LMFDB - Embedded newform 77.2.f.a.64.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [77,2,Mod(15,77)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("77.15"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(77, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.614848095564$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.1
Root			$-0.628998 - 0.456994i$ of defining polynomial
Character	$\chi$	$=$	77.64
Dual form			77.2.f.a.71.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.240256 + 0.739431i) q^{2} +(-0.500000 + 0.363271i) q^{3} +(1.12900 + 0.820265i) q^{4} +(-0.0687611 - 0.211625i) q^{5} +(-0.148486 - 0.456994i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-2.13577 + 1.55173i) q^{8} +(-0.809017 + 2.48990i) q^{9} +0.173002 q^{10} +(0.660531 - 3.25018i) q^{11} -0.862478 q^{12} +(2.01774 - 6.20997i) q^{13} +(-0.628998 + 0.456994i) q^{14} +(0.111258 + 0.0808336i) q^{15} +(0.228211 + 0.702362i) q^{16} +(-1.33947 - 4.12246i) q^{17} +(-1.64674 - 1.19643i) q^{18} +(-2.35829 + 1.71340i) q^{19} +(0.0959574 - 0.295327i) q^{20} -0.618034 q^{21} +(2.24459 + 1.26929i) q^{22} -3.89796 q^{23} +(0.504188 - 1.55173i) q^{24} +(4.00503 - 2.90982i) q^{25} +(4.10707 + 2.98396i) q^{26} +(-1.07295 - 3.30220i) q^{27} +(0.431239 + 1.32722i) q^{28} +(3.05322 + 2.21829i) q^{29} +(-0.0865012 + 0.0628468i) q^{30} +(-2.12900 + 6.55238i) q^{31} -5.85410 q^{32} +(0.850433 + 1.86504i) q^{33} +3.37009 q^{34} +(0.0687611 - 0.211625i) q^{35} +(-2.95576 + 2.14748i) q^{36} +(4.57379 + 3.32305i) q^{37} +(-0.700347 - 2.15545i) q^{38} +(1.24703 + 3.83797i) q^{39} +(0.475243 + 0.345285i) q^{40} +(-1.08255 + 0.786521i) q^{41} +(0.148486 - 0.456994i) q^{42} -4.70820 q^{43} +(3.41175 - 3.12764i) q^{44} +0.582554 q^{45} +(0.936507 - 2.88227i) q^{46} +(-4.89094 + 3.55348i) q^{47} +(-0.369254 - 0.268279i) q^{48} +(0.309017 + 0.951057i) q^{49} +(1.18938 + 3.66055i) q^{50} +(2.16731 + 1.57464i) q^{51} +(7.37184 - 5.35596i) q^{52} +(-0.530865 + 1.63383i) q^{53} +2.69953 q^{54} +(-0.733239 + 0.0837016i) q^{55} -2.63996 q^{56} +(0.556717 - 1.71340i) q^{57} +(-2.37383 + 1.72469i) q^{58} +(7.71239 + 5.60338i) q^{59} +(0.0593050 + 0.182522i) q^{60} +(-2.97566 - 9.15813i) q^{61} +(-4.33353 - 3.14850i) q^{62} +(-2.11803 + 1.53884i) q^{63} +(0.950059 - 2.92398i) q^{64} -1.45293 q^{65} +(-1.58339 + 0.180749i) q^{66} +1.27155 q^{67} +(1.86925 - 5.75297i) q^{68} +(1.94898 - 1.41602i) q^{69} +(0.139962 + 0.101688i) q^{70} +(-2.87670 - 8.85357i) q^{71} +(-2.13577 - 6.57324i) q^{72} +(-4.52169 - 3.28520i) q^{73} +(-3.55605 + 2.58362i) q^{74} +(-0.945459 + 2.90982i) q^{75} -4.06794 q^{76} +(2.44479 - 2.24120i) q^{77} -3.13752 q^{78} +(-1.39971 + 4.30785i) q^{79} +(0.132945 - 0.0965905i) q^{80} +(-4.61803 - 3.35520i) q^{81} +(-0.321489 - 0.989441i) q^{82} +(3.48688 + 10.7315i) q^{83} +(-0.697759 - 0.506952i) q^{84} +(-0.780313 + 0.566931i) q^{85} +(1.13117 - 3.48139i) q^{86} -2.33245 q^{87} +(3.63267 + 7.96663i) q^{88} +7.92157 q^{89} +(-0.139962 + 0.430759i) q^{90} +(5.28251 - 3.83797i) q^{91} +(-4.40079 - 3.19736i) q^{92} +(-1.31579 - 4.04959i) q^{93} +(-1.45248 - 4.47026i) q^{94} +(0.524757 + 0.381258i) q^{95} +(2.92705 - 2.12663i) q^{96} +(-2.79781 + 8.61078i) q^{97} -0.777484 q^{98} +(7.55825 + 4.27411i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 4 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} - 2 q^{9} - 28 q^{10} + 5 q^{11} - 14 q^{12} + 5 q^{13} + q^{14} + 6 q^{15} - 3 q^{16} - 11 q^{17} + 4 q^{18} - 9 q^{19} + 21 q^{20}+ \cdots + 4 q^{98}+O(q^{100}) $ 8 * q - q^2 - 4 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 - 2 * q^9 - 28 * q^10 + 5 * q^11 - 14 * q^12 + 5 * q^13 + q^14 + 6 * q^15 - 3 * q^16 - 11 * q^17 + 4 * q^18 - 9 * q^19 + 21 * q^20 + 4 * q^21 - q^22 - 16 * q^23 + 21 * q^24 + 5 * q^25 + 21 * q^26 - 22 * q^27 + 7 * q^28 - 9 * q^29 + 14 * q^30 - 11 * q^31 - 20 * q^32 + 10 * q^33 - 24 * q^34 - 3 * q^35 - 2 * q^36 + 6 * q^37 + 35 * q^38 - 5 * q^39 - 16 * q^40 - 22 * q^41 - 3 * q^42 + 16 * q^43 + 29 * q^44 + 18 * q^45 + 29 * q^46 + 7 * q^47 + 4 * q^48 - 2 * q^49 - 34 * q^50 + 3 * q^51 + 21 * q^52 + 2 * q^53 + 4 * q^54 + 26 * q^55 - 18 * q^56 - 3 * q^57 - 39 * q^58 + 25 * q^59 - 38 * q^60 + 7 * q^61 - 5 * q^62 - 8 * q^63 + q^64 + 24 * q^65 + 18 * q^66 - 30 * q^67 + 8 * q^68 + 8 * q^69 - 2 * q^70 - 14 * q^71 + 3 * q^72 + 3 * q^73 - 9 * q^74 + 5 * q^75 - 52 * q^76 - 5 * q^77 - 18 * q^78 - 9 * q^79 - 33 * q^80 - 28 * q^81 + 31 * q^82 + 23 * q^83 + 4 * q^84 - 10 * q^85 - 17 * q^86 + 12 * q^87 - 7 * q^88 - 34 * q^89 + 2 * q^90 + 5 * q^91 - 34 * q^92 + 8 * q^93 - 30 * q^94 + 24 * q^95 + 10 * q^96 + 30 * q^97 + 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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	$-0.988639\pi$
$2$	−0.240256	+	0.739431i	−0.169887	+	0.522857i	0.829477	+	0.558542i	$0.188639\pi$
$3$	−0.500000	+	0.363271i	−0.288675	+	0.209735i	−0.722692	−	0.691170i	$-0.757096\pi$
$3$	−0.500000	+	0.363271i	−0.288675	+	0.209735i	0.434017	+	0.900905i	$0.357096\pi$
$4$	1.12900	+	0.820265i	0.564499	+	0.410133i
$5$	−0.0687611	−	0.211625i	−0.0307509	−	0.0946416i	0.934503	−	0.355955i	$-0.115844\pi$
$5$	−0.0687611	−	0.211625i	−0.0307509	−	0.0946416i	−0.965254	+	0.261313i	$0.915844\pi$
$6$	−0.148486	−	0.456994i	−0.0606193	−	0.186567i
$7$	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
$9$	−0.809017	+	2.48990i	−0.269672	+	0.829966i
$10$	0.173002			0.0547082
$11$	0.660531	−	3.25018i	0.199158	−	0.979967i
$11$	0.660531	−	3.25018i	0.199158	−	0.979967i
$12$	−0.862478			−0.248976
$13$	2.01774	−	6.20997i	0.559620	−	1.72233i	−0.123798	−	0.992307i	$-0.539507\pi$
$13$	2.01774	−	6.20997i	0.559620	−	1.72233i	0.683418	−	0.730027i	$-0.260493\pi$
$14$	−0.628998	+	0.456994i	−0.168107	+	0.122137i
$15$	0.111258	+	0.0808336i	0.0287267	+	0.0208711i
$16$	0.228211	+	0.702362i	0.0570529	+	0.175591i
$17$	−1.33947	−	4.12246i	−0.324869	−	0.999844i	−0.971500	−	0.237041i	$-0.923822\pi$
$17$	−1.33947	−	4.12246i	−0.324869	−	0.999844i	0.646631	−	0.762803i	$-0.276178\pi$
$18$	−1.64674	−	1.19643i	−0.388140	−	0.282000i
$19$	−2.35829	+	1.71340i	−0.541029	+	0.393080i	−0.824467	−	0.565910i	$-0.808525\pi$
$19$	−2.35829	+	1.71340i	−0.541029	+	0.393080i	0.283438	+	0.958991i	$0.408525\pi$
$20$	0.0959574	−	0.295327i	0.0214567	−	0.0660370i
$21$	−0.618034			−0.134866
$22$	2.24459	+	1.26929i	0.478549	+	0.270614i
$23$	−3.89796			−0.812780			−0.406390	−	0.913700i	$-0.633213\pi$
$23$	−3.89796			−0.812780			−0.406390	+	0.913700i	$0.633213\pi$
$24$	0.504188	−	1.55173i	0.102917	−	0.316746i
$25$	4.00503	−	2.90982i	0.801006	−	0.581965i
$26$	4.10707	+	2.98396i	0.805463	+	0.585203i
$27$	−1.07295	−	3.30220i	−0.206489	−	0.635508i
$28$	0.431239	+	1.32722i	0.0814965	+	0.250820i
$29$	3.05322	+	2.21829i	0.566969	+	0.411927i	0.834003	−	0.551760i	$-0.186044\pi$
$29$	3.05322	+	2.21829i	0.566969	+	0.411927i	−0.267034	+	0.963687i	$0.586044\pi$
$30$	−0.0865012	+	0.0628468i	−0.0157929	+	0.0114742i
$31$	−2.12900	+	6.55238i	−0.382379	+	1.17684i	0.555984	+	0.831193i	$0.312341\pi$
$31$	−2.12900	+	6.55238i	−0.382379	+	1.17684i	−0.938364	+	0.345650i	$0.887659\pi$
$32$	−5.85410			−1.03487
$33$	0.850433	+	1.86504i	0.148041	+	0.324662i
$34$	3.37009			0.577966
$35$	0.0687611	−	0.211625i	0.0116228	−	0.0357712i
$36$	−2.95576	+	2.14748i	−0.492626	+	0.357914i
$37$	4.57379	+	3.32305i	0.751926	+	0.546306i	0.896423	−	0.443199i	$-0.146156\pi$
$37$	4.57379	+	3.32305i	0.751926	+	0.546306i	−0.144497	+	0.989505i	$0.546156\pi$
$38$	−0.700347	−	2.15545i	−0.113611	−	0.349660i
$39$	1.24703	+	3.83797i	0.199685	+	0.614567i
$40$	0.475243	+	0.345285i	0.0751426	+	0.0545943i
$41$	−1.08255	+	0.786521i	−0.169066	+	0.122834i	−0.669101	−	0.743171i	$-0.733321\pi$
$41$	−1.08255	+	0.786521i	−0.169066	+	0.122834i	0.500035	+	0.866005i	$0.333321\pi$
$42$	0.148486	−	0.456994i	0.0229119	−	0.0705157i
$43$	−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
$45$	0.582554			0.0868420
$46$	0.936507	−	2.88227i	0.138080	−	0.424968i
$47$	−4.89094	+	3.55348i	−0.713417	+	0.518328i	−0.884274	−	0.466968i	$-0.845346\pi$
$47$	−4.89094	+	3.55348i	−0.713417	+	0.518328i	0.170857	+	0.985296i	$0.445346\pi$
$48$	−0.369254	−	0.268279i	−0.0532972	−	0.0387227i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	1.18938	+	3.66055i	0.168204	+	0.517679i
$51$	2.16731	+	1.57464i	0.303484	+	0.220494i
$52$	7.37184	−	5.35596i	1.02229	−	0.742738i
$53$	−0.530865	+	1.63383i	−0.0729199	+	0.224424i	−0.980873	−	0.194646i	$-0.937644\pi$
$53$	−0.530865	+	1.63383i	−0.0729199	+	0.224424i	0.907954	+	0.419071i	$0.137644\pi$
$54$	2.69953			0.367360
$55$	−0.733239	+	0.0837016i	−0.0988700	+	0.0112863i
$56$	−2.63996			−0.352780
$57$	0.556717	−	1.71340i	0.0737389	−	0.226945i
$58$	−2.37383	+	1.72469i	−0.311699	+	0.226463i
$59$	7.71239	+	5.60338i	1.00407	+	0.729498i	0.962957	−	0.269657i	$-0.0869102\pi$
$59$	7.71239	+	5.60338i	1.00407	+	0.729498i	0.0411113	+	0.999155i	$0.486910\pi$
$60$	0.0593050	+	0.182522i	0.00765624	+	0.0235635i
$61$	−2.97566	−	9.15813i	−0.380994	−	1.17258i	−0.939345	−	0.342974i	$-0.888566\pi$
