LMFDB - Embedded newform 315.2.l.c.121.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.15
Character	$\chi$	$=$	315.121
Dual form			315.2.l.c.151.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.89985 q^{2} +(0.960253 - 1.44150i) q^{3} +1.60945 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.82434 - 2.73864i) q^{6} +(1.72052 + 2.00992i) q^{7} -0.741992 q^{8} +(-1.15583 - 2.76840i) q^{9} +O(q^{10})$	\(q+1.89985 q^{2} +(0.960253 - 1.44150i) q^{3} +1.60945 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.82434 - 2.73864i) q^{6} +(1.72052 + 2.00992i) q^{7} -0.741992 q^{8} +(-1.15583 - 2.76840i) q^{9} +(-0.949927 - 1.64532i) q^{10} +(2.47977 - 4.29509i) q^{11} +(1.54548 - 2.32002i) q^{12} +(-2.81852 + 4.88183i) q^{13} +(3.26875 + 3.81856i) q^{14} +(-1.72850 - 0.110854i) q^{15} -4.62857 q^{16} +(1.93945 + 3.35923i) q^{17} +(-2.19591 - 5.25956i) q^{18} +(-0.540078 + 0.935442i) q^{19} +(-0.804724 - 1.39382i) q^{20} +(4.54944 - 0.550097i) q^{21} +(4.71121 - 8.16005i) q^{22} +(2.68704 + 4.65410i) q^{23} +(-0.712500 + 1.06958i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-5.35479 + 9.27476i) q^{26} +(-5.10054 - 0.992240i) q^{27} +(2.76909 + 3.23487i) q^{28} +(-2.83238 - 4.90583i) q^{29} +(-3.28390 - 0.210607i) q^{30} +0.424059 q^{31} -7.30963 q^{32} +(-3.81016 - 7.69896i) q^{33} +(3.68468 + 6.38204i) q^{34} +(0.880383 - 2.49498i) q^{35} +(-1.86025 - 4.45560i) q^{36} +(0.891603 - 1.54430i) q^{37} +(-1.02607 + 1.77720i) q^{38} +(4.33065 + 8.75068i) q^{39} +(0.370996 + 0.642584i) q^{40} +(-4.04814 + 7.01159i) q^{41} +(8.64327 - 1.04511i) q^{42} +(-3.60053 - 6.23630i) q^{43} +(3.99106 - 6.91272i) q^{44} +(-1.81959 + 2.38518i) q^{45} +(5.10499 + 8.84211i) q^{46} +10.6119 q^{47} +(-4.44460 + 6.67208i) q^{48} +(-1.07959 + 6.91625i) q^{49} +(-0.949927 + 1.64532i) q^{50} +(6.70468 + 0.429993i) q^{51} +(-4.53627 + 7.85704i) q^{52} +(1.94432 + 3.36765i) q^{53} +(-9.69028 - 1.88511i) q^{54} -4.95954 q^{55} +(-1.27662 - 1.49135i) q^{56} +(0.829826 + 1.67678i) q^{57} +(-5.38111 - 9.32036i) q^{58} -8.29222 q^{59} +(-2.78193 - 0.178414i) q^{60} -6.05593 q^{61} +0.805650 q^{62} +(3.57565 - 7.08624i) q^{63} -4.63009 q^{64} +5.63705 q^{65} +(-7.23874 - 14.6269i) q^{66} -1.34169 q^{67} +(3.12145 + 5.40650i) q^{68} +(9.28911 + 0.595741i) q^{69} +(1.67260 - 4.74010i) q^{70} +5.02270 q^{71} +(0.857617 + 2.05413i) q^{72} +(-5.89623 - 10.2126i) q^{73} +(1.69392 - 2.93395i) q^{74} +(0.768247 + 1.55235i) q^{75} +(-0.869227 + 1.50554i) q^{76} +(12.8993 - 2.40566i) q^{77} +(8.22760 + 16.6250i) q^{78} +8.24977 q^{79} +(2.31429 + 4.00846i) q^{80} +(-6.32811 + 6.39961i) q^{81} +(-7.69089 + 13.3210i) q^{82} +(-2.91400 - 5.04719i) q^{83} +(7.32208 - 0.885353i) q^{84} +(1.93945 - 3.35923i) q^{85} +(-6.84048 - 11.8481i) q^{86} +(-9.79154 - 0.627963i) q^{87} +(-1.83997 + 3.18692i) q^{88} +(8.26047 - 14.3076i) q^{89} +(-3.45696 + 4.53150i) q^{90} +(-14.6614 + 2.73428i) q^{91} +(4.32466 + 7.49052i) q^{92} +(0.407203 - 0.611279i) q^{93} +20.1611 q^{94} +1.08016 q^{95} +(-7.01909 + 10.5368i) q^{96} +(4.81694 + 8.34318i) q^{97} +(-2.05106 + 13.1399i) q^{98} +(-14.7567 - 1.90061i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) $ 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.89985			1.34340			0.671700	−	0.740823i	$-0.265564\pi$
$2$	1.89985			1.34340			0.671700	+	0.740823i	$0.265564\pi$
$3$	0.960253	−	1.44150i	0.554402	−	0.832249i
$3$	0.960253	−	1.44150i	0.554402	−	0.832249i
$4$	1.60945			0.804724
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	1.82434	−	2.73864i	0.744784	−	1.11804i
$7$	1.72052	+	2.00992i	0.650297	+	0.759680i
$7$	1.72052	+	2.00992i	0.650297	+	0.759680i
$8$	−0.741992			−0.262334
$9$	−1.15583	−	2.76840i	−0.385277	−	0.922801i
$10$	−0.949927	−	1.64532i	−0.300393	−	0.520297i
$11$	2.47977	−	4.29509i	0.747679	−	1.29502i	−0.201253	−	0.979539i	$-0.564501\pi$
$11$	2.47977	−	4.29509i	0.747679	−	1.29502i	0.948932	−	0.315479i	$-0.102165\pi$
$12$	1.54548	−	2.32002i	0.446141	−	0.669731i
$13$	−2.81852	+	4.88183i	−0.781718	+	1.35397i	0.149223	+	0.988804i	$0.452323\pi$
$13$	−2.81852	+	4.88183i	−0.781718	+	1.35397i	−0.930940	+	0.365171i	$0.881010\pi$
$14$	3.26875	+	3.81856i	0.873609	+	1.02055i
$15$	−1.72850	−	0.110854i	−0.446297	−	0.0286225i
$16$	−4.62857			−1.15714
$17$	1.93945	+	3.35923i	0.470386	+	0.814732i	0.999426	−	0.0338642i	$-0.0107814\pi$
$17$	1.93945	+	3.35923i	0.470386	+	0.814732i	−0.529040	+	0.848597i	$0.677448\pi$
$18$	−2.19591	−	5.25956i	−0.517581	−	1.23969i
$19$	−0.540078	+	0.935442i	−0.123902	+	0.214605i	−0.921303	−	0.388845i	$-0.872874\pi$
$19$	−0.540078	+	0.935442i	−0.123902	+	0.214605i	0.797401	+	0.603450i	$0.206208\pi$
$20$	−0.804724	−	1.39382i	−0.179942	−	0.311668i
$21$	4.54944	−	0.550097i	0.992769	−	0.120041i
$22$	4.71121	−	8.16005i	1.00443	−	1.73973i
$23$	2.68704	+	4.65410i	0.560287	+	0.970446i	0.997471	+	0.0710739i	$0.0226426\pi$
$23$	2.68704	+	4.65410i	0.560287	+	0.970446i	−0.437184	+	0.899372i	$0.644024\pi$
$24$	−0.712500	+	1.06958i	−0.145438	+	0.218327i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−5.35479	+	9.27476i	−1.05016	+	1.81893i
$27$	−5.10054	−	0.992240i	−0.981598	−	0.190957i
$28$	2.76909	+	3.23487i	0.523310	+	0.611333i
$29$	−2.83238	−	4.90583i	−0.525960	−	0.910989i	−0.999543	−	0.0302399i	$-0.990373\pi$
$29$	−2.83238	−	4.90583i	−0.525960	−	0.910989i	0.473583	−	0.880749i	$-0.342960\pi$
$30$	−3.28390	−	0.210607i	−0.599555	−	0.0384514i
$31$	0.424059			0.0761632			0.0380816	−	0.999275i	$-0.487875\pi$
$31$	0.424059			0.0761632			0.0380816	+	0.999275i	$0.487875\pi$
$32$	−7.30963			−1.29217
$33$	−3.81016	−	7.69896i	−0.663263	−	1.34022i
$34$	3.68468	+	6.38204i	0.631917	+	1.09451i
$35$	0.880383	−	2.49498i	0.148812	−	0.421729i
$36$	−1.86025	−	4.45560i	−0.310041	−	0.742600i
$37$	0.891603	−	1.54430i	0.146579	−	0.253882i	−0.783382	−	0.621540i	$-0.786507\pi$
$37$	0.891603	−	1.54430i	0.146579	−	0.253882i	0.929961	+	0.367659i	$0.119841\pi$
$38$	−1.02607	+	1.77720i	−0.166450	+	0.288300i
$39$	4.33065	+	8.75068i	0.693458	+	1.40123i
$40$	0.370996	+	0.642584i	0.0586596	+	0.101601i
$41$	−4.04814	+	7.01159i	−0.632214	+	1.09503i	0.354884	+	0.934910i	$0.384520\pi$
$41$	−4.04814	+	7.01159i	−0.632214	+	1.09503i	−0.987098	+	0.160116i	$0.948813\pi$
$42$	8.64327	−	1.04511i	1.33369	−	0.161263i
$43$	−3.60053	−	6.23630i	−0.549076	−	0.951027i	−0.998338	−	0.0576271i	$-0.981647\pi$
$43$	−3.60053	−	6.23630i	−0.549076	−	0.951027i	0.449263	−	0.893400i	$-0.351687\pi$
$44$	3.99106	−	6.91272i	0.601675	−	1.04213i
$45$	−1.81959	+	2.38518i	−0.271249	+	0.355562i
$46$	5.10499	+	8.84211i	0.752690	+	1.30370i
$47$	10.6119			1.54791			0.773953	−	0.633243i	$-0.218277\pi$
$47$	10.6119			1.54791			0.773953	+	0.633243i	$0.218277\pi$
$48$	−4.44460	+	6.67208i	−0.641523	+	0.963031i
$49$	−1.07959	+	6.91625i	−0.154227	+	0.988035i
$50$	−0.949927	+	1.64532i	−0.134340	+	0.232684i
$51$	6.70468	+	0.429993i	0.938843	+	0.0602111i
$52$	−4.53627	+	7.85704i	−0.629067	+	1.08958i
$53$	1.94432	+	3.36765i	0.267072	+	0.462583i	0.968104	−	0.250547i	$-0.0806104\pi$
$53$	1.94432	+	3.36765i	0.267072	+	0.462583i	−0.701032	+	0.713130i	$0.747277\pi$
$54$	−9.69028	−	1.88511i	−1.31868	−	0.256531i
$55$	−4.95954			−0.668745
$56$	−1.27662	−	1.49135i	−0.170595	−	0.199290i
$57$	0.829826	+	1.67678i	0.109913	+	0.222095i
$58$	−5.38111	−	9.32036i	−0.706575	−	1.22382i
$59$	−8.29222			−1.07955			−0.539777	−	0.841808i	$-0.681492\pi$
$59$	−8.29222			−1.07955			−0.539777	+	0.841808i	$0.681492\pi$
$60$	−2.78193	−	0.178414i	−0.359146	−	0.0230332i
$61$	−6.05593			−0.775382			−0.387691	−	0.921789i	$-0.626727\pi$
$61$	−6.05593			−0.775382			−0.387691	+	0.921789i	$0.626727\pi$
$62$	0.805650			0.102318
$63$	3.57565	−	7.08624i	0.450489	−	0.892782i
$64$	−4.63009			−0.578761
$65$	5.63705			0.699190
$66$	−7.23874	−	14.6269i	−0.891028	−	1.80045i
$67$	−1.34169			−0.163913			−0.0819566	−	0.996636i	$-0.526117\pi$
$67$	−1.34169			−0.163913			−0.0819566	+	0.996636i	$0.526117\pi$
$68$	3.12145	+	5.40650i	0.378531	+	0.655635i
$69$	9.28911	+	0.595741i	1.11828	+	0.0717188i
$70$	1.67260	−	4.74010i	0.199914	−	0.566550i
$71$	5.02270			0.596085			0.298043	−	0.954553i	$-0.403666\pi$
$71$	5.02270			0.596085			0.298043	+	0.954553i	$0.403666\pi$
$72$	0.857617	+	2.05413i	0.101071	+	0.242082i
$73$	−5.89623	−	10.2126i	−0.690102	−	1.19529i	−0.971804	−	0.235790i	$-0.924232\pi$
$73$	−5.89623	−	10.2126i	−0.690102	−	1.19529i	0.281702	−	0.959502i	$-0.409101\pi$
$74$	1.69392	−	2.93395i	0.196914	−	0.341064i
$75$	0.768247	+	1.55235i	0.0887095	+	0.179250i
$76$	−0.869227	+	1.50554i	−0.0997071	+	0.172698i
$77$	12.8993	−	2.40566i	1.47001	−	0.274150i
$78$	8.22760	+	16.6250i	0.931592	+	1.88241i
$79$	8.24977			0.928171			0.464086	−	0.885790i	$-0.346383\pi$
