LMFDB - Embedded newform 315.2.k.b.16.2

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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.2
Character	$\chi$	$=$	315.16
Dual form			315.2.k.b.256.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16277 - 2.01398i) q^{2} +(0.434379 - 1.67670i) q^{3} +(-1.70408 + 2.95156i) q^{4} -1.00000 q^{5} +(-3.88192 + 1.07479i) q^{6} +(0.459529 - 2.60554i) q^{7} +3.27475 q^{8} +(-2.62263 - 1.45664i) q^{9} +O(q^{10})$	\(q+(-1.16277 - 2.01398i) q^{2} +(0.434379 - 1.67670i) q^{3} +(-1.70408 + 2.95156i) q^{4} -1.00000 q^{5} +(-3.88192 + 1.07479i) q^{6} +(0.459529 - 2.60554i) q^{7} +3.27475 q^{8} +(-2.62263 - 1.45664i) q^{9} +(1.16277 + 2.01398i) q^{10} -2.95729 q^{11} +(4.20865 + 4.13933i) q^{12} +(1.00448 + 1.73980i) q^{13} +(-5.78184 + 2.10417i) q^{14} +(-0.434379 + 1.67670i) q^{15} +(-0.399631 - 0.692181i) q^{16} +(-1.98046 - 3.43026i) q^{17} +(0.115867 + 6.97568i) q^{18} +(-2.55847 + 4.43140i) q^{19} +(1.70408 - 2.95156i) q^{20} +(-4.16909 - 1.90228i) q^{21} +(3.43866 + 5.95593i) q^{22} +0.433062 q^{23} +(1.42248 - 5.49077i) q^{24} +1.00000 q^{25} +(2.33596 - 4.04599i) q^{26} +(-3.58157 + 3.76462i) q^{27} +(6.90732 + 5.79638i) q^{28} +(1.68214 - 2.91356i) q^{29} +(3.88192 - 1.07479i) q^{30} +(4.53268 - 7.85083i) q^{31} +(2.34539 - 4.06234i) q^{32} +(-1.28459 + 4.95849i) q^{33} +(-4.60565 + 7.97722i) q^{34} +(-0.459529 + 2.60554i) q^{35} +(8.76855 - 5.25860i) q^{36} +(0.0400194 - 0.0693157i) q^{37} +11.8997 q^{38} +(3.35345 - 0.928469i) q^{39} -3.27475 q^{40} +(-0.435072 - 0.753568i) q^{41} +(1.01654 + 10.6084i) q^{42} +(-1.02431 + 1.77416i) q^{43} +(5.03947 - 8.72862i) q^{44} +(2.62263 + 1.45664i) q^{45} +(-0.503553 - 0.872180i) q^{46} +(1.92386 + 3.33223i) q^{47} +(-1.33417 + 0.369391i) q^{48} +(-6.57767 - 2.39464i) q^{49} +(-1.16277 - 2.01398i) q^{50} +(-6.61178 + 1.83060i) q^{51} -6.84684 q^{52} +(-4.24749 - 7.35687i) q^{53} +(11.7464 + 2.83582i) q^{54} +2.95729 q^{55} +(1.50484 - 8.53250i) q^{56} +(6.31877 + 6.21469i) q^{57} -7.82380 q^{58} +(-5.89034 + 10.2024i) q^{59} +(-4.20865 - 4.13933i) q^{60} +(-7.50487 - 12.9988i) q^{61} -21.0819 q^{62} +(-5.00052 + 6.16399i) q^{63} -12.5072 q^{64} +(-1.00448 - 1.73980i) q^{65} +(11.4800 - 3.17846i) q^{66} +(4.54700 - 7.87563i) q^{67} +13.4995 q^{68} +(0.188113 - 0.726115i) q^{69} +(5.78184 - 2.10417i) q^{70} -2.95233 q^{71} +(-8.58847 - 4.77015i) q^{72} +(-5.84200 - 10.1186i) q^{73} -0.186134 q^{74} +(0.434379 - 1.67670i) q^{75} +(-8.71969 - 15.1029i) q^{76} +(-1.35896 + 7.70534i) q^{77} +(-5.76922 - 5.67419i) q^{78} +(6.15121 + 10.6542i) q^{79} +(0.399631 + 0.692181i) q^{80} +(4.75637 + 7.64048i) q^{81} +(-1.01178 + 1.75246i) q^{82} +(-0.126085 + 0.218385i) q^{83} +(12.7192 - 9.06367i) q^{84} +(1.98046 + 3.43026i) q^{85} +4.76417 q^{86} +(-4.15446 - 4.08603i) q^{87} -9.68441 q^{88} +(8.58029 - 14.8615i) q^{89} +(-0.115867 - 6.97568i) q^{90} +(4.99471 - 1.81771i) q^{91} +(-0.737974 + 1.27821i) q^{92} +(-11.1946 - 11.0102i) q^{93} +(4.47403 - 7.74925i) q^{94} +(2.55847 - 4.43140i) q^{95} +(-5.79253 - 5.69711i) q^{96} +(7.67728 - 13.2974i) q^{97} +(2.82557 + 16.0317i) q^{98} +(7.75588 + 4.30773i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9} + q^{10} - 2 q^{11} - 16 q^{12} - 4 q^{13} - 13 q^{14} - q^{15} - 5 q^{16} - 7 q^{17} - 12 q^{18} - 2 q^{19} + 7 q^{20} - 5 q^{21} + 19 q^{22} - 2 q^{23} - 30 q^{24} + 24 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 3 q^{30} + 8 q^{31} + 17 q^{32} + q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} + 70 q^{38} - 8 q^{39} - 12 q^{40} + 20 q^{41} - 15 q^{42} + 31 q^{43} - 7 q^{44} - 9 q^{45} - 10 q^{46} - 31 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} - 37 q^{51} + 8 q^{52} + 8 q^{53} + 111 q^{54} + 2 q^{55} + 45 q^{56} + 5 q^{57} - 90 q^{58} - 21 q^{59} + 16 q^{60} + 5 q^{61} + 14 q^{62} - 9 q^{63} - 56 q^{64} + 4 q^{65} + 46 q^{66} + 43 q^{67} + 96 q^{68} + 26 q^{69} + 13 q^{70} + 24 q^{71} - 69 q^{72} - 18 q^{73} - 18 q^{74} + q^{75} - 13 q^{76} + 5 q^{77} + 19 q^{78} + 40 q^{79} + 5 q^{80} - 39 q^{81} + 5 q^{82} - 60 q^{83} + 47 q^{84} + 7 q^{85} - 24 q^{86} - 61 q^{87} - 100 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} - 8 q^{93} - 11 q^{94} + 2 q^{95} + 6 q^{96} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9 + q^10 - 2 * q^11 - 16 * q^12 - 4 * q^13 - 13 * q^14 - q^15 - 5 * q^16 - 7 * q^17 - 12 * q^18 - 2 * q^19 + 7 * q^20 - 5 * q^21 + 19 * q^22 - 2 * q^23 - 30 * q^24 + 24 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 3 * q^30 + 8 * q^31 + 17 * q^32 + q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 + 70 * q^38 - 8 * q^39 - 12 * q^40 + 20 * q^41 - 15 * q^42 + 31 * q^43 - 7 * q^44 - 9 * q^45 - 10 * q^46 - 31 * q^47 - 36 * q^48 - 11 * q^49 - q^50 - 37 * q^51 + 8 * q^52 + 8 * q^53 + 111 * q^54 + 2 * q^55 + 45 * q^56 + 5 * q^57 - 90 * q^58 - 21 * q^59 + 16 * q^60 + 5 * q^61 + 14 * q^62 - 9 * q^63 - 56 * q^64 + 4 * q^65 + 46 * q^66 + 43 * q^67 + 96 * q^68 + 26 * q^69 + 13 * q^70 + 24 * q^71 - 69 * q^72 - 18 * q^73 - 18 * q^74 + q^75 - 13 * q^76 + 5 * q^77 + 19 * q^78 + 40 * q^79 + 5 * q^80 - 39 * q^81 + 5 * q^82 - 60 * q^83 + 47 * q^84 + 7 * q^85 - 24 * q^86 - 61 * q^87 - 100 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 - 8 * q^93 - 11 * q^94 + 2 * q^95 + 6 * q^96 + 6 * q^97 - 15 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.16277	−	2.01398i	−0.822205	−	1.42410i	−0.904037	−	0.427454i	$-0.859410\pi$
$2$	−1.16277	−	2.01398i	−0.822205	−	1.42410i	0.0818322	−	0.996646i	$-0.473923\pi$
$3$	0.434379	−	1.67670i	0.250789	−	0.968042i
$3$	0.434379	−	1.67670i	0.250789	−	0.968042i
$4$	−1.70408	+	2.95156i	−0.852041	+	1.47578i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−3.88192	+	1.07479i	−1.58479	+	0.438780i
$7$	0.459529	−	2.60554i	0.173686	−	0.984801i
$7$	0.459529	−	2.60554i	0.173686	−	0.984801i
$8$	3.27475			1.15780
$9$	−2.62263	−	1.45664i	−0.874210	−	0.485548i
$10$	1.16277	+	2.01398i	0.367701	+	0.636877i
$11$	−2.95729			−0.891657			−0.445829	−	0.895118i	$-0.647091\pi$
$11$	−2.95729			−0.891657			−0.445829	+	0.895118i	$0.647091\pi$
$12$	4.20865	+	4.13933i	1.21493	+	1.19492i
$13$	1.00448	+	1.73980i	0.278592	+	0.482535i	0.971035	−	0.238937i	$-0.0767991\pi$
$13$	1.00448	+	1.73980i	0.278592	+	0.482535i	−0.692443	+	0.721472i	$0.743466\pi$
$14$	−5.78184	+	2.10417i	−1.54526	+	0.562362i
$15$	−0.434379	+	1.67670i	−0.112156	+	0.432921i
$16$	−0.399631	−	0.692181i	−0.0999077	−	0.173045i
$17$	−1.98046	−	3.43026i	−0.480332	−	0.831960i	0.519413	−	0.854523i	$-0.326151\pi$
$17$	−1.98046	−	3.43026i	−0.480332	−	0.831960i	−0.999745	+	0.0225634i	$0.992817\pi$
$18$	0.115867	+	6.97568i	0.0273100	+	1.64418i
$19$	−2.55847	+	4.43140i	−0.586953	+	1.01663i	0.407676	+	0.913127i	$0.366339\pi$
$19$	−2.55847	+	4.43140i	−0.586953	+	1.01663i	−0.994629	+	0.103506i	$0.966994\pi$
$20$	1.70408	−	2.95156i	0.381044	−	0.659988i
$21$	−4.16909	−	1.90228i	−0.909770	−	0.415112i
$22$	3.43866	+	5.95593i	0.733125	+	1.26981i
$23$	0.433062			0.0902998			0.0451499	−	0.998980i	$-0.485623\pi$
$23$	0.433062			0.0902998			0.0451499	+	0.998980i	$0.485623\pi$
$24$	1.42248	−	5.49077i	0.290363	−	1.12080i
$25$	1.00000			0.200000
$26$	2.33596	−	4.04599i	0.458119	−	0.793485i
$27$	−3.58157	+	3.76462i	−0.689273	+	0.724502i
$28$	6.90732	+	5.79638i	1.30536	+	1.09541i
$29$	1.68214	−	2.91356i	0.312366	−	0.541034i	−0.666508	−	0.745498i	$-0.732212\pi$
$29$	1.68214	−	2.91356i	0.312366	−	0.541034i	0.978874	+	0.204464i	$0.0655451\pi$
$30$	3.88192	−	1.07479i	0.708739	−	0.196228i
$31$	4.53268	−	7.85083i	0.814093	−	1.41005i	−0.0958844	−	0.995392i	$-0.530568\pi$
$31$	4.53268	−	7.85083i	0.814093	−	1.41005i	0.909977	−	0.414658i	$-0.136099\pi$
$32$	2.34539	−	4.06234i	0.414611	−	0.718127i
$33$	−1.28459	+	4.95849i	−0.223618	+	0.863162i
$34$	−4.60565	+	7.97722i	−0.789863	+	1.36808i
$35$	−0.459529	+	2.60554i	−0.0776746	+	0.440416i
$36$	8.76855	−	5.25860i	1.46142	−	0.876433i
$37$	0.0400194	−	0.0693157i	0.00657916	−	0.0113954i	−0.862717	−	0.505687i	$-0.831239\pi$
$37$	0.0400194	−	0.0693157i	0.00657916	−	0.0113954i	0.869296	+	0.494291i	$0.164572\pi$
$38$	11.8997			1.93038
$39$	3.35345	−	0.928469i	0.536982	−	0.148674i
$40$	−3.27475			−0.517784
$41$	−0.435072	−	0.753568i	−0.0679469	−	0.117687i	0.830051	−	0.557688i	$-0.188312\pi$
$41$	−0.435072	−	0.753568i	−0.0679469	−	0.117687i	−0.897997	+	0.440001i	$0.854978\pi$
$42$	1.01654	+	10.6084i	0.156856	+	1.63691i
$43$	−1.02431	+	1.77416i	−0.156206	+	0.270557i	−0.933497	−	0.358584i	$-0.883260\pi$
$43$	−1.02431	+	1.77416i	−0.156206	+	0.270557i	0.777292	+	0.629141i	$0.216593\pi$
$44$	5.03947	−	8.72862i	0.759729	−	1.31589i
$45$	2.62263	+	1.45664i	0.390959	+	0.217144i
$46$	−0.503553	−	0.872180i	−0.0742449	−	0.128596i
$47$	1.92386	+	3.33223i	0.280624	+	0.486055i	0.971539	−	0.236881i	$-0.0761252\pi$
$47$	1.92386	+	3.33223i	0.280624	+	0.486055i	−0.690915	+	0.722936i	$0.742792\pi$
$48$	−1.33417	+	0.369391i	−0.192571	+	0.0533170i
$49$	−6.57767	−	2.39464i	−0.939667	−	0.342092i
$50$	−1.16277	−	2.01398i	−0.164441	−	0.284820i
$51$	−6.61178	+	1.83060i	−0.925834	+	0.256335i
$52$	−6.84684			−0.949486
$53$	−4.24749	−	7.35687i	−0.583438	−	1.01054i	−0.995068	−	0.0991931i	$-0.968374\pi$
