LMFDB - Embedded newform 385.2.i.a.331.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(221,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("385.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.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:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.310217769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 $ x^8 + 4x^6 - 2x^5 + 15x^4 - 4x^3 + 5*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.3
Root			$0.346911 + 0.600868i$ of defining polynomial
Character	$\chi$	$=$	385.331
Dual form			385.2.i.a.221.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.873734 - 1.51335i) q^{2} +(1.22065 + 2.11422i) q^{3} +(-0.526823 - 0.912484i) q^{4} +(-0.500000 + 0.866025i) q^{5} +4.26608 q^{6} +(-1.89234 + 1.84906i) q^{7} +1.65372 q^{8} +(-1.47995 + 2.56335i) q^{9} +O(q^{10})$	\(q+(0.873734 - 1.51335i) q^{2} +(1.22065 + 2.11422i) q^{3} +(-0.526823 - 0.912484i) q^{4} +(-0.500000 + 0.866025i) q^{5} +4.26608 q^{6} +(-1.89234 + 1.84906i) q^{7} +1.65372 q^{8} +(-1.47995 + 2.56335i) q^{9} +(0.873734 + 1.51335i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.28613 - 2.22764i) q^{12} +1.88258 q^{13} +(1.14488 + 4.47937i) q^{14} -2.44129 q^{15} +(2.49856 - 4.32763i) q^{16} +(1.28613 + 2.22764i) q^{17} +(2.58617 + 4.47937i) q^{18} +(-1.53360 + 2.65627i) q^{19} +1.05365 q^{20} +(-6.21921 - 1.74378i) q^{21} -1.74747 q^{22} +(2.91917 - 5.05615i) q^{23} +(2.01861 + 3.49634i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.64488 - 2.84901i) q^{26} +0.0978926 q^{27} +(2.68417 + 0.752606i) q^{28} -2.56286 q^{29} +(-2.13304 + 3.69453i) q^{30} +(-1.42423 - 2.46684i) q^{31} +(-2.71243 - 4.69807i) q^{32} +(1.22065 - 2.11422i) q^{33} +4.49494 q^{34} +(-0.655163 - 2.56335i) q^{35} +3.11869 q^{36} +(2.49179 - 4.31590i) q^{37} +(2.67991 + 4.64174i) q^{38} +(2.29796 + 3.98019i) q^{39} +(-0.826862 + 1.43217i) q^{40} +1.57928 q^{41} +(-8.07289 + 7.88825i) q^{42} -10.7818 q^{43} +(-0.526823 + 0.912484i) q^{44} +(-1.47995 - 2.56335i) q^{45} +(-5.10115 - 8.83546i) q^{46} +(2.43922 - 4.22485i) q^{47} +12.1994 q^{48} +(0.161936 - 6.99813i) q^{49} -1.74747 q^{50} +(-3.13981 + 5.43832i) q^{51} +(-0.991787 - 1.71783i) q^{52} +(0.952493 + 1.64977i) q^{53} +(0.0855321 - 0.148146i) q^{54} +1.00000 q^{55} +(-3.12942 + 3.05784i) q^{56} -7.48791 q^{57} +(-2.23926 + 3.87850i) q^{58} +(-4.18406 - 7.24700i) q^{59} +(1.28613 + 2.22764i) q^{60} +(3.44806 - 5.97222i) q^{61} -4.97760 q^{62} +(-1.93922 - 7.58726i) q^{63} +0.514463 q^{64} +(-0.941291 + 1.63036i) q^{65} +(-2.13304 - 3.69453i) q^{66} +(-7.30708 - 12.6562i) q^{67} +(1.35512 - 2.34714i) q^{68} +14.2531 q^{69} +(-4.45169 - 1.24819i) q^{70} +4.51573 q^{71} +(-2.44743 + 4.23907i) q^{72} +(-0.0504965 - 0.0874625i) q^{73} +(-4.35432 - 7.54190i) q^{74} +(1.22065 - 2.11422i) q^{75} +3.23174 q^{76} +(2.54751 + 0.714287i) q^{77} +8.03124 q^{78} +(-4.59764 + 7.96335i) q^{79} +(2.49856 + 4.32763i) q^{80} +(4.55934 + 7.89702i) q^{81} +(1.37987 - 2.39001i) q^{82} +7.62375 q^{83} +(1.68525 + 6.59359i) q^{84} -2.57226 q^{85} +(-9.42044 + 16.3167i) q^{86} +(-3.12834 - 5.41844i) q^{87} +(-0.826862 - 1.43217i) q^{88} +(-7.09557 + 12.2899i) q^{89} -5.17233 q^{90} +(-3.56249 + 3.48101i) q^{91} -6.15154 q^{92} +(3.47696 - 6.02227i) q^{93} +(-4.26245 - 7.38279i) q^{94} +(-1.53360 - 2.65627i) q^{95} +(6.62184 - 11.4694i) q^{96} +1.79824 q^{97} +(-10.4491 - 6.35957i) q^{98} +2.95990 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 4 q^{5} + 14 q^{6} + q^{7} - 18 q^{8} + q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 4 * q^5 + 14 * q^6 + q^7 - 18 * q^8 + q^9	\( 8 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 4 q^{5} + 14 q^{6} + q^{7} - 18 q^{8} + q^{9} + 3 q^{10} - 4 q^{11} + 3 q^{12} - 12 q^{13} + q^{14} - 6 q^{15} - 5 q^{16} + 3 q^{17} - q^{18} + 3 q^{19} + 6 q^{20} - 18 q^{21} - 6 q^{22} + 6 q^{23} + 4 q^{24} - 4 q^{25} + 5 q^{26} + 6 q^{27} - 20 q^{28} - 16 q^{29} - 7 q^{30} - 10 q^{31} - 4 q^{32} + 3 q^{33} + 20 q^{34} + q^{35} - 16 q^{36} + 9 q^{37} + 23 q^{38} + 13 q^{39} + 9 q^{40} + 30 q^{41} - 16 q^{42} - 4 q^{43} - 3 q^{44} + q^{45} - 16 q^{46} + 15 q^{47} - 2 q^{48} - 19 q^{49} - 6 q^{50} - q^{51} + 3 q^{52} + 30 q^{53} + 13 q^{54} + 8 q^{55} - 24 q^{56} - 12 q^{57} + q^{58} - 17 q^{59} + 3 q^{60} + 32 q^{62} - 11 q^{63} + 10 q^{64} + 6 q^{65} - 7 q^{66} + 25 q^{67} + 19 q^{68} + 12 q^{69} + q^{70} - 26 q^{71} - 26 q^{72} - 3 q^{73} + 16 q^{74} + 3 q^{75} + 80 q^{76} - 2 q^{77} - 10 q^{78} + 4 q^{79} - 5 q^{80} + 16 q^{81} + 27 q^{82} + 36 q^{83} - 24 q^{84} - 6 q^{85} + 10 q^{86} - 20 q^{87} + 9 q^{88} - 25 q^{89} + 2 q^{90} - 3 q^{91} - 52 q^{92} - 10 q^{93} - 23 q^{94} + 3 q^{95} + 7 q^{96} - 46 q^{97} - 60 q^{98} - 2 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 4 * q^5 + 14 * q^6 + q^7 - 18 * q^8 + q^9 + 3 * q^10 - 4 * q^11 + 3 * q^12 - 12 * q^13 + q^14 - 6 * q^15 - 5 * q^16 + 3 * q^17 - q^18 + 3 * q^19 + 6 * q^20 - 18 * q^21 - 6 * q^22 + 6 * q^23 + 4 * q^24 - 4 * q^25 + 5 * q^26 + 6 * q^27 - 20 * q^28 - 16 * q^29 - 7 * q^30 - 10 * q^31 - 4 * q^32 + 3 * q^33 + 20 * q^34 + q^35 - 16 * q^36 + 9 * q^37 + 23 * q^38 + 13 * q^39 + 9 * q^40 + 30 * q^41 - 16 * q^42 - 4 * q^43 - 3 * q^44 + q^45 - 16 * q^46 + 15 * q^47 - 2 * q^48 - 19 * q^49 - 6 * q^50 - q^51 + 3 * q^52 + 30 * q^53 + 13 * q^54 + 8 * q^55 - 24 * q^56 - 12 * q^57 + q^58 - 17 * q^59 + 3 * q^60 + 32 * q^62 - 11 * q^63 + 10 * q^64 + 6 * q^65 - 7 * q^66 + 25 * q^67 + 19 * q^68 + 12 * q^69 + q^70 - 26 * q^71 - 26 * q^72 - 3 * q^73 + 16 * q^74 + 3 * q^75 + 80 * q^76 - 2 * q^77 - 10 * q^78 + 4 * q^79 - 5 * q^80 + 16 * q^81 + 27 * q^82 + 36 * q^83 - 24 * q^84 - 6 * q^85 + 10 * q^86 - 20 * q^87 + 9 * q^88 - 25 * q^89 + 2 * q^90 - 3 * q^91 - 52 * q^92 - 10 * q^93 - 23 * q^94 + 3 * q^95 + 7 * q^96 - 46 * q^97 - 60 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.873734	−	1.51335i	0.617823	−	1.07010i	−0.372059	−	0.928209i	$-0.621348\pi$
$2$	0.873734	−	1.51335i	0.617823	−	1.07010i	0.989882	−	0.141892i	$-0.0453187\pi$
$3$	1.22065	+	2.11422i	0.704740	+	1.22065i	0.966785	+	0.255590i	$0.0822697\pi$
$3$	1.22065	+	2.11422i	0.704740	+	1.22065i	−0.262045	+	0.965056i	$0.584397\pi$
$4$	−0.526823	−	0.912484i	−0.263411	−	0.456242i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	4.26608			1.74162
$7$	−1.89234	+	1.84906i	−0.715239	+	0.698880i
$7$	−1.89234	+	1.84906i	−0.715239	+	0.698880i
$8$	1.65372			0.584680
$9$	−1.47995	+	2.56335i	−0.493317	+	0.854450i
$10$	0.873734	+	1.51335i	0.276299	+	0.478564i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	1.28613	−	2.22764i	0.371273	−	0.643064i
$13$	1.88258			0.522134			0.261067	−	0.965321i	$-0.415926\pi$
$13$	1.88258			0.522134			0.261067	+	0.965321i	$0.415926\pi$
$14$	1.14488	+	4.47937i	0.305981	+	1.19716i
$15$	−2.44129			−0.630339
$16$	2.49856	−	4.32763i	0.624640	−	1.08191i
$17$	1.28613	+	2.22764i	0.311932	+	0.540282i	0.978781	−	0.204911i	$-0.0656906\pi$
$17$	1.28613	+	2.22764i	0.311932	+	0.540282i	−0.666849	+	0.745193i	$0.732357\pi$
$18$	2.58617	+	4.47937i	0.609565	+	1.05580i
$19$	−1.53360	+	2.65627i	−0.351831	+	0.609390i	−0.986570	−	0.163337i	$-0.947774\pi$
$19$	−1.53360	+	2.65627i	−0.351831	+	0.609390i	0.634739	+	0.772726i	$0.281108\pi$
$20$	1.05365			0.235602
$21$	−6.21921	−	1.74378i	−1.35714	−	0.380525i
$22$	−1.74747			−0.372562
$23$	2.91917	−	5.05615i	0.608689	−	1.05428i	−0.382768	−	0.923844i	$-0.625029\pi$
$23$	2.91917	−	5.05615i	0.608689	−	1.05428i	0.991457	−	0.130435i	$-0.0416374\pi$
$24$	2.01861	+	3.49634i	0.412047	+	0.713687i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.64488	−	2.84901i	0.322587	−	0.558737i
$27$	0.0978926			0.0188394
$28$	2.68417	+	0.752606i	0.507261	+	0.142229i
$29$	−2.56286			−0.475911			−0.237955	−	0.971276i	$-0.576477\pi$
$29$	−2.56286			−0.475911			−0.237955	+	0.971276i	$0.576477\pi$
$30$	−2.13304	+	3.69453i	−0.389438	+	0.674526i
$31$	−1.42423	−	2.46684i	−0.255799	−	0.443058i	0.709313	−	0.704894i	$-0.249005\pi$
$31$	−1.42423	−	2.46684i	−0.255799	−	0.443058i	−0.965112	+	0.261836i	$0.915672\pi$
$32$	−2.71243	−	4.69807i	−0.479495	−	0.830510i
$33$	1.22065	−	2.11422i	0.212487	−	0.368038i
$34$	4.49494			0.770875
$35$	−0.655163	−	2.56335i	−0.110743	−	0.433285i
$36$	3.11869			0.519781
$37$	2.49179	−	4.31590i	0.409647	−	0.709530i	−0.585203	−	0.810887i	$-0.698985\pi$
$37$	2.49179	−	4.31590i	0.409647	−	0.709530i	0.994850	+	0.101357i	$0.0323184\pi$
$38$	2.67991	+	4.64174i	0.434739	+	0.752990i
$39$	2.29796	+	3.98019i	0.367969	+	0.637341i
$40$	−0.826862	+	1.43217i	−0.130738	+	0.226445i
$41$	1.57928			0.246642			0.123321	−	0.992367i	$-0.460645\pi$
$41$	1.57928			0.246642			0.123321	+	0.992367i	$0.460645\pi$
$42$	−8.07289	+	7.88825i	−1.24567	+	1.21718i
$43$	−10.7818			−1.64421			−0.822105	−	0.569335i	$-0.807201\pi$
$43$	−10.7818			−1.64421			−0.822105	+	0.569335i	$0.807201\pi$
$44$	−0.526823	+	0.912484i	−0.0794216	+	0.137562i
$45$	−1.47995	−	2.56335i	−0.220618	−	0.382122i
$46$	−5.10115	−	8.83546i	−0.752124	−	1.30272i
