LMFDB - Embedded newform 370.2.q.e.273.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(97,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("370.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.q (of order $12$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			273.2
Root			$-0.424637 + 3.22544i$ of defining polynomial
Character	$\chi$	$=$	370.273
Dual form			370.2.q.e.267.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.46593 - 0.392794i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.57872 + 1.58356i) q^{5} +(1.07313 - 1.07313i) q^{6} +(0.578728 + 0.155070i) q^{7} +1.00000 q^{8} +(-0.603425 - 0.348387i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.46593 - 0.392794i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.57872 + 1.58356i) q^{5} +(1.07313 - 1.07313i) q^{6} +(0.578728 + 0.155070i) q^{7} +1.00000 q^{8} +(-0.603425 - 0.348387i) q^{9} +(-2.16076 + 0.575432i) q^{10} -2.03593i q^{11} +(0.392794 + 1.46593i) q^{12} +(2.26005 + 3.91452i) q^{13} +(-0.423658 + 0.423658i) q^{14} +(-1.69227 - 2.94149i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(5.58598 + 3.22507i) q^{17} +(0.603425 - 0.348387i) q^{18} +(-0.311316 + 1.16185i) q^{19} +(0.582041 - 2.15899i) q^{20} +(-0.787462 - 0.454641i) q^{21} +(1.76316 + 1.01796i) q^{22} -4.39871 q^{23} +(-1.46593 - 0.392794i) q^{24} +(-0.0152997 + 4.99998i) q^{25} -4.52010 q^{26} +(3.96713 + 3.96713i) q^{27} +(-0.155070 - 0.578728i) q^{28} +(-5.43667 + 5.43667i) q^{29} +(3.39354 + 0.00519203i) q^{30} +(5.48443 + 5.48443i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.799699 + 2.98452i) q^{33} +(-5.58598 + 3.22507i) q^{34} +(0.668086 + 1.16126i) q^{35} +0.696775i q^{36} +(6.05437 + 0.586988i) q^{37} +(-0.850530 - 0.850530i) q^{38} +(-1.77547 - 6.62614i) q^{39} +(1.57872 + 1.58356i) q^{40} +(-1.10366 + 0.637200i) q^{41} +(0.787462 - 0.454641i) q^{42} +3.83333 q^{43} +(-1.76316 + 1.01796i) q^{44} +(-0.400946 - 1.50556i) q^{45} +(2.19935 - 3.80939i) q^{46} +(-3.13110 + 3.13110i) q^{47} +(1.07313 - 1.07313i) q^{48} +(-5.75130 - 3.32051i) q^{49} +(-4.32246 - 2.51324i) q^{50} +(-6.92185 - 6.92185i) q^{51} +(2.26005 - 3.91452i) q^{52} +(-0.370259 + 0.0992105i) q^{53} +(-5.41920 + 1.45207i) q^{54} +(3.22400 - 3.21415i) q^{55} +(0.578728 + 0.155070i) q^{56} +(0.912731 - 1.58090i) q^{57} +(-1.98996 - 7.42663i) q^{58} +(10.2327 - 2.74186i) q^{59} +(-1.70127 + 2.93629i) q^{60} +(2.46273 - 9.19103i) q^{61} +(-7.49187 + 2.00744i) q^{62} +(-0.295194 - 0.295194i) q^{63} +1.00000 q^{64} +(-2.63088 + 9.75885i) q^{65} +(-2.18482 - 2.18482i) q^{66} +(-0.204369 + 0.762716i) q^{67} -6.45014i q^{68} +(6.44818 + 1.72778i) q^{69} +(-1.33972 - 0.00204974i) q^{70} +(-8.36217 - 14.4837i) q^{71} +(-0.603425 - 0.348387i) q^{72} +(3.81312 - 3.81312i) q^{73} +(-3.53553 + 4.94975i) q^{74} +(1.98639 - 7.32359i) q^{75} +(1.16185 - 0.311316i) q^{76} +(0.315710 - 1.17825i) q^{77} +(6.62614 + 1.77547i) q^{78} +(3.16370 - 11.8071i) q^{79} +(-2.16076 + 0.575432i) q^{80} +(-3.21209 - 5.56350i) q^{81} -1.27440i q^{82} +(-0.974119 + 0.261014i) q^{83} +0.909282i q^{84} +(3.71162 + 13.9372i) q^{85} +(-1.91666 + 3.31976i) q^{86} +(10.1052 - 5.83426i) q^{87} -2.03593i q^{88} +(2.11336 + 7.88715i) q^{89} +(1.50433 + 0.405551i) q^{90} +(0.700931 + 2.61591i) q^{91} +(2.19935 + 3.80939i) q^{92} +(-5.88552 - 10.1940i) q^{93} +(-1.14606 - 4.27716i) q^{94} +(-2.33133 + 1.34124i) q^{95} +(0.392794 + 1.46593i) q^{96} +15.7440i q^{97} +(5.75130 - 3.32051i) q^{98} +(-0.709291 + 1.22853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} + 16 q^{8} - 24 q^{9}+O(q^{10}) $ 16 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 + 16 * q^8 - 24 * q^9	$ 16 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} + 16 q^{8} - 24 q^{9} - 4 q^{10} + 16 q^{12} - 4 q^{13} + 8 q^{15} - 8 q^{16} + 24 q^{18} - 24 q^{19} + 8 q^{20} - 12 q^{21} - 8 q^{23} - 8 q^{24} + 32 q^{25} + 8 q^{26} + 16 q^{27} + 16 q^{29} - 4 q^{30} + 24 q^{31} - 8 q^{32} + 12 q^{33} - 20 q^{35} - 4 q^{40} - 36 q^{41} + 12 q^{42} - 16 q^{43} + 4 q^{45} + 4 q^{46} + 32 q^{47} - 8 q^{48} + 24 q^{49} - 16 q^{50} - 16 q^{51} - 4 q^{52} - 48 q^{53} - 8 q^{54} - 24 q^{55} + 20 q^{57} - 8 q^{58} - 8 q^{59} - 4 q^{60} + 8 q^{61} - 12 q^{62} + 16 q^{63} + 16 q^{64} + 24 q^{65} - 24 q^{66} - 8 q^{67} - 8 q^{69} + 28 q^{70} + 4 q^{71} - 24 q^{72} + 48 q^{73} - 36 q^{75} + 24 q^{76} - 60 q^{77} + 20 q^{79} - 4 q^{80} + 16 q^{81} + 24 q^{83} + 8 q^{85} + 8 q^{86} + 12 q^{87} - 8 q^{89} - 8 q^{90} - 8 q^{91} + 4 q^{92} + 36 q^{93} - 28 q^{94} + 28 q^{95} + 16 q^{96} - 24 q^{98} + 8 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 + 16 * q^8 - 24 * q^9 - 4 * q^10 + 16 * q^12 - 4 * q^13 + 8 * q^15 - 8 * q^16 + 24 * q^18 - 24 * q^19 + 8 * q^20 - 12 * q^21 - 8 * q^23 - 8 * q^24 + 32 * q^25 + 8 * q^26 + 16 * q^27 + 16 * q^29 - 4 * q^30 + 24 * q^31 - 8 * q^32 + 12 * q^33 - 20 * q^35 - 4 * q^40 - 36 * q^41 + 12 * q^42 - 16 * q^43 + 4 * q^45 + 4 * q^46 + 32 * q^47 - 8 * q^48 + 24 * q^49 - 16 * q^50 - 16 * q^51 - 4 * q^52 - 48 * q^53 - 8 * q^54 - 24 * q^55 + 20 * q^57 - 8 * q^58 - 8 * q^59 - 4 * q^60 + 8 * q^61 - 12 * q^62 + 16 * q^63 + 16 * q^64 + 24 * q^65 - 24 * q^66 - 8 * q^67 - 8 * q^69 + 28 * q^70 + 4 * q^71 - 24 * q^72 + 48 * q^73 - 36 * q^75 + 24 * q^76 - 60 * q^77 + 20 * q^79 - 4 * q^80 + 16 * q^81 + 24 * q^83 + 8 * q^85 + 8 * q^86 + 12 * q^87 - 8 * q^89 - 8 * q^90 - 8 * q^91 + 4 * q^92 + 36 * q^93 - 28 * q^94 + 28 * q^95 + 16 * q^96 - 24 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.46593	−	0.392794i	−0.846353	−	0.226780i	−0.190518	−	0.981684i	$-0.561017\pi$
$3$	−1.46593	−	0.392794i	−0.846353	−	0.226780i	−0.655835	+	0.754904i	$0.727683\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.57872	+	1.58356i	0.706024	+	0.708188i
$5$	1.57872	+	1.58356i	0.706024	+	0.708188i
$6$	1.07313	−	1.07313i	0.438104	−	0.438104i
$7$	0.578728	+	0.155070i	0.218739	+	0.0586108i	0.366524	−	0.930409i	$-0.380548\pi$
$7$	0.578728	+	0.155070i	0.218739	+	0.0586108i	−0.147785	+	0.989019i	$0.547214\pi$
$8$	1.00000			0.353553
$9$	−0.603425	−	0.348387i	−0.201142	−	0.116129i
$10$	−2.16076	+	0.575432i	−0.683292	+	0.181967i
$11$		−	2.03593i		−	0.613855i	−0.951733	−	0.306927i	$-0.900699\pi$
$11$		−	2.03593i		−	0.613855i	0.951733	−	0.306927i	$-0.0993009\pi$
$12$	0.392794	+	1.46593i	0.113390	+	0.423176i
$13$	2.26005	+	3.91452i	0.626826	+	1.08569i	0.988185	+	0.153267i	$0.0489795\pi$
$13$	2.26005	+	3.91452i	0.626826	+	1.08569i	−0.361359	+	0.932427i	$0.617687\pi$
$14$	−0.423658	+	0.423658i	−0.113227	+	0.113227i
$15$	−1.69227	−	2.94149i	−0.436943	−	0.759488i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	5.58598	+	3.22507i	1.35480	+	0.782194i	0.988917	−	0.148467i	$-0.0474337\pi$
$17$	5.58598	+	3.22507i	1.35480	+	0.782194i	0.365883	+	0.930661i	$0.380767\pi$
$18$	0.603425	−	0.348387i	0.142229	−	0.0821157i
$19$	−0.311316	+	1.16185i	−0.0714207	+	0.266546i	−0.992398	−	0.123071i	$-0.960726\pi$
$19$	−0.311316	+	1.16185i	−0.0714207	+	0.266546i	0.920977	+	0.389617i	$0.127392\pi$
$20$	0.582041	−	2.15899i	0.130148	−	0.482764i
$21$	−0.787462	−	0.454641i	−0.171838	−	0.0992108i
$22$	1.76316	+	1.01796i	0.375908	+	0.217030i
$23$	−4.39871			−0.917194			−0.458597	−	0.888644i	$-0.651648\pi$
$23$	−4.39871			−0.917194			−0.458597	+	0.888644i	$0.651648\pi$
$24$	−1.46593	−	0.392794i	−0.299231	−	0.0801787i
$25$	−0.0152997	+	4.99998i	−0.00305994	+	0.999995i
$26$	−4.52010			−0.886465
$27$	3.96713	+	3.96713i	0.763474	+	0.763474i
$28$	−0.155070	−	0.578728i	−0.0293054	−	0.109369i
$29$	−5.43667	+	5.43667i	−1.00956	+	1.00956i	−0.00961005	+	0.999954i	$0.503059\pi$
$29$	−5.43667	+	5.43667i	−1.00956	+	1.00956i	−0.999954	+	0.00961005i	$0.996941\pi$
$30$	3.39354	+	0.00519203i	0.619572	+	0.000947930i
$31$	5.48443	+	5.48443i	0.985032	+	0.985032i	0.999890	−	0.0148573i	$-0.00472940\pi$
$31$	5.48443	+	5.48443i	0.985032	+	0.985032i	−0.0148573	+	0.999890i	$0.504729\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.799699	+	2.98452i	−0.139210	+	0.519538i
$34$	−5.58598	+	3.22507i	−0.957988	+	0.553095i
$35$	0.668086	+	1.16126i	0.112927	+	0.196289i
$36$			0.696775i			0.116129i
$37$	6.05437	+	0.586988i	0.995333	+	0.0965003i
$37$	6.05437	+	0.586988i	0.995333	+	0.0965003i
$38$	−0.850530	−	0.850530i	−0.137974	−	0.137974i
$39$	−1.77547	−	6.62614i	−0.284302	−	1.06103i
$40$	1.57872	+	1.58356i	0.249617	+	0.250382i
$41$	−1.10366	+	0.637200i	−0.172363	+	0.0995140i	−0.583700	−	0.811970i	$-0.698395\pi$
$41$	−1.10366	+	0.637200i	−0.172363	+	0.0995140i	0.411336	+	0.911484i	$0.365062\pi$
$42$	0.787462	−	0.454641i	0.121508	−	0.0701527i
$43$	3.83333			0.584577			0.292288	−	0.956330i	$-0.405583\pi$
$43$	3.83333			0.584577			0.292288	+	0.956330i	$0.405583\pi$
$44$	−1.76316	+	1.01796i	−0.265807	+	0.153464i
$45$	−0.400946	−	1.50556i	−0.0597695	−	0.224436i
$46$	2.19935	−	3.80939i	0.324277	−	0.561664i
$47$	−3.13110	+	3.13110i	−0.456718	+	0.456718i	−0.897576	−	0.440859i	$-0.854674\pi$
$47$	−3.13110	+	3.13110i	−0.456718	+	0.456718i	0.440859	+	0.897576i	$0.354674\pi$
$48$	1.07313	−	1.07313i	0.154893	−	0.154893i
$49$	−5.75130	−	3.32051i	−0.821614	−	0.474359i
$50$	−4.32246	−	2.51324i	−0.611288	−	0.355426i
$51$	−6.92185	−	6.92185i	−0.969253	−	0.969253i
$52$	2.26005	−	3.91452i	0.313413	−	0.542847i
$53$	−0.370259	+	0.0992105i	−0.0508589	+	0.0136276i	−0.284159	−	0.958777i	$-0.591714\pi$
$53$	−0.370259	+	0.0992105i	−0.0508589	+	0.0136276i	0.233300	+	0.972405i	$0.425048\pi$
$54$	−5.41920	+	1.45207i	−0.737459	+	0.197602i
$55$	3.22400	−	3.21415i	0.434724	−	0.433396i
