LMFDB - Embedded newform 68.2.i.b.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [68,2,Mod(3,68)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(68, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 1]))

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

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

chi := DirichletCharacter("68.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 68 = 2^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	68.i (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.542982733745$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	68.11
Dual form			68.2.i.b.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.114599 + 1.40956i) q^{2} +(0.935416 - 0.186066i) q^{3} +(-1.97373 + 0.323068i) q^{4} +(0.763429 + 0.510107i) q^{5} +(0.369469 + 1.29720i) q^{6} +(-0.225807 - 0.337944i) q^{7} +(-0.681573 - 2.74508i) q^{8} +(-1.93126 + 0.799952i) q^{9} +O(q^{10})$	\(q+(0.114599 + 1.40956i) q^{2} +(0.935416 - 0.186066i) q^{3} +(-1.97373 + 0.323068i) q^{4} +(0.763429 + 0.510107i) q^{5} +(0.369469 + 1.29720i) q^{6} +(-0.225807 - 0.337944i) q^{7} +(-0.681573 - 2.74508i) q^{8} +(-1.93126 + 0.799952i) q^{9} +(-0.631540 + 1.13456i) q^{10} +(0.892912 - 4.48897i) q^{11} +(-1.78615 + 0.669448i) q^{12} +(-1.21544 + 1.21544i) q^{13} +(0.450476 - 0.357017i) q^{14} +(0.809037 + 0.335114i) q^{15} +(3.79125 - 1.27530i) q^{16} +(2.80335 - 3.02345i) q^{17} +(-1.34890 - 2.63055i) q^{18} +(-1.29031 + 3.11507i) q^{19} +(-1.67161 - 0.760176i) q^{20} +(-0.274103 - 0.274103i) q^{21} +(6.42981 + 0.744184i) q^{22} +(-1.22170 - 0.243011i) q^{23} +(-1.14832 - 2.44097i) q^{24} +(-1.59080 - 3.84054i) q^{25} +(-1.85253 - 1.57395i) q^{26} +(-4.03671 + 2.69724i) q^{27} +(0.554862 + 0.594060i) q^{28} +(-3.14845 + 4.71199i) q^{29} +(-0.379650 + 1.17879i) q^{30} +(1.67369 + 8.41419i) q^{31} +(2.23209 + 5.19786i) q^{32} -4.36520i q^{33} +(4.58300 + 3.60501i) q^{34} -0.373182i q^{35} +(3.55335 - 2.20282i) q^{36} +(1.30555 + 6.56346i) q^{37} +(-4.53876 - 1.46178i) q^{38} +(-0.910791 + 1.36310i) q^{39} +(0.879951 - 2.44335i) q^{40} +(1.11203 - 0.743033i) q^{41} +(0.354954 - 0.417777i) q^{42} +(2.03481 + 4.91247i) q^{43} +(-0.312126 + 9.14851i) q^{44} +(-1.88244 - 0.374440i) q^{45} +(0.202534 - 1.74991i) q^{46} +(-9.03666 - 9.03666i) q^{47} +(3.30911 - 1.89836i) q^{48} +(2.61557 - 6.31454i) q^{49} +(5.23117 - 2.68246i) q^{50} +(2.05974 - 3.34979i) q^{51} +(2.00629 - 2.79163i) q^{52} +(2.36069 + 0.977830i) q^{53} +(-4.26453 - 5.38089i) q^{54} +(2.97153 - 2.97153i) q^{55} +(-0.773779 + 0.850191i) q^{56} +(-0.627364 + 3.15397i) q^{57} +(-7.00265 - 3.89795i) q^{58} +(11.1640 - 4.62429i) q^{59} +(-1.70509 - 0.400052i) q^{60} +(2.41467 + 3.61380i) q^{61} +(-11.6685 + 3.32342i) q^{62} +(0.706429 + 0.472021i) q^{63} +(-7.07092 + 3.74194i) q^{64} +(-1.54791 + 0.307898i) q^{65} +(6.15302 - 0.500246i) q^{66} -8.38234 q^{67} +(-4.55628 + 6.87316i) q^{68} -1.18801 q^{69} +(0.526023 - 0.0427662i) q^{70} +(13.3275 - 2.65100i) q^{71} +(3.51222 + 4.75622i) q^{72} +(-5.16828 - 3.45333i) q^{73} +(-9.10200 + 2.59242i) q^{74} +(-2.20266 - 3.29651i) q^{75} +(1.54034 - 6.56518i) q^{76} +(-1.71864 + 0.711886i) q^{77} +(-2.02574 - 1.12761i) q^{78} +(1.81098 - 9.10440i) q^{79} +(3.54489 + 0.960342i) q^{80} +(1.16022 - 1.16022i) q^{81} +(1.17479 + 1.48232i) q^{82} +(-3.70474 - 1.53455i) q^{83} +(0.629561 + 0.452453i) q^{84} +(3.68244 - 0.878180i) q^{85} +(-6.69125 + 3.43116i) q^{86} +(-2.06837 + 4.99349i) q^{87} +(-12.9312 + 0.608447i) q^{88} +(6.88729 + 6.88729i) q^{89} +(0.312072 - 2.69632i) q^{90} +(0.685206 + 0.136296i) q^{91} +(2.48982 + 0.0849468i) q^{92} +(3.13119 + 7.55935i) q^{93} +(11.7021 - 13.7733i) q^{94} +(-2.57408 + 1.71994i) q^{95} +(3.05508 + 4.44685i) q^{96} +(4.91684 - 7.35857i) q^{97} +(9.20048 + 2.96317i) q^{98} +(1.86652 + 9.38364i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) $ 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9	$ 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9} + 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 24 q^{20} - 16 q^{21} - 8 q^{22} + 8 q^{24} + 16 q^{25} - 16 q^{26} + 40 q^{28} + 56 q^{30} + 32 q^{32} + 56 q^{34} + 56 q^{36} - 16 q^{37} + 32 q^{38} + 56 q^{40} - 48 q^{41} + 40 q^{42} + 24 q^{44} - 64 q^{45} + 8 q^{46} - 32 q^{48} - 16 q^{49} - 16 q^{52} + 48 q^{53} - 24 q^{54} - 48 q^{56} + 64 q^{57} - 64 q^{58} - 112 q^{60} + 16 q^{61} - 64 q^{62} - 56 q^{64} + 96 q^{65} - 96 q^{66} - 32 q^{68} + 32 q^{69} - 80 q^{70} - 64 q^{72} + 64 q^{73} - 16 q^{74} - 64 q^{76} + 16 q^{77} - 112 q^{78} - 24 q^{80} + 64 q^{81} - 40 q^{82} - 80 q^{85} + 64 q^{86} + 56 q^{88} - 16 q^{89} + 48 q^{90} + 104 q^{92} - 16 q^{93} + 88 q^{94} + 144 q^{96} - 16 q^{97} + 72 q^{98}+O(q^{100}) $ 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9 + 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 24 * q^20 - 16 * q^21 - 8 * q^22 + 8 * q^24 + 16 * q^25 - 16 * q^26 + 40 * q^28 + 56 * q^30 + 32 * q^32 + 56 * q^34 + 56 * q^36 - 16 * q^37 + 32 * q^38 + 56 * q^40 - 48 * q^41 + 40 * q^42 + 24 * q^44 - 64 * q^45 + 8 * q^46 - 32 * q^48 - 16 * q^49 - 16 * q^52 + 48 * q^53 - 24 * q^54 - 48 * q^56 + 64 * q^57 - 64 * q^58 - 112 * q^60 + 16 * q^61 - 64 * q^62 - 56 * q^64 + 96 * q^65 - 96 * q^66 - 32 * q^68 + 32 * q^69 - 80 * q^70 - 64 * q^72 + 64 * q^73 - 16 * q^74 - 64 * q^76 + 16 * q^77 - 112 * q^78 - 24 * q^80 + 64 * q^81 - 40 * q^82 - 80 * q^85 + 64 * q^86 + 56 * q^88 - 16 * q^89 + 48 * q^90 + 104 * q^92 - 16 * q^93 + 88 * q^94 + 144 * q^96 - 16 * q^97 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/68\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{7}{16}\right)$

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 $

$2$	0.114599	+	1.40956i	0.0810336	+	0.996711i
$2$	0.114599	+	1.40956i	0.0810336	+	0.996711i
$3$	0.935416	−	0.186066i	0.540063	−	0.107425i	0.0824809	−	0.996593i	$-0.473716\pi$
$3$	0.935416	−	0.186066i	0.540063	−	0.107425i	0.457582	+	0.889167i	$0.348716\pi$
$4$	−1.97373	+	0.323068i	−0.986867	+	0.161534i
$5$	0.763429	+	0.510107i	0.341416	+	0.228127i	0.714443	−	0.699694i	$-0.246680\pi$
$5$	0.763429	+	0.510107i	0.341416	+	0.228127i	−0.373027	+	0.927820i	$0.621680\pi$
$6$	0.369469	+	1.29720i	0.150835	+	0.529582i
$7$	−0.225807	−	0.337944i	−0.0853469	−	0.127731i	0.786340	−	0.617794i	$-0.211974\pi$
$7$	−0.225807	−	0.337944i	−0.0853469	−	0.127731i	−0.871687	+	0.490064i	$0.836974\pi$
$8$	−0.681573	−	2.74508i	−0.240972	−	0.970532i
$9$	−1.93126	+	0.799952i	−0.643752	+	0.266651i
$10$	−0.631540	+	1.13456i	−0.199710	+	0.358779i
$11$	0.892912	−	4.48897i	0.269223	−	1.35348i	−0.575294	−	0.817947i	$-0.695112\pi$
$11$	0.892912	−	4.48897i	0.269223	−	1.35348i	0.844517	−	0.535529i	$-0.179888\pi$
$12$	−1.78615	+	0.669448i	−0.515617	+	0.193253i
$13$	−1.21544	+	1.21544i	−0.337103	+	0.337103i	−0.855276	−	0.518173i	$-0.826612\pi$
$13$	−1.21544	+	1.21544i	−0.337103	+	0.337103i	0.518173	+	0.855276i	$0.326612\pi$
$14$	0.450476	−	0.357017i	0.120395	−	0.0954168i
$15$	0.809037	+	0.335114i	0.208893	+	0.0865261i
$16$	3.79125	−	1.27530i	0.947813	−	0.318826i
$17$	2.80335	−	3.02345i	0.679912	−	0.733294i
$17$	2.80335	−	3.02345i	0.679912	−	0.733294i
$18$	−1.34890	−	2.63055i	−0.317939	−	0.620027i
$19$	−1.29031	+	3.11507i	−0.296016	+	0.714647i	0.703974	+	0.710226i	$0.251407\pi$
$19$	−1.29031	+	3.11507i	−0.296016	+	0.714647i	−0.999990	+	0.00442090i	$0.998593\pi$
$20$	−1.67161	−	0.760176i	−0.373782	−	0.169980i
$21$	−0.274103	−	0.274103i	−0.0598142	−	0.0598142i
$22$	6.42981	+	0.744184i	1.37084	+	0.158661i
$23$	−1.22170	−	0.243011i	−0.254742	−	0.0506713i	0.0660673	−	0.997815i	$-0.478955\pi$
$23$	−1.22170	−	0.243011i	−0.254742	−	0.0506713i	−0.320809	+	0.947144i	$0.603955\pi$
$24$	−1.14832	−	2.44097i	−0.234400	−	0.498262i
$25$	−1.59080	−	3.84054i	−0.318161	−	0.768107i
$26$	−1.85253	−	1.57395i	−0.363311	−	0.308677i
$27$	−4.03671	+	2.69724i	−0.776865	+	0.519084i
$28$	0.554862	+	0.594060i	0.104859	+	0.112267i
$29$	−3.14845	+	4.71199i	−0.584653	+	0.874995i	−0.999389	−	0.0349470i	$-0.988874\pi$
$29$	−3.14845	+	4.71199i	−0.584653	+	0.874995i	0.414737	+	0.909942i	$0.363874\pi$
$30$	−0.379650	+	1.17879i	−0.0693143	+	0.215217i
$31$	1.67369	+	8.41419i	0.300603	+	1.51123i	0.775588	+	0.631239i	$0.217453\pi$
$31$	1.67369	+	8.41419i	0.300603	+	1.51123i	−0.474985	+	0.879994i	$0.657547\pi$
$32$	2.23209	+	5.19786i	0.394582	+	0.918861i
$33$		−	4.36520i		−	0.759883i
$34$	4.58300	+	3.60501i	0.785978	+	0.618254i
$35$		−	0.373182i		−	0.0630792i
$36$	3.55335	−	2.20282i	0.592224	−	0.367137i
$37$	1.30555	+	6.56346i	0.214632	+	1.07903i	0.926380	+	0.376591i	$0.122904\pi$
$37$	1.30555	+	6.56346i	0.214632	+	1.07903i	−0.711748	+	0.702435i	$0.752096\pi$
$38$	−4.53876	−	1.46178i	−0.736284	−	0.237133i
$39$	−0.910791	+	1.36310i	−0.145843	+	0.218270i
$40$	0.879951	−	2.44335i	0.139133	−	0.386327i
$41$	1.11203	−	0.743033i	0.173670	−	0.116042i	−0.465697	−	0.884944i	$-0.654196\pi$
$41$	1.11203	−	0.743033i	0.173670	−	0.116042i	0.639367	+	0.768902i	$0.279196\pi$
$42$	0.354954	−	0.417777i	0.0547705	−	0.0644645i
$43$	2.03481	+	4.91247i	0.310306	+	0.749145i	0.999694	+	0.0247525i	$0.00787977\pi$
$43$	2.03481	+	4.91247i	0.310306	+	0.749145i	−0.689387	+	0.724393i	$0.742120\pi$
$44$	−0.312126	+	9.14851i	−0.0470547	+	1.37919i
$45$	−1.88244	−	0.374440i	−0.280617	−	0.0558182i
$46$	0.202534	−	1.74991i	0.0298620	−	0.258010i
$47$	−9.03666	−	9.03666i	−1.31813	−	1.31813i	−0.915253	−	0.402879i	$-0.868010\pi$
$47$	−9.03666	−	9.03666i	−1.31813	−	1.31813i	−0.402879	−	0.915253i	$-0.631990\pi$
$48$	3.30911	−	1.89836i	0.477629	−	0.274005i
$49$	2.61557	−	6.31454i	0.373652	−	0.902077i
$50$	5.23117	−	2.68246i	0.739800	−	0.379357i
$51$	2.05974	−	3.34979i	0.288421	−	0.469064i
$52$	2.00629	−	2.79163i	0.278222	−	0.387129i