$47$	2.43922	−	4.22485i	0.355796	−	0.616257i	−0.631458	−	0.775410i	$-0.717543\pi$
$47$	2.43922	−	4.22485i	0.355796	−	0.616257i	0.987254	+	0.159153i	$0.0508763\pi$
$48$	12.1994			1.76084
$49$	0.161936	−	6.99813i	0.0231338	−	0.999732i
$50$	−1.74747			−0.247129
$51$	−3.13981	+	5.43832i	−0.439662	+	0.761517i
$52$	−0.991787	−	1.71783i	−0.137536	−	0.238220i
$53$	0.952493	+	1.64977i	0.130835	+	0.226613i	0.923999	−	0.382396i	$-0.124901\pi$
$53$	0.952493	+	1.64977i	0.130835	+	0.226613i	−0.793164	+	0.609008i	$0.791568\pi$
$54$	0.0855321	−	0.148146i	0.0116394	−	0.0201601i
$55$	1.00000			0.134840
$56$	−3.12942	+	3.05784i	−0.418186	+	0.408621i
$57$	−7.48791			−0.991798
$58$	−2.23926	+	3.87850i	−0.294029	+	0.509273i
$59$	−4.18406	−	7.24700i	−0.544718	−	0.943480i	−0.998625	−	0.0524302i	$-0.983303\pi$
$59$	−4.18406	−	7.24700i	−0.544718	−	0.943480i	0.453906	−	0.891049i	$-0.350030\pi$
$60$	1.28613	+	2.22764i	0.166038	+	0.287587i
$61$	3.44806	−	5.97222i	0.441479	−	0.764665i	−0.556320	−	0.830968i	$-0.687787\pi$
$61$	3.44806	−	5.97222i	0.441479	−	0.764665i	0.997800	+	0.0663033i	$0.0211205\pi$
$62$	−4.97760			−0.632155
$63$	−1.93922	−	7.58726i	−0.244318	−	0.955905i
$64$	0.514463			0.0643078
$65$	−0.941291	+	1.63036i	−0.116753	+	0.202222i
$66$	−2.13304	−	3.69453i	−0.262559	−	0.454766i
$67$	−7.30708	−	12.6562i	−0.892702	−	1.54621i	−0.836623	−	0.547780i	$-0.815473\pi$
$67$	−7.30708	−	12.6562i	−0.892702	−	1.54621i	−0.0560798	−	0.998426i	$-0.517860\pi$
$68$	1.35512	−	2.34714i	0.164333	−	0.284633i
$69$	14.2531			1.71587
$70$	−4.45169	−	1.24819i	−0.532079	−	0.149188i
$71$	4.51573			0.535919			0.267959	−	0.963430i	$-0.413651\pi$
$71$	4.51573			0.535919			0.267959	+	0.963430i	$0.413651\pi$
$72$	−2.44743	+	4.23907i	−0.288432	+	0.499579i
$73$	−0.0504965	−	0.0874625i	−0.00591017	−	0.0102367i	0.863055	−	0.505110i	$-0.168548\pi$
$73$	−0.0504965	−	0.0874625i	−0.00591017	−	0.0102367i	−0.868965	+	0.494873i	$0.835215\pi$
$74$	−4.35432	−	7.54190i	−0.506179	−	0.876728i
$75$	1.22065	−	2.11422i	0.140948	−	0.244129i
$76$	3.23174			0.370706
$77$	2.54751	+	0.714287i	0.290315	+	0.0814006i
$78$	8.03124			0.909359
$79$	−4.59764	+	7.96335i	−0.517275	+	0.895947i	0.482524	+	0.875883i	$0.339720\pi$
$79$	−4.59764	+	7.96335i	−0.517275	+	0.895947i	−0.999799	+	0.0200636i	$0.993613\pi$
$80$	2.49856	+	4.32763i	0.279348	+	0.483844i
$81$	4.55934	+	7.89702i	0.506594	+	0.877446i
$82$	1.37987	−	2.39001i	0.152381	−	0.263932i
$83$	7.62375			0.836815			0.418408	−	0.908259i	$-0.362588\pi$
$83$	7.62375			0.836815			0.418408	+	0.908259i	$0.362588\pi$
$84$	1.68525	+	6.59359i	0.183875	+	0.719420i
$85$	−2.57226			−0.279000
$86$	−9.42044	+	16.3167i	−1.01583	+	1.75947i
$87$	−3.12834	−	5.41844i	−0.335393	−	0.580918i
$88$	−0.826862	−	1.43217i	−0.0881438	−	0.152669i
$89$	−7.09557	+	12.2899i	−0.752129	+	1.30272i	0.194661	+	0.980871i	$0.437639\pi$
$89$	−7.09557	+	12.2899i	−0.752129	+	1.30272i	−0.946789	+	0.321854i	$0.895694\pi$
$90$	−5.17233			−0.545212
$91$	−3.56249	+	3.48101i	−0.373451	+	0.364909i
$92$	−6.15154			−0.641342
$93$	3.47696	−	6.02227i	0.360544	−	0.624481i
$94$	−4.26245	−	7.38279i	−0.439639	−	0.761476i
$95$	−1.53360	−	2.65627i	−0.157344	−	0.272527i
$96$	6.62184	−	11.4694i	0.675838	−	1.17059i
$97$	1.79824			0.182583			0.0912916	−	0.995824i	$-0.470900\pi$
$97$	1.79824			0.182583			0.0912916	+	0.995824i	$0.470900\pi$
$98$	−10.4491	−	6.35957i	−1.05552	−	0.642414i
$99$	2.95990			0.297481
$100$	−0.526823	+	0.912484i	−0.0526823	+	0.0912484i
$101$	5.38322	+	9.32401i	0.535650	+	0.927773i	0.999132	+	0.0416666i	$0.0132667\pi$
$101$	5.38322	+	9.32401i	0.535650	+	0.927773i	−0.463481	+	0.886107i	$0.653400\pi$
$102$	5.48672	+	9.50329i	0.543267	+	0.940965i
$103$	−2.31817	+	4.01520i	−0.228417	+	0.395629i	−0.957339	−	0.288967i	$-0.906688\pi$
$103$	−2.31817	+	4.01520i	−0.228417	+	0.395629i	0.728922	+	0.684596i	$0.240021\pi$
$104$	3.11327			0.305281
$105$	4.61976	−	4.51410i	0.450843	−	0.440531i
$106$	3.32890			0.323332
$107$	0.818538	−	1.41775i	0.0791311	−	0.137059i	−0.823744	−	0.566962i	$-0.808119\pi$
$107$	0.818538	−	1.41775i	0.0791311	−	0.137059i	0.902875	+	0.429903i	$0.141452\pi$
$108$	−0.0515721	−	0.0893254i	−0.00496252	−	0.00859534i
$109$	8.32506	+	14.4194i	0.797396	+	1.38113i	0.921307	+	0.388837i	$0.127123\pi$
$109$	8.32506	+	14.4194i	0.797396	+	1.38113i	−0.123910	+	0.992293i	$0.539544\pi$
$110$	0.873734	−	1.51335i	0.0833073	−	0.144292i
$111$	12.1664			1.15478
$112$	3.27393	+	12.8094i	0.309357	+	1.21037i
$113$	−15.0135			−1.41236			−0.706178	−	0.708034i	$-0.749582\pi$
$113$	−15.0135			−1.41236			−0.706178	+	0.708034i	$0.749582\pi$
$114$	−6.54244	+	11.3318i	−0.612756	+	1.06132i
$115$	2.91917	+	5.05615i	0.272214	+	0.471488i
$116$	1.35017	+	2.33857i	0.125360	+	0.217130i
$117$	−2.78613	+	4.82572i	−0.257578	+	0.446138i
$118$	−14.6230			−1.34616
$119$	−6.55284	−	1.83733i	−0.600698	−	0.168428i
$120$	−4.03722			−0.368546
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−6.02538	−	10.4363i	−0.545513	−	0.944856i
$123$	1.92774	+	3.33895i	0.173819	+	0.301063i
$124$	−1.50063	+	2.59918i	−0.134761	+	0.233413i
$125$	1.00000			0.0894427
$126$	−13.1766	−	3.69453i	−1.17386	−	0.329135i
$127$	10.5179			0.933311			0.466656	−	0.884439i	$-0.345459\pi$
$127$	10.5179			0.933311			0.466656	+	0.884439i	$0.345459\pi$
$128$	5.87437	−	10.1747i	0.519226	−	0.899325i
$129$	−13.1608	−	22.7951i	−1.15874	−	2.00700i
$130$	1.64488	+	2.84901i	0.144265	+	0.249875i
$131$	−10.3426	+	17.9139i	−0.903637	+	1.56514i	−0.0808998	+	0.996722i	$0.525779\pi$
$131$	−10.3426	+	17.9139i	−0.903637	+	1.56514i	−0.822737	+	0.568422i	$0.807554\pi$
$132$	−2.57226			−0.223886
$133$	−2.00951	−	7.86229i	−0.174247	−	0.681747i
$134$	−25.5378			−2.20613
$135$	−0.0489463	+	0.0847775i	−0.00421263	+	0.00729648i
$136$	2.12690	+	3.68390i	0.182380	+	0.315892i
$137$	10.8074	+	18.7190i	0.923343	+	1.59928i	0.794205	+	0.607649i	$0.207887\pi$
$137$	10.8074	+	18.7190i	0.923343	+	1.59928i	0.129137	+	0.991627i	$0.458779\pi$
$138$	12.4534	−	21.5699i	1.06010	−	1.83615i
$139$	−16.4798			−1.39780			−0.698898	−	0.715221i	$-0.746326\pi$
$139$	−16.4798			−1.39780			−0.698898	+	0.715221i	$0.746326\pi$
$140$	−1.99386	+	1.94826i	−0.168512	+	0.164658i
$141$	11.9097			1.00298
$142$	3.94555	−	6.83389i	0.331103	−	0.573488i
$143$	−0.941291	−	1.63036i	−0.0787147	−	0.136338i
$144$	7.39549	+	12.8094i	0.616291	+	1.06745i
$145$	1.28143	−	2.21950i	0.106417	−	0.184319i
$146$	−0.176482			−0.0146058
$147$	14.9932	−	8.19986i	1.23662	−	0.676313i
$148$	−5.25092			−0.431623
$149$	−4.47226	+	7.74618i	−0.366382	+	0.634592i	−0.988997	−	0.147936i	$-0.952737\pi$
$149$	−4.47226	+	7.74618i	−0.366382	+	0.634592i	0.622615	+	0.782528i	$0.286070\pi$
$150$	−2.13304	−	3.69453i	−0.174162	−	0.301657i
$151$	−6.97137	−	12.0748i	−0.567322	−	0.982631i	−0.996829	−	0.0795678i	$-0.974646\pi$
$151$	−6.97137	−	12.0748i	−0.567322	−	0.982631i	0.429507	−	0.903064i	$-0.358687\pi$
$152$	−2.53615	+	4.39273i	−0.205709	+	0.356298i
$153$	−7.61363			−0.615525
$154$	3.30681	−	3.23118i	0.266471	−	0.260376i
$155$	2.84846			0.228794
$156$	2.42124	−	4.19371i	0.193854	−	0.335766i
$157$	1.50144	+	2.60057i	0.119828	+	0.207548i	0.919699	−	0.392623i	$-0.128432\pi$
$157$	1.50144	+	2.60057i	0.119828	+	0.207548i	−0.799871	+	0.600171i	$0.795099\pi$
$158$	8.03423	+	13.9157i	0.639169	+	1.10707i
$159$	−2.32531	+	4.02756i	−0.184409	+	0.319406i
$160$	5.42487			0.428873
$161$	3.82506	+	14.9657i	0.301457	+	1.17946i
$162$	15.9346			1.25194
$163$	11.1349	−	19.2861i	0.872150	−	1.51061i	0.0123812	−	0.999923i	$-0.496059\pi$
$163$	11.1349	−	19.2861i	0.872150	−	1.51061i	0.859768	−	0.510684i	$-0.170608\pi$
$164$	−0.832002	−	1.44107i	−0.0649685	−	0.112529i
$165$	1.22065	+	2.11422i	0.0950271	+	0.164592i
$166$	6.66113	−	11.5374i	0.517004	−	0.895477i
$167$	−7.35385			−0.569058			−0.284529	−	0.958667i	$-0.591837\pi$
$167$	−7.35385			−0.569058			−0.284529	+	0.958667i	$0.591837\pi$
$168$	−10.2848	−	2.88374i	−0.793493	−	0.222485i
$169$	−9.45589			−0.727376
$170$	−2.24747	+	3.89273i	−0.172373	+	0.298559i
$171$	−4.53929	−	7.86229i	−0.347129	−	0.601244i
$172$	5.68011	+	9.83823i	0.433104	+	0.750158i
$173$	11.6054	−	20.1012i	0.882343	−	1.52826i	0.0336144	−	0.999435i	$-0.489298\pi$
$173$	11.6054	−	20.1012i	0.882343	−	1.52826i	0.848729	−	0.528828i	$-0.177368\pi$
$174$	−10.9333			−0.828855
$175$	2.54751	+	0.714287i	0.192573	+	0.0539950i
$176$	−4.99712			−0.376672
$177$	10.2145	−	17.6920i	0.767769	−	1.32982i
$178$	12.3993	+	21.4762i	0.929365	+	1.60971i
$179$	9.45799	+	16.3817i	0.706923	+	1.22443i	0.965993	+	0.258568i	$0.0832507\pi$
$179$	9.45799	+	16.3817i	0.706923	+	1.22443i	−0.259070	+	0.965859i	$0.583416\pi$
$180$	−1.55934	+	2.70086i	−0.116227	+	0.201310i
$181$	21.8510			1.62417			0.812086	−	0.583538i	$-0.198332\pi$
$181$	21.8510			1.62417			0.812086	+	0.583538i	$0.198332\pi$
$182$	2.15532	+	8.43279i	0.159763	+	0.625080i
$183$	16.8355			1.24451
$184$	4.82750	−	8.36147i	0.355888	−	0.616416i
$185$	2.49179	+	4.31590i	0.183200	+	0.317311i
$186$	−6.07588	−	10.5237i	−0.445505	−	0.771638i
