LMFDB - Embedded newform 585.2.bs.a.334.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(289,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("585.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bs (of order $6$, degree $2$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 8x^{10} + 54x^{8} - 78x^{6} + 92x^{4} - 10x^{2} + 1 $ x^12 - 8x^10 + 54x^8 - 78x^6 + 92x^4 - 10*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			334.1
Root			$-2.20467 + 1.27287i$ of defining polynomial
Character	$\chi$	$=$	585.334
Dual form			585.2.bs.a.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.20467 - 1.27287i) q^{2} +(2.24039 + 3.88048i) q^{4} +(0.817544 + 2.08125i) q^{5} +(-2.54486 + 1.46928i) q^{7} -6.31544i q^{8} +O(q^{10})$	\(q+(-2.20467 - 1.27287i) q^{2} +(2.24039 + 3.88048i) q^{4} +(0.817544 + 2.08125i) q^{5} +(-2.54486 + 1.46928i) q^{7} -6.31544i q^{8} +(0.846746 - 5.62912i) q^{10} +(-0.317544 + 0.550003i) q^{11} +(3.60484 - 0.0716710i) q^{13} +7.48079 q^{14} +(-3.55794 + 6.16253i) q^{16} +(1.05998 - 0.611979i) q^{17} +(0.682456 + 1.18205i) q^{19} +(-6.24464 + 7.83529i) q^{20} +(1.40016 - 0.808385i) q^{22} +(-1.86449 - 1.07646i) q^{23} +(-3.66324 + 3.40304i) q^{25} +(-8.03872 - 4.43048i) q^{26} +(-11.4030 - 6.58351i) q^{28} +(-1.50000 + 2.59808i) q^{29} -8.96157 q^{31} +(4.74954 - 2.74215i) q^{32} -3.11588 q^{34} +(-5.13847 - 4.09531i) q^{35} +(-1.05998 - 0.611979i) q^{37} -3.47471i q^{38} +(13.1440 - 5.16315i) q^{40} +(-4.98079 + 8.62698i) q^{41} +(1.18412 - 0.683650i) q^{43} -2.84570 q^{44} +(2.74039 + 4.74650i) q^{46} +6.16379i q^{47} +(0.817544 - 1.41603i) q^{49} +(12.4079 - 2.83976i) q^{50} +(8.35437 + 13.8279i) q^{52} +0.642285i q^{53} +(-1.40430 - 0.211239i) q^{55} +(9.27912 + 16.0719i) q^{56} +(6.61402 - 3.81861i) q^{58} +(-3.79833 - 6.57890i) q^{59} +(1.13509 + 1.96603i) q^{61} +(19.7574 + 11.4069i) q^{62} +0.270178 q^{64} +(3.09628 + 7.44399i) q^{65} +(-6.95421 - 4.01502i) q^{67} +(4.74954 + 2.74215i) q^{68} +(6.11588 + 15.5694i) q^{70} +(1.31754 + 2.28205i) q^{71} +10.3263i q^{73} +(1.55794 + 2.69843i) q^{74} +(-3.05794 + 5.29650i) q^{76} -1.86624i q^{77} -1.03843 q^{79} +(-15.7346 - 2.36683i) q^{80} +(21.9620 - 12.6798i) q^{82} +11.8452i q^{83} +(2.14026 + 1.70576i) q^{85} -3.48079 q^{86} +(3.47351 + 2.00543i) q^{88} +(6.27912 - 10.8758i) q^{89} +(-9.06851 + 5.47890i) q^{91} -9.64680i q^{92} +(7.84570 - 13.5891i) q^{94} +(-1.90220 + 2.38674i) q^{95} +(-12.8031 + 7.39190i) q^{97} +(-3.60484 + 2.08125i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 6 q^{5}+O(q^{10}) $ 12 * q + 4 * q^4 + 6 * q^5	$ 12 q + 4 q^{4} + 6 q^{5} + 7 q^{10} + 44 q^{14} - 16 q^{16} + 12 q^{19} + q^{20} - 2 q^{25} - 24 q^{26} - 18 q^{29} - 16 q^{31} + 16 q^{34} - 10 q^{35} + 70 q^{40} - 14 q^{41} + 4 q^{44} + 10 q^{46} + 6 q^{49} + 31 q^{50} - 26 q^{55} + 16 q^{56} + 4 q^{59} + 6 q^{61} - 12 q^{64} - 23 q^{65} + 20 q^{70} + 12 q^{71} - 8 q^{74} - 10 q^{76} - 104 q^{79} - 33 q^{80} + 21 q^{85} + 4 q^{86} - 20 q^{89} - 44 q^{91} + 56 q^{94} - 20 q^{95}+O(q^{100}) $ 12 * q + 4 * q^4 + 6 * q^5 + 7 * q^10 + 44 * q^14 - 16 * q^16 + 12 * q^19 + q^20 - 2 * q^25 - 24 * q^26 - 18 * q^29 - 16 * q^31 + 16 * q^34 - 10 * q^35 + 70 * q^40 - 14 * q^41 + 4 * q^44 + 10 * q^46 + 6 * q^49 + 31 * q^50 - 26 * q^55 + 16 * q^56 + 4 * q^59 + 6 * q^61 - 12 * q^64 - 23 * q^65 + 20 * q^70 + 12 * q^71 - 8 * q^74 - 10 * q^76 - 104 * q^79 - 33 * q^80 + 21 * q^85 + 4 * q^86 - 20 * q^89 - 44 * q^91 + 56 * q^94 - 20 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.20467	−	1.27287i	−1.55894	−	0.900055i	−0.997359	−	0.0726333i	$-0.976860\pi$
$2$	−2.20467	−	1.27287i	−1.55894	−	0.900055i	−0.561582	−	0.827421i	$-0.689807\pi$
$3$		0			0
$3$		0			0
$4$	2.24039	+	3.88048i	1.12020	+	1.94024i
$5$	0.817544	+	2.08125i	0.365617	+	0.930765i
$5$	0.817544	+	2.08125i	0.365617	+	0.930765i
$6$		0			0
$7$	−2.54486	+	1.46928i	−0.961867	+	0.555334i	−0.896747	−	0.442543i	$-0.854076\pi$
$7$	−2.54486	+	1.46928i	−0.961867	+	0.555334i	−0.0651198	+	0.997877i	$0.520743\pi$
$8$		−	6.31544i		−	2.23284i
$9$		0			0
$10$	0.846746	−	5.62912i	0.267765	−	1.78008i
$11$	−0.317544	+	0.550003i	−0.0957433	+	0.165832i	−0.909919	−	0.414787i	$-0.863856\pi$
$11$	−0.317544	+	0.550003i	−0.0957433	+	0.165832i	0.814175	+	0.580619i	$0.197189\pi$
$12$		0			0
$13$	3.60484	−	0.0716710i	0.999802	−	0.0198779i
$13$	3.60484	−	0.0716710i	0.999802	−	0.0198779i
$14$	7.48079			1.99932
$15$		0			0
$16$	−3.55794	+	6.16253i	−0.889484	+	1.54063i
$17$	1.05998	−	0.611979i	0.257082	−	0.148427i	−0.365920	−	0.930646i	$-0.619246\pi$
$17$	1.05998	−	0.611979i	0.257082	−	0.148427i	0.623003	+	0.782220i	$0.285912\pi$
$18$		0			0
$19$	0.682456	+	1.18205i	0.156566	+	0.271180i	0.933628	−	0.358244i	$-0.116624\pi$
$19$	0.682456	+	1.18205i	0.156566	+	0.271180i	−0.777062	+	0.629424i	$0.783291\pi$
$20$	−6.24464	+	7.83529i	−1.39634	+	1.75202i
$21$		0			0
$22$	1.40016	−	0.808385i	0.298516	−	0.172348i
$23$	−1.86449	−	1.07646i	−0.388773	−	0.224458i	0.292856	−	0.956157i	$-0.405394\pi$
$23$	−1.86449	−	1.07646i	−0.388773	−	0.224458i	−0.681628	+	0.731699i	$0.738728\pi$
$24$		0			0
$25$	−3.66324	+	3.40304i	−0.732648	+	0.680607i
$26$	−8.03872	−	4.43048i	−1.57652	−	0.868888i
$27$		0			0
$28$	−11.4030	−	6.58351i	−2.15496	−	1.24417i
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$	−8.96157			−1.60955			−0.804773	−	0.593583i	$-0.797713\pi$
$31$	−8.96157			−1.60955			−0.804773	+	0.593583i	$0.797713\pi$
$32$	4.74954	−	2.74215i	0.839607	−	0.484747i
$33$		0			0
$34$	−3.11588			−0.534368
$35$	−5.13847	−	4.09531i	−0.868561	−	0.692233i
$36$		0			0
$37$	−1.05998	−	0.611979i	−0.174259	−	0.100609i	0.410333	−	0.911936i	$-0.365412\pi$
$37$	−1.05998	−	0.611979i	−0.174259	−	0.100609i	−0.584593	+	0.811327i	$0.698746\pi$
$38$		−	3.47471i		−	0.563672i
$39$		0			0
$40$	13.1440	−	5.16315i	2.07825	−	0.816366i
$41$	−4.98079	+	8.62698i	−0.777868	+	1.34731i	0.155300	+	0.987867i	$0.450366\pi$
$41$	−4.98079	+	8.62698i	−0.777868	+	1.34731i	−0.933168	+	0.359440i	$0.882968\pi$
$42$		0			0
$43$	1.18412	−	0.683650i	0.180576	−	0.104256i	−0.406987	−	0.913434i	$-0.633421\pi$
$43$	1.18412	−	0.683650i	0.180576	−	0.104256i	0.587563	+	0.809178i	$0.300087\pi$
$44$	−2.84570			−0.429005
$45$		0			0
$46$	2.74039	+	4.74650i	0.404049	+	0.699833i
$47$			6.16379i			0.899081i	0.893260	+	0.449540i	$0.148412\pi$
$47$			6.16379i			0.899081i	−0.893260	+	0.449540i	$0.851588\pi$
$48$		0			0
$49$	0.817544	−	1.41603i	0.116792	−	0.202290i
$50$	12.4079	−	2.83976i	1.75474	−	0.401603i
$51$		0			0
$52$	8.35437	+	13.8279i	1.15854	+	1.91759i
$53$			0.642285i			0.0882246i	0.999027	+	0.0441123i	$0.0140459\pi$
$53$			0.642285i			0.0882246i	−0.999027	+	0.0441123i	$0.985954\pi$
$54$		0			0
$55$	−1.40430	−	0.211239i	−0.189356	−	0.0284834i
$56$	9.27912	+	16.0719i	1.23997	+	2.14770i
$57$		0			0
$58$	6.61402	−	3.81861i	0.868464	−	0.501408i
$59$	−3.79833	−	6.57890i	−0.494501	−	0.856500i	0.505479	−	0.862839i	$-0.331316\pi$
$59$	−3.79833	−	6.57890i	−0.494501	−	0.856500i	−0.999980	+	0.00633858i	$0.997982\pi$
$60$		0			0
$61$	1.13509	+	1.96603i	0.145333	+	0.251725i	0.929497	−	0.368829i	$-0.120241\pi$
$61$	1.13509	+	1.96603i	0.145333	+	0.251725i	−0.784164	+	0.620554i	$0.786908\pi$
$62$	19.7574	+	11.4069i	2.50919	+	1.44868i
$63$		0			0
$64$	0.270178			0.0337722
$65$	3.09628	+	7.44399i	0.384046	+	0.923314i
$66$		0			0
$67$	−6.95421	−	4.01502i	−0.849592	−	0.490512i	0.0109212	−	0.999940i	$-0.496524\pi$
$67$	−6.95421	−	4.01502i	−0.849592	−	0.490512i	−0.860513	+	0.509428i	$0.829857\pi$
$68$	4.74954	+	2.74215i	0.575966	+	0.332534i
$69$		0			0
$70$	6.11588	+	15.5694i	0.730987	+	1.86090i