$61$	−2.97566	−	9.15813i	−0.380994	−	1.17258i	0.558351	−	0.829605i	$-0.311434\pi$
$62$	−4.33353	−	3.14850i	−0.550359	−	0.399859i
$63$	−2.11803	+	1.53884i	−0.266847	+	0.193876i
$64$	0.950059	−	2.92398i	0.118757	−	0.365498i
$65$	−1.45293			−0.180213
$66$	−1.58339	+	0.180749i	−0.194902	+	0.0222487i
$67$	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
$69$	1.94898	−	1.41602i	0.234629	−	0.170468i
$70$	0.139962	+	0.101688i	0.0167287	+	0.0121541i
$71$	−2.87670	−	8.85357i	−0.341401	−	1.05072i	−0.963482	−	0.267772i	$-0.913713\pi$
$71$	−2.87670	−	8.85357i	−0.341401	−	1.05072i	0.622081	−	0.782953i	$-0.286287\pi$
$72$	−2.13577	−	6.57324i	−0.251703	−	0.774663i
$73$	−4.52169	−	3.28520i	−0.529223	−	0.384503i	0.290844	−	0.956771i	$-0.406064\pi$
$73$	−4.52169	−	3.28520i	−0.529223	−	0.384503i	−0.820067	+	0.572267i	$0.806064\pi$
$74$	−3.55605	+	2.58362i	−0.413382	+	0.300340i
$75$	−0.945459	+	2.90982i	−0.109172	+	0.335997i
$76$	−4.06794			−0.466625
$77$	2.44479	−	2.24120i	0.278610	−	0.255409i
$78$	−3.13752			−0.355254
$79$	−1.39971	+	4.30785i	−0.157479	+	0.484671i	−0.998404	−	0.0564813i	$-0.982012\pi$
$79$	−1.39971	+	4.30785i	−0.157479	+	0.484671i	0.840924	+	0.541153i	$0.182012\pi$
$80$	0.132945	−	0.0965905i	0.0148638	−	0.0107991i
$81$	−4.61803	−	3.35520i	−0.513115	−	0.372800i
$82$	−0.321489	−	0.989441i	−0.0355025	−	0.109265i
$83$	3.48688	+	10.7315i	0.382734	+	1.17793i	0.938111	+	0.346336i	$0.112574\pi$
$83$	3.48688	+	10.7315i	0.382734	+	1.17793i	−0.555376	+	0.831599i	$0.687426\pi$
$84$	−0.697759	−	0.506952i	−0.0761318	−	0.0553130i
$85$	−0.780313	+	0.566931i	−0.0846368	+	0.0614922i
$86$	1.13117	−	3.48139i	0.121978	−	0.375408i
$87$	−2.33245			−0.250065
$88$	3.63267	+	7.96663i	0.387244	+	0.849245i
$89$	7.92157			0.839684			0.419842	−	0.907597i	$-0.362085\pi$
$89$	7.92157			0.839684			0.419842	+	0.907597i	$0.362085\pi$
$90$	−0.139962	+	0.430759i	−0.0147533	+	0.0454059i
$91$	5.28251	−	3.83797i	0.553758	−	0.402329i
$92$	−4.40079	−	3.19736i	−0.458814	−	0.333348i
$93$	−1.31579	−	4.04959i	−0.136441	−	0.419923i
$94$	−1.45248	−	4.47026i	−0.149811	−	0.461072i
$95$	0.524757	+	0.381258i	0.0538389	+	0.0391162i
$96$	2.92705	−	2.12663i	0.298741	−	0.217048i
$97$	−2.79781	+	8.61078i	−0.284075	+	0.874292i	0.702600	+	0.711585i	$0.252023\pi$
$97$	−2.79781	+	8.61078i	−0.284075	+	0.874292i	−0.986674	+	0.162707i	$0.947977\pi$
$98$	−0.777484			−0.0785378
$99$	7.55825	+	4.27411i	0.759633	+	0.429564i
$100$	6.90849			0.690849
$101$	−5.93627	+	18.2700i	−0.590681	+	1.81793i	−0.0155316	+	0.999879i	$0.504944\pi$
$101$	−5.93627	+	18.2700i	−0.590681	+	1.81793i	−0.575149	+	0.818049i	$0.695056\pi$
$102$	−1.68505	+	1.22426i	−0.166845	+	0.121220i
$103$	−13.1371	−	9.54464i	−1.29443	−	0.940461i	−0.294549	−	0.955636i	$-0.595169\pi$
$103$	−13.1371	−	9.54464i	−1.29443	−	0.940461i	−0.999885	+	0.0151755i	$0.995169\pi$
$104$	5.32676	+	16.3941i	0.522332	+	1.60757i
$105$	0.0424967	+	0.130791i	0.00414726	+	0.0127639i
$106$	−1.08057	−	0.785077i	−0.104954	−	0.0762534i
$107$	4.36332	−	3.17014i	0.421818	−	0.306469i	−0.356551	−	0.934276i	$-0.616047\pi$
$107$	4.36332	−	3.17014i	0.421818	−	0.306469i	0.778369	+	0.627807i	$0.216047\pi$
$108$	1.49732	−	4.60828i	0.144080	−	0.443432i
$109$	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
$111$	−3.49406			−0.331642
$112$	−0.228211	+	0.702362i	−0.0215640	+	0.0663670i
$113$	13.3457	−	9.69624i	1.25546	−	0.912145i	0.256935	−	0.966429i	$-0.417287\pi$
$113$	13.3457	−	9.69624i	1.25546	−	0.912145i	0.998526	+	0.0542834i	$0.0172875\pi$
$114$	1.13319	+	0.823308i	0.106133	+	0.0771098i
$115$	0.268028	+	0.824906i	0.0249937	+	0.0769228i
$116$	1.62749	+	5.00890i	0.151109	+	0.465065i
$117$	13.8298	+	10.0479i	1.27857	+	0.928932i
$118$	−5.99626	+	4.35654i	−0.552001	+	0.401052i
$119$	1.33947	−	4.12246i	0.122789	−	0.377906i
$120$	−0.363054			−0.0331421
$121$	−10.1274	−	4.29369i	−0.920673	−	0.390336i
$122$	7.48673			0.677816
$123$	0.255556	−	0.786521i	0.0230427	−	0.0709182i
$124$	−7.77832	+	5.65128i	−0.698514	+	0.507500i
$125$	−1.79128	−	1.30144i	−0.160217	−	0.116404i
$126$	−0.628998	−	1.93586i	−0.0560356	−	0.172460i
$127$	0.617194	+	1.89953i	0.0547671	+	0.168556i	0.974699	−	0.223523i	$-0.0717559\pi$
$127$	0.617194	+	1.89953i	0.0547671	+	0.168556i	−0.919931	+	0.392079i	$0.871756\pi$
$128$	−7.53831	−	5.47690i	−0.666299	−	0.484094i
$129$	2.35410	−	1.71036i	0.207267	−	0.150588i
$130$	0.349074	−	1.07434i	0.0306158	−	0.0942258i
$131$	1.37009			0.119706			0.0598528	−	0.998207i	$-0.480937\pi$
$131$	1.37009			0.119706			0.0598528	+	0.998207i	$0.480937\pi$
$132$	−0.569693	+	2.80321i	−0.0495854	+	0.243988i
$133$	−2.91501			−0.252763
$134$	−0.305497	+	0.940223i	−0.0263909	+	0.0812229i
$135$	−0.625051	+	0.454126i	−0.0537958	+	0.0390849i
$136$	9.25776	+	6.72615i	0.793846	+	0.576763i
$137$	0.772308	+	2.37692i	0.0659827	+	0.203074i	0.978612	−	0.205714i	$-0.0659516\pi$
$137$	0.772308	+	2.37692i	0.0659827	+	0.203074i	−0.912629	+	0.408788i	$0.865952\pi$
$138$	0.578793	+	1.78134i	0.0492702	+	0.151638i
$139$	3.85302	+	2.79938i	0.326809	+	0.237441i	0.739075	−	0.673623i	$-0.235263\pi$
$139$	3.85302	+	2.79938i	0.326809	+	0.237441i	−0.412266	+	0.911063i	$0.635263\pi$
$140$	0.251220	−	0.182522i	0.0212320	−	0.0154259i
$141$	1.15459	−	3.55348i	0.0972344	−	0.299257i
$142$	7.23775			0.607378
$143$	−18.8508	−	10.6599i	−1.57638	−	0.891426i
$144$	−1.93344			−0.161120
$145$	0.259504	−	0.798670i	0.0215506	−	0.0663260i
$146$	3.51554	−	2.55419i	0.290948	−	0.211386i
$147$	−0.500000	−	0.363271i	−0.0412393	−	0.0299621i
$148$	2.43801	+	7.50344i	0.200404	+	0.616779i
$149$	−2.23415	−	6.87600i	−0.183028	−	0.563304i	0.816880	−	0.576807i	$-0.195702\pi$
$149$	−2.23415	−	6.87600i	−0.183028	−	0.563304i	−0.999909	+	0.0135034i	$0.995702\pi$
$150$	−1.92446	−	1.39820i	−0.157132	−	0.114163i
$151$	−6.58514	+	4.78439i	−0.535891	+	0.389348i	−0.822557	−	0.568683i	$-0.807453\pi$
$151$	−6.58514	+	4.78439i	−0.535891	+	0.389348i	0.286666	+	0.958031i	$0.407453\pi$
$152$	2.37804	−	7.31886i	0.192885	−	0.593638i
$153$	11.3482			0.917445
$154$	1.06984	+	2.34622i	0.0862103	+	0.189064i
$155$	1.53304			0.123137
$156$	−1.74026	+	5.35596i	−0.139332	+	0.428820i
$157$	−16.3028	+	11.8447i	−1.30111	+	0.945311i	−0.999966	−	0.00826862i	$-0.997368\pi$
$157$	−16.3028	+	11.8447i	−1.30111	+	0.945311i	−0.301143	+	0.953579i	$0.597368\pi$
$158$	−2.84907	−	2.06997i	−0.226660	−	0.164678i
$159$	−0.328093	−	1.00977i	−0.0260194	−	0.0800796i
$160$	0.402535	+	1.23887i	0.0318232	+	0.0979416i
$161$	−3.15351	−	2.29116i	−0.248532	−	0.180569i
$162$	3.59045	−	2.60861i	0.282092	−	0.204952i
$163$	2.29739	−	7.07062i	0.179945	−	0.553814i	−0.819880	−	0.572536i	$-0.805960\pi$
$163$	2.29739	−	7.07062i	0.179945	−	0.553814i	0.999825	+	0.0187219i	$0.00595970\pi$
$164$	−1.86736			−0.145816
$165$	0.336213	−	0.308216i	0.0261742	−	0.0239945i
$166$	−8.77295			−0.680913
$167$	−0.683275	+	2.10290i	−0.0528734	+	0.162728i	−0.974006	−	0.226520i	$-0.927265\pi$
$167$	−0.683275	+	2.10290i	−0.0528734	+	0.162728i	0.921133	+	0.389248i	$0.127265\pi$
$168$	1.31998	−	0.959022i	0.101839	−	0.0739902i
$169$	−23.9752	−	17.4190i	−1.84424	−	1.33992i
$170$	−0.231732	−	0.713196i	−0.0177730	−	0.0546997i
$171$	−2.35829	−	7.25807i	−0.180343	−	0.555038i
$172$	−5.31555	−	3.86198i	−0.405307	−	0.294473i
$173$	8.38320	−	6.09075i	0.637363	−	0.463071i	−0.221581	−	0.975142i	$-0.571122\pi$
$173$	8.38320	−	6.09075i	0.637363	−	0.463071i	0.858943	+	0.512071i	$0.171122\pi$
$174$	0.560385	−	1.72469i	0.0424827	−	0.130748i
$175$	4.95049			0.374222
$176$	2.43355	−	0.277797i	0.183436	−	0.0209398i
$177$	−5.89174			−0.442851
$178$	−1.90320	+	5.85746i	−0.142651	+	0.439035i
$179$	18.9386	−	13.7597i	1.41554	−	1.02845i	0.423051	−	0.906106i	$-0.360959\pi$
$179$	18.9386	−	13.7597i	1.41554	−	1.02845i	0.992488	−	0.122343i	$-0.0390408\pi$
$180$	0.657702	+	0.477849i	0.0490222	+	0.0356167i
$181$	−4.23851	−	13.0448i	−0.315046	−	0.969611i	−0.975736	−	0.218952i	$-0.929736\pi$
$181$	−4.23851	−	13.0448i	−0.315046	−	0.969611i	0.660690	−	0.750659i	$-0.270264\pi$
$182$	1.56876	+	4.82815i	0.116284	+	0.357886i
$183$	4.81471	+	3.49809i	0.355914	+	0.258587i
$184$	8.32516	−	6.04858i	0.613739	−	0.445907i
$185$	0.388742	−	1.19643i	0.0285809	−	0.0879629i
$186$	3.31052			0.242739
$187$	−14.2835	+	1.63051i	−1.04451	+	0.119235i
$188$	−8.43666			−0.615306
$189$	1.07295	−	3.30220i	0.0780456	−	0.240200i
$190$	−0.407990	+	0.296422i	−0.0295987	+	0.0215047i
$191$	9.72838	+	7.06808i	0.703921	+	0.511429i	0.881207	−	0.472731i	$-0.156732\pi$
$191$	9.72838	+	7.06808i	0.703921	+	0.511429i	−0.177286	+	0.984159i	$0.556732\pi$
$192$	0.587169	+	1.80712i	0.0423753	+	0.130418i
$193$	4.90840	+	15.1065i	0.353315	+	1.08739i	0.956980	+	0.290153i	$0.0937062\pi$
$193$	4.90840	+	15.1065i	0.353315	+	1.08739i	−0.603666	+	0.797238i	$0.706294\pi$
$194$	−5.69489	−	4.13758i	−0.408869	−	0.297061i
$195$	0.726463	−	0.527806i	0.0520231	−	0.0377970i
$196$	−0.431239	+	1.32722i	−0.0308028	+	0.0948012i
$197$	12.3035			0.876590			0.438295	−	0.898831i	$-0.355582\pi$
$197$	12.3035			0.876590			0.438295	+	0.898831i	$0.355582\pi$
$198$	−4.97632	+	4.56193i	−0.353652	+	0.324202i
