
$272$	5.26258	−	9.11506i	0.319091	−	0.552682i
$273$	−3.87085	−	2.29802i	−0.234275	−	0.139083i
$274$	−0.0734686	−	0.127251i	−0.00443840	−	0.00768754i
$275$	2.56147	+	4.43660i	0.154463	+	0.267537i
$276$	1.97865	−	1.11052i	0.119101	−	0.0668457i
$277$	6.19683	−	10.7332i	0.372331	−	0.644897i	−0.617592	−	0.786498i	$-0.711892\pi$
$277$	6.19683	−	10.7332i	0.372331	−	0.644897i	0.989924	+	0.141602i	$0.0452252\pi$
$278$	−1.77581			−0.106506
$279$	−10.9140	+	17.8849i	−0.653403	+	1.07074i
$280$	5.68769			0.339905
$281$	−5.78362	+	10.0175i	−0.345022	+	0.597595i	−0.985358	−	0.170500i	$-0.945462\pi$
$281$	−5.78362	+	10.0175i	−0.345022	+	0.597595i	0.640336	+	0.768095i	$0.278795\pi$
$282$	0.0677691	−	5.57448i	0.00403559	−	0.331956i
$283$	−7.09436	−	12.2878i	−0.421716	−	0.730433i	0.574392	−	0.818581i	$-0.305239\pi$
$283$	−7.09436	−	12.2878i	−0.421716	−	0.730433i	−0.996107	+	0.0881474i	$0.971905\pi$
$284$	−0.932484	−	1.61511i	−0.0553328	−	0.0958392i
$285$	0.0954803	−	7.85392i	0.00565576	−	0.465226i
$286$	−1.54076	+	2.66868i	−0.0911071	+	0.157802i
$287$	−11.7989			−0.696470
$288$	−8.68214	+	14.2275i	−0.511600	+	0.838365i
$289$	11.8367			0.696274
$290$	1.00182	−	1.73521i	0.0588291	−	0.101895i
$291$	10.5216	−	5.90527i	0.616785	−	0.346173i
$292$	1.61571	+	2.79849i	0.0945521	+	0.163769i
$293$	−8.78426	−	15.2148i	−0.513182	−	0.888857i	−0.999883	−	0.0152888i	$-0.995133\pi$
$293$	−8.78426	−	15.2148i	−0.513182	−	0.888857i	0.486701	−	0.873569i	$-0.338200\pi$
$294$	0.219667	+	0.130411i	0.0128112	+	0.00760571i
$295$	−0.409124	+	0.708623i	−0.0238201	+	0.0412576i
$296$	−23.2816			−1.35321
$297$	22.5526	+	14.1415i	1.30864	+	0.820574i
$298$	13.3027			0.770602
$299$	−0.399834	+	0.692533i	−0.0231230	+	0.0400502i
$300$	−2.43984	−	1.44847i	−0.140864	−	0.0836276i
$301$	8.64949	+	14.9814i	0.498549	+	0.863511i
$302$	6.51724	+	11.2882i	0.375025	+	0.649562i
$303$	18.4996	−	10.3830i	1.06277	−	0.596485i
$304$	4.44410	−	7.69741i	0.254887	−	0.441477i
$305$	4.24792			0.243235
$306$	−9.68748	−	0.235577i	−0.553796	−	0.0134670i
$307$	28.4980			1.62647			0.813233	−	0.581938i	$-0.197705\pi$
$307$	28.4980			1.62647			0.813233	+	0.581938i	$0.197705\pi$
$308$	10.9058	−	18.8894i	0.621417	−	1.07633i
$309$	0.354086	−	29.1260i	0.0201432	−	1.65692i
$310$	2.10048	+	3.63813i	0.119299	+	0.206632i
$311$	10.5961	+	18.3530i	0.600851	+	1.04070i	0.992693	+	0.120671i	$0.0385047\pi$
$311$	10.5961	+	18.3530i	0.600851	+	1.04070i	−0.391842	+	0.920033i	$0.628162\pi$
$312$	0.0460772	−	3.79017i	0.00260861	−	0.214576i
$313$	−6.29174	+	10.8976i	−0.355630	+	0.615970i	−0.987226	−	0.159329i	$-0.949067\pi$
$313$	−6.29174	+	10.8976i	−0.355630	+	0.615970i	0.631595	+	0.775298i	$0.282400\pi$
$314$	6.38874			0.360537
$315$	3.73319	+	6.84518i	0.210342	+	0.385682i
$316$	−11.9195			−0.670523
$317$	6.36185	−	11.0190i	0.357317	−	0.618891i	−0.630195	−	0.776437i	$-0.717025\pi$
$317$	6.36185	−	11.0190i	0.357317	−	0.618891i	0.987512	+	0.157546i	$0.0503582\pi$
$318$	−8.79599	+	4.93679i	−0.493255	+	0.276841i
$319$	−8.53229	−	14.7784i	−0.477717	−	0.827430i
$320$	−0.289057	−	0.500662i	−0.0161588	−	0.0279879i
$321$	−7.60340	−	4.51394i	−0.424380	−	0.251944i
$322$	−0.625074	+	1.08266i	−0.0348340	+	0.0603343i
$323$	24.3518			1.35497
$324$	−14.7262	−	0.716637i	−0.818123	−	0.0398132i
$325$	1.00000			0.0554700
$326$	−4.69809	+	8.13733i	−0.260203	+	0.450685i
$327$	−9.17366	−	5.44617i	−0.507305	−	0.301174i
$328$	−4.96749	−	8.60394i	−0.274284	−	0.475073i
$329$	−6.95355	−	12.0439i	−0.383362	−	0.664002i
$330$	4.65438	−	2.61229i	0.256215	−	0.143802i
$331$	3.46381	−	5.99949i	0.190388	−	0.329762i	−0.754991	−	0.655735i	$-0.772359\pi$
$331$	3.46381	−	5.99949i	0.190388	−	0.329762i	0.945379	+	0.325974i	$0.105692\pi$
$332$	26.3182			1.44440
$333$	−15.2812	−	28.0196i	−0.837404	−	1.53546i
$334$	−14.6193			−0.799930
$335$	−4.82116	+	8.35049i	−0.263408	+	0.456236i
$336$	−0.107255	+	8.82249i	−0.00585125	+	0.481306i
$337$	1.11915	+	1.93843i	0.0609642	+	0.105593i	0.894897	−	0.446273i	$-0.147249\pi$
$337$	1.11915	+	1.93843i	0.0609642	+	0.105593i	−0.833932	+	0.551867i	$0.813916\pi$
$338$	0.300757	+	0.520926i	0.0163590	+	0.0283346i
$339$	−0.0668270	+	5.49699i	−0.00362955	+	0.298555i
$340$	4.39850	−	7.61842i	0.238542	−	0.413167i
$341$	35.7785			1.93752
$342$	−8.18081	−	0.198938i	−0.442367	−	0.0107573i
$343$	18.8303			1.01674
$344$	−7.28307	+	12.6146i	−0.392677	+	0.680136i
$345$	1.20783	−	0.677901i	0.0650275	−	0.0364969i
$346$	−4.11842	−	7.13331i	−0.221407	−	0.383489i
$347$	−13.2274	−	22.9105i	−0.710082	−	1.22990i	−0.964826	−	0.262890i	$-0.915324\pi$
$347$	−13.2274	−	22.9105i	−0.710082	−	1.22990i	0.254743	−	0.967009i	$-0.418009\pi$
$348$	8.12714	+	4.82488i	0.435661	+	0.258640i
$349$	−8.41711	+	14.5789i	−0.450558	+	0.780389i	−0.998421	−	0.0561794i	$-0.982108\pi$
$349$	−8.41711	+	14.5789i	−0.450558	+	0.780389i	0.547863	+	0.836568i	$0.315441\pi$
$350$	1.56333			0.0835637
$351$	4.59174	−	2.43227i	0.245089	−	0.129825i
$352$	28.4621			1.51703
$353$	−16.4476	+	28.4880i	−0.875416	+	1.51626i	−0.0190964	+	0.999818i	$0.506079\pi$
$353$	−16.4476	+	28.4880i	−0.875416	+	1.51626i	−0.856319	+	0.516447i	$0.827254\pi$
$354$	0.733044	+	0.435190i	0.0389609	+	0.0231301i
$355$	−0.569219	−	0.985917i	−0.0302110	−	0.0523270i
$356$	3.88394	+	6.72718i	0.205848	+	0.356540i
$357$	−21.0802	+	11.8314i	−1.11568	+	0.626182i
$358$	−1.49708	+	2.59301i	−0.0791229	+	0.137045i
$359$	−3.73239			−0.196988			−0.0984941	−	0.995138i	$-0.531403\pi$
$359$	−3.73239			−0.196988			−0.0984941	+	0.995138i	$0.531403\pi$
$360$	−3.41987	+	5.60419i	−0.180243	+	0.295367i
$361$	1.56438			0.0823355
$362$	7.35911	−	12.7463i	0.386786	−	0.669933i
$363$	0.320976	−	26.4025i	0.0168468	−	1.38577i
$364$	−2.12882	−	3.68722i	−0.111580	−	0.193263i
$365$	0.986281	+	1.70829i	0.0516243	+	0.0894159i
$366$	0.0537995	−	4.42538i	0.00281214	−	0.231318i
$367$	12.1488	−	21.0423i	0.634160	−	1.09840i	−0.352532	−	0.935800i	$-0.614679\pi$
$367$	12.1488	−	21.0423i	0.634160	−	1.09840i	0.986692	−	0.162598i	$-0.0519874\pi$
