LMFDB - Embedded newform 819.2.do.e.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(361,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 5]))

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

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

chi := DirichletCharacter("819.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.do (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.3
Root			$-1.18541 - 0.771231i$ of defining polynomial
Character	$\chi$	$=$	819.361
Dual form			819.2.do.e.667.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.433001 - 0.249993i) q^{2} +(-0.875007 - 1.51556i) q^{4} +(-0.902810 + 0.521238i) q^{5} +(1.52469 + 2.16225i) q^{7} +1.87496i q^{8} +O(q^{10})$	\(q+(-0.433001 - 0.249993i) q^{2} +(-0.875007 - 1.51556i) q^{4} +(-0.902810 + 0.521238i) q^{5} +(1.52469 + 2.16225i) q^{7} +1.87496i q^{8} +0.521224 q^{10} -3.96730i q^{11} +(-3.57504 - 0.468096i) q^{13} +(-0.119647 - 1.31742i) q^{14} +(-1.28129 + 2.21925i) q^{16} +(0.0710177 + 0.123006i) q^{17} -5.50977i q^{19} +(1.57993 + 0.912173i) q^{20} +(-0.991800 + 1.71785i) q^{22} +(-2.19549 + 3.80270i) q^{23} +(-1.95662 + 3.38897i) q^{25} +(1.43097 + 1.09642i) q^{26} +(1.94289 - 4.20274i) q^{28} +(-4.19880 - 7.27253i) q^{29} +(-2.46516 - 1.42326i) q^{31} +(4.35712 - 2.51558i) q^{32} -0.0710158i q^{34} +(-2.50355 - 1.15737i) q^{35} +(-0.730221 - 0.421593i) q^{37} +(-1.37740 + 2.38574i) q^{38} +(-0.977298 - 1.69273i) q^{40} +(-10.4766 + 6.04869i) q^{41} +(2.41161 - 4.17704i) q^{43} +(-6.01267 + 3.47142i) q^{44} +(1.90130 - 1.09772i) q^{46} +(-3.94602 + 2.27824i) q^{47} +(-2.35062 + 6.59353i) q^{49} +(1.69444 - 0.978285i) q^{50} +(2.41875 + 5.82776i) q^{52} +(-0.139800 + 0.242141i) q^{53} +(2.06791 + 3.58172i) q^{55} +(-4.05412 + 2.85873i) q^{56} +4.19868i q^{58} +(-9.33705 + 5.39075i) q^{59} -5.86354 q^{61} +(0.711612 + 1.23255i) q^{62} +2.60963 q^{64} +(3.47157 - 1.44084i) q^{65} +5.14447i q^{67} +(0.124282 - 0.215263i) q^{68} +(0.794706 + 1.12701i) q^{70} +(3.20326 + 1.84940i) q^{71} +(-5.72686 - 3.30640i) q^{73} +(0.210791 + 0.365101i) q^{74} +(-8.35036 + 4.82108i) q^{76} +(8.57829 - 6.04892i) q^{77} +(-5.96135 - 10.3254i) q^{79} -2.67142i q^{80} +6.04853 q^{82} -2.87321i q^{83} +(-0.128231 - 0.0740342i) q^{85} +(-2.08846 + 1.20578i) q^{86} +7.43852 q^{88} +(-1.51351 - 0.873824i) q^{89} +(-4.43870 - 8.44381i) q^{91} +7.68427 q^{92} +2.27818 q^{94} +(2.87190 + 4.97427i) q^{95} +(2.34079 + 1.35145i) q^{97} +(2.66616 - 2.26737i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7}+O(q^{10}) $ 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7	$ 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7} - 24 q^{10} - 2 q^{13} - 4 q^{14} - 8 q^{16} - 17 q^{17} + 3 q^{20} - 15 q^{22} - 3 q^{23} - 5 q^{25} + 9 q^{26} + 27 q^{28} + q^{29} - 18 q^{31} - 18 q^{32} - 18 q^{35} + 15 q^{37} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} - 30 q^{46} - 15 q^{47} + 9 q^{49} - 18 q^{50} + 47 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{59} - 10 q^{61} - 41 q^{62} + 2 q^{64} + 3 q^{65} + 11 q^{68} - 3 q^{70} - 30 q^{71} - 42 q^{73} + 33 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} - 10 q^{82} - 21 q^{85} - 57 q^{86} + 28 q^{88} - 48 q^{89} - 16 q^{91} + 66 q^{92} - 2 q^{94} - 2 q^{95} - 3 q^{97} + 36 q^{98}+O(q^{100}) $ 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7 - 24 * q^10 - 2 * q^13 - 4 * q^14 - 8 * q^16 - 17 * q^17 + 3 * q^20 - 15 * q^22 - 3 * q^23 - 5 * q^25 + 9 * q^26 + 27 * q^28 + q^29 - 18 * q^31 - 18 * q^32 - 18 * q^35 + 15 * q^37 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 - 33 * q^44 - 30 * q^46 - 15 * q^47 + 9 * q^49 - 18 * q^50 + 47 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^59 - 10 * q^61 - 41 * q^62 + 2 * q^64 + 3 * q^65 + 11 * q^68 - 3 * q^70 - 30 * q^71 - 42 * q^73 + 33 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 - 10 * q^82 - 21 * q^85 - 57 * q^86 + 28 * q^88 - 48 * q^89 - 16 * q^91 + 66 * q^92 - 2 * q^94 - 2 * q^95 - 3 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.433001	−	0.249993i	−0.306178	−	0.176772i	0.339037	−	0.940773i	$-0.389899\pi$
$2$	−0.433001	−	0.249993i	−0.306178	−	0.176772i	−0.645215	+	0.764001i	$0.723232\pi$
$3$		0			0
$3$		0			0
$4$	−0.875007	−	1.51556i	−0.437503	−	0.757778i
$5$	−0.902810	+	0.521238i	−0.403749	+	0.233105i	−0.688100	−	0.725616i	$-0.741555\pi$
$5$	−0.902810	+	0.521238i	−0.403749	+	0.233105i	0.284351	+	0.958720i	$0.408222\pi$
$6$		0			0
$7$	1.52469	+	2.16225i	0.576280	+	0.817252i
$7$	1.52469	+	2.16225i	0.576280	+	0.817252i
$8$			1.87496i			0.662897i
$9$		0			0
$10$	0.521224			0.164825
$11$		−	3.96730i		−	1.19619i	−0.801426	−	0.598094i	$-0.795925\pi$
$11$		−	3.96730i		−	1.19619i	0.801426	−	0.598094i	$-0.204075\pi$
$12$		0			0
$13$	−3.57504	−	0.468096i	−0.991537	−	0.129827i
$13$	−3.57504	−	0.468096i	−0.991537	−	0.129827i
$14$	−0.119647	−	1.31742i	−0.0319770	−	0.352095i
$15$		0			0
$16$	−1.28129	+	2.21925i	−0.320322	+	0.554813i
$17$	0.0710177	+	0.123006i	0.0172243	+	0.0298334i	0.874509	−	0.485009i	$-0.161184\pi$
$17$	0.0710177	+	0.123006i	0.0172243	+	0.0298334i	−0.857285	+	0.514843i	$0.827850\pi$
$18$		0			0
$19$		−	5.50977i		−	1.26403i	−0.774957	−	0.632014i	$-0.782229\pi$
$19$		−	5.50977i		−	1.26403i	0.774957	−	0.632014i	$-0.217771\pi$
$20$	1.57993	+	0.912173i	0.353283	+	0.203968i
$21$		0			0
$22$	−0.991800	+	1.71785i	−0.211452	+	0.366246i
$23$	−2.19549	+	3.80270i	−0.457791	+	0.792917i	−0.998844	−	0.0480711i	$-0.984693\pi$
$23$	−2.19549	+	3.80270i	−0.457791	+	0.792917i	0.541053	+	0.840989i	$0.318026\pi$
$24$		0			0
$25$	−1.95662	+	3.38897i	−0.391325	+	0.677794i
$26$	1.43097	+	1.09642i	0.280637	+	0.215026i
$27$		0			0
$28$	1.94289	−	4.20274i	0.367171	−	0.794243i
$29$	−4.19880	−	7.27253i	−0.779697	−	1.35047i	−0.932116	−	0.362159i	$-0.882040\pi$
$29$	−4.19880	−	7.27253i	−0.779697	−	1.35047i	0.152419	−	0.988316i	$-0.451294\pi$
$30$		0			0
$31$	−2.46516	−	1.42326i	−0.442756	−	0.255625i	0.262010	−	0.965065i	$-0.415615\pi$
$31$	−2.46516	−	1.42326i	−0.442756	−	0.255625i	−0.704766	+	0.709440i	$0.748948\pi$
$32$	4.35712	−	2.51558i	0.770237	−	0.444696i
$33$		0			0
$34$		−	0.0710158i		−	0.0121791i
$35$	−2.50355	−	1.15737i	−0.423178	−	0.195631i
$36$		0			0
$37$	−0.730221	−	0.421593i	−0.120048	−	0.0693095i	0.438774	−	0.898598i	$-0.355413\pi$
$37$	−0.730221	−	0.421593i	−0.120048	−	0.0693095i	−0.558821	+	0.829288i	$0.688746\pi$
$38$	−1.37740	+	2.38574i	−0.223445	+	0.387017i
$39$		0			0
$40$	−0.977298	−	1.69273i	−0.154524	−	0.267644i
$41$	−10.4766	+	6.04869i	−1.63618	+	0.944647i	−0.654044	+	0.756457i	$0.726929\pi$
$41$	−10.4766	+	6.04869i	−1.63618	+	0.944647i	−0.982133	+	0.188190i	$0.939738\pi$
$42$		0			0
$43$	2.41161	−	4.17704i	0.367768	−	0.636993i	−0.621448	−	0.783455i	$-0.713455\pi$
$43$	2.41161	−	4.17704i	0.367768	−	0.636993i	0.989216	+	0.146463i	$0.0467888\pi$
$44$	−6.01267	+	3.47142i	−0.906444	+	0.523336i
$45$		0			0
$46$	1.90130	−	1.09772i	0.280331	−	0.161849i
$47$	−3.94602	+	2.27824i	−0.575587	+	0.332315i	−0.759378	−	0.650650i	$-0.774496\pi$
$47$	−3.94602	+	2.27824i	−0.575587	+	0.332315i	0.183791	+	0.982965i	$0.441163\pi$
$48$		0			0
$49$	−2.35062	+	6.59353i	−0.335803	+	0.941932i
$50$	1.69444	−	0.978285i	0.239630	−	0.138350i
$51$		0			0
$52$	2.41875	+	5.82776i	0.335421	+	0.808164i
$53$	−0.139800	+	0.242141i	−0.0192030	+	0.0332606i	−0.875467	−	0.483278i	$-0.839446\pi$
$53$	−0.139800	+	0.242141i	−0.0192030	+	0.0332606i	0.856264	+	0.516538i	$0.172780\pi$
$54$		0			0
$55$	2.06791	+	3.58172i	0.278837	+	0.482959i
$56$	−4.05412	+	2.85873i	−0.541754	+	0.382014i
$57$		0			0
$58$			4.19868i			0.551314i
$59$	−9.33705	+	5.39075i	−1.21558	+	0.701815i	−0.963969	−	0.266013i	$-0.914294\pi$