$71$	1.31754	+	2.28205i	0.156364	+	0.270830i	0.933555	−	0.358435i	$-0.116689\pi$
$71$	1.31754	+	2.28205i	0.156364	+	0.270830i	−0.777191	+	0.629265i	$0.783356\pi$
$72$		0			0
$73$			10.3263i			1.20860i	0.796756	+	0.604301i	$0.206547\pi$
$73$			10.3263i			1.20860i	−0.796756	+	0.604301i	$0.793453\pi$
$74$	1.55794	+	2.69843i	0.181107	+	0.313686i
$75$		0			0
$76$	−3.05794	+	5.29650i	−0.350770	+	0.607551i
$77$		−	1.86624i		−	0.212678i
$78$		0			0
$79$	−1.03843			−0.116832			−0.0584161	−	0.998292i	$-0.518605\pi$
$79$	−1.03843			−0.116832			−0.0584161	+	0.998292i	$0.518605\pi$
$80$	−15.7346	−	2.36683i	−1.75918	−	0.264620i
$81$		0			0
$82$	21.9620	−	12.6798i	2.42530	−	1.40025i
$83$			11.8452i			1.30018i	0.759855	+	0.650092i	$0.225270\pi$
$83$			11.8452i			1.30018i	−0.759855	+	0.650092i	$0.774730\pi$
$84$		0			0
$85$	2.14026	+	1.70576i	0.232144	+	0.185016i
$86$	−3.48079			−0.375343
$87$		0			0
$88$	3.47351	+	2.00543i	0.370277	+	0.213780i
$89$	6.27912	−	10.8758i	0.665585	−	1.15283i	−0.313541	−	0.949575i	$-0.601515\pi$
$89$	6.27912	−	10.8758i	0.665585	−	1.15283i	0.979126	−	0.203253i	$-0.0651513\pi$
$90$		0			0
$91$	−9.06851	+	5.47890i	−0.950638	+	0.574344i
$92$		−	9.64680i		−	1.00575i
$93$		0			0
$94$	7.84570	−	13.5891i	0.809222	−	1.40161i
$95$	−1.90220	+	2.38674i	−0.195162	+	0.244874i
$96$		0			0
$97$	−12.8031	+	7.39190i	−1.29996	+	0.750534i	−0.980397	−	0.197031i	$-0.936870\pi$
$97$	−12.8031	+	7.39190i	−1.29996	+	0.750534i	−0.319565	+	0.947564i	$0.603537\pi$
$98$	−3.60484	+	2.08125i	−0.364144	+	0.210238i
$99$		0			0
$100$	−21.4125	−	6.59098i	−2.14125	−	0.659098i
$101$	6.61588	−	11.4590i	0.658304	−	1.14022i	−0.322750	−	0.946484i	$-0.604607\pi$
$101$	6.61588	−	11.4590i	0.658304	−	1.14022i	0.981054	−	0.193732i	$-0.0620593\pi$
$102$		0			0
$103$		−	10.9686i		−	1.08077i	−0.841419	−	0.540383i	$-0.818279\pi$
$103$		−	10.9686i		−	1.08077i	0.841419	−	0.540383i	$-0.181721\pi$
$104$	−0.452633	−	22.7661i	−0.0443843	−	2.23240i
$105$		0			0
$106$	0.817544	−	1.41603i	0.0794069	−	0.137537i
$107$	−9.24360	−	5.33680i	−0.893613	−	0.515928i	−0.0184903	−	0.999829i	$-0.505886\pi$
$107$	−9.24360	−	5.33680i	−0.893613	−	0.515928i	−0.875123	+	0.483901i	$0.839219\pi$
$108$		0			0
$109$	3.27018			0.313226			0.156613	−	0.987660i	$-0.449942\pi$
$109$	3.27018			0.313226			0.156613	+	0.987660i	$0.449942\pi$
$110$	2.82715	+	2.25321i	0.269558	+	0.214835i
$111$		0			0
$112$		−	20.9104i		−	1.97584i
$113$	−4.78895	+	2.76490i	−0.450507	+	0.260100i	−0.708044	−	0.706168i	$-0.750422\pi$
$113$	−4.78895	+	2.76490i	−0.450507	+	0.260100i	0.257537	+	0.966268i	$0.417089\pi$
$114$		0			0
$115$	0.716091	−	4.76053i	0.0667759	−	0.443922i
$116$	−13.4424			−1.24809
$117$		0			0
$118$			19.3391i			1.78031i
$119$	−1.79833	+	3.11480i	−0.164853	+	0.285533i
$120$		0			0
$121$	5.29833	+	9.17698i	0.481666	+	0.834271i
$122$		−	5.77928i		−	0.523231i
$123$		0			0
$124$	−20.0774	−	34.7752i	−1.80301	−	3.12290i
$125$	−10.0774	−	4.84201i	−0.901354	−	0.433082i
$126$		0			0
$127$	14.9231	+	8.61586i	1.32421	+	0.764534i	0.984397	−	0.175959i	$-0.0563027\pi$
$127$	14.9231	+	8.61586i	1.32421	+	0.764534i	0.339813	+	0.940493i	$0.389636\pi$
$128$	−10.0947	−	5.82819i	−0.892256	−	0.515144i
$129$		0			0
$130$	2.64894	−	20.3527i	0.232327	−	1.78505i
$131$	−10.0000			−0.873704			−0.436852	−	0.899533i	$-0.643907\pi$
$131$	−10.0000			−0.873704			−0.436852	+	0.899533i	$0.643907\pi$
$132$		0			0
$133$	−3.47351	−	2.00543i	−0.301191	−	0.173893i
$134$	10.2212	+	17.7036i	0.882975	+	1.52936i
$135$		0			0
$136$	−3.86491	−	6.69422i	−0.331413	−	0.574025i
$137$	7.51044	−	4.33616i	0.641661	−	0.370463i	−0.143593	−	0.989637i	$-0.545866\pi$
$137$	7.51044	−	4.33616i	0.641661	−	0.370463i	0.785254	+	0.619174i	$0.212532\pi$
$138$		0			0
$139$	7.16324	+	12.4071i	0.607578	+	1.05236i	0.991638	+	0.129048i	$0.0411922\pi$
$139$	7.16324	+	12.4071i	0.607578	+	1.05236i	−0.384060	+	0.923308i	$0.625474\pi$
$140$	4.37953	−	29.1148i	0.370137	−	2.46065i
$141$		0			0
$142$		−	6.70825i		−	0.562944i
$143$	−1.10528	+	2.00543i	−0.0924279	+	0.167703i
$144$		0			0
$145$	−6.63357	−	0.997839i	−0.550888	−	0.0828660i
$146$	13.1440	−	22.7661i	1.08781	−	1.88414i
$147$		0			0
$148$		−	5.48429i		−	0.450806i
$149$	8.57745	+	14.8566i	0.702692	+	1.21710i	0.967518	+	0.252802i	$0.0813521\pi$
$149$	8.57745	+	14.8566i	0.702692	+	1.21710i	−0.264826	+	0.964296i	$0.585315\pi$
$150$		0			0
$151$	−21.3828			−1.74011			−0.870053	−	0.492957i	$-0.835916\pi$
$151$	−21.3828			−1.74011			−0.870053	+	0.492957i	$0.835916\pi$
$152$	7.46515	−	4.31000i	0.605503	−	0.349587i
$153$		0			0
$154$	−2.37548	+	4.11446i	−0.191422	+	0.331552i
$155$	−7.32648	−	18.6513i	−0.588477	−	1.49811i
$156$		0			0
$157$		−	18.3646i		−	1.46566i	−0.680413	−	0.732829i	$-0.738200\pi$
$157$		−	18.3646i		−	1.46566i	0.680413	−	0.732829i	$-0.261800\pi$
$158$	2.28939	+	1.32178i	0.182134	+	0.105155i
$159$		0			0
$160$	9.59006	+	7.64317i	0.758161	+	0.604245i
$161$	6.32648			0.498597
$162$		0			0
$163$	3.47351	−	2.00543i	0.272066	−	0.157078i	−0.357760	−	0.933814i	$-0.616459\pi$
$163$	3.47351	−	2.00543i	0.272066	−	0.157078i	0.629826	+	0.776736i	$0.283126\pi$
$164$	−44.6357			−3.48546
$165$		0			0
$166$	15.0774	−	26.1149i	1.17024	−	2.02691i
$167$	2.54486	+	1.46928i	0.196927	+	0.113696i	0.595221	−	0.803562i	$-0.297064\pi$
$167$	2.54486	+	1.46928i	0.196927	+	0.113696i	−0.398294	+	0.917258i	$0.630398\pi$
$168$		0			0
$169$	12.9897	−	0.516725i	0.999210	−	0.0397480i
$170$	−2.54737	−	6.48493i	−0.195374	−	0.497371i
$171$		0			0
$172$	5.30577	+	3.06329i	0.404561	+	0.233574i
$173$	1.18412	−	0.683650i	0.0900267	−	0.0519769i	−0.454311	−	0.890843i	$-0.650114\pi$
$173$	1.18412	−	0.683650i	0.0900267	−	0.0519769i	0.544337	+	0.838866i	$0.316781\pi$
$174$		0			0
$175$	4.32244	−	14.0426i	0.326746	−	1.06152i
$176$	−2.25961	−	3.91375i	−0.170324	−	0.295010i
$177$		0			0
$178$	−27.6868	+	15.9850i	−2.07522	+	1.19813i
$179$	−3.89306	+	6.74299i	−0.290981	+	0.503994i	−0.974042	−	0.226367i	$-0.927315\pi$
$179$	−3.89306	+	6.74299i	−0.290981	+	0.503994i	0.683061	+	0.730362i	$0.260648\pi$
$180$		0			0
$181$	−3.86684			−0.287420			−0.143710	−	0.989620i	$-0.545903\pi$
$181$	−3.86684			−0.287420			−0.143710	+	0.989620i	$0.545903\pi$
$182$	26.9670	−	0.536155i	1.99893	−	0.0397425i
$183$		0			0
$184$	−6.79833	+	11.7751i	−0.501180	+	0.868069i
$185$	0.407104	−	2.70640i	0.0299309	−	0.198979i
$186$		0			0
$187$			0.777322i			0.0568434i
$188$	−23.9184	+	13.8093i	−1.74443	+	1.00715i
$189$		0			0
$190$	7.23175	−	2.84073i	0.524646	−	0.206088i
$191$	2.47185	+	4.28136i	0.178857	+	0.309789i	0.941489	−	0.337043i	$-0.109427\pi$
$191$	2.47185	+	4.28136i	0.178857	+	0.309789i	−0.762633	+	0.646832i	$0.776094\pi$
$192$		0			0
$193$	4.29240	+	2.47822i	0.308974	+	0.178386i	0.646467	−	0.762942i	$-0.276246\pi$
$193$	4.29240	+	2.47822i	0.308974	+	0.178386i	−0.337493	+	0.941328i	$0.609579\pi$
$194$	37.6357			2.70208
$195$		0			0
$196$	7.32648			0.523320
$197$	5.84174	+	3.37273i	0.416207	+	0.240297i	0.693453	−	0.720502i	$-0.256088\pi$
$197$	5.84174	+	3.37273i	0.416207	+	0.240297i	−0.277246	+	0.960799i	$0.589422\pi$
$198$		0			0
$199$	2.58772	+	4.48207i	0.183439	+	0.317725i	0.943049	−	0.332653i	$-0.107944\pi$
$199$	2.58772	+	4.48207i	0.183439	+	0.317725i	−0.759611	+	0.650378i	$0.774610\pi$
$200$	21.4917	+	23.1350i	1.51969	+	1.63589i
$201$		0			0
$202$	−29.1717	+	16.8423i	−2.05251	+	1.18502i
$203$		−	8.81566i		−	0.618738i
$204$		0			0
$205$	−22.0269	−	3.31335i	−1.53843	−	0.231414i
$206$	−13.9616	+	24.1822i	−0.972749	+	1.68485i
$207$		0			0
$208$	−12.3841	+	22.4699i	−0.858684	+	1.55801i
$209$	−0.866840			−0.0599606
$210$		0			0
