LMFDB - Embedded newform 930.2.y.b.29.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(29,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 3]))

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

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

chi := DirichletCharacter("930.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.y (of order $10$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.17
Character	$\chi$	$=$	930.29
Dual form			930.2.y.b.449.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.0766541 + 1.73035i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.02596 - 1.98681i) q^{5} +(-1.07909 + 1.35483i) q^{6} +(-2.19882 + 0.714440i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.98825 - 0.265277i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.0766541 + 1.73035i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.02596 - 1.98681i) q^{5} +(-1.07909 + 1.35483i) q^{6} +(-2.19882 + 0.714440i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.98825 - 0.265277i) q^{9} +(0.337800 - 2.21041i) q^{10} +(-0.734441 - 2.26038i) q^{11} +(-1.66935 + 0.461806i) q^{12} +(-0.942922 + 0.685073i) q^{13} +(-2.19882 - 0.714440i) q^{14} +(3.51653 - 1.62297i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.14288 - 0.696265i) q^{17} +(-2.26162 - 1.97106i) q^{18} +(-2.09132 - 1.51943i) q^{19} +(1.57253 - 1.58970i) q^{20} +(-1.06769 - 3.85950i) q^{21} +(0.734441 - 2.26038i) q^{22} +(-0.939222 - 0.305172i) q^{23} +(-1.62198 - 0.607611i) q^{24} +(-2.89482 + 4.07676i) q^{25} -1.16552 q^{26} +(0.688085 - 5.15039i) q^{27} +(-1.35895 - 1.87043i) q^{28} +(-0.0467931 - 0.0339972i) q^{29} +(3.79889 + 0.753951i) q^{30} +(-1.01658 - 5.47417i) q^{31} -1.00000 q^{32} +(3.96755 - 1.09758i) q^{33} +(-1.32438 - 1.82285i) q^{34} +(3.67535 + 3.63565i) q^{35} +(-0.671126 - 2.92397i) q^{36} -5.14314 q^{37} +(-0.798814 - 2.45850i) q^{38} +(-1.11314 - 1.68410i) q^{39} +(2.20661 - 0.361785i) q^{40} +(1.21463 - 1.67179i) q^{41} +(1.40478 - 3.74997i) q^{42} +(-3.98227 - 2.89329i) q^{43} +(1.92279 - 1.39699i) q^{44} +(2.53876 + 6.20924i) q^{45} +(-0.580471 - 0.798950i) q^{46} +(-0.515217 + 0.374327i) q^{47} +(-0.955062 - 1.44494i) q^{48} +(-1.33873 + 0.972645i) q^{49} +(-4.73822 + 1.59664i) q^{50} +(1.36905 - 3.65458i) q^{51} +(-0.942922 - 0.685073i) q^{52} +(5.38488 + 1.74965i) q^{53} +(3.58400 - 3.76231i) q^{54} +(-3.73743 + 3.77824i) q^{55} -2.31198i q^{56} +(2.78947 - 3.50226i) q^{57} +(-0.0178734 - 0.0550086i) q^{58} +(2.75885 + 3.79723i) q^{59} +(2.63020 + 2.84289i) q^{60} +11.0451i q^{61} +(2.39521 - 5.02623i) q^{62} +(6.76015 - 1.55163i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(2.32851 + 1.17055i) q^{65} +(3.85495 + 1.44411i) q^{66} +6.15029i q^{67} -2.25316i q^{68} +(0.600050 - 1.60179i) q^{69} +(0.836440 + 5.10162i) q^{70} +(-3.33910 - 1.08494i) q^{71} +(1.17571 - 2.76002i) q^{72} +(1.70047 + 5.23350i) q^{73} +(-4.16089 - 3.02306i) q^{74} +(-6.83234 - 5.32157i) q^{75} +(0.798814 - 2.45850i) q^{76} +(3.22981 + 4.44545i) q^{77} +(0.0893415 - 2.01675i) q^{78} +(-14.2376 - 4.62607i) q^{79} +(1.99783 + 1.00432i) q^{80} +(8.85926 + 1.58543i) q^{81} +(1.96531 - 0.638568i) q^{82} +(6.71473 - 9.24203i) q^{83} +(3.34067 - 2.20808i) q^{84} +(0.815161 + 4.97184i) q^{85} +(-1.52109 - 4.68144i) q^{86} +(0.0624140 - 0.0783625i) q^{87} +2.37670 q^{88} +(3.68728 + 11.3483i) q^{89} +(-1.59580 + 6.51563i) q^{90} +(1.58387 - 2.18001i) q^{91} -0.987556i q^{92} +(9.55018 - 1.33942i) q^{93} -0.636843 q^{94} +(-0.873220 + 5.71393i) q^{95} +(0.0766541 - 1.73035i) q^{96} +(-7.60762 + 2.47186i) q^{97} -1.65476 q^{98} +(1.59506 + 6.94940i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9	$ 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9} + 2 q^{10} - 35 q^{15} - 32 q^{16} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 20 q^{23} - 10 q^{25} - 48 q^{31} - 128 q^{32} + 8 q^{33} + 10 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{38} + 4 q^{39} - 3 q^{40} + 5 q^{45} + 10 q^{46} - 6 q^{47} + 46 q^{49} + 5 q^{50} + 34 q^{51} + 20 q^{53} + 35 q^{60} + 8 q^{62} - 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} - 6 q^{72} + 5 q^{75} + 12 q^{76} - 50 q^{77} - 4 q^{78} - 10 q^{79} - 2 q^{80} - 24 q^{81} + 40 q^{83} - 30 q^{85} + 4 q^{87} - 5 q^{90} + 20 q^{91} + 26 q^{93} - 4 q^{94} + 26 q^{95} + 124 q^{98}+O(q^{100}) $ 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9 + 2 * q^10 - 35 * q^15 - 32 * q^16 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 20 * q^23 - 10 * q^25 - 48 * q^31 - 128 * q^32 + 8 * q^33 + 10 * q^34 - 16 * q^35 - 4 * q^36 - 12 * q^38 + 4 * q^39 - 3 * q^40 + 5 * q^45 + 10 * q^46 - 6 * q^47 + 46 * q^49 + 5 * q^50 + 34 * q^51 + 20 * q^53 + 35 * q^60 + 8 * q^62 - 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 - 6 * q^72 + 5 * q^75 + 12 * q^76 - 50 * q^77 - 4 * q^78 - 10 * q^79 - 2 * q^80 - 24 * q^81 + 40 * q^83 - 30 * q^85 + 4 * q^87 - 5 * q^90 + 20 * q^91 + 26 * q^93 - 4 * q^94 + 26 * q^95 + 124 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.0766541	+	1.73035i	−0.0442562	+	0.999020i
$3$	−0.0766541	+	1.73035i	−0.0442562	+	0.999020i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.02596	−	1.98681i	−0.458822	−	0.888528i
$5$	−1.02596	−	1.98681i	−0.458822	−	0.888528i
$6$	−1.07909	+	1.35483i	−0.440537	+	0.553107i
$7$	−2.19882	+	0.714440i	−0.831076	+	0.270033i	−0.693499	−	0.720458i	$-0.743932\pi$
$7$	−2.19882	+	0.714440i	−0.831076	+	0.270033i	−0.137578	+	0.990491i	$0.543932\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−2.98825	−	0.265277i	−0.996083	−	0.0884258i
$10$	0.337800	−	2.21041i	0.106822	−	0.698991i
$11$	−0.734441	−	2.26038i	−0.221442	−	0.681529i	−0.998633	−	0.0522644i	$-0.983356\pi$
$11$	−0.734441	−	2.26038i	−0.221442	−	0.681529i	0.777191	−	0.629265i	$-0.216644\pi$
$12$	−1.66935	+	0.461806i	−0.481900	+	0.133312i
$13$	−0.942922	+	0.685073i	−0.261519	+	0.190005i	−0.710817	−	0.703377i	$-0.751674\pi$
$13$	−0.942922	+	0.685073i	−0.261519	+	0.190005i	0.449297	+	0.893382i	$0.351674\pi$
$14$	−2.19882	−	0.714440i	−0.587660	−	0.190942i
$15$	3.51653	−	1.62297i	0.907963	−	0.419050i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−2.14288	−	0.696265i	−0.519726	−	0.168869i	0.0373951	−	0.999301i	$-0.488094\pi$
$17$	−2.14288	−	0.696265i	−0.519726	−	0.168869i	−0.557121	+	0.830431i	$0.688094\pi$
$18$	−2.26162	−	1.97106i	−0.533068	−	0.464584i
$19$	−2.09132	−	1.51943i	−0.479782	−	0.348582i	0.321459	−	0.946923i	$-0.395827\pi$
$19$	−2.09132	−	1.51943i	−0.479782	−	0.348582i	−0.801241	+	0.598341i	$0.795827\pi$
$20$	1.57253	−	1.58970i	0.351628	−	0.355468i
$21$	−1.06769	−	3.85950i	−0.232988	−	0.842213i
$22$	0.734441	−	2.26038i	0.156583	−	0.481914i
$23$	−0.939222	−	0.305172i	−0.195841	−	0.0636327i	0.209454	−	0.977818i	$-0.432831\pi$
$23$	−0.939222	−	0.305172i	−0.195841	−	0.0636327i	−0.405295	+	0.914186i	$0.632831\pi$
$24$	−1.62198	−	0.607611i	−0.331085	−	0.124028i
$25$	−2.89482	+	4.07676i	−0.578965	+	0.815353i
$26$	−1.16552			−0.228576
$27$	0.688085	−	5.15039i	0.132422	−	0.991193i
$28$	−1.35895	−	1.87043i	−0.256817	−	0.353478i
$29$	−0.0467931	−	0.0339972i	−0.00868926	−	0.00631311i	0.583432	−	0.812162i	$-0.301709\pi$
$29$	−0.0467931	−	0.0339972i	−0.00868926	−	0.00631311i	−0.592121	+	0.805849i	$0.701709\pi$
$30$	3.79889	+	0.753951i	0.693579	+	0.137652i
$31$	−1.01658	−	5.47417i	−0.182583	−	0.983191i
$31$	−1.01658	−	5.47417i	−0.182583	−	0.983191i
$32$	−1.00000			−0.176777
$33$	3.96755	−	1.09758i	0.690662	−	0.191063i
$34$	−1.32438	−	1.82285i	−0.227128	−	0.312615i
$35$	3.67535	+	3.63565i	0.621248	+	0.614538i
$36$	−0.671126	−	2.92397i	−0.111854	−	0.487328i
$37$	−5.14314			−0.845527			−0.422763	−	0.906240i	$-0.638940\pi$
$37$	−5.14314			−0.845527			−0.422763	+	0.906240i	$0.638940\pi$
$38$	−0.798814	−	2.45850i	−0.129585	−	0.398821i
$39$	−1.11314	−	1.68410i	−0.178245	−	0.269672i
$40$	2.20661	−	0.361785i	0.348895	−	0.0572033i
$41$	1.21463	−	1.67179i	0.189693	−	0.261090i	−0.703568	−	0.710628i	$-0.748411\pi$
$41$	1.21463	−	1.67179i	0.189693	−	0.261090i	0.893262	+	0.449537i	$0.148411\pi$
$42$	1.40478	−	3.74997i	0.216763	−	0.578633i
$43$	−3.98227	−	2.89329i	−0.607291	−	0.441223i	0.241168	−	0.970483i	$-0.422469\pi$
$43$	−3.98227	−	2.89329i	−0.607291	−	0.441223i	−0.848459	+	0.529261i	$0.822469\pi$
$44$	1.92279	−	1.39699i	0.289872	−	0.210604i
$45$	2.53876	+	6.20924i	0.378456	+	0.925619i
$46$	−0.580471	−	0.798950i	−0.0855858	−	0.117799i
$47$	−0.515217	+	0.374327i	−0.0751522	+	0.0546012i	−0.624727	−	0.780843i	$-0.714790\pi$
$47$	−0.515217	+	0.374327i	−0.0751522	+	0.0546012i	0.549575	+	0.835444i	$0.314790\pi$
$48$	−0.955062	−	1.44494i	−0.137851	−	0.208559i
$49$	−1.33873	+	0.972645i	−0.191247	+	0.138949i
$50$	−4.73822	+	1.59664i	−0.670086	+	0.225798i
$51$	1.36905	−	3.65458i	0.191705	−	0.511743i
$52$	−0.942922	−	0.685073i	−0.130760	−	0.0950025i
$53$	5.38488	+	1.74965i	0.739670	+	0.240333i	0.654530	−	0.756036i	$-0.272866\pi$
$53$	5.38488	+	1.74965i	0.739670	+	0.240333i	0.0851396	+	0.996369i	$0.472866\pi$
$54$	3.58400	−	3.76231i	0.487720	−	0.511985i
$55$	−3.73743	+	3.77824i	−0.503955	+	0.509458i
$56$		−	2.31198i		−	0.308951i
$57$	2.78947	−	3.50226i	0.369474	−	0.463885i
$58$	−0.0178734	−	0.0550086i	−0.00234689	−	0.00722298i
$59$	2.75885	+	3.79723i	0.359172	+	0.494358i	0.949918	−	0.312500i	$-0.101166\pi$
$59$	2.75885	+	3.79723i	0.359172	+	0.494358i	−0.590746	+	0.806858i	$0.701166\pi$
$60$	2.63020	+	2.84289i	0.339558	+	0.367016i
$61$			11.0451i			1.41418i	0.707123	+	0.707091i	$0.249993\pi$
