LMFDB - Embedded newform 585.2.bs.a.334.6

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			334.6
Root			$2.20467 - 1.27287i$ of defining polynomial
Character	$\chi$	$=$	585.334
Dual form			585.2.bs.a.289.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.20467 + 1.27287i) q^{2} +(2.24039 + 3.88048i) q^{4} +(0.817544 - 2.08125i) q^{5} +(2.54486 - 1.46928i) q^{7} +6.31544i q^{8} +O(q^{10})$	\(q+(2.20467 + 1.27287i) q^{2} +(2.24039 + 3.88048i) q^{4} +(0.817544 - 2.08125i) q^{5} +(2.54486 - 1.46928i) q^{7} +6.31544i q^{8} +(4.45158 - 3.54786i) q^{10} +(-0.317544 + 0.550003i) q^{11} +(-3.60484 + 0.0716710i) q^{13} +7.48079 q^{14} +(-3.55794 + 6.16253i) q^{16} +(-1.05998 + 0.611979i) q^{17} +(0.682456 + 1.18205i) q^{19} +(9.90788 - 1.49037i) q^{20} +(-1.40016 + 0.808385i) q^{22} +(1.86449 + 1.07646i) q^{23} +(-3.66324 - 3.40304i) q^{25} +(-8.03872 - 4.43048i) q^{26} +(11.4030 + 6.58351i) q^{28} +(-1.50000 + 2.59808i) q^{29} -8.96157 q^{31} +(-4.74954 + 2.74215i) q^{32} -3.11588 q^{34} +(-0.977401 - 6.49770i) q^{35} +(1.05998 + 0.611979i) q^{37} +3.47471i q^{38} +(13.1440 + 5.16315i) q^{40} +(-4.98079 + 8.62698i) q^{41} +(-1.18412 + 0.683650i) q^{43} -2.84570 q^{44} +(2.74039 + 4.74650i) q^{46} -6.16379i q^{47} +(0.817544 - 1.41603i) q^{49} +(-3.74464 - 12.1654i) q^{50} +(-8.35437 - 13.8279i) q^{52} -0.642285i q^{53} +(0.885090 + 1.11054i) q^{55} +(9.27912 + 16.0719i) q^{56} +(-6.61402 + 3.81861i) q^{58} +(-3.79833 - 6.57890i) q^{59} +(1.13509 + 1.96603i) q^{61} +(-19.7574 - 11.4069i) q^{62} +0.270178 q^{64} +(-2.79795 + 7.56118i) q^{65} +(6.95421 + 4.01502i) q^{67} +(-4.74954 - 2.74215i) q^{68} +(6.11588 - 15.5694i) q^{70} +(1.31754 + 2.28205i) q^{71} -10.3263i q^{73} +(1.55794 + 2.69843i) q^{74} +(-3.05794 + 5.29650i) q^{76} +1.86624i q^{77} -1.03843 q^{79} +(9.91702 + 12.4431i) q^{80} +(-21.9620 + 12.6798i) q^{82} -11.8452i q^{83} +(0.407104 + 2.70640i) q^{85} -3.48079 q^{86} +(-3.47351 - 2.00543i) q^{88} +(6.27912 - 10.8758i) q^{89} +(-9.06851 + 5.47890i) q^{91} +9.64680i q^{92} +(7.84570 - 13.5891i) q^{94} +(3.01808 - 0.453987i) q^{95} +(12.8031 - 7.39190i) q^{97} +(3.60484 - 2.08125i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.0231403\pi$
$2$	2.20467	+	1.27287i	1.55894	+	0.900055i	0.561582	+	0.827421i	$0.310193\pi$
$3$		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	0.0651198	−	0.997877i	$-0.479257\pi$
$7$	2.54486	−	1.46928i	0.961867	−	0.555334i	0.896747	+	0.442543i	$0.145924\pi$
$8$			6.31544i			2.23284i
$9$		0			0
$10$	4.45158	−	3.54786i	1.40771	−	1.12193i
$11$	−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	−0.623003	−	0.782220i	$-0.714088\pi$
$17$	−1.05998	+	0.611979i	−0.257082	+	0.148427i	0.365920	+	0.930646i	$0.380754\pi$
$18$		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	$0.783291\pi$
$20$	9.90788	−	1.49037i	2.21547	−	0.333256i
$21$		0			0
$22$	−1.40016	+	0.808385i	−0.298516	+	0.172348i
$23$	1.86449	+	1.07646i	0.388773	+	0.224458i	0.681628	−	0.731699i	$-0.261272\pi$
$23$	1.86449	+	1.07646i	0.388773	+	0.224458i	−0.292856	+	0.956157i	$0.594606\pi$
$24$		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
$35$	−0.977401	−	6.49770i	−0.165211	−	1.09831i
$36$		0			0
$37$	1.05998	+	0.611979i	0.174259	+	0.100609i	0.584593	−	0.811327i	$-0.301254\pi$
$37$	1.05998	+	0.611979i	0.174259	+	0.100609i	−0.410333	+	0.911936i	$0.634588\pi$
$38$			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	−0.587563	−	0.809178i	$-0.699913\pi$
$43$	−1.18412	+	0.683650i	−0.180576	+	0.104256i	0.406987	+	0.913434i	$0.366579\pi$
$44$	−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	$-0.851588\pi$
$47$		−	6.16379i		−	0.899081i	0.893260	−	0.449540i	$-0.148412\pi$
$48$		0			0
$49$	0.817544	−	1.41603i	0.116792	−	0.202290i
$50$	−3.74464	−	12.1654i	−0.529571	−	1.72045i
$51$		0			0
$52$	−8.35437	−	13.8279i	−1.15854	−	1.91759i
$53$		−	0.642285i		−	0.0882246i	−0.999027	−	0.0441123i	$-0.985954\pi$
