LMFDB - Embedded newform 572.2.bk.a.31.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(31,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 12, 15]))

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

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

chi := DirichletCharacter("572.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bk (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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$80$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			31.7
Character	$\chi$	$=$	572.31
Dual form			572.2.bk.a.203.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37479 + 0.331572i) q^{2} +(1.89320 + 2.60576i) q^{3} +(1.78012 - 0.911688i) q^{4} +(-3.02502 - 1.54132i) q^{5} +(-3.46676 - 2.95466i) q^{6} +(-0.922158 + 0.146055i) q^{7} +(-2.14501 + 1.84362i) q^{8} +(-2.27875 + 7.01328i) q^{9} +O(q^{10})$	\(q+(-1.37479 + 0.331572i) q^{2} +(1.89320 + 2.60576i) q^{3} +(1.78012 - 0.911688i) q^{4} +(-3.02502 - 1.54132i) q^{5} +(-3.46676 - 2.95466i) q^{6} +(-0.922158 + 0.146055i) q^{7} +(-2.14501 + 1.84362i) q^{8} +(-2.27875 + 7.01328i) q^{9} +(4.66983 + 1.11599i) q^{10} +(-3.25973 + 0.611685i) q^{11} +(5.74576 + 2.91256i) q^{12} +(-1.98867 - 3.00752i) q^{13} +(1.21935 - 0.506558i) q^{14} +(-1.71063 - 10.8005i) q^{15} +(2.33765 - 3.24583i) q^{16} +(3.56213 - 1.15741i) q^{17} +(0.807406 - 10.3974i) q^{18} +(-0.700372 - 0.110928i) q^{19} +(-6.79009 + 0.0141323i) q^{20} +(-2.12641 - 2.12641i) q^{21} +(4.27864 - 1.92178i) q^{22} -6.09630 q^{23} +(-8.86496 - 2.09904i) q^{24} +(3.83612 + 5.27996i) q^{25} +(3.73123 + 3.47533i) q^{26} +(-13.3993 + 4.35369i) q^{27} +(-1.50839 + 1.10072i) q^{28} +(-6.25168 - 4.54211i) q^{29} +(5.93291 + 14.2813i) q^{30} +(2.86494 - 1.45976i) q^{31} +(-2.13756 + 5.23745i) q^{32} +(-7.76522 - 7.33604i) q^{33} +(-4.51343 + 2.77230i) q^{34} +(3.01466 + 0.979523i) q^{35} +(2.33747 + 14.5620i) q^{36} +(1.08496 + 6.85019i) q^{37} +(0.999649 - 0.0797209i) q^{38} +(4.07193 - 10.8758i) q^{39} +(9.33030 - 2.27084i) q^{40} +(0.459342 - 2.90017i) q^{41} +(3.62844 + 2.21832i) q^{42} -1.66833 q^{43} +(-5.24504 + 4.06073i) q^{44} +(17.7030 - 17.7030i) q^{45} +(8.38116 - 2.02136i) q^{46} +(0.394064 - 2.48802i) q^{47} +(12.8835 - 0.0536294i) q^{48} +(-5.82835 + 1.89375i) q^{49} +(-7.02456 - 5.98691i) q^{50} +(9.75974 + 7.09087i) q^{51} +(-6.28200 - 3.54070i) q^{52} +(-3.33094 + 10.2516i) q^{53} +(16.9777 - 10.4283i) q^{54} +(10.8035 + 3.17394i) q^{55} +(1.70876 - 2.01340i) q^{56} +(-1.03689 - 2.03501i) q^{57} +(10.1008 + 4.17159i) q^{58} +(0.803695 - 0.127293i) q^{59} +(-12.8918 - 17.6666i) q^{60} +(-4.40460 - 13.5560i) q^{61} +(-3.45469 + 2.95681i) q^{62} +(1.07704 - 6.80017i) q^{63} +(1.20212 - 7.90917i) q^{64} +(1.38021 + 12.1630i) q^{65} +(13.1080 + 7.51082i) q^{66} +(5.51848 + 5.51848i) q^{67} +(5.28582 - 5.30787i) q^{68} +(-11.5415 - 15.8855i) q^{69} +(-4.46932 - 0.347064i) q^{70} +(-6.27371 + 12.3129i) q^{71} +(-8.04189 - 19.2447i) q^{72} +(0.911449 + 5.75466i) q^{73} +(-3.76293 - 9.05785i) q^{74} +(-6.49580 + 19.9920i) q^{75} +(-1.34788 + 0.441056i) q^{76} +(2.91665 - 1.04017i) q^{77} +(-1.99194 + 16.3022i) q^{78} +(0.545807 + 0.177343i) q^{79} +(-12.0743 + 6.21560i) q^{80} +(-18.8146 - 13.6696i) q^{81} +(0.330116 + 4.13945i) q^{82} +(-2.94275 + 5.77547i) q^{83} +(-5.72389 - 1.84664i) q^{84} +(-12.5594 - 1.98922i) q^{85} +(2.29361 - 0.553172i) q^{86} -24.8895i q^{87} +(5.86443 - 7.32178i) q^{88} +(0.876154 + 0.876154i) q^{89} +(-18.4681 + 30.2078i) q^{90} +(2.27314 + 2.48295i) q^{91} +(-10.8521 + 5.55792i) q^{92} +(9.22769 + 4.70174i) q^{93} +(0.283203 + 3.55118i) q^{94} +(1.94766 + 1.41506i) q^{95} +(-17.6944 + 4.34554i) q^{96} +(-4.11683 - 8.07973i) q^{97} +(7.38487 - 4.53603i) q^{98} +(3.13820 - 24.2553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9}+O(q^{10}) $ 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9	$ 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9} - 12 q^{13} + 4 q^{14} - 36 q^{16} - 10 q^{18} - 60 q^{20} - 56 q^{21} - 44 q^{22} - 14 q^{24} + 26 q^{26} - 14 q^{28} - 24 q^{29} - 16 q^{32} - 28 q^{33} + 12 q^{34} - 12 q^{37} + 4 q^{40} - 36 q^{41} - 8 q^{42} + 26 q^{44} - 16 q^{45} - 50 q^{46} + 48 q^{48} + 36 q^{50} - 52 q^{52} - 40 q^{53} + 116 q^{54} - 36 q^{57} - 70 q^{58} + 52 q^{60} - 8 q^{61} - 48 q^{65} - 228 q^{66} - 44 q^{68} - 68 q^{70} - 38 q^{72} - 12 q^{73} - 12 q^{74} + 108 q^{76} + 108 q^{78} + 62 q^{80} - 168 q^{81} - 36 q^{84} - 52 q^{85} - 62 q^{86} + 16 q^{89} - 80 q^{92} - 4 q^{93} - 124 q^{94} - 132 q^{96} - 4 q^{97} - 108 q^{98}+O(q^{100}) $ 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9 - 12 * q^13 + 4 * q^14 - 36 * q^16 - 10 * q^18 - 60 * q^20 - 56 * q^21 - 44 * q^22 - 14 * q^24 + 26 * q^26 - 14 * q^28 - 24 * q^29 - 16 * q^32 - 28 * q^33 + 12 * q^34 - 12 * q^37 + 4 * q^40 - 36 * q^41 - 8 * q^42 + 26 * q^44 - 16 * q^45 - 50 * q^46 + 48 * q^48 + 36 * q^50 - 52 * q^52 - 40 * q^53 + 116 * q^54 - 36 * q^57 - 70 * q^58 + 52 * q^60 - 8 * q^61 - 48 * q^65 - 228 * q^66 - 44 * q^68 - 68 * q^70 - 38 * q^72 - 12 * q^73 - 12 * q^74 + 108 * q^76 + 108 * q^78 + 62 * q^80 - 168 * q^81 - 36 * q^84 - 52 * q^85 - 62 * q^86 + 16 * q^89 - 80 * q^92 - 4 * q^93 - 124 * q^94 - 132 * q^96 - 4 * q^97 - 108 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.37479	+	0.331572i	−0.972126	+	0.234457i
$2$	−1.37479	+	0.331572i	−0.972126	+	0.234457i
$3$	1.89320	+	2.60576i	1.09304	+	1.50444i	0.844303	+	0.535866i	$0.180015\pi$
$3$	1.89320	+	2.60576i	1.09304	+	1.50444i	0.248735	+	0.968572i	$0.419985\pi$
$4$	1.78012	−	0.911688i	0.890060	−	0.455844i
$5$	−3.02502	−	1.54132i	−1.35283	−	0.689300i	−0.380908	−	0.924613i	$-0.624389\pi$
$5$	−3.02502	−	1.54132i	−1.35283	−	0.689300i	−0.971920	+	0.235313i	$0.924389\pi$
$6$	−3.46676	−	2.95466i	−1.41530	−	1.20623i
$7$	−0.922158	+	0.146055i	−0.348543	+	0.0552038i	−0.328252	−	0.944590i	$-0.606459\pi$
$7$	−0.922158	+	0.146055i	−0.348543	+	0.0552038i	−0.0202914	+	0.999794i	$0.506459\pi$
$8$	−2.14501	+	1.84362i	−0.758375	+	0.651819i
$9$	−2.27875	+	7.01328i	−0.759584	+	2.33776i
$10$	4.66983	+	1.11599i	1.47673	+	0.352907i
$11$	−3.25973	+	0.611685i	−0.982846	+	0.184430i
$11$	−3.25973	+	0.611685i	−0.982846	+	0.184430i
$12$	5.74576	+	2.91256i	1.65866	+	0.840785i
$13$	−1.98867	−	3.00752i	−0.551559	−	0.834136i
$13$	−1.98867	−	3.00752i	−0.551559	−	0.834136i
$14$	1.21935	−	0.506558i	0.325885	−	0.135383i
$15$	−1.71063	−	10.8005i	−0.441683	−	2.78868i
$16$	2.33765	−	3.24583i	0.584413	−	0.811457i
$17$	3.56213	−	1.15741i	0.863943	−	0.280712i	0.156669	−	0.987651i	$-0.449924\pi$
$17$	3.56213	−	1.15741i	0.863943	−	0.280712i	0.707275	+	0.706939i	$0.249924\pi$
$18$	0.807406	−	10.3974i	0.190307	−	2.45069i
$19$	−0.700372	−	0.110928i	−0.160676	−	0.0254486i	0.0755779	−	0.997140i	$-0.475920\pi$
$19$	−0.700372	−	0.110928i	−0.160676	−	0.0254486i	−0.236254	+	0.971691i	$0.575920\pi$
$20$	−6.79009	+	0.0141323i	−1.51831	+	0.00316008i
$21$	−2.12641	−	2.12641i	−0.464021	−	0.464021i
$22$	4.27864	−	1.92178i	0.912209	−	0.409725i
$23$	−6.09630			−1.27117			−0.635583	−	0.772033i	$-0.719240\pi$
$23$	−6.09630			−1.27117			−0.635583	+	0.772033i	$0.719240\pi$
$24$	−8.86496	−	2.09904i	−1.80955	−	0.428465i
$25$	3.83612	+	5.27996i	0.767223	+	1.05599i
$26$	3.73123	+	3.47533i	0.731754	+	0.681569i
$27$	−13.3993	+	4.35369i	−2.57869	+	0.837868i
$28$	−1.50839	+	1.10072i	−0.285060	+	0.208016i
$29$	−6.25168	−	4.54211i	−1.16091	−	0.843449i	−0.171016	−	0.985268i	$-0.554705\pi$
$29$	−6.25168	−	4.54211i	−1.16091	−	0.843449i	−0.989893	+	0.141819i	$0.954705\pi$
$30$	5.93291	+	14.2813i	1.08320	+	2.60739i
$31$	2.86494	−	1.45976i	0.514559	−	0.262181i	−0.177373	−	0.984144i	$-0.556760\pi$
$31$	2.86494	−	1.45976i	0.514559	−	0.262181i	0.691932	+	0.721963i	$0.256760\pi$
$32$	−2.13756	+	5.23745i	−0.377871	+	0.925858i
$33$	−7.76522	−	7.33604i	−1.35175	−	1.27704i
$34$	−4.51343	+	2.77230i	−0.774047	+	0.475445i
$35$	3.01466	+	0.979523i	0.509571	+	0.165570i
$36$	2.33747	+	14.5620i	0.389578	+	2.42700i
$37$	1.08496	+	6.85019i	0.178367	+	1.12616i	0.900643	+	0.434559i	$0.143096\pi$
$37$	1.08496	+	6.85019i	0.178367	+	1.12616i	−0.722276	+	0.691604i	$0.756904\pi$
$38$	0.999649	−	0.0797209i	0.162164	−	0.0129324i
$39$	4.07193	−	10.8758i	0.652031	−	1.74153i
$40$	9.33030	−	2.27084i	1.47525	−	0.359051i
$41$	0.459342	−	2.90017i	0.0717372	−	0.452931i	−0.925506	−	0.378732i	$-0.876360\pi$
$41$	0.459342	−	2.90017i	0.0717372	−	0.452931i	0.997243	−	0.0741986i	$-0.0236399\pi$
$42$	3.62844	+	2.21832i	0.559881	+	0.342294i
$43$	−1.66833			−0.254418			−0.127209	−	0.991876i	$-0.540602\pi$
$43$	−1.66833			−0.254418			−0.127209	+	0.991876i	$0.540602\pi$
$44$	−5.24504	+	4.06073i	−0.790720	+	0.612178i
$45$	17.7030	−	17.7030i	2.63900	−	2.63900i
$46$	8.38116	−	2.02136i	1.23573	−	0.298034i
$47$	0.394064	−	2.48802i	0.0574802	−	0.362916i	−0.942136	−	0.335230i	$-0.891186\pi$
$47$	0.394064	−	2.48802i	0.0574802	−	0.362916i	0.999617	−	0.0276861i	$-0.00881388\pi$
$48$	12.8835	−	0.0536294i	1.85957	−	0.00774073i
$49$	−5.82835	+	1.89375i	−0.832622	+	0.270535i
$50$	−7.02456	−	5.98691i	−0.993423	−	0.846677i
$51$	9.75974	+	7.09087i	1.36664	+	0.992920i
$52$	−6.28200	−	3.54070i	−0.871156	−	0.491006i
$53$	−3.33094	+	10.2516i	−0.457539	+	1.40816i	0.410589	+	0.911821i	$0.365323\pi$
$53$	−3.33094	+	10.2516i	−0.457539	+	1.40816i	−0.868128	+	0.496340i	$0.834677\pi$
$54$	16.9777	−	10.4283i	2.31037	−	1.41911i
$55$	10.8035	+	3.17394i	1.45675	+	0.427974i
$56$	1.70876	−	2.01340i	0.228343	−	0.269052i
$57$	−1.03689	−	2.03501i	−0.137340	−	0.269544i
$58$	10.1008	+	4.17159i	1.32630	+	0.547756i
$59$	0.803695	−	0.127293i	0.104632	−	0.0165721i	−0.103899	−	0.994588i	$-0.533132\pi$
