LMFDB - Embedded newform 684.3.s.a.445.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			445.10
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.21812 - 2.01989i) q^{3} +(-2.05295 - 3.55582i) q^{5} +(-6.48935 - 11.2399i) q^{7} +(0.840121 + 8.96070i) q^{9} +O(q^{10})$	\(q+(-2.21812 - 2.01989i) q^{3} +(-2.05295 - 3.55582i) q^{5} +(-6.48935 - 11.2399i) q^{7} +(0.840121 + 8.96070i) q^{9} +(-7.93892 - 13.7506i) q^{11} +0.390460i q^{13} +(-2.62865 + 12.0340i) q^{15} +(7.48023 - 12.9561i) q^{17} +(-9.33801 - 16.5469i) q^{19} +(-8.30912 + 38.0391i) q^{21} -18.6837 q^{23} +(4.07076 - 7.05077i) q^{25} +(16.2361 - 21.5729i) q^{27} +(13.2027 + 7.62259i) q^{29} +(12.7235 + 7.34592i) q^{31} +(-10.1652 + 46.5363i) q^{33} +(-26.6447 + 46.1499i) q^{35} +35.7838i q^{37} +(0.788684 - 0.866087i) q^{39} +(19.8233 - 11.4450i) q^{41} +16.0986 q^{43} +(30.1379 - 21.3832i) q^{45} +(21.4855 - 37.2140i) q^{47} +(-59.7232 + 103.444i) q^{49} +(-42.7620 + 13.6291i) q^{51} +(17.6872 - 10.2117i) q^{53} +(-32.5965 + 56.4588i) q^{55} +(-12.7101 + 55.5649i) q^{57} +(-60.1406 + 34.7222i) q^{59} +(38.0444 - 65.8948i) q^{61} +(95.2654 - 67.5920i) q^{63} +(1.38840 - 0.801596i) q^{65} +44.8495i q^{67} +(41.4427 + 37.7389i) q^{69} +(20.3029 + 11.7219i) q^{71} +(33.0816 - 57.2991i) q^{73} +(-23.2712 + 7.41698i) q^{75} +(-103.037 + 178.465i) q^{77} +120.865i q^{79} +(-79.5884 + 15.0562i) q^{81} +(-65.1021 - 112.760i) q^{83} -61.4263 q^{85} +(-13.8885 - 43.5758i) q^{87} +(-113.522 + 65.5419i) q^{89} +(4.38872 - 2.53383i) q^{91} +(-13.3844 - 41.9942i) q^{93} +(-39.6675 + 67.1744i) q^{95} +144.324i q^{97} +(116.546 - 82.6905i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.21812	−	2.01989i	−0.739374	−	0.673295i
$3$	−2.21812	−	2.01989i	−0.739374	−	0.673295i
$4$		0			0
$5$	−2.05295	−	3.55582i	−0.410591	−	0.711164i	0.584364	−	0.811492i	$-0.301344\pi$
$5$	−2.05295	−	3.55582i	−0.410591	−	0.711164i	−0.994954	+	0.100328i	$0.968011\pi$
$6$		0			0
$7$	−6.48935	−	11.2399i	−0.927049	−	1.60570i	−0.788231	−	0.615379i	$-0.789003\pi$
$7$	−6.48935	−	11.2399i	−0.927049	−	1.60570i	−0.138818	−	0.990318i	$-0.544330\pi$
$8$		0			0
$9$	0.840121	+	8.96070i	0.0933468	+	0.995634i
$10$		0			0
$11$	−7.93892	−	13.7506i	−0.721720	−	1.25006i	−0.960310	−	0.278936i	$-0.910018\pi$
$11$	−7.93892	−	13.7506i	−0.721720	−	1.25006i	0.238590	−	0.971120i	$-0.423315\pi$
$12$		0			0
$13$			0.390460i			0.0300354i	0.999887	+	0.0150177i	$0.00478046\pi$
$13$			0.390460i			0.0300354i	−0.999887	+	0.0150177i	$0.995220\pi$
$14$		0			0
$15$	−2.62865	+	12.0340i	−0.175243	+	0.802265i
$16$		0			0
$17$	7.48023	−	12.9561i	0.440014	−	0.762126i	−0.557676	−	0.830059i	$-0.688307\pi$
$17$	7.48023	−	12.9561i	0.440014	−	0.762126i	0.997690	+	0.0679325i	$0.0216402\pi$
$18$		0			0
$19$	−9.33801	−	16.5469i	−0.491474	−	0.870892i
$19$	−9.33801	−	16.5469i	−0.491474	−	0.870892i
$20$		0			0
$21$	−8.30912	+	38.0391i	−0.395672	+	1.81139i
$22$		0			0
$23$	−18.6837			−0.812335			−0.406167	−	0.913799i	$-0.633135\pi$
$23$	−18.6837			−0.812335			−0.406167	+	0.913799i	$0.633135\pi$
$24$		0			0
$25$	4.07076	−	7.05077i	0.162831	−	0.282031i
$26$		0			0
$27$	16.2361	−	21.5729i	0.601337	−	0.798995i
$28$		0			0
$29$	13.2027	+	7.62259i	0.455266	+	0.262848i	0.710052	−	0.704150i	$-0.248672\pi$
$29$	13.2027	+	7.62259i	0.455266	+	0.262848i	−0.254785	+	0.966998i	$0.582005\pi$
$30$		0			0
$31$	12.7235	+	7.34592i	0.410436	+	0.236965i	0.690977	−	0.722877i	$-0.257181\pi$
$31$	12.7235	+	7.34592i	0.410436	+	0.236965i	−0.280541	+	0.959842i	$0.590514\pi$
$32$		0			0
$33$	−10.1652	+	46.5363i	−0.308036	+	1.41019i
$34$		0			0
$35$	−26.6447	+	46.1499i	−0.761276	+	1.31857i
$36$		0			0
$37$			35.7838i			0.967131i	0.875308	+	0.483565i	$0.160658\pi$
$37$			35.7838i			0.967131i	−0.875308	+	0.483565i	$0.839342\pi$
$38$		0			0
$39$	0.788684	−	0.866087i	0.0202227	−	0.0222074i
$40$		0			0
$41$	19.8233	−	11.4450i	0.483496	−	0.279146i	−0.238377	−	0.971173i	$-0.576615\pi$
