LMFDB - Embedded newform 175.2.s.a.13.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(13,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([19, 10]))

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

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

chi := DirichletCharacter("175.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.s (of order $20$, degree $8$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.10
Character	$\chi$	$=$	175.13
Dual form			175.2.s.a.27.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.437303 + 0.0692620i) q^{2} +(2.82799 + 1.44093i) q^{3} +(-1.71568 + 0.557457i) q^{4} +(-2.19504 + 0.426380i) q^{5} +(-1.33649 - 0.434253i) q^{6} +(-1.52822 + 2.15975i) q^{7} +(1.50065 - 0.764621i) q^{8} +(4.15790 + 5.72286i) q^{9} +O(q^{10})$	\(q+(-0.437303 + 0.0692620i) q^{2} +(2.82799 + 1.44093i) q^{3} +(-1.71568 + 0.557457i) q^{4} +(-2.19504 + 0.426380i) q^{5} +(-1.33649 - 0.434253i) q^{6} +(-1.52822 + 2.15975i) q^{7} +(1.50065 - 0.764621i) q^{8} +(4.15790 + 5.72286i) q^{9} +(0.930365 - 0.338490i) q^{10} +(2.41860 + 1.75722i) q^{11} +(-5.65518 - 0.895693i) q^{12} +(0.482157 - 3.04422i) q^{13} +(0.518708 - 1.05031i) q^{14} +(-6.82194 - 1.95711i) q^{15} +(2.31560 - 1.68238i) q^{16} +(0.763071 - 0.388804i) q^{17} +(-2.21464 - 2.21464i) q^{18} +(1.72594 - 5.31191i) q^{19} +(3.52829 - 1.95517i) q^{20} +(-7.43387 + 3.90570i) q^{21} +(-1.17937 - 0.600919i) q^{22} +(0.214665 + 1.35534i) q^{23} +5.34561 q^{24} +(4.63640 - 1.87184i) q^{25} +1.36464i q^{26} +(2.02271 + 12.7709i) q^{27} +(1.41797 - 4.55736i) q^{28} +(-4.22812 + 1.37380i) q^{29} +(3.11881 + 0.383348i) q^{30} +(5.16783 + 1.67913i) q^{31} +(-3.27794 + 3.27794i) q^{32} +(4.30775 + 8.45444i) q^{33} +(-0.306764 + 0.222877i) q^{34} +(2.43364 - 5.39235i) q^{35} +(-10.3239 - 7.50072i) q^{36} +(0.429395 - 2.71109i) q^{37} +(-0.386847 + 2.44245i) q^{38} +(5.75006 - 7.91428i) q^{39} +(-2.96797 + 2.31822i) q^{40} +(-6.23753 - 8.58522i) q^{41} +(2.98034 - 2.22286i) q^{42} +(4.86378 + 4.86378i) q^{43} +(-5.12911 - 1.66655i) q^{44} +(-11.5669 - 10.7891i) q^{45} +(-0.187747 - 0.577827i) q^{46} +(0.788291 - 1.54711i) q^{47} +(8.97271 - 1.42114i) q^{48} +(-2.32906 - 6.60117i) q^{49} +(-1.89786 + 1.13969i) q^{50} +2.71820 q^{51} +(0.869797 + 5.49168i) q^{52} +(-5.16846 + 10.1437i) q^{53} +(-1.76908 - 5.44465i) q^{54} +(-6.05817 - 2.82592i) q^{55} +(-0.641942 + 4.40955i) q^{56} +(12.5351 - 12.5351i) q^{57} +(1.75382 - 0.893614i) q^{58} +(0.0470722 - 0.0342000i) q^{59} +(12.7953 - 0.445177i) q^{60} +(3.65341 - 5.02849i) q^{61} +(-2.37621 - 0.376354i) q^{62} +(-18.7142 + 0.234228i) q^{63} +(-2.15835 + 2.97071i) q^{64} +(0.239642 + 6.88777i) q^{65} +(-2.46936 - 3.39879i) q^{66} +(-0.445112 - 0.873581i) q^{67} +(-1.09244 + 1.09244i) q^{68} +(-1.34589 + 4.14221i) q^{69} +(-0.690752 + 2.52665i) q^{70} +(-2.53019 - 7.78713i) q^{71} +(10.6154 + 5.40881i) q^{72} +(-4.88695 + 0.774018i) q^{73} +1.21531i q^{74} +(15.8089 + 1.38719i) q^{75} +10.0757i q^{76} +(-7.49131 + 2.53816i) q^{77} +(-1.96636 + 3.85920i) q^{78} +(8.47048 - 2.75222i) q^{79} +(-4.36550 + 4.68023i) q^{80} +(-6.12400 + 18.8477i) q^{81} +(3.32232 + 3.32232i) q^{82} +(-0.465755 - 0.914096i) q^{83} +(10.5769 - 10.8450i) q^{84} +(-1.50919 + 1.17880i) q^{85} +(-2.46382 - 1.79007i) q^{86} +(-13.9366 - 2.20735i) q^{87} +(4.97308 + 0.787659i) q^{88} +(8.07045 + 5.86353i) q^{89} +(5.80550 + 3.91694i) q^{90} +(5.83792 + 5.69359i) q^{91} +(-1.12384 - 2.20566i) q^{92} +(12.1951 + 12.1951i) q^{93} +(-0.237566 + 0.731153i) q^{94} +(-1.52362 + 12.3958i) q^{95} +(-13.9933 + 4.54670i) q^{96} +(0.309632 - 0.607687i) q^{97} +(1.47572 + 2.72540i) q^{98} +21.1476i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 16 q^{2} - 20 q^{4} - 14 q^{7} - 12 q^{8} - 20 q^{9}+O(q^{10}) $ 144 * q - 16 * q^2 - 20 * q^4 - 14 * q^7 - 12 * q^8 - 20 * q^9	$ 144 q - 16 q^{2} - 20 q^{4} - 14 q^{7} - 12 q^{8} - 20 q^{9} - 12 q^{11} - 10 q^{14} - 20 q^{15} + 12 q^{16} - 28 q^{18} - 6 q^{21} + 16 q^{22} - 8 q^{23} - 20 q^{25} - 70 q^{28} + 40 q^{30} - 20 q^{32} - 40 q^{35} - 28 q^{36} + 4 q^{37} - 60 q^{39} - 30 q^{42} + 72 q^{43} - 20 q^{44} - 12 q^{46} + 140 q^{50} - 32 q^{51} - 104 q^{53} - 22 q^{56} + 120 q^{57} - 32 q^{58} - 120 q^{60} + 48 q^{63} + 40 q^{64} - 20 q^{65} - 16 q^{67} + 90 q^{70} - 12 q^{71} - 64 q^{72} + 74 q^{77} + 60 q^{78} - 20 q^{79} - 8 q^{81} + 190 q^{84} - 12 q^{86} + 92 q^{88} - 6 q^{91} - 20 q^{92} - 160 q^{93} + 80 q^{95} + 162 q^{98}+O(q^{100}) $ 144 * q - 16 * q^2 - 20 * q^4 - 14 * q^7 - 12 * q^8 - 20 * q^9 - 12 * q^11 - 10 * q^14 - 20 * q^15 + 12 * q^16 - 28 * q^18 - 6 * q^21 + 16 * q^22 - 8 * q^23 - 20 * q^25 - 70 * q^28 + 40 * q^30 - 20 * q^32 - 40 * q^35 - 28 * q^36 + 4 * q^37 - 60 * q^39 - 30 * q^42 + 72 * q^43 - 20 * q^44 - 12 * q^46 + 140 * q^50 - 32 * q^51 - 104 * q^53 - 22 * q^56 + 120 * q^57 - 32 * q^58 - 120 * q^60 + 48 * q^63 + 40 * q^64 - 20 * q^65 - 16 * q^67 + 90 * q^70 - 12 * q^71 - 64 * q^72 + 74 * q^77 + 60 * q^78 - 20 * q^79 - 8 * q^81 + 190 * q^84 - 12 * q^86 + 92 * q^88 - 6 * q^91 - 20 * q^92 - 160 * q^93 + 80 * q^95 + 162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	−0.437303	+	0.0692620i	−0.309220	+	0.0489756i	−0.309116	−	0.951024i	$-0.600033\pi$
$2$	−0.437303	+	0.0692620i	−0.309220	+	0.0489756i	−0.000103993		1.00000i	$0.500033\pi$
$3$	2.82799	+	1.44093i	1.63274	+	0.831924i	0.998259	+	0.0589881i	$0.0187874\pi$
$3$	2.82799	+	1.44093i	1.63274	+	0.831924i	0.634484	+	0.772936i	$0.281213\pi$
$4$	−1.71568	+	0.557457i	−0.857838	+	0.278729i
$5$	−2.19504	+	0.426380i	−0.981652	+	0.190683i
$5$	−2.19504	+	0.426380i	−0.981652	+	0.190683i
$6$	−1.33649	−	0.434253i	−0.545621	−	0.177283i
$7$	−1.52822	+	2.15975i	−0.577614	+	0.816310i
$7$	−1.52822	+	2.15975i	−0.577614	+	0.816310i
$8$	1.50065	−	0.764621i	0.530561	−	0.270334i
$9$	4.15790	+	5.72286i	1.38597	+	1.90762i
$10$	0.930365	−	0.338490i	0.294207	−	0.107040i
$11$	2.41860	+	1.75722i	0.729235	+	0.529821i	0.889321	−	0.457283i	$-0.151177\pi$
$11$	2.41860	+	1.75722i	0.729235	+	0.529821i	−0.160086	+	0.987103i	$0.551177\pi$
$12$	−5.65518	−	0.895693i	−1.63251	−	0.258564i
$13$	0.482157	−	3.04422i	0.133726	−	0.844315i	−0.826060	−	0.563583i	$-0.809423\pi$
$13$	0.482157	−	3.04422i	0.133726	−	0.844315i	0.959786	−	0.280733i	$-0.0905774\pi$
$14$	0.518708	−	1.05031i	0.138631	−	0.280708i
$15$	−6.82194	−	1.95711i	−1.76142	−	0.505323i
$16$	2.31560	−	1.68238i	0.578901	−	0.420596i
$17$	0.763071	−	0.388804i	0.185072	−	0.0942989i	−0.358999	−	0.933338i	$-0.616882\pi$
$17$	0.763071	−	0.388804i	0.185072	−	0.0942989i	0.544071	+	0.839039i	$0.316882\pi$
$18$	−2.21464	−	2.21464i	−0.521995	−	0.521995i
$19$	1.72594	−	5.31191i	0.395959	−	1.21864i	−0.532254	−	0.846585i	$-0.678655\pi$
$19$	1.72594	−	5.31191i	0.395959	−	1.21864i	0.928213	−	0.372050i	$-0.121345\pi$
$20$	3.52829	−	1.95517i	0.788949	−	0.437190i
$21$	−7.43387	+	3.90570i	−1.62220	+	0.852293i
$22$	−1.17937	−	0.600919i	−0.251442	−	0.128116i
$23$	0.214665	+	1.35534i	0.0447607	+	0.282608i	0.999909	−	0.0135212i	$-0.00430406\pi$
$23$	0.214665	+	1.35534i	0.0447607	+	0.282608i	−0.955148	+	0.296129i	$0.904304\pi$
$24$	5.34561			1.09117
$25$	4.63640	−	1.87184i	0.927280	−	0.374369i
$26$			1.36464i			0.267628i
$27$	2.02271	+	12.7709i	0.389271	+	2.45776i
$28$	1.41797	−	4.55736i	0.267971	−	0.861259i
$29$	−4.22812	+	1.37380i	−0.785142	+	0.255108i	−0.674034	−	0.738700i	$-0.735440\pi$
$29$	−4.22812	+	1.37380i	−0.785142	+	0.255108i	−0.111108	+	0.993808i	$0.535440\pi$
$30$	3.11881	+	0.383348i	0.569414	+	0.0699894i
$31$	5.16783	+	1.67913i	0.928169	+	0.301581i	0.733814	−	0.679351i	$-0.237738\pi$
$31$	5.16783	+	1.67913i	0.928169	+	0.301581i	0.194356	+	0.980931i	$0.437738\pi$
$32$	−3.27794	+	3.27794i	−0.579464	+	0.579464i
$33$	4.30775	+	8.45444i	0.749883	+	1.47173i
$34$	−0.306764	+	0.222877i	−0.0526096	+	0.0382231i
$35$	2.43364	−	5.39235i	0.411360	−	0.911473i
$36$	−10.3239	−	7.50072i	−1.72064	−	1.25012i
$37$	0.429395	−	2.71109i	0.0705921	−	0.445701i	−0.926923	−	0.375251i	$-0.877556\pi$
$37$	0.429395	−	2.71109i	0.0705921	−	0.445701i	0.997515	−	0.0704500i	$-0.0224435\pi$
$38$	−0.386847	+	2.44245i	−0.0627548	+	0.396219i
$39$	5.75006	−	7.91428i	0.920747	−	1.26730i
$40$	−2.96797	+	2.31822i	−0.469278	+	0.366543i
$41$	−6.23753	−	8.58522i	−0.974138	−	1.34079i	−0.939928	−	0.341371i	$-0.889109\pi$
$41$	−6.23753	−	8.58522i	−0.974138	−	1.34079i	−0.0342096	−	0.999415i	$-0.510891\pi$
$42$	2.98034	−	2.22286i	0.459876	−	0.342994i
$43$	4.86378	+	4.86378i	0.741720	+	0.741720i	0.972909	−	0.231189i	$-0.0742616\pi$
$43$	4.86378	+	4.86378i	0.741720	+	0.741720i	−0.231189	+	0.972909i	$0.574262\pi$
$44$	−5.12911	−	1.66655i	−0.773242	−	0.251242i
$45$	−11.5669	−	10.7891i	−1.72429	−	1.60834i
$46$	−0.187747	−	0.577827i	−0.0276818	−	0.0851959i
$47$	0.788291	−	1.54711i	0.114984	−	0.225669i	−0.826341	−	0.563170i	$-0.809582\pi$
$47$	0.788291	−	1.54711i	0.114984	−	0.225669i	0.941325	+	0.337501i	$0.109582\pi$
$48$	8.97271	−	1.42114i	1.29510	−	0.205124i
$49$	−2.32906	−	6.60117i	−0.332723	−	0.943024i
$50$	−1.89786	+	1.13969i	−0.268398	+	0.161176i
$51$	2.71820			0.380624
$52$	0.869797	+	5.49168i	0.120619	+	0.761559i
$53$	−5.16846	+	10.1437i	−0.709943	+	1.39334i	0.200494	+	0.979695i	$0.435745\pi$
$53$	−5.16846	+	10.1437i	−0.709943	+	1.39334i	−0.910437	+	0.413647i	$0.864255\pi$
$54$	−1.76908	−	5.44465i	−0.240741	−	0.740923i
$55$	−6.05817	−	2.82592i	−0.816883	−	0.381046i
$56$	−0.641942	+	4.40955i	−0.0857831	+	0.589251i
$57$	12.5351	−	12.5351i	1.66031	−	1.66031i
$58$	1.75382	−	0.893614i	0.230287	−	0.117337i
$59$	0.0470722	−	0.0342000i	0.00612828	−	0.00445246i	−0.584717	−	0.811237i	$-0.698794\pi$
