LMFDB - Embedded newform 315.2.k.c.16.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(16,315)]

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([4, 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("315.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.k (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			16.4
Character	$\chi$	$=$	315.16
Dual form			315.2.k.c.256.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.949927 - 1.64532i) q^{2} +(-1.72850 + 0.110854i) q^{3} +(-0.804724 + 1.39382i) q^{4} +1.00000 q^{5} +(1.82434 + 2.73864i) q^{6} +(0.880383 - 2.49498i) q^{7} -0.741992 q^{8} +(2.97542 - 0.383223i) q^{9} +O(q^{10})$	\(q+(-0.949927 - 1.64532i) q^{2} +(-1.72850 + 0.110854i) q^{3} +(-0.804724 + 1.39382i) q^{4} +1.00000 q^{5} +(1.82434 + 2.73864i) q^{6} +(0.880383 - 2.49498i) q^{7} -0.741992 q^{8} +(2.97542 - 0.383223i) q^{9} +(-0.949927 - 1.64532i) q^{10} -4.95954 q^{11} +(1.23645 - 2.49843i) q^{12} +(-2.81852 - 4.88183i) q^{13} +(-4.94135 + 0.921536i) q^{14} +(-1.72850 + 0.110854i) q^{15} +(2.31429 + 4.00846i) q^{16} +(1.93945 + 3.35923i) q^{17} +(-3.45696 - 4.53150i) q^{18} +(-0.540078 + 0.935442i) q^{19} +(-0.804724 + 1.39382i) q^{20} +(-1.24516 + 4.41017i) q^{21} +(4.71121 + 8.16005i) q^{22} -5.37409 q^{23} +(1.28253 - 0.0822531i) q^{24} +1.00000 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} +(1.82434 + 2.73864i) q^{30} +(-0.212029 + 0.367245i) q^{31} +(3.65482 - 6.33033i) q^{32} +(8.57257 - 0.549787i) 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} +2.05214 q^{38} +(5.41299 + 8.12579i) q^{39} -0.741992 q^{40} +(-4.04814 - 7.01159i) q^{41} +(8.43896 - 2.14064i) q^{42} +(-3.60053 + 6.23630i) q^{43} +(3.99106 - 6.91272i) q^{44} +(2.97542 - 0.383223i) q^{45} +(5.10499 + 8.84211i) q^{46} +(-5.30595 - 9.19018i) q^{47} +(-4.44460 - 6.67208i) q^{48} +(-5.44985 - 4.39308i) q^{49} +(-0.949927 - 1.64532i) q^{50} +(-3.72473 - 5.59143i) q^{51} +9.07253 q^{52} +(1.94432 + 3.36765i) q^{53} +(6.47769 + 7.44947i) q^{54} -4.95954 q^{55} +(-0.653237 + 1.85126i) q^{56} +(0.829826 - 1.67678i) q^{57} +10.7622 q^{58} +(4.14611 - 7.18127i) q^{59} +(1.23645 - 2.49843i) q^{60} +(3.02796 + 5.24459i) q^{61} +0.805650 q^{62} +(1.66338 - 7.76100i) q^{63} -4.63009 q^{64} +(-2.81852 - 4.88183i) q^{65} +(-9.04789 - 13.5824i) q^{66} +(0.670844 - 1.16194i) q^{67} -6.24289 q^{68} +(9.28911 - 0.595741i) q^{69} +(-4.94135 + 0.921536i) q^{70} +5.02270 q^{71} +(-2.20774 + 0.284349i) q^{72} +(-5.89623 - 10.2126i) q^{73} -3.38783 q^{74} +(-1.72850 + 0.110854i) q^{75} +(-0.869227 - 1.50554i) q^{76} +(-4.36630 + 12.3740i) q^{77} +(8.22760 - 16.6250i) q^{78} +(-4.12488 - 7.14451i) q^{79} +(2.31429 + 4.00846i) q^{80} +(8.70628 - 2.28050i) q^{81} +(-7.69089 + 13.3210i) q^{82} +(-2.91400 + 5.04719i) q^{83} +(-5.14498 - 5.28450i) q^{84} +(1.93945 + 3.35923i) q^{85} +13.6810 q^{86} +(4.35194 - 8.79370i) q^{87} +3.67994 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} +(0.325782 - 0.658288i) q^{93} +(-10.0805 + 17.4600i) q^{94} +(-0.540078 + 0.935442i) q^{95} +(-5.61560 + 11.3471i) 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} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) $ 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.949927	−	1.64532i	−0.671700	−	1.16342i	−0.977422	−	0.211298i	$-0.932231\pi$
$2$	−0.949927	−	1.64532i	−0.671700	−	1.16342i	0.305722	−	0.952121i	$-0.401102\pi$
$3$	−1.72850	+	0.110854i	−0.997950	+	0.0640018i
$3$	−1.72850	+	0.110854i	−0.997950	+	0.0640018i
$4$	−0.804724	+	1.39382i	−0.402362	+	0.696911i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.82434	+	2.73864i	0.744784	+	1.11804i
$7$	0.880383	−	2.49498i	0.332753	−	0.943014i
$7$	0.880383	−	2.49498i	0.332753	−	0.943014i
$8$	−0.741992			−0.262334
$9$	2.97542	−	0.383223i	0.991808	−	0.127741i
$10$	−0.949927	−	1.64532i	−0.300393	−	0.520297i
$11$	−4.95954			−1.49536			−0.747679	−	0.664060i	$-0.768832\pi$
$11$	−4.95954			−1.49536			−0.747679	+	0.664060i	$0.768832\pi$
$12$	1.23645	−	2.49843i	0.356933	−	0.721234i
$13$	−2.81852	−	4.88183i	−0.781718	−	1.35397i	−0.930940	−	0.365171i	$-0.881010\pi$
$13$	−2.81852	−	4.88183i	−0.781718	−	1.35397i	0.149223	−	0.988804i	$-0.452323\pi$
$14$	−4.94135	+	0.921536i	−1.32063	+	0.246291i
$15$	−1.72850	+	0.110854i	−0.446297	+	0.0286225i
$16$	2.31429	+	4.00846i	0.578572	+	1.00212i
$17$	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	$0.677448\pi$
$18$	−3.45696	−	4.53150i	−0.814814	−	1.06808i
$19$	−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
$21$	−1.24516	+	4.41017i	−0.271717	+	0.962377i
$22$	4.71121	+	8.16005i	1.00443	+	1.73973i
$23$	−5.37409			−1.12057			−0.560287	−	0.828298i	$-0.689309\pi$
$23$	−5.37409			−1.12057			−0.560287	+	0.828298i	$0.689309\pi$
$24$	1.28253	−	0.0822531i	0.261796	−	0.0167898i
$25$	1.00000			0.200000
$26$	−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	0.473583	+	0.880749i	$0.342960\pi$
$29$	−2.83238	+	4.90583i	−0.525960	+	0.910989i	−0.999543	+	0.0302399i	$0.990373\pi$
$30$	1.82434	+	2.73864i	0.333077	+	0.500004i
$31$	−0.212029	+	0.367245i	−0.0380816	+	0.0659592i	−0.884438	−	0.466658i	$-0.845458\pi$
$31$	−0.212029	+	0.367245i	−0.0380816	+	0.0659592i	0.846356	+	0.532617i	$0.178791\pi$
$32$	3.65482	−	6.33033i	0.646086	−	1.11905i
$33$	8.57257	−	0.549787i	1.49229	−	0.0957056i
$34$	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	$0.119841\pi$
$38$	2.05214			0.332901
$39$	5.41299	+	8.12579i	0.866772	+	1.30117i
$40$	−0.741992			−0.117319
$41$	−4.04814	−	7.01159i	−0.632214	−	1.09503i	−0.987098	−	0.160116i	$-0.948813\pi$
$41$	−4.04814	−	7.01159i	−0.632214	−	1.09503i	0.354884	−	0.934910i	$-0.384520\pi$
$42$	8.43896	−	2.14064i	1.30216	−	0.330309i
$43$	−3.60053	+	6.23630i	−0.549076	+	0.951027i	0.449263	+	0.893400i	$0.351687\pi$
$43$	−3.60053	+	6.23630i	−0.549076	+	0.951027i	−0.998338	+	0.0576271i	$0.981647\pi$
$44$	3.99106	−	6.91272i	0.601675	−	1.04213i
$45$	2.97542	−	0.383223i	0.443550	−	0.0571276i
$46$	5.10499	+	8.84211i	0.752690	+	1.30370i
$47$	−5.30595	−	9.19018i	−0.773953	−	1.34053i	−0.935381	−	0.353641i	$-0.884943\pi$
$47$	−5.30595	−	9.19018i	−0.773953	−	1.34053i	0.161428	−	0.986884i	$-0.448390\pi$
$48$	−4.44460	−	6.67208i	−0.641523	−	0.963031i
$49$	−5.44985	−	4.39308i	−0.778550	−	0.627582i
$50$	−0.949927	−	1.64532i	−0.134340	−	0.232684i
$51$	−3.72473	−	5.59143i	−0.521566	−	0.782957i
$52$	9.07253			1.25813
$53$	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	$0.747277\pi$
$54$	6.47769	+	7.44947i	0.881502	+	1.01374i
$55$	−4.95954			−0.668745
$56$	−0.653237	+	1.85126i	−0.0872925	+	0.247385i
$57$	0.829826	−	1.67678i	0.109913	−	0.222095i
$58$	10.7622			1.41315
$59$	4.14611	−	7.18127i	0.539777	−	0.934922i	−0.459138	−	0.888365i	$-0.651842\pi$
$59$	4.14611	−	7.18127i	0.539777	−	0.934922i	0.998916	−	0.0465570i	$-0.0148249\pi$
$60$	1.23645	−	2.49843i	0.159625	−	0.322546i
$61$	3.02796	+	5.24459i	0.387691	+	0.671501i	0.992139	−	0.125144i	$-0.0399394\pi$
$61$	3.02796	+	5.24459i	0.387691	+	0.671501i	−0.604447	+	0.796645i	$0.706606\pi$
$62$	0.805650			0.102318
$63$	1.66338	−	7.76100i	0.209566	−	0.977795i
$64$	−4.63009			−0.578761
$65$	−2.81852	−	4.88183i	−0.349595	−	0.605516i
$66$	−9.04789	−	13.5824i	−1.11372	−	1.67188i
$67$	0.670844	−	1.16194i	0.0819566	−	0.141953i	−0.822134	−	0.569294i	$-0.807216\pi$
$67$	0.670844	−	1.16194i	0.0819566	−	0.141953i	0.904090	+	0.427341i	$0.140550\pi$
$68$	−6.24289			−0.757062
$69$	9.28911	−	0.595741i	1.11828	−	0.0717188i
$70$	−4.94135	+	0.921536i	−0.590604	+	0.110145i
$71$	5.02270			0.596085			0.298043	−	0.954553i	$-0.403666\pi$
$71$	5.02270			0.596085			0.298043	+	0.954553i	$0.403666\pi$
