LMFDB - Embedded newform 315.2.cg.e.283.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(157,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 3, 2]))

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

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

chi := DirichletCharacter("315.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.cg (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			283.13
Character	$\chi$	$=$	315.283
Dual form			315.2.cg.e.187.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.252864 - 0.943703i) q^{2} +(1.54348 - 0.785915i) q^{3} +(0.905417 - 0.522743i) q^{4} +(-0.290604 - 2.21710i) q^{5} +(-1.13196 - 1.25786i) q^{6} +(-1.88490 + 1.85665i) q^{7} +(-2.10394 - 2.10394i) q^{8} +(1.76468 - 2.42609i) q^{9} +O(q^{10})$	\(q+(-0.252864 - 0.943703i) q^{2} +(1.54348 - 0.785915i) q^{3} +(0.905417 - 0.522743i) q^{4} +(-0.290604 - 2.21710i) q^{5} +(-1.13196 - 1.25786i) q^{6} +(-1.88490 + 1.85665i) q^{7} +(-2.10394 - 2.10394i) q^{8} +(1.76468 - 2.42609i) q^{9} +(-2.01880 + 0.834870i) q^{10} -1.63342 q^{11} +(0.986664 - 1.51842i) q^{12} +(0.137573 + 0.513429i) q^{13} +(2.22875 + 1.30930i) q^{14} +(-2.19100 - 3.19367i) q^{15} +(-0.407995 + 0.706668i) q^{16} +(0.989992 - 0.265268i) q^{17} +(-2.73573 - 1.05186i) q^{18} +(2.99374 + 5.18531i) q^{19} +(-1.42209 - 1.85549i) q^{20} +(-1.45014 + 4.34708i) q^{21} +(0.413034 + 1.54146i) q^{22} +(5.24887 + 5.24887i) q^{23} +(-4.90091 - 1.59387i) q^{24} +(-4.83110 + 1.28860i) q^{25} +(0.449737 - 0.259656i) q^{26} +(0.817045 - 5.13151i) q^{27} +(-0.736068 + 2.66636i) q^{28} +(5.82340 - 3.36214i) q^{29} +(-2.45985 + 2.87521i) q^{30} +(7.23702 - 4.17830i) q^{31} +(-4.97801 - 1.33385i) q^{32} +(-2.52116 + 1.28373i) q^{33} +(-0.500668 - 0.867182i) q^{34} +(4.66415 + 3.63947i) q^{35} +(0.329546 - 3.11909i) q^{36} +(-5.49748 - 1.47305i) q^{37} +(4.13638 - 4.13638i) q^{38} +(0.615853 + 0.684348i) q^{39} +(-4.05324 + 5.27606i) q^{40} +(-6.13816 - 3.54387i) q^{41} +(4.46904 + 0.269277i) q^{42} +(-1.98612 + 7.41230i) q^{43} +(-1.47893 + 0.853858i) q^{44} +(-5.89172 - 3.20744i) q^{45} +(3.62612 - 6.28062i) q^{46} +(1.90773 - 0.511176i) q^{47} +(-0.0743522 + 1.41138i) q^{48} +(0.105686 - 6.99920i) q^{49} +(2.43767 + 4.23328i) q^{50} +(1.31956 - 1.18749i) q^{51} +(0.392952 + 0.392952i) q^{52} +(-1.35099 + 0.361997i) q^{53} +(-5.04922 + 0.526530i) q^{54} +(0.474678 + 3.62146i) q^{55} +(7.87199 + 0.0594290i) q^{56} +(8.69599 + 5.65061i) q^{57} +(-4.64539 - 4.64539i) q^{58} +(-0.552610 - 0.957148i) q^{59} +(-3.65323 - 1.74628i) q^{60} +(11.8958 + 6.86804i) q^{61} +(-5.77305 - 5.77305i) q^{62} +(1.17817 + 7.84933i) q^{63} +6.66703i q^{64} +(1.09835 - 0.454218i) q^{65} +(1.84897 + 2.05461i) q^{66} +(-5.39935 - 1.44675i) q^{67} +(0.757689 - 0.757689i) q^{68} +(12.2267 + 3.97637i) q^{69} +(2.25518 - 5.32186i) q^{70} -6.35753 q^{71} +(-8.81711 + 1.39158i) q^{72} +(1.62714 + 6.07255i) q^{73} +5.56047i q^{74} +(-6.44399 + 5.78576i) q^{75} +(5.42116 + 3.12991i) q^{76} +(3.07883 - 3.03269i) q^{77} +(0.490094 - 0.754229i) q^{78} +(5.83478 + 3.36871i) q^{79} +(1.68532 + 0.699207i) q^{80} +(-2.77184 - 8.56253i) q^{81} +(-1.79224 + 6.68871i) q^{82} +(-3.78491 - 1.01416i) q^{83} +(0.959425 + 4.69397i) q^{84} +(-0.875822 - 2.11783i) q^{85} +7.49722 q^{86} +(6.34596 - 9.76610i) q^{87} +(3.43661 + 3.43661i) q^{88} +(9.04644 + 15.6689i) q^{89} +(-1.53706 + 6.37108i) q^{90} +(-1.21257 - 0.712336i) q^{91} +(7.49622 + 2.00861i) q^{92} +(7.88643 - 12.1368i) q^{93} +(-0.964796 - 1.67108i) q^{94} +(10.6264 - 8.14430i) q^{95} +(-8.73177 + 1.85351i) q^{96} +(-0.0399199 + 0.148983i) q^{97} +(-6.63189 + 1.67011i) q^{98} +(-2.88246 + 3.96283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 2 q^{2} - 12 q^{3} - 24 q^{6} + 6 q^{7} - 16 q^{8}+O(q^{10}) $ 160 * q - 2 * q^2 - 12 * q^3 - 24 * q^6 + 6 * q^7 - 16 * q^8	$ 160 q - 2 q^{2} - 12 q^{3} - 24 q^{6} + 6 q^{7} - 16 q^{8} - 24 q^{10} + 32 q^{11} - 12 q^{12} + 16 q^{15} + 76 q^{16} - 6 q^{17} - 44 q^{18} - 60 q^{20} - 60 q^{21} + 8 q^{22} - 16 q^{23} - 4 q^{25} - 36 q^{26} + 36 q^{27} + 22 q^{28} - 44 q^{30} + 48 q^{31} - 6 q^{32} + 60 q^{33} - 36 q^{35} - 32 q^{36} - 4 q^{37} + 12 q^{41} + 2 q^{42} - 4 q^{43} - 24 q^{45} - 16 q^{46} - 54 q^{47} + 18 q^{48} - 44 q^{50} - 4 q^{51} + 8 q^{53} - 92 q^{56} - 4 q^{57} - 56 q^{58} - 28 q^{60} - 24 q^{61} + 54 q^{63} + 62 q^{65} + 12 q^{66} + 12 q^{67} + 2 q^{70} - 40 q^{71} + 28 q^{72} + 36 q^{73} + 36 q^{75} - 96 q^{76} - 110 q^{77} - 62 q^{78} + 36 q^{80} - 16 q^{81} - 66 q^{82} + 138 q^{83} - 20 q^{85} + 32 q^{86} + 48 q^{87} - 92 q^{88} - 18 q^{90} - 48 q^{91} - 26 q^{92} + 40 q^{93} - 94 q^{95} + 132 q^{96} - 48 q^{97} + 102 q^{98}+O(q^{100}) $ 160 * q - 2 * q^2 - 12 * q^3 - 24 * q^6 + 6 * q^7 - 16 * q^8 - 24 * q^10 + 32 * q^11 - 12 * q^12 + 16 * q^15 + 76 * q^16 - 6 * q^17 - 44 * q^18 - 60 * q^20 - 60 * q^21 + 8 * q^22 - 16 * q^23 - 4 * q^25 - 36 * q^26 + 36 * q^27 + 22 * q^28 - 44 * q^30 + 48 * q^31 - 6 * q^32 + 60 * q^33 - 36 * q^35 - 32 * q^36 - 4 * q^37 + 12 * q^41 + 2 * q^42 - 4 * q^43 - 24 * q^45 - 16 * q^46 - 54 * q^47 + 18 * q^48 - 44 * q^50 - 4 * q^51 + 8 * q^53 - 92 * q^56 - 4 * q^57 - 56 * q^58 - 28 * q^60 - 24 * q^61 + 54 * q^63 + 62 * q^65 + 12 * q^66 + 12 * q^67 + 2 * q^70 - 40 * q^71 + 28 * q^72 + 36 * q^73 + 36 * q^75 - 96 * q^76 - 110 * q^77 - 62 * q^78 + 36 * q^80 - 16 * q^81 - 66 * q^82 + 138 * q^83 - 20 * q^85 + 32 * q^86 + 48 * q^87 - 92 * q^88 - 18 * q^90 - 48 * q^91 - 26 * q^92 + 40 * q^93 - 94 * q^95 + 132 * q^96 - 48 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.252864	−	0.943703i	−0.178802	−	0.667298i	−0.995873	−	0.0907609i	$-0.971070\pi$
$2$	−0.252864	−	0.943703i	−0.178802	−	0.667298i	0.817071	−	0.576538i	$-0.195597\pi$
$3$	1.54348	−	0.785915i	0.891130	−	0.453748i
$3$	1.54348	−	0.785915i	0.891130	−	0.453748i
$4$	0.905417	−	0.522743i	0.452708	−	0.261371i
$5$	−0.290604	−	2.21710i	−0.129962	−	0.991519i
$5$	−0.290604	−	2.21710i	−0.129962	−	0.991519i
$6$	−1.13196	−	1.25786i	−0.462121	−	0.513519i
$7$	−1.88490	+	1.85665i	−0.712425	+	0.701749i
$7$	−1.88490	+	1.85665i	−0.712425	+	0.701749i
$8$	−2.10394	−	2.10394i	−0.743854	−	0.743854i
$9$	1.76468	−	2.42609i	0.588225	−	0.808697i
$10$	−2.01880	+	0.834870i	−0.638402	+	0.264009i
$11$	−1.63342			−0.492495			−0.246247	−	0.969207i	$-0.579198\pi$
$11$	−1.63342			−0.492495			−0.246247	+	0.969207i	$0.579198\pi$
$12$	0.986664	−	1.51842i	0.284825	−	0.438331i
$13$	0.137573	+	0.513429i	0.0381558	+	0.142400i	0.982376	−	0.186915i	$-0.0598490\pi$
$13$	0.137573	+	0.513429i	0.0381558	+	0.142400i	−0.944220	+	0.329315i	$0.893182\pi$
$14$	2.22875	+	1.30930i	0.595659	+	0.349926i
$15$	−2.19100	−	3.19367i	−0.565713	−	0.824602i
$16$	−0.407995	+	0.706668i	−0.101999	+	0.176667i
$17$	0.989992	−	0.265268i	0.240108	−	0.0643369i	−0.136758	−	0.990604i	$-0.543668\pi$
$17$	0.989992	−	0.265268i	0.240108	−	0.0643369i	0.376866	+	0.926268i	$0.377002\pi$
$18$	−2.73573	−	1.05186i	−0.644818	−	0.247925i
$19$	2.99374	+	5.18531i	0.686811	+	1.18959i	0.972864	+	0.231377i	$0.0743232\pi$
$19$	2.99374	+	5.18531i	0.686811	+	1.18959i	−0.286053	+	0.958214i	$0.592343\pi$
$20$	−1.42209	−	1.85549i	−0.317989	−	0.414901i
$21$	−1.45014	+	4.34708i	−0.316446	+	0.948611i
$22$	0.413034	+	1.54146i	0.0880591	+	0.328641i
$23$	5.24887	+	5.24887i	1.09446	+	1.09446i	0.995046	+	0.0994192i	$0.0316985\pi$
$23$	5.24887	+	5.24887i	1.09446	+	1.09446i	0.0994192	+	0.995046i	$0.468302\pi$
$24$	−4.90091	−	1.59387i	−1.00039	−	0.325348i
$25$	−4.83110	+	1.28860i	−0.966220	+	0.257720i
$26$	0.449737	−	0.259656i	0.0882006	−	0.0509227i
$27$	0.817045	−	5.13151i	0.157240	−	0.987560i
$28$	−0.736068	+	2.66636i	−0.139104	+	0.503895i
$29$	5.82340	−	3.36214i	1.08138	−	0.624334i	0.150110	−	0.988669i	$-0.452037\pi$
$29$	5.82340	−	3.36214i	1.08138	−	0.624334i	0.931268	+	0.364335i	$0.118704\pi$
$30$	−2.45985	+	2.87521i	−0.449105	+	0.524940i
$31$	7.23702	−	4.17830i	1.29981	−	0.750444i	0.319437	−	0.947608i	$-0.396506\pi$
$31$	7.23702	−	4.17830i	1.29981	−	0.750444i	0.980371	+	0.197164i	$0.0631730\pi$
$32$	−4.97801	−	1.33385i	−0.879997	−	0.235794i
$33$	−2.52116	+	1.28373i	−0.438877	+	0.223469i
$34$	−0.500668	−	0.867182i	−0.0858638	−	0.148720i
$35$	4.66415	+	3.63947i	0.788385	+	0.615182i
$36$	0.329546	−	3.11909i	0.0549243	−	0.519849i
$37$	−5.49748	−	1.47305i	−0.903780	−	0.242167i	−0.223141	−	0.974786i	$-0.571631\pi$
$37$	−5.49748	−	1.47305i	−0.903780	−	0.242167i	−0.680639	+	0.732619i	$0.738298\pi$
$38$	4.13638	−	4.13638i	0.671009	−	0.671009i
$39$	0.615853	+	0.684348i	0.0986153	+	0.109583i
$40$	−4.05324	+	5.27606i	−0.640873	+	0.834218i
$41$	−6.13816	−	3.54387i	−0.958619	−	0.553459i	−0.0628714	−	0.998022i	$-0.520026\pi$
$41$	−6.13816	−	3.54387i	−0.958619	−	0.553459i	−0.895748	+	0.444563i	$0.853359\pi$
$42$	4.46904	+	0.269277i	0.689588	+	0.0415503i
$43$	−1.98612	+	7.41230i	−0.302880	+	1.13036i	0.631874	+	0.775071i	$0.282286\pi$
$43$	−1.98612	+	7.41230i	−0.302880	+	1.13036i	−0.934755	+	0.355294i	$0.884381\pi$
$44$	−1.47893	+	0.853858i	−0.222956	+	0.128724i
$45$	−5.89172	−	3.20744i	−0.878285	−	0.478137i
$46$	3.62612	−	6.28062i	0.534642	−	0.926027i
$47$	1.90773	−	0.511176i	0.278272	−	0.0745627i	−0.116984	−	0.993134i	$-0.537323\pi$
$47$	1.90773	−	0.511176i	0.278272	−	0.0745627i	0.395256	+	0.918571i	$0.370656\pi$
$48$	−0.0743522	+	1.41138i	−0.0107318	+	0.203715i
$49$	0.105686	−	6.99920i	0.0150980	−	0.999886i
$50$	2.43767	+	4.23328i	0.344738	+	0.598676i
$51$	1.31956	−	1.18749i	0.184775	−	0.166281i
$52$	0.392952	+	0.392952i	0.0544926	+	0.0544926i
$53$	−1.35099	+	0.361997i	−0.185573	+	0.0497241i	−0.350409	−	0.936597i	$-0.613957\pi$
$53$	−1.35099	+	0.361997i	−0.185573	+	0.0497241i	0.164836	+	0.986321i	$0.447291\pi$
$54$	−5.04922	+	0.526530i	−0.687112	+	0.0716516i