$59$	0.803695	−	0.127293i	0.104632	−	0.0165721i	0.208531	+	0.978016i	$0.433132\pi$
$60$	−12.8918	−	17.6666i	−1.66433	−	2.28075i
$61$	−4.40460	−	13.5560i	−0.563951	−	1.73566i	−0.671048	−	0.741414i	$-0.734156\pi$
$61$	−4.40460	−	13.5560i	−0.563951	−	1.73566i	0.107097	−	0.994249i	$-0.465844\pi$
$62$	−3.45469	+	2.95681i	−0.438746	+	0.375515i
$63$	1.07704	−	6.80017i	0.135694	−	0.856741i
$64$	1.20212	−	7.90917i	0.150264	−	0.988646i
$65$	1.38021	+	12.1630i	0.171194	+	1.50863i
$66$	13.1080	+	7.51082i	1.61348	+	0.924518i
$67$	5.51848	+	5.51848i	0.674189	+	0.674189i	0.958679	−	0.284490i	$-0.0918242\pi$
$67$	5.51848	+	5.51848i	0.674189	+	0.674189i	−0.284490	+	0.958679i	$0.591824\pi$
$68$	5.28582	−	5.30787i	0.641000	−	0.643674i
$69$	−11.5415	−	15.8855i	−1.38943	−	1.91239i
$70$	−4.46932	−	0.347064i	−0.534186	−	0.0414821i
$71$	−6.27371	+	12.3129i	−0.744553	+	1.46127i	0.137692	+	0.990475i	$0.456032\pi$
$71$	−6.27371	+	12.3129i	−0.744553	+	1.46127i	−0.882244	+	0.470792i	$0.843968\pi$
$72$	−8.04189	−	19.2447i	−0.947746	−	2.26801i
$73$	0.911449	+	5.75466i	0.106677	+	0.673532i	0.981841	+	0.189706i	$0.0607534\pi$
$73$	0.911449	+	5.75466i	0.106677	+	0.673532i	−0.875164	+	0.483826i	$0.839247\pi$
$74$	−3.76293	−	9.05785i	−0.437432	−	1.05295i
$75$	−6.49580	+	19.9920i	−0.750070	+	2.30848i
$76$	−1.34788	+	0.441056i	−0.154612	+	0.0505926i
$77$	2.91665	−	1.04017i	0.332383	−	0.118539i
$78$	−1.99194	+	16.3022i	−0.225543	+	1.84586i
$79$	0.545807	+	0.177343i	0.0614081	+	0.0199527i	0.339560	−	0.940584i	$-0.389722\pi$
$79$	0.545807	+	0.177343i	0.0614081	+	0.0199527i	−0.278152	+	0.960537i	$0.589722\pi$
$80$	−12.0743	+	6.21560i	−1.34995	+	0.694926i
$81$	−18.8146	−	13.6696i	−2.09051	−	1.51885i
$82$	0.330116	+	4.13945i	0.0364552	+	0.457125i
$83$	−2.94275	+	5.77547i	−0.323009	+	0.633940i	−0.994224	−	0.107322i	$-0.965772\pi$
$83$	−2.94275	+	5.77547i	−0.323009	+	0.633940i	0.671216	+	0.741262i	$0.265772\pi$
$84$	−5.72389	−	1.84664i	−0.624528	−	0.201485i
$85$	−12.5594	−	1.98922i	−1.36226	−	0.215761i
$86$	2.29361	−	0.553172i	0.247326	−	0.0596500i
$87$		−	24.8895i		−	2.66844i
$88$	5.86443	−	7.32178i	0.625150	−	0.780504i
$89$	0.876154	+	0.876154i	0.0928722	+	0.0928722i	0.752016	−	0.659144i	$-0.229081\pi$
$89$	0.876154	+	0.876154i	0.0928722	+	0.0928722i	−0.659144	+	0.752016i	$0.729081\pi$
$90$	−18.4681	+	30.2078i	−1.94671	+	3.18418i
$91$	2.27314	+	2.48295i	0.238289	+	0.260284i
$92$	−10.8521	+	5.55792i	−1.13141	+	0.579453i
$93$	9.22769	+	4.70174i	0.956866	+	0.487548i
$94$	0.283203	+	3.55118i	0.0292101	+	0.366277i
$95$	1.94766	+	1.41506i	0.199826	+	0.145182i
$96$	−17.6944	+	4.34554i	−1.80592	+	0.443515i
$97$	−4.11683	−	8.07973i	−0.418001	−	0.820373i	−0.999974	−	0.00716495i	$-0.997719\pi$
$97$	−4.11683	−	8.07973i	−0.418001	−	0.820373i	0.581974	−	0.813208i	$-0.302281\pi$
$98$	7.38487	−	4.53603i	0.745985	−	0.458209i
$99$	3.13820	−	24.2553i	0.315401	−	2.43775i
$100$	11.6424	+	5.90162i	1.16424	+	0.590162i
$101$	12.2496	+	3.98015i	1.21888	+	0.396040i	0.846676	−	0.532109i	$-0.178600\pi$
$101$	12.2496	+	3.98015i	1.21888	+	0.396040i	0.372209	+	0.928149i	$0.378600\pi$
$102$	−15.7688	−	6.51242i	−1.56134	−	0.644826i
$103$	5.32908	+	3.87180i	0.525090	+	0.381500i	0.818518	−	0.574481i	$-0.194796\pi$
$103$	5.32908	+	3.87180i	0.525090	+	0.381500i	−0.293428	+	0.955981i	$0.594796\pi$
$104$	9.81045	+	2.78479i	0.961994	+	0.273071i
$105$	3.15494	+	9.70992i	0.307891	+	0.947591i
$106$	1.18021	−	15.1982i	0.114633	−	1.47618i
$107$	−7.24913	−	9.97758i	−0.700800	−	0.964569i	−0.999946	−	0.0103615i	$-0.996702\pi$
$107$	−7.24913	−	9.97758i	−0.700800	−	0.964569i	0.299146	−	0.954207i	$-0.403298\pi$
$108$	−19.8831	+	19.9661i	−1.91325	+	1.92123i
$109$	−7.69902	+	7.69902i	−0.737433	+	0.737433i	−0.972080	−	0.234648i	$-0.924606\pi$
$109$	−7.69902	+	7.69902i	−0.737433	+	0.737433i	0.234648	+	0.972080i	$0.424606\pi$
$110$	−15.9050	−	0.781356i	−1.51649	−	0.0744993i
$111$	−15.7959	+	15.7959i	−1.49928	+	1.49928i
$112$	−1.68161	+	3.33459i	−0.158897	+	0.315089i
$113$	2.79687	−	2.03204i	0.263107	−	0.191159i	−0.448409	−	0.893829i	$-0.648009\pi$
$113$	2.79687	−	2.03204i	0.263107	−	0.191159i	0.711516	+	0.702670i	$0.248009\pi$
$114$	2.10027	+	2.45392i	0.196708	+	0.229831i
$115$	18.4414	+	9.39636i	1.71967	+	0.876215i
$116$	−15.2697	−	2.38592i	−1.41776	−	0.221527i
$117$	25.6243	−	7.09372i	2.36896	−	0.655815i
$118$	−1.06271	+	0.441485i	−0.0978302	+	0.0406419i
$119$	−3.11580	+	1.58758i	−0.285625	+	0.145533i
$120$	23.5814	+	20.0134i	2.15267	+	1.82696i
$121$	10.2517	−	3.98786i	0.931971	−	0.362533i
$122$	10.5502	+	17.1762i	0.955170	+	1.55506i
$123$	8.42679	−	4.29366i	0.759818	−	0.387146i
$124$	3.76909	−	5.21048i	0.338474	−	0.467915i
$125$	−0.810672	−	5.11838i	−0.0725087	−	0.457802i
$126$	0.774039	+	9.70596i	0.0689569	+	0.864675i
$127$	2.92089	+	8.98958i	0.259187	+	0.797697i	0.992976	+	0.118318i	$0.0377504\pi$
$127$	2.92089	+	8.98958i	0.259187	+	0.797697i	−0.733788	+	0.679378i	$0.762250\pi$
$128$	0.969801	+	11.2721i	0.0857191	+	0.996319i
$129$	−3.15847	−	4.34727i	−0.278088	−	0.382755i
$130$	−5.93041	−	16.2640i	−0.520132	−	1.42644i
$131$		−	0.0126254i		−	0.00110309i	−1.00000		0.000551545i	$-0.999824\pi$
$131$		−	0.0126254i		−	0.00110309i	1.00000		0.000551545i	$-0.000175562\pi$
$132$	−20.5112	−	5.97957i	−1.78527	−	0.520455i
$133$	0.662055			0.0574075
$134$	−9.41655	−	5.75700i	−0.813466	−	0.497329i
$135$	47.2435	+	7.48263i	4.06607	+	0.644003i
$136$	−5.50698	+	9.04987i	−0.472219	+	0.776020i
$137$	4.28924	−	8.41811i	0.366455	−	0.719208i	−0.631989	−	0.774977i	$-0.717761\pi$
$137$	4.28924	−	8.41811i	0.366455	−	0.719208i	0.998444	+	0.0557695i	$0.0177612\pi$
$138$	21.1344	+	18.0125i	1.79908	+	1.53332i
$139$	−10.1339	+	13.9482i	−0.859550	+	1.18307i	0.122127	+	0.992514i	$0.461028\pi$
$139$	−10.1339	+	13.9482i	−0.859550	+	1.18307i	−0.981677	+	0.190554i	$0.938972\pi$
$140$	6.25947	−	1.00476i	0.529022	−	0.0849179i
$141$	7.22924	−	3.68348i	0.608812	−	0.310205i
$142$	4.54246	−	19.0078i	0.381195	−	1.59510i
$143$	8.32219	+	8.58726i	0.695937	+	0.718103i
$144$	17.4370	+	23.7910i	1.45308	+	1.98258i
$145$	11.9106	+	23.3758i	0.989119	+	1.94126i
$146$	−3.16114	−	7.60926i	−0.261618	−	0.629747i
$147$	−15.9689	−	11.6021i	−1.31709	−	0.956922i
$148$	8.17660	+	11.2050i	0.672112	+	0.921045i
$149$	−8.96786	−	4.56935i	−0.734676	−	0.374336i	0.0462749	−	0.998929i	$-0.485265\pi$
$149$	−8.96786	−	4.56935i	−0.734676	−	0.374336i	−0.780951	+	0.624593i	$0.785265\pi$
$150$	2.30159	−	29.6387i	0.187924	−	2.41999i
$151$	−0.549464	+	3.46918i	−0.0447147	+	0.282318i	−0.999907	−	0.0136697i	$-0.995649\pi$
$151$	−0.549464	+	3.46918i	−0.0447147	+	0.282318i	0.955192	+	0.295987i	$0.0956487\pi$
$152$	1.70681	−	1.05328i	0.138441	−	0.0854323i
$153$			27.6196i			2.23292i
$154$	−3.66490	+	2.39710i	−0.295326	+	0.193164i
$155$	−10.9164			−0.876830
$156$	−2.66684	−	23.0726i	−0.213518	−	1.84729i
$157$	4.42725	−	3.21659i	0.353333	−	0.256712i	−0.396933	−	0.917848i	$-0.629925\pi$
$157$	4.42725	−	3.21659i	0.353333	−	0.256712i	0.750266	+	0.661136i	$0.229925\pi$
$158$	−0.809174	−	0.0628362i	−0.0643745	−	0.00499898i
$159$	−33.0193	+	10.7286i	−2.61860	+	0.850834i
$160$	14.5387	−	12.5487i	1.14939	−	0.992060i
$161$	5.62175	−	0.890398i	0.443056	−	0.0701732i
$162$	30.3987	+	12.5545i	2.38835	+	0.986376i
$163$	−5.11271	−	10.0343i	−0.400459	−	0.785945i	0.599436	−	0.800422i	$-0.295391\pi$
$163$	−5.11271	−	10.0343i	−0.400459	−	0.785945i	−0.999895	+	0.0144778i	$0.995391\pi$
$164$	−1.82637	−	5.58143i	−0.142615	−	0.435836i
$165$	12.1827	+	34.1603i	0.948422	+	2.65938i
$166$	2.13069	−	8.91582i	0.165373	−	0.692002i
$167$	3.17736	+	6.23593i	0.245872	+	0.482550i	0.980653	−	0.195754i	$-0.0627153\pi$
$167$	3.17736	+	6.23593i	0.245872	+	0.482550i	−0.734781	+	0.678304i	$0.762715\pi$
$168$	8.48147	+	0.640870i	0.654360	+	0.0494442i
$169$	−5.09036	+	11.9620i	−0.391566	+	0.920150i
$170$	17.9262	−	1.42960i	1.37488	−	0.109645i
$171$	2.37394	−	4.65913i	0.181540	−	0.356292i
$172$	−2.96982	+	1.52099i	−0.226447	+	0.115975i
$173$	1.65427	+	2.27690i	0.125772	+	0.173110i	0.867259	−	0.497857i	$-0.165879\pi$
$173$	1.65427	+	2.27690i	0.125772	+	0.173110i	−0.741488	+	0.670966i	$0.765879\pi$
$174$	8.25268	+	34.2180i	0.625634	+	2.59406i
$175$	−4.30867	−	4.30867i	−0.325705	−	0.325705i
$176$	−5.63468	+	12.0104i	−0.424730	+	0.905320i
$177$	1.85325	+	1.85325i	0.139299	+	0.139299i
$178$	−1.49504	−	0.914024i	−0.112058	−	0.0685090i
$179$	−11.2577	+	8.17919i	−0.841439	+	0.611341i	−0.922772	−	0.385346i	$-0.874082\pi$
$179$	−11.2577	+	8.17919i	−0.841439	+	0.611341i	0.0813333	+	0.996687i	$0.474082\pi$
$180$	15.3738	−	47.6530i	1.14590	−	3.55185i
$181$	−13.7540	+	4.46893i	−1.02232	+	0.332173i	−0.771751	−	0.635925i	$-0.780619\pi$
$181$	−13.7540	+	4.46893i	−1.02232	+	0.332173i	−0.250572	+	0.968098i	$0.580619\pi$
$182$	−3.94837	−	2.65984i	−0.292673	−	0.197160i
$183$	26.9848	−	37.1414i	1.99478	−	2.74557i
$184$	13.0766	−	11.2393i	0.964020	−	0.828570i
$185$	7.27631	−	22.3942i	0.534965	−	1.64645i
$186$	−14.2451	−	3.40428i	−1.04450	−	0.249614i
$187$	−10.9036	+	5.95173i	−0.797351	+	0.435234i
$188$	−1.56682	−	4.78824i	−0.114272	−	0.349219i
$189$	11.7204	−	5.97183i	0.852532	−	0.434387i
$190$	−3.14683	−	1.29962i	−0.228295	−	0.0942846i
$191$	−10.4274	+	14.3521i	−0.754501	+	1.03848i	0.243150	+	0.969989i	$0.421819\pi$
$191$	−10.4274	+	14.3521i	−0.754501	+	1.03848i	−0.997652	+	0.0684934i	$0.978181\pi$
$192$	22.8853	−	11.8412i	1.65160	−	0.854564i
$193$	−2.82848	+	5.55121i	−0.203599	+	0.399585i	−0.970117	−	0.242638i	$-0.921987\pi$
$193$	−2.82848	+	5.55121i	−0.203599	+	0.399585i	0.766518	+	0.642222i	$0.221987\pi$
$194$	8.33881	+	9.74294i	0.598692	+	0.699503i
$195$	−29.0808	+	26.6234i	−2.08252	+	1.90654i