$53$	−4.24749	−	7.35687i	−0.583438	−	1.01054i	0.411630	−	0.911351i	$-0.364959\pi$
$54$	11.7464	+	2.83582i	1.59849	+	0.385906i
$55$	2.95729			0.398761
$56$	1.50484	−	8.53250i	0.201093	−	1.14020i
$57$	6.31877	+	6.21469i	0.836941	+	0.823155i
$58$	−7.82380			−1.02732
$59$	−5.89034	+	10.2024i	−0.766857	+	1.32824i	0.172402	+	0.985027i	$0.444847\pi$
$59$	−5.89034	+	10.2024i	−0.766857	+	1.32824i	−0.939259	+	0.343209i	$0.888486\pi$
$60$	−4.20865	−	4.13933i	−0.543335	−	0.534385i
$61$	−7.50487	−	12.9988i	−0.960901	−	1.66433i	−0.720247	−	0.693717i	$-0.755972\pi$
$61$	−7.50487	−	12.9988i	−0.960901	−	1.66433i	−0.240653	−	0.970611i	$-0.577362\pi$
$62$	−21.0819			−2.67740
$63$	−5.00052	+	6.16399i	−0.630006	+	0.776590i
$64$	−12.5072			−1.56340
$65$	−1.00448	−	1.73980i	−0.124590	−	0.215796i
$66$	11.4800	−	3.17846i	1.41309	−	0.391241i
$67$	4.54700	−	7.87563i	0.555504	−	0.962162i	−0.442360	−	0.896838i	$-0.645859\pi$
$67$	4.54700	−	7.87563i	0.555504	−	0.962162i	0.997864	−	0.0653239i	$-0.0208081\pi$
$68$	13.4995			1.63705
$69$	0.188113	−	0.726115i	0.0226462	−	0.0874139i
$70$	5.78184	−	2.10417i	0.691062	−	0.251496i
$71$	−2.95233			−0.350377			−0.175189	−	0.984535i	$-0.556054\pi$
$71$	−2.95233			−0.350377			−0.175189	+	0.984535i	$0.556054\pi$
$72$	−8.58847	−	4.77015i	−1.01216	−	0.562168i
$73$	−5.84200	−	10.1186i	−0.683754	−	1.18430i	−0.973827	−	0.227292i	$-0.927013\pi$
$73$	−5.84200	−	10.1186i	−0.683754	−	1.18430i	0.290073	−	0.957005i	$-0.406320\pi$
$74$	−0.186134			−0.0216377
$75$	0.434379	−	1.67670i	0.0501578	−	0.193608i
$76$	−8.71969	−	15.1029i	−1.00022	−	1.73243i
$77$	−1.35896	+	7.70534i	−0.154868	+	0.878105i
$78$	−5.76922	−	5.67419i	−0.653235	−	0.642475i
$79$	6.15121	+	10.6542i	0.692065	+	1.19869i	0.971160	+	0.238428i	$0.0766322\pi$
$79$	6.15121	+	10.6542i	0.692065	+	1.19869i	−0.279095	+	0.960264i	$0.590034\pi$
$80$	0.399631	+	0.692181i	0.0446801	+	0.0773881i
$81$	4.75637	+	7.64048i	0.528486	+	0.848942i
$82$	−1.01178	+	1.75246i	−0.111733	+	0.193526i
$83$	−0.126085	+	0.218385i	−0.0138396	+	0.0239709i	−0.872862	−	0.487967i	$-0.837739\pi$
$83$	−0.126085	+	0.218385i	−0.0138396	+	0.0239709i	0.859023	+	0.511938i	$0.171072\pi$
$84$	12.7192	−	9.06367i	1.38778	−	0.988927i
$85$	1.98046	+	3.43026i	0.214811	+	0.372064i
$86$	4.76417			0.513733
$87$	−4.15446	−	4.08603i	−0.445405	−	0.438069i
$88$	−9.68441			−1.03236
$89$	8.58029	−	14.8615i	0.909508	−	1.57531i	0.0947600	−	0.995500i	$-0.469792\pi$
$89$	8.58029	−	14.8615i	0.909508	−	1.57531i	0.814748	−	0.579815i	$-0.196875\pi$
$90$	−0.115867	−	6.97568i	−0.0122134	−	0.735301i
$91$	4.99471	−	1.81771i	0.523588	−	0.190548i
$92$	−0.737974	+	1.27821i	−0.0769391	+	0.133262i
$93$	−11.1946	−	11.0102i	−1.16082	−	1.14170i
$94$	4.47403	−	7.74925i	0.461461	−	0.799274i
$95$	2.55847	−	4.43140i	0.262493	−	0.454652i
$96$	−5.79253	−	5.69711i	−0.591198	−	0.581459i
$97$	7.67728	−	13.2974i	0.779510	−	1.35015i	−0.152714	−	0.988270i	$-0.548801\pi$
$97$	7.67728	−	13.2974i	0.779510	−	1.35015i	0.932224	−	0.361881i	$-0.117865\pi$
$98$	2.82557	+	16.0317i	0.285426	+	1.61945i
$99$	7.75588	+	4.30773i	0.779496	+	0.432943i
$100$	−1.70408	+	2.95156i	−0.170408	+	0.295156i
$101$	−5.69006			−0.566182			−0.283091	−	0.959093i	$-0.591360\pi$
$101$	−5.69006			−0.566182			−0.283091	+	0.959093i	$0.591360\pi$
$102$	11.3748	+	11.1874i	1.12627	+	1.10772i
$103$	−16.8024			−1.65559			−0.827796	−	0.561029i	$-0.810406\pi$
$103$	−16.8024			−1.65559			−0.827796	+	0.561029i	$0.810406\pi$
$104$	3.28941	+	5.69743i	0.322553	+	0.558679i
$105$	4.16909	+	1.90228i	0.406862	+	0.185644i
$106$	−9.87774	+	17.1087i	−0.959411	+	1.66175i
$107$	7.47266	−	12.9430i	0.722409	−	1.25125i	−0.237623	−	0.971358i	$-0.576368\pi$
$107$	7.47266	−	12.9430i	0.722409	−	1.25125i	0.960032	−	0.279892i	$-0.0902985\pi$
$108$	−5.00821	−	16.9864i	−0.481915	−	1.63452i
$109$	8.06216	+	13.9641i	0.772215	+	1.33752i	0.936346	+	0.351077i	$0.114185\pi$
$109$	8.06216	+	13.9641i	0.772215	+	1.33752i	−0.164131	+	0.986439i	$0.552482\pi$
$110$	−3.43866	−	5.95593i	−0.327863	−	0.567876i
$111$	−0.0988379	−	0.0972098i	−0.00938128	−	0.00922675i
$112$	−1.98715	+	0.723176i	−0.187768	+	0.0683337i
$113$	5.41997	+	9.38766i	0.509868	+	0.883117i	0.999935	+	0.0114319i	$0.00363896\pi$
$113$	5.41997	+	9.38766i	0.509868	+	0.883117i	−0.490067	+	0.871685i	$0.663028\pi$
$114$	5.16897	−	19.9522i	0.484118	−	1.86869i
$115$	−0.433062			−0.0403833
$116$	5.73302	+	9.92988i	0.532298	+	0.921966i
$117$	−0.100093	−	6.02603i	−0.00925358	−	0.557106i
$118$	27.3965			2.52205
$119$	−9.84775	+	3.58386i	−0.902742	+	0.328532i
$120$	−1.42248	+	5.49077i	−0.129855	+	0.501237i
$121$	−2.25442			−0.204947
$122$	−17.4529	+	30.2294i	−1.58011	+	2.73684i
$123$	−1.45249	+	0.402151i	−0.130967	+	0.0362607i
$124$	15.4481	+	26.7569i	1.38728	+	2.40284i
$125$	−1.00000			−0.0894427
$126$	18.2286	+	2.90363i	1.62394	+	0.258676i
$127$	−6.40805			−0.568623			−0.284311	−	0.958732i	$-0.591765\pi$
$127$	−6.40805			−0.568623			−0.284311	+	0.958732i	$0.591765\pi$
$128$	9.85221	+	17.0645i	0.870821	+	1.50831i
$129$	2.52979	+	2.48812i	0.222735	+	0.219066i
$130$	−2.33596	+	4.04599i	−0.204877	+	0.354857i
$131$	0.112153			0.00979886			0.00489943	−	0.999988i	$-0.498440\pi$
$131$	0.112153			0.00979886			0.00489943	+	0.999988i	$0.498440\pi$
$132$	−12.4462	−	12.2412i	−1.08330	−	1.06546i
$133$	10.3705	+	8.70255i	0.899236	+	0.754607i
$134$	−21.1485			−1.82695
$135$	3.58157	−	3.76462i	0.308252	−	0.324007i
$136$	−6.48552	−	11.2333i	−0.556129	−	0.963243i
$137$	19.2284			1.64279			0.821396	−	0.570358i	$-0.193196\pi$
$137$	19.2284			1.64279			0.821396	+	0.570358i	$0.193196\pi$
$138$	−1.68112	+	0.465450i	−0.143106	+	0.0396217i
$139$	−6.94402	−	12.0274i	−0.588984	−	1.02015i	−0.994366	−	0.106003i	$-0.966195\pi$
$139$	−6.94402	−	12.0274i	−0.588984	−	1.02015i	0.405381	−	0.914148i	$-0.367139\pi$
$140$	−6.90732	−	5.79638i	−0.583775	−	0.489884i
$141$	6.42282	−	1.77828i	0.540899	−	0.149759i
$142$	3.43289	+	5.94594i	0.288082	+	0.498972i
$143$	−2.97053	−	5.14511i	−0.248408	−	0.430256i
$144$	0.0398219	+	2.39745i	0.00331849	+	0.199788i
$145$	−1.68214	+	2.91356i	−0.139694	+	0.241958i
$146$	−13.5858	+	23.5313i	−1.12437	+	1.94747i
$147$	−6.87229	+	9.98857i	−0.566817	+	0.823844i
$148$	0.136393	+	0.236239i	0.0112114	+	0.0194188i
$149$	−11.3094			−0.926501			−0.463250	−	0.886227i	$-0.653317\pi$
$149$	−11.3094			−0.926501			−0.463250	+	0.886227i	$0.653317\pi$
$150$	−3.88192	+	1.07479i	−0.316958	+	0.0877560i
$151$	10.5143			0.855644			0.427822	−	0.903863i	$-0.359281\pi$
$151$	10.5143			0.855644			0.427822	+	0.903863i	$0.359281\pi$
$152$	−8.37836	+	14.5117i	−0.679575	+	1.17706i
$153$	0.197346	+	11.8811i	0.0159545	+	0.960532i
$154$	17.0986	−	6.22264i	1.37784	−	0.501435i
$155$	−4.53268	+	7.85083i	−0.364073	+	0.630594i
$156$	−2.97413	+	11.4801i	−0.238121	+	0.919142i
$157$	−1.04398	+	1.80823i	−0.0833187	+	0.144312i	−0.904674	−	0.426105i	$-0.859885\pi$
$157$	−1.04398	+	1.80823i	−0.0833187	+	0.144312i	0.821355	+	0.570418i	$0.193219\pi$
$158$	14.3049	−	24.7769i	1.13804	−	1.97114i
$159$	−14.1803	+	3.92609i	−1.12457	+	0.311359i
$160$	−2.34539	+	4.06234i	−0.185420	+	0.321156i
$161$	0.199005	−	1.12836i	0.0156838	−	0.0889273i
$162$	9.85721	−	18.4634i	0.774455	−	1.45062i
$163$	9.73811	−	16.8669i	0.762748	−	1.32112i	−0.178681	−	0.983907i	$-0.557183\pi$
$163$	9.73811	−	16.8669i	0.762748	−	1.32112i	0.941429	−	0.337211i	$-0.109484\pi$
$164$	2.96560			0.231574
$165$	1.28459	−	4.95849i	0.100005	−	0.386018i
$166$	0.586432			0.0455160
$167$	0.328916	+	0.569700i	0.0254523	+	0.0440847i	0.878471	−	0.477796i	$-0.158564\pi$
$167$	0.328916	+	0.569700i	0.0254523	+	0.0440847i	−0.853019	+	0.521880i	$0.825231\pi$
$168$	−13.6527	−	6.22951i	−1.05333	−	0.480617i
$169$	4.48205	−	7.76315i	0.344773	−	0.597165i
$170$	4.60565	−	7.97722i	0.353237	−	0.611825i
$171$	13.1649	−	7.89514i	1.00674	−	0.603756i
$172$	−3.49102	−	6.04663i	−0.266188	−	0.461051i
$173$	6.14977	+	10.6517i	0.467558	+	0.809835i	0.999313	−	0.0370638i	$-0.0118005\pi$
$173$	6.14977	+	10.6517i	0.467558	+	0.809835i	−0.531755	+	0.846898i	$0.678467\pi$
$174$	−3.39850	+	13.1181i	−0.257639	+	0.994484i
$175$	0.459529	−	2.60554i	0.0347371	−	0.196960i
$176$	1.18182	+	2.04698i	0.0890834	+	0.154297i
$177$	14.5477	+	14.3080i	1.09347	+	1.07546i
$178$	−39.9077			−2.99121
$179$	10.3534	+	17.9326i	0.773849	+	1.34035i	0.935439	+	0.353488i	$0.115004\pi$
$179$	10.3534	+	17.9326i	0.773849	+	1.34035i	−0.161590	+	0.986858i	$0.551662\pi$
$180$	−8.76855	+	5.25860i	−0.653569	+	0.391953i
$181$	9.89856			0.735754			0.367877	−	0.929874i	$-0.380085\pi$
$181$	9.89856			0.735754			0.367877	+	0.929874i	$0.380085\pi$
$182$	−9.46856	−	7.94568i	−0.701856	−	0.588973i
$183$	−25.0551	+	6.93699i	−1.85212	+	0.512797i
$184$	1.41817			0.104549
$185$	−0.0400194	+	0.0693157i	−0.00294229	+	0.00509619i
$186$	−9.15754	+	35.3480i	−0.671463	+	2.59184i
$187$	5.85680	+	10.1443i	0.428292	+	0.741823i
$188$	−13.1137			−0.956413
$189$	8.16303	+	11.0619i	0.593773	+	0.804633i
$190$	−11.8997			−0.863293
$191$	7.15823	+	12.3984i	0.517951	+	0.897118i	0.999783	+	0.0208537i	$0.00663843\pi$
$191$	7.15823	+	12.3984i	0.517951	+	0.897118i	−0.481831	+	0.876264i	$0.660028\pi$
$192$	−5.43285	+	20.9707i	−0.392082	+	1.51343i
$193$	2.94156	−	5.09492i	0.211738	−	0.366741i	−0.740521	−	0.672034i	$-0.765421\pi$
