LMFDB - Embedded newform 315.2.i.d.106.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(106,315)]

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, 0]))

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

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

chi := DirichletCharacter("315.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			106.2
Root			$0.669131 + 0.743145i$ of defining polynomial
Character	$\chi$	$=$	315.106
Dual form			315.2.i.d.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 + 0.181049i) q^{2} +(-1.28716 - 1.15897i) q^{3} +(0.978148 + 1.69420i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.344375 - 0.111894i) q^{6} +(0.500000 - 0.866025i) q^{7} -0.827091 q^{8} +(0.313585 + 2.98357i) q^{9} +O(q^{10})$	\(q+(-0.104528 + 0.181049i) q^{2} +(-1.28716 - 1.15897i) q^{3} +(0.978148 + 1.69420i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.344375 - 0.111894i) q^{6} +(0.500000 - 0.866025i) q^{7} -0.827091 q^{8} +(0.313585 + 2.98357i) q^{9} -0.209057 q^{10} +(-1.10453 + 1.91310i) q^{11} +(0.704489 - 3.31436i) q^{12} +(1.24441 + 2.15539i) q^{13} +(0.104528 + 0.181049i) q^{14} +(0.360114 - 1.69420i) q^{15} +(-1.86984 + 3.23866i) q^{16} -0.209057 q^{17} +(-0.572949 - 0.255093i) q^{18} +7.22851 q^{19} +(-0.978148 + 1.69420i) q^{20} +(-1.64728 + 0.535233i) q^{21} +(-0.230909 - 0.399947i) q^{22} +(1.42928 + 2.47559i) q^{23} +(1.06460 + 0.958572i) q^{24} +(-0.500000 + 0.866025i) q^{25} -0.520307 q^{26} +(3.05422 - 4.20378i) q^{27} +1.95630 q^{28} +(-2.41637 + 4.18527i) q^{29} +(0.269091 + 0.242290i) q^{30} +(1.99165 + 3.44964i) q^{31} +(-1.21799 - 2.10963i) q^{32} +(3.63893 - 1.18236i) q^{33} +(0.0218524 - 0.0378495i) q^{34} +1.00000 q^{35} +(-4.74803 + 3.44964i) q^{36} +0.739681 q^{37} +(-0.755585 + 1.30871i) q^{38} +(0.896261 - 4.21658i) q^{39} +(-0.413545 - 0.716282i) q^{40} +(-1.09714 - 1.90030i) q^{41} +(0.0752842 - 0.354185i) q^{42} +(2.65185 - 4.59313i) q^{43} -4.32157 q^{44} +(-2.42705 + 1.76336i) q^{45} -0.597604 q^{46} +(4.30757 - 7.46094i) q^{47} +(6.16030 - 2.00160i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.104528 - 0.181049i) q^{50} +(0.269091 + 0.242290i) q^{51} +(-2.43444 + 4.21658i) q^{52} -7.93863 q^{53} +(0.441835 + 0.992377i) q^{54} -2.20906 q^{55} +(-0.413545 + 0.716282i) q^{56} +(-9.30428 - 8.37761i) q^{57} +(-0.505159 - 0.874960i) q^{58} +(-7.01712 - 12.1540i) q^{59} +(3.22256 - 1.04707i) q^{60} +(-0.206824 + 0.358229i) q^{61} -0.832738 q^{62} +(2.74064 + 1.22021i) q^{63} -6.97010 q^{64} +(-1.24441 + 2.15539i) q^{65} +(-0.166307 + 0.782414i) q^{66} +(2.19098 + 3.79489i) q^{67} +(-0.204489 - 0.354185i) q^{68} +(1.02941 - 4.84299i) q^{69} +(-0.104528 + 0.181049i) q^{70} -8.07039 q^{71} +(-0.259364 - 2.46768i) q^{72} -16.0446 q^{73} +(-0.0773178 + 0.133918i) q^{74} +(1.64728 - 0.535233i) q^{75} +(7.07055 + 12.2466i) q^{76} +(1.10453 + 1.91310i) q^{77} +(0.669721 + 0.603019i) q^{78} +(7.86101 - 13.6157i) q^{79} -3.73968 q^{80} +(-8.80333 + 1.87121i) q^{81} +0.458728 q^{82} +(-1.56365 + 2.70832i) q^{83} +(-2.51807 - 2.26728i) q^{84} +(-0.104528 - 0.181049i) q^{85} +(0.554387 + 0.960226i) q^{86} +(7.96086 - 2.58664i) q^{87} +(0.913545 - 1.58231i) q^{88} +10.1477 q^{89} +(-0.0655572 - 0.623735i) q^{90} +2.48883 q^{91} +(-2.79610 + 4.84299i) q^{92} +(1.43444 - 6.74852i) q^{93} +(0.900528 + 1.55976i) q^{94} +(3.61426 + 6.26007i) q^{95} +(-0.877232 + 4.12705i) q^{96} +(5.95300 - 10.3109i) q^{97} +0.209057 q^{98} +(-6.05422 - 2.69551i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 8 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + 4 * q^7 + 6 * q^8 - 3 * q^9	$ 8 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{9} + 2 q^{10} - 7 q^{11} + 3 q^{12} + 8 q^{13} - q^{14} + 3 q^{15} + 9 q^{16} + 2 q^{17} - 18 q^{18} + 6 q^{19} + q^{20} - 7 q^{22} + 8 q^{23} + 6 q^{24} - 4 q^{25} - 6 q^{26} - 2 q^{28} - q^{29} - 3 q^{30} + 9 q^{34} + 8 q^{35} - 6 q^{36} - 42 q^{37} - 8 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} + 3 q^{42} + 7 q^{43} + 6 q^{44} - 6 q^{45} - 46 q^{46} + 2 q^{47} + 30 q^{48} - 4 q^{49} + q^{50} - 3 q^{51} + 7 q^{52} - 16 q^{53} - 36 q^{54} - 14 q^{55} + 3 q^{56} - 24 q^{57} + 19 q^{58} - 19 q^{59} + 15 q^{60} + 12 q^{61} + 30 q^{62} + 3 q^{63} - 14 q^{64} - 8 q^{65} - 9 q^{66} + 22 q^{67} + q^{68} + 51 q^{69} + q^{70} + 26 q^{71} - 21 q^{72} - 8 q^{73} - 9 q^{74} + 13 q^{76} + 7 q^{77} - 21 q^{78} + 24 q^{79} + 18 q^{80} + 9 q^{81} + 19 q^{83} - 12 q^{84} + q^{85} + 27 q^{86} + 45 q^{87} + q^{88} + 30 q^{89} - 27 q^{90} + 16 q^{91} - 3 q^{92} - 15 q^{93} + 7 q^{94} + 3 q^{95} + 30 q^{96} + 12 q^{97} - 2 q^{98} - 24 q^{99}+O(q^{100}) $ 8 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + 4 * q^7 + 6 * q^8 - 3 * q^9 + 2 * q^10 - 7 * q^11 + 3 * q^12 + 8 * q^13 - q^14 + 3 * q^15 + 9 * q^16 + 2 * q^17 - 18 * q^18 + 6 * q^19 + q^20 - 7 * q^22 + 8 * q^23 + 6 * q^24 - 4 * q^25 - 6 * q^26 - 2 * q^28 - q^29 - 3 * q^30 + 9 * q^34 + 8 * q^35 - 6 * q^36 - 42 * q^37 - 8 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 + 3 * q^42 + 7 * q^43 + 6 * q^44 - 6 * q^45 - 46 * q^46 + 2 * q^47 + 30 * q^48 - 4 * q^49 + q^50 - 3 * q^51 + 7 * q^52 - 16 * q^53 - 36 * q^54 - 14 * q^55 + 3 * q^56 - 24 * q^57 + 19 * q^58 - 19 * q^59 + 15 * q^60 + 12 * q^61 + 30 * q^62 + 3 * q^63 - 14 * q^64 - 8 * q^65 - 9 * q^66 + 22 * q^67 + q^68 + 51 * q^69 + q^70 + 26 * q^71 - 21 * q^72 - 8 * q^73 - 9 * q^74 + 13 * q^76 + 7 * q^77 - 21 * q^78 + 24 * q^79 + 18 * q^80 + 9 * q^81 + 19 * q^83 - 12 * q^84 + q^85 + 27 * q^86 + 45 * q^87 + q^88 + 30 * q^89 - 27 * q^90 + 16 * q^91 - 3 * q^92 - 15 * q^93 + 7 * q^94 + 3 * q^95 + 30 * q^96 + 12 * q^97 - 2 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.104528	+	0.181049i	−0.0739128	+	0.128021i	−0.900613	−	0.434622i	$-0.856882\pi$
$2$	−0.104528	+	0.181049i	−0.0739128	+	0.128021i	0.826700	+	0.562643i	$0.190215\pi$
$3$	−1.28716	−	1.15897i	−0.743145	−	0.669131i
$3$	−1.28716	−	1.15897i	−0.743145	−	0.669131i
$4$	0.978148	+	1.69420i	0.489074	+	0.847101i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.344375	−	0.111894i	0.140590	−	0.0456806i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−0.827091			−0.292421
$9$	0.313585	+	2.98357i	0.104528	+	0.994522i
$10$	−0.209057			−0.0661096
$11$	−1.10453	+	1.91310i	−0.333028	+	0.576821i	−0.983104	−	0.183048i	$-0.941404\pi$
$11$	−1.10453	+	1.91310i	−0.333028	+	0.576821i	0.650076	+	0.759869i	$0.274737\pi$
$12$	0.704489	−	3.31436i	0.203368	−	0.956773i
$13$	1.24441	+	2.15539i	0.345139	+	0.597798i	0.985379	−	0.170377i	$-0.0544986\pi$
$13$	1.24441	+	2.15539i	0.345139	+	0.597798i	−0.640240	+	0.768175i	$0.721165\pi$
$14$	0.104528	+	0.181049i	0.0279364	+	0.0483873i
$15$	0.360114	−	1.69420i	0.0929809	−	0.437441i
$16$	−1.86984	+	3.23866i	−0.467460	+	0.809665i
$17$	−0.209057			−0.0507038			−0.0253519	−	0.999679i	$-0.508071\pi$
$17$	−0.209057			−0.0507038			−0.0253519	+	0.999679i	$0.508071\pi$
$18$	−0.572949	−	0.255093i	−0.135045	−	0.0601261i
$19$	7.22851			1.65833			0.829167	−	0.559001i	$-0.188815\pi$
$19$	7.22851			1.65833			0.829167	+	0.559001i	$0.188815\pi$
$20$	−0.978148	+	1.69420i	−0.218720	+	0.378835i
$21$	−1.64728	+	0.535233i	−0.359466	+	0.116797i
$22$	−0.230909	−	0.399947i	−0.0492300	−	0.0852689i
$23$	1.42928	+	2.47559i	0.298026	+	0.516197i	0.975684	−	0.219180i	$-0.0703383\pi$
$23$	1.42928	+	2.47559i	0.298026	+	0.516197i	−0.677658	+	0.735377i	$0.737005\pi$
$24$	1.06460	+	0.958572i	0.217311	+	0.195668i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.520307			−0.102041
$27$	3.05422	−	4.20378i	0.587785	−	0.809017i
$28$	1.95630			0.369705
$29$	−2.41637	+	4.18527i	−0.448708	+	0.777186i	−0.998302	−	0.0582462i	$-0.981449\pi$
$29$	−2.41637	+	4.18527i	−0.448708	+	0.777186i	0.549594	+	0.835432i	$0.314782\pi$
$30$	0.269091	+	0.242290i	0.0491290	+	0.0442360i
$31$	1.99165	+	3.44964i	0.357711	+	0.619574i	0.987578	−	0.157129i	$-0.0502238\pi$
$31$	1.99165	+	3.44964i	0.357711	+	0.619574i	−0.629867	+	0.776703i	$0.716890\pi$
$32$	−1.21799	−	2.10963i	−0.215313	−	0.372933i
$33$	3.63893	−	1.18236i	0.633457	−	0.205823i
$34$	0.0218524	−	0.0378495i	0.00374766	−	0.00649113i
$35$	1.00000			0.169031
$36$	−4.74803	+	3.44964i	−0.791338	+	0.574941i
$37$	0.739681			0.121603			0.0608014	−	0.998150i	$-0.480634\pi$
$37$	0.739681			0.121603			0.0608014	+	0.998150i	$0.480634\pi$
$38$	−0.755585	+	1.30871i	−0.122572	+	0.212301i
$39$	0.896261	−	4.21658i	0.143517	−	0.675193i
$40$	−0.413545	−	0.716282i	−0.0653873	−	0.113254i
$41$	−1.09714	−	1.90030i	−0.171344	−	0.296776i	0.767546	−	0.640994i	$-0.221478\pi$
$41$	−1.09714	−	1.90030i	−0.171344	−	0.296776i	−0.938890	+	0.344217i	$0.888144\pi$
$42$	0.0752842	−	0.354185i	0.0116166	−	0.0546519i
$43$	2.65185	−	4.59313i	0.404403	−	0.700446i	−0.589849	−	0.807514i	$-0.700813\pi$
$43$	2.65185	−	4.59313i	0.404403	−	0.700446i	0.994252	+	0.107067i	$0.0341461\pi$
$44$	−4.32157			−0.651501
$45$	−2.42705	+	1.76336i	−0.361803	+	0.262866i
$46$	−0.597604			−0.0881118
$47$	4.30757	−	7.46094i	0.628324	−	1.08829i	−0.359564	−	0.933121i	$-0.617074\pi$
$47$	4.30757	−	7.46094i	0.628324	−	1.08829i	0.987888	−	0.155169i	$-0.0495922\pi$
$48$	6.16030	−	2.00160i	0.889162	−	0.288906i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−0.104528	−	0.181049i	−0.0147826	−	0.0256041i
