LMFDB - Embedded newform 336.2.bq.b.109.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(37,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("336.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bq (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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$30$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			109.4
Character	$\chi$	$=$	336.109
Dual form			336.2.bq.b.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30822 + 0.537189i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.42286 - 1.40552i) q^{4} +(-1.52423 - 0.408415i) q^{5} +(1.12460 - 0.857476i) q^{6} +(1.09198 + 2.40989i) q^{7} +(-1.10637 + 2.60306i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-1.30822 + 0.537189i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.42286 - 1.40552i) q^{4} +(-1.52423 - 0.408415i) q^{5} +(1.12460 - 0.857476i) q^{6} +(1.09198 + 2.40989i) q^{7} +(-1.10637 + 2.60306i) q^{8} +(0.866025 - 0.500000i) q^{9} +(2.21341 - 0.284503i) q^{10} +(-0.686571 - 2.56232i) q^{11} +(-1.01060 + 1.72589i) q^{12} +(-0.948125 - 0.948125i) q^{13} +(-2.72311 - 2.56606i) q^{14} +1.57800 q^{15} +(0.0490361 - 3.99970i) q^{16} +(-2.32148 + 4.02093i) q^{17} +(-0.864353 + 1.11933i) q^{18} +(-1.53566 + 5.73117i) q^{19} +(-2.74279 + 1.56121i) q^{20} +(-1.67849 - 2.04515i) q^{21} +(2.27463 + 2.98324i) q^{22} +(-5.02785 + 2.90283i) q^{23} +(0.394951 - 2.80072i) q^{24} +(-2.17366 - 1.25496i) q^{25} +(1.74967 + 0.731030i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(4.94087 + 1.89414i) q^{28} +(-6.50787 - 6.50787i) q^{29} +(-2.06436 + 0.847682i) q^{30} +(-1.32781 + 2.29984i) q^{31} +(2.08445 + 5.25881i) q^{32} +(1.32635 + 2.29731i) q^{33} +(0.877002 - 6.50731i) q^{34} +(-0.680182 - 4.11920i) q^{35} +(0.529470 - 1.92864i) q^{36} +(-10.3258 - 2.76679i) q^{37} +(-1.06975 - 8.32255i) q^{38} +(1.16121 + 0.670426i) q^{39} +(2.74949 - 3.51580i) q^{40} -3.43864i q^{41} +(3.29447 + 1.77383i) q^{42} +(3.31394 - 3.31394i) q^{43} +(-4.57828 - 2.68082i) q^{44} +(-1.52423 + 0.408415i) q^{45} +(5.01814 - 6.49844i) q^{46} +(3.52421 + 6.10411i) q^{47} +(0.987833 + 3.87610i) q^{48} +(-4.61517 + 5.26309i) q^{49} +(3.51777 + 0.474096i) q^{50} +(1.20169 - 4.48476i) q^{51} +(-2.68165 - 0.0164379i) q^{52} +(2.81379 + 10.5012i) q^{53} +(0.545198 - 1.30490i) q^{54} +4.18596i q^{55} +(-7.48124 + 0.176244i) q^{56} -5.93335i q^{57} +(12.0096 + 5.01774i) q^{58} +(1.68748 + 6.29775i) q^{59} +(2.24526 - 2.21790i) q^{60} +(-0.738851 + 2.75743i) q^{61} +(0.501616 - 3.72197i) q^{62} +(2.15063 + 1.54104i) q^{63} +(-5.55188 - 5.75992i) q^{64} +(1.05793 + 1.83239i) q^{65} +(-2.96925 - 2.29288i) q^{66} +(12.7774 - 3.42370i) q^{67} +(2.34835 + 8.98408i) q^{68} +(4.10522 - 4.10522i) q^{69} +(3.10262 + 5.02342i) q^{70} +2.52175i q^{71} +(0.343385 + 2.80751i) q^{72} +(-7.51613 - 4.33944i) q^{73} +(14.9946 - 1.92735i) q^{74} +(2.42441 + 0.649617i) q^{75} +(5.87024 + 10.3130i) q^{76} +(5.42519 - 4.45255i) q^{77} +(-1.87926 - 0.253271i) q^{78} +(1.62052 + 2.80682i) q^{79} +(-1.70828 + 6.07642i) q^{80} +(0.500000 - 0.866025i) q^{81} +(1.84720 + 4.49849i) q^{82} +(-2.40354 - 2.40354i) q^{83} +(-5.26276 - 0.550804i) q^{84} +(5.18068 - 5.18068i) q^{85} +(-2.55513 + 6.11555i) q^{86} +(7.97048 + 4.60176i) q^{87} +(7.42948 + 1.04769i) q^{88} +(9.99029 - 5.76790i) q^{89} +(1.77462 - 1.35309i) q^{90} +(1.24955 - 3.32021i) q^{91} +(-3.07392 + 11.1970i) q^{92} +(0.687326 - 2.56513i) q^{93} +(-7.88949 - 6.09232i) q^{94} +(4.68140 - 8.10842i) q^{95} +(-3.37450 - 4.54013i) q^{96} +5.78600 q^{97} +(3.21037 - 9.36448i) q^{98} +(-1.87575 - 1.87575i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8}+O(q^{10}) $ 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8	$ 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8} - 8 q^{10} + 4 q^{11} + 8 q^{13} + 32 q^{14} + 8 q^{15} + 12 q^{16} - 16 q^{17} - 4 q^{18} - 8 q^{19} - 64 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{24} - 8 q^{26} - 8 q^{28} - 64 q^{29} - 52 q^{31} - 4 q^{33} + 32 q^{34} - 8 q^{35} + 24 q^{37} - 40 q^{38} - 60 q^{40} + 24 q^{42} - 32 q^{43} - 12 q^{44} - 8 q^{45} + 4 q^{46} - 8 q^{47} + 32 q^{48} + 20 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{54} - 104 q^{56} + 4 q^{58} + 52 q^{59} - 16 q^{60} + 4 q^{61} - 144 q^{62} + 8 q^{63} - 64 q^{64} + 24 q^{65} + 24 q^{66} + 12 q^{68} + 24 q^{69} - 48 q^{70} + 4 q^{72} + 16 q^{74} + 16 q^{75} - 8 q^{76} + 8 q^{77} - 56 q^{78} + 28 q^{79} + 68 q^{80} + 60 q^{81} + 28 q^{82} + 8 q^{83} + 24 q^{84} - 80 q^{85} + 36 q^{86} + 40 q^{88} + 8 q^{90} + 36 q^{91} - 184 q^{92} + 4 q^{93} + 60 q^{94} - 16 q^{95} + 36 q^{96} + 24 q^{97} + 124 q^{98} - 8 q^{99}+O(q^{100}) $ 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8 - 8 * q^10 + 4 * q^11 + 8 * q^13 + 32 * q^14 + 8 * q^15 + 12 * q^16 - 16 * q^17 - 4 * q^18 - 8 * q^19 - 64 * q^20 + 12 * q^21 + 24 * q^22 - 8 * q^24 - 8 * q^26 - 8 * q^28 - 64 * q^29 - 52 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 24 * q^37 - 40 * q^38 - 60 * q^40 + 24 * q^42 - 32 * q^43 - 12 * q^44 - 8 * q^45 + 4 * q^46 - 8 * q^47 + 32 * q^48 + 20 * q^49 - 16 * q^50 - 8 * q^51 - 16 * q^52 + 4 * q^54 - 104 * q^56 + 4 * q^58 + 52 * q^59 - 16 * q^60 + 4 * q^61 - 144 * q^62 + 8 * q^63 - 64 * q^64 + 24 * q^65 + 24 * q^66 + 12 * q^68 + 24 * q^69 - 48 * q^70 + 4 * q^72 + 16 * q^74 + 16 * q^75 - 8 * q^76 + 8 * q^77 - 56 * q^78 + 28 * q^79 + 68 * q^80 + 60 * q^81 + 28 * q^82 + 8 * q^83 + 24 * q^84 - 80 * q^85 + 36 * q^86 + 40 * q^88 + 8 * q^90 + 36 * q^91 - 184 * q^92 + 4 * q^93 + 60 * q^94 - 16 * q^95 + 36 * q^96 + 24 * q^97 + 124 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.30822	+	0.537189i	−0.925048	+	0.379850i
$2$	−1.30822	+	0.537189i	−0.925048	+	0.379850i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	1.42286	−	1.40552i	0.711428	−	0.702759i
$5$	−1.52423	−	0.408415i	−0.681655	−	0.182649i	−0.0986558	−	0.995122i	$-0.531454\pi$
$5$	−1.52423	−	0.408415i	−0.681655	−	0.182649i	−0.582999	+	0.812473i	$0.698121\pi$
$6$	1.12460	−	0.857476i	0.459118	−	0.350063i
$7$	1.09198	+	2.40989i	0.412728	+	0.910854i
$7$	1.09198	+	2.40989i	0.412728	+	0.910854i
$8$	−1.10637	+	2.60306i	−0.391162	+	0.920322i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	2.21341	−	0.284503i	0.699943	−	0.0899677i
$11$	−0.686571	−	2.56232i	−0.207009	−	0.772568i	−0.988828	−	0.149062i	$-0.952375\pi$
$11$	−0.686571	−	2.56232i	−0.207009	−	0.772568i	0.781819	−	0.623506i	$-0.214292\pi$
$12$	−1.01060	+	1.72589i	−0.291735	+	0.498221i
$13$	−0.948125	−	0.948125i	−0.262963	−	0.262963i	0.563294	−	0.826257i	$-0.309534\pi$
$13$	−0.948125	−	0.948125i	−0.262963	−	0.262963i	−0.826257	+	0.563294i	$0.809534\pi$
$14$	−2.72311	−	2.56606i	−0.727782	−	0.685809i
$15$	1.57800			0.407437
$16$	0.0490361	−	3.99970i	0.0122590	−	0.999925i
$17$	−2.32148	+	4.02093i	−0.563042	+	0.975218i	0.434187	+	0.900823i	$0.357036\pi$
$17$	−2.32148	+	4.02093i	−0.563042	+	0.975218i	−0.997229	+	0.0743949i	$0.976297\pi$
$18$	−0.864353	+	1.11933i	−0.203730	+	0.263828i
$19$	−1.53566	+	5.73117i	−0.352305	+	1.31482i	0.531536	+	0.847035i	$0.321615\pi$
$19$	−1.53566	+	5.73117i	−0.352305	+	1.31482i	−0.883842	+	0.467786i	$0.845052\pi$
$20$	−2.74279	+	1.56121i	−0.613307	+	0.349098i
$21$	−1.67849	−	2.04515i	−0.366278	−	0.446289i
$22$	2.27463	+	2.98324i	0.484953	+	0.636030i
$23$	−5.02785	+	2.90283i	−1.04838	+	0.605282i	−0.922195	−	0.386725i	$-0.873606\pi$
$23$	−5.02785	+	2.90283i	−1.04838	+	0.605282i	−0.126184	+	0.992007i	$0.540273\pi$
$24$	0.394951	−	2.80072i	0.0806191	−	0.571694i
$25$	−2.17366	−	1.25496i	−0.434732	−	0.250993i
$26$	1.74967	+	0.731030i	0.343139	+	0.143367i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	4.94087	+	1.89414i	0.933738	+	0.357958i
$29$	−6.50787	−	6.50787i	−1.20848	−	1.20848i	−0.971519	−	0.236961i	$-0.923849\pi$
$29$	−6.50787	−	6.50787i	−1.20848	−	1.20848i	−0.236961	−	0.971519i	$-0.576151\pi$
$30$	−2.06436	+	0.847682i	−0.376899	+	0.154765i
$31$	−1.32781	+	2.29984i	−0.238482	+	0.413063i	−0.960279	−	0.279042i	$-0.909983\pi$
$31$	−1.32781	+	2.29984i	−0.238482	+	0.413063i	0.721797	+	0.692105i	$0.243316\pi$
$32$	2.08445	+	5.25881i	0.368481	+	0.929635i
$33$	1.32635	+	2.29731i	0.230888	+	0.399910i
$34$	0.877002	−	6.50731i	0.150405	−	1.11600i
$35$	−0.680182	−	4.11920i	−0.114972	−	0.696273i
$36$	0.529470	−	1.92864i	0.0882450	−	0.321440i
$37$	−10.3258	−	2.76679i	−1.69755	−	0.454857i	−0.725229	−	0.688508i	$-0.758266\pi$
$37$	−10.3258	−	2.76679i	−1.69755	−	0.454857i	−0.972321	+	0.233651i	$0.924933\pi$
$38$	−1.06975	−	8.32255i	−0.173536	−	1.35010i
$39$	1.16121	+	0.670426i	0.185943	+	0.107354i
$40$	2.74949	−	3.51580i	0.434733	−	0.555897i
$41$		−	3.43864i		−	0.537026i	−0.963276	−	0.268513i	$-0.913468\pi$
$41$		−	3.43864i		−	0.537026i	0.963276	−	0.268513i	$-0.0865322\pi$
$42$	3.29447	+	1.77383i	0.508347	+	0.273708i
$43$	3.31394	−	3.31394i	0.505371	−	0.505371i	−0.407731	−	0.913102i	$-0.633680\pi$
$43$	3.31394	−	3.31394i	0.505371	−	0.505371i	0.913102	+	0.407731i	$0.133680\pi$
$44$	−4.57828	−	2.68082i	−0.690201	−	0.404149i
$45$	−1.52423	+	0.408415i	−0.227218	+	0.0608830i
$46$	5.01814	−	6.49844i	0.739885	−	0.958142i
$47$	3.52421	+	6.10411i	0.514059	+	0.890376i	0.999867	+	0.0163105i	$0.00519203\pi$
$47$	3.52421	+	6.10411i	0.514059	+	0.890376i	−0.485808	+	0.874065i	$0.661475\pi$
$48$	0.987833	+	3.87610i	0.142581	+	0.559467i
$49$	−4.61517	+	5.26309i	−0.659311	+	0.751871i
$50$	3.51777	+	0.474096i	0.497488	+	0.0670473i
$51$	1.20169	−	4.48476i	0.168270	−	0.627992i
$52$	−2.68165	−	0.0164379i	−0.371878	−	0.00227952i
$53$	2.81379	+	10.5012i	0.386504	+	1.44245i	0.835783	+	0.549060i	$0.185014\pi$