$61$			11.0451i			1.41418i	−0.707123	+	0.707091i	$0.750007\pi$
$62$	2.39521	−	5.02623i	0.304192	−	0.638332i
$63$	6.76015	−	1.55163i	0.851699	−	0.195487i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	2.32851	+	1.17055i	0.288816	+	0.145189i
$66$	3.85495	+	1.44411i	0.474512	+	0.177758i
$67$			6.15029i			0.751377i	0.926746	+	0.375689i	$0.122594\pi$
$67$			6.15029i			0.751377i	−0.926746	+	0.375689i	$0.877406\pi$
$68$		−	2.25316i		−	0.273236i
$69$	0.600050	−	1.60179i	0.0722375	−	0.192833i
$70$	0.836440	+	5.10162i	0.0999736	+	0.609761i
$71$	−3.33910	−	1.08494i	−0.396279	−	0.128759i	0.104097	−	0.994567i	$-0.466805\pi$
$71$	−3.33910	−	1.08494i	−0.396279	−	0.128759i	−0.500376	+	0.865808i	$0.666805\pi$
$72$	1.17571	−	2.76002i	0.138559	−	0.325271i
$73$	1.70047	+	5.23350i	0.199025	+	0.612535i	0.999906	+	0.0137119i	$0.00436477\pi$
$73$	1.70047	+	5.23350i	0.199025	+	0.612535i	−0.800881	+	0.598823i	$0.795635\pi$
$74$	−4.16089	−	3.02306i	−0.483693	−	0.351424i
$75$	−6.83234	−	5.32157i	−0.788931	−	0.614482i
$76$	0.798814	−	2.45850i	0.0916303	−	0.282009i
$77$	3.22981	+	4.44545i	0.368071	+	0.506606i
$78$	0.0893415	−	2.01675i	0.0101159	−	0.228352i
$79$	−14.2376	−	4.62607i	−1.60185	−	0.520474i	−0.634289	−	0.773096i	$-0.718707\pi$
$79$	−14.2376	−	4.62607i	−1.60185	−	0.520474i	−0.967565	+	0.252622i	$0.918707\pi$
$80$	1.99783	+	1.00432i	0.223365	+	0.112286i
$81$	8.85926	+	1.58543i	0.984362	+	0.176159i
$82$	1.96531	−	0.638568i	0.217032	−	0.0705181i
$83$	6.71473	−	9.24203i	0.737037	−	1.01444i	−0.261746	−	0.965137i	$-0.584298\pi$
$83$	6.71473	−	9.24203i	0.737037	−	1.01444i	0.998784	−	0.0493082i	$-0.0157017\pi$
$84$	3.34067	−	2.20808i	0.364497	−	0.240921i
$85$	0.815161	+	4.97184i	0.0884166	+	0.539272i
$86$	−1.52109	−	4.68144i	−0.164024	−	0.504813i
$87$	0.0624140	−	0.0783625i	0.00669148	−	0.00840135i
$88$	2.37670			0.253357
$89$	3.68728	+	11.3483i	0.390851	+	1.20292i	0.932146	+	0.362083i	$0.117934\pi$
$89$	3.68728	+	11.3483i	0.390851	+	1.20292i	−0.541295	+	0.840833i	$0.682066\pi$
$90$	−1.59580	+	6.51563i	−0.168212	+	0.686808i
$91$	1.58387	−	2.18001i	0.166035	−	0.228528i
$92$		−	0.987556i		−	0.102960i
$93$	9.55018	−	1.33942i	0.990308	−	0.138891i
$94$	−0.636843			−0.0656854
$95$	−0.873220	+	5.71393i	−0.0895905	+	0.586237i
$96$	0.0766541	−	1.73035i	0.00782347	−	0.176603i
$97$	−7.60762	+	2.47186i	−0.772436	+	0.250980i	−0.668608	−	0.743615i	$-0.733109\pi$
$97$	−7.60762	+	2.47186i	−0.772436	+	0.250980i	−0.103829	+	0.994595i	$0.533109\pi$
$98$	−1.65476			−0.167156
$99$	1.59506	+	6.94940i	0.160310	+	0.698441i
$100$	−4.77178	−	1.49335i	−0.477178	−	0.149335i
$101$	−6.96271	−	2.26232i	−0.692815	−	0.225109i	−0.0586178	−	0.998280i	$-0.518669\pi$
$101$	−6.96271	−	2.26232i	−0.692815	−	0.225109i	−0.634197	+	0.773171i	$0.718669\pi$
$102$	3.25569	−	2.15191i	0.322361	−	0.213071i
$103$	0.682353	−	0.939178i	0.0672342	−	0.0925399i	−0.774076	−	0.633093i	$-0.781785\pi$
$103$	0.682353	−	0.939178i	0.0672342	−	0.0925399i	0.841310	+	0.540553i	$0.181785\pi$
$104$	−0.360164	−	1.10847i	−0.0353170	−	0.108695i
$105$	−6.57270	+	6.08097i	−0.641430	+	0.593442i
$106$	3.32804	+	4.58065i	0.323248	+	0.444912i
$107$	1.66206	−	5.11530i	0.160677	−	0.494514i	−0.838014	−	0.545648i	$-0.816284\pi$
$107$	1.66206	−	5.11530i	0.160677	−	0.494514i	0.998692	+	0.0511339i	$0.0162835\pi$
$108$	5.11094	−	0.937151i	0.491801	−	0.0901774i
$109$	−2.45021	+	1.78018i	−0.234687	+	0.170510i	−0.698913	−	0.715207i	$-0.746333\pi$
$109$	−2.45021	+	1.78018i	−0.234687	+	0.170510i	0.464226	+	0.885717i	$0.346333\pi$
$110$	−5.24444	+	0.859855i	−0.500038	+	0.0819840i
$111$	0.394243	−	8.89945i	0.0374198	−	0.844699i
$112$	1.35895	−	1.87043i	0.128408	−	0.176739i
$113$	−2.59305	−	7.98058i	−0.243933	−	0.750750i	−0.995810	−	0.0914461i	$-0.970851\pi$
$113$	−2.59305	−	7.98058i	−0.243933	−	0.750750i	0.751877	−	0.659304i	$-0.229149\pi$
$114$	4.31530	−	1.19378i	0.404165	−	0.111807i
$115$	0.357283	+	2.17915i	0.0333169	+	0.203207i
$116$	0.0178734	−	0.0550086i	0.00165950	−	0.00510742i
$117$	2.99942	−	1.79703i	0.277296	−	0.166136i
$118$			4.69364i			0.432084i
$119$	5.20926			0.477532
$120$	0.456871	+	3.84594i	0.0417065	+	0.351085i
$121$	4.32929	−	3.14541i	0.393572	−	0.285947i
$122$	−6.49216	+	8.93569i	−0.587772	+	0.808999i
$123$	2.79969	+	2.22989i	0.252439	+	0.201062i
$124$	4.89211	−	2.65843i	0.439324	−	0.238734i
$125$	11.0697	+	1.56888i	0.990106	+	0.140325i
$126$	6.38110	+	2.71822i	0.568473	+	0.242158i
$127$	−15.6424	+	11.3648i	−1.38804	+	1.00847i	−0.391958	+	0.919983i	$0.628202\pi$
$127$	−15.6424	+	11.3648i	−1.38804	+	1.00847i	−0.996078	+	0.0884840i	$0.971798\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	5.31167	−	6.66896i	0.467667	−	0.587169i
$130$	1.19577	+	2.31566i	0.104876	+	0.203097i
$131$	7.90497	−	2.56848i	0.690660	−	0.224409i	0.0574037	−	0.998351i	$-0.481718\pi$
$131$	7.90497	−	2.56848i	0.690660	−	0.224409i	0.633257	+	0.773942i	$0.281718\pi$
$132$	2.26990	+	3.43419i	0.197569	+	0.298908i
$133$	5.68399	+	1.84684i	0.492864	+	0.160141i
$134$	−3.61505	+	4.97569i	−0.312293	+	0.429834i
$135$	−10.9388	+	3.91699i	−0.941461	+	0.337121i
$136$	1.32438	−	1.82285i	0.113564	−	0.156308i
$137$	1.44126	+	1.98373i	0.123135	+	0.169481i	0.866134	−	0.499811i	$-0.166597\pi$
$137$	1.44126	+	1.98373i	0.123135	+	0.169481i	−0.742999	+	0.669292i	$0.766597\pi$
$138$	1.42696	−	0.943177i	0.121471	−	0.0802886i
$139$	−11.0992	−	15.2768i	−0.941423	−	1.29576i	−0.955234	−	0.295853i	$-0.904396\pi$
$139$	−11.0992	−	15.2768i	−0.941423	−	1.29576i	0.0138108	−	0.999905i	$-0.495604\pi$
$140$	−2.32197	+	4.61895i	−0.196242	+	0.390372i
$141$	−0.608225	−	0.920202i	−0.0512218	−	0.0774950i
$142$	−2.06368	−	2.84041i	−0.173180	−	0.238362i
$143$	2.24104	+	1.62821i	0.187405	+	0.136158i
$144$	2.57347	−	1.54183i	0.214456	−	0.128486i
$145$	−0.0195382	+	0.127849i	−0.00162256	+	0.0106172i
$146$	−1.70047	+	5.23350i	−0.140732	+	0.433128i
$147$	−1.58040	−	2.39103i	−0.130349	−	0.197209i
$148$	−1.58932	−	4.89142i	−0.130641	−	0.402072i
$149$			15.5615i			1.27485i	0.770514	+	0.637423i	$0.220000\pi$
$149$			15.5615i			1.27485i	−0.770514	+	0.637423i	$0.780000\pi$
$150$	−2.39954	−	8.32119i	−0.195922	−	0.679422i
$151$	9.71319	−	3.15601i	0.790448	−	0.256832i	0.114153	−	0.993463i	$-0.463585\pi$
$151$	9.71319	−	3.15601i	0.790448	−	0.256832i	0.676295	+	0.736631i	$0.263585\pi$
$152$	2.09132	−	1.51943i	0.169629	−	0.123242i
$153$	6.21877	+	2.64907i	0.502757	+	0.214165i
$154$			5.49488i			0.442790i
$155$	−9.83318	+	7.63601i	−0.789820	+	0.613339i
$156$	1.25770	−	1.57907i	0.100696	−	0.126427i
$157$	4.78698	−	6.58872i	0.382043	−	0.525837i	−0.574081	−	0.818798i	$-0.694641\pi$
$157$	4.78698	−	6.58872i	0.382043	−	0.525837i	0.956124	+	0.292961i	$0.0946407\pi$
$158$	−8.79931	−	12.1112i	−0.700036	−	0.963517i
$159$	−3.44029	+	9.18363i	−0.272833	+	0.728309i
$160$	1.02596	+	1.98681i	0.0811090	+	0.157071i
$161$	2.28321			0.179942
$162$	6.23540	+	6.48998i	0.489899	+	0.509901i
$163$	−17.1297	−	5.56577i	−1.34170	−	0.435945i	−0.451808	−	0.892115i	$-0.649221\pi$
$163$	−17.1297	−	5.56577i	−1.34170	−	0.435945i	−0.889892	+	0.456171i	$0.849221\pi$
$164$	1.96531	+	0.638568i	0.153465	+	0.0498638i
$165$	−6.25121	−	6.75670i	−0.486656	−	0.526008i
$166$	10.8647	−	3.53014i	0.843261	−	0.273992i
$167$	−13.5676	+	18.6742i	−1.04989	+	1.44505i	−0.160989	+	0.986956i	$0.551468\pi$
$167$	−13.5676	+	18.6742i	−1.04989	+	1.44505i	−0.888903	+	0.458096i	$0.848532\pi$
$168$	4.00054	+	0.177222i	0.308648	+	0.0136730i
$169$	−3.59744	+	11.0718i	−0.276726	+	0.851676i
$170$	−2.26290	+	4.50144i	−0.173556	+	0.345245i
$171$	5.84632	+	5.09523i	0.447079	+	0.389642i
$172$	1.52109	−	4.68144i	0.115982	−	0.356957i
$173$	−10.2188	+	7.42441i	−0.776923	+	0.564468i	−0.904054	−	0.427418i	$-0.859423\pi$
$173$	−10.2188	+	7.42441i	−0.776923	+	0.564468i	0.127131	+	0.991886i	$0.459423\pi$
$174$	0.0965543	−	0.0267106i	0.00731976	−	0.00202493i
$175$	3.45260	−	11.0322i	0.260992	−	0.833960i
$176$	1.92279	+	1.39699i	0.144936	+	0.105302i
$177$	−6.78203	+	4.48272i	−0.509769	+	0.336942i
$178$	−3.68728	+	11.3483i	−0.276374	+	0.850590i
$179$	2.89608	+	8.91321i	0.216463	+	0.666205i	0.999046	+	0.0436591i	$0.0139015\pi$
$179$	2.89608	+	8.91321i	0.216463	+	0.666205i	−0.782583	+	0.622546i	$0.786098\pi$
$180$	−5.12082	+	4.33327i	−0.381683	+	0.322983i
$181$		−	4.48683i		−	0.333503i	−0.985999	−	0.166752i	$-0.946672\pi$
$181$		−	4.48683i		−	0.333503i	0.985999	−	0.166752i	$-0.0533278\pi$
$182$	2.56276	−	0.832691i	0.189964	−	0.0617232i
$183$	−19.1120	−	0.846653i	−1.41280	−	0.0625864i
$184$	0.580471	−	0.798950i	0.0427929	−	0.0588994i
$185$	5.27664	+	10.2184i	0.387946	+	0.751275i
$186$	8.51355	+	4.52984i	0.624244	+	0.332144i
$187$			5.35509i			0.391603i
$188$	−0.515217	−	0.374327i	−0.0375761	−	0.0273006i
$189$	2.16667	+	11.8164i	0.157602	+	0.859516i
$190$	−4.06502	+	4.10940i	−0.294907	+	0.298128i
$191$		−	16.0896i		−	1.16420i	−0.813116	−	0.582102i	$-0.802231\pi$
$191$		−	16.0896i		−	1.16420i	0.813116	−	0.582102i	$-0.197769\pi$
$192$	1.07909	−	1.35483i	0.0778767	−	0.0977764i
$193$	−0.673299	+	0.218768i	−0.0484651	+	0.0157473i	−0.333149	−	0.942874i	$-0.608111\pi$
$193$	−0.673299	+	0.218768i	−0.0484651	+	0.0157473i	0.284684	+	0.958621i	$0.408111\pi$
$194$	−7.60762	−	2.47186i	−0.546195	−	0.177470i
$195$	−2.20396	+	3.93941i	−0.157829	+	0.282107i
$196$	−1.33873	−	0.972645i	−0.0956236	−	0.0694746i
$197$	−20.9215	+	6.79780i	−1.49059	+	0.484323i	−0.937258	−	0.348635i	$-0.886645\pi$