$59$	−9.33705	+	5.39075i	−1.21558	+	0.701815i	−0.251611	+	0.967829i	$0.580960\pi$
$60$		0			0
$61$	−5.86354			−0.750749			−0.375374	−	0.926873i	$-0.622486\pi$
$61$	−5.86354			−0.750749			−0.375374	+	0.926873i	$0.622486\pi$
$62$	0.711612	+	1.23255i	0.0903748	+	0.156534i
$63$		0			0
$64$	2.60963			0.326204
$65$	3.47157	−	1.44084i	0.430595	−	0.178714i
$66$		0			0
$67$			5.14447i			0.628497i	0.949341	+	0.314248i	$0.101753\pi$
$67$			5.14447i			0.628497i	−0.949341	+	0.314248i	$0.898247\pi$
$68$	0.124282	−	0.215263i	0.0150714	−	0.0261044i
$69$		0			0
$70$	0.794706	+	1.12701i	0.0949856	+	0.134704i
$71$	3.20326	+	1.84940i	0.380157	+	0.219484i	0.677887	−	0.735167i	$-0.262896\pi$
$71$	3.20326	+	1.84940i	0.380157	+	0.219484i	−0.297730	+	0.954650i	$0.596229\pi$
$72$		0			0
$73$	−5.72686	−	3.30640i	−0.670278	−	0.386985i	0.125904	−	0.992042i	$-0.459817\pi$
$73$	−5.72686	−	3.30640i	−0.670278	−	0.386985i	−0.796182	+	0.605057i	$0.793150\pi$
$74$	0.210791	+	0.365101i	0.0245040	+	0.0424421i
$75$		0			0
$76$	−8.35036	+	4.82108i	−0.957852	+	0.553016i
$77$	8.57829	−	6.04892i	0.977587	−	0.689339i
$78$		0			0
$79$	−5.96135	−	10.3254i	−0.670705	−	1.16169i	−0.977705	−	0.209985i	$-0.932658\pi$
$79$	−5.96135	−	10.3254i	−0.670705	−	1.16169i	0.307000	−	0.951710i	$-0.400675\pi$
$80$		−	2.67142i		−	0.298674i
$81$		0			0
$82$	6.04853			0.667948
$83$		−	2.87321i		−	0.315376i	−0.987489	−	0.157688i	$-0.949596\pi$
$83$		−	2.87321i		−	0.315376i	0.987489	−	0.157688i	$-0.0504040\pi$
$84$		0			0
$85$	−0.128231	−	0.0740342i	−0.0139086	−	0.00803013i
$86$	−2.08846	+	1.20578i	−0.225205	+	0.130022i
$87$		0			0
$88$	7.43852			0.792949
$89$	−1.51351	−	0.873824i	−0.160432	−	0.0926252i	0.417635	−	0.908615i	$-0.362859\pi$
$89$	−1.51351	−	0.873824i	−0.160432	−	0.0926252i	−0.578066	+	0.815990i	$0.696193\pi$
$90$		0			0
$91$	−4.43870	−	8.44381i	−0.465302	−	0.885152i
$92$	7.68427			0.801141
$93$		0			0
$94$	2.27818			0.234976
$95$	2.87190	+	4.97427i	0.294650	+	0.510350i
$96$		0			0
$97$	2.34079	+	1.35145i	0.237671	+	0.137219i	0.614106	−	0.789224i	$-0.289517\pi$
$97$	2.34079	+	1.35145i	0.237671	+	0.137219i	−0.376435	+	0.926443i	$0.622850\pi$
$98$	2.66616	−	2.26737i	0.269323	−	0.229039i
$99$		0			0
$100$	6.84823			0.684823
$101$	11.4722			1.14153			0.570765	−	0.821114i	$-0.306647\pi$
$101$	11.4722			1.14153			0.570765	+	0.821114i	$0.306647\pi$
$102$		0			0
$103$	2.08475	+	3.61090i	0.205417	+	0.355792i	0.950265	−	0.311441i	$-0.100812\pi$
$103$	2.08475	+	3.61090i	0.205417	+	0.355792i	−0.744849	+	0.667233i	$0.767478\pi$
$104$	0.877660	−	6.70304i	0.0860617	−	0.657287i
$105$		0			0
$106$	0.121067	−	0.0698982i	0.0117591	−	0.00678911i
$107$	4.24371	−	7.35032i	0.410255	−	0.710583i	−0.584662	−	0.811277i	$-0.698773\pi$
$107$	4.24371	−	7.35032i	0.410255	−	0.710583i	0.994917	+	0.100694i	$0.0321063\pi$
$108$		0			0
$109$	−5.56886	−	3.21518i	−0.533400	−	0.307958i	0.209000	−	0.977916i	$-0.432979\pi$
$109$	−5.56886	−	3.21518i	−0.533400	−	0.307958i	−0.742400	+	0.669957i	$0.766312\pi$
$110$		−	2.06785i		−	0.197162i
$111$		0			0
$112$	−6.75214	+	0.613225i	−0.638018	+	0.0579443i
$113$	5.48164	−	9.49448i	0.515670	−	0.893166i	−0.484165	−	0.874977i	$-0.660877\pi$
$113$	5.48164	−	9.49448i	0.515670	−	0.893166i	0.999835	−	0.0181892i	$-0.00579012\pi$
$114$		0			0
$115$		−	4.57749i		−	0.426853i
$116$	−7.34795	+	12.7270i	−0.682240	+	1.18167i
$117$		0			0
$118$	5.39060			0.496245
$119$	−0.157690	+	0.341105i	−0.0144554	+	0.0312690i
$120$		0			0
$121$	−4.73951			−0.430864
$122$	2.53892	+	1.46584i	0.229863	+	0.132711i
$123$		0			0
$124$			4.98145i			0.447348i
$125$		−	9.29184i		−	0.831087i
$126$		0			0
$127$	−1.00394	−	1.73887i	−0.0890849	−	0.154300i	0.818040	−	0.575162i	$-0.195061\pi$
$127$	−1.00394	−	1.73887i	−0.0890849	−	0.154300i	−0.907125	+	0.420862i	$0.861728\pi$
$128$	−9.84421	−	5.68356i	−0.870113	−	0.502360i
$129$		0			0
$130$	−1.86339	−	0.243983i	−0.163430	−	0.0213987i
$131$	−6.22511	−	10.7822i	−0.543890	−	0.942046i	−0.998676	−	0.0514449i	$-0.983617\pi$
$131$	−6.22511	−	10.7822i	−0.543890	−	0.942046i	0.454785	−	0.890601i	$-0.349716\pi$
$132$		0			0
$133$	11.9135	−	8.40071i	1.03303	−	0.728434i
$134$	1.28608	−	2.22756i	0.111101	−	0.192432i
$135$		0			0
$136$	−0.230631	+	0.133155i	−0.0197765	+	0.0114180i
$137$	−4.54246	+	2.62259i	−0.388088	+	0.224063i	−0.681332	−	0.731975i	$-0.738599\pi$
$137$	−4.54246	+	2.62259i	−0.388088	+	0.224063i	0.293243	+	0.956038i	$0.405265\pi$
$138$		0			0
$139$	10.3693	−	17.9601i	0.879510	−	1.52336i	0.0276301	−	0.999618i	$-0.491204\pi$
$139$	10.3693	−	17.9601i	0.879510	−	1.52336i	0.851880	−	0.523737i	$-0.175463\pi$
$140$	0.436567	+	4.80698i	0.0368966	+	0.406264i
$141$		0			0
$142$	−0.924676	−	1.60159i	−0.0775971	−	0.134402i
$143$	−1.85708	+	14.1833i	−0.155297	+	1.18606i
$144$		0			0
$145$	7.58143	+	4.37714i	0.629604	+	0.363502i
$146$	1.65316	+	2.86335i	0.136816	+	0.236973i
$147$		0			0
$148$			1.47559i			0.121293i
$149$		−	0.0113760i		−	0.000931956i	−1.00000		0.000465978i	$-0.999852\pi$
$149$		−	0.0113760i		−	0.000931956i	1.00000		0.000465978i	$-0.000148325\pi$
$150$		0			0
$151$	16.3726	+	9.45271i	1.33238	+	0.769251i	0.985664	−	0.168719i	$-0.0539631\pi$
$151$	16.3726	+	9.45271i	1.33238	+	0.769251i	0.346717	+	0.937970i	$0.387296\pi$
$152$	10.3306			0.837920
$153$		0			0
$154$	−5.22660	+	0.474676i	−0.421171	+	0.0382505i
$155$	2.96743			0.238350
$156$		0			0
$157$	−9.89687	+	17.1419i	−0.789856	+	1.36807i	0.136198	+	0.990682i	$0.456512\pi$
$157$	−9.89687	+	17.1419i	−0.789856	+	1.36807i	−0.926054	+	0.377390i	$0.876822\pi$
$158$			5.96119i			0.474247i
$159$		0			0
$160$	−2.62243	+	4.54219i	−0.207321	+	0.359091i
$161$	−11.5698	+	1.05076i	−0.911830	+	0.0828117i
$162$		0			0
$163$			8.93255i			0.699651i	0.936815	+	0.349825i	$0.113759\pi$
$163$			8.93255i			0.699651i	−0.936815	+	0.349825i	$0.886241\pi$
$164$	18.3343	+	10.5853i	1.43167	+	0.826572i
$165$		0			0
$166$	−0.718284	+	1.24410i	−0.0557496	+	0.0965612i
$167$	−5.31279	+	3.06734i	−0.411116	+	0.237358i	−0.691269	−	0.722597i	$-0.742948\pi$
$167$	−5.31279	+	3.06734i	−0.411116	+	0.237358i	0.280153	+	0.959955i	$0.409615\pi$
$168$		0			0
$169$	12.5618	+	3.34692i	0.966290	+	0.257456i
$170$	0.0370161	+	0.0641138i	0.00283900	+	0.00491730i
$171$		0			0
$172$	−8.44072			−0.643599
$173$	24.2628			1.84466			0.922332	−	0.386399i	$-0.126281\pi$
$173$	24.2628			1.84466			0.922332	+	0.386399i	$0.126281\pi$
$174$		0			0
$175$	−10.3110	+	0.936441i	−0.779441	+	0.0707883i
$176$	8.80446	+	5.08325i	0.663661	+	0.383165i
$177$		0			0
$178$	0.436901	+	0.756734i	0.0327471	+	0.0567196i
$179$	−4.13675			−0.309195			−0.154598	−	0.987978i	$-0.549408\pi$
$179$	−4.13675			−0.309195			−0.154598	+	0.987978i	$0.549408\pi$
$180$		0			0
$181$	−7.86568			−0.584651			−0.292326	−	0.956319i	$-0.594429\pi$
$181$	−7.86568			−0.584651			−0.292326	+	0.956319i	$0.594429\pi$
$182$	−0.188936	+	4.76582i	−0.0140049	+	0.353266i
$183$		0			0
$184$	−7.12989	−	4.11645i	−0.525623	−	0.303468i
$185$	0.879001			0.0646254
$186$		0			0
$187$	0.488003	−	0.281749i	0.0356863	−	0.0206035i
$188$	6.90560	+	3.98695i	0.503642	+	0.290778i
$189$		0			0
$190$		−	2.87182i		−	0.208344i
$191$	6.47866			0.468780			0.234390	−	0.972143i	$-0.424691\pi$
$191$	6.47866			0.468780			0.234390	+	0.972143i	$0.424691\pi$
$192$		0			0
$193$		−	4.82928i		−	0.347619i	−0.984779	−	0.173810i	$-0.944392\pi$
$193$		−	4.82928i		−	0.347619i	0.984779	−	0.173810i	$-0.0556077\pi$
$194$	−0.675708	−	1.17036i	−0.0485130	−	0.0840270i
$195$		0			0
$196$	12.0497	−	2.20689i	0.860690	−	0.157635i
$197$	22.3748	−	12.9181i	1.59414	−	0.920377i	0.601554	−	0.798832i	$-0.294548\pi$
$197$	22.3748	−	12.9181i	1.59414	−	0.920377i	0.992586	−	0.121545i	$-0.0387850\pi$