$79$	8.24977			0.928171			0.464086	+	0.885790i	$0.346383\pi$
$80$	2.31429	+	4.00846i	0.258745	+	0.448160i
$81$	−6.32811	+	6.39961i	−0.703124	+	0.711068i
$82$	−7.69089	+	13.3210i	−0.849316	+	1.47106i
$83$	−2.91400	−	5.04719i	−0.319853	−	0.554001i	0.660604	−	0.750734i	$-0.270300\pi$
$83$	−2.91400	−	5.04719i	−0.319853	−	0.554001i	−0.980457	+	0.196733i	$0.936967\pi$
$84$	7.32208	−	0.885353i	0.798905	−	0.0965999i
$85$	1.93945	−	3.35923i	0.210363	−	0.364359i
$86$	−6.84048	−	11.8481i	−0.737628	−	1.27761i
$87$	−9.79154	−	0.627963i	−1.04976	−	0.0673247i
$88$	−1.83997	+	3.18692i	−0.196142	+	0.339727i
$89$	8.26047	−	14.3076i	0.875608	−	1.51660i	0.0194946	−	0.999810i	$-0.493794\pi$
$89$	8.26047	−	14.3076i	0.875608	−	1.51660i	0.856114	−	0.516788i	$-0.172872\pi$
$90$	−3.45696	+	4.53150i	−0.364396	+	0.477662i
$91$	−14.6614	+	2.73428i	−1.53694	+	0.286631i
$92$	4.32466	+	7.49052i	0.450877	+	0.780941i
$93$	0.407203	−	0.611279i	0.0422250	−	0.0633867i
$94$	20.1611			2.07946
$95$	1.08016			0.110822
$96$	−7.01909	+	10.5368i	−0.716383	+	1.07541i
$97$	4.81694	+	8.34318i	0.489086	+	0.847121i	0.999921	−	0.0125571i	$-0.00399716\pi$
$97$	4.81694	+	8.34318i	0.489086	+	0.847121i	−0.510835	+	0.859679i	$0.670664\pi$
$98$	−2.05106	+	13.1399i	−0.207189	+	1.32733i
$99$	−14.7567	−	1.90061i	−1.48311	−	0.191019i
$100$	−0.804724	+	1.39382i	−0.0804724	+	0.139382i
$101$	0.631548	−	1.09387i	0.0628414	−	0.108844i	−0.832893	−	0.553434i	$-0.813317\pi$
$101$	0.631548	−	1.09387i	0.0628414	−	0.108844i	0.895734	+	0.444590i	$0.146650\pi$
$102$	12.7379	+	0.816924i	1.26124	+	0.0808876i
$103$	−7.58307	−	13.1343i	−0.747182	−	1.29416i	−0.949168	−	0.314769i	$-0.898073\pi$
$103$	−7.58307	−	13.1343i	−0.747182	−	1.29416i	0.201986	−	0.979388i	$-0.435260\pi$
$104$	2.09132	−	3.62228i	0.205071	−	0.355194i
$105$	−2.75112	−	3.66488i	−0.268482	−	0.357656i
$106$	3.69392	+	6.39805i	0.358785	+	0.621434i
$107$	1.56144	−	2.70449i	0.150950	−	0.261453i	−0.780627	−	0.624997i	$-0.785100\pi$
$107$	1.56144	−	2.70449i	0.150950	−	0.261453i	0.931577	+	0.363544i	$0.118433\pi$
$108$	−8.20905	−	1.59696i	−0.789916	−	0.153667i
$109$	−1.95948	−	3.39393i	−0.187685	−	0.325079i	0.756793	−	0.653654i	$-0.226765\pi$
$109$	−1.95948	−	3.39393i	−0.187685	−	0.325079i	−0.944478	+	0.328575i	$0.893432\pi$
$110$	−9.42241			−0.898392
$111$	−1.36994	−	2.76816i	−0.130029	−	0.262742i
$112$	−7.96357	−	9.30308i	−0.752487	−	0.879059i
$113$	5.52663	−	9.57241i	0.519902	−	0.900497i	−0.479830	−	0.877361i	$-0.659302\pi$
$113$	5.52663	−	9.57241i	0.519902	−	0.900497i	0.999732	−	0.0231353i	$-0.00736487\pi$
$114$	1.57655	+	3.18564i	0.147657	+	0.298363i
$115$	2.68704	−	4.65410i	0.250568	−	0.433997i
$116$	−4.55857	−	7.89567i	−0.423252	−	0.733095i
$117$	16.7726	+	2.16025i	1.55063	+	0.199715i
$118$	−15.7540			−1.45027
$119$	−3.41492	+	9.67778i	−0.313045	+	0.887161i
$120$	1.28253	+	0.0822531i	0.117079	+	0.00750864i
$121$	−6.79854	−	11.7754i	−0.618049	−	1.07049i
$122$	−11.5054			−1.04165
$123$	6.21995	+	12.5683i	0.560834	+	1.13324i
$124$	0.682500			0.0612903
$125$	1.00000			0.0894427
$126$	6.79321	−	13.4628i	0.605187	−	1.19936i
$127$	−2.02599			−0.179777			−0.0898887	−	0.995952i	$-0.528651\pi$
$127$	−2.02599			−0.179777			−0.0898887	+	0.995952i	$0.528651\pi$
$128$	5.82276			0.514664
$129$	−12.4470	−	0.798269i	−1.09590	−	0.0702836i
$130$	10.7096			0.939292
$131$	1.53667	+	2.66158i	0.134259	+	0.232544i	0.925314	−	0.379201i	$-0.123801\pi$
$131$	1.53667	+	2.66158i	0.134259	+	0.232544i	−0.791055	+	0.611745i	$0.790468\pi$
$132$	−6.13225	−	12.3911i	−0.533744	−	1.07850i
$133$	−2.80938	+	0.523936i	−0.243604	+	0.0454310i
$134$	−2.54901			−0.220201
$135$	1.69096	+	4.91331i	0.145535	+	0.422871i
$136$	−1.43906	−	2.49252i	−0.123398	−	0.213732i
$137$	1.88153	−	3.25890i	0.160750	−	0.278427i	−0.774388	−	0.632711i	$-0.781942\pi$
$137$	1.88153	−	3.25890i	0.160750	−	0.278427i	0.935138	+	0.354284i	$0.115275\pi$
$138$	17.6480	+	1.13182i	1.50229	+	0.0963470i
$139$	−8.30302	+	14.3813i	−0.704253	+	1.21980i	0.262707	+	0.964876i	$0.415385\pi$
$139$	−8.30302	+	14.3813i	−0.704253	+	1.21980i	−0.966960	+	0.254926i	$0.917949\pi$
$140$	1.41693	−	4.01554i	0.119752	−	0.339375i
$141$	10.1901	−	15.2970i	0.858162	−	1.28824i
$142$	9.54241			0.800781
$143$	13.9786	+	24.2116i	1.16895	+	2.02468i
$144$	5.34984	+	12.8138i	0.445820	+	1.06781i
$145$	−2.83238	+	4.90583i	−0.235216	+	0.407407i
$146$	−11.2020	−	19.4024i	−0.927083	−	1.60575i
$147$	8.93308	+	8.19757i	0.736788	+	0.676124i
$148$	1.43499	−	2.48547i	0.117955	−	0.204305i
$149$	−11.3200	−	19.6067i	−0.927366	−	1.60625i	−0.787710	−	0.616046i	$-0.788734\pi$
$149$	−11.3200	−	19.6067i	−0.927366	−	1.60625i	−0.139656	−	0.990200i	$-0.544600\pi$
$150$	1.45956	+	2.94924i	0.119172	+	0.240805i
$151$	−2.30325	+	3.98934i	−0.187436	+	0.324648i	−0.944395	−	0.328814i	$-0.893351\pi$
$151$	−2.30325	+	3.98934i	−0.187436	+	0.324648i	0.756959	+	0.653463i	$0.226684\pi$
$152$	0.400733	−	0.694091i	0.0325038	−	0.0562982i
$153$	7.05802	−	9.25188i	0.570607	−	0.747970i
$154$	24.5068	−	4.57040i	1.97482	−	0.368293i
$155$	−0.212029	−	0.367245i	−0.0170306	−	0.0294979i
$156$	6.96995	+	14.0838i	0.558043	+	1.12760i
$157$	8.40747			0.670989			0.335495	−	0.942042i	$-0.391097\pi$
$157$	8.40747			0.670989			0.335495	+	0.942042i	$0.391097\pi$
$158$	15.6734			1.24691
$159$	6.72150	+	0.431072i	0.533050	+	0.0341862i
$160$	3.65482	+	6.33033i	0.288939	+	0.500456i
$161$	−4.73125	+	13.4082i	−0.372875	+	1.05672i
$162$	−12.0225	+	12.1583i	−0.944576	+	0.955248i
$163$	−6.83197	+	11.8333i	−0.535121	+	0.926856i	0.464037	+	0.885816i	$0.346401\pi$
$163$	−6.83197	+	11.8333i	−0.535121	+	0.926856i	−0.999157	+	0.0410405i	$0.986933\pi$
$164$	−6.51528	+	11.2848i	−0.508758	+	0.881194i
$165$	−4.76241	+	7.14917i	−0.370753	+	0.556562i
$166$	−5.53617	−	9.58893i	−0.429690	−	0.744246i
$167$	0.161363	−	0.279489i	0.0124866	−	0.0216275i	−0.859715	−	0.510775i	$-0.829359\pi$
$167$	0.161363	−	0.279489i	0.0124866	−	0.0216275i	0.872201	+	0.489147i	$0.162692\pi$
$168$	−3.37565	+	0.408168i	−0.260437	+	0.0314908i
$169$	−9.38815	−	16.2608i	−0.722166	−	1.25083i
$170$	3.68468	−	6.38204i	0.282602	−	0.489481i
$171$	3.21392	+	0.413941i	0.245774	+	0.0316548i
$172$	−5.79486	−	10.0370i	−0.441854	−	0.765314i
$173$	10.2701			0.780820			0.390410	−	0.920641i	$-0.372333\pi$
$173$	10.2701			0.780820			0.390410	+	0.920641i	$0.372333\pi$
$174$	−18.6025	−	1.19304i	−1.41025	−	0.0904441i
$175$	−2.60091	+	0.485056i	−0.196610	+	0.0366668i
$176$	−11.4778	+	19.8801i	−0.865172	+	1.49852i
$177$	−7.96262	+	11.9532i	−0.598507	+	0.898458i
$178$	15.6937	−	27.1823i	1.17629	−	2.03740i
$179$	−6.71395	−	11.6289i	−0.501824	−	0.869185i	−0.999998	−	0.00210780i	$-0.999329\pi$
$179$	−6.71395	−	11.6289i	−0.501824	−	0.869185i	0.498173	−	0.867077i	$-0.334004\pi$
$180$	−2.92854	+	3.83882i	−0.218280	+	0.286129i
$181$	10.5458			0.783864			0.391932	−	0.919994i	$-0.371807\pi$
$181$	10.5458			0.783864			0.391932	+	0.919994i	$0.371807\pi$
$182$	−27.8546	+	5.19474i	−2.06472	+	0.385060i
$183$	−5.81522	+	8.72961i	−0.429873	+	0.645311i
$184$	−1.99377	−	3.45330i	−0.146982	−	0.254581i
$185$	−1.78321			−0.131104
$186$	0.773627	−	1.16134i	0.0567251	−	0.0851537i
$187$	19.2376			1.40679
$188$	17.0793			1.24564
$189$	−6.78127	−	11.9589i	−0.493265	−	0.869879i
$190$	2.05214			0.148878
$191$	19.6326			1.42057			0.710283	−	0.703917i	$-0.248567\pi$
$191$	19.6326			1.42057			0.710283	+	0.703917i	$0.248567\pi$
$192$	−4.44606	+	6.67427i	−0.320867	+	0.481674i
$193$	26.5059			1.90794			0.953968	−	0.299909i	$-0.0969562\pi$
$193$	26.5059			1.90794			0.953968	+	0.299909i	$0.0969562\pi$
$194$	9.15148	+	15.8508i	0.657038	+	1.13802i
$195$	5.41299	−	8.12579i	0.387632	−	0.581900i
$196$	−1.73754	+	11.1313i	−0.124110	+	0.795096i
$197$	−18.1946			−1.29631			−0.648154	−	0.761509i	$-0.724459\pi$
$197$	−18.1946			−1.29631			−0.648154	+	0.761509i	$0.724459\pi$
$198$	−28.0357	−	3.61089i	−1.99241	−	0.256615i
$199$	6.54080	+	11.3290i	0.463665	+	0.803091i	0.999140	−	0.0414600i	$-0.0132009\pi$
$199$	6.54080	+	11.3290i	0.463665	+	0.803091i	−0.535475	+	0.844551i	$0.679868\pi$
$200$	0.370996	−	0.642584i	0.0262334	−	0.0454376i
$201$	−1.28836	+	1.93404i	−0.0908738	+	0.136417i
$202$	1.19985	−	2.07820i	0.0844211	−	0.146222i
$203$	4.98716	−	14.1335i	0.350030	−	0.991975i
$204$	10.7908	+	0.692051i	0.755510	+	0.0484533i
$205$	8.09629			0.565469
$206$	−14.4067	−	24.9532i	−1.00376	−	1.73857i
$207$	9.77865	−	12.8182i	0.679663	−	0.890924i
$208$	13.0457	−	22.5959i	0.904560	−	1.56674i
$209$	2.67854	+	4.63936i	0.185278	+	0.320912i
$210$	−5.22672	−	6.96274i	−0.360678	−	0.480475i
$211$	−10.8596	+	18.8094i	−0.747606	+	1.29489i	0.201361	+	0.979517i	$0.435464\pi$
$211$	−10.8596	+	18.8094i	−0.747606	+	1.29489i	−0.948967	+	0.315375i	$0.897870\pi$
