LMFDB - Embedded newform 416.2.bd.a.83.19

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			83.19
Character	$\chi$	$=$	416.83
Dual form			416.2.bd.a.411.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.757760 - 1.19407i) q^{2} +(-2.82515 - 1.17022i) q^{3} +(-0.851600 + 1.80963i) q^{4} +(0.899503 - 2.17159i) q^{5} +(0.743468 + 4.26017i) q^{6} +2.64760i q^{7} +(2.80614 - 0.354399i) q^{8} +(4.49077 + 4.49077i) q^{9} +O(q^{10})$	\(q+(-0.757760 - 1.19407i) q^{2} +(-2.82515 - 1.17022i) q^{3} +(-0.851600 + 1.80963i) q^{4} +(0.899503 - 2.17159i) q^{5} +(0.743468 + 4.26017i) q^{6} +2.64760i q^{7} +(2.80614 - 0.354399i) q^{8} +(4.49077 + 4.49077i) q^{9} +(-3.27464 + 0.571477i) q^{10} +(5.77603 + 2.39251i) q^{11} +(4.52357 - 4.11594i) q^{12} +(-1.01875 - 3.45863i) q^{13} +(3.16142 - 2.00625i) q^{14} +(-5.08247 + 5.08247i) q^{15} +(-2.54955 - 3.08217i) q^{16} -1.08697 q^{17} +(1.95936 - 8.76521i) q^{18} +(2.28731 + 5.52206i) q^{19} +(3.16377 + 3.47710i) q^{20} +(3.09827 - 7.47989i) q^{21} +(-1.52002 - 8.70992i) q^{22} +(-0.961319 - 0.961319i) q^{23} +(-8.34249 - 2.28256i) q^{24} +(-0.371172 - 0.371172i) q^{25} +(-3.35788 + 3.83727i) q^{26} +(-3.92128 - 9.46682i) q^{27} +(-4.79120 - 2.25470i) q^{28} +(2.08624 - 5.03663i) q^{29} +(9.92011 + 2.21753i) q^{30} +(-2.29862 - 2.29862i) q^{31} +(-1.74837 + 5.37989i) q^{32} +(-13.5184 - 13.5184i) q^{33} +(0.823659 + 1.29791i) q^{34} +(5.74952 + 2.38153i) q^{35} +(-11.9510 + 4.30231i) q^{36} +(3.15093 + 1.30516i) q^{37} +(4.86049 - 6.91560i) q^{38} +(-1.16923 + 10.9633i) q^{39} +(1.75452 - 6.41257i) q^{40} +6.50731 q^{41} +(-11.2792 + 1.96841i) q^{42} +(-3.53570 - 8.53592i) q^{43} +(-9.24844 + 8.41504i) q^{44} +(13.7916 - 5.71266i) q^{45} +(-0.419432 + 1.87633i) q^{46} +(0.374148 + 0.374148i) q^{47} +(3.59607 + 11.6911i) q^{48} -0.00980685 q^{49} +(-0.161946 + 0.724465i) q^{50} +(3.07085 + 1.27199i) q^{51} +(7.12643 + 1.10181i) q^{52} +(4.36222 + 10.5313i) q^{53} +(-8.33264 + 11.8559i) q^{54} +(10.3911 - 10.3911i) q^{55} +(0.938308 + 7.42954i) q^{56} -18.2773i q^{57} +(-7.59495 + 1.32544i) q^{58} +(2.23176 - 5.38795i) q^{59} +(-4.86918 - 13.5256i) q^{60} +(3.69576 - 8.92236i) q^{61} +(-1.00291 + 4.48652i) q^{62} +(-11.8898 + 11.8898i) q^{63} +(7.74880 - 1.98898i) q^{64} +(-8.42711 - 0.898742i) q^{65} +(-5.89821 + 26.3856i) q^{66} +(1.11846 - 0.463281i) q^{67} +(0.925660 - 1.96701i) q^{68} +(1.59092 + 3.84083i) q^{69} +(-1.51304 - 8.66994i) q^{70} +5.48277 q^{71} +(14.1932 + 11.0102i) q^{72} +13.2430i q^{73} +(-0.829201 - 4.75143i) q^{74} +(0.614267 + 1.48297i) q^{75} +(-11.9408 - 0.563389i) q^{76} +(-6.33442 + 15.2926i) q^{77} +(13.9770 - 6.91143i) q^{78} -2.73529 q^{79} +(-8.98655 + 2.76417i) q^{80} +12.2813i q^{81} +(-4.93098 - 7.77018i) q^{82} +(0.835389 + 2.01681i) q^{83} +(10.8974 + 11.9766i) q^{84} +(-0.977729 + 2.36045i) q^{85} +(-7.51327 + 10.6900i) q^{86} +(-11.7879 + 11.7879i) q^{87} +(17.0562 + 4.66669i) q^{88} -11.1773 q^{89} +(-17.2720 - 12.1393i) q^{90} +(9.15709 - 2.69725i) q^{91} +(2.55830 - 0.920977i) q^{92} +(3.80408 + 9.18385i) q^{93} +(0.163244 - 0.730273i) q^{94} +14.0491 q^{95} +(11.2351 - 13.1530i) q^{96} +(11.6113 - 11.6113i) q^{97} +(0.00743124 + 0.0117101i) q^{98} +(15.1946 + 36.6830i) 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 $

$2$	−0.757760	−	1.19407i	−0.535817	−	0.844334i
$2$	−0.757760	−	1.19407i	−0.535817	−	0.844334i
$3$	−2.82515	−	1.17022i	−1.63110	−	0.675625i	−0.635748	−	0.771896i	$-0.719308\pi$
$3$	−2.82515	−	1.17022i	−1.63110	−	0.675625i	−0.995355	+	0.0962713i	$0.969308\pi$
$4$	−0.851600	+	1.80963i	−0.425800	+	0.904817i
$5$	0.899503	−	2.17159i	0.402270	−	0.971165i	−0.584844	−	0.811146i	$-0.698844\pi$
$5$	0.899503	−	2.17159i	0.402270	−	0.971165i	0.987114	−	0.160020i	$-0.0511557\pi$
$6$	0.743468	+	4.26017i	0.303520	+	1.73921i
$7$			2.64760i			1.00070i	0.865823	+	0.500350i	$0.166795\pi$
$7$			2.64760i			1.00070i	−0.865823	+	0.500350i	$0.833205\pi$
$8$	2.80614	−	0.354399i	0.992119	−	0.125299i
$9$	4.49077	+	4.49077i	1.49692	+	1.49692i
$10$	−3.27464	+	0.571477i	−1.03553	+	0.180717i
$11$	5.77603	+	2.39251i	1.74154	+	0.721369i	0.998649	+	0.0519539i	$0.0165449\pi$
$11$	5.77603	+	2.39251i	1.74154	+	0.721369i	0.742889	+	0.669415i	$0.233455\pi$
$12$	4.52357	−	4.11594i	1.30584	−	1.18817i
$13$	−1.01875	−	3.45863i	−0.282550	−	0.959252i
$13$	−1.01875	−	3.45863i	−0.282550	−	0.959252i
$14$	3.16142	−	2.00625i	0.844925	−	0.536192i
$15$	−5.08247	+	5.08247i	−1.31229	+	1.31229i
$16$	−2.54955	−	3.08217i	−0.637389	−	0.770543i
$17$	−1.08697			−0.263628			−0.131814	−	0.991274i	$-0.542080\pi$
$17$	−1.08697			−0.263628			−0.131814	+	0.991274i	$0.542080\pi$
$18$	1.95936	−	8.76521i	0.461826	−	2.06598i
$19$	2.28731	+	5.52206i	0.524745	+	1.26685i	0.934926	+	0.354843i	$0.115466\pi$
$19$	2.28731	+	5.52206i	0.524745	+	1.26685i	−0.410180	+	0.912004i	$0.634534\pi$
$20$	3.16377	+	3.47710i	0.707441	+	0.777503i
$21$	3.09827	−	7.47989i	0.676098	−	1.63225i
$22$	−1.52002	−	8.70992i	−0.324070	−	1.85696i
$23$	−0.961319	−	0.961319i	−0.200449	−	0.200449i	0.599743	−	0.800192i	$-0.295269\pi$
$23$	−0.961319	−	0.961319i	−0.200449	−	0.200449i	−0.800192	+	0.599743i	$0.795269\pi$
$24$	−8.34249	−	2.28256i	−1.70290	−	0.465925i
$25$	−0.371172	−	0.371172i	−0.0742345	−	0.0742345i
$26$	−3.35788	+	3.83727i	−0.658534	+	0.752551i
$27$	−3.92128	−	9.46682i	−0.754652	−	1.82189i
$28$	−4.79120	−	2.25470i	−0.905451	−	0.426098i
$29$	2.08624	−	5.03663i	0.387405	−	0.935278i	−0.603083	−	0.797678i	$-0.706061\pi$
$29$	2.08624	−	5.03663i	0.387405	−	0.935278i	0.990488	−	0.137600i	$-0.0439388\pi$
$30$	9.92011	+	2.21753i	1.81116	+	0.404863i
$31$	−2.29862	−	2.29862i	−0.412845	−	0.412845i	0.469883	−	0.882728i	$-0.344296\pi$
$31$	−2.29862	−	2.29862i	−0.412845	−	0.412845i	−0.882728	+	0.469883i	$0.844296\pi$
$32$	−1.74837	+	5.37989i	−0.309072	+	0.951039i
$33$	−13.5184	−	13.5184i	−2.35325	−	2.35325i
$34$	0.823659	+	1.29791i	0.141256	+	0.222590i
$35$	5.74952	+	2.38153i	0.971845	+	0.402552i
$36$	−11.9510	+	4.30231i	−1.99183	+	0.717051i
$37$	3.15093	+	1.30516i	0.518010	+	0.214567i	0.626343	−	0.779548i	$-0.284551\pi$
$37$	3.15093	+	1.30516i	0.518010	+	0.214567i	−0.108332	+	0.994115i	$0.534551\pi$
$38$	4.86049	−	6.91560i	0.788475	−	1.12186i
$39$	−1.16923	+	10.9633i	−0.187226	+	1.75554i
$40$	1.75452	−	6.41257i	0.277414	−	1.01392i
$41$	6.50731			1.01627			0.508136	−	0.861277i	$-0.330335\pi$
$41$	6.50731			1.01627			0.508136	+	0.861277i	$0.330335\pi$
$42$	−11.2792	+	1.96841i	−1.74043	+	0.303732i
$43$	−3.53570	−	8.53592i	−0.539189	−	1.30172i	−0.925290	−	0.379260i	$-0.876179\pi$
$43$	−3.53570	−	8.53592i	−0.539189	−	1.30172i	0.386102	−	0.922456i	$-0.373821\pi$
$44$	−9.24844	+	8.41504i	−1.39425	+	1.26861i
$45$	13.7916	−	5.71266i	2.05593	−	0.851592i
$46$	−0.419432	+	1.87633i	−0.0618419	+	0.276650i
$47$	0.374148	+	0.374148i	0.0545751	+	0.0545751i	0.733868	−	0.679293i	$-0.237713\pi$
$47$	0.374148	+	0.374148i	0.0545751	+	0.0545751i	−0.679293	+	0.733868i	$0.737713\pi$
$48$	3.59607	+	11.6911i	0.519049	+	1.68747i
$49$	−0.00980685			−0.00140098
$50$	−0.161946	+	0.724465i	−0.0229026	+	0.102455i
