LMFDB - Embedded newform 819.2.gh.d.262.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(19,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("819.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.gh (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			262.5
Character	$\chi$	$=$	819.262
Dual form			819.2.gh.d.397.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.170536 - 0.636449i) q^{2} +(1.35607 - 0.782925i) q^{4} +(1.02345 - 3.81958i) q^{5} +(-2.47383 + 0.938166i) q^{7} +(-1.66138 - 1.66138i) q^{8} +O(q^{10})$	\(q+(-0.170536 - 0.636449i) q^{2} +(1.35607 - 0.782925i) q^{4} +(1.02345 - 3.81958i) q^{5} +(-2.47383 + 0.938166i) q^{7} +(-1.66138 - 1.66138i) q^{8} -2.60550 q^{10} +(1.90358 + 1.90358i) q^{11} +(-0.360197 - 3.58751i) q^{13} +(1.01897 + 1.41448i) q^{14} +(0.791792 - 1.37142i) q^{16} +(-1.67332 - 2.89827i) q^{17} +(4.69300 + 4.69300i) q^{19} +(-1.60257 - 5.98088i) q^{20} +(0.886905 - 1.53616i) q^{22} +(-5.65887 - 3.26715i) q^{23} +(-9.21158 - 5.31831i) q^{25} +(-2.22184 + 0.841048i) q^{26} +(-2.62016 + 3.20904i) q^{28} +(1.95916 + 3.39337i) q^{29} +(1.41145 - 0.378198i) q^{31} +(-5.54684 - 1.48627i) q^{32} +(-1.55924 + 1.55924i) q^{34} +(1.05155 + 10.4092i) q^{35} +(-2.02635 + 0.542959i) q^{37} +(2.18653 - 3.78718i) q^{38} +(-8.04609 + 4.64541i) q^{40} +(0.717157 - 2.67647i) q^{41} +(9.41379 + 5.43505i) q^{43} +(4.07175 + 1.09102i) q^{44} +(-1.11433 + 4.15875i) q^{46} +(-1.76755 - 0.473614i) q^{47} +(5.23969 - 4.64173i) q^{49} +(-1.81393 + 6.76967i) q^{50} +(-3.29720 - 4.58290i) q^{52} +(-3.90136 + 6.75735i) q^{53} +(9.21911 - 5.32265i) q^{55} +(5.66861 + 2.55132i) q^{56} +(1.82560 - 1.82560i) q^{58} +(0.574097 + 0.153829i) q^{59} -5.48741i q^{61} +(-0.481407 - 0.833822i) q^{62} +0.616576i q^{64} +(-14.0714 - 2.29585i) q^{65} +(-2.33126 + 2.33126i) q^{67} +(-4.53826 - 2.62016i) q^{68} +(6.44557 - 2.44439i) q^{70} +(0.629931 + 2.35094i) q^{71} +(-0.670194 - 2.50120i) q^{73} +(0.691132 + 1.19708i) q^{74} +(10.0383 + 2.68975i) q^{76} +(-6.49502 - 2.92327i) q^{77} +(-6.72164 - 11.6422i) q^{79} +(-4.42790 - 4.42790i) q^{80} -1.82574 q^{82} +(0.485609 + 0.485609i) q^{83} +(-12.7827 + 3.42512i) q^{85} +(1.85375 - 6.91827i) q^{86} -6.32514i q^{88} +(2.12574 + 7.93338i) q^{89} +(4.25675 + 8.53698i) q^{91} -10.2317 q^{92} +1.20573i q^{94} +(22.7283 - 13.1222i) q^{95} +(7.37323 - 1.97565i) q^{97} +(-3.84778 - 2.54321i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7}+O(q^{10}) $ 40 * q - 8 * q^7	$ 40 q - 8 q^{7} - 4 q^{11} + 18 q^{14} + 32 q^{16} - 4 q^{17} + 14 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} + 24 q^{25} + 32 q^{26} + 16 q^{28} - 8 q^{29} + 14 q^{31} + 26 q^{32} - 24 q^{34} - 26 q^{35} + 36 q^{37} + 8 q^{38} - 30 q^{40} + 2 q^{41} - 66 q^{43} + 32 q^{44} - 26 q^{46} + 4 q^{47} - 14 q^{49} + 20 q^{50} + 2 q^{52} + 8 q^{53} - 42 q^{55} - 46 q^{56} + 24 q^{58} - 14 q^{59} - 24 q^{62} - 28 q^{65} - 44 q^{67} + 18 q^{68} - 4 q^{70} + 6 q^{71} + 14 q^{73} + 20 q^{74} - 64 q^{76} - 24 q^{77} - 20 q^{80} + 48 q^{82} + 12 q^{83} + 2 q^{85} + 60 q^{86} + 2 q^{89} - 14 q^{91} - 236 q^{92} - 24 q^{95} - 62 q^{97} + 88 q^{98}+O(q^{100}) $ 40 * q - 8 * q^7 - 4 * q^11 + 18 * q^14 + 32 * q^16 - 4 * q^17 + 14 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 + 24 * q^25 + 32 * q^26 + 16 * q^28 - 8 * q^29 + 14 * q^31 + 26 * q^32 - 24 * q^34 - 26 * q^35 + 36 * q^37 + 8 * q^38 - 30 * q^40 + 2 * q^41 - 66 * q^43 + 32 * q^44 - 26 * q^46 + 4 * q^47 - 14 * q^49 + 20 * q^50 + 2 * q^52 + 8 * q^53 - 42 * q^55 - 46 * q^56 + 24 * q^58 - 14 * q^59 - 24 * q^62 - 28 * q^65 - 44 * q^67 + 18 * q^68 - 4 * q^70 + 6 * q^71 + 14 * q^73 + 20 * q^74 - 64 * q^76 - 24 * q^77 - 20 * q^80 + 48 * q^82 + 12 * q^83 + 2 * q^85 + 60 * q^86 + 2 * q^89 - 14 * q^91 - 236 * q^92 - 24 * q^95 - 62 * q^97 + 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.170536	−	0.636449i	−0.120587	−	0.450038i	0.879057	−	0.476717i	$-0.158173\pi$
$2$	−0.170536	−	0.636449i	−0.120587	−	0.450038i	−0.999644	+	0.0266793i	$0.991507\pi$
$3$		0			0
$3$		0			0
$4$	1.35607	−	0.782925i	0.678033	−	0.391462i
$5$	1.02345	−	3.81958i	0.457702	−	1.70817i	−0.222320	−	0.974974i	$-0.571363\pi$
$5$	1.02345	−	3.81958i	0.457702	−	1.70817i	0.680021	−	0.733192i	$-0.261970\pi$
$6$		0			0
$7$	−2.47383	+	0.938166i	−0.935021	+	0.354594i
$7$	−2.47383	+	0.938166i	−0.935021	+	0.354594i
$8$	−1.66138	−	1.66138i	−0.587385	−	0.587385i
$9$		0			0
$10$	−2.60550			−0.823932
$11$	1.90358	+	1.90358i	0.573952	+	0.573952i	0.933230	−	0.359278i	$-0.116977\pi$
$11$	1.90358	+	1.90358i	0.573952	+	0.573952i	−0.359278	+	0.933230i	$0.616977\pi$
$12$		0			0
$13$	−0.360197	−	3.58751i	−0.0999006	−	0.994997i
$13$	−0.360197	−	3.58751i	−0.0999006	−	0.994997i
$14$	1.01897	+	1.41448i	0.272332	+	0.378035i
$15$		0			0
$16$	0.791792	−	1.37142i	0.197948	−	0.342856i
$17$	−1.67332	−	2.89827i	−0.405839	−	0.702934i	0.588580	−	0.808439i	$-0.299687\pi$
$17$	−1.67332	−	2.89827i	−0.405839	−	0.702934i	−0.994419	+	0.105505i	$0.966354\pi$
$18$		0			0
$19$	4.69300	+	4.69300i	1.07665	+	1.07665i	0.996808	+	0.0798395i	$0.0254408\pi$
$19$	4.69300	+	4.69300i	1.07665	+	1.07665i	0.0798395	+	0.996808i	$0.474559\pi$
$20$	−1.60257	−	5.98088i	−0.358346	−	1.33737i
$21$		0			0
$22$	0.886905	−	1.53616i	0.189089	−	0.327511i
$23$	−5.65887	−	3.26715i	−1.17996	−	0.681248i	−0.223952	−	0.974600i	$-0.571896\pi$
$23$	−5.65887	−	3.26715i	−1.17996	−	0.681248i	−0.956004	+	0.293352i	$0.905229\pi$
$24$		0			0
$25$	−9.21158	−	5.31831i	−1.84232	−	1.06366i
$26$	−2.22184	+	0.841048i	−0.435740	+	0.164943i
$27$		0			0
$28$	−2.62016	+	3.20904i	−0.495165	+	0.606451i
$29$	1.95916	+	3.39337i	0.363808	+	0.630133i	0.988584	−	0.150670i	$-0.0481432\pi$
$29$	1.95916	+	3.39337i	0.363808	+	0.630133i	−0.624776	+	0.780804i	$0.714810\pi$
$30$		0			0
$31$	1.41145	−	0.378198i	0.253504	−	0.0679263i	−0.129829	−	0.991536i	$-0.541443\pi$
$31$	1.41145	−	0.378198i	0.253504	−	0.0679263i	0.383333	+	0.923610i	$0.374776\pi$
$32$	−5.54684	−	1.48627i	−0.980551	−	0.262738i
$33$		0			0
$34$	−1.55924	+	1.55924i	−0.267408	+	0.267408i
$35$	1.05155	+	10.4092i	0.177744	+	1.75947i
$36$		0			0
$37$	−2.02635	+	0.542959i	−0.333130	+	0.0892619i	−0.421507	−	0.906825i	$-0.638499\pi$
$37$	−2.02635	+	0.542959i	−0.333130	+	0.0892619i	0.0883769	+	0.996087i	$0.471832\pi$
$38$	2.18653	−	3.78718i	0.354702	−	0.614362i
$39$		0			0
$40$	−8.04609	+	4.64541i	−1.27220	+	0.734505i
$41$	0.717157	−	2.67647i	0.112001	−	0.417994i	−0.887044	−	0.461685i	$-0.847245\pi$
$41$	0.717157	−	2.67647i	0.112001	−	0.417994i	0.999045	+	0.0436912i	$0.0139118\pi$
$42$		0			0
$43$	9.41379	+	5.43505i	1.43559	+	0.828838i	0.997539	−	0.0701122i	$-0.0223357\pi$
$43$	9.41379	+	5.43505i	1.43559	+	0.828838i	0.438051	+	0.898950i	$0.355669\pi$
$44$	4.07175	+	1.09102i	0.613839	+	0.164478i
$45$		0			0
$46$	−1.11433	+	4.15875i	−0.164300	+	0.613175i
$47$	−1.76755	−	0.473614i	−0.257824	−	0.0690838i	0.127592	−	0.991827i	$-0.459275\pi$
$47$	−1.76755	−	0.473614i	−0.257824	−	0.0690838i	−0.385416	+	0.922743i	$0.625942\pi$
$48$		0			0
$49$	5.23969	−	4.64173i	0.748527	−	0.663105i
$50$	−1.81393	+	6.76967i	−0.256528	+	0.957375i
$51$		0			0
$52$	−3.29720	−	4.58290i	−0.457240	−	0.635534i
$53$	−3.90136	+	6.75735i	−0.535892	+	0.928193i	0.463227	+	0.886240i	$0.346691\pi$
$53$	−3.90136	+	6.75735i	−0.535892	+	0.928193i	−0.999120	+	0.0419532i	$0.986642\pi$
$54$		0			0
$55$	9.21911	−	5.32265i	1.24310	−	0.717707i
$56$	5.66861	+	2.55132i	0.757500	+	0.340934i
$57$		0			0
$58$	1.82560	−	1.82560i	0.239713	−	0.239713i
$59$	0.574097	+	0.153829i	0.0747410	+	0.0200268i	0.295996	−	0.955189i	$-0.404349\pi$
$59$	0.574097	+	0.153829i	0.0747410	+	0.0200268i	−0.221255	+	0.975216i	$0.571015\pi$
$60$		0			0
$61$		−	5.48741i		−	0.702590i	−0.936265	−	0.351295i	$-0.885741\pi$