$199$	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
$201$	−0.635774	+	0.461917i	−0.0448440	+	0.0325811i
$202$	−12.0832	−	8.77892i	−0.850168	−	0.617683i
$203$	1.16623	+	3.58928i	0.0818530	+	0.251918i
$204$	1.15526	+	3.55553i	0.0808845	+	0.248937i
$205$	0.240885	+	0.175013i	0.0168242	+	0.0122235i
$206$	10.2139	−	7.42080i	0.711633	−	0.517032i
$207$	3.15351	−	9.70552i	0.219184	−	0.674580i
$208$	4.82212			0.334354
$209$	4.01114	+	8.79663i	0.277456	+	0.608476i
$210$	−0.106921			−0.00737828
$211$	2.76058	−	8.49620i	0.190046	−	0.584903i	−0.809952	−	0.586496i	$-0.800507\pi$
$211$	2.76058	−	8.49620i	0.190046	−	0.584903i	0.999999	+	0.00159295i	$0.000507051\pi$
$212$	−1.93952	+	1.40915i	−0.133207	+	0.0967805i
$213$	4.65459	+	3.38176i	0.318928	+	0.231714i
$214$	1.29579	+	3.98802i	0.0885781	+	0.272615i
$215$	0.323742	+	0.996374i	0.0220790	+	0.0679521i
$216$	7.41570	+	5.38782i	0.504574	+	0.366595i
$217$	−5.57379	+	4.04959i	−0.378373	+	0.274904i
$218$	−1.29714	+	3.99220i	−0.0878537	+	0.270386i
$219$	3.45426			0.233417
$220$	−0.896483	−	0.506952i	−0.0604409	−	0.0341787i
$221$	−28.3031			−1.90387
$222$	0.839469	−	2.58362i	0.0563415	−	0.173401i
$223$	−0.578645	+	0.420410i	−0.0387489	+	0.0281527i	−0.606991	−	0.794709i	$-0.707624\pi$
$223$	−0.578645	+	0.420410i	−0.0387489	+	0.0281527i	0.568242	+	0.822861i	$0.307624\pi$
$224$	−4.73607	−	3.44095i	−0.316442	−	0.229908i
$225$	4.00503	+	12.3262i	0.267002	+	0.821747i
$226$	3.96331	+	12.1978i	0.263636	+	0.811387i
$227$	4.30528	+	3.12797i	0.285751	+	0.207611i	0.721422	−	0.692496i	$-0.243489\pi$
$227$	4.30528	+	3.12797i	0.285751	+	0.207611i	−0.435671	+	0.900106i	$0.643489\pi$
$228$	2.03397	−	1.47777i	0.134703	−	0.0978675i
$229$	−2.04208	+	6.28489i	−0.134945	+	0.415317i	−0.995581	−	0.0939024i	$-0.970066\pi$
$229$	−2.04208	+	6.28489i	−0.134945	+	0.415317i	0.860637	+	0.509219i	$0.170066\pi$
$230$	−0.674356			−0.0444657
$231$	−0.408230	+	2.00872i	−0.0268596	+	0.132164i
$232$	−9.96318			−0.654115
$233$	−2.95332	+	9.08937i	−0.193478	+	0.595464i	0.806513	+	0.591217i	$0.201352\pi$
$233$	−2.95332	+	9.08937i	−0.193478	+	0.595464i	−0.999991	+	0.00424788i	$0.998648\pi$
$234$	−10.7524	+	7.81211i	−0.702910	+	0.510694i
$235$	1.08831	+	0.790705i	0.0709936	+	0.0515799i
$236$	4.11102	+	12.6524i	0.267604	+	0.823602i
$237$	−0.865066	−	2.66240i	−0.0561921	−	0.172941i
$238$	2.72646	+	1.98089i	0.176730	+	0.128402i
$239$	−21.7194	+	15.7801i	−1.40491	+	1.02073i	−0.410872	+	0.911693i	$0.634776\pi$
$239$	−21.7194	+	15.7801i	−1.40491	+	1.02073i	−0.994038	+	0.109034i	$0.965224\pi$
$240$	−0.0313842	+	0.0965905i	−0.00202584	+	0.00623489i
$241$	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
$243$	13.9443			0.894525
$244$	4.15258	−	12.7803i	0.265842	−	0.818177i
$245$	0.180019	−	0.130791i	0.0115010	−	0.00835596i
$246$	0.520180	+	0.377933i	0.0331654	+	0.0240961i
$247$	5.88173	+	18.1021i	0.374245	+	1.15181i
$248$	−5.62047	−	17.2980i	−0.356900	−	1.09843i
$249$	−5.64188	−	4.09907i	−0.357540	−	0.259768i
$250$	1.39269	−	1.01185i	0.0880814	−	0.0639949i
$251$	9.07680	−	27.9355i	0.572923	−	1.76328i	−0.0702229	−	0.997531i	$-0.522371\pi$
$251$	9.07680	−	27.9355i	0.572923	−	1.76328i	0.643146	−	0.765744i	$-0.277629\pi$
$252$	−3.65351			−0.230150
$253$	−2.57472	+	12.6691i	−0.161871	+	0.796498i
$254$	−1.55285			−0.0974348
$255$	0.184207	−	0.566931i	0.0115355	−	0.0355026i
$256$	10.8355	−	7.87245i	0.677218	−	0.492028i
$257$	13.6856	+	9.94320i	0.853687	+	0.620240i	0.926160	−	0.377130i	$-0.123089\pi$
$257$	13.6856	+	9.94320i	0.853687	+	0.620240i	−0.0724730	+	0.997370i	$0.523089\pi$
$258$	0.699104	+	2.15162i	0.0435243	+	0.133954i
$259$	1.74703	+	5.37681i	0.108555	+	0.334099i
$260$	−1.64035	−	1.19178i	−0.101730	−	0.0739114i
$261$	−7.99343	+	5.80757i	−0.494781	+	0.359480i
$262$	−0.329173	+	1.01309i	−0.0203364	+	0.0625889i
$263$	−8.18034			−0.504421			−0.252211	−	0.967672i	$-0.581158\pi$
$263$	−8.18034			−0.504421			−0.252211	+	0.967672i	$0.581158\pi$
$264$	−4.71038	−	2.66367i	−0.289904	−	0.163938i
$265$	0.382263			0.0234822
$266$	0.700347	−	2.15545i	0.0429411	−	0.132159i
$267$	−3.96078	+	2.87768i	−0.242396	+	0.176111i
$268$	1.43558	+	1.04301i	0.0876917	+	0.0637118i
$269$	−1.93048	−	5.94140i	−0.117703	−	0.362254i	0.874798	−	0.484488i	$-0.160994\pi$
$269$	−1.93048	−	5.94140i	−0.117703	−	0.362254i	−0.992501	+	0.122234i	$0.960994\pi$
$270$	−0.185623	−	0.571288i	−0.0112966	−	0.0347675i
$271$	−6.36444	−	4.62403i	−0.386612	−	0.280890i	0.377454	−	0.926028i	$-0.376800\pi$
$271$	−6.36444	−	4.62403i	−0.386612	−	0.280890i	−0.764066	+	0.645138i	$0.776800\pi$
$272$	2.58978	−	1.88159i	0.157029	−	0.114088i
$273$	−1.24703	+	3.83797i	−0.0754738	+	0.232284i
$274$	−1.94312			−0.117388
$275$	−6.81202	−	14.9391i	−0.410780	−	0.900862i
$276$	3.36190			0.202363
$277$	3.72293	−	11.4580i	0.223689	−	0.688444i	−0.774733	−	0.632289i	$-0.782116\pi$
$277$	3.72293	−	11.4580i	0.223689	−	0.688444i	0.998422	−	0.0561556i	$-0.0178843\pi$
$278$	−2.99566	+	2.17648i	−0.179668	+	0.130536i
$279$	−14.5924	−	10.6020i	−0.873622	−	0.634724i
$280$	0.181527	+	0.558682i	0.0108483	+	0.0333876i
$281$	6.53723	+	20.1195i	0.389978	+	1.20023i	0.932804	+	0.360384i	$0.117354\pi$
$281$	6.53723	+	20.1195i	0.389978	+	1.20023i	−0.542826	+	0.839846i	$0.682646\pi$
$282$	2.35015	+	1.70749i	0.139950	+	0.101679i
$283$	20.2281	−	14.6966i	1.20244	−	0.873623i	0.207916	−	0.978147i	$-0.433332\pi$
$283$	20.2281	−	14.6966i	1.20244	−	0.873623i	0.994522	+	0.104524i	$0.0333319\pi$
$284$	4.01448	−	12.3553i	0.238216	−	0.733153i
$285$	−0.400878			−0.0237460
$286$	12.4113	−	11.3777i	0.733894	−	0.672780i
$287$	−1.33811			−0.0789861
$288$	4.73607	−	14.5761i	0.279075	−	0.858906i
$289$	−1.44723	+	1.05147i	−0.0851312	+	0.0618515i
$290$	0.528215	+	0.383770i	0.0310178	+	0.0225358i
$291$	−1.72914	−	5.32176i	−0.101364	−	0.311967i
$292$	−2.41024	−	7.41796i	−0.141049	−	0.434104i
$293$	0.368173	+	0.267494i	0.0215089	+	0.0156271i	0.598488	−	0.801132i	$-0.295769\pi$
$293$	0.368173	+	0.267494i	0.0215089	+	0.0156271i	−0.576979	+	0.816759i	$0.695769\pi$
$294$	0.388742	−	0.282438i	0.0226719	−	0.0164721i
$295$	0.655503	−	2.01743i	0.0381648	−	0.117459i
$296$	−14.9251			−0.867502
$297$	−11.4415	+	1.30608i	−0.663901	+	0.0757864i
$298$	5.62110			0.325621
$299$	−7.86507	+	24.2062i	−0.454849	+	1.39988i
$300$	−3.45425	+	2.50966i	−0.199431	+	0.144895i
$301$	−3.80902	−	2.76741i	−0.219548	−	0.159511i
$302$	−1.95561	−	6.01874i	−0.112533	−	0.346339i
$303$	−3.66881	−	11.2915i	−0.210768	−	0.648677i
$304$	−1.74162	−	1.26536i	−0.0998885	−	0.0725732i
$305$	−1.73348	+	1.25945i	−0.0992588	+	0.0721157i
$306$	−2.72646	+	8.39119i	−0.155862	+	0.479692i
$307$	−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
$309$	10.0358			0.570918
$310$	−0.368322	+	1.13358i	−0.0209193	+	0.0643829i
$311$	−0.110807	+	0.0805059i	−0.00628328	+	0.00456507i	−0.590922	−	0.806728i	$-0.701236\pi$
$311$	−0.110807	+	0.0805059i	−0.00628328	+	0.00456507i	0.584639	+	0.811293i	$0.301236\pi$
$312$	−8.61887	−	6.26198i	−0.487948	−	0.354515i
$313$	−4.72485	−	14.5416i	−0.267064	−	0.821939i	−0.991211	−	0.132293i	$-0.957766\pi$
$313$	−4.72485	−	14.5416i	−0.267064	−	0.821939i	0.724146	−	0.689646i	$-0.242234\pi$
$314$	−4.84150	−	14.9006i	−0.273221	−	0.840889i
$315$	0.471296	+	0.342417i	0.0265545	+	0.0192930i
$316$	−5.11385	+	3.71543i	−0.287676	+	0.209009i
$317$	−10.1953	+	31.3778i	−0.572622	+	1.76235i	0.0715138	+	0.997440i	$0.477217\pi$
$317$	−10.1953	+	31.3778i	−0.572622	+	1.76235i	−0.644136	+	0.764911i	$0.722783\pi$
$318$	0.825478			0.0462905
$319$	9.22661	−	8.45828i	0.516591	−	0.473573i
$320$	−0.684115			−0.0382432
$321$	−1.03004	+	3.17014i	−0.0574912	+	0.176940i
$322$	2.45181	−	1.78134i	0.136634	−	0.0992703i
$323$	10.2223	+	7.42692i	0.568783	+	0.413245i
$324$	−2.46160	−	7.57602i	−0.136756	−	0.420890i
$325$	−9.98880	−	30.7424i	−0.554079	−	1.70528i
$326$	4.67628	+	3.39752i	0.258995	+	0.188171i
$327$	−2.69951	+	1.96131i	−0.149283	+	0.108461i
$328$	1.09162	−	3.35966i	0.0602747	−	0.185506i
$329$	−6.04554			−0.333301
$330$	0.147127	+	0.322657i	0.00809908	+	0.0177617i
$331$	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
$333$	−11.9743	+	8.69986i	−0.656190	+	0.476750i
$334$	−1.39079	−	1.01047i	−0.0761008	−	0.0552905i
$335$	−0.0874331	−	0.269091i	−0.00477698	−	0.0147020i
$336$	−0.141042	−	0.434084i	−0.00769449	−	0.0236812i
$337$	−4.55497	−	3.30938i	−0.248125	−	0.180273i	0.456770	−	0.889585i	$-0.349006\pi$
$337$	−4.55497	−	3.30938i	−0.248125	−	0.180273i	−0.704895	+	0.709311i	$0.749006\pi$
$338$	18.6403	−	13.5430i	1.01390	−	0.736641i
$339$	−3.15050	+	9.69624i	−0.171112	+	0.526627i
$340$	−1.34600			−0.0729974
$341$	19.8902	+	11.2477i	1.07711	+	0.609096i
$342$	5.93344			0.320844
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	10.0557	−	7.30586i	0.542165	−	0.393906i
$345$	−0.433679	−	0.315086i	−0.0233485	−	0.0169637i
$346$	2.48958	+	7.66214i	0.133841	+	0.411919i
$347$	2.69791	+	8.30331i	0.144831	+	0.445745i	0.996989	−	0.0775398i	$-0.0247065\pi$
$347$	2.69791	+	8.30331i	0.144831	+	0.445745i	−0.852158	+	0.523285i	$0.824706\pi$
$348$	−2.63333	−	1.91323i	−0.141162	−	0.102560i