$187$	1.28613	−	2.22764i	0.0940510	−	0.162901i
$188$	−5.14014			−0.374883
$189$	−0.185246	+	0.181009i	−0.0134747	+	0.0131665i
$190$	−5.35982			−0.388842
$191$	−1.57378	+	2.72586i	−0.113875	+	0.197237i	−0.917329	−	0.398129i	$-0.869660\pi$
$191$	−1.57378	+	2.72586i	−0.113875	+	0.197237i	0.803455	+	0.595366i	$0.202993\pi$
$192$	0.627976	+	1.08769i	0.0453203	+	0.0784970i
$193$	−10.6195	−	18.3935i	−0.764409	−	1.32400i	−0.940558	−	0.339632i	$-0.889697\pi$
$193$	−10.6195	−	18.3935i	−0.764409	−	1.32400i	0.176149	−	0.984363i	$-0.443636\pi$
$194$	1.57118	−	2.72137i	0.112804	−	0.195383i
$195$	−4.59593			−0.329121
$196$	−6.47099	+	3.53901i	−0.462214	+	0.252786i
$197$	8.39202			0.597906			0.298953	−	0.954268i	$-0.403363\pi$
$197$	8.39202			0.597906			0.298953	+	0.954268i	$0.403363\pi$
$198$	2.58617	−	4.47937i	0.183791	−	0.318335i
$199$	−11.7326	−	20.3215i	−0.831705	−	1.44056i	−0.896685	−	0.442669i	$-0.854032\pi$
$199$	−11.7326	−	20.3215i	−0.831705	−	1.44056i	0.0649802	−	0.997887i	$-0.479302\pi$
$200$	−0.826862	−	1.43217i	−0.0584680	−	0.101269i
$201$	17.8387	−	30.8976i	1.25825	−	2.17935i
$202$	18.8140			1.32375
$203$	4.84981	−	4.73888i	0.340390	−	0.332604i
$204$	6.61650			0.463248
$205$	−0.789641	+	1.36770i	−0.0551509	+	0.0955242i
$206$	4.05094	+	7.01643i	0.282242	+	0.488858i
$207$	8.64045	+	14.9657i	0.600553	+	1.04019i
$208$	4.70375	−	8.14713i	0.326146	−	0.564902i
$209$	3.06719			0.212162
$210$	−2.79498	−	10.9355i	−0.192872	−	0.754618i
$211$	0.283774			0.0195358			0.00976791	−	0.999952i	$-0.496891\pi$
$211$	0.283774			0.0195358			0.00976791	+	0.999952i	$0.496891\pi$
$212$	1.00359	−	1.73827i	0.0689268	−	0.119385i
$213$	5.51211	+	9.54725i	0.377683	+	0.654167i
$214$	−1.43037	−	2.47747i	−0.0977780	−	0.169357i
$215$	5.39091	−	9.33732i	0.367657	−	0.636800i
$216$	0.161887			0.0110150
$217$	7.25648	+	2.03462i	0.492602	+	0.138119i
$218$	29.0956			1.97060
$219$	0.123277	−	0.213521i	0.00833026	−	0.0144284i
$220$	−0.526823	−	0.912484i	−0.0355184	−	0.0615197i
$221$	2.42124	+	4.19371i	0.162870	+	0.282100i
$222$	10.6302	−	18.4120i	0.713450	−	1.23573i
$223$	−27.4540			−1.83845			−0.919226	−	0.393729i	$-0.871185\pi$
$223$	−27.4540			−1.83845			−0.919226	+	0.393729i	$0.871185\pi$
$224$	13.8199	+	3.87491i	0.923380	+	0.258903i
$225$	2.95990			0.197327
$226$	−13.1179	+	22.7208i	−0.872586	+	1.51136i
$227$	−1.39793	−	2.42129i	−0.0927840	−	0.160707i	0.815898	−	0.578196i	$-0.196243\pi$
$227$	−1.39793	−	2.42129i	−0.0927840	−	0.160707i	−0.908682	+	0.417490i	$0.862910\pi$
$228$	3.94480	+	6.83260i	0.261251	+	0.452500i
$229$	6.42487	−	11.1282i	0.424567	−	0.735372i	−0.571813	−	0.820384i	$-0.693760\pi$
$229$	6.42487	−	11.1282i	0.424567	−	0.735372i	0.996380	+	0.0850124i	$0.0270930\pi$
$230$	10.2023			0.672720
$231$	1.59944	+	6.25788i	0.105236	+	0.411738i
$232$	−4.23826			−0.278255
$233$	9.23419	−	15.9941i	0.604952	−	1.04781i	−0.387107	−	0.922035i	$-0.626526\pi$
$233$	9.23419	−	15.9941i	0.604952	−	1.04781i	0.992059	−	0.125773i	$-0.0401411\pi$
$234$	4.86867	+	8.43279i	0.318275	+	0.551268i
$235$	2.43922	+	4.22485i	0.159117	+	0.275599i
$236$	−4.40852	+	7.63578i	−0.286970	+	0.497047i
$237$	−22.4484			−1.45818
$238$	−8.50597	+	8.31142i	−0.551360	+	0.538749i
$239$	−21.0893			−1.36415			−0.682075	−	0.731282i	$-0.738922\pi$
$239$	−21.0893			−1.36415			−0.682075	+	0.731282i	$0.738922\pi$
$240$	−6.09971	+	10.5650i	−0.393735	+	0.681969i
$241$	4.68550	+	8.11552i	0.301819	+	0.522767i	0.976548	−	0.215299i	$-0.0690727\pi$
$241$	4.68550	+	8.11552i	0.301819	+	0.522767i	−0.674729	+	0.738066i	$0.735739\pi$
$242$	0.873734	+	1.51335i	0.0561658	+	0.0972820i
$243$	−10.9838	+	19.0246i	−0.704614	+	1.22043i
$244$	−7.26608			−0.465163
$245$	5.97959	+	3.63930i	0.382022	+	0.232507i
$246$	6.73734			0.429557
$247$	−2.88712	+	5.00064i	−0.183703	+	0.318183i
$248$	−2.35528	−	4.07947i	−0.149561	−	0.259047i
$249$	9.30590	+	16.1183i	0.589737	+	1.02145i
$250$	0.873734	−	1.51335i	0.0552598	−	0.0957128i
$251$	−14.4075			−0.909393			−0.454696	−	0.890647i	$-0.650252\pi$
$251$	−14.4075			−0.909393			−0.454696	+	0.890647i	$0.650252\pi$
$252$	−5.90163	+	5.76665i	−0.371768	+	0.363265i
$253$	−5.83834			−0.367053
$254$	9.18983	−	15.9173i	0.576622	−	0.998738i
$255$	−3.13981	−	5.43832i	−0.196623	−	0.340561i
$256$	−9.75081	−	16.8889i	−0.609426	−	1.05556i
$257$	−8.15372	+	14.1227i	−0.508615	+	0.880948i	0.491335	+	0.870971i	$0.336509\pi$
$257$	−8.15372	+	14.1227i	−0.508615	+	0.880948i	−0.999950	+	0.00997684i	$0.996824\pi$
$258$	−45.9961			−2.86359
$259$	3.26505	+	12.7746i	0.202880	+	0.793778i
$260$	1.98357			0.123016
$261$	3.79290	−	6.56950i	0.234775	−	0.406642i
$262$	18.0734	+	31.3040i	1.11658	+	1.93397i
$263$	13.1596	+	22.7931i	0.811456	+	1.40548i	0.911845	+	0.410535i	$0.134658\pi$
$263$	13.1596	+	22.7931i	0.811456	+	1.40548i	−0.100388	+	0.994948i	$0.532009\pi$
$264$	2.01861	−	3.49634i	0.124237	−	0.215185i
$265$	−1.90499			−0.117022
$266$	−13.6542	−	3.82845i	−0.837192	−	0.234738i
$267$	−34.6447			−2.12022
$268$	−7.69908	+	13.3352i	−0.470296	+	0.814577i
$269$	−0.235108	−	0.407219i	−0.0143348	−	0.0248286i	0.858769	−	0.512363i	$-0.171230\pi$
$269$	−0.235108	−	0.407219i	−0.0143348	−	0.0248286i	−0.873104	+	0.487534i	$0.837896\pi$
$270$	0.0855321	+	0.148146i	0.00520532	+	0.00901587i
$271$	−8.99413	+	15.5783i	−0.546355	+	0.946314i	0.452166	+	0.891934i	$0.350652\pi$
$271$	−8.99413	+	15.5783i	−0.546355	+	0.946314i	−0.998520	+	0.0543801i	$0.982682\pi$
$272$	12.8539			0.779381
$273$	−11.7082	−	3.28281i	−0.708610	−	0.198685i
$274$	37.7713			2.28185
$275$	−0.500000	+	0.866025i	−0.0301511	+	0.0522233i
$276$	−7.50885	−	13.0057i	−0.451980	−	0.782851i
$277$	−12.4853	−	21.6251i	−0.750168	−	1.29933i	−0.947741	−	0.319041i	$-0.896639\pi$
$277$	−12.4853	−	21.6251i	−0.750168	−	1.29933i	0.197573	−	0.980288i	$-0.436694\pi$
$278$	−14.3989	+	24.9397i	−0.863592	+	1.49578i
$279$	8.43116			0.504761
$280$	−1.08346	−	4.23907i	−0.0647490	−	0.253333i
$281$	−22.4277			−1.33793			−0.668964	−	0.743295i	$-0.733262\pi$
$281$	−22.4277			−1.33793			−0.668964	+	0.743295i	$0.733262\pi$
$282$	10.4059	−	18.0235i	0.619662	−	1.07329i
$283$	10.6232	+	18.3999i	0.631483	+	1.09376i	0.987249	+	0.159185i	$0.0508867\pi$
$283$	10.6232	+	18.3999i	0.631483	+	1.09376i	−0.355766	+	0.934575i	$0.615780\pi$
$284$	−2.37899	−	4.12053i	−0.141167	−	0.244509i
$285$	3.74396	−	6.48472i	0.221773	−	0.384122i
$286$	−3.28975			−0.194527
$287$	−2.98855	+	2.92019i	−0.176408	+	0.172373i
$288$	16.0571			0.946172
$289$	5.19175	−	8.99237i	0.305397	−	0.528963i
$290$	−2.23926	−	3.87850i	−0.131494	−	0.227754i
$291$	2.19501	+	3.80187i	0.128674	+	0.222869i
$292$	−0.0532054	+	0.0921545i	−0.00311361	+	0.00539293i
$293$	−16.3043			−0.952510			−0.476255	−	0.879307i	$-0.658006\pi$
$293$	−16.3043			−0.952510			−0.476255	+	0.879307i	$0.658006\pi$
$294$	0.690833	−	29.8546i	0.0402902	−	1.74115i
$295$	8.36812			0.487211
$296$	4.12073	−	7.13731i	0.239512	−	0.414848i
$297$	−0.0489463	−	0.0847775i	−0.00284015	−	0.00491929i
$298$	7.81514	+	13.5362i	0.452719	+	0.784132i
$299$	5.49557	−	9.51861i	0.317817	−	0.550475i
$300$	−2.57226			−0.148509
$301$	20.4029	−	19.9362i	1.17600	−	1.14911i
$302$	−24.3645			−1.40202
$303$	−13.1420	+	22.7626i	−0.754988	+	1.30768i
$304$	7.66357	+	13.2737i	0.439536	+	0.761298i
$305$	3.44806	+	5.97222i	0.197436	+	0.341968i
$306$	−6.65228	+	11.5221i	−0.380286	+	0.658674i
$307$	1.80820			0.103199			0.0515996	−	0.998668i	$-0.483568\pi$
$307$	1.80820			0.103199			0.0515996	+	0.998668i	$0.483568\pi$
$308$	−0.690310	−	2.70086i	−0.0393340	−	0.153896i
$309$	−11.3187			−0.643897
$310$	2.48880	−	4.31073i	0.141354	−	0.244833i
$311$	15.1903	+	26.3104i	0.861363	+	1.49192i	0.870614	+	0.491967i	$0.163722\pi$
$311$	15.1903	+	26.3104i	0.861363	+	1.49192i	−0.00925081	+	0.999957i	$0.502945\pi$
$312$	3.80020	+	6.58214i	0.215144	+	0.372640i
$313$	−8.89162	+	15.4007i	−0.502584	+	0.870501i	0.497412	+	0.867515i	$0.334284\pi$
$313$	−8.89162	+	15.4007i	−0.502584	+	0.870501i	−0.999996	+	0.00298627i	$0.999049\pi$
$314$	5.24743			0.296130
$315$	7.54037	+	2.11422i	0.424852	+	0.119123i
$316$	9.68857			0.545025
$317$	−2.85850	+	4.95106i	−0.160549	+	0.278079i	−0.935066	−	0.354474i	$-0.884660\pi$
$317$	−2.85850	+	4.95106i	−0.160549	+	0.278079i	0.774517	+	0.632554i	$0.217993\pi$
$318$	4.06341	+	7.03803i	0.227865	+	0.394673i
$319$	1.28143	+	2.21950i	0.0717462	+	0.124268i
$320$	−0.257231	+	0.445538i	−0.0143797	+	0.0249063i
$321$	3.99658			0.223067
$322$	25.9905	+	7.28738i	1.44839	+	0.406110i
$323$	−7.88961			−0.438990
$324$	4.80393	−	8.32066i	0.266885	−	0.462259i
$325$	−0.941291	−	1.63036i	−0.0522134	−	0.0904363i
$326$	−19.4578	−	33.7019i	−1.07767	−	1.86658i
$327$	−20.3239	+	35.2020i	−1.12391	+	1.94668i
$328$	2.61170			0.144207
$329$	3.19617	+	12.5051i	0.176210	+	0.689430i
$330$	4.26608			0.234840
$331$	4.04516	−	7.00643i	0.222342	−	0.385108i	−0.733177	−	0.680038i	$-0.761963\pi$
$331$	4.04516	−	7.00643i	0.222342	−	0.385108i	0.955519	+	0.294930i	$0.0952964\pi$
$332$	−4.01637	−	6.95655i	−0.220427	−	0.381790i
$333$	7.37544	+	12.7746i	0.404172	+	0.700046i
