LMFDB - Embedded newform 416.2.bd.a.83.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(83,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 6]))

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

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

chi := DirichletCharacter("416.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bd (of order $8$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			83.4
Character	$\chi$	$=$	416.83
Dual form			416.2.bd.a.411.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37663 - 0.323857i) q^{2} +(-2.65712 - 1.10062i) q^{3} +(1.79023 + 0.891665i) q^{4} +(-1.41696 + 3.42085i) q^{5} +(3.30144 + 2.37567i) q^{6} +0.353777i q^{7} +(-2.17572 - 1.80728i) q^{8} +(3.72762 + 3.72762i) q^{9} +O(q^{10})$	\(q+(-1.37663 - 0.323857i) q^{2} +(-2.65712 - 1.10062i) q^{3} +(1.79023 + 0.891665i) q^{4} +(-1.41696 + 3.42085i) q^{5} +(3.30144 + 2.37567i) q^{6} +0.353777i q^{7} +(-2.17572 - 1.80728i) q^{8} +(3.72762 + 3.72762i) q^{9} +(3.05851 - 4.25036i) q^{10} +(2.46532 + 1.02117i) q^{11} +(-3.77548 - 4.33962i) q^{12} +(-3.60380 + 0.112275i) q^{13} +(0.114573 - 0.487021i) q^{14} +(7.53009 - 7.53009i) q^{15} +(2.40987 + 3.19258i) q^{16} +1.59116 q^{17} +(-3.92434 - 6.33878i) q^{18} +(-1.92428 - 4.64563i) q^{19} +(-5.58695 + 4.86066i) q^{20} +(0.389372 - 0.940028i) q^{21} +(-3.06313 - 2.20419i) q^{22} +(2.45672 + 2.45672i) q^{23} +(3.79204 + 7.19678i) q^{24} +(-6.15891 - 6.15891i) q^{25} +(4.99747 + 1.01256i) q^{26} +(-2.50021 - 6.03605i) q^{27} +(-0.315451 + 0.633343i) q^{28} +(-3.12000 + 7.53235i) q^{29} +(-12.8048 + 7.92748i) q^{30} +(-5.89587 - 5.89587i) q^{31} +(-2.28356 - 5.17546i) q^{32} +(-5.42675 - 5.42675i) q^{33} +(-2.19044 - 0.515309i) q^{34} +(-1.21022 - 0.501289i) q^{35} +(3.34952 + 9.99709i) q^{36} +(-9.34063 - 3.86902i) q^{37} +(1.14451 + 7.01852i) q^{38} +(9.69931 + 3.66807i) q^{39} +(9.26533 - 4.88197i) q^{40} +1.57288 q^{41} +(-0.840458 + 1.16797i) q^{42} +(0.399110 + 0.963538i) q^{43} +(3.50296 + 4.02637i) q^{44} +(-18.0335 + 7.46973i) q^{45} +(-2.58638 - 4.17763i) q^{46} +(-8.53183 - 8.53183i) q^{47} +(-2.88951 - 11.1354i) q^{48} +6.87484 q^{49} +(6.48394 + 10.4732i) q^{50} +(-4.22791 - 1.75126i) q^{51} +(-6.55176 - 3.01239i) q^{52} +(-1.84534 - 4.45505i) q^{53} +(1.48705 + 9.11913i) q^{54} +(-6.98654 + 6.98654i) q^{55} +(0.639372 - 0.769719i) q^{56} +14.4619i q^{57} +(6.73450 - 9.35884i) q^{58} +(0.791741 - 1.91143i) q^{59} +(20.1949 - 6.76629i) q^{60} +(2.66607 - 6.43647i) q^{61} +(6.20702 + 10.0259i) q^{62} +(-1.31875 + 1.31875i) q^{63} +(1.46751 + 7.86425i) q^{64} +(4.72238 - 12.4872i) q^{65} +(5.71314 + 9.22813i) q^{66} +(14.2881 - 5.91831i) q^{67} +(2.84855 + 1.41878i) q^{68} +(-3.82390 - 9.23172i) q^{69} +(1.50368 + 1.08203i) q^{70} -8.29142 q^{71} +(-1.37342 - 14.8471i) q^{72} -2.92849i q^{73} +(11.6056 + 8.35125i) q^{74} +(9.58637 + 23.1436i) q^{75} +(0.697433 - 10.0326i) q^{76} +(-0.361266 + 0.872174i) q^{77} +(-12.1645 - 8.19078i) q^{78} +0.975544 q^{79} +(-14.3360 + 3.72003i) q^{80} +2.97534i q^{81} +(-2.16528 - 0.509389i) q^{82} +(-1.97848 - 4.77649i) q^{83} +(1.53526 - 1.33568i) q^{84} +(-2.25462 + 5.44313i) q^{85} +(-0.237379 - 1.45569i) q^{86} +(16.5804 - 16.5804i) q^{87} +(-3.51832 - 6.67730i) q^{88} +5.86136 q^{89} +(27.2447 - 4.44278i) q^{90} +(-0.0397203 - 1.27494i) q^{91} +(2.20753 + 6.58868i) q^{92} +(9.17695 + 22.1551i) q^{93} +(8.98209 + 14.5083i) q^{94} +18.6187 q^{95} +(0.371507 + 16.2651i) q^{96} +(-0.254086 + 0.254086i) q^{97} +(-9.46413 - 2.22647i) q^{98} +(5.38325 + 12.9963i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24} - 4 q^{26} - 8 q^{27} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 44 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 4 q^{37} - 28 q^{39} - 8 q^{40} - 8 q^{41} - 48 q^{42} - 32 q^{43} + 12 q^{44} - 36 q^{45} - 48 q^{46} - 8 q^{47} - 8 q^{48} - 168 q^{49} + 76 q^{50} - 4 q^{52} - 8 q^{53} - 28 q^{54} - 40 q^{55} + 56 q^{56} + 32 q^{58} + 52 q^{59} - 36 q^{60} - 8 q^{61} + 72 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} - 4 q^{67} - 64 q^{68} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 8 q^{74} - 68 q^{76} + 56 q^{77} - 48 q^{78} - 16 q^{79} + 28 q^{80} - 88 q^{82} + 36 q^{83} + 100 q^{84} - 24 q^{85} + 96 q^{86} - 8 q^{87} + 64 q^{88} - 8 q^{89} - 64 q^{90} + 72 q^{91} - 8 q^{92} - 40 q^{93} - 56 q^{94} + 36 q^{96} - 8 q^{97} + 52 q^{98} - 44 q^{99}+O(q^{100}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.37663	−	0.323857i	−0.973426	−	0.229002i
$2$	−1.37663	−	0.323857i	−0.973426	−	0.229002i
$3$	−2.65712	−	1.10062i	−1.53409	−	0.635441i	−0.553737	−	0.832692i	$-0.686799\pi$
$3$	−2.65712	−	1.10062i	−1.53409	−	0.635441i	−0.980353	+	0.197251i	$0.936799\pi$
$4$	1.79023	+	0.891665i	0.895116	+	0.445833i
$5$	−1.41696	+	3.42085i	−0.633685	+	1.52985i	0.201271	+	0.979535i	$0.435493\pi$
$5$	−1.41696	+	3.42085i	−0.633685	+	1.52985i	−0.834957	+	0.550316i	$0.814507\pi$
$6$	3.30144	+	2.37567i	1.34781	+	0.969864i
$7$			0.353777i			0.133715i	0.997763	+	0.0668575i	$0.0212973\pi$
$7$			0.353777i			0.133715i	−0.997763	+	0.0668575i	$0.978703\pi$
$8$	−2.17572	−	1.80728i	−0.769233	−	0.638968i
$9$	3.72762	+	3.72762i	1.24254	+	1.24254i
$10$	3.05851	−	4.25036i	0.967184	−	1.34408i
$11$	2.46532	+	1.02117i	0.743323	+	0.307894i	0.722014	−	0.691879i	$-0.243217\pi$
$11$	2.46532	+	1.02117i	0.743323	+	0.307894i	0.0213089	+	0.999773i	$0.493217\pi$
$12$	−3.77548	−	4.33962i	−1.08989	−	1.25274i
$13$	−3.60380	+	0.112275i	−0.999515	+	0.0311395i
$13$	−3.60380	+	0.112275i	−0.999515	+	0.0311395i
$14$	0.114573	−	0.487021i	0.0306210	−	0.130162i
$15$	7.53009	−	7.53009i	1.94426	−	1.94426i
$16$	2.40987	+	3.19258i	0.602467	+	0.798144i
$17$	1.59116			0.385913			0.192957	−	0.981207i	$-0.438192\pi$
$17$	1.59116			0.385913			0.192957	+	0.981207i	$0.438192\pi$
$18$	−3.92434	−	6.33878i	−0.924977	−	1.49406i
$19$	−1.92428	−	4.64563i	−0.441461	−	1.06578i	−0.975436	−	0.220281i	$-0.929303\pi$
$19$	−1.92428	−	4.64563i	−0.441461	−	1.06578i	0.533976	−	0.845500i	$-0.320697\pi$
$20$	−5.58695	+	4.86066i	−1.24928	+	1.08688i
$21$	0.389372	−	0.940028i	0.0849680	−	0.205131i
$22$	−3.06313	−	2.20419i	−0.653061	−	0.469935i
$23$	2.45672	+	2.45672i	0.512262	+	0.512262i	0.915219	−	0.402957i	$-0.132018\pi$
$23$	2.45672	+	2.45672i	0.512262	+	0.512262i	−0.402957	+	0.915219i	$0.632018\pi$
$24$	3.79204	+	7.19678i	0.774046	+	1.46904i
$25$	−6.15891	−	6.15891i	−1.23178	−	1.23178i
$26$	4.99747	+	1.01256i	0.980085	+	0.198579i
$27$	−2.50021	−	6.03605i	−0.481166	−	1.16164i
$28$	−0.315451	+	0.633343i	−0.0596146	+	0.119691i
$29$	−3.12000	+	7.53235i	−0.579369	+	1.39872i	0.314010	+	0.949420i	$0.398327\pi$
$29$	−3.12000	+	7.53235i	−0.579369	+	1.39872i	−0.893380	+	0.449302i	$0.851673\pi$
$30$	−12.8048	+	7.92748i	−2.33783	+	1.44735i
$31$	−5.89587	−	5.89587i	−1.05893	−	1.05893i	−0.998151	−	0.0607782i	$-0.980642\pi$
$31$	−5.89587	−	5.89587i	−1.05893	−	1.05893i	−0.0607782	−	0.998151i	$-0.519358\pi$
$32$	−2.28356	−	5.17546i	−0.403680	−	0.914900i
$33$	−5.42675	−	5.42675i	−0.944675	−	0.944675i
$34$	−2.19044	−	0.515309i	−0.375658	−	0.0883748i
$35$	−1.21022	−	0.501289i	−0.204564	−	0.0847333i
$36$	3.34952	+	9.99709i	0.558253	+	1.66618i
$37$	−9.34063	−	3.86902i	−1.53559	−	0.636062i	−0.554951	−	0.831883i	$-0.687263\pi$
$37$	−9.34063	−	3.86902i	−1.53559	−	0.636062i	−0.980640	+	0.195821i	$0.937263\pi$