$198$		0			0
$199$	8.55731	+	14.8217i	0.606612	+	1.05068i	0.991795	+	0.127842i	$0.0408050\pi$
$199$	8.55731	+	14.8217i	0.606612	+	1.05068i	−0.385183	+	0.922840i	$0.625862\pi$
$200$	−6.35417	−	3.66858i	−0.449308	−	0.259408i
$201$		0			0
$202$	−4.96749	−	2.86798i	−0.349511	−	0.201790i
$203$	9.32312	−	20.1672i	0.654355	−	1.41546i
$204$		0			0
$205$	6.30561	−	10.9216i	0.440403	−	0.762800i
$206$		−	2.08470i		−	0.145248i
$207$		0			0
$208$	5.61947	−	7.33415i	0.389640	−	0.508532i
$209$	−21.8589			−1.51201
$210$		0			0
$211$	−9.14557	−	15.8406i	−0.629607	−	1.09051i	−0.987631	−	0.156799i	$-0.949883\pi$
$211$	−9.14557	−	15.8406i	−0.629607	−	1.09051i	0.358024	−	0.933713i	$-0.383451\pi$
$212$	0.489304			0.0336055
$213$		0			0
$214$	−3.67506	+	2.12180i	−0.251222	+	0.145043i
$215$			5.02810i			0.342913i
$216$		0			0
$217$	−0.681174	−	7.50032i	−0.0462411	−	0.509155i
$218$	1.60755	+	2.78435i	0.108877	+	0.188580i
$219$		0			0
$220$	3.61887	−	6.26806i	0.243984	−	0.422593i
$221$	−0.196312	−	0.472995i	−0.0132054	−	0.0318171i
$222$		0			0
$223$	−9.96682	+	5.75435i	−0.667428	+	0.385340i	−0.795101	−	0.606477i	$-0.792582\pi$
$223$	−9.96682	+	5.75435i	−0.667428	+	0.385340i	0.127674	+	0.991816i	$0.459249\pi$
$224$	12.0826	+	5.58567i	0.807301	+	0.373208i
$225$		0			0
$226$	−4.74711	+	2.74075i	−0.315773	+	0.182312i
$227$	−15.5057	+	8.95223i	−1.02915	+	0.594181i	−0.916741	−	0.399481i	$-0.869190\pi$
$227$	−15.5057	+	8.95223i	−1.02915	+	0.594181i	−0.112410	+	0.993662i	$0.535857\pi$
$228$		0			0
$229$	3.34589	−	1.93175i	0.221103	−	0.127654i	−0.385358	−	0.922767i	$-0.625922\pi$
$229$	3.34589	−	1.93175i	0.221103	−	0.127654i	0.606461	+	0.795113i	$0.292589\pi$
$230$	−1.14434	+	1.98206i	−0.0754556	+	0.130693i
$231$		0			0
$232$	13.6357	−	7.87256i	0.895226	−	0.516859i
$233$	−12.5321	−	21.7062i	−0.821004	−	1.42202i	−0.904935	−	0.425549i	$-0.860081\pi$
$233$	−12.5321	−	21.7062i	−0.821004	−	1.42202i	0.0839312	−	0.996472i	$-0.473252\pi$
$234$		0			0
$235$	2.37501	−	4.11363i	0.154928	−	0.268344i
$236$	16.3400	+	9.43388i	1.06364	+	0.614093i
$237$		0			0
$238$	0.153554	−	0.108277i	0.00995340	−	0.00701858i
$239$		−	7.80462i		−	0.504839i	−0.967618	−	0.252419i	$-0.918774\pi$
$239$		−	7.80462i		−	0.504839i	0.967618	−	0.252419i	$-0.0812263\pi$
$240$		0			0
$241$	18.8493	−	10.8826i	1.21419	−	0.701012i	0.250519	−	0.968112i	$-0.419399\pi$
$241$	18.8493	−	10.8826i	1.21419	−	0.701012i	0.963669	+	0.267100i	$0.0860655\pi$
$242$	2.05221	+	1.18484i	0.131921	+	0.0761647i
$243$		0			0
$244$	5.13063	+	8.88652i	0.328455	+	0.568901i
$245$	−1.31463	−	7.17793i	−0.0839888	−	0.458581i
$246$		0			0
$247$	−2.57910	+	19.6976i	−0.164104	+	1.25333i
$248$	2.66855	−	4.62207i	0.169453	−	0.293502i
$249$		0			0
$250$	−2.32290	+	4.02338i	−0.146913	+	0.254461i
$251$	−3.83990	+	6.65090i	−0.242372	+	0.419801i	−0.961390	−	0.275191i	$-0.911259\pi$
$251$	−3.83990	+	6.65090i	−0.242372	+	0.419801i	0.719017	+	0.694992i	$0.244592\pi$
$252$		0			0
$253$	15.0865	+	8.71017i	0.948478	+	0.547604i
$254$			1.00391i			0.0629909i
$255$		0			0
$256$	0.232070	+	0.401958i	0.0145044	+	0.0251224i
$257$	−6.81187	+	11.7985i	−0.424913	+	0.735971i	−0.996412	−	0.0846316i	$-0.973029\pi$
$257$	−6.81187	+	11.7985i	−0.424913	+	0.735971i	0.571499	+	0.820603i	$0.306362\pi$
$258$		0			0
$259$	−0.201775	−	2.22172i	−0.0125377	−	0.138051i
$260$	−5.22132	−	4.00061i	−0.323813	−	0.248107i
$261$		0			0
$262$			6.22494i			0.384578i
$263$	11.7232			0.722880			0.361440	−	0.932395i	$-0.382285\pi$
$263$	11.7232			0.722880			0.361440	+	0.932395i	$0.382285\pi$
$264$		0			0
$265$		−	0.291476i		−	0.0179052i
$266$	−7.25867	+	0.659227i	−0.445057	+	0.0404198i
$267$		0			0
$268$	7.79673	−	4.50144i	0.476261	−	0.274970i
$269$	4.59938	+	7.96636i	0.280429	+	0.485717i	0.971490	−	0.237079i	$-0.0761899\pi$
$269$	4.59938	+	7.96636i	0.280429	+	0.485717i	−0.691061	+	0.722796i	$0.742857\pi$
$270$		0			0
$271$	2.22022	+	1.28184i	0.134869	+	0.0778665i	0.565916	−	0.824463i	$-0.308523\pi$
$271$	2.22022	+	1.28184i	0.134869	+	0.0778665i	−0.431048	+	0.902329i	$0.641856\pi$
$272$	−0.363976			−0.0220693
$273$		0			0
$274$	2.62252			0.158432
$275$	13.4451	+	7.76252i	0.810769	+	0.468097i
$276$		0			0
$277$	−0.466941	−	0.808765i	−0.0280558	−	0.0485940i	0.851657	−	0.524100i	$-0.175598\pi$
$277$	−0.466941	−	0.808765i	−0.0280558	−	0.0485940i	−0.879712	+	0.475506i	$0.842265\pi$
$278$	−8.97981	+	5.18450i	−0.538573	+	0.310945i
$279$		0			0
$280$	2.17002	−	4.69405i	0.129683	−	0.280523i
$281$		−	6.45288i		−	0.384947i	−0.981302	−	0.192473i	$-0.938349\pi$
$281$		−	6.45288i		−	0.384947i	0.981302	−	0.192473i	$-0.0616509\pi$
$282$		0			0
$283$	−22.1746			−1.31814			−0.659071	−	0.752081i	$-0.729050\pi$
$283$	−22.1746			−1.31814			−0.659071	+	0.752081i	$0.729050\pi$
$284$		−	6.47296i		−	0.384099i
$285$		0			0
$286$	4.34984	−	5.67711i	0.257211	−	0.335695i
$287$	−29.0524	−	13.4307i	−1.71491	−	0.792788i
$288$		0			0
$289$	8.48991	−	14.7050i	0.499407	−	0.864998i
$290$	−2.18851	−	3.79061i	−0.128514	−	0.222593i
$291$		0			0
$292$			11.5725i			0.677229i
$293$	20.9600	+	12.1013i	1.22450	+	0.706964i	0.965874	−	0.259014i	$-0.0833976\pi$
$293$	20.9600	+	12.1013i	1.22450	+	0.706964i	0.258624	+	0.965978i	$0.416731\pi$
$294$		0			0
$295$	5.61972	−	9.73364i	0.327193	−	0.566714i
$296$	0.790469	−	1.36913i	0.0459451	−	0.0795792i
$297$		0			0
$298$	−0.00284392	+	0.00492581i	−0.000164744	+	0.000285345i
$299$	9.62898	−	12.5671i	0.556858	−	0.726773i
$300$		0			0
$301$	12.7088	−	1.15420i	0.732521	−	0.0665270i
$302$	−4.72623	−	8.18607i	−0.271964	−	0.471055i
$303$		0			0
$304$	12.2276	+	7.05959i	0.701299	+	0.404895i
$305$	5.29366	−	3.05630i	0.303114	−	0.175003i
$306$		0			0
$307$			24.2924i			1.38644i	0.720726	+	0.693220i	$0.243809\pi$
$307$			24.2924i			1.38644i	−0.720726	+	0.693220i	$0.756191\pi$
$308$	−16.6735	−	7.70803i	−0.950063	−	0.439206i
$309$		0			0
$310$	−1.28490	−	0.741837i	−0.0729774	−	0.0421335i
$311$	−1.99355	+	3.45294i	−0.113044	+	0.195798i	−0.916996	−	0.398896i	$-0.869393\pi$
$311$	−1.99355	+	3.45294i	−0.113044	+	0.195798i	0.803952	+	0.594694i	$0.202727\pi$
$312$		0			0
$313$	−14.2377	−	24.6604i	−0.804763	−	1.39389i	−0.916451	−	0.400147i	$-0.868959\pi$
$313$	−14.2377	−	24.6604i	−0.804763	−	1.39389i	0.111688	−	0.993743i	$-0.464374\pi$
$314$	8.57071	−	4.94830i	0.483673	−	0.279249i
$315$		0			0
$316$	−10.4324	+	18.0695i	−0.586871	+	1.01649i
$317$	−14.5632	+	8.40806i	−0.817950	+	0.472244i	−0.849709	−	0.527252i	$-0.823222\pi$
$317$	−14.5632	+	8.40806i	−0.817950	+	0.472244i	0.0317591	+	0.999496i	$0.489889\pi$
$318$		0			0
$319$	−28.8523	+	16.6579i	−1.61542	+	0.932664i
$320$	−2.35600	+	1.36024i	−0.131704	+	0.0760396i
$321$		0			0
$322$	5.27243	+	2.43740i	0.293821	+	0.135831i
$323$	0.677736	−	0.391291i	0.0377102	−	0.0217720i
$324$		0			0
$325$	8.58136	−	11.1998i	0.476008	−	0.621253i
$326$	2.23308	−	3.86780i	0.123679	−	0.214218i
$327$		0			0
$328$	−11.3410	−	19.6432i	−0.626204	−	1.08462i
$329$	−10.9426	−	5.05866i	−0.603285	−	0.278893i
$330$		0			0
$331$			6.20917i			0.341287i	0.985333	+	0.170644i	$0.0545846\pi$
$331$			6.20917i			0.341287i	−0.985333	+	0.170644i	$0.945415\pi$
$332$	−4.35451	+	2.51408i	−0.238985	+	0.137978i
$333$		0			0
$334$	3.06726			0.167833
$335$	−2.68149	−	4.64448i	−0.146505	−	0.253755i
$336$		0			0
$337$	7.69650			0.419255			0.209628	−	0.977781i	$-0.432775\pi$
$337$	7.69650			0.419255			0.209628	+	0.977781i	$0.432775\pi$
$338$	−4.60255	−	4.58958i	−0.250346	−	0.249640i
$339$		0			0
$340$			0.259122i			0.0140528i
$341$	−5.64651	+	9.78005i	−0.305776	+	0.529619i
$342$		0			0
$343$	−17.8408	+	4.97049i	−0.963313	+	0.268381i
$344$	7.83177	+	4.52167i	0.422261	+	0.243792i
$345$		0			0