$334$	−6.42531	+	11.1290i	−0.351577	+	0.608949i
$335$	14.6142			0.798457
$336$	−23.0855	+	22.5575i	−1.25942	+	1.23061i
$337$	11.3367			0.617549			0.308775	−	0.951135i	$-0.400081\pi$
$337$	11.3367			0.617549			0.308775	+	0.951135i	$0.400081\pi$
$338$	−8.26193	+	14.3101i	−0.449390	+	0.778366i
$339$	−18.3262	−	31.7419i	−0.995344	−	1.72399i
$340$	1.35512	+	2.34714i	0.0734919	+	0.127292i
$341$	−1.42423	+	2.46684i	−0.0771264	+	0.133587i
$342$	−15.8645			−0.857857
$343$	12.6335	+	13.5423i	0.682147	+	0.731215i
$344$	−17.8301			−0.961337
$345$	−7.12654	+	12.3435i	−0.383680	+	0.664553i
$346$	−20.2801	−	35.1262i	−1.09026	−	1.88839i
$347$	0.203382	+	0.352268i	0.0109181	+	0.0189108i	0.871433	−	0.490515i	$-0.163191\pi$
$347$	0.203382	+	0.352268i	0.0109181	+	0.0189108i	−0.860515	+	0.509426i	$0.829858\pi$
$348$	−3.29616	+	5.70912i	−0.176693	+	0.306041i
$349$	4.87916			0.261175			0.130588	−	0.991437i	$-0.458314\pi$
$349$	4.87916			0.261175			0.130588	+	0.991437i	$0.458314\pi$
$350$	3.30681	−	3.23118i	0.176757	−	0.172714i
$351$	0.184291			0.00983671
$352$	−2.71243	+	4.69807i	−0.144573	+	0.250408i
$353$	−4.49867	−	7.79193i	−0.239440	−	0.414723i	0.721114	−	0.692817i	$-0.243631\pi$
$353$	−4.49867	−	7.79193i	−0.239440	−	0.414723i	−0.960554	+	0.278094i	$0.910297\pi$
$354$	−17.8495	−	30.9163i	−0.948692	−	1.64318i
$355$	−2.25787	+	3.91074i	−0.119835	+	0.207560i
$356$	14.9524			0.792477
$357$	−4.11418	−	16.0969i	−0.217745	−	0.851937i
$358$	33.0551			1.74701
$359$	2.34846	−	4.06765i	0.123947	−	0.214683i	−0.797374	−	0.603486i	$-0.793778\pi$
$359$	2.34846	−	4.06765i	0.123947	−	0.214683i	0.921321	+	0.388803i	$0.127111\pi$
$360$	−2.44743	−	4.23907i	−0.128991	−	0.223419i
$361$	4.79616	+	8.30720i	0.252430	+	0.437221i
$362$	19.0920	−	33.0683i	1.00345	−	1.73803i
$363$	−2.44129			−0.128135
$364$	5.05317	+	1.41684i	0.264858	+	0.0742627i
$365$	0.100993			0.00528621
$366$	14.7097	−	25.4780i	0.768889	−	1.33176i
$367$	−2.29586	−	3.97655i	−0.119843	−	0.207574i	0.799862	−	0.600184i	$-0.204906\pi$
$367$	−2.29586	−	3.97655i	−0.119843	−	0.207574i	−0.919705	+	0.392609i	$0.871572\pi$
$368$	−14.5874	−	25.2662i	−0.760423	−	1.31709i
$369$	−2.33726	+	4.04825i	−0.121673	+	0.210744i
$370$	8.70864			0.452741
$371$	−4.85296	−	1.36071i	−0.251953	−	0.0706444i
$372$	−7.32697			−0.379886
$373$	6.53376	−	11.3168i	0.338305	−	0.585962i	−0.645809	−	0.763499i	$-0.723480\pi$
$373$	6.53376	−	11.3168i	0.338305	−	0.585962i	0.984114	+	0.177537i	$0.0568131\pi$
$374$	−2.24747	−	3.89273i	−0.116214	−	0.201288i
$375$	1.22065	+	2.11422i	0.0630339	+	0.109178i
$376$	4.03379	−	6.98673i	0.208027	−	0.360313i
$377$	−4.82479			−0.248489
$378$	0.112075	+	0.438497i	0.00576451	+	0.0225539i
$379$	−10.4099			−0.534719			−0.267359	−	0.963597i	$-0.586151\pi$
$379$	−10.4099			−0.534719			−0.267359	+	0.963597i	$0.586151\pi$
$380$	−1.61587	+	2.79877i	−0.0828923	+	0.143574i
$381$	12.8386	+	22.2371i	0.657742	+	1.13924i
$382$	2.75013	+	4.76336i	0.140709	+	0.243715i
$383$	11.4726	−	19.8711i	0.586221	−	1.01536i	−0.408502	−	0.912758i	$-0.633949\pi$
$383$	11.4726	−	19.8711i	0.586221	−	1.01536i	0.994722	−	0.102606i	$-0.0327181\pi$
$384$	28.6821			1.46368
$385$	−1.89234	+	1.84906i	−0.0964428	+	0.0942369i
$386$	−37.1145			−1.88908
$387$	15.9565	−	27.6376i	0.811117	−	1.40490i
$388$	−0.947352	−	1.64086i	−0.0480945	−	0.0833022i
$389$	−5.83327	−	10.1035i	−0.295759	−	0.512269i	0.679402	−	0.733766i	$-0.262239\pi$
$389$	−5.83327	−	10.1035i	−0.295759	−	0.512269i	−0.975161	+	0.221497i	$0.928906\pi$
$390$	−4.01562	+	6.95526i	−0.203339	+	0.352193i
$391$	15.0177			0.759477
$392$	0.267798	−	11.5730i	0.0135258	−	0.584523i
$393$	−50.4986			−2.54732
$394$	7.33239	−	12.7001i	0.369401	−	0.639820i
$395$	−4.59764	−	7.96335i	−0.231332	−	0.400679i
$396$	−1.55934	−	2.70086i	−0.0783600	−	0.135723i
$397$	1.20748	−	2.09142i	0.0606017	−	0.104965i	−0.834133	−	0.551564i	$-0.814031\pi$
$397$	1.20748	−	2.09142i	0.0606017	−	0.104965i	0.894735	+	0.446598i	$0.147365\pi$
$398$	−41.0048			−2.05539
$399$	14.1697	−	13.8456i	0.709373	−	0.693148i
$400$	−4.99712			−0.249856
$401$	16.9248	−	29.3146i	0.845183	−	1.46390i	−0.0402794	−	0.999188i	$-0.512825\pi$
$401$	16.9248	−	29.3146i	0.845183	−	1.46390i	0.885462	−	0.464711i	$-0.153842\pi$
$402$	−31.1726	−	53.9925i	−1.55475	−	2.69290i
$403$	−2.68123	−	4.64403i	−0.133562	−	0.231336i
$404$	5.67200	−	9.82420i	0.282193	−	0.488772i
$405$	−9.11869			−0.453111
$406$	−2.93415	−	11.4800i	−0.145620	−	0.569742i
$407$	−4.98357			−0.247027
$408$	−5.19238	+	8.99347i	−0.257061	+	0.445243i
$409$	4.58528	+	7.94194i	0.226728	+	0.392704i	0.956836	−	0.290627i	$-0.0938640\pi$
$409$	4.58528	+	7.94194i	0.226728	+	0.392704i	−0.730109	+	0.683331i	$0.760531\pi$
$410$	1.37987	+	2.39001i	0.0681471	+	0.118034i
$411$	−26.3841	+	45.6986i	−1.30143	+	2.25415i
$412$	4.88507			0.240670
$413$	21.3178	+	5.97724i	1.04898	+	0.294121i
$414$	30.1978			1.48414
$415$	−3.81188	+	6.60236i	−0.187118	+	0.324097i
$416$	−5.10638	−	8.84450i	−0.250361	−	0.433637i
$417$	−20.1160	−	34.8419i	−0.985083	−	1.70621i
$418$	2.67991	−	4.64174i	0.131079	−	0.227035i
$419$	−9.98307			−0.487705			−0.243852	−	0.969812i	$-0.578411\pi$
$419$	−9.98307			−0.487705			−0.243852	+	0.969812i	$0.578411\pi$
$420$	−6.55284	−	1.83733i	−0.319746	−	0.0896525i
$421$	−16.5141			−0.804846			−0.402423	−	0.915454i	$-0.631832\pi$
$421$	−16.5141			−0.804846			−0.402423	+	0.915454i	$0.631832\pi$
$422$	0.247943	−	0.429450i	0.0120697	−	0.0209053i
$423$	7.21984	+	12.5051i	0.351041	+	0.608020i
$424$	1.57516	+	2.72826i	0.0764965	+	0.132496i
$425$	1.28613	−	2.22764i	0.0623864	−	0.108056i
$426$	19.2645			0.933367
$427$	4.51809	+	17.6772i	0.218646	+	0.855459i
$428$	−1.72490			−0.0833761
$429$	2.29796	−	3.98019i	0.110947	−	0.192165i
$430$	−9.42044	−	16.3167i	−0.454294	−	0.786860i
$431$	8.22769	+	14.2508i	0.396314	+	0.686436i	0.993268	−	0.115840i	$-0.0369559\pi$
$431$	8.22769	+	14.2508i	0.396314	+	0.686436i	−0.596954	+	0.802275i	$0.703623\pi$
$432$	0.244591	−	0.423643i	0.0117679	−	0.0203825i
$433$	−17.9836			−0.864235			−0.432118	−	0.901817i	$-0.642234\pi$
$433$	−17.9836			−0.864235			−0.432118	+	0.901817i	$0.642234\pi$
$434$	9.41933	−	9.20389i	0.452142	−	0.441801i
$435$	6.25668			0.299985
$436$	8.77167	−	15.1930i	0.420087	−	0.727611i
$437$	8.95365	+	15.5082i	0.428311	+	0.741857i
$438$	−0.215422	−	0.373122i	−0.0102933	−	0.0178285i
$439$	−11.5363	+	19.9815i	−0.550598	+	0.953663i	0.447634	+	0.894217i	$0.352267\pi$
$439$	−11.5363	+	19.9815i	−0.550598	+	0.953663i	−0.998232	+	0.0594464i	$0.981066\pi$
$440$	1.65372			0.0788382
$441$	17.6990	+	10.7720i	0.842809	+	0.512952i
$442$	8.46209			0.402500
$443$	−4.81514	+	8.34006i	−0.228774	+	0.396248i	−0.957445	−	0.288616i	$-0.906805\pi$
$443$	−4.81514	+	8.34006i	−0.228774	+	0.396248i	0.728671	+	0.684864i	$0.240138\pi$
$444$	−6.40952	−	11.1016i	−0.304182	−	0.526859i
$445$	−7.09557	−	12.2899i	−0.336362	−	0.582596i
$446$	−23.9875	+	41.5475i	−1.13584	+	1.96733i
$447$	−21.8362			−1.03282
$448$	−0.973540	+	0.951273i	−0.0459955	+	0.0449434i
$449$	−5.45196			−0.257294			−0.128647	−	0.991690i	$-0.541063\pi$
$449$	−5.45196			−0.257294			−0.128647	+	0.991690i	$0.541063\pi$
$450$	2.58617	−	4.47937i	0.121913	−	0.211160i
$451$	−0.789641	−	1.36770i	−0.0371827	−	0.0644024i
$452$	7.90948	+	13.6996i	0.372031	+	0.644376i
$453$	17.0192	−	29.4780i	0.799630	−	1.38500i
$454$	−4.88568			−0.229296
$455$	−1.23340	−	4.82572i	−0.0578226	−	0.226233i
$456$	−12.3829			−0.579884
$457$	−13.1926	+	22.8503i	−0.617125	+	1.06889i	0.372883	+	0.927879i	$0.378369\pi$
$457$	−13.1926	+	22.8503i	−0.617125	+	1.06889i	−0.990008	+	0.141013i	$0.954964\pi$
$458$	−11.2273	−	19.4462i	−0.524615	−	0.908660i
$459$	0.125902	+	0.218069i	0.00587662	+	0.0101786i
$460$	3.07577	−	5.32739i	0.143408	−	0.248391i
$461$	14.6685			0.683182			0.341591	−	0.939849i	$-0.389034\pi$
$461$	14.6685			0.683182			0.341591	+	0.939849i	$0.389034\pi$
$462$	10.8679	+	3.04721i	0.505619	+	0.141769i
$463$	29.7719			1.38362			0.691809	−	0.722081i	$-0.256814\pi$
$463$	29.7719			1.38362			0.691809	+	0.722081i	$0.256814\pi$
$464$	−6.40345	+	11.0911i	−0.297273	+	0.514892i
$465$	3.47696	+	6.02227i	0.161240	+	0.279276i
$466$	−16.1365	−	27.9492i	−0.747507	−	1.29472i
$467$	−3.50506	+	6.07095i	−0.162195	+	0.280930i	−0.935656	−	0.352914i	$-0.885191\pi$
$467$	−3.50506	+	6.07095i	−0.162195	+	0.280930i	0.773461	+	0.633844i	$0.218524\pi$
$468$	5.87119			0.271396
$469$	37.2297	+	10.4387i	1.71911	+	0.482015i
$470$	8.52491			0.393225
$471$	−3.66545	+	6.34874i	−0.168895	+	0.292535i
$472$	−6.91928	−	11.9845i	−0.318486	−	0.551633i
$473$	5.39091	+	9.33732i	0.247874	+	0.429331i
$474$	−19.6139	+	33.9723i	−0.900896	+	1.56040i
$475$	3.06719			0.140732
$476$	1.77565	+	6.94731i	0.0813869	+	0.318430i
$477$	−5.63857			−0.258172
$478$	−18.4264	+	31.9155i	−0.842804	+	1.45978i
$479$	−6.97660	−	12.0838i	−0.318769	−	0.552124i	0.661463	−	0.749978i	$-0.269936\pi$
$479$	−6.97660	−	12.0838i	−0.318769	−	0.552124i	−0.980231	+	0.197854i	$0.936603\pi$
$480$	6.62184	+	11.4694i	0.302244	+	0.523502i