$212$	3.12927	+	5.42006i	0.214919	+	0.372251i
$213$	4.82306	−	7.24021i	0.330471	−	0.496091i
$214$	2.96650	−	5.13814i	0.202786	−	0.351236i
$215$	−3.60053	+	6.23630i	−0.245554	+	0.425312i
$216$	3.78456	+	0.736234i	0.257507	+	0.0500944i
$217$	0.729603	+	0.852325i	0.0495287	+	0.0578596i
$218$	−3.72273	−	6.44797i	−0.252135	−	0.436711i
$219$	−20.3833	−	1.30725i	−1.37737	−	0.0883355i
$220$	−7.98213			−0.538155
$221$	−21.8656			−1.47084
$222$	−2.60269	−	5.25911i	−0.174681	−	0.352968i
$223$	4.00079	+	6.92958i	0.267913	+	0.464039i	0.968323	−	0.249702i	$-0.0803327\pi$
$223$	4.00079	+	6.92958i	0.267913	+	0.464039i	−0.700410	+	0.713741i	$0.746999\pi$
$224$	−12.5764	−	14.6918i	−0.840296	−	0.981638i
$225$	2.97542	+	0.383223i	0.198362	+	0.0255482i
$226$	10.4998	−	18.1862i	0.698436	−	1.20973i
$227$	−3.69487	+	6.39970i	−0.245237	+	0.424763i	−0.962198	−	0.272350i	$-0.912199\pi$
$227$	−3.69487	+	6.39970i	−0.245237	+	0.424763i	0.716961	+	0.697113i	$0.245533\pi$
$228$	1.33556	+	2.69869i	0.0884497	+	0.178725i
$229$	2.74321	+	4.75137i	0.181276	+	0.313980i	0.942315	−	0.334726i	$-0.108644\pi$
$229$	2.74321	+	4.75137i	0.181276	+	0.313980i	−0.761039	+	0.648706i	$0.775311\pi$
$230$	5.10499	−	8.84211i	0.336613	−	0.583031i
$231$	8.91885	−	20.9044i	0.586817	−	1.37541i
$232$	2.10160	+	3.64009i	0.137977	+	0.238983i
$233$	1.08520	−	1.87963i	0.0710941	−	0.123139i	−0.828287	−	0.560304i	$-0.810684\pi$
$233$	1.08520	−	1.87963i	0.0710941	−	0.123139i	0.899381	+	0.437166i	$0.144018\pi$
$234$	31.8655	+	4.10416i	2.08311	+	0.268297i
$235$	−5.30595	−	9.19018i	−0.346122	−	0.599501i
$236$	−13.3459			−0.868744
$237$	7.92186	−	11.8920i	0.514580	−	0.772470i
$238$	−6.48785	+	18.3864i	−0.420545	+	1.19181i
$239$	−2.54202	+	4.40291i	−0.164430	+	0.284801i	−0.936453	−	0.350794i	$-0.885912\pi$
$239$	−2.54202	+	4.40291i	−0.164430	+	0.284801i	0.772023	+	0.635595i	$0.219245\pi$
$240$	8.00049	+	0.513097i	0.516429	+	0.0331203i
$241$	4.42918	−	7.67156i	0.285308	−	0.494169i	−0.687376	−	0.726302i	$-0.741237\pi$
$241$	4.42918	−	7.67156i	0.285308	−	0.494169i	0.972684	+	0.232134i	$0.0745707\pi$
$242$	−12.9162	−	22.3716i	−0.830287	−	1.43810i
$243$	3.14843	+	15.2672i	0.201972	+	0.979391i
$244$	−9.74670			−0.623969
$245$	6.52944	−	2.52317i	0.417151	−	0.161200i
$246$	11.8170	+	23.8779i	0.753425	+	1.52240i
$247$	−3.04444	−	5.27313i	−0.193713	−	0.335521i
$248$	−0.314648			−0.0199802
$249$	−10.0737	−	0.646059i	−0.638394	−	0.0409423i
$250$	1.89985			0.120157
$251$	−0.251384			−0.0158672			−0.00793360	−	0.999969i	$-0.502525\pi$
$251$	−0.251384			−0.0158672			−0.00793360	+	0.999969i	$0.502525\pi$
$252$	5.75482	−	11.4049i	0.362519	−	0.718443i
$253$	26.6530			1.67566
$254$	−3.84908			−0.241513
$255$	−2.97996	−	6.02142i	−0.186612	−	0.377076i
$256$	20.3226			1.27016
$257$	−6.56553	−	11.3718i	−0.409546	−	0.709355i	0.585293	−	0.810822i	$-0.300980\pi$
$257$	−6.56553	−	11.3718i	−0.409546	−	0.709355i	−0.994839	+	0.101467i	$0.967646\pi$
$258$	−23.6475	−	1.51659i	−1.47223	−	0.0944190i
$259$	4.63795	−	0.864954i	0.288188	−	0.0537457i
$260$	9.07253			0.562655
$261$	−10.3076	+	13.5115i	−0.638022	+	0.836339i
$262$	2.91944	+	5.05662i	0.180364	+	0.312399i
$263$	−12.9665	+	22.4587i	−0.799551	+	1.38486i	0.120358	+	0.992731i	$0.461596\pi$
$263$	−12.9665	+	22.4587i	−0.799551	+	1.38486i	−0.919909	+	0.392132i	$0.871738\pi$
$264$	2.82711	+	5.71257i	0.173996	+	0.351584i
$265$	1.94432	−	3.36765i	0.119438	−	0.206873i
$266$	−5.33742	+	0.995402i	−0.327258	+	0.0610320i
$267$	−12.6922	−	25.6463i	−0.776748	−	1.56953i
$268$	−2.15938			−0.131905
$269$	2.36259	+	4.09213i	0.144050	+	0.249501i	0.929018	−	0.370035i	$-0.120654\pi$
$269$	2.36259	+	4.09213i	0.144050	+	0.249501i	−0.784968	+	0.619536i	$0.787321\pi$
$270$	3.21258	+	9.33458i	0.195512	+	0.568084i
$271$	−10.1944	+	17.6573i	−0.619268	+	1.07260i	0.370352	+	0.928892i	$0.379237\pi$
$271$	−10.1944	+	17.6573i	−0.619268	+	1.07260i	−0.989620	+	0.143712i	$0.954096\pi$
$272$	−8.97689	−	15.5484i	−0.544304	−	0.942762i
$273$	−10.1372	+	23.7600i	−0.613533	+	1.43802i
$274$	3.57463	−	6.19144i	0.215951	−	0.374039i
$275$	2.47977	+	4.29509i	0.149536	+	0.259004i
$276$	14.9503	+	0.958814i	0.899904	+	0.0577138i
$277$	−1.65123	+	2.86002i	−0.0992128	+	0.171842i	−0.911359	−	0.411612i	$-0.864966\pi$
$277$	−1.65123	+	2.86002i	−0.0992128	+	0.171842i	0.812146	+	0.583454i	$0.198299\pi$
$278$	−15.7745	+	27.3223i	−0.946094	+	1.63868i
$279$	−0.490140	−	1.17397i	−0.0293439	−	0.0702835i
$280$	−0.653237	+	1.85126i	−0.0390384	+	0.110634i
$281$	13.6426	+	23.6297i	0.813849	+	1.40963i	0.910151	+	0.414276i	$0.135965\pi$
$281$	13.6426	+	23.6297i	0.813849	+	1.40963i	−0.0963023	+	0.995352i	$0.530702\pi$
$282$	19.3597	−	29.0621i	1.15286	−	1.73063i
$283$	−13.6462			−0.811185			−0.405593	−	0.914054i	$-0.632935\pi$
$283$	−13.6462			−0.811185			−0.405593	+	0.914054i	$0.632935\pi$
$284$	8.08378			0.479684
$285$	1.03722	−	1.55704i	0.0614397	−	0.0922311i
$286$	26.5573	+	45.9986i	1.57037	+	2.71995i
$287$	−21.0577	+	3.92715i	−1.24300	+	0.231813i
$288$	8.44869	+	20.2360i	0.497844	+	1.19242i
$289$	0.977058	−	1.69231i	0.0574740	−	0.0995479i
$290$	−5.38111	+	9.32036i	−0.315990	+	0.547310i
$291$	16.6521	+	1.06796i	0.976166	+	0.0626047i
$292$	−9.48968	−	16.4366i	−0.555341	−	0.961880i
$293$	−5.55114	+	9.61486i	−0.324301	+	0.561706i	−0.981371	−	0.192124i	$-0.938463\pi$
$293$	−5.55114	+	9.61486i	−0.324301	+	0.561706i	0.657069	+	0.753830i	$0.271796\pi$
$294$	16.9715	+	15.5742i	0.989801	+	0.908305i
$295$	4.14611	+	7.18127i	0.241396	+	0.418110i
$296$	−0.661562	+	1.14586i	−0.0384525	+	0.0666017i
$297$	−16.9099	+	19.4467i	−0.981213	+	1.12841i
$298$	−21.5063	−	37.2499i	−1.24582	−	2.15783i
$299$	−30.2940			−1.75195
$300$	1.23645	+	2.49843i	0.0713867	+	0.144247i
$301$	6.33969	−	17.9665i	0.365414	−	1.03557i
$302$	−4.37584	+	7.57918i	−0.251801	+	0.436133i
$303$	−0.970370	−	1.96077i	−0.0557463	−	0.112643i
$304$	2.49979	−	4.32976i	0.143373	−	0.248329i
$305$	3.02796	+	5.24459i	0.173381	+	0.300304i
$306$	13.4092	−	17.5772i	0.766554	−	1.00482i
$307$	−11.1997			−0.639198			−0.319599	−	0.947553i	$-0.603548\pi$
$307$	−11.1997			−0.639198			−0.319599	+	0.947553i	$0.603548\pi$
$308$	20.7608	−	3.87178i	1.18295	−	0.220615i
$309$	−26.2147	−	1.68123i	−1.49130	−	0.0956419i
$310$	−0.402825	−	0.697713i	−0.0228789	−	0.0396274i
$311$	6.67593			0.378558			0.189279	−	0.981923i	$-0.439385\pi$
$311$	6.67593			0.378558			0.189279	+	0.981923i	$0.439385\pi$
$312$	−3.21331	−	6.49294i	−0.181918	−	0.367590i
$313$	−13.7157			−0.775257			−0.387629	−	0.921816i	$-0.626706\pi$
$313$	−13.7157			−0.775257			−0.387629	+	0.921816i	$0.626706\pi$
$314$	15.9730			0.901407
$315$	−7.92468	+	0.446518i	−0.446505	+	0.0251584i
$316$	13.2776			0.746922
$317$	−2.04912			−0.115090			−0.0575451	−	0.998343i	$-0.518327\pi$
$317$	−2.04912			−0.115090			−0.0575451	+	0.998343i	$0.518327\pi$
$318$	12.7699	+	0.818973i	0.716099	+	0.0459258i
$319$	−28.0946			−1.57300
$320$	2.31505	+	4.00978i	0.129415	+	0.224153i
$321$	−2.39914	−	4.84780i	−0.133907	−	0.270578i
$322$	−8.98870	+	25.4737i	−0.500920	+	1.41959i
$323$	−4.18982			−0.233128
$324$	−10.1848	+	10.2998i	−0.565820	+	0.572213i
$325$	−2.81852	−	4.88183i	−0.156344	−	0.270795i
$326$	−12.9797	+	22.4816i	−0.718881	+	1.24514i
$327$	−6.77394	−	0.434435i	−0.374599	−	0.0240243i
$328$	3.00369	−	5.20255i	0.165851	−	0.287263i
$329$	18.2580	+	21.3291i	1.00660	+	1.17591i
$330$	−9.04789	+	13.5824i	−0.498070	+	0.747686i
$331$	−5.54024			−0.304519			−0.152259	−	0.988341i	$-0.548655\pi$
$331$	−5.54024			−0.304519			−0.152259	+	0.988341i	$0.548655\pi$
$332$	−4.68993	−	8.12320i	−0.257393	−	0.445818i
$333$	−5.30579	−	0.683366i	−0.290755	−	0.0374482i
$334$	0.306566	−	0.530988i	0.0167745	−	0.0290543i
$335$	0.670844	+	1.16194i	0.0366521	+	0.0634833i
$336$	−21.0574	+	2.54617i	−1.14878	+	0.138905i
$337$	−11.1267	+	19.2721i	−0.606112	+	1.04982i	0.385762	+	0.922598i	$0.373939\pi$
$337$	−11.1267	+	19.2721i	−0.606112	+	1.04982i	−0.991875	+	0.127219i	$0.959395\pi$
$338$	−17.8361	−	30.8931i	−0.970157	−	1.68036i
$339$	−8.49164	−	17.1586i	−0.461203	−	0.931925i
$340$	3.12145	−	5.40650i	0.169284	−	0.293209i
$341$	1.05157	−	1.82137i	0.0569456	−	0.0986327i
$342$	6.10598	+	0.786427i	0.330173	+	0.0425251i
$343$	−15.7586	+	9.72968i	−0.850884	+	0.525353i
$344$	2.67157	+	4.62729i	0.144041	+	0.249487i
$345$	−4.12863	−	8.34247i	−0.222278	−	0.449144i
$346$	19.5117			1.04895
$347$	14.7511			0.791878			0.395939	−	0.918277i	$-0.370419\pi$
$347$	14.7511			0.791878			0.395939	+	0.918277i	$0.370419\pi$
$348$	−15.7590	−	1.01067i	−0.844769	−	0.0541778i
$349$	−4.59282	−	7.95501i	−0.245848	−	0.425822i	0.716521	−	0.697565i	$-0.245733\pi$
$349$	−4.59282	−	7.95501i	−0.245848	−	0.425822i	−0.962370	+	0.271743i	$0.912400\pi$