$53$	2.81379	+	10.5012i	0.386504	+	1.44245i	−0.449279	+	0.893392i	$0.648319\pi$
$54$	0.545198	−	1.30490i	0.0741920	−	0.177574i
$55$			4.18596i			0.564435i
$56$	−7.48124	+	0.176244i	−0.999723	+	0.0235516i
$57$		−	5.93335i		−	0.785891i
$58$	12.0096	+	5.01774i	1.57694	+	0.658861i
$59$	1.68748	+	6.29775i	0.219691	+	0.819897i	0.984462	+	0.175596i	$0.0561852\pi$
$59$	1.68748	+	6.29775i	0.219691	+	0.819897i	−0.764772	+	0.644302i	$0.777148\pi$
$60$	2.24526	−	2.21790i	0.289862	−	0.286330i
$61$	−0.738851	+	2.75743i	−0.0946001	+	0.353053i	−0.996959	−	0.0779339i	$-0.975168\pi$
$61$	−0.738851	+	2.75743i	−0.0946001	+	0.353053i	0.902358	+	0.430986i	$0.141834\pi$
$62$	0.501616	−	3.72197i	0.0637053	−	0.472690i
$63$	2.15063	+	1.54104i	0.270953	+	0.194153i
$64$	−5.55188	−	5.75992i	−0.693985	−	0.719989i
$65$	1.05793	+	1.83239i	0.131220	+	0.227280i
$66$	−2.96925	−	2.29288i	−0.365489	−	0.282233i
$67$	12.7774	−	3.42370i	1.56101	−	0.418272i	0.628029	−	0.778190i	$-0.283862\pi$
$67$	12.7774	−	3.42370i	1.56101	−	0.418272i	0.932984	+	0.359918i	$0.117195\pi$
$68$	2.34835	+	8.98408i	0.284779	+	1.08948i
$69$	4.10522	−	4.10522i	0.494211	−	0.494211i
$70$	3.10262	+	5.02342i	0.370834	+	0.600414i
$71$			2.52175i			0.299277i	0.988741	+	0.149638i	$0.0478110\pi$
$71$			2.52175i			0.299277i	−0.988741	+	0.149638i	$0.952189\pi$
$72$	0.343385	+	2.80751i	0.0404683	+	0.330868i
$73$	−7.51613	−	4.33944i	−0.879696	−	0.507893i	−0.00913815	−	0.999958i	$-0.502909\pi$
$73$	−7.51613	−	4.33944i	−0.879696	−	0.507893i	−0.870558	+	0.492065i	$0.836242\pi$
$74$	14.9946	−	1.92735i	1.74309	−	0.224050i
$75$	2.42441	+	0.649617i	0.279946	+	0.0750114i
$76$	5.87024	+	10.3130i	0.673363	+	1.18299i
$77$	5.42519	−	4.45255i	0.618258	−	0.507416i
$78$	−1.87926	−	0.253271i	−0.212784	−	0.0286773i
$79$	1.62052	+	2.80682i	0.182323	+	0.315792i	0.942671	−	0.333723i	$-0.108305\pi$
$79$	1.62052	+	2.80682i	0.182323	+	0.315792i	−0.760348	+	0.649516i	$0.774972\pi$
$80$	−1.70828	+	6.07642i	−0.190992	+	0.679365i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	1.84720	+	4.49849i	0.203989	+	0.496775i
$83$	−2.40354	−	2.40354i	−0.263822	−	0.263822i	0.562783	−	0.826605i	$-0.309731\pi$
$83$	−2.40354	−	2.40354i	−0.263822	−	0.263822i	−0.826605	+	0.562783i	$0.809731\pi$
$84$	−5.26276	−	0.550804i	−0.574214	−	0.0600976i
$85$	5.18068	−	5.18068i	0.561923	−	0.561923i
$86$	−2.55513	+	6.11555i	−0.275527	+	0.659457i
$87$	7.97048	+	4.60176i	0.854525	+	0.493360i
$88$	7.42948	+	1.04769i	0.791985	+	0.111684i
$89$	9.99029	−	5.76790i	1.05897	−	0.611396i	0.133822	−	0.991005i	$-0.457275\pi$
$89$	9.99029	−	5.76790i	1.05897	−	0.611396i	0.925147	+	0.379610i	$0.123942\pi$
$90$	1.77462	−	1.35309i	0.187061	−	0.142629i
$91$	1.24955	−	3.32021i	0.130988	−	0.348053i
$92$	−3.07392	+	11.1970i	−0.320479	+	1.16737i
$93$	0.687326	−	2.56513i	0.0712723	−	0.265992i
$94$	−7.88949	−	6.09232i	−0.813739	−	0.628375i
$95$	4.68140	−	8.10842i	0.480301	−	0.831906i
$96$	−3.37450	−	4.54013i	−0.344408	−	0.463375i
$97$	5.78600			0.587479			0.293740	−	0.955885i	$-0.405100\pi$
$97$	5.78600			0.587479			0.293740	+	0.955885i	$0.405100\pi$
$98$	3.21037	−	9.36448i	0.324296	−	0.945956i
$99$	−1.87575	−	1.87575i	−0.188520	−	0.188520i
$100$	−4.85668	+	1.26949i	−0.485668	+	0.126949i
$101$	−0.915365	−	3.41619i	−0.0910822	−	0.339924i	0.905314	−	0.424743i	$-0.139635\pi$
$101$	−0.915365	−	3.41619i	−0.0910822	−	0.339924i	−0.996396	+	0.0848191i	$0.972969\pi$
$102$	0.837098	+	6.51257i	0.0828850	+	0.644840i
$103$	−11.8368	+	6.83396i	−1.16631	+	0.673370i	−0.952808	−	0.303573i	$-0.901820\pi$
$103$	−11.8368	+	6.83396i	−1.16631	+	0.673370i	−0.213502	+	0.976943i	$0.568487\pi$
$104$	3.51701	−	1.41905i	0.344871	−	0.139149i
$105$	1.72313	+	3.80280i	0.168161	+	0.371115i
$106$	−9.32218	−	12.2263i	−0.905450	−	1.18752i
$107$	−5.84188	−	1.56533i	−0.564756	−	0.151326i	−0.0348656	−	0.999392i	$-0.511100\pi$
$107$	−5.84188	−	1.56533i	−0.564756	−	0.151326i	−0.529891	+	0.848066i	$0.677767\pi$
$108$	−0.0122593	+	1.99996i	−0.00117965	+	0.192446i
$109$	−4.85248	+	1.30022i	−0.464783	+	0.124538i	−0.483608	−	0.875284i	$-0.660674\pi$
$109$	−4.85248	+	1.30022i	−0.464783	+	0.124538i	0.0188251	+	0.999823i	$0.494007\pi$
$110$	−2.24865	−	5.47614i	−0.214401	−	0.522129i
$111$	10.6900			1.01465
$112$	9.69240	−	4.24941i	0.915845	−	0.401531i
$113$	7.89759			0.742943			0.371472	−	0.928444i	$-0.378853\pi$
$113$	7.89759			0.742943			0.371472	+	0.928444i	$0.378853\pi$
$114$	3.18733	+	7.76210i	0.298521	+	0.726987i
$115$	8.84915	−	2.37112i	0.825187	−	0.221108i
$116$	−18.4067	−	0.112828i	−1.70902	−	0.0104758i
$117$	−1.29516	−	0.347038i	−0.119738	−	0.0320837i
$118$	−5.59067	−	7.33232i	−0.514663	−	0.674995i
$119$	−12.2250	−	1.20377i	−1.12066	−	0.110349i
$120$	−1.74585	+	4.10762i	−0.159374	+	0.374973i
$121$	3.43219	−	1.98158i	0.312017	−	0.180143i
$122$	−0.514685	−	4.00421i	−0.0465974	−	0.362524i
$123$	0.889987	+	3.32148i	0.0802474	+	0.299487i
$124$	1.34318	+	5.13860i	0.120621	+	0.461460i
$125$	8.37967	+	8.37967i	0.749500	+	0.749500i
$126$	−3.64131	−	0.860721i	−0.324394	−	0.0766791i
$127$	−2.55209			−0.226461			−0.113231	−	0.993569i	$-0.536120\pi$
$127$	−2.55209			−0.226461			−0.113231	+	0.993569i	$0.536120\pi$
$128$	10.3572	+	4.55280i	0.915458	+	0.402415i
$129$	−2.34331	+	4.05873i	−0.206317	+	0.357351i
$130$	−2.36834	−	1.82885i	−0.207717	−	0.160401i
$131$	3.32215	−	12.3984i	0.290258	−	1.08326i	−0.654653	−	0.755929i	$-0.727185\pi$
$131$	3.32215	−	12.3984i	0.290258	−	1.08326i	0.944911	−	0.327328i	$-0.106148\pi$
$132$	5.11612	+	1.40453i	0.445301	+	0.122248i
$133$	−15.4884	+	2.55752i	−1.34302	+	0.221765i
$134$	−14.8765	+	11.3428i	−1.28513	+	0.979872i
$135$	1.36658	−	0.788998i	0.117617	−	0.0679061i
$136$	−7.89830	−	10.4916i	−0.677274	−	0.899648i
$137$	13.5589	+	7.82823i	1.15841	+	0.668811i	0.950923	−	0.309426i	$-0.100137\pi$
$137$	13.5589	+	7.82823i	1.15841	+	0.668811i	0.207491	+	0.978237i	$0.433470\pi$
$138$	−3.16524	+	7.57580i	−0.269443	+	0.644895i
$139$	−10.6286	+	10.6286i	−0.901505	+	0.901505i	−0.995566	−	0.0940614i	$-0.970015\pi$
$139$	−10.6286	+	10.6286i	−0.901505	+	0.901505i	0.0940614	+	0.995566i	$0.470015\pi$
$140$	−6.75742	−	4.90502i	−0.571106	−	0.414550i
$141$	−4.98399	−	4.98399i	−0.419727	−	0.419727i
$142$	−1.35466	−	3.29900i	−0.113680	−	0.276846i
$143$	−1.77844	+	3.08035i	−0.148721	+	0.257592i
$144$	−1.95738	−	3.48836i	−0.163115	−	0.290697i
$145$	7.26155	+	12.5774i	0.603039	+	1.04449i
$146$	12.1638	+	1.63934i	1.00668	+	0.135673i
$147$	3.09573	−	6.27825i	0.255331	−	0.517822i
$148$	−18.5809	+	10.5763i	−1.52734	+	0.869370i
$149$	−6.68563	−	1.79141i	−0.547708	−	0.146758i	−0.0256551	−	0.999671i	$-0.508167\pi$
$149$	−6.68563	−	1.79141i	−0.547708	−	0.146758i	−0.522053	+	0.852913i	$0.674834\pi$
$150$	−3.52061	+	0.452525i	−0.287457	+	0.0369485i
$151$	−8.48885	−	4.90104i	−0.690813	−	0.398841i	0.113104	−	0.993583i	$-0.463921\pi$
$151$	−8.48885	−	4.90104i	−0.690813	−	0.398841i	−0.803917	+	0.594742i	$0.797254\pi$
$152$	−13.2196	−	10.3382i	−1.07225	−	0.838542i
$153$			4.64297i			0.375362i
$154$	−4.70546	+	8.73925i	−0.379177	+	0.704229i
$155$	2.96317	−	2.96317i	0.238008	−	0.238008i
$156$	2.59453	−	0.678185i	0.207729	−	0.0542983i
$157$	7.79462	−	2.08856i	0.622079	−	0.166685i	0.0660061	−	0.997819i	$-0.478974\pi$
$157$	7.79462	−	2.08856i	0.622079	−	0.166685i	0.556073	+	0.831134i	$0.312308\pi$
$158$	−3.62779	−	2.80140i	−0.288611	−	0.222868i
$159$	−5.43583	−	9.41513i	−0.431089	−	0.746668i
$160$	−1.02939	−	8.86694i	−0.0813803	−	0.700993i
$161$	−12.4858	−	8.94676i	−0.984020	−	0.705104i
$162$	−0.188888	+	1.40154i	−0.0148405	+	0.110116i
$163$	−1.89999	+	7.09085i	−0.148819	+	0.555399i	0.850737	+	0.525592i	$0.176156\pi$
$163$	−1.89999	+	7.09085i	−0.148819	+	0.555399i	−0.999556	+	0.0298071i	$0.990511\pi$
$164$	−4.83308	−	4.89269i	−0.377400	−	0.382055i
$165$	−1.08341	−	4.04333i	−0.0843430	−	0.314773i
$166$	4.43550	+	1.85319i	0.344261	+	0.143835i
$167$		−	6.64657i		−	0.514327i	−0.966368	−	0.257164i	$-0.917212\pi$
$167$		−	6.64657i		−	0.514327i	0.966368	−	0.257164i	$-0.0827879\pi$
$168$	7.18071	−	2.10653i	0.554004	−	0.162522i
$169$		−	11.2021i		−	0.861701i
$170$	−3.99444	+	9.56044i	−0.306359	+	0.733252i
$171$	1.53566	+	5.73117i	0.117435	+	0.438274i
$172$	0.0574544	−	9.37305i	0.00438086	−	0.714688i
$173$	2.63642	−	9.83924i	0.200443	−	0.748063i	−0.790347	−	0.612659i	$-0.790100\pi$
$173$	2.63642	−	9.83924i	0.200443	−	0.748063i	0.990790	−	0.135404i	$-0.0432334\pi$
$174$	−12.8991	−	1.73844i	−0.977879	−	0.131790i
$175$	0.650743	−	6.60869i	0.0491915	−	0.499570i
$176$	−10.2822	+	2.62043i	−0.775047	+	0.197522i
$177$	−3.25996	−	5.64641i	−0.245033	−	0.424410i
$178$	−9.97100	+	12.9123i	−0.747358	+	0.967820i
$179$	3.80096	−	1.01846i	0.284097	−	0.0761235i	−0.113957	−	0.993486i	$-0.536353\pi$
$179$	3.80096	−	1.01846i	0.284097	−	0.0761235i	0.398053	+	0.917362i	$0.369686\pi$
$180$	−1.59472	+	2.72345i	−0.118863	+	0.202994i
$181$	−14.7450	+	14.7450i	−1.09599	+	1.09599i	−0.101116	+	0.994875i	$0.532241\pi$
$181$	−14.7450	+	14.7450i	−1.09599	+	1.09599i	−0.994875	+	0.101116i	$0.967759\pi$
$182$	0.148900	+	5.01480i	0.0110372	+	0.371722i
$183$		−	2.85470i		−	0.211025i
$184$	−1.99358	−	16.2994i	−0.146969	−	1.20161i
$185$	14.6088	+	8.43442i	1.07406	+	0.620111i
$186$	0.478792	+	3.72497i	0.0351067	+	0.273128i
$187$	11.8968	+	3.18773i	0.869977	+	0.233110i
$188$	13.5939	+	3.73193i	0.991436	+	0.272179i
$189$	−2.47620	−	0.931908i	−0.180117	−	0.0677863i
$190$	−1.76852	+	13.1224i	−0.128302	+	0.951996i
$191$	3.57089	+	6.18497i	0.258381	+	0.447529i	0.965808	−	0.259257i	$-0.0834778\pi$
$191$	3.57089	+	6.18497i	0.258381	+	0.447529i	−0.707428	+	0.706786i	$0.750144\pi$
$192$	6.85348	+	4.12672i	0.494607	+	0.297820i