$481$	4.69099	−	8.12504i	0.213891	−	0.370470i
$482$	16.3755			0.745885
$483$	−26.9717	+	26.3548i	−1.22726	+	1.19919i
$484$	1.05365			0.0478930
$485$	−0.899118	+	1.55732i	−0.0408269	+	0.0707142i
$486$	19.1939	+	33.2449i	0.870654	+	1.50802i
$487$	−3.36066	−	5.82084i	−0.152286	−	0.263767i	0.779781	−	0.626052i	$-0.215330\pi$
$487$	−3.36066	−	5.82084i	−0.152286	−	0.263767i	−0.932068	+	0.362285i	$0.881997\pi$
$488$	5.70215	−	9.87641i	0.258124	−	0.447084i
$489$	54.3669			2.45855
$490$	10.7321	−	5.86944i	0.484828	−	0.265154i
$491$	−25.9471			−1.17098			−0.585489	−	0.810681i	$-0.699097\pi$
$491$	−25.9471			−1.17098			−0.585489	+	0.810681i	$0.699097\pi$
$492$	2.03116	−	3.51807i	0.0915717	−	0.158607i
$493$	−3.29616	−	5.70912i	−0.148452	−	0.257126i
$494$	5.04515	+	8.73846i	0.226992	+	0.393162i
$495$	−1.47995	+	2.56335i	−0.0665188	+	0.115214i
$496$	−14.2341			−0.639130
$497$	−8.54532	+	8.34987i	−0.383310	+	0.374543i
$498$	32.5235			1.45741
$499$	−10.4025	+	18.0176i	−0.465679	+	0.806580i	−0.999232	−	0.0391865i	$-0.987523\pi$
$499$	−10.4025	+	18.0176i	−0.465679	+	0.806580i	0.533552	+	0.845767i	$0.320857\pi$
$500$	−0.526823	−	0.912484i	−0.0235602	−	0.0408075i
$501$	−8.97644	−	15.5476i	−0.401038	−	0.694618i
$502$	−12.5883	+	21.8036i	−0.561844	+	0.973143i
$503$	30.1238			1.34315			0.671576	−	0.740936i	$-0.265618\pi$
$503$	30.1238			1.34315			0.671576	+	0.740936i	$0.265618\pi$
$504$	−3.20693	−	12.5472i	−0.142848	−	0.558898i
$505$	−10.7664			−0.479100
$506$	−5.10115	+	8.83546i	−0.226774	+	0.392784i
$507$	−11.5423	−	19.9918i	−0.512611	−	0.887868i
$508$	−5.54106	−	9.59740i	−0.245845	−	0.425816i
$509$	5.27979	−	9.14486i	0.234022	−	0.405339i	−0.724966	−	0.688785i	$-0.758144\pi$
$509$	5.27979	−	9.14486i	0.234022	−	0.405339i	0.958988	+	0.283446i	$0.0914778\pi$
$510$	−10.9734			−0.485912
$511$	0.257280	+	0.0721380i	0.0113814	+	0.00319120i
$512$	−10.5810			−0.467618
$513$	−0.150128	+	0.260029i	−0.00662830	+	0.0114806i
$514$	14.2484	+	24.6789i	0.628469	+	1.08854i
$515$	−2.31817	−	4.01520i	−0.102151	−	0.176931i
$516$	−13.8668	+	24.0180i	−0.610451	+	1.05733i
$517$	−4.87843			−0.214553
$518$	22.1853	+	6.22047i	0.974767	+	0.273312i
$519$	56.6644			2.48729
$520$	−1.55664	+	2.69617i	−0.0682630	+	0.118235i
$521$	7.45591	+	12.9140i	0.326650	+	0.565774i	0.981845	−	0.189686i	$-0.0607470\pi$
$521$	7.45591	+	12.9140i	0.326650	+	0.565774i	−0.655195	+	0.755460i	$0.727414\pi$
$522$	−6.62798	−	11.4800i	−0.290099	−	0.502466i
$523$	−3.43089	+	5.94248i	−0.150022	+	0.259847i	−0.931235	−	0.364418i	$-0.881268\pi$
$523$	−3.43089	+	5.94248i	−0.150022	+	0.259847i	0.781213	+	0.624265i	$0.214601\pi$
$524$	21.7949			0.952113
$525$	1.59944	+	6.25788i	0.0698054	+	0.273116i
$526$	45.9920			2.00535
$527$	3.66349	−	6.34534i	0.159584	−	0.276408i
$528$	−6.09971	−	10.5650i	−0.265456	−	0.459783i
$529$	−5.54308	−	9.60089i	−0.241003	−	0.417430i
$530$	−1.66445	+	2.88291i	−0.0722991	+	0.125226i
$531$	24.7688			1.07487
$532$	−6.11556	+	5.97568i	−0.265143	+	0.259079i
$533$	2.97313			0.128780
$534$	−30.2702	+	52.4296i	−1.30992	+	2.26885i
$535$	0.818538	+	1.41775i	0.0353885	+	0.0612947i
$536$	−12.0839	−	20.9299i	−0.521945	−	0.904035i
$537$	−23.0897	+	39.9925i	−0.996394	+	1.72581i
$538$	−0.821688			−0.0354255
$539$	−6.14152	+	3.35882i	−0.264534	+	0.144675i
$540$	0.103144			0.00443862
$541$	6.88385	−	11.9232i	0.295960	−	0.512618i	−0.679248	−	0.733909i	$-0.737694\pi$
$541$	6.88385	−	11.9232i	0.295960	−	0.512618i	0.975208	+	0.221291i	$0.0710272\pi$
$542$	15.7170	+	27.2226i	0.675101	+	1.16931i
$543$	26.6723	+	46.1978i	1.14462	+	1.98254i
$544$	6.97707	−	12.0846i	0.299140	−	0.518125i
$545$	−16.6501			−0.713213
$546$	−15.1979	+	14.8503i	−0.650409	+	0.635533i
$547$	−8.87135			−0.379312			−0.189656	−	0.981851i	$-0.560737\pi$
$547$	−8.87135			−0.379312			−0.189656	+	0.981851i	$0.560737\pi$
$548$	11.3872	−	19.7233i	0.486438	−	0.842535i
$549$	10.2059	+	17.6772i	0.435579	+	0.754444i
$550$	0.873734	+	1.51335i	0.0372562	+	0.0645295i
$551$	3.93039	−	6.80763i	0.167440	−	0.290015i
$552$	23.5706			1.00323
$553$	−6.02441	−	23.5707i	−0.256184	−	1.00233i
$554$	−43.6353			−1.85389
$555$	−6.08318	+	10.5364i	−0.258217	+	0.447244i
$556$	8.68193	+	15.0375i	0.368196	+	0.637734i
$557$	−6.28170	−	10.8802i	−0.266164	−	0.461010i	0.701704	−	0.712469i	$-0.252423\pi$
$557$	−6.28170	−	10.8802i	−0.266164	−	0.461010i	−0.967868	+	0.251459i	$0.919090\pi$
$558$	7.36660	−	12.7593i	0.311853	−	0.540145i
$559$	−20.2976			−0.858499
$560$	−12.7302	−	3.56938i	−0.537949	−	0.150834i
$561$	6.27963			0.265126
$562$	−19.5959	+	33.9411i	−0.826603	+	1.43172i
$563$	7.24233	+	12.5441i	0.305228	+	0.528670i	0.977312	−	0.211805i	$-0.0679341\pi$
$563$	7.24233	+	12.5441i	0.305228	+	0.528670i	−0.672084	+	0.740475i	$0.734601\pi$
$564$	−6.27429	−	10.8674i	−0.264195	−	0.457600i
$565$	7.50677	−	13.0021i	0.315812	−	0.547003i
$566$	37.1274			1.56058
$567$	−23.2299	−	6.51336i	−0.975565	−	0.273536i
$568$	7.46777			0.313341
$569$	17.2222	−	29.8298i	0.721993	−	1.25053i	−0.238207	−	0.971214i	$-0.576560\pi$
$569$	17.2222	−	29.8298i	0.721993	−	1.25053i	0.960200	−	0.279314i	$-0.0901070\pi$
$570$	−6.54244	−	11.3318i	−0.274033	−	0.474639i
$571$	−22.9894	−	39.8189i	−0.962078	−	1.66637i	−0.717269	−	0.696796i	$-0.754608\pi$
$571$	−22.9894	−	39.8189i	−0.962078	−	1.66637i	−0.244809	−	0.969571i	$-0.578725\pi$
$572$	−0.991787	+	1.71783i	−0.0414687	+	0.0718259i
$573$	−7.68410			−0.321008
$574$	1.80808	+	7.07419i	0.0754679	+	0.295271i
$575$	−5.83834			−0.243475
$576$	−0.761379	+	1.31875i	−0.0317241	+	0.0549478i
$577$	20.1984	+	34.9846i	0.840868	+	1.45643i	0.889161	+	0.457594i	$0.151289\pi$
$577$	20.1984	+	34.9846i	0.840868	+	1.45643i	−0.0482930	+	0.998833i	$0.515378\pi$
$578$	−9.07242	−	15.7139i	−0.377363	−	0.653612i
$579$	25.9253	−	44.9040i	1.07742	−	1.86615i
$580$	−2.70034			−0.112126
$581$	−14.4268	+	14.0968i	−0.598523	+	0.584833i
$582$	7.67142			0.317991
$583$	0.952493	−	1.64977i	0.0394482	−	0.0683263i
$584$	−0.0835072	−	0.144639i	−0.00345555	−	0.00598520i
$585$	−2.78613	−	4.82572i	−0.115192	−	0.199519i
$586$	−14.2457	+	24.6742i	−0.588483	+	1.01928i
$587$	−21.4627			−0.885860			−0.442930	−	0.896556i	$-0.646061\pi$
$587$	−21.4627			−0.885860			−0.442930	+	0.896556i	$0.646061\pi$
$588$	−15.3810	−	9.36122i	−0.634303	−	0.386050i
$589$	8.73678			0.359993
$590$	7.31151	−	12.6639i	0.301010	−	0.521365i
$591$	10.2437	+	17.7426i	0.421368	+	0.729832i
$592$	−12.4518	−	21.5671i	−0.511764	−	0.886402i
$593$	5.80084	−	10.0474i	0.238212	−	0.412595i	−0.721989	−	0.691904i	$-0.756772\pi$
$593$	5.80084	−	10.0474i	0.238212	−	0.412595i	0.960201	+	0.279309i	$0.0901053\pi$
$594$	−0.171064			−0.00701885
$595$	4.86760	−	4.75626i	0.199552	−	0.194988i
$596$	9.42436			0.386037
$597$	28.6428	−	49.6108i	1.17227	−	2.03043i
$598$	−9.60334	−	16.6335i	−0.392710	−	0.680193i
$599$	6.88817	+	11.9307i	0.281443	+	0.487473i	0.971740	−	0.236052i	$-0.0758537\pi$
$599$	6.88817	+	11.9307i	0.281443	+	0.487473i	−0.690297	+	0.723526i	$0.742520\pi$
$600$	2.01861	−	3.49634i	0.0824094	−	0.142737i
$601$	−28.9935			−1.18267			−0.591335	−	0.806426i	$-0.701399\pi$
$601$	−28.9935			−1.18267			−0.591335	+	0.806426i	$0.701399\pi$
$602$	−12.3438	−	48.2958i	−0.503097	−	1.96839i
$603$	43.2565			1.76154
$604$	−7.34536	+	12.7225i	−0.298879	+	0.517673i
$605$	−0.500000	−	0.866025i	−0.0203279	−	0.0352089i
$606$	22.9652	+	39.7769i	0.932899	+	1.61583i
$607$	−20.7447	+	35.9308i	−0.842000	+	1.45839i	0.0462017	+	0.998932i	$0.485288\pi$
$607$	−20.7447	+	35.9308i	−0.842000	+	1.45839i	−0.888201	+	0.459454i	$0.848045\pi$
$608$	16.6391			0.674805
$609$	15.9389	+	4.46907i	0.645878	+	0.181096i
$610$	12.0508			0.487921
$611$	4.59203	−	7.95362i	0.185773	−	0.321769i
$612$	4.01103	+	6.94731i	0.162136	+	0.280828i
$613$	−17.1114	−	29.6379i	−0.691124	−	1.19706i	−0.971470	−	0.237163i	$-0.923782\pi$
$613$	−17.1114	−	29.6379i	−0.691124	−	1.19706i	0.280346	−	0.959899i	$-0.409551\pi$
$614$	1.57988	−	2.73644i	0.0637589	−	0.110434i
$615$	−3.85549			−0.155468
$616$	4.21287	+	1.18123i	0.169742	+	0.0475933i
$617$	30.4992			1.22785			0.613926	−	0.789363i	$-0.289589\pi$
$617$	30.4992			1.22785			0.613926	+	0.789363i	$0.289589\pi$
$618$	−9.88952	+	17.1291i	−0.397815	+	0.689035i
$619$	−19.2573	−	33.3547i	−0.774018	−	1.34064i	−0.935345	−	0.353737i	$-0.884911\pi$
$619$	−19.2573	−	33.3547i	−0.774018	−	1.34064i	0.161327	−	0.986901i	$-0.448422\pi$
$620$	−1.50063	−	2.59918i	−0.0602670	−	0.104385i
$621$	0.285765	−	0.494959i	0.0114673	−	0.0198620i
$622$	53.0891			2.12868
$623$	−9.29750	−	36.3768i	−0.372497	−	1.45741i
$624$	22.9664			0.919393
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	15.5378	+	26.9123i	0.621016	+	1.07563i
$627$	3.74396	+	6.48472i	0.149519	+	0.258975i
$628$	1.58199	−	2.74008i	0.0631281	−	0.109341i
$629$	12.8190			0.511128
$630$	9.78784	−	9.56397i	0.389957	−	0.381038i
$631$	2.18173			0.0868534			0.0434267	−	0.999057i	$-0.486172\pi$
$631$	2.18173			0.0868534			0.0434267	+	0.999057i	$0.486172\pi$
$632$	−7.60323	+	13.1692i	−0.302440	+	0.523842i