$38$	1.14451	+	7.01852i	0.185664	+	1.13855i
$39$	9.69931	+	3.66807i	1.55313	+	0.587362i
$40$	9.26533	−	4.88197i	1.46498	−	0.771907i
$41$	1.57288			0.245643			0.122821	−	0.992429i	$-0.460806\pi$
$41$	1.57288			0.245643			0.122821	+	0.992429i	$0.460806\pi$
$42$	−0.840458	+	1.16797i	−0.129685	+	0.180222i
$43$	0.399110	+	0.963538i	0.0608638	+	0.146938i	0.951386	−	0.308002i	$-0.0996605\pi$
$43$	0.399110	+	0.963538i	0.0608638	+	0.146938i	−0.890522	+	0.454941i	$0.849660\pi$
$44$	3.50296	+	4.02637i	0.528091	+	0.606999i
$45$	−18.0335	+	7.46973i	−2.68828	+	1.11352i
$46$	−2.58638	−	4.17763i	−0.381340	−	0.615958i
$47$	−8.53183	−	8.53183i	−1.24449	−	1.24449i	−0.958117	−	0.286378i	$-0.907549\pi$
$47$	−8.53183	−	8.53183i	−1.24449	−	1.24449i	−0.286378	−	0.958117i	$-0.592451\pi$
$48$	−2.88951	−	11.1354i	−0.417064	−	1.60726i
$49$	6.87484			0.982120
$50$	6.48394	+	10.4732i	0.916968	+	1.48113i
$51$	−4.22791	−	1.75126i	−0.592026	−	0.245225i
$52$	−6.55176	−	3.01239i	−0.908565	−	0.417743i
$53$	−1.84534	−	4.45505i	−0.253477	−	0.611948i	0.745003	−	0.667061i	$-0.232448\pi$
$53$	−1.84534	−	4.45505i	−0.253477	−	0.611948i	−0.998480	+	0.0551131i	$0.982448\pi$
$54$	1.48705	+	9.11913i	0.202363	+	1.24096i
$55$	−6.98654	+	6.98654i	−0.942065	+	0.942065i
$56$	0.639372	−	0.769719i	0.0854397	−	0.102858i
$57$			14.4619i			1.91553i
$58$	6.73450	−	9.35884i	0.884283	−	1.22888i
$59$	0.791741	−	1.91143i	0.103076	−	0.248847i	−0.863925	−	0.503621i	$-0.832001\pi$
$59$	0.791741	−	1.91143i	0.103076	−	0.248847i	0.967001	+	0.254774i	$0.0820009\pi$
$60$	20.1949	−	6.76629i	2.60715	−	0.873524i
$61$	2.66607	−	6.43647i	0.341355	−	0.824105i	−0.656224	−	0.754566i	$-0.727847\pi$
$61$	2.66607	−	6.43647i	0.341355	−	0.824105i	0.997579	−	0.0695386i	$-0.0221527\pi$
$62$	6.20702	+	10.0259i	0.788293	+	1.27329i
$63$	−1.31875	+	1.31875i	−0.166146	+	0.166146i
$64$	1.46751	+	7.86425i	0.183439	+	0.983031i
$65$	4.72238	−	12.4872i	0.585739	−	1.54884i
$66$	5.71314	+	9.22813i	0.703239	+	1.13590i
$67$	14.2881	−	5.91831i	1.74557	−	0.723037i	0.747280	−	0.664509i	$-0.231359\pi$
$67$	14.2881	−	5.91831i	1.74557	−	0.723037i	0.998286	−	0.0585284i	$-0.0186408\pi$
$68$	2.84855	+	1.41878i	0.345437	+	0.172053i
$69$	−3.82390	−	9.23172i	−0.460344	−	1.11137i
$70$	1.50368	+	1.08203i	0.179724	+	0.129327i
$71$	−8.29142			−0.984011			−0.492005	−	0.870592i	$-0.663736\pi$
$71$	−8.29142			−0.984011			−0.492005	+	0.870592i	$0.663736\pi$
$72$	−1.37342	−	14.8471i	−0.161859	−	1.74975i
$73$		−	2.92849i		−	0.342754i	−0.985206	−	0.171377i	$-0.945178\pi$
$73$		−	2.92849i		−	0.342754i	0.985206	−	0.171377i	$-0.0548216\pi$
$74$	11.6056	+	8.35125i	1.34912	+	0.970813i
$75$	9.58637	+	23.1436i	1.10694	+	2.67239i
$76$	0.697433	−	10.0326i	0.0800010	−	1.15082i
$77$	−0.361266	+	0.872174i	−0.0411701	+	0.0993935i
$78$	−12.1645	−	8.19078i	−1.37735	−	0.927424i
$79$	0.975544			0.109757			0.0548787	−	0.998493i	$-0.482523\pi$
$79$	0.975544			0.109757			0.0548787	+	0.998493i	$0.482523\pi$
$80$	−14.3360	+	3.72003i	−1.60282	+	0.415912i
$81$			2.97534i			0.330593i
$82$	−2.16528	−	0.509389i	−0.239115	−	0.0562526i
$83$	−1.97848	−	4.77649i	−0.217167	−	0.524287i	0.777325	−	0.629099i	$-0.216576\pi$
$83$	−1.97848	−	4.77649i	−0.217167	−	0.524287i	−0.994492	+	0.104812i	$0.966576\pi$
$84$	1.53526	−	1.33568i	0.167510	−	0.145735i
$85$	−2.25462	+	5.44313i	−0.244547	+	0.590390i
$86$	−0.237379	−	1.45569i	−0.0255973	−	0.156971i
$87$	16.5804	−	16.5804i	1.77761	−	1.77761i
$88$	−3.51832	−	6.67730i	−0.375054	−	0.711802i
$89$	5.86136			0.621303			0.310652	−	0.950524i	$-0.399453\pi$
$89$	5.86136			0.621303			0.310652	+	0.950524i	$0.399453\pi$
$90$	27.2447	−	4.44278i	2.87184	−	0.468310i
$91$	−0.0397203	−	1.27494i	−0.00416382	−	0.133650i
$92$	2.20753	+	6.58868i	0.230151	+	0.686917i
$93$	9.17695	+	22.1551i	0.951606	+	2.29738i
$94$	8.98209	+	14.5083i	0.926432	+	1.49642i
$95$	18.6187			1.91023
$96$	0.371507	+	16.2651i	0.0379168	+	1.66005i
$97$	−0.254086	+	0.254086i	−0.0257986	+	0.0257986i	−0.719888	−	0.694090i	$-0.755807\pi$
$97$	−0.254086	+	0.254086i	−0.0257986	+	0.0257986i	0.694090	+	0.719888i	$0.255807\pi$
$98$	−9.46413	−	2.22647i	−0.956021	−	0.224907i
$99$	5.38325	+	12.9963i	0.541037	+	1.30618i
$100$	−5.53419	−	16.5176i	−0.553419	−	1.65176i
$101$	−1.78843	−	4.31765i	−0.177955	−	0.429622i	0.809582	−	0.587007i	$-0.199694\pi$
$101$	−1.78843	−	4.31765i	−0.177955	−	0.429622i	−0.987537	+	0.157385i	$0.949694\pi$
$102$	5.25312	+	3.78008i	0.520136	+	0.374283i
$103$	−2.77664	+	2.77664i	−0.273591	+	0.273591i	−0.830544	−	0.556953i	$-0.811970\pi$
$103$	−2.77664	+	2.77664i	−0.273591	+	0.273591i	0.556953	+	0.830544i	$0.311970\pi$
$104$	8.04378	+	6.26878i	0.788757	+	0.614705i
$105$	2.66397	+	2.66397i	0.259977	+	0.259977i
$106$	1.09756	+	6.73059i	0.106604	+	0.653733i
$107$	−8.49296	+	3.51790i	−0.821046	+	0.340088i	−0.753352	−	0.657618i	$-0.771564\pi$
$107$	−8.49296	+	3.51790i	−0.821046	+	0.340088i	−0.0676940	+	0.997706i	$0.521564\pi$
$108$	0.906171	−	13.0353i	0.0871964	−	1.25432i
$109$	−6.49096	+	2.68864i	−0.621721	+	0.257525i	−0.671231	−	0.741248i	$-0.734234\pi$
$109$	−6.49096	+	2.68864i	−0.621721	+	0.257525i	0.0495096	+	0.998774i	$0.484234\pi$
$110$	11.8805	−	7.35526i	1.13277	−	0.701296i
$111$	20.5609	+	20.5609i	1.95155	+	1.95155i
$112$	−1.12946	+	0.852555i	−0.106724	+	0.0805589i
$113$			5.63040i			0.529664i	0.964295	+	0.264832i	$0.0853165\pi$
$113$			5.63040i			0.529664i	−0.964295	+	0.264832i	$0.914684\pi$
$114$	4.68360	−	19.9087i	0.438659	−	1.86462i
$115$	−11.8852	+	4.92300i	−1.10830	+	0.459072i
$116$	−12.3019	+	10.7027i	−1.14220	+	0.993717i
$117$	−13.8521	−	13.0151i	−1.28063	−	1.20325i
$118$	−1.70897	+	2.37493i	−0.157323	+	0.218630i
$119$			0.562916i			0.0516024i
$120$	−29.9923	+	2.77442i	−2.73791	+	0.253269i
$121$	−2.74315	−	2.74315i	−0.249377	−	0.249377i
$122$	−5.75470	+	7.99722i	−0.521006	+	0.724034i
$123$	−4.17933	−	1.73114i	−0.376838	−	0.156091i
$124$	−5.29784	−	15.8121i	−0.475760	−	1.41997i
$125$	12.6914	−	5.25695i	1.13515	−	0.470195i
$126$	2.24251	−	1.38834i	0.199779	−	0.123683i
$127$	1.50867			0.133873			0.0669363	−	0.997757i	$-0.478678\pi$
$127$	1.50867			0.133873			0.0669363	+	0.997757i	$0.478678\pi$
$128$	0.526671	−	11.3014i	0.0465516	−	0.998916i
$129$		−	2.99950i		−	0.264092i
$130$	−10.5450	+	15.6609i	−0.924861	+	1.37355i
$131$	−12.6190	−	5.22695i	−1.10253	−	0.456681i	−0.244168	−	0.969733i	$-0.578515\pi$
$131$	−12.6190	−	5.22695i	−1.10253	−	0.456681i	−0.858358	+	0.513052i	$0.828515\pi$
$132$	−4.87630	−	14.5540i	−0.424427	−	1.26676i
$133$	1.64352	−	0.680767i	0.142511	−	0.0590300i
$134$	−21.5861	+	3.52004i	−1.86476	+	0.304085i
$135$	24.1911			2.08204
$136$	−3.46192	−	2.87567i	−0.296857	−	0.246586i
$137$			4.14276i			0.353940i	0.984216	+	0.176970i	$0.0566295\pi$
$137$			4.14276i			0.353940i	−0.984216	+	0.176970i	$0.943371\pi$
$138$	2.27435	+	13.9471i	0.193605	+	1.18725i
$139$	−10.2116	+	4.22977i	−0.866133	+	0.358764i	−0.771103	−	0.636710i	$-0.780295\pi$
$139$	−10.2116	+	4.22977i	−0.866133	+	0.358764i	−0.0950300	+	0.995474i	$0.530295\pi$
$140$	−1.71959	−	1.97653i	−0.145332	−	0.167048i
$141$	13.2798	+	32.0604i	1.11836	+	2.69997i
$142$	11.4142	+	2.68524i	0.957861	+	0.225340i
$143$	−8.99919	−	3.40330i	−0.752550	−	0.284598i
$144$	−2.91765	+	20.8838i	−0.243137	+	1.74031i
$145$	−21.3461	−	21.3461i	−1.77270	−	1.77270i
$146$	−0.948414	+	4.03146i	−0.0784913	+	0.333646i
$147$	−18.2673	−	7.56656i	−1.50666	−	0.624079i