$350$	−4.94135	+	0.921536i	−0.264126	+	0.0492582i
$351$	19.2199	−	22.1033i	1.02588	−	1.17979i
$352$	−18.1262	+	31.3955i	−0.966131	+	1.67339i
$353$	5.61562	−	9.72653i	0.298889	−	0.517691i	−0.676993	−	0.735990i	$-0.736717\pi$
$353$	5.61562	−	9.72653i	0.298889	−	0.517691i	0.975882	+	0.218298i	$0.0700506\pi$
$354$	−15.1278	+	22.7094i	−0.804035	+	1.20699i
$355$	−2.51135	−	4.34979i	−0.133289	−	0.230863i
$356$	13.2948	−	23.0273i	0.704623	−	1.22044i
$357$	10.6713	+	14.2157i	0.564786	+	0.752375i
$358$	−12.7555	−	22.0932i	−0.674151	−	1.16766i
$359$	−4.84085	+	8.38460i	−0.255490	+	0.442522i	−0.965029	−	0.262145i	$-0.915570\pi$
$359$	−4.84085	+	8.38460i	−0.255490	+	0.442522i	0.709538	+	0.704667i	$0.248904\pi$
$360$	1.35012	−	1.76979i	0.0711578	−	0.0932759i
$361$	8.91663	+	15.4441i	0.469296	+	0.812845i
$362$	20.0355			1.05304
$363$	−23.5025	−	1.50729i	−1.23356	−	0.0791124i
$364$	−23.5968	+	4.40069i	−1.23681	+	0.230659i
$365$	−5.89623	+	10.2126i	−0.308623	+	0.534551i
$366$	−11.0481	+	16.5850i	−0.577492	+	0.866911i
$367$	−8.76907	+	15.1885i	−0.457742	+	0.792832i	−0.998841	−	0.0481268i	$-0.984675\pi$
$367$	−8.76907	+	15.1885i	−0.457742	+	0.792832i	0.541100	+	0.840958i	$0.318008\pi$
$368$	−12.4372	−	21.5418i	−0.648333	−	1.12295i
$369$	24.0899	+	3.10269i	1.25407	+	0.161519i
$370$	−3.38783			−0.176125
$371$	−3.42349	+	9.70206i	−0.177738	+	0.503706i
$372$	0.655372	−	0.983822i	0.0339795	−	0.0510088i
$373$	18.6891	+	32.3704i	0.967684	+	1.67608i	0.702224	+	0.711956i	$0.252190\pi$
$373$	18.6891	+	32.3704i	0.967684	+	1.67608i	0.265460	+	0.964122i	$0.414476\pi$
$374$	36.5486			1.88988
$375$	0.960253	−	1.44150i	0.0495872	−	0.0744386i
$376$	−7.87395			−0.406068
$377$	31.9325			1.64461
$378$	−12.8834	−	22.7201i	−0.662652	−	1.16860i
$379$	23.8371			1.22443			0.612214	−	0.790692i	$-0.290279\pi$
$379$	23.8371			1.22443			0.612214	+	0.790692i	$0.290279\pi$
$380$	1.73845			0.0891808
$381$	−1.94546	+	2.92046i	−0.0996689	+	0.149620i
$382$	37.2991			1.90839
$383$	−4.57197	−	7.91889i	−0.233617	−	0.404636i	0.725253	−	0.688483i	$-0.241723\pi$
$383$	−4.57197	−	7.91889i	−0.233617	−	0.404636i	−0.958870	+	0.283846i	$0.908389\pi$
$384$	5.59132	−	8.39350i	0.285331	−	0.428329i
$385$	−8.53302	−	9.96831i	−0.434883	−	0.508032i
$386$	50.3573			2.56312
$387$	−13.1030	+	17.1758i	−0.666063	+	0.873096i
$388$	7.75261	+	13.4279i	0.393579	+	0.681699i
$389$	2.32182	−	4.02152i	0.117721	−	0.203899i	−0.801143	−	0.598473i	$-0.795774\pi$
$389$	2.32182	−	4.02152i	0.117721	−	0.203899i	0.918864	+	0.394574i	$0.129108\pi$
$390$	10.2839	−	15.4378i	0.520745	−	0.781724i
$391$	−10.4228	+	18.0528i	−0.527103	+	0.912968i
$392$	0.801047	−	5.13180i	0.0404590	−	0.259195i
$393$	5.31225	+	0.340692i	0.267968	+	0.0171856i
$394$	−34.5670			−1.74146
$395$	−4.12488	−	7.14451i	−0.207545	−	0.359479i
$396$	−23.7502	−	3.05894i	−1.19349	−	0.153717i
$397$	10.4639	−	18.1240i	0.525167	−	0.909615i	−0.474404	−	0.880307i	$-0.657336\pi$
$397$	10.4639	−	18.1240i	0.525167	−	0.909615i	0.999570	−	0.0293079i	$-0.00933033\pi$
$398$	12.4266	+	21.5234i	0.622887	+	1.07887i
$399$	−1.94247	+	4.55283i	−0.0972449	+	0.227927i
$400$	2.31429	−	4.00846i	0.115714	−	0.200423i
$401$	−7.42294	−	12.8569i	−0.370684	−	0.642044i	0.618987	−	0.785401i	$-0.287543\pi$
$401$	−7.42294	−	12.8569i	−0.370684	−	0.642044i	−0.989671	+	0.143358i	$0.954210\pi$
$402$	−2.44770	+	3.67439i	−0.122080	+	0.183262i
$403$	−1.19522	+	2.07018i	−0.0595381	+	0.103123i
$404$	1.01644	−	1.76053i	0.0505700	−	0.0875898i
$405$	8.70628	+	2.28050i	0.432619	+	0.113319i
$406$	9.47488	−	26.8515i	0.470230	−	1.33262i
$407$	−4.42194	−	7.65903i	−0.219188	−	0.379644i
$408$	−4.97482	−	0.319052i	−0.246290	−	0.0157954i
$409$	10.1336			0.501073			0.250536	−	0.968107i	$-0.419393\pi$
$409$	10.1336			0.501073			0.250536	+	0.968107i	$0.419393\pi$
$410$	15.3818			0.759652
$411$	−2.89096	−	5.84159i	−0.142600	−	0.288144i
$412$	−12.2046	−	21.1389i	−0.601275	−	1.04144i
$413$	−14.2670	−	16.6667i	−0.702031	−	0.820116i
$414$	18.5780	−	24.3526i	0.913059	−	1.19687i
$415$	−2.91400	+	5.04719i	−0.143043	+	0.247757i
$416$	20.6024	−	35.6844i	1.01011	−	1.74957i
$417$	12.7575	+	25.7784i	0.624740	+	1.26237i
$418$	5.08883	+	8.81412i	0.248903	+	0.431113i
$419$	−0.759103	+	1.31480i	−0.0370846	+	0.0642324i	−0.883972	−	0.467540i	$-0.845140\pi$
$419$	−0.759103	+	1.31480i	−0.0370846	+	0.0642324i	0.846887	+	0.531772i	$0.178474\pi$
$420$	−4.42778	−	5.89843i	−0.216054	−	0.287814i
$421$	−14.2107	−	24.6136i	−0.692586	−	1.19959i	−0.970988	−	0.239129i	$-0.923138\pi$
$421$	−14.2107	−	24.6136i	−0.692586	−	1.19959i	0.278402	−	0.960465i	$-0.410195\pi$
$422$	−20.6317	+	35.7351i	−1.00433	+	1.73956i
$423$	−12.2656	−	29.3780i	−0.596372	−	1.42841i
$424$	−1.44267	−	2.49877i	−0.0700621	−	0.121351i
$425$	−3.87890			−0.188154
$426$	9.16312	−	13.7554i	0.443955	−	0.666449i
$427$	−10.4194	−	12.1720i	−0.504229	−	0.589042i
$428$	2.51305	−	4.35273i	0.121473	−	0.210397i
$429$	48.3240	+	3.09917i	2.33310	+	0.149630i
$430$	−6.84048	+	11.8481i	−0.329877	+	0.571364i
$431$	−3.58814	−	6.21484i	−0.172835	−	0.299358i	0.766575	−	0.642155i	$-0.221959\pi$
$431$	−3.58814	−	6.21484i	−0.172835	−	0.299358i	−0.939410	+	0.342796i	$0.888626\pi$
$432$	23.6082	+	4.59266i	1.13585	+	0.220964i
$433$	−7.11022			−0.341696			−0.170848	−	0.985297i	$-0.554651\pi$
$433$	−7.11022			−0.341696			−0.170848	+	0.985297i	$0.554651\pi$
$434$	1.38614	+	1.61929i	0.0665369	+	0.0777286i
$435$	4.35194	+	8.79370i	0.208659	+	0.421626i
$436$	−3.15369	−	5.46235i	−0.151034	−	0.261599i
$437$	−5.80485			−0.277684
$438$	−38.7253	−	2.48358i	−1.85036	−	0.118670i
$439$	−34.1127			−1.62811			−0.814056	−	0.580787i	$-0.802745\pi$
$439$	−34.1127			−1.62811			−0.814056	+	0.580787i	$0.802745\pi$
$440$	3.67994			0.175434
$441$	20.3948	−	5.00527i	0.971180	−	0.238346i
$442$	−41.5414			−1.97592
$443$	13.1332			0.623976			0.311988	−	0.950086i	$-0.399005\pi$
$443$	13.1332			0.623976			0.311988	+	0.950086i	$0.399005\pi$
$444$	−2.20485	−	4.45521i	−0.104638	−	0.211435i
$445$	−16.5209			−0.783168
$446$	7.60093	+	13.1652i	0.359914	+	0.623390i
$447$	−39.1331	−	2.50973i	−1.85093	−	0.118706i
$448$	−7.96619	−	9.30613i	−0.376367	−	0.439673i
$449$	−21.5648			−1.01771			−0.508854	−	0.860853i	$-0.669931\pi$
$449$	−21.5648			−1.01771			−0.508854	+	0.860853i	$0.669931\pi$
$450$	5.65287	+	0.728069i	0.266479	+	0.0343215i
$451$	20.0770	+	34.7743i	0.945387	+	1.63746i
$452$	8.89483	−	15.4063i	0.418378	−	0.724651i
$453$	3.53893	+	7.15091i	0.166273	+	0.335979i
$454$	−7.01972	+	12.1585i	−0.329452	+	0.570627i
$455$	9.69868	+	11.3300i	0.454681	+	0.531160i
$456$	−0.615725	−	1.24416i	−0.0288339	−	0.0582631i
$457$	31.0608			1.45296			0.726482	−	0.687185i	$-0.241154\pi$
$457$	31.0608			1.45296			0.726482	+	0.687185i	$0.241154\pi$
$458$	5.21169	+	9.02692i	0.243526	+	0.421800i
$459$	−6.55908	−	19.0583i	−0.306152	−	0.889563i
$460$	4.32466	−	7.49052i	0.201638	−	0.349248i
$461$	8.82780	+	15.2902i	0.411152	+	0.712135i	0.995016	−	0.0997158i	$-0.0317933\pi$
$461$	8.82780	+	15.2902i	0.411152	+	0.712135i	−0.583864	+	0.811851i	$0.698460\pi$
$462$	16.9445	−	39.7153i	0.788331	−	1.84772i
$463$	10.6941	−	18.5227i	0.496997	−	0.860824i	−0.502997	−	0.864288i	$-0.667769\pi$
$463$	10.6941	−	18.5227i	0.496997	−	0.860824i	0.999994	+	0.00346411i	$0.00110266\pi$
$464$	13.1099	+	22.7070i	0.608611	+	1.05415i
$465$	−0.732985	−	0.0470087i	−0.0339914	−	0.00217998i
$466$	2.06173	−	3.57102i	0.0955078	−	0.165424i
$467$	6.51071	−	11.2769i	0.301280	−	0.521832i	−0.675146	−	0.737684i	$-0.735920\pi$
$467$	6.51071	−	11.2769i	0.301280	−	0.521832i	0.976426	+	0.215852i	$0.0692529\pi$
$468$	26.9946	+	3.47681i	1.24783	+	0.160715i
$469$	−2.30841	−	2.69669i	−0.106592	−	0.124522i
$470$	−10.0805	−	17.4600i	−0.464981	−	0.805370i
$471$	8.07330	−	12.1193i	0.371998	−	0.558430i
$472$	6.15276			0.283204
$473$	−35.7140			−1.64213
$474$	15.0504	−	22.5931i	0.691287	−	1.03774i
$475$	−0.540078	−	0.935442i	−0.0247805	−	0.0429210i
$476$	−5.49613	+	15.5759i	−0.251915	+	0.713920i
$477$	7.07572	−	9.27509i	0.323975	−	0.424677i
$478$	−4.82947	+	8.36489i	−0.220895	+	0.382601i
$479$	14.8801	−	25.7731i	0.679890	−	1.17760i	−0.295124	−	0.955459i	$-0.595361\pi$
$479$	14.8801	−	25.7731i	0.679890	−	1.17760i	0.975014	−	0.222145i	$-0.0713057\pi$
$480$	12.6347	+	0.810304i	0.576692	+	0.0369852i
$481$	5.02601	+	8.70530i	0.229166	+	0.396927i
$482$	8.41479	−	14.5748i	0.383283	−	0.663866i
$483$	14.7847	+	19.6954i	0.672729	+	0.896171i
$484$	−10.9419	−	18.9519i	−0.497359	−	0.861450i
$485$	4.81694	−	8.34318i	0.218726	−	0.378844i
$486$	5.98156	+	29.0055i	0.271329	+	1.31571i
$487$	7.27767	+	12.6053i	0.329783	+	0.571201i	0.982469	−	0.186428i	$-0.0596911\pi$
$487$	7.27767	+	12.6053i	0.329783	+	0.571201i	−0.652686	+	0.757629i	$0.726358\pi$