$633$	0.346387	+	0.599961i	0.0137677	+	0.0238463i
$634$	4.99513	+	8.65182i	0.198382	+	0.343608i
$635$	−5.25894	+	9.10875i	−0.208695	+	0.361470i
$636$	4.90011			0.194302
$637$	0.304858	−	13.1745i	0.0120789	−	0.521995i
$638$	4.47851			0.177306
$639$	−6.68306	+	11.5754i	−0.264378	+	0.457916i
$640$	5.87437	+	10.1747i	0.232205	+	0.402191i
$641$	20.5410	+	35.5781i	0.811321	+	1.40525i	0.911940	+	0.410324i	$0.134584\pi$
$641$	20.5410	+	35.5781i	0.811321	+	1.40525i	−0.100619	+	0.994925i	$0.532082\pi$
$642$	3.49195	−	6.04823i	0.137816	−	0.238705i
$643$	−36.7462			−1.44913			−0.724565	−	0.689206i	$-0.757959\pi$
$643$	−36.7462			−1.44913			−0.724565	+	0.689206i	$0.757959\pi$
$644$	11.6408	−	11.3746i	0.458713	−	0.448221i
$645$	26.3215			1.03641
$646$	−6.89342	+	11.9398i	−0.271218	+	0.469763i
$647$	19.1792	+	33.2193i	0.754012	+	1.30599i	0.945864	+	0.324563i	$0.105217\pi$
$647$	19.1792	+	33.2193i	0.754012	+	1.30599i	−0.191852	+	0.981424i	$0.561449\pi$
$648$	7.53990	+	13.0595i	0.296195	+	0.513025i
$649$	−4.18406	+	7.24700i	−0.164239	+	0.284470i
$650$	−3.28975			−0.129035
$651$	4.55595	+	17.8253i	0.178562	+	0.698630i
$652$	−23.4644			−0.918937
$653$	7.21254	−	12.4925i	0.282249	−	0.488869i	−0.689690	−	0.724105i	$-0.742253\pi$
$653$	7.21254	−	12.4925i	0.282249	−	0.488869i	0.971938	+	0.235236i	$0.0755863\pi$
$654$	35.5154	+	61.5144i	1.38876	+	2.40540i
$655$	−10.3426	−	17.9139i	−0.404119	−	0.699954i
$656$	3.94593	−	6.83456i	0.154063	−	0.266845i
$657$	0.298929			0.0116623
$658$	21.7173	+	6.08923i	0.846627	+	0.237383i
$659$	21.0717			0.820835			0.410418	−	0.911898i	$-0.365383\pi$
$659$	21.0717			0.820835			0.410418	+	0.911898i	$0.365383\pi$
$660$	1.28613	−	2.22764i	0.0500625	−	0.0867107i
$661$	11.0082	+	19.0668i	0.428170	+	0.741612i	0.996711	−	0.0810432i	$-0.0258252\pi$
$661$	11.0082	+	19.0668i	0.428170	+	0.741612i	−0.568541	+	0.822655i	$0.692492\pi$
$662$	−7.06879	−	12.2435i	−0.274736	−	0.475857i
$663$	−5.91096	+	10.2381i	−0.229562	+	0.397614i
$664$	12.6076			0.489269
$665$	7.81370	+	2.19086i	0.303002	+	0.0849578i
$666$	25.7767			0.998827
$667$	−7.48141	+	12.9582i	−0.289681	+	0.501743i
$668$	3.87417	+	6.71027i	0.149896	+	0.259628i
$669$	−33.5115	−	58.0437i	−1.29563	−	2.24410i
$670$	12.7689	−	22.1164i	0.493306	−	0.854430i
$671$	−6.89613			−0.266222
$672$	8.67676	+	33.9482i	0.334713	+	1.30958i
$673$	29.4552			1.13542			0.567708	−	0.823230i	$-0.307830\pi$
$673$	29.4552			1.13542			0.567708	+	0.823230i	$0.307830\pi$
$674$	9.90526	−	17.1564i	0.381536	−	0.660840i
$675$	−0.0489463	−	0.0847775i	−0.00188394	−	0.00326309i
$676$	4.98158	+	8.62835i	0.191599	+	0.331859i
$677$	12.7669	−	22.1129i	0.490671	−	0.849867i	−0.509271	−	0.860606i	$-0.670085\pi$
$677$	12.7669	−	22.1129i	0.490671	−	0.849867i	0.999942	+	0.0107391i	$0.00341843\pi$
$678$	−64.0490			−2.45979
$679$	−3.40288	+	3.32505i	−0.130591	+	0.127604i
$680$	−4.25380			−0.163126
$681$	3.41276	−	5.91107i	0.130777	−	0.226513i
$682$	2.48880	+	4.31073i	0.0953010	+	0.165066i
$683$	−8.51844	−	14.7544i	−0.325949	−	0.564560i	0.655755	−	0.754974i	$-0.272350\pi$
$683$	−8.51844	−	14.7544i	−0.325949	−	0.564560i	−0.981704	+	0.190414i	$0.939017\pi$
$684$	−4.78281	+	8.28407i	−0.182875	+	0.316749i
$685$	−21.6149			−0.825863
$686$	31.5326	−	7.28662i	1.20392	−	0.278204i
$687$	31.3699			1.19684
$688$	−26.9390	+	46.6597i	−1.02704	+	1.77889i
$689$	1.79315	+	3.10582i	0.0683134	+	0.118322i
$690$	12.4534	+	21.5699i	0.474093	+	0.821153i
$691$	21.7098	−	37.6025i	0.825881	−	1.43047i	−0.0753636	−	0.997156i	$-0.524012\pi$
$691$	21.7098	−	37.6025i	0.825881	−	1.43047i	0.901244	−	0.433311i	$-0.142655\pi$
$692$	−24.4560			−0.929677
$693$	−5.60115	+	5.47304i	−0.212770	+	0.207904i
$694$	0.710808			0.0269819
$695$	8.23989	−	14.2719i	0.312557	−	0.541364i
$696$	−5.17341	−	8.96061i	−0.196098	−	0.339651i
$697$	2.03116	+	3.51807i	0.0769356	+	0.133256i
$698$	4.26309	−	7.38389i	0.161360	−	0.279484i
$699$	45.0867			1.70534
$700$	−0.690310	−	2.70086i	−0.0260912	−	0.102083i
$701$	−19.0563			−0.719746			−0.359873	−	0.933001i	$-0.617180\pi$
$701$	−19.0563			−0.719746			−0.359873	+	0.933001i	$0.617180\pi$
$702$	0.161021	−	0.278897i	0.00607735	−	0.0105263i
$703$	7.64279	+	13.2377i	0.288253	+	0.499270i
$704$	−0.257231	−	0.445538i	−0.00969477	−	0.0167918i
$705$	−5.95484	+	10.3141i	−0.224272	+	0.388451i
$706$	−15.7226			−0.591727
$707$	−27.4276	−	7.69033i	−1.03152	−	0.289225i
$708$	−21.5249			−0.808957
$709$	−9.47641	+	16.4136i	−0.355894	+	0.616427i	−0.987271	−	0.159050i	$-0.949157\pi$
$709$	−9.47641	+	16.4136i	−0.355894	+	0.616427i	0.631377	+	0.775476i	$0.282490\pi$
$710$	3.94555	+	6.83389i	0.148074	+	0.256471i
$711$	−13.6086	−	23.5707i	−0.510361	−	0.883971i
$712$	−11.7341	+	20.3241i	−0.439754	+	0.761677i
$713$	−16.6303			−0.622809
$714$	−27.9549	−	7.83820i	−1.04619	−	0.293337i
$715$	1.88258			0.0704046
$716$	9.96537	−	17.2605i	0.372423	−	0.645056i
$717$	−25.7425	−	44.5873i	−0.961372	−	1.66514i
$718$	−4.10386	−	7.10810i	−0.153155	−	0.265272i
$719$	16.6173	−	28.7820i	0.619721	−	1.07339i	−0.369816	−	0.929105i	$-0.620579\pi$
$719$	16.6173	−	28.7820i	0.619721	−	1.07339i	0.989537	−	0.144283i	$-0.0460874\pi$
$720$	−14.7910			−0.551228
$721$	−3.03756	−	11.8846i	−0.113125	−	0.442605i
$722$	16.7623			0.623828
$723$	−11.4387	+	19.8123i	−0.425409	+	0.736829i
$724$	−11.5116	−	19.9387i	−0.427826	−	0.741016i
$725$	1.28143	+	2.21950i	0.0475911	+	0.0824301i
$726$	−2.13304	+	3.69453i	−0.0791645	+	0.137117i
$727$	9.83280			0.364678			0.182339	−	0.983236i	$-0.441633\pi$
$727$	9.83280			0.364678			0.182339	+	0.983236i	$0.441633\pi$
$728$	−5.89138	+	5.75663i	−0.218349	+	0.213355i
$729$	−26.2735			−0.973091
$730$	0.0882410	−	0.152838i	0.00326595	−	0.00565679i
$731$	−13.8668	−	24.0180i	−0.512882	−	0.888337i
$732$	−8.86931	−	15.3621i	−0.327819	−	0.567799i
$733$	8.35122	−	14.4647i	0.308459	−	0.534267i	−0.669566	−	0.742752i	$-0.733520\pi$
$733$	8.35122	−	14.4647i	0.308459	−	0.534267i	0.978026	+	0.208485i	$0.0668533\pi$
$734$	−8.02390			−0.296167
$735$	−0.395334	+	17.0845i	−0.0145821	+	0.630170i
$736$	−31.6722			−1.16745
$737$	−7.30708	+	12.6562i	−0.269160	+	0.466199i
$738$	4.08429	+	7.07419i	0.150345	+	0.260405i
$739$	13.8823	+	24.0449i	0.510670	+	0.884506i	0.999924	+	0.0123645i	$0.00393584\pi$
$739$	13.8823	+	24.0449i	0.510670	+	0.884506i	−0.489254	+	0.872141i	$0.662731\pi$
$740$	2.62546	−	4.54743i	0.0965139	−	0.167167i
$741$	−14.0966			−0.517852
$742$	−6.29943	+	6.15535i	−0.231259	+	0.225970i
$743$	16.1302			0.591759			0.295880	−	0.955225i	$-0.404387\pi$
$743$	16.1302			0.591759			0.295880	+	0.955225i	$0.404387\pi$
$744$	5.74993	−	9.95918i	0.210803	−	0.365121i
$745$	−4.47226	−	7.74618i	−0.163851	−	0.283798i
$746$	−11.4175	−	19.7757i	−0.418026	−	0.724042i
$747$	−11.2828	+	19.5423i	−0.412815	+	0.715017i
$748$	−2.71025			−0.0990965
$749$	1.07255	+	4.19640i	0.0391902	+	0.153333i
$750$	4.26608			0.155775
$751$	15.0946	−	26.1446i	0.550809	−	0.954029i	−0.447408	−	0.894330i	$-0.647653\pi$
$751$	15.0946	−	26.1446i	0.550809	−	0.954029i	0.998216	−	0.0596987i	$-0.0190140\pi$
$752$	−12.1891	−	21.1121i	−0.444489	−	0.769878i
$753$	−17.5864	−	30.4606i	−0.640885	−	1.11005i
$754$	−4.21558	+	7.30160i	−0.153522	+	0.265909i
$755$	13.9427			0.507429
$756$	0.262760	+	0.0736745i	0.00955650	+	0.00267952i
$757$	13.3060			0.483615			0.241807	−	0.970324i	$-0.422260\pi$
$757$	13.3060			0.483615			0.241807	+	0.970324i	$0.422260\pi$
$758$	−9.09546	+	15.7538i	−0.330362	+	0.572203i
$759$	−7.12654	−	12.3435i	−0.258677	−	0.448042i
$760$	−2.53615	−	4.39273i	−0.0919957	−	0.159341i
$761$	−4.08844	+	7.08139i	−0.148206	+	0.256700i	−0.930564	−	0.366128i	$-0.880683\pi$
$761$	−4.08844	+	7.08139i	−0.148206	+	0.256700i	0.782358	+	0.622828i	$0.214017\pi$
$762$	44.8701			1.62547
$763$	−42.4163	−	11.8930i	−1.53557	−	0.430554i
$764$	3.31641			0.119984
$765$	3.80681	−	6.59359i	0.137636	−	0.238392i
$766$	−20.0479	−	34.7240i	−0.724361	−	1.25463i
$767$	−7.87683	−	13.6431i	−0.284416	−	0.492623i
$768$	23.8046	−	41.2307i	0.858973	−	1.48779i
$769$	−54.6122			−1.96936			−0.984682	−	0.174358i	$-0.944215\pi$
$769$	−54.6122			−1.96936			−0.984682	+	0.174358i	$0.944215\pi$
$770$	1.14488	+	4.47937i	0.0412585	+	0.161425i
$771$	−39.8112			−1.43377
$772$	−11.1892	+	19.3803i	−0.402708	+	0.697511i
$773$	19.8490	+	34.3794i	0.713918	+	1.23654i	0.963375	+	0.268157i	$0.0864144\pi$
$773$	19.8490	+	34.3794i	0.713918	+	1.23654i	−0.249457	+	0.968386i	$0.580252\pi$
$774$	−27.8836	−	48.2958i	−1.00225	−	1.73595i
$775$	−1.42423	+	2.46684i	−0.0511599	+	0.0886115i
$776$	2.97379			0.106753
$777$	−23.0229	+	22.4964i	−0.825943	+	0.807052i
$778$	−20.3869			−0.730906
$779$	−2.42198	+	4.19500i	−0.0867765	+	0.150301i
$780$	2.42124	+	4.19371i	0.0866944	+	0.150159i
$781$	−2.25787	−	3.91074i	−0.0807928	−	0.139937i
$782$	13.1215	−	22.7271i	0.469223	−	0.812718i
$783$	−0.250885			−0.00896589
$784$	−29.8807	−	18.1860i	−1.06717	−	0.649502i
$785$	−3.00288			−0.107177
$786$	−44.1223	+	76.4221i	−1.57379	+	2.72589i
$787$	−11.4636	−	19.8555i	−0.408633	−	0.707773i	0.586104	−	0.810236i	$-0.300661\pi$
