LMFDB - Embedded newform 315.2.l.b.121.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.9
Character	$\chi$	$=$	315.121
Dual form			315.2.l.b.151.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.19807 q^{2} +(-0.773328 + 1.54983i) q^{3} -0.564635 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.926499 + 1.85680i) q^{6} +(0.433740 + 2.60996i) q^{7} -3.07261 q^{8} +(-1.80393 - 2.39705i) q^{9} +O(q^{10})$	\(q+1.19807 q^{2} +(-0.773328 + 1.54983i) q^{3} -0.564635 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.926499 + 1.85680i) q^{6} +(0.433740 + 2.60996i) q^{7} -3.07261 q^{8} +(-1.80393 - 2.39705i) q^{9} +(0.599034 + 1.03756i) q^{10} +(-0.0568723 + 0.0985057i) q^{11} +(0.436648 - 0.875086i) q^{12} +(-1.79716 + 3.11277i) q^{13} +(0.519650 + 3.12690i) q^{14} +(-1.72885 + 0.105192i) q^{15} -2.55192 q^{16} +(1.61936 + 2.80482i) q^{17} +(-2.16123 - 2.87183i) q^{18} +(0.951626 - 1.64826i) q^{19} +(-0.282317 - 0.488988i) q^{20} +(-4.38040 - 1.34613i) q^{21} +(-0.0681368 + 0.118016i) q^{22} +(0.300208 + 0.519975i) q^{23} +(2.37613 - 4.76201i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.15312 + 3.72931i) q^{26} +(5.11004 - 0.942072i) q^{27} +(-0.244905 - 1.47367i) q^{28} +(1.57537 + 2.72863i) q^{29} +(-2.07128 + 0.126027i) q^{30} +5.81891 q^{31} +3.08784 q^{32} +(-0.108686 - 0.164319i) q^{33} +(1.94011 + 3.36036i) q^{34} +(-2.04342 + 1.68061i) q^{35} +(1.01856 + 1.35346i) q^{36} +(-1.60007 + 2.77141i) q^{37} +(1.14011 - 1.97473i) q^{38} +(-3.43446 - 5.19248i) q^{39} +(-1.53630 - 2.66095i) q^{40} +(4.74928 - 8.22599i) q^{41} +(-5.24802 - 1.61275i) q^{42} +(0.780850 + 1.35247i) q^{43} +(0.0321120 - 0.0556197i) q^{44} +(1.17394 - 2.76077i) q^{45} +(0.359669 + 0.622965i) q^{46} +8.66129 q^{47} +(1.97347 - 3.95503i) q^{48} +(-6.62374 + 2.26409i) q^{49} +(-0.599034 + 1.03756i) q^{50} +(-5.59928 + 0.340688i) q^{51} +(1.01474 - 1.75758i) q^{52} +(-5.54540 - 9.60491i) q^{53} +(6.12217 - 1.12867i) q^{54} -0.113745 q^{55} +(-1.33271 - 8.01936i) q^{56} +(1.81861 + 2.74950i) q^{57} +(1.88740 + 3.26908i) q^{58} +14.3279 q^{59} +(0.976171 - 0.0593950i) q^{60} -13.5921 q^{61} +6.97145 q^{62} +(5.47376 - 5.74787i) q^{63} +8.80328 q^{64} -3.59432 q^{65} +(-0.130213 - 0.196866i) q^{66} +4.63189 q^{67} +(-0.914348 - 1.58370i) q^{68} +(-1.03803 + 0.0631589i) q^{69} +(-2.44815 + 2.01348i) q^{70} +6.64762 q^{71} +(5.54276 + 7.36518i) q^{72} +(6.73961 + 11.6733i) q^{73} +(-1.91699 + 3.32033i) q^{74} +(-0.955526 - 1.44464i) q^{75} +(-0.537321 + 0.930667i) q^{76} +(-0.281763 - 0.105708i) q^{77} +(-4.11472 - 6.22094i) q^{78} -17.4616 q^{79} +(-1.27596 - 2.21003i) q^{80} +(-2.49169 + 8.64821i) q^{81} +(5.68996 - 9.85530i) q^{82} +(0.0205902 + 0.0356633i) q^{83} +(2.47333 + 0.760071i) q^{84} +(-1.61936 + 2.80482i) q^{85} +(0.935511 + 1.62035i) q^{86} +(-5.44718 + 0.331433i) q^{87} +(0.174746 - 0.302669i) q^{88} +(-1.22344 + 2.11906i) q^{89} +(1.40646 - 3.30759i) q^{90} +(-8.90370 - 3.34037i) q^{91} +(-0.169508 - 0.293596i) q^{92} +(-4.49993 + 9.01830i) q^{93} +10.3768 q^{94} +1.90325 q^{95} +(-2.38791 + 4.78562i) q^{96} +(-2.36579 - 4.09767i) q^{97} +(-7.93569 + 2.71253i) q^{98} +(0.338716 - 0.0413715i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9} + q^{10} + q^{11} - 7 q^{12} - 4 q^{13} + 8 q^{14} - q^{15} + 10 q^{16} - 7 q^{17} + 18 q^{18} - 2 q^{19} + 7 q^{20} - 17 q^{21} + 19 q^{22} + q^{23} + 18 q^{24} - 12 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 16 q^{31} - 34 q^{32} + 7 q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} - 35 q^{38} - 17 q^{39} + 6 q^{40} + 20 q^{41} - 36 q^{42} + 31 q^{43} - 7 q^{44} + 6 q^{45} - 10 q^{46} + 62 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} + 14 q^{51} - 4 q^{52} + 8 q^{53} - 51 q^{54} + 2 q^{55} + 5 q^{57} + 45 q^{58} + 42 q^{59} - 23 q^{60} - 10 q^{61} + 14 q^{62} + 18 q^{63} - 56 q^{64} - 8 q^{65} + 4 q^{66} - 86 q^{67} - 48 q^{68} + 26 q^{69} - 5 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{73} + 9 q^{74} + 4 q^{75} - 13 q^{76} + 35 q^{77} + 19 q^{78} - 80 q^{79} + 5 q^{80} + 21 q^{81} + 5 q^{82} - 60 q^{83} + 35 q^{84} + 7 q^{85} + 12 q^{86} + 68 q^{87} + 50 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} + 7 q^{93} + 22 q^{94} - 4 q^{95} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9 + q^10 + q^11 - 7 * q^12 - 4 * q^13 + 8 * q^14 - q^15 + 10 * q^16 - 7 * q^17 + 18 * q^18 - 2 * q^19 + 7 * q^20 - 17 * q^21 + 19 * q^22 + q^23 + 18 * q^24 - 12 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 16 * q^31 - 34 * q^32 + 7 * q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 - 35 * q^38 - 17 * q^39 + 6 * q^40 + 20 * q^41 - 36 * q^42 + 31 * q^43 - 7 * q^44 + 6 * q^45 - 10 * q^46 + 62 * q^47 - 36 * q^48 - 11 * q^49 - q^50 + 14 * q^51 - 4 * q^52 + 8 * q^53 - 51 * q^54 + 2 * q^55 + 5 * q^57 + 45 * q^58 + 42 * q^59 - 23 * q^60 - 10 * q^61 + 14 * q^62 + 18 * q^63 - 56 * q^64 - 8 * q^65 + 4 * q^66 - 86 * q^67 - 48 * q^68 + 26 * q^69 - 5 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^73 + 9 * q^74 + 4 * q^75 - 13 * q^76 + 35 * q^77 + 19 * q^78 - 80 * q^79 + 5 * q^80 + 21 * q^81 + 5 * q^82 - 60 * q^83 + 35 * q^84 + 7 * q^85 + 12 * q^86 + 68 * q^87 + 50 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 + 7 * q^93 + 22 * q^94 - 4 * q^95 + 6 * q^97 - 15 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.19807			0.847162			0.423581	−	0.905858i	$-0.360773\pi$
$2$	1.19807			0.847162			0.423581	+	0.905858i	$0.360773\pi$
$3$	−0.773328	+	1.54983i	−0.446481	+	0.894793i
$3$	−0.773328	+	1.54983i	−0.446481	+	0.894793i
$4$	−0.564635			−0.282317
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.926499	+	1.85680i	−0.378242	+	0.758034i
$7$	0.433740	+	2.60996i	0.163938	+	0.986471i
$7$	0.433740	+	2.60996i	0.163938	+	0.986471i
$8$	−3.07261			−1.08633
$9$	−1.80393	−	2.39705i	−0.601309	−	0.799016i
$10$	0.599034	+	1.03756i	0.189431	+	0.328104i
$11$	−0.0568723	+	0.0985057i	−0.0171476	+	0.0297006i	−0.874472	−	0.485076i	$-0.838792\pi$
$11$	−0.0568723	+	0.0985057i	−0.0171476	+	0.0297006i	0.857324	+	0.514777i	$0.172125\pi$
$12$	0.436648	−	0.875086i	0.126049	−	0.252616i
$13$	−1.79716	+	3.11277i	−0.498442	+	0.863327i	−0.999998	−	0.00179772i	$-0.999428\pi$
$13$	−1.79716	+	3.11277i	−0.498442	+	0.863327i	0.501556	+	0.865125i	$0.332761\pi$
$14$	0.519650	+	3.12690i	0.138882	+	0.835700i
$15$	−1.72885	+	0.105192i	−0.446388	+	0.0271604i
$16$	−2.55192			−0.637980
$17$	1.61936	+	2.80482i	0.392753	+	0.680269i	0.992812	−	0.119688i	$-0.0381893\pi$
$17$	1.61936	+	2.80482i	0.392753	+	0.680269i	−0.600058	+	0.799956i	$0.704856\pi$
$18$	−2.16123	−	2.87183i	−0.509406	−	0.676896i
$19$	0.951626	−	1.64826i	0.218318	−	0.378138i	−0.735976	−	0.677008i	$-0.763276\pi$
$19$	0.951626	−	1.64826i	0.218318	−	0.378138i	0.954294	+	0.298870i	$0.0966097\pi$
$20$	−0.282317	−	0.488988i	−0.0631281	−	0.109341i
$21$	−4.38040	−	1.34613i	−0.955882	−	0.293750i
$22$	−0.0681368	+	0.118016i	−0.0145268	+	0.0251612i
$23$	0.300208	+	0.519975i	0.0625976	+	0.108422i	0.895626	−	0.444808i	$-0.146728\pi$
$23$	0.300208	+	0.519975i	0.0625976	+	0.108422i	−0.833028	+	0.553231i	$0.813395\pi$
$24$	2.37613	−	4.76201i	0.485026	−	0.972040i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.15312	+	3.72931i	−0.422261	+	0.731378i
$27$	5.11004	−	0.942072i	0.983428	−	0.181302i
$28$	−0.244905	−	1.47367i	−0.0462826	−	0.278498i
$29$	1.57537	+	2.72863i	0.292539	+	0.506693i	0.974410	−	0.224780i	$-0.0721664\pi$
$29$	1.57537	+	2.72863i	0.292539	+	0.506693i	−0.681870	+	0.731473i	$0.738833\pi$
$30$	−2.07128	+	0.126027i	−0.378163	+	0.0230093i
$31$	5.81891			1.04511			0.522554	−	0.852606i	$-0.324979\pi$
$31$	5.81891			1.04511			0.522554	+	0.852606i	$0.324979\pi$
$32$	3.08784			0.545858
$33$	−0.108686	−	0.164319i	−0.0189198	−	0.0286043i
$34$	1.94011	+	3.36036i	0.332725	+	0.576297i
$35$	−2.04342	+	1.68061i	−0.345401	+	0.284075i
$36$	1.01856	+	1.35346i	0.169760	+	0.225576i
$37$	−1.60007	+	2.77141i	−0.263050	+	0.455616i	−0.967051	−	0.254583i	$-0.918062\pi$
$37$	−1.60007	+	2.77141i	−0.263050	+	0.455616i	0.704001	+	0.710199i	$0.251395\pi$
$38$	1.14011	−	1.97473i	0.184951	−	0.320344i
$39$	−3.43446	−	5.19248i	−0.549954	−	0.831462i
$40$	−1.53630	−	2.66095i	−0.242911	−	0.420734i
$41$	4.74928	−	8.22599i	0.741713	−	1.28468i	−0.210002	−	0.977701i	$-0.567347\pi$
$41$	4.74928	−	8.22599i	0.741713	−	1.28468i	0.951715	−	0.306983i	$-0.0993196\pi$
$42$	−5.24802	−	1.61275i	−0.809787	−	0.248853i
$43$	0.780850	+	1.35247i	0.119079	+	0.206250i	0.919403	−	0.393317i	$-0.128673\pi$
$43$	0.780850	+	1.35247i	0.119079	+	0.206250i	−0.800324	+	0.599567i	$0.795339\pi$
$44$	0.0321120	−	0.0556197i	0.00484107	−	0.00838499i
$45$	1.17394	−	2.76077i	0.175001	−	0.411552i
$46$	0.359669	+	0.622965i	0.0530303	+	0.0918512i
$47$	8.66129			1.26338			0.631689	−	0.775222i	$-0.282362\pi$
$47$	8.66129			1.26338			0.631689	+	0.775222i	$0.282362\pi$
$48$	1.97347	−	3.95503i	0.284846	−	0.570860i
$49$	−6.62374	+	2.26409i	−0.946248	+	0.323441i
$50$	−0.599034	+	1.03756i	−0.0847162	+	0.146733i
$51$	−5.59928	+	0.340688i	−0.784056	+	0.0477058i
$52$	1.01474	−	1.75758i	0.140719	−	0.243732i
$53$	−5.54540	−	9.60491i	−0.761719	−	1.31934i	−0.941964	−	0.335714i	$-0.891023\pi$
$53$	−5.54540	−	9.60491i	−0.761719	−	1.31934i	0.180245	−	0.983622i	$-0.442311\pi$
$54$	6.12217	−	1.12867i	0.833122	−	0.153592i