$53$		−	0.642285i		−	0.0882246i	0.999027	−	0.0441123i	$-0.0140459\pi$
$54$		0			0
$55$	0.885090	+	1.11054i	0.119345	+	0.149746i
$56$	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
$65$	−2.79795	+	7.56118i	−0.347043	+	0.937849i
$66$		0			0
$67$	6.95421	+	4.01502i	0.849592	+	0.490512i	0.860513	−	0.509428i	$-0.170143\pi$
$67$	6.95421	+	4.01502i	0.849592	+	0.490512i	−0.0109212	+	0.999940i	$0.503476\pi$
$68$	−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	$-0.793453\pi$
$73$		−	10.3263i		−	1.20860i	0.796756	−	0.604301i	$-0.206547\pi$
$74$	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	$0.518605\pi$
$80$	9.91702	+	12.4431i	1.10876	+	1.39118i
$81$		0			0
$82$	−21.9620	+	12.6798i	−2.42530	+	1.40025i
$83$		−	11.8452i		−	1.30018i	−0.759855	−	0.650092i	$-0.774730\pi$
$83$		−	11.8452i		−	1.30018i	0.759855	−	0.650092i	$-0.225270\pi$
$84$		0			0
$85$	0.407104	+	2.70640i	0.0441566	+	0.293551i
$86$	−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
$95$	3.01808	−	0.453987i	0.309648	−	0.0465781i
$96$		0			0
$97$	12.8031	−	7.39190i	1.29996	−	0.750534i	0.319565	−	0.947564i	$-0.396463\pi$
$97$	12.8031	−	7.39190i	1.29996	−	0.750534i	0.980397	+	0.197031i	$0.0631299\pi$
$98$	3.60484	−	2.08125i	0.364144	−	0.210238i
$99$		0			0
$100$	4.99829	−	21.8393i	0.499829	−	2.18393i
$101$	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	$0.181721\pi$
$103$			10.9686i			1.08077i	−0.841419	+	0.540383i	$0.818279\pi$
$104$	−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	0.875123	−	0.483901i	$-0.160781\pi$
$107$	9.24360	+	5.33680i	0.893613	+	0.515928i	0.0184903	+	0.999829i	$0.494114\pi$
$108$		0			0
$109$	3.27018			0.313226			0.156613	−	0.987660i	$-0.449942\pi$
$109$	3.27018			0.313226			0.156613	+	0.987660i	$0.449942\pi$
$110$	0.537759	+	3.57499i	0.0512733	+	0.340862i
$111$		0			0
$112$			20.9104i			1.97584i
$113$	4.78895	−	2.76490i	0.450507	−	0.260100i	−0.257537	−	0.966268i	$-0.582911\pi$
$113$	4.78895	−	2.76490i	0.450507	−	0.260100i	0.708044	+	0.706168i	$0.249578\pi$
$114$		0			0
$115$	3.76470	−	3.00042i	0.351060	−	0.279790i
$116$	−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	−0.339813	−	0.940493i	$-0.610364\pi$
$127$	−14.9231	−	8.61586i	−1.32421	−	0.764534i	−0.984397	+	0.175959i	$0.943697\pi$
$128$	10.0947	+	5.82819i	0.892256	+	0.515144i
$129$		0			0
$130$	−15.7930	+	13.1085i	−1.38513	+	1.14969i
$131$	−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	−0.785254	−	0.619174i	$-0.787468\pi$
$137$	−7.51044	+	4.33616i	−0.641661	+	0.370463i	0.143593	+	0.989637i	$0.454134\pi$
$138$		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	$0.625474\pi$
$140$	23.0244	−	18.3502i	1.94592	−	1.55087i
$141$		0			0
$142$			6.70825i			0.562944i
$143$	1.10528	−	2.00543i	0.0924279	−	0.167703i
$144$		0			0
$145$	4.18094	+	5.24592i	0.347208	+	0.435650i
$146$	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	$0.261800\pi$
$157$			18.3646i			1.46566i	−0.680413	+	0.732829i	$0.738200\pi$
$158$	−2.28939	−	1.32178i	−0.182134	−	0.105155i
$159$		0			0
$160$	1.82415	+	12.1268i	0.144211	+	0.958709i
$161$	6.32648			0.498597
$162$		0			0
$163$	−3.47351	+	2.00543i	−0.272066	+	0.157078i	−0.629826	−	0.776736i	$-0.716874\pi$
$163$	−3.47351	+	2.00543i	−0.272066	+	0.157078i	0.357760	+	0.933814i	$0.383541\pi$
$164$	−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	0.398294	−	0.917258i	$-0.369602\pi$
$167$	−2.54486	−	1.46928i	−0.196927	−	0.113696i	−0.595221	+	0.803562i	$0.702936\pi$
$168$		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	−0.544337	−	0.838866i	$-0.683219\pi$
$173$	−1.18412	+	0.683650i	−0.0900267	+	0.0519769i	0.454311	+	0.890843i	$0.349886\pi$
$174$		0			0
$175$	−14.3224	−	3.27794i	−1.08267	−	0.247789i
$176$	−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
$185$	2.14026	−	1.70576i	0.157355	−	0.125410i
$186$		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	0.337493	−	0.941328i	$-0.390421\pi$