$53$	2.36069	+	0.977830i	0.324266	+	0.134315i	0.538877	−	0.842384i	$-0.318849\pi$
$53$	2.36069	+	0.977830i	0.324266	+	0.134315i	−0.214612	+	0.976699i	$0.568849\pi$
$54$	−4.26453	−	5.38089i	−0.580329	−	0.732247i
$55$	2.97153	−	2.97153i	0.400681	−	0.400681i
$56$	−0.773779	+	0.850191i	−0.103401	+	0.113612i
$57$	−0.627364	+	3.15397i	−0.0830964	+	0.417754i
$58$	−7.00265	−	3.89795i	−0.919494	−	0.511826i
$59$	11.1640	−	4.62429i	1.45343	−	0.602032i	0.490420	−	0.871486i	$-0.336844\pi$
$59$	11.1640	−	4.62429i	1.45343	−	0.602032i	0.963013	+	0.269455i	$0.0868435\pi$
$60$	−1.70509	−	0.400052i	−0.220126	−	0.0516465i
$61$	2.41467	+	3.61380i	0.309166	+	0.462700i	0.953219	−	0.302281i	$-0.0977482\pi$
$61$	2.41467	+	3.61380i	0.309166	+	0.462700i	−0.644052	+	0.764981i	$0.722748\pi$
$62$	−11.6685	+	3.32342i	−1.48190	+	0.422075i
$63$	0.706429	+	0.472021i	0.0890018	+	0.0594691i
$64$	−7.07092	+	3.74194i	−0.883865	+	0.467743i
$65$	−1.54791	+	0.307898i	−0.191994	+	0.0381900i
$66$	6.15302	−	0.500246i	0.757384	−	0.0615761i
$67$	−8.38234			−1.02407			−0.512033	−	0.858966i	$-0.671107\pi$
$67$	−8.38234			−1.02407			−0.512033	+	0.858966i	$0.671107\pi$
$68$	−4.55628	+	6.87316i	−0.552531	+	0.833493i
$69$	−1.18801			−0.143020
$70$	0.526023	−	0.0427662i	0.0628718	−	0.00511154i
$71$	13.3275	−	2.65100i	1.58168	−	0.314615i	0.675451	−	0.737405i	$-0.263949\pi$
$71$	13.3275	−	2.65100i	1.58168	−	0.314615i	0.906228	+	0.422789i	$0.138949\pi$
$72$	3.51222	+	4.75622i	0.413919	+	0.560526i
$73$	−5.16828	−	3.45333i	−0.604902	−	0.404182i	0.215060	−	0.976601i	$-0.431005\pi$
$73$	−5.16828	−	3.45333i	−0.604902	−	0.404182i	−0.819962	+	0.572419i	$0.806005\pi$
$74$	−9.10200	+	2.59242i	−1.05809	+	0.301363i
$75$	−2.20266	−	3.29651i	−0.254341	−	0.380648i
$76$	1.54034	−	6.56518i	0.176689	−	0.753078i
$77$	−1.71864	+	0.711886i	−0.195858	+	0.0811269i
$78$	−2.02574	−	1.12761i	−0.229370	−	0.127677i
$79$	1.81098	−	9.10440i	0.203751	−	1.02433i	−0.734563	−	0.678540i	$-0.762613\pi$
$79$	1.81098	−	9.10440i	0.203751	−	1.02433i	0.938314	−	0.345785i	$-0.112387\pi$
$80$	3.54489	+	0.960342i	0.396331	+	0.107369i
$81$	1.16022	−	1.16022i	0.128913	−	0.128913i
$82$	1.17479	+	1.48232i	0.129734	+	0.163695i
$83$	−3.70474	−	1.53455i	−0.406648	−	0.168439i	0.169977	−	0.985448i	$-0.445631\pi$
$83$	−3.70474	−	1.53455i	−0.406648	−	0.168439i	−0.576625	+	0.817009i	$0.695631\pi$
$84$	0.629561	+	0.452453i	0.0686907	+	0.0493666i
$85$	3.68244	−	0.878180i	0.399417	−	0.0952520i
$86$	−6.69125	+	3.43116i	−0.721536	+	0.369992i
$87$	−2.06837	+	4.99349i	−0.221753	+	0.535358i
$88$	−12.9312	+	0.608447i	−1.37847	+	0.0648607i
$89$	6.88729	+	6.88729i	0.730051	+	0.730051i	0.970630	−	0.240578i	$-0.0773371\pi$
$89$	6.88729	+	6.88729i	0.730051	+	0.730051i	−0.240578	+	0.970630i	$0.577337\pi$
$90$	0.312072	−	2.69632i	0.0328952	−	0.284218i
$91$	0.685206	+	0.136296i	0.0718291	+	0.0142877i
$92$	2.48982	+	0.0849468i	0.259581	+	0.00885632i
$93$	3.13119	+	7.55935i	0.324689	+	0.783868i
$94$	11.7021	−	13.7733i	1.20698	−	1.42061i
$95$	−2.57408	+	1.71994i	−0.264095	+	0.176462i
$96$	3.05508	+	4.44685i	0.311808	+	0.453855i
$97$	4.91684	−	7.35857i	0.499230	−	0.747150i	−0.493206	−	0.869912i	$-0.664175\pi$
$97$	4.91684	−	7.35857i	0.499230	−	0.747150i	0.992436	+	0.122762i	$0.0391753\pi$
$98$	9.20048	+	2.96317i	0.929388	+	0.299325i
$99$	1.86652	+	9.38364i	0.187592	+	0.943091i
$100$	4.38058	+	7.06626i	0.438058	+	0.706626i
$101$		−	6.84404i		−	0.681007i	−0.940243	−	0.340504i	$-0.889402\pi$
$101$		−	6.84404i		−	0.681007i	0.940243	−	0.340504i	$-0.110598\pi$
$102$	4.95778	+	2.51945i	0.490894	+	0.249462i
$103$			0.284275i			0.0280104i	0.999902	+	0.0140052i	$0.00445815\pi$
$103$			0.284275i			0.0280104i	−0.999902	+	0.0140052i	$0.995542\pi$
$104$	4.16489	+	2.50807i	0.408401	+	0.245937i
$105$	−0.0694364	−	0.349080i	−0.00677630	−	0.0340667i
$106$	−1.10778	+	3.43960i	−0.107597	+	0.334083i
$107$	−7.64175	+	11.4367i	−0.738756	+	1.10563i	0.251701	+	0.967805i	$0.419010\pi$
$107$	−7.64175	+	11.4367i	−0.738756	+	1.10563i	−0.990457	+	0.137821i	$0.955990\pi$
$108$	7.09599	−	6.62777i	0.682812	−	0.637757i
$109$	−13.9748	+	9.33769i	−1.33855	+	0.894389i	−0.998933	−	0.0461763i	$-0.985296\pi$
$109$	−13.9748	+	9.33769i	−1.33855	+	0.894389i	−0.339614	+	0.940565i	$0.610296\pi$
$110$	4.52909	+	3.84802i	0.431832	+	0.366895i
$111$	2.44247	+	5.89665i	0.231829	+	0.559685i
$112$	−1.28707	−	0.993259i	−0.121617	−	0.0938541i
$113$	5.17999	+	1.03036i	0.487292	+	0.0969285i	0.432621	−	0.901576i	$-0.357589\pi$
$113$	5.17999	+	1.03036i	0.487292	+	0.0969285i	0.0546714	+	0.998504i	$0.482589\pi$
$114$	−4.51762	−	0.522868i	−0.423114	−	0.0489710i
$115$	−0.808719	−	0.808719i	−0.0754134	−	0.0754134i
$116$	4.69191	−	10.3174i	0.435633	−	0.957945i
$117$	1.37503	−	3.31962i	0.127122	−	0.306899i
$118$	7.79761	+	15.2065i	0.717829	+	1.39987i
$119$	−1.65477	−	0.264659i	−0.151693	−	0.0242612i
$120$	0.368497	−	2.44928i	0.0336390	−	0.223587i
$121$	−9.19089	−	3.80699i	−0.835535	−	0.346090i
$122$	−4.81716	+	3.81776i	−0.436126	+	0.345644i
$123$	0.901956	−	0.901956i	0.0813266	−	0.0813266i
$124$	−6.02177	−	16.0667i	−0.540771	−	1.44283i
$125$	1.64025	−	8.24609i	0.146708	−	0.737552i
$126$	−0.584387	+	1.04985i	−0.0520614	+	0.0935280i
$127$	−7.85185	+	3.25234i	−0.696739	+	0.288599i	−0.702805	−	0.711383i	$-0.748069\pi$
$127$	−7.85185	+	3.25234i	−0.696739	+	0.288599i	0.00606555	+	0.999982i	$0.498069\pi$
$128$	−6.08482	−	9.53808i	−0.537827	−	0.843055i
$129$	2.81744	+	4.21660i	0.248062	+	0.371251i
$130$	−0.611390	−	2.14659i	−0.0536224	−	0.188268i
$131$	−2.69398	−	1.80006i	−0.235374	−	0.157272i	0.432290	−	0.901735i	$-0.357706\pi$
$131$	−2.69398	−	1.80006i	−0.235374	−	0.157272i	−0.667664	+	0.744463i	$0.732706\pi$
$132$	1.41026	+	8.61574i	0.122747	+	0.749904i
$133$	1.34408	−	0.267354i	0.116546	−	0.0231825i
$134$	−0.960606	−	11.8154i	−0.0829837	−	1.02070i
$135$	−4.45762			−0.383651
$136$	−10.2103	−	5.63471i	−0.875525	−	0.483173i
$137$	−8.43609			−0.720744			−0.360372	−	0.932809i	$-0.617350\pi$
$137$	−8.43609			−0.720744			−0.360372	+	0.932809i	$0.617350\pi$
$138$	−0.136145	−	1.67458i	−0.0115894	−	0.142550i
$139$	10.0965	−	2.00832i	0.856377	−	0.170344i	0.252672	−	0.967552i	$-0.418691\pi$
$139$	10.0965	−	2.00832i	0.856377	−	0.170344i	0.603705	+	0.797208i	$0.293691\pi$
$140$	0.120563	+	0.736561i	0.0101895	+	0.0622508i
$141$	−10.1345	−	6.77162i	−0.853475	−	0.570274i
$142$	5.26406	+	18.4821i	0.441750	+	1.55098i
$143$	4.37080	+	6.54136i	0.365504	+	0.547016i
$144$	−6.30170	+	5.49576i	−0.525142	+	0.457980i
$145$	−4.80724	+	1.99122i	−0.399219	+	0.165362i
$146$	4.27541	−	7.68076i	0.353836	−	0.635665i
$147$	1.27172	−	6.39339i	0.104890	−	0.527318i
$148$	−4.69726	−	12.5327i	−0.386113	−	1.03019i
$149$	7.60542	−	7.60542i	0.623060	−	0.623060i	−0.323253	−	0.946313i	$-0.604776\pi$
$149$	7.60542	−	7.60542i	0.623060	−	0.623060i	0.946313	+	0.323253i	$0.104776\pi$
$150$	4.39421	−	3.48256i	0.358786	−	0.284350i
$151$	−11.0709	−	4.58573i	−0.900940	−	0.373182i	−0.116359	−	0.993207i	$-0.537122\pi$
$151$	−11.0709	−	4.58573i	−0.900940	−	0.373182i	−0.784582	+	0.620026i	$0.787122\pi$
$152$	9.43056	+	1.41884i	0.764919	+	0.115083i
$153$	−2.99537	+	8.08160i	−0.242161	+	0.653358i
$154$	−1.20040	−	2.34096i	−0.0967312	−	0.188640i
$155$	−3.01440	+	7.27739i	−0.242122	+	0.584534i
$156$	1.35729	−	2.98464i	0.108670	−	0.238962i
$157$	−2.70792	−	2.70792i	−0.216116	−	0.216116i	0.590744	−	0.806859i	$-0.298834\pi$
$157$	−2.70792	−	2.70792i	−0.216116	−	0.216116i	−0.806859	+	0.590744i	$0.798834\pi$
$158$	13.0408	+	1.50933i	1.03747	+	0.120076i
$159$	2.39017	+	0.475434i	0.189553	+	0.0377044i
$160$	−0.947421	+	5.10680i	−0.0749002	+	0.403728i
$161$	0.193744	+	0.467739i	0.0152692	+	0.0368630i
$162$	1.76836	+	1.50244i	0.138936	+	0.118043i
$163$	10.0958	−	6.74581i	0.790766	−	0.528373i	−0.0933542	−	0.995633i	$-0.529759\pi$
$163$	10.0958	−	6.74581i	0.790766	−	0.528373i	0.884120	+	0.467260i	$0.154759\pi$
$164$	−1.95480	+	1.82581i	−0.152644	+	0.142572i
$165$	2.22672	−	3.33252i	0.173350	−	0.259436i
$166$	1.73849	−	5.39792i	0.134933	−	0.418960i
$167$	−0.797843	−	4.01103i	−0.0617390	−	0.310383i	0.937560	−	0.347824i	$-0.113079\pi$
$167$	−0.797843	−	4.01103i	−0.0617390	−	0.310383i	−0.999299	+	0.0374412i	$0.988079\pi$
$168$	−0.565614	+	0.939256i	−0.0436380	+	0.0724652i
$169$			10.0454i			0.772724i
$170$	1.65985	+	5.08999i	0.127305	+	0.390384i
$171$		−	7.04819i		−	0.538988i
$172$	−5.60325	−	9.03853i	−0.427244	−	0.689182i
$173$	1.08850	+	5.47224i	0.0827568	+	0.416047i	0.999849	+	0.0173716i	$0.00552983\pi$
$173$	1.08850	+	5.47224i	0.0827568	+	0.416047i	−0.917092	+	0.398675i	$0.869470\pi$
$174$	−7.27567	−	2.34325i	−0.551567	−	0.177641i
$175$	−0.938671	+	1.40482i	−0.0709569	+	0.106194i
$176$	−2.33954	−	18.1576i	−0.176349	−	1.36868i
$177$	9.58259	−	6.40288i	0.720272	−	0.481270i
$178$	−8.91879	+	10.4973i	−0.668492	+	0.786809i
$179$	2.50373	+	6.04454i	0.187138	+	0.451790i	0.989406	−	0.145173i	$-0.0463739\pi$
$179$	2.50373	+	6.04454i	0.187138	+	0.451790i	−0.802269	+	0.596963i	$0.796374\pi$
$180$	3.83640	+	0.130889i	0.285948	+	0.00975590i
$181$	17.8909	+	3.55872i	1.32982	+	0.264517i	0.808324	−	0.588738i	$-0.200375\pi$
$181$	17.8909	+	3.55872i	1.32982	+	0.264517i	0.521494	+	0.853255i	$0.325375\pi$
$182$	−0.113594	+	0.981460i	−0.00842014	+	0.0727506i
$183$	2.93112	+	2.93112i	0.216675	+	0.216675i
$184$	0.165592	+	3.51929i	0.0122076	+	0.259445i
$185$	−2.35137	+	5.67671i	−0.172876	+	0.417360i
$186$	−10.2966	+	5.27990i	−0.754980	+	0.387141i
$187$	−11.0690	−	15.2838i	−0.809447	−	1.11766i
$188$	20.7554	+	14.9165i	1.51374	+	1.08790i
$189$	1.82303	+	0.755124i	0.132606	+	0.0549272i
$190$	−2.71935	−	3.43122i	−0.197283	−	0.248927i
$191$	6.75213	−	6.75213i	0.488567	−	0.488567i	−0.419287	−	0.907854i	$-0.637720\pi$
$191$	6.75213	−	6.75213i	0.488567	−	0.488567i	0.907854	+	0.419287i	$0.137720\pi$