$41$	19.8233	−	11.4450i	0.483496	−	0.279146i	0.721872	+	0.692027i	$0.243282\pi$
$42$		0			0
$43$	16.0986			0.374387			0.187193	−	0.982323i	$-0.440061\pi$
$43$	16.0986			0.374387			0.187193	+	0.982323i	$0.440061\pi$
$44$		0			0
$45$	30.1379	−	21.3832i	0.669731	−	0.475183i
$46$		0			0
$47$	21.4855	−	37.2140i	0.457139	−	0.791787i	−0.541670	−	0.840591i	$-0.682208\pi$
$47$	21.4855	−	37.2140i	0.457139	−	0.791787i	0.998808	+	0.0488042i	$0.0155410\pi$
$48$		0			0
$49$	−59.7232	+	103.444i	−1.21884	+	2.11110i
$50$		0			0
$51$	−42.7620	+	13.6291i	−0.838471	+	0.267237i
$52$		0			0
$53$	17.6872	−	10.2117i	0.333720	−	0.192674i	−0.323771	−	0.946135i	$-0.604951\pi$
$53$	17.6872	−	10.2117i	0.333720	−	0.192674i	0.657492	+	0.753462i	$0.271617\pi$
$54$		0			0
$55$	−32.5965	+	56.4588i	−0.592663	+	1.02652i
$56$		0			0
$57$	−12.7101	+	55.5649i	−0.222984	+	0.974822i
$58$		0			0
$59$	−60.1406	+	34.7222i	−1.01933	+	0.588511i	−0.913910	−	0.405916i	$-0.866952\pi$
$59$	−60.1406	+	34.7222i	−1.01933	+	0.588511i	−0.105421	+	0.994428i	$0.533619\pi$
$60$		0			0
$61$	38.0444	−	65.8948i	0.623679	−	1.08024i	−0.365116	−	0.930962i	$-0.618971\pi$
$61$	38.0444	−	65.8948i	0.623679	−	1.08024i	0.988795	−	0.149281i	$-0.0476959\pi$
$62$		0			0
$63$	95.2654	−	67.5920i	1.51215	−	1.07289i
$64$		0			0
$65$	1.38840	−	0.801596i	0.0213601	−	0.0123322i
$66$		0			0
$67$			44.8495i			0.669396i	0.942325	+	0.334698i	$0.108634\pi$
$67$			44.8495i			0.669396i	−0.942325	+	0.334698i	$0.891366\pi$
$68$		0			0
$69$	41.4427	+	37.7389i	0.600619	+	0.546941i
$70$		0			0
$71$	20.3029	+	11.7219i	0.285957	+	0.165097i	0.636117	−	0.771593i	$-0.280540\pi$
$71$	20.3029	+	11.7219i	0.285957	+	0.165097i	−0.350160	+	0.936690i	$0.613873\pi$
$72$		0			0
$73$	33.0816	−	57.2991i	0.453173	−	0.784919i	−0.545408	−	0.838171i	$-0.683625\pi$
$73$	33.0816	−	57.2991i	0.453173	−	0.784919i	0.998581	+	0.0532517i	$0.0169586\pi$
$74$		0			0
$75$	−23.2712	+	7.41698i	−0.310283	+	0.0988931i
$76$		0			0
$77$	−103.037	+	178.465i	−1.33814	+	2.31773i
$78$		0			0
$79$			120.865i			1.52994i	0.644068	+	0.764968i	$0.277245\pi$
$79$			120.865i			1.52994i	−0.644068	+	0.764968i	$0.722755\pi$
$80$		0			0
$81$	−79.5884	+	15.0562i	−0.982573	+	0.185878i
$82$		0			0
$83$	−65.1021	−	112.760i	−0.784363	−	1.35856i	−0.929379	−	0.369127i	$-0.879657\pi$
$83$	−65.1021	−	112.760i	−0.784363	−	1.35856i	0.145016	−	0.989429i	$-0.453677\pi$
$84$		0			0
$85$	−61.4263			−0.722662
$86$		0			0
$87$	−13.8885	−	43.5758i	−0.159637	−	0.500872i
$88$		0			0
$89$	−113.522	+	65.5419i	−1.27553	+	0.736426i	−0.976023	−	0.217669i	$-0.930155\pi$
$89$	−113.522	+	65.5419i	−1.27553	+	0.736426i	−0.299505	+	0.954095i	$0.596821\pi$
$90$		0			0
$91$	4.38872	−	2.53383i	0.0482277	−	0.0278443i
$92$		0			0
$93$	−13.3844	−	41.9942i	−0.143918	−	0.451550i
$94$		0			0
$95$	−39.6675	+	67.1744i	−0.417552	+	0.707099i
$96$		0			0
$97$			144.324i			1.48788i	0.668249	+	0.743938i	$0.267044\pi$
$97$			144.324i			1.48788i	−0.668249	+	0.743938i	$0.732956\pi$
$98$		0			0
$99$	116.546	−	82.6905i	1.17723	−	0.835258i
$100$		0			0
$101$	90.9289	−	157.493i	0.900286	−	1.55934i	0.0731633	−	0.997320i	$-0.476691\pi$
$101$	90.9289	−	157.493i	0.900286	−	1.55934i	0.827123	−	0.562021i	$-0.189976\pi$
$102$		0			0
$103$	123.209	+	71.1348i	1.19621	+	0.690629i	0.959707	−	0.281002i	$-0.0906669\pi$
$103$	123.209	+	71.1348i	1.19621	+	0.690629i	0.236498	+	0.971632i	$0.424000\pi$
$104$		0			0
$105$	152.319	−	48.5469i	1.45065	−	0.462351i
$106$		0			0
$107$			7.60032i			0.0710310i	0.999369	+	0.0355155i	$0.0113073\pi$
$107$			7.60032i			0.0710310i	−0.999369	+	0.0355155i	$0.988693\pi$
$108$		0			0
$109$	−48.7475	−	28.1444i	−0.447225	−	0.258205i	0.259433	−	0.965761i	$-0.416464\pi$
$109$	−48.7475	−	28.1444i	−0.447225	−	0.258205i	−0.706657	+	0.707556i	$0.749798\pi$
$110$		0			0
$111$	72.2793	−	79.3729i	0.651165	−	0.715071i
$112$		0			0
$113$	42.3909	+	24.4744i	0.375141	+	0.216588i	0.675702	−	0.737175i	$-0.263841\pi$
$113$	42.3909	+	24.4744i	0.375141	+	0.216588i	−0.300561	+	0.953763i	$0.597174\pi$