$196$	−8.64866	+	8.68473i	−0.617761	+	0.620338i
$197$	11.8294	−	11.8294i	0.842813	−	0.842813i	−0.146411	−	0.989224i	$-0.546772\pi$
$197$	11.8294	−	11.8294i	0.842813	−	0.842813i	0.989224	+	0.146411i	$0.0467721\pi$
$198$	3.72800	+	34.3865i	0.264938	+	2.44375i
$199$	11.4300			0.810254			0.405127	−	0.914260i	$-0.367227\pi$
$199$	11.4300			0.810254			0.405127	+	0.914260i	$0.367227\pi$
$200$	−17.9628	−	4.25321i	−1.27016	−	0.300747i
$201$	−3.93227	+	24.8274i	−0.277361	+	1.75119i
$202$	−18.1604	−	1.41024i	−1.27776	−	0.0992244i
$203$	6.42844	+	3.27545i	0.451188	+	0.229892i
$204$	23.8382	+	3.72475i	1.66901	+	0.260785i
$205$	−5.85962	+	8.06507i	−0.409253	+	0.563289i
$206$	−8.61017	−	3.55596i	−0.599899	−	0.247755i
$207$	13.8919	−	42.7550i	0.965557	−	2.97168i
$208$	−14.4107	−	0.575642i	−0.999203	−	0.0399136i
$209$	2.35088	−	0.0668119i	0.162614	−	0.00462147i
$210$	−7.55694	−	12.3031i	−0.521478	−	0.848991i
$211$	−6.35222	−	2.06396i	−0.437305	−	0.142089i	0.0820871	−	0.996625i	$-0.473841\pi$
$211$	−6.35222	−	2.06396i	−0.437305	−	0.142089i	−0.519392	+	0.854536i	$0.673841\pi$
$212$	3.41677	+	21.2858i	0.234664	+	1.46191i
$213$	−43.9617	+	6.96286i	−3.01221	+	0.477087i
$214$	13.2744	+	11.3135i	0.907417	+	0.773375i
$215$	5.04672	+	2.57143i	0.344183	+	0.175370i
$216$	20.7150	−	34.0419i	1.40948	−	2.31626i
$217$	−2.42872	+	1.76457i	−0.164872	+	0.119787i
$218$	8.03179	−	13.1374i	0.543981	−	0.889774i
$219$	−13.2697	+	13.2697i	−0.896685	+	0.896685i
$220$	22.1252	−	4.19947i	1.49168	−	0.283128i
$221$	−10.5648	−	8.41148i	−0.710668	−	0.565817i
$222$	16.4786	−	26.9536i	1.10597	−	1.80901i
$223$	3.98798	+	0.631633i	0.267055	+	0.0422973i	0.288526	−	0.957472i	$-0.406835\pi$
$223$	3.98798	+	0.631633i	0.267055	+	0.0422973i	−0.0214710	+	0.999769i	$0.506835\pi$
$224$	1.20621	−	5.14195i	0.0805934	−	0.343561i
$225$	−45.7714	+	14.8720i	−3.05143	+	0.991468i
$226$	−3.17135	+	3.72101i	−0.210955	+	0.247518i
$227$	−3.10225	−	19.5868i	−0.205903	−	1.30002i	−0.846600	−	0.532229i	$-0.821354\pi$
$227$	−3.10225	−	19.5868i	−0.205903	−	1.30002i	0.640697	−	0.767794i	$-0.278646\pi$
$228$	−3.70109	−	2.67724i	−0.245110	−	0.177305i
$229$	−2.53588	+	1.29210i	−0.167576	+	0.0853841i	−0.535767	−	0.844366i	$-0.679977\pi$
$229$	−2.53588	+	1.29210i	−0.167576	+	0.0853841i	0.368191	+	0.929750i	$0.379977\pi$
$230$	−28.4687	−	6.80340i	−1.87717	−	0.448603i
$231$	8.23223	+	5.63084i	0.541641	+	0.370482i
$232$	21.7838	−	1.78287i	1.43018	−	0.117051i
$233$	14.0800	+	4.57487i	0.922411	+	0.299709i	0.731455	−	0.681889i	$-0.238841\pi$
$233$	14.0800	+	4.57487i	0.922411	+	0.299709i	0.190955	+	0.981599i	$0.438841\pi$
$234$	−32.8760	+	18.2487i	−2.14917	+	1.19296i
$235$	−5.02690	+	6.91893i	−0.327919	+	0.451341i
$236$	1.31462	−	0.959315i	0.0855746	−	0.0624461i
$237$	0.571205	+	1.75799i	0.0371038	+	0.114194i
$238$	3.75719	−	3.21571i	0.243542	−	0.208443i
$239$	8.90005	+	1.40963i	0.575697	+	0.0911814i	0.437492	−	0.899222i	$-0.355867\pi$
$239$	8.90005	+	1.40963i	0.575697	+	0.0911814i	0.138205	+	0.990404i	$0.455867\pi$
$240$	−39.0554	−	19.6954i	−2.52102	−	1.27133i
$241$	−9.91690	−	9.91690i	−0.638804	−	0.638804i	0.311457	−	0.950260i	$-0.399183\pi$
$241$	−9.91690	−	9.91690i	−0.638804	−	0.638804i	−0.950260	+	0.311457i	$0.899183\pi$
$242$	−12.7717	+	8.88166i	−0.820995	+	0.570935i
$243$		−	32.6393i		−	2.09381i
$244$	−20.1995	−	20.1156i	−1.29314	−	1.28777i
$245$	20.5497	+	3.25476i	1.31287	+	0.207939i
$246$	−10.1614	+	8.69699i	−0.647870	+	0.554500i
$247$	1.05919	+	2.32698i	0.0673948	+	0.148062i
$248$	−3.45407	+	8.41306i	−0.219334	+	0.534230i
$249$	−20.6207	+	3.26600i	−1.30678	+	0.206974i
$250$	2.81162	+	6.76792i	0.177823	+	0.428041i
$251$	3.90876	−	12.0299i	0.246719	−	0.759322i	−0.748630	−	0.662988i	$-0.769288\pi$
$251$	3.90876	−	12.0299i	0.246719	−	0.759322i	0.995349	−	0.0963343i	$-0.0307118\pi$
$252$	−4.28237	−	13.0870i	−0.269764	−	0.824406i
$253$	19.8723	−	3.72902i	1.24936	−	0.234441i
$254$	−6.99633	−	11.3903i	−0.438989	−	0.714694i
$255$	−18.5941	−	36.4929i	−1.16440	−	2.28527i
$256$	−5.07078	−	15.1752i	−0.316924	−	0.948451i
$257$	7.70638	−	10.6069i	0.480710	−	0.661641i	−0.497931	−	0.867217i	$-0.665907\pi$
$257$	7.70638	−	10.6069i	0.480710	−	0.661641i	0.978641	+	0.205576i	$0.0659066\pi$
$258$	5.78369	+	4.92933i	0.360077	+	0.306887i
$259$	−2.00101	−	6.15849i	−0.124337	−	0.382670i
$260$	13.5458	+	20.3932i	0.840074	+	1.26474i
$261$	46.1011	−	33.4944i	2.85359	−	2.07325i
$262$	0.00418625	+	0.0173574i	0.000258627	+	0.00107234i
$263$			7.85916i			0.484617i	0.970199	+	0.242308i	$0.0779046\pi$
$263$			7.85916i			0.484617i	−0.970199	+	0.242308i	$0.922095\pi$
$264$	30.1813	+	1.41974i	1.85753	+	0.0873787i
$265$	25.8771	−	25.8771i	1.58962	−	1.58962i
$266$	−0.910190	+	0.219519i	−0.0558073	+	0.0134596i
$267$	−0.624317	+	3.94178i	−0.0382076	+	0.241233i
$268$	14.8547	+	4.79242i	0.907394	+	0.292744i
$269$	−3.59674	−	11.0696i	−0.219297	−	0.674926i	−0.998821	−	0.0485537i	$-0.984539\pi$
$269$	−3.59674	−	11.0696i	−0.219297	−	0.674926i	0.779524	−	0.626373i	$-0.215461\pi$
$270$	−67.4311	+	5.37756i	−4.10373	+	0.327268i
$271$	−10.9156	+	1.72886i	−0.663073	+	0.105021i	−0.478895	−	0.877872i	$-0.658962\pi$
$271$	−10.9156	+	1.72886i	−0.663073	+	0.105021i	−0.184179	+	0.982893i	$0.558962\pi$
$272$	4.57027	−	14.2677i	0.277114	−	0.865104i
$273$	−2.16649	+	10.6240i	−0.131122	+	0.642992i
$274$	−3.10561	+	12.9954i	−0.187617	+	0.785079i
$275$	−15.7344	−	14.8648i	−0.948819	−	0.896378i
$276$	−35.0279	−	17.7559i	−2.10843	−	1.06878i
$277$	−5.82876	−	1.89388i	−0.350216	−	0.113792i	0.128626	−	0.991693i	$-0.458943\pi$
$277$	−5.82876	−	1.89388i	−0.350216	−	0.113792i	−0.478842	+	0.877901i	$0.658943\pi$
$278$	9.30725	−	22.5360i	0.558212	−	1.35162i
$279$	3.70921	+	23.4191i	0.222065	+	1.40206i
$280$	−8.27234	+	3.45681i	−0.494367	+	0.206584i
$281$	−7.68645	+	15.0855i	−0.458535	+	0.899926i	0.539775	+	0.841809i	$0.318509\pi$
$281$	−7.68645	+	15.0855i	−0.458535	+	0.899926i	−0.998310	+	0.0581161i	$0.981491\pi$
$282$	−8.71738	+	7.46105i	−0.519112	+	0.444299i
$283$	−16.5639	+	12.0344i	−0.984620	+	0.715369i	−0.958736	−	0.284296i	$-0.908240\pi$
$283$	−16.5639	+	12.0344i	−0.984620	+	0.715369i	−0.0258840	+	0.999665i	$0.508240\pi$
$284$	0.0575234	+	27.6380i	0.00341338	+	1.64001i
$285$			7.75413i			0.459315i
$286$	−14.2886	−	9.04631i	−0.844903	−	0.534920i
$287$			2.74151i			0.161826i
$288$	−31.8607	−	26.9261i	−1.87741	−	1.58664i
$289$	−2.40411	+	1.74669i	−0.141418	+	0.102746i
$290$	−24.1254	−	28.1877i	−1.41669	−	1.65524i
$291$	13.2599	−	26.0240i	0.777309	−	1.52555i
$292$	6.86894	+	9.41303i	0.401974	+	0.550856i
$293$	−0.363283	−	2.29368i	−0.0212232	−	0.133998i	0.974802	−	0.223073i	$-0.0716089\pi$
$293$	−0.363283	−	2.29368i	−0.0212232	−	0.133998i	−0.996025	+	0.0890750i	$0.971609\pi$
$294$	25.8008	+	10.6556i	1.50474	+	0.621448i
$295$	−2.62739	−	0.853690i	−0.152972	−	0.0497038i
$296$	−14.9564	−	12.6934i	−0.869324	−	0.737791i
$297$	41.0150	−	22.3880i	2.37993	−	1.29908i
$298$	13.8440	+	3.30843i	0.801963	+	0.191652i
$299$	12.1235	+	18.3347i	0.701123	+	1.06033i
$300$	6.66318	+	41.5103i	0.384699	+	2.39660i
$301$	1.53846	−	0.243668i	0.0886755	−	0.0140448i
$302$	−0.394884	−	4.95159i	−0.0227230	−	0.284932i
$303$	12.8197	+	39.4549i	0.736470	+	2.26662i
$304$	−1.99728	+	2.01398i	−0.114552	+	0.115509i
$305$	−7.57012	+	47.7959i	−0.433464	+	2.73678i
$306$	−9.15791	−	37.9713i	−0.523523	−	2.17068i
$307$	12.9404	−	12.9404i	0.738548	−	0.738548i	−0.233749	−	0.972297i	$-0.575099\pi$
$307$	12.9404	−	12.9404i	0.738548	−	0.738548i	0.972297	+	0.233749i	$0.0750994\pi$
$308$	4.24367	−	4.51070i	0.241805	−	0.257021i
$309$			21.2164i			1.20696i
$310$	15.0079	−	3.61959i	0.852390	−	0.205579i
$311$	−10.4906	+	7.62190i	−0.594870	+	0.432198i	−0.844054	−	0.536258i	$-0.819838\pi$
$311$	−10.4906	+	7.62190i	−0.594870	+	0.432198i	0.249184	+	0.968456i	$0.419838\pi$
$312$	11.3166	+	30.8359i	0.640677	+	1.74574i
$313$	5.90393	+	18.1704i	0.333710	+	1.02705i	0.967354	+	0.253429i	$0.0815585\pi$
$313$	5.90393	+	18.1704i	0.333710	+	1.02705i	−0.633644	+	0.773625i	$0.718442\pi$
$314$	−5.02003	+	5.89010i	−0.283297	+	0.332398i
$315$	−13.7393	+	18.9106i	−0.774123	+	1.06549i
$316$	1.13328	−	0.181913i	0.0637522	−	0.0102334i
$317$	−2.59456	−	5.09211i	−0.145725	−	0.286002i	0.806594	−	0.591106i	$-0.201309\pi$
$317$	−2.59456	−	5.09211i	−0.145725	−	0.286002i	−0.952319	+	0.305105i	$0.901309\pi$
$318$	41.8374	−	25.6979i	2.34612	−	1.44107i
$319$	23.1571	+	10.9820i	1.29655	+	0.614874i
$320$	−15.8270	+	22.0725i	−0.884756	+	1.23389i
$321$	12.2752	−	37.7790i	0.685132	−	2.10862i
$322$	−7.43352	+	3.08813i	−0.414254	+	0.172095i
$323$	−2.62321	+	0.415475i	−0.145959	+	0.0231176i
$324$	−45.9547	−	7.18050i	−2.55304	−	0.398917i
$325$	8.25081	−	22.0373i	0.457673	−	1.22241i
$326$	10.3560	+	12.0998i	0.573567	+	0.670147i
$327$	−34.6376	−	5.48606i	−1.91546	−	0.303380i
$328$	4.36153	+	7.06774i	0.240825	+	0.390251i
$329$			2.35191i			0.129665i
$330$	−28.0753	−	42.9240i	−1.54550	−	2.36289i
$331$	−3.70552	−	3.70552i	−0.203674	−	0.203674i	0.597898	−	0.801572i	$-0.296003\pi$
$331$	−3.70552	−	3.70552i	−0.203674	−	0.203674i	−0.801572	+	0.597898i	$0.796003\pi$
$332$	0.0269819	+	12.9639i	0.00148083	+	0.711486i
$333$	−50.5146	−	8.00073i	−2.76818	−	0.438437i
$334$	−6.43588	−	7.51959i	−0.352156	−	0.411454i
$335$	−8.18772	−	25.1992i	−0.447343	−	1.37678i
$336$	−11.8728	+	1.93116i	−0.647713	+	0.105353i
$337$	11.2656	−	15.5057i	0.613674	−	0.844650i	−0.383200	−	0.923666i	$-0.625178\pi$
$337$	11.2656	−	15.5057i	0.613674	−	0.844650i	0.996873	+	0.0790161i	$0.0251778\pi$
$338$	3.03194	−	18.1330i	0.164916	−	0.986308i
$339$	10.5900	+	3.44091i	0.575172	+	0.186885i
$340$	−24.1708	+	7.90924i	−1.31085	+	0.428939i