$59$	0.0470722	−	0.0342000i	0.00612828	−	0.00445246i	0.590845	+	0.806785i	$0.298794\pi$
$60$	12.7953	−	0.445177i	1.65186	−	0.0574721i
$61$	3.65341	−	5.02849i	0.467771	−	0.643832i	−0.508326	−	0.861164i	$-0.669736\pi$
$61$	3.65341	−	5.02849i	0.467771	−	0.643832i	0.976098	+	0.217333i	$0.0697356\pi$
$62$	−2.37621	−	0.376354i	−0.301779	−	0.0477970i
$63$	−18.7142	+	0.234228i	−2.35776	+	0.0295099i
$64$	−2.15835	+	2.97071i	−0.269794	+	0.371339i
$65$	0.239642	+	6.88777i	0.0297239	+	0.854323i
$66$	−2.46936	−	3.39879i	−0.303958	−	0.418362i
$67$	−0.445112	−	0.873581i	−0.0543791	−	0.106725i	0.862218	−	0.506538i	$-0.169075\pi$
$67$	−0.445112	−	0.873581i	−0.0543791	−	0.106725i	−0.916597	+	0.399813i	$0.869075\pi$
$68$	−1.09244	+	1.09244i	−0.132478	+	0.132478i
$69$	−1.34589	+	4.14221i	−0.162026	+	0.498664i
$70$	−0.690752	+	2.52665i	−0.0825606	+	0.301992i
$71$	−2.53019	−	7.78713i	−0.300279	−	0.924162i	−0.981397	−	0.191989i	$-0.938506\pi$
$71$	−2.53019	−	7.78713i	−0.300279	−	0.924162i	0.681118	−	0.732173i	$-0.261494\pi$
$72$	10.6154	+	5.40881i	1.25103	+	0.637434i
$73$	−4.88695	+	0.774018i	−0.571975	+	0.0905919i	−0.435721	−	0.900082i	$-0.643506\pi$
$73$	−4.88695	+	0.774018i	−0.571975	+	0.0905919i	−0.136254	+	0.990674i	$0.543506\pi$
$74$			1.21531i			0.141277i
$75$	15.8089	+	1.38719i	1.82546	+	0.160179i
$76$			10.0757i			1.15576i
$77$	−7.49131	+	2.53816i	−0.853715	+	0.289250i
$78$	−1.96636	+	3.85920i	−0.222647	+	0.436968i
$79$	8.47048	−	2.75222i	0.953003	−	0.309649i	0.209068	−	0.977901i	$-0.432957\pi$
$79$	8.47048	−	2.75222i	0.953003	−	0.309649i	0.743935	+	0.668252i	$0.232957\pi$
$80$	−4.36550	+	4.68023i	−0.488078	+	0.523265i
$81$	−6.12400	+	18.8477i	−0.680445	+	2.09419i
$82$	3.32232	+	3.32232i	0.366889	+	0.366889i
$83$	−0.465755	−	0.914096i	−0.0511233	−	0.100335i	0.864031	−	0.503438i	$-0.167932\pi$
$83$	−0.465755	−	0.914096i	−0.0511233	−	0.100335i	−0.915155	+	0.403103i	$0.867932\pi$
$84$	10.5769	−	10.8450i	1.15403	−	1.18328i
$85$	−1.50919	+	1.17880i	−0.163695	+	0.127859i
$86$	−2.46382	−	1.79007i	−0.265681	−	0.193028i
$87$	−13.9366	−	2.20735i	−1.49416	−	0.236652i
$88$	4.97308	+	0.787659i	0.530133	+	0.0839648i
$89$	8.07045	+	5.86353i	0.855466	+	0.621533i	0.926648	−	0.375931i	$-0.122677\pi$
$89$	8.07045	+	5.86353i	0.855466	+	0.621533i	−0.0711814	+	0.997463i	$0.522677\pi$
$90$	5.80550	+	3.91694i	0.611953	+	0.412882i
$91$	5.83792	+	5.69359i	0.611981	+	0.596851i
$92$	−1.12384	−	2.20566i	−0.117168	−	0.229956i
$93$	12.1951	+	12.1951i	1.26457	+	1.26457i
$94$	−0.237566	+	0.731153i	−0.0245031	+	0.0754127i
$95$	−1.52362	+	12.3958i	−0.156320	+	1.27178i
$96$	−13.9933	+	4.54670i	−1.42819	+	0.464046i
$97$	0.309632	−	0.607687i	0.0314384	−	0.0617013i	−0.874753	−	0.484569i	$-0.838976\pi$
$97$	0.309632	−	0.607687i	0.0314384	−	0.0617013i	0.906191	+	0.422868i	$0.138976\pi$
$98$	1.47572	+	2.72540i	0.149070	+	0.275307i
$99$			21.1476i			2.12542i
$100$	−6.91109	+	5.79607i	−0.691109	+	0.579607i
$101$			6.52607i			0.649368i	0.945823	+	0.324684i	$0.105258\pi$
$101$			6.52607i			0.649368i	−0.945823	+	0.324684i	$0.894742\pi$
$102$	−1.18868	+	0.188268i	−0.117697	+	0.0186413i
$103$	−6.23891	−	3.17888i	−0.614738	−	0.313224i	0.118753	−	0.992924i	$-0.462110\pi$
$103$	−6.23891	−	3.17888i	−0.614738	−	0.313224i	−0.733491	+	0.679699i	$0.762110\pi$
$104$	−1.60413	−	4.93699i	−0.157297	−	0.484112i
$105$	14.6523	−	11.7428i	1.42992	−	1.14598i
$106$	1.55761	−	4.79384i	0.151289	−	0.465619i
$107$	−2.79953	+	2.79953i	−0.270641	+	0.270641i	−0.829358	−	0.558718i	$-0.811294\pi$
$107$	−2.79953	+	2.79953i	−0.270641	+	0.270641i	0.558718	+	0.829358i	$0.311294\pi$
$108$	−10.5895	−	20.7831i	−1.01898	−	1.99986i
$109$	−10.3895	−	14.3000i	−0.995138	−	1.36969i	−0.928262	−	0.371928i	$-0.878697\pi$
$109$	−10.3895	−	14.3000i	−0.995138	−	1.36969i	−0.0668759	−	0.997761i	$-0.521303\pi$
$110$	2.84498	+	0.816181i	0.271258	+	0.0778198i
$111$	5.12084	−	7.04823i	0.486048	−	0.668988i
$112$	0.0947740	+	7.57219i	0.00895530	+	0.715504i
$113$	6.00704	+	0.951422i	0.565095	+	0.0895023i	0.432444	−	0.901661i	$-0.357651\pi$
$113$	6.00704	+	0.951422i	0.565095	+	0.0895023i	0.132651	+	0.991163i	$0.457651\pi$
$114$	−4.61342	+	6.34983i	−0.432086	+	0.594716i
$115$	−1.04909	−	2.88350i	−0.0978280	−	0.268888i
$116$	6.48825	−	4.71399i	0.602419	−	0.437683i
$117$	19.4264	−	9.89825i	1.79597	−	0.915093i
$118$	−0.0182161	+	0.0182161i	−0.00167692	+	0.00167692i
$119$	−0.326423	+	2.24223i	−0.0299231	+	0.205544i
$120$	−11.7338	+	2.27926i	−1.07115	+	0.208067i
$121$	−0.637367	−	1.96162i	−0.0579425	−	0.178329i
$122$	−1.24936	+	2.45201i	−0.113112	+	0.221995i
$123$	−5.26895	−	33.2668i	−0.475085	−	2.99957i
$124$	−9.80236			−0.880278
$125$	−9.37896	+	6.08564i	−0.838880	+	0.544316i
$126$	8.16753	−	1.39861i	0.727622	−	0.124598i
$127$	−3.09449	+	0.490120i	−0.274592	+	0.0434911i	−0.292212	−	0.956354i	$-0.594391\pi$
$127$	−3.09449	+	0.490120i	−0.274592	+	0.0434911i	0.0176197	+	0.999845i	$0.494391\pi$
$128$	4.94723	−	9.70950i	0.437278	−	0.858206i
$129$	6.74635	+	20.7631i	0.593983	+	1.82809i
$130$	−0.581857	−	2.99544i	−0.0510322	−	0.262718i
$131$	−7.46859	−	2.42669i	−0.652534	−	0.212021i	−0.0360029	−	0.999352i	$-0.511463\pi$
$131$	−7.46859	−	2.42669i	−0.652534	−	0.212021i	−0.616531	+	0.787331i	$0.711463\pi$
$132$	−12.1037	−	12.1037i	−1.05349	−	1.05349i
$133$	8.83478	+	11.8454i	0.766072	+	1.02713i
$134$	0.255155	+	0.351190i	0.0220420	+	0.0303382i
$135$	−9.88519	−	27.1702i	−0.850782	−	2.33844i
$136$	0.847818	−	1.16692i	0.0726998	−	0.100063i
$137$	−1.88413	+	11.8960i	−0.160972	+	1.01634i	0.766444	+	0.642311i	$0.222024\pi$
$137$	−1.88413	+	11.8960i	−0.160972	+	1.01634i	−0.927417	+	0.374029i	$0.877976\pi$
$138$	0.301662	−	1.90462i	0.0256792	−	0.162132i
$139$	−10.2633	−	7.45673i	−0.870522	−	0.632472i	0.0602047	−	0.998186i	$-0.480825\pi$
$139$	−10.2633	−	7.45673i	−0.870522	−	0.632472i	−0.930727	+	0.365715i	$0.880825\pi$
$140$	−1.16933	+	10.6082i	−0.0988264	+	0.896554i
$141$	4.45856	−	3.23933i	0.375479	−	0.272801i
$142$	1.64581	+	3.23009i	0.138114	+	0.271063i
$143$	6.51550	−	6.51550i	0.544854	−	0.544854i
$144$	19.2561	+	6.25668i	1.60467	+	0.521390i
$145$	8.69512	−	4.81833i	0.722091	−	0.400140i
$146$	2.08347	−	0.676960i	0.172429	−	0.0560256i
$147$	2.92528	−	22.0241i	0.241273	−	1.81652i
$148$	0.774616	+	4.89073i	0.0636730	+	0.402016i
$149$		−	3.07944i		−	0.252278i	−0.992013	−	0.126139i	$-0.959741\pi$
$149$		−	3.07944i		−	0.252278i	0.992013	−	0.126139i	$-0.0402585\pi$
$150$	−7.00936	+	0.488335i	−0.572312	+	0.0398724i
$151$	10.5337			0.857222			0.428611	−	0.903489i	$-0.359003\pi$
$151$	10.5337			0.857222			0.428611	+	0.903489i	$0.359003\pi$
$152$	−1.47155	−	9.29102i	−0.119359	−	0.753601i
$153$	5.39784	+	2.75034i	0.436390	+	0.222352i
$154$	3.10018	−	1.62881i	0.249819	−	0.131253i
$155$	−12.0595	−	1.48230i	−0.968645	−	0.119061i
$156$	−5.45337	+	16.7838i	−0.436619	+	1.34378i
$157$	8.81242	+	8.81242i	0.703307	+	0.703307i	0.965119	−	0.261812i	$-0.0843199\pi$
$157$	8.81242	+	8.81242i	0.703307	+	0.703307i	−0.261812	+	0.965119i	$0.584320\pi$
$158$	−3.51354	+	1.79024i	−0.279522	+	0.142424i
$159$	−29.2328	+	21.2388i	−2.31831	+	1.68435i
$160$	5.79757	−	8.59287i	0.458338	−	0.679326i
$161$	−3.25526	−	1.60764i	−0.256550	−	0.126700i
$162$	1.37261	−	8.66633i	0.107843	−	0.680891i
$163$	−13.1076	−	2.07604i	−1.02667	−	0.162608i	−0.379686	−	0.925115i	$-0.623968\pi$
$163$	−13.1076	−	2.07604i	−1.02667	−	0.162608i	−0.646979	+	0.762508i	$0.723968\pi$
$164$	15.4875	+	11.2523i	1.20937	+	0.878657i
$165$	−13.0605	−	16.7211i	−1.01676	−	1.30174i
$166$	0.266988	+	0.367478i	0.0207223	+	0.0285218i
$167$	−5.99531	+	3.05476i	−0.463931	+	0.236385i	−0.670301	−	0.742089i	$-0.733835\pi$
$167$	−5.99531	+	3.05476i	−0.463931	+	0.236385i	0.206370	+	0.978474i	$0.433835\pi$
$168$	−8.16928	+	11.5452i	−0.630274	+	0.890731i
$169$	3.32892	+	1.08163i	0.256071	+	0.0832025i
$170$	0.578329	−	0.620022i	0.0443558	−	0.0475535i
$171$	37.5756	−	12.2090i	2.87348	−	0.933649i
$172$	−11.0560	−	5.63333i	−0.843014	−	0.429537i
$173$	−7.01830	+	1.11159i	−0.533592	+	0.0845126i	−0.417415	−	0.908716i	$-0.637064\pi$
$173$	−7.01830	+	1.11159i	−0.533592	+	0.0845126i	−0.116177	+	0.993229i	$0.537064\pi$
$174$	6.24742			0.473616
$175$	−3.04274	+	12.8741i	−0.230009	+	0.973188i
$176$	8.55683			0.644995
$177$	0.182400	−	0.0288893i	0.0137100	−	0.00217145i
$178$	−3.93535	−	2.00516i	−0.294967	−	0.150293i
$179$	−11.1912	+	3.63625i	−0.836472	+	0.271786i	−0.695769	−	0.718266i	$-0.744936\pi$
$179$	−11.1912	+	3.63625i	−0.836472	+	0.271786i	−0.140703	+	0.990052i	$0.544936\pi$
$180$	25.8594	+	12.0625i	1.92745	+	0.899085i
$181$	15.3486	+	4.98705i	1.14085	+	0.370684i	0.817689	−	0.575660i	$-0.195255\pi$
$181$	15.3486	+	4.98705i	1.14085	+	0.370684i	0.323160	+	0.946344i	$0.395255\pi$
$182$	−2.94729	−	2.08548i	−0.218468	−	0.154586i
$183$	17.5775	−	8.95620i	1.29937	−	0.662062i
$184$	1.35846	+	1.86976i	0.100147	+	0.137840i
$185$	0.213418	+	6.13405i	0.0156908	+	0.450984i
$186$	−6.17759	−	4.48829i	−0.452963	−	0.329097i
$187$	2.52878	+	0.400519i	0.184923	+	0.0292889i
$188$	−0.490006	+	3.09377i	−0.0357373	+	0.225637i
$189$	−30.6731	−	15.1482i	−2.23114	−	1.10187i
$190$	−0.192270	−	5.52623i	−0.0139488	−	0.400915i
$191$	9.19433	−	6.68007i	0.665278	−	0.483353i	−0.203163	−	0.979145i	$-0.565122\pi$
$191$	9.19433	−	6.68007i	0.665278	−	0.483353i	0.868441	+	0.495792i	$0.165122\pi$
$192$	−10.3844	+	5.29112i	−0.749429	+	0.381853i
$193$	−2.14105	−	2.14105i	−0.154116	−	0.154116i	0.625837	−	0.779954i	$-0.284757\pi$
$193$	−2.14105	−	2.14105i	−0.154116	−	0.154116i	−0.779954	+	0.625837i	$0.784757\pi$
$194$	−0.0933134	+	0.287189i	−0.00669951	+	0.0206190i
$195$	−9.24712	+	19.8239i	−0.662200	+	1.41962i
$196$	7.67579	+	10.0271i	0.548271	+	0.716223i
$197$	10.9562	+	5.58244i	0.780594	+	0.397733i	0.798414	−	0.602109i	$-0.205673\pi$