$72$	−2.20774	+	0.284349i	−0.260185	+	0.0335108i
$73$	−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	$-0.409101\pi$
$74$	−3.38783			−0.393827
$75$	−1.72850	+	0.110854i	−0.199590	+	0.0128004i
$76$	−0.869227	−	1.50554i	−0.0997071	−	0.172698i
$77$	−4.36630	+	12.3740i	−0.497586	+	1.41014i
$78$	8.22760	−	16.6250i	0.931592	−	1.88241i
$79$	−4.12488	−	7.14451i	−0.464086	−	0.803820i	0.535074	−	0.844805i	$-0.320284\pi$
$79$	−4.12488	−	7.14451i	−0.464086	−	0.803820i	−0.999160	+	0.0409853i	$0.986950\pi$
$80$	2.31429	+	4.00846i	0.258745	+	0.448160i
$81$	8.70628	−	2.28050i	0.967364	−	0.253389i
$82$	−7.69089	+	13.3210i	−0.849316	+	1.47106i
$83$	−2.91400	+	5.04719i	−0.319853	+	0.554001i	−0.980457	−	0.196733i	$-0.936967\pi$
$83$	−2.91400	+	5.04719i	−0.319853	+	0.554001i	0.660604	+	0.750734i	$0.270300\pi$
$84$	−5.14498	−	5.28450i	−0.561363	−	0.576586i
$85$	1.93945	+	3.35923i	0.210363	+	0.364359i
$86$	13.6810			1.47526
$87$	4.35194	−	8.79370i	0.466577	−	0.942784i
$88$	3.67994			0.392283
$89$	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
$93$	0.325782	−	0.658288i	0.0337820	−	0.0682613i
$94$	−10.0805	+	17.4600i	−1.03973	+	1.80086i
$95$	−0.540078	+	0.935442i	−0.0554108	+	0.0959743i
$96$	−5.61560	+	11.3471i	−0.573140	+	1.15811i
$97$	4.81694	−	8.34318i	0.489086	−	0.847121i	−0.510835	−	0.859679i	$-0.670664\pi$
$97$	4.81694	−	8.34318i	0.489086	−	0.847121i	0.999921	+	0.0125571i	$0.00399716\pi$
$98$	−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
$101$	−1.26310			−0.125683			−0.0628414	−	0.998024i	$-0.520016\pi$
$101$	−1.26310			−0.125683			−0.0628414	+	0.998024i	$0.520016\pi$
$102$	−5.66148	+	11.4398i	−0.560570	+	1.13271i
$103$	15.1661			1.49436			0.747182	−	0.664619i	$-0.231406\pi$
$103$	15.1661			1.49436			0.747182	+	0.664619i	$0.231406\pi$
$104$	2.09132	+	3.62228i	0.205071	+	0.355194i
$105$	−1.24516	+	4.41017i	−0.121515	+	0.430388i
$106$	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	$0.118433\pi$
$108$	2.72152	−	7.90772i	0.261878	−	0.760921i
$109$	−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	$0.893432\pi$
$110$	4.71121	+	8.16005i	0.449196	+	0.778030i
$111$	−1.36994	+	2.76816i	−0.130029	+	0.262742i
$112$	12.0385	−	2.24512i	1.13753	−	0.212144i
$113$	5.52663	+	9.57241i	0.519902	+	0.900497i	0.999732	+	0.0231353i	$0.00736487\pi$
$113$	5.52663	+	9.57241i	0.519902	+	0.900497i	−0.479830	+	0.877361i	$0.659302\pi$
$114$	−3.54712	+	0.227488i	−0.332218	+	0.0213062i
$115$	−5.37409			−0.501136
$116$	−4.55857	−	7.89567i	−0.423252	−	0.733095i
$117$	−10.2571	−	13.4454i	−0.948272	−	1.24303i
$118$	−15.7540			−1.45027
$119$	10.0887	−	1.88148i	0.924827	−	0.172475i
$120$	1.28253	−	0.0822531i	0.117079	−	0.00750864i
$121$	13.5971			1.23610
$122$	5.75269	−	9.96396i	0.520824	−	0.902094i
$123$	7.77448	+	11.6708i	0.701001	+	1.05232i
$124$	−0.341250	−	0.591062i	−0.0306452	−	0.0530790i
$125$	1.00000			0.0894427
$126$	−14.3494	+	4.63560i	−1.27835	+	0.412972i
$127$	−2.02599			−0.179777			−0.0898887	−	0.995952i	$-0.528651\pi$
$127$	−2.02599			−0.179777			−0.0898887	+	0.995952i	$0.528651\pi$
$128$	−2.91138	−	5.04266i	−0.257332	−	0.445712i
$129$	5.53219	−	11.1786i	0.487083	−	0.984219i
$130$	−5.35479	+	9.27476i	−0.469646	+	0.813450i
$131$	−3.07333			−0.268518			−0.134259	−	0.990946i	$-0.542865\pi$
$131$	−3.07333			−0.268518			−0.134259	+	0.990946i	$0.542865\pi$
$132$	−6.13225	+	12.3911i	−0.533744	+	1.07850i
$133$	1.85843	+	2.17103i	0.161147	+	0.188252i
$134$	−2.54901			−0.220201
$135$	−5.10054	+	0.992240i	−0.438984	+	0.0853984i
$136$	−1.43906	−	2.49252i	−0.123398	−	0.213732i
$137$	−3.76306			−0.321500			−0.160750	−	0.986995i	$-0.551391\pi$
$137$	−3.76306			−0.321500			−0.160750	+	0.986995i	$0.551391\pi$
$138$	−9.80416	−	14.7177i	−0.834586	−	1.25285i
$139$	−8.30302	−	14.3813i	−0.704253	−	1.21980i	−0.966960	−	0.254926i	$-0.917949\pi$
$139$	−8.30302	−	14.3813i	−0.704253	−	1.21980i	0.262707	−	0.964876i	$-0.415385\pi$
$140$	2.76909	+	3.23487i	0.234031	+	0.273396i
$141$	10.1901	+	15.2970i	0.858162	+	1.28824i
$142$	−4.77120	−	8.26397i	−0.400390	−	0.693497i
$143$	13.9786	+	24.2116i	1.16895	+	2.02468i
$144$	8.42212	+	11.0400i	0.701843	+	0.919998i
$145$	−2.83238	+	4.90583i	−0.235216	+	0.407407i
$146$	−11.2020	+	19.4024i	−0.927083	+	1.60575i
$147$	9.90706	+	6.98929i	0.817120	+	0.576467i
$148$	1.43499	+	2.48547i	0.117955	+	0.204305i
$149$	22.6399			1.85473			0.927366	−	0.374154i	$-0.122067\pi$
$149$	22.6399			1.85473			0.927366	+	0.374154i	$0.122067\pi$
$150$	1.82434	+	2.73864i	0.148957	+	0.223609i
$151$	4.60650			0.374872			0.187436	−	0.982277i	$-0.439982\pi$
$151$	4.60650			0.374872			0.187436	+	0.982277i	$0.439982\pi$
$152$	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
$156$	−15.6819	+	1.00573i	−1.25555	+	0.0805228i
$157$	−4.20374	+	7.28108i	−0.335495	+	0.581094i	−0.983580	−	0.180474i	$-0.942237\pi$
$157$	−4.20374	+	7.28108i	−0.335495	+	0.581094i	0.648085	+	0.761568i	$0.275570\pi$
$158$	−7.83668	+	13.5735i	−0.623453	+	1.07985i
$159$	−3.73407	−	5.60545i	−0.296131	−	0.444541i
$160$	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	$0.986933\pi$
$164$	13.0306			1.01752
$165$	8.57257	−	0.549787i	0.667374	−	0.0428008i
$166$	11.0723			0.859381
$167$	0.161363	+	0.279489i	0.0124866	+	0.0216275i	0.872201	−	0.489147i	$-0.162692\pi$
$167$	0.161363	+	0.279489i	0.0124866	+	0.0216275i	−0.859715	+	0.510775i	$0.829359\pi$
$168$	0.923901	−	3.27231i	0.0712805	−	0.252464i
$169$	−9.38815	+	16.2608i	−0.722166	+	1.25083i
$170$	3.68468	−	6.38204i	0.282602	−	0.489481i
$171$	−1.24848	+	2.99030i	−0.0954733	+	0.228674i
$172$	−5.79486	−	10.0370i	−0.441854	−	0.765314i
$173$	−5.13504	−	8.89415i	−0.390410	−	0.676210i	0.602094	−	0.798425i	$-0.294333\pi$
$173$	−5.13504	−	8.89415i	−0.390410	−	0.676210i	−0.992504	+	0.122216i	$0.961000\pi$
$174$	−18.6025	+	1.19304i	−1.41025	+	0.0904441i
$175$	0.880383	−	2.49498i	0.0665507	−	0.188603i
$176$	−11.4778	−	19.8801i	−0.865172	−	1.49852i
$177$	−6.37047	+	12.8724i	−0.478834	+	0.967552i
$178$	−31.3874			−2.35258
$179$	−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	$-0.334004\pi$
$180$	−1.86025	+	4.45560i	−0.138655	+	0.332101i
$181$	10.5458			0.783864			0.391932	−	0.919994i	$-0.371807\pi$
$181$	10.5458			0.783864			0.391932	+	0.919994i	$0.371807\pi$
$182$	18.4261	+	21.5254i	1.36583	+	1.59557i
$183$	−5.81522	−	8.72961i	−0.429873	−	0.645311i
$184$	3.98753			0.293965
$185$	0.891603	−	1.54430i	0.0655519	−	0.113539i
$186$	−1.39257	+	0.0893097i	−0.102108	+	0.00654851i
$187$	−9.61879	−	16.6602i	−0.703396	−	1.21832i
$188$	17.0793			1.24564
$189$	−2.01481	+	13.5993i	−0.146556	+	0.989202i
$190$	2.05214			0.148878
$191$	−9.81630	−	17.0023i	−0.710283	−	1.23025i	−0.964751	−	0.263164i	$-0.915234\pi$
$191$	−9.81630	−	17.0023i	−0.710283	−	1.23025i	0.254468	−	0.967081i	$-0.418100\pi$
$192$	8.00311	−	0.513266i	0.577575	−	0.0370418i
$193$	−13.2529	+	22.9548i	−0.953968	+	1.65232i	−0.217255	+	0.976115i	$0.569710\pi$
$193$	−13.2529	+	22.9548i	−0.953968	+	1.65232i	−0.736713	+	0.676206i	$0.763623\pi$
$194$	−18.3030			−1.31408
$195$	5.41299	+	8.12579i	0.387632	+	0.581900i
$196$	10.5088	−	4.06091i	0.750628	−	0.290065i
$197$	−18.1946			−1.29631			−0.648154	−	0.761509i	$-0.724459\pi$
$197$	−18.1946			−1.29631			−0.648154	+	0.761509i	$0.724459\pi$
$198$	17.1449	+	22.4741i	1.21844	+	1.59717i
$199$	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	$0.679868\pi$
$200$	−0.741992			−0.0524668
$201$	−1.03075	+	2.08277i	−0.0727034	+	0.146907i
$202$	1.19985	+	2.07820i	0.0844211	+	0.146222i
$203$	9.74636	+	11.3857i	0.684060	+	0.799122i
$204$	10.7908	−	0.692051i	0.755510	−	0.0484533i
$205$	−4.04814	−	7.01159i	−0.282735	−	0.489711i
$206$	−14.4067	−	24.9532i	−1.00376	−	1.73857i