$193$	4.67901	−	8.10429i	0.336803	−	0.583359i	−0.647027	−	0.762467i	$-0.723988\pi$
$193$	4.67901	−	8.10429i	0.336803	−	0.583359i	0.983829	+	0.179108i	$0.0573211\pi$
$194$	−7.56933	+	3.10818i	−0.543446	+	0.223154i
$195$	−1.49614	−	1.49614i	−0.107141	−	0.107141i
$196$	0.830648	+	13.9753i	0.0593320	+	0.998238i
$197$	0.576057	−	0.576057i	0.0410423	−	0.0410423i	−0.686288	−	0.727330i	$-0.740761\pi$
$197$	0.576057	−	0.576057i	0.0410423	−	0.0410423i	0.727330	+	0.686288i	$0.240761\pi$
$198$	3.46151	+	1.44625i	0.245999	+	0.102781i
$199$	16.9674	+	9.79615i	1.20279	+	0.694430i	0.961174	−	0.275942i	$-0.0889897\pi$
$199$	16.9674	+	9.79615i	1.20279	+	0.694430i	0.241614	+	0.970372i	$0.422323\pi$
$200$	5.67163	−	4.26972i	0.401045	−	0.301915i
$201$	−11.4559	+	6.61409i	−0.808040	+	0.466522i
$202$	3.03264	+	3.97739i	0.213375	+	0.279848i
$203$	8.57683	−	22.7897i	0.601975	−	1.59952i
$204$	−4.59359	−	8.07016i	−0.321615	−	0.565024i
$205$	−1.40440	+	5.24127i	−0.0980872	+	0.366066i
$206$	11.8139	−	15.2989i	0.823114	−	1.06592i
$207$	−2.90283	+	5.02785i	−0.201761	+	0.349460i
$208$	−3.83871	+	3.74572i	−0.266167	+	0.259719i
$209$	15.7394			1.08872
$210$	−4.29706	−	4.04924i	−0.296525	−	0.279424i
$211$	−3.27921	−	3.27921i	−0.225750	−	0.225750i	0.585164	−	0.810915i	$-0.301030\pi$
$211$	−3.27921	−	3.27921i	−0.225750	−	0.225750i	−0.810915	+	0.585164i	$0.801030\pi$
$212$	18.7633	+	10.9869i	1.28867	+	0.754581i
$213$	−0.652678	−	2.43583i	−0.0447207	−	0.166900i
$214$	8.48332	−	1.09041i	0.579908	−	0.0745389i
$215$	−6.40465	+	3.69773i	−0.436794	+	0.252183i
$216$	−1.05832	−	2.62297i	−0.0720096	−	0.178470i
$217$	−6.99230	−	0.688516i	−0.474668	−	0.0467395i
$218$	5.64963	−	4.30766i	0.382641	−	0.291752i
$219$	8.38315	+	2.24626i	0.566481	+	0.151788i
$220$	5.88344	+	5.95602i	0.396662	+	0.401554i
$221$	6.01340	−	1.61129i	0.404505	−	0.108387i
$222$	−13.9849	+	5.74258i	−0.938604	+	0.385416i
$223$	−29.3171			−1.96322			−0.981608	−	0.190906i	$-0.938857\pi$
$223$	−29.3171			−1.96322			−0.981608	+	0.190906i	$0.938857\pi$
$224$	−10.3970	+	10.7658i	−0.694679	+	0.719320i
$225$	−2.50993			−0.167329
$226$	−10.3318	+	4.24250i	−0.687258	+	0.282207i
$227$	−18.5702	+	4.97587i	−1.23255	+	0.330260i	−0.815571	−	0.578657i	$-0.803577\pi$
$227$	−18.5702	+	4.97587i	−1.23255	+	0.330260i	−0.416976	+	0.908917i	$0.636910\pi$
$228$	−8.33943	−	8.44230i	−0.552292	−	0.559105i
$229$	−7.98916	−	2.14069i	−0.527939	−	0.141461i	−0.0150025	−	0.999887i	$-0.504776\pi$
$229$	−7.98916	−	2.14069i	−0.527939	−	0.141461i	−0.512936	+	0.858427i	$0.671442\pi$
$230$	−10.3029	+	7.85560i	−0.679350	+	0.517983i
$231$	−4.08793	+	5.70498i	−0.268966	+	0.375360i
$232$	24.1405	−	9.74026i	1.58490	−	0.639480i
$233$	−8.96009	+	5.17311i	−0.586995	+	0.338902i	−0.763908	−	0.645325i	$-0.776722\pi$
$233$	−8.96009	+	5.17311i	−0.586995	+	0.338902i	0.176913	+	0.984226i	$0.443389\pi$
$234$	1.88078	−	0.241747i	0.122950	−	0.0158035i
$235$	−2.87868	−	10.7434i	−0.187785	−	0.700822i
$236$	11.2526	+	6.58901i	0.732485	+	0.428908i
$237$	−2.29176	−	2.29176i	−0.148866	−	0.148866i
$238$	16.6396	−	4.99235i	1.07859	−	0.323606i
$239$	24.8219			1.60559			0.802796	−	0.596253i	$-0.203345\pi$
$239$	24.8219			1.60559			0.802796	+	0.596253i	$0.203345\pi$
$240$	0.0773788	−	6.31151i	0.00499478	−	0.407406i
$241$	6.67972	−	11.5696i	0.430279	−	0.745264i	−0.566618	−	0.823980i	$-0.691749\pi$
$241$	6.67972	−	11.5696i	0.430279	−	0.745264i	0.996897	+	0.0787158i	$0.0250820\pi$
$242$	−3.42556	+	4.43606i	−0.220203	+	0.285161i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	2.82434	+	4.96189i	0.180810	+	0.317653i
$245$	9.18410	−	6.13724i	0.586751	−	0.392094i
$246$	−2.94855	−	3.86711i	−0.187993	−	0.246558i
$247$	6.88987	−	3.97787i	0.438392	−	0.253106i
$248$	−4.51757	−	6.00085i	−0.286866	−	0.381054i
$249$	2.94372	+	1.69956i	0.186551	+	0.107705i
$250$	−15.4639	−	6.46094i	−0.978021	−	0.408626i
$251$	−13.7393	+	13.7393i	−0.867215	+	0.867215i	−0.992163	−	0.124948i	$-0.960123\pi$
$251$	−13.7393	+	13.7393i	−0.867215	+	0.867215i	0.124948	+	0.992163i	$0.460123\pi$
$252$	5.22599	−	0.830066i	0.329207	−	0.0522892i
$253$	10.8900	+	10.8900i	0.684645	+	0.684645i
$254$	3.33868	−	1.37096i	0.209488	−	0.0860214i
$255$	−3.66329	+	6.34501i	−0.229404	+	0.397340i
$256$	−15.9952	−	0.392260i	−0.999699	−	0.0245162i
$257$	9.87229	+	17.0993i	0.615816	+	1.06663i	0.990241	+	0.139368i	$0.0445071\pi$
$257$	9.87229	+	17.0993i	0.615816	+	1.06663i	−0.374424	+	0.927258i	$0.622160\pi$
$258$	0.885246	−	6.56849i	0.0551130	−	0.408936i
$259$	−4.60786	−	27.9053i	−0.286318	−	1.73395i
$260$	4.08073	+	1.12028i	0.253076	+	0.0694770i
$261$	−8.88991	−	2.38204i	−0.550272	−	0.147445i
$262$	2.31422	+	18.0045i	0.142973	+	1.11232i
$263$	−12.2727	−	7.08567i	−0.756769	−	0.436921i	0.0713652	−	0.997450i	$-0.477264\pi$
$263$	−12.2727	−	7.08567i	−0.756769	−	0.436921i	−0.828135	+	0.560529i	$0.810598\pi$
$264$	−7.44749	+	0.910900i	−0.458361	+	0.0560620i
$265$		−	17.1554i		−	1.05385i
$266$	18.8883	−	11.6660i	1.15812	−	0.715289i
$267$	−8.15704	+	8.15704i	−0.499203	+	0.499203i
$268$	13.3684	−	22.8304i	0.816603	−	1.39459i
$269$	−15.6840	+	4.20253i	−0.956273	+	0.256233i	−0.703022	−	0.711168i	$-0.748167\pi$
$269$	−15.6840	+	4.20253i	−0.956273	+	0.256233i	−0.253251	+	0.967401i	$0.581500\pi$
$270$	−1.36395	+	1.76629i	−0.0830071	+	0.107493i
$271$	3.24426	+	5.61922i	0.197075	+	0.341343i	0.947579	−	0.319523i	$-0.103523\pi$
$271$	3.24426	+	5.61922i	0.197075	+	0.341343i	−0.750504	+	0.660866i	$0.770189\pi$
$272$	15.9687	+	9.48240i	0.968242	+	0.574955i
$273$	−0.347639	+	3.53049i	−0.0210401	+	0.213675i
$274$	−21.9432	−	2.95732i	−1.32564	−	0.178658i
$275$	−1.72324	+	6.43123i	−0.103916	+	0.387818i
$276$	0.0711731	−	11.6111i	0.00428412	−	0.698907i
$277$	6.92228	+	25.8343i	0.415920	+	1.55223i	0.782986	+	0.622039i	$0.213695\pi$
$277$	6.92228	+	25.8343i	0.415920	+	1.55223i	−0.367067	+	0.930195i	$0.619638\pi$
$278$	8.19492	−	19.6140i	0.491499	−	1.17637i
$279$			2.65562i			0.158988i
$280$	11.4751	+	2.78682i	0.685768	+	0.166544i
$281$			15.4474i			0.921513i	0.887527	+	0.460757i	$0.152422\pi$
$281$			15.4474i			0.921513i	−0.887527	+	0.460757i	$0.847578\pi$
$282$	9.19747	+	3.84278i	0.547701	+	0.228834i
$283$	1.38014	+	5.15076i	0.0820409	+	0.306181i	0.994737	−	0.102457i	$-0.0326705\pi$
$283$	1.38014	+	5.15076i	0.0820409	+	0.306181i	−0.912696	+	0.408638i	$0.866004\pi$
$284$	3.54437	+	3.58809i	0.210320	+	0.212914i
$285$	−2.42327	+	9.04377i	−0.143542	+	0.535707i
$286$	0.671854	−	4.98513i	0.0397276	−	0.294777i
$287$	8.28677	−	3.75492i	0.489152	−	0.221646i
$288$	4.43459	+	3.51204i	0.261311	+	0.206949i
$289$	−2.27857	−	3.94659i	−0.134033	−	0.232152i
$290$	−16.2561	−	12.5531i	−0.954591	−	0.737143i
$291$	−5.58884	+	1.49753i	−0.327624	+	0.0877866i
$292$	−16.7935	+	4.38966i	−0.982767	+	0.256886i
$293$	8.40672	−	8.40672i	0.491126	−	0.491126i	−0.417535	−	0.908661i	$-0.637106\pi$
$293$	8.40672	−	8.40672i	0.491126	−	0.491126i	0.908661	+	0.417535i	$0.137106\pi$
$294$	−0.677269	+	9.87630i	−0.0394991	+	0.575998i
$295$		−	10.2884i		−	0.599013i
$296$	18.6263	−	23.8176i	1.08263	−	1.38437i
$297$	2.29731	+	1.32635i	0.133303	+	0.0769628i
$298$	9.70857	−	1.24790i	0.562403	−	0.0722889i
$299$	7.51928	+	2.01479i	0.434851	+	0.116518i
$300$	4.36263	−	2.48323i	0.251876	−	0.143370i
$301$	11.6050	+	4.36749i	0.668900	+	0.251738i
$302$	13.7380	+	1.85150i	0.790535	+	0.106542i
$303$	1.76835	+	3.06287i	0.101589	+	0.175957i
$304$	22.8477	+	6.42323i	1.31040	+	0.368397i
$305$	2.25235	−	3.90119i	0.128969	−	0.223381i
$306$	−2.49415	−	6.07400i	−0.142581	−	0.347227i
$307$	19.2364	+	19.2364i	1.09788	+	1.09788i	0.994658	+	0.103221i	$0.0329148\pi$
$307$	19.2364	+	19.2364i	1.09788	+	1.09788i	0.103221	+	0.994658i	$0.467085\pi$
$308$	1.46112	−	13.9605i	0.0832551	−	0.795476i
$309$	9.66467	−	9.66467i	0.549804	−	0.549804i
$310$	−2.28469	+	5.46825i	−0.129761	+	0.310576i
$311$	−6.10637	−	3.52551i	−0.346260	−	0.199914i	0.316777	−	0.948500i	$-0.397399\pi$
$311$	−6.10637	−	3.52551i	−0.346260	−	0.199914i	−0.663037	+	0.748587i	$0.730733\pi$
$312$	−3.02989	+	2.28097i	−0.171534	+	0.129134i
$313$	23.1264	−	13.3520i	1.30718	−	0.754701i	0.325556	−	0.945523i	$-0.394448\pi$
$313$	23.1264	−	13.3520i	1.30718	−	0.754701i	0.981625	+	0.190821i	$0.0611151\pi$
$314$	−9.07509	+	6.91948i	−0.512137	+	0.390489i
$315$	−2.64866	−	3.22724i	−0.149235	−	0.181835i
$316$	6.25081	+	1.71603i	0.351635	+	0.0965344i
$317$	2.50459	−	9.34728i	0.140672	−	0.524995i	−0.859238	−	0.511576i	$-0.829062\pi$
$317$	2.50459	−	9.34728i	0.140672	−	0.524995i	0.999910	−	0.0134191i	$-0.00427155\pi$
$318$	12.1689	+	9.39695i	0.682400	+	0.526955i
$319$	−12.2071	+	21.1433i	−0.683467	+	1.18380i
$320$	6.10989	+	11.0469i	0.341553	+	0.617540i
$321$	6.04796			0.337564
$322$	21.1402	+	4.99705i	1.17810	+	0.278475i
$323$	−19.4796	−	19.4796i	−1.08387	−	1.08387i
$324$	−0.505787	−	1.93499i	−0.0280993	−	0.107499i
$325$	0.871041	+	3.25077i	0.0483166	+	0.180320i
$326$	−1.32354	−	10.2970i	−0.0733038	−	0.570299i
$327$	4.35061	−	2.51183i	0.240590	−	0.138904i
$328$	8.95101	+	3.80442i	0.494237	+	0.210064i
$329$	−10.8619	+	15.1585i	−0.598836	+	0.835716i
$330$	3.58936	+	4.70755i	0.197588	+	0.259142i
$331$	18.4381	+	4.94047i	1.01345	+	0.271553i	0.727070	−	0.686563i	$-0.240881\pi$
$331$	18.4381	+	4.94047i	1.01345	+	0.271553i	0.286380	+	0.958116i	$0.407548\pi$
$332$	−6.79810	−	0.0416706i	−0.373094	−	0.00228697i
$333$	−10.3258	+	2.76679i	−0.565850	+	0.151619i
$334$	3.57047	+	8.69515i	0.195367	+	0.475777i
$335$	−20.8740			−1.14047
$336$	−8.26231	+	6.61319i	−0.450746	+	0.360779i
$337$	24.6418			1.34232			0.671162	−	0.741311i	$-0.265796\pi$
$337$	24.6418			1.34232			0.671162	+	0.741311i	$0.265796\pi$