$197$	10.9562	+	5.58244i	0.780594	+	0.397733i	−0.0178200	+	0.999841i	$0.505673\pi$
$198$	−1.46473	−	9.24792i	−0.104094	−	0.657221i
$199$	−6.17091			−0.437444			−0.218722	−	0.975787i	$-0.570189\pi$
$199$	−6.17091			−0.437444			−0.218722	+	0.975787i	$0.570189\pi$
$200$	5.52638	−	6.35408i	0.390774	−	0.449301i
$201$		−	3.11186i		−	0.219494i
$202$	−0.452008	−	2.85387i	−0.0318032	−	0.200797i
$203$	3.49444	−	11.2312i	0.245262	−	0.788273i
$204$	−4.66356	+	1.51528i	−0.326514	+	0.106091i
$205$	17.3522	+	16.1853i	1.21193	+	1.13043i
$206$	2.94847	+	0.958015i	0.205429	+	0.0667481i
$207$	−6.86387	+	6.86387i	−0.477072	+	0.477072i
$208$	−4.00506	−	7.86038i	−0.277701	−	0.545019i
$209$	13.5085	−	9.81453i	0.934405	−	0.678885i
$210$	−5.59418	+	6.15002i	−0.386035	+	0.424391i
$211$	−8.75641	−	6.36190i	−0.602816	−	0.437971i	0.244061	−	0.969760i	$-0.421520\pi$
$211$	−8.75641	−	6.36190i	−0.602816	−	0.437971i	−0.846877	+	0.531788i	$0.821520\pi$
$212$	3.21274	−	20.2845i	0.220652	−	1.39314i
$213$	4.06538	−	25.6678i	0.278555	−	1.75873i
$214$	1.03034	−	1.41814i	0.0704326	−	0.0969422i
$215$	−12.7500	−	8.60237i	−0.869544	−	0.586677i
$216$	12.8003	+	17.6181i	0.870949	+	1.19876i
$217$	−11.5241	+	8.59515i	−0.782307	+	0.583477i
$218$	5.53382	+	5.53382i	0.374798	+	0.374798i
$219$	−14.9356	−	4.85287i	−1.00925	−	0.327926i
$220$	11.9692	+	1.47119i	0.806962	+	0.0991875i
$221$	−0.815686	−	2.51042i	−0.0548690	−	0.168869i
$222$	−1.75118	+	3.43689i	−0.117532	+	0.230669i
$223$	−21.7024	+	3.43732i	−1.45330	+	0.230180i	−0.832603	−	0.553870i	$-0.813150\pi$
$223$	−21.7024	+	3.43732i	−1.45330	+	0.230180i	−0.620697	+	0.784050i	$0.713150\pi$
$224$	−2.07012	−	12.0890i	−0.138316	−	0.807729i
$225$	29.9900	+	18.7505i	1.99933	+	1.25003i
$226$	−2.69279			−0.179122
$227$	−2.32135	−	14.6564i	−0.154073	−	0.972781i	−0.936660	−	0.350240i	$-0.886100\pi$
$227$	−2.32135	−	14.6564i	−0.154073	−	0.972781i	0.782587	−	0.622542i	$-0.213900\pi$
$228$	−14.5184	+	28.4939i	−0.961502	+	1.88705i
$229$	−9.06535	−	27.9003i	−0.599055	−	1.84370i	−0.533405	−	0.845860i	$-0.679088\pi$
$229$	−9.06535	−	27.9003i	−0.599055	−	1.84370i	−0.0656503	−	0.997843i	$-0.520912\pi$
$230$	0.658486	+	1.18830i	0.0434193	+	0.0783542i
$231$	−24.8427	−	3.61660i	−1.63453	−	0.237955i
$232$	−5.29450	+	5.29450i	−0.347601	+	0.347601i
$233$	−9.85778	+	5.02279i	−0.645804	+	0.329054i	−0.746031	−	0.665911i	$-0.768043\pi$
$233$	−9.85778	+	5.02279i	−0.645804	+	0.329054i	0.100227	+	0.994965i	$0.468043\pi$
$234$	−7.80965	+	5.67405i	−0.510533	+	0.370924i
$235$	−1.07067	+	3.73207i	−0.0698430	+	0.243454i
$236$	−0.0616957	+	0.0849168i	−0.00401605	+	0.00552762i
$237$	27.9202	+	4.42213i	1.81361	+	0.287248i
$238$	−0.0125554	−	1.00314i	−0.000813844	−	0.0650239i
$239$	11.2435	−	15.4754i	0.727283	−	1.00102i	−0.271967	−	0.962307i	$-0.587674\pi$
$239$	11.2435	−	15.4754i	0.727283	−	1.00102i	0.999250	−	0.0387131i	$-0.0123259\pi$
$240$	−19.0895	+	6.94524i	−1.23222	+	0.448313i
$241$	3.30581	+	4.55006i	0.212946	+	0.293095i	0.902106	−	0.431514i	$-0.142020\pi$
$241$	3.30581	+	4.55006i	0.212946	+	0.293095i	−0.689160	+	0.724609i	$0.742020\pi$
$242$	0.414588	+	0.813675i	0.0266507	+	0.0523050i
$243$	−17.0481	+	17.0481i	−1.09364	+	1.09364i
$244$	−3.46490	+	10.6639i	−0.221818	+	0.682685i
$245$	7.92700	+	13.4968i	0.506437	+	0.862277i
$246$	4.60825	+	14.1827i	0.293811	+	0.904258i
$247$	−15.3384	−	7.81533i	−0.975962	−	0.497278i
$248$	9.03902	−	1.43164i	0.573978	−	0.0909092i
$249$		−	3.25618i		−	0.206352i
$250$	3.67995	−	3.31087i	0.232740	−	0.209398i
$251$		−	19.7255i		−	1.24506i	−0.782596	−	0.622530i	$-0.786105\pi$
$251$		−	19.7255i		−	1.24506i	0.782596	−	0.622530i	$-0.213895\pi$
$252$	31.9769	−	10.8342i	2.01435	−	0.682490i
$253$	−1.86244	+	3.65524i	−0.117090	+	0.229803i
$254$	1.31928	−	0.428662i	0.0827793	−	0.0268966i
$255$	−5.96656	+	1.15899i	−0.373641	+	0.0725787i
$256$	0.778481	−	2.39592i	0.0486550	−	0.149745i
$257$	−2.76628	−	2.76628i	−0.172556	−	0.172556i	0.615546	−	0.788101i	$-0.288936\pi$
$257$	−2.76628	−	2.76628i	−0.172556	−	0.172556i	−0.788101	+	0.615546i	$0.788936\pi$
$258$	−4.38829	−	8.61251i	−0.273203	−	0.536192i
$259$	5.19908	+	5.07055i	0.323055	+	0.315068i
$260$	−4.25078	−	11.6836i	−0.263622	−	0.724586i
$261$	−25.4421	−	18.4848i	−1.57483	−	1.14418i
$262$	3.43412	+	0.543911i	0.212160	+	0.0336029i
$263$	12.8706	+	2.03851i	0.793638	+	0.125700i	0.540073	−	0.841618i	$-0.318397\pi$
$263$	12.8706	+	2.03851i	0.793638	+	0.125700i	0.253565	+	0.967318i	$0.418397\pi$
$264$	12.9289	+	9.39338i	0.795718	+	0.578123i
$265$	7.01992	−	24.4695i	0.431230	−	1.50315i
$266$	−4.68391	−	4.56811i	−0.287189	−	0.280089i
$267$	14.3742	+	28.2110i	0.879689	+	1.72649i
$268$	1.25065	+	1.25065i	0.0763957	+	0.0763957i
$269$	−2.20892	+	6.79836i	−0.134680	+	0.414503i	−0.995540	−	0.0943389i	$-0.969926\pi$
$269$	−2.20892	+	6.79836i	−0.134680	+	0.414503i	0.860860	+	0.508842i	$0.169926\pi$
$270$	6.20468	+	11.1969i	0.377605	+	0.681424i
$271$	2.05858	−	0.668873i	0.125050	−	0.0406311i	−0.245824	−	0.969315i	$-0.579058\pi$
$271$	2.05858	−	0.668873i	0.125050	−	0.0406311i	0.370873	+	0.928683i	$0.379058\pi$
$272$	1.11285	−	2.18409i	0.0674766	−	0.132430i
$273$	8.30551	+	24.5135i	0.502672	+	1.48363i
$274$		−	5.33263i		−	0.322156i
$275$	14.5028	+	3.61991i	0.874554	+	0.218289i
$276$		−	7.85697i		−	0.472934i
$277$	26.5717	−	4.20855i	1.59654	−	0.252867i	0.706148	−	0.708064i	$-0.250431\pi$
$277$	26.5717	−	4.20855i	1.59654	−	0.252867i	0.890391	+	0.455197i	$0.150431\pi$
$278$	5.00464	+	2.54999i	0.300159	+	0.152938i
$279$	11.8779	+	36.5564i	0.711111	+	2.18857i
$280$	−0.471059	−	9.95285i	−0.0281511	−	0.594797i
$281$	−7.74687	+	23.8424i	−0.462139	+	1.42232i	0.400406	+	0.916338i	$0.368869\pi$
$281$	−7.74687	+	23.8424i	−0.462139	+	1.42232i	−0.862545	+	0.505980i	$0.831131\pi$
$282$	−1.72538	+	1.72538i	−0.102745	+	0.102745i
$283$	7.41454	+	14.5519i	0.440749	+	0.865018i	0.999366	+	0.0355926i	$0.0113319\pi$
$283$	7.41454	+	14.5519i	0.440749	+	0.865018i	−0.558618	+	0.829425i	$0.688668\pi$
$284$	8.68198	+	11.9497i	0.515181	+	0.709086i
$285$	−22.1703	+	32.8597i	−1.31325	+	1.94644i
$286$	−2.39797	+	3.30052i	−0.141795	+	0.195164i
$287$	28.0743	−	0.351380i	1.65717	−	0.0207413i
$288$	−32.3886	−	5.12985i	−1.90851	−	0.302279i
$289$	−9.56124	+	13.1599i	−0.562426	+	0.774113i
$290$	−3.46868	+	2.70931i	−0.203688	+	0.159096i
$291$	1.75128	−	1.27238i	0.102662	−	0.0745880i
$292$	7.95295	−	4.05223i	0.465411	−	0.237139i
$293$	16.2278	−	16.2278i	0.948038	−	0.948038i	−0.0506772	−	0.998715i	$-0.516138\pi$
$293$	16.2278	−	16.2278i	0.948038	−	0.948038i	0.998715	+	0.0506772i	$0.0161380\pi$
$294$	0.246200	+	9.83381i	0.0143587	+	0.573520i
$295$	−0.0887432	+	0.0951410i	−0.00516683	+	0.00553932i
$296$	−1.42859	−	4.39674i	−0.0830349	−	0.255555i
$297$	−17.5491	+	34.4420i	−1.01830	+	1.99853i
$298$	0.213288	+	1.34665i	0.0123555	+	0.0780093i
$299$	4.22946			0.244596
$300$	−27.8963	+	6.43282i	−1.61059	+	0.371399i
$301$	−17.9375	+	3.07162i	−1.03390	+	0.177045i
$302$	−4.60643	+	0.729586i	−0.265070	+	0.0419830i
$303$	−9.40363	+	18.4557i	−0.540225	+	1.06025i
$304$	−4.94007	−	15.2040i	−0.283332	−	0.872007i
$305$	−5.87533	+	12.5955i	−0.336421	+	0.721215i
$306$	−2.55099	−	0.828866i	−0.145830	−	0.0473831i
$307$	−3.94765	−	3.94765i	−0.225304	−	0.225304i	0.585424	−	0.810728i	$-0.300928\pi$
$307$	−3.94765	−	3.94765i	−0.225304	−	0.225304i	−0.810728	+	0.585424i	$0.800928\pi$
$308$	11.4378	−	8.53075i	0.651727	−	0.486084i
$309$	−13.0630	−	17.9797i	−0.743129	−	1.02283i
$310$	5.37634	−	0.187055i	0.305355	−	0.0106240i
$311$	6.50647	−	8.95539i	0.368948	−	0.507814i	−0.583666	−	0.811994i	$-0.698382\pi$
$311$	6.50647	−	8.95539i	0.368948	−	0.507814i	0.952615	+	0.304180i	$0.0983824\pi$
$312$	2.57742	−	16.2732i	0.145918	−	0.921289i
$313$	−4.95706	+	31.2977i	−0.280190	+	1.76905i	0.299388	+	0.954132i	$0.403218\pi$
$313$	−4.95706	+	31.2977i	−0.280190	+	1.76905i	−0.579578	+	0.814917i	$0.696782\pi$
$314$	−4.46406	−	3.24333i	−0.251922	−	0.183032i
$315$	40.9784	−	8.49349i	2.30887	−	0.478554i
$316$	−12.9983	+	9.44385i	−0.731214	+	0.531258i
$317$	−12.2250	−	23.9929i	−0.686625	−	1.34758i	−0.926323	−	0.376729i	$-0.877049\pi$
$317$	−12.2250	−	23.9929i	−0.686625	−	1.34758i	0.239699	−	0.970847i	$-0.422951\pi$
$318$	11.3125	−	11.3125i	0.634375	−	0.634375i
$319$	−12.6402	−	4.10705i	−0.707715	−	0.229950i
$320$	3.47101	−	7.44111i	0.194035	−	0.415971i
$321$	−11.9510	+	3.88311i	−0.667039	+	0.216734i
$322$	1.53488	+	0.477561i	0.0855356	+	0.0266134i
$323$	−0.748274	−	4.72442i	−0.0416351	−	0.262874i
$324$		−	35.7505i		−	1.98614i
$325$	−3.46283	−	15.0168i	−0.192083	−	0.832980i
$326$	5.87578			0.325429
$327$	−8.77622	−	55.4109i	−0.485326	−	3.06423i
$328$	−15.9248	−	8.11409i	−0.879300	−	0.448026i
$329$	2.13668	+	4.06684i	0.117799	+	0.224212i
$330$	6.86953	+	6.40759i	0.378155	+	0.352726i
$331$	2.72188	−	8.37709i	0.149608	−	0.460447i	−0.847967	−	0.530050i	$-0.822173\pi$
$331$	2.72188	−	8.37709i	0.149608	−	0.460447i	0.997575	+	0.0696030i	$0.0221733\pi$
$332$	1.30865	+	1.30865i	0.0718217	+	0.0718217i
$333$	17.3006	−	8.81509i	0.948066	−	0.483064i
$334$	2.41019	−	1.75110i	0.131880	−	0.0958161i
$335$	1.34952	+	1.72776i	0.0737319	+	0.0943975i
$336$	−10.6430	+	21.5507i	−0.580624	+	1.17568i
$337$	−0.873192	+	5.51312i	−0.0475658	+	0.300319i	−0.999990	−	0.00445672i	$-0.998581\pi$
$337$	−0.873192	+	5.51312i	−0.0475658	+	0.300319i	0.952424	+	0.304775i	$0.0985814\pi$
$338$	−1.53066	−	0.242433i	−0.0832571	−	0.0131866i
$339$	15.6169	+	11.3464i	0.848196	+	0.616250i
$340$	1.93216	−	2.86375i	0.104786	−	0.155309i
$341$	9.54832	+	13.1421i	0.517070	+	0.711686i
$342$	−15.5863	+	7.94161i	−0.842810	+	0.429433i
$343$	17.8162	+	5.05786i	0.961986	+	0.273099i