$368$	1.56735			0.0817038
$369$	7.09443	−	11.6257i	0.369321	−	0.605211i
$370$	−6.39924			−0.332680
$371$	−12.5811	+	21.7911i	−0.653179	+	1.13134i
$372$	−17.2807	+	9.69886i	−0.895963	+	0.502862i
$373$	4.95877	+	8.58884i	0.256755	+	0.444713i	0.965371	−	0.260882i	$-0.0840132\pi$
$373$	4.95877	+	8.58884i	0.256755	+	0.444713i	−0.708615	+	0.705595i	$0.750680\pi$
$374$	8.27385	+	14.3307i	0.427831	+	0.741025i
$375$	−1.48936	−	0.884196i	−0.0769103	−	0.0456597i
$376$	5.85505	−	10.1412i	0.301951	−	0.522994i
$377$	−3.33101			−0.171556
$378$	7.17842	−	3.80245i	0.369218	−	0.195577i
$379$	−15.6671			−0.804763			−0.402381	−	0.915472i	$-0.631817\pi$
$379$	−15.6671			−0.804763			−0.402381	+	0.915472i	$0.631817\pi$
$380$	3.71441	−	6.43355i	0.190545	−	0.330034i
$381$	21.2763	+	12.6312i	1.09002	+	0.647115i
$382$	−3.68508	−	6.38274i	−0.188545	−	0.326570i
$383$	8.13515	+	14.0905i	0.415687	+	0.719991i	0.995500	−	0.0947585i	$-0.0302079\pi$
$383$	8.13515	+	14.0905i	0.415687	+	0.719991i	−0.579813	+	0.814749i	$0.696875\pi$
$384$	−17.3084	+	9.71439i	−0.883265	+	0.495736i
$385$	6.65727	−	11.5307i	0.339286	−	0.587660i
$386$	−3.38615			−0.172350
$387$	−19.9621	−	0.485433i	−1.01473	−	0.0246759i
$388$	11.4116			0.579335
$389$	−12.8990	+	22.3417i	−0.654005	+	1.13277i	0.328138	+	0.944630i	$0.393579\pi$
$389$	−12.8990	+	22.3417i	−0.654005	+	1.13277i	−0.982142	+	0.188139i	$0.939754\pi$
$390$	0.0126649	−	1.04178i	0.000641312	−	0.0527523i
$391$	2.14710	+	3.71889i	0.108584	+	0.188072i
$392$	0.268299	+	0.464708i	0.0135512	+	0.0234713i
$393$	−0.360660	+	29.6668i	−0.0181929	+	1.49649i
$394$	2.58178	−	4.47177i	0.130068	−	0.225285i
$395$	−7.27604			−0.366097
$396$	12.0547	+	22.1035i	0.605771	+	1.11074i
$397$	10.3951			0.521713			0.260857	−	0.965378i	$-0.415995\pi$
$397$	10.3951			0.521713			0.260857	+	0.965378i	$0.415995\pi$
$398$	4.33049	−	7.50064i	0.217068	−	0.375973i
$399$	−17.8017	+	9.99126i	−0.891198	+	0.500189i
$400$	−0.980001	−	1.69741i	−0.0490000	−	0.0848705i
$401$	−0.0423001	−	0.0732660i	−0.00211237	−	0.00365873i	0.864967	−	0.501828i	$-0.167339\pi$
$401$	−0.0423001	−	0.0732660i	−0.00211237	−	0.00365873i	−0.867080	+	0.498170i	$0.834006\pi$
$402$	8.63828	+	5.12832i	0.430838	+	0.255777i
$403$	3.49199	−	6.04830i	0.173948	−	0.301287i
$404$	20.0644			0.998243
$405$	−8.98936	−	0.437459i	−0.446685	−	0.0217375i
$406$	−5.20748			−0.258443
$407$	−27.2504	+	47.1991i	−1.35075	+	2.33957i
$408$	−17.5026	−	10.3908i	−0.866508	−	0.514423i
$409$	10.4697	+	18.1341i	0.517694	+	0.896671i	0.999789	+	0.0205527i	$0.00654257\pi$
$409$	10.4697	+	18.1341i	0.517694	+	0.896671i	−0.482095	+	0.876119i	$0.660124\pi$
$410$	−1.36538	−	2.36490i	−0.0674311	−	0.116794i
$411$	0.368964	−	0.207082i	0.0181996	−	0.0102146i
$412$	13.7748	−	23.8586i	0.678634	−	1.17543i
$413$	2.12663			0.104644
$414$	−0.690923	−	1.26687i	−0.0339570	−	0.0622635i
$415$	16.0655			0.788624
$416$	2.77790	−	4.81146i	0.136198	−	0.235901i
$417$	0.0621596	−	5.11306i	0.00304397	−	0.250387i
$418$	6.98704	+	12.1019i	0.341747	+	0.591924i
$419$	−10.7091	−	18.5488i	−0.523176	−	0.906167i	−0.999636	−	0.0269711i	$-0.991414\pi$
$419$	−10.7091	−	18.5488i	−0.523176	−	0.906167i	0.476460	−	0.879196i	$-0.341920\pi$
$420$	−0.0896446	+	7.37389i	−0.00437421	+	0.359809i
$421$	13.9364	−	24.1385i	0.679217	−	1.17644i	−0.296000	−	0.955188i	$-0.595653\pi$
$421$	13.9364	−	24.1385i	0.679217	−	1.17644i	0.975217	−	0.221251i	$-0.0710139\pi$
$422$	−9.07139			−0.441588
$423$	16.0481	+	0.390252i	0.780285	+	0.0189747i
$424$	−21.1871			−1.02894
$425$	2.68499	−	4.65054i	0.130241	−	0.225584i
$426$	−1.03431	+	0.580512i	−0.0501126	+	0.0281259i
$427$	−5.52018	−	9.56122i	−0.267140	−	0.462700i
$428$	−4.18157	−	7.24270i	−0.202124	−	0.350089i
$429$	−7.62992	−	4.52969i	−0.368376	−	0.218695i
$430$	−2.00184	+	3.46729i	−0.0965374	+	0.167208i
$431$	0.802560			0.0386580			0.0193290	−	0.999813i	$-0.493847\pi$
$431$	0.802560			0.0386580			0.0193290	+	0.999813i	$0.493847\pi$
$432$	−8.62847	−	5.41044i	−0.415138	−	0.260310i
$433$	−22.8580			−1.09848			−0.549242	−	0.835663i	$-0.685083\pi$
$433$	−22.8580			−1.09848			−0.549242	+	0.835663i	$0.685083\pi$
$434$	5.45914	−	9.45551i	0.262047	−	0.453879i
$435$	4.96108	+	2.94526i	0.237865	+	0.141215i
$436$	−5.04516	−	8.73847i	−0.241619	−	0.418497i
$437$	1.81317	+	3.14050i	0.0867355	+	0.150230i
$438$	1.79214	−	1.00585i	0.0856319	−	0.0480612i
$439$	−19.2250	+	33.2987i	−0.917559	+	1.58926i	−0.114448	+	0.993429i	$0.536510\pi$
$439$	−19.2250	+	33.2987i	−0.917559	+	1.58926i	−0.803111	+	0.595829i	$0.796823\pi$
$440$	11.2111			0.534470
$441$	−0.383177	+	0.627917i	−0.0182465	+	0.0299008i
$442$	3.23011			0.153641
$443$	−17.2644	+	29.9028i	−0.820257	+	1.42073i	0.0852336	+	0.996361i	$0.472836\pi$
$443$	−17.2644	+	29.9028i	−0.820257	+	1.42073i	−0.905491	+	0.424366i	$0.860497\pi$
$444$	0.366945	−	30.1838i	0.0174144	−	1.43246i
$445$	2.37088	+	4.10649i	0.112391	+	0.194666i
$446$	−1.50435	−	2.60561i	−0.0712329	−	0.123379i
$447$	−0.465638	+	38.3020i	−0.0220239	+	1.81162i
$448$	−0.751260	+	1.30122i	−0.0354937	+	0.0614769i
$449$	−31.3590			−1.47992			−0.739962	−	0.672649i	$-0.765157\pi$
$449$	−31.3590			−1.47992			−0.739962	+	0.672649i	$0.765157\pi$
$450$	−0.939996	+	1.54038i	−0.0443118	+	0.0726143i
$451$	−23.2572			−1.09514
$452$	−2.59973	+	4.50286i	−0.122281	+	0.211797i
$453$	−32.7299	+	18.3698i	−1.53779	+	0.863088i
$454$	−1.12747	−	1.95284i	−0.0529150	−	0.0916514i
$455$	−1.29950	−	2.25080i	−0.0609215	−	0.105519i
$456$	−14.7805	−	8.77477i	−0.692158	−	0.410916i
$457$	6.51806	−	11.2896i	0.304902	−	0.528105i	−0.672338	−	0.740245i	$-0.734710\pi$
$457$	6.51806	−	11.2896i	0.304902	−	0.528105i	0.977239	+	0.212139i	$0.0680430\pi$
$458$	9.04004			0.422413
$459$	1.01739	−	27.8847i	0.0474875	−	1.30155i
$460$	1.31000			0.0610791
$461$	20.1102	−	34.8318i	0.936623	−	1.62228i	0.164910	−	0.986309i	$-0.447267\pi$
$461$	20.1102	−	34.8318i	0.936623	−	1.62228i	0.771713	−	0.635970i	$-0.219400\pi$
$462$	−11.9281	−	7.08141i	−0.554946	−	0.329457i