$346$	−10.5058	−	6.06553i	−0.564795	−	0.326085i
$347$	15.2047	+	26.3353i	0.816231	+	1.41375i	0.908440	+	0.418015i	$0.137274\pi$
$347$	15.2047	+	26.3353i	0.816231	+	1.41375i	−0.0922088	+	0.995740i	$0.529393\pi$
$348$		0			0
$349$	−13.9933	+	8.07906i	−0.749046	+	0.432462i	−0.825349	−	0.564623i	$-0.809022\pi$
$349$	−13.9933	+	8.07906i	−0.749046	+	0.432462i	0.0763028	+	0.997085i	$0.475688\pi$
$350$	4.69880	+	2.17221i	0.251161	+	0.116110i
$351$		0			0
$352$	−9.98008	−	17.2860i	−0.531940	−	0.921347i
$353$		−	11.8424i		−	0.630306i	−0.949041	−	0.315153i	$-0.897944\pi$
$353$		−	11.8424i		−	0.630306i	0.949041	−	0.315153i	$-0.102056\pi$
$354$		0			0
$355$	−3.85591			−0.204651
$356$			3.05841i			0.162095i
$357$		0			0
$358$	1.79122	+	1.03416i	0.0946688	+	0.0546571i
$359$	−27.1631	+	15.6826i	−1.43362	+	0.827698i	−0.997394	−	0.0721417i	$-0.977017\pi$
$359$	−27.1631	+	15.6826i	−1.43362	+	0.827698i	−0.436221	+	0.899840i	$0.643683\pi$
$360$		0			0
$361$	−11.3575			−0.597765
$362$	3.40585	+	1.96637i	0.179007	+	0.103350i
$363$		0			0
$364$	−8.91318	+	14.1155i	−0.467178	+	0.739852i
$365$	6.89369			0.360832
$366$		0			0
$367$	24.0774			1.25683			0.628415	−	0.777878i	$-0.283704\pi$
$367$	24.0774			1.25683			0.628415	+	0.777878i	$0.283704\pi$
$368$	−5.62610	−	9.74470i	−0.293281	−	0.507977i
$369$		0			0
$370$	−0.380608	−	0.219744i	−0.0197869	−	0.0114240i
$371$	−0.736720	+	0.0669084i	−0.0382486	+	0.00347371i
$372$		0			0
$373$	−18.3922			−0.952314			−0.476157	−	0.879360i	$-0.657971\pi$
$373$	−18.3922			−0.952314			−0.476157	+	0.879360i	$0.657971\pi$
$374$	−0.281741			−0.0145685
$375$		0			0
$376$	−4.27160	−	7.39862i	−0.220291	−	0.381555i
$377$	11.6066	+	27.9650i	0.597771	+	1.44027i
$378$		0			0
$379$	−7.04719	+	4.06870i	−0.361990	+	0.208995i	−0.669953	−	0.742403i	$-0.733686\pi$
$379$	−7.04719	+	4.06870i	−0.361990	+	0.208995i	0.307963	+	0.951398i	$0.400353\pi$
$380$	5.02586	−	8.70504i	0.257821	−	0.446559i
$381$		0			0
$382$	−2.80527	−	1.61962i	−0.143530	−	0.0828671i
$383$			22.3711i			1.14311i	0.820564	+	0.571555i	$0.193660\pi$
$383$			22.3711i			1.14311i	−0.820564	+	0.571555i	$0.806340\pi$
$384$		0			0
$385$	−4.59164	+	9.93236i	−0.234012	+	0.506200i
$386$	−1.20729	+	2.09108i	−0.0614493	+	0.106433i
$387$		0			0
$388$		−	4.73012i		−	0.240136i
$389$	10.6973	−	18.5283i	0.542374	−	0.939420i	−0.456393	−	0.889778i	$-0.650859\pi$
$389$	10.6973	−	18.5283i	0.542374	−	0.939420i	0.998767	−	0.0496415i	$-0.0158079\pi$
$390$		0			0
$391$	−0.623674			−0.0315406
$392$	−12.3626	−	4.40731i	−0.624404	−	0.222603i
$393$		0			0
$394$	−12.9178			−0.650788
$395$	10.7639	+	6.21456i	0.541592	+	0.312689i
$396$		0			0
$397$			1.19673i			0.0600622i	0.999549	+	0.0300311i	$0.00956063\pi$
$397$			1.19673i			0.0600622i	−0.999549	+	0.0300311i	$0.990439\pi$
$398$		−	8.55708i		−	0.428928i
$399$		0			0
$400$	−5.01399	−	8.68449i	−0.250699	−	0.434224i
$401$	−31.4150	−	18.1375i	−1.56879	−	0.905741i	−0.996310	−	0.0858220i	$-0.972648\pi$
$401$	−31.4150	−	18.1375i	−1.56879	−	0.905741i	−0.572479	−	0.819919i	$-0.694018\pi$
$402$		0			0
$403$	8.14682	+	6.24214i	0.405822	+	0.310943i
$404$	−10.0383	−	17.3868i	−0.499423	−	0.865026i
$405$		0			0
$406$	−9.07859	+	6.40171i	−0.450563	+	0.317711i
$407$	−1.67259	+	2.89701i	−0.0829072	+	0.143599i
$408$		0			0
$409$	−12.7066	+	7.33616i	−0.628301	+	0.362750i	−0.780094	−	0.625662i	$-0.784829\pi$
$409$	−12.7066	+	7.33616i	−0.628301	+	0.362750i	0.151793	+	0.988412i	$0.451495\pi$
$410$	−5.46067	+	3.15272i	−0.269683	+	0.155702i
$411$		0			0
$412$	3.64834	−	6.31912i	0.179741	−	0.311321i
$413$	−25.8923	−	11.9698i	−1.27407	−	0.588993i
$414$		0			0
$415$	1.49763	+	2.59397i	0.0735156	+	0.127333i
$416$	−16.7544	+	6.95375i	−0.821451	+	0.340936i
$417$		0			0
$418$	9.46494	+	5.46458i	0.462945	+	0.267282i
$419$	−2.96674	−	5.13855i	−0.144935	−	0.251034i	0.784414	−	0.620238i	$-0.212964\pi$
$419$	−2.96674	−	5.13855i	−0.144935	−	0.251034i	−0.929349	+	0.369203i	$0.879631\pi$
$420$		0			0
$421$		−	2.63174i		−	0.128263i	−0.997941	−	0.0641317i	$-0.979572\pi$
$421$		−	2.63174i		−	0.128263i	0.997941	−	0.0641317i	$-0.0204278\pi$
$422$			9.14532i			0.445187i
$423$		0			0
$424$	−0.454004	−	0.262119i	−0.0220484	−	0.0127296i
$425$	−0.555819			−0.0269612
$426$		0			0
$427$	−8.94010	−	12.6784i	−0.432642	−	0.613551i
$428$	−14.8531			−0.717952
$429$		0			0
$430$	1.25699	−	2.17717i	0.0606175	−	0.104993i
$431$			18.8377i			0.907378i	0.891160	+	0.453689i	$0.149892\pi$
$431$			18.8377i			0.907378i	−0.891160	+	0.453689i	$0.850108\pi$
$432$		0			0
$433$	9.56773	−	16.5718i	0.459796	−	0.796389i	−0.539154	−	0.842207i	$-0.681256\pi$
$433$	9.56773	−	16.5718i	0.459796	−	0.796389i	0.998950	+	0.0458176i	$0.0145893\pi$
$434$	−1.58008	+	3.41794i	−0.0758463	+	0.164066i
$435$		0			0
$436$			11.2532i			0.538931i
$437$	20.9520	+	12.0966i	1.00227	+	0.578660i
$438$		0			0
$439$	−0.632554	+	1.09561i	−0.0301901	+	0.0522908i	−0.880726	−	0.473627i	$-0.842945\pi$
$439$	−0.632554	+	1.09561i	−0.0301901	+	0.0522908i	0.850536	+	0.525918i	$0.176278\pi$
$440$	−6.71557	+	3.87724i	−0.320152	+	0.184840i
$441$		0			0
$442$	−0.0332422	+	0.253884i	−0.00158117	+	0.0120760i
$443$	−10.4696	−	18.1339i	−0.497426	−	0.861568i	0.502569	−	0.864537i	$-0.332388\pi$
$443$	−10.4696	−	18.1339i	−0.497426	−	0.861568i	−0.999996	+	0.00296930i	$0.999055\pi$
$444$		0			0
$445$	1.82188			0.0863654
$446$	5.75419			0.272469
$447$		0			0
$448$	3.97889	+	5.64267i	0.187985	+	0.266591i
$449$	−15.4700	−	8.93162i	−0.730075	−	0.421509i	0.0883746	−	0.996087i	$-0.471833\pi$
$449$	−15.4700	−	8.93162i	−0.730075	−	0.421509i	−0.818450	+	0.574578i	$0.805166\pi$
$450$		0			0
$451$	23.9970	+	41.5640i	1.12997	+	1.95717i
$452$	−19.1859			−0.902429
$453$		0			0
$454$	8.95199			0.420138
$455$	8.40853	+	5.30954i	0.394198	+	0.248915i
$456$		0			0
$457$	−5.68629	−	3.28298i	−0.265994	−	0.153571i	0.361072	−	0.932538i	$-0.382411\pi$
$457$	−5.68629	−	3.28298i	−0.265994	−	0.153571i	−0.627066	+	0.778966i	$0.715744\pi$
$458$	−1.93170			−0.0902624
$459$		0			0
$460$	−6.93744	+	4.00533i	−0.323460	+	0.186749i
$461$	4.42854	+	2.55682i	0.206258	+	0.119083i	0.599571	−	0.800322i	$-0.295338\pi$
$461$	4.42854	+	2.55682i	0.206258	+	0.119083i	−0.393313	+	0.919404i	$0.628671\pi$
$462$		0			0
$463$		−	33.3239i		−	1.54869i	−0.632761	−	0.774347i	$-0.718079\pi$
$463$		−	33.3239i		−	1.54869i	0.632761	−	0.774347i	$-0.281921\pi$
$464$	21.5194			0.999015
$465$		0			0
$466$			12.5317i			0.580522i
$467$	6.47472	+	11.2145i	0.299614	+	0.518947i	0.976048	−	0.217557i	$-0.0698087\pi$
$467$	6.47472	+	11.2145i	0.299614	+	0.518947i	−0.676433	+	0.736504i	$0.736475\pi$
$468$		0			0
$469$	−11.1236	+	7.84374i	−0.513641	+	0.362190i
$470$	−2.05676	+	1.18747i	−0.0948713	+	0.0547740i
$471$		0			0
$472$	−10.1074	−	17.5066i	−0.465231	−	0.805805i
$473$	−16.5716	−	9.56761i	−0.761962	−	0.439919i
$474$		0			0
$475$	18.6724	+	10.7805i	0.856750	+	0.494645i
$476$	0.654942	−	0.0594814i	0.0300192	−	0.00272633i
$477$		0			0
$478$	−1.95110	+	3.37941i	−0.0892414	+	0.154571i
$479$			27.0119i			1.23421i	0.786882	+	0.617104i	$0.211694\pi$
$479$			27.0119i			1.23421i	−0.786882	+	0.617104i	$0.788306\pi$
$480$		0			0
$481$	2.41322	+	1.84903i	0.110033	+	0.0843083i
$482$	−10.8823			−0.495677
$483$		0			0
$484$	4.14710	+	7.18299i	0.188505	+	0.326499i
$485$	−2.81771			−0.127946
$486$		0			0
$487$	27.7854	−	16.0419i	1.25908	−	0.726928i	0.286182	−	0.958175i	$-0.407614\pi$
$487$	27.7854	−	16.0419i	1.25908	−	0.726928i	0.972895	+	0.231247i	$0.0742805\pi$
$488$		−	10.9939i		−	0.497669i
$489$		0			0
$490$	−1.22520	+	3.43670i	−0.0553488	+	0.155254i
$491$	14.3020	+	24.7718i	0.645440	+	1.11793i	0.984200	+	0.177061i	$0.0566591\pi$