$192$	−5.91800	+	4.81593i	−0.427095	+	0.347560i
$193$	−1.86434	+	9.37269i	−0.134198	+	0.674661i	0.853850	+	0.520519i	$0.174261\pi$
$193$	−1.86434	+	9.37269i	−0.134198	+	0.674661i	−0.988049	+	0.154142i	$0.950739\pi$
$194$	10.9358	+	6.08731i	0.785147	+	0.437044i
$195$	−1.39065	+	0.576026i	−0.0995864	+	0.0412501i
$196$	−3.12241	+	13.3082i	−0.223029	+	0.950587i
$197$	−10.3618	−	15.5076i	−0.738251	−	1.10487i	−0.990541	−	0.137219i	$-0.956184\pi$
$197$	−10.3618	−	15.5076i	−0.738251	−	1.10487i	0.252290	−	0.967652i	$-0.418816\pi$
$198$	−13.0129	+	3.70633i	−0.924788	+	0.263398i
$199$	7.79360	+	5.20752i	0.552474	+	0.369151i	0.800250	−	0.599666i	$-0.204700\pi$
$199$	7.79360	+	5.20752i	0.552474	+	0.369151i	−0.247777	+	0.968817i	$0.579700\pi$
$200$	−9.45833	+	6.98448i	−0.668805	+	0.493878i
$201$	−7.84098	+	1.55967i	−0.553060	+	0.110010i
$202$	9.64710	−	0.784319i	0.678768	−	0.0551845i
$203$	2.30333			0.161662
$204$	−2.98316	+	7.27703i	−0.208863	+	0.509494i
$205$	1.22798			0.0857659
$206$	−0.400703	+	0.0325776i	−0.0279183	+	0.00226979i
$207$	2.55381	−	0.507984i	0.177502	−	0.0353074i
$208$	−3.05799	+	6.15810i	−0.212033	+	0.426987i
$209$	12.8313	+	8.57363i	0.887562	+	0.593050i
$210$	0.484093	−	0.137879i	0.0334056	−	0.00951456i
$211$	8.84331	+	13.2350i	0.608799	+	0.911132i	0.999958	−	0.00919145i	$-0.00292577\pi$
$211$	8.84331	+	13.2350i	0.608799	+	0.911132i	−0.391159	+	0.920323i	$0.627926\pi$
$212$	−4.97528	−	1.16731i	−0.341704	−	0.0801713i
$213$	11.9735	−	4.95957i	0.820408	−	0.339824i
$214$	−16.9965	−	9.46090i	−1.16185	−	0.646734i
$215$	−0.952452	+	4.78830i	−0.0649567	+	0.326559i
$216$	10.1555	+	9.24271i	0.690991	+	0.628887i
$217$	2.46559	−	2.46559i	0.167375	−	0.167375i
$218$	−14.7636	−	18.6283i	−0.999915	−	1.26167i
$219$	−5.47704	−	2.26867i	−0.370104	−	0.153302i
$220$	−4.90500	+	6.82502i	−0.330695	+	0.460142i
$221$	0.267518	+	7.08213i	0.0179952	+	0.476395i
$222$	−8.03179	+	4.11857i	−0.539059	+	0.276420i
$223$	6.11461	−	14.7620i	0.409464	−	0.988534i	−0.575815	−	0.817580i	$-0.695315\pi$
$223$	6.11461	−	14.7620i	0.409464	−	0.988534i	0.985279	−	0.170954i	$-0.0546850\pi$
$224$	1.25256	−	1.92803i	0.0836904	−	0.128822i
$225$	6.14449	+	6.14449i	0.409633	+	0.409633i
$226$	−0.858742	+	7.41960i	−0.0571227	+	0.493544i
$227$	−5.72927	−	1.13962i	−0.380265	−	0.0756394i	0.00125698	−	0.999999i	$-0.499600\pi$
$227$	−5.72927	−	1.13962i	−0.380265	−	0.0756394i	−0.381522	+	0.924360i	$0.624600\pi$
$228$	0.219301	−	6.42778i	0.0145236	−	0.425690i
$229$	−3.41246	−	8.23841i	−0.225502	−	0.544409i	0.770118	−	0.637901i	$-0.220197\pi$
$229$	−3.41246	−	8.23841i	−0.225502	−	0.544409i	−0.995620	+	0.0934918i	$0.970197\pi$
$230$	1.04726	−	1.23262i	0.0690544	−	0.0812764i
$231$	−1.47519	+	0.985691i	−0.0970604	+	0.0648537i
$232$	15.0807	+	5.43118i	0.990095	+	0.356575i
$233$	−7.13584	+	10.6795i	−0.467484	+	0.699640i	−0.988042	−	0.154187i	$-0.950724\pi$
$233$	−7.13584	+	10.6795i	−0.467484	+	0.699640i	0.520557	+	0.853827i	$0.325724\pi$
$234$	4.83679	+	1.55777i	0.316191	+	0.101835i
$235$	−2.28918	−	11.5085i	−0.149330	−	0.750732i
$236$	−20.5409	+	12.7339i	−1.33710	+	0.828904i
$237$		−	8.85337i		−	0.575088i
$238$	0.183419	−	2.36283i	0.0118893	−	0.153160i
$239$			19.5305i			1.26332i	0.775244	+	0.631662i	$0.217627\pi$
$239$			19.5305i			1.26332i	−0.775244	+	0.631662i	$0.782373\pi$
$240$	3.49464	+	0.238736i	0.225578	+	0.0154103i
$241$	−1.27829	−	6.42638i	−0.0823417	−	0.413960i	−0.999867	−	0.0162832i	$-0.994817\pi$
$241$	−1.27829	−	6.42638i	−0.0823417	−	0.413960i	0.917526	−	0.397676i	$-0.130183\pi$
$242$	4.31293	−	13.3914i	0.277245	−	0.860832i
$243$	8.96114	−	13.4113i	0.574857	−	0.860334i
$244$	−5.93342	−	6.35258i	−0.379848	−	0.406683i
$245$	5.21789	−	3.48648i	0.333359	−	0.222743i
$246$	1.37473	+	1.16800i	0.0876493	+	0.0744690i
$247$	−2.21790	−	5.35448i	−0.141121	−	0.340697i
$248$	21.9569	−	10.3293i	1.39426	−	0.655910i
$249$	−3.75100	−	0.746120i	−0.237710	−	0.0472835i
$250$	11.8113	+	1.36704i	0.747015	+	0.0864593i
$251$	2.67687	+	2.67687i	0.168963	+	0.168963i	0.786523	−	0.617561i	$-0.211879\pi$
$251$	2.67687	+	2.67687i	0.168963	+	0.168963i	−0.617561	+	0.786523i	$0.711879\pi$
$252$	−1.54680	−	0.703419i	−0.0974392	−	0.0443112i
$253$	−2.18174	+	5.26718i	−0.137165	+	0.331145i
$254$	−5.48420	−	10.6950i	−0.344109	−	0.671062i
$255$	3.28121	−	1.50664i	0.205478	−	0.0943495i
$256$	12.7472	−	9.66999i	0.796700	−	0.604374i
$257$	−4.20491	−	1.74173i	−0.262295	−	0.108646i	0.247661	−	0.968847i	$-0.420338\pi$
$257$	−4.20491	−	1.74173i	−0.262295	−	0.108646i	−0.509956	+	0.860201i	$0.670338\pi$
$258$	−5.62069	+	4.45458i	−0.349929	+	0.277330i
$259$	1.92328	−	1.92328i	0.119507	−	0.119507i
$260$	2.95569	−	1.10779i	0.183304	−	0.0687022i
$261$	2.31110	−	11.6187i	0.143053	−	0.719177i
$262$	2.22857	−	4.00361i	0.137681	−	0.247344i
$263$	−0.848600	+	0.351502i	−0.0523269	+	0.0216745i	−0.408693	−	0.912672i	$-0.634015\pi$
$263$	−0.848600	+	0.351502i	−0.0523269	+	0.0216745i	0.356366	+	0.934346i	$0.384015\pi$
$264$	−11.9828	+	2.97520i	−0.737491	+	0.183111i
$265$	1.30342	+	1.95071i	0.0800685	+	0.119831i
$266$	0.530882	+	1.86393i	0.0325505	+	0.114285i
$267$	7.72397	+	5.16099i	0.472699	+	0.315848i
$268$	16.5445	−	2.70807i	1.01062	−	0.165422i
$269$	−15.2617	+	3.03575i	−0.930525	+	0.185093i	−0.637005	−	0.770860i	$-0.719827\pi$
$269$	−15.2617	+	3.03575i	−0.930525	+	0.185093i	−0.293520	+	0.955953i	$0.594827\pi$
$270$	−0.510838	−	6.28330i	−0.0310886	−	0.382389i
$271$	−18.0694			−1.09764			−0.548818	−	0.835942i	$-0.684922\pi$
$271$	−18.0694			−1.09764			−0.548818	+	0.835942i	$0.684922\pi$
$272$	6.77239	−	15.0378i	0.410637	−	0.911799i
$273$	0.666313			0.0403271
$274$	−0.966766	−	11.8912i	−0.0584045	−	0.718374i
$275$	−18.6605	+	3.71180i	−1.12527	+	0.223830i
$276$	2.34482	−	0.383809i	0.141142	−	0.0231026i
$277$	10.8598	+	7.25627i	0.652501	+	0.435987i	0.837266	−	0.546795i	$-0.184152\pi$
$277$	10.8598	+	7.25627i	0.652501	+	0.435987i	−0.184765	+	0.982783i	$0.559152\pi$
$278$	3.98791	+	14.0015i	0.239179	+	0.839757i
$279$	−9.96326	−	14.9111i	−0.596485	−	0.892703i
$280$	−1.02441	+	0.254350i	−0.0612204	+	0.0152003i
$281$	−23.5059	+	9.73646i	−1.40224	+	0.580828i	−0.950333	−	0.311235i	$-0.899257\pi$
$281$	−23.5059	+	9.73646i	−1.40224	+	0.580828i	−0.451911	+	0.892063i	$0.649257\pi$
$282$	8.38363	−	15.0612i	0.499238	−	0.896879i
$283$	−5.93767	+	29.8507i	−0.352958	+	1.77444i	0.241589	+	0.970379i	$0.422331\pi$
$283$	−5.93767	+	29.8507i	−0.352958	+	1.77444i	−0.594547	+	0.804061i	$0.702669\pi$
$284$	−25.4484	+	9.53805i	−1.51009	+	0.565979i
$285$	−2.08781	+	2.08781i	−0.123671	+	0.123671i
$286$	−8.71957	+	6.91055i	−0.515599	+	0.408629i
$287$	−0.502207	−	0.208021i	−0.0296443	−	0.0122791i
$288$	−8.46878	−	8.25283i	−0.499028	−	0.486303i
$289$	−1.28248	−	16.9516i	−0.0754398	−	0.997150i
$290$	−3.35766	−	6.54791i	−0.197168	−	0.384507i
$291$	3.23011	−	7.79819i	0.189353	−	0.457138i
$292$	11.3165	+	5.14626i	0.662247	+	0.301162i
$293$	−22.9097	−	22.9097i	−1.33840	−	1.33840i	−0.897614	−	0.440782i	$-0.854701\pi$
$293$	−22.9097	−	22.9097i	−1.33840	−	1.33840i	−0.440782	−	0.897614i	$-0.645299\pi$
$294$	9.15762	+	1.05990i	0.534083	+	0.0618146i
$295$	10.8818	+	2.16453i	0.633564	+	0.126024i
$296$	17.1274	−	8.05732i	0.995509	−	0.468322i
$297$	8.50341	+	20.5291i	0.493418	+	1.19122i
$298$	11.5919	+	9.84874i	0.671500	+	0.570522i
$299$	1.78027	−	1.18954i	0.102956	−	0.0687927i
$300$	5.41245	+	5.79482i	0.312488	+	0.334564i
$301$	1.20067	−	1.79692i	0.0692052	−	0.103573i
$302$	5.19516	−	16.1307i	0.298948	−	0.928218i
$303$	−1.27344	−	6.40202i	−0.0731573	−	0.367787i
$304$	−0.919215	+	13.4556i	−0.0527206	+	0.771729i
$305$			3.99062i			0.228502i
$306$	−11.7348	−	3.29602i	−0.670833	−	0.188421i
$307$			1.89027i			0.107883i	0.998544	+	0.0539417i	$0.0171785\pi$
$307$			1.89027i			0.107883i	−0.998544	+	0.0539417i	$0.982821\pi$
$308$	3.16216	−	1.96031i	0.180181	−	0.111699i
$309$	0.0528939	+	0.265915i	0.00300903	+	0.0151274i
$310$	−10.6034	−	3.41500i	−0.602232	−	0.193959i
$311$	−8.66570	+	12.9691i	−0.491387	+	0.735413i	−0.991437	−	0.130584i	$-0.958315\pi$
$311$	−8.66570	+	12.9691i	−0.491387	+	0.735413i	0.500050	+	0.865996i	$0.333315\pi$
$312$	4.36258	+	1.57115i	0.246982	+	0.0889486i
$313$	13.2017	−	8.82111i	0.746206	−	0.498599i	−0.123393	−	0.992358i	$-0.539378\pi$
$313$	13.2017	−	8.82111i	0.746206	−	0.498599i	0.869599	+	0.493759i	$0.164378\pi$
$314$	3.50666	−	4.12731i	0.197892	−	0.232917i
$315$	0.298527	+	0.720709i	0.0168201	+	0.0406074i
$316$	−0.633044	+	18.5547i	−0.0356115	+	1.04379i
$317$	−15.6845	−	3.11985i	−0.880932	−	0.175228i	−0.266156	−	0.963930i	$-0.585754\pi$
$317$	−15.6845	−	3.11985i	−0.880932	−	0.175228i	−0.614776	+	0.788702i	$0.710754\pi$
$318$	−0.396244	+	3.42358i	−0.0222202	+	0.191985i
$319$	18.3407	+	18.3407i	1.02688	+	1.02688i
$320$	−7.30693	−	0.750216i	−0.408470	−	0.0419384i
$321$	−5.02024	+	12.1199i	−0.280203	+	0.676469i
$322$	−0.637105	+	0.326696i	−0.0355045	+	0.0182061i
$323$	5.80109	+	12.6338i	0.322781	+	0.702964i
$324$	−1.91514	+	2.66480i	−0.106396	+	0.148044i
$325$	6.60147	+	2.73442i	0.366184	+	0.151678i
$326$	10.6656	+	13.4576i	0.590714	+	0.745349i
$327$	−11.3349	+	11.3349i	−0.626820	+	0.626820i
$328$	−2.79761	−	2.54617i	−0.154472	−	0.140589i
$329$	−1.01334	+	5.09442i	−0.0558674	+	0.280865i
$330$	4.95257	+	2.75679i	0.272630	+	0.151757i
$331$	−20.9274	+	8.66841i	−1.15027	+	0.476459i	−0.874625	−	0.484799i	$-0.838893\pi$
$331$	−20.9274	+	8.66841i	−1.15027	+	0.476459i	−0.275649	+	0.961259i	$0.588893\pi$
$332$	7.80794	+	1.83192i	0.428516	+	0.100539i
$333$	−7.77181	−	11.6313i	−0.425893	−	0.637394i
$334$	5.56236	−	1.58427i	0.304359	−	0.0866874i
$335$	−6.39932	−	4.27589i	−0.349632	−	0.233617i
$336$	−1.38876	−	0.689630i	−0.0757630	−	0.0376224i
$337$	7.52435	−	1.49669i	0.409878	−	0.0815297i	0.0141550	−	0.999900i	$-0.495494\pi$