$463$	15.0393	+	26.0488i	0.698935	+	1.21059i	0.968836	+	0.247703i	$0.0796758\pi$
$463$	15.0393	+	26.0488i	0.698935	+	1.21059i	−0.269901	+	0.962888i	$0.586991\pi$
$464$	3.26439	+	5.65409i	0.151546	+	0.262485i
$465$	−10.5487	+	5.92050i	−0.489185	+	0.274557i
$466$	1.29010	−	2.23453i	0.0597629	−	0.103512i
$467$	−15.9026			−0.735882			−0.367941	−	0.929849i	$-0.619937\pi$
$467$	−15.9026			−0.735882			−0.367941	+	0.929849i	$0.619937\pi$
$468$	4.91309	+	0.119475i	0.227108	+	0.00552273i
$469$	25.0604			1.15718
$470$	1.60933	−	2.78745i	0.0742330	−	0.128575i
$471$	−0.223628	+	18.3949i	−0.0103042	+	0.847594i
$472$	0.895333	+	1.55076i	0.0412110	+	0.0713796i
$473$	17.0492	+	29.5301i	0.783924	+	1.35780i
$474$	−0.0921502	+	7.58000i	−0.00423260	+	0.348161i
$475$	2.26740	−	3.92725i	0.104035	−	0.180195i
$476$	−22.8634			−1.04794
$477$	−13.9065	−	25.4989i	−0.636734	−	1.16751i
$478$	10.7141			0.490054
$479$	9.89919	−	17.1459i	0.452306	−	0.783416i	−0.546223	−	0.837640i	$-0.683935\pi$
$479$	9.89919	−	17.1459i	0.452306	−	0.783416i	0.998529	+	0.0542235i	$0.0172683\pi$
$480$	−8.39157	+	4.70980i	−0.383021	+	0.214972i
$481$	5.31928	+	9.21326i	0.242538	+	0.420088i
$482$	−4.84009	−	8.38328i	−0.220460	−	0.381848i
$483$	−3.09540	−	1.83766i	−0.140845	−	0.0836163i
$484$	12.4867	−	21.6276i	0.567578	−	0.983073i
$485$	6.96601			0.316310
$486$	−0.569583	+	9.35935i	−0.0258368	+	0.424549i
$487$	28.2257			1.27903			0.639514	−	0.768779i	$-0.279135\pi$
$487$	28.2257			1.27903			0.639514	+	0.768779i	$0.279135\pi$
$488$	4.64811	−	8.05076i	0.210410	−	0.364441i
$489$	−23.2652	−	13.8119i	−1.05209	−	0.624597i
$490$	0.0737454	+	0.127731i	0.00333148	+	0.00577029i
$491$	−1.71512	−	2.97067i	−0.0774022	−	0.134065i	0.824726	−	0.565532i	$-0.191329\pi$
$491$	−1.71512	−	2.97067i	−0.0774022	−	0.134065i	−0.902128	+	0.431468i	$0.857996\pi$
$492$	11.2330	−	6.30456i	0.506423	−	0.284232i
$493$	−8.94372	+	15.4910i	−0.402805	+	0.697679i
$494$	2.72774			0.122727
$495$	7.35858	+	13.4927i	0.330744	+	0.606451i
$496$	−13.6886			−0.614636
$497$	−1.47940	+	2.56240i	−0.0663602	+	0.114939i
$498$	0.203468	−	16.7366i	0.00911761	−	0.749987i
$499$	−17.6912	−	30.6421i	−0.791967	−	1.37173i	−0.924747	−	0.380582i	$-0.875724\pi$
$499$	−17.6912	−	30.6421i	−0.791967	−	1.37173i	0.132780	−	0.991145i	$-0.457610\pi$
$500$	−0.819091	−	1.41871i	−0.0366309	−	0.0634465i
$501$	0.511724	−	42.0929i	0.0228622	−	1.88057i
$502$	−4.16551	+	7.21487i	−0.185916	+	0.322015i
$503$	−13.9869			−0.623645			−0.311822	−	0.950140i	$-0.600939\pi$
$503$	−13.9869			−0.623645			−0.311822	+	0.950140i	$0.600939\pi$
$504$	17.0580	+	0.414811i	0.759825	+	0.0184772i
$505$	12.2480			0.545028
$506$	−1.23210	+	2.13406i	−0.0547734	+	0.0948704i
$507$	−1.51042	+	0.847727i	−0.0670800	+	0.0376489i
$508$	11.7011	+	20.2670i	0.519154	+	0.899201i
$509$	0.997337	+	1.72744i	0.0442062	+	0.0765673i	0.887282	−	0.461228i	$-0.152591\pi$
$509$	0.997337	+	1.72744i	0.0442062	+	0.0765673i	−0.843076	+	0.537795i	$0.819257\pi$
$510$	−4.81081	−	2.85605i	−0.213026	−	0.126468i
$511$	2.56334	−	4.43984i	0.113396	−	0.196407i
$512$	−19.4680			−0.860371
$513$	0.859153	−	23.5478i	0.0379325	−	1.03966i
$514$	2.70632			0.119371
$515$	8.40857	−	14.5641i	0.370526	−	0.641770i
$516$	−16.2396	−	9.64106i	−0.714911	−	0.424424i
$517$	−13.7063	−	23.7400i	−0.602803	−	1.04409i
$518$	8.31581	+	14.4034i	0.365376	+	0.632849i
$519$	20.6829	−	11.6084i	0.907879	−	0.509551i
$520$	1.09421	−	1.89522i	0.0479842	−	0.0831110i
$521$	−13.4590			−0.589648			−0.294824	−	0.955552i	$-0.595261\pi$
$521$	−13.4590			−0.589648			−0.294824	+	0.955552i	$0.595261\pi$
$522$	3.13113	−	5.13102i	0.137046	−	0.224579i
$523$	−14.1211			−0.617475			−0.308737	−	0.951147i	$-0.599906\pi$
$523$	−14.1211			−0.617475			−0.308737	+	0.951147i	$0.599906\pi$
$524$	−14.0305	+	24.3016i	−0.612927	+	1.06162i
$525$	−0.0547220	+	4.50127i	−0.00238827	+	0.196451i
$526$	5.15511	+	8.92892i	0.224774	+	0.389319i
$527$	−18.7519	−	32.4792i	−0.816845	−	1.41482i
$528$	−0.211413	+	17.3902i	−0.00920058	+	0.756812i
$529$	11.1803	−	19.3648i	0.486098	−	0.841947i
$530$	−5.82355			−0.252959
$531$	−1.27869	+	2.09540i	−0.0554904	+	0.0909327i
$532$	−19.3075			−0.837086
$533$	−2.26990	+	3.93158i	−0.0983203	+	0.170296i
$534$	4.30807	−	2.41792i	0.186428	−	0.104634i
$535$	−2.55257	−	4.42118i	−0.110357	−	0.191144i
$536$	10.5507	+	18.2744i	0.455721	+	0.789332i
$537$	−7.41359	−	4.40126i	−0.319920	−	0.189928i
$538$	0.544570	−	0.943224i	0.0234781	−	0.0406653i
$539$	1.25614			0.0541060
$540$	−7.21173	−	4.52208i	−0.310344	−	0.194599i
$541$	27.8421			1.19703			0.598513	−	0.801113i	$-0.295758\pi$
$541$	27.8421			1.19703			0.598513	+	0.801113i	$0.295758\pi$
$542$	5.91579	−	10.2464i	0.254105	−	0.440122i
$543$	36.4426	+	21.6351i	1.56390	+	0.928449i
$544$	−14.9173	−	25.8374i	−0.639572	−	1.10777i
$545$	−3.07973	−	5.33425i	−0.131921	−	0.228494i
$546$	−2.36129	+	1.32528i	−0.101054	+	0.0567168i
$547$	−21.1814	+	36.6873i	−0.905652	+	1.56863i	−0.0856117	+	0.996329i	$0.527284\pi$
$547$	−21.1814	+	36.6873i	−0.905652	+	1.56863i	−0.820040	+	0.572306i	$0.806049\pi$
$548$	0.400174			0.0170946
$549$	12.7400	+	0.309807i	0.543730	+	0.0132222i
$550$	3.08152			0.131397
$551$	−7.55272	+	13.0817i	−0.321757	+	0.557299i
$552$	0.0368464	−	3.03088i	0.00156829	−	0.129003i
$553$	9.45521	+	16.3769i	0.402077	+	0.696417i
$554$	−3.72748	−	6.45618i	−0.158365	−	0.274297i
$555$	0.223995	−	18.4252i	0.00950807	−	0.782104i
$556$	2.41815	−	4.18837i	0.102553	−	0.177626i
$557$	0.190749			0.00808228			0.00404114	−	0.999992i	$-0.498714\pi$
$557$	0.190749			0.00808228			0.00404114	+	0.999992i	$0.498714\pi$
$558$	6.03423	+	11.0644i	0.255450	+	0.468392i
$559$	6.65602			0.281520
$560$	−2.54702	+	4.41157i	−0.107631	+	0.186423i
$561$	−41.5517	+	23.3211i	−1.75432	+	0.984617i
$562$	3.47892	+	6.02567i	0.146750	+	0.254178i
$563$	13.5087	+	23.3978i	0.569325	+	0.986100i	0.996633	+	0.0819938i	$0.0261288\pi$
$563$	13.5087	+	23.3978i	0.569325	+	0.986100i	−0.427308	+	0.904106i	$0.640538\pi$
$564$	13.0555	+	7.75070i	0.549735	+	0.326363i