$51$	3.07085	+	1.27199i	0.430004	+	0.178114i
$52$	7.12643	+	1.10181i	0.988258	+	0.152793i
$53$	4.36222	+	10.5313i	0.599198	+	1.44659i	0.874401	+	0.485205i	$0.161255\pi$
$53$	4.36222	+	10.5313i	0.599198	+	1.44659i	−0.275203	+	0.961386i	$0.588745\pi$
$54$	−8.33264	+	11.8559i	−1.13393	+	1.61338i
$55$	10.3911	−	10.3911i	1.40114	−	1.40114i
$56$	0.938308	+	7.42954i	0.125387	+	0.992814i
$57$		−	18.2773i		−	2.42089i
$58$	−7.59495	+	1.32544i	−0.997265	+	0.174039i
$59$	2.23176	−	5.38795i	0.290551	−	0.701451i	−0.709444	−	0.704762i	$-0.751054\pi$
$59$	2.23176	−	5.38795i	0.290551	−	0.701451i	0.999995	+	0.00331069i	$0.00105383\pi$
$60$	−4.86918	−	13.5256i	−0.628608	−	1.74615i
$61$	3.69576	−	8.92236i	0.473194	−	1.14239i	−0.489549	−	0.871976i	$-0.662839\pi$
$61$	3.69576	−	8.92236i	0.473194	−	1.14239i	0.962744	−	0.270416i	$-0.0871613\pi$
$62$	−1.00291	+	4.48652i	−0.127370	+	0.569788i
$63$	−11.8898	+	11.8898i	−1.49797	+	1.49797i
$64$	7.74880	−	1.98898i	0.968600	−	0.248623i
$65$	−8.42711	−	0.898742i	−1.04525	−	0.111475i
$66$	−5.89821	+	26.3856i	−0.726019	+	3.24785i
$67$	1.11846	−	0.463281i	0.136642	−	0.0565988i	−0.313315	−	0.949649i	$-0.601440\pi$
$67$	1.11846	−	0.463281i	0.136642	−	0.0565988i	0.449956	+	0.893051i	$0.351440\pi$
$68$	0.925660	−	1.96701i	0.112253	−	0.238535i
$69$	1.59092	+	3.84083i	0.191525	+	0.462381i
$70$	−1.51304	−	8.66994i	−0.180843	−	1.03626i
$71$	5.48277			0.650685			0.325343	−	0.945596i	$-0.394520\pi$
$71$	5.48277			0.650685			0.325343	+	0.945596i	$0.394520\pi$
$72$	14.1932	+	11.0102i	1.67269	+	1.29756i
$73$			13.2430i			1.54998i	0.631976	+	0.774988i	$0.282244\pi$
$73$			13.2430i			1.54998i	−0.631976	+	0.774988i	$0.717756\pi$
$74$	−0.829201	−	4.75143i	−0.0963926	−	0.552342i
$75$	0.614267	+	1.48297i	0.0709294	+	0.171239i
$76$	−11.9408	−	0.563389i	−1.36970	−	0.0646251i
$77$	−6.33442	+	15.2926i	−0.721874	+	1.74276i
$78$	13.9770	−	6.91143i	1.58258	−	0.782566i
$79$	−2.73529			−0.307744			−0.153872	−	0.988091i	$-0.549174\pi$
$79$	−2.73529			−0.307744			−0.153872	+	0.988091i	$0.549174\pi$
$80$	−8.98655	+	2.76417i	−1.00473	+	0.309044i
$81$			12.2813i			1.36458i
$82$	−4.93098	−	7.77018i	−0.544536	−	0.858073i
$83$	0.835389	+	2.01681i	0.0916958	+	0.221373i	0.963073	−	0.269240i	$-0.0867726\pi$
$83$	0.835389	+	2.01681i	0.0916958	+	0.221373i	−0.871377	+	0.490614i	$0.836773\pi$
$84$	10.8974	+	11.9766i	1.18900	+	1.30676i
$85$	−0.977729	+	2.36045i	−0.106050	+	0.256026i
$86$	−7.51327	+	10.6900i	−0.810177	+	1.15274i
$87$	−11.7879	+	11.7879i	−1.26380	+	1.26380i
$88$	17.0562	+	4.66669i	1.81820	+	0.497471i
$89$	−11.1773			−1.18479			−0.592395	−	0.805648i	$-0.701817\pi$
$89$	−11.1773			−1.18479			−0.592395	+	0.805648i	$0.701817\pi$
$90$	−17.2720	−	12.1393i	−1.82063	−	1.27959i
$91$	9.15709	−	2.69725i	0.959924	−	0.282748i
$92$	2.55830	−	0.920977i	0.266721	−	0.0960185i
$93$	3.80408	+	9.18385i	0.394464	+	0.952321i
$94$	0.163244	−	0.730273i	0.0168374	−	0.0753219i
$95$	14.0491			1.44141
$96$	11.2351	−	13.1530i	1.14667	−	1.34243i
$97$	11.6113	−	11.6113i	1.17895	−	1.17895i	0.198936	−	0.980013i	$-0.436252\pi$
$97$	11.6113	−	11.6113i	1.17895	−	1.17895i	0.980013	−	0.198936i	$-0.0637484\pi$
$98$	0.00743124	+	0.0117101i	0.000750669	+	0.00118289i
$99$	15.1946	+	36.6830i	1.52711	+	3.68678i
$100$	0.987777	−	0.355596i	0.0987777	−	0.0355596i
$101$	−2.63674	−	6.36565i	−0.262365	−	0.633406i	0.736718	−	0.676200i	$-0.236374\pi$
$101$	−2.63674	−	6.36565i	−0.262365	−	0.633406i	−0.999084	+	0.0427933i	$0.986374\pi$
$102$	−0.808125	−	4.63066i	−0.0800163	−	0.458504i
$103$	7.73145	−	7.73145i	0.761802	−	0.761802i	−0.214846	−	0.976648i	$-0.568925\pi$
$103$	7.73145	−	7.73145i	0.761802	−	0.761802i	0.976648	+	0.214846i	$0.0689248\pi$
$104$	−4.08449	−	9.34435i	−0.400517	−	0.916289i
$105$	−13.4564	−	13.4564i	−1.31321	−	1.31321i
$106$	9.26963	−	13.1890i	0.900346	−	1.28103i
$107$	−2.11027	+	0.874102i	−0.204007	+	0.0845026i	−0.482348	−	0.875980i	$-0.660216\pi$
$107$	−2.11027	+	0.874102i	−0.204007	+	0.0845026i	0.278340	+	0.960483i	$0.410216\pi$
$108$	20.4708	+	0.965853i	1.96981	+	0.0929392i
$109$	−3.26015	+	1.35040i	−0.312266	+	0.129345i	−0.533312	−	0.845919i	$-0.679053\pi$
$109$	−3.26015	+	1.35040i	−0.312266	+	0.129345i	0.221046	+	0.975263i	$0.429053\pi$
$110$	−20.2817	−	4.53373i	−1.93378	−	0.432275i
$111$	−7.37455	−	7.37455i	−0.699962	−	0.699962i
$112$	8.16037	−	6.75021i	0.771082	−	0.637835i
$113$			2.67729i			0.251859i	0.992039	+	0.125929i	$0.0401912\pi$
$113$			2.67729i			0.251859i	−0.992039	+	0.125929i	$0.959809\pi$
$114$	−21.8244	+	13.8498i	−2.04404	+	1.29715i
$115$	−2.95230	+	1.22288i	−0.275304	+	0.114035i
$116$	7.33781	+	8.06452i	0.681299	+	0.748772i
$117$	10.9570	−	20.1069i	1.01297	−	1.85888i
$118$	−8.12472	+	1.41789i	−0.747941	+	0.130528i
$119$		−	2.87785i		−	0.263813i
$120$	−12.4609	+	16.0633i	−1.13752	+	1.46637i
$121$	19.8602	+	19.8602i	1.80548	+	1.80548i
$122$	−13.4544	+	2.34801i	−1.21811	+	0.212579i
$123$	−18.3842	−	7.61497i	−1.65764	−	0.686619i
$124$	6.11718	−	2.20216i	0.549339	−	0.197760i
$125$	9.71805	−	4.02535i	0.869209	−	0.360038i
$126$	23.2068	+	5.18761i	2.06743	+	0.462149i
$127$	0.627273			0.0556615			0.0278307	−	0.999613i	$-0.491140\pi$
$127$	0.627273			0.0556615			0.0278307	+	0.999613i	$0.491140\pi$
$128$	−8.24671	−	7.74543i	−0.728913	−	0.684606i
$129$			28.2528i			2.48752i
$130$	5.31257	+	10.7436i	0.465943	+	0.942274i
$131$	−2.06667	−	0.856043i	−0.180566	−	0.0747929i	0.290569	−	0.956854i	$-0.406155\pi$
$131$	−2.06667	−	0.856043i	−0.180566	−	0.0747929i	−0.471135	+	0.882061i	$0.656155\pi$
$132$	35.9757	−	12.9511i	3.13128	−	1.12725i
$133$	−14.6202	+	6.05590i	−1.26773	+	0.525113i
$134$	−1.40071	−	0.984462i	−0.121003	−	0.0850445i
$135$	−24.0853			−2.07293
$136$	−3.05017	+	0.385220i	−0.261550	+	0.0330323i
$137$			7.09311i			0.606005i	0.952990	+	0.303003i	$0.0979891\pi$
$137$			7.09311i			0.606005i	−0.952990	+	0.303003i	$0.902011\pi$
$138$	3.38067	−	4.81010i	0.287782	−	0.409463i
$139$	−7.14389	+	2.95910i	−0.605937	+	0.250987i	−0.664490	−	0.747297i	$-0.731351\pi$
$139$	−7.14389	+	2.95910i	−0.605937	+	0.250987i	0.0585531	+	0.998284i	$0.481351\pi$
$140$	−9.20598	+	8.37641i	−0.778048	+	0.707936i
$141$	−0.619192	−	1.49486i	−0.0521453	−	0.125890i
$142$	−4.15462	−	6.54681i	−0.348648	−	0.549396i
$143$	2.39049	−	22.4145i	0.199902	−	1.87440i
$144$	2.39186	−	25.2908i	0.199321	−	2.10756i
$145$	−9.06092	−	9.06092i	−0.752469	−	0.752469i
$146$	15.8130	−	10.0350i	1.30870	−	0.830503i
$147$	0.0277059	+	0.0114761i	0.00228514	+	0.000946537i
$148$	−5.04520	+	4.59057i	−0.414713	+	0.377342i
$149$	14.6080	+	6.05085i	1.19674	+	0.495705i	0.889943	−	0.456071i	$-0.150744\pi$
$149$	14.6080	+	6.05085i	1.19674	+	0.495705i	0.306794	+	0.951776i	$0.400744\pi$
$150$	1.30530	−	1.85721i	0.106578	−	0.151641i
$151$	−8.48791			−0.690736			−0.345368	−	0.938467i	$-0.612246\pi$
$151$	−8.48791			−0.690736			−0.345368	+	0.938467i	$0.612246\pi$
$152$	8.37552	+	14.6850i	0.679345	+	1.19111i
$153$	−4.88131	−	4.88131i	−0.394630	−	0.394630i
$154$	23.0604	−	4.02442i	1.85826	−	0.324297i
$155$	−7.05929	+	2.92405i	−0.567016	+	0.234866i
$156$	−18.8439	−	11.4523i	−1.50872	−	0.916914i
