LMFDB - Embedded newform 369.2.u.a.307.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [369,2,Mod(46,369)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(369, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("369.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 369 = 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	369.u (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.94647983459$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 41)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			307.2
Character	$\chi$	$=$	369.307
Dual form			369.2.u.a.244.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.290902 - 0.0945196i) q^{2} +(-1.54234 - 1.12058i) q^{4} +(2.03721 - 2.80398i) q^{5} +(1.29765 + 0.661185i) q^{7} +(0.702328 + 0.966671i) q^{8} +O(q^{10})$	\(q+(-0.290902 - 0.0945196i) q^{2} +(-1.54234 - 1.12058i) q^{4} +(2.03721 - 2.80398i) q^{5} +(1.29765 + 0.661185i) q^{7} +(0.702328 + 0.966671i) q^{8} +(-0.857659 + 0.623126i) q^{10} +(-0.285814 + 1.80456i) q^{11} +(-2.91004 - 5.71127i) q^{13} +(-0.314993 - 0.314993i) q^{14} +(1.06531 + 3.27868i) q^{16} +(-3.14295 - 0.497794i) q^{17} +(1.51872 - 2.98065i) q^{19} +(-6.28416 + 2.04185i) q^{20} +(0.253710 - 0.497934i) q^{22} +(1.67386 - 5.15161i) q^{23} +(-2.16699 - 6.66932i) q^{25} +(0.306707 + 1.93647i) q^{26} +(-1.26051 - 2.47389i) q^{28} +(0.335113 - 0.0530767i) q^{29} +(-3.04183 + 2.21002i) q^{31} -3.44421i q^{32} +(0.867237 + 0.441879i) q^{34} +(4.49754 - 2.29161i) q^{35} +(0.993200 + 0.721602i) q^{37} +(-0.723527 + 0.723527i) q^{38} +4.14132 q^{40} +(6.22198 + 1.51227i) q^{41} +(7.02832 + 2.28364i) q^{43} +(2.46297 - 2.46297i) q^{44} +(-0.973857 + 1.34040i) q^{46} +(1.40824 - 0.717533i) q^{47} +(-2.86777 - 3.94715i) q^{49} +2.14494i q^{50} +(-1.91165 + 12.0697i) q^{52} +(-1.12895 + 0.178807i) q^{53} +(4.47768 + 4.47768i) q^{55} +(0.272226 + 1.71877i) q^{56} +(-0.102502 - 0.0162347i) q^{58} +(-4.16549 + 12.8200i) q^{59} +(-4.39785 + 1.42895i) q^{61} +(1.09376 - 0.355385i) q^{62} +(1.80507 - 5.55543i) q^{64} +(-21.9426 - 3.47537i) q^{65} +(1.04355 + 6.58873i) q^{67} +(4.28969 + 4.28969i) q^{68} +(-1.52494 + 0.241527i) q^{70} +(1.29298 - 8.16358i) q^{71} +8.99466i q^{73} +(-0.220718 - 0.303792i) q^{74} +(-5.68244 + 2.89535i) q^{76} +(-1.56403 + 2.15271i) q^{77} +(7.20521 - 7.20521i) q^{79} +(11.3636 + 3.69226i) q^{80} +(-1.66705 - 1.02802i) q^{82} +7.11449 q^{83} +(-7.79865 + 7.79865i) q^{85} +(-1.82870 - 1.32863i) q^{86} +(-1.94515 + 0.991103i) q^{88} +(12.9260 + 6.58613i) q^{89} -9.33529i q^{91} +(-8.35446 + 6.06987i) q^{92} +(-0.477479 + 0.0756253i) q^{94} +(-5.26374 - 10.3307i) q^{95} +(0.514313 + 3.24724i) q^{97} +(0.461156 + 1.41929i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) $ 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8	$ 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) $ 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8 + 6 * q^10 + 16 * q^11 - 14 * q^14 - 20 * q^16 - 8 * q^17 + 16 * q^19 - 20 * q^20 + 6 * q^22 - 12 * q^23 - 8 * q^25 + 28 * q^26 + 18 * q^28 - 40 * q^29 - 12 * q^31 - 16 * q^34 + 36 * q^35 - 46 * q^38 - 44 * q^40 + 4 * q^41 + 48 * q^44 + 70 * q^46 + 12 * q^47 - 30 * q^49 + 20 * q^52 + 26 * q^53 + 20 * q^55 - 106 * q^56 - 20 * q^58 - 6 * q^59 + 30 * q^61 + 10 * q^62 + 70 * q^64 - 68 * q^65 - 22 * q^67 + 20 * q^68 - 20 * q^70 - 4 * q^71 - 10 * q^74 - 128 * q^76 + 20 * q^77 - 2 * q^79 + 70 * q^80 - 90 * q^82 - 80 * q^83 - 56 * q^85 + 46 * q^86 + 10 * q^88 + 72 * q^89 - 18 * q^94 + 40 * q^95 - 22 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/369\mathbb{Z}\right)^\times$.

$n$	$83$	$334$
$\chi(n)$	$1$	$e\left(\frac{17}{20}\right)$

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 $

$2$	−0.290902	−	0.0945196i	−0.205698	−	0.0668355i	0.204356	−	0.978897i	$-0.434490\pi$
$2$	−0.290902	−	0.0945196i	−0.205698	−	0.0668355i	−0.410054	+	0.912061i	$0.634490\pi$
$3$		0			0
$3$		0			0
$4$	−1.54234	−	1.12058i	−0.771172	−	0.560289i
$5$	2.03721	−	2.80398i	0.911069	−	1.25398i	−0.0557316	−	0.998446i	$-0.517749\pi$
$5$	2.03721	−	2.80398i	0.911069	−	1.25398i	0.966800	−	0.255533i	$-0.0822509\pi$
$6$		0			0
$7$	1.29765	+	0.661185i	0.490465	+	0.249905i	0.681689	−	0.731642i	$-0.261246\pi$
$7$	1.29765	+	0.661185i	0.490465	+	0.249905i	−0.191224	+	0.981546i	$0.561246\pi$
$8$	0.702328	+	0.966671i	0.248310	+	0.341770i
$9$		0			0
$10$	−0.857659	+	0.623126i	−0.271216	+	0.197050i
$11$	−0.285814	+	1.80456i	−0.0861761	+	0.544095i	0.906395	+	0.422431i	$0.138823\pi$
$11$	−0.285814	+	1.80456i	−0.0861761	+	0.544095i	−0.992571	+	0.121664i	$0.961177\pi$
$12$		0			0
$13$	−2.91004	−	5.71127i	−0.807099	−	1.58402i	−0.811731	−	0.584031i	$-0.801475\pi$
$13$	−2.91004	−	5.71127i	−0.807099	−	1.58402i	0.00463289	−	0.999989i	$-0.498525\pi$
$14$	−0.314993	−	0.314993i	−0.0841854	−	0.0841854i
$15$		0			0
$16$	1.06531	+	3.27868i	0.266327	+	0.819670i
$17$	−3.14295	−	0.497794i	−0.762277	−	0.120733i	−0.236821	−	0.971553i	$-0.576105\pi$
$17$	−3.14295	−	0.497794i	−0.762277	−	0.120733i	−0.525456	+	0.850821i	$0.676105\pi$
$18$		0			0
$19$	1.51872	−	2.98065i	0.348417	−	0.683808i	−0.648588	−	0.761140i	$-0.724640\pi$
$19$	1.51872	−	2.98065i	0.348417	−	0.683808i	0.997005	+	0.0773320i	$0.0246401\pi$
$20$	−6.28416	+	2.04185i	−1.40518	+	0.456571i
$21$		0			0
$22$	0.253710	−	0.497934i	0.0540911	−	0.106160i
$23$	1.67386	−	5.15161i	0.349024	−	1.07419i	−0.610370	−	0.792117i	$-0.708979\pi$
$23$	1.67386	−	5.15161i	0.349024	−	1.07419i	0.959394	−	0.282069i	$-0.0910208\pi$
$24$		0			0
$25$	−2.16699	−	6.66932i	−0.433399	−	1.33386i
$26$	0.306707	+	1.93647i	0.0601502	+	0.379773i
$27$		0			0
$28$	−1.26051	−	2.47389i	−0.238214	−	0.467522i
$29$	0.335113	−	0.0530767i	0.0622289	−	0.00985609i	−0.125242	−	0.992126i	$-0.539971\pi$
$29$	0.335113	−	0.0530767i	0.0622289	−	0.00985609i	0.187471	+	0.982270i	$0.439971\pi$
$30$		0			0
$31$	−3.04183	+	2.21002i	−0.546329	+	0.396931i	−0.826430	−	0.563039i	$-0.809632\pi$
$31$	−3.04183	+	2.21002i	−0.546329	+	0.396931i	0.280101	+	0.959971i	$0.409632\pi$
$32$		−	3.44421i		−	0.608856i
$33$		0			0
$34$	0.867237	+	0.441879i	0.148730	+	0.0757817i
$35$	4.49754	−	2.29161i	0.760222	−	0.387353i
$36$		0			0
$37$	0.993200	+	0.721602i	0.163281	+	0.118631i	0.666425	−	0.745572i	$-0.267824\pi$
$37$	0.993200	+	0.721602i	0.163281	+	0.118631i	−0.503144	+	0.864202i	$0.667824\pi$
$38$	−0.723527	+	0.723527i	−0.117372	+	0.117372i
$39$		0			0
$40$	4.14132			0.654800
$41$	6.22198	+	1.51227i	0.971710	+	0.236176i
$41$	6.22198	+	1.51227i	0.971710	+	0.236176i
$42$		0			0
$43$	7.02832	+	2.28364i	1.07181	+	0.348252i	0.791192	−	0.611568i	$-0.209461\pi$
$43$	7.02832	+	2.28364i	1.07181	+	0.348252i	0.280617	+	0.959820i	$0.409461\pi$
$44$	2.46297	−	2.46297i	0.371307	−	0.371307i
$45$		0			0
$46$	−0.973857	+	1.34040i	−0.143587	+	0.197631i
$47$	1.40824	−	0.717533i	0.205413	−	0.104663i	−0.348258	−	0.937399i	$-0.613227\pi$
$47$	1.40824	−	0.717533i	0.205413	−	0.104663i	0.553671	+	0.832736i	$0.313227\pi$
$48$		0			0
$49$	−2.86777	−	3.94715i	−0.409681	−	0.563878i
$50$			2.14494i			0.303340i
$51$		0			0
$52$	−1.91165	+	12.0697i	−0.265098	+	1.67376i
$53$	−1.12895	+	0.178807i	−0.155073	+	0.0245611i	−0.233488	−	0.972360i	$-0.575014\pi$
$53$	−1.12895	+	0.178807i	−0.155073	+	0.0245611i	0.0784154	+	0.996921i	$0.475014\pi$
$54$		0			0
$55$	4.47768	+	4.47768i	0.603771	+	0.603771i
$56$	0.272226	+	1.71877i	0.0363778	+	0.229680i
$57$		0			0
$58$	−0.102502	−	0.0162347i	−0.0134591	−	0.00213172i
$59$	−4.16549	+	12.8200i	−0.542300	+	1.66903i	0.185024	+	0.982734i	$0.440764\pi$
$59$	−4.16549	+	12.8200i	−0.542300	+	1.66903i	−0.727324	+	0.686294i	$0.759236\pi$
$60$		0			0
$61$	−4.39785	+	1.42895i	−0.563087	+	0.182958i	−0.576710	−	0.816949i	$-0.695664\pi$
$61$	−4.39785	+	1.42895i	−0.563087	+	0.182958i	0.0136225	+	0.999907i	$0.495664\pi$
$62$	1.09376	−	0.355385i	0.138908	−	0.0451340i
$63$		0			0
$64$	1.80507	−	5.55543i	0.225634	−	0.694429i