$56$	0.578728	+	0.155070i	0.0773357	+	0.0207221i
$57$	0.912731	−	1.58090i	0.120894	−	0.209395i
$58$	−1.98996	−	7.42663i	−0.261294	−	0.975164i
$59$	10.2327	−	2.74186i	1.33219	−	0.356959i	0.478659	−	0.878001i	$-0.341123\pi$
$59$	10.2327	−	2.74186i	1.33219	−	0.356959i	0.853531	+	0.521042i	$0.174456\pi$
$60$	−1.70127	+	2.93629i	−0.219632	+	0.379074i
$61$	2.46273	−	9.19103i	0.315320	−	1.17679i	−0.608371	−	0.793653i	$-0.708177\pi$
$61$	2.46273	−	9.19103i	0.315320	−	1.17679i	0.923691	−	0.383138i	$-0.125157\pi$
$62$	−7.49187	+	2.00744i	−0.951468	+	0.254945i
$63$	−0.295194	−	0.295194i	−0.0371910	−	0.0371910i
$64$	1.00000			0.125000
$65$	−2.63088	+	9.75885i	−0.326321	+	1.21044i
$66$	−2.18482	−	2.18482i	−0.268932	−	0.268932i
$67$	−0.204369	+	0.762716i	−0.0249677	+	0.0931806i	−0.977285	−	0.211928i	$-0.932026\pi$
$67$	−0.204369	+	0.762716i	−0.0249677	+	0.0931806i	0.952318	+	0.305108i	$0.0986926\pi$
$68$		−	6.45014i		−	0.782194i
$69$	6.44818	+	1.72778i	0.776270	+	0.208001i
$70$	−1.33972	−	0.00204974i	−0.160128	−	0.000244991i
$71$	−8.36217	−	14.4837i	−0.992407	−	1.71890i	−0.602725	−	0.797949i	$-0.705918\pi$
$71$	−8.36217	−	14.4837i	−0.992407	−	1.71890i	−0.389681	−	0.920950i	$-0.627415\pi$
$72$	−0.603425	−	0.348387i	−0.0711143	−	0.0410578i
$73$	3.81312	−	3.81312i	0.446292	−	0.446292i	−0.447828	−	0.894120i	$-0.647802\pi$
$73$	3.81312	−	3.81312i	0.446292	−	0.446292i	0.894120	+	0.447828i	$0.147802\pi$
$74$	−3.53553	+	4.94975i	−0.410997	+	0.575396i
$75$	1.98639	−	7.32359i	0.229368	−	0.845655i
$76$	1.16185	−	0.311316i	0.133273	−	0.0357104i
$77$	0.315710	−	1.17825i	0.0359785	−	0.134274i
$78$	6.62614	+	1.77547i	0.750262	+	0.201032i
$79$	3.16370	−	11.8071i	0.355944	−	1.32840i	−0.523347	−	0.852119i	$-0.675317\pi$
$79$	3.16370	−	11.8071i	0.355944	−	1.32840i	0.879292	−	0.476283i	$-0.158016\pi$
$80$	−2.16076	+	0.575432i	−0.241580	+	0.0643352i
$81$	−3.21209	−	5.56350i	−0.356899	−	0.618167i
$82$		−	1.27440i		−	0.140734i
$83$	−0.974119	+	0.261014i	−0.106923	+	0.0286501i	−0.311884	−	0.950120i	$-0.600960\pi$
$83$	−0.974119	+	0.261014i	−0.106923	+	0.0286501i	0.204961	+	0.978770i	$0.434293\pi$
$84$			0.909282i			0.0992108i
$85$	3.71162	+	13.9372i	0.402581	+	1.51170i
$86$	−1.91666	+	3.31976i	−0.206679	+	0.357979i
$87$	10.1052	−	5.83426i	1.08340	−	0.625499i
$88$		−	2.03593i		−	0.217030i
$89$	2.11336	+	7.88715i	0.224015	+	0.836036i	0.982797	+	0.184691i	$0.0591284\pi$
$89$	2.11336	+	7.88715i	0.224015	+	0.836036i	−0.758781	+	0.651345i	$0.774205\pi$
$90$	1.50433	+	0.405551i	0.158570	+	0.0427489i
$91$	0.700931	+	2.61591i	0.0734775	+	0.274222i
$92$	2.19935	+	3.80939i	0.229299	+	0.397157i
$93$	−5.88552	−	10.1940i	−0.610300	−	1.05707i
$94$	−1.14606	−	4.27716i	−0.118207	−	0.441155i
$95$	−2.33133	+	1.34124i	−0.239189	+	0.137608i
$96$	0.392794	+	1.46593i	0.0400893	+	0.149615i
$97$			15.7440i			1.59856i	0.600957	+	0.799282i	$0.294786\pi$
$97$			15.7440i			1.59856i	−0.600957	+	0.799282i	$0.705214\pi$
$98$	5.75130	−	3.32051i	0.580969	−	0.335423i
$99$	−0.709291	+	1.22853i	−0.0712864	+	0.123472i
$100$	4.33776	−	2.48674i	0.433776	−	0.248674i
$101$		−	2.83229i		−	0.281823i	−0.990022	−	0.140912i	$-0.954997\pi$
$101$		−	2.83229i		−	0.281823i	0.990022	−	0.140912i	$-0.0450034\pi$
$102$	9.45543	−	2.53357i	0.936227	−	0.250861i
$103$		−	1.86000i		−	0.183271i	−0.995793	−	0.0916354i	$-0.970791\pi$
$103$		−	1.86000i		−	0.183271i	0.995793	−	0.0916354i	$-0.0292094\pi$
$104$	2.26005	+	3.91452i	0.221616	+	0.383851i
$105$	−0.523230	−	1.96474i	−0.0510620	−	0.191739i
$106$	0.0992105	−	0.370259i	0.00963617	−	0.0359627i
$107$	−9.82137	−	2.63163i	−0.949467	−	0.254409i	−0.249331	−	0.968418i	$-0.580211\pi$
$107$	−9.82137	−	2.63163i	−0.949467	−	0.254409i	−0.700136	+	0.714009i	$0.746877\pi$
$108$	1.45207	−	5.41920i	0.139725	−	0.521463i
$109$	7.40247	−	1.98349i	0.709028	−	0.189983i	0.113757	−	0.993509i	$-0.463711\pi$
$109$	7.40247	−	1.98349i	0.709028	−	0.189983i	0.595271	+	0.803525i	$0.297045\pi$
$110$	1.17154	+	4.39914i	0.111702	+	0.419442i
$111$	−8.64470	−	3.23860i	−0.820518	−	0.307394i
$112$	−0.423658	+	0.423658i	−0.0400319	+	0.0400319i
$113$	4.57128	+	2.63923i	0.430029	+	0.248278i	0.699359	−	0.714770i	$-0.253469\pi$
$113$	4.57128	+	2.63923i	0.430029	+	0.248278i	−0.269330	+	0.963048i	$0.586802\pi$
$114$	0.912731	+	1.58090i	0.0854851	+	0.148065i
$115$	−6.94432	−	6.96560i	−0.647561	−	0.649546i
$116$	7.42663	+	1.98996i	0.689545	+	0.184763i
$117$		−	3.14949i		−	0.291171i
$118$	−2.74186	+	10.2327i	−0.252408	+	0.942000i
$119$	2.73265	+	2.73265i	0.250502	+	0.250502i
$120$	−1.69227	−	2.94149i	−0.154483	−	0.268520i
$121$	6.85501			0.623182
$122$	6.72830	+	6.72830i	0.609152	+	0.609152i
$123$	1.86818	−	0.500576i	0.168448	−	0.0451355i
$124$	2.00744	−	7.49187i	0.180273	−	0.672790i
$125$	−7.94190	+	7.86932i	−0.710345	+	0.703854i
$126$	0.403243	−	0.108049i	0.0359237	−	0.00962573i
$127$	−3.82781	−	14.2856i	−0.339664	−	1.26764i	−0.898724	−	0.438515i	$-0.855505\pi$
$127$	−3.82781	−	14.2856i	−0.339664	−	1.26764i	0.559060	−	0.829127i	$-0.311162\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−5.61937	−	1.50571i	−0.494758	−	0.132570i
$130$	−7.13597	−	7.15784i	−0.625866	−	0.627784i
$131$	−1.12935	+	0.302609i	−0.0986720	+	0.0264391i	−0.307817	−	0.951446i	$-0.599599\pi$
$131$	−1.12935	+	0.302609i	−0.0986720	+	0.0264391i	0.209145	+	0.977885i	$0.432932\pi$
$132$	2.98452	−	0.799699i	0.259769	−	0.0696048i
$133$	−0.360334	+	0.624117i	−0.0312449	+	0.0541178i
$134$	−0.558347	−	0.558347i	−0.0482338	−	0.0482338i
$135$	−0.0191938	+	12.5451i	−0.00165194	+	1.07971i
$136$	5.58598	+	3.22507i	0.478994	+	0.276547i
$137$	−8.27041	+	8.27041i	−0.706589	+	0.706589i	−0.965816	−	0.259227i	$-0.916532\pi$
$137$	−8.27041	+	8.27041i	−0.706589	+	0.706589i	0.259227	+	0.965816i	$0.416532\pi$
$138$	−4.72040	+	4.72040i	−0.401827	+	0.401827i
$139$	−7.00906	+	12.1400i	−0.594500	+	1.02970i	0.399117	+	0.916900i	$0.369317\pi$
$139$	−7.00906	+	12.1400i	−0.594500	+	1.02970i	−0.993617	+	0.112805i	$0.964017\pi$
$140$	0.671637	−	1.15921i	0.0567637	−	0.0979711i
$141$	5.81983	−	3.36008i	0.490118	−	0.282970i
$142$	16.7243			1.40347
$143$	7.96968	−	4.60130i	0.666458	−	0.384780i
$144$	0.603425	−	0.348387i	0.0502854	−	0.0290323i
$145$	−17.1922	−	0.0263037i	−1.42774	−	0.00218440i
$146$	1.39570	+	5.20882i	0.115509	+	0.431085i
$147$	7.12670	+	7.12670i	0.587800	+	0.587800i
$148$	−2.51884	−	5.53674i	−0.207047	−	0.455117i
$149$		−	3.58283i		−	0.293517i	−0.989172	−	0.146759i	$-0.953116\pi$
$149$		−	3.58283i		−	0.293517i	0.989172	−	0.146759i	$-0.0468840\pi$
$150$	5.34922	+	5.38205i	0.436762	+	0.439443i
$151$	−4.05219	+	2.33953i	−0.329763	+	0.190389i	−0.655736	−	0.754991i	$-0.727641\pi$
$151$	−4.05219	+	2.33953i	−0.329763	+	0.190389i	0.325973	+	0.945379i	$0.394308\pi$
$152$	−0.311316	+	1.16185i	−0.0252510	+	0.0942381i
$153$	−2.24715	−	3.89217i	−0.181671	−	0.314663i
$154$	0.862537	+	0.862537i	0.0695052	+	0.0695052i
$155$	−0.0265348	+	17.3433i	−0.00213132	+	1.39304i
$156$	−4.85067	+	4.85067i	−0.388364	+	0.388364i
$157$	−6.08343	−	22.7037i	−0.485511	−	1.81195i	−0.577749	−	0.816214i	$-0.696069\pi$
$157$	−6.08343	−	22.7037i	−0.485511	−	1.81195i	0.0922381	−	0.995737i	$-0.470598\pi$
$158$	8.64340	+	8.64340i	0.687632	+	0.687632i
$159$	0.581741			0.0461350
$160$	0.582041	−	2.15899i	0.0460144	−	0.170683i
$161$	−2.54565	−	0.682106i	−0.200626	−	0.0537575i
$162$	6.42418			0.504731
$163$	−0.687018	−	0.396650i	−0.0538114	−	0.0310680i	0.472853	−	0.881141i	$-0.343224\pi$
$163$	−0.687018	−	0.396650i	−0.0538114	−	0.0310680i	−0.526664	+	0.850073i	$0.676558\pi$
$164$	1.10366	+	0.637200i	0.0861816	+	0.0497570i
$165$	−5.98865	+	3.44534i	−0.466216	+	0.268219i
$166$	0.261014	−	0.974119i	0.0202587	−	0.0756063i
$167$	−17.2360	+	9.95122i	−1.33376	+	0.770048i	−0.985874	−	0.167488i	$-0.946435\pi$
$167$	−17.2360	+	9.95122i	−1.33376	+	0.770048i	−0.347888	+	0.937536i	$0.613101\pi$
$168$	−0.787462	−	0.454641i	−0.0607540	−	0.0350763i
$169$	−3.71567	+	6.43573i	−0.285821	+	0.495056i
$170$	−13.9258	−	3.75424i	−1.06806	−	0.287937i
$171$	0.592628	−	0.592628i	0.0453194	−	0.0453194i
$172$	−1.91666	−	3.31976i	−0.146144	−	0.253129i
$173$	−3.17278	−	11.8410i	−0.241222	−	0.900253i	−0.975245	−	0.221128i	$-0.929026\pi$
$173$	−3.17278	−	11.8410i	−0.241222	−	0.900253i	0.734023	−	0.679125i	$-0.237640\pi$
$174$			11.6685i			0.884589i
$175$	−0.784199	+	2.89125i	−0.0592799	+	0.218558i
$176$	1.76316	+	1.01796i	0.132903	+	0.0767318i
$177$	−16.0774			−1.20845
$178$	−7.88715	−	2.11336i	−0.591167	−	0.158403i
$179$	5.49311	−	5.49311i	0.410575	−	0.410575i	−0.471364	−	0.881939i	$-0.656238\pi$
$179$	5.49311	−	5.49311i	0.410575	−	0.410575i	0.881939	+	0.471364i	$0.156238\pi$
$180$	−1.10338	+	1.10001i	−0.0822412	+	0.0819899i
$181$	−3.07920	−	5.33333i	−0.228875	−	0.396423i	0.728600	−	0.684939i	$-0.240171\pi$
$181$	−3.07920	−	5.33333i	−0.228875	−	0.396423i	−0.957475	+	0.288516i	$0.906838\pi$
$182$	−2.61591	−	0.700931i	−0.193904	−	0.0519564i
$183$	−7.22036	+	12.5060i	−0.533744	+	0.924472i
$184$	−4.39871			−0.324277
$185$	8.62862	+	10.5141i	0.634389	+	0.773014i
$186$	11.7710			0.863094
$187$	6.56600	−	11.3727i	0.480154	−	0.831651i
$188$	4.27716	+	1.14606i	0.311944	+	0.0835851i
$189$	1.68071	+	2.91107i	0.122253	+	0.211749i
$190$	0.00411503	−	2.68961i	0.000298536	−	0.195125i
$191$	−2.76449	+	2.76449i	−0.200031	+	0.200031i	−0.800013	−	0.599982i	$-0.795174\pi$
$191$	−2.76449	+	2.76449i	−0.200031	+	0.200031i	0.599982	+	0.800013i	$0.295174\pi$
$192$	−1.46593	−	0.392794i	−0.105794	−	0.0283474i
$193$	−2.71669			−0.195552			−0.0977759	−	0.995208i	$-0.531173\pi$