$55$	0.474678	+	3.62146i	0.0640056	+	0.488318i
$56$	7.87199	+	0.0594290i	1.05194	+	0.00794154i
$57$	8.69599	+	5.65061i	1.15181	+	0.748441i
$58$	−4.64539	−	4.64539i	−0.609970	−	0.609970i
$59$	−0.552610	−	0.957148i	−0.0719437	−	0.124610i	0.827809	−	0.561009i	$-0.189587\pi$
$59$	−0.552610	−	0.957148i	−0.0719437	−	0.124610i	−0.899753	+	0.436399i	$0.856254\pi$
$60$	−3.65323	−	1.74628i	−0.471630	−	0.225443i
$61$	11.8958	+	6.86804i	1.52310	+	0.879363i	0.999627	+	0.0273211i	$0.00869765\pi$
$61$	11.8958	+	6.86804i	1.52310	+	0.879363i	0.523474	+	0.852042i	$0.324636\pi$
$62$	−5.77305	−	5.77305i	−0.733178	−	0.733178i
$63$	1.17817	+	7.84933i	0.148436	+	0.988922i
$64$			6.66703i			0.833378i
$65$	1.09835	−	0.454218i	0.136233	−	0.0563388i
$66$	1.84897	+	2.05461i	0.227592	+	0.252905i
$67$	−5.39935	−	1.44675i	−0.659635	−	0.176749i	−0.0865538	−	0.996247i	$-0.527585\pi$
$67$	−5.39935	−	1.44675i	−0.659635	−	0.176749i	−0.573081	+	0.819498i	$0.694252\pi$
$68$	0.757689	−	0.757689i	0.0918833	−	0.0918833i
$69$	12.2267	+	3.97637i	1.47192	+	0.478699i
$70$	2.25518	−	5.32186i	0.269545	−	0.636084i
$71$	−6.35753			−0.754500			−0.377250	−	0.926112i	$-0.623130\pi$
$71$	−6.35753			−0.754500			−0.377250	+	0.926112i	$0.623130\pi$
$72$	−8.81711	+	1.39158i	−1.03911	+	0.163999i
$73$	1.62714	+	6.07255i	0.190442	+	0.710739i	0.993400	+	0.114703i	$0.0365917\pi$
$73$	1.62714	+	6.07255i	0.190442	+	0.710739i	−0.802958	+	0.596036i	$0.796742\pi$
$74$			5.56047i			0.646391i
$75$	−6.44399	+	5.78576i	−0.744088	+	0.668082i
$76$	5.42116	+	3.12991i	0.621850	+	0.359025i
$77$	3.07883	−	3.03269i	0.350865	−	0.345607i
$78$	0.490094	−	0.754229i	0.0554922	−	0.0853996i
$79$	5.83478	+	3.36871i	0.656465	+	0.379010i	0.790929	−	0.611908i	$-0.209598\pi$
$79$	5.83478	+	3.36871i	0.656465	+	0.379010i	−0.134464	+	0.990918i	$0.542931\pi$
$80$	1.68532	+	0.699207i	0.188425	+	0.0781737i
$81$	−2.77184	−	8.56253i	−0.307982	−	0.951392i
$82$	−1.79224	+	6.68871i	−0.197919	+	0.738645i
$83$	−3.78491	−	1.01416i	−0.415448	−	0.111319i	0.0450392	−	0.998985i	$-0.485659\pi$
$83$	−3.78491	−	1.01416i	−0.415448	−	0.111319i	−0.460488	+	0.887666i	$0.652325\pi$
$84$	0.959425	+	4.69397i	0.104682	+	0.512154i
$85$	−0.875822	−	2.11783i	−0.0949962	−	0.229711i
$86$	7.49722			0.808446
$87$	6.34596	−	9.76610i	0.680358	−	1.04704i
$88$	3.43661	+	3.43661i	0.366344	+	0.366344i
$89$	9.04644	+	15.6689i	0.958921	+	1.66090i	0.725128	+	0.688614i	$0.241780\pi$
$89$	9.04644	+	15.6689i	0.958921	+	1.66090i	0.233793	+	0.972286i	$0.424886\pi$
$90$	−1.53706	+	6.37108i	−0.162021	+	0.671570i
$91$	−1.21257	−	0.712336i	−0.127112	−	0.0746731i
$92$	7.49622	+	2.00861i	0.781535	+	0.209412i
$93$	7.88643	−	12.1368i	0.817785	−	1.25853i
$94$	−0.964796	−	1.67108i	−0.0995111	−	0.172358i
$95$	10.6264	−	8.14430i	1.09024	−	0.835587i
$96$	−8.73177	+	1.85351i	−0.891183	+	0.189173i
$97$	−0.0399199	+	0.148983i	−0.00405325	+	0.0151270i	−0.967923	−	0.251248i	$-0.919159\pi$
$97$	−0.0399199	+	0.148983i	−0.00405325	+	0.0151270i	0.963870	+	0.266375i	$0.0858258\pi$
$98$	−6.63189	+	1.67011i	−0.669922	+	0.168707i
$99$	−2.88246	+	3.96283i	−0.289698	+	0.398279i
$100$	−3.70055	+	3.69214i	−0.370055	+	0.369214i
$101$			8.14296i			0.810255i	0.914260	+	0.405127i	$0.132773\pi$
$101$			8.14296i			0.810255i	−0.914260	+	0.405127i	$0.867227\pi$
$102$	−1.45430	−	0.944998i	−0.143997	−	0.0935687i
$103$	7.26124	−	7.26124i	0.715471	−	0.715471i	−0.252203	−	0.967674i	$-0.581155\pi$
$103$	7.26124	−	7.26124i	0.715471	−	0.715471i	0.967674	+	0.252203i	$0.0811551\pi$
$104$	0.790777	−	1.36967i	0.0775421	−	0.134307i
$105$	10.0593	+	1.95183i	0.981691	+	0.190479i
$106$	0.683235	+	1.18340i	0.0663616	+	0.114942i
$107$	1.22899	+	0.329306i	0.118811	+	0.0318352i	0.317734	−	0.948180i	$-0.397078\pi$
$107$	1.22899	+	0.329306i	0.118811	+	0.0318352i	−0.198924	+	0.980015i	$0.563745\pi$
$108$	−1.94270	−	5.07326i	−0.186936	−	0.488175i
$109$	−10.0397	−	5.79643i	−0.961630	−	0.555197i	−0.0649556	−	0.997888i	$-0.520691\pi$
$109$	−10.0397	−	5.79643i	−0.961630	−	0.555197i	−0.896674	+	0.442691i	$0.854024\pi$
$110$	3.29755	−	1.36369i	0.314409	−	0.130023i
$111$	−9.64295	+	2.04693i	−0.915269	+	0.194286i
$112$	−0.543008	−	2.08950i	−0.0513094	−	0.197440i
$113$	−20.1005	+	5.38592i	−1.89090	+	0.506664i	−0.892438	+	0.451170i	$0.851007\pi$
$113$	−20.1005	+	5.38592i	−1.89090	+	0.506664i	−0.998459	+	0.0554944i	$0.982327\pi$
$114$	3.13359	−	9.63527i	0.293487	−	0.902425i
$115$	10.1119	−	13.1626i	0.942944	−	1.22742i
$116$	3.51507	−	6.08828i	0.326366	−	0.565282i
$117$	1.48840	+	0.572271i	0.137602	+	0.0529065i
$118$	−0.763528	+	0.763528i	−0.0702884	+	0.0702884i
$119$	−1.37353	+	2.33807i	−0.125911	+	0.214331i
$120$	−2.10956	+	11.3290i	−0.192576	+	1.03419i
$121$	−8.33194			−0.757449
$122$	3.47337	−	12.9628i	0.314464	−	1.17359i
$123$	−12.2593	−	0.645827i	−1.10539	−	0.0582323i
$124$	4.36835	−	7.56620i	0.392289	−	0.679465i
$125$	4.26089	+	10.3366i	0.381106	+	0.924531i
$126$	7.10951	−	3.09666i	0.633366	−	0.275872i
$127$	−1.86063	+	1.86063i	−0.165104	+	0.165104i	−0.784824	−	0.619719i	$-0.787246\pi$
$127$	−1.86063	+	1.86063i	−0.165104	+	0.165104i	0.619719	+	0.784824i	$0.287246\pi$
$128$	−3.66433	+	0.981855i	−0.323884	+	0.0867846i
$129$	2.75989	+	13.0017i	0.242995	+	1.14473i
$130$	−0.706379	−	0.921656i	−0.0619535	−	0.0808346i
$131$		−	2.10752i		−	0.184135i	−0.995753	−	0.0920674i	$-0.970652\pi$
$131$		−	2.10752i		−	0.184135i	0.995753	−	0.0920674i	$-0.0293475\pi$
$132$	−1.61164	+	2.48022i	−0.140275	+	0.215876i
$133$	−15.2702	−	4.21545i	−1.32409	−	0.365526i
$134$			5.46121i			0.471777i
$135$	−11.6145	−	0.320235i	−0.999620	−	0.0275614i
$136$	−2.64099	−	1.52478i	−0.226463	−	0.130748i
$137$	−9.56652	+	9.56652i	−0.817323	+	0.817323i	−0.985719	−	0.168396i	$-0.946141\pi$
$137$	−9.56652	+	9.56652i	−0.817323	+	0.817323i	0.168396	+	0.985719i	$0.446141\pi$
$138$	0.660816	−	12.5439i	0.0562524	−	1.06780i
$139$	−6.44269	+	11.1591i	−0.546461	+	0.946499i	0.452052	+	0.891992i	$0.350692\pi$
$139$	−6.44269	+	11.1591i	−0.546461	+	0.946499i	−0.998513	+	0.0545074i	$0.982641\pi$
$140$	6.12550	+	0.857084i	0.517699	+	0.0724368i
$141$	2.54281	−	2.28831i	0.214144	−	0.192710i
$142$	1.60759	+	5.99961i	0.134906	+	0.503476i
$143$	−0.224714	−	0.838645i	−0.0187915	−	0.0701310i
$144$	0.994463	+	2.23687i	0.0828719	+	0.186406i
$145$	−9.14652	−	11.9340i	−0.759577	−	0.991067i
$146$	5.31924	−	3.07106i	0.440223	−	0.254163i
$147$	−5.33765	−	10.8862i	−0.440242	−	0.897879i
$148$	−5.74753	+	1.54005i	−0.472444	+	0.126591i
$149$			3.66315i			0.300097i	0.988679	+	0.150049i	$0.0479430\pi$
$149$			3.66315i			0.300097i	−0.988679	+	0.150049i	$0.952057\pi$
$150$	7.08949	+	4.61820i	0.578855	+	0.377074i
$151$	1.99730			0.162538			0.0812691	−	0.996692i	$-0.474103\pi$
$151$	1.99730			0.162538			0.0812691	+	0.996692i	$0.474103\pi$
$152$	4.61092	−	17.2082i	0.373995	−	1.39577i
$153$	1.10345	−	2.86992i	0.0892088	−	0.232020i
$154$	−3.64049	−	2.13864i	−0.293359	−	0.172337i
$155$	−11.3668	−	14.8310i	−0.913005	−	1.19125i
$156$	0.915341	+	0.297688i	0.0732859	+	0.0238341i
$157$	2.18660	−	8.16051i	0.174510	−	0.651280i	−0.822125	−	0.569307i	$-0.807211\pi$
$157$	2.18660	−	8.16051i	0.174510	−	0.651280i	0.996635	−	0.0819723i	$-0.0261219\pi$
$158$	1.70366	−	6.35813i	0.135536	−	0.505826i
$159$	−1.80073	+	1.62050i	−0.142807	+	0.128514i
$160$	−1.51066	+	11.4244i	−0.119428	+	0.903178i
$161$	−19.6389	−	0.148263i	−1.54776	−	0.0116847i
$162$	−7.37958	+	4.78095i	−0.579795	+	0.375627i
$163$	0.573913	−	2.14187i	0.0449523	−	0.167764i	−0.939801	−	0.341723i	$-0.888989\pi$
$163$	0.573913	−	2.14187i	0.0449523	−	0.167764i	0.984753	+	0.173959i	$0.0556561\pi$
$164$	−7.41012			−0.578633
$165$	3.57882	+	5.21661i	0.278611	+	0.406112i
$166$			3.82828i			0.297132i
$167$	−1.31306	+	0.351833i	−0.101607	+	0.0272256i	−0.309265	−	0.950976i	$-0.600083\pi$
$167$	−1.31306	+	0.351833i	−0.101607	+	0.0272256i	0.207657	+	0.978202i	$0.433416\pi$
$168$	12.1970	−	6.09499i	0.941018	−	0.470238i
$169$	11.0136	−	6.35873i	0.847204	−	0.489133i
$170$	−1.77714	+	1.36204i	−0.136300	+	0.104464i
$171$	17.8630	+	1.88730i	1.36602	+	0.144326i
$172$	2.07646	+	7.74945i	0.158328	+	0.590890i
$173$	−0.530773	−	1.98087i	−0.0403539	−	0.150603i	0.942809	−	0.333333i	$-0.108173\pi$
$173$	−0.530773	−	1.98087i	−0.0403539	−	0.150603i	−0.983163	+	0.182730i	$0.941507\pi$
$174$	−10.8210	−	3.51920i	−0.820335	−	0.266790i
$175$	6.71365	−	11.3985i	0.507505	−	0.861649i
$176$	0.666427	−	1.15429i	0.0502339	−	0.0870076i
$177$	−1.60518	−	1.04304i	−0.120653	−	0.0783995i
$178$	12.4993	−	12.4993i	0.936859	−	0.936859i
$179$	−14.6028	−	8.43092i	−1.09146	−	0.630157i	−0.157498	−	0.987519i	$-0.550343\pi$
$179$	−14.6028	−	8.43092i	−1.09146	−	0.630157i	−0.933966	+	0.357362i	$0.883676\pi$
$180$	−7.01112	+	0.175784i	−0.522578	+	0.0131022i
$181$		−	20.3678i		−	1.51392i	−0.653459	−	0.756962i	$-0.726683\pi$
$181$		−	20.3678i		−	1.51392i	0.653459	−	0.756962i	$-0.273317\pi$
$182$	−0.365618	+	1.32443i	−0.0271014	+	0.0981732i
$183$	23.7587	+	1.25162i	1.75629	+	0.0925223i
$184$		−	22.0866i		−	1.62824i
$185$	−1.66831	+	12.6166i	−0.122656	+	0.927588i
$186$	−13.4477	−	4.37348i	−0.986036	−	0.320679i
$187$	−1.61707	+	0.433294i	−0.118252	+	0.0316856i
$188$	1.46008	−	1.46008i	0.106487	−	0.106487i
$189$	7.98739	+	11.1894i	0.580997	+	0.813906i
$190$	−10.3728	−	7.96873i	−0.752524	−	0.578113i
$191$	−8.61703	+	14.9251i	−0.623506	+	1.07994i	0.365322	+	0.930881i	$0.380959\pi$
$191$	−8.61703	+	14.9251i	−0.623506	+	1.07994i	−0.988828	+	0.149063i	$0.952374\pi$
$192$	5.23972	+	10.2904i	0.378144	+	0.742648i
$193$	2.79962	−	10.4483i	0.201521	−	0.752088i	−0.788960	−	0.614444i	$-0.789380\pi$
$193$	2.79962	−	10.4483i	0.201521	−	0.752088i	0.990482	−	0.137644i	$-0.0439530\pi$
$194$	0.150690			0.0108189
$195$	1.33830	−	1.56428i	0.0958377	−	0.112021i
$196$	−3.56309	−	6.39244i	−0.254507	−	0.456603i