$207$	−15.9902	+	2.05948i	−1.11139	+	0.143143i
$208$	13.0457	−	22.5959i	0.904560	−	1.56674i
$209$	2.67854	−	4.63936i	0.185278	−	0.320912i
$210$	8.43896	−	2.14064i	0.582344	−	0.147718i
$211$	−10.8596	−	18.8094i	−0.747606	−	1.29489i	−0.948967	−	0.315375i	$-0.897870\pi$
$211$	−10.8596	−	18.8094i	−0.747606	−	1.29489i	0.201361	−	0.979517i	$-0.435464\pi$
$212$	−6.25855			−0.429839
$213$	−8.68174	+	0.556788i	−0.594863	+	0.0381505i
$214$	−5.93301			−0.405572
$215$	−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
$219$	11.3237	+	16.9988i	0.765188	+	1.14867i
$220$	3.99106	−	6.91272i	0.269077	−	0.466056i
$221$	10.9328	−	18.9361i	0.735418	−	1.27378i
$222$	5.85586	−	0.375556i	0.393020	−	0.0252056i
$223$	4.00079	−	6.92958i	0.267913	−	0.464039i	−0.700410	−	0.713741i	$-0.746999\pi$
$223$	4.00079	−	6.92958i	0.267913	−	0.464039i	0.968323	+	0.249702i	$0.0803327\pi$
$224$	−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
$227$	7.38974			0.490474			0.245237	−	0.969463i	$-0.421134\pi$
$227$	7.38974			0.490474			0.245237	+	0.969463i	$0.421134\pi$
$228$	1.66935	+	2.50598i	0.110556	+	0.165962i
$229$	−5.48641			−0.362552			−0.181276	−	0.983432i	$-0.558023\pi$
$229$	−5.48641			−0.362552			−0.181276	+	0.983432i	$0.558023\pi$
$230$	5.10499	+	8.84211i	0.336613	+	0.583031i
$231$	6.17544	−	21.8724i	0.406314	−	1.43910i
$232$	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	$0.144018\pi$
$234$	−12.3784	+	29.6484i	−0.809204	+	1.93818i
$235$	−5.30595	−	9.19018i	−0.346122	−	0.599501i
$236$	6.67295	+	11.5579i	0.434372	+	0.752354i
$237$	7.92186	+	11.8920i	0.514580	+	0.772470i
$238$	−12.6791	−	14.8118i	−0.821867	−	0.960109i
$239$	−2.54202	−	4.40291i	−0.164430	−	0.284801i	0.772023	−	0.635595i	$-0.219245\pi$
$239$	−2.54202	−	4.40291i	−0.164430	−	0.284801i	−0.936453	+	0.350794i	$0.885912\pi$
$240$	−4.44460	−	6.67208i	−0.286898	−	0.430681i
$241$	−8.85835			−0.570617			−0.285308	−	0.958436i	$-0.592096\pi$
$241$	−8.85835			−0.570617			−0.285308	+	0.958436i	$0.592096\pi$
$242$	−12.9162	−	22.3716i	−0.830287	−	1.43810i
$243$	−14.7960	+	4.90698i	−0.949164	+	0.314783i
$244$	−9.74670			−0.623969
$245$	−5.44985	−	4.39308i	−0.348178	−	0.280663i
$246$	11.8170	−	23.8779i	0.753425	−	1.52240i
$247$	6.08889			0.387427
$248$	0.157324	−	0.272493i	0.00999009	−	0.0173033i
$249$	4.47734	−	9.04710i	0.283740	−	0.573337i
$250$	−0.949927	−	1.64532i	−0.0600787	−	0.104059i
$251$	−0.251384			−0.0158672			−0.00793360	−	0.999969i	$-0.502525\pi$
$251$	−0.251384			−0.0158672			−0.00793360	+	0.999969i	$0.502525\pi$
$252$	9.47890	+	8.56392i	0.597115	+	0.539476i
$253$	26.6530			1.67566
$254$	1.92454	+	3.33340i	0.120756	+	0.209156i
$255$	−3.72473	−	5.59143i	−0.233251	−	0.350149i
$256$	−10.1613	+	17.5999i	−0.635081	+	1.09999i
$257$	13.1311			0.819093			0.409546	−	0.912289i	$-0.365687\pi$
$257$	13.1311			0.819093			0.409546	+	0.912289i	$0.365687\pi$
$258$	−23.6475	+	1.51659i	−1.47223	+	0.0944190i
$259$	−3.06805	−	3.58411i	−0.190639	−	0.222706i
$260$	9.07253			0.562655
$261$	−6.54750	+	15.6823i	−0.405280	+	0.970713i
$262$	2.91944	+	5.05662i	0.180364	+	0.312399i
$263$	25.9331			1.59910			0.799551	−	0.600599i	$-0.205071\pi$
$263$	25.9331			1.59910			0.799551	+	0.600599i	$0.205071\pi$
$264$	−6.36078	+	0.407938i	−0.391479	+	0.0251068i
$265$	1.94432	+	3.36765i	0.119438	+	0.206873i
$266$	1.80667	−	5.12004i	0.110774	−	0.313930i
$267$	−12.6922	+	25.6463i	−0.776748	+	1.56953i
$268$	1.07969	+	1.87007i	0.0659525	+	0.114233i
$269$	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	$0.787321\pi$
$270$	6.47769	+	7.44947i	0.394220	+	0.453360i
$271$	−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
$273$	25.0392	−	6.35149i	1.51544	−	0.384410i
$274$	3.57463	+	6.19144i	0.215951	+	0.374039i
$275$	−4.95954			−0.299072
$276$	−6.64481	+	13.4268i	−0.399971	+	0.808197i
$277$	3.30246			0.198426			0.0992128	−	0.995066i	$-0.468368\pi$
$277$	3.30246			0.198426			0.0992128	+	0.995066i	$0.468368\pi$
$278$	−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	−0.0963023	−	0.995352i	$-0.530702\pi$
$281$	13.6426	−	23.6297i	0.813849	−	1.40963i	0.910151	−	0.414276i	$-0.135965\pi$
$282$	15.4887	−	31.2971i	0.922338	−	1.86371i
$283$	6.82312	−	11.8180i	0.405593	−	0.702507i	−0.588798	−	0.808280i	$-0.700399\pi$
$283$	6.82312	−	11.8180i	0.405593	−	0.702507i	0.994390	+	0.105773i	$0.0337318\pi$
$284$	−4.04189	+	7.00076i	−0.239842	+	0.415419i
$285$	0.829826	−	1.67678i	0.0491547	−	0.0993239i
$286$	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
$290$	10.7622			0.631980
$291$	−7.40120	+	14.9552i	−0.433866	+	0.876687i
$292$	18.9794			1.11068
$293$	−5.55114	−	9.61486i	−0.324301	−	0.561706i	0.657069	−	0.753830i	$-0.271796\pi$
$293$	−5.55114	−	9.61486i	−0.324301	−	0.561706i	−0.981371	+	0.192124i	$0.938463\pi$
$294$	2.08865	−	22.9396i	0.121813	−	1.33787i
$295$	4.14611	−	7.18127i	0.241396	−	0.418110i
$296$	−0.661562	+	1.14586i	−0.0384525	+	0.0666017i
$297$	25.2963	−	4.92106i	1.46784	−	0.285549i
$298$	−21.5063	−	37.2499i	−1.24582	−	2.15783i
$299$	15.1470	+	26.2354i	0.875973	+	1.51723i
$300$	1.23645	−	2.49843i	0.0713867	−	0.144247i
$301$	12.3896	+	14.4736i	0.714125	+	0.834243i
$302$	−4.37584	−	7.57918i	−0.251801	−	0.436133i
$303$	2.18326	−	0.140020i	0.125425	−	0.00804392i
$304$	−4.99958			−0.286745
$305$	3.02796	+	5.24459i	0.173381	+	0.300304i
$306$	8.51772	−	20.4013i	0.486926	−	1.16627i
$307$	−11.1997			−0.639198			−0.319599	−	0.947553i	$-0.603548\pi$
$307$	−11.1997			−0.639198			−0.319599	+	0.947553i	$0.603548\pi$
$308$	−13.7334	−	16.0435i	−0.782536	−	0.914161i
$309$	−26.2147	+	1.68123i	−1.49130	+	0.0956419i
$310$	0.805650			0.0457578
$311$	−3.33797	+	5.78153i	−0.189279	+	0.327840i	−0.945010	−	0.327041i	$-0.893948\pi$
$311$	−3.33797	+	5.78153i	−0.189279	+	0.327840i	0.755731	+	0.654882i	$0.227282\pi$
$312$	−4.01640	−	6.02927i	−0.227384	−	0.341340i
$313$	6.85785	+	11.8781i	0.387629	+	0.671393i	0.992130	−	0.125212i	$-0.0399610\pi$
$313$	6.85785	+	11.8781i	0.387629	+	0.671393i	−0.604501	+	0.796604i	$0.706628\pi$
$314$	15.9730			0.901407
$315$	1.66338	−	7.76100i	0.0937207	−	0.437283i
$316$	13.2776			0.746922
$317$	1.02456	+	1.77459i	0.0575451	+	0.0996710i	0.893363	−	0.449336i	$-0.148339\pi$
$317$	1.02456	+	1.77459i	0.0575451	+	0.0996710i	−0.835818	+	0.549007i	$0.815006\pi$
$318$	−5.67568	+	11.4685i	−0.318277	+	0.643123i
$319$	14.0473	−	24.3307i	0.786499	−	1.36226i
$320$	−4.63009			−0.258830
$321$	−2.39914	+	4.84780i	−0.133907	+	0.270578i
$322$	26.5552	−	4.95241i	1.47986	−	0.275987i
$323$	−4.18982			−0.233128
$324$	−3.82753	+	13.9702i	−0.212641	+	0.776121i
$325$	−2.81852	−	4.88183i	−0.156344	−	0.270795i
$326$	25.9595			1.43776
$327$	3.76320	+	5.64918i	0.208105	+	0.312401i
$328$	3.00369	+	5.20255i	0.165851	+	0.287263i
$329$	−27.6006	+	5.14737i	−1.52167	+	0.283784i
$330$	−9.04789	−	13.5824i	−0.498070	−	0.747686i
$331$	2.77012	+	4.79799i	0.152259	+	0.263721i	0.932058	−	0.362310i	$-0.118012\pi$
$331$	2.77012	+	4.79799i	0.152259	+	0.263721i	−0.779798	+	0.626031i	$0.784678\pi$
$332$	−4.68993	−	8.12320i	−0.257393	−	0.445818i
$333$	2.06108	−	4.93663i	0.112947	−	0.270526i
$334$	0.306566	−	0.530988i	0.0167745	−	0.0290543i
$335$	0.670844	−	1.16194i	0.0366521	−	0.0634833i
$336$	−20.5596	+	5.21520i	−1.12162	+	0.284513i
$337$	−11.1267	−	19.2721i	−0.606112	−	1.04982i	−0.991875	−	0.127219i	$-0.959395\pi$
$337$	−11.1267	−	19.2721i	−0.606112	−	1.04982i	0.385762	−	0.922598i	$-0.373939\pi$
$338$	35.6722			1.94031
$339$	−10.6139	−	15.9333i	−0.576469	−	0.865376i
$340$	−6.24289			−0.338568
$341$	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
$345$	9.28911	−	0.595741i	0.500109	−	0.0320736i
$346$	−9.75583	+	16.8976i	−0.524477	+	0.908420i