$193$	2.94156	−	5.09492i	0.211738	−	0.366741i	0.952258	+	0.305293i	$0.0987544\pi$
$194$	−35.7078			−2.56367
$195$	−3.35345	+	0.928469i	−0.240145	+	0.0664890i
$196$	18.2768	−	15.3337i	1.30549	−	1.09526i
$197$	21.2370			1.51307			0.756536	−	0.653952i	$-0.226890\pi$
$197$	21.2370			1.51307			0.756536	+	0.653952i	$0.226890\pi$
$198$	−0.342651	−	20.6291i	−0.0243512	−	1.46605i
$199$	−1.38845	−	2.40486i	−0.0984246	−	0.170476i	0.812608	−	0.582810i	$-0.198047\pi$
$199$	−1.38845	−	2.40486i	−0.0984246	−	0.170476i	−0.911033	+	0.412334i	$0.864714\pi$
$200$	3.27475			0.231560
$201$	−11.2299	−	11.0450i	−0.792098	−	0.779051i
$202$	6.61625	+	11.4597i	0.465518	+	0.806300i
$203$	−6.81839	−	5.72175i	−0.478557	−	0.401588i
$204$	5.86389	−	22.6345i	0.410554	−	1.58473i
$205$	0.435072	+	0.753568i	0.0303868	+	0.0526314i
$206$	19.5374	+	33.8398i	1.36124	+	2.35773i
$207$	−1.13576	−	0.630818i	−0.0789409	−	0.0438449i
$208$	0.802839	−	1.39056i	0.0556669	−	0.0964179i
$209$	7.56614	−	13.1049i	0.523361	−	0.906488i
$210$	−1.01654	−	10.6084i	−0.0701482	−	0.732049i
$211$	12.9601	+	22.4476i	0.892212	+	1.54536i	0.837217	+	0.546870i	$0.184181\pi$
$211$	12.9601	+	22.4476i	0.892212	+	1.54536i	0.0549949	+	0.998487i	$0.482486\pi$
$212$	28.9523			1.98845
$213$	−1.28243	+	4.95017i	−0.0878707	+	0.339180i
$214$	−34.7560			−2.37587
$215$	1.02431	−	1.77416i	0.0698574	−	0.120997i
$216$	−11.7288	+	12.3282i	−0.798041	+	0.838828i
$217$	−18.3727	−	15.4178i	−1.24722	−	1.04663i
$218$	18.7489	−	32.4741i	1.26984	−	2.19942i
$219$	−19.5035	+	5.39994i	−1.31793	+	0.364894i
$220$	−5.03947	+	8.72862i	−0.339761	+	0.588484i
$221$	3.97865	−	6.89123i	0.267633	−	0.463554i
$222$	−0.0808528	+	0.312091i	−0.00542648	+	0.0209462i
$223$	7.06550	−	12.2378i	0.473141	−	0.819504i	−0.526386	−	0.850246i	$-0.676453\pi$
$223$	7.06550	−	12.2378i	0.473141	−	0.819504i	0.999527	+	0.0307411i	$0.00978674\pi$
$224$	−9.50681	−	7.97778i	−0.635201	−	0.533038i
$225$	−2.62263	−	1.45664i	−0.174842	−	0.0971097i
$226$	12.6044	−	21.8314i	0.838431	−	1.45221i
$227$	−4.32133			−0.286817			−0.143408	−	0.989664i	$-0.545806\pi$
$227$	−4.32133			−0.286817			−0.143408	+	0.989664i	$0.545806\pi$
$228$	−29.1107	+	8.05988i	−1.92790	+	0.533778i
$229$	7.27691			0.480872			0.240436	−	0.970665i	$-0.422710\pi$
$229$	7.27691			0.480872			0.240436	+	0.970665i	$0.422710\pi$
$230$	0.503553	+	0.872180i	0.0332033	+	0.0575098i
$231$	12.3292	+	5.62561i	0.811203	+	0.370138i
$232$	5.50860	−	9.54118i	0.361657	−	0.626409i
$233$	1.98252	−	3.43383i	0.129879	−	0.224958i	−0.793750	−	0.608244i	$-0.791874\pi$
$233$	1.98252	−	3.43383i	0.129879	−	0.224958i	0.923630	+	0.383286i	$0.125208\pi$
$234$	−12.0199	+	7.20849i	−0.785767	+	0.471234i
$235$	−1.92386	−	3.33223i	−0.125499	−	0.217370i
$236$	−20.0753	−	34.7714i	−1.30679	−	2.26342i
$237$	20.5358	−	5.68575i	1.33395	−	0.369329i
$238$	18.6685	+	15.6660i	1.21010	+	1.01547i
$239$	−8.06282	−	13.9652i	−0.521540	−	0.903334i	−0.999686	−	0.0250538i	$-0.992024\pi$
$239$	−8.06282	−	13.9652i	−0.521540	−	0.903334i	0.478146	−	0.878280i	$-0.341309\pi$
$240$	1.33417	−	0.369391i	0.0861202	−	0.0238441i
$241$	−1.54003			−0.0992022			−0.0496011	−	0.998769i	$-0.515795\pi$
$241$	−1.54003			−0.0992022			−0.0496011	+	0.998769i	$0.515795\pi$
$242$	2.62138	+	4.54036i	0.168509	+	0.291865i
$243$	14.8768	−	4.65613i	0.954350	−	0.298691i
$244$	51.1557			3.27491
$245$	6.57767	+	2.39464i	0.420232	+	0.152988i
$246$	2.49884	+	2.45768i	0.159320	+	0.156696i
$247$	−10.2797			−0.654081
$248$	14.8434	−	25.7095i	0.942557	−	1.63256i
$249$	0.311398	+	0.306268i	0.0197340	+	0.0194090i
$250$	1.16277	+	2.01398i	0.0735402	+	0.127375i
$251$	−6.88146			−0.434354			−0.217177	−	0.976132i	$-0.569685\pi$
$251$	−6.88146			−0.434354			−0.217177	+	0.976132i	$0.569685\pi$
$252$	−9.67208	−	25.2633i	−0.609284	−	1.59144i
$253$	−1.28069			−0.0805164
$254$	7.45111	+	12.9057i	0.467524	+	0.809776i
$255$	6.61178	−	1.83060i	0.414045	−	0.114637i
$256$	10.4046	−	18.0213i	0.650288	−	1.12633i
$257$	12.8005			0.798475			0.399237	−	0.916848i	$-0.369275\pi$
$257$	12.8005			0.798475			0.399237	+	0.916848i	$0.369275\pi$
$258$	2.06945	−	7.98806i	0.128839	−	0.497315i
$259$	−0.162215	−	0.136125i	−0.0100795	−	0.00845838i
$260$	6.84684			0.424623
$261$	−8.65565	+	5.19089i	−0.535771	+	0.321308i
$262$	−0.130409	−	0.225874i	−0.00805667	−	0.0139546i
$263$	−7.66776			−0.472814			−0.236407	−	0.971654i	$-0.575970\pi$
$263$	−7.66776			−0.472814			−0.236407	+	0.971654i	$0.575970\pi$
$264$	−4.20670	+	16.2378i	−0.258905	+	0.999369i
$265$	4.24749	+	7.35687i	0.260921	+	0.451929i
$266$	5.46825	−	31.0051i	0.335280	−	1.90104i
$267$	−21.1911	−	20.8421i	−1.29688	−	1.27551i
$268$	15.4969	+	26.8415i	0.946625	+	1.63960i
$269$	−3.44232	−	5.96227i	−0.209882	−	0.363526i	0.741795	−	0.670626i	$-0.233975\pi$
$269$	−3.44232	−	5.96227i	−0.209882	−	0.363526i	−0.951677	+	0.307100i	$0.900641\pi$
$270$	−11.7464	−	2.83582i	−0.714865	−	0.172582i
$271$	−2.16184	+	3.74442i	−0.131322	+	0.227457i	−0.924187	−	0.381941i	$-0.875256\pi$
$271$	−2.16184	+	3.74442i	−0.131322	+	0.227457i	0.792864	+	0.609398i	$0.208589\pi$
$272$	−1.58291	+	2.74167i	−0.0959777	+	0.166238i
$273$	−0.878154	−	9.16420i	−0.0531483	−	0.554643i
$274$	−22.3583	−	38.7256i	−1.35071	−	2.33950i
$275$	−2.95729			−0.178331
$276$	1.82261	+	1.79259i	0.109708	+	0.107901i
$277$	−10.8173			−0.649946			−0.324973	−	0.945723i	$-0.605355\pi$
$277$	−10.8173			−0.649946			−0.324973	+	0.945723i	$0.605355\pi$
$278$	−16.1486	+	27.9703i	−0.968532	+	1.67755i
$279$	−23.3234	+	13.9873i	−1.39634	+	0.837399i
$280$	−1.50484	+	8.53250i	−0.0899317	+	0.509914i
$281$	−7.45465	+	12.9118i	−0.444707	+	0.770255i	−0.998032	−	0.0627106i	$-0.980026\pi$
$281$	−7.45465	+	12.9118i	−0.444707	+	0.770255i	0.553325	+	0.832966i	$0.313359\pi$
$282$	−11.0497	−	10.8677i	−0.658001	−	0.647162i
$283$	−6.85754	+	11.8776i	−0.407638	+	0.706050i	−0.994625	−	0.103547i	$-0.966981\pi$
$283$	−6.85754	+	11.8776i	−0.407638	+	0.706050i	0.586986	+	0.809597i	$0.300314\pi$
$284$	5.03102	−	8.71398i	0.298536	−	0.517079i
$285$	−6.31877	−	6.21469i	−0.374292	−	0.368126i
$286$	−6.90811	+	11.9652i	−0.408485	+	0.707517i
$287$	−2.16338	+	0.787312i	−0.127700	+	0.0464736i
$288$	−12.0685	+	7.23761i	−0.711143	+	0.426480i
$289$	0.655553	−	1.13545i	0.0385620	−	0.0667913i
$290$	7.82380			0.459429
$291$	−18.9609	−	18.6486i	−1.11151	−	1.09320i
$292$	39.8210			2.33035
$293$	−4.89324	−	8.47534i	−0.285866	−	0.495135i	0.686953	−	0.726702i	$-0.258948\pi$
$293$	−4.89324	−	8.47534i	−0.285866	−	0.495135i	−0.972819	+	0.231568i	$0.925615\pi$
$294$	28.1077	+	2.22622i	1.63928	+	0.129836i
$295$	5.89034	−	10.2024i	0.342949	−	0.594005i
$296$	0.131054	−	0.226992i	0.00761735	−	0.0131936i
$297$	10.5917	−	11.1331i	0.614595	−	0.646007i
$298$	13.1502	+	22.7769i	0.761773	+	1.31943i
$299$	0.435001	+	0.753444i	0.0251568	+	0.0435728i
$300$	4.20865	+	4.13933i	0.242987	+	0.238984i
$301$	4.15194	+	3.48416i	0.239314	+	0.200824i
$302$	−12.2258	−	21.1757i	−0.703515	−	1.21852i
$303$	−2.47164	+	9.54051i	−0.141992	+	0.548088i
$304$	4.08977			0.234564
$305$	7.50487	+	12.9988i	0.429728	+	0.744310i
$306$	23.6989	−	14.2125i	1.35478	−	0.812475i
$307$	−11.5120			−0.657025			−0.328513	−	0.944500i	$-0.606547\pi$
$307$	−11.5120			−0.657025			−0.328513	+	0.944500i	$0.606547\pi$
$308$	−20.4270	−	17.1416i	−1.16394	−	0.976733i
$309$	−7.29863	+	28.1726i	−0.415204	+	1.60268i
$310$	21.0819			1.19737
$311$	−8.34864	+	14.4603i	−0.473408	+	0.819967i	−0.999537	−	0.0304382i	$-0.990310\pi$
$311$	−8.34864	+	14.4603i	−0.473408	+	0.819967i	0.526129	+	0.850405i	$0.323643\pi$
$312$	10.9817	−	3.04051i	0.621717	−	0.172135i
$313$	−2.24518	−	3.88877i	−0.126905	−	0.219806i	0.795571	−	0.605860i	$-0.207171\pi$
$313$	−2.24518	−	3.88877i	−0.126905	−	0.219806i	−0.922476	+	0.386054i	$0.873838\pi$
$314$	4.85565			0.274020
$315$	5.00052	−	6.16399i	0.281747	−	0.347302i
$316$	−41.9287			−2.35867
$317$	5.84319	+	10.1207i	0.328186	+	0.568435i	0.982152	−	0.188089i	$-0.0602294\pi$
$317$	5.84319	+	10.1207i	0.328186	+	0.568435i	−0.653966	+	0.756524i	$0.726896\pi$
$318$	24.3955	+	23.9937i	1.36803	+	1.34550i
$319$	−4.97459	+	8.61624i	−0.278523	+	0.482417i
$320$	12.5072			0.699172
$321$	−18.4556	−	18.1516i	−1.03009	−	1.01312i
$322$	−2.50390	+	0.911236i	−0.139537	+	0.0507812i
$323$	20.2678			1.12773
$324$	−30.6566	+	1.01870i	−1.70314	+	0.0565943i
$325$	1.00448	+	1.73980i	0.0557183	+	0.0965070i
$326$	−45.2929			−2.50854
$327$	26.9156	−	7.45211i	1.48843	−	0.412102i
$328$	−1.42476	−	2.46775i	−0.0786690	−	0.136259i
$329$	9.56632	−	3.48144i	0.527408	−	0.191938i
$330$	−11.4800	+	3.17846i	−0.631952	+	0.174968i
$331$	3.62981	+	6.28701i	0.199512	+	0.345565i	0.948370	−	0.317165i	$-0.102731\pi$
$331$	3.62981	+	6.28701i	0.199512	+	0.345565i	−0.748858	+	0.662730i	$0.769398\pi$
$332$	−0.429718	−	0.744293i	−0.0235838	−	0.0408484i
$333$	−0.205925	+	0.123495i	−0.0112846	+	0.00676750i
$334$	0.764910	−	1.32486i	0.0418540	−	0.0724933i
$335$	−4.54700	+	7.87563i	−0.248429	+	0.430292i
$336$	0.349373	+	3.64597i	0.0190599	+	0.198904i
$337$	3.31859	+	5.74796i	0.180775	+	0.313111i	0.942145	−	0.335207i	$-0.108806\pi$
$337$	3.31859	+	5.74796i	0.180775	+	0.313111i	−0.761370	+	0.648318i	$0.775473\pi$
$338$	−20.8465			−1.13390
$339$	18.0946	−	5.00984i	0.982763	−	0.272097i
$340$	−13.4995			−0.732112