$55$	−0.113745			−0.0153373
$56$	−1.33271	−	8.01936i	−0.178091	−	1.07163i
$57$	1.81861	+	2.74950i	0.240880	+	0.364181i
$58$	1.88740	+	3.26908i	0.247828	+	0.429251i
$59$	14.3279			1.86533			0.932667	−	0.360738i	$-0.117475\pi$
$59$	14.3279			1.86533			0.932667	+	0.360738i	$0.117475\pi$
$60$	0.976171	−	0.0593950i	0.126023	−	0.00766786i
$61$	−13.5921			−1.74029			−0.870143	−	0.492799i	$-0.835974\pi$
$61$	−13.5921			−1.74029			−0.870143	+	0.492799i	$0.835974\pi$
$62$	6.97145			0.885375
$63$	5.47376	−	5.74787i	0.689628	−	0.724163i
$64$	8.80328			1.10041
$65$	−3.59432			−0.445820
$66$	−0.130213	−	0.196866i	−0.0160281	−	0.0242325i
$67$	4.63189			0.565876			0.282938	−	0.959138i	$-0.408691\pi$
$67$	4.63189			0.565876			0.282938	+	0.959138i	$0.408691\pi$
$68$	−0.914348	−	1.58370i	−0.110881	−	0.192052i
$69$	−1.03803	+	0.0631589i	−0.124964	+	0.00760343i
$70$	−2.44815	+	2.01348i	−0.292610	+	0.240657i
$71$	6.64762			0.788927			0.394464	−	0.918912i	$-0.370930\pi$
$71$	6.64762			0.788927			0.394464	+	0.918912i	$0.370930\pi$
$72$	5.54276	+	7.36518i	0.653220	+	0.867995i
$73$	6.73961	+	11.6733i	0.788812	+	1.36626i	0.926695	+	0.375814i	$0.122637\pi$
$73$	6.73961	+	11.6733i	0.788812	+	1.36626i	−0.137884	+	0.990448i	$0.544030\pi$
$74$	−1.91699	+	3.32033i	−0.222846	+	0.385981i
$75$	−0.955526	−	1.44464i	−0.110335	−	0.166812i
$76$	−0.537321	+	0.930667i	−0.0616349	+	0.106755i
$77$	−0.281763	−	0.105708i	−0.0321099	−	0.0120466i
$78$	−4.11472	−	6.22094i	−0.465900	−	0.704383i
$79$	−17.4616			−1.96459			−0.982293	−	0.187349i	$-0.940010\pi$
$79$	−17.4616			−1.96459			−0.982293	+	0.187349i	$0.940010\pi$
$80$	−1.27596	−	2.21003i	−0.142657	−	0.247088i
$81$	−2.49169	+	8.64821i	−0.276854	+	0.960912i
$82$	5.68996	−	9.85530i	0.628351	−	1.08834i
$83$	0.0205902	+	0.0356633i	0.00226007	+	0.00391455i	0.867153	−	0.498041i	$-0.165947\pi$
$83$	0.0205902	+	0.0356633i	0.00226007	+	0.00391455i	−0.864893	+	0.501956i	$0.832614\pi$
$84$	2.47333	+	0.760071i	0.269862	+	0.0829306i
$85$	−1.61936	+	2.80482i	−0.175645	+	0.304225i
$86$	0.935511	+	1.62035i	0.100879	+	0.174727i
$87$	−5.44718	+	0.331433i	−0.583999	+	0.0355334i
$88$	0.174746	−	0.302669i	0.0186280	−	0.0322646i
$89$	−1.22344	+	2.11906i	−0.129685	+	0.224620i	−0.923554	−	0.383468i	$-0.874730\pi$
$89$	−1.22344	+	2.11906i	−0.129685	+	0.224620i	0.793870	+	0.608088i	$0.208063\pi$
$90$	1.40646	−	3.30759i	0.148254	−	0.348651i
$91$	−8.90370	−	3.34037i	−0.933361	−	0.350166i
$92$	−0.169508	−	0.293596i	−0.0176724	−	0.0306095i
$93$	−4.49993	+	9.01830i	−0.466621	+	0.935155i
$94$	10.3768			1.07029
$95$	1.90325			0.195269
$96$	−2.38791	+	4.78562i	−0.243715	+	0.488430i
$97$	−2.36579	−	4.09767i	−0.240210	−	0.416055i	0.720564	−	0.693388i	$-0.243883\pi$
$97$	−2.36579	−	4.09767i	−0.240210	−	0.416055i	−0.960774	+	0.277333i	$0.910550\pi$
$98$	−7.93569	+	2.71253i	−0.801625	+	0.274007i
$99$	0.338716	−	0.0413715i	0.0340423	−	0.00415799i
$100$	0.282317	−	0.488988i	0.0282317	−	0.0488988i
$101$	−5.12926	+	8.88413i	−0.510380	+	0.884004i	0.489548	+	0.871977i	$0.337162\pi$
$101$	−5.12926	+	8.88413i	−0.510380	+	0.884004i	−0.999928	+	0.0120277i	$0.996171\pi$
$102$	−6.70832	+	0.408167i	−0.664222	+	0.0404146i
$103$	1.94910	+	3.37595i	0.192051	+	0.332642i	0.945930	−	0.324372i	$-0.105153\pi$
$103$	1.94910	+	3.37595i	0.192051	+	0.332642i	−0.753879	+	0.657013i	$0.771819\pi$
$104$	5.52196	−	9.56432i	0.541473	−	0.937858i
$105$	−1.02442	−	4.46661i	−0.0999731	−	0.435896i
$106$	−6.64376	−	11.5073i	−0.645299	−	1.11769i
$107$	5.35082	−	9.26789i	0.517283	−	0.895961i	−0.482515	−	0.875887i	$-0.660277\pi$
$107$	5.35082	−	9.26789i	0.517283	−	0.895961i	0.999799	−	0.0200731i	$-0.00638991\pi$
$108$	−2.88531	+	0.531926i	−0.277639	+	0.0511846i
$109$	−4.95253	−	8.57803i	−0.474366	−	0.821627i	0.525203	−	0.850977i	$-0.323989\pi$
$109$	−4.95253	−	8.57803i	−0.474366	−	0.821627i	−0.999569	+	0.0293504i	$0.990656\pi$
$110$	−0.136274			−0.0129932
$111$	−3.05782	−	4.62304i	−0.290235	−	0.438799i
$112$	−1.10687	−	6.66039i	−0.104589	−	0.629348i
$113$	−4.19621	+	7.26806i	−0.394747	+	0.683721i	−0.993069	−	0.117534i	$-0.962501\pi$
$113$	−4.19621	+	7.26806i	−0.394747	+	0.683721i	0.598322	+	0.801256i	$0.295834\pi$
$114$	2.17881	+	3.29409i	0.204064	+	0.308520i
$115$	−0.300208	+	0.519975i	−0.0279945	+	0.0484879i
$116$	−0.889510	−	1.54068i	−0.0825890	−	0.143048i
$117$	10.7034	−	1.30734i	0.989531	−	0.120863i
$118$	17.1658			1.58024
$119$	−6.61807	+	5.44303i	−0.606678	+	0.498962i
$120$	5.31208	−	0.323213i	0.484925	−	0.0295052i
$121$	5.49353	+	9.51507i	0.499412	+	0.865007i
$122$	−16.2842			−1.47430
$123$	9.07612	+	13.7220i	0.818366	+	1.23727i
$124$	−3.28556			−0.295052
$125$	−1.00000			−0.0894427
$126$	6.55793	−	6.88633i	0.584227	−	0.613483i
$127$	−9.00068			−0.798681			−0.399341	−	0.916803i	$-0.630761\pi$
$127$	−9.00068			−0.798681			−0.399341	+	0.916803i	$0.630761\pi$
$128$	4.37124			0.386367
$129$	−2.69995	+	0.164278i	−0.237718	+	0.0144639i
$130$	−4.30624			−0.377682
$131$	−4.62304	−	8.00735i	−0.403917	−	0.699605i	0.590278	−	0.807200i	$-0.299018\pi$
$131$	−4.62304	−	8.00735i	−0.403917	−	0.699605i	−0.994195	+	0.107595i	$0.965685\pi$
$132$	0.0613678	+	0.0927804i	0.00534138	+	0.00807550i
$133$	4.71465	+	1.76878i	0.408812	+	0.153373i
$134$	5.54932			0.479388
$135$	3.37088	+	3.95439i	0.290119	+	0.340340i
$136$	−4.97566	−	8.61810i	−0.426660	−	0.738996i
$137$	6.15355	−	10.6583i	0.525733	−	0.910597i	−0.473818	−	0.880623i	$-0.657124\pi$
$137$	6.15355	−	10.6583i	0.525733	−	0.910597i	0.999551	−	0.0299735i	$-0.00954230\pi$
$138$	−1.24363	+	0.0756686i	−0.105865	+	0.00644134i
$139$	−10.3521	+	17.9304i	−0.878053	+	1.52083i	−0.0245786	+	0.999698i	$0.507824\pi$
$139$	−10.3521	+	17.9304i	−0.878053	+	1.52083i	−0.853474	+	0.521135i	$0.825509\pi$
$140$	1.15378	−	0.948929i	0.0975126	−	0.0801992i
$141$	−6.69802	+	13.4235i	−0.564075	+	1.13046i
$142$	7.96430			0.668349
$143$	−0.204417	−	0.354061i	−0.0170942	−	0.0296080i
$144$	4.60348	+	6.11707i	0.383623	+	0.509756i
$145$	−1.57537	+	2.72863i	−0.130828	+	0.226600i
$146$	8.07451	+	13.9855i	0.668251	+	1.15744i
$147$	1.61338	−	12.0165i	0.133069	−	0.991107i
$148$	0.903456	−	1.56483i	0.0742636	−	0.128628i
$149$	4.54523	+	7.87257i	0.372360	+	0.644946i	0.989928	−	0.141571i	$-0.0452155\pi$
$149$	4.54523	+	7.87257i	0.372360	+	0.644946i	−0.617568	+	0.786517i	$0.711882\pi$
$150$	−1.14478	−	1.73077i	−0.0934712	−	0.141317i
$151$	4.54913	−	7.87932i	0.370203	−	0.641210i	−0.619394	−	0.785080i	$-0.712622\pi$
$151$	4.54913	−	7.87932i	0.370203	−	0.641210i	0.989596	+	0.143871i	$0.0459549\pi$
$152$	−2.92397	+	5.06446i	−0.237165	+	0.410782i
$153$	3.80207	−	8.94138i	0.307379	−	0.722868i
$154$	−0.337571	−	0.126646i	−0.0272023	−	0.0102054i
$155$	2.90945	+	5.03932i	0.233693	+	0.404768i
$156$	1.93922	+	2.93185i	0.155262	+	0.234736i
$157$	0.0436206			0.00348131			0.00174065	−	0.999998i	$-0.499446\pi$
$157$	0.0436206			0.00348131			0.00174065	+	0.999998i	$0.499446\pi$
$158$	−20.9202			−1.66432
$159$	19.1744	−	1.16666i	1.52063	−	0.0925223i
$160$	1.54392	+	2.67415i	0.122058	+	0.211410i
$161$	−1.22690	+	1.00906i	−0.0966932	+	0.0795253i
$162$	−2.98521	+	10.3611i	−0.234540	+	0.814048i
$163$	6.83035	−	11.8305i	0.534995	−	0.926638i	−0.464169	−	0.885747i	$-0.653647\pi$
$163$	6.83035	−	11.8305i	0.534995	−	0.926638i	0.999164	−	0.0408913i	$-0.0130197\pi$
$164$	−2.68161	+	4.64468i	−0.209398	+	0.362689i
$165$	0.0879618	−	0.176284i	0.00684782	−	0.0137237i
$166$	0.0246684	+	0.0427270i	0.00191464	+	0.00331626i
$167$	5.04540	−	8.73888i	0.390424	−	0.676235i	−0.602081	−	0.798435i	$-0.705662\pi$
$167$	5.04540	−	8.73888i	0.390424	−	0.676235i	0.992505	+	0.122200i	$0.0389949\pi$
$168$	13.4592	+	4.13612i	1.03840	+	0.319109i
$169$	0.0404366	+	0.0700382i	0.00311051	+	0.00538756i
$170$	−1.94011	+	3.36036i	−0.148799	+	0.257728i
$171$	−5.66763	+	0.692256i	−0.433415	+	0.0529381i
$172$	−0.440895	−	0.763653i	−0.0336179	−	0.0582280i
$173$	3.24820			0.246956			0.123478	−	0.992347i	$-0.460595\pi$
$173$	3.24820			0.246956			0.123478	+	0.992347i	$0.460595\pi$
$174$	−6.52609	+	0.397079i	−0.494741	+	0.0301025i
$175$	−2.47716	−	0.929348i	−0.187256	−	0.0702521i
$176$	0.145133	−	0.251378i	0.0109398	−	0.0189484i
$177$	−11.0802	+	22.2058i	−0.832836	+	1.66909i
$178$	−1.46577	+	2.53878i	−0.109864	+	0.190290i
$179$	−7.29241	−	12.6308i	−0.545060	−	0.944072i	−0.998603	−	0.0528375i	$-0.983173\pi$
$179$	−7.29241	−	12.6308i	−0.545060	−	0.944072i	0.453543	−	0.891234i	$-0.350160\pi$
$180$	−0.662848	+	1.55883i	−0.0494058	+	0.116188i
$181$	−7.23510			−0.537781			−0.268890	−	0.963171i	$-0.586657\pi$
$181$	−7.23510			−0.537781			−0.268890	+	0.963171i	$0.586657\pi$
$182$	−10.6672	−	4.00199i	−0.790707	−	0.296647i
$183$	10.5111	−	21.0654i	0.777005	−	1.55720i
$184$	−0.922420	−	1.59768i	−0.0680017	−	0.117782i
$185$	−3.20014			−0.235279
$186$	−5.39121	+	10.8045i	−0.395303	+	0.792227i
$187$	−0.368387			−0.0269392
$188$	−4.89046			−0.356674
$189$	4.67519	+	12.9284i	0.340070	+	0.940400i
$190$	2.28022			0.165425
$191$	7.61296			0.550855			0.275427	−	0.961322i	$-0.411181\pi$
$191$	7.61296			0.550855			0.275427	+	0.961322i	$0.411181\pi$
$192$	−6.80782	+	13.6436i	−0.491312	+	0.984639i
$193$	10.3077			0.741966			0.370983	−	0.928640i	$-0.379021\pi$
$193$	10.3077			0.741966			0.370983	+	0.928640i	$0.379021\pi$
$194$	−2.83438	−	4.90928i	−0.203496	−	0.352466i
$195$	2.77959	−	5.57057i	0.199050	−	0.398917i