$211$	7.00894	−	12.1398i	0.482515	−	0.835741i	−0.517283	−	0.855814i	$-0.673057\pi$
$211$	7.00894	−	12.1398i	0.482515	−	0.835741i	0.999799	+	0.0200732i	$0.00638994\pi$
$212$	−2.49237	+	1.43897i	−0.171177	+	0.0988289i
$213$		0			0
$214$	13.5861	+	23.5318i	0.928726	+	1.60860i
$215$	2.39092	+	1.90553i	0.163059	+	0.129956i
$216$		0			0
$217$	22.8060	−	13.1670i	1.54817	−	0.893836i
$218$	−7.20968	−	4.16251i	−0.488301	−	0.281921i
$219$		0			0
$220$	−2.32648	−	5.92262i	−0.156852	−	0.399303i
$221$	3.77719	−	2.28205i	0.254081	−	0.153508i
$222$		0			0
$223$	−0.00719226	−	0.00415245i	−0.000481629	−	0.000278069i	0.499759	−	0.866164i	$-0.333422\pi$
$223$	−0.00719226	−	0.00415245i	−0.000481629	−	0.000278069i	−0.500241	+	0.865886i	$0.666755\pi$
$224$	−8.05794	+	13.9568i	−0.538394	+	0.932525i
$225$		0			0
$226$	14.0774			0.936418
$227$	−9.75454	+	5.63179i	−0.647431	+	0.373795i	−0.787471	−	0.616351i	$-0.788610\pi$
$227$	−9.75454	+	5.63179i	−0.647431	+	0.373795i	0.140040	+	0.990146i	$0.455277\pi$
$228$		0			0
$229$	16.5404			1.09302			0.546509	−	0.837453i	$-0.315957\pi$
$229$	16.5404			1.09302			0.546509	+	0.837453i	$0.315957\pi$
$230$	−7.63828	+	9.58393i	−0.503653	+	0.631946i
$231$		0			0
$232$	16.4080	+	9.47315i	1.07724	+	0.621943i
$233$			6.94941i			0.455271i	0.973746	+	0.227636i	$0.0730995\pi$
$233$			6.94941i			0.455271i	−0.973746	+	0.227636i	$0.926900\pi$
$234$		0			0
$235$	−12.8284	+	5.03917i	−0.836833	+	0.328719i
$236$	17.0195	−	29.4787i	1.10788	−	1.91890i
$237$		0			0
$238$	7.92947	−	4.57808i	0.513991	−	0.296753i
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$		0			0
$241$	−9.88605	−	17.1231i	−0.636817	−	1.10300i	−0.986127	−	0.165992i	$-0.946917\pi$
$241$	−9.88605	−	17.1231i	−0.636817	−	1.10300i	0.349310	−	0.937007i	$-0.386416\pi$
$242$		−	26.9763i		−	1.73410i
$243$		0			0
$244$	−5.08609	+	8.80937i	−0.325604	+	0.563962i
$245$	3.61549	+	0.543852i	0.230985	+	0.0347454i
$246$		0			0
$247$	2.54486	+	4.21218i	0.161926	+	0.268015i
$248$			56.5962i			3.59386i
$249$		0			0
$250$	16.0543	+	23.5023i	1.01536	+	1.48642i
$251$	1.83676	+	3.18136i	0.115935	+	0.200806i	0.918153	−	0.396226i	$-0.129680\pi$
$251$	1.83676	+	3.18136i	0.115935	+	0.200806i	−0.802218	+	0.597031i	$0.796347\pi$
$252$		0			0
$253$	1.18412	−	0.683650i	0.0744447	−	0.0429807i
$254$	−21.9337	−	37.9903i	−1.37624	−	2.38372i
$255$		0			0
$256$	14.5669	+	25.2306i	0.910430	+	1.57691i
$257$	−11.4877	−	6.63242i	−0.716583	−	0.413719i	0.0969108	−	0.995293i	$-0.469104\pi$
$257$	−11.4877	−	6.63242i	−0.716583	−	0.413719i	−0.813494	+	0.581574i	$0.802437\pi$
$258$		0			0
$259$	3.59666			0.223486
$260$	−21.9493	+	28.6925i	−1.36124	+	1.77943i
$261$		0			0
$262$	22.0467	+	12.7287i	1.36205	+	0.786381i
$263$	26.2150	+	15.1352i	1.61649	+	0.933279i	0.987819	+	0.155605i	$0.0497327\pi$
$263$	26.2150	+	15.1352i	1.61649	+	0.933279i	0.628667	+	0.777674i	$0.283601\pi$
$264$		0			0
$265$	−1.33676	+	0.525096i	−0.0821164	+	0.0322564i
$266$	5.10530	+	8.84265i	0.313026	+	0.542177i
$267$		0			0
$268$		−	35.9809i		−	2.19788i
$269$	11.1248	+	19.2687i	0.678292	+	1.17484i	0.975495	+	0.220022i	$0.0706129\pi$
$269$	11.1248	+	19.2687i	0.678292	+	1.17484i	−0.297203	+	0.954814i	$0.596054\pi$
$270$		0			0
$271$	5.91421	−	10.2437i	0.359262	−	0.622261i	−0.628575	−	0.777749i	$-0.716362\pi$
$271$	5.91421	−	10.2437i	0.359262	−	0.622261i	0.987838	+	0.155488i	$0.0496950\pi$
$272$			8.70953i			0.528093i
$273$		0			0
$274$	−22.0774			−1.33375
$275$	−0.708438	−	3.09541i	−0.0427204	−	0.186660i
$276$		0			0
$277$	−14.5363	+	8.39254i	−0.873402	+	0.504259i	−0.868477	−	0.495729i	$-0.834901\pi$
$277$	−14.5363	+	8.39254i	−0.873402	+	0.504259i	−0.00492452	+	0.999988i	$0.501568\pi$
$278$		−	36.4715i		−	2.18741i
$279$		0			0
$280$	−25.8636	+	32.4517i	−1.54565	+	1.93936i
$281$	10.5967			0.632144			0.316072	−	0.948735i	$-0.397636\pi$
$281$	10.5967			0.632144			0.316072	+	0.948735i	$0.397636\pi$
$282$		0			0
$283$	7.63458	+	4.40783i	0.453829	+	0.262018i	0.709446	−	0.704760i	$-0.248945\pi$
$283$	7.63458	+	4.40783i	0.453829	+	0.262018i	−0.255617	+	0.966778i	$0.582279\pi$
$284$	−5.90364	+	10.2254i	−0.350316	+	0.606766i
$285$		0			0
$286$	4.98943	−	3.01445i	0.295031	−	0.178248i
$287$		−	29.2726i		−	1.72791i
$288$		0			0
$289$	−7.75096	+	13.4251i	−0.455939	+	0.789710i
$290$	13.3548	+	10.6436i	0.784218	+	0.625013i
$291$		0			0
$292$	−40.0709	+	23.1350i	−2.34497	+	1.35387i
$293$	24.4675	−	14.1263i	1.42940	−	0.825267i	0.432331	−	0.901715i	$-0.357691\pi$
$293$	24.4675	−	14.1263i	1.42940	−	0.825267i	0.997074	+	0.0764476i	$0.0243578\pi$
$294$		0			0
$295$	10.5871	−	13.2838i	0.616403	−	0.773415i
$296$	−3.86491	+	6.69422i	−0.224643	+	0.389094i
$297$		0			0
$298$		−	43.6719i		−	2.52984i
$299$	−6.79833	−	3.74685i	−0.393158	−	0.216686i
$300$		0			0
$301$	−2.00894	+	3.47959i	−0.115793	+	0.200560i
$302$	47.1421	+	27.2175i	2.71272	+	1.56619i
$303$		0			0
$304$	−9.71254			−0.557052
$305$	−3.16383	+	3.96973i	−0.181160	+	0.227306i
$306$		0			0
$307$		−	12.7219i		−	0.726077i	−0.931774	−	0.363039i	$-0.881739\pi$
$307$		−	12.7219i		−	0.726077i	0.931774	−	0.363039i	$-0.118261\pi$
$308$	7.24190	−	4.18112i	0.412646	−	0.238241i
$309$		0			0
$310$	−7.58818	+	50.4457i	−0.430980	+	2.86513i
$311$	−27.9231			−1.58338			−0.791688	−	0.610925i	$-0.790798\pi$
$311$	−27.9231			−1.58338			−0.791688	+	0.610925i	$0.790798\pi$
$312$		0			0
$313$			24.5807i			1.38938i	0.719307	+	0.694692i	$0.244460\pi$
$313$			24.5807i			1.38938i	−0.719307	+	0.694692i	$0.755540\pi$
$314$	−23.3758	+	40.4880i	−1.31917	+	2.28487i
$315$		0			0
$316$	−2.32648	−	4.02959i	−0.130875	−	0.226682i
$317$		−	0.234377i		−	0.0131639i	−0.999978	−	0.00658196i	$-0.997905\pi$
$317$		−	0.234377i		−	0.0131639i	0.999978	−	0.00658196i	$-0.00209512\pi$
$318$		0			0
$319$	−0.952633	−	1.65001i	−0.0533372	−	0.0923828i
$320$	0.220882	+	0.562309i	0.0123477	+	0.0314340i
$321$		0			0
$322$	−13.9478	−	8.05279i	−0.777283	−	0.448764i
$323$	1.44678	+	0.835296i	0.0805008	+	0.0464771i
$324$		0			0
$325$	−12.9615	+	12.5299i	−0.718975	+	0.695036i
$326$	−10.2106			−0.565513
$327$		0			0
$328$	54.4831	+	31.4558i	3.00833	+	1.73686i
$329$	−9.05631	−	15.6860i	−0.499290	−	0.864796i
$330$		0			0
$331$	9.16324	+	15.8712i	0.503657	+	0.872360i	0.999991	+	0.00422829i	$0.00134591\pi$
$331$	9.16324	+	15.8712i	0.503657	+	0.872360i	−0.496334	+	0.868132i	$0.665321\pi$
$332$	−45.9652	+	26.5380i	−2.52267	+	1.45646i
$333$		0			0
$334$	−3.74039	−	6.47855i	−0.204665	−	0.354491i
$335$	2.67089	−	17.7559i	0.145926	−	0.970110i
$336$		0			0
$337$			21.2949i			1.16001i	0.814614	+	0.580003i	$0.196949\pi$
$337$			21.2949i			1.16001i	−0.814614	+	0.580003i	$0.803051\pi$
$338$	−29.2958	−	15.3950i	−1.59348	−	0.837379i
$339$		0			0
$340$	−1.82415	+	12.1268i	−0.0989283	+	0.657669i
$341$	2.84570	−	4.92889i	0.154103	−	0.266915i
$342$		0			0
$343$		−	15.7651i		−	0.851234i
$344$	−4.31754	−	7.47821i	−0.232786	−	0.403198i
$345$		0			0
$346$	−3.48079			−0.187128
$347$	−3.30407	+	1.90761i	−0.177372	+	0.102406i	−0.586057	−	0.810270i	$-0.699321\pi$
$347$	−3.30407	+	1.90761i	−0.177372	+	0.102406i	0.408685	+	0.912675i	$0.365987\pi$
$348$		0			0
$349$	12.1632	−	21.0674i	0.651083	−	1.12771i	−0.331777	−	0.943358i	$-0.607648\pi$
$349$	12.1632	−	21.0674i	0.651083	−	1.12771i	0.982860	−	0.184352i	$-0.0590185\pi$
$350$	−27.4039	+	25.4574i	−1.46480	+	1.36075i
$351$		0			0
$352$			3.48301i			0.185645i
$353$	−23.4338	−	13.5295i	−1.24726	−	0.720104i	−0.276696	−	0.960958i	$-0.589239\pi$
$353$	−23.4338	−	13.5295i	−1.24726	−	0.720104i	−0.970562	+	0.240853i	$0.922573\pi$
$354$		0			0
$355$	−3.67238	+	4.60783i	−0.194910	+	0.244558i
$356$	56.2708			2.98235
$357$		0			0
$358$	17.1659	−	9.91073i	0.907245	−	0.523798i