$114$		0			0
$115$	38.3568	+	66.4359i	0.333537	+	0.577703i
$116$		0			0
$117$	−3.49879	+	0.328034i	−0.0299042	+	0.00280371i
$118$		0			0
$119$	−194.167			−1.63166
$120$		0			0
$121$	−65.5530	+	113.541i	−0.541760	+	0.938356i
$122$		0			0
$123$	−67.0881	−	14.6545i	−0.545432	−	0.119142i
$124$		0			0
$125$	−136.076			−1.08861
$126$		0			0
$127$	198.477	−	114.591i	1.56281	−	0.902288i	0.565838	−	0.824516i	$-0.308553\pi$
$127$	198.477	−	114.591i	1.56281	−	0.902288i	0.996971	−	0.0777721i	$-0.0247807\pi$
$128$		0			0
$129$	−35.7087	−	32.5174i	−0.276812	−	0.252073i
$130$		0			0
$131$	32.2676	+	55.8891i	0.246317	+	0.426634i	0.962501	−	0.271278i	$-0.0874461\pi$
$131$	32.2676	+	55.8891i	0.246317	+	0.426634i	−0.716184	+	0.697912i	$0.754113\pi$
$132$		0			0
$133$	−125.388	+	212.337i	−0.942767	+	1.59652i
$134$		0			0
$135$	−110.041	−	13.4446i	−0.815120	−	0.0995894i
$136$		0			0
$137$	49.4849	−	85.7103i	0.361204	−	0.625623i	−0.626956	−	0.779055i	$-0.715699\pi$
$137$	49.4849	−	85.7103i	0.361204	−	0.625623i	0.988159	+	0.153432i	$0.0490326\pi$
$138$		0			0
$139$	123.733			0.890166			0.445083	−	0.895489i	$-0.353174\pi$
$139$	123.733			0.890166			0.445083	+	0.895489i	$0.353174\pi$
$140$		0			0
$141$	−122.825	+	39.1469i	−0.871103	+	0.277637i
$142$		0			0
$143$	5.36906	−	3.09983i	0.0375459	−	0.0216771i
$144$		0			0
$145$		−	62.5953i		−	0.431692i
$146$		0			0
$147$	341.418	−	108.816i	2.32257	−	0.740248i
$148$		0			0
$149$	−76.3395	−	132.224i	−0.512345	−	0.887408i	−0.999898	−	0.0143143i	$-0.995443\pi$
$149$	−76.3395	−	132.224i	−0.512345	−	0.887408i	0.487552	−	0.873094i	$-0.337890\pi$
$150$		0			0
$151$	−77.0133	+	44.4637i	−0.510022	+	0.294461i	−0.732843	−	0.680398i	$-0.761807\pi$
$151$	−77.0133	+	44.4637i	−0.510022	+	0.294461i	0.222821	+	0.974859i	$0.428474\pi$
$152$		0			0
$153$	122.380	+	56.1434i	0.799872	+	0.366950i
$154$		0			0
$155$		−	60.3234i		−	0.389183i
$156$		0			0
$157$	−95.5975	−	165.580i	−0.608901	−	1.05465i	−0.991422	−	0.130701i	$-0.958277\pi$
$157$	−95.5975	−	165.580i	−0.608901	−	1.05465i	0.382521	−	0.923947i	$-0.375056\pi$
$158$		0			0
$159$	−59.8588	−	13.0753i	−0.376470	−	0.0822346i
$160$		0			0
$161$	121.245	+	210.002i	0.753074	+	1.30436i
$162$		0			0
$163$	13.9541			0.0856080			0.0428040	−	0.999083i	$-0.486371\pi$
$163$	13.9541			0.0856080			0.0428040	+	0.999083i	$0.486371\pi$
$164$		0			0
$165$	186.343	−	59.3912i	1.12935	−	0.359947i
$166$		0			0
$167$		−	238.675i		−	1.42919i	−0.699538	−	0.714596i	$-0.746611\pi$
$167$		−	238.675i		−	1.42919i	0.699538	−	0.714596i	$-0.253389\pi$
$168$		0			0
$169$	168.848			0.999098
$170$		0			0
$171$	140.427	−	97.5766i	0.821212	−	0.570623i
$172$		0			0
$173$		−	141.566i		−	0.818300i	−0.912467	−	0.409150i	$-0.865825\pi$
$173$		−	141.566i		−	0.818300i	0.912467	−	0.409150i	$-0.134175\pi$
$174$		0			0
$175$	−105.666			−0.603808
$176$		0			0
$177$	203.534	+	44.4591i	1.14991	+	0.251181i
$178$		0			0
$179$		−	253.540i		−	1.41643i	−0.705998	−	0.708214i	$-0.749501\pi$
$179$		−	253.540i		−	1.41643i	0.705998	−	0.708214i	$-0.250499\pi$
$180$		0			0
$181$	−200.068	+	115.509i	−1.10535	+	0.638173i	−0.937620	−	0.347661i	$-0.886976\pi$
$181$	−200.068	+	115.509i	−1.10535	+	0.638173i	−0.167727	+	0.985833i	$0.553643\pi$
$182$		0			0
$183$	−217.487	+	69.3173i	−1.18845	+	0.378783i
$184$		0			0
$185$	127.241	−	73.4626i	0.687789	−	0.397095i
$186$		0			0
$187$	−237.540			−1.27027
$188$		0			0
$189$	−347.838	−	42.4980i	−1.84041	−	0.224857i
$190$		0			0
$191$	−135.073	−	233.954i	−0.707190	−	1.22489i	−0.965895	−	0.258933i	$-0.916629\pi$
$191$	−135.073	−	233.954i	−0.707190	−	1.22489i	0.258705	−	0.965956i	$-0.416704\pi$
$192$		0			0
$193$	21.6562	−	12.5032i	0.112208	−	0.0647835i	−0.442845	−	0.896598i	$-0.646031\pi$
$193$	21.6562	−	12.5032i	0.112208	−	0.0647835i	0.555054	+	0.831814i	$0.312698\pi$
$194$		0			0
$195$	−4.69878	−	1.02638i	−0.0240963	−	0.00526350i
$196$		0			0
$197$	243.933			1.23824			0.619119	−	0.785297i	$-0.287490\pi$