$344$	11.0178	+	3.57990i	0.594040	+	0.193015i
$345$	1.18812	−	9.66618i	0.0639661	−	0.520410i
$346$	2.99213	−	0.972203i	0.160858	−	0.0522660i
$347$	20.1228	+	10.2531i	1.08025	+	0.550415i	0.901191	−	0.433423i	$-0.142694\pi$
$347$	20.1228	+	10.2531i	1.08025	+	0.550415i	0.179060	+	0.983838i	$0.442694\pi$
$348$	25.1413	−	3.98199i	1.34771	−	0.213457i
$349$	2.68079			0.143500			0.0717498	−	0.997423i	$-0.477142\pi$
$349$	2.68079			0.143500			0.0717498	+	0.997423i	$0.477142\pi$
$350$	0.438914	−	5.84062i	0.0234609	−	0.312194i
$351$	39.8527			2.12718
$352$	−13.6881	+	2.16798i	−0.729578	+	0.115554i
$353$	−25.4558	−	12.9704i	−1.35488	−	0.690344i	−0.382542	−	0.923938i	$-0.624951\pi$
$353$	−25.4558	−	12.9704i	−1.35488	−	0.690344i	−0.972334	+	0.233594i	$0.924951\pi$
$354$	−0.0777631	+	0.0252668i	−0.00413306	+	0.00134291i
$355$	8.87415	+	16.0142i	0.470991	+	0.849948i
$356$	−17.1150	−	5.56098i	−0.907091	−	0.294732i
$357$	−4.15402	+	5.87065i	−0.219854	+	0.310708i
$358$	4.64211	−	2.36527i	0.245343	−	0.125008i
$359$	4.45197	+	6.12761i	0.234966	+	0.323403i	0.910175	−	0.414223i	$-0.135947\pi$
$359$	4.45197	+	6.12761i	0.234966	+	0.323403i	−0.675209	+	0.737626i	$0.735947\pi$
$360$	−25.6074	−	7.34636i	−1.34963	−	0.387187i
$361$	−9.86615	−	7.16818i	−0.519271	−	0.377273i
$362$	−7.05738	−	1.11778i	−0.370928	−	0.0587492i
$363$	1.02409	−	6.46584i	0.0537507	−	0.339369i
$364$	−13.1899	−	6.51397i	−0.691340	−	0.341425i
$365$	10.3970	−	3.78270i	0.544206	−	0.197996i
$366$	−7.06639	+	5.13403i	−0.369366	+	0.268360i
$367$	−30.0325	+	15.3023i	−1.56768	+	0.798774i	−0.999705	−	0.0242713i	$-0.992273\pi$
$367$	−30.0325	+	15.3023i	−1.56768	+	0.798774i	−0.567976	+	0.823045i	$0.692273\pi$
$368$	2.77728	+	2.77728i	0.144776	+	0.144776i
$369$	23.1970	−	71.3929i	1.20759	−	3.71657i
$370$	−0.518184	−	2.66765i	−0.0269391	−	0.138685i
$371$	−14.0093	−	26.6644i	−0.727325	−	1.38435i
$372$	−27.7210	−	14.1246i	−1.43727	−	0.732325i
$373$	−3.04834	−	19.2465i	−0.157837	−	0.996544i	−0.931710	−	0.363203i	$-0.881683\pi$
$373$	−3.04834	−	19.2465i	−0.157837	−	0.996544i	0.773873	−	0.633341i	$-0.218317\pi$
$374$	−1.13358			−0.0586162
$375$	−35.2927	+	3.69568i	−1.82251	+	0.190844i
$376$		−	2.92442i		−	0.150815i
$377$	2.14353	+	13.5337i	0.110397	+	0.697022i
$378$	14.4626	+	4.49988i	0.743878	+	0.231449i
$379$	19.0116	−	6.17725i	0.976562	−	0.317304i	0.223100	−	0.974796i	$-0.428382\pi$
$379$	19.0116	−	6.17725i	0.976562	−	0.317304i	0.753462	+	0.657491i	$0.228382\pi$
$380$	−4.29606	−	22.1165i	−0.220383	−	1.13455i
$381$	−9.45744	−	3.07291i	−0.484519	−	0.157430i
$382$	−3.55803	+	3.55803i	−0.182045	+	0.182045i
$383$	9.67059	+	18.9796i	0.494144	+	0.969813i	0.994574	+	0.104035i	$0.0331755\pi$
$383$	9.67059	+	18.9796i	0.494144	+	0.969813i	−0.500429	+	0.865777i	$0.666825\pi$
$384$	27.9815	−	20.3297i	1.42792	−	1.03745i
$385$	15.3615	−	8.76551i	0.782895	−	0.446732i
$386$	1.08458	+	0.787995i	0.0552037	+	0.0401079i
$387$	−7.61161	+	48.0578i	−0.386920	+	2.44292i
$388$	−0.192469	+	1.21520i	−0.00977113	+	0.0616925i
$389$	−15.4924	+	21.3234i	−0.785495	+	1.08114i	0.209159	+	0.977882i	$0.432927\pi$
$389$	−15.4924	+	21.3234i	−0.785495	+	1.08114i	−0.994654	+	0.103260i	$0.967073\pi$
$390$	2.67075	−	9.30952i	0.135239	−	0.471406i
$391$	0.690767	+	0.950759i	0.0349336	+	0.0480820i
$392$	−8.54251	−	8.12522i	−0.431462	−	0.410385i
$393$	−17.6244	−	17.6244i	−0.889035	−	0.889035i
$394$	−5.17781	−	1.68237i	−0.260854	−	0.0847568i
$395$	−17.4195	+	9.65289i	−0.876472	+	0.485689i
$396$	−11.7889	−	36.2825i	−0.592414	−	1.82326i
$397$	−11.0445	+	21.6760i	−0.554306	+	1.08789i	0.428551	+	0.903517i	$0.359024\pi$
$397$	−11.0445	+	21.6760i	−0.554306	+	1.08789i	−0.982857	+	0.184369i	$0.940976\pi$
$398$	2.69856	−	0.427409i	0.135266	−	0.0214241i
$399$	7.91626	+	46.2290i	0.396309	+	2.31435i
$400$	7.58690	−	12.1346i	0.379345	−	0.606732i
$401$	16.0932			0.803655			0.401827	−	0.915715i	$-0.368375\pi$
$401$	16.0932			0.803655			0.401827	+	0.915715i	$0.368375\pi$
$402$	0.215534	+	1.36083i	0.0107498	+	0.0678718i
$403$	7.60335	−	14.9224i	0.378750	−	0.743338i
$404$	−3.63800	−	11.1966i	−0.180997	−	0.557053i
$405$	5.40612	−	43.9827i	0.268632	−	2.18552i
$406$	−0.750238	+	5.15345i	−0.0372337	+	0.255761i
$407$	5.80251	−	5.80251i	0.287620	−	0.287620i
$408$	4.07908	−	2.07839i	0.201945	−	0.102896i
$409$	−5.69426	+	4.13712i	−0.281563	+	0.204568i	−0.719599	−	0.694390i	$-0.755674\pi$
$409$	−5.69426	+	4.13712i	−0.281563	+	0.204568i	0.438036	+	0.898958i	$0.355674\pi$
$410$	−8.70919	−	5.87605i	−0.430116	−	0.290197i
$411$	−22.4696	+	30.9268i	−1.10834	+	1.52550i
$412$	12.4760	+	1.97601i	0.614650	+	0.0973510i
$413$	0.00192659	+	0.153930i	9.48014e−5	+	0.00757438i
$414$	2.52618	−	3.47699i	0.124155	−	0.170885i
$415$	1.41210	+	1.80789i	0.0693174	+	0.0887457i
$416$	8.39831	+	11.5593i	0.411761	+	0.566740i
$417$	−18.2799	−	35.8763i	−0.895171	−	1.75687i
$418$	−5.22755	+	5.22755i	−0.255688	+	0.255688i
$419$	−9.23428	+	28.4202i	−0.451124	+	1.38842i	0.424502	+	0.905427i	$0.360449\pi$
$419$	−9.23428	+	28.4202i	−0.451124	+	1.38842i	−0.875626	+	0.482990i	$0.839551\pi$
$420$	−18.5925	+	28.3149i	−0.907223	+	1.38163i
$421$	9.81104	+	30.1953i	0.478161	+	1.47163i	0.841647	+	0.540028i	$0.181586\pi$
$421$	9.81104	+	30.1953i	0.478161	+	1.47163i	−0.363486	+	0.931600i	$0.618414\pi$
$422$	4.26984	+	2.17559i	0.207853	+	0.105906i
$423$	12.1315	−	1.92144i	0.589854	−	0.0934237i
$424$			19.1741i			0.931175i
$425$	2.81012	−	3.23100i	0.136311	−	0.156727i
$426$			11.5062i			0.557476i
$427$	5.27706	+	15.5751i	0.255375	+	0.753733i
$428$	3.24247	−	6.36370i	0.156731	−	0.307601i
$429$	27.8142	−	9.03738i	1.34288	−	0.436329i
$430$	6.17144	+	2.87875i	0.297613	+	0.138826i
$431$	−5.13268	+	15.7968i	−0.247233	+	0.760904i	0.748029	+	0.663666i	$0.231001\pi$
$431$	−5.13268	+	15.7968i	−0.247233	+	0.760904i	−0.995261	+	0.0972373i	$0.968999\pi$
$432$	26.1693	+	26.1693i	1.25907	+	1.25907i
$433$	6.10599	+	11.9837i	0.293435	+	0.575899i	0.989913	−	0.141680i	$-0.0452503\pi$
$433$	6.10599	+	11.9837i	0.293435	+	0.575899i	−0.696477	+	0.717579i	$0.745250\pi$
$434$	4.44421	−	4.55687i	0.213329	−	0.218737i
$435$	31.5327	−	1.09709i	1.51187	−	0.0526017i
$436$	25.7967	+	18.7424i	1.23544	+	0.897599i
$437$	7.56994	+	1.19896i	0.362120	+	0.0573541i
$438$	6.86749	+	1.08770i	0.328142	+	0.0519725i
$439$	27.6583	+	20.0949i	1.32006	+	0.959079i	0.999931	+	0.0117051i	$0.00372594\pi$
$439$	27.6583	+	20.0949i	1.32006	+	0.959079i	0.320128	+	0.947374i	$0.396274\pi$
$440$	−11.2520	+	0.391482i	−0.536416	+	0.0186632i
$441$	28.0935	−	40.7759i	1.33779	−	1.94171i
$442$	0.530579	+	1.04132i	0.0252371	+	0.0495305i
$443$	−25.4171	−	25.4171i	−1.20760	−	1.20760i	−0.971801	−	0.235804i	$-0.924228\pi$
$443$	−25.4171	−	25.4171i	−1.20760	−	1.20760i	−0.235804	−	0.971801i	$-0.575772\pi$
$444$	−4.85661	+	14.9471i	−0.230485	+	0.709359i
$445$	−20.2151	−	9.42959i	−0.958286	−	0.447006i
$446$	9.25245	−	3.00630i	0.438116	−	0.142353i
$447$	4.43728	−	8.70865i	0.209876	−	0.411905i
$448$	−3.11756	−	9.20141i	−0.147291	−	0.434726i
$449$		−	10.9088i		−	0.514817i	−0.966303	−	0.257409i	$-0.917131\pi$
$449$		−	10.9088i		−	0.514817i	0.966303	−	0.257409i	$-0.0828687\pi$
$450$	−14.4134	−	6.12249i	−0.679454	−	0.288617i
$451$		−	31.7249i		−	1.49387i
$452$	−10.8365	+	1.71634i	−0.509707	+	0.0807296i
$453$	29.7893	+	15.1784i	1.39962	+	0.713143i
$454$	2.03027	+	6.24852i	0.0952851	+	0.293257i
$455$	−15.2421	−	10.0085i	−0.714561	−	0.469205i
$456$	9.22621	−	28.3954i	0.432057	−	1.32973i
$457$	18.0865	−	18.0865i	0.846053	−	0.846053i	−0.143585	−	0.989638i	$-0.545863\pi$
$457$	18.0865	−	18.0865i	0.846053	−	0.846053i	0.989638	+	0.143585i	$0.0458630\pi$
$458$	5.89673	+	11.5730i	0.275536	+	0.540770i
$459$	6.50885	+	8.95867i	0.303807	+	0.418155i
$460$	3.40732	+	4.36233i	0.158867	+	0.203395i
$461$	−13.1276	+	18.0685i	−0.611411	+	0.841535i	−0.996693	−	0.0812637i	$-0.974104\pi$
$461$	−13.1276	+	18.0685i	−0.611411	+	0.841535i	0.385281	+	0.922799i	$0.374104\pi$
$462$	11.1143	−	0.139107i	0.517083	−	0.00647185i
$463$	−19.9895	−	3.16603i	−0.928991	−	0.147138i	−0.326440	−	0.945218i	$-0.605849\pi$
$463$	−19.9895	−	3.16603i	−0.928991	−	0.147138i	−0.602551	+	0.798080i	$0.705849\pi$
$464$	−7.47938	+	10.2945i	−0.347222	+	0.477909i
$465$	−31.9684	−	21.5689i	−1.48250	−	1.00023i
$466$	3.96295	−	2.87925i	0.183580	−	0.133379i
$467$	20.9396	−	10.6693i	0.968970	−	0.493715i	0.103475	−	0.994632i	$-0.467004\pi$
$467$	20.9396	−	10.6693i	0.968970	−	0.493715i	0.865495	+	0.500917i	$0.167004\pi$
$468$	−27.8116	+	27.8116i	−1.28559	+	1.28559i
$469$	2.56695	+	0.373696i	0.118531	+	0.0172557i
$470$	0.209718	−	1.70620i	0.00967355	−	0.0787013i
$471$	12.2233	+	37.6196i	0.563222	+	1.73342i
$472$	0.0444891	−	0.0873147i	0.00204778	−	0.00401899i
$473$	3.21683	+	20.3103i	0.147910	+	0.933867i
$474$	−12.5159			−0.574874
$475$	−1.94090	−	27.8588i	−0.0890544	−	1.27825i
$476$	−0.689909	−	4.02890i	−0.0316219	−	0.184664i
$477$	−79.5408	+	12.5980i	−3.64192	+	0.576824i
$478$	−3.84497	+	7.54618i	−0.175865	+	0.345154i
$479$	−3.77957	−	11.6323i	−0.172693	−	0.531494i	0.826828	−	0.562455i	$-0.190143\pi$
$479$	−3.77957	−	11.6323i	−0.172693	−	0.531494i	−0.999521	+	0.0309613i	$0.990143\pi$
$480$	28.7772	−	15.9467i	1.31350	−	0.727862i
$481$	−8.04614	−	2.61435i	−0.366872	−	0.119204i
$482$	−1.76079	−	1.76079i	−0.0802017	−	0.0802017i
$483$	−6.88934	−	9.23701i	−0.313476	−	0.420299i
$484$	2.18703	+	3.01019i	0.0994106	+	0.136827i
$485$	−0.420549	+	1.46592i	−0.0190961	+	0.0665640i
$486$	6.27442	−	8.63599i	0.284613	−	0.391737i
$487$	−0.212746	+	1.34323i	−0.00964045	+	0.0608674i	−0.992040	−	0.125926i	$-0.959810\pi$
$487$	−0.212746	+	1.34323i	−0.00964045	+	0.0608674i	0.982399	+	0.186794i	$0.0598097\pi$
$488$	1.63761	−	10.3395i	0.0741313	−	0.468047i