$349$	−14.9401	+	10.8546i	−0.799724	+	0.581034i	−0.910833	−	0.412774i	$-0.864560\pi$
$349$	−14.9401	+	10.8546i	−0.799724	+	0.581034i	0.111109	+	0.993808i	$0.464560\pi$
$350$	−1.18938	+	3.66055i	−0.0635752	+	0.195664i
$351$	−22.6715			−1.21011
$352$	−3.86681	+	19.0269i	−0.206102	+	1.01414i
$353$	−23.4857			−1.25002			−0.625009	−	0.780618i	$-0.714905\pi$
$353$	−23.4857			−1.25002			−0.625009	+	0.780618i	$0.714905\pi$
$354$	1.41553	−	4.35654i	0.0752343	−	0.231547i
$355$	−1.67583	+	1.21756i	−0.0889439	+	0.0646215i
$356$	8.94343	+	6.49778i	0.474001	+	0.344382i
$357$	0.827838	+	2.54782i	0.0438138	+	0.134845i
$358$	5.62425	+	17.3097i	0.297251	+	0.914844i
$359$	−12.0391	−	8.74695i	−0.635402	−	0.461647i	0.222865	−	0.974849i	$-0.428459\pi$
$359$	−12.0391	−	8.74695i	−0.635402	−	0.461647i	−0.858267	+	0.513203i	$0.828459\pi$
$360$	−1.24420	+	0.903967i	−0.0655753	+	0.0476432i
$361$	−3.24552	+	9.98870i	−0.170817	+	0.525721i
$362$	10.6641			0.560490
$363$	6.62347	−	1.53215i	0.347642	−	0.0804168i
$364$	9.11210			0.477604
$365$	−0.384314	+	1.18280i	−0.0201159	+	0.0619104i
$366$	−3.74336	+	2.71971i	−0.195669	+	0.142162i
$367$	27.6894	+	20.1175i	1.44537	+	1.05012i	0.986885	+	0.161424i	$0.0516085\pi$
$367$	27.6894	+	20.1175i	1.44537	+	1.05012i	0.458487	+	0.888701i	$0.348391\pi$
$368$	−0.889558	−	2.73778i	−0.0463714	−	0.142717i
$369$	−1.08255	−	3.33176i	−0.0563555	−	0.173444i
$370$	0.791277	+	0.574896i	0.0411365	+	0.0298874i
$371$	−1.38982	+	1.00977i	−0.0721560	+	0.0524244i
$372$	1.83621	−	5.65128i	0.0952032	−	0.293005i
$373$	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
$375$	1.36841			0.0706646
$376$	4.93191	−	15.1788i	0.254344	−	0.782789i
$377$	19.9361	−	14.4845i	1.02676	−	0.745987i
$378$	2.18397	+	1.58674i	0.112331	+	0.0816133i
$379$	−1.89252	−	5.82457i	−0.0972121	−	0.299188i	0.890612	−	0.454764i	$-0.150277\pi$
$379$	−1.89252	−	5.82457i	−0.0972121	−	0.299188i	−0.987824	+	0.155576i	$0.950277\pi$
$380$	0.279717	+	0.860879i	0.0143492	+	0.0441622i
$381$	−0.998641	−	0.725555i	−0.0511619	−	0.0371713i
$382$	−7.56367	+	5.49532i	−0.386991	+	0.281165i
$383$	1.35689	−	4.17607i	0.0693338	−	0.213387i	−0.910386	−	0.413760i	$-0.864215\pi$
$383$	1.35689	−	4.17607i	0.0693338	−	0.213387i	0.979720	+	0.200373i	$0.0642153\pi$
$384$	5.75876			0.293875
$385$	−0.642402	−	0.363271i	−0.0327398	−	0.0185140i
$386$	−12.3495			−0.628573
$387$	3.80902	−	11.7229i	0.193623	−	0.595911i
$388$	−10.2218	+	7.42661i	−0.518936	+	0.377029i
$389$	−8.49145	−	6.16940i	−0.430533	−	0.312801i	0.351329	−	0.936252i	$-0.385730\pi$
$389$	−8.49145	−	6.16940i	−0.430533	−	0.312801i	−0.781862	+	0.623451i	$0.785730\pi$
$390$	0.215740	+	0.663978i	0.0109244	+	0.0336218i
$391$	5.22119	+	16.0692i	0.264047	+	0.812654i
$392$	−2.13577	−	1.55173i	−0.107873	−	0.0783742i
$393$	−0.685047	+	0.497716i	−0.0345560	+	0.0251064i
$394$	−2.95600	+	9.09762i	−0.148921	+	0.458331i
$395$	1.00789			0.0507127
$396$	5.02734	+	11.0252i	0.252634	+	0.554038i
$397$	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
$399$	1.45750	−	1.05894i	0.0729664	−	0.0530132i
$400$	2.95774	+	2.14893i	0.147887	+	0.107446i
$401$	−1.46009	−	4.49370i	−0.0729135	−	0.224405i	0.907958	−	0.419061i	$-0.137641\pi$
$401$	−1.46009	−	4.49370i	−0.0729135	−	0.224405i	−0.980871	+	0.194657i	$0.937641\pi$
$402$	−0.188807	−	0.581090i	−0.00941686	−	0.0289821i
$403$	36.3943	+	26.4420i	1.81293	+	1.31717i
$404$	−21.6882	+	15.7574i	−1.07903	+	0.783961i
$405$	−0.392503	+	1.20800i	−0.0195036	+	0.0600260i
$406$	−2.93422			−0.145623
$407$	13.8217	−	12.6707i	0.685114	−	0.628062i
$408$	−7.07230			−0.350131
$409$	0.761863	−	2.34477i	0.0376717	−	0.115942i	−0.930452	−	0.366413i	$-0.880586\pi$
$409$	0.761863	−	2.34477i	0.0376717	−	0.115942i	0.968124	+	0.250472i	$0.0805857\pi$
$410$	−0.187285	+	0.136070i	−0.00924932	+	0.00672003i
$411$	−1.24962	−	0.907902i	−0.0616392	−	0.0447835i
$412$	−7.00259	−	21.5518i	−0.344993	−	1.06178i
$413$	2.94587	+	9.06646i	0.144957	+	0.446131i
$414$	6.41892	+	4.66362i	0.315472	+	0.229204i
$415$	2.03129	−	1.47582i	0.0997122	−	0.0724452i
$416$	−11.8121	+	36.3538i	−0.579134	+	1.78239i
$417$	−2.94345			−0.144141
$418$	−7.46820	+	0.852519i	−0.365282	+	0.0416981i
$419$	−14.3399			−0.700548			−0.350274	−	0.936647i	$-0.613912\pi$
$419$	−14.3399			−0.700548			−0.350274	+	0.936647i	$0.613912\pi$
$420$	−0.0593050	+	0.182522i	−0.00289379	+	0.00890616i
$421$	14.0087	−	10.1779i	0.682744	−	0.496043i	−0.191523	−	0.981488i	$-0.561343\pi$
$421$	14.0087	−	10.1779i	0.682744	−	0.496043i	0.874267	+	0.485446i	$0.161343\pi$
$422$	5.61911	+	4.08253i	0.273534	+	0.198734i
$423$	−4.89094	−	15.0528i	−0.237806	−	0.731891i
$424$	−1.40146	−	4.31326i	−0.0680611	−	0.209470i
$425$	−17.3602	−	12.6130i	−0.842096	−	0.611818i
$426$	−3.61887	+	2.62927i	−0.175335	+	0.127388i
$427$	2.97566	−	9.15813i	0.144002	−	0.443193i
$428$	7.52653			0.363808
$429$	13.2978	−	1.51799i	0.642024	−	0.0732891i
$430$	−0.814531			−0.0392802
$431$	8.61919	−	26.5272i	0.415172	−	1.27777i	−0.496925	−	0.867794i	$-0.665538\pi$
$431$	8.61919	−	26.5272i	0.415172	−	1.27777i	0.912097	−	0.409975i	$-0.134462\pi$
$432$	2.07448	−	1.50720i	0.0998085	−	0.0725151i
$433$	23.9040	+	17.3673i	1.14875	+	0.834619i	0.988315	−	0.152426i	$-0.0487087\pi$
$433$	23.9040	+	17.3673i	1.14875	+	0.834619i	0.160440	+	0.987046i	$0.448709\pi$
$434$	−1.65526	−	5.09437i	−0.0794551	−	0.244538i
$435$	0.160382	+	0.493605i	0.00768973	+	0.0236666i
$436$	6.09548	+	4.42862i	0.291920	+	0.212093i
$437$	9.19251	−	6.67875i	0.439738	−	0.319488i
$438$	−0.829907	+	2.55419i	−0.0396545	+	0.122044i
$439$	−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
$441$	−2.61803			−0.124668
$442$	6.79997	−	20.9282i	0.323442	−	0.995451i
$443$	−8.35449	+	6.06989i	−0.396934	+	0.288389i	−0.768291	−	0.640101i	$-0.778893\pi$
$443$	−8.35449	+	6.06989i	−0.396934	+	0.288389i	0.371357	+	0.928490i	$0.378893\pi$
$444$	−3.94479	−	2.86606i	−0.187211	−	0.136017i
$445$	−0.544696	−	1.67640i	−0.0258211	−	0.0794691i
$446$	−0.171842	−	0.528874i	−0.00813694	−	0.0250429i
$447$	3.61493	+	2.62640i	0.170980	+	0.124224i
$448$	2.48729	−	1.80712i	0.117513	−	0.0853784i
$449$	−0.852224	+	2.62287i	−0.0402189	+	0.123781i	−0.969150	−	0.246471i	$-0.920729\pi$
$449$	−0.852224	+	2.62287i	−0.0402189	+	0.123781i	0.928931	+	0.370253i	$0.120729\pi$
$450$	−10.0766			−0.475016
$451$	1.84128	+	4.03802i	0.0867025	+	0.190143i
$452$	23.0208			1.08281
$453$	1.55454	−	4.78439i	0.0730387	−	0.224790i
$454$	−3.34729	+	2.43195i	−0.157096	+	0.114137i
$455$	−1.17544	−	0.854009i	−0.0551056	−	0.0400365i
$456$	1.46971	+	4.52331i	0.0688255	+	0.211823i
$457$	−12.4628	−	38.3566i	−0.582986	−	1.79425i	−0.607213	−	0.794539i	$-0.707713\pi$
$457$	−12.4628	−	38.3566i	−0.582986	−	1.79425i	0.0242276	−	0.999706i	$-0.492287\pi$
$458$	−4.15662	−	3.01996i	−0.194226	−	0.141114i
$459$	−12.1760	+	8.84638i	−0.568327	+	0.412914i
$460$	−0.374038	+	1.15117i	−0.0174396	+	0.0536736i
$461$	−34.2251			−1.59402			−0.797011	−	0.603965i	$-0.793587\pi$
$461$	−34.2251			−1.59402			−0.797011	+	0.603965i	$0.793587\pi$
$462$	−1.38723	−	0.784466i	−0.0645400	−	0.0364967i
$463$	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
$465$	−0.766520	+	0.556910i	−0.0355465	+	0.0258261i
$466$	−6.01142	−	4.36755i	−0.278473	−	0.202323i
$467$	−8.83555	−	27.1930i	−0.408860	−	1.25834i	−0.917629	−	0.397439i	$-0.869899\pi$
$467$	−8.83555	−	27.1930i	−0.408860	−	1.25834i	0.508768	−	0.860904i	$-0.330101\pi$
$468$	7.37184	+	22.6882i	0.340764	+	1.04876i
$469$	1.02870	+	0.747397i	0.0475011	+	0.0345116i
$470$	−0.846145	+	0.614760i	−0.0390298	+	0.0283568i
$471$	3.84858	−	11.8447i	0.177333	−	0.545775i
$472$	−25.1669			−1.15840
$473$	−3.10991	+	15.3025i	−0.142994	+	0.703611i
$474$	2.17650			0.0999699
$475$	−4.45933	+	13.7244i	−0.204608	+	0.629719i
$476$	4.89377	−	3.55553i	0.224306	−	0.162968i
$477$	−3.63860	−	2.64360i	−0.166600	−	0.121042i
$478$	−6.45006	−	19.8512i	−0.295019	−	0.907975i
$479$	−1.57511	−	4.84769i	−0.0719686	−	0.221497i	0.908602	−	0.417663i	$-0.137151\pi$
$479$	−1.57511	−	4.84769i	−0.0719686	−	0.221497i	−0.980571	+	0.196166i	$0.937151\pi$
$480$	−0.651315	−	0.473208i	−0.0297283	−	0.0215989i
$481$	29.8648	−	21.6980i	1.36172	−	0.989344i
$482$	−4.53274	+	13.9503i	−0.206461	+	0.635421i
$483$	2.40907			0.109617
$484$	−7.91185	−	13.1547i	−0.359629	−	0.597942i
$485$	2.01464			0.0914800
$486$	−3.35019	+	10.3108i	−0.151968	+	0.467709i
$487$	−23.6138	+	17.1564i	−1.07004	+	0.777433i	−0.975920	−	0.218128i	$-0.930005\pi$
$487$	−23.6138	+	17.1564i	−1.07004	+	0.777433i	−0.0941240	+	0.995560i	$0.530005\pi$
$488$	20.5663	+	14.9423i	0.930992	+	0.676405i
$489$	1.41986	+	4.36989i	0.0642084	+	0.197613i
$490$	0.0534607	+	0.164535i	0.00241511	+	0.00743294i
$491$	−24.3870	−	17.7182i	−1.10057	−	0.799610i	−0.119416	−	0.992844i	$-0.538102\pi$
$491$	−24.3870	−	17.7182i	−1.10057	−	0.799610i	−0.981153	+	0.193235i	$0.938102\pi$
$492$	0.933679	−	0.678357i	0.0420935	−	0.0305827i
$493$	5.05514	−	15.5581i	0.227672	−	0.700703i
$494$	−14.7984			−0.665810
$495$	0.384795	−	1.89341i	0.0172952	−	0.0851023i
$496$	−5.08801			−0.228458
$497$	2.87670	−	8.85357i	0.129038	−	0.397137i