$148$	−13.2720	−	15.2552i	−1.09095	−	1.25397i
$149$	16.8714	+	6.98838i	1.38216	+	0.572510i	0.945059	−	0.326901i	$-0.106004\pi$
$149$	16.8714	+	6.98838i	1.38216	+	0.572510i	0.437103	+	0.899411i	$0.356004\pi$
$150$	−5.70170	−	34.9648i	−0.465542	−	2.85486i
$151$	−10.4562			−0.850914			−0.425457	−	0.904979i	$-0.639887\pi$
$151$	−10.4562			−0.850914			−0.425457	+	0.904979i	$0.639887\pi$
$152$	−4.20923	+	13.5853i	−0.341414	+	1.10191i
$153$	5.93124	+	5.93124i	0.479512	+	0.479512i
$154$	0.779791	−	1.08366i	0.0628374	−	0.0873242i
$155$	28.5231	−	11.8147i	2.29103	−	0.948977i
$156$	14.0933	+	15.2152i	1.12837	+	1.21819i
$157$	0.894726	−	2.16006i	0.0714069	−	0.172392i	−0.884146	−	0.467210i	$-0.845259\pi$
$157$	0.894726	−	2.16006i	0.0714069	−	0.172392i	0.955553	+	0.294818i	$0.0952592\pi$
$158$	−1.34297	−	0.315937i	−0.106841	−	0.0251346i
$159$			13.8686i			1.09985i
$160$	20.9402	−	0.478288i	1.65547	−	0.0378120i
$161$	−0.869132	+	0.869132i	−0.0684972	+	0.0684972i
$162$	0.963586	−	4.09595i	0.0757065	−	0.321808i
$163$	4.27941	+	10.3314i	0.335190	+	0.809219i	0.998164	+	0.0605769i	$0.0192940\pi$
$163$	4.27941	+	10.3314i	0.335190	+	0.809219i	−0.662974	+	0.748643i	$0.730706\pi$
$164$	2.81582	+	1.40248i	0.219879	+	0.109515i
$165$	26.2536	−	10.8746i	2.04384	−	0.846586i
$166$	1.17675	+	7.21621i	0.0913332	+	0.560087i
$167$		−	18.8148i		−	1.45593i	−0.685615	−	0.727965i	$-0.740466\pi$
$167$		−	18.8148i		−	1.45593i	0.685615	−	0.727965i	$-0.259534\pi$
$168$	−2.54605	+	1.34153i	−0.196432	+	0.103502i
$169$	12.9748	−	0.809233i	0.998061	−	0.0622487i
$170$	4.86657	−	6.76301i	0.373249	−	0.518699i
$171$	10.1441	−	24.4901i	0.775742	−	1.87281i
$172$	−0.144653	+	2.08083i	−0.0110297	+	0.158662i
$173$	−2.07624	+	5.01250i	−0.157854	+	0.381093i	−0.982943	−	0.183909i	$-0.941125\pi$
$173$	−2.07624	+	5.01250i	−0.157854	+	0.381093i	0.825089	+	0.565002i	$0.191125\pi$
$174$	−28.1949	+	17.4555i	−2.13745	+	1.32330i
$175$	2.17888	−	2.17888i	0.164708	−	0.164708i
$176$	2.68093	+	10.3316i	0.202083	+	0.778775i
$177$	−4.20750	+	4.20750i	−0.316255	+	0.316255i
$178$	−8.06894	−	1.89825i	−0.604793	−	0.142280i
$179$	−15.6779	−	6.49400i	−1.17182	−	0.485384i	−0.290027	−	0.957019i	$-0.593664\pi$
$179$	−15.6779	−	6.49400i	−1.17182	−	0.485384i	−0.881794	+	0.471634i	$0.843664\pi$
$180$	−38.9447	−	2.70731i	−2.90277	−	0.201791i
$181$	21.9954	−	9.11080i	1.63491	−	0.677200i	0.639137	−	0.769093i	$-0.279292\pi$
$181$	21.9954	−	9.11080i	1.63491	−	0.677200i	0.995769	+	0.0918931i	$0.0292918\pi$
$182$	−0.358219	+	1.76799i	−0.0265530	+	0.131052i
$183$	−14.1682	+	14.1682i	−1.04734	+	1.04734i
$184$	−0.905166	−	9.78511i	−0.0667297	−	0.721368i
$185$	26.4707	−	26.4707i	1.94616	−	1.94616i
$186$	−5.45819	−	33.4715i	−0.400214	−	2.45425i
$187$	3.92273	+	1.62485i	0.286858	+	0.118821i
$188$	−7.66642	−	22.8815i	−0.559131	−	1.66880i
$189$	2.13541	−	0.884518i	0.155329	−	0.0643392i
$190$	−25.6310	−	6.02979i	−1.85947	−	0.437447i
$191$		−	4.98552i		−	0.360739i	−0.983599	−	0.180370i	$-0.942271\pi$
$191$		−	4.98552i		−	0.360739i	0.983599	−	0.180370i	$-0.0577294\pi$
$192$	4.75616	−	22.5114i	0.343246	−	1.62462i
$193$	7.82300	+	7.82300i	0.563112	+	0.563112i	0.930190	−	0.367078i	$-0.119642\pi$
$193$	7.82300	+	7.82300i	0.563112	+	0.563112i	−0.367078	+	0.930190i	$0.619642\pi$
$194$	0.432071	−	0.267496i	0.0310209	−	0.0192051i
$195$	−26.2915	+	27.9824i	−1.88277	+	2.00386i
$196$	12.3076	+	6.13006i	0.879112	+	0.437861i
$197$	−6.87393	+	16.5951i	−0.489747	+	1.18235i	0.465101	+	0.885258i	$0.346018\pi$
$197$	−6.87393	+	16.5951i	−0.489747	+	1.18235i	−0.954848	+	0.297096i	$0.903982\pi$
$198$	−3.20180	−	19.6346i	−0.227542	−	1.39537i
$199$	−12.4837	+	12.4837i	−0.884943	+	0.884943i	−0.994032	−	0.109089i	$-0.965207\pi$
$199$	−12.4837	+	12.4837i	−0.884943	+	0.884943i	0.109089	+	0.994032i	$0.465207\pi$
$200$	2.26921	+	24.5309i	0.160458	+	1.73460i
$201$	−44.4789			−3.13730
$202$	1.06371	+	6.52301i	0.0748421	+	0.458957i
$203$	−2.66477	−	1.10378i	−0.187030	−	0.0774704i
$204$	−6.00740	−	6.90504i	−0.420602	−	0.483449i
$205$	−2.22871	+	5.38059i	−0.155660	+	0.375797i
$206$	4.72165	−	2.92318i	0.328973	−	0.203668i
$207$			18.3155i			1.27301i
$208$	−9.04313	−	11.2348i	−0.627028	−	0.778997i
$209$		−	13.4180i		−	0.928143i
$210$	−2.80456	−	4.53005i	−0.193533	−	0.312603i
$211$	7.42408	−	17.9233i	0.511095	−	1.23389i	−0.432152	−	0.901801i	$-0.642246\pi$
$211$	7.42408	−	17.9233i	0.511095	−	1.23389i	0.943247	−	0.332092i	$-0.107754\pi$
$212$	0.668821	−	9.62100i	0.0459348	−	0.660773i
$213$	22.0313	+	9.12567i	1.50956	+	0.625280i
$214$	12.8310	−	2.09235i	0.877108	−	0.143030i
$215$	−3.86164			−0.263362
$216$	−5.46904	+	17.6513i	−0.372121	+	1.20102i
$217$	2.08582	−	2.08582i	0.141595	−	0.141595i
$218$	9.80640	−	1.59913i	0.664174	−	0.108307i
$219$	−3.22315	+	7.78136i	−0.217800	+	0.525816i
$220$	−18.7372	+	6.27788i	−1.26326	+	0.423255i
$221$	−5.73423	+	0.178647i	−0.385726	+	0.0120171i
$222$	−21.6460	−	34.9636i	−1.45278	−	2.34660i
$223$	13.7154	+	13.7154i	0.918450	+	0.918450i	0.996917	−	0.0784671i	$-0.0250025\pi$
$223$	13.7154	+	13.7154i	0.918450	+	0.918450i	−0.0784671	+	0.996917i	$0.525003\pi$
$224$	1.83096	−	0.807871i	0.122336	−	0.0539781i
$225$		−	45.9161i		−	3.06107i
$226$	1.82345	−	7.75099i	0.121294	−	0.515588i
$227$	−12.1243	+	5.02203i	−0.804715	+	0.333324i	−0.746843	−	0.665000i	$-0.768432\pi$
$227$	−12.1243	+	5.02203i	−0.804715	+	0.333324i	−0.0578720	+	0.998324i	$0.518432\pi$
$228$	−12.8952	+	25.8902i	−0.854004	+	1.71462i
$229$	−18.7008	−	7.74614i	−1.23579	−	0.511879i	−0.333391	−	0.942789i	$-0.608193\pi$
$229$	−18.7008	−	7.74614i	−1.23579	−	0.511879i	−0.902395	+	0.430910i	$0.858193\pi$
$230$	17.9559	−	2.92806i	1.18397	−	0.193070i
$231$	1.91986	−	1.91986i	0.126317	−	0.126317i
$232$	20.4013	−	10.7496i	1.33941	−	0.705744i
$233$	−9.84366	+	9.84366i	−0.644880	+	0.644880i	−0.951751	−	0.306871i	$-0.900718\pi$
$233$	−9.84366	+	9.84366i	−0.644880	+	0.644880i	0.306871	+	0.951751i	$0.400718\pi$
$234$	14.8542	+	22.4031i	0.971052	+	1.46454i
$235$	41.2754	−	17.0968i	2.69251	−	1.11527i
$236$	3.12176	−	2.71594i	0.203209	−	0.176793i
$237$	−2.59214	−	1.07370i	−0.168378	−	0.0697443i
$238$	0.182305	−	0.774928i	0.0118170	−	0.0502311i
$239$	−1.97560	+	1.97560i	−0.127791	+	0.127791i	−0.768109	−	0.640319i	$-0.778802\pi$
$239$	−1.97560	+	1.97560i	−0.127791	+	0.127791i	0.640319	+	0.768109i	$0.278802\pi$
$240$	42.1869	+	5.89387i	2.72315	+	0.380448i
$241$	−16.0083	+	16.0083i	−1.03119	+	1.03119i	−0.0316884	+	0.999498i	$0.510088\pi$
$241$	−16.0083	+	16.0083i	−1.03119	+	1.03119i	−0.999498	+	0.0316884i	$0.989912\pi$
$242$	2.88792	+	4.66469i	0.185642	+	0.299858i
$243$	−4.22593	+	10.2023i	−0.271094	+	0.654478i
$244$	10.5121	−	9.14553i	0.672966	−	0.585482i
$245$	−9.74140	+	23.5178i	−0.622355	+	1.50250i
$246$	5.19276	+	3.73665i	0.331079	+	0.238240i
$247$	7.45633	+	16.5259i	0.474435	+	1.05152i
$248$	2.17230	+	23.4832i	0.137941	+	1.49119i
$249$			14.8693i			0.942301i
$250$	−19.1739	+	3.12668i	−1.21266	+	0.197749i
$251$	2.90534	−	1.20343i	0.183384	−	0.0759600i	−0.289102	−	0.957298i	$-0.593357\pi$
$251$	2.90534	−	1.20343i	0.183384	−	0.0759600i	0.472486	+	0.881338i	$0.343357\pi$
$252$	−3.53674	+	1.18498i	−0.222794	+	0.0746468i
$253$	3.54788	+	8.56534i	0.223053	+	0.538499i
$254$	−2.07688	−	0.488593i	−0.130315	−	0.0306571i
$255$	11.9816	−	11.9816i	0.750316	−	0.750316i
$256$	−4.38509	+	15.3874i	−0.274068	+	0.961710i
