LMFDB - Embedded newform 693.2.m.g.379.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			379.2
Root			$-0.628998 + 0.456994i$ of defining polynomial
Character	$\chi$	$=$	693.379
Dual form			693.2.m.g.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.240256 + 0.739431i) q^{2} +(1.12900 - 0.820265i) q^{4} +(0.0687611 - 0.211625i) q^{5} +(0.809017 - 0.587785i) q^{7} +(2.13577 + 1.55173i) q^{8} +O(q^{10})$	\(q+(0.240256 + 0.739431i) q^{2} +(1.12900 - 0.820265i) q^{4} +(0.0687611 - 0.211625i) q^{5} +(0.809017 - 0.587785i) q^{7} +(2.13577 + 1.55173i) q^{8} +0.173002 q^{10} +(-0.660531 - 3.25018i) q^{11} +(2.01774 + 6.20997i) q^{13} +(0.628998 + 0.456994i) q^{14} +(0.228211 - 0.702362i) q^{16} +(1.33947 - 4.12246i) q^{17} +(-2.35829 - 1.71340i) q^{19} +(-0.0959574 - 0.295327i) q^{20} +(2.24459 - 1.26929i) q^{22} +3.89796 q^{23} +(4.00503 + 2.90982i) q^{25} +(-4.10707 + 2.98396i) q^{26} +(0.431239 - 1.32722i) q^{28} +(-3.05322 + 2.21829i) q^{29} +(-2.12900 - 6.55238i) q^{31} +5.85410 q^{32} +3.37009 q^{34} +(-0.0687611 - 0.211625i) q^{35} +(4.57379 - 3.32305i) q^{37} +(0.700347 - 2.15545i) q^{38} +(0.475243 - 0.345285i) q^{40} +(1.08255 + 0.786521i) q^{41} -4.70820 q^{43} +(-3.41175 - 3.12764i) q^{44} +(0.936507 + 2.88227i) q^{46} +(4.89094 + 3.55348i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-1.18938 + 3.66055i) q^{50} +(7.37184 + 5.35596i) q^{52} +(0.530865 + 1.63383i) q^{53} +(-0.733239 - 0.0837016i) q^{55} +2.63996 q^{56} +(-2.37383 - 1.72469i) q^{58} +(-7.71239 + 5.60338i) q^{59} +(-2.97566 + 9.15813i) q^{61} +(4.33353 - 3.14850i) q^{62} +(0.950059 + 2.92398i) q^{64} +1.45293 q^{65} +1.27155 q^{67} +(-1.86925 - 5.75297i) q^{68} +(0.139962 - 0.101688i) q^{70} +(2.87670 - 8.85357i) q^{71} +(-4.52169 + 3.28520i) q^{73} +(3.55605 + 2.58362i) q^{74} -4.06794 q^{76} +(-2.44479 - 2.24120i) q^{77} +(-1.39971 - 4.30785i) q^{79} +(-0.132945 - 0.0965905i) q^{80} +(-0.321489 + 0.989441i) q^{82} +(-3.48688 + 10.7315i) q^{83} +(-0.780313 - 0.566931i) q^{85} +(-1.13117 - 3.48139i) q^{86} +(3.63267 - 7.96663i) q^{88} -7.92157 q^{89} +(5.28251 + 3.83797i) q^{91} +(4.40079 - 3.19736i) q^{92} +(-1.45248 + 4.47026i) q^{94} +(-0.524757 + 0.381258i) q^{95} +(-2.79781 - 8.61078i) q^{97} +0.777484 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 3 q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8}+O(q^{10}) $ 8 * q + q^2 + 3 * q^4 - 3 * q^5 + 2 * q^7 - 3 * q^8	$ 8 q + q^{2} + 3 q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8} - 28 q^{10} - 5 q^{11} + 5 q^{13} - q^{14} - 3 q^{16} + 11 q^{17} - 9 q^{19} - 21 q^{20} - q^{22} + 16 q^{23} + 5 q^{25} - 21 q^{26} + 7 q^{28} + 9 q^{29} - 11 q^{31} + 20 q^{32} - 24 q^{34} + 3 q^{35} + 6 q^{37} - 35 q^{38} - 16 q^{40} + 22 q^{41} + 16 q^{43} - 29 q^{44} + 29 q^{46} - 7 q^{47} - 2 q^{49} + 34 q^{50} + 21 q^{52} - 2 q^{53} + 26 q^{55} + 18 q^{56} - 39 q^{58} - 25 q^{59} + 7 q^{61} + 5 q^{62} + q^{64} - 24 q^{65} - 30 q^{67} - 8 q^{68} - 2 q^{70} + 14 q^{71} + 3 q^{73} + 9 q^{74} - 52 q^{76} + 5 q^{77} - 9 q^{79} + 33 q^{80} + 31 q^{82} - 23 q^{83} - 10 q^{85} + 17 q^{86} - 7 q^{88} + 34 q^{89} + 5 q^{91} + 34 q^{92} - 30 q^{94} - 24 q^{95} + 30 q^{97} - 4 q^{98}+O(q^{100}) $ 8 * q + q^2 + 3 * q^4 - 3 * q^5 + 2 * q^7 - 3 * q^8 - 28 * q^10 - 5 * q^11 + 5 * q^13 - q^14 - 3 * q^16 + 11 * q^17 - 9 * q^19 - 21 * q^20 - q^22 + 16 * q^23 + 5 * q^25 - 21 * q^26 + 7 * q^28 + 9 * q^29 - 11 * q^31 + 20 * q^32 - 24 * q^34 + 3 * q^35 + 6 * q^37 - 35 * q^38 - 16 * q^40 + 22 * q^41 + 16 * q^43 - 29 * q^44 + 29 * q^46 - 7 * q^47 - 2 * q^49 + 34 * q^50 + 21 * q^52 - 2 * q^53 + 26 * q^55 + 18 * q^56 - 39 * q^58 - 25 * q^59 + 7 * q^61 + 5 * q^62 + q^64 - 24 * q^65 - 30 * q^67 - 8 * q^68 - 2 * q^70 + 14 * q^71 + 3 * q^73 + 9 * q^74 - 52 * q^76 + 5 * q^77 - 9 * q^79 + 33 * q^80 + 31 * q^82 - 23 * q^83 - 10 * q^85 + 17 * q^86 - 7 * q^88 + 34 * q^89 + 5 * q^91 + 34 * q^92 - 30 * q^94 - 24 * q^95 + 30 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.240256	+	0.739431i	0.169887	+	0.522857i	0.999363	−	0.0356845i	$-0.0113611\pi$
$2$	0.240256	+	0.739431i	0.169887	+	0.522857i	−0.829477	+	0.558542i	$0.811361\pi$
$3$		0			0
$3$		0			0
$4$	1.12900	−	0.820265i	0.564499	−	0.410133i
$5$	0.0687611	−	0.211625i	0.0307509	−	0.0946416i	−0.934503	−	0.355955i	$-0.884156\pi$
$5$	0.0687611	−	0.211625i	0.0307509	−	0.0946416i	0.965254	+	0.261313i	$0.0841556\pi$
$6$		0			0
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	2.13577	+	1.55173i	0.755110	+	0.548620i
$9$		0			0
$10$	0.173002			0.0547082
$11$	−0.660531	−	3.25018i	−0.199158	−	0.979967i
$11$	−0.660531	−	3.25018i	−0.199158	−	0.979967i
$12$		0			0
$13$	2.01774	+	6.20997i	0.559620	+	1.72233i	0.683418	+	0.730027i	$0.260493\pi$
$13$	2.01774	+	6.20997i	0.559620	+	1.72233i	−0.123798	+	0.992307i	$0.539507\pi$
$14$	0.628998	+	0.456994i	0.168107	+	0.122137i
$15$		0			0
$16$	0.228211	−	0.702362i	0.0570529	−	0.175591i
$17$	1.33947	−	4.12246i	0.324869	−	0.999844i	−0.646631	−	0.762803i	$-0.723822\pi$
$17$	1.33947	−	4.12246i	0.324869	−	0.999844i	0.971500	−	0.237041i	$-0.0761775\pi$
$18$		0			0
$19$	−2.35829	−	1.71340i	−0.541029	−	0.393080i	0.283438	−	0.958991i	$-0.408525\pi$
$19$	−2.35829	−	1.71340i	−0.541029	−	0.393080i	−0.824467	+	0.565910i	$0.808525\pi$
$20$	−0.0959574	−	0.295327i	−0.0214567	−	0.0660370i
$21$		0			0
$22$	2.24459	−	1.26929i	0.478549	−	0.270614i
$23$	3.89796			0.812780			0.406390	−	0.913700i	$-0.366787\pi$
$23$	3.89796			0.812780			0.406390	+	0.913700i	$0.366787\pi$
$24$		0			0
$25$	4.00503	+	2.90982i	0.801006	+	0.581965i
$26$	−4.10707	+	2.98396i	−0.805463	+	0.585203i
$27$		0			0
$28$	0.431239	−	1.32722i	0.0814965	−	0.250820i
$29$	−3.05322	+	2.21829i	−0.566969	+	0.411927i	−0.834003	−	0.551760i	$-0.813956\pi$
$29$	−3.05322	+	2.21829i	−0.566969	+	0.411927i	0.267034	+	0.963687i	$0.413956\pi$
$30$		0			0
$31$	−2.12900	−	6.55238i	−0.382379	−	1.17684i	−0.938364	−	0.345650i	$-0.887659\pi$
$31$	−2.12900	−	6.55238i	−0.382379	−	1.17684i	0.555984	−	0.831193i	$-0.312341\pi$
$32$	5.85410			1.03487
$33$		0			0
$34$	3.37009			0.577966
$35$	−0.0687611	−	0.211625i	−0.0116228	−	0.0357712i
$36$		0			0
$37$	4.57379	−	3.32305i	0.751926	−	0.546306i	−0.144497	−	0.989505i	$-0.546156\pi$
$37$	4.57379	−	3.32305i	0.751926	−	0.546306i	0.896423	+	0.443199i	$0.146156\pi$
$38$	0.700347	−	2.15545i	0.113611	−	0.349660i
$39$		0			0
$40$	0.475243	−	0.345285i	0.0751426	−	0.0545943i
$41$	1.08255	+	0.786521i	0.169066	+	0.122834i	0.669101	−	0.743171i	$-0.266679\pi$
$41$	1.08255	+	0.786521i	0.169066	+	0.122834i	−0.500035	+	0.866005i	$0.666679\pi$
$42$		0			0
$43$	−4.70820			−0.717994			−0.358997	−	0.933339i	$-0.616881\pi$
$43$	−4.70820			−0.717994			−0.358997	+	0.933339i	$0.616881\pi$
$44$	−3.41175	−	3.12764i	−0.514341	−	0.471510i
$45$		0			0
$46$	0.936507	+	2.88227i	0.138080	+	0.424968i
$47$	4.89094	+	3.55348i	0.713417	+	0.518328i	0.884274	−	0.466968i	$-0.154654\pi$
$47$	4.89094	+	3.55348i	0.713417	+	0.518328i	−0.170857	+	0.985296i	$0.554654\pi$
$48$		0			0
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−1.18938	+	3.66055i	−0.168204	+	0.517679i
$51$		0			0
$52$	7.37184	+	5.35596i	1.02229	+	0.742738i
$53$	0.530865	+	1.63383i	0.0729199	+	0.224424i	0.980873	−	0.194646i	$-0.0623559\pi$
$53$	0.530865	+	1.63383i	0.0729199	+	0.224424i	−0.907954	+	0.419071i	$0.862356\pi$
$54$		0			0
$55$	−0.733239	−	0.0837016i	−0.0988700	−	0.0112863i
$56$	2.63996			0.352780
$57$		0			0
$58$	−2.37383	−	1.72469i	−0.311699	−	0.226463i
$59$	−7.71239	+	5.60338i	−1.00407	+	0.729498i	−0.962957	−	0.269657i	$-0.913090\pi$
$59$	−7.71239	+	5.60338i	−1.00407	+	0.729498i	−0.0411113	+	0.999155i	$0.513090\pi$
$60$		0			0
$61$	−2.97566	+	9.15813i	−0.380994	+	1.17258i	0.558351	+	0.829605i	$0.311434\pi$
$61$	−2.97566	+	9.15813i	−0.380994	+	1.17258i	−0.939345	+	0.342974i	$0.888566\pi$
$62$	4.33353	−	3.14850i	0.550359	−	0.399859i