$196$	3.73999	−	1.27838i	0.267142	−	0.0913129i
$197$	−12.0738			−0.860221			−0.430110	−	0.902776i	$-0.641525\pi$
$197$	−12.0738			−0.860221			−0.430110	+	0.902776i	$0.641525\pi$
$198$	0.405805	−	0.0495658i	0.0288393	−	0.00352249i
$199$	−6.42977	−	11.1367i	−0.455795	−	0.789459i	0.542939	−	0.839772i	$-0.317312\pi$
$199$	−6.42977	−	11.1367i	−0.455795	−	0.789459i	−0.998734	+	0.0503128i	$0.983978\pi$
$200$	1.53630	−	2.66095i	0.108633	−	0.188158i
$201$	−3.58197	+	7.17864i	−0.252653	+	0.506342i
$202$	−6.14519	+	10.6438i	−0.432374	+	0.748894i
$203$	−6.43829	+	5.29517i	−0.451880	+	0.371648i
$204$	3.16155	−	0.192364i	0.221353	−	0.0134682i
$205$	9.49856			0.663408
$206$	2.33516	+	4.04461i	0.162698	+	0.281801i
$207$	0.704853	−	1.65761i	0.0489906	−	0.115212i
$208$	4.58620	−	7.94354i	0.317996	−	0.550785i
$209$	0.108242	+	0.187481i	0.00748727	+	0.0129683i
$210$	−1.22732	−	5.35129i	−0.0846934	−	0.369274i
$211$	6.51474	−	11.2839i	0.448493	−	0.776813i	−0.549795	−	0.835300i	$-0.685294\pi$
$211$	6.51474	−	11.2839i	0.448493	−	0.776813i	0.998288	+	0.0584864i	$0.0186274\pi$
$212$	3.13112	+	5.42326i	0.215046	+	0.372471i
$213$	−5.14079	+	10.3027i	−0.352241	+	0.705927i
$214$	6.41064	−	11.1036i	0.438222	−	0.759023i
$215$	−0.780850	+	1.35247i	−0.0532536	+	0.0922379i
$216$	−15.7011	+	2.89461i	−1.06833	+	0.196954i
$217$	2.52389	+	15.1871i	0.171333	+	1.03097i
$218$	−5.93347	−	10.2771i	−0.401865	−	0.696051i
$219$	−23.3036	+	1.41791i	−1.57471	+	0.0958132i
$220$	0.0642241			0.00432999
$221$	−11.6410			−0.783059
$222$	−3.66347	−	5.53871i	−0.245876	−	0.371734i
$223$	12.8217	+	22.2078i	0.858604	+	1.48715i	0.873261	+	0.487253i	$0.162001\pi$
$223$	12.8217	+	22.2078i	0.858604	+	1.48715i	−0.0146565	+	0.999893i	$0.504665\pi$
$224$	1.33932	+	8.05913i	0.0894871	+	0.538473i
$225$	2.97787	−	0.363723i	0.198525	−	0.0242482i
$226$	−5.02735	+	8.70762i	−0.334414	+	0.579222i
$227$	−13.0179	+	22.5477i	−0.864031	+	1.49655i	0.00397458	+	0.999992i	$0.498735\pi$
$227$	−13.0179	+	22.5477i	−0.864031	+	1.49655i	−0.868006	+	0.496554i	$0.834598\pi$
$228$	−1.02685	−	1.55246i	−0.0680046	−	0.102814i
$229$	0.745635	+	1.29148i	0.0492730	+	0.0853433i	0.889610	−	0.456721i	$-0.150976\pi$
$229$	0.745635	+	1.29148i	0.0492730	+	0.0853433i	−0.840337	+	0.542064i	$0.817643\pi$
$230$	−0.359669	+	0.622965i	−0.0237159	+	0.0410771i
$231$	0.381725	−	0.354937i	0.0251156	−	0.0233531i
$232$	−4.84050	−	8.38399i	−0.317794	−	0.550436i
$233$	2.91829	−	5.05463i	0.191184	−	0.331140i	−0.754459	−	0.656347i	$-0.772101\pi$
$233$	2.91829	−	5.05463i	0.191184	−	0.331140i	0.945643	+	0.325207i	$0.105434\pi$
$234$	12.8234	−	1.56628i	0.838292	−	0.102391i
$235$	4.33064	+	7.50090i	0.282500	+	0.489305i
$236$	−8.09003			−0.526616
$237$	13.5036	−	27.0625i	0.877151	−	1.75790i
$238$	−7.92889	+	6.52111i	−0.513954	+	0.422701i
$239$	−1.54594	+	2.67764i	−0.0999983	+	0.173202i	−0.911684	−	0.410893i	$-0.865217\pi$
$239$	−1.54594	+	2.67764i	−0.0999983	+	0.173202i	0.811685	+	0.584095i	$0.198550\pi$
$240$	4.41189	−	0.268441i	0.284786	−	0.0173278i
$241$	11.2046	−	19.4069i	0.721751	−	1.25011i	−0.238546	−	0.971131i	$-0.576671\pi$
$241$	11.2046	−	19.4069i	0.721751	−	1.25011i	0.960297	−	0.278979i	$-0.0899960\pi$
$242$	6.58162	+	11.3997i	0.423083	+	0.732801i
$243$	−11.4763	−	10.5496i	−0.736207	−	0.676756i
$244$	7.67455			0.491313
$245$	−5.27262	−	4.60428i	−0.336856	−	0.294157i
$246$	10.8738	+	16.4398i	0.693288	+	1.04816i
$247$	3.42045	+	5.92439i	0.217638	+	0.376960i
$248$	−17.8792			−1.13533
$249$	−0.0711949	+	0.00433184i	−0.00451179	+	0.000274520i
$250$	−1.19807			−0.0757724
$251$	20.4501			1.29080			0.645398	−	0.763846i	$-0.276692\pi$
$251$	20.4501			1.29080			0.645398	+	0.763846i	$0.276692\pi$
$252$	−3.09067	+	3.24545i	−0.194694	+	0.204444i
$253$	−0.0682940			−0.00429361
$254$	−10.7834			−0.676612
$255$	−3.09469	−	4.67878i	−0.193797	−	0.292996i
$256$	−12.3695			−0.773095
$257$	5.72256	+	9.91177i	0.356964	+	0.618279i	0.987452	−	0.157920i	$-0.0504787\pi$
$257$	5.72256	+	9.91177i	0.356964	+	0.618279i	−0.630488	+	0.776199i	$0.717145\pi$
$258$	−3.23472	+	0.196817i	−0.201385	+	0.0122533i
$259$	−7.92726	−	2.97405i	−0.492576	−	0.184798i
$260$	2.02948			0.125863
$261$	3.69879	−	8.69849i	0.228949	−	0.538423i
$262$	−5.53872	−	9.59334i	−0.342183	−	0.592678i
$263$	2.74843	−	4.76042i	0.169475	−	0.293540i	−0.768760	−	0.639537i	$-0.779126\pi$
$263$	2.74843	−	4.76042i	0.169475	−	0.293540i	0.938236	+	0.345997i	$0.112459\pi$
$264$	0.333949	+	0.504888i	0.0205531	+	0.0310737i
$265$	5.54540	−	9.60491i	0.340651	−	0.590025i
$266$	5.64847	+	2.11912i	0.346330	+	0.129932i
$267$	−2.33806	−	3.53485i	−0.143087	−	0.216329i
$268$	−2.61533			−0.159757
$269$	−1.42378	−	2.46605i	−0.0868091	−	0.150358i	0.819352	−	0.573291i	$-0.194334\pi$
$269$	−1.42378	−	2.46605i	−0.0868091	−	0.150358i	−0.906161	+	0.422934i	$0.861000\pi$
$270$	4.03854	+	4.73762i	0.245778	+	0.288323i
$271$	12.0863	−	20.9342i	0.734193	−	1.27166i	−0.220883	−	0.975300i	$-0.570894\pi$
$271$	12.0863	−	20.9342i	0.734193	−	1.27166i	0.955076	−	0.296360i	$-0.0957728\pi$
$272$	−4.13248	−	7.15767i	−0.250569	−	0.433997i
$273$	12.0625	−	11.2160i	0.730054	−	0.678822i
$274$	7.37237	−	12.7693i	0.445381	−	0.771422i
$275$	−0.0568723	−	0.0985057i	−0.00342953	−	0.00594011i
$276$	0.586108	−	0.0356617i	0.0352795	−	0.00214658i
$277$	12.1727	−	21.0838i	0.731389	−	1.26680i	−0.224901	−	0.974382i	$-0.572206\pi$
$277$	12.1727	−	21.0838i	0.731389	−	1.26680i	0.956290	−	0.292421i	$-0.0944608\pi$
$278$	−12.4025	+	21.4818i	−0.743853	+	1.28839i
$279$	−10.4969	−	13.9482i	−0.628433	−	0.835058i
$280$	6.27862	−	5.16384i	0.375219	−	0.308599i
$281$	−5.05886	−	8.76220i	−0.301786	−	0.522709i	0.674754	−	0.738042i	$-0.264250\pi$
$281$	−5.05886	−	8.76220i	−0.301786	−	0.522709i	−0.976541	+	0.215333i	$0.930916\pi$
$282$	−8.02467	+	16.0823i	−0.477862	+	0.957684i
$283$	16.1280			0.958709			0.479354	−	0.877621i	$-0.340871\pi$
$283$	16.1280			0.958709			0.479354	+	0.877621i	$0.340871\pi$
$284$	−3.75348			−0.222728
$285$	−1.47184	+	2.94971i	−0.0871841	+	0.174726i
$286$	−0.244905	−	0.424189i	−0.0144816	−	0.0250828i
$287$	23.5294	+	8.82747i	1.38890	+	0.521069i
$288$	−5.57024	−	7.40170i	−0.328230	−	0.436150i
$289$	3.25533	−	5.63839i	0.191490	−	0.331670i
$290$	−1.88740	+	3.26908i	−0.110832	+	0.191967i
$291$	8.18021	−	0.497724i	0.479532	−	0.0291771i
$292$	−3.80542	−	6.59118i	−0.222695	−	0.385719i
$293$	−3.39638	+	5.88270i	−0.198419	+	0.343671i	−0.948016	−	0.318223i	$-0.896914\pi$
$293$	−3.39638	+	5.88270i	−0.198419	+	0.343671i	0.749597	+	0.661894i	$0.230247\pi$
$294$	1.93294	−	14.3966i	0.112731	−	0.839627i
$295$	7.16395	+	12.4083i	0.417101	+	0.722441i
$296$	4.91639	−	8.51543i	0.285759	−	0.494950i
$297$	−0.197820	+	0.556945i	−0.0114787	+	0.0323173i
$298$	5.44549	+	9.43186i	0.315449	+	0.546373i
$299$	−2.15808			−0.124805
$300$	0.539523	+	0.815691i	0.0311494	+	0.0470939i
$301$	−3.19121	+	2.62461i	−0.183938	+	0.151280i
$302$	5.45016	−	9.43995i	0.313621	−	0.543208i
$303$	−9.80227	−	14.8198i	−0.563126	−	0.851376i
$304$	−2.42847	+	4.20623i	−0.139282	+	0.241244i
$305$	−6.79604	−	11.7711i	−0.389140	−	0.674010i
$306$	4.55514	−	10.7124i	0.260400	−	0.612386i
$307$	−17.6686			−1.00840			−0.504199	−	0.863587i	$-0.668212\pi$
$307$	−17.6686			−1.00840			−0.504199	+	0.863587i	$0.668212\pi$
$308$	0.159093	+	0.0596865i	0.00906518	+	0.00340096i
$309$	−6.73943	+	0.410060i	−0.383393	+	0.0233275i
$310$	3.48572	+	6.03745i	0.197976	+	0.342904i
$311$	21.9124			1.24254			0.621270	−	0.783597i	$-0.286617\pi$
$311$	21.9124			1.24254			0.621270	+	0.783597i	$0.286617\pi$
$312$	10.5528	+	15.9544i	0.597432	+	0.903242i
$313$	−19.1773			−1.08396			−0.541981	−	0.840391i	$-0.682326\pi$
$313$	−19.1773			−1.08396			−0.541981	+	0.840391i	$0.682326\pi$
$314$	0.0522605			0.00294923
$315$	7.71468	+	1.86648i	0.434673	+	0.105164i
$316$	9.85944			0.554637
$317$	0.837213			0.0470226			0.0235113	−	0.999724i	$-0.492515\pi$
$317$	0.837213			0.0470226			0.0235113	+	0.999724i	$0.492515\pi$
$318$	22.9722	−	1.39774i	1.28822	−	0.0783813i
$319$	−0.358380			−0.0200654
$320$	4.40164	+	7.62386i	0.246059	+	0.426187i
$321$	10.2257	+	15.4600i	0.570742	+	0.862891i
$322$	−1.46991	+	1.20893i	−0.0819148	+	0.0673708i
$323$	6.16411			0.342980
$324$	1.40689	−	4.88308i	0.0781607	−	0.271282i
$325$	−1.79716	−	3.11277i	−0.0996885	−	0.172665i
$326$	8.18323	−	14.1738i	0.453227	−	0.785012i
$327$	17.1244	−	1.04193i	0.946982	−	0.0576190i
$328$	−14.5927	+	25.2752i	−0.805745	+	1.39559i
$329$	3.75675	+	22.6056i	0.207116	+	1.24629i
$330$	0.105384	−	0.211201i	0.00580121	−	0.0116262i
$331$	25.5137			1.40236			0.701179	−	0.712985i	$-0.252657\pi$
$331$	25.5137			1.40236			0.701179	+	0.712985i	$0.252657\pi$
$332$	−0.0116259	−	0.0201367i	−0.000638056	−	0.00110515i
$333$	9.52961	−	1.16397i	0.522219	−	0.0637849i
$334$	6.04472	−	10.4698i	0.330753	−	0.572880i
$335$	2.31595	+	4.01134i	0.126534	+	0.219163i
$336$	11.1784	+	3.43521i	0.609834	+	0.187406i
$337$	11.2945	−	19.5627i	0.615252	−	1.06565i	−0.375088	−	0.926989i	$-0.622388\pi$
$337$	11.2945	−	19.5627i	0.615252	−	1.06565i	0.990340	−	0.138658i	$-0.0442790\pi$
$338$	0.0484458	+	0.0839105i	0.00263510	+	0.00456413i
$339$	−8.01918	−	12.1240i	−0.435542	−	0.658485i
$340$	0.914348	−	1.58370i	0.0495875	−	0.0858881i
$341$	−0.330935	+	0.573195i	−0.0179211	+	0.0310403i
$342$	−6.79021	+	0.829369i	−0.367172	+	0.0448472i