$337$	7.52435	−	1.49669i	0.409878	−	0.0815297i	0.395723	+	0.918370i	$0.370494\pi$
$338$	−14.1596	+	1.15119i	−0.770182	+	0.0626166i
$339$	5.03716			0.273581
$340$	−6.98444	+	2.92297i	−0.378785	+	0.158521i
$341$	39.2655			2.12635
$342$	9.93486	−	0.807714i	0.537216	−	0.0436762i
$343$	−5.51499	+	1.09700i	−0.297782	+	0.0592325i
$344$	12.0983	−	8.93393i	0.652294	−	0.481685i
$345$	−0.906963	−	0.606014i	−0.0488293	−	0.0326267i
$346$	−7.58872	+	2.16142i	−0.407972	+	0.116198i
$347$	5.34876	+	8.00499i	0.287137	+	0.429730i	0.946796	−	0.321835i	$-0.104299\pi$
$347$	5.34876	+	8.00499i	0.287137	+	0.429730i	−0.659659	+	0.751565i	$0.729299\pi$
$348$	2.46918	−	10.5241i	0.132362	−	0.564148i
$349$	20.0918	−	8.32229i	1.07549	−	0.445482i	0.226564	−	0.973996i	$-0.427251\pi$
$349$	20.0918	−	8.32229i	1.07549	−	0.445482i	0.848924	+	0.528514i	$0.177251\pi$
$350$	−2.08775	−	1.16213i	−0.111595	−	0.0621182i
$351$	1.62804	−	8.18472i	0.0868984	−	0.436868i
$352$	25.3261	−	5.37856i	1.34989	−	0.286678i
$353$	1.76014	−	1.76014i	0.0936828	−	0.0936828i	−0.658712	−	0.752395i	$-0.728899\pi$
$353$	1.76014	−	1.76014i	0.0936828	−	0.0936828i	0.752395	+	0.658712i	$0.228899\pi$
$354$	10.1234	+	12.7735i	0.538054	+	0.678904i
$355$	11.5269	+	4.77458i	0.611782	+	0.253409i
$356$	−15.8187	−	11.3686i	−0.838392	−	0.602535i
$357$	−1.59714	+	0.0603300i	−0.0845298	+	0.00319300i
$358$	−8.23323	+	4.22186i	−0.435140	+	0.223132i
$359$	0.686366	−	1.65703i	0.0362250	−	0.0874549i	−0.904732	−	0.425982i	$-0.859929\pi$
$359$	0.686366	−	1.65703i	0.0362250	−	0.0874549i	0.940957	+	0.338527i	$0.109929\pi$
$360$	0.255151	+	5.42265i	0.0134476	+	0.285799i
$361$	5.39624	+	5.39624i	0.284012	+	0.284012i
$362$	−2.96596	+	25.6261i	−0.155887	+	1.34688i
$363$	−9.30566	−	1.85101i	−0.488420	−	0.0971528i
$364$	−1.39645	−	0.0476435i	−0.0731937	−	0.00249720i
$365$	−2.18405	−	5.27275i	−0.114318	−	0.275988i
$366$	−3.79570	+	4.46751i	−0.198404	+	0.233520i
$367$	24.9067	−	16.6422i	1.30012	−	0.868713i	0.303661	−	0.952780i	$-0.401791\pi$
$367$	24.9067	−	16.6422i	1.30012	−	0.868713i	0.996460	+	0.0840669i	$0.0267909\pi$
$368$	−4.94168	+	0.636719i	−0.257603	+	0.0331913i
$369$	−1.55322	+	2.32456i	−0.0808573	+	0.121012i
$370$	−8.27114	−	2.66386i	−0.429996	−	0.138487i
$371$	−0.202608	−	1.01858i	−0.0105189	−	0.0528821i
$372$	−8.62232	−	13.9086i	−0.447046	−	0.721126i
$373$			9.74301i			0.504474i	0.967666	+	0.252237i	$0.0811662\pi$
$373$			9.74301i			0.504474i	−0.967666	+	0.252237i	$0.918834\pi$
$374$	20.2750	−	17.3540i	1.04840	−	0.897354i
$375$		−	8.01872i		−	0.414085i
$376$	−18.6472	+	30.9655i	−0.961656	+	1.59692i
$377$	−1.90039	−	9.55390i	−0.0978750	−	0.492051i
$378$	−0.855478	+	2.65621i	−0.0440010	+	0.136621i
$379$	14.0499	−	21.0271i	0.721693	−	1.08009i	−0.271366	−	0.962476i	$-0.587476\pi$
$379$	14.0499	−	21.0271i	0.721693	−	1.08009i	0.993059	−	0.117614i	$-0.0375245\pi$
$380$	4.52488	−	4.22631i	0.232122	−	0.216805i
$381$	−6.73960	+	4.50326i	−0.345280	+	0.230709i
$382$	10.2913	+	8.74377i	0.526551	+	0.447370i
$383$	−9.99151	−	24.1216i	−0.510543	−	1.23256i	−0.943569	−	0.331177i	$-0.892554\pi$
$383$	−9.99151	−	24.1216i	−0.510543	−	1.23256i	0.433026	−	0.901381i	$-0.357446\pi$
$384$	−7.46655	−	7.78990i	−0.381026	−	0.397526i
$385$	−1.67520	−	0.333218i	−0.0853762	−	0.0169824i
$386$	−13.4250	−	1.55381i	−0.683317	−	0.0790869i
$387$	−7.85949	−	7.85949i	−0.399520	−	0.399520i
$388$	−7.32722	+	16.1123i	−0.371983	+	0.817980i
$389$	−5.63360	+	13.6007i	−0.285635	+	0.689584i	−0.999948	−	0.0102429i	$-0.996740\pi$
$389$	−5.63360	+	13.6007i	−0.285635	+	0.689584i	0.714313	+	0.699827i	$0.246740\pi$
$390$	−0.971311	−	1.89419i	−0.0491842	−	0.0959163i
$391$	−4.15958	+	3.01250i	−0.210359	+	0.152349i
$392$	−19.1166	−	2.87612i	−0.965534	−	0.145266i
$393$	−2.85492	−	1.18255i	−0.144012	−	0.0596516i
$394$	20.6715	−	16.3828i	1.04141	−	0.825355i
$395$	6.02677	−	6.02677i	0.303240	−	0.303240i
$396$	−6.71557	−	17.9178i	−0.337470	−	0.900403i
$397$	−0.885181	+	4.45011i	−0.0444260	+	0.223344i	−0.996620	−	0.0821494i	$-0.973822\pi$
$397$	−0.885181	+	4.45011i	−0.0444260	+	0.223344i	0.952194	+	0.305494i	$0.0988215\pi$
$398$	−6.44719	+	11.5823i	−0.323168	+	0.580571i
$399$	1.20753	−	0.500175i	0.0604520	−	0.0250400i
$400$	−10.9290	−	12.5317i	−0.546449	−	0.626585i
$401$	8.28246	+	12.3956i	0.413606	+	0.619006i	0.978522	−	0.206143i	$-0.0660912\pi$
$401$	8.28246	+	12.3956i	0.413606	+	0.619006i	−0.564915	+	0.825149i	$0.691091\pi$
$402$	−3.09702	−	10.8736i	−0.154465	−	0.542327i
$403$	−12.2612	−	8.19268i	−0.610775	−	0.408107i
$404$	2.21109	+	13.5083i	0.110006	+	0.672064i
$405$	1.47758	−	0.293909i	0.0734216	−	0.0146045i
$406$	0.263959	+	3.24669i	0.0131001	+	0.161130i
$407$	30.6289			1.51822
$408$	−10.5993	−	3.37102i	−0.524743	−	0.166890i
$409$	−17.9088			−0.885532			−0.442766	−	0.896637i	$-0.646003\pi$
$409$	−17.9088			−0.885532			−0.442766	+	0.896637i	$0.646003\pi$
$410$	0.140725	+	1.73092i	0.00694992	+	0.0854838i
$411$	−7.89126	+	1.56967i	−0.389247	+	0.0774260i
$412$	−0.0918403	−	0.561083i	−0.00452465	−	0.0276426i
$413$	−4.08366	−	2.72862i	−0.200944	−	0.134266i
$414$	1.00870	+	3.54154i	0.0495749	+	0.174057i
$415$	−2.04552	−	3.06133i	−0.100411	−	0.150275i
$416$	−9.03067	−	3.60472i	−0.442765	−	0.176736i
$417$	9.07078	−	3.75724i	0.444198	−	0.183993i
$418$	−10.6146	+	19.0691i	−0.519178	+	0.932701i
$419$	0.580401	−	2.91787i	0.0283545	−	0.142548i	−0.964015	−	0.265848i	$-0.914348\pi$
$419$	0.580401	−	2.91787i	0.0283545	−	0.142548i	0.992369	+	0.123301i	$0.0393480\pi$
$420$	0.249826	+	0.666559i	0.0121902	+	0.0325247i
$421$	−23.4894	+	23.4894i	−1.14480	+	1.14480i	−0.157243	+	0.987560i	$0.550261\pi$
$421$	−23.4894	+	23.4894i	−1.14480	+	1.14480i	−0.987560	+	0.157243i	$0.949739\pi$
$422$	−17.6421	+	13.9819i	−0.858802	+	0.680629i
$423$	24.6810	+	10.2232i	1.20003	+	0.497069i
$424$	1.07524	−	7.14674i	0.0522182	−	0.347076i
$425$	−16.0712	−	5.95665i	−0.779570	−	0.288940i
$426$	8.36297	+	16.3090i	0.405187	+	0.790173i
$427$	0.676014	−	1.63204i	0.0327146	−	0.0789801i
$428$	11.3880	−	25.0418i	0.550457	−	1.21044i
$429$	5.30564	+	5.30564i	0.256159	+	0.256159i
$430$	−6.85855	−	0.793807i	−0.330749	−	0.0382808i
$431$	3.60329	+	0.716739i	0.173564	+	0.0345241i	0.281107	−	0.959676i	$-0.409298\pi$
$431$	3.60329	+	0.716739i	0.173564	+	0.0345241i	−0.107543	+	0.994200i	$0.534298\pi$
$432$	−11.8644	+	15.3739i	−0.570825	+	0.739679i
$433$	−7.48956	−	18.0814i	−0.359925	−	0.868937i	−0.995310	−	0.0967405i	$-0.969158\pi$
$433$	−7.48956	−	18.0814i	−0.359925	−	0.868937i	0.635384	−	0.772196i	$-0.280842\pi$
$434$	3.75796	+	3.19285i	0.180388	+	0.153262i
$435$	−4.12627	+	2.75708i	−0.197839	+	0.132192i
$436$	24.5659	−	22.9450i	1.17649	−	1.09886i
$437$	2.33336	−	3.49212i	0.111620	−	0.167051i
$438$	2.57016	−	7.98022i	0.122807	−	0.381310i
$439$	−5.00530	−	25.1633i	−0.238890	−	1.20098i	−0.894913	−	0.446240i	$-0.852763\pi$
$439$	−5.00530	−	25.1633i	−0.238890	−	1.20098i	0.656023	−	0.754740i	$-0.272237\pi$
$440$	−10.1824	−	6.13177i	−0.485427	−	0.292321i
$441$			14.2873i			0.680348i
$442$	−9.95205	+	1.18869i	−0.473371	+	0.0565401i
$443$		−	13.7486i		−	0.653215i	−0.945160	−	0.326607i	$-0.894095\pi$
$443$		−	13.7486i		−	0.653215i	0.945160	−	0.326607i	$-0.105905\pi$
$444$	−6.72581	−	10.8493i	−0.319193	−	0.514887i
$445$	1.74470	+	8.77121i	0.0827068	+	0.415795i
$446$	21.5086	+	6.92722i	1.01846	+	0.328013i
$447$	5.69912	−	8.52934i	0.269559	−	0.403424i
$448$	2.86123	+	1.54462i	0.135180	+	0.0729763i
$449$	24.8776	−	16.6227i	1.17404	−	0.784472i	0.193564	−	0.981088i	$-0.437995\pi$
$449$	24.8776	−	16.6227i	1.17404	−	0.784472i	0.980481	+	0.196616i	$0.0629952\pi$
$450$	−7.95690	+	9.36520i	−0.375092	+	0.441480i
$451$	−2.34251	−	5.65532i	−0.110305	−	0.266299i
$452$	−10.5568	−	0.360173i	−0.496550	−	0.0169411i
$453$	−11.2092	−	2.22965i	−0.526653	−	0.104758i
$454$	0.949802	−	8.20636i	0.0445764	−	0.385144i
$455$	0.453580	+	0.453580i	0.0212642	+	0.0212642i
$456$	9.08550	−	0.427498i	0.425467	−	0.0200194i
$457$	14.6714	−	35.4200i	0.686301	−	1.65688i	−0.0658030	−	0.997833i	$-0.520961\pi$
$457$	14.6714	−	35.4200i	0.686301	−	1.65688i	0.752104	−	0.659044i	$-0.229039\pi$
$458$	11.2215	−	5.75419i	0.524346	−	0.268875i
$459$	−3.16133	+	19.7661i	−0.147558	+	0.922602i
$460$	1.85747	+	1.33492i	0.0866048	+	0.0622412i
$461$	23.5936	+	9.77281i	1.09887	+	0.455165i	0.857090	−	0.515167i	$-0.172270\pi$
$461$	23.5936	+	9.77281i	1.09887	+	0.455165i	0.241776	+	0.970332i	$0.422270\pi$
$462$	−1.55845	−	1.96641i	−0.0725056	−	0.0914859i
$463$	−24.0274	+	24.0274i	−1.11665	+	1.11665i	−0.124417	+	0.992230i	$0.539706\pi$
$463$	−24.0274	+	24.0274i	−1.11665	+	1.11665i	−0.992230	+	0.124417i	$0.960294\pi$
$464$	−5.92736	+	21.8796i	−0.275171	+	1.01573i
$465$	−1.46564	+	7.36827i	−0.0679674	+	0.341695i
$466$	−15.8712	−	8.83455i	−0.735221	−	0.409253i
$467$	18.9361	−	7.84360i	0.876260	−	0.362959i	0.101215	−	0.994865i	$-0.467727\pi$
$467$	18.9361	−	7.84360i	0.876260	−	0.362959i	0.775045	+	0.631906i	$0.217727\pi$
$468$	−1.64148	+	6.99628i	−0.0758776	+	0.323403i
$469$	1.89279	+	2.83276i	0.0874009	+	0.130805i
$470$	15.9596	−	4.54561i	0.736163	−	0.209673i
$471$	−3.03688	−	2.02918i	−0.139932	−	0.0934997i
$472$	−20.3031	−	27.4943i	−0.934528	−	1.26553i
$473$	23.8689	−	4.74781i	1.09749	−	0.218305i
$474$	12.4794	−	1.01459i	0.573197	−	0.0466014i
$475$	14.0162			0.643106
$476$	3.35158	−	0.0122377i	0.153619	−	0.000560915i
$477$	−5.34131			−0.244562
$478$	−27.5295	+	2.23817i	−1.25917	+	0.102372i
$479$	−32.7511	+	6.51459i	−1.49643	+	0.297659i	−0.874352	−	0.485293i	$-0.838713\pi$
$479$	−32.7511	+	6.51459i	−1.49643	+	0.297659i	−0.622082	+	0.782952i	$0.713713\pi$
$480$	0.0639684	+	4.95327i	0.00291974	+	0.226085i
$481$	−9.56432	−	6.39068i	−0.436096	−	0.291390i
$482$	8.91190	−	2.53828i	0.405926	−	0.115616i