$65$	−21.9426	−	3.47537i	−2.72165	−	0.431067i
$66$		0			0
$67$	1.04355	+	6.58873i	0.127490	+	0.804941i	0.965713	+	0.259613i	$0.0835950\pi$
$67$	1.04355	+	6.58873i	0.127490	+	0.804941i	−0.838223	+	0.545328i	$0.816405\pi$
$68$	4.28969	+	4.28969i	0.520201	+	0.520201i
$69$		0			0
$70$	−1.52494	+	0.241527i	−0.182265	+	0.0288680i
$71$	1.29298	−	8.16358i	0.153449	−	0.968839i	−0.784011	−	0.620746i	$-0.786830\pi$
$71$	1.29298	−	8.16358i	0.153449	−	0.968839i	0.937460	−	0.348092i	$-0.113170\pi$
$72$		0			0
$73$			8.99466i			1.05274i	0.850254	+	0.526372i	$0.176448\pi$
$73$			8.99466i			1.05274i	−0.850254	+	0.526372i	$0.823552\pi$
$74$	−0.220718	−	0.303792i	−0.0256579	−	0.0353151i
$75$		0			0
$76$	−5.68244	+	2.89535i	−0.651820	+	0.332119i
$77$	−1.56403	+	2.15271i	−0.178238	+	0.245324i
$78$		0			0
$79$	7.20521	−	7.20521i	0.810649	−	0.810649i	−0.174082	−	0.984731i	$-0.555696\pi$
$79$	7.20521	−	7.20521i	0.810649	−	0.810649i	0.984731	+	0.174082i	$0.0556958\pi$
$80$	11.3636	+	3.69226i	1.27049	+	0.412807i
$81$		0			0
$82$	−1.66705	−	1.02802i	−0.184094	−	0.113526i
$83$	7.11449			0.780916			0.390458	−	0.920621i	$-0.372317\pi$
$83$	7.11449			0.780916			0.390458	+	0.920621i	$0.372317\pi$
$84$		0			0
$85$	−7.79865	+	7.79865i	−0.845883	+	0.845883i
$86$	−1.82870	−	1.32863i	−0.197194	−	0.143270i
$87$		0			0
$88$	−1.94515	+	0.991103i	−0.207354	+	0.105652i
$89$	12.9260	+	6.58613i	1.37015	+	0.698128i	0.975355	−	0.220639i	$-0.0708144\pi$
$89$	12.9260	+	6.58613i	1.37015	+	0.698128i	0.394798	+	0.918768i	$0.370814\pi$
$90$		0			0
$91$		−	9.33529i		−	0.978604i
$92$	−8.35446	+	6.06987i	−0.871013	+	0.632828i
$93$		0			0
$94$	−0.477479	+	0.0756253i	−0.0492482	+	0.00780016i
$95$	−5.26374	−	10.3307i	−0.540048	−	1.05990i
$96$		0			0
$97$	0.514313	+	3.24724i	0.0522205	+	0.329707i	0.999944	+	0.0106137i	$0.00337850\pi$
$97$	0.514313	+	3.24724i	0.0522205	+	0.329707i	−0.947723	+	0.319094i	$0.896621\pi$
$98$	0.461156	+	1.41929i	0.0465838	+	0.143370i
$99$		0			0
$100$	−4.13125	+	12.7147i	−0.413125	+	1.27147i
$101$	−2.96889	+	5.82677i	−0.295415	+	0.579785i	−0.990237	−	0.139397i	$-0.955484\pi$
$101$	−2.96889	+	5.82677i	−0.295415	+	0.579785i	0.694821	+	0.719183i	$0.255484\pi$
$102$		0			0
$103$	15.6950	−	5.09961i	1.54647	−	0.502479i	0.593319	−	0.804967i	$-0.297817\pi$
$103$	15.6950	−	5.09961i	1.54647	−	0.502479i	0.953153	+	0.302488i	$0.0978173\pi$
$104$	3.47712	−	6.82423i	0.340959	−	0.669171i
$105$		0			0
$106$	0.345313	+	0.0546922i	0.0335397	+	0.00531217i
$107$	2.13141	+	6.55981i	0.206051	+	0.634160i	0.999669	+	0.0257432i	$0.00819521\pi$
$107$	2.13141	+	6.55981i	0.206051	+	0.634160i	−0.793617	+	0.608417i	$0.791805\pi$
$108$		0			0
$109$	0.909585	+	0.909585i	0.0871225	+	0.0871225i	0.749325	−	0.662202i	$-0.230378\pi$
$109$	0.909585	+	0.909585i	0.0871225	+	0.0871225i	−0.662202	+	0.749325i	$0.730378\pi$
$110$	−0.879336	−	1.72579i	−0.0838414	−	0.164548i
$111$		0			0
$112$	−0.785419	+	4.95894i	−0.0742151	+	0.468576i
$113$	5.72258	−	4.15770i	0.538335	−	0.391123i	−0.285131	−	0.958489i	$-0.592037\pi$
$113$	5.72258	−	4.15770i	0.538335	−	0.391123i	0.823466	+	0.567365i	$0.192037\pi$
$114$		0			0
$115$	−11.0350	−	15.1884i	−1.02902	−	1.41633i
$116$	−0.576336	−	0.293658i	−0.0535115	−	0.0272655i
$117$		0			0
$118$	2.42349	−	3.33565i	0.223101	−	0.307072i
$119$	−3.74931	−	2.72403i	−0.343699	−	0.249712i
$120$		0			0
$121$	7.28688	+	2.36765i	0.662444	+	0.215241i
$122$	1.41441			0.128054
$123$		0			0
$124$	7.16805			0.643710
$125$	−6.63390	−	2.15548i	−0.593354	−	0.192792i
$126$		0			0
$127$	4.45174	+	3.23438i	0.395028	+	0.287005i	0.767513	−	0.641034i	$-0.221494\pi$
$127$	4.45174	+	3.23438i	0.395028	+	0.287005i	−0.372485	+	0.928038i	$0.621494\pi$
$128$	−5.09910	+	7.01831i	−0.450701	+	0.620337i
$129$		0			0
$130$	6.05466	+	3.08500i	0.531029	+	0.270573i
$131$	4.78432	+	6.58506i	0.418008	+	0.575339i	0.965149	−	0.261702i	$-0.0842836\pi$
$131$	4.78432	+	6.58506i	0.418008	+	0.575339i	−0.547140	+	0.837041i	$0.684284\pi$
$132$		0			0
$133$	3.94152	−	2.86368i	0.341773	−	0.248313i
$134$	0.319193	−	2.01531i	0.0275741	−	0.174096i
$135$		0			0
$136$	−1.72618	−	3.38781i	−0.148018	−	0.290502i
$137$	−0.0757881	−	0.0757881i	−0.00647501	−	0.00647501i	0.703862	−	0.710337i	$-0.251457\pi$
$137$	−0.0757881	−	0.0757881i	−0.00647501	−	0.00647501i	−0.710337	+	0.703862i	$0.751457\pi$
$138$		0			0
$139$	4.01271	+	12.3499i	0.340354	+	1.04750i	0.964024	+	0.265814i	$0.0856408\pi$
$139$	4.01271	+	12.3499i	0.340354	+	1.04750i	−0.623670	+	0.781688i	$0.714359\pi$
$140$	−9.50468	−	1.50539i	−0.803292	−	0.127229i
$141$		0			0
$142$	−1.14775	+	2.25259i	−0.0963170	+	0.189033i
$143$	11.1380	−	3.61897i	0.931409	−	0.302633i
$144$		0			0
$145$	0.533870	−	1.04778i	0.0443355	−	0.0870133i
$146$	0.850172	−	2.61656i	0.0703607	−	0.216548i
$147$		0			0
$148$	−0.723245	−	2.22592i	−0.0594504	−	0.182969i
$149$	−0.0276020	−	0.174272i	−0.00226125	−	0.0142769i	0.986532	−	0.163569i	$-0.0523006\pi$
$149$	−0.0276020	−	0.174272i	−0.00226125	−	0.0142769i	−0.988793	+	0.149292i	$0.952301\pi$
$150$		0			0
$151$	−8.96384	−	17.5925i	−0.729467	−	1.43166i	−0.895281	−	0.445502i	$-0.853025\pi$
$151$	−8.96384	−	17.5925i	−0.729467	−	1.43166i	0.165814	−	0.986157i	$-0.446975\pi$
$152$	3.94794	−	0.625293i	0.320221	−	0.0507180i
$153$		0			0
$154$	0.658453	−	0.478394i	0.0530596	−	0.0385501i
$155$			13.0315i			1.04672i
$156$		0			0
$157$	−3.16869	−	1.61453i	−0.252889	−	0.128853i	0.322951	−	0.946416i	$-0.395325\pi$
$157$	−3.16869	−	1.61453i	−0.252889	−	0.128853i	−0.575840	+	0.817562i	$0.695325\pi$
$158$	−2.77704	+	1.41497i	−0.220929	+	0.112569i
$159$		0			0
$160$	−9.65749	−	7.01658i	−0.763492	−	0.554709i
$161$	5.57826	−	5.57826i	0.439628	−	0.439628i
$162$		0			0
$163$	−4.06263			−0.318210			−0.159105	−	0.987262i	$-0.550861\pi$
$163$	−4.06263			−0.318210			−0.159105	+	0.987262i	$0.550861\pi$
$164$	−7.90183	−	9.30465i	−0.617029	−	0.726571i
$165$		0			0
$166$	−2.06961	−	0.672459i	−0.160633	−	0.0521929i
$167$	−4.42614	+	4.42614i	−0.342505	+	0.342505i	−0.857308	−	0.514803i	$-0.827865\pi$
$167$	−4.42614	+	4.42614i	−0.342505	+	0.342505i	0.514803	+	0.857308i	$0.327865\pi$
$168$		0			0
$169$	−16.5090	+	22.7227i	−1.26993	+	1.74790i
$170$	3.00577	−	1.53151i	0.230532	−	0.117462i
$171$		0			0
$172$	−8.28109	−	11.3979i	−0.631428	−	0.869085i
$173$		−	5.09639i		−	0.387472i	−0.981054	−	0.193736i	$-0.937940\pi$
$173$		−	5.09639i		−	0.387472i	0.981054	−	0.193736i	$-0.0620605\pi$
$174$		0			0
$175$	1.59766	−	10.0872i	0.120772	−	0.762523i
$176$	−6.22105	+	0.985317i	−0.468929	+	0.0742710i
$177$		0			0
$178$	−3.13768	−	3.13768i	−0.235179	−	0.235179i
$179$	−1.40815	−	8.89068i	−0.105250	−	0.664521i	−0.982749	−	0.184943i	$-0.940790\pi$
$179$	−1.40815	−	8.89068i	−0.105250	−	0.664521i	0.877500	−	0.479578i	$-0.159210\pi$
$180$		0			0
$181$	−11.7410	−	1.85960i	−0.872704	−	0.138223i	−0.296012	−	0.955184i	$-0.595657\pi$
$181$	−11.7410	−	1.85960i	−0.872704	−	0.138223i	−0.576692	+	0.816961i	$0.695657\pi$
$182$	−0.882368	+	2.71565i	−0.0654055	+	0.201297i
$183$		0			0
$184$	6.15552	−	2.00005i	0.453791	−	0.147446i
$185$	4.04672	−	1.31486i	0.297521	−	0.0966703i
$186$		0			0
$187$	1.79660	−	5.52935i	0.131380	−	0.404346i
$188$	−2.97604	−	0.471358i	−0.217050	−	0.0343773i
$189$		0			0
$190$	0.554778	+	3.50273i	0.0402479	+	0.254115i
$191$	−12.4651	−	12.4651i	−0.901943	−	0.901943i	0.0936612	−	0.995604i	$-0.470143\pi$
$191$	−12.4651	−	12.4651i	−0.901943	−	0.901943i	−0.995604	+	0.0936612i	$0.970143\pi$
$192$		0			0
$193$	13.5277	−	2.14258i	0.973749	−	0.154227i	0.350767	−	0.936463i	$-0.385921\pi$
$193$	13.5277	−	2.14258i	0.973749	−	0.154227i	0.622982	+	0.782236i	$0.285921\pi$
$194$	0.157314	−	0.993240i	0.0112945	−	0.0713105i
$195$		0			0
$196$			9.30142i			0.664387i
$197$	−2.51439	−	3.46077i	−0.179143	−	0.246569i	0.709997	−	0.704205i	$-0.248696\pi$
$197$	−2.51439	−	3.46077i	−0.179143	−	0.246569i	−0.889140	+	0.457636i	$0.848696\pi$