$61$		−	5.48741i		−	0.702590i	0.936265	−	0.351295i	$-0.114259\pi$
$62$	−0.481407	−	0.833822i	−0.0611388	−	0.105896i
$63$		0			0
$64$			0.616576i			0.0770720i
$65$	−14.0714	−	2.29585i	−1.74535	−	0.284765i
$66$		0			0
$67$	−2.33126	+	2.33126i	−0.284809	+	0.284809i	−0.835023	−	0.550214i	$-0.814546\pi$
$67$	−2.33126	+	2.33126i	−0.284809	+	0.284809i	0.550214	+	0.835023i	$0.314546\pi$
$68$	−4.53826	−	2.62016i	−0.550345	−	0.317742i
$69$		0			0
$70$	6.44557	−	2.44439i	0.770393	−	0.292161i
$71$	0.629931	+	2.35094i	0.0747591	+	0.279005i	0.993179	−	0.116603i	$-0.0372006\pi$
$71$	0.629931	+	2.35094i	0.0747591	+	0.279005i	−0.918419	+	0.395608i	$0.870534\pi$
$72$		0			0
$73$	−0.670194	−	2.50120i	−0.0784402	−	0.292743i	0.915551	−	0.402202i	$-0.131755\pi$
$73$	−0.670194	−	2.50120i	−0.0784402	−	0.292743i	−0.993991	+	0.109459i	$0.965088\pi$
$74$	0.691132	+	1.19708i	0.0803424	+	0.139157i
$75$		0			0
$76$	10.0383	+	2.68975i	1.15147	+	0.308535i
$77$	−6.49502	−	2.92327i	−0.740177	−	0.333137i
$78$		0			0
$79$	−6.72164	−	11.6422i	−0.756244	−	1.30985i	−0.944754	−	0.327781i	$-0.893699\pi$
$79$	−6.72164	−	11.6422i	−0.756244	−	1.30985i	0.188510	−	0.982071i	$-0.439634\pi$
$80$	−4.42790	−	4.42790i	−0.495054	−	0.495054i
$81$		0			0
$82$	−1.82574			−0.201619
$83$	0.485609	+	0.485609i	0.0533025	+	0.0533025i	0.733256	−	0.679953i	$-0.238000\pi$
$83$	0.485609	+	0.485609i	0.0533025	+	0.0533025i	−0.679953	+	0.733256i	$0.738000\pi$
$84$		0			0
$85$	−12.7827	+	3.42512i	−1.38648	+	0.371507i
$86$	1.85375	−	6.91827i	0.199895	−	0.746017i
$87$		0			0
$88$		−	6.32514i		−	0.674262i
$89$	2.12574	+	7.93338i	0.225328	+	0.840937i	0.982273	+	0.187458i	$0.0600247\pi$
$89$	2.12574	+	7.93338i	0.225328	+	0.840937i	−0.756944	+	0.653479i	$0.773309\pi$
$90$		0			0
$91$	4.25675	+	8.53698i	0.446229	+	0.894919i
$92$	−10.2317			−1.06673
$93$		0			0
$94$			1.20573i			0.124361i
$95$	22.7283	−	13.1222i	2.33188	−	1.34631i
$96$		0			0
$97$	7.37323	−	1.97565i	0.748638	−	0.200597i	0.135724	−	0.990747i	$-0.456664\pi$
$97$	7.37323	−	1.97565i	0.748638	−	0.200597i	0.612914	+	0.790150i	$0.289997\pi$
$98$	−3.84778	−	2.54321i	−0.388685	−	0.256903i
$99$		0			0
$100$	−16.6553			−1.66553
$101$	13.5609			1.34936			0.674681	−	0.738110i	$-0.264281\pi$
$101$	13.5609			1.34936			0.674681	+	0.738110i	$0.264281\pi$
$102$		0			0
$103$	−2.89216	−	5.00937i	−0.284973	−	0.493588i	0.687630	−	0.726062i	$-0.258651\pi$
$103$	−2.89216	−	5.00937i	−0.284973	−	0.493588i	−0.972603	+	0.232474i	$0.925318\pi$
$104$	−5.36179	+	6.55864i	−0.525767	+	0.643127i
$105$		0			0
$106$	4.96603	+	1.33064i	0.482343	+	0.129244i
$107$	3.38467	−	5.86241i	0.327208	−	0.566741i	−0.654749	−	0.755847i	$-0.727226\pi$
$107$	3.38467	−	5.86241i	0.327208	−	0.566741i	0.981957	+	0.189106i	$0.0605589\pi$
$108$		0			0
$109$	−1.07769	−	4.02199i	−0.103224	−	0.385237i	0.894914	−	0.446239i	$-0.147237\pi$
$109$	−1.07769	−	4.02199i	−0.103224	−	0.385237i	−0.998138	+	0.0610023i	$0.980570\pi$
$110$	−4.95979	−	4.95979i	−0.472897	−	0.472897i
$111$		0			0
$112$	−0.672136	+	4.13551i	−0.0635109	+	0.390769i
$113$	8.98623	−	15.5646i	0.845353	−	1.46420i	−0.0399604	−	0.999201i	$-0.512723\pi$
$113$	8.98623	−	15.5646i	0.845353	−	1.46420i	0.885314	−	0.464994i	$-0.153943\pi$
$114$		0			0
$115$	−18.2707	+	18.2707i	−1.70375	+	1.70375i
$116$	5.31351	+	3.06776i	0.493347	+	0.284834i
$117$		0			0
$118$		−	0.391617i		−	0.0360513i
$119$	6.85857	+	5.59999i	0.628724	+	0.513350i
$120$		0			0
$121$		−	3.75274i		−	0.341158i
$122$	−3.49246	+	0.935801i	−0.316192	+	0.0847234i
$123$		0			0
$124$	1.61792	−	1.61792i	0.145294	−	0.145294i
$125$	−15.7607	+	15.7607i	−1.40968	+	1.40968i
$126$		0			0
$127$	10.5135	−	6.07000i	0.932926	−	0.538625i	0.0451906	−	0.998978i	$-0.485610\pi$
$127$	10.5135	−	6.07000i	0.932926	−	0.538625i	0.887736	+	0.460353i	$0.152277\pi$
$128$	−10.7013	+	2.86739i	−0.945866	+	0.253444i
$129$		0			0
$130$	0.938494	+	9.34728i	0.0823113	+	0.819810i
$131$	12.0751	−	6.97154i	1.05500	−	0.609107i	0.130958	−	0.991388i	$-0.458195\pi$
$131$	12.0751	−	6.97154i	1.05500	−	0.609107i	0.924046	+	0.382281i	$0.124861\pi$
$132$		0			0
$133$	−16.0125	−	7.20687i	−1.38846	−	0.624915i
$134$	1.88130	+	1.08617i	0.162519	+	0.0938305i
$135$		0			0
$136$	−2.03511	+	7.59513i	−0.174509	+	0.651277i
$137$	−4.02872	+	15.0354i	−0.344197	+	1.28456i	0.549351	+	0.835591i	$0.314875\pi$
$137$	−4.02872	+	15.0354i	−0.344197	+	1.28456i	−0.893548	+	0.448968i	$0.851792\pi$
$138$		0			0
$139$	12.6736	+	7.31710i	1.07496	+	0.620629i	0.929532	−	0.368740i	$-0.120211\pi$
$139$	12.6736	+	7.31710i	1.07496	+	0.620629i	0.145428	+	0.989369i	$0.453544\pi$
$140$	9.57556	+	13.2922i	0.809282	+	1.12340i
$141$		0			0
$142$	1.38883	−	0.801839i	0.116548	−	0.0672888i
$143$	6.14347	−	7.51480i	0.513743	−	0.628419i
$144$		0			0
$145$	14.9664	−	4.01022i	1.24289	−	0.333031i
$146$	−1.47759	+	0.853089i	−0.122286	+	0.0706021i
$147$		0			0
$148$	−2.32277	+	2.32277i	−0.190930	+	0.190930i
$149$	−1.98626	+	1.98626i	−0.162721	+	0.162721i	−0.783771	−	0.621050i	$-0.786706\pi$
$149$	−1.98626	+	1.98626i	−0.162721	+	0.162721i	0.621050	+	0.783771i	$0.286706\pi$
$150$		0			0
$151$	−8.14633	+	2.18280i	−0.662939	+	0.177634i	−0.574572	−	0.818454i	$-0.694831\pi$
$151$	−8.14633	+	2.18280i	−0.662939	+	0.177634i	−0.0883669	+	0.996088i	$0.528165\pi$
$152$		−	15.5937i		−	1.26481i
$153$		0			0
$154$	−0.752876	+	4.63228i	−0.0606685	+	0.373279i
$155$		−	5.77822i		−	0.464118i
$156$		0			0
$157$	15.0399	+	8.68326i	1.20031	+	0.693000i	0.960624	−	0.277850i	$-0.0896220\pi$
$157$	15.0399	+	8.68326i	1.20031	+	0.693000i	0.239687	+	0.970850i	$0.422955\pi$
$158$	−6.26340	+	6.26340i	−0.498290	+	0.498290i
$159$		0			0
$160$	−11.3538	+	19.6654i	−0.897600	+	1.55469i
$161$	17.0642	+	2.77342i	1.34485	+	0.218576i
$162$		0			0
$163$	16.7917	+	16.7917i	1.31523	+	1.31523i	0.917507	+	0.397719i	$0.130198\pi$
$163$	16.7917	+	16.7917i	1.31523	+	1.31523i	0.397719	+	0.917507i	$0.369802\pi$
$164$	−1.12296	−	4.19094i	−0.0876884	−	0.327258i
$165$		0			0
$166$	0.226252	−	0.391880i	0.0175605	−	0.0304158i
$167$	20.3791	+	5.46055i	1.57698	+	0.422550i	0.937989	−	0.346665i	$-0.112686\pi$
$167$	20.3791	+	5.46055i	1.57698	+	0.422550i	0.638989	+	0.769216i	$0.279353\pi$
$168$		0			0
$169$	−12.7405	+	2.58442i	−0.980040	+	0.198802i
$170$	4.35983	+	7.55145i	0.334384	+	0.579170i
$171$		0			0
$172$	17.0210			1.29784
$173$	15.9512			1.21275			0.606375	−	0.795179i	$-0.292623\pi$
$173$	15.9512			1.21275			0.606375	+	0.795179i	$0.292623\pi$
$174$		0			0
$175$	27.7773	+	4.51460i	2.09977	+	0.341272i
$176$	4.11786	−	1.10338i	0.310396	−	0.0831702i
$177$		0			0
$178$	4.68668	−	2.70586i	0.351282	−	0.202813i
$179$		−	2.88915i		−	0.215945i	−0.994154	−	0.107973i	$-0.965564\pi$
$179$		−	2.88915i		−	0.215945i	0.994154	−	0.107973i	$-0.0344359\pi$
$180$		0			0
$181$	−16.0175			−1.19057			−0.595284	−	0.803515i	$-0.702960\pi$
$181$	−16.0175			−1.19057			−0.595284	+	0.803515i	$0.702960\pi$
$182$	4.70743	−	4.16507i	0.348938	−	0.308736i
$183$		0			0
$184$	3.97355	+	14.8295i	0.292934	+	1.09324i
$185$			8.29549i			0.609897i
$186$		0			0
$187$	2.33180	−	8.70240i	0.170518	−	0.636383i
$188$	−2.76772	+	0.741609i	−0.201857	+	0.0540874i
$189$		0			0
$190$	−12.2276	−	12.2276i	−0.887084	−	0.887084i
$191$	−21.3735			−1.54653			−0.773267	−	0.634081i	$-0.781379\pi$
$191$	−21.3735			−1.54653			−0.773267	+	0.634081i	$0.781379\pi$
$192$		0			0
$193$	−6.57884	−	6.57884i	−0.473555	−	0.473555i	0.429508	−	0.903063i	$-0.358687\pi$
$193$	−6.57884	−	6.57884i	−0.473555	−	0.473555i	−0.903063	+	0.429508i	$0.858687\pi$
$194$	−2.51480	−	4.35577i	−0.180552	−	0.312726i
$195$		0			0
$196$	3.47123	−	10.3968i	0.247945	−	0.742627i
$197$	2.84864	+	0.763291i	0.202957	+	0.0543823i	0.358865	−	0.933389i	$-0.383164\pi$