$157$	5.50863	−	13.2990i	0.439637	−	1.06138i	−0.536438	−	0.843940i	$-0.680230\pi$
$157$	5.50863	−	13.2990i	0.439637	−	1.06138i	0.976074	−	0.217437i	$-0.0697696\pi$
$158$	2.07269	+	3.26612i	0.164894	+	0.259839i
$159$		−	34.8574i		−	2.76437i
$160$	10.1103	+	8.63598i	0.799286	+	0.682734i
$161$	2.54519	−	2.54519i	0.200589	−	0.200589i
$162$	14.6647	−	9.30625i	1.15217	−	0.731168i
$163$	−1.06661	−	2.57501i	−0.0835430	−	0.201691i	0.876588	−	0.481242i	$-0.159814\pi$
$163$	−1.06661	−	2.57501i	−0.0835430	−	0.201691i	−0.960131	+	0.279551i	$0.909814\pi$
$164$	−5.54163	+	11.7759i	−0.432728	+	0.919540i
$165$	−41.5163	+	17.1966i	−3.23204	+	1.33876i
$166$	1.77518	−	2.52577i	0.137781	−	0.196037i
$167$		−	8.56469i		−	0.662756i	−0.943498	−	0.331378i	$-0.892487\pi$
$167$		−	8.56469i		−	0.662756i	0.943498	−	0.331378i	$-0.107513\pi$
$168$	6.04331	−	22.0876i	0.466251	−	1.70410i
$169$	−10.9243	+	7.04697i	−0.840331	+	0.542074i
$170$	3.55942	−	0.621176i	0.272995	−	0.0476420i
$171$	−14.5265	+	35.0701i	−1.11087	+	2.68188i
$172$	18.4579	+	0.870878i	1.40740	+	0.0664038i
$173$	2.78463	−	6.72269i	0.211712	−	0.511117i	−0.781975	−	0.623310i	$-0.785788\pi$
$173$	2.78463	−	6.72269i	0.211712	−	0.511117i	0.993686	+	0.112193i	$0.0357875\pi$
$174$	23.0079	+	5.14316i	1.74423	+	0.389902i
$175$	0.982717	−	0.982717i	0.0742865	−	0.0742865i
$176$	−7.35218	−	23.9025i	−0.554191	−	1.80172i
$177$	−12.6101	+	12.6101i	−0.947836	+	0.947836i
$178$	8.46970	+	13.3464i	0.634831	+	1.00036i
$179$	−6.51758	−	2.69967i	−0.487147	−	0.201783i	0.125571	−	0.992085i	$-0.459924\pi$
$179$	−6.51758	−	2.69967i	−0.487147	−	0.201783i	−0.612718	+	0.790302i	$0.709924\pi$
$180$	−1.40709	+	29.8226i	−0.104878	+	2.22285i
$181$	−7.57485	+	3.13761i	−0.563034	+	0.233216i	−0.646002	−	0.763336i	$-0.723560\pi$
$181$	−7.57485	+	3.13761i	−0.563034	+	0.233216i	0.0829677	+	0.996552i	$0.473560\pi$
$182$	−10.1596	−	8.89033i	−0.753078	−	0.658995i
$183$	−20.8822	+	20.8822i	−1.54366	+	1.54366i
$184$	−3.03828	−	2.35690i	−0.223985	−	0.173753i
$185$	5.66855	−	5.66855i	0.416760	−	0.416760i
$186$	8.08358	−	11.5015i	0.592717	−	0.843330i
$187$	−6.27835	−	2.60058i	−0.459118	−	0.190173i
$188$	−0.995696	+	0.358447i	−0.0726186	+	0.0261424i
$189$	25.0644	−	10.3820i	1.82317	−	0.755180i
$190$	−10.6458	−	16.7756i	−0.772331	−	1.21703i
$191$			2.45562i			0.177683i	0.996046	+	0.0888413i	$0.0283164\pi$
$191$			2.45562i			0.177683i	−0.996046	+	0.0888413i	$0.971684\pi$
$192$	−24.2191	−	3.44859i	−1.74786	−	0.248881i
$193$	5.41219	+	5.41219i	0.389578	+	0.389578i	0.874537	−	0.484959i	$-0.161165\pi$
$193$	5.41219	+	5.41219i	0.389578	+	0.389578i	−0.484959	+	0.874537i	$0.661165\pi$
$194$	−22.6633	−	5.06611i	−1.62713	−	0.363726i
$195$	22.7562	+	12.4006i	1.62960	+	0.888028i
$196$	0.00835152	−	0.0177468i	0.000596537	−	0.00126763i
$197$	−0.329537	+	0.795572i	−0.0234785	+	0.0566822i	−0.935184	−	0.354162i	$-0.884766\pi$
$197$	−0.329537	+	0.795572i	−0.0234785	+	0.0566822i	0.911705	+	0.410844i	$0.134766\pi$
$198$	32.2882	−	45.9403i	2.29462	−	3.26483i
$199$	−16.9240	+	16.9240i	−1.19971	+	1.19971i	−0.225454	+	0.974254i	$0.572386\pi$
$199$	−16.9240	+	16.9240i	−1.19971	+	1.19971i	−0.974254	+	0.225454i	$0.927614\pi$
$200$	−1.17310	−	0.910017i	−0.0829509	−	0.0643479i
$201$	−3.70196			−0.261116
$202$	−5.60301	+	7.97209i	−0.394227	+	0.560914i
$203$	13.3350	+	5.52354i	0.935933	+	0.387676i
$204$	−4.91696	+	4.47388i	−0.344256	+	0.313235i
$205$	5.85335	−	14.1312i	0.408815	−	0.986968i
$206$	−15.0905	−	3.37330i	−1.05140	−	0.235029i
$207$		−	8.63412i		−	0.600113i
$208$	−8.06274	+	11.9579i	−0.559051	+	0.829134i
$209$			37.3680i			2.58480i
$210$	−5.87113	+	26.2645i	−0.405147	+	1.81242i
$211$	−2.48562	+	6.00081i	−0.171117	+	0.413113i	−0.986052	−	0.166440i	$-0.946773\pi$
$211$	−2.48562	+	6.00081i	−0.171117	+	0.413113i	0.814935	+	0.579553i	$0.196773\pi$
$212$	−22.7727	−	1.07446i	−1.56404	−	0.0737943i
$213$	−15.4897	−	6.41603i	−1.06133	−	0.439619i
$214$	2.64281	+	1.85745i	0.180659	+	0.126972i
$215$	−21.7169			−1.48108
$216$	−14.3587	−	25.1755i	−0.976985	−	1.71297i
$217$	6.08584	−	6.08584i	0.413134	−	0.413134i
$218$	4.08288	+	2.86957i	0.276528	+	0.194352i
$219$	15.4972	−	37.4135i	1.04720	−	2.52817i
$220$	9.95504	+	27.6532i	0.671169	+	1.86438i
$221$	1.10735	+	3.75942i	0.0744882	+	0.252886i
$222$	−3.21758	+	14.3939i	−0.215950	+	0.966053i
$223$	0.426879	+	0.426879i	0.0285859	+	0.0285859i	0.721255	−	0.692669i	$-0.243565\pi$
$223$	0.426879	+	0.426879i	0.0285859	+	0.0285859i	−0.692669	+	0.721255i	$0.743565\pi$
$224$	−14.2438	−	4.62900i	−0.951705	−	0.309288i
$225$		−	3.33370i		−	0.222246i
$226$	3.19687	−	2.02875i	0.212653	−	0.134950i
$227$	23.4772	−	9.72456i	1.55823	−	0.645442i	0.573452	−	0.819239i	$-0.305604\pi$
$227$	23.4772	−	9.72456i	1.55823	−	0.645442i	0.984781	+	0.173797i	$0.0556038\pi$
$228$	33.0753	+	15.5650i	2.19046	+	1.03082i
$229$	−21.0868	−	8.73445i	−1.39346	−	0.577189i	−0.445413	−	0.895325i	$-0.646943\pi$
$229$	−21.0868	−	8.73445i	−1.39346	−	0.577189i	−0.948045	+	0.318136i	$0.896943\pi$
$230$	3.69734	+	2.59860i	0.243796	+	0.171347i
$231$	35.7914	−	35.7914i	2.35490	−	2.35490i
$232$	4.06930	−	14.8728i	0.267162	−	0.976449i
$233$	−6.76040	+	6.76040i	−0.442888	+	0.442888i	−0.892982	−	0.450093i	$-0.851391\pi$
$233$	−6.76040	+	6.76040i	−0.442888	+	0.442888i	0.450093	+	0.892982i	$0.351391\pi$
$234$	−32.3117	+	2.15284i	−2.11228	+	0.140735i
$235$	1.14904	−	0.475950i	0.0749554	−	0.0310475i
$236$	7.84965	+	8.62705i	0.510969	+	0.561573i
$237$	7.72760	+	3.20088i	0.501962	+	0.207919i
$238$	−3.43636	+	2.18072i	−0.222746	+	0.141355i
$239$	−4.67775	+	4.67775i	−0.302578	+	0.302578i	−0.842022	−	0.539443i	$-0.818635\pi$
$239$	−4.67775	+	4.67775i	−0.302578	+	0.302578i	0.539443	+	0.842022i	$0.318635\pi$
$240$	28.6231	+	2.70700i	1.84761	+	0.174736i
$241$	18.0291	−	18.0291i	1.16136	−	1.16136i	0.177179	−	0.984179i	$-0.443303\pi$
$241$	18.0291	−	18.0291i	1.16136	−	1.16136i	0.984179	−	0.177179i	$-0.0566971\pi$
$242$	8.66520	−	38.7638i	0.557020	−	2.49183i
$243$	2.60789	−	6.29600i	0.167296	−	0.403889i
$244$	12.9989	+	14.2863i	0.832170	+	0.914585i
$245$	−0.00882129	+	0.0212965i	−0.000563572	+	0.00136058i
$246$	4.83798	+	27.7223i	0.308458	+	1.76751i
$247$	16.7686	−	13.5366i	1.06696	−	0.861312i
$248$	−7.26488	−	5.63562i	−0.461320	−	0.357862i
$249$		−	6.67537i		−	0.423035i
$250$	−12.1705	−	8.55378i	−0.769730	−	0.540988i
$251$	−11.0253	+	4.56684i	−0.695913	+	0.288257i	−0.702461	−	0.711722i	$-0.747916\pi$
$251$	−11.0253	+	4.56684i	−0.695913	+	0.288257i	0.00654819	+	0.999979i	$0.497916\pi$
$252$	−11.3908	−	31.6415i	−0.717554	−	1.99323i
$253$	−3.25264	−	7.85257i	−0.204492	−	0.493687i
$254$	−0.475322	−	0.749007i	−0.0298244	−	0.0469969i
$255$	5.52447	−	5.52447i	0.345956	−	0.345956i
$256$	−2.99955	+	15.7163i	−0.187472	+	0.982270i
$257$			10.7788i			0.672365i	0.941797	+	0.336182i	$0.109136\pi$
$257$			10.7788i			0.672365i	−0.941797	+	0.336182i	$0.890864\pi$
$258$	33.7358	−	21.4089i	2.10030	−	1.33286i
$259$	−3.45555	+	8.34243i	−0.214717	+	0.518373i
$260$	8.80292	−	14.4846i	0.545934	−	0.898298i
$261$	31.9871	−	13.2495i	1.97995	−	0.820124i
$262$	0.543866	+	3.11642i	0.0336002	+	0.192533i