$787$	−11.4636	−	19.8555i	−0.408633	−	0.707773i	−0.994737	+	0.102463i	$0.967328\pi$
$788$	−4.42111	−	7.65758i	−0.157495	−	0.272790i
$789$	−32.1264	+	55.6446i	−1.14373	+	1.98100i
$790$	−16.0685			−0.571690
$791$	28.4108	−	27.7610i	1.01017	−	0.987067i
$792$	4.89486			0.173931
$793$	6.49126	−	11.2432i	0.230512	−	0.399258i
$794$	−2.11003	−	3.65469i	−0.0748823	−	0.129700i
$795$	−2.32531	−	4.02756i	−0.0824703	−	0.142843i
$796$	−12.3621	+	21.4117i	−0.438161	+	0.758918i
$797$	26.4654			0.937451			0.468725	−	0.883344i	$-0.344713\pi$
$797$	26.4654			0.937451			0.468725	+	0.883344i	$0.344713\pi$
$798$	−8.57273	−	33.5411i	−0.303471	−	1.18734i
$799$	12.5486			0.443937
$800$	−2.71243	+	4.69807i	−0.0958990	+	0.166102i
$801$	−21.0022	−	36.3768i	−0.742075	−	1.28531i
$802$	−29.5755	−	51.2263i	−1.04435	−	1.80886i
$803$	−0.0504965	+	0.0874625i	−0.00178198	+	0.00308648i
$804$	−37.5914			−1.32575
$805$	−14.8732	−	4.17025i	−0.524211	−	0.146982i
$806$	−9.37073			−0.330070
$807$	0.573967	−	0.994140i	0.0202046	−	0.0349954i
$808$	8.90235	+	15.4193i	0.313184	+	0.542450i
$809$	12.3312	+	21.3583i	0.433542	+	0.750916i	0.997175	−	0.0751085i	$-0.0239303\pi$
$809$	12.3312	+	21.3583i	0.433542	+	0.750916i	−0.563634	+	0.826025i	$0.690597\pi$
$810$	−7.96731	+	13.7998i	−0.279943	+	0.484875i
$811$	−36.8401			−1.29363			−0.646815	−	0.762647i	$-0.723900\pi$
$811$	−36.8401			−1.29363			−0.646815	+	0.762647i	$0.723900\pi$
$812$	−6.87915	−	1.92882i	−0.241411	−	0.0676884i
$813$	−43.9146			−1.54015
$814$	−4.35432	+	7.54190i	−0.152619	+	0.264344i
$815$	11.1349	+	19.2861i	0.390037	+	0.675564i
$816$	15.6900	+	27.1759i	0.549261	+	0.951348i
$817$	16.5349	−	28.6394i	0.578485	−	1.00196i
$818$	16.0253			0.560310
$819$	−3.65073	−	14.2836i	−0.127567	−	0.499111i
$820$	1.66400			0.0581096
$821$	4.19328	−	7.26297i	0.146346	−	0.253479i	−0.783528	−	0.621356i	$-0.786582\pi$
$821$	4.19328	−	7.26297i	0.146346	−	0.253479i	0.929874	+	0.367877i	$0.119915\pi$
$822$	46.1054	+	79.8569i	1.60811	+	2.78533i
$823$	25.4346	+	44.0540i	0.886594	+	1.53563i	0.843876	+	0.536539i	$0.180269\pi$
$823$	25.4346	+	44.0540i	0.886594	+	1.53563i	0.0427186	+	0.999087i	$0.486398\pi$
$824$	−3.83362	+	6.64003i	−0.133550	+	0.231316i
$825$	−2.44129			−0.0849948
$826$	27.6718	−	27.0389i	0.962825	−	0.940803i
$827$	38.3029			1.33192			0.665961	−	0.745987i	$-0.268022\pi$
$827$	38.3029			1.33192			0.665961	+	0.745987i	$0.268022\pi$
$828$	9.10397	−	15.7685i	0.316385	−	0.547995i
$829$	1.98520	+	3.43847i	0.0689489	+	0.119423i	0.898439	−	0.439099i	$-0.144702\pi$
$829$	1.98520	+	3.43847i	0.0689489	+	0.119423i	−0.829490	+	0.558522i	$0.811369\pi$
$830$	6.66113	+	11.5374i	0.231211	+	0.400470i
$831$	30.4802	−	52.7933i	1.05735	−	1.83138i
$832$	0.968518			0.0335773
$833$	15.7976	−	8.63975i	0.547353	−	0.299350i
$834$	−70.3040			−2.43443
$835$	3.67692	−	6.36862i	0.127245	−	0.220395i
$836$	−1.61587	−	2.79877i	−0.0558860	−	0.0967973i
$837$	−0.139422	−	0.241485i	−0.00481912	−	0.00834695i
$838$	−8.72255	+	15.1079i	−0.301316	+	0.521894i
$839$	−34.3262			−1.18507			−0.592537	−	0.805543i	$-0.701874\pi$
$839$	−34.3262			−1.18507			−0.592537	+	0.805543i	$0.701874\pi$
$840$	7.63981	−	7.46507i	0.263599	−	0.257569i
$841$	−22.4318			−0.773509
$842$	−14.4289	+	24.9916i	−0.497253	+	0.861267i
$843$	−27.3763	−	47.4172i	−0.942891	−	1.63313i
$844$	−0.149499	−	0.258939i	−0.00514596	−	0.00891306i
$845$	4.72794	−	8.18904i	0.162646	−	0.281711i
$846$	25.2329			0.867525
$847$	−0.655163	−	2.56335i	−0.0225117	−	0.0880777i
$848$	9.51944			0.326899
$849$	−25.9343	+	44.9195i	−0.890062	+	1.54163i
$850$	−2.24747	−	3.89273i	−0.0770875	−	0.133520i
$851$	−14.5479	−	25.1977i	−0.498695	−	0.863766i
$852$	5.80781	−	10.0594i	0.198972	−	0.344630i
$853$	11.6335			0.398322			0.199161	−	0.979967i	$-0.436178\pi$
$853$	11.6335			0.398322			0.199161	+	0.979967i	$0.436178\pi$
$854$	30.6994	+	8.60771i	1.05051	+	0.294550i
$855$	9.07859			0.310481
$856$	1.35364	−	2.34457i	0.0462663	−	0.0801356i
$857$	24.1495	+	41.8282i	0.824932	+	1.42882i	0.901971	+	0.431796i	$0.142120\pi$
$857$	24.1495	+	41.8282i	0.824932	+	1.42882i	−0.0770396	+	0.997028i	$0.524547\pi$
$858$	−4.01562	−	6.95526i	−0.137091	−	0.237449i
$859$	−2.13320	+	3.69481i	−0.0727838	+	0.126065i	−0.900120	−	0.435641i	$-0.856522\pi$
$859$	−2.13320	+	3.69481i	−0.0727838	+	0.126065i	0.827337	+	0.561707i	$0.189855\pi$
$860$	−11.3602			−0.387380
$861$	−9.82188	−	2.75393i	−0.334729	−	0.0938535i
$862$	28.7553			0.979408
$863$	12.6118	−	21.8443i	0.429310	−	0.743588i	−0.567502	−	0.823372i	$-0.692090\pi$
$863$	12.6118	−	21.8443i	0.429310	−	0.743588i	0.996812	+	0.0797847i	$0.0254233\pi$
$864$	−0.265527	−	0.459906i	−0.00903341	−	0.0156463i
$865$	11.6054	+	20.1012i	0.394596	+	0.683460i
$866$	−15.7129	+	27.2155i	−0.533945	+	0.924820i
$867$	25.3491			0.860902
$868$	−1.96632	−	7.69330i	−0.0667413	−	0.261128i
$869$	9.19528			0.311929
$870$	5.46667	−	9.46856i	0.185338	−	0.321014i
$871$	−13.7562	−	23.8264i	−0.466111	−	0.807327i
$872$	13.7673	+	23.8457i	0.466221	+	0.807519i
$873$	−2.66130	+	4.60951i	−0.0900714	+	0.156008i
$874$	31.2924			1.05848
$875$	−1.89234	+	1.84906i	−0.0639729	+	0.0625097i
$876$	−0.259780			−0.00877715
$877$	−0.564155	+	0.977145i	−0.0190502	+	0.0329958i	−0.875393	−	0.483411i	$-0.839398\pi$
$877$	−0.564155	+	0.977145i	−0.0190502	+	0.0329958i	0.856343	+	0.516407i	$0.172731\pi$
$878$	20.1593	+	34.9170i	0.680344	+	1.17839i
$879$	−19.9018	−	34.4710i	−0.671272	−	1.16268i
$880$	2.49856	−	4.32763i	0.0842265	−	0.145885i
$881$	28.1086			0.947003			0.473501	−	0.880793i	$-0.342990\pi$
$881$	28.1086			0.947003			0.473501	+	0.880793i	$0.342990\pi$
$882$	31.7660	−	17.3730i	1.06962	−	0.584978i
$883$	17.9702			0.604745			0.302372	−	0.953190i	$-0.402221\pi$
$883$	17.9702			0.604745			0.302372	+	0.953190i	$0.402221\pi$
$884$	2.55113	−	4.41869i	0.0858038	−	0.148617i
$885$	10.2145	+	17.6920i	0.343357	+	0.594712i
$886$	8.41430	+	14.5740i	0.282684	+	0.489623i
$887$	2.97199	−	5.14764i	0.0997897	−	0.172841i	−0.811808	−	0.583925i	$-0.801516\pi$
$887$	2.97199	−	5.14764i	0.0997897	−	0.172841i	0.911598	+	0.411084i	$0.134850\pi$
$888$	20.1198			0.675176
$889$	−19.9035	+	19.4482i	−0.667541	+	0.652272i
$890$	−24.7986			−0.831250
$891$	4.55934	−	7.89702i	0.152744	−	0.264560i
$892$	14.4634	+	25.0513i	0.484270	+	0.838780i
$893$	7.48155	+	12.9584i	0.250361	+	0.433637i
$894$	−19.0790	+	33.0458i	−0.638098	+	1.10522i
$895$	−18.9160			−0.632291
$896$	7.69734	+	30.1161i	0.257150	+	1.00611i
$897$	26.8326			0.895914
$898$	−4.76356	+	8.25074i	−0.158962	+	0.275331i
$899$	3.65010	+	6.32216i	0.121738	+	0.210856i
$900$	−1.55934	−	2.70086i	−0.0519781	−	0.0900288i
$901$	−2.45006	+	4.24362i	−0.0816232	+	0.141375i
$902$	−2.75975			−0.0918895
$903$	67.0543	+	18.8011i	2.23143	+	0.625663i
$904$	−24.8283			−0.825776
$905$	−10.9255	+	18.9235i	−0.363176	+	0.629039i
$906$	−29.7404	−	51.5119i	−0.988060	−	1.71137i
$907$	4.48691	+	7.77156i	0.148985	+	0.258050i	0.930853	−	0.365394i	$-0.119066\pi$
$907$	4.48691	+	7.77156i	0.148985	+	0.258050i	−0.781867	+	0.623445i	$0.785733\pi$
$908$	−1.47292	+	2.55118i	−0.0488807	+	0.0846639i
$909$	−31.8676			−1.05698
$910$	−8.38067	−	2.34983i	−0.277816	−	0.0778961i
$911$	48.2124			1.59735			0.798673	−	0.601765i	$-0.205536\pi$
$911$	48.2124			1.59735			0.798673	+	0.601765i	$0.205536\pi$
$912$	−18.7090	+	32.4049i	−0.619517	+	1.07303i
$913$	−3.81188	−	6.60236i	−0.126155	−	0.218506i
$914$	23.0537	+	39.9302i	0.762549	+	1.32077i
$915$	−8.41773	+	14.5799i	−0.278282	+	0.481998i
$916$	−13.5391			−0.447343
$917$	−13.5522	−	53.0234i	−0.447532	−	1.75099i
$918$	0.440021			0.0145229
$919$	6.01747	−	10.4226i	0.198498	−	0.343809i	−0.749544	−	0.661955i	$-0.769727\pi$
$919$	6.01747	−	10.4226i	0.198498	−	0.343809i	0.948042	+	0.318146i	$0.103060\pi$
$920$	4.82750	+	8.36147i	0.159158	+	0.275669i
$921$	2.20717	+	3.82292i	0.0727286	+	0.125970i
$922$	12.8164	−	22.1987i	0.422086	−	0.731074i
$923$	8.50124			0.279822
$924$	4.86760	−	4.75626i	0.160132	−	0.156470i
$925$	−4.98357			−0.163859
$926$	26.0127	−	45.0554i	0.854832	−	1.48061i
$927$	−6.86157	−	11.8846i	−0.225363	−	0.390341i
$928$	6.95158	+	12.0405i	0.228197	+	0.395248i
$929$	21.2817	−	36.8609i	0.698229	−	1.20937i	−0.270851	−	0.962621i	$-0.587305\pi$
$929$	21.2817	−	36.8609i	0.698229	−	1.20937i	0.969080	−	0.246747i	$-0.0793616\pi$
$930$	12.1518			0.398472
$931$	18.3406	+	11.1624i	0.601087	+	0.365835i
$932$	−19.4591			−0.637405
$933$	−37.0839	+	64.2313i	−1.21407	+	2.10284i
$934$	6.12499	+	10.6088i	0.200416	+	0.347130i
$935$	1.28613	+	2.22764i	0.0420609	+	0.0728516i
$936$	−4.60749	+	7.98040i	−0.150600	+	0.260848i
$937$	−17.7793			−0.580824			−0.290412	−	0.956902i	$-0.593792\pi$
$937$	−17.7793			−0.580824			−0.290412	+	0.956902i	$0.593792\pi$
$938$	48.3263	−	47.2210i	1.57791	−	1.54182i
$939$	−43.4141			−1.41676
$940$	2.57007	−	4.45149i	0.0838265	−	0.145192i
$941$	−11.5993	−	20.0905i	−0.378125	−	0.654932i	0.612664	−	0.790343i	$-0.290098\pi$
$941$	−11.5993	−	20.0905i	−0.378125	−	0.654932i	−0.990789	+	0.135411i	$0.956764\pi$