$193$	−4.29240	−	2.47822i	−0.308974	−	0.178386i	−0.646467	+	0.762942i	$0.723754\pi$
$194$	37.6357			2.70208
$195$		0			0
$196$	7.32648			0.523320
$197$	−5.84174	−	3.37273i	−0.416207	−	0.240297i	0.277246	−	0.960799i	$-0.410578\pi$
$197$	−5.84174	−	3.37273i	−0.416207	−	0.240297i	−0.693453	+	0.720502i	$0.743912\pi$
$198$		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
$205$	13.8829	+	17.4192i	0.969625	+	1.21661i
$206$	−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
$215$	0.454782	+	3.02336i	0.0310158	+	0.206191i
$216$		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	0.500241	−	0.865886i	$-0.333245\pi$
$223$	0.00719226	+	0.00415245i	0.000481629	+	0.000278069i	−0.499759	+	0.866164i	$0.666578\pi$
$224$	−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	−0.140040	−	0.990146i	$-0.544723\pi$
$227$	9.75454	−	5.63179i	0.647431	−	0.373795i	0.787471	+	0.616351i	$0.211390\pi$
$228$		0			0
$229$	16.5404			1.09302			0.546509	−	0.837453i	$-0.315957\pi$
$229$	16.5404			1.09302			0.546509	+	0.837453i	$0.315957\pi$
$230$	12.1191	−	1.82298i	0.799108	−	0.120204i
$231$		0			0
$232$	−16.4080	−	9.47315i	−1.07724	−	0.621943i
$233$		−	6.94941i		−	0.455271i	−0.973746	−	0.227636i	$-0.926900\pi$
$233$		−	6.94941i		−	0.455271i	0.973746	−	0.227636i	$-0.0730995\pi$
$234$		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
$245$	−2.27874	−	2.85918i	−0.145583	−	0.182667i
$246$		0			0
$247$	−2.54486	−	4.21218i	−0.161926	−	0.268015i
$248$		−	56.5962i		−	3.59386i
$249$		0			0
$250$	−28.3807	−	2.15223i	−1.79496	−	0.136119i
$251$	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	0.813494	−	0.581574i	$-0.197563\pi$
$257$	11.4877	+	6.63242i	0.716583	+	0.413719i	−0.0969108	+	0.995293i	$0.530896\pi$
$258$		0			0
$259$	3.59666			0.223486
$260$	−35.6095	+	6.08264i	−2.20841	+	0.377230i
$261$		0			0
$262$	−22.0467	−	12.7287i	−1.36205	−	0.786381i
$263$	−26.2150	−	15.1352i	−1.61649	−	0.933279i	−0.987819	−	0.155605i	$-0.950267\pi$
$263$	−26.2150	−	15.1352i	−1.61649	−	0.933279i	−0.628667	−	0.777674i	$-0.716399\pi$
$264$		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
$275$	3.03492	−	0.934179i	0.183013	−	0.0563331i
$276$		0			0
$277$	14.5363	−	8.39254i	0.873402	−	0.504259i	0.00492452	−	0.999988i	$-0.498432\pi$
$277$	14.5363	−	8.39254i	0.873402	−	0.504259i	0.868477	+	0.495729i	$0.165099\pi$
$278$			36.4715i			2.18741i
$279$		0			0
$280$	41.0358	−	6.17271i	2.45236	−	0.368890i
$281$	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	0.255617	−	0.966778i	$-0.417721\pi$
$283$	−7.63458	−	4.40783i	−0.453829	−	0.262018i	−0.709446	+	0.704760i	$0.751055\pi$
$284$	−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
$290$	2.54024	+	16.8873i	0.149168	+	0.991659i
$291$		0			0
$292$	40.0709	−	23.1350i	2.34497	−	1.35387i
$293$	−24.4675	+	14.1263i	−1.42940	+	0.825267i	−0.997074	−	0.0764476i	$-0.975642\pi$
$293$	−24.4675	+	14.1263i	−1.42940	+	0.825267i	−0.432331	+	0.901715i	$0.642309\pi$
$294$		0			0
$295$	−16.7977	+	2.52675i	−0.977999	+	0.147113i
$296$	−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
$305$	5.01980	−	0.755091i	0.287433	−	0.0432364i
$306$		0			0
$307$			12.7219i			0.726077i	0.931774	+	0.363039i	$0.118261\pi$
$307$			12.7219i			0.726077i	−0.931774	+	0.363039i	$0.881739\pi$
$308$	−7.24190	+	4.18112i	−0.412646	+	0.238241i
$309$		0			0
$310$	−39.8932	+	31.7944i	−2.26578	+	1.80580i
$311$	−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	$-0.755540\pi$
$313$		−	24.5807i		−	1.38938i	0.719307	−	0.694692i	$-0.244460\pi$
$314$	−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	$0.00209512\pi$
$317$			0.234377i			0.0131639i	−0.999978	+	0.00658196i	$0.997905\pi$
$318$		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
$325$	13.4493	+	12.0048i	0.746033	+	0.665909i
$326$	−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
$335$	14.0416	−	11.1910i	0.767177	−	0.611431i