$491$	14.3020	+	24.7718i	0.645440	+	1.11793i	−0.338760	+	0.940873i	$0.610008\pi$
$492$		0			0
$493$	0.596378	−	1.03296i	0.0268595	−	0.0465220i
$494$	6.04103	−	7.88433i	0.271799	−	0.354733i
$495$		0			0
$496$	6.31716	−	3.64721i	0.283649	−	0.163765i
$497$	0.885125	+	9.74601i	0.0397033	+	0.437168i
$498$		0			0
$499$	−1.55726	+	0.899082i	−0.0697123	+	0.0402484i	−0.534451	−	0.845199i	$-0.679482\pi$
$499$	−1.55726	+	0.899082i	−0.0697123	+	0.0402484i	0.464739	+	0.885448i	$0.346148\pi$
$500$	−14.0823	+	8.13042i	−0.629780	+	0.363603i
$501$		0			0
$502$	3.32536	−	1.91990i	0.148418	−	0.0856893i
$503$	14.5386	−	25.1816i	0.648245	−	1.12279i	−0.335297	−	0.942112i	$-0.608837\pi$
$503$	14.5386	−	25.1816i	0.648245	−	1.12279i	0.983542	−	0.180681i	$-0.0578300\pi$
$504$		0			0
$505$	−10.3572	+	5.97976i	−0.460891	+	0.266096i
$506$	−4.35497	−	7.54303i	−0.193602	−	0.335329i
$507$		0			0
$508$	−1.75690	+	3.04304i	−0.0779499	+	0.135013i
$509$	−20.0843	−	11.5957i	−0.890220	−	0.513969i	−0.0162054	−	0.999869i	$-0.505159\pi$
$509$	−20.0843	−	11.5957i	−0.890220	−	0.513969i	−0.874014	+	0.485900i	$0.838492\pi$
$510$		0			0
$511$	−1.58245	−	17.4241i	−0.0700033	−	0.770798i
$512$			22.5022i			0.994464i
$513$		0			0
$514$	5.89910	−	3.40585i	0.260198	−	0.150225i
$515$	−3.76427	−	2.17330i	−0.165874	−	0.0957671i
$516$		0			0
$517$	9.03847	+	15.6551i	0.397511	+	0.688510i
$518$	−0.468046	+	1.01245i	−0.0205648	+	0.0444844i
$519$		0			0
$520$	2.70151	+	6.50904i	0.118469	+	0.285440i
$521$	16.6255	−	28.7962i	0.728376	−	1.26158i	−0.229193	−	0.973381i	$-0.573609\pi$
$521$	16.6255	−	28.7962i	0.728376	−	1.26158i	0.957569	−	0.288203i	$-0.0930579\pi$
$522$		0			0
$523$	−19.3560	+	33.5256i	−0.846380	+	1.46597i	0.0380367	+	0.999276i	$0.487890\pi$
$523$	−19.3560	+	33.5256i	−0.846380	+	1.46597i	−0.884417	+	0.466697i	$0.845444\pi$
$524$	−10.8940	+	18.8690i	−0.475908	+	0.824296i
$525$		0			0
$526$	−5.07614	−	2.93071i	−0.221330	−	0.127785i
$527$		−	0.404307i		−	0.0176119i
$528$		0			0
$529$	1.85966	+	3.22102i	0.0808546	+	0.140044i
$530$	−0.0728671	+	0.126210i	−0.00316514	+	0.00548219i
$531$		0			0
$532$	−23.1561	−	10.7049i	−1.00394	−	0.464115i
$533$	40.2857	−	16.7202i	1.74497	−	0.724233i
$534$		0			0
$535$			8.84793i			0.382529i
$536$	−9.64566			−0.416629
$537$		0			0
$538$		−	4.59926i		−	0.198288i
$539$	26.1585	+	9.32562i	1.12673	+	0.401683i
$540$		0			0
$541$	19.6306	−	11.3337i	0.843986	−	0.487275i	−0.0146313	−	0.999893i	$-0.504657\pi$
$541$	19.6306	−	11.3337i	0.843986	−	0.487275i	0.858617	+	0.512618i	$0.171324\pi$
$542$	−0.640905	−	1.11008i	−0.0275292	−	0.0476820i
$543$		0			0
$544$	0.618865	+	0.357302i	0.0265336	+	0.0153192i
$545$	6.70349			0.287146
$546$		0			0
$547$	−9.21134			−0.393848			−0.196924	−	0.980419i	$-0.563095\pi$
$547$	−9.21134			−0.393848			−0.196924	+	0.980419i	$0.563095\pi$
$548$	7.94936	+	4.58957i	0.339580	+	0.196057i
$549$		0			0
$550$	−3.88116	−	6.72236i	−0.165493	−	0.286642i
$551$	−40.0699	+	23.1344i	−1.70704	+	0.985558i
$552$		0			0
$553$	13.2367	−	28.6329i	0.562884	−	1.21760i
$554$			0.466928i			0.0198379i
$555$		0			0
$556$	−36.2927			−1.53915
$557$			11.3281i			0.479986i	0.970775	+	0.239993i	$0.0771451\pi$
$557$			11.3281i			0.479986i	−0.970775	+	0.239993i	$0.922855\pi$
$558$		0			0
$559$	−10.5769	+	13.8042i	−0.447354	+	0.583855i
$560$	5.77627	−	4.07310i	0.244092	−	0.172120i
$561$		0			0
$562$	−1.61318	+	2.79411i	−0.0680478	+	0.117862i
$563$	−16.3193	−	28.2659i	−0.687777	−	1.19127i	−0.972555	−	0.232672i	$-0.925253\pi$
$563$	−16.3193	−	28.2659i	−0.687777	−	1.19127i	0.284778	−	0.958594i	$-0.408080\pi$
$564$		0			0
$565$			11.4290i			0.480820i
$566$	9.60161	+	5.54349i	0.403586	+	0.233010i
$567$		0			0
$568$	−3.46755	+	6.00597i	−0.145495	+	0.252005i
$569$	−17.5045	+	30.3188i	−0.733829	+	1.27103i	0.221407	+	0.975182i	$0.428935\pi$
$569$	−17.5045	+	30.3188i	−0.733829	+	1.27103i	−0.955235	+	0.295847i	$0.904398\pi$
$570$		0			0
$571$	13.1273	−	22.7371i	0.549360	−	0.951519i	−0.448959	−	0.893552i	$-0.648205\pi$
$571$	13.1273	−	22.7371i	0.549360	−	0.951519i	0.998319	−	0.0579663i	$-0.0184616\pi$
$572$	23.1205	−	9.59594i	0.966716	−	0.401226i
$573$		0			0
$574$	9.22215	+	13.0784i	0.384925	+	0.545882i
$575$	−8.59149	−	14.8809i	−0.358290	−	0.620576i
$576$		0			0
$577$	−21.2806	−	12.2863i	−0.885922	−	0.511487i	−0.0133154	−	0.999911i	$-0.504239\pi$
$577$	−21.2806	−	12.2863i	−0.885922	−	0.511487i	−0.872606	+	0.488424i	$0.837572\pi$
$578$	−7.35228	+	4.24484i	−0.305815	+	0.176562i
$579$		0			0
$580$		−	15.3201i		−	0.636133i
$581$	6.21259	−	4.38077i	0.257742	−	0.181745i
$582$		0			0
$583$	0.960646	+	0.554629i	0.0397859	+	0.0229704i
$584$	6.19936	−	10.7376i	0.256531	−	0.444325i
$585$		0			0
$586$	−6.05048	−	10.4797i	−0.249943	−	0.432914i
$587$	−17.7777	+	10.2640i	−0.733765	+	0.423639i	−0.819798	−	0.572653i	$-0.805914\pi$
$587$	−17.7777	+	10.2640i	−0.733765	+	0.423639i	0.0860331	+	0.996292i	$0.472581\pi$
$588$		0			0
$589$	−7.84184	+	13.5825i	−0.323117	+	0.559656i
$590$	−4.86669	+	2.80978i	−0.200358	+	0.115677i
$591$		0			0
$592$	1.87124	−	1.08036i	0.0769077	−	0.0444027i
$593$	33.1545	−	19.1417i	1.36149	−	0.786057i	0.371669	−	0.928365i	$-0.378786\pi$
$593$	33.1545	−	19.1417i	1.36149	−	0.786057i	0.989822	+	0.142308i	$0.0454524\pi$
$594$		0			0
$595$	−0.0354328	−	0.390146i	−0.00145260	−	0.0159944i
$596$	−0.0172409	+	0.00995405i	−0.000706216	+	0.000407734i
$597$		0			0
$598$	−7.31105	+	3.03438i	−0.298971	+	0.124085i
$599$	7.03567	−	12.1861i	0.287470	−	0.497912i	−0.685735	−	0.727851i	$-0.740519\pi$
$599$	7.03567	−	12.1861i	0.287470	−	0.497912i	0.973205	+	0.229939i	$0.0738526\pi$
$600$		0			0
$601$	10.1171	+	17.5233i	0.412685	+	0.714791i	0.995182	−	0.0980417i	$-0.0312579\pi$
$601$	10.1171	+	17.5233i	0.412685	+	0.714791i	−0.582498	+	0.812832i	$0.697925\pi$
$602$	−5.79145	−	2.67734i	−0.236042	−	0.109120i
$603$		0			0
$604$		−	33.0847i		−	1.34620i
$605$	4.27887	−	2.47041i	0.173961	−	0.100436i
$606$		0			0
$607$	6.55127			0.265908			0.132954	−	0.991122i	$-0.457554\pi$
$607$	6.55127			0.265908			0.132954	+	0.991122i	$0.457554\pi$
$608$	−13.8603	−	24.0067i	−0.562108	−	0.973600i
$609$		0			0
$610$	−3.05621			−0.123742
$611$	15.1736	−	6.29767i	0.613859	−	0.254776i
$612$		0			0
$613$		−	33.3244i		−	1.34596i	−0.739660	−	0.672980i	$-0.765014\pi$
$613$		−	33.3244i		−	1.34596i	0.739660	−	0.672980i	$-0.234986\pi$
$614$	6.07294	−	10.5186i	0.245084	−	0.424498i
$615$		0			0
$616$	11.3415	+	16.0839i	0.456961	+	0.648040i
$617$	−5.85466	−	3.38019i	−0.235700	−	0.136081i	0.377499	−	0.926010i	$-0.376784\pi$
$617$	−5.85466	−	3.38019i	−0.235700	−	0.136081i	−0.613199	+	0.789929i	$0.710117\pi$
$618$		0			0
$619$	−15.2582	−	8.80931i	−0.613278	−	0.354076i	0.160970	−	0.986959i	$-0.448538\pi$
$619$	−15.2582	−	8.80931i	−0.613278	−	0.354076i	−0.774247	+	0.632883i	$0.781871\pi$
$620$	−2.59652	−	4.49731i	−0.104279	−	0.180616i
$621$		0			0
$622$	1.72642	−	0.996751i	0.0692233	−	0.0399661i
$623$	−0.418213	−	4.60489i	−0.0167554	−	0.184491i
$624$		0			0
$625$	−4.93986	−	8.55609i	−0.197594	−	0.342244i
$626$			14.2373i			0.569038i
$627$		0			0
$628$	34.6393			1.38226
$629$		−	0.119762i		−	0.00477524i
$630$		0			0
$631$	13.6416	+	7.87596i	0.543062	+	0.313537i	0.746319	−	0.665588i	$-0.231819\pi$
$631$	13.6416	+	7.87596i	0.543062	+	0.313537i	−0.203257	+	0.979125i	$0.565153\pi$
$632$	19.3596	−	11.1773i	0.770084	−	0.444608i
$633$		0			0
$634$	8.40783			0.333918
$635$	1.81273	+	1.04658i	0.0719359	+	0.0415322i
$636$		0			0
$637$	11.4899	−	22.4718i	0.455248	−	0.890364i
$638$	16.6575			0.659475
$639$		0			0
$640$	11.8499			0.468410
$641$	10.4702	+	18.1350i	0.413550	+	0.716289i	0.995275	−	0.0970962i	$-0.0309554\pi$
$641$	10.4702	+	18.1350i	0.413550	+	0.716289i	−0.581725	+	0.813385i	$0.697622\pi$