$343$	−8.78214	−	16.3056i	−0.474191	−	0.880422i
$344$	−2.39924	−	4.15561i	−0.129359	−	0.224056i
$345$	−0.573712	−	0.867381i	−0.0308876	−	0.0466982i
$346$	3.89156			0.209212
$347$	−25.1822			−1.35185			−0.675924	−	0.736971i	$-0.736255\pi$
$347$	−25.1822			−1.35185			−0.675924	+	0.736971i	$0.736255\pi$
$348$	3.07567	−	0.187139i	0.164873	−	0.0100317i
$349$	−1.91474	−	3.31642i	−0.102494	−	0.177524i	0.810218	−	0.586129i	$-0.199349\pi$
$349$	−1.91474	−	3.31642i	−0.102494	−	0.177524i	−0.912711	+	0.408605i	$0.866015\pi$
$350$	−2.96780	−	1.11342i	−0.158636	−	0.0595149i
$351$	−6.25110	+	17.5994i	−0.333659	+	0.939388i
$352$	−0.175612	+	0.304170i	−0.00936017	+	0.0162123i
$353$	17.7531	−	30.7492i	0.944901	−	1.63662i	0.188951	−	0.981986i	$-0.439491\pi$
$353$	17.7531	−	30.7492i	0.944901	−	1.63662i	0.755950	−	0.654630i	$-0.227175\pi$
$354$	−13.2748	+	26.6040i	−0.705547	+	1.41399i
$355$	3.32381	+	5.75701i	0.176410	+	0.305550i
$356$	0.690797	−	1.19650i	0.0366122	−	0.0634142i
$357$	−3.31781	−	14.4661i	−0.175597	−	0.765628i
$358$	−8.73680	−	15.1326i	−0.461754	−	0.799781i
$359$	18.6809	−	32.3563i	0.985942	−	1.70770i	0.348270	−	0.937394i	$-0.386769\pi$
$359$	18.6809	−	32.3563i	0.985942	−	1.70770i	0.637672	−	0.770308i	$-0.279897\pi$
$360$	−3.60706	+	8.48276i	−0.190109	+	0.447081i
$361$	7.68882	+	13.3174i	0.404675	+	0.700917i
$362$	−8.66814			−0.455587
$363$	−18.9950	+	1.15575i	−0.996980	+	0.0606612i
$364$	5.02733	+	1.88609i	0.263504	+	0.0988580i
$365$	−6.73961	+	11.6733i	−0.352767	+	0.611011i
$366$	12.5930	−	25.2377i	0.658249	−	1.31920i
$367$	−14.2727	+	24.7210i	−0.745028	+	1.29043i	0.205154	+	0.978730i	$0.434230\pi$
$367$	−14.2727	+	24.7210i	−0.745028	+	1.29043i	−0.950182	+	0.311696i	$0.899103\pi$
$368$	−0.766106	−	1.32693i	−0.0399360	−	0.0691712i
$369$	−28.2855	+	3.45484i	−1.47248	+	0.179852i
$370$	−3.83399			−0.199319
$371$	22.6631	−	18.6393i	1.17661	−	0.967703i
$372$	2.54081	−	5.09205i	0.131735	−	0.264010i
$373$	−10.9068	−	18.8912i	−0.564734	−	0.978148i	−0.997074	−	0.0764377i	$-0.975645\pi$
$373$	−10.9068	−	18.8912i	−0.564734	−	0.978148i	0.432340	−	0.901711i	$-0.357688\pi$
$374$	−0.441353			−0.0228218
$375$	0.773328	−	1.54983i	0.0399345	−	0.0800327i
$376$	−26.6127			−1.37245
$377$	−11.3248			−0.583256
$378$	5.60120	+	15.4890i	0.288095	+	0.796671i
$379$	−11.5179			−0.591632			−0.295816	−	0.955245i	$-0.595592\pi$
$379$	−11.5179			−0.591632			−0.295816	+	0.955245i	$0.595592\pi$
$380$	−1.07464			−0.0551279
$381$	6.96048	−	13.9495i	0.356596	−	0.714655i
$382$	9.12084			0.466663
$383$	−1.53315	−	2.65549i	−0.0783403	−	0.135689i	0.824194	−	0.566308i	$-0.191629\pi$
$383$	−1.53315	−	2.65549i	−0.0783403	−	0.135689i	−0.902534	+	0.430619i	$0.858295\pi$
$384$	−3.38040	+	6.77467i	−0.172505	+	0.345718i
$385$	−0.0493356	−	0.296868i	−0.00251437	−	0.0151298i
$386$	12.3493			0.628565
$387$	1.83335	−	4.31150i	0.0931942	−	0.219166i
$388$	1.33581	+	2.31369i	0.0678153	+	0.117460i
$389$	−2.82404	+	4.89139i	−0.143185	+	0.248003i	−0.928694	−	0.370846i	$-0.879068\pi$
$389$	−2.82404	+	4.89139i	−0.143185	+	0.248003i	0.785510	+	0.618850i	$0.212401\pi$
$390$	3.33013	−	6.67392i	0.168628	−	0.337947i
$391$	−0.972291	+	1.68406i	−0.0491708	+	0.0851664i
$392$	20.3521	−	6.95664i	1.02794	−	0.351363i
$393$	15.9851	−	0.972614i	0.806343	−	0.0490619i
$394$	−14.4652			−0.728746
$395$	−8.73081	−	15.1222i	−0.439295	−	0.760881i
$396$	−0.191251	+	0.0233598i	−0.00961072	+	0.00117387i
$397$	−18.0441	+	31.2534i	−0.905609	+	1.56856i	−0.0855123	+	0.996337i	$0.527253\pi$
$397$	−18.0441	+	31.2534i	−0.905609	+	1.56856i	−0.820097	+	0.572224i	$0.806081\pi$
$398$	−7.70330	−	13.3425i	−0.386132	−	0.668800i
$399$	−6.38728	+	5.93905i	−0.319764	+	0.297324i
$400$	1.27596	−	2.21003i	0.0637980	−	0.110501i
$401$	−14.6836	−	25.4327i	−0.733264	−	1.27005i	−0.955481	−	0.295053i	$-0.904663\pi$
$401$	−14.6836	−	25.4327i	−0.733264	−	1.27005i	0.222217	−	0.974997i	$-0.428671\pi$
$402$	−4.29145	+	8.60049i	−0.214038	+	0.428953i
$403$	−10.4575	+	18.1129i	−0.520926	+	0.902270i
$404$	2.89616	−	5.01629i	0.144089	−	0.249570i
$405$	−8.73541	+	2.16624i	−0.434066	+	0.107641i
$406$	−7.71351	+	6.34397i	−0.382815	+	0.314846i
$407$	−0.181999	−	0.315232i	−0.00902137	−	0.0156255i
$408$	17.2044	−	1.04680i	0.851744	−	0.0518243i
$409$	27.3302			1.35139			0.675696	−	0.737181i	$-0.263843\pi$
$409$	27.3302			1.35139			0.675696	+	0.737181i	$0.263843\pi$
$410$	11.3799			0.562014
$411$	11.7597	+	17.7793i	0.580066	+	0.876987i
$412$	−1.10053	−	1.90618i	−0.0542193	−	0.0939106i
$413$	6.21459	+	37.3952i	0.305800	+	1.84010i
$414$	0.844461	−	1.98593i	0.0415030	−	0.0976031i
$415$	−0.0205902	+	0.0356633i	−0.00101073	+	0.00175064i
$416$	−5.54934	+	9.61174i	−0.272079	+	0.471254i
$417$	−19.7834	−	29.9100i	−0.968796	−	1.46470i
$418$	0.129681	+	0.224615i	0.00634293	+	0.0109863i
$419$	2.99144	−	5.18132i	0.146141	−	0.253124i	−0.783657	−	0.621194i	$-0.786648\pi$
$419$	2.99144	−	5.18132i	0.146141	−	0.253124i	0.929798	+	0.368070i	$0.119981\pi$
$420$	0.578423	+	2.52200i	0.0282241	+	0.123061i
$421$	12.6243	+	21.8660i	0.615273	+	1.06568i	0.990337	+	0.138685i	$0.0442876\pi$
$421$	12.6243	+	21.8660i	0.615273	+	1.06568i	−0.375063	+	0.926999i	$0.622379\pi$
$422$	7.80510	−	13.5188i	0.379946	−	0.658086i
$423$	−15.6243	−	20.7615i	−0.759681	−	1.00946i
$424$	17.0388	+	29.5121i	0.827478	+	1.43323i
$425$	−3.23873			−0.157101
$426$	−6.15901	+	12.3433i	−0.298405	+	0.598034i
$427$	−5.89543	−	35.4747i	−0.285300	−	1.71674i
$428$	−3.02126	+	5.23297i	−0.146038	+	0.252945i
$429$	0.706814	−	0.0430061i	0.0341253	−	0.00207635i
$430$	−0.935511	+	1.62035i	−0.0451144	+	0.0781404i
$431$	12.2647	+	21.2431i	0.590771	+	1.02325i	0.994129	+	0.108203i	$0.0345097\pi$
$431$	12.2647	+	21.2431i	0.590771	+	1.02325i	−0.403358	+	0.915042i	$0.632157\pi$
$432$	−13.0404	+	2.40409i	−0.627407	+	0.115667i
$433$	−10.0912			−0.484951			−0.242476	−	0.970158i	$-0.577959\pi$
$433$	−10.0912			−0.484951			−0.242476	+	0.970158i	$0.577959\pi$
$434$	3.02380	+	18.1952i	0.145147	+	0.873396i
$435$	−3.01062	−	4.55168i	−0.144348	−	0.218236i
$436$	2.79637	+	4.84346i	0.133922	+	0.231959i
$437$	1.14274			0.0546647
$438$	−27.9193	+	1.69875i	−1.33403	+	0.0811692i
$439$	−2.96072			−0.141307			−0.0706537	−	0.997501i	$-0.522509\pi$
$439$	−2.96072			−0.141307			−0.0706537	+	0.997501i	$0.522509\pi$
$440$	0.349492			0.0166614
$441$	17.3759	+	11.7932i	0.827422	+	0.561580i
$442$	−13.9467			−0.663378
$443$	−30.8278			−1.46467			−0.732337	−	0.680943i	$-0.761570\pi$
$443$	−30.8278			−1.46467			−0.732337	+	0.680943i	$0.761570\pi$
$444$	1.72655	+	2.61033i	0.0819385	+	0.123881i
$445$	−2.44688			−0.115993
$446$	15.3613	+	26.6065i	0.727376	+	1.25985i
$447$	−15.7161	+	0.956243i	−0.743344	+	0.0452287i
$448$	3.81833	+	22.9762i	0.180399	+	1.08552i
$449$	−27.5418			−1.29978			−0.649890	−	0.760029i	$-0.725185\pi$
$449$	−27.5418			−1.29978			−0.649890	+	0.760029i	$0.725185\pi$
$450$	3.56769	−	0.435765i	0.168182	−	0.0205421i
$451$	0.540205	+	0.935662i	0.0254372	+	0.0440586i
$452$	2.36933	−	4.10380i	0.111444	−	0.193026i
$453$	8.69361	+	13.1437i	0.408462	+	0.617543i
$454$	−15.5964	+	27.0137i	−0.731974	+	1.26782i
$455$	−1.55900	−	9.38101i	−0.0730871	−	0.439789i
$456$	−5.58786	−	8.44814i	−0.261675	−	0.395620i
$457$	−6.59646			−0.308569			−0.154285	−	0.988026i	$-0.549307\pi$
$457$	−6.59646			−0.308569			−0.154285	+	0.988026i	$0.549307\pi$
$458$	0.893321	+	1.54728i	0.0417421	+	0.0722995i
$459$	10.9173	+	12.8072i	0.509578	+	0.597788i
$460$	0.169508	−	0.293596i	0.00790334	−	0.0136890i
$461$	14.1891	+	24.5762i	0.660852	+	1.14463i	0.980392	+	0.197056i	$0.0631382\pi$
$461$	14.1891	+	24.5762i	0.660852	+	1.14463i	−0.319540	+	0.947573i	$0.603528\pi$
$462$	0.457332	−	0.425239i	0.0212770	−	0.0197839i
$463$	−13.5765	+	23.5151i	−0.630952	+	1.09284i	0.356406	+	0.934331i	$0.384002\pi$
$463$	−13.5765	+	23.5151i	−0.630952	+	1.09284i	−0.987358	+	0.158509i	$0.949331\pi$
$464$	−4.02022	−	6.96323i	−0.186634	−	0.323260i
$465$	−10.0600	+	0.612102i	−0.466523	+	0.0283856i
$466$	3.49631	−	6.05579i	0.161963	−	0.280529i
$467$	−2.55322	+	4.42231i	−0.118149	+	0.204640i	−0.919034	−	0.394178i	$-0.871029\pi$
$467$	−2.55322	+	4.42231i	−0.118149	+	0.204640i	0.800885	+	0.598818i	$0.204363\pi$
$468$	−6.04352	+	0.738167i	−0.279362	+	0.0341218i
$469$	2.00904	+	12.0890i	0.0927688	+	0.558220i
$470$	5.18840	+	8.98658i	0.239323	+	0.414520i
$471$	−0.0337331	+	0.0676044i	−0.00155434	+	0.00311505i
$472$	−44.0240			−2.02637
$473$	−0.177635			−0.00816766
$474$	16.1782	−	32.4227i	0.743088	−	1.48922i
$475$	0.951626	+	1.64826i	0.0436636	+	0.0756275i
$476$	3.73679	−	3.07332i	0.171276	−	0.140865i
$477$	−13.0199	+	30.6191i	−0.596142	+	1.40195i
$478$	−1.85214	+	3.20799i	−0.0847147	+	0.146730i
$479$	8.51637	−	14.7508i	0.389123	−	0.673980i	−0.603209	−	0.797583i	$-0.706112\pi$
$479$	8.51637	−	14.7508i	0.389123	−	0.673980i	0.992332	+	0.123603i	$0.0394449\pi$
$480$	−5.33842	+	0.324816i	−0.243665	+	0.0148257i
$481$	−5.75117	−	9.96131i	−0.262231	−	0.454197i
$482$	13.4239	−	23.2508i	0.611440	−	1.05905i
$483$	−0.615077	−	2.68182i	−0.0279870	−	0.122027i
$484$	−3.10184	−	5.37254i	−0.140993	−	0.244206i
$485$	2.36579	−	4.09767i	0.107425	−	0.186066i
$486$	−13.7494	−	12.6391i	−0.623686	−	0.573322i
$487$	16.2711	+	28.1823i	0.737312	+	1.27706i	0.953701	+	0.300755i	$0.0972387\pi$