$198$		0			0
$199$	3.37859	−	1.72148i	0.239502	−	0.122032i	−0.330120	−	0.943939i	$-0.607089\pi$
$199$	3.37859	−	1.72148i	0.239502	−	0.122032i	0.569623	+	0.821906i	$0.307089\pi$
$200$	4.92510	−	6.77882i	0.348257	−	0.479335i
$201$		0			0
$202$	1.41440	−	1.41440i	0.0995167	−	0.0995167i
$203$	0.469952	+	0.152697i	0.0329842	+	0.0107172i
$204$		0			0
$205$	16.9159	−	14.3655i	1.18145	−	1.00333i
$206$	−5.04771			−0.351690
$207$		0			0
$208$	15.6253	−	15.6253i	1.08342	−	1.08342i
$209$	4.94468	+	3.59252i	0.342031	+	0.248500i
$210$		0			0
$211$	1.22845	−	0.625927i	0.0845701	−	0.0430906i	−0.411194	−	0.911548i	$-0.634888\pi$
$211$	1.22845	−	0.625927i	0.0845701	−	0.0430906i	0.495764	+	0.868457i	$0.334888\pi$
$212$	1.94159	+	0.989290i	0.133349	+	0.0679447i
$213$		0			0
$214$		−	2.10972i		−	0.144217i
$215$	20.7215	−	15.0550i	1.41319	−	1.02674i
$216$		0			0
$217$	−5.40846	+	0.856616i	−0.367150	+	0.0581509i
$218$	−0.178626	−	0.350573i	−0.0120981	−	0.0237438i
$219$		0			0
$220$	−1.88853	−	11.9237i	−0.127325	−	0.803897i
$221$	6.30305	+	19.3988i	0.423989	+	1.30490i
$222$		0			0
$223$	−0.544037	+	1.67437i	−0.0364314	+	0.112124i	−0.967618	−	0.252417i	$-0.918774\pi$
$223$	−0.544037	+	1.67437i	−0.0364314	+	0.112124i	0.931187	+	0.364542i	$0.118774\pi$
$224$	2.27726	−	4.46937i	0.152156	−	0.298623i
$225$		0			0
$226$	−2.05769	+	0.668585i	−0.136876	+	0.0444736i
$227$	−0.0104794	+	0.0205670i	−0.000695544	+	0.00136508i	−0.891354	−	0.453308i	$-0.850244\pi$
$227$	−0.0104794	+	0.0205670i	−0.000695544	+	0.00136508i	0.890658	+	0.454673i	$0.150244\pi$
$228$		0			0
$229$	−23.8647	−	3.77980i	−1.57703	−	0.249776i	−0.694308	−	0.719678i	$-0.744289\pi$
$229$	−23.8647	−	3.77980i	−1.57703	−	0.249776i	−0.882719	+	0.469902i	$0.844289\pi$
$230$	1.77450	+	5.46136i	0.117007	+	0.360111i
$231$		0			0
$232$	0.286667	+	0.286667i	0.0188206	+	0.0188206i
$233$	−8.63167	−	16.9406i	−0.565480	−	1.10982i	−0.979855	−	0.199710i	$-0.936000\pi$
$233$	−8.63167	−	16.9406i	−0.565480	−	1.10982i	0.414375	−	0.910106i	$-0.364000\pi$
$234$		0			0
$235$	0.856929	−	5.41044i	0.0558999	−	0.352938i
$236$	20.7905	−	15.1052i	1.35335	−	0.983263i
$237$		0			0
$238$	0.833205	+	1.14681i	0.0540087	+	0.0743366i
$239$	−15.9440	−	8.12387i	−1.03133	−	0.525490i	−0.145433	−	0.989368i	$-0.546457\pi$
$239$	−15.9440	−	8.12387i	−1.03133	−	0.525490i	−0.885899	+	0.463878i	$0.846457\pi$
$240$		0			0
$241$	−3.38611	+	4.66058i	−0.218118	+	0.300214i	−0.904029	−	0.427472i	$-0.859404\pi$
$241$	−3.38611	+	4.66058i	−0.218118	+	0.300214i	0.685910	+	0.727686i	$0.259404\pi$
$242$	−1.89598	−	1.37751i	−0.121878	−	0.0885495i
$243$		0			0
$244$	8.38425	+	2.72421i	0.536747	+	0.174400i
$245$	−16.9100			−1.08034
$246$		0			0
$247$	−21.4428			−1.36437
$248$	−4.27273	−	1.38829i	−0.271318	−	0.0881567i
$249$		0			0
$250$	1.72608	+	1.25407i	0.109167	+	0.0793142i
$251$	−14.5918	+	20.0839i	−0.921025	+	1.26768i	0.0422335	+	0.999108i	$0.486553\pi$
$251$	−14.5918	+	20.0839i	−0.921025	+	1.26768i	−0.963259	+	0.268575i	$0.913447\pi$
$252$		0			0
$253$	8.81797	+	4.49298i	0.554381	+	0.282471i
$254$	−0.989306	−	1.36166i	−0.0620746	−	0.0854383i
$255$		0			0
$256$	−7.30476	+	5.30722i	−0.456548	+	0.331701i
$257$	−1.77211	+	11.1887i	−0.110541	+	0.697931i	0.868716	+	0.495311i	$0.164946\pi$
$257$	−1.77211	+	11.1887i	−0.110541	+	0.697931i	−0.979257	+	0.202620i	$0.935054\pi$
$258$		0			0
$259$	0.811713	+	1.59308i	0.0504374	+	0.0989889i
$260$	29.9487	+	29.9487i	1.85734	+	1.85734i
$261$		0			0
$262$	−0.769350	−	2.36782i	−0.0475306	−	0.146284i
$263$	5.50072	+	0.871229i	0.339189	+	0.0537223i	0.323706	−	0.946158i	$-0.395071\pi$
$263$	5.50072	+	0.871229i	0.339189	+	0.0537223i	0.0154834	+	0.999880i	$0.495071\pi$
$264$		0			0
$265$	−1.79853	+	3.52981i	−0.110483	+	0.216835i
$266$	−1.41727	+	0.460499i	−0.0868983	+	0.0282350i
$267$		0			0
$268$	5.77367	−	11.3315i	0.352683	−	0.692180i
$269$	−2.20004	+	6.77102i	−0.134139	+	0.412836i	−0.995455	−	0.0952327i	$-0.969640\pi$
$269$	−2.20004	+	6.77102i	−0.134139	+	0.412836i	0.861316	+	0.508069i	$0.169640\pi$
$270$		0			0
$271$	4.59561	+	14.1438i	0.279164	+	0.859177i	0.988088	+	0.153892i	$0.0491809\pi$
$271$	4.59561	+	14.1438i	0.279164	+	0.859177i	−0.708924	+	0.705285i	$0.750819\pi$
$272$	−1.71610	−	10.8350i	−0.104054	−	0.656970i
$273$		0			0
$274$	0.0148834	+	0.0292103i	0.000899140	+	0.00176466i
$275$	12.6545	−	2.00428i	0.763097	−	0.120863i
$276$		0			0
$277$	−6.93372	+	5.03764i	−0.416607	+	0.302683i	−0.776271	−	0.630399i	$-0.782891\pi$
$277$	−6.93372	+	5.03764i	−0.416607	+	0.302683i	0.359664	+	0.933082i	$0.382891\pi$
$278$		−	3.97188i		−	0.238217i
$279$		0			0
$280$	5.37398	+	2.73818i	0.321157	+	0.163637i
$281$	−10.9370	+	5.57269i	−0.652448	+	0.332439i	−0.748691	−	0.662919i	$-0.769317\pi$
$281$	−10.9370	+	5.57269i	−0.652448	+	0.332439i	0.0962434	+	0.995358i	$0.469317\pi$
$282$		0			0
$283$	17.0898	+	12.4165i	1.01588	+	0.738083i	0.965435	−	0.260644i	$-0.0839347\pi$
$283$	17.0898	+	12.4165i	1.01588	+	0.738083i	0.0504491	+	0.998727i	$0.483935\pi$
$284$	−11.1422	+	11.1422i	−0.661166	+	0.661166i
$285$		0			0
$286$	−3.58214			−0.211816
$287$	7.07406	+	6.07627i	0.417569	+	0.358671i
$288$		0			0
$289$	−6.53764	−	2.12421i	−0.384567	−	0.124953i
$290$	−0.254339	+	0.254339i	−0.0149353	+	0.0149353i
$291$		0			0
$292$	10.0792	−	13.8729i	0.589842	−	0.811848i
$293$	23.6770	−	12.0640i	1.38323	−	0.704789i	0.405387	−	0.914145i	$-0.367137\pi$
$293$	23.6770	−	12.0640i	1.38323	−	0.704789i	0.977839	+	0.209356i	$0.0671367\pi$
$294$		0			0
$295$	27.4612	+	37.7971i	1.59885	+	2.20063i
$296$			1.46690i			0.0852618i
$297$		0			0
$298$	−0.00844269	+	0.0533050i	−0.000489072	+	0.00308788i
$299$	−34.2932	+	5.43151i	−1.98323	+	0.314113i
$300$		0			0
$301$	7.61039	+	7.61039i	0.438655	+	0.438655i
$302$	0.944756	+	5.96495i	0.0543646	+	0.343244i
$303$		0			0
$304$	11.3905	+	1.80408i	0.653289	+	0.103471i
$305$	−4.95261	+	15.2426i	−0.283586	+	0.872787i
$306$		0			0
$307$	6.65182	−	2.16131i	0.379639	−	0.123352i	−0.112980	−	0.993597i	$-0.536040\pi$
$307$	6.65182	−	2.16131i	0.379639	−	0.123352i	0.492619	+	0.870245i	$0.336040\pi$
$308$	4.82455	−	1.56759i	0.274905	−	0.0893219i
$309$		0			0
$310$	1.23173	−	3.79089i	0.0699578	−	0.215308i
$311$	3.25192	+	0.515053i	0.184399	+	0.0292060i	0.247951	−	0.968773i	$-0.420243\pi$
$311$	3.25192	+	0.515053i	0.184399	+	0.0292060i	−0.0635517	+	0.997979i	$0.520243\pi$
$312$		0			0
$313$	−1.77802	−	11.2260i	−0.100499	−	0.634528i	−0.985595	−	0.169120i	$-0.945907\pi$
$313$	−1.77802	−	11.2260i	−0.100499	−	0.634528i	0.885096	−	0.465408i	$-0.154093\pi$
$314$	0.769173	+	0.769173i	0.0434069	+	0.0434069i
$315$		0			0
$316$	−19.1869	+	3.03891i	−1.07935	+	0.170952i
$317$	−4.29092	+	27.0918i	−0.241002	+	1.52163i	0.509334	+	0.860569i	$0.329892\pi$
$317$	−4.29092	+	27.0918i	−0.241002	+	1.52163i	−0.750336	+	0.661057i	$0.770108\pi$
$318$		0			0
$319$			0.619901i			0.0347078i
$320$	−11.9000	−	16.3790i	−0.665231	−	0.915612i
$321$		0			0
$322$	−2.14998	+	1.09547i	−0.119814	+	0.0610481i
$323$	−6.25700	+	8.61202i	−0.348149	+	0.479185i
$324$		0			0
$325$	−31.7843	+	31.7843i	−1.76307	+	1.76307i
$326$	1.18183	+	0.383998i	0.0654552	+	0.0212677i
$327$		0			0
$328$	2.90801	+	7.07672i	0.160568	+	0.390746i
$329$	2.30182			0.126903
$330$		0			0
$331$	−10.6130	+	10.6130i	−0.583344	+	0.583344i	−0.935821	−	0.352477i	$-0.885340\pi$
$331$	−10.6130	+	10.6130i	−0.583344	+	0.583344i	0.352477	+	0.935821i	$0.385340\pi$
$332$	−10.9730	−	7.97234i	−0.602221	−	0.437539i
$333$		0			0
$334$	1.70593	−	0.869213i	0.0933442	−	0.0475612i
$335$	20.6006	+	10.4965i	1.12553	+	0.573487i
$336$		0			0
$337$		−	11.4038i		−	0.621207i	−0.950540	−	0.310603i	$-0.899469\pi$
$337$		−	11.4038i		−	0.621207i	0.950540	−	0.310603i	$-0.100531\pi$
$338$	6.95025	−	5.04965i	0.378044	−	0.274665i
$339$		0			0
$340$	20.7672	−	3.28920i	1.12626	−	0.178382i
$341$	−3.11871	−	6.12082i	−0.168888	−	0.331461i
$342$		0			0
$343$	−2.70637	−	17.0873i	−0.146130	−	0.922629i