$341$	−8.44602	+	6.51087i	−0.457378	+	0.352583i
$342$	−1.71885	+	7.19248i	−0.0929446	+	0.388925i
$343$	10.9213	−	5.56468i	0.589695	−	0.300465i
$344$	3.57858	−	3.07577i	0.192944	−	0.165834i
$345$	10.4285	+	65.8431i	0.561452	+	3.54487i
$346$	−3.02923	−	2.58176i	−0.162853	−	0.138796i
$347$	−11.3888	+	3.70046i	−0.611385	+	0.198651i	−0.598312	−	0.801264i	$-0.704161\pi$
$347$	−11.3888	+	3.70046i	−0.611385	+	0.198651i	−0.0130733	+	0.999915i	$0.504161\pi$
$348$	−22.6915	−	44.3063i	−1.21639	−	2.37507i
$349$	−26.3522	−	4.17378i	−1.41060	−	0.223418i	−0.595789	−	0.803141i	$-0.703161\pi$
$349$	−26.3522	−	4.17378i	−1.41060	−	0.223418i	−0.814813	+	0.579723i	$0.803161\pi$
$350$	7.35218	+	4.49490i	0.392990	+	0.240263i
$351$	39.7406	+	31.6406i	2.12120	+	1.68885i
$352$	3.76421	−	18.3802i	0.200633	−	0.979667i
$353$	−0.927206	+	0.927206i	−0.0493502	+	0.0493502i	−0.731351	−	0.682001i	$-0.761110\pi$
$353$	−0.927206	+	0.927206i	−0.0493502	+	0.0493502i	0.682001	+	0.731351i	$0.261110\pi$
$354$	−3.16232	−	1.93335i	−0.168075	−	0.102756i
$355$	37.9561	−	27.5768i	2.01450	−	1.46362i
$356$	2.35844	+	0.760880i	0.124997	+	0.0403266i
$357$	−10.0357	−	5.11344i	−0.531145	−	0.270632i
$358$	12.7650	−	14.9774i	0.674652	−	0.791582i
$359$	5.97724	−	0.946701i	0.315467	−	0.0499650i	0.00330653	−	0.999995i	$-0.498947\pi$
$359$	5.97724	−	0.946701i	0.315467	−	0.0499650i	0.312160	+	0.950030i	$0.398947\pi$
$360$	−5.33542	+	70.6106i	−0.281201	+	3.72151i
$361$	−17.5919	−	5.71594i	−0.925887	−	0.300839i
$362$	17.4271	−	10.7043i	0.915947	−	0.562605i
$363$	29.7999	+	19.1636i	1.56409	+	1.00583i
$364$	6.31013	+	2.34756i	0.330741	+	0.123046i
$365$	6.11264	−	18.8128i	0.319950	−	0.984705i
$366$	−24.7835	+	60.0093i	−1.29546	+	3.13673i
$367$	14.9119	−	20.5245i	0.778396	−	1.07137i	−0.217061	−	0.976158i	$-0.569647\pi$
$367$	14.9119	−	20.5245i	0.778396	−	1.07137i	0.995457	−	0.0952117i	$-0.0303528\pi$
$368$	−14.2510	+	19.7875i	−0.742885	+	1.03150i
$369$	19.2930	+	9.83027i	1.00435	+	0.511743i
$370$	−2.57814	+	33.2000i	−0.134031	+	1.72599i
$371$	1.57435	−	9.94007i	0.0817363	−	0.516062i
$372$	20.7129	−	0.0431100i	1.07391	−	0.00223515i
$373$	8.49204			0.439701			0.219851	−	0.975534i	$-0.429443\pi$
$373$	8.49204			0.439701			0.219851	+	0.975534i	$0.429443\pi$
$374$	13.0168	−	11.7977i	0.673082	−	0.610047i
$375$	11.8025	−	11.8025i	0.609480	−	0.609480i
$376$	3.74171	+	6.06334i	0.192964	+	0.312693i
$377$	−1.22794	+	27.8348i	−0.0632424	+	1.43357i
$378$	−14.1330	+	12.0962i	−0.726924	+	0.622161i
$379$	15.0226	−	29.4836i	0.771661	−	1.51447i	−0.0837310	−	0.996488i	$-0.526684\pi$
$379$	15.0226	−	29.4836i	0.771661	−	1.51447i	0.855392	−	0.517981i	$-0.173316\pi$
$380$	4.75716	+	0.743314i	0.244037	+	0.0381312i
$381$	−17.8949	+	24.6302i	−0.916783	+	1.26184i
$382$	9.57679	−	23.1886i	0.489991	−	1.18643i
$383$	20.1038	−	10.2434i	1.02726	−	0.523414i	0.142661	−	0.989772i	$-0.454434\pi$
$383$	20.1038	−	10.2434i	1.02726	−	0.523414i	0.884596	+	0.466358i	$0.154434\pi$
$384$	−27.5363	+	23.8673i	−1.40521	+	1.21797i
$385$	−10.4261	−	1.34896i	−0.531365	−	0.0687491i
$386$	2.04795	−	8.56962i	0.104238	−	0.436182i
$387$	3.80170	−	11.7004i	0.193252	−	0.594767i
$388$	−14.6946	−	10.6296i	−0.746008	−	0.539637i
$389$	15.7712	−	21.7071i	0.799629	−	1.10060i	−0.193212	−	0.981157i	$-0.561891\pi$
$389$	15.7712	−	21.7071i	0.799629	−	1.10060i	0.992842	−	0.119438i	$-0.0381094\pi$
$390$	31.1526	−	46.2441i	1.57747	−	2.34166i
$391$	−21.7158	+	7.05589i	−1.09822	+	0.356832i
$392$	9.01051	−	14.8074i	0.455099	−	0.747886i
$393$	0.0328989	−	0.0239025i	0.00165953	−	0.00120572i
$394$	−12.3407	+	20.1854i	−0.621717	+	1.01692i
$395$	−1.37773	−	1.37773i	−0.0693211	−	0.0693211i
$396$	−16.5269	−	46.0383i	−0.830506	−	2.31351i
$397$	20.0713	+	20.0713i	1.00735	+	1.00735i	0.999973	+	0.00737835i	$0.00234862\pi$
$397$	20.0713	+	20.0713i	1.00735	+	1.00735i	0.00737835	+	0.999973i	$0.497651\pi$
$398$	−15.7140	+	3.78989i	−0.787670	+	0.189970i
$399$	1.25340	+	1.72516i	0.0627486	+	0.0863660i
$400$	26.1053	−	0.108667i	1.30527	−	0.00543336i
$401$	8.11655	−	15.9296i	0.405321	−	0.795487i	−0.594643	−	0.803990i	$-0.702707\pi$
$401$	8.11655	−	15.9296i	0.405321	−	0.795487i	0.999964	+	0.00850270i	$0.00270653\pi$
$402$	−2.82601	−	35.4364i	−0.140949	−	1.76741i
$403$	−10.0877	−	5.71338i	−0.502504	−	0.284604i
$404$	25.4345	−	4.08271i	1.26541	−	0.203122i
$405$	35.8452	+	70.3503i	1.78116	+	3.49573i
$406$	−9.92383	−	2.37158i	−0.492512	−	0.117700i
$407$	−7.72684	−	21.6661i	−0.383005	−	1.07395i
$408$	−34.0076	+	2.78331i	−1.68363	+	0.137794i
$409$	−8.03768	−	15.7748i	−0.397438	−	0.780015i	0.602397	−	0.798197i	$-0.294212\pi$
$409$	−8.03768	−	15.7748i	−0.397438	−	0.780015i	−0.999835	+	0.0181813i	$0.994212\pi$
$410$	5.38161	−	13.0307i	0.265779	−	0.643540i
$411$	30.0560	−	4.76040i	1.48255	−	0.234813i
$412$	13.0163	+	2.03381i	0.641266	+	0.100199i
$413$	−0.722542	+	0.234768i	−0.0355540	+	0.0115522i
$414$	−4.92219	+	63.3856i	−0.241912	+	3.11523i
$415$	17.8037	−	12.9352i	0.873950	−	0.634962i
$416$	20.0026	−	3.98681i	0.980710	−	0.195469i
$417$	−55.5312			−2.71937
$418$	−3.20982	+	0.871339i	−0.156997	+	0.0426186i
$419$		−	36.0916i		−	1.76319i	−0.472006	−	0.881596i	$-0.656470\pi$
$419$		−	36.0916i		−	1.76319i	0.472006	−	0.881596i	$-0.343530\pi$
$420$	14.4686	+	14.4085i	0.705995	+	0.703062i
$421$	2.20888	−	13.9463i	0.107654	−	0.679702i	−0.873551	−	0.486733i	$-0.838188\pi$
$421$	2.20888	−	13.9463i	0.107654	−	0.679702i	0.981205	−	0.192969i	$-0.0618115\pi$
$422$	9.41734	+	0.731301i	0.458429	+	0.0355992i
$423$	16.5512	+	8.43327i	0.804748	+	0.410040i
$424$	−11.7551	−	28.1307i	−0.570880	−	1.36615i
$425$	19.7758	+	14.3680i	0.959267	+	0.696949i
$426$	58.1297	−	24.1490i	2.81639	−	1.17002i
$427$	6.04166	+	11.8574i	0.292376	+	0.573821i
$428$	−22.0008	−	11.1523i	−1.06345	−	0.539068i
$429$	−6.62081	+	37.9430i	−0.319656	+	1.83191i
$430$	−7.79081	−	1.86184i	−0.375706	−	0.0897857i
$431$	17.0904	−	8.70797i	0.823214	−	0.419448i	0.00896159	−	0.999960i	$-0.497147\pi$
$431$	17.0904	−	8.70797i	0.823214	−	0.419448i	0.814252	+	0.580512i	$0.197147\pi$
$432$	−17.1915	+	53.6692i	−0.827127	+	2.58216i
$433$	17.8385	−	24.5526i	0.857262	−	1.17992i	−0.124953	−	0.992163i	$-0.539878\pi$
$433$	17.8385	−	24.5526i	0.857262	−	1.17992i	0.982215	−	0.187758i	$-0.0601220\pi$
$434$	2.75391	−	3.23122i	0.132192	−	0.155103i
$435$	−38.3628	+	75.2912i	−1.83935	+	3.60994i
$436$	−6.68607	+	20.7243i	−0.320205	+	0.992513i
$437$	4.26968	+	0.676251i	0.204246	+	0.0323495i
$438$	13.8433	−	22.6430i	0.661457	−	1.08193i
$439$	−26.5857			−1.26886			−0.634432	−	0.772978i	$-0.718766\pi$
$439$	−26.5857			−1.26886			−0.634432	+	0.772978i	$0.718766\pi$
$440$	−29.0252	+	13.1095i	−1.38372	+	0.624972i
$441$		−	45.1912i		−	2.15196i
$442$	17.3135	+	8.06104i	0.823519	+	0.383425i
$443$	−2.44772	−	3.36900i	−0.116295	−	0.160066i	0.746901	−	0.664935i	$-0.231541\pi$
$443$	−2.44772	−	3.36900i	−0.116295	−	0.160066i	−0.863196	+	0.504869i	$0.831541\pi$
$444$	−13.7177	+	42.5195i	−0.651012	+	2.01789i
$445$	−1.29994	−	4.00082i	−0.0616233	−	0.189657i
$446$	−5.69208	+	0.453937i	−0.269528	+	0.0214945i
$447$	−5.07128	−	32.0188i	−0.239863	−	1.51444i
$448$	0.0466370	+	7.46908i	0.00220339	+	0.352881i
$449$	32.6396	−	16.6307i	1.54036	−	0.784851i	0.541902	−	0.840441i	$-0.317704\pi$
$449$	32.6396	−	16.6307i	1.54036	−	0.784851i	0.998454	+	0.0555908i	$0.0177042\pi$
$450$	57.9951	−	35.6225i	2.73391	−	1.67926i
$451$	0.276661	+	9.73475i	0.0130275	+	0.458392i
$452$	3.12617	−	6.16715i	0.147043	−	0.290078i
$453$	−10.0801	+	5.13607i	−0.473604	+	0.241313i
$454$	10.7594	+	25.8992i	0.504964	+	1.21551i
$455$	−3.04924	−	11.0146i	−0.142951	−	0.516373i
$456$	5.97593	+	2.45348i	0.279849	+	0.114895i
$457$	8.79676	+	4.48217i	0.411495	+	0.209667i	0.647468	−	0.762092i	$-0.275828\pi$
$457$	8.79676	+	4.48217i	0.411495	+	0.209667i	−0.235973	+	0.971760i	$0.575828\pi$
$458$	3.05789	−	2.61720i	0.142886	−	0.122294i
$459$	−42.6910	+	31.0168i	−1.99265	+	1.44774i
$460$	41.3944	−	0.0861548i	1.93003	−	0.00401699i
$461$	0.218649	−	0.218649i	0.0101835	−	0.0101835i	−0.701997	−	0.712180i	$-0.747708\pi$
$461$	0.218649	−	0.218649i	0.0101835	−	0.0101835i	0.712180	+	0.701997i	$0.247708\pi$
$462$	−13.1847	−	5.01166i	−0.613406	−	0.233164i
$463$	−21.1407	+	21.1407i	−0.982492	+	0.982492i	−0.999849	−	0.0173571i	$-0.994475\pi$
$463$	−21.1407	+	21.1407i	−0.982492	+	0.982492i	0.0173571	+	0.999849i	$0.494475\pi$
$464$	−29.3572	+	9.67401i	−1.36287	+	0.449104i
$465$	−20.6670	−	28.4457i	−0.958409	−	1.31914i
$466$	−20.8740	−	1.62096i	−0.966969	−	0.0750897i
$467$	10.6558	+	32.7952i	0.493092	+	1.51758i	0.819908	+	0.572495i	$0.194024\pi$
$467$	10.6558	+	32.7952i	0.493092	+	1.51758i	−0.326816	+	0.945088i	$0.605976\pi$
$468$	39.1470	−	35.9890i	1.80957	−	1.66359i
$469$	−5.89491	−	4.28290i	−0.272202	−	0.197766i
$470$	4.61682	−	11.1789i	0.212958	−	0.515644i
$471$	16.7633	+	5.44673i	0.772413	+	0.250972i
$472$	−1.48925	+	1.75475i	−0.0685484	+	0.0807691i
$473$	5.43830	−	1.02049i	0.250053	−	0.0469223i
$474$	−1.36819	−	2.22748i	−0.0628431	−	0.102311i
$475$	−2.10101	−	4.12347i	−0.0964011	−	0.189198i
$476$	−4.09912	+	5.66672i	−0.187883	+	0.259734i
$477$	−64.3067	−	46.7215i	−2.94440	−	2.13923i
$478$	−12.7031	+	1.01306i	−0.581028	+	0.0463363i
$479$	−1.47203	−	0.750036i	−0.0672587	−	0.0342700i	0.420038	−	0.907507i	$-0.362017\pi$
$479$	−1.47203	−	0.750036i	−0.0672587	−	0.0342700i	−0.487296	+	0.873237i	$0.662017\pi$
$480$	60.2236	+	14.1274i	2.74882	+	0.644824i
$481$	18.4444	−	16.8858i	0.840994	−	0.769928i
$482$	16.9219	+	10.3455i	0.770770	+	0.471226i
$483$	12.9632	+	12.9632i	0.589848	+	0.589848i
$484$	14.6135	−	16.4452i	0.664252	−	0.747509i
$485$			30.7867i			1.39795i
$486$	10.8223	+	44.8723i	0.490908	+	2.03545i
