LMFDB - Embedded newform 891.2.n.e.676.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(136,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("891.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.n (of order $15$, degree $8$, not 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} - 15x^{12} + 116x^{10} + 69x^{8} - 814x^{6} + 2420x^{4} - 7986x^{2} + 14641 $ x^16 - x^14 - 15x^12 + 116x^10 + 69x^8 - 814x^6 + 2420x^4 - 7986x^2 + 14641
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			676.1
Root			$-1.03271 + 1.14694i$ of defining polynomial
Character	$\chi$	$=$	891.676
Dual form			891.2.n.e.460.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.03271 + 1.14694i) q^{2} +(-0.0399263 - 0.379874i) q^{4} +(1.03271 + 1.14694i) q^{5} +(0.215659 + 0.0960175i) q^{7} +(-2.02029 - 1.46782i) q^{8} -2.38197 q^{10} +(0.899280 - 3.19238i) q^{11} +(4.14350 + 0.880728i) q^{13} +(-0.332840 + 0.148190i) q^{14} +(4.51712 - 0.960143i) q^{16} +(-1.83812 + 5.65714i) q^{17} +(3.73607 + 2.71441i) q^{19} +(0.394460 - 0.438093i) q^{20} +(2.73278 + 4.32823i) q^{22} +(-3.74582 + 6.48795i) q^{23} +(0.273659 - 2.60369i) q^{25} +(-5.28918 + 3.84281i) q^{26} +(0.0278640 - 0.0857567i) q^{28} +(1.74277 + 0.775932i) q^{29} +(2.32991 + 0.495239i) q^{31} +(-1.06644 + 1.84712i) q^{32} +(-4.59017 - 7.95041i) q^{34} +(0.112587 + 0.346506i) q^{35} +(-5.04508 + 3.66547i) q^{37} +(-6.97155 + 1.48185i) q^{38} +(-0.402863 - 3.83299i) q^{40} +(5.10118 - 2.27119i) q^{41} +(5.35410 + 9.27358i) q^{43} +(-1.24861 - 0.214153i) q^{44} +(-3.57295 - 10.9964i) q^{46} +(-0.0997045 + 0.948625i) q^{47} +(-4.64662 - 5.16060i) q^{49} +(2.70367 + 3.00273i) q^{50} +(0.169131 - 1.60917i) q^{52} +(-2.79197 - 8.59279i) q^{53} +(4.59017 - 2.26538i) q^{55} +(-0.294756 - 0.510532i) q^{56} +(-2.68973 + 1.19754i) q^{58} +(0.882794 + 8.39922i) q^{59} +(-4.23170 + 0.899475i) q^{61} +(-2.97414 + 2.16084i) q^{62} +(1.83688 + 5.65334i) q^{64} +(3.26889 + 5.66189i) q^{65} +(-1.92705 + 3.33775i) q^{67} +(2.22239 + 0.472383i) q^{68} +(-0.513692 - 0.228710i) q^{70} +(-2.38463 + 7.33912i) q^{71} +(5.23607 - 3.80423i) q^{73} +(1.00604 - 9.57179i) q^{74} +(0.881966 - 1.52761i) q^{76} +(0.500462 - 0.602118i) q^{77} +(-0.353210 + 0.392279i) q^{79} +(5.76611 + 4.18932i) q^{80} +(-2.66312 + 8.19624i) q^{82} +(-4.30865 + 0.915833i) q^{83} +(-8.38666 + 3.73398i) q^{85} +(-16.1655 - 3.43608i) q^{86} +(-6.50266 + 5.12954i) q^{88} -16.7518 q^{89} +(0.809017 + 0.587785i) q^{91} +(2.61416 + 1.16390i) q^{92} +(-0.985051 - 1.09401i) q^{94} +(0.745005 + 7.08825i) q^{95} +(-8.56378 + 9.51105i) q^{97} +10.7175 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4} + 6 q^{7} - 56 q^{10} + 6 q^{13} - 2 q^{16} + 24 q^{19} - 28 q^{22} - 8 q^{25} + 72 q^{28} - 12 q^{31} + 16 q^{34} - 36 q^{37} + 16 q^{40} + 32 q^{43} - 84 q^{46} + 44 q^{49} - 6 q^{52} - 16 q^{55}+ \cdots + 54 q^{97}+O(q^{100}) $ 16 * q - 2 * q^4 + 6 * q^7 - 56 * q^10 + 6 * q^13 - 2 * q^16 + 24 * q^19 - 28 * q^22 - 8 * q^25 + 72 * q^28 - 12 * q^31 + 16 * q^34 - 36 * q^37 + 16 * q^40 + 32 * q^43 - 84 * q^46 + 44 * q^49 - 6 * q^52 - 16 * q^55 - 28 * q^58 - 42 * q^61 + 92 * q^64 - 4 * q^67 - 26 * q^70 + 48 * q^73 + 32 * q^76 - 30 * q^79 + 20 * q^82 - 46 * q^85 + 14 * q^88 + 4 * q^91 + 26 * q^94 + 54 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.03271	+	1.14694i	−0.730237	+	0.811010i	−0.987878	−	0.155231i	$-0.950388\pi$
$2$	−1.03271	+	1.14694i	−0.730237	+	0.811010i	0.257642	+	0.966241i	$0.417055\pi$
$3$		0			0
$3$		0			0
$4$	−0.0399263	−	0.379874i	−0.0199632	−	0.189937i
$5$	1.03271	+	1.14694i	0.461842	+	0.512928i	0.928410	−	0.371558i	$-0.121176\pi$
$5$	1.03271	+	1.14694i	0.461842	+	0.512928i	−0.466568	+	0.884486i	$0.654510\pi$
$6$		0			0
$7$	0.215659	+	0.0960175i	0.0815114	+	0.0362912i	0.447087	−	0.894490i	$-0.352461\pi$
$7$	0.215659	+	0.0960175i	0.0815114	+	0.0362912i	−0.365576	+	0.930781i	$0.619128\pi$
$8$	−2.02029	−	1.46782i	−0.714279	−	0.518954i
$9$		0			0
$10$	−2.38197			−0.753244
$11$	0.899280	−	3.19238i	0.271143	−	0.962539i
$11$	0.899280	−	3.19238i	0.271143	−	0.962539i
$12$		0			0
$13$	4.14350	+	0.880728i	1.14920	+	0.244270i	0.742857	−	0.669450i	$-0.233470\pi$
$13$	4.14350	+	0.880728i	1.14920	+	0.244270i	0.406343	+	0.913720i	$0.366804\pi$
$14$	−0.332840	+	0.148190i	−0.0889551	+	0.0396054i
$15$		0			0
$16$	4.51712	−	0.960143i	1.12928	−	0.240036i
$17$	−1.83812	+	5.65714i	−0.445809	+	1.37206i	0.435785	+	0.900051i	$0.356471\pi$
$17$	−1.83812	+	5.65714i	−0.445809	+	1.37206i	−0.881594	+	0.472008i	$0.843529\pi$
$18$		0			0
$19$	3.73607	+	2.71441i	0.857113	+	0.622729i	0.927098	−	0.374819i	$-0.122295\pi$
$19$	3.73607	+	2.71441i	0.857113	+	0.622729i	−0.0699852	+	0.997548i	$0.522295\pi$
$20$	0.394460	−	0.438093i	0.0882040	−	0.0979605i
$21$		0			0
$22$	2.73278	+	4.32823i	0.582630	+	0.922781i
$23$	−3.74582	+	6.48795i	−0.781057	+	1.35283i	0.150269	+	0.988645i	$0.451986\pi$
$23$	−3.74582	+	6.48795i	−0.781057	+	1.35283i	−0.931326	+	0.364185i	$0.881347\pi$
$24$		0			0
$25$	0.273659	−	2.60369i	0.0547318	−	0.520738i
$26$	−5.28918	+	3.84281i	−1.03729	+	0.753638i
$27$		0			0
$28$	0.0278640	−	0.0857567i	0.00526581	−	0.0162065i
$29$	1.74277	+	0.775932i	0.323624	+	0.144087i	0.562118	−	0.827057i	$-0.309987\pi$
$29$	1.74277	+	0.775932i	0.323624	+	0.144087i	−0.238493	+	0.971144i	$0.576653\pi$
$30$		0			0
$31$	2.32991	+	0.495239i	0.418465	+	0.0889475i	0.412332	−	0.911034i	$-0.364714\pi$
$31$	2.32991	+	0.495239i	0.418465	+	0.0889475i	0.00613311	+	0.999981i	$0.498048\pi$
$32$	−1.06644	+	1.84712i	−0.188521	+	0.326528i
$33$		0			0
$34$	−4.59017	−	7.95041i	−0.787208	−	1.36348i
$35$	0.112587	+	0.346506i	0.0190306	+	0.0585703i
$36$		0			0
$37$	−5.04508	+	3.66547i	−0.829407	+	0.602599i	−0.919391	−	0.393344i	$-0.871318\pi$
$37$	−5.04508	+	3.66547i	−0.829407	+	0.602599i	0.0899846	+	0.995943i	$0.471318\pi$
$38$	−6.97155	+	1.48185i	−1.13093	+	0.240388i
$39$		0			0
$40$	−0.402863	−	3.83299i	−0.0636983	−	0.606049i
$41$	5.10118	−	2.27119i	0.796670	−	0.354700i	0.0323002	−	0.999478i	$-0.489717\pi$
$41$	5.10118	−	2.27119i	0.796670	−	0.354700i	0.764370	+	0.644778i	$0.223050\pi$
$42$		0			0
$43$	5.35410	+	9.27358i	0.816493	+	1.41421i	0.908251	+	0.418426i	$0.137418\pi$
$43$	5.35410	+	9.27358i	0.816493	+	1.41421i	−0.0917581	+	0.995781i	$0.529249\pi$
$44$	−1.24861	−	0.214153i	−0.188234	−	0.0322847i
$45$		0			0
$46$	−3.57295	−	10.9964i	−0.526803	−	1.62133i
$47$	−0.0997045	+	0.948625i	−0.0145434	+	0.138371i	−0.999384	−	0.0350896i	$-0.988828\pi$
$47$	−0.0997045	+	0.948625i	−0.0145434	+	0.138371i	0.984841	+	0.173461i	$0.0554950\pi$
$48$		0			0
$49$	−4.64662	−	5.16060i	−0.663804	−	0.737229i
$50$	2.70367	+	3.00273i	0.382357	+	0.424650i
$51$		0			0
$52$	0.169131	−	1.60917i	0.0234542	−	0.223152i
$53$	−2.79197	−	8.59279i	−0.383506	−	1.18031i	−0.937558	−	0.347829i	$-0.886919\pi$
$53$	−2.79197	−	8.59279i	−0.383506	−	1.18031i	0.554052	−	0.832482i	$-0.313081\pi$
$54$		0			0
$55$	4.59017	−	2.26538i	0.618938	−	0.305464i
$56$	−0.294756	−	0.510532i	−0.0393884	−	0.0682227i
$57$		0			0
$58$	−2.68973	+	1.19754i	−0.353178	+	0.157245i
$59$	0.882794	+	8.39922i	0.114930	+	1.09349i	0.888215	+	0.459427i	$0.151945\pi$
$59$	0.882794	+	8.39922i	0.114930	+	1.09349i	−0.773285	+	0.634058i	$0.781388\pi$
$60$		0			0
$61$	−4.23170	+	0.899475i	−0.541814	+	0.115166i	−0.470685	−	0.882301i	$-0.655993\pi$
$61$	−4.23170	+	0.899475i	−0.541814	+	0.115166i	−0.0711282	+	0.997467i	$0.522660\pi$
$62$	−2.97414	+	2.16084i	−0.377716	+	0.274427i
$63$		0			0
$64$	1.83688	+	5.65334i	0.229610	+	0.706667i
$65$	3.26889	+	5.66189i	0.405456	+	0.702271i
$66$		0			0
$67$	−1.92705	+	3.33775i	−0.235427	+	0.407771i	−0.959397	−	0.282061i	$-0.908982\pi$
$67$	−1.92705	+	3.33775i	−0.235427	+	0.407771i	0.723970	+	0.689832i	$0.242315\pi$
$68$	2.22239	+	0.472383i	0.269504	+	0.0572849i
$69$		0			0