$197$	2.84864	+	0.763291i	0.202957	+	0.0543823i	−0.155908	+	0.987772i	$0.549830\pi$
$198$		0			0
$199$	−2.82344	−	4.89035i	−0.200149	−	0.346668i	0.748428	−	0.663217i	$-0.230809\pi$
$199$	−2.82344	−	4.89035i	−0.200149	−	0.346668i	−0.948576	+	0.316549i	$0.897476\pi$
$200$	6.46819	+	24.1396i	0.457370	+	1.70693i
$201$		0			0
$202$	−2.31262	−	8.63083i	−0.162716	−	0.607263i
$203$	−8.03019	−	6.55661i	−0.563609	−	0.460184i
$204$		0			0
$205$	−9.48899	−	5.47847i	−0.662740	−	0.382633i
$206$	−2.69499	+	2.69499i	−0.187769	+	0.187769i
$207$		0			0
$208$	−5.20520	−	2.34658i	−0.360916	−	0.162706i
$209$			17.8670i			1.23589i
$210$		0			0
$211$	4.36155	+	7.55442i	0.300261	+	0.520068i	0.976195	−	0.216895i	$-0.0695928\pi$
$211$	4.36155	+	7.55442i	0.300261	+	0.520068i	−0.675934	+	0.736962i	$0.736259\pi$
$212$			12.2179i			0.839127i
$213$		0			0
$214$	−4.30834	−	1.15442i	−0.294512	−	0.0789142i
$215$	30.3942	−	30.3942i	2.07287	−	2.07287i
$216$		0			0
$217$	−3.13689	+	2.25978i	−0.212946	+	0.153404i
$218$	−2.37601	+	1.37179i	−0.160924	+	0.0929093i
$219$		0			0
$220$	8.33448	−	14.4357i	0.561910	−	0.973257i
$221$	−9.79487	+	7.04700i	−0.658874	+	0.474033i
$222$		0			0
$223$	−2.60725	+	9.73040i	−0.174595	+	0.651596i	0.822026	+	0.569450i	$0.192844\pi$
$223$	−2.60725	+	9.73040i	−0.174595	+	0.651596i	−0.996620	+	0.0821456i	$0.973823\pi$
$224$	15.1163	−	1.52707i	1.01000	−	0.102032i
$225$		0			0
$226$	−11.4386	−	3.06495i	−0.760882	−	0.203878i
$227$	−1.12923	+	4.21434i	−0.0749495	+	0.279715i	−0.993222	−	0.116234i	$-0.962918\pi$
$227$	−1.12923	+	4.21434i	−0.0749495	+	0.279715i	0.918272	+	0.395949i	$0.129584\pi$
$228$		0			0
$229$	16.3054	+	4.36901i	1.07749	+	0.288713i	0.753567	−	0.657371i	$-0.228331\pi$
$229$	16.3054	+	4.36901i	1.07749	+	0.288713i	0.323923	+	0.946083i	$0.394998\pi$
$230$	14.7442	+	8.51257i	0.972204	+	0.561302i
$231$		0			0
$232$	2.38276	−	8.89258i	0.156436	−	0.583827i
$233$	3.04241	−	1.75654i	0.199315	−	0.115075i	−0.397021	−	0.917810i	$-0.629956\pi$
$233$	3.04241	−	1.75654i	0.199315	−	0.115075i	0.596336	+	0.802735i	$0.296623\pi$
$234$		0			0
$235$	−3.61801	+	6.26658i	−0.236013	+	0.408787i
$236$	0.898949	−	0.240873i	0.0585166	−	0.0156795i
$237$		0			0
$238$	2.39447	−	5.32013i	0.155211	−	0.344853i
$239$	−15.0576	+	15.0576i	−0.973998	+	0.973998i	−0.999670	−	0.0256726i	$-0.991827\pi$
$239$	−15.0576	+	15.0576i	−0.973998	+	0.973998i	0.0256726	+	0.999670i	$0.491827\pi$
$240$		0			0
$241$	10.6221	+	2.84619i	0.684232	+	0.183339i	0.584157	−	0.811641i	$-0.301425\pi$
$241$	10.6221	+	2.84619i	0.684232	+	0.183339i	0.100075	+	0.994980i	$0.468092\pi$
$242$	−2.38843	+	0.639978i	−0.153534	+	0.0411393i
$243$		0			0
$244$	−4.29623	−	7.44128i	−0.275038	−	0.476379i
$245$	−12.3669	−	24.7640i	−0.790091	−	1.58211i
$246$		0			0
$247$	15.1458	−	18.5266i	0.963703	−	1.17882i
$248$	−2.97328	−	1.71663i	−0.188804	−	0.109006i
$249$		0			0
$250$	12.7186	+	7.34310i	0.804397	+	0.464419i
$251$	11.0284	−	19.1018i	0.696107	−	1.20569i	−0.273700	−	0.961815i	$-0.588247\pi$
$251$	11.0284	−	19.1018i	0.696107	−	1.20569i	0.969806	−	0.243877i	$-0.0784193\pi$
$252$		0			0
$253$	−4.55284	−	16.9914i	−0.286235	−	1.06824i
$254$	−5.65619	−	5.65619i	−0.354901	−	0.354901i
$255$		0			0
$256$	4.26648	+	7.38975i	0.266655	+	0.461860i
$257$	−3.31994	+	5.75030i	−0.207092	+	0.358694i	−0.950797	−	0.309814i	$-0.899733\pi$
$257$	−3.31994	+	5.75030i	−0.207092	+	0.358694i	0.743705	+	0.668508i	$0.233067\pi$
$258$		0			0
$259$	4.50346	−	3.24424i	0.279832	−	0.201587i
$260$	−20.8793	+	7.90354i	−1.29488	+	0.490157i
$261$		0			0
$262$	−6.49627	−	6.49627i	−0.401341	−	0.401341i
$263$	−1.05208			−0.0648739			−0.0324369	−	0.999474i	$-0.510327\pi$
$263$	−1.05208			−0.0648739			−0.0324369	+	0.999474i	$0.510327\pi$
$264$		0			0
$265$	21.8173	+	21.8173i	1.34023	+	1.34023i
$266$	−1.85610	+	11.4202i	−0.113805	+	0.700216i
$267$		0			0
$268$	−1.33614	+	4.98655i	−0.0816178	+	0.304602i
$269$	−6.04641	+	3.49090i	−0.368656	+	0.212844i	−0.672871	−	0.739760i	$-0.734939\pi$
$269$	−6.04641	+	3.49090i	−0.368656	+	0.212844i	0.304215	+	0.952603i	$0.401606\pi$
$270$		0			0
$271$	−6.55082	−	24.4480i	−0.397934	−	1.48511i	−0.816725	−	0.577027i	$-0.804213\pi$
$271$	−6.55082	−	24.4480i	−0.397934	−	1.48511i	0.418792	−	0.908082i	$-0.362454\pi$
$272$	−5.29968			−0.321340
$273$		0			0
$274$	10.2563			0.619606
$275$	−7.41116	−	27.6588i	−0.446910	−	1.66789i
$276$		0			0
$277$	22.6117	−	13.0549i	1.35861	−	0.784392i	0.369171	−	0.929362i	$-0.379642\pi$
$277$	22.6117	−	13.0549i	1.35861	−	0.784392i	0.989436	+	0.144970i	$0.0463084\pi$
$278$	2.49566	−	9.31393i	0.149680	−	0.558612i
$279$		0			0
$280$	15.5465	−	19.0405i	0.929082	−	1.13789i
$281$	13.0103	+	13.0103i	0.776131	+	0.776131i	0.979171	−	0.203039i	$-0.0650819\pi$
$281$	13.0103	+	13.0103i	0.776131	+	0.776131i	−0.203039	+	0.979171i	$0.565082\pi$
$282$		0			0
$283$	−6.29709			−0.374323			−0.187162	−	0.982329i	$-0.559929\pi$
$283$	−6.29709			−0.374323			−0.187162	+	0.982329i	$0.559929\pi$
$284$	2.69483	+	2.69483i	0.159909	+	0.159909i
$285$		0			0
$286$	−5.83047	−	2.62846i	−0.344763	−	0.155424i
$287$	0.736845	+	7.29394i	0.0434946	+	0.430548i
$288$		0			0
$289$	2.90001	−	5.02297i	0.170589	−	0.295469i
$290$	−5.10461	−	8.84144i	−0.299753	−	0.519187i
$291$		0			0
$292$	−2.86708	−	2.86708i	−0.167783	−	0.167783i
$293$	−3.07465	−	11.4748i	−0.179623	−	0.670362i	−0.995718	−	0.0924444i	$-0.970532\pi$
$293$	−3.07465	−	11.4748i	−0.179623	−	0.670362i	0.816095	−	0.577918i	$-0.196135\pi$
$294$		0			0
$295$	1.17512	−	2.03537i	0.0684182	−	0.118504i
$296$	4.26859	+	2.46447i	0.248107	+	0.143245i
$297$		0			0
$298$	1.60288	+	0.925424i	0.0928524	+	0.0536084i
$299$	−9.68264	+	21.4781i	−0.559962	+	1.24211i
$300$		0			0
$301$	−28.3871	−	4.61371i	−1.63621	−	0.265930i
$302$	2.77849	+	4.81248i	0.159884	+	0.276927i
$303$		0			0
$304$	10.1520	−	2.72021i	0.582255	−	0.156015i
$305$	−20.9596	−	5.61610i	−1.20014	−	0.321577i
$306$		0			0
$307$	−14.8912	+	14.8912i	−0.849885	+	0.849885i	−0.990118	−	0.140234i	$-0.955215\pi$
$307$	−14.8912	+	14.8912i	−0.849885	+	0.849885i	0.140234	+	0.990118i	$0.455215\pi$
$308$	−11.0964	+	1.12097i	−0.632275	+	0.0638733i
$309$		0			0
$310$	−3.67754	+	0.985395i	−0.208870	+	0.0559667i
$311$	−10.6266	+	18.4058i	−0.602580	+	1.04370i	0.389849	+	0.920879i	$0.372527\pi$
$311$	−10.6266	+	18.4058i	−0.602580	+	1.04370i	−0.992429	+	0.122820i	$0.960806\pi$
$312$		0			0
$313$	4.47455	−	2.58338i	0.252916	−	0.146021i	−0.368183	−	0.929754i	$-0.620020\pi$
$313$	4.47455	−	2.58338i	0.252916	−	0.146021i	0.621099	+	0.783732i	$0.286687\pi$
$314$	2.96162	−	11.0529i	0.167134	−	0.623752i
$315$		0			0
$316$	−18.2300	−	10.5251i	−1.02552	−	0.592082i
$317$	6.11134	+	1.63753i	0.343247	+	0.0919728i	0.426325	−	0.904570i	$-0.359808\pi$
$317$	6.11134	+	1.63753i	0.343247	+	0.0919728i	−0.0830772	+	0.996543i	$0.526475\pi$
$318$		0			0
$319$	−2.73013	+	10.1890i	−0.152858	+	0.570474i
$320$	2.35506	+	0.631036i	0.131652	+	0.0352760i
$321$		0			0
$322$	−1.14493	−	11.3335i	−0.0638042	−	0.631590i
$323$	5.74870	−	21.4545i	0.319866	−	1.19376i
$324$		0			0
$325$	−15.7615	+	34.9623i	−0.874292	+	1.93936i
$326$	7.82347	−	13.5506i	0.433302	−	0.750501i
$327$		0			0
$328$	−5.63808	+	3.25515i	−0.311311	+	0.179736i
$329$	4.81696	−	0.486616i	0.265567	−	0.0268280i
$330$		0			0
$331$	−3.87092	+	3.87092i	−0.212765	+	0.212765i	−0.805441	−	0.592676i	$-0.798071\pi$
$331$	−3.87092	+	3.87092i	−0.212765	+	0.212765i	0.592676	+	0.805441i	$0.298071\pi$
$332$	1.03871	+	0.278322i	0.0570068	+	0.0152749i
$333$		0			0
$334$		−	13.9015i		−	0.760654i
$335$	6.51850	+	11.2904i	0.356144	+	0.616859i
$336$		0			0
$337$			23.5704i			1.28396i	0.766722	+	0.641980i	$0.221887\pi$
$337$			23.5704i			1.28396i	−0.766722	+	0.641980i	$0.778113\pi$
$338$	3.81757	+	7.66796i	0.207649	+	0.417082i
$339$		0			0