$489$	−34.0767	−	24.7582i	−1.54100	−	1.11960i
$490$	−4.40131	−	5.35314i	−0.198831	−	0.241830i
$491$	−15.0688	+	10.9482i	−0.680048	+	0.494084i	−0.873373	−	0.487051i	$-0.838073\pi$
$491$	−15.0688	+	10.9482i	−0.680048	+	0.494084i	0.193326	+	0.981135i	$0.438073\pi$
$492$	27.5846	+	54.1379i	1.24361	+	2.44072i
$493$	−2.69222	+	2.69222i	−0.121251	+	0.121251i
$494$	7.24885	+	2.35530i	0.326141	+	0.105970i
$495$	−9.01693	−	46.4199i	−0.405281	−	2.08642i
$496$	14.7916	−	4.80607i	0.664161	−	0.215799i
$497$	20.6850	+	6.43589i	0.927848	+	0.288689i
$498$	0.225529	+	1.42394i	0.0101062	+	0.0638081i
$499$			22.7838i			1.01994i	0.860191	+	0.509971i	$0.170344\pi$
$499$			22.7838i			1.01994i	−0.860191	+	0.509971i	$0.829656\pi$
$500$	12.6988	−	15.6694i	0.567907	−	0.700755i
$501$	−21.3564			−0.954134
$502$	1.36623	+	8.62601i	0.0609776	+	0.384998i
$503$	7.59633	+	3.87053i	0.338704	+	0.172578i	0.615067	−	0.788475i	$-0.289129\pi$
$503$	7.59633	+	3.87053i	0.338704	+	0.172578i	−0.276363	+	0.961053i	$0.589129\pi$
$504$	−27.9044	+	14.6607i	−1.24296	+	0.653041i
$505$	−2.78259	−	14.3250i	−0.123823	−	0.637453i
$506$	0.561281	−	1.72744i	0.0249520	−	0.0767942i
$507$	7.85561	+	7.85561i	0.348880	+	0.348880i
$508$	5.03593	−	2.56593i	0.223433	−	0.113845i
$509$	−22.4839	+	16.3355i	−0.996581	+	0.724059i	−0.961353	−	0.275320i	$-0.911216\pi$
$509$	−22.4839	+	16.3355i	−0.996581	+	0.724059i	−0.0352289	+	0.999379i	$0.511216\pi$
$510$	2.52892	−	0.920085i	0.111983	−	0.0407420i
$511$	5.79667	−	11.7375i	0.256430	−	0.519236i
$512$	−3.58389	+	22.6278i	−0.158387	+	1.00002i
$513$	71.3289	+	11.2974i	3.14925	+	0.498792i
$514$	1.40130	+	1.01810i	0.0618087	+	0.0449067i
$515$	15.0501	+	4.31762i	0.663185	+	0.190257i
$516$	−23.1491	−	31.8620i	−1.01908	−	1.40265i
$517$	4.62516	−	2.35664i	0.203414	−	0.103645i
$518$	−2.62477	−	1.85727i	−0.115326	−	0.0816036i
$519$	−21.4494	−	6.96935i	−0.941526	−	0.305920i
$520$	5.62615	+	10.1529i	0.246723	+	0.445235i
$521$	−42.5775	+	13.8343i	−1.86535	+	0.606090i	−0.872219	+	0.489116i	$0.837319\pi$
$521$	−42.5775	+	13.8343i	−1.86535	+	0.606090i	−0.993135	+	0.116974i	$0.962681\pi$
$522$	12.4062	+	6.32128i	0.543005	+	0.276675i
$523$	−32.7999	+	5.19499i	−1.43424	+	0.227161i	−0.824689	−	0.565587i	$-0.808650\pi$
$523$	−32.7999	+	5.19499i	−1.43424	+	0.227161i	−0.609550	+	0.792748i	$0.708650\pi$
$524$	14.1665			0.618865
$525$	−27.1555	+	32.0234i	−1.18516	+	1.39762i
$526$	−5.76956			−0.251565
$527$	4.59627	−	0.727978i	0.200217	−	0.0317112i
$528$	24.1987	+	12.3298i	1.05311	+	0.536587i
$529$	20.0834	−	6.52550i	0.873193	−	0.283718i
$530$	−1.37502	+	11.1868i	−0.0597272	+	0.485924i
$531$	0.391443	+	0.127188i	0.0169872	+	0.00551947i
$532$	−21.7609	−	15.3979i	−0.943455	−	0.667582i
$533$	−29.1428	+	14.8490i	−1.26231	+	0.643181i
$534$	−8.23984	−	11.3412i	−0.356573	−	0.490781i
$535$	4.95141	−	7.33874i	0.214068	−	0.317281i
$536$	−1.33592	−	0.970600i	−0.0577028	−	0.0419236i
$537$	−36.8883	−	5.84254i	−1.59185	−	0.252124i
$538$	0.495100	−	3.12594i	0.0213453	−	0.134769i
$539$	5.96661	−	20.0583i	0.257000	−	0.863971i
$540$	32.1060	+	41.1047i	1.38162	+	1.76886i
$541$	−7.16628	+	5.20661i	−0.308103	+	0.223850i	−0.731082	−	0.682290i	$-0.760984\pi$
$541$	−7.16628	+	5.20661i	−0.308103	+	0.223850i	0.422979	+	0.906139i	$0.360984\pi$
$542$	−0.853895	+	0.435081i	−0.0366779	+	0.0186883i
$543$	36.2196	+	36.2196i	1.55433	+	1.55433i
$544$	−1.22683	+	3.77578i	−0.0525998	+	0.161885i
$545$	28.9027	+	26.9591i	1.23805	+	1.15480i
$546$	−5.32988	−	10.1446i	−0.228098	−	0.434148i
$547$	11.0624	+	5.63659i	0.472995	+	0.241003i	0.674204	−	0.738545i	$-0.264487\pi$
$547$	11.0624	+	5.63659i	0.472995	+	0.241003i	−0.201209	+	0.979548i	$0.564487\pi$
$548$	−3.39892	−	21.4599i	−0.145195	−	0.916723i
$549$	43.9678			1.87650
$550$	−6.59285	−	0.578504i	−0.281120	−	0.0246675i
$551$			24.8305i			1.05781i
$552$	1.14751	+	7.24512i	0.0488414	+	0.308373i
$553$	−7.00066	+	22.5001i	−0.297698	+	0.956804i
$554$	−11.3284	+	3.68082i	−0.481297	+	0.156383i
$555$	−8.23522	+	17.6546i	−0.349565	+	0.749394i
$556$	21.7653	+	7.07198i	0.923055	+	0.299919i
$557$	19.7643	−	19.7643i	0.837438	−	0.837438i	−0.151083	−	0.988521i	$-0.548276\pi$
$557$	19.7643	−	19.7643i	0.837438	−	0.837438i	0.988521	+	0.151083i	$0.0482760\pi$
$558$	−7.72620	−	15.1635i	−0.327076	−	0.641923i
$559$	17.1515	−	12.4613i	0.725433	−	0.527058i
$560$	−3.43666	−	16.5808i	−0.145226	−	0.700668i
$561$	6.57425	+	4.77647i	0.277565	+	0.201663i
$562$	1.73636	−	10.9629i	0.0732437	−	0.462443i
$563$	3.79742	−	23.9760i	0.160042	−	1.01047i	−0.768664	−	0.639652i	$-0.779078\pi$
$563$	3.79742	−	23.9760i	0.160042	−	1.01047i	0.928707	−	0.370815i	$-0.120922\pi$
$564$	−5.84366	+	8.04311i	−0.246062	+	0.338676i
$565$	−13.5914	+	0.472875i	−0.571793	+	0.0198940i
$566$	−4.25029	−	5.85002i	−0.178653	−	0.245895i
$567$	−31.3476	−	42.0299i	−1.31648	−	1.76509i
$568$	−9.75115	−	9.75115i	−0.409149	−	0.409149i
$569$	21.2622	+	6.90849i	0.891356	+	0.289619i	0.718665	−	0.695357i	$-0.244754\pi$
$569$	21.2622	+	6.90849i	0.891356	+	0.289619i	0.172691	+	0.984976i	$0.444754\pi$
$570$	7.41920	−	15.9052i	0.310756	−	0.666195i
$571$	−3.46064	−	10.6507i	−0.144823	−	0.445720i	0.852165	−	0.523273i	$-0.175289\pi$
$571$	−3.46064	−	10.6507i	−0.144823	−	0.445720i	−0.996988	+	0.0775532i	$0.975289\pi$
$572$	−7.54638	+	14.8106i	−0.315530	+	0.619263i
$573$	35.6270	−	5.64277i	1.48834	−	0.235730i
$574$	−12.2526	+	2.09814i	−0.511415	+	0.0875747i
$575$	3.53226	+	5.88208i	0.147305	+	0.245300i
$576$	−25.9752			−1.08230
$577$	6.29545	+	39.7479i	0.262083	+	1.65473i	0.670484	+	0.741924i	$0.266086\pi$
$577$	6.29545	+	39.7479i	0.262083	+	1.65473i	−0.408402	+	0.912802i	$0.633914\pi$
$578$	3.26968	−	6.41710i	0.136001	−	0.266916i
$579$	−2.96976	−	9.13999i	−0.123419	−	0.379845i
$580$	−12.2320	+	13.1139i	−0.507907	+	0.544523i
$581$	2.68600	+	0.391027i	0.111434	+	0.0162225i
$582$	−0.677711	+	0.677711i	−0.0280920	+	0.0280920i
$583$	−30.3251	+	15.4514i	−1.25594	+	0.639932i
$584$	−6.74179	+	4.89820i	−0.278977	+	0.202689i
$585$	−38.4213	+	30.0101i	−1.58853	+	1.24076i
$586$	−5.97249	+	8.22043i	−0.246721	+	0.339583i
$587$	−32.8107	−	5.19670i	−1.35424	−	0.214491i	−0.563235	−	0.826297i	$-0.690443\pi$
$587$	−32.8107	−	5.19670i	−1.35424	−	0.214491i	−0.791008	+	0.611806i	$0.790443\pi$
$588$	7.25866	+	39.4169i	0.299342	+	1.62553i
$589$	17.8388	−	24.5529i	0.735033	−	1.01169i
$590$	0.0322180	−	0.0477520i	0.00132639	−	0.00196592i
$591$	22.9400	+	31.5742i	0.943626	+	1.29879i
$592$	−3.56679	−	7.00022i	−0.146594	−	0.287707i
$593$	32.3722	−	32.3722i	1.32937	−	1.32937i	0.423445	−	0.905922i	$-0.360821\pi$
$593$	32.3722	−	32.3722i	1.32937	−	1.32937i	0.905922	−	0.423445i	$-0.139179\pi$
$594$	5.28875	−	16.2771i	0.217000	−	0.667857i
$595$	−0.239530	−	5.06095i	−0.00981977	−	0.207479i
$596$	1.71666	+	5.28333i	0.0703170	+	0.216414i
$597$	−17.4513	−	8.89188i	−0.714234	−	0.363920i
$598$	−1.84956	+	0.292941i	−0.0756340	+	0.0119792i
$599$		−	21.7950i		−	0.890520i	−0.895401	−	0.445260i	$-0.853111\pi$
$599$		−	21.7950i		−	0.890520i	0.895401	−	0.445260i	$-0.146889\pi$
$600$	24.7844	−	10.0061i	1.01182	−	0.408499i
$601$			27.7666i			1.13262i	0.824191	+	0.566312i	$0.191630\pi$
$601$			27.7666i			1.13262i	−0.824191	+	0.566312i	$0.808370\pi$
$602$	7.63138	−	2.58562i	0.311032	−	0.105382i
$603$	3.14865	−	6.17957i	0.128223	−	0.251652i
$604$	−18.0725	+	5.87210i	−0.735358	+	0.238932i
$605$	2.23544	+	4.03406i	0.0908836	+	0.164008i
$606$	2.83396	−	8.72203i	0.115122	−	0.354308i
$607$	24.6559	+	24.6559i	1.00075	+	1.00075i	1.00000		0.000750532i	$0.000238902\pi$
$607$	24.6559	+	24.6559i	1.00075	+	1.00075i	0.000750532		1.00000i	$0.499761\pi$
$608$	11.7546	+	23.0697i	0.476712	+	0.935599i
$609$	26.0656	−	26.7264i	1.05623	−	1.08301i
$610$	1.69691	−	5.91497i	0.0687060	−	0.239490i
$611$	−4.32966	−	3.14568i	−0.175159	−	0.127261i
$612$	−10.7942	−	1.70963i	−0.436328	−	0.0691075i
$613$	−46.5842	−	7.37822i	−1.88152	−	0.298003i	−0.893113	−	0.449833i	$-0.851484\pi$
$613$	−46.5842	−	7.37822i	−1.88152	−	0.298003i	−0.988407	+	0.151829i	$0.951484\pi$
$614$	1.99974	+	1.45290i	0.0807029	+	0.0586341i
$615$	25.7499	+	70.7754i	1.03833	+	2.85394i
$616$	−9.30114	+	9.53691i	−0.374753	+	0.384253i
$617$	14.1085	+	27.6895i	0.567987	+	1.11474i	0.979143	+	0.203172i	$0.0651250\pi$
$617$	14.1085	+	27.6895i	0.567987	+	1.11474i	−0.411156	+	0.911565i	$0.634875\pi$
$618$	6.95781	+	6.95781i	0.279884	+	0.279884i
$619$	10.2075	−	31.4153i	0.410272	−	1.26269i	−0.506140	−	0.862451i	$-0.668928\pi$
$619$	10.2075	−	31.4153i	0.410272	−	1.26269i	0.916412	−	0.400236i	$-0.131072\pi$
$620$	21.5166	−	4.17954i	0.864127	−	0.167854i
$621$	−16.8747	+	5.48293i	−0.677159	+	0.220022i
$622$	−2.22503	+	4.36687i	−0.0892157	+	0.175096i
$623$	−24.9972	+	8.46940i	−1.00149	+	0.339319i
$624$		−	28.0001i		−	1.12090i
$625$	17.9924	−	17.3572i	0.719696	−	0.694289i
$626$		−	14.0299i		−	0.560747i
$627$	52.3441	−	8.29050i	2.09042	−	0.331091i
$628$	−20.0318	−	10.2067i	−0.799356	−	0.407292i
$629$	−0.726426	−	2.23571i	−0.0289645	−	0.0891436i
$630$	−17.3317	+	6.55248i	−0.690512	+	0.261057i
$631$	−0.569361	+	1.75231i	−0.0226659	+	0.0697584i	−0.961750	−	0.273930i	$-0.911676\pi$
$631$	−0.569361	+	1.75231i	−0.0226659	+	0.0697584i	0.939084	+	0.343688i	$0.111676\pi$
$632$	10.6068	−	10.6068i	0.421917	−	0.421917i
$633$	−15.5960	−	30.6088i	−0.619885	−	1.21659i
$634$	7.00783	+	9.64545i	0.278316	+	0.383070i
$635$	6.58356	−	2.39526i	0.261261	−	0.0950531i
$636$	38.3142	−	52.7350i	1.51926	−	2.09108i
$637$	−21.2184	+	3.90738i	−0.840704	+	0.154816i
$638$	5.81205	+	0.920539i	0.230101	+	0.0364445i
$639$	34.0444	−	46.8580i	1.34677	−	1.85368i
$640$	−6.71944	+	23.4221i	−0.265609	+	0.925841i
$641$	−12.4103	+	9.01658i	−0.490176	+	0.356133i	−0.805252	−	0.592933i	$-0.797970\pi$