$197$	243.933			1.23824			0.619119	+	0.785297i	$0.287490\pi$
$198$		0			0
$199$	−86.3189	−	149.509i	−0.433763	−	0.751300i	0.563431	−	0.826163i	$-0.309481\pi$
$199$	−86.3189	−	149.509i	−0.433763	−	0.751300i	−0.997194	+	0.0748635i	$0.976148\pi$
$200$		0			0
$201$	90.5910	−	99.4817i	0.450701	−	0.494934i
$202$		0			0
$203$		−	197.863i		−	0.974693i
$204$		0			0
$205$	−81.3927	−	46.9921i	−0.397038	−	0.229230i
$206$		0			0
$207$	−15.6966	−	167.419i	−0.0758289	−	0.808788i
$208$		0			0
$209$	−153.397	+	259.768i	−0.733957	+	1.24291i
$210$		0			0
$211$	−69.6073	+	40.1878i	−0.329892	+	0.190463i	−0.655793	−	0.754941i	$-0.727666\pi$
$211$	−69.6073	+	40.1878i	−0.329892	+	0.190463i	0.325901	+	0.945404i	$0.394332\pi$
$212$		0			0
$213$	−21.3574	−	67.0101i	−0.100270	−	0.314602i
$214$		0			0
$215$	−33.0497	−	57.2438i	−0.153720	−	0.266250i
$216$		0			0
$217$		−	190.681i		−	0.878714i
$218$		0			0
$219$	−189.117	+	60.2752i	−0.863547	+	0.275229i
$220$		0			0
$221$	5.05885	+	2.92073i	0.0228907	+	0.0132160i
$222$		0			0
$223$		−	130.404i		−	0.584772i	−0.956300	−	0.292386i	$-0.905551\pi$
$223$		−	130.404i		−	0.584772i	0.956300	−	0.292386i	$-0.0944493\pi$
$224$		0			0
$225$	66.5998	+	30.5534i	0.295999	+	0.135793i
$226$		0			0
$227$	−32.0290	+	18.4920i	−0.141097	+	0.0814624i	−0.568887	−	0.822416i	$-0.692626\pi$
$227$	−32.0290	+	18.4920i	−0.141097	+	0.0814624i	0.427790	+	0.903878i	$0.359292\pi$
$228$		0			0
$229$	−79.1349	+	137.066i	−0.345567	+	0.598540i	−0.985457	−	0.169927i	$-0.945647\pi$
$229$	−79.1349	+	137.066i	−0.345567	+	0.598540i	0.639889	+	0.768467i	$0.278980\pi$
$230$		0			0
$231$	589.027	−	187.734i	2.54990	−	0.812703i
$232$		0			0
$233$	−125.476	+	217.331i	−0.538525	+	0.932753i	0.460459	+	0.887681i	$0.347685\pi$
$233$	−125.476	+	217.331i	−0.538525	+	0.932753i	−0.998984	+	0.0450717i	$0.985648\pi$
$234$		0			0
$235$	−176.435			−0.750787
$236$		0			0
$237$	244.133	−	268.093i	1.03010	−	1.13119i
$238$		0			0
$239$	−87.5050	+	151.563i	−0.366130	+	0.634155i	−0.988957	−	0.148204i	$-0.952651\pi$
$239$	−87.5050	+	151.563i	−0.366130	+	0.634155i	0.622827	+	0.782360i	$0.285984\pi$
$240$		0			0
$241$	296.093	+	170.949i	1.22860	+	0.709333i	0.966737	−	0.255772i	$-0.0823298\pi$
$241$	296.093	+	170.949i	1.22860	+	0.709333i	0.261863	+	0.965105i	$0.415663\pi$
$242$		0			0
$243$	206.948	+	127.363i	0.851640	+	0.524128i
$244$		0			0
$245$	490.436			2.00178
$246$		0			0
$247$	6.46092	−	3.64612i	0.0261576	−	0.0147616i
$248$		0			0
$249$	−83.3583	+	381.615i	−0.334772	+	1.53259i
$250$		0			0
$251$	−138.459	−	239.818i	−0.551630	−	0.955451i	−0.998157	−	0.0606811i	$-0.980673\pi$
$251$	−138.459	−	239.818i	−0.551630	−	0.955451i	0.446527	−	0.894770i	$-0.352661\pi$
$252$		0			0
$253$	148.328	+	256.912i	0.586278	+	1.01546i
$254$		0			0
$255$	136.251	+	124.074i	0.534317	+	0.486565i
$256$		0			0
$257$		−	94.7767i		−	0.368781i	−0.982853	−	0.184390i	$-0.940969\pi$
$257$		−	94.7767i		−	0.368781i	0.982853	−	0.184390i	$-0.0590311\pi$
$258$		0			0
$259$	402.206	−	232.214i	1.55292	−	0.896578i
$260$		0			0
$261$	−57.2119	+	124.710i	−0.219203	+	0.477814i
$262$		0			0
$263$	104.855			0.398688			0.199344	−	0.979930i	$-0.436119\pi$
$263$	104.855			0.398688			0.199344	+	0.979930i	$0.436119\pi$
$264$		0			0
$265$	−72.6219	−	41.9283i	−0.274045	−	0.158220i
$266$		0			0
$267$	384.193	+	83.9215i	1.43892	+	0.314313i
$268$		0			0
$269$	122.868	+	70.9381i	0.456760	+	0.263711i	0.710681	−	0.703514i	$-0.248387\pi$
$269$	122.868	+	70.9381i	0.456760	+	0.263711i	−0.253921	+	0.967225i	$0.581720\pi$
$270$		0			0
$271$	−48.7803	+	84.4900i	−0.180001	+	0.311771i	−0.941881	−	0.335948i	$-0.890943\pi$
$271$	−48.7803	+	84.4900i	−0.180001	+	0.311771i	0.761879	+	0.647719i	$0.224277\pi$
$272$		0			0
$273$	−14.8528	−	3.24437i	−0.0544057	−	0.0118842i
$274$		0			0
$275$	−129.270			−0.470072
$276$		0			0
$277$	85.1441	+	147.474i	0.307379	+	0.532397i	0.977788	−	0.209595i	$-0.0672146\pi$
$277$	85.1441	+	147.474i	0.307379	+	0.532397i	−0.670409	+	0.741992i	$0.733881\pi$