$347$	−7.37553	+	12.7748i	−0.395939	+	0.685787i	−0.993221	−	0.116245i	$-0.962914\pi$
$347$	−7.37553	+	12.7748i	−0.395939	+	0.685787i	0.597281	+	0.802032i	$0.296248\pi$
$348$	8.75475	+	13.1423i	0.469304	+	0.704503i
$349$	−4.59282	+	7.95501i	−0.245848	+	0.425822i	−0.962370	−	0.271743i	$-0.912400\pi$
$349$	−4.59282	+	7.95501i	−0.245848	+	0.425822i	0.716521	+	0.697565i	$0.245733\pi$
$350$	−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
$353$	−11.2312			−0.597778			−0.298889	−	0.954288i	$-0.596616\pi$
$353$	−11.2312			−0.597778			−0.298889	+	0.954288i	$0.596616\pi$
$354$	27.2308	−	1.74640i	1.44730	−	0.0928201i
$355$	5.02270			0.266577
$356$	13.2948	+	23.0273i	0.704623	+	1.22044i
$357$	−17.2297	+	4.37052i	−0.911892	+	0.231312i
$358$	−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	$0.248904\pi$
$360$	−2.20774	+	0.284349i	−0.116358	+	0.0149865i
$361$	8.91663	+	15.4441i	0.469296	+	0.812845i
$362$	−10.0178	−	17.3513i	−0.526521	−	0.911962i
$363$	−23.5025	+	1.50729i	−1.23356	+	0.0791124i
$364$	7.98730	−	22.6358i	0.418649	−	1.18644i
$365$	−5.89623	−	10.2126i	−0.308623	−	0.534551i
$366$	−8.83898	+	17.8604i	−0.462021	+	0.933578i
$367$	17.5381			0.915483			0.457742	−	0.889085i	$-0.348659\pi$
$367$	17.5381			0.915483			0.457742	+	0.889085i	$0.348659\pi$
$368$	−12.4372	−	21.5418i	−0.648333	−	1.12295i
$369$	−14.7319	−	19.3111i	−0.766915	−	1.00530i
$370$	−3.38783			−0.176125
$371$	10.1140	−	1.88620i	0.525091	−	0.0979268i
$372$	0.655372	+	0.983822i	0.0339795	+	0.0510088i
$373$	−37.3782			−1.93537			−0.967684	−	0.252166i	$-0.918857\pi$
$373$	−37.3782			−1.93537			−0.967684	+	0.252166i	$0.918857\pi$
$374$	−18.2743	+	31.6520i	−0.944942	+	1.63669i
$375$	−1.72850	+	0.110854i	−0.0892593	+	0.00572449i
$376$	3.93698	+	6.81904i	0.203034	+	0.351665i
$377$	31.9325			1.64461
$378$	24.2891	−	9.60333i	1.24930	−	0.493942i
$379$	23.8371			1.22443			0.612214	−	0.790692i	$-0.290279\pi$
$379$	23.8371			1.22443			0.612214	+	0.790692i	$0.290279\pi$
$380$	−0.869227	−	1.50554i	−0.0445904	−	0.0772328i
$381$	3.50192	−	0.224590i	0.179409	−	0.0115061i
$382$	−18.6495	+	32.3020i	−0.954194	+	1.65271i
$383$	9.14395			0.467234			0.233617	−	0.972329i	$-0.424944\pi$
$383$	9.14395			0.467234			0.233617	+	0.972329i	$0.424944\pi$
$384$	5.59132	+	8.39350i	0.285331	+	0.428329i
$385$	−4.36630	+	12.3740i	−0.222527	+	0.630636i
$386$	50.3573			2.56312
$387$	−8.32320	+	19.9354i	−0.423092	+	1.01338i
$388$	7.75261	+	13.4279i	0.393579	+	0.681699i
$389$	−4.64365			−0.235442			−0.117721	−	0.993047i	$-0.537559\pi$
$389$	−4.64365			−0.235442			−0.117721	+	0.993047i	$0.537559\pi$
$390$	8.22760	−	16.6250i	0.416621	−	0.841841i
$391$	−10.4228	−	18.0528i	−0.527103	−	0.912968i
$392$	4.04375	+	3.25963i	0.204240	+	0.164636i
$393$	5.31225	−	0.340692i	0.267968	−	0.0171856i
$394$	17.2835	+	29.9359i	0.870731	+	1.50815i
$395$	−4.12488	−	7.14451i	−0.207545	−	0.359479i
$396$	9.22598	−	22.0977i	0.463623	−	1.11045i
$397$	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
$399$	−3.45297	−	3.54661i	−0.172865	−	0.177553i
$400$	2.31429	+	4.00846i	0.115714	+	0.200423i
$401$	14.8459			0.741368			0.370684	−	0.928759i	$-0.379123\pi$
$401$	14.8459			0.741368			0.370684	+	0.928759i	$0.379123\pi$
$402$	4.40597	−	0.282569i	0.219750	−	0.0140933i
$403$	2.39044			0.119076
$404$	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
$408$	2.76372	+	4.14880i	0.136824	+	0.205396i
$409$	−5.06678	+	8.77592i	−0.250536	+	0.433942i	−0.963674	−	0.267083i	$-0.913940\pi$
$409$	−5.06678	+	8.77592i	−0.250536	+	0.433942i	0.713137	+	0.701024i	$0.247274\pi$
$410$	−7.69089	+	13.3210i	−0.379826	+	0.657878i
$411$	6.50445	−	0.417151i	0.320841	−	0.0205766i
$412$	−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
$416$	−41.2047			−2.02023
$417$	15.9460	+	23.9376i	0.780879	+	1.17223i
$418$	−10.1777			−0.497806
$419$	−0.759103	−	1.31480i	−0.0370846	−	0.0642324i	0.846887	−	0.531772i	$-0.178474\pi$
$419$	−0.759103	−	1.31480i	−0.0370846	−	0.0642324i	−0.883972	+	0.467540i	$0.845140\pi$
$420$	−5.14498	−	5.28450i	−0.251049	−	0.257857i
$421$	−14.2107	+	24.6136i	−0.692586	+	1.19959i	0.278402	+	0.960465i	$0.410195\pi$
$421$	−14.2107	+	24.6136i	−0.692586	+	1.19959i	−0.970988	+	0.239129i	$0.923138\pi$
$422$	−20.6317	+	35.7351i	−1.00433	+	1.73956i
$423$	−19.3093	−	25.3113i	−0.938853	−	1.23068i
$424$	−1.44267	−	2.49877i	−0.0700621	−	0.121351i
$425$	1.93945	+	3.35923i	0.0940772	+	0.162946i
$426$	9.16312	+	13.7554i	0.443955	+	0.666449i
$427$	15.7509	−	2.93746i	0.762240	−	0.142154i
$428$	2.51305	+	4.35273i	0.121473	+	0.210397i
$429$	−26.8460	−	40.3002i	−1.29613	−	1.94571i
$430$	13.6810			0.659755
$431$	−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	$0.888626\pi$
$432$	−15.7815	−	18.1490i	−0.759286	−	0.873193i
$433$	−7.11022			−0.341696			−0.170848	−	0.985297i	$-0.554651\pi$
$433$	−7.11022			−0.341696			−0.170848	+	0.985297i	$0.554651\pi$
$434$	0.709280	−	2.01008i	0.0340465	−	0.0964869i
$435$	4.35194	−	8.79370i	0.208659	−	0.421626i
$436$	6.30737			0.302068
$437$	2.90242	−	5.02715i	0.138842	−	0.240481i
$438$	17.2118	−	34.7788i	0.822411	−	1.66180i
$439$	17.0564	+	29.5425i	0.814056	+	1.40999i	0.910004	+	0.414599i	$0.136078\pi$
$439$	17.0564	+	29.5425i	0.814056	+	1.40999i	−0.0959483	+	0.995386i	$0.530588\pi$
$440$	3.67994			0.175434
$441$	−17.8991	−	10.9827i	−0.852340	−	0.522988i
$442$	−41.5414			−1.97592
$443$	−6.56659	−	11.3737i	−0.311988	−	0.540379i	0.666805	−	0.745233i	$-0.267662\pi$
$443$	−6.56659	−	11.3737i	−0.311988	−	0.540379i	−0.978793	+	0.204853i	$0.934328\pi$
$444$	−2.75590	−	4.13706i	−0.130789	−	0.196336i
$445$	8.26047	−	14.3076i	0.391584	−	0.678243i
$446$	−15.2019			−0.719829
$447$	−39.1331	+	2.50973i	−1.85093	+	0.118706i
$448$	−4.07625	+	11.5520i	−0.192585	+	0.545780i
$449$	−21.5648			−1.01771			−0.508854	−	0.860853i	$-0.669931\pi$
$449$	−21.5648			−1.01771			−0.508854	+	0.860853i	$0.669931\pi$
$450$	−3.45696	−	4.53150i	−0.162963	−	0.213617i
$451$	20.0770	+	34.7743i	0.945387	+	1.63746i
$452$	−17.7897			−0.836755
$453$	−7.96233	+	0.510650i	−0.374103	+	0.0239924i
$454$	−7.01972	−	12.1585i	−0.329452	−	0.570627i
$455$	−14.6614	+	2.73428i	−0.687339	+	0.128185i
$456$	−0.615725	+	1.24416i	−0.0288339	+	0.0582631i
$457$	−15.5304	−	26.8995i	−0.726482	−	1.25830i	−0.958361	−	0.285560i	$-0.907821\pi$
$457$	−15.5304	−	26.8995i	−0.726482	−	1.25830i	0.231878	−	0.972745i	$-0.425513\pi$
$458$	5.21169	+	9.02692i	0.243526	+	0.421800i
$459$	−13.2254	−	15.2095i	−0.617309	−	0.709917i
$460$	4.32466	−	7.49052i	0.201638	−	0.349248i
$461$	8.82780	−	15.2902i	0.411152	−	0.712135i	−0.583864	−	0.811851i	$-0.698460\pi$
$461$	8.82780	−	15.2902i	0.411152	−	0.712135i	0.995016	+	0.0997158i	$0.0317933\pi$
$462$	−41.8534	+	10.6166i	−1.94720	+	0.493930i
$463$	10.6941	+	18.5227i	0.496997	+	0.860824i	0.999994	−	0.00346411i	$-0.00110266\pi$
$463$	10.6941	+	18.5227i	0.496997	+	0.860824i	−0.502997	+	0.864288i	$0.667769\pi$
$464$	−26.2198			−1.21722
$465$	0.325782	−	0.658288i	0.0151078	−	0.0305274i
$466$	−4.12346			−0.191016
$467$	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
$471$	6.45902	−	13.0514i	0.297616	−	0.601375i
$472$	−3.07638	+	5.32845i	−0.141602	+	0.245262i
$473$	17.8570	−	30.9292i	0.821065	−	1.42213i
$474$	12.0410	−	24.3306i	0.553062	−	1.11754i
$475$	−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
$479$	−29.7602			−1.35978			−0.679890	−	0.733314i	$-0.737972\pi$
$479$	−29.7602			−1.35978			−0.679890	+	0.733314i	$0.737972\pi$
$480$	−5.61560	+	11.3471i	−0.256316	+	0.517923i
$481$	−10.0520			−0.458332
$482$	8.41479	+	14.5748i	0.383283	+	0.663866i
$483$	6.69161	−	23.7006i	0.304479	−	1.07842i
$484$	−10.9419	+	18.9519i	−0.497359	+	0.861450i