$483$	0.268261	+	0.401482i	0.0122063	+	0.0182680i
$484$	19.3703	+	4.54470i	0.880468	+	0.206577i
$485$	7.50732	−	3.10963i	0.340890	−	0.141201i
$486$	19.9310	+	11.0944i	0.904088	+	0.503251i
$487$	−4.00924	+	20.1558i	−0.181676	+	0.913346i	0.777142	+	0.629325i	$0.216669\pi$
$487$	−4.00924	+	20.1558i	−0.181676	+	0.913346i	−0.958818	+	0.284021i	$0.908331\pi$
$488$	8.27440	−	9.09152i	0.374565	−	0.411554i
$489$	8.18863	−	8.18863i	0.370303	−	0.370303i
$490$	5.51238	+	6.95539i	0.249024	+	0.314213i
$491$	12.2562	+	5.07668i	0.553114	+	0.229107i	0.641693	−	0.766962i	$-0.278233\pi$
$491$	12.2562	+	5.07668i	0.553114	+	0.229107i	−0.0885788	+	0.996069i	$0.528233\pi$
$492$	−1.48883	+	2.07161i	−0.0671215	+	0.0933956i
$493$	5.42025	+	22.7285i	0.244116	+	1.02364i
$494$	7.29331	−	3.73988i	0.328141	−	0.168265i
$495$	−3.36170	+	8.11586i	−0.151097	+	0.364781i
$496$	17.0760	+	29.7659i	0.766735	+	1.33653i
$497$	−3.90532	−	3.90532i	−0.175178	−	0.175178i
$498$	0.621843	−	5.37278i	0.0278655	−	0.240760i
$499$	6.36354	+	1.26579i	0.284871	+	0.0566644i	0.335458	−	0.942055i	$-0.391109\pi$
$499$	6.36354	+	1.26579i	0.284871	+	0.0566644i	−0.0505864	+	0.998720i	$0.516109\pi$
$500$	−0.573364	+	16.8055i	−0.0256416	+	0.751564i
$501$	−1.49263	−	3.60353i	−0.0666858	−	0.160994i
$502$	−3.46645	+	4.07998i	−0.154715	+	0.182099i
$503$	−31.5587	+	21.0869i	−1.40713	+	0.940216i	−0.407498	+	0.913206i	$0.633599\pi$
$503$	−31.5587	+	21.0869i	−1.40713	+	0.940216i	−0.999635	+	0.0270102i	$0.991401\pi$
$504$	0.814252	−	2.26092i	0.0362697	−	0.100709i
$505$	3.49119	−	5.22494i	0.155356	−	0.232507i
$506$	−7.67445	−	2.47168i	−0.341171	−	0.109880i
$507$	1.86911	+	9.39664i	0.0830100	+	0.417319i
$508$	14.4467	−	8.95595i	0.640970	−	0.397356i
$509$			2.06900i			0.0917069i	0.998948	+	0.0458535i	$0.0146007\pi$
$509$			2.06900i			0.0917069i	−0.998948	+	0.0458535i	$0.985399\pi$
$510$	2.49973	+	4.45242i	0.110690	+	0.197156i
$511$			2.52637i			0.111760i
$512$	15.0913	+	16.8598i	0.666946	+	0.745106i
$513$	−3.19352	−	16.0549i	−0.140997	−	0.708841i
$514$	1.97320	−	6.12668i	0.0870341	−	0.270236i
$515$	−0.145011	+	0.217024i	−0.00638993	+	0.00956321i
$516$	−6.92313	−	7.41222i	−0.304774	−	0.326305i
$517$	−48.6342	+	32.4964i	−2.13893	+	1.42919i
$518$	2.93139	+	2.49058i	0.128798	+	0.109430i
$519$	2.03639	+	4.91629i	0.0893877	+	0.215801i
$520$	1.90022	+	4.03927i	0.0833300	+	0.177134i
$521$	−7.47703	−	1.48727i	−0.327575	−	0.0651586i	0.0285635	−	0.999592i	$-0.490907\pi$
$521$	−7.47703	−	1.48727i	−0.327575	−	0.0651586i	−0.356138	+	0.934433i	$0.615907\pi$
$522$	16.6421	+	1.92615i	0.728404	+	0.0843053i
$523$	12.1077	+	12.1077i	0.529433	+	0.529433i	0.920403	−	0.390970i	$-0.127861\pi$
$523$	12.1077	+	12.1077i	0.529433	+	0.529433i	−0.390970	+	0.920403i	$0.627861\pi$
$524$	5.89874	+	2.68250i	0.257687	+	0.117185i
$525$	−0.616659	+	1.48875i	−0.0269132	+	0.0649743i
$526$	−0.592712	−	1.15587i	−0.0258435	−	0.0503985i
$527$	30.1318	+	18.5276i	1.31256	+	0.807075i
$528$	−5.56695	−	16.5496i	−0.242270	−	0.720227i
$529$	−19.8157	−	8.20795i	−0.861554	−	0.356867i
$530$	−2.60027	+	2.06080i	−0.112949	+	0.0895156i
$531$	−17.8614	+	17.8614i	−0.775118	+	0.775118i
$532$	−2.56648	+	0.961915i	−0.111271	+	0.0417043i
$533$	−0.448491	+	2.25472i	−0.0194263	+	0.0976626i
$534$	−6.38959	+	11.4789i	−0.276504	+	0.496739i
$535$	−11.6679	+	4.83299i	−0.504446	+	0.208948i
$536$	5.71318	+	23.0102i	0.246772	+	0.993889i
$537$	3.46671	+	5.18830i	0.149600	+	0.223892i
$538$	−6.02806	−	21.1645i	−0.259888	−	0.912466i
$539$	−26.0103	−	17.3795i	−1.12034	−	0.748589i
$540$	8.79816	−	1.44012i	0.378612	−	0.0619727i
$541$	36.8713	−	7.33416i	1.58522	−	0.315320i	0.677704	−	0.735335i	$-0.262975\pi$
$541$	36.8713	−	7.33416i	1.58522	−	0.315320i	0.907517	+	0.420014i	$0.137975\pi$
$542$	−2.07073	−	25.4699i	−0.0889453	−	1.09403i
$543$	17.3976			0.746601
$544$	21.9728	+	7.82280i	0.942076	+	0.335400i
$545$	−15.4320			−0.661035
$546$	0.0763586	+	0.939209i	0.00326785	+	0.0401944i
$547$	−19.5071	+	3.88020i	−0.834063	+	0.165905i	−0.593607	−	0.804755i	$-0.702297\pi$
$547$	−19.5071	+	3.88020i	−0.834063	+	0.165905i	−0.240455	+	0.970660i	$0.577297\pi$
$548$	16.6506	−	2.72543i	0.711278	−	0.116425i
$549$	−7.55421	−	5.04756i	−0.322406	−	0.215425i
$550$	−7.37049	−	25.8778i	−0.314279	−	1.10343i
$551$	−10.6157	−	15.8876i	−0.452245	−	0.676833i
$552$	0.809717	+	3.26119i	0.0344639	+	0.138805i
$553$	−3.48571	+	1.44383i	−0.148227	+	0.0613978i
$554$	−8.98366	+	16.1391i	−0.381679	+	0.685685i
$555$	−1.14327	+	5.74759i	−0.0485290	+	0.243972i
$556$	−19.2790	+	7.22577i	−0.817614	+	0.306441i
$557$	−7.97634	+	7.97634i	−0.337969	+	0.337969i	−0.855602	−	0.517634i	$-0.826813\pi$
$557$	−7.97634	+	7.97634i	−0.337969	+	0.337969i	0.517634	+	0.855602i	$0.326813\pi$
$558$	19.8763	−	15.7526i	0.841432	−	0.666862i
$559$	−8.44402	−	3.49763i	−0.357144	−	0.147934i
$560$	−0.475919	−	1.41483i	−0.0201113	−	0.0597873i
$561$	−13.1979	−	12.2372i	−0.557218	−	0.516654i
$562$	−16.4179	−	32.0172i	−0.692547	−	1.35057i
$563$	3.58432	−	8.65330i	0.151061	−	0.364693i	−0.830175	−	0.557502i	$-0.811760\pi$
$563$	3.58432	−	8.65330i	0.151061	−	0.364693i	0.981236	+	0.192809i	$0.0617598\pi$
$564$	22.1904	+	10.0913i	0.934385	+	0.424919i
$565$	3.42896	+	3.42896i	0.144257	+	0.144257i
$566$	−42.7569	−	4.94867i	−1.79721	−	0.208008i
$567$	−0.654075	−	0.130104i	−0.0274686	−	0.00546384i
$568$	−16.3608	−	34.7781i	−0.686485	−	1.45926i
$569$	2.18702	+	5.27993i	0.0916846	+	0.221346i	0.963069	−	0.269255i	$-0.0867773\pi$
$569$	2.18702	+	5.27993i	0.0916846	+	0.221346i	−0.871384	+	0.490601i	$0.836777\pi$
$570$	−3.18216	−	2.70364i	−0.133286	−	0.113243i
$571$	−5.02334	+	3.35649i	−0.210220	+	0.140465i	−0.656223	−	0.754567i	$-0.727847\pi$
$571$	−5.02334	+	3.35649i	−0.210220	+	0.140465i	0.446003	+	0.895031i	$0.352847\pi$
$572$	−10.7401	−	11.4988i	−0.449066	−	0.480791i
$573$	5.05971	−	7.57240i	0.211373	−	0.316341i
$574$	0.235666	−	0.731731i	0.00983651	−	0.0305419i
$575$	1.01019	+	5.07856i	0.0421278	+	0.211791i
$576$	10.6624	−	12.8830i	0.444265	−	0.536793i
$577$			9.73764i			0.405383i	0.979243	+	0.202692i	$0.0649689\pi$
$577$			9.73764i			0.405383i	−0.979243	+	0.202692i	$0.935031\pi$
$578$	23.7473	−	3.75036i	0.987758	−	0.155994i
$579$			9.11426i			0.378776i
$580$	8.84491	−	5.48321i	0.367265	−	0.227678i
$581$	0.317963	+	1.59851i	0.0131913	+	0.0663172i
$582$	11.3622	+	3.65939i	0.470978	+	0.151686i
$583$	6.49734	−	9.72395i	0.269092	−	0.402725i
$584$	−5.95712	+	16.5410i	−0.246507	+	0.684473i
$585$	2.74310	−	1.83288i	0.113413	−	0.0757803i
$586$	29.6672	−	34.9180i	1.22554	−	1.44245i
$587$	−9.50544	−	22.9482i	−0.392331	−	0.947172i	−0.989431	−	0.145005i	$-0.953680\pi$
$587$	−9.50544	−	22.9482i	−0.392331	−	0.947172i	0.597100	−	0.802167i	$-0.296320\pi$
$588$	−0.444543	+	13.0297i	−0.0183327	+	0.537336i
$589$	−28.3704	−	5.64322i	−1.16898	−	0.232525i
$590$	−1.80400	+	15.5867i	−0.0742693	+	0.641693i
$591$	−12.5781	−	12.5781i	−0.517393	−	0.517393i
$592$	13.3201	+	23.2188i	0.547452	+	0.954286i
$593$	4.11126	−	9.92545i	0.168829	−	0.407589i	−0.816708	−	0.577052i	$-0.804203\pi$
$593$	4.11126	−	9.92545i	0.168829	−	0.407589i	0.985537	+	0.169462i	$0.0542031\pi$
$594$	−27.9625	+	14.3387i	−1.14732	+	0.588324i
$595$	−1.12830	−	1.04616i	−0.0462556	−	0.0428883i
$596$	−12.5540	+	17.4681i	−0.514232	+	0.715523i
$597$	8.25921	+	3.42107i	0.338027	+	0.140015i
$598$	1.88074	+	2.37308i	0.0769094	+	0.0970425i
$599$	18.0672	−	18.0672i	0.738206	−	0.738206i	−0.234024	−	0.972231i	$-0.575190\pi$
$599$	18.0672	−	18.0672i	0.738206	−	0.738206i	0.972231	+	0.234024i	$0.0751896\pi$
$600$	−7.54790	+	8.29327i	−0.308142	+	0.338571i
$601$	4.81521	−	24.2077i	0.196416	−	0.987452i	−0.749244	−	0.662295i	$-0.769583\pi$
$601$	4.81521	−	24.2077i	0.196416	−	0.987452i	0.945660	−	0.325157i	$-0.105417\pi$
$602$	2.67047	+	1.48649i	0.108840	+	0.0605847i
$603$	16.1884	−	6.70547i	0.659244	−	0.273068i
$604$	23.3326	+	5.47435i	0.949390	+	0.222748i
$605$	−5.07462	−	7.59470i	−0.206313	−	0.308769i
$606$	8.87812	−	2.52866i	0.360649	−	0.102720i
$607$	33.8738	+	22.6337i	1.37489	+	0.918675i	0.999965	−	0.00837899i	$-0.00266715\pi$
$607$	33.8738	+	22.6337i	1.37489	+	0.918675i	0.374929	+	0.927054i	$0.377667\pi$
$608$	−19.0718	+	0.246300i	−0.773464	+	0.00998880i
$609$	2.15457	−	0.428571i	0.0873076	−	0.0173666i
$610$	−5.62503	+	0.457320i	−0.227751	+	0.0185164i
$611$	21.9671			0.888692
$612$	3.30115	−	16.9186i	0.133441	−	0.683895i
$613$	−5.39160			−0.217765			−0.108882	−	0.994055i	$-0.534727\pi$
$613$	−5.39160			−0.217765			−0.108882	+	0.994055i	$0.534727\pi$
$614$	−2.66445	+	0.216623i	−0.107529	+	0.00874218i
$615$	1.14867	−	0.228485i	0.0463190	−	0.00921341i
$616$	3.12557	+	4.23261i	0.125933	+	0.170537i
$617$	28.1032	+	18.7780i	1.13139	+	0.755973i	0.972863	−	0.231381i	$-0.0743245\pi$
$617$	28.1032	+	18.7780i	1.13139	+	0.755973i	0.158530	+	0.987354i	$0.449324\pi$
$618$	−0.368763	+	0.105031i	−0.0148338	+	0.00422496i
$619$	−14.6522	−	21.9285i	−0.588921	−	0.881382i	0.410616	−	0.911808i	$-0.365314\pi$
$619$	−14.6522	−	21.9285i	−0.588921	−	0.881382i	−0.999537	+	0.0304262i	$0.990314\pi$
$620$	3.59852	−	15.3375i	0.144520	−	0.615969i
$621$	5.58710	−	2.31425i	0.224203	−	0.0928677i
$622$	−19.2739	−	10.7286i	−0.772813	−	0.430178i
$623$	0.772320	−	3.88271i	0.0309423	−	0.155558i
$624$	−1.71468	+	6.32938i	−0.0686422	+	0.253378i
$625$	−9.23850	+	9.23850i	−0.369540	+	0.369540i
$626$	13.9468	+	17.5978i	0.557427	+	0.703348i
$627$	13.5979	+	5.63244i	0.543048	+	0.224938i
$628$	6.21956	+	4.46987i	0.248187	+	0.178367i
$629$	23.5042	+	14.4524i	0.937174	+	0.576255i
$630$	−0.981674	+	0.503386i	−0.0391108	+	0.0200554i
$631$	6.39692	−	15.4435i	0.254657	−	0.614797i	−0.743912	−	0.668278i	$-0.767032\pi$
$631$	6.39692	−	15.4435i	0.254657	−	0.614797i	0.998569	+	0.0534811i	$0.0170317\pi$
$632$	−26.2266	+	1.23403i	−1.04324	+	0.0490873i