$487$	16.2711	+	28.1823i	0.737312	+	1.27706i	−0.216389	+	0.976307i	$0.569428\pi$
$488$	41.7631			1.89053
$489$	13.0532	+	19.7347i	0.590284	+	0.892436i
$490$	−6.31696	−	5.51624i	−0.285371	−	0.249198i
$491$	−1.00773	+	1.74543i	−0.0454781	+	0.0787703i	−0.887868	−	0.460098i	$-0.847814\pi$
$491$	−1.00773	+	1.74543i	−0.0454781	+	0.0787703i	0.842390	+	0.538868i	$0.181148\pi$
$492$	−5.12469	−	7.74789i	−0.231039	−	0.349302i
$493$	−5.10220	+	8.83727i	−0.229792	+	0.398011i
$494$	4.09792	+	7.09781i	0.184374	+	0.319346i
$495$	0.205187	+	0.272651i	0.00922247	+	0.0122548i
$496$	−14.8494			−0.666757
$497$	2.88334	+	17.3500i	0.129335	+	0.778254i
$498$	−0.0852962	+	0.00518984i	−0.00382222	+	0.000232562i
$499$	−6.33204	−	10.9674i	−0.283461	−	0.490969i	0.688774	−	0.724976i	$-0.258149\pi$
$499$	−6.33204	−	10.9674i	−0.283461	−	0.490969i	−0.972235	+	0.234008i	$0.924816\pi$
$500$	0.564635			0.0252512
$501$	9.64201	+	14.5775i	0.430773	+	0.651275i
$502$	24.5005			1.09351
$503$	−2.36917			−0.105636			−0.0528180	−	0.998604i	$-0.516820\pi$
$503$	−2.36917			−0.105636			−0.0528180	+	0.998604i	$0.516820\pi$
$504$	−16.8187	+	17.6609i	−0.749164	+	0.786680i
$505$	−10.2585			−0.456498
$506$	−0.0818208			−0.00363738
$507$	−0.139818	+	0.00850721i	−0.00620953	+	0.000377818i
$508$	5.08210			0.225482
$509$	8.31506	+	14.4021i	0.368559	+	0.638362i	0.989340	−	0.145621i	$-0.0465180\pi$
$509$	8.31506	+	14.4021i	0.368559	+	0.638362i	−0.620782	+	0.783983i	$0.713185\pi$
$510$	−3.70764	−	5.60549i	−0.164177	−	0.248215i
$511$	−27.5437	+	22.6533i	−1.21846	+	1.00212i
$512$	−23.5620			−1.04130
$513$	3.31006	−	9.31919i	0.146143	−	0.411452i
$514$	6.85601	+	11.8750i	0.302406	+	0.523782i
$515$	−1.94910	+	3.37595i	−0.0858878	+	0.148762i
$516$	1.52449	−	0.0927572i	0.0671118	−	0.00408341i
$517$	−0.492587	+	0.853186i	−0.0216640	+	0.0375231i
$518$	−9.49739	−	3.56311i	−0.417291	−	0.156554i
$519$	−2.51192	+	5.03415i	−0.110261	+	0.220975i
$520$	11.0439			0.484308
$521$	5.90682	+	10.2309i	0.258783	+	0.448225i	0.965916	−	0.258856i	$-0.0833454\pi$
$521$	5.90682	+	10.2309i	0.258783	+	0.448225i	−0.707134	+	0.707080i	$0.750012\pi$
$522$	4.43140	−	10.4214i	0.193957	−	0.456131i
$523$	0.674962	−	1.16907i	0.0295140	−	0.0511198i	−0.850891	−	0.525342i	$-0.823937\pi$
$523$	0.674962	−	1.16907i	0.0295140	−	0.0511198i	0.880405	+	0.474222i	$0.157271\pi$
$524$	2.61033	+	4.52122i	0.114033	+	0.197511i
$525$	3.35598	−	3.12048i	0.146467	−	0.136189i
$526$	3.29280	−	5.70330i	0.143573	−	0.248676i
$527$	9.42293	+	16.3210i	0.410469	+	0.710953i
$528$	0.277357	+	0.419330i	0.0120704	+	0.0182490i
$529$	11.3198	−	19.6064i	0.492163	−	0.852451i
$530$	6.64376	−	11.5073i	0.288586	−	0.499846i
$531$	−25.8465	−	34.3447i	−1.12164	−	1.49043i
$532$	−2.66206	−	0.998716i	−0.115415	−	0.0432998i
$533$	17.0704	+	29.5668i	0.739402	+	1.28068i
$534$	−2.80115	−	4.23499i	−0.121218	−	0.183266i
$535$	10.7016			0.462672
$536$	−14.2320			−0.614728
$537$	25.2150	−	1.53421i	1.08811	−	0.0662058i
$538$	−1.70578	−	2.95450i	−0.0735413	−	0.127377i
$539$	0.153682	−	0.781239i	0.00661955	−	0.0336504i
$540$	−1.90331	−	2.23278i	−0.0819056	−	0.0960837i
$541$	−0.745947	+	1.29202i	−0.0320708	+	0.0555482i	−0.881615	−	0.471969i	$-0.843544\pi$
$541$	−0.745947	+	1.29202i	−0.0320708	+	0.0555482i	0.849545	+	0.527517i	$0.176877\pi$
$542$	14.4803	−	25.0805i	0.621980	−	1.07730i
$543$	5.59510	−	11.2132i	0.240109	−	0.481202i
$544$	5.00033	+	8.66083i	0.214388	+	0.371330i
$545$	4.95253	−	8.57803i	0.212143	−	0.367443i
$546$	14.4517	−	13.4375i	0.618474	−	0.575072i
$547$	22.3572	+	38.7239i	0.955927	+	1.65571i	0.732232	+	0.681055i	$0.238478\pi$
$547$	22.3572	+	38.7239i	0.955927	+	1.65571i	0.223694	+	0.974659i	$0.428188\pi$
$548$	−3.47451	+	6.01802i	−0.148424	+	0.257077i
$549$	24.5191	+	32.5809i	1.04645	+	1.39052i
$550$	−0.0681368	−	0.118016i	−0.00290536	−	0.00503224i
$551$	5.99666			0.255466
$552$	3.18946	−	0.194062i	0.135752	−	0.00825984i
$553$	−7.57381	−	45.5741i	−0.322071	−	1.93801i
$554$	14.5838	−	25.2598i	0.619604	−	1.07319i
$555$	2.47476	−	4.95967i	0.105048	−	0.210526i
$556$	5.84515	−	10.1241i	0.247890	−	0.429357i
$557$	−1.83356	−	3.17581i	−0.0776903	−	0.134564i	0.824563	−	0.565771i	$-0.191421\pi$
$557$	−1.83356	−	3.17581i	−0.0776903	−	0.134564i	−0.902253	+	0.431207i	$0.858088\pi$
$558$	−12.5760	−	16.7109i	−0.532384	−	0.707429i
$559$	−5.61325			−0.237415
$560$	5.21464	−	4.28877i	0.220359	−	0.181234i
$561$	0.284884	−	0.570937i	0.0120278	−	0.0241050i
$562$	−6.06085	−	10.4977i	−0.255662	−	0.442819i
$563$	32.7475			1.38014			0.690072	−	0.723741i	$-0.257579\pi$
$563$	32.7475			1.38014			0.690072	+	0.723741i	$0.257579\pi$
$564$	3.78193	−	7.57937i	0.159248	−	0.319149i
$565$	−8.39243			−0.353072
$566$	19.3224			0.812181
$567$	−23.6522	−	2.75212i	−0.993298	−	0.115578i
$568$	−20.4255			−0.857035
$569$	−19.3140			−0.809684			−0.404842	−	0.914387i	$-0.632673\pi$
$569$	−19.3140			−0.809684			−0.404842	+	0.914387i	$0.632673\pi$
$570$	−1.76336	+	3.53395i	−0.0738590	+	0.148021i
$571$	−19.7075			−0.824733			−0.412367	−	0.911018i	$-0.635298\pi$
$571$	−19.7075			−0.824733			−0.412367	+	0.911018i	$0.635298\pi$
$572$	0.115421	+	0.199915i	0.00482599	+	0.00835886i
$573$	−5.88732	+	11.7988i	−0.245946	+	0.492901i
$574$	28.1898	+	10.5759i	1.17662	+	0.441430i
$575$	−0.600415			−0.0250391
$576$	−15.8805	−	21.1019i	−0.661687	−	0.879245i
$577$	−5.79830	−	10.0429i	−0.241386	−	0.418093i	0.719723	−	0.694261i	$-0.244269\pi$
$577$	−5.79830	−	10.0429i	−0.241386	−	0.418093i	−0.961109	+	0.276168i	$0.910935\pi$
$578$	3.90010	−	6.75517i	0.162223	−	0.280978i
$579$	−7.97125	+	15.9752i	−0.331274	+	0.663906i
$580$	0.889510	−	1.54068i	0.0369349	−	0.0639731i
$581$	−0.0841487	+	0.0692081i	−0.00349108	+	0.00287124i
$582$	9.80044	−	0.596307i	0.406241	−	0.0247177i
$583$	1.26152			0.0522467
$584$	−20.7082	−	35.8676i	−0.856910	−	1.48421i
$585$	6.48389	+	8.61576i	0.268076	+	0.356218i
$586$	−4.06909	+	7.04787i	−0.168093	+	0.291145i
$587$	−3.95014	−	6.84185i	−0.163040	−	0.282393i	0.772918	−	0.634506i	$-0.218797\pi$
$587$	−3.95014	−	6.84185i	−0.163040	−	0.282393i	−0.935957	+	0.352113i	$0.885463\pi$
$588$	−0.910971	+	6.78495i	−0.0375678	+	0.279807i
$589$	5.53742	−	9.59110i	0.228166	−	0.395194i
$590$	8.58290	+	14.8660i	0.353352	+	0.612024i
$591$	9.33699	−	18.7123i	0.384072	−	0.769720i
$592$	4.08325	−	7.07240i	0.167821	−	0.290674i
$593$	0.0464247	−	0.0804099i	0.00190643	−	0.00330204i	−0.865071	−	0.501650i	$-0.832726\pi$
$593$	0.0464247	−	0.0804099i	0.00190643	−	0.00330204i	0.866977	+	0.498348i	$0.166060\pi$
$594$	−0.237002	+	0.667258i	−0.00972430	+	0.0273779i
$595$	−8.02284	−	3.00990i	−0.328904	−	0.123394i
$596$	−2.56639	−	4.44512i	−0.105124	−	0.182079i
$597$	22.2323	−	1.35272i	0.909907	−	0.0553632i
$598$	−2.58553			−0.105730
$599$	6.49795			0.265499			0.132750	−	0.991150i	$-0.457619\pi$
$599$	6.49795			0.265499			0.132750	+	0.991150i	$0.457619\pi$
$600$	2.93595	+	4.43879i	0.119860	+	0.181213i
$601$	−2.30404	−	3.99071i	−0.0939836	−	0.162784i	0.815200	−	0.579179i	$-0.196627\pi$
$601$	−2.30404	−	3.99071i	−0.0939836	−	0.162784i	−0.909184	+	0.416395i	$0.863293\pi$
$602$	−3.82328	+	3.14446i	−0.155825	+	0.128158i
$603$	−8.35560	−	11.1029i	−0.340267	−	0.452144i
$604$	−2.56859	+	4.44893i	−0.104515	+	0.181025i
$605$	−5.49353	+	9.51507i	−0.223344	+	0.386843i
$606$	−11.7438	−	17.7551i	−0.477059	−	0.721253i
$607$	0.887377	+	1.53698i	0.0360175	+	0.0623842i	0.883472	−	0.468483i	$-0.155199\pi$
$607$	0.887377	+	1.53698i	0.0360175	+	0.0623842i	−0.847455	+	0.530868i	$0.821866\pi$
$608$	2.93847	−	5.08957i	0.119171	−	0.206409i
$609$	−3.22769	−	14.0731i	−0.130792	−	0.570272i
$610$	−8.14211	−	14.1025i	−0.329664	−	0.570995i
$611$	−15.5657	+	26.9606i	−0.629721	+	1.09071i
$612$	−2.14678	+	5.04861i	−0.0867785	+	0.204078i
$613$	5.19451	+	8.99715i	0.209804	+	0.363392i	0.951653	−	0.307176i	$-0.0993840\pi$
$613$	5.19451	+	8.99715i	0.209804	+	0.363392i	−0.741848	+	0.670568i	$0.766051\pi$
$614$	−21.1681			−0.854276
$615$	−7.34550	+	14.7211i	−0.296199	+	0.593613i
$616$	0.865747	+	0.324800i	0.0348819	+	0.0130866i
$617$	−7.21167	+	12.4910i	−0.290331	+	0.502868i	−0.973888	−	0.227029i	$-0.927099\pi$
$617$	−7.21167	+	12.4910i	−0.290331	+	0.502868i	0.683557	+	0.729897i	$0.260432\pi$
$618$	−8.07429	+	0.491280i	−0.324796	+	0.0197622i
$619$	−3.33641	+	5.77882i	−0.134101	+	0.232271i	−0.925254	−	0.379349i	$-0.876148\pi$
$619$	−3.33641	+	5.77882i	−0.134101	+	0.232271i	0.791152	+	0.611619i	$0.209481\pi$
$620$	−1.64278	−	2.84538i	−0.0659756	−	0.114273i
$621$	2.02393	+	2.37428i	0.0812174	+	0.0952764i
$622$	26.2525			1.05263
$623$	−6.06132	−	2.27401i	−0.242841	−	0.0911061i
$624$	8.76447	+	13.2508i	0.350860	+	0.530456i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−22.9756			−0.918291
$627$	−0.374270	+	0.0227724i	−0.0149469	+	0.000909443i
$628$	−0.0246297			−0.000982833
$629$	−10.3644			−0.413255
$630$	9.24270	+	2.23617i	0.368238	+	0.0890910i
$631$	16.7108			0.665248			0.332624	−	0.943060i	$-0.392066\pi$
$631$	16.7108			0.665248			0.332624	+	0.943060i	$0.392066\pi$
$632$	53.6527			2.13419
$633$	12.4500	+	18.8229i	0.494843	+	0.748141i
$634$	1.00304			0.0398357
$635$	−4.50034	−	7.79482i	−0.178591	−	0.309328i
$636$	−10.8265	+	0.658738i	−0.429299	+	0.0261206i
$637$	4.85634	−	24.6871i	0.192415	−	0.978139i
$638$	−0.429364			−0.0169987
$639$	−11.9918	−	15.9347i	−0.474389	−	0.630366i
$640$	2.18562	+	3.78560i	0.0863942	+	0.149639i