$641$	−12.4103	+	9.01658i	−0.490176	+	0.356133i	0.315076	+	0.949066i	$0.397970\pi$
$642$	4.95725	−	2.52584i	0.195647	−	0.0996871i
$643$	4.15929	−	4.15929i	0.164027	−	0.164027i	−0.620321	−	0.784348i	$-0.712998\pi$
$643$	4.15929	−	4.15929i	0.164027	−	0.164027i	0.784348	+	0.620321i	$0.212998\pi$
$644$	6.48116	+	0.943526i	0.255393	+	0.0371801i
$645$	−23.6615	−	42.6994i	−0.931671	−	1.68129i
$646$	0.654445	+	2.01418i	0.0257488	+	0.0792467i
$647$	12.4207	−	24.3771i	0.488310	−	0.958362i	−0.507029	−	0.861929i	$-0.669256\pi$
$647$	12.4207	−	24.3771i	0.488310	−	0.958362i	0.995339	−	0.0964335i	$-0.0307435\pi$
$648$	5.22137	+	32.9665i	0.205115	+	1.29504i
$649$	0.173946			0.00682796
$650$	2.55440	+	6.32703i	0.100192	+	0.248166i
$651$	−44.9751	+	7.70154i	−1.76271	+	0.301847i
$652$	23.6457	−	3.74511i	0.926036	−	0.146670i
$653$	−9.49843	+	18.6417i	−0.371702	+	0.729507i	−0.998776	−	0.0494529i	$-0.984252\pi$
$653$	−9.49843	+	18.6417i	−0.371702	+	0.729507i	0.627074	+	0.778959i	$0.284252\pi$
$654$	7.67574	+	23.6235i	0.300145	+	0.923751i
$655$	17.4286	+	2.14223i	0.680990	+	0.0837037i
$656$	−28.8873	−	9.38604i	−1.12786	−	0.366463i
$657$	−24.7491	−	24.7491i	−0.965553	−	0.965553i
$658$	−1.21606	−	1.63045i	−0.0474068	−	0.0635615i
$659$	5.15199	+	7.09111i	0.200693	+	0.276230i	0.897487	−	0.441041i	$-0.145391\pi$
$659$	5.15199	+	7.09111i	0.200693	+	0.276230i	−0.696794	+	0.717272i	$0.745391\pi$
$660$	31.7289	+	21.4073i	1.23504	+	0.833279i
$661$	14.7218	−	20.2629i	0.572613	−	0.788134i	−0.420248	−	0.907409i	$-0.638057\pi$
$661$	14.7218	−	20.2629i	0.572613	−	0.788134i	0.992861	+	0.119275i	$0.0380571\pi$
$662$	−0.610073	+	3.85185i	−0.0237112	+	0.149706i
$663$	1.31060	−	8.27481i	0.0508995	−	0.321367i
$664$	−1.39787	−	1.01561i	−0.0542480	−	0.0394135i
$665$	−24.4433	−	22.2341i	−0.947872	−	0.862203i
$666$	−6.95505	+	5.05314i	−0.269503	+	0.195805i
$667$	−2.76959	−	5.43563i	−0.107239	−	0.210469i
$668$	8.58311	−	8.58311i	0.332091	−	0.332091i
$669$	−66.3272	−	21.5510i	−2.56436	−	0.833210i
$670$	−0.709815	−	0.662084i	−0.0274226	−	0.0255785i
$671$	17.6723	−	5.74207i	0.682231	−	0.221670i
$672$	11.5652	−	37.1705i	0.446136	−	1.43388i
$673$	−0.908113	−	5.73360i	−0.0350052	−	0.221014i	0.963984	−	0.265959i	$-0.0856887\pi$
$673$	−0.908113	−	5.73360i	−0.0350052	−	0.221014i	−0.998989	+	0.0449453i	$0.985689\pi$
$674$		−	2.47138i		−	0.0951941i
$675$	33.2832	+	55.4248i	1.28107	+	2.13330i
$676$	−6.31432			−0.242858
$677$	0.858091	+	5.41777i	0.0329791	+	0.208222i	0.998675	−	0.0514520i	$-0.0163849\pi$
$677$	0.858091	+	5.41777i	0.0329791	+	0.208222i	−0.965696	+	0.259674i	$0.916385\pi$
$678$	−7.61521	−	3.88014i	−0.292460	−	0.149016i
$679$	0.839267	+	1.59741i	0.0322081	+	0.0613030i
$680$	−1.36344	+	2.92293i	−0.0522856	+	0.112089i
$681$	14.5542	−	44.7932i	0.557718	−	1.71648i
$682$	−5.08576	−	5.08576i	−0.194744	−	0.194744i
$683$	−7.85213	+	4.00086i	−0.300454	+	0.153089i	−0.597718	−	0.801706i	$-0.703926\pi$
$683$	−7.85213	+	4.00086i	−0.300454	+	0.153089i	0.297264	+	0.954795i	$0.403926\pi$
$684$	−57.6615	+	41.8935i	−2.20474	+	1.60184i
$685$	−0.936451	−	26.9154i	−0.0357800	−	1.02839i
$686$	−8.14141	−	0.977832i	−0.310840	−	0.0373338i
$687$	14.5657	−	91.9644i	0.555717	−	3.50866i
$688$	19.4453	+	3.07984i	0.741346	+	0.117418i
$689$	28.3876	+	20.6248i	1.08148	+	0.785742i
$690$	0.149932	+	4.30934i	0.00570782	+	0.164054i
$691$	−13.7324	−	18.9010i	−0.522405	−	0.719029i	0.463544	−	0.886074i	$-0.346577\pi$
$691$	−13.7324	−	18.9010i	−0.522405	−	0.719029i	−0.985949	+	0.167045i	$0.946577\pi$
$692$	11.4215	−	5.81953i	0.434179	−	0.221225i
$693$	−45.6736	−	32.3183i	−1.73500	−	1.22767i
$694$	−9.50993	−	3.08996i	−0.360992	−	0.117293i
$695$	25.7078	+	11.9917i	0.975151	+	0.454873i
$696$	−22.6018	+	7.34379i	−0.856721	+	0.278365i
$697$	−8.09765	−	4.12596i	−0.306720	−	0.156282i
$698$	−1.17232	+	0.185677i	−0.0443729	+	0.00702798i
$699$	−35.1152			−1.32818
$700$	−1.95639	−	23.7839i	−0.0739446	−	0.898948i
$701$	−26.2540			−0.991601			−0.495800	−	0.868437i	$-0.665125\pi$
$701$	−26.2540			−0.991601			−0.495800	+	0.868437i	$0.665125\pi$
$702$	−17.4277	+	2.76028i	−0.657766	+	0.104180i
$703$	−13.6600	−	6.96010i	−0.515196	−	0.262505i
$704$	−10.4404	+	3.39228i	−0.393486	+	0.127851i
$705$	−8.40553	+	9.01151i	−0.316571	+	0.339393i
$706$	12.0303	+	3.90887i	0.452765	+	0.147112i
$707$	−14.0947	−	9.97329i	−0.530085	−	0.375084i
$708$	−0.296835	+	0.151245i	−0.0111557	+	0.00568413i
$709$	14.7378	+	20.2849i	0.553490	+	0.761814i	0.990481	−	0.137652i	$-0.0439557\pi$
$709$	14.7378	+	20.2849i	0.553490	+	0.761814i	−0.436991	+	0.899466i	$0.643956\pi$
$710$	−4.98987	−	6.38843i	−0.187267	−	0.239754i
$711$	50.9700	+	37.0318i	1.91152	+	1.38880i
$712$	16.5943	+	2.62828i	0.621899	+	0.0984991i
$713$	−1.16644	+	7.36462i	−0.0436836	+	0.275807i
$714$	1.40995	−	2.85497i	0.0527662	−	0.106844i
$715$	−11.5237	+	17.0799i	−0.430962	+	0.638751i
$716$	17.1735	−	12.4773i	0.641803	−	0.466297i
$717$	54.0957	−	27.5631i	2.02024	−	1.02936i
$718$	−2.37127	−	2.37127i	−0.0884950	−	0.0884950i
$719$	−1.82953	+	5.63072i	−0.0682300	+	0.209990i	−0.979358	−	0.202133i	$-0.935213\pi$
$719$	−1.82953	+	5.63072i	−0.0682300	+	0.209990i	0.911128	+	0.412123i	$0.135213\pi$
$720$	−44.9356	−	5.52325i	−1.67465	−	0.205839i
$721$	16.4000	−	8.61645i	0.610769	−	0.320893i
$722$	4.81098	+	2.45132i	0.179046	+	0.0912286i
$723$	2.79248	+	17.6310i	0.103853	+	0.655704i
$724$	−29.1132			−1.08198
$725$	−17.0317	+	14.2839i	−0.632542	+	0.530489i
$726$			2.89846i			0.107572i
$727$	0.672407	+	4.24541i	0.0249382	+	0.157454i	0.997015	−	0.0772100i	$-0.0246012\pi$
$727$	0.672407	+	4.24541i	0.0249382	+	0.157454i	−0.972077	+	0.234663i	$0.924601\pi$
$728$	13.1141	+	4.08031i	0.486042	+	0.151226i
$729$	−16.2341	+	5.27477i	−0.601262	+	0.195362i
$730$	−4.28466	+	2.37431i	−0.158582	+	0.0878770i
$731$	5.60247	+	1.82035i	0.207215	+	0.0673282i
$732$	−25.1647	+	25.1647i	−0.930113	+	0.930113i
$733$	−1.43780	−	2.82184i	−0.0531063	−	0.104227i	0.862928	−	0.505327i	$-0.168628\pi$
$733$	−1.43780	−	2.82184i	−0.0531063	−	0.104227i	−0.916034	+	0.401100i	$0.868628\pi$
$734$	12.0734	−	8.77185i	0.445638	−	0.323775i
$735$	2.96954	+	49.5911i	0.109533	+	1.82919i
$736$	−5.14639	−	3.73907i	−0.189699	−	0.137824i
$737$	0.458523	−	2.89500i	0.0168899	−	0.106639i
$738$	−5.19929	+	32.8270i	−0.191388	+	1.20838i
$739$	3.02368	−	4.16174i	0.111228	−	0.153092i	−0.749774	−	0.661694i	$-0.769838\pi$
$739$	3.02368	−	4.16174i	0.111228	−	0.153092i	0.861002	+	0.508602i	$0.169838\pi$
$740$	−3.78562	−	10.4051i	−0.139162	−	0.382498i
$741$	−32.1157	−	44.2034i	−1.17980	−	1.62385i
$742$	7.97313	+	10.6901i	0.292703	+	0.392447i
$743$	9.62030	+	9.62030i	0.352935	+	0.352935i	0.861200	−	0.508266i	$-0.169713\pi$
$743$	9.62030	+	9.62030i	0.352935	+	0.352935i	−0.508266	+	0.861200i	$0.669713\pi$
$744$	27.6252	+	8.97596i	1.01279	+	0.329075i
$745$	1.31301	+	6.75950i	0.0481051	+	0.247649i
$746$	2.66610	+	8.20540i	0.0976128	+	0.300421i
$747$	3.29468	−	6.46617i	0.120546	−	0.236585i
$748$	−4.56184	+	0.722524i	−0.166797	+	0.0264181i
$749$	−1.76798	−	10.3246i	−0.0646007	−	0.377252i
$750$	15.1776	−	4.06057i	0.554208	−	0.148271i
$751$	24.2819			0.886058			0.443029	−	0.896507i	$-0.353904\pi$
$751$	24.2819			0.886058			0.443029	+	0.896507i	$0.353904\pi$
$752$	−0.777460	−	4.90869i	−0.0283511	−	0.179002i
$753$	28.4231	−	55.7835i	1.03580	−	2.03286i
$754$	−1.87474	−	5.76987i	−0.0682741	−	0.210126i
$755$	−23.1219	+	4.49137i	−0.841493	+	0.163458i
$756$	61.0697	+	8.89051i	2.22108	+	0.323345i
$757$	−4.83512	+	4.83512i	−0.175736	+	0.175736i	−0.789494	−	0.613758i	$-0.789657\pi$
$757$	−4.83512	+	4.83512i	−0.175736	+	0.175736i	0.613758	+	0.789494i	$0.289657\pi$
$758$	−7.88599	+	4.01811i	−0.286432	+	0.145944i
$759$	−10.5339	+	7.65335i	−0.382357	+	0.277799i
$760$	7.19163	+	19.7667i	0.260868	+	0.717014i
$761$	18.0919	−	24.9013i	0.655830	−	0.902672i	−0.343505	−	0.939151i	$-0.611614\pi$
$761$	18.0919	−	24.9013i	0.655830	−	0.902672i	0.999334	+	0.0364788i	$0.0116141\pi$
$762$	4.34860	+	0.688751i	0.157533	+	0.0249508i
$763$	46.7620	−	0.585276i	1.69290	−	0.0211884i
$764$	−12.0506	+	16.5863i	−0.435977	+	0.600071i
$765$	−13.0212	−	3.73557i	−0.470782	−	0.135060i
$766$	−5.54354	−	7.63003i	−0.200296	−	0.275684i
$767$	−0.0814161	−	0.159788i	−0.00293977	−	0.00576961i
$768$	5.65390	−	5.65390i	0.204017	−	0.204017i
$769$	−15.2426	+	46.9119i	−0.549662	+	1.69169i	0.159976	+	0.987121i	$0.448858\pi$
$769$	−15.2426	+	46.9119i	−0.549662	+	1.69169i	−0.709639	+	0.704566i	$0.751142\pi$
$770$	−6.11052	+	4.89715i	−0.220208	+	0.176481i
$771$	−3.83699	−	11.8090i	−0.138186	−	0.425292i
$772$	4.86690	+	2.47981i	0.175163	+	0.0892502i
$773$	3.51573	−	0.556836i	0.126452	−	0.0200280i	−0.0928877	−	0.995677i	$-0.529610\pi$
$773$	3.51573	−	0.556836i	0.126452	−	0.0200280i	0.219340	+	0.975649i	$0.429610\pi$
$774$		−	21.5430i		−	0.774348i
$775$	27.1032	−	1.88825i	0.973575	−	0.0678280i
$776$		−	1.14868i		−	0.0412352i
$777$	7.39664	+	21.8310i	0.265353	+	0.783183i
$778$	5.29796	−	10.3978i	0.189941	−	0.372780i
$779$	−56.3695	+	18.3156i	−2.01965	+	0.656223i
$780$	4.81411	−	39.1662i	0.172373	−	1.40238i
$781$	7.56415	−	23.2801i	0.270666	−	0.833026i
$782$	−0.367926	−	0.367926i	−0.0131570	−	0.0131570i
$783$	−26.0969	−	51.2180i	−0.932627	−	1.83038i
$784$	−16.4989	−	11.3673i	−0.589246	−	0.405975i
$785$	−23.1010	−	15.5862i	−0.824512	−	0.556294i
$786$	8.92792	+	6.48651i	0.318448	+	0.231366i
$787$	−43.2919	−	6.85676i	−1.54319	−	0.244417i	−0.673938	−	0.738788i	$-0.735399\pi$
$787$	−43.2919	−	6.85676i	−1.54319	−	0.244417i	−0.869251	+	0.494371i	$0.835399\pi$
$788$	−21.9092	−	3.47008i	−0.780483	−	0.123616i
$789$	33.4607	+	24.3107i	1.19123	+	0.865482i
$790$	6.94904	−	5.42775i	0.247236	−	0.193111i