$263$	12.8376	+	12.8376i	0.791602	+	0.791602i	0.981755	−	0.190153i	$-0.0608983\pi$
$263$	12.8376	+	12.8376i	0.791602	+	0.791602i	−0.190153	+	0.981755i	$0.560898\pi$
$264$	−42.7254	−	33.1436i	−2.62957	−	2.03985i
$265$	26.7936			1.64592
$266$	18.3098	+	12.8686i	1.12264	+	0.789027i
$267$	31.5775	+	13.0798i	1.93251	+	0.800474i
$268$	−0.114111	+	2.41853i	−0.00697043	+	0.147735i
$269$	−2.62050	−	1.08545i	−0.159775	−	0.0661809i	0.301363	−	0.953510i	$-0.402558\pi$
$269$	−2.62050	−	1.08545i	−0.159775	−	0.0661809i	−0.461137	+	0.887329i	$0.652558\pi$
$270$	18.2509	+	28.7595i	1.11071	+	1.75025i
$271$	16.7350	+	16.7350i	1.01658	+	1.01658i	0.999860	+	0.0167180i	$0.00532175\pi$
$271$	16.7350	+	16.7350i	1.01658	+	1.01658i	0.0167180	+	0.999860i	$0.494678\pi$
$272$	2.77128	+	3.35021i	0.168033	+	0.203137i
$273$	−29.0266	−	3.09565i	−1.75677	−	0.187357i
$274$	8.46966	−	5.37487i	0.511671	−	0.324708i
$275$	−1.25587	−	3.03194i	−0.0757317	−	0.182833i
$276$	−8.30532	−	0.391861i	−0.499922	−	0.0235872i
$277$	0.772334	−	0.319911i	0.0464051	−	0.0192216i	−0.359360	−	0.933199i	$-0.617005\pi$
$277$	0.772334	−	0.319911i	0.0464051	−	0.0192216i	0.405765	+	0.913977i	$0.367005\pi$
$278$	8.94672	+	6.28802i	0.536589	+	0.377130i
$279$		−	20.6452i		−	1.23599i
$280$	16.9779	+	4.64527i	1.01463	+	0.277608i
$281$	24.0078			1.43219			0.716094	−	0.698004i	$-0.245928\pi$
$281$	24.0078			1.43219			0.716094	+	0.698004i	$0.245928\pi$
$282$	−1.31577	+	1.87210i	−0.0783528	+	0.111482i
$283$	−6.66435	+	2.76046i	−0.396154	+	0.164093i	−0.571862	−	0.820350i	$-0.693779\pi$
$283$	−6.66435	+	2.76046i	−0.396154	+	0.164093i	0.175707	+	0.984442i	$0.443779\pi$
$284$	−4.66913	+	9.92181i	−0.277062	+	0.588751i
$285$	−39.6909	−	16.4405i	−2.35109	−	0.973851i
$286$	−28.5759	+	14.1304i	−1.68973	+	0.835550i
$287$			17.2288i			1.01698i
$288$	−32.0114	+	16.3083i	−1.88629	+	0.960975i
$289$	−15.8185			−0.930500
$290$	−3.95336	+	17.6854i	−0.232149	+	1.03852i
$291$	−46.3914	+	19.2160i	−2.71951	+	1.12646i
$292$	−23.9650	−	11.2777i	−1.40244	−	0.659980i
$293$	−10.5707	−	4.37854i	−0.617548	−	0.255797i	0.0519040	−	0.998652i	$-0.483471\pi$
$293$	−10.5707	−	4.37854i	−0.617548	−	0.255797i	−0.669452	+	0.742855i	$0.733471\pi$
$294$	−0.00729109	−	0.0417789i	−0.000425225	−	0.00243659i
$295$	−9.69295	−	9.69295i	−0.564345	−	0.564345i
$296$	9.30450	+	2.54577i	0.540813	+	0.147970i
$297$		−	64.0623i		−	3.71727i
$298$	−3.84426	−	22.0281i	−0.222692	−	1.27605i
$299$	−2.34551	+	4.30420i	−0.135644	+	0.248918i
$300$	−3.20675	−	0.151300i	−0.185142	−	0.00873532i
$301$	22.5997	−	9.36112i	1.30263	−	0.539566i
$302$	6.43180	+	10.1351i	0.370108	+	0.583212i
$303$			21.0695i			1.21041i
$304$	11.1883	−	21.1287i	0.641693	−	1.21181i
$305$	−16.0514	−	16.0514i	−0.919100	−	0.919100i
$306$	−2.12976	+	9.52748i	−0.121750	+	0.544650i
$307$	−1.83964	+	0.762002i	−0.104994	+	0.0434897i	−0.434562	−	0.900642i	$-0.643097\pi$
$307$	−1.83964	+	0.762002i	−0.104994	+	0.0434897i	0.329568	+	0.944132i	$0.393097\pi$
$308$	−22.2797	−	24.4862i	−1.26950	−	1.39523i
$309$	−30.8900	+	12.7951i	−1.75727	+	0.727886i
$310$	8.84077	+	6.21355i	0.502122	+	0.352906i
$311$	21.1350	+	21.1350i	1.19846	+	1.19846i	0.974628	+	0.223830i	$0.0718559\pi$
$311$	21.1350	+	21.1350i	1.19846	+	1.19846i	0.223830	+	0.974628i	$0.428144\pi$
$312$	0.604383	+	31.1790i	0.0342165	+	1.76516i
$313$	−10.4099	+	10.4099i	−0.588405	+	0.588405i	−0.937199	−	0.348794i	$-0.886591\pi$
$313$	−10.4099	+	10.4099i	−0.588405	+	0.588405i	0.348794	+	0.937199i	$0.386591\pi$
$314$	−20.0542	+	3.49977i	−1.13172	+	0.197504i
$315$	15.1248	+	36.5146i	0.852189	+	2.05737i
$316$	2.32937	−	4.94987i	0.131037	−	0.278452i
$317$	8.43756	+	20.3701i	0.473901	+	1.14410i	0.962425	+	0.271547i	$0.0875352\pi$
$317$	8.43756	+	20.3701i	0.473901	+	1.14410i	−0.488525	+	0.872550i	$0.662465\pi$
$318$	−41.6221	+	26.4135i	−2.33405	+	1.48120i
$319$	24.1004	−	24.1004i	1.34936	−	1.34936i
$320$	2.65081	−	18.6163i	0.148185	−	1.04068i
$321$	6.98472			0.389849
$322$	−4.96778	−	1.11049i	−0.276844	−	0.0618852i
$323$	−2.48623	−	6.00229i	−0.138338	−	0.333976i
$324$	−22.2246	−	10.4587i	−1.23470	−	0.581040i
$325$	−0.905618	+	1.66188i	−0.0502346	+	0.0921846i
$326$	−2.26651	+	3.22484i	−0.125531	+	0.178608i
$327$	10.7907			0.596727
$328$	18.2604	−	2.30619i	1.00826	−	0.127338i
$329$	−0.990596	+	0.990596i	−0.0546133	+	0.0546133i
$330$	51.9934	+	36.5424i	2.86214	+	2.01160i
$331$	6.27576	−	15.1510i	0.344947	−	0.832776i	−0.652253	−	0.758001i	$-0.726176\pi$
$331$	6.27576	−	15.1510i	0.344947	−	0.832776i	0.997200	−	0.0747751i	$-0.0238239\pi$
$332$	−4.36110	−	0.205765i	−0.239346	−	0.0112928i
$333$	8.28894	+	20.0113i	0.454231	+	1.09661i
$334$	−10.2268	+	6.48998i	−0.559587	+	0.355116i
$335$		−	2.84556i		−	0.155470i
$336$	−30.9535	+	9.52098i	−1.68865	+	0.519412i
$337$	10.6765			0.581584			0.290792	−	0.956786i	$-0.406081\pi$
$337$	10.6765			0.581584			0.290792	+	0.956786i	$0.406081\pi$
$338$	16.6926	+	7.70445i	0.907955	+	0.419067i
$339$	3.13301	−	7.56377i	0.170162	−	0.410807i
$340$	−3.43891	−	3.77949i	−0.186501	−	0.204972i
$341$	−7.77744	−	18.7764i	−0.421172	−	1.01680i
$342$	52.8837	−	9.22905i	2.85962	−	0.499050i
$343$			18.5073i			0.999298i
$344$	−12.9468	−	22.6999i	−0.698043	−	1.22390i
$345$	9.77175			0.526093
$346$	−10.1374	+	1.76915i	−0.544992	+	0.0951099i
$347$	13.5419	+	32.6930i	0.726966	+	1.75505i	0.652451	+	0.757831i	$0.273741\pi$
$347$	13.5419	+	32.6930i	0.726966	+	1.75505i	0.0745143	+	0.997220i	$0.476259\pi$
$348$	−11.2932	−	31.3704i	−0.605379	−	1.68163i
$349$	−8.38088	+	3.47147i	−0.448618	+	0.185824i	−0.595542	−	0.803324i	$-0.703063\pi$
$349$	−8.38088	+	3.47147i	−0.448618	+	0.185824i	0.146924	+	0.989148i	$0.453063\pi$
$350$	−1.91810	−	0.428768i	−0.102527	−	0.0229186i
$351$	−28.7474	+	23.2066i	−1.53443	+	1.23868i
$352$	−22.9701	+	26.8914i	−1.22431	+	1.43332i
$353$	−12.2601	+	12.2601i	−0.652539	+	0.652539i	−0.953604	−	0.301065i	$-0.902658\pi$
$353$	−12.2601	+	12.2601i	−0.652539	+	0.652539i	0.301065	+	0.953604i	$0.402658\pi$
$354$	24.6128	+	5.50192i	1.30816	+	0.292424i
$355$	4.93177	−	11.9063i	0.261751	−	0.631923i
$356$	9.51858	−	20.2268i	0.504484	−	1.07202i
$357$	−3.36771	+	8.13038i	−0.178238	+	0.430305i
$358$	1.71517	+	9.82813i	0.0906494	+	0.519433i
$359$		−	31.3319i		−	1.65363i	−0.562471	−	0.826817i	$-0.690149\pi$
$359$		−	31.3319i		−	1.65363i	0.562471	−	0.826817i	$-0.309851\pi$
$360$	36.6765	−	20.9182i	1.93302	−	1.10249i
$361$	−11.8263	+	11.8263i	−0.622438	+	0.622438i
$362$	9.48643	+	6.66734i	0.498596	+	0.350428i
$363$	−32.8674	−	79.3490i	−1.72509	−	4.16474i
$364$	−2.91715	+	18.8680i	−0.152900	+	0.988950i
$365$	28.7584	+	11.9121i	1.50528	+	0.623509i
$366$	40.7585	+	9.11109i	2.13048	+	0.476244i
$367$	−14.4963			−0.756700			−0.378350	−	0.925663i	$-0.623508\pi$
$367$	−14.4963			−0.756700			−0.378350	+	0.925663i	$0.623508\pi$
$368$	−0.512014	+	5.41389i	−0.0266906	+	0.282218i
$369$	29.2228	+	29.2228i	1.52128	+	1.52128i
$370$	−11.0640	−	2.47324i	−0.575192	−	0.128578i
$371$	−27.8828	+	11.5494i	−1.44760	+	0.599617i
$372$	−19.8590	−	0.936983i	−1.02964	−	0.0485803i
$373$	−11.3171	−	27.3219i	−0.585978	−	1.41468i	−0.887317	−	0.461159i	$-0.847434\pi$