$338$	6.01766	+	14.6548i	0.327317	+	0.797115i
$339$	−7.62849	+	2.04405i	−0.414323	+	0.111017i
$340$	0.0898185	−	14.6529i	0.00487109	−	0.794664i
$341$	6.80455	+	1.82327i	0.368487	+	0.0987358i
$342$	−5.08770	−	6.67267i	−0.275111	−	0.360817i
$343$	−17.7232	−	5.37491i	−0.956961	−	0.290218i
$344$	4.95994	+	12.2928i	0.267422	+	0.662785i
$345$	−7.93393	+	4.58066i	−0.427148	+	0.246614i
$346$	1.83653	+	14.2881i	0.0987325	+	0.768133i
$347$	−2.26524	−	8.45398i	−0.121604	−	0.453834i	0.878092	−	0.478493i	$-0.158817\pi$
$347$	−2.26524	−	8.45398i	−0.121604	−	0.453834i	−0.999696	+	0.0246590i	$0.992150\pi$
$348$	17.8087	−	4.65502i	0.954646	−	0.249535i
$349$	−3.93101	−	3.93101i	−0.210422	−	0.210422i	0.594025	−	0.804447i	$-0.297538\pi$
$349$	−3.93101	−	3.93101i	−0.210422	−	0.210422i	−0.804447	+	0.594025i	$0.797538\pi$
$350$	2.69880	+	8.99516i	0.144257	+	0.480811i
$351$	1.34085			0.0715694
$352$	12.0436	−	8.95156i	0.641927	−	0.477120i
$353$	−13.2508	+	22.9510i	−0.705268	+	1.22156i	0.261327	+	0.965250i	$0.415840\pi$
$353$	−13.2508	+	22.9510i	−0.705268	+	1.22156i	−0.966595	+	0.256310i	$0.917493\pi$
$354$	7.29791	+	5.63551i	0.387880	+	0.299524i
$355$	1.02992	−	3.84372i	0.0546626	−	0.204004i
$356$	6.10786	−	22.2484i	0.323716	−	1.17916i
$357$	12.1200	−	2.00131i	0.641459	−	0.105921i
$358$	−4.42536	+	3.37420i	−0.233888	+	0.178332i
$359$	21.6271	−	12.4864i	1.14144	−	0.659009i	0.194651	−	0.980873i	$-0.437643\pi$
$359$	21.6271	−	12.4864i	1.14144	−	0.659009i	0.946786	+	0.321864i	$0.104309\pi$
$360$	0.623232	−	4.41952i	0.0328472	−	0.232929i
$361$	−14.0336	−	8.10230i	−0.738611	−	0.426437i
$362$	11.3688	−	27.2106i	0.597532	−	1.43016i
$363$	−2.80237	+	2.80237i	−0.147086	+	0.147086i
$364$	−2.88869	−	6.48045i	−0.151408	−	0.339668i
$365$	9.68399	+	9.68399i	0.506883	+	0.506883i
$366$	1.53351	+	3.73456i	0.0801581	+	0.195209i
$367$	−2.73006	+	4.72860i	−0.142508	+	0.246831i	−0.928440	−	0.371481i	$-0.878850\pi$
$367$	−2.73006	+	4.72860i	−0.142508	+	0.246831i	0.785932	+	0.618312i	$0.212183\pi$
$368$	11.3639	+	20.2522i	0.592385	+	1.05572i
$369$	−1.71932	−	2.97795i	−0.0895043	−	0.155026i
$370$	−23.6424	−	3.18633i	−1.22911	−	0.165649i
$371$	−22.2342	+	18.2480i	−1.15434	+	0.947389i
$372$	−2.62738	−	4.61586i	−0.136223	−	0.239321i
$373$	−11.9145	−	3.19249i	−0.616912	−	0.165301i	−0.0631882	−	0.998002i	$-0.520127\pi$
$373$	−11.9145	−	3.19249i	−0.616912	−	0.165301i	−0.553723	+	0.832701i	$0.686794\pi$
$374$	−17.2759	+	2.22057i	−0.893317	+	0.114823i
$375$	−10.2630	−	5.92532i	−0.529977	−	0.305982i
$376$	−19.7885	+	2.42032i	−1.02051	+	0.124819i
$377$			12.3405i			0.635570i
$378$	3.74001	−	0.111049i	0.192365	−	0.00571174i
$379$	19.7865	−	19.7865i	1.01636	−	1.01636i	0.0165001	−	0.999864i	$-0.494748\pi$
$379$	19.7865	−	19.7865i	1.01636	−	1.01636i	0.999864	−	0.0165001i	$-0.00525240\pi$
$380$	−4.73558	−	18.1169i	−0.242930	−	0.929378i
$381$	2.46513	−	0.660530i	0.126292	−	0.0338400i
$382$	−7.99399	−	6.17303i	−0.409008	−	0.315839i
$383$	−16.7191	−	28.9584i	−0.854308	−	1.47971i	−0.877285	−	0.479969i	$-0.840648\pi$
$383$	−16.7191	−	28.9584i	−0.854308	−	1.47971i	0.0229769	−	0.999736i	$-0.492686\pi$
$384$	−11.1827	−	1.71702i	−0.570663	−	0.0876215i
$385$	−10.0877	+	4.57097i	−0.514118	+	0.232958i
$386$	−1.76762	+	13.1157i	−0.0899695	+	0.667570i
$387$	1.21298	−	4.52692i	0.0616595	−	0.230116i
$388$	8.23264	−	8.13233i	0.417949	−	0.412856i
$389$	8.37902	+	31.2709i	0.424833	+	1.58550i	0.764287	+	0.644877i	$0.223091\pi$
$389$	8.37902	+	31.2709i	0.424833	+	1.58550i	−0.339453	+	0.940623i	$0.610242\pi$
$390$	2.76098	+	1.15356i	0.139808	+	0.0584129i
$391$		−	26.9555i		−	1.36320i
$392$	−8.59407	−	17.8365i	−0.434066	−	0.900881i
$393$			12.8358i			0.647481i
$394$	−0.444155	+	1.06306i	−0.0223762	+	0.0535561i
$395$	−1.32369	−	4.94008i	−0.0666021	−	0.248562i
$396$	−5.30531	−	0.0325202i	−0.266602	−	0.00163420i
$397$	−2.66507	+	9.94619i	−0.133756	+	0.499185i	−1.00000		0.000436625i	$-0.999861\pi$
$397$	−2.66507	+	9.94619i	−0.133756	+	0.499185i	0.866244	+	0.499622i	$0.166528\pi$
$398$	−27.4594	−	3.70075i	−1.37642	−	0.185502i
$399$	14.2987	−	6.47908i	0.715832	−	0.324359i
$400$	−5.12607	+	8.63246i	−0.256303	+	0.431623i
$401$	−11.9519	−	20.7012i	−0.596848	−	1.03377i	−0.993283	−	0.115708i	$-0.963086\pi$
$401$	−11.9519	−	20.7012i	−0.596848	−	1.03377i	0.396435	−	0.918063i	$-0.370247\pi$
$402$	11.4338	−	14.8067i	0.570267	−	0.738489i
$403$	3.43946	−	0.921602i	0.171332	−	0.0459082i
$404$	−6.10395	−	3.57418i	−0.303683	−	0.177822i
$405$	−1.11581	+	1.11581i	−0.0554451	+	0.0554451i
$406$	1.02204	+	34.4212i	0.0507230	+	1.70830i
$407$			28.3575i			1.40563i
$408$	10.3446	+	8.08989i	0.512134	+	0.400509i
$409$	−6.41138	−	3.70161i	−0.317022	−	0.183033i	0.333042	−	0.942912i	$-0.391925\pi$
$409$	−6.41138	−	3.70161i	−0.317022	−	0.183033i	−0.650064	+	0.759879i	$0.725258\pi$
$410$	−0.978304	−	7.61114i	−0.0483150	−	0.375888i
$411$	−15.1230	−	4.05219i	−0.745962	−	0.199880i
$412$	−7.23675	+	26.3605i	−0.356529	+	1.29869i
$413$	−13.3342	+	10.9436i	−0.656134	+	0.538501i
$414$	1.09662	−	8.13688i	0.0538960	−	0.399906i
$415$	2.68189	+	4.64518i	0.131649	+	0.228023i
$416$	3.00970	−	6.96233i	0.147562	−	0.341356i
$417$	7.51555	−	13.0173i	0.368038	−	0.637460i
$418$	−20.5906	+	8.45505i	−1.00712	+	0.413550i
$419$	−1.97973	−	1.97973i	−0.0967163	−	0.0967163i	0.657093	−	0.753809i	$-0.271786\pi$
$419$	−1.97973	−	1.97973i	−0.0967163	−	0.0967163i	−0.753809	+	0.657093i	$0.771786\pi$
$420$	7.79668	+	2.98894i	0.380439	+	0.145845i
$421$	17.2068	−	17.2068i	0.838606	−	0.838606i	−0.150069	−	0.988675i	$-0.547950\pi$
$421$	17.2068	−	17.2068i	0.838606	−	0.838606i	0.988675	+	0.150069i	$0.0479497\pi$
$422$	6.05148	+	2.52836i	0.294581	+	0.123079i
$423$	6.10411	+	3.52421i	0.296792	+	0.171353i
$424$	−30.4484	−	4.29377i	−1.47871	−	0.208524i
$425$	10.0922	−	5.82676i	0.489546	−	0.282639i
$426$	2.16234	+	2.83597i	0.104766	+	0.137403i
$427$	−7.45192	+	1.23050i	−0.360624	+	0.0595478i
$428$	−10.5123	+	5.98364i	−0.508129	+	0.289230i
$429$	0.920590	−	3.43569i	0.0444465	−	0.165877i
$430$	6.39229	−	8.27794i	0.308263	−	0.399198i
$431$	0.296697	−	0.513893i	0.0142914	−	0.0247534i	−0.858791	−	0.512326i	$-0.828784\pi$
$431$	0.296697	−	0.513893i	0.0142914	−	0.0247534i	0.873083	+	0.487572i	$0.162117\pi$
$432$	2.79354	+	2.86289i	0.134404	+	0.137741i
$433$	−39.1849			−1.88311			−0.941553	−	0.336865i	$-0.890633\pi$
$433$	−39.1849			−1.88311			−0.941553	+	0.336865i	$0.890633\pi$
$434$	9.51730	−	2.85546i	0.456845	−	0.137066i
$435$	−10.2694	−	10.2694i	−0.492379	−	0.492379i
$436$	−5.07690	+	8.67027i	−0.243139	+	0.415231i
$437$	−8.91554	−	33.2733i	−0.426488	−	1.59168i
$438$	−12.1736	+	1.56475i	−0.581679	+	0.0747666i
$439$	29.8184	−	17.2156i	1.42315	−	0.821658i	0.426586	−	0.904447i	$-0.359716\pi$
$439$	29.8184	−	17.2156i	1.42315	−	0.821658i	0.996567	+	0.0827889i	$0.0263827\pi$
$440$	−10.8963	−	4.63123i	−0.519462	−	0.220785i
$441$	−1.36531	+	6.86556i	−0.0650148	+	0.326931i
$442$	−7.00126	+	5.33824i	−0.333016	+	0.253914i
$443$	−15.9669	−	4.27832i	−0.758610	−	0.203269i	−0.141276	−	0.989970i	$-0.545121\pi$
$443$	−15.9669	−	4.27832i	−0.758610	−	0.203269i	−0.617334	+	0.786701i	$0.711787\pi$
$444$	15.2104	−	15.0251i	0.721853	−	0.713057i
$445$	−17.5832	+	4.71140i	−0.833522	+	0.223342i
$446$	38.3531	−	15.7488i	1.81607	−	0.745728i
$447$	6.92148			0.327375
$448$	7.81826	−	19.6691i	0.369378	−	0.929279i
$449$	−16.6418			−0.785376			−0.392688	−	0.919672i	$-0.628455\pi$
$449$	−16.6418			−0.785376			−0.392688	+	0.919672i	$0.628455\pi$
$450$	3.28353	−	1.34831i	0.154787	−	0.0635598i
$451$	−8.81090	+	2.36087i	−0.414889	+	0.111169i
$452$	11.2371	−	11.1002i	0.528550	−	0.522110i
$453$	9.46808	+	2.53697i	0.444849	+	0.119197i
$454$	21.6208	−	16.4852i	1.01472	−	0.773690i
$455$	−3.26062	+	4.55042i	−0.152860	+	0.213327i
$456$	15.4449	+	6.56449i	0.723273	+	0.307411i
$457$	−13.3213	+	7.69107i	−0.623145	+	0.359773i	−0.778093	−	0.628150i	$-0.783813\pi$
$457$	−13.3213	+	7.69107i	−0.623145	+	0.359773i	0.154947	+	0.987923i	$0.450479\pi$
$458$	11.6015	−	1.49121i	0.542103	−	0.0696796i
$459$	−1.20169	−	4.48476i	−0.0560900	−	0.209331i
$460$	9.25840	−	15.8114i	0.431675	−	0.737210i
$461$	17.8707	+	17.8707i	0.832321	+	0.832321i	0.987834	−	0.155513i	$-0.0497031\pi$
$461$	17.8707	+	17.8707i	0.832321	+	0.832321i	−0.155513	+	0.987834i	$0.549703\pi$
$462$	2.28324	−	9.65933i	0.106226	−	0.449393i
$463$	−22.0370			−1.02415			−0.512073	−	0.858942i	$-0.671122\pi$
$463$	−22.0370			−1.02415			−0.512073	+	0.858942i	$0.671122\pi$
$464$	−26.3486	+	25.7104i	−1.22320	+	1.19357i
$465$	−2.09528	+	3.62913i	−0.0971663	+	0.168297i
$466$	8.94279	−	11.5808i	0.414267	−	0.536471i
$467$	−10.1477	+	37.8718i	−0.469580	+	1.75250i	0.171660	+	0.985156i	$0.445087\pi$
$467$	−10.1477	+	37.8718i	−0.469580	+	1.75250i	−0.641240	+	0.767340i	$0.721580\pi$
$468$	−2.33060	+	1.32659i	−0.107732	+	0.0613217i
$469$	22.2034	+	27.0537i	1.02526	+	1.24922i
$470$	9.53717	+	12.5083i	0.439917	+	0.576964i
$471$	−6.98847	+	4.03479i	−0.322012	+	0.185913i
$472$	−18.2604	−	2.57505i	−0.840504	−	0.118526i
$473$	−10.7666	−	6.21610i	−0.495049	−	0.285817i
$474$	4.22923	+	1.76701i	0.194255	+	0.0811614i
$475$	10.5304	−	10.5304i	0.483169	−	0.483169i
$476$	−19.0863	+	15.4697i	−0.874821	+	0.709052i
$477$	7.68742	+	7.68742i	0.351983	+	0.351983i
$478$	−32.4723	+	13.3340i	−1.48525	+	0.609884i
$479$	−7.64455	+	13.2407i	−0.349288	+	0.604985i	−0.986123	−	0.166015i	$-0.946910\pi$
$479$	−7.64455	+	13.2407i	−0.349288	+	0.604985i	0.636835	+	0.771000i	$0.280243\pi$
$480$	3.28925	+	8.29838i	0.150133	+	0.378768i
$481$	7.16688	+	12.4134i	0.326782	+	0.566002i
$482$	−2.52344	+	18.7238i	−0.114940	+	0.852847i
$483$	14.3760	+	5.41034i	0.654129	+	0.246179i