$63$		0			0
$64$	0.950059	+	2.92398i	0.118757	+	0.365498i
$65$	1.45293			0.180213
$66$		0			0
$67$	1.27155			0.155344			0.0776722	−	0.996979i	$-0.475251\pi$
$67$	1.27155			0.155344			0.0776722	+	0.996979i	$0.475251\pi$
$68$	−1.86925	−	5.75297i	−0.226680	−	0.697650i
$69$		0			0
$70$	0.139962	−	0.101688i	0.0167287	−	0.0121541i
$71$	2.87670	−	8.85357i	0.341401	−	1.05072i	−0.622081	−	0.782953i	$-0.713713\pi$
$71$	2.87670	−	8.85357i	0.341401	−	1.05072i	0.963482	−	0.267772i	$-0.0862874\pi$
$72$		0			0
$73$	−4.52169	+	3.28520i	−0.529223	+	0.384503i	−0.820067	−	0.572267i	$-0.806064\pi$
$73$	−4.52169	+	3.28520i	−0.529223	+	0.384503i	0.290844	+	0.956771i	$0.406064\pi$
$74$	3.55605	+	2.58362i	0.413382	+	0.300340i
$75$		0			0
$76$	−4.06794			−0.466625
$77$	−2.44479	−	2.24120i	−0.278610	−	0.255409i
$78$		0			0
$79$	−1.39971	−	4.30785i	−0.157479	−	0.484671i	0.840924	−	0.541153i	$-0.182012\pi$
$79$	−1.39971	−	4.30785i	−0.157479	−	0.484671i	−0.998404	+	0.0564813i	$0.982012\pi$
$80$	−0.132945	−	0.0965905i	−0.0148638	−	0.0107991i
$81$		0			0
$82$	−0.321489	+	0.989441i	−0.0355025	+	0.109265i
$83$	−3.48688	+	10.7315i	−0.382734	+	1.17793i	0.555376	+	0.831599i	$0.312574\pi$
$83$	−3.48688	+	10.7315i	−0.382734	+	1.17793i	−0.938111	+	0.346336i	$0.887426\pi$
$84$		0			0
$85$	−0.780313	−	0.566931i	−0.0846368	−	0.0614922i
$86$	−1.13117	−	3.48139i	−0.121978	−	0.375408i
$87$		0			0
$88$	3.63267	−	7.96663i	0.387244	−	0.849245i
$89$	−7.92157			−0.839684			−0.419842	−	0.907597i	$-0.637915\pi$
$89$	−7.92157			−0.839684			−0.419842	+	0.907597i	$0.637915\pi$
$90$		0			0
$91$	5.28251	+	3.83797i	0.553758	+	0.402329i
$92$	4.40079	−	3.19736i	0.458814	−	0.333348i
$93$		0			0
$94$	−1.45248	+	4.47026i	−0.149811	+	0.461072i
$95$	−0.524757	+	0.381258i	−0.0538389	+	0.0391162i
$96$		0			0
$97$	−2.79781	−	8.61078i	−0.284075	−	0.874292i	−0.986674	−	0.162707i	$-0.947977\pi$
$97$	−2.79781	−	8.61078i	−0.284075	−	0.874292i	0.702600	−	0.711585i	$-0.252023\pi$
$98$	0.777484			0.0785378
$99$		0			0
$100$	6.90849			0.690849
$101$	5.93627	+	18.2700i	0.590681	+	1.81793i	0.575149	+	0.818049i	$0.304944\pi$
$101$	5.93627	+	18.2700i	0.590681	+	1.81793i	0.0155316	+	0.999879i	$0.495056\pi$
$102$		0			0
$103$	−13.1371	+	9.54464i	−1.29443	+	0.940461i	−0.999885	−	0.0151755i	$-0.995169\pi$
$103$	−13.1371	+	9.54464i	−1.29443	+	0.940461i	−0.294549	+	0.955636i	$0.595169\pi$
$104$	−5.32676	+	16.3941i	−0.522332	+	1.60757i
$105$		0			0
$106$	−1.08057	+	0.785077i	−0.104954	+	0.0762534i
$107$	−4.36332	−	3.17014i	−0.421818	−	0.306469i	0.356551	−	0.934276i	$-0.383953\pi$
$107$	−4.36332	−	3.17014i	−0.421818	−	0.306469i	−0.778369	+	0.627807i	$0.783953\pi$
$108$		0			0
$109$	5.39901			0.517132			0.258566	−	0.965994i	$-0.416750\pi$
$109$	5.39901			0.517132			0.258566	+	0.965994i	$0.416750\pi$
$110$	−0.114273	−	0.562290i	−0.0108955	−	0.0536122i
$111$		0			0
$112$	−0.228211	−	0.702362i	−0.0215640	−	0.0663670i
$113$	−13.3457	−	9.69624i	−1.25546	−	0.912145i	−0.256935	−	0.966429i	$-0.582713\pi$
$113$	−13.3457	−	9.69624i	−1.25546	−	0.912145i	−0.998526	+	0.0542834i	$0.982713\pi$
$114$		0			0
$115$	0.268028	−	0.824906i	0.0249937	−	0.0769228i
$116$	−1.62749	+	5.00890i	−0.151109	+	0.465065i
$117$		0			0
$118$	−5.99626	−	4.35654i	−0.552001	−	0.401052i
$119$	−1.33947	−	4.12246i	−0.122789	−	0.377906i
$120$		0			0
$121$	−10.1274	+	4.29369i	−0.920673	+	0.390336i
$122$	−7.48673			−0.677816
$123$		0			0
$124$	−7.77832	−	5.65128i	−0.698514	−	0.507500i
$125$	1.79128	−	1.30144i	0.160217	−	0.116404i
$126$		0			0
$127$	0.617194	−	1.89953i	0.0547671	−	0.168556i	−0.919931	−	0.392079i	$-0.871756\pi$
$127$	0.617194	−	1.89953i	0.0547671	−	0.168556i	0.974699	+	0.223523i	$0.0717559\pi$
$128$	7.53831	−	5.47690i	0.666299	−	0.484094i
$129$		0			0
$130$	0.349074	+	1.07434i	0.0306158	+	0.0942258i
$131$	−1.37009			−0.119706			−0.0598528	−	0.998207i	$-0.519063\pi$
$131$	−1.37009			−0.119706			−0.0598528	+	0.998207i	$0.519063\pi$
$132$		0			0
$133$	−2.91501			−0.252763
$134$	0.305497	+	0.940223i	0.0263909	+	0.0812229i
$135$		0			0
$136$	9.25776	−	6.72615i	0.793846	−	0.576763i
$137$	−0.772308	+	2.37692i	−0.0659827	+	0.203074i	−0.978612	−	0.205714i	$-0.934048\pi$
$137$	−0.772308	+	2.37692i	−0.0659827	+	0.203074i	0.912629	+	0.408788i	$0.134048\pi$
$138$		0			0
$139$	3.85302	−	2.79938i	0.326809	−	0.237441i	−0.412266	−	0.911063i	$-0.635263\pi$
$139$	3.85302	−	2.79938i	0.326809	−	0.237441i	0.739075	+	0.673623i	$0.235263\pi$
$140$	−0.251220	−	0.182522i	−0.0212320	−	0.0154259i
$141$		0			0
$142$	7.23775			0.607378
$143$	18.8508	−	10.6599i	1.57638	−	0.891426i
$144$		0			0
$145$	0.259504	+	0.798670i	0.0215506	+	0.0663260i
$146$	−3.51554	−	2.55419i	−0.290948	−	0.211386i
$147$		0			0
$148$	2.43801	−	7.50344i	0.200404	−	0.616779i
$149$	2.23415	−	6.87600i	0.183028	−	0.563304i	−0.816880	−	0.576807i	$-0.804298\pi$
$149$	2.23415	−	6.87600i	0.183028	−	0.563304i	0.999909	+	0.0135034i	$0.00429840\pi$
$150$		0			0
$151$	−6.58514	−	4.78439i	−0.535891	−	0.389348i	0.286666	−	0.958031i	$-0.407453\pi$
$151$	−6.58514	−	4.78439i	−0.535891	−	0.389348i	−0.822557	+	0.568683i	$0.807453\pi$
$152$	−2.37804	−	7.31886i	−0.192885	−	0.593638i
$153$		0			0
$154$	1.06984	−	2.34622i	0.0862103	−	0.189064i
$155$	−1.53304			−0.123137
$156$		0			0
$157$	−16.3028	−	11.8447i	−1.30111	−	0.945311i	−0.301143	−	0.953579i	$-0.597368\pi$
$157$	−16.3028	−	11.8447i	−1.30111	−	0.945311i	−0.999966	+	0.00826862i	$0.997368\pi$
$158$	2.84907	−	2.06997i	0.226660	−	0.164678i
$159$		0			0
$160$	0.402535	−	1.23887i	0.0318232	−	0.0979416i
$161$	3.15351	−	2.29116i	0.248532	−	0.180569i
$162$		0			0
$163$	2.29739	+	7.07062i	0.179945	+	0.553814i	0.999825	−	0.0187219i	$-0.00595970\pi$
$163$	2.29739	+	7.07062i	0.179945	+	0.553814i	−0.819880	+	0.572536i	$0.805960\pi$
$164$	1.86736			0.145816
$165$		0			0
$166$	−8.77295			−0.680913
$167$	0.683275	+	2.10290i	0.0528734	+	0.162728i	0.974006	−	0.226520i	$-0.0727350\pi$
$167$	0.683275	+	2.10290i	0.0528734	+	0.162728i	−0.921133	+	0.389248i	$0.872735\pi$
$168$		0			0
$169$	−23.9752	+	17.4190i	−1.84424	+	1.33992i
$170$	0.231732	−	0.713196i	0.0177730	−	0.0546997i
$171$		0			0
$172$	−5.31555	+	3.86198i	−0.405307	+	0.294473i
$173$	−8.38320	−	6.09075i	−0.637363	−	0.463071i	0.221581	−	0.975142i	$-0.428878\pi$
$173$	−8.38320	−	6.09075i	−0.637363	−	0.463071i	−0.858943	+	0.512071i	$0.828878\pi$
$174$		0			0
$175$	4.95049			0.374222
$176$	−2.43355	−	0.277797i	−0.183436	−	0.0209398i
$177$		0			0
$178$	−1.90320	−	5.85746i	−0.142651	−	0.439035i
$179$	−18.9386	−	13.7597i	−1.41554	−	1.02845i	−0.992488	−	0.122343i	$-0.960959\pi$
$179$	−18.9386	−	13.7597i	−1.41554	−	1.02845i	−0.423051	−	0.906106i	$-0.639041\pi$
$180$		0			0
$181$	−4.23851	+	13.0448i	−0.315046	+	0.969611i	0.660690	+	0.750659i	$0.270264\pi$
$181$	−4.23851	+	13.0448i	−0.315046	+	0.969611i	−0.975736	+	0.218952i	$0.929736\pi$
$182$	−1.56876	+	4.82815i	−0.116284	+	0.357886i
$183$		0			0
$184$	8.32516	+	6.04858i	0.613739	+	0.445907i
$185$	−0.388742	−	1.19643i	−0.0285809	−	0.0879629i
$186$		0			0
$187$	−14.2835	−	1.63051i	−1.04451	−	0.119235i
$188$	8.43666			0.615306
$189$		0			0
$190$	−0.407990	−	0.296422i	−0.0295987	−	0.0215047i
$191$	−9.72838	+	7.06808i	−0.703921	+	0.511429i	−0.881207	−	0.472731i	$-0.843268\pi$
$191$	−9.72838	+	7.06808i	−0.703921	+	0.511429i	0.177286	+	0.984159i	$0.443268\pi$
$192$		0			0
$193$	4.90840	−	15.1065i	0.353315	−	1.08739i	−0.603666	−	0.797238i	$-0.706294\pi$
$193$	4.90840	−	15.1065i	0.353315	−	1.08739i	0.956980	−	0.290153i	$-0.0937062\pi$
$194$	5.69489	−	4.13758i	0.408869	−	0.297061i
$195$		0			0
$196$	−0.431239	−	1.32722i	−0.0308028	−	0.0948012i
$197$	−12.3035			−0.876590			−0.438295	−	0.898831i	$-0.644418\pi$
$197$	−12.3035			−0.876590			−0.438295	+	0.898831i	$0.644418\pi$
$198$		0			0
$199$	15.2615			1.08186			0.540929	−	0.841068i	$-0.318073\pi$