$341$	−13.4045	+	23.2172i	−0.725892	+	1.25728i
$342$	−31.2084	−	17.3336i	−1.68756	−	0.937294i
$343$	−9.26196	+	16.0380i	−0.500099	+	0.865968i
$344$	−3.35437	+	5.80993i	−0.180855	+	0.313251i
$345$	−0.188113	+	0.726115i	−0.0101277	+	0.0390927i
$346$	14.3016	−	24.7710i	0.768857	−	1.33170i
$347$	−1.45046	+	2.51227i	−0.0778649	+	0.134866i	−0.902329	−	0.431049i	$-0.858144\pi$
$347$	−1.45046	+	2.51227i	−0.0778649	+	0.134866i	0.824464	+	0.565915i	$0.191477\pi$
$348$	19.1397	−	5.29921i	1.02600	−	0.284067i
$349$	−3.58299	+	6.20592i	−0.191793	+	0.332195i	−0.945845	−	0.324620i	$-0.894764\pi$
$349$	−3.58299	+	6.20592i	−0.191793	+	0.332195i	0.754051	+	0.656815i	$0.228097\pi$
$350$	−5.78184	+	2.10417i	−0.309052	+	0.112472i
$351$	−10.1473	−	2.44975i	−0.541623	−	0.130758i
$352$	−6.93602	+	12.0135i	−0.369691	+	0.640324i
$353$	1.73212			0.0921913			0.0460956	−	0.998937i	$-0.485322\pi$
$353$	1.73212			0.0921913			0.0460956	+	0.998937i	$0.485322\pi$
$354$	11.9005	−	45.9357i	0.632503	−	2.44145i
$355$	2.95233			0.156693
$356$	29.2430	+	50.6504i	1.54988	+	2.68447i
$357$	1.73140	+	18.0685i	0.0916353	+	0.956284i
$358$	24.0773	−	41.7031i	1.27252	−	2.20408i
$359$	2.90961	−	5.03960i	0.153564	−	0.265980i	−0.778972	−	0.627059i	$-0.784258\pi$
$359$	2.90961	−	5.03960i	0.153564	−	0.265980i	0.932535	+	0.361079i	$0.117592\pi$
$360$	8.58847	+	4.77015i	0.452652	+	0.251409i
$361$	−3.59153	−	6.22071i	−0.189028	−	0.327406i
$362$	−11.5098	−	19.9355i	−0.604940	−	1.04779i
$363$	−0.979273	+	3.77998i	−0.0513985	+	0.198397i
$364$	−3.14632	+	17.8397i	−0.164912	+	0.935055i
$365$	5.84200	+	10.1186i	0.305784	+	0.529633i
$366$	43.1043	+	42.3943i	2.25310	+	2.21598i
$367$	−4.23385			−0.221005			−0.110502	−	0.993876i	$-0.535246\pi$
$367$	−4.23385			−0.221005			−0.110502	+	0.993876i	$0.535246\pi$
$368$	−0.173065	−	0.299757i	−0.00902164	−	0.0156259i
$369$	0.0433536	+	2.61007i	0.00225690	+	0.135875i
$370$	0.186134			0.00967665
$371$	−21.1205	+	7.68631i	−1.09652	+	0.399053i
$372$	51.5736	−	14.2792i	2.67397	−	0.740341i
$373$	−5.41347			−0.280299			−0.140149	−	0.990130i	$-0.544758\pi$
$373$	−5.41347			−0.280299			−0.140149	+	0.990130i	$0.544758\pi$
$374$	13.6203	−	23.5910i	0.704287	−	1.21986i
$375$	−0.434379	+	1.67670i	−0.0224312	+	0.0865843i
$376$	6.30017	+	10.9122i	0.324907	+	0.562755i
$377$	6.75869			0.348090
$378$	12.7867	−	29.3026i	0.657674	−	1.50717i
$379$	16.3583			0.840268			0.420134	−	0.907462i	$-0.361983\pi$
$379$	16.3583			0.840268			0.420134	+	0.907462i	$0.361983\pi$
$380$	8.71969	+	15.1029i	0.447310	+	0.774764i
$381$	−2.78353	+	10.7444i	−0.142604	+	0.550451i
$382$	16.6468	−	28.8331i	0.851724	−	1.47523i
$383$	−2.51914			−0.128722			−0.0643611	−	0.997927i	$-0.520501\pi$
$383$	−2.51914			−0.128722			−0.0643611	+	0.997927i	$0.520501\pi$
$384$	32.8917	−	9.10670i	1.67850	−	0.464725i
$385$	1.35896	−	7.70534i	0.0692591	−	0.392701i
$386$	−13.6814			−0.696367
$387$	5.27071	−	3.16090i	0.267925	−	0.160678i
$388$	26.1655	+	45.3199i	1.32835	+	2.30077i
$389$	35.2983			1.78969			0.894847	−	0.446373i	$-0.147285\pi$
$389$	35.2983			1.78969			0.894847	+	0.446373i	$0.147285\pi$
$390$	5.76922	+	5.67419i	0.292136	+	0.287324i
$391$	−0.857663	−	1.48552i	−0.0433739	−	0.0751258i
$392$	−21.5402	−	7.84186i	−1.08795	−	0.396074i
$393$	0.0487170	−	0.188047i	0.00245745	−	0.00948571i
$394$	−24.6938	−	42.7709i	−1.24406	−	2.15477i
$395$	−6.15121	−	10.6542i	−0.309501	−	0.536071i
$396$	−25.9312	+	15.5512i	−1.30309	+	0.781478i
$397$	−7.06116	+	12.2303i	−0.354390	+	0.613821i	−0.987013	−	0.160639i	$-0.948645\pi$
$397$	−7.06116	+	12.2303i	−0.354390	+	0.613821i	0.632624	+	0.774459i	$0.281978\pi$
$398$	−3.22890	+	5.59262i	−0.161850	+	0.280333i
$399$	19.0963	−	13.6080i	0.956009	−	0.681251i
$400$	−0.399631	−	0.692181i	−0.0199815	−	0.0346090i
$401$	1.84888			0.0923285			0.0461643	−	0.998934i	$-0.485300\pi$
$401$	1.84888			0.0923285			0.0461643	+	0.998934i	$0.485300\pi$
$402$	−9.18647	+	35.4597i	−0.458180	+	1.76857i
$403$	18.2119			0.907198
$404$	9.69633	−	16.7945i	0.482411	−	0.835560i
$405$	−4.75637	−	7.64048i	−0.236346	−	0.379658i
$406$	−3.59526	+	20.3852i	−0.178430	+	1.01170i
$407$	−0.118349	+	0.204987i	−0.00586635	+	0.0101608i
$408$	−21.6519	+	5.99477i	−1.07193	+	0.296785i
$409$	11.9200	−	20.6460i	0.589406	−	1.02088i	−0.404904	−	0.914359i	$-0.632695\pi$
$409$	11.9200	−	20.6460i	0.589406	−	1.02088i	0.994310	−	0.106522i	$-0.0339714\pi$
$410$	1.01178	−	1.75246i	0.0499683	−	0.0865476i
$411$	8.35241	−	32.2402i	0.411994	−	1.59029i
$412$	28.6327	−	49.5934i	1.41063	−	2.44329i
$413$	23.8759	+	20.0358i	1.17486	+	0.985897i
$414$	0.0501775	+	3.02090i	0.00246609	+	0.148469i
$415$	0.126085	−	0.218385i	0.00618926	−	0.0107201i
$416$	9.42357			0.462029
$417$	−23.1827	+	6.41858i	−1.13526	+	0.314319i
$418$	−35.1908			−1.72124
$419$	13.9024	+	24.0796i	0.679175	+	1.17637i	0.975230	+	0.221195i	$0.0709957\pi$
$419$	13.9024	+	24.0796i	0.679175	+	1.17637i	−0.296054	+	0.955171i	$0.595671\pi$
$420$	−12.7192	+	9.06367i	−0.620632	+	0.442262i
$421$	−15.7054	+	27.2025i	−0.765434	+	1.32577i	0.174583	+	0.984643i	$0.444142\pi$
$421$	−15.7054	+	27.2025i	−0.765434	+	1.32577i	−0.940017	+	0.341128i	$0.889191\pi$
$422$	30.1394	−	52.2029i	1.46716	−	2.54120i
$423$	−0.191707	−	11.5416i	−0.00932109	−	0.561171i
$424$	−13.9095	−	24.0919i	−0.675505	−	1.17001i
$425$	−1.98046	−	3.43026i	−0.0960664	−	0.166392i
$426$	11.4607	−	3.17313i	0.555274	−	0.153739i
$427$	−37.3176	+	13.5809i	−1.80593	+	0.657226i
$428$	25.4681	+	44.1120i	1.23104	+	2.13223i
$429$	−9.91713	+	2.74575i	−0.478804	+	0.132566i
$430$	−4.76417			−0.229748
$431$	−17.5172	−	30.3406i	−0.843772	−	1.46146i	−0.886683	−	0.462378i	$-0.846996\pi$
$431$	−17.5172	−	30.3406i	−0.843772	−	1.46146i	0.0429109	−	0.999079i	$-0.486337\pi$
$432$	4.03710	+	0.974634i	0.194235	+	0.0468921i
$433$	−28.3872			−1.36420			−0.682101	−	0.731258i	$-0.738933\pi$
$433$	−28.3872			−1.36420			−0.682101	+	0.731258i	$0.738933\pi$
$434$	−9.68775	+	54.9297i	−0.465027	+	2.63671i
$435$	4.15446	+	4.08603i	0.199191	+	0.195910i
$436$	−54.9544			−2.63184
$437$	−1.10798	+	1.91907i	−0.0530017	+	0.0918017i
$438$	33.5536	+	33.0009i	1.60325	+	1.57684i
$439$	5.19524	+	8.99841i	0.247955	+	0.429471i	0.962958	−	0.269650i	$-0.0869081\pi$
$439$	5.19524	+	8.99841i	0.247955	+	0.429471i	−0.715003	+	0.699121i	$0.753575\pi$
$440$	9.68441			0.461686
$441$	13.7626	+	15.8616i	0.655364	+	0.755313i
$442$	−18.5051			−0.880197
$443$	−7.13847	−	12.3642i	−0.339159	−	0.587440i	0.645116	−	0.764085i	$-0.276809\pi$
$443$	−7.13847	−	12.3642i	−0.339159	−	0.587440i	−0.984275	+	0.176644i	$0.943476\pi$
$444$	0.455348	−	0.126072i	0.0216099	−	0.00598312i
$445$	−8.58029	+	14.8615i	−0.406745	+	0.704502i
$446$	−32.8623			−1.55608
$447$	−4.91256	+	18.9624i	−0.232356	+	0.896891i
$448$	−5.74741	+	32.5879i	−0.271539	+	1.53963i
$449$	7.89891			0.372773			0.186386	−	0.982477i	$-0.440322\pi$
$449$	7.89891			0.372773			0.186386	+	0.982477i	$0.440322\pi$
$450$	0.115867	+	6.97568i	0.00546200	+	0.328837i
$451$	1.28664	+	2.22852i	0.0605854	+	0.104937i
$452$	−36.9443			−1.73771
$453$	4.56721	−	17.6294i	0.214586	−	0.828299i
$454$	5.02472	+	8.70307i	0.235822	+	0.408456i
$455$	−4.99471	+	1.81771i	−0.234156	+	0.0852156i
$456$	20.6924	+	20.3516i	0.969011	+	0.953050i
$457$	−13.6926	−	23.7163i	−0.640513	−	1.10940i	−0.985318	−	0.170726i	$-0.945389\pi$
$457$	−13.6926	−	23.7163i	−0.640513	−	1.10940i	0.344806	−	0.938674i	$-0.387945\pi$
$458$	−8.46140	−	14.6556i	−0.395375	−	0.684810i
$459$	20.0068	+	4.83002i	0.933836	+	0.225446i
$460$	0.737974	−	1.27821i	0.0344082	−	0.0595968i
$461$	16.7801	−	29.0640i	0.781528	−	1.35365i	−0.149524	−	0.988758i	$-0.547774\pi$
$461$	16.7801	−	29.0640i	0.781528	−	1.35365i	0.931052	−	0.364888i	$-0.118893\pi$
$462$	−3.00622	−	31.3721i	−0.139862	−	1.45956i
$463$	3.99562	+	6.92062i	0.185692	+	0.321629i	0.943810	−	0.330490i	$-0.107214\pi$
$463$	3.99562	+	6.92062i	0.185692	+	0.321629i	−0.758117	+	0.652118i	$0.773881\pi$
$464$	−2.68894			−0.124831
$465$	11.1946	+	11.0102i	0.519136	+	0.510584i
$466$	−9.22090			−0.427150
$467$	−17.7951	+	30.8220i	−0.823460	+	1.42627i	0.0796308	+	0.996824i	$0.474626\pi$
$467$	−17.7951	+	30.8220i	−0.823460	+	1.42627i	−0.903091	+	0.429450i	$0.858707\pi$
$468$	17.9567	+	9.97342i	0.830050	+	0.461021i
$469$	−18.4308	−	15.4665i	−0.851055	−	0.714175i
$470$	−4.47403	+	7.74925i	−0.206372	+	0.357446i
$471$	2.57837	+	2.53590i	0.118805	+	0.116848i
$472$	−19.2894	+	33.4103i	−0.887868	+	1.53783i
$473$	3.02919	−	5.24671i	0.139282	−	0.241244i
$474$	−35.3295	−	34.7476i	−1.62274	−	1.59601i
$475$	−2.55847	+	4.43140i	−0.117391	+	0.203327i
$476$	6.20340	−	35.1734i	0.284332	−	1.61217i
$477$	0.423249	+	25.4814i	0.0193792	+	1.16671i
$478$	−18.7505	+	32.4767i	−0.857626	+	1.48545i
$479$	−4.19182			−0.191529			−0.0957647	−	0.995404i	$-0.530530\pi$
$479$	−4.19182			−0.191529			−0.0957647	+	0.995404i	$0.530530\pi$
$480$	5.79253	+	5.69711i	0.264392	+	0.260036i
$481$	0.160794			0.00733159
$482$	1.79071	+	3.10160i	0.0815645	+	0.141274i
$483$	−1.80548	−	0.823807i	−0.0821520	−	0.0374845i
$484$	3.84172	−	6.65405i	0.174624	−	0.302457i
$485$	−7.67728	+	13.2974i	−0.348608	+	0.603806i
$486$	−26.6758	−	24.5477i	−1.21004	−	1.11350i
$487$	−2.62050	−	4.53883i	−0.118746	−	0.205674i	0.800525	−	0.599299i	$-0.204554\pi$