$488$	4.49345			0.203409
$489$	10.4973	+	21.2112i	0.474703	+	0.959205i
$490$	12.4050	−	4.79366i	0.560400	−	0.216555i
$491$	10.6020	−	18.3632i	0.478462	−	0.828720i	−0.521234	−	0.853414i	$-0.674528\pi$
$491$	10.6020	−	18.3632i	0.478462	−	0.828720i	0.999695	+	0.0246944i	$0.00786128\pi$
$492$	10.0107	+	20.2280i	0.451317	+	0.911949i
$493$	10.9865	−	19.0292i	0.494808	−	0.857033i
$494$	−5.78400	−	10.0182i	−0.260234	−	0.450739i
$495$	5.73239	+	13.7300i	0.257652	+	0.617118i
$496$	−1.96279			−0.0881317
$497$	8.64168	+	10.0953i	0.387633	+	0.452834i
$498$	−19.1386	−	1.22742i	−0.857619	−	0.0550019i
$499$	6.48145	+	11.2262i	0.290149	+	0.502554i	0.973845	−	0.227214i	$-0.0729616\pi$
$499$	6.48145	+	11.2262i	0.290149	+	0.502554i	−0.683695	+	0.729767i	$0.739628\pi$
$500$	1.60945			0.0719767
$501$	−0.247933	−	0.500984i	−0.0110768	−	0.0223823i
$502$	−0.477592			−0.0213160
$503$	37.0834			1.65347			0.826733	−	0.562594i	$-0.190197\pi$
$503$	37.0834			1.65347			0.826733	+	0.562594i	$0.190197\pi$
$504$	−2.65310	+	5.25793i	−0.118179	+	0.234207i
$505$	−1.26310			−0.0562071
$506$	50.6369			2.25108
$507$	−32.4548	−	2.08143i	−1.44137	−	0.0924397i
$508$	−3.26072			−0.144671
$509$	−0.0890596	−	0.154256i	−0.00394750	−	0.00683727i	0.864045	−	0.503415i	$-0.167923\pi$
$509$	−0.0890596	−	0.154256i	−0.00394750	−	0.00683727i	−0.867992	+	0.496577i	$0.834590\pi$
$510$	−5.66148	−	11.4398i	−0.250695	−	0.506564i
$511$	10.3819	−	29.4220i	0.459268	−	1.30155i
$512$	26.9644			1.19167
$513$	3.68287	−	4.23537i	0.162603	−	0.186996i
$514$	−12.4735	−	21.6048i	−0.550185	−	0.952948i
$515$	−7.58307	+	13.1343i	−0.334150	+	0.578765i
$516$	−20.0328	−	1.28477i	−0.881897	−	0.0565589i
$517$	26.3151	−	45.5791i	1.15734	−	2.00457i
$518$	8.81144	−	1.64329i	0.387152	−	0.0722019i
$519$	9.86187	−	14.8043i	0.432888	−	0.649836i
$520$	−4.18265			−0.183421
$521$	−14.1889	−	24.5760i	−0.621628	−	1.07669i	−0.989183	−	0.146690i	$-0.953138\pi$
$521$	−14.1889	−	24.5760i	−0.621628	−	1.07669i	0.367554	−	0.930002i	$-0.380195\pi$
$522$	−19.5829	+	25.6698i	−0.857119	+	1.12354i
$523$	7.88941	−	13.6649i	0.344980	−	0.597522i	−0.640370	−	0.768066i	$-0.721219\pi$
$523$	7.88941	−	13.6649i	0.344980	−	0.597522i	0.985350	+	0.170544i	$0.0545524\pi$
$524$	2.47318	+	4.28368i	0.108042	+	0.187133i
$525$	−1.79832	+	4.21498i	−0.0784852	+	0.183957i
$526$	−24.6345	+	42.6683i	−1.07412	+	1.86042i
$527$	0.822441	+	1.42451i	0.0358261	+	0.0620526i
$528$	17.6356	+	35.6352i	0.767490	+	1.55082i
$529$	−2.94041	+	5.09293i	−0.127844	+	0.221432i
$530$	3.69392	−	6.39805i	0.160454	−	0.277914i
$531$	9.58440	+	22.9562i	0.415927	+	0.996214i
$532$	−4.52156	+	0.843247i	−0.196034	+	0.0365594i
$533$	−22.8196	−	39.5247i	−0.988426	−	1.71200i
$534$	−24.1133	−	48.7243i	−1.04348	−	2.10851i
$535$	−3.12287			−0.135014
$536$	0.995522			0.0430000
$537$	−23.2101	−	1.48854i	−1.00159	−	0.0642353i
$538$	4.48858	+	7.77444i	0.193516	+	0.335180i
$539$	27.0288	+	21.7877i	1.16421	+	0.938461i
$540$	2.72152	+	7.90772i	0.117115	+	0.340294i
$541$	2.15961	−	3.74055i	0.0928489	−	0.160819i	−0.815860	−	0.578250i	$-0.803736\pi$
$541$	2.15961	−	3.74055i	0.0928489	−	0.160819i	0.908709	+	0.417431i	$0.137069\pi$
$542$	−19.3679	+	33.5463i	−0.831925	+	1.44094i
$543$	10.1266	−	15.2018i	0.434576	−	0.652370i
$544$	−14.1767	−	24.5547i	−0.607820	−	1.05277i
$545$	−1.95948	+	3.39393i	−0.0839351	+	0.145380i
$546$	−19.2592	+	45.1406i	−0.824220	+	1.93184i
$547$	−6.34548	−	10.9907i	−0.271313	−	0.469928i	0.697885	−	0.716209i	$-0.254124\pi$
$547$	−6.34548	−	10.9907i	−0.271313	−	0.469928i	−0.969198	+	0.246282i	$0.920791\pi$
$548$	3.02822	−	5.24504i	0.129359	−	0.224057i
$549$	6.99963	+	16.7653i	0.298737	+	0.715524i
$550$	4.71121	+	8.16005i	0.200887	+	0.347946i
$551$	6.11882			0.260671
$552$	−6.89245	−	0.442035i	−0.293362	−	0.0188143i
$553$	14.1939	+	16.5814i	0.603587	+	0.705113i
$554$	−3.13710	+	5.43361i	−0.133283	+	0.230852i
$555$	−1.71233	+	2.57049i	−0.0726842	+	0.109111i
$556$	−13.3633	+	23.1459i	−0.566729	+	0.981604i
$557$	0.832500	+	1.44193i	0.0352742	+	0.0610966i	0.883124	−	0.469141i	$-0.155436\pi$
$557$	0.832500	+	1.44193i	0.0352742	+	0.0610966i	−0.847849	+	0.530237i	$0.822103\pi$
$558$	−0.931194	−	2.23036i	−0.0394206	−	0.0944188i
$559$	40.5927			1.71689
$560$	−4.07492	+	11.5482i	−0.172197	+	0.488000i
$561$	18.4729	−	27.7309i	0.779928	−	1.17080i
$562$	25.9190	+	44.8929i	1.09332	+	1.89369i
$563$	−1.03276			−0.0435255			−0.0217627	−	0.999763i	$-0.506928\pi$
$563$	−1.03276			−0.0435255			−0.0217627	+	0.999763i	$0.506928\pi$
$564$	16.4005	−	24.6198i	0.690584	−	1.03668i
$565$	−11.0533			−0.465014
$566$	−25.9259			−1.08975
$567$	−23.7504	−	1.70834i	−0.997423	−	0.0717437i
$568$	−3.72681			−0.156373
$569$	−40.2940			−1.68921			−0.844607	−	0.535387i	$-0.820166\pi$
$569$	−40.2940			−1.68921			−0.844607	+	0.535387i	$0.820166\pi$
$570$	1.97057	−	2.95815i	0.0825381	−	0.123903i
$571$	22.2175			0.929774			0.464887	−	0.885370i	$-0.346095\pi$
$571$	22.2175			0.929774			0.464887	+	0.885370i	$0.346095\pi$
$572$	22.4978	+	38.9674i	0.940681	+	1.62931i
$573$	18.8523	−	28.3003i	0.787564	−	1.18226i
$574$	−40.0066	+	7.46102i	−1.66984	+	0.311417i
$575$	−5.37409			−0.224115
$576$	5.35160	+	12.8180i	0.222983	+	0.534082i
$577$	3.99702	+	6.92304i	0.166398	+	0.288210i	0.937151	−	0.348924i	$-0.113453\pi$
$577$	3.99702	+	6.92304i	0.166398	+	0.288210i	−0.770753	+	0.637134i	$0.780120\pi$
$578$	1.85627	−	3.21515i	0.0772106	−	0.133733i
$579$	25.4523	−	38.2082i	1.05776	−	1.58788i
$580$	−4.55857	+	7.89567i	−0.189284	+	0.327850i
$581$	5.13087	−	14.5407i	0.212864	−	0.603251i
$582$	31.6367	+	2.02896i	1.31138	+	0.0841032i
$583$	19.2858			0.798738
$584$	4.37496	+	7.57765i	0.181037	+	0.313565i
$585$	−6.51547	−	15.6056i	−0.269382	−	0.645213i
$586$	−10.5464	+	18.2668i	−0.435666	+	0.754596i
$587$	−9.83730	−	17.0387i	−0.406029	−	0.703263i	0.588412	−	0.808561i	$-0.299753\pi$
$587$	−9.83730	−	17.0387i	−0.406029	−	0.703263i	−0.994441	+	0.105299i	$0.966420\pi$
$588$	14.3773	+	13.1936i	0.592911	+	0.544093i
$589$	−0.229025	+	0.396682i	−0.00943679	+	0.0163450i
$590$	7.87700	+	13.6434i	0.324291	+	0.561689i
$591$	−17.4714	+	26.2274i	−0.718676	+	1.07885i
$592$	−4.12685	+	7.14791i	−0.169612	+	0.293777i
$593$	2.39541	−	4.14898i	0.0983678	−	0.170378i	−0.812641	−	0.582764i	$-0.801971\pi$
$593$	2.39541	−	4.14898i	0.0983678	−	0.170378i	0.911009	+	0.412386i	$0.135305\pi$
$594$	−32.1264	+	36.9460i	−1.31816	+	1.51591i
$595$	10.0887	−	1.88148i	0.413595	−	0.0771334i
$596$	−18.2189	−	31.5560i	−0.746274	−	1.29258i
$597$	22.6115	+	1.45015i	0.925428	+	0.0593507i
$598$	−57.5542			−2.35356
$599$	3.47430			0.141956			0.0709779	−	0.997478i	$-0.477388\pi$
$599$	3.47430			0.141956			0.0709779	+	0.997478i	$0.477388\pi$
$600$	−0.570034	−	1.15183i	−0.0232715	−	0.0470234i
$601$	−11.6008	−	20.0932i	−0.473207	−	0.819618i	0.526323	−	0.850285i	$-0.323570\pi$
$601$	−11.6008	−	20.0932i	−0.473207	−	0.819618i	−0.999530	+	0.0306665i	$0.990237\pi$
$602$	12.0445	−	34.1337i	0.490897	−	1.39119i
$603$	1.55076	+	3.71433i	0.0631520	+	0.151259i
$604$	−3.70696	+	6.42064i	−0.150834	+	0.261252i
$605$	−6.79854	+	11.7754i	−0.276400	+	0.478738i
$606$	−1.84356	−	3.72518i	−0.0748896	−	0.151325i
$607$	−22.2826	−	38.5947i	−0.904425	−	1.56651i	−0.821688	−	0.569938i	$-0.806967\pi$
$607$	−22.2826	−	38.5947i	−0.904425	−	1.56651i	−0.0827369	−	0.996571i	$-0.526366\pi$
$608$	3.94777	−	6.83774i	0.160103	−	0.277307i
$609$	−15.5844	−	20.7607i	−0.631513	−	0.841265i
$610$	5.75269	+	9.96396i	0.232920	+	0.403429i
$611$	−29.9099	+	51.8055i	−1.21003	+	2.09583i
$612$	11.3595	−	14.8904i	0.459181	−	0.601909i
$613$	9.93289	+	17.2043i	0.401186	+	0.694874i	0.993869	−	0.110561i	$-0.0352649\pi$
$613$	9.93289	+	17.2043i	0.401186	+	0.694874i	−0.592684	+	0.805435i	$0.701932\pi$
$614$	−21.2777			−0.858699
$615$	7.77448	−	11.6708i	0.313497	−	0.470611i
$616$	−9.57119	+	1.78498i	−0.385634	+	0.0719188i
$617$	−8.25212	+	14.2931i	−0.332218	+	0.575418i	−0.982946	−	0.183892i	$-0.941130\pi$
$617$	−8.25212	+	14.2931i	−0.332218	+	0.575418i	0.650729	+	0.759310i	$0.274464\pi$
$618$	−49.8041	−	3.19410i	−2.00341	−	0.128485i
$619$	−10.6299	+	18.4115i	−0.427251	+	0.740020i	−0.996628	−	0.0820567i	$-0.973851\pi$
$619$	−10.6299	+	18.4115i	−0.427251	+	0.740020i	0.569377	+	0.822077i	$0.307184\pi$
$620$	−0.341250	−	0.591062i	−0.0137049	−	0.0237376i
$621$	−9.08738	−	26.4046i	−0.364664	−	1.05958i
$622$	12.6833			0.508554
$623$	42.9694	−	8.01358i	1.72153	−	0.321057i
$624$	−20.0447	−	40.5032i	−0.802431	−	1.62142i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−26.0578			−1.04148
$627$	9.25971	+	0.593855i	0.369797	+	0.0237163i
$628$	13.5314			0.539961
$629$	6.91688			0.275794
$630$	−15.0557	+	0.848320i	−0.599835	+	0.0337979i