$278$		0			0
$279$	−55.1353	+	120.183i	−0.197618	+	0.430764i
$280$		0			0
$281$	−424.449	−	245.056i	−1.51050	−	0.872085i	−0.999925	−	0.0122499i	$-0.996101\pi$
$281$	−424.449	−	245.056i	−1.51050	−	0.872085i	−0.510571	−	0.859835i	$-0.670566\pi$
$282$		0			0
$283$	218.630	+	378.679i	0.772545	+	1.33809i	0.936164	+	0.351564i	$0.114350\pi$
$283$	218.630	+	378.679i	0.772545	+	1.33809i	−0.163619	+	0.986524i	$0.552317\pi$
$284$		0			0
$285$	223.672	−	68.8772i	0.784814	−	0.241674i
$286$		0			0
$287$	−257.281	−	148.541i	−0.896449	−	0.517565i
$288$		0			0
$289$	32.5922	+	56.4514i	0.112776	+	0.195333i
$290$		0			0
$291$	291.518	−	320.128i	1.00178	−	1.10010i
$292$		0			0
$293$	232.886	+	134.457i	0.794831	+	0.458896i	0.841661	−	0.540007i	$-0.181578\pi$
$293$	232.886	+	134.457i	0.794831	+	0.458896i	−0.0468294	+	0.998903i	$0.514912\pi$
$294$		0			0
$295$	246.932	+	142.566i	0.837056	+	0.483275i
$296$		0			0
$297$	−425.538	−	51.9911i	−1.43279	−	0.175054i
$298$		0			0
$299$		−	7.29523i		−	0.0243988i
$300$		0			0
$301$	−104.470	−	180.947i	−0.347075	−	0.601152i
$302$		0			0
$303$	−519.810	+	165.674i	−1.71554	+	0.546777i
$304$		0			0
$305$	−312.413			−1.02431
$306$		0			0
$307$	222.433	+	128.422i	0.724536	+	0.418311i	0.816420	−	0.577459i	$-0.195956\pi$
$307$	222.433	+	128.422i	0.724536	+	0.418311i	−0.0918838	+	0.995770i	$0.529289\pi$
$308$		0			0
$309$	−129.609	−	406.654i	−0.419445	−	1.31603i
$310$		0			0
$311$	77.6546	−	134.502i	0.249693	−	0.432482i	−0.713747	−	0.700403i	$-0.753004\pi$
$311$	77.6546	−	134.502i	0.249693	−	0.432482i	0.963441	+	0.267922i	$0.0863369\pi$
$312$		0			0
$313$	−82.9289	+	143.637i	−0.264949	+	0.458905i	−0.967550	−	0.252679i	$-0.918688\pi$
$313$	−82.9289	+	143.637i	−0.264949	+	0.458905i	0.702602	+	0.711584i	$0.252022\pi$
$314$		0			0
$315$	−435.920	−	199.983i	−1.38387	−	0.634868i
$316$		0			0
$317$	−240.589	−	138.904i	−0.758957	−	0.438184i	0.0699642	−	0.997550i	$-0.477711\pi$
$317$	−240.589	−	138.904i	−0.758957	−	0.438184i	−0.828921	+	0.559366i	$0.811045\pi$
$318$		0			0
$319$		−	242.061i		−	0.758811i
$320$		0			0
$321$	15.3518	−	16.8584i	0.0478248	−	0.0525185i
$322$		0			0
$323$	−284.235	−	2.79038i	−0.879985	−	0.00863893i
$324$		0			0
$325$	2.75304	+	1.58947i	0.00847090	+	0.00489067i
$326$		0			0
$327$	51.2794	+	160.892i	0.156818	+	0.492025i
$328$		0			0
$329$	−557.708			−1.69516
$330$		0			0
$331$	−231.109	+	133.431i	−0.698213	+	0.403113i	−0.806682	−	0.590986i	$-0.798739\pi$
$331$	−231.109	+	133.431i	−0.698213	+	0.403113i	0.108468	+	0.994100i	$0.465405\pi$
$332$		0			0
$333$	−320.648	+	30.0628i	−0.962908	+	0.0902786i
$334$		0			0
$335$	159.477	−	92.0740i	0.476050	−	0.274848i
$336$		0			0
$337$	339.761	−	196.161i	1.00819	−	0.582080i	0.0975308	−	0.995233i	$-0.468906\pi$
$337$	339.761	−	196.161i	1.00819	−	0.582080i	0.910662	+	0.413152i	$0.135572\pi$
$338$		0			0
$339$	−44.5927	−	139.912i	−0.131542	−	0.412720i
$340$		0			0
$341$		−	233.275i		−	0.684090i
$342$		0			0
$343$	914.303			2.66561
$344$		0			0
$345$	49.1129	−	224.839i	0.142356	−	0.651707i
$346$		0			0
$347$	234.248	+	405.730i	0.675067	+	1.16925i	0.976449	+	0.215747i	$0.0692186\pi$
$347$	234.248	+	405.730i	0.675067	+	1.16925i	−0.301382	+	0.953503i	$0.597448\pi$
$348$		0			0
$349$	−292.595	−	506.789i	−0.838380	−	1.45212i	−0.891248	−	0.453515i	$-0.850170\pi$
$349$	−292.595	−	506.789i	−0.838380	−	1.45212i	0.0528684	−	0.998601i	$-0.483164\pi$
$350$		0			0
$351$	8.42334	+	6.33955i	0.0239981	+	0.0180614i
$352$		0			0
$353$	−4.23602	−	7.33701i	−0.0120001	−	0.0207847i	0.859963	−	0.510356i	$-0.170486\pi$
$353$	−4.23602	−	7.33701i	−0.0120001	−	0.0207847i	−0.871963	+	0.489572i	$0.837153\pi$
$354$		0			0
$355$		−	96.2580i		−	0.271149i
$356$		0			0
$357$	430.687	+	392.196i	1.20640	+	1.09859i
$358$		0			0
$359$	−134.445	+	232.865i	−0.374498	+	0.648650i	−0.990252	−	0.139289i	$-0.955518\pi$
$359$	−134.445	+	232.865i	−0.374498	+	0.648650i	0.615754	+	0.787939i	$0.288852\pi$