$336$		0			0
$337$		−	21.2949i		−	1.16001i	−0.814614	−	0.580003i	$-0.803051\pi$
$337$		−	21.2949i		−	1.16001i	0.814614	−	0.580003i	$-0.196949\pi$
$338$	29.2958	+	15.3950i	1.59348	+	0.837379i
$339$		0			0
$340$	−9.59006	+	7.64317i	−0.520094	+	0.414509i
$341$	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	−0.408685	−	0.912675i	$-0.634013\pi$
$347$	3.30407	−	1.90761i	0.177372	−	0.102406i	0.586057	+	0.810270i	$0.300679\pi$
$348$		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	0.970562	−	0.240853i	$-0.0774272\pi$
$353$	23.4338	+	13.5295i	1.24726	+	0.720104i	0.276696	+	0.960958i	$0.410761\pi$
$354$		0			0
$355$	5.82669	−	0.876465i	0.309248	−	0.0465179i
$356$	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	0.648617	−	0.761115i	$-0.275348\pi$
$367$	6.01118	+	3.47055i	0.313781	+	0.181161i	−0.334836	+	0.942276i	$0.608681\pi$
$368$	−13.2675	+	7.65998i	−0.691615	+	0.399304i
$369$		0			0
$370$	6.88980	−	1.03638i	0.358184	−	0.0538789i
$371$	−0.943693	−	1.63452i	−0.0489941	−	0.0848603i
$372$		0			0
$373$	−2.00301	+	1.15644i	−0.103712	+	0.0598781i	−0.550959	−	0.834532i	$-0.685738\pi$
$373$	−2.00301	+	1.15644i	−0.103712	+	0.0598781i	0.447247	+	0.894411i	$0.352405\pi$
$374$	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	$0.124231\pi$
$380$	8.52337	+	10.6945i	0.437240	+	0.548615i
$381$		0			0
$382$			12.5854i			0.643923i
$383$	−17.8929	+	10.3305i	−0.914283	+	0.527861i	−0.881807	−	0.471611i	$-0.843673\pi$
$383$	−17.8929	+	10.3305i	−0.914283	+	0.527861i	−0.0324760	+	0.999473i	$0.510339\pi$
$384$		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	−0.689969	−	0.723839i	$-0.742376\pi$
$397$	−8.13113	+	4.69451i	−0.408090	+	0.235611i	0.281879	+	0.959450i	$0.409042\pi$
$398$			13.1753i			0.660420i
$399$		0			0
$400$	34.0049	−	10.4670i	1.70024	−	0.523352i
$401$	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	$0.481985\pi$
$410$	8.43492	+	56.0749i	0.416571	+	2.76934i
$411$		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
$425$	5.96554	+	1.36532i	0.289371	+	0.0662277i
$426$		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	−0.505323	−	0.862930i	$-0.668627\pi$
$433$	−0.221929	+	0.128130i	−0.0106652	+	0.00615756i	0.494658	+	0.869088i	$0.335293\pi$
$434$	−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	$0.224692\pi$
$440$	−7.01356	+	5.58973i	−0.334358	+	0.266480i
$441$		0			0
$442$	11.2322	−	0.223318i	0.534263	−	0.0106221i
$443$			4.32246i			0.205366i	0.994714	+	0.102683i	$0.0327428\pi$
$443$			4.32246i			0.205366i	−0.994714	+	0.102683i	$0.967257\pi$
$444$		0			0
$445$	−17.5017	−	21.9599i	−0.829663	−	1.04100i
$446$	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
$455$	3.98907	+	23.3531i	0.187010	+	1.09481i
$456$		0			0
$457$	13.3594	+	7.71304i	0.624925	+	0.360801i	0.778784	−	0.627292i	$-0.215837\pi$
$457$	13.3594	+	7.71304i	0.624925	+	0.360801i	−0.153859	+	0.988093i	$0.549170\pi$
$458$	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	$-0.947690\pi$
$463$		−	7.04045i		−	0.327197i	0.986527	−	0.163599i	$-0.0523102\pi$
$464$	−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	$-0.856663\pi$
$467$		−	18.8113i		−	0.870482i	0.900314	−	0.435241i	$-0.143337\pi$
$468$		0			0
$469$	23.5967			1.08959
$470$	−21.8683	−	27.4386i	−1.00871	−	1.26565i
$471$		0			0
$472$	41.5486	−	23.9881i	1.91243	−	1.10414i
$473$		−	0.868356i		−	0.0399271i
$474$		0			0
$475$	1.52255	−	6.65255i	0.0698594	−	0.305240i
$476$	−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
$485$	−4.91728	−	32.6898i	−0.223282	−	1.48437i
$486$		0			0
$487$	−27.9935	+	16.1620i	−1.26851	+	0.732372i	−0.974705	−	0.223495i	$-0.928253\pi$
$487$	−27.9935	+	16.1620i	−1.26851	+	0.732372i	−0.293800	+	0.955867i	$0.594920\pi$
$488$	−12.4163	+	7.16858i	−0.562062	+	0.324506i
$489$		0			0
$490$	−1.38451	−	9.20411i	−0.0625456	−	0.415799i
$491$	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	$0.724498\pi$