$359$	27.0039			1.42521			0.712605	−	0.701566i	$-0.247515\pi$
$359$	27.0039			1.42521			0.712605	+	0.701566i	$0.247515\pi$
$360$		0			0
$361$	8.56851	−	14.8411i	0.450974	−	0.781110i
$362$	8.52512	+	4.92198i	0.448071	+	0.258694i
$363$		0			0
$364$	−41.5777	−	22.9152i	−2.17927	−	1.20108i
$365$	−21.4917	+	8.44221i	−1.12492	+	0.441885i
$366$		0			0
$367$	−6.01118	−	3.47055i	−0.313781	−	0.181161i	0.334836	−	0.942276i	$-0.391319\pi$
$367$	−6.01118	−	3.47055i	−0.313781	−	0.181161i	−0.648617	+	0.761115i	$0.724652\pi$
$368$	13.2675	−	7.65998i	0.691615	−	0.399304i
$369$		0			0
$370$	−4.34243	+	5.44855i	−0.225752	+	0.283257i
$371$	−0.943693	−	1.63452i	−0.0489941	−	0.0848603i
$372$		0			0
$373$	2.00301	−	1.15644i	0.103712	−	0.0598781i	−0.447247	−	0.894411i	$-0.647595\pi$
$373$	2.00301	−	1.15644i	0.103712	−	0.0598781i	0.550959	+	0.834532i	$0.314262\pi$
$374$	0.989429	−	1.71374i	0.0511622	−	0.0886154i
$375$		0			0
$376$	38.9270			2.00751
$377$	−5.22105	+	9.47315i	−0.268898	+	0.487892i
$378$		0			0
$379$	2.58772	−	4.48207i	0.132922	−	0.230228i	−0.791880	−	0.610677i	$-0.790897\pi$
$379$	2.58772	−	4.48207i	0.132922	−	0.230228i	0.924802	+	0.380449i	$0.124231\pi$
$380$	−13.5234	−	2.03422i	−0.693734	−	0.104353i
$381$		0			0
$382$		−	12.5854i		−	0.643923i
$383$	17.8929	−	10.3305i	0.914283	−	0.527861i	0.0324760	−	0.999473i	$-0.489661\pi$
$383$	17.8929	−	10.3305i	0.914283	−	0.527861i	0.881807	+	0.471611i	$0.156327\pi$
$384$		0			0
$385$	3.88412	−	1.52574i	0.197953	−	0.0777587i
$386$	−6.30890	−	10.9273i	−0.321115	−	0.556187i
$387$		0			0
$388$	−57.3682	−	33.1215i	−2.91243	−	1.68149i
$389$	19.7477			1.00125			0.500624	−	0.865665i	$-0.333104\pi$
$389$	19.7477			1.00125			0.500624	+	0.865665i	$0.333104\pi$
$390$		0			0
$391$	−2.63509			−0.133262
$392$	−8.94284	−	5.16315i	−0.451681	−	0.260778i
$393$		0			0
$394$	−8.58609	−	14.8715i	−0.432561	−	0.749218i
$395$	−0.848960	−	2.16123i	−0.0427158	−	0.108743i
$396$		0			0
$397$	8.13113	−	4.69451i	0.408090	−	0.235611i	−0.281879	−	0.959450i	$-0.590958\pi$
$397$	8.13113	−	4.69451i	0.408090	−	0.235611i	0.689969	+	0.723839i	$0.257624\pi$
$398$		−	13.1753i		−	0.660420i
$399$		0			0
$400$	−7.93772	−	34.6826i	−0.396886	−	1.73413i
$401$	12.2510	−	21.2193i	0.611784	−	1.05964i	−0.379156	−	0.925333i	$-0.623786\pi$
$401$	12.2510	−	21.2193i	0.611784	−	1.05964i	0.990940	−	0.134308i	$-0.0428812\pi$
$402$		0			0
$403$	−32.3050	+	0.642285i	−1.60923	+	0.0319945i
$404$	59.2887			2.94972
$405$		0			0
$406$	−11.2212	+	19.4357i	−0.556898	+	0.964575i
$407$	0.673180	−	0.388661i	0.0333683	−	0.0192652i
$408$		0			0
$409$	18.0582	+	31.2778i	0.892922	+	1.54659i	0.836355	+	0.548188i	$0.184682\pi$
$409$	18.0582	+	31.2778i	0.892922	+	1.54659i	0.0565671	+	0.998399i	$0.481985\pi$
$410$	44.3448	+	35.3423i	2.19003	+	1.74543i
$411$		0			0
$412$	42.5633	−	24.5739i	2.09694	−	1.21067i
$413$	19.3324	+	11.1616i	0.951288	+	0.549226i
$414$		0			0
$415$	−24.6530	+	9.68401i	−1.21017	+	0.475370i
$416$	16.9248	−	10.2254i	0.829805	−	0.501341i
$417$		0			0
$418$	1.91110	+	1.10337i	0.0934749	+	0.0539678i
$419$	3.43342	−	5.94686i	0.167734	−	0.290523i	−0.769889	−	0.638178i	$-0.779689\pi$
$419$	3.43342	−	5.94686i	0.167734	−	0.290523i	0.937623	+	0.347655i	$0.113022\pi$
$420$		0			0
$421$	33.9795			1.65606			0.828029	−	0.560686i	$-0.189462\pi$
$421$	33.9795			1.65606			0.828029	+	0.560686i	$0.189462\pi$
$422$	−30.9049	+	17.8429i	−1.50443	+	0.868580i
$423$		0			0
$424$	4.05631			0.196992
$425$	−1.80037	+	5.84897i	−0.0873308	+	0.283717i
$426$		0			0
$427$	−5.77729	−	3.33552i	−0.279582	−	0.161417i
$428$		−	47.8261i		−	2.31176i
$429$		0			0
$430$	−2.84570	−	7.24440i	−0.137232	−	0.349356i
$431$	−8.12482	+	14.0726i	−0.391359	+	0.677853i	−0.992629	−	0.121193i	$-0.961328\pi$
$431$	−8.12482	+	14.0726i	−0.391359	+	0.677853i	0.601270	+	0.799046i	$0.294661\pi$
$432$		0			0
$433$	0.221929	−	0.128130i	0.0106652	−	0.00615756i	−0.494658	−	0.869088i	$-0.664707\pi$
$433$	0.221929	−	0.128130i	0.0106652	−	0.00615756i	0.505323	+	0.862930i	$0.331373\pi$
$434$	−67.0396			−3.21800
$435$		0			0
$436$	7.32648	+	12.6898i	0.350875	+	0.607733i
$437$		−	2.93855i		−	0.140570i
$438$		0			0
$439$	−3.79833	+	6.57890i	−0.181284	+	0.313994i	−0.942318	−	0.334718i	$-0.891359\pi$
$439$	−3.79833	+	6.57890i	−0.181284	+	0.313994i	0.761034	+	0.648712i	$0.224692\pi$
$440$	−1.33407	+	8.86879i	−0.0635991	+	0.422803i
$441$		0			0
$442$	−11.2322	+	0.223318i	−0.534263	+	0.0106221i
$443$		−	4.32246i		−	0.205366i	−0.994714	−	0.102683i	$-0.967257\pi$
$443$		−	4.32246i		−	0.205366i	0.994714	−	0.102683i	$-0.0327428\pi$
$444$		0			0
$445$	27.7687	+	4.17703i	1.31636	+	0.198010i
$446$	0.0105711	+	0.0183096i	0.000500554	+	0.000866986i
$447$		0			0
$448$	−0.687565	+	0.396966i	−0.0324844	+	0.0187549i
$449$	−1.64403	−	2.84754i	−0.0775865	−	0.134384i	0.824622	−	0.565685i	$-0.191388\pi$
$449$	−1.64403	−	2.84754i	−0.0775865	−	0.134384i	−0.902208	+	0.431301i	$0.858055\pi$
$450$		0			0
$451$	−3.16324	−	5.47890i	−0.148951	−	0.257991i
$452$	−21.4583	−	12.3889i	−1.00931	−	0.582727i
$453$		0			0
$454$	28.6741			1.34574
$455$	−18.8169	−	14.3946i	−0.882149	−	0.674831i
$456$		0			0
$457$	−13.3594	−	7.71304i	−0.624925	−	0.360801i	0.153859	−	0.988093i	$-0.450830\pi$
$457$	−13.3594	−	7.71304i	−0.624925	−	0.360801i	−0.778784	+	0.627292i	$0.784163\pi$
$458$	−36.4661	−	21.0537i	−1.70395	−	0.983775i
$459$		0			0
$460$	20.0774	−	7.88669i	0.936116	−	0.367719i
$461$	12.9424	+	22.4168i	0.602786	+	1.04406i	0.992397	+	0.123076i	$0.0392760\pi$
$461$	12.9424	+	22.4168i	0.602786	+	1.04406i	−0.389611	+	0.920979i	$0.627391\pi$
$462$		0			0
$463$			7.04045i			0.327197i	0.986527	+	0.163599i	$0.0523102\pi$
$463$			7.04045i			0.327197i	−0.986527	+	0.163599i	$0.947690\pi$
$464$	−10.6738	−	18.4876i	−0.495519	−	0.858265i
$465$		0			0
$466$	8.84570	−	15.3212i	0.409769	−	0.709741i
$467$			18.8113i			0.870482i	0.900314	+	0.435241i	$0.143337\pi$
$467$			18.8113i			0.870482i	−0.900314	+	0.435241i	$0.856663\pi$
$468$		0			0
$469$	23.5967			1.08959
$470$	34.6967	+	5.21916i	1.60044	+	0.240742i
$471$		0			0
$472$	−41.5486	+	23.9881i	−1.91243	+	1.10414i
$473$			0.868356i			0.0399271i
$474$		0			0
$475$	−6.52255	−	2.00771i	−0.299275	−	0.0921199i
$476$	−16.1159			−0.738670
$477$		0			0
$478$	−8.81870	−	5.09148i	−0.403358	−	0.232879i
$479$	9.73876	−	16.8680i	0.444975	−	0.770720i	−0.553075	−	0.833131i	$-0.686546\pi$
$479$	9.73876	−	16.8680i	0.444975	−	0.770720i	0.998051	+	0.0624114i	$0.0198791\pi$
$480$		0			0
$481$	−3.86491	−	2.13011i	−0.176225	−	0.0971249i
$482$			50.3346i			2.29268i
$483$		0			0
$484$	−23.7407	+	41.1201i	−1.07912	+	1.86909i
$485$	−25.8516	−	20.6034i	−1.17386	−	0.935552i
$486$		0			0
$487$	27.9935	−	16.1620i	1.26851	−	0.732372i	0.293800	−	0.955867i	$-0.405080\pi$
$487$	27.9935	−	16.1620i	1.26851	−	0.732372i	0.974705	+	0.223495i	$0.0717467\pi$
$488$	12.4163	−	7.16858i	0.562062	−	0.324506i
$489$		0			0
$490$	−7.27874	−	5.80107i	−0.328820	−	0.262066i
$491$	14.3354	−	24.8297i	0.646949	−	1.12055i	−0.336899	−	0.941541i	$-0.609378\pi$
$491$	14.3354	−	24.8297i	0.646949	−	1.12055i	0.983848	−	0.179007i	$-0.0572885\pi$
$492$		0			0
$493$			3.67187i			0.165373i
$494$	−0.249036	−	12.5258i	−0.0112046	−	0.563561i
$495$		0			0
$496$	31.8847	−	55.2260i	1.43167	−	2.47972i
$497$	−6.70593	−	3.87167i	−0.300802	−	0.173668i
$498$		0			0
$499$	−28.9616			−1.29650			−0.648249	−	0.761428i	$-0.724498\pi$
$499$	−28.9616			−1.29650			−0.648249	+	0.761428i	$0.724498\pi$
$500$	−3.78816	−	49.9533i	−0.169412	−	2.23398i
$501$		0			0
$502$		−	9.35181i		−	0.417392i
$503$	24.3433	−	14.0546i	1.08542	−	0.626665i	0.153063	−	0.988216i	$-0.451086\pi$