$565$	−1.58696	+	2.74870i	−0.0667639	+	0.115639i
$566$	−8.53471			−0.358740
$567$	10.6970	+	20.8017i	0.449234	+	0.873591i
$568$	−2.49138			−0.104536
$569$	6.91429	−	11.9759i	0.289862	−	0.502056i	−0.683914	−	0.729562i	$-0.739724\pi$
$569$	6.91429	−	11.9759i	0.289862	−	0.502056i	0.973777	+	0.227506i	$0.0730572\pi$
$570$	−4.06259	−	2.41186i	−0.170163	−	0.101022i
$571$	21.8081	+	37.7728i	0.912642	+	1.58074i	0.810318	+	0.585991i	$0.199295\pi$
$571$	21.8081	+	37.7728i	0.912642	+	1.58074i	0.102324	+	0.994751i	$0.467372\pi$
$572$	−4.19616	−	7.26796i	−0.175450	−	0.303889i
$573$	18.5067	−	10.3869i	0.773127	−	0.433920i
$574$	−3.54861	+	6.14638i	−0.148116	+	0.256545i
$575$	0.799668			0.0333485
$576$	−0.830402	−	1.52262i	−0.0346001	−	0.0634427i
$577$	−15.4561			−0.643445			−0.321723	−	0.946834i	$-0.604262\pi$
$577$	−15.4561			−0.643445			−0.321723	+	0.946834i	$0.604262\pi$
$578$	3.55996	−	6.16603i	0.148075	−	0.256473i
$579$	0.118527	−	9.74965i	0.00492580	−	0.405182i
$580$	2.72840	+	4.72572i	0.113291	+	0.196225i
$581$	−20.8771	−	36.1602i	−0.866129	−	1.50018i
$582$	0.0882237	−	7.25701i	0.00365699	−	0.300813i
$583$	−24.7989	+	42.9530i	−1.02707	+	1.77893i
$584$	4.31678			0.178630
$585$	2.99911	+	0.0729314i	0.123998	+	0.00301534i
$586$	−10.5677			−0.436548
$587$	−16.4720	+	28.5303i	−0.679871	+	1.17757i	0.295149	+	0.955451i	$0.404631\pi$
$587$	−16.4720	+	28.5303i	−0.679871	+	1.17757i	−0.975019	+	0.222120i	$0.928702\pi$
$588$	−0.606706	+	0.340516i	−0.0250201	+	0.0140426i
$589$	−15.8354	−	27.4278i	−0.652488	−	1.13014i
$590$	0.246093	+	0.426246i	0.0101315	+	0.0175483i
$591$	12.7851	+	7.59017i	0.525908	+	0.312218i
$592$	10.4258	−	18.0580i	0.428497	−	0.742179i
$593$	−13.4309			−0.551540			−0.275770	−	0.961224i	$-0.588933\pi$
$593$	−13.4309			−0.551540			−0.275770	+	0.961224i	$0.588933\pi$
$594$	14.1495	−	7.49511i	0.580563	−	0.307528i
$595$	−13.9566			−0.572164
$596$	−18.1144	+	31.3751i	−0.741996	+	1.28517i
$597$	21.4448	+	12.7312i	0.877678	+	0.521055i
$598$	0.240506	+	0.416568i	0.00983501	+	0.0170347i
$599$	−11.5386	−	19.9854i	−0.471454	−	0.816582i	0.528013	−	0.849236i	$-0.322937\pi$
$599$	−11.5386	−	19.9854i	−0.471454	−	0.816582i	−0.999467	+	0.0326545i	$0.989604\pi$
$600$	−3.30542	+	1.85518i	−0.134943	+	0.0757374i
$601$	−7.62485	+	13.2066i	−0.311024	+	0.538710i	−0.978584	−	0.205846i	$-0.934005\pi$
$601$	−7.62485	+	13.2066i	−0.311024	+	0.538710i	0.667560	+	0.744556i	$0.267339\pi$
$602$	10.4056			0.424100
$603$	−15.0682	+	24.6925i	−0.613625	+	1.00555i
$604$	−35.4985			−1.44441
$605$	7.62230	−	13.2022i	0.309891	−	0.536746i
$606$	0.155119	−	12.7596i	0.00630130	−	0.518325i
$607$	13.3156	+	23.0633i	0.540463	+	0.936109i	0.998877	+	0.0473707i	$0.0150842\pi$
$607$	13.3156	+	23.0633i	0.540463	+	0.936109i	−0.458414	+	0.888739i	$0.651582\pi$
$608$	−12.5972	−	21.8190i	−0.510884	−	0.884877i
$609$	0.182280	−	14.9938i	0.00738634	−	0.607578i
$610$	1.27759	−	2.21285i	0.0517282	−	0.0895958i
$611$	−5.35095			−0.216476
$612$	13.7472	−	22.5277i	0.555698	−	0.910630i
$613$	−6.15713			−0.248684			−0.124342	−	0.992239i	$-0.539682\pi$
$613$	−6.15713			−0.248684			−0.124342	+	0.992239i	$0.539682\pi$
$614$	8.57096	−	14.8453i	0.345896	−	0.599109i
$615$	6.85699	−	3.84851i	0.276501	−	0.155187i
$616$	−14.5689	−	25.2340i	−0.586997	−	1.01671i
$617$	0.163116	+	0.282525i	0.00656680	+	0.0113740i	0.869290	−	0.494302i	$-0.164576\pi$
$617$	0.163116	+	0.282525i	0.00656680	+	0.0113740i	−0.862723	+	0.505676i	$0.831243\pi$
$618$	−15.0660	−	8.94429i	−0.606043	−	0.359792i
$619$	10.0672	−	17.4369i	0.404636	−	0.700849i	−0.589643	−	0.807664i	$-0.700732\pi$
$619$	10.0672	−	17.4369i	0.404636	−	0.700849i	0.994279	+	0.106814i	$0.0340650\pi$
$620$	−11.4410			−0.459482
$621$	3.67187	−	1.94501i	0.147347	−	0.0780506i
$622$	12.7474			0.511125
$623$	6.16192	−	10.6728i	0.246872	−	0.427595i
$624$	2.91915	+	1.73302i	0.116860	+	0.0693765i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	3.78457	+	6.55506i	0.151262	+	0.261993i
$627$	−35.0893	+	19.6940i	−1.40133	+	0.786502i
$628$	−8.69965	+	15.0682i	−0.347154	+	0.601288i
$629$	57.1288			2.27788
$630$	4.68861	+	0.114016i	0.186799	+	0.00454251i
$631$	5.53688			0.220420			0.110210	−	0.993908i	$-0.464848\pi$
$631$	5.53688			0.220420			0.110210	+	0.993908i	$0.464848\pi$
$632$	−7.96150	+	13.7897i	−0.316691	+	0.548526i
$633$	0.317530	−	26.1190i	0.0126207	−	1.03814i
$634$	−3.82674	−	6.62811i	−0.151979	−	0.263236i
$635$	7.14276	+	12.3716i	0.283452	+	0.490953i
$636$	0.333934	−	27.4684i	0.0132413	−	1.08919i
$637$	0.122600	−	0.212349i	0.00485758	−	0.00841357i
$638$	−10.2646			−0.406379
$639$	−1.63525	−	2.99839i	−0.0646894	−	0.118614i
$640$	−11.4593			−0.452970
$641$	13.3715	−	23.1602i	0.528144	−	0.914773i	−0.471317	−	0.881964i	$-0.656221\pi$
$641$	13.3715	−	23.1602i	0.528144	−	0.914773i	0.999462	−	0.0328090i	$-0.0104453\pi$
$642$	−4.63820	+	2.60321i	−0.183055	+	0.102740i
$643$	−11.2515	−	19.4881i	−0.443715	−	0.768536i	0.554247	−	0.832352i	$-0.313006\pi$
$643$	−11.2515	−	19.4881i	−0.443715	−	0.768536i	−0.997962	+	0.0638158i	$0.979673\pi$
$644$	−1.70235	−	2.94855i	−0.0670819	−	0.116189i
$645$	−9.91322	−	5.88522i	−0.390333	−	0.231730i
$646$	7.32396	−	12.6855i	0.288157	−	0.499103i
$647$	−26.4570			−1.04013			−0.520066	−	0.854126i	$-0.674093\pi$
$647$	−26.4570			−1.04013			−0.520066	+	0.854126i	$0.674093\pi$
$648$	−10.6653	+	16.5582i	−0.418973	+	0.650467i
$649$	4.19184			0.164544
$650$	0.300757	−	0.520926i	0.0117967	−	0.0204324i
$651$	27.0339	+	16.0493i	1.05954	+	0.629023i
$652$	−12.7949	−	22.1615i	−0.501088	−	0.867910i
$653$	22.2416	+	38.5235i	0.870380	+	1.50754i	0.861604	+	0.507581i	$0.169460\pi$
$653$	22.2416	+	38.5235i	0.870380	+	1.50754i	0.00877580	+	0.999961i	$0.497207\pi$
$654$	−5.59609	+	3.14083i	−0.218825	+	0.122816i
$655$	−8.56471	+	14.8345i	−0.334651	+	0.579632i
$656$	8.89802			0.347409
$657$	2.83338	+	5.19528i	0.110541	+	0.202687i
$658$	−8.36531			−0.326114
$659$	−12.8331	+	22.2276i	−0.499908	+	0.865866i	−1.00000		0.000106459i	$-0.999966\pi$