$197$	−20.9215	+	6.79780i	−1.49059	+	0.484323i	−0.553335	+	0.832959i	$0.686645\pi$
$198$	−2.79432	+	6.55974i	−0.198584	+	0.466180i
$199$	−1.13307	−	1.55954i	−0.0803214	−	0.110553i	0.766966	−	0.641688i	$-0.221766\pi$
$199$	−1.13307	−	1.55954i	−0.0803214	−	0.110553i	−0.847287	+	0.531135i	$0.821766\pi$
$200$	−2.98268	−	4.01293i	−0.210907	−	0.283757i
$201$	−10.6422	−	0.471445i	−0.750641	−	0.0332531i
$202$	−4.30319	−	5.92283i	−0.302771	−	0.416729i
$203$	0.127179	+	0.0413228i	0.00892618	+	0.00290029i
$204$	3.89877	+	0.172714i	0.272968	+	0.0120924i
$205$	−4.56769	−	0.698048i	−0.319021	−	0.0487538i
$206$	1.10407	−	0.358734i	0.0769242	−	0.0249942i
$207$	2.72567	+	1.16108i	0.189447	+	0.0807008i
$208$	0.360164	−	1.10847i	0.0249729	−	0.0768586i
$209$	−1.89854	+	5.84311i	−0.131325	+	0.404176i
$210$	−8.89173	+	1.05628i	−0.613588	+	0.0728900i
$211$	18.7889			1.29348			0.646741	−	0.762710i	$-0.276131\pi$
$211$	18.7889			1.29348			0.646741	+	0.762710i	$0.276131\pi$
$212$			5.66200i			0.388867i
$213$	2.13329	−	5.69467i	0.146170	−	0.390192i
$214$	4.35133	−	3.16143i	0.297451	−	0.216111i
$215$	−1.66278	+	10.8804i	−0.113400	+	0.742038i
$216$	4.68568	+	2.24597i	0.318820	+	0.152819i
$217$	6.14624	+	11.3104i	0.417234	+	0.767803i
$218$	−3.02862			−0.205124
$219$	−9.18616	+	2.54124i	−0.620743	+	0.171721i
$220$	−4.74825	−	2.38697i	−0.320127	−	0.160929i
$221$	2.49756	−	0.811508i	0.168004	−	0.0545879i
$222$	5.54992	−	6.96808i	0.372486	−	0.467667i
$223$	1.15132			0.0770980			0.0385490	−	0.999257i	$-0.487726\pi$
$223$	1.15132			0.0770980			0.0385490	+	0.999257i	$0.487726\pi$
$224$	2.19882	−	0.714440i	0.146915	−	0.0477355i
$225$	9.73192	−	11.4144i	0.648795	−	0.760963i
$226$	2.59305	−	7.98058i	0.172487	−	0.530860i
$227$	4.72616	+	3.43375i	0.313686	+	0.227906i	0.733476	−	0.679715i	$-0.237896\pi$
$227$	4.72616	+	3.43375i	0.313686	+	0.227906i	−0.419791	+	0.907621i	$0.637896\pi$
$228$	4.19284	+	1.57068i	0.277677	+	0.104021i
$229$	−2.28116	+	3.13974i	−0.150743	+	0.207480i	−0.877710	−	0.479193i	$-0.840929\pi$
$229$	−2.28116	+	3.13974i	−0.150743	+	0.207480i	0.726967	+	0.686673i	$0.240929\pi$
$230$	−0.991823	+	1.97297i	−0.0653988	+	0.130094i
$231$	−7.93978	+	5.24795i	−0.522399	+	0.345290i
$232$	0.0467931	−	0.0339972i	0.00307212	−	0.00223202i
$233$	1.64759	−	1.19705i	0.107937	−	0.0784211i	−0.532507	−	0.846425i	$-0.678750\pi$
$233$	1.64759	−	1.19705i	0.107937	−	0.0784211i	0.640445	+	0.768004i	$0.278750\pi$
$234$	3.48285	+	0.309185i	0.227681	+	0.0202120i
$235$	1.27231	+	0.639595i	0.0829962	+	0.0417226i
$236$	−2.75885	+	3.79723i	−0.179586	+	0.247179i
$237$	9.09611	−	24.2815i	0.590856	−	1.57725i
$238$	4.21438	+	3.06192i	0.273178	+	0.198475i
$239$	6.61255	−	20.3513i	0.427730	−	1.31642i	−0.472625	−	0.881263i	$-0.656694\pi$
$239$	6.61255	−	20.3513i	0.427730	−	1.31642i	0.900356	−	0.435155i	$-0.143306\pi$
$240$	−1.89097	+	3.37997i	−0.122062	+	0.218176i
$241$	15.8223	−	5.14097i	1.01920	−	0.331159i	0.248690	−	0.968583i	$-0.420000\pi$
$241$	15.8223	−	5.14097i	1.01920	−	0.331159i	0.770513	+	0.637424i	$0.220000\pi$
$242$	5.35130			0.343994
$243$	−3.42245	+	15.2081i	−0.219550	+	0.975601i
$244$	−10.5045	+	3.41313i	−0.672484	+	0.218503i
$245$	3.30594	+	1.66191i	0.211209	+	0.106176i
$246$	0.954300	+	3.44963i	0.0608439	+	0.219941i
$247$	3.01288			0.191705
$248$	5.52039	+	0.724791i	0.350545	+	0.0460243i
$249$	15.4773	+	12.3273i	0.980832	+	0.781211i
$250$	8.03342	+	7.77587i	0.508078	+	0.491789i
$251$	5.80653	−	4.21869i	0.366505	−	0.266282i	−0.389255	−	0.921130i	$-0.627268\pi$
$251$	5.80653	−	4.21869i	0.366505	−	0.266282i	0.755760	+	0.654848i	$0.227268\pi$
$252$	3.56469	+	5.94980i	0.224554	+	0.374802i
$253$			2.34713i			0.147562i
$254$	−19.3350			−1.21319
$255$	−8.66553	+	1.02940i	−0.542656	+	0.0644638i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	4.70089	−	14.4679i	0.293234	−	0.902481i	−0.690575	−	0.723261i	$-0.742643\pi$
$257$	4.70089	−	14.4679i	0.293234	−	0.902481i	0.983809	−	0.179220i	$-0.0573574\pi$
$258$	8.21715	−	2.27318i	0.511577	−	0.141522i
$259$	11.3088	−	3.67447i	0.702697	−	0.228320i
$260$	−0.393712	+	2.57626i	−0.0244170	+	0.159773i
$261$	0.130811	+	0.114005i	0.00809698	+	0.00705674i
$262$	7.90497	+	2.56848i	0.488371	+	0.158681i
$263$	−3.25661	−	4.48234i	−0.200811	−	0.276393i	0.696721	−	0.717342i	$-0.254642\pi$
$263$	−3.25661	−	4.48234i	−0.200811	−	0.276393i	−0.897532	+	0.440950i	$0.854642\pi$
$264$	−0.182184	+	4.11253i	−0.0112126	+	0.253109i
$265$	−2.04843	−	12.4938i	−0.125834	−	0.767488i
$266$	3.51290	+	4.83509i	0.215390	+	0.296458i
$267$	−19.9192	+	5.51041i	−1.21904	+	0.337232i
$268$	−5.84927	+	1.90054i	−0.357301	+	0.116094i
$269$	20.3957	+	14.8183i	1.24355	+	0.903489i	0.997829	−	0.0658526i	$-0.0209767\pi$
$269$	20.3957	+	14.8183i	1.24355	+	0.903489i	0.245717	+	0.969342i	$0.420977\pi$
$270$	−11.1520	−	3.26075i	−0.678690	−	0.198443i
$271$	23.3452	+	7.58532i	1.41812	+	0.460775i	0.915005	−	0.403443i	$-0.132187\pi$
$271$	23.3452	+	7.58532i	1.41812	+	0.460775i	0.503116	+	0.864219i	$0.332187\pi$
$272$	2.14288	−	0.696265i	0.129931	−	0.0422173i
$273$	3.65078	+	2.90777i	0.220956	+	0.175986i
$274$			2.45202i			0.148132i
$275$	11.3411	+	3.54925i	0.683894	+	0.214028i
$276$	1.70882	+	0.0757002i	0.102859	+	0.00455662i
$277$	−2.27846	−	1.65540i	−0.136900	−	0.0994634i	0.517228	−	0.855848i	$-0.326964\pi$
$277$	−2.27846	−	1.65540i	−0.136900	−	0.0994634i	−0.654127	+	0.756384i	$0.726964\pi$
$278$		−	18.8831i		−	1.13253i
$279$	1.58561	+	16.6279i	0.0949279	+	0.995484i
$280$	−4.59346	+	2.37199i	−0.274512	+	0.141753i
$281$	8.60887	−	11.8491i	0.513562	−	0.706858i	−0.470953	−	0.882158i	$-0.656090\pi$
$281$	8.60887	−	11.8491i	0.513562	−	0.706858i	0.984515	+	0.175301i	$0.0560898\pi$
$282$	0.0488166	−	1.10196i	0.00290699	−	0.0656210i
$283$	−25.0922	+	8.15295i	−1.49158	+	0.484643i	−0.937548	−	0.347855i	$-0.886910\pi$
$283$	−25.0922	+	8.15295i	−1.49158	+	0.484643i	−0.554028	+	0.832498i	$0.686910\pi$
$284$		−	3.51094i		−	0.208336i
$285$	−9.82019	−	1.94898i	−0.581698	−	0.115447i
$286$	0.856002	+	2.63450i	0.0506165	+	0.155781i
$287$	−1.47636	+	4.54375i	−0.0871465	+	0.268209i
$288$	2.98825	+	0.265277i	0.176084	+	0.0156316i
$289$	−9.64612	−	7.00832i	−0.567419	−	0.412254i
$290$	−0.0909542	+	0.0919474i	−0.00534102	+	0.00539934i
$291$	−3.69405	−	13.3533i	−0.216549	−	0.782787i
$292$	−4.45188	+	3.23448i	−0.260527	+	0.189284i
$293$	8.78246	−	27.0296i	0.513077	−	1.57909i	−0.273677	−	0.961822i	$-0.588240\pi$
$293$	8.78246	−	27.0296i	0.513077	−	1.57909i	0.786754	−	0.617267i	$-0.211760\pi$
$294$	0.126844	−	2.86332i	0.00739771	−	0.166992i
$295$	4.71392	−	9.37711i	0.274455	−	0.545956i
$296$	1.58932	−	4.89142i	0.0923772	−	0.284308i
$297$	−12.1472	+	2.22733i	−0.704851	+	0.129243i
$298$	−9.14681	+	12.5895i	−0.529861	+	0.729291i
$299$	1.09468	−	0.355682i	0.0633068	−	0.0205696i
$300$	2.94980	−	8.14240i	0.170307	−	0.470102i
$301$	10.8234	+	3.51673i	0.623850	+	0.202701i
$302$	9.71319	+	3.15601i	0.558931	+	0.181608i
$303$	4.44833	−	11.8745i	0.255550	−	0.682174i
$304$	2.58502			0.148261
$305$	21.9445	−	11.3318i	1.25654	−	0.648858i
$306$	3.47400	+	5.79844i	0.198595	+	0.331475i
$307$	15.3837	+	21.1738i	0.877991	+	1.20845i	0.976973	+	0.213362i	$0.0684414\pi$
$307$	15.3837	+	21.1738i	0.877991	+	1.20845i	−0.0989818	+	0.995089i	$0.531559\pi$
$308$	−3.22981	+	4.44545i	−0.184035	+	0.253303i
$309$	1.57280	+	1.25270i	0.0894737	+	0.0712638i
$310$	−12.4435	+	0.397868i	−0.706746	+	0.0225974i
$311$		−	18.0258i		−	1.02215i	−0.859536	−	0.511075i	$-0.829248\pi$
$311$		−	18.0258i		−	1.02215i	0.859536	−	0.511075i	$-0.170752\pi$
$312$	1.94566	−	0.538242i	0.110151	−	0.0304720i
$313$	12.9421	−	9.40301i	0.731533	−	0.531490i	−0.158515	−	0.987357i	$-0.550671\pi$
$313$	12.9421	−	9.40301i	0.731533	−	0.531490i	0.890048	+	0.455867i	$0.150671\pi$
$314$	7.74550	−	2.51667i	0.437104	−	0.142024i
$315$	−10.0184	−	11.8392i	−0.564473	−	0.667065i
$316$		−	14.9703i		−	0.842144i
$317$	−7.23665	−	22.2721i	−0.406451	−	1.25093i	−0.919678	−	0.392674i	$-0.871550\pi$
$317$	−7.23665	−	22.2721i	−0.406451	−	1.25093i	0.513227	−	0.858253i	$-0.328450\pi$
$318$	−8.18125	+	5.40756i	−0.458782	+	0.303241i
$319$	−0.0424796	+	0.130739i	−0.00237840	+	0.00731997i
$320$	−0.337800	+	2.21041i	−0.0188836	+	0.123565i
$321$	8.72387	+	3.26806i	0.486919	+	0.182405i
$322$	1.84715	+	1.34204i	0.102938	+	0.0747887i
$323$	3.42353	+	4.71209i	0.190490	+	0.262188i
$324$	1.22983	+	8.91558i	0.0683238	+	0.495310i
$325$	−0.0632871	−	5.82723i	−0.00351054	−	0.323237i
$326$	−10.5867	−	14.5714i	−0.586344	−	0.807034i
$327$	−2.89252	−	4.37619i	−0.159957	−	0.242004i
$328$	1.21463	+	1.67179i	0.0670667	+	0.0923093i
$329$	0.865436	−	1.19117i	0.0477130	−	0.0656713i
$330$	−1.08585	−	9.14065i	−0.0597739	−	0.503176i
$331$	−10.7986	+	14.8630i	−0.593545	+	0.816945i	−0.995098	−	0.0988911i	$-0.968470\pi$
$331$	−10.7986	+	14.8630i	−0.593545	+	0.816945i	0.401553	+	0.915836i	$0.368470\pi$
$332$	10.8647	+	3.53014i	0.596276	+	0.193742i
$333$	15.3690	+	1.36436i	0.842215	+	0.0747664i
$334$	−21.9528	+	7.13291i	−1.20121	+	0.390295i
$335$	12.2194	−	6.30993i	0.667620	−	0.344748i
$336$	3.13233	+	2.49483i	0.170883	+	0.136104i
$337$	−1.37409	−	4.22900i	−0.0748513	−	0.230369i	0.906630	−	0.421927i	$-0.138646\pi$
$337$	−1.37409	−	4.22900i	−0.0748513	−	0.230369i	−0.981481	+	0.191558i	$0.938646\pi$
$338$	−9.41823	+	6.84275i	−0.512284	+	0.372196i
$339$	14.0080	−	3.87515i	0.760810	−	0.210469i
$340$	−4.47660	+	2.31165i	−0.242778	+	0.125367i
$341$	−11.6271	+	6.31830i	−0.629641	+	0.342155i
$342$	1.73487	+	7.55851i	0.0938111	+	0.408717i