$360$		0			0
$361$	−186.603	+	309.031i	−0.516906	+	0.856042i
$362$		0			0
$363$	374.745	−	119.438i	1.03235	−	0.329031i
$364$		0			0
$365$	−271.660			−0.744275
$366$		0			0
$367$	−300.091	+	519.773i	−0.817686	+	1.41627i	0.0896967	+	0.995969i	$0.471410\pi$
$367$	−300.091	+	519.773i	−0.817686	+	1.41627i	−0.907383	+	0.420305i	$0.861923\pi$
$368$		0			0
$369$	119.209	+	168.016i	0.323060	+	0.455327i
$370$		0			0
$371$	−229.557	−	132.535i	−0.618751	−	0.357236i
$372$		0			0
$373$	−468.871	−	270.703i	−1.25703	−	0.725745i	−0.284531	−	0.958667i	$-0.591838\pi$
$373$	−468.871	−	270.703i	−1.25703	−	0.725745i	−0.972495	+	0.232922i	$0.925171\pi$
$374$		0			0
$375$	301.833	+	274.858i	0.804888	+	0.732955i
$376$		0			0
$377$	−2.97632	+	5.15513i	−0.00789474	+	0.0136741i
$378$		0			0
$379$		−	387.805i		−	1.02323i	−0.859214	−	0.511617i	$-0.829047\pi$
$379$		−	387.805i		−	1.02323i	0.859214	−	0.511617i	$-0.170953\pi$
$380$		0			0
$381$	−671.706	−	146.725i	−1.76301	−	0.385104i
$382$		0			0
$383$	83.5548	−	48.2404i	0.218159	−	0.125954i	−0.386939	−	0.922105i	$-0.626467\pi$
$383$	83.5548	−	48.2404i	0.218159	−	0.125954i	0.605097	+	0.796151i	$0.293134\pi$
$384$		0			0
$385$	846.119			2.19771
$386$		0			0
$387$	13.5248	+	144.255i	0.0349478	+	0.372752i
$388$		0			0
$389$	−173.311	+	300.183i	−0.445530	+	0.771680i	−0.998089	−	0.0617937i	$-0.980318\pi$
$389$	−173.311	+	300.183i	−0.445530	+	0.771680i	0.552559	+	0.833474i	$0.313651\pi$
$390$		0			0
$391$	−139.758	+	242.069i	−0.357438	+	0.619102i
$392$		0			0
$393$	41.3162	−	189.146i	0.105130	−	0.481286i
$394$		0			0
$395$	429.774	−	248.130i	1.08804	−	0.628177i
$396$		0			0
$397$	42.6512	−	73.8740i	0.107434	−	0.186081i	−0.807296	−	0.590146i	$-0.799070\pi$
$397$	42.6512	−	73.8740i	0.107434	−	0.186081i	0.914730	+	0.404066i	$0.132403\pi$
$398$		0			0
$399$	707.022	−	217.720i	1.77199	−	0.545663i
$400$		0			0
$401$	−418.030	+	241.350i	−1.04247	+	0.601870i	−0.920532	−	0.390668i	$-0.872244\pi$
$401$	−418.030	+	241.350i	−1.04247	+	0.601870i	−0.121937	+	0.992538i	$0.538911\pi$
$402$		0			0
$403$	−2.86829	+	4.96802i	−0.00711734	+	0.0123276i
$404$		0			0
$405$	216.928	+	252.092i	0.535625	+	0.622450i
$406$		0			0
$407$	492.050	−	284.085i	1.20897	−	0.697998i
$408$		0			0
$409$			539.601i			1.31932i	0.751566	+	0.659658i	$0.229299\pi$
$409$			539.601i			1.31932i	−0.751566	+	0.659658i	$0.770701\pi$
$410$		0			0
$411$	−282.889	+	90.1621i	−0.688293	+	0.219372i
$412$		0			0
$413$	780.546	+	450.648i	1.88994	+	1.09116i
$414$		0			0
$415$	−267.303	+	462.983i	−0.644104	+	1.11562i
$416$		0			0
$417$	−274.455	−	249.927i	−0.658165	−	0.599345i
$418$		0			0
$419$	−345.181	+	597.871i	−0.823820	+	1.42690i	0.0789970	+	0.996875i	$0.474828\pi$
$419$	−345.181	+	597.871i	−0.823820	+	1.42690i	−0.902817	+	0.430024i	$0.858505\pi$
$420$		0			0
$421$		−	426.877i		−	1.01396i	−0.861958	−	0.506980i	$-0.830762\pi$
$421$		−	426.877i		−	1.01396i	0.861958	−	0.506980i	$-0.169238\pi$
$422$		0			0
$423$	351.514	+	161.261i	0.831002	+	0.381232i
$424$		0			0
$425$	−60.9005	−	105.483i	−0.143295	−	0.248195i
$426$		0			0
$427$	−987.533			−2.31272
$428$		0			0
$429$	−18.1705	−	3.96910i	−0.0423556	−	0.00925197i
$430$		0			0
$431$	−132.173	+	76.3101i	−0.306666	+	0.177054i	−0.645434	−	0.763816i	$-0.723323\pi$
$431$	−132.173	+	76.3101i	−0.306666	+	0.177054i	0.338768	+	0.940870i	$0.389990\pi$
$432$		0			0
$433$	−272.158	+	157.131i	−0.628541	+	0.362889i	−0.780187	−	0.625546i	$-0.784876\pi$
$433$	−272.158	+	157.131i	−0.628541	+	0.362889i	0.151646	+	0.988435i	$0.451543\pi$
$434$		0			0
$435$	−126.435	+	138.844i	−0.290656	+	0.319182i
$436$		0			0
$437$	174.469	+	309.158i	0.399242	+	0.707456i
$438$		0			0
$439$		−	679.923i		−	1.54880i	−0.632697	−	0.774399i	$-0.718052\pi$
$439$		−	679.923i		−	1.54880i	0.632697	−	0.774399i	$-0.281948\pi$
$440$		0			0
$441$	−977.103	−	448.257i	−2.21565	−	1.01646i
$442$		0			0
$443$	−51.4605	+	89.1323i	−0.116164	+	0.201201i	−0.918244	−	0.396014i	$-0.870393\pi$