$193$	−2.71669			−0.195552			−0.0977759	+	0.995208i	$0.531173\pi$
$194$	−13.6347	−	7.87201i	−0.978916	−	0.565177i
$195$	7.68990	−	13.2724i	0.550685	−	0.950453i
$196$			6.64103i			0.474359i
$197$	1.68054	+	6.27187i	0.119734	+	0.446852i	0.999597	−	0.0283740i	$-0.00903292\pi$
$197$	1.68054	+	6.27187i	0.119734	+	0.446852i	−0.879864	+	0.475226i	$0.842366\pi$
$198$	−0.709291	−	1.22853i	−0.0504071	−	0.0873077i
$199$	7.80886	−	7.80886i	0.553555	−	0.553555i	−0.373910	−	0.927465i	$-0.621983\pi$
$199$	7.80886	−	7.80886i	0.553555	−	0.553555i	0.927465	+	0.373910i	$0.121983\pi$
$200$	−0.0152997	+	4.99998i	−0.00108185	+	0.353552i
$201$	0.599180	−	1.03781i	0.0422629	−	0.0732015i
$202$	2.45283	+	1.41614i	0.172581	+	0.0996396i
$203$	−3.98941	+	2.30329i	−0.280002	+	0.161659i
$204$	−2.53357	+	9.45543i	−0.177386	+	0.662012i
$205$	−2.75141	−	0.741753i	−0.192167	−	0.0518063i
$206$	1.61080	+	0.929998i	0.112230	+	0.0647960i
$207$	2.65429	+	1.53245i	0.184486	+	0.106513i
$208$	−4.52010			−0.313413
$209$	2.36543	+	0.633816i	0.163620	+	0.0438419i
$210$	1.96313	+	0.529239i	0.135469	+	0.0365210i
$211$	15.5424			1.06998			0.534991	−	0.844858i	$-0.320315\pi$
$211$	15.5424			1.06998			0.534991	+	0.844858i	$0.320315\pi$
$212$	0.271048	+	0.271048i	0.0186157	+	0.0186157i
$213$	6.56921	+	24.5166i	0.450115	+	1.67985i
$214$	7.18974	−	7.18974i	0.491480	−	0.491480i
$215$	6.05174	+	6.07029i	0.412725	+	0.413990i
$216$	3.96713	+	3.96713i	0.269929	+	0.269929i
$217$	2.32352	+	4.02446i	0.157731	+	0.273198i
$218$	−1.98349	+	7.40247i	−0.134339	+	0.501358i
$219$	−7.08752	+	4.09198i	−0.478931	+	0.276511i
$220$	−4.39554	−	1.18499i	−0.296347	−	0.0798921i
$221$			29.1553i			1.96120i
$222$	7.12706	−	5.86723i	0.478337	−	0.393783i
$223$	18.5992	+	18.5992i	1.24550	+	1.24550i	0.957688	+	0.287808i	$0.0929264\pi$
$223$	18.5992	+	18.5992i	1.24550	+	1.24550i	0.287808	+	0.957688i	$0.407074\pi$
$224$	−0.155070	−	0.578728i	−0.0103610	−	0.0386679i
$225$	1.75116	−	3.01178i	0.116744	−	0.200785i
$226$	−4.57128	+	2.63923i	−0.304077	+	0.175559i
$227$	14.2760	−	8.24225i	0.947531	−	0.547057i	0.0552179	−	0.998474i	$-0.482415\pi$
$227$	14.2760	−	8.24225i	0.947531	−	0.547057i	0.892313	+	0.451417i	$0.149081\pi$
$228$	−1.82546			−0.120894
$229$	24.6249	−	14.2172i	1.62726	−	0.939499i	0.642353	−	0.766409i	$-0.277958\pi$
$229$	24.6249	−	14.2172i	1.62726	−	0.939499i	0.984906	−	0.173090i	$-0.0553750\pi$
$230$	9.50455	−	2.53116i	0.626711	−	0.166900i
$231$	−0.925616	+	1.60321i	−0.0609010	+	0.105484i
$232$	−5.43667	+	5.43667i	−0.356935	+	0.356935i
$233$	8.01937	−	8.01937i	0.525366	−	0.525366i	−0.393821	−	0.919187i	$-0.628847\pi$
$233$	8.01937	−	8.01937i	0.525366	−	0.525366i	0.919187	+	0.393821i	$0.128847\pi$
$234$	2.72754	+	1.57475i	0.178305	+	0.102944i
$235$	−9.90139	−	0.0151489i	−0.645895	−	0.000988204i
$236$	−7.49089	−	7.49089i	−0.487615	−	0.487615i
$237$	−9.27551	+	16.0657i	−0.602509	+	1.04358i
$238$	−3.73287	+	1.00022i	−0.241966	+	0.0648347i
$239$	−5.82100	+	1.55973i	−0.376529	+	0.100891i	−0.442120	−	0.896956i	$-0.645773\pi$
$239$	−5.82100	+	1.55973i	−0.376529	+	0.100891i	0.0655909	+	0.997847i	$0.479107\pi$
$240$	3.39354	+	0.00519203i	0.219052	+	0.000335144i
$241$	−14.6525	−	3.92614i	−0.943853	−	0.252905i	−0.246101	−	0.969244i	$-0.579150\pi$
$241$	−14.6525	−	3.92614i	−0.943853	−	0.252905i	−0.697752	+	0.716339i	$0.745816\pi$
$242$	−3.42750	+	5.93661i	−0.220328	+	0.381620i
$243$	−1.83283	−	6.84022i	−0.117576	−	0.438800i
$244$	−9.19103	+	2.46273i	−0.588395	+	0.157660i
$245$	−3.82146	−	14.3497i	−0.244144	−	0.916766i
$246$	−0.500576	+	1.86818i	−0.0319156	+	0.119111i
$247$	−5.25166	+	1.40718i	−0.334155	+	0.0895367i
$248$	5.48443	+	5.48443i	0.348262	+	0.348262i
$249$	1.53051			0.0969922
$250$	−2.84409	−	10.8125i	−0.179876	−	0.683846i
$251$	10.1166	+	10.1166i	0.638554	+	0.638554i	0.950199	−	0.311644i	$-0.100880\pi$
$251$	10.1166	+	10.1166i	0.638554	+	0.638554i	−0.311644	+	0.950199i	$0.600880\pi$
$252$	−0.108049	+	0.403243i	−0.00680642	+	0.0254019i
$253$			8.95545i			0.563024i
$254$	14.2856	+	3.82781i	0.896358	+	0.240178i
$255$	0.0334893	−	21.8888i	0.00209718	−	1.37073i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.56308	−	3.78920i	−0.409394	−	0.236364i	0.281135	−	0.959668i	$-0.409289\pi$
$257$	−6.56308	−	3.78920i	−0.409394	−	0.236364i	−0.690529	+	0.723304i	$0.742622\pi$
$258$	4.11367	−	4.11367i	0.256106	−	0.256106i
$259$	3.41281	+	1.27856i	0.212062	+	0.0794456i
$260$	9.76685	−	2.60101i	0.605715	−	0.161308i
$261$	5.17468	−	1.38655i	0.320305	−	0.0858255i
$262$	0.302609	−	1.12935i	0.0186953	−	0.0697717i
$263$	−25.8089	−	6.91548i	−1.59145	−	0.426427i	−0.649002	−	0.760787i	$-0.724813\pi$
$263$	−25.8089	−	6.91548i	−1.59145	−	0.426427i	−0.942446	+	0.334360i	$0.891480\pi$
$264$	−0.799699	+	2.98452i	−0.0492181	+	0.183684i
$265$	−0.741639	−	0.429700i	−0.0455585	−	0.0263962i
$266$	−0.360334	−	0.624117i	−0.0220935	−	0.0382671i
$267$		−	12.3921i		−	0.758384i
$268$	0.762716	−	0.204369i	0.0465903	−	0.0124838i
$269$		−	16.1826i		−	0.986670i	−0.869839	−	0.493335i	$-0.835778\pi$
$269$		−	16.1826i		−	0.986670i	0.869839	−	0.493335i	$-0.164222\pi$
$270$	−10.8548	−	6.28919i	−0.660603	−	0.382748i
$271$	−14.3377	+	24.8336i	−0.870951	+	1.50853i	−0.00993755	+	0.999951i	$0.503163\pi$
$271$	−14.3377	+	24.8336i	−0.870951	+	1.50853i	−0.861014	+	0.508581i	$0.830170\pi$
$272$	−5.58598	+	3.22507i	−0.338700	+	0.195549i
$273$		−	4.11005i		−	0.248752i
$274$	−3.02718	−	11.2976i	−0.182879	−	0.682512i
$275$	10.1796	+	0.0311491i	0.613852	+	0.00187836i
$276$	−1.72778	−	6.44818i	−0.104000	−	0.388135i
$277$	5.05462	+	8.75485i	0.303703	+	0.526028i	0.976972	−	0.213369i	$-0.0684438\pi$
$277$	5.05462	+	8.75485i	0.303703	+	0.526028i	−0.673269	+	0.739398i	$0.735110\pi$
$278$	−7.00906	−	12.1400i	−0.420375	−	0.728111i
$279$	−1.39873	−	5.22014i	−0.0837400	−	0.312522i
$280$	0.668086	+	1.16126i	0.0399258	+	0.0693985i
$281$	−0.0150119	−	0.0560250i	−0.000895532	−	0.00334217i	0.965477	−	0.260490i	$-0.0838840\pi$
$281$	−0.0150119	−	0.0560250i	−0.000895532	−	0.00334217i	−0.966372	+	0.257148i	$0.917217\pi$
$282$			6.72016i			0.400180i
$283$	16.4514	−	9.49821i	0.977933	−	0.564610i	0.0762878	−	0.997086i	$-0.475693\pi$
$283$	16.4514	−	9.49821i	0.977933	−	0.564610i	0.901646	+	0.432476i	$0.142360\pi$
$284$	−8.36217	+	14.4837i	−0.496203	+	0.859449i
$285$	3.94438	−	1.05043i	0.233645	−	0.0622221i
$286$			9.20260i			0.544161i
$287$	−0.737531	+	0.197621i	−0.0435351	+	0.0116652i
$288$			0.696775i			0.0410578i
$289$	12.3021	+	21.3079i	0.723656	+	1.25341i
$290$	8.61890	−	14.8758i	0.506119	−	0.873535i
$291$	6.18415	−	23.0796i	0.362521	−	1.35295i
$292$	−5.20882	−	1.39570i	−0.304823	−	0.0816771i
$293$	4.87500	−	18.1938i	0.284801	−	1.06289i	−0.664184	−	0.747569i	$-0.731221\pi$
$293$	4.87500	−	18.1938i	0.284801	−	1.06289i	0.948985	−	0.315322i	$-0.102112\pi$
$294$	−9.73525	+	2.60855i	−0.567772	+	0.152134i
$295$	20.4965	+	11.8755i	1.19335	+	0.691419i
$296$	6.05437	+	0.586988i	0.351903	+	0.0341180i
$297$	8.07678	−	8.07678i	0.468662	−	0.468662i
$298$	3.10282	+	1.79142i	0.179742	+	0.103774i
$299$	−9.94131	−	17.2189i	−0.574921	−	0.995792i
$300$	−7.33560	+	1.94153i	−0.423521	+	0.112094i
$301$	2.21845	+	0.594433i	0.127869	+	0.0342625i
$302$		−	4.67907i		−	0.269250i
$303$	−1.11251	+	4.15193i	−0.0639118	+	0.238522i
$304$	−0.850530	−	0.850530i	−0.0487813	−	0.0487813i
$305$	18.4425	−	10.6102i	1.05601	−	0.607537i
$306$	4.49429			0.256922
$307$	−0.0672646	−	0.0672646i	−0.00383899	−	0.00383899i	0.705185	−	0.709024i	$-0.250864\pi$
$307$	−0.0672646	−	0.0672646i	−0.00383899	−	0.00383899i	−0.709024	+	0.705185i	$0.750864\pi$
$308$	−1.17825	+	0.315710i	−0.0671368	+	0.0179893i
$309$	−0.730594	+	2.72661i	−0.0415621	+	0.155112i
$310$	−15.0064	−	8.69461i	−0.852308	−	0.493821i
$311$	−26.9341	+	7.21697i	−1.52729	+	0.409237i	−0.922135	−	0.386869i	$-0.873557\pi$
$311$	−26.9341	+	7.21697i	−1.52729	+	0.409237i	−0.605158	+	0.796106i	$0.706890\pi$
$312$	−1.77547	−	6.62614i	−0.100516	−	0.375131i
$313$	−0.166143	+	0.287768i	−0.00939094	+	0.0162656i	−0.870683	−	0.491845i	$-0.836323\pi$
$313$	−0.166143	+	0.287768i	−0.00939094	+	0.0162656i	0.861292	+	0.508111i	$0.169656\pi$
$314$	22.7037	+	6.08343i	1.28124	+	0.343308i
$315$	0.00142821	−	0.933485i	8.04704e−5	−	0.0525959i
$316$	−11.8071	+	3.16370i	−0.664201	+	0.177972i
$317$	−4.56417	+	1.22297i	−0.256349	+	0.0686886i	−0.384705	−	0.923040i	$-0.625697\pi$
$317$	−4.56417	+	1.22297i	−0.256349	+	0.0686886i	0.128356	+	0.991728i	$0.459030\pi$
$318$	−0.290870	+	0.503802i	−0.0163112	+	0.0282518i
$319$	11.0687	+	11.0687i	0.619726	+	0.619726i
$320$	1.57872	+	1.58356i	0.0882530	+	0.0885235i
$321$	13.3637	+	7.71554i	0.745889	+	0.430639i
$322$	1.86355	−	1.86355i	0.103852	−	0.103852i
$323$	−5.48604	+	5.48604i	−0.305251	+	0.305251i
$324$	−3.21209	+	5.56350i	−0.178449	+	0.309084i
$325$	−19.6071	+	11.2403i	−1.08761	+	0.623500i
$326$	0.687018	−	0.396650i	0.0380504	−	0.0219684i
$327$	−11.6306			−0.643172
$328$	−1.10366	+	0.637200i	−0.0609396	+	0.0351835i
$329$	−2.29759	+	1.32651i	−0.126670	+	0.0731331i
$330$	0.0105706	−	6.90899i	0.000581891	−	0.380327i
$331$	−2.87977	−	10.7475i	−0.158287	−	0.590734i	−0.998801	−	0.0489451i	$-0.984414\pi$
$331$	−2.87977	−	10.7475i	−0.158287	−	0.590734i	0.840515	−	0.541788i	$-0.182253\pi$
$332$	0.713105	+	0.713105i	0.0391367	+	0.0391367i
$333$	−3.44886	−	2.46347i	−0.188996	−	0.134997i
$334$		−	19.9024i		−	1.08901i
$335$	−1.53044	+	0.880483i	−0.0836171	+	0.0481059i
$336$	0.787462	−	0.454641i	0.0429596	−	0.0248027i
$337$	4.97727	−	18.5754i	0.271129	−	1.01187i	−0.687262	−	0.726410i	$-0.741188\pi$