$340$	−14.6526	+	14.6526i	−0.794649	+	0.794649i
$341$	3.40675	+	1.96689i	0.184486	+	0.106513i
$342$		0			0
$343$	−8.60739	+	16.3986i	−0.464755	+	0.885439i
$344$	−6.61018	−	24.6695i	−0.356397	−	1.33009i
$345$		0			0
$346$	−2.72026	−	10.1521i	−0.146242	−	0.545783i
$347$	8.51855	+	14.7546i	0.457300	+	0.792067i	0.998817	−	0.0486230i	$-0.0154833\pi$
$347$	8.51855	+	14.7546i	0.457300	+	0.792067i	−0.541517	+	0.840690i	$0.682150\pi$
$348$		0			0
$349$	−16.3863	−	4.39071i	−0.877140	−	0.235029i	−0.207967	−	0.978136i	$-0.566685\pi$
$349$	−16.3863	−	4.39071i	−0.877140	−	0.235029i	−0.669173	+	0.743107i	$0.733351\pi$
$350$	−1.86372	−	18.4488i	−0.0996202	−	0.986129i
$351$		0			0
$352$	−7.72963	−	13.3881i	−0.411990	−	0.713588i
$353$	24.5444	+	24.5444i	1.30637	+	1.30637i	0.924019	+	0.382347i	$0.124884\pi$
$353$	24.5444	+	24.5444i	1.30637	+	1.30637i	0.382347	+	0.924019i	$0.375116\pi$
$354$		0			0
$355$	9.62428			0.510804
$356$	9.09389	+	9.09389i	0.481975	+	0.481975i
$357$		0			0
$358$	−1.83880	+	0.492704i	−0.0971835	+	0.0260402i
$359$	−4.32153	+	16.1282i	−0.228081	+	0.851212i	0.753065	+	0.657946i	$0.228575\pi$
$359$	−4.32153	+	16.1282i	−0.228081	+	0.851212i	−0.981146	+	0.193266i	$0.938092\pi$
$360$		0			0
$361$			25.0484i			1.31834i
$362$	2.73155	+	10.1943i	0.143567	+	0.535801i
$363$		0			0
$364$	12.4562	+	8.24399i	0.652885	+	0.432103i
$365$	−10.2394			−0.535956
$366$		0			0
$367$		−	3.91533i		−	0.204379i	−0.994765	−	0.102189i	$-0.967415\pi$
$367$		−	3.91533i		−	0.204379i	0.994765	−	0.102189i	$-0.0325848\pi$
$368$	−8.96130	+	5.17381i	−0.467140	+	0.269703i
$369$		0			0
$370$	5.27966	−	1.41468i	0.274476	−	0.0735458i
$371$	3.31178	−	20.3767i	0.171939	−	1.05790i
$372$		0			0
$373$	−28.4227			−1.47167			−0.735836	−	0.677160i	$-0.763211\pi$
$373$	−28.4227			−1.47167			−0.735836	+	0.677160i	$0.763211\pi$
$374$	−5.93630			−0.306959
$375$		0			0
$376$	2.14972	+	3.72342i	0.110863	+	0.192021i
$377$	11.4681	−	8.25081i	0.590637	−	0.424938i
$378$		0			0
$379$	13.2091	+	3.53938i	0.678508	+	0.181806i	0.581584	−	0.813486i	$-0.302433\pi$
$379$	13.2091	+	3.53938i	0.678508	+	0.181806i	0.0969237	+	0.995292i	$0.469100\pi$
$380$	20.5474	−	35.5891i	1.05406	−	1.82568i
$381$		0			0
$382$	3.64496	+	13.6032i	0.186492	+	0.695999i
$383$	−21.4595	−	21.4595i	−1.09653	−	1.09653i	−0.994814	−	0.101714i	$-0.967567\pi$
$383$	−21.4595	−	21.4595i	−1.09653	−	1.09653i	−0.101714	−	0.994814i	$-0.532433\pi$
$384$		0			0
$385$	−17.8130	+	21.8164i	−0.907834	+	1.11187i
$386$	−3.06517	+	5.30903i	−0.156013	+	0.270222i
$387$		0			0
$388$	8.45180	−	8.45180i	0.429075	−	0.429075i
$389$	−15.8430	−	9.14693i	−0.803270	−	0.463768i	0.0413436	−	0.999145i	$-0.486836\pi$
$389$	−15.8430	−	9.14693i	−0.803270	−	0.463768i	−0.844613	+	0.535377i	$0.820170\pi$
$390$		0			0
$391$			21.8679i			1.10591i
$392$	−16.4168	−	0.993431i	−0.829172	−	0.0501758i
$393$		0			0
$394$		−	1.94319i		−	0.0978963i
$395$	−51.3476	+	13.7586i	−2.58358	+	0.692268i
$396$		0			0
$397$	−1.64039	+	1.64039i	−0.0823287	+	0.0823287i	−0.747072	−	0.664743i	$-0.768541\pi$
$397$	−1.64039	+	1.64039i	−0.0823287	+	0.0823287i	0.664743	+	0.747072i	$0.268541\pi$
$398$	−2.63096	+	2.63096i	−0.131878	+	0.131878i
$399$		0			0
$400$	−14.5873	+	8.42198i	−0.729365	+	0.421099i
$401$	−12.9824	+	3.47862i	−0.648309	+	0.173714i	−0.567964	−	0.823053i	$-0.692269\pi$
$401$	−12.9824	+	3.47862i	−0.648309	+	0.173714i	−0.0803450	+	0.996767i	$0.525602\pi$
$402$		0			0
$403$	−1.86519	−	4.92738i	−0.0929118	−	0.245450i
$404$	18.3895	−	10.6172i	0.914911	−	0.528224i
$405$		0			0
$406$	−2.80351	+	6.22895i	−0.139136	+	0.309138i
$407$	−4.89089	−	2.82376i	−0.242433	−	0.139969i
$408$		0			0
$409$	5.29697	−	19.7685i	0.261918	−	0.977492i	−0.702192	−	0.711988i	$-0.747795\pi$
$409$	5.29697	−	19.7685i	0.261918	−	0.977492i	0.964110	−	0.265504i	$-0.0855383\pi$
$410$	−1.86855	+	6.97354i	−0.0922813	+	0.344398i
$411$		0			0
$412$	−7.84392	−	4.52869i	−0.386442	−	0.223113i
$413$	−1.56454	+	0.158052i	−0.0769858	+	0.00777722i
$414$		0			0
$415$	2.35182	−	1.35782i	0.115446	−	0.0666529i
$416$	−3.33406	+	20.4347i	−0.163466	+	1.00189i
$417$		0			0
$418$	11.3715	−	3.04697i	0.556196	−	0.149032i
$419$	−25.2902	+	14.6013i	−1.23551	+	0.713321i	−0.968173	−	0.250282i	$-0.919477\pi$
$419$	−25.2902	+	14.6013i	−1.23551	+	0.713321i	−0.267336	+	0.963604i	$0.586143\pi$
$420$		0			0
$421$	−27.2327	+	27.2327i	−1.32724	+	1.32724i	−0.419470	+	0.907769i	$0.637784\pi$
$421$	−27.2327	+	27.2327i	−1.32724	+	1.32724i	−0.907769	+	0.419470i	$0.862216\pi$
$422$	4.06421	−	4.06421i	0.197842	−	0.197842i
$423$		0			0
$424$	17.7081	−	4.74488i	0.859982	−	0.230432i
$425$			35.5969i			1.72670i
$426$		0			0
$427$	5.14810	+	13.5749i	0.249134	+	0.656936i
$428$		−	10.5998i		−	0.512358i
$429$		0			0
$430$	−24.5277	−	14.1610i	−1.18283	−	0.682906i
$431$	6.07435	−	6.07435i	0.292591	−	0.292591i	−0.545512	−	0.838103i	$-0.683665\pi$
$431$	6.07435	−	6.07435i	0.292591	−	0.292591i	0.838103	+	0.545512i	$0.183665\pi$
$432$		0			0
$433$	7.61560	−	13.1906i	0.365983	−	0.633900i	−0.622951	−	0.782261i	$-0.714066\pi$
$433$	7.61560	−	13.1906i	0.365983	−	0.633900i	0.988933	+	0.148361i	$0.0473997\pi$
$434$	1.97318	+	1.61110i	0.0947159	+	0.0773351i
$435$		0			0
$436$	−4.61034	−	4.61034i	−0.220795	−	0.220795i
$437$	−11.2243	−	41.8898i	−0.536933	−	2.00386i
$438$		0			0
$439$	−1.43313	+	2.48226i	−0.0683996	+	0.118472i	−0.898197	−	0.439593i	$-0.855123\pi$
$439$	−1.43313	+	2.48226i	−0.0683996	+	0.118472i	0.829797	+	0.558065i	$0.188456\pi$
$440$	−24.1593	−	6.47348i	−1.15175	−	0.308611i
$441$		0			0
$442$	6.15544	+	5.03217i	0.292784	+	0.239356i
$443$	−10.5160	−	18.2142i	−0.499628	−	0.865382i	0.500372	−	0.865811i	$-0.333197\pi$
$443$	−10.5160	−	18.2142i	−0.499628	−	0.865382i	−1.00000		0.000429119i	$0.999863\pi$
$444$		0			0
$445$	32.4778			1.53959
$446$	6.63754			0.314297
$447$		0			0
$448$	−0.578451	−	1.52530i	−0.0273292	−	0.0720639i
$449$	−6.15599	+	1.64949i	−0.290519	+	0.0778444i	−0.401135	−	0.916019i	$-0.631384\pi$
$449$	−6.15599	+	1.64949i	−0.290519	+	0.0778444i	0.110616	+	0.993863i	$0.464718\pi$
$450$		0			0
$451$	6.46004	−	3.72971i	0.304192	−	0.175625i
$452$		−	28.1422i		−	1.32370i
$453$		0			0
$454$	2.87479			0.134920
$455$	36.9642	−	7.52179i	1.73291	−	0.352627i
$456$		0			0
$457$	−4.14196	−	15.4580i	−0.193753	−	0.723095i	−0.992586	−	0.121543i	$-0.961216\pi$
$457$	−4.14196	−	15.4580i	−0.193753	−	0.723095i	0.798834	−	0.601552i	$-0.205451\pi$
$458$		−	11.1226i		−	0.519726i
$459$		0			0
$460$	−10.4717	+	39.0809i	−0.488245	+	1.82216i
$461$	29.9787	−	8.03276i	1.39625	−	0.374123i	0.519250	−	0.854622i	$-0.326211\pi$
$461$	29.9787	−	8.03276i	1.39625	−	0.374123i	0.876995	+	0.480499i	$0.159545\pi$
$462$		0			0
$463$	−2.20061	−	2.20061i	−0.102271	−	0.102271i	0.654120	−	0.756391i	$-0.273039\pi$
$463$	−2.20061	−	2.20061i	−0.102271	−	0.102271i	−0.756391	+	0.654120i	$0.773039\pi$
$464$	6.20500			0.288060
$465$		0			0
$466$	−1.63679	−	1.63679i	−0.0758228	−	0.0758228i
$467$	−2.25883	−	3.91240i	−0.104526	−	0.181044i	0.809018	−	0.587783i	$-0.199999\pi$
$467$	−2.25883	−	3.91240i	−0.104526	−	0.181044i	−0.913544	+	0.406739i	$0.866666\pi$
$468$		0			0
$469$	3.58004	−	7.95426i	0.165311	−	0.367294i
$470$	4.60536	+	1.23400i	0.212430	+	0.0569203i
$471$		0			0
$472$	−0.698223	−	1.20936i	−0.0321383	−	0.0556652i
$473$	7.57386	+	28.2660i	0.348246	+	1.29967i
$474$		0			0
$475$	−18.2711	−	68.1887i	−0.838336	−	3.12871i
$476$	13.6850	+	2.22421i	0.627253	+	0.101946i
$477$		0			0
$478$	12.1513	+	7.01556i	0.555787	+	0.320884i
$479$	22.0309	−	22.0309i	1.00662	−	1.00662i	0.00663726	−	0.999978i	$-0.497887\pi$
$479$	22.0309	−	22.0309i	1.00662	−	1.00662i	0.999978	−	0.00663726i	$-0.00211272\pi$
$480$		0			0
$481$	2.67776	+	7.07399i	0.122095	+	0.322546i
$482$		−	7.24583i		−	0.330038i
$483$		0			0