$257$			20.2150i			1.26098i	0.776198	+	0.630490i	$0.217146\pi$
$257$			20.2150i			1.26098i	−0.776198	+	0.630490i	$0.782854\pi$
$258$	−0.971412	+	4.12921i	−0.0604775	+	0.257074i
$259$	1.36877	−	3.30450i	0.0850511	−	0.205332i
$260$	19.5885	−	18.1441i	1.21483	−	1.12525i
$261$	−39.7079	+	16.4475i	−2.45786	+	1.01808i
$262$	15.6789	+	11.2823i	0.968646	+	0.697025i
$263$	−6.40220	−	6.40220i	−0.394776	−	0.394776i	0.481610	−	0.876386i	$-0.340052\pi$
$263$	−6.40220	−	6.40220i	−0.394776	−	0.394776i	−0.876386	+	0.481610i	$0.840052\pi$
$264$	1.99945	+	21.6147i	0.123058	+	1.33029i
$265$	17.8548			1.09681
$266$	−2.48299	+	0.404901i	−0.152242	+	0.0248261i
$267$	−15.5744	−	6.45111i	−0.953135	−	0.394801i
$268$	30.8561	+	2.14502i	1.88484	+	0.131028i
$269$	20.1893	+	8.36268i	1.23096	+	0.509881i	0.900879	−	0.434070i	$-0.142923\pi$
$269$	20.1893	+	8.36268i	1.23096	+	0.509881i	0.330084	+	0.943952i	$0.392923\pi$
$270$	−33.3023	−	7.83448i	−2.02671	−	0.476791i
$271$	−21.7642	−	21.7642i	−1.32208	−	1.32208i	−0.912091	−	0.409988i	$-0.865533\pi$
$271$	−21.7642	−	21.7642i	−1.32208	−	1.32208i	−0.409988	−	0.912091i	$-0.634467\pi$
$272$	3.83449	+	5.07990i	0.232500	+	0.308014i
$273$	−1.29768	+	3.43139i	−0.0785392	+	0.207677i
$274$	1.34166	−	5.70305i	0.0810528	−	0.344534i
$275$	−8.89440	−	21.4730i	−0.536353	−	1.29487i
$276$	1.38593	−	19.9366i	0.0834229	−	1.20004i
$277$	19.2556	−	7.97591i	1.15695	−	0.479226i	0.280095	−	0.959972i	$-0.409634\pi$
$277$	19.2556	−	7.97591i	1.15695	−	0.479226i	0.876860	+	0.480746i	$0.159634\pi$
$278$	15.4274	−	2.51574i	0.925274	−	0.150884i
$279$		−	43.9551i		−	2.63152i
$280$	1.72713	+	3.27786i	0.103216	+	0.195890i
$281$	−30.1434			−1.79821			−0.899103	−	0.437737i	$-0.855780\pi$
$281$	−30.1434			−1.79821			−0.899103	+	0.437737i	$0.855780\pi$
$282$	−7.89847	−	48.4361i	−0.470347	−	2.88433i
$283$	3.68558	−	1.52662i	0.219085	−	0.0907480i	−0.270441	−	0.962736i	$-0.587170\pi$
$283$	3.68558	−	1.52662i	0.219085	−	0.0907480i	0.489527	+	0.871988i	$0.337170\pi$
$284$	−14.8436	−	7.39317i	−0.880804	−	0.438704i
$285$	−49.4720	−	20.4920i	−2.93047	−	1.21384i
$286$	11.2864	+	7.59955i	0.667378	+	0.449371i
$287$			0.556449i			0.0328461i
$288$	10.7799	−	27.8044i	0.635211	−	1.63839i
$289$	−14.4682			−0.851071
$290$	22.4726	+	36.2988i	1.31964	+	2.13154i
$291$	0.954790	−	0.395487i	0.0559708	−	0.0231838i
$292$	2.61124	−	5.24268i	0.152811	−	0.306805i
$293$	7.49438	+	3.10427i	0.437826	+	0.181354i	0.590698	−	0.806892i	$-0.298852\pi$
$293$	7.49438	+	3.10427i	0.437826	+	0.181354i	−0.152872	+	0.988246i	$0.548852\pi$
$294$	22.6969	+	16.3324i	1.32371	+	0.952523i
$295$	5.41685	+	5.41685i	0.315381	+	0.315381i
$296$	13.3302	+	25.2990i	0.774803	+	1.47047i
$297$		−	17.4339i		−	1.01162i
$298$	−20.9625	−	15.0844i	−1.21433	−	0.873814i
$299$	−9.12937	−	8.57771i	−0.527965	−	0.496062i
$300$	−3.47446	+	49.9802i	−0.200598	+	2.88561i
$301$	−0.340877	+	0.141196i	−0.0196478	+	0.00813840i
$302$	14.3944	+	3.38632i	0.828302	+	0.194861i
$303$			13.4409i			0.772159i
$304$	10.1943	−	17.3388i	0.584681	−	0.994447i
$305$	18.2405	+	18.2405i	1.04445	+	1.04445i
$306$	−6.24426	−	10.0860i	−0.356961	−	0.576579i
$307$	−0.366292	+	0.151723i	−0.0209054	+	0.00865930i	−0.393112	−	0.919491i	$-0.628601\pi$
$307$	−0.366292	+	0.151723i	−0.0209054	+	0.00865930i	0.372206	+	0.928150i	$0.378601\pi$
$308$	−1.42444	+	1.23927i	−0.0811649	+	0.0706137i
$309$	10.4339	−	4.32186i	0.593563	−	0.245862i
$310$	−43.0921	+	7.02702i	−2.44747	+	0.399108i
$311$	8.51083	+	8.51083i	0.482605	+	0.482605i	0.905963	−	0.423358i	$-0.139149\pi$
$311$	8.51083	+	8.51083i	0.482605	+	0.482605i	−0.423358	+	0.905963i	$0.639149\pi$
$312$	−14.4738	−	25.5100i	−0.819416	−	1.44422i
$313$	−14.1585	+	14.1585i	−0.800285	+	0.800285i	−0.983140	−	0.182855i	$-0.941466\pi$
$313$	−14.1585	+	14.1585i	−0.800285	+	0.800285i	0.182855	+	0.983140i	$0.441466\pi$
$314$	−1.93126	+	2.68384i	−0.108987	+	0.151458i
$315$	−2.64262	−	6.37985i	−0.148895	−	0.359464i
$316$	1.74645	+	0.869859i	0.0982456	+	0.0489334i
$317$	−6.31088	−	15.2358i	−0.354454	−	0.855728i	−0.996059	−	0.0886929i	$-0.971731\pi$
$317$	−6.31088	−	15.2358i	−0.354454	−	0.855728i	0.641605	−	0.767035i	$-0.278269\pi$
$318$	4.49146	−	19.0920i	0.251868	−	1.07063i
$319$	−15.3836	+	15.3836i	−0.861317	+	0.861317i
$320$	−28.9818	−	6.12321i	−1.62013	−	0.342298i
$321$	26.4387			1.47566
$322$	1.47795	−	0.915000i	0.0823629	−	0.0509910i
$323$	−3.06184	−	7.39195i	−0.170366	−	0.411299i
$324$	−2.65301	+	5.32655i	−0.147389	+	0.295919i
$325$	22.8870	+	21.5040i	1.26954	+	1.19283i
$326$	−2.54527	−	15.6085i	−0.140970	−	0.864474i
$327$	20.2064			1.11742
$328$	−3.42215	−	2.84263i	−0.188956	−	0.156958i
$329$	3.01836	−	3.01836i	0.166408	−	0.166408i
$330$	−39.6634	+	6.46789i	−2.18340	+	0.356046i
$331$	−4.25527	+	10.2731i	−0.233891	+	0.564662i	−0.996629	−	0.0820456i	$-0.973855\pi$
$331$	−4.25527	+	10.2731i	−0.233891	+	0.564662i	0.762738	+	0.646708i	$0.223855\pi$
$332$	0.717077	−	10.3152i	0.0393547	−	0.566118i
$333$	−20.3961	−	49.2405i	−1.11770	−	2.69836i
$334$	−6.09330	+	25.9010i	−0.333410	+	1.41724i
$335$			57.2634i			3.12863i
$336$	3.93945	−	1.02224i	0.214914	−	0.0557678i
$337$	−2.85453			−0.155496			−0.0777480	−	0.996973i	$-0.524773\pi$
$337$	−2.85453			−0.155496			−0.0777480	+	0.996973i	$0.524773\pi$
$338$	−18.1236	−	3.08797i	−0.985793	−	0.167963i
$339$	6.19691	−	14.9607i	0.336570	−	0.812552i
$340$	−8.88973	+	7.73410i	−0.482113	+	0.419440i
$341$	−8.51454	−	20.5559i	−0.461088	−	1.11316i
$342$	−21.8961	+	30.4287i	−1.18400	+	1.64539i
$343$			4.90860i			0.265039i
$344$	0.873026	−	2.81769i	0.0470704	−	0.151920i
$345$	36.9987			1.99194
$346$	4.48156	−	6.22796i	0.240930	−	0.334817i
$347$	−3.27675	−	7.91078i	−0.175905	−	0.424673i	0.811195	−	0.584776i	$-0.198817\pi$
$347$	−3.27675	−	7.91078i	−0.175905	−	0.424673i	−0.987100	+	0.160103i	$0.948817\pi$
$348$	44.4670	−	14.8986i	2.38368	−	0.798651i
$349$	10.4538	−	4.33012i	0.559581	−	0.231786i	−0.0849220	−	0.996388i	$-0.527064\pi$
$349$	10.4538	−	4.33012i	0.559581	−	0.231786i	0.644503	+	0.764601i	$0.277064\pi$
$350$	−3.70516	+	2.29387i	−0.198049	+	0.122612i
$351$	9.68797	+	21.4720i	0.517106	+	1.14609i
$352$	−0.344690	−	15.0911i	−0.0183721	−	0.804357i
$353$	0.176228	−	0.176228i	0.00937969	−	0.00937969i	−0.702401	−	0.711781i	$-0.747889\pi$
$353$	0.176228	−	0.176228i	0.00937969	−	0.00937969i	0.711781	+	0.702401i	$0.247889\pi$
$354$	7.15481	−	4.42955i	0.380274	−	0.235428i
$355$	11.7486	−	28.3637i	0.623553	−	1.50539i
$356$	10.4932	+	5.22637i	0.556139	+	0.276997i
$357$	0.619554	−	1.49574i	0.0327903	−	0.0791628i
$358$	19.4796	+	14.0173i	1.02953	+	0.740835i
$359$		−	0.365637i		−	0.0192976i	−0.999953	−	0.00964878i	$-0.996929\pi$
$359$		−	0.365637i		−	0.0192976i	0.999953	−	0.00964878i	$-0.00307135\pi$
$360$	52.7358	+	16.3395i	2.77942	+	0.861168i
$361$	−4.44400	+	4.44400i	−0.233895	+	0.233895i
$362$	−33.2302	+	5.41884i	−1.74654	+	0.284808i
$363$	4.26972	+	10.3080i	0.224102	+	0.541031i
$364$	1.06571	−	2.31786i	0.0558585	−	0.121489i
$365$	10.0179	+	4.14957i	0.524363	+	0.217198i
$366$	24.0928	−	14.9159i	1.25935	−	0.779665i
$367$	7.56357			0.394815			0.197408	−	0.980322i	$-0.436748\pi$
$367$	7.56357			0.394815			0.197408	+	0.980322i	$0.436748\pi$
$368$	−1.92290	+	13.7636i	−0.100238	+	0.717480i
$369$	5.86310	+	5.86310i	0.305221	+	0.305221i
$370$	−45.0131	+	27.8676i	−2.34012	+	1.44877i
$371$	1.57609	−	0.652839i	0.0818267	−	0.0338937i