$337$	4.97727	−	18.5754i	0.271129	−	1.01187i	0.958391	−	0.285458i	$-0.0921457\pi$
$338$	−3.71567	−	6.43573i	−0.202106	−	0.350057i
$339$	−5.66448	−	5.66448i	−0.307652	−	0.307652i
$340$	10.2142	−	10.1830i	0.553940	−	0.552248i
$341$	11.1659	−	11.1659i	0.604667	−	0.604667i
$342$	0.216917	+	0.809545i	0.0117295	+	0.0437752i
$343$	−5.77913	−	5.77913i	−0.312044	−	0.312044i
$344$	3.83333			0.206679
$345$	7.44381	+	12.9387i	0.400761	+	0.696598i
$346$	11.8410	+	3.17278i	0.636575	+	0.170570i
$347$	−9.35647			−0.502282			−0.251141	−	0.967951i	$-0.580806\pi$
$347$	−9.35647			−0.502282			−0.251141	+	0.967951i	$0.580806\pi$
$348$	−10.1052	−	5.83426i	−0.541698	−	0.312749i
$349$	−22.9567	−	13.2541i	−1.22884	−	0.709473i	−0.262056	−	0.965053i	$-0.584400\pi$
$349$	−22.9567	−	13.2541i	−1.22884	−	0.709473i	−0.966788	+	0.255580i	$0.917734\pi$
$350$	−2.11180	−	2.12476i	−0.112880	−	0.113573i
$351$	−6.56350	+	24.4953i	−0.350334	+	1.30746i
$352$	−1.76316	+	1.01796i	−0.0939769	+	0.0542576i
$353$	−17.8939	−	10.3311i	−0.952397	−	0.549867i	−0.0585724	−	0.998283i	$-0.518655\pi$
$353$	−17.8939	−	10.3311i	−0.952397	−	0.549867i	−0.893825	+	0.448416i	$0.851988\pi$
$354$	8.03871	−	13.9235i	0.427253	−	0.740024i
$355$	9.73424	−	36.1076i	0.516640	−	1.91639i
$356$	5.77380	−	5.77380i	0.306011	−	0.306011i
$357$	−2.93250	−	5.07924i	−0.155204	−	0.268822i
$358$	2.01062	+	7.50373i	0.106265	+	0.396585i
$359$			6.46994i			0.341470i	0.985317	+	0.170735i	$0.0546143\pi$
$359$			6.46994i			0.341470i	−0.985317	+	0.170735i	$0.945386\pi$
$360$	−0.400946	−	1.50556i	−0.0211317	−	0.0793501i
$361$	15.2015	+	8.77660i	0.800080	+	0.461926i
$362$	6.15840			0.323678
$363$	−10.0489	−	2.69260i	−0.527432	−	0.141325i
$364$	1.91498	−	1.91498i	0.100372	−	0.100372i
$365$	12.0581	+	0.0184486i	0.631152	+	0.000965646i
$366$	−7.22036	−	12.5060i	−0.377414	−	0.653700i
$367$	−20.2501	−	5.42600i	−1.05705	−	0.283235i	−0.311886	−	0.950120i	$-0.600961\pi$
$367$	−20.2501	−	5.42600i	−1.05705	−	0.283235i	−0.745161	+	0.666885i	$0.767627\pi$
$368$	2.19935	−	3.80939i	0.114649	−	0.198578i
$369$	0.887970			0.0462259
$370$	−13.4198	+	2.21554i	−0.697663	+	0.115180i
$371$	−0.229663			−0.0119235
$372$	−5.88552	+	10.1940i	−0.305150	+	0.528535i
$373$	34.0846	+	9.13295i	1.76484	+	0.472886i	0.987689	−	0.156433i	$-0.0499995\pi$
$373$	34.0846	+	9.13295i	1.76484	+	0.472886i	0.777147	+	0.629319i	$0.216666\pi$
$374$	6.56600	+	11.3727i	0.339520	+	0.588066i
$375$	14.7333	−	8.41632i	0.760822	−	0.434617i
$376$	−3.13110	+	3.13110i	−0.161474	+	0.161474i
$377$	−33.5691	−	8.99482i	−1.72890	−	0.463257i
$378$	−3.36141			−0.172892
$379$	18.9131	+	10.9195i	0.971503	+	0.560897i	0.899694	−	0.436521i	$-0.143790\pi$
$379$	18.9131	+	10.9195i	0.971503	+	0.560897i	0.0718086	+	0.997418i	$0.477123\pi$
$380$	2.32721	+	1.34837i	0.119383	+	0.0691698i
$381$			22.4452i			1.14990i
$382$	−1.01187	−	3.77636i	−0.0517719	−	0.193215i
$383$	9.85267	+	17.0653i	0.503448	+	0.871998i	0.999992	+	0.00398611i	$0.00126882\pi$
$383$	9.85267	+	17.0653i	0.503448	+	0.871998i	−0.496544	+	0.868012i	$0.665398\pi$
$384$	1.07313	−	1.07313i	0.0547630	−	0.0547630i
$385$	2.36424	−	1.36017i	0.120493	−	0.0693209i
$386$	1.35835	−	2.35272i	0.0691380	−	0.119751i
$387$	−2.31312	−	1.33548i	−0.117583	−	0.0678864i
$388$	13.6347	−	7.87201i	0.692198	−	0.399641i
$389$	3.02794	−	11.3004i	0.153523	−	0.572954i	−0.845705	−	0.533651i	$-0.820820\pi$
$389$	3.02794	−	11.3004i	0.153523	−	0.572954i	0.999227	−	0.0393031i	$-0.0125138\pi$
$390$	7.64925	+	13.2958i	0.387335	+	0.673260i
$391$	−24.5711	−	14.1861i	−1.24261	−	0.717424i
$392$	−5.75130	−	3.32051i	−0.290484	−	0.167711i
$393$	1.77441			0.0895072
$394$	−6.27187	−	1.68054i	−0.315972	−	0.0846645i
$395$	23.6918	−	13.6302i	1.19206	−	0.685809i
$396$	1.41858			0.0712864
$397$	22.5548	+	22.5548i	1.13199	+	1.13199i	0.989845	+	0.142149i	$0.0454011\pi$
$397$	22.5548	+	22.5548i	1.13199	+	1.13199i	0.142149	+	0.989845i	$0.454599\pi$
$398$	2.85824	+	10.6671i	0.143271	+	0.534693i
$399$	0.773372	−	0.773372i	0.0387170	−	0.0387170i
$400$	−4.32246	−	2.51324i	−0.216123	−	0.125662i
$401$	7.60001	+	7.60001i	0.379526	+	0.379526i	0.870931	−	0.491405i	$-0.163516\pi$
$401$	7.60001	+	7.60001i	0.379526	+	0.379526i	−0.491405	+	0.870931i	$0.663516\pi$
$402$	0.599180	+	1.03781i	0.0298844	+	0.0517612i
$403$	−9.07384	+	33.8640i	−0.452000	+	1.68689i
$404$	−2.45283	+	1.41614i	−0.122033	+	0.0704558i
$405$	3.73914	−	13.8697i	0.185799	−	0.689192i
$406$		−	4.60658i		−	0.228621i
$407$	1.19507	−	12.3263i	0.0592372	−	0.610990i
$408$	−6.92185	−	6.92185i	−0.342683	−	0.342683i
$409$	−2.29363	−	8.55993i	−0.113413	−	0.423261i	0.885751	−	0.464161i	$-0.153644\pi$
$409$	−2.29363	−	8.55993i	−0.113413	−	0.423261i	−0.999163	+	0.0409000i	$0.986978\pi$
$410$	2.01808	−	2.01192i	0.0996661	−	0.0993616i
$411$	15.3724	−	8.87524i	0.758263	−	0.437783i
$412$	−1.61080	+	0.929998i	−0.0793586	+	0.0458177i
$413$	6.34715			0.312323
$414$	−2.65429	+	1.53245i	−0.130451	+	0.0753160i
$415$	−1.95119	−	1.13050i	−0.0957802	−	0.0554943i
$416$	2.26005	−	3.91452i	0.110808	−	0.191925i
$417$	15.0433	−	15.0433i	0.736673	−	0.736673i
$418$	−1.73162	+	1.73162i	−0.0846961	+	0.0846961i
$419$	−19.2058	−	11.0885i	−0.938263	−	0.541707i	−0.0488478	−	0.998806i	$-0.515555\pi$
$419$	−19.2058	−	11.0885i	−0.938263	−	0.541707i	−0.889415	+	0.457100i	$0.848888\pi$
$420$	−1.43990	+	1.43550i	−0.0702599	+	0.0700452i
$421$	−18.3815	−	18.3815i	−0.895860	−	0.895860i	0.0992065	−	0.995067i	$-0.468370\pi$
$421$	−18.3815	−	18.3815i	−0.895860	−	0.895860i	−0.995067	+	0.0992065i	$0.968370\pi$
$422$	−7.77120	+	13.4601i	−0.378296	+	0.655228i
$423$	2.98022	−	0.798546i	0.144903	−	0.0388267i
$424$	−0.370259	+	0.0992105i	−0.0179813	+	0.00481809i
$425$	−16.2107	+	27.8804i	−0.786336	+	1.35240i
$426$	−24.5166	−	6.56921i	−1.18783	−	0.318279i
$427$	2.85050	−	4.93721i	0.137945	−	0.238928i
$428$	2.63163	+	9.82137i	0.127204	+	0.474734i
$429$	−13.4903	+	3.61472i	−0.651319	+	0.174520i
$430$	−8.28290	+	2.20582i	−0.399437	+	0.106374i
$431$	7.44919	−	27.8008i	0.358815	−	1.33912i	−0.516800	−	0.856106i	$-0.672877\pi$
$431$	7.44919	−	27.8008i	0.358815	−	1.33912i	0.875615	−	0.483010i	$-0.160456\pi$
$432$	−5.41920	+	1.45207i	−0.260731	+	0.0698627i
$433$	−17.4049	−	17.4049i	−0.836424	−	0.836424i	0.151962	−	0.988386i	$-0.451441\pi$
$433$	−17.4049	−	17.4049i	−0.836424	−	0.836424i	−0.988386	+	0.151962i	$0.951441\pi$
$434$	−4.64704			−0.223065
$435$	25.1922	+	6.79156i	1.20787	+	0.325630i
$436$	−5.41898	−	5.41898i	−0.259522	−	0.259522i
$437$	1.36939	−	5.11062i	0.0655067	−	0.244474i
$438$		−	8.18397i		−	0.391045i
$439$	−21.2845	−	5.70316i	−1.01585	−	0.272197i	−0.287780	−	0.957696i	$-0.592917\pi$
$439$	−21.2845	−	5.70316i	−1.01585	−	0.272197i	−0.728073	+	0.685499i	$0.759584\pi$
$440$	3.22400	−	3.21415i	0.153698	−	0.153229i
$441$	2.31365	+	4.00736i	0.110174	+	0.190827i
$442$	−25.2492	−	14.5776i	−1.20098	−	0.693388i
$443$	−3.32530	+	3.32530i	−0.157990	+	0.157990i	−0.781675	−	0.623686i	$-0.785635\pi$
$443$	−3.32530	+	3.32530i	−0.157990	+	0.157990i	0.623686	+	0.781675i	$0.285635\pi$
$444$	1.51764	+	9.10583i	0.0720239	+	0.432143i
$445$	−9.15335	+	15.7982i	−0.433911	+	0.748907i
$446$	−25.4070	+	6.80779i	−1.20306	+	0.322358i
$447$	−1.40731	+	5.25217i	−0.0665637	+	0.248419i
$448$	0.578728	+	0.155070i	0.0273423	+	0.00732635i
$449$	2.82477	−	10.5422i	0.133309	−	0.497516i	−0.866690	−	0.498847i	$-0.833757\pi$
$449$	2.82477	−	10.5422i	0.133309	−	0.497516i	0.999999	+	0.00133097i	$0.000423660\pi$
$450$	1.73270	+	3.02244i	0.0816801	+	0.142479i
$451$	1.29729	+	2.24698i	0.0610871	+	0.105806i
$452$		−	5.27845i		−	0.248278i
$453$	6.85916	−	1.83791i	0.322272	−	0.0863524i
$454$			16.4845i			0.773656i
$455$	−3.03587	+	5.23975i	−0.142324	+	0.245643i
$456$	0.912731	−	1.58090i	0.0427426	−	0.0740323i
$457$	−17.6788	+	10.2069i	−0.826980	+	0.477457i	−0.852818	−	0.522209i	$-0.825108\pi$
$457$	−17.6788	+	10.2069i	−0.826980	+	0.477457i	0.0258373	+	0.999666i	$0.491775\pi$
$458$			28.4344i			1.32865i
$459$	9.36605	+	34.9546i	0.437170	+	1.63154i
$460$	−2.56023	+	9.49676i	−0.119371	+	0.442789i
$461$	1.88507	+	7.03518i	0.0877965	+	0.327661i	0.995829	−	0.0912386i	$-0.0290826\pi$
$461$	1.88507	+	7.03518i	0.0877965	+	0.327661i	−0.908033	+	0.418900i	$0.862416\pi$
$462$	−0.925616	−	1.60321i	−0.0430635	−	0.0745882i
$463$	5.42314	+	9.39316i	0.252035	+	0.436537i	0.964086	−	0.265591i	$-0.0855669\pi$
$463$	5.42314	+	9.39316i	0.252035	+	0.436537i	−0.712051	+	0.702128i	$0.752234\pi$
$464$	−1.98996	−	7.42663i	−0.0923815	−	0.344772i
$465$	6.85122	−	25.4135i	0.317718	−	1.17852i
$466$	2.93529	+	10.9547i	0.135975	+	0.507465i
$467$			13.4387i			0.621867i	0.950432	+	0.310934i	$0.100642\pi$
$467$			13.4387i			0.621867i	−0.950432	+	0.310934i	$0.899358\pi$
$468$	−2.72754	+	1.57475i	−0.126081	+	0.0727927i
$469$	−0.236548	+	0.409713i	−0.0109228	+	0.0189188i
$470$	4.96381	−	8.56728i	0.228964	−	0.395179i
$471$			35.6715i			1.64365i
$472$	10.2327	−	2.74186i	0.471000	−	0.126204i
$473$		−	7.80437i		−	0.358845i
$474$	−9.27551	−	16.0657i	−0.426038	−	0.737920i
$475$	−5.80444	−	1.57435i	−0.266326	−	0.0722360i
$476$	1.00022	−	3.73287i	0.0458450	−	0.171096i
$477$	0.257987	+	0.0691273i	0.0118124	+	0.00316512i
$478$	1.55973	−	5.82100i	0.0713404	−	0.266246i
$479$	14.3897	−	3.85570i	0.657480	−	0.176171i	0.0853716	−	0.996349i	$-0.472792\pi$
$479$	14.3897	−	3.85570i	0.657480	−	0.176171i	0.572109	+	0.820178i	$0.306126\pi$
$480$	−1.70127	+	2.93629i	−0.0776518	+	0.134023i
$481$	11.3854	+	25.0266i	0.519130	+	1.14112i
$482$	10.7264	−	10.7264i	0.488574	−	0.488574i
$483$	3.46381	+	1.99983i	0.157609	+	0.0909956i