$641$	12.9502	−	22.4303i	0.511501	−	0.885945i	−0.488410	−	0.872614i	$-0.662423\pi$
$641$	12.9502	−	22.4303i	0.511501	−	0.885945i	0.999911	−	0.0133311i	$-0.00424355\pi$
$642$	12.2511	+	18.5221i	0.483511	+	0.731008i
$643$	14.7993	−	25.6331i	0.583626	−	1.01087i	−0.411419	−	0.911446i	$-0.634967\pi$
$643$	14.7993	−	25.6331i	0.583626	−	1.01087i	0.995045	−	0.0994234i	$-0.0316998\pi$
$644$	0.692750	−	0.569752i	0.0272982	−	0.0224514i
$645$	−1.49225	−	2.25609i	−0.0587571	−	0.0888334i
$646$	7.38502			0.290560
$647$	−8.82748	−	15.2896i	−0.347044	−	0.601098i	0.638679	−	0.769473i	$-0.279481\pi$
$647$	−8.82748	−	15.2896i	−0.347044	−	0.601098i	−0.985723	+	0.168375i	$0.946148\pi$
$648$	7.65597	−	26.5725i	0.300755	−	1.04387i
$649$	−0.814860	+	1.41138i	−0.0319861	+	0.0554015i
$650$	−2.15312	−	3.72931i	−0.0844522	−	0.146276i
$651$	−25.4892	−	7.83301i	−0.998999	−	0.307000i
$652$	−3.85665	+	6.67992i	−0.151038	+	0.261606i
$653$	−0.409006	−	0.708418i	−0.0160056	−	0.0277226i	0.857912	−	0.513797i	$-0.171762\pi$
$653$	−0.409006	−	0.708418i	−0.0160056	−	0.0277226i	−0.873917	+	0.486075i	$0.838428\pi$
$654$	20.5162	−	1.24831i	0.802246	−	0.0488126i
$655$	4.62304	−	8.00735i	0.180637	−	0.312873i
$656$	−12.1198	+	20.9921i	−0.473198	+	0.819603i
$657$	15.8238	−	37.2131i	0.617346	−	1.45182i
$658$	4.50084	+	27.0830i	0.175461	+	1.05581i
$659$	−12.5468	−	21.7318i	−0.488755	−	0.846549i	0.511161	−	0.859485i	$-0.329216\pi$
$659$	−12.5468	−	21.7318i	−0.488755	−	0.846549i	−0.999916	+	0.0129359i	$0.995882\pi$
$660$	−0.0496663	+	0.0995362i	−0.00193326	+	0.00387444i
$661$	−41.0131			−1.59522			−0.797612	−	0.603171i	$-0.793904\pi$
$661$	−41.0131			−1.59522			−0.797612	+	0.603171i	$0.793904\pi$
$662$	30.5671			1.18802
$663$	9.00232	−	18.0416i	0.349621	−	0.700676i
$664$	−0.0632655	−	0.109579i	−0.00245518	−	0.00425249i
$665$	0.825516	+	4.96740i	0.0320121	+	0.192628i
$666$	11.4171	−	1.39451i	0.442404	−	0.0540361i
$667$	−0.945878	+	1.63831i	−0.0366246	+	0.0634356i
$668$	−2.84881	+	4.93428i	−0.110224	+	0.190913i
$669$	−44.3337	+	2.69748i	−1.71404	+	0.104291i
$670$	2.77466	+	4.80585i	0.107195	+	0.185666i
$671$	0.773012	−	1.33890i	0.0298418	−	0.0516875i
$672$	−13.5260	−	4.15663i	−0.521776	−	0.160346i
$673$	9.07484	+	15.7181i	0.349809	+	0.605888i	0.986215	−	0.165467i	$-0.0529130\pi$
$673$	9.07484	+	15.7181i	0.349809	+	0.605888i	−0.636406	+	0.771354i	$0.719580\pi$
$674$	13.5316	−	23.4374i	0.521218	−	0.902776i
$675$	−1.73916	+	4.89646i	−0.0669404	+	0.188465i
$676$	−0.0228319	−	0.0395460i	−0.000878150	−	0.00152100i
$677$	−35.6203			−1.36900			−0.684500	−	0.729012i	$-0.739980\pi$
$677$	−35.6203			−1.36900			−0.684500	+	0.729012i	$0.739980\pi$
$678$	−9.60752	−	14.5254i	−0.368975	−	0.557843i
$679$	9.66860	−	7.95193i	0.371047	−	0.305167i
$680$	4.97566	−	8.61810i	0.190808	−	0.330489i
$681$	−24.8780	−	37.6124i	−0.953325	−	1.44131i
$682$	−0.396482	+	0.686727i	−0.0151821	+	0.0262961i
$683$	25.2198	+	43.6820i	0.965009	+	1.67144i	0.709591	+	0.704614i	$0.248880\pi$
$683$	25.2198	+	43.6820i	0.965009	+	1.67144i	0.255418	+	0.966831i	$0.417787\pi$
$684$	3.20014	−	0.390872i	0.122360	−	0.0149454i
$685$	12.3071			0.470230
$686$	−10.5216	−	19.5353i	−0.401717	−	0.745860i
$687$	−2.57819	+	0.156870i	−0.0983640	+	0.00598495i
$688$	−1.99267	−	3.45140i	−0.0759697	−	0.131583i
$689$	39.8638			1.51869
$690$	−0.687346	−	1.03918i	−0.0261668	−	0.0395610i
$691$	8.16900			0.310763			0.155382	−	0.987855i	$-0.450339\pi$
$691$	8.16900			0.310763			0.155382	+	0.987855i	$0.450339\pi$
$692$	−1.83405			−0.0697200
$693$	0.254893	+	0.866090i	0.00968257	+	0.0329000i
$694$	−30.1699			−1.14523
$695$	−20.7042			−0.785355
$696$	16.7370	−	1.01836i	0.634415	−	0.0386010i
$697$	30.7632			1.16524
$698$	−2.29398	−	3.97330i	−0.0868286	−	0.150391i
$699$	5.57701	+	8.43173i	0.210942	+	0.318917i
$700$	1.39869	+	0.524742i	0.0528655	+	0.0198334i
$701$	−50.2753			−1.89887			−0.949437	−	0.313959i	$-0.898345\pi$
$701$	−50.2753			−1.89887			−0.949437	+	0.313959i	$0.898345\pi$
$702$	−7.48924	+	21.0853i	−0.282663	+	0.795814i
$703$	3.04534	+	5.27468i	0.114857	+	0.198938i
$704$	−0.500662	+	0.867173i	−0.0188694	+	0.0326828i
$705$	−14.9741	+	0.911098i	−0.563957	+	0.0343139i
$706$	21.2694	−	36.8396i	0.800484	−	1.38648i
$707$	−25.4120	−	9.53373i	−0.955715	−	0.358553i
$708$	6.25625	−	12.5381i	0.235124	−	0.471212i
$709$	45.2555			1.69961			0.849804	−	0.527099i	$-0.176720\pi$
$709$	45.2555			1.69961			0.849804	+	0.527099i	$0.176720\pi$
$710$	3.98215	+	6.89728i	0.149447	+	0.258850i
$711$	31.4995	+	41.8564i	1.18132	+	1.56974i
$712$	3.75915	−	6.51104i	0.140880	−	0.244012i
$713$	1.74688	+	3.02569i	0.0654212	+	0.113313i
$714$	−3.97496	−	17.3314i	−0.148759	−	0.648610i
$715$	0.204417	−	0.354061i	0.00764476	−	0.0132411i
$716$	4.11755	+	7.13180i	0.153880	+	0.266528i
$717$	−2.95436	−	4.46663i	−0.110333	−	0.166809i
$718$	22.3810	−	38.7651i	0.835252	−	1.44670i
$719$	−1.80843	+	3.13229i	−0.0674431	+	0.116815i	−0.897775	−	0.440454i	$-0.854817\pi$
$719$	−1.80843	+	3.13229i	−0.0674431	+	0.116815i	0.830332	+	0.557269i	$0.188151\pi$
$720$	−2.99580	+	7.04527i	−0.111647	+	0.262562i
$721$	−7.96567	+	6.55136i	−0.296657	+	0.243985i
$722$	9.21172	+	15.9552i	0.342825	+	0.593790i
$723$	21.4126	+	32.3731i	0.796342	+	1.20397i
$724$	4.08519			0.151825
$725$	−3.15075			−0.117016
$726$	−22.7573	+	1.38467i	−0.844603	+	0.0513898i
$727$	2.79978	+	4.84936i	0.103838	+	0.179853i	0.913263	−	0.407371i	$-0.133554\pi$
$727$	2.79978	+	4.84936i	0.103838	+	0.179853i	−0.809425	+	0.587223i	$0.800221\pi$
$728$	27.3575	+	10.2636i	1.01394	+	0.380396i
$729$	25.2250	−	9.62805i	0.934259	−	0.356594i
$730$	−8.07451	+	13.9855i	−0.298851	+	0.517625i
$731$	−2.52896	+	4.38029i	−0.0935370	+	0.162011i
$732$	−5.93495	+	11.8942i	−0.219362	+	0.439623i
$733$	3.88698	+	6.73245i	0.143569	+	0.248669i	0.928838	−	0.370486i	$-0.120809\pi$
$733$	3.88698	+	6.73245i	0.143569	+	0.248669i	−0.785269	+	0.619154i	$0.787475\pi$
$734$	−17.0996	+	29.6174i	−0.631159	+	1.09320i
$735$	11.2133	−	4.61104i	0.413609	−	0.170081i
$736$	0.926993	+	1.60560i	0.0341694	+	0.0591832i
$737$	−0.263426	+	0.456268i	−0.00970343	+	0.0168068i
$738$	−33.8879	+	4.13914i	−1.24743	+	0.152364i
$739$	−10.0240	−	17.3620i	−0.368738	−	0.638673i	0.620631	−	0.784103i	$-0.286877\pi$
$739$	−10.0240	−	17.3620i	−0.368738	−	0.638673i	−0.989369	+	0.145430i	$0.953543\pi$
$740$	1.80691			0.0664234
$741$	−11.8269	+	0.719607i	−0.434472	+	0.0264354i
$742$	27.1519	−	22.3311i	0.996779	−	0.819801i
$743$	12.2777	−	21.2656i	0.450425	−	0.780159i	−0.547987	−	0.836487i	$-0.684606\pi$
$743$	12.2777	−	21.2656i	0.450425	−	0.780159i	0.998412	+	0.0563275i	$0.0179391\pi$
$744$	13.8265	−	27.7097i	0.506904	−	1.01589i
$745$	−4.54523	+	7.87257i	−0.166524	+	0.288428i
$746$	−13.0671	−	22.6329i	−0.478421	−	0.828650i
$747$	0.0483434	−	0.113690i	0.00176879	−	0.00415969i
$748$	0.208004			0.00760539
$749$	26.5096	+	9.94554i	0.968641	+	0.363402i
$750$	0.926499	−	1.85680i	0.0338310	−	0.0678006i
$751$	21.2934	+	36.8813i	0.777008	+	1.34582i	0.933659	+	0.358164i	$0.116597\pi$
$751$	21.2934	+	36.8813i	0.777008	+	1.34582i	−0.156651	+	0.987654i	$0.550070\pi$
$752$	−22.1029			−0.806010
$753$	−15.8146	+	31.6940i	−0.576316	+	1.15500i
$754$	−13.5679			−0.494112
$755$	9.09825			0.331119
$756$	−2.63978	−	7.29980i	−0.0960077	−	0.265491i
$757$	23.3325			0.848034			0.424017	−	0.905654i	$-0.360620\pi$
$757$	23.3325			0.848034			0.424017	+	0.905654i	$0.360620\pi$
$758$	−13.7992			−0.501208
$759$	0.0528136	−	0.105844i	0.00191701	−	0.00384189i
$760$	−5.84794			−0.212127
$761$	−10.0625	−	17.4288i	−0.364766	−	0.631794i	0.623972	−	0.781446i	$-0.285518\pi$
$761$	−10.0625	−	17.4288i	−0.364766	−	0.631794i	−0.988739	+	0.149653i	$0.952184\pi$
$762$	8.33912	−	16.7124i	0.302095	−	0.605428i
$763$	20.2402	−	16.6465i	0.732744	−	0.602645i
$764$	−4.29854			−0.155516
$765$	9.64450	−	1.17800i	0.348698	−	0.0425906i
$766$	−1.83682	−	3.18146i	−0.0663669	−	0.114951i
$767$	−25.7495	+	44.5995i	−0.929762	+	1.61039i
$768$	9.56569	−	19.1706i	0.345172	−	0.691760i
$769$	−1.23565	+	2.14022i	−0.0445588	+	0.0771782i	−0.887445	−	0.460914i	$-0.847522\pi$
$769$	−1.23565	+	2.14022i	−0.0445588	+	0.0771782i	0.842886	+	0.538092i	$0.180855\pi$
$770$	−0.0591073	−	0.355668i	−0.00213008	−	0.0128174i
$771$	−19.7869	+	1.20393i	−0.712609	+	0.0433586i
$772$	−5.82009			−0.209470
$773$	−14.8023	−	25.6384i	−0.532403	−	0.922149i	−0.999284	−	0.0378289i	$-0.987956\pi$
$773$	−14.8023	−	25.6384i	−0.532403	−	0.922149i	0.466881	−	0.884320i	$-0.345378\pi$
$774$	2.19647	−	5.16547i	0.0789505	−	0.185669i
$775$	−2.90945	+	5.03932i	−0.104511	+	0.181018i
$776$	7.26914	+	12.5905i	0.260947	+	0.451973i
$777$	10.7396	−	9.98597i	0.385282	−	0.358245i
$778$	−3.38339	+	5.86021i	−0.121301	+	0.210099i
$779$	−9.03907	−	15.6561i	−0.323858	−	0.560939i
$780$	−1.56945	+	3.14534i	−0.0561954	+	0.112621i
$781$	−0.378065	+	0.654828i	−0.0135282	+	0.0234316i
$782$	−1.16487	+	2.01761i	−0.0416557	+	0.0721497i
$783$	10.6208	+	12.4593i	0.379556	+	0.445258i
$784$	16.9032	−	5.77776i	0.603687	−	0.206349i
$785$	0.0218103	+	0.0377766i	0.000778444	+	0.00134830i
$786$	19.1513	−	1.16526i	0.683103	−	0.0415633i
$787$	−26.3687			−0.939941			−0.469971	−	0.882682i	$-0.655735\pi$
$787$	−26.3687			−0.939941			−0.469971	+	0.882682i	$0.655735\pi$
$788$	6.81727			0.242855
$789$	5.25239	+	7.94095i	0.186990	+	0.282705i