$484$	2.09837	−	7.64350i	0.0953804	−	0.347432i
$485$	−8.81917	−	2.36309i	−0.400458	−	0.107302i
$486$	−0.180294	−	1.40267i	−0.00817829	−	0.0636266i
$487$	−1.78564	−	1.03094i	−0.0809153	−	0.0467165i	0.458996	−	0.888438i	$-0.348209\pi$
$487$	−1.78564	−	1.03094i	−0.0809153	−	0.0467165i	−0.539912	+	0.841722i	$0.681542\pi$
$488$	−6.36032	−	4.97402i	−0.287918	−	0.225163i
$489$		−	7.34099i		−	0.331971i
$490$	−8.71793	+	12.9624i	−0.393836	+	0.585583i
$491$	−21.5673	+	21.5673i	−0.973320	+	0.973320i	−0.999653	−	0.0263328i	$-0.991617\pi$
$491$	−21.5673	+	21.5673i	−0.973320	+	0.973320i	0.0263328	+	0.999653i	$0.491617\pi$
$492$	5.93472	+	3.47509i	0.267558	+	0.156669i
$493$	41.2755	−	11.0598i	1.85896	−	0.498106i
$494$	−6.87657	+	8.90507i	−0.309391	+	0.400658i
$495$	2.09298	+	3.62515i	0.0940724	+	0.162938i
$496$	9.13354	+	5.42362i	0.410108	+	0.243528i
$497$	−6.07715	+	2.75369i	−0.272598	+	0.123520i
$498$	−4.76400	−	0.642053i	−0.213480	−	0.0287711i
$499$	−7.21290	+	26.9189i	−0.322894	+	1.20506i	0.593519	+	0.804820i	$0.297738\pi$
$499$	−7.21290	+	26.9189i	−0.322894	+	1.20506i	−0.916412	+	0.400235i	$0.868928\pi$
$500$	23.7008	+	0.145280i	1.05993	+	0.00649712i
$501$	1.72026	+	6.42010i	0.0768555	+	0.286829i
$502$	10.5933	−	25.3545i	0.472804	−	1.13163i
$503$			12.1554i			0.541982i	0.962582	+	0.270991i	$0.0873513\pi$
$503$			12.1554i			0.541982i	−0.962582	+	0.270991i	$0.912649\pi$
$504$	−6.39082	+	3.89325i	−0.284670	+	0.173419i
$505$			5.58090i			0.248347i
$506$	−20.0964	−	8.39644i	−0.893392	−	0.373267i
$507$	2.89932	+	10.8204i	0.128763	+	0.480551i
$508$	−3.63126	+	3.58701i	−0.161111	+	0.159148i
$509$	10.4118	−	38.8575i	0.461497	−	1.72233i	−0.206755	−	0.978393i	$-0.566290\pi$
$509$	10.4118	−	38.8575i	0.461497	−	1.72233i	0.668251	−	0.743936i	$-0.267043\pi$
$510$	1.38391	−	10.2685i	0.0612804	−	0.454697i
$511$	2.25015	−	22.8516i	0.0995408	−	1.01090i
$512$	21.1359	−	8.07928i	0.934083	−	0.357057i
$513$	−2.96667	−	5.13843i	−0.130982	−	0.226867i
$514$	−22.1006	−	17.0663i	−0.974818	−	0.752762i
$515$	20.8330	−	5.58219i	0.918012	−	0.245981i
$516$	2.37043	+	9.06854i	0.104352	+	0.399220i
$517$	13.2210	−	13.2210i	0.581461	−	0.581461i
$518$	21.0185	+	34.0309i	0.923500	+	1.49523i
$519$			10.1863i			0.447130i
$520$	−5.94028	+	0.726554i	−0.260499	+	0.0318615i
$521$	1.15705	+	0.668020i	0.0506911	+	0.0292665i	0.525131	−	0.851021i	$-0.324016\pi$
$521$	1.15705	+	0.668020i	0.0506911	+	0.0292665i	−0.474440	+	0.880288i	$0.657350\pi$
$522$	12.9095	−	1.65934i	0.565035	−	0.0726272i
$523$	−42.1404	−	11.2915i	−1.84267	−	0.493742i	−0.843604	−	0.536965i	$-0.819571\pi$
$523$	−42.1404	−	11.2915i	−1.84267	−	0.493742i	−0.999065	+	0.0432236i	$0.986237\pi$
$524$	−12.6993	−	22.3105i	−0.554771	−	0.974641i
$525$	1.08188	+	6.55193i	0.0472173	+	0.285949i
$526$	19.8617	+	2.67680i	0.866013	+	0.116714i
$527$	−6.16498	−	10.6781i	−0.268551	−	0.465144i
$528$	9.25359	−	5.19236i	0.402711	−	0.225969i
$529$	5.35286	−	9.27142i	0.232733	−	0.403105i
$530$	9.21571	+	22.4430i	0.400305	+	0.974861i
$531$	4.61027	+	4.61027i	0.200069	+	0.200069i
$532$	−18.4432	+	25.4083i	−0.799612	+	1.10159i
$533$	−3.26027	+	3.26027i	−0.141218	+	0.141218i
$534$	6.28929	−	15.0530i	0.272164	−	0.651409i
$535$	8.26505	+	4.77183i	0.357329	+	0.206304i
$536$	−5.22449	+	37.0484i	−0.225663	+	1.60025i
$537$	−3.40784	+	1.96752i	−0.147059	+	0.0849047i
$538$	18.2606	−	13.9231i	0.787269	−	0.600268i
$539$	16.6544	+	8.21206i	0.717354	+	0.353718i
$540$	0.835501	−	3.04339i	0.0359543	−	0.130967i
$541$	1.55998	−	5.82192i	0.0670687	−	0.250304i	−0.924249	−	0.381789i	$-0.875308\pi$
$541$	1.55998	−	5.82192i	0.0670687	−	0.250304i	0.991318	+	0.131485i	$0.0419747\pi$
$542$	−7.26277	−	5.60837i	−0.311963	−	0.240900i
$543$	10.4263	−	18.0589i	0.447436	−	0.774982i
$544$	−25.9843	−	3.82684i	−1.11407	−	0.164074i
$545$	7.92731			0.339569
$546$	−1.44175	−	4.80538i	−0.0617013	−	0.205651i
$547$	31.5510	+	31.5510i	1.34902	+	1.34902i	0.886725	+	0.462298i	$0.152975\pi$
$547$	31.5510	+	31.5510i	1.34902	+	1.34902i	0.462298	+	0.886725i	$0.347025\pi$
$548$	30.2951	−	7.91883i	1.29414	−	0.338276i
$549$	0.738851	+	2.75743i	0.0315334	+	0.117684i
$550$	−1.20041	−	9.33915i	−0.0511859	−	0.398223i
$551$	47.2916	−	27.3038i	2.01469	−	1.16318i
$552$	6.14425	+	15.2281i	0.261517	+	0.648149i
$553$	−4.99458	+	6.97027i	−0.212391	+	0.296406i
$554$	−22.9338	−	30.0783i	−0.974362	−	1.27790i
$555$	−16.2941	−	4.36598i	−0.691644	−	0.185325i
$556$	−0.184270	+	30.0616i	−0.00781479	+	1.27490i
$557$	−31.4752	+	8.43375i	−1.33365	+	0.357350i	−0.854073	−	0.520152i	$-0.825875\pi$
$557$	−31.4752	+	8.43375i	−1.33365	+	0.357350i	−0.479573	+	0.877502i	$0.659208\pi$
$558$	−1.42657	−	3.47413i	−0.0603916	−	0.147071i
$559$	−6.28405			−0.265787
$560$	−16.5089	+	2.51853i	−0.697630	+	0.106428i
$561$	−12.3164			−0.520000
$562$	−8.29816	−	20.2085i	−0.350037	−	0.852444i
$563$	15.9505	−	4.27392i	0.672233	−	0.180124i	0.0934725	−	0.995622i	$-0.470203\pi$
$563$	15.9505	−	4.27392i	0.672233	−	0.180124i	0.578760	+	0.815498i	$0.303537\pi$
$564$	−14.0966	−	0.0864084i	−0.593573	−	0.00363845i
$565$	−12.0377	−	3.22550i	−0.506431	−	0.135698i
$566$	−4.57245	−	5.99691i	−0.192195	−	0.252069i
$567$	2.63302	+	0.259267i	0.110576	+	0.0108882i
$568$	−6.56428	−	2.79000i	−0.275431	−	0.117066i
$569$	−28.2824	+	16.3288i	−1.18566	+	0.684540i	−0.957317	−	0.289041i	$-0.906664\pi$
$569$	−28.2824	+	16.3288i	−1.18566	+	0.684540i	−0.228341	+	0.973581i	$0.573330\pi$
$570$	−1.68805	−	13.1330i	−0.0707048	−	0.550079i
$571$	4.35009	+	16.2348i	0.182046	+	0.679404i	0.995244	+	0.0974167i	$0.0310580\pi$
$571$	4.35009	+	16.2348i	0.182046	+	0.679404i	−0.813198	+	0.581987i	$0.802275\pi$
$572$	1.79903	+	6.88253i	0.0752210	+	0.287773i
$573$	−5.05000	−	5.05000i	−0.210967	−	0.210967i
$574$	−8.82378	+	9.36380i	−0.368297	+	0.390838i
$575$	14.5718			0.607686
$576$	−7.68803	−	2.21229i	−0.320334	−	0.0921789i
$577$	16.1306	−	27.9391i	0.671527	−	1.16312i	−0.305944	−	0.952049i	$-0.598972\pi$
$577$	16.1306	−	27.9391i	0.671527	−	1.16312i	0.977471	−	0.211069i	$-0.0676945\pi$
$578$	5.10092	+	3.93897i	0.212170	+	0.163840i
$579$	−2.42203	+	9.03916i	−0.100656	+	0.375655i
$580$	28.0099	+	7.68955i	1.16305	+	0.319291i
$581$	3.16766	−	8.41687i	0.131417	−	0.349191i
$582$	6.50696	−	4.96135i	0.269722	−	0.205655i
$583$	24.9756	−	14.4196i	1.03438	−	0.597201i
$584$	19.6115	−	14.7639i	0.811529	−	0.610936i
$585$	1.83239	+	1.05793i	0.0757599	+	0.0437400i
$586$	−6.48181	+	15.5138i	−0.267761	+	0.640869i
$587$	−23.5697	+	23.5697i	−0.972826	+	0.972826i	−0.999640	−	0.0268139i	$-0.991464\pi$
$587$	−23.5697	+	23.5697i	−0.972826	+	0.972826i	0.0268139	+	0.999640i	$0.491464\pi$
$588$	−4.41943	−	13.2842i	−0.182254	−	0.547829i
$589$	−11.1417	−	11.1417i	−0.459085	−	0.459085i
$590$	5.52681	+	13.4594i	0.227535	+	0.554116i
$591$	−0.407334	+	0.705523i	−0.0167555	+	0.0290213i
$592$	−11.5727	+	41.1644i	−0.475633	+	1.69185i
$593$	−13.2569	−	22.9617i	−0.544397	−	0.942923i	−0.998645	−	0.0520473i	$-0.983425\pi$
$593$	−13.2569	−	22.9617i	−0.544397	−	0.942923i	0.454248	−	0.890875i	$-0.349908\pi$
$594$	−3.71788	−	0.501065i	−0.152546	−	0.0205590i
$595$	18.1421	+	6.82770i	0.743752	+	0.279908i
$596$	−12.0306	+	6.84786i	−0.492791	+	0.280499i
$597$	−18.9247	−	5.07086i	−0.774537	−	0.207536i
$598$	−10.9192	+	1.40350i	−0.446518	+	0.0573935i
$599$	−4.72855	−	2.73003i	−0.193203	−	0.111546i	0.400278	−	0.916394i	$-0.368914\pi$
$599$	−4.72855	−	2.73003i	−0.193203	−	0.111546i	−0.593481	+	0.804848i	$0.702247\pi$
$600$	−4.37329	+	5.59216i	−0.178539	+	0.228299i
$601$		−	35.4315i		−	1.44528i	−0.691224	−	0.722640i	$-0.742928\pi$
$601$		−	35.4315i		−	1.44528i	0.691224	−	0.722640i	$-0.257072\pi$
$602$	−17.5280	+	0.520444i	−0.714387	+	0.0212117i
$603$	9.35373	−	9.35373i	0.380913	−	0.380913i
$604$	−18.9669	+	4.95776i	−0.771753	+	0.201729i
$605$	−6.04074	+	1.61861i	−0.245591	+	0.0658059i
$606$	−3.95872	−	3.05696i	−0.160812	−	0.124180i
$607$	−18.8417	−	32.6347i	−0.764760	−	1.32460i	−0.940373	−	0.340144i	$-0.889524\pi$
$607$	−18.8417	−	32.6347i	−0.764760	−	1.32460i	0.175613	−	0.984459i	$-0.443809\pi$
$608$	−33.3402	+	3.87056i	−1.35212	+	0.156972i
$609$	−2.38617	+	24.2330i	−0.0966925	+	0.981971i
$610$	−0.850886	+	6.31354i	−0.0344514	+	0.255628i
$611$	2.44607	−	9.12885i	0.0989574	−	0.369314i
$612$	6.52577	+	6.60627i	0.263789	+	0.267043i
$613$	5.19339	+	19.3820i	0.209759	+	0.782831i	0.987946	+	0.154799i	$0.0494729\pi$
$613$	5.19339	+	19.3820i	0.209759	+	0.782831i	−0.778187	+	0.628033i	$0.783860\pi$
$614$	−35.4989	−	14.8318i	−1.43262	−	0.598562i
$615$		−	5.42617i		−	0.218804i
$616$	5.58799	+	19.0483i	0.225147	+	0.767478i
$617$		−	22.9976i		−	0.925850i	−0.886397	−	0.462925i	$-0.846800\pi$
$617$		−	22.9976i		−	0.925850i	0.886397	−	0.462925i	$-0.153200\pi$
$618$	−7.45172	+	17.8352i	−0.299752	+	0.717438i
$619$	−7.07021	−	26.3864i	−0.284176	−	1.06056i	−0.949440	−	0.313950i	$-0.898348\pi$
$619$	−7.07021	−	26.3864i	−0.284176	−	1.06056i	0.665264	−	0.746608i	$-0.268319\pi$
$620$	0.0513732	−	8.38096i	0.00206320	−	0.336588i
$621$	1.50262	−	5.60784i	0.0602979	−	0.225035i
$622$	9.88232	+	1.33186i	0.396245	+	0.0534026i
$623$	24.8092	+	17.7771i	0.993959	+	0.712226i
$624$	2.73844	−	4.61162i	0.109625	−	0.184613i
$625$	−3.07531	−	5.32659i	−0.123012	−	0.213063i
$626$	−23.0817	+	29.8906i	−0.922532	+	1.19467i
$627$	−15.2031	+	4.07366i	−0.607154	+	0.162686i
$628$	8.15511	−	13.9272i	0.325424	−	0.555756i
$629$	35.0962	−	35.0962i	1.39938	−	1.39938i
$630$	5.19866	+	2.79910i	0.207119	+	0.111519i
$631$			4.18210i			0.166487i	0.996529	+	0.0832434i	$0.0265279\pi$
$631$			4.18210i			0.166487i	−0.996529	+	0.0832434i	$0.973472\pi$
$632$	−9.09924	+	1.11293i	−0.361948	+	0.0442698i
$633$	4.01620	+	2.31875i	0.159630	+	0.0921622i