$344$	2.72866	+	8.39794i	0.147119	+	0.452787i
$345$		0			0
$346$	−0.481709	+	1.48255i	−0.0258968	+	0.0797023i
$347$	15.1544	−	29.7422i	0.813531	−	1.59665i	0.0110717	−	0.999939i	$-0.496476\pi$
$347$	15.1544	−	29.7422i	0.813531	−	1.59665i	0.802460	−	0.596706i	$-0.203524\pi$
$348$		0			0
$349$	−4.88104	+	1.58595i	−0.261276	+	0.0848938i	−0.436726	−	0.899595i	$-0.643862\pi$
$349$	−4.88104	+	1.58595i	−0.261276	+	0.0848938i	0.175450	+	0.984488i	$0.443862\pi$
$350$	−1.41820	+	2.78338i	−0.0758061	+	0.148778i
$351$		0			0
$352$	6.21527	+	0.984402i	0.331275	+	0.0524688i
$353$	−7.91928	−	24.3730i	−0.421501	−	1.29725i	−0.906305	−	0.422624i	$-0.861109\pi$
$353$	−7.91928	−	24.3730i	−0.421501	−	1.29725i	0.484804	−	0.874623i	$-0.338891\pi$
$354$		0			0
$355$	−20.2564	−	20.2564i	−1.07510	−	1.07510i
$356$	−12.5561	−	24.6427i	−0.665471	−	1.30606i
$357$		0			0
$358$	−0.430712	+	2.71941i	−0.0227638	+	0.143725i
$359$	1.10482	−	0.802698i	0.0583101	−	0.0423648i	−0.558248	−	0.829674i	$-0.688526\pi$
$359$	1.10482	−	0.802698i	0.0583101	−	0.0423648i	0.616559	+	0.787309i	$0.288526\pi$
$360$		0			0
$361$	4.59015	+	6.31780i	0.241587	+	0.332516i
$362$	3.23972	+	1.65072i	0.170276	+	0.0867598i
$363$		0			0
$364$	−10.4609	+	14.3982i	−0.548302	+	0.754672i
$365$	25.2208	+	18.3240i	1.32012	+	0.959123i
$366$		0			0
$367$	8.38455	+	2.72431i	0.437670	+	0.142208i	0.519560	−	0.854434i	$-0.326096\pi$
$367$	8.38455	+	2.72431i	0.437670	+	0.142208i	−0.0818904	+	0.996641i	$0.526096\pi$
$368$	18.6737			0.973432
$369$		0			0
$370$	−1.30148			−0.0676606
$371$	−1.58320	−	0.514413i	−0.0821956	−	0.0267070i
$372$		0			0
$373$	−13.1261	−	9.53664i	−0.679641	−	0.493788i	0.193597	−	0.981081i	$-0.437984\pi$
$373$	−13.1261	−	9.53664i	−0.679641	−	0.493788i	−0.873239	+	0.487293i	$0.837984\pi$
$374$	−1.04527	+	1.43868i	−0.0540494	+	0.0743926i
$375$		0			0
$376$	1.68266	+	0.857359i	0.0867767	+	0.0442149i
$377$	−1.27833	−	1.75946i	−0.0658371	−	0.0906170i
$378$		0			0
$379$	−9.20110	+	6.68499i	−0.472629	+	0.343385i	−0.798465	−	0.602041i	$-0.794354\pi$
$379$	−9.20110	+	6.68499i	−0.472629	+	0.343385i	0.325836	+	0.945426i	$0.394354\pi$
$380$	−3.45783	+	21.8319i	−0.177383	+	1.11995i
$381$		0			0
$382$	2.44792	+	4.80431i	0.125246	+	0.245810i
$383$	−3.21049	−	3.21049i	−0.164048	−	0.164048i	0.620309	−	0.784357i	$-0.287007\pi$
$383$	−3.21049	−	3.21049i	−0.164048	−	0.164048i	−0.784357	+	0.620309i	$0.787007\pi$
$384$		0			0
$385$	2.84988	+	8.77104i	0.145243	+	0.447014i
$386$	−4.13776	−	0.655357i	−0.210606	−	0.0333568i
$387$		0			0
$388$	2.84554	−	5.58469i	0.144461	−	0.283520i
$389$	24.2065	−	7.86516i	1.22732	−	0.398780i	0.377576	−	0.925979i	$-0.376758\pi$
$389$	24.2065	−	7.86516i	1.22732	−	0.398780i	0.849742	+	0.527199i	$0.176758\pi$
$390$		0			0
$391$	−7.82530	+	15.3580i	−0.395742	+	0.776688i
$392$	1.80148	−	5.54438i	0.0909884	−	0.280033i
$393$		0			0
$394$	0.404331	+	1.24440i	0.0203699	+	0.0626920i
$395$	−5.52473	−	34.8818i	−0.277980	−	1.75509i
$396$		0			0
$397$	10.4510	+	20.5112i	0.524519	+	1.02943i	0.989558	+	0.144136i	$0.0460402\pi$
$397$	10.4510	+	20.5112i	0.524519	+	1.02943i	−0.465039	+	0.885290i	$0.653960\pi$
$398$	−1.14555	+	0.181438i	−0.0574213	+	0.00909464i
$399$		0			0
$400$	19.5581	−	14.2098i	0.977903	−	0.710488i
$401$			21.8245i			1.08986i	0.838481	+	0.544931i	$0.183444\pi$
$401$			21.8245i			1.08986i	−0.838481	+	0.544931i	$0.816556\pi$
$402$		0			0
$403$	21.4739	+	10.9415i	1.06969	+	0.545034i
$404$	11.1084	−	5.66001i	0.552664	−	0.281596i
$405$		0			0
$406$	−0.122277	−	0.0888395i	−0.00606851	−	0.00440903i
$407$	−1.58604	+	1.58604i	−0.0786173	+	0.0786173i
$408$		0			0
$409$	−3.45570			−0.170874			−0.0854368	−	0.996344i	$-0.527229\pi$
$409$	−3.45570			−0.170874			−0.0854368	+	0.996344i	$0.527229\pi$
$410$	−6.27867	+	2.58007i	−0.310082	+	0.127421i
$411$		0			0
$412$	−29.9216	−	9.72211i	−1.47413	−	0.478974i
$413$	−13.8818	+	13.8818i	−0.683077	+	0.683077i
$414$		0			0
$415$	14.4937	−	19.9489i	0.711468	−	0.979252i
$416$	−19.6708	+	10.0228i	−0.964440	+	0.491407i
$417$		0			0
$418$	−1.09885	−	1.51244i	−0.0537466	−	0.0739759i
$419$			18.7536i			0.916172i	0.888908	+	0.458086i	$0.151465\pi$
$419$			18.7536i			0.916172i	−0.888908	+	0.458086i	$0.848535\pi$
$420$		0			0
$421$	−0.976054	+	6.16256i	−0.0475699	+	0.300345i	−0.999990	−	0.00444331i	$-0.998586\pi$
$421$	−0.976054	+	6.16256i	−0.0475699	+	0.300345i	0.952420	+	0.304788i	$0.0985856\pi$
$422$	−0.416521	+	0.0659704i	−0.0202759	+	0.00321139i
$423$		0			0
$424$	−0.965738	−	0.965738i	−0.0469004	−	0.0469004i
$425$	3.49080	+	22.0401i	0.169329	+	1.06910i
$426$		0			0
$427$	−6.65167	−	1.05352i	−0.321897	−	0.0509834i
$428$	4.06341	−	12.5059i	0.196412	−	0.604495i
$429$		0			0
$430$	−7.45090	+	2.42094i	−0.359314	+	0.116748i
$431$	−6.05658	+	1.96790i	−0.291735	+	0.0947906i	−0.451228	−	0.892408i	$-0.649014\pi$
$431$	−6.05658	+	1.96790i	−0.291735	+	0.0947906i	0.159493	+	0.987199i	$0.449014\pi$
$432$		0			0
$433$	−0.625179	+	1.92410i	−0.0300442	+	0.0924664i	−0.964954	−	0.262418i	$-0.915480\pi$
$433$	−0.625179	+	1.92410i	−0.0300442	+	0.0924664i	0.934910	+	0.354885i	$0.115480\pi$
$434$	1.65430	+	0.262015i	0.0794088	+	0.0125771i
$435$		0			0
$436$	−0.383632	−	2.42216i	−0.0183726	−	0.116000i
$437$	−12.8130	−	12.8130i	−0.612931	−	0.612931i
$438$		0			0
$439$	21.7512	−	3.44505i	1.03813	−	0.164423i	0.385974	−	0.922510i	$-0.373865\pi$
$439$	21.7512	−	3.44505i	1.03813	−	0.164423i	0.652154	+	0.758086i	$0.273865\pi$
$440$	−1.18365	+	7.47325i	−0.0564281	+	0.356273i
$441$		0			0
$442$		−	6.23891i		−	0.296754i
$443$	9.35155	+	12.8713i	0.444305	+	0.611534i	0.971162	−	0.238420i	$-0.0766296\pi$
$443$	9.35155	+	12.8713i	0.444305	+	0.611534i	−0.526857	+	0.849954i	$0.676630\pi$
$444$		0			0
$445$	44.8004	−	22.8269i	2.12374	−	1.08210i
$446$	0.316523	−	0.435656i	0.0149878	−	0.0206289i
$447$		0			0
$448$	6.01552	−	6.01552i	0.284206	−	0.284206i
$449$	−21.4180	−	6.95914i	−1.01078	−	0.328422i	−0.243615	−	0.969872i	$-0.578333\pi$
$449$	−21.4180	−	6.95914i	−1.01078	−	0.328422i	−0.767165	+	0.641450i	$0.778333\pi$
$450$		0			0
$451$	−4.50730	+	10.7957i	−0.212240	+	0.508350i
$452$	−13.4852			−0.634291
$453$		0			0
$454$	0.00499247	−	0.00499247i	0.000234308	−	0.000234308i
$455$	−26.1760	−	19.0180i	−1.22715	−	0.891576i
$456$		0			0
$457$	3.27733	−	1.66988i	0.153307	−	0.0781138i	−0.375654	−	0.926760i	$-0.622582\pi$
$457$	3.27733	−	1.66988i	0.153307	−	0.0781138i	0.528961	+	0.848646i	$0.322582\pi$
$458$	6.58502	+	3.35524i	0.307698	+	0.156780i
$459$		0			0
$460$			35.7914i			1.66878i
$461$	3.11530	−	2.26340i	0.145094	−	0.105417i	−0.512870	−	0.858466i	$-0.671418\pi$
$461$	3.11530	−	2.26340i	0.145094	−	0.105417i	0.657964	+	0.753049i	$0.271418\pi$
$462$		0			0
$463$	−31.3684	+	4.96826i	−1.45781	+	0.230895i	−0.834469	−	0.551054i	$-0.814226\pi$
$463$	−31.3684	+	4.96826i	−1.45781	+	0.230895i	−0.623342	+	0.781949i	$0.714226\pi$
$464$	0.531020	+	1.04218i	0.0246520	+	0.0483822i
$465$		0			0
$466$	0.909746	+	5.74391i	0.0421432	+	0.266082i
$467$	−9.68505	−	29.8075i	−0.448171	−	1.37933i	−0.878969	−	0.476879i	$-0.841768\pi$
$467$	−9.68505	−	29.8075i	−0.448171	−	1.37933i	0.430798	−	0.902448i	$-0.358232\pi$
$468$		0			0
$469$	−3.00221	+	9.23984i	−0.138629	+	0.426656i
$470$	−0.760675	+	1.49291i	−0.0350873	+	0.0688627i
$471$		0			0
$472$	−15.3183	+	4.97722i	−0.705082	+	0.229095i
$473$	−6.12975	+	12.0303i	−0.281846	+	0.553155i
$474$		0			0
$475$	−23.1700	−	3.66976i	−1.06311	−	0.168380i
$476$	2.73023	+	8.40279i	0.125140	+	0.385141i
$477$		0			0
$478$	3.87027	+	3.87027i	0.177022	+	0.177022i
$479$	18.7953	+	36.8879i	0.858780	+	1.68545i	0.718711	+	0.695309i	$0.244732\pi$
$479$	18.7953	+	36.8879i	0.858780	+	1.68545i	0.140069	+	0.990142i	$0.455268\pi$
$480$		0			0
$481$	1.23101	−	7.77232i	0.0561294	−	0.354387i
$482$	1.42554	−	1.03572i	0.0649316	−	0.0471756i
$483$		0			0
$484$	−8.58574	−	11.8173i	−0.390261	−	0.537148i