$790$	−10.4601	−	18.1174i	−0.372154	−	0.644589i
$791$	−20.7894	−	7.79949i	−0.739185	−	0.277318i
$792$	−1.04074	+	0.127118i	−0.0369811	+	0.00451695i
$793$	24.4271	−	42.3090i	0.867432	−	1.50244i
$794$	−21.6181	+	37.4436i	−0.767197	+	1.32882i
$795$	10.5975	+	16.0221i	0.375856	+	0.568247i
$796$	3.63047	+	6.28816i	0.128679	+	0.222878i
$797$	−6.17736	+	10.6995i	−0.218813	+	0.378996i	−0.954445	−	0.298385i	$-0.903552\pi$
$797$	−6.17736	+	10.6995i	−0.218813	+	0.378996i	0.735632	+	0.677381i	$0.236885\pi$
$798$	−7.65239	+	7.11538i	−0.270892	+	0.251882i
$799$	14.0258	+	24.2933i	0.496196	+	0.859437i
$800$	−1.54392	+	2.67415i	−0.0545858	+	0.0945454i
$801$	7.28650	−	0.889987i	0.257456	−	0.0314462i
$802$	−17.5919	−	30.4701i	−0.621193	−	1.07594i
$803$	−1.53319			−0.0541050
$804$	2.02251	−	4.05331i	0.0713283	−	0.142949i
$805$	−1.48732	−	0.557995i	−0.0524213	−	0.0196667i
$806$	−12.5288	+	21.7005i	−0.441308	+	0.764368i
$807$	4.92300	−	0.299539i	0.173298	−	0.0105443i
$808$	15.7602	−	27.2974i	0.554441	−	0.960320i
$809$	−4.41689	−	7.65028i	−0.155290	−	0.268970i	0.777875	−	0.628419i	$-0.216298\pi$
$809$	−4.41689	−	7.65028i	−0.155290	−	0.268970i	−0.933164	+	0.359450i	$0.882964\pi$
$810$	−10.4656	+	2.59530i	−0.367724	+	0.0911895i
$811$	−3.11073			−0.109233			−0.0546163	−	0.998507i	$-0.517394\pi$
$811$	−3.11073			−0.109233			−0.0546163	+	0.998507i	$0.517394\pi$
$812$	3.63528	−	2.98984i	0.127573	−	0.104923i
$813$	23.0976	+	34.9207i	0.810069	+	1.22472i
$814$	−0.218048	−	0.377669i	−0.00764256	−	0.0132373i
$815$	13.6607			0.478514
$816$	14.2889	−	0.869408i	0.500212	−	0.0304354i
$817$	2.97231			0.103988
$818$	32.7434			1.14485
$819$	8.05459	+	27.3684i	0.281450	+	0.956329i
$820$	−5.36322			−0.187292
$821$	−56.5411			−1.97330			−0.986650	−	0.162857i	$-0.947929\pi$
$821$	−56.5411			−1.97330			−0.986650	+	0.162857i	$0.947929\pi$
$822$	14.0890	+	21.3008i	0.491409	+	0.742949i
$823$	−25.0291			−0.872458			−0.436229	−	0.899836i	$-0.643686\pi$
$823$	−25.0291			−0.872458			−0.436229	+	0.899836i	$0.643686\pi$
$824$	−5.98883	−	10.3730i	−0.208631	−	0.361359i
$825$	0.196648	−	0.0119650i	0.00684639	−	0.000416568i
$826$	7.44549	+	44.8020i	0.259062	+	1.55886i
$827$	8.46606			0.294394			0.147197	−	0.989107i	$-0.452975\pi$
$827$	8.46606			0.294394			0.147197	+	0.989107i	$0.452975\pi$
$828$	−0.397984	+	0.935944i	−0.0138309	+	0.0325263i
$829$	−14.6895	−	25.4430i	−0.510189	−	0.883673i	−0.999930	−	0.0118051i	$-0.996242\pi$
$829$	−14.6895	−	25.4430i	−0.510189	−	0.883673i	0.489742	−	0.871868i	$-0.337091\pi$
$830$	−0.0246684	+	0.0427270i	−0.000856254	+	0.00148308i
$831$	23.2627	+	35.1703i	0.806975	+	1.22004i
$832$	−15.8209	+	27.4026i	−0.548491	+	0.950014i
$833$	−17.0766	−	14.9120i	−0.591669	−	0.516671i
$834$	−23.7018	−	35.8342i	−0.820727	−	1.24084i
$835$	10.0908			0.349206
$836$	−0.0611173	−	0.105858i	−0.00211379	−	0.00366118i
$837$	29.7349	−	5.48183i	1.02779	−	0.189480i
$838$	3.58394	−	6.20757i	0.123805	−	0.214437i
$839$	18.6218	+	32.2540i	0.642897	+	1.11353i	0.984783	+	0.173789i	$0.0556010\pi$
$839$	18.6218	+	32.2540i	0.642897	+	1.11353i	−0.341886	+	0.939741i	$0.611066\pi$
$840$	3.14764	+	13.7241i	0.108604	+	0.473527i
$841$	9.53640	−	16.5175i	0.328841	−	0.569570i
$842$	15.1248	+	26.1970i	0.521236	+	0.902807i
$843$	17.4921	−	1.06430i	0.602458	−	0.0366565i
$844$	−3.67845	+	6.37126i	−0.126617	+	0.219308i
$845$	−0.0404366	+	0.0700382i	−0.00139106	+	0.00240939i
$846$	−18.7190	−	24.8737i	−0.643573	−	0.855176i
$847$	−22.4512	+	18.4649i	−0.771431	+	0.634463i
$848$	14.1514	+	24.5109i	0.485961	+	0.841709i
$849$	−12.4722	+	24.9956i	−0.428045	+	0.857846i
$850$	−3.88021			−0.133090
$851$	−1.92142			−0.0658653
$852$	2.90267	−	5.81724i	0.0994438	−	0.199295i
$853$	−17.8799	−	30.9688i	−0.612195	−	1.06035i	−0.990870	−	0.134823i	$-0.956954\pi$
$853$	−17.8799	−	30.9688i	−0.612195	−	1.06035i	0.378675	−	0.925530i	$-0.376380\pi$
$854$	−7.06312	−	42.5011i	−0.241695	−	1.45436i
$855$	−3.43333	−	4.56219i	−0.117417	−	0.156023i
$856$	−16.4410	+	28.4766i	−0.561940	+	0.973309i
$857$	4.92399	−	8.52860i	0.168200	−	0.291331i	−0.769587	−	0.638542i	$-0.779538\pi$
$857$	4.92399	−	8.52860i	0.168200	−	0.291331i	0.937787	+	0.347211i	$0.112871\pi$
$858$	0.846811	−	0.0515241i	0.0289097	−	0.00175901i
$859$	−0.178891	−	0.309849i	−0.00610369	−	0.0105719i	0.862957	−	0.505277i	$-0.168610\pi$
$859$	−0.178891	−	0.309849i	−0.00610369	−	0.0105719i	−0.869061	+	0.494705i	$0.835276\pi$
$860$	0.440895	−	0.763653i	0.0150344	−	0.0260403i
$861$	−31.8770	+	29.6400i	−1.08637	+	1.01013i
$862$	14.6940	+	25.4507i	0.500479	+	0.866854i
$863$	−5.16897	+	8.95291i	−0.175954	+	0.304761i	−0.940491	−	0.339819i	$-0.889634\pi$
$863$	−5.16897	+	8.95291i	−0.175954	+	0.304761i	0.764537	+	0.644580i	$0.222968\pi$
$864$	15.7790	−	2.90897i	0.536812	−	0.0989650i
$865$	1.62410	+	2.81302i	0.0552211	+	0.0956457i
$866$	−12.0899			−0.410832
$867$	6.22110	+	9.40552i	0.211280	+	0.319428i
$868$	−1.42508	−	8.57516i	−0.0483703	−	0.291060i
$869$	0.993082	−	1.72007i	0.0336880	−	0.0583493i
$870$	−3.60692	−	5.45322i	−0.122286	−	0.184881i
$871$	−8.32425	+	14.4180i	−0.282057	+	0.488536i
$872$	15.2172	+	26.3569i	0.515318	+	0.892558i
$873$	−5.55460	+	13.0628i	−0.187995	+	0.442109i
$874$	1.36908			0.0463099
$875$	−0.433740	−	2.60996i	−0.0146631	−	0.0882326i
$876$	13.1580	−	0.800598i	0.444568	−	0.0270497i
$877$	7.29934	+	12.6428i	0.246481	+	0.426918i	0.962547	−	0.271115i	$-0.0873924\pi$
$877$	7.29934	+	12.6428i	0.246481	+	0.426918i	−0.716066	+	0.698033i	$0.754059\pi$
$878$	−3.54714			−0.119710
$879$	−6.49065	−	9.81306i	−0.218924	−	0.330986i
$880$	0.290267			0.00978489
$881$	−42.5010			−1.43189			−0.715947	−	0.698154i	$-0.754005\pi$
$881$	−42.5010			−1.43189			−0.715947	+	0.698154i	$0.754005\pi$
$882$	20.8175	+	14.1290i	0.700960	+	0.475749i
$883$	−50.9798			−1.71561			−0.857804	−	0.513978i	$-0.828171\pi$
$883$	−50.9798			−1.71561			−0.857804	+	0.513978i	$0.828171\pi$
$884$	6.57292			0.221071
$885$	−24.7708	+	1.50718i	−0.832663	+	0.0506633i
$886$	−36.9338			−1.24081
$887$	−8.54995	−	14.8090i	−0.287079	−	0.497236i	0.686032	−	0.727571i	$-0.259351\pi$
$887$	−8.54995	−	14.8090i	−0.287079	−	0.497236i	−0.973111	+	0.230335i	$0.926018\pi$
$888$	9.39547	+	14.2048i	0.315291	+	0.476681i
$889$	−3.90396	−	23.4914i	−0.130935	−	0.787876i
$890$	−2.93153			−0.0982651
$891$	−0.710189	−	0.737288i	−0.0237922	−	0.0247001i
$892$	−7.23957	−	12.5393i	−0.242399	−	0.419847i
$893$	8.24230	−	14.2761i	0.275818	−	0.477731i
$894$	−18.8289	+	1.14564i	−0.629733	+	0.0383160i
$895$	7.29241	−	12.6308i	0.243758	−	0.422202i
$896$	1.89598	+	11.4087i	0.0633403	+	0.381139i
$897$	1.66891	−	3.34466i	0.0557232	−	0.111675i
$898$	−32.9970			−1.10112
$899$	9.16695	+	15.8776i	0.305735	+	0.529549i
$900$	−1.68141	+	0.205371i	−0.0560469	+	0.00684569i
$901$	17.9600	−	31.1077i	0.598335	−	1.03635i
$902$	0.647202	+	1.12099i	0.0215495	+	0.0373247i
$903$	−1.59984	−	6.97550i	−0.0532392	−	0.232130i
$904$	12.8933	−	22.3319i	0.428825	−	0.742747i
$905$	−3.61755	−	6.26578i	−0.120251	−	0.208282i
$906$	10.4155	+	15.7470i	0.346033	+	0.523158i
$907$	9.03355	−	15.6466i	0.299954	−	0.519536i	−0.676171	−	0.736745i	$-0.736362\pi$
$907$	9.03355	−	15.6466i	0.299954	−	0.519536i	0.976125	+	0.217209i	$0.0696953\pi$
$908$	7.35038	−	12.7312i	0.243931	−	0.422501i
$909$	30.5485	−	3.73126i	1.01323	−	0.123758i
$910$	−1.86779	−	11.2391i	−0.0619165	−	0.372572i
$911$	−23.2208	−	40.2197i	−0.769340	−	1.33254i	−0.937921	−	0.346849i	$-0.887252\pi$
$911$	−23.2208	−	40.2197i	−0.769340	−	1.33254i	0.168581	−	0.985688i	$-0.446082\pi$
$912$	−4.64093	−	7.01651i	−0.153677	−	0.232340i
$913$	−0.00468404			−0.000155019
$914$	−7.90300			−0.261408
$915$	23.4987	−	1.42978i	0.776843	−	0.0472669i
$916$	−0.421011	−	0.729213i	−0.0139106	−	0.0240939i
$917$	18.8936	−	15.5390i	0.623922	−	0.513144i
$918$	13.0797	+	15.3439i	0.431695	+	0.506423i
$919$	8.01109	−	13.8756i	0.264262	−	0.457714i	−0.703108	−	0.711083i	$-0.748205\pi$
$919$	8.01109	−	13.8756i	0.264262	−	0.457714i	0.967370	+	0.253368i	$0.0815384\pi$
$920$	0.922420	−	1.59768i	0.0304113	−	0.0526739i
$921$	13.6636	−	27.3832i	0.450231	−	0.902308i
$922$	16.9995	+	29.4440i	0.559848	+	0.969686i
$923$	−11.9468	+	20.6925i	−0.393235	+	0.681103i
$924$	−0.215535	+	0.200410i	−0.00709058	+	0.00659300i
$925$	−1.60007	−	2.77141i	−0.0526100	−	0.0911232i
$926$	−16.2655	+	28.1727i	−0.534518	+	0.925812i
$927$	4.57627	−	10.7621i	0.150304	−	0.353473i
$928$	4.86450	+	8.42556i	0.159685	+	0.276583i
$929$	−10.3972			−0.341121			−0.170561	−	0.985347i	$-0.554558\pi$
$929$	−10.3972			−0.341121			−0.170561	+	0.985347i	$0.554558\pi$
$930$	−12.0526	+	0.733340i	−0.395221	+	0.0240472i
$931$	−2.57151	+	13.0722i	−0.0842778	+	0.428425i
$932$	−1.64777	+	2.85402i	−0.0539745	+	0.0934865i
$933$	−16.9455	+	33.9605i	−0.554770	+	1.11182i
$934$	−3.05893	+	5.29823i	−0.100091	+	0.173363i
$935$	−0.184194	−	0.319033i	−0.00602378	−	0.0104335i
$936$	−32.8874	+	4.01693i	−1.07496	+	0.131297i
$937$	33.7051			1.10110			0.550549	−	0.834803i	$-0.314418\pi$
$937$	33.7051			1.10110			0.550549	+	0.834803i	$0.314418\pi$
$938$	2.40696	+	14.4835i	0.0785901	+	0.472903i
$939$	14.8303	−	29.7214i	0.483969	−	0.969922i
$940$	−2.44523	−	4.23527i	−0.0797547	−	0.138139i
$941$	−43.5453			−1.41954			−0.709768	−	0.704435i	$-0.751200\pi$
$941$	−43.5453			−1.41954			−0.709768	+	0.704435i	$0.751200\pi$