$197$	4.66542	−	4.66542i	0.332398	−	0.332398i	−0.521099	−	0.853496i	$-0.674478\pi$
$197$	4.66542	−	4.66542i	0.332398	−	0.332398i	0.853496	+	0.521099i	$0.174478\pi$
$198$	4.46860	+	1.71812i	0.317570	+	0.122102i
$199$	2.58318	−	4.47420i	0.183117	−	0.317168i	−0.759823	−	0.650130i	$-0.774715\pi$
$199$	2.58318	−	4.47420i	0.183117	−	0.317168i	0.942940	+	0.332962i	$0.108048\pi$
$200$	12.8755	+	7.45320i	0.910432	+	0.527021i
$201$	−9.47082	+	2.01039i	−0.668020	+	0.141802i
$202$	7.68453	−	2.05906i	0.540682	−	0.144875i
$203$	−4.73419	+	17.1493i	−0.332275	+	1.20365i
$204$	0.574001	−	1.76496i	0.0401881	−	0.123572i
$205$	−6.07335	+	14.6388i	−0.424181	+	1.02242i
$206$	−8.68856	−	5.01634i	−0.605360	−	0.349505i
$207$	21.9968	−	3.47168i	1.52888	−	0.241299i
$208$	−0.418953	−	0.112258i	−0.0290492	−	0.00778370i
$209$	−4.89003	−	8.46978i	−0.338251	−	0.585867i
$210$	−0.701704	−	9.98657i	−0.0484222	−	0.689139i
$211$	0.273339	−	0.473437i	0.0188174	−	0.0325927i	−0.856463	−	0.516208i	$-0.827343\pi$
$211$	0.273339	−	0.473437i	0.0188174	−	0.0325927i	0.875281	+	0.483615i	$0.160677\pi$
$212$	−1.03398	+	1.03398i	−0.0710139	+	0.0710139i
$213$	−9.81273	+	4.99648i	−0.672357	+	0.342353i
$214$		−	1.24307i		−	0.0849744i
$215$	17.0110	+	2.24939i	1.16014	+	0.153407i
$216$	−12.5154	+	9.07737i	−0.851565	+	0.617637i
$217$	−5.88341	+	21.3123i	−0.399392	+	1.44677i
$218$	−2.93142	+	10.9402i	−0.198541	+	0.740965i
$219$	7.28397	+	8.09409i	0.492205	+	0.546948i
$220$	2.32287	+	3.03080i	0.156608	+	0.204336i
$221$	0.272392	+	0.471797i	0.0183231	+	0.0317365i
$222$	4.37005	+	8.58248i	0.293299	+	0.576019i
$223$	25.6042	+	6.86061i	1.71458	+	0.459421i	0.976540	−	0.215335i	$-0.0690844\pi$
$223$	25.6042	+	6.86061i	1.71458	+	0.459421i	0.738041	+	0.674756i	$0.235751\pi$
$224$	11.8596	−	6.72826i	0.792400	−	0.449551i
$225$	−5.39907	+	13.9946i	−0.359938	+	0.932976i
$226$	10.1654	+	17.6070i	0.676193	+	1.17120i
$227$	−12.0327	−	12.0327i	−0.798640	−	0.798640i	0.184241	−	0.982881i	$-0.441017\pi$
$227$	−12.0327	−	12.0327i	−0.798640	−	0.798640i	−0.982881	+	0.184241i	$0.941017\pi$
$228$	10.8273	+	0.570388i	0.717056	+	0.0377749i
$229$	−13.9913			−0.924574			−0.462287	−	0.886730i	$-0.652971\pi$
$229$	−13.9913			−0.924574			−0.462287	+	0.886730i	$0.652971\pi$
$230$	−14.9786	−	6.21431i	−0.987657	−	0.409759i
$231$	2.36868	−	7.10061i	0.155848	−	0.467186i
$232$	−19.3258	−	5.17833i	−1.26880	−	0.339974i
$233$	−3.18669	+	11.8929i	−0.208767	+	0.779130i	0.779501	+	0.626401i	$0.215473\pi$
$233$	−3.18669	+	11.8929i	−0.208767	+	0.779130i	−0.988268	+	0.152729i	$0.951194\pi$
$234$	0.163691	−	1.54931i	0.0107008	−	0.101282i
$235$	−1.68772	−	4.08110i	−0.110095	−	0.266221i
$236$	−1.00068	−	0.577745i	−0.0651390	−	0.0376080i
$237$	11.6534	+	0.613908i	0.756970	+	0.0398776i
$238$	2.55376	+	0.704984i	0.165536	+	0.0456973i
$239$	−6.57367	−	3.79531i	−0.425215	−	0.245498i	0.272091	−	0.962272i	$-0.412285\pi$
$239$	−6.57367	−	3.79531i	−0.425215	−	0.245498i	−0.697306	+	0.716773i	$0.745618\pi$
$240$	3.15078	−	0.245306i	0.203382	−	0.0158344i
$241$			6.02593i			0.388164i	0.980985	+	0.194082i	$0.0621728\pi$
$241$			6.02593i			0.388164i	−0.980985	+	0.194082i	$0.937827\pi$
$242$	2.10685	+	7.86287i	0.135433	+	0.505445i
$243$	−11.0077	−	11.0377i	−0.706145	−	0.708068i
$244$	14.3609			0.919361
$245$	−15.5487	+	1.79968i	−0.993368	+	0.114977i
$246$	2.49048	+	11.7325i	0.158787	+	0.748034i
$247$	−2.25043	+	2.25043i	−0.143191	+	0.143191i
$248$	−24.0171	−	6.43537i	−1.52509	−	0.408646i
$249$	−6.63900	+	1.40927i	−0.420729	+	0.0893092i
$250$	8.67723	−	6.63476i	0.548796	−	0.419619i
$251$		−	4.81059i		−	0.303642i	−0.988408	−	0.151821i	$-0.951486\pi$
$251$		−	4.81059i		−	0.303642i	0.988408	−	0.151821i	$-0.0485137\pi$
$252$	5.16991	+	6.49103i	0.325674	+	0.408896i
$253$	−8.57361	−	8.57361i	−0.539018	−	0.539018i
$254$	2.22637	+	1.28540i	0.139695	+	0.0806529i
$255$	−3.01625	−	2.58051i	−0.188885	−	0.161598i
$256$	8.52019	+	14.7574i	0.532512	+	0.922337i
$257$	−11.5783	−	11.5783i	−0.722235	−	0.722235i	0.246825	−	0.969060i	$-0.420613\pi$
$257$	−11.5783	−	11.5783i	−0.722235	−	0.722235i	−0.969060	+	0.246825i	$0.920613\pi$
$258$	11.5718	−	5.89218i	0.720431	−	0.366831i
$259$	13.0971	−	7.43037i	0.813816	−	0.461701i
$260$	0.757022	−	0.985408i	0.0469485	−	0.0611124i
$261$	2.11955	−	20.0612i	0.131197	−	1.24176i
$262$	−1.98887	+	0.532917i	−0.122873	+	0.0329237i
$263$	5.89707	+	5.89707i	0.363629	+	0.363629i	0.865147	−	0.501518i	$-0.167225\pi$
$263$	5.89707	+	5.89707i	0.363629	+	0.363629i	−0.501518	+	0.865147i	$0.667225\pi$
$264$	8.00524	+	2.60347i	0.492688	+	0.160232i
$265$	1.19519	+	2.89009i	0.0734198	+	0.177537i
$266$	−0.116839	+	15.4765i	−0.00716383	+	0.948923i
$267$	26.2775	+	17.0749i	1.60815	+	1.04497i
$268$	−5.64494	+	1.51256i	−0.344819	+	0.0923941i
$269$	1.86662	−	3.23307i	0.113810	−	0.197124i	−0.803494	−	0.595313i	$-0.797028\pi$
$269$	1.86662	−	3.23307i	0.113810	−	0.197124i	0.917303	+	0.398189i	$0.130361\pi$
$270$	2.63470	+	11.0416i	0.160342	+	0.671973i
$271$	5.54325	−	3.20039i	0.336728	−	0.194410i	−0.322096	−	0.946707i	$-0.604387\pi$
$271$	5.54325	−	3.20039i	0.336728	−	0.194410i	0.658824	+	0.752297i	$0.271054\pi$
$272$	−0.216456	+	0.807824i	−0.0131246	+	0.0489815i
$273$	−2.43142	−	0.146502i	−0.147156	−	0.00886672i
$274$	11.4470	+	6.60892i	0.691537	+	0.399259i
$275$	7.89121	−	2.10482i	0.475858	−	0.126925i
$276$	13.1489	−	2.79114i	0.791470	−	0.168007i
$277$	0.406069	−	0.406069i	0.0243983	−	0.0243983i	−0.694802	−	0.719201i	$-0.744508\pi$
$277$	0.406069	−	0.406069i	0.0243983	−	0.0243983i	0.719201	+	0.694802i	$0.244508\pi$
$278$	12.1600	+	3.25825i	0.729306	+	0.195417i
$279$	2.63407	−	24.9310i	0.157697	−	1.49258i
$280$	−2.15587	−	17.4703i	−0.128838	−	1.04405i
$281$	2.21693	+	3.83984i	0.132251	+	0.229065i	0.924544	−	0.381075i	$-0.124446\pi$
$281$	2.21693	+	3.83984i	0.132251	+	0.229065i	−0.792293	+	0.610141i	$0.791113\pi$
$282$	−2.80247	−	1.82103i	−0.166885	−	0.108441i
$283$	7.19375	+	1.92756i	0.427624	+	0.114582i	0.466211	−	0.884674i	$-0.345619\pi$
$283$	7.19375	+	1.92756i	0.427624	+	0.114582i	−0.0385865	+	0.999255i	$0.512286\pi$
$284$	−5.75621	+	3.32335i	−0.341568	+	0.197205i
$285$	10.0009	−	20.9220i	0.592402	−	1.23931i
$286$	−0.734609	+	0.424127i	−0.0434383	+	0.0250791i
$287$	18.1495	−	4.71659i	1.07133	−	0.278412i
$288$	−12.0206	+	9.72329i	−0.708322	+	0.572950i
$289$	−13.8127	+	7.97477i	−0.812513	+	0.469104i
$290$	−8.94935	+	11.6493i	−0.525524	+	0.684069i
$291$	0.0554724	+	0.261327i	0.00325185	+	0.0153192i
$292$	4.64762	+	4.64762i	0.271981	+	0.271981i
$293$	4.98512	+	18.6047i	0.291234	+	1.08690i	0.944163	+	0.329480i	$0.106873\pi$
$293$	4.98512	+	18.6047i	0.291234	+	1.08690i	−0.652929	+	0.757419i	$0.726460\pi$
$294$	−8.92364	+	7.78989i	−0.520437	+	0.454316i
$295$	−1.96151	+	1.50334i	−0.114203	+	0.0875281i
$296$	8.46716	+	14.6656i	0.492144	+	0.852418i
$297$	−1.33458	+	8.38192i	−0.0774400	+	0.486368i
$298$	3.45692	−	0.926280i	0.200254	−	0.0536580i
$299$	−1.97282	+	3.41702i	−0.114091	+	0.197611i
$300$	−2.81003	+	8.60707i	−0.162237	+	0.496929i
$301$	−10.0184	−	17.6590i	−0.577452	−	1.01785i
$302$	−0.505047	−	1.88486i	−0.0290622	−	0.108462i
$303$	6.39967	+	12.5685i	0.367652	+	0.722042i
$304$	−4.88572			−0.280215
$305$	11.7702	−	28.3701i	0.673960	−	1.62447i
$306$	−2.98738	−	0.315629i	−0.170777	−	0.0180433i
$307$	−6.54479	−	6.54479i	−0.373531	−	0.373531i	0.495231	−	0.868761i	$-0.335084\pi$
$307$	−6.54479	−	6.54479i	−0.373531	−	0.373531i	−0.868761	+	0.495231i	$0.835084\pi$
$308$	1.20231	−	4.35529i	0.0685078	−	0.248166i
$309$	5.50088	−	16.9143i	0.312934	−	0.962221i
$310$	−11.1218	+	14.4771i	−0.631675	+	0.822246i
$311$	−21.3328	+	12.3165i	−1.20967	+	0.698406i	−0.962688	−	0.270613i	$-0.912773\pi$
$311$	−21.3328	+	12.3165i	−1.20967	+	0.698406i	−0.246986	+	0.969019i	$0.579440\pi$
$312$	0.144110	−	2.73554i	0.00815860	−	0.154869i
$313$	6.56755	+	24.5104i	0.371220	+	1.38541i	0.858790	+	0.512327i	$0.171216\pi$
$313$	6.56755	+	24.5104i	0.371220	+	1.38541i	−0.487571	+	0.873083i	$0.662117\pi$
$314$	−8.25401			−0.465801
$315$	17.0604	−	4.89318i	0.961244	−	0.275699i
$316$	7.04388			0.396249
$317$	−2.75779	−	10.2922i	−0.154893	−	0.578069i	−0.999114	−	0.0420744i	$-0.986603\pi$
$317$	−2.75779	−	10.2922i	−0.154893	−	0.578069i	0.844221	−	0.535995i	$-0.180063\pi$
$318$	1.98461	+	1.28959i	0.111291	+	0.0723165i
$319$	−9.51206	+	5.49179i	−0.532573	+	0.307481i
$320$	14.7815	−	1.93746i	0.826311	−	0.108308i
$321$	2.15573	−	0.457601i	0.120321	−	0.0255408i
$322$	4.82606	+	18.5708i	0.268946	+	1.03491i
$323$	4.33927	+	4.33927i	0.241444	+	0.241444i
$324$	−6.98567	−	6.30370i	−0.388093	−	0.350205i
$325$	−1.32623	−	2.30315i	−0.0735661	−	0.127756i
$326$	−2.16641			−0.119986
$327$	−20.0516	−	1.05633i	−1.10886	−	0.0584151i
$328$	5.45823	+	20.3704i	0.301380	+	1.12477i
$329$	−2.64681	+	4.50551i	−0.145923	+	0.248397i
$330$	4.01797	−	4.69643i	0.221182	−	0.258530i
$331$	−3.12351	+	5.41009i	−0.171684	+	0.297365i	−0.939009	−	0.343893i	$-0.888254\pi$
$331$	−3.12351	+	5.41009i	−0.171684	+	0.297365i	0.767325	+	0.641259i	$0.221587\pi$
$332$	−3.95707	+	1.06029i	−0.217173	+	0.0581912i
$333$	−13.2750	+	10.7379i	−0.727466	+	0.588436i
$334$	0.664051	+	1.15017i	0.0363352	+	0.0629345i
$335$	−1.63853	+	12.3913i	−0.0895222	+	0.677011i
$336$	−2.48029	−	2.79835i	−0.135311	−	0.152663i
$337$	−3.31266	−	12.3630i	−0.180452	−	0.673457i	−0.995558	−	0.0941452i	$-0.969988\pi$
$337$	−3.31266	−	12.3630i	−0.180452	−	0.673457i	0.815106	−	0.579311i	$-0.196678\pi$
$338$	−8.78571	−	8.78571i	−0.477880	−	0.477880i
$339$	−26.7919	+	24.1104i	−1.45514	+	1.30949i
$340$	−1.90006	−	1.45969i	−0.103045	−	0.0791627i
$341$	−11.8211	+	6.82491i	−0.640148	+	0.369590i
$342$	−2.73587	−	17.3346i	−0.147939	−	0.937348i
$343$	12.7959	+	13.3890i	0.690912	+	0.722939i
$344$	19.7737	−	11.4163i	1.06613	−	0.615528i