$631$	9.83777			0.391635			0.195818	−	0.980640i	$-0.437264\pi$
$631$	9.83777			0.391635			0.195818	+	0.980640i	$0.437264\pi$
$632$	−6.12126			−0.243491
$633$	16.6857	+	33.7159i	0.663198	+	1.34009i
$634$	−3.89303			−0.154612
$635$	1.01299	+	1.75456i	0.0401994	+	0.0696275i
$636$	10.8179	+	0.693787i	0.428958	+	0.0275105i
$637$	−30.7211	−	24.7640i	−1.21721	−	0.981185i
$638$	−53.3757			−2.11316
$639$	−5.80539	−	13.9049i	−0.229658	−	0.550068i
$640$	−2.91138	−	5.04266i	−0.115082	−	0.199329i
$641$	−1.36762	+	2.36879i	−0.0540178	+	0.0935616i	−0.891770	−	0.452489i	$-0.850536\pi$
$641$	−1.36762	+	2.36879i	−0.0540178	+	0.0935616i	0.837752	+	0.546051i	$0.183869\pi$
$642$	−4.55802	−	9.21012i	−0.179891	−	0.363494i
$643$	−13.6815	+	23.6971i	−0.539546	+	0.934522i	0.459382	+	0.888239i	$0.348071\pi$
$643$	−13.6815	+	23.6971i	−0.539546	+	0.934522i	−0.998928	+	0.0462829i	$0.985262\pi$
$644$	−7.61471	+	21.5799i	−0.300062	+	0.850366i
$645$	5.53219	+	11.1786i	0.217830	+	0.440156i
$646$	−7.96004			−0.313184
$647$	6.27552	+	10.8695i	0.246716	+	0.427325i	0.962613	−	0.270882i	$-0.0873152\pi$
$647$	6.27552	+	10.8695i	0.246716	+	0.427325i	−0.715897	+	0.698206i	$0.753982\pi$
$648$	4.69541	−	4.74846i	0.184453	−	0.186537i
$649$	−20.5628	+	35.6158i	−0.807161	+	1.39804i
$650$	−5.35479	−	9.27476i	−0.210032	−	0.363786i
$651$	1.92923	−	0.233273i	0.0756124	−	0.00914271i
$652$	−10.9957	+	19.0451i	−0.430625	+	0.745864i
$653$	3.40827	+	5.90330i	0.133376	+	0.231014i	0.924976	−	0.380026i	$-0.124085\pi$
$653$	3.40827	+	5.90330i	0.133376	+	0.231014i	−0.791600	+	0.611040i	$0.790752\pi$
$654$	−12.8695	−	0.825363i	−0.503237	−	0.0322742i
$655$	1.53667	−	2.66158i	0.0600425	−	0.103997i
$656$	18.7371	−	32.4537i	0.731562	−	1.26710i
$657$	−21.4575	+	28.1272i	−0.837136	+	1.09734i
$658$	34.6876	+	40.5222i	1.35226	+	1.57972i
$659$	12.8692	+	22.2901i	0.501313	+	0.868300i	0.999999	+	0.00151714i	$0.000482920\pi$
$659$	12.8692	+	22.2901i	0.501313	+	0.868300i	−0.498686	+	0.866783i	$0.666184\pi$
$660$	−7.66486	+	11.5062i	−0.298354	+	0.447879i
$661$	−36.1443			−1.40585			−0.702925	−	0.711264i	$-0.748123\pi$
$661$	−36.1443			−1.40585			−0.702925	+	0.711264i	$0.748123\pi$
$662$	−10.5256			−0.409091
$663$	−20.9965	+	31.5191i	−0.815435	+	1.22410i
$664$	2.16216	+	3.74498i	0.0839083	+	0.145333i
$665$	1.85843	+	2.17103i	0.0720670	+	0.0841889i
$666$	−10.0802	−	1.29830i	−0.390601	−	0.0503079i
$667$	15.2215	−	26.3643i	0.589377	−	1.02083i
$668$	0.259705	−	0.449822i	0.0100483	−	0.0174041i
$669$	13.8307	+	0.887011i	0.534727	+	0.0342938i
$670$	1.27451	+	2.20751i	0.0492385	+	0.0852835i
$671$	−15.0173	+	26.0108i	−0.579737	+	1.00413i
$672$	−33.2547	+	4.02101i	−1.28283	+	0.155114i
$673$	21.2313	+	36.7737i	0.818408	+	1.41752i	0.906855	+	0.421443i	$0.138476\pi$
$673$	21.2313	+	36.7737i	0.818408	+	1.41752i	−0.0884474	+	0.996081i	$0.528191\pi$
$674$	−21.1392	+	36.6142i	−0.814252	+	1.41033i
$675$	3.40957	−	3.92107i	0.131235	−	0.150922i
$676$	−15.1097	−	26.1708i	−0.581144	−	1.00657i
$677$	16.0206			0.615722			0.307861	−	0.951431i	$-0.400387\pi$
$677$	16.0206			0.615722			0.307861	+	0.951431i	$0.400387\pi$
$678$	−16.1329	−	32.5988i	−0.619580	−	1.25195i
$679$	−8.48150	+	24.0363i	−0.325490	+	0.922429i
$680$	−1.43906	+	2.49252i	−0.0551854	+	0.0955838i
$681$	5.67715	+	11.4715i	0.217549	+	0.439588i
$682$	1.99783	−	3.46034i	0.0765008	−	0.132503i
$683$	−1.73764	−	3.00967i	−0.0664888	−	0.115162i	0.830865	−	0.556475i	$-0.187846\pi$
$683$	−1.73764	−	3.00967i	−0.0664888	−	0.115162i	−0.897353	+	0.441313i	$0.854513\pi$
$684$	5.17263	+	0.666216i	0.197781	+	0.0254734i
$685$	−3.76306			−0.143779
$686$	−29.9390	+	18.4850i	−1.14308	+	0.705760i
$687$	9.48326	+	0.608192i	0.361809	+	0.0232040i
$688$	16.6653	+	28.8652i	0.635359	+	1.10047i
$689$	−21.9204			−0.835101
$690$	−7.84379	−	15.8495i	−0.298608	−	0.603380i
$691$	36.2643			1.37956			0.689780	−	0.724019i	$-0.257707\pi$
$691$	36.2643			1.37956			0.689780	+	0.724019i	$0.257707\pi$
$692$	16.5292			0.628344
$693$	−21.5692	−	32.9300i	−0.819348	−	1.25091i
$694$	28.0249			1.06381
$695$	16.6060			0.629903
$696$	7.26525	+	0.465944i	0.275388	+	0.0176616i
$697$	−31.4047			−1.18954
$698$	−8.72570	−	15.1134i	−0.330273	−	0.572049i
$699$	−1.66741	−	3.36924i	−0.0630672	−	0.127436i
$700$	−4.18603	+	0.780672i	−0.158217	+	0.0295066i
$701$	−40.8817			−1.54408			−0.772040	−	0.635574i	$-0.780764\pi$
$701$	−40.8817			−1.54408			−0.772040	+	0.635574i	$0.780764\pi$
$702$	36.5151	−	41.9930i	1.37817	−	1.58492i
$703$	0.963069	+	1.66808i	0.0363228	+	0.0629130i
$704$	−11.4816	+	19.8867i	−0.432728	+	0.749507i
$705$	−18.3427	−	1.17638i	−0.690825	−	0.0443049i
$706$	10.6689	−	18.4790i	0.401528	−	0.695466i
$707$	3.28520	−	0.612673i	0.123553	−	0.0230419i
$708$	−12.8154	+	19.2381i	−0.481633	+	0.723011i
$709$	40.5323			1.52222			0.761110	−	0.648622i	$-0.224655\pi$
$709$	40.5323			1.52222			0.761110	+	0.648622i	$0.224655\pi$
$710$	−4.77120	−	8.26397i	−0.179060	−	0.310141i
$711$	−9.53533	−	22.8387i	−0.357603	−	0.856517i
$712$	−6.12921	+	10.6161i	−0.229702	+	0.397855i
$713$	1.13946	+	1.97361i	0.0426733	+	0.0739122i
$714$	20.2740	+	27.0078i	0.758734	+	1.01074i
$715$	13.9786	−	24.2116i	0.522770	−	0.905464i
$716$	−10.8058	−	18.7161i	−0.403830	−	0.699454i
$717$	3.90580	+	7.89222i	0.145865	+	0.294740i
$718$	−9.19691	+	15.9295i	−0.343226	+	0.594484i
$719$	−4.34752	+	7.53012i	−0.162135	+	0.280826i	−0.935634	−	0.352971i	$-0.885171\pi$
$719$	−4.34752	+	7.53012i	−0.162135	+	0.280826i	0.773499	+	0.633797i	$0.218505\pi$
$720$	8.42212	−	11.0400i	0.313874	−	0.411436i
$721$	13.3520	−	37.8392i	0.497255	−	1.40921i
$722$	16.9403	+	29.3415i	0.630453	+	1.09198i
$723$	−6.80541	−	13.7513i	−0.253096	−	0.511416i
$724$	16.9729			0.630794
$725$	5.66476			0.210384
$726$	−44.6514	−	2.86364i	−1.65717	−	0.106280i
$727$	10.5850	+	18.3338i	0.392578	+	0.679964i	0.992789	−	0.119877i	$-0.0382501\pi$
$727$	10.5850	+	18.3338i	0.392578	+	0.679964i	−0.600211	+	0.799842i	$0.704917\pi$
$728$	10.8787	−	2.02882i	0.403191	−	0.0751930i
$729$	25.0309	+	10.1219i	0.927071	+	0.374886i
$730$	−11.2020	+	19.4024i	−0.414604	+	0.718115i
$731$	13.9661	−	24.1900i	0.516555	−	0.894699i
$732$	−9.35929	+	14.0498i	−0.345929	+	0.519297i
$733$	1.54156	+	2.67007i	0.0569390	+	0.0986212i	0.893090	−	0.449878i	$-0.148533\pi$
$733$	1.54156	+	2.67007i	0.0569390	+	0.0986212i	−0.836151	+	0.548499i	$0.815199\pi$
$734$	−16.6600	+	28.8559i	−0.614930	+	1.06509i
$735$	2.63277	−	11.8351i	0.0971111	−	0.436543i
$736$	−19.6413	−	34.0197i	−0.723988	−	1.25398i
$737$	−3.32708	+	5.76267i	−0.122555	+	0.212271i
$738$	45.7673	+	5.89465i	1.68472	+	0.216985i
$739$	−9.40466	−	16.2893i	−0.345956	−	0.599213i	0.639571	−	0.768732i	$-0.279112\pi$
$739$	−9.40466	−	16.2893i	−0.345956	−	0.599213i	−0.985527	+	0.169519i	$0.945779\pi$
$740$	−2.86998			−0.105502
$741$	−10.5246	−	0.674979i	−0.386632	−	0.0247960i
$742$	−6.50412	+	18.4325i	−0.238774	+	0.676678i
$743$	7.14920	−	12.3828i	0.262279	−	0.454280i	−0.704568	−	0.709636i	$-0.748859\pi$
$743$	7.14920	−	12.3828i	0.262279	−	0.454280i	0.966847	+	0.255356i	$0.0821927\pi$
$744$	−0.302142	+	0.453565i	−0.0110771	+	0.0166285i
$745$	−11.3200	+	19.6067i	−0.414731	+	0.718335i
$746$	35.5065	+	61.4991i	1.29999	+	2.25164i
$747$	−10.6046	+	13.9008i	−0.388001	+	0.508604i
$748$	30.9619			1.13208
$749$	8.12231	−	1.51477i	0.296783	−	0.0553485i
$750$	1.82434	−	2.73864i	0.0666155	−	0.100001i
$751$	−1.46616	−	2.53946i	−0.0535009	−	0.0926663i	0.838035	−	0.545617i	$-0.183705\pi$
$751$	−1.46616	−	2.53946i	−0.0535009	−	0.0926663i	−0.891536	+	0.452951i	$0.850371\pi$
$752$	−49.1180			−1.79115
$753$	−0.241392	+	0.362369i	−0.00879681	+	0.0132055i
$754$	60.6672			2.20937
$755$	4.60650			0.167648
$756$	−10.9141	−	19.2472i	−0.396942	−	0.700013i
$757$	45.0838			1.63860			0.819299	−	0.573366i	$-0.194363\pi$
$757$	45.0838			1.63860			0.819299	+	0.573366i	$0.194363\pi$
$758$	45.2870			1.64490
$759$	25.5936	−	38.4203i	0.928990	−	1.39457i
$760$	−0.801467			−0.0290723
$761$	−2.43832	−	4.22329i	−0.0883890	−	0.153094i	0.818441	−	0.574590i	$-0.194839\pi$
$761$	−2.43832	−	4.22329i	−0.0883890	−	0.153094i	−0.906830	+	0.421496i	$0.861505\pi$
$762$	−3.69609	+	5.54844i	−0.133895	+	0.200999i
$763$	3.45019	−	9.77775i	0.124905	−	0.353978i
$764$	31.5976			1.14316
$765$	−11.5414	−	1.48649i	−0.417279	−	0.0537440i
$766$	−8.68608	−	15.0447i	−0.313841	−	0.543589i
$767$	23.3718	−	40.4812i	0.843907	−	1.46169i
$768$	19.5148	−	29.2950i	0.704180	−	1.05709i
$769$	9.30829	−	16.1224i	0.335666	−	0.581390i	−0.647947	−	0.761686i	$-0.724372\pi$
$769$	9.30829	−	16.1224i	0.335666	−	0.581390i	0.983612	+	0.180296i	$0.0577054\pi$
$770$	−16.2115	−	18.9383i	−0.584222	−	0.682490i
$771$	−22.6970	−	1.45563i	−0.817413	−	0.0524234i
$772$	42.6598			1.53536