$942$	−0.0404145	+	0.0809947i	−0.00131677	+	0.00263895i
$943$	5.70308			0.185718
$944$	−36.5636			−1.19005
$945$	−8.85869	+	10.5130i	−0.288173	+	0.341989i
$946$	−0.212819			−0.00691933
$947$	40.8971			1.32898			0.664488	−	0.747299i	$-0.268650\pi$
$947$	40.8971			1.32898			0.664488	+	0.747299i	$0.268650\pi$
$948$	−7.62458	+	15.2804i	−0.247635	+	0.496285i
$949$	−48.4486			−1.57271
$950$	1.14011	+	1.97473i	0.0369901	+	0.0640687i
$951$	−0.647440	+	1.29754i	−0.0209947	+	0.0420755i
$952$	20.3347	−	16.7243i	0.659052	−	0.542037i
$953$	60.8815			1.97215			0.986073	−	0.166314i	$-0.0531865\pi$
$953$	60.8815			1.97215			0.986073	+	0.166314i	$0.0531865\pi$
$954$	−15.5988	+	36.6838i	−0.505029	+	1.18768i
$955$	3.80648	+	6.59302i	0.123175	+	0.213345i
$956$	0.872889	−	1.51189i	0.0282312	−	0.0488979i
$957$	0.277145	−	0.555427i	0.00895884	−	0.0179544i
$958$	10.2032	−	17.6724i	0.329650	−	0.570970i
$959$	30.4866	+	11.4376i	0.984465	+	0.369339i
$960$	−15.2196	+	0.926034i	−0.491210	+	0.0298876i
$961$	2.85971			0.0922487
$962$	−6.89029	−	11.9343i	−0.222152	−	0.384778i
$963$	−31.8681	+	3.89243i	−1.02693	+	0.125432i
$964$	−6.32650	+	10.9578i	−0.203763	+	0.352928i
$965$	5.15386	+	8.92675i	0.165909	+	0.287362i
$966$	−0.736904	−	3.21300i	−0.0237095	−	0.103377i
$967$	−11.8510	+	20.5265i	−0.381102	+	0.660088i	−0.991220	−	0.132222i	$-0.957789\pi$
$967$	−11.8510	+	20.5265i	−0.381102	+	0.660088i	0.610118	+	0.792311i	$0.291122\pi$
$968$	−16.8795	−	29.2361i	−0.542526	−	0.939683i
$969$	−4.76688	+	9.55330i	−0.153134	+	0.306896i
$970$	2.83438	−	4.90928i	0.0910063	−	0.157628i
$971$	25.0995	−	43.4737i	0.805483	−	1.39514i	−0.110482	−	0.993878i	$-0.535239\pi$
$971$	25.0995	−	43.4737i	0.805483	−	1.39514i	0.915965	−	0.401259i	$-0.131427\pi$
$972$	6.47994	+	5.95666i	0.207844	+	0.191060i
$973$	−51.2875	−	19.2414i	−1.64420	−	0.616851i
$974$	19.4938	+	33.7643i	0.624623	+	1.08188i
$975$	6.21405	−	0.378093i	0.199009	−	0.0121087i
$976$	34.6859			1.11027
$977$	−40.4495			−1.29409			−0.647047	−	0.762450i	$-0.723996\pi$
$977$	−40.4495			−1.29409			−0.647047	+	0.762450i	$0.723996\pi$
$978$	15.6386	+	23.6435i	0.500066	+	0.756037i
$979$	−0.139160	−	0.241032i	−0.00444757	−	0.00770341i
$980$	2.97711	+	2.59974i	0.0951002	+	0.0830456i
$981$	−11.6280	+	27.3456i	−0.371252	+	0.873078i
$982$	−1.20732	+	2.09115i	−0.0385273	+	0.0667312i
$983$	26.6895	−	46.2275i	0.851262	−	1.47443i	−0.0288089	−	0.999585i	$-0.509171\pi$
$983$	26.6895	−	46.2275i	0.851262	−	1.47443i	0.880070	−	0.474843i	$-0.157495\pi$
$984$	−27.8873	−	42.1621i	−0.889015	−	1.34408i
$985$	−6.03689	−	10.4562i	−0.192351	−	0.333162i
$986$	−6.11278	+	10.5876i	−0.194671	+	0.337179i
$987$	−37.9399	−	11.6592i	−1.20764	−	0.371117i
$988$	−1.93130	−	3.34511i	−0.0614429	−	0.106422i
$989$	−0.468835	+	0.812045i	−0.0149081	+	0.0258215i
$990$	0.245828	+	0.326655i	0.00781292	+	0.0103818i
$991$	3.36119	+	5.82175i	0.106772	+	0.184934i	0.914461	−	0.404675i	$-0.132615\pi$
$991$	3.36119	+	5.82175i	0.106772	+	0.184934i	−0.807689	+	0.589609i	$0.799282\pi$
$992$	17.9679			0.570480
$993$	−19.7304	+	39.5418i	−0.626126	+	1.25482i
$994$	3.45443	+	20.7865i	0.109568	+	0.659307i
$995$	6.42977	−	11.1367i	0.203838	−	0.353057i
$996$	0.0401991	−	0.00244591i	0.00127376	−	7.75016e-5i
$997$	−15.3643	+	26.6118i	−0.486592	+	0.842803i	−0.999881	−	0.0154133i	$-0.995094\pi$
$997$	−15.3643	+	26.6118i	−0.486592	+	0.842803i	0.513289	+	0.858216i	$0.328427\pi$
$998$	−7.58621	−	13.1397i	−0.240137	−	0.415930i
$999$	−5.56557	+	15.6694i	−0.176087	+	0.495757i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.b.121.9	yes	24
3.2	odd	2		945.2.l.b.226.4		24
7.4	even	3		315.2.k.b.256.4	yes	24
9.2	odd	6		945.2.k.b.856.9		24
9.7	even	3		315.2.k.b.16.4	✓	24
21.11	odd	6		945.2.k.b.361.9		24
63.11	odd	6		945.2.l.b.46.4		24
63.25	even	3	inner	315.2.l.b.151.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.b.16.4	✓	24	9.7	even	3
315.2.k.b.256.4	yes	24	7.4	even	3
315.2.l.b.121.9	yes	24	1.1	even	1	trivial
315.2.l.b.151.9	yes	24	63.25	even	3	inner
945.2.k.b.361.9		24	21.11	odd	6
945.2.k.b.856.9		24	9.2	odd	6
945.2.l.b.46.4		24	63.11	odd	6
945.2.l.b.226.4		24	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.19807 q^{2} +(-0.773328 + 1.54983i) q^{3} -0.564635 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.926499 + 1.85680i) q^{6} +(0.433740 + 2.60996i) q^{7} -3.07261 q^{8} +(-1.80393 - 2.39705i) q^{9} +O(q^{10})\)	\(q+1.19807 q^{2} +(-0.773328 + 1.54983i) q^{3} -0.564635 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.926499 + 1.85680i) q^{6} +(0.433740 + 2.60996i) q^{7} -3.07261 q^{8} +(-1.80393 - 2.39705i) q^{9} +(0.599034 + 1.03756i) q^{10} +(-0.0568723 + 0.0985057i) q^{11} +(0.436648 - 0.875086i) q^{12} +(-1.79716 + 3.11277i) q^{13} +(0.519650 + 3.12690i) q^{14} +(-1.72885 + 0.105192i) q^{15} -2.55192 q^{16} +(1.61936 + 2.80482i) q^{17} +(-2.16123 - 2.87183i) q^{18} +(0.951626 - 1.64826i) q^{19} +(-0.282317 - 0.488988i) q^{20} +(-4.38040 - 1.34613i) q^{21} +(-0.0681368 + 0.118016i) q^{22} +(0.300208 + 0.519975i) q^{23} +(2.37613 - 4.76201i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.15312 + 3.72931i) q^{26} +(5.11004 - 0.942072i) q^{27} +(-0.244905 - 1.47367i) q^{28} +(1.57537 + 2.72863i) q^{29} +(-2.07128 + 0.126027i) q^{30} +5.81891 q^{31} +3.08784 q^{32} +(-0.108686 - 0.164319i) q^{33} +(1.94011 + 3.36036i) q^{34} +(-2.04342 + 1.68061i) q^{35} +(1.01856 + 1.35346i) q^{36} +(-1.60007 + 2.77141i) q^{37} +(1.14011 - 1.97473i) q^{38} +(-3.43446 - 5.19248i) q^{39} +(-1.53630 - 2.66095i) q^{40} +(4.74928 - 8.22599i) q^{41} +(-5.24802 - 1.61275i) q^{42} +(0.780850 + 1.35247i) q^{43} +(0.0321120 - 0.0556197i) q^{44} +(1.17394 - 2.76077i) q^{45} +(0.359669 + 0.622965i) q^{46} +8.66129 q^{47} +(1.97347 - 3.95503i) q^{48} +(-6.62374 + 2.26409i) q^{49} +(-0.599034 + 1.03756i) q^{50} +(-5.59928 + 0.340688i) q^{51} +(1.01474 - 1.75758i) q^{52} +(-5.54540 - 9.60491i) q^{53} +(6.12217 - 1.12867i) q^{54} -0.113745 q^{55} +(-1.33271 - 8.01936i) q^{56} +(1.81861 + 2.74950i) q^{57} +(1.88740 + 3.26908i) q^{58} +14.3279 q^{59} +(0.976171 - 0.0593950i) q^{60} -13.5921 q^{61} +6.97145 q^{62} +(5.47376 - 5.74787i) q^{63} +8.80328 q^{64} -3.59432 q^{65} +(-0.130213 - 0.196866i) q^{66} +4.63189 q^{67} +(-0.914348 - 1.58370i) q^{68} +(-1.03803 + 0.0631589i) q^{69} +(-2.44815 + 2.01348i) q^{70} +6.64762 q^{71} +(5.54276 + 7.36518i) q^{72} +(6.73961 + 11.6733i) q^{73} +(-1.91699 + 3.32033i) q^{74} +(-0.955526 - 1.44464i) q^{75} +(-0.537321 + 0.930667i) q^{76} +(-0.281763 - 0.105708i) q^{77} +(-4.11472 - 6.22094i) q^{78} -17.4616 q^{79} +(-1.27596 - 2.21003i) q^{80} +(-2.49169 + 8.64821i) q^{81} +(5.68996 - 9.85530i) q^{82} +(0.0205902 + 0.0356633i) q^{83} +(2.47333 + 0.760071i) q^{84} +(-1.61936 + 2.80482i) q^{85} +(0.935511 + 1.62035i) q^{86} +(-5.44718 + 0.331433i) q^{87} +(0.174746 - 0.302669i) q^{88} +(-1.22344 + 2.11906i) q^{89} +(1.40646 - 3.30759i) q^{90} +(-8.90370 - 3.34037i) q^{91} +(-0.169508 - 0.293596i) q^{92} +(-4.49993 + 9.01830i) q^{93} +10.3768 q^{94} +1.90325 q^{95} +(-2.38791 + 4.78562i) q^{96} +(-2.36579 - 4.09767i) q^{97} +(-7.93569 + 2.71253i) q^{98} +(0.338716 - 0.0413715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9} + q^{10} + q^{11} - 7 q^{12} - 4 q^{13} + 8 q^{14} - q^{15} + 10 q^{16} - 7 q^{17} + 18 q^{18} - 2 q^{19} + 7 q^{20} - 17 q^{21} + 19 q^{22} + q^{23} + 18 q^{24} - 12 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 16 q^{31} - 34 q^{32} + 7 q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} - 35 q^{38} - 17 q^{39} + 6 q^{40} + 20 q^{41} - 36 q^{42} + 31 q^{43} - 7 q^{44} + 6 q^{45} - 10 q^{46} + 62 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} + 14 q^{51} - 4 q^{52} + 8 q^{53} - 51 q^{54} + 2 q^{55} + 5 q^{57} + 45 q^{58} + 42 q^{59} - 23 q^{60} - 10 q^{61} + 14 q^{62} + 18 q^{63} - 56 q^{64} - 8 q^{65} + 4 q^{66} - 86 q^{67} - 48 q^{68} + 26 q^{69} - 5 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{73} + 9 q^{74} + 4 q^{75} - 13 q^{76} + 35 q^{77} + 19 q^{78} - 80 q^{79} + 5 q^{80} + 21 q^{81} + 5 q^{82} - 60 q^{83} + 35 q^{84} + 7 q^{85} + 12 q^{86} + 68 q^{87} + 50 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} + 7 q^{93} + 22 q^{94} - 4 q^{95} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9 + q^10 + q^11 - 7 * q^12 - 4 * q^13 + 8 * q^14 - q^15 + 10 * q^16 - 7 * q^17 + 18 * q^18 - 2 * q^19 + 7 * q^20 - 17 * q^21 + 19 * q^22 + q^23 + 18 * q^24 - 12 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 16 * q^31 - 34 * q^32 + 7 * q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 - 35 * q^38 - 17 * q^39 + 6 * q^40 + 20 * q^41 - 36 * q^42 + 31 * q^43 - 7 * q^44 + 6 * q^45 - 10 * q^46 + 62 * q^47 - 36 * q^48 - 11 * q^49 - q^50 + 14 * q^51 - 4 * q^52 + 8 * q^53 - 51 * q^54 + 2 * q^55 + 5 * q^57 + 45 * q^58 + 42 * q^59 - 23 * q^60 - 10 * q^61 + 14 * q^62 + 18 * q^63 - 56 * q^64 - 8 * q^65 + 4 * q^66 - 86 * q^67 - 48 * q^68 + 26 * q^69 - 5 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^73 + 9 * q^74 + 4 * q^75 - 13 * q^76 + 35 * q^77 + 19 * q^78 - 80 * q^79 + 5 * q^80 + 21 * q^81 + 5 * q^82 - 60 * q^83 + 35 * q^84 + 7 * q^85 + 12 * q^86 + 68 * q^87 + 50 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 + 7 * q^93 + 22 * q^94 - 4 * q^95 + 6 * q^97 - 15 * q^98 - q^99

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