$659$	−12.8331	+	22.2276i	−0.499908	+	0.865866i	0.500092	+	0.865972i	$0.333299\pi$
$660$	−0.176701	+	14.5348i	−0.00687806	+	0.565768i
$661$	−5.26875	−	9.12575i	−0.204931	−	0.354950i	0.745180	−	0.666863i	$-0.232364\pi$
$661$	−5.26875	−	9.12575i	−0.204931	−	0.354950i	−0.950111	+	0.311913i	$0.899030\pi$
$662$	−2.08353	−	3.60877i	−0.0809785	−	0.140259i
$663$	−0.113065	+	9.30039i	−0.00439108	+	0.361197i
$664$	17.5790	−	30.4477i	0.682197	−	1.18160i
$665$	−11.7859			−0.457039
$666$	−19.1920	−	0.466705i	−0.743676	−	0.0180845i
$667$	−2.66370			−0.103139
$668$	19.9073	−	34.4804i	0.770236	−	1.33409i
$669$	7.55491	−	4.24022i	0.292090	−	0.163937i
$670$	2.89999	+	5.02294i	0.112037	+	0.194053i
$671$	−10.8809	−	18.8463i	−0.420054	−	0.727555i
$672$	21.5057	+	12.7674i	0.829599	+	0.492512i
$673$	16.7207	−	28.9611i	0.644536	−	1.11637i	−0.339873	−	0.940471i	$-0.610384\pi$
$673$	16.7207	−	28.9611i	0.644536	−	1.11637i	0.984409	−	0.175897i	$-0.0562826\pi$
$674$	1.34637			0.0518603
$675$	−4.40228	−	2.76042i	−0.169444	−	0.106249i
$676$	−1.63818			−0.0630070
$677$	−3.32779	+	5.76390i	−0.127897	+	0.221525i	−0.922862	−	0.385131i	$-0.874156\pi$
$677$	−3.32779	+	5.76390i	−0.127897	+	0.221525i	0.794964	+	0.606656i	$0.207489\pi$
$678$	2.84343	+	1.68807i	0.109201	+	0.0648299i
$679$	−9.05232	−	15.6791i	−0.347396	−	0.601708i
$680$	−5.87587	−	10.1773i	−0.225329	−	0.390282i
$681$	5.66224	−	3.17795i	0.216977	−	0.121779i
$682$	10.7606	−	18.6380i	0.412046	−	0.713685i
$683$	5.46952			0.209285			0.104643	−	0.994510i	$-0.466630\pi$
$683$	5.46952			0.209285			0.104643	+	0.994510i	$0.466630\pi$
$684$	11.6091	−	19.0240i	0.443887	−	0.727402i
$685$	0.244279			0.00933343
$686$	5.66333	−	9.80918i	0.216227	−	0.374516i
$687$	−0.316432	+	26.0288i	−0.0120726	+	0.993059i
$688$	−6.52290	−	11.2980i	−0.248683	−	0.430732i
$689$	4.84075	+	8.38443i	0.184418	+	0.319421i
$690$	0.0101277	−	0.833074i	0.000385555	−	0.0317146i
$691$	−11.7110	+	20.2841i	−0.445508	+	0.771642i	−0.998087	−	0.0618182i	$-0.980310\pi$
$691$	−11.7110	+	20.2841i	−0.445508	+	0.771642i	0.552580	+	0.833460i	$0.313643\pi$
$692$	22.4325			0.852754
$693$	20.8069	−	34.0964i	0.790387	−	1.29522i
$694$	−15.9129			−0.604045
$695$	1.47612	−	2.55672i	0.0559925	−	0.0969818i
$696$	11.0104	−	6.17962i	0.417347	−	0.234238i
$697$	12.1893	+	21.1125i	0.461703	+	0.799694i
$698$	5.06301	+	8.76938i	0.191638	+	0.331926i
$699$	6.38865	+	3.79278i	0.241641	+	0.143456i
$700$	−2.12882	+	3.68722i	−0.0804617	+	0.139364i
$701$	−43.7946			−1.65410			−0.827050	−	0.562129i	$-0.809983\pi$
$701$	−43.7946			−1.65410			−0.827050	+	0.562129i	$0.809983\pi$
$702$	0.113962	−	3.12348i	0.00430120	−	0.117888i
$703$	48.2437			1.81954
$704$	−1.48083	+	2.56487i	−0.0558107	+	0.0966670i
$705$	7.96949	+	4.73128i	0.300149	+	0.178190i
$706$	9.89343	+	17.1359i	0.372344	+	0.644919i
$707$	−15.9163	−	27.5678i	−0.598593	−	1.03679i
$708$	−2.02462	+	1.13633i	−0.0760899	+	0.0427057i
$709$	4.95137	−	8.57603i	0.185953	−	0.322080i	−0.757944	−	0.652319i	$-0.773796\pi$
$709$	4.95137	−	8.57603i	0.185953	−	0.322080i	0.943897	+	0.330240i	$0.107130\pi$
$710$	−0.684786			−0.0256996
$711$	−21.8217	−	0.530652i	−0.818376	−	0.0199010i
$712$	10.3770			0.388893
$713$	2.79243	−	4.83663i	0.104577	−	0.181133i
$714$	−0.176758	+	14.5396i	−0.00661502	+	0.544131i
$715$	−2.56147	−	4.43660i	−0.0957937	−	0.165920i
$716$	−4.07718	−	7.06189i	−0.152371	−	0.263915i
$717$	−0.375032	+	30.8490i	−0.0140058	+	1.15208i
$718$	−1.12254	+	1.94430i	−0.0418929	+	0.0725607i
$719$	1.51958			0.0566708			0.0283354	−	0.999598i	$-0.490979\pi$
$719$	1.51958			0.0566708			0.0283354	+	0.999598i	$0.490979\pi$
$720$	−2.81534	−	5.16220i	−0.104921	−	0.192384i
$721$	−43.7078			−1.62776
$722$	0.470497	−	0.814924i	0.0175101	−	0.0303283i
$723$	24.3072	−	13.6425i	0.903994	−	0.507370i
$724$	20.0420	+	34.7138i	0.744856	+	1.29013i
$725$	1.66550	+	2.88474i	0.0618553	+	0.107136i
$726$	−13.6572	−	8.10793i	−0.506866	−	0.300913i
$727$	−24.0013	+	41.5714i	−0.890158	+	1.54180i	−0.0504720	+	0.998725i	$0.516073\pi$
$727$	−24.0013	+	41.5714i	−0.890158	+	1.54180i	−0.839686	+	0.543073i	$0.817261\pi$
$728$	−5.68769			−0.210800
$729$	−26.9282	−	1.96760i	−0.997341	−	0.0728739i
$730$	1.18652			0.0439152
$731$	17.8713	−	30.9541i	0.660995	−	1.14488i
$732$	10.3643	+	6.15300i	0.383074	+	0.227421i
$733$	−7.75216	−	13.4271i	−0.286333	−	0.495943i	0.686599	−	0.727037i	$-0.259103\pi$
$733$	−7.75216	−	13.4271i	−0.286333	−	0.495943i	−0.972931	+	0.231094i	$0.925770\pi$
$734$	−7.30765	−	12.6572i	−0.269730	−	0.467186i
$735$	−0.370353	+	0.207862i	−0.0136607	+	0.00766712i
$736$	2.22140	−	3.84757i	0.0818818	−	0.141823i
$737$	49.3971			1.81957
$738$	−3.92244	−	7.19218i	−0.144387	−	0.264748i
$739$	−28.8573			−1.06153			−0.530766	−	0.847519i	$-0.678096\pi$
$739$	−28.8573			−1.06153			−0.530766	+	0.847519i	$0.678096\pi$
$740$	8.71394	−	15.0930i	0.320331	−	0.554829i
$741$	−0.0954803	+	7.85392i	−0.00350756	+	0.288521i
$742$	7.56771	+	13.1077i	0.277819	+	0.481197i
$743$	−3.52892	−	6.11228i	−0.129464	−	0.224238i	0.794005	−	0.607911i	$-0.207992\pi$
$743$	−3.52892	−	6.11228i	−0.129464	−	0.224238i	−0.923469	+	0.383673i	$0.874659\pi$
$744$	−0.321802	+	26.4704i	−0.0117978	+	0.970453i
$745$	−11.0576	+	19.1524i	−0.405121	+	0.701690i
$746$	5.96554			0.218414
$747$	48.1823	+	1.17168i	1.76290	+	0.0428695i
$748$	−45.0666			−1.64780
$749$	−6.63413	+	11.4906i	−0.242406	+	0.419859i
$750$	−0.908536	+	0.509919i	−0.0331750	+	0.0186196i
$751$	19.8046	+	34.3026i	0.722681	+	1.25172i	0.959921	+	0.280269i	$0.0904238\pi$
$751$	19.8046	+	34.3026i	0.722681	+	1.25172i	−0.237240	+	0.971451i	$0.576243\pi$
$752$	5.24393	+	9.08276i	0.191227	+	0.331214i
$753$	−20.6278	−	12.2462i	−0.751719	−	0.446276i
$754$	−1.00182	+	1.73521i	−0.0364843	+	0.0631926i
$755$	−21.6695			−0.788632
$756$	−0.806643	+	22.1086i	−0.0293373	+	0.804082i
$757$	7.29994			0.265321			0.132660	−	0.991162i	$-0.457648\pi$
$757$	7.29994			0.265321			0.132660	+	0.991162i	$0.457648\pi$
$758$	−4.71197	+	8.16138i	−0.171147	+	0.296435i