$199$	15.2615			1.08186			0.540929	+	0.841068i	$0.318073\pi$
$200$	4.03857	+	12.4294i	0.285570	+	0.878895i
$201$		0			0
$202$	−12.0832	+	8.77892i	−0.850168	+	0.617683i
$203$	−1.16623	+	3.58928i	−0.0818530	+	0.251918i
$204$		0			0
$205$	0.240885	−	0.175013i	0.0168242	−	0.0122235i
$206$	−10.2139	−	7.42080i	−0.711633	−	0.517032i
$207$		0			0
$208$	4.82212			0.334354
$209$	−4.01114	+	8.79663i	−0.277456	+	0.608476i
$210$		0			0
$211$	2.76058	+	8.49620i	0.190046	+	0.584903i	0.999999	−	0.00159295i	$-0.000507051\pi$
$211$	2.76058	+	8.49620i	0.190046	+	0.584903i	−0.809952	+	0.586496i	$0.800507\pi$
$212$	1.93952	+	1.40915i	0.133207	+	0.0967805i
$213$		0			0
$214$	1.29579	−	3.98802i	0.0885781	−	0.272615i
$215$	−0.323742	+	0.996374i	−0.0220790	+	0.0679521i
$216$		0			0
$217$	−5.57379	−	4.04959i	−0.378373	−	0.274904i
$218$	1.29714	+	3.99220i	0.0878537	+	0.270386i
$219$		0			0
$220$	−0.896483	+	0.506952i	−0.0604409	+	0.0341787i
$221$	28.3031			1.90387
$222$		0			0
$223$	−0.578645	−	0.420410i	−0.0387489	−	0.0281527i	0.568242	−	0.822861i	$-0.307624\pi$
$223$	−0.578645	−	0.420410i	−0.0387489	−	0.0281527i	−0.606991	+	0.794709i	$0.707624\pi$
$224$	4.73607	−	3.44095i	0.316442	−	0.229908i
$225$		0			0
$226$	3.96331	−	12.1978i	0.263636	−	0.811387i
$227$	−4.30528	+	3.12797i	−0.285751	+	0.207611i	−0.721422	−	0.692496i	$-0.756511\pi$
$227$	−4.30528	+	3.12797i	−0.285751	+	0.207611i	0.435671	+	0.900106i	$0.356511\pi$
$228$		0			0
$229$	−2.04208	−	6.28489i	−0.134945	−	0.415317i	0.860637	−	0.509219i	$-0.170066\pi$
$229$	−2.04208	−	6.28489i	−0.134945	−	0.415317i	−0.995581	+	0.0939024i	$0.970066\pi$
$230$	0.674356			0.0444657
$231$		0			0
$232$	−9.96318			−0.654115
$233$	2.95332	+	9.08937i	0.193478	+	0.595464i	0.999991	+	0.00424788i	$0.00135215\pi$
$233$	2.95332	+	9.08937i	0.193478	+	0.595464i	−0.806513	+	0.591217i	$0.798648\pi$
$234$		0			0
$235$	1.08831	−	0.790705i	0.0709936	−	0.0515799i
$236$	−4.11102	+	12.6524i	−0.267604	+	0.823602i
$237$		0			0
$238$	2.72646	−	1.98089i	0.176730	−	0.128402i
$239$	21.7194	+	15.7801i	1.40491	+	1.02073i	0.994038	+	0.109034i	$0.0347756\pi$
$239$	21.7194	+	15.7801i	1.40491	+	1.02073i	0.410872	+	0.911693i	$0.365224\pi$
$240$		0			0
$241$	18.8663			1.21529			0.607643	−	0.794210i	$-0.292115\pi$
$241$	18.8663			1.21529			0.607643	+	0.794210i	$0.292115\pi$
$242$	−5.60806	−	6.45693i	−0.360500	−	0.415067i
$243$		0			0
$244$	4.15258	+	12.7803i	0.265842	+	0.818177i
$245$	−0.180019	−	0.130791i	−0.0115010	−	0.00835596i
$246$		0			0
$247$	5.88173	−	18.1021i	0.374245	−	1.15181i
$248$	5.62047	−	17.2980i	0.356900	−	1.09843i
$249$		0			0
$250$	1.39269	+	1.01185i	0.0880814	+	0.0639949i
$251$	−9.07680	−	27.9355i	−0.572923	−	1.76328i	−0.643146	−	0.765744i	$-0.722371\pi$
$251$	−9.07680	−	27.9355i	−0.572923	−	1.76328i	0.0702229	−	0.997531i	$-0.477629\pi$
$252$		0			0
$253$	−2.57472	−	12.6691i	−0.161871	−	0.796498i
$254$	1.55285			0.0974348
$255$		0			0
$256$	10.8355	+	7.87245i	0.677218	+	0.492028i
$257$	−13.6856	+	9.94320i	−0.853687	+	0.620240i	−0.926160	−	0.377130i	$-0.876911\pi$
$257$	−13.6856	+	9.94320i	−0.853687	+	0.620240i	0.0724730	+	0.997370i	$0.476911\pi$
$258$		0			0
$259$	1.74703	−	5.37681i	0.108555	−	0.334099i
$260$	1.64035	−	1.19178i	0.101730	−	0.0739114i
$261$		0			0
$262$	−0.329173	−	1.01309i	−0.0203364	−	0.0625889i
$263$	8.18034			0.504421			0.252211	−	0.967672i	$-0.418842\pi$
$263$	8.18034			0.504421			0.252211	+	0.967672i	$0.418842\pi$
$264$		0			0
$265$	0.382263			0.0234822
$266$	−0.700347	−	2.15545i	−0.0429411	−	0.132159i
$267$		0			0
$268$	1.43558	−	1.04301i	0.0876917	−	0.0637118i
$269$	1.93048	−	5.94140i	0.117703	−	0.362254i	−0.874798	−	0.484488i	$-0.839006\pi$
$269$	1.93048	−	5.94140i	0.117703	−	0.362254i	0.992501	+	0.122234i	$0.0390059\pi$
$270$		0			0
$271$	−6.36444	+	4.62403i	−0.386612	+	0.280890i	−0.764066	−	0.645138i	$-0.776800\pi$
$271$	−6.36444	+	4.62403i	−0.386612	+	0.280890i	0.377454	+	0.926028i	$0.376800\pi$
$272$	−2.58978	−	1.88159i	−0.157029	−	0.114088i
$273$		0			0
$274$	−1.94312			−0.117388
$275$	6.81202	−	14.9391i	0.410780	−	0.900862i
$276$		0			0
$277$	3.72293	+	11.4580i	0.223689	+	0.688444i	0.998422	+	0.0561556i	$0.0178843\pi$
$277$	3.72293	+	11.4580i	0.223689	+	0.688444i	−0.774733	+	0.632289i	$0.782116\pi$
$278$	2.99566	+	2.17648i	0.179668	+	0.130536i
$279$		0			0
$280$	0.181527	−	0.558682i	0.0108483	−	0.0333876i
$281$	−6.53723	+	20.1195i	−0.389978	+	1.20023i	0.542826	+	0.839846i	$0.317354\pi$
$281$	−6.53723	+	20.1195i	−0.389978	+	1.20023i	−0.932804	+	0.360384i	$0.882646\pi$
$282$		0			0
$283$	20.2281	+	14.6966i	1.20244	+	0.873623i	0.994522	−	0.104524i	$-0.0333319\pi$
$283$	20.2281	+	14.6966i	1.20244	+	0.873623i	0.207916	+	0.978147i	$0.433332\pi$
$284$	−4.01448	−	12.3553i	−0.238216	−	0.733153i
$285$		0			0
$286$	12.4113	+	11.3777i	0.733894	+	0.672780i
$287$	1.33811			0.0789861
$288$		0			0
$289$	−1.44723	−	1.05147i	−0.0851312	−	0.0618515i
$290$	−0.528215	+	0.383770i	−0.0310178	+	0.0225358i
$291$		0			0
$292$	−2.41024	+	7.41796i	−0.141049	+	0.434104i
$293$	−0.368173	+	0.267494i	−0.0215089	+	0.0156271i	−0.598488	−	0.801132i	$-0.704231\pi$
$293$	−0.368173	+	0.267494i	−0.0215089	+	0.0156271i	0.576979	+	0.816759i	$0.304231\pi$
$294$		0			0
$295$	0.655503	+	2.01743i	0.0381648	+	0.117459i
$296$	14.9251			0.867502
$297$		0			0
$298$	5.62110			0.325621
$299$	7.86507	+	24.2062i	0.454849	+	1.39988i
$300$		0			0
$301$	−3.80902	+	2.76741i	−0.219548	+	0.159511i
$302$	1.95561	−	6.01874i	0.112533	−	0.346339i
$303$		0			0
$304$	−1.74162	+	1.26536i	−0.0998885	+	0.0725732i
$305$	1.73348	+	1.25945i	0.0992588	+	0.0721157i
$306$		0			0
$307$	−8.03578			−0.458626			−0.229313	−	0.973353i	$-0.573648\pi$
$307$	−8.03578			−0.458626			−0.229313	+	0.973353i	$0.573648\pi$
$308$	−4.59855	−	0.524938i	−0.262026	−	0.0299111i
$309$		0			0
$310$	−0.368322	−	1.13358i	−0.0209193	−	0.0643829i
$311$	0.110807	+	0.0805059i	0.00628328	+	0.00456507i	0.590922	−	0.806728i	$-0.298764\pi$
$311$	0.110807	+	0.0805059i	0.00628328	+	0.00456507i	−0.584639	+	0.811293i	$0.698764\pi$
$312$		0			0
$313$	−4.72485	+	14.5416i	−0.267064	+	0.821939i	0.724146	+	0.689646i	$0.242234\pi$
$313$	−4.72485	+	14.5416i	−0.267064	+	0.821939i	−0.991211	+	0.132293i	$0.957766\pi$
$314$	4.84150	−	14.9006i	0.273221	−	0.840889i
$315$		0			0
$316$	−5.11385	−	3.71543i	−0.287676	−	0.209009i
$317$	10.1953	+	31.3778i	0.572622	+	1.76235i	0.644136	+	0.764911i	$0.277217\pi$
$317$	10.1953	+	31.3778i	0.572622	+	1.76235i	−0.0715138	+	0.997440i	$0.522783\pi$
$318$		0			0
$319$	9.22661	+	8.45828i	0.516591	+	0.473573i
$320$	0.684115			0.0382432
$321$		0			0
$322$	2.45181	+	1.78134i	0.136634	+	0.0992703i
$323$	−10.2223	+	7.42692i	−0.568783	+	0.413245i
$324$		0			0
$325$	−9.98880	+	30.7424i	−0.554079	+	1.70528i
$326$	−4.67628	+	3.39752i	−0.258995	+	0.188171i
$327$		0			0
$328$	1.09162	+	3.35966i	0.0602747	+	0.185506i
$329$	6.04554			0.333301
$330$		0			0
$331$	29.5335			1.62331			0.811653	−	0.584140i	$-0.198568\pi$
$331$	29.5335			1.62331			0.811653	+	0.584140i	$0.198568\pi$
$332$	4.86600	+	14.9760i	0.267056	+	0.821915i
$333$		0			0
$334$	−1.39079	+	1.01047i	−0.0761008	+	0.0552905i
$335$	0.0874331	−	0.269091i	0.00477698	−	0.0147020i
$336$		0			0
$337$	−4.55497	+	3.30938i	−0.248125	+	0.180273i	−0.704895	−	0.709311i	$-0.749006\pi$
$337$	−4.55497	+	3.30938i	−0.248125	+	0.180273i	0.456770	+	0.889585i	$0.349006\pi$
$338$	−18.6403	−	13.5430i	−1.01390	−	0.736641i
$339$		0			0
$340$	−1.34600			−0.0729974
$341$	−19.8902	+	11.2477i	−1.07711	+	0.609096i
$342$		0			0
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	−10.0557	−	7.30586i	−0.542165	−	0.393906i
$345$		0			0
$346$	2.48958	−	7.66214i	0.133841	−	0.411919i
$347$	−2.69791	+	8.30331i	−0.144831	+	0.445745i	−0.996989	−	0.0775398i	$-0.975294\pi$
$347$	−2.69791	+	8.30331i	−0.144831	+	0.445745i	0.852158	+	0.523285i	$0.175294\pi$
$348$		0			0