$484$	−2.93811	−	5.08896i	−0.133551	−	0.231316i
$485$		−	30.1846i		−	1.37061i
$486$		0			0
$487$	−9.25651	−	2.48028i	−0.419453	−	0.112392i	0.0429183	−	0.999079i	$-0.486334\pi$
$487$	−9.25651	−	2.48028i	−0.419453	−	0.112392i	−0.462371	+	0.886687i	$0.653001\pi$
$488$	−9.11665	+	9.11665i	−0.412691	+	0.412691i
$489$		0			0
$490$	−13.6520	+	12.0940i	−0.616735	+	0.546353i
$491$	0.411322	−	0.237477i	0.0185627	−	0.0107172i	−0.490690	−	0.871334i	$-0.663255\pi$
$491$	0.411322	−	0.237477i	0.0185627	−	0.0107172i	0.509253	+	0.860617i	$0.329922\pi$
$492$		0			0
$493$	6.55661	−	11.3564i	0.295295	−	0.511466i
$494$	−14.3741	−	6.48008i	−0.646723	−	0.291552i
$495$		0			0
$496$	0.598908	−	2.23515i	0.0268918	−	0.100361i
$497$	−3.76391	−	5.22484i	−0.168835	−	0.234366i
$498$		0			0
$499$	3.41717	+	0.915629i	0.152974	+	0.0409892i	0.334493	−	0.942398i	$-0.391435\pi$
$499$	3.41717	+	0.915629i	0.152974	+	0.0409892i	−0.181520	+	0.983387i	$0.558102\pi$
$500$	−9.03308	+	33.7119i	−0.403971	+	1.50764i
$501$		0			0
$502$	−14.0380	−	3.76148i	−0.626548	−	0.167883i
$503$	10.2816	+	5.93609i	0.458434	+	0.264677i	0.711386	−	0.702802i	$-0.248068\pi$
$503$	10.2816	+	5.93609i	0.458434	+	0.264677i	−0.252951	+	0.967479i	$0.581401\pi$
$504$		0			0
$505$	13.8789	−	51.7969i	0.617605	−	2.30493i
$506$	−10.0378	+	5.79530i	−0.446233	+	0.257633i
$507$		0			0
$508$	9.50471	−	16.4626i	0.421703	−	0.730411i
$509$	11.3092	−	3.03030i	0.501272	−	0.134315i	0.000681842	−	1.00000i	$-0.499783\pi$
$509$	11.3092	−	3.03030i	0.501272	−	0.134315i	0.500590	+	0.865684i	$0.333116\pi$
$510$		0			0
$511$	4.00449	+	5.55879i	0.177148	+	0.245906i
$512$	−11.6921	+	11.6921i	−0.516723	+	0.516723i
$513$		0			0
$514$	4.22595	+	1.13234i	0.186399	+	0.0499453i
$515$	−22.0937	+	5.91998i	−0.973563	+	0.260865i
$516$		0			0
$517$	−2.46312	−	4.26625i	−0.108328	−	0.187629i
$518$	−2.83280	−	2.31297i	−0.124466	−	0.101626i
$519$		0			0
$520$	19.5637	+	27.1922i	0.857924	+	1.19246i
$521$	−11.1559	−	6.44088i	−0.488750	−	0.282180i	0.235306	−	0.971921i	$-0.424391\pi$
$521$	−11.1559	−	6.44088i	−0.488750	−	0.282180i	−0.724056	+	0.689741i	$0.757724\pi$
$522$		0			0
$523$	−33.3427	−	19.2504i	−1.45798	−	0.841763i	−0.459064	−	0.888403i	$-0.651815\pi$
$523$	−33.3427	−	19.2504i	−1.45798	−	0.841763i	−0.998912	+	0.0466401i	$0.985149\pi$
$524$	10.9164	−	18.9077i	0.476885	−	0.825988i
$525$		0			0
$526$	0.179417	+	0.669594i	0.00782296	+	0.0291957i
$527$	−3.45793	−	3.45793i	−0.150630	−	0.150630i
$528$		0			0
$529$	9.84855	+	17.0582i	0.428198	+	0.741660i
$530$	10.1650	−	17.6063i	0.441539	−	0.764768i
$531$		0			0
$532$	−27.3564	+	2.76359i	−1.18605	+	0.119817i
$533$	−9.86018	−	1.60876i	−0.427092	−	0.0696829i
$534$		0			0
$535$	−18.9279	−	18.9279i	−0.818324	−	0.818324i
$536$	7.74621			0.334585
$537$		0			0
$538$	3.25291	+	3.25291i	0.140243	+	0.140243i
$539$	18.8101	+	1.13826i	0.810209	+	0.0490283i
$540$		0			0
$541$	0.0403040	−	0.150417i	0.00173280	−	0.00646691i	−0.965054	−	0.262051i	$-0.915601\pi$
$541$	0.0403040	−	0.150417i	0.00173280	−	0.00646691i	0.966787	+	0.255584i	$0.0822678\pi$
$542$	−14.4428	+	8.33853i	−0.620369	+	0.358170i
$543$		0			0
$544$	4.97401	+	18.5632i	0.213259	+	0.795893i
$545$	−16.4653			−0.705295
$546$		0			0
$547$	43.5439			1.86180			0.930902	−	0.365270i	$-0.119023\pi$
$547$	43.5439			1.86180			0.930902	+	0.365270i	$0.119023\pi$
$548$	6.30837	+	23.5431i	0.269480	+	1.00571i
$549$		0			0
$550$	−16.3396	+	9.43366i	−0.696722	+	0.402253i
$551$	−6.73073	+	25.1194i	−0.286739	+	1.07012i
$552$		0			0
$553$	27.5505	+	22.4949i	1.17157	+	0.956580i
$554$	−12.1649	−	12.1649i	−0.516837	−	0.516837i
$555$		0			0
$556$	22.9150			0.971811
$557$	13.9786	+	13.9786i	0.592293	+	0.592293i	0.938250	−	0.345958i	$-0.112446\pi$
$557$	13.9786	+	13.9786i	0.592293	+	0.592293i	−0.345958	+	0.938250i	$0.612446\pi$
$558$		0			0
$559$	16.1075	−	35.7298i	0.681275	−	1.51121i
$560$	15.1080	+	6.79977i	0.638428	+	0.287343i
$561$		0			0
$562$	6.06169	−	10.4991i	0.255697	−	0.442880i
$563$	9.23041	+	15.9875i	0.389016	+	0.673795i	0.992317	−	0.123718i	$-0.0394819\pi$
$563$	9.23041	+	15.9875i	0.389016	+	0.673795i	−0.603302	+	0.797513i	$0.706149\pi$
$564$		0			0
$565$	−50.2532	−	50.2532i	−2.11417	−	2.11417i
$566$	1.07388	+	4.00778i	0.0451386	+	0.168460i
$567$		0			0
$568$	2.85924	−	4.95234i	0.119971	−	0.207796i
$569$	−21.1562	−	12.2146i	−0.886915	−	0.512061i	−0.0139829	−	0.999902i	$-0.504451\pi$
$569$	−21.1562	−	12.2146i	−0.886915	−	0.512061i	−0.872932	+	0.487842i	$0.837784\pi$
$570$		0			0
$571$	4.47758	+	2.58513i	0.187381	+	0.108184i	0.590756	−	0.806850i	$-0.298830\pi$
$571$	4.47758	+	2.58513i	0.187381	+	0.108184i	−0.403375	+	0.915035i	$0.632163\pi$
$572$	2.44742	−	15.0004i	0.102332	−	0.627199i
$573$		0			0
$574$	4.51656	−	1.71284i	0.188518	−	0.0714927i
$575$	34.7514	+	60.1912i	1.44923	+	2.51015i
$576$		0			0
$577$	14.4591	−	3.87429i	0.601939	−	0.161289i	0.0550348	−	0.998484i	$-0.482473\pi$
$577$	14.4591	−	3.87429i	0.601939	−	0.161289i	0.546904	+	0.837195i	$0.315806\pi$
$578$	−3.69142	−	0.989114i	−0.153543	−	0.0411417i
$579$		0			0
$580$	17.1557	−	17.1557i	0.712350	−	0.712350i
$581$	−1.65690	−	0.745733i	−0.0687397	−	0.0309382i
$582$		0			0
$583$	−20.2897	+	5.43662i	−0.840315	+	0.225162i
$584$	−3.04199	+	5.26888i	−0.125878	+	0.218028i
$585$		0			0
$586$	−6.77876	+	3.91372i	−0.280028	+	0.161674i
$587$	−6.32266	+	23.5965i	−0.260964	+	0.973931i	0.703710	+	0.710487i	$0.251525\pi$
$587$	−6.32266	+	23.5965i	−0.260964	+	0.973931i	−0.964675	+	0.263444i	$0.915141\pi$
$588$		0			0
$589$	8.39882	+	4.84906i	0.346068	+	0.199802i
$590$	−1.49581	−	0.400801i	−0.0615815	−	0.0165007i
$591$		0			0
$592$	−0.859821	+	3.20890i	−0.0353384	+	0.131885i
$593$	−37.5507	−	10.0617i	−1.54202	−	0.413184i	−0.615105	−	0.788446i	$-0.710886\pi$
$593$	−37.5507	−	10.0617i	−1.54202	−	0.413184i	−0.926919	+	0.375262i	$0.877553\pi$
$594$		0			0
$595$	28.4090	−	20.4655i	1.16465	−	0.839004i
$596$	−1.13841	+	4.24859i	−0.0466309	+	0.174029i
$597$		0			0
$598$	15.3210	+	2.49972i	0.626521	+	0.102221i
$599$	9.62419	−	16.6696i	0.393234	−	0.681101i	−0.599640	−	0.800270i	$-0.704690\pi$
$599$	9.62419	−	16.6696i	0.393234	−	0.681101i	0.992874	+	0.119169i	$0.0380230\pi$
$600$		0			0
$601$	−29.6061	+	17.0931i	−1.20766	+	0.697243i	−0.962247	−	0.272176i	$-0.912257\pi$
$601$	−29.6061	+	17.0931i	−1.20766	+	0.697243i	−0.245412	+	0.969419i	$0.578923\pi$
$602$	1.90464	+	18.8538i	0.0776272	+	0.768422i
$603$		0			0
$604$	−9.33799	+	9.33799i	−0.379957	+	0.379957i
$605$	−14.3339	−	3.84075i	−0.582755	−	0.156149i
$606$		0			0
$607$			30.2148i			1.22638i	0.789935	+	0.613191i	$0.210114\pi$
$607$			30.2148i			1.22638i	−0.789935	+	0.613191i	$0.789886\pi$
$608$	−19.0562	−	33.0063i	−0.772832	−	1.33858i
$609$		0			0
$610$			14.2974i			0.578887i
$611$	−1.06243	+	6.51172i	−0.0429814	+	0.263436i
$612$		0			0
$613$	−5.91438	+	5.91438i	−0.238880	+	0.238880i	−0.816386	−	0.577506i	$-0.804026\pi$
$613$	−5.91438	+	5.91438i	−0.238880	+	0.238880i	0.577506	+	0.816386i	$0.304026\pi$
$614$	12.0170	+	6.93800i	0.484965	+	0.279995i
$615$		0			0
$616$	5.93403	+	15.6473i	0.239089	+	0.630449i
$617$	7.87008	+	29.3715i	0.316837	+	1.18245i	0.922267	+	0.386554i	$0.126335\pi$
$617$	7.87008	+	29.3715i	0.316837	+	1.18245i	−0.605429	+	0.795899i	$0.706998\pi$
$618$		0			0
$619$	−2.19775	−	8.20212i	−0.0883351	−	0.329671i	0.907590	−	0.419858i	$-0.137920\pi$
$619$	−2.19775	−	8.20212i	−0.0883351	−	0.329671i	−0.995925	+	0.0901871i	$0.971253\pi$
$620$	−4.52391	−	7.83564i	−0.181685	−	0.314687i
$621$		0			0
$622$	13.5266	+	3.62444i	0.542367	+	0.145327i
$623$	−12.7016	−	17.6316i	−0.508878	−	0.706393i
$624$		0			0
$625$	17.4772	+	30.2714i	0.699089	+	1.21086i
$626$	−2.40726	−	2.40726i	−0.0962136	−	0.0962136i
$627$		0			0
$628$	27.1934			1.08513
$629$	4.96437	+	4.96437i	0.197942	+	0.197942i