$484$	−3.42750	−	5.93661i	−0.155796	−	0.269846i
$485$	−24.9315	+	24.8554i	−1.13208	+	1.12862i
$486$	6.84022	+	1.83283i	0.310279	+	0.0831389i
$487$			19.9809i			0.905422i	0.891657	+	0.452711i	$0.149543\pi$
$487$			19.9809i			0.905422i	−0.891657	+	0.452711i	$0.850457\pi$
$488$	2.46273	−	9.19103i	0.111482	−	0.416058i
$489$	0.851316	+	0.851316i	0.0384978	+	0.0384978i
$490$	14.3379	+	3.86535i	0.647720	+	0.174619i
$491$	37.4035			1.68800			0.843999	−	0.536345i	$-0.180195\pi$
$491$	37.4035			1.68800			0.843999	+	0.536345i	$0.180195\pi$
$492$	−1.36760	−	1.36760i	−0.0616562	−	0.0616562i
$493$	−47.9028	+	12.8355i	−2.15743	+	0.578082i
$494$	1.40718	−	5.25166i	0.0633120	−	0.236284i
$495$	−3.06521	+	0.816297i	−0.137771	+	0.0366898i
$496$	−7.49187	+	2.00744i	−0.336395	+	0.0901367i
$497$	−2.59344	−	9.67884i	−0.116332	−	0.434155i
$498$	−0.765256	+	1.32546i	−0.0342919	+	0.0593954i
$499$	4.65546	+	1.24743i	0.208407	+	0.0558425i	0.361512	−	0.932367i	$-0.382261\pi$
$499$	4.65546	+	1.24743i	0.208407	+	0.0558425i	−0.153105	+	0.988210i	$0.548927\pi$
$500$	10.7860	+	2.94322i	0.482364	+	0.131625i
$501$	29.1755	−	7.81755i	1.30346	−	0.349262i
$502$	−13.8195	+	3.70293i	−0.616796	+	0.165270i
$503$	−0.898560	+	1.55635i	−0.0400648	+	0.0693943i	−0.885362	−	0.464901i	$-0.846090\pi$
$503$	−0.898560	+	1.55635i	−0.0400648	+	0.0693943i	0.845298	+	0.534296i	$0.179423\pi$
$504$	−0.295194	−	0.295194i	−0.0131490	−	0.0131490i
$505$	4.48509	−	4.47139i	0.199584	−	0.198974i
$506$	−7.75564	−	4.47772i	−0.344780	−	0.199059i
$507$	7.97481	−	7.97481i	0.354174	−	0.354174i
$508$	−10.4578	+	10.4578i	−0.463989	+	0.463989i
$509$	19.6160	−	33.9759i	0.869463	−	1.50595i	0.00691570	−	0.999976i	$-0.497799\pi$
$509$	19.6160	−	33.9759i	0.869463	−	1.50595i	0.862547	−	0.505977i	$-0.168868\pi$
$510$	18.9395	+	10.9734i	0.838655	+	0.485910i
$511$	2.79806	−	1.61546i	0.123779	−	0.0714637i
$512$	1.00000			0.0441942
$513$	−5.84422	+	3.37416i	−0.258029	+	0.148973i
$514$	6.56308	−	3.78920i	0.289485	−	0.167134i
$515$	2.94541	−	2.93641i	0.129790	−	0.129394i
$516$	1.50571	+	5.61937i	0.0662850	+	0.247379i
$517$	6.37468	+	6.37468i	0.280358	+	0.280358i
$518$	−2.81367	+	2.31630i	−0.123625	+	0.101772i
$519$			18.6042i			0.816635i
$520$	−2.63088	+	9.75885i	−0.115372	+	0.427954i
$521$	26.5926	−	15.3533i	1.16504	−	0.672638i	0.212536	−	0.977153i	$-0.431828\pi$
$521$	26.5926	−	15.3533i	1.16504	−	0.672638i	0.952508	+	0.304515i	$0.0984944\pi$
$522$	−1.38655	+	5.17468i	−0.0606878	+	0.226490i
$523$	21.1142	+	36.5709i	0.923261	+	1.59914i	0.794334	+	0.607481i	$0.207820\pi$
$523$	21.1142	+	36.5709i	0.923261	+	1.59914i	0.128927	+	0.991654i	$0.458847\pi$
$524$	0.826744	+	0.826744i	0.0361165	+	0.0361165i
$525$	2.28524	−	3.93033i	0.0997362	−	0.171534i
$526$	18.8935	−	18.8935i	0.823794	−	0.823794i
$527$	12.9483	+	48.3236i	0.564035	+	2.10501i
$528$	−2.18482	−	2.18482i	−0.0950820	−	0.0950820i
$529$	−3.65136			−0.158755
$530$	0.742950	−	0.427428i	0.0322717	−	0.0185663i
$531$	−7.12992	−	1.91046i	−0.309412	−	0.0829067i
$532$	0.720668			0.0312449
$533$	−4.98867	−	2.88021i	−0.216083	−	0.124756i
$534$	10.7319	+	6.19605i	0.464413	+	0.268129i
$535$	−11.3378	−	19.7073i	−0.490177	−	0.852020i
$536$	−0.204369	+	0.762716i	−0.00882740	+	0.0329443i
$537$	−10.2102	+	5.89484i	−0.440601	+	0.254381i
$538$	14.0145	+	8.09130i	0.604210	+	0.348841i
$539$	−6.76032	+	11.7092i	−0.291188	+	0.504352i
$540$	10.8740	−	6.25595i	0.467943	−	0.269213i
$541$	−8.09430	+	8.09430i	−0.348001	+	0.348001i	−0.859365	−	0.511363i	$-0.829141\pi$
$541$	−8.09430	+	8.09430i	−0.348001	+	0.348001i	0.511363	+	0.859365i	$0.329141\pi$
$542$	−14.3377	−	24.8336i	−0.615856	−	1.06669i
$543$	2.41898	+	9.02775i	0.103808	+	0.387418i
$544$		−	6.45014i		−	0.276547i
$545$	14.8274	+	8.59086i	0.635135	+	0.367992i
$546$	3.55941	+	2.05503i	0.152329	+	0.0879470i
$547$	13.3403			0.570390			0.285195	−	0.958470i	$-0.407942\pi$
$547$	13.3403			0.570390			0.285195	+	0.958470i	$0.407942\pi$
$548$	11.2976	+	3.02718i	0.482609	+	0.129315i
$549$	−4.68811	+	4.68811i	−0.200084	+	0.200084i
$550$	−5.11677	+	8.80020i	−0.218180	+	0.375242i
$551$	−4.62405	−	8.00909i	−0.196991	−	0.341199i
$552$	6.44818	+	1.72778i	0.274453	+	0.0735394i
$553$	3.66185	−	6.34250i	0.155718	−	0.269711i
$554$	−10.1092			−0.429500
$555$	−8.51903	−	18.8022i	−0.361613	−	0.798109i
$556$	14.0181			0.594500
$557$	20.9029	−	36.2049i	0.885685	−	1.53405i	0.0407575	−	0.999169i	$-0.487023\pi$
$557$	20.9029	−	36.2049i	0.885685	−	1.53405i	0.844927	−	0.534882i	$-0.179644\pi$
$558$	5.22014	+	1.39873i	0.220986	+	0.0592131i
$559$	8.66352	+	15.0057i	0.366428	+	0.634672i
$560$	−1.33972	−	0.00204974i	−0.0566136	−	8.66174e-5i
$561$	−14.0924	+	14.0924i	−0.594981	+	0.594981i
$562$	0.0560250	+	0.0150119i	0.00236327	+	0.000633237i
$563$	−18.7518			−0.790295			−0.395148	−	0.918618i	$-0.629307\pi$
$563$	−18.7518			−0.790295			−0.395148	+	0.918618i	$0.629307\pi$
$564$	−5.81983	−	3.36008i	−0.245059	−	0.141485i
$565$	3.03739	+	11.4055i	0.127784	+	0.479832i
$566$			18.9964i			0.798479i
$567$	−0.996195	−	3.71785i	−0.0418363	−	0.156135i
$568$	−8.36217	−	14.4837i	−0.350869	−	0.607722i
$569$	5.69966	−	5.69966i	0.238942	−	0.238942i	−0.577470	−	0.816412i	$-0.695960\pi$
$569$	5.69966	−	5.69966i	0.238942	−	0.238942i	0.816412	+	0.577470i	$0.195960\pi$
$570$	−1.06249	+	3.94115i	−0.0445030	+	0.165077i
$571$	8.12850	−	14.0790i	0.340167	−	0.589187i	−0.644296	−	0.764776i	$-0.722850\pi$
$571$	8.12850	−	14.0790i	0.340167	−	0.589187i	0.984464	+	0.175589i	$0.0561830\pi$
$572$	−7.96968	−	4.60130i	−0.333229	−	0.192390i
$573$	5.13841	−	2.96666i	0.214660	−	0.123934i
$574$	0.197621	−	0.737531i	0.00824853	−	0.0307839i
$575$	0.0672990	−	21.9934i	0.00280656	−	0.917190i
$576$	−0.603425	−	0.348387i	−0.0251427	−	0.0145161i
$577$	18.7466	+	10.8233i	0.780430	+	0.450582i	0.836583	−	0.547841i	$-0.184550\pi$
$577$	18.7466	+	10.8233i	0.780430	+	0.450582i	−0.0561525	+	0.998422i	$0.517883\pi$
$578$	−24.6043			−1.02340
$579$	3.98247	+	1.06710i	0.165506	+	0.0443471i
$580$	8.57334	+	14.9021i	0.355988	+	0.618774i
$581$	−0.604225			−0.0250675
$582$	16.8954	+	16.8954i	0.700338	+	0.700338i
$583$	0.201985	+	0.753819i	0.00836537	+	0.0312200i
$584$	3.81312	−	3.81312i	0.157788	−	0.157788i
$585$	4.98740	−	4.97216i	0.206204	−	0.205574i
$586$	13.3188	+	13.3188i	0.550193	+	0.550193i
$587$	−19.9109	−	34.4867i	−0.821810	−	1.42342i	−0.904333	−	0.426827i	$-0.859631\pi$
$587$	−19.9109	−	34.4867i	−0.821810	−	1.42342i	0.0825233	−	0.996589i	$-0.473702\pi$
$588$	2.60855	−	9.73525i	0.107575	−	0.401475i
$589$	−8.07945	+	4.66467i	−0.332908	+	0.192204i
$590$	−20.5327	+	11.8127i	−0.845320	+	0.486323i
$591$		−	9.85420i		−	0.405348i
$592$	−3.53553	+	4.94975i	−0.145310	+	0.203433i
$593$	15.5586	+	15.5586i	0.638915	+	0.638915i	0.950288	−	0.311373i	$-0.100789\pi$
$593$	15.5586	+	15.5586i	0.638915	+	0.638915i	−0.311373	+	0.950288i	$0.600789\pi$
$594$	2.95631	+	11.0331i	0.121299	+	0.452693i
$595$	−0.0132211	+	8.64140i	−0.000542013	+	0.354263i
$596$	−3.10282	+	1.79142i	−0.127097	+	0.0733793i
$597$	−14.5145	+	8.37994i	−0.594038	+	0.342968i
$598$	19.8826			0.813061
$599$	−15.5409	+	8.97253i	−0.634983	+	0.366608i	−0.782679	−	0.622425i	$-0.786148\pi$
$599$	−15.5409	+	8.97253i	−0.634983	+	0.366608i	0.147696	+	0.989033i	$0.452814\pi$
$600$	1.98639	−	7.32359i	0.0810939	−	0.298984i
$601$	−12.7730	+	22.1236i	−0.521024	+	0.902439i	0.478678	+	0.877991i	$0.341116\pi$
$601$	−12.7730	+	22.1236i	−0.521024	+	0.902439i	−0.999701	+	0.0244484i	$0.992217\pi$
$602$	−1.62402	+	1.62402i	−0.0661901	+	0.0661901i
$603$	0.389042	−	0.389042i	0.0158430	−	0.0158430i
$604$	4.05219	+	2.33953i	0.164881	+	0.0951943i
$605$	10.8221	+	10.8553i	0.439982	+	0.441330i
$606$	−3.03942	−	3.03942i	−0.123468	−	0.123468i
$607$	−3.97161	+	6.87904i	−0.161203	+	0.279212i	−0.935300	−	0.353855i	$-0.884871\pi$
$607$	−3.97161	+	6.87904i	−0.161203	+	0.279212i	0.774097	+	0.633066i	$0.218204\pi$
$608$	1.16185	−	0.311316i	0.0471191	−	0.0126255i
$609$	6.75290	−	1.80943i	0.273641	−	0.0733220i
$610$	−0.0325529	+	21.2767i	−0.00131803	+	0.861470i
$611$	−19.3332	−	5.18032i	−0.782138	−	0.209573i
$612$	−2.24715	+	3.89217i	−0.0908355	+	0.157332i
$613$	0.295928	+	1.10442i	0.0119524	+	0.0446070i	0.971644	−	0.236447i	$-0.0759828\pi$
$613$	0.295928	+	1.10442i	0.0119524	+	0.0446070i	−0.959692	+	0.281054i	$0.909316\pi$
$614$	0.0918851	−	0.0246205i	0.00370818	−	0.000993604i
$615$	3.74201	+	2.16809i	0.150893	+	0.0874260i
$616$	0.315710	−	1.17825i	0.0127203	−	0.0474729i
$617$	13.4207	−	3.59608i	0.540299	−	0.144773i	0.0216589	−	0.999765i	$-0.493105\pi$
$617$	13.4207	−	3.59608i	0.540299	−	0.144773i	0.518640	+	0.854993i	$0.326439\pi$
$618$	−1.99602	−	1.99602i	−0.0802917	−	0.0802917i
$619$	−3.73473			−0.150112			−0.0750558	−	0.997179i	$-0.523913\pi$
$619$	−3.73473			−0.150112			−0.0750558	+	0.997179i	$0.523913\pi$
$620$	15.0330	−	8.64865i	0.603739	−	0.347338i
$621$	−17.4502	−	17.4502i	−0.700254	−	0.700254i
$622$	7.21697	−	26.9341i	0.289374	−	1.07996i
$623$			4.89223i			0.196003i
$624$	6.62614	+	1.77547i	0.265258	+	0.0710756i
$625$	−24.9995	−	0.152996i	−0.999981	−	0.00611986i
$626$	−0.166143	−	0.287768i	−0.00664040	−	0.0115015i
$627$	−3.21859	−	1.85825i	−0.128538	−	0.0742115i
$628$	−16.6203	+	16.6203i	−0.663220	+	0.663220i
$629$	31.9266	+	22.8047i	1.27300	+	0.909282i
$630$	0.807708	+	0.467979i	0.0321798	+	0.0186447i
$631$	−29.8147	+	7.98884i	−1.18691	+	0.318031i	−0.797662	−	0.603104i	$-0.793930\pi$
$631$	−29.8147	+	7.98884i	−1.18691	+	0.318031i	−0.389244	+	0.921135i	$0.627264\pi$
$632$	3.16370	−	11.8071i	0.125845	−	0.469661i