$349$	−14.9401	−	10.8546i	−0.799724	−	0.581034i	0.111109	−	0.993808i	$-0.464560\pi$
$349$	−14.9401	−	10.8546i	−0.799724	−	0.581034i	−0.910833	+	0.412774i	$0.864560\pi$
$350$	1.18938	+	3.66055i	0.0635752	+	0.195664i
$351$		0			0
$352$	−3.86681	−	19.0269i	−0.206102	−	1.01414i
$353$	23.4857			1.25002			0.625009	−	0.780618i	$-0.285095\pi$
$353$	23.4857			1.25002			0.625009	+	0.780618i	$0.285095\pi$
$354$		0			0
$355$	−1.67583	−	1.21756i	−0.0889439	−	0.0646215i
$356$	−8.94343	+	6.49778i	−0.474001	+	0.344382i
$357$		0			0
$358$	5.62425	−	17.3097i	0.297251	−	0.914844i
$359$	12.0391	−	8.74695i	0.635402	−	0.461647i	−0.222865	−	0.974849i	$-0.571541\pi$
$359$	12.0391	−	8.74695i	0.635402	−	0.461647i	0.858267	+	0.513203i	$0.171541\pi$
$360$		0			0
$361$	−3.24552	−	9.98870i	−0.170817	−	0.525721i
$362$	−10.6641			−0.560490
$363$		0			0
$364$	9.11210			0.477604
$365$	0.384314	+	1.18280i	0.0201159	+	0.0619104i
$366$		0			0
$367$	27.6894	−	20.1175i	1.44537	−	1.05012i	0.458487	−	0.888701i	$-0.348391\pi$
$367$	27.6894	−	20.1175i	1.44537	−	1.05012i	0.986885	−	0.161424i	$-0.0516085\pi$
$368$	0.889558	−	2.73778i	0.0463714	−	0.142717i
$369$		0			0
$370$	0.791277	−	0.574896i	0.0411365	−	0.0298874i
$371$	1.38982	+	1.00977i	0.0721560	+	0.0524244i
$372$		0			0
$373$	3.01739			0.156235			0.0781173	−	0.996944i	$-0.475109\pi$
$373$	3.01739			0.156235			0.0781173	+	0.996944i	$0.475109\pi$
$374$	−2.22605	−	10.9534i	−0.115106	−	0.566388i
$375$		0			0
$376$	4.93191	+	15.1788i	0.254344	+	0.782789i
$377$	−19.9361	−	14.4845i	−1.02676	−	0.745987i
$378$		0			0
$379$	−1.89252	+	5.82457i	−0.0972121	+	0.299188i	−0.987824	−	0.155576i	$-0.950277\pi$
$379$	−1.89252	+	5.82457i	−0.0972121	+	0.299188i	0.890612	+	0.454764i	$0.150277\pi$
$380$	−0.279717	+	0.860879i	−0.0143492	+	0.0441622i
$381$		0			0
$382$	−7.56367	−	5.49532i	−0.386991	−	0.281165i
$383$	−1.35689	−	4.17607i	−0.0693338	−	0.213387i	0.910386	−	0.413760i	$-0.135785\pi$
$383$	−1.35689	−	4.17607i	−0.0693338	−	0.213387i	−0.979720	+	0.200373i	$0.935785\pi$
$384$		0			0
$385$	−0.642402	+	0.363271i	−0.0327398	+	0.0185140i
$386$	12.3495			0.628573
$387$		0			0
$388$	−10.2218	−	7.42661i	−0.518936	−	0.377029i
$389$	8.49145	−	6.16940i	0.430533	−	0.312801i	−0.351329	−	0.936252i	$-0.614270\pi$
$389$	8.49145	−	6.16940i	0.430533	−	0.312801i	0.781862	+	0.623451i	$0.214270\pi$
$390$		0			0
$391$	5.22119	−	16.0692i	0.264047	−	0.812654i
$392$	2.13577	−	1.55173i	0.107873	−	0.0783742i
$393$		0			0
$394$	−2.95600	−	9.09762i	−0.148921	−	0.458331i
$395$	−1.00789			−0.0507127
$396$		0			0
$397$	11.3888			0.571589			0.285794	−	0.958291i	$-0.407743\pi$
$397$	11.3888			0.571589			0.285794	+	0.958291i	$0.407743\pi$
$398$	3.66666	+	11.2848i	0.183793	+	0.565657i
$399$		0			0
$400$	2.95774	−	2.14893i	0.147887	−	0.107446i
$401$	1.46009	−	4.49370i	0.0729135	−	0.224405i	−0.907958	−	0.419061i	$-0.862359\pi$
$401$	1.46009	−	4.49370i	0.0729135	−	0.224405i	0.980871	+	0.194657i	$0.0623592\pi$
$402$		0			0
$403$	36.3943	−	26.4420i	1.81293	−	1.31717i
$404$	21.6882	+	15.7574i	1.07903	+	0.783961i
$405$		0			0
$406$	−2.93422			−0.145623
$407$	−13.8217	−	12.6707i	−0.685114	−	0.628062i
$408$		0			0
$409$	0.761863	+	2.34477i	0.0376717	+	0.115942i	0.968124	−	0.250472i	$-0.0805857\pi$
$409$	0.761863	+	2.34477i	0.0376717	+	0.115942i	−0.930452	+	0.366413i	$0.880586\pi$
$410$	0.187285	+	0.136070i	0.00924932	+	0.00672003i
$411$		0			0
$412$	−7.00259	+	21.5518i	−0.344993	+	1.06178i
$413$	−2.94587	+	9.06646i	−0.144957	+	0.446131i
$414$		0			0
$415$	2.03129	+	1.47582i	0.0997122	+	0.0724452i
$416$	11.8121	+	36.3538i	0.579134	+	1.78239i
$417$		0			0
$418$	−7.46820	−	0.852519i	−0.365282	−	0.0416981i
$419$	14.3399			0.700548			0.350274	−	0.936647i	$-0.386088\pi$
$419$	14.3399			0.700548			0.350274	+	0.936647i	$0.386088\pi$
$420$		0			0
$421$	14.0087	+	10.1779i	0.682744	+	0.496043i	0.874267	−	0.485446i	$-0.161343\pi$
$421$	14.0087	+	10.1779i	0.682744	+	0.496043i	−0.191523	+	0.981488i	$0.561343\pi$
$422$	−5.61911	+	4.08253i	−0.273534	+	0.198734i
$423$		0			0
$424$	−1.40146	+	4.31326i	−0.0680611	+	0.209470i
$425$	17.3602	−	12.6130i	0.842096	−	0.611818i
$426$		0			0
$427$	2.97566	+	9.15813i	0.144002	+	0.443193i
$428$	−7.52653			−0.363808
$429$		0			0
$430$	−0.814531			−0.0392802
$431$	−8.61919	−	26.5272i	−0.415172	−	1.27777i	−0.912097	−	0.409975i	$-0.865538\pi$
$431$	−8.61919	−	26.5272i	−0.415172	−	1.27777i	0.496925	−	0.867794i	$-0.334462\pi$
$432$		0			0
$433$	23.9040	−	17.3673i	1.14875	−	0.834619i	0.160440	−	0.987046i	$-0.448709\pi$
$433$	23.9040	−	17.3673i	1.14875	−	0.834619i	0.988315	+	0.152426i	$0.0487087\pi$
$434$	1.65526	−	5.09437i	0.0794551	−	0.244538i
$435$		0			0
$436$	6.09548	−	4.42862i	0.291920	−	0.212093i
$437$	−9.19251	−	6.67875i	−0.439738	−	0.319488i
$438$		0			0
$439$	−33.6655			−1.60677			−0.803384	−	0.595461i	$-0.796970\pi$
$439$	−33.6655			−1.60677			−0.803384	+	0.595461i	$0.796970\pi$
$440$	−1.43615	−	1.31656i	−0.0684658	−	0.0627644i
$441$		0			0
$442$	6.79997	+	20.9282i	0.323442	+	0.995451i
$443$	8.35449	+	6.06989i	0.396934	+	0.288389i	0.768291	−	0.640101i	$-0.221107\pi$
$443$	8.35449	+	6.06989i	0.396934	+	0.288389i	−0.371357	+	0.928490i	$0.621107\pi$
$444$		0			0
$445$	−0.544696	+	1.67640i	−0.0258211	+	0.0794691i
$446$	0.171842	−	0.528874i	0.00813694	−	0.0250429i
$447$		0			0
$448$	2.48729	+	1.80712i	0.117513	+	0.0853784i
$449$	0.852224	+	2.62287i	0.0402189	+	0.123781i	0.969150	−	0.246471i	$-0.0792712\pi$
$449$	0.852224	+	2.62287i	0.0402189	+	0.123781i	−0.928931	+	0.370253i	$0.879271\pi$
$450$		0			0
$451$	1.84128	−	4.03802i	0.0867025	−	0.190143i
$452$	−23.0208			−1.08281
$453$		0			0
$454$	−3.34729	−	2.43195i	−0.157096	−	0.114137i
$455$	1.17544	−	0.854009i	0.0551056	−	0.0400365i
$456$		0			0
$457$	−12.4628	+	38.3566i	−0.582986	+	1.79425i	0.0242276	+	0.999706i	$0.492287\pi$
$457$	−12.4628	+	38.3566i	−0.582986	+	1.79425i	−0.607213	+	0.794539i	$0.707713\pi$
$458$	4.15662	−	3.01996i	0.194226	−	0.141114i
$459$		0			0
$460$	−0.374038	−	1.15117i	−0.0174396	−	0.0536736i
$461$	34.2251			1.59402			0.797011	−	0.603965i	$-0.206413\pi$
$461$	34.2251			1.59402			0.797011	+	0.603965i	$0.206413\pi$
$462$		0			0
$463$	0.707349			0.0328733			0.0164367	−	0.999865i	$-0.494768\pi$
$463$	0.707349			0.0328733			0.0164367	+	0.999865i	$0.494768\pi$
$464$	0.861267	+	2.65071i	0.0399833	+	0.123056i
$465$		0			0
$466$	−6.01142	+	4.36755i	−0.278473	+	0.202323i
$467$	8.83555	−	27.1930i	0.408860	−	1.25834i	−0.508768	−	0.860904i	$-0.669899\pi$
$467$	8.83555	−	27.1930i	0.408860	−	1.25834i	0.917629	−	0.397439i	$-0.130101\pi$
$468$		0			0
$469$	1.02870	−	0.747397i	0.0475011	−	0.0345116i
$470$	0.846145	+	0.614760i	0.0390298	+	0.0283568i
$471$		0			0
$472$	−25.1669			−1.15840
$473$	3.10991	+	15.3025i	0.142994	+	0.703611i
$474$		0			0
$475$	−4.45933	−	13.7244i	−0.204608	−	0.629719i
$476$	−4.89377	−	3.55553i	−0.224306	−	0.162968i
$477$		0			0
$478$	−6.45006	+	19.8512i	−0.295019	+	0.907975i
$479$	1.57511	−	4.84769i	0.0719686	−	0.221497i	−0.908602	−	0.417663i	$-0.862849\pi$
$479$	1.57511	−	4.84769i	0.0719686	−	0.221497i	0.980571	+	0.196166i	$0.0628493\pi$
$480$		0			0
$481$	29.8648	+	21.6980i	1.36172	+	0.989344i
$482$	4.53274	+	13.9503i	0.206461	+	0.635421i
$483$		0			0
$484$	−7.91185	+	13.1547i	−0.359629	+	0.597942i
$485$	−2.01464			−0.0914800
$486$		0			0
$487$	−23.6138	−	17.1564i	−1.07004	−	0.777433i	−0.0941240	−	0.995560i	$-0.530005\pi$
$487$	−23.6138	−	17.1564i	−1.07004	−	0.777433i	−0.975920	+	0.218128i	$0.930005\pi$
$488$	−20.5663	+	14.9423i	−0.930992	+	0.676405i
$489$		0			0
$490$	0.0534607	−	0.164535i	0.00241511	−	0.00743294i
$491$	24.3870	−	17.7182i	1.10057	−	0.799610i	0.119416	−	0.992844i	$-0.461898\pi$
$491$	24.3870	−	17.7182i	1.10057	−	0.799610i	0.981153	+	0.193235i	$0.0618979\pi$
$492$		0			0
$493$	5.05514	+	15.5581i	0.227672	+	0.700703i
$494$	14.7984			0.665810
$495$		0			0