$791$	−11.2349	+	11.5197i	−0.399469	+	0.409595i
$792$	16.1699	+	31.7353i	0.574573	+	1.12766i
$793$	−13.5463	−	13.5463i	−0.481044	−	0.481044i
$794$	3.32846	−	10.2439i	0.118122	−	0.363544i
$795$	55.1113	−	59.0844i	1.95459	−	2.09551i
$796$	10.5873	−	3.44002i	0.375256	−	0.121928i
$797$	6.92880	−	13.5985i	0.245431	−	0.481685i	−0.735124	−	0.677933i	$-0.762876\pi$
$797$	6.92880	−	13.5985i	0.245431	−	0.481685i	0.980554	+	0.196248i	$0.0628759\pi$
$798$	−6.66372	−	19.6678i	−0.235893	−	0.696232i
$799$		−	1.48704i		−	0.0526078i
$800$	−9.06206	+	21.3337i	−0.320392	+	0.754259i
$801$			70.5660i			2.49333i
$802$	−7.03759	+	1.11465i	−0.248506	+	0.0393595i
$803$	−13.1797	−	6.71540i	−0.465102	−	0.236981i
$804$	1.73473	+	5.33894i	0.0611791	+	0.188290i
$805$	7.83089	+	2.14086i	0.276002	+	0.0754554i
$806$	−2.29141	+	7.05224i	−0.0807115	+	0.248405i
$807$	−16.0428	+	16.0428i	−0.564733	+	0.564733i
$808$	4.98997	+	9.79336i	0.175546	+	0.344529i
$809$	29.5073	+	40.6133i	1.03742	+	1.42789i	0.899226	+	0.437484i	$0.144130\pi$
$809$	29.5073	+	40.6133i	1.03742	+	1.42789i	0.138196	+	0.990405i	$0.455870\pi$
$810$	0.682215	+	19.6082i	0.0239706	+	0.688962i
$811$	−11.4410	+	15.7472i	−0.401749	+	0.552961i	−0.961182	−	0.275915i	$-0.911019\pi$
$811$	−11.4410	+	15.7472i	−0.401749	+	0.552961i	0.559433	+	0.828876i	$0.311019\pi$
$812$	0.265554	+	21.2170i	0.00931911	+	0.744572i
$813$	6.78545	+	1.07471i	0.237976	+	0.0376917i
$814$	−2.13556	+	2.93935i	−0.0748514	+	0.103024i
$815$	29.6568	−	1.03183i	1.03883	−	0.0361435i
$816$	6.29428	−	4.57306i	0.220344	−	0.160089i
$817$	34.2306	−	17.4413i	1.19758	−	0.610195i
$818$	2.20357	−	2.20357i	0.0770461	−	0.0770461i
$819$	−8.31013	+	57.0830i	−0.290379	+	1.99464i
$820$	−38.7934	−	18.0957i	−1.35472	−	0.631929i
$821$	1.67476	+	5.15438i	0.0584495	+	0.179889i	0.976019	−	0.217687i	$-0.0698513\pi$
$821$	1.67476	+	5.15438i	0.0584495	+	0.179889i	−0.917569	+	0.397576i	$0.869851\pi$
$822$	7.68398	−	15.0807i	0.268009	−	0.525998i
$823$	0.777653	+	4.90991i	0.0271073	+	0.171149i	0.997528	−	0.0702719i	$-0.0223867\pi$
$823$	0.777653	+	4.90991i	0.0271073	+	0.171149i	−0.970421	+	0.241420i	$0.922387\pi$
$824$	−11.7931			−0.410831
$825$	35.7979	+	31.1347i	1.24632	+	1.08397i
$826$	−0.0115040	−	0.0671804i	−0.000400274	−	0.00233751i
$827$	−33.9914	+	5.38372i	−1.18200	+	0.187210i	−0.716338	−	0.697753i	$-0.754183\pi$
$827$	−33.9914	+	5.38372i	−1.18200	+	0.187210i	−0.465660	+	0.884964i	$0.654183\pi$
$828$	7.94986	−	15.6025i	0.276277	−	0.542224i
$829$	−10.3277	−	31.7855i	−0.358697	−	1.10396i	−0.953835	−	0.300332i	$-0.902902\pi$
$829$	−10.3277	−	31.7855i	−0.358697	−	1.10396i	0.595138	−	0.803624i	$-0.297098\pi$
$830$	−0.742735	−	0.692790i	−0.0257807	−	0.0240471i
$831$	81.2089	+	26.3864i	2.81710	+	0.915333i
$832$	8.00284	+	8.00284i	0.277449	+	0.277449i
$833$	−4.34381	−	4.13162i	−0.150504	−	0.143152i
$834$	10.4787	+	14.4227i	0.362849	+	0.499418i
$835$	11.8575	−	9.26161i	0.410344	−	0.320511i
$836$	−17.7051	+	24.3690i	−0.612344	+	0.842819i
$837$	−10.9910	+	69.3942i	−0.379903	+	2.39861i
$838$	2.06974	−	13.0678i	0.0714979	−	0.451420i
$839$	−19.1479	−	13.9117i	−0.661058	−	0.480286i	0.205962	−	0.978560i	$-0.433968\pi$
$839$	−19.1479	−	13.9117i	−0.661058	−	0.480286i	−0.867020	+	0.498273i	$0.833968\pi$
$840$	13.0093	−	28.8254i	0.448862	−	0.994570i
$841$	−7.47184	+	5.42861i	−0.257650	+	0.187193i
$842$	−6.38178	−	12.5250i	−0.219931	−	0.431638i
$843$	−56.2634	+	56.2634i	−1.93782	+	1.93782i
$844$	18.5697	+	6.03365i	0.639194	+	0.207687i
$845$	−7.76830	−	0.954839i	−0.267238	−	0.0328475i
$846$	−5.17206	+	1.68050i	−0.177819	+	0.0577769i
$847$	5.21064	+	1.62123i	0.179040	+	0.0557062i
$848$	5.09746	+	32.1841i	0.175047	+	1.10521i
$849$			51.8364i			1.77902i
$850$	−1.00509	+	1.60756i	−0.0344743	+	0.0551389i
$851$	3.76663			0.129119
$852$	7.33382	+	46.3039i	0.251253	+	1.58635i
$853$	−0.962940	−	0.490642i	−0.0329704	−	0.0167993i	0.437428	−	0.899254i	$-0.355890\pi$
$853$	−0.962940	−	0.490642i	−0.0329704	−	0.0167993i	−0.470398	+	0.882454i	$0.655890\pi$
$854$	−3.38644	−	6.44554i	−0.115882	−	0.220562i
$855$	−77.2742	+	42.8208i	−2.64272	+	1.46444i
$856$	−2.06054	+	6.34170i	−0.0704279	+	0.216755i
$857$	−29.3167	−	29.3167i	−1.00144	−	1.00144i	−0.999999	−	0.00143911i	$-0.999542\pi$
$857$	−29.3167	−	29.3167i	−1.00144	−	1.00144i	−0.00143911	−	0.999999i	$-0.500458\pi$
$858$	−11.5373	+	5.87854i	−0.393877	+	0.200690i
$859$	36.9931	−	26.8770i	1.26219	−	0.917033i	0.263325	−	0.964707i	$-0.415181\pi$
$859$	36.9931	−	26.8770i	1.26219	−	0.917033i	0.998863	+	0.0476742i	$0.0151809\pi$
$860$	26.6704	+	7.65130i	0.909451	+	0.260907i
$861$	79.9002	+	39.4595i	2.72299	+	1.34478i
$862$	1.15042	−	7.26347i	0.0391835	−	0.247395i
$863$	−6.36436	−	1.00802i	−0.216645	−	0.0343133i	0.0471681	−	0.998887i	$-0.484980\pi$
$863$	−6.36436	−	1.00802i	−0.216645	−	0.0343133i	−0.263814	+	0.964574i	$0.584980\pi$
$864$	−48.4926	−	35.2320i	−1.64975	−	1.19862i
$865$	14.9315	−	5.43245i	0.507686	−	0.184709i
$866$	−3.50018	−	4.81759i	−0.118941	−	0.163708i
$867$	−46.0017	+	23.4390i	−1.56230	+	0.796032i
$868$	14.9802	−	21.1707i	0.508461	−	0.718580i
$869$	25.3229	+	8.22792i	0.859022	+	0.279113i
$870$	−13.7133	+	2.66378i	−0.464926	+	0.0903105i
$871$	−2.87399	+	0.933816i	−0.0973814	+	0.0316411i
$872$	−26.5252	−	13.5152i	−0.898255	−	0.457684i
$873$	4.76513	−	0.754722i	0.161275	−	0.0255435i
$874$	−3.39340			−0.114784
$875$	1.18968	−	29.5565i	0.0402184	−	0.999191i
$876$	28.3299			0.957178
$877$	26.0262	−	4.12215i	0.878844	−	0.139195i	0.299322	−	0.954152i	$-0.403239\pi$
$877$	26.0262	−	4.12215i	0.878844	−	0.139195i	0.579522	+	0.814957i	$0.303239\pi$
$878$	−13.4869	−	6.87191i	−0.455160	−	0.231916i
$879$	69.2753	−	22.5089i	2.33660	−	0.759207i
$880$	−18.7826	+	3.64846i	−0.633161	+	0.122990i
$881$	27.5787	+	8.96086i	0.929150	+	0.301899i	0.734215	−	0.678917i	$-0.237551\pi$
$881$	27.5787	+	8.96086i	0.929150	+	0.301899i	0.194935	+	0.980816i	$0.437551\pi$
$882$	−9.46117	+	19.7772i	−0.318574	+	0.665934i
$883$	42.0851	−	21.4434i	1.41628	−	0.721629i	0.432602	−	0.901585i	$-0.357596\pi$
$883$	42.0851	−	21.4434i	1.41628	−	0.721629i	0.983675	+	0.179956i	$0.0575956\pi$
$884$	2.79891	+	3.85236i	0.0941374	+	0.129569i
$885$	−0.388057	+	0.141185i	−0.0130444	+	0.00474588i
$886$	12.8754	+	9.35455i	0.432559	+	0.314272i
$887$	−41.5454	−	6.58015i	−1.39496	−	0.220940i	−0.586718	−	0.809791i	$-0.699580\pi$
$887$	−41.5454	−	6.58015i	−1.39496	−	0.220940i	−0.808241	+	0.588852i	$0.799580\pi$
$888$	2.29538	−	14.4924i	0.0770278	−	0.486335i
$889$	3.67054	−	7.43235i	0.123106	−	0.249273i
$890$	9.49322	+	2.72345i	0.318213	+	0.0912904i
$891$	−47.9311	+	34.8240i	−1.60575	+	1.16665i
$892$	35.3181	−	17.9955i	1.18254	−	0.602533i
$893$	−6.85755	−	6.85755i	−0.229479	−	0.229479i
$894$	−1.33726	+	4.11565i	−0.0447245	+	0.137648i
$895$	23.0148	−	12.7534i	0.769299	−	0.426300i
$896$	13.4096	+	25.5231i	0.447984	+	0.852666i
$897$	11.9609	+	6.09438i	0.399362	+	0.203485i
$898$	0.755564	+	4.77044i	0.0252135	+	0.159192i
$899$	−24.1570			−0.805680
$900$	−61.9057	−	15.4517i	−2.06352	−	0.515056i
$901$			9.74988i			0.324815i
$902$	2.19733	+	13.8734i	0.0731631	+	0.461933i
$903$	−55.1532	−	17.1603i	−1.83538	−	0.571058i
$904$	9.74196	−	3.16536i	0.324013	−	0.105278i
$905$	−35.8171	−	4.40245i	−1.19060	−	0.146342i
$906$	−14.0782	−	4.57429i	−0.467718	−	0.151971i
$907$	−14.6541	+	14.6541i	−0.486582	+	0.486582i	−0.907226	−	0.420644i	$-0.861804\pi$
$907$	−14.6541	+	14.6541i	−0.486582	+	0.486582i	0.420644	+	0.907226i	$0.361804\pi$
$908$	12.1530	+	23.8516i	0.403312	+	0.791544i
$909$	−37.3477	+	27.1347i	−1.23875	+	0.900002i
$910$	7.35863	+	3.32104i	0.243936	+	0.110092i
$911$	−8.97934	−	6.52388i	−0.297499	−	0.216146i	0.429015	−	0.903297i	$-0.358861\pi$
$911$	−8.97934	−	6.52388i	−0.297499	−	0.216146i	−0.726514	+	0.687152i	$0.758861\pi$
$912$	7.93744	−	50.1150i	0.262835	−	1.65947i
$913$	0.479788	−	3.02926i	0.0158787	−	0.100254i
$914$	−6.65659	+	9.16201i	−0.220180	+	0.303052i
$915$	−34.7647	+	27.1539i	−1.14928	+	0.897682i
$916$	31.1064	+	42.8143i	1.02779	+	1.41462i
$917$	16.6547	−	12.4218i	0.549988	−	0.410204i
$918$	−3.46684	−	3.46684i	−0.114423	−	0.114423i
$919$	−27.9059	−	9.06719i	−0.920532	−	0.299099i	−0.189847	−	0.981814i	$-0.560799\pi$
$919$	−27.9059	−	9.06719i	−0.920532	−	0.299099i	−0.730685	+	0.682715i	$0.760799\pi$
$920$	−3.77910	−	3.52498i	−0.124593	−	0.116215i
$921$	−5.47562	−	16.8522i	−0.180428	−	0.555300i
$922$	4.48926	−	8.81066i	0.147846	−	0.290164i
$923$	−24.9257	+	3.94784i	−0.820440	+	0.129945i
$924$	44.6381	−	7.64383i	1.46849	−	0.251464i
$925$	−3.08390	−	13.3735i	−0.101398	−	0.439717i
$926$	8.96075			0.294469
$927$	−7.74846	−	48.9218i	−0.254493	−	1.60680i
$928$	9.35630	−	18.3628i	0.307136	−	0.602787i
$929$	−4.42172	−	13.6087i	−0.145072	−	0.446486i	0.851948	−	0.523626i	$-0.175421\pi$
$929$	−4.42172	−	13.6087i	−0.145072	−	0.446486i	−0.997020	+	0.0771402i	$0.975421\pi$
$930$	15.4738	+	7.21796i	0.507405	+	0.236686i
$931$	−39.0846	+	0.978525i	−1.28095	+	0.0320699i
$932$	14.1128	−	14.1128i	0.462279	−	0.462279i
$933$	31.3044	−	15.9504i	1.02486	−	0.522192i
$934$	−8.41799	+	6.11602i	−0.275445	+	0.200122i
$935$	−5.72154	+	0.199066i	−0.187114	+	0.00651015i
$936$	21.5839	−	29.7077i	0.705492	−	0.971026i
$937$	14.0017	+	2.21764i	0.457414	+	0.0724473i	0.380890	−	0.924620i	$-0.375618\pi$
$937$	14.0017	+	2.21764i	0.457414	+	0.0724473i	0.0765244	+	0.997068i	$0.475618\pi$
$938$	−1.14842	+	0.0143737i	−0.0374972	+	0.000469317i
$939$	−59.1164	+	81.3668i	−1.92919	+	2.65530i
$940$	−0.243542	−	6.99989i	−0.00794348	−	0.228311i
$941$	−20.6293	−	28.3938i	−0.672496	−	0.925611i	0.327318	−	0.944914i	$-0.393855\pi$
$941$	−20.6293	−	28.3938i	−0.672496	−	0.925611i	−0.999814	+	0.0193033i	$0.993855\pi$