$373$	−11.3171	−	27.3219i	−0.585978	−	1.41468i	0.301339	−	0.953517i	$-0.402566\pi$
$374$	1.65221	+	9.46739i	0.0854338	+	0.489547i
$375$	−32.1655			−1.66102
$376$	1.18251	+	0.917313i	0.0609832	+	0.0473068i
$377$	−19.5452	−	2.08447i	−1.00663	−	0.107356i
$378$	−31.3896	−	22.0615i	−1.61451	−	1.13472i
$379$	−18.2142	−	7.54458i	−0.935602	−	0.387539i	−0.137801	−	0.990460i	$-0.544004\pi$
$379$	−18.2142	−	7.54458i	−0.935602	−	0.387539i	−0.797801	+	0.602921i	$0.794004\pi$
$380$	−11.9642	+	25.4237i	−0.613752	+	1.30421i
$381$	−1.77214	−	0.734045i	−0.0907896	−	0.0376063i
$382$	2.93218	−	1.86077i	0.150023	−	0.0952053i
$383$	10.6892	+	10.6892i	0.546194	+	0.546194i	0.925338	−	0.379144i	$-0.123781\pi$
$383$	10.6892	+	10.6892i	0.546194	+	0.546194i	−0.379144	+	0.925338i	$0.623781\pi$
$384$	14.2344	+	31.5325i	0.726396	+	1.60914i
$385$	27.5115	+	27.5115i	1.40212	+	1.40212i
$386$	2.36139	−	10.5637i	0.120191	−	0.537677i
$387$	22.4549	−	54.2108i	1.14144	−	2.75569i
$388$	11.1240	+	30.9004i	0.564736	+	1.56873i
$389$	7.85086	+	18.9536i	0.398054	+	0.960988i	0.988127	+	0.153638i	$0.0490990\pi$
$389$	7.85086	+	18.9536i	0.398054	+	0.960988i	−0.590073	+	0.807350i	$0.700901\pi$
$390$	−2.43649	−	36.5691i	−0.123377	−	1.85175i
$391$	1.04492	+	1.04492i	0.0528439	+	0.0528439i
$392$	−0.0275194	+	0.00347554i	−0.00138994	+	0.000175541i
$393$	4.83691	+	4.83691i	0.243990	+	0.243990i
$394$	1.19968	−	0.209363i	0.0604389	−	0.0105476i
$395$	−2.46040	+	5.93993i	−0.123796	+	0.298870i
$396$	−79.3225	−	3.74259i	−3.98611	−	0.188072i
$397$	−8.45983	−	20.4238i	−0.424587	−	1.02504i	−0.980977	−	0.194122i	$-0.937814\pi$
$397$	−8.45983	−	20.4238i	−0.424587	−	1.02504i	0.556391	−	0.830921i	$-0.312186\pi$
$398$	33.0327	+	7.38407i	1.65578	+	0.370130i
$399$	48.3911			2.42259
$400$	−0.197692	+	2.09034i	−0.00988462	+	0.104517i
$401$	−10.4272	+	10.4272i	−0.520709	+	0.520709i	−0.917786	−	0.397076i	$-0.870025\pi$
$401$	−10.4272	+	10.4272i	−0.520709	+	0.520709i	0.397076	+	0.917786i	$0.370025\pi$
$402$	2.80520	+	4.42039i	0.139910	+	0.220469i
$403$	−5.60837	+	10.2918i	−0.279373	+	0.512672i
$404$	13.7650	+	0.649456i	0.684832	+	0.0323117i
$405$	26.6699	+	11.0470i	1.32524	+	0.548931i
$406$	−3.50924	−	20.1084i	−0.174161	−	0.997964i
$407$	15.0773	+	15.0773i	0.747353	+	0.747353i
$408$	9.06800	+	2.48106i	0.448933	+	0.122831i
$409$			36.2137i			1.79065i	0.445411	+	0.895326i	$0.353058\pi$
$409$			36.2137i			1.79065i	−0.445411	+	0.895326i	$0.646942\pi$
$410$	−21.3091	+	3.71878i	−1.05238	+	0.183657i
$411$	8.30048	−	20.0391i	0.409432	−	0.988457i
$412$	7.40699	+	20.5752i	0.364916	+	1.01367i
$413$	14.2652	+	5.90882i	0.701942	+	0.290754i
$414$	−10.3097	+	6.54259i	−0.506696	+	0.321551i
$415$	5.13112			0.251877
$416$	20.3882	+	0.566225i	0.999615	+	0.0277614i
$417$	23.6454			1.15792
$418$	44.6200	−	28.3160i	2.18243	−	1.38498i
$419$	1.44481	+	0.598459i	0.0705835	+	0.0292366i	0.417696	−	0.908587i	$-0.362838\pi$
$419$	1.44481	+	0.598459i	0.0705835	+	0.0292366i	−0.347112	+	0.937824i	$0.612838\pi$
$420$	35.8105	−	12.8917i	1.74738	−	0.629048i
$421$	−1.17500	+	2.83671i	−0.0572662	+	0.138253i	−0.949923	−	0.312484i	$-0.898839\pi$
$421$	−1.17500	+	2.83671i	−0.0572662	+	0.138253i	0.892657	+	0.450737i	$0.148839\pi$
$422$	9.04888	−	1.57918i	0.440493	−	0.0768731i
$423$			3.36042i			0.163389i
$424$	15.9733	+	28.0064i	0.775732	+	1.36011i
$425$	0.403452	+	0.403452i	0.0195703	+	0.0195703i
$426$	4.07627	+	23.3575i	0.197496	+	1.13168i
$427$	23.6229	+	9.78492i	1.14319	+	0.473525i
$428$	0.215300	−	4.56320i	0.0104069	−	0.220571i
$429$	−32.9834	+	60.5271i	−1.59245	+	2.92228i
$430$	16.4562	+	25.9315i	0.793589	+	1.25053i
$431$	9.64730	−	9.64730i	0.464694	−	0.464694i	−0.435496	−	0.900191i	$-0.643427\pi$
$431$	9.64730	−	9.64730i	0.464694	−	0.464694i	0.900191	+	0.435496i	$0.143427\pi$
$432$	−19.1808	+	36.2222i	−0.922838	+	1.74274i
$433$	−3.86613			−0.185794			−0.0928971	−	0.995676i	$-0.529613\pi$
$433$	−3.86613			−0.185794			−0.0928971	+	0.995676i	$0.529613\pi$
$434$	−11.8785	−	2.65531i	−0.570187	−	0.127459i
$435$	14.9953	+	36.2017i	0.718967	+	1.73574i
$436$	0.332617	−	7.04969i	0.0159295	−	0.337619i
$437$	3.10963	−	7.50730i	0.148754	−	0.359123i
$438$	−56.4174	+	9.84575i	−2.69573	+	0.470448i
$439$	−16.4792	−	16.4792i	−0.786509	−	0.786509i	0.194411	−	0.980920i	$-0.437720\pi$
$439$	−16.4792	−	16.4792i	−0.786509	−	0.786509i	−0.980920	+	0.194411i	$0.937720\pi$
$440$	25.4763	−	32.8415i	1.21453	−	1.56566i
$441$	−0.0440403	−	0.0440403i	−0.00209716	−	0.00209716i
$442$	3.64990	−	4.17098i	0.173608	−	0.198393i
$443$	−4.31269	−	10.4117i	−0.204902	−	0.494677i	0.787705	−	0.616053i	$-0.211269\pi$
$443$	−4.31269	−	10.4117i	−0.204902	−	0.494677i	−0.992607	+	0.121376i	$0.961269\pi$
$444$	19.6254	−	7.06508i	0.931381	−	0.335294i
$445$	−10.0540	+	24.2725i	−0.476605	+	1.15063i
$446$	0.186251	−	0.833194i	0.00881924	−	0.0394529i
$447$	−34.1892	−	34.1892i	−1.61709	−	1.61709i
$448$	5.26604	+	20.5158i	0.248797	+	0.969279i
$449$	−0.830268	−	0.830268i	−0.0391828	−	0.0391828i	0.687244	−	0.726427i	$-0.258820\pi$
$449$	−0.830268	−	0.830268i	−0.0391828	−	0.0391828i	−0.726427	+	0.687244i	$0.758820\pi$
$450$	−3.98066	+	2.52614i	−0.187650	+	0.119083i
$451$	37.5864	+	15.5688i	1.76988	+	0.733106i
$452$	−4.84492	−	2.27998i	−0.227886	−	0.107241i
$453$	23.9797	+	9.93270i	1.12666	+	0.466679i
$454$	−29.4018	−	20.6645i	−1.37990	−	0.969831i
$455$	2.37951	−	22.3117i	0.111553	−	1.04599i
$456$	−6.47747	−	51.2887i	−0.303335	−	2.40181i
$457$	−31.4019			−1.46892			−0.734460	−	0.678651i	$-0.762565\pi$
$457$	−31.4019			−1.46892			−0.734460	+	0.678651i	$0.762565\pi$
$458$	5.54922	+	31.7978i	0.259298	+	1.48581i
$459$	4.26230	+	10.2901i	0.198947	+	0.480301i
$460$	0.301209	−	6.38400i	0.0140439	−	0.297655i
$461$	−26.7134	+	11.0650i	−1.24417	+	0.515351i	−0.905014	−	0.425381i	$-0.860140\pi$
$461$	−26.7134	+	11.0650i	−1.24417	+	0.515351i	−0.339152	+	0.940732i	$0.610140\pi$
$462$	−69.8587	−	15.6161i	−3.25012	−	0.726527i
$463$	−17.9440	−	17.9440i	−0.833927	−	0.833927i	0.154125	−	0.988051i	$-0.450744\pi$
$463$	−17.9440	−	17.9440i	−0.833927	−	0.833927i	−0.988051	+	0.154125i	$0.950744\pi$
$464$	−20.8427	+	6.41101i	−0.967599	+	0.297624i
$465$	23.3654			1.08354
$466$	13.1951	+	2.94962i	0.611253	+	0.136639i
$467$	7.29041	+	3.01979i	0.337360	+	0.139739i	0.544931	−	0.838481i	$-0.316556\pi$
$467$	7.29041	+	3.01979i	0.337360	+	0.139739i	−0.207571	+	0.978220i	$0.566556\pi$
$468$	27.0552	+	36.9511i	1.25063	+	1.70807i
$469$	1.22658	+	2.96124i	0.0566384	+	0.136737i
$470$	−1.43902	−	1.01138i	−0.0663769	−	0.0466516i
$471$	−31.1255	+	31.1255i	−1.43419	+	1.43419i
$472$	4.35314	−	15.9103i	0.200370	−	0.732329i
$473$		−	57.7629i		−	2.65594i
$474$	−2.03360	−	11.6528i	−0.0934063	−	0.535230i
$475$	1.20065	−	2.89862i	0.0550896	−	0.132998i
$476$	5.20787	+	2.45078i	0.238702	+	0.112331i
$477$	−27.7041	+	66.8835i	−1.26848	+	3.06239i
$478$	9.13016	+	2.04094i	0.417604	+	0.0933506i
$479$	11.4813	−	11.4813i	0.524594	−	0.524594i	−0.394362	−	0.918955i	$-0.629034\pi$
$479$	11.4813	−	11.4813i	0.524594	−	0.524594i	0.918955	+	0.394362i	$0.129034\pi$
$480$	−18.4571	−	36.2292i	−0.842445	−	1.65363i
$481$	1.30406	−	12.2276i	0.0594598	−	0.557529i