$487$	−19.4217	−	3.07609i	−0.880079	−	0.139391i	−0.299989	−	0.953943i	$-0.596983\pi$
$487$	−19.4217	−	3.07609i	−0.880079	−	0.139391i	−0.580091	+	0.814552i	$0.696983\pi$
$488$	34.4400	+	20.9572i	1.55902	+	0.948689i
$489$	16.4675	−	32.3194i	0.744688	−	1.46153i
$490$	−29.3308	+	2.33910i	−1.32503	+	0.105670i
$491$	11.8658	+	8.62100i	0.535496	+	0.389060i	0.822409	−	0.568896i	$-0.192629\pi$
$491$	11.8658	+	8.62100i	0.535496	+	0.389060i	−0.286914	+	0.957956i	$0.592629\pi$
$492$	11.0862	−	15.3258i	0.499805	−	0.690942i
$493$	−27.5264	−	8.94386i	−1.23973	−	0.402811i
$494$	−2.22774	−	2.84792i	−0.100231	−	0.128134i
$495$	−46.8783	+	68.5356i	−2.10702	+	3.08045i
$496$	1.95910	−	12.7115i	0.0879662	−	0.570764i
$497$	3.98699	−	12.2707i	0.178841	−	0.550416i
$498$	27.2663	−	11.3273i	1.22183	−	0.507590i
$499$	−1.63039	−	10.2939i	−0.0729864	−	0.460818i	−0.996931	−	0.0782908i	$-0.975054\pi$
$499$	−1.63039	−	10.2939i	−0.0729864	−	0.460818i	0.923944	−	0.382527i	$-0.124946\pi$
$500$	−6.10946	−	8.37225i	−0.273223	−	0.374418i
$501$	−10.2340	+	20.0853i	−0.457220	+	0.897345i
$502$	−1.38495	+	17.8347i	−0.0618133	+	0.796002i
$503$	0.356391	+	0.490530i	0.0158907	+	0.0218717i	0.816888	−	0.576796i	$-0.195697\pi$
$503$	0.356391	+	0.490530i	0.0158907	+	0.0218717i	−0.800998	+	0.598667i	$0.795697\pi$
$504$	10.2267	+	16.5721i	0.455533	+	0.738179i
$505$	−30.9207	−	30.9207i	−1.37595	−	1.37595i
$506$	−26.0839	+	11.7157i	−1.15957	+	0.520828i
$507$	−40.8071	+	9.38207i	−1.81230	+	0.416672i
$508$	13.3952	+	13.3396i	0.594317	+	0.591849i
$509$	−0.117408	+	0.741288i	−0.00520404	+	0.0328570i	−0.990154	−	0.139984i	$-0.955295\pi$
$509$	−0.117408	+	0.741288i	−0.00520404	+	0.0328570i	0.984950	+	0.172841i	$0.0552948\pi$
$510$	37.6630	+	44.0049i	1.66775	+	1.94857i
$511$	−1.68100	−	5.17358i	−0.0743630	−	0.228866i
$512$	12.0030	+	19.1815i	0.530461	+	0.847709i
$513$	9.86743	−	1.56285i	0.435658	−	0.0690014i
$514$	−7.07772	+	17.1376i	−0.312185	+	0.755905i
$515$	−10.1529	−	19.9261i	−0.447388	−	0.878049i
$516$	−9.58581	−	4.85911i	−0.421992	−	0.213910i
$517$	0.237345	+	8.35133i	0.0104384	+	0.367291i
$518$	4.79297	+	7.80317i	0.210591	+	0.342852i
$519$	−2.80121	+	8.62125i	−0.122960	+	0.378431i
$520$	−25.3845	−	23.5451i	−1.11318	−	1.03252i
$521$	36.7280	+	26.6845i	1.60908	+	1.16907i	0.866279	+	0.499561i	$0.166505\pi$
$521$	36.7280	+	26.6845i	1.60908	+	1.16907i	0.742806	+	0.669507i	$0.233495\pi$
$522$	−52.2737	+	61.3338i	−2.28796	+	2.68451i
$523$	−17.5435	+	5.70023i	−0.767124	+	0.249254i	−0.666333	−	0.745654i	$-0.732137\pi$
$523$	−17.5435	+	5.70023i	−0.767124	+	0.249254i	−0.100791	+	0.994908i	$0.532137\pi$
$524$	−0.0115105	−	0.0224748i	−0.000502837	−	0.000981816i
$525$	3.07021	−	19.3845i	0.133995	−	0.846011i
$526$	−2.60588	−	10.8047i	−0.113622	−	0.471109i
$527$	8.51575	−	8.51575i	0.370952	−	0.370952i
$528$	−41.9639	+	8.05546i	−1.82624	+	0.350569i
$529$	14.1648			0.615863
$530$	−26.9956	+	44.1558i	−1.17261	+	1.91801i
$531$	−0.938682	+	5.92660i	−0.0407353	+	0.257193i
$532$	1.17854	−	0.603588i	0.0510961	−	0.0261689i
$533$	−9.63581	+	4.38601i	−0.417373	+	0.189979i
$534$	−0.448679	−	5.62615i	−0.0194162	−	0.243467i
$535$	6.55008	+	41.3556i	0.283185	+	1.78796i
$536$	−22.0112	−	1.66319i	−0.950737	−	0.0718388i
$537$	−42.6260	−	13.8500i	−1.83945	−	0.597673i
$538$	8.61515	+	14.0259i	0.371426	+	0.604698i
$539$	17.8405	−	9.73822i	0.768444	−	0.419455i
$540$	90.9209	−	29.7513i	3.91261	−	1.28029i
$541$	−25.6800	+	13.0846i	−1.10407	+	0.562551i	−0.908393	−	0.418118i	$-0.862690\pi$
$541$	−25.6800	+	13.0846i	−1.10407	+	0.562551i	−0.195676	+	0.980669i	$0.562690\pi$
$542$	14.4334	−	5.99612i	0.619968	−	0.257555i
$543$	−37.6839	−	27.3790i	−1.61717	−	1.17494i
$544$	−1.55242	+	21.1305i	−0.0665595	+	0.905962i
$545$	35.1563	−	11.4230i	1.50593	−	0.489307i
$546$	−0.544138	−	15.3241i	−0.0232869	−	0.655812i
$547$	23.2608	+	32.0157i	0.994559	+	1.36889i	0.928605	+	0.371070i	$0.121009\pi$
$547$	23.2608	+	32.0157i	0.994559	+	1.36889i	0.0659535	+	0.997823i	$0.478991\pi$
$548$	−0.0393279	−	18.8957i	−0.00168000	−	0.807184i
$549$	105.109			4.48593
$550$	26.5603	+	15.2189i	1.13253	+	0.648936i
$551$	3.87466	+	3.87466i	0.165066	+	0.165066i
$552$	54.0435	+	12.7964i	2.30024	+	0.544650i
$553$	−0.529222	−	0.0838205i	−0.0225048	−	0.00356441i
$554$	8.64130	+	0.671038i	0.367134	+	0.0285097i
$555$	72.1295	−	23.4363i	3.06172	−	0.994815i
$556$	−5.32324	+	34.0684i	−0.225756	+	1.44482i
$557$	−1.61722	−	10.2107i	−0.0685236	−	0.432641i	−0.997970	−	0.0636841i	$-0.979715\pi$
$557$	−1.61722	−	10.2107i	−0.0685236	−	0.432641i	0.929447	−	0.368957i	$-0.120285\pi$
$558$	−12.8645	−	30.9665i	−0.544598	−	1.31092i
$559$	3.31776	+	5.01753i	0.140326	+	0.212219i
$560$	10.2266	−	7.49528i	0.432152	−	0.316734i
$561$	−36.1515	−	17.1444i	−1.52632	−	0.723838i
$562$	5.56535	−	23.2881i	0.234760	−	0.982348i
$563$	−4.13846	+	12.7369i	−0.174415	+	0.536795i	−0.999606	−	0.0280587i	$-0.991067\pi$
$563$	−4.13846	+	12.7369i	−0.174415	+	0.536795i	0.825191	+	0.564854i	$0.191067\pi$
$564$	9.51073	−	13.1479i	0.400474	−	0.553624i
$565$	−11.5926	+	1.83609i	−0.487704	+	0.0772448i
$566$	18.7817	−	22.0369i	0.789452	−	0.926280i
$567$	19.3466	+	9.85758i	0.812480	+	0.413979i
$568$	−9.24309	−	37.9775i	−0.387831	−	1.59350i
$569$	−14.7454	−	20.2954i	−0.618161	−	0.850825i	0.379057	−	0.925374i	$-0.376249\pi$
$569$	−14.7454	−	20.2954i	−0.618161	−	0.850825i	−0.997217	+	0.0745481i	$0.976249\pi$
$570$	−2.57105	−	10.6603i	−0.107690	−	0.446512i
$571$	−24.0415			−1.00610			−0.503052	−	0.864256i	$-0.667790\pi$
$571$	−24.0415			−1.00610			−0.503052	+	0.864256i	$0.667790\pi$
$572$	22.6434	+	7.69911i	0.946768	+	0.321916i
$573$	−57.1393			−2.38703
$574$	−0.909008	−	3.76901i	−0.0379413	−	0.157315i
$575$	−23.3861	−	32.1882i	−0.975268	−	1.34234i
$576$	52.7298	+	26.4538i	2.19708	+	1.10224i
$577$	−16.3664	−	8.33908i	−0.681341	−	0.347160i	0.0788262	−	0.996888i	$-0.474883\pi$
$577$	−16.3664	−	8.33908i	−0.681341	−	0.347160i	−0.760167	+	0.649728i	$0.774883\pi$
$578$	2.72600	−	3.19847i	0.113387	−	0.133039i
$579$	−19.8200	+	3.13918i	−0.823692	+	0.130460i
$580$	42.5137	+	30.7530i	1.76529	+	1.27695i
$581$	1.87014	−	5.75570i	0.0775865	−	0.238787i
$582$	−9.60079	+	40.1743i	−0.397965	+	1.66528i
$583$	4.58722	−	35.4548i	0.189983	−	1.46839i
$584$	−12.5645	−	10.6634i	−0.519922	−	0.441256i
$585$	−88.4475	−	18.0366i	−3.65685	−	0.745723i
$586$	1.25996	+	3.03289i	0.0520485	+	0.125287i
$587$	4.69963	+	29.6723i	0.193974	+	1.22471i	0.871940	+	0.489613i	$0.162862\pi$
$587$	4.69963	+	29.6723i	0.193974	+	1.22471i	−0.677966	+	0.735094i	$0.737138\pi$
$588$	−39.0040	−	6.09443i	−1.60850	−	0.251330i
$589$	−2.16845	+	0.704573i	−0.0893496	+	0.0290314i
$590$	3.89518	+	0.302479i	0.160362	+	0.0124529i
$591$	53.2202	+	8.42925i	2.18919	+	0.346733i
$592$	24.7708	+	12.4917i	1.01807	+	0.513407i
$593$	6.01591	+	6.01591i	0.247044	+	0.247044i	0.819756	−	0.572712i	$-0.194109\pi$
$593$	6.01591	+	6.01591i	0.247044	+	0.247044i	−0.572712	+	0.819756i	$0.694109\pi$
$594$	−48.9639	+	44.3783i	−2.00901	+	1.82087i
$595$	11.8723			0.486718
$596$	−20.1297	+	0.0418962i	−0.824544	+	0.00171613i
$597$	21.6393	+	29.7840i	0.885639	+	1.21898i
$598$	−22.7467	−	21.1867i	−0.930181	−	0.866387i
$599$	−40.4486	+	13.1426i	−1.65269	+	0.536990i	−0.979320	−	0.202318i	$-0.935152\pi$
$599$	−40.4486	+	13.1426i	−1.65269	+	0.536990i	−0.673367	+	0.739309i	$0.735152\pi$
$600$	−22.9242	−	54.8588i	−0.935876	−	2.23960i
$601$	0.629636	+	0.457458i	0.0256834	+	0.0186601i	0.600553	−	0.799585i	$-0.294947\pi$
$601$	0.629636	+	0.457458i	0.0256834	+	0.0186601i	−0.574869	+	0.818245i	$0.694947\pi$
$602$	−2.03428	+	0.845106i	−0.0829109	+	0.0344439i
$603$	−51.2778	+	26.1274i	−2.08819	+	1.06399i
$604$	2.18470	+	6.67649i	0.0888941	+	0.271663i
$605$	−37.1581	−	3.73781i	−1.51069	−	0.151964i
$606$	−30.7065	−	49.9917i	−1.24737	−	2.03077i
$607$	−37.1610	−	12.0743i	−1.50832	−	0.490082i	−0.565887	−	0.824483i	$-0.691466\pi$
$607$	−37.1610	−	12.0743i	−1.50832	−	0.490082i	−0.942431	+	0.334401i	$0.891466\pi$
$608$	2.07807	−	3.43105i	0.0842768	−	0.139147i
$609$	3.63525	+	22.9521i	0.147308	+	0.930065i
$610$	−5.44043	−	68.2195i	−0.220277	−	2.76213i
$611$	−8.26645	+	3.76271i	−0.334425	+	0.152223i
$612$	25.1805	+	49.1663i	1.01786	+	1.98743i
$613$	−3.61765	+	22.8409i	−0.146115	+	0.922536i	0.800304	+	0.599595i	$0.204672\pi$
$613$	−3.61765	+	22.8409i	−0.146115	+	0.922536i	−0.946419	+	0.322941i	$0.895328\pi$
$614$	−13.4997	+	22.0811i	−0.544804	+	0.891120i
$615$	−32.1091			−1.29476
$616$	−4.33854	+	7.60837i	−0.174805	+	0.306550i
$617$	−3.60282	+	3.60282i	−0.145044	+	0.145044i	−0.775900	−	0.630856i	$-0.782704\pi$
$617$	−3.60282	+	3.60282i	−0.145044	+	0.145044i	0.630856	+	0.775900i	$0.282704\pi$
$618$	−7.03478	−	29.1682i	−0.282980	−	1.17332i
$619$	−6.00439	+	37.9102i	−0.241337	+	1.52374i	0.507888	+	0.861423i	$0.330426\pi$
$619$	−6.00439	+	37.9102i	−0.241337	+	1.52374i	−0.749224	+	0.662316i	$0.769574\pi$
$620$	−19.4326	+	9.95240i	−0.780431	+	0.399698i
$621$	81.6860	−	26.5414i	3.27795	−	1.06507i
$622$	11.8953	−	13.9570i	0.476957	−	0.559623i
$623$	−0.935920	−	0.679986i	−0.0374968	−	0.0272430i
$624$	−25.7823	−	38.6407i	−1.03212	−	1.54687i
$625$	4.64705	−	14.3021i	0.185882	−	0.572086i
$626$	−14.1415	−	23.0230i	−0.565209	−	0.920186i
$627$	4.62477	+	5.99934i	0.184696	+	0.239591i
$628$	4.94851	−	9.76218i	0.197467	−	0.389553i
$629$	11.7932	+	23.1455i	0.470227	+	0.922872i
$630$	12.6185	−	30.5537i	0.502734	−	1.21729i
$631$	−8.67320	+	1.37370i	−0.345274	+	0.0546861i	−0.326664	−	0.945141i	$-0.605924\pi$
$631$	−8.67320	+	1.37370i	−0.345274	+	0.0546861i	−0.0186109	+	0.999827i	$0.505924\pi$
$632$	−1.49771	+	0.625859i	−0.0595759	+	0.0248953i
$633$	−6.64781	−	20.4598i	−0.264227	−	0.813206i