$372$	−3.32607	+	47.8456i	−0.172449	+	2.48068i
$373$	−11.2013	−	27.0424i	−0.579982	−	1.40020i	−0.892829	−	0.450396i	$-0.851283\pi$
$373$	−11.2013	−	27.0424i	−0.579982	−	1.40020i	0.312847	−	0.949804i	$-0.398717\pi$
$374$	−4.87393	−	3.50722i	−0.252025	−	0.181354i
$375$	−39.5084			−2.04021
$376$	3.14350	+	33.9822i	0.162114	+	1.75250i
$377$	10.3982	−	27.4954i	0.535533	−	1.41608i
$378$	−3.22614	+	0.526086i	−0.165935	+	0.0270589i
$379$	−6.36739	−	2.63746i	−0.327071	−	0.135477i	0.213105	−	0.977029i	$-0.431642\pi$
$379$	−6.36739	−	2.63746i	−0.327071	−	0.135477i	−0.540176	+	0.841552i	$0.681642\pi$
$380$	33.3317	+	16.6016i	1.70988	+	0.851644i
$381$	−4.00871	−	1.66046i	−0.205372	−	0.0850681i
$382$	−1.61460	+	6.86323i	−0.0826100	+	0.351153i
$383$	16.6127	+	16.6127i	0.848868	+	0.848868i	0.989992	−	0.141124i	$-0.0450715\pi$
$383$	16.6127	+	16.6127i	0.848868	+	0.848868i	−0.141124	+	0.989992i	$0.545071\pi$
$384$	−13.8380	+	29.4496i	−0.706166	+	1.50285i
$385$	−2.47168	−	2.47168i	−0.125968	−	0.125968i
$386$	−8.23585	−	13.3029i	−0.419194	−	0.677101i
$387$	−2.10397	+	5.07943i	−0.106951	+	0.258202i
$388$	−0.681434	+	0.228314i	−0.0345946	+	0.0115909i
$389$	6.34049	+	15.3073i	0.321475	+	0.776110i	0.999169	+	0.0407656i	$0.0129797\pi$
$389$	6.34049	+	15.3073i	0.321475	+	0.776110i	−0.677693	+	0.735345i	$0.737020\pi$
$390$	45.2560	−	30.0068i	2.29163	−	1.51945i
$391$	3.90904	+	3.90904i	0.197689	+	0.197689i
$392$	−14.9577	−	12.4247i	−0.755479	−	0.627544i
$393$	27.7773	+	27.7773i	1.40118	+	1.40118i
$394$	14.8373	−	20.6192i	0.747494	−	1.03878i
$395$	−1.38231	+	3.33719i	−0.0695516	+	0.167912i
$396$	−1.95109	+	28.0665i	−0.0980461	+	1.41039i
$397$	−5.23840	−	12.6466i	−0.262908	−	0.634716i	0.736208	−	0.676755i	$-0.236614\pi$
$397$	−5.23840	−	12.6466i	−0.262908	−	0.634716i	−0.999116	+	0.0420396i	$0.986614\pi$
$398$	21.2283	−	13.1425i	1.06408	−	0.658773i
$399$	−5.11629			−0.256135
$400$	4.82064	−	34.5049i	0.241032	−	1.72525i
$401$	23.9777	−	23.9777i	1.19739	−	1.19739i	0.222445	−	0.974945i	$-0.428596\pi$
$401$	23.9777	−	23.9777i	1.19739	−	1.19739i	0.974945	−	0.222445i	$-0.0714039\pi$
$402$	61.2311	+	14.4048i	3.05393	+	0.718448i
$403$	21.9095	+	20.5856i	1.09139	+	1.02544i
$404$	0.648193	−	9.32427i	0.0322488	−	0.463900i
$405$	−10.1782	−	4.21595i	−0.505759	−	0.209492i
$406$	3.31094	+	2.38251i	0.164319	+	0.118242i
$407$	−19.0767	−	19.0767i	−0.945599	−	0.945599i
$408$	6.03374	+	11.4512i	0.298715	+	0.566921i
$409$		−	1.21937i		−	0.0602939i	−0.999545	−	0.0301470i	$-0.990402\pi$
$409$		−	1.21937i		−	0.0602939i	0.999545	−	0.0301470i	$-0.00959753\pi$
$410$	4.81066	−	6.68531i	0.237582	−	0.330164i
$411$	4.55958	−	11.0078i	0.224908	−	0.542975i
$412$	−7.44667	+	2.49500i	−0.366871	+	0.122920i
$413$	0.676220	+	0.280100i	0.0332746	+	0.0137828i
$414$	5.93160	−	25.2136i	0.291522	−	1.23918i
$415$	19.1431			0.939697
$416$	8.81057	+	18.3949i	0.431974	+	0.901886i
$417$	31.7887			1.55670
$418$	−4.34552	+	18.4717i	−0.212546	+	0.903478i
$419$	−11.5662	−	4.79088i	−0.565046	−	0.234050i	0.0818282	−	0.996646i	$-0.473924\pi$
$419$	−11.5662	−	4.79088i	−0.565046	−	0.234050i	−0.646874	+	0.762597i	$0.723924\pi$
$420$	2.39376	+	7.14450i	0.116803	+	0.348616i
$421$	2.81125	−	6.78695i	0.137012	−	0.330776i	−0.840450	−	0.541890i	$-0.817709\pi$
$421$	2.81125	−	6.78695i	0.137012	−	0.330776i	0.977461	+	0.211114i	$0.0677091\pi$
$422$	−16.0248	+	22.2695i	−0.780077	+	1.08406i
$423$		−	63.6068i		−	3.09267i
$424$	−4.03655	+	13.0280i	−0.196032	+	0.632695i
$425$	−9.79981	−	9.79981i	−0.475361	−	0.475361i
$426$	−27.3736	−	19.6977i	−1.32626	−	0.954356i
$427$	2.27707	+	0.943194i	0.110195	+	0.0456444i
$428$	−18.3412	−	1.27502i	−0.886554	−	0.0616304i
$429$	20.1662	+	18.9476i	0.973634	+	0.914800i
$430$	5.31606	+	1.25062i	0.256363	+	0.0603104i
$431$	−11.4808	+	11.4808i	−0.553009	+	0.553009i	−0.927308	−	0.374299i	$-0.877883\pi$
$431$	−11.4808	+	11.4808i	−0.553009	+	0.553009i	0.374299	+	0.927308i	$0.377883\pi$
$432$	13.2454	−	22.5282i	0.637268	−	1.08389i
$433$	10.0079			0.480949			0.240475	−	0.970655i	$-0.422697\pi$
$433$	10.0079			0.480949			0.240475	+	0.970655i	$0.422697\pi$
$434$	−3.54692	+	2.19590i	−0.170258	+	0.105407i
$435$	33.2253	+	80.2131i	1.59303	+	3.84592i
$436$	−14.0177	−	0.974466i	−0.671326	−	0.0466684i
$437$	6.68560	−	16.1405i	0.319815	−	0.772103i
$438$	6.95714	−	9.66823i	0.332425	−	0.461966i
$439$	11.3029	+	11.3029i	0.539457	+	0.539457i	0.923370	−	0.383912i	$-0.125424\pi$
$439$	11.3029	+	11.3029i	0.539457	+	0.539457i	−0.383912	+	0.923370i	$0.625424\pi$
$440$	27.8274	−	2.57415i	1.32662	−	0.122718i
$441$	25.6268	+	25.6268i	1.22032	+	1.22032i
$442$	7.95178	+	1.61114i	0.378228	+	0.0766342i
$443$	0.195059	+	0.470913i	0.00926752	+	0.0223738i	0.928446	−	0.371468i	$-0.121146\pi$
$443$	0.195059	+	0.470913i	0.00926752	+	0.0223738i	−0.919178	+	0.393842i	$0.871146\pi$
$444$	18.4754	+	55.1422i	0.876801	+	2.61693i
$445$	−8.30533	+	20.0509i	−0.393711	+	0.950502i
$446$	−14.4392	−	23.3229i	−0.683716	−	1.10437i
$447$	−37.1379	−	37.1379i	−1.75656	−	1.75656i
$448$	−2.78219	+	0.519172i	−0.131446	+	0.0245286i
$449$	−27.7903	−	27.7903i	−1.31151	−	1.31151i	−0.920305	−	0.391202i	$-0.872059\pi$
$449$	−27.7903	−	27.7903i	−1.31151	−	1.31151i	−0.391202	−	0.920305i	$-0.627941\pi$
$450$	−14.8703	+	63.2096i	−0.700991	+	2.97973i
$451$	3.87766	+	1.60618i	0.182592	+	0.0756320i
$452$	−5.02043	+	10.0797i	−0.236141	+	0.474111i
$453$	27.7834	+	11.5083i	1.30538	+	0.540706i
$454$	18.3171	−	2.98696i	0.859663	−	0.140185i
$455$	4.41767	+	1.67067i	0.207104	+	0.0783222i
$456$	26.1366	−	31.4650i	1.22396	−	1.47349i
$457$	−10.4561			−0.489114			−0.244557	−	0.969635i	$-0.578643\pi$
$457$	−10.4561			−0.489114			−0.244557	+	0.969635i	$0.578643\pi$
$458$	23.2355	+	16.7200i	1.08572	+	0.781274i
$459$	−3.97824	−	9.60432i	−0.185688	−	0.448291i
$460$	−25.6669	−	1.78428i	−1.19672	−	0.0831924i
$461$	23.5526	−	9.75582i	1.09696	−	0.454374i	0.240528	−	0.970642i	$-0.422679\pi$
$461$	23.5526	−	9.75582i	1.09696	−	0.454374i	0.856427	+	0.516268i	$0.172679\pi$
$462$	−3.26470	+	2.02118i	−0.151887	+	0.0940337i
$463$	22.0162	+	22.0162i	1.02318	+	1.02318i	0.999725	+	0.0234560i	$0.00746696\pi$
$463$	22.0162	+	22.0162i	1.02318	+	1.02318i	0.0234560	+	0.999725i	$0.492533\pi$
$464$	−31.5664	+	8.19111i	−1.46543	+	0.380263i
$465$	−88.7928			−4.11767
$466$	16.7390	−	10.3632i	0.775421	−	0.480064i
$467$	−26.1364	−	10.8261i	−1.20945	−	0.500970i	−0.315408	−	0.948956i	$-0.602141\pi$
$467$	−26.1364	−	10.8261i	−1.20945	−	0.500970i	−0.894040	+	0.447986i	$0.852141\pi$
$468$	−13.1934	−	35.6515i	−0.609866	−	1.64799i
$469$	2.09376	+	5.05479i	0.0966810	+	0.233409i
$470$	−62.3580	+	10.1687i	−2.87636	+	0.469047i
$471$	−4.75479	+	4.75479i	−0.219089	+	0.219089i
$472$	−5.17709	+	2.72784i	−0.238295	+	0.125559i
$473$			2.78299i			0.127962i
$474$	3.22070	+	2.31757i	0.147932	+	0.106450i
$475$	−16.7605	+	40.4635i	−0.769026	+	1.85659i
$476$	−0.501933	+	1.00775i	−0.0230060	+	0.0461902i
$477$	9.72800	−	23.4855i	0.445414	−	1.07533i
$478$	3.35949	−	2.07986i	0.153659	−	0.0951307i
$479$	−20.9333	+	20.9333i	−0.956469	+	0.956469i	−0.999091	−	0.0426225i	$-0.986429\pi$
$479$	−20.9333	+	20.9333i	−0.956469	+	0.956469i	0.0426225	+	0.999091i	$0.486429\pi$
$480$	−56.1670	−	21.7762i	−2.56366	−	0.993944i
$481$	34.0962	+	12.8945i	1.55465	+	0.587936i
$482$	27.2220	−	16.8531i	1.23993	−	0.767640i
$483$	3.26597	−	1.35281i	0.148607	−	0.0615549i