$487$	−2.62050	−	4.53883i	−0.118746	−	0.205674i	−0.919271	+	0.393625i	$0.871221\pi$
$488$	−24.5766	−	42.5679i	−1.11253	−	1.92696i
$489$	−24.0507	−	23.6545i	−1.08761	−	1.06969i
$490$	−2.82557	−	16.0317i	−0.127646	−	0.724240i
$491$	−1.74427	−	3.02116i	−0.0787177	−	0.136343i	0.823979	−	0.566620i	$-0.191749\pi$
$491$	−1.74427	−	3.02116i	−0.0787177	−	0.136343i	−0.902697	+	0.430277i	$0.858416\pi$
$492$	1.28819	−	4.97241i	0.0580763	−	0.224174i
$493$	−13.3257			−0.600158
$494$	11.9529	+	20.7031i	0.537788	+	0.931477i
$495$	−7.75588	−	4.30773i	−0.348601	−	0.193618i
$496$	−7.24559			−0.325337
$497$	−1.35668	+	7.69241i	−0.0608555	+	0.345052i
$498$	0.254734	−	0.983270i	0.0114149	−	0.0440614i
$499$	−7.06665			−0.316347			−0.158173	−	0.987411i	$-0.550561\pi$
$499$	−7.06665			−0.316347			−0.158173	+	0.987411i	$0.550561\pi$
$500$	1.70408	−	2.95156i	0.0762089	−	0.131998i
$501$	1.09809	−	0.304027i	0.0490590	−	0.0135829i
$502$	8.00157	+	13.8591i	0.357128	+	0.618563i
$503$	−4.16784			−0.185835			−0.0929174	−	0.995674i	$-0.529619\pi$
$503$	−4.16784			−0.185835			−0.0929174	+	0.995674i	$0.529619\pi$
$504$	−16.3755	+	20.1856i	−0.729421	+	0.899136i
$505$	5.69006			0.253204
$506$	1.48915	+	2.57929i	0.0662010	+	0.114663i
$507$	−11.0695	−	10.8872i	−0.491615	−	0.483517i
$508$	10.9199	−	18.9137i	0.484490	−	0.839162i
$509$	19.9963			0.886319			0.443159	−	0.896443i	$-0.353858\pi$
$509$	19.9963			0.886319			0.443159	+	0.896443i	$0.353858\pi$
$510$	−11.3748	−	11.1874i	−0.503684	−	0.495388i
$511$	−29.0491	+	10.5717i	−1.28505	+	0.467666i
$512$	−8.98394			−0.397038
$513$	−7.51920	−	25.5030i	−0.331981	−	1.12599i
$514$	−14.8841	−	25.7800i	−0.656510	−	1.13711i
$515$	16.8024			0.740404
$516$	−11.6548	+	3.22686i	−0.513074	+	0.142055i
$517$	−5.68942	−	9.85437i	−0.250221	−	0.433395i
$518$	−0.0855340	+	0.484980i	−0.00375815	+	0.0213088i
$519$	20.5310	−	5.68442i	0.901212	−	0.249518i
$520$	−3.28941	−	5.69743i	−0.144250	−	0.249849i
$521$	−9.66649	−	16.7429i	−0.423497	−	0.733518i	0.572782	−	0.819708i	$-0.305864\pi$
$521$	−9.66649	−	16.7429i	−0.423497	−	0.733518i	−0.996279	+	0.0861898i	$0.972531\pi$
$522$	20.5189	+	11.3965i	0.898089	+	0.498811i
$523$	3.14491	−	5.44714i	0.137517	−	0.238187i	−0.789039	−	0.614343i	$-0.789421\pi$
$523$	3.14491	−	5.44714i	0.137517	−	0.238187i	0.926556	+	0.376156i	$0.122754\pi$
$524$	−0.191118	+	0.331026i	−0.00834904	+	0.0144610i
$525$	−4.16909	−	1.90228i	−0.181954	−	0.0830224i
$526$	8.91586	+	15.4427i	0.388750	+	0.673335i
$527$	−35.9072			−1.56414
$528$	3.94553	−	1.09240i	0.171707	−	0.0475405i
$529$	−22.8125			−0.991846
$530$	9.87774	−	17.1087i	0.429062	−	0.743156i
$531$	30.3094	−	18.1769i	1.31532	−	0.788811i
$532$	−43.3582	+	15.7792i	−1.87982	+	0.684117i
$533$	0.874040	−	1.51388i	0.0378589	−	0.0655735i
$534$	−17.3351	+	66.9131i	−0.750162	+	2.89562i
$535$	−7.47266	+	12.9430i	−0.323071	+	0.559576i
$536$	14.8903	−	25.7908i	0.643163	−	1.11399i
$537$	34.5649	−	9.56996i	1.49158	−	0.412974i
$538$	−8.00527	+	13.8655i	−0.345132	+	0.597786i
$539$	19.4521	+	7.08166i	0.837861	+	0.305029i
$540$	5.00821	+	16.9864i	0.215519	+	0.730980i
$541$	13.1057	−	22.6998i	0.563460	−	0.975941i	−0.433732	−	0.901042i	$-0.642803\pi$
$541$	13.1057	−	22.6998i	0.563460	−	0.975941i	0.997191	−	0.0748985i	$-0.0238633\pi$
$542$	10.0549			0.431896
$543$	4.29973	−	16.5969i	0.184519	−	0.712241i
$544$	−18.5798			−0.796604
$545$	−8.06216	−	13.9641i	−0.345345	−	0.598155i
$546$	−17.4354	+	12.4245i	−0.746168	+	0.531718i
$547$	13.7438	−	23.8049i	0.587642	−	1.01783i	−0.406898	−	0.913474i	$-0.633390\pi$
$547$	13.7438	−	23.8049i	0.587642	−	1.01783i	0.994540	−	0.104353i	$-0.0332770\pi$
$548$	−32.7668	+	56.7537i	−1.39973	+	2.42440i
$549$	0.747836	+	45.0230i	0.0319169	+	1.92154i
$550$	3.43866	+	5.95593i	0.146625	+	0.253962i
$551$	8.60742	+	14.9085i	0.366688	+	0.635123i
$552$	0.616025	−	2.37785i	0.0262198	−	0.101208i
$553$	30.5866	−	11.1313i	1.30067	−	0.473351i
$554$	12.5780	+	21.7858i	0.534389	+	0.925588i
$555$	0.0988379	+	0.0972098i	0.00419543	+	0.00412633i
$556$	47.3328			2.00736
$557$	10.3852	+	17.9877i	0.440035	+	0.762162i	0.997692	−	0.0679092i	$-0.0216328\pi$
$557$	10.3852	+	17.9877i	0.440035	+	0.762162i	−0.557657	+	0.830072i	$0.688299\pi$
$558$	55.2900	+	30.7088i	2.34061	+	1.30001i
$559$	−4.11558			−0.174071
$560$	1.98715	−	0.723176i	0.0839722	−	0.0305598i
$561$	19.5530	−	5.41362i	0.825527	−	0.228563i
$562$	34.6723			1.46256
$563$	14.2317	−	24.6500i	0.599794	−	1.03887i	−0.393058	−	0.919514i	$-0.628583\pi$
$563$	14.2317	−	24.6500i	0.599794	−	1.03887i	0.992851	−	0.119359i	$-0.0380840\pi$
$564$	−5.69631	+	21.9877i	−0.239858	+	0.925848i
$565$	−5.41997	−	9.38766i	−0.228020	−	0.394942i
$566$	31.8950			1.34065
$567$	22.0933	−	8.88189i	0.927830	−	0.373004i
$568$	−9.66816			−0.405667
$569$	1.97056	+	3.41311i	0.0826101	+	0.143085i	0.904370	−	0.426749i	$-0.140341\pi$
$569$	1.97056	+	3.41311i	0.0826101	+	0.143085i	−0.821760	+	0.569833i	$0.807008\pi$
$570$	−5.16897	+	19.9522i	−0.216504	+	0.835704i
$571$	−0.365579	+	0.633202i	−0.0152990	+	0.0264987i	−0.873574	−	0.486692i	$-0.838203\pi$
$571$	−0.365579	+	0.633202i	−0.0152990	+	0.0264987i	0.858275	+	0.513191i	$0.171537\pi$
$572$	20.2481			0.846616
$573$	23.8978	−	6.61657i	0.998344	−	0.276411i
$574$	4.10115	+	3.44154i	0.171179	+	0.143647i
$575$	0.433062			0.0180600
$576$	32.8017	+	18.2185i	1.36674	+	0.759104i
$577$	5.81896	+	10.0787i	0.242247	+	0.419583i	0.961354	−	0.275316i	$-0.0887824\pi$
$577$	5.81896	+	10.0787i	0.242247	+	0.419583i	−0.719107	+	0.694899i	$0.755449\pi$
$578$	−3.04904			−0.126823
$579$	−7.26489	−	7.14523i	−0.301919	−	0.296945i
$580$	−5.73302	−	9.92988i	−0.238051	−	0.412316i
$581$	0.511072	+	0.428873i	0.0212028	+	0.0177927i
$582$	−15.5107	+	59.8711i	−0.642939	+	2.48174i
$583$	12.5611	+	21.7564i	0.520227	+	0.901059i
$584$	−19.1311	−	33.1360i	−0.791650	−	1.37118i
$585$	0.100093	+	6.02603i	0.00413833	+	0.249146i
$586$	−11.3795	+	19.7098i	−0.470081	+	0.814204i
$587$	12.2189	−	21.1637i	0.504327	−	0.873520i	−0.495660	−	0.868517i	$-0.665074\pi$
$587$	12.2189	−	21.1637i	0.504327	−	0.873520i	0.999987	−	0.00500395i	$-0.00159281\pi$
$588$	−17.7709	−	37.3053i	−0.732860	−	1.53845i
$589$	23.1934	+	40.1722i	0.955669	+	1.65527i
$590$	−27.3965			−1.12790
$591$	9.22490	−	35.6080i	0.379462	−	1.46472i
$592$	−0.0639720			−0.00262923
$593$	13.2758	−	22.9944i	0.545174	−	0.944268i	−0.453422	−	0.891296i	$-0.649797\pi$
$593$	13.2758	−	22.9944i	0.545174	−	0.944268i	0.998596	−	0.0529726i	$-0.0168696\pi$
$594$	−34.7376	−	8.38634i	−1.42530	−	0.344096i
$595$	9.84775	−	3.58386i	0.403718	−	0.146924i
$596$	19.2721	−	33.3803i	0.789417	−	1.36731i
$597$	−4.63534	+	1.28339i	−0.189712	+	0.0525255i
$598$	1.01161	−	1.75217i	0.0413680	−	0.0716515i
$599$	−13.1831	+	22.8338i	−0.538647	+	0.932964i	0.460330	+	0.887748i	$0.347731\pi$
$599$	−13.1831	+	22.8338i	−0.538647	+	0.932964i	−0.998977	+	0.0452165i	$0.985602\pi$
$600$	1.42248	−	5.49077i	0.0580727	−	0.224160i
$601$	8.67608	−	15.0274i	0.353905	−	0.612981i	−0.633025	−	0.774131i	$-0.718187\pi$
$601$	8.67608	−	15.0274i	0.353905	−	0.612981i	0.986930	+	0.161150i	$0.0515204\pi$
$602$	2.18927	−	12.4132i	0.0892281	−	0.505925i
$603$	−23.3971	+	14.0315i	−0.952803	+	0.571407i
$604$	−17.9173	+	31.0337i	−0.729044	+	1.26274i
$605$	2.25442			0.0916552
$606$	22.0884	−	6.11560i	0.897279	−	0.248429i
$607$	−26.9404			−1.09348			−0.546738	−	0.837303i	$-0.684131\pi$
$607$	−26.9404			−1.09348			−0.546738	+	0.837303i	$0.684131\pi$
$608$	12.0012	+	20.7868i	0.486715	+	0.843014i
$609$	−12.5554	+	8.94697i	−0.508771	+	0.362550i
$610$	17.4529	−	30.2294i	0.706648	−	1.22395i
$611$	−3.86495	+	6.69429i	−0.156359	+	0.270822i
$612$	−35.4041	−	19.6639i	−1.43113	−	0.794868i
$613$	−11.9877	−	20.7633i	−0.484179	−	0.838623i	0.515655	−	0.856796i	$-0.327548\pi$
$613$	−11.9877	−	20.7633i	−0.484179	−	0.838623i	−0.999835	+	0.0181727i	$0.994215\pi$
$614$	13.3859	+	23.1850i	0.540209	+	0.935670i
$615$	1.45249	−	0.402151i	0.0585701	−	0.0162163i
$616$	−4.45027	+	25.2331i	−0.179306	+	1.01667i
$617$	−23.1081	−	40.0243i	−0.930295	−	1.61132i	−0.782816	−	0.622254i	$-0.786217\pi$
$617$	−23.1081	−	40.0243i	−0.930295	−	1.61132i	−0.147480	−	0.989065i	$-0.547116\pi$
$618$	65.2258	−	18.0590i	2.62376	−	0.726441i
$619$	34.2821			1.37792			0.688958	−	0.724802i	$-0.258069\pi$
$619$	34.2821			1.37792			0.688958	+	0.724802i	$0.258069\pi$
$620$	−15.4481	−	26.7569i	−0.620411	−	1.07458i
$621$	−1.55104	+	1.63032i	−0.0622412	+	0.0654223i
$622$	38.8303			1.55695
$623$	−34.7793	−	29.1856i	−1.39340	−	1.16929i
$624$	−1.98281	−	1.95015i	−0.0793759	−	0.0780684i
$625$	1.00000			0.0400000
$626$	−5.22127	+	9.04350i	−0.208684	+	0.361451i
$627$	−18.6865	−	18.3786i	−0.746265	−	0.733972i
$628$	−3.55806	−	6.16274i	−0.141982	−	0.245920i
$629$	−0.317028			−0.0126407
$630$	−18.2286	−	2.90363i	−0.726246	−	0.115683i
$631$	26.8165			1.06755			0.533774	−	0.845627i	$-0.320773\pi$
$631$	26.8165			1.06755			0.533774	+	0.845627i	$0.320773\pi$
$632$	20.1437	+	34.8899i	0.801273	+	1.38785i
$633$	43.2675	−	11.9794i	1.71973	−	0.476140i
$634$	13.5886	−	23.5361i	0.539672	−	0.934740i
$635$	6.40805			0.254296
$636$	12.5763	−	48.5443i	0.498682	−	1.92491i
$637$	−2.44090	−	13.8492i	−0.0967121	−	0.548726i
$638$	23.1373			0.916013
$639$	7.74287	+	4.30050i	0.306303	+	0.170125i