$482$	−35.1897	−	7.86626i	−1.60285	−	0.358299i
$483$	−10.1690	+	4.21213i	−0.462705	+	0.191659i
$484$	−52.8527	+	19.0268i	−2.40240	+	0.864854i
$485$	−14.7706	−	35.6594i	−0.670698	−	1.61921i
$486$	−9.49402	+	1.65686i	−0.430657	+	0.0751566i
$487$	−31.5564			−1.42996			−0.714979	−	0.699146i	$-0.753564\pi$
$487$	−31.5564			−1.42996			−0.714979	+	0.699146i	$0.753564\pi$
$488$	7.20874	−	26.3471i	0.326324	−	1.19268i
$489$			8.52297i			0.385422i
$490$	0.0321139	−	0.00560439i	0.00145076	−	0.000253181i
$491$	−7.80660	−	18.8468i	−0.352307	−	0.850545i	−0.996335	−	0.0855422i	$-0.972738\pi$
$491$	−7.80660	−	18.8468i	−0.352307	−	0.850545i	0.644027	−	0.765002i	$-0.277262\pi$
$492$	29.4363	−	26.7837i	1.32709	−	1.20750i
$493$	−2.26767	+	5.47464i	−0.102131	+	0.246565i
$494$	−28.8702	−	9.76537i	−1.29893	−	0.439365i
$495$	93.3281			4.19479
$496$	−1.22428	+	12.9452i	−0.0549720	+	0.581257i
$497$			14.5162i			0.651141i
$498$	−7.97086	+	5.05833i	−0.357183	+	0.226669i
$499$	−11.1888	−	27.0123i	−0.500881	−	1.20923i	−0.949004	−	0.315263i	$-0.897907\pi$
$499$	−11.1888	−	27.0123i	−0.500881	−	1.20923i	0.448123	−	0.893972i	$-0.352093\pi$
$500$	−0.991485	+	21.0141i	−0.0443406	+	0.939780i
$501$	−10.0225	+	24.1966i	−0.447774	+	1.08102i
$502$	13.8077	+	9.70444i	0.616267	+	0.433130i
$503$	12.2315	−	12.2315i	0.545377	−	0.545377i	−0.379723	−	0.925100i	$-0.623981\pi$
$503$	12.2315	−	12.2315i	0.545377	−	0.545377i	0.925100	+	0.379723i	$0.123981\pi$
$504$	−29.1506	+	37.5780i	−1.29847	+	1.67386i
$505$	−16.1954			−0.720684
$506$	−6.91179	+	9.83424i	−0.307267	+	0.437185i
$507$	39.1093	−	7.12496i	1.73691	−	0.316431i
$508$	−0.534186	+	1.13513i	−0.0237007	+	0.0503634i
$509$	−8.72720	−	21.0693i	−0.386826	−	0.933881i	−0.990608	−	0.136732i	$-0.956340\pi$
$509$	−8.72720	−	21.0693i	−0.386826	−	0.933881i	0.603782	−	0.797150i	$-0.293660\pi$
$510$	−10.7828	−	2.41037i	−0.477471	−	0.106733i
$511$	−35.0622			−1.55106
$512$	21.0393	−	8.32753i	0.929815	−	0.368028i
$513$	43.3071	−	43.3071i	1.91206	−	1.91206i
$514$	12.8707	−	8.16776i	0.567700	−	0.360265i
$515$	−9.83509	−	23.7440i	−0.433386	−	1.04629i
$516$	−51.1273	−	24.0601i	−2.25075	−	1.05919i
$517$	1.26594	+	3.05624i	0.0556759	+	0.134413i
$518$	12.5799	−	2.19540i	0.552729	−	0.0964601i
$519$	−15.7340	+	15.7340i	−0.690647	+	0.690647i
$520$	−23.9661	+	0.464567i	−1.05098	+	0.0203726i
$521$	−8.68779	−	8.68779i	−0.380619	−	0.380619i	0.490706	−	0.871325i	$-0.336739\pi$
$521$	−8.68779	−	8.68779i	−0.380619	−	0.380619i	−0.871325	+	0.490706i	$0.836739\pi$
$522$	−40.0594	−	28.1549i	−1.75335	−	1.23231i
$523$	−14.1034	+	5.84180i	−0.616697	+	0.255444i	−0.669089	−	0.743182i	$-0.733315\pi$
$523$	−14.1034	+	5.84180i	−0.616697	+	0.255444i	0.0523921	+	0.998627i	$0.483315\pi$
$524$	3.30910	−	3.01091i	0.144559	−	0.131532i
$525$	−3.92632	+	1.62634i	−0.171359	+	0.0709791i
$526$	5.60117	−	25.0568i	0.244223	−	1.09253i
$527$	2.49852	+	2.49852i	0.108837	+	0.108837i
$528$	−7.20013	+	76.1320i	−0.313345	+	3.31322i
$529$		−	21.1517i		−	0.919640i
$530$	−20.3031	−	31.9934i	−0.881911	−	1.38970i
$531$	34.2183	−	14.1737i	1.48495	−	0.615086i
$532$	1.49163	−	31.6145i	0.0646704	−	1.37066i
$533$	−6.62932	−	22.5064i	−0.287148	−	0.974861i
$534$	−8.30996	−	47.6171i	−0.359607	−	2.06060i
$535$			5.36890i			0.232118i
$536$	2.97436	−	1.69641i	0.128473	−	0.0732738i
$537$	15.2540	+	15.2540i	0.658257	+	0.658257i
$538$	0.689612	+	3.95157i	0.0297313	+	0.170364i
$539$	−0.0566447	−	0.0234630i	−0.00243986	−	0.00101062i
$540$	20.5110	−	43.5855i	0.882654	−	1.87562i
$541$	−4.10564	+	1.70061i	−0.176515	+	0.0731150i	−0.469191	−	0.883097i	$-0.655454\pi$
$541$	−4.10564	+	1.70061i	−0.176515	+	0.0731150i	0.292676	+	0.956212i	$0.405454\pi$
$542$	7.30163	−	32.6638i	0.313632	−	1.40303i
$543$	25.0718			1.07593
$544$	1.90042	−	5.84775i	0.0814799	−	0.250720i
$545$			8.29441i			0.355294i
$546$	18.2987	+	37.0055i	0.783114	+	1.58369i
$547$	−19.2177	−	7.96023i	−0.821689	−	0.340355i	−0.0680819	−	0.997680i	$-0.521688\pi$
$547$	−19.2177	−	7.96023i	−0.821689	−	0.340355i	−0.753607	+	0.657325i	$0.771688\pi$
$548$	−12.8359	−	6.04049i	−0.548324	−	0.258037i
$549$	56.6651	−	23.4714i	2.41841	−	1.00174i
$550$	−2.66869	+	3.79707i	−0.113793	+	0.161908i
$551$	32.5844			1.38814
$552$	5.82553	+	10.2141i	0.247951	+	0.434739i
$553$		−	7.24195i		−	0.307959i
$554$	−0.967240	−	0.679804i	−0.0410941	−	0.0288821i
$555$	−22.6480	+	9.38109i	−0.961352	+	0.398205i
$556$	0.728856	−	15.4478i	0.0309104	−	0.655133i
$557$	−2.54460	−	6.14321i	−0.107818	−	0.260296i	0.860757	−	0.509015i	$-0.169990\pi$
$557$	−2.54460	−	6.14321i	−0.107818	−	0.260296i	−0.968576	+	0.248719i	$0.919990\pi$
$558$	−24.6517	+	15.6441i	−1.04359	+	0.662266i
$559$	−25.9207	+	20.9246i	−1.09633	+	0.885018i
$560$	−7.31843	−	23.7928i	−0.309260	−	1.00543i
$561$	14.6941	+	14.6941i	0.620383	+	0.620383i
$562$	−18.1922	−	28.6670i	−0.767391	−	1.20924i
$563$	17.3599	+	7.19070i	0.731632	+	0.303052i	0.717223	−	0.696844i	$-0.245413\pi$
$563$	17.3599	+	7.19070i	0.731632	+	0.303052i	0.0144097	+	0.999896i	$0.495413\pi$
$564$	3.23246	+	0.152513i	0.136111	+	0.00642197i
$565$	5.81399	+	2.40823i	0.244596	+	0.101315i
$566$	8.34616	+	5.86592i	0.350815	+	0.246563i
$567$	−32.5159			−1.36554
$568$	15.3854	−	1.94309i	0.645557	−	0.0815302i
$569$	−7.30940	−	7.30940i	−0.306426	−	0.306426i	0.537095	−	0.843521i	$-0.319521\pi$
$569$	−7.30940	−	7.30940i	−0.306426	−	0.306426i	−0.843521	+	0.537095i	$0.819521\pi$
$570$	10.4451	+	59.8516i	0.437496	+	2.50691i
$571$	−9.38796	+	3.88862i	−0.392874	+	0.162734i	−0.570370	−	0.821388i	$-0.693200\pi$
$571$	−9.38796	+	3.88862i	−0.392874	+	0.162734i	0.177496	+	0.984121i	$0.443200\pi$
$572$	38.5264	+	23.4141i	1.61087	+	0.978994i
$573$	2.87361	−	6.93751i	0.120047	−	0.289819i
$574$	20.5724	−	13.0553i	0.858673	−	0.544917i
$575$			0.713630i			0.0297604i
$576$	43.7301	+	25.8660i	1.82209	+	1.07775i
$577$	−12.6144	+	12.6144i	−0.525145	+	0.525145i	−0.919121	−	0.393976i	$-0.871099\pi$
$577$	−12.6144	+	12.6144i	−0.525145	+	0.525145i	0.393976	+	0.919121i	$0.371099\pi$
$578$	11.9866	+	18.8884i	0.498578	+	0.785653i
$579$	−8.95684	−	21.6237i	−0.372233	−	0.898651i
$580$	24.1132	−	8.68067i	1.00125	−	0.360445i
$581$	−5.33970	+	2.21178i	−0.221528	+	0.0917600i
$582$	58.0987	+	40.8335i	2.40827	+	1.69260i
$583$			71.2660i			2.95154i
$584$	4.69331	+	37.1617i	0.194210	+	1.53776i
$585$	−33.8081	−	41.8802i	−1.39779	−	1.73153i
$586$	2.78179	+	15.9400i	0.114915	+	0.658477i
$587$	6.62324	−	15.9899i	0.273370	−	0.659974i	−0.726253	−	0.687428i	$-0.758740\pi$
$587$	6.62324	−	15.9899i	0.273370	−	0.659974i	0.999623	+	0.0274534i	$0.00873978\pi$
$588$	−0.0443620	+	0.0403644i	−0.00182946	+	0.00166460i
$589$	7.43547	−	17.9508i	0.306373	−	0.739650i
$590$	−4.22912	+	18.9190i	−0.174110	+	0.778882i
$591$	1.86198	−	1.86198i	0.0765918	−	0.0765918i
$592$	−4.01075	−	13.0393i	−0.164841	−	0.535912i
$593$	−26.2711	+	26.2711i	−1.07882	+	1.07882i	−0.0822082	+	0.996615i	$0.526197\pi$
$593$	−26.2711	+	26.2711i	−1.07882	+	1.07882i	−0.996615	+	0.0822082i	$0.973803\pi$
$594$	−76.4948	+	48.5439i	−3.13862	+	1.99178i
$595$	−6.24953	−	2.58864i	−0.256206	−	0.106124i
$596$	−23.3900	+	21.2823i	−0.958093	+	0.871758i