$485$	10.1530	+	5.17320i	0.461023	+	0.234903i
$486$		0			0
$487$	19.1905	−	26.4134i	0.869602	−	1.19691i	−0.109591	−	0.993977i	$-0.534954\pi$
$487$	19.1905	−	26.4134i	0.869602	−	1.19691i	0.979194	−	0.202928i	$-0.0650458\pi$
$488$	−4.47006	−	3.24769i	−0.202350	−	0.147016i
$489$		0			0
$490$	4.91914	+	1.59833i	0.222224	+	0.0722050i
$491$	40.3633			1.82157			0.910786	−	0.412880i	$-0.135477\pi$
$491$	40.3633			1.82157			0.910786	+	0.412880i	$0.135477\pi$
$492$		0			0
$493$	−1.07966			−0.0486256
$494$	6.23774	+	2.02677i	0.280649	+	0.0911885i
$495$		0			0
$496$	−10.4864	−	7.61884i	−0.470855	−	0.342096i
$497$	7.07548	−	9.73856i	0.317379	−	0.436834i
$498$		0			0
$499$	−9.86612	−	5.02704i	−0.441668	−	0.225041i	0.218992	−	0.975727i	$-0.429723\pi$
$499$	−9.86612	−	5.02704i	−0.441668	−	0.225041i	−0.660660	+	0.750686i	$0.729723\pi$
$500$	7.81637	+	10.7583i	0.349559	+	0.481126i
$501$		0			0
$502$	6.14309	−	4.46322i	0.274180	−	0.199203i
$503$	−5.39469	+	34.0608i	−0.240538	+	1.51869i	0.511333	+	0.859383i	$0.329152\pi$
$503$	−5.39469	+	34.0608i	−0.240538	+	1.51869i	−0.751870	+	0.659311i	$0.770848\pi$
$504$		0			0
$505$	10.2899	+	20.1951i	0.457895	+	0.898669i
$506$	−2.14049	−	2.14049i	−0.0951562	−	0.0951562i
$507$		0			0
$508$	−3.24174	−	9.97706i	−0.143829	−	0.442660i
$509$	−20.1967	−	3.19884i	−0.895202	−	0.141786i	−0.308152	−	0.951337i	$-0.599711\pi$
$509$	−20.1967	−	3.19884i	−0.895202	−	0.141786i	−0.587050	+	0.809551i	$0.699711\pi$
$510$		0			0
$511$	−5.94713	+	11.6719i	−0.263086	+	0.516335i
$512$	19.1276	−	6.21495i	0.845331	−	0.274665i
$513$		0			0
$514$	1.57306	−	3.08731i	0.0693847	−	0.136175i
$515$	17.6748	−	54.3974i	0.778844	−	2.39704i
$516$		0			0
$517$	0.892336	+	2.74633i	0.0392449	+	0.120783i
$518$	−0.0855515	−	0.540151i	−0.00375892	−	0.0237329i
$519$		0			0
$520$	−12.0514	−	23.6522i	−0.528488	−	1.03722i
$521$	−27.5874	+	4.36942i	−1.20863	+	0.191428i	−0.728050	−	0.685525i	$-0.759573\pi$
$521$	−27.5874	+	4.36942i	−1.20863	+	0.191428i	−0.480577	+	0.876952i	$0.659573\pi$
$522$		0			0
$523$	29.2671	−	21.2638i	1.27976	−	0.929800i	0.280214	−	0.959937i	$-0.409594\pi$
$523$	29.2671	−	21.2638i	1.27976	−	0.929800i	0.999546	+	0.0301373i	$0.00959445\pi$
$524$		−	15.5176i		−	0.677891i
$525$		0			0
$526$	−1.51782	−	0.773368i	−0.0661801	−	0.0337204i
$527$	10.6605	−	5.43177i	0.464377	−	0.236612i
$528$		0			0
$529$	−5.12993	−	3.72711i	−0.223040	−	0.162048i
$530$	0.856831	−	0.856831i	0.0372184	−	0.0372184i
$531$		0			0
$532$	−9.28817			−0.402693
$533$	−9.46924	−	39.9361i	−0.410158	−	1.72983i
$534$		0			0
$535$	22.7357	+	7.38728i	0.982950	+	0.319380i
$536$	−5.63622	+	5.63622i	−0.243448	+	0.243448i
$537$		0			0
$538$	1.27999	−	1.76175i	0.0551842	−	0.0759546i
$539$	7.94250	−	4.04691i	0.342108	−	0.174313i
$540$		0			0
$541$	−20.5933	−	28.3442i	−0.885374	−	1.21861i	−0.974903	−	0.222628i	$-0.928536\pi$
$541$	−20.5933	−	28.3442i	−0.885374	−	1.21861i	0.0895294	−	0.995984i	$-0.471464\pi$
$542$		−	4.54884i		−	0.195389i
$543$		0			0
$544$	−1.71451	+	10.8250i	−0.0735088	+	0.464116i
$545$	4.40348	−	0.697442i	0.188624	−	0.0298751i
$546$		0			0
$547$	−9.29596	−	9.29596i	−0.397467	−	0.397467i	0.479872	−	0.877339i	$-0.340683\pi$
$547$	−9.29596	−	9.29596i	−0.397467	−	0.397467i	−0.877339	+	0.479872i	$0.840683\pi$
$548$	0.0319648	+	0.201818i	0.00136547	+	0.00862123i
$549$		0			0
$550$	−3.87067	−	0.613054i	−0.165046	−	0.0261407i
$551$	0.350739	−	1.07946i	0.0149420	−	0.0459866i
$552$		0			0
$553$	14.1138	−	4.58585i	0.600180	−	0.195010i
$554$	2.49319	−	0.810085i	0.105925	−	0.0344172i
$555$		0			0
$556$	7.65001	−	23.5443i	0.324433	−	0.998501i
$557$	−28.1382	−	4.45665i	−1.19225	−	0.188834i	−0.471399	−	0.881920i	$-0.656251\pi$
$557$	−28.1382	−	4.45665i	−1.19225	−	0.188834i	−0.720855	+	0.693086i	$0.756251\pi$
$558$		0			0
$559$	−7.41019	−	46.7861i	−0.313418	−	1.97884i
$560$	12.3047	+	12.3047i	0.519969	+	0.519969i
$561$		0			0
$562$	3.70832	−	0.587341i	0.156426	−	0.0247755i
$563$	−2.11661	+	13.3638i	−0.0892046	+	0.563216i	0.902089	+	0.431549i	$0.142033\pi$
$563$	−2.11661	+	13.3638i	−0.0892046	+	0.563216i	−0.991294	+	0.131667i	$0.957967\pi$
$564$		0			0
$565$		−	24.5161i		−	1.03140i
$566$	−3.79785	−	5.22730i	−0.159636	−	0.219720i
$567$		0			0
$568$	8.79959	−	4.48362i	0.369223	−	0.188128i
$569$	26.6643	−	36.7002i	1.11782	−	1.53855i	0.308467	−	0.951235i	$-0.400184\pi$
$569$	26.6643	−	36.7002i	1.11782	−	1.53855i	0.809357	−	0.587317i	$-0.199816\pi$
$570$		0			0
$571$	−1.62367	+	1.62367i	−0.0679486	+	0.0679486i	−0.740264	−	0.672316i	$-0.765300\pi$
$571$	−1.62367	+	1.62367i	−0.0679486	+	0.0679486i	0.672316	+	0.740264i	$0.265300\pi$
$572$	−21.2340	−	6.89935i	−0.887839	−	0.288476i
$573$		0			0
$574$	−1.48353	−	2.43623i	−0.0619213	−	0.101686i
$575$	−37.9850			−1.58409
$576$		0			0
$577$	−4.24210	+	4.24210i	−0.176601	+	0.176601i	−0.789872	−	0.613271i	$-0.789853\pi$
$577$	−4.24210	+	4.24210i	−0.176601	+	0.176601i	0.613271	+	0.789872i	$0.289853\pi$
$578$	1.70103	+	1.23587i	0.0707535	+	0.0514054i
$579$		0			0
$580$	−1.99753	+	1.01779i	−0.0829429	+	0.0422615i
$581$	9.23210	+	4.70399i	0.383012	+	0.195154i
$582$		0			0
$583$		−	2.08835i		−	0.0864908i
$584$	−8.69487	+	6.31720i	−0.359796	+	0.261407i
$585$		0			0
$586$	−8.02797	+	1.27151i	−0.331632	+	0.0525254i
$587$	16.5667	+	32.5140i	0.683780	+	1.34199i	0.928111	+	0.372303i	$0.121432\pi$
$587$	16.5667	+	32.5140i	0.683780	+	1.34199i	−0.244331	+	0.969692i	$0.578568\pi$
$588$		0			0
$589$	1.96761	+	12.4230i	0.0810741	+	0.511882i
$590$	−4.41594	−	13.5909i	−0.181801	−	0.559527i
$591$		0			0
$592$	−1.30784	+	4.02511i	−0.0537518	+	0.165431i
$593$	0.226552	−	0.444634i	0.00930339	−	0.0182589i	−0.886308	−	0.463096i	$-0.846738\pi$
$593$	0.226552	−	0.444634i	0.00930339	−	0.0182589i	0.895611	+	0.444837i	$0.146738\pi$
$594$		0			0
$595$	−15.2763	+	4.96356i	−0.626266	+	0.203486i
$596$	−0.152714	+	0.299718i	−0.00625541	+	0.0122769i
$597$		0			0
$598$	10.4893	+	1.66135i	0.428941	+	0.0679376i
$599$	7.58173	+	23.3342i	0.309781	+	0.953409i	0.977850	+	0.209309i	$0.0671214\pi$
$599$	7.58173	+	23.3342i	0.309781	+	0.953409i	−0.668068	+	0.744100i	$0.732879\pi$
$600$		0			0
$601$	5.35213	+	5.35213i	0.218318	+	0.218318i	0.807789	−	0.589471i	$-0.200664\pi$
$601$	5.35213	+	5.35213i	0.218318	+	0.218318i	−0.589471	+	0.807789i	$0.700664\pi$
$602$	−1.49454	−	2.93320i	−0.0609130	−	0.119548i
$603$		0			0
$604$	−5.88848	+	37.1784i	−0.239599	+	1.51277i
$605$	21.4838	−	15.6089i	0.873440	−	0.634591i
$606$		0			0
$607$	21.2236	+	29.2118i	0.861440	+	1.18567i	0.981224	+	0.192870i	$0.0617796\pi$
$607$	21.2236	+	29.2118i	0.861440	+	1.18567i	−0.119785	+	0.992800i	$0.538220\pi$
$608$	−10.2660	−	5.23077i	−0.416340	−	0.212136i
$609$		0			0
$610$	2.88144	−	3.96597i	0.116666	−	0.160577i
$611$	−8.19604	−	5.95477i	−0.331576	−	0.240904i
$612$		0			0
$613$	−30.2951	−	9.84349i	−1.22361	−	0.397575i	−0.375214	−	0.926938i	$-0.622431\pi$
$613$	−30.2951	−	9.84349i	−1.22361	−	0.397575i	−0.848395	+	0.529364i	$0.822431\pi$
$614$	−2.13931			−0.0863355
$615$		0			0
$616$	−3.17942			−0.128103
$617$	−18.2794	−	5.93935i	−0.735903	−	0.239109i	−0.0829983	−	0.996550i	$-0.526450\pi$
$617$	−18.2794	−	5.93935i	−0.735903	−	0.239109i	−0.652904	+	0.757440i	$0.726450\pi$
$618$		0			0
$619$	−31.0258	−	22.5415i	−1.24703	−	0.906021i	−0.248985	−	0.968507i	$-0.580097\pi$
$619$	−31.0258	−	22.5415i	−1.24703	−	0.906021i	−0.998046	+	0.0624862i	$0.980097\pi$
$620$	14.6028	−	20.0991i	0.586464	−	0.807199i
$621$		0			0
$622$	−0.897305	−	0.457200i	−0.0359787	−	0.0183320i
$623$	12.4188	+	17.0930i	0.497547	+	0.684815i
$624$		0			0
$625$	8.80773	−	6.39919i	0.352309	−	0.255968i
$626$	−0.543845	+	3.43370i	−0.0217364	+	0.137238i
$627$		0			0
$628$	3.07801	+	6.04093i	0.122826	+	0.241059i
$629$	−2.76237	−	2.76237i	−0.110143	−	0.110143i
$630$		0			0
$631$	−11.7225	−	36.0782i	−0.466666	−	1.43625i	−0.856875	−	0.515525i	$-0.827597\pi$
$631$	−11.7225	−	36.0782i	−0.466666	−	1.43625i	0.390208	−	0.920727i	$-0.372403\pi$