$759$	−6.10141	−	3.62225i	−0.221467	−	0.131479i
$760$	−4.96201	−	8.59445i	−0.179991	−	0.311754i
$761$	17.3506	+	30.0521i	0.628958	+	1.08939i	0.987761	+	0.155974i	$0.0498516\pi$
$761$	17.3506	+	30.0521i	0.628958	+	1.08939i	−0.358803	+	0.933413i	$0.616815\pi$
$762$	12.9789	−	7.28446i	0.470176	−	0.263888i
$763$	−8.00422	+	13.8637i	−0.289772	+	0.501900i
$764$	20.0721			0.726184
$765$	8.39176	−	13.7517i	0.303405	−	0.497193i
$766$	9.78681			0.353612
$767$	0.409124	−	0.708623i	0.0147726	−	0.0255869i
$768$	−0.120787	+	9.93555i	−0.00435852	+	0.358518i
$769$	−11.3006	−	19.5732i	−0.407510	−	0.705827i	0.587100	−	0.809514i	$-0.300269\pi$
$769$	−11.3006	−	19.5732i	−0.407510	−	0.705827i	−0.994610	+	0.103687i	$0.966936\pi$
$770$	−4.00444	−	6.93589i	−0.144310	−	0.249952i
$771$	−0.0947305	+	7.79224i	−0.00341163	+	0.280631i
$772$	4.61097	−	7.98644i	0.165953	−	0.287438i
$773$	3.33276			0.119871			0.0599355	−	0.998202i	$-0.480910\pi$
$773$	3.33276			0.119871			0.0599355	+	0.998202i	$0.480910\pi$
$774$	−6.25663	+	10.2528i	−0.224890	+	0.368530i
$775$	−6.98397			−0.250872
$776$	7.62226	−	13.2021i	0.273623	−	0.473929i
$777$	−41.7624	+	23.4393i	−1.49822	+	0.840881i
$778$	7.75892	+	13.4388i	0.278171	+	0.481806i
$779$	10.2935	+	17.8289i	0.368804	+	0.638788i
$780$	2.43984	+	1.44847i	0.0873605	+	0.0518636i
$781$	−2.91608	+	5.05080i	−0.104346	+	0.180732i
$782$	2.58302			0.0923686
$783$	14.6640	+	9.19500i	0.524050	+	0.328602i
$784$	−0.480591			−0.0171640
$785$	−5.31055	+	9.19815i	−0.189542	+	0.328296i
$786$	15.3457	+	9.11037i	0.547365	+	0.324956i
$787$	−10.7058	−	18.5430i	−0.381621	−	0.660987i	0.609673	−	0.792653i	$-0.291301\pi$
$787$	−10.7058	−	18.5430i	−0.381621	−	0.660987i	−0.991294	+	0.131666i	$0.957967\pi$
$788$	7.03130	+	12.1786i	0.250480	+	0.433843i
$789$	−25.8893	+	14.5304i	−0.921682	+	0.517298i
$790$	−2.18832	+	3.79028i	−0.0778569	+	0.134852i
$791$	8.24902			0.293301
$792$	33.6235	+	0.817644i	1.19476	+	0.0290537i
$793$	−4.24792			−0.150848
$794$	3.12639	−	5.41506i	0.110951	−	0.192173i
$795$	0.203844	−	16.7676i	0.00722961	−	0.594686i
$796$	11.7938	+	20.4275i	0.418020	+	0.724033i
$797$	1.61678	+	2.80035i	0.0572694	+	0.0991935i	0.893239	−	0.449583i	$-0.148427\pi$
$797$	1.61678	+	2.80035i	0.0572694	+	0.0991935i	−0.835969	+	0.548776i	$0.815094\pi$
$798$	−0.149268	+	12.2783i	−0.00528401	+	0.434647i
$799$	−14.3672	+	24.8848i	−0.508276	+	0.880360i
$800$	−5.55580			−0.196427
$801$	6.81105	+	12.4887i	0.240657	+	0.441268i
$802$	−0.0508882			−0.00179693
$803$	5.05266	−	8.75147i	0.178305	−	0.308833i
$804$	−23.8583	+	13.3906i	−0.841419	+	0.472250i
$805$	−1.03917	−	1.79989i	−0.0366259	−	0.0634379i
$806$	−2.10048	−	3.63813i	−0.0739861	−	0.128148i
$807$	2.69674	+	1.60098i	0.0949297	+	0.0563573i
$808$	13.4018	−	23.2127i	0.471475	−	0.816619i
$809$	22.3591			0.786106			0.393053	−	0.919516i	$-0.371419\pi$
$809$	22.3591			0.786106			0.393053	+	0.919516i	$0.371419\pi$
$810$	−2.93150	+	4.55122i	−0.103002	+	0.159914i
$811$	−45.4604			−1.59633			−0.798166	−	0.602438i	$-0.794196\pi$
$811$	−45.4604			−1.59633			−0.798166	+	0.602438i	$0.794196\pi$
$812$	7.09111	−	12.2822i	0.248849	−	0.431019i
$813$	29.2953	+	17.3918i	1.02743	+	0.609958i
$814$	16.3915	+	28.3909i	0.574521	+	0.995099i
$815$	−7.81044	−	13.5281i	−0.273588	−	0.473868i
$816$	15.8974	−	8.92247i	0.556520	−	0.312349i
$817$	15.0918	−	26.1398i	0.527997	−	0.914517i
$818$	12.5953			0.440386
$819$	−3.73319	−	6.84518i	−0.130448	−	0.239190i
$820$	7.43702			0.259712
$821$	15.1115	−	26.1738i	0.527394	−	0.913473i	−0.472096	−	0.881547i	$-0.656503\pi$
$821$	15.1115	−	26.1738i	0.527394	−	0.913473i	0.999490	−	0.0319261i	$-0.0101641\pi$
$822$	0.00309377	−	0.254484i	0.000107908	−	0.00887615i
$823$	−2.39544	−	4.14903i	−0.0834999	−	0.144626i	0.821251	−	0.570567i	$-0.193277\pi$
$823$	−2.39544	−	4.14903i	−0.0834999	−	0.144626i	−0.904751	+	0.425941i	$0.859943\pi$
$824$	−18.4014	−	31.8722i	−0.641045	−	1.11032i
$825$	−0.107864	+	8.87255i	−0.00375534	+	0.308903i
$826$	0.639597	−	1.10781i	0.0222544	−	0.0385458i
$827$	22.0981			0.768426			0.384213	−	0.923244i	$-0.374473\pi$
$827$	22.0981			0.768426			0.384213	+	0.923244i	$0.374473\pi$
$828$	3.92884	+	0.0955402i	0.136537	+	0.00332025i
$829$	−16.9618			−0.589108			−0.294554	−	0.955635i	$-0.595171\pi$
$829$	−16.9618			−0.589108			−0.294554	+	0.955635i	$0.595171\pi$
$830$	4.83181	−	8.36894i	0.167715	−	0.290490i
$831$	18.7196	−	10.5064i	0.649375	−	0.364464i
$832$	0.289057	+	0.500662i	0.0100213	+	0.0173573i
$833$	−0.658358	−	1.14031i	−0.0228108	−	0.0395094i
$834$	−2.64483	−	1.57017i	−0.0915830	−	0.0543704i
$835$	12.1521	−	21.0480i	0.420539	−	0.728396i
$836$	−38.0575			−1.31624
$837$	−32.0686	+	16.9869i	−1.10845	+	0.587154i
$838$	−12.8834			−0.445049
$839$	22.3677	−	38.7420i	0.772220	−	1.33752i	−0.164124	−	0.986440i	$-0.552480\pi$
$839$	22.3677	−	38.7420i	0.772220	−	1.33752i	0.936344	−	0.351084i	$-0.114187\pi$
$840$	8.47103	+	5.02903i	0.292278	+	0.173518i
$841$	8.95219	+	15.5056i	0.308696	+	0.534678i
$842$	−8.38292	−	14.5196i	−0.288894	−	0.500380i
$843$	−17.4713	+	9.80586i	−0.601745	+	0.337732i
$844$	12.3527	−	21.3954i	0.425196	−	0.736461i
$845$	−1.00000			−0.0344010
$846$	5.02987	−	8.24250i	0.172930	−	0.283383i
$847$	−39.6207			−1.36138
$848$	9.48788	−	16.4335i	0.325815	−	0.564328i
$849$	0.298744	−	24.5738i	0.0102529	−	0.843369i
$850$	−1.61506	−	2.79736i	−0.0553960	−	0.0959487i
$851$	4.25366	+	7.36755i	0.145814	+	0.252556i
$852$	0.0392670	−	3.22998i	0.00134526	−	0.110657i
$853$	1.75767	−	3.04438i	0.0601816	−	0.104238i	−0.834365	−	0.551212i	$-0.814165\pi$
$853$	1.75767	−	3.04438i	0.0601816	−	0.104238i	0.894546	+	0.446975i	$0.147499\pi$
$854$	−6.64092			−0.227248
$855$	7.08660	−	11.6129i	0.242357	−	0.397153i
$856$	−11.1722			−0.381857
$857$	−2.50084	+	4.33159i	−0.0854271	+	0.147964i	−0.905573	−	0.424190i	$-0.860559\pi$
$857$	−2.50084	+	4.33159i	−0.0854271	+	0.147964i	0.820146	+	0.572154i	$0.193892\pi$
$858$	−4.65438	+	2.61229i	−0.158898	+	0.0891821i