$642$		0			0
$643$	−16.3952	−	9.46576i	−0.646563	−	0.373293i	0.140575	−	0.990070i	$-0.455105\pi$
$643$	−16.3952	−	9.46576i	−0.646563	−	0.373293i	−0.787138	+	0.616777i	$0.788438\pi$
$644$	11.7162	+	16.6153i	0.461681	+	0.654734i
$645$		0			0
$646$	−0.391280			−0.0153947
$647$	−37.6768			−1.48123			−0.740614	−	0.671930i	$-0.765465\pi$
$647$	−37.6768			−1.48123			−0.740614	+	0.671930i	$0.765465\pi$
$648$		0			0
$649$	21.3867	+	37.0429i	0.839503	+	1.45406i
$650$	−6.51562	+	2.70424i	−0.255563	+	0.106069i
$651$		0			0
$652$	13.5378	−	7.81604i	0.530180	−	0.306100i
$653$	14.5163	−	25.1430i	0.568066	−	0.983920i	−0.428691	−	0.903451i	$-0.641025\pi$
$653$	14.5163	−	25.1430i	0.568066	−	0.983920i	0.996757	−	0.0804686i	$-0.0256417\pi$
$654$		0			0
$655$	11.2402	+	6.48952i	0.439190	+	0.253567i
$656$		−	31.0004i		−	1.21036i
$657$		0			0
$658$	3.47352	+	4.92598i	0.135412	+	0.192035i
$659$	−0.709152	+	1.22829i	−0.0276247	+	0.0478473i	−0.879507	−	0.475886i	$-0.842128\pi$
$659$	−0.709152	+	1.22829i	−0.0276247	+	0.0478473i	0.851883	+	0.523733i	$0.175461\pi$
$660$		0			0
$661$			4.59298i			0.178646i	0.996003	+	0.0893231i	$0.0284704\pi$
$661$			4.59298i			0.178646i	−0.996003	+	0.0893231i	$0.971530\pi$
$662$	1.55225	−	2.68858i	0.0603300	−	0.104495i
$663$		0			0
$664$	5.38715			0.209062
$665$	−6.37684	+	13.7940i	−0.247283	+	0.534908i
$666$		0			0
$667$	36.8736			1.42775
$668$	9.29746	+	5.36789i	0.359730	+	0.207690i
$669$		0			0
$670$			2.68142i			0.103592i
$671$			23.2624i			0.898036i
$672$		0			0
$673$	−2.10111	−	3.63924i	−0.0809920	−	0.140282i	0.822684	−	0.568499i	$-0.192475\pi$
$673$	−2.10111	−	3.63924i	−0.0809920	−	0.140282i	−0.903676	+	0.428216i	$0.859142\pi$
$674$	−3.33259	−	1.92407i	−0.128367	−	0.0741126i
$675$		0			0
$676$	−5.91919	−	21.9666i	−0.227661	−	0.844871i
$677$	4.04354	+	7.00361i	0.155406	+	0.269171i	0.933207	−	0.359340i	$-0.116998\pi$
$677$	4.04354	+	7.00361i	0.155406	+	0.269171i	−0.777801	+	0.628511i	$0.783665\pi$
$678$		0			0
$679$	0.646806	+	7.12191i	0.0248222	+	0.273314i
$680$	0.138811	−	0.240427i	0.00532315	−	0.00921997i
$681$		0			0
$682$	4.88989	−	2.82318i	0.187244	−	0.108105i
$683$	−21.3792	+	12.3433i	−0.818051	+	0.472302i	−0.849744	−	0.527196i	$-0.823243\pi$
$683$	−21.3792	+	12.3433i	−0.818051	+	0.472302i	0.0316929	+	0.999498i	$0.489910\pi$
$684$		0			0
$685$	2.73398	−	4.73540i	0.104460	−	0.180930i
$686$	8.96768	+	2.30785i	0.342388	+	0.0881142i
$687$		0			0
$688$	6.17994	+	10.7040i	0.235608	+	0.408085i
$689$	0.613136	−	0.800222i	0.0233586	−	0.0304860i
$690$		0			0
$691$	−9.74859	−	5.62835i	−0.370854	−	0.214113i	0.302978	−	0.952998i	$-0.402019\pi$
$691$	−9.74859	−	5.62835i	−0.370854	−	0.214113i	−0.673831	+	0.738885i	$0.735353\pi$
$692$	−21.2301	−	36.7716i	−0.807047	−	1.39785i
$693$		0			0
$694$		−	15.2043i		−	0.577147i
$695$			21.6194i			0.820071i
$696$		0			0
$697$	−1.48805	−	0.859128i	−0.0563640	−	0.0325418i
$698$	8.07884			0.305789
$699$		0			0
$700$	10.4415	+	14.8076i	0.394650	+	0.559673i
$701$	−22.2305			−0.839635			−0.419818	−	0.907608i	$-0.637906\pi$
$701$	−22.2305			−0.839635			−0.419818	+	0.907608i	$0.637906\pi$
$702$		0			0
$703$	−2.32288	+	4.02335i	−0.0876091	+	0.151743i
$704$		−	10.3532i		−	0.390201i
$705$		0			0
$706$	−2.96052	+	5.12776i	−0.111420	+	0.192986i
$707$	17.4916	+	24.8058i	0.657841	+	0.932918i
$708$		0			0
$709$			23.7741i			0.892854i	0.894820	+	0.446427i	$0.147304\pi$
$709$			23.7741i			0.892854i	−0.894820	+	0.446427i	$0.852696\pi$
$710$	1.66961	+	0.963952i	0.0626595	+	0.0361765i
$711$		0			0
$712$	1.63838	−	2.83776i	0.0614010	−	0.106350i
$713$	10.8245	−	6.24951i	0.405380	−	0.234046i
$714$		0			0
$715$	−5.71626	−	13.7728i	−0.213776	−	0.515072i
$716$	3.61969	+	6.26948i	0.135274	+	0.234301i
$717$		0			0
$718$	15.6822			0.585255
$719$	20.7808			0.774992			0.387496	−	0.921871i	$-0.373340\pi$
$719$	20.7808			0.774992			0.387496	+	0.921871i	$0.373340\pi$
$720$		0			0
$721$	−4.62904	+	10.0133i	−0.172394	+	0.372913i
$722$	4.91782	+	2.83931i	0.183022	+	0.105668i
$723$		0			0
$724$	6.88252	+	11.9209i	0.255787	+	0.443036i
$725$	32.8618			1.22046
$726$		0			0
$727$	−26.7719			−0.992915			−0.496457	−	0.868061i	$-0.665366\pi$
$727$	−26.7719			−0.992915			−0.496457	+	0.868061i	$0.665366\pi$
$728$	15.8318	−	8.32236i	0.586765	−	0.308447i
$729$		0			0
$730$	−2.98497	−	1.72338i	−0.110479	−	0.0637850i
$731$	0.685069			0.0253382
$732$		0			0
$733$	−4.55224	+	2.62824i	−0.168141	+	0.0970761i	−0.581709	−	0.813397i	$-0.697616\pi$
$733$	−4.55224	+	2.62824i	−0.168141	+	0.0970761i	0.413568	+	0.910473i	$0.364282\pi$
$734$	−10.4255	−	6.01919i	−0.384814	−	0.222172i
$735$		0			0
$736$			22.0917i			0.814312i
$737$	20.4097			0.751800
$738$		0			0
$739$		−	7.15001i		−	0.263017i	−0.991315	−	0.131509i	$-0.958018\pi$
$739$		−	7.15001i		−	0.263017i	0.991315	−	0.131509i	$-0.0419821\pi$
$740$	−0.769132	−	1.33218i	−0.0282738	−	0.0489717i
$741$		0			0
$742$	0.335727	+	0.155204i	0.0123249	+	0.00569771i
$743$	0.618032	−	0.356821i	0.0226734	−	0.0130905i	−0.488620	−	0.872496i	$-0.662500\pi$
$743$	0.618032	−	0.356821i	0.0226734	−	0.0130905i	0.511294	+	0.859406i	$0.329166\pi$
$744$		0			0
$745$	0.00592959	+	0.0102703i	0.000217243	+	0.000376276i
$746$	7.96386	+	4.59794i	0.291578	+	0.168342i
$747$		0			0
$748$	−0.854012	−	0.493064i	−0.0312258	−	0.0180282i
$749$	22.3636	−	2.03104i	0.817147	−	0.0742127i
$750$		0			0
$751$	−12.8507	+	22.2580i	−0.468927	+	0.812205i	−0.999369	−	0.0355158i	$-0.988693\pi$
$751$	−12.8507	+	22.2580i	−0.468927	+	0.812205i	0.530442	+	0.847721i	$0.322026\pi$
$752$		−	11.6763i		−	0.425791i
$753$		0			0
$754$	1.96539	−	15.0104i	0.0715752	−	0.546648i
$755$	−19.7084			−0.717263
$756$		0			0
$757$	−8.19425	−	14.1928i	−0.297825	−	0.515848i	0.677813	−	0.735234i	$-0.262928\pi$
$757$	−8.19425	−	14.1928i	−0.297825	−	0.515848i	−0.975638	+	0.219386i	$0.929594\pi$
$758$	4.06859			0.147778
$759$		0			0
$760$	−9.32654	+	5.38468i	−0.338309	+	0.195323i
$761$		−	8.31998i		−	0.301599i	−0.988564	−	0.150800i	$-0.951815\pi$
$761$		−	8.31998i		−	0.301599i	0.988564	−	0.150800i	$-0.0481848\pi$
$762$		0			0
$763$	−1.53879	−	16.9434i	−0.0557079	−	0.613392i
$764$	−5.66888	−	9.81878i	−0.205093	−	0.355231i
$765$		0			0
$766$	5.59263	−	9.68671i	0.202070	−	0.349995i
$767$	35.9037	−	14.9015i	1.29641	−	0.538061i
$768$		0			0
$769$	22.1346	−	12.7794i	0.798194	−	0.460838i	−0.0446452	−	0.999003i	$-0.514216\pi$
$769$	22.1346	−	12.7794i	0.798194	−	0.460838i	0.842839	+	0.538165i	$0.180882\pi$
$770$	4.47121	−	3.15284i	0.161131	−	0.113621i
$771$		0			0
$772$	−7.31905	+	4.22565i	−0.263418	+	0.152085i
$773$	−7.27528	+	4.20038i	−0.261674	+	0.151077i	−0.625098	−	0.780546i	$-0.714941\pi$
$773$	−7.27528	+	4.20038i	−0.261674	+	0.151077i	0.363424	+	0.931624i	$0.381608\pi$
$774$		0			0
$775$	9.64678	−	5.56957i	0.346523	−	0.200065i
$776$	−2.53392	+	4.38887i	−0.0909623	+	0.157551i
$777$		0			0
$778$	−9.26388	+	5.34850i	−0.332126	+	0.191753i
$779$	33.3269	+	57.7238i	1.19406	+	2.06817i
$780$		0			0
$781$	7.33714	−	12.7083i	0.262544	−	0.454739i
$782$	0.270052	+	0.155914i	0.00965703	+	0.00557549i
$783$		0			0
$784$	−11.6209	−	13.6648i	−0.415032	−	0.488029i
$785$		−	20.6345i		−	0.736476i
$786$		0			0
$787$	−30.3667	+	17.5322i	−1.08246	+	0.624956i	−0.931558	−	0.363593i	$-0.881550\pi$
$787$	−30.3667	+	17.5322i	−1.08246	+	0.624956i	−0.150898	+	0.988549i	$0.548216\pi$
$788$	−39.1562	−	22.6069i	−1.39488	−	0.805336i
$789$		0			0
$790$	−3.10720	−	5.38182i	−0.110549	−	0.191477i
$791$	28.8872	−	2.62352i	1.02711	−	0.0932816i
$792$		0			0
$793$	20.9624	+	2.74470i	0.744395	+	0.0974671i
$794$	0.299175	−	0.518186i	0.0106173	−	0.0183897i
$795$		0			0
$796$	14.9754	−	25.9382i	0.530789	−	0.919354i