$633$	10.7348	+	10.7348i	0.426668	+	0.426668i
$634$	2.60019	−	22.4659i	0.103267	−	0.892234i
$635$	−7.65337	−	1.52235i	−0.303715	−	0.0604126i
$636$	−4.87116	−	0.166192i	−0.193154	−	0.00658996i
$637$	4.49588	+	10.8540i	0.178133	+	0.430052i
$638$	−23.7505	+	27.9542i	−0.940293	+	1.10672i
$639$	−23.6181	+	15.7811i	−0.934316	+	0.624290i
$640$	0.220111	−	10.3856i	0.00870065	−	0.410525i
$641$	3.08829	−	4.62195i	0.121980	−	0.182556i	−0.765454	−	0.643490i	$-0.777486\pi$
$641$	3.08829	−	4.62195i	0.121980	−	0.182556i	0.887434	+	0.460934i	$0.152486\pi$
$642$	−17.6591	−	5.68741i	−0.696950	−	0.224464i
$643$	−3.62984	−	18.2484i	−0.143147	−	0.719648i	−0.983969	−	0.178337i	$-0.942928\pi$
$643$	−3.62984	−	18.2484i	−0.143147	−	0.719648i	0.840822	−	0.541311i	$-0.182072\pi$
$644$	−0.533511	−	0.860600i	−0.0210233	−	0.0339124i
$645$			4.65627i			0.183340i
$646$	−17.1433	+	9.62481i	−0.674496	+	0.378683i
$647$		−	19.3474i		−	0.760626i	−0.924858	−	0.380313i	$-0.875816\pi$
$647$		−	19.3474i		−	0.760626i	0.924858	−	0.380313i	$-0.124184\pi$
$648$	−3.97567	−	2.39412i	−0.156179	−	0.0940500i
$649$	−10.7898	−	54.2441i	−0.423537	−	2.12927i
$650$	−3.09782	+	9.61855i	−0.121506	+	0.377271i
$651$	1.84759	−	2.76512i	0.0724129	−	0.108374i
$652$	−17.7471	+	16.5761i	−0.695030	+	0.649169i
$653$	−9.15351	+	6.11618i	−0.358205	+	0.239345i	−0.721631	−	0.692278i	$-0.756607\pi$
$653$	−9.15351	+	6.11618i	−0.358205	+	0.239345i	0.363426	+	0.931623i	$0.381607\pi$
$654$	−17.2762	−	14.6782i	−0.675552	−	0.573965i
$655$	−1.13844	−	2.74843i	−0.0444824	−	0.107390i
$656$	3.26839	−	4.23520i	0.127609	−	0.165357i
$657$	12.7438	+	2.53489i	0.497182	+	0.0988956i
$658$	−7.29704	−	0.844557i	−0.284468	−	0.0329242i
$659$	0.830341	+	0.830341i	0.0323455	+	0.0323455i	0.723095	−	0.690749i	$-0.242719\pi$
$659$	0.830341	+	0.830341i	0.0323455	+	0.0323455i	−0.690749	+	0.723095i	$0.742719\pi$
$660$	−3.31832	+	7.29688i	−0.129165	+	0.284031i
$661$	−8.66926	+	20.9295i	−0.337195	+	0.814061i	0.660787	+	0.750573i	$0.270223\pi$
$661$	−8.66926	+	20.9295i	−0.337195	+	0.814061i	−0.997983	+	0.0634882i	$0.979777\pi$
$662$	−14.6169	−	28.5051i	−0.568103	−	1.10788i
$663$	1.56798	+	6.57496i	0.0608954	+	0.255350i
$664$	−1.68742	+	11.2157i	−0.0654846	+	0.435254i
$665$	1.16249	+	0.481518i	0.0450794	+	0.0186725i
$666$	15.5045	−	12.2878i	0.600786	−	0.476142i
$667$	4.99152	−	4.99152i	0.193273	−	0.193273i
$668$	2.87057	+	7.65895i	0.111066	+	0.296334i
$669$	2.97300	−	14.9463i	0.114943	−	0.577857i
$670$	5.29378	−	9.51026i	0.204517	−	0.367413i
$671$	18.3783	−	7.61256i	0.709488	−	0.293880i
$672$	0.812927	−	2.03657i	0.0313593	−	0.0785625i
$673$	23.2736	+	34.8315i	0.897133	+	1.34265i	0.939139	+	0.343537i	$0.111625\pi$
$673$	23.2736	+	34.8315i	0.897133	+	1.34265i	−0.0420063	+	0.999117i	$0.513375\pi$
$674$	2.97196	+	10.4345i	0.114475	+	0.401923i
$675$	16.7805	+	11.2123i	0.645880	+	0.431563i
$676$	−3.24535	−	19.8270i	−0.124821	−	0.762575i
$677$	−13.3893	+	2.66331i	−0.514594	+	0.102359i	−0.445555	−	0.895255i	$-0.646994\pi$
$677$	−13.3893	+	2.66331i	−0.514594	+	0.102359i	−0.0690397	+	0.997614i	$0.521994\pi$
$678$	0.577253	+	7.10019i	0.0221693	+	0.272681i
$679$	−3.59704			−0.138042
$680$	−4.92052	−	9.51004i	−0.188694	−	0.364693i
$681$	−5.57129			−0.213492
$682$	4.49978	+	55.3472i	0.172305	+	2.11935i
$683$	2.47247	−	0.491805i	0.0946064	−	0.0188184i	−0.147560	−	0.989053i	$-0.547142\pi$
$683$	2.47247	−	0.491805i	0.0946064	−	0.0188184i	0.242166	+	0.970235i	$0.422142\pi$
$684$	2.27705	+	13.9112i	0.0870650	+	0.531910i
$685$	−6.44036	−	4.30331i	−0.246073	−	0.164421i
$686$	−2.17830	−	7.64802i	−0.0831680	−	0.292003i
$687$	−4.72496	−	7.07140i	−0.180268	−	0.269791i
$688$	13.9794	+	16.0294i	0.532959	+	0.611116i
$689$	−4.05777	+	1.68079i	−0.154589	+	0.0640328i
$690$	0.750277	−	1.34787i	0.0285626	−	0.0513125i
$691$	−0.907837	+	4.56400i	−0.0345357	+	0.173623i	−0.994204	−	0.107513i	$-0.965711\pi$
$691$	−0.907837	+	4.56400i	−0.0345357	+	0.173623i	0.959668	+	0.281136i	$0.0907112\pi$
$692$	−3.91631	−	10.4491i	−0.148876	−	0.397215i
$693$	2.74967	−	2.74967i	0.104451	−	0.104451i
$694$	−10.6706	+	8.45678i	−0.405049	+	0.321015i
$695$	8.73244	+	3.61710i	0.331240	+	0.137204i
$696$	15.1173	+	2.27442i	0.573019	+	0.0862115i
$697$	0.870879	−	5.44514i	0.0329869	−	0.206249i
$698$	14.0333	+	27.3669i	0.531167	+	1.03585i
$699$	−4.68788	+	11.3176i	−0.177312	+	0.428069i
$700$	1.39883	−	3.07600i	0.0528710	−	0.116262i
$701$	−3.51127	−	3.51127i	−0.132619	−	0.132619i	0.637681	−	0.770300i	$-0.279894\pi$
$701$	−3.51127	−	3.51127i	−0.132619	−	0.132619i	−0.770300	+	0.637681i	$0.779894\pi$
$702$	11.7234	+	1.35687i	0.442473	+	0.0512117i
$703$	−22.1302	−	4.40198i	−0.834657	−	0.166024i
$704$	10.4838	+	35.0824i	0.395122	+	1.32222i
$705$	−4.28268	−	10.3393i	−0.161295	−	0.389401i
$706$	2.68274	+	2.27932i	0.100966	+	0.0857833i
$707$	−2.31290	+	1.54543i	−0.0869856	+	0.0581219i
$708$	−16.8449	+	15.7334i	−0.633071	+	0.591298i
$709$	−10.2706	+	15.3711i	−0.385721	+	0.577273i	−0.972624	−	0.232385i	$-0.925347\pi$
$709$	−10.2706	+	15.3711i	−0.385721	+	0.577273i	0.586903	+	0.809657i	$0.300347\pi$
$710$	−5.40911	+	16.7950i	−0.203000	+	0.630305i
$711$	3.78562	+	19.0316i	0.141972	+	0.713741i
$712$	14.2120	−	23.6003i	0.532616	−	0.884460i
$713$		−	10.6863i		−	0.400206i
$714$	−0.268070	−	2.24436i	−0.0100323	−	0.0839931i
$715$			7.22344i			0.270141i
$716$	−6.89450	−	11.1214i	−0.257659	−	0.415628i
$717$	3.63396	+	18.2692i	0.135713	+	0.682275i
$718$	2.41435	+	0.777582i	0.0901028	+	0.0290191i
$719$	5.19183	−	7.77013i	0.193623	−	0.289777i	−0.721937	−	0.691959i	$-0.756748\pi$
$719$	5.19183	−	7.77013i	0.193623	−	0.289777i	0.915560	+	0.402182i	$0.131748\pi$
$720$	−7.61432	+	0.981080i	−0.283769	+	0.0365627i
$721$	0.0960690	−	0.0641912i	0.00357780	−	0.00239061i
$722$	−6.98793	+	8.22474i	−0.260064	+	0.306093i
$723$	−2.39146	−	5.77350i	−0.0889394	−	0.214719i
$724$	−36.4615	−	1.24398i	−1.35508	−	0.0462323i
$725$	23.1051	+	4.59590i	0.858103	+	0.170687i
$726$	1.54270	−	13.3290i	0.0572549	−	0.494687i
$727$	4.71286	+	4.71286i	0.174790	+	0.174790i	0.789080	−	0.614290i	$-0.210557\pi$
$727$	4.71286	+	4.71286i	0.174790	+	0.174790i	−0.614290	+	0.789080i	$0.710557\pi$
$728$	−0.0928746	−	1.97384i	−0.00344216	−	0.0731553i
$729$	4.00329	−	9.66480i	0.148270	−	0.357955i
$730$	7.18199	−	3.68280i	0.265817	−	0.136307i
$731$	20.5569	+	7.61922i	0.760324	+	0.281807i
$732$	−6.73221	−	4.83831i	−0.248830	−	0.178829i
$733$	39.9546	+	16.5498i	1.47576	+	0.611279i	0.968164	−	0.250317i	$-0.0805349\pi$
$733$	39.9546	+	16.5498i	1.47576	+	0.611279i	0.507594	+	0.861596i	$0.330535\pi$
$734$	26.3124	+	33.2004i	0.971210	+	1.22545i
$735$	4.23218	−	4.23218i	0.156106	−	0.156106i
$736$	−1.46381	−	6.89264i	−0.0539566	−	0.254066i
$737$	−7.48469	+	37.6281i	−0.275702	+	1.38605i
$738$	−3.45460	−	1.92297i	−0.127166	−	0.0707854i
$739$	−9.16633	+	3.79682i	−0.337189	+	0.139668i	−0.544852	−	0.838532i	$-0.683414\pi$
$739$	−9.16633	+	3.79682i	−0.337189	+	0.139668i	0.207663	+	0.978200i	$0.433414\pi$
$740$	2.80701	−	11.9640i	0.103188	−	0.439804i
$741$	−3.07094	−	4.59599i	−0.112814	−	0.168838i
$742$	1.41254	−	0.402317i	0.0518558	−	0.0147695i
$743$	−28.8467	−	19.2748i	−1.05828	−	0.707122i	−0.100594	−	0.994928i	$-0.532074\pi$
$743$	−28.8467	−	19.2748i	−1.05828	−	0.707122i	−0.957689	+	0.287805i	$0.907074\pi$
$744$	18.6169	−	13.7476i	0.682528	−	0.504012i
$745$	9.68577	−	1.92662i	0.354859	−	0.0705859i
$746$	−13.7334	+	1.11654i	−0.502815	+	0.0408793i
$747$	8.38237			0.306695
$748$	26.7850	+	26.5901i	0.979358	+	0.972232i
$749$	5.59052			0.204273
$750$	11.3029	−	0.918935i	0.412723	−	0.0335548i
$751$	4.72926	−	0.940707i	0.172573	−	0.0343269i	−0.108047	−	0.994146i	$-0.534460\pi$
$751$	4.72926	−	0.940707i	0.172573	−	0.0343269i	0.280620	+	0.959819i	$0.409460\pi$
$752$	−45.7847	−	22.7358i	−1.66960	−	0.829089i
$753$	3.00206	+	2.00591i	0.109401	+	0.0730996i
$754$	13.2490	−	3.77358i	0.482502	−	0.137426i
$755$	−6.11266	−	9.14824i	−0.222463	−	0.332939i
$756$	−3.84214	−	0.901451i	−0.139737	−	0.0327855i
$757$	3.21103	−	1.33005i	0.116707	−	0.0483416i	−0.323566	−	0.946206i	$-0.604882\pi$
$757$	3.21103	−	1.33005i	0.116707	−	0.0483416i	0.440273	+	0.897864i	$0.354882\pi$
$758$	31.2491	+	17.3945i	1.13502	+	0.631796i
$759$	−1.06079	+	5.33295i	−0.0385043	+	0.193574i
$760$	6.47580	+	5.89378i	0.234902	+	0.213790i
$761$	−1.64912	+	1.64912i	−0.0597806	+	0.0597806i	−0.736365	−	0.676584i	$-0.763459\pi$
$761$	−1.64912	+	1.64912i	−0.0597806	+	0.0597806i	0.676584	+	0.736365i	$0.263459\pi$
$762$	−7.11997	−	8.98382i	−0.257929	−	0.325450i
$763$	6.31123	+	2.61420i	0.228482	+	0.0946403i
$764$	−11.1455	+	15.5083i	−0.403231	+	0.561071i
$765$	−6.40923	+	4.64177i	−0.231726	+	0.167823i
$766$	32.8560	−	16.8480i	1.18713	−	0.608742i
$767$	−7.94866	+	19.1898i	−0.287010	+	0.692903i
$768$	10.1247	−	11.4173i	0.365343	−	0.411986i
$769$	−2.15644	−	2.15644i	−0.0777632	−	0.0777632i	0.667155	−	0.744919i	$-0.267512\pi$
$769$	−2.15644	−	2.15644i	−0.0777632	−	0.0777632i	−0.744919	+	0.667155i	$0.767512\pi$
$770$	0.277716	−	2.39949i	0.0100082	−	0.0864715i
$771$	−4.25741	−	0.846852i	−0.153327	−	0.0304986i
$772$	0.651699	−	19.1015i	0.0234552	−	0.687478i
$773$	−14.9831	−	36.1723i	−0.538903	−	1.30103i	−0.925489	−	0.378773i	$-0.876346\pi$
$773$	−14.9831	−	36.1723i	−0.538903	−	1.30103i	0.386587	−	0.922253i	$-0.373654\pi$
$774$	10.1778	−	11.9791i	0.365832	−	0.430581i
$775$	29.6525	−	19.8132i	1.06515	−	0.711710i
$776$	−23.5511	−	8.48171i	−0.845433	−	0.304476i
$777$	1.44121	−	2.15692i	0.0517031	−	0.0773791i
$778$	−19.8167	−	6.38229i	−0.710462	−	0.228816i
$779$	0.879747	+	4.42279i	0.0315202	+	0.158463i
$780$	2.55868	−	1.58620i	0.0916153	−	0.0567949i
$781$		−	62.1937i		−	2.22547i
$782$	−4.72299	−	5.51796i	−0.168894	−	0.197322i
$783$		−	27.5131i		−	0.983236i