$597$	67.6175	−	28.0081i	2.76740	−	1.14629i
$598$	6.91684	−	0.460849i	0.282850	−	0.0188455i
$599$	15.4881	−	15.4881i	0.632827	−	0.632827i	−0.315949	−	0.948776i	$-0.602323\pi$
$599$	15.4881	−	15.4881i	0.632827	−	0.632827i	0.948776	+	0.315949i	$0.102323\pi$
$600$	2.24928	+	3.94372i	0.0918265	+	0.161002i
$601$	1.53528	−	1.53528i	0.0626256	−	0.0626256i	−0.675100	−	0.737726i	$-0.735900\pi$
$601$	1.53528	−	1.53528i	0.0626256	−	0.0626256i	0.737726	+	0.675100i	$0.235900\pi$
$602$	−28.3030	−	19.8922i	−1.15354	−	0.810744i
$603$	7.10323	+	2.94225i	0.289266	+	0.119818i
$604$	7.22831	−	15.3600i	0.294116	−	0.624990i
$605$	60.9927	−	25.2640i	2.47970	−	1.02713i
$606$	25.1584	−	15.9656i	1.02199	−	0.648559i
$607$		−	25.2987i		−	1.02684i	−0.858136	−	0.513422i	$-0.828378\pi$
$607$		−	25.2987i		−	1.02684i	0.858136	−	0.513422i	$-0.171622\pi$
$608$	−33.7071	+	2.65086i	−1.36700	+	0.107506i
$609$	−31.2097	−	31.2097i	−1.26468	−	1.26468i
$610$	−7.00336	+	31.3295i	−0.283558	+	1.26850i
$611$	0.912878	−	1.67520i	0.0369311	−	0.0677715i
$612$	12.9903	−	4.67646i	0.525102	−	0.189035i
$613$	2.77210	−	6.69244i	0.111964	−	0.270305i	−0.857958	−	0.513719i	$-0.828267\pi$
$613$	2.77210	−	6.69244i	0.111964	−	0.270305i	0.969923	+	0.243414i	$0.0782673\pi$
$614$	2.30388	+	1.61924i	0.0929772	+	0.0653471i
$615$	−33.0732	+	33.0732i	−1.33364	+	1.33364i
$616$	−12.3555	+	45.1581i	−0.497819	+	1.81947i
$617$	−8.47710			−0.341275			−0.170638	−	0.985334i	$-0.554583\pi$
$617$	−8.47710			−0.341275			−0.170638	+	0.985334i	$0.554583\pi$
$618$	38.6854	+	27.1892i	1.55615	+	1.09371i
$619$	4.15215	+	1.71988i	0.166889	+	0.0691277i	0.464564	−	0.885540i	$-0.346211\pi$
$619$	4.15215	+	1.71988i	0.166889	+	0.0691277i	−0.297675	+	0.954667i	$0.596211\pi$
$620$	0.720225	−	15.2649i	0.0289249	−	0.613052i
$621$	−5.33103	+	12.8702i	−0.213927	+	0.516465i
$622$	9.22140	−	41.2520i	0.369745	−	1.65405i
$623$		−	29.5930i		−	1.18562i
$624$	36.7719	−	24.3479i	1.47205	−	0.974694i
$625$		−	27.3490i		−	1.09396i
$626$	20.3184	+	4.54195i	0.812088	+	0.181533i
$627$	43.7287	−	105.570i	1.74635	−	4.21607i
$628$	19.3752	+	21.2941i	0.773155	+	0.849725i
$629$	−3.42496	−	1.41866i	−0.136562	−	0.0565658i
$630$	32.1400	−	45.7294i	1.28049	−	1.82190i
$631$	−21.2981			−0.847864			−0.423932	−	0.905694i	$-0.639350\pi$
$631$	−21.2981			−0.847864			−0.423932	+	0.905694i	$0.639350\pi$
$632$	−7.67559	+	0.969383i	−0.305318	+	0.0385600i
$633$	14.0445	−	14.0445i	0.558219	−	0.558219i
$634$	17.9296	−	25.5106i	0.712076	−	1.01316i
$635$	0.564234	−	1.36218i	0.0223909	−	0.0540565i
$636$	63.0792	+	29.6846i	2.50125	+	1.17707i
$637$	0.00999073	+	0.0339183i	0.000395847	+	0.00134389i
$638$	−47.0398	−	10.5152i	−1.86232	−	0.416301i
$639$	24.6218	+	24.6218i	0.974025	+	0.974025i
$640$	−24.2379	+	10.9415i	−0.958085	+	0.432499i
$641$		−	8.78867i		−	0.347132i	−0.984822	−	0.173566i	$-0.944471\pi$
$641$		−	8.78867i		−	0.347132i	0.984822	−	0.173566i	$-0.0555289\pi$
$642$	−5.29274	−	8.34024i	−0.208888	−	0.329163i
$643$	−37.9154	+	15.7051i	−1.49524	+	0.619347i	−0.972449	−	0.233117i	$-0.925108\pi$
$643$	−37.9154	+	15.7051i	−1.49524	+	0.619347i	−0.522787	+	0.852463i	$0.675108\pi$
$644$	2.43838	+	6.77336i	0.0960857	+	0.266908i
$645$	61.3536	+	25.4135i	2.41580	+	1.00066i
$646$	−5.28318	+	7.51702i	−0.207864	+	0.295753i
$647$	18.3403	−	18.3403i	0.721030	−	0.721030i	−0.247785	−	0.968815i	$-0.579703\pi$
$647$	18.3403	−	18.3403i	0.721030	−	0.721030i	0.968815	+	0.247785i	$0.0797025\pi$
$648$	4.35247	+	34.4629i	0.170981	+	1.35383i
$649$	25.7814	−	25.7814i	1.01201	−	1.01201i
$650$	2.67064	−	0.177937i	0.104751	−	0.00697927i
$651$	−24.3152	+	10.0717i	−0.952988	+	0.394741i
$652$	5.56816	+	0.262716i	0.218066	+	0.0102888i
$653$	30.7101	+	12.7205i	1.20178	+	0.497793i	0.891573	−	0.452876i	$-0.149602\pi$
$653$	30.7101	+	12.7205i	1.20178	+	0.497793i	0.310206	+	0.950670i	$0.399602\pi$
$654$	−8.17675	−	12.8848i	−0.319736	−	0.503837i
$655$	−3.71795	+	3.71795i	−0.145272	+	0.145272i
$656$	−16.5907	−	20.0566i	−0.647760	−	0.783080i
$657$	−59.4712	+	59.4712i	−2.32019	+	2.32019i
$658$	1.93347	+	0.432206i	0.0753747	+	0.0168491i
$659$	−12.4839	+	30.1387i	−0.486303	+	1.17404i	0.470264	+	0.882526i	$0.344159\pi$
$659$	−12.4839	+	30.1387i	−0.486303	+	1.17404i	−0.956567	+	0.291513i	$0.905841\pi$
$660$	4.23571	−	89.7740i	0.164875	−	3.49445i
$661$	6.42611	−	15.5140i	0.249947	−	0.603425i	−0.748252	−	0.663414i	$-0.769107\pi$
$661$	6.42611	−	15.5140i	0.249947	−	0.603425i	0.998199	+	0.0599894i	$0.0191067\pi$
$662$	−22.8469	+	3.98715i	−0.887970	+	0.154965i
$663$	1.27091	−	11.9168i	0.0493581	−	0.462809i
$664$	3.05897	+	5.36337i	0.118711	+	0.208139i
$665$			37.1965i			1.44242i
$666$	17.6138	−	25.0613i	0.682521	−	0.971106i
$667$	−6.84735	+	2.83627i	−0.265130	+	0.109821i
$668$	15.4990	+	7.29369i	0.599673	+	0.282201i
$669$	−0.706457	−	1.70554i	−0.0273132	−	0.0659399i
$670$	−3.39779	+	2.15625i	−0.131268	+	0.0833033i
$671$	42.6937	−	42.6937i	1.64817	−	1.64817i
$672$	34.8240	+	29.7460i	1.34337	+	1.14748i
$673$			23.8980i			0.921199i	0.887608	+	0.460600i	$0.152366\pi$
$673$			23.8980i			0.921199i	−0.887608	+	0.460600i	$0.847634\pi$
$674$	−8.09020	−	12.7484i	−0.311623	−	0.491051i
$675$	−2.05835	+	4.96929i	−0.0792259	+	0.191268i
$676$	−3.44930	−	25.7702i	−0.132665	−	0.991161i
$677$	−29.3087	+	12.1400i	−1.12642	+	0.466580i	−0.866564	−	0.499067i	$-0.833676\pi$
$677$	−29.3087	+	12.1400i	−1.12642	+	0.466580i	−0.259860	+	0.965646i	$0.583676\pi$
$678$	−11.4057	+	1.99048i	−0.438034	+	0.0764440i
$679$	30.7421	+	30.7421i	1.17977	+	1.17977i
$680$	−1.90710	+	6.97024i	−0.0731340	+	0.267296i
$681$	−77.7064			−2.97772
$682$	−16.5269	+	23.5148i	−0.632847	+	0.900428i
$683$	0.433500	+	0.179562i	0.0165874	+	0.00687073i	0.390962	−	0.920407i	$-0.372142\pi$
$683$	0.433500	+	0.179562i	0.0165874	+	0.00687073i	−0.374374	+	0.927278i	$0.622142\pi$
$684$	−51.0932	−	56.1533i	−1.95360	−	2.14708i
$685$	15.4033	+	6.38027i	0.588531	+	0.243778i
$686$	22.0989	−	14.0241i	0.843742	−	0.535441i
$687$	49.3524	+	49.3524i	1.88291	+	1.88291i
$688$	−17.2947	+	32.6604i	−0.659355	+	1.24517i
$689$	31.9800	−	25.8161i	1.21834	−	0.983517i
$690$	−7.40464	−	11.6681i	−0.281890	−	0.444199i
$691$	−15.0338	−	36.2947i	−0.571912	−	1.38072i	−0.899925	−	0.436044i	$-0.856379\pi$
$691$	−15.0338	−	36.2947i	−0.571912	−	1.38072i	0.328013	−	0.944673i	$-0.393621\pi$
$692$	9.79422	+	10.7642i	0.372321	+	0.409194i
$693$	−97.1221	+	40.2293i	−3.68936	+	1.52818i
$694$	28.7762	−	40.9433i	1.09233	−	1.55419i
$695$			18.1753i			0.689430i
$696$	−28.9008	+	37.2561i	−1.09548	+	1.41219i
$697$	−7.07322			−0.267917
$698$	10.4959	+	7.37680i	0.397274	+	0.279216i
$699$	27.0103	−	11.1880i	1.02162	−	0.423170i
$700$	0.941477	+	2.61524i	0.0355845	+	0.0988468i
$701$	−25.3437	−	10.4977i	−0.957220	−	0.396493i	−0.151280	−	0.988491i	$-0.548339\pi$
$701$	−25.3437	−	10.4977i	−0.957220	−	0.396493i	−0.805940	+	0.591998i	$0.798339\pi$
$702$	49.4939	+	16.7414i	1.86803	+	0.631863i
$703$			20.3850i			0.768833i
$704$	49.5160	+	7.05065i	1.86620	+	0.265732i
$705$	−3.80319			−0.143236
$706$	23.9296	+	5.34919i	0.900602	+	0.201319i
$707$	16.8537	−	6.98104i	0.633850	−	0.262549i