$632$	12.0255	+	1.90465i	0.478348	+	0.0757629i
$633$		0			0
$634$	3.80894	−	7.47546i	0.151272	−	0.296889i
$635$	18.1383	−	5.89349i	0.719796	−	0.233876i
$636$		0			0
$637$	−14.1979	+	27.8649i	−0.562541	+	1.10405i
$638$	0.0585928	−	0.180330i	0.00231971	−	0.00713934i
$639$		0			0
$640$	9.29127	+	28.5956i	0.367270	+	1.13034i
$641$	−4.45397	−	28.1213i	−0.175921	−	1.11072i	−0.904723	−	0.426000i	$-0.859923\pi$
$641$	−4.45397	−	28.1213i	−0.175921	−	1.11072i	0.728802	−	0.684725i	$-0.240077\pi$
$642$		0			0
$643$	14.8198	+	29.0856i	0.584437	+	1.14702i	0.974111	+	0.226070i	$0.0725878\pi$
$643$	14.8198	+	29.0856i	0.584437	+	1.14702i	−0.389674	+	0.920953i	$0.627412\pi$
$644$	−14.8545	+	2.35272i	−0.585348	+	0.0927100i
$645$		0			0
$646$	2.63417	−	1.91384i	0.103640	−	0.0752990i
$647$			35.7053i			1.40372i	0.712315	+	0.701860i	$0.247647\pi$
$647$			35.7053i			1.40372i	−0.712315	+	0.701860i	$0.752353\pi$
$648$		0			0
$649$	−21.9440	−	11.1810i	−0.861376	−	0.438893i
$650$	12.2503	−	6.24185i	0.480497	−	0.244826i
$651$		0			0
$652$	6.26597	+	4.55250i	0.245394	+	0.178290i
$653$	−13.7761	+	13.7761i	−0.539102	+	0.539102i	−0.923265	−	0.384163i	$-0.874490\pi$
$653$	−13.7761	+	13.7761i	−0.539102	+	0.539102i	0.384163	+	0.923265i	$0.374490\pi$
$654$		0			0
$655$	28.2111			1.10230
$656$	1.67009	+	22.0109i	0.0652061	+	0.859382i
$657$		0			0
$658$	−0.669603	−	0.217567i	−0.0261038	−	0.00848165i
$659$	−10.7415	+	10.7415i	−0.418431	+	0.418431i	−0.884663	−	0.466231i	$-0.845611\pi$
$659$	−10.7415	+	10.7415i	−0.418431	+	0.418431i	0.466231	+	0.884663i	$0.345611\pi$
$660$		0			0
$661$	−6.05918	+	8.33975i	−0.235675	+	0.324379i	−0.910430	−	0.413663i	$-0.864249\pi$
$661$	−6.05918	+	8.33975i	−0.235675	+	0.324379i	0.674755	+	0.738042i	$0.264249\pi$
$662$	4.09048	−	2.08420i	0.158981	−	0.0810048i
$663$		0			0
$664$	4.99670	+	6.87737i	0.193910	+	0.266894i
$665$		−	16.8859i		−	0.654806i
$666$		0			0
$667$	0.287502	−	1.81522i	0.0111321	−	0.0702854i
$668$	11.7865	−	1.86679i	0.456032	−	0.0722284i
$669$		0			0
$670$	−5.00062	−	5.00062i	−0.193191	−	0.193191i
$671$	−1.32165	−	8.34459i	−0.0510219	−	0.322139i
$672$		0			0
$673$	−22.8825	−	3.62423i	−0.882055	−	0.139704i	−0.301054	−	0.953607i	$-0.597339\pi$
$673$	−22.8825	−	3.62423i	−0.882055	−	0.139704i	−0.581001	+	0.813903i	$0.697339\pi$
$674$	−1.07789	+	3.31739i	−0.0415186	+	0.127781i
$675$		0			0
$676$	50.9253	−	16.5466i	1.95866	−	0.636408i
$677$	−10.7253	+	3.48486i	−0.412206	+	0.133934i	−0.507777	−	0.861489i	$-0.669532\pi$
$677$	−10.7253	+	3.48486i	−0.412206	+	0.133934i	0.0955705	+	0.995423i	$0.469532\pi$
$678$		0			0
$679$	−1.47963	+	4.55384i	−0.0567830	+	0.174760i
$680$	−13.0159	−	2.06152i	−0.499139	−	0.0790558i
$681$		0			0
$682$	0.328701	+	2.07533i	0.0125866	+	0.0794687i
$683$	6.92268	+	6.92268i	0.264889	+	0.264889i	0.827037	−	0.562148i	$-0.190025\pi$
$683$	6.92268	+	6.92268i	0.264889	+	0.264889i	−0.562148	+	0.827037i	$0.690025\pi$
$684$		0			0
$685$	−0.366905	+	0.0581120i	−0.0140187	+	0.00222035i
$686$	−0.827801	+	5.22653i	−0.0316056	+	0.199550i
$687$		0			0
$688$			25.4764i			0.971278i
$689$	4.30649	+	5.92737i	0.164064	+	0.225815i
$690$		0			0
$691$	−32.0987	+	16.3551i	−1.22109	+	0.622178i	−0.941199	−	0.337852i	$-0.890300\pi$
$691$	−32.0987	+	16.3551i	−1.22109	+	0.622178i	−0.279895	+	0.960031i	$0.590300\pi$
$692$	−5.71091	+	7.86039i	−0.217096	+	0.298807i
$693$		0			0
$694$	−7.21966	+	7.21966i	−0.274055	+	0.274055i
$695$	42.8035	+	13.9077i	1.62363	+	0.527550i
$696$		0			0
$697$	−18.8026	−	7.85023i	−0.712198	−	0.297349i
$698$	1.56981			0.0594180
$699$		0			0
$700$	−13.7677	+	13.7677i	−0.520369	+	0.520369i
$701$	−41.7632	−	30.3427i	−1.57737	−	1.14603i	−0.919630	−	0.392787i	$-0.871511\pi$
$701$	−41.7632	−	30.3427i	−1.57737	−	1.14603i	−0.657744	−	0.753242i	$-0.728489\pi$
$702$		0			0
$703$	3.65923	−	1.86447i	0.138011	−	0.0703199i
$704$	9.50919	+	4.84517i	0.358391	+	0.182609i
$705$		0			0
$706$			7.83868i			0.295013i
$707$	−7.70515	+	5.59812i	−0.289782	+	0.210539i
$708$		0			0
$709$	48.3157	−	7.65246i	1.81453	−	0.287394i	0.845438	−	0.534074i	$-0.179340\pi$
$709$	48.3157	−	7.65246i	1.81453	−	0.287394i	0.969097	+	0.246680i	$0.0793395\pi$
$710$	3.97800	+	7.80726i	0.149292	+	0.293001i
$711$		0			0
$712$	2.71167	+	17.1208i	0.101624	+	0.641630i
$713$	6.29357	+	19.3696i	0.235696	+	0.725398i
$714$		0			0
$715$	12.5430	−	38.6035i	0.469082	−	1.44369i
$716$	−7.79086	+	15.2904i	−0.291158	+	0.571430i
$717$		0			0
$718$	−0.397264	+	0.129079i	−0.0148258	+	0.00481718i
$719$	−9.42790	+	18.5033i	−0.351601	+	0.690056i	−0.997292	−	0.0735426i	$-0.976570\pi$
$719$	−9.42790	+	18.5033i	−0.351601	+	0.690056i	0.645691	+	0.763599i	$0.276570\pi$
$720$		0			0
$721$	23.7384	+	3.75979i	0.884063	+	0.140022i
$722$	−0.738126	−	2.27172i	−0.0274702	−	0.0845446i
$723$		0			0
$724$	16.0249	+	16.0249i	0.595561	+	0.595561i
$725$	−1.08017	−	2.11996i	−0.0401166	−	0.0787333i
$726$		0			0
$727$	−2.24680	+	14.1858i	−0.0833293	+	0.526121i	0.910348	+	0.413844i	$0.135814\pi$
$727$	−2.24680	+	14.1858i	−0.0833293	+	0.526121i	−0.993677	+	0.112276i	$0.964186\pi$
$728$	9.02416	−	6.55643i	0.334457	−	0.242998i
$729$		0			0
$730$	−5.60480	−	7.71435i	−0.207443	−	0.285521i
$731$	−20.9529	−	10.6760i	−0.774970	−	0.394867i
$732$		0			0
$733$	14.2196	−	19.5717i	0.525214	−	0.722895i	−0.461177	−	0.887308i	$-0.652573\pi$
$733$	14.2196	−	19.5717i	0.525214	−	0.722895i	0.986392	+	0.164413i	$0.0525728\pi$
$734$	−2.18158	−	1.58501i	−0.0805235	−	0.0585038i
$735$		0			0
$736$	−17.7432	−	5.76512i	−0.654024	−	0.212505i
$737$	−12.1880			−0.448951
$738$		0			0
$739$	0.683852			0.0251559			0.0125780	−	0.999921i	$-0.495996\pi$
$739$	0.683852			0.0251559			0.0125780	+	0.999921i	$0.495996\pi$
$740$	−7.71484	−	2.50670i	−0.283603	−	0.0921482i
$741$		0			0
$742$	0.411933	+	0.299287i	0.0151225	+	0.0109872i
$743$	17.7873	−	24.4821i	0.652553	−	0.898162i	−0.346654	−	0.937993i	$-0.612682\pi$
$743$	17.7873	−	24.4821i	0.652553	−	0.898162i	0.999206	+	0.0398315i	$0.0126821\pi$
$744$		0			0
$745$	−0.544888	−	0.277634i	−0.0199631	−	0.0101717i
$746$	2.91699	+	4.01489i	0.106799	+	0.146996i
$747$		0			0
$748$	−8.96705	+	6.51494i	−0.327868	+	0.238210i
$749$	−1.57142	+	9.92158i	−0.0574186	+	0.362527i
$750$		0			0
$751$	8.69372	+	17.0624i	0.317238	+	0.622615i	0.993473	−	0.114072i	$-0.0363893\pi$
$751$	8.69372	+	17.0624i	0.317238	+	0.622615i	−0.676234	+	0.736687i	$0.736389\pi$
$752$	3.85277	+	3.85277i	0.140496	+	0.140496i
$753$		0			0
$754$	0.205563	+	0.632658i	0.00748616	+	0.0230400i
$755$	−67.5904	−	10.7053i	−2.45986	−	0.389604i
$756$		0			0
$757$	16.5655	−	32.5117i	0.602085	−	1.18166i	−0.365901	−	0.930654i	$-0.619239\pi$
$757$	16.5655	−	32.5117i	0.602085	−	1.18166i	0.967986	−	0.251005i	$-0.0807609\pi$
$758$	3.30848	−	1.07499i	0.120169	−	0.0390454i
$759$		0			0
$760$	6.28949	−	12.3438i	0.228144	−	0.447757i
$761$	5.94946	−	18.3106i	0.215668	−	0.663758i	−0.783438	−	0.621470i	$-0.786536\pi$
$761$	5.94946	−	18.3106i	0.215668	−	0.663758i	0.999106	−	0.0422871i	$-0.0134644\pi$
$762$		0			0
$763$	0.578918	+	1.78173i	0.0209582	+	0.0645028i
$764$	5.25735	+	33.1936i	0.190204	+	1.20090i
$765$		0			0
$766$	0.630481	+	1.23739i	0.0227802	+	0.0447087i
$767$	85.3404	−	13.5166i	3.08146	−	0.488056i
$768$		0			0
$769$	−14.1385	+	10.2722i	−0.509848	+	0.370427i	−0.812766	−	0.582590i	$-0.802039\pi$
$769$	−14.1385	+	10.2722i	−0.509848	+	0.370427i	0.302918	+	0.953017i	$0.402039\pi$
$770$		−	2.82088i		−	0.101657i
$771$		0			0
$772$	−23.2654	−	11.8543i	−0.837339	−	0.426646i
$773$	37.4355	−	19.0743i	1.34646	−	0.686056i	0.375843	−	0.926683i	$-0.377353\pi$
$773$	37.4355	−	19.0743i	1.34646	−	0.686056i	0.970618	+	0.240627i	$0.0773530\pi$
$774$		0			0
$775$	21.3310	+	15.4979i	0.766231	+	0.556700i
$776$	−2.77780	+	2.77780i	−0.0997172	+	0.0997172i
$777$		0			0
$778$	−7.78512			−0.279110
$779$	13.9570	−	16.2488i	0.500060	−	0.582175i
$780$		0			0