$496$	−5.08801			−0.228458
$497$	−2.87670	−	8.85357i	−0.129038	−	0.397137i
$498$		0			0
$499$	−4.81450	+	3.49794i	−0.215526	+	0.156589i	−0.690311	−	0.723513i	$-0.742526\pi$
$499$	−4.81450	+	3.49794i	−0.215526	+	0.156589i	0.474784	+	0.880102i	$0.342526\pi$
$500$	0.954823	−	2.93864i	0.0427010	−	0.131420i
$501$		0			0
$502$	18.4757	−	13.4233i	0.824609	−	0.599113i
$503$	−4.02773	−	2.92632i	−0.179588	−	0.130478i	0.494360	−	0.869257i	$-0.335403\pi$
$503$	−4.02773	−	2.92632i	−0.179588	−	0.130478i	−0.673947	+	0.738779i	$0.735403\pi$
$504$		0			0
$505$	4.27456			0.190216
$506$	8.74933	−	4.94765i	0.388955	−	0.219950i
$507$		0			0
$508$	−0.861305	−	2.65083i	−0.0382142	−	0.117611i
$509$	−17.2551	−	12.5366i	−0.764821	−	0.555675i	0.135565	−	0.990769i	$-0.456715\pi$
$509$	−17.2551	−	12.5366i	−0.764821	−	0.555675i	−0.900385	+	0.435094i	$0.856715\pi$
$510$		0			0
$511$	−1.72713	+	5.31556i	−0.0764038	+	0.235147i
$512$	2.54091	−	7.82012i	0.112293	−	0.345604i
$513$		0			0
$514$	−10.6404	−	7.73068i	−0.469327	−	0.340986i
$515$	1.11656	+	3.43643i	0.0492017	+	0.151427i
$516$		0			0
$517$	8.31884	−	18.2436i	0.365862	−	0.802354i
$518$	4.39552			0.193128
$519$		0			0
$520$	3.10312	+	2.25455i	0.136081	+	0.0988686i
$521$	−17.9103	+	13.0126i	−0.784664	+	0.570092i	−0.906375	−	0.422473i	$-0.861162\pi$
$521$	−17.9103	+	13.0126i	−0.784664	+	0.570092i	0.121711	+	0.992566i	$0.461162\pi$
$522$		0			0
$523$	1.51773	−	4.67108i	0.0663655	−	0.204252i	−0.912375	−	0.409356i	$-0.865753\pi$
$523$	1.51773	−	4.67108i	0.0663655	−	0.204252i	0.978740	+	0.205104i	$0.0657533\pi$
$524$	−1.54683	+	1.12384i	−0.0675737	+	0.0490952i
$525$		0			0
$526$	1.96537	+	6.04880i	0.0856944	+	0.263740i
$527$	−29.8637			−1.30088
$528$		0			0
$529$	−7.80592			−0.339388
$530$	0.0918410	+	0.282657i	0.00398932	+	0.0122779i
$531$		0			0
$532$	−3.29104	+	2.39108i	−0.142685	+	0.103666i
$533$	−2.69996	+	8.30962i	−0.116948	+	0.359929i
$534$		0			0
$535$	−0.970907	+	0.705405i	−0.0419760	+	0.0304973i
$536$	2.71574	+	1.97310i	0.117302	+	0.0852250i
$537$		0			0
$538$	4.85707			0.209403
$539$	−3.29522	−	0.376160i	−0.141935	−	0.0162024i
$540$		0			0
$541$	5.99013	+	18.4357i	0.257536	+	0.792614i	0.993319	+	0.115397i	$0.0368141\pi$
$541$	5.99013	+	18.4357i	0.257536	+	0.792614i	−0.735784	+	0.677217i	$0.763186\pi$
$542$	−4.94825	−	3.59511i	−0.212546	−	0.154423i
$543$		0			0
$544$	7.84139	−	24.1333i	0.336197	−	1.03471i
$545$	0.371242	−	1.14257i	0.0159023	−	0.0489422i
$546$		0			0
$547$	−11.6904	−	8.49354i	−0.499843	−	0.363158i	0.309114	−	0.951025i	$-0.399968\pi$
$547$	−11.6904	−	8.49354i	−0.499843	−	0.363158i	−0.808957	+	0.587868i	$0.799968\pi$
$548$	1.07777	+	3.31703i	0.0460400	+	0.141697i
$549$		0			0
$550$	12.6831	+	1.44781i	0.540808	+	0.0617349i
$551$	11.0012			0.468667
$552$		0			0
$553$	−3.66448	−	2.66240i	−0.155829	−	0.113217i
$554$	−7.57795	+	5.50570i	−0.321956	+	0.233915i
$555$		0			0
$556$	2.05382	−	6.32100i	0.0871012	−	0.268070i
$557$	14.9432	−	10.8569i	0.633164	−	0.460021i	−0.224331	−	0.974513i	$-0.572020\pi$
$557$	14.9432	−	10.8569i	0.633164	−	0.460021i	0.857495	+	0.514492i	$0.172020\pi$
$558$		0			0
$559$	−9.49993	−	29.2378i	−0.401804	−	1.23663i
$560$	−0.164330			−0.00694419
$561$		0			0
$562$	−16.4476			−0.693801
$563$	−9.66724	−	29.7527i	−0.407426	−	1.25393i	−0.918853	−	0.394600i	$-0.870883\pi$
$563$	−9.66724	−	29.7527i	−0.407426	−	1.25393i	0.511427	−	0.859327i	$-0.329117\pi$
$564$		0			0
$565$	−2.96963	+	2.15757i	−0.124933	+	0.0907695i
$566$	−6.00720	+	18.4883i	−0.252502	+	0.777120i
$567$		0			0
$568$	19.8823	−	14.4454i	0.834244	−	0.606114i
$569$	1.40449	+	1.02042i	0.0588794	+	0.0427784i	0.616836	−	0.787092i	$-0.288414\pi$
$569$	1.40449	+	1.02042i	0.0588794	+	0.0427784i	−0.557956	+	0.829870i	$0.688414\pi$
$570$		0			0
$571$	12.5309			0.524403			0.262201	−	0.965013i	$-0.415551\pi$
$571$	12.5309			0.524403			0.262201	+	0.965013i	$0.415551\pi$
$572$	12.5385	−	27.4976i	0.524262	−	1.14973i
$573$		0			0
$574$	0.321489	+	0.989441i	0.0134187	+	0.0412985i
$575$	15.6114	+	11.3424i	0.651042	+	0.473009i
$576$		0			0
$577$	6.23893	−	19.2015i	0.259730	−	0.799368i	−0.733130	−	0.680088i	$-0.761942\pi$
$577$	6.23893	−	19.2015i	0.259730	−	0.799368i	0.992861	−	0.119280i	$-0.0380585\pi$
$578$	0.429788	−	1.32275i	0.0178768	−	0.0550192i
$579$		0			0
$580$	0.948101	+	0.688835i	0.0393677	+	0.0286023i
$581$	3.48688	+	10.7315i	0.144660	+	0.445218i
$582$		0			0
$583$	4.95961	−	2.80461i	0.205406	−	0.116155i
$584$	−14.7550			−0.610568
$585$		0			0
$586$	−0.286249	−	0.207972i	−0.0118248	−	0.00859125i
$587$	−0.00677611	+	0.00492314i	−0.000279680	+	0.000203200i	−0.587925	−	0.808915i	$-0.700055\pi$
$587$	−0.00677611	+	0.00492314i	−0.000279680	+	0.000203200i	0.587645	+	0.809119i	$0.300055\pi$
$588$		0			0
$589$	−6.20604	+	19.1002i	−0.255716	+	0.787012i
$590$	−1.33426	+	0.969399i	−0.0549307	+	0.0399095i
$591$		0			0
$592$	−1.29020	−	3.97082i	−0.0530267	−	0.163200i
$593$	0.439298			0.0180398			0.00901989	−	0.999959i	$-0.497129\pi$
$593$	0.439298			0.0180398			0.00901989	+	0.999959i	$0.497129\pi$
$594$		0			0
$595$	−0.964520			−0.0395415
$596$	−3.11779	−	9.59558i	−0.127710	−	0.393050i
$597$		0			0
$598$	−16.0092	+	11.6314i	−0.654664	+	0.475641i
$599$	−13.9572	+	42.9558i	−0.570275	+	1.75512i	0.0814591	+	0.996677i	$0.474042\pi$
$599$	−13.9572	+	42.9558i	−0.570275	+	1.75512i	−0.651734	+	0.758448i	$0.725958\pi$
$600$		0			0
$601$	−9.01541	+	6.55008i	−0.367746	+	0.267183i	−0.756276	−	0.654253i	$-0.772983\pi$
$601$	−9.01541	+	6.55008i	−0.367746	+	0.267183i	0.388529	+	0.921436i	$0.372983\pi$
$602$	−2.96145	−	2.15162i	−0.120700	−	0.0876935i
$603$		0			0
$604$	−11.3591			−0.462194
$605$	0.212282	+	2.43845i	0.00863047	+	0.0991371i
$606$		0			0
$607$	−11.0318	−	33.9525i	−0.447768	−	1.37809i	−0.879419	−	0.476049i	$-0.842069\pi$
$607$	−11.0318	−	33.9525i	−0.447768	−	1.37809i	0.431651	−	0.902041i	$-0.357931\pi$
$608$	−13.8057	−	10.0304i	−0.559894	−	0.406787i
$609$		0			0
$610$	−0.514796	+	1.58438i	−0.0208435	+	0.0641496i
$611$	−12.1983	+	37.5426i	−0.493491	+	1.51881i
$612$		0			0
$613$	−13.9135	−	10.1087i	−0.561960	−	0.408288i	0.270216	−	0.962800i	$-0.412905\pi$
$613$	−13.9135	−	10.1087i	−0.561960	−	0.408288i	−0.832176	+	0.554512i	$0.812905\pi$
$614$	−1.93064	−	5.94191i	−0.0779144	−	0.239796i
$615$		0			0
$616$	−1.74378	−	8.58036i	−0.0702587	−	0.345713i
$617$	16.8852			0.679774			0.339887	−	0.940466i	$-0.389611\pi$
$617$	16.8852			0.679774			0.339887	+	0.940466i	$0.389611\pi$
$618$		0			0
$619$	−25.1355	−	18.2620i	−1.01028	−	0.734013i	−0.0460139	−	0.998941i	$-0.514652\pi$
$619$	−25.1355	−	18.2620i	−1.01028	−	0.734013i	−0.964268	+	0.264928i	$0.914652\pi$
$620$	−1.73080	+	1.25750i	−0.0695106	+	0.0505024i
$621$		0			0
$622$	−0.0329066	+	0.101276i	−0.00131943	+	0.00406080i
$623$	−6.40868	+	4.65618i	−0.256758	+	0.186546i
$624$		0			0
$625$	7.49668	+	23.0724i	0.299867	+	0.922896i
$626$	−11.8877			−0.475127
$627$		0			0
$628$	−28.1217			−1.12218
$629$	−7.57271	−	23.3064i	−0.301944	−	0.929287i
$630$		0			0
$631$	−5.86832	+	4.26359i	−0.233614	+	0.169731i	−0.698434	−	0.715675i	$-0.746119\pi$
$631$	−5.86832	+	4.26359i	−0.233614	+	0.169731i	0.464819	+	0.885406i	$0.346119\pi$
$632$	3.69517	−	11.3726i	0.146986	−	0.452376i
$633$		0			0
$634$	−20.7522	+	15.0774i	−0.824176	+	0.598799i
$635$	−0.359549	−	0.261227i	−0.0142683	−	0.0103665i
$636$		0			0
$637$	6.52954			0.258710
$638$	−4.03757	+	8.85460i	−0.159849	+	0.350557i
$639$		0			0
$640$	−0.640707	−	1.97189i	−0.0253262	−	0.0779459i
$641$	−16.7870	−	12.1965i	−0.663047	−	0.481732i	0.204643	−	0.978837i	$-0.434397\pi$
$641$	−16.7870	−	12.1965i	−0.663047	−	0.481732i	−0.867691	+	0.497104i	$0.834397\pi$
$642$		0			0
$643$	2.19750	−	6.76322i	0.0866611	−	0.266715i	−0.898330	−	0.439322i	$-0.855219\pi$
$643$	2.19750	−	6.76322i	0.0866611	−	0.266715i	0.984991	+	0.172606i	$0.0552188\pi$
$644$	1.68095	−	5.17343i	0.0662387	−	0.203862i