$630$		0			0
$631$	−32.0135	+	8.57800i	−1.27444	+	0.341485i	−0.831730	−	0.555180i	$-0.812649\pi$
$631$	−32.0135	+	8.57800i	−1.27444	+	0.341485i	−0.442709	+	0.896665i	$0.645983\pi$
$632$	−8.17494	+	30.5093i	−0.325182	+	1.21359i
$633$		0			0
$634$		−	4.16882i		−	0.165565i
$635$	−12.4247	−	46.3696i	−0.493060	−	1.84012i
$636$		0			0
$637$	−18.5396	−	17.1255i	−0.734566	−	0.678538i
$638$	6.95037			0.275168
$639$		0			0
$640$			43.8089i			1.73170i
$641$	−0.941730	+	0.543708i	−0.0371961	+	0.0214752i	−0.518483	−	0.855088i	$-0.673503\pi$
$641$	−0.941730	+	0.543708i	−0.0371961	+	0.0214752i	0.481287	+	0.876563i	$0.340170\pi$
$642$		0			0
$643$	−22.6036	+	6.05661i	−0.891398	+	0.238849i	−0.675318	−	0.737526i	$-0.735994\pi$
$643$	−22.6036	+	6.05661i	−0.891398	+	0.238849i	−0.216080	+	0.976376i	$0.569327\pi$
$644$	25.3116	−	9.59907i	0.997416	−	0.378256i
$645$		0			0
$646$	−14.6350			−0.575808
$647$	4.95844			0.194936			0.0974681	−	0.995239i	$-0.468926\pi$
$647$	4.95844			0.194936			0.0974681	+	0.995239i	$0.468926\pi$
$648$		0			0
$649$	0.800015	+	1.38567i	0.0314033	+	0.0543922i
$650$	24.9396	+	4.06907i	0.978213	+	0.159602i
$651$		0			0
$652$	35.9173	+	9.62400i	1.40663	+	0.376905i
$653$	−13.5594	+	23.4855i	−0.530619	+	0.919059i	0.468743	+	0.883335i	$0.344707\pi$
$653$	−13.5594	+	23.4855i	−0.530619	+	0.919059i	−0.999362	+	0.0357243i	$0.988626\pi$
$654$		0			0
$655$	−14.2701	−	53.2567i	−0.557578	−	2.08091i
$656$	−3.10273	−	3.10273i	−0.121141	−	0.121141i
$657$		0			0
$658$	−1.13117	−	2.98276i	−0.0440977	−	0.116280i
$659$	−2.99955	+	5.19537i	−0.116846	+	0.202383i	−0.918516	−	0.395384i	$-0.870612\pi$
$659$	−2.99955	+	5.19537i	−0.116846	+	0.202383i	0.801670	+	0.597766i	$0.203945\pi$
$660$		0			0
$661$	18.5058	−	18.5058i	0.719793	−	0.719793i	−0.248769	−	0.968563i	$-0.580026\pi$
$661$	18.5058	−	18.5058i	0.719793	−	0.719793i	0.968563	+	0.248769i	$0.0800261\pi$
$662$	3.12378	+	1.80351i	0.121409	+	0.0700955i
$663$		0			0
$664$		−	1.61356i		−	0.0626183i
$665$	−43.9152	+	53.7850i	−1.70296	+	2.08569i
$666$		0			0
$667$		−	25.6035i		−	0.991373i
$668$	31.9105	−	8.55040i	1.23466	−	0.330825i
$669$		0			0
$670$	6.07411	−	6.07411i	0.234663	−	0.234663i
$671$	10.4457	−	10.4457i	0.403253	−	0.403253i
$672$		0			0
$673$	−32.5368	+	18.7852i	−1.25420	+	0.724114i	−0.971941	−	0.235223i	$-0.924418\pi$
$673$	−32.5368	+	18.7852i	−1.25420	+	0.724114i	−0.282262	+	0.959337i	$0.591085\pi$
$674$	15.0013	−	4.01960i	0.577830	−	0.154829i
$675$		0			0
$676$	−15.2536	+	13.4795i	−0.586676	+	0.518443i
$677$	−6.13983	+	3.54483i	−0.235973	+	0.136239i	−0.613324	−	0.789831i	$-0.710168\pi$
$677$	−6.13983	+	3.54483i	−0.235973	+	0.136239i	0.377352	+	0.926070i	$0.376835\pi$
$678$		0			0
$679$	−16.3866	+	11.8047i	−0.628862	+	0.453025i
$680$	26.9273	+	15.5465i	1.03262	+	0.596181i
$681$		0			0
$682$	0.670851	−	2.50365i	0.0256882	−	0.0958697i
$683$	−0.00660203	+	0.0246391i	−0.000252620	+	0.000942790i	−0.966052	−	0.258348i	$-0.916822\pi$
$683$	−0.00660203	+	0.0246391i	−0.000252620	+	0.000942790i	0.965799	+	0.259290i	$0.0834887\pi$
$684$		0			0
$685$	53.3056	+	30.7760i	2.03670	+	1.17589i
$686$	11.9047	+	2.68162i	0.454525	+	0.102385i
$687$		0			0
$688$	14.9075	−	8.60687i	0.568344	−	0.328134i
$689$	25.6473	+	11.5622i	0.977085	+	0.440484i
$690$		0			0
$691$	11.2460	−	3.01335i	0.427816	−	0.114633i	−0.0384846	−	0.999259i	$-0.512253\pi$
$691$	11.2460	−	3.01335i	0.427816	−	0.114633i	0.466301	+	0.884626i	$0.345586\pi$
$692$	21.6309	−	12.4886i	0.822284	−	0.474746i
$693$		0			0
$694$	7.93781	−	7.93781i	0.301315	−	0.301315i
$695$	40.9190	−	40.9190i	1.55215	−	1.55215i
$696$		0			0
$697$	−8.95716	+	2.40006i	−0.339276	+	0.0909089i
$698$			11.1778i			0.423088i
$699$		0			0
$700$	41.2025	−	15.6255i	1.55731	−	0.590587i
$701$		−	23.4707i		−	0.886478i	−0.896404	−	0.443239i	$-0.853829\pi$
$701$		−	23.4707i		−	0.886478i	0.896404	−	0.443239i	$-0.146171\pi$
$702$		0			0
$703$	−12.0578	−	6.96155i	−0.454767	−	0.262560i
$704$	−1.17370	+	1.17370i	−0.0442356	+	0.0442356i
$705$		0			0
$706$	11.4356	−	19.8070i	0.430383	−	0.745445i
$707$	−33.5474	+	12.7224i	−1.26168	+	0.478475i
$708$		0			0
$709$	21.9010	+	21.9010i	0.822510	+	0.822510i	0.986467	−	0.163958i	$-0.0524261\pi$
$709$	21.9010	+	21.9010i	0.822510	+	0.822510i	−0.163958	+	0.986467i	$0.552426\pi$
$710$	−1.64129	−	6.12537i	−0.0615964	−	0.229881i
$711$		0			0
$712$	9.64868	−	16.7120i	0.361600	−	0.626309i
$713$	−9.22286	−	2.47126i	−0.345399	−	0.0925493i
$714$		0			0
$715$	−22.4158	−	31.1565i	−0.838303	−	1.16519i
$716$	−2.26199	−	3.91788i	−0.0845344	−	0.146418i
$717$		0			0
$718$	11.0017			0.410581
$719$	−18.4370			−0.687585			−0.343793	−	0.939046i	$-0.611712\pi$
$719$	−18.4370			−0.687585			−0.343793	+	0.939046i	$0.611712\pi$
$720$		0			0
$721$	11.8543	+	9.67901i	0.441479	+	0.360465i
$722$	15.9421	−	4.27166i	0.593302	−	0.158975i
$723$		0			0
$724$	−21.7207	+	12.5405i	−0.807244	+	0.466063i
$725$		−	41.6777i		−	1.54787i
$726$		0			0
$727$	−43.1639			−1.60086			−0.800430	−	0.599426i	$-0.795395\pi$
$727$	−43.1639			−1.60086			−0.800430	+	0.599426i	$0.795395\pi$
$728$	7.11108	−	21.2552i	0.263554	−	0.787771i
$729$		0			0
$730$	1.74619	+	6.51687i	0.0646294	+	0.241200i
$731$		−	36.3783i		−	1.34550i
$732$		0			0
$733$	−1.04974	+	3.91767i	−0.0387729	+	0.144702i	−0.982599	−	0.185741i	$-0.940532\pi$
$733$	−1.04974	+	3.91767i	−0.0387729	+	0.144702i	0.943826	+	0.330443i	$0.107198\pi$
$734$	−2.49191	+	0.667706i	−0.0919781	+	0.0246455i
$735$		0			0
$736$	26.5330	+	26.5330i	0.978018	+	0.978018i
$737$	−8.87551			−0.326933
$738$		0			0
$739$	30.2816	+	30.2816i	1.11393	+	1.11393i	0.992614	+	0.121312i	$0.0387101\pi$
$739$	30.2816	+	30.2816i	1.11393	+	1.11393i	0.121312	+	0.992614i	$0.461290\pi$
$740$	6.49475	+	11.2492i	0.238752	+	0.413530i
$741$		0			0
$742$	−13.5335	+	1.36717i	−0.496830	+	0.0501905i
$743$	−28.2948	−	7.58157i	−1.03804	−	0.278141i	−0.300736	−	0.953707i	$-0.597232\pi$
$743$	−28.2948	−	7.58157i	−1.03804	−	0.278141i	−0.737299	+	0.675567i	$0.763899\pi$
$744$		0			0
$745$	5.55382	+	9.61950i	0.203476	+	0.352431i
$746$	4.84710	+	18.0896i	0.177465	+	0.662308i
$747$		0			0
$748$	−3.65125	−	13.6267i	−0.133503	−	0.498240i
$749$	−2.87317	+	17.6780i	−0.104984	+	0.645940i
$750$		0			0
$751$	11.4245	+	6.59592i	0.416885	+	0.240688i	0.693744	−	0.720222i	$-0.255960\pi$
$751$	11.4245	+	6.59592i	0.416885	+	0.240688i	−0.276859	+	0.960911i	$0.589293\pi$
$752$	−2.04906	+	2.04906i	−0.0747215	+	0.0747215i
$753$		0			0
$754$	−7.20695	−	5.89180i	−0.262462	−	0.214567i
$755$			33.3495i			1.21371i
$756$		0			0
$757$	23.1688	+	40.1295i	0.842083	+	1.45853i	0.888130	+	0.459592i	$0.152004\pi$
$757$	23.1688	+	40.1295i	0.842083	+	1.45853i	−0.0460469	+	0.998939i	$0.514662\pi$
$758$		−	9.01054i		−	0.327278i
$759$		0			0
$760$	−59.5612	−	15.9594i	−2.16051	−	0.578907i
$761$	−1.13588	+	1.13588i	−0.0411757	+	0.0411757i	−0.727395	−	0.686219i	$-0.759269\pi$
$761$	−1.13588	+	1.13588i	−0.0411757	+	0.0411757i	0.686219	+	0.727395i	$0.259269\pi$
$762$		0			0
$763$	6.43932	+	8.93868i	0.233119	+	0.323602i
$764$	−28.9839	+	16.7339i	−1.04860	+	0.605410i
$765$		0			0
$766$	−9.99826	+	17.3175i	−0.361252	+	0.625706i
$767$	0.345075	−	2.11499i	0.0124599	−	0.0763678i
$768$		0			0
$769$	3.99954	−	14.9265i	0.144227	−	0.538263i	−0.855562	−	0.517701i	$-0.826788\pi$
$769$	3.99954	−	14.9265i	0.144227	−	0.538263i	0.999789	−	0.0205616i	$-0.00654542\pi$
$770$	16.9228	+	7.61658i	0.609855	+	0.274482i
$771$		0			0
$772$	−14.0721	−	3.77060i	−0.506465	−	0.135707i
$773$	4.47957	−	16.7180i	0.161119	−	0.601304i	−0.837384	−	0.546614i	$-0.815916\pi$
$773$	4.47957	−	16.7180i	0.161119	−	0.601304i	0.998503	−	0.0546899i	$-0.0174170\pi$
$774$		0			0
$775$	−15.0131	−	4.02274i	−0.539286	−	0.144501i
$776$	−15.5320	−	8.96741i	−0.557567	−	0.321911i