$51$	0.269091	+	0.242290i	0.0376802	+	0.0339274i
$52$	−2.43444	+	4.21658i	−0.337596	+	0.584734i
$53$	−7.93863			−1.09045			−0.545227	−	0.838288i	$-0.683557\pi$
$53$	−7.93863			−1.09045			−0.545227	+	0.838288i	$0.683557\pi$
$54$	0.441835	+	0.992377i	0.0601261	+	0.135045i
$55$	−2.20906			−0.297869
$56$	−0.413545	+	0.716282i	−0.0552623	+	0.0957172i
$57$	−9.30428	−	8.37761i	−1.23238	−	1.10964i
$58$	−0.505159	−	0.874960i	−0.0663306	−	0.114888i
$59$	−7.01712	−	12.1540i	−0.913551	−	1.58232i	−0.809009	−	0.587796i	$-0.799996\pi$
$59$	−7.01712	−	12.1540i	−0.913551	−	1.58232i	−0.104542	−	0.994520i	$-0.533338\pi$
$60$	3.22256	−	1.04707i	0.416031	−	0.135177i
$61$	−0.206824	+	0.358229i	−0.0264811	+	0.0458666i	−0.878962	−	0.476891i	$-0.841764\pi$
$61$	−0.206824	+	0.358229i	−0.0264811	+	0.0458666i	0.852481	+	0.522758i	$0.175097\pi$
$62$	−0.832738			−0.105758
$63$	2.74064	+	1.22021i	0.345288	+	0.153732i
$64$	−6.97010			−0.871263
$65$	−1.24441	+	2.15539i	−0.154351	+	0.267343i
$66$	−0.166307	+	0.782414i	−0.0204710	+	0.0963085i
$67$	2.19098	+	3.79489i	0.267671	+	0.463620i	0.968260	−	0.249945i	$-0.0804126\pi$
$67$	2.19098	+	3.79489i	0.267671	+	0.463620i	−0.700589	+	0.713565i	$0.747079\pi$
$68$	−0.204489	−	0.354185i	−0.0247979	−	0.0429512i
$69$	1.02941	−	4.84299i	0.123926	−	0.583028i
$70$	−0.104528	+	0.181049i	−0.0124935	+	0.0216394i
$71$	−8.07039			−0.957779			−0.478889	−	0.877875i	$-0.658960\pi$
$71$	−8.07039			−0.957779			−0.478889	+	0.877875i	$0.658960\pi$
$72$	−0.259364	−	2.46768i	−0.0305663	−	0.290819i
$73$	−16.0446			−1.87787			−0.938937	−	0.344090i	$-0.888187\pi$
$73$	−16.0446			−1.87787			−0.938937	+	0.344090i	$0.888187\pi$
$74$	−0.0773178	+	0.133918i	−0.00898801	+	0.0155677i
$75$	1.64728	−	0.535233i	0.190211	−	0.0618034i
$76$	7.07055	+	12.2466i	0.811048	+	1.40478i
$77$	1.10453	+	1.91310i	0.125873	+	0.218018i
$78$	0.669721	+	0.603019i	0.0758310	+	0.0682785i
$79$	7.86101	−	13.6157i	0.884432	−	1.53188i	0.0380692	−	0.999275i	$-0.487879\pi$
$79$	7.86101	−	13.6157i	0.884432	−	1.53188i	0.846363	−	0.532606i	$-0.178787\pi$
$80$	−3.73968			−0.418109
$81$	−8.80333	+	1.87121i	−0.978148	+	0.207912i
$82$	0.458728			0.0506580
$83$	−1.56365	+	2.70832i	−0.171633	+	0.297276i	−0.938991	−	0.343942i	$-0.888238\pi$
$83$	−1.56365	+	2.70832i	−0.171633	+	0.297276i	0.767358	+	0.641219i	$0.221571\pi$
$84$	−2.51807	−	2.26728i	−0.274744	−	0.247381i
$85$	−0.104528	−	0.181049i	−0.0113377	−	0.0196375i
$86$	0.554387	+	0.960226i	0.0597811	+	0.103544i
$87$	7.96086	−	2.58664i	0.853494	−	0.277317i
$88$	0.913545	−	1.58231i	0.0973843	−	0.168675i
$89$	10.1477			1.07565			0.537826	−	0.843056i	$-0.319246\pi$
$89$	10.1477			1.07565			0.537826	+	0.843056i	$0.319246\pi$
$90$	−0.0655572	−	0.623735i	−0.00691034	−	0.0657474i
$91$	2.48883			0.260900
$92$	−2.79610	+	4.84299i	−0.291514	+	0.504917i
$93$	1.43444	−	6.74852i	0.148745	−	0.699789i
$94$	0.900528	+	1.55976i	0.0928824	+	0.160877i
$95$	3.61426	+	6.26007i	0.370815	+	0.642270i
$96$	−0.877232	+	4.12705i	−0.0895322	+	0.421216i
$97$	5.95300	−	10.3109i	0.604436	−	1.04691i	−0.387704	−	0.921784i	$-0.626732\pi$
$97$	5.95300	−	10.3109i	0.604436	−	1.04691i	0.992140	−	0.125130i	$-0.0399348\pi$
$98$	0.209057			0.0211179
$99$	−6.05422	−	2.69551i	−0.608472	−	0.270909i
$100$	−1.95630			−0.195630
$101$	5.73357	−	9.93083i	0.570511	−	0.988155i	−0.426002	−	0.904722i	$-0.640078\pi$
$101$	5.73357	−	9.93083i	0.570511	−	0.988155i	0.996513	−	0.0834324i	$-0.0265883\pi$
$102$	−0.0719940	+	0.0233923i	−0.00712846	+	0.00231618i
$103$	−2.69663	−	4.67070i	−0.265707	−	0.460218i	0.702042	−	0.712136i	$-0.252272\pi$
$103$	−2.69663	−	4.67070i	−0.265707	−	0.460218i	−0.967749	+	0.251918i	$0.918939\pi$
$104$	−1.02924	−	1.78270i	−0.100926	−	0.174808i
$105$	−1.28716	−	1.15897i	−0.125614	−	0.113104i
$106$	0.829812	−	1.43728i	0.0805985	−	0.139601i
$107$	17.6475			1.70605			0.853023	−	0.521873i	$-0.174767\pi$
$107$	17.6475			1.70605			0.853023	+	0.521873i	$0.174767\pi$
$108$	10.1095	+	1.06255i	0.972789	+	0.102244i
$109$	7.37559			0.706453			0.353227	−	0.935538i	$-0.385084\pi$
$109$	7.37559			0.706453			0.353227	+	0.935538i	$0.385084\pi$
$110$	0.230909	−	0.399947i	0.0220163	−	0.0381334i
$111$	−0.952092	−	0.857267i	−0.0903685	−	0.0813682i
$112$	1.86984	+	3.23866i	0.176683	+	0.306025i
$113$	6.77553	+	11.7356i	0.637388	+	1.10399i	0.986004	+	0.166723i	$0.0533185\pi$
$113$	6.77553	+	11.7356i	0.637388	+	1.10399i	−0.348616	+	0.937266i	$0.613348\pi$
$114$	2.48932	−	0.808828i	0.233146	−	0.0757537i
$115$	−1.42928	+	2.47559i	−0.133281	+	0.230850i
$116$	−9.45426			−0.877806
$117$	−6.04052	+	4.38869i	−0.558446	+	0.405735i
$118$	2.93395			0.270092
$119$	−0.104528	+	0.181049i	−0.00958211	+	0.0165967i
$120$	−0.297847	+	1.40126i	−0.0271896	+	0.127917i
$121$	3.06003	+	5.30013i	0.278185	+	0.481830i
$122$	−0.0432379	−	0.0748903i	−0.00391458	−	0.00678025i
$123$	−0.790188	+	3.71754i	−0.0712488	+	0.335199i
$124$	−3.89626	+	6.74852i	−0.349895	+	0.606035i
$125$	−1.00000			−0.0894427
$126$	−0.507392	+	0.368642i	−0.0452021	+	0.0328412i
$127$	−7.93802			−0.704386			−0.352193	−	0.935927i	$-0.614564\pi$
$127$	−7.93802			−0.704386			−0.352193	+	0.935927i	$0.614564\pi$
$128$	3.16456	−	5.48118i	0.279710	−	0.484473i
$129$	−8.73666	+	2.83871i	−0.769220	+	0.249935i
$130$	−0.260154	−	0.450599i	−0.0228170	−	0.0395202i
$131$	6.96379	+	12.0616i	0.608429	+	1.05383i	0.991499	+	0.130111i	$0.0415333\pi$
$131$	6.96379	+	12.0616i	0.608429	+	1.05383i	−0.383070	+	0.923719i	$0.625133\pi$
$132$	5.56257	+	5.00856i	0.484159	+	0.435939i
$133$	3.61426	−	6.26007i	0.313396	−	0.542817i
$134$	−0.916080			−0.0791373
$135$	5.16769	+	0.543146i	0.444764	+	0.0467465i
$136$	0.172909			0.0148268
$137$	−1.35867	+	2.35329i	−0.116079	+	0.201055i	−0.918211	−	0.396093i	$-0.870366\pi$
$137$	−1.35867	+	2.35329i	−0.116079	+	0.201055i	0.802132	+	0.597147i	$0.203699\pi$
$138$	0.769214	+	0.692603i	0.0654799	+	0.0589583i
$139$	1.02264	+	1.77127i	0.0867394	+	0.150237i	0.906131	−	0.422997i	$-0.139022\pi$
$139$	1.02264	+	1.77127i	0.0867394	+	0.150237i	−0.819392	+	0.573234i	$0.805689\pi$
$140$	0.978148	+	1.69420i	0.0826686	+	0.143186i
$141$	−14.1915	+	4.61111i	−1.19514	+	0.388326i
$142$	0.843585	−	1.46113i	0.0707921	−	0.122615i
$143$	−5.49797			−0.459763
$144$	−10.2491	−	4.56320i	−0.854092	−	0.380266i
$145$	−4.83274			−0.401337
$146$	1.67711	−	2.90484i	0.138799	−	0.240407i
$147$	−0.360114	+	1.69420i	−0.0297017	+	0.139735i
$148$	0.723518	+	1.25317i	0.0594728	+	0.103010i
$149$	−1.64212	−	2.84423i	−0.134528	−	0.233009i	0.790889	−	0.611959i	$-0.209618\pi$
$149$	−1.64212	−	2.84423i	−0.134528	−	0.233009i	−0.925417	+	0.378951i	$0.876285\pi$
$150$	−0.0752842	+	0.354185i	−0.00614693	+	0.0289190i
$151$	1.11724	−	1.93512i	0.0909200	−	0.157478i	−0.816978	−	0.576668i	$-0.804353\pi$
$151$	1.11724	−	1.93512i	0.0909200	−	0.157478i	0.907899	+	0.419190i	$0.137686\pi$
$152$	−5.97864			−0.484931
$153$	−0.0655572	−	0.623735i	−0.00529999	−	0.0504260i
$154$	−0.461819			−0.0372144
$155$	−1.99165	+	3.44964i	−0.159973	+	0.277082i
$156$	8.02041	−	2.60599i	0.642147	−	0.208646i
$157$	0.375062	+	0.649627i	0.0299332	+	0.0518459i	0.880604	−	0.473853i	$-0.157137\pi$
$157$	0.375062	+	0.649627i	0.0299332	+	0.0518459i	−0.850671	+	0.525699i	$0.823804\pi$
$158$	1.64340	+	2.84645i	0.130742	+	0.226451i
$159$	10.2183	+	9.20061i	0.810365	+	0.729656i
$160$	1.21799	−	2.10963i	0.0962909	−	0.166781i
$161$	2.85857			0.225287
$162$	0.581419	−	1.78942i	0.0456806	−	0.140590i
$163$	−21.0896			−1.65187			−0.825934	−	0.563767i	$-0.809352\pi$
$163$	−21.0896			−1.65187			−0.825934	+	0.563767i	$0.809352\pi$
$164$	2.14632	−	3.71754i	0.167600	−	0.290291i
$165$	2.84342	+	2.56023i	0.221360	+	0.199313i
$166$	−0.326891	−	0.566192i	−0.0253717	−	0.0439450i
$167$	−2.47437	−	4.28573i	−0.191472	−	0.331640i	0.754266	−	0.656569i	$-0.227993\pi$
$167$	−2.47437	−	4.28573i	−0.191472	−	0.331640i	−0.945738	+	0.324929i	$0.894660\pi$
$168$	1.36245	−	0.442686i	0.105115	−	0.0341540i
$169$	3.40286	−	5.89393i	0.261759	−	0.453379i
$170$	0.0437048			0.00335201
$171$	2.26676	+	21.5667i	0.173343	+	1.64925i
$172$	10.3756			0.791131
$173$	−8.56756	+	14.8395i	−0.651380	+	1.12822i	0.331409	+	0.943487i	$0.392476\pi$
$173$	−8.56756	+	14.8395i	−0.651380	+	1.12822i	−0.982788	+	0.184735i	$0.940857\pi$
$174$	−0.363829	+	1.71168i	−0.0275818	+	0.129762i
$175$	0.500000	+	0.866025i	0.0377964	+	0.0654654i
$176$	−4.13058	−	7.15438i	−0.311355	−	0.539282i
$177$	−5.05392	+	23.7768i	−0.379876	+	1.78718i
$178$	−1.06072	+	1.83722i	−0.0795044	+	0.137706i
$179$	22.4030			1.67448			0.837239	−	0.546837i	$-0.184168\pi$
$179$	22.4030			1.67448			0.837239	+	0.546837i	$0.184168\pi$
$180$	−5.36149	−	2.38709i	−0.399622	−	0.177923i
$181$	−5.69164			−0.423056			−0.211528	−	0.977372i	$-0.567844\pi$
$181$	−5.69164			−0.423056			−0.211528	+	0.977372i	$0.567844\pi$
$182$	−0.260154	+	0.450599i	−0.0192839	+	0.0334006i
$183$	0.681393	−	0.221398i	0.0503700	−	0.0163662i
$184$	−1.18215	−	2.04754i	−0.0871491	−	0.150947i
$185$	0.369841	+	0.640583i	0.0271912	+	0.0470966i
$186$	1.07187	+	0.965117i	0.0785934	+	0.0707658i
$187$	0.230909	−	0.399947i	0.0168858	−	0.0292470i
$188$	16.8538			1.22919
$189$	−2.11347	−	4.74692i	−0.153732	−	0.345288i
$190$	−1.51117			−0.109632
$191$	12.0980	−	20.9544i	0.875384	−	1.51621i	0.0190312	−	0.999819i	$-0.493942\pi$