$503$	24.3433	−	14.0546i	1.08542	−	0.626665i	0.932352	+	0.361551i	$0.117753\pi$
$504$		0			0
$505$	29.2579	+	4.40105i	1.30196	+	0.195844i
$506$	−3.48079			−0.154740
$507$		0			0
$508$			77.2116i			3.42571i
$509$	−10.5563	+	18.2841i	−0.467900	+	0.810427i	−0.999327	−	0.0366773i	$-0.988323\pi$
$509$	−10.5563	+	18.2841i	−0.467900	+	0.810427i	0.531427	+	0.847104i	$0.321656\pi$
$510$		0			0
$511$	−15.1722	−	26.2790i	−0.671178	−	1.16251i
$512$		−	50.8542i		−	2.24746i
$513$		0			0
$514$	16.8844	+	29.2447i	0.744740	+	1.28993i
$515$	22.8284	−	8.96730i	1.00594	−	0.395147i
$516$		0			0
$517$	−3.39010	−	1.95728i	−0.149097	−	0.0860809i
$518$	−7.92947	−	4.57808i	−0.348401	−	0.201149i
$519$		0			0
$520$	47.0121	−	19.5544i	2.06162	−	0.857516i
$521$	−0.673516			−0.0295073			−0.0147536	−	0.999891i	$-0.504696\pi$
$521$	−0.673516			−0.0295073			−0.0147536	+	0.999891i	$0.504696\pi$
$522$		0			0
$523$	25.8618	+	14.9313i	1.13086	+	0.652900i	0.944150	−	0.329516i	$-0.106886\pi$
$523$	25.8618	+	14.9313i	1.13086	+	0.652900i	0.186706	+	0.982416i	$0.440219\pi$
$524$	−22.4039	−	38.8048i	−0.978720	−	1.69519i
$525$		0			0
$526$	−38.5304	−	66.7366i	−1.68000	−	2.90985i
$527$	−9.49907	+	5.48429i	−0.413786	+	0.238899i
$528$		0			0
$529$	−9.18246	−	15.9045i	−0.399237	−	0.691499i
$530$	3.61549	+	0.543852i	0.157047	+	0.0236234i
$531$		0			0
$532$		−	17.9718i		−	0.779177i
$533$	−17.3366	+	31.4558i	−0.750933	+	1.36250i
$534$		0			0
$535$	3.55018	−	23.6014i	0.153488	−	1.02038i
$536$	−25.3566	+	43.9189i	−1.09524	+	1.89701i
$537$		0			0
$538$		−	56.6418i		−	2.44200i
$539$	0.519213	+	0.899304i	0.0223641	+	0.0387358i
$540$		0			0
$541$	6.28806			0.270345			0.135172	−	0.990822i	$-0.456841\pi$
$541$	6.28806			0.270345			0.135172	+	0.990822i	$0.456841\pi$
$542$	−26.0778	+	15.0560i	−1.12014	+	0.646712i
$543$		0			0
$544$	3.35627	−	5.81323i	0.143899	−	0.249240i
$545$	2.67352	+	6.80607i	0.114521	+	0.291540i
$546$		0			0
$547$			3.03789i			0.129891i	0.997889	+	0.0649454i	$0.0206873\pi$
$547$			3.03789i			0.129891i	−0.997889	+	0.0649454i	$0.979313\pi$
$548$	33.6527	+	19.4294i	1.43757	+	0.829983i
$549$		0			0
$550$	−2.37818	+	7.72612i	−0.101406	+	0.329443i
$551$	−4.09473			−0.174442
$552$		0			0
$553$	2.64265	−	1.52574i	0.112377	−	0.0648809i
$554$	42.7304			1.81544
$555$		0			0
$556$	−32.0970	+	55.5936i	−1.36121	+	2.35769i
$557$	−17.9264	−	10.3498i	−0.759566	−	0.438536i	0.0695738	−	0.997577i	$-0.477836\pi$
$557$	−17.9264	−	10.3498i	−0.759566	−	0.438536i	−0.829140	+	0.559041i	$0.811169\pi$
$558$		0			0
$559$	4.21955	−	2.54931i	0.178468	−	0.107824i
$560$	43.5198	−	17.0952i	1.83905	−	0.722402i
$561$		0			0
$562$	−23.3622	−	13.4882i	−0.985475	−	0.568964i
$563$	−9.49188	+	5.48014i	−0.400035	+	0.230960i	−0.686499	−	0.727131i	$-0.740853\pi$
$563$	−9.49188	+	5.48014i	−0.400035	+	0.230960i	0.286464	+	0.958091i	$0.407520\pi$
$564$		0			0
$565$	−9.66965	−	7.70660i	−0.406805	−	0.324219i
$566$	−11.2212	−	19.4357i	−0.471661	−	0.816941i
$567$		0			0
$568$	14.4122	−	8.32087i	0.604721	−	0.349136i
$569$	−21.3566	+	36.9907i	−0.895314	+	1.55073i	−0.0618981	+	0.998082i	$0.519715\pi$
$569$	−21.3566	+	36.9907i	−0.895314	+	1.55073i	−0.833416	+	0.552647i	$0.813618\pi$
$570$		0			0
$571$	−23.6145			−0.988238			−0.494119	−	0.869394i	$-0.664509\pi$
$571$	−23.6145			−0.988238			−0.494119	+	0.869394i	$0.664509\pi$
$572$	−10.2583	+	0.203954i	−0.428920	+	0.00852774i
$573$		0			0
$574$	−37.2602	+	64.5366i	−1.55521	+	2.69370i
$575$	10.4933	−	2.40158i	0.437601	−	0.100153i
$576$		0			0
$577$			18.3646i			0.764530i	0.924053	+	0.382265i	$0.124856\pi$
$577$			18.3646i			0.764530i	−0.924053	+	0.382265i	$0.875144\pi$
$578$	34.1767	−	19.7319i	1.42156	−	0.820740i
$579$		0			0
$580$	−10.9897	−	27.9770i	−0.456324	−	1.16168i
$581$	−17.4039	−	30.1445i	−0.722037	−	1.25060i
$582$		0			0
$583$	−0.353259	−	0.203954i	−0.0146305	−	0.00844691i
$584$	65.2151			2.69862
$585$		0			0
$586$	−71.9237			−2.97114
$587$	0.608726	+	0.351448i	0.0251248	+	0.0145058i	0.512510	−	0.858681i	$-0.328716\pi$
$587$	0.608726	+	0.351448i	0.0251248	+	0.0145058i	−0.487385	+	0.873187i	$0.662049\pi$
$588$		0			0
$589$	−6.11588	−	10.5930i	−0.252000	−	0.436477i
$590$	−40.2496	+	15.8106i	−1.65705	+	0.650912i
$591$		0			0
$592$	7.54267	−	4.35476i	0.310002	−	0.178980i
$593$			37.1593i			1.52595i	0.646428	+	0.762975i	$0.276262\pi$
$593$			37.1593i			1.52595i	−0.646428	+	0.762975i	$0.723738\pi$
$594$		0			0
$595$	−7.95291	−	1.19630i	−0.326037	−	0.0490434i
$596$	−38.4337	+	66.5692i	−1.57431	+	2.72678i
$597$		0			0
$598$	10.2189	+	16.9140i	0.417880	+	0.691663i
$599$	−15.6914			−0.641133			−0.320567	−	0.947226i	$-0.603873\pi$
$599$	−15.6914			−0.641133			−0.320567	+	0.947226i	$0.603873\pi$
$600$		0			0
$601$	−6.00193	+	10.3956i	−0.244824	+	0.424047i	−0.962082	−	0.272760i	$-0.912063\pi$
$601$	−6.00193	+	10.3956i	−0.244824	+	0.424047i	0.717258	+	0.696807i	$0.245397\pi$
$602$	8.85812	−	5.11424i	0.361030	−	0.208441i
$603$		0			0
$604$	−47.9059	−	82.9754i	−1.94926	−	3.37622i
$605$	−14.7680	+	18.5298i	−0.600405	+	0.753342i
$606$		0			0
$607$	−33.5035	+	19.3433i	−1.35987	+	0.785119i	−0.989606	−	0.143809i	$-0.954065\pi$
$607$	−33.5035	+	19.3433i	−1.35987	+	0.785119i	−0.370261	+	0.928928i	$0.620732\pi$
$608$	6.48269	+	3.74278i	0.262908	+	0.151790i
$609$		0			0
$610$	12.0282	−	4.72482i	0.487006	−	0.191302i
$611$	0.441765	+	22.2195i	0.0178719	+	0.898903i
$612$		0			0
$613$	14.9684	+	8.64201i	0.604568	+	0.349047i	0.770836	−	0.637033i	$-0.219839\pi$
$613$	14.9684	+	8.64201i	0.604568	+	0.349047i	−0.166269	+	0.986081i	$0.553172\pi$
$614$	−16.1933	+	28.0477i	−0.653509	+	1.13191i
$615$		0			0
$616$	−11.7861			−0.474877
$617$	22.9229	−	13.2345i	0.922841	−	0.532803i	0.0383009	−	0.999266i	$-0.487805\pi$
$617$	22.9229	−	13.2345i	0.922841	−	0.532803i	0.884540	+	0.466464i	$0.154472\pi$
$618$		0			0
$619$	31.0039			1.24615			0.623075	−	0.782162i	$-0.285883\pi$
$619$	31.0039			1.24615			0.623075	+	0.782162i	$0.285883\pi$
$620$	55.9618	−	70.2165i	2.24748	−	2.81996i
$621$		0			0
$622$	61.5615	+	35.5425i	2.46839	+	1.42513i
$623$			36.9030i			1.47849i
$624$		0			0
$625$	1.83869	−	24.9323i	0.0735475	−	0.997292i
$626$	31.2881	−	54.1925i	1.25052	−	2.16597i
$627$		0			0
$628$	71.2635	−	41.1440i	2.84372	−	1.64182i
$629$	−1.49807			−0.0597320
$630$		0			0
$631$	10.3566	+	17.9381i	0.412288	+	0.714104i	0.995140	−	0.0984745i	$-0.0313963\pi$
$631$	10.3566	+	17.9381i	0.412288	+	0.714104i	−0.582851	+	0.812579i	$0.698063\pi$
$632$			6.55812i			0.260868i
$633$		0			0
$634$	−0.298331	+	0.516725i	−0.0118482	+	0.0205218i
$635$	−5.73149	+	38.1026i	−0.227447	+	1.51206i
$636$		0			0
$637$	2.84563	−	5.16315i	0.112748	−	0.204571i
$638$			4.85031i			0.192026i
$639$		0			0
$640$	3.87707	−	25.7745i	0.153254	−	1.01883i
$641$	10.5947	+	18.3506i	0.418467	+	0.724806i	0.995785	−	0.0917132i	$-0.0292343\pi$
$641$	10.5947	+	18.3506i	0.418467	+	0.724806i	−0.577319	+	0.816519i	$0.695901\pi$
$642$		0			0
$643$	−9.98843	+	5.76682i	−0.393905	+	0.227421i	−0.683851	−	0.729622i	$-0.739696\pi$
$643$	−9.98843	+	5.76682i	−0.393905	+	0.227421i	0.289946	+	0.957043i	$0.406363\pi$
$644$	14.1738	+	24.5498i	0.558526	+	0.967396i
$645$		0			0
$646$	−2.12645	−	3.68311i	−0.0836639	−	0.144910i
$647$	30.1779	+	17.4232i	1.18641	+	0.684977i	0.957490	−	0.288467i	$-0.0931456\pi$
$647$	30.1779	+	17.4232i	1.18641	+	0.684977i	0.228925	+	0.973444i	$0.426479\pi$
$648$		0			0
$649$	4.82456			0.189380
$650$	44.5249	−	11.1262i	1.74641	−	0.436404i
$651$		0			0
$652$	15.5641	+	8.98591i	0.609535	+	0.351915i
$653$	19.3324	+	11.1616i	0.756537	+	0.436787i	0.828051	−	0.560653i	$-0.189450\pi$
$653$	19.3324	+	11.1616i	0.756537	+	0.436787i	−0.0715139	+	0.997440i	$0.522783\pi$