$498$	4.38647	−	3.18696i	0.196563	−	0.142811i
$499$	−4.81450	−	3.49794i	−0.215526	−	0.156589i	0.474784	−	0.880102i	$-0.342526\pi$
$499$	−4.81450	−	3.49794i	−0.215526	−	0.156589i	−0.690311	+	0.723513i	$0.742526\pi$
$500$	−0.954823	−	2.93864i	−0.0427010	−	0.131420i
$501$	−0.422287	−	1.29967i	−0.0188664	−	0.0580648i
$502$	18.4757	+	13.4233i	0.824609	+	0.599113i
$503$	4.02773	−	2.92632i	0.179588	−	0.130478i	−0.494360	−	0.869257i	$-0.664597\pi$
$503$	4.02773	−	2.92632i	0.179588	−	0.130478i	0.673947	+	0.738779i	$0.264597\pi$
$504$	2.13577	−	6.57324i	0.0951349	−	0.292795i
$505$	4.27456			0.190216
$506$	−8.74933	−	4.94765i	−0.388955	−	0.219950i
$507$	18.3154			0.813416
$508$	−0.861305	+	2.65083i	−0.0382142	+	0.117611i
$509$	17.2551	−	12.5366i	0.764821	−	0.555675i	−0.135565	−	0.990769i	$-0.543285\pi$
$509$	17.2551	−	12.5366i	0.764821	−	0.555675i	0.900385	+	0.435094i	$0.143285\pi$
$510$	0.374949	+	0.272417i	0.0166030	+	0.0120628i
$511$	−1.72713	−	5.31556i	−0.0764038	−	0.235147i
$512$	−2.54091	−	7.82012i	−0.112293	−	0.345604i
$513$	8.18830	+	5.94915i	0.361522	+	0.262661i
$514$	−10.6404	+	7.73068i	−0.469327	+	0.340986i
$515$	−1.11656	+	3.43643i	−0.0492017	+	0.151427i
$516$	4.06072			0.178763
$517$	8.31884	+	18.2436i	0.365862	+	0.802354i
$518$	−4.39552			−0.193128
$519$	−1.97900	+	6.09075i	−0.0868686	+	0.267354i
$520$	3.10312	−	2.25455i	0.136081	−	0.0988686i
$521$	17.9103	+	13.0126i	0.784664	+	0.570092i	0.906375	−	0.422473i	$-0.138838\pi$
$521$	17.9103	+	13.0126i	0.784664	+	0.570092i	−0.121711	+	0.992566i	$0.538838\pi$
$522$	−2.37383	−	7.30590i	−0.103900	−	0.319771i
$523$	1.51773	+	4.67108i	0.0663655	+	0.204252i	0.978740	−	0.205104i	$-0.0657533\pi$
$523$	1.51773	+	4.67108i	0.0663655	+	0.204252i	−0.912375	+	0.409356i	$0.865753\pi$
$524$	1.54683	+	1.12384i	0.0675737	+	0.0490952i
$525$	−2.47524	+	1.79837i	−0.108028	+	0.0784873i
$526$	1.96537	−	6.04880i	0.0856944	−	0.263740i
$527$	29.8637			1.30088
$528$	−1.11586	+	1.02294i	−0.0485615	+	0.0445176i
$529$	−7.80592			−0.339388
$530$	−0.0918410	+	0.282657i	−0.00398932	+	0.0122779i
$531$	−20.1913	+	14.6698i	−0.876228	+	0.636617i
$532$	−3.29104	−	2.39108i	−0.142685	−	0.103666i
$533$	2.69996	+	8.30962i	0.116948	+	0.359929i
$534$	−1.17624	−	3.62011i	−0.0509010	−	0.156657i
$535$	−0.970907	−	0.705405i	−0.0419760	−	0.0304973i
$536$	−2.71574	+	1.97310i	−0.117302	+	0.0852250i
$537$	−4.47080	+	13.7597i	−0.192929	+	0.593775i
$538$	4.85707			0.209403
$539$	3.29522	−	0.376160i	0.141935	−	0.0162024i
$540$	−1.07818			−0.0463977
$541$	5.99013	−	18.4357i	0.257536	−	0.792614i	−0.735784	−	0.677217i	$-0.763186\pi$
$541$	5.99013	−	18.4357i	0.257536	−	0.792614i	0.993319	−	0.115397i	$-0.0368141\pi$
$542$	4.94825	−	3.59511i	0.212546	−	0.154423i
$543$	6.85805	+	4.98266i	0.294307	+	0.213827i
$544$	7.84139	+	24.1333i	0.336197	+	1.03471i
$545$	−0.371242	−	1.14257i	−0.0159023	−	0.0489422i
$546$	−2.53831	−	1.84419i	−0.108630	−	0.0789240i
$547$	−11.6904	+	8.49354i	−0.499843	+	0.363158i	−0.808957	−	0.587868i	$-0.799968\pi$
$547$	−11.6904	+	8.49354i	−0.499843	+	0.363158i	0.309114	+	0.951025i	$0.399968\pi$
$548$	−1.07777	+	3.31703i	−0.0460400	+	0.141697i
$549$	25.2102			1.07594
$550$	12.6831	−	1.44781i	0.540808	−	0.0617349i
$551$	−11.0012			−0.468667
$552$	−1.96530	+	6.04858i	−0.0836489	+	0.257445i
$553$	−3.66448	+	2.66240i	−0.155829	+	0.113217i
$554$	7.57795	+	5.50570i	0.321956	+	0.233915i
$555$	0.240256	+	0.739431i	0.0101983	+	0.0313871i
$556$	2.05382	+	6.32100i	0.0871012	+	0.268070i
$557$	−14.9432	−	10.8569i	−0.633164	−	0.460021i	0.224331	−	0.974513i	$-0.427980\pi$
$557$	−14.9432	−	10.8569i	−0.633164	−	0.460021i	−0.857495	+	0.514492i	$0.827980\pi$
$558$	11.3453	−	8.24287i	0.480286	−	0.348949i
$559$	−9.49993	+	29.2378i	−0.401804	+	1.23663i
$560$	0.164330			0.00694419
$561$	6.54945	−	6.00405i	0.276518	−	0.253491i
$562$	−16.4476			−0.693801
$563$	9.66724	−	29.7527i	0.407426	−	1.25393i	−0.511427	−	0.859327i	$-0.670883\pi$
$563$	9.66724	−	29.7527i	0.407426	−	1.25393i	0.918853	−	0.394600i	$-0.129117\pi$
$564$	4.21833	−	3.06479i	0.177624	−	0.129051i
$565$	−2.96963	−	2.15757i	−0.124933	−	0.0907695i
$566$	6.00720	+	18.4883i	0.252502	+	0.777120i
$567$	−1.76393	−	5.42882i	−0.0740782	−	0.227989i
$568$	19.8823	+	14.4454i	0.834244	+	0.606114i
$569$	−1.40449	+	1.02042i	−0.0588794	+	0.0427784i	−0.616836	−	0.787092i	$-0.711586\pi$
$569$	−1.40449	+	1.02042i	−0.0588794	+	0.0427784i	0.557956	+	0.829870i	$0.311586\pi$
$570$	0.0963134	−	0.296422i	0.00403412	−	0.0124158i
$571$	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
$573$	−7.43182			−0.310469
$574$	0.321489	−	0.989441i	0.0134187	−	0.0412985i
$575$	−15.6114	+	11.3424i	−0.651042	+	0.473009i
$576$	6.51180	+	4.73110i	0.271325	+	0.197129i
$577$	6.23893	+	19.2015i	0.259730	+	0.799368i	0.992861	+	0.119280i	$0.0380585\pi$
$577$	6.23893	+	19.2015i	0.259730	+	0.799368i	−0.733130	+	0.680088i	$0.761942\pi$
$578$	−0.429788	−	1.32275i	−0.0178768	−	0.0550192i
$579$	−7.94196	−	5.77017i	−0.330057	−	0.239800i
$580$	0.948101	−	0.688835i	0.0393677	−	0.0286023i
$581$	−3.48688	+	10.7315i	−0.144660	+	0.445218i
$582$	4.35051			0.180334
$583$	4.95961	+	2.80461i	0.205406	+	0.116155i
$584$	14.7550			0.610568
$585$	1.17544	−	3.61764i	0.0485986	−	0.149571i
$586$	−0.286249	+	0.207972i	−0.0118248	+	0.00859125i
$587$	0.00677611	+	0.00492314i	0.000279680	+	0.000203200i	0.587925	−	0.808915i	$-0.299945\pi$
$587$	0.00677611	+	0.00492314i	0.000279680	+	0.000203200i	−0.587645	+	0.809119i	$0.699945\pi$
$588$	−0.266520	−	0.820265i	−0.0109911	−	0.0338272i
$589$	−6.20604	−	19.1002i	−0.255716	−	0.787012i
$590$	1.33426	+	0.969399i	0.0549307	+	0.0399095i
$591$	−6.15177	+	4.46952i	−0.253050	+	0.183851i
$592$	−1.29020	+	3.97082i	−0.0530267	+	0.163200i
$593$	−0.439298			−0.0180398			−0.00901989	−	0.999959i	$-0.502871\pi$
$593$	−0.439298			−0.0180398			−0.00901989	+	0.999959i	$0.502871\pi$
$594$	1.78312	−	8.77397i	0.0731624	−	0.360001i
$595$	−0.964520			−0.0395415
$596$	3.11779	−	9.59558i	0.127710	−	0.393050i
$597$	−7.63075	+	5.54406i	−0.312306	+	0.226903i
$598$	−16.0092	−	11.6314i	−0.654664	−	0.475641i
$599$	13.9572	+	42.9558i	0.570275	+	1.75512i	0.651734	+	0.758448i	$0.274042\pi$
$599$	13.9572	+	42.9558i	0.570275	+	1.75512i	−0.0814591	+	0.996677i	$0.525958\pi$
$600$	−2.49598	−	7.68182i	−0.101898	−	0.313609i
$601$	−9.01541	−	6.55008i	−0.367746	−	0.267183i	0.388529	−	0.921436i	$-0.372983\pi$
$601$	−9.01541	−	6.55008i	−0.367746	−	0.267183i	−0.756276	+	0.654253i	$0.772983\pi$
$602$	2.96145	−	2.15162i	0.120700	−	0.0876935i
$603$	−1.02870	+	3.16603i	−0.0418921	+	0.128931i
$604$	−11.3591			−0.462194
$605$	−0.212282	+	2.43845i	−0.00863047	+	0.0991371i
$606$	9.23071			0.374972
$607$	−11.0318	+	33.9525i	−0.447768	+	1.37809i	0.431651	+	0.902041i	$0.357931\pi$
$607$	−11.0318	+	33.9525i	−0.447768	+	1.37809i	−0.879419	+	0.476049i	$0.842069\pi$
$608$	13.8057	−	10.0304i	0.559894	−	0.406787i
$609$	−1.88699	−	1.37098i	−0.0764649	−	0.0555550i
$610$	−0.514796	−	1.58438i	−0.0208435	−	0.0641496i
$611$	12.1983	+	37.5426i	0.493491	+	1.51881i
$612$	12.8121	+	9.30850i	0.517897	+	0.376274i
$613$	−13.9135	+	10.1087i	−0.561960	+	0.408288i	−0.832176	−	0.554512i	$-0.812905\pi$
$613$	−13.9135	+	10.1087i	−0.561960	+	0.408288i	0.270216	+	0.962800i	$0.412905\pi$
$614$	1.93064	−	5.94191i	0.0779144	−	0.239796i
$615$	−0.184020			−0.00742040
$616$	−1.74378	+	8.58036i	−0.0702587	+	0.345713i
$617$	−16.8852			−0.679774			−0.339887	−	0.940466i	$-0.610389\pi$
$617$	−16.8852			−0.679774			−0.339887	+	0.940466i	$0.610389\pi$
$618$	−2.41117	+	7.42080i	−0.0969913	+	0.298509i
$619$	−25.1355	+	18.2620i	−1.01028	+	0.734013i	−0.964268	−	0.264928i	$-0.914652\pi$
$619$	−25.1355	+	18.2620i	−1.01028	+	0.734013i	−0.0460139	+	0.998941i	$0.514652\pi$
$620$	1.73080	+	1.25750i	0.0695106	+	0.0505024i
$621$	4.18231	+	12.8718i	0.167830	+	0.516529i
$622$	−0.0329066	−	0.101276i	−0.00131943	−	0.00406080i
$623$	6.40868	+	4.65618i	0.256758	+	0.186546i
$624$	−2.41106	+	1.75174i	−0.0965196	+	0.0701256i
$625$	7.49668	−	23.0724i	0.299867	−	0.922896i
$626$	11.8877			0.475127
$627$	−5.20113	−	2.94118i	−0.207713	−	0.117460i
$628$	−28.1217			−1.12218
$629$	7.57271	−	23.3064i	0.301944	−	0.929287i
$630$	−0.366425	+	0.266223i	−0.0145987	+	0.0106066i
$631$	−5.86832	−	4.26359i	−0.233614	−	0.169731i	0.464819	−	0.885406i	$-0.346119\pi$
$631$	−5.86832	−	4.26359i	−0.233614	−	0.169731i	−0.698434	+	0.715675i	$0.746119\pi$
$632$	−3.69517	−	11.3726i	−0.146986	−	0.452376i
$633$	1.70613	+	5.25094i	0.0678128	+	0.208706i
$634$	−20.7522	−	15.0774i	−0.824176	−	0.598799i
$635$	0.359549	−	0.261227i	0.0142683	−	0.0103665i
$636$	0.457859	−	1.40915i	0.0181553	−	0.0558763i
$637$	6.52954			0.258710
$638$	4.03757	+	8.85460i	0.159849	+	0.350557i
$639$	24.3718			0.964132
$640$	−0.640707	+	1.97189i	−0.0253262	+	0.0779459i
$641$	16.7870	−	12.1965i	0.663047	−	0.481732i	−0.204643	−	0.978837i	$-0.565603\pi$
$641$	16.7870	−	12.1965i	0.663047	−	0.481732i	0.867691	+	0.497104i	$0.165603\pi$
$642$	−2.09663	−	1.52329i	−0.0827472	−	0.0601194i
$643$	2.19750	+	6.76322i	0.0866611	+	0.266715i	0.984991	−	0.172606i	$-0.0552188\pi$