$485$	4.81694	−	8.34318i	0.218726	−	0.378844i
$486$	22.1287	+	19.6829i	1.00378	+	0.892835i
$487$	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	$0.726358\pi$
$488$	−2.24673	−	3.89144i	−0.101705	−	0.176157i
$489$	10.4973	−	21.2112i	0.474703	−	0.959205i
$490$	−2.05106	+	13.1399i	−0.0926576	+	0.593599i
$491$	10.6020	+	18.3632i	0.478462	+	0.828720i	0.999695	−	0.0246944i	$-0.00786128\pi$
$491$	10.6020	+	18.3632i	0.478462	+	0.828720i	−0.521234	+	0.853414i	$0.674528\pi$
$492$	−22.5233	+	1.44449i	−1.01543	+	0.0651228i
$493$	−21.9731			−0.989617
$494$	−5.78400	−	10.0182i	−0.260234	−	0.450739i
$495$	−14.7567	+	1.90061i	−0.663266	+	0.0854262i
$496$	−1.96279			−0.0881317
$497$	4.42190	−	12.5315i	0.198349	−	0.562117i
$498$	−19.1386	+	1.22742i	−0.857619	+	0.0550019i
$499$	−12.9629			−0.580299			−0.290149	−	0.956981i	$-0.593705\pi$
$499$	−12.9629			−0.580299			−0.290149	+	0.956981i	$0.593705\pi$
$500$	−0.804724	+	1.39382i	−0.0359883	+	0.0623336i
$501$	−0.309898	−	0.465208i	−0.0138452	−	0.0207840i
$502$	0.238796	+	0.413607i	0.0106580	+	0.0184602i
$503$	37.0834			1.65347			0.826733	−	0.562594i	$-0.190197\pi$
$503$	37.0834			1.65347			0.826733	+	0.562594i	$0.190197\pi$
$504$	−1.23421	+	5.75861i	−0.0549762	+	0.256509i
$505$	−1.26310			−0.0562071
$506$	−25.3184	−	43.8528i	−1.12554	−	1.94950i
$507$	14.4248	−	29.1474i	0.640630	−	1.29448i
$508$	1.63036	−	2.82387i	0.0723356	−	0.125289i
$509$	0.178119			0.00789500			0.00394750	−	0.999992i	$-0.498743\pi$
$509$	0.178119			0.00789500			0.00394750	+	0.999992i	$0.498743\pi$
$510$	−5.66148	+	11.4398i	−0.250695	+	0.506564i
$511$	−30.6711	+	5.72001i	−1.35681	+	0.253038i
$512$	26.9644			1.19167
$513$	1.82650	−	5.30714i	0.0806420	−	0.234316i
$514$	−12.4735	−	21.6048i	−0.550185	−	0.952948i
$515$	15.1661			0.668300
$516$	11.1291	+	16.7066i	0.489930	+	0.735466i
$517$	26.3151	+	45.5791i	1.15734	+	2.00457i
$518$	−2.98259	+	8.45257i	−0.131047	+	0.371385i
$519$	9.86187	+	14.8043i	0.432888	+	0.649836i
$520$	2.09132	+	3.62228i	0.0917106	+	0.158847i
$521$	−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	$-0.380195\pi$
$522$	32.0222	−	4.12434i	1.40157	−	0.180517i
$523$	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
$525$	−1.24516	+	4.41017i	−0.0543433	+	0.192475i
$526$	−24.6345	−	42.6683i	−1.07412	−	1.86042i
$527$	−1.64488			−0.0716522
$528$	22.0432	+	33.0905i	0.959306	+	1.44008i
$529$	5.88081			0.255687
$530$	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
$534$	54.2531	−	3.47943i	2.34776	−	0.150570i
$535$	1.56144	−	2.70449i	0.0675068	−	0.116925i
$536$	−0.497761	+	0.862147i	−0.0215000	+	0.0372391i
$537$	12.8942	+	19.3563i	0.556425	+	0.835286i
$538$	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	$0.137069\pi$
$542$	38.7359			1.66385
$543$	−18.2284	+	1.16905i	−0.782257	+	0.0501687i
$544$	28.3533			1.21564
$545$	−1.95948	−	3.39393i	−0.0839351	−	0.145380i
$546$	−34.2357	−	35.1641i	−1.46515	−	1.50488i
$547$	−6.34548	+	10.9907i	−0.271313	+	0.469928i	−0.969198	−	0.246282i	$-0.920791\pi$
$547$	−6.34548	+	10.9907i	−0.271313	+	0.469928i	0.697885	+	0.716209i	$0.254124\pi$
$548$	3.02822	−	5.24504i	0.129359	−	0.224057i
$549$	11.0193	+	14.4445i	0.470293	+	0.616475i
$550$	4.71121	+	8.16005i	0.200887	+	0.347946i
$551$	−3.05941	−	5.29905i	−0.130335	−	0.225747i
$552$	−6.89245	+	0.442035i	−0.293362	+	0.0188143i
$553$	−21.4569	+	4.00160i	−0.912439	+	0.170165i
$554$	−3.13710	−	5.43361i	−0.133283	−	0.230852i
$555$	−1.36994	+	2.76816i	−0.0581508	+	0.117502i
$556$	26.7266			1.13346
$557$	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	$0.822103\pi$
$558$	2.39715	−	0.308744i	0.101479	−	0.0130702i
$559$	40.5927			1.71689
$560$	12.0385	−	2.24512i	0.508719	−	0.0948735i
$561$	18.4729	+	27.7309i	0.779928	+	1.17080i
$562$	−51.8379			−2.18665
$563$	0.516378	−	0.894393i	0.0217627	−	0.0376942i	−0.854939	−	0.518729i	$-0.826405\pi$
$563$	0.516378	−	0.894393i	0.0217627	−	0.0376942i	0.876702	+	0.481034i	$0.159739\pi$
$564$	−29.5216	+	1.89332i	−1.24308	+	0.0797230i
$565$	5.52663	+	9.57241i	0.232507	+	0.402714i
$566$	−25.9259			−1.08975
$567$	1.97505	−	23.7297i	0.0829444	−	0.996554i
$568$	−3.72681			−0.156373
$569$	20.1470	+	34.8957i	0.844607	+	1.46290i	0.885962	+	0.463758i	$0.153499\pi$
$569$	20.1470	+	34.8957i	0.844607	+	1.46290i	−0.0413548	+	0.999145i	$0.513167\pi$
$570$	−3.54712	+	0.227488i	−0.148572	+	0.00952844i
$571$	−11.1088	+	19.2409i	−0.464887	+	0.805208i	−0.999196	−	0.0400812i	$-0.987238\pi$
$571$	−11.1088	+	19.2409i	−0.464887	+	0.805208i	0.534310	+	0.845289i	$0.320572\pi$
$572$	−44.9956			−1.88136
$573$	18.8523	+	28.3003i	0.787564	+	1.18226i
$574$	26.4647	+	30.9162i	1.10462	+	1.29042i
$575$	−5.37409			−0.224115
$576$	−13.7765	+	1.77436i	−0.574020	+	0.0739316i
$577$	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	$0.780120\pi$
$578$	−3.71254			−0.154421
$579$	20.3631	−	41.1465i	0.846261	−	1.70999i
$580$	−4.55857	−	7.89567i	−0.189284	−	0.327850i
$581$	10.0272	+	11.7138i	0.415999	+	0.485972i
$582$	31.6367	−	2.02896i	1.31138	−	0.0841032i
$583$	−9.64292	−	16.7020i	−0.399369	−	0.691727i
$584$	4.37496	+	7.57765i	0.181037	+	0.313565i
$585$	−10.2571	−	13.4454i	−0.424080	−	0.555898i
$586$	−10.5464	+	18.2668i	−0.435666	+	0.754596i
$587$	−9.83730	+	17.0387i	−0.406029	+	0.703263i	−0.994441	−	0.105299i	$-0.966420\pi$
$587$	−9.83730	+	17.0387i	−0.406029	+	0.703263i	0.588412	+	0.808561i	$0.299753\pi$
$588$	−17.7143	+	8.18423i	−0.730525	+	0.337512i
$589$	−0.229025	−	0.396682i	−0.00943679	−	0.0163450i
$590$	−15.7540			−0.648582
$591$	31.4493	−	2.01695i	1.29365	−	0.0829661i
$592$	8.25370			0.339225
$593$	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
$597$	−12.5616	−	18.8571i	−0.514113	−	0.771769i
$598$	28.7771	−	49.8434i	1.17678	−	2.03825i
$599$	−1.73715	+	3.00883i	−0.0709779	+	0.122937i	−0.899330	−	0.437270i	$-0.855945\pi$
$599$	−1.73715	+	3.00883i	−0.0709779	+	0.122937i	0.828352	+	0.560208i	$0.189279\pi$
$600$	1.28253	−	0.0822531i	0.0523592	−	0.00335797i
$601$	−11.6008	+	20.0932i	−0.473207	+	0.819618i	−0.999530	−	0.0306665i	$-0.990237\pi$
$601$	−11.6008	+	20.0932i	−0.473207	+	0.819618i	0.526323	+	0.850285i	$0.323570\pi$
$602$	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
$605$	13.5971			0.552800
$606$	−2.30432	−	3.45916i	−0.0936065	−	0.140519i
$607$	44.5653			1.80885			0.904425	−	0.426633i	$-0.140301\pi$
$607$	44.5653			1.80885			0.904425	+	0.426633i	$0.140301\pi$
$608$	3.94777	+	6.83774i	0.160103	+	0.277307i
$609$	−18.1087	−	18.5998i	−0.733803	−	0.753703i
$610$	5.75269	−	9.96396i	0.232920	−	0.403429i
$611$	−29.9099	+	51.8055i	−1.21003	+	2.09583i
$612$	−18.5752	+	2.39242i	−0.750860	+	0.0967079i
$613$	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	$0.701932\pi$
$614$	10.6389	+	18.4270i	0.429349	+	0.743655i
$615$	7.77448	+	11.6708i	0.313497	+	0.470611i
$616$	3.23976	−	9.18139i	0.130534	−	0.369929i
$617$	−8.25212	−	14.2931i	−0.332218	−	0.575418i	0.650729	−	0.759310i	$-0.274464\pi$
$617$	−8.25212	−	14.2931i	−0.332218	−	0.575418i	−0.982946	+	0.183892i	$0.941130\pi$
$618$	27.6682	+	41.5345i	1.11298	+	1.67076i
$619$	21.2597			0.854501			0.427251	−	0.904133i	$-0.359482\pi$
$619$	21.2597			0.854501			0.427251	+	0.904133i	$0.359482\pi$
$620$	−0.341250	−	0.591062i	−0.0137049	−	0.0237376i
$621$	27.4107	−	5.33238i	1.09995	−	0.213981i
$622$	12.6833			0.508554
$623$	−28.4247	−	33.2058i	−1.13881	−	1.33036i
$624$	−20.0447	+	40.5032i	−0.802431	+	1.62142i
$625$	1.00000			0.0400000
$626$	13.0289	−	22.5668i	0.520740	−	0.901949i
$627$	−4.11556	+	8.31607i	−0.164360	+	0.332112i
$628$	−6.76569	−	11.7185i	−0.269981	−	0.467620i
$629$	6.91688			0.275794
$630$	−14.3494	+	4.63560i	−0.571695	+	0.184687i