$634$	5.25539	+	6.14032i	0.208718	+	0.243863i
$635$	5.02010	−	31.6957i	0.199217	−	1.25780i
$636$	−48.9971	+	49.2015i	−1.94286	+	1.95097i
$637$	17.2862	+	13.7628i	0.684903	+	0.545304i
$638$	−35.4776	−	7.41972i	−1.40457	−	0.293750i
$639$	−72.0572	−	72.0572i	−2.85054	−	2.85054i
$640$	14.4402	−	35.5929i	0.570800	−	1.40693i
$641$	−6.47096	−	8.90651i	−0.255587	−	0.351786i	0.661871	−	0.749618i	$-0.269763\pi$
$641$	−6.47096	−	8.90651i	−0.255587	−	0.351786i	−0.917458	+	0.397832i	$0.869763\pi$
$642$	−4.34932	+	56.0085i	−0.171654	+	2.21048i
$643$	4.00991	−	7.86988i	0.158135	−	0.310358i	−0.798322	−	0.602231i	$-0.794279\pi$
$643$	4.00991	−	7.86988i	0.158135	−	0.310358i	0.956457	+	0.291873i	$0.0942785\pi$
$644$	9.19562	−	6.71030i	0.362358	−	0.264423i
$645$	2.85389	+	18.0188i	0.112372	+	0.709489i
$646$	3.46861	−	1.44098i	0.136471	−	0.0566944i
$647$	−0.948919	+	2.92047i	−0.0373059	+	0.114816i	−0.967975	−	0.251046i	$-0.919226\pi$
$647$	−0.948919	+	2.92047i	−0.0373059	+	0.114816i	0.930669	+	0.365861i	$0.119226\pi$
$648$	65.5592	−	5.36561i	2.57541	−	0.210781i
$649$	−2.54197	+	0.906548i	−0.0997809	+	0.0355851i
$650$	−4.03620	+	33.0325i	−0.158313	+	1.29564i
$651$	−9.19610	−	2.98799i	−0.360424	−	0.117109i
$652$	−18.2494	−	13.2010i	−0.714700	−	0.516991i
$653$	−4.93859	−	3.58810i	−0.193262	−	0.140413i	0.486946	−	0.873432i	$-0.338111\pi$
$653$	−4.93859	−	3.58810i	−0.193262	−	0.140413i	−0.680208	+	0.733019i	$0.738111\pi$
$654$	49.4386	−	3.94267i	1.93320	−	0.154171i
$655$	−0.0194599	+	0.0381922i	−0.000760361	+	0.00149229i
$656$	−8.33968	−	8.27053i	−0.325610	−	0.322910i
$657$	−42.4360	−	6.72120i	−1.65559	−	0.262219i
$658$	−0.779828	−	3.23339i	−0.0304008	−	0.126051i
$659$			41.6355i			1.62189i	0.585124	+	0.810944i	$0.301046\pi$
$659$			41.6355i			1.62189i	−0.585124	+	0.810944i	$0.698954\pi$
$660$	52.8302	+	49.7027i	2.05641	+	1.93467i
$661$	−5.29097	−	5.29097i	−0.205795	−	0.205795i	0.596682	−	0.802477i	$-0.296485\pi$
$661$	−5.29097	−	5.29097i	−0.205795	−	0.205795i	−0.802477	+	0.596682i	$0.796485\pi$
$662$	6.32297	+	3.86568i	0.245749	+	0.150244i
$663$	1.91699	−	43.4540i	0.0744498	−	1.68761i
$664$	−4.33556	−	17.8137i	−0.168253	−	0.691307i
$665$	−2.00273	−	1.02044i	−0.0776625	−	0.0395710i
$666$	72.1000	−	5.74990i	2.79382	−	0.222804i
$667$	38.1121	+	27.6901i	1.47571	+	1.07216i
$668$	11.3413	+	8.20393i	0.438808	+	0.317420i
$669$	5.90414	+	11.5875i	0.228267	+	0.448000i
$670$	19.6118	+	31.9289i	0.757670	+	1.23352i
$671$	22.6498	+	41.4945i	0.874385	+	1.60188i
$672$	15.6823	−	6.59163i	0.604958	−	0.254278i
$673$	46.3122	+	15.0477i	1.78520	+	0.580047i	0.999268	−	0.0382622i	$-0.0121822\pi$
$673$	46.3122	+	15.0477i	1.78520	+	0.580047i	0.785935	+	0.618310i	$0.212182\pi$
$674$	−10.3466	+	25.0525i	−0.398534	+	0.964986i
$675$	−74.3886	−	54.0464i	−2.86322	−	2.08025i
$676$	1.84412	+	25.9345i	0.0709277	+	0.997481i
$677$	−3.35132	−	10.3143i	−0.128802	−	0.396411i	0.865773	−	0.500437i	$-0.166827\pi$
$677$	−3.35132	−	10.3143i	−0.128802	−	0.396411i	−0.994575	+	0.104026i	$0.966827\pi$
$678$	−15.7000	−	1.21918i	−0.602957	−	0.0468224i
$679$	4.97646	+	6.84950i	0.190979	+	0.262860i
$680$	30.6074	−	18.8880i	1.17374	−	0.724320i
$681$	45.1654	−	45.1654i	1.73074	−	1.73074i
$682$	9.45272	−	11.7516i	0.361963	−	0.449991i
$683$	25.2360	−	25.2360i	0.965630	−	0.965630i	−0.0337985	−	0.999429i	$-0.510760\pi$
$683$	25.2360	−	25.2360i	0.965630	−	0.965630i	0.999429	+	0.0337985i	$0.0107604\pi$
$684$	−0.0217666	−	10.4581i	−0.000832266	−	0.399875i
$685$	−25.9500	+	18.8538i	−0.991500	+	0.720367i
$686$	−13.1695	+	11.2715i	−0.502812	+	0.430348i
$687$	−8.16782	−	4.16171i	−0.311622	−	0.158779i
$688$	−3.89997	+	5.41510i	−0.148685	+	0.206449i
$689$	37.4559	−	10.3692i	1.42696	−	0.395033i
$690$	−36.1688	−	87.0629i	−1.37692	−	3.31443i
$691$	−25.1927	+	12.8363i	−0.958375	+	0.488317i	−0.861933	−	0.507022i	$-0.830746\pi$
$691$	−25.1927	+	12.8363i	−0.958375	+	0.488317i	−0.0964421	+	0.995339i	$0.530746\pi$
$692$	5.02062	+	2.54498i	0.190855	+	0.0967458i
$693$	0.648701	+	22.8255i	0.0246421	+	0.867071i
$694$	14.4303	−	8.86359i	0.547768	−	0.336457i
$695$	52.1539	−	26.5738i	1.97831	−	1.00800i
$696$	45.8869	+	53.3882i	1.73934	+	2.02367i
$697$	−1.72044	−	10.8624i	−0.0651663	−	0.411444i
$698$	37.6128	−	2.99958i	1.42367	−	0.113536i
$699$	14.7352	+	45.3502i	0.557336	+	1.71530i
$700$	−11.5981	−	3.74179i	−0.438368	−	0.141426i
$701$	17.8137	+	24.5184i	0.672813	+	0.926048i	0.999820	−	0.0189743i	$-0.00604006\pi$
$701$	17.8137	+	24.5184i	0.672813	+	0.926048i	−0.327007	+	0.945022i	$0.606040\pi$
$702$	−65.1263	−	30.3224i	−2.45803	−	1.14444i
$703$		−	4.91803i		−	0.185487i
$704$	0.919350	+	26.5171i	0.0346493	+	0.999400i
$705$	−27.5460			−1.03744
$706$	0.967281	−	1.58215i	0.0364041	−	0.0595451i
$707$	−11.8774	−	1.88120i	−0.446697	−	0.0707498i
$708$	4.98859	+	1.60942i	0.187483	+	0.0604857i
$709$	−14.0160	+	27.5079i	−0.526382	+	1.03308i	0.462810	+	0.886457i	$0.346841\pi$
$709$	−14.0160	+	27.5079i	−0.526382	+	1.03308i	−0.989192	+	0.146625i	$0.953159\pi$
$710$	−43.0382	+	50.4976i	−1.61520	+	1.89514i
$711$	−2.48752	+	3.42377i	−0.0932891	+	0.128401i
$712$	−3.49466	−	0.264060i	−0.130968	−	0.00989608i
$713$	−17.4655	+	8.89913i	−0.654089	+	0.333275i
$714$	15.4925	+	3.70237i	0.579791	+	0.138558i
$715$	−11.9390	−	38.8038i	−0.446494	−	1.45118i
$716$	−12.5832	+	24.8234i	−0.470255	+	0.927695i
$717$	13.1764	+	25.8601i	0.492082	+	0.965764i
$718$	−7.90357	+	3.28341i	−0.294959	+	0.122536i
$719$	−21.1217	−	15.3458i	−0.787707	−	0.572302i	0.119575	−	0.992825i	$-0.461847\pi$
$719$	−21.1217	−	15.3458i	−0.787707	−	0.572302i	−0.907282	+	0.420523i	$0.861847\pi$
$720$	−16.0774	−	98.8442i	−0.599170	−	3.68370i
$721$	−5.47975	−	2.79207i	−0.204077	−	0.103982i
$722$	26.0804	+	2.02527i	0.970613	+	0.0753727i
$723$	7.06644	−	44.6157i	0.262804	−	1.65928i
$724$	−20.4094	+	20.4945i	−0.758510	+	0.761674i
$725$		−	50.4327i		−	1.87302i
$726$	−47.3228	−	16.4653i	−1.75632	−	0.611083i
$727$	49.7849			1.84642			0.923210	−	0.384297i	$-0.125556\pi$
$727$	49.7849			1.84642			0.923210	+	0.384297i	$0.125556\pi$
$728$	−9.45352	−	1.13515i	−0.350371	−	0.0420714i
$729$	28.6062	−	20.7836i	1.05949	−	0.769765i
$730$	−2.16583	+	27.8905i	−0.0801608	+	1.03227i
$731$	−5.94280	+	1.93093i	−0.219802	+	0.0714181i
$732$	14.1748	−	90.7179i	0.523917	−	3.35303i
$733$	35.1236	−	5.56303i	1.29732	−	0.205475i	0.530691	−	0.847565i	$-0.321933\pi$
$733$	35.1236	−	5.56303i	1.29732	−	0.205475i	0.766629	+	0.642090i	$0.221933\pi$
$734$	−13.6955	+	33.1613i	−0.505509	+	1.22401i
$735$	30.4236	+	59.7096i	1.12219	+	2.20242i
$736$	13.0312	−	31.9290i	0.480337	−	1.17692i
$737$	−21.3643	−	14.6132i	−0.786965	−	0.538283i
$738$	−29.7833	−	7.11757i	−1.09634	−	0.262001i
$739$	2.00312	+	3.93135i	0.0736861	+	0.144617i	0.924911	−	0.380185i	$-0.124140\pi$
$739$	2.00312	+	3.93135i	0.0736861	+	0.144617i	−0.851225	+	0.524802i	$0.824140\pi$
$740$	−7.46381	−	46.4981i	−0.274375	−	1.70930i
$741$	−4.05831	+	7.16544i	−0.149086	+	0.263229i
$742$	1.13144	+	14.1876i	0.0415365	+	0.520842i
$743$	−2.55623	+	5.01688i	−0.0937788	+	0.184051i	−0.933131	−	0.359537i	$-0.882935\pi$
$743$	−2.55623	+	5.01688i	−0.0937788	+	0.184051i	0.839352	+	0.543588i	$0.182935\pi$
$744$	−28.4617	+	6.92710i	−1.04346	+	0.253960i
$745$	20.0851	+	27.6447i	0.735860	+	1.01282i
$746$	−11.6748	+	2.81573i	−0.427445	+	0.103091i
$747$	−33.7992	−	33.7992i	−1.23665	−	1.23665i
$748$	−13.9836	+	20.5355i	−0.511291	+	0.750852i
$749$	8.14213	+	8.14213i	0.297507	+	0.297507i
$750$	−12.3127	+	20.1394i	−0.449594	+	0.735388i
$751$	36.8775	−	26.7931i	1.34568	−	0.977693i	0.346464	−	0.938063i	$-0.387382\pi$
$751$	36.8775	−	26.7931i	1.34568	−	0.977693i	0.999214	−	0.0396292i	$-0.0126177\pi$
$752$	−7.15451	−	7.09520i	−0.260898	−	0.258735i
$753$	38.7472	−	12.5897i	1.41203	−	0.458795i
$754$	−7.54109	−	38.6743i	−0.274630	−	1.40844i
$755$	7.00926	−	9.64742i	0.255093	−	0.351105i
$756$	15.4192	−	21.3159i	0.560792	−	0.775252i
$757$	10.6928	−	32.9091i	0.388637	−	1.19610i	−0.545170	−	0.838325i	$-0.683535\pi$
$757$	10.6928	−	32.9091i	0.388637	−	1.19610i	0.933807	−	0.357776i	$-0.116465\pi$
$758$	−10.8771	+	45.5150i	−0.395074	+	1.65318i
$759$	47.3391	+	44.7227i	1.71830	+	1.62333i
$760$	−6.78658	+	0.555439i	−0.246175	+	0.0201479i
$761$	−38.2973	+	19.5134i	−1.38828	+	0.707362i	−0.978773	−	0.204947i	$-0.934298\pi$
$761$	−38.2973	+	19.5134i	−1.38828	+	0.707362i	−0.409502	+	0.912309i	$0.634298\pi$
$762$	16.4351	−	39.7949i	0.595381	−	1.44162i
$763$	5.97523	−	8.22420i	0.216318	−	0.297736i
$764$	−5.47740	+	35.0550i	−0.198165	+	1.26825i
$765$	42.5708	−	83.5498i	1.53915	−	3.02075i
$766$	−24.2422	+	20.7485i	−0.875906	+	0.749672i
$767$	−1.98112	−	2.16399i	−0.0715342	−	0.0781370i
$768$	29.9430	−	41.9429i	1.08048	−	1.51349i
$769$	−12.3039	+	12.3039i	−0.443690	+	0.443690i	−0.893250	−	0.449560i	$-0.851581\pi$
$769$	−12.3039	+	12.3039i	−0.443690	+	0.443690i	0.449560	+	0.893250i	$0.351581\pi$
$770$	14.7811	−	1.60248i	0.532673	−	0.0577495i
$771$	42.2288			1.52083
$772$	0.0259342	+	12.4605i	0.000933393	+	0.448464i
$773$	−3.75142	+	23.6855i	−0.134929	+	0.851909i	0.823653	+	0.567094i	$0.191932\pi$
$773$	−3.75142	+	23.6855i	−0.134929	+	0.851909i	−0.958582	+	0.284815i	$0.908068\pi$
$774$	−1.34702	+	17.3462i	−0.0484175	+	0.623498i
$775$	18.6977	+	9.52697i	0.671642	+	0.342219i
$776$	23.7266	+	9.74121i	0.851736	+	0.349689i
$777$	12.2592	−	16.8734i	0.439798	−	0.605330i
$778$	−14.4846	+	35.0721i	−0.519298	+	1.25740i
$779$	−0.643421	+	1.98025i	−0.0230529	+	0.0709497i
$780$	−27.4951	+	73.9055i	−0.984483	+	2.64624i
$781$	12.9190	−	43.9741i	0.462279	−	1.57352i
$782$	27.5152	−	16.9008i	0.983942	−	0.604370i
$783$	103.543	+	33.6432i	3.70033	+	1.20231i
$784$	−7.47788	+	23.3447i	−0.267067	+	0.833741i