$191$	12.0980	−	20.9544i	0.875384	−	1.51621i	0.856353	−	0.516391i	$-0.172725\pi$
$192$	8.97167	+	8.07813i	0.647474	+	0.582989i
$193$	−10.0583	−	17.4215i	−0.724014	−	1.25403i	−0.959379	−	0.282122i	$-0.908962\pi$
$193$	−10.0583	−	17.4215i	−0.724014	−	1.25403i	0.235365	−	0.971907i	$-0.424372\pi$
$194$	1.24452	+	2.15557i	0.0893511	+	0.154761i
$195$	4.09979	−	1.33210i	0.293592	−	0.0953940i
$196$	0.978148	−	1.69420i	0.0698677	−	0.121014i
$197$	2.57340			0.183347			0.0916734	−	0.995789i	$-0.470778\pi$
$197$	2.57340			0.183347			0.0916734	+	0.995789i	$0.470778\pi$
$198$	1.12086	−	0.814351i	0.0796559	−	0.0578734i
$199$	−24.5589			−1.74093			−0.870467	−	0.492227i	$-0.836183\pi$
$199$	−24.5589			−1.74093			−0.870467	+	0.492227i	$0.836183\pi$
$200$	0.413545	−	0.716282i	0.0292421	−	0.0506488i
$201$	1.57801	−	7.42393i	0.111304	−	0.523644i
$202$	1.19864	+	2.07611i	0.0843362	+	0.146075i
$203$	2.41637	+	4.18527i	0.169596	+	0.293749i
$204$	−0.147278	+	0.692889i	−0.0103115	+	0.0485120i
$205$	1.09714	−	1.90030i	0.0766273	−	0.132722i
$206$	1.12750			0.0785565
$207$	−6.93789	+	5.04067i	−0.482217	+	0.350351i
$208$	−9.30743			−0.645354
$209$	−7.98410	+	13.8289i	−0.552271	+	0.956562i
$210$	0.344375	−	0.111894i	0.0237641	−	0.00772143i
$211$	5.97825	+	10.3546i	0.411560	+	0.712842i	0.995061	−	0.0992703i	$-0.0316508\pi$
$211$	5.97825	+	10.3546i	0.411560	+	0.712842i	−0.583501	+	0.812113i	$0.698318\pi$
$212$	−7.76515	−	13.4496i	−0.533312	−	0.923724i
$213$	10.3879	+	9.35332i	0.711768	+	0.640879i
$214$	−1.84466	+	3.19505i	−0.126099	+	0.218409i
$215$	5.30369			0.361709
$216$	−2.52612	+	3.47690i	−0.171881	+	0.236573i
$217$	3.98331			0.270404
$218$	−0.770959	+	1.33534i	−0.0522159	+	0.0904407i
$219$	20.6520	+	18.5951i	1.39553	+	1.25654i
$220$	−2.16078	−	3.74259i	−0.145680	−	0.252325i
$221$	−0.260154	−	0.450599i	−0.0174998	−	0.0303106i
$222$	0.254728	−	0.0827660i	0.0170962	−	0.00555489i
$223$	3.40424	−	5.89632i	0.227965	−	0.394847i	−0.729240	−	0.684258i	$-0.760126\pi$
$223$	3.40424	−	5.89632i	0.227965	−	0.394847i	0.957205	+	0.289411i	$0.0934595\pi$
$224$	−2.43599			−0.162761
$225$	−2.74064	−	1.22021i	−0.182709	−	0.0813473i
$226$	−2.83294			−0.188444
$227$	10.0236	−	17.3613i	0.665287	−	1.15231i	−0.313921	−	0.949449i	$-0.601643\pi$
$227$	10.0236	−	17.3613i	0.665287	−	1.15231i	0.979207	−	0.202861i	$-0.0650240\pi$
$228$	5.09240	−	23.9579i	0.337253	−	1.58665i
$229$	10.6324	+	18.4159i	0.702611	+	1.21696i	0.967547	+	0.252692i	$0.0813158\pi$
$229$	10.6324	+	18.4159i	0.702611	+	1.21696i	−0.264936	+	0.964266i	$0.585351\pi$
$230$	−0.298802	−	0.517540i	−0.0197024	−	0.0341256i
$231$	0.795511	−	3.74259i	0.0523408	−	0.246244i
$232$	1.99856	−	3.46160i	0.131212	−	0.227265i
$233$	−5.44631			−0.356799			−0.178400	−	0.983958i	$-0.557092\pi$
$233$	−5.44631			−0.356799			−0.178400	+	0.983958i	$0.557092\pi$
$234$	−0.163161	−	1.55237i	−0.0106661	−	0.101482i
$235$	8.61515			0.561990
$236$	13.7276	−	23.7768i	0.893588	−	1.54774i
$237$	−25.8985	+	8.41494i	−1.68229	+	0.546609i
$238$	−0.0218524	−	0.0378495i	−0.00141648	−	0.00245342i
$239$	9.33432	+	16.1675i	0.603787	+	1.04579i	0.992242	+	0.124322i	$0.0396755\pi$
$239$	9.33432	+	16.1675i	0.603787	+	1.04579i	−0.388455	+	0.921468i	$0.626991\pi$
$240$	4.81359	+	4.33417i	0.310716	+	0.279770i
$241$	2.31671	−	4.01266i	0.149232	−	0.258478i	−0.781712	−	0.623640i	$-0.785653\pi$
$241$	2.31671	−	4.01266i	0.149232	−	0.258478i	0.930944	+	0.365162i	$0.118986\pi$
$242$	−1.27944			−0.0822457
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	−0.809217			−0.0518048
$245$	0.500000	−	0.866025i	0.0319438	−	0.0553283i
$246$	−0.590458	−	0.531651i	−0.0376463	−	0.0338968i
$247$	8.99527	+	15.5803i	0.572355	+	0.991348i
$248$	−1.64728	−	2.85317i	−0.104602	−	0.181176i
$249$	5.15152	−	1.67383i	0.326465	−	0.106075i
$250$	0.104528	−	0.181049i	0.00661096	−	0.0114505i
$251$	9.53378			0.601767			0.300884	−	0.953661i	$-0.402718\pi$
$251$	9.53378			0.601767			0.300884	+	0.953661i	$0.402718\pi$
$252$	0.613466	+	5.83674i	0.0386447	+	0.367680i
$253$	−6.31474			−0.397004
$254$	0.829749	−	1.43717i	0.0520631	−	0.0901759i
$255$	−0.0752842	+	0.354185i	−0.00471448	+	0.0221799i
$256$	−6.30853	−	10.9267i	−0.394283	−	0.682918i
$257$	−15.1971	−	26.3221i	−0.947967	−	1.64193i	−0.749699	−	0.661779i	$-0.769802\pi$
$257$	−15.1971	−	26.3221i	−0.947967	−	1.64193i	−0.198268	−	0.980148i	$-0.563532\pi$
$258$	0.399285	−	1.87849i	0.0248584	−	0.116949i
$259$	0.369841	−	0.640583i	0.0229808	−	0.0398039i
$260$	−4.86889			−0.301955
$261$	−13.2448	−	5.89695i	−0.819831	−	0.365012i
$262$	−2.91166			−0.179883
$263$	−4.89433	+	8.47723i	−0.301797	+	0.522728i	−0.976543	−	0.215322i	$-0.930920\pi$
$263$	−4.89433	+	8.47723i	−0.301797	+	0.522728i	0.674746	+	0.738050i	$0.264253\pi$
$264$	−3.00973	+	0.977920i	−0.185236	+	0.0601868i
$265$	−3.96931	−	6.87505i	−0.243833	−	0.422331i
$266$	0.755585	+	1.30871i	0.0463279	+	0.0802423i
$267$	−13.0617	−	11.7608i	−0.799365	−	0.719752i
$268$	−4.28621	+	7.42393i	−0.261822	+	0.453489i
$269$	23.2210			1.41581			0.707903	−	0.706309i	$-0.249641\pi$
$269$	23.2210			1.41581			0.707903	+	0.706309i	$0.249641\pi$
$270$	−0.638506	+	0.878828i	−0.0388583	+	0.0534838i
$271$	−3.68277			−0.223713			−0.111856	−	0.993724i	$-0.535680\pi$
$271$	−3.68277			−0.223713			−0.111856	+	0.993724i	$0.535680\pi$
$272$	0.390903	−	0.677064i	0.0237020	−	0.0410530i
$273$	−3.20353	−	2.88447i	−0.193887	−	0.174576i
$274$	−0.284039	−	0.491971i	−0.0171595	−	0.0297210i
$275$	−1.10453	−	1.91310i	−0.0666056	−	0.115364i
$276$	9.21191	−	2.99313i	0.554492	−	0.180165i
$277$	−1.61301	+	2.79382i	−0.0969165	+	0.167864i	−0.910407	−	0.413714i	$-0.864231\pi$
$277$	−1.61301	+	2.79382i	−0.0969165	+	0.167864i	0.813490	+	0.581578i	$0.197565\pi$
$278$	−0.427581			−0.0256446
$279$	−9.66769	+	7.02399i	−0.578789	+	0.420515i
$280$	−0.827091			−0.0494281
$281$	3.10670	−	5.38096i	0.185330	−	0.321001i	−0.758358	−	0.651839i	$-0.773998\pi$
$281$	3.10670	−	5.38096i	0.185330	−	0.321001i	0.943688	+	0.330838i	$0.107331\pi$
$282$	0.648585	−	3.05135i	0.0386227	−	0.181705i
$283$	−13.3210	−	23.0727i	−0.791852	−	1.37153i	−0.924819	−	0.380408i	$-0.875784\pi$
$283$	−13.3210	−	23.0727i	−0.791852	−	1.37153i	0.132967	−	0.991121i	$-0.457550\pi$
$284$	−7.89403	−	13.6729i	−0.468424	−	0.811335i
$285$	2.60309	−	12.2466i	0.154193	−	0.725423i
$286$	0.574694	−	0.995399i	0.0339824	−	0.0588592i
$287$	−2.19427			−0.129524
$288$	5.91227	−	4.29551i	0.348384	−	0.253116i
$289$	−16.9563			−0.997429
$290$	0.505159	−	0.874960i	0.0296639	−	0.0513794i
$291$	−19.6125	+	6.37249i	−1.14971	+	0.373562i
$292$	−15.6939	−	27.1827i	−0.918419	−	1.59075i
$293$	13.6507	+	23.6437i	0.797482	+	1.38128i	0.921251	+	0.388968i	$0.127168\pi$
$293$	13.6507	+	23.6437i	0.797482	+	1.38128i	−0.123769	+	0.992311i	$0.539498\pi$
$294$	−0.269091	−	0.242290i	−0.0156937	−	0.0141307i
$295$	7.01712	−	12.1540i	0.408552	−	0.707634i
$296$	−0.611784			−0.0355592
$297$	4.66877	+	10.4862i	0.270909	+	0.608472i
$298$	0.686593			0.0397733
$299$	−3.55724	+	6.16133i	−0.205721	+	0.356319i
$300$	2.51807	+	2.26728i	0.145381	+	0.130902i
$301$	−2.65185	−	4.59313i	−0.152850	−	0.264744i
$302$	0.233568	+	0.404551i	0.0134403	+	0.0232793i
$303$	−18.8896	+	6.13759i	−1.08518	+	0.352595i
$304$	−13.5162	+	23.4107i	−0.775205	+	1.34269i
$305$	−0.413648			−0.0236854
$306$	0.119779	+	0.0533290i	0.00684731	+	0.00304862i
$307$	−0.831362			−0.0474483			−0.0237242	−	0.999719i	$-0.507552\pi$
$307$	−0.831362			−0.0474483			−0.0237242	+	0.999719i	$0.507552\pi$
$308$	−2.16078	+	3.74259i	−0.123122	+	0.213254i
$309$	−1.94219	+	9.13727i	−0.110487	+	0.519801i
$310$	−0.416369	−	0.721172i	−0.0236482	−	0.0409598i
$311$	−13.3270	−	23.0831i	−0.755708	−	1.30892i	−0.945022	−	0.327007i	$-0.893960\pi$
$311$	−13.3270	−	23.0831i	−0.755708	−	1.30892i	0.189314	−	0.981917i	$-0.439374\pi$
$312$	−0.741290	+	3.48749i	−0.0419673	+	0.197440i
$313$	−1.74927	+	3.02983i	−0.0988747	+	0.171256i	−0.911219	−	0.411922i	$-0.864858\pi$
$313$	−1.74927	+	3.02983i	−0.0988747	+	0.171256i	0.812344	+	0.583178i	$0.198191\pi$
$314$	−0.156819			−0.00884980
$315$	0.313585	+	2.98357i	0.0176685	+	0.168105i
$316$	30.7569			1.73021
$317$	−7.22036	+	12.5060i	−0.405536	+	0.702409i	−0.994384	−	0.105835i	$-0.966248\pi$
$317$	−7.22036	+	12.5060i	−0.405536	+	0.702409i	0.588848	+	0.808244i	$0.299582\pi$
$318$	−2.73386	+	0.888286i	−0.153307	+	0.0498126i
$319$	−5.33790	−	9.24551i	−0.298865	−	0.517649i
$320$	−3.48505	−	6.03629i	−0.194820	−	0.337439i
$321$	−22.7152	−	20.4529i	−1.26784	−	1.14157i
$322$	−0.298802	+	0.517540i	−0.0166516	+	0.0288414i
$323$	−1.51117			−0.0840838
$324$	−11.7812	−	13.0843i	−0.654508	−	0.726905i
$325$	−2.48883			−0.138055
$326$	2.20447	−	3.81825i	0.122094	−	0.211473i
$327$	−9.49360	−	8.54807i	−0.524997	−	0.472710i
$328$	0.907432	+	1.57172i	0.0501045	+	0.0867836i
$329$	−4.30757	−	7.46094i	−0.237484	−	0.411335i
$330$	−0.760744	+	0.247181i	−0.0418776	+	0.0136068i
$331$	−2.69683	+	4.67105i	−0.148231	+	0.256744i	−0.930574	−	0.366104i	$-0.880691\pi$
$331$	−2.69683	+	4.67105i	−0.148231	+	0.256744i	0.782343	+	0.622848i	$0.214025\pi$
$332$	−6.11791			−0.335764
$333$	0.231953	+	2.20689i	0.0127110	+	0.120937i
$334$	1.03457			0.0566090
$335$	−2.19098	+	3.79489i	−0.119706	+	0.207337i
$336$	1.34671	−	6.33577i	0.0734691	−	0.345645i