$70$	−0.513692	−	0.228710i	−0.0613979	−	0.0273361i
$71$	−2.38463	+	7.33912i	−0.283003	+	0.870994i	0.703987	+	0.710213i	$0.251401\pi$
$71$	−2.38463	+	7.33912i	−0.283003	+	0.870994i	−0.986990	+	0.160781i	$0.948599\pi$
$72$		0			0
$73$	5.23607	−	3.80423i	0.612835	−	0.445251i	−0.237576	−	0.971369i	$-0.576353\pi$
$73$	5.23607	−	3.80423i	0.612835	−	0.445251i	0.850412	+	0.526118i	$0.176353\pi$
$74$	1.00604	−	9.57179i	0.116949	−	1.11270i
$75$		0			0
$76$	0.881966	−	1.52761i	0.101168	−	0.175229i
$77$	0.500462	−	0.602118i	0.0570329	−	0.0686178i
$78$		0			0
$79$	−0.353210	+	0.392279i	−0.0397392	+	0.0441349i	−0.762687	−	0.646768i	$-0.776120\pi$
$79$	−0.353210	+	0.392279i	−0.0397392	+	0.0441349i	0.722947	+	0.690903i	$0.242787\pi$
$80$	5.76611	+	4.18932i	0.644670	+	0.468380i
$81$		0			0
$82$	−2.66312	+	8.19624i	−0.294092	+	0.905123i
$83$	−4.30865	+	0.915833i	−0.472936	+	0.100526i	−0.438213	−	0.898871i	$-0.644388\pi$
$83$	−4.30865	+	0.915833i	−0.472936	+	0.100526i	−0.0347234	+	0.999397i	$0.511055\pi$
$84$		0			0
$85$	−8.38666	+	3.73398i	−0.909661	+	0.405007i
$86$	−16.1655	−	3.43608i	−1.74317	−	0.370522i
$87$		0			0
$88$	−6.50266	+	5.12954i	−0.693186	+	0.546811i
$89$	−16.7518			−1.77569			−0.887844	−	0.460145i	$-0.847798\pi$
$89$	−16.7518			−1.77569			−0.887844	+	0.460145i	$0.847798\pi$
$90$		0			0
$91$	0.809017	+	0.587785i	0.0848080	+	0.0616166i
$92$	2.61416	+	1.16390i	0.272545	+	0.121345i
$93$		0			0
$94$	−0.985051	−	1.09401i	−0.101600	−	0.112839i
$95$	0.745005	+	7.08825i	0.0764360	+	0.727239i
$96$		0			0
$97$	−8.56378	+	9.51105i	−0.869520	+	0.965700i	−0.999667	−	0.0257944i	$-0.991788\pi$
$97$	−8.56378	+	9.51105i	−0.869520	+	0.965700i	0.130147	+	0.991495i	$0.458455\pi$
$98$	10.7175			1.08263
$99$		0			0
$100$	−1.00000			−0.100000
$101$	7.07830	−	7.86125i	0.704318	−	0.782224i	−0.279740	−	0.960076i	$-0.590248\pi$
$101$	7.07830	−	7.86125i	0.704318	−	0.782224i	0.984057	+	0.177852i	$0.0569148\pi$
$102$		0			0
$103$	−0.725874	−	6.90623i	−0.0715225	−	0.680491i	−0.970270	−	0.242025i	$-0.922188\pi$
$103$	−0.725874	−	6.90623i	−0.0715225	−	0.680491i	0.898748	−	0.438466i	$-0.144478\pi$
$104$	−7.07830	−	7.86125i	−0.694085	−	0.770859i
$105$		0			0
$106$	12.7387	+	5.67165i	1.23729	+	0.550879i
$107$	7.60422	+	5.52479i	0.735128	+	0.534102i	0.891182	−	0.453647i	$-0.149877\pi$
$107$	7.60422	+	5.52479i	0.735128	+	0.534102i	−0.156054	+	0.987749i	$0.549877\pi$
$108$		0			0
$109$	−0.291796			−0.0279490			−0.0139745	−	0.999902i	$-0.504448\pi$
$109$	−0.291796			−0.0279490			−0.0139745	+	0.999902i	$0.504448\pi$
$110$	−2.14205	+	7.60414i	−0.204237	+	0.725027i
$111$		0			0
$112$	1.06635	+	0.226659i	0.100760	+	0.0214173i
$113$	10.3295	−	4.59899i	0.971717	−	0.432636i	0.141415	−	0.989950i	$-0.454835\pi$
$113$	10.3295	−	4.59899i	0.971717	−	0.432636i	0.830302	+	0.557314i	$0.188168\pi$
$114$		0			0
$115$	−11.3096	+	2.40394i	−1.05463	+	0.224168i
$116$	0.225173	−	0.693013i	0.0209068	−	0.0643446i
$117$		0			0
$118$	−10.5451	−	7.66145i	−0.970754	−	0.705294i
$119$	−0.939591	+	1.04352i	−0.0861322	+	0.0956595i
$120$		0			0
$121$	−9.38259	−	5.74169i	−0.852963	−	0.521972i
$122$	3.33848	−	5.78241i	0.302251	−	0.523515i
$123$		0			0
$124$	0.0951031	−	0.904846i	0.00854051	−	0.0812576i
$125$	9.51192	−	6.91082i	0.850772	−	0.618122i
$126$		0			0
$127$	−2.23607	+	6.88191i	−0.198419	+	0.610671i	0.801501	+	0.597994i	$0.204035\pi$
$127$	−2.23607	+	6.88191i	−0.198419	+	0.610671i	−0.999920	+	0.0126769i	$0.995965\pi$
$128$	−12.2780	−	5.46650i	−1.08523	−	0.483175i
$129$		0			0
$130$	−9.86968	−	2.09786i	−0.865628	−	0.183995i
$131$	6.06086	−	10.4977i	0.529540	−	0.917190i	−0.469866	−	0.882738i	$-0.655698\pi$
$131$	6.06086	−	10.4977i	0.529540	−	0.917190i	0.999406	−	0.0344525i	$-0.0109687\pi$
$132$		0			0
$133$	0.545085	+	0.944115i	0.0472649	+	0.0818651i
$134$	−1.83812	−	5.65714i	−0.158789	−	0.488703i
$135$		0			0
$136$	12.0172	−	8.73102i	1.03047	−	0.748679i
$137$	10.3472	−	2.19936i	0.884021	−	0.187904i	0.256537	−	0.966534i	$-0.417418\pi$
$137$	10.3472	−	2.19936i	0.884021	−	0.187904i	0.627483	+	0.778630i	$0.284085\pi$
$138$		0			0
$139$	1.42347	+	13.5434i	0.120737	+	1.14874i	0.872264	+	0.489036i	$0.162651\pi$
$139$	1.42347	+	13.5434i	0.120737	+	1.14874i	−0.751526	+	0.659703i	$0.770682\pi$
$140$	0.127133	−	0.0566034i	0.0107447	−	0.00478386i
$141$		0			0
$142$	−5.95492	−	10.3142i	−0.499725	−	0.865550i
$143$	6.53779	−	12.4356i	0.546717	−	1.03992i
$144$		0			0
$145$	0.909830	+	2.80017i	0.0755573	+	0.232541i
$146$	−1.04412	+	9.93413i	−0.0864119	+	0.822154i
$147$		0			0
$148$	1.59385	+	1.77015i	0.131013	+	0.145505i
$149$	9.14373	+	10.1551i	0.749083	+	0.831941i	0.990360	−	0.138515i	$-0.0442329\pi$
$149$	9.14373	+	10.1551i	0.749083	+	0.831941i	−0.241277	+	0.970456i	$0.577566\pi$
$150$		0			0
$151$	0.916080	−	8.71592i	0.0745496	−	0.709292i	−0.891865	−	0.452302i	$-0.850603\pi$
$151$	0.916080	−	8.71592i	0.0745496	−	0.709292i	0.966414	−	0.256989i	$-0.0827305\pi$
$152$	−3.56365	−	10.9678i	−0.289050	−	0.889605i
$153$		0			0
$154$	0.173762	+	1.19581i	0.0140021	+	0.0963615i
$155$	1.83812	+	3.18371i	0.147641	+	0.255722i
$156$		0			0
$157$	9.73152	−	4.33275i	0.776660	−	0.345791i	0.0201699	−	0.999797i	$-0.493579\pi$
$157$	9.73152	−	4.33275i	0.776660	−	0.345791i	0.756490	+	0.654005i	$0.226913\pi$
$158$	−0.0851578	−	0.810222i	−0.00677479	−	0.0644578i
$159$		0			0
$160$	−3.21986	+	0.684403i	−0.254552	+	0.0541068i
$161$	−1.43078	+	1.03952i	−0.112761	+	0.0819256i
$162$		0			0
$163$	1.11803	+	3.44095i	0.0875712	+	0.269516i	0.985247	−	0.171141i	$-0.0547454\pi$
$163$	1.11803	+	3.44095i	0.0875712	+	0.269516i	−0.897675	+	0.440657i	$0.854745\pi$
$164$	−1.06644	−	1.84712i	−0.0832747	−	0.144236i
$165$		0			0
$166$	3.39919	−	5.88756i	0.263828	−	0.456964i
$167$	−7.54818	−	1.60441i	−0.584096	−	0.124153i	−0.0936196	−	0.995608i	$-0.529844\pi$
$167$	−7.54818	−	1.60441i	−0.584096	−	0.124153i	−0.490476	+	0.871455i	$0.663177\pi$
$168$		0			0
$169$	4.51682	+	2.01102i	0.347447	+	0.154694i
$170$	4.37833	−	13.4751i	0.335803	−	1.03350i
$171$		0			0
$172$	3.30902	−	2.40414i	0.252310	−	0.183314i
$173$	−0.284567	+	2.70747i	−0.0216352	+	0.205845i	−0.999999	−	0.00104456i	$-0.999668\pi$
$173$	−0.284567	+	2.70747i	−0.0216352	+	0.205845i	0.978364	+	0.206890i	$0.0663342\pi$
$174$		0			0
$175$	0.309017	−	0.535233i	0.0233595	−	0.0404598i
$176$	0.997012	−	15.2838i	0.0751526	−	1.15206i
$177$		0			0
$178$	17.2998	−	19.2133i	1.29667	−	1.44010i
$179$	15.0959	+	10.9678i	1.12832	+	0.819771i	0.985449	−	0.169971i	$-0.0543674\pi$
$179$	15.0959	+	10.9678i	1.12832	+	0.819771i	0.142868	+	0.989742i	$0.454367\pi$
$180$		0			0
$181$	2.39919	−	7.38394i	0.178330	−	0.548844i	−0.821440	−	0.570295i	$-0.806829\pi$
$181$	2.39919	−	7.38394i	0.178330	−	0.548844i	0.999770	+	0.0214515i	$0.00682876\pi$
$182$	−1.50964	+	0.320883i	−0.111902	+	0.0237854i
$183$		0			0
$184$	17.0908	−	7.60931i	1.25995	−	0.560966i
$185$	−9.41419	−	2.00105i	−0.692145	−	0.147120i
$186$		0			0
$187$	16.4068	+	10.9553i	1.19978	+	0.801133i
$188$	0.364338			0.0265721
$189$		0			0
$190$	−8.89919	−	6.46564i	−0.645615	−	0.469067i
$191$	3.35841	+	1.49526i	0.243006	+	0.108193i	0.524626	−	0.851333i	$-0.324205\pi$
$191$	3.35841	+	1.49526i	0.243006	+	0.108193i	−0.281620	+	0.959526i	$0.590872\pi$
$192$		0			0
$193$	6.43572	+	7.14759i	0.463253	+	0.514495i	0.928827	−	0.370514i	$-0.120819\pi$
$193$	6.43572	+	7.14759i	0.463253	+	0.514495i	−0.465573	+	0.885009i	$0.654152\pi$
$194$	−2.06470	−	19.6443i	−0.148237	−	1.41038i
$195$		0			0
$196$	−1.77485	+	1.97117i	−0.126775	+	0.140798i
$197$	12.1217			0.863637			0.431818	−	0.901961i	$-0.357872\pi$
$197$	12.1217			0.863637			0.431818	+	0.901961i	$0.357872\pi$
$198$		0			0
$199$	−26.4164			−1.87261			−0.936305	−	0.351189i	$-0.885778\pi$
$199$	−26.4164			−1.87261			−0.936305	+	0.351189i	$0.885778\pi$
$200$	−4.37463	+	4.85852i	−0.309333	+	0.343549i