$633$	−22.7840	−	6.10495i	−0.905582	−	0.242650i
$634$	1.22297	−	4.56417i	0.0485702	−	0.181266i
$635$	16.5790	−	28.6145i	0.657918	−	1.13553i
$636$	−0.290870	−	0.503802i	−0.0115338	−	0.0199771i
$637$		−	30.0181i		−	1.18936i
$638$	−15.1201	+	4.05141i	−0.598609	+	0.160397i
$639$			11.6531i			0.460989i
$640$	−2.16076	+	0.575432i	−0.0854115	+	0.0227459i
$641$	8.39991	−	14.5491i	0.331776	−	0.574654i	−0.651084	−	0.759006i	$-0.725685\pi$
$641$	8.39991	−	14.5491i	0.331776	−	0.574654i	0.982860	+	0.184352i	$0.0590187\pi$
$642$	−13.3637	+	7.71554i	−0.527423	+	0.304508i
$643$			12.1107i			0.477598i	0.971069	+	0.238799i	$0.0767537\pi$
$643$			12.1107i			0.477598i	−0.971069	+	0.238799i	$0.923246\pi$
$644$	0.682106	+	2.54565i	0.0268787	+	0.100313i
$645$	−6.48703	−	11.2757i	−0.255427	−	0.443979i
$646$	−2.00803	−	7.49407i	−0.0790049	−	0.294850i
$647$	15.4144	+	26.6986i	0.606004	+	1.04963i	0.991892	+	0.127084i	$0.0405618\pi$
$647$	15.4144	+	26.6986i	0.606004	+	1.04963i	−0.385888	+	0.922546i	$0.626105\pi$
$648$	−3.21209	−	5.56350i	−0.126183	−	0.218555i
$649$	−5.58221	−	20.8331i	−0.219121	−	0.817771i
$650$	0.0691563	−	22.6004i	0.00271253	−	0.886461i
$651$	−1.82533	−	6.81222i	−0.0715403	−	0.266992i
$652$			0.793300i			0.0310680i
$653$	−38.7254	+	22.3581i	−1.51544	+	0.874941i	−0.515605	+	0.856826i	$0.672433\pi$
$653$	−38.7254	+	22.3581i	−1.51544	+	0.874941i	−0.999836	+	0.0181144i	$0.994234\pi$
$654$	5.81528	−	10.0724i	0.227396	−	0.393861i
$655$	−2.26213	−	1.31066i	−0.0883887	−	0.0512117i
$656$		−	1.27440i		−	0.0497570i
$657$	−3.62937	+	0.972488i	−0.141595	+	0.0379404i
$658$		−	2.65303i		−	0.103426i
$659$	18.7286	+	32.4389i	0.729563	+	1.26364i	0.957068	+	0.289863i	$0.0936098\pi$
$659$	18.7286	+	32.4389i	0.729563	+	1.26364i	−0.227505	+	0.973777i	$0.573057\pi$
$660$	5.97808	+	3.46365i	0.232696	+	0.134822i
$661$	2.86805	−	10.7037i	0.111554	−	0.416326i	−0.887452	−	0.460901i	$-0.847526\pi$
$661$	2.86805	−	10.7037i	0.111554	−	0.416326i	0.999006	+	0.0445742i	$0.0141931\pi$
$662$	10.7475	+	2.87977i	0.417712	+	0.111926i
$663$	11.4520	−	42.7395i	0.444759	−	1.65986i
$664$	−0.974119	+	0.261014i	−0.0378032	+	0.0101293i
$665$	−1.55719	+	0.414695i	−0.0603852	+	0.0160812i
$666$	3.85786	−	1.75506i	0.149489	−	0.0680073i
$667$	23.9143	−	23.9143i	0.925966	−	0.925966i
$668$	17.2360	+	9.95122i	0.666881	+	0.385024i
$669$	−19.9594	−	34.5707i	−0.771676	−	1.33658i
$670$	0.00270139	−	1.76565i	0.000104364	−	0.0682128i
$671$	−18.7123	−	5.01393i	−0.722379	−	0.193561i
$672$			0.909282i			0.0350763i
$673$	3.26096	−	12.1701i	0.125701	−	0.469121i	−0.874163	−	0.485633i	$-0.838589\pi$
$673$	3.26096	−	12.1701i	0.125701	−	0.469121i	0.999864	+	0.0165114i	$0.00525596\pi$
$674$	13.5982	+	13.5982i	0.523781	+	0.523781i
$675$	−19.8962	+	19.7749i	−0.765807	+	0.761134i
$676$	7.43134			0.285821
$677$	−22.9134	−	22.9134i	−0.880633	−	0.880633i	0.112966	−	0.993599i	$-0.463965\pi$
$677$	−22.9134	−	22.9134i	−0.880633	−	0.880633i	−0.993599	+	0.112966i	$0.963965\pi$
$678$	7.73782	−	2.07334i	0.297169	−	0.0796263i
$679$	−2.44142	+	9.11150i	−0.0936931	+	0.349667i
$680$	3.71162	+	13.9372i	0.142334	+	0.534467i
$681$	−24.1651	+	6.47501i	−0.926007	+	0.248123i
$682$	4.08700	+	15.2529i	0.156499	+	0.584063i
$683$	−5.31104	+	9.19898i	−0.203221	+	0.351989i	−0.949564	−	0.313572i	$-0.898474\pi$
$683$	−5.31104	+	9.19898i	−0.203221	+	0.351989i	0.746343	+	0.665561i	$0.231808\pi$
$684$	−0.809545	−	0.216917i	−0.0309537	−	0.00829402i
$685$	−26.1533	−	0.0400139i	−0.999266	−	0.00152885i
$686$	7.89444	−	2.11531i	0.301411	−	0.0807629i
$687$	−41.6827	+	11.1688i	−1.59029	+	0.426118i
$688$	−1.91666	+	3.31976i	−0.0730721	+	0.126565i
$689$	−1.22517	−	1.22517i	−0.0466751	−	0.0466751i
$690$	−14.9272	−	0.0228382i	−0.568268	−	0.000869436i
$691$	5.88296	+	3.39653i	0.223798	+	0.129210i	0.607708	−	0.794161i	$-0.292089\pi$
$691$	5.88296	+	3.39653i	0.223798	+	0.129210i	−0.383909	+	0.923371i	$0.625423\pi$
$692$	−8.66819	+	8.66819i	−0.329515	+	0.329515i
$693$	−0.600994	+	0.600994i	−0.0228299	+	0.0228299i
$694$	4.67824	−	8.10294i	0.177583	−	0.307583i
$695$	−30.2898	+	8.06647i	−1.14896	+	0.305979i
$696$	10.1052	−	5.83426i	0.383038	−	0.221147i
$697$	−8.22006			−0.311357
$698$	22.9567	−	13.2541i	0.868924	−	0.501673i
$699$	−14.9058	+	8.60584i	−0.563788	+	0.325503i
$700$	2.89600	−	0.766490i	0.109458	−	0.0289706i
$701$	−4.29704	−	16.0368i	−0.162297	−	0.605701i	−0.998370	−	0.0570819i	$-0.981820\pi$
$701$	−4.29704	−	16.0368i	−0.162297	−	0.605701i	0.836072	−	0.548619i	$-0.184846\pi$
$702$	−17.9318	−	17.9318i	−0.676793	−	0.676793i
$703$	−2.56681	+	6.85151i	−0.0968091	+	0.258410i
$704$		−	2.03593i		−	0.0767318i
$705$	14.5088	+	3.91141i	0.546431	+	0.147312i
$706$	17.8939	−	10.3311i	0.673446	−	0.388815i
$707$	0.439202	−	1.63912i	0.0165179	−	0.0616456i
$708$	8.03871	+	13.9235i	0.302113	+	0.523276i
$709$	4.55454	+	4.55454i	0.171049	+	0.171049i	0.787440	−	0.616391i	$-0.211406\pi$
$709$	4.55454	+	4.55454i	0.171049	+	0.171049i	−0.616391	+	0.787440i	$0.711406\pi$
$710$	26.4030	+	26.4839i	0.990887	+	0.993924i
$711$	−6.02250	+	6.02250i	−0.225861	+	0.225861i
$712$	2.11336	+	7.88715i	0.0792014	+	0.295584i
$713$	−24.1244	−	24.1244i	−0.903466	−	0.903466i
$714$	5.86500			0.219492
$715$	19.8683	+	5.35629i	0.743032	+	0.200314i
$716$	−7.50373	−	2.01062i	−0.280428	−	0.0751404i
$717$	9.14580			0.341556
$718$	−5.60313	−	3.23497i	−0.209107	−	0.120728i
$719$	8.28834	+	4.78528i	0.309103	+	0.178461i	0.646525	−	0.762893i	$-0.276222\pi$
$719$	8.28834	+	4.78528i	0.309103	+	0.178461i	−0.337422	+	0.941354i	$0.609555\pi$
$720$	1.50433	+	0.405551i	0.0560630	+	0.0151140i
$721$	0.288429	−	1.07643i	0.0107416	−	0.0400884i
$722$	−15.2015	+	8.77660i	−0.565742	+	0.326631i
$723$	19.9374	+	11.5109i	0.741479	+	0.428093i
$724$	−3.07920	+	5.33333i	−0.114437	+	0.198212i
$725$	−27.1000	−	27.2664i	−1.00647	−	1.01265i
$726$	7.35633	−	7.35633i	0.273019	−	0.273019i
$727$	−8.59617	−	14.8890i	−0.318814	−	0.552202i	0.661427	−	0.750010i	$-0.269951\pi$
$727$	−8.59617	−	14.8890i	−0.318814	−	0.552202i	−0.980241	+	0.197807i	$0.936618\pi$
$728$	0.700931	+	2.61591i	0.0259782	+	0.0969521i
$729$			30.0197i			1.11184i
$730$	−6.04505	+	10.4334i	−0.223737	+	0.386159i
$731$	21.4129	+	12.3627i	0.791985	+	0.457253i
$732$	14.4407			0.533744
$733$	−9.75498	−	2.61384i	−0.360309	−	0.0965444i	0.0741233	−	0.997249i	$-0.476384\pi$
$733$	−9.75498	−	2.61384i	−0.360309	−	0.0965444i	−0.434432	+	0.900705i	$0.643051\pi$
$734$	14.8241	−	14.8241i	0.547167	−	0.547167i
$735$	−0.0344804	+	22.5366i	−0.00127183	+	0.831274i
$736$	2.19935	+	3.80939i	0.0810693	+	0.140416i
$737$	1.55283	+	0.416080i	0.0571993	+	0.0153265i
$738$	−0.443985	+	0.769004i	−0.0163433	+	0.0283074i
$739$	−35.2004			−1.29487			−0.647434	−	0.762122i	$-0.724158\pi$
$739$	−35.2004			−1.29487			−0.647434	+	0.762122i	$0.724158\pi$
$740$	4.79119	−	12.7297i	0.176128	−	0.467952i
$741$	8.25128			0.303118
$742$	0.114832	−	0.198894i	0.00421560	−	0.00730164i
$743$	21.4177	+	5.73886i	0.785740	+	0.210538i	0.629314	−	0.777151i	$-0.283336\pi$
$743$	21.4177	+	5.73886i	0.785740	+	0.210538i	0.156426	+	0.987690i	$0.450003\pi$
$744$	−5.88552	−	10.1940i	−0.215773	−	0.373731i
$745$	5.67362	−	5.65628i	0.207865	−	0.207230i
$746$	−24.9517	+	24.9517i	−0.913546	+	0.913546i
$747$	0.678742	+	0.181868i	0.0248339	+	0.00665421i
$748$	−13.1320			−0.480154
$749$	−5.27581	−	3.04599i	−0.192774	−	0.111298i
$750$	−0.0778802	+	16.9675i	−0.00284378	+	0.619567i
$751$		−	54.5209i		−	1.98950i	−0.102354	−	0.994748i	$-0.532637\pi$
$751$		−	54.5209i		−	1.98950i	0.102354	−	0.994748i	$-0.467363\pi$
$752$	−1.14606	−	4.27716i	−0.0417926	−	0.155972i
$753$	−10.8565	−	18.8039i	−0.395631	−	0.685253i
$754$	24.5743	−	24.5743i	0.894943	−	0.894943i
$755$	−10.1020	−	2.72341i	−0.367651	−	0.0991150i
$756$	1.68071	−	2.91107i	0.0611267	−	0.105875i
$757$	33.7676	+	19.4957i	1.22731	+	0.708585i	0.966465	−	0.256797i	$-0.0826672\pi$
$757$	33.7676	+	19.4957i	1.22731	+	0.708585i	0.260840	+	0.965382i	$0.416001\pi$
$758$	−18.9131	+	10.9195i	−0.686956	+	0.396614i
$759$	3.51764	−	13.1280i	0.127682	−	0.476517i
$760$	−2.33133	+	1.34124i	−0.0845661	+	0.0486519i
$761$	45.6597	+	26.3617i	1.65516	+	0.955609i	0.974900	+	0.222642i	$0.0714682\pi$
$761$	45.6597	+	26.3617i	1.65516	+	0.955609i	0.680264	+	0.732967i	$0.261865\pi$
$762$	−19.4381	−	11.2226i	−0.704167	−	0.406551i
$763$	4.59159			0.166227
$764$	3.77636	+	1.01187i	0.136624	+	0.0366083i
$765$	2.61586	−	9.70313i	0.0945767	−	0.350817i
$766$	−19.7053			−0.711983
$767$	33.8596	+	33.8596i	1.22260	+	1.22260i
$768$	0.392794	+	1.46593i	0.0141737	+	0.0528970i
$769$	34.7685	−	34.7685i	1.25378	−	1.25378i	0.299773	−	0.954010i	$-0.403089\pi$
$769$	34.7685	−	34.7685i	1.25378	−	1.25378i	0.954010	−	0.299773i	$-0.0969111\pi$
$770$	−0.00417312	+	2.72758i	−0.000150389	+	0.0982950i
$771$	8.13262	+	8.13262i	0.292889	+	0.292889i
$772$	1.35835	+	2.35272i	0.0488880	+	0.0846764i
$773$	8.15785	−	30.4455i	0.293418	−	1.09505i	−0.649048	−	0.760747i	$-0.724833\pi$
$773$	8.15785	−	30.4455i	0.293418	−	1.09505i	0.942466	−	0.334302i	$-0.108501\pi$
$774$	2.31312	−	1.33548i	0.0831435	−	0.0480029i
$775$	−27.5059	+	27.3381i	−0.988042	+	0.982014i
$776$			15.7440i			0.565177i
$777$	−4.50072	−	3.21480i	−0.161462	−	0.115330i
$778$	8.27249	+	8.27249i	0.296583	+	0.296583i
$779$	−0.396741	−	1.48066i	−0.0142147	−	0.0530500i
$780$	−15.3391	−	0.0234685i	−0.549229	−	0.000840307i
$781$	−29.4877	+	17.0248i	−1.05515	+	0.609193i
$782$	24.5711	−	14.1861i	0.878661	−	0.507295i
$783$	−43.1359			−1.54155
$784$	5.75130	−	3.32051i	0.205404	−	0.118590i
$785$	26.3485	−	45.4762i	0.940419	−	1.62311i