$343$	11.7614	−	16.1881i	0.635053	−	0.874076i
$344$	3.98227	−	2.89329i	0.214710	−	0.155996i
$345$	−3.79808	+	0.451186i	−0.204482	+	0.0242910i
$346$	−12.6312			−0.679056
$347$		−	4.13258i		−	0.221848i	−0.993829	−	0.110924i	$-0.964619\pi$
$347$		−	4.13258i		−	0.221848i	0.993829	−	0.110924i	$-0.0353811\pi$
$348$	0.0938142	+	0.0351439i	0.00502897	+	0.00188391i
$349$	−6.92567	+	21.3150i	−0.370723	+	1.14097i	0.575597	+	0.817734i	$0.304770\pi$
$349$	−6.92567	+	21.3150i	−0.370723	+	1.14097i	−0.946319	+	0.323233i	$0.895230\pi$
$350$	9.27780	−	6.89589i	0.495919	−	0.368601i
$351$	2.87958	+	5.32781i	0.153701	+	0.284377i
$352$	0.734441	+	2.26038i	0.0391458	+	0.120478i
$353$	−16.1662	+	22.2509i	−0.860440	+	1.18429i	0.121024	+	0.992650i	$0.461382\pi$
$353$	−16.1662	+	22.2509i	−0.860440	+	1.18429i	−0.981464	+	0.191645i	$0.938618\pi$
$354$	−8.12165	−	0.359786i	−0.431661	−	0.0191224i
$355$	1.27021	+	7.74727i	0.0674156	+	0.411182i
$356$	−9.65343	+	7.01363i	−0.511631	+	0.371722i
$357$	−0.399311	+	9.01386i	−0.0211338	+	0.477064i
$358$	−2.89608	+	8.91321i	−0.153062	+	0.471078i
$359$	−12.1783	−	16.7620i	−0.642748	−	0.884667i	0.356010	−	0.934482i	$-0.384137\pi$
$359$	−12.1783	−	16.7620i	−0.642748	−	0.884667i	−0.998758	+	0.0498151i	$0.984137\pi$
$360$	−6.68986	+	0.495742i	−0.352587	+	0.0261279i
$361$	−3.80637	−	11.7148i	−0.200336	−	0.616569i
$362$	2.63729	−	3.62992i	0.138613	−	0.190784i
$363$	5.11082	+	7.73231i	0.268248	+	0.405841i
$364$	2.56276	+	0.832691i	0.134325	+	0.0436449i
$365$	8.65336	−	8.74785i	0.452938	−	0.457884i
$366$	−14.9642	−	11.9187i	−0.782194	−	0.623000i
$367$	28.7379			1.50010			0.750052	−	0.661378i	$-0.230028\pi$
$367$	28.7379			1.50010			0.750052	+	0.661378i	$0.230028\pi$
$368$	0.939222	−	0.305172i	0.0489603	−	0.0159082i
$369$	−4.07310	+	4.67352i	−0.212037	+	0.243294i
$370$	−1.73736	+	11.3684i	−0.0903208	+	0.591016i
$371$	−13.0904			−0.679620
$372$	4.22503	+	8.66886i	0.219058	+	0.449459i
$373$		−	15.9044i		−	0.823499i	−0.911297	−	0.411750i	$-0.864918\pi$
$373$		−	15.9044i		−	0.823499i	0.911297	−	0.411750i	$-0.135082\pi$
$374$	−3.14764	+	4.33236i	−0.162761	+	0.224021i
$375$	−3.56325	+	19.0343i	−0.184006	+	0.982925i
$376$	−0.196795	−	0.605674i	−0.0101490	−	0.0312353i
$377$	0.0674127			0.00347193
$378$	−5.19262	+	10.8332i	−0.267080	+	0.557199i
$379$	0.679661	+	2.09178i	0.0349118	+	0.107448i	0.966994	−	0.254800i	$-0.0820096\pi$
$379$	0.679661	+	2.09178i	0.0349118	+	0.107448i	−0.932082	+	0.362247i	$0.882010\pi$
$380$	−5.70411	+	0.935221i	−0.292615	+	0.0479758i
$381$	−18.4662	−	27.9380i	−0.946050	−	1.43131i
$382$	9.45723	−	13.0168i	0.483874	−	0.665996i
$383$	−33.9827	+	11.0416i	−1.73644	+	0.564202i	−0.994355	−	0.106109i	$-0.966161\pi$
$383$	−33.9827	+	11.0416i	−1.73644	+	0.564202i	−0.742080	+	0.670311i	$0.766161\pi$
$384$	1.66935	−	0.461806i	0.0851887	−	0.0235665i
$385$	5.51862	−	10.9779i	0.281255	−	0.559483i
$386$	−0.673299	−	0.218768i	−0.0342700	−	0.0111350i
$387$	11.1325	+	9.70228i	0.565897	+	0.493194i
$388$	−4.70177	−	6.47142i	−0.238696	−	0.328537i
$389$	6.64984	−	20.4661i	0.337160	−	1.03767i	−0.628488	−	0.777820i	$-0.716326\pi$
$389$	6.64984	−	20.4661i	0.337160	−	1.03767i	0.965648	−	0.259854i	$-0.0836743\pi$
$390$	−4.09857	+	1.89160i	−0.207539	+	0.0957848i
$391$	1.80016	+	1.30789i	0.0910381	+	0.0661431i
$392$	−0.511350	−	1.57377i	−0.0258271	−	0.0794875i
$393$	3.83843	+	13.8753i	0.193623	+	0.699915i
$394$	−20.9215	−	6.79780i	−1.05401	−	0.342468i
$395$	5.41603	+	33.0335i	0.272510	+	1.66210i
$396$	−6.11637	+	3.66448i	−0.307359	+	0.184147i
$397$			8.07639i			0.405342i	0.979247	+	0.202671i	$0.0649622\pi$
$397$			8.07639i			0.405342i	−0.979247	+	0.202671i	$0.935038\pi$
$398$		−	1.92770i		−	0.0966268i
$399$	−3.63139	+	9.69374i	−0.181797	+	0.485294i
$400$	−0.0542996	−	4.99971i	−0.00271498	−	0.249985i
$401$	15.7633	+	11.4527i	0.787183	+	0.571922i	0.907126	−	0.420859i	$-0.138271\pi$
$401$	15.7633	+	11.4527i	0.787183	+	0.571922i	−0.119943	+	0.992781i	$0.538271\pi$
$402$	−8.33259	−	6.63672i	−0.415592	−	0.331009i
$403$	4.70876	+	4.46529i	0.234560	+	0.222432i
$404$		−	7.32102i		−	0.364234i
$405$	−5.93927	−	19.2282i	−0.295125	−	0.955459i
$406$	0.0786006	+	0.108185i	0.00390088	+	0.00536911i
$407$	3.77733	+	11.6254i	0.187235	+	0.576251i
$408$	3.05265	+	2.43137i	0.151129	+	0.120371i
$409$		−	5.20959i		−	0.257598i	−0.991671	−	0.128799i	$-0.958888\pi$
$409$		−	5.20959i		−	0.257598i	0.991671	−	0.128799i	$-0.0411122\pi$
$410$	−3.28504	−	3.24955i	−0.162236	−	0.160484i
$411$	−3.54303	+	2.34183i	−0.174765	+	0.115514i
$412$	1.10407	+	0.358734i	0.0543936	+	0.0176736i
$413$	−8.77912	−	6.37840i	−0.431992	−	0.313861i
$414$	1.52265	+	2.54145i	0.0748341	+	0.124905i
$415$	−25.2512	−	3.85896i	−1.23953	−	0.189429i
$416$	0.942922	−	0.685073i	0.0462305	−	0.0335885i
$417$	27.2850	−	18.0345i	1.33615	−	0.883155i
$418$	−4.97045	+	3.61124i	−0.243113	+	0.176632i
$419$	−7.12259	−	9.80341i	−0.347961	−	0.478928i	0.598784	−	0.800910i	$-0.295651\pi$
$419$	−7.12259	−	9.80341i	−0.347961	−	0.478928i	−0.946746	+	0.321983i	$0.895651\pi$
$420$	−7.81442	−	4.37188i	−0.381305	−	0.213326i
$421$	−27.6382	+	20.0803i	−1.34700	+	0.978656i	−0.347849	+	0.937550i	$0.613088\pi$
$421$	−27.6382	+	20.0803i	−1.34700	+	0.978656i	−0.999155	+	0.0411054i	$0.986912\pi$
$422$	15.2006	+	11.0438i	0.739951	+	0.537606i
$423$	1.63890	−	0.981907i	0.0796859	−	0.0477420i
$424$	−3.32804	+	4.58065i	−0.161624	+	0.222456i
$425$	9.04178	−	6.72046i	0.438591	−	0.325990i
$426$	5.07311	−	3.35317i	0.245793	−	0.162461i
$427$	−7.89107	−	24.2862i	−0.381876	−	1.17529i
$428$	5.37854			0.259982
$429$	−2.98917	+	3.75299i	−0.144318	+	0.181196i
$430$	−7.74056	+	7.82508i	−0.373283	+	0.377359i
$431$	−11.4658	−	15.7813i	−0.552287	−	0.760158i	0.438033	−	0.898959i	$-0.355675\pi$
$431$	−11.4658	−	15.7813i	−0.552287	−	0.760158i	−0.990320	+	0.138801i	$0.955675\pi$
$432$	2.47065	+	4.57120i	0.118869	+	0.219932i
$433$	35.2945			1.69615			0.848074	−	0.529878i	$-0.177762\pi$
$433$	35.2945			1.69615			0.848074	+	0.529878i	$0.177762\pi$
$434$	−1.67570	+	12.7630i	−0.0804362	+	0.612644i
$435$	−0.219726	−	0.0436081i	−0.0105350	−	0.00209085i
$436$	−2.45021	−	1.78018i	−0.117344	−	0.0852552i
$437$	1.50053	+	2.06530i	0.0717800	+	0.0987966i
$438$	−8.92546	−	3.34358i	−0.426475	−	0.159762i
$439$	−8.10148			−0.386663			−0.193331	−	0.981134i	$-0.561929\pi$
$439$	−8.10148			−0.386663			−0.193331	+	0.981134i	$0.561929\pi$
$440$	−2.43839	−	4.72205i	−0.116246	−	0.225115i
$441$	4.25848	−	2.55137i	0.202785	−	0.121494i
$442$	2.49756	+	0.811508i	0.118797	+	0.0385995i
$443$	0.792833	−	2.44009i	0.0376686	−	0.115932i	−0.930454	−	0.366409i	$-0.880587\pi$
$443$	0.792833	−	2.44009i	0.0376686	−	0.115932i	0.968123	+	0.250476i	$0.0805873\pi$
$444$	8.58571	−	2.37513i	0.407460	−	0.112719i
$445$	18.7639	−	18.9688i	0.889494	−	0.899207i
$446$	0.931436	+	0.676728i	0.0441048	+	0.0320440i
$447$	−26.9269	−	1.19285i	−1.27360	−	0.0564199i
$448$	2.19882	+	0.714440i	0.103885	+	0.0337541i
$449$	16.8363	−	12.2323i	0.794556	−	0.577279i	−0.114756	−	0.993394i	$-0.536609\pi$
$449$	16.8363	−	12.2323i	0.794556	−	0.577279i	0.909312	+	0.416115i	$0.136609\pi$
$450$	14.5825	−	3.51420i	0.687427	−	0.165661i
$451$	−4.67096	−	1.51769i	−0.219947	−	0.0714650i
$452$	6.78869	−	4.93227i	0.319313	−	0.231994i
$453$	4.71645	+	17.0492i	0.221598	+	0.801040i
$454$	1.80523	+	5.55593i	0.0847237	+	0.260753i
$455$	−5.95626	−	0.910252i	−0.279234	−	0.0426733i
$456$	2.46885	+	3.73520i	0.115615	+	0.174917i
$457$	2.67042	−	8.21869i	0.124917	−	0.384454i	−0.868969	−	0.494866i	$-0.835217\pi$
$457$	2.67042	−	8.21869i	0.124917	−	0.384454i	0.993886	+	0.110412i	$0.0352170\pi$
$458$	−3.69099	+	1.19927i	−0.172469	+	0.0560384i
$459$	−5.06052	+	10.5576i	−0.236205	+	0.492787i
$460$	−1.96209	+	1.01319i	−0.0914827	+	0.0472402i
$461$	−8.26243	−	25.4291i	−0.384820	−	1.18435i	−0.936611	−	0.350371i	$-0.886056\pi$
$461$	−8.26243	−	25.4291i	−0.384820	−	1.18435i	0.551791	−	0.833982i	$-0.313944\pi$
$462$	−9.50808	−	0.421205i	−0.442356	−	0.0195962i
$463$	−25.2681	−	18.3584i	−1.17431	−	0.853185i	−0.182790	−	0.983152i	$-0.558513\pi$
$463$	−25.2681	−	18.3584i	−1.17431	−	0.853185i	−0.991518	+	0.129967i	$0.958513\pi$
$464$	0.0578394			0.00268513
$465$	−12.4592	−	17.6002i	−0.577784	−	0.816190i
$466$	2.03654			0.0943407
$467$	−0.684174	−	0.497081i	−0.0316598	−	0.0230022i	0.571843	−	0.820363i	$-0.306229\pi$
$467$	−0.684174	−	0.497081i	−0.0316598	−	0.0230022i	−0.603503	+	0.797361i	$0.706229\pi$
$468$	2.63595	+	2.29730i	0.121847	+	0.106193i
$469$	−4.39401	−	13.5234i	−0.202897	−	0.624452i
$470$	0.653374	+	1.26529i	0.0301379	+	0.0583633i
$471$	11.0339	+	8.78823i	0.508414	+	0.404940i
$472$	−4.46392	+	1.45041i	−0.205468	+	0.0667607i
$473$	−3.61518	+	11.1264i	−0.166226	+	0.511592i
$474$	21.6312	−	14.2976i	0.993554	−	0.656708i
$475$	12.2484	−	4.12733i	0.561994	−	0.189375i
$476$	1.60975	+	4.95430i	0.0737827	+	0.227080i
$477$	−15.6272	−	6.65688i	−0.715521	−	0.304798i
$478$	17.3119	−	12.5778i	0.791827	−	0.575296i
$479$	−28.1947	−	9.16103i	−1.28825	−	0.418578i	−0.416772	−	0.909011i	$-0.636839\pi$
$479$	−28.1947	−	9.16103i	−1.28825	−	0.418578i	−0.871479	+	0.490433i	$0.836839\pi$
$480$	−3.51653	+	1.62297i	−0.160507	+	0.0740782i
$481$	4.84958	−	3.52343i	0.221122	−	0.160654i
$482$	15.8223	+	5.14097i	0.720686	+	0.234165i
$483$	−0.175017	+	3.95076i	−0.00796355	+	0.179766i
$484$	4.32929	+	3.14541i	0.196786	+	0.142973i
$485$	12.7162	+	12.5789i	0.577413	+	0.571176i
$486$	−11.7079	+	10.2920i	−0.531082	+	0.466853i