$201$		0			0
$202$	1.70656	+	16.2368i	0.120073	+	1.14242i
$203$	0.301341	+	0.334673i	0.0211500	+	0.0234894i
$204$		0			0
$205$	7.87297	+	3.50527i	0.549872	+	0.244819i
$206$	8.67066	+	6.29960i	0.604113	+	0.438914i
$207$		0			0
$208$	19.5623			1.35640
$209$	12.0252	−	9.48594i	0.831801	−	0.656156i
$210$		0			0
$211$	−10.7933	−	2.29419i	−0.743042	−	0.157939i	−0.179190	−	0.983814i	$-0.557348\pi$
$211$	−10.7933	−	2.29419i	−0.743042	−	0.157939i	−0.563852	+	0.825876i	$0.690681\pi$
$212$	−3.15270	+	1.40367i	−0.216528	+	0.0964047i
$213$		0			0
$214$	−14.1896	+	3.01609i	−0.969979	+	0.206175i
$215$	−5.10701	+	15.7178i	−0.348295	+	1.07194i
$216$		0			0
$217$	0.454915	+	0.330515i	0.0308816	+	0.0224368i
$218$	0.301341	−	0.334673i	0.0204094	−	0.0226669i
$219$		0			0
$220$	−1.04383	−	1.65324i	−0.0703749	−	0.111461i
$221$	−12.5986	+	21.8215i	−0.847477	+	1.46787i
$222$		0			0
$223$	2.00489	−	19.0753i	0.134257	−	1.27737i	−0.695205	−	0.718812i	$-0.744686\pi$
$223$	2.00489	−	19.0753i	0.134257	−	1.27737i	0.829462	−	0.558563i	$-0.188647\pi$
$224$	−0.407343	+	0.295952i	−0.0272167	+	0.0197741i
$225$		0			0
$226$	−5.39261	+	16.5967i	−0.358711	+	1.10400i
$227$	8.58672	+	3.82305i	0.569921	+	0.253745i	0.671403	−	0.741092i	$-0.265692\pi$
$227$	8.58672	+	3.82305i	0.569921	+	0.253745i	−0.101482	+	0.994837i	$0.532359\pi$
$228$		0			0
$229$	9.31966	+	1.98095i	0.615860	+	0.130905i	0.505271	−	0.862961i	$-0.331393\pi$
$229$	9.31966	+	1.98095i	0.615860	+	0.130905i	0.110590	+	0.993866i	$0.464726\pi$
$230$	8.92241	−	15.4541i	0.588326	−	1.01901i
$231$		0			0
$232$	−2.38197	−	4.12569i	−0.156384	−	0.270865i
$233$	1.29161	+	3.97517i	0.0846162	+	0.260422i	0.984409	−	0.175896i	$-0.0562823\pi$
$233$	1.29161	+	3.97517i	0.0846162	+	0.260422i	−0.899793	+	0.436318i	$0.856282\pi$
$234$		0			0
$235$	−1.19098	+	0.865300i	−0.0776912	+	0.0564459i
$236$	3.15540	−	0.670700i	0.205399	−	0.0436588i
$237$		0			0
$238$	−0.226532	−	2.15531i	−0.0146839	−	0.139708i
$239$	14.5593	−	6.48221i	0.941762	−	0.419299i	0.122339	−	0.992488i	$-0.460961\pi$
$239$	14.5593	−	6.48221i	0.941762	−	0.419299i	0.819423	+	0.573189i	$0.194294\pi$
$240$		0			0
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	16.2749	−	4.83178i	1.04619	−	0.310598i
$243$		0			0
$244$	0.510643	+	1.57160i	0.0326906	+	0.100611i
$245$	1.12029	−	10.6588i	0.0715725	−	0.680967i
$246$		0			0
$247$	13.0897	+	14.5376i	0.832880	+	0.925007i
$248$	−3.98017	−	4.42043i	−0.252741	−	0.280698i
$249$		0			0
$250$	−1.89676	+	18.0465i	−0.119962	+	1.14136i
$251$	−4.56050	−	14.0358i	−0.287856	−	0.885931i	−0.985528	−	0.169513i	$-0.945780\pi$
$251$	−4.56050	−	14.0358i	−0.287856	−	0.885931i	0.697672	−	0.716418i	$-0.254220\pi$
$252$		0			0
$253$	17.3435	+	17.7926i	1.09037	+	1.11861i
$254$	−5.58394	−	9.67166i	−0.350367	−	0.606854i
$255$		0			0
$256$	8.08862	−	3.60129i	0.505539	−	0.225080i
$257$	−1.65134	−	15.7114i	−0.103008	−	0.980051i	−0.916922	−	0.399066i	$-0.869334\pi$
$257$	−1.65134	−	15.7114i	−0.103008	−	0.980051i	0.813914	−	0.580985i	$-0.197332\pi$
$258$		0			0
$259$	−1.43997	+	0.306074i	−0.0894751	+	0.0190185i
$260$	2.02029	−	1.46782i	0.125293	−	0.0910306i
$261$		0			0
$262$	5.78115	+	17.7926i	0.357161	+	1.09923i
$263$	−2.31504	−	4.00977i	−0.142752	−	0.247253i	0.785780	−	0.618506i	$-0.212262\pi$
$263$	−2.31504	−	4.00977i	−0.142752	−	0.247253i	−0.928532	+	0.371253i	$0.878928\pi$
$264$		0			0
$265$	6.97214	−	12.0761i	0.428295	−	0.741829i
$266$	−1.64576	−	0.349817i	−0.100908	−	0.0214487i
$267$		0			0
$268$	1.34486	+	0.598772i	0.0821506	+	0.0365758i
$269$	8.30632	−	25.5642i	0.506445	−	1.55868i	−0.291882	−	0.956454i	$-0.594281\pi$
$269$	8.30632	−	25.5642i	0.506445	−	1.55868i	0.798327	−	0.602224i	$-0.205719\pi$
$270$		0			0
$271$	24.2984	−	17.6538i	1.47602	−	1.07239i	0.497209	−	0.867631i	$-0.334358\pi$
$271$	24.2984	−	17.6538i	1.47602	−	1.07239i	0.978812	−	0.204761i	$-0.0656418\pi$
$272$	−2.87133	+	27.3189i	−0.174100	+	1.65645i
$273$		0			0
$274$	−8.16312	+	14.1389i	−0.493152	+	0.854164i
$275$	−8.06588	−	3.21507i	−0.486391	−	0.193876i
$276$		0			0
$277$	14.4653	−	16.0653i	0.869135	−	0.965272i	−0.130522	−	0.991445i	$-0.541665\pi$
$277$	14.4653	−	16.0653i	0.869135	−	0.965272i	0.999657	+	0.0261732i	$0.00833214\pi$
$278$	−17.0036	−	12.3538i	−1.01981	−	0.740932i
$279$		0			0
$280$	0.281153	−	0.865300i	0.0168021	−	0.0517116i
$281$	8.61731	−	1.83167i	0.514066	−	0.109268i	0.0564277	−	0.998407i	$-0.482029\pi$
$281$	8.61731	−	1.83167i	0.514066	−	0.109268i	0.457638	+	0.889139i	$0.348696\pi$
$282$		0			0
$283$	6.34391	−	2.82449i	0.377106	−	0.167898i	−0.209426	−	0.977825i	$-0.567159\pi$
$283$	6.34391	−	2.82449i	0.377106	−	0.167898i	0.586532	+	0.809926i	$0.300493\pi$
$284$	2.88315	+	0.612832i	0.171083	+	0.0363649i
$285$		0			0
$286$	7.51127	+	20.3408i	0.444151	+	1.20278i
$287$	1.31819			0.0778102
$288$		0			0
$289$	−14.8713	−	10.8046i	−0.874784	−	0.635568i
$290$	−4.15122	−	1.84824i	−0.243768	−	0.108533i
$291$		0			0
$292$	−1.65418	−	1.83716i	−0.0968037	−	0.107511i
$293$	2.14986	+	20.4545i	0.125596	+	1.19497i	0.857837	+	0.513921i	$0.171808\pi$
$293$	2.14986	+	20.4545i	0.125596	+	1.19497i	−0.732241	+	0.681045i	$0.761526\pi$
$294$		0			0
$295$	−8.72174	+	9.68648i	−0.507800	+	0.563969i
$296$	15.5728			0.905150
$297$		0			0
$298$	−21.0902			−1.22172
$299$	−21.2349	+	23.5838i	−1.22805	+	1.36388i
$300$		0			0
$301$	0.264234	+	2.51402i	0.0152302	+	0.144905i
$302$	9.05061	+	10.0517i	0.520804	+	0.578411i
$303$		0			0
$304$	19.4825	+	8.67416i	1.11740	+	0.497497i
$305$	−5.40177	−	3.92461i	−0.309304	−	0.224723i
$306$		0			0
$307$	−16.2705			−0.928607			−0.464304	−	0.885676i	$-0.653695\pi$
$307$	−16.2705			−0.928607			−0.464304	+	0.885676i	$0.653695\pi$
$308$	−0.248711	−	0.166072i	−0.0141716	−	0.00946283i
$309$		0			0
$310$	−5.54978	−	1.17964i	−0.315206	−	0.0669991i
$311$	22.0204	−	9.80409i	1.24866	−	0.555939i	0.327400	−	0.944886i	$-0.393828\pi$
$311$	22.0204	−	9.80409i	1.24866	−	0.555939i	0.921260	+	0.388947i	$0.127161\pi$
$312$		0			0
$313$	−0.339930	+	0.0722543i	−0.0192140	+	0.00408406i	−0.217509	−	0.976058i	$-0.569793\pi$
$313$	−0.339930	+	0.0722543i	−0.0192140	+	0.00408406i	0.198295	+	0.980142i	$0.436460\pi$
$314$	−5.08043	+	15.6360i	−0.286705	+	0.882389i
$315$		0			0
$316$	0.163119	+	0.118513i	0.00917616	+	0.00666687i
$317$	7.07830	−	7.86125i	0.397557	−	0.441532i	−0.510817	−	0.859689i	$-0.670657\pi$
$317$	7.07830	−	7.86125i	0.397557	−	0.441532i	0.908375	+	0.418157i	$0.137324\pi$
$318$		0			0
$319$	4.04431	−	4.86581i	0.226438	−	0.272433i
$320$	−4.58708	+	7.94506i	−0.256426	+	0.444142i
$321$		0			0
$322$	0.285309	−	2.71454i	0.0158997	−	0.151275i
$323$	−22.2232	+	16.1461i	−1.23653	+	0.898391i
$324$		0			0
$325$	3.42705	−	10.5474i	0.190099	−	0.585063i
$326$	−5.10118	−	2.27119i	−0.282528	−	0.125790i
$327$		0			0
$328$	−13.6396	−	2.89918i	−0.753118	−	0.160080i
$329$	−0.112587	+	0.195006i	−0.00620711	+	0.0107510i
$330$		0			0
$331$	−10.3541	−	17.9338i	−0.569113	−	0.985732i	−0.996654	−	0.0817366i	$-0.973953\pi$
$331$	−10.3541	−	17.9338i	−0.569113	−	0.985732i	0.427541	−	0.903996i	$-0.359380\pi$
$332$	0.519929	+	1.60018i	0.0285348	+	0.0878212i
$333$		0			0
$334$	9.63525	−	7.00042i	0.527218	−	0.383046i
$335$	−5.81829	+	1.23672i	−0.317887	+	0.0675690i
$336$		0			0
$337$	−0.486316	−	4.62699i	−0.0264913	−	0.252048i	−0.999750	−	0.0223382i	$-0.992889\pi$
$337$	−0.486316	−	4.62699i	−0.0264913	−	0.252048i	0.973259	−	0.229710i	$-0.0737777\pi$
$338$	−6.97108	+	3.10373i	−0.379177	+	0.168820i
$339$		0			0
$340$	1.75329	+	3.03679i	0.0950854	+	0.164693i
$341$	3.67624	−	6.99262i	0.199079	−	0.378671i
$342$		0			0
$343$	−1.01722	−	3.13068i	−0.0549248	−	0.169041i
$344$	2.79516	−	26.5942i	0.150705	−	1.43386i
$345$		0			0
$346$	−2.81144	−	3.12242i	−0.151144	−	0.167862i
$347$	1.76408	+	1.95921i	0.0947008	+	0.105176i	0.788632	−	0.614865i	$-0.210790\pi$