$484$	−2.46490	−	7.35684i	−0.112041	−	0.334402i
$485$	−0.509161	−	1.22922i	−0.0231198	−	0.0558161i
$486$	9.12165	−	12.6762i	0.413766	−	0.575005i
$487$	−26.1553			−1.18521			−0.592605	−	0.805493i	$-0.701901\pi$
$487$	−26.1553			−1.18521			−0.592605	+	0.805493i	$0.701901\pi$
$488$	−17.4331	+	9.18562i	−0.789159	+	0.415813i
$489$		−	32.1618i		−	1.45441i
$490$	21.0267	−	29.2206i	0.949891	−	1.32005i
$491$	2.91967	+	7.04871i	0.131763	+	0.318104i	0.975967	−	0.217918i	$-0.0699265\pi$
$491$	2.91967	+	7.04871i	0.131763	+	0.318104i	−0.844204	+	0.536022i	$0.819926\pi$
$492$	−5.93839	−	6.82570i	−0.267723	−	0.307726i
$493$	−4.96442	+	11.9852i	−0.223586	+	0.539785i
$494$	−4.91259	−	25.1649i	−0.221028	−	1.13222i
$495$	−52.0863			−2.34111
$496$	4.61476	−	33.0313i	0.207209	−	1.48315i
$497$		−	2.93331i		−	0.131577i
$498$	4.81552	−	20.4695i	0.215789	−	0.917260i
$499$	−5.20677	−	12.5702i	−0.233087	−	0.562722i	0.763451	−	0.645866i	$-0.223504\pi$
$499$	−5.20677	−	12.5702i	−0.233087	−	0.562722i	−0.996537	+	0.0831447i	$0.973504\pi$
$500$	27.4080	+	1.90531i	1.22572	+	0.0852082i
$501$	−20.7078	+	49.9931i	−0.925157	+	2.23353i
$502$	−4.38933	+	0.715767i	−0.195905	+	0.0319463i
$503$	−8.12326	+	8.12326i	−0.362198	+	0.362198i	−0.864622	−	0.502423i	$-0.832442\pi$
$503$	−8.12326	+	8.12326i	−0.362198	+	0.362198i	0.502423	+	0.864622i	$0.332442\pi$
$504$	5.25256	−	0.485884i	0.233967	−	0.0216430i
$505$	17.3042			0.770025
$506$	−2.11018	−	12.9403i	−0.0938089	−	0.575268i
$507$	−35.3662	−	12.1300i	−1.57067	−	0.538713i
$508$	2.70086	+	1.34523i	0.119832	+	0.0596847i
$509$	−3.12959	−	7.55550i	−0.138717	−	0.334892i	0.839220	−	0.543791i	$-0.183012\pi$
$509$	−3.12959	−	7.55550i	−0.138717	−	0.334892i	−0.977937	+	0.208900i	$0.933012\pi$
$510$	−20.3746	+	12.6139i	−0.902200	+	0.558553i
$511$	1.03603			0.0458314
$512$	11.0200	−	19.7626i	0.487018	−	0.873392i
$513$	−23.2301	+	23.2301i	−1.02564	+	1.02564i
$514$	6.54679	−	27.8287i	0.288767	−	1.22747i
$515$	−5.56408	−	13.4329i	−0.245183	−	0.591923i
$516$	2.67455	−	5.36981i	0.117741	−	0.236393i
$517$	−12.3213	−	29.7462i	−0.541888	−	1.30823i
$518$	−2.95448	+	4.10580i	−0.129812	+	0.180398i
$519$	11.0337	−	11.0337i	0.484324	−	0.484324i
$520$	−32.8423	+	18.6339i	−1.44023	+	0.817152i
$521$	−14.0233	−	14.0233i	−0.614373	−	0.614373i	0.329709	−	0.944082i	$-0.393049\pi$
$521$	−14.0233	−	14.0233i	−0.614373	−	0.614373i	−0.944082	+	0.329709i	$0.893049\pi$
$522$	59.9898	−	9.78253i	2.62568	−	0.428170i
$523$	−6.69070	+	2.77138i	−0.292564	+	0.121184i	−0.524138	−	0.851633i	$-0.675612\pi$
$523$	−6.69070	+	2.77138i	−0.292564	+	0.121184i	0.231574	+	0.972817i	$0.425612\pi$
$524$	−17.9302	−	20.6094i	−0.783285	−	0.900324i
$525$	−8.18765	+	3.39144i	−0.357339	+	0.148014i
$526$	6.74007	+	10.8869i	0.293881	+	0.474690i
$527$	−9.38128	−	9.38128i	−0.408655	−	0.408655i
$528$	4.24757	−	30.4030i	0.184852	−	1.32312i
$529$		−	10.9290i		−	0.475175i
$530$	−24.5796	−	5.78242i	−1.06767	−	0.251172i
$531$	10.0764	−	4.17378i	0.437278	−	0.181127i
$532$	3.54929	+	0.246736i	0.153881	+	0.0106973i
$533$	−5.66835	+	0.176595i	−0.245523	+	0.00764918i
$534$	19.3509	+	13.9247i	0.837396	+	0.602580i
$535$		−	34.0379i		−	1.47159i
$536$	−41.7829	−	12.9459i	−1.80475	−	0.559177i
$537$	34.5107	+	34.5107i	1.48925	+	1.48925i
$538$	−25.0849	−	18.0508i	−1.08149	−	0.778224i
$539$	16.9487	+	7.02038i	0.730032	+	0.302389i
$540$	43.3078	+	21.5704i	1.86367	+	0.928242i
$541$	3.28934	−	1.36249i	0.141420	−	0.0585780i	−0.310851	−	0.950459i	$-0.600614\pi$
$541$	3.28934	−	1.36249i	0.141420	−	0.0585780i	0.452271	+	0.891881i	$0.350614\pi$
$542$	22.9128	+	37.0097i	0.984187	+	1.58970i
$543$	−68.4719			−2.93841
$544$	−3.63351	−	8.23498i	−0.155786	−	0.353072i
$545$		−	26.0143i		−	1.11433i
$546$	2.89771	−	4.30350i	0.124011	−	0.184173i
$547$	11.5180	+	4.77093i	0.492476	+	0.203990i	0.615079	−	0.788466i	$-0.289124\pi$
$547$	11.5180	+	4.77093i	0.492476	+	0.203990i	−0.122603	+	0.992456i	$0.539124\pi$
$548$	−3.69395	+	7.41650i	−0.157798	+	0.316817i
$549$	33.9308	−	14.0546i	1.44813	−	0.599835i
$550$	5.29013	+	32.4409i	0.225572	+	1.38329i
$551$	40.9963			1.74650
$552$	−8.36451	+	26.9965i	−0.356017	+	1.14905i
$553$			0.345125i			0.0146762i
$554$	−29.0909	+	4.74384i	−1.23595	+	0.201547i
$555$	−99.4698	+	41.2017i	−4.22226	+	1.74892i
$556$	−22.0526	−	1.53303i	−0.935239	−	0.0650148i
$557$	−7.00735	−	16.9172i	−0.296911	−	0.716807i	−0.999984	−	0.00568880i	$-0.998189\pi$
$557$	−7.00735	−	16.9172i	−0.296911	−	0.716807i	0.703073	−	0.711118i	$-0.251811\pi$
$558$	−14.2352	+	60.5100i	−0.602624	+	2.56159i
$559$	−1.54650	−	3.42759i	−0.0654098	−	0.144972i
$560$	−1.31606	−	5.07175i	−0.0556137	−	0.214321i
$561$	−8.63483	−	8.63483i	−0.364563	−	0.364563i
$562$	41.4964	+	9.76217i	1.75042	+	0.411792i
$563$	−1.44990	−	0.600569i	−0.0611061	−	0.0253110i	0.351921	−	0.936030i	$-0.385529\pi$
$563$	−1.44990	−	0.600569i	−0.0611061	−	0.0253110i	−0.413027	+	0.910719i	$0.635529\pi$
$564$	−4.81311	+	69.2367i	−0.202669	+	2.91539i
$565$	−19.2608	−	7.97807i	−0.810307	−	0.335640i
$566$	−5.56810	+	0.907988i	−0.234045	+	0.0381656i
$567$	−1.05261			−0.0442053
$568$	18.0398	+	14.9849i	0.756933	+	0.628752i
$569$	−25.2684	−	25.2684i	−1.05931	−	1.05931i	−0.998127	−	0.0611796i	$-0.980514\pi$
$569$	−25.2684	−	25.2684i	−1.05931	−	1.05931i	−0.0611796	−	0.998127i	$-0.519486\pi$
$570$	61.4683	+	44.2318i	2.57462	+	1.85267i
$571$	20.4365	−	8.46509i	0.855242	−	0.354253i	0.0883972	−	0.996085i	$-0.471826\pi$
$571$	20.4365	−	8.46509i	0.855242	−	0.354253i	0.766845	+	0.641832i	$0.221826\pi$
$572$	−13.0760	−	14.1170i	−0.546737	−	0.590260i
$573$	−5.48714	+	13.2471i	−0.229229	+	0.553407i
$574$	0.180210	−	0.766025i	0.00752182	−	0.0319733i
$575$		−	30.2614i		−	1.26199i
$576$	−23.8446	+	34.7852i	−0.993525	+	1.44939i
$577$	−14.7312	+	14.7312i	−0.613267	+	0.613267i	−0.943796	−	0.330529i	$-0.892773\pi$
$577$	−14.7312	+	14.7312i	−0.613267	+	0.613267i	0.330529	+	0.943796i	$0.392773\pi$
$578$	19.9174	+	4.68564i	0.828455	+	0.194897i
$579$	−12.1765	−	29.3968i	−0.506040	−	1.22169i
$580$	−19.1809	−	57.2481i	−0.796444	−	2.37710i
$581$	1.68981	−	0.699942i	0.0701051	−	0.0290385i
$582$	−1.44248	+	0.235224i	−0.0597925	+	0.00975036i
$583$		−	12.8675i		−	0.532919i
$584$	−5.29259	+	6.37158i	−0.219009	+	0.263658i
$585$	64.1506	−	28.9442i	2.65230	−	1.19669i
$586$	−9.31166	−	6.70055i	−0.384661	−	0.276797i
$587$	1.90840	−	4.60730i	0.0787683	−	0.190163i	−0.879590	−	0.475733i	$-0.842183\pi$
$587$	1.90840	−	4.60730i	0.0787683	−	0.190163i	0.958358	+	0.285570i	$0.0921828\pi$
$588$	−25.9559	−	29.8342i	−1.07040	−	1.23034i
$589$	−16.0447	+	38.7354i	−0.661111	+	1.59606i
$590$	−5.70273	−	9.21130i	−0.234778	−	0.379223i
$591$	36.5297	−	36.5297i	1.50263	−	1.50263i
$592$	−10.1575	−	39.1445i	−0.417472	−	1.60883i
$593$	−29.4587	+	29.4587i	−1.20973	+	1.20973i	−0.238610	+	0.971116i	$0.576692\pi$
$593$	−29.4587	+	29.4587i	−1.20973	+	1.20973i	−0.971116	+	0.238610i	$0.923308\pi$
$594$	−5.64611	+	24.0001i	−0.231663	+	0.984738i
$595$	−1.92565	−	0.797631i	−0.0789440	−	0.0326997i
$596$	23.9725	+	27.5545i	0.981952	+	1.12868i
$597$	46.9103	−	19.4309i	1.91991	−	0.795253i
$598$	9.78983	+	14.7650i	0.400336	+	0.603785i
$599$	7.80699	−	7.80699i	0.318985	−	0.318985i	−0.529392	−	0.848377i	$-0.677580\pi$
$599$	7.80699	−	7.80699i	0.318985	−	0.318985i	0.848377	+	0.529392i	$0.177580\pi$
$600$	20.9695	−	67.6791i	0.856077	−	2.76299i