$797$	12.2876	−	21.2828i	0.435250	−	0.753875i	−0.562066	−	0.827092i	$-0.689993\pi$
$797$	12.2876	−	21.2828i	0.435250	−	0.753875i	0.997316	+	0.0732173i	$0.0233267\pi$
$798$		0			0
$799$	−0.560475	−	0.323590i	−0.0198282	−	0.0114478i
$800$			19.6882i			0.696083i
$801$		0			0
$802$	9.06848	+	15.7071i	0.320219	+	0.554636i
$803$	−13.1175	+	22.7202i	−0.462907	+	0.801778i
$804$		0			0
$805$	9.89765	−	6.97926i	0.348846	−	0.245987i
$806$	−1.96709	−	4.73951i	−0.0692877	−	0.166942i
$807$		0			0
$808$			21.5099i			0.756717i
$809$	31.8012			1.11807			0.559035	−	0.829144i	$-0.311172\pi$
$809$	31.8012			1.11807			0.559035	+	0.829144i	$0.311172\pi$
$810$		0			0
$811$			10.3633i			0.363905i	0.983307	+	0.181953i	$0.0582418\pi$
$811$			10.3633i			0.363905i	−0.983307	+	0.181953i	$0.941758\pi$
$812$	−38.7223	+	3.51673i	−1.35889	+	0.123413i
$813$		0			0
$814$	1.44847	−	0.836272i	0.0507687	−	0.0293113i
$815$	−4.65598	−	8.06439i	−0.163092	−	0.282483i
$816$		0			0
$817$	−23.0145	−	13.2874i	−0.805176	−	0.464868i
$818$	7.33597			0.256496
$819$		0			0
$820$	−22.0698			−0.770711
$821$	−3.51253	−	2.02796i	−0.122588	−	0.0707762i	0.437452	−	0.899242i	$-0.355881\pi$
$821$	−3.51253	−	2.02796i	−0.122588	−	0.0707762i	−0.560040	+	0.828465i	$0.689214\pi$
$822$		0			0
$823$	4.35848	+	7.54912i	0.151927	+	0.263146i	0.931936	−	0.362623i	$-0.118119\pi$
$823$	4.35848	+	7.54912i	0.151927	+	0.263146i	−0.780009	+	0.625769i	$0.784785\pi$
$824$	−6.77027	+	3.90882i	−0.235854	+	0.136170i
$825$		0			0
$826$	8.21902	+	11.6558i	0.285976	+	0.405557i
$827$			23.5788i			0.819915i	0.912105	+	0.409957i	$0.134456\pi$
$827$			23.5788i			0.819915i	−0.912105	+	0.409957i	$0.865544\pi$
$828$		0			0
$829$	29.0406			1.00862			0.504311	−	0.863522i	$-0.331747\pi$
$829$	29.0406			1.00862			0.504311	+	0.863522i	$0.331747\pi$
$830$		−	1.49759i		−	0.0519820i
$831$		0			0
$832$	−9.32953	−	1.22156i	−0.323443	−	0.0423499i
$833$	−0.977980	+	0.179116i	−0.0338850	+	0.00620601i
$834$		0			0
$835$	3.19763	−	5.53846i	0.110659	−	0.191666i
$836$	19.1267	+	33.1284i	0.661511	+	1.14577i
$837$		0			0
$838$			2.96666i			0.102482i
$839$	10.0090	+	5.77871i	0.345550	+	0.199503i	0.662723	−	0.748864i	$-0.269400\pi$
$839$	10.0090	+	5.77871i	0.345550	+	0.199503i	−0.317174	+	0.948367i	$0.602734\pi$
$840$		0			0
$841$	−20.7598	+	35.9570i	−0.715855	+	1.23990i
$842$	−0.657918	+	1.13955i	−0.0226734	+	0.0392714i
$843$		0			0
$844$	−16.0049	+	27.7212i	−0.550910	+	0.954205i
$845$	−13.0854	+	3.52603i	−0.450153	+	0.121299i
$846$		0			0
$847$	−7.22630	−	10.2480i	−0.248298	−	0.352125i
$848$	−0.358248	−	0.620504i	−0.0123023	−	0.0213082i
$849$		0			0
$850$	0.240670	+	0.138951i	0.00825493	+	0.00476598i
$851$	3.20638	−	1.85121i	0.109913	−	0.0634586i
$852$		0			0
$853$		−	1.51845i		−	0.0519906i	−0.999662	−	0.0259953i	$-0.991725\pi$
$853$		−	1.51845i		−	0.0519906i	0.999662	−	0.0259953i	$-0.00827550\pi$
$854$	0.701554	+	7.72473i	0.0240067	+	0.264335i
$855$		0			0
$856$	13.7815	+	7.95678i	0.471043	+	0.271957i
$857$	3.00060	−	5.19718i	0.102498	−	0.177532i	−0.810215	−	0.586133i	$-0.800650\pi$
$857$	3.00060	−	5.19718i	0.102498	−	0.177532i	0.912713	+	0.408600i	$0.133983\pi$
$858$		0			0
$859$	−0.838021	−	1.45150i	−0.0285929	−	0.0495244i	0.851375	−	0.524558i	$-0.175769\pi$
$859$	−0.838021	−	1.45150i	−0.0285929	−	0.0495244i	−0.879968	+	0.475033i	$0.842436\pi$
$860$	7.62036	−	4.39962i	0.259852	−	0.150026i
$861$		0			0
$862$	4.70929	−	8.15673i	0.160399	−	0.277819i
$863$	36.4167	−	21.0252i	1.23964	−	0.715706i	0.270619	−	0.962687i	$-0.412772\pi$
$863$	36.4167	−	21.0252i	1.23964	−	0.715706i	0.969021	+	0.246980i	$0.0794383\pi$
$864$		0			0
$865$	−21.9047	+	12.6467i	−0.744781	+	0.429999i
$866$	−8.28567	+	4.78374i	−0.281559	+	0.162558i
$867$		0			0
$868$	−10.7711	+	7.59519i	−0.365596	+	0.257798i
$869$	−40.9639	+	23.6505i	−1.38960	+	0.802288i
$870$		0			0
$871$	2.40811	−	18.3917i	0.0815956	−	0.623178i
$872$	6.02832	−	10.4414i	0.204145	−	0.353589i
$873$		0			0
$874$	−6.04815	−	10.4757i	−0.204582	−	0.354346i
$875$	20.0912	−	14.1672i	0.679208	−	0.478939i
$876$		0			0
$877$			30.8630i			1.04217i	0.853505	+	0.521084i	$0.174472\pi$
$877$			30.8630i			1.04217i	−0.853505	+	0.521084i	$0.825528\pi$
$878$	0.547793	−	0.316268i	0.0184871	−	0.0106735i
$879$		0			0
$880$	−10.5983			−0.357270
$881$	27.8669	+	48.2669i	0.938860	+	1.62615i	0.767601	+	0.640928i	$0.221450\pi$
$881$	27.8669	+	48.2669i	0.938860	+	1.62615i	0.171260	+	0.985226i	$0.445216\pi$
$882$		0			0
$883$	−2.92007			−0.0982681			−0.0491341	−	0.998792i	$-0.515646\pi$
$883$	−2.92007			−0.0982681			−0.0491341	+	0.998792i	$0.515646\pi$
$884$	−0.545076	+	0.711396i	−0.0183329	+	0.0239268i
$885$		0			0
$886$			10.4693i			0.351724i
$887$	0.939545	−	1.62734i	0.0315468	−	0.0546407i	−0.849821	−	0.527071i	$-0.823290\pi$
$887$	0.939545	−	1.62734i	0.0315468	−	0.0546407i	0.881368	+	0.472431i	$0.156623\pi$
$888$		0			0
$889$	2.22917	−	4.82200i	0.0747639	−	0.161725i
$890$	−0.788876	−	0.455458i	−0.0264432	−	0.0152670i
$891$		0			0
$892$	17.4421	+	10.0702i	0.584004	+	0.337175i
$893$	12.5526	+	21.7417i	0.420055	+	0.727557i
$894$		0			0
$895$	3.73470	−	2.15623i	0.124837	−	0.0720748i
$896$	−2.72015	−	29.9513i	−0.0908740	−	1.00060i
$897$		0			0
$898$	4.46569	+	7.73480i	0.149022	+	0.258114i
$899$			23.9039i			0.797241i
$900$		0			0
$901$	−0.0397131			−0.00132304
$902$		−	23.9964i		−	0.798991i
$903$		0			0
$904$	17.8017	+	10.2778i	0.592077	+	0.341836i
$905$	7.10121	−	4.09989i	0.236052	−	0.136285i
$906$		0			0
$907$	35.6164			1.18262			0.591311	−	0.806444i	$-0.298611\pi$
$907$	35.6164			1.18262			0.591311	+	0.806444i	$0.298611\pi$
$908$	27.1352	+	15.6665i	0.900514	+	0.519912i
$909$		0			0
$910$	−2.31355	−	4.40111i	−0.0766935	−	0.145896i
$911$	−44.2844			−1.46721			−0.733604	−	0.679577i	$-0.762163\pi$
$911$	−44.2844			−1.46721			−0.733604	+	0.679577i	$0.762163\pi$
$912$		0			0
$913$	−11.3989			−0.377249
$914$	1.64145	+	2.84307i	0.0542943	+	0.0940404i
$915$		0			0
$916$	−5.85535	−	3.38059i	−0.193466	−	0.111698i
$917$	13.8224	−	29.8998i	0.456456	−	0.987378i
$918$		0			0
$919$	26.1128			0.861382			0.430691	−	0.902499i	$-0.358270\pi$
$919$	26.1128			0.861382			0.430691	+	0.902499i	$0.358270\pi$
$920$	8.58259			0.282959
$921$		0			0
$922$	−1.27838	−	2.21421i	−0.0421010	−	0.0729211i
$923$	−10.5861	−	8.11111i	−0.348445	−	0.266981i
$924$		0			0
$925$	2.85753	−	1.64980i	0.0939551	−	0.0542450i
$926$	−8.33076	+	14.4293i	−0.273766	+	0.474176i
$927$		0			0
$928$	−36.5893	−	21.1248i	−1.20110	−	0.693457i
$929$			10.0231i			0.328849i	0.986390	+	0.164424i	$0.0525766\pi$
$929$			10.0231i			0.328849i	−0.986390	+	0.164424i	$0.947423\pi$
$930$		0			0
$931$	36.3288	+	12.9514i	1.19063	+	0.424464i
$932$	−21.9313	+	37.9861i	−0.718384	+	1.24428i
$933$		0			0
$934$		−	6.47455i		−	0.211854i
$935$	−0.293716	+	0.508731i	−0.00960554	+	0.0166373i
$936$		0			0
$937$	−0.916838			−0.0299518			−0.0149759	−	0.999888i	$-0.504767\pi$
$937$	−0.916838			−0.0299518			−0.0149759	+	0.999888i	$0.504767\pi$
$938$	6.77742	−	0.615520i	0.221291	−	0.0200975i
$939$		0			0
$940$	−8.31259			−0.271127
$941$	−14.8001	−	8.54482i	−0.482468	−	0.278553i	0.238976	−	0.971025i	$-0.423188\pi$
$941$	−14.8001	−	8.54482i	−0.482468	−	0.278553i	−0.721445	+	0.692472i	$0.756522\pi$
$942$		0			0
$943$		−	53.1193i		−	1.72980i
$944$		−	27.6284i		−	0.899227i
$945$		0			0
$946$	4.78368	+	8.28557i	0.155531	+	0.269387i
$947$	−18.8408	−	10.8777i	−0.612243	−	0.353479i	0.161600	−	0.986856i	$-0.448335\pi$
$947$	−18.8408	−	10.8777i	−0.612243	−	0.353479i	−0.773843	+	0.633378i	$0.781668\pi$
$948$		0			0
$949$	18.9260	+	14.5012i	0.614364	+	0.470730i
$950$	−5.39012	−	9.33597i	−0.174879	−	0.302899i
$951$		0			0