$640$	−9.85221	−	17.0645i	−0.389443	−	0.674535i
$641$	15.9325			0.629294			0.314647	−	0.949209i	$-0.398114\pi$
$641$	15.9325			0.629294			0.314647	+	0.949209i	$0.398114\pi$
$642$	−15.0973	+	58.2753i	−0.595842	+	2.29994i
$643$	18.2048	+	31.5317i	0.717929	+	1.24349i	0.961819	+	0.273686i	$0.0882430\pi$
$643$	18.2048	+	31.5317i	0.717929	+	1.24349i	−0.243890	+	0.969803i	$0.578424\pi$
$644$	2.99130	+	2.51019i	0.117874	+	0.0989155i
$645$	−2.52979	−	2.48812i	−0.0996103	−	0.0979695i
$646$	−23.5668	−	40.8190i	−0.927225	−	1.60600i
$647$	2.57737	+	4.46414i	0.101327	+	0.175503i	0.912232	−	0.409675i	$-0.134358\pi$
$647$	2.57737	+	4.46414i	0.101327	+	0.175503i	−0.810905	+	0.585178i	$0.801025\pi$
$648$	15.5759	+	25.0207i	0.611881	+	0.982906i
$649$	17.4195	−	30.1714i	0.683774	−	1.18433i
$650$	2.33596	−	4.04599i	0.0916237	−	0.158697i
$651$	−33.8316	+	24.1084i	−1.32597	+	0.944882i
$652$	33.1891	+	57.4852i	1.29979	+	2.25129i
$653$	−28.9844			−1.13425			−0.567124	−	0.823633i	$-0.691944\pi$
$653$	−28.9844			−1.13425			−0.567124	+	0.823633i	$0.691944\pi$
$654$	−46.3051	−	45.5424i	−1.81067	−	1.78085i
$655$	−0.112153			−0.00438218
$656$	−0.347737	+	0.602297i	−0.0135768	+	0.0235158i
$657$	0.582136	+	35.0471i	0.0227113	+	1.36732i
$658$	−18.1350	−	15.2183i	−0.706977	−	0.593270i
$659$	6.18409	−	10.7112i	0.240898	−	0.417248i	−0.720072	−	0.693899i	$-0.755891\pi$
$659$	6.18409	−	10.7112i	0.240898	−	0.417248i	0.960970	+	0.276651i	$0.0892247\pi$
$660$	12.4462	+	12.2412i	0.484468	+	0.476488i
$661$	−2.45608	+	4.25405i	−0.0955303	+	0.165463i	−0.909830	−	0.414982i	$-0.863788\pi$
$661$	−2.45608	+	4.25405i	−0.0955303	+	0.165463i	0.814300	+	0.580445i	$0.197121\pi$
$662$	8.44128	−	14.6207i	0.328080	−	0.568251i
$663$	−9.82626	−	9.66440i	−0.381620	−	0.375334i
$664$	−0.412897	+	0.715158i	−0.0160235	+	0.0277535i
$665$	−10.3705	−	8.70255i	−0.402150	−	0.337470i
$666$	0.488161	+	0.271131i	0.0189159	+	0.0105061i
$667$	0.728473	−	1.26175i	0.0282066	−	0.0488552i
$668$	−2.24200			−0.0867457
$669$	−17.4500	−	17.1626i	−0.674656	−	0.663543i
$670$	21.1485			0.817038
$671$	22.1941	+	38.4413i	0.856794	+	1.48401i
$672$	−17.5059	+	12.4747i	−0.675304	+	0.481221i
$673$	−14.0727	+	24.3746i	−0.542461	+	0.939570i	0.456301	+	0.889826i	$0.349174\pi$
$673$	−14.0727	+	24.3746i	−0.542461	+	0.939570i	−0.998762	+	0.0497447i	$0.984159\pi$
$674$	7.71753	−	13.3672i	0.297268	−	0.514884i
$675$	−3.58157	+	3.76462i	−0.137855	+	0.144900i
$676$	15.2756	+	26.4581i	0.587522	+	1.01762i
$677$	−10.2332	−	17.7244i	−0.393294	−	0.681205i	0.599588	−	0.800309i	$-0.295331\pi$
$677$	−10.2332	−	17.7244i	−0.393294	−	0.681205i	−0.992882	+	0.119104i	$0.961998\pi$
$678$	−31.1296	−	30.6169i	−1.19553	−	1.17583i
$679$	−31.1191	−	26.1140i	−1.19424	−	1.00216i
$680$	6.48552	+	11.2333i	0.248708	+	0.430776i
$681$	−1.87709	+	7.24556i	−0.0719304	+	0.277650i
$682$	62.3454			2.38733
$683$	−9.41989	−	16.3157i	−0.360442	−	0.624304i	0.627592	−	0.778543i	$-0.284041\pi$
$683$	−9.41989	−	16.3157i	−0.360442	−	0.624304i	−0.988034	+	0.154239i	$0.950707\pi$
$684$	0.868888	+	52.3109i	0.0332228	+	2.00016i
$685$	−19.2284			−0.734679
$686$	43.0697	+	0.00491509i	1.64441	+	0.000187659i
$687$	3.16094	−	12.2012i	0.120597	−	0.465504i
$688$	1.63738			0.0624247
$689$	8.53301	−	14.7796i	0.325082	−	0.563058i
$690$	1.68112	−	0.465450i	0.0639990	−	0.0177194i
$691$	17.0192	+	29.4782i	0.647442	+	1.12140i	0.983732	+	0.179644i	$0.0574944\pi$
$691$	17.0192	+	29.4782i	0.647442	+	1.12140i	−0.336290	+	0.941758i	$0.609172\pi$
$692$	−41.9189			−1.59352
$693$	14.7880	−	18.2287i	0.561750	−	0.692452i
$694$	6.74624			0.256084
$695$	6.94402	+	12.0274i	0.263402	+	0.456225i
$696$	−13.6049	−	13.3808i	−0.515691	−	0.507196i
$697$	−1.72329	+	2.98482i	−0.0652742	+	0.113058i
$698$	16.6648			0.630773
$699$	−4.89633	−	4.81568i	−0.185196	−	0.182146i
$700$	6.90732	+	5.79638i	0.261072	+	0.219083i
$701$	−44.6921			−1.68800			−0.843998	−	0.536346i	$-0.819804\pi$
$701$	−44.6921			−1.68800			−0.843998	+	0.536346i	$0.819804\pi$
$702$	6.86525	+	23.2850i	0.259112	+	0.878836i
$703$	0.204777	+	0.354684i	0.00772331	+	0.0133772i
$704$	36.9874			1.39401
$705$	−6.42282	+	1.77828i	−0.241897	+	0.0669741i
$706$	−2.01406	−	3.48845i	−0.0758001	−	0.131290i
$707$	−2.61475	+	14.8257i	−0.0983377	+	0.557577i
$708$	−67.0214	+	18.5562i	−2.51882	+	0.697384i
$709$	15.6579	+	27.1203i	0.588045	+	1.01852i	0.994488	+	0.104847i	$0.0334354\pi$
$709$	15.6579	+	27.1203i	0.588045	+	1.01852i	−0.406444	+	0.913676i	$0.633231\pi$
$710$	−3.43289	−	5.94594i	−0.128834	−	0.223147i
$711$	−0.612948	−	36.9022i	−0.0229873	−	1.38394i
$712$	28.0983	−	48.6677i	1.05303	−	1.82390i
$713$	1.96293	−	3.39990i	0.0735124	−	0.127327i
$714$	34.3763	−	24.4965i	1.28650	−	0.916759i
$715$	2.97053	+	5.14511i	0.111092	+	0.192416i
$716$	−70.5722			−2.63741
$717$	−26.9177	+	7.45271i	−1.00526	+	0.278327i
$718$	−13.5329			−0.505043
$719$	21.5997	−	37.4118i	0.805533	−	1.39522i	−0.110398	−	0.993887i	$-0.535213\pi$
$719$	21.5997	−	37.4118i	0.805533	−	1.39522i	0.915931	−	0.401336i	$-0.131454\pi$
$720$	−0.0398219	−	2.39745i	−0.00148407	−	0.0893478i
$721$	−7.72120	+	43.7794i	−0.287553	+	1.63043i
$722$	−8.35227	+	14.4665i	−0.310839	+	0.538389i
$723$	−0.668958	+	2.58217i	−0.0248788	+	0.0960319i
$724$	−16.8680	+	29.2162i	−0.626893	+	1.08581i
$725$	1.68214	−	2.91356i	0.0624732	−	0.108207i
$726$	8.75148	−	2.42302i	0.324798	−	0.0899267i
$727$	−0.462646	+	0.801327i	−0.0171586	+	0.0297196i	−0.874477	−	0.485067i	$-0.838795\pi$
$727$	−0.462646	+	0.801327i	−0.0171586	+	0.0297196i	0.857319	+	0.514786i	$0.172129\pi$
$728$	16.3565	−	5.95256i	0.606211	−	0.220617i
$729$	−1.34474	−	26.9665i	−0.0498051	−	0.998759i
$730$	13.5858	−	23.5313i	0.502834	−	0.870934i
$731$	8.11443			0.300123
$732$	22.2210	−	85.7726i	0.821311	−	3.17025i
$733$	−32.2085			−1.18965			−0.594824	−	0.803856i	$-0.702778\pi$
$733$	−32.2085			−1.18965			−0.594824	+	0.803856i	$0.702778\pi$
$734$	4.92300	+	8.52689i	0.181711	+	0.314733i
$735$	6.87229	−	9.98857i	0.253488	−	0.368434i
$736$	1.01570	−	1.75925i	0.0374393	−	0.0648467i
$737$	−13.4468	+	23.2905i	−0.495319	+	0.857918i
$738$	5.20623	−	3.12224i	0.191644	−	0.114931i
$739$	3.96081	+	6.86033i	0.145701	+	0.252361i	0.929634	−	0.368484i	$-0.120123\pi$
$739$	3.96081	+	6.86033i	0.145701	+	0.252361i	−0.783933	+	0.620845i	$0.786790\pi$
$740$	−0.136393	−	0.236239i	−0.00501390	−	0.00868433i
$741$	−4.46528	+	17.2359i	−0.164036	+	0.633178i
$742$	40.0384	+	33.5988i	1.46986	+	1.23345i
$743$	−9.01322	−	15.6114i	−0.330663	−	0.572725i	0.651979	−	0.758237i	$-0.273939\pi$
$743$	−9.01322	−	15.6114i	−0.330663	−	0.572725i	−0.982642	+	0.185512i	$0.940606\pi$
$744$	−36.6594	−	36.0556i	−1.34400	−	1.32186i
$745$	11.3094			0.414344
$746$	6.29464	+	10.9026i	0.230463	+	0.399174i
$747$	0.648784	−	0.389083i	0.0237378	−	0.0142358i
$748$	−39.9219			−1.45969
$749$	−30.2896	−	25.4180i	−1.10676	−	0.928753i
$750$	3.88192	−	1.07479i	0.141748	−	0.0392457i
$751$	12.6122			0.460227			0.230113	−	0.973164i	$-0.426090\pi$
$751$	12.6122			0.460227			0.230113	+	0.973164i	$0.426090\pi$
$752$	1.53767	−	2.66332i	0.0560730	−	0.0971213i
$753$	−2.98916	+	11.5381i	−0.108931	+	0.420473i
$754$	−7.85882	−	13.6119i	−0.286201	−	0.495715i
$755$	−10.5143			−0.382656
$756$	−46.5602	+	5.24332i	−1.69338	+	0.190698i
$757$	31.5254			1.14581			0.572905	−	0.819622i	$-0.305816\pi$
$757$	31.5254			1.14581			0.572905	+	0.819622i	$0.305816\pi$
$758$	−19.0210	−	32.9453i	−0.690872	−	1.19663i
$759$	−0.556306	+	2.14733i	−0.0201926	+	0.0779433i
$760$	8.37836	−	14.5117i	0.303915	−	0.526396i
$761$	10.0827			0.365497			0.182748	−	0.983160i	$-0.441501\pi$
$761$	10.0827			0.365497			0.182748	+	0.983160i	$0.441501\pi$
$762$	24.8756	−	6.88729i	0.901147	−	0.249500i
$763$	40.0887	−	14.5894i	1.45131	−	0.528171i
$764$	−48.7928			−1.76526
$765$	−0.197346	−	11.8811i	−0.00713508	−	0.429563i
$766$	2.92919	+	5.07351i	0.105836	+	0.183313i
$767$	−23.6668			−0.854560
$768$	−25.6967	−	25.2735i	−0.927251	−	0.911977i
$769$	4.49619	+	7.78763i	0.162137	+	0.280829i	0.935635	−	0.352970i	$-0.114828\pi$
$769$	4.49619	+	7.78763i	0.162137	+	0.280829i	−0.773498	+	0.633799i	$0.781495\pi$
$770$	−17.0986	+	6.22264i	−0.616190	+	0.224248i
$771$	5.56028	−	21.4626i	0.200249	−	0.772957i
$772$	10.0253	+	17.3643i	0.360819	+	0.624956i
$773$	−17.8964	−	30.9974i	−0.643688	−	1.11490i	−0.984603	−	0.174806i	$-0.944070\pi$
$773$	−17.8964	−	30.9974i	−0.643688	−	1.11490i	0.340915	−	0.940094i	$-0.389263\pi$
$774$	−12.4946	−	6.93970i	−0.449111	−	0.249442i
$775$	4.53268	−	7.85083i	0.162819	−	0.282010i
$776$	25.1412	−	43.5459i	0.902517	−	1.56321i
$777$	−0.298703	+	0.212855i	−0.0107159	+	0.00763614i
$778$	−41.0439	−	71.0901i	−1.47149	−	2.54870i
$779$	4.45248			0.159527
$780$	2.97413	−	11.4801i	0.106491	−	0.411053i
$781$	8.73091			0.312416
$782$	−1.99453	+	3.45464i	−0.0713244	+	0.123538i
$783$	4.94373	+	16.7677i	0.176674	+	0.599230i
$784$	0.971113	+	5.50991i	0.0346826	+	0.196782i
$785$	1.04398	−	1.80823i	0.0372613	−	0.0645384i
$786$	−0.435370	+	0.120541i	−0.0155291	+	0.00429955i
$787$	6.28045	−	10.8781i	0.223874	−	0.387761i	−0.732107	−	0.681189i	$-0.761463\pi$
$787$	6.28045	−	10.8781i	0.223874	−	0.387761i	0.955981	+	0.293429i	$0.0947963\pi$
$788$	−36.1896	+	62.6822i	−1.28920	+	2.23296i
$789$	−3.33071	+	12.8565i	−0.118577	+	0.457704i