$601$	−15.2437	+	15.2437i	−0.621805	+	0.621805i	−0.945993	−	0.324188i	$-0.894909\pi$
$601$	−15.2437	+	15.2437i	−0.621805	+	0.621805i	0.324188	+	0.945993i	$0.394909\pi$
$602$	0.514990	−	0.0839793i	0.0209894	−	0.00342274i
$603$	75.3217	+	31.1993i	3.06734	+	1.27053i
$604$	−18.7191	−	9.32344i	−0.761667	−	0.379365i
$605$	13.2708	−	5.49696i	0.539536	−	0.223483i
$606$	4.35293	−	18.5032i	0.176826	−	0.751639i
$607$		−	41.2527i		−	1.67439i	−0.546902	−	0.837197i	$-0.684193\pi$
$607$		−	41.2527i		−	1.67439i	0.546902	−	0.837197i	$-0.315807\pi$
$608$	−19.6490	+	20.5676i	−0.796874	+	0.834127i
$609$	5.86578	+	5.86578i	0.237693	+	0.237693i
$610$	−19.2031	−	31.0177i	−0.777511	−	1.25587i
$611$	31.7049	+	29.7891i	1.28264	+	1.20514i
$612$	5.32962	+	15.9070i	0.215437	+	0.643002i
$613$	8.64630	−	20.8740i	0.349221	−	0.843093i	−0.647492	−	0.762073i	$-0.724182\pi$
$613$	8.64630	−	20.8740i	0.349221	−	0.843093i	0.996712	−	0.0810209i	$-0.0258180\pi$
$614$	0.553386	−	0.0902406i	0.0223329	−	0.00364181i
$615$	11.8439	−	11.8439i	0.477593	−	0.477593i
$616$	2.36227	−	1.24470i	0.0951787	−	0.0501503i
$617$	38.0732			1.53277			0.766385	−	0.642382i	$-0.222054\pi$
$617$	38.0732			1.53277			0.766385	+	0.642382i	$0.222054\pi$
$618$	−15.7633	+	2.57052i	−0.634093	+	0.103401i
$619$	−2.84679	−	1.17918i	−0.114422	−	0.0473952i	0.324738	−	0.945804i	$-0.394724\pi$
$619$	−2.84679	−	1.17918i	−0.114422	−	0.0473952i	−0.439160	+	0.898409i	$0.644724\pi$
$620$	61.5978	+	4.28208i	2.47383	+	0.171972i
$621$	8.68657	−	20.9712i	0.348580	−	0.841546i
$622$	−8.95999	−	14.4726i	−0.359263	−	0.580298i
$623$			2.07361i			0.0830776i
$624$	11.6634	+	39.8054i	0.466911	+	1.59349i
$625$			7.31421i			0.292568i
$626$	24.0763	−	14.9057i	0.962284	−	0.595751i
$627$	−14.7681	+	35.6533i	−0.589780	+	1.42385i
$628$	3.52782	−	3.06921i	0.140775	−	0.122475i
$629$	−14.8624	−	6.15623i	−0.592605	−	0.245465i
$630$	1.57175	+	9.63853i	0.0626202	+	0.384008i
$631$	−22.2524			−0.885853			−0.442927	−	0.896558i	$-0.646060\pi$
$631$	−22.2524			−0.885853			−0.442927	+	0.896558i	$0.646060\pi$
$632$	−2.12251	−	1.76308i	−0.0844290	−	0.0701314i
$633$	−39.4534	+	39.4534i	−1.56813	+	1.56813i
$634$	3.75353	+	23.0179i	0.149072	+	0.914159i
$635$	−2.13773	+	5.16093i	−0.0848330	+	0.204805i
$636$	−12.3662	+	24.8281i	−0.490350	+	0.984496i
$637$	−24.7756	+	0.771872i	−0.981644	+	0.0305827i
$638$	26.1597	−	16.1955i	1.03567	−	0.641185i
$639$	−30.9073	−	30.9073i	−1.22267	−	1.22267i
$640$	37.9143	+	17.8154i	1.49869	+	0.704215i
$641$			22.7437i			0.898322i	0.893451	+	0.449161i	$0.148277\pi$
$641$			22.7437i			0.898322i	−0.893451	+	0.449161i	$0.851723\pi$
$642$	−36.3964	−	8.56237i	−1.43645	−	0.337930i
$643$	−14.2276	+	5.89327i	−0.561082	+	0.232408i	−0.645155	−	0.764052i	$-0.723207\pi$
$643$	−14.2276	+	5.89327i	−0.561082	+	0.232408i	0.0840729	+	0.996460i	$0.473207\pi$
$644$	−2.33092	+	0.780973i	−0.0918512	+	0.0307747i
$645$	10.2609	+	4.25019i	0.404021	+	0.167351i
$646$	1.82110	+	11.1676i	0.0716501	+	0.439383i
$647$	−16.0729	+	16.0729i	−0.631892	+	0.631892i	−0.948542	−	0.316650i	$-0.897442\pi$
$647$	−16.0729	+	16.0729i	−0.631892	+	0.631892i	0.316650	+	0.948542i	$0.397442\pi$
$648$	5.37726	−	6.47351i	0.211239	−	0.254303i
$649$	3.90379	−	3.90379i	0.153237	−	0.153237i
$650$	−24.5427	−	37.0152i	−0.962645	−	1.45186i
$651$	−7.83797	+	3.24659i	−0.307194	+	0.127244i
$652$	−1.55102	+	22.3115i	−0.0607427	+	0.873784i
$653$	−21.2018	−	8.78207i	−0.829690	−	0.343669i	−0.0729100	−	0.997339i	$-0.523229\pi$
$653$	−21.2018	−	8.78207i	−0.829690	−	0.343669i	−0.756780	+	0.653670i	$0.773229\pi$
$654$	−27.8168	−	6.54401i	−1.08772	−	0.255891i
$655$	35.7613	−	35.7613i	1.39731	−	1.39731i
$656$	3.79043	+	5.02154i	0.147991	+	0.196058i
$657$	10.9163	−	10.9163i	0.425886	−	0.425886i
$658$	−5.13270	+	3.17766i	−0.200093	+	0.123878i
$659$	−7.90917	+	19.0944i	−0.308098	+	0.743814i	0.691669	+	0.722215i	$0.256876\pi$
$659$	−7.90917	+	19.0944i	−0.308098	+	0.743814i	−0.999767	+	0.0215990i	$0.993124\pi$
$660$	56.6965	+	3.94136i	2.20691	+	0.153417i
$661$	−13.2440	+	31.9740i	−0.515134	+	1.24364i	0.425728	+	0.904851i	$0.360018\pi$
$661$	−13.2440	+	31.9740i	−0.515134	+	1.24364i	−0.940862	+	0.338791i	$0.889982\pi$
$662$	9.18497	−	12.7642i	0.356984	−	0.496095i
$663$	15.4332	+	5.83650i	0.599375	+	0.226671i
$664$	−4.32780	+	13.9680i	−0.167951	+	0.542062i
$665$			6.58685i			0.255427i
$666$	12.1310	+	74.3915i	0.470067	+	2.88261i
$667$	−26.1699	+	10.8399i	−1.01330	+	0.419723i
$668$	16.7765	−	33.6828i	0.649101	−	1.30323i
$669$	−21.3481	−	51.5388i	−0.825364	−	1.99260i
$670$	18.5452	−	78.8307i	0.716463	−	3.04549i
$671$	13.1455	−	13.1455i	0.507475	−	0.507475i
$672$	−5.75423	+	0.131431i	−0.221974	+	0.00507004i
$673$			3.14540i			0.121246i	0.998161	+	0.0606231i	$0.0193088\pi$
$673$			3.14540i			0.121246i	−0.998161	+	0.0606231i	$0.980691\pi$
$674$	3.92963	+	0.924460i	0.151364	+	0.0356089i
$675$	−21.7769	+	52.5740i	−0.838192	+	2.02358i
$676$	23.9495	+	10.1205i	0.921133	+	0.389248i
$677$	−20.8407	+	8.63252i	−0.800975	+	0.331775i	−0.745347	−	0.666677i	$-0.767716\pi$
$677$	−20.8407	+	8.63252i	−0.800975	+	0.331775i	−0.0556280	+	0.998452i	$0.517716\pi$
$678$	−13.3760	+	18.5884i	−0.513702	+	0.713884i
$679$	−0.0898899	−	0.0898899i	−0.00344966	−	0.00344966i
$680$	14.7426	−	7.76800i	0.565354	−	0.297889i
$681$	37.7430			1.44631
$682$	5.06420	+	31.0554i	0.193918	+	1.18917i
$683$	42.8294	+	17.7405i	1.63882	+	0.678822i	0.996178	−	0.0873440i	$-0.0278379\pi$
$683$	42.8294	+	17.7405i	1.63882	+	0.678822i	0.642643	+	0.766166i	$0.277838\pi$
$684$	39.9974	−	34.7979i	1.52934	−	1.33053i
$685$	−14.1718	−	5.87013i	−0.541475	−	0.224286i
$686$	1.58969	−	6.75734i	0.0606945	−	0.257996i
$687$	41.1649	+	41.1649i	1.57054	+	1.57054i
$688$	−2.11437	+	3.59619i	−0.0806094	+	0.137103i
$689$	7.15044	+	15.8479i	0.272410	+	0.603758i
$690$	−50.9336	−	11.9823i	−1.93901	−	0.456158i
$691$	17.8719	+	43.1467i	0.679881	+	1.64138i	0.764232	+	0.644941i	$0.223118\pi$
$691$	17.8719	+	43.1467i	0.679881	+	1.64138i	−0.0843517	+	0.996436i	$0.526882\pi$
$692$	−8.18643	+	7.12222i	−0.311201	+	0.270746i
$693$	−4.59780	+	1.90447i	−0.174656	+	0.0723448i
$694$	1.94892	+	11.9514i	0.0739799	+	0.453670i
$695$		−	40.9256i		−	1.55240i
$696$	−66.0398	+	6.10897i	−2.50323	+	0.231560i
$697$	2.50271			0.0947967
$698$	−15.7934	+	2.57543i	−0.597791	+	0.0974816i
$699$	36.9899	−	15.3217i	1.39909	−	0.579520i
$700$	5.84353	−	1.95787i	0.220865	−	0.0740005i
$701$	−21.1619	−	8.76555i	−0.799274	−	0.331070i	−0.0546083	−	0.998508i	$-0.517391\pi$
$701$	−21.1619	−	8.76555i	−0.799274	−	0.331070i	−0.744666	+	0.667438i	$0.767391\pi$
$702$	−6.38290	−	32.6966i	−0.240907	−	1.23405i
$703$			50.8382i			1.91740i
$704$	−4.41284	+	20.8865i	−0.166315	+	0.787189i
$705$	−128.491			−4.83924
$706$	−0.299675	+	0.185529i	−0.0112784	+	0.00698247i
$707$	1.52748	−	0.632705i	0.0574469	−	0.0237953i
$708$	−11.2841	+	3.78072i	−0.424082	+	0.142088i
$709$	−5.42719	−	2.24801i	−0.203822	−	0.0844260i	0.278437	−	0.960455i	$-0.410184\pi$
$709$	−5.42719	−	2.24801i	−0.203822	−	0.0844260i	−0.482259	+	0.876029i	$0.660184\pi$
$710$	−25.3594	+	35.2415i	−0.951720	+	1.32259i
$711$	3.63646	+	3.63646i	0.136378	+	0.136378i
$712$	−12.7527	−	10.5931i	−0.477927	−	0.396993i
$713$		−	28.9690i		−	1.08490i
$714$	−1.33730	+	1.85843i	−0.0500473	+	0.0695500i
$715$	24.3937	−	25.9625i	0.912273	−	0.970944i
$716$	−22.2766	−	25.6052i	−0.832516	−	0.956911i
$717$	7.42379	−	3.07503i	0.277246	−	0.114839i