$643$	2.19750	+	6.76322i	0.0866611	+	0.266715i	−0.898330	+	0.439322i	$0.855219\pi$
$644$	−1.68095	−	5.17343i	−0.0662387	−	0.203862i
$645$	−0.523825	−	0.380581i	−0.0206256	−	0.0149854i
$646$	−7.94766	+	5.77431i	−0.312696	+	0.227187i
$647$	8.52234	−	26.2291i	0.335048	−	1.03117i	−0.631651	−	0.775253i	$-0.717622\pi$
$647$	8.52234	−	26.2291i	0.335048	−	1.03117i	0.966699	−	0.255918i	$-0.0823777\pi$
$648$	15.0694			0.591984
$649$	23.3063	−	21.3655i	0.914852	−	0.838669i
$650$	25.1317			0.985748
$651$	1.31579	−	4.04959i	0.0515700	−	0.158716i
$652$	8.39353	−	6.09826i	0.328716	−	0.238826i
$653$	−13.0690	−	9.49516i	−0.511428	−	0.371574i	0.301937	−	0.953328i	$-0.402367\pi$
$653$	−13.0690	−	9.49516i	−0.511428	−	0.371574i	−0.813365	+	0.581753i	$0.802367\pi$
$654$	−0.801680	−	2.46732i	−0.0313482	−	0.0964797i
$655$	−0.0942092	−	0.289946i	−0.00368106	−	0.0113291i
$656$	−0.799474	−	0.580852i	−0.0312142	−	0.0226785i
$657$	11.8379	−	8.60076i	0.461842	−	0.335548i
$658$	1.45248	−	4.47026i	0.0566234	−	0.174269i
$659$	−13.2085			−0.514531			−0.257266	−	0.966341i	$-0.582822\pi$
$659$	−13.2085			−0.514531			−0.257266	+	0.966341i	$0.582822\pi$
$660$	0.632403	−	0.0721907i	0.0246162	−	0.00281002i
$661$	−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
$663$	14.1515	−	10.2817i	0.549600	−	0.399308i
$664$	−24.0996	−	17.5094i	−0.935245	−	0.679495i
$665$	0.200439	+	0.616888i	0.00777270	+	0.0239219i
$666$	−3.55605	−	10.9444i	−0.137794	−	0.424087i
$667$	−11.9013	−	8.64682i	−0.460821	−	0.334806i
$668$	−2.49635	+	1.81371i	−0.0965869	+	0.0701745i
$669$	0.136599	−	0.420410i	0.00528124	−	0.0162540i
$670$	0.219981			0.00849861
$671$	−31.7311	+	3.62221i	−1.22497	+	0.139834i
$672$	3.61803			0.139569
$673$	−9.26654	+	28.5195i	−0.357199	+	1.09935i	0.597524	+	0.801851i	$0.296151\pi$
$673$	−9.26654	+	28.5195i	−0.357199	+	1.09935i	−0.954723	+	0.297495i	$0.903849\pi$
$674$	3.54142	−	2.57299i	0.136410	−	0.0991079i
$675$	−13.9060	−	10.1033i	−0.535242	−	0.388876i
$676$	−12.7797	−	39.3320i	−0.491528	−	1.51277i
$677$	3.89019	+	11.9728i	0.149512	+	0.460151i	0.997564	−	0.0697626i	$-0.0222242\pi$
$677$	3.89019	+	11.9728i	0.149512	+	0.460151i	−0.848051	+	0.529914i	$0.822224\pi$
$678$	−6.41278	−	4.65916i	−0.246281	−	0.178934i
$679$	−7.32477	+	5.32176i	−0.281099	+	0.204230i
$680$	0.786849	−	2.42167i	0.0301743	−	0.0928668i
$681$	−3.28894			−0.126033
$682$	−13.0956	+	12.0051i	−0.501457	+	0.459699i
$683$	−28.5342			−1.09183			−0.545916	−	0.837840i	$-0.683818\pi$
$683$	−28.5342			−1.09183			−0.545916	+	0.837840i	$0.683818\pi$
$684$	3.29104	−	10.1288i	0.125836	−	0.387283i
$685$	0.449911	−	0.326879i	0.0171902	−	0.0124894i
$686$	−0.628998	−	0.456994i	−0.0240153	−	0.0174481i
$687$	−1.26208	−	3.88427i	−0.0481513	−	0.148194i
$688$	−1.07447	−	3.30687i	−0.0409636	−	0.126073i
$689$	9.07491	+	6.59331i	0.345726	+	0.251185i
$690$	0.337178	−	0.244974i	0.0128362	−	0.00932601i
$691$	7.84107	−	24.1323i	0.298288	−	0.918037i	−0.683809	−	0.729661i	$-0.739678\pi$
$691$	7.84107	−	24.1323i	0.298288	−	0.918037i	0.982097	−	0.188376i	$-0.0603223\pi$
$692$	14.4606			0.549711
$693$	3.60249	+	7.90045i	0.136847	+	0.300113i
$694$	−6.78791			−0.257666
$695$	0.327482	−	1.00788i	0.0124221	−	0.0382312i
$696$	4.98159	−	3.61934i	0.188827	−	0.137191i
$697$	4.69245	+	3.40927i	0.177739	+	0.129135i
$698$	−4.43679	−	13.6551i	−0.167935	−	0.516851i
$699$	−1.82525	−	5.61754i	−0.0690373	−	0.212475i
$700$	5.58909	+	4.06071i	0.211248	+	0.153480i
$701$	36.9738	−	26.8630i	1.39648	−	1.01460i	0.401363	−	0.915919i	$-0.368537\pi$
$701$	36.9738	−	26.8630i	1.39648	−	1.01460i	0.995119	−	0.0986843i	$-0.0314634\pi$
$702$	5.44695	−	16.7640i	0.205582	−	0.632716i
$703$	−16.4800			−0.621556
$704$	−8.87594	−	5.01925i	−0.334525	−	0.189170i
$705$	−0.831396			−0.0313122
$706$	5.64257	−	17.3661i	0.212361	−	0.653580i
$707$	−15.5413	+	11.2915i	−0.584493	+	0.424659i
$708$	−6.65177	−	4.83279i	−0.249989	−	0.181627i
$709$	11.9065	+	36.6446i	0.447160	+	1.37622i	0.880098	+	0.474793i	$0.157477\pi$
$709$	11.9065	+	36.6446i	0.447160	+	1.37622i	−0.432938	+	0.901424i	$0.642523\pi$
$710$	−0.497676	−	1.53169i	−0.0186774	−	0.0574833i
$711$	−9.59373	−	6.97025i	−0.359793	−	0.261405i
$712$	−16.9187	+	12.2921i	−0.634054	+	0.460667i
$713$	8.29874	−	25.5409i	0.310790	−	0.956515i
$714$	−2.08283			−0.0779480
$715$	−0.959703	+	4.72228i	−0.0358908	+	0.176603i
$716$	32.6683			1.22087
$717$	5.12725	−	15.7801i	0.191481	−	0.589317i
$718$	9.36025	−	6.80062i	0.349321	−	0.253797i
$719$	−4.61312	−	3.35163i	−0.172040	−	0.124995i	0.498433	−	0.866928i	$-0.333909\pi$
$719$	−4.61312	−	3.35163i	−0.172040	−	0.124995i	−0.670473	+	0.741934i	$0.733909\pi$
$720$	0.132945	+	0.409164i	0.00495458	+	0.0152486i
$721$	−5.01791	−	15.4435i	−0.186877	−	0.575148i
$722$	−6.60620	−	4.79969i	−0.245857	−	0.178626i
$723$	−9.43316	+	6.85359i	−0.350823	+	0.254888i
$724$	5.91491	−	18.2042i	0.219826	−	0.676555i
$725$	18.6831			0.693872
$726$	−0.458411	+	5.26571i	−0.0170132	+	0.195429i
$727$	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
$729$	6.88197	−	5.00004i	0.254888	−	0.185187i
$730$	−0.782263	−	0.568347i	−0.0289529	−	0.0210355i
$731$	6.30649	+	19.4094i	0.233254	+	0.717882i
$732$	2.56644	+	7.89868i	0.0948582	+	0.291944i
$733$	−7.12900	−	5.17952i	−0.263316	−	0.191310i	0.448292	−	0.893887i	$-0.352033\pi$
$733$	−7.12900	−	5.17952i	−0.263316	−	0.191310i	−0.711607	+	0.702577i	$0.752033\pi$
$734$	−21.5280	+	15.6410i	−0.794614	+	0.577321i
$735$	−0.0424967	+	0.130791i	−0.00156752	+	0.00482432i
$736$	22.8190			0.841121
$737$	0.839897	−	4.13277i	0.0309380	−	0.152232i
$738$	2.72370			0.100261
$739$	0.148578	−	0.457276i	0.00546553	−	0.0168212i	−0.948287	−	0.317416i	$-0.897185\pi$
$739$	0.148578	−	0.457276i	0.00546553	−	0.0168212i	0.953752	+	0.300594i	$0.0971850\pi$
$740$	1.42027	−	1.03189i	0.0522103	−	0.0379330i
$741$	−9.51683	−	6.91438i	−0.349610	−	0.254006i
$742$	−0.412739	−	1.27028i	−0.0151521	−	0.0466335i
$743$	10.2730	+	31.6172i	0.376881	+	1.15992i	0.942201	+	0.335049i	$0.108753\pi$
$743$	10.2730	+	31.6172i	0.376881	+	1.15992i	−0.565319	+	0.824872i	$0.691247\pi$
$744$	9.09412	+	6.60726i	0.333407	+	0.242234i
$745$	−1.30151	+	0.945603i	−0.0476837	+	0.0346442i
$746$	−0.724946	+	2.23116i	−0.0265422	+	0.0816884i
$747$	−29.5413			−1.08086
$748$	−17.4635	−	9.87543i	−0.638530	−	0.361082i
$749$	5.39336			0.197069
$750$	−0.328769	+	1.01185i	−0.0120050	+	0.0369475i
$751$	−22.6578	+	16.4619i	−0.826796	+	0.600703i	−0.918651	−	0.395070i	$-0.870720\pi$
$751$	−22.6578	+	16.4619i	−0.826796	+	0.600703i	0.0918547	+	0.995772i	$0.470720\pi$
$752$	−3.61200	−	2.62427i	−0.131716	−	0.0956973i
$753$	5.60977	+	17.2651i	0.204432	+	0.629176i
$754$	5.92049	+	18.2214i	0.215611	+	0.663584i
$755$	1.46530	+	1.06460i	0.0533276	+	0.0387448i
$756$	3.92003	−	2.84807i	0.142570	−	0.103583i
$757$	−6.87465	+	21.1580i	−0.249863	+	0.769001i	0.744935	+	0.667137i	$0.232481\pi$
$757$	−6.87465	+	21.1580i	−0.249863	+	0.769001i	−0.994798	+	0.101864i	$0.967519\pi$
$758$	4.76156			0.172948
$759$	−3.31495	−	7.26986i	−0.120325	−	0.263879i
$760$	−1.71237			−0.0621142
$761$	−14.9025	+	45.8651i	−0.540214	+	1.66261i	0.191891	+	0.981416i	$0.438538\pi$
$761$	−14.9025	+	45.8651i	−0.540214	+	1.66261i	−0.732105	+	0.681192i	$0.761462\pi$
$762$	0.776427	−	0.564108i	0.0281270	−	0.0204355i
$763$	4.36789	+	3.17346i	0.158128	+	0.114887i
$764$	5.18562	+	15.9597i	0.187609	+	0.577402i
$765$	−0.780313	−	2.40156i	−0.0282123	−	0.0868284i
$766$	2.76192	+	2.00665i	0.0997922	+	0.0725033i
$767$	50.3584	−	36.5875i	1.81834	−	1.32110i
$768$	−2.55791	+	7.87245i	−0.0923007	+	0.284072i
$769$	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
$771$	−10.4549			−0.376524
$772$	−6.84977	+	21.0814i	−0.246528	+	0.758737i
$773$	0.473736	−	0.344189i	0.0170391	−	0.0123796i	−0.579233	−	0.815162i	$-0.696648\pi$
$773$	0.473736	−	0.344189i	0.0170391	−	0.0123796i	0.596272	+	0.802782i	$0.296648\pi$
$774$	7.75318	+	5.63301i	0.278682	+	0.202475i
$775$	10.5396	+	32.4375i	0.378593	+	1.16519i
$776$	−7.38612	−	22.7321i	−0.265146	−	0.816036i
$777$	−2.82676	−	2.05376i	−0.101409	−	0.0736782i
$778$	6.60197	−	4.79661i	0.236692	−	0.171967i
$779$	1.20535	−	3.70969i	0.0431862	−	0.132913i
$780$	1.25312			0.0448688
$781$	−30.6759	+	3.50175i	−1.09767	+	0.125302i
$782$	−13.1365			−0.469760
$783$	4.04930	−	12.4625i	0.144710	−	0.445372i
$784$	−0.597465	+	0.434084i	−0.0213380	+	0.0155030i
$785$	3.62764	+	2.63563i	0.129476	+	0.0940698i
$786$	−0.203440	−	0.626124i	−0.00725647	−	0.0223331i
$787$	9.49195	+	29.2132i	0.338351	+	1.04134i	0.965048	+	0.262075i	$0.0844067\pi$
$787$	9.49195	+	29.2132i	0.338351	+	1.04134i	−0.626696	+	0.779264i	$0.715593\pi$
$788$	13.8907	+	10.0922i	0.494834	+	0.359518i
$789$	4.09017	−	2.97168i	0.145614	−	0.105795i
$790$	−0.242153	+	0.745269i	−0.00861540	+	0.0265155i
$791$	16.4962			0.586538
$792$	−22.7750	+	2.59984i	−0.809274	+	0.0923811i
$793$	−62.8758			−2.23278
$794$	−2.73623	+	8.42125i	−0.0971052	+	0.298859i
$795$	−0.191132	+	0.138865i	−0.00677874	+	0.00492504i
$796$	17.2302	+	12.5185i	0.610708	+	0.443705i
$797$	−3.34767	−	10.3031i	−0.118581	−	0.364953i	0.874096	−	0.485752i	$-0.161454\pi$