$773$	19.5690	+	33.8945i	0.703847	+	1.21910i	0.967106	+	0.254374i	$0.0818693\pi$
$773$	19.5690	+	33.8945i	0.703847	+	1.21910i	−0.263259	+	0.964725i	$0.584797\pi$
$774$	−24.8938	+	32.6316i	−0.894789	+	1.17292i
$775$	−0.212029	+	0.367245i	−0.00761632	+	0.0131918i
$776$	−3.57413	−	6.19057i	−0.128304	−	0.222229i
$777$	3.20678	−	7.51617i	0.115042	−	0.269641i
$778$	4.41113	−	7.64030i	0.158147	−	0.273918i
$779$	−4.37262	−	7.57361i	−0.156666	−	0.271353i
$780$	8.71192	−	13.0780i	0.311937	−	0.468269i
$781$	12.4552	−	21.5730i	0.445681	−	0.771941i
$782$	−19.8018	+	34.2977i	−0.708110	+	1.22648i
$783$	9.57890	+	27.8327i	0.342322	+	0.994661i
$784$	4.99696	−	32.0124i	0.178463	−	1.14330i
$785$	−4.20374	−	7.28108i	−0.150038	−	0.259873i
$786$	10.0925	+	0.647265i	0.359988	+	0.0230872i
$787$	−46.9548			−1.67376			−0.836879	−	0.547388i	$-0.815622\pi$
$787$	−46.9548			−1.67376			−0.836879	+	0.547388i	$0.815622\pi$
$788$	−29.2832			−1.04317
$789$	19.9230	+	40.2572i	0.709278	+	1.43320i
$790$	−7.83668	−	13.5735i	−0.278817	−	0.482924i
$791$	28.7485	−	5.36145i	1.02218	−	0.190631i
$792$	10.9494	+	1.41024i	0.389070	+	0.0501107i
$793$	17.0688	−	29.5640i	0.606130	−	1.04985i
$794$	19.8798	−	34.4329i	0.705509	−	1.22198i
$795$	−2.98743	−	6.03652i	−0.105953	−	0.214093i
$796$	10.5271	+	18.2334i	0.373122	+	0.646266i
$797$	−9.63386	+	16.6863i	−0.341249	+	0.591061i	−0.984665	−	0.174456i	$-0.944183\pi$
$797$	−9.63386	+	16.6863i	−0.341249	+	0.591061i	0.643416	+	0.765517i	$0.277517\pi$
$798$	−3.69040	+	8.64972i	−0.130639	+	0.306197i
$799$	20.5813	+	35.6478i	0.728113	+	1.26113i
$800$	3.65482	−	6.33033i	0.129217	−	0.223811i
$801$	−49.1568	−	6.33121i	−1.73687	−	0.223702i
$802$	−14.1025	−	24.4263i	−0.497977	−	0.862522i
$803$	−58.4852			−2.06390
$804$	−2.07355	+	3.11274i	−0.0731284	+	0.109778i
$805$	13.9775	−	2.60673i	0.492642	−	0.0918753i
$806$	−2.27074	+	3.93304i	−0.0799835	+	0.138535i
$807$	8.16747	+	0.523807i	0.287509	+	0.0184389i
$808$	−0.468604	+	0.811646i	−0.0164854	+	0.0285536i
$809$	−24.4939	−	42.4246i	−0.861159	−	1.49157i	−0.870811	−	0.491617i	$-0.836406\pi$
$809$	−24.4939	−	42.4246i	−0.861159	−	1.49157i	0.00965287	−	0.999953i	$-0.496927\pi$
$810$	16.5407	+	4.33262i	0.581180	+	0.152233i
$811$	−34.7360			−1.21975			−0.609873	−	0.792499i	$-0.708780\pi$
$811$	−34.7360			−1.21975			−0.609873	+	0.792499i	$0.708780\pi$
$812$	8.02657	−	22.7471i	0.281677	−	0.798266i
$813$	15.6637	+	31.6507i	0.549350	+	1.11004i
$814$	−8.40105	−	14.5510i	−0.294457	−	0.510014i
$815$	13.6639			0.478627
$816$	−31.0331	−	1.99025i	−1.08638	−	0.0696728i
$817$	7.77826			0.272127
$818$	19.2523			0.673141
$819$	24.5157	+	37.4284i	0.856649	+	1.30785i
$820$	13.0306			0.455047
$821$	−29.8436			−1.04155			−0.520774	−	0.853695i	$-0.674356\pi$
$821$	−29.8436			−1.04155			−0.520774	+	0.853695i	$0.674356\pi$
$822$	−5.49240	−	11.0982i	−0.191570	−	0.387093i
$823$	39.2953			1.36975			0.684873	−	0.728662i	$-0.259858\pi$
$823$	39.2953			1.36975			0.684873	+	0.728662i	$0.259858\pi$
$824$	5.62658	+	9.74552i	0.196011	+	0.339501i
$825$	8.57257	+	0.549787i	0.298459	+	0.0191411i
$826$	−27.1052	−	31.6644i	−0.943109	−	1.10174i
$827$	45.4517			1.58051			0.790255	−	0.612778i	$-0.209948\pi$
$827$	45.4517			1.58051			0.790255	+	0.612778i	$0.209948\pi$
$828$	15.7382	−	20.6302i	0.546941	−	0.716948i
$829$	−11.3925	−	19.7323i	−0.395676	−	0.685331i	0.597511	−	0.801861i	$-0.296156\pi$
$829$	−11.3925	−	19.7323i	−0.395676	−	0.685331i	−0.993187	+	0.116529i	$0.962823\pi$
$830$	−5.53617	+	9.58893i	−0.192163	+	0.332837i
$831$	2.53711	+	5.12658i	0.0880113	+	0.177839i
$832$	13.0500	−	22.6033i	0.452428	−	0.783629i
$833$	−25.3271	+	9.78714i	−0.877531	+	0.339104i
$834$	24.2375	+	48.9752i	0.839275	+	1.69587i
$835$	−0.322726			−0.0111684
$836$	4.31097	+	7.46681i	0.149098	+	0.258245i
$837$	−2.16293	−	0.420768i	−0.0747616	−	0.0145439i
$838$	−1.44218	+	2.49794i	−0.0498194	+	0.0862898i
$839$	−17.0440	−	29.5210i	−0.588423	−	1.01918i	−0.994439	−	0.105313i	$-0.966416\pi$
$839$	−17.0440	−	29.5210i	−0.588423	−	1.01918i	0.406016	−	0.913866i	$-0.366918\pi$
$840$	2.04131	+	2.71931i	0.0704318	+	0.0938252i
$841$	−1.54476	+	2.67560i	−0.0532676	+	0.0922622i
$842$	−26.9982	−	46.7623i	−0.930420	−	1.61153i
$843$	47.1625	+	3.02468i	1.62436	+	0.104176i
$844$	−17.4780	+	30.2727i	−0.601617	+	1.04203i
$845$	−9.38815	+	16.2608i	−0.322962	+	0.559387i
$846$	−23.3028	−	55.8140i	−0.801166	−	1.91892i
$847$	11.9706	−	33.9244i	0.411316	−	1.16566i
$848$	−8.99941	−	15.5874i	−0.309041	−	0.535275i
$849$	−13.1038	+	19.6710i	−0.449723	+	0.675108i
$850$	−7.36935			−0.252767
$851$	9.58310			0.328504
$852$	7.76247	−	11.6527i	0.265938	−	0.399217i
$853$	−5.23794	−	9.07238i	−0.179344	−	0.310632i	0.762312	−	0.647209i	$-0.224064\pi$
$853$	−5.23794	−	9.07238i	−0.179344	−	0.310632i	−0.941656	+	0.336577i	$0.890731\pi$
$854$	−19.7953	−	23.1249i	−0.677381	−	0.791319i
$855$	−1.24848	−	2.99030i	−0.0426970	−	0.102266i
$856$	−1.15857	+	2.00671i	−0.0395993	+	0.0685879i
$857$	28.7072	−	49.7222i	0.980618	−	1.69848i	0.320627	−	0.947205i	$-0.396106\pi$
$857$	28.7072	−	49.7222i	0.980618	−	1.69848i	0.659990	−	0.751274i	$-0.270560\pi$
$858$	91.8085	+	5.88798i	3.13429	+	0.201012i
$859$	0.954670	+	1.65354i	0.0325729	+	0.0564180i	0.881852	−	0.471526i	$-0.156297\pi$
$859$	0.954670	+	1.65354i	0.0325729	+	0.0564180i	−0.849279	+	0.527944i	$0.822963\pi$
$860$	−5.79486	+	10.0370i	−0.197603	+	0.342259i
$861$	−14.5597	+	34.1257i	−0.496194	+	1.16300i
$862$	−6.81695	−	11.8073i	−0.232186	−	0.402158i
$863$	−4.12970	+	7.15285i	−0.140577	+	0.243486i	−0.927714	−	0.373292i	$-0.878229\pi$
$863$	−4.12970	+	7.15285i	−0.140577	+	0.243486i	0.787137	+	0.616778i	$0.211562\pi$
$864$	37.2830	+	7.25291i	1.26839	+	0.246749i
$865$	−5.13504	−	8.89415i	−0.174597	−	0.302410i
$866$	−13.5084			−0.459034
$867$	−1.50124	−	3.03348i	−0.0509850	−	0.103022i
$868$	1.17426	+	1.37177i	0.0398569	+	0.0465610i
$869$	20.4575	−	35.4335i	0.693974	−	1.20200i
$870$	8.26805	+	16.7068i	0.280313	+	0.566412i
$871$	3.78158	−	6.54989i	0.128134	−	0.221934i
$872$	1.45392	+	2.51827i	0.0492360	+	0.0852793i
$873$	17.5297	−	22.9785i	0.593291	−	0.777705i
$874$	−11.0284			−0.373040
$875$	1.72052	+	2.00992i	0.0581643	+	0.0679478i
$876$	−32.8058	−	2.10394i	−1.10841	−	0.0710857i
$877$	11.4872	+	19.8964i	0.387895	+	0.671854i	0.992166	−	0.124925i	$-0.0398690\pi$
$877$	11.4872	+	19.8964i	0.387895	+	0.671854i	−0.604271	+	0.796779i	$0.706536\pi$
$878$	−64.8092			−2.18721
$879$	8.52930	+	17.2347i	0.287686	+	0.581311i
$880$	22.9556			0.773833
$881$	−23.5449			−0.793246			−0.396623	−	0.917982i	$-0.629818\pi$
$881$	−23.5449			−0.793246			−0.396623	+	0.917982i	$0.629818\pi$
$882$	38.7471	−	9.50928i	1.30468	−	0.320194i
$883$	40.4456			1.36110			0.680551	−	0.732701i	$-0.261740\pi$
$883$	40.4456			1.36110			0.680551	+	0.732701i	$0.261740\pi$
$884$	−35.1915			−1.18362
$885$	14.3331	+	0.919228i	0.481802	+	0.0308995i
$886$	24.9511			0.838249
$887$	−16.4128	−	28.4278i	−0.551088	−	0.954512i	−0.998196	−	0.0600326i	$-0.980880\pi$
$887$	−16.4128	−	28.4278i	−0.551088	−	0.954512i	0.447108	−	0.894480i	$-0.352454\pi$
$888$	1.01649	+	2.05396i	0.0341111	+	0.0689262i
$889$	−3.48576	−	4.07208i	−0.116909	−	0.136573i
$890$	−31.3874			−1.05211
$891$	11.7946	+	43.0494i	0.395135	+	1.44221i
$892$	6.43907	+	11.1528i	0.215596	+	0.373423i
$893$	−5.73125	+	9.92682i	−0.191789	+	0.332188i
$894$	−74.3471	−	4.76812i	−2.48654	−	0.159470i
$895$	−6.71395	+	11.6289i	−0.224423	+	0.388711i
$896$	10.0182	+	11.7033i	0.334685	+	0.390980i
$897$	−29.0899	+	43.6687i	−0.971283	+	1.45806i
$898$	−40.9701			−1.36719
$899$	−1.20110	−	2.08036i	−0.0400588	−	0.0693838i
$900$	4.78879	+	0.616778i	0.159626	+	0.0205593i
$901$	−7.54181	+	13.0628i	−0.251254	+	0.435185i
$902$	38.1433	+	66.0661i	1.27003	+	2.19976i
$903$	−19.8110	−	26.3910i	−0.659268	−	0.878238i
$904$	−4.10072	+	7.10266i	−0.136388	+	0.236231i
$905$	−5.27290	−	9.13294i	−0.175277	−	0.303589i
$906$	6.72345	+	13.5857i	0.223372	+	0.451354i
$907$	0.275277	−	0.476793i	0.00914041	−	0.0158317i	−0.861419	−	0.507895i	$-0.830424\pi$
$907$	0.275277	−	0.476793i	0.00914041	−	0.0158317i	0.870559	+	0.492063i	$0.163757\pi$
$908$	−5.94670	+	10.3000i	−0.197348	+	0.341817i
$909$	−3.75825	−	0.484048i	−0.124653	−	0.0160549i
$910$	18.4261	+	21.5254i	0.610819	+	0.713561i
$911$	2.20974	+	3.82739i	0.0732120	+	0.126807i	0.900307	−	0.435255i	$-0.143342\pi$
$911$	2.20974	+	3.82739i	0.0732120	+	0.126807i	−0.827095	+	0.562062i	$0.810008\pi$
$912$	−3.84091	−	7.76110i	−0.127185	−	0.256996i
$913$	−28.9042			−0.956590
$914$	59.0111			1.95191
$915$	10.4677	+	0.671326i	0.346051	+	0.0221933i
$916$	4.41505	+	7.64709i	0.145877	+	0.252667i
$917$	−2.70571	+	7.66790i	−0.0893504	+	0.253216i
$918$	−12.4613	−	36.2079i	−0.411284	−	1.19504i