$777$		0			0
$778$	−3.11976	+	11.6431i	−0.111849	+	0.417426i
$779$	15.9263	−	9.19503i	0.570617	−	0.329446i
$780$		0			0
$781$	−3.27608	+	5.67433i	−0.117227	+	0.203043i
$782$	13.9178	−	3.72927i	0.497701	−	0.133358i
$783$		0			0
$784$	−2.21704	−	10.8611i	−0.0791800	−	0.387897i
$785$	48.5590	−	48.5590i	1.73314	−	1.73314i
$786$		0			0
$787$	13.8560	+	3.71270i	0.493912	+	0.132343i	0.497173	−	0.867651i	$-0.334371\pi$
$787$	13.8560	+	3.71270i	0.493912	+	0.132343i	−0.00326103	+	0.999995i	$0.501038\pi$
$788$	4.46054	−	1.19520i	0.158900	−	0.0425772i
$789$		0			0
$790$	17.5132	+	30.3338i	0.623093	+	1.07923i
$791$	−7.62823	+	46.9348i	−0.271229	+	1.66881i
$792$		0			0
$793$	−19.6861	+	1.97655i	−0.699076	+	0.0701892i
$794$	1.32377	+	0.764279i	0.0469788	+	0.0271232i
$795$		0			0
$796$	−7.65755	−	4.42109i	−0.271415	−	0.156701i
$797$	−25.7962	+	44.6803i	−0.913747	+	1.58266i	−0.105022	+	0.994470i	$0.533491\pi$
$797$	−25.7962	+	44.6803i	−0.913747	+	1.58266i	−0.808725	+	0.588187i	$0.799842\pi$
$798$		0			0
$799$	1.58501	+	5.91536i	0.0560738	+	0.209270i
$800$	43.1907	+	43.1907i	1.52702	+	1.52702i
$801$		0			0
$802$	4.42793	+	7.66940i	0.156356	+	0.270816i
$803$	3.48547	−	6.03701i	0.122999	−	0.213041i
$804$		0			0
$805$	28.0577	−	62.3396i	0.988904	−	2.19718i
$806$	−2.81795	+	2.02740i	−0.0992580	+	0.0714120i
$807$		0			0
$808$	−22.5298	−	22.5298i	−0.792595	−	0.792595i
$809$	−2.29691			−0.0807551			−0.0403776	−	0.999184i	$-0.512856\pi$
$809$	−2.29691			−0.0807551			−0.0403776	+	0.999184i	$0.512856\pi$
$810$		0			0
$811$	−8.78392	−	8.78392i	−0.308445	−	0.308445i	0.535861	−	0.844306i	$-0.319987\pi$
$811$	−8.78392	−	8.78392i	−0.308445	−	0.308445i	−0.844306	+	0.535861i	$0.819987\pi$
$812$	−16.0228	−	2.60416i	−0.562290	−	0.0913880i
$813$		0			0
$814$	−0.963106	+	3.59436i	−0.0337568	+	0.125982i
$815$	81.3226	−	46.9516i	2.84861	−	1.64464i
$816$		0			0
$817$	18.6722	+	69.6856i	0.653257	+	2.43799i
$818$	−13.4850			−0.471492
$819$		0			0
$820$	−17.1569			−0.599145
$821$	8.35682	+	31.1881i	0.291655	+	1.08847i	0.943838	+	0.330409i	$0.107187\pi$
$821$	8.35682	+	31.1881i	0.291655	+	1.08847i	−0.652183	+	0.758062i	$0.726147\pi$
$822$		0			0
$823$	−9.84808	+	5.68579i	−0.343282	+	0.198194i	−0.661723	−	0.749749i	$-0.730174\pi$
$823$	−9.84808	+	5.68579i	−0.343282	+	0.198194i	0.318440	+	0.947943i	$0.396841\pi$
$824$	−3.51748	+	13.1274i	−0.122537	+	0.457315i
$825$		0			0
$826$	0.367402	+	0.968794i	0.0127835	+	0.0337087i
$827$	20.9552	+	20.9552i	0.728685	+	0.728685i	0.970358	−	0.241673i	$-0.0776960\pi$
$827$	20.9552	+	20.9552i	0.728685	+	0.728685i	−0.241673	+	0.970358i	$0.577696\pi$
$828$		0			0
$829$	−36.1999			−1.25728			−0.628638	−	0.777698i	$-0.716387\pi$
$829$	−36.1999			−1.25728			−0.628638	+	0.777698i	$0.716387\pi$
$830$	−1.26526	−	1.26526i	−0.0439177	−	0.0439177i
$831$		0			0
$832$	2.21197	−	0.222089i	0.0766864	−	0.00769954i
$833$	−22.2207	−	7.41895i	−0.769900	−	0.257051i
$834$		0			0
$835$	41.7140	−	72.2507i	1.44357	−	2.50034i
$836$	13.9885	+	24.2288i	0.483804	+	0.837972i
$837$		0			0
$838$	13.6059	+	13.6059i	0.470008	+	0.470008i
$839$	2.14726	+	8.01368i	0.0741316	+	0.276663i	0.993035	−	0.117820i	$-0.0375905\pi$
$839$	2.14726	+	8.01368i	0.0741316	+	0.276663i	−0.918903	+	0.394483i	$0.870924\pi$
$840$		0			0
$841$	6.82335	−	11.8184i	0.235288	−	0.407531i
$842$	21.9764	+	12.6881i	0.757356	+	0.437260i
$843$		0			0
$844$	11.8291	+	6.82953i	0.407174	+	0.235082i
$845$	−3.16791	+	51.3084i	−0.108980	+	1.76506i
$846$		0			0
$847$	3.52070	+	9.28365i	0.120973	+	0.318990i
$848$	6.17812	+	10.7008i	0.212158	+	0.367468i
$849$		0			0
$850$	22.6556	−	6.07055i	0.777081	−	0.208218i
$851$	13.2408	+	3.54786i	0.453888	+	0.121619i
$852$		0			0
$853$	0.875083	−	0.875083i	0.0299623	−	0.0299623i	−0.691967	−	0.721929i	$-0.743256\pi$
$853$	0.875083	−	0.875083i	0.0299623	−	0.0299623i	0.721929	+	0.691967i	$0.243256\pi$
$854$	7.76181	−	5.59152i	0.265604	−	0.191338i
$855$		0			0
$856$	−15.3629	+	4.11647i	−0.525092	+	0.140698i
$857$	1.31117	−	2.27101i	0.0447886	−	0.0775761i	−0.842762	−	0.538286i	$-0.819072\pi$
$857$	1.31117	−	2.27101i	0.0447886	−	0.0775761i	0.887551	+	0.460710i	$0.152405\pi$
$858$		0			0
$859$	6.83308	−	3.94508i	0.233142	−	0.134605i	−0.378879	−	0.925446i	$-0.623690\pi$
$859$	6.83308	−	3.94508i	0.233142	−	0.134605i	0.612021	+	0.790842i	$0.290357\pi$
$860$	17.4201	−	65.0128i	0.594022	−	2.21692i
$861$		0			0
$862$	−4.90191	−	2.83012i	−0.166960	−	0.0963943i
$863$	21.9947	+	5.89346i	0.748708	+	0.200616i	0.612945	−	0.790126i	$-0.289985\pi$
$863$	21.9947	+	5.89346i	0.748708	+	0.200616i	0.135763	+	0.990741i	$0.456651\pi$
$864$		0			0
$865$	16.3253	−	60.9269i	0.555077	−	2.07158i
$866$	−9.69389	−	2.59747i	−0.329412	−	0.0882656i
$867$		0			0
$868$	−2.48459	+	5.52035i	−0.0843324	+	0.187373i
$869$	9.36674	−	34.9571i	0.317745	−	1.18584i
$870$		0			0
$871$	9.20315	+	7.52373i	0.311837	+	0.254932i
$872$	−4.89160	+	8.47249i	−0.165650	+	0.286915i
$873$		0			0
$874$	−24.7466	+	14.2874i	−0.837065	+	0.483280i
$875$	24.2031	−	53.7753i	0.818214	−	1.81794i
$876$		0			0
$877$	−27.2001	+	27.2001i	−0.918483	+	0.918483i	−0.996919	−	0.0784363i	$-0.975007\pi$
$877$	−27.2001	+	27.2001i	−0.918483	+	0.918483i	0.0784363	+	0.996919i	$0.475007\pi$
$878$	1.82423	+	0.488801i	0.0615648	+	0.0164962i
$879$		0			0
$880$		−	16.8577i		−	0.568274i
$881$	−20.4737	−	35.4615i	−0.689777	−	1.19473i	−0.971910	−	0.235354i	$-0.924375\pi$
$881$	−20.4737	−	35.4615i	−0.689777	−	1.19473i	0.282133	−	0.959375i	$-0.408958\pi$
$882$		0			0
$883$		−	2.58549i		−	0.0870086i	−0.999053	−	0.0435043i	$-0.986148\pi$
$883$		−	2.58549i		−	0.0870086i	0.999053	−	0.0435043i	$-0.0138522\pi$
$884$	−7.76521	+	17.2248i	−0.261172	+	0.579334i
$885$		0			0
$886$	−9.79905	+	9.79905i	−0.329206	+	0.329206i
$887$	50.4735	+	29.1409i	1.69474	+	0.978456i	0.950596	+	0.310432i	$0.100474\pi$
$887$	50.4735	+	29.1409i	1.69474	+	0.978456i	0.744140	+	0.668024i	$0.232860\pi$
$888$		0			0
$889$	−20.3141	+	24.8796i	−0.681312	+	0.834435i
$890$	−5.53863	−	20.6704i	−0.185655	−	0.692875i
$891$		0			0
$892$	4.08257	+	15.2363i	0.136694	+	0.510151i
$893$	−6.07245	−	10.5178i	−0.203207	−	0.351964i
$894$		0			0
$895$	−11.0353	−	2.95691i	−0.368870	−	0.0988385i
$896$	23.7830	−	17.1330i	0.794535	−	0.572373i
$897$		0			0
$898$	2.09964	+	3.63668i	0.0700658	+	0.121358i
$899$	4.04863	+	4.04863i	0.135030	+	0.135030i
$900$		0			0
$901$	26.1128			0.869945
$902$	−3.47544	−	3.47544i	−0.115720	−	0.115720i
$903$		0			0
$904$	−40.7882	+	10.9292i	−1.35660	+	0.363499i
$905$	−16.3931	+	61.1799i	−0.544925	+	2.03369i
$906$		0			0
$907$			36.5574i			1.21387i	0.794753	+	0.606934i	$0.207601\pi$
$907$			36.5574i			1.21387i	−0.794753	+	0.606934i	$0.792399\pi$
$908$	1.76820	+	6.59902i	0.0586798	+	0.218996i
$909$		0			0
$910$	−11.0910	−	22.2431i	−0.367662	−	0.737352i
$911$	0.732987			0.0242849			0.0121425	−	0.999926i	$-0.496135\pi$
$911$	0.732987			0.0242849			0.0121425	+	0.999926i	$0.496135\pi$
$912$		0			0
$913$			1.84880i			0.0611862i
$914$	−9.13188	+	5.27229i	−0.302056	+	0.174392i
$915$		0			0
$916$	25.5318	−	6.84122i	0.843594	−	0.226040i
$917$	−23.3312	+	28.5748i	−0.770465	+	0.943625i
$918$		0			0
$919$	33.0929			1.09163			0.545817	−	0.837905i	$-0.316219\pi$
$919$	33.0929			1.09163			0.545817	+	0.837905i	$0.316219\pi$
$920$	60.7091			2.00152
$921$		0			0
$922$	−10.2249	−	17.7100i	−0.336739	−	0.583249i
$923$	8.20712	−	3.10669i	0.270141	−	0.102258i
$924$		0			0
$925$	21.5535	+	5.77524i	0.708675	+	0.189889i
$926$	−1.02529	+	1.77586i	−0.0336932	+	0.0583583i
$927$		0			0
$928$	−5.82370	−	21.7343i	−0.191172	−	0.713464i
$929$	−5.19717	−	5.19717i	−0.170514	−	0.170514i	0.616691	−	0.787205i	$-0.288473\pi$
$929$	−5.19717	−	5.19717i	−0.170514	−	0.170514i	−0.787205	+	0.616691i	$0.788473\pi$
$930$		0			0