$631$	9.83777			0.391635			0.195818	−	0.980640i	$-0.437264\pi$
$631$	9.83777			0.391635			0.195818	+	0.980640i	$0.437264\pi$
$632$	3.06063	+	5.30117i	0.121745	+	0.210869i
$633$	20.8559	+	31.3082i	0.828949	+	1.24439i
$634$	1.94652	−	3.37147i	0.0773061	−	0.133898i
$635$	−2.02599			−0.0803989
$636$	10.8179	−	0.693787i	0.428958	−	0.0275105i
$637$	−6.08570	+	38.9872i	−0.241124	+	1.54473i
$638$	−53.3757			−2.11316
$639$	14.9447	−	1.92482i	0.591202	−	0.0761446i
$640$	−2.91138	−	5.04266i	−0.115082	−	0.199329i
$641$	2.73524			0.108036			0.0540178	−	0.998540i	$-0.482797\pi$
$641$	2.73524			0.108036			0.0540178	+	0.998540i	$0.482797\pi$
$642$	10.2552	−	0.657700i	0.404741	−	0.0259573i
$643$	−13.6815	−	23.6971i	−0.539546	−	0.934522i	−0.998928	−	0.0462829i	$-0.985262\pi$
$643$	−13.6815	−	23.6971i	−0.539546	−	0.934522i	0.459382	−	0.888239i	$-0.348071\pi$
$644$	−14.8814	−	17.3845i	−0.586408	−	0.685044i
$645$	5.53219	−	11.1786i	0.217830	−	0.440156i
$646$	3.98002	+	6.89360i	0.156592	+	0.271225i
$647$	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	$0.753982\pi$
$648$	−6.45999	+	1.69212i	−0.253772	+	0.0664726i
$649$	−20.5628	+	35.6158i	−0.807161	+	1.39804i
$650$	−5.35479	+	9.27476i	−0.210032	+	0.363786i
$651$	−1.35560	−	1.39236i	−0.0531303	−	0.0545711i
$652$	−10.9957	−	19.0451i	−0.430625	−	0.745864i
$653$	−6.81654			−0.266752			−0.133376	−	0.991066i	$-0.542582\pi$
$653$	−6.81654			−0.266752			−0.133376	+	0.991066i	$0.542582\pi$
$654$	5.71996	−	11.5580i	0.223668	−	0.451953i
$655$	−3.07333			−0.120085
$656$	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	−0.498686	−	0.866783i	$-0.666184\pi$
$659$	12.8692	−	22.2901i	0.501313	−	0.868300i	0.999999	−	0.00151714i	$-0.000482920\pi$
$660$	−6.13225	+	12.3911i	−0.238697	+	0.482322i
$661$	18.0721	−	31.3019i	0.702925	−	1.21750i	−0.264511	−	0.964383i	$-0.585210\pi$
$661$	18.0721	−	31.3019i	0.702925	−	1.21750i	0.967435	−	0.253118i	$-0.0814563\pi$
$662$	5.26282	−	9.11548i	0.204545	−	0.354283i
$663$	−16.7982	+	33.9430i	−0.652386	+	1.31824i
$664$	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
$668$	−0.519410			−0.0200966
$669$	−6.14720	+	12.4213i	−0.237664	+	0.480234i
$670$	−2.54901			−0.0984769
$671$	−15.0173	−	26.0108i	−0.579737	−	1.00413i
$672$	23.3670	+	24.0006i	0.901400	+	0.925845i
$673$	21.2313	−	36.7737i	0.818408	−	1.41752i	−0.0884474	−	0.996081i	$-0.528191\pi$
$673$	21.2313	−	36.7737i	0.818408	−	1.41752i	0.906855	−	0.421443i	$-0.138476\pi$
$674$	−21.1392	+	36.6142i	−0.814252	+	1.41033i
$675$	−5.10054	+	0.992240i	−0.196320	+	0.0381913i
$676$	−15.1097	−	26.1708i	−0.581144	−	1.00657i
$677$	−8.01031	−	13.8743i	−0.307861	−	0.533231i	0.670033	−	0.742331i	$-0.266280\pi$
$677$	−8.01031	−	13.8743i	−0.307861	−	0.533231i	−0.977894	+	0.209100i	$0.932947\pi$
$678$	−16.1329	+	32.5988i	−0.619580	+	1.25195i
$679$	−16.5753	−	19.3634i	−0.636102	−	0.743097i
$680$	−1.43906	−	2.49252i	−0.0551854	−	0.0955838i
$681$	−12.7732	+	0.819185i	−0.489469	+	0.0313912i
$682$	−3.99565			−0.153002
$683$	−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	$0.854513\pi$
$684$	−3.16328	−	4.14652i	−0.120951	−	0.158546i
$685$	−3.76306			−0.143779
$686$	30.9780	+	16.6855i	1.18274	+	0.637055i
$687$	9.48326	−	0.608192i	0.361809	−	0.0232040i
$688$	−33.3306			−1.27072
$689$	10.9602	−	18.9836i	0.417550	−	0.723218i
$690$	−9.80416	−	14.7177i	−0.373238	−	0.560292i
$691$	−18.1322	−	31.4058i	−0.689780	−	1.19473i	−0.971909	−	0.235358i	$-0.924374\pi$
$691$	−18.1322	−	31.4058i	−0.689780	−	1.19473i	0.282128	−	0.959377i	$-0.408960\pi$
$692$	16.5292			0.628344
$693$	−8.24959	+	38.4910i	−0.313376	+	1.46215i
$694$	28.0249			1.06381
$695$	−8.30302	−	14.3813i	−0.314952	−	0.545512i
$696$	−3.22910	+	6.52486i	−0.122399	+	0.247324i
$697$	15.7024	−	27.1973i	0.594769	−	1.03017i
$698$	17.4514			0.660545
$699$	−1.66741	+	3.36924i	−0.0630672	+	0.127436i
$700$	2.76909	+	3.23487i	0.104662	+	0.122267i
$701$	−40.8817			−1.54408			−0.772040	−	0.635574i	$-0.780764\pi$
$701$	−40.8817			−1.54408			−0.772040	+	0.635574i	$0.780764\pi$
$702$	18.1095	−	52.6195i	0.683498	−	1.98599i
$703$	0.963069	+	1.66808i	0.0363228	+	0.0629130i
$704$	22.9631			0.865456
$705$	10.1901	+	15.2970i	0.383782	+	0.576120i
$706$	10.6689	+	18.4790i	0.401528	+	0.695466i
$707$	−1.11201	+	3.15140i	−0.0418214	+	0.118521i
$708$	−12.8154	−	19.2381i	−0.481633	−	0.723011i
$709$	−20.2661	−	35.1020i	−0.761110	−	1.31828i	−0.942279	−	0.334830i	$-0.891321\pi$
$709$	−20.2661	−	35.1020i	−0.761110	−	1.31828i	0.181168	−	0.983452i	$-0.442012\pi$
$710$	−4.77120	−	8.26397i	−0.179060	−	0.310141i
$711$	−15.0112	−	19.6772i	−0.562964	−	0.737952i
$712$	−6.12921	+	10.6161i	−0.229702	+	0.397855i
$713$	1.13946	−	1.97361i	0.0426733	−	0.0739122i
$714$	23.5579	+	24.1967i	0.881631	+	0.905539i
$715$	13.9786	+	24.2116i	0.522770	+	0.905464i
$716$	21.6115			0.807660
$717$	4.88196	+	7.32863i	0.182320	+	0.273693i
$718$	18.3938			0.686451
$719$	−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
$723$	15.3117	−	0.981987i	0.569447	−	0.0365205i
$724$	−8.48646	+	14.6990i	−0.315397	+	0.546284i
$725$	−2.83238	+	4.90583i	−0.105192	+	0.182198i
$726$	24.8057	+	37.2374i	0.920625	+	1.38201i
$727$	10.5850	−	18.3338i	0.392578	−	0.679964i	−0.600211	−	0.799842i	$-0.704917\pi$
$727$	10.5850	−	18.3338i	0.392578	−	0.679964i	0.992789	+	0.119877i	$0.0382501\pi$
$728$	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
$731$	−27.9322			−1.03311
$732$	16.8472	−	1.08046i	0.622689	−	0.0399351i
$733$	−3.08313			−0.113878			−0.0569390	−	0.998378i	$-0.518134\pi$
$733$	−3.08313			−0.113878			−0.0569390	+	0.998378i	$0.518134\pi$
$734$	−16.6600	−	28.8559i	−0.614930	−	1.06509i
$735$	9.90706	+	6.98929i	0.365427	+	0.257804i
$736$	−19.6413	+	34.0197i	−0.723988	+	1.25398i
$737$	−3.32708	+	5.76267i	−0.122555	+	0.212271i
$738$	−17.7787	+	42.5830i	−0.654444	+	1.56750i
$739$	−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	$0.945779\pi$
$740$	1.43499	+	2.48547i	0.0527512	+	0.0913678i
$741$	−10.5246	+	0.674979i	−0.386632	+	0.0247960i
$742$	−12.7110	−	14.8490i	−0.466634	−	0.545123i
$743$	7.14920	+	12.3828i	0.262279	+	0.454280i	0.966847	−	0.255356i	$-0.0821927\pi$
$743$	7.14920	+	12.3828i	0.262279	+	0.454280i	−0.704568	+	0.709636i	$0.748859\pi$
$744$	−0.241728	+	0.488445i	−0.00886216	+	0.0179073i
$745$	22.6399			0.829462
$746$	35.5065	+	61.4991i	1.29999	+	2.25164i
$747$	−6.73618	+	16.1342i	−0.246464	+	0.590321i
$748$	30.9619			1.13208
$749$	−5.37298	−	6.27674i	−0.196325	−	0.229347i
$750$	1.82434	+	2.73864i	0.0666155	+	0.100001i
$751$	2.93232			0.107002			0.0535009	−	0.998568i	$-0.482962\pi$
$751$	2.93232			0.107002			0.0535009	+	0.998568i	$0.482962\pi$
$752$	24.5590	−	42.5374i	0.895574	−	1.55118i
$753$	0.434517	−	0.0278670i	0.0158347	−	0.00101553i
$754$	−30.3336	−	52.5393i	−1.10468	−	1.91337i
$755$	4.60650			0.167648
$756$	−17.3336	−	13.7520i	−0.630418	−	0.500154i
$757$	45.0838			1.63860			0.819299	−	0.573366i	$-0.194363\pi$
$757$	45.0838			1.63860			0.819299	+	0.573366i	$0.194363\pi$
$758$	−22.6435	−	39.2197i	−0.822449	−	1.42452i
$759$	−46.0697	+	2.95460i	−1.67223	+	0.107245i
$760$	0.400733	−	0.694091i	0.0145361	−	0.0251773i
$761$	4.87664			0.176778			0.0883890	−	0.996086i	$-0.471828\pi$
$761$	4.87664			0.176778			0.0883890	+	0.996086i	$0.471828\pi$
$762$	−3.69609	−	5.54844i	−0.133895	−	0.200999i
$763$	−10.1929	+	1.90092i	−0.369007	+	0.0688179i
$764$	31.5976			1.14316
$765$	7.05802	+	9.25188i	0.255183	+	0.334502i
$766$	−8.68608	−	15.0447i	−0.313841	−	0.543589i
$767$	−46.7436			−1.68781
$768$	15.6128	−	31.5478i	0.563377	−	1.13838i
$769$	9.30829	+	16.1224i	0.335666	+	0.581390i	0.983612	−	0.180296i	$-0.0577054\pi$