$347$	1.76408	+	1.95921i	0.0947008	+	0.105176i	−0.693931	+	0.720041i	$0.744123\pi$
$348$		0			0
$349$	1.37772	−	13.1081i	0.0737477	−	0.701662i	−0.893713	−	0.448640i	$-0.851909\pi$
$349$	1.37772	−	13.1081i	0.0737477	−	0.701662i	0.967460	−	0.253023i	$-0.0814247\pi$
$350$	0.294756	+	0.907165i	0.0157554	+	0.0484900i
$351$		0			0
$352$	4.93769	+	5.06555i	0.263180	+	0.269995i
$353$	−1.76854	−	3.06319i	−0.0941296	−	0.163037i	0.815115	−	0.579299i	$-0.196673\pi$
$353$	−1.76854	−	3.06319i	−0.0941296	−	0.163037i	−0.909245	+	0.416261i	$0.863340\pi$
$354$		0			0
$355$	−10.8802	+	4.84416i	−0.577460	+	0.257102i
$356$	0.668838	+	6.36357i	0.0354483	+	0.337268i
$357$		0			0
$358$	−28.1691	+	5.98752i	−1.48878	+	0.316450i
$359$	−21.1567	+	15.3713i	−1.11661	+	0.811264i	−0.983692	−	0.179863i	$-0.942434\pi$
$359$	−21.1567	+	15.3713i	−1.11661	+	0.811264i	−0.132917	+	0.991127i	$0.542434\pi$
$360$		0			0
$361$	0.718847	+	2.21238i	0.0378341	+	0.116441i
$362$	5.99128	+	10.3772i	0.314895	+	0.545413i
$363$		0			0
$364$	0.190983	−	0.330792i	0.0100102	−	0.0173382i
$365$	9.77057	+	2.07680i	0.511415	+	0.108705i
$366$		0			0
$367$	−5.51274	−	2.45443i	−0.287763	−	0.128120i	0.257779	−	0.966204i	$-0.417009\pi$
$367$	−5.51274	−	2.45443i	−0.287763	−	0.128120i	−0.545542	+	0.838084i	$0.683676\pi$
$368$	−10.6909	+	32.9034i	−0.557304	+	1.71521i
$369$		0			0
$370$	12.0172	−	8.73102i	0.624746	−	0.453904i
$371$	0.222946	−	2.12119i	0.0115748	−	0.110127i
$372$		0			0
$373$	−6.20820	+	10.7529i	−0.321449	+	0.556765i	−0.980787	−	0.195081i	$-0.937503\pi$
$373$	−6.20820	+	10.7529i	−0.321449	+	0.556765i	0.659339	+	0.751846i	$0.270836\pi$
$374$	−29.5086	+	7.50393i	−1.52585	+	0.388019i
$375$		0			0
$376$	1.59385	−	1.77015i	0.0821964	−	0.0912883i
$377$	6.53779	+	4.74998i	0.336713	+	0.244636i
$378$		0			0
$379$	0.545085	−	1.67760i	0.0279991	−	0.0861725i	−0.936080	−	0.351786i	$-0.885574\pi$
$379$	0.545085	−	1.67760i	0.0279991	−	0.0861725i	0.964080	+	0.265613i	$0.0855745\pi$
$380$	2.66289	−	0.566016i	0.136604	−	0.0290360i
$381$		0			0
$382$	−5.18324	+	2.30773i	−0.265198	+	0.118074i
$383$	−13.8070	−	2.93476i	−0.705503	−	0.149959i	−0.158831	−	0.987306i	$-0.550772\pi$
$383$	−13.8070	−	2.93476i	−0.705503	−	0.149959i	−0.546673	+	0.837346i	$0.684106\pi$
$384$		0			0
$385$	1.20743	−	0.0478135i	0.0615362	−	0.00243680i
$386$	−14.8441			−0.755545
$387$		0			0
$388$	3.95492	+	2.87341i	0.200780	+	0.145875i
$389$	−17.7906	−	7.92087i	−0.902017	−	0.401604i	−0.0972951	−	0.995256i	$-0.531019\pi$
$389$	−17.7906	−	7.92087i	−0.902017	−	0.401604i	−0.804722	+	0.593652i	$0.797686\pi$
$390$		0			0
$391$	−29.8180	−	33.1162i	−1.50796	−	1.67476i
$392$	1.81266	+	17.2463i	0.0915532	+	0.871071i
$393$		0			0
$394$	−12.5182	+	13.9029i	−0.630659	+	0.700418i
$395$	−0.814685			−0.0409913
$396$		0			0
$397$	−2.41641			−0.121276			−0.0606380	−	0.998160i	$-0.519314\pi$
$397$	−2.41641			−0.121276			−0.0606380	+	0.998160i	$0.519314\pi$
$398$	27.2805	−	30.2981i	1.36745	−	1.51871i
$399$		0			0
$400$	−1.26377	−	12.0239i	−0.0631883	−	0.601197i
$401$	2.21609	+	2.46122i	0.110666	+	0.122907i	0.795933	−	0.605385i	$-0.206981\pi$
$401$	2.21609	+	2.46122i	0.110666	+	0.122907i	−0.685266	+	0.728293i	$0.740314\pi$
$402$		0			0
$403$	9.21783	+	4.10404i	0.459173	+	0.204437i
$404$	−3.26889	−	2.37499i	−0.162634	−	0.118160i
$405$		0			0
$406$	−0.695048			−0.0344947
$407$	7.16463	+	19.4021i	0.355137	+	0.961727i
$408$		0			0
$409$	22.4429	+	4.77038i	1.10973	+	0.235880i	0.726088	−	0.687602i	$-0.241337\pi$
$409$	22.4429	+	4.77038i	1.10973	+	0.235880i	0.383641	+	0.923482i	$0.374670\pi$
$410$	−12.1508	+	5.40990i	−0.600087	+	0.267176i
$411$		0			0
$412$	−2.59451	+	0.551481i	−0.127822	+	0.0271695i
$413$	−0.616090	+	1.89613i	−0.0303158	+	0.0933024i
$414$		0			0
$415$	−5.50000	−	3.99598i	−0.269984	−	0.196155i
$416$	−6.04559	+	6.71431i	−0.296410	+	0.329196i
$417$		0			0
$418$	−1.53875	+	23.5884i	−0.0752627	+	1.15375i
$419$	8.03814	−	13.9225i	0.392689	−	0.680157i	−0.600114	−	0.799914i	$-0.704878\pi$
$419$	8.03814	−	13.9225i	0.392689	−	0.680157i	0.992803	+	0.119757i	$0.0382115\pi$
$420$		0			0
$421$	−2.32208	+	22.0931i	−0.113171	+	1.07675i	0.779612	+	0.626263i	$0.215417\pi$
$421$	−2.32208	+	22.0931i	−0.113171	+	1.07675i	−0.892783	+	0.450488i	$0.851250\pi$
$422$	13.7777	−	10.0101i	0.670687	−	0.487282i
$423$		0			0
$424$	−6.97214	+	21.4580i	−0.338597	+	1.04209i
$425$	14.2264	+	6.33402i	0.690084	+	0.307245i
$426$		0			0
$427$	−0.998969	−	0.212337i	−0.0483435	−	0.0102757i
$428$	1.79511	−	3.10923i	0.0867701	−	0.150290i
$429$		0			0
$430$	−12.7533	−	22.0893i	−0.615018	−	1.06524i
$431$	−1.69895	−	5.22884i	−0.0818357	−	0.251864i	0.901764	−	0.432228i	$-0.142272\pi$
$431$	−1.69895	−	5.22884i	−0.0818357	−	0.251864i	−0.983600	+	0.180364i	$0.942272\pi$
$432$		0			0
$433$	−23.1803	+	16.8415i	−1.11398	+	0.809351i	−0.983285	−	0.182072i	$-0.941720\pi$
$433$	−23.1803	+	16.8415i	−1.11398	+	0.809351i	−0.130691	+	0.991423i	$0.541720\pi$
$434$	−0.848877	+	0.180434i	−0.0407474	+	0.00866113i
$435$		0			0
$436$	0.0116503	+	0.110846i	0.000557950	+	0.00530854i
$437$	−31.6056	+	14.0717i	−1.51190	+	0.673142i
$438$		0			0
$439$	12.5000	+	21.6506i	0.596592	+	1.03333i	0.993320	+	0.115392i	$0.0368124\pi$
$439$	12.5000	+	21.6506i	0.596592	+	1.03333i	−0.396728	+	0.917936i	$0.629854\pi$
$440$	−12.5986	−	2.16084i	−0.600617	−	0.103014i
$441$		0			0
$442$	−12.0172	−	36.9852i	−0.571601	−	1.75921i
$443$	−1.96500	+	18.6957i	−0.0933598	+	0.888259i	0.843164	+	0.537656i	$0.180690\pi$
$443$	−1.96500	+	18.6957i	−0.0933598	+	0.888259i	−0.936524	+	0.350603i	$0.885977\pi$
$444$		0			0
$445$	−17.2998	−	19.2133i	−0.820088	−	0.910800i
$446$	19.8077	+	21.9987i	0.937924	+	1.04167i
$447$		0			0
$448$	−0.146680	+	1.39557i	−0.00692997	+	0.0659343i
$449$	−0.139165	−	0.428305i	−0.00656760	−	0.0202130i	0.947719	−	0.319106i	$-0.103383\pi$
$449$	−0.139165	−	0.428305i	−0.00656760	−	0.0202130i	−0.954287	+	0.298893i	$0.903383\pi$
$450$		0			0
$451$	−2.66312	−	18.3273i	−0.125401	−	0.863001i
$452$	−2.15945	−	3.74028i	−0.101572	−	0.175928i
$453$		0			0
$454$	−13.2524	+	5.90036i	−0.621967	+	0.276917i
$455$	0.161325	+	1.53491i	0.00756304	+	0.0719576i
$456$		0			0
$457$	−23.3873	+	4.97113i	−1.09401	+	0.232540i	−0.719369	−	0.694628i	$-0.755569\pi$
$457$	−23.3873	+	4.97113i	−1.09401	+	0.232540i	−0.374645	+	0.927168i	$0.622235\pi$
$458$	−11.8965	+	8.64335i	−0.555889	+	0.403877i
$459$		0			0
$460$	1.36475	+	4.20025i	0.0636316	+	0.195838i
$461$	−9.80668	−	16.9857i	−0.456743	−	0.791101i	0.542044	−	0.840350i	$-0.317651\pi$
$461$	−9.80668	−	16.9857i	−0.456743	−	0.791101i	−0.998787	+	0.0492488i	$0.984317\pi$
$462$		0			0
$463$	0.718847	−	1.24508i	0.0334077	−	0.0578638i	−0.848838	−	0.528653i	$-0.822697\pi$
$463$	0.718847	−	1.24508i	0.0334077	−	0.0578638i	0.882246	+	0.470789i	$0.156031\pi$
$464$	8.61731	+	1.83167i	0.400049	+	0.0850329i
$465$		0			0
$466$	−5.89314	−	2.62380i	−0.272995	−	0.121545i
$467$	−1.50036	+	4.61763i	−0.0694283	+	0.213678i	−0.979751	−	0.200222i	$-0.935834\pi$
$467$	−1.50036	+	4.61763i	−0.0694283	+	0.213678i	0.910322	+	0.413900i	$0.135834\pi$
$468$		0			0
$469$	−0.736068	+	0.534785i	−0.0339885	+	0.0246941i
$470$	0.237493	−	2.25959i	0.0109547	−	0.104227i
$471$		0			0
$472$	10.5451	−	18.2646i	0.485377	−	0.840697i
$473$	34.4196	−	8.75279i	1.58262	−	0.402454i
$474$		0			0
$475$	8.08990	−	8.98475i	0.371190	−	0.412248i
$476$	0.433921	+	0.315262i	0.0198887	+	0.0144500i
$477$		0			0
$478$	−7.60081	+	23.3929i	−0.347653	+	1.06997i
$479$	−36.0110	+	7.65438i	−1.64538	+	0.349737i	−0.935157	−	0.354234i	$-0.884742\pi$
$479$	−36.0110	+	7.65438i	−1.64538	+	0.349737i	−0.710228	+	0.703972i	$0.751408\pi$
$480$		0			0
$481$	−24.1326	+	10.7445i	−1.10035	+	0.489908i
$482$	21.1349	+	4.49236i	0.962668	+	0.204621i
$483$		0			0
$484$	−1.80650	+	3.79344i	−0.0821138	+	0.172429i
$485$	−19.7525			−0.896916