$708$	−12.0809	−	33.5585i	−0.454030	−	1.26121i
$709$	13.2912	+	5.50540i	0.499162	+	0.206760i	0.618036	−	0.786150i	$-0.287929\pi$
$709$	13.2912	+	5.50540i	0.499162	+	0.206760i	−0.118874	+	0.992909i	$0.537929\pi$
$710$	−17.9541	+	3.13328i	−0.673805	+	0.117590i
$711$	−12.2835	−	12.2835i	−0.460668	−	0.460668i
$712$	−31.3650	+	3.96122i	−1.17545	+	0.148453i
$713$			4.41942i			0.165509i
$714$	12.2602	−	2.13959i	0.458825	−	0.0800723i
$715$	−46.5250	−	25.3531i	−1.73994	−	0.948152i
$716$	10.4358	−	9.49539i	0.390004	−	0.354860i
$717$	18.6893	−	7.74138i	0.697966	−	0.289107i
$718$	−37.4124	+	23.7421i	−1.39622	+	0.886045i
$719$			2.99679i			0.111761i	0.998437	+	0.0558807i	$0.0177967\pi$
$719$			2.99679i			0.111761i	−0.998437	+	0.0558807i	$0.982203\pi$
$720$	−52.7697	−	27.9432i	−1.96661	−	1.04138i
$721$	20.4698	+	20.4698i	0.762336	+	0.762336i
$722$	23.0829	+	5.15993i	0.859058	+	0.192033i
$723$	−72.0330	+	29.8370i	−2.67894	+	1.10965i
$724$	0.772825	−	16.3797i	0.0287218	−	0.608747i
$725$	−2.64381	+	1.09510i	−0.0981887	+	0.0406711i
$726$	−69.8425	+	99.3735i	−2.59210	+	3.68810i
$727$	1.11583	+	1.11583i	0.0413839	+	0.0413839i	0.727496	−	0.686112i	$-0.240684\pi$
$727$	1.11583	+	1.11583i	0.0413839	+	0.0413839i	−0.686112	+	0.727496i	$0.740684\pi$
$728$	24.7402	−	10.8141i	0.916931	−	0.400797i
$729$	11.3171	−	11.3171i	0.419152	−	0.419152i
$730$	−7.56807	−	43.3660i	−0.280107	−	1.60505i
$731$	3.84318	+	9.27826i	0.142145	+	0.343169i
$732$	−20.0059	−	55.5725i	−0.739438	−	2.05402i
$733$	9.82994	+	23.7316i	0.363077	+	0.876546i	0.994847	+	0.101390i	$0.0323289\pi$
$733$	9.82994	+	23.7316i	0.363077	+	0.876546i	−0.631770	+	0.775156i	$0.717671\pi$
$734$	10.9847	+	17.3096i	0.405453	+	0.638908i
$735$	0.0498430	−	0.0498430i	0.00183849	−	0.00183849i
$736$	6.85254	−	3.49104i	0.252588	−	0.128682i
$737$	7.56866			0.278795
$738$	12.7502	−	57.0379i	0.469341	−	2.09960i
$739$	−2.00313	−	4.83599i	−0.0736864	−	0.177895i	0.882745	−	0.469853i	$-0.155693\pi$
$739$	−2.00313	−	4.83599i	−0.0736864	−	0.177895i	−0.956431	+	0.291958i	$0.905693\pi$
$740$	5.43066	+	15.0853i	0.199635	+	0.554548i
$741$	−63.2146	+	18.6200i	−2.32225	+	0.684023i
$742$	34.9193	+	24.5423i	1.28193	+	0.900976i
$743$	−11.1494			−0.409032			−0.204516	−	0.978863i	$-0.565562\pi$
$743$	−11.1494			−0.409032			−0.204516	+	0.978863i	$0.565562\pi$
$744$	13.9295	+	24.4230i	0.510680	+	0.895390i
$745$	26.2800	−	26.2800i	0.962823	−	0.962823i
$746$	−24.0486	+	34.2169i	−0.880482	+	1.25277i
$747$	−5.30547	+	12.8085i	−0.194117	+	0.468640i
$748$	10.0527	−	9.14686i	0.367564	−	0.334442i
$749$	−2.31428	−	5.58716i	−0.0845618	−	0.204150i
$750$	24.3737	+	38.4079i	0.890003	+	1.40246i
$751$			22.1687i			0.808947i	0.914550	+	0.404474i	$0.132545\pi$
$751$			22.1687i			0.808947i	−0.914550	+	0.404474i	$0.867455\pi$
$752$	0.199277	−	2.10710i	0.00726690	−	0.0768380i
$753$	36.4925			1.32986
$754$	12.3216	+	24.9179i	0.448725	+	0.907455i
$755$	−7.63490	+	18.4323i	−0.277862	+	0.670819i
$756$	−2.55720	+	54.1987i	−0.0930043	+	1.97119i
$757$	14.7347	+	35.5726i	0.535540	+	1.29291i	0.927808	+	0.373058i	$0.121691\pi$
$757$	14.7347	+	35.5726i	0.535540	+	1.29291i	−0.392268	+	0.919851i	$0.628309\pi$
$758$	4.79326	+	27.4660i	0.174099	+	0.997611i
$759$			25.9910i			0.943415i
$760$	39.4237	−	4.97899i	1.43005	−	0.180607i
$761$	17.4224			0.631563			0.315781	−	0.948832i	$-0.397733\pi$
$761$	17.4224			0.631563			0.315781	+	0.948832i	$0.397733\pi$
$762$	0.466357	+	2.67229i	0.0168943	+	0.0968068i
$763$	−3.57532	−	8.63159i	−0.129435	−	0.312485i
$764$	−4.44378	−	2.09121i	−0.160770	−	0.0756572i
$765$	−14.9910	+	6.20946i	−0.541999	+	0.224504i
$766$	4.66380	−	20.8635i	0.168510	−	0.753830i
$767$	−20.9086	−	2.22987i	−0.754964	−	0.0805161i
$768$	26.8657	−	40.8909i	0.969432	−	1.47552i
$769$	5.75237	−	5.75237i	0.207436	−	0.207436i	−0.595741	−	0.803177i	$-0.703141\pi$
$769$	5.75237	−	5.75237i	0.207436	−	0.207436i

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)

\(f(q)\)	\(=\)	\(q+(-0.757760 - 1.19407i) q^{2} +(-2.82515 - 1.17022i) q^{3} +(-0.851600 + 1.80963i) q^{4} +(0.899503 - 2.17159i) q^{5} +(0.743468 + 4.26017i) q^{6} +2.64760i q^{7} +(2.80614 - 0.354399i) q^{8} +(4.49077 + 4.49077i) q^{9} +O(q^{10})\)	\(q+(-0.757760 - 1.19407i) q^{2} +(-2.82515 - 1.17022i) q^{3} +(-0.851600 + 1.80963i) q^{4} +(0.899503 - 2.17159i) q^{5} +(0.743468 + 4.26017i) q^{6} +2.64760i q^{7} +(2.80614 - 0.354399i) q^{8} +(4.49077 + 4.49077i) q^{9} +(-3.27464 + 0.571477i) q^{10} +(5.77603 + 2.39251i) q^{11} +(4.52357 - 4.11594i) q^{12} +(-1.01875 - 3.45863i) q^{13} +(3.16142 - 2.00625i) q^{14} +(-5.08247 + 5.08247i) q^{15} +(-2.54955 - 3.08217i) q^{16} -1.08697 q^{17} +(1.95936 - 8.76521i) q^{18} +(2.28731 + 5.52206i) q^{19} +(3.16377 + 3.47710i) q^{20} +(3.09827 - 7.47989i) q^{21} +(-1.52002 - 8.70992i) q^{22} +(-0.961319 - 0.961319i) q^{23} +(-8.34249 - 2.28256i) q^{24} +(-0.371172 - 0.371172i) q^{25} +(-3.35788 + 3.83727i) q^{26} +(-3.92128 - 9.46682i) q^{27} +(-4.79120 - 2.25470i) q^{28} +(2.08624 - 5.03663i) q^{29} +(9.92011 + 2.21753i) q^{30} +(-2.29862 - 2.29862i) q^{31} +(-1.74837 + 5.37989i) q^{32} +(-13.5184 - 13.5184i) q^{33} +(0.823659 + 1.29791i) q^{34} +(5.74952 + 2.38153i) q^{35} +(-11.9510 + 4.30231i) q^{36} +(3.15093 + 1.30516i) q^{37} +(4.86049 - 6.91560i) q^{38} +(-1.16923 + 10.9633i) q^{39} +(1.75452 - 6.41257i) q^{40} +6.50731 q^{41} +(-11.2792 + 1.96841i) q^{42} +(-3.53570 - 8.53592i) q^{43} +(-9.24844 + 8.41504i) q^{44} +(13.7916 - 5.71266i) q^{45} +(-0.419432 + 1.87633i) q^{46} +(0.374148 + 0.374148i) q^{47} +(3.59607 + 11.6911i) q^{48} -0.00980685 q^{49} +(-0.161946 + 0.724465i) q^{50} +(3.07085 + 1.27199i) q^{51} +(7.12643 + 1.10181i) q^{52} +(4.36222 + 10.5313i) q^{53} +(-8.33264 + 11.8559i) q^{54} +(10.3911 - 10.3911i) q^{55} +(0.938308 + 7.42954i) q^{56} -18.2773i q^{57} +(-7.59495 + 1.32544i) q^{58} +(2.23176 - 5.38795i) q^{59} +(-4.86918 - 13.5256i) q^{60} +(3.69576 - 8.92236i) q^{61} +(-1.00291 + 4.48652i) q^{62} +(-11.8898 + 11.8898i) q^{63} +(7.74880 - 1.98898i) q^{64} +(-8.42711 - 0.898742i) q^{65} +(-5.89821 + 26.3856i) q^{66} +(1.11846 - 0.463281i) q^{67} +(0.925660 - 1.96701i) q^{68} +(1.59092 + 3.84083i) q^{69} +(-1.51304 - 8.66994i) q^{70} +5.48277 q^{71} +(14.1932 + 11.0102i) q^{72} +13.2430i q^{73} +(-0.829201 - 4.75143i) q^{74} +(0.614267 + 1.48297i) q^{75} +(-11.9408 - 0.563389i) q^{76} +(-6.33442 + 15.2926i) q^{77} +(13.9770 - 6.91143i) q^{78} -2.73529 q^{79} +(-8.98655 + 2.76417i) q^{80} +12.2813i q^{81} +(-4.93098 - 7.77018i) q^{82} +(0.835389 + 2.01681i) q^{83} +(10.8974 + 11.9766i) q^{84} +(-0.977729 + 2.36045i) q^{85} +(-7.51327 + 10.6900i) q^{86} +(-11.7879 + 11.7879i) q^{87} +(17.0562 + 4.66669i) q^{88} -11.1773 q^{89} +(-17.2720 - 12.1393i) q^{90} +(9.15709 - 2.69725i) q^{91} +(2.55830 - 0.920977i) q^{92} +(3.80408 + 9.18385i) q^{93} +(0.163244 - 0.730273i) q^{94} +14.0491 q^{95} +(11.2351 - 13.1530i) q^{96} +(11.6113 - 11.6113i) q^{97} +(0.00743124 + 0.0117101i) q^{98} +(15.1946 + 36.6830i) 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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