$654$		0			0
$655$	−8.17544	−	20.8125i	−0.319441	−	0.813214i
$656$	−35.4427	−	61.3885i	−1.38380	−	2.39682i
$657$		0			0
$658$			46.1100i			1.79755i
$659$	0.433420	+	0.750705i	0.0168836	+	0.0292433i	0.874344	−	0.485307i	$-0.161292\pi$
$659$	0.433420	+	0.750705i	0.0168836	+	0.0292433i	−0.857460	+	0.514550i	$0.827959\pi$
$660$		0			0
$661$	−6.65430	+	11.5256i	−0.258822	+	0.448293i	−0.965927	−	0.258816i	$-0.916668\pi$
$661$	−6.65430	+	11.5256i	−0.258822	+	0.448293i	0.707104	+	0.707109i	$0.250001\pi$
$662$		−	46.6544i		−	1.81328i
$663$		0			0
$664$	74.8079			2.90311
$665$	1.33407	−	8.86879i	0.0517328	−	0.343917i
$666$		0			0
$667$	5.59346	−	3.22939i	0.216580	−	0.125042i
$668$			13.1670i			0.509448i
$669$		0			0
$670$	−28.4894	+	35.7464i	−1.10064	+	1.38100i
$671$	−1.44176			−0.0556587
$672$		0			0
$673$	4.77457	+	2.75660i	0.184046	+	0.106259i	0.589192	−	0.807993i	$-0.299446\pi$
$673$	4.77457	+	2.75660i	0.184046	+	0.106259i	−0.405146	+	0.914252i	$0.632779\pi$
$674$	27.1056	−	46.9483i	1.04407	−	1.80838i
$675$		0			0
$676$	31.1072	+	49.2486i	1.19643	+	1.89418i
$677$		−	4.80479i		−	0.184663i	−0.995728	−	0.0923316i	$-0.970568\pi$
$677$		−	4.80479i		−	0.184663i	0.995728	−	0.0923316i	$-0.0294320\pi$
$678$		0			0
$679$	21.7215	−	37.6227i	0.833594	−	1.44383i
$680$	10.7726	−	13.5167i	0.413112	−	0.518341i
$681$		0			0
$682$	−12.5477	+	7.24440i	−0.480475	+	0.277403i
$683$	−10.1866	+	5.88126i	−0.389781	+	0.225040i	−0.682065	−	0.731291i	$-0.738918\pi$
$683$	−10.1866	+	5.88126i	−0.389781	+	0.225040i	0.292284	+	0.956331i	$0.405585\pi$
$684$		0			0
$685$	15.1648	+	12.0861i	0.579416	+	0.461788i
$686$	−20.0669	+	34.7569i	−0.766157	+	1.32702i
$687$		0			0
$688$			9.72953i			0.370935i
$689$	0.0460332	+	2.31533i	0.00175372	+	0.0882071i
$690$		0			0
$691$	−2.43342	+	4.21481i	−0.0925717	+	0.160339i	−0.908593	−	0.417684i	$-0.862842\pi$
$691$	−2.43342	+	4.21481i	−0.0925717	+	0.160339i	0.816021	+	0.578022i	$0.196175\pi$
$692$	5.30577	+	3.06329i	0.201695	+	0.116449i
$693$		0			0
$694$	9.71254			0.368683
$695$	−19.9661	+	25.0519i	−0.757356	+	0.950272i
$696$		0			0
$697$			12.1925i			0.461825i
$698$	−53.6320	+	30.9644i	−2.03000	+	1.17202i
$699$		0			0
$700$	64.1758	−	14.6877i	2.42562	−	0.555145i
$701$	−21.3828			−0.807617			−0.403808	−	0.914844i	$-0.632314\pi$
$701$	−21.3828			−0.807617			−0.403808	+	0.914844i	$0.632314\pi$
$702$		0			0
$703$		−	1.67059i		−	0.0630076i
$704$	−0.0857934	+	0.148599i	−0.00323346	+	0.00560052i
$705$		0			0
$706$	34.4427	+	59.6564i	1.29627	+	2.24520i
$707$			38.8822i			1.46232i
$708$		0			0
$709$	−13.0582	−	22.6175i	−0.490412	−	0.849419i	0.509527	−	0.860455i	$-0.329820\pi$
$709$	−13.0582	−	22.6175i	−0.490412	−	0.849419i	−0.999939	+	0.0110357i	$0.996487\pi$
$710$	13.9616	−	5.48429i	0.523969	−	0.205822i
$711$		0			0
$712$	−68.6851	−	39.6554i	−2.57408	−	1.48615i
$713$	16.7087	+	9.64680i	0.625748	+	0.361276i
$714$		0			0
$715$	−5.07743	−	0.660834i	−0.189885	−	0.0247138i
$716$	−34.8880			−1.30383
$717$		0			0
$718$	−59.5347	−	34.3724i	−2.22182	−	1.28277i
$719$	−18.3387	−	31.7635i	−0.683918	−	1.18458i	−0.973776	−	0.227510i	$-0.926941\pi$
$719$	−18.3387	−	31.7635i	−0.683918	−	1.18458i	0.289858	−	0.957070i	$-0.406392\pi$
$720$		0			0
$721$	16.1159	+	27.9135i	0.600187	+	1.03955i
$722$	−37.7815	+	21.8132i	−1.40608	+	0.811803i
$723$		0			0
$724$	−8.66324	−	15.0052i	−0.321967	−	0.557663i
$725$	−3.34648	−	14.6219i	−0.124285	−	0.543045i
$726$		0			0
$727$			26.2596i			0.973916i	0.873425	+	0.486958i	$0.161893\pi$
$727$			26.2596i			0.973916i	−0.873425	+	0.486958i	$0.838107\pi$
$728$	34.6016	+	57.2716i	1.28242	+	2.12263i
$729$		0			0
$730$	58.1279	+	8.74375i	2.15141	+	0.323621i
$731$	0.836758	−	1.44931i	0.0309486	−	0.0536046i
$732$		0			0
$733$			31.7811i			1.17386i	0.809637	+	0.586931i	$0.199664\pi$
$733$			31.7811i			1.17386i	−0.809637	+	0.586931i	$0.800336\pi$
$734$	8.83513	+	15.3029i	0.326110	+	0.564840i
$735$		0			0
$736$	−11.8073			−0.435222
$737$	4.41654	−	2.54989i	0.162685	−	0.0939265i
$738$		0			0
$739$	−17.0685	+	29.5635i	−0.627875	+	1.08751i	0.360102	+	0.932913i	$0.382742\pi$
$739$	−17.0685	+	29.5635i	−0.627875	+	1.08751i	−0.987977	+	0.154599i	$0.950591\pi$
$740$	11.4142	−	4.48365i	0.419595	−	0.164822i
$741$		0			0
$742$			4.80479i			0.176390i
$743$	2.70254	+	1.56031i	0.0991465	+	0.0572423i	0.548753	−	0.835984i	$-0.315103\pi$
$743$	2.70254	+	1.56031i	0.0991465	+	0.0572423i	−0.449607	+	0.893227i	$0.648436\pi$
$744$		0			0
$745$	−23.9079	+	29.9978i	−0.875917	+	1.09903i
$746$	−5.88798			−0.215574
$747$		0			0
$748$	−3.01638	+	1.74151i	−0.110290	+	0.0636758i
$749$	31.3649			1.14605
$750$		0			0
$751$	−0.742024	+	1.28522i	−0.0270769	+	0.0468985i	−0.879246	−	0.476367i	$-0.841953\pi$
$751$	−0.742024	+	1.28522i	−0.0270769	+	0.0468985i	0.852169	+	0.523266i	$0.175287\pi$
$752$	−37.9845	−	21.9304i	−1.38515	−	0.799718i
$753$		0			0
$754$	23.5688	−	14.2395i	0.858325	−	0.518572i
$755$	−17.4814	−	44.5030i	−0.636213	−	1.61963i
$756$		0			0
$757$	4.41654	+	2.54989i	0.160522	+	0.0926774i	0.578109	−	0.815960i	$-0.303791\pi$
$757$	4.41654	+	2.54989i	0.160522	+	0.0926774i	−0.417587	+	0.908637i	$0.637124\pi$
$758$	−11.4102	+	6.58767i	−0.414436	+	0.239275i
$759$		0			0
$760$	15.0733	+	12.0132i	0.546766	+	0.435766i
$761$	−14.8931	−	25.7955i	−0.539873	−	0.935088i	−0.998910	−	0.0466707i	$-0.985139\pi$
$761$	−14.8931	−	25.7955i	−0.539873	−	0.935088i	0.459037	−	0.888417i	$-0.348194\pi$
$762$		0			0
$763$	−8.32215	+	4.80479i	−0.301282	+	0.173945i
$764$	−11.0758	+	19.1839i	−0.400709	+	0.694048i
$765$		0			0
$766$	−52.5973			−1.90042
$767$	−14.1639	−	23.4437i	−0.511428	−	0.846501i
$768$		0			0
$769$	9.54930	−	16.5399i	0.344356	−	0.596443i	−0.640880	−	0.767641i	$-0.721430\pi$
$769$	9.54930	−	16.5399i	0.344356	−	0.596443i	0.985237	+	0.171198i	$0.0547638\pi$
$770$	−10.5053	−	1.58023i	−0.378584	−	0.0569476i
$771$		0			0
$772$			22.2088i			0.799311i
$773$	−42.6350	+	24.6153i	−1.53347	+	0.885351i	−0.534275	+	0.845311i	$0.679415\pi$
$773$	−42.6350	+	24.6153i	−1.53347	+	0.885351i	−0.999198	+	0.0400400i	$0.987251\pi$
$774$		0			0
$775$	32.8284	−	30.4966i	1.17923	−	1.09547i
$776$	46.6831	+	80.8574i	1.67582	+	2.90261i
$777$		0			0
$778$	−43.5373	−	25.1362i	−1.56089	−	0.901178i
$779$	−13.5967			−0.487151
$780$		0			0
$781$	−1.67352			−0.0598831
$782$	5.80951	+	3.35412i	0.207748	+	0.119943i
$783$		0			0
$784$	5.81754	+	10.0763i	0.207769	+	0.359867i
$785$	38.2215	−	15.0139i	1.36418	−	0.535869i
$786$		0			0
$787$	8.47263	−	4.89168i	0.302017	−	0.174369i	−0.341332	−	0.939943i	$-0.610878\pi$
$787$	8.47263	−	4.89168i	0.302017	−	0.174369i	0.643349	+	0.765573i	$0.277545\pi$
$788$			30.2250i			1.07672i
$789$		0			0
$790$	−0.879284	+	5.84543i	−0.0312835	+	0.207971i
$791$	8.12482	−	14.0726i	0.288885	−	0.500364i
$792$		0			0
$793$	4.23272	+	7.00587i	0.150308	+	0.248786i
$794$	−23.9020			−0.848250
$795$		0			0
$796$	−11.5950	+	20.0832i	−0.410975	+	0.711830i
$797$	14.3216	−	8.26856i	0.507296	−	0.292887i	−0.224426	−	0.974491i	$-0.572051\pi$
$797$	14.3216	−	8.26856i	0.507296	−	0.292887i	0.731721	+	0.681604i	$0.238717\pi$
$798$		0			0
$799$	3.77211	+	6.53348i	0.133448	+	0.231138i
$800$	−8.06708	+	26.2080i	−0.285214	+	0.926592i
$801$		0			0
$802$	−54.0188	+	31.1878i	−1.90747	+	1.10128i
$803$	−5.67950	−	3.27906i	−0.200425	−	0.115715i
$804$		0			0
$805$	5.17218	+	13.1670i	0.182295	+	0.464077i
$806$	72.0396	+	39.7041i	2.53749	+	1.39852i
$807$		0			0
$808$	−72.3688	−	41.7821i	−2.54592	−	1.46989i
$809$	15.9212	−	27.5764i	0.559760	−	0.969533i	−0.437756	−	0.899094i	$-0.644227\pi$
$809$	15.9212	−	27.5764i	0.559760	−	0.969533i	0.997516	−	0.0704392i	$-0.0224401\pi$