$790$	−14.3049	+	24.7769i	−0.508946	+	0.881521i
$791$	26.9505	−	9.80803i	0.958251	−	0.348734i
$792$	25.3986	+	14.1067i	0.902500	+	0.501261i
$793$	15.0769	−	26.1140i	0.535398	−	0.927336i
$794$	32.8421			1.16552
$795$	14.1803	−	3.92609i	0.502922	−	0.139244i
$796$	9.46413			0.335447
$797$	−3.44704	−	5.97045i	−0.122101	−	0.211484i	0.798495	−	0.602001i	$-0.205630\pi$
$797$	−3.44704	−	5.97045i	−0.122101	−	0.211484i	−0.920596	+	0.390517i	$0.872296\pi$
$798$	−49.6108	−	22.6366i	−1.75620	−	0.801325i
$799$	7.62026	−	13.1987i	0.269586	−	0.466936i
$800$	2.34539	−	4.06234i	0.0829222	−	0.143625i
$801$	−44.1508	+	26.4778i	−1.55999	+	0.935545i
$802$	−2.14982	−	3.72361i	−0.0759130	−	0.131485i
$803$	17.2765	+	29.9238i	0.609674	+	1.05599i
$804$	51.7365	−	14.3243i	1.82461	−	0.505179i
$805$	−0.199005	+	1.12836i	−0.00701400	+	0.0397695i
$806$	−21.1763	−	36.6784i	−0.745902	−	1.29194i
$807$	−11.4922	+	3.18184i	−0.404545	+	0.112006i
$808$	−18.6336			−0.655526
$809$	−8.42797	−	14.5977i	−0.296312	−	0.513227i	0.678977	−	0.734159i	$-0.262423\pi$
$809$	−8.42797	−	14.5977i	−0.296312	−	0.513227i	−0.975289	+	0.220932i	$0.929090\pi$
$810$	−9.85721	+	18.4634i	−0.346347	+	0.648737i
$811$	6.95388			0.244184			0.122092	−	0.992519i	$-0.461040\pi$
$811$	6.95388			0.244184			0.122092	+	0.992519i	$0.461040\pi$
$812$	28.5072	−	10.3745i	1.00041	−	0.364075i
$813$	5.33920	+	5.25125i	0.187254	+	0.184169i
$814$	0.550453			0.0192934
$815$	−9.73811	+	16.8669i	−0.341111	+	0.590822i
$816$	3.90937	+	3.84498i	0.136855	+	0.134601i
$817$	−5.24134	−	9.07826i	−0.183371	−	0.317608i
$818$	−55.4410			−1.93845
$819$	−15.7470	−	2.50834i	−0.550246	−	0.0876484i
$820$	−2.96560			−0.103563
$821$	−11.9271	−	20.6583i	−0.416258	−	0.720979i	0.579302	−	0.815113i	$-0.303325\pi$
$821$	−11.9271	−	20.6583i	−0.416258	−	0.720979i	−0.995560	+	0.0941337i	$0.969992\pi$
$822$	−74.6431	+	20.6664i	−2.60348	+	0.720824i
$823$	−15.0857	+	26.1291i	−0.525853	+	0.910804i	0.473694	+	0.880690i	$0.342920\pi$
$823$	−15.0857	+	26.1291i	−0.525853	+	0.910804i	−0.999546	+	0.0301141i	$0.990413\pi$
$824$	−55.0238			−1.91685
$825$	−1.28459	+	4.95849i	−0.0447236	+	0.172632i
$826$	12.5895	−	71.3827i	0.438045	−	2.48372i
$827$	−21.2692			−0.739603			−0.369802	−	0.929111i	$-0.620574\pi$
$827$	−21.2692			−0.739603			−0.369802	+	0.929111i	$0.620574\pi$
$828$	3.79733	−	2.27730i	0.131966	−	0.0791417i
$829$	−5.63065	−	9.75257i	−0.195561	−	0.338721i	0.751524	−	0.659706i	$-0.229319\pi$
$829$	−5.63065	−	9.75257i	−0.195561	−	0.338721i	−0.947084	+	0.320985i	$0.895986\pi$
$830$	−0.586432			−0.0203554
$831$	−4.69879	+	18.1373i	−0.162999	+	0.629175i
$832$	−12.5632	−	21.7600i	−0.435549	−	0.754393i
$833$	4.81257	+	27.3056i	0.166746	+	0.946082i
$834$	39.8831	+	39.2261i	1.38104	+	1.35829i
$835$	−0.328916	−	0.569700i	−0.0113826	−	0.0197153i
$836$	25.7867	+	44.6638i	0.891850	+	1.54473i
$837$	13.3213	+	45.1821i	0.460451	+	1.56172i
$838$	32.3306	−	55.9982i	1.11684	−	1.93443i
$839$	−16.5892	+	28.7333i	−0.572722	+	0.991984i	0.423563	+	0.905867i	$0.360779\pi$
$839$	−16.5892	+	28.7333i	−0.572722	+	0.991984i	−0.996285	+	0.0861170i	$0.972554\pi$
$840$	13.6527	+	6.22951i	0.471065	+	0.214938i
$841$	8.84079	+	15.3127i	0.304855	+	0.528024i
$842$	73.0473			2.51737
$843$	18.4111	+	18.1078i	0.634111	+	0.623666i
$844$	−88.3405			−3.04081
$845$	−4.48205	+	7.76315i	−0.154187	+	0.267060i
$846$	−23.0216	+	13.8063i	−0.791500	+	0.474671i
$847$	−1.03597	+	5.87398i	−0.0355964	+	0.201832i
$848$	−3.39486	+	5.88006i	−0.116580	+	0.201922i
$849$	16.9364	+	16.6574i	0.581255	+	0.571680i
$850$	−4.60565	+	7.97722i	−0.157973	+	0.273617i
$851$	0.0173309	−	0.0300180i	0.000594096	−	0.00102900i
$852$	−12.4253	−	12.2207i	−0.425685	−	0.418673i
$853$	−1.95782	+	3.39105i	−0.0670346	+	0.116107i	−0.897595	−	0.440822i	$-0.854687\pi$
$853$	−1.95782	+	3.39105i	−0.0670346	+	0.116107i	0.830560	+	0.556929i	$0.188020\pi$
$854$	70.7436	+	59.3656i	2.42080	+	2.03145i
$855$	−13.1649	+	7.89514i	−0.450230	+	0.270008i
$856$	24.4711	−	42.3852i	0.836405	−	1.44870i
$857$	17.9574			0.613412			0.306706	−	0.951804i	$-0.400773\pi$
$857$	17.9574			0.613412			0.306706	+	0.951804i	$0.400773\pi$
$858$	17.0613	+	16.7802i	0.582462	+	0.572868i
$859$	48.1738			1.64367			0.821835	−	0.569725i	$-0.192950\pi$
$859$	48.1738			1.64367			0.821835	+	0.569725i	$0.192950\pi$
$860$	3.49102	+	6.04663i	0.119043	+	0.206188i
$861$	0.380358	+	3.96932i	0.0129626	+	0.135274i
$862$	−40.7370	+	70.5585i	−1.38751	+	2.40323i
$863$	−22.0723	+	38.2303i	−0.751349	+	1.30137i	0.195821	+	0.980640i	$0.437263\pi$
$863$	−22.0723	+	38.2303i	−0.751349	+	1.30137i	−0.947169	+	0.320734i	$0.896070\pi$
$864$	6.89299	+	23.3791i	0.234504	+	0.795372i
$865$	−6.14977	−	10.6517i	−0.209098	−	0.362169i
$866$	33.0079	+	57.1713i	1.12165	+	1.94276i
$867$	−1.61905	−	1.59238i	−0.0549858	−	0.0540801i
$868$	76.8151	−	27.9551i	2.60727	−	0.948858i
$869$	−18.1909	−	31.5076i	−0.617085	−	1.06882i
$870$	3.39850	−	13.1181i	0.115220	−	0.444747i
$871$	18.2694			0.619035
$872$	26.4016	+	45.7289i	0.894071	+	1.54858i
$873$	−39.5043	+	23.6912i	−1.33702	+	0.801826i
$874$	5.15330			0.174313
$875$	−0.459529	+	2.60554i	−0.0155349	+	0.0880833i
$876$	17.2974	−	66.7677i	0.584425	−	2.25587i
$877$	28.5861			0.965283			0.482641	−	0.875818i	$-0.339677\pi$
$877$	28.5861			0.965283			0.482641	+	0.875818i	$0.339677\pi$
$878$	12.0818	−	20.9262i	0.407740	−	0.706226i
$879$	−16.3361	+	4.52297i	−0.551003	+	0.152556i
$880$	−1.18182	−	2.04698i	−0.0398393	−	0.0690037i
$881$	−25.1883			−0.848615			−0.424308	−	0.905518i	$-0.639482\pi$
$881$	−25.1883			−0.848615			−0.424308	+	0.905518i	$0.639482\pi$
$882$	15.9421	−	46.1611i	0.536799	−	1.55433i
$883$	−0.466663			−0.0157044			−0.00785222	−	0.999969i	$-0.502499\pi$
$883$	−0.466663			−0.0157044			−0.00785222	+	0.999969i	$0.502499\pi$
$884$	13.5599	+	23.4864i	0.456069	+	0.789934i
$885$	−14.5477	−	14.3080i	−0.489014	−	0.480959i
$886$	−16.6008	+	28.7535i	−0.557716	+	0.965992i
$887$	5.03726			0.169135			0.0845673	−	0.996418i	$-0.473049\pi$
$887$	5.03726			0.169135			0.0845673	+	0.996418i	$0.473049\pi$
$888$	−0.323670	−	0.318338i	−0.0108616	−	0.0106827i
$889$	−2.94469	+	16.6964i	−0.0987616	+	0.559980i
$890$	39.9077			1.33771
$891$	−14.0660	−	22.5951i	−0.471228	−	0.756965i
$892$	24.0804	+	41.7085i	0.806272	+	1.39650i
$893$	−19.6886			−0.658853
$894$	43.9022	−	12.1552i	1.46831	−	0.406530i
$895$	−10.3534	−	17.9326i	−0.346076	−	0.599421i
$896$	48.9897	−	17.8287i	1.63663	−	0.595614i
$897$	1.45225	−	0.402085i	0.0484893	−	0.0134252i
$898$	−9.18464	−	15.9083i	−0.306496	−	0.530866i
$899$	−15.2492	−	26.4124i	−0.508590	−	0.880904i
$900$	8.76855	−	5.25860i	0.292285	−	0.175287i
$901$	−16.8240	+	29.1400i	−0.560488	+	0.970794i
$902$	2.99213	−	5.18253i	0.0996271	−	0.172559i
$903$	7.64540	−	5.44810i	0.254423	−	0.181301i
$904$	17.7491	+	30.7423i	0.590325	+	1.02247i
$905$	−9.89856			−0.329039
$906$	−40.8158	+	11.3007i	−1.35602	+	0.375440i
$907$	−59.4915			−1.97538			−0.987691	−	0.156418i	$-0.950005\pi$
$907$	−59.4915			−1.97538			−0.987691	+	0.156418i	$0.950005\pi$
$908$	7.36390	−	12.7546i	0.244380	−	0.423278i
$909$	14.9229	+	8.28840i	0.494962	+	0.274909i
$910$	9.46856	+	7.94568i	0.313880	+	0.263397i
$911$	24.2229	−	41.9552i	0.802540	−	1.39004i	−0.115400	−	0.993319i	$-0.536815\pi$
$911$	24.2229	−	41.9552i	0.802540	−	1.39004i	0.917940	−	0.396720i	$-0.129852\pi$
$912$	1.77651	−	6.85731i	0.0588262	−	0.227068i
$913$	0.372870	−	0.645829i	0.0123402	−	0.0213738i
$914$	−31.8428	+	55.1533i	−1.05326	+	1.82431i
$915$	25.0551	−	6.93699i	0.828294	−	0.229330i
$916$	−12.4005	+	21.4782i	−0.409723	+	0.709661i
$917$	0.0515376	−	0.292219i	0.00170192	−	0.00964993i
$918$	−13.5358	−	45.9095i	−0.446747	−	1.51524i
$919$	−7.16949	+	12.4179i	−0.236500	+	0.409630i	−0.959707	−	0.281001i	$-0.909334\pi$
$919$	−7.16949	+	12.4179i	−0.236500	+	0.409630i	0.723208	+	0.690631i	$0.242667\pi$
$920$	−1.41817			−0.0467558
$921$	−5.00058	+	19.3022i	−0.164775	+	0.636028i
$922$	−78.0459			−2.57030
$923$	−2.96555	−	5.13648i	−0.0976122	−	0.169069i
$924$	−37.6143	+	26.8039i	−1.23742	+	0.881784i
$925$	0.0400194	−	0.0693157i	0.00131583	−	0.00227909i
$926$	9.29200	−	16.0942i	0.305354	−	0.528889i
$927$	44.0666	+	24.4752i	1.44734	+	0.803870i
$928$	−7.89058	−	13.6669i	−0.259021	−	0.448637i
$929$	23.2562	+	40.2809i	0.763011	+	1.32157i	0.941292	+	0.337594i	$0.109613\pi$
$929$	23.2562	+	40.2809i	0.763011	+	1.32157i	−0.178281	+	0.983980i	$0.557054\pi$
$930$	9.15754	−	35.3480i	0.300288	−	1.15911i
$931$	27.4404	−	23.0216i	0.899322	−	0.754504i
$932$	6.75677	+	11.7031i	0.221325	+	0.383347i
$933$	20.6190	+	20.2794i	0.675037	+	0.663917i
$934$	82.7667			2.70821
$935$	−5.85680	−	10.1443i	−0.191538	−	0.331753i
$936$	−0.327779	−	19.7338i	−0.0107138	−	0.645018i
$937$	−53.0098			−1.73175			−0.865877	−	0.500256i	$-0.833239\pi$
$937$	−53.0098			−1.73175			−0.865877	+	0.500256i	$0.833239\pi$
$938$	−9.71835	+	55.1033i	−0.317315	+	1.79919i
$939$	−7.49554	+	2.07529i	−0.244608	+	0.0677245i
$940$	13.1137			0.427721
$941$	−25.7438	+	44.5896i	−0.839225	+	1.45358i	0.0513188	+	0.998682i	$0.483658\pi$
$941$	−25.7438	+	44.5896i	−0.839225	+	1.45358i	−0.890544	+	0.454898i	$0.849676\pi$
$942$	2.10919	−	8.14146i	0.0687212	−	0.265263i
$943$	−0.188414	−	0.326342i	−0.00613559	−	0.0106272i