$645$		0			0
$646$	−7.94766	−	5.77431i	−0.312696	−	0.227187i
$647$	−8.52234	−	26.2291i	−0.335048	−	1.03117i	−0.966699	−	0.255918i	$-0.917622\pi$
$647$	−8.52234	−	26.2291i	−0.335048	−	1.03117i	0.631651	−	0.775253i	$-0.282378\pi$
$648$		0			0
$649$	23.3063	+	21.3655i	0.914852	+	0.838669i
$650$	−25.1317			−0.985748
$651$		0			0
$652$	8.39353	+	6.09826i	0.328716	+	0.238826i
$653$	13.0690	−	9.49516i	0.511428	−	0.371574i	−0.301937	−	0.953328i	$-0.597633\pi$
$653$	13.0690	−	9.49516i	0.511428	−	0.371574i	0.813365	+	0.581753i	$0.197633\pi$
$654$		0			0
$655$	−0.0942092	+	0.289946i	−0.00368106	+	0.0113291i
$656$	0.799474	−	0.580852i	0.0312142	−	0.0226785i
$657$		0			0
$658$	1.45248	+	4.47026i	0.0566234	+	0.174269i
$659$	13.2085			0.514531			0.257266	−	0.966341i	$-0.417178\pi$
$659$	13.2085			0.514531			0.257266	+	0.966341i	$0.417178\pi$
$660$		0			0
$661$	−4.90660			−0.190845			−0.0954223	−	0.995437i	$-0.530420\pi$
$661$	−4.90660			−0.190845			−0.0954223	+	0.995437i	$0.530420\pi$
$662$	7.09559	+	21.8380i	0.275778	+	0.848757i
$663$		0			0
$664$	−24.0996	+	17.5094i	−0.935245	+	0.679495i
$665$	−0.200439	+	0.616888i	−0.00777270	+	0.0239219i
$666$		0			0
$667$	−11.9013	+	8.64682i	−0.460821	+	0.334806i
$668$	2.49635	+	1.81371i	0.0965869	+	0.0701745i
$669$		0			0
$670$	0.219981			0.00849861
$671$	31.7311	+	3.62221i	1.22497	+	0.139834i
$672$		0			0
$673$	−9.26654	−	28.5195i	−0.357199	−	1.09935i	−0.954723	−	0.297495i	$-0.903849\pi$
$673$	−9.26654	−	28.5195i	−0.357199	−	1.09935i	0.597524	−	0.801851i	$-0.296151\pi$
$674$	−3.54142	−	2.57299i	−0.136410	−	0.0991079i
$675$		0			0
$676$	−12.7797	+	39.3320i	−0.491528	+	1.51277i
$677$	−3.89019	+	11.9728i	−0.149512	+	0.460151i	−0.997564	−	0.0697626i	$-0.977776\pi$
$677$	−3.89019	+	11.9728i	−0.149512	+	0.460151i	0.848051	+	0.529914i	$0.177776\pi$
$678$		0			0
$679$	−7.32477	−	5.32176i	−0.281099	−	0.204230i
$680$	−0.786849	−	2.42167i	−0.0301743	−	0.0928668i
$681$		0			0
$682$	−13.0956	−	12.0051i	−0.501457	−	0.459699i
$683$	28.5342			1.09183			0.545916	−	0.837840i	$-0.316182\pi$
$683$	28.5342			1.09183			0.545916	+	0.837840i	$0.316182\pi$
$684$		0			0
$685$	0.449911	+	0.326879i	0.0171902	+	0.0124894i
$686$	0.628998	−	0.456994i	0.0240153	−	0.0174481i
$687$		0			0
$688$	−1.07447	+	3.30687i	−0.0409636	+	0.126073i
$689$	−9.07491	+	6.59331i	−0.345726	+	0.251185i
$690$		0			0
$691$	7.84107	+	24.1323i	0.298288	+	0.918037i	0.982097	+	0.188376i	$0.0603223\pi$
$691$	7.84107	+	24.1323i	0.298288	+	0.918037i	−0.683809	+	0.729661i	$0.739678\pi$
$692$	−14.4606			−0.549711
$693$		0			0
$694$	−6.78791			−0.257666
$695$	−0.327482	−	1.00788i	−0.0124221	−	0.0382312i
$696$		0			0
$697$	4.69245	−	3.40927i	0.177739	−	0.129135i
$698$	4.43679	−	13.6551i	0.167935	−	0.516851i
$699$		0			0
$700$	5.58909	−	4.06071i	0.211248	−	0.153480i
$701$	−36.9738	−	26.8630i	−1.39648	−	1.01460i	−0.995119	−	0.0986843i	$-0.968537\pi$
$701$	−36.9738	−	26.8630i	−1.39648	−	1.01460i	−0.401363	−	0.915919i	$-0.631463\pi$
$702$		0			0
$703$	−16.4800			−0.621556
$704$	8.87594	−	5.01925i	0.334525	−	0.189170i
$705$		0			0
$706$	5.64257	+	17.3661i	0.212361	+	0.653580i
$707$	15.5413	+	11.2915i	0.584493	+	0.424659i
$708$		0			0
$709$	11.9065	−	36.6446i	0.447160	−	1.37622i	−0.432938	−	0.901424i	$-0.642523\pi$
$709$	11.9065	−	36.6446i	0.447160	−	1.37622i	0.880098	−	0.474793i	$-0.157477\pi$
$710$	0.497676	−	1.53169i	0.0186774	−	0.0574833i
$711$		0			0
$712$	−16.9187	−	12.2921i	−0.634054	−	0.460667i
$713$	−8.29874	−	25.5409i	−0.310790	−	0.956515i
$714$		0			0
$715$	−0.959703	−	4.72228i	−0.0358908	−	0.176603i
$716$	−32.6683			−1.22087
$717$		0			0
$718$	9.36025	+	6.80062i	0.349321	+	0.253797i
$719$	4.61312	−	3.35163i	0.172040	−	0.124995i	−0.498433	−	0.866928i	$-0.666091\pi$
$719$	4.61312	−	3.35163i	0.172040	−	0.124995i	0.670473	+	0.741934i	$0.266091\pi$
$720$		0			0
$721$	−5.01791	+	15.4435i	−0.186877	+	0.575148i
$722$	6.60620	−	4.79969i	0.245857	−	0.178626i
$723$		0			0
$724$	5.91491	+	18.2042i	0.219826	+	0.676555i
$725$	−18.6831			−0.693872
$726$		0			0
$727$	11.8221			0.438458			0.219229	−	0.975673i	$-0.429646\pi$
$727$	11.8221			0.438458			0.219229	+	0.975673i	$0.429646\pi$
$728$	5.32676	+	16.3941i	0.197423	+	0.607605i
$729$		0			0
$730$	−0.782263	+	0.568347i	−0.0289529	+	0.0210355i
$731$	−6.30649	+	19.4094i	−0.233254	+	0.717882i
$732$		0			0
$733$	−7.12900	+	5.17952i	−0.263316	+	0.191310i	−0.711607	−	0.702577i	$-0.752033\pi$
$733$	−7.12900	+	5.17952i	−0.263316	+	0.191310i	0.448292	+	0.893887i	$0.352033\pi$
$734$	21.5280	+	15.6410i	0.794614	+	0.577321i
$735$		0			0
$736$	22.8190			0.841121
$737$	−0.839897	−	4.13277i	−0.0309380	−	0.152232i
$738$		0			0
$739$	0.148578	+	0.457276i	0.00546553	+	0.0168212i	0.953752	−	0.300594i	$-0.0971850\pi$
$739$	0.148578	+	0.457276i	0.00546553	+	0.0168212i	−0.948287	+	0.317416i	$0.897185\pi$
$740$	−1.42027	−	1.03189i	−0.0522103	−	0.0379330i
$741$		0			0
$742$	−0.412739	+	1.27028i	−0.0151521	+	0.0466335i
$743$	−10.2730	+	31.6172i	−0.376881	+	1.15992i	0.565319	+	0.824872i	$0.308753\pi$
$743$	−10.2730	+	31.6172i	−0.376881	+	1.15992i	−0.942201	+	0.335049i	$0.891247\pi$
$744$		0			0
$745$	−1.30151	−	0.945603i	−0.0476837	−	0.0346442i
$746$	0.724946	+	2.23116i	0.0265422	+	0.0816884i
$747$		0			0
$748$	−17.4635	+	9.87543i	−0.638530	+	0.361082i
$749$	−5.39336			−0.197069
$750$		0			0
$751$	−22.6578	−	16.4619i	−0.826796	−	0.600703i	0.0918547	−	0.995772i	$-0.470720\pi$
$751$	−22.6578	−	16.4619i	−0.826796	−	0.600703i	−0.918651	+	0.395070i	$0.870720\pi$
$752$	3.61200	−	2.62427i	0.131716	−	0.0956973i
$753$		0			0
$754$	5.92049	−	18.2214i	0.215611	−	0.663584i
$755$	−1.46530	+	1.06460i	−0.0533276	+	0.0387448i
$756$		0			0
$757$	−6.87465	−	21.1580i	−0.249863	−	0.769001i	−0.994798	−	0.101864i	$-0.967519\pi$
$757$	−6.87465	−	21.1580i	−0.249863	−	0.769001i	0.744935	−	0.667137i	$-0.232481\pi$
$758$	−4.76156			−0.172948
$759$		0			0
$760$	−1.71237			−0.0621142
$761$	14.9025	+	45.8651i	0.540214	+	1.66261i	0.732105	+	0.681192i	$0.238538\pi$
$761$	14.9025	+	45.8651i	0.540214	+	1.66261i	−0.191891	+	0.981416i	$0.561462\pi$
$762$		0			0
$763$	4.36789	−	3.17346i	0.158128	−	0.114887i
$764$	−5.18562	+	15.9597i	−0.187609	+	0.577402i
$765$		0			0
$766$	2.76192	−	2.00665i	0.0997922	−	0.0725033i
$767$	−50.3584	−	36.5875i	−1.81834	−	1.32110i
$768$		0			0
$769$	43.6883			1.57544			0.787721	−	0.616032i	$-0.211261\pi$
$769$	43.6883			1.57544			0.787721	+	0.616032i	$0.211261\pi$
$770$	−0.422955	−	0.387734i	−0.0152422	−	0.0139730i
$771$		0			0
$772$	−6.84977	−	21.0814i	−0.246528	−	0.758737i
$773$	−0.473736	−	0.344189i	−0.0170391	−	0.0123796i	0.579233	−	0.815162i	$-0.303352\pi$
$773$	−0.473736	−	0.344189i	−0.0170391	−	0.0123796i	−0.596272	+	0.802782i	$0.703352\pi$
$774$		0			0
$775$	10.5396	−	32.4375i	0.378593	−	1.16519i
$776$	7.38612	−	22.7321i	0.265146	−	0.816036i
$777$		0			0
$778$	6.60197	+	4.79661i	0.236692	+	0.171967i
$779$	−1.20535	−	3.70969i	−0.0431862	−	0.132913i
$780$		0			0
$781$	−30.6759	−	3.50175i	−1.09767	−	0.125302i
$782$	13.1365			0.469760
$783$		0			0
$784$	−0.597465	−	0.434084i	−0.0213380	−	0.0155030i
$785$	−3.62764	+	2.63563i	−0.129476	+	0.0940698i
$786$		0			0
$787$	9.49195	−	29.2132i	0.338351	−	1.04134i	−0.626696	−	0.779264i	$-0.715593\pi$
$787$	9.49195	−	29.2132i	0.338351	−	1.04134i	0.965048	−	0.262075i	$-0.0844067\pi$
$788$	−13.8907	+	10.0922i	−0.494834	+	0.359518i
$789$		0			0
$790$	−0.242153	−	0.745269i	−0.00861540	−	0.0265155i
$791$	−16.4962			−0.586538
$792$		0			0
$793$	−62.8758			−2.23278
$794$	2.73623	+	8.42125i	0.0971052	+	0.298859i
$795$		0			0
$796$	17.2302	−	12.5185i	0.610708	−	0.443705i
$797$	3.34767	−	10.3031i	0.118581	−	0.364953i	−0.874096	−	0.485752i	$-0.838546\pi$
$797$	3.34767	−	10.3031i	0.118581	−	0.364953i	0.992677	+	0.120799i	$0.0385456\pi$
$798$		0			0
$799$	21.2003	−	15.4029i	0.750014	−	0.544917i