$786$	−0.887205	+	1.53668i	−0.0316456	+	0.0548117i
$787$	33.6848	−	33.6848i	1.20073	−	1.20073i	0.226791	−	0.973943i	$-0.427177\pi$
$787$	33.6848	−	33.6848i	1.20073	−	1.20073i	0.973943	−	0.226791i	$-0.0728234\pi$
$788$	4.59133	−	4.59133i	0.163559	−	0.163559i
$789$	35.1176	+	20.2752i	1.25022	+	0.721815i
$790$	−0.0418185	+	27.3328i	−0.00148783	+	0.972457i
$791$	2.23626	+	2.23626i	0.0795122	+	0.0795122i
$792$	−0.709291	+	1.22853i	−0.0252036	+	0.0436538i
$793$	41.5444	−	11.1318i	1.47528	−	0.395301i
$794$	−30.8105	+	8.25564i	−1.09342	+	0.292982i
$795$	0.918405	+	0.921219i	0.0325725	+	0.0326723i
$796$	−10.6671	−	2.85824i	−0.378085	−	0.101308i
$797$	−22.6296	+	39.1956i	−0.801581	+	1.38838i	0.116994	+	0.993133i	$0.462674\pi$
$797$	−22.6296	+	39.1956i	−0.801581	+	1.38838i	−0.918575	+	0.395246i	$0.870659\pi$
$798$	0.283074	+	1.05645i	0.0100207	+	0.0373978i
$799$	−27.5883	+	7.39226i	−0.976003	+	0.261519i
$800$	4.33776	−	2.48674i	0.153363	−	0.0879195i
$801$	1.47253	−	5.49557i	0.0520294	−	0.194176i
$802$	−10.3818	+	2.78180i	−0.366594	+	0.0982287i
$803$	−7.76323	−	7.76323i	−0.273959	−	0.273959i
$804$	−1.19836			−0.0422629
$805$	−2.93872	−	5.10804i	−0.103576	−	0.180035i
$806$	−24.7902	−	24.7902i	−0.873197	−	0.873197i
$807$	−6.35642	+	23.7225i	−0.223757	+	0.835071i
$808$		−	2.83229i		−	0.0996396i
$809$	−38.4611	−	10.3056i	−1.35222	−	0.362326i	−0.491266	−	0.871009i	$-0.663466\pi$
$809$	−38.4611	−	10.3056i	−1.35222	−	0.362326i	−0.860954	+	0.508683i	$0.830133\pi$
$810$	10.1420	+	10.1731i	0.356352	+	0.357445i
$811$	1.92162	+	3.32834i	0.0674770	+	0.116874i	0.897790	−	0.440424i	$-0.145172\pi$
$811$	1.92162	+	3.32834i	0.0674770	+	0.116874i	−0.830313	+	0.557297i	$0.811838\pi$
$812$	3.98941	+	2.30329i	0.140001	+	0.0808296i
$813$	30.7724	−	30.7724i	1.07924	−	1.07924i
$814$	10.0773	+	7.19809i	0.353210	+	0.252293i
$815$	−0.456490	−	1.71413i	−0.0159902	−	0.0600434i
$816$	9.45543	−	2.53357i	0.331006	−	0.0886928i
$817$	−1.19337	+	4.45374i	−0.0417509	+	0.155816i
$818$	8.55993	+	2.29363i	0.299291	+	0.0801948i
$819$	0.488391	−	1.82270i	0.0170658	−	0.0636903i
$820$	0.733330	+	2.75367i	0.0256090	+	0.0961624i
$821$	12.0892	+	20.9392i	0.421917	+	0.730782i	0.996127	−	0.0879264i	$-0.0280240\pi$
$821$	12.0892	+	20.9392i	0.421917	+	0.730782i	−0.574210	+	0.818708i	$0.694691\pi$
$822$			17.7505i			0.619119i
$823$	41.2132	−	11.0430i	1.43660	−	0.384936i	0.545259	−	0.838268i	$-0.316431\pi$
$823$	41.2132	−	11.0430i	1.43660	−	0.384936i	0.891342	+	0.453332i	$0.149765\pi$
$824$		−	1.86000i		−	0.0647960i
$825$	−14.9103	−	4.04414i	−0.519109	−	0.140799i
$826$	−3.17358	+	5.49679i	−0.110423	+	0.191258i
$827$	5.40417	−	3.12010i	0.187921	−	0.108496i	−0.403088	−	0.915161i	$-0.632063\pi$
$827$	5.40417	−	3.12010i	0.187921	−	0.108496i	0.591009	+	0.806665i	$0.298730\pi$
$828$		−	3.06491i		−	0.106513i
$829$	0.708796	+	2.64526i	0.0246175	+	0.0918737i	0.977142	−	0.212589i	$-0.0681897\pi$
$829$	0.708796	+	2.64526i	0.0246175	+	0.0918737i	−0.952524	+	0.304463i	$0.901523\pi$
$830$	1.95464	−	1.12453i	0.0678466	−	0.0390330i
$831$	−3.97084	−	14.8194i	−0.137747	−	0.514079i
$832$	2.26005	+	3.91452i	0.0783532	+	0.135712i
$833$	−21.4178	−	37.0967i	−0.742082	−	1.28532i
$834$	5.50623	+	20.5495i	0.190665	+	0.711572i
$835$	−42.9691	−	11.5840i	−1.48701	−	0.400882i
$836$	−0.633816	−	2.36543i	−0.0219210	−	0.0818102i
$837$			43.5149i			1.50409i
$838$	19.2058	−	11.0885i	0.663452	−	0.383044i
$839$	26.0250	−	45.0765i	0.898481	−	1.55622i	0.0690451	−	0.997614i	$-0.478005\pi$
$839$	26.0250	−	45.0765i	0.898481	−	1.55622i	0.829436	−	0.558602i	$-0.188662\pi$
$840$	−0.523230	−	1.96474i	−0.0180531	−	0.0677900i
$841$		−	30.1147i		−	1.03844i
$842$	25.1096	−	6.72810i	0.865335	−	0.231866i
$843$			0.0880251i			0.00303174i
$844$	−7.77120	−	13.4601i	−0.267496	−	0.463316i
$845$	−16.0573	+	4.27623i	−0.552389	+	0.147107i
$846$	−0.798546	+	2.98022i	−0.0274546	+	0.102462i
$847$	3.96718	+	1.06300i	0.136314	+	0.0365252i
$848$	0.0992105	−	0.370259i	0.00340690	−	0.0127147i
$849$	−27.8473	+	7.46167i	−0.955718	+	0.256084i
$850$	−16.0398	−	27.9791i	−0.550161	−	0.959676i
$851$	−26.6314	−	2.58199i	−0.912914	−	0.0885095i
$852$	17.9474	−	17.9474i	0.614868	−	0.614868i
$853$	−8.37182	−	4.83347i	−0.286646	−	0.165495i	0.349782	−	0.936831i	$-0.386256\pi$
$853$	−8.37182	−	4.83347i	−0.286646	−	0.165495i	−0.636428	+	0.771336i	$0.719589\pi$
$854$	2.85050	+	4.93721i	0.0975421	+	0.168948i
$855$	1.87405	+	0.00286725i	0.0640912	+	9.80579e-5i
$856$	−9.82137	−	2.63163i	−0.335687	−	0.0899472i
$857$			33.2215i			1.13482i	0.823434	+	0.567412i	$0.192055\pi$
$857$			33.2215i			1.13482i	−0.823434	+	0.567412i	$0.807945\pi$
$858$	3.61472	−	13.4903i	0.123405	−	0.460552i
$859$	−4.72012	−	4.72012i	−0.161048	−	0.161048i	0.621983	−	0.783031i	$-0.286327\pi$
$859$	−4.72012	−	4.72012i	−0.161048	−	0.161048i	−0.783031	+	0.621983i	$0.786327\pi$
$860$	2.23115	−	8.27611i	0.0760817	−	0.282213i
$861$	1.15879			0.0394914
$862$	20.3516	+	20.3516i	0.693177	+	0.693177i
$863$	31.0995	−	8.33308i	1.05864	−	0.283661i	0.312821	−	0.949812i	$-0.398726\pi$
$863$	31.0995	−	8.33308i	1.05864	−	0.283661i	0.745817	+	0.666151i	$0.232059\pi$
$864$	1.45207	−	5.41920i	0.0494004	−	0.184365i
$865$	13.7419	−	23.7178i	0.467239	−	0.806430i
$866$	23.7755	−	6.37062i	0.807924	−	0.216483i
$867$	−9.66441	−	36.0681i	−0.328221	−	1.22494i
$868$	2.32352	−	4.02446i	0.0788655	−	0.136599i
$869$	−24.0384	−	6.44107i	−0.815446	−	0.218498i
$870$	−18.4778	+	18.4213i	−0.626455	+	0.624541i
$871$	−3.44755	+	0.923769i	−0.116816	+	0.0313007i
$872$	7.40247	−	1.98349i	0.250679	−	0.0671693i
$873$	5.48502	−	9.50033i	0.185640	−	0.321537i
$874$	3.74123	+	3.74123i	0.126549	+	0.126549i
$875$	−5.81649	+	3.32265i	−0.196633	+	0.112326i
$876$	7.08752	+	4.09198i	0.239465	+	0.138255i
$877$	−16.9697	+	16.9697i	−0.573025	+	0.573025i	−0.932972	−	0.359948i	$-0.882795\pi$
$877$	−16.9697	+	16.9697i	−0.573025	+	0.573025i	0.359948	+	0.932972i	$0.382795\pi$
$878$	15.5813	−	15.5813i	0.525844	−	0.525844i
$879$	−14.2928	+	24.7558i	−0.482084	+	0.834994i
$880$	1.17154	+	4.39914i	0.0394925	+	0.148295i
$881$	18.5012	−	10.6817i	0.623323	−	0.359876i	−0.154839	−	0.987940i	$-0.549486\pi$
$881$	18.5012	−	10.6817i	0.623323	−	0.359876i	0.778162	+	0.628064i	$0.216152\pi$
$882$	−4.62730			−0.155809
$883$	17.5366	−	10.1248i	0.590154	−	0.340726i	−0.175004	−	0.984568i	$-0.555994\pi$
$883$	17.5366	−	10.1248i	0.590154	−	0.340726i	0.765158	+	0.643842i	$0.222661\pi$
$884$	25.2492	−	14.5776i	0.849223	−	0.490299i
$885$	−25.3817	−	25.4595i	−0.853197	−	0.855812i
$886$	−1.21714	−	4.54244i	−0.0408907	−	0.152606i
$887$	28.2385	+	28.2385i	0.948156	+	0.948156i	0.998721	−	0.0505644i	$-0.0161020\pi$
$887$	28.2385	+	28.2385i	0.948156	+	0.948156i	−0.0505644	+	0.998721i	$0.516102\pi$
$888$	−8.64470	−	3.23860i	−0.290097	−	0.108680i
$889$		−	8.86105i		−	0.297190i
$890$	−9.10497	−	15.8261i	−0.305199	−	0.530493i
$891$	−11.3269	+	6.53958i	−0.379465	+	0.219084i
$892$	6.80779	−	25.4070i	0.227942	−	0.850690i
$893$	−2.66309	−	4.61261i	−0.0891170	−	0.154355i
$894$	−3.84485	−	3.84485i	−0.128591	−	0.128591i
$895$	17.3707	+	0.0265768i	0.580639	+	0.000888364i
$896$	−0.423658	+	0.423658i	−0.0141534	+	0.0141534i
$897$	7.80977	+	29.1464i	0.260761	+	0.973171i
$898$	7.71741	+	7.71741i	0.257533	+	0.257533i
$899$	−59.6340			−1.98891
$900$	−3.48386	−	0.0106604i	−0.116129	−	0.000355348i
$901$	−2.38822	−	0.639921i	−0.0795631	−	0.0213189i
$902$	−2.59458			−0.0863902
$903$	−3.01860	−	1.74279i	−0.100453	−	0.0579964i
$904$	4.57128	+	2.63923i	0.152038	+	0.0877794i
$905$	3.58444	−	13.2959i	0.119151	−	0.441971i
$906$	−1.83791	+	6.85916i	−0.0610604	+	0.227880i
$907$	41.4768	−	23.9466i	1.37721	−	0.795135i	0.385391	−	0.922754i	$-0.374067\pi$
$907$	41.4768	−	23.9466i	1.37721	−	0.795135i	0.991823	+	0.127619i	$0.0407334\pi$
$908$	−14.2760	−	8.24225i	−0.473766	−	0.273529i
$909$	−0.986734	+	1.70907i	−0.0327279	+	0.0566864i
$910$	−3.01982	−	5.24901i	−0.100106	−	0.174003i
$911$	−19.6371	+	19.6371i	−0.650605	+	0.650605i	−0.953139	−	0.302534i	$-0.902168\pi$
$911$	−19.6371	+	19.6371i	−0.650605	+	0.650605i	0.302534	+	0.953139i	$0.402168\pi$
$912$	0.912731	+	1.58090i	0.0302236	+	0.0523487i
$913$	0.531406	+	1.98323i	0.0175870	+	0.0656355i
$914$		−	20.4137i		−	0.675227i
$915$	−31.2029	+	8.30964i	−1.03154	+	0.274708i
$916$	−24.6249	−	14.2172i	−0.813630	−	0.469749i
$917$	−0.700513			−0.0231330
$918$	−34.9546	−	9.36605i	−1.15367	−	0.309126i
$919$	−38.7347	+	38.7347i	−1.27774	+	1.27774i	−0.335811	+	0.941929i	$0.609010\pi$
$919$	−38.7347	+	38.7347i	−1.27774	+	1.27774i	−0.941929	+	0.335811i	$0.890990\pi$
$920$	−6.94432	−	6.96560i	−0.228947	−	0.229649i
$921$	0.0721838	+	0.125026i	0.00237854	+	0.00411974i
$922$	−7.03518	−	1.88507i	−0.231691	−	0.0620815i
$923$	37.7979	−	65.4678i	1.24413	−	2.15490i
$924$	1.85123			0.0609010
$925$	−3.02756	+	30.2627i	−0.0995455	+	0.995033i
$926$	−10.8463			−0.356431
$927$	−0.647999	+	1.12237i	−0.0212831	+	0.0368634i
$928$	7.42663	+	1.98996i	0.243791	+	0.0653236i
$929$	−1.95592	−	3.38775i	−0.0641716	−	0.111149i	0.832155	−	0.554544i	$-0.187107\pi$
$929$	−1.95592	−	3.38775i	−0.0641716	−	0.111149i	−0.896326	+	0.443395i	$0.853774\pi$
$930$	18.5831	+	18.6401i	0.609365	+	0.611233i
$931$	5.64839	−	5.64839i	0.185119	−	0.185119i
$932$	−10.9547	−	2.93529i	−0.358832	−	0.0961487i
$933$	42.3182			1.38543
$934$	−11.6382	−	6.71933i	−0.380814	−	0.219863i
$935$	28.3751	−	7.55657i	0.927965	−	0.247126i
$936$		−	3.14949i		−	0.102944i
$937$	5.57229	+	20.7961i	0.182039	+	0.679378i	0.995245	+	0.0974022i	$0.0310533\pi$