$859$	24.4865	+	42.4119i	0.835469	+	1.44707i	0.893648	+	0.448768i	$0.148137\pi$
$859$	24.4865	+	42.4119i	0.835469	+	1.44707i	−0.0581792	+	0.998306i	$0.518529\pi$
$860$	−5.45188	−	9.44294i	−0.185908	−	0.322001i
$861$	−17.5729	−	10.4326i	−0.598883	−	0.355541i
$862$	0.241375	−	0.418075i	0.00822128	−	0.0142397i
$863$	−10.6834			−0.363666			−0.181833	−	0.983329i	$-0.558203\pi$
$863$	−10.6834			−0.363666			−0.181833	+	0.983329i	$0.558203\pi$
$864$	−25.5108	+	13.5132i	−0.867894	+	0.459729i
$865$	13.6935			0.465593
$866$	−6.87469	+	11.9073i	−0.233611	+	0.404627i
$867$	17.6291	+	10.4659i	0.598715	+	0.355442i
$868$	14.8676	+	25.7514i	0.504639	+	0.874061i
$869$	18.6374	+	32.2809i	0.632230	+	1.09505i
$870$	3.02634	−	1.69855i	0.102603	−	0.0575861i
$871$	4.82116	−	8.35049i	0.163359	−	0.282946i
$872$	−13.4795			−0.456472
$873$	20.8918	+	0.508040i	0.707082	+	0.0171946i
$874$	2.18129			0.0737832
$875$	−1.29950	+	2.25080i	−0.0439311	+	0.0760909i
$876$	−0.0680375	+	5.59656i	−0.00229877	+	0.189090i
$877$	−10.6797	−	18.4978i	−0.360628	−	0.624627i	0.627436	−	0.778668i	$-0.284104\pi$
$877$	−10.6797	−	18.4978i	−0.360628	−	0.624627i	−0.988064	+	0.154041i	$0.950771\pi$
$878$	11.5641	+	20.0296i	0.390269	+	0.675966i
$879$	0.369906	−	30.4273i	0.0124766	−	1.02629i
$880$	−5.02049	+	8.69575i	−0.169241	+	0.293134i
$881$	45.2544			1.52466			0.762330	−	0.647189i	$-0.224056\pi$
$881$	45.2544			1.52466			0.762330	+	0.647189i	$0.224056\pi$
$882$	0.211855	+	0.388457i	0.00713354	+	0.0130800i
$883$	20.4837			0.689330			0.344665	−	0.938726i	$-0.387992\pi$
$883$	20.4837			0.689330			0.344665	+	0.938726i	$0.387992\pi$
$884$	−4.39850	+	7.61842i	−0.147938	+	0.256235i
$885$	−1.23589	+	0.693651i	−0.0415441	+	0.0233168i
$886$	10.3848	+	17.9870i	0.348884	+	0.604284i
$887$	−6.15937	−	10.6683i	−0.206811	−	0.358208i	0.743897	−	0.668294i	$-0.232975\pi$
$887$	−6.15937	−	10.6683i	−0.206811	−	0.358208i	−0.950708	+	0.310086i	$0.899642\pi$
$888$	−34.6747	−	20.5855i	−1.16361	−	0.690803i
$889$	18.5640	−	32.1538i	0.622617	−	1.07841i
$890$	2.85224			0.0956072
$891$	21.0852	+	41.0028i	0.706380	+	1.37364i
$892$	8.19398			0.274355
$893$	−12.1327	+	21.0145i	−0.406006	+	0.703223i
$894$	19.8125	+	11.7621i	0.662628	+	0.393385i
$895$	−2.48885	−	4.31081i	−0.0831930	−	0.144094i
$896$	14.8914	+	25.7927i	0.497487	+	0.861673i
$897$	−1.20783	+	0.677901i	−0.0403283	+	0.0226344i
$898$	−9.43144	+	16.3357i	−0.314731	+	0.545131i
$899$	23.2637			0.775887
$900$	−2.35308	−	4.31460i	−0.0784359	−	0.143820i
$901$	51.9895			1.73202
$902$	−6.99475	+	12.1153i	−0.232900	+	0.403394i
$903$	−0.364231	+	29.9605i	−0.0121208	+	0.997023i
$904$	3.47293	+	6.01529i	0.115508	+	0.200066i
$905$	12.2343	+	21.1905i	0.406682	+	0.704395i
$906$	−0.274441	+	22.5747i	−0.00911770	+	0.749994i
$907$	−21.3166	+	36.9214i	−0.707805	+	1.22595i	0.257864	+	0.966181i	$0.416981\pi$
$907$	−21.3166	+	36.9214i	−0.707805	+	1.22595i	−0.965670	+	0.259773i	$0.916352\pi$
$908$	6.14120			0.203803
$909$	36.7331	+	0.893263i	1.21836	+	0.0296277i
$910$	−1.56333			−0.0518240
$911$	16.4417	−	28.4779i	0.544739	−	0.943515i	−0.453884	−	0.891061i	$-0.649962\pi$
$911$	16.4417	−	28.4779i	0.544739	−	0.943515i	0.998623	−	0.0524549i	$-0.0167046\pi$
$912$	13.4249	−	7.53477i	0.444543	−	0.249501i
$913$	−41.1514	−	71.2763i	−1.36191	−	2.35890i
$914$	−3.92070	−	6.79085i	−0.129685	−	0.224621i
$915$	6.32669	+	3.75599i	0.209154	+	0.124169i
$916$	−12.3100	+	21.3215i	−0.406733	+	0.704482i
$917$	44.5193			1.47016
$918$	−14.2199	−	8.91649i	−0.469325	−	0.294288i
$919$	−53.2590			−1.75685			−0.878427	−	0.477877i	$-0.841406\pi$
$919$	−53.2590			−1.75685			−0.878427	+	0.477877i	$0.841406\pi$
$920$	0.875003	−	1.51555i	0.0288480	−	0.0499662i
$921$	42.4438	+	25.1978i	1.39857	+	0.830296i
$922$	−12.0965	−	20.9518i	−0.398378	−	0.690011i
$923$	0.569219	+	0.985917i	0.0187361	+	0.0324518i
$924$	32.9447	−	18.4903i	1.08380	−	0.608287i
$925$	5.31928	−	9.21326i	0.174897	−	0.302930i
$926$	18.0927			0.594562
$927$	26.2804	−	43.0661i	0.863163	−	1.41448i
$928$	18.5064			0.607503
$929$	−24.4988	+	42.4331i	−0.803778	+	1.39218i	0.113334	+	0.993557i	$0.463847\pi$
$929$	−24.4988	+	42.4331i	−0.803778	+	1.39218i	−0.917113	+	0.398628i	$0.869486\pi$
$930$	−0.0884512	+	7.27573i	−0.00290043	+	0.238581i
$931$	−0.555965	−	0.962959i	−0.0182210	−	0.0315597i
$932$	3.51351	+	6.08558i	0.115089	+	0.199340i
$933$	−0.446203	+	36.7033i	−0.0146080	+	1.20161i
$934$	−4.78280	+	8.28405i	−0.156498	+	0.271063i
$935$	−27.5101			−0.899677
$936$	3.41987	−	5.60419i	0.111782	−	0.183179i
$937$	−51.7278			−1.68987			−0.844937	−	0.534865i	$-0.820362\pi$
$937$	−51.7278			−1.68987			−0.844937	+	0.534865i	$0.820362\pi$
$938$	7.53708	−	13.0546i	0.246094	−	0.426248i
$939$	−19.0063	+	10.6674i	−0.620247	+	0.348116i
$940$	4.38291	+	7.59142i	0.142955	+	0.247605i
$941$	6.20121	+	10.7408i	0.202154	+	0.350141i	0.949222	−	0.314607i	$-0.101873\pi$
$941$	6.20121	+	10.7408i	0.202154	+	0.350141i	−0.747068	+	0.664747i	$0.768539\pi$
$942$	9.51514	+	5.64889i	0.310020	+	0.184051i
$943$	−1.81517	+	3.14396i	−0.0591100	+	0.102381i
$944$	−1.60377			−0.0521981
$945$	−0.492401	+	13.4958i	−0.0160178	+	0.439019i
$946$	20.5107			0.666859
$947$	1.73015	−	2.99670i	0.0562222	−	0.0973798i	−0.836544	−	0.547899i	$-0.815428\pi$
$947$	1.73015	−	2.99670i	0.0562222	−	0.0973798i	0.892767	+	0.450519i	$0.148761\pi$
$948$	−17.7524	−	10.5391i	−0.576571	−	0.342296i
$949$	−0.986281	−	1.70829i	−0.0320160	−	0.0554534i
$950$	−1.36387	−	2.36229i	−0.0442498	−	0.0766429i
$951$	19.2181	−	10.7862i	0.623189	−	0.349767i
$952$	−15.2714	+	26.4508i	−0.494949	+	0.857276i
$953$	21.5313			0.697467			0.348733	−	0.937222i	$-0.386612\pi$
$953$	21.5313			0.697467			0.348733	+	0.937222i	$0.386612\pi$
$954$	−17.4655	−	0.424720i	−0.565466	−	0.0137508i
$955$	12.2527			0.396488
$956$	−14.5896	+	25.2700i	−0.471862	+	0.817289i
$957$	0.359295	−	29.5545i	0.0116144	−	0.955363i
$958$	−5.95450	−	10.3135i	−0.192381	−	0.333214i
$959$	−0.317441	−	0.549824i	−0.0102507	−	0.0177547i
$960$	0.0121722	−	1.00125i	0.000392857	−	0.0323152i