$634$	1.74471	+	13.5737i	0.0692911	+	0.539080i
$635$	3.88997	+	1.04231i	0.154369	+	0.0413629i
$636$	−20.9675	−	5.75621i	−0.831417	−	0.228249i
$637$	9.36584	−	0.614309i	0.371088	−	0.0243398i
$638$	4.61156	−	34.2176i	0.182573	−	1.35469i
$639$	1.26088	+	2.18390i	0.0498795	+	0.0863938i
$640$	−13.9273	−	11.1696i	−0.550526	−	0.441515i
$641$	−6.01646	+	10.4208i	−0.237636	+	0.411598i	−0.960035	−	0.279878i	$-0.909706\pi$
$641$	−6.01646	+	10.4208i	−0.237636	+	0.411598i	0.722399	+	0.691476i	$0.243039\pi$
$642$	−7.91204	+	3.24890i	−0.312263	+	0.128224i
$643$	9.87295	+	9.87295i	0.389351	+	0.389351i	0.874456	−	0.485105i	$-0.161219\pi$
$643$	9.87295	+	9.87295i	0.389351	+	0.389351i	−0.485105	+	0.874456i	$0.661219\pi$
$644$	−30.3403	+	4.81908i	−1.19558	+	0.189898i
$645$	5.22938	−	5.22938i	0.205907	−	0.205907i
$646$	35.9478	+	15.0193i	1.41435	+	0.590926i
$647$	4.83599	+	2.79206i	0.190122	+	0.109767i	0.592040	−	0.805909i	$-0.298323\pi$
$647$	4.83599	+	2.79206i	0.190122	+	0.109767i	−0.401917	+	0.915676i	$0.631656\pi$
$648$	1.70113	+	2.25968i	0.0668268	+	0.0887686i
$649$	14.9783	−	8.64771i	0.587948	−	0.339452i
$650$	−2.88579	−	3.78479i	−0.113190	−	0.148452i
$651$	6.93224	−	1.14468i	0.271696	−	0.0448637i
$652$	7.26292	+	12.7597i	0.284438	+	0.499710i
$653$	−5.18433	+	19.3482i	−0.202878	+	0.757152i	0.787207	+	0.616688i	$0.211526\pi$
$653$	−5.18433	+	19.3482i	−0.202878	+	0.757152i	−0.990086	+	0.140464i	$0.955141\pi$
$654$	−4.34221	+	5.62312i	−0.169794	+	0.219881i
$655$	−10.1274	+	17.5412i	−0.395711	+	0.685392i
$656$	−13.7535	−	0.168618i	−0.536986	−	0.00658342i
$657$	−8.67888			−0.338595
$658$	6.06672	−	25.6655i	0.236505	−	1.00055i
$659$	−0.587147	−	0.587147i	−0.0228720	−	0.0228720i	0.695578	−	0.718450i	$-0.255148\pi$
$659$	−0.587147	−	0.587147i	−0.0228720	−	0.0228720i	−0.718450	+	0.695578i	$0.755148\pi$
$660$	−7.22450	−	4.23032i	−0.281213	−	0.164665i
$661$	−0.494002	−	1.84364i	−0.0192145	−	0.0717094i	0.955653	−	0.294495i	$-0.0951515\pi$
$661$	−0.494002	−	1.84364i	−0.0192145	−	0.0717094i	−0.974867	+	0.222786i	$0.928485\pi$
$662$	−26.7750	+	3.44154i	−1.04064	+	0.133759i
$663$	−5.39147	+	3.11276i	−0.209387	+	0.120890i
$664$	8.91577	−	3.59735i	0.345999	−	0.139604i
$665$	24.6524	+	2.42747i	0.955979	+	0.0941332i
$666$	12.0221	−	9.16646i	0.465846	−	0.355193i
$667$	51.6118	+	13.8293i	1.99842	+	0.535474i
$668$	−9.34188	−	9.45711i	−0.361448	−	0.365907i
$669$	28.3181	−	7.58782i	1.09484	−	0.293362i
$670$	27.3077	−	11.2133i	1.05499	−	0.433207i
$671$	7.57268			0.292340
$672$	7.25635	−	13.0899i	0.279920	−	0.504954i
$673$	−44.0319			−1.69731			−0.848653	−	0.528950i	$-0.822586\pi$
$673$	−44.0319			−1.69731			−0.848653	+	0.528950i	$0.822586\pi$
$674$	−32.2368	+	13.2373i	−1.24171	+	0.509882i
$675$	2.42441	−	0.649617i	0.0933154	−	0.0250038i
$676$	−15.7448	−	15.9390i	−0.605569	−	0.613038i
$677$	−23.1127	−	6.19302i	−0.888291	−	0.238017i	−0.214310	−	0.976766i	$-0.568750\pi$
$677$	−23.1127	−	6.19302i	−0.888291	−	0.238017i	−0.673981	+	0.738749i	$0.735417\pi$
$678$	8.88167	−	6.77200i	0.341098	−	0.260077i
$679$	6.31817	+	13.9436i	0.242469	+	0.535108i
$680$	7.75387	+	19.2174i	0.297347	+	0.736953i
$681$	16.6496	−	9.61264i	0.638013	−	0.368357i
$682$	−9.88126	+	1.27009i	−0.378373	+	0.0486345i
$683$	−3.05497	−	11.4013i	−0.116895	−	0.436258i	0.882527	−	0.470262i	$-0.155841\pi$
$683$	−3.05497	−	11.4013i	−0.116895	−	0.436258i	−0.999422	+	0.0340042i	$0.989174\pi$
$684$	10.2403	+	5.99623i	0.391548	+	0.229272i
$685$	−17.4697	−	17.4697i	−0.667481	−	0.667481i
$686$	26.0731	−	2.48915i	0.995474	−	0.0950364i
$687$	8.27099			0.315558
$688$	−13.0922	−	13.4173i	−0.499137	−	0.511528i
$689$	7.28864	−	12.6243i	0.277675	−	0.480947i
$690$	7.91861	−	10.2545i	0.301456	−	0.390382i
$691$	−5.21291	+	19.4548i	−0.198308	+	0.740097i	0.793077	+	0.609121i	$0.208478\pi$
$691$	−5.21291	+	19.4548i	−0.198308	+	0.740097i	−0.991386	+	0.130976i	$0.958189\pi$
$692$	−10.0780	−	17.7053i	−0.383108	−	0.673056i
$693$	2.47208	−	6.56862i	0.0939065	−	0.249521i
$694$	7.50481	+	9.84277i	0.284879	+	0.373626i
$695$	20.5413	−	11.8595i	0.779174	−	0.449856i
$696$	−20.7970	+	15.6564i	−0.788307	+	0.593454i
$697$	13.8265	+	7.98275i	0.523717	+	0.302368i
$698$	7.25430	+	3.03091i	0.274579	+	0.114722i
$699$	7.31589	−	7.31589i	0.276712	−	0.276712i
$700$	−8.36272	−	10.3178i	−0.316081	−	0.389978i
$701$	1.28742	+	1.28742i	0.0486251	+	0.0486251i	0.731001	−	0.682376i	$-0.239053\pi$
$701$	1.28742	+	1.28742i	0.0486251	+	0.0486251i	−0.682376	+	0.731001i	$0.739053\pi$
$702$	−1.75412	+	0.720291i	−0.0662051	+	0.0271856i
$703$	31.7139	−	54.9300i	1.19611	−	2.07173i
$704$	−10.9470	+	18.1803i	−0.412580	+	0.685195i
$705$	5.56119	+	9.63226i	0.209446	+	0.362772i
$706$	5.00584	−	37.1431i	0.188397	−	1.39790i
$707$	7.23310	−	5.93633i	0.272029	−	0.223259i
$708$	−12.5746	−	3.45210i	−0.472582	−	0.129738i
$709$	38.1980	+	10.2351i	1.43456	+	0.384388i	0.890624	−	0.454741i	$-0.150268\pi$
$709$	38.1980	+	10.2351i	1.43456	+	0.384388i	0.543932	+	0.839129i	$0.316935\pi$
$710$	0.717446	+	5.58168i	0.0269253	+	0.209477i
$711$	2.80682	+	1.62052i	0.105264	+	0.0607743i
$712$	3.96122	+	32.3868i	0.148453	+	1.21375i
$713$		−	15.4176i		−	0.577395i
$714$	−14.7805	+	9.12889i	−0.553146	+	0.341640i
$715$	3.96881	−	3.96881i	0.148425	−	0.148425i
$716$	3.97674	−	6.79144i	0.148618	−	0.253808i
$717$	−23.9761	+	6.42437i	−0.895403	+	0.239922i
$718$	−21.5854	+	27.9528i	−0.805559	+	1.04319i
$719$	7.67559	+	13.2945i	0.286251	+	0.495801i	0.972912	−	0.231177i	$-0.0742575\pi$
$719$	7.67559	+	13.2945i	0.286251	+	0.495801i	−0.686661	+	0.726978i	$0.740924\pi$
$720$	1.55880	+	6.11648i	0.0580929	+	0.227948i
$721$	−29.3946	−	21.0628i	−1.09471	−	0.784420i
$722$	22.7114	+	3.06086i	0.845233	+	0.113913i
$723$	−3.45768	+	12.9042i	−0.128592	+	0.479913i
$724$	−0.255638	+	41.7045i	−0.00950071	+	1.54994i
$725$	5.97876	+	22.3130i	0.222046	+	0.828686i
$726$	2.16070	−	5.17151i	0.0801912	−	0.191933i
$727$			29.4581i			1.09254i	0.837609	+	0.546270i	$0.183953\pi$
$727$			29.4581i			1.09254i	−0.837609	+	0.546270i	$0.816047\pi$
$728$	7.26025	+	6.92605i	0.269083	+	0.256697i
$729$		−	1.00000i		−	0.0370370i
$730$	−17.8709	−	7.46661i	−0.661431	−	0.276352i
$731$	5.63185	+	21.0183i	0.208301	+	0.777391i
$732$	−4.01233	−	4.06183i	−0.148300	−	0.150129i
$733$	−0.468633	+	1.74896i	−0.0173093	+	0.0645993i	−0.974040	−	0.226375i	$-0.927313\pi$
$733$	−0.468633	+	1.74896i	−0.0173093	+	0.0645993i	0.956731	+	0.290974i	$0.0939793\pi$
$734$	1.03135	−	7.65259i	0.0380679	−	0.282462i
$735$	−7.28273	+	8.30514i	−0.268627	+	0.306340i
$736$	−25.7457	−	20.3897i	−0.949000	−	0.751575i
$737$	−17.5452	−	30.3892i	−0.646287	−	1.11940i
$738$	3.84897	+	2.97220i	0.141682	+	0.109408i
$739$	19.0268	−	5.09822i	0.699913	−	0.187541i	0.108721	−	0.994072i	$-0.465324\pi$
$739$	19.0268	−	5.09822i	0.699913	−	0.187541i	0.591192	+	0.806531i	$0.298658\pi$
$740$	32.6410	−	8.53204i	1.19991	−	0.313644i
$741$	−5.62556	+	5.62556i	−0.206660	+	0.206660i
$742$	19.2845	−	35.8163i	0.707956	−	1.31486i
$743$			36.0203i			1.32146i	0.750626	+	0.660728i	$0.229752\pi$
$743$			36.0203i			1.32146i	−0.750626	+	0.660728i	$0.770248\pi$
$744$	5.91677	+	4.62715i	0.216919	+	0.169639i
$745$	9.45878	+	5.46103i	0.346543	+	0.200077i
$746$	17.3018	−	2.22390i	0.633463	−	0.0814226i
$747$	−3.28329	−	0.879755i	−0.120129	−	0.0321886i
$748$	21.4078	−	12.1854i	0.782745	−	0.445543i
$749$	−2.60693	−	15.7876i	−0.0952550	−	0.576867i
$750$	16.6092	+	2.23845i	0.606481	+	0.0817365i
$751$	17.9149	+	31.0295i	0.653723	+	1.13228i	0.982212	+	0.187774i	$0.0601274\pi$
$751$	17.9149	+	31.0295i	0.653723	+	1.13228i	−0.328489	+	0.944508i	$0.606539\pi$
$752$	24.5874	−	13.7965i	0.896611	−	0.503105i
$753$	9.71513	−	16.8271i	0.354039	−	0.613213i
$754$	−6.62921	−	16.1441i	−0.241421	−	0.587933i
$755$	10.9373	+	10.9373i	0.398048	+	0.398048i
$756$	−4.83308	+	2.15437i	−0.175778	+	0.0783536i
$757$	13.2556	−	13.2556i	0.481784	−	0.481784i	−0.423917	−	0.905701i	$-0.639345\pi$
$757$	13.2556	−	13.2556i	0.481784	−	0.481784i	0.905701	+	0.423917i	$0.139345\pi$
$758$	−15.2559	+	36.5141i	−0.554120	+	1.32625i
$759$	−13.3374	−	7.70036i	−0.484117	−	0.279505i
$760$	15.9274	+	21.1569i	0.577746	+	0.767442i
$761$	−29.2352	+	16.8790i	−1.05978	+	0.611862i	−0.925370	−	0.379064i	$-0.876246\pi$
$761$	−29.2352	+	16.8790i	−1.05978	+	0.611862i	−0.134406	+	0.990926i	$0.542913\pi$
$762$	−2.87009	+	2.18836i	−0.103972	+	0.0792758i
$763$	−8.43218	−	10.2742i	−0.305265	−	0.371949i
$764$	13.7739	+	3.78136i	0.498324	+	0.136805i
$765$	1.89626	−	7.07693i	0.0685594	−	0.255867i
$766$	37.4284	+	28.9025i	1.35234	+	1.04429i
$767$	4.37112	−	7.57100i	0.157832	−	0.273373i
$768$	15.5517	−	3.76097i	0.561173	−	0.135712i
$769$	53.2751			1.92115			0.960575	−	0.278021i	$-0.0896784\pi$
$769$	53.2751			1.92115			0.960575	+	0.278021i	$0.0896784\pi$
$770$	10.7414	−	11.3988i	0.387094	−	0.410785i
$771$	−13.9615	−	13.9615i	−0.502812	−	0.502812i
$772$	−4.73317	−	18.1077i	−0.170350	−	0.651709i
$773$	8.61943	+	32.1681i	0.310019	+	1.15701i	0.928538	+	0.371237i	$0.121066\pi$
$773$	8.61943	+	32.1681i	0.310019	+	1.15701i	−0.618519	+	0.785770i	$0.712267\pi$
$774$	0.844967	+	6.57379i	0.0303717	+	0.236290i
$775$	5.77243	−	3.33271i	0.207352	−	0.119715i
$776$	−6.40147	+	15.0613i	−0.229799	+	0.540670i
$777$	11.6733	+	25.7619i	0.418776	+	0.924202i
$778$	−27.7600	−	36.4080i	−0.995244	−	1.30529i
$779$	19.7075	+	5.28060i	0.706093	+	0.189197i
$780$	−4.23164	−	0.0259389i	−0.151517	−	0.000928760i
$781$	6.46153	−	1.73136i	0.231212	−	0.0619530i
$782$	14.4802	+	35.2636i	0.517811	+	1.26102i
$783$	9.20351			0.328907
$784$	20.8245	+	18.7174i	0.743732	+	0.668478i
$785$	−12.7338			−0.454488
$786$	−6.89526	−	16.7920i	−0.245946	−	0.598951i