$500$	−41.3667	−	28.2573i	−1.84998	−	1.26370i
$501$		0			0
$502$			9.35181i			0.417392i
$503$	−24.3433	+	14.0546i	−1.08542	+	0.626665i	−0.932352	−	0.361551i	$-0.882247\pi$
$503$	−24.3433	+	14.0546i	−1.08542	+	0.626665i	−0.153063	+	0.988216i	$0.548914\pi$
$504$		0			0
$505$	−18.4404	−	23.1376i	−0.820587	−	1.02961i
$506$	−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
$520$	−47.7522	−	17.6703i	−2.09407	−	0.774893i
$521$	−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	−0.186706	−	0.982416i	$-0.559781\pi$
$523$	−25.8618	−	14.9313i	−1.13086	−	0.652900i	−0.944150	+	0.329516i	$0.893114\pi$
$524$	−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
$530$	−2.27874	−	2.85918i	−0.0989820	−	0.124195i
$531$		0			0
$532$			17.9718i			0.779177i
$533$	17.3366	−	31.4558i	0.750933	−	1.36250i
$534$		0			0
$535$	18.6643	−	14.8752i	0.806928	−	0.643112i
$536$	−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	$-0.979313\pi$
$547$		−	3.03789i		−	0.129891i	0.997889	−	0.0649454i	$-0.0206873\pi$
$548$	−33.6527	−	19.4294i	−1.43757	−	0.829983i
$549$		0			0
$550$	7.88011	+	1.80350i	0.336009	+	0.0769015i
$551$	−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	0.829140	−	0.559041i	$-0.188831\pi$
$557$	17.9264	+	10.3498i	0.759566	+	0.438536i	−0.0695738	+	0.997577i	$0.522164\pi$
$558$		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	−0.286464	−	0.958091i	$-0.592480\pi$
$563$	9.49188	−	5.48014i	0.400035	−	0.230960i	0.686499	+	0.727131i	$0.259147\pi$
$564$		0			0
$565$	−1.83929	−	12.2275i	−0.0773794	−	0.514413i
$566$	−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
$575$	−3.16683	−	10.2883i	−0.132066	−	0.429050i
$576$		0			0
$577$		−	18.3646i		−	0.764530i	−0.924053	−	0.382265i	$-0.875144\pi$
$577$		−	18.3646i		−	0.764530i	0.924053	−	0.382265i	$-0.124856\pi$
$578$	−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	0.487385	−	0.873187i	$-0.337951\pi$
$587$	−0.608726	−	0.351448i	−0.0251248	−	0.0145058i	−0.512510	+	0.858681i	$0.671284\pi$
$588$		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	$-0.723738\pi$
$593$		−	37.1593i		−	1.52595i	0.646428	−	0.762975i	$-0.276262\pi$
$594$		0			0
$595$	5.01248	+	6.28927i	0.205492	+	0.257835i
$596$	−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
$605$	23.4313	−	3.52459i	0.952616	−	0.143295i
$606$		0			0
$607$	33.5035	−	19.3433i	1.35987	−	0.785119i	0.370261	−	0.928928i	$-0.379268\pi$
$607$	33.5035	−	19.3433i	1.35987	−	0.785119i	0.989606	+	0.143809i	$0.0459350\pi$
$608$	−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	0.166269	−	0.986081i	$-0.446828\pi$
$613$	−14.9684	−	8.64201i	−0.604568	−	0.349047i	−0.770836	+	0.637033i	$0.780161\pi$
$614$	−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	−0.884540	−	0.466464i	$-0.845528\pi$
$617$	−22.9229	+	13.2345i	−0.922841	+	0.532803i	−0.0383009	+	0.999266i	$0.512195\pi$
$618$		0			0
$619$	31.0039			1.24615			0.623075	−	0.782162i	$-0.285883\pi$
$619$	31.0039			1.24615			0.623075	+	0.782162i	$0.285883\pi$
$620$	−88.7902	+	13.3560i	−3.56590	+	0.536392i
$621$		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
$635$	−30.1321	+	24.0149i	−1.19576	+	0.953003i
$636$		0			0
$637$	−2.84563	+	5.16315i	−0.112748	+	0.204571i
$638$		−	4.85031i		−	0.192026i
$639$		0			0
$640$	20.3828	−	16.2449i	0.805702	−	0.642136i
$641$	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	−0.289946	−	0.957043i	$-0.593637\pi$
$643$	9.98843	−	5.76682i	0.393905	−	0.227421i	0.683851	+	0.729622i	$0.260304\pi$
$644$	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	−0.228925	−	0.973444i	$-0.573521\pi$
$647$	−30.1779	−	17.4232i	−1.18641	−	0.684977i	−0.957490	+	0.288467i	$0.906854\pi$
$648$		0			0
$649$	4.82456			0.189380
$650$	14.3707	+	43.5860i	0.563666	+	1.70958i
$651$		0			0
$652$	−15.5641	−	8.98591i	−0.609535	−	0.351915i
$653$	−19.3324	−	11.1616i	−0.756537	−	0.436787i	0.0715139	−	0.997440i	$-0.477217\pi$