$486$		0			0
$487$	13.6631	+	9.92684i	0.619135	+	0.449828i	0.852619	−	0.522533i	$-0.175013\pi$
$487$	13.6631	+	9.92684i	0.619135	+	0.449828i	−0.233484	+	0.972361i	$0.575013\pi$
$488$	9.86952	+	4.39419i	0.446772	+	0.198916i
$489$		0			0
$490$	11.0681	+	12.2924i	0.500006	+	0.555313i
$491$	3.23206	+	30.7510i	0.145861	+	1.38777i	0.785387	+	0.619005i	$0.212464\pi$
$491$	3.23206	+	30.7510i	0.145861	+	1.38777i	−0.639526	+	0.768769i	$0.720870\pi$
$492$		0			0
$493$	−7.59298	+	8.43285i	−0.341970	+	0.379797i
$494$	−30.1917			−1.35839
$495$		0			0
$496$	11.0000			0.493915
$497$	−1.21895	+	1.35378i	−0.0546774	+	0.0607254i
$498$		0			0
$499$	1.01838	+	9.68927i	0.0455891	+	0.433751i	0.993381	+	0.114863i	$0.0366429\pi$
$499$	1.01838	+	9.68927i	0.0455891	+	0.433751i	−0.947792	+	0.318889i	$0.896690\pi$
$500$	−3.00501	−	3.33740i	−0.134388	−	0.149253i
$501$		0			0
$502$	20.8079	+	9.26428i	0.928702	+	0.413485i
$503$	9.03500	+	6.56431i	0.402851	+	0.292688i	0.770701	−	0.637197i	$-0.219906\pi$
$503$	9.03500	+	6.56431i	0.402851	+	0.292688i	−0.367850	+	0.929885i	$0.619906\pi$
$504$		0			0
$505$	16.3262			0.726508
$506$	−38.3178	+	1.51737i	−1.70343	+	0.0674551i
$507$		0			0
$508$	2.70353	+	0.574654i	0.119950	+	0.0254961i
$509$	−7.58820	+	3.37849i	−0.336341	+	0.149749i	−0.567956	−	0.823059i	$-0.692266\pi$
$509$	−7.58820	+	3.37849i	−0.336341	+	0.149749i	0.231615	+	0.972808i	$0.425599\pi$
$510$		0			0
$511$	1.49448	−	0.317661i	0.0661118	−	0.0140525i
$512$	4.08358	−	12.5680i	0.180470	−	0.555431i
$513$		0			0
$514$	19.7254	+	14.3314i	0.870051	+	0.632129i
$515$	7.17142	−	7.96467i	0.316011	−	0.350965i
$516$		0			0
$517$	2.93871	+	1.17137i	0.129244	+	0.0515170i
$518$	1.13602	−	1.96764i	0.0499138	−	0.0864533i
$519$		0			0
$520$	1.70656	−	16.2368i	0.0748375	−	0.712031i
$521$	−4.40491	+	3.20036i	−0.192983	+	0.140210i	−0.680081	−	0.733137i	$-0.738055\pi$
$521$	−4.40491	+	3.20036i	−0.192983	+	0.140210i	0.487098	+	0.873347i	$0.338055\pi$
$522$		0			0
$523$	5.70163	−	17.5478i	0.249315	−	0.767312i	−0.745582	−	0.666414i	$-0.767828\pi$
$523$	5.70163	−	17.5478i	0.249315	−	0.767312i	0.994897	−	0.100898i	$-0.0321716\pi$
$524$	−4.22979	−	1.88323i	−0.184779	−	0.0822691i
$525$		0			0
$526$	6.98974	+	1.48572i	0.304767	+	0.0647803i
$527$	−7.08429	+	12.2704i	−0.308597	+	0.534505i
$528$		0			0
$529$	−16.5623	−	28.6868i	−0.720100	−	1.24725i
$530$	6.65037	+	20.4677i	0.288874	+	0.889062i
$531$		0			0
$532$	0.336881	−	0.244758i	0.0146056	−	0.0106116i
$533$	23.1370	−	4.91793i	1.00218	−	0.213019i
$534$		0			0
$535$	1.51635	+	14.4271i	0.0655575	+	0.623738i
$536$	8.79243	−	3.91464i	0.379775	−	0.169087i
$537$		0			0
$538$	20.7426	+	35.9273i	0.894279	+	1.54894i
$539$	−20.6532	+	10.1930i	−0.889597	+	0.439042i
$540$		0			0
$541$	−12.2467	−	37.6915i	−0.526527	−	1.62048i	−0.761276	−	0.648428i	$-0.775427\pi$
$541$	−12.2467	−	37.6915i	−0.526527	−	1.62048i	0.234749	−	0.972056i	$-0.424573\pi$
$542$	−4.84531	+	46.1001i	−0.208124	+	1.98017i
$543$		0			0
$544$	−8.48920	−	9.42822i	−0.363972	−	0.404231i
$545$	−0.301341	−	0.334673i	−0.0129080	−	0.0143358i
$546$		0			0
$547$	0.944356	−	8.98495i	0.0403778	−	0.384169i	−0.955607	−	0.294645i	$-0.904799\pi$
$547$	0.944356	−	8.98495i	0.0403778	−	0.384169i	0.995985	−	0.0895241i	$-0.0285346\pi$
$548$	−1.24861	−	3.84281i	−0.0533378	−	0.164157i
$549$		0			0
$550$	12.0172	−	5.93085i	0.512416	−	0.252892i
$551$	4.40491	+	7.62953i	0.187656	+	0.325029i
$552$		0			0
$553$	−0.113839	+	0.0506842i	−0.00484091	+	0.00215531i
$554$	3.48753	+	33.1817i	0.148171	+	1.40975i
$555$		0			0
$556$	5.08796	−	1.08148i	0.215777	−	0.0458649i
$557$	14.3242	−	10.4071i	0.606935	−	0.440964i	−0.241399	−	0.970426i	$-0.577606\pi$
$557$	14.3242	−	10.4071i	0.606935	−	0.440964i	0.848334	+	0.529462i	$0.177606\pi$
$558$		0			0
$559$	14.0172	+	43.1406i	0.592865	+	1.82465i
$560$	0.841263	+	1.45711i	0.0355499	+	0.0615742i
$561$		0			0
$562$	−6.79837	+	11.7751i	−0.286772	+	0.496704i
$563$	−39.6589	−	8.42976i	−1.67142	−	0.355272i	−0.727671	−	0.685926i	$-0.759397\pi$
$563$	−39.6589	−	8.42976i	−1.67142	−	0.355272i	−0.943752	+	0.330654i	$0.892731\pi$
$564$		0			0
$565$	15.9421	+	7.09790i	0.670691	+	0.298611i
$566$	−3.31190	+	10.1930i	−0.139209	+	0.428443i
$567$		0			0
$568$	15.5902	−	11.3269i	0.654149	−	0.475267i
$569$	3.10326	−	29.5256i	0.130096	−	1.23778i	−0.713445	−	0.700711i	$-0.752866\pi$
$569$	3.10326	−	29.5256i	0.130096	−	1.23778i	0.843541	−	0.537065i	$-0.180467\pi$
$570$		0			0
$571$	17.4894	−	30.2925i	0.731907	−	1.26770i	−0.224160	−	0.974552i	$-0.571964\pi$
$571$	17.4894	−	30.2925i	0.731907	−	1.26770i	0.956067	−	0.293148i	$-0.0947027\pi$
$572$	−4.98499	−	1.98702i	−0.208433	−	0.0830816i
$573$		0			0
$574$	−1.36131	+	1.51188i	−0.0568199	+	0.0631049i
$575$	15.8675	+	11.5284i	0.661722	+	0.480769i
$576$		0			0
$577$	−10.0902	+	31.0543i	−0.420059	+	1.29281i	0.487587	+	0.873074i	$0.337877\pi$
$577$	−10.0902	+	31.0543i	−0.420059	+	1.29281i	−0.907647	+	0.419735i	$0.862123\pi$
$578$	27.7501	−	5.89846i	1.15425	−	0.245344i
$579$		0			0
$580$	1.02738	−	0.457421i	0.0426598	−	0.0189934i
$581$	−1.01714	−	0.216199i	−0.0421979	−	0.00896944i
$582$		0			0
$583$	−29.9422	+	1.18570i	−1.24008	+	0.0491066i
$584$	−16.1623			−0.668801
$585$		0			0
$586$	−25.6803	−	18.6579i	−1.06085	−	0.770749i
$587$	−8.33245	−	3.70985i	−0.343917	−	0.153122i	0.227507	−	0.973776i	$-0.426942\pi$
$587$	−8.33245	−	3.70985i	−0.343917	−	0.153122i	−0.571425	+	0.820655i	$0.693609\pi$
$588$		0			0
$589$	7.36044	+	8.17459i	0.303282	+	0.336828i
$590$	−2.10278	−	20.0067i	−0.0865703	−	0.823661i
$591$		0			0
$592$	−19.2699	+	21.4014i	−0.791987	+	0.879591i
$593$	1.09301			0.0448847			0.0224424	−	0.999748i	$-0.492856\pi$
$593$	1.09301			0.0448847			0.0224424	+	0.999748i	$0.492856\pi$
$594$		0			0
$595$	−2.16718			−0.0888459
$596$	3.49259	−	3.87892i	0.143062	−	0.158887i
$597$		0			0
$598$	−5.11967	−	48.7104i	−0.209359	−	1.99192i
$599$	−8.26169	−	9.17553i	−0.337563	−	0.374902i	0.550333	−	0.834945i	$-0.314501\pi$
$599$	−8.26169	−	9.17553i	−0.337563	−	0.374902i	−0.887897	+	0.460043i	$0.847834\pi$
$600$		0			0
$601$	32.3036	+	14.3825i	1.31769	+	0.586674i	0.940604	−	0.339504i	$-0.110259\pi$
$601$	32.3036	+	14.3825i	1.31769	+	0.586674i	0.377086	+	0.926178i	$0.376926\pi$
$602$	−3.15631	−	2.29319i	−0.128641	−	0.0934635i
$603$		0			0
$604$	−3.34752			−0.136209
$605$	−3.10412	−	16.6908i	−0.126200	−	0.678577i
$606$		0			0
$607$	25.8055	+	5.48512i	1.04741	+	0.222634i	0.699307	−	0.714822i	$-0.253492\pi$
$607$	25.8055	+	5.48512i	1.04741	+	0.222634i	0.348104	+	0.937456i	$0.386825\pi$
$608$	−8.99813	+	4.00623i	−0.364922	+	0.162474i
$609$		0			0
$610$	10.0798	−	2.14252i	0.408118	−	0.0867481i
$611$	−1.24861	+	3.84281i	−0.0505132	+	0.155464i
$612$		0			0
$613$	−34.7426	−	25.2420i	−1.40324	−	1.01952i	−0.994262	−	0.106972i	$-0.965885\pi$
$613$	−34.7426	−	25.2420i	−1.40324	−	1.01952i	−0.408980	−	0.912543i	$-0.634115\pi$
$614$	16.8027	−	18.6613i	0.678103	−	0.753110i
$615$		0			0
$616$	−1.89488	+	0.481862i	−0.0763469	+	0.0194148i
$617$	0.884268	−	1.53160i	0.0355993	−	0.0616598i	−0.847677	−	0.530513i	$-0.821999\pi$
$617$	0.884268	−	1.53160i	0.0355993	−	0.0616598i	0.883276	+	0.468853i	$0.155333\pi$
$618$		0			0
$619$	3.01968	−	28.7303i	0.121371	−	1.15477i	−0.749069	−	0.662492i	$-0.769499\pi$
$619$	3.01968	−	28.7303i	0.121371	−	1.15477i	0.870440	−	0.492275i	$-0.163835\pi$
$620$	1.13602	−	0.825366i	0.0456236	−	0.0331475i
$621$		0			0
$622$	−11.4959	+	35.3808i	−0.460945	+	1.41864i
$623$	−3.61268	−	1.60847i	−0.144739	−	0.0644419i
$624$		0			0
$625$	4.94525	+	1.05114i	0.197810	+	0.0420458i
$626$	0.268178	−	0.464498i	0.0107185	−	0.0185651i
$627$		0			0
$628$	−2.03444	−	3.52376i	−0.0811831	−	0.140613i
$629$	−11.4626	−	35.2783i	−0.457045	−	1.40664i
$630$		0			0
$631$	15.8713	−	11.5312i	0.631827	−	0.459049i	−0.225205	−	0.974311i	$-0.572305\pi$