$487$	−1.02270	+	3.14754i	−0.0463429	+	0.142629i	−0.971550	−	0.236833i	$-0.923891\pi$
$487$	−1.02270	+	3.14754i	−0.0463429	+	0.142629i	0.925208	+	0.379461i	$0.123891\pi$
$488$	−10.5045	−	3.41313i	−0.475518	−	0.154505i
$489$	10.9438	−	29.2138i	0.494896	−	1.32109i
$490$	1.69771	+	3.28770i	0.0766949	+	0.148523i
$491$	24.1722			1.09088			0.545439	−	0.838151i	$-0.316363\pi$
$491$	24.1722			1.09088			0.545439	+	0.838151i	$0.316363\pi$
$492$	−1.25560	+	3.35173i	−0.0566067	+	0.151108i
$493$	0.0766011	+	0.105432i	0.00344994	+	0.00474843i
$494$	2.43747	+	1.77092i	0.109667	+	0.0796777i
$495$	12.1707	−	10.2989i	0.547030	−	0.462900i
$496$	4.04007	+	3.83117i	0.181404	+	0.172025i
$497$	8.11722			0.364107
$498$	5.27557	+	19.0703i	0.236404	+	0.854561i
$499$	16.8509	+	23.1933i	0.754352	+	1.03828i	0.997663	+	0.0683280i	$0.0217664\pi$
$499$	16.8509	+	23.1933i	0.754352	+	1.03828i	−0.243311	+	0.969948i	$0.578234\pi$
$500$	1.92864	+	11.0127i	0.0862513	+	0.492505i
$501$	−31.2729	−	24.9082i	−1.39717	−	1.11282i
$502$	7.17727			0.320337
$503$	−7.54898	−	23.2334i	−0.336592	−	1.03592i	−0.965932	−	0.258795i	$-0.916675\pi$
$503$	−7.54898	−	23.2334i	−0.336592	−	1.03592i	0.629340	−	0.777130i	$-0.283325\pi$
$504$	−0.613315	+	6.90876i	−0.0273192	+	0.307741i
$505$	2.64864	+	16.1546i	0.117863	+	0.718871i
$506$	−1.37961	+	1.89886i	−0.0613309	+	0.0844148i
$507$	−18.8824	−	7.07355i	−0.838595	−	0.314147i
$508$	−15.6424	−	11.3648i	−0.694018	−	0.504234i
$509$	5.78216	−	4.20099i	0.256290	−	0.186205i	−0.452220	−	0.891906i	$-0.649368\pi$
$509$	5.78216	−	4.20099i	0.256290	−	0.186205i	0.708510	+	0.705701i	$0.249368\pi$
$510$	−7.61563	−	4.26066i	−0.337226	−	0.188665i
$511$	−7.47805	−	10.2927i	−0.330809	−	0.455320i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−9.26469	+	9.72563i	−0.409046	+	0.429397i
$514$	12.3071	−	8.94163i	0.542843	−	0.394398i
$515$	−2.56603	−	0.392148i	−0.113073	−	0.0172801i
$516$	7.98395	+	2.99088i	0.351474	+	0.131666i
$517$	1.22452	+	0.889664i	0.0538542	+	0.0391274i
$518$	11.3088	+	3.67447i	0.496882	+	0.161447i
$519$	−12.0635	−	18.2513i	−0.529531	−	0.801143i
$520$	−1.83281	+	1.85282i	−0.0803739	+	0.0812516i
$521$			28.4290i			1.24550i	0.782422	+	0.622749i	$0.213984\pi$
$521$			28.4290i			1.24550i	−0.782422	+	0.622749i	$0.786016\pi$
$522$	0.0388175	+	0.169121i	0.00169900	+	0.00740221i
$523$	7.51108	+	23.1167i	0.328437	+	1.01082i	0.969865	+	0.243641i	$0.0783419\pi$
$523$	7.51108	+	23.1167i	0.328437	+	1.01082i	−0.641429	+	0.767182i	$0.721658\pi$
$524$	4.88554	+	6.72437i	0.213426	+	0.293755i
$525$	18.8250	+	6.81988i	0.821592	+	0.297644i
$526$		−	5.54047i		−	0.241576i
$527$	−1.63307	+	12.4383i	−0.0711377	+	0.541822i
$528$	−2.56468	+	3.22002i	−0.111613	+	0.140134i
$529$	−17.8184	−	12.9458i	−0.774712	−	0.562861i
$530$	5.68646	−	11.3117i	0.247004	−	0.491350i
$531$	−7.23681	−	12.0789i	−0.314051	−	0.524181i
$532$			5.97650i			0.259114i
$533$			2.40848i			0.104323i
$534$	−19.3539	−	7.25020i	−0.837526	−	0.313747i
$535$	−11.8683	+	1.94588i	−0.513112	+	0.0841276i
$536$	−5.84927	−	1.90054i	−0.252650	−	0.0820910i
$537$	−15.6450	+	4.32801i	−0.675132	+	0.186767i
$538$	7.79045	+	23.9766i	0.335870	+	1.03370i
$539$	3.18176	+	2.31168i	0.137048	+	0.0995713i
$540$	−7.10555	−	9.19299i	−0.305774	−	0.395604i
$541$	−9.91477	+	30.5145i	−0.426269	+	1.31192i	0.475504	+	0.879713i	$0.342266\pi$
$541$	−9.91477	+	30.5145i	−0.426269	+	1.31192i	−0.901774	+	0.432209i	$0.857734\pi$
$542$	14.4281	+	19.8586i	0.619742	+	0.853001i
$543$	7.76380	+	0.343934i	0.333177	+	0.0147596i
$544$	2.14288	+	0.696265i	0.0918754	+	0.0298521i
$545$	6.05069	+	3.04171i	0.259183	+	0.130292i
$546$	1.24440	+	4.49831i	0.0532556	+	0.192510i
$547$	9.96238	−	3.23697i	0.425961	−	0.138403i	−0.0881885	−	0.996104i	$-0.528108\pi$
$547$	9.96238	−	3.23697i	0.425961	−	0.138403i	0.514149	+	0.857701i	$0.328108\pi$
$548$	−1.44126	+	1.98373i	−0.0615676	+	0.0847405i
$549$	2.93002	−	33.0055i	0.125050	−	1.40864i
$550$	7.08894	+	9.53753i	0.302274	+	0.406682i
$551$	0.0462029	+	0.142198i	0.00196831	+	0.00605784i
$552$	1.33797	+	1.06566i	0.0569478	+	0.0453576i
$553$	34.6110			1.47181
$554$	−0.870296	−	2.67849i	−0.0369753	−	0.113798i
$555$	−18.0860	+	8.34717i	−0.767708	+	0.354318i
$556$	11.0992	−	15.2768i	0.470711	−	0.647879i
$557$		−	1.85791i		−	0.0787221i	−0.999225	−	0.0393611i	$-0.987468\pi$
$557$		−	1.85791i		−	0.0787221i	0.999225	−	0.0393611i	$-0.0125323\pi$
$558$	−8.49083	+	14.3842i	−0.359445	+	0.608933i
$559$	5.73709			0.242653
$560$	−5.11041	−	0.780987i	−0.215954	−	0.0330027i
$561$	−9.26620	−	0.410489i	−0.391219	−	0.0173309i
$562$	13.9294	−	4.52595i	0.587578	−	0.190916i
$563$	35.0269			1.47621			0.738105	−	0.674686i	$-0.235721\pi$
$563$	35.0269			1.47621			0.738105	+	0.674686i	$0.235721\pi$
$564$	0.687212	−	0.862814i	0.0289368	−	0.0363310i
$565$	−13.1955	+	13.3396i	−0.555140	+	0.561202i
$566$	−25.0922	−	8.15295i	−1.05470	−	0.342694i
$567$	−20.6126	+	2.84333i	−0.865648	+	0.119409i
$568$	2.06368	−	2.84041i	0.0865901	−	0.119181i
$569$	−9.01229	−	27.7370i	−0.377815	−	1.16279i	−0.941560	−	0.336846i	$-0.890640\pi$
$569$	−9.01229	−	27.7370i	−0.377815	−	1.16279i	0.563745	−	0.825949i	$-0.309360\pi$
$570$	−6.79912	−	7.34892i	−0.284784	−	0.307812i
$571$	5.49457	+	7.56263i	0.229941	+	0.316486i	0.908360	−	0.418189i	$-0.137335\pi$
$571$	5.49457	+	7.56263i	0.229941	+	0.316486i	−0.678420	+	0.734675i	$0.737335\pi$
$572$	−0.856002	+	2.63450i	−0.0357912	+	0.110154i
$573$	27.8407	+	1.23333i	1.16306	+	0.0515233i
$574$	−3.86515	+	2.80819i	−0.161328	+	0.117212i
$575$	3.96299	−	2.94557i	0.165268	−	0.122839i
$576$	2.26162	+	1.97106i	0.0942341	+	0.0821276i
$577$	−3.94067	+	5.42387i	−0.164052	+	0.225799i	−0.883127	−	0.469134i	$-0.844566\pi$
$577$	−3.94067	+	5.42387i	−0.164052	+	0.225799i	0.719074	+	0.694933i	$0.244566\pi$
$578$	−3.68449	−	11.3397i	−0.153255	−	0.471669i
$579$	−0.326935	−	1.18182i	−0.0135870	−	0.0491146i
$580$	−0.127629	+	0.0209255i	−0.00529950	+	0.000868882i
$581$	−8.16161	+	25.1188i	−0.338601	+	1.04211i
$582$	4.86035	−	12.9744i	0.201468	−	0.537806i
$583$		−	13.4569i		−	0.557327i
$584$	−5.50283			−0.227709
$585$	−6.64764	−	4.11560i	−0.274846	−	0.170159i
$586$	22.9928	−	16.7052i	0.949823	−	0.690087i
$587$	12.2563	−	16.8694i	0.505873	−	0.696274i	−0.477344	−	0.878717i	$-0.658400\pi$
$587$	12.2563	−	16.8694i	0.505873	−	0.696274i	0.983216	+	0.182443i	$0.0584004\pi$
$588$	1.78564	−	2.24192i	0.0736385	−	0.0924552i
$589$	−6.19166	+	12.9929i	−0.255123	+	0.535362i
$590$	9.32536	−	4.81547i	0.383919	−	0.198250i
$591$	−10.1589	−	36.7226i	−0.417881	−	1.51057i
$592$	4.16089	−	3.02306i	0.171011	−	0.124247i
$593$	0.938135	+	2.88728i	0.0385246	+	0.118566i	0.968469	−	0.249133i	$-0.0801456\pi$
$593$	0.938135	+	2.88728i	0.0385246	+	0.118566i	−0.929945	+	0.367699i	$0.880146\pi$
$594$	−11.1365	−	5.33799i	−0.456935	−	0.219020i
$595$	−5.34448	−	10.3498i	−0.219102	−	0.424301i
$596$	−14.7999	+	4.80876i	−0.606226	+	0.196975i
$597$	2.78541	−	1.84107i	0.113999	−	0.0753501i
$598$	1.09468	+	0.355682i	0.0447647	+	0.0145449i
$599$	−10.6546	+	14.6648i	−0.435335	+	0.599188i	−0.969168	−	0.246403i	$-0.920751\pi$
$599$	−10.6546	+	14.6648i	−0.435335	+	0.599188i	0.533832	+	0.845590i	$0.320751\pi$
$600$	7.17242	−	4.85349i	0.292813	−	0.198143i
$601$	1.33815	−	1.84180i	0.0545842	−	0.0751287i	−0.780852	−	0.624716i	$-0.785215\pi$
$601$	1.33815	−	1.84180i	0.0545842	−	0.0751287i	0.835437	+	0.549587i	$0.185215\pi$
$602$	6.68922	+	9.20692i	0.272632	+	0.375246i
$603$	1.63153	−	18.3786i	0.0664411	−	0.748434i
$604$	6.00308	+	8.26253i	0.244262	+	0.336198i
$605$	−10.6910	−	5.37441i	−0.434651	−	0.218501i
$606$	10.5785	−	6.99203i	0.429720	−	0.284032i
$607$	−21.5743	−	29.6945i	−0.875673	−	1.20526i	−0.977601	−	0.210469i	$-0.932501\pi$
$607$	−21.5743	−	29.6945i	−0.875673	−	1.20526i	0.101927	−	0.994792i	$-0.467499\pi$
$608$	2.09132	+	1.51943i	0.0848143	+	0.0616212i
$609$	−0.0812518	+	0.216896i	−0.00329249	+	0.00878908i
$610$	24.4142	+	3.73105i	0.988501	+	0.151066i
$611$	0.229368	−	0.705923i	0.00927924	−	0.0285586i
$612$	−0.597713	+	6.73301i	−0.0241611	+	0.272166i
$613$	3.16008	+	9.72572i	0.127634	+	0.392818i	0.994372	−	0.105946i	$-0.0337872\pi$
$613$	3.16008	+	9.72572i	0.127634	+	0.392818i	−0.866737	+	0.498765i	$0.833787\pi$
$614$			26.1722i			1.05623i
$615$	1.55800	−	7.85022i	0.0628247	−	0.316551i
$616$	−5.22594	+	1.69801i	−0.210559	+	0.0684148i
$617$	−8.91808	+	6.47937i	−0.359028	+	0.260849i	−0.752647	−	0.658425i	$-0.771223\pi$
$617$	−8.91808	+	6.47937i	−0.359028	+	0.260849i	0.393618	+	0.919274i	$0.371223\pi$
$618$	0.536105	+	1.93793i	0.0215653	+	0.0779550i
$619$		−	35.5220i		−	1.42775i	−0.700273	−	0.713876i	$-0.746938\pi$
$619$		−	35.5220i		−	1.42775i	0.700273	−	0.713876i	$-0.253062\pi$
$620$	−10.3009	−	6.99225i	−0.413694	−	0.280815i
$621$	−2.21802	+	4.62738i	−0.0890060	+	0.185690i
$622$	10.5953	−	14.5832i	0.424833	−	0.584732i
$623$	−16.2153	−	22.3185i	−0.649654	−	0.894172i
$624$	1.89044	+	0.708180i	0.0756781	+	0.0283499i
$625$	−8.23999	−	23.6030i	−0.329600	−	0.944121i
$626$	15.9974			0.639383
$627$	−9.96512	−	3.73305i	−0.397968	−	0.149084i
$628$	7.74550	+	2.51667i	0.309079	+	0.100426i
$629$	11.0212	+	3.58099i	0.439442	+	0.142783i
$630$	−1.14614	−	15.4668i	−0.0456635	−	0.616212i
$631$	14.0087	−	4.55170i	0.557677	−	0.181200i	−0.0165986	−	0.999862i	$-0.505284\pi$
$631$	14.0087	−	4.55170i	0.557677	−	0.181200i	0.574276	+	0.818662i	$0.305284\pi$
$632$	8.79931	−	12.1112i	0.350018	−	0.481758i
$633$	−1.44025	+	32.5115i	−0.0572447	+	1.29221i
$634$	7.23665	−	22.2721i	0.287404	−	0.884539i