$810$		0			0
$811$	13.3470			0.468678			0.234339	−	0.972155i	$-0.424707\pi$
$811$	13.3470			0.468678			0.234339	+	0.972155i	$0.424707\pi$
$812$	34.2089	−	19.7505i	1.20050	−	0.693108i
$813$		0			0
$814$	−1.97886			−0.0693589
$815$	7.01356	+	5.58973i	0.245674	+	0.195800i
$816$		0			0
$817$	1.61621	+	0.933121i	0.0565441	+	0.0326458i
$818$		−	91.9431i		−	3.21472i
$819$		0			0
$820$	−36.4917	−	92.8982i	−1.27434	−	3.24415i
$821$	5.83676	−	10.1096i	0.203704	−	0.352826i	−0.746015	−	0.665929i	$-0.768035\pi$
$821$	5.83676	−	10.1096i	0.203704	−	0.352826i	0.949719	+	0.313103i	$0.101369\pi$
$822$		0			0
$823$	28.0867	−	16.2159i	0.979041	−	0.565249i	0.0770602	−	0.997026i	$-0.475447\pi$
$823$	28.0867	−	16.2159i	0.979041	−	0.565249i	0.901980	+	0.431777i	$0.142113\pi$
$824$	−69.2714			−2.41318
$825$		0			0
$826$	−28.4145	−	49.2154i	−0.988667	−	1.71242i
$827$			27.3319i			0.950425i	0.879871	+	0.475212i	$0.157629\pi$
$827$			27.3319i			0.950425i	−0.879871	+	0.475212i	$0.842371\pi$
$828$		0			0
$829$	1.77018	−	3.06604i	0.0614808	−	0.106488i	−0.833647	−	0.552298i	$-0.813751\pi$
$829$	1.77018	−	3.06604i	0.0614808	−	0.106488i	0.895128	+	0.445810i	$0.147084\pi$
$830$	66.6783	+	10.0299i	2.31444	+	0.348143i
$831$		0			0
$832$	0.973947	−	0.0193639i	0.0337655	−	0.000671322i
$833$		−	2.00128i		−	0.0693402i
$834$		0			0
$835$	−0.977401	+	6.49770i	−0.0338244	+	0.224862i
$836$	−1.94206	−	3.36375i	−0.0671676	−	0.116338i
$837$		0			0
$838$	−15.1391	+	8.74059i	−0.522973	+	0.301939i
$839$	−22.3950	−	38.7893i	−0.773161	−	1.33915i	−0.935822	−	0.352472i	$-0.885341\pi$
$839$	−22.3950	−	38.7893i	−0.773161	−	1.33915i	0.162661	−	0.986682i	$-0.447992\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	−74.9136	−	43.2514i	−2.58169	−	1.49054i
$843$		0			0
$844$	62.8111			2.16205
$845$	11.6951	+	26.6125i	0.402324	+	0.915497i
$846$		0			0
$847$	−26.9670	−	15.5694i	−0.926598	−	0.534972i
$848$	−3.95810	−	2.28521i	−0.135922	−	0.0784744i
$849$		0			0
$850$	11.4142	−	10.6034i	0.391504	−	0.363695i
$851$	1.31754	+	2.28205i	0.0451648	+	0.0782278i
$852$		0			0
$853$		−	31.3732i		−	1.07420i	−0.843519	−	0.537099i	$-0.819520\pi$
$853$		−	31.3732i		−	1.07420i	0.843519	−	0.537099i	$-0.180480\pi$
$854$	8.49136	+	14.7075i	0.290568	+	0.503279i
$855$		0			0
$856$	−33.7042	+	58.3774i	−1.15199	+	1.99530i
$857$		−	21.2813i		−	0.726955i	−0.931603	−	0.363478i	$-0.881589\pi$
$857$		−	21.2813i		−	0.726955i	0.931603	−	0.363478i	$-0.118411\pi$
$858$		0			0
$859$	−56.8502			−1.93970			−0.969851	−	0.243698i	$-0.921639\pi$
$859$	−56.8502			−1.93970			−0.969851	+	0.243698i	$0.921639\pi$
$860$	−2.03778	+	13.5470i	−0.0694877	+	0.461950i
$861$		0			0
$862$	35.8251	−	20.6837i	1.22021	−	0.704488i
$863$		−	32.8011i		−	1.11656i	−0.829651	−	0.558282i	$-0.811461\pi$
$863$		−	32.8011i		−	1.11656i	0.829651	−	0.558282i	$-0.188539\pi$
$864$		0			0
$865$	2.39092	+	1.90553i	0.0812936	+	0.0647901i
$866$	−0.652374			−0.0221686
$867$		0			0
$868$	102.189	+	58.9986i	3.46851	+	2.00254i
$869$	0.329747	−	0.571138i	0.0111859	−	0.0193745i
$870$		0			0
$871$	−25.3566	−	13.9751i	−0.859174	−	0.473527i
$872$		−	20.6526i		−	0.699385i
$873$		0			0
$874$	−3.74039	+	6.47855i	−0.126521	+	0.219140i
$875$	32.7599	−	2.48432i	1.10749	−	0.0839854i
$876$		0			0
$877$	31.2333	−	18.0325i	1.05467	−	0.608916i	0.130719	−	0.991419i	$-0.458271\pi$
$877$	31.2333	−	18.0325i	1.05467	−	0.608916i	0.923954	+	0.382504i	$0.124938\pi$
$878$	16.7482	−	9.66956i	0.565223	−	0.326332i
$879$		0			0
$880$	6.29819	−	7.90248i	0.212312	−	0.266393i
$881$	−23.0198	+	39.8715i	−0.775557	+	1.34330i	0.158924	+	0.987291i	$0.449198\pi$
$881$	−23.0198	+	39.8715i	−0.775557	+	1.34330i	−0.934481	+	0.356013i	$0.884136\pi$
$882$		0			0
$883$			0.802236i			0.0269974i	0.999909	+	0.0134987i	$0.00429690\pi$
$883$			0.802236i			0.0269974i	−0.999909	+	0.0134987i	$0.995703\pi$
$884$	17.3178	+	9.54459i	0.582462	+	0.321019i
$885$		0			0
$886$	−5.50193	+	9.52962i	−0.184841	+	0.320154i
$887$	−7.12365	−	4.11284i	−0.239189	−	0.138096i	0.375615	−	0.926776i	$-0.377431\pi$
$887$	−7.12365	−	4.11284i	−0.239189	−	0.138096i	−0.614804	+	0.788680i	$0.710765\pi$
$888$		0			0
$889$	−50.6363			−1.69829
$890$	−55.9041	−	44.5549i	−1.87391	−	1.49348i
$891$		0			0
$892$		−	0.0372125i		−	0.00124597i
$893$	−7.28589	+	4.20651i	−0.243813	+	0.140766i
$894$		0			0
$895$	−17.2166	−	2.58977i	−0.575488	−	0.0865664i
$896$	34.2529			1.14431
$897$		0			0
$898$			8.37054i			0.279328i
$899$	13.4424	−	23.2829i	0.448328	−	0.776527i
$900$		0			0
$901$	0.393064	+	0.680808i	0.0130949	+	0.0226810i
$902$			16.1056i			0.536257i
$903$		0			0
$904$	17.4616	+	30.2443i	0.580763	+	1.00591i
$905$	−3.16131	−	8.04788i	−0.105086	−	0.267521i
$906$		0			0
$907$	−26.3583	−	15.2180i	−0.875213	−	0.505305i	−0.00613601	−	0.999981i	$-0.501953\pi$
$907$	−26.3583	−	15.2180i	−0.875213	−	0.505305i	−0.869077	+	0.494677i	$0.835286\pi$
$908$	−43.7080	−	25.2348i	−1.45050	−	0.837447i
$909$		0			0
$910$	23.1626	+	55.6869i	0.767833	+	1.84600i
$911$	−43.6145			−1.44501			−0.722507	−	0.691363i	$-0.757010\pi$
$911$	−43.6145			−1.44501			−0.722507	+	0.691363i	$0.757010\pi$
$912$		0			0
$913$	−6.51492	−	3.76139i	−0.215612	−	0.124484i
$914$	19.6354	+	34.0095i	0.649481	+	1.12493i
$915$		0			0
$916$	37.0569	+	64.1844i	1.22439	+	2.12071i
$917$	25.4486	−	14.6928i	0.840387	−	0.485198i
$918$		0			0
$919$	−18.5109	−	32.0618i	−0.610617	−	1.05762i	−0.991137	−	0.132847i	$-0.957588\pi$
$919$	−18.5109	−	32.0618i	−0.610617	−	1.05762i	0.380519	−	0.924773i	$-0.375745\pi$
$920$	−30.0648	−	4.52243i	−0.991208	−	0.149100i
$921$		0			0
$922$		−	65.8957i		−	2.17016i
$923$	4.91309	+	8.13201i	0.161716	+	0.267668i
$924$		0			0
$925$	5.96554	−	1.36532i	0.196146	−	0.0448914i
$926$	8.96157	−	15.5219i	0.294496	−	0.510081i
$927$		0			0
$928$			16.4529i			0.540092i
$929$	2.38412	+	4.12942i	0.0782206	+	0.135482i	0.902482	−	0.430727i	$-0.141743\pi$
$929$	2.38412	+	4.12942i	0.0782206	+	0.135482i	−0.824262	+	0.566209i	$0.808409\pi$
$930$		0			0
$931$	2.23175			0.0731427
$932$	−26.9670	+	15.5694i	−0.883334	+	0.509993i
$933$		0			0
$934$	23.9443	−	41.4727i	0.783481	−	1.35703i
$935$	−1.61780	+	0.635495i	−0.0529079	+	0.0207829i
$936$		0			0
$937$		−	43.6264i		−	1.42521i	−0.701565	−	0.712606i	$-0.747515\pi$
$937$		−	43.6264i		−	1.42521i	0.701565	−	0.712606i	$-0.252485\pi$
$938$	−52.0230	−	30.0355i	−1.69861	−	0.980693i
$939$		0			0
$940$	−48.2951	−	38.4906i	−1.57521	−	1.25543i
$941$	−18.2675			−0.595504			−0.297752	−	0.954643i	$-0.596237\pi$
$941$	−18.2675			−0.595504			−0.297752	+	0.954643i	$0.596237\pi$
$942$		0			0
$943$	18.5732	−	10.7233i	0.604828	−	0.349197i
$944$	54.0569			1.75940
$945$		0			0
$946$	1.10530	−	1.91444i	0.0359365	−	0.0622439i
$947$	17.3057	+	9.99146i	0.562360	+	0.324679i	0.754092	−	0.656769i	$-0.228077\pi$
$947$	17.3057	+	9.99146i	0.562360	+	0.324679i	−0.191732	+	0.981447i	$0.561410\pi$
$948$		0			0
$949$	0.740096	+	37.2246i	0.0240245	+	1.20836i
$950$	11.8246	+	12.7287i	0.383639	+	0.412973i
$951$		0			0
$952$	19.6713	+	11.3572i	0.637551	+	0.368090i
$953$	34.5228	−	19.9317i	1.11830	−	0.645652i	0.177335	−	0.984150i	$-0.443252\pi$
$953$	34.5228	−	19.9317i	1.11830	−	0.645652i	0.940967	+	0.338498i	$0.109919\pi$
$954$		0			0
$955$	−6.88976	+	8.64475i	−0.222948	+	0.279737i
$956$	8.96157	+	15.5219i	0.289838	+	0.502014i
$957$		0			0
$958$	−42.9416	+	24.7923i	−1.38738	+	0.801004i
$959$	−12.7420	+	22.0698i	−0.411461	+	0.712672i
$960$		0			0
$961$	49.3098			1.59064
$962$	5.80951	+	9.61574i	0.187306	+	0.310024i
$963$		0			0
$964$	44.2973	−	76.7252i	1.42672	−	2.47115i
$965$	−1.64858	+	10.9596i	−0.0530696	+	0.352803i
$966$		0			0