$784$	1.86333	−	27.2756i	0.0665476	−	0.974130i
$785$	−0.685976	−	3.44863i	−0.0244835	−	0.123087i
$786$	1.33970	−	4.15971i	0.0477856	−	0.148372i
$787$	−14.5329	+	21.7500i	−0.518041	+	0.775304i	−0.994594	−	0.103842i	$-0.966886\pi$
$787$	−14.5329	+	21.7500i	−0.518041	+	0.775304i	0.476552	+	0.879146i	$0.341886\pi$
$788$	25.4615	+	27.2603i	0.907030	+	0.971108i
$789$	−0.728392	+	0.486696i	−0.0259314	+	0.0173268i
$790$	9.18577	+	7.80445i	0.326815	+	0.277670i
$791$	−0.821472	−	1.98321i	−0.0292082	−	0.0705148i
$792$	24.4866	−	11.5194i	0.870095	−	0.409323i
$793$	−7.32725	−	1.45748i	−0.260198	−	0.0517567i
$794$	−6.37415	−	0.737742i	−0.226210	−	0.0261815i
$795$	1.58220	+	1.58220i	0.0561149	+	0.0561149i
$796$	−17.0649	−	7.76039i	−0.604849	−	0.275060i
$797$	−11.0879	+	26.7685i	−0.392752	+	0.948188i	0.596585	+	0.802550i	$0.296524\pi$
$797$	−11.0879	+	26.7685i	−0.392752	+	0.948188i	−0.989338	+	0.145639i	$0.953476\pi$
$798$	0.843409	+	1.64477i	0.0298563	+	0.0582241i
$799$	−52.6548	+	1.98897i	−1.86279	+	0.0703646i
$800$	16.4118	−	16.8412i	0.580243	−	0.595426i
$801$	−18.8106	−	7.79161i	−0.664641	−	0.275303i
$802$	−16.5232	+	13.0952i	−0.583454	+	0.462406i
$803$	−20.1167	+	20.1167i	−0.709904	+	0.709904i
$804$	14.9721	−	5.61154i	0.528026	−	0.197904i
$805$	−0.0906872	+	0.455916i	−0.00319631	+	0.0160689i
$806$	10.1430	−	18.2218i	0.357271	−	0.641837i
$807$	−13.7112	+	5.67938i	−0.482658	+	0.199924i
$808$	−18.7874	+	4.66471i	−0.660939	+	0.164104i
$809$	4.93037	+	7.37882i	0.173342	+	0.259425i	0.907961	−	0.419055i	$-0.137639\pi$
$809$	4.93037	+	7.37882i	0.173342	+	0.259425i	−0.734618	+	0.678481i	$0.762639\pi$
$810$	0.583613	+	2.04906i	0.0205061	+	0.0719967i
$811$	4.20198	+	2.80767i	0.147551	+	0.0985907i	0.627155	−	0.778895i	$-0.284219\pi$
$811$	4.20198	+	2.80767i	0.147551	+	0.0985907i	−0.479603	+	0.877485i	$0.659219\pi$
$812$	−4.54616	+	0.744133i	−0.159539	+	0.0261139i
$813$	−16.9024	+	3.36209i	−0.592792	+	0.117914i
$814$	3.51004	+	43.1734i	0.123027	+	1.51323i
$815$	11.1485			0.390516
$816$	3.53699	−	15.3267i	0.123819	−	0.536541i
$817$	−17.9282			−0.627230
$818$	−2.05232	−	25.2435i	−0.0717578	−	0.882620i
$819$	−1.43234	+	0.284910i	−0.0500499	+	0.00995555i
$820$	−2.42371	+	0.396722i	−0.0846395	+	0.0138541i
$821$	4.94868	+	3.30660i	0.172710	+	0.115401i	0.638921	−	0.769273i	$-0.279381\pi$
$821$	4.94868	+	3.30660i	0.172710	+	0.115401i	−0.466211	+	0.884674i	$0.654381\pi$
$822$	−3.11688	−	10.9433i	−0.108714	−	0.381693i
$823$	29.8490	+	44.6722i	1.04047	+	1.55717i	0.812029	+	0.583617i	$0.198363\pi$
$823$	29.8490	+	44.6722i	1.04047	+	1.55717i	0.228442	+	0.973557i	$0.426637\pi$
$824$	0.780357	−	0.193754i	0.0271850	−	0.00674974i
$825$	−16.7647	+	6.94416i	−0.583672	+	0.241765i
$826$	3.37817	−	6.06888i	0.117542	−	0.211163i
$827$	3.98075	−	20.0126i	0.138424	−	0.695905i	−0.847777	−	0.530353i	$-0.822059\pi$
$827$	3.98075	−	20.0126i	0.138424	−	0.695905i	0.986201	−	0.165552i	$-0.0529406\pi$
$828$	−4.87643	+	1.82768i	−0.169468	+	0.0635163i
$829$	13.1038	−	13.1038i	0.455114	−	0.455114i	−0.441933	−	0.897048i	$-0.645707\pi$
$829$	13.1038	−	13.1038i	0.455114	−	0.455114i	0.897048	+	0.441933i	$0.145707\pi$
$830$	4.08073	−	3.23411i	0.141644	−	0.112258i
$831$	11.5086	+	4.76700i	0.399228	+	0.165365i
$832$	4.04617	−	13.1424i	0.140276	−	0.455631i
$833$	−11.7593	−	25.6099i	−0.407437	−	0.887330i
$834$	6.33557	+	12.3553i	0.219383	+	0.427828i
$835$	1.43696	−	3.46912i	0.0497279	−	0.120054i
$836$	−28.0955	−	12.7767i	−0.971704	−	0.441890i
$837$	−29.4513	−	29.4513i	−1.01799	−	1.01799i
$838$	4.17944	+	0.483727i	0.144376	+	0.0167101i
$839$	10.9012	+	2.16839i	0.376352	+	0.0748610i	0.379642	−	0.925134i	$-0.376047\pi$
$839$	10.9012	+	2.16839i	0.376352	+	0.0748610i	−0.00329014	+	0.999995i	$0.501047\pi$
$840$	−0.910927	+	0.428532i	−0.0314300	+	0.0147858i
$841$	−1.19229	−	2.87843i	−0.0411133	−	0.0992562i
$842$	−35.8016	−	30.4179i	−1.23381	−	1.04827i
$843$	−20.1762	+	13.4813i	−0.694904	+	0.464320i
$844$	−21.7301	−	23.2653i	−0.747982	−	0.800824i
$845$	−5.12423	+	7.66895i	−0.176279	+	0.263820i
$846$	−11.5818	+	35.9610i	−0.398192	+	1.23636i
$847$	0.788816	+	3.96565i	0.0271040	+	0.136261i
$848$	10.1970	+	0.696607i	0.350167	+	0.0239216i
$849$			29.0276i			0.996225i
$850$	6.55453	−	23.3360i	0.224819	−	0.800420i
$851$		−	8.33584i		−	0.285749i
$852$	−22.0302	+	13.6571i	−0.754741	+	0.467885i
$853$	9.54079	+	47.9648i	0.326670	+	1.64228i	0.699681	+	0.714456i	$0.253326\pi$
$853$	9.54079	+	47.9648i	0.326670	+	1.64228i	−0.373011	+	0.927827i	$0.621674\pi$
$854$	2.37794	+	0.765854i	0.0813713	+	0.0262070i
$855$	3.59533	−	5.38079i	0.122958	−	0.184019i
$856$	36.6030	+	13.1823i	1.25107	+	0.450561i
$857$	35.4449	−	23.6835i	1.21077	−	0.809014i	0.224556	−	0.974461i	$-0.427907\pi$
$857$	35.4449	−	23.6835i	1.21077	−	0.809014i	0.986219	+	0.165447i	$0.0529067\pi$
$858$	−6.87061	+	8.08665i	−0.234559	+	0.276074i
$859$	12.4250	+	29.9967i	0.423937	+	1.02347i	0.981175	+	0.193121i	$0.0618609\pi$
$859$	12.4250	+	29.9967i	0.423937	+	1.02347i	−0.557238	+	0.830353i	$0.688139\pi$
$860$	0.332938	−	9.75853i	0.0113531	−	0.332763i
$861$	−0.508478	−	0.101143i	−0.0173289	−	0.00344693i
$862$	−0.597356	+	5.16120i	−0.0203460	+	0.175791i
$863$	1.19042	+	1.19042i	0.0405224	+	0.0405224i	0.727078	−	0.686555i	$-0.240878\pi$
$863$	1.19042	+	1.19042i	0.0405224	+	0.0405224i	−0.686555	+	0.727078i	$0.740878\pi$
$864$	−23.0302	−	14.9618i	−0.783503	−	0.509009i
$865$	−1.96044	+	4.73291i	−0.0666569	+	0.160924i
$866$	24.6286	−	12.6291i	0.836913	−	0.429155i
$867$	−4.35375	−	15.6181i	−0.147861	−	0.530420i
$868$	−4.06987	+	5.66298i	−0.138140	+	0.192214i
$869$	−39.2523	−	16.2589i	−1.33154	−	0.551544i
$870$	−4.35915	−	5.50028i	−0.147789	−	0.186477i
$871$	10.1882	−	10.1882i	0.345215	−	0.345215i
$872$	35.1576	+	31.9977i	1.19059	+	1.08358i
$873$	−3.60917	+	18.1445i	−0.122152	+	0.614099i
$874$	5.18977	+	2.88883i	0.175546	+	0.0977160i
$875$	−3.15709	+	1.30771i	−0.106729	+	0.0442087i
$876$	11.5432	+	2.70828i	0.390007	+	0.0915044i
$877$	−13.9469	−	20.8730i	−0.470953	−	0.704830i	0.517614	−	0.855614i	$-0.326820\pi$
$877$	−13.9469	−	20.8730i	−0.470953	−	0.704830i	−0.988567	+	0.150784i	$0.951820\pi$
$878$	34.8957	−	9.93897i	1.17767	−	0.335424i
$879$	−25.6928	−	17.1674i	−0.866596	−	0.579041i
$880$	7.47622	−	15.0554i	0.252023	−	0.507518i
$881$	−50.1420	+	9.97387i	−1.68933	+	0.336028i	−0.943818	−	0.330466i	$-0.892794\pi$
$881$	−50.1420	+	9.97387i	−1.68933	+	0.336028i	−0.745510	+	0.666494i	$0.767794\pi$
$882$	−20.1389	+	1.63731i	−0.678111	+	0.0551311i
$883$	−49.6632			−1.67130			−0.835650	−	0.549263i	$-0.814909\pi$
$883$	−49.6632			−1.67130			−0.835650	+	0.549263i	$0.814909\pi$
$884$	−2.81602	−	13.8918i	−0.0947131	−	0.467232i
$885$	10.5818			0.355703
$886$	19.3795	−	1.57557i	0.651067	−	0.0529323i
$887$	18.7263	−	3.72489i	0.628768	−	0.125070i	0.129588	−	0.991568i	$-0.458635\pi$
$887$	18.7263	−	3.72489i	0.628768	−	0.125070i	0.499180	+	0.866498i	$0.333635\pi$
$888$	14.5220	−	10.7238i	0.487328	−	0.359866i
$889$	2.87211	+	1.91908i	0.0963275	+	0.0643640i
$890$	−12.1636	+	3.46444i	−0.407726	+	0.116128i
$891$	−4.17222	−	6.24417i	−0.139775	−	0.209187i
$892$	−7.29948	+	31.1116i	−0.244405	+	1.04169i
$893$	39.8099	−	16.4898i	1.33219	−	0.551810i
$894$	12.6758	+	7.05582i	0.423941	+	0.235982i
$895$	−1.17194	+	5.89174i	−0.0391737	+	0.196939i
$896$	−1.84934	+	4.21009i	−0.0617821	+	0.140649i
$897$	1.44396	−	1.44396i	0.0482124	−	0.0482124i
$898$	26.2816	+	33.1616i	0.877029	+	1.10662i
$899$	−44.9171	−	18.6053i	−1.49807	−	0.620520i
$900$	−14.1127	−	10.1425i	−0.470423	−	0.338083i
$901$	9.57425	−	4.39623i	0.318965	−	0.146460i
$902$	7.70308	−	3.95001i	0.256485	−	0.131521i
$903$	0.788776	−	1.90427i	0.0262488	−	0.0633703i
$904$	−0.702110	−	14.9217i	−0.0233518	−	0.496290i
$905$	11.8431	+	11.8431i	0.393677	+	0.393677i
$906$	1.85827	−	16.0556i	0.0617367	−	0.533410i
$907$	40.6907	+	8.09389i	1.35111	+	0.268753i	0.816989	−	0.576653i	$-0.195642\pi$
$907$	40.6907	+	8.09389i	1.35111	+	0.268753i	0.534124	+	0.845406i	$0.320642\pi$
$908$	11.6762	+	0.398366i	0.387489	+	0.0132202i
$909$	5.47490	+	13.2176i	0.181591	+	0.438400i
$910$	−0.587370	+	0.691330i	−0.0194711	+	0.0229174i
$911$	3.59828	−	2.40430i	0.119216	−	0.0796579i	−0.494532	−	0.869159i	$-0.664661\pi$
$911$	3.59828	−	2.40430i	0.119216	−	0.0796579i	0.613749	+	0.789501i	$0.289661\pi$
$912$	1.64377	+	12.7576i	0.0544307	+	0.422446i
$913$	−10.1966	+	15.2602i	−0.337457	+	0.505040i
$914$	51.6080	+	16.6212i	1.70704	+	0.549781i
$915$	0.742518	+	3.73289i	0.0245469	+	0.123406i
$916$	9.39686	+	15.1580i	0.310481	+	0.500833i
$917$			1.31688i			0.0434871i
$918$	−28.2238	−	2.19092i	−0.931525	−	0.0723111i
$919$			38.4158i			1.26722i	0.773652	+	0.633611i	$0.218428\pi$
$919$			38.4158i			1.26722i	−0.773652	+	0.633611i	$0.781572\pi$
$920$	−1.66880	+	2.77120i	−0.0550186	+	0.0913637i
$921$	0.351715	+	1.76819i	0.0115894	+	0.0582638i
$922$	−11.0716	+	34.3767i	−0.364623	+	1.13214i
$923$	−12.9766	+	19.4209i	−0.427131	+	0.639246i
$924$	2.59319	−	2.42208i	0.0853097	−	0.0796806i
$925$	23.1303	−	15.4552i	0.760521	−	0.508164i
$926$	−36.6216	−	31.1146i	−1.20346	−	1.02249i
$927$	−0.227406	−	0.549008i	−0.00746901	−	0.0180318i
$928$	−31.5199	−	5.84762i	−1.03469	−	0.191957i
$929$	38.9826	+	7.75412i	1.27898	+	0.254404i	0.787407	−	0.616433i	$-0.211423\pi$
$929$	38.9826	+	7.75412i	1.27898	+	0.254404i	0.491571	+	0.870838i	$0.336423\pi$
$930$	−10.5540	−	1.22152i	−0.346079	−	0.0400551i
$931$	16.2954	+	16.2954i	0.534059	+	0.534059i
$932$	10.6340	−	23.3839i	0.348329	−	0.765966i
$933$	−5.69293	+	13.7439i	−0.186378	+	0.449956i
$934$	13.2261	+	25.7928i	0.432771	+	0.843966i
$935$	−0.654033	−	17.3145i	−0.0213892	−	0.566245i
$936$	−10.0498	−	1.51201i	−0.328488	−	0.0494215i
$937$	30.2238	+	12.5191i	0.987369	+	0.408982i	0.817150	−	0.576425i	$-0.195553\pi$