$337$	5.83652	+	10.1091i	0.317935	+	0.550680i	0.980057	−	0.198716i	$-0.0636772\pi$
$337$	5.83652	+	10.1091i	0.317935	+	0.550680i	−0.662122	+	0.749396i	$0.730344\pi$
$338$	0.711392	+	1.23217i	0.0386946	+	0.0670211i
$339$	4.87992	−	22.9582i	0.265041	−	1.24692i
$340$	0.204489	−	0.354185i	0.0110899	−	0.0192084i
$341$	−8.79935			−0.476512
$342$	−4.14157	−	1.84395i	−0.223950	−	0.0997091i
$343$	−1.00000			−0.0539949
$344$	−2.19332	+	3.79894i	−0.118256	+	0.204825i
$345$	4.70886	−	1.53000i	0.253516	−	0.0823725i
$346$	−1.79111	−	3.10229i	−0.0962906	−	0.166780i
$347$	17.6064	+	30.4952i	0.945163	+	1.63707i	0.755425	+	0.655236i	$0.227431\pi$
$347$	17.6064	+	30.4952i	0.945163	+	1.63707i	0.189738	+	0.981835i	$0.439236\pi$
$348$	12.1692	+	10.9572i	0.652337	+	0.587367i
$349$	15.0792	−	26.1180i	0.807172	−	1.39806i	−0.107643	−	0.994190i	$-0.534330\pi$
$349$	15.0792	−	26.1180i	0.807172	−	1.39806i	0.914815	−	0.403874i	$-0.132336\pi$
$350$	−0.209057			−0.0111746
$351$	12.8615	+	1.35180i	0.686496	+	0.0721536i
$352$	5.38124			0.286821
$353$	1.44532	−	2.50338i	0.0769269	−	0.133241i	−0.824996	−	0.565139i	$-0.808823\pi$
$353$	1.44532	−	2.50338i	0.0769269	−	0.133241i	0.901923	+	0.431898i	$0.142156\pi$
$354$	−3.77648	−	3.40036i	−0.200718	−	0.180727i
$355$	−4.03519	−	6.98916i	−0.214166	−	0.370946i
$356$	9.92593	+	17.1922i	0.526073	+	0.911186i
$357$	0.344375	−	0.111894i	0.0182263	−	0.00592207i
$358$	−2.34175	+	4.05603i	−0.123765	+	0.214368i
$359$	−29.6466			−1.56469			−0.782345	−	0.622846i	$-0.785976\pi$
$359$	−29.6466			−1.56469			−0.782345	+	0.622846i	$0.785976\pi$
$360$	2.00739	−	1.45846i	0.105799	−	0.0768674i
$361$	33.2514			1.75007
$362$	0.594938	−	1.03046i	0.0312692	−	0.0541599i
$363$	2.20392	−	10.3686i	0.115676	−	0.544212i
$364$	2.43444	+	4.21658i	0.127599	+	0.221009i
$365$	−8.02228	−	13.8950i	−0.419905	−	0.727297i
$366$	−0.0311411	+	0.146508i	−0.00162777	+	0.00765807i
$367$	−13.6688	+	23.6751i	−0.713506	+	1.23583i	0.250028	+	0.968239i	$0.419560\pi$
$367$	−13.6688	+	23.6751i	−0.713506	+	1.23583i	−0.963533	+	0.267589i	$0.913773\pi$
$368$	−10.6901			−0.557262
$369$	5.32561	−	3.86928i	0.277240	−	0.201427i
$370$	−0.154636			−0.00803912
$371$	−3.96931	+	6.87505i	−0.206076	+	0.356935i
$372$	12.8365	−	4.17082i	0.665539	−	0.216247i
$373$	9.96619	+	17.2619i	0.516030	+	0.893790i	0.999827	+	0.0186094i	$0.00592390\pi$
$373$	9.96619	+	17.2619i	0.516030	+	0.893790i	−0.483797	+	0.875180i	$0.660743\pi$
$374$	0.0482732	+	0.0836116i	0.00249615	+	0.00432345i
$375$	1.28716	+	1.15897i	0.0664689	+	0.0598489i
$376$	−3.56276	+	6.17087i	−0.183735	+	0.318238i
$377$	−12.0279			−0.619466
$378$	1.08034	+	0.113548i	0.0555667	+	0.00584030i
$379$	21.2461			1.09134			0.545668	−	0.838001i	$-0.316276\pi$
$379$	21.2461			1.09134			0.545668	+	0.838001i	$0.316276\pi$
$380$	−7.07055	+	12.2466i	−0.362712	+	0.628235i
$381$	10.2175	+	9.19991i	0.523460	+	0.471326i
$382$	2.52918	+	4.38067i	0.129404	+	0.224135i
$383$	0.457904	+	0.793112i	0.0233978	+	0.0405261i	0.877487	−	0.479600i	$-0.159218\pi$
$383$	0.457904	+	0.793112i	0.0233978	+	0.0405261i	−0.854089	+	0.520126i	$0.825885\pi$
$384$	−10.4258	+	3.38756i	−0.532041	+	0.172871i
$385$	−1.10453	+	1.91310i	−0.0562920	+	0.0975006i
$386$	4.20552			0.214056
$387$	14.5355	+	6.47162i	0.738881	+	0.328971i
$388$	23.2917			1.18246
$389$	−12.2298	+	21.1826i	−0.620075	+	1.07400i	0.369396	+	0.929272i	$0.379564\pi$
$389$	−12.2298	+	21.1826i	−0.620075	+	1.07400i	−0.989471	+	0.144729i	$0.953769\pi$
$390$	−0.187370	+	0.881505i	−0.00948783	+	0.0446367i
$391$	−0.298802	−	0.517540i	−0.0151111	−	0.0261731i
$392$	0.413545	+	0.716282i	0.0208872	+	0.0361777i
$393$	5.01551	−	23.5961i	0.252999	−	1.19027i
$394$	−0.268993	+	0.465910i	−0.0135517	+	0.0234722i
$395$	15.7220			0.791060
$396$	−1.35518	−	12.8937i	−0.0681004	−	0.647932i
$397$	10.0648			0.505137			0.252568	−	0.967579i	$-0.418725\pi$
$397$	10.0648			0.505137			0.252568	+	0.967579i	$0.418725\pi$
$398$	2.56710	−	4.44635i	0.128677	−	0.222875i
$399$	−11.9074	+	3.86894i	−0.596114	+	0.193689i
$400$	−1.86984	−	3.23866i	−0.0934920	−	0.161933i
$401$	−4.27067	−	7.39702i	−0.213267	−	0.369389i	0.739468	−	0.673192i	$-0.235077\pi$
$401$	−4.27067	−	7.39702i	−0.213267	−	0.369389i	−0.952735	+	0.303802i	$0.901744\pi$
$402$	1.17915	+	1.06171i	0.0588105	+	0.0529532i
$403$	−4.95689	+	8.58558i	−0.246920	+	0.427678i
$404$	22.4331			1.11609
$405$	−6.02218	−	6.68830i	−0.299244	−	0.332344i
$406$	−1.01032			−0.0501412
$407$	−0.816999	+	1.41508i	−0.0404971	+	0.0701431i
$408$	−0.222562	−	0.200396i	−0.0110185	−	0.00992109i
$409$	−3.01836	−	5.22796i	−0.149248	−	0.258506i	0.781701	−	0.623653i	$-0.214352\pi$
$409$	−3.01836	−	5.22796i	−0.149248	−	0.258506i	−0.930950	+	0.365147i	$0.881019\pi$
$410$	0.229364	+	0.397270i	0.0113275	+	0.0196198i
$411$	4.47622	−	1.45441i	0.220795	−	0.0717408i
$412$	5.27540	−	9.13727i	0.259901	−	0.450161i
$413$	−14.0342			−0.690580
$414$	−0.187400	−	1.78299i	−0.00921019	−	0.0876291i
$415$	−3.12729			−0.153513
$416$	3.03138	−	5.25050i	0.148626	−	0.257427i
$417$	0.736535	−	3.46512i	0.0360683	−	0.169688i
$418$	−1.66913	−	2.89102i	−0.0816398	−	0.141404i
$419$	−9.93710	−	17.2116i	−0.485459	−	0.840840i	0.514401	−	0.857550i	$-0.328014\pi$
$419$	−9.93710	−	17.2116i	−0.485459	−	0.840840i	−0.999860	+	0.0167097i	$0.994681\pi$
$420$	0.704489	−	3.31436i	0.0343755	−	0.161724i
$421$	16.1049	−	27.8944i	0.784902	−	1.35949i	−0.144155	−	0.989555i	$-0.546046\pi$
$421$	16.1049	−	27.8944i	0.784902	−	1.35949i	0.929057	−	0.369936i	$-0.120620\pi$
$422$	−2.49959			−0.121678
$423$	23.6110	+	10.5123i	1.14801	+	0.511125i
$424$	6.56596			0.318871
$425$	0.104528	−	0.181049i	0.00507038	−	0.00878215i
$426$	−2.77924	+	0.903029i	−0.134655	+	0.0437519i
$427$	0.206824	+	0.358229i	0.0100089	+	0.0173359i
$428$	17.2618	+	29.8984i	0.834382	+	1.44519i
$429$	7.07679	+	6.37197i	0.341671	+	0.307642i
$430$	−0.554387	+	0.960226i	−0.0267349	+	0.0463062i
$431$	8.89203			0.428314			0.214157	−	0.976799i	$-0.431300\pi$
$431$	8.89203			0.428314			0.214157	+	0.976799i	$0.431300\pi$
$432$	7.90369	+	17.7520i	0.380266	+	0.854092i
$433$	−6.06725			−0.291574			−0.145787	−	0.989316i	$-0.546571\pi$
$433$	−6.06725			−0.291574			−0.145787	+	0.989316i	$0.546571\pi$
$434$	−0.416369	+	0.721172i	−0.0199863	+	0.0346174i
$435$	6.22053	+	5.60099i	0.298252	+	0.268547i
$436$	7.21442	+	12.4957i	0.345508	+	0.598437i
$437$	10.3316	+	17.8948i	0.494227	+	0.856027i
$438$	−5.52534	+	1.79529i	−0.264011	+	0.0857824i
$439$	−13.8852	+	24.0499i	−0.662706	+	1.14784i	0.317196	+	0.948360i	$0.397259\pi$
$439$	−13.8852	+	24.0499i	−0.662706	+	1.14784i	−0.979902	+	0.199480i	$0.936075\pi$
$440$	1.82709			0.0871031
$441$	2.42705	−	1.76336i	0.115574	−	0.0839693i
$442$	0.108774			0.00517384
$443$	17.0252	−	29.4886i	0.808893	−	1.40104i	−0.104737	−	0.994500i	$-0.533400\pi$
$443$	17.0252	−	29.4886i	0.808893	−	1.40104i	0.913631	−	0.406545i	$-0.133266\pi$
$444$	0.521097	−	2.45157i	0.0247302	−	0.116346i
$445$	5.07384	+	8.78815i	0.240523	+	0.416598i
$446$	0.711681	+	1.23267i	0.0336991	+	0.0583685i
$447$	−1.18270	+	5.56416i	−0.0559398	+	0.263176i
$448$	−3.48505	+	6.03629i	−0.164653	+	0.285188i
$449$	−0.508887			−0.0240159			−0.0120079	−	0.999928i	$-0.503822\pi$
$449$	−0.508887			−0.0240159			−0.0120079	+	0.999928i	$0.503822\pi$
$450$	0.507392	−	0.368642i	0.0239187	−	0.0173779i
$451$	4.84727			0.228249
$452$	−13.2549	+	22.9582i	−0.623460	+	1.07986i
$453$	−3.68082	+	1.19597i	−0.172940	+	0.0561917i
$454$	2.09549	+	3.62950i	0.0983464	+	0.170341i
$455$	1.24441	+	2.15539i	0.0583391	+	0.101046i
$456$	7.69549	+	6.92905i	0.360374	+	0.324482i
$457$	−9.50481	+	16.4628i	−0.444616	+	0.770098i	−0.998025	−	0.0628118i	$-0.979993\pi$
$457$	−9.50481	+	16.4628i	−0.444616	+	0.770098i	0.553409	+	0.832909i	$0.313327\pi$
$458$	−4.44557			−0.207728
$459$	−0.638506	+	0.878828i	−0.0298029	+	0.0410202i
$460$	−5.59220			−0.260738
$461$	−6.47352	+	11.2125i	−0.301502	+	0.522216i	−0.976476	−	0.215625i	$-0.930821\pi$
$461$	−6.47352	+	11.2125i	−0.301502	+	0.522216i	0.674975	+	0.737841i	$0.264155\pi$
$462$	0.594437	+	0.535233i	0.0276557	+	0.0249013i
$463$	8.51258	+	14.7442i	0.395613	+	0.685222i	0.993179	−	0.116597i	$-0.0371987\pi$
$463$	8.51258	+	14.7442i	0.395613	+	0.685222i	−0.597566	+	0.801820i	$0.703865\pi$
$464$	−9.03645	−	15.6516i	−0.419507	−	0.726607i
$465$	6.56161	−	2.13200i	0.304288	−	0.0988690i
$466$	0.569294	−	0.986046i	0.0263720	−	0.0456777i
$467$	−31.1794			−1.44281			−0.721405	−	0.692513i	$-0.756504\pi$
$467$	−31.1794			−1.44281			−0.721405	+	0.692513i	$0.756504\pi$
$468$	−13.3438	−	5.94106i	−0.616819	−	0.274626i
$469$	4.38197			0.202340
$470$	−0.900528	+	1.55976i	−0.0415383	+	0.0719464i
$471$	0.270130	−	1.27086i	0.0124469	−	0.0585582i
$472$	5.80380	+	10.0525i	0.267141	+	0.462702i
$473$	5.85808	+	10.1465i	0.269355	+	0.466536i
$474$	1.18362	−	5.56849i	0.0543655	−	0.255769i
$475$	−3.61426	+	6.26007i	−0.165833	+	0.287232i
$476$	−0.408977			−0.0187454
$477$	−2.48944	−	23.6854i	−0.113983	−	1.08448i
$478$	−3.90281			−0.178510
$479$	6.77784	−	11.7396i	0.309687	−	0.536394i	−0.668606	−	0.743616i	$-0.733109\pi$
$479$	6.77784	−	11.7396i	0.309687	−	0.536394i	0.978294	+	0.207222i	$0.0664422\pi$
$480$	−4.01275	+	1.30382i	−0.183156	+	0.0595110i
$481$	0.920470	+	1.59430i	0.0419698	+	0.0726939i
$482$	0.484324	+	0.838874i	0.0220604	+	0.0382097i