$787$	−30.7264	+	8.23310i	−1.09528	+	0.293478i	−0.760840	−	0.648940i	$-0.775213\pi$
$787$	−30.7264	+	8.23310i	−1.09528	+	0.293478i	−0.334437	+	0.942418i	$0.608546\pi$
$788$	0.00998722	−	1.62930i	0.000355780	−	0.0580416i
$789$	13.6885	+	3.66781i	0.487322	+	0.130578i
$790$	4.38543	+	5.75162i	0.156027	+	0.204633i
$791$	8.62399	+	19.0324i	0.306634	+	0.676713i
$792$	6.95796	−	2.80741i	0.247240	−	0.0997571i
$793$	3.31491	−	1.91386i	0.117716	−	0.0679633i
$794$	−1.85650	−	14.4434i	−0.0658846	−	0.512578i
$795$	4.44015	+	16.5709i	0.157476	+	0.587708i
$796$	37.9109	−	9.90952i	1.34371	−	0.351234i
$797$	−21.8956	−	21.8956i	−0.775581	−	0.775581i	0.203495	−	0.979076i	$-0.434770\pi$
$797$	−21.8956	−	21.8956i	−0.775581	−	0.775581i	−0.979076	+	0.203495i	$0.934770\pi$
$798$	−15.2253	+	16.1572i	−0.538971	+	0.571957i
$799$	−32.7256			−1.15775
$800$	2.06874	−	14.0468i	0.0731410	−	0.496629i
$801$	5.76790	−	9.99029i	0.203799	−	0.352990i
$802$	26.7561	+	20.6613i	0.944791	+	0.729575i
$803$	−5.95867	+	22.2380i	−0.210277	+	0.784763i
$804$	−7.00392	+	25.5124i	−0.247009	+	0.899754i
$805$	15.3772	+	18.7363i	0.541976	+	0.660368i
$806$	−4.00449	+	3.05330i	−0.141052	+	0.107548i
$807$	14.0619	−	8.11866i	0.495003	−	0.285790i
$808$	9.90529	+	1.39682i	0.348467	+	0.0491401i
$809$	−41.2490	−	23.8151i	−1.45024	−	0.837295i	−0.451743	−	0.892148i	$-0.649198\pi$
$809$	−41.2490	−	23.8151i	−1.45024	−	0.837295i	−0.998494	+	0.0548526i	$0.982531\pi$
$810$	0.860320	−	2.05912i	0.0302286	−	0.0723502i
$811$	−16.2417	+	16.2417i	−0.570322	+	0.570322i	−0.932218	−	0.361896i	$-0.882129\pi$
$811$	−16.2417	+	16.2417i	−0.570322	+	0.570322i	0.361896	+	0.932218i	$0.382129\pi$
$812$	−19.8278	−	44.4813i	−0.695818	−	1.56099i
$813$	−4.58807	−	4.58807i	−0.160911	−	0.160911i
$814$	−15.2334	−	37.0978i	−0.533929	−	1.30028i
$815$	5.79203	−	10.0321i	0.202886	−	0.351409i
$816$	−17.8788	−	5.02631i	−0.625882	−	0.175956i
$817$	13.9037	+	24.0818i	0.486427	+	0.842517i
$818$	10.3759	+	1.39838i	0.362786	+	0.0488933i
$819$	−0.577963	−	3.50016i	−0.0201957	−	0.122306i
$820$	5.36846	+	9.43148i	0.187475	+	0.329362i
$821$	3.64694	+	0.977195i	0.127279	+	0.0341043i	0.321896	−	0.946775i	$-0.395680\pi$
$821$	3.64694	+	0.977195i	0.127279	+	0.0341043i	−0.194617	+	0.980879i	$0.562346\pi$
$822$	21.9609	−	2.82276i	0.765975	−	0.0984552i
$823$	−38.1796	−	22.0430i	−1.33086	−	0.768370i	−0.345425	−	0.938446i	$-0.612265\pi$
$823$	−38.1796	−	22.0430i	−1.33086	−	0.768370i	−0.985431	+	0.170076i	$0.945599\pi$
$824$	−4.69336	−	38.3727i	−0.163501	−	1.33678i
$825$		−	6.65810i		−	0.231805i
$826$	11.5652	−	21.4796i	0.402406	−	0.747372i
$827$	30.6996	−	30.6996i	1.06753	−	1.06753i	0.0699816	−	0.997548i	$-0.477706\pi$
$827$	30.6996	−	30.6996i	1.06753	−	1.06753i	0.997548	−	0.0699816i	$-0.0222940\pi$
$828$	2.93643	+	11.2339i	0.102048	+	0.390405i
$829$	−16.9527	+	4.54247i	−0.588793	+	0.157767i	−0.540901	−	0.841086i	$-0.681917\pi$
$829$	−16.9527	+	4.54247i	−0.588793	+	0.157767i	−0.0478913	+	0.998853i	$0.515250\pi$
$830$	−6.00383	−	4.63621i	−0.208396	−	0.160925i
$831$	−13.3728	−	23.1624i	−0.463898	−	0.803495i
$832$	−0.197244	+	10.7250i	−0.00683822	+	0.371822i
$833$	−10.4485	−	30.7755i	−0.362018	−	1.06631i
$834$	−2.83920	+	21.0667i	−0.0983134	+	0.729481i
$835$	−2.71456	+	10.1309i	−0.0939413	+	0.350594i
$836$	22.3949	−	22.1221i	0.774545	−	0.765107i
$837$	−0.687326	−	2.56513i	−0.0237574	−	0.0886640i
$838$	3.65341	+	1.52643i	0.126205	+	0.0527295i
$839$		−	25.8629i		−	0.892888i	−0.894812	−	0.446444i	$-0.852690\pi$
$839$		−	25.8629i		−	0.892888i	0.894812	−	0.446444i	$-0.147310\pi$
$840$	−11.8054	+	0.278112i	−0.407324	+	0.00959579i
$841$			55.7046i			1.92085i
$842$	−13.2669	+	31.7534i	−0.457206	+	1.09430i
$843$	−3.99808	−	14.9210i	−0.137701	−	0.513907i
$844$	−9.27484	−	0.0568524i	−0.319253	−	0.00195694i
$845$	−4.57512	+	17.0746i	−0.157389	+	0.587383i
$846$	−9.87866	−	1.33136i	−0.339635	−	0.0457732i
$847$	8.52325	+	6.10738i	0.292863	+	0.209852i
$848$	42.1397	−	10.7394i	1.44708	−	0.368792i
$849$	−2.66623	−	4.61804i	−0.0915047	−	0.158491i
$850$	−10.0728	+	13.0441i	−0.345493	+	0.447409i
$851$	59.9480	−	16.0630i	2.05499	−	0.550634i
$852$	−4.35226	−	2.54848i	−0.149106	−	0.0873094i
$853$	−17.4950	+	17.4950i	−0.599017	+	0.599017i	−0.940051	−	0.341034i	$-0.889223\pi$
$853$	−17.4950	+	17.4950i	−0.599017	+	0.599017i	0.341034	+	0.940051i	$0.389223\pi$
$854$	9.08770	−	5.61284i	0.310975	−	0.192068i
$855$		−	9.36280i		−	0.320201i
$856$	10.5379	−	13.4750i	0.360180	−	0.460565i
$857$	−32.1948	−	18.5877i	−1.09975	−	0.634944i	−0.163598	−	0.986527i	$-0.552310\pi$
$857$	−32.1948	−	18.5877i	−1.09975	−	0.634944i	−0.936157	+	0.351583i	$0.885643\pi$
$858$	0.641284	+	4.98915i	0.0218931	+	0.170327i
$859$	−22.8200	−	6.11459i	−0.778607	−	0.208627i	−0.152436	−	0.988313i	$-0.548712\pi$
$859$	−22.8200	−	6.11459i	−0.778607	−	0.208627i	−0.626170	+	0.779686i	$0.715379\pi$
$860$	−3.91567	+	14.2632i	−0.133523	+	0.486371i
$861$	−7.03256	+	5.77175i	−0.239669	+	0.196701i
$862$	−0.112085	+	0.831666i	−0.00381763	+	0.0283266i
$863$	−12.9042	−	22.3508i	−0.439266	−	0.760830i	0.558367	−	0.829594i	$-0.311428\pi$
$863$	−12.9042	−	22.3508i	−0.439266	−	0.760830i	−0.997633	+	0.0687634i	$0.978095\pi$
$864$	−5.19247	−	2.24462i	−0.176651	−	0.0763634i
$865$	−8.03699	+	13.9205i	−0.273266	+	0.473310i
$866$	51.2623	−	21.0497i	1.74196	−	0.715298i
$867$	3.22238	+	3.22238i	0.109438	+	0.109438i
$868$	−10.9168	+	8.84815i	−0.370539	+	0.300326i
$869$	6.07937	−	6.07937i	0.206229	−	0.206229i
$870$	18.9512	+	7.91797i	0.642505	+	0.268444i
$871$	−15.3607	−	8.86851i	−0.520478	−	0.300498i
$872$	1.98410	−	14.0698i	0.0671901	−	0.476465i
$873$	5.01082	−	2.89300i	0.169591	−	0.0979132i
$874$	29.5375	+	38.7393i	0.999120	+	1.31038i
$875$	−11.0437	+	29.3445i	−0.373345	+	0.992025i
$876$	15.0852	−	8.58657i	0.509681	−	0.290113i
$877$	−2.35089	+	8.77365i	−0.0793840	+	0.296265i	−0.994192	−	0.107625i	$-0.965675\pi$
$877$	−2.35089	+	8.77365i	−0.0793840	+	0.296265i	0.914808	+	0.403890i	$0.132342\pi$
$878$	−29.7608	+	38.5399i	−1.00438	+	1.30066i
$879$	−5.94445	+	10.2961i	−0.200501	+	0.347279i
$880$	16.7426	+	0.205263i	0.564392	+	0.00691942i
$881$	45.6752			1.53884			0.769418	−	0.638745i	$-0.220546\pi$
$881$	45.6752			1.53884			0.769418	+	0.638745i	$0.220546\pi$
$882$	−1.90198	−	9.71506i	−0.0640431	−	0.327123i
$883$	4.59704	+	4.59704i	0.154703	+	0.154703i	0.780215	−	0.625512i	$-0.215110\pi$
$883$	4.59704	+	4.59704i	0.154703	+	0.154703i	−0.625512	+	0.780215i	$0.715110\pi$
$884$	6.29151	−	10.7446i	0.211606	−	0.361379i
$885$	2.66283	+	9.93783i	0.0895101	+	0.334056i
$886$	23.1864	−	2.98028i	0.778963	−	0.100125i
$887$	−17.7874	+	10.2696i	−0.597243	+	0.344818i	−0.767956	−	0.640503i	$-0.778726\pi$
$887$	−17.7874	+	10.2696i	−0.597243	+	0.344818i	0.170713	+	0.985321i	$0.445393\pi$
$888$	−11.8272	+	27.8269i	−0.396894	+	0.933808i
$889$	−2.78682	−	6.15027i	−0.0934670	−	0.206273i
$890$	20.4717	−	15.6090i	0.686212	−	0.523215i
$891$	−2.56232	−	0.686571i	−0.0858409	−	0.0230010i
$892$	−41.7140	+	41.2057i	−1.39669	+	1.37967i
$893$	−40.3957	+	10.8240i	−1.35179	+	0.362211i
$894$	−9.05478	+	3.71814i	−0.302837	+	0.124353i
$895$	−6.20947			−0.207560
$896$	0.338072	+	29.9313i	0.0112942	+	0.999936i
$897$	−7.78453			−0.259918
$898$	21.7711	−	8.93981i	0.726511	−	0.298325i
$899$	23.6082	−	6.32581i	0.787379	−	0.210978i
$900$	−3.57127	+	3.52775i	−0.119042	+	0.117592i
$901$	−48.7568	−	13.0643i	−1.62432	−	0.435236i
$902$	10.2583	−	7.82165i	0.341565	−	0.260432i
$903$	−12.3399	−	1.21509i	−0.410647	−	0.0404355i
$904$	−8.73768	+	20.5579i	−0.290611	+	0.683747i
$905$	28.4969	−	16.4527i	0.947269	−	0.546906i
$906$	−13.7491	+	1.76725i	−0.456784	+	0.0587131i
$907$	−0.797702	−	2.97706i	−0.0264873	−	0.0988518i	0.951417	−	0.307906i	$-0.0996282\pi$
$907$	−0.797702	−	2.97706i	−0.0264873	−	0.0988518i	−0.977904	+	0.209054i	$0.932962\pi$
$908$	−19.4290	+	33.1807i	−0.644775	+	1.10114i
$909$	−2.50082	−	2.50082i	−0.0829471	−	0.0829471i
$910$	1.82116	−	7.70450i	0.0603710	−	0.255402i
$911$	15.3790			0.509528			0.254764	−	0.967003i	$-0.418002\pi$
$911$	15.3790			0.509528			0.254764	+	0.967003i	$0.418002\pi$
$912$	−23.7316	−	0.290948i	−0.785832	−	0.00963426i
$913$	−4.50843	+	7.80882i	−0.149207	+	0.258434i
$914$	13.2956	−	17.2177i	0.439780	−	0.569509i
$915$	−1.16590	+	4.35121i	−0.0385436	+	0.143847i
$916$	−14.3762	+	8.18302i	−0.475003	+	0.270375i
$917$	33.5066	−	5.53277i	1.10649	−	0.182708i
$918$	3.98123	+	5.22150i	0.131400	+	0.172335i
$919$	−35.2740	+	20.3654i	−1.16358	+	0.671794i	−0.952160	−	0.305601i	$-0.901143\pi$
$919$	−35.2740	+	20.3654i	−1.16358	+	0.671794i	−0.211422	+	0.977395i	$0.567809\pi$
$920$	−3.61827	+	25.6582i	−0.119291	+	0.845927i
$921$	−23.5597	−	13.6022i	−0.776318	−	0.448207i
$922$	−32.9786	−	13.7788i	−1.08609	−	0.453779i
$923$	2.39094	−	2.39094i	0.0786987	−	0.0786987i
$924$	2.20192	+	13.8630i	0.0724379	+	0.456060i
$925$	18.9726	+	18.9726i	0.623814	+	0.623814i
$926$	28.8291	−	11.8380i	0.947384	−	0.389022i
$927$	−6.83396	+	11.8368i	−0.224457	+	0.388770i
$928$	20.6583	−	47.7889i	0.678143	−	1.56875i
$929$	7.95906	+	13.7855i	0.261128	+	0.452287i	0.966542	−	0.256508i	$-0.0825721\pi$
$929$	7.95906	+	13.7855i	0.261128	+	0.452287i	−0.705414	+	0.708796i	$0.749239\pi$
$930$	0.791548	−	5.87325i	0.0259559	−	0.192591i
$931$	−23.0764	−	34.5327i	−0.756297	−	1.13176i
$932$	−5.47801	+	19.9542i	−0.179438	+	0.653620i
$933$	6.81077	+	1.82494i	0.222975	+	0.0597459i
$934$	−7.06891	−	54.9957i	−0.231302	−	1.79951i
$935$	−16.8314	−	9.71763i	−0.550447	−	0.317801i
$936$	2.33629	−	2.98744i	0.0763642	−	0.0976475i
$937$		−	1.34667i		−	0.0439937i	−0.999758	−	0.0219969i	$-0.992998\pi$
$937$		−	1.34667i		−	0.0439937i	0.999758	−	0.0219969i	$-0.00700239\pi$