$345$	5.26291	−	28.2634i	0.283345	−	1.52165i
$346$	−1.73514	+	1.00178i	−0.0932817	+	0.0538562i
$347$	12.9433	+	3.46816i	0.694835	+	0.186181i	0.588916	−	0.808194i	$-0.299555\pi$
$347$	12.9433	+	3.46816i	0.694835	+	0.186181i	0.105919	+	0.994375i	$0.466222\pi$
$348$	0.640579	−	12.1597i	0.0343386	−	0.651828i
$349$	−15.4350	−	26.7341i	−0.826215	−	1.43105i	−0.900987	−	0.433846i	$-0.857156\pi$
$349$	−15.4350	−	26.7341i	−0.826215	−	1.43105i	0.0747724	−	0.997201i	$-0.476177\pi$
$350$	−12.4545	−	3.45341i	−0.665720	−	0.184592i
$351$	2.74707	−	0.286463i	0.146628	−	0.0152902i
$352$	8.13118	+	2.17874i	0.433394	+	0.116127i
$353$	11.6226	−	11.6226i	0.618609	−	0.618609i	−0.326566	−	0.945174i	$-0.605891\pi$
$353$	11.6226	−	11.6226i	0.618609	−	0.618609i	0.945174	+	0.326566i	$0.105891\pi$
$354$	−0.578424	+	1.77856i	−0.0307429	+	0.0945294i
$355$	1.84752	+	14.0953i	0.0980563	+	0.748101i
$356$	16.3816	+	9.45792i	0.868223	+	0.501269i
$357$	−0.282485	+	4.68825i	−0.0149507	+	0.248129i
$358$	−4.26376	+	15.9126i	−0.225347	+	0.841005i
$359$	−1.40486	+	0.811094i	−0.0741455	+	0.0428079i	−0.536614	−	0.843828i	$-0.680297\pi$
$359$	−1.40486	+	0.811094i	−0.0741455	+	0.0428079i	0.462469	+	0.886635i	$0.346964\pi$
$360$	5.64756	+	19.1441i	0.297652	+	1.00898i
$361$	−8.42494	+	14.5924i	−0.443418	+	0.768022i
$362$	−19.2211	+	5.15028i	−1.01024	+	0.270693i
$363$	−12.8602	+	6.54819i	−0.674986	+	0.343691i
$364$	−1.47025	−	0.0110995i	−0.0770620	−	0.000581774i
$365$	12.9906	−	5.37224i	0.679961	−	0.281196i
$366$	−4.82656	−	22.7376i	−0.252288	−	1.18851i
$367$	1.71374	+	1.71374i	0.0894563	+	0.0894563i	0.750419	−	0.660963i	$-0.229852\pi$
$367$	1.71374	+	1.71374i	0.0894563	+	0.0894563i	−0.660963	+	0.750419i	$0.729852\pi$
$368$	−5.85072	+	1.56770i	−0.304990	+	0.0817218i
$369$	−19.4296	+	8.63796i	−1.01146	+	0.449674i
$370$	12.3281	−	1.61589i	0.640909	−	0.0840063i
$371$	1.87438	−	3.19065i	0.0973129	−	0.165650i
$372$	0.796078	−	15.1114i	0.0412747	−	0.783492i
$373$	−22.6169	−	22.6169i	−1.17106	−	1.17106i	−0.981958	−	0.189099i	$-0.939443\pi$
$373$	−22.6169	−	22.6169i	−1.17106	−	1.17106i	−0.189099	−	0.981958i	$-0.560557\pi$
$374$	0.817800	+	1.41647i	0.0422875	+	0.0732440i
$375$	14.7003	+	12.6056i	0.759119	+	0.650952i
$376$	−5.08924	−	2.93827i	−0.262457	−	0.151530i
$377$	2.52736	+	2.52736i	0.130166	+	0.130166i
$378$	8.53969	−	10.3671i	0.439234	−	0.533227i
$379$		−	30.9678i		−	1.59071i	−0.606146	−	0.795353i	$-0.707285\pi$
$379$		−	30.9678i		−	1.59071i	0.606146	−	0.795353i	$-0.292715\pi$
$380$	5.36392	−	12.9288i	0.275163	−	0.663236i
$381$	−1.40955	+	4.33415i	−0.0722136	+	0.222045i
$382$	16.2638	+	4.35788i	0.832129	+	0.222968i
$383$	13.3140	−	13.3140i	0.680313	−	0.680313i	−0.279758	−	0.960071i	$-0.590254\pi$
$383$	13.3140	−	13.3140i	0.680313	−	0.680313i	0.960071	+	0.279758i	$0.0902542\pi$
$384$	−4.88418	+	4.39533i	−0.249245	+	0.224298i
$385$	−7.61851	−	5.94478i	−0.388275	−	0.302974i
$386$	−10.5681			−0.537900
$387$	14.4781	+	17.8988i	0.735961	+	0.909847i
$388$	0.0417357	+	0.155760i	0.00211881	+	0.00790750i
$389$		−	23.6875i		−	1.20101i	−0.799622	−	0.600503i	$-0.794967\pi$
$389$		−	23.6875i		−	1.20101i	0.799622	−	0.600503i	$-0.205033\pi$
$390$	−1.81463	−	0.867407i	−0.0918872	−	0.0439228i
$391$	6.58870	+	3.80399i	0.333205	+	0.192376i
$392$	−14.9482	+	14.5035i	−0.755000	+	0.732539i
$393$	−1.65633	−	3.25292i	−0.0835508	−	0.164088i
$394$	−5.58249	−	3.22305i	−0.281242	−	0.162375i
$395$	5.77318	−	13.9153i	0.290480	−	0.700154i
$396$	−0.538286	+	5.09479i	−0.0270499	+	0.256023i
$397$	−6.22065	+	23.2158i	−0.312205	+	1.16517i	0.614358	+	0.789027i	$0.289415\pi$
$397$	−6.22065	+	23.2158i	−0.312205	+	1.16517i	−0.926563	+	0.376139i	$0.877252\pi$
$398$	−4.87551	−	1.30639i	−0.244387	−	0.0654834i
$399$	−26.8823	+	5.49461i	−1.34580	+	0.275075i
$400$	1.06045	−	3.93973i	0.0530227	−	0.196986i
$401$	34.2145			1.70859			0.854295	−	0.519789i	$-0.173989\pi$
$401$	34.2145			1.70859			0.854295	+	0.519789i	$0.173989\pi$
$402$	4.29204	+	8.42928i	0.214068	+	0.420414i
$403$	3.14087	+	3.14087i	0.156458	+	0.156458i
$404$	4.25667	+	7.37277i	0.211777	+	0.366809i
$405$	−18.1785	+	8.63376i	−0.903297	+	0.429015i
$406$	17.3810	+	0.131216i	0.862603	+	0.00651216i
$407$	8.97969	+	2.40610i	0.445107	+	0.119266i
$408$	−5.27466	−	0.277872i	−0.261135	−	0.0137567i
$409$	0.0455144	+	0.0788332i	0.00225054	+	0.00389805i	0.867148	−	0.498050i	$-0.165950\pi$
$409$	0.0455144	+	0.0788332i	0.00225054	+	0.00389805i	−0.864898	+	0.501948i	$0.832617\pi$
$410$	15.3504	+	2.02981i	0.758102	+	0.100245i
$411$	−7.24728	+	22.2842i	−0.357482	+	1.09920i
$412$	2.77869	−	10.3702i	0.136896	−	0.510903i
$413$	2.81870	+	0.778123i	0.138699	+	0.0382889i
$414$	−8.83844	−	19.8806i	−0.434386	−	0.977076i
$415$	−1.14860	+	8.68627i	−0.0563825	+	0.426392i
$416$		−	2.73936i		−	0.134308i
$417$	−1.17410	+	22.2872i	−0.0574960	+	1.09141i
$418$	−6.75644	+	6.75644i	−0.330468	+	0.330468i
$419$	13.7216	−	23.7665i	0.670343	−	1.16107i	−0.307464	−	0.951560i	$-0.599480\pi$
$419$	13.7216	−	23.7665i	0.670343	−	1.16107i	0.977807	−	0.209508i	$-0.0671862\pi$
$420$	10.1282	−	3.49123i	0.494206	−	0.170355i
$421$	−5.94319	−	10.2939i	−0.289653	−	0.501695i	0.684074	−	0.729413i	$-0.260207\pi$
$421$	−5.94319	−	10.2939i	−0.289653	−	0.501695i	−0.973727	+	0.227719i	$0.926873\pi$
$422$	−0.515901	−	0.138235i	−0.0251137	−	0.00672919i
$423$	2.12637	−	5.53040i	0.103388	−	0.268897i
$424$	3.60402	+	2.08078i	0.175027	+	0.101052i
$425$	−4.44093	+	2.55724i	−0.215417	+	0.124044i
$426$	7.19648	+	7.99687i	0.348670	+	0.387450i
$427$	−35.1739	+	9.14079i	−1.70219	+	0.442354i
$428$	1.28489	−	0.344285i	0.0621074	−	0.0166416i
$429$	−1.00595	−	1.11783i	−0.0485675	−	0.0539692i
$430$	−2.17872	−	16.6221i	−0.105067	−	0.801590i
$431$	−11.1221	+	19.2640i	−0.535732	+	0.927915i	0.463396	+	0.886152i	$0.346631\pi$
$431$	−11.1221	+	19.2640i	−0.535732	+	0.927915i	−0.999128	+	0.0417634i	$0.986702\pi$
$432$	3.29293	+	2.67101i	0.158431	+	0.128509i
$433$	5.23695	−	5.23695i	0.251672	−	0.251672i	−0.569984	−	0.821656i	$-0.693051\pi$
$433$	5.23695	−	5.23695i	0.251672	−	0.251672i	0.821656	+	0.569984i	$0.193051\pi$
$434$	21.6002	+	0.163069i	1.03684	+	0.00782756i
$435$	−23.4966	−	11.2316i	−1.12658	−	0.538513i
$436$	−12.1202			−0.580450
$437$	−11.5033	+	42.9307i	−0.550275	+	2.05366i
$438$	5.79656	−	8.92060i	0.276970	−	0.426243i
$439$	−9.77505	+	16.9309i	−0.466538	+	0.808067i	−0.999269	−	0.0382173i	$-0.987832\pi$
$439$	−9.77505	+	16.9309i	−0.466538	+	0.808067i	0.532732	+	0.846284i	$0.321165\pi$
$440$	6.62064	−	8.61802i	0.315626	−	0.410848i
$441$	−16.7942	−	12.6077i	−0.799724	−	0.600368i
$442$	0.376358	−	0.376358i	0.0179015	−	0.0179015i
$443$	36.2031	−	9.70060i	1.72006	−	0.460889i	0.742207	−	0.670170i	$-0.233779\pi$
$443$	36.2031	−	9.70060i	1.72006	−	0.460889i	0.977856	+	0.209281i	$0.0671123\pi$
$444$	−7.66087	+	6.89411i	−0.363569	+	0.327180i
$445$	32.1107	−	24.6103i	1.52219	−	1.16664i
$446$		−	25.8975i		−	1.22628i
$447$	2.87892	+	5.65401i	0.136168	+	0.267425i
$448$	−12.3784	−	12.5667i	−0.584822	−	0.593719i
$449$			18.6203i			0.878748i	0.898304	+	0.439374i	$0.144800\pi$
$449$			18.6203i			0.878748i	−0.898304	+	0.439374i	$0.855200\pi$
$450$	14.5720	+	1.55637i	0.686931	+	0.0733678i
$451$	10.0262	+	5.78862i	0.472115	+	0.272576i
$452$	−15.3839	+	15.3839i	−0.723597	+	0.723597i
$453$	3.08280	−	1.56971i	0.144843	−	0.0737514i
$454$	−8.31267	+	14.3980i	−0.390133	+	0.675730i
$455$	−1.22695	+	2.89540i	−0.0575201	+	0.135738i
$456$	−6.40730	−	30.1843i	−0.300049	−	1.41351i
$457$	−7.55435	−	28.1932i	−0.353378	−	1.31882i	−0.882514	−	0.470286i	$-0.844151\pi$
$457$	−7.55435	−	28.1932i	−0.353378	−	1.31882i	0.529136	−	0.848537i	$-0.322516\pi$
$458$	3.53791	+	13.2037i	0.165316	+	0.616967i
$459$	−0.552357	−	5.29690i	−0.0257818	−	0.247238i
$460$	2.27486	−	17.2036i	0.106066	−	0.802122i
$461$	−13.2237	+	7.63473i	−0.615891	+	0.355585i	−0.775267	−	0.631633i	$-0.782385\pi$
$461$	−13.2237	+	7.63473i	−0.615891	+	0.355585i	0.159377	+	0.987218i	$0.449052\pi$
$462$	−7.29982	−	0.439842i	−0.339618	−	0.0204633i
$463$	39.9841	−	10.7137i	1.85822	−	0.497908i	0.858333	−	0.513092i	$-0.171500\pi$
$463$	39.9841	−	10.7137i	1.85822	−	0.497908i	0.999885	+	0.0151842i	$0.00483345\pi$
$464$			5.48695i			0.254725i
$465$	−29.2004	−	13.9580i	−1.35414	−	0.647288i
$466$	12.0292			0.557240
$467$	4.67993	−	17.4657i	0.216561	−	0.808217i	−0.769050	−	0.639189i	$-0.779270\pi$
$467$	4.67993	−	17.4657i	0.216561	−	0.808217i	0.985611	−	0.169029i	$-0.0540630\pi$
$468$	1.64677	−	0.259905i	0.0761220	−	0.0120141i
$469$	12.8633	−	7.29773i	0.593973	−	0.336978i
$470$	−3.42457	+	2.62467i	−0.157964	+	0.121067i
$471$	−3.03848	−	14.3141i	−0.140006	−	0.659558i
$472$	−0.851123	+	3.17644i	−0.0391761	+	0.146207i
$473$	3.24417	−	12.1074i	0.149167	−	0.556698i
$474$	−2.36739	−	11.1526i	−0.108738	−	0.512255i
$475$	−21.1448	−	21.1930i	−0.970191	−	0.972402i
$476$	−0.0214021	+	2.83493i	−0.000980965	+	0.129939i
$477$	−1.50582	+	3.91643i	−0.0689469	+	0.179321i
$478$	−1.91940	+	7.16329i	−0.0877912	+	0.327641i
$479$	8.15139			0.372447			0.186223	−	0.982507i	$-0.440375\pi$
$479$	8.15139			0.372447			0.186223	+	0.982507i	$0.440375\pi$
$480$	6.64692	+	18.8206i	0.303389	+	0.859039i
$481$		−	3.02522i		−	0.137938i
$482$	5.68668	−	1.52374i	0.259021	−	0.0694045i
$483$	−30.4288	+	15.2057i	−1.38456	+	0.691882i
$484$	−7.54388	+	4.35546i	−0.342903	+	0.197975i
$485$	0.341912	+	0.0452115i	0.0155254	+	0.00205295i
$486$	−7.63283	+	13.1790i	−0.346232	+	0.597813i
$487$	−1.05326	−	3.93080i	−0.0477276	−	0.178122i	0.937947	−	0.346777i	$-0.112724\pi$
$487$	−1.05326	−	3.93080i	−0.0477276	−	0.178122i	−0.985675	+	0.168656i	$0.946057\pi$
$488$	−10.5781	−	39.4779i	−0.478847	−	1.78708i
$489$	−0.797504	−	3.75699i	−0.0360644	−	0.169897i
$490$	5.63006	+	14.2182i	0.254340	+	0.642315i