$942$	−7.95091	−	15.6045i	−0.259055	−	0.508423i
$943$	10.2969	−	10.2969i	0.335314	−	0.335314i
$944$	0.0514631	−	0.158387i	0.00167498	−	0.00515506i
$945$	73.7877	+	20.1725i	2.40031	+	0.656213i
$946$	−2.81346	−	8.65893i	−0.0914734	−	0.281526i
$947$	13.6010	+	6.93008i	0.441974	+	0.225197i	0.660793	−	0.750568i	$-0.270220\pi$
$947$	13.6010	+	6.93008i	0.441974	+	0.225197i	−0.218818	+	0.975766i	$0.570220\pi$
$948$	−50.3672	+	7.97738i	−1.63585	+	0.259093i
$949$			15.2502i			0.495042i
$950$	2.77832	+	12.0483i	0.0901405	+	0.390899i
$951$		−	85.4672i		−	2.77147i
$952$	1.22461	+	3.61439i	0.0396897	+	0.117143i
$953$	11.5341	−	22.6369i	0.373625	−	0.733280i	−0.625264	−	0.780413i	$-0.715009\pi$
$953$	11.5341	−	22.6369i	0.373625	−	0.733280i	0.998889	+	0.0471336i	$0.0150086\pi$
$954$	33.9109	−	11.0183i	1.09790	−	0.356731i
$955$	−17.3337	+	18.5833i	−0.560904	+	0.601341i
$956$	−10.6634	+	32.8185i	−0.344879	+	1.06143i
$957$	−29.8284	−	29.8284i	−0.964215	−	0.964215i
$958$	2.45849	+	4.82506i	0.0794303	+	0.155891i
$959$	−22.8129	−	22.2489i	−0.736668	−	0.718456i
$960$	20.5381	−	16.0419i	0.662866	−	0.517750i
$961$	−1.19255	−	0.866439i	−0.0384694	−	0.0279496i
$962$	3.69967	+	0.585971i	0.119282	+	0.0188925i
$963$	−27.6614	−	4.38114i	−0.891378	−	0.141180i
$964$	−8.20817	−	5.96358i	−0.264367	−	0.192074i
$965$	5.61260	+	3.78679i	0.180676	+	0.121901i
$966$	3.65250	+	3.56220i	0.117517	+	0.114612i
$967$	5.00859	+	9.82991i	0.161065	+	0.316109i	0.957409	−	0.288736i	$-0.0932351\pi$
$967$	5.00859	+	9.82991i	0.161065	+	0.316109i	−0.796343	+	0.604845i	$0.793235\pi$
$968$	−2.45636	−	2.45636i	−0.0789504	−	0.0789504i
$969$	4.69146	−	14.4388i	0.150712	−	0.463842i
$970$	0.0823749	−	0.670179i	0.00264490	−	0.0215181i
$971$	33.5408	−	10.8981i	1.07638	−	0.349736i	0.283409	−	0.958999i	$-0.408535\pi$
$971$	33.5408	−	10.8981i	1.07638	−	0.349736i	0.792968	+	0.609263i	$0.208535\pi$
$972$	19.7455	−	38.7527i	0.633337	−	1.24299i
$973$	31.7893	−	10.7707i	1.01912	−	0.345291i
$974$		−	0.602132i		−	0.0192936i
$975$	11.8453	−	47.4570i	0.379353	−	1.51984i
$976$		−	17.7904i		−	0.569457i
$977$	−28.5499	+	4.52186i	−0.913393	+	0.144667i	−0.595403	−	0.803427i	$-0.703008\pi$
$977$	−28.5499	+	4.52186i	−0.913393	+	0.144667i	−0.317990	+	0.948094i	$0.603008\pi$
$978$	16.6167	+	8.46661i	0.531342	+	0.270732i
$979$	9.21572	+	28.3631i	0.294536	+	0.906487i
$980$	−21.1240	−	18.7371i	−0.674782	−	0.598535i
$981$	38.6381	−	118.916i	1.23362	−	3.79669i
$982$	5.83136	−	5.83136i	0.186086	−	0.186086i
$983$	8.98984	+	17.6435i	0.286731	+	0.562742i	0.988779	−	0.149389i	$-0.0477305\pi$
$983$	8.98984	+	17.6435i	0.286731	+	0.562742i	−0.702047	+	0.712130i	$0.747731\pi$
$984$	−33.3434	−	45.8932i	−1.06295	−	1.46302i
$985$	−26.4295	−	7.58219i	−0.842112	−	0.241589i
$986$	0.990846	−	1.36378i	0.0315550	−	0.0434317i
$987$	0.182482	+	14.5798i	0.00580846	+	0.464081i
$988$	30.6725	+	4.85805i	0.975823	+	0.154555i
$989$	−5.54800	+	7.63617i	−0.176416	+	0.242816i
$990$	7.15826	+	19.6750i	0.227505	+	0.625313i
$991$	−3.58816	+	2.60695i	−0.113982	+	0.0828125i	−0.643316	−	0.765601i	$-0.722442\pi$
$991$	−3.58816	+	2.60695i	−0.113982	+	0.0828125i	0.529334	+	0.848413i	$0.322442\pi$
$992$	−22.4439	+	11.4358i	−0.712596	+	0.363086i
$993$	19.7683	−	19.7683i	0.627328	−	0.627328i
$994$	−9.49137	−	1.38175i	−0.301048	−	0.0438265i
$995$	13.5454	−	2.63115i	0.429418	−	0.0834132i
$996$	1.81518	+	5.58655i	0.0575162	+	0.177017i
$997$	3.85288	−	7.56170i	0.122022	−	0.239481i	−0.821913	−	0.569613i	$-0.807093\pi$
$997$	3.85288	−	7.56170i	0.122022	−	0.239481i	0.943935	+	0.330132i	$0.107093\pi$
$998$	−1.57805	−	9.96342i	−0.0499523	−	0.315387i
$999$	35.4916			1.12291

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.s.a.13.10	yes	144
5.2	odd	4		875.2.s.b.832.10		144
5.3	odd	4		875.2.s.a.832.9		144
5.4	even	2		875.2.s.c.293.9		144
7.6	odd	2	inner	175.2.s.a.13.9	✓	144
25.2	odd	20	inner	175.2.s.a.27.9	yes	144
25.11	even	5		875.2.s.b.468.9		144
25.14	even	10		875.2.s.a.468.10		144
25.23	odd	20		875.2.s.c.657.10		144
35.13	even	4		875.2.s.a.832.10		144
35.27	even	4		875.2.s.b.832.9		144
35.34	odd	2		875.2.s.c.293.10		144
175.27	even	20	inner	175.2.s.a.27.10	yes	144
175.48	even	20		875.2.s.c.657.9		144
175.111	odd	10		875.2.s.b.468.10		144
175.139	odd	10		875.2.s.a.468.9		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.s.a.13.9	✓	144	7.6	odd	2	inner
175.2.s.a.13.10	yes	144	1.1	even	1	trivial
175.2.s.a.27.9	yes	144	25.2	odd	20	inner
175.2.s.a.27.10	yes	144	175.27	even	20	inner
875.2.s.a.468.9		144	175.139	odd	10
875.2.s.a.468.10		144	25.14	even	10
875.2.s.a.832.9		144	5.3	odd	4
875.2.s.a.832.10		144	35.13	even	4
875.2.s.b.468.9		144	25.11	even	5
875.2.s.b.468.10		144	175.111	odd	10
875.2.s.b.832.9		144	35.27	even	4
875.2.s.b.832.10		144	5.2	odd	4
875.2.s.c.293.9		144	5.4	even	2
875.2.s.c.293.10		144	35.34	odd	2
875.2.s.c.657.9		144	175.48	even	20
875.2.s.c.657.10		144	25.23	odd	20

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.s (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.437303 + 0.0692620i) q^{2} +(2.82799 + 1.44093i) q^{3} +(-1.71568 + 0.557457i) q^{4} +(-2.19504 + 0.426380i) q^{5} +(-1.33649 - 0.434253i) q^{6} +(-1.52822 + 2.15975i) q^{7} +(1.50065 - 0.764621i) q^{8} +(4.15790 + 5.72286i) q^{9} +O(q^{10})\)	\(q+(-0.437303 + 0.0692620i) q^{2} +(2.82799 + 1.44093i) q^{3} +(-1.71568 + 0.557457i) q^{4} +(-2.19504 + 0.426380i) q^{5} +(-1.33649 - 0.434253i) q^{6} +(-1.52822 + 2.15975i) q^{7} +(1.50065 - 0.764621i) q^{8} +(4.15790 + 5.72286i) q^{9} +(0.930365 - 0.338490i) q^{10} +(2.41860 + 1.75722i) q^{11} +(-5.65518 - 0.895693i) q^{12} +(0.482157 - 3.04422i) q^{13} +(0.518708 - 1.05031i) q^{14} +(-6.82194 - 1.95711i) q^{15} +(2.31560 - 1.68238i) q^{16} +(0.763071 - 0.388804i) q^{17} +(-2.21464 - 2.21464i) q^{18} +(1.72594 - 5.31191i) q^{19} +(3.52829 - 1.95517i) q^{20} +(-7.43387 + 3.90570i) q^{21} +(-1.17937 - 0.600919i) q^{22} +(0.214665 + 1.35534i) q^{23} +5.34561 q^{24} +(4.63640 - 1.87184i) q^{25} +1.36464i q^{26} +(2.02271 + 12.7709i) q^{27} +(1.41797 - 4.55736i) q^{28} +(-4.22812 + 1.37380i) q^{29} +(3.11881 + 0.383348i) q^{30} +(5.16783 + 1.67913i) q^{31} +(-3.27794 + 3.27794i) q^{32} +(4.30775 + 8.45444i) q^{33} +(-0.306764 + 0.222877i) q^{34} +(2.43364 - 5.39235i) q^{35} +(-10.3239 - 7.50072i) q^{36} +(0.429395 - 2.71109i) q^{37} +(-0.386847 + 2.44245i) q^{38} +(5.75006 - 7.91428i) q^{39} +(-2.96797 + 2.31822i) q^{40} +(-6.23753 - 8.58522i) q^{41} +(2.98034 - 2.22286i) q^{42} +(4.86378 + 4.86378i) q^{43} +(-5.12911 - 1.66655i) q^{44} +(-11.5669 - 10.7891i) q^{45} +(-0.187747 - 0.577827i) q^{46} +(0.788291 - 1.54711i) q^{47} +(8.97271 - 1.42114i) q^{48} +(-2.32906 - 6.60117i) q^{49} +(-1.89786 + 1.13969i) q^{50} +2.71820 q^{51} +(0.869797 + 5.49168i) q^{52} +(-5.16846 + 10.1437i) q^{53} +(-1.76908 - 5.44465i) q^{54} +(-6.05817 - 2.82592i) q^{55} +(-0.641942 + 4.40955i) q^{56} +(12.5351 - 12.5351i) q^{57} +(1.75382 - 0.893614i) q^{58} +(0.0470722 - 0.0342000i) q^{59} +(12.7953 - 0.445177i) q^{60} +(3.65341 - 5.02849i) q^{61} +(-2.37621 - 0.376354i) q^{62} +(-18.7142 + 0.234228i) q^{63} +(-2.15835 + 2.97071i) q^{64} +(0.239642 + 6.88777i) q^{65} +(-2.46936 - 3.39879i) q^{66} +(-0.445112 - 0.873581i) q^{67} +(-1.09244 + 1.09244i) q^{68} +(-1.34589 + 4.14221i) q^{69} +(-0.690752 + 2.52665i) q^{70} +(-2.53019 - 7.78713i) q^{71} +(10.6154 + 5.40881i) q^{72} +(-4.88695 + 0.774018i) q^{73} +1.21531i q^{74} +(15.8089 + 1.38719i) q^{75} +10.0757i q^{76} +(-7.49131 + 2.53816i) q^{77} +(-1.96636 + 3.85920i) q^{78} +(8.47048 - 2.75222i) q^{79} +(-4.36550 + 4.68023i) q^{80} +(-6.12400 + 18.8477i) q^{81} +(3.32232 + 3.32232i) q^{82} +(-0.465755 - 0.914096i) q^{83} +(10.5769 - 10.8450i) q^{84} +(-1.50919 + 1.17880i) q^{85} +(-2.46382 - 1.79007i) q^{86} +(-13.9366 - 2.20735i) q^{87} +(4.97308 + 0.787659i) q^{88} +(8.07045 + 5.86353i) q^{89} +(5.80550 + 3.91694i) q^{90} +(5.83792 + 5.69359i) q^{91} +(-1.12384 - 2.20566i) q^{92} +(12.1951 + 12.1951i) q^{93} +(-0.237566 + 0.731153i) q^{94} +(-1.52362 + 12.3958i) q^{95} +(-13.9933 + 4.54670i) q^{96} +(0.309632 - 0.607687i) q^{97} +(1.47572 + 2.72540i) q^{98} +21.1476i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 16 q^{2} - 20 q^{4} - 14 q^{7} - 12 q^{8} - 20 q^{9}+O(q^{10}) \) 144 * q - 16 * q^2 - 20 * q^4 - 14 * q^7 - 12 * q^8 - 20 * q^9	\( 144 q - 16 q^{2} - 20 q^{4} - 14 q^{7} - 12 q^{8} - 20 q^{9} - 12 q^{11} - 10 q^{14} - 20 q^{15} + 12 q^{16} - 28 q^{18} - 6 q^{21} + 16 q^{22} - 8 q^{23} - 20 q^{25} - 70 q^{28} + 40 q^{30} - 20 q^{32} - 40 q^{35} - 28 q^{36} + 4 q^{37} - 60 q^{39} - 30 q^{42} + 72 q^{43} - 20 q^{44} - 12 q^{46} + 140 q^{50} - 32 q^{51} - 104 q^{53} - 22 q^{56} + 120 q^{57} - 32 q^{58} - 120 q^{60} + 48 q^{63} + 40 q^{64} - 20 q^{65} - 16 q^{67} + 90 q^{70} - 12 q^{71} - 64 q^{72} + 74 q^{77} + 60 q^{78} - 20 q^{79} - 8 q^{81} + 190 q^{84} - 12 q^{86} + 92 q^{88} - 6 q^{91} - 20 q^{92} - 160 q^{93} + 80 q^{95} + 162 q^{98}+O(q^{100}) \) 144 * q - 16 * q^2 - 20 * q^4 - 14 * q^7 - 12 * q^8 - 20 * q^9 - 12 * q^11 - 10 * q^14 - 20 * q^15 + 12 * q^16 - 28 * q^18 - 6 * q^21 + 16 * q^22 - 8 * q^23 - 20 * q^25 - 70 * q^28 + 40 * q^30 - 20 * q^32 - 40 * q^35 - 28 * q^36 + 4 * q^37 - 60 * q^39 - 30 * q^42 + 72 * q^43 - 20 * q^44 - 12 * q^46 + 140 * q^50 - 32 * q^51 - 104 * q^53 - 22 * q^56 + 120 * q^57 - 32 * q^58 - 120 * q^60 + 48 * q^63 + 40 * q^64 - 20 * q^65 - 16 * q^67 + 90 * q^70 - 12 * q^71 - 64 * q^72 + 74 * q^77 + 60 * q^78 - 20 * q^79 - 8 * q^81 + 190 * q^84 - 12 * q^86 + 92 * q^88 - 6 * q^91 - 20 * q^92 - 160 * q^93 + 80 * q^95 + 162 * q^98

Introduction

L-functions

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