$938$	−43.5798	−	23.4646i	−1.42293	−	0.766146i
$939$	−18.8826	+	18.8826i	−0.616211	+	0.616211i
$940$	−19.1960	−	11.2403i	−0.626104	−	0.366617i
$941$	1.21897	−	0.326622i	0.0397373	−	0.0106476i	−0.238896	−	0.971045i	$-0.576785\pi$
$941$	1.21897	−	0.326622i	0.0397373	−	0.0106476i	0.278633	+	0.960398i	$0.410119\pi$
$942$	6.97497	−	9.03251i	0.227257	−	0.294295i
$943$	9.98180	+	17.2890i	0.325052	+	0.563007i
$944$	25.2719	−	6.44058i	0.822529	−	0.209623i
$945$	3.39368	+	2.43176i	0.110396	+	0.0791050i
$946$	17.4243	+	2.34830i	0.566512	+	0.0763498i
$947$	1.41517	−	5.28148i	0.0459868	−	0.171625i	−0.939113	−	0.343608i	$-0.888351\pi$
$947$	1.41517	−	5.28148i	0.0459868	−	0.171625i	0.985100	+	0.171983i	$0.0550175\pi$
$948$	−6.48196	−	0.0397328i	−0.210524	−	0.00129046i
$949$	3.01190	+	11.2406i	0.0977704	+	0.364884i
$950$	−8.11924	+	19.4329i	−0.263423	+	0.630487i
$951$			9.67701i			0.313799i
$952$	16.6589	−	30.4907i	0.539918	−	0.988208i
$953$			10.6064i			0.343574i	0.985134	+	0.171787i	$0.0549541\pi$
$953$			10.6064i			0.343574i	−0.985134	+	0.171787i	$0.945046\pi$
$954$	−14.1864	−	5.92720i	−0.459302	−	0.191900i
$955$	−2.91681	−	10.8857i	−0.0943859	−	0.352253i
$956$	35.3179	−	34.8876i	1.14226	−	1.12834i
$957$	6.31886	−	23.5823i	0.204260	−	0.762308i
$958$	2.88793	−	21.4283i	0.0933048	−	0.692317i
$959$	−4.05921	+	41.2237i	−0.131079	+	1.33118i
$960$	−8.76084	−	9.08912i	−0.282755	−	0.293350i
$961$	11.9738	+	20.7393i	0.386253	+	0.669009i
$962$	−16.0442	−	12.3894i	−0.517285	−	0.399451i
$963$	−5.84188	+	1.56533i	−0.188252	+	0.0504420i
$964$	−6.75703	−	25.8504i	−0.217629	−	0.832584i
$965$	−10.4418	+	10.4418i	−0.336133	+	0.336133i
$966$	−21.7132	+	0.644713i	−0.698612	+	0.0207433i
$967$			5.90611i			0.189928i	0.995481	+	0.0949638i	$0.0302735\pi$
$967$			5.90611i			0.189928i	−0.995481	+	0.0949638i	$0.969726\pi$
$968$	1.36089	+	11.1266i	0.0437406	+	0.357621i
$969$	23.8576	+	13.7742i	0.766415	+	0.442490i
$970$	12.8068	−	1.64613i	0.411202	−	0.0528541i
$971$	8.32330	+	2.23022i	0.267108	+	0.0715713i	0.389887	−	0.920863i	$-0.372514\pi$
$971$	8.32330	+	2.23022i	0.267108	+	0.0715713i	−0.122779	+	0.992434i	$0.539181\pi$
$972$	0.989364	+	1.73815i	0.0317339	+	0.0557511i
$973$	−37.2199	−	14.0076i	−1.19322	−	0.449063i
$974$	2.88982	+	0.389466i	0.0925958	+	0.0124793i
$975$	−1.68272	−	2.91456i	−0.0538902	−	0.0933406i
$976$	10.9927	+	3.09039i	0.351866	+	0.0989211i
$977$	7.82690	−	13.5566i	0.250405	−	0.433714i	−0.713233	−	0.700927i	$-0.752770\pi$
$977$	7.82690	−	13.5566i	0.250405	−	0.433714i	0.963637	+	0.267214i	$0.0861030\pi$
$978$	3.94350	+	9.60360i	0.126099	+	0.307089i
$979$	−21.6382	−	21.6382i	−0.691561	−	0.691561i
$980$	4.44165	−	21.6408i	0.141883	−	0.691291i
$981$	−3.55226	+	3.55226i	−0.113415	+	0.113415i
$982$	16.6290	−	39.8005i	0.530652	−	1.27008i
$983$	20.1401	+	11.6279i	0.642369	+	0.370872i	0.785527	−	0.618828i	$-0.212392\pi$
$983$	20.1401	+	11.6279i	0.642369	+	0.370872i	−0.143157	+	0.989700i	$0.545725\pi$
$984$	−9.63067	−	1.35810i	−0.307014	−	0.0432946i
$985$	−1.11331	+	0.642771i	−0.0354731	+	0.0204804i
$986$	−48.0561	+	36.6413i	−1.53042	+	1.16690i
$987$	6.56848	−	17.4533i	0.209077	−	0.555544i
$988$	4.21232	−	15.3438i	0.134012	−	0.488151i
$989$	−7.04218	+	26.2818i	−0.223928	+	0.835712i
$990$	−4.68546	−	3.61815i	−0.148914	−	0.114992i
$991$	−13.4607	+	23.3146i	−0.427593	+	0.740614i	−0.996659	−	0.0816787i	$-0.973972\pi$
$991$	−13.4607	+	23.3146i	−0.427593	+	0.740614i	0.569065	+	0.822292i	$0.307305\pi$
$992$	−14.8622	−	2.18882i	−0.471874	−	0.0694952i
$993$	−19.0885			−0.605756
$994$	6.47097	−	6.86701i	0.205247	−	0.217808i
$995$	−21.8613	−	21.8613i	−0.693050	−	0.693050i
$996$	6.57725	−	1.71923i	0.208408	−	0.0544758i
$997$	−8.09416	−	30.2078i	−0.256345	−	0.956691i	−0.967337	−	0.253492i	$-0.918421\pi$
$997$	−8.09416	−	30.2078i	−0.256345	−	0.956691i	0.710993	−	0.703199i	$-0.248246\pi$
$998$	−5.02452	−	39.0904i	−0.159048	−	1.23739i
$999$	9.25785	−	5.34502i	0.292905	−	0.169109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bq.b.109.4	yes	120
7.2	even	3	inner	336.2.bq.b.205.23	yes	120
16.5	even	4	inner	336.2.bq.b.277.23	yes	120
112.37	even	12	inner	336.2.bq.b.37.4	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bq.b.37.4	✓	120	112.37	even	12	inner
336.2.bq.b.109.4	yes	120	1.1	even	1	trivial
336.2.bq.b.205.23	yes	120	7.2	even	3	inner
336.2.bq.b.277.23	yes	120	16.5	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30822 + 0.537189i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.42286 - 1.40552i) q^{4} +(-1.52423 - 0.408415i) q^{5} +(1.12460 - 0.857476i) q^{6} +(1.09198 + 2.40989i) q^{7} +(-1.10637 + 2.60306i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-1.30822 + 0.537189i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.42286 - 1.40552i) q^{4} +(-1.52423 - 0.408415i) q^{5} +(1.12460 - 0.857476i) q^{6} +(1.09198 + 2.40989i) q^{7} +(-1.10637 + 2.60306i) q^{8} +(0.866025 - 0.500000i) q^{9} +(2.21341 - 0.284503i) q^{10} +(-0.686571 - 2.56232i) q^{11} +(-1.01060 + 1.72589i) q^{12} +(-0.948125 - 0.948125i) q^{13} +(-2.72311 - 2.56606i) q^{14} +1.57800 q^{15} +(0.0490361 - 3.99970i) q^{16} +(-2.32148 + 4.02093i) q^{17} +(-0.864353 + 1.11933i) q^{18} +(-1.53566 + 5.73117i) q^{19} +(-2.74279 + 1.56121i) q^{20} +(-1.67849 - 2.04515i) q^{21} +(2.27463 + 2.98324i) q^{22} +(-5.02785 + 2.90283i) q^{23} +(0.394951 - 2.80072i) q^{24} +(-2.17366 - 1.25496i) q^{25} +(1.74967 + 0.731030i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(4.94087 + 1.89414i) q^{28} +(-6.50787 - 6.50787i) q^{29} +(-2.06436 + 0.847682i) q^{30} +(-1.32781 + 2.29984i) q^{31} +(2.08445 + 5.25881i) q^{32} +(1.32635 + 2.29731i) q^{33} +(0.877002 - 6.50731i) q^{34} +(-0.680182 - 4.11920i) q^{35} +(0.529470 - 1.92864i) q^{36} +(-10.3258 - 2.76679i) q^{37} +(-1.06975 - 8.32255i) q^{38} +(1.16121 + 0.670426i) q^{39} +(2.74949 - 3.51580i) q^{40} -3.43864i q^{41} +(3.29447 + 1.77383i) q^{42} +(3.31394 - 3.31394i) q^{43} +(-4.57828 - 2.68082i) q^{44} +(-1.52423 + 0.408415i) q^{45} +(5.01814 - 6.49844i) q^{46} +(3.52421 + 6.10411i) q^{47} +(0.987833 + 3.87610i) q^{48} +(-4.61517 + 5.26309i) q^{49} +(3.51777 + 0.474096i) q^{50} +(1.20169 - 4.48476i) q^{51} +(-2.68165 - 0.0164379i) q^{52} +(2.81379 + 10.5012i) q^{53} +(0.545198 - 1.30490i) q^{54} +4.18596i q^{55} +(-7.48124 + 0.176244i) q^{56} -5.93335i q^{57} +(12.0096 + 5.01774i) q^{58} +(1.68748 + 6.29775i) q^{59} +(2.24526 - 2.21790i) q^{60} +(-0.738851 + 2.75743i) q^{61} +(0.501616 - 3.72197i) q^{62} +(2.15063 + 1.54104i) q^{63} +(-5.55188 - 5.75992i) q^{64} +(1.05793 + 1.83239i) q^{65} +(-2.96925 - 2.29288i) q^{66} +(12.7774 - 3.42370i) q^{67} +(2.34835 + 8.98408i) q^{68} +(4.10522 - 4.10522i) q^{69} +(3.10262 + 5.02342i) q^{70} +2.52175i q^{71} +(0.343385 + 2.80751i) q^{72} +(-7.51613 - 4.33944i) q^{73} +(14.9946 - 1.92735i) q^{74} +(2.42441 + 0.649617i) q^{75} +(5.87024 + 10.3130i) q^{76} +(5.42519 - 4.45255i) q^{77} +(-1.87926 - 0.253271i) q^{78} +(1.62052 + 2.80682i) q^{79} +(-1.70828 + 6.07642i) q^{80} +(0.500000 - 0.866025i) q^{81} +(1.84720 + 4.49849i) q^{82} +(-2.40354 - 2.40354i) q^{83} +(-5.26276 - 0.550804i) q^{84} +(5.18068 - 5.18068i) q^{85} +(-2.55513 + 6.11555i) q^{86} +(7.97048 + 4.60176i) q^{87} +(7.42948 + 1.04769i) q^{88} +(9.99029 - 5.76790i) q^{89} +(1.77462 - 1.35309i) q^{90} +(1.24955 - 3.32021i) q^{91} +(-3.07392 + 11.1970i) q^{92} +(0.687326 - 2.56513i) q^{93} +(-7.88949 - 6.09232i) q^{94} +(4.68140 - 8.10842i) q^{95} +(-3.37450 - 4.54013i) q^{96} +5.78600 q^{97} +(3.21037 - 9.36448i) q^{98} +(-1.87575 - 1.87575i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8}+O(q^{10}) \) 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8	\( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8} - 8 q^{10} + 4 q^{11} + 8 q^{13} + 32 q^{14} + 8 q^{15} + 12 q^{16} - 16 q^{17} - 4 q^{18} - 8 q^{19} - 64 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{24} - 8 q^{26} - 8 q^{28} - 64 q^{29} - 52 q^{31} - 4 q^{33} + 32 q^{34} - 8 q^{35} + 24 q^{37} - 40 q^{38} - 60 q^{40} + 24 q^{42} - 32 q^{43} - 12 q^{44} - 8 q^{45} + 4 q^{46} - 8 q^{47} + 32 q^{48} + 20 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{54} - 104 q^{56} + 4 q^{58} + 52 q^{59} - 16 q^{60} + 4 q^{61} - 144 q^{62} + 8 q^{63} - 64 q^{64} + 24 q^{65} + 24 q^{66} + 12 q^{68} + 24 q^{69} - 48 q^{70} + 4 q^{72} + 16 q^{74} + 16 q^{75} - 8 q^{76} + 8 q^{77} - 56 q^{78} + 28 q^{79} + 68 q^{80} + 60 q^{81} + 28 q^{82} + 8 q^{83} + 24 q^{84} - 80 q^{85} + 36 q^{86} + 40 q^{88} + 8 q^{90} + 36 q^{91} - 184 q^{92} + 4 q^{93} + 60 q^{94} - 16 q^{95} + 36 q^{96} + 24 q^{97} + 124 q^{98} - 8 q^{99}+O(q^{100}) \) 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8 - 8 * q^10 + 4 * q^11 + 8 * q^13 + 32 * q^14 + 8 * q^15 + 12 * q^16 - 16 * q^17 - 4 * q^18 - 8 * q^19 - 64 * q^20 + 12 * q^21 + 24 * q^22 - 8 * q^24 - 8 * q^26 - 8 * q^28 - 64 * q^29 - 52 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 24 * q^37 - 40 * q^38 - 60 * q^40 + 24 * q^42 - 32 * q^43 - 12 * q^44 - 8 * q^45 + 4 * q^46 - 8 * q^47 + 32 * q^48 + 20 * q^49 - 16 * q^50 - 8 * q^51 - 16 * q^52 + 4 * q^54 - 104 * q^56 + 4 * q^58 + 52 * q^59 - 16 * q^60 + 4 * q^61 - 144 * q^62 + 8 * q^63 - 64 * q^64 + 24 * q^65 + 24 * q^66 + 12 * q^68 + 24 * q^69 - 48 * q^70 + 4 * q^72 + 16 * q^74 + 16 * q^75 - 8 * q^76 + 8 * q^77 - 56 * q^78 + 28 * q^79 + 68 * q^80 + 60 * q^81 + 28 * q^82 + 8 * q^83 + 24 * q^84 - 80 * q^85 + 36 * q^86 + 40 * q^88 + 8 * q^90 + 36 * q^91 - 184 * q^92 + 4 * q^93 + 60 * q^94 - 16 * q^95 + 36 * q^96 + 24 * q^97 + 124 * q^98 - 8 * q^99

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