$491$	14.1237	−	24.4629i	0.637392	−	1.10399i	−0.348612	−	0.937267i	$-0.613347\pi$
$491$	14.1237	−	24.4629i	0.637392	−	1.10399i	0.986003	−	0.166727i	$-0.0533199\pi$
$492$	−11.4374	+	5.82372i	−0.515637	+	0.262554i
$493$	4.87325	−	4.87325i	0.219480	−	0.219480i
$494$	2.69279	+	1.55468i	0.121154	+	0.0699485i
$495$	9.62365	+	5.23909i	0.432551	+	0.235480i
$496$			6.81890i			0.306178i
$497$	11.9833	−	11.8037i	0.537524	−	0.529469i
$498$	3.00870	+	5.90888i	0.134823	+	0.264783i
$499$			24.7679i			1.10876i	0.832262	+	0.554382i	$0.187045\pi$
$499$			24.7679i			1.10876i	−0.832262	+	0.554382i	$0.812955\pi$
$500$	9.26125	+	7.13156i	0.414176	+	0.318933i
$501$	−1.75017	+	1.57500i	−0.0781918	+	0.0703657i
$502$	−4.53977	+	1.21643i	−0.202620	+	0.0542918i
$503$	22.1184	−	22.1184i	0.986211	−	0.986211i	−0.0136949	−	0.999906i	$-0.504359\pi$
$503$	22.1184	−	22.1184i	0.986211	−	0.986211i	0.999906	+	0.0136949i	$0.00435937\pi$
$504$	14.0357	−	18.9933i	0.625199	−	0.846028i
$505$	18.0538	−	2.36638i	0.803383	−	0.105302i
$506$	−5.92298	+	10.2589i	−0.263308	+	0.456064i
$507$	12.0019	−	18.4704i	0.533025	−	0.820298i
$508$	−0.712015	+	2.65728i	−0.0315906	+	0.117898i
$509$	−1.37539			−0.0609630			−0.0304815	−	0.999535i	$-0.509704\pi$
$509$	−1.37539			−0.0609630			−0.0304815	+	0.999535i	$0.509704\pi$
$510$	−1.67253	+	3.49896i	−0.0740610	+	0.154937i
$511$	−14.3416	−	8.42512i	−0.634435	−	0.372706i
$512$	6.40718	−	6.40718i	0.283160	−	0.283160i
$513$	29.0545	−	11.1258i	1.28279	−	0.491215i
$514$	−7.99874	+	13.8542i	−0.352809	+	0.611084i
$515$	−18.2091	−	13.9888i	−0.802387	−	0.616419i
$516$	9.29538	+	10.3292i	0.409206	+	0.454718i
$517$	−3.11613	+	0.834965i	−0.137047	+	0.0367217i
$518$	−10.3239	−	10.4809i	−0.453604	−	0.460505i
$519$	−2.37603	−	2.64030i	−0.104296	−	0.115896i
$520$	−3.26650	−	1.35521i	−0.143245	−	0.0594297i
$521$	−22.4862	−	12.9824i	−0.985140	−	0.568771i	−0.0813222	−	0.996688i	$-0.525914\pi$
$521$	−22.4862	−	12.9824i	−0.985140	−	0.568771i	−0.903818	+	0.427917i	$0.859248\pi$
$522$	−19.4678	+	3.07253i	−0.852080	+	0.134481i
$523$	2.60320	+	0.697525i	0.113830	+	0.0305006i	0.315284	−	0.948997i	$-0.397900\pi$
$523$	2.60320	+	0.697525i	0.113830	+	0.0305006i	−0.201454	+	0.979498i	$0.564567\pi$
$524$	−1.10169	−	1.90818i	−0.0481276	−	0.0833594i
$525$	1.40412	−	22.8698i	0.0612808	−	0.998121i
$526$	4.07392	−	7.05624i	0.177631	−	0.307667i
$527$	6.05623	−	6.05623i	0.263813	−	0.263813i
$528$	0.121448	−	2.30538i	0.00528536	−	0.100329i
$529$			32.1013i			1.39571i
$530$	2.42516	−	1.85870i	0.105342	−	0.0807368i
$531$	−3.29731	−	0.348374i	−0.143091	−	0.0151182i
$532$	−16.0295	+	4.16565i	−0.694967	+	0.180604i
$533$	0.975080	−	3.63905i	0.0422354	−	0.157625i
$534$	9.46903	−	29.1157i	0.409765	−	1.25996i
$535$	0.372958	−	2.82049i	0.0161244	−	0.121940i
$536$	8.31601	+	14.4038i	0.359197	+	0.622148i
$537$	−29.1651	−	1.53643i	−1.25857	−	0.0663020i
$538$	−3.52306	−	0.944001i	−0.151890	−	0.0406988i
$539$	−0.172630	+	11.4326i	−0.00743569	+	0.492439i
$540$	−10.6834	+	5.78147i	−0.459740	+	0.248795i
$541$	−10.0369	−	17.3845i	−0.431522	−	0.747418i	0.565482	−	0.824760i	$-0.308690\pi$
$541$	−10.0369	−	17.3845i	−0.431522	−	0.747418i	−0.997005	+	0.0773420i	$0.975357\pi$
$542$	−4.42191	−	4.42191i	−0.189937	−	0.189937i
$543$	−16.0073	−	31.4373i	−0.686940	−	1.34910i
$544$	−5.28202			−0.226465
$545$	−9.93371	+	23.9435i	−0.425513	+	1.02563i
$546$	0.476564	+	2.33158i	0.0203950	+	0.0997823i
$547$	14.4892	+	3.88238i	0.619515	+	0.165999i	0.554907	−	0.831912i	$-0.312754\pi$
$547$	14.4892	+	3.88238i	0.619515	+	0.165999i	0.0646077	+	0.997911i	$0.479420\pi$
$548$	−3.66086	+	13.6625i	−0.156384	+	0.583634i
$549$	37.6547	−	16.7404i	1.60706	−	0.714464i
$550$	−3.98173	−	6.91472i	−0.169782	−	0.294845i
$551$	34.8675	+	20.1307i	1.48540	+	0.857598i
$552$	−17.3582	−	34.0903i	−0.738813	−	1.45098i
$553$	−17.2525	+	4.48348i	−0.733651	+	0.190657i
$554$	−0.485889	−	0.280528i	−0.0206434	−	0.0119185i
$555$	7.34054	+	20.7846i	0.311589	+	0.882256i
$556$			13.4715i			0.571317i
$557$	−0.0632745	−	0.236144i	−0.00268103	−	0.0100057i	0.964572	−	0.263818i	$-0.0849820\pi$
$557$	−0.0632745	−	0.236144i	−0.00268103	−	0.0100057i	−0.967253	+	0.253813i	$0.918315\pi$
$558$	−24.1935	+	3.81839i	−1.02419	+	0.161645i
$559$	−4.07892			−0.172520
$560$	−4.47485	+	1.81112i	−0.189097	+	0.0765339i
$561$	−2.15539	+	1.93966i	−0.0910008	+	0.0818926i
$562$	3.06308	−	3.06308i	0.129208	−	0.129208i
$563$	0.0758206	+	0.0203161i	0.00319546	+	0.000856220i	0.260416	−	0.965496i	$-0.416140\pi$
$563$	0.0758206	+	0.0203161i	0.00319546	+	0.000856220i	−0.257221	+	0.966353i	$0.582807\pi$
$564$	1.10611	−	3.40111i	0.0465756	−	0.143213i
$565$	17.7824	+	42.9998i	0.748112	+	1.80901i
$566$		−	7.27618i		−	0.305840i
$567$	21.1223	+	10.9932i	0.887052	+	0.461669i
$568$	13.3758	+	13.3758i	0.561238	+	0.561238i
$569$	12.7781	+	7.37743i	0.535685	+	0.309278i	0.743328	−	0.668927i	$-0.233246\pi$
$569$	12.7781	+	7.37743i	0.535685	+	0.309278i	−0.207643	+	0.978205i	$0.566579\pi$
$570$	−22.2730	−	4.14744i	−0.932914	−	0.173717i
$571$	14.7758	+	25.5924i	0.618347	+	1.07101i	0.989787	+	0.142552i	$0.0455308\pi$
$571$	14.7758	+	25.5924i	0.618347	+	1.07101i	−0.371440	+	0.928457i	$0.621136\pi$
$572$	−0.641855	−	0.641855i	−0.0268373	−	0.0268373i
$573$	−1.57035	+	29.8089i	−0.0656023	+	1.24529i
$574$	−9.04043	−	15.9351i	−0.377340	−	0.665118i
$575$	−32.1215	−	18.5941i	−1.33956	−	0.775429i
$576$	16.1748	+	11.7651i	0.673951	+	0.490214i
$577$	−8.07441	+	2.16353i	−0.336142	+	0.0900690i	−0.422942	−	0.906157i	$-0.639003\pi$
$577$	−8.07441	+	2.16353i	−0.336142	+	0.0900690i	0.0867998	+	0.996226i	$0.472336\pi$
$578$	11.0186	+	11.0186i	0.458312	+	0.458312i
$579$	−3.89034	−	18.3271i	−0.161677	−	0.761648i
$580$	−14.5198	−	6.02400i	−0.602903	−	0.250133i
$581$	9.01713	−	5.11567i	0.374094	−	0.212234i
$582$	0.232588	−	0.118430i	0.00964106	−	0.00490907i
$583$	2.20673	−	0.591293i	0.0913936	−	0.0244888i
$584$	9.35288	−	16.1997i	0.387025	−	0.670347i
$585$	0.836251	−	3.46623i	0.0345747	−	0.143311i
$586$	16.2968	−	9.40894i	0.673213	−	0.388680i
$587$	−2.34352	+	8.74614i	−0.0967275	+	0.360992i	−0.997276	−	0.0737643i	$-0.976499\pi$
$587$	−2.34352	+	8.74614i	−0.0967275	+	0.360992i	0.900548	+	0.434756i	$0.143165\pi$
$588$	−10.5235	−	7.06633i	−0.433981	−	0.291411i
$589$	43.3315	+	25.0175i	1.78544	+	1.03083i
$590$	1.91470	+	1.47094i	0.0788271	+	0.0605575i
$591$	3.53437	−	10.8676i	0.145385	−	0.447034i
$592$	3.28390	−	3.28390i	0.134967	−	0.134967i
$593$	−27.9474	−	7.48847i	−1.14766	−	0.307515i	−0.365633	−	0.930759i	$-0.619148\pi$
$593$	−27.9474	−	7.48847i	−1.14766	−	0.307515i	−0.782027	+	0.623244i	$0.785814\pi$
$594$	8.24750	−	0.860044i	0.338399	−	0.0352880i
$595$	5.58291	+	2.36580i	0.228877	+	0.0969882i
$596$	1.91489	+	3.31668i	0.0784367	+	0.135856i
$597$	0.470754	−	8.93602i	0.0192667	−	0.365727i
$598$	3.72351	+	0.997711i	0.152266	+	0.0407994i
$599$	8.70341	−	5.02492i	0.355612	−	0.205313i	−0.311542	−	0.950232i	$-0.600846\pi$
$599$	8.70341	−	5.02492i	0.355612	−	0.205313i	0.667154	+	0.744920i	$0.267512\pi$
$600$	25.7306	+	1.38487i	1.05045	+	0.0565371i
$601$	−27.4153	+	15.8282i	−1.11829	+	0.645647i	−0.940965	−	0.338505i	$-0.890079\pi$
$601$	−27.4153	+	15.8282i	−1.11829	+	0.645647i	−0.177329	+	0.984152i	$0.556746\pi$
$602$	−14.1315	+	13.9197i	−0.575957	+	0.567326i
$603$	−13.0380	+	10.5463i	−0.530950	+	0.429477i
$604$	1.80839	−	1.04408i	0.0735824	−	0.0424828i
$605$	2.42129	+	18.4728i	0.0984396	+	0.751025i
$606$	10.2427	−	9.21752i	0.416081	−	0.374436i
$607$	7.81669	+	7.81669i	0.317270	+	0.317270i	0.847718	−	0.530448i	$-0.177976\pi$
$607$	7.81669	+	7.81669i	0.317270	+	0.317270i	−0.530448	+	0.847718i	$0.677976\pi$
$608$	−7.98642	−	29.8057i	−0.323892	−	1.20878i
$609$	6.17077	+	30.1903i	0.250052	+	1.22337i
$610$	−29.7492	−	3.93378i	−1.20451	−	0.159274i
$611$	0.524905	+	0.909162i	0.0212354	+	0.0367807i
$612$	−0.501147	−	3.17530i	−0.0202577	−	0.128354i
$613$	−23.0984	+	6.18919i	−0.932934	+	0.249979i	−0.693105	−	0.720836i	$-0.743758\pi$
$613$	−23.0984	+	6.18919i	−0.932934	+	0.249979i	−0.239829	+	0.970815i	$0.577091\pi$
$614$	−4.52139	+	7.83128i	−0.182468	+	0.316045i
$615$	2.13074	+	27.3679i	0.0859197	+	1.10358i
$616$	−12.8583	−	0.0970726i	−0.518074	−	0.00391117i
$617$	−1.79766	−	6.70895i	−0.0723709	−	0.270092i	0.920253	−	0.391323i	$-0.127982\pi$
$617$	−1.79766	−	6.70895i	−0.0723709	−	0.270092i	−0.992624	+	0.121231i	$0.961316\pi$
$618$	−17.3531	−	0.914168i	−0.698042	−	0.0367732i
$619$	−31.3954			−1.26189			−0.630945	−	0.775828i	$-0.717333\pi$
$619$	−31.3954			−1.26189			−0.630945	+	0.775828i	$0.717333\pi$
$620$	−18.0445	−	7.48631i	−0.724685	−	0.300658i
$621$	31.2232	−	22.6461i	1.25294	−	0.908756i
$622$	17.0174	+	17.0174i	0.682337	+	0.682337i
$623$	−46.1433	−	12.7382i	−1.84869	−	0.510345i
$624$	−0.734872	+	0.155993i	−0.0294184	+	0.00624471i
$625$	21.6790	−	12.4507i	0.867161	−	0.498027i
$626$	21.4698	−	12.3956i	0.858107	−	0.495429i
$627$	−14.2042	−	9.22981i	−0.567261	−	0.368603i
$628$	−2.28606	−	8.53169i	−0.0912237	−	0.340452i
$629$	−5.83322			−0.232586
$630$	−8.93167	−	14.8626i	−0.355846	−	0.592141i
$631$	−36.8622			−1.46746			−0.733730	−	0.679441i	$-0.762222\pi$
$631$	−36.8622			−1.46746			−0.733730	+	0.679441i	$0.762222\pi$
$632$	−5.18846	−	19.3636i	−0.206386	−	0.770242i
$633$	0.0498127	−	0.945563i	0.00197988	−	0.0375827i
$634$	−9.01545	+	5.20507i	−0.358049	+	0.206720i
$635$	4.66592	+	3.58451i	0.185161	+	0.142247i
$636$	−0.783308	+	2.40855i	−0.0310602	+	0.0955051i
$637$	3.60813	−	0.908638i	0.142959	−	0.0360015i
$638$	7.58787	+	7.58787i	0.300407	+	0.300407i
$639$	−11.2190	+	15.4239i	−0.443816	+	0.610162i
$640$	3.24174	+	7.83888i	0.128141	+	0.309859i
$641$	15.0643			0.595004			0.297502	−	0.954721i	$-0.403846\pi$
$641$	15.0643			0.595004			0.297502	+	0.954721i	$0.403846\pi$
$642$	−0.976946	−	1.91865i	−0.0385570	−	0.0757233i