$937$	30.2238	+	12.5191i	0.987369	+	0.408982i	0.170219	+	0.985406i	$0.445553\pi$
$938$	−3.77604	+	2.99264i	−0.123292	+	0.0977130i
$939$	10.7078	−	10.7078i	0.349436	−	0.349436i
$940$	8.23628	+	21.9752i	0.268638	+	0.716751i
$941$	11.1265	−	55.9366i	0.362713	−	1.82348i	−0.180127	−	0.983643i	$-0.557651\pi$
$941$	11.1265	−	55.9366i	0.362713	−	1.82348i	0.542840	−	0.839836i	$-0.317349\pi$
$942$	2.51223	−	4.51322i	0.0818530	−	0.147049i
$943$	−1.53913	+	0.637528i	−0.0501209	+	0.0207608i
$944$	36.4283	−	31.7694i	1.18564	−	1.03401i
$945$	1.00656	+	1.50642i	0.0327434	+	0.0490040i
$946$	9.42768	+	33.1006i	0.306520	+	1.07619i
$947$	33.5745	+	22.4338i	1.09103	+	0.729000i	0.964796	−	0.263000i	$-0.0847121\pi$
$947$	33.5745	+	22.4338i	1.09103	+	0.729000i	0.126231	+	0.992001i	$0.459712\pi$
$948$	2.86024	+	17.4742i	0.0928964	+	0.567535i
$949$	10.4791	−	2.08442i	0.340165	−	0.0676630i
$950$	1.60624	+	19.7567i	0.0521132	+	0.640991i
$951$	−15.2521			−0.494583
$952$	0.401337	+	4.72286i	0.0130074	+	0.153069i
$953$	8.96145			0.290290			0.145145	−	0.989410i	$-0.453635\pi$
$953$	8.96145			0.290290			0.145145	+	0.989410i	$0.453635\pi$
$954$	−0.612108	−	7.52891i	−0.0198177	−	0.243758i
$955$	8.59908	−	1.71046i	0.278260	−	0.0553493i
$956$	−6.30970	−	38.5481i	−0.204070	−	1.24673i
$957$	20.5688	+	13.7436i	0.664894	+	0.444268i
$958$	−12.9360	−	45.4181i	−0.417942	−	1.46739i
$959$	1.90493	+	2.85092i	0.0615133	+	0.0920611i
$960$	−6.97461	+	0.657806i	−0.225105	+	0.0212306i
$961$	−39.3571	+	16.3022i	−1.26958	+	0.525879i
$962$	7.91200	−	14.2139i	0.255093	−	0.458274i
$963$	5.60937	−	28.2002i	0.180759	−	0.908739i
$964$	4.59916	+	12.2710i	0.148129	+	0.395222i
$965$	−6.20437	+	6.20437i	−0.199726	+	0.199726i
$966$	−0.535171	+	0.424141i	−0.0172188	+	0.0136465i
$967$	−24.7485	−	10.2512i	−0.795857	−	0.329655i	−0.0525615	−	0.998618i	$-0.516739\pi$
$967$	−24.7485	−	10.2512i	−0.795857	−	0.329655i	−0.743296	+	0.668963i	$0.766739\pi$
$968$	−4.18623	+	27.8245i	−0.134551	+	0.894312i
$969$	7.77715	+	10.7385i	0.249838	+	0.344970i
$970$	5.24355	+	10.2257i	0.168360	+	0.328327i
$971$	−3.71697	+	8.97356i	−0.119283	+	0.287975i	−0.972232	−	0.234020i	$-0.924812\pi$
$971$	−3.71697	+	8.97356i	−0.119283	+	0.287975i	0.852949	+	0.521995i	$0.174812\pi$
$972$	−13.3541	+	29.3654i	−0.428334	+	0.941895i
$973$	−2.95857	−	2.95857i	−0.0948473	−	0.0948473i
$974$	−28.8703	−	3.34144i	−0.925065	−	0.107067i
$975$	6.68391	+	1.32951i	0.214056	+	0.0425785i
$976$	13.7633	+	10.6214i	0.440553	+	0.339983i
$977$	13.8857	+	33.5230i	0.444242	+	1.07250i	0.974445	+	0.224625i	$0.0721158\pi$
$977$	13.8857	+	33.5230i	0.444242	+	1.07250i	−0.530203	+	0.847871i	$0.677884\pi$
$978$	12.4808	+	10.6040i	0.399092	+	0.339078i
$979$	37.0666	−	24.7671i	1.18465	−	0.791560i
$980$	−9.17235	+	8.56712i	−0.293000	+	0.273667i
$981$	19.5193	−	29.2127i	0.623203	−	0.932689i
$982$	−5.75135	+	17.8576i	−0.183533	+	0.569860i
$983$	2.38654	+	11.9979i	0.0761187	+	0.382674i	1.00000		4.70595e-6i	$-1.49795e-6\pi$
$983$	2.38654	+	11.9979i	0.0761187	+	0.382674i	−0.923881	+	0.382679i	$0.875001\pi$
$984$	−3.09069	−	1.86119i	−0.0985275	−	0.0593326i
$985$		−	17.1246i		−	0.545635i
$986$	−31.4161	+	10.2448i	−1.00049	+	0.326262i
$987$			4.95395i			0.157686i
$988$	6.10740	+	9.85179i	0.194302	+	0.313427i
$989$	−1.29214	−	6.49605i	−0.0410878	−	0.206562i
$990$	−11.8251	−	3.80846i	−0.375825	−	0.121041i
$991$	−0.753137	+	1.12715i	−0.0239242	+	0.0358051i	−0.843239	−	0.537539i	$-0.819354\pi$
$991$	−0.753137	+	1.12715i	−0.0239242	+	0.0358051i	0.819315	+	0.573344i	$0.194354\pi$
$992$	−40.0000	+	27.4808i	−1.27000	+	0.872517i
$993$	−17.9629	+	12.0024i	−0.570036	+	0.380886i
$994$	5.05725	−	5.95234i	0.160406	−	0.188797i
$995$	3.29347	+	7.95114i	0.104410	+	0.252068i
$996$	7.64453	+	0.260813i	0.242226	+	0.00826419i
$997$	−28.3234	−	5.63388i	−0.897012	−	0.178427i	−0.275009	−	0.961442i	$-0.588681\pi$
$997$	−28.3234	−	5.63388i	−0.897012	−	0.178427i	−0.622003	+	0.783015i	$0.713681\pi$
$998$	−1.05495	+	9.11487i	−0.0333939	+	0.288526i
$999$	−22.9734	−	22.9734i	−0.726845	−	0.726845i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	68.2.i.b.11.5	✓	48
3.2	odd	2		612.2.bd.d.487.2		48
4.3	odd	2	inner	68.2.i.b.11.6	yes	48
12.11	even	2		612.2.bd.d.487.1		48
17.14	odd	16	inner	68.2.i.b.31.6	yes	48
51.14	even	16		612.2.bd.d.235.1		48
68.31	even	16	inner	68.2.i.b.31.5	yes	48
204.167	odd	16		612.2.bd.d.235.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.2.i.b.11.5	✓	48	1.1	even	1	trivial
68.2.i.b.11.6	yes	48	4.3	odd	2	inner
68.2.i.b.31.5	yes	48	68.31	even	16	inner
68.2.i.b.31.6	yes	48	17.14	odd	16	inner
612.2.bd.d.235.1		48	51.14	even	16
612.2.bd.d.235.2		48	204.167	odd	16
612.2.bd.d.487.1		48	12.11	even	2
612.2.bd.d.487.2		48	3.2	odd	2

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:	\( N \)	\(=\)	\( 68 = 2^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	68.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.114599 + 1.40956i) q^{2} +(0.935416 - 0.186066i) q^{3} +(-1.97373 + 0.323068i) q^{4} +(0.763429 + 0.510107i) q^{5} +(0.369469 + 1.29720i) q^{6} +(-0.225807 - 0.337944i) q^{7} +(-0.681573 - 2.74508i) q^{8} +(-1.93126 + 0.799952i) q^{9} +O(q^{10})\)	\(q+(0.114599 + 1.40956i) q^{2} +(0.935416 - 0.186066i) q^{3} +(-1.97373 + 0.323068i) q^{4} +(0.763429 + 0.510107i) q^{5} +(0.369469 + 1.29720i) q^{6} +(-0.225807 - 0.337944i) q^{7} +(-0.681573 - 2.74508i) q^{8} +(-1.93126 + 0.799952i) q^{9} +(-0.631540 + 1.13456i) q^{10} +(0.892912 - 4.48897i) q^{11} +(-1.78615 + 0.669448i) q^{12} +(-1.21544 + 1.21544i) q^{13} +(0.450476 - 0.357017i) q^{14} +(0.809037 + 0.335114i) q^{15} +(3.79125 - 1.27530i) q^{16} +(2.80335 - 3.02345i) q^{17} +(-1.34890 - 2.63055i) q^{18} +(-1.29031 + 3.11507i) q^{19} +(-1.67161 - 0.760176i) q^{20} +(-0.274103 - 0.274103i) q^{21} +(6.42981 + 0.744184i) q^{22} +(-1.22170 - 0.243011i) q^{23} +(-1.14832 - 2.44097i) q^{24} +(-1.59080 - 3.84054i) q^{25} +(-1.85253 - 1.57395i) q^{26} +(-4.03671 + 2.69724i) q^{27} +(0.554862 + 0.594060i) q^{28} +(-3.14845 + 4.71199i) q^{29} +(-0.379650 + 1.17879i) q^{30} +(1.67369 + 8.41419i) q^{31} +(2.23209 + 5.19786i) q^{32} -4.36520i q^{33} +(4.58300 + 3.60501i) q^{34} -0.373182i q^{35} +(3.55335 - 2.20282i) q^{36} +(1.30555 + 6.56346i) q^{37} +(-4.53876 - 1.46178i) q^{38} +(-0.910791 + 1.36310i) q^{39} +(0.879951 - 2.44335i) q^{40} +(1.11203 - 0.743033i) q^{41} +(0.354954 - 0.417777i) q^{42} +(2.03481 + 4.91247i) q^{43} +(-0.312126 + 9.14851i) q^{44} +(-1.88244 - 0.374440i) q^{45} +(0.202534 - 1.74991i) q^{46} +(-9.03666 - 9.03666i) q^{47} +(3.30911 - 1.89836i) q^{48} +(2.61557 - 6.31454i) q^{49} +(5.23117 - 2.68246i) q^{50} +(2.05974 - 3.34979i) q^{51} +(2.00629 - 2.79163i) q^{52} +(2.36069 + 0.977830i) q^{53} +(-4.26453 - 5.38089i) q^{54} +(2.97153 - 2.97153i) q^{55} +(-0.773779 + 0.850191i) q^{56} +(-0.627364 + 3.15397i) q^{57} +(-7.00265 - 3.89795i) q^{58} +(11.1640 - 4.62429i) q^{59} +(-1.70509 - 0.400052i) q^{60} +(2.41467 + 3.61380i) q^{61} +(-11.6685 + 3.32342i) q^{62} +(0.706429 + 0.472021i) q^{63} +(-7.07092 + 3.74194i) q^{64} +(-1.54791 + 0.307898i) q^{65} +(6.15302 - 0.500246i) q^{66} -8.38234 q^{67} +(-4.55628 + 6.87316i) q^{68} -1.18801 q^{69} +(0.526023 - 0.0427662i) q^{70} +(13.3275 - 2.65100i) q^{71} +(3.51222 + 4.75622i) q^{72} +(-5.16828 - 3.45333i) q^{73} +(-9.10200 + 2.59242i) q^{74} +(-2.20266 - 3.29651i) q^{75} +(1.54034 - 6.56518i) q^{76} +(-1.71864 + 0.711886i) q^{77} +(-2.02574 - 1.12761i) q^{78} +(1.81098 - 9.10440i) q^{79} +(3.54489 + 0.960342i) q^{80} +(1.16022 - 1.16022i) q^{81} +(1.17479 + 1.48232i) q^{82} +(-3.70474 - 1.53455i) q^{83} +(0.629561 + 0.452453i) q^{84} +(3.68244 - 0.878180i) q^{85} +(-6.69125 + 3.43116i) q^{86} +(-2.06837 + 4.99349i) q^{87} +(-12.9312 + 0.608447i) q^{88} +(6.88729 + 6.88729i) q^{89} +(0.312072 - 2.69632i) q^{90} +(0.685206 + 0.136296i) q^{91} +(2.48982 + 0.0849468i) q^{92} +(3.13119 + 7.55935i) q^{93} +(11.7021 - 13.7733i) q^{94} +(-2.57408 + 1.71994i) q^{95} +(3.05508 + 4.44685i) q^{96} +(4.91684 - 7.35857i) q^{97} +(9.20048 + 2.96317i) q^{98} +(1.86652 + 9.38364i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9	\( 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9} + 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 24 q^{20} - 16 q^{21} - 8 q^{22} + 8 q^{24} + 16 q^{25} - 16 q^{26} + 40 q^{28} + 56 q^{30} + 32 q^{32} + 56 q^{34} + 56 q^{36} - 16 q^{37} + 32 q^{38} + 56 q^{40} - 48 q^{41} + 40 q^{42} + 24 q^{44} - 64 q^{45} + 8 q^{46} - 32 q^{48} - 16 q^{49} - 16 q^{52} + 48 q^{53} - 24 q^{54} - 48 q^{56} + 64 q^{57} - 64 q^{58} - 112 q^{60} + 16 q^{61} - 64 q^{62} - 56 q^{64} + 96 q^{65} - 96 q^{66} - 32 q^{68} + 32 q^{69} - 80 q^{70} - 64 q^{72} + 64 q^{73} - 16 q^{74} - 64 q^{76} + 16 q^{77} - 112 q^{78} - 24 q^{80} + 64 q^{81} - 40 q^{82} - 80 q^{85} + 64 q^{86} + 56 q^{88} - 16 q^{89} + 48 q^{90} + 104 q^{92} - 16 q^{93} + 88 q^{94} + 144 q^{96} - 16 q^{97} + 72 q^{98}+O(q^{100}) \) 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9 + 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 24 * q^20 - 16 * q^21 - 8 * q^22 + 8 * q^24 + 16 * q^25 - 16 * q^26 + 40 * q^28 + 56 * q^30 + 32 * q^32 + 56 * q^34 + 56 * q^36 - 16 * q^37 + 32 * q^38 + 56 * q^40 - 48 * q^41 + 40 * q^42 + 24 * q^44 - 64 * q^45 + 8 * q^46 - 32 * q^48 - 16 * q^49 - 16 * q^52 + 48 * q^53 - 24 * q^54 - 48 * q^56 + 64 * q^57 - 64 * q^58 - 112 * q^60 + 16 * q^61 - 64 * q^62 - 56 * q^64 + 96 * q^65 - 96 * q^66 - 32 * q^68 + 32 * q^69 - 80 * q^70 - 64 * q^72 + 64 * q^73 - 16 * q^74 - 64 * q^76 + 16 * q^77 - 112 * q^78 - 24 * q^80 + 64 * q^81 - 40 * q^82 - 80 * q^85 + 64 * q^86 + 56 * q^88 - 16 * q^89 + 48 * q^90 + 104 * q^92 - 16 * q^93 + 88 * q^94 + 144 * q^96 - 16 * q^97 + 72 * q^98

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