$800$	23.4458	+	17.0344i	0.828936	+	0.602257i
$801$		0			0
$802$	3.67358			0.129719
$803$	13.6642	+	12.5263i	0.482200	+	0.442045i
$804$		0			0
$805$	−0.268028	−	0.824906i	−0.00944675	−	0.0290741i
$806$	28.2960	+	20.5582i	0.996684	+	0.724133i
$807$		0			0
$808$	−15.6715	+	48.2320i	−0.551322	+	1.69679i
$809$	11.9250	−	36.7013i	0.419260	−	1.29035i	−0.489125	−	0.872214i	$-0.662684\pi$
$809$	11.9250	−	36.7013i	0.419260	−	1.29035i	0.908385	−	0.418136i	$-0.137316\pi$
$810$		0			0
$811$	41.1737	+	29.9144i	1.44580	+	1.05044i	0.986789	+	0.162010i	$0.0517977\pi$
$811$	41.1737	+	29.9144i	1.44580	+	1.05044i	0.459015	+	0.888428i	$0.348202\pi$
$812$	1.62749	+	5.00890i	0.0571137	+	0.175778i
$813$		0			0
$814$	6.04836	−	13.2644i	0.211995	−	0.464916i
$815$	1.65429			0.0579473
$816$		0			0
$817$	11.1033	+	8.06703i	0.388456	+	0.282230i
$818$	−1.55076	+	1.12669i	−0.0542209	+	0.0393938i
$819$		0			0
$820$	0.128402	−	0.395180i	0.00448398	−	0.0138003i
$821$	−32.6110	+	23.6933i	−1.13813	+	0.826901i	−0.986858	−	0.161590i	$-0.948338\pi$
$821$	−32.6110	+	23.6933i	−1.13813	+	0.826901i	−0.151274	+	0.988492i	$0.548338\pi$
$822$		0			0
$823$	7.93609	+	24.4248i	0.276635	+	0.851395i	0.988782	+	0.149365i	$0.0477228\pi$
$823$	7.93609	+	24.4248i	0.276635	+	0.851395i	−0.712147	+	0.702030i	$0.752277\pi$
$824$	−42.8685			−1.49340
$825$		0			0
$826$	−7.41179			−0.257889
$827$	9.87486	+	30.3917i	0.343382	+	1.05682i	0.962444	+	0.271480i	$0.0875131\pi$
$827$	9.87486	+	30.3917i	0.343382	+	1.05682i	−0.619062	+	0.785342i	$0.712487\pi$
$828$		0			0
$829$	−39.1566	+	28.4489i	−1.35996	+	0.988072i	−0.361518	+	0.932365i	$0.617741\pi$
$829$	−39.1566	+	28.4489i	−1.35996	+	0.988072i	−0.998447	+	0.0557070i	$0.982259\pi$
$830$	−0.603238	+	1.85658i	−0.0209387	+	0.0644427i
$831$		0			0
$832$	−16.2409	+	11.7997i	−0.563050	+	0.409080i
$833$	−3.50678	−	2.54782i	−0.121503	−	0.0882768i
$834$		0			0
$835$	0.492010			0.0170267
$836$	2.68700	+	13.2216i	0.0929319	+	0.457278i
$837$		0			0
$838$	3.44524	+	10.6033i	0.119014	+	0.366287i
$839$	−30.5133	−	22.1692i	−1.05344	−	0.765366i	−0.0805734	−	0.996749i	$-0.525675\pi$
$839$	−30.5133	−	22.1692i	−1.05344	−	0.765366i	−0.972863	+	0.231382i	$0.925675\pi$
$840$		0			0
$841$	−4.56017	+	14.0348i	−0.157247	+	0.483957i
$842$	−4.16021	+	12.8038i	−0.143370	+	0.441248i
$843$		0			0
$844$	10.0858	+	7.32779i	0.347169	+	0.252233i
$845$	2.03773	+	6.27150i	0.0701001	+	0.215746i
$846$		0			0
$847$	−5.66947	+	9.42641i	−0.194805	+	0.323895i
$848$	1.26869			0.0435671
$849$		0			0
$850$	13.4973	+	9.80638i	0.462954	+	0.336356i
$851$	17.8284	−	12.9531i	0.611151	−	0.444027i
$852$		0			0
$853$	2.87035	−	8.83403i	0.0982789	−	0.302471i	−0.889815	−	0.456321i	$-0.849167\pi$
$853$	2.87035	−	8.83403i	0.0982789	−	0.302471i	0.988094	+	0.153849i	$0.0491670\pi$
$854$	−6.05689	+	4.40059i	−0.207262	+	0.150585i
$855$		0			0
$856$	−4.39986	−	13.5414i	−0.150384	−	0.462835i
$857$	29.7644			1.01673			0.508365	−	0.861141i	$-0.330250\pi$
$857$	29.7644			1.01673			0.508365	+	0.861141i	$0.330250\pi$
$858$		0			0
$859$	33.2611			1.13485			0.567427	−	0.823424i	$-0.307939\pi$
$859$	33.2611			1.13485			0.567427	+	0.823424i	$0.307939\pi$
$860$	0.451787	+	1.39046i	0.0154058	+	0.0474142i
$861$		0			0
$862$	17.5442	−	12.7466i	0.597558	−	0.434151i
$863$	5.73772	−	17.6589i	0.195314	−	0.601116i	−0.804658	−	0.593738i	$-0.797652\pi$
$863$	5.73772	−	17.6589i	0.195314	−	0.601116i	0.999973	−	0.00737787i	$-0.00234847\pi$
$864$		0			0
$865$	−1.86539	+	1.35529i	−0.0634253	+	0.0460812i
$866$	18.5850	+	13.5028i	0.631544	+	0.458844i
$867$		0			0
$868$	−9.61454			−0.326339
$869$	−13.0768	+	7.39477i	−0.443599	+	0.250850i
$870$		0			0
$871$	2.56565	+	7.89627i	0.0869339	+	0.267555i
$872$	11.5311	+	8.37782i	0.390491	+	0.283709i
$873$		0			0
$874$	2.72992	−	8.40184i	0.0923411	−	0.284197i
$875$	0.684207	−	2.10577i	0.0231304	−	0.0711881i
$876$		0			0
$877$	18.1965	+	13.2205i	0.614452	+	0.446426i	0.850979	−	0.525199i	$-0.176009\pi$
$877$	18.1965	+	13.2205i	0.614452	+	0.446426i	−0.236527	+	0.971625i	$0.576009\pi$
$878$	−8.08834	−	24.8934i	−0.272968	−	0.840110i
$879$		0			0
$880$	−0.226122	+	0.495898i	−0.00762259	+	0.0167167i
$881$	−7.06565			−0.238048			−0.119024	−	0.992891i	$-0.537977\pi$
$881$	−7.06565			−0.238048			−0.119024	+	0.992891i	$0.537977\pi$
$882$		0			0
$883$	16.1304	+	11.7194i	0.542830	+	0.394389i	0.825135	−	0.564936i	$-0.191099\pi$
$883$	16.1304	+	11.7194i	0.542830	+	0.394389i	−0.282305	+	0.959325i	$0.591099\pi$
$884$	31.9541	−	23.2160i	1.07473	−	0.780839i
$885$		0			0
$886$	−2.48105	+	7.63590i	−0.0833527	+	0.256533i
$887$	5.62656	−	4.08793i	0.188921	−	0.137259i	−0.489304	−	0.872113i	$-0.662749\pi$
$887$	5.62656	−	4.08793i	0.188921	−	0.137259i	0.678226	+	0.734854i	$0.262749\pi$
$888$		0			0
$889$	−0.617194	−	1.89953i	−0.0207000	−	0.0637081i
$890$	−1.37045			−0.0459376
$891$		0			0
$892$	−0.998136			−0.0334201
$893$	−5.44574	−	16.7603i	−0.182235	−	0.560861i
$894$		0			0
$895$	−4.21414	+	3.06175i	−0.140863	+	0.102343i
$896$	2.87938	−	8.86181i	0.0961933	−	0.296052i
$897$		0			0
$898$	−1.73468	+	1.26032i	−0.0578872	+	0.0420575i
$899$	21.0354	+	15.2831i	0.701570	+	0.509721i
$900$		0			0
$901$	7.44650			0.248079
$902$	3.42822	+	0.391342i	0.114147	+	0.0130303i
$903$		0			0
$904$	−13.4575	−	41.4179i	−0.447590	−	1.37754i
$905$	2.46916	+	1.79395i	0.0820776	+	0.0596329i
$906$		0			0
$907$	−7.24340	+	22.2929i	−0.240513	+	0.740224i	0.755829	+	0.654769i	$0.227234\pi$
$907$	−7.24340	+	22.2929i	−0.240513	+	0.740224i	−0.996342	+	0.0854543i	$0.972766\pi$
$908$	−2.29489	+	7.06294i	−0.0761586	+	0.234392i
$909$		0			0
$910$	0.913888	+	0.663978i	0.0302951	+	0.0220107i
$911$	−14.4650	−	44.5186i	−0.479246	−	1.47497i	−0.840145	−	0.542362i	$-0.817530\pi$
$911$	−14.4650	−	44.5186i	−0.479246	−	1.47497i	0.360899	−	0.932605i	$-0.382470\pi$
$912$		0			0
$913$	37.1825	+	4.24450i	1.23056	+	0.140473i
$914$	−31.3563			−1.03718
$915$		0			0
$916$	−7.46078	−	5.42058i	−0.246511	−	0.179101i
$917$	−1.10843	+	0.805321i	−0.0366036	+	0.0265940i
$918$		0			0
$919$	3.28402	−	10.1072i	0.108330	−	0.333405i	−0.882168	−	0.470935i	$-0.843916\pi$
$919$	3.28402	−	10.1072i	0.108330	−	0.333405i	0.990498	+	0.137530i	$0.0439165\pi$
$920$	1.85248	−	1.34590i	0.0610744	−	0.0443732i
$921$		0			0
$922$	8.22278	+	25.3071i	0.270803	+	0.833445i
$923$	60.7848			2.00075
$924$		0			0
$925$	27.9876			0.920228
$926$	0.169945	+	0.523036i	0.00558473	+	0.0171880i
$927$		0			0
$928$	−17.8739	+	12.9861i	−0.586738	+	0.426290i
$929$	11.3319	−	34.8762i	0.371789	−	1.14425i	−0.573830	−	0.818974i	$-0.694543\pi$
$929$	11.3319	−	34.8762i	0.371789	−	1.14425i	0.945619	−	0.325275i	$-0.105457\pi$
$930$		0			0
$931$	−2.35829	+	1.71340i	−0.0772898	+	0.0561543i
$932$	10.7900	+	7.83938i	0.353438	+	0.256787i
$933$		0			0
$934$	22.2302			0.727393
$935$	−1.32721	+	2.91064i	−0.0434043	+	0.0951880i
$936$		0			0
$937$	−12.4278	−	38.2490i	−0.406000	−	1.24954i	−0.920057	−	0.391784i	$-0.871858\pi$
$937$	−12.4278	−	38.2490i	−0.406000	−	1.24954i	0.514057	−	0.857756i	$-0.328142\pi$
$938$	0.799801	+	0.581090i	0.0261144	+	0.0189732i
$939$		0			0
$940$	0.580114	−	1.78541i	0.0189212	−	0.0582336i
$941$	−7.69751	+	23.6905i	−0.250932	+	0.772288i	0.743672	+	0.668544i	$0.233082\pi$
$941$	−7.69751	+	23.6905i	−0.250932	+	0.772288i	−0.994604	+	0.103744i	$0.966918\pi$
$942$		0			0
$943$	4.21975	+	3.06583i	0.137414	+	0.0998371i
$944$	2.17555	+	6.69565i	0.0708081	+	0.217925i
$945$		0			0
$946$	−10.5680	+	5.97609i	−0.343595	+	0.194299i
$947$	32.2061			1.04656			0.523279	−	0.852161i	$-0.324708\pi$
$947$	32.2061			1.04656			0.523279	+	0.852161i	$0.324708\pi$
$948$		0			0
$949$	−29.5246	−	21.4508i	−0.958408	−	0.696324i
$950$	9.07688	−	6.59474i	0.294493	−	0.213962i
$951$		0			0
$952$	3.53615	−	10.8831i	0.114607	−	0.352725i
$953$	36.4552	−	26.4863i	1.18090	−	0.857975i	0.188628	−	0.982049i	$-0.439596\pi$