$483$	−3.67945	−	3.31299i	−0.167421	−	0.150746i
$484$	−5.98633	+	10.3686i	−0.272106	+	0.471301i
$485$	11.9060			0.540624
$486$	−2.82227	+	1.62944i	−0.128021	+	0.0739128i
$487$	5.50906			0.249639			0.124820	−	0.992179i	$-0.460165\pi$
$487$	5.50906			0.249639			0.124820	+	0.992179i	$0.460165\pi$
$488$	0.171062	−	0.296288i	0.00774362	−	0.0134123i
$489$	27.1458	+	24.4422i	1.22758	+	1.10532i
$490$	0.104528	+	0.181049i	0.00472211	+	0.00817894i
$491$	−5.13183	−	8.88859i	−0.231596	−	0.401136i	0.726682	−	0.686974i	$-0.241061\pi$
$491$	−5.13183	−	8.88859i	−0.231596	−	0.401136i	−0.958278	+	0.285838i	$0.907728\pi$
$492$	−7.07118	+	2.29757i	−0.318794	+	0.103582i
$493$	0.505159	−	0.874960i	0.0227512	−	0.0394062i
$494$	−3.76105			−0.169217
$495$	−0.692728	−	6.59087i	−0.0311358	−	0.296237i
$496$	−14.8963			−0.668863
$497$	−4.03519	+	6.98916i	−0.181003	+	0.313507i
$498$	−0.235436	+	1.10764i	−0.0105501	+	0.0496345i
$499$	−12.0666	−	20.8999i	−0.540174	−	0.935609i	−0.998894	−	0.0470277i	$-0.985025\pi$
$499$	−12.0666	−	20.8999i	−0.540174	−	0.935609i	0.458720	−	0.888581i	$-0.348308\pi$
$500$	−0.978148	−	1.69420i	−0.0437441	−	0.0757670i
$501$	−1.78211	+	8.38416i	−0.0796187	+	0.374577i
$502$	−0.996552	+	1.72608i	−0.0444783	+	0.0770386i
$503$	−33.9679			−1.51455			−0.757277	−	0.653094i	$-0.773471\pi$
$503$	−33.9679			−1.51455			−0.757277	+	0.653094i	$0.773471\pi$
$504$	−2.26676	−	1.00922i	−0.100969	−	0.0449544i
$505$	11.4671			0.510281
$506$	0.660070	−	1.14327i	0.0293437	−	0.0508248i
$507$	−11.2109	+	3.64265i	−0.497895	+	0.161776i
$508$	−7.76456	−	13.4486i	−0.344497	−	0.596685i
$509$	0.519250	+	0.899367i	0.0230154	+	0.0398638i	0.877304	−	0.479936i	$-0.159340\pi$
$509$	0.519250	+	0.899367i	0.0230154	+	0.0398638i	−0.854288	+	0.519799i	$0.826007\pi$
$510$	−0.0562553	−	0.0506525i	−0.00249103	−	0.00224293i
$511$	−8.02228	+	13.8950i	−0.354885	+	0.614678i
$512$	15.2959			0.675991
$513$	22.0775	−	30.3870i	0.974744	−	1.34162i
$514$	6.35410			0.280268
$515$	2.69663	−	4.67070i	0.118828	−	0.205816i
$516$	−13.3551	−	12.0250i	−0.587925	−	0.529370i
$517$	9.51568	+	16.4816i	0.418499	+	0.724861i
$518$	0.0773178	+	0.133918i	0.00339715	+	0.00588403i
$519$	28.2263	−	9.17129i	1.23900	−	0.402575i
$520$	1.02924	−	1.78270i	0.0451353	−	0.0781767i
$521$	−32.6154			−1.42891			−0.714453	−	0.699683i	$-0.753324\pi$
$521$	−32.6154			−1.42891			−0.714453	+	0.699683i	$0.753324\pi$
$522$	2.45209	−	1.78155i	0.107325	−	0.0779763i
$523$	27.0228			1.18162			0.590812	−	0.806809i	$-0.298807\pi$
$523$	27.0228			1.18162			0.590812	+	0.806809i	$0.298807\pi$
$524$	−13.6232	+	23.5961i	−0.595133	+	1.03080i
$525$	0.360114	−	1.69420i	0.0157166	−	0.0739410i
$526$	−1.02319	−	1.77222i	−0.0446134	−	0.0772726i
$527$	−0.416369	−	0.721172i	−0.0181373	−	0.0314147i
$528$	−2.97496	+	13.9961i	−0.129468	+	0.609101i
$529$	7.41429	−	12.8419i	0.322361	−	0.558345i
$530$	1.65962			0.0720895
$531$	34.0618	−	24.7474i	1.47816	−	1.07394i
$532$	14.1411			0.613095
$533$	2.73059	−	4.72951i	0.118275	−	0.204858i
$534$	3.49461	−	1.13547i	0.151226	−	0.0491364i
$535$	8.82374	+	15.2832i	0.381483	+	0.660749i
$536$	−1.81214	−	3.13872i	−0.0782726	−	0.135572i
$537$	−28.8363	−	25.9644i	−1.24438	−	1.12045i
$538$	−2.42725	+	4.20412i	−0.104646	+	0.181253i
$539$	2.20906			0.0951508
$540$	4.13456	+	9.28638i	0.177923	+	0.399622i
$541$	−35.7007			−1.53489			−0.767447	−	0.641113i	$-0.778473\pi$
$541$	−35.7007			−1.53489			−0.767447	+	0.641113i	$0.778473\pi$
$542$	0.384955	−	0.666761i	0.0165352	−	0.0286398i
$543$	7.32607	+	6.59643i	0.314392	+	0.283080i
$544$	0.254630	+	0.441032i	0.0109172	+	0.0189091i
$545$	3.68779	+	6.38745i	0.157968	+	0.273608i
$546$	0.857091	−	0.278486i	0.0366801	−	0.0119181i
$547$	−9.20386	+	15.9415i	−0.393528	+	0.681611i	−0.992912	−	0.118851i	$-0.962079\pi$
$547$	−9.20386	+	15.9415i	−0.393528	+	0.681611i	0.599384	+	0.800462i	$0.295412\pi$
$548$	−5.31592			−0.227085
$549$	−1.13366	−	0.504737i	−0.0483833	−	0.0215416i
$550$	0.461819			0.0196920
$551$	−17.4667	+	30.2533i	−0.744109	+	1.28883i
$552$	−0.851415	+	4.00559i	−0.0362386	+	0.170489i
$553$	−7.86101	−	13.6157i	−0.334284	−	0.578997i
$554$	−0.337211	−	0.584067i	−0.0143267	−	0.0248146i
$555$	0.266369	−	1.25317i	0.0113067	−	0.0531941i
$556$	−2.00059	+	3.46512i	−0.0848439	+	0.146954i
$557$	35.9397			1.52281			0.761407	−	0.648275i	$-0.224509\pi$
$557$	35.9397			1.52281			0.761407	+	0.648275i	$0.224509\pi$
$558$	−0.261134	−	2.48453i	−0.0110547	−	0.105178i
$559$	13.2000			0.558300
$560$	−1.86984	+	3.23866i	−0.0790152	+	0.136858i
$561$	−0.760744	+	0.247181i	−0.0321186	+	0.0104360i
$562$	0.649477	+	1.12493i	0.0273965	+	0.0474522i
$563$	−5.53684	−	9.59008i	−0.233350	−	0.404174i	0.725442	−	0.688283i	$-0.241635\pi$
$563$	−5.53684	−	9.59008i	−0.233350	−	0.404174i	−0.958792	+	0.284110i	$0.908302\pi$
$564$	−21.6936	−	19.5330i	−0.913464	−	0.822487i
$565$	−6.77553	+	11.7356i	−0.285049	+	0.493719i
$566$	5.56970			0.234112
$567$	−2.78115	+	8.55951i	−0.116797	+	0.359466i
$568$	6.67494			0.280074
$569$	−3.58412	+	6.20788i	−0.150254	+	0.260248i	−0.931321	−	0.364200i	$-0.881343\pi$
$569$	−3.58412	+	6.20788i	−0.150254	+	0.260248i	0.781067	+	0.624448i	$0.214676\pi$
$570$	1.94512	+	1.75140i	0.0814723	+	0.0733580i
$571$	4.67955	+	8.10521i	0.195833	+	0.339193i	0.947173	−	0.320722i	$-0.103926\pi$
$571$	4.67955	+	8.10521i	0.195833	+	0.339193i	−0.751340	+	0.659915i	$0.770592\pi$
$572$	−5.37782	−	9.31466i	−0.224858	−	0.389466i
$573$	−39.8577	+	12.9506i	−1.66508	+	0.541017i
$574$	0.229364	−	0.397270i	0.00957347	−	0.0165817i
$575$	−2.85857			−0.119211
$576$	−2.18572	−	20.7958i	−0.0910718	−	0.866490i
$577$	−8.63400			−0.359438			−0.179719	−	0.983718i	$-0.557519\pi$
$577$	−8.63400			−0.359438			−0.179719	+	0.983718i	$0.557519\pi$
$578$	1.77242	−	3.06991i	0.0737228	−	0.127692i
$579$	−7.24428	+	34.0816i	−0.301062	+	1.41639i
$580$	−4.72713	−	8.18763i	−0.196283	−	0.339973i
$581$	1.56365	+	2.70832i	0.0648710	+	0.112360i
$582$	0.896335	−	4.21692i	0.0371543	−	0.174797i
$583$	8.76844	−	15.1874i	0.363152	−	0.628997i
$584$	13.2703			0.549129
$585$	−6.82098	−	3.03689i	−0.282013	−	0.125560i
$586$	−5.70754			−0.235776
$587$	21.4070	−	37.0781i	0.883563	−	1.53038i	0.0362112	−	0.999344i	$-0.488471\pi$
$587$	21.4070	−	37.0781i	0.883563	−	1.53038i	0.847352	−	0.531032i	$-0.178196\pi$
$588$	−3.22256	+	1.04707i	−0.132896	+	0.0431806i
$589$	14.3967	+	24.9358i	0.593205	+	1.02746i
$590$	1.46698	+	2.54088i	0.0603945	+	0.104606i
$591$	−3.31238	−	2.98248i	−0.136253	−	0.122683i
$592$	−1.38309	+	2.39558i	−0.0568445	+	0.0984575i
$593$	−21.9382			−0.900895			−0.450447	−	0.892803i	$-0.648736\pi$
$593$	−21.9382			−0.900895			−0.450447	+	0.892803i	$0.648736\pi$
$594$	−2.38653	−	0.250835i	−0.0979207	−	0.0102919i
$595$	−0.209057			−0.00857050
$596$	3.21247	−	5.56416i	0.131588	−	0.227917i
$597$	31.6113	+	28.4630i	1.29377	+	1.16491i
$598$	−0.743667	−	1.28807i	−0.0304108	−	0.0526730i
$599$	−9.23318	−	15.9923i	−0.377258	−	0.653429i	0.613405	−	0.789769i	$-0.289800\pi$
$599$	−9.23318	−	15.9923i	−0.377258	−	0.653429i	−0.990662	+	0.136340i	$0.956466\pi$
$600$	−1.36245	+	0.442686i	−0.0556217	+	0.0180726i
$601$	0.864194	−	1.49683i	0.0352512	−	0.0610569i	−0.847862	−	0.530218i	$-0.822110\pi$
$601$	0.864194	−	1.49683i	0.0352512	−	0.0610569i	0.883113	+	0.469161i	$0.155444\pi$
$602$	1.10877			0.0451902
$603$	−10.6353	+	7.72696i	−0.433101	+	0.314666i
$604$	4.37132			0.177866
$605$	−3.06003	+	5.30013i	−0.124408	+	0.215481i
$606$	0.863295	−	4.06148i	0.0350689	−	0.164986i
$607$	−11.3399	−	19.6413i	−0.460273	−	0.797217i	0.538701	−	0.842497i	$-0.318915\pi$
$607$	−11.3399	−	19.6413i	−0.460273	−	0.797217i	−0.998974	+	0.0452803i	$0.985582\pi$
$608$	−8.80428	−	15.2495i	−0.357061	−	0.618448i
$609$	1.74033	−	8.18763i	0.0705219	−	0.331780i
$610$	0.0432379	−	0.0748903i	0.00175065	−	0.00303222i
$611$	21.4416			0.867436
$612$	0.992608	−	0.721172i	0.0401238	−	0.0291517i
$613$	18.5227			0.748125			0.374062	−	0.927404i	$-0.377965\pi$
$613$	18.5227			0.748125			0.374062	+	0.927404i	$0.377965\pi$
$614$	0.0869010	−	0.150517i	0.00350704	−	0.00607437i
$615$	−3.61458	+	1.17445i	−0.145754	+	0.0473583i
$616$	−0.913545	−	1.58231i	−0.0368078	−	0.0637530i
$617$	11.0939	+	19.2152i	0.446623	+	0.773573i	0.998164	−	0.0605745i	$-0.0192933\pi$
$617$	11.0939	+	19.2152i	0.446623	+	0.773573i	−0.551541	+	0.834148i	$0.685960\pi$
$618$	−1.45128	−	1.30673i	−0.0583789	−	0.0525646i
$619$	−4.64395	+	8.04356i	−0.186656	+	0.323298i	−0.944133	−	0.329564i	$-0.893098\pi$
$619$	−4.64395	+	8.04356i	−0.186656	+	0.323298i	0.757477	+	0.652862i	$0.226432\pi$
$620$	−7.79252			−0.312955
$621$	14.7722	+	1.55262i	0.592787	+	0.0623045i
$622$	5.57222			0.223426
$623$	5.07384	−	8.78815i	0.203279	−	0.352090i
$624$	11.9802	+	10.7870i	0.479592	+	0.431826i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.365697	−	0.633406i	−0.0146162	−	0.0253160i
$627$	26.3041	−	8.54671i	1.05048	−	0.341323i
$628$	−0.733733	+	1.27086i	−0.0292791	+	0.0507129i
$629$	−0.154636			−0.00616572
$630$	−0.572949	−	0.255093i	−0.0228268	−	0.0101632i
$631$	26.6838			1.06227			0.531133	−	0.847288i	$-0.321766\pi$
$631$	26.6838			1.06227			0.531133	+	0.847288i	$0.321766\pi$
$632$	−6.50177	+	11.2614i	−0.258626	+	0.447954i
$633$	4.30570	−	20.2567i	0.171136	−	0.805132i
$634$	−1.50947	−	2.61447i	−0.0599486	−	0.103834i