$643$	4.70433	+	17.5568i	0.185521	+	0.692372i	0.994518	+	0.104561i	$0.0333437\pi$
$643$	4.70433	+	17.5568i	0.185521	+	0.692372i	−0.808998	+	0.587812i	$0.799990\pi$
$644$	−17.8589	+	10.1319i	−0.703739	+	0.399251i
$645$	28.0240	−	9.89731i	1.10344	−	0.389706i
$646$	2.99774	−	5.19223i	0.117944	−	0.204286i
$647$	−3.91026	+	1.04775i	−0.153728	+	0.0411913i	−0.334862	−	0.942267i	$-0.608690\pi$
$647$	−3.91026	+	1.04775i	−0.153728	+	0.0411913i	0.181134	+	0.983458i	$0.442023\pi$
$648$	−12.1832	+	23.8468i	−0.478603	+	0.936791i
$649$	0.902644	+	1.56342i	0.0354319	+	0.0613698i
$650$	−1.83813	+	1.83395i	−0.0720974	+	0.0719335i
$651$	7.66871	+	37.5190i	0.300560	+	1.47049i
$652$	−0.600017	−	2.23930i	−0.0234985	−	0.0876976i
$653$	16.3529	+	16.3529i	0.639940	+	0.639940i	0.950540	−	0.310601i	$-0.100530\pi$
$653$	16.3529	+	16.3529i	0.639940	+	0.639940i	−0.310601	+	0.950540i	$0.600530\pi$
$654$	4.07348	+	19.1899i	0.159286	+	0.750383i
$655$	−4.67259	+	0.612453i	−0.182573	+	0.0239305i
$656$	5.00868	−	2.89176i	0.195556	−	0.112904i
$657$	17.6039	+	6.76851i	0.686795	+	0.264065i
$658$	4.92115	+	1.35852i	0.191846	+	0.0529605i
$659$	−38.7647	+	22.3808i	−1.51006	+	0.871834i	−0.510129	+	0.860098i	$0.670402\pi$
$659$	−38.7647	+	22.3808i	−1.51006	+	0.871834i	−0.999931	+	0.0117356i	$0.996264\pi$
$660$	5.96726	+	2.85240i	0.232275	+	0.111030i
$661$	−15.1919	+	8.77106i	−0.590897	+	0.341155i	−0.765452	−	0.643493i	$-0.777485\pi$
$661$	−15.1919	+	8.77106i	−0.590897	+	0.341155i	0.174555	+	0.984647i	$0.444151\pi$
$662$	5.89534	+	1.57965i	0.229129	+	0.0613949i
$663$	0.791225	+	0.514133i	0.0307286	+	0.0199673i
$664$	5.82948	+	10.0970i	0.226228	+	0.391838i
$665$	−4.90851	+	35.0807i	−0.190344	+	1.36037i
$666$	13.4902	+	9.81242i	0.522735	+	0.380224i
$667$	48.2137	+	12.9188i	1.86684	+	0.500219i
$668$	−1.00495	+	1.00495i	−0.0388825	+	0.0388825i
$669$	44.9114	−	9.53345i	1.73638	−	0.368585i
$670$	12.1081	−	1.58705i	0.467775	−	0.0613130i
$671$	−19.4308	−	11.2184i	−0.750119	−	0.433081i
$672$	13.0172	−	19.7055i	0.502148	−	0.760158i
$673$	−12.8090	+	47.8039i	−0.493751	+	1.84270i	0.0431629	+	0.999068i	$0.486257\pi$
$673$	−12.8090	+	47.8039i	−0.493751	+	1.84270i	−0.536914	+	0.843637i	$0.680410\pi$
$674$	−10.8294	+	6.25233i	−0.417131	+	0.240831i
$675$	2.66523	+	25.8437i	0.102585	+	0.994724i
$676$	6.64796	−	11.5146i	0.255691	−	0.442869i
$677$	36.1964	−	9.69880i	1.39114	−	0.372755i	0.515986	−	0.856597i	$-0.327426\pi$
$677$	36.1964	−	9.69880i	1.39114	−	0.372755i	0.875155	+	0.483842i	$0.160759\pi$
$678$	29.5277	+	19.1869i	1.13401	+	0.736870i
$679$	−0.201365	−	0.354936i	−0.00772768	−	0.0136212i
$680$	−2.61310	+	6.29845i	−0.100208	+	0.241535i
$681$	−28.0290	−	9.11560i	−1.07407	−	0.349311i
$682$	9.42982	+	9.42982i	0.361086	+	0.361086i
$683$	25.2542	−	6.76683i	0.966324	−	0.258926i	0.259049	−	0.965864i	$-0.416591\pi$
$683$	25.2542	−	6.76683i	0.966324	−	0.258926i	0.707275	+	0.706939i	$0.249924\pi$
$684$	17.1600	−	7.62896i	0.656130	−	0.291701i
$685$	23.9900	+	18.4299i	0.916612	+	0.704170i
$686$	9.39962	−	15.4611i	0.358879	−	0.590308i
$687$	−21.5954	+	10.9960i	−0.823916	+	0.419524i
$688$	−4.42771	−	4.42771i	−0.168805	−	0.168805i
$689$	−0.371719	−	0.643836i	−0.0141614	−	0.0245282i
$690$	−28.0031	+	2.18019i	−1.06606	+	0.0829985i
$691$	18.3023	+	10.5668i	0.696251	+	0.401980i	0.805949	−	0.591984i	$-0.201655\pi$
$691$	18.3023	+	10.5668i	0.696251	+	0.401980i	−0.109699	+	0.993965i	$0.534989\pi$
$692$	−1.51606	−	1.51606i	−0.0576318	−	0.0576318i
$693$	−1.92445	−	12.8212i	−0.0731039	−	0.487039i
$694$		−	13.0916i		−	0.496952i
$695$	26.6131	+	11.0412i	1.00949	+	0.418818i
$696$	−33.8988	+	7.19577i	−1.28493	+	0.272755i
$697$	−7.01680	−	1.88015i	−0.265780	−	0.0712156i
$698$	−21.3261	+	21.3261i	−0.807206	+	0.807206i
$699$	4.42820	+	20.8610i	0.167490	+	0.789034i
$700$	0.120149	−	13.8299i	0.00454122	−	0.522723i
$701$	17.0822			0.645186			0.322593	−	0.946538i	$-0.395446\pi$
$701$	17.0822			0.645186			0.322593	+	0.946538i	$0.395446\pi$
$702$	−0.964972	−	2.51998i	−0.0364205	−	0.0951106i
$703$	−8.81983	−	32.9160i	−0.332646	−	1.24145i
$704$		−	10.8901i		−	0.410434i
$705$	−5.81237	−	4.97269i	−0.218906	−	0.187282i
$706$	−13.9072	−	8.02934i	−0.523405	−	0.302188i
$707$	−15.1186	−	15.3487i	−0.568595	−	0.577246i
$708$	−1.99860	−	0.105287i	−0.0751119	−	0.00395693i
$709$	37.8779	+	21.8688i	1.42254	+	0.821302i	0.996515	−	0.0834117i	$-0.0265817\pi$
$709$	37.8779	+	21.8688i	1.42254	+	0.821302i	0.426021	+	0.904713i	$0.359915\pi$
$710$	12.8346	−	5.30771i	0.481674	−	0.199195i
$711$	18.4693	−	8.21103i	0.692653	−	0.307938i
$712$	13.9332	−	51.9995i	0.522170	−	1.94877i
$713$	59.9175	+	16.0548i	2.24393	+	0.601259i
$714$	4.49574	−	0.918909i	0.168249	−	0.0343893i
$715$	−1.79406	+	0.741928i	−0.0670940	+	0.0277465i
$716$	−17.6288			−0.658820
$717$	−13.1291	−	0.691649i	−0.490316	−	0.0258301i
$718$	1.12067	+	1.12067i	0.0418230	+	0.0418230i
$719$	9.10099	+	15.7634i	0.339410	+	0.587875i	0.984322	−	0.176382i	$-0.0564394\pi$
$719$	9.10099	+	15.7634i	0.339410	+	0.587875i	−0.644912	+	0.764257i	$0.723106\pi$
$720$	4.67039	−	2.85487i	0.174055	−	0.106395i
$721$	−0.205105	+	27.1683i	−0.00763851	+	1.01180i
$722$	15.9013	+	4.26073i	0.591784	+	0.158568i
$723$	4.73587	+	9.30091i	0.176129	+	0.345905i
$724$	−10.6471	−	18.4413i	−0.395696	−	0.685366i
$725$	−23.8010	+	23.7469i	−0.883946	+	0.881936i
$726$	9.43143	+	10.4804i	0.350033	+	0.388964i
$727$	12.6674	−	47.2752i	0.469806	−	1.75334i	−0.170635	−	0.985334i	$-0.554582\pi$
$727$	12.6674	−	47.2752i	0.469806	−	1.75334i	0.640441	−	0.768007i	$-0.278752\pi$
$728$	1.05246	+	4.04988i	0.0390067	+	0.150099i
$729$	−25.6649	−	8.38535i	−0.950551	−	0.310569i
$730$	−8.35466	−	10.9008i	−0.309220	−	0.403458i
$731$			7.86497i			0.290896i
$732$	22.1658	−	11.2864i	0.819270	−	0.417158i
$733$	14.0880	−	14.0880i	0.520350	−	0.520350i	−0.397327	−	0.917677i	$-0.630062\pi$
$733$	14.0880	−	14.0880i	0.520350	−	0.520350i	0.917677	+	0.397327i	$0.130062\pi$
$734$	1.18391	−	2.05060i	0.0436991	−	0.0756890i
$735$	−22.5847	+	14.9977i	−0.833049	+	0.553199i
$736$	−19.1277	−	33.1302i	−0.705057	−	1.22119i
$737$	8.81940	+	2.36315i	0.324867	+	0.0870478i
$738$	13.0647	+	16.1515i	0.480919	+	0.594546i
$739$	41.8852	+	24.1825i	1.54077	+	0.889566i	0.998790	+	0.0491770i	$0.0156598\pi$
$739$	41.8852	+	24.1825i	1.54077	+	0.889566i	0.541984	+	0.840389i	$0.317673\pi$
$740$	5.08470	+	12.2953i	0.186917	+	0.451986i
$741$	−1.70485	+	5.24214i	−0.0626293	+	0.192575i
$742$	−3.48498	−	0.962055i	−0.127938	−	0.0353181i
$743$	−31.7951	+	8.51948i	−1.16645	+	0.312549i	−0.789539	−	0.613700i	$-0.789680\pi$
$743$	−31.7951	+	8.51948i	−1.16645	+	0.312549i	−0.376911	+	0.926250i	$0.623014\pi$
$744$	−42.1276	+	8.94253i	−1.54447	+	0.327849i
$745$	8.12159	−	1.06453i	0.297552	−	0.0390012i
$746$	−15.6246	+	27.0626i	−0.572057	+	0.990832i
$747$	−9.13960	+	7.39288i	−0.334401	+	0.270491i
$748$	−1.23762	+	1.23762i	−0.0452520	+	0.0452520i
$749$	−2.92792	+	1.66109i	−0.106984	+	0.0606950i
$750$	8.17879	−	17.0602i	0.298647	−	0.622951i
$751$	−13.5203			−0.493364			−0.246682	−	0.969096i	$-0.579340\pi$
$751$	−13.5203			−0.493364			−0.246682	+	0.969096i	$0.579340\pi$
$752$	−0.417115	+	1.55669i	−0.0152106	+	0.0567667i
$753$	−3.78071	−	7.42506i	−0.137777	−	0.270584i
$754$	1.74600	−	3.02416i	0.0635855	−	0.110133i
$755$	−0.580424	−	4.42823i	−0.0211238	−	0.161160i
$756$	13.0811	+	5.95568i	0.475754	+	0.216606i
$757$	28.4104	−	28.4104i	1.03260	−	1.03260i	0.0331447	−	0.999451i	$-0.489448\pi$
$757$	28.4104	−	28.4104i	1.03260	−	1.03260i	0.999451	−	0.0331447i	$-0.0105522\pi$
$758$	−29.2244	+	7.83064i	−1.06148	+	0.284422i
$759$	−19.9713	−	6.49509i	−0.724914	−	0.235757i
$760$	−39.4923	−	5.22213i	−1.43254	−	0.189426i
$761$		−	15.8150i		−	0.573292i	−0.958037	−	0.286646i	$-0.907460\pi$
$761$		−	15.8150i		−	0.573292i	0.958037	−	0.286646i	$-0.0925404\pi$
$762$	4.44657	+	0.234248i	0.161082	+	0.00848590i
$763$	29.6858	−	7.71457i	1.07470	−	0.279286i
$764$			18.0179i			0.651866i
$765$	−6.68359	−	1.61246i	−0.241646	−	0.0582985i
$766$	−15.9311	−	9.19781i	−0.575613	−	0.332330i
$767$	0.415403	−	0.415403i	0.0149993	−	0.0149993i
$768$	24.7488	+	16.0816i	0.893046	+	0.580296i
$769$	10.7002	−	18.5333i	0.385860	−	0.668328i	−0.606028	−	0.795443i	$-0.707238\pi$
$769$	10.7002	−	18.5333i	0.385860	−	0.668328i	0.991888	+	0.127115i	$0.0405716\pi$
$770$	−3.68365	+	8.69283i	−0.132750	+	0.313268i
$771$	−26.9705	−	8.77136i	−0.971319	−	0.315893i
$772$	−2.92697	−	10.9236i	−0.105344	−	0.393148i
$773$	2.38488	+	8.90050i	0.0857782	+	0.320129i	0.995460	−	0.0951763i	$-0.0303415\pi$
$773$	2.38488	+	8.90050i	0.0857782	+	0.320129i	−0.909682	+	0.415305i	$0.863675\pi$
$774$	13.2302	−	18.1889i	0.475548	−	0.653788i
$775$	−29.5786	+	29.5114i	−1.06250	+	1.06008i
$776$	0.397440	−	0.229462i	0.0142673	−	0.00823722i
$777$	14.3755	−	21.7619i	0.515720	−	0.780703i
$778$	−22.3540	+	5.98973i	−0.801430	+	0.214742i
$779$		−	42.4376i		−	1.52049i
$780$	0.394003	−	2.11592i	0.0141076	−	0.0757619i
$781$	10.3845			0.371587
$782$	1.92378	−	7.17966i	0.0687944	−	0.256744i
$783$	−12.4949	−	32.6299i	−0.446531	−	1.16610i
$784$	4.90300	+	2.93033i	0.175107	+	0.104654i
$785$	−18.7281	−	2.47645i	−0.668436	−	0.0883882i
$786$	−2.65096	+	2.38563i	−0.0945567	+	0.0850926i
$787$	−13.4497	+	50.1948i	−0.479428	+	1.78925i	0.124509	+	0.992219i	$0.460265\pi$
$787$	−13.4497	+	50.1948i	−0.479428	+	1.78925i	−0.603937	+	0.797032i	$0.706402\pi$
$788$	1.78534	−	6.66297i	0.0636000	−	0.237358i
$789$	13.7366	+	4.46743i	0.489036	+	0.159045i
$790$	−14.5917	−	1.92948i	−0.519150	−	0.0686480i
$791$	27.8877	−	47.4716i	0.991571	−	1.68789i
$792$	14.4020	−	2.27303i	0.511754	−	0.0807686i
$793$	−1.88971	+	7.05250i	−0.0671056	+	0.250442i
$794$	23.4818			0.833336
$795$	4.11611	+	3.52149i	0.145984	+	0.124894i
$796$		−	5.40136i		−	0.191446i