$785$	−18.3503	+	2.90640i	−0.654950	+	0.103734i
$786$	−0.0373038	+	0.0437693i	−0.00133058	+	0.00156120i
$787$	−33.6317	−	17.1362i	−1.19884	−	0.610840i	−0.263525	−	0.964653i	$-0.584885\pi$
$787$	−33.6317	−	17.1362i	−1.19884	−	0.610840i	−0.935316	+	0.353812i	$0.884885\pi$
$788$	10.2731	−	31.8426i	0.365963	−	1.13435i
$789$	−20.4791	+	14.8789i	−0.729076	+	0.529704i
$790$	2.35091	+	1.43728i	0.0836418	+	0.0511361i
$791$	−2.28236	+	2.28236i	−0.0811515	+	0.0811515i
$792$	37.9861	+	57.8134i	1.34978	+	2.05431i
$793$	−32.0105	+	40.2053i	−1.13673	+	1.42773i
$794$	−34.2491	−	20.9389i	−1.21545	−	0.743092i
$795$	116.420	+	18.4391i	4.12899	+	0.653968i
$796$	20.3468	−	10.4206i	0.721175	−	0.369350i
$797$	−17.1157	+	5.56122i	−0.606268	+	0.196988i	−0.596034	−	0.802959i	$-0.703258\pi$
$797$	−17.1157	+	5.56122i	−0.606268	+	0.196988i	−0.0102341	+	0.999948i	$0.503258\pi$
$798$	−2.29519	−	1.95615i	−0.0812487	−	0.0692468i
$799$	−1.47595	−	9.31876i	−0.0522152	−	0.329674i
$800$	−35.8534	+	8.80521i	−1.26761	+	0.311311i
$801$	−8.14125	+	4.14817i	−0.287657	+	0.146569i
$802$	−5.87676	+	24.5912i	−0.207516	+	0.868345i
$803$	−6.49112	−	18.2011i	−0.229067	−	0.642304i
$804$	15.6349	+	47.7808i	0.551401	+	1.68510i
$805$	−18.3783	−	5.97146i	−0.647749	−	0.210466i
$806$	15.7629	+	4.50993i	0.555224	+	0.158855i
$807$	22.0355	−	30.3292i	0.775685	−	1.06764i
$808$	−33.6135	+	14.0463i	−1.18252	+	0.494146i
$809$	7.53152	+	23.1796i	0.264794	+	0.814953i	0.991741	+	0.128259i	$0.0409388\pi$
$809$	7.53152	+	23.1796i	0.264794	+	0.814953i	−0.726947	+	0.686694i	$0.759061\pi$
$810$	−72.6061	−	84.8318i	−2.55112	−	2.98069i
$811$	−21.3778	−	3.38590i	−0.750675	−	0.118895i	−0.230639	−	0.973040i	$-0.574081\pi$
$811$	−21.3778	−	3.38590i	−0.750675	−	0.118895i	−0.520036	+	0.854144i	$0.674081\pi$
$812$	14.4296	−	0.0300325i	0.506379	−	0.00105393i
$813$	−25.1703	−	25.1703i	−0.882761	−	0.882761i
$814$	17.8067	+	27.2244i	0.624125	+	0.954216i
$815$			38.2342i			1.33928i
$816$	45.8306	−	15.1025i	1.60439	−	0.528692i
$817$	1.16845	+	0.185064i	0.0408789	+	0.00647458i
$818$	16.2807	+	19.0221i	0.569240	+	0.665091i
$819$	−22.5935	+	10.2841i	−0.789482	+	0.359355i
$820$	−3.07799	+	19.6989i	−0.107488	+	0.687917i
$821$	17.7974	−	2.81883i	0.621132	−	0.0983777i	0.162066	−	0.986780i	$-0.448184\pi$
$821$	17.7974	−	2.81883i	0.621132	−	0.0983777i	0.459066	+	0.888402i	$0.348184\pi$
$822$	−39.7424	+	16.5103i	−1.38617	+	0.575863i
$823$	−8.69691	+	26.7663i	−0.303155	+	0.933016i	0.677204	+	0.735795i	$0.263191\pi$
$823$	−8.69691	+	26.7663i	−0.303155	+	0.933016i	−0.980359	+	0.197220i	$0.936809\pi$
$824$	−18.5691	+	1.51976i	−0.646884	+	0.0529434i
$825$	8.94573	−	69.1420i	0.311450	−	2.40721i
$826$	0.915504	−	0.562333i	0.0318545	−	0.0195661i
$827$	−23.7711	−	46.6534i	−0.826603	−	1.62230i	−0.781987	−	0.623295i	$-0.785794\pi$
$827$	−23.7711	−	46.6534i	−0.826603	−	1.62230i	−0.0446158	−	0.999004i	$-0.514206\pi$
$828$	−14.2499	−	88.7742i	−0.495219	−	3.08512i
$829$	−1.84404	+	2.53810i	−0.0640461	+	0.0881518i	−0.839838	−	0.542836i	$-0.817350\pi$
$829$	−1.84404	+	2.53810i	−0.0640461	+	0.0881518i	0.775792	+	0.630988i	$0.217350\pi$
$830$	−20.1875	+	23.6864i	−0.700719	+	0.822167i
$831$	−6.09999	−	18.7738i	−0.211606	−	0.651258i
$832$	−26.1776	+	12.1134i	−0.907545	+	0.419955i
$833$	−18.5695	+	13.4915i	−0.643396	+	0.467454i
$834$	76.3439	−	18.4126i	2.64357	−	0.637576i
$835$		−	23.7611i		−	0.822287i
$836$	4.12393	−	2.26220i	0.142629	−	0.0782398i
$837$	−32.0328	+	32.0328i	−1.10722	+	1.10722i
$838$	11.9670	+	49.6186i	0.413393	+	1.71404i
$839$	7.90678	−	49.9214i	0.272972	−	1.72348i	−0.346146	−	0.938181i	$-0.612510\pi$
$839$	7.90678	−	49.9214i	0.272972	−	1.72348i	0.619118	−	0.785298i	$-0.287490\pi$
$840$	−24.6688	−	15.0113i	−0.851154	−	0.517940i
$841$	9.49125	+	29.2111i	0.327284	+	1.00728i
$842$	1.58746	+	19.9057i	0.0547074	+	0.685996i
$843$	−53.8612	+	8.53078i	−1.85508	+	0.293815i
$844$	−13.1894	+	2.11714i	−0.453998	+	0.0728751i
$845$	33.8356	−	28.3392i	1.16398	−	0.974898i
$846$	−25.5508	−	6.10608i	−0.878454	−	0.209931i
$847$	−8.87122	+	5.17475i	−0.304819	+	0.177806i
$848$	25.4882	+	34.7762i	0.875270	+	1.19422i
$849$	−62.7174	−	20.3781i	−2.15246	−	0.699375i
$850$	−31.9517	−	13.1959i	−1.09593	−	0.452615i
$851$	−6.61426	−	41.7608i	−0.226734	−	1.43154i
$852$	−71.9092	+	52.4741i	−2.46357	+	1.79773i
$853$	−11.9751	+	23.5024i	−0.410019	+	0.804708i	−0.999996	−	0.00271170i	$-0.999137\pi$
$853$	−11.9751	+	23.5024i	−0.410019	+	0.804708i	0.589977	+	0.807420i	$0.299137\pi$
$854$	−12.2376	−	14.2983i	−0.418763	−	0.489277i
$855$	−14.3624	+	10.4349i	−0.491185	+	0.356867i
$856$	33.9443	+	8.03732i	1.16019	+	0.274710i
$857$			34.2414i			1.16967i	0.811154	+	0.584833i	$0.198840\pi$
$857$			34.2414i			1.16967i	−0.811154	+	0.584833i	$0.801160\pi$
$858$	−3.47861	−	54.3592i	−0.118758	−	1.85579i
$859$		−	14.1353i		−	0.482292i	−0.970489	−	0.241146i	$-0.922477\pi$
$859$		−	14.1353i		−	0.482292i	0.970489	−	0.241146i	$-0.0775232\pi$
$860$	11.3281	−	0.0235773i	0.386285	−	0.000803980i
$861$	−7.14371	+	5.19021i	−0.243457	+	0.176882i
$862$	−20.6084	+	17.6384i	−0.701925	+	0.600765i
$863$	−14.6817	+	28.8145i	−0.499772	+	0.980858i	0.494004	+	0.869460i	$0.335533\pi$
$863$	−14.6817	+	28.8145i	−0.499772	+	0.980858i	−0.993776	+	0.111398i	$0.964467\pi$
$864$	5.83958	−	79.4843i	0.198666	−	2.70411i
$865$	−1.49474	−	9.43742i	−0.0508227	−	0.320882i
$866$	−16.3833	+	39.6695i	−0.556727	+	1.34802i
$867$	−9.10291	−	2.95771i	−0.309151	−	0.100449i
$868$	−2.71468	+	5.35538i	−0.0921422	+	0.181773i
$869$	−1.88766	−	0.244230i	−0.0640345	−	0.00828492i
$870$	27.7764	−	116.230i	0.941709	−	3.94056i
$871$	5.62248	−	27.5714i	0.190511	−	0.934220i
$872$	2.32037	−	30.7085i	0.0785778	−	1.03992i
$873$	66.0466	−	10.4608i	2.23534	−	0.354043i
$874$	−6.09416	+	0.486002i	−0.206138	+	0.0164393i
$875$	1.49514	+	4.60155i	0.0505448	+	0.155561i
$876$	−11.5238	+	35.7195i	−0.389355	+	1.20685i
$877$	−0.705560	+	4.45473i	−0.0238251	+	0.150426i	−0.996733	−	0.0807675i	$-0.974263\pi$
$877$	−0.705560	+	4.45473i	−0.0238251	+	0.150426i	0.972908	+	0.231193i	$0.0742629\pi$
$878$	36.5498	−	8.81508i	1.23350	−	0.297494i
$879$	5.28902	−	5.28902i	0.178394	−	0.178394i
$880$	35.5569	−	27.6469i	1.19862	−	0.931975i
$881$		−	11.3945i		−	0.383892i	−0.981406	−	0.191946i	$-0.938520\pi$
$881$		−	11.3945i		−	0.383892i	0.981406	−	0.191946i	$-0.0614798\pi$
$882$	14.9842	+	62.1286i	0.504543	+	2.09198i
$883$	−7.58678	+	5.51212i	−0.255315	+	0.185498i	−0.708079	−	0.706133i	$-0.750438\pi$
$883$	−7.58678	+	5.51212i	−0.255315	+	0.185498i	0.452764	+	0.891630i	$0.350438\pi$
$884$	−26.4753	−	5.34160i	−0.890461	−	0.179657i
$885$	−2.74965	−	8.46256i	−0.0924285	−	0.284466i
$886$	4.48218	+	3.82009i	0.150582	+	0.128338i
$887$	−4.37357	+	6.01970i	−0.146850	+	0.202122i	−0.876105	−	0.482120i	$-0.839867\pi$
$887$	−4.37357	+	6.01970i	−0.146850	+	0.202122i	0.729255	+	0.684242i	$0.239867\pi$
$888$	4.76066	−	63.0040i	0.159757	−	2.11428i
$889$	−4.00650	−	7.86320i	−0.134374	−	0.263723i
$890$	3.11372	+	5.06927i	0.104372	+	0.169922i
$891$	69.6921	+	33.0507i	2.33477	+	1.10724i
$892$	7.67492	−	2.51141i	0.256975	−	0.0840881i
$893$	−0.551983	+	1.69883i	−0.0184714	+	0.0568492i
$894$	17.5885	+	42.3378i	0.588248	+	1.41599i
$895$	46.6614	−	7.39045i	1.55972	−	0.247035i
$896$	−2.54066	−	10.2530i	−0.0848774	−	0.342528i
$897$	−24.8237	+	66.3024i	−0.828840	+	2.21377i
$898$	−39.3584	+	33.6862i	−1.31341	+	1.12412i
$899$	−24.5411	−	3.88693i	−0.818491	−	0.129636i
$900$	−67.9199	+	68.2032i	−2.26400	+	2.27344i
$901$			40.3727i			1.34501i
$902$	−3.60813	−	13.2915i	−0.120138	−	0.442560i
$903$	3.54755	+	3.54755i	0.118055	+	0.118055i
$904$	−2.25298	+	9.51512i	−0.0749331	+	0.316468i
$905$	48.4940	+	7.68069i	1.61199	+	0.255315i
$906$	12.1551	−	10.4033i	0.403826	−	0.345627i
$907$	−0.856152	−	2.63497i	−0.0284281	−	0.0874926i	0.935836	−	0.352436i	$-0.114647\pi$
$907$	−0.856152	−	2.63497i	−0.0284281	−	0.0874926i	−0.964264	+	0.264944i	$0.914647\pi$
$908$	−23.3794	−	32.0386i	−0.775874	−	1.06324i
$909$	−55.8278	+	76.8403i	−1.85169	+	2.54863i
$910$	7.84422	+	14.1318i	0.260033	+	0.468464i
$911$	47.5840	+	15.4610i	1.57653	+	0.512245i	0.961160	−	0.275993i	$-0.0890067\pi$
$911$	47.5840	+	15.4610i	1.57653	+	0.512245i	0.615370	+	0.788239i	$0.289007\pi$
$912$	−9.02919	−	1.39158i	−0.298986	−	0.0460798i
$913$	6.05980	−	20.6265i	0.200550	−	0.682638i
$914$	−13.5799	−	3.24530i	−0.449183	−	0.107345i
$915$	−138.876	+	70.7611i	−4.59111	+	2.33929i
$916$	−3.33618	+	4.61202i	−0.110231	+	0.152385i
$917$	0.00184402	+	0.0116427i	6.08948e−5	+	0.000384474i
$918$	48.4070	−	56.7969i	1.59767	−	1.87458i
$919$	−29.6167	+	9.62305i	−0.976965	+	0.317435i	−0.753624	−	0.657305i	$-0.771696\pi$
$919$	−29.6167	+	9.62305i	−0.976965	+	0.317435i	−0.223341	+	0.974740i	$0.571696\pi$
$920$	−56.8803	+	13.8437i	−1.87529	+	0.456413i
$921$	58.2184	+	9.22088i	1.91836	+	0.303838i
$922$	−0.228099	+	0.373095i	−0.00751206	+	0.0122872i
$923$	49.5075	−	5.61792i	1.62956	−	0.184916i
$924$	19.7879	+	2.51834i	0.650975	+	0.0828473i
$925$	−32.0067	+	32.0067i	−1.05237	+	1.05237i
$926$	22.0545	−	36.0738i	0.724754	−	1.18546i
$927$	−39.2977	+	28.5514i	−1.29070	+	0.937752i
$928$	37.1524	−	23.0338i	1.21959	−	0.756121i
$929$	18.7458	+	9.55147i	0.615030	+	0.313374i	0.733610	−	0.679571i	$-0.237834\pi$
$929$	18.7458	+	9.55147i	0.615030	+	0.313374i	−0.118579	+	0.992945i	$0.537834\pi$
$930$	37.8447	+	32.2544i	1.24098	+	1.05766i
$931$	4.29209	−	0.679800i	0.140667	−	0.0222795i
$932$	29.2349	−	4.69275i	0.957621	−	0.153716i
$933$	−39.7217	−	12.9064i	−1.30043	−	0.422536i
$934$	−25.5236	−	41.5535i	−0.835156	−	1.35967i
$935$	42.1571	−	1.19810i	1.37869	−	0.0391822i
$936$	−41.8861	+	62.4575i	−1.36909	+	2.04149i