$635$	38.6282	+	19.4186i	1.53291	+	0.770602i
$636$	−9.79726	−	0.434015i	−0.388486	−	0.0172098i
$637$	0.595986	−	1.83426i	0.0236138	−	0.0726759i
$638$	−0.111213	+	0.0808011i	−0.00440297	+	0.00319894i
$639$	9.69026	+	4.12786i	0.383341	+	0.163296i
$640$	−1.57253	+	1.58970i	−0.0621597	+	0.0628385i
$641$	36.1620	+	26.2732i	1.42831	+	1.03773i	0.990328	+	0.138747i	$0.0443074\pi$
$641$	36.1620	+	26.2732i	1.42831	+	1.03773i	0.437984	+	0.898983i	$0.355693\pi$
$642$	5.13684	+	7.77168i	0.202735	+	0.306724i
$643$	−2.02047	+	6.21838i	−0.0796797	+	0.245229i	−0.982959	−	0.183824i	$-0.941152\pi$
$643$	−2.02047	+	6.21838i	−0.0796797	+	0.245229i	0.903280	+	0.429053i	$0.141152\pi$
$644$	0.705550	+	2.17146i	0.0278026	+	0.0855675i
$645$	−18.6995	−	3.71122i	−0.736292	−	0.146129i
$646$			5.82446i			0.229160i
$647$	−21.3344	+	6.93198i	−0.838743	+	0.272524i	−0.696724	−	0.717340i	$-0.745360\pi$
$647$	−21.3344	+	6.93198i	−0.838743	+	0.272524i	−0.142020	+	0.989864i	$0.545360\pi$
$648$	−4.24549	+	7.93573i	−0.166779	+	0.311745i
$649$	6.55696	−	9.02488i	0.257383	−	0.354258i
$650$	3.37396	−	4.75153i	0.132338	−	0.186370i
$651$	−20.0422	+	9.76818i	−0.785516	+	0.382845i
$652$		−	18.0112i		−	0.705373i
$653$	−26.6774	−	19.3822i	−1.04397	−	0.758486i	−0.0729104	−	0.997338i	$-0.523229\pi$
$653$	−26.6774	−	19.3822i	−1.04397	−	0.758486i	−0.971056	+	0.238853i	$0.923229\pi$
$654$	0.232156	−	5.24059i	0.00907803	−	0.204923i
$655$	−13.2132	−	13.0705i	−0.516284	−	0.510707i
$656$			2.06645i			0.0806813i
$657$	−3.69309	−	16.0901i	−0.144081	−	0.627735i
$658$	1.40030	−	0.454987i	0.0545896	−	0.0177372i
$659$	−39.1874	−	12.7328i	−1.52652	−	0.495998i	−0.578904	−	0.815396i	$-0.696519\pi$
$659$	−39.1874	−	12.7328i	−1.52652	−	0.495998i	−0.947621	+	0.319398i	$0.896519\pi$
$660$	4.49427	−	8.03319i	0.174939	−	0.312691i
$661$	25.6214	+	18.6150i	0.996555	+	0.724040i	0.961347	−	0.275340i	$-0.0887906\pi$
$661$	25.6214	+	18.6150i	0.996555	+	0.724040i	0.0352082	+	0.999380i	$0.488791\pi$
$662$	−17.4725	+	5.67716i	−0.679088	+	0.220649i
$663$	1.21275	+	4.38388i	0.0470992	+	0.170256i
$664$	6.71473	+	9.24203i	0.260582	+	0.358660i
$665$	−2.16221	−	13.1878i	−0.0838469	−	0.511400i
$666$	11.6318	+	10.1374i	0.450724	+	0.392818i
$667$	0.0335741	+	0.0462108i	0.00129999	+	0.00178929i
$668$	−21.9528	−	7.13291i	−0.849380	−	0.275980i
$669$	−0.0882533	+	1.99219i	−0.00341207	+	0.0770225i
$670$	13.5946	+	2.07757i	0.525206	+	0.0802635i
$671$	24.9661	−	8.11198i	0.963806	−	0.313160i
$672$	1.06769	+	3.85950i	0.0411869	+	0.148884i
$673$	8.54587	−	26.3015i	0.329419	−	1.01385i	−0.639987	−	0.768385i	$-0.721060\pi$
$673$	8.54587	−	26.3015i	0.329419	−	1.01385i	0.969406	−	0.245462i	$-0.0789396\pi$
$674$	1.37409	−	4.22900i	0.0529278	−	0.162895i
$675$	19.0050	+	17.7146i	0.731504	+	0.681837i
$676$	−11.6416			−0.447753
$677$		−	36.0601i		−	1.38590i	−0.720985	−	0.692950i	$-0.756311\pi$
$677$		−	36.0601i		−	1.38590i	0.720985	−	0.692950i	$-0.243689\pi$
$678$	13.6105	+	5.09863i	0.522707	+	0.195812i
$679$	14.9618	−	10.8704i	0.574181	−	0.417167i
$680$	−4.98040	−	0.761119i	−0.190990	−	0.0291876i
$681$	−6.30389	+	7.91471i	−0.241565	+	0.303292i
$682$	−13.1203	−	1.72261i	−0.502403	−	0.0659622i
$683$	−21.3687			−0.817651			−0.408825	−	0.912613i	$-0.634062\pi$
$683$	−21.3687			−0.817651			−0.408825	+	0.912613i	$0.634062\pi$
$684$	−3.03924	+	7.13469i	−0.116208	+	0.272802i
$685$	2.46261	−	4.89873i	0.0940916	−	0.187171i
$686$	19.0303	−	6.18331i	0.726579	−	0.236080i
$687$	−5.25801	−	4.18788i	−0.200605	−	0.159778i
$688$	4.92236			0.187663
$689$	−6.27616	+	2.03925i	−0.239103	+	0.0776892i
$690$	−3.33791	−	1.86744i	−0.127072	−	0.0710922i
$691$	−9.10804	+	28.0317i	−0.346486	+	1.06637i	0.614297	+	0.789075i	$0.289440\pi$
$691$	−9.10804	+	28.0317i	−0.346486	+	1.06637i	−0.960783	+	0.277300i	$0.910560\pi$
$692$	−10.2188	−	7.42441i	−0.388462	−	0.282234i
$693$	−8.47219	−	14.1409i	−0.321832	−	0.537168i
$694$	2.42907	−	3.34332i	0.0922061	−	0.126911i
$695$	−18.9647	+	37.7253i	−0.719371	+	1.43100i
$696$	0.0552402	+	0.0835746i	0.00209388	+	0.00316789i
$697$	−3.76682	+	2.73676i	−0.142678	+	0.103662i
$698$	−18.1316	+	13.1734i	−0.686293	+	0.498621i
$699$	1.94502	+	2.94268i	0.0735673	+	0.111302i
$700$	11.5592	−	0.125540i	0.436897	−	0.00474495i
$701$	−26.2868	+	36.1807i	−0.992838	+	1.36652i	−0.0632205	+	0.998000i	$0.520137\pi$
$701$	−26.2868	+	36.1807i	−0.992838	+	1.36652i	−0.929618	+	0.368525i	$0.879863\pi$
$702$	−0.801974	+	6.00286i	−0.0302685	+	0.226563i
$703$	10.7560	+	7.81467i	0.405669	+	0.294736i
$704$	−0.734441	+	2.26038i	−0.0276803	+	0.0851911i
$705$	−1.20425	+	2.15251i	−0.0453548	+	0.0810684i
$706$	−26.1575	+	8.49908i	−0.984449	+	0.319867i
$707$	16.9260			0.636569
$708$	−6.35908	−	5.06486i	−0.238989	−	0.190349i
$709$	−13.0054	+	4.22571i	−0.488428	+	0.158700i	−0.542869	−	0.839817i	$-0.682662\pi$
$709$	−13.0054	+	4.22571i	−0.488428	+	0.158700i	0.0544416	+	0.998517i	$0.482662\pi$
$710$	−3.52611	+	7.01428i	−0.132333	+	0.263241i
$711$	41.3183	+	17.6008i	1.54956	+	0.660080i
$712$	−11.9323			−0.447182
$713$	−0.715772	+	5.45169i	−0.0268059	+	0.204168i
$714$	−5.62126	+	7.05766i	−0.210370	+	0.264126i
$715$	0.935735	−	6.12300i	0.0349945	−	0.228987i
$716$	−7.58203	+	5.50867i	−0.283354	+	0.205869i
$717$	34.7081	+	13.0021i	1.29620	+	0.485571i
$718$		−	20.7190i		−	0.773227i
$719$	−0.465778			−0.0173706			−0.00868529	−	0.999962i	$-0.502765\pi$
$719$	−0.465778			−0.0173706			−0.00868529	+	0.999962i	$0.502765\pi$
$720$	−5.70360	−	3.53114i	−0.212561	−	0.131598i
$721$	−0.829385	+	2.55258i	−0.0308879	+	0.0950632i
$722$	3.80637	−	11.7148i	0.141659	−	0.435980i
$723$	7.68286	+	27.7722i	0.285729	+	1.03286i
$724$	4.26723	−	1.38651i	0.158590	−	0.0515291i
$725$	0.274056	−	0.0923485i	0.0101782	−	0.00342974i
$726$	−0.410199	+	9.25963i	−0.0152239	+	0.343657i
$727$	−27.6297	−	8.97743i	−1.02473	−	0.332955i	−0.252025	−	0.967721i	$-0.581096\pi$
$727$	−27.6297	−	8.97743i	−1.02473	−	0.332955i	−0.772704	+	0.634766i	$0.781096\pi$
$728$	1.58387	+	2.18001i	0.0587022	+	0.0807967i
$729$	−26.0531	−	7.08781i	−0.964929	−	0.262512i
$730$	12.1426	−	1.99084i	0.449417	−	0.0736844i
$731$	6.51905	+	8.97270i	0.241116	+	0.331867i
$732$	−5.10070	−	18.4382i	−0.188527	−	0.681495i
$733$	21.9190	−	7.12192i	0.809597	−	0.263054i	0.125170	−	0.992135i	$-0.460052\pi$
$733$	21.9190	−	7.12192i	0.809597	−	0.263054i	0.684427	+	0.729081i	$0.260052\pi$
$734$	23.2494	+	16.8917i	0.858152	+	0.623484i
$735$	−3.12911	+	5.59305i	−0.115419	+	0.206303i
$736$	0.939222	+	0.305172i	0.0346202	+	0.0112488i
$737$	13.9020	−	4.51702i	0.512085	−	0.166387i
$738$	−6.04223	+	1.38685i	−0.222418	+	0.0510506i
$739$			27.3954i			1.00776i	0.863775	+	0.503878i	$0.168094\pi$
$739$			27.3954i			1.00776i	−0.863775	+	0.503878i	$0.831906\pi$
$740$	−8.08774	+	8.17606i	−0.297311	+	0.300558i
$741$	−0.230949	+	5.21334i	−0.00848413	+	0.191517i
$742$	−10.5904	−	7.69435i	−0.388784	−	0.282468i
$743$		−	46.4139i		−	1.70276i	−0.524548	−	0.851381i	$-0.675766\pi$
$743$		−	46.4139i		−	1.70276i	0.524548	−	0.851381i	$-0.324234\pi$
$744$	−1.67730	+	9.49667i	−0.0614930	+	0.348165i
$745$	30.9177	−	15.9654i	1.13274	−	0.584928i
$746$	9.34838	−	12.8669i	0.342268	−	0.471092i
$747$	−22.5170	+	25.8362i	−0.823853	+	0.945298i
$748$	−5.09299	+	1.65481i	−0.186218	+	0.0605060i
$749$			12.4351i			0.454367i
$750$	−14.0708	+	13.3046i	−0.513793	+	0.485816i
$751$	7.09675	+	21.8415i	0.258964	+	0.797009i	0.993023	+	0.117923i	$0.0376237\pi$
$751$	7.09675	+	21.8415i	0.258964	+	0.797009i	−0.734059	+	0.679086i	$0.762376\pi$
$752$	0.196795	−	0.605674i	0.00717639	−	0.0220867i
$753$	6.85474	+	10.3707i	0.249801	+	0.377931i
$754$	0.0545380	+	0.0396242i	0.00198616	+	0.00144303i
$755$	−16.2357	−	16.0603i	−0.590878	−	0.584495i
$756$	−10.5685	+	5.71209i	−0.384373	+	0.207747i
$757$	−16.8855	+	12.2680i	−0.613712	+	0.445888i	−0.850720	−	0.525620i	$-0.823833\pi$
$757$	−16.8855	+	12.2680i	−0.613712	+	0.445888i	0.237007	+	0.971508i	$0.423833\pi$
$758$	−0.679661	+	2.09178i	−0.0246864	+	0.0759769i
$759$	−4.06136	−	0.179917i	−0.147418	−	0.00653056i
$760$	−5.16443	−	2.59618i	−0.187334	−	0.0941735i
$761$	1.36968	−	4.21543i	0.0496507	−	0.152809i	−0.923157	−	0.384423i	$-0.874401\pi$
$761$	1.36968	−	4.21543i	0.0496507	−	0.152809i	0.972808	+	0.231614i	$0.0744005\pi$
$762$	1.48211	−	33.4564i	0.0536911	−	1.21200i
$763$	4.11574	−	5.66483i	0.149000	−	0.205080i
$764$	15.3021	−	4.97196i	0.553612	−	0.179879i
$765$	−1.11699	−	15.0733i	−0.0403847	−	0.544978i
$766$	−33.9827	−	11.0416i	−1.22784	−	0.398951i
$767$	−5.20276	−	1.69048i	−0.187861	−	0.0610397i
$768$	1.62198	+	0.607611i	0.0585280	+	0.0219253i
$769$	27.5186			0.992346			0.496173	−	0.868224i	$-0.334738\pi$
$769$	27.5186			0.992346			0.496173	+	0.868224i	$0.334738\pi$
$770$	10.9173	−	5.63751i	0.393431	−	0.203162i
$771$	24.6742	+	9.24323i	0.888619	+	0.332887i
$772$	−0.416122	−	0.572743i	−0.0149766	−	0.0206135i
$773$	−24.9987	+	34.4077i	−0.899140	+	1.23756i	0.0716014	+	0.997433i	$0.477189\pi$
$773$	−24.9987	+	34.4077i	−0.899140	+	1.23756i	−0.970742	+	0.240127i	$0.922811\pi$
$774$	3.30352	+	14.3928i	0.118743	+	0.517339i
$775$	25.2597	+	11.7024i	0.907356	+	0.420363i
$776$		−	7.99912i		−	0.287152i
$777$	5.49126	+	19.8500i	0.196998	+	0.712113i
$778$	17.4095	−	12.6488i	0.624161	−	0.453480i
$779$	−5.08036	+	1.65071i	−0.182023	+	0.0591428i
$780$	−4.42766	−	0.878741i	−0.158536	−	0.0314640i
$781$			8.34446i			0.298588i
$782$	0.687601	+	2.11622i	0.0245886	+	0.0756758i
$783$	−0.207296	+	0.217610i	−0.00740817	+	0.00777674i