$937$	5.57229	+	20.7961i	0.182039	+	0.679378i	−0.813206	+	0.581975i	$0.802280\pi$
$938$	−0.236548	−	0.409713i	−0.00772357	−	0.0133776i
$939$	0.356586	−	0.356586i	0.0116367	−	0.0116367i
$940$	4.93758	+	8.58243i	0.161046	+	0.279928i
$941$	19.2703	−	33.3771i	0.628194	−	1.08806i	−0.359720	−	0.933060i	$-0.617128\pi$
$941$	19.2703	−	33.3771i	0.628194	−	1.08806i	0.987914	−	0.155004i	$-0.0495389\pi$
$942$	−30.8924	−	17.8357i	−1.00653	−	0.581119i
$943$	4.85469	−	2.80286i	0.158091	−	0.0912736i
$944$	−2.74186	+	10.2327i	−0.0892398	+	0.333047i
$945$	−1.95648	+	7.25725i	−0.0636443	+	0.236078i
$946$	6.75878	+	3.90219i	0.219747	+	0.126871i
$947$	−18.0327	−	10.4112i	−0.585986	−	0.338319i	0.177523	−	0.984117i	$-0.443192\pi$
$947$	−18.0327	−	10.4112i	−0.585986	−	0.338319i	−0.763509	+	0.645798i	$0.776525\pi$
$948$	18.5510			0.602509
$949$	23.5444	+	6.30871i	0.764284	+	0.204789i
$950$	4.26564	−	4.23962i	0.138396	−	0.137551i
$951$	7.17111			0.232539
$952$	2.73265	+	2.73265i	0.0885658	+	0.0885658i
$953$	−8.38583	−	31.2963i	−0.271644	−	1.01379i	−0.958057	−	0.286577i	$-0.907483\pi$
$953$	−8.38583	−	31.2963i	−0.271644	−	1.01379i	0.686414	−	0.727211i	$-0.259184\pi$
$954$	−0.188859	+	0.188859i	−0.00611455	+	0.00611455i
$955$	−8.74206	−	0.0133751i	−0.282887	−	0.000432809i
$956$	4.26127	+	4.26127i	0.137819	+	0.137819i
$957$	−11.8781	−	20.5735i	−0.383965	−	0.665047i
$958$	−3.85570	+	14.3897i	−0.124572	+	0.464909i
$959$	−6.06881	+	3.50383i	−0.195972	+	0.113144i
$960$	−1.69227	−	2.94149i	−0.0546179	−	0.0949361i
$961$			29.1579i			0.940577i
$962$	−27.3664	−	2.65325i	−0.882328	−	0.0855442i
$963$	5.00963	+	5.00963i	0.161433	+	0.161433i
$964$	3.92614	+	14.6525i	0.126452	+	0.471927i
$965$	−4.28889	−	4.30203i	−0.138064	−	0.138487i
$966$	−3.46381	+	1.99983i	−0.111446	+	0.0643436i
$967$	−16.8260	+	9.71450i	−0.541088	+	0.312397i	−0.745520	−	0.666483i	$-0.767799\pi$
$967$	−16.8260	+	9.71450i	−0.541088	+	0.312397i	0.204432	+	0.978881i	$0.434465\pi$
$968$	6.85501			0.220328
$969$	10.1970	−	5.88724i	0.327575	−	0.189126i
$970$	−9.05961	−	34.0190i	−0.290887	−	1.09229i
$971$	−14.9573	+	25.9068i	−0.480003	+	0.831390i	−0.999737	−	0.0229382i	$-0.992698\pi$
$971$	−14.9573	+	25.9068i	−0.480003	+	0.831390i	0.519733	+	0.854328i	$0.326031\pi$
$972$	−5.00739	+	5.00739i	−0.160612	+	0.160612i
$973$	−5.93889	+	5.93889i	−0.190392	+	0.190392i
$974$	−17.3040	−	9.99046i	−0.554455	−	0.320115i
$975$	33.1577	−	8.77592i	1.06190	−	0.281054i
$976$	6.72830	+	6.72830i	0.215368	+	0.215368i
$977$	29.9834	−	51.9328i	0.959254	−	1.66148i	0.234937	−	0.972011i	$-0.424512\pi$
$977$	29.9834	−	51.9328i	0.959254	−	1.66148i	0.724317	−	0.689467i	$-0.242155\pi$
$978$	−1.16292	+	0.311603i	−0.0371861	+	0.00996397i
$979$	16.0577	−	4.30264i	0.513205	−	0.137513i
$980$	−10.5164	+	10.4843i	−0.335935	+	0.334909i
$981$	−5.15785	−	1.38204i	−0.164678	−	0.0441252i
$982$	−18.7018	+	32.3924i	−0.596797	+	1.03368i
$983$	−1.05669	−	3.94363i	−0.0337032	−	0.125782i	0.947025	−	0.321161i	$-0.104073\pi$
$983$	−1.05669	−	3.94363i	−0.0337032	−	0.125782i	−0.980728	+	0.195379i	$0.937406\pi$
$984$	1.86818	−	0.500576i	0.0595553	−	0.0159578i
$985$	−7.27875	+	12.5627i	−0.231920	+	0.400282i
$986$	12.8355	−	47.9028i	0.408766	−	1.52554i
$987$	3.88915	−	1.04209i	0.123793	−	0.0331702i
$988$	3.84448	+	3.84448i	0.122309	+	0.122309i
$989$	−16.8617			−0.536171
$990$	0.825672	−	3.06270i	0.0262416	−	0.0973390i
$991$	−13.7908	−	13.7908i	−0.438080	−	0.438080i	0.453285	−	0.891366i	$-0.350252\pi$
$991$	−13.7908	−	13.7908i	−0.438080	−	0.438080i	−0.891366	+	0.453285i	$0.850252\pi$
$992$	2.00744	−	7.49187i	0.0637363	−	0.237867i
$993$			16.8861i			0.535865i
$994$	9.67884	+	2.59344i	0.306994	+	0.0822588i
$995$	24.6937	+	0.0377808i	0.782844	+	0.00119773i
$996$	−0.765256	−	1.32546i	−0.0242481	−	0.0419989i
$997$	39.2557	+	22.6643i	1.24324	+	0.717785i	0.969753	−	0.244090i	$-0.0784892\pi$
$997$	39.2557	+	22.6643i	1.24324	+	0.717785i	0.273488	+	0.961875i	$0.411823\pi$
$998$	−3.40804	+	3.40804i	−0.107880	+	0.107880i
$999$	21.6898	+	26.3471i	0.686235	+	0.833586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.q.e.273.2	yes	16
5.2	odd	4		370.2.r.e.347.2	yes	16
37.8	odd	12		370.2.r.e.193.2	yes	16
185.82	even	12	inner	370.2.q.e.267.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.e.267.2	✓	16	185.82	even	12	inner
370.2.q.e.273.2	yes	16	1.1	even	1	trivial
370.2.r.e.193.2	yes	16	37.8	odd	12
370.2.r.e.347.2	yes	16	5.2	odd	4

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.46593 - 0.392794i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.57872 + 1.58356i) q^{5} +(1.07313 - 1.07313i) q^{6} +(0.578728 + 0.155070i) q^{7} +1.00000 q^{8} +(-0.603425 - 0.348387i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.46593 - 0.392794i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.57872 + 1.58356i) q^{5} +(1.07313 - 1.07313i) q^{6} +(0.578728 + 0.155070i) q^{7} +1.00000 q^{8} +(-0.603425 - 0.348387i) q^{9} +(-2.16076 + 0.575432i) q^{10} -2.03593i q^{11} +(0.392794 + 1.46593i) q^{12} +(2.26005 + 3.91452i) q^{13} +(-0.423658 + 0.423658i) q^{14} +(-1.69227 - 2.94149i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(5.58598 + 3.22507i) q^{17} +(0.603425 - 0.348387i) q^{18} +(-0.311316 + 1.16185i) q^{19} +(0.582041 - 2.15899i) q^{20} +(-0.787462 - 0.454641i) q^{21} +(1.76316 + 1.01796i) q^{22} -4.39871 q^{23} +(-1.46593 - 0.392794i) q^{24} +(-0.0152997 + 4.99998i) q^{25} -4.52010 q^{26} +(3.96713 + 3.96713i) q^{27} +(-0.155070 - 0.578728i) q^{28} +(-5.43667 + 5.43667i) q^{29} +(3.39354 + 0.00519203i) q^{30} +(5.48443 + 5.48443i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.799699 + 2.98452i) q^{33} +(-5.58598 + 3.22507i) q^{34} +(0.668086 + 1.16126i) q^{35} +0.696775i q^{36} +(6.05437 + 0.586988i) q^{37} +(-0.850530 - 0.850530i) q^{38} +(-1.77547 - 6.62614i) q^{39} +(1.57872 + 1.58356i) q^{40} +(-1.10366 + 0.637200i) q^{41} +(0.787462 - 0.454641i) q^{42} +3.83333 q^{43} +(-1.76316 + 1.01796i) q^{44} +(-0.400946 - 1.50556i) q^{45} +(2.19935 - 3.80939i) q^{46} +(-3.13110 + 3.13110i) q^{47} +(1.07313 - 1.07313i) q^{48} +(-5.75130 - 3.32051i) q^{49} +(-4.32246 - 2.51324i) q^{50} +(-6.92185 - 6.92185i) q^{51} +(2.26005 - 3.91452i) q^{52} +(-0.370259 + 0.0992105i) q^{53} +(-5.41920 + 1.45207i) q^{54} +(3.22400 - 3.21415i) q^{55} +(0.578728 + 0.155070i) q^{56} +(0.912731 - 1.58090i) q^{57} +(-1.98996 - 7.42663i) q^{58} +(10.2327 - 2.74186i) q^{59} +(-1.70127 + 2.93629i) q^{60} +(2.46273 - 9.19103i) q^{61} +(-7.49187 + 2.00744i) q^{62} +(-0.295194 - 0.295194i) q^{63} +1.00000 q^{64} +(-2.63088 + 9.75885i) q^{65} +(-2.18482 - 2.18482i) q^{66} +(-0.204369 + 0.762716i) q^{67} -6.45014i q^{68} +(6.44818 + 1.72778i) q^{69} +(-1.33972 - 0.00204974i) q^{70} +(-8.36217 - 14.4837i) q^{71} +(-0.603425 - 0.348387i) q^{72} +(3.81312 - 3.81312i) q^{73} +(-3.53553 + 4.94975i) q^{74} +(1.98639 - 7.32359i) q^{75} +(1.16185 - 0.311316i) q^{76} +(0.315710 - 1.17825i) q^{77} +(6.62614 + 1.77547i) q^{78} +(3.16370 - 11.8071i) q^{79} +(-2.16076 + 0.575432i) q^{80} +(-3.21209 - 5.56350i) q^{81} -1.27440i q^{82} +(-0.974119 + 0.261014i) q^{83} +0.909282i q^{84} +(3.71162 + 13.9372i) q^{85} +(-1.91666 + 3.31976i) q^{86} +(10.1052 - 5.83426i) q^{87} -2.03593i q^{88} +(2.11336 + 7.88715i) q^{89} +(1.50433 + 0.405551i) q^{90} +(0.700931 + 2.61591i) q^{91} +(2.19935 + 3.80939i) q^{92} +(-5.88552 - 10.1940i) q^{93} +(-1.14606 - 4.27716i) q^{94} +(-2.33133 + 1.34124i) q^{95} +(0.392794 + 1.46593i) q^{96} +15.7440i q^{97} +(5.75130 - 3.32051i) q^{98} +(-0.709291 + 1.22853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} + 16 q^{8} - 24 q^{9}+O(q^{10}) \) 16 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 + 16 * q^8 - 24 * q^9	\( 16 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} + 16 q^{8} - 24 q^{9} - 4 q^{10} + 16 q^{12} - 4 q^{13} + 8 q^{15} - 8 q^{16} + 24 q^{18} - 24 q^{19} + 8 q^{20} - 12 q^{21} - 8 q^{23} - 8 q^{24} + 32 q^{25} + 8 q^{26} + 16 q^{27} + 16 q^{29} - 4 q^{30} + 24 q^{31} - 8 q^{32} + 12 q^{33} - 20 q^{35} - 4 q^{40} - 36 q^{41} + 12 q^{42} - 16 q^{43} + 4 q^{45} + 4 q^{46} + 32 q^{47} - 8 q^{48} + 24 q^{49} - 16 q^{50} - 16 q^{51} - 4 q^{52} - 48 q^{53} - 8 q^{54} - 24 q^{55} + 20 q^{57} - 8 q^{58} - 8 q^{59} - 4 q^{60} + 8 q^{61} - 12 q^{62} + 16 q^{63} + 16 q^{64} + 24 q^{65} - 24 q^{66} - 8 q^{67} - 8 q^{69} + 28 q^{70} + 4 q^{71} - 24 q^{72} + 48 q^{73} - 36 q^{75} + 24 q^{76} - 60 q^{77} + 20 q^{79} - 4 q^{80} + 16 q^{81} + 24 q^{83} + 8 q^{85} + 8 q^{86} + 12 q^{87} - 8 q^{89} - 8 q^{90} - 8 q^{91} + 4 q^{92} + 36 q^{93} - 28 q^{94} + 28 q^{95} + 16 q^{96} - 24 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 + 16 * q^8 - 24 * q^9 - 4 * q^10 + 16 * q^12 - 4 * q^13 + 8 * q^15 - 8 * q^16 + 24 * q^18 - 24 * q^19 + 8 * q^20 - 12 * q^21 - 8 * q^23 - 8 * q^24 + 32 * q^25 + 8 * q^26 + 16 * q^27 + 16 * q^29 - 4 * q^30 + 24 * q^31 - 8 * q^32 + 12 * q^33 - 20 * q^35 - 4 * q^40 - 36 * q^41 + 12 * q^42 - 16 * q^43 + 4 * q^45 + 4 * q^46 + 32 * q^47 - 8 * q^48 + 24 * q^49 - 16 * q^50 - 16 * q^51 - 4 * q^52 - 48 * q^53 - 8 * q^54 - 24 * q^55 + 20 * q^57 - 8 * q^58 - 8 * q^59 - 4 * q^60 + 8 * q^61 - 12 * q^62 + 16 * q^63 + 16 * q^64 + 24 * q^65 - 24 * q^66 - 8 * q^67 - 8 * q^69 + 28 * q^70 + 4 * q^71 - 24 * q^72 + 48 * q^73 - 36 * q^75 + 24 * q^76 - 60 * q^77 + 20 * q^79 - 4 * q^80 + 16 * q^81 + 24 * q^83 + 8 * q^85 + 8 * q^86 + 12 * q^87 - 8 * q^89 - 8 * q^90 - 8 * q^91 + 4 * q^92 + 36 * q^93 - 28 * q^94 + 28 * q^95 + 16 * q^96 - 24 * q^98 + 8 * q^99

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