$931$	46.3735	+	2.80621i	1.51983	+	0.0919697i
$932$	2.75048	−	4.76396i	0.0900948	−	0.156049i
$933$		0			0
$934$	−2.10484	+	2.10484i	−0.0688723	+	0.0688723i
$935$	−30.8530	−	17.8130i	−1.00900	−	0.582547i
$936$		0			0
$937$			47.7381i			1.55954i	0.626068	+	0.779768i	$0.284663\pi$
$937$			47.7381i			1.55954i	−0.626068	+	0.779768i	$0.715337\pi$
$938$	−5.67301	−	0.922025i	−0.185230	−	0.0301052i
$939$		0			0
$940$			11.3305i			0.369561i
$941$	−35.8550	+	9.60732i	−1.16884	+	0.313190i	−0.790491	−	0.612473i	$-0.790175\pi$
$941$	−35.8550	+	9.60732i	−1.16884	+	0.313190i	−0.378349	+	0.925663i	$0.623508\pi$
$942$		0			0
$943$	−12.8027	+	12.8027i	−0.416914	+	0.416914i
$944$	0.665530	−	0.665530i	0.0216611	−	0.0216611i
$945$		0			0
$946$	16.6983	−	9.64075i	0.542908	−	0.313448i
$947$	−6.41300	+	1.71836i	−0.208394	+	0.0558391i	−0.361506	−	0.932370i	$-0.617737\pi$
$947$	−6.41300	+	1.71836i	−0.208394	+	0.0558391i	0.153112	+	0.988209i	$0.451071\pi$
$948$		0			0
$949$	−8.73168	+	3.30525i	−0.283442	+	0.107293i
$950$	−40.2828	+	23.2573i	−1.30695	+	0.754565i
$951$		0			0
$952$	−2.09098	−	20.6984i	−0.0677690	−	0.670838i
$953$	−17.6451	−	10.1874i	−0.571581	−	0.330003i	0.186199	−	0.982512i	$-0.440383\pi$
$953$	−17.6451	−	10.1874i	−0.571581	−	0.330003i	−0.757781	+	0.652509i	$0.773716\pi$
$954$		0			0
$955$	−21.8748	+	81.6378i	−0.707851	+	2.64174i
$956$	−8.63015	+	32.2081i	−0.279119	+	1.04169i
$957$		0			0
$958$	−17.7786	−	10.2645i	−0.574400	−	0.331630i
$959$	−4.13932	−	40.9746i	−0.133666	−	1.32314i
$960$		0			0
$961$	−24.9976	+	14.4324i	−0.806375	+	0.465561i
$962$	4.04558	−	2.91063i	0.130435	−	0.0938424i
$963$		0			0
$964$	16.6327	−	4.45671i	0.535702	−	0.143541i
$965$	−31.8615	+	18.3952i	−1.02566	+	0.592164i
$966$		0			0
$967$	−20.9933	+	20.9933i	−0.675099	+	0.675099i	−0.958887	−	0.283788i	$-0.908409\pi$
$967$	−20.9933	+	20.9933i	−0.675099	+	0.675099i	0.283788	+	0.958887i	$0.408409\pi$
$968$	−6.23472	+	6.23472i	−0.200391	+	0.200391i
$969$		0			0
$970$	−19.2110	+	5.14756i	−0.616827	+	0.165278i
$971$			38.6692i			1.24096i	0.784224	+	0.620478i	$0.213061\pi$
$971$			38.6692i			1.24096i	−0.784224	+	0.620478i	$0.786939\pi$
$972$		0			0
$973$	−38.2170	−	6.21134i	−1.22518	−	0.199127i
$974$			6.31428i			0.202323i
$975$		0			0
$976$	−7.52556	−	4.34488i	−0.240887	−	0.139076i
$977$	40.0093	−	40.0093i	1.28001	−	1.28001i	0.339352	−	0.940659i	$-0.389792\pi$
$977$	40.0093	−	40.0093i	1.28001	−	1.28001i	0.940659	−	0.339352i	$-0.110208\pi$
$978$		0			0
$979$	−11.0553	+	19.1484i	−0.353330	+	0.611985i
$980$	−36.1586	−	23.8992i	−1.15504	−	0.763433i
$981$		0			0
$982$	−0.221287	−	0.221287i	−0.00706156	−	0.00706156i
$983$	−5.46396	−	20.3918i	−0.174273	−	0.650396i	−0.996674	−	0.0814882i	$-0.974033\pi$
$983$	−5.46396	−	20.3918i	−0.174273	−	0.650396i	0.822401	−	0.568908i	$-0.192634\pi$
$984$		0			0
$985$	5.83090	−	10.0994i	0.185788	−	0.321794i
$986$	−8.34590	−	2.23628i	−0.265788	−	0.0712176i
$987$		0			0
$988$	6.03375	−	36.9813i	0.191959	−	1.17653i
$989$	−35.5143	−	61.5125i	−1.12929	−	1.95599i
$990$		0			0
$991$	36.0112			1.14393			0.571967	−	0.820277i	$-0.306181\pi$
$991$	36.0112			1.14393			0.571967	+	0.820277i	$0.306181\pi$
$992$	−8.39120			−0.266421
$993$		0			0
$994$	−2.68346	+	3.28656i	−0.0851143	+	0.104243i
$995$	−21.5687	+	5.77932i	−0.683774	+	0.183217i
$996$		0			0
$997$	28.2485	−	16.3093i	0.894639	−	0.516520i	0.0191818	−	0.999816i	$-0.493894\pi$
$997$	28.2485	−	16.3093i	0.894639	−	0.516520i	0.875457	+	0.483296i	$0.160561\pi$
$998$		−	2.33101i		−	0.0737867i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.gh.d.262.5		40
3.2	odd	2		273.2.cg.b.262.6	yes	40
7.5	odd	6		819.2.et.d.145.5		40
13.7	odd	12		819.2.et.d.514.5		40
21.5	even	6		273.2.bt.b.145.6	✓	40
39.20	even	12		273.2.bt.b.241.6	yes	40
91.33	even	12	inner	819.2.gh.d.397.5		40
273.215	odd	12		273.2.cg.b.124.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.145.6	✓	40	21.5	even	6
273.2.bt.b.241.6	yes	40	39.20	even	12
273.2.cg.b.124.6	yes	40	273.215	odd	12
273.2.cg.b.262.6	yes	40	3.2	odd	2
819.2.et.d.145.5		40	7.5	odd	6
819.2.et.d.514.5		40	13.7	odd	12
819.2.gh.d.262.5		40	1.1	even	1	trivial
819.2.gh.d.397.5		40	91.33	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.gh (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.170536 - 0.636449i) q^{2} +(1.35607 - 0.782925i) q^{4} +(1.02345 - 3.81958i) q^{5} +(-2.47383 + 0.938166i) q^{7} +(-1.66138 - 1.66138i) q^{8} +O(q^{10})\)	\(q+(-0.170536 - 0.636449i) q^{2} +(1.35607 - 0.782925i) q^{4} +(1.02345 - 3.81958i) q^{5} +(-2.47383 + 0.938166i) q^{7} +(-1.66138 - 1.66138i) q^{8} -2.60550 q^{10} +(1.90358 + 1.90358i) q^{11} +(-0.360197 - 3.58751i) q^{13} +(1.01897 + 1.41448i) q^{14} +(0.791792 - 1.37142i) q^{16} +(-1.67332 - 2.89827i) q^{17} +(4.69300 + 4.69300i) q^{19} +(-1.60257 - 5.98088i) q^{20} +(0.886905 - 1.53616i) q^{22} +(-5.65887 - 3.26715i) q^{23} +(-9.21158 - 5.31831i) q^{25} +(-2.22184 + 0.841048i) q^{26} +(-2.62016 + 3.20904i) q^{28} +(1.95916 + 3.39337i) q^{29} +(1.41145 - 0.378198i) q^{31} +(-5.54684 - 1.48627i) q^{32} +(-1.55924 + 1.55924i) q^{34} +(1.05155 + 10.4092i) q^{35} +(-2.02635 + 0.542959i) q^{37} +(2.18653 - 3.78718i) q^{38} +(-8.04609 + 4.64541i) q^{40} +(0.717157 - 2.67647i) q^{41} +(9.41379 + 5.43505i) q^{43} +(4.07175 + 1.09102i) q^{44} +(-1.11433 + 4.15875i) q^{46} +(-1.76755 - 0.473614i) q^{47} +(5.23969 - 4.64173i) q^{49} +(-1.81393 + 6.76967i) q^{50} +(-3.29720 - 4.58290i) q^{52} +(-3.90136 + 6.75735i) q^{53} +(9.21911 - 5.32265i) q^{55} +(5.66861 + 2.55132i) q^{56} +(1.82560 - 1.82560i) q^{58} +(0.574097 + 0.153829i) q^{59} -5.48741i q^{61} +(-0.481407 - 0.833822i) q^{62} +0.616576i q^{64} +(-14.0714 - 2.29585i) q^{65} +(-2.33126 + 2.33126i) q^{67} +(-4.53826 - 2.62016i) q^{68} +(6.44557 - 2.44439i) q^{70} +(0.629931 + 2.35094i) q^{71} +(-0.670194 - 2.50120i) q^{73} +(0.691132 + 1.19708i) q^{74} +(10.0383 + 2.68975i) q^{76} +(-6.49502 - 2.92327i) q^{77} +(-6.72164 - 11.6422i) q^{79} +(-4.42790 - 4.42790i) q^{80} -1.82574 q^{82} +(0.485609 + 0.485609i) q^{83} +(-12.7827 + 3.42512i) q^{85} +(1.85375 - 6.91827i) q^{86} -6.32514i q^{88} +(2.12574 + 7.93338i) q^{89} +(4.25675 + 8.53698i) q^{91} -10.2317 q^{92} +1.20573i q^{94} +(22.7283 - 13.1222i) q^{95} +(7.37323 - 1.97565i) q^{97} +(-3.84778 - 2.54321i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7}+O(q^{10}) \) 40 * q - 8 * q^7	\( 40 q - 8 q^{7} - 4 q^{11} + 18 q^{14} + 32 q^{16} - 4 q^{17} + 14 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} + 24 q^{25} + 32 q^{26} + 16 q^{28} - 8 q^{29} + 14 q^{31} + 26 q^{32} - 24 q^{34} - 26 q^{35} + 36 q^{37} + 8 q^{38} - 30 q^{40} + 2 q^{41} - 66 q^{43} + 32 q^{44} - 26 q^{46} + 4 q^{47} - 14 q^{49} + 20 q^{50} + 2 q^{52} + 8 q^{53} - 42 q^{55} - 46 q^{56} + 24 q^{58} - 14 q^{59} - 24 q^{62} - 28 q^{65} - 44 q^{67} + 18 q^{68} - 4 q^{70} + 6 q^{71} + 14 q^{73} + 20 q^{74} - 64 q^{76} - 24 q^{77} - 20 q^{80} + 48 q^{82} + 12 q^{83} + 2 q^{85} + 60 q^{86} + 2 q^{89} - 14 q^{91} - 236 q^{92} - 24 q^{95} - 62 q^{97} + 88 q^{98}+O(q^{100}) \) 40 * q - 8 * q^7 - 4 * q^11 + 18 * q^14 + 32 * q^16 - 4 * q^17 + 14 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 + 24 * q^25 + 32 * q^26 + 16 * q^28 - 8 * q^29 + 14 * q^31 + 26 * q^32 - 24 * q^34 - 26 * q^35 + 36 * q^37 + 8 * q^38 - 30 * q^40 + 2 * q^41 - 66 * q^43 + 32 * q^44 - 26 * q^46 + 4 * q^47 - 14 * q^49 + 20 * q^50 + 2 * q^52 + 8 * q^53 - 42 * q^55 - 46 * q^56 + 24 * q^58 - 14 * q^59 - 24 * q^62 - 28 * q^65 - 44 * q^67 + 18 * q^68 - 4 * q^70 + 6 * q^71 + 14 * q^73 + 20 * q^74 - 64 * q^76 - 24 * q^77 - 20 * q^80 + 48 * q^82 + 12 * q^83 + 2 * q^85 + 60 * q^86 + 2 * q^89 - 14 * q^91 - 236 * q^92 - 24 * q^95 - 62 * q^97 + 88 * q^98

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