$631$	15.8713	−	11.5312i	0.631827	−	0.459049i	0.857033	+	0.515262i	$0.172305\pi$
$632$	1.28938	−	0.274067i	0.0512889	−	0.0109018i
$633$		0			0
$634$	1.70656	+	16.2368i	0.0677760	+	0.644846i
$635$	−10.2024	+	4.54238i	−0.404868	+	0.180259i
$636$		0			0
$637$	−14.7082	−	25.4754i	−0.582760	−	1.00937i
$638$	1.40420	+	9.66356i	0.0555927	+	0.382584i
$639$		0			0
$640$	−6.40983	−	19.7274i	−0.253371	−	0.779795i
$641$	1.28161	−	12.1937i	0.0506206	−	0.481623i	−0.939616	−	0.342229i	$-0.888818\pi$
$641$	1.28161	−	12.1937i	0.0506206	−	0.481623i	0.990237	−	0.139394i	$-0.0445153\pi$
$642$		0			0
$643$	18.8421	+	20.9263i	0.743059	+	0.825251i	0.989595	−	0.143883i	$-0.0459588\pi$
$643$	18.8421	+	20.9263i	0.743059	+	0.825251i	−0.246535	+	0.969134i	$0.579292\pi$
$644$	0.452011	+	0.502009i	0.0178117	+	0.0197819i
$645$		0			0
$646$	4.43150	−	42.1629i	0.174355	−	1.65888i
$647$	12.1913	+	37.5210i	0.479290	+	1.47510i	0.840084	+	0.542456i	$0.182506\pi$
$647$	12.1913	+	37.5210i	0.479290	+	1.47510i	−0.360794	+	0.932645i	$0.617494\pi$
$648$		0			0
$649$	27.6074	+	4.73504i	1.08368	+	0.185867i
$650$	8.55807	+	14.8230i	0.335675	+	0.581407i
$651$		0			0
$652$	1.26249	−	0.562096i	0.0494429	−	0.0220134i
$653$	−4.37033	−	41.5809i	−0.171024	−	1.62719i	−0.657474	−	0.753478i	$-0.728375\pi$
$653$	−4.37033	−	41.5809i	−0.171024	−	1.62719i	0.486449	−	0.873709i	$-0.338292\pi$
$654$		0			0
$655$	18.2994	−	3.88965i	0.715016	−	0.151981i
$656$	20.8620	−	15.1571i	0.814523	−	0.591785i
$657$		0			0
$658$	−0.107391	−	0.330515i	−0.00418653	−	0.0128848i
$659$	−1.76854	−	3.06319i	−0.0688924	−	0.119325i	0.829522	−	0.558475i	$-0.188613\pi$
$659$	−1.76854	−	3.06319i	−0.0688924	−	0.119325i	−0.898414	+	0.439150i	$0.855280\pi$
$660$		0			0
$661$	−11.2812	+	19.5395i	−0.438786	+	0.760000i	−0.997596	−	0.0692960i	$-0.977925\pi$
$661$	−11.2812	+	19.5395i	−0.438786	+	0.760000i	0.558810	+	0.829296i	$0.311258\pi$
$662$	31.2618	+	6.64491i	1.21503	+	0.258262i
$663$		0			0
$664$	10.0490	+	4.47410i	0.389977	+	0.173629i
$665$	−0.519929	+	1.60018i	−0.0201620	+	0.0620522i
$666$		0			0
$667$	−11.5623	+	8.40051i	−0.447694	+	0.325269i
$668$	−0.308104	+	2.93141i	−0.0119209	+	0.113420i
$669$		0			0
$670$	4.59017	−	7.95041i	0.177334	−	0.307151i
$671$	−0.934015	+	14.3181i	−0.0360572	+	0.552743i
$672$		0			0
$673$	9.20987	−	10.2286i	0.355014	−	0.394283i	−0.539012	−	0.842298i	$-0.681202\pi$
$673$	9.20987	−	10.2286i	0.355014	−	0.394283i	0.894026	+	0.448015i	$0.147869\pi$
$674$	5.80911	+	4.22056i	0.223759	+	0.162570i
$675$		0			0
$676$	0.583592	−	1.79611i	0.0224459	−	0.0690812i
$677$	−6.03854	+	1.28353i	−0.232080	+	0.0493301i	−0.322483	−	0.946575i	$-0.604518\pi$
$677$	−6.03854	+	1.28353i	−0.232080	+	0.0493301i	0.0904034	+	0.995905i	$0.471184\pi$
$678$		0			0
$679$	−2.76008	+	1.22887i	−0.105922	+	0.0471596i
$680$	22.4243	+	4.76643i	0.859932	+	0.182784i
$681$		0			0
$682$	4.22363	+	11.4378i	0.161731	+	0.437975i
$683$	31.7351			1.21431			0.607155	−	0.794584i	$-0.292311\pi$
$683$	31.7351			1.21431			0.607155	+	0.794584i	$0.292311\pi$
$684$		0			0
$685$	13.2082	+	9.59632i	0.504660	+	0.366657i
$686$	4.64121	+	2.06640i	0.177202	+	0.0788954i
$687$		0			0
$688$	33.0891	+	36.7491i	1.26151	+	1.40105i
$689$	−4.00060	−	38.0632i	−0.152411	−	1.45009i
$690$		0			0
$691$	−8.27091	+	9.18578i	−0.314640	+	0.349443i	−0.879633	−	0.475652i	$-0.842212\pi$
$691$	−8.27091	+	9.18578i	−0.314640	+	0.349443i	0.564993	+	0.825096i	$0.308879\pi$
$692$	1.03986			0.0395295
$693$		0			0
$694$	−4.06888			−0.154453
$695$	−14.0635	+	15.6191i	−0.533459	+	0.592466i
$696$		0			0
$697$	3.47189	+	33.0328i	0.131507	+	1.25121i
$698$	13.6115	+	15.1171i	0.515202	+	0.572190i
$699$		0			0
$700$	−0.215659	−	0.0960175i	−0.00815114	−	0.00362912i
$701$	−31.0760	−	22.5780i	−1.17372	−	0.852760i	−0.182274	−	0.983248i	$-0.558346\pi$
$701$	−31.0760	−	22.5780i	−1.17372	−	0.852760i	−0.991450	+	0.130488i	$0.958346\pi$
$702$		0			0
$703$	−28.7984			−1.08615
$704$	19.6995	−	0.780089i	0.742452	−	0.0294007i
$705$		0			0
$706$	5.33969	+	1.13499i	0.200962	+	0.0427158i
$707$	2.28132	−	1.01571i	0.0857977	−	0.0381996i
$708$		0			0
$709$	38.9287	−	8.27455i	1.46200	−	0.310757i	0.592851	−	0.805312i	$-0.298002\pi$
$709$	38.9287	−	8.27455i	1.46200	−	0.310757i	0.869146	+	0.494555i	$0.164669\pi$
$710$	5.68010	−	17.4815i	0.213170	−	0.656070i
$711$		0			0
$712$	33.8435	+	24.5887i	1.26834	+	0.921501i
$713$	−11.9405	+	13.2613i	−0.447176	+	0.496639i
$714$		0			0
$715$	21.0146	−	5.34393i	0.785900	−	0.199852i
$716$	3.56365	−	6.17242i	0.133180	−	0.230674i
$717$		0			0
$718$	4.21884	−	40.1396i	0.157446	−	1.49800i
$719$	28.7609	−	20.8960i	1.07260	−	0.779291i	0.0962240	−	0.995360i	$-0.469323\pi$
$719$	28.7609	−	20.8960i	1.07260	−	0.779291i	0.976378	+	0.216069i	$0.0693235\pi$
$720$		0			0
$721$	0.506578	−	1.55909i	0.0188659	−	0.0580634i
$722$	−3.27984	−	1.46028i	−0.122063	−	0.0543459i
$723$		0			0
$724$	−2.90075	−	0.616574i	−0.107806	−	0.0229148i
$725$	2.49721	−	4.32530i	0.0927441	−	0.160638i
$726$		0			0
$727$	0.281153	+	0.486971i	0.0104274	+	0.0180608i	0.871192	−	0.490942i	$-0.163347\pi$
$727$	0.281153	+	0.486971i	0.0104274	+	0.0180608i	−0.860765	+	0.509003i	$0.830014\pi$
$728$	−0.771681	−	2.37499i	−0.0286004	−	0.0880230i
$729$		0			0
$730$	−12.4721	+	9.06154i	−0.461614	+	0.335383i
$731$	−62.3034	+	13.2430i	−2.30438	+	0.489810i
$732$		0			0
$733$	−1.74066	−	16.5613i	−0.0642927	−	0.611704i	−0.978470	−	0.206389i	$-0.933829\pi$
$733$	−1.74066	−	16.5613i	−0.0642927	−	0.611704i	0.914177	−	0.405315i	$-0.132838\pi$
$734$	8.50815	−	3.78807i	0.314041	−	0.139820i
$735$		0			0
$736$	−7.98936	−	13.8380i	−0.294492	−	0.510074i
$737$	8.92241	+	9.15345i	0.328661	+	0.337172i
$738$		0			0
$739$	4.25329	+	13.0903i	0.156460	+	0.481534i	0.998306	−	0.0581840i	$-0.0185310\pi$
$739$	4.25329	+	13.0903i	0.156460	+	0.481534i	−0.841846	+	0.539718i	$0.818531\pi$
$740$	−0.384271	+	3.65610i	−0.0141261	+	0.134401i
$741$		0			0
$742$	2.20264	+	2.44628i	0.0808615	+	0.0898058i
$743$	−29.4966	−	32.7593i	−1.08213	−	1.20182i	−0.978293	−	0.207227i	$-0.933556\pi$
$743$	−29.4966	−	32.7593i	−1.08213	−	1.20182i	−0.103832	−	0.994595i	$-0.533111\pi$
$744$		0			0
$745$	−2.20452	+	20.9746i	−0.0807675	+	0.768451i
$746$	−5.92170	−	18.2251i	−0.216809	−	0.667269i
$747$		0			0
$748$	3.50658	−	6.66991i	0.128213	−	0.243876i
$749$	1.10944	+	1.92161i	0.0405381	+	0.0702140i
$750$		0			0
$751$	33.3504	−	14.8486i	1.21697	−	0.541832i	0.305107	−	0.952318i	$-0.401308\pi$
$751$	33.3504	−	14.8486i	1.21697	−	0.541832i	0.911867	+	0.410486i	$0.134641\pi$
$752$	0.460439	+	4.38078i	0.0167905	+	0.159751i
$753$		0			0
$754$	−12.1996	+	2.59310i	−0.444283	+	0.0944352i
$755$	10.9427	−	7.95034i	0.398246	−	0.289342i
$756$		0			0
$757$	−1.57953	−	4.86128i	−0.0574089	−	0.176686i	0.918240	−	0.396024i	$-0.129610\pi$
$757$	−1.57953	−	4.86128i	−0.0574089	−	0.176686i	−0.975649	+	0.219338i	$0.929610\pi$
$758$	1.36119	+	2.35766i	0.0494407	+	0.0856339i
$759$		0			0
$760$	8.89919	−	15.4138i	0.322807	−	0.559119i
$761$	−6.88742	−	1.46397i	−0.249669	−	0.0530687i	0.0813771	−	0.996683i	$-0.474068\pi$
$761$	−6.88742	−	1.46397i	−0.249669	−	0.0530687i	−0.331046	+	0.943615i	$0.607402\pi$
$762$		0			0
$763$	−0.0629284	−	0.0280175i	−0.00227816	−	0.00101430i
$764$	0.433921	−	1.33547i	0.0156987	−	0.0483156i
$765$		0			0
$766$	17.6246	−	12.8050i	0.636803	−	0.462665i
$767$	−3.73957	+	35.5797i	−0.135028	+	1.28471i
$768$		0			0
$769$	−5.63525	+	9.76055i	−0.203212	+	0.351974i	−0.949562	−	0.313580i	$-0.898472\pi$
$769$	−5.63525	+	9.76055i	−0.203212	+	0.351974i	0.746349	+	0.665555i	$0.231805\pi$
$770$	−1.19208	+	1.43423i	−0.0429597	+	0.0516859i
$771$		0			0
$772$	2.45823	−	2.73014i	0.0884735	−	0.0982598i
$773$	−39.1141	−	28.4181i	−1.40684	−	1.02213i	−0.993773	−	0.111426i	$-0.964458\pi$
$773$	−39.1141	−	28.4181i	−1.40684	−	1.02213i	−0.413065	−	0.910702i	$-0.635542\pi$