$443$	−51.4605	+	89.1323i	−0.116164	+	0.201201i	0.802081	+	0.597216i	$0.203726\pi$
$444$		0			0
$445$	466.111	+	269.109i	1.04744	+	0.604739i
$446$		0			0
$447$	−97.7469	+	447.485i	−0.218673	+	1.00109i
$448$		0			0
$449$			723.036i			1.61033i	0.593053	+	0.805163i	$0.297922\pi$
$449$			723.036i			1.61033i	−0.593053	+	0.805163i	$0.702078\pi$
$450$		0			0
$451$	−314.752	−	181.722i	−0.697897	−	0.402931i
$452$		0			0
$453$	260.636	+	56.9324i	0.575356	+	0.125679i
$454$		0			0
$455$	−18.0197	−	10.4037i	−0.0396037	−	0.0228652i
$456$		0			0
$457$	68.0568	+	117.878i	0.148921	+	0.257938i	0.930829	−	0.365455i	$-0.119087\pi$
$457$	68.0568	+	117.878i	0.148921	+	0.257938i	−0.781908	+	0.623394i	$0.785753\pi$
$458$		0			0
$459$	−158.051	−	371.727i	−0.344339	−	0.809864i
$460$		0			0
$461$	793.339			1.72091			0.860455	−	0.509527i	$-0.170180\pi$
$461$	793.339			1.72091			0.860455	+	0.509527i	$0.170180\pi$
$462$		0			0
$463$	−13.1918	+	22.8488i	−0.0284919	+	0.0493495i	−0.879920	−	0.475122i	$-0.842404\pi$
$463$	−13.1918	+	22.8488i	−0.0284919	+	0.0493495i	0.851428	+	0.524472i	$0.175737\pi$
$464$		0			0
$465$	−121.846	+	133.804i	−0.262035	+	0.287752i
$466$		0			0
$467$	220.125			0.471361			0.235680	−	0.971831i	$-0.424268\pi$
$467$	220.125			0.471361			0.235680	+	0.971831i	$0.424268\pi$
$468$		0			0
$469$	504.103	−	291.044i	1.07485	−	0.620563i
$470$		0			0
$471$	−122.405	+	560.372i	−0.259884	+	1.18975i
$472$		0			0
$473$	−127.806	−	221.366i	−0.270202	−	0.468004i
$474$		0			0
$475$	−154.682	−	1.51853i	−0.325645	−	0.00319691i
$476$		0			0
$477$	106.363	+	149.911i	0.222984	+	0.314278i
$478$		0			0
$479$	−117.813	+	204.057i	−0.245955	+	0.426007i	−0.962400	−	0.271637i	$-0.912435\pi$
$479$	−117.813	+	204.057i	−0.245955	+	0.426007i	0.716445	+	0.697644i	$0.245768\pi$
$480$		0			0
$481$	−13.9721			−0.0290481
$482$		0			0
$483$	155.245	−	710.712i	0.321418	−	1.47145i
$484$		0			0
$485$	513.190	−	296.290i	1.05812	−	0.610908i
$486$		0			0
$487$			511.738i			1.05080i	0.850856	+	0.525398i	$0.176084\pi$
$487$			511.738i			1.05080i	−0.850856	+	0.525398i	$0.823916\pi$
$488$		0			0
$489$	−30.9519	−	28.1857i	−0.0632963	−	0.0576395i
$490$		0			0
$491$	−29.5262	−	51.1408i	−0.0601348	−	0.104156i	0.834391	−	0.551173i	$-0.185820\pi$
$491$	−29.5262	−	51.1408i	−0.0601348	−	0.104156i	−0.894526	+	0.447017i	$0.852486\pi$
$492$		0			0
$493$	197.519	−	114.038i	0.400647	−	0.231314i
$494$		0			0
$495$	−533.295	−	244.655i	−1.07736	−	0.494253i
$496$		0			0
$497$		−	304.270i		−	0.612213i
$498$		0			0
$499$	137.211	+	237.656i	0.274971	+	0.476264i	0.970128	−	0.242594i	$-0.0779983\pi$
$499$	137.211	+	237.656i	0.274971	+	0.476264i	−0.695157	+	0.718858i	$0.744665\pi$
$500$		0			0
$501$	−482.096	+	529.410i	−0.962268	+	1.05671i
$502$		0			0
$503$	301.952	+	522.996i	0.600302	+	1.03975i	0.992775	+	0.119990i	$0.0382863\pi$
$503$	301.952	+	522.996i	0.600302	+	1.03975i	−0.392473	+	0.919763i	$0.628380\pi$
$504$		0			0
$505$	−746.691			−1.47860
$506$		0			0
$507$	−374.524	−	341.053i	−0.738707	−	0.672688i
$508$		0			0
$509$		−	684.790i		−	1.34536i	−0.739932	−	0.672682i	$-0.765142\pi$
$509$		−	684.790i		−	1.34536i	0.739932	−	0.672682i	$-0.234858\pi$
$510$		0			0
$511$	−858.713			−1.68046
$512$		0			0
$513$	−508.578	−	67.2102i	−0.991381	−	0.131014i
$514$		0			0
$515$		−	584.146i		−	1.13426i
$516$		0			0
$517$	−682.287			−1.31970
$518$		0			0
$519$	−285.947	+	314.010i	−0.550957	+	0.605029i
$520$		0			0
$521$			868.338i			1.66668i	0.552763	+	0.833338i	$0.313573\pi$
$521$			868.338i			1.66668i	−0.552763	+	0.833338i	$0.686427\pi$
$522$		0			0
$523$	−746.158	+	430.795i	−1.42669	+	0.823699i	−0.996858	−	0.0792098i	$-0.974760\pi$
$523$	−746.158	+	430.795i	−1.42669	+	0.823699i	−0.429831	+	0.902909i	$0.641427\pi$
$524$		0			0
$525$	234.381	+	213.434i	0.446440	+	0.406541i
$526$		0			0
$527$	190.350	−	109.898i	0.361195	−	0.208536i
$528$		0			0
$529$	−179.919			−0.340112
$530$		0			0
$531$	−361.660	−	509.731i	−0.681093	−	0.959945i
$532$		0			0