$635$	−3.96901	−	6.87453i	−0.157505	−	0.272807i
$636$	−5.59267	+	26.3114i	−0.221764	+	1.04332i
$637$	1.24441	−	2.15539i	0.0493055	−	0.0853997i
$638$	2.23185			0.0883597
$639$	−2.53076	−	24.0785i	−0.100115	−	0.952532i
$640$	6.32912			0.250181
$641$	3.28872	−	5.69624i	0.129897	−	0.224988i	−0.793740	−	0.608258i	$-0.791869\pi$
$641$	3.28872	−	5.69624i	0.129897	−	0.224988i	0.923636	+	0.383270i	$0.125202\pi$
$642$	6.07735	−	1.97465i	0.239854	−	0.0779332i
$643$	−3.68215	−	6.37767i	−0.145210	−	0.251511i	0.784241	−	0.620456i	$-0.213052\pi$
$643$	−3.68215	−	6.37767i	−0.145210	−	0.251511i	−0.929451	+	0.368945i	$0.879719\pi$
$644$	2.79610	+	4.84299i	0.110182	+	0.190841i
$645$	−6.82673	−	6.14681i	−0.268802	−	0.242030i
$646$	0.157960	−	0.273595i	0.00621487	−	0.0107645i
$647$	11.8899			0.467438			0.233719	−	0.972304i	$-0.424910\pi$
$647$	11.8899			0.467438			0.233719	+	0.972304i	$0.424910\pi$
$648$	7.28115	−	1.54766i	0.286031	−	0.0607977i
$649$	31.0024			1.21695
$650$	0.260154	−	0.450599i	0.0102041	−	0.0176740i
$651$	−5.12717	−	4.61653i	−0.200950	−	0.180936i
$652$	−20.6288	−	35.7301i	−0.807885	−	1.39930i
$653$	2.57811	+	4.46541i	0.100889	+	0.174745i	0.912051	−	0.410076i	$-0.134498\pi$
$653$	2.57811	+	4.46541i	0.100889	+	0.174745i	−0.811162	+	0.584821i	$0.801165\pi$
$654$	2.53997	−	0.825286i	0.0993206	−	0.0322712i
$655$	−6.96379	+	12.0616i	−0.272098	+	0.471287i
$656$	8.20588			0.320386
$657$	−5.03134	−	47.8700i	−0.196291	−	1.86759i
$658$	1.80106			0.0702125
$659$	−2.91467	+	5.04835i	−0.113539	+	0.196656i	−0.917195	−	0.398439i	$-0.869552\pi$
$659$	−2.91467	+	5.04835i	−0.113539	+	0.196656i	0.803656	+	0.595095i	$0.202885\pi$
$660$	−1.55626	+	7.32161i	−0.0605772	+	0.284993i
$661$	−6.57455	−	11.3875i	−0.255720	−	0.442921i	0.709371	−	0.704836i	$-0.248979\pi$
$661$	−6.57455	−	11.3875i	−0.255720	−	0.442921i	−0.965091	+	0.261915i	$0.915646\pi$
$662$	−0.563791	−	0.976514i	−0.0219124	−	0.0379533i
$663$	−0.187370	+	0.881505i	−0.00727683	+	0.0342348i
$664$	1.29328	−	2.24002i	0.0501889	−	0.0869298i
$665$	7.22851			0.280310
$666$	−0.423800	−	0.188688i	−0.0164219	−	0.00731150i
$667$	−13.8147			−0.534908
$668$	4.84060	−	8.38416i	0.187288	−	0.324393i
$669$	−11.2155	+	3.64413i	−0.433615	+	0.140890i
$670$	−0.458040	−	0.793349i	−0.0176956	−	0.0306497i
$671$	−0.456885	−	0.791349i	−0.0176379	−	0.0305497i
$672$	3.13552	+	2.82323i	0.120955	+	0.108909i
$673$	11.0088	−	19.0677i	0.424356	−	0.735006i	−0.572004	−	0.820251i	$-0.693834\pi$
$673$	11.0088	−	19.0677i	0.424356	−	0.735006i	0.996360	+	0.0852445i	$0.0271671\pi$
$674$	−2.44033			−0.0939979
$675$	2.11347	+	4.74692i	0.0813473	+	0.182709i
$676$	13.3140			0.512077
$677$	1.58248	−	2.74093i	0.0608195	−	0.105342i	−0.834012	−	0.551746i	$-0.813962\pi$
$677$	1.58248	−	2.74093i	0.0608195	−	0.105342i	0.894832	+	0.446403i	$0.147295\pi$
$678$	3.64646	+	3.28329i	0.140042	+	0.126094i
$679$	−5.95300	−	10.3109i	−0.228455	−	0.395696i
$680$	0.0864545	+	0.149744i	0.00331538	+	0.00574241i
$681$	−33.0232	+	10.7299i	−1.26545	+	0.411170i
$682$	0.919783	−	1.59311i	0.0352203	−	0.0610033i
$683$	−23.4933			−0.898946			−0.449473	−	0.893294i	$-0.648388\pi$
$683$	−23.4933			−0.898946			−0.449473	+	0.893294i	$0.648388\pi$
$684$	−34.3212	+	24.9358i	−1.31230	+	0.953444i
$685$	−2.71734			−0.103824
$686$	0.104528	−	0.181049i	0.00399092	−	0.00691247i
$687$	7.65777	−	36.0270i	0.292162	−	1.37451i
$688$	9.91706	+	17.1769i	0.378084	+	0.654861i
$689$	−9.87894	−	17.1108i	−0.376358	−	0.651871i
$690$	−0.215205	+	1.01246i	−0.00819272	+	0.0385437i
$691$	−25.3039	+	43.8276i	−0.962604	+	1.66728i	−0.246684	+	0.969096i	$0.579341\pi$
$691$	−25.3039	+	43.8276i	−0.962604	+	1.66728i	−0.715919	+	0.698183i	$0.753992\pi$
$692$	−33.5214			−1.27429
$693$	−5.36149	+	3.89535i	−0.203666	+	0.147972i
$694$	−7.36149			−0.279439
$695$	−1.02264	+	1.77127i	−0.0387910	+	0.0671880i
$696$	−6.58436	+	2.13939i	−0.249579	+	0.0810933i
$697$	0.229364	+	0.397270i	0.00868778	+	0.0150477i
$698$	3.15242	+	5.46014i	0.119321	+	0.206669i
$699$	7.01029	+	6.31209i	0.265154	+	0.238745i
$700$	−0.978148	+	1.69420i	−0.0369705	+	0.0640348i
$701$	−47.3661			−1.78899			−0.894496	−	0.447076i	$-0.852465\pi$
$701$	−47.3661			−1.78899			−0.894496	+	0.447076i	$0.852465\pi$
$702$	−1.58913	+	2.18725i	−0.0599780	+	0.0825526i
$703$	5.34679			0.201658
$704$	7.69868	−	13.3345i	0.290155	−	0.502563i
$705$	−11.0891	−	9.98468i	−0.417640	−	0.376045i
$706$	0.302155	+	0.523348i	0.0113718	+	0.0196965i
$707$	−5.73357	−	9.93083i	−0.215633	−	0.373487i
$708$	−45.2262	+	14.6949i	−1.69970	+	0.552268i
$709$	13.5583	−	23.4837i	0.509193	−	0.881948i	−0.490751	−	0.871300i	$-0.663277\pi$
$709$	13.5583	−	23.4837i	0.509193	−	0.881948i	0.999943	−	0.0106476i	$-0.00338929\pi$
$710$	1.68717			0.0633184
$711$	43.0883	+	19.1842i	1.61594	+	0.719462i
$712$	−8.39306			−0.314543
$713$	−5.69328	+	9.86104i	−0.213215	+	0.369299i
$714$	−0.0157387	+	0.0740447i	−0.000589006	+	0.00277105i
$715$	−2.74898	−	4.76138i	−0.102806	−	0.178065i
$716$	21.9134	+	37.9552i	0.818944	+	1.41845i
$717$	6.72283	−	31.6284i	0.251069	−	1.18119i
$718$	3.09892	−	5.36748i	0.115651	−	0.200313i
$719$	−13.6974			−0.510828			−0.255414	−	0.966832i	$-0.582212\pi$
$719$	−13.6974			−0.510828			−0.255414	+	0.966832i	$0.582212\pi$
$720$	−1.17271	−	11.1576i	−0.0437043	−	0.415819i
$721$	−5.39326			−0.200855
$722$	−3.47571	+	6.02011i	−0.129353	+	0.224045i
$723$	−7.63253	+	2.47996i	−0.283857	+	0.0922307i
$724$	−5.56726	−	9.64278i	−0.206906	−	0.358371i
$725$	−2.41637	−	4.18527i	−0.0897417	−	0.155437i
$726$	1.64685	+	1.48283i	0.0611205	+	0.0550331i
$727$	−0.456096	+	0.789981i	−0.0169156	+	0.0292988i	−0.874359	−	0.485279i	$-0.838718\pi$
$727$	−0.456096	+	0.789981i	−0.0169156	+	0.0292988i	0.857444	+	0.514578i	$0.172051\pi$
$728$	−2.05849			−0.0762927
$729$	−8.34346	−	25.6785i	−0.309017	−	0.951057i
$730$	3.35423			0.124145
$731$	−0.554387	+	0.960226i	−0.0205047	+	0.0355153i
$732$	1.04160	+	0.937856i	0.0384985	+	0.0346642i
$733$	12.7913	+	22.1553i	0.472459	+	0.818323i	0.999503	−	0.0315149i	$-0.0100332\pi$
$733$	12.7913	+	22.1553i	0.472459	+	0.818323i	−0.527044	+	0.849838i	$0.676700\pi$
$734$	−2.85756	−	4.94943i	−0.105474	−	0.182687i
$735$	−1.64728	+	0.535233i	−0.0607608	+	0.0197424i
$736$	3.48172	−	6.03051i	0.128338	−	0.222288i
$737$	−9.68001			−0.356568
$738$	0.143850	+	1.36865i	0.00529521	+	0.0503805i
$739$	−46.2781			−1.70237			−0.851183	−	0.524869i	$-0.824114\pi$
$739$	−46.2781			−1.70237			−0.851183	+	0.524869i	$0.824114\pi$
$740$	−0.723518	+	1.25317i	−0.0265970	+	0.0460674i
$741$	6.47864	−	30.4796i	0.237999	−	1.11970i
$742$	−0.829812	−	1.43728i	−0.0304634	−	0.0527641i
$743$	−11.1220	−	19.2639i	−0.408028	−	0.706725i	0.586641	−	0.809847i	$-0.300450\pi$
$743$	−11.1220	−	19.2639i	−0.408028	−	0.706725i	−0.994669	+	0.103122i	$0.967117\pi$
$744$	−1.18641	+	5.58164i	−0.0434961	+	0.204633i
$745$	1.64212	−	2.84423i	0.0601626	−	0.104205i
$746$	−4.16700			−0.152565
$747$	−8.57078	−	3.81596i	−0.313588	−	0.139619i
$748$	0.903454			0.0330335
$749$	8.82374	−	15.2832i	0.322412	−	0.558435i
$750$	−0.344375	+	0.111894i	−0.0125748	+	0.00408580i
$751$	−10.4029	−	18.0184i	−0.379609	−	0.657501i	0.611397	−	0.791324i	$-0.290608\pi$
$751$	−10.4029	−	18.0184i	−0.379609	−	0.657501i	−0.991005	+	0.133823i	$0.957275\pi$
$752$	16.1090	+	27.9015i	0.587433	+	1.01746i
$753$	−12.2715	−	11.0494i	−0.447200	−	0.402661i
$754$	1.25725	−	2.17763i	0.0457865	−	0.0793045i
$755$	2.23449			0.0813213
$756$	5.97496	−	8.22383i	0.217307	−	0.299098i
$757$	−41.4984			−1.50828			−0.754142	−	0.656712i	$-0.771947\pi$
$757$	−41.4984			−1.50828			−0.754142	+	0.656712i	$0.771947\pi$
$758$	−2.22082	+	3.84657i	−0.0806637	+	0.139714i
$759$	8.12811	+	7.31858i	0.295032	+	0.265648i
$760$	−2.98932	−	5.17765i	−0.108434	−	0.187813i
$761$	9.96767	+	17.2645i	0.361328	+	0.625838i	0.988180	−	0.153301i	$-0.0489903\pi$
$761$	9.96767	+	17.2645i	0.361328	+	0.625838i	−0.626852	+	0.779138i	$0.715657\pi$
$762$	−2.73366	+	0.888219i	−0.0990299	+	0.0321768i
$763$	3.68779	−	6.38745i	0.133507	−	0.231241i
$764$	47.3347			1.71251
$765$	0.507392	−	0.368642i	0.0183448	−	0.0133283i
$766$	−0.191456			−0.00691758
$767$	17.4644	−	30.2493i	0.630603	−	1.09224i
$768$	−4.54357	+	21.3758i	−0.163952	+	0.771334i
$769$	5.57449	+	9.65531i	0.201021	+	0.348179i	0.948858	−	0.315704i	$-0.102241\pi$
$769$	5.57449	+	9.65531i	0.201021	+	0.348179i	−0.747836	+	0.663883i	$0.768907\pi$
$770$	−0.230909	−	0.399947i	−0.00832139	−	0.0144131i
$771$	−10.9453	+	51.4938i	−0.394187	+	1.85450i
$772$	19.6770	−	34.0816i	0.708193	−	1.22663i
$773$	34.9747			1.25795			0.628976	−	0.777425i	$-0.283474\pi$
$773$	34.9747			1.25795			0.628976	+	0.777425i	$0.283474\pi$
$774$	−2.69105	+	1.95516i	−0.0967278	+	0.0702769i
$775$	−3.98331			−0.143085
$776$	−4.92368	+	8.52806i	−0.176750	+	0.306139i
$777$	−1.21846	+	0.395902i	−0.0437120	+	0.0142029i
$778$	−2.55672	−	4.42837i	−0.0916629	−	0.158765i
$779$	−7.93066	−	13.7363i	−0.284146	−	0.492155i
$780$	6.26706	+	5.64288i	0.224397	+	0.202048i
$781$	8.91397	−	15.4394i	0.318967	−	0.552467i
$782$	0.124933			0.00446760
$783$	10.2138	+	22.9406i	0.365012	+	0.819831i
$784$	3.73968			0.133560
$785$	−0.375062	+	0.649627i	−0.0133866	+	0.0231862i
$786$	3.74778	+	3.37452i	0.133679	+	0.120365i
$787$	−21.3292	−	36.9433i	−0.760304	−	1.31688i	−0.942694	−	0.333659i	$-0.891717\pi$