$942$	6.40526	+	11.0942i	0.208695	+	0.361470i
$943$	4.61019	−	7.98508i	0.150128	−	0.260030i
$944$	−41.8165			−1.36101
$945$	−0.0641356	−	0.250933i	−0.00208633	−	0.00816285i
$946$	18.8409			0.612570
$947$	26.5153	−	45.9259i	0.861632	−	1.49239i	−0.00872124	−	0.999962i	$-0.502776\pi$
$947$	26.5153	−	45.9259i	0.861632	−	1.49239i	0.870353	−	0.492428i	$-0.163891\pi$
$948$	11.8263	+	20.4838i	0.384101	+	0.665282i
$949$	−0.0950638	−	0.164655i	−0.00308590	−	0.00534494i
$950$	2.67991	−	4.64174i	0.0869478	−	0.150598i
$951$	−13.9568			−0.452582
$952$	−10.8366	−	3.03844i	−0.351216	−	0.0984763i
$953$	−41.6025			−1.34764			−0.673818	−	0.738898i	$-0.735347\pi$
$953$	−41.6025			−1.34764			−0.673818	+	0.738898i	$0.735347\pi$
$954$	−4.92661	+	8.53314i	−0.159505	+	0.276271i
$955$	−1.57378	−	2.72586i	−0.0509263	−	0.0882069i
$956$	11.1103	+	19.2436i	0.359333	+	0.622383i
$957$	−3.12834	+	5.41844i	−0.101125	+	0.175153i
$958$	−24.3828			−0.787772
$959$	−55.0641	−	15.4392i	−1.77811	−	0.498559i
$960$	−1.25595			−0.0405357
$961$	11.4431	−	19.8201i	0.369133	−	0.639358i
$962$	−8.19736	−	14.1982i	−0.264294	−	0.457770i
$963$	2.42279	+	4.19640i	0.0780734	+	0.135227i
$964$	4.93686	−	8.55089i	0.159005	−	0.275406i
$965$	21.2390			0.683708
$966$	16.3180	+	63.8448i	0.525023	+	2.05417i
$967$	23.1656			0.744955			0.372478	−	0.928041i	$-0.378508\pi$
$967$	23.1656			0.744955			0.372478	+	0.928041i	$0.378508\pi$
$968$	−0.826862	+	1.43217i	−0.0265763	+	0.0460316i
$969$	−9.63041	−	16.6804i	−0.309373	−	0.535851i
$970$	1.57118	+	2.72137i	0.0504476	+	0.0873778i
$971$	−14.6257	+	25.3325i	−0.469362	+	0.812959i	−0.999386	−	0.0350234i	$-0.988849\pi$
$971$	−14.6257	+	25.3325i	−0.469362	+	0.812959i	0.530024	+	0.847982i	$0.322183\pi$
$972$	23.1462			0.742414
$973$	31.1854	−	30.4721i	0.999759	−	0.976892i
$974$	−11.7453			−0.376344
$975$	2.29796	−	3.98019i	0.0735938	−	0.127468i
$976$	−17.2304	−	29.8439i	−0.551532	−	0.955281i
$977$	3.54292	+	6.13652i	0.113348	+	0.196325i	0.917118	−	0.398615i	$-0.130509\pi$
$977$	3.54292	+	6.13652i	0.113348	+	0.196325i	−0.803770	+	0.594940i	$0.797176\pi$
$978$	47.5022	−	82.2762i	1.51895	−	2.63090i
$979$	14.1911			0.453551
$980$	0.170624	−	7.37355i	0.00545037	−	0.235539i
$981$	−49.2827			−1.57348
$982$	−22.6709	+	39.2671i	−0.723457	+	1.25306i
$983$	−9.92549	−	17.1914i	−0.316574	−	0.548322i	0.663197	−	0.748445i	$-0.269199\pi$
$983$	−9.92549	−	17.1914i	−0.316574	−	0.548322i	−0.979771	+	0.200123i	$0.935866\pi$
$984$	3.18796	+	5.52170i	0.101628	+	0.176025i
$985$	−4.19601	+	7.26770i	−0.133696	+	0.231568i
$986$	−11.5199			−0.366868
$987$	−22.5372	+	22.0217i	−0.717367	+	0.700960i
$988$	6.08401			0.193558
$989$	−31.4739	+	54.5144i	−1.00081	+	1.73346i
$990$	2.58617	+	4.47937i	0.0821938	+	0.142364i
$991$	8.03974	+	13.9252i	0.255391	+	0.442350i	0.965002	−	0.262244i	$-0.0844625\pi$
$991$	8.03974	+	13.9252i	0.255391	+	0.442350i	−0.709611	+	0.704594i	$0.751129\pi$
$992$	−7.72626	+	13.3823i	−0.245309	+	0.424888i
$993$	19.7508			0.626774
$994$	5.16995	+	20.2276i	0.163981	+	0.641582i
$995$	23.4653			0.743900
$996$	9.80512	−	16.9830i	0.310687	−	0.538126i
$997$	−11.4092	−	19.7613i	−0.361332	−	0.625846i	0.626848	−	0.779142i	$-0.284345\pi$
$997$	−11.4092	−	19.7613i	−0.361332	−	0.625846i	−0.988180	+	0.153296i	$0.951011\pi$
$998$	18.1780	+	31.4853i	0.575415	+	0.996649i
$999$	0.243927	−	0.422495i	0.00771752	−	0.0133671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.i.a.331.3	yes	8
7.2	even	3		2695.2.a.j.1.2		4
7.4	even	3	inner	385.2.i.a.221.3	✓	8
7.5	odd	6		2695.2.a.k.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.a.221.3	✓	8	7.4	even	3	inner
385.2.i.a.331.3	yes	8	1.1	even	1	trivial
2695.2.a.j.1.2		4	7.2	even	3
2695.2.a.k.1.2		4	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.873734 - 1.51335i) q^{2} +(1.22065 + 2.11422i) q^{3} +(-0.526823 - 0.912484i) q^{4} +(-0.500000 + 0.866025i) q^{5} +4.26608 q^{6} +(-1.89234 + 1.84906i) q^{7} +1.65372 q^{8} +(-1.47995 + 2.56335i) q^{9} +O(q^{10})\)	\(q+(0.873734 - 1.51335i) q^{2} +(1.22065 + 2.11422i) q^{3} +(-0.526823 - 0.912484i) q^{4} +(-0.500000 + 0.866025i) q^{5} +4.26608 q^{6} +(-1.89234 + 1.84906i) q^{7} +1.65372 q^{8} +(-1.47995 + 2.56335i) q^{9} +(0.873734 + 1.51335i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.28613 - 2.22764i) q^{12} +1.88258 q^{13} +(1.14488 + 4.47937i) q^{14} -2.44129 q^{15} +(2.49856 - 4.32763i) q^{16} +(1.28613 + 2.22764i) q^{17} +(2.58617 + 4.47937i) q^{18} +(-1.53360 + 2.65627i) q^{19} +1.05365 q^{20} +(-6.21921 - 1.74378i) q^{21} -1.74747 q^{22} +(2.91917 - 5.05615i) q^{23} +(2.01861 + 3.49634i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.64488 - 2.84901i) q^{26} +0.0978926 q^{27} +(2.68417 + 0.752606i) q^{28} -2.56286 q^{29} +(-2.13304 + 3.69453i) q^{30} +(-1.42423 - 2.46684i) q^{31} +(-2.71243 - 4.69807i) q^{32} +(1.22065 - 2.11422i) q^{33} +4.49494 q^{34} +(-0.655163 - 2.56335i) q^{35} +3.11869 q^{36} +(2.49179 - 4.31590i) q^{37} +(2.67991 + 4.64174i) q^{38} +(2.29796 + 3.98019i) q^{39} +(-0.826862 + 1.43217i) q^{40} +1.57928 q^{41} +(-8.07289 + 7.88825i) q^{42} -10.7818 q^{43} +(-0.526823 + 0.912484i) q^{44} +(-1.47995 - 2.56335i) q^{45} +(-5.10115 - 8.83546i) q^{46} +(2.43922 - 4.22485i) q^{47} +12.1994 q^{48} +(0.161936 - 6.99813i) q^{49} -1.74747 q^{50} +(-3.13981 + 5.43832i) q^{51} +(-0.991787 - 1.71783i) q^{52} +(0.952493 + 1.64977i) q^{53} +(0.0855321 - 0.148146i) q^{54} +1.00000 q^{55} +(-3.12942 + 3.05784i) q^{56} -7.48791 q^{57} +(-2.23926 + 3.87850i) q^{58} +(-4.18406 - 7.24700i) q^{59} +(1.28613 + 2.22764i) q^{60} +(3.44806 - 5.97222i) q^{61} -4.97760 q^{62} +(-1.93922 - 7.58726i) q^{63} +0.514463 q^{64} +(-0.941291 + 1.63036i) q^{65} +(-2.13304 - 3.69453i) q^{66} +(-7.30708 - 12.6562i) q^{67} +(1.35512 - 2.34714i) q^{68} +14.2531 q^{69} +(-4.45169 - 1.24819i) q^{70} +4.51573 q^{71} +(-2.44743 + 4.23907i) q^{72} +(-0.0504965 - 0.0874625i) q^{73} +(-4.35432 - 7.54190i) q^{74} +(1.22065 - 2.11422i) q^{75} +3.23174 q^{76} +(2.54751 + 0.714287i) q^{77} +8.03124 q^{78} +(-4.59764 + 7.96335i) q^{79} +(2.49856 + 4.32763i) q^{80} +(4.55934 + 7.89702i) q^{81} +(1.37987 - 2.39001i) q^{82} +7.62375 q^{83} +(1.68525 + 6.59359i) q^{84} -2.57226 q^{85} +(-9.42044 + 16.3167i) q^{86} +(-3.12834 - 5.41844i) q^{87} +(-0.826862 - 1.43217i) q^{88} +(-7.09557 + 12.2899i) q^{89} -5.17233 q^{90} +(-3.56249 + 3.48101i) q^{91} -6.15154 q^{92} +(3.47696 - 6.02227i) q^{93} +(-4.26245 - 7.38279i) q^{94} +(-1.53360 - 2.65627i) q^{95} +(6.62184 - 11.4694i) q^{96} +1.79824 q^{97} +(-10.4491 - 6.35957i) q^{98} +2.95990 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 4 q^{5} + 14 q^{6} + q^{7} - 18 q^{8} + q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 4 * q^5 + 14 * q^6 + q^7 - 18 * q^8 + q^9	\( 8 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 4 q^{5} + 14 q^{6} + q^{7} - 18 q^{8} + q^{9} + 3 q^{10} - 4 q^{11} + 3 q^{12} - 12 q^{13} + q^{14} - 6 q^{15} - 5 q^{16} + 3 q^{17} - q^{18} + 3 q^{19} + 6 q^{20} - 18 q^{21} - 6 q^{22} + 6 q^{23} + 4 q^{24} - 4 q^{25} + 5 q^{26} + 6 q^{27} - 20 q^{28} - 16 q^{29} - 7 q^{30} - 10 q^{31} - 4 q^{32} + 3 q^{33} + 20 q^{34} + q^{35} - 16 q^{36} + 9 q^{37} + 23 q^{38} + 13 q^{39} + 9 q^{40} + 30 q^{41} - 16 q^{42} - 4 q^{43} - 3 q^{44} + q^{45} - 16 q^{46} + 15 q^{47} - 2 q^{48} - 19 q^{49} - 6 q^{50} - q^{51} + 3 q^{52} + 30 q^{53} + 13 q^{54} + 8 q^{55} - 24 q^{56} - 12 q^{57} + q^{58} - 17 q^{59} + 3 q^{60} + 32 q^{62} - 11 q^{63} + 10 q^{64} + 6 q^{65} - 7 q^{66} + 25 q^{67} + 19 q^{68} + 12 q^{69} + q^{70} - 26 q^{71} - 26 q^{72} - 3 q^{73} + 16 q^{74} + 3 q^{75} + 80 q^{76} - 2 q^{77} - 10 q^{78} + 4 q^{79} - 5 q^{80} + 16 q^{81} + 27 q^{82} + 36 q^{83} - 24 q^{84} - 6 q^{85} + 10 q^{86} - 20 q^{87} + 9 q^{88} - 25 q^{89} + 2 q^{90} - 3 q^{91} - 52 q^{92} - 10 q^{93} - 23 q^{94} + 3 q^{95} + 7 q^{96} - 46 q^{97} - 60 q^{98} - 2 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 4 * q^5 + 14 * q^6 + q^7 - 18 * q^8 + q^9 + 3 * q^10 - 4 * q^11 + 3 * q^12 - 12 * q^13 + q^14 - 6 * q^15 - 5 * q^16 + 3 * q^17 - q^18 + 3 * q^19 + 6 * q^20 - 18 * q^21 - 6 * q^22 + 6 * q^23 + 4 * q^24 - 4 * q^25 + 5 * q^26 + 6 * q^27 - 20 * q^28 - 16 * q^29 - 7 * q^30 - 10 * q^31 - 4 * q^32 + 3 * q^33 + 20 * q^34 + q^35 - 16 * q^36 + 9 * q^37 + 23 * q^38 + 13 * q^39 + 9 * q^40 + 30 * q^41 - 16 * q^42 - 4 * q^43 - 3 * q^44 + q^45 - 16 * q^46 + 15 * q^47 - 2 * q^48 - 19 * q^49 - 6 * q^50 - q^51 + 3 * q^52 + 30 * q^53 + 13 * q^54 + 8 * q^55 - 24 * q^56 - 12 * q^57 + q^58 - 17 * q^59 + 3 * q^60 + 32 * q^62 - 11 * q^63 + 10 * q^64 + 6 * q^65 - 7 * q^66 + 25 * q^67 + 19 * q^68 + 12 * q^69 + q^70 - 26 * q^71 - 26 * q^72 - 3 * q^73 + 16 * q^74 + 3 * q^75 + 80 * q^76 - 2 * q^77 - 10 * q^78 + 4 * q^79 - 5 * q^80 + 16 * q^81 + 27 * q^82 + 36 * q^83 - 24 * q^84 - 6 * q^85 + 10 * q^86 - 20 * q^87 + 9 * q^88 - 25 * q^89 + 2 * q^90 - 3 * q^91 - 52 * q^92 - 10 * q^93 - 23 * q^94 + 3 * q^95 + 7 * q^96 - 46 * q^97 - 60 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more