$781$	14.3621	+	4.66653i	0.513916	+	0.166982i
$782$	3.72803	−	3.72803i	0.133314	−	0.133314i
$783$		0			0
$784$	9.88637	−	13.6074i	0.353085	−	0.485979i
$785$	−10.9824	+	5.59582i	−0.391979	+	0.199723i
$786$		0			0
$787$	12.6296	+	17.3831i	0.450195	+	0.619640i	0.972439	−	0.233156i	$-0.0749051\pi$
$787$	12.6296	+	17.3831i	0.450195	+	0.619640i	−0.522244	+	0.852796i	$0.674905\pi$
$788$			8.15527i			0.290519i
$789$		0			0
$790$	−1.68986	+	10.6694i	−0.0601226	+	0.379599i
$791$	10.1749	−	1.61155i	0.361778	−	0.0573000i
$792$		0			0
$793$	20.9590	+	20.9590i	0.744276	+	0.744276i
$794$	−1.10149	−	6.95455i	−0.0390905	−	0.246808i
$795$		0			0
$796$	−7.14001	−	1.13087i	−0.253071	−	0.0400825i
$797$	−7.95385	+	24.4794i	−0.281740	+	0.867106i	0.705617	+	0.708593i	$0.250670\pi$
$797$	−7.95385	+	24.4794i	−0.281740	+	0.867106i	−0.987357	+	0.158513i	$0.949330\pi$
$798$		0			0
$799$	−4.78320	+	1.55416i	−0.169217	+	0.0549821i
$800$	−22.9705	+	7.46358i	−0.812131	+	0.263877i
$801$		0			0
$802$	2.06284	−	6.34877i	0.0728414	−	0.224183i
$803$	−16.2314	−	2.57080i	−0.572793	−	0.0907215i
$804$		0			0
$805$	−4.27724	−	27.0054i	−0.150753	−	0.951816i
$806$	−5.21259	−	5.21259i	−0.183606	−	0.183606i
$807$		0			0
$808$	−7.71770	+	1.22236i	−0.271508	+	0.0430026i
$809$	2.48312	−	15.6778i	0.0873018	−	0.551202i	−0.904807	−	0.425822i	$-0.859985\pi$
$809$	2.48312	−	15.6778i	0.0873018	−	0.551202i	0.992109	−	0.125380i	$-0.0400150\pi$
$810$		0			0
$811$			46.8407i			1.64480i	0.568910	+	0.822400i	$0.307365\pi$
$811$			46.8407i			1.64480i	−0.568910	+	0.822400i	$0.692635\pi$
$812$	−0.553720	−	0.762130i	−0.0194318	−	0.0267455i
$813$		0			0
$814$	0.611295	−	0.311470i	0.0214259	−	0.0109170i
$815$	−8.27644	+	11.3915i	−0.289911	+	0.399028i
$816$		0			0
$817$	17.4808	−	17.4808i	0.611574	−	0.611574i
$818$	1.00527	+	0.326632i	0.0351484	+	0.0114204i
$819$		0			0
$820$	−42.1878	+	3.20102i	−1.47326	+	0.111785i
$821$	4.49527			0.156886			0.0784431	−	0.996919i	$-0.475005\pi$
$821$	4.49527			0.156886			0.0784431	+	0.996919i	$0.475005\pi$
$822$		0			0
$823$	−10.4358	+	10.4358i	−0.363769	+	0.363769i	−0.865199	−	0.501429i	$-0.832808\pi$
$823$	−10.4358	+	10.4358i	−0.363769	+	0.363769i	0.501429	+	0.865199i	$0.332808\pi$
$824$	15.9527	+	11.5903i	0.555737	+	0.403767i
$825$		0			0
$826$	5.35033	−	2.72613i	0.186162	−	0.0948541i
$827$	−32.6277	−	16.6247i	−1.13458	−	0.578096i	−0.217205	−	0.976126i	$-0.569694\pi$
$827$	−32.6277	−	16.6247i	−1.13458	−	0.578096i	−0.917372	+	0.398030i	$0.869694\pi$
$828$		0			0
$829$			24.1722i			0.839534i	0.907632	+	0.419767i	$0.137888\pi$
$829$			24.1722i			0.839534i	−0.907632	+	0.419767i	$0.862112\pi$
$830$	−6.10180	+	4.43322i	−0.211797	+	0.153879i
$831$		0			0
$832$	−36.9814	+	5.85727i	−1.28210	+	0.203064i
$833$	7.04838	+	13.8332i	0.244212	+	0.479293i
$834$		0			0
$835$	3.39383	+	21.4278i	0.117448	+	0.741539i
$836$	−3.60070	−	11.0818i	−0.124533	−	0.383273i
$837$		0			0
$838$	1.77258	−	5.45544i	0.0612328	−	0.188455i
$839$	13.7897	−	27.0638i	0.476074	−	0.934347i	−0.520674	−	0.853756i	$-0.674319\pi$
$839$	13.7897	−	27.0638i	0.476074	−	0.934347i	0.996747	−	0.0805911i	$-0.0256808\pi$
$840$		0			0
$841$	−27.4712	+	8.92592i	−0.947281	+	0.307790i
$842$	0.866418	−	1.70044i	0.0298588	−	0.0586011i
$843$		0			0
$844$	−2.59610	−	0.411181i	−0.0893613	−	0.0141534i
$845$	30.0817	+	92.5821i	1.03484	+	3.18492i
$846$		0			0
$847$	7.89036	+	7.89036i	0.271116	+	0.271116i
$848$	−1.78893	−	3.51097i	−0.0614320	−	0.120567i
$849$		0			0
$850$	1.06774	−	6.74143i	0.0366231	−	0.231229i
$851$	5.37990	−	3.90872i	0.184420	−	0.133989i
$852$		0			0
$853$	−0.247241	−	0.340298i	−0.00846537	−	0.0116516i	0.804763	−	0.593596i	$-0.202292\pi$
$853$	−0.247241	−	0.340298i	−0.00846537	−	0.0116516i	−0.813229	+	0.581944i	$0.802292\pi$
$854$	1.83540	+	0.935184i	0.0628062	+	0.0320013i
$855$		0			0
$856$	−4.84423	+	6.66751i	−0.165572	+	0.227891i
$857$	43.6766	+	31.7329i	1.49196	+	1.08397i	0.973449	+	0.228906i	$0.0735147\pi$
$857$	43.6766	+	31.7329i	1.49196	+	1.08397i	0.518514	+	0.855069i	$0.326485\pi$
$858$		0			0
$859$	−39.5195	−	12.8407i	−1.34839	−	0.438117i	−0.456237	−	0.889858i	$-0.650803\pi$
$859$	−39.5195	−	12.8407i	−1.34839	−	0.438117i	−0.892149	+	0.451741i	$0.850803\pi$
$860$	−48.8300			−1.66509
$861$		0			0
$862$	1.94787			0.0663449
$863$	−5.06646	−	1.64619i	−0.172464	−	0.0560371i	0.221512	−	0.975158i	$-0.428901\pi$
$863$	−5.06646	−	1.64619i	−0.172464	−	0.0560371i	−0.393976	+	0.919121i	$0.628901\pi$
$864$		0			0
$865$	−14.2902	−	10.3824i	−0.485881	−	0.353013i
$866$	0.363731	−	0.500633i	0.0123601	−	0.0170122i
$867$		0			0
$868$	9.30162	+	4.73941i	0.315718	+	0.160866i
$869$	10.9429	+	15.0616i	0.371211	+	0.510929i
$870$		0			0
$871$	34.5932	−	25.1334i	1.17215	−	0.851614i
$872$	−0.240443	+	1.51810i	−0.00814242	+	0.0514092i
$873$		0			0
$874$	2.51625	+	4.93841i	0.0851134	+	0.167044i
$875$	−7.18330	−	7.18330i	−0.242840	−	0.242840i
$876$		0			0
$877$	9.32212	+	28.6905i	0.314786	+	0.968811i	0.975843	+	0.218475i	$0.0701082\pi$
$877$	9.32212	+	28.6905i	0.314786	+	0.968811i	−0.661057	+	0.750336i	$0.729892\pi$
$878$	−6.65309	−	1.05375i	−0.224531	−	0.0355622i
$879$		0			0
$880$	−9.91078	+	19.4510i	−0.334092	+	0.655693i
$881$	11.5811	−	3.76294i	0.390179	−	0.126777i	−0.107356	−	0.994221i	$-0.534239\pi$
$881$	11.5811	−	3.76294i	0.390179	−	0.126777i	0.497535	+	0.867444i	$0.334239\pi$
$882$		0			0
$883$	5.32064	−	10.4423i	0.179054	−	0.351413i	−0.783983	−	0.620782i	$-0.786815\pi$
$883$	5.32064	−	10.4423i	0.179054	−	0.351413i	0.963037	+	0.269369i	$0.0868152\pi$
$884$	12.0164	−	36.9827i	0.404156	−	1.24386i
$885$		0			0
$886$	−1.50379	−	4.62818i	−0.0505208	−	0.155487i
$887$	−5.47072	−	34.5408i	−0.183689	−	1.15976i	−0.891385	−	0.453248i	$-0.850265\pi$
$887$	−5.47072	−	34.5408i	−0.183689	−	1.15976i	0.707696	−	0.706517i	$-0.249735\pi$
$888$		0			0
$889$	3.63827	+	7.14052i	0.122024	+	0.239485i
$890$	−15.1901	+	2.40588i	−0.509173	+	0.0806451i
$891$		0			0
$892$	2.71536	−	1.97283i	0.0909170	−	0.0660551i
$893$		−	5.28719i		−	0.176929i
$894$		0			0
$895$	−27.7980	−	14.1638i	−0.929184	−	0.473443i
$896$	−11.2573	+	5.73586i	−0.376078	+	0.191622i
$897$		0			0
$898$	5.57276	+	4.04885i	0.185966	+	0.135112i
$899$	−0.902057	+	0.902057i	−0.0300853	+	0.0300853i
$900$		0			0
$901$	3.63723			0.121174
$902$	2.33159	−	2.71446i	0.0776333	−	0.0903815i
$903$		0			0
$904$	8.03825	+	2.61179i	0.267348	+	0.0868668i
$905$	−29.1333	+	29.1333i	−0.968422	+	0.968422i
$906$		0			0
$907$	−5.59498	+	7.70083i	−0.185778	+	0.255702i	−0.891740	−	0.452548i	$-0.850515\pi$
$907$	−5.59498	+	7.70083i	−0.185778	+	0.255702i	0.705962	+	0.708250i	$0.250515\pi$
$908$	0.0392099	−	0.0199784i	0.00130122	−	0.000663007i
$909$		0			0
$910$	5.81706	+	8.00650i	0.192834	+	0.265413i
$911$			36.1439i			1.19750i	0.800936	+	0.598750i	$0.204336\pi$
$911$			36.1439i			1.19750i	−0.800936	+	0.598750i	$0.795664\pi$
$912$		0			0
$913$	−2.03342	+	12.8385i	−0.0672963	+	0.424892i
$914$	−1.11122	+	0.175999i	−0.0367558	+	0.00582154i
$915$		0			0
$916$	32.5721	+	32.5721i	1.07621	+	1.07621i
$917$	1.85443	+	11.7084i	0.0612387	+	0.386646i
$918$		0			0
$919$	55.4813	+	8.78737i	1.83016	+	0.289869i	0.973950	−	0.226763i	$-0.0728143\pi$
$919$	55.4813	+	8.78737i	1.83016	+	0.289869i	0.856208	+	0.516631i	$0.172814\pi$
$920$	6.93199	−	21.3345i	0.228541	−	0.703377i
$921$		0			0
$922$	−1.12018	+	0.363969i	−0.0368912	+	0.0119867i
$923$	−50.3870	+	16.3717i	−1.65851	+	0.538882i
$924$		0			0
$925$	2.66034	−	8.18769i	0.0874714	−	0.269209i
$926$	9.59470	+	1.51965i	0.315302	+	0.0499389i
$927$		0			0
$928$	−0.182807	−	1.15420i	−0.00600094	−	0.0378884i
$929$	−37.3268	−	37.3268i	−1.22465	−	1.22465i	−0.965959	−	0.258694i	$-0.916708\pi$
$929$	−37.3268	−	37.3268i	−1.22465	−	1.22465i	−0.258694	−	0.965959i	$-0.583292\pi$
$930$		0			0
$931$	−16.1204	+	2.55322i	−0.528324	+	0.0836784i
$932$	−5.67028	+	35.8007i	−0.185736	+	1.17269i
$933$		0			0
$934$			9.58648i			0.313679i