$797$	4.61563	−	1.23676i	0.163494	−	0.0438081i	−0.176143	−	0.984365i	$-0.556362\pi$
$797$	4.61563	−	1.23676i	0.163494	−	0.0438081i	0.339638	+	0.940556i	$0.389696\pi$
$798$	11.9828	+	23.9795i	0.424188	+	0.848864i
$799$	1.75304	−	1.01212i	0.0620182	−	0.0358062i
$800$	25.7681	+	0.0293272i	0.911039	+	0.00103687i
$801$	53.9782	+	5.70303i	1.90723	+	0.201507i
$802$	−8.65162	−	32.2883i	−0.305499	−	1.14014i
$803$	−2.65780	−	9.91903i	−0.0937916	−	0.350035i
$804$	−7.52412	+	6.77104i	−0.265355	+	0.238796i
$805$	5.37843	+	43.5846i	0.189565	+	1.53615i
$806$	2.16984	−	3.75827i	0.0764292	−	0.132379i
$807$	0.340168	−	6.45719i	0.0119745	−	0.227304i
$808$	17.1323	−	17.1323i	0.602711	−	0.602711i
$809$	−16.7030	−	9.64348i	−0.587246	−	0.339047i	0.176762	−	0.984254i	$-0.443438\pi$
$809$	−16.7030	−	9.64348i	−0.587246	−	0.339047i	−0.764008	+	0.645207i	$0.776771\pi$
$810$	12.7444	+	14.9719i	0.447792	+	0.526060i
$811$		−	7.57899i		−	0.266134i	−0.991107	−	0.133067i	$-0.957517\pi$
$811$		−	7.57899i		−	0.266134i	0.991107	−	0.133067i	$-0.0424826\pi$
$812$	4.67826	+	18.0020i	0.164175	+	0.631748i
$813$	6.04066	−	9.29627i	0.211855	−	0.326034i
$814$		−	9.08258i		−	0.318344i
$815$	−4.91553	−	0.649988i	−0.172184	−	0.0227681i
$816$	0.300785	+	1.41698i	0.0105296	+	0.0496042i
$817$	−44.3810	+	11.8918i	−1.55269	+	0.416043i
$818$	0.0628861	−	0.0628861i	0.00219876	−	0.00219876i
$819$	−3.86799	+	1.68476i	−0.135158	+	0.0588703i
$820$	2.15341	+	16.4290i	0.0752003	+	0.573726i
$821$	−11.4071	+	19.7576i	−0.398110	+	0.689547i	−0.993493	−	0.113895i	$-0.963667\pi$
$821$	−11.4071	+	19.7576i	−0.398110	+	0.689547i	0.595383	+	0.803442i	$0.297000\pi$
$822$	22.8623	+	1.20440i	0.797413	+	0.0420081i
$823$	1.93083	−	7.20595i	0.0673044	−	0.251183i	−0.924074	−	0.382214i	$-0.875162\pi$
$823$	1.93083	−	7.20595i	0.0673044	−	0.251183i	0.991378	+	0.131030i	$0.0418285\pi$
$824$	−30.5544			−1.06441
$825$	10.5257	−	9.45058i	0.366459	−	0.329027i
$826$	0.0215670	−	2.85678i	0.000750414	−	0.0994000i
$827$	−21.2830	+	21.2830i	−0.740083	+	0.740083i	−0.972594	−	0.232511i	$-0.925306\pi$
$827$	−21.2830	+	21.2830i	−0.740083	+	0.740083i	0.232511	+	0.972594i	$0.425306\pi$
$828$	18.1015	−	14.6420i	0.629069	−	0.508844i
$829$	−4.24336	+	7.34971i	−0.147378	+	0.255266i	−0.930258	−	0.366907i	$-0.880417\pi$
$829$	−4.24336	+	7.34971i	−0.147378	+	0.255266i	0.782880	+	0.622173i	$0.213750\pi$
$830$	8.48769	−	1.11251i	0.294612	−	0.0386159i
$831$	0.307625	−	0.945896i	0.0106714	−	0.0328128i
$832$	−3.42304	+	0.917202i	−0.118673	+	0.0317983i
$833$	−1.75203	−	6.95719i	−0.0607044	−	0.241052i
$834$	21.3294	−	4.52764i	0.738576	−	0.156779i
$835$	1.16163	+	2.80894i	0.0401998	+	0.0972074i
$836$	−8.85503	−	5.11246i	−0.306258	−	0.176818i
$837$	−15.5280	−	40.5507i	−0.536727	−	1.40164i
$838$	−25.8982	−	6.93939i	−0.894637	−	0.239717i
$839$	−0.839410	−	1.45390i	−0.0289797	−	0.0501942i	0.851172	−	0.524887i	$-0.175892\pi$
$839$	−0.839410	−	1.45390i	−0.0289797	−	0.0501942i	−0.880152	+	0.474693i	$0.842559\pi$
$840$	−17.0577	−	25.2708i	−0.588547	−	0.871924i
$841$	8.10798	−	14.0434i	0.279586	−	0.484256i
$842$	−8.21157	+	8.21157i	−0.282989	+	0.282989i
$843$	6.43958	+	4.18440i	0.221791	+	0.144118i
$844$		−	0.571544i		−	0.0196733i
$845$	−17.2986	−	22.5705i	−0.595089	−	0.776450i
$846$	−5.75673	−	0.608223i	−0.197921	−	0.0209111i
$847$	15.7049	−	15.4695i	0.539625	−	0.531539i
$848$	0.295386	−	1.10240i	0.0101436	−	0.0378564i
$849$	12.6183	−	2.67852i	0.433060	−	0.0919267i
$850$	3.53622	+	3.54428i	0.121291	+	0.121568i
$851$	−21.1237	−	36.5874i	−0.724112	−	1.25420i
$852$	−6.27274	+	9.65342i	−0.214901	+	0.330721i
$853$	−41.0407	−	10.9968i	−1.40521	−	0.376524i	−0.524995	−	0.851105i	$-0.675933\pi$
$853$	−41.0407	−	10.9968i	−1.40521	−	0.376524i	−0.880212	+	0.474581i	$0.842599\pi$
$854$	17.5204	+	30.8824i	0.599537	+	1.05677i
$855$	−1.00671	−	40.1526i	−0.0344289	−	1.37319i
$856$	−1.89287	−	3.27855i	−0.0646971	−	0.112059i
$857$	−36.4574	−	36.4574i	−1.24536	−	1.24536i	−0.957747	−	0.287613i	$-0.907138\pi$
$857$	−36.4574	−	36.4574i	−1.24536	−	1.24536i	−0.287613	−	0.957747i	$-0.592862\pi$
$858$	−0.800529	+	1.23197i	−0.0273296	+	0.0420588i
$859$	−19.3844			−0.661387			−0.330694	−	0.943738i	$-0.607283\pi$
$859$	−19.3844			−0.661387			−0.330694	+	0.943738i	$0.607283\pi$
$860$	16.5779	−	6.85574i	0.565302	−	0.233779i
$861$	24.3066	−	21.5440i	0.828368	−	0.734216i
$862$	20.9919	+	5.62476i	0.714986	+	0.191580i
$863$	−0.109624	+	0.409122i	−0.00373165	+	0.0139267i	−0.967767	−	0.251849i	$-0.918961\pi$
$863$	−0.109624	+	0.409122i	−0.00373165	+	0.0139267i	0.964035	+	0.265776i	$0.0856280\pi$
$864$	−10.9120	+	24.4549i	−0.371232	+	0.831973i
$865$	−4.23755	+	1.75243i	−0.144081	+	0.0595843i
$866$	−6.26636	−	3.61788i	−0.212939	−	0.122941i
$867$	−15.0522	+	23.1645i	−0.511199	+	0.786709i
$868$	5.81391	+	22.3720i	0.197337	+	0.759356i
$869$	−9.53065	−	5.50253i	−0.323305	−	0.186660i
$870$	−4.65781	+	25.0139i	−0.157915	+	0.848050i
$871$		−	2.97121i		−	0.100676i
$872$	8.92760	+	33.3182i	0.302327	+	1.12830i
$873$	0.291001	+	0.359756i	0.00984890	+	0.0121759i
$874$	43.4226			1.46879
$875$	−27.2228	−	11.5724i	−0.920298	−	0.391219i
$876$	10.8262	+	3.52089i	0.365782	+	0.118960i
$877$	27.6571	−	27.6571i	0.933913	−	0.933913i	−0.0640351	−	0.997948i	$-0.520397\pi$
$877$	27.6571	−	27.6571i	0.933913	−	0.933913i	0.997948	+	0.0640351i	$0.0203970\pi$
$878$	18.4495	+	4.94352i	0.622640	+	0.166836i
$879$	22.3162	+	24.7982i	0.752706	+	0.836422i
$880$	−2.75284	−	1.14210i	−0.0927982	−	0.0385001i
$881$			34.8974i			1.17572i	0.808961	+	0.587862i	$0.200030\pi$
$881$			34.8974i			1.17572i	−0.808961	+	0.587862i	$0.799970\pi$
$882$	−7.65129	+	19.0368i	−0.257632	+	0.641002i
$883$	−38.1289	−	38.1289i	−1.28314	−	1.28314i	−0.938872	−	0.344268i	$-0.888127\pi$
$883$	−38.1289	−	38.1289i	−1.28314	−	1.28314i	−0.344268	−	0.938872i	$-0.611873\pi$
$884$	0.493257	+	0.284782i	0.0165900	+	0.00957825i
$885$	−1.84605	+	3.86196i	−0.0620543	+	0.129818i
$886$	−18.3090	−	31.7121i	−0.615102	−	1.06539i
$887$	33.3655	+	33.3655i	1.12030	+	1.12030i	0.991695	+	0.128609i	$0.0410511\pi$
$887$	33.3655	+	33.3655i	1.12030	+	1.12030i	0.128609	+	0.991695i	$0.458949\pi$
$888$	24.5948	+	15.9816i	0.825347	+	0.536306i
$889$	0.0525565	−	6.96165i	0.00176269	−	0.233486i
$890$	−31.3445	−	24.0798i	−1.05067	−	0.807157i
$891$	4.52758	+	13.9862i	0.151680	+	0.468556i
$892$	26.7688	−	7.17267i	0.896285	−	0.240159i
$893$	8.36186	+	8.36186i	0.279819	+	0.279819i
$894$	4.60773	−	4.14655i	0.154105	−	0.138681i
$895$	−14.4486	+	34.8260i	−0.482964	+	1.16410i
$896$	5.08393	−	8.65409i	0.169842	−	0.289113i
$897$	−0.359522	+	6.82458i	−0.0120041	+	0.227866i
$898$	17.5721	−	4.70842i	0.586387	−	0.157122i
$899$	28.0960	−	48.6638i	0.937055	−	1.62303i
$900$	2.42719	+	15.4933i	0.0809064	+	0.516444i
$901$	−1.24144	+	0.716748i	−0.0413585	+	0.0238783i
$902$	2.92747	−	10.9255i	0.0974742	−	0.363779i
$903$	−29.3417	−	19.3827i	−0.976430	−	0.645015i
$904$	53.6218	+	30.9586i	1.78344	+	1.02967i
$905$	−45.1574	+	5.91895i	−1.50108	+	0.196753i
$906$	−2.26087	−	2.51232i	−0.0751124	−	0.0834664i
$907$	17.7517	−	17.7517i	0.589436	−	0.589436i	−0.348043	−	0.937479i	$-0.613154\pi$
$907$	17.7517	−	17.7517i	0.589436	−	0.589436i	0.937479	+	0.348043i	$0.113154\pi$
$908$	−17.1846	−	4.60461i	−0.570293	−	0.152809i
$909$	19.7556	+	14.3697i	0.655251	+	0.476612i
$910$	3.04265	+	0.425729i	0.100863	+	0.0141128i
$911$	18.7147	+	32.4148i	0.620045	+	1.07395i	0.989477	+	0.144692i	$0.0462191\pi$
$911$	18.7147	+	32.4148i	0.620045	+	1.07395i	−0.369431	+	0.929258i	$0.620448\pi$
$912$	−7.54103	+	3.83976i	−0.249708	+	0.127147i
$913$	6.18235	+	1.65656i	0.204606	+	0.0548240i
$914$	−24.6958	+	14.2581i	−0.816864	+	0.471617i
$915$	−4.12939	−	53.0391i	−0.136513	−	1.75342i
$916$	−12.6680	+	7.31387i	−0.418562	+	0.241657i
$917$	3.91293	+	3.97246i	0.129216	+	0.131182i
$918$	−4.85902	+	1.86066i	−0.160372	+	0.0614108i
$919$	−31.8867	+	18.4098i	−1.05184	+	0.607283i	−0.923165	−	0.384403i	$-0.874407\pi$
$919$	−31.8867	+	18.4098i	−1.05184	+	0.607283i	−0.128680	+	0.991686i	$0.541074\pi$
$920$	−48.9683	+	6.41845i	−1.61444	+	0.211610i
$921$	−15.2454	−	4.95812i	−0.502353	−	0.163376i
$922$	10.5487	+	10.5487i	0.347404	+	0.347404i
$923$	−0.874623	−	3.26414i	−0.0287886	−	0.107440i
$924$	−1.56714	−	7.66722i	−0.0515553	−	0.252233i
$925$	28.4570	+	0.0323876i	0.935662	+	0.00106490i
$926$	−20.2211	−	35.0240i	−0.664507	−	1.15096i
$927$	−4.80270	−	30.4302i	−0.157741	−	0.999458i
$928$	−33.4736	+	8.96921i	−1.09882	+	0.294429i
$929$	5.43502	−	9.41374i	0.178317	−	0.308855i	−0.762987	−	0.646414i	$-0.776268\pi$
$929$	5.43502	−	9.41374i	0.178317	−	0.308855i	0.941304	+	0.337559i	$0.109601\pi$
$930$	−5.78849	+	31.0860i	−0.189812	+	1.01935i
$931$	36.6094	−	20.4058i	1.19982	−	0.668772i
$932$	3.33164	+	12.4339i	0.109132	+	0.407284i
$933$	−23.2471	+	35.7761i	−0.761077	+	1.17126i
$934$	−17.6658			−0.578044
$935$	1.43058	+	3.45930i	0.0467851	+	0.113131i
$936$	−1.92747	−	4.33552i	−0.0630014	−	0.141711i
$937$	−22.9760	−	22.9760i	−0.750592	−	0.750592i	0.223998	−	0.974590i	$-0.428089\pi$
$937$	−22.9760	−	22.9760i	−0.750592	−	0.750592i	−0.974590	+	0.223998i	$0.928089\pi$
$938$	−10.1396	−	10.2938i	−0.331068	−	0.336105i
$939$	29.4000	+	32.6699i	0.959432	+	1.06614i
$940$	−3.66146	−	2.81285i	−0.119424	−	0.0917449i
$941$	31.4547	−	18.1604i	1.02539	−	0.592012i	0.109732	−	0.993961i	$-0.465001\pi$
$941$	31.4547	−	18.1604i	1.02539	−	0.592012i	0.915662	+	0.401949i	$0.131667\pi$
$942$	−12.7399	+	6.48695i	−0.415089	+	0.211356i
$943$	−13.6171	−	50.8197i	−0.443434	−	1.65492i
$944$	0.901848			0.0293527
$945$	22.4868	−	20.9605i	0.731495	−	0.681846i
$946$	−12.2461			−0.398155
$947$	−2.99339	−	11.1715i	−0.0972723	−	0.363025i	0.900082	−	0.435721i	$-0.143506\pi$
$947$	−2.99339	−	11.1715i	−0.0972723	−	0.363025i	−0.997354	+	0.0726957i	$0.976840\pi$