$961$	−8.88794	+	15.3944i	−0.286708	+	0.496592i
$962$	6.39924			0.206320
$963$	−7.33300	−	13.4458i	−0.236303	−	0.433284i
$964$	26.3633			0.849105
$965$	2.81469	−	4.87519i	0.0906081	−	0.156938i
$966$	−1.88824	+	1.05978i	−0.0607533	+	0.0340980i
$967$	25.9833	+	45.0043i	0.835565	+	1.44724i	0.893569	+	0.448925i	$0.148193\pi$
$967$	25.9833	+	45.0043i	0.835565	+	1.44724i	−0.0580042	+	0.998316i	$0.518474\pi$
$968$	−16.6808	−	28.8919i	−0.536140	−	0.928621i
$969$	36.2686	+	21.5317i	1.16511	+	0.691698i
$970$	2.09507	−	3.62877i	0.0672688	−	0.116513i
$971$	−1.67242			−0.0536705			−0.0268352	−	0.999640i	$-0.508543\pi$
$971$	−1.67242			−0.0536705			−0.0268352	+	0.999640i	$0.508543\pi$
$972$	−21.2990	−	14.0882i	−0.683166	−	0.451879i
$973$	−7.67288			−0.245981
$974$	8.48907	−	14.7035i	0.272007	−	0.471131i
$975$	1.48936	+	0.884196i	0.0476977	+	0.0283169i
$976$	4.16297	+	7.21047i	0.133253	+	0.230802i
$977$	12.0669	+	20.9005i	0.386055	+	0.668668i	0.991915	−	0.126904i	$-0.0405040\pi$
$977$	12.0669	+	20.9005i	0.386055	+	0.668668i	−0.605860	+	0.795572i	$0.707171\pi$
$978$	−14.1921	+	7.96539i	−0.453815	+	0.254705i
$979$	12.1459	−	21.0373i	0.388185	−	0.672356i
$980$	−0.401681			−0.0128312
$981$	−8.84743	−	16.2226i	−0.282477	−	0.517949i
$982$	−2.06333			−0.0658436
$983$	−13.0206	+	22.5523i	−0.415293	+	0.719308i	−0.995459	−	0.0951901i	$-0.969654\pi$
$983$	−13.0206	+	22.5523i	−0.415293	+	0.719308i	0.580167	+	0.814498i	$0.302987\pi$
$984$	0.209181	−	17.2066i	0.00666845	−	0.548527i
$985$	4.29214	+	7.43420i	0.136759	+	0.236873i
$986$	5.37977	+	9.31804i	0.171327	+	0.296747i
$987$	0.292815	−	24.0860i	0.00932039	−	0.766667i
$988$	−3.71441	+	6.43355i	−0.118171	+	0.204678i
$989$	5.32261			0.169249
$990$	9.24184	+	0.224740i	0.293725	+	0.00714270i
$991$	−31.4180			−0.998026			−0.499013	−	0.866594i	$-0.666304\pi$
$991$	−31.4180			−0.998026			−0.499013	+	0.866594i	$0.666304\pi$
$992$	−19.4008	+	33.6031i	−0.615975	+	1.06690i
$993$	10.4636	−	5.87272i	0.332052	−	0.186365i
$994$	0.889880	+	1.54132i	0.0282253	+	0.0488876i
$995$	7.19933	+	12.4696i	0.228234	+	0.395313i
$996$	39.1973	+	23.2704i	1.24201	+	0.737352i
$997$	15.2244	−	26.3694i	0.482161	−	0.835127i	−0.517629	−	0.855605i	$-0.673185\pi$
$997$	15.2244	−	26.3694i	0.482161	−	0.835127i	0.999790	+	0.0204775i	$0.00651866\pi$
$998$	−21.2830			−0.673701
$999$	2.01556	−	55.2428i	0.0637695	−	1.74780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.h.196.9	✓	30
3.2	odd	2		1755.2.i.h.586.7		30
9.2	odd	6		5265.2.a.bl.1.9		15
9.4	even	3	inner	585.2.i.h.391.9	yes	30
9.5	odd	6		1755.2.i.h.1171.7		30
9.7	even	3		5265.2.a.bk.1.7		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.h.196.9	✓	30	1.1	even	1	trivial
585.2.i.h.391.9	yes	30	9.4	even	3	inner
1755.2.i.h.586.7		30	3.2	odd	2
1755.2.i.h.1171.7		30	9.5	odd	6
5265.2.a.bk.1.7		15	9.7	even	3
5265.2.a.bl.1.9		15	9.2	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.300757 - 0.520926i) q^{2} +(1.48936 + 0.884196i) q^{3} +(0.819091 + 1.41871i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.908536 - 0.509919i) q^{6} +(1.29950 - 2.25080i) q^{7} +2.18842 q^{8} +(1.43640 + 2.63377i) q^{9} +O(q^{10})\)	\(q+(0.300757 - 0.520926i) q^{2} +(1.48936 + 0.884196i) q^{3} +(0.819091 + 1.41871i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.908536 - 0.509919i) q^{6} +(1.29950 - 2.25080i) q^{7} +2.18842 q^{8} +(1.43640 + 2.63377i) q^{9} +0.601514 q^{10} +(2.56147 - 4.43660i) q^{11} +(-0.0344920 + 2.83720i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-0.781667 - 1.35389i) q^{14} +(-0.0210550 + 1.73192i) q^{15} +(-0.980001 + 1.69741i) q^{16} -5.36998 q^{17} +(1.80401 + 0.0438692i) q^{18} -4.53480 q^{19} +(-0.819091 + 1.41871i) q^{20} +(3.92557 - 2.20324i) q^{21} +(-1.54076 - 2.66868i) q^{22} +(-0.399834 - 0.692533i) q^{23} +(3.25934 + 1.93499i) q^{24} +(-0.500000 + 0.866025i) q^{25} -0.601514 q^{26} +(-0.189458 + 5.19270i) q^{27} +4.25763 q^{28} +(1.66550 - 2.88474i) q^{29} +(0.895871 + 0.531856i) q^{30} +(3.49199 + 6.04830i) q^{31} +(2.77790 + 4.81146i) q^{32} +(7.73779 - 4.34286i) q^{33} +(-1.61506 + 2.79736i) q^{34} +2.59900 q^{35} +(-2.56001 + 4.19512i) q^{36} -10.6386 q^{37} +(-1.36387 + 2.36229i) q^{38} +(0.0210550 - 1.73192i) q^{39} +(1.09421 + 1.89522i) q^{40} +(-2.26990 - 3.93158i) q^{41} +(0.0329160 - 2.70757i) q^{42} +(-3.32801 + 5.76428i) q^{43} +8.39232 q^{44} +(-1.56272 + 2.56084i) q^{45} -0.481011 q^{46} +(2.67547 - 4.63406i) q^{47} +(-2.96042 + 1.66155i) q^{48} +(0.122600 + 0.212349i) q^{49} +(0.300757 + 0.520926i) q^{50} +(-7.99784 - 4.74811i) q^{51} +(0.819091 - 1.41871i) q^{52} -9.68150 q^{53} +(2.64803 + 1.66043i) q^{54} +5.12295 q^{55} +(2.84385 - 4.92569i) q^{56} +(-6.75395 - 4.00965i) q^{57} +(-1.00182 - 1.73521i) q^{58} +(0.409124 + 0.708623i) q^{59} +(-2.47434 + 1.38873i) q^{60} +(2.12396 - 3.67881i) q^{61} +4.20095 q^{62} +(7.79470 + 0.189549i) q^{63} -0.578115 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.0648816 - 5.33696i) q^{66} +(4.82116 + 8.35049i) q^{67} +(-4.39850 - 7.61842i) q^{68} +(0.0168370 - 1.38496i) q^{69} +(0.781667 - 1.35389i) q^{70} -1.13844 q^{71} +(3.14343 + 5.76379i) q^{72} +1.97256 q^{73} +(-3.19962 + 5.54190i) q^{74} +(-1.51042 + 0.847727i) q^{75} +(-3.71441 - 6.43355i) q^{76} +(-6.65727 - 11.5307i) q^{77} +(-0.895871 - 0.531856i) q^{78} +(-3.63802 + 6.30124i) q^{79} -1.96000 q^{80} +(-4.87353 + 7.56629i) q^{81} -2.73075 q^{82} +(8.03275 - 13.9131i) q^{83} +(6.34116 + 3.76458i) q^{84} +(-2.68499 - 4.65054i) q^{85} +(2.00184 + 3.46729i) q^{86} +(5.03121 - 2.82379i) q^{87} +(5.60557 - 9.70913i) q^{88} +4.74177 q^{89} +(0.864012 + 1.58425i) q^{90} -2.59900 q^{91} +(0.655001 - 1.13449i) q^{92} +(-0.147048 + 12.0957i) q^{93} +(-1.60933 - 2.78745i) q^{94} +(-2.26740 - 3.92725i) q^{95} +(-0.116978 + 9.62221i) q^{96} +(3.48300 - 6.03274i) q^{97} +0.147491 q^{98} +(15.3643 + 0.373624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

Introduction

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