$797$	−3.34767	−	10.3031i	−0.118581	−	0.364953i	−0.992677	+	0.120799i	$0.961454\pi$
$798$	0.432838	+	1.33214i	0.0153223	+	0.0471572i
$799$	21.2003	+	15.4029i	0.750014	+	0.544917i
$800$	−23.4458	+	17.0344i	−0.828936	+	0.602257i
$801$	−6.40868	+	19.7239i	−0.226440	+	0.696910i
$802$	3.67358			0.129719
$803$	−13.6642	+	12.5263i	−0.482200	+	0.442045i
$804$	−1.09668			−0.0386770
$805$	−0.268028	+	0.824906i	−0.00944675	+	0.0290741i
$806$	−28.2960	+	20.5582i	−0.996684	+	0.724133i
$807$	3.12358	+	2.26941i	0.109955	+	0.0798872i
$808$	−15.6715	−	48.2320i	−0.551322	−	1.69679i
$809$	−11.9250	−	36.7013i	−0.419260	−	1.29035i	−0.908385	−	0.418136i	$-0.862684\pi$
$809$	−11.9250	−	36.7013i	−0.419260	−	1.29035i	0.489125	−	0.872214i	$-0.337316\pi$
$810$	−0.798931	−	0.580458i	−0.0280716	−	0.0203952i
$811$	41.1737	−	29.9144i	1.44580	−	1.05044i	0.459015	−	0.888428i	$-0.348202\pi$
$811$	41.1737	−	29.9144i	1.44580	−	1.05044i	0.986789	−	0.162010i	$-0.0517977\pi$
$812$	−1.62749	+	5.00890i	−0.0571137	+	0.175778i
$813$	4.86200			0.170518
$814$	6.04836	+	13.2644i	0.211995	+	0.464916i
$815$	−1.65429			−0.0579473
$816$	−0.611364	+	1.88159i	−0.0214020	+	0.0658687i
$817$	11.1033	−	8.06703i	0.388456	−	0.282230i
$818$	1.55076	+	1.12669i	0.0542209	+	0.0393938i
$819$	5.28251	+	16.2579i	0.184586	+	0.568097i
$820$	0.128402	+	0.395180i	0.00448398	+	0.0138003i
$821$	32.6110	+	23.6933i	1.13813	+	0.826901i	0.986858	−	0.161590i	$-0.0516623\pi$
$821$	32.6110	+	23.6933i	1.13813	+	0.826901i	0.151274	+	0.988492i	$0.451662\pi$
$822$	0.971560	−	0.705880i	0.0338870	−	0.0246204i
$823$	7.93609	−	24.4248i	0.276635	−	0.851395i	−0.712147	−	0.702030i	$-0.752277\pi$
$823$	7.93609	−	24.4248i	0.276635	−	0.851395i	0.988782	−	0.149365i	$-0.0477228\pi$
$824$	42.8685			1.49340
$825$	8.83296	+	4.99494i	0.307524	+	0.173902i
$826$	−7.41179			−0.257889
$827$	−9.87486	+	30.3917i	−0.343382	+	1.05682i	0.619062	+	0.785342i	$0.287513\pi$
$827$	−9.87486	+	30.3917i	−0.343382	+	1.05682i	−0.962444	+	0.271480i	$0.912487\pi$
$828$	11.5214	−	8.37079i	0.400397	−	0.290905i
$829$	−39.1566	−	28.4489i	−1.35996	−	0.988072i	−0.998447	−	0.0557070i	$-0.982259\pi$
$829$	−39.1566	−	28.4489i	−1.35996	−	0.988072i	−0.361518	−	0.932365i	$-0.617741\pi$
$830$	0.603238	+	1.85658i	0.0209387	+	0.0644427i
$831$	2.30090	+	7.08143i	0.0798172	+	0.245652i
$832$	−16.2409	−	11.7997i	−0.563050	−	0.409080i
$833$	3.50678	−	2.54782i	0.121503	−	0.0882768i
$834$	0.707180	−	2.17648i	0.0244876	−	0.0753652i
$835$	0.492010			0.0170267
$836$	−2.68700	+	13.2216i	−0.0929319	+	0.457278i
$837$	23.9216			0.826850
$838$	3.44524	−	10.6033i	0.119014	−	0.366287i
$839$	30.5133	−	22.1692i	1.05344	−	0.765366i	0.0805734	−	0.996749i	$-0.474325\pi$
$839$	30.5133	−	22.1692i	1.05344	−	0.765366i	0.972863	+	0.231382i	$0.0743249\pi$
$840$	−0.293717	−	0.213398i	−0.0101342	−	0.00736292i
$841$	−4.56017	−	14.0348i	−0.157247	−	0.483957i
$842$	4.16021	+	12.8038i	0.143370	+	0.441248i
$843$	−10.5775	−	7.68497i	−0.364307	−	0.264685i
$844$	10.0858	−	7.32779i	0.347169	−	0.252233i
$845$	−2.03773	+	6.27150i	−0.0701001	+	0.215746i
$846$	12.3056			0.423074
$847$	−5.66947	−	9.42641i	−0.194805	−	0.323895i
$848$	−1.26869			−0.0435671
$849$	−4.77522	+	14.6966i	−0.163885	+	0.504386i
$850$	13.4973	−	9.80638i	0.462954	−	0.336356i
$851$	−17.8284	−	12.9531i	−0.611151	−	0.444027i
$852$	2.48109	+	7.63600i	0.0850007	+	0.261605i
$853$	2.87035	+	8.83403i	0.0982789	+	0.302471i	0.988094	−	0.153849i	$-0.0491670\pi$
$853$	2.87035	+	8.83403i	0.0982789	+	0.302471i	−0.889815	+	0.456321i	$0.849167\pi$
$854$	6.05689	+	4.40059i	0.207262	+	0.150585i
$855$	−1.37383	+	0.998146i	−0.0469840	+	0.0341359i
$856$	−4.39986	+	13.5414i	−0.150384	+	0.462835i
$857$	−29.7644			−1.01673			−0.508365	−	0.861141i	$-0.669750\pi$
$857$	−29.7644			−1.01673			−0.508365	+	0.861141i	$0.669750\pi$
$858$	−2.07243	+	10.1975i	−0.0707516	+	0.348138i
$859$	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
$861$	0.669055	−	0.486097i	0.0228013	−	0.0165661i
$862$	17.5442	+	12.7466i	0.597558	+	0.434151i
$863$	−5.73772	−	17.6589i	−0.195314	−	0.601116i	−0.999973	−	0.00737787i	$-0.997652\pi$
$863$	−5.73772	−	17.6589i	−0.195314	−	0.601116i	0.804658	−	0.593738i	$-0.202348\pi$
$864$	6.28115	+	19.3314i	0.213689	+	0.657668i
$865$	−1.86539	−	1.35529i	−0.0634253	−	0.0460812i
$866$	−18.5850	+	13.5028i	−0.631544	+	0.458844i
$867$	0.341645	−	1.05147i	0.0116029	−	0.0357100i
$868$	−9.61454			−0.326339
$869$	13.0768	+	7.39477i	0.443599	+	0.250850i
$870$	−0.403520			−0.0136806
$871$	2.56565	−	7.89627i	0.0869339	−	0.267555i
$872$	−11.5311	+	8.37782i	−0.390491	+	0.283709i
$873$	−19.1765	−	13.9325i	−0.649026	−	0.471545i
$874$	2.72992	+	8.40184i	0.0923411	+	0.284197i
$875$	−0.684207	−	2.10577i	−0.0231304	−	0.0711881i
$876$	3.89985	+	2.83341i	0.131764	+	0.0957321i
$877$	18.1965	−	13.2205i	0.614452	−	0.446426i	−0.236527	−	0.971625i	$-0.576009\pi$
$877$	18.1965	−	13.2205i	0.614452	−	0.446426i	0.850979	+	0.525199i	$0.176009\pi$
$878$	8.08834	−	24.8934i	0.272968	−	0.840110i
$879$	−0.281259			−0.00948664
$880$	−0.226122	−	0.495898i	−0.00762259	−	0.0167167i
$881$	7.06565			0.238048			0.119024	−	0.992891i	$-0.462023\pi$
$881$	7.06565			0.238048			0.119024	+	0.992891i	$0.462023\pi$
$882$	0.628998	−	1.93586i	0.0211795	−	0.0651837i
$883$	16.1304	−	11.7194i	0.542830	−	0.394389i	−0.282305	−	0.959325i	$-0.591099\pi$
$883$	16.1304	−	11.7194i	0.542830	−	0.394389i	0.825135	+	0.564936i	$0.191099\pi$
$884$	−31.9541	−	23.2160i	−1.07473	−	0.780839i
$885$	0.405123	+	1.24684i	0.0136181	+	0.0419121i
$886$	−2.48105	−	7.63590i	−0.0833527	−	0.256533i
$887$	−5.62656	−	4.08793i	−0.188921	−	0.137259i	0.489304	−	0.872113i	$-0.337251\pi$
$887$	−5.62656	−	4.08793i	−0.188921	−	0.137259i	−0.678226	+	0.734854i	$0.737251\pi$
$888$	7.46253	−	5.42185i	0.250426	−	0.181945i
$889$	−0.617194	+	1.89953i	−0.0207000	+	0.0637081i
$890$	1.37045			0.0459376
$891$	−13.9554	+	12.7933i	−0.467522	+	0.428590i
$892$	−0.998136			−0.0334201
$893$	5.44574	−	16.7603i	0.182235	−	0.560861i
$894$	−2.81055	+	2.04198i	−0.0939988	+	0.0682941i
$895$	−4.21414	−	3.06175i	−0.140863	−	0.102343i
$896$	−2.87938	−	8.86181i	−0.0961933	−	0.296052i
$897$	−4.86088	−	14.9602i	−0.162300	−	0.499508i
$898$	−1.73468	−	1.26032i	−0.0578872	−	0.0420575i
$899$	−21.0354	+	15.2831i	−0.701570	+	0.509721i
$900$	−5.58909	+	17.2014i	−0.186303	+	0.573382i
$901$	7.44650			0.248079
$902$	−3.42822	+	0.391342i	−0.114147	+	0.0130303i
$903$	2.90983			0.0968331
$904$	−13.4575	+	41.4179i	−0.447590	+	1.37754i
$905$	−2.46916	+	1.79395i	−0.0820776	+	0.0596329i
$906$	3.16424	+	2.29895i	0.105125	+	0.0763776i
$907$	−7.24340	−	22.2929i	−0.240513	−	0.740224i	−0.996342	−	0.0854543i	$-0.972766\pi$
$907$	−7.24340	−	22.2929i	−0.240513	−	0.740224i	0.755829	−	0.654769i	$-0.227234\pi$
$908$	2.29489	+	7.06294i	0.0761586	+	0.234392i
$909$	−40.6878	−	29.5614i	−1.34953	−	0.980490i
$910$	0.913888	−	0.663978i	0.0302951	−	0.0220107i
$911$	14.4650	−	44.5186i	0.479246	−	1.47497i	−0.360899	−	0.932605i	$-0.617530\pi$
$911$	14.4650	−	44.5186i	0.479246	−	1.47497i	0.840145	−	0.542362i	$-0.182470\pi$
$912$	1.33048			0.0440564
$913$	37.1825	−	4.24450i	1.23056	−	0.140473i
$914$	31.3563			1.03718
$915$	0.409219	−	1.25945i	0.0135284	−	0.0416360i
$916$	−7.46078	+	5.42058i	−0.246511	+	0.179101i
$917$	1.10843	+	0.805321i	0.0366036	+	0.0265940i
$918$	−3.61594	−	11.1287i	−0.119344	−	0.367302i
$919$	3.28402	+	10.1072i	0.108330	+	0.333405i	0.990498	−	0.137530i	$-0.0439165\pi$
$919$	3.28402	+	10.1072i	0.108330	+	0.333405i	−0.882168	+	0.470935i	$0.843916\pi$
$920$	−1.85248	−	1.34590i	−0.0610744	−	0.0443732i
$921$	4.01789	−	2.91917i	0.132394	−	0.0961898i
$922$	8.22278	−	25.3071i	0.270803	−	0.833445i
$923$	−60.7848			−2.00075
$924$	−2.10858	+	1.93299i	−0.0693671	+	0.0635907i
$925$	27.9876			0.920228
$926$	−0.169945	+	0.523036i	−0.00558473	+	0.0171880i
$927$	34.3933	−	24.9882i	1.12962	−	0.820720i
$928$	−17.8739	−	12.9861i	−0.586738	−	0.426290i
$929$	−11.3319	−	34.8762i	−0.371789	−	1.14425i	−0.945619	−	0.325275i	$-0.894543\pi$
$929$	−11.3319	−	34.8762i	−0.371789	−	1.14425i	0.573830	−	0.818974i	$-0.305457\pi$
$930$	−0.227635	−	0.700590i	−0.00746446	−	0.0229733i
$931$	−2.35829	−	1.71340i	−0.0772898	−	0.0561543i
$932$	−10.7900	+	7.83938i	−0.353438	+	0.256787i
$933$	0.0261579	−	0.0805059i	0.000856373	−	0.00263564i
$934$	22.2302			0.727393
$935$	1.32721	+	2.91064i	0.0434043	+	0.0951880i
$936$	−45.1290			−1.47509
$937$	−12.4278	+	38.2490i	−0.406000	+	1.24954i	0.514057	+	0.857756i	$0.328142\pi$
$937$	−12.4278	+	38.2490i	−0.406000	+	1.24954i	−0.920057	+	0.391784i	$0.871858\pi$
$938$	−0.799801	+	0.581090i	−0.0261144	+	0.0189732i
$939$	7.64497	+	5.55439i	0.249484	+	0.181261i
$940$	0.580114	+	1.78541i	0.0189212	+	0.0582336i
$941$	7.69751	+	23.6905i	0.250932	+	0.772288i	0.994604	+	0.103744i	$0.0330823\pi$
$941$	7.69751	+	23.6905i	0.250932	+	0.772288i	−0.743672	+	0.668544i	$0.766918\pi$
$942$	7.83371	+	5.69152i	0.255236	+	0.185440i
$943$	4.21975	−	3.06583i	0.137414	−	0.0998371i
$944$	−2.17555	+	6.69565i	−0.0708081	+	0.217925i
$945$	−0.772605			−0.0251328
$946$	−10.5680	−	5.97609i	−0.343595	−	0.194299i