$935$	−11.8442	−	16.3021i	−0.387345	−	0.533135i
$936$		0			0
$937$	8.13713	−	4.14608i	0.265829	−	0.135446i	−0.315997	−	0.948760i	$-0.602339\pi$
$937$	8.13713	−	4.14608i	0.265829	−	0.135446i	0.581825	+	0.813314i	$0.302339\pi$
$938$	1.74669	−	2.40412i	0.0570315	−	0.0784972i
$939$		0			0
$940$	−7.38450	+	7.38450i	−0.240856	+	0.240856i
$941$	33.6652	+	10.9385i	1.09745	+	0.356584i	0.801122	−	0.598501i	$-0.204237\pi$
$941$	33.6652	+	10.9385i	1.09745	+	0.356584i	0.296331	+	0.955085i	$0.404237\pi$
$942$		0			0
$943$	18.2053	−	29.5219i	0.592847	−	0.961366i
$944$	−46.4703			−1.51248
$945$		0			0
$946$	2.92026	−	2.92026i	0.0949457	−	0.0949457i
$947$	21.7998	+	15.8385i	0.708399	+	0.514682i	0.882657	−	0.470018i	$-0.155753\pi$
$947$	21.7998	+	15.8385i	0.708399	+	0.514682i	−0.174258	+	0.984700i	$0.555753\pi$
$948$		0			0
$949$	51.3709	−	26.1748i	1.66757	−	0.849669i
$950$	6.39331	+	3.25756i	0.207427	+	0.105689i
$951$		0			0
$952$		−	5.53751i		−	0.179472i
$953$	37.0784	−	26.9390i	1.20109	−	0.872640i	0.206695	−	0.978405i	$-0.433729\pi$
$953$	37.0784	−	26.9390i	1.20109	−	0.872640i	0.994391	+	0.105765i	$0.0337291\pi$
$954$		0			0
$955$	−60.3459	+	9.55786i	−1.95275	+	0.309285i
$956$	15.4877	+	30.3963i	0.500908	+	0.983087i
$957$		0			0
$958$	−1.98096	−	12.5073i	−0.0640018	−	0.404092i
$959$	−0.0482364	−	0.148456i	−0.00155763	−	0.00479390i
$960$		0			0
$961$	−5.21097	+	16.0377i	−0.168096	+	0.517346i
$962$	−1.09274	+	2.14462i	−0.0352314	+	0.0691455i
$963$		0			0
$964$	10.4451	−	3.39382i	0.336414	−	0.109307i
$965$	21.5511	−	42.2965i	0.693755	−	1.36157i
$966$		0			0
$967$	12.8592	+	2.03670i	0.413524	+	0.0654957i	0.359730	−	0.933056i	$-0.382869\pi$
$967$	12.8592	+	2.03670i	0.413524	+	0.0654957i	0.0537936	+	0.998552i	$0.482869\pi$
$968$	2.82904	+	8.70689i	0.0909287	+	0.279850i
$969$		0			0
$970$	−2.46455	−	2.46455i	−0.0791318	−	0.0791318i
$971$	−14.6907	−	28.8321i	−0.471447	−	0.925268i	−0.997211	−	0.0746367i	$-0.976220\pi$
$971$	−14.6907	−	28.8321i	−0.471447	−	0.925268i	0.525763	−	0.850631i	$-0.323780\pi$
$972$		0			0
$973$	−2.95845	+	18.6789i	−0.0948437	+	0.598819i
$974$	−8.07912	+	5.86982i	−0.258872	+	0.188081i
$975$		0			0
$976$	−9.37013	−	12.8969i	−0.299931	−	0.412819i
$977$	33.8782	+	17.2618i	1.08386	+	0.552254i	0.902292	−	0.431125i	$-0.141883\pi$
$977$	33.8782	+	17.2618i	1.08386	+	0.552254i	0.181567	+	0.983379i	$0.441883\pi$
$978$		0			0
$979$	−15.5795	+	21.4433i	−0.497922	+	0.685331i
$980$	26.0810	+	18.9490i	0.833127	+	0.605302i
$981$		0			0
$982$	−11.7418	−	3.81513i	−0.374694	−	0.121746i
$983$	2.64592			0.0843918			0.0421959	−	0.999109i	$-0.486565\pi$
$983$	2.64592			0.0843918			0.0421959	+	0.999109i	$0.486565\pi$
$984$		0			0
$985$	−14.8263			−0.472404
$986$	0.314076	+	0.102049i	0.0100022	+	0.00324992i
$987$		0			0
$988$	33.0722	+	24.0283i	1.05217	+	0.764443i
$989$	23.5289	−	32.3847i	0.748175	−	1.02977i
$990$		0			0
$991$	8.06220	+	4.10790i	0.256104	+	0.130492i	0.577330	−	0.816511i	$-0.304095\pi$
$991$	8.06220	+	4.10790i	0.256104	+	0.130492i	−0.321225	+	0.947003i	$0.604095\pi$
$992$	7.61177	+	10.4767i	0.241674	+	0.332636i
$993$		0			0
$994$	−2.97875	+	2.16419i	−0.0944803	+	0.0686439i
$995$	2.05591	−	12.9805i	0.0651768	−	0.411510i
$996$		0			0
$997$	−17.3045	−	33.9621i	−0.548040	−	1.07559i	−0.984421	−	0.175828i	$-0.943740\pi$
$997$	−17.3045	−	33.9621i	−0.548040	−	1.07559i	0.436381	−	0.899762i	$-0.356260\pi$
$998$	2.39491	+	2.39491i	0.0758097	+	0.0758097i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	369.2.u.a.307.2		24
3.2	odd	2		41.2.g.a.20.2	✓	24
12.11	even	2		656.2.bs.d.225.1		24
41.39	even	20	inner	369.2.u.a.244.2		24
123.11	even	40		1681.2.a.m.1.12		24
123.71	even	40		1681.2.a.m.1.11		24
123.80	odd	20		41.2.g.a.39.2	yes	24
492.203	even	20		656.2.bs.d.449.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.20.2	✓	24	3.2	odd	2
41.2.g.a.39.2	yes	24	123.80	odd	20
369.2.u.a.244.2		24	41.39	even	20	inner
369.2.u.a.307.2		24	1.1	even	1	trivial
656.2.bs.d.225.1		24	12.11	even	2
656.2.bs.d.449.1		24	492.203	even	20
1681.2.a.m.1.11		24	123.71	even	40
1681.2.a.m.1.12		24	123.11	even	40

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:	\( N \)	\(=\)	\( 369 = 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	369.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.290902 - 0.0945196i) q^{2} +(-1.54234 - 1.12058i) q^{4} +(2.03721 - 2.80398i) q^{5} +(1.29765 + 0.661185i) q^{7} +(0.702328 + 0.966671i) q^{8} +O(q^{10})\)	\(q+(-0.290902 - 0.0945196i) q^{2} +(-1.54234 - 1.12058i) q^{4} +(2.03721 - 2.80398i) q^{5} +(1.29765 + 0.661185i) q^{7} +(0.702328 + 0.966671i) q^{8} +(-0.857659 + 0.623126i) q^{10} +(-0.285814 + 1.80456i) q^{11} +(-2.91004 - 5.71127i) q^{13} +(-0.314993 - 0.314993i) q^{14} +(1.06531 + 3.27868i) q^{16} +(-3.14295 - 0.497794i) q^{17} +(1.51872 - 2.98065i) q^{19} +(-6.28416 + 2.04185i) q^{20} +(0.253710 - 0.497934i) q^{22} +(1.67386 - 5.15161i) q^{23} +(-2.16699 - 6.66932i) q^{25} +(0.306707 + 1.93647i) q^{26} +(-1.26051 - 2.47389i) q^{28} +(0.335113 - 0.0530767i) q^{29} +(-3.04183 + 2.21002i) q^{31} -3.44421i q^{32} +(0.867237 + 0.441879i) q^{34} +(4.49754 - 2.29161i) q^{35} +(0.993200 + 0.721602i) q^{37} +(-0.723527 + 0.723527i) q^{38} +4.14132 q^{40} +(6.22198 + 1.51227i) q^{41} +(7.02832 + 2.28364i) q^{43} +(2.46297 - 2.46297i) q^{44} +(-0.973857 + 1.34040i) q^{46} +(1.40824 - 0.717533i) q^{47} +(-2.86777 - 3.94715i) q^{49} +2.14494i q^{50} +(-1.91165 + 12.0697i) q^{52} +(-1.12895 + 0.178807i) q^{53} +(4.47768 + 4.47768i) q^{55} +(0.272226 + 1.71877i) q^{56} +(-0.102502 - 0.0162347i) q^{58} +(-4.16549 + 12.8200i) q^{59} +(-4.39785 + 1.42895i) q^{61} +(1.09376 - 0.355385i) q^{62} +(1.80507 - 5.55543i) q^{64} +(-21.9426 - 3.47537i) q^{65} +(1.04355 + 6.58873i) q^{67} +(4.28969 + 4.28969i) q^{68} +(-1.52494 + 0.241527i) q^{70} +(1.29298 - 8.16358i) q^{71} +8.99466i q^{73} +(-0.220718 - 0.303792i) q^{74} +(-5.68244 + 2.89535i) q^{76} +(-1.56403 + 2.15271i) q^{77} +(7.20521 - 7.20521i) q^{79} +(11.3636 + 3.69226i) q^{80} +(-1.66705 - 1.02802i) q^{82} +7.11449 q^{83} +(-7.79865 + 7.79865i) q^{85} +(-1.82870 - 1.32863i) q^{86} +(-1.94515 + 0.991103i) q^{88} +(12.9260 + 6.58613i) q^{89} -9.33529i q^{91} +(-8.35446 + 6.06987i) q^{92} +(-0.477479 + 0.0756253i) q^{94} +(-5.26374 - 10.3307i) q^{95} +(0.514313 + 3.24724i) q^{97} +(0.461156 + 1.41929i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8}+O(q^{10}) \) 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8	\( 24 q + 10 q^{2} + 10 q^{5} - 8 q^{7} + 10 q^{8} + 6 q^{10} + 16 q^{11} - 14 q^{14} - 20 q^{16} - 8 q^{17} + 16 q^{19} - 20 q^{20} + 6 q^{22} - 12 q^{23} - 8 q^{25} + 28 q^{26} + 18 q^{28} - 40 q^{29} - 12 q^{31} - 16 q^{34} + 36 q^{35} - 46 q^{38} - 44 q^{40} + 4 q^{41} + 48 q^{44} + 70 q^{46} + 12 q^{47} - 30 q^{49} + 20 q^{52} + 26 q^{53} + 20 q^{55} - 106 q^{56} - 20 q^{58} - 6 q^{59} + 30 q^{61} + 10 q^{62} + 70 q^{64} - 68 q^{65} - 22 q^{67} + 20 q^{68} - 20 q^{70} - 4 q^{71} - 10 q^{74} - 128 q^{76} + 20 q^{77} - 2 q^{79} + 70 q^{80} - 90 q^{82} - 80 q^{83} - 56 q^{85} + 46 q^{86} + 10 q^{88} + 72 q^{89} - 18 q^{94} + 40 q^{95} - 22 q^{97} - 6 q^{98}+O(q^{100}) \) 24 * q + 10 * q^2 + 10 * q^5 - 8 * q^7 + 10 * q^8 + 6 * q^10 + 16 * q^11 - 14 * q^14 - 20 * q^16 - 8 * q^17 + 16 * q^19 - 20 * q^20 + 6 * q^22 - 12 * q^23 - 8 * q^25 + 28 * q^26 + 18 * q^28 - 40 * q^29 - 12 * q^31 - 16 * q^34 + 36 * q^35 - 46 * q^38 - 44 * q^40 + 4 * q^41 + 48 * q^44 + 70 * q^46 + 12 * q^47 - 30 * q^49 + 20 * q^52 + 26 * q^53 + 20 * q^55 - 106 * q^56 - 20 * q^58 - 6 * q^59 + 30 * q^61 + 10 * q^62 + 70 * q^64 - 68 * q^65 - 22 * q^67 + 20 * q^68 - 20 * q^70 - 4 * q^71 - 10 * q^74 - 128 * q^76 + 20 * q^77 - 2 * q^79 + 70 * q^80 - 90 * q^82 - 80 * q^83 - 56 * q^85 + 46 * q^86 + 10 * q^88 + 72 * q^89 - 18 * q^94 + 40 * q^95 - 22 * q^97 - 6 * q^98

Introduction

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