$787$	−21.3292	−	36.9433i	−0.760304	−	1.31688i	0.182390	−	0.983226i	$-0.441617\pi$
$788$	2.51716	+	4.35985i	0.0896701	+	0.155313i
$789$	16.1246	−	5.23922i	0.574053	−	0.186521i
$790$	−1.64340	+	2.84645i	−0.0584695	+	0.101272i
$791$	13.5511			0.481820
$792$	5.00739	+	2.22943i	0.177930	+	0.0792195i
$793$	−1.02950			−0.0365586
$794$	−1.05206	+	1.82221i	−0.0373361	+	0.0646680i
$795$	−2.85881	+	13.4496i	−0.101391	+	0.477009i
$796$	−24.0222	−	41.6077i	−0.851445	−	1.47475i
$797$	4.13403	+	7.16035i	0.146435	+	0.253633i	0.929907	−	0.367794i	$-0.119887\pi$
$797$	4.13403	+	7.16035i	0.146435	+	0.253633i	−0.783472	+	0.621427i	$0.786553\pi$
$798$	0.544193	−	2.56023i	0.0192642	−	0.0906310i
$799$	−0.900528	+	1.55976i	−0.0318584	+	0.0551804i
$800$	2.43599			0.0861252
$801$	3.18216	+	30.2763i	0.112436	+	1.06976i
$802$	1.78563			0.0630527
$803$	17.7217	−	30.6948i	0.625384	−	1.08320i
$804$	14.1212	−	4.58824i	0.498015	−	0.161815i
$805$	1.42928	+	2.47559i	0.0503756	+	0.0872532i
$806$	−1.03627	−	1.79487i	−0.0365011	−	0.0632218i
$807$	−29.8892	−	26.9123i	−1.05215	−	0.947359i
$808$	−4.74218	+	8.21370i	−0.166829	+	0.288957i
$809$	−7.79155			−0.273936			−0.136968	−	0.990575i	$-0.543736\pi$
$809$	−7.79155			−0.273936			−0.136968	+	0.990575i	$0.543736\pi$
$810$	1.84040	−	0.391188i	0.0646650	−	0.0137450i
$811$	−31.4280			−1.10359			−0.551793	−	0.833981i	$-0.686056\pi$
$811$	−31.4280			−1.10359			−0.551793	+	0.833981i	$0.686056\pi$
$812$	−4.72713	+	8.18763i	−0.165890	+	0.287330i
$813$	4.74033	+	4.26822i	0.166251	+	0.149693i
$814$	−0.170799	−	0.295833i	−0.00598651	−	0.0103689i
$815$	−10.5448	−	18.2642i	−0.369369	−	0.639766i
$816$	−1.28785	+	0.418449i	−0.0450839	+	0.0146486i
$817$	19.1689	−	33.2015i	0.670635	−	1.16157i
$818$	1.26202			0.0441255
$819$	0.780461	+	7.42559i	0.0272715	+	0.259471i
$820$	4.29265			0.149906
$821$	−20.6628	+	35.7890i	−0.721136	+	1.24904i	0.239408	+	0.970919i	$0.423047\pi$
$821$	−20.6628	+	35.7890i	−0.721136	+	1.24904i	−0.960545	+	0.278126i	$0.910287\pi$
$822$	−0.204573	+	0.962440i	−0.00713530	+	0.0335690i
$823$	22.6315	+	39.1989i	0.788885	+	1.36639i	0.926650	+	0.375924i	$0.122675\pi$
$823$	22.6315	+	39.1989i	0.788885	+	1.36639i	−0.137765	+	0.990465i	$0.543992\pi$
$824$	2.23036	+	3.86309i	0.0776982	+	0.134577i
$825$	−0.795511	+	3.74259i	−0.0276962	+	0.130300i
$826$	1.46698	−	2.54088i	0.0510427	−	0.0884085i
$827$	39.9978			1.39086			0.695430	−	0.718594i	$-0.255214\pi$
$827$	39.9978			1.39086			0.695430	+	0.718594i	$0.255214\pi$
$828$	−15.3262	−	6.82366i	−0.532622	−	0.237139i
$829$	41.0978			1.42739			0.713693	−	0.700459i	$-0.247021\pi$
$829$	41.0978			1.42739			0.713693	+	0.700459i	$0.247021\pi$
$830$	0.326891	−	0.566192i	0.0113466	−	0.0196528i
$831$	5.31416	−	1.72667i	0.184346	−	0.0598977i
$832$	−8.67370	−	15.0233i	−0.300706	−	0.520839i
$833$	0.104528	+	0.181049i	0.00362170	+	0.00627296i
$834$	0.550367	+	0.495553i	0.0190577	+	0.0171596i
$835$	2.47437	−	4.28573i	0.0856291	−	0.148314i
$836$	−31.2385			−1.08041
$837$	20.5845	+	2.16352i	0.711504	+	0.0747821i
$838$	4.15484			0.143527
$839$	0.600564	−	1.04021i	0.0207338	−	0.0359119i	−0.855472	−	0.517848i	$-0.826733\pi$
$839$	0.600564	−	1.04021i	0.0207338	−	0.0359119i	0.876206	+	0.481937i	$0.160066\pi$
$840$	1.06460	+	0.958572i	0.0367323	+	0.0330739i
$841$	2.82232	+	4.88841i	0.0973215	+	0.168566i
$842$	3.36683	+	5.83152i	0.116029	+	0.200968i
$843$	−10.2352	+	3.32562i	−0.352519	+	0.114540i
$844$	−11.6952	+	20.2567i	−0.402566	+	0.697265i
$845$	6.80573			0.234124
$846$	−4.37126	+	3.17590i	−0.150287	+	0.109190i
$847$	6.12007			0.210288
$848$	14.8440	−	25.7105i	0.509744	−	0.882902i
$849$	−9.59416	+	45.1370i	−0.329271	+	1.54910i
$850$	0.0218524	+	0.0378495i	0.000749531	+	0.00129823i
$851$	1.05721	+	1.83115i	0.0362409	+	0.0627710i
$852$	−5.68549	+	26.7481i	−0.194782	+	0.916376i
$853$	−17.4107	+	30.1562i	−0.596131	+	1.03253i	0.397255	+	0.917708i	$0.369963\pi$
$853$	−17.4107	+	30.1562i	−0.596131	+	1.03253i	−0.993386	+	0.114821i	$0.963371\pi$
$854$	−0.0864759			−0.00295914
$855$	−17.5440	+	12.7464i	−0.599991	+	0.435919i
$856$	−14.5961			−0.498883
$857$	6.87227	−	11.9031i	0.234752	−	0.406603i	−0.724448	−	0.689329i	$-0.757905\pi$
$857$	6.87227	−	11.9031i	0.234752	−	0.406603i	0.959201	+	0.282726i	$0.0912387\pi$
$858$	−1.89336	+	0.615191i	−0.0646383	+	0.0210023i
$859$	−10.3260	−	17.8852i	−0.352319	−	0.610234i	0.634336	−	0.773057i	$-0.281273\pi$
$859$	−10.3260	−	17.8852i	−0.352319	−	0.610234i	−0.986655	+	0.162823i	$0.947940\pi$
$860$	5.18779	+	8.98552i	0.176902	+	0.306404i
$861$	2.82439	+	2.54309i	0.0962550	+	0.0866684i
$862$	−0.929471	+	1.60989i	−0.0316579	+	0.0548331i
$863$	35.9288			1.22303			0.611515	−	0.791233i	$-0.290560\pi$
$863$	35.9288			1.22303			0.611515	+	0.791233i	$0.290560\pi$
$864$	−12.5884	−	1.32310i	−0.428267	−	0.0450127i
$865$	−17.1351			−0.582612
$866$	0.634201	−	1.09847i	0.0215510	−	0.0373274i
$867$	21.8255	+	19.6518i	0.741234	+	0.667410i
$868$	3.89626	+	6.74852i	0.132248	+	0.229060i
$869$	17.3654	+	30.0778i	0.589081	+	1.02032i
$870$	−1.66427	+	0.540755i	−0.0564242	+	0.0183333i
$871$	−5.45298	+	9.44484i	−0.184767	+	0.320026i
$872$	−6.10028			−0.206582
$873$	32.6300	+	14.5278i	1.10436	+	0.491693i
$874$	−4.31978			−0.146119
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$	−11.3032	+	53.1774i	−0.381900	+	1.79670i
$877$	16.9171	+	29.3012i	0.571249	+	0.989432i	0.996438	+	0.0843278i	$0.0268743\pi$
$877$	16.9171	+	29.3012i	0.571249	+	0.989432i	−0.425189	+	0.905105i	$0.639792\pi$
$878$	−2.90280	−	5.02780i	−0.0979649	−	0.169680i
$879$	9.83160	−	46.2540i	0.331612	−	1.56011i
$880$	4.13058	−	7.15438i	0.139242	−	0.241174i
$881$	39.0617			1.31602			0.658011	−	0.753008i	$-0.271398\pi$
$881$	39.0617			1.31602			0.658011	+	0.753008i	$0.271398\pi$
$882$	0.0655572	+	0.623735i	0.00220743	+	0.0210023i
$883$	−20.1056			−0.676606			−0.338303	−	0.941037i	$-0.609853\pi$
$883$	−20.1056			−0.676606			−0.338303	+	0.941037i	$0.609853\pi$
$884$	0.508937	−	0.881505i	0.0171174	−	0.0296482i
$885$	−23.1183	+	7.51159i	−0.777113	+	0.252499i
$886$	3.55924	+	6.16479i	0.119575	+	0.207110i
$887$	−22.3440	−	38.7009i	−0.750237	−	1.29945i	−0.947707	−	0.319140i	$-0.896606\pi$
$887$	−22.3440	−	38.7009i	−0.750237	−	1.29945i	0.197470	−	0.980309i	$-0.436728\pi$
$888$	0.787466	+	0.709038i	0.0264256	+	0.0237938i
$889$	−3.96901	+	6.87453i	−0.133116	+	0.230564i
$890$	−2.12144			−0.0711109
$891$	6.14373	−	18.9084i	0.205823	−	0.633457i
$892$	13.3194			0.445967
$893$	31.1373	−	53.9315i	1.04197	−	1.80475i
$894$	−0.883758	−	0.795739i	−0.0295573	−	0.0266135i
$895$	11.2015	+	19.4016i	0.374425	+	0.648523i
$896$	−3.16456	−	5.48118i	−0.105721	−	0.183113i
$897$	11.7195	−	3.80791i	0.391304	−	0.127142i
$898$	0.0531932	−	0.0921333i	0.00177508	−	0.00307453i
$899$	−19.2503			−0.642033
$900$	−0.613466	−	5.83674i	−0.0204489	−	0.194558i
$901$	1.65962			0.0552901
$902$	−0.506678	+	0.877592i	−0.0168705	+	0.0292206i
$903$	−1.90993	+	8.98552i	−0.0635586	+	0.299020i
$904$	−5.60398	−	9.70637i	−0.186386	−	0.322829i
$905$	−2.84582	−	4.92910i	−0.0945982	−	0.163849i
$906$	0.168222	−	0.791421i	0.00558879	−	0.0262932i
$907$	−15.5293	+	26.8975i	−0.515642	+	0.893118i	0.484193	+	0.874961i	$0.339113\pi$
$907$	−15.5293	+	26.8975i	−0.515642	+	0.893118i	−0.999835	+	0.0181569i	$0.994220\pi$
$908$	39.2181			1.30150
$909$	31.4272	+	13.9923i	1.04238	+	0.464096i
$910$	−0.520307			−0.0172480
$911$	−12.4227	+	21.5168i	−0.411583	+	0.712882i	−0.995063	−	0.0992453i	$-0.968357\pi$
$911$	−12.4227	+	21.5168i	−0.411583	+	0.712882i	0.583480	+	0.812127i	$0.301690\pi$
$912$	44.5298	−	14.4686i	1.47453	−	0.479103i
$913$	−3.45419	−	5.98282i	−0.114317	−	0.198003i
$914$	−1.98705	−	3.44166i	−0.0657256	−	0.113840i
$915$	0.532432	+	0.479404i	0.0176017	+	0.0158486i
$916$	−20.8002	+	36.0270i	−0.687257	+	1.19036i
$917$	13.9276			0.459929
$918$	−0.0923686	−	0.207463i	−0.00304862	−	0.00684731i
$919$	−15.5187			−0.511914			−0.255957	−	0.966688i	$-0.582391\pi$
$919$	−15.5187			−0.511914			−0.255957	+	0.966688i	$0.582391\pi$
$920$	1.18215	−	2.04754i	0.0389743	−	0.0675054i
$921$	1.07010	+	0.963522i	0.0352610	+	0.0317491i
$922$	−1.35333	−	2.34404i	−0.0445697	−	0.0771969i
$923$	−10.0429	−	17.3948i	−0.330566	−	0.572558i
$924$	7.11882	−	2.31305i	0.234192	−	0.0760936i
$925$	−0.369841	+	0.640583i	−0.0121603	+	0.0210622i
$926$	−3.55923			−0.116964
$927$	13.0897	−	9.51024i	0.429923	−	0.312357i
$928$	11.7725			0.386451
$929$	−6.77388	+	11.7327i	−0.222244	+	0.384938i	−0.955489	−	0.295027i	$-0.904671\pi$
$929$	−6.77388	+	11.7327i	−0.222244	+	0.384938i	0.733245	+	0.679964i	$0.238005\pi$
$930$	−0.299880	+	1.41083i	−0.00983346	+	0.0462628i
$931$	−3.61426	−	6.26007i	−0.118452	−	0.205166i
$932$	−5.32729	−	9.22714i	−0.174501	−	0.302245i
$933$	−9.59850	+	45.1574i	−0.314241	+	1.47839i
$934$	3.25914	−	5.64499i	0.106642	−	0.184710i
$935$	0.461819			0.0151031
$936$	4.99606	−	3.62985i	0.163301	−	0.118645i
$937$	12.8207			0.418833			0.209416	−	0.977827i	$-0.432844\pi$
$937$	12.8207			0.418833			0.209416	+	0.977827i	$0.432844\pi$
$938$	−0.458040	+	0.793349i	−0.0149555	+	0.0259038i
$939$	5.76307	−	1.87254i	0.188071	−	0.0611079i
$940$	8.42689	+	14.5958i	0.274855	+	0.476062i
$941$	12.7185	+	22.0291i	0.414612	+	0.718129i	0.995388	−	0.0959348i	$-0.0305840\pi$