$774$		0			0
$775$	1.92705	−	5.93085i	0.0692217	−	0.213043i
$776$	31.2618	−	6.64491i	1.12223	−	0.238538i
$777$		0			0
$778$	27.4573	−	12.2248i	0.984391	−	0.438279i
$779$	25.2233	+	5.36138i	0.903719	+	0.192091i
$780$		0			0
$781$	21.2848	+	14.2126i	0.761631	+	0.508565i
$782$	68.7758			2.45942
$783$		0			0
$784$	−25.9443	−	18.8496i	−0.926581	−	0.673201i
$785$	15.0193	+	6.68700i	0.536060	+	0.238669i
$786$		0			0
$787$	−29.2926	−	32.5327i	−1.04417	−	1.15967i	−0.986904	−	0.161307i	$-0.948429\pi$
$787$	−29.2926	−	32.5327i	−1.04417	−	1.15967i	−0.0572638	−	0.998359i	$-0.518238\pi$
$788$	−0.483976	−	4.60472i	−0.0172409	−	0.164036i
$789$		0			0
$790$	0.841334	−	0.934396i	0.0299333	−	0.0332443i
$791$	2.66923			0.0949069
$792$		0			0
$793$	−18.3262			−0.650784
$794$	2.49545	−	2.77148i	0.0885602	−	0.0983561i
$795$		0			0
$796$	1.05471	+	10.0349i	0.0373832	+	0.355677i
$797$	−2.06542	−	2.29388i	−0.0731610	−	0.0812535i	0.705453	−	0.708757i	$-0.250744\pi$
$797$	−2.06542	−	2.29388i	−0.0731610	−	0.0812535i	−0.778614	+	0.627503i	$0.784077\pi$
$798$		0			0
$799$	−5.18324	−	2.30773i	−0.183370	−	0.0816415i
$800$	4.51750	+	3.28216i	0.159718	+	0.116042i
$801$		0			0
$802$	−5.11146			−0.180492
$803$	−7.43585	−	20.1366i	−0.262405	−	0.710605i
$804$		0			0
$805$	−2.66984	−	0.567493i	−0.0940996	−	0.0200015i
$806$	−14.2264	+	6.33402i	−0.501105	+	0.223106i
$807$		0			0
$808$	−25.8391	+	5.49228i	−0.909018	+	0.193218i
$809$	7.96856	−	24.5247i	0.280160	−	0.862243i	−0.707648	−	0.706565i	$-0.750244\pi$
$809$	7.96856	−	24.5247i	0.280160	−	0.862243i	0.987808	−	0.155678i	$-0.0497562\pi$
$810$		0			0
$811$	−5.83688	−	4.24074i	−0.204961	−	0.148913i	0.480570	−	0.876956i	$-0.340430\pi$
$811$	−5.83688	−	4.24074i	−0.204961	−	0.148913i	−0.685531	+	0.728044i	$0.740430\pi$
$812$	0.115102	−	0.127834i	0.00403929	−	0.00448608i
$813$		0			0
$814$	−29.6521	−	11.8194i	−1.03930	−	0.414268i
$815$	−2.79197	+	4.83583i	−0.0977984	+	0.169392i
$816$		0			0
$817$	−5.16902	+	49.1800i	−0.180841	+	1.72059i
$818$	−28.6484	+	20.8142i	−1.00167	+	0.727753i
$819$		0			0
$820$	1.01722	−	3.13068i	0.0355229	−	0.109328i
$821$	27.5029	+	12.2451i	0.959859	+	0.427357i	0.826017	−	0.563646i	$-0.190602\pi$
$821$	27.5029	+	12.2451i	0.959859	+	0.427357i	0.133842	+	0.991003i	$0.457268\pi$
$822$		0			0
$823$	−53.6891	−	11.4120i	−1.87148	−	0.397796i	−0.875188	−	0.483783i	$-0.839262\pi$
$823$	−53.6891	−	11.4120i	−1.87148	−	0.397796i	−0.996296	+	0.0859867i	$0.972596\pi$
$824$	−8.67066	+	15.0180i	−0.302057	+	0.523178i
$825$		0			0
$826$	−1.53851	−	2.66477i	−0.0535315	−	0.0927193i
$827$	10.2140	+	31.4355i	0.355176	+	1.09312i	0.955907	+	0.293669i	$0.0948763\pi$
$827$	10.2140	+	31.4355i	0.355176	+	1.09312i	−0.600731	+	0.799451i	$0.705124\pi$
$828$		0			0
$829$	7.30902	−	5.31031i	0.253853	−	0.184435i	−0.453580	−	0.891216i	$-0.649853\pi$
$829$	7.30902	−	5.31031i	0.253853	−	0.184435i	0.707433	+	0.706781i	$0.249853\pi$
$830$	10.2631	−	2.18148i	0.356236	−	0.0757204i
$831$		0			0
$832$	2.63206	+	25.0424i	0.0912503	+	0.868189i
$833$	37.7353	−	16.8008i	1.30745	−	0.582115i
$834$		0			0
$835$	−5.95492	−	10.3142i	−0.206078	−	0.356938i
$836$	−4.08358	−	4.18932i	−0.141234	−	0.144891i
$837$		0			0
$838$	7.66718	+	23.5972i	0.264858	+	0.815151i
$839$	5.08281	−	48.3597i	0.175478	−	1.66956i	−0.452830	−	0.891597i	$-0.649586\pi$
$839$	5.08281	−	48.3597i	0.175478	−	1.66956i	0.628308	−	0.777965i	$-0.283748\pi$
$840$		0			0
$841$	−16.9696	−	18.8467i	−0.585159	−	0.649885i
$842$	−22.9414	−	25.4791i	−0.790614	−	0.878066i
$843$		0			0
$844$	−0.440565	+	4.19169i	−0.0151649	+	0.144284i
$845$	2.35805	+	7.25732i	0.0811193	+	0.249660i
$846$		0			0
$847$	−1.47214	−	2.13914i	−0.0505832	−	0.0735017i
$848$	−20.8620	−	36.1340i	−0.716403	−	1.24085i
$849$		0			0
$850$	−21.9566	+	9.77569i	−0.753104	+	0.335303i
$851$	−4.88340	−	46.4624i	−0.167401	−	1.59271i
$852$		0			0
$853$	−20.7175	+	4.40364i	−0.709354	+	0.150778i	−0.548439	−	0.836191i	$-0.684778\pi$
$853$	−20.7175	+	4.40364i	−0.709354	+	0.150778i	−0.160915	+	0.986968i	$0.551444\pi$
$854$	1.27518	−	0.926476i	0.0436359	−	0.0317033i
$855$		0			0
$856$	−7.25329	−	22.3233i	−0.247912	−	0.762996i
$857$	20.4976	+	35.5029i	0.700186	+	1.21276i	0.968401	+	0.249398i	$0.0802327\pi$
$857$	20.4976	+	35.5029i	0.700186	+	1.21276i	−0.268216	+	0.963359i	$0.586434\pi$
$858$		0			0
$859$	−7.79180	+	13.4958i	−0.265853	+	0.460470i	−0.967787	−	0.251772i	$-0.918987\pi$
$859$	−7.79180	+	13.4958i	−0.265853	+	0.460470i	0.701934	+	0.712242i	$0.252320\pi$
$860$	6.17467	+	1.31247i	0.210554	+	0.0447547i
$861$		0			0
$862$	7.75170	+	3.45128i	0.264024	+	0.117551i
$863$	7.63080	−	23.4852i	0.259755	−	0.799445i	−0.733100	−	0.680121i	$-0.761927\pi$
$863$	7.63080	−	23.4852i	0.259755	−	0.799445i	0.992855	−	0.119324i	$-0.0380728\pi$
$864$		0			0
$865$	−3.39919	+	2.46965i	−0.115576	+	0.0839708i
$866$	4.62237	−	43.9789i	0.157074	−	1.49446i
$867$		0			0
$868$	0.107391	−	0.186006i	0.00364508	−	0.00631347i
$869$	0.934671	+	1.48035i	0.0317065	+	0.0502174i
$870$		0			0
$871$	−10.9244	+	12.1328i	−0.370159	+	0.411103i
$872$	0.589512	+	0.428305i	0.0199634	+	0.0145043i
$873$		0			0
$874$	16.5000	−	50.7818i	0.558121	−	1.71772i
$875$	2.71489	−	0.577068i	0.0917800	−	0.0195084i
$876$		0			0
$877$	2.30932	−	1.02817i	0.0779802	−	0.0347190i	−0.367376	−	0.930073i	$-0.619744\pi$
$877$	2.30932	−	1.02817i	0.0779802	−	0.0347190i	0.445356	+	0.895354i	$0.353077\pi$
$878$	−37.7409	−	8.02207i	−1.27369	−	0.270732i
$879$		0			0
$880$	18.5592	−	14.6402i	0.625632	−	0.493522i
$881$	47.8114			1.61081			0.805403	−	0.592728i	$-0.201949\pi$
$881$	47.8114			1.61081			0.805403	+	0.592728i	$0.201949\pi$
$882$		0			0
$883$	40.3607	+	29.3238i	1.35825	+	0.986823i	0.998554	+	0.0537512i	$0.0171178\pi$
$883$	40.3607	+	29.3238i	1.35825	+	0.986823i	0.359691	+	0.933072i	$0.382882\pi$
$884$	8.79243	+	3.91464i	0.295721	+	0.131664i
$885$		0			0
$886$	−19.4136	−	21.5610i	−0.652212	−	0.724355i
$887$	−1.72195	−	16.3832i	−0.0578173	−	0.550095i	−0.984640	−	0.174596i	$-0.944138\pi$
$887$	−1.72195	−	16.3832i	−0.0578173	−	0.550095i	0.926823	−	0.375499i	$-0.122529\pi$
$888$		0			0
$889$	−1.14301	+	1.26944i	−0.0383354	+	0.0425757i
$890$	39.9022			1.33753
$891$		0			0
$892$	−7.32624			−0.245301
$893$	−2.94746	+	3.27349i	−0.0986330	+	0.109543i
$894$		0			0
$895$	3.01025	+	28.6406i	0.100622	+	0.957350i
$896$	−2.12297	−	2.35780i	−0.0709235	−	0.0787686i
$897$		0			0
$898$	0.634958	+	0.282702i	0.0211888	+	0.00943388i
$899$	3.67624	+	2.67094i	0.122609	+	0.0890809i
$900$		0			0
$901$	53.7426			1.79043
$902$	23.7706	+	15.8724i	0.791475	+	0.528493i
$903$		0			0
$904$	−27.6190	−	5.87061i	−0.918596	−	0.195254i
$905$	10.9466	−	4.87375i	0.363878	−	0.162009i
$906$		0			0
$907$	−45.8431	+	9.74425i	−1.52220	+	0.323553i	−0.891695	−	0.452637i	$-0.850483\pi$
$907$	−45.8431	+	9.74425i	−1.52220	+	0.323553i	−0.630500	+	0.776189i	$0.717150\pi$
$908$	1.10944	−	3.41451i	0.0368181	−	0.113314i
$909$		0			0
$910$	−1.92705	−	1.40008i	−0.0638811	−	0.0464123i
$911$	−25.3658	+	28.1715i	−0.840405	+	0.933364i	−0.998538	−	0.0540535i	$-0.982786\pi$
$911$	−25.3658	+	28.1715i	−0.840405	+	0.933364i	0.158133	+	0.987418i	$0.449453\pi$
$912$		0			0
$913$	−0.951000	+	14.5785i	−0.0314735	+	0.482476i
$914$	18.4508	−	31.9577i	0.610297	−	1.05707i
$915$		0			0
$916$	0.380413	−	3.61938i	0.0125692	−	0.119588i
$917$	2.31504	−	1.68198i	0.0764495	−	0.0555438i
$918$		0			0
$919$	−0.871323	+	2.68166i	−0.0287423	+	0.0884597i	−0.964399	−	0.264453i	$-0.914809\pi$
$919$	−0.871323	+	2.68166i	−0.0287423	+	0.0884597i	0.935656	+	0.352912i	$0.114809\pi$
$920$	26.3773	+	11.7439i	0.869633	+	0.387186i
$921$		0			0
$922$	29.6090	+	6.29359i	0.975121	+	0.207268i
$923$	−16.3445	+	28.3094i	−0.537985	+	0.931817i
$924$		0			0
$925$	8.16312	+	14.1389i	0.268402	+	0.464885i
$926$	0.685672	+	2.11028i	0.0225326	+	0.0693482i
$927$		0			0