$784$	0.511350	−	1.57377i	0.0182625	−	0.0562061i
$785$	−18.0018	−	2.75108i	−0.642511	−	0.0981903i
$786$	−5.05033	+	13.4815i	−0.180139	+	0.480869i
$787$	−17.6719	−	12.8394i	−0.629936	−	0.457675i	0.226442	−	0.974025i	$-0.427291\pi$
$787$	−17.6719	−	12.8394i	−0.629936	−	0.457675i	−0.856378	+	0.516349i	$0.827291\pi$
$788$	−12.9302	−	17.7969i	−0.460619	−	0.633987i
$789$	8.00566	−	5.29149i	0.285009	−	0.188382i
$790$	−15.0350	+	29.9082i	−0.534920	+	1.06408i
$791$	11.4033	+	15.6953i	0.405455	+	0.558060i
$792$	−7.10217	−	0.630485i	−0.252365	−	0.0224033i
$793$	−7.56671	−	10.4147i	−0.268702	−	0.369836i
$794$	−4.74718	+	6.53394i	−0.168471	+	0.231881i
$795$	21.7757	−	2.58680i	0.772305	−	0.0917445i
$796$	1.13307	−	1.55954i	0.0401607	−	0.0552765i
$797$	8.03647	+	2.61121i	0.284666	+	0.0924937i	0.447870	−	0.894099i	$-0.352183\pi$
$797$	8.03647	+	2.61121i	0.284666	+	0.0924937i	−0.163204	+	0.986592i	$0.552183\pi$
$798$	−8.63569	+	5.70793i	−0.305700	+	0.202058i
$799$	1.36468	−	0.443412i	0.0482790	−	0.0156868i
$800$	2.89482	−	4.07676i	0.102347	−	0.144135i
$801$	−8.00807	−	34.8897i	−0.282951	−	1.23277i
$802$	6.02105	+	18.5309i	0.212611	+	0.654349i
$803$	10.5808	−	7.68739i	0.373388	−	0.271282i
$804$	−2.84024	−	10.2670i	−0.100168	−	0.362089i
$805$	−2.34247	−	4.53630i	−0.0825613	−	0.159883i
$806$	1.18484	+	6.38023i	0.0417341	+	0.224734i
$807$	−27.2044	+	34.1558i	−0.957639	+	1.20234i
$808$	4.30319	−	5.92283i	0.151386	−	0.208364i
$809$	−39.6455	+	28.8041i	−1.39386	+	1.01270i	−0.398432	+	0.917198i	$0.630445\pi$
$809$	−39.6455	+	28.8041i	−1.39386	+	1.01270i	−0.995429	+	0.0955013i	$0.969555\pi$
$810$	6.49710	−	19.0470i	0.228285	−	0.669243i
$811$	−25.9388			−0.910836			−0.455418	−	0.890278i	$-0.650510\pi$
$811$	−25.9388			−0.910836			−0.455418	+	0.890278i	$0.650510\pi$
$812$			0.133723i			0.00469277i
$813$	−14.9148	+	39.8140i	−0.523085	+	1.39634i
$814$	−3.77733	+	11.6254i	−0.132395	+	0.407471i
$815$	6.51619	+	39.7436i	0.228252	+	1.39216i
$816$	1.04052	+	3.76132i	0.0364256	+	0.131672i
$817$	3.93205	+	12.1016i	0.137565	+	0.423382i
$818$	3.06212	−	4.21465i	0.107065	−	0.147362i
$819$	−5.31131	+	6.09426i	−0.185592	+	0.212951i
$820$	−0.747612	−	4.55984i	−0.0261077	−	0.159237i
$821$	−2.06278	+	1.49870i	−0.0719916	+	0.0523050i	−0.623199	−	0.782063i	$-0.714167\pi$
$821$	−2.06278	+	1.49870i	−0.0719916	+	0.0523050i	0.551207	+	0.834368i	$0.314167\pi$
$822$	−4.24286	−	0.187957i	−0.147987	−	0.00655576i
$823$	−1.77656	+	5.46769i	−0.0619270	+	0.190592i	−0.977234	−	0.212166i	$-0.931948\pi$
$823$	−1.77656	+	5.46769i	−0.0619270	+	0.190592i	0.915307	+	0.402758i	$0.131948\pi$
$824$	0.682353	+	0.939178i	0.0237709	+	0.0327178i
$825$	−7.01080	+	19.3520i	−0.244085	+	0.673752i
$826$	−3.35332	−	10.3205i	−0.116677	−	0.359095i
$827$	−4.06440	+	5.59417i	−0.141333	+	0.194528i	−0.873815	−	0.486258i	$-0.838362\pi$
$827$	−4.06440	+	5.59417i	−0.141333	+	0.194528i	0.732482	+	0.680786i	$0.238362\pi$
$828$	−0.261976	+	2.95106i	−0.00910430	+	0.102557i
$829$	23.8269	+	7.74183i	0.827542	+	0.268885i	0.692010	−	0.721888i	$-0.256725\pi$
$829$	23.8269	+	7.74183i	0.827542	+	0.268885i	0.135533	+	0.990773i	$0.456725\pi$
$830$	−18.1604	−	17.9642i	−0.630357	−	0.623548i
$831$	3.03908	−	3.81565i	0.105425	−	0.132364i
$832$	1.16552			0.0404070
$833$	3.54596	−	1.15215i	0.122860	−	0.0399197i
$834$	32.6745	+	1.44747i	1.13142	+	0.0501217i
$835$	51.0218	+	7.79730i	1.76568	+	0.269837i
$836$	−6.14381			−0.212488
$837$	−28.8936	+	1.46907i	−0.998710	+	0.0507785i
$838$		−	12.1177i		−	0.418598i
$839$	21.6110	−	29.7450i	0.746094	−	1.02691i	−0.252151	−	0.967688i	$-0.581138\pi$
$839$	21.6110	−	29.7450i	0.746094	−	1.02691i	0.998245	−	0.0592221i	$-0.0188620\pi$
$840$	−3.75227	−	8.13013i	−0.129466	−	0.280516i
$841$	−8.96046	−	27.5775i	−0.308981	−	0.950947i
$842$	−34.1627			−1.17732
$843$	19.8432	+	15.8047i	0.683437	+	0.544342i
$844$	5.80609	+	17.8693i	0.199854	+	0.615087i
$845$	25.6884	−	4.21175i	0.883707	−	0.144889i
$846$	1.90305	+	0.168940i	0.0654281	+	0.00580828i
$847$	−7.27212	+	10.0092i	−0.249873	+	0.343921i
$848$	−5.38488	+	1.74965i	−0.184917	+	0.0600833i
$849$	−12.1841	−	44.0433i	−0.418156	−	1.51156i
$850$	11.2651	−	0.122346i	0.386391	−	0.00419643i
$851$	4.83055	+	1.56954i	0.165589	+	0.0538032i
$852$	6.07517	+	0.269128i	0.208132	+	0.00922017i
$853$	23.7053	+	32.6275i	0.811653	+	1.11714i	0.991066	+	0.133371i	$0.0425801\pi$
$853$	23.7053	+	32.6275i	0.811653	+	1.11714i	−0.179413	+	0.983774i	$0.557420\pi$
$854$	7.89107	−	24.2862i	0.270027	−	0.831058i
$855$	4.12518	−	16.8430i	0.141078	−	0.576019i
$856$	4.35133	+	3.16143i	0.148725	+	0.108055i
$857$	8.17143	+	25.1491i	0.279131	+	0.859076i	0.988097	+	0.153834i	$0.0491620\pi$
$857$	8.17143	+	25.1491i	0.279131	+	0.859076i	−0.708966	+	0.705243i	$0.750838\pi$
$858$	−4.62424	+	1.27924i	−0.157869	+	0.0436726i
$859$	−19.2045	−	6.23993i	−0.655250	−	0.212904i	−0.0375225	−	0.999296i	$-0.511947\pi$
$859$	−19.2045	−	6.23993i	−0.655250	−	0.212904i	−0.617728	+	0.786392i	$0.711947\pi$
$860$	−10.8617	+	1.78084i	−0.370381	+	0.0607261i
$861$	−7.74913	−	2.90291i	−0.264090	−	0.0989310i
$862$		−	19.5068i		−	0.664403i
$863$			11.6676i			0.397170i	0.980084	+	0.198585i	$0.0636346\pi$
$863$			11.6676i			0.397170i	−0.980084	+	0.198585i	$0.936365\pi$
$864$	−0.688085	+	5.15039i	−0.0234091	+	0.175220i
$865$	25.2350	+	12.6857i	0.858015	+	0.431328i
$866$	28.5539	+	20.7456i	0.970300	+	0.704964i
$867$	12.8663	−	16.1540i	0.436962	−	0.548618i
$868$	−8.85758	+	9.34054i	−0.300646	+	0.317039i
$869$			35.5799i			1.20697i
$870$	−0.152129	−	0.164431i	−0.00515767	−	0.00557474i
$871$	−4.21339	−	5.79924i	−0.142765	−	0.196500i
$872$	−0.935896	−	2.88039i	−0.0316935	−	0.0975424i
$873$	23.3892	−	5.36842i	0.791604	−	0.181693i
$874$			2.55285i			0.0863514i
$875$	−25.4612	+	4.45897i	−0.860745	+	0.150741i
$876$	−5.25554	−	7.95127i	−0.177568	−	0.268648i
$877$	−54.8432	−	17.8196i	−1.85192	−	0.601726i	−0.996480	−	0.0838268i	$-0.973286\pi$
$877$	−54.8432	−	17.8196i	−1.85192	−	0.601726i	−0.855442	−	0.517899i	$-0.826714\pi$
$878$	−6.55424	−	4.76193i	−0.221195	−	0.160707i
$879$	46.0976	+	17.2687i	1.55483	+	0.582459i
$880$	0.802851	−	5.25347i	0.0270641	−	0.177094i
$881$	−18.2862	+	13.2857i	−0.616077	+	0.447606i	−0.851549	−	0.524275i	$-0.824336\pi$
$881$	−18.2862	+	13.2857i	−0.616077	+	0.447606i	0.235472	+	0.971881i	$0.424336\pi$
$882$	4.94484	+	0.438971i	0.166501	+	0.0147809i
$883$	−39.3204	+	28.5679i	−1.32324	+	0.961387i	−0.323349	+	0.946280i	$0.604809\pi$
$883$	−39.3204	+	28.5679i	−1.32324	+	0.961387i	−0.999886	+	0.0151071i	$0.995191\pi$
$884$	1.54358	+	2.12456i	0.0519162	+	0.0714565i
$885$	15.8644	+	8.87553i	0.533275	+	0.298348i
$886$	2.07566	−	1.50806i	0.0697333	−	0.0506642i
$887$	−18.8385	−	13.6870i	−0.632535	−	0.459564i	0.224742	−	0.974418i	$-0.427846\pi$
$887$	−18.8385	−	13.6870i	−0.632535	−	0.459564i	−0.857278	+	0.514855i	$0.827846\pi$
$888$	8.34205	+	3.12503i	0.279941	+	0.104869i
$889$	26.2753	−	36.1648i	0.881244	−	1.21293i
$890$	26.3299	−	4.31693i	0.882580	−	0.144704i
$891$	−2.92293	−	21.1897i	−0.0979219	−	0.709880i
$892$	0.355777	+	1.09497i	0.0119123	+	0.0366623i
$893$	1.64625			0.0550897
$894$	−21.0832	−	16.7923i	−0.705126	−	0.561617i
$895$	14.7376	−	14.8985i	0.492624	−	0.498003i
$896$	1.35895	+	1.87043i	0.0453992	+	0.0624866i
$897$	0.531545	+	1.92144i	0.0177478	+	0.0641551i
$898$	20.8109			0.694467
$899$	−0.138538	+	0.290714i	−0.00462049	+	0.00969586i
$900$	13.8631	+	5.72835i	0.462104	+	0.190945i
$901$	−10.3209	−	7.49861i	−0.343841	−	0.249815i
$902$	−2.88681	−	3.97335i	−0.0961202	−	0.132298i
$903$	−6.91485	+	18.4587i	−0.230112	+	0.614268i
$904$	8.39128			0.279090
$905$	−8.91447	+	4.60329i	−0.296327	+	0.153019i
$906$	−6.20556	+	16.5653i	−0.206166	+	0.550346i
$907$	37.8253	+	12.2902i	1.25597	+	0.408089i	0.860056	−	0.510199i	$-0.170428\pi$
$907$	37.8253	+	12.2902i	1.25597	+	0.408089i	0.395912	+	0.918288i	$0.370428\pi$
$908$	−1.80523	+	5.55593i	−0.0599087	+	0.184380i
$909$	20.2062	+	8.60742i	0.670196	+	0.285490i
$910$	−4.28368	−	4.23741i	−0.142003	−	0.140469i
$911$	18.2550	+	13.2630i	0.604816	+	0.439424i	0.847585	−	0.530660i	$-0.178056\pi$
$911$	18.2550	+	13.2630i	0.604816	+	0.439424i	−0.242769	+	0.970084i	$0.578056\pi$
$912$	−0.198152	+	4.47299i	−0.00656147	+	0.148116i
$913$	−25.8220	−	8.39009i	−0.854585	−	0.277671i
$914$	6.99124	−	5.07943i	0.231250	−	0.168013i
$915$	17.9259	+	38.8404i	0.592612	+	1.28403i
$916$	−3.69099	−	1.19927i	−0.121954	−	0.0396252i
$917$	−15.5466	+	11.2953i	−0.513393	+	0.373002i
$918$	−10.2997	+	5.56678i	−0.339939	+	0.183731i
$919$	7.69385	+	23.6792i	0.253797	+	0.781106i	0.994064	+	0.108793i	$0.0346987\pi$
$919$	7.69385	+	23.6792i	0.253797	+	0.781106i	−0.740268	+	0.672312i	$0.765301\pi$
$920$	−2.18290	−	0.333597i	−0.0719681	−	0.0109984i
$921$	−37.8173	+	24.9961i	−1.24612	+	0.823650i
$922$	8.26243	−	25.4291i	0.272109	−	0.837464i
$923$	3.89178	−	1.26452i	0.128099	−	0.0416220i
$924$	−7.44462	−	5.92947i	−0.244910	−	0.195065i
$925$	14.8885	−	20.9674i	0.489530	−	0.689403i
$926$	−9.65156	−	29.7044i	−0.317170	−	0.976149i
$927$	−2.28818	+	2.62548i	−0.0751537	+	0.0862322i
$928$	0.0467931	+	0.0339972i	0.00153606	+	0.00111601i
$929$	−0.394430			−0.0129408			−0.00647041	−	0.999979i	$-0.502060\pi$
$929$	−0.394430			−0.0129408			−0.00647041	+	0.999979i	$0.502060\pi$
$930$	0.265396	−	21.5622i	0.00870269	−	0.707053i
$931$	4.27759			0.140192
$932$	1.64759	+	1.19705i	0.0539687	+	0.0392105i
$933$	31.1910	+	1.38175i	1.02115	+	0.0452365i
$934$	−0.261331	−	0.804294i	−0.00855101	−	0.0263173i