$953$	36.4552	−	26.4863i	1.18090	−	0.857975i	0.992273	+	0.124074i	$0.0395960\pi$
$954$		0			0
$955$	0.826849	+	2.54478i	0.0267562	+	0.0823471i
$956$	37.4650			1.21170
$957$		0			0
$958$	3.96296			0.128038
$959$	0.772308	+	2.37692i	0.0249391	+	0.0767547i
$960$		0			0
$961$	−13.3216	+	9.67867i	−0.429727	+	0.312215i
$962$	−8.86901	+	27.2960i	−0.285948	+	0.880059i
$963$		0			0
$964$	21.3000	−	15.4754i	0.686028	−	0.498428i
$965$	−2.85941	−	2.07748i	−0.0920476	−	0.0668765i
$966$		0			0
$967$	1.81387			0.0583300			0.0291650	−	0.999575i	$-0.490715\pi$
$967$	1.81387			0.0583300			0.0291650	+	0.999575i	$0.490715\pi$
$968$	−28.2925	−	6.54464i	−0.909355	−	0.210353i
$969$		0			0
$970$	−0.484029	−	1.48969i	−0.0155412	−	0.0478310i
$971$	18.6510	+	13.5507i	0.598539	+	0.434864i	0.845360	−	0.534197i	$-0.179386\pi$
$971$	18.6510	+	13.5507i	0.598539	+	0.434864i	−0.246821	+	0.969061i	$0.579386\pi$
$972$		0			0
$973$	1.47172	−	4.52950i	0.0471813	−	0.145209i
$974$	7.01266	−	21.5827i	0.224700	−	0.691555i
$975$		0			0
$976$	5.75325	+	4.17998i	0.184157	+	0.133798i
$977$	2.19232	+	6.74726i	0.0701385	+	0.215864i	0.979981	−	0.199089i	$-0.0637981\pi$
$977$	2.19232	+	6.74726i	0.0701385	+	0.215864i	−0.909843	+	0.414953i	$0.863798\pi$
$978$		0			0
$979$	5.23244	+	25.7466i	0.167229	+	0.822863i
$980$	−0.310525			−0.00991935
$981$		0			0
$982$	18.9605	+	13.7756i	0.605053	+	0.439597i
$983$	31.0260	−	22.5417i	0.989576	−	0.718969i	0.0297474	−	0.999557i	$-0.490530\pi$
$983$	31.0260	−	22.5417i	0.989576	−	0.718969i	0.959828	+	0.280589i	$0.0905297\pi$
$984$		0			0
$985$	−0.846005	+	2.60374i	−0.0269560	+	0.0829619i
$986$	−10.2896	+	7.47586i	−0.327689	+	0.238080i
$987$		0			0
$988$	−8.20806	−	25.2618i	−0.261133	−	0.803685i
$989$	−18.3524			−0.583572
$990$		0			0
$991$	20.2722			0.643967			0.321984	−	0.946745i	$-0.395650\pi$
$991$	20.2722			0.643967			0.321984	+	0.946745i	$0.395650\pi$
$992$	−12.4634	−	38.3583i	−0.395712	−	1.21788i
$993$		0			0
$994$	5.85546	−	4.25424i	0.185724	−	0.134936i
$995$	1.04940	−	3.22971i	0.0332681	−	0.102389i
$996$		0			0
$997$	−12.4675	+	9.05819i	−0.394851	+	0.286876i	−0.767440	−	0.641120i	$-0.778470\pi$
$997$	−12.4675	+	9.05819i	−0.394851	+	0.286876i	0.372590	+	0.927996i	$0.378470\pi$
$998$	−3.74319	−	2.71959i	−0.118489	−	0.0860871i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.g.379.2		8
3.2	odd	2		77.2.f.a.71.1	yes	8
11.3	even	5		7623.2.a.ch.1.3		4
11.8	odd	10		7623.2.a.co.1.2		4
11.9	even	5	inner	693.2.m.g.64.2		8
21.2	odd	6		539.2.q.c.214.1		16
21.5	even	6		539.2.q.b.214.1		16
21.11	odd	6		539.2.q.c.324.2		16
21.17	even	6		539.2.q.b.324.2		16
21.20	even	2		539.2.f.d.148.1		8
33.2	even	10		847.2.f.q.372.2		8
33.5	odd	10		847.2.f.p.323.2		8
33.8	even	10		847.2.a.k.1.3		4
33.14	odd	10		847.2.a.l.1.2		4
33.17	even	10		847.2.f.s.323.1		8
33.20	odd	10		77.2.f.a.64.1	✓	8
33.26	odd	10		847.2.f.p.729.2		8
33.29	even	10		847.2.f.s.729.1		8
33.32	even	2		847.2.f.q.148.2		8
231.20	even	10		539.2.f.d.295.1		8
231.41	odd	10		5929.2.a.bb.1.3		4
231.53	odd	30		539.2.q.c.471.1		16
231.86	odd	30		539.2.q.c.361.2		16
231.146	even	10		5929.2.a.bi.1.2		4
231.152	even	30		539.2.q.b.361.2		16
231.185	even	30		539.2.q.b.471.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.64.1	✓	8	33.20	odd	10
77.2.f.a.71.1	yes	8	3.2	odd	2
539.2.f.d.148.1		8	21.20	even	2
539.2.f.d.295.1		8	231.20	even	10
539.2.q.b.214.1		16	21.5	even	6
539.2.q.b.324.2		16	21.17	even	6
539.2.q.b.361.2		16	231.152	even	30
539.2.q.b.471.1		16	231.185	even	30
539.2.q.c.214.1		16	21.2	odd	6
539.2.q.c.324.2		16	21.11	odd	6
539.2.q.c.361.2		16	231.86	odd	30
539.2.q.c.471.1		16	231.53	odd	30
693.2.m.g.64.2		8	11.9	even	5	inner
693.2.m.g.379.2		8	1.1	even	1	trivial
847.2.a.k.1.3		4	33.8	even	10
847.2.a.l.1.2		4	33.14	odd	10
847.2.f.p.323.2		8	33.5	odd	10
847.2.f.p.729.2		8	33.26	odd	10
847.2.f.q.148.2		8	33.32	even	2
847.2.f.q.372.2		8	33.2	even	10
847.2.f.s.323.1		8	33.17	even	10
847.2.f.s.729.1		8	33.29	even	10
5929.2.a.bb.1.3		4	231.41	odd	10
5929.2.a.bi.1.2		4	231.146	even	10
7623.2.a.ch.1.3		4	11.3	even	5
7623.2.a.co.1.2		4	11.8	odd	10

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.240256 + 0.739431i) q^{2} +(1.12900 - 0.820265i) q^{4} +(0.0687611 - 0.211625i) q^{5} +(0.809017 - 0.587785i) q^{7} +(2.13577 + 1.55173i) q^{8} +O(q^{10})\)	\(q+(0.240256 + 0.739431i) q^{2} +(1.12900 - 0.820265i) q^{4} +(0.0687611 - 0.211625i) q^{5} +(0.809017 - 0.587785i) q^{7} +(2.13577 + 1.55173i) q^{8} +0.173002 q^{10} +(-0.660531 - 3.25018i) q^{11} +(2.01774 + 6.20997i) q^{13} +(0.628998 + 0.456994i) q^{14} +(0.228211 - 0.702362i) q^{16} +(1.33947 - 4.12246i) q^{17} +(-2.35829 - 1.71340i) q^{19} +(-0.0959574 - 0.295327i) q^{20} +(2.24459 - 1.26929i) q^{22} +3.89796 q^{23} +(4.00503 + 2.90982i) q^{25} +(-4.10707 + 2.98396i) q^{26} +(0.431239 - 1.32722i) q^{28} +(-3.05322 + 2.21829i) q^{29} +(-2.12900 - 6.55238i) q^{31} +5.85410 q^{32} +3.37009 q^{34} +(-0.0687611 - 0.211625i) q^{35} +(4.57379 - 3.32305i) q^{37} +(0.700347 - 2.15545i) q^{38} +(0.475243 - 0.345285i) q^{40} +(1.08255 + 0.786521i) q^{41} -4.70820 q^{43} +(-3.41175 - 3.12764i) q^{44} +(0.936507 + 2.88227i) q^{46} +(4.89094 + 3.55348i) q^{47} +(0.309017 - 0.951057i) q^{49} +(-1.18938 + 3.66055i) q^{50} +(7.37184 + 5.35596i) q^{52} +(0.530865 + 1.63383i) q^{53} +(-0.733239 - 0.0837016i) q^{55} +2.63996 q^{56} +(-2.37383 - 1.72469i) q^{58} +(-7.71239 + 5.60338i) q^{59} +(-2.97566 + 9.15813i) q^{61} +(4.33353 - 3.14850i) q^{62} +(0.950059 + 2.92398i) q^{64} +1.45293 q^{65} +1.27155 q^{67} +(-1.86925 - 5.75297i) q^{68} +(0.139962 - 0.101688i) q^{70} +(2.87670 - 8.85357i) q^{71} +(-4.52169 + 3.28520i) q^{73} +(3.55605 + 2.58362i) q^{74} -4.06794 q^{76} +(-2.44479 - 2.24120i) q^{77} +(-1.39971 - 4.30785i) q^{79} +(-0.132945 - 0.0965905i) q^{80} +(-0.321489 + 0.989441i) q^{82} +(-3.48688 + 10.7315i) q^{83} +(-0.780313 - 0.566931i) q^{85} +(-1.13117 - 3.48139i) q^{86} +(3.63267 - 7.96663i) q^{88} -7.92157 q^{89} +(5.28251 + 3.83797i) q^{91} +(4.40079 - 3.19736i) q^{92} +(-1.45248 + 4.47026i) q^{94} +(-0.524757 + 0.381258i) q^{95} +(-2.79781 - 8.61078i) q^{97} +0.777484 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 3 q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8}+O(q^{10}) \) 8 * q + q^2 + 3 * q^4 - 3 * q^5 + 2 * q^7 - 3 * q^8	\( 8 q + q^{2} + 3 q^{4} - 3 q^{5} + 2 q^{7} - 3 q^{8} - 28 q^{10} - 5 q^{11} + 5 q^{13} - q^{14} - 3 q^{16} + 11 q^{17} - 9 q^{19} - 21 q^{20} - q^{22} + 16 q^{23} + 5 q^{25} - 21 q^{26} + 7 q^{28} + 9 q^{29} - 11 q^{31} + 20 q^{32} - 24 q^{34} + 3 q^{35} + 6 q^{37} - 35 q^{38} - 16 q^{40} + 22 q^{41} + 16 q^{43} - 29 q^{44} + 29 q^{46} - 7 q^{47} - 2 q^{49} + 34 q^{50} + 21 q^{52} - 2 q^{53} + 26 q^{55} + 18 q^{56} - 39 q^{58} - 25 q^{59} + 7 q^{61} + 5 q^{62} + q^{64} - 24 q^{65} - 30 q^{67} - 8 q^{68} - 2 q^{70} + 14 q^{71} + 3 q^{73} + 9 q^{74} - 52 q^{76} + 5 q^{77} - 9 q^{79} + 33 q^{80} + 31 q^{82} - 23 q^{83} - 10 q^{85} + 17 q^{86} - 7 q^{88} + 34 q^{89} + 5 q^{91} + 34 q^{92} - 30 q^{94} - 24 q^{95} + 30 q^{97} - 4 q^{98}+O(q^{100}) \) 8 * q + q^2 + 3 * q^4 - 3 * q^5 + 2 * q^7 - 3 * q^8 - 28 * q^10 - 5 * q^11 + 5 * q^13 - q^14 - 3 * q^16 + 11 * q^17 - 9 * q^19 - 21 * q^20 - q^22 + 16 * q^23 + 5 * q^25 - 21 * q^26 + 7 * q^28 + 9 * q^29 - 11 * q^31 + 20 * q^32 - 24 * q^34 + 3 * q^35 + 6 * q^37 - 35 * q^38 - 16 * q^40 + 22 * q^41 + 16 * q^43 - 29 * q^44 + 29 * q^46 - 7 * q^47 - 2 * q^49 + 34 * q^50 + 21 * q^52 - 2 * q^53 + 26 * q^55 + 18 * q^56 - 39 * q^58 - 25 * q^59 + 7 * q^61 + 5 * q^62 + q^64 - 24 * q^65 - 30 * q^67 - 8 * q^68 - 2 * q^70 + 14 * q^71 + 3 * q^73 + 9 * q^74 - 52 * q^76 + 5 * q^77 - 9 * q^79 + 33 * q^80 + 31 * q^82 - 23 * q^83 - 10 * q^85 + 17 * q^86 - 7 * q^88 + 34 * q^89 + 5 * q^91 + 34 * q^92 - 30 * q^94 - 24 * q^95 + 30 * q^97 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more