$947$	−32.2061			−1.04656			−0.523279	−	0.852161i	$-0.675292\pi$
$947$	−32.2061			−1.04656			−0.523279	+	0.852161i	$0.675292\pi$
$948$	1.20722	−	3.71543i	0.0392085	−	0.120671i
$949$	−29.5246	+	21.4508i	−0.958408	+	0.696324i
$950$	−9.07688	−	6.59474i	−0.294493	−	0.213962i
$951$	−6.30101	−	19.3925i	−0.204324	−	0.628846i
$952$	3.53615	+	10.8831i	0.114607	+	0.352725i
$953$	−36.4552	−	26.4863i	−1.18090	−	0.857975i	−0.188628	−	0.982049i	$-0.560404\pi$
$953$	−36.4552	−	26.4863i	−1.18090	−	0.857975i	−0.992273	+	0.124074i	$0.960404\pi$
$954$	2.82896	−	2.05536i	0.0915908	−	0.0665446i
$955$	0.826849	−	2.54478i	0.0267562	−	0.0823471i
$956$	−37.4650			−1.21170
$957$	−1.54066	+	7.58090i	−0.0498024	+	0.245056i
$958$	3.96296			0.128038
$959$	−0.772308	+	2.37692i	−0.0249391	+	0.0767547i
$960$	0.342058	−	0.248519i	0.0110399	−	0.00802093i
$961$	−13.3216	−	9.67867i	−0.429727	−	0.312215i
$962$	8.86901	+	27.2960i	0.285948	+	0.880059i
$963$	4.36332	+	13.4289i	0.140606	+	0.432741i
$964$	21.3000	+	15.4754i	0.686028	+	0.498428i
$965$	2.85941	−	2.07748i	0.0920476	−	0.0668765i
$966$	−0.578793	+	1.78134i	−0.0186224	+	0.0573138i
$967$	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
$969$	−7.80912			−0.250865
$970$	−0.484029	+	1.48969i	−0.0155412	+	0.0478310i
$971$	−18.6510	+	13.5507i	−0.598539	+	0.434864i	−0.845360	−	0.534197i	$-0.820614\pi$
$971$	−18.6510	+	13.5507i	−0.598539	+	0.434864i	0.246821	+	0.969061i	$0.420614\pi$
$972$	15.7431	+	11.4380i	0.504959	+	0.366874i
$973$	1.47172	+	4.52950i	0.0471813	+	0.145209i
$974$	−7.01266	−	21.5827i	−0.224700	−	0.691555i
$975$	16.1622	+	11.7425i	0.517605	+	0.376062i
$976$	5.75325	−	4.17998i	0.184157	−	0.133798i
$977$	−2.19232	+	6.74726i	−0.0701385	+	0.215864i	−0.979981	−	0.199089i	$-0.936202\pi$
$977$	−2.19232	+	6.74726i	−0.0701385	+	0.215864i	0.909843	+	0.414953i	$0.136202\pi$
$978$	−3.57236			−0.114232
$979$	5.23244	−	25.7466i	0.167229	−	0.822863i
$980$	0.310525			0.00991935
$981$	−4.36789	+	13.4430i	−0.139456	+	0.429202i
$982$	18.9605	−	13.7756i	0.605053	−	0.439597i
$983$	−31.0260	−	22.5417i	−0.989576	−	0.718969i	−0.0297474	−	0.999557i	$-0.509470\pi$
$983$	−31.0260	−	22.5417i	−0.989576	−	0.718969i	−0.959828	+	0.280589i	$0.909470\pi$
$984$	0.674659	+	2.07639i	0.0215073	+	0.0661928i
$985$	−0.846005	−	2.60374i	−0.0269560	−	0.0829619i
$986$	10.2896	+	7.47586i	0.327689	+	0.238080i
$987$	3.02277	−	2.19617i	0.0962158	−	0.0699048i
$988$	−8.20806	+	25.2618i	−0.261133	+	0.803685i
$989$	18.3524			0.583572
$990$	1.30760	+	0.739431i	0.0415581	+	0.0235007i
$991$	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
$993$	−14.7667	+	10.7287i	−0.468608	+	0.340464i
$994$	5.85546	+	4.25424i	0.185724	+	0.134936i
$995$	−1.04940	−	3.22971i	−0.0332681	−	0.102389i
$996$	−3.00735	−	9.25568i	−0.0952916	−	0.293277i
$997$	−12.4675	−	9.05819i	−0.394851	−	0.286876i	0.372590	−	0.927996i	$-0.378470\pi$
$997$	−12.4675	−	9.05819i	−0.394851	−	0.286876i	−0.767440	+	0.641120i	$0.778470\pi$
$998$	3.74319	−	2.71959i	0.118489	−	0.0860871i
$999$	6.06593	−	18.6690i	0.191918	−	0.590662i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.f.a.64.1	✓	8
3.2	odd	2		693.2.m.g.64.2		8
7.2	even	3		539.2.q.c.361.2		16
7.3	odd	6		539.2.q.b.471.1		16
7.4	even	3		539.2.q.c.471.1		16
7.5	odd	6		539.2.q.b.361.2		16
7.6	odd	2		539.2.f.d.295.1		8
11.2	odd	10		847.2.f.s.729.1		8
11.3	even	5		847.2.f.p.323.2		8
11.4	even	5		847.2.a.l.1.2		4
11.5	even	5	inner	77.2.f.a.71.1	yes	8
11.6	odd	10		847.2.f.q.148.2		8
11.7	odd	10		847.2.a.k.1.3		4
11.8	odd	10		847.2.f.s.323.1		8
11.9	even	5		847.2.f.p.729.2		8
11.10	odd	2		847.2.f.q.372.2		8
33.5	odd	10		693.2.m.g.379.2		8
33.26	odd	10		7623.2.a.ch.1.3		4
33.29	even	10		7623.2.a.co.1.2		4
77.5	odd	30		539.2.q.b.214.1		16
77.16	even	15		539.2.q.c.214.1		16
77.27	odd	10		539.2.f.d.148.1		8
77.38	odd	30		539.2.q.b.324.2		16
77.48	odd	10		5929.2.a.bi.1.2		4
77.60	even	15		539.2.q.c.324.2		16
77.62	even	10		5929.2.a.bb.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.64.1	✓	8	1.1	even	1	trivial
77.2.f.a.71.1	yes	8	11.5	even	5	inner
539.2.f.d.148.1		8	77.27	odd	10
539.2.f.d.295.1		8	7.6	odd	2
539.2.q.b.214.1		16	77.5	odd	30
539.2.q.b.324.2		16	77.38	odd	30
539.2.q.b.361.2		16	7.5	odd	6
539.2.q.b.471.1		16	7.3	odd	6
539.2.q.c.214.1		16	77.16	even	15
539.2.q.c.324.2		16	77.60	even	15
539.2.q.c.361.2		16	7.2	even	3
539.2.q.c.471.1		16	7.4	even	3
693.2.m.g.64.2		8	3.2	odd	2
693.2.m.g.379.2		8	33.5	odd	10
847.2.a.k.1.3		4	11.7	odd	10
847.2.a.l.1.2		4	11.4	even	5
847.2.f.p.323.2		8	11.3	even	5
847.2.f.p.729.2		8	11.9	even	5
847.2.f.q.148.2		8	11.6	odd	10
847.2.f.q.372.2		8	11.10	odd	2
847.2.f.s.323.1		8	11.8	odd	10
847.2.f.s.729.1		8	11.2	odd	10
5929.2.a.bb.1.3		4	77.62	even	10
5929.2.a.bi.1.2		4	77.48	odd	10
7623.2.a.ch.1.3		4	33.26	odd	10
7623.2.a.co.1.2		4	33.29	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.240256 + 0.739431i) q^{2} +(-0.500000 + 0.363271i) q^{3} +(1.12900 + 0.820265i) q^{4} +(-0.0687611 - 0.211625i) q^{5} +(-0.148486 - 0.456994i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-2.13577 + 1.55173i) q^{8} +(-0.809017 + 2.48990i) q^{9} +0.173002 q^{10} +(0.660531 - 3.25018i) q^{11} -0.862478 q^{12} +(2.01774 - 6.20997i) q^{13} +(-0.628998 + 0.456994i) q^{14} +(0.111258 + 0.0808336i) q^{15} +(0.228211 + 0.702362i) q^{16} +(-1.33947 - 4.12246i) q^{17} +(-1.64674 - 1.19643i) q^{18} +(-2.35829 + 1.71340i) q^{19} +(0.0959574 - 0.295327i) q^{20} -0.618034 q^{21} +(2.24459 + 1.26929i) q^{22} -3.89796 q^{23} +(0.504188 - 1.55173i) q^{24} +(4.00503 - 2.90982i) q^{25} +(4.10707 + 2.98396i) q^{26} +(-1.07295 - 3.30220i) q^{27} +(0.431239 + 1.32722i) q^{28} +(3.05322 + 2.21829i) q^{29} +(-0.0865012 + 0.0628468i) q^{30} +(-2.12900 + 6.55238i) q^{31} -5.85410 q^{32} +(0.850433 + 1.86504i) q^{33} +3.37009 q^{34} +(0.0687611 - 0.211625i) q^{35} +(-2.95576 + 2.14748i) q^{36} +(4.57379 + 3.32305i) q^{37} +(-0.700347 - 2.15545i) q^{38} +(1.24703 + 3.83797i) q^{39} +(0.475243 + 0.345285i) q^{40} +(-1.08255 + 0.786521i) q^{41} +(0.148486 - 0.456994i) q^{42} -4.70820 q^{43} +(3.41175 - 3.12764i) q^{44} +0.582554 q^{45} +(0.936507 - 2.88227i) q^{46} +(-4.89094 + 3.55348i) q^{47} +(-0.369254 - 0.268279i) q^{48} +(0.309017 + 0.951057i) q^{49} +(1.18938 + 3.66055i) q^{50} +(2.16731 + 1.57464i) q^{51} +(7.37184 - 5.35596i) q^{52} +(-0.530865 + 1.63383i) q^{53} +2.69953 q^{54} +(-0.733239 + 0.0837016i) q^{55} -2.63996 q^{56} +(0.556717 - 1.71340i) q^{57} +(-2.37383 + 1.72469i) q^{58} +(7.71239 + 5.60338i) q^{59} +(0.0593050 + 0.182522i) q^{60} +(-2.97566 - 9.15813i) q^{61} +(-4.33353 - 3.14850i) q^{62} +(-2.11803 + 1.53884i) q^{63} +(0.950059 - 2.92398i) q^{64} -1.45293 q^{65} +(-1.58339 + 0.180749i) q^{66} +1.27155 q^{67} +(1.86925 - 5.75297i) q^{68} +(1.94898 - 1.41602i) q^{69} +(0.139962 + 0.101688i) q^{70} +(-2.87670 - 8.85357i) q^{71} +(-2.13577 - 6.57324i) q^{72} +(-4.52169 - 3.28520i) q^{73} +(-3.55605 + 2.58362i) q^{74} +(-0.945459 + 2.90982i) q^{75} -4.06794 q^{76} +(2.44479 - 2.24120i) q^{77} -3.13752 q^{78} +(-1.39971 + 4.30785i) q^{79} +(0.132945 - 0.0965905i) q^{80} +(-4.61803 - 3.35520i) q^{81} +(-0.321489 - 0.989441i) q^{82} +(3.48688 + 10.7315i) q^{83} +(-0.697759 - 0.506952i) q^{84} +(-0.780313 + 0.566931i) q^{85} +(1.13117 - 3.48139i) q^{86} -2.33245 q^{87} +(3.63267 + 7.96663i) q^{88} +7.92157 q^{89} +(-0.139962 + 0.430759i) q^{90} +(5.28251 - 3.83797i) q^{91} +(-4.40079 - 3.19736i) q^{92} +(-1.31579 - 4.04959i) q^{93} +(-1.45248 - 4.47026i) q^{94} +(0.524757 + 0.381258i) q^{95} +(2.92705 - 2.12663i) q^{96} +(-2.79781 + 8.61078i) q^{97} -0.777484 q^{98} +(7.55825 + 4.27411i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 4 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} - 2 q^{9} - 28 q^{10} + 5 q^{11} - 14 q^{12} + 5 q^{13} + q^{14} + 6 q^{15} - 3 q^{16} - 11 q^{17} + 4 q^{18} - 9 q^{19} + 21 q^{20}+ \cdots + 4 q^{98}+O(q^{100}) \) 8 * q - q^2 - 4 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 - 2 * q^9 - 28 * q^10 + 5 * q^11 - 14 * q^12 + 5 * q^13 + q^14 + 6 * q^15 - 3 * q^16 - 11 * q^17 + 4 * q^18 - 9 * q^19 + 21 * q^20 + 4 * q^21 - q^22 - 16 * q^23 + 21 * q^24 + 5 * q^25 + 21 * q^26 - 22 * q^27 + 7 * q^28 - 9 * q^29 + 14 * q^30 - 11 * q^31 - 20 * q^32 + 10 * q^33 - 24 * q^34 - 3 * q^35 - 2 * q^36 + 6 * q^37 + 35 * q^38 - 5 * q^39 - 16 * q^40 - 22 * q^41 - 3 * q^42 + 16 * q^43 + 29 * q^44 + 18 * q^45 + 29 * q^46 + 7 * q^47 + 4 * q^48 - 2 * q^49 - 34 * q^50 + 3 * q^51 + 21 * q^52 + 2 * q^53 + 4 * q^54 + 26 * q^55 - 18 * q^56 - 3 * q^57 - 39 * q^58 + 25 * q^59 - 38 * q^60 + 7 * q^61 - 5 * q^62 - 8 * q^63 + q^64 + 24 * q^65 + 18 * q^66 - 30 * q^67 + 8 * q^68 + 8 * q^69 - 2 * q^70 - 14 * q^71 + 3 * q^72 + 3 * q^73 - 9 * q^74 + 5 * q^75 - 52 * q^76 - 5 * q^77 - 18 * q^78 - 9 * q^79 - 33 * q^80 - 28 * q^81 + 31 * q^82 + 23 * q^83 + 4 * q^84 - 10 * q^85 - 17 * q^86 + 12 * q^87 - 7 * q^88 - 34 * q^89 + 2 * q^90 + 5 * q^91 - 34 * q^92 + 8 * q^93 - 30 * q^94 + 24 * q^95 + 10 * q^96 + 30 * q^97 + 4 * q^98

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