$967$			43.8607i			1.41047i	0.708975	+	0.705233i	$0.249158\pi$
$967$			43.8607i			1.41047i	−0.708975	+	0.705233i	$0.750842\pi$
$968$	57.9566	−	33.4613i	1.86280	−	1.07549i
$969$		0			0
$970$	30.7688	+	78.3294i	0.987928	+	2.51501i
$971$	30.4897	+	52.8098i	0.978462	+	1.69475i	0.668002	+	0.744159i	$0.267150\pi$
$971$	30.4897	+	52.8098i	0.978462	+	1.69475i	0.310459	+	0.950587i	$0.399517\pi$
$972$		0			0
$973$	−36.4589	−	21.0496i	−1.16882	−	0.674818i
$974$	−82.2887			−2.63670
$975$		0			0
$976$	−16.1543			−0.517087
$977$	−44.4875	−	25.6849i	−1.42328	−	0.821731i	−0.426703	−	0.904392i	$-0.640325\pi$
$977$	−44.4875	−	25.6849i	−1.42328	−	0.821731i	−0.996578	+	0.0826604i	$0.973658\pi$
$978$		0			0
$979$	3.98780	+	6.90707i	0.127451	+	0.220751i
$980$	5.98973	+	15.2483i	0.191335	+	0.487088i
$981$		0			0
$982$	−63.2099	+	36.4942i	−2.01711	+	1.16458i
$983$		−	37.3026i		−	1.18977i	−0.803811	−	0.594885i	$-0.797198\pi$
$983$		−	37.3026i		−	1.18977i	0.803811	−	0.594885i	$-0.202802\pi$
$984$		0			0
$985$	−2.24363	+	14.9155i	−0.0714880	+	0.475248i
$986$	4.67381	−	8.09528i	0.148845	−	0.257806i
$987$		0			0
$988$	−10.6438	+	19.3122i	−0.338623	+	0.614403i
$989$	−2.94369			−0.0936040
$990$		0			0
$991$	25.7810	−	44.6541i	0.818962	−	1.41848i	−0.0874859	−	0.996166i	$-0.527883\pi$
$991$	25.7810	−	44.6541i	0.818962	−	1.41848i	0.906448	−	0.422318i	$-0.138783\pi$
$992$	−42.5633	+	24.5739i	−1.35139	+	0.780223i
$993$		0			0
$994$	9.85627	+	17.0716i	0.312622	+	0.541477i
$995$	−7.21274	+	9.05000i	−0.228659	+	0.286904i
$996$		0			0
$997$	−19.8743	+	11.4744i	−0.629425	+	0.363399i	−0.780529	−	0.625119i	$-0.785050\pi$
$997$	−19.8743	+	11.4744i	−0.629425	+	0.363399i	0.151104	+	0.988518i	$0.451717\pi$
$998$	63.8508	+	36.8643i	2.02116	+	1.16692i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bs.a.334.1		12
3.2	odd	2		65.2.n.a.9.6	yes	12
5.4	even	2	inner	585.2.bs.a.334.6		12
12.11	even	2		1040.2.dh.a.529.5		12
13.3	even	3	inner	585.2.bs.a.289.6		12
15.2	even	4		325.2.e.e.126.1		12
15.8	even	4		325.2.e.e.126.6		12
15.14	odd	2		65.2.n.a.9.1	✓	12
39.2	even	12		845.2.l.f.699.12		24
39.5	even	4		845.2.l.f.654.11		24
39.8	even	4		845.2.l.f.654.1		24
39.11	even	12		845.2.l.f.699.2		24
39.17	odd	6		845.2.b.e.339.6		6
39.20	even	12		845.2.d.d.844.12		12
39.23	odd	6		845.2.n.e.484.6		12
39.29	odd	6		65.2.n.a.29.1	yes	12
39.32	even	12		845.2.d.d.844.2		12
39.35	odd	6		845.2.b.d.339.1		6
39.38	odd	2		845.2.n.e.529.1		12
60.59	even	2		1040.2.dh.a.529.2		12
65.29	even	6	inner	585.2.bs.a.289.1		12
156.107	even	6		1040.2.dh.a.289.2		12
195.17	even	12		4225.2.a.bq.1.1		6
195.29	odd	6		65.2.n.a.29.6	yes	12
195.44	even	4		845.2.l.f.654.2		24
195.59	even	12		845.2.d.d.844.1		12
195.68	even	12		325.2.e.e.276.6		12
195.74	odd	6		845.2.b.d.339.6		6
195.89	even	12		845.2.l.f.699.11		24
195.107	even	12		325.2.e.e.276.1		12
195.113	even	12		4225.2.a.br.1.1		6
195.119	even	12		845.2.l.f.699.1		24
195.134	odd	6		845.2.b.e.339.1		6
195.149	even	12		845.2.d.d.844.11		12
195.152	even	12		4225.2.a.br.1.6		6
195.164	even	4		845.2.l.f.654.12		24
195.173	even	12		4225.2.a.bq.1.6		6
195.179	odd	6		845.2.n.e.484.1		12
195.194	odd	2		845.2.n.e.529.6		12
780.419	even	6		1040.2.dh.a.289.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.1	✓	12	15.14	odd	2
65.2.n.a.9.6	yes	12	3.2	odd	2
65.2.n.a.29.1	yes	12	39.29	odd	6
65.2.n.a.29.6	yes	12	195.29	odd	6
325.2.e.e.126.1		12	15.2	even	4
325.2.e.e.126.6		12	15.8	even	4
325.2.e.e.276.1		12	195.107	even	12
325.2.e.e.276.6		12	195.68	even	12
585.2.bs.a.289.1		12	65.29	even	6	inner
585.2.bs.a.289.6		12	13.3	even	3	inner
585.2.bs.a.334.1		12	1.1	even	1	trivial
585.2.bs.a.334.6		12	5.4	even	2	inner
845.2.b.d.339.1		6	39.35	odd	6
845.2.b.d.339.6		6	195.74	odd	6
845.2.b.e.339.1		6	195.134	odd	6
845.2.b.e.339.6		6	39.17	odd	6
845.2.d.d.844.1		12	195.59	even	12
845.2.d.d.844.2		12	39.32	even	12
845.2.d.d.844.11		12	195.149	even	12
845.2.d.d.844.12		12	39.20	even	12
845.2.l.f.654.1		24	39.8	even	4
845.2.l.f.654.2		24	195.44	even	4
845.2.l.f.654.11		24	39.5	even	4
845.2.l.f.654.12		24	195.164	even	4
845.2.l.f.699.1		24	195.119	even	12
845.2.l.f.699.2		24	39.11	even	12
845.2.l.f.699.11		24	195.89	even	12
845.2.l.f.699.12		24	39.2	even	12
845.2.n.e.484.1		12	195.179	odd	6
845.2.n.e.484.6		12	39.23	odd	6
845.2.n.e.529.1		12	39.38	odd	2
845.2.n.e.529.6		12	195.194	odd	2
1040.2.dh.a.289.2		12	156.107	even	6
1040.2.dh.a.289.5		12	780.419	even	6
1040.2.dh.a.529.2		12	60.59	even	2
1040.2.dh.a.529.5		12	12.11	even	2
4225.2.a.bq.1.1		6	195.17	even	12
4225.2.a.bq.1.6		6	195.173	even	12
4225.2.a.br.1.1		6	195.113	even	12
4225.2.a.br.1.6		6	195.152	even	12

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.20467 - 1.27287i) q^{2} +(2.24039 + 3.88048i) q^{4} +(0.817544 + 2.08125i) q^{5} +(-2.54486 + 1.46928i) q^{7} -6.31544i q^{8} +O(q^{10})\)	\(q+(-2.20467 - 1.27287i) q^{2} +(2.24039 + 3.88048i) q^{4} +(0.817544 + 2.08125i) q^{5} +(-2.54486 + 1.46928i) q^{7} -6.31544i q^{8} +(0.846746 - 5.62912i) q^{10} +(-0.317544 + 0.550003i) q^{11} +(3.60484 - 0.0716710i) q^{13} +7.48079 q^{14} +(-3.55794 + 6.16253i) q^{16} +(1.05998 - 0.611979i) q^{17} +(0.682456 + 1.18205i) q^{19} +(-6.24464 + 7.83529i) q^{20} +(1.40016 - 0.808385i) q^{22} +(-1.86449 - 1.07646i) q^{23} +(-3.66324 + 3.40304i) q^{25} +(-8.03872 - 4.43048i) q^{26} +(-11.4030 - 6.58351i) q^{28} +(-1.50000 + 2.59808i) q^{29} -8.96157 q^{31} +(4.74954 - 2.74215i) q^{32} -3.11588 q^{34} +(-5.13847 - 4.09531i) q^{35} +(-1.05998 - 0.611979i) q^{37} -3.47471i q^{38} +(13.1440 - 5.16315i) q^{40} +(-4.98079 + 8.62698i) q^{41} +(1.18412 - 0.683650i) q^{43} -2.84570 q^{44} +(2.74039 + 4.74650i) q^{46} +6.16379i q^{47} +(0.817544 - 1.41603i) q^{49} +(12.4079 - 2.83976i) q^{50} +(8.35437 + 13.8279i) q^{52} +0.642285i q^{53} +(-1.40430 - 0.211239i) q^{55} +(9.27912 + 16.0719i) q^{56} +(6.61402 - 3.81861i) q^{58} +(-3.79833 - 6.57890i) q^{59} +(1.13509 + 1.96603i) q^{61} +(19.7574 + 11.4069i) q^{62} +0.270178 q^{64} +(3.09628 + 7.44399i) q^{65} +(-6.95421 - 4.01502i) q^{67} +(4.74954 + 2.74215i) q^{68} +(6.11588 + 15.5694i) q^{70} +(1.31754 + 2.28205i) q^{71} +10.3263i q^{73} +(1.55794 + 2.69843i) q^{74} +(-3.05794 + 5.29650i) q^{76} -1.86624i q^{77} -1.03843 q^{79} +(-15.7346 - 2.36683i) q^{80} +(21.9620 - 12.6798i) q^{82} +11.8452i q^{83} +(2.14026 + 1.70576i) q^{85} -3.48079 q^{86} +(3.47351 + 2.00543i) q^{88} +(6.27912 - 10.8758i) q^{89} +(-9.06851 + 5.47890i) q^{91} -9.64680i q^{92} +(7.84570 - 13.5891i) q^{94} +(-1.90220 + 2.38674i) q^{95} +(-12.8031 + 7.39190i) q^{97} +(-3.60484 + 2.08125i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 6 q^{5}+O(q^{10}) \) 12 * q + 4 * q^4 + 6 * q^5	\( 12 q + 4 q^{4} + 6 q^{5} + 7 q^{10} + 44 q^{14} - 16 q^{16} + 12 q^{19} + q^{20} - 2 q^{25} - 24 q^{26} - 18 q^{29} - 16 q^{31} + 16 q^{34} - 10 q^{35} + 70 q^{40} - 14 q^{41} + 4 q^{44} + 10 q^{46} + 6 q^{49} + 31 q^{50} - 26 q^{55} + 16 q^{56} + 4 q^{59} + 6 q^{61} - 12 q^{64} - 23 q^{65} + 20 q^{70} + 12 q^{71} - 8 q^{74} - 10 q^{76} - 104 q^{79} - 33 q^{80} + 21 q^{85} + 4 q^{86} - 20 q^{89} - 44 q^{91} + 56 q^{94} - 20 q^{95}+O(q^{100}) \) 12 * q + 4 * q^4 + 6 * q^5 + 7 * q^10 + 44 * q^14 - 16 * q^16 + 12 * q^19 + q^20 - 2 * q^25 - 24 * q^26 - 18 * q^29 - 16 * q^31 + 16 * q^34 - 10 * q^35 + 70 * q^40 - 14 * q^41 + 4 * q^44 + 10 * q^46 + 6 * q^49 + 31 * q^50 - 26 * q^55 + 16 * q^56 + 4 * q^59 + 6 * q^61 - 12 * q^64 - 23 * q^65 + 20 * q^70 + 12 * q^71 - 8 * q^74 - 10 * q^76 - 104 * q^79 - 33 * q^80 + 21 * q^85 + 4 * q^86 - 20 * q^89 - 44 * q^91 + 56 * q^94 - 20 * q^95

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