$928$	−3.29180	+	2.39163i	−0.108058	+	0.0785091i
$929$	−0.848877	+	0.180434i	−0.0278508	+	0.00591986i	−0.221816	−	0.975089i	$-0.571198\pi$
$929$	−0.848877	+	0.180434i	−0.0278508	+	0.00591986i	0.193965	+	0.981008i	$0.437865\pi$
$930$		0			0
$931$	−3.35211	−	31.8932i	−0.109861	−	1.04526i
$932$	1.45849	−	0.649362i	0.0477745	−	0.0212706i
$933$		0			0
$934$	−3.74671	−	6.48949i	−0.122596	−	0.212343i
$935$	4.37833	+	30.1313i	0.143187	+	0.985399i
$936$		0			0
$937$	10.2533	+	31.5564i	0.334960	+	1.03090i	0.966742	+	0.255755i	$0.0823241\pi$
$937$	10.2533	+	31.5564i	0.334960	+	1.03090i	−0.631781	+	0.775147i	$0.717676\pi$
$938$	0.146779	−	1.39650i	0.00479249	−	0.0455975i
$939$		0			0
$940$	0.376256	+	0.417875i	0.0122721	+	0.0136296i
$941$	−30.2280	−	33.5716i	−0.985404	−	1.09440i	−0.995529	−	0.0944529i	$-0.969890\pi$
$941$	−30.2280	−	33.5716i	−0.985404	−	1.09440i	0.0101257	−	0.999949i	$-0.496777\pi$
$942$		0			0
$943$	−4.37272	+	41.6037i	−0.142395	+	1.35480i
$944$	12.0521	+	37.0927i	0.392264	+	1.20726i
$945$		0			0
$946$	−25.5066	+	48.5164i	−0.829290	+	1.57740i
$947$	12.6682	+	21.9420i	0.411662	+	0.713020i	0.995072	−	0.0991584i	$-0.0316151\pi$
$947$	12.6682	+	21.9420i	0.411662	+	0.713020i	−0.583410	+	0.812178i	$0.698282\pi$
$948$		0			0
$949$	25.0461	−	11.1513i	0.813032	−	0.361985i
$950$	1.95045	+	18.5573i	0.0632809	+	0.602078i
$951$		0			0
$952$	3.42995	−	0.729059i	0.111165	−	0.0236289i
$953$	37.6834	−	27.3786i	1.22068	−	0.886879i	0.224527	−	0.974468i	$-0.427916\pi$
$953$	37.6834	−	27.3786i	1.22068	−	0.886879i	0.996157	+	0.0875894i	$0.0279163\pi$
$954$		0			0
$955$	1.75329	+	5.39607i	0.0567351	+	0.174613i
$956$	−3.04372	−	5.27188i	−0.0984409	−	0.170505i
$957$		0			0
$958$	28.4098	−	49.2073i	0.917880	−	1.58981i
$959$	2.44264	+	0.519200i	0.0788770	+	0.0167658i
$960$		0			0
$961$	−23.1367	−	10.3011i	−0.746344	−	0.332294i
$962$	12.5986	−	38.7746i	0.406197	−	1.25014i
$963$		0			0
$964$	−4.32624	+	3.14320i	−0.139339	+	0.101236i
$965$	−1.55163	+	14.7628i	−0.0499488	+	0.475231i
$966$		0			0
$967$	−21.3435	+	36.9680i	−0.686359	+	1.18881i	0.286648	+	0.958036i	$0.407459\pi$
$967$	−21.3435	+	36.9680i	−0.686359	+	1.18881i	−0.973008	+	0.230773i	$0.925874\pi$
$968$	10.5277	+	25.3719i	0.338374	+	0.815482i
$969$		0			0
$970$	20.3986	−	22.6550i	0.654961	−	0.727408i
$971$	−10.5784	−	7.68563i	−0.339476	−	0.246644i	0.404965	−	0.914332i	$-0.367284\pi$
$971$	−10.5784	−	7.68563i	−0.339476	−	0.246644i	−0.744441	+	0.667689i	$0.767284\pi$
$972$		0			0
$973$	−0.993422	+	3.05744i	−0.0318477	+	0.0980170i
$974$	−25.4955	+	5.41925i	−0.816930	+	0.173644i
$975$		0			0
$976$	−18.2515	+	8.12607i	−0.584215	+	0.260109i
$977$	28.0223	+	5.95633i	0.896513	+	0.190560i	0.633051	−	0.774110i	$-0.281802\pi$
$977$	28.0223	+	5.95633i	0.896513	+	0.190560i	0.263462	+	0.964670i	$0.415136\pi$
$978$		0			0
$979$	−15.0646	+	53.4781i	−0.481466	+	1.70917i
$980$	−4.09373			−0.130769
$981$		0			0
$982$	−38.6074	−	28.0499i	−1.23201	−	0.895109i
$983$	−36.0897	−	16.0681i	−1.15108	−	0.512494i	−0.259673	−	0.965696i	$-0.583615\pi$
$983$	−36.0897	−	16.0681i	−1.15108	−	0.512494i	−0.891408	+	0.453202i	$0.850282\pi$
$984$		0			0
$985$	12.5182	+	13.9029i	0.398864	+	0.442983i
$986$	−1.83064	−	17.4174i	−0.0582995	−	0.554683i
$987$		0			0
$988$	4.99983	−	5.55288i	0.159066	−	0.176661i
$989$	−80.2220			−2.55091
$990$		0			0
$991$	−24.7295			−0.785558			−0.392779	−	0.919633i	$-0.628486\pi$
$991$	−24.7295			−0.785558			−0.392779	+	0.919633i	$0.628486\pi$
$992$	−3.39947	+	3.77550i	−0.107933	+	0.119872i
$993$		0			0
$994$	−0.293885	−	2.79613i	−0.00932146	−	0.0886878i
$995$	−27.2805	−	30.2981i	−0.864850	−	0.960513i
$996$		0			0
$997$	−3.41908	−	1.52227i	−0.108283	−	0.0482108i	0.351880	−	0.936045i	$-0.385542\pi$
$997$	−3.41908	−	1.52227i	−0.108283	−	0.0482108i	−0.460163	+	0.887834i	$0.652209\pi$
$998$	−12.1647	−	8.83819i	−0.385068	−	0.279768i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.e.676.1		16
3.2	odd	2	inner	891.2.n.e.676.2		16
9.2	odd	6	inner	891.2.n.e.379.1		16
9.4	even	3		99.2.f.c.82.1	yes	8
9.5	odd	6		99.2.f.c.82.2	yes	8
9.7	even	3	inner	891.2.n.e.379.2		16
11.9	even	5	inner	891.2.n.e.757.2		16
33.20	odd	10	inner	891.2.n.e.757.1		16
99.14	odd	30		1089.2.a.v.1.3		4
99.20	odd	30	inner	891.2.n.e.460.2		16
99.31	even	15		99.2.f.c.64.1	✓	8
99.41	even	30		1089.2.a.w.1.2		4
99.58	even	15		1089.2.a.v.1.2		4
99.85	odd	30		1089.2.a.w.1.3		4
99.86	odd	30		99.2.f.c.64.2	yes	8
99.97	even	15	inner	891.2.n.e.460.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.f.c.64.1	✓	8	99.31	even	15
99.2.f.c.64.2	yes	8	99.86	odd	30
99.2.f.c.82.1	yes	8	9.4	even	3
99.2.f.c.82.2	yes	8	9.5	odd	6
891.2.n.e.379.1		16	9.2	odd	6	inner
891.2.n.e.379.2		16	9.7	even	3	inner
891.2.n.e.460.1		16	99.97	even	15	inner
891.2.n.e.460.2		16	99.20	odd	30	inner
891.2.n.e.676.1		16	1.1	even	1	trivial
891.2.n.e.676.2		16	3.2	odd	2	inner
891.2.n.e.757.1		16	33.20	odd	10	inner
891.2.n.e.757.2		16	11.9	even	5	inner
1089.2.a.v.1.2		4	99.58	even	15
1089.2.a.v.1.3		4	99.14	odd	30
1089.2.a.w.1.2		4	99.41	even	30
1089.2.a.w.1.3		4	99.85	odd	30

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.03271 + 1.14694i) q^{2} +(-0.0399263 - 0.379874i) q^{4} +(1.03271 + 1.14694i) q^{5} +(0.215659 + 0.0960175i) q^{7} +(-2.02029 - 1.46782i) q^{8} -2.38197 q^{10} +(0.899280 - 3.19238i) q^{11} +(4.14350 + 0.880728i) q^{13} +(-0.332840 + 0.148190i) q^{14} +(4.51712 - 0.960143i) q^{16} +(-1.83812 + 5.65714i) q^{17} +(3.73607 + 2.71441i) q^{19} +(0.394460 - 0.438093i) q^{20} +(2.73278 + 4.32823i) q^{22} +(-3.74582 + 6.48795i) q^{23} +(0.273659 - 2.60369i) q^{25} +(-5.28918 + 3.84281i) q^{26} +(0.0278640 - 0.0857567i) q^{28} +(1.74277 + 0.775932i) q^{29} +(2.32991 + 0.495239i) q^{31} +(-1.06644 + 1.84712i) q^{32} +(-4.59017 - 7.95041i) q^{34} +(0.112587 + 0.346506i) q^{35} +(-5.04508 + 3.66547i) q^{37} +(-6.97155 + 1.48185i) q^{38} +(-0.402863 - 3.83299i) q^{40} +(5.10118 - 2.27119i) q^{41} +(5.35410 + 9.27358i) q^{43} +(-1.24861 - 0.214153i) q^{44} +(-3.57295 - 10.9964i) q^{46} +(-0.0997045 + 0.948625i) q^{47} +(-4.64662 - 5.16060i) q^{49} +(2.70367 + 3.00273i) q^{50} +(0.169131 - 1.60917i) q^{52} +(-2.79197 - 8.59279i) q^{53} +(4.59017 - 2.26538i) q^{55} +(-0.294756 - 0.510532i) q^{56} +(-2.68973 + 1.19754i) q^{58} +(0.882794 + 8.39922i) q^{59} +(-4.23170 + 0.899475i) q^{61} +(-2.97414 + 2.16084i) q^{62} +(1.83688 + 5.65334i) q^{64} +(3.26889 + 5.66189i) q^{65} +(-1.92705 + 3.33775i) q^{67} +(2.22239 + 0.472383i) q^{68} +(-0.513692 - 0.228710i) q^{70} +(-2.38463 + 7.33912i) q^{71} +(5.23607 - 3.80423i) q^{73} +(1.00604 - 9.57179i) q^{74} +(0.881966 - 1.52761i) q^{76} +(0.500462 - 0.602118i) q^{77} +(-0.353210 + 0.392279i) q^{79} +(5.76611 + 4.18932i) q^{80} +(-2.66312 + 8.19624i) q^{82} +(-4.30865 + 0.915833i) q^{83} +(-8.38666 + 3.73398i) q^{85} +(-16.1655 - 3.43608i) q^{86} +(-6.50266 + 5.12954i) q^{88} -16.7518 q^{89} +(0.809017 + 0.587785i) q^{91} +(2.61416 + 1.16390i) q^{92} +(-0.985051 - 1.09401i) q^{94} +(0.745005 + 7.08825i) q^{95} +(-8.56378 + 9.51105i) q^{97} +10.7175 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4} + 6 q^{7} - 56 q^{10} + 6 q^{13} - 2 q^{16} + 24 q^{19} - 28 q^{22} - 8 q^{25} + 72 q^{28} - 12 q^{31} + 16 q^{34} - 36 q^{37} + 16 q^{40} + 32 q^{43} - 84 q^{46} + 44 q^{49} - 6 q^{52} - 16 q^{55}+ \cdots + 54 q^{97}+O(q^{100}) \) 16 * q - 2 * q^4 + 6 * q^7 - 56 * q^10 + 6 * q^13 - 2 * q^16 + 24 * q^19 - 28 * q^22 - 8 * q^25 + 72 * q^28 - 12 * q^31 + 16 * q^34 - 36 * q^37 + 16 * q^40 + 32 * q^43 - 84 * q^46 + 44 * q^49 - 6 * q^52 - 16 * q^55 - 28 * q^58 - 42 * q^61 + 92 * q^64 - 4 * q^67 - 26 * q^70 + 48 * q^73 + 32 * q^76 - 30 * q^79 + 20 * q^82 - 46 * q^85 + 14 * q^88 + 4 * q^91 + 26 * q^94 + 54 * q^97

Introduction

L-functions

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