$653$	−19.3324	−	11.1616i	−0.756537	−	0.436787i	−0.828051	+	0.560653i	$0.810550\pi$
$654$		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
$665$	7.01356	−	5.58973i	0.271974	−	0.216760i
$666$		0			0
$667$	−5.59346	+	3.22939i	−0.216580	+	0.125042i
$668$		−	13.1670i		−	0.509448i
$669$		0			0
$670$	45.2020	−	6.79940i	1.74630	−	0.262684i
$671$	−1.44176			−0.0556587
$672$		0			0
$673$	−4.77457	−	2.75660i	−0.184046	−	0.106259i	0.405146	−	0.914252i	$-0.367221\pi$
$673$	−4.77457	−	2.75660i	−0.184046	−	0.106259i	−0.589192	+	0.807993i	$0.700554\pi$
$674$	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	$0.0294320\pi$
$677$			4.80479i			0.184663i	−0.995728	+	0.0923316i	$0.970568\pi$
$678$		0			0
$679$	21.7215	−	37.6227i	0.833594	−	1.44383i
$680$	−17.0921	+	2.57104i	−0.655453	+	0.0985949i
$681$		0			0
$682$	12.5477	−	7.24440i	0.480475	−	0.277403i
$683$	10.1866	−	5.88126i	0.389781	−	0.225040i	−0.292284	−	0.956331i	$-0.594415\pi$
$683$	10.1866	−	5.88126i	0.389781	−	0.225040i	0.682065	+	0.731291i	$0.261082\pi$
$684$		0			0
$685$	2.88453	+	19.1761i	0.110212	+	0.732683i
$686$	−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
$695$	31.6786	−	4.76518i	1.20164	−	0.180753i
$696$		0			0
$697$		−	12.1925i		−	0.461825i
$698$	53.6320	−	30.9644i	2.03000	−	1.17202i
$699$		0			0
$700$	−19.3679	−	62.9218i	−0.732039	−	2.37822i
$701$	−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
$715$	−3.27020	−	3.93989i	−0.122299	−	0.147344i
$716$	−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
$725$	14.3362	−	4.41283i	0.532434	−	0.163888i
$726$		0			0
$727$		−	26.2596i		−	0.973916i	−0.873425	−	0.486958i	$-0.838107\pi$
$727$		−	26.2596i		−	0.973916i	0.873425	−	0.486958i	$-0.161893\pi$
$728$	−34.6016	−	57.2716i	−1.28242	−	2.12263i
$729$		0			0
$730$	−36.6363	−	45.9684i	−1.35597	−	1.70137i
$731$	0.836758	−	1.44931i	0.0309486	−	0.0536046i
$732$		0			0
$733$		−	31.7811i		−	1.17386i	−0.809637	−	0.586931i	$-0.800336\pi$
$733$		−	31.7811i		−	1.17386i	0.809637	−	0.586931i	$-0.199664\pi$
$734$	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	0.449607	−	0.893227i	$-0.351564\pi$
$743$	−2.70254	−	1.56031i	−0.0991465	−	0.0572423i	−0.548753	+	0.835984i	$0.684897\pi$
$744$		0			0
$745$	37.9328	−	5.70594i	1.38975	−	0.209050i
$746$	−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	0.417587	−	0.908637i	$-0.362876\pi$
$757$	−4.41654	−	2.54989i	−0.160522	−	0.0926774i	−0.578109	+	0.815960i	$0.696209\pi$
$758$	11.4102	−	6.58767i	0.414436	−	0.239275i
$759$		0			0
$760$	2.86713	+	19.0605i	0.104002	+	0.691397i
$761$	−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	$0.0547638\pi$
$770$	6.62117	+	8.30773i	0.238610	+	0.299390i
$771$		0			0
$772$		−	22.2088i		−	0.799311i
$773$	42.6350	−	24.6153i	1.53347	−	0.885351i	0.534275	−	0.845311i	$-0.320585\pi$
$773$	42.6350	−	24.6153i	1.53347	−	0.885351i	0.999198	−	0.0400400i	$-0.0127485\pi$
$774$		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	−0.643349	−	0.765573i	$-0.722455\pi$
$787$	−8.47263	+	4.89168i	−0.302017	+	0.174369i	0.341332	+	0.939943i	$0.389122\pi$
$788$		−	30.2250i		−	1.07672i
$789$		0			0
$790$	−4.62264	+	3.68419i	−0.164466	+	0.131078i
$791$	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	−0.731721	−	0.681604i	$-0.761283\pi$
$797$	−14.3216	+	8.26856i	−0.507296	+	0.292887i	0.224426	+	0.974491i	$0.427949\pi$
$798$		0			0
$799$	3.77211	+	6.53348i	0.133448	+	0.231138i
$800$	26.7303	+	6.11770i	0.945060	+	0.216293i
$801$		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
$815$	1.33407	+	8.86879i	0.0467303	+	0.310660i
$816$		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	−0.901980	−	0.431777i	$-0.857887\pi$
$823$	−28.0867	+	16.2159i	−0.979041	+	0.565249i	−0.0770602	+	0.997026i	$0.524553\pi$
$824$	−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	$-0.842371\pi$
$827$		−	27.3319i		−	0.950425i	0.879871	−	0.475212i	$-0.157629\pi$
$828$		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	$0.147084\pi$