$919$	−8.72249	+	15.1078i	−0.287728	+	0.498360i	−0.973267	−	0.229676i	$-0.926233\pi$
$919$	−8.72249	+	15.1078i	−0.287728	+	0.498360i	0.685539	+	0.728036i	$0.259567\pi$
$920$	−1.99377	+	3.45330i	−0.0657325	+	0.113852i
$921$	−10.7545	+	16.1443i	−0.354373	+	0.531972i
$922$	16.7715	+	29.0492i	0.552341	+	0.956683i
$923$	−14.1566	+	24.5200i	−0.465970	+	0.807084i
$924$	14.3544	−	33.6445i	0.472226	−	1.10682i
$925$	0.891603	+	1.54430i	0.0293157	+	0.0507763i
$926$	20.3172	−	35.1905i	0.667666	−	1.15643i
$927$	−27.5962	+	36.1740i	−0.906378	+	1.18811i
$928$	20.7037	+	35.8598i	0.679631	+	1.17716i
$929$	5.41645			0.177708			0.0888539	−	0.996045i	$-0.471680\pi$
$929$	5.41645			0.177708			0.0888539	+	0.996045i	$0.471680\pi$
$930$	−1.39257	−	0.0893097i	−0.0456640	−	0.00292858i
$931$	−5.88669	−	4.74520i	−0.192928	−	0.155518i
$932$	1.74658	−	3.02516i	0.0572111	−	0.0990925i
$933$	6.41058	−	9.62334i	0.209873	−	0.315054i
$934$	12.3694	−	21.4244i	0.404739	−	0.701029i
$935$	−9.61879	−	16.6602i	−0.314568	−	0.544848i
$936$	−12.4451	−	1.60289i	−0.406782	−	0.0523920i
$937$	2.77753			0.0907380			0.0453690	−	0.998970i	$-0.485554\pi$
$937$	2.77753			0.0907380			0.0453690	+	0.998970i	$0.485554\pi$
$938$	−4.38564	−	5.12332i	−0.143196	−	0.167282i
$939$	−13.1705	+	19.7711i	−0.429804	+	0.645207i
$940$	−8.53966	−	14.7911i	−0.278533	−	0.482433i
$941$	58.2492			1.89887			0.949435	−	0.313964i	$-0.101657\pi$
$941$	58.2492			1.89887			0.949435	+	0.313964i	$0.101657\pi$
$942$	15.3381	−	23.0250i	0.499742	−	0.750195i
$943$	−43.5102			−1.41689
$944$	38.3811			1.24920
$945$	−6.96604	+	11.8522i	−0.226605	+	0.385552i
$946$	−67.8514			−2.20604
$947$	−60.3701			−1.96176			−0.980882	−	0.194602i	$-0.937658\pi$
$947$	−60.3701			−1.96176			−0.980882	+	0.194602i	$0.937658\pi$
$948$	12.7498	−	19.1396i	0.414095	−	0.621625i
$949$	66.4747			2.15786
$950$	−1.02607	−	1.77720i	−0.0332901	−	0.0576601i
$951$	−1.96767	+	2.95380i	−0.0638062	+	0.0957837i
$952$	2.53384	−	7.18084i	0.0821224	−	0.232732i
$953$	−57.0129			−1.84683			−0.923415	−	0.383803i	$-0.874614\pi$
$953$	−57.0129			−1.84683			−0.923415	+	0.383803i	$0.874614\pi$
$954$	13.4428	−	17.6213i	0.435228	−	0.570511i
$955$	−9.81630	−	17.0023i	−0.317648	−	0.550183i
$956$	−4.09125	+	7.08625i	−0.132321	+	0.229186i
$957$	−26.9779	+	40.4983i	−0.872073	+	1.30913i
$958$	28.2701	−	48.9652i	0.913364	−	1.58199i
$959$	9.78737	−	1.82529i	0.316051	−	0.0589418i
$960$	8.00311	+	0.513266i	0.258299	+	0.0165656i
$961$	−30.8202			−0.994199
$962$	9.54868	+	16.5388i	0.307862	+	0.533232i
$963$	−9.29187	−	1.19676i	−0.299426	−	0.0385650i
$964$	7.12853	−	12.3470i	0.229594	−	0.397669i
$965$	−13.2529	−	22.9548i	−0.426627	−	0.738940i
$966$	28.0889	+	37.4184i	0.903745	+	1.20392i
$967$	−13.2885	+	23.0163i	−0.427328	+	0.740154i	−0.996635	−	0.0819715i	$-0.973878\pi$
$967$	−13.2885	+	23.0163i	−0.427328	+	0.740154i	0.569307	+	0.822125i	$0.307212\pi$
$968$	5.04446	+	8.73726i	0.162135	+	0.280826i
$969$	−4.02328	+	6.03961i	−0.129246	+	0.194020i
$970$	9.15148	−	15.8508i	0.293836	−	0.508939i
$971$	5.29519	−	9.17153i	0.169931	−	0.294328i	−0.768465	−	0.639892i	$-0.778979\pi$
$971$	5.29519	−	9.17153i	0.169931	−	0.294328i	0.938395	+	0.345564i	$0.112312\pi$
$972$	5.06724	+	24.5718i	0.162532	+	0.788140i
$973$	−43.1908	+	8.05486i	−1.38463	+	0.258227i
$974$	13.8265	+	23.9482i	0.443030	+	0.767351i
$975$	−9.74363	−	0.624891i	−0.312046	−	0.0200125i
$976$	28.0303			0.897228
$977$	−1.82409			−0.0583579			−0.0291789	−	0.999574i	$-0.509289\pi$
$977$	−1.82409			−0.0583579			−0.0291789	+	0.999574i	$0.509289\pi$
$978$	19.9433	+	40.2983i	0.637716	+	1.28860i
$979$	−40.9682	−	70.9589i	−1.30935	−	2.26786i
$980$	10.5088	−	4.06091i	0.335691	−	0.129721i
$981$	−7.13092	+	9.34744i	−0.227673	+	0.298441i
$982$	20.1423	−	34.8874i	0.642765	−	1.11330i
$983$	3.94428	−	6.83169i	0.125803	−	0.217897i	−0.796244	−	0.604976i	$-0.793183\pi$
$983$	3.94428	−	6.83169i	0.125803	−	0.217897i	0.922047	+	0.387079i	$0.126516\pi$
$984$	−4.61516	−	9.32558i	−0.147126	−	0.297288i
$985$	9.09728	+	15.7570i	0.289863	+	0.502058i
$986$	20.8728	−	36.1528i	0.664726	−	1.15134i
$987$	48.2782	−	5.83758i	1.53671	−	0.185812i
$988$	−4.89987	−	8.48683i	−0.155886	−	0.270002i
$989$	19.3496	−	33.5144i	0.615280	−	1.06570i
$990$	10.8907	+	26.0850i	0.346129	+	0.829037i
$991$	−26.4744	−	45.8551i	−0.840988	−	1.45663i	−0.889060	−	0.457790i	$-0.848641\pi$
$991$	−26.4744	−	45.8551i	−0.840988	−	1.45663i	0.0480725	−	0.998844i	$-0.484692\pi$
$992$	−3.09971			−0.0984160
$993$	−5.32003	+	7.98624i	−0.168826	+	0.253436i
$994$	16.4179	+	19.1795i	0.520746	+	0.608337i
$995$	6.54080	−	11.3290i	0.207357	−	0.359153i
$996$	−16.2131	−	1.03980i	−0.513731	−	0.0329473i
$997$	15.8271	−	27.4133i	0.501249	−	0.868189i	−0.498750	−	0.866746i	$-0.666207\pi$
$997$	15.8271	−	27.4133i	0.501249	−	0.868189i	0.999999	−	0.00144314i	$-0.000459366\pi$
$998$	12.3138	+	21.3281i	0.389787	+	0.675131i
$999$	−6.07997	+	6.99208i	−0.192362	+	0.221220i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.c.121.15	yes	36
3.2	odd	2		945.2.l.c.226.4		36
7.4	even	3		315.2.k.c.256.4	yes	36
9.2	odd	6		945.2.k.c.856.15		36
9.7	even	3		315.2.k.c.16.4	✓	36
21.11	odd	6		945.2.k.c.361.15		36
63.11	odd	6		945.2.l.c.46.4		36
63.25	even	3	inner	315.2.l.c.151.15	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.4	✓	36	9.7	even	3
315.2.k.c.256.4	yes	36	7.4	even	3
315.2.l.c.121.15	yes	36	1.1	even	1	trivial
315.2.l.c.151.15	yes	36	63.25	even	3	inner
945.2.k.c.361.15		36	21.11	odd	6
945.2.k.c.856.15		36	9.2	odd	6
945.2.l.c.46.4		36	63.11	odd	6
945.2.l.c.226.4		36	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)

\(f(q)\)	\(=\)	\(q+1.89985 q^{2} +(0.960253 - 1.44150i) q^{3} +1.60945 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.82434 - 2.73864i) q^{6} +(1.72052 + 2.00992i) q^{7} -0.741992 q^{8} +(-1.15583 - 2.76840i) q^{9} +O(q^{10})\)	\(q+1.89985 q^{2} +(0.960253 - 1.44150i) q^{3} +1.60945 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.82434 - 2.73864i) q^{6} +(1.72052 + 2.00992i) q^{7} -0.741992 q^{8} +(-1.15583 - 2.76840i) q^{9} +(-0.949927 - 1.64532i) q^{10} +(2.47977 - 4.29509i) q^{11} +(1.54548 - 2.32002i) q^{12} +(-2.81852 + 4.88183i) q^{13} +(3.26875 + 3.81856i) q^{14} +(-1.72850 - 0.110854i) q^{15} -4.62857 q^{16} +(1.93945 + 3.35923i) q^{17} +(-2.19591 - 5.25956i) q^{18} +(-0.540078 + 0.935442i) q^{19} +(-0.804724 - 1.39382i) q^{20} +(4.54944 - 0.550097i) q^{21} +(4.71121 - 8.16005i) q^{22} +(2.68704 + 4.65410i) q^{23} +(-0.712500 + 1.06958i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-5.35479 + 9.27476i) q^{26} +(-5.10054 - 0.992240i) q^{27} +(2.76909 + 3.23487i) q^{28} +(-2.83238 - 4.90583i) q^{29} +(-3.28390 - 0.210607i) q^{30} +0.424059 q^{31} -7.30963 q^{32} +(-3.81016 - 7.69896i) q^{33} +(3.68468 + 6.38204i) q^{34} +(0.880383 - 2.49498i) q^{35} +(-1.86025 - 4.45560i) q^{36} +(0.891603 - 1.54430i) q^{37} +(-1.02607 + 1.77720i) q^{38} +(4.33065 + 8.75068i) q^{39} +(0.370996 + 0.642584i) q^{40} +(-4.04814 + 7.01159i) q^{41} +(8.64327 - 1.04511i) q^{42} +(-3.60053 - 6.23630i) q^{43} +(3.99106 - 6.91272i) q^{44} +(-1.81959 + 2.38518i) q^{45} +(5.10499 + 8.84211i) q^{46} +10.6119 q^{47} +(-4.44460 + 6.67208i) q^{48} +(-1.07959 + 6.91625i) q^{49} +(-0.949927 + 1.64532i) q^{50} +(6.70468 + 0.429993i) q^{51} +(-4.53627 + 7.85704i) q^{52} +(1.94432 + 3.36765i) q^{53} +(-9.69028 - 1.88511i) q^{54} -4.95954 q^{55} +(-1.27662 - 1.49135i) q^{56} +(0.829826 + 1.67678i) q^{57} +(-5.38111 - 9.32036i) q^{58} -8.29222 q^{59} +(-2.78193 - 0.178414i) q^{60} -6.05593 q^{61} +0.805650 q^{62} +(3.57565 - 7.08624i) q^{63} -4.63009 q^{64} +5.63705 q^{65} +(-7.23874 - 14.6269i) q^{66} -1.34169 q^{67} +(3.12145 + 5.40650i) q^{68} +(9.28911 + 0.595741i) q^{69} +(1.67260 - 4.74010i) q^{70} +5.02270 q^{71} +(0.857617 + 2.05413i) q^{72} +(-5.89623 - 10.2126i) q^{73} +(1.69392 - 2.93395i) q^{74} +(0.768247 + 1.55235i) q^{75} +(-0.869227 + 1.50554i) q^{76} +(12.8993 - 2.40566i) q^{77} +(8.22760 + 16.6250i) q^{78} +8.24977 q^{79} +(2.31429 + 4.00846i) q^{80} +(-6.32811 + 6.39961i) q^{81} +(-7.69089 + 13.3210i) q^{82} +(-2.91400 - 5.04719i) q^{83} +(7.32208 - 0.885353i) q^{84} +(1.93945 - 3.35923i) q^{85} +(-6.84048 - 11.8481i) q^{86} +(-9.79154 - 0.627963i) q^{87} +(-1.83997 + 3.18692i) q^{88} +(8.26047 - 14.3076i) q^{89} +(-3.45696 + 4.53150i) q^{90} +(-14.6614 + 2.73428i) q^{91} +(4.32466 + 7.49052i) q^{92} +(0.407203 - 0.611279i) q^{93} +20.1611 q^{94} +1.08016 q^{95} +(-7.01909 + 10.5368i) q^{96} +(4.81694 + 8.34318i) q^{97} +(-2.05106 + 13.1399i) q^{98} +(-14.7567 - 1.90061i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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