$769$	9.30829	+	16.1224i	0.335666	+	0.581390i	−0.647947	+	0.761686i	$0.724372\pi$
$770$	24.5068	−	4.57040i	0.883165	−	0.164706i
$771$	−22.6970	+	1.45563i	−0.817413	+	0.0524234i
$772$	−21.3299	−	36.9445i	−0.767681	−	1.32966i
$773$	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	$0.584797\pi$
$774$	40.7067	−	5.24287i	1.46317	−	0.188451i
$775$	−0.212029	+	0.367245i	−0.00761632	+	0.0131918i
$776$	−3.57413	+	6.19057i	−0.128304	+	0.222229i
$777$	5.70043	+	5.85502i	0.204502	+	0.210048i
$778$	4.41113	+	7.64030i	0.158147	+	0.273918i
$779$	8.74525			0.313331
$780$	−15.6819	+	1.00573i	−0.561501	+	0.0360109i
$781$	−24.9103			−0.891361
$782$	−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
$786$	−5.60680	−	8.41673i	−0.199988	−	0.300215i
$787$	23.4774	−	40.6640i	0.836879	−	1.44952i	−0.0556129	−	0.998452i	$-0.517711\pi$
$787$	23.4774	−	40.6640i	0.836879	−	1.44952i	0.892492	−	0.451064i	$-0.148955\pi$
$788$	14.6416	−	25.3600i	0.521585	−	0.903412i
$789$	−44.8253	+	2.87479i	−1.59582	+	0.102345i
$790$	−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
$794$	−39.7597			−1.41102
$795$	−3.73407	−	5.60545i	−0.132434	−	0.198805i
$796$	−21.0541			−0.746244
$797$	−9.63386	−	16.6863i	−0.341249	−	0.591061i	0.643416	−	0.765517i	$-0.277517\pi$
$797$	−9.63386	−	16.6863i	−0.341249	−	0.591061i	−0.984665	+	0.174456i	$0.944183\pi$
$798$	−2.55524	+	9.05027i	−0.0904547	+	0.320376i
$799$	20.5813	−	35.6478i	0.728113	−	1.26113i
$800$	3.65482	−	6.33033i	0.129217	−	0.223811i
$801$	19.0954	−	45.7366i	0.674703	−	1.61602i
$802$	−14.1025	−	24.4263i	−0.497977	−	0.862522i
$803$	29.2426	+	50.6497i	1.03195	+	1.78739i
$804$	−2.07355	−	3.11274i	−0.0731284	−	0.109778i
$805$	−4.73125	+	13.4082i	−0.166755	+	0.472578i
$806$	−2.27074	−	3.93304i	−0.0799835	−	0.138535i
$807$	−4.53737	−	6.81133i	−0.159723	−	0.239770i
$808$	0.937208			0.0329709
$809$	−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	$-0.496927\pi$
$810$	−12.0225	−	12.1583i	−0.422427	−	0.427200i
$811$	−34.7360			−1.21975			−0.609873	−	0.792499i	$-0.708780\pi$
$811$	−34.7360			−1.21975			−0.609873	+	0.792499i	$0.708780\pi$
$812$	−23.7128	+	4.42232i	−0.832157	+	0.155193i
$813$	15.6637	−	31.6507i	0.549350	−	1.11004i
$814$	16.8021			0.588913
$815$	−6.83197	+	11.8333i	−0.239313	+	0.414503i
$816$	13.7929	−	27.8706i	0.482850	−	0.975666i
$817$	−3.88913	−	6.73617i	−0.136063	−	0.235669i
$818$	19.2523			0.673141
$819$	−42.5761	+	13.7543i	−1.48773	+	0.480613i
$820$	13.0306			0.455047
$821$	14.9218	+	25.8453i	0.520774	+	0.902006i	0.999708	+	0.0241558i	$0.00768978\pi$
$821$	14.9218	+	25.8453i	0.520774	+	0.902006i	−0.478935	+	0.877851i	$0.658977\pi$
$822$	−6.86510	−	10.3056i	−0.239448	−	0.359451i
$823$	−19.6476	+	34.0307i	−0.684873	+	1.18624i	0.288603	+	0.957449i	$0.406809\pi$
$823$	−19.6476	+	34.0307i	−0.684873	+	1.18624i	−0.973477	+	0.228787i	$0.926524\pi$
$824$	−11.2532			−0.392022
$825$	8.57257	−	0.549787i	0.298459	−	0.0191411i
$826$	−13.8696	+	39.3059i	−0.482584	+	1.36763i
$827$	45.4517			1.58051			0.790255	−	0.612778i	$-0.209948\pi$
$827$	45.4517			1.58051			0.790255	+	0.612778i	$0.209948\pi$
$828$	9.99714	−	23.9448i	0.347425	−	0.832139i
$829$	−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	$0.962823\pi$
$830$	11.0723			0.384327
$831$	−5.70830	+	0.366092i	−0.198019	+	0.0126996i
$832$	13.0500	+	22.6033i	0.452428	+	0.783629i
$833$	4.18762	−	26.8275i	0.145093	−	0.929516i
$834$	24.2375	−	48.9752i	0.839275	−	1.69587i
$835$	0.161363	+	0.279489i	0.00558419	+	0.00967210i
$836$	4.31097	+	7.46681i	0.149098	+	0.258245i
$837$	0.717067	−	2.08353i	0.0247855	−	0.0720174i
$838$	−1.44218	+	2.49794i	−0.0498194	+	0.0862898i
$839$	−17.0440	+	29.5210i	−0.588423	+	1.01918i	0.406016	+	0.913866i	$0.366918\pi$
$839$	−17.0440	+	29.5210i	−0.588423	+	1.01918i	−0.994439	+	0.105313i	$0.966416\pi$
$840$	0.923901	−	3.27231i	0.0318776	−	0.112905i
$841$	−1.54476	−	2.67560i	−0.0532676	−	0.0922622i
$842$	53.9964			1.86084
$843$	−20.9618	+	42.3562i	−0.721962	+	1.45883i
$844$	34.9559			1.20323
$845$	−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
$849$	−10.4837	+	21.1838i	−0.359799	+	0.727025i
$850$	3.68468	−	6.38204i	0.126383	−	0.218902i
$851$	−4.79155	+	8.29921i	−0.164252	+	0.284493i
$852$	6.21034	−	12.5489i	0.212763	−	0.429917i
$853$	−5.23794	+	9.07238i	−0.179344	+	0.310632i	−0.941656	−	0.336577i	$-0.890731\pi$
$853$	−5.23794	+	9.07238i	−0.179344	+	0.310632i	0.762312	+	0.647209i	$0.224064\pi$
$854$	−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
$857$	−57.4143			−1.96124			−0.980618	−	0.195931i	$-0.937227\pi$
$857$	−57.4143			−1.96124			−0.980618	+	0.195931i	$0.937227\pi$
$858$	−40.8051	+	82.4525i	−1.39306	+	2.81488i
$859$	−1.90934			−0.0651459			−0.0325729	−	0.999469i	$-0.510370\pi$
$859$	−1.90934			−0.0651459			−0.0325729	+	0.999469i	$0.510370\pi$
$860$	−5.79486	−	10.0370i	−0.197603	−	0.342259i
$861$	35.9629	−	9.12242i	1.22561	−	0.310891i
$862$	−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	$0.211562\pi$
$864$	−12.3603	+	35.9145i	−0.420506	+	1.22184i
$865$	−5.13504	−	8.89415i	−0.174597	−	0.302410i
$866$	6.75420	+	11.6986i	0.229517	+	0.397535i
$867$	−1.50124	+	3.03348i	−0.0509850	+	0.103022i
$868$	−1.77512	+	0.331051i	−0.0602515	+	0.0112366i
$869$	20.4575	+	35.4335i	0.693974	+	1.20200i
$870$	−18.6025	+	1.19304i	−0.630684	+	0.0404478i
$871$	−7.56316			−0.256268
$872$	1.45392	+	2.51827i	0.0492360	+	0.0852793i
$873$	11.1351	−	26.6704i	0.376867	−	0.902658i
$874$	−11.0284			−0.373040
$875$	0.880383	−	2.49498i	0.0297624	−	0.0843457i
$876$	−32.8058	+	2.10394i	−1.10841	+	0.0710857i
$877$	−22.9744			−0.775790			−0.387895	−	0.921704i	$-0.626798\pi$
$877$	−22.9744			−0.775790			−0.387895	+	0.921704i	$0.626798\pi$
$878$	32.4046	−	56.1264i	1.09360	−	1.89418i
$879$	10.6610	+	16.0039i	0.359587	+	0.539799i
$880$	−11.4778	−	19.8801i	−0.386917	−	0.670159i
$881$	−23.5449			−0.793246			−0.396623	−	0.917982i	$-0.629818\pi$
$881$	−23.5449			−0.793246			−0.396623	+	0.917982i	$0.629818\pi$
$882$	−1.06728	+	39.8827i	−0.0359371	+	1.34292i
$883$	40.4456			1.36110			0.680551	−	0.732701i	$-0.261740\pi$
$883$	40.4456			1.36110			0.680551	+	0.732701i	$0.261740\pi$
$884$	17.5957	+	30.4767i	0.591809	+	1.02504i
$885$	−6.37047	+	12.8724i	−0.214141	+	0.432702i
$886$	−12.4756	+	21.6083i	−0.419125	+	0.725945i
$887$	32.8256			1.10218			0.551088	−	0.834447i	$-0.314213\pi$
$887$	32.8256			1.10218			0.551088	+	0.834447i	$0.314213\pi$
$888$	1.01649	−	2.05396i	0.0341111	−	0.0689262i
$889$	−1.78365	+	5.05480i	−0.0598215	+	0.169533i
$890$	−31.3874			−1.05211
$891$	−43.1792	+	11.3103i	−1.44656	+	0.378908i
$892$	6.43907	+	11.1528i	0.215596	+	0.373423i
$893$	11.4625			0.383578
$894$	41.3029	+	62.0024i	1.38138	+	2.07367i
$895$	−6.71395	−	11.6289i	−0.224423	−	0.388711i
$896$	−15.1445	+	2.82437i	−0.505941	+	0.0943554i
$897$	−29.0899	−	43.6687i	−0.971283	−	1.45806i
$898$	20.4850	+	35.4811i	0.683594	+	1.18402i
$899$	−1.20110	−	2.08036i	−0.0400588	−	0.0693838i
$900$	−1.86025	+	4.45560i	−0.0620083	+	0.148520i
$901$	−7.54181	+	13.0628i	−0.251254	+	0.435185i
$902$	38.1433	−	66.0661i	1.27003	−	2.19976i
$903$	−23.0199	−	23.6441i	−0.766054	−	0.786828i
$904$	−4.10072	−	7.10266i	−0.136388	−	0.236231i
$905$	10.5458			0.350555
$906$	8.40382	+	12.6155i	0.279198	+	0.419123i
$907$	−0.550553			−0.0182808			−0.00914041	−	0.999958i	$-0.502910\pi$
$907$	−0.550553			−0.0182808			−0.00914041	+	0.999958i	$0.502910\pi$
$908$	−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	−0.827095	−	0.562062i	$-0.810008\pi$
$911$	2.20974	−	3.82739i	0.0732120	−	0.126807i	0.900307	+	0.435255i	$0.143342\pi$
$912$	8.64177	−	0.554225i	0.286158	−	0.0183522i
$913$	14.4521	−	25.0318i	0.478295	−	0.828431i