$948$	10.8721	−	5.53589i	0.353110	−	0.179797i
$949$	−2.89397	+	1.67084i	−0.0939424	+	0.0542377i
$950$	−14.6531	+	25.3134i	−0.475410	+	0.821274i
$951$	−12.3454	−	13.7185i	−0.400328	−	0.444852i
$952$	7.80897	−	2.02935i	0.253090	−	0.0657716i
$953$	39.2129	+	39.2129i	1.27023	+	1.27023i	0.945967	+	0.324263i	$0.105116\pi$
$953$	39.2129	+	39.2129i	1.27023	+	1.27023i	0.324263	+	0.945967i	$0.394884\pi$
$954$	4.07672	+	0.430722i	0.131989	+	0.0139452i
$955$	35.5947	+	14.7675i	1.15182	+	0.477866i
$956$	−7.93588			−0.256665
$957$	−10.3656	+	15.9521i	−0.335073	+	0.515660i
$958$	−2.06120	−	7.69249i	−0.0665942	−	0.248533i
$959$	0.270221	−	35.7936i	0.00872591	−	1.15584i
$960$	21.2923	−	14.6074i	0.687206	−	0.471453i
$961$	19.4163	−	33.6300i	0.626333	−	1.08484i
$962$	−2.85490	+	0.764969i	−0.0920458	+	0.0246636i
$963$	2.96769	−	2.40052i	0.0956325	−	0.0773556i
$964$	3.15001	+	5.45598i	0.101455	+	0.175725i
$965$	−23.9786	−	3.17073i	−0.771900	−	0.102069i
$966$	22.0440	+	24.8708i	0.709254	+	0.800205i
$967$	−0.320359	−	1.19560i	−0.0103021	−	0.0384478i	0.960583	−	0.277992i	$-0.0896688\pi$
$967$	−0.320359	−	1.19560i	−0.0103021	−	0.0384478i	−0.970886	+	0.239544i	$0.923002\pi$
$968$	17.5299	+	17.5299i	0.563432	+	0.563432i
$969$	10.1079	+	3.28729i	0.324712	+	0.105603i
$970$	−0.0437911	−	0.334096i	−0.00140605	−	0.0107272i
$971$	−36.8435	+	21.2716i	−1.18237	+	0.682639i	−0.956561	−	0.291533i	$-0.905835\pi$
$971$	−36.8435	+	21.2716i	−1.18237	+	0.682639i	−0.225805	+	0.974173i	$0.572501\pi$
$972$	−15.7364	−	4.23951i	−0.504746	−	0.135982i
$973$	−8.57468	−	32.9955i	−0.274892	−	1.05779i
$974$	−3.44318	+	1.98792i	−0.110327	+	0.0636971i
$975$	−3.85709	−	2.51257i	−0.123526	−	0.0804665i
$976$	−9.70686	+	5.60426i	−0.310709	+	0.179388i
$977$	7.08909	+	1.89952i	0.226800	+	0.0607709i	0.370429	−	0.928861i	$-0.379211\pi$
$977$	7.08909	+	1.89952i	0.226800	+	0.0607709i	−0.143629	+	0.989632i	$0.545877\pi$
$978$	−3.34382	+	1.70262i	−0.106924	+	0.0544436i
$979$	−14.7766	−	25.5939i	−0.472264	−	0.817985i
$980$	−13.1373	+	9.75741i	−0.419654	+	0.311689i
$981$	−31.7795	+	14.1284i	−1.01464	+	0.451086i
$982$	−26.6571	−	7.14274i	−0.850661	−	0.227934i
$983$	−21.3401	+	21.3401i	−0.680645	+	0.680645i	−0.960146	−	0.279500i	$-0.909831\pi$
$983$	−21.3401	+	21.3401i	−0.680645	+	0.680645i	0.279500	+	0.960146i	$0.409831\pi$
$984$	24.4341	+	27.1516i	0.778929	+	0.865562i
$985$	−11.6995	−	8.98794i	−0.372778	−	0.286380i
$986$	−5.83117	−	3.36663i	−0.185702	−	0.107215i
$987$	−0.544355	+	9.03435i	−0.0173270	+	0.287566i
$988$	−0.861181	+	3.21397i	−0.0273978	+	0.102250i
$989$	−49.3310	+	28.4813i	−1.56864	+	0.905652i
$990$	2.51067	−	10.4066i	0.0797943	−	0.330745i
$991$	−25.4329	+	44.0511i	−0.807903	+	1.39933i	0.106411	+	0.994322i	$0.466064\pi$
$991$	−25.4329	+	44.0511i	−0.807903	+	1.39933i	−0.914314	+	0.405007i	$0.867269\pi$
$992$	−41.5992	+	11.1465i	−1.32078	+	0.353901i
$993$	−0.569223	+	10.8052i	−0.0180637	+	0.342892i
$994$	−14.1693	−	8.32393i	−0.449424	−	0.264019i
$995$	−10.6705	−	4.42696i	−0.338276	−	0.140344i
$996$	−5.27437	+	4.74647i	−0.167125	+	0.150398i
$997$	−4.43771	−	4.43771i	−0.140544	−	0.140544i	0.633334	−	0.773878i	$-0.281686\pi$
$997$	−4.43771	−	4.43771i	−0.140544	−	0.140544i	−0.773878	+	0.633334i	$0.781686\pi$
$998$	23.3735	−	6.26292i	0.739876	−	0.198249i
$999$	−12.0506	+	27.0069i	−0.381265	+	0.854459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.cg.e.283.13	yes	160
3.2	odd	2		945.2.cj.e.388.28		160
5.2	odd	4	inner	315.2.cg.e.157.28	yes	160
7.5	odd	6		315.2.bs.e.103.13	yes	160
9.2	odd	6		945.2.bv.e.73.28		160
9.7	even	3		315.2.bs.e.178.13	yes	160
15.2	even	4		945.2.cj.e.577.13		160
21.5	even	6		945.2.bv.e.523.28		160
35.12	even	12		315.2.bs.e.292.13	yes	160
45.2	even	12		945.2.bv.e.262.28		160
45.7	odd	12		315.2.bs.e.52.13	✓	160
63.47	even	6		945.2.cj.e.208.13		160
63.61	odd	6	inner	315.2.cg.e.313.28	yes	160
105.47	odd	12		945.2.bv.e.712.28		160
315.47	odd	12		945.2.cj.e.397.28		160
315.187	even	12	inner	315.2.cg.e.187.13	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.e.52.13	✓	160	45.7	odd	12
315.2.bs.e.103.13	yes	160	7.5	odd	6
315.2.bs.e.178.13	yes	160	9.7	even	3
315.2.bs.e.292.13	yes	160	35.12	even	12
315.2.cg.e.157.28	yes	160	5.2	odd	4	inner
315.2.cg.e.187.13	yes	160	315.187	even	12	inner
315.2.cg.e.283.13	yes	160	1.1	even	1	trivial
315.2.cg.e.313.28	yes	160	63.61	odd	6	inner
945.2.bv.e.73.28		160	9.2	odd	6
945.2.bv.e.262.28		160	45.2	even	12
945.2.bv.e.523.28		160	21.5	even	6
945.2.bv.e.712.28		160	105.47	odd	12
945.2.cj.e.208.13		160	63.47	even	6
945.2.cj.e.388.28		160	3.2	odd	2
945.2.cj.e.397.28		160	315.47	odd	12
945.2.cj.e.577.13		160	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.252864 - 0.943703i) q^{2} +(1.54348 - 0.785915i) q^{3} +(0.905417 - 0.522743i) q^{4} +(-0.290604 - 2.21710i) q^{5} +(-1.13196 - 1.25786i) q^{6} +(-1.88490 + 1.85665i) q^{7} +(-2.10394 - 2.10394i) q^{8} +(1.76468 - 2.42609i) q^{9} +O(q^{10})\)	\(q+(-0.252864 - 0.943703i) q^{2} +(1.54348 - 0.785915i) q^{3} +(0.905417 - 0.522743i) q^{4} +(-0.290604 - 2.21710i) q^{5} +(-1.13196 - 1.25786i) q^{6} +(-1.88490 + 1.85665i) q^{7} +(-2.10394 - 2.10394i) q^{8} +(1.76468 - 2.42609i) q^{9} +(-2.01880 + 0.834870i) q^{10} -1.63342 q^{11} +(0.986664 - 1.51842i) q^{12} +(0.137573 + 0.513429i) q^{13} +(2.22875 + 1.30930i) q^{14} +(-2.19100 - 3.19367i) q^{15} +(-0.407995 + 0.706668i) q^{16} +(0.989992 - 0.265268i) q^{17} +(-2.73573 - 1.05186i) q^{18} +(2.99374 + 5.18531i) q^{19} +(-1.42209 - 1.85549i) q^{20} +(-1.45014 + 4.34708i) q^{21} +(0.413034 + 1.54146i) q^{22} +(5.24887 + 5.24887i) q^{23} +(-4.90091 - 1.59387i) q^{24} +(-4.83110 + 1.28860i) q^{25} +(0.449737 - 0.259656i) q^{26} +(0.817045 - 5.13151i) q^{27} +(-0.736068 + 2.66636i) q^{28} +(5.82340 - 3.36214i) q^{29} +(-2.45985 + 2.87521i) q^{30} +(7.23702 - 4.17830i) q^{31} +(-4.97801 - 1.33385i) q^{32} +(-2.52116 + 1.28373i) q^{33} +(-0.500668 - 0.867182i) q^{34} +(4.66415 + 3.63947i) q^{35} +(0.329546 - 3.11909i) q^{36} +(-5.49748 - 1.47305i) q^{37} +(4.13638 - 4.13638i) q^{38} +(0.615853 + 0.684348i) q^{39} +(-4.05324 + 5.27606i) q^{40} +(-6.13816 - 3.54387i) q^{41} +(4.46904 + 0.269277i) q^{42} +(-1.98612 + 7.41230i) q^{43} +(-1.47893 + 0.853858i) q^{44} +(-5.89172 - 3.20744i) q^{45} +(3.62612 - 6.28062i) q^{46} +(1.90773 - 0.511176i) q^{47} +(-0.0743522 + 1.41138i) q^{48} +(0.105686 - 6.99920i) q^{49} +(2.43767 + 4.23328i) q^{50} +(1.31956 - 1.18749i) q^{51} +(0.392952 + 0.392952i) q^{52} +(-1.35099 + 0.361997i) q^{53} +(-5.04922 + 0.526530i) q^{54} +(0.474678 + 3.62146i) q^{55} +(7.87199 + 0.0594290i) q^{56} +(8.69599 + 5.65061i) q^{57} +(-4.64539 - 4.64539i) q^{58} +(-0.552610 - 0.957148i) q^{59} +(-3.65323 - 1.74628i) q^{60} +(11.8958 + 6.86804i) q^{61} +(-5.77305 - 5.77305i) q^{62} +(1.17817 + 7.84933i) q^{63} +6.66703i q^{64} +(1.09835 - 0.454218i) q^{65} +(1.84897 + 2.05461i) q^{66} +(-5.39935 - 1.44675i) q^{67} +(0.757689 - 0.757689i) q^{68} +(12.2267 + 3.97637i) q^{69} +(2.25518 - 5.32186i) q^{70} -6.35753 q^{71} +(-8.81711 + 1.39158i) q^{72} +(1.62714 + 6.07255i) q^{73} +5.56047i q^{74} +(-6.44399 + 5.78576i) q^{75} +(5.42116 + 3.12991i) q^{76} +(3.07883 - 3.03269i) q^{77} +(0.490094 - 0.754229i) q^{78} +(5.83478 + 3.36871i) q^{79} +(1.68532 + 0.699207i) q^{80} +(-2.77184 - 8.56253i) q^{81} +(-1.79224 + 6.68871i) q^{82} +(-3.78491 - 1.01416i) q^{83} +(0.959425 + 4.69397i) q^{84} +(-0.875822 - 2.11783i) q^{85} +7.49722 q^{86} +(6.34596 - 9.76610i) q^{87} +(3.43661 + 3.43661i) q^{88} +(9.04644 + 15.6689i) q^{89} +(-1.53706 + 6.37108i) q^{90} +(-1.21257 - 0.712336i) q^{91} +(7.49622 + 2.00861i) q^{92} +(7.88643 - 12.1368i) q^{93} +(-0.964796 - 1.67108i) q^{94} +(10.6264 - 8.14430i) q^{95} +(-8.73177 + 1.85351i) q^{96} +(-0.0399199 + 0.148983i) q^{97} +(-6.63189 + 1.67011i) q^{98} +(-2.88246 + 3.96283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 2 q^{2} - 12 q^{3} - 24 q^{6} + 6 q^{7} - 16 q^{8}+O(q^{10}) \) 160 * q - 2 * q^2 - 12 * q^3 - 24 * q^6 + 6 * q^7 - 16 * q^8	\( 160 q - 2 q^{2} - 12 q^{3} - 24 q^{6} + 6 q^{7} - 16 q^{8} - 24 q^{10} + 32 q^{11} - 12 q^{12} + 16 q^{15} + 76 q^{16} - 6 q^{17} - 44 q^{18} - 60 q^{20} - 60 q^{21} + 8 q^{22} - 16 q^{23} - 4 q^{25} - 36 q^{26} + 36 q^{27} + 22 q^{28} - 44 q^{30} + 48 q^{31} - 6 q^{32} + 60 q^{33} - 36 q^{35} - 32 q^{36} - 4 q^{37} + 12 q^{41} + 2 q^{42} - 4 q^{43} - 24 q^{45} - 16 q^{46} - 54 q^{47} + 18 q^{48} - 44 q^{50} - 4 q^{51} + 8 q^{53} - 92 q^{56} - 4 q^{57} - 56 q^{58} - 28 q^{60} - 24 q^{61} + 54 q^{63} + 62 q^{65} + 12 q^{66} + 12 q^{67} + 2 q^{70} - 40 q^{71} + 28 q^{72} + 36 q^{73} + 36 q^{75} - 96 q^{76} - 110 q^{77} - 62 q^{78} + 36 q^{80} - 16 q^{81} - 66 q^{82} + 138 q^{83} - 20 q^{85} + 32 q^{86} + 48 q^{87} - 92 q^{88} - 18 q^{90} - 48 q^{91} - 26 q^{92} + 40 q^{93} - 94 q^{95} + 132 q^{96} - 48 q^{97} + 102 q^{98}+O(q^{100}) \) 160 * q - 2 * q^2 - 12 * q^3 - 24 * q^6 + 6 * q^7 - 16 * q^8 - 24 * q^10 + 32 * q^11 - 12 * q^12 + 16 * q^15 + 76 * q^16 - 6 * q^17 - 44 * q^18 - 60 * q^20 - 60 * q^21 + 8 * q^22 - 16 * q^23 - 4 * q^25 - 36 * q^26 + 36 * q^27 + 22 * q^28 - 44 * q^30 + 48 * q^31 - 6 * q^32 + 60 * q^33 - 36 * q^35 - 32 * q^36 - 4 * q^37 + 12 * q^41 + 2 * q^42 - 4 * q^43 - 24 * q^45 - 16 * q^46 - 54 * q^47 + 18 * q^48 - 44 * q^50 - 4 * q^51 + 8 * q^53 - 92 * q^56 - 4 * q^57 - 56 * q^58 - 28 * q^60 - 24 * q^61 + 54 * q^63 + 62 * q^65 + 12 * q^66 + 12 * q^67 + 2 * q^70 - 40 * q^71 + 28 * q^72 + 36 * q^73 + 36 * q^75 - 96 * q^76 - 110 * q^77 - 62 * q^78 + 36 * q^80 - 16 * q^81 - 66 * q^82 + 138 * q^83 - 20 * q^85 + 32 * q^86 + 48 * q^87 - 92 * q^88 - 18 * q^90 - 48 * q^91 - 26 * q^92 + 40 * q^93 - 94 * q^95 + 132 * q^96 - 48 * q^97 + 102 * q^98

Introduction

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