$952$	−0.639556	−	0.295661i	−0.0207281	−	0.00958243i
$953$	8.90406	−	15.4223i	0.288431	−	0.499577i	−0.685005	−	0.728539i	$-0.740200\pi$
$953$	8.90406	−	15.4223i	0.288431	−	0.499577i	0.973435	+	0.228962i	$0.0735331\pi$
$954$		0			0
$955$	−5.84900	+	3.37692i	−0.189269	+	0.109275i
$956$	−11.8283	+	6.82909i	−0.382556	+	0.220869i
$957$		0			0
$958$	6.75281	−	11.6962i	0.218173	−	0.377887i
$959$	−12.5965	−	5.82327i	−0.406763	−	0.188043i
$960$		0			0
$961$	−11.4487	−	19.8297i	−0.369311	−	0.639666i
$962$	−0.582683	−	1.40392i	−0.0187865	−	0.0452642i
$963$		0			0
$964$	−32.9865	−	19.0447i	−1.06242	−	0.613390i
$965$	2.51720	+	4.35992i	0.0810316	+	0.140351i
$966$		0			0
$967$			35.3813i			1.13779i	0.822412	+	0.568893i	$0.192628\pi$
$967$			35.3813i			1.13779i	−0.822412	+	0.568893i	$0.807372\pi$
$968$		−	8.88637i		−	0.285619i
$969$		0			0
$970$	1.22007	+	0.704409i	0.0391742	+	0.0226172i
$971$	−49.7067			−1.59516			−0.797582	−	0.603211i	$-0.793888\pi$
$971$	−49.7067			−1.59516			−0.797582	+	0.603211i	$0.793888\pi$
$972$		0			0
$973$	54.6441	−	4.96274i	1.75181	−	0.159098i
$974$	−16.0415			−0.514002
$975$		0			0
$976$	7.51287	−	13.0127i	0.240481	−	0.416526i
$977$		−	61.2801i		−	1.96052i	−0.197702	−	0.980262i	$-0.563348\pi$
$977$		−	61.2801i		−	1.96052i	0.197702	−	0.980262i	$-0.436652\pi$
$978$		0			0
$979$	−3.46673	+	6.00455i	−0.110797	+	0.191906i
$980$	−9.72825	+	8.27314i	−0.310757	+	0.264276i
$981$		0			0
$982$		−	14.3016i		−	0.456383i
$983$	−6.05318	−	3.49481i	−0.193067	−	0.111467i	0.400351	−	0.916362i	$-0.368888\pi$
$983$	−6.05318	−	3.49481i	−0.193067	−	0.111467i	−0.593417	+	0.804895i	$0.702222\pi$
$984$		0			0
$985$	−13.4668	+	23.3252i	−0.429088	+	0.743203i
$986$	−0.516464	+	0.298181i	−0.0164476	+	0.00949601i
$987$		0			0
$988$	32.1096	−	13.3268i	1.02154	−	0.423981i
$989$	10.5893	+	18.3413i	0.336722	+	0.583219i
$990$		0			0
$991$	−32.7341			−1.03983			−0.519917	−	0.854217i	$-0.674037\pi$
$991$	−32.7341			−1.03983			−0.519917	+	0.854217i	$0.674037\pi$
$992$	−14.3213			−0.454703
$993$		0			0
$994$	2.05318	−	4.44131i	0.0651228	−	0.140870i
$995$	−15.4512	−	8.92078i	−0.489838	−	0.282808i
$996$		0			0
$997$	−28.8948	−	50.0473i	−0.915109	−	1.58502i	−0.806742	−	0.590904i	$-0.798771\pi$
$997$	−28.8948	−	50.0473i	−0.915109	−	1.58502i	−0.108367	−	0.994111i	$-0.534562\pi$
$998$	0.899058			0.0284592
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.do.e.361.3		12
3.2	odd	2		91.2.u.b.88.4	yes	12
7.2	even	3		819.2.bm.f.478.4		12
13.4	even	6		819.2.bm.f.550.3		12
21.2	odd	6		91.2.k.b.23.3	yes	12
21.5	even	6		637.2.k.i.569.3		12
21.11	odd	6		637.2.q.g.491.3		12
21.17	even	6		637.2.q.i.491.3		12
21.20	even	2		637.2.u.g.361.4		12
39.2	even	12		1183.2.e.j.508.8		24
39.11	even	12		1183.2.e.j.508.5		24
39.17	odd	6		91.2.k.b.4.4	✓	12
91.30	even	6	inner	819.2.do.e.667.3		12
273.2	even	12		1183.2.e.j.170.8		24
273.11	even	12		8281.2.a.cp.1.8		12
273.17	even	6		637.2.q.i.589.3		12
273.80	odd	12		8281.2.a.co.1.5		12
273.95	odd	6		637.2.q.g.589.3		12
273.128	even	12		1183.2.e.j.170.5		24
273.158	even	12		8281.2.a.cp.1.5		12
273.173	even	6		637.2.u.g.30.4		12
273.206	odd	12		8281.2.a.co.1.8		12
273.212	odd	6		91.2.u.b.30.4	yes	12
273.251	even	6		637.2.k.i.459.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.4	✓	12	39.17	odd	6
91.2.k.b.23.3	yes	12	21.2	odd	6
91.2.u.b.30.4	yes	12	273.212	odd	6
91.2.u.b.88.4	yes	12	3.2	odd	2
637.2.k.i.459.4		12	273.251	even	6
637.2.k.i.569.3		12	21.5	even	6
637.2.q.g.491.3		12	21.11	odd	6
637.2.q.g.589.3		12	273.95	odd	6
637.2.q.i.491.3		12	21.17	even	6
637.2.q.i.589.3		12	273.17	even	6
637.2.u.g.30.4		12	273.173	even	6
637.2.u.g.361.4		12	21.20	even	2
819.2.bm.f.478.4		12	7.2	even	3
819.2.bm.f.550.3		12	13.4	even	6
819.2.do.e.361.3		12	1.1	even	1	trivial
819.2.do.e.667.3		12	91.30	even	6	inner
1183.2.e.j.170.5		24	273.128	even	12
1183.2.e.j.170.8		24	273.2	even	12
1183.2.e.j.508.5		24	39.11	even	12
1183.2.e.j.508.8		24	39.2	even	12
8281.2.a.co.1.5		12	273.80	odd	12
8281.2.a.co.1.8		12	273.206	odd	12
8281.2.a.cp.1.5		12	273.158	even	12
8281.2.a.cp.1.8		12	273.11	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.do (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.433001 - 0.249993i) q^{2} +(-0.875007 - 1.51556i) q^{4} +(-0.902810 + 0.521238i) q^{5} +(1.52469 + 2.16225i) q^{7} +1.87496i q^{8} +O(q^{10})\)	\(q+(-0.433001 - 0.249993i) q^{2} +(-0.875007 - 1.51556i) q^{4} +(-0.902810 + 0.521238i) q^{5} +(1.52469 + 2.16225i) q^{7} +1.87496i q^{8} +0.521224 q^{10} -3.96730i q^{11} +(-3.57504 - 0.468096i) q^{13} +(-0.119647 - 1.31742i) q^{14} +(-1.28129 + 2.21925i) q^{16} +(0.0710177 + 0.123006i) q^{17} -5.50977i q^{19} +(1.57993 + 0.912173i) q^{20} +(-0.991800 + 1.71785i) q^{22} +(-2.19549 + 3.80270i) q^{23} +(-1.95662 + 3.38897i) q^{25} +(1.43097 + 1.09642i) q^{26} +(1.94289 - 4.20274i) q^{28} +(-4.19880 - 7.27253i) q^{29} +(-2.46516 - 1.42326i) q^{31} +(4.35712 - 2.51558i) q^{32} -0.0710158i q^{34} +(-2.50355 - 1.15737i) q^{35} +(-0.730221 - 0.421593i) q^{37} +(-1.37740 + 2.38574i) q^{38} +(-0.977298 - 1.69273i) q^{40} +(-10.4766 + 6.04869i) q^{41} +(2.41161 - 4.17704i) q^{43} +(-6.01267 + 3.47142i) q^{44} +(1.90130 - 1.09772i) q^{46} +(-3.94602 + 2.27824i) q^{47} +(-2.35062 + 6.59353i) q^{49} +(1.69444 - 0.978285i) q^{50} +(2.41875 + 5.82776i) q^{52} +(-0.139800 + 0.242141i) q^{53} +(2.06791 + 3.58172i) q^{55} +(-4.05412 + 2.85873i) q^{56} +4.19868i q^{58} +(-9.33705 + 5.39075i) q^{59} -5.86354 q^{61} +(0.711612 + 1.23255i) q^{62} +2.60963 q^{64} +(3.47157 - 1.44084i) q^{65} +5.14447i q^{67} +(0.124282 - 0.215263i) q^{68} +(0.794706 + 1.12701i) q^{70} +(3.20326 + 1.84940i) q^{71} +(-5.72686 - 3.30640i) q^{73} +(0.210791 + 0.365101i) q^{74} +(-8.35036 + 4.82108i) q^{76} +(8.57829 - 6.04892i) q^{77} +(-5.96135 - 10.3254i) q^{79} -2.67142i q^{80} +6.04853 q^{82} -2.87321i q^{83} +(-0.128231 - 0.0740342i) q^{85} +(-2.08846 + 1.20578i) q^{86} +7.43852 q^{88} +(-1.51351 - 0.873824i) q^{89} +(-4.43870 - 8.44381i) q^{91} +7.68427 q^{92} +2.27818 q^{94} +(2.87190 + 4.97427i) q^{95} +(2.34079 + 1.35145i) q^{97} +(2.66616 - 2.26737i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7}+O(q^{10}) \) 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7	\( 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7} - 24 q^{10} - 2 q^{13} - 4 q^{14} - 8 q^{16} - 17 q^{17} + 3 q^{20} - 15 q^{22} - 3 q^{23} - 5 q^{25} + 9 q^{26} + 27 q^{28} + q^{29} - 18 q^{31} - 18 q^{32} - 18 q^{35} + 15 q^{37} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} - 30 q^{46} - 15 q^{47} + 9 q^{49} - 18 q^{50} + 47 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{59} - 10 q^{61} - 41 q^{62} + 2 q^{64} + 3 q^{65} + 11 q^{68} - 3 q^{70} - 30 q^{71} - 42 q^{73} + 33 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} - 10 q^{82} - 21 q^{85} - 57 q^{86} + 28 q^{88} - 48 q^{89} - 16 q^{91} + 66 q^{92} - 2 q^{94} - 2 q^{95} - 3 q^{97} + 36 q^{98}+O(q^{100}) \) 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7 - 24 * q^10 - 2 * q^13 - 4 * q^14 - 8 * q^16 - 17 * q^17 + 3 * q^20 - 15 * q^22 - 3 * q^23 - 5 * q^25 + 9 * q^26 + 27 * q^28 + q^29 - 18 * q^31 - 18 * q^32 - 18 * q^35 + 15 * q^37 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 - 33 * q^44 - 30 * q^46 - 15 * q^47 + 9 * q^49 - 18 * q^50 + 47 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^59 - 10 * q^61 - 41 * q^62 + 2 * q^64 + 3 * q^65 + 11 * q^68 - 3 * q^70 - 30 * q^71 - 42 * q^73 + 33 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 - 10 * q^82 - 21 * q^85 - 57 * q^86 + 28 * q^88 - 48 * q^89 - 16 * q^91 + 66 * q^92 - 2 * q^94 - 2 * q^95 - 3 * q^97 + 36 * q^98

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