$914$	−29.5055	+	51.1051i	−0.975957	+	1.69041i
$915$	−5.81522	−	8.72961i	−0.192245	−	0.288592i
$916$	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	$0.259567\pi$
$920$	3.98753			0.131465
$921$	19.3586	−	1.24153i	0.637887	−	0.0409098i
$922$	−33.5431			−1.10468
$923$	−14.1566	−	24.5200i	−0.465970	−	0.807084i
$924$	25.5167	+	26.2087i	0.839439	+	0.862204i
$925$	0.891603	−	1.54430i	0.0293157	−	0.0507763i
$926$	20.3172	−	35.1905i	0.667666	−	1.15643i
$927$	45.1257	−	5.81202i	1.48212	−	0.190892i
$928$	20.7037	+	35.8598i	0.679631	+	1.17716i
$929$	−2.70822	−	4.69078i	−0.0888539	−	0.153900i	0.818173	−	0.574972i	$-0.194987\pi$
$929$	−2.70822	−	4.69078i	−0.0888539	−	0.153900i	−0.907027	+	0.421073i	$0.861654\pi$
$930$	−1.39257	+	0.0893097i	−0.0456640	+	0.00292858i
$931$	7.05281	−	2.72542i	0.231146	−	0.0893219i
$932$	1.74658	+	3.02516i	0.0572111	+	0.0990925i
$933$	5.12877	−	10.3634i	0.167908	−	0.339282i
$934$	−24.7388			−0.809478
$935$	−9.61879	−	16.6602i	−0.314568	−	0.544848i
$936$	7.61071	+	9.97636i	0.248764	+	0.326088i
$937$	2.77753			0.0907380			0.0453690	−	0.998970i	$-0.485554\pi$
$937$	2.77753			0.0907380			0.0453690	+	0.998970i	$0.485554\pi$
$938$	−2.24411	+	6.35973i	−0.0732727	+	0.207653i
$939$	−13.1705	−	19.7711i	−0.429804	−	0.645207i
$940$	17.0793			0.557066
$941$	−29.1246	+	50.4453i	−0.949435	+	1.64447i	−0.202817	+	0.979217i	$0.565010\pi$
$941$	−29.1246	+	50.4453i	−0.949435	+	1.64447i	−0.746618	+	0.665253i	$0.768324\pi$
$942$	−27.6093	+	1.77067i	−0.899559	+	0.0576916i
$943$	21.7551	+	37.6809i	0.708443	+	1.22706i
$944$	38.3811			1.24920
$945$	−2.01481	+	13.5993i	−0.0655416	+	0.442385i
$946$	−67.8514			−2.20604
$947$	30.1850	+	52.2820i	0.980882	+	1.69894i	0.658972	+	0.752168i	$0.270992\pi$
$947$	30.1850	+	52.2820i	0.980882	+	1.69894i	0.321911	+	0.946770i	$0.395675\pi$
$948$	−22.9503	+	1.47188i	−0.745390	+	0.0478043i
$949$	−33.2373	+	57.5688i	−1.07893	+	1.86876i
$950$	2.05214			0.0665801
$951$	−1.96767	−	2.95380i	−0.0638062	−	0.0957837i
$952$	−7.48571	+	1.39605i	−0.242613	+	0.0452462i
$953$	−57.0129			−1.84683			−0.923415	−	0.383803i	$-0.874614\pi$
$953$	−57.0129			−1.84683			−0.923415	+	0.383803i	$0.874614\pi$
$954$	8.53908	−	20.4525i	0.276463	−	0.662174i
$955$	−9.81630	−	17.0023i	−0.317648	−	0.550183i
$956$	8.18250			0.264641
$957$	−21.5836	+	43.6128i	−0.697699	+	1.40980i
$958$	28.2701	+	48.9652i	0.913364	+	1.58199i
$959$	−3.31293	+	9.38876i	−0.106980	+	0.303179i
$960$	8.00311	−	0.513266i	0.258299	−	0.0165656i
$961$	15.4101	+	26.6911i	0.497100	+	0.861002i
$962$	9.54868	+	16.5388i	0.307862	+	0.533232i
$963$	3.60951	−	8.64538i	0.116315	−	0.278593i
$964$	7.12853	−	12.3470i	0.229594	−	0.397669i
$965$	−13.2529	+	22.9548i	−0.426627	+	0.738940i
$966$	−45.3517	+	11.5040i	−1.45917	+	0.370135i
$967$	−13.2885	−	23.0163i	−0.427328	−	0.740154i	0.569307	−	0.822125i	$-0.307212\pi$
$967$	−13.2885	−	23.0163i	−0.427328	−	0.740154i	−0.996635	+	0.0819715i	$0.973878\pi$
$968$	−10.0889			−0.324270
$969$	7.24210	−	0.464459i	0.232650	−	0.0149206i
$970$	−18.3030			−0.587673
$971$	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
$975$	5.41299	+	8.12579i	0.173354	+	0.260234i
$976$	−14.0152	+	24.2750i	−0.448614	+	0.777023i
$977$	0.912046	−	1.57971i	0.0291789	−	0.0505394i	−0.851067	−	0.525057i	$-0.824044\pi$
$977$	0.912046	−	1.57971i	0.0291789	−	0.0505394i	0.880246	+	0.474517i	$0.157377\pi$
$978$	−44.8710	+	2.87772i	−1.43482	+	0.0920194i
$979$	−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
$983$	−7.88856			−0.251606			−0.125803	−	0.992055i	$-0.540151\pi$
$983$	−7.88856			−0.251606			−0.125803	+	0.992055i	$0.540151\pi$
$984$	−5.76861	−	8.65963i	−0.183896	−	0.276059i
$985$	−18.1946			−0.579727
$986$	20.8728	+	36.1528i	0.664726	+	1.15134i
$987$	47.1370	−	11.9569i	1.50039	−	0.380591i
$988$	−4.89987	+	8.48683i	−0.155886	+	0.270002i
$989$	19.3496	−	33.5144i	0.615280	−	1.06570i
$990$	17.1449	+	22.4741i	0.544902	+	0.714275i
$991$	−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	$-0.484692\pi$
$992$	1.54986	+	2.68443i	0.0492080	+	0.0852307i
$993$	−5.32003	−	7.98624i	−0.168826	−	0.253436i
$994$	−24.8189	+	4.62860i	−0.787208	+	0.146810i
$995$	6.54080	+	11.3290i	0.207357	+	0.359153i
$996$	9.00703	+	13.5210i	0.285399	+	0.428431i
$997$	−31.6542			−1.00250			−0.501249	−	0.865303i	$-0.667126\pi$
$997$	−31.6542			−1.00250			−0.501249	+	0.865303i	$0.667126\pi$
$998$	12.3138	+	21.3281i	0.389787	+	0.675131i
$999$	−3.01533	+	8.76145i	−0.0954009	+	0.277200i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.4	✓	36	1.1	even	1	trivial
315.2.k.c.256.4	yes	36	63.4	even	3	inner
315.2.l.c.121.15	yes	36	9.4	even	3
315.2.l.c.151.15	yes	36	7.4	even	3
945.2.k.c.361.15		36	63.32	odd	6
945.2.k.c.856.15		36	3.2	odd	2
945.2.l.c.46.4		36	21.11	odd	6
945.2.l.c.226.4		36	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.949927 - 1.64532i) q^{2} +(-1.72850 + 0.110854i) q^{3} +(-0.804724 + 1.39382i) q^{4} +1.00000 q^{5} +(1.82434 + 2.73864i) q^{6} +(0.880383 - 2.49498i) q^{7} -0.741992 q^{8} +(2.97542 - 0.383223i) q^{9} +O(q^{10})\)	\(q+(-0.949927 - 1.64532i) q^{2} +(-1.72850 + 0.110854i) q^{3} +(-0.804724 + 1.39382i) q^{4} +1.00000 q^{5} +(1.82434 + 2.73864i) q^{6} +(0.880383 - 2.49498i) q^{7} -0.741992 q^{8} +(2.97542 - 0.383223i) q^{9} +(-0.949927 - 1.64532i) q^{10} -4.95954 q^{11} +(1.23645 - 2.49843i) q^{12} +(-2.81852 - 4.88183i) q^{13} +(-4.94135 + 0.921536i) q^{14} +(-1.72850 + 0.110854i) q^{15} +(2.31429 + 4.00846i) q^{16} +(1.93945 + 3.35923i) q^{17} +(-3.45696 - 4.53150i) q^{18} +(-0.540078 + 0.935442i) q^{19} +(-0.804724 + 1.39382i) q^{20} +(-1.24516 + 4.41017i) q^{21} +(4.71121 + 8.16005i) q^{22} -5.37409 q^{23} +(1.28253 - 0.0822531i) q^{24} +1.00000 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} +(1.82434 + 2.73864i) q^{30} +(-0.212029 + 0.367245i) q^{31} +(3.65482 - 6.33033i) q^{32} +(8.57257 - 0.549787i) 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} +2.05214 q^{38} +(5.41299 + 8.12579i) q^{39} -0.741992 q^{40} +(-4.04814 - 7.01159i) q^{41} +(8.43896 - 2.14064i) q^{42} +(-3.60053 + 6.23630i) q^{43} +(3.99106 - 6.91272i) q^{44} +(2.97542 - 0.383223i) q^{45} +(5.10499 + 8.84211i) q^{46} +(-5.30595 - 9.19018i) q^{47} +(-4.44460 - 6.67208i) q^{48} +(-5.44985 - 4.39308i) q^{49} +(-0.949927 - 1.64532i) q^{50} +(-3.72473 - 5.59143i) q^{51} +9.07253 q^{52} +(1.94432 + 3.36765i) q^{53} +(6.47769 + 7.44947i) q^{54} -4.95954 q^{55} +(-0.653237 + 1.85126i) q^{56} +(0.829826 - 1.67678i) q^{57} +10.7622 q^{58} +(4.14611 - 7.18127i) q^{59} +(1.23645 - 2.49843i) q^{60} +(3.02796 + 5.24459i) q^{61} +0.805650 q^{62} +(1.66338 - 7.76100i) q^{63} -4.63009 q^{64} +(-2.81852 - 4.88183i) q^{65} +(-9.04789 - 13.5824i) q^{66} +(0.670844 - 1.16194i) q^{67} -6.24289 q^{68} +(9.28911 - 0.595741i) q^{69} +(-4.94135 + 0.921536i) q^{70} +5.02270 q^{71} +(-2.20774 + 0.284349i) q^{72} +(-5.89623 - 10.2126i) q^{73} -3.38783 q^{74} +(-1.72850 + 0.110854i) q^{75} +(-0.869227 - 1.50554i) q^{76} +(-4.36630 + 12.3740i) q^{77} +(8.22760 - 16.6250i) q^{78} +(-4.12488 - 7.14451i) q^{79} +(2.31429 + 4.00846i) q^{80} +(8.70628 - 2.28050i) q^{81} +(-7.69089 + 13.3210i) q^{82} +(-2.91400 + 5.04719i) q^{83} +(-5.14498 - 5.28450i) q^{84} +(1.93945 + 3.35923i) q^{85} +13.6810 q^{86} +(4.35194 - 8.79370i) q^{87} +3.67994 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} +(0.325782 - 0.658288i) q^{93} +(-10.0805 + 17.4600i) q^{94} +(-0.540078 + 0.935442i) q^{95} +(-5.61560 + 11.3471i) q^{96} +(4.81694 - 8.34318i) q^{97} +(-2.05106 + 13.1399i) q^{98} +(-14.7567 + 1.90061i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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