$937$	−9.19979	+	28.3140i	−0.300544	+	0.924979i	0.680759	+	0.732508i	$0.261650\pi$
$937$	−9.19979	+	28.3140i	−0.300544	+	0.924979i	−0.981303	+	0.192471i	$0.938350\pi$
$938$	9.52438	+	3.93352i	0.310982	+	0.128434i
$939$	−36.1705	+	49.7845i	−1.18038	+	1.62466i
$940$	−2.64057	+	16.8995i	−0.0861260	+	0.551200i
$941$	−53.0869	−	27.0491i	−1.73058	−	0.881776i	−0.973574	−	0.228373i	$-0.926659\pi$
$941$	−53.0869	−	27.0491i	−1.73058	−	0.881776i	−0.757010	−	0.653403i	$-0.773341\pi$
$942$	−24.8521	−	1.92988i	−0.809726	−	0.0628790i
$943$	−2.80029	+	17.6803i	−0.0911899	+	0.575750i
$944$	1.46559	−	2.90622i	0.0477008	−	0.0945894i
$945$	−44.6588			−1.45275
$946$	−7.13818	+	3.20616i	−0.232082	+	0.104241i
$947$	−30.5558	+	30.5558i	−0.992931	+	0.992931i	−0.999975	−	0.00704374i	$-0.997758\pi$
$947$	−30.5558	+	30.5558i	−0.992931	+	0.992931i	0.00704374	+	0.999975i	$0.497758\pi$
$948$	2.61955	+	2.60867i	0.0850791	+	0.0847256i
$949$	15.4947	−	14.1853i	0.502979	−	0.460476i
$950$	4.25569	+	4.97229i	0.138073	+	0.161322i
$951$	8.35682	−	16.4012i	0.270989	−	0.531845i
$952$	3.75652	−	9.14973i	0.121749	−	0.296544i
$953$	10.5609	−	14.5358i	0.342101	−	0.470862i	−0.602953	−	0.797777i	$-0.706009\pi$
$953$	10.5609	−	14.5358i	0.342101	−	0.470862i	0.945054	+	0.326915i	$0.106009\pi$
$954$	103.900	+	42.9102i	3.36389	+	1.38927i
$955$	53.6643	−	27.3433i	1.73654	−	0.884810i
$956$	17.1283	−	5.60476i	0.553969	−	0.181271i
$957$	15.2246	+	81.1331i	0.492140	+	2.62266i
$958$	2.27243	+	0.543062i	0.0734189	+	0.0175455i
$959$	−2.72585	+	8.38930i	−0.0880222	+	0.270905i
$960$	−87.4793	+	0.546222i	−2.82338	+	0.0176292i
$961$	−12.1444	+	16.7153i	−0.391753	+	0.539202i
$962$	−19.7584	+	29.3302i	−0.637037	+	0.945644i
$963$	86.4945	−	28.1038i	2.78725	−	0.905631i
$964$	−26.6944	−	8.61215i	−0.859768	−	0.277379i
$965$	17.1124	−	12.4329i	0.550868	−	0.400229i
$966$	−22.1201	−	13.5235i	−0.711701	−	0.435113i
$967$	−39.0126	−	39.0126i	−1.25456	−	1.25456i	−0.953654	−	0.300906i	$-0.902711\pi$
$967$	−39.0126	−	39.0126i	−1.25456	−	1.25456i	−0.300906	−	0.953654i	$-0.597289\pi$
$968$	−14.6378	+	27.4542i	−0.470478	+	0.882412i
$969$	−6.04887	−	6.04887i	−0.194318	−	0.194318i
$970$	−10.2080	−	42.3254i	−0.327760	−	1.35899i
$971$	3.87532	+	5.33392i	0.124365	+	0.171174i	0.866660	−	0.498900i	$-0.166262\pi$
$971$	3.87532	+	5.33392i	0.124365	+	0.171174i	−0.742295	+	0.670074i	$0.766262\pi$
$972$	−29.7568	−	58.1018i	−0.954450	−	1.86361i
$973$	7.30789	−	14.3425i	0.234280	−	0.459801i
$974$	27.7207	−	2.21070i	0.888230	−	0.0708353i
$975$	73.0444	−	20.2213i	2.33929	−	0.647601i
$976$	−54.2967	−	17.3925i	−1.73799	−	0.556721i
$977$	−19.7346	−	38.7313i	−0.631366	−	1.23913i	−0.956022	−	0.293293i	$-0.905249\pi$
$977$	−19.7346	−	38.7313i	−0.631366	−	1.23913i	0.324657	−	0.945832i	$-0.394751\pi$
$978$	−11.9233	+	49.8927i	−0.381264	+	1.59539i
$979$	−3.39196	−	2.32010i	−0.108407	−	0.0741506i
$980$	39.5483	−	12.9411i	1.26332	−	0.413388i
$981$	−36.4512	−	71.5395i	−1.16380	−	2.28408i
$982$	−19.1715	−	7.91774i	−0.611788	−	0.252665i
$983$	−3.33574	+	0.528329i	−0.106393	+	0.0168511i	−0.209404	−	0.977829i	$-0.567152\pi$
$983$	−3.33574	+	0.528329i	−0.106393	+	0.0168511i	0.103011	+	0.994680i	$0.467152\pi$
$984$	−10.1596	+	24.7457i	−0.323877	+	0.788866i
$985$	−54.0172	+	17.5513i	−1.72113	+	0.559230i
$986$	40.8086	+	3.16898i	1.29961	+	0.100921i
$987$	−6.12851	+	4.45262i	−0.195073	+	0.141729i
$988$	4.00697	+	3.17665i	0.127479	+	0.101063i
$989$	10.1706			0.323407
$990$	41.7235	−	109.766i	1.32606	−	3.48859i
$991$			17.3545i			0.551285i	0.961260	+	0.275643i	$0.0888906\pi$
$991$			17.3545i			0.551285i	−0.961260	+	0.275643i	$0.911109\pi$
$992$	1.52143	+	18.1253i	0.0483053	+	0.575479i
$993$	2.64042	−	16.6710i	0.0837913	−	0.529037i
$994$	−1.41267	+	18.1917i	−0.0448071	+	0.577005i
$995$	−34.5761	−	17.6174i	−1.09613	−	0.558509i
$996$	−33.7297	+	24.6135i	−1.06877	+	0.779909i
$997$	19.5604	+	14.2115i	0.619485	+	0.450082i	0.852741	−	0.522333i	$-0.174938\pi$
$997$	19.5604	+	14.2115i	0.619485	+	0.450082i	−0.233257	+	0.972415i	$0.574938\pi$
$998$	5.65463	+	13.6114i	0.178994	+	0.430861i
$999$	−44.3613	−	87.0640i	−1.40353	−	2.75458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bk.a.31.7	✓	640
4.3	odd	2	inner	572.2.bk.a.31.63	yes	640
11.5	even	5	inner	572.2.bk.a.291.58	yes	640
13.8	odd	4	inner	572.2.bk.a.515.35	yes	640
44.27	odd	10	inner	572.2.bk.a.291.35	yes	640
52.47	even	4	inner	572.2.bk.a.515.58	yes	640
143.60	odd	20	inner	572.2.bk.a.203.63	yes	640
572.203	even	20	inner	572.2.bk.a.203.7	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bk.a.31.7	✓	640	1.1	even	1	trivial
572.2.bk.a.31.63	yes	640	4.3	odd	2	inner
572.2.bk.a.203.7	yes	640	572.203	even	20	inner
572.2.bk.a.203.63	yes	640	143.60	odd	20	inner
572.2.bk.a.291.35	yes	640	44.27	odd	10	inner
572.2.bk.a.291.58	yes	640	11.5	even	5	inner
572.2.bk.a.515.35	yes	640	13.8	odd	4	inner
572.2.bk.a.515.58	yes	640	52.47	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37479 + 0.331572i) q^{2} +(1.89320 + 2.60576i) q^{3} +(1.78012 - 0.911688i) q^{4} +(-3.02502 - 1.54132i) q^{5} +(-3.46676 - 2.95466i) q^{6} +(-0.922158 + 0.146055i) q^{7} +(-2.14501 + 1.84362i) q^{8} +(-2.27875 + 7.01328i) q^{9} +O(q^{10})\)	\(q+(-1.37479 + 0.331572i) q^{2} +(1.89320 + 2.60576i) q^{3} +(1.78012 - 0.911688i) q^{4} +(-3.02502 - 1.54132i) q^{5} +(-3.46676 - 2.95466i) q^{6} +(-0.922158 + 0.146055i) q^{7} +(-2.14501 + 1.84362i) q^{8} +(-2.27875 + 7.01328i) q^{9} +(4.66983 + 1.11599i) q^{10} +(-3.25973 + 0.611685i) q^{11} +(5.74576 + 2.91256i) q^{12} +(-1.98867 - 3.00752i) q^{13} +(1.21935 - 0.506558i) q^{14} +(-1.71063 - 10.8005i) q^{15} +(2.33765 - 3.24583i) q^{16} +(3.56213 - 1.15741i) q^{17} +(0.807406 - 10.3974i) q^{18} +(-0.700372 - 0.110928i) q^{19} +(-6.79009 + 0.0141323i) q^{20} +(-2.12641 - 2.12641i) q^{21} +(4.27864 - 1.92178i) q^{22} -6.09630 q^{23} +(-8.86496 - 2.09904i) q^{24} +(3.83612 + 5.27996i) q^{25} +(3.73123 + 3.47533i) q^{26} +(-13.3993 + 4.35369i) q^{27} +(-1.50839 + 1.10072i) q^{28} +(-6.25168 - 4.54211i) q^{29} +(5.93291 + 14.2813i) q^{30} +(2.86494 - 1.45976i) q^{31} +(-2.13756 + 5.23745i) q^{32} +(-7.76522 - 7.33604i) q^{33} +(-4.51343 + 2.77230i) q^{34} +(3.01466 + 0.979523i) q^{35} +(2.33747 + 14.5620i) q^{36} +(1.08496 + 6.85019i) q^{37} +(0.999649 - 0.0797209i) q^{38} +(4.07193 - 10.8758i) q^{39} +(9.33030 - 2.27084i) q^{40} +(0.459342 - 2.90017i) q^{41} +(3.62844 + 2.21832i) q^{42} -1.66833 q^{43} +(-5.24504 + 4.06073i) q^{44} +(17.7030 - 17.7030i) q^{45} +(8.38116 - 2.02136i) q^{46} +(0.394064 - 2.48802i) q^{47} +(12.8835 - 0.0536294i) q^{48} +(-5.82835 + 1.89375i) q^{49} +(-7.02456 - 5.98691i) q^{50} +(9.75974 + 7.09087i) q^{51} +(-6.28200 - 3.54070i) q^{52} +(-3.33094 + 10.2516i) q^{53} +(16.9777 - 10.4283i) q^{54} +(10.8035 + 3.17394i) q^{55} +(1.70876 - 2.01340i) q^{56} +(-1.03689 - 2.03501i) q^{57} +(10.1008 + 4.17159i) q^{58} +(0.803695 - 0.127293i) q^{59} +(-12.8918 - 17.6666i) q^{60} +(-4.40460 - 13.5560i) q^{61} +(-3.45469 + 2.95681i) q^{62} +(1.07704 - 6.80017i) q^{63} +(1.20212 - 7.90917i) q^{64} +(1.38021 + 12.1630i) q^{65} +(13.1080 + 7.51082i) q^{66} +(5.51848 + 5.51848i) q^{67} +(5.28582 - 5.30787i) q^{68} +(-11.5415 - 15.8855i) q^{69} +(-4.46932 - 0.347064i) q^{70} +(-6.27371 + 12.3129i) q^{71} +(-8.04189 - 19.2447i) q^{72} +(0.911449 + 5.75466i) q^{73} +(-3.76293 - 9.05785i) q^{74} +(-6.49580 + 19.9920i) q^{75} +(-1.34788 + 0.441056i) q^{76} +(2.91665 - 1.04017i) q^{77} +(-1.99194 + 16.3022i) q^{78} +(0.545807 + 0.177343i) q^{79} +(-12.0743 + 6.21560i) q^{80} +(-18.8146 - 13.6696i) q^{81} +(0.330116 + 4.13945i) q^{82} +(-2.94275 + 5.77547i) q^{83} +(-5.72389 - 1.84664i) q^{84} +(-12.5594 - 1.98922i) q^{85} +(2.29361 - 0.553172i) q^{86} -24.8895i q^{87} +(5.86443 - 7.32178i) q^{88} +(0.876154 + 0.876154i) q^{89} +(-18.4681 + 30.2078i) q^{90} +(2.27314 + 2.48295i) q^{91} +(-10.8521 + 5.55792i) q^{92} +(9.22769 + 4.70174i) q^{93} +(0.283203 + 3.55118i) q^{94} +(1.94766 + 1.41506i) q^{95} +(-17.6944 + 4.34554i) q^{96} +(-4.11683 - 8.07973i) q^{97} +(7.38487 - 4.53603i) q^{98} +(3.13820 - 24.2553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9}+O(q^{10}) \) 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9	\( 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9} - 12 q^{13} + 4 q^{14} - 36 q^{16} - 10 q^{18} - 60 q^{20} - 56 q^{21} - 44 q^{22} - 14 q^{24} + 26 q^{26} - 14 q^{28} - 24 q^{29} - 16 q^{32} - 28 q^{33} + 12 q^{34} - 12 q^{37} + 4 q^{40} - 36 q^{41} - 8 q^{42} + 26 q^{44} - 16 q^{45} - 50 q^{46} + 48 q^{48} + 36 q^{50} - 52 q^{52} - 40 q^{53} + 116 q^{54} - 36 q^{57} - 70 q^{58} + 52 q^{60} - 8 q^{61} - 48 q^{65} - 228 q^{66} - 44 q^{68} - 68 q^{70} - 38 q^{72} - 12 q^{73} - 12 q^{74} + 108 q^{76} + 108 q^{78} + 62 q^{80} - 168 q^{81} - 36 q^{84} - 52 q^{85} - 62 q^{86} + 16 q^{89} - 80 q^{92} - 4 q^{93} - 124 q^{94} - 132 q^{96} - 4 q^{97} - 108 q^{98}+O(q^{100}) \) 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9 - 12 * q^13 + 4 * q^14 - 36 * q^16 - 10 * q^18 - 60 * q^20 - 56 * q^21 - 44 * q^22 - 14 * q^24 + 26 * q^26 - 14 * q^28 - 24 * q^29 - 16 * q^32 - 28 * q^33 + 12 * q^34 - 12 * q^37 + 4 * q^40 - 36 * q^41 - 8 * q^42 + 26 * q^44 - 16 * q^45 - 50 * q^46 + 48 * q^48 + 36 * q^50 - 52 * q^52 - 40 * q^53 + 116 * q^54 - 36 * q^57 - 70 * q^58 + 52 * q^60 - 8 * q^61 - 48 * q^65 - 228 * q^66 - 44 * q^68 - 68 * q^70 - 38 * q^72 - 12 * q^73 - 12 * q^74 + 108 * q^76 + 108 * q^78 + 62 * q^80 - 168 * q^81 - 36 * q^84 - 52 * q^85 - 62 * q^86 + 16 * q^89 - 80 * q^92 - 4 * q^93 - 124 * q^94 - 132 * q^96 - 4 * q^97 - 108 * q^98

Introduction

L-functions

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