$830$	−42.0253	−	52.7301i	−1.45872	−	1.83029i
$831$		0			0
$832$	−0.973947	+	0.0193639i	−0.0337655	+	0.000671322i
$833$			2.00128i			0.0693402i
$834$		0			0
$835$	−5.13847	+	4.09531i	−0.177824	+	0.141724i
$836$	−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
$845$	9.54424	−	27.4574i	0.328332	−	0.944562i
$846$		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	$0.180480\pi$
$853$			31.3732i			1.07420i	−0.843519	+	0.537099i	$0.819520\pi$
$854$	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	$0.118411\pi$
$857$			21.2813i			0.726955i	−0.931603	+	0.363478i	$0.881589\pi$
$858$		0			0
$859$	−56.8502			−1.93970			−0.969851	−	0.243698i	$-0.921639\pi$
$859$	−56.8502			−1.93970			−0.969851	+	0.243698i	$0.921639\pi$
$860$	−10.7132	+	8.53829i	−0.365317	+	0.291153i
$861$		0			0
$862$	−35.8251	+	20.6837i	−1.22021	+	0.704488i
$863$			32.8011i			1.11656i	0.829651	+	0.558282i	$0.188539\pi$
$863$			32.8011i			1.11656i	−0.829651	+	0.558282i	$0.811461\pi$
$864$		0			0
$865$	0.454782	+	3.02336i	0.0154630	+	0.102797i
$866$	−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
$875$	−18.5315	+	27.1288i	−0.626478	+	0.917120i
$876$		0			0
$877$	−31.2333	+	18.0325i	−1.05467	+	0.608916i	−0.923954	−	0.382504i	$-0.875062\pi$
$877$	−31.2333	+	18.0325i	−1.05467	+	0.608916i	−0.130719	+	0.991419i	$0.541729\pi$
$878$	−16.7482	+	9.66956i	−0.565223	+	0.326332i
$879$		0			0
$880$	−9.99285	+	1.50315i	−0.336859	+	0.0506712i
$881$	−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	$-0.995703\pi$
$883$		−	0.802236i		−	0.0269974i	0.999909	−	0.0134987i	$-0.00429690\pi$
$884$	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	0.614804	−	0.788680i	$-0.289235\pi$
$887$	7.12365	+	4.11284i	0.239189	+	0.138096i	−0.375615	+	0.926776i	$0.622569\pi$
$888$		0			0
$889$	−50.6363			−1.69829
$890$	−10.6336	−	70.6918i	−0.356440	−	2.36959i
$891$		0			0
$892$			0.0372125i			0.00124597i
$893$	7.28589	−	4.20651i	0.243813	−	0.140766i
$894$		0			0
$895$	10.8511	+	13.6151i	0.362713	+	0.455104i
$896$	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	0.869077	−	0.494677i	$-0.164714\pi$
$907$	26.3583	+	15.2180i	0.875213	+	0.505305i	0.00613601	+	0.999981i	$0.498047\pi$
$908$	43.7080	+	25.2348i	1.45050	+	0.837447i
$909$		0			0
$910$	−20.9309	+	56.5636i	−0.693852	+	1.87506i
$911$	−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	$-0.375745\pi$
$920$	18.9490	+	23.7757i	0.624728	+	0.783861i
$921$		0			0
$922$			65.8957i			2.17016i
$923$	−4.91309	−	8.13201i	−0.161716	−	0.267668i
$924$		0			0
$925$	−1.80037	−	5.84897i	−0.0591958	−	0.192313i
$926$	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	$0.252485\pi$
$937$			43.6264i			1.42521i	−0.701565	+	0.712606i	$0.747515\pi$
$938$	52.0230	+	30.0355i	1.69861	+	0.980693i
$939$		0			0
$940$	−9.18631	−	61.0701i	−0.299625	−	1.99189i
$941$	−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	0.191732	−	0.981447i	$-0.438590\pi$
$947$	−17.3057	−	9.99146i	−0.562360	−	0.324679i	−0.754092	+	0.656769i	$0.771923\pi$
$948$		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	−0.940967	−	0.338498i	$-0.890081\pi$
$953$	−34.5228	+	19.9317i	−1.11830	+	0.645652i	−0.177335	+	0.984150i	$0.556748\pi$
$954$		0			0
$955$	10.9315	−	1.64434i	0.353734	−	0.0532095i
$956$	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
$965$	−8.66704	+	6.90753i	−0.279002	+	0.222361i
$966$		0			0
$967$		−	43.8607i		−	1.41047i	−0.708975	−	0.705233i	$-0.750842\pi$
$967$		−	43.8607i		−	1.41047i	0.708975	−	0.705233i	$-0.249158\pi$
$968$	−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	0.996578	−	0.0826604i	$-0.0263417\pi$
$977$	44.4875	+	25.6849i	1.42328	+	0.821731i	0.426703	+	0.904392i	$0.359675\pi$
$978$		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	$0.202802\pi$
$983$			37.3026i			1.18977i	−0.803811	+	0.594885i	$0.797198\pi$
$984$		0			0
$985$	−11.7954	+	9.40079i	−0.375832	+	0.299534i