$944$	9.41585			0.306460
$945$	−8.16303	−	11.0619i	−0.265543	−	0.359843i
$946$	−14.0890			−0.458074
$947$	15.4562	+	26.7709i	0.502258	+	0.869936i	0.999997	+	0.00260888i	$0.000830432\pi$
$947$	15.4562	+	26.7709i	0.502258	+	0.869936i	−0.497739	+	0.867327i	$0.665836\pi$
$948$	−18.2129	+	70.3017i	−0.591529	+	2.28329i
$949$	11.7363	−	20.3279i	0.380976	−	0.659870i
$950$	11.8997			0.386076
$951$	19.5075	−	5.40104i	0.632574	−	0.175141i
$952$	−32.2490	+	11.7363i	−1.04519	+	0.380375i
$953$	−19.2506			−0.623588			−0.311794	−	0.950150i	$-0.600930\pi$
$953$	−19.2506			−0.623588			−0.311794	+	0.950150i	$0.600930\pi$
$954$	50.8270	−	30.4815i	1.64559	−	0.986876i
$955$	−7.15823	−	12.3984i	−0.231635	−	0.401203i
$956$	54.9588			1.77750
$957$	12.2860	+	12.0836i	0.397149	+	0.390607i
$958$	4.87414	+	8.44226i	0.157476	+	0.272757i
$959$	8.83600	−	50.1003i	0.285329	−	1.61782i
$960$	5.43285	−	20.9707i	0.175345	−	0.676828i
$961$	−25.5903	−	44.3238i	−0.825495	−	1.42980i
$962$	−0.186967	−	0.323837i	−0.00602807	−	0.0104409i
$963$	−38.4514	+	23.0597i	−1.23908	+	0.743090i
$964$	2.62434	−	4.54550i	0.0845244	−	0.146401i
$965$	−2.94156	+	5.09492i	−0.0946920	+	0.164011i
$966$	0.440227	+	4.59410i	0.0141641	+	0.147813i
$967$	−9.18403	−	15.9072i	−0.295338	−	0.511541i	0.679725	−	0.733467i	$-0.262099\pi$
$967$	−9.18403	−	15.9072i	−0.295338	−	0.511541i	−0.975064	+	0.221926i	$0.928766\pi$
$968$	−7.38267			−0.237288
$969$	8.80390	−	33.9829i	0.282822	−	1.09169i
$970$	35.7078			1.14651
$971$	−9.62981	+	16.6793i	−0.309035	+	0.535265i	−0.978152	−	0.207893i	$-0.933339\pi$
$971$	−9.62981	+	16.6793i	−0.309035	+	0.535265i	0.669116	+	0.743158i	$0.266673\pi$
$972$	−11.6085	+	51.8443i	−0.372344	+	1.66291i
$973$	−34.5288	+	12.5660i	−1.10694	+	0.402847i
$974$	−6.09409	+	10.5553i	−0.195267	+	0.338213i
$975$	3.35345	−	0.928469i	0.107396	−	0.0297348i
$976$	−5.99835	+	10.3895i	−0.192003	+	0.332558i
$977$	29.7715	−	51.5657i	0.952475	−	1.64973i	0.212430	−	0.977176i	$-0.431862\pi$
$977$	29.7715	−	51.5657i	0.952475	−	1.64973i	0.740044	−	0.672558i	$-0.234804\pi$
$978$	−19.6743	+	75.9424i	−0.629114	+	2.42837i
$979$	−25.3744	+	43.9498i	−0.810970	+	1.40464i
$980$	−18.2768	+	15.3337i	−0.583831	+	0.489817i
$981$	−0.803368	−	48.3663i	−0.0256496	−	1.54422i
$982$	−4.05638	+	7.02585i	−0.129444	+	0.224204i
$983$	−9.56801			−0.305172			−0.152586	−	0.988290i	$-0.548760\pi$
$983$	−9.56801			−0.305172			−0.152586	+	0.988290i	$0.548760\pi$
$984$	−4.75655	+	1.31695i	−0.151633	+	0.0419827i
$985$	−21.2370			−0.676667
$986$	15.4947	+	26.8377i	0.493453	+	0.854685i
$987$	−1.68192	−	17.5521i	−0.0535360	−	0.558689i
$988$	17.5174	−	30.3411i	0.557304	−	0.965279i
$989$	−0.443591	+	0.768321i	−0.0141054	+	0.0244312i
$990$	0.342651	+	20.6291i	0.0108902	+	0.655636i
$991$	7.44111	+	12.8884i	0.236375	+	0.409413i	0.959671	−	0.281125i	$-0.0907074\pi$
$991$	7.44111	+	12.8884i	0.236375	+	0.409413i	−0.723297	+	0.690537i	$0.757374\pi$
$992$	−21.2618	−	36.8266i	−0.675064	−	1.16925i
$993$	12.1181	−	3.35514i	0.384557	−	0.106472i
$994$	17.0699	−	6.21220i	0.541424	−	0.197039i
$995$	1.38845	+	2.40486i	0.0440168	+	0.0762393i
$996$	−1.43462	+	0.397202i	−0.0454575	+	0.0125858i
$997$	7.16008			0.226762			0.113381	−	0.993552i	$-0.463832\pi$
$997$	7.16008			0.226762			0.113381	+	0.993552i	$0.463832\pi$
$998$	8.21692	+	14.2321i	0.260102	+	0.450510i
$999$	0.117615	+	0.398917i	0.00372117	+	0.0126212i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.b.16.2	✓	24
3.2	odd	2		945.2.k.b.856.11		24
7.4	even	3		315.2.l.b.151.11	yes	24
9.4	even	3		315.2.l.b.121.11	yes	24
9.5	odd	6		945.2.l.b.226.2		24
21.11	odd	6		945.2.l.b.46.2		24
63.4	even	3	inner	315.2.k.b.256.2	yes	24
63.32	odd	6		945.2.k.b.361.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.b.16.2	✓	24	1.1	even	1	trivial
315.2.k.b.256.2	yes	24	63.4	even	3	inner
315.2.l.b.121.11	yes	24	9.4	even	3
315.2.l.b.151.11	yes	24	7.4	even	3
945.2.k.b.361.11		24	63.32	odd	6
945.2.k.b.856.11		24	3.2	odd	2
945.2.l.b.46.2		24	21.11	odd	6
945.2.l.b.226.2		24	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)

\(f(q)\)	\(=\)	\(q+(-1.16277 - 2.01398i) q^{2} +(0.434379 - 1.67670i) q^{3} +(-1.70408 + 2.95156i) q^{4} -1.00000 q^{5} +(-3.88192 + 1.07479i) q^{6} +(0.459529 - 2.60554i) q^{7} +3.27475 q^{8} +(-2.62263 - 1.45664i) q^{9} +O(q^{10})\)	\(q+(-1.16277 - 2.01398i) q^{2} +(0.434379 - 1.67670i) q^{3} +(-1.70408 + 2.95156i) q^{4} -1.00000 q^{5} +(-3.88192 + 1.07479i) q^{6} +(0.459529 - 2.60554i) q^{7} +3.27475 q^{8} +(-2.62263 - 1.45664i) q^{9} +(1.16277 + 2.01398i) q^{10} -2.95729 q^{11} +(4.20865 + 4.13933i) q^{12} +(1.00448 + 1.73980i) q^{13} +(-5.78184 + 2.10417i) q^{14} +(-0.434379 + 1.67670i) q^{15} +(-0.399631 - 0.692181i) q^{16} +(-1.98046 - 3.43026i) q^{17} +(0.115867 + 6.97568i) q^{18} +(-2.55847 + 4.43140i) q^{19} +(1.70408 - 2.95156i) q^{20} +(-4.16909 - 1.90228i) q^{21} +(3.43866 + 5.95593i) q^{22} +0.433062 q^{23} +(1.42248 - 5.49077i) q^{24} +1.00000 q^{25} +(2.33596 - 4.04599i) q^{26} +(-3.58157 + 3.76462i) q^{27} +(6.90732 + 5.79638i) q^{28} +(1.68214 - 2.91356i) q^{29} +(3.88192 - 1.07479i) q^{30} +(4.53268 - 7.85083i) q^{31} +(2.34539 - 4.06234i) q^{32} +(-1.28459 + 4.95849i) q^{33} +(-4.60565 + 7.97722i) q^{34} +(-0.459529 + 2.60554i) q^{35} +(8.76855 - 5.25860i) q^{36} +(0.0400194 - 0.0693157i) q^{37} +11.8997 q^{38} +(3.35345 - 0.928469i) q^{39} -3.27475 q^{40} +(-0.435072 - 0.753568i) q^{41} +(1.01654 + 10.6084i) q^{42} +(-1.02431 + 1.77416i) q^{43} +(5.03947 - 8.72862i) q^{44} +(2.62263 + 1.45664i) q^{45} +(-0.503553 - 0.872180i) q^{46} +(1.92386 + 3.33223i) q^{47} +(-1.33417 + 0.369391i) q^{48} +(-6.57767 - 2.39464i) q^{49} +(-1.16277 - 2.01398i) q^{50} +(-6.61178 + 1.83060i) q^{51} -6.84684 q^{52} +(-4.24749 - 7.35687i) q^{53} +(11.7464 + 2.83582i) q^{54} +2.95729 q^{55} +(1.50484 - 8.53250i) q^{56} +(6.31877 + 6.21469i) q^{57} -7.82380 q^{58} +(-5.89034 + 10.2024i) q^{59} +(-4.20865 - 4.13933i) q^{60} +(-7.50487 - 12.9988i) q^{61} -21.0819 q^{62} +(-5.00052 + 6.16399i) q^{63} -12.5072 q^{64} +(-1.00448 - 1.73980i) q^{65} +(11.4800 - 3.17846i) q^{66} +(4.54700 - 7.87563i) q^{67} +13.4995 q^{68} +(0.188113 - 0.726115i) q^{69} +(5.78184 - 2.10417i) q^{70} -2.95233 q^{71} +(-8.58847 - 4.77015i) q^{72} +(-5.84200 - 10.1186i) q^{73} -0.186134 q^{74} +(0.434379 - 1.67670i) q^{75} +(-8.71969 - 15.1029i) q^{76} +(-1.35896 + 7.70534i) q^{77} +(-5.76922 - 5.67419i) q^{78} +(6.15121 + 10.6542i) q^{79} +(0.399631 + 0.692181i) q^{80} +(4.75637 + 7.64048i) q^{81} +(-1.01178 + 1.75246i) q^{82} +(-0.126085 + 0.218385i) q^{83} +(12.7192 - 9.06367i) q^{84} +(1.98046 + 3.43026i) q^{85} +4.76417 q^{86} +(-4.15446 - 4.08603i) q^{87} -9.68441 q^{88} +(8.58029 - 14.8615i) q^{89} +(-0.115867 - 6.97568i) q^{90} +(4.99471 - 1.81771i) q^{91} +(-0.737974 + 1.27821i) q^{92} +(-11.1946 - 11.0102i) q^{93} +(4.47403 - 7.74925i) q^{94} +(2.55847 - 4.43140i) q^{95} +(-5.79253 - 5.69711i) q^{96} +(7.67728 - 13.2974i) q^{97} +(2.82557 + 16.0317i) q^{98} +(7.75588 + 4.30773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9} + q^{10} - 2 q^{11} - 16 q^{12} - 4 q^{13} - 13 q^{14} - q^{15} - 5 q^{16} - 7 q^{17} - 12 q^{18} - 2 q^{19} + 7 q^{20} - 5 q^{21} + 19 q^{22} - 2 q^{23} - 30 q^{24} + 24 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 3 q^{30} + 8 q^{31} + 17 q^{32} + q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} + 70 q^{38} - 8 q^{39} - 12 q^{40} + 20 q^{41} - 15 q^{42} + 31 q^{43} - 7 q^{44} - 9 q^{45} - 10 q^{46} - 31 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} - 37 q^{51} + 8 q^{52} + 8 q^{53} + 111 q^{54} + 2 q^{55} + 45 q^{56} + 5 q^{57} - 90 q^{58} - 21 q^{59} + 16 q^{60} + 5 q^{61} + 14 q^{62} - 9 q^{63} - 56 q^{64} + 4 q^{65} + 46 q^{66} + 43 q^{67} + 96 q^{68} + 26 q^{69} + 13 q^{70} + 24 q^{71} - 69 q^{72} - 18 q^{73} - 18 q^{74} + q^{75} - 13 q^{76} + 5 q^{77} + 19 q^{78} + 40 q^{79} + 5 q^{80} - 39 q^{81} + 5 q^{82} - 60 q^{83} + 47 q^{84} + 7 q^{85} - 24 q^{86} - 61 q^{87} - 100 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} - 8 q^{93} - 11 q^{94} + 2 q^{95} + 6 q^{96} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9 + q^10 - 2 * q^11 - 16 * q^12 - 4 * q^13 - 13 * q^14 - q^15 - 5 * q^16 - 7 * q^17 - 12 * q^18 - 2 * q^19 + 7 * q^20 - 5 * q^21 + 19 * q^22 - 2 * q^23 - 30 * q^24 + 24 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 3 * q^30 + 8 * q^31 + 17 * q^32 + q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 + 70 * q^38 - 8 * q^39 - 12 * q^40 + 20 * q^41 - 15 * q^42 + 31 * q^43 - 7 * q^44 - 9 * q^45 - 10 * q^46 - 31 * q^47 - 36 * q^48 - 11 * q^49 - q^50 - 37 * q^51 + 8 * q^52 + 8 * q^53 + 111 * q^54 + 2 * q^55 + 45 * q^56 + 5 * q^57 - 90 * q^58 - 21 * q^59 + 16 * q^60 + 5 * q^61 + 14 * q^62 - 9 * q^63 - 56 * q^64 + 4 * q^65 + 46 * q^66 + 43 * q^67 + 96 * q^68 + 26 * q^69 + 13 * q^70 + 24 * q^71 - 69 * q^72 - 18 * q^73 - 18 * q^74 + q^75 - 13 * q^76 + 5 * q^77 + 19 * q^78 + 40 * q^79 + 5 * q^80 - 39 * q^81 + 5 * q^82 - 60 * q^83 + 47 * q^84 + 7 * q^85 - 24 * q^86 - 61 * q^87 - 100 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 - 8 * q^93 - 11 * q^94 + 2 * q^95 + 6 * q^96 + 6 * q^97 - 15 * q^98 - q^99

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