$718$	−0.118414	+	0.503347i	−0.00441918	+	0.0187848i
$719$			29.1752i			1.08805i	0.839069	+	0.544025i	$0.183100\pi$
$719$			29.1752i			1.08805i	−0.839069	+	0.544025i	$0.816900\pi$
$720$	−67.3061	−	39.5724i	−2.50835	−	1.47477i
$721$	−0.982312	−	0.982312i	−0.0365832	−	0.0365832i
$722$	7.55697	−	4.67853i	0.281241	−	0.174117i
$723$	60.1550	−	24.9170i	2.23719	−	0.926674i
$724$	47.5007	+	3.30209i	1.76535	+	0.122721i
$725$	65.6068	−	27.1752i	2.43658	−	1.00926i
$726$	−2.53951	−	15.5731i	−0.0942500	−	0.577974i
$727$	−0.875628	−	0.875628i	−0.0324752	−	0.0324752i	0.690683	−	0.723158i	$-0.257310\pi$
$727$	−0.875628	−	0.875628i	−0.0324752	−	0.0324752i	−0.723158	+	0.690683i	$0.757310\pi$
$728$	−2.21775	+	2.84570i	−0.0821953	+	0.105469i
$729$	28.7693	−	28.7693i	1.06553	−	1.06553i
$730$	−12.4472	−	8.95681i	−0.460690	−	0.331506i
$731$	0.635049	+	1.53314i	0.0234881	+	0.0567054i
$732$	−37.9975	+	12.7310i	−1.40443	+	0.470553i
$733$	−0.221050	−	0.533662i	−0.00816467	−	0.0197113i	0.919745	−	0.392517i	$-0.128396\pi$
$733$	−0.221050	−	0.533662i	−0.00816467	−	0.0197113i	−0.927909	+	0.372806i	$0.878396\pi$
$734$	−10.4123	−	2.44952i	−0.384323	−	0.0904134i
$735$	51.7681	−	51.7681i	1.90950	−	1.90950i
$736$	7.10459	−	18.3247i	0.261879	−	0.675459i
$737$	41.2683			1.52014
$738$	−6.17252	−	9.97014i	−0.227214	−	0.367006i
$739$	14.3778	+	34.7112i	0.528897	+	1.27687i	0.932246	+	0.361825i	$0.117846\pi$
$739$	14.3778	+	34.7112i	0.528897	+	1.27687i	−0.403349	+	0.915046i	$0.632154\pi$
$740$	70.9916	−	23.7857i	2.60970	−	0.874379i
$741$	−1.62371	−	52.1178i	−0.0596484	−	1.91460i
$742$	−2.38113	+	0.388290i	−0.0874140	+	0.0142546i
$743$	−27.0184			−0.991210			−0.495605	−	0.868548i	$-0.665054\pi$
$743$	−27.0184			−0.991210			−0.495605	+	0.868548i	$0.665054\pi$
$744$	20.0739	−	64.7886i	0.735946	−	2.37527i
$745$	−47.8124	+	47.8124i	−1.75171	+	1.75171i
$746$	6.66222	+	40.8550i	0.243921	+	1.49581i
$747$	10.4299	−	25.1800i	0.381609	−	0.921286i
$748$	5.57377	+	6.40661i	0.203797	+	0.234249i
$749$	−1.24455	−	3.00461i	−0.0454749	−	0.109786i
$750$	54.3886	+	12.7951i	1.98599	+	0.467211i
$751$			27.8107i			1.01483i	0.861703	+	0.507414i	$0.169398\pi$
$751$			27.8107i			1.01483i	−0.861703	+	0.507414i	$0.830602\pi$
$752$	6.67795	−	47.7991i	0.243520	−	1.74305i
$753$	−9.04437			−0.329595
$754$	−23.2190	+	34.4835i	−0.845588	+	1.25582i
$755$	14.8161	−	35.7691i	0.539212	−	1.30177i
$756$	4.61158	+	0.320582i	0.167722	+	0.0116595i
$757$	−3.97154	−	9.58814i	−0.144348	−	0.348487i	0.835126	−	0.550059i	$-0.185395\pi$
$757$	−3.97154	−	9.58814i	−0.144348	−	0.348487i	−0.979474	+	0.201572i	$0.935395\pi$
$758$	7.91139	+	5.69293i	0.287355	+	0.206777i
$759$		−	26.6640i		−	0.967842i
$760$	−40.5090	−	33.6490i	−1.46941	−	1.22058i
$761$	4.70902			0.170702			0.0853509	−	0.996351i	$-0.472799\pi$
$761$	4.70902			0.170702			0.0853509	+	0.996351i	$0.472799\pi$
$762$	4.98077	+	3.58410i	0.180434	+	0.129838i
$763$	−0.951180	−	2.29635i	−0.0344350	−	0.0831335i
$764$	4.44541	−	8.92524i	0.160829	−	0.322904i
$765$	−28.6942	+	11.8855i	−1.03744	+	0.429723i
$766$	−17.4894	−	28.2497i	−0.631918	−	1.02070i
$767$	−2.63867	+	6.97731i	−0.0952769	+	0.251936i
$768$	28.5873	−	36.0598i	1.03155	−	1.30120i
$769$	−36.1755	+	36.1755i	−1.30452	+	1.30452i

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bd (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37663 - 0.323857i) q^{2} +(-2.65712 - 1.10062i) q^{3} +(1.79023 + 0.891665i) q^{4} +(-1.41696 + 3.42085i) q^{5} +(3.30144 + 2.37567i) q^{6} +0.353777i q^{7} +(-2.17572 - 1.80728i) q^{8} +(3.72762 + 3.72762i) q^{9} +O(q^{10})\)	\(q+(-1.37663 - 0.323857i) q^{2} +(-2.65712 - 1.10062i) q^{3} +(1.79023 + 0.891665i) q^{4} +(-1.41696 + 3.42085i) q^{5} +(3.30144 + 2.37567i) q^{6} +0.353777i q^{7} +(-2.17572 - 1.80728i) q^{8} +(3.72762 + 3.72762i) q^{9} +(3.05851 - 4.25036i) q^{10} +(2.46532 + 1.02117i) q^{11} +(-3.77548 - 4.33962i) q^{12} +(-3.60380 + 0.112275i) q^{13} +(0.114573 - 0.487021i) q^{14} +(7.53009 - 7.53009i) q^{15} +(2.40987 + 3.19258i) q^{16} +1.59116 q^{17} +(-3.92434 - 6.33878i) q^{18} +(-1.92428 - 4.64563i) q^{19} +(-5.58695 + 4.86066i) q^{20} +(0.389372 - 0.940028i) q^{21} +(-3.06313 - 2.20419i) q^{22} +(2.45672 + 2.45672i) q^{23} +(3.79204 + 7.19678i) q^{24} +(-6.15891 - 6.15891i) q^{25} +(4.99747 + 1.01256i) q^{26} +(-2.50021 - 6.03605i) q^{27} +(-0.315451 + 0.633343i) q^{28} +(-3.12000 + 7.53235i) q^{29} +(-12.8048 + 7.92748i) q^{30} +(-5.89587 - 5.89587i) q^{31} +(-2.28356 - 5.17546i) q^{32} +(-5.42675 - 5.42675i) q^{33} +(-2.19044 - 0.515309i) q^{34} +(-1.21022 - 0.501289i) q^{35} +(3.34952 + 9.99709i) q^{36} +(-9.34063 - 3.86902i) q^{37} +(1.14451 + 7.01852i) q^{38} +(9.69931 + 3.66807i) q^{39} +(9.26533 - 4.88197i) q^{40} +1.57288 q^{41} +(-0.840458 + 1.16797i) q^{42} +(0.399110 + 0.963538i) q^{43} +(3.50296 + 4.02637i) q^{44} +(-18.0335 + 7.46973i) q^{45} +(-2.58638 - 4.17763i) q^{46} +(-8.53183 - 8.53183i) q^{47} +(-2.88951 - 11.1354i) q^{48} +6.87484 q^{49} +(6.48394 + 10.4732i) q^{50} +(-4.22791 - 1.75126i) q^{51} +(-6.55176 - 3.01239i) q^{52} +(-1.84534 - 4.45505i) q^{53} +(1.48705 + 9.11913i) q^{54} +(-6.98654 + 6.98654i) q^{55} +(0.639372 - 0.769719i) q^{56} +14.4619i q^{57} +(6.73450 - 9.35884i) q^{58} +(0.791741 - 1.91143i) q^{59} +(20.1949 - 6.76629i) q^{60} +(2.66607 - 6.43647i) q^{61} +(6.20702 + 10.0259i) q^{62} +(-1.31875 + 1.31875i) q^{63} +(1.46751 + 7.86425i) q^{64} +(4.72238 - 12.4872i) q^{65} +(5.71314 + 9.22813i) q^{66} +(14.2881 - 5.91831i) q^{67} +(2.84855 + 1.41878i) q^{68} +(-3.82390 - 9.23172i) q^{69} +(1.50368 + 1.08203i) q^{70} -8.29142 q^{71} +(-1.37342 - 14.8471i) q^{72} -2.92849i q^{73} +(11.6056 + 8.35125i) q^{74} +(9.58637 + 23.1436i) q^{75} +(0.697433 - 10.0326i) q^{76} +(-0.361266 + 0.872174i) q^{77} +(-12.1645 - 8.19078i) q^{78} +0.975544 q^{79} +(-14.3360 + 3.72003i) q^{80} +2.97534i q^{81} +(-2.16528 - 0.509389i) q^{82} +(-1.97848 - 4.77649i) q^{83} +(1.53526 - 1.33568i) q^{84} +(-2.25462 + 5.44313i) q^{85} +(-0.237379 - 1.45569i) q^{86} +(16.5804 - 16.5804i) q^{87} +(-3.51832 - 6.67730i) q^{88} +5.86136 q^{89} +(27.2447 - 4.44278i) q^{90} +(-0.0397203 - 1.27494i) q^{91} +(2.20753 + 6.58868i) q^{92} +(9.17695 + 22.1551i) q^{93} +(8.98209 + 14.5083i) q^{94} +18.6187 q^{95} +(0.371507 + 16.2651i) q^{96} +(-0.254086 + 0.254086i) q^{97} +(-9.46413 - 2.22647i) q^{98} +(5.38325 + 12.9963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24} - 4 q^{26} - 8 q^{27} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 44 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 4 q^{37} - 28 q^{39} - 8 q^{40} - 8 q^{41} - 48 q^{42} - 32 q^{43} + 12 q^{44} - 36 q^{45} - 48 q^{46} - 8 q^{47} - 8 q^{48} - 168 q^{49} + 76 q^{50} - 4 q^{52} - 8 q^{53} - 28 q^{54} - 40 q^{55} + 56 q^{56} + 32 q^{58} + 52 q^{59} - 36 q^{60} - 8 q^{61} + 72 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} - 4 q^{67} - 64 q^{68} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 8 q^{74} - 68 q^{76} + 56 q^{77} - 48 q^{78} - 16 q^{79} + 28 q^{80} - 88 q^{82} + 36 q^{83} + 100 q^{84} - 24 q^{85} + 96 q^{86} - 8 q^{87} + 64 q^{88} - 8 q^{89} - 64 q^{90} + 72 q^{91} - 8 q^{92} - 40 q^{93} - 56 q^{94} + 36 q^{96} - 8 q^{97} + 52 q^{98} - 44 q^{99}+O(q^{100}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

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