$986$	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
$995$	11.4439	−	1.72142i	0.362796	−	0.0545727i
$996$		0			0
$997$	19.8743	−	11.4744i	0.629425	−	0.363399i	−0.151104	−	0.988518i	$-0.548283\pi$
$997$	19.8743	−	11.4744i	0.629425	−	0.363399i	0.780529	+	0.625119i	$0.214950\pi$
$998$	−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.334.6		12
3.2	odd	2		65.2.n.a.9.1	✓	12
5.4	even	2	inner	585.2.bs.a.334.1		12
12.11	even	2		1040.2.dh.a.529.2		12
13.3	even	3	inner	585.2.bs.a.289.1		12
15.2	even	4		325.2.e.e.126.6		12
15.8	even	4		325.2.e.e.126.1		12
15.14	odd	2		65.2.n.a.9.6	yes	12
39.2	even	12		845.2.l.f.699.1		24
39.5	even	4		845.2.l.f.654.2		24
39.8	even	4		845.2.l.f.654.12		24
39.11	even	12		845.2.l.f.699.11		24
39.17	odd	6		845.2.b.e.339.1		6
39.20	even	12		845.2.d.d.844.1		12
39.23	odd	6		845.2.n.e.484.1		12
39.29	odd	6		65.2.n.a.29.6	yes	12
39.32	even	12		845.2.d.d.844.11		12
39.35	odd	6		845.2.b.d.339.6		6
39.38	odd	2		845.2.n.e.529.6		12
60.59	even	2		1040.2.dh.a.529.5		12
65.29	even	6	inner	585.2.bs.a.289.6		12
156.107	even	6		1040.2.dh.a.289.5		12
195.17	even	12		4225.2.a.bq.1.6		6
195.29	odd	6		65.2.n.a.29.1	yes	12
195.44	even	4		845.2.l.f.654.11		24
195.59	even	12		845.2.d.d.844.12		12
195.68	even	12		325.2.e.e.276.1		12
195.74	odd	6		845.2.b.d.339.1		6
195.89	even	12		845.2.l.f.699.2		24
195.107	even	12		325.2.e.e.276.6		12
195.113	even	12		4225.2.a.br.1.6		6
195.119	even	12		845.2.l.f.699.12		24
195.134	odd	6		845.2.b.e.339.6		6
195.149	even	12		845.2.d.d.844.2		12
195.152	even	12		4225.2.a.br.1.1		6
195.164	even	4		845.2.l.f.654.1		24
195.173	even	12		4225.2.a.bq.1.1		6
195.179	odd	6		845.2.n.e.484.6		12
195.194	odd	2		845.2.n.e.529.1		12
780.419	even	6		1040.2.dh.a.289.2		12

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

\(f(q)\)	\(=\)	\(q+(2.20467 + 1.27287i) q^{2} +(2.24039 + 3.88048i) q^{4} +(0.817544 - 2.08125i) q^{5} +(2.54486 - 1.46928i) q^{7} +6.31544i q^{8} +O(q^{10})\)	\(q+(2.20467 + 1.27287i) q^{2} +(2.24039 + 3.88048i) q^{4} +(0.817544 - 2.08125i) q^{5} +(2.54486 - 1.46928i) q^{7} +6.31544i q^{8} +(4.45158 - 3.54786i) q^{10} +(-0.317544 + 0.550003i) q^{11} +(-3.60484 + 0.0716710i) q^{13} +7.48079 q^{14} +(-3.55794 + 6.16253i) q^{16} +(-1.05998 + 0.611979i) q^{17} +(0.682456 + 1.18205i) q^{19} +(9.90788 - 1.49037i) q^{20} +(-1.40016 + 0.808385i) q^{22} +(1.86449 + 1.07646i) q^{23} +(-3.66324 - 3.40304i) q^{25} +(-8.03872 - 4.43048i) q^{26} +(11.4030 + 6.58351i) q^{28} +(-1.50000 + 2.59808i) q^{29} -8.96157 q^{31} +(-4.74954 + 2.74215i) q^{32} -3.11588 q^{34} +(-0.977401 - 6.49770i) q^{35} +(1.05998 + 0.611979i) q^{37} +3.47471i q^{38} +(13.1440 + 5.16315i) q^{40} +(-4.98079 + 8.62698i) q^{41} +(-1.18412 + 0.683650i) q^{43} -2.84570 q^{44} +(2.74039 + 4.74650i) q^{46} -6.16379i q^{47} +(0.817544 - 1.41603i) q^{49} +(-3.74464 - 12.1654i) q^{50} +(-8.35437 - 13.8279i) q^{52} -0.642285i q^{53} +(0.885090 + 1.11054i) q^{55} +(9.27912 + 16.0719i) q^{56} +(-6.61402 + 3.81861i) q^{58} +(-3.79833 - 6.57890i) q^{59} +(1.13509 + 1.96603i) q^{61} +(-19.7574 - 11.4069i) q^{62} +0.270178 q^{64} +(-2.79795 + 7.56118i) q^{65} +(6.95421 + 4.01502i) q^{67} +(-4.74954 - 2.74215i) q^{68} +(6.11588 - 15.5694i) q^{70} +(1.31754 + 2.28205i) q^{71} -10.3263i q^{73} +(1.55794 + 2.69843i) q^{74} +(-3.05794 + 5.29650i) q^{76} +1.86624i q^{77} -1.03843 q^{79} +(9.91702 + 12.4431i) q^{80} +(-21.9620 + 12.6798i) q^{82} -11.8452i q^{83} +(0.407104 + 2.70640i) q^{85} -3.48079 q^{86} +(-3.47351 - 2.00543i) q^{88} +(6.27912 - 10.8758i) q^{89} +(-9.06851 + 5.47890i) q^{91} +9.64680i q^{92} +(7.84570 - 13.5891i) q^{94} +(3.01808 - 0.453987i) q^{95} +(12.8031 - 7.39190i) q^{97} +(3.60484 - 2.08125i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 6 q^{5}+O(q^{10}) \) 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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