$941$	12.7185	+	22.0291i	0.414612	+	0.718129i	−0.580776	+	0.814064i	$0.697251\pi$
$942$	0.201852	+	0.181748i	0.00657668	+	0.00592167i
$943$	3.13624	−	5.43213i	0.102130	−	0.176894i
$944$	52.4836			1.70819
$945$	3.05422	−	4.20378i	0.0993538	−	0.136749i
$946$	−2.44934			−0.0796351
$947$	18.8010	−	32.5643i	0.610950	−	1.05820i	−0.380130	−	0.924933i	$-0.624121\pi$
$947$	18.8010	−	32.5643i	0.610950	−	1.05820i	0.991081	−	0.133264i	$-0.0425458\pi$
$948$	−39.5892	−	35.6463i	−1.28580	−	1.15774i
$949$	−19.9661	−	34.5823i	−0.648126	−	1.12259i
$950$	−0.755585	−	1.30871i	−0.0245144	−	0.0424602i
$951$	23.7879	−	7.72916i	0.771375	−	0.250635i
$952$	0.0864545	−	0.149744i	0.00280201	−	0.00485322i
$953$	−39.7536			−1.28775			−0.643873	−	0.765133i	$-0.722673\pi$
$953$	−39.7536			−1.28775			−0.643873	+	0.765133i	$0.722673\pi$
$954$	4.54843	+	2.02509i	0.147261	+	0.0655647i
$955$	24.1961			0.782967
$956$	−18.2607	+	31.6284i	−0.590593	+	1.02294i
$957$	−3.84450	+	18.0869i	−0.124275	+	0.584668i
$958$	1.41695	+	2.45424i	0.0457797	+	0.0792928i
$959$	1.35867	+	2.35329i	0.0438738	+	0.0759916i
$960$	−2.51003	+	11.8088i	−0.0810108	+	0.381126i
$961$	7.56664	−	13.1058i	0.244085	−	0.422768i
$962$	−0.384861			−0.0124084
$963$	5.53399	+	52.6524i	0.178330	+	1.69670i
$964$	9.06434			0.291943
$965$	10.0583	−	17.4215i	0.323789	−	0.560819i
$966$	0.984419	−	0.319857i	0.0316732	−	0.0102912i
$967$	−5.88940	−	10.2007i	−0.189390	−	0.328034i	0.755657	−	0.654968i	$-0.227318\pi$
$967$	−5.88940	−	10.2007i	−0.189390	−	0.328034i	−0.945047	+	0.326934i	$0.893984\pi$
$968$	−2.53093	−	4.38369i	−0.0813470	−	0.140897i
$969$	1.94512	+	1.75140i	0.0624864	+	0.0562630i
$970$	−1.24452	+	2.15557i	−0.0399590	+	0.0692111i
$971$	53.8520			1.72819			0.864096	−	0.503327i	$-0.167891\pi$
$971$	53.8520			1.72819			0.864096	+	0.503327i	$0.167891\pi$
$972$			30.4956i			0.978148i
$973$	2.04528			0.0655688
$974$	−0.575853	+	0.997407i	−0.0184515	+	0.0319590i
$975$	3.20353	+	2.88447i	0.102595	+	0.0923771i
$976$	−0.773455	−	1.33966i	−0.0247577	−	0.0428816i
$977$	15.4790	+	26.8104i	0.495217	+	0.857741i	0.999985	−	0.00551414i	$-0.00175521\pi$
$977$	15.4790	+	26.8104i	0.495217	+	0.857741i	−0.504768	+	0.863255i	$0.668422\pi$
$978$	−7.26274	+	2.35981i	−0.232237	+	0.0754583i
$979$	−11.2084	+	19.4135i	−0.358222	+	0.620459i
$980$	1.95630			0.0624916
$981$	2.31288	+	22.0056i	0.0738445	+	0.702583i
$982$	2.14569			0.0684717
$983$	−20.3154	+	35.1872i	−0.647959	+	1.12230i	0.335650	+	0.941987i	$0.391044\pi$
$983$	−20.3154	+	35.1872i	−0.647959	+	1.12230i	−0.983610	+	0.180311i	$0.942289\pi$
$984$	0.653557	−	3.07474i	0.0208346	−	0.0980193i
$985$	1.28670	+	2.22863i	0.0409976	+	0.0710099i
$986$	0.105607	+	0.182917i	0.00336321	+	0.00582525i
$987$	−3.10243	+	14.5958i	−0.0987515	+	0.464589i
$988$	−17.5974	+	30.4796i	−0.559848	+	0.969685i
$989$	15.1610			0.482091
$990$	1.26568	+	0.563516i	0.0402259	+	0.0179097i
$991$	−54.5615			−1.73320			−0.866602	−	0.499000i	$-0.833701\pi$
$991$	−54.5615			−1.73320			−0.866602	+	0.499000i	$0.833701\pi$
$992$	4.85164	−	8.40329i	0.154040	−	0.266805i
$993$	8.88486	−	2.88687i	0.281952	−	0.0916119i
$994$	−0.843585	−	1.46113i	−0.0267569	−	0.0463443i
$995$	−12.2794	−	21.2686i	−0.389284	−	0.674261i
$996$	7.87476	+	7.09046i	0.249521	+	0.224670i
$997$	−15.0875	+	26.1323i	−0.477826	+	0.827619i	−0.999677	−	0.0254177i	$-0.991908\pi$
$997$	−15.0875	+	26.1323i	−0.477826	+	0.827619i	0.521851	+	0.853037i	$0.325242\pi$
$998$	5.04520			0.159703
$999$	2.25915	−	3.10945i	0.0714764	−	0.0983788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.i.d.106.2	✓	8
3.2	odd	2		945.2.i.c.316.3		8
9.2	odd	6		2835.2.a.q.1.2		4
9.4	even	3	inner	315.2.i.d.211.2	yes	8
9.5	odd	6		945.2.i.c.631.3		8
9.7	even	3		2835.2.a.l.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.i.d.106.2	✓	8	1.1	even	1	trivial
315.2.i.d.211.2	yes	8	9.4	even	3	inner
945.2.i.c.316.3		8	3.2	odd	2
945.2.i.c.631.3		8	9.5	odd	6
2835.2.a.l.1.3		4	9.7	even	3
2835.2.a.q.1.2		4	9.2	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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 + 0.181049i) q^{2} +(-1.28716 - 1.15897i) q^{3} +(0.978148 + 1.69420i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.344375 - 0.111894i) q^{6} +(0.500000 - 0.866025i) q^{7} -0.827091 q^{8} +(0.313585 + 2.98357i) q^{9} +O(q^{10})\)	\(q+(-0.104528 + 0.181049i) q^{2} +(-1.28716 - 1.15897i) q^{3} +(0.978148 + 1.69420i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.344375 - 0.111894i) q^{6} +(0.500000 - 0.866025i) q^{7} -0.827091 q^{8} +(0.313585 + 2.98357i) q^{9} -0.209057 q^{10} +(-1.10453 + 1.91310i) q^{11} +(0.704489 - 3.31436i) q^{12} +(1.24441 + 2.15539i) q^{13} +(0.104528 + 0.181049i) q^{14} +(0.360114 - 1.69420i) q^{15} +(-1.86984 + 3.23866i) q^{16} -0.209057 q^{17} +(-0.572949 - 0.255093i) q^{18} +7.22851 q^{19} +(-0.978148 + 1.69420i) q^{20} +(-1.64728 + 0.535233i) q^{21} +(-0.230909 - 0.399947i) q^{22} +(1.42928 + 2.47559i) q^{23} +(1.06460 + 0.958572i) q^{24} +(-0.500000 + 0.866025i) q^{25} -0.520307 q^{26} +(3.05422 - 4.20378i) q^{27} +1.95630 q^{28} +(-2.41637 + 4.18527i) q^{29} +(0.269091 + 0.242290i) q^{30} +(1.99165 + 3.44964i) q^{31} +(-1.21799 - 2.10963i) q^{32} +(3.63893 - 1.18236i) q^{33} +(0.0218524 - 0.0378495i) q^{34} +1.00000 q^{35} +(-4.74803 + 3.44964i) q^{36} +0.739681 q^{37} +(-0.755585 + 1.30871i) q^{38} +(0.896261 - 4.21658i) q^{39} +(-0.413545 - 0.716282i) q^{40} +(-1.09714 - 1.90030i) q^{41} +(0.0752842 - 0.354185i) q^{42} +(2.65185 - 4.59313i) q^{43} -4.32157 q^{44} +(-2.42705 + 1.76336i) q^{45} -0.597604 q^{46} +(4.30757 - 7.46094i) q^{47} +(6.16030 - 2.00160i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.104528 - 0.181049i) q^{50} +(0.269091 + 0.242290i) q^{51} +(-2.43444 + 4.21658i) q^{52} -7.93863 q^{53} +(0.441835 + 0.992377i) q^{54} -2.20906 q^{55} +(-0.413545 + 0.716282i) q^{56} +(-9.30428 - 8.37761i) q^{57} +(-0.505159 - 0.874960i) q^{58} +(-7.01712 - 12.1540i) q^{59} +(3.22256 - 1.04707i) q^{60} +(-0.206824 + 0.358229i) q^{61} -0.832738 q^{62} +(2.74064 + 1.22021i) q^{63} -6.97010 q^{64} +(-1.24441 + 2.15539i) q^{65} +(-0.166307 + 0.782414i) q^{66} +(2.19098 + 3.79489i) q^{67} +(-0.204489 - 0.354185i) q^{68} +(1.02941 - 4.84299i) q^{69} +(-0.104528 + 0.181049i) q^{70} -8.07039 q^{71} +(-0.259364 - 2.46768i) q^{72} -16.0446 q^{73} +(-0.0773178 + 0.133918i) q^{74} +(1.64728 - 0.535233i) q^{75} +(7.07055 + 12.2466i) q^{76} +(1.10453 + 1.91310i) q^{77} +(0.669721 + 0.603019i) q^{78} +(7.86101 - 13.6157i) q^{79} -3.73968 q^{80} +(-8.80333 + 1.87121i) q^{81} +0.458728 q^{82} +(-1.56365 + 2.70832i) q^{83} +(-2.51807 - 2.26728i) q^{84} +(-0.104528 - 0.181049i) q^{85} +(0.554387 + 0.960226i) q^{86} +(7.96086 - 2.58664i) q^{87} +(0.913545 - 1.58231i) q^{88} +10.1477 q^{89} +(-0.0655572 - 0.623735i) q^{90} +2.48883 q^{91} +(-2.79610 + 4.84299i) q^{92} +(1.43444 - 6.74852i) q^{93} +(0.900528 + 1.55976i) q^{94} +(3.61426 + 6.26007i) q^{95} +(-0.877232 + 4.12705i) q^{96} +(5.95300 - 10.3109i) q^{97} +0.209057 q^{98} +(-6.05422 - 2.69551i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 8 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + 4 * q^7 + 6 * q^8 - 3 * q^9	\( 8 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{9} + 2 q^{10} - 7 q^{11} + 3 q^{12} + 8 q^{13} - q^{14} + 3 q^{15} + 9 q^{16} + 2 q^{17} - 18 q^{18} + 6 q^{19} + q^{20} - 7 q^{22} + 8 q^{23} + 6 q^{24} - 4 q^{25} - 6 q^{26} - 2 q^{28} - q^{29} - 3 q^{30} + 9 q^{34} + 8 q^{35} - 6 q^{36} - 42 q^{37} - 8 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} + 3 q^{42} + 7 q^{43} + 6 q^{44} - 6 q^{45} - 46 q^{46} + 2 q^{47} + 30 q^{48} - 4 q^{49} + q^{50} - 3 q^{51} + 7 q^{52} - 16 q^{53} - 36 q^{54} - 14 q^{55} + 3 q^{56} - 24 q^{57} + 19 q^{58} - 19 q^{59} + 15 q^{60} + 12 q^{61} + 30 q^{62} + 3 q^{63} - 14 q^{64} - 8 q^{65} - 9 q^{66} + 22 q^{67} + q^{68} + 51 q^{69} + q^{70} + 26 q^{71} - 21 q^{72} - 8 q^{73} - 9 q^{74} + 13 q^{76} + 7 q^{77} - 21 q^{78} + 24 q^{79} + 18 q^{80} + 9 q^{81} + 19 q^{83} - 12 q^{84} + q^{85} + 27 q^{86} + 45 q^{87} + q^{88} + 30 q^{89} - 27 q^{90} + 16 q^{91} - 3 q^{92} - 15 q^{93} + 7 q^{94} + 3 q^{95} + 30 q^{96} + 12 q^{97} - 2 q^{98} - 24 q^{99}+O(q^{100}) \) 8 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + 4 * q^7 + 6 * q^8 - 3 * q^9 + 2 * q^10 - 7 * q^11 + 3 * q^12 + 8 * q^13 - q^14 + 3 * q^15 + 9 * q^16 + 2 * q^17 - 18 * q^18 + 6 * q^19 + q^20 - 7 * q^22 + 8 * q^23 + 6 * q^24 - 4 * q^25 - 6 * q^26 - 2 * q^28 - q^29 - 3 * q^30 + 9 * q^34 + 8 * q^35 - 6 * q^36 - 42 * q^37 - 8 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 + 3 * q^42 + 7 * q^43 + 6 * q^44 - 6 * q^45 - 46 * q^46 + 2 * q^47 + 30 * q^48 - 4 * q^49 + q^50 - 3 * q^51 + 7 * q^52 - 16 * q^53 - 36 * q^54 - 14 * q^55 + 3 * q^56 - 24 * q^57 + 19 * q^58 - 19 * q^59 + 15 * q^60 + 12 * q^61 + 30 * q^62 + 3 * q^63 - 14 * q^64 - 8 * q^65 - 9 * q^66 + 22 * q^67 + q^68 + 51 * q^69 + q^70 + 26 * q^71 - 21 * q^72 - 8 * q^73 - 9 * q^74 + 13 * q^76 + 7 * q^77 - 21 * q^78 + 24 * q^79 + 18 * q^80 + 9 * q^81 + 19 * q^83 - 12 * q^84 + q^85 + 27 * q^86 + 45 * q^87 + q^88 + 30 * q^89 - 27 * q^90 + 16 * q^91 - 3 * q^92 - 15 * q^93 + 7 * q^94 + 3 * q^95 + 30 * q^96 + 12 * q^97 - 2 * q^98 - 24 * q^99

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