$935$	10.6395	−	5.49409i	0.347950	−	0.179676i
$936$	0.782208	+	3.40793i	0.0255673	+	0.111392i
$937$	22.1010	−	7.18105i	0.722008	−	0.234595i	0.0751143	−	0.997175i	$-0.476068\pi$
$937$	22.1010	−	7.18105i	0.722008	−	0.234595i	0.646893	+	0.762580i	$0.276068\pi$
$938$	4.39401	−	13.5234i	0.143470	−	0.441554i
$939$	15.2785	+	23.1153i	0.498594	+	0.754338i
$940$	−0.215126	+	1.40768i	−0.00701664	+	0.0459135i
$941$	11.3514	+	34.9359i	0.370044	+	1.13888i	0.946762	+	0.321935i	$0.104333\pi$
$941$	11.3514	+	34.9359i	0.370044	+	1.13888i	−0.576718	+	0.816943i	$0.695667\pi$
$942$	3.76100	+	13.5954i	0.122540	+	0.442961i
$943$	−1.65099	+	1.19951i	−0.0537636	+	0.0390616i
$944$	−4.46392	−	1.45041i	−0.145288	−	0.0472070i
$945$	21.2540	−	16.4279i	0.691392	−	0.534399i
$946$	−9.46467	+	6.87648i	−0.307723	+	0.223574i
$947$	54.5575	+	17.7268i	1.77288	+	0.576044i	0.998399	−	0.0565548i	$-0.0180115\pi$
$947$	54.5575	+	17.7268i	1.77288	+	0.576044i	0.774480	+	0.632598i	$0.218012\pi$
$948$	25.9039	+	1.14753i	0.841319	+	0.0372702i
$949$	−5.18874	−	3.76984i	−0.168434	−	0.122374i
$950$	12.3351	+	3.86034i	0.400205	+	0.125246i
$951$	39.0934	−	10.8147i	1.26769	−	0.350691i
$952$	−1.60975	+	4.95430i	−0.0521723	+	0.160570i
$953$	−10.6268	−	3.45287i	−0.344237	−	0.111849i	0.131796	−	0.991277i	$-0.457926\pi$
$953$	−10.6268	−	3.45287i	−0.344237	−	0.111849i	−0.476033	+	0.879427i	$0.657926\pi$
$954$	−8.72986	−	14.5710i	−0.282640	−	0.471753i
$955$	−31.9670	+	16.5073i	−1.03443	+	0.534162i
$956$	21.3987			0.692082
$957$	−0.222968	−	0.0835264i	−0.00720754	−	0.00270003i
$958$	−17.4253	−	23.9839i	−0.562986	−	0.774884i
$959$	−4.58633	−	3.33216i	−0.148100	−	0.107601i
$960$	−3.79889	−	0.753951i	−0.122609	−	0.0243337i
$961$	−28.9331	+	11.1298i	−0.933327	+	0.359027i
$962$	5.99441			0.193268
$963$	−6.32362	+	14.8449i	−0.203776	+	0.478369i
$964$	9.77872	+	13.4592i	0.314951	+	0.433493i
$965$	1.12543	+	1.11327i	0.0362288	+	0.0358374i
$966$	−2.46379	+	3.09336i	−0.0792711	+	0.0995271i
$967$	21.2998			0.684955			0.342477	−	0.939526i	$-0.388734\pi$
$967$	21.2998			0.684955			0.342477	+	0.939526i	$0.388734\pi$
$968$	1.65364	+	5.08938i	0.0531500	+	0.163579i
$969$	−8.41601	+	5.56272i	−0.270361	+	0.178700i
$970$	2.89397	+	17.6509i	0.0929196	+	0.566737i
$971$	−14.6392	+	20.1491i	−0.469793	+	0.646615i	−0.976504	−	0.215501i	$-0.930861\pi$
$971$	−14.6392	+	20.1491i	−0.469793	+	0.646615i	0.506710	+	0.862117i	$0.330861\pi$
$972$	−15.5214	+	1.44462i	−0.497848	+	0.0463363i
$973$	35.3195	+	25.6611i	1.13229	+	0.822658i
$974$	−2.67746	+	1.94529i	−0.0857914	+	0.0623311i
$975$	10.0880	+	0.337172i	0.323075	+	0.0107981i
$976$	−6.49216	−	8.93569i	−0.207809	−	0.286024i
$977$	−3.45280	+	2.50860i	−0.110465	+	0.0802574i	−0.641646	−	0.767001i	$-0.721748\pi$
$977$	−3.45280	+	2.50860i	−0.110465	+	0.0802574i	0.531181	+	0.847258i	$0.321748\pi$
$978$	26.0251	−	17.2018i	0.832192	−	0.550054i
$979$	22.9433	−	16.6693i	0.733271	−	0.532753i
$980$	−0.558979	+	3.65769i	−0.0178559	+	0.116841i
$981$	7.79407	−	4.66964i	0.248846	−	0.149090i
$982$	19.5557	+	14.2081i	0.624049	+	0.453398i
$983$	−4.66748	−	1.51656i	−0.148870	−	0.0483706i	0.233634	−	0.972325i	$-0.424938\pi$
$983$	−4.66748	−	1.51656i	−0.148870	−	0.0483706i	−0.382504	+	0.923954i	$0.624938\pi$
$984$	−2.98590	+	1.97359i	−0.0951870	+	0.0629157i
$985$	34.9705	+	34.5927i	1.11425	+	1.10222i
$986$			0.130322i			0.00415028i
$987$	1.99481	+	1.58882i	0.0634954	+	0.0505726i
$988$	0.931030	+	2.86542i	0.0296200	+	0.0911610i
$989$	2.85729	+	3.93272i	0.0908564	+	0.125053i
$990$	15.8998	−	1.17823i	0.505329	−	0.0374466i
$991$		−	7.23305i		−	0.229765i	−0.993379	−	0.114883i	$-0.963351\pi$
$991$		−	7.23305i		−	0.229765i	0.993379	−	0.114883i	$-0.0366492\pi$
$992$	1.01658	+	5.47417i	0.0322763	+	0.173805i
$993$	−24.8905	−	19.8247i	−0.789876	−	0.629118i
$994$	6.56697	+	4.77118i	0.208292	+	0.151333i
$995$	−1.93603	+	3.85122i	−0.0613762	+	0.122092i
$996$	−6.94122	+	18.5291i	−0.219941	+	0.587117i
$997$			32.2900i			1.02263i	0.859392	+	0.511317i	$0.170842\pi$
$997$			32.2900i			1.02263i	−0.859392	+	0.511317i	$0.829158\pi$
$998$			28.6685i			0.907487i
$999$	−3.53892	+	26.4892i	−0.111966	+	0.838081i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.y.b.29.17	yes	128
3.2	odd	2		930.2.y.a.29.3	✓	128
5.4	even	2		930.2.y.a.29.16	yes	128
15.14	odd	2	inner	930.2.y.b.29.30	yes	128
31.15	odd	10	inner	930.2.y.b.449.30	yes	128
93.77	even	10		930.2.y.a.449.16	yes	128
155.139	odd	10		930.2.y.a.449.3	yes	128
465.449	even	10	inner	930.2.y.b.449.17	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.y.a.29.3	✓	128	3.2	odd	2
930.2.y.a.29.16	yes	128	5.4	even	2
930.2.y.a.449.3	yes	128	155.139	odd	10
930.2.y.a.449.16	yes	128	93.77	even	10
930.2.y.b.29.17	yes	128	1.1	even	1	trivial
930.2.y.b.29.30	yes	128	15.14	odd	2	inner
930.2.y.b.449.17	yes	128	465.449	even	10	inner
930.2.y.b.449.30	yes	128	31.15	odd	10	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.0766541 + 1.73035i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.02596 - 1.98681i) q^{5} +(-1.07909 + 1.35483i) q^{6} +(-2.19882 + 0.714440i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.98825 - 0.265277i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.0766541 + 1.73035i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.02596 - 1.98681i) q^{5} +(-1.07909 + 1.35483i) q^{6} +(-2.19882 + 0.714440i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.98825 - 0.265277i) q^{9} +(0.337800 - 2.21041i) q^{10} +(-0.734441 - 2.26038i) q^{11} +(-1.66935 + 0.461806i) q^{12} +(-0.942922 + 0.685073i) q^{13} +(-2.19882 - 0.714440i) q^{14} +(3.51653 - 1.62297i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.14288 - 0.696265i) q^{17} +(-2.26162 - 1.97106i) q^{18} +(-2.09132 - 1.51943i) q^{19} +(1.57253 - 1.58970i) q^{20} +(-1.06769 - 3.85950i) q^{21} +(0.734441 - 2.26038i) q^{22} +(-0.939222 - 0.305172i) q^{23} +(-1.62198 - 0.607611i) q^{24} +(-2.89482 + 4.07676i) q^{25} -1.16552 q^{26} +(0.688085 - 5.15039i) q^{27} +(-1.35895 - 1.87043i) q^{28} +(-0.0467931 - 0.0339972i) q^{29} +(3.79889 + 0.753951i) q^{30} +(-1.01658 - 5.47417i) q^{31} -1.00000 q^{32} +(3.96755 - 1.09758i) q^{33} +(-1.32438 - 1.82285i) q^{34} +(3.67535 + 3.63565i) q^{35} +(-0.671126 - 2.92397i) q^{36} -5.14314 q^{37} +(-0.798814 - 2.45850i) q^{38} +(-1.11314 - 1.68410i) q^{39} +(2.20661 - 0.361785i) q^{40} +(1.21463 - 1.67179i) q^{41} +(1.40478 - 3.74997i) q^{42} +(-3.98227 - 2.89329i) q^{43} +(1.92279 - 1.39699i) q^{44} +(2.53876 + 6.20924i) q^{45} +(-0.580471 - 0.798950i) q^{46} +(-0.515217 + 0.374327i) q^{47} +(-0.955062 - 1.44494i) q^{48} +(-1.33873 + 0.972645i) q^{49} +(-4.73822 + 1.59664i) q^{50} +(1.36905 - 3.65458i) q^{51} +(-0.942922 - 0.685073i) q^{52} +(5.38488 + 1.74965i) q^{53} +(3.58400 - 3.76231i) q^{54} +(-3.73743 + 3.77824i) q^{55} -2.31198i q^{56} +(2.78947 - 3.50226i) q^{57} +(-0.0178734 - 0.0550086i) q^{58} +(2.75885 + 3.79723i) q^{59} +(2.63020 + 2.84289i) q^{60} +11.0451i q^{61} +(2.39521 - 5.02623i) q^{62} +(6.76015 - 1.55163i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(2.32851 + 1.17055i) q^{65} +(3.85495 + 1.44411i) q^{66} +6.15029i q^{67} -2.25316i q^{68} +(0.600050 - 1.60179i) q^{69} +(0.836440 + 5.10162i) q^{70} +(-3.33910 - 1.08494i) q^{71} +(1.17571 - 2.76002i) q^{72} +(1.70047 + 5.23350i) q^{73} +(-4.16089 - 3.02306i) q^{74} +(-6.83234 - 5.32157i) q^{75} +(0.798814 - 2.45850i) q^{76} +(3.22981 + 4.44545i) q^{77} +(0.0893415 - 2.01675i) q^{78} +(-14.2376 - 4.62607i) q^{79} +(1.99783 + 1.00432i) q^{80} +(8.85926 + 1.58543i) q^{81} +(1.96531 - 0.638568i) q^{82} +(6.71473 - 9.24203i) q^{83} +(3.34067 - 2.20808i) q^{84} +(0.815161 + 4.97184i) q^{85} +(-1.52109 - 4.68144i) q^{86} +(0.0624140 - 0.0783625i) q^{87} +2.37670 q^{88} +(3.68728 + 11.3483i) q^{89} +(-1.59580 + 6.51563i) q^{90} +(1.58387 - 2.18001i) q^{91} -0.987556i q^{92} +(9.55018 - 1.33942i) q^{93} -0.636843 q^{94} +(-0.873220 + 5.71393i) q^{95} +(0.0766541 - 1.73035i) q^{96} +(-7.60762 + 2.47186i) q^{97} -1.65476 q^{98} +(1.59506 + 6.94940i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9	\( 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9} + 2 q^{10} - 35 q^{15} - 32 q^{16} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 20 q^{23} - 10 q^{25} - 48 q^{31} - 128 q^{32} + 8 q^{33} + 10 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{38} + 4 q^{39} - 3 q^{40} + 5 q^{45} + 10 q^{46} - 6 q^{47} + 46 q^{49} + 5 q^{50} + 34 q^{51} + 20 q^{53} + 35 q^{60} + 8 q^{62} - 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} - 6 q^{72} + 5 q^{75} + 12 q^{76} - 50 q^{77} - 4 q^{78} - 10 q^{79} - 2 q^{80} - 24 q^{81} + 40 q^{83} - 30 q^{85} + 4 q^{87} - 5 q^{90} + 20 q^{91} + 26 q^{93} - 4 q^{94} + 26 q^{95} + 124 q^{98}+O(q^{100}) \) 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9 + 2 * q^10 - 35 * q^15 - 32 * q^16 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 20 * q^23 - 10 * q^25 - 48 * q^31 - 128 * q^32 + 8 * q^33 + 10 * q^34 - 16 * q^35 - 4 * q^36 - 12 * q^38 + 4 * q^39 - 3 * q^40 + 5 * q^45 + 10 * q^46 - 6 * q^47 + 46 * q^49 + 5 * q^50 + 34 * q^51 + 20 * q^53 + 35 * q^60 + 8 * q^62 - 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 - 6 * q^72 + 5 * q^75 + 12 * q^76 - 50 * q^77 - 4 * q^78 - 10 * q^79 - 2 * q^80 - 24 * q^81 + 40 * q^83 - 30 * q^85 + 4 * q^87 - 5 * q^90 + 20 * q^91 + 26 * q^93 - 4 * q^94 + 26 * q^95 + 124 * q^98

Introduction

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