$533$	4.46881	+	7.74021i	0.00838426	+	0.0145220i
$534$		0			0
$535$	27.0254	−	15.6031i	0.0505147	−	0.0291647i
$536$		0			0
$537$	−512.123	+	562.383i	−0.953674	+	1.04727i
$538$		0			0
$539$	1896.55			3.51865
$540$		0			0
$541$	−395.214	−	684.531i	−0.730526	−	1.26531i	−0.956659	−	0.291211i	$-0.905942\pi$
$541$	−395.214	−	684.531i	−0.730526	−	1.26531i	0.226133	−	0.974096i	$-0.427392\pi$
$542$		0			0
$543$	677.090	+	147.901i	1.24694	+	0.272377i
$544$		0			0
$545$			231.116i			0.424067i
$546$		0			0
$547$	−391.263	−	225.896i	−0.715288	−	0.412972i	0.0977278	−	0.995213i	$-0.468843\pi$
$547$	−391.263	−	225.896i	−0.715288	−	0.412972i	−0.813016	+	0.582241i	$0.802176\pi$
$548$		0			0
$549$	622.426	+	285.545i	1.13374	+	0.520118i
$550$		0			0
$551$	2.84348	−	289.645i	0.00516058	−	0.525671i
$552$		0			0
$553$	1358.51	−	784.334i	2.45661	−	1.41833i
$554$		0			0
$555$	−430.622	−	94.0632i	−0.775895	−	0.169483i
$556$		0			0
$557$	−510.833	−	884.789i	−0.917115	−	1.58849i	−0.803775	−	0.594934i	$-0.797178\pi$
$557$	−510.833	−	884.789i	−0.917115	−	1.58849i	−0.113341	−	0.993556i	$-0.536155\pi$
$558$		0			0
$559$			6.28587i			0.0112448i
$560$		0			0
$561$	526.892	+	479.804i	0.939202	+	0.855265i
$562$		0			0
$563$	264.370	+	152.634i	0.469574	+	0.271109i	0.716061	−	0.698037i	$-0.245943\pi$
$563$	264.370	+	152.634i	0.469574	+	0.271109i	−0.246487	+	0.969146i	$0.579276\pi$
$564$		0			0
$565$		−	200.979i		−	0.355716i
$566$		0			0
$567$	685.706	+	796.859i	1.20936	+	1.40540i
$568$		0			0
$569$	−576.757	+	332.991i	−1.01363	+	0.585221i	−0.912253	−	0.409626i	$-0.865659\pi$
$569$	−576.757	+	332.991i	−1.01363	+	0.585221i	−0.101380	+	0.994848i	$0.532326\pi$
$570$		0			0
$571$	111.463	−	193.060i	0.195207	−	0.338108i	−0.751761	−	0.659435i	$-0.770795\pi$
$571$	111.463	−	193.060i	0.195207	−	0.338108i	0.946968	+	0.321327i	$0.104129\pi$
$572$		0			0
$573$	−172.951	+	791.770i	−0.301834	+	1.38180i
$574$		0			0
$575$	−76.0569	+	131.734i	−0.132273	+	0.229103i
$576$		0			0
$577$	−422.219			−0.731749			−0.365875	−	0.930664i	$-0.619230\pi$
$577$	−422.219			−0.731749			−0.365875	+	0.930664i	$0.619230\pi$
$578$		0			0
$579$	−73.2912	−	16.0094i	−0.126582	−	0.0276501i
$580$		0			0
$581$	−844.940	+	1463.48i	−1.45429	+	2.51890i
$582$		0			0
$583$	−280.834	−	162.140i	−0.481706	−	0.278113i
$584$		0			0
$585$	8.34929	+	11.7676i	0.0142723	+	0.0201156i
$586$		0			0
$587$	−48.5657			−0.0827354			−0.0413677	−	0.999144i	$-0.513172\pi$
$587$	−48.5657			−0.0827354			−0.0413677	+	0.999144i	$0.513172\pi$
$588$		0			0
$589$	2.74027	−	279.132i	0.00465242	−	0.473908i
$590$		0			0
$591$	−541.073	−	492.717i	−0.915521	−	0.833700i
$592$		0			0
$593$	545.462	+	944.768i	0.919835	+	1.59320i	0.799664	+	0.600448i	$0.205011\pi$
$593$	545.462	+	944.768i	0.919835	+	1.59320i	0.120171	+	0.992753i	$0.461656\pi$
$594$		0			0
$595$	398.616	+	690.424i	0.669944	+	1.16038i
$596$		0			0
$597$	−110.525	+	505.983i	−0.185134	+	0.847542i
$598$		0			0
$599$			588.855i			0.983063i	0.870860	+	0.491532i	$0.163563\pi$
$599$			588.855i			0.983063i	−0.870860	+	0.491532i	$0.836437\pi$
$600$		0			0
$601$	838.716	−	484.233i	1.39553	−	0.805712i	0.401613	−	0.915809i	$-0.368450\pi$
$601$	838.716	−	484.233i	1.39553	−	0.805712i	0.993921	+	0.110097i	$0.0351163\pi$
$602$		0			0
$603$	−401.883	+	37.6791i	−0.666473	+	0.0624860i
$604$		0			0
$605$	538.309			0.889767
$606$		0			0
$607$	129.306	+	74.6547i	0.213024	+	0.122990i	0.602716	−	0.797956i	$-0.294085\pi$
$607$	129.306	+	74.6547i	0.213024	+	0.122990i	−0.389692	+	0.920945i	$0.627418\pi$
$608$		0			0
$609$	−399.660	+	438.883i	−0.656256	+	0.720662i
$610$		0			0
$611$	14.5306	+	8.38923i	0.0237816	+	0.0137303i
$612$		0			0
$613$	480.397	−	832.071i	0.783681	−	1.35738i	−0.146102	−	0.989269i	$-0.546673\pi$
$613$	480.397	−	832.071i	0.783681	−	1.35738i	0.929784	−	0.368106i	$-0.119994\pi$
$614$		0			0
$615$	85.6202	+	268.638i	0.139220	+	0.436810i
$616$		0			0
$617$	546.118			0.885119			0.442559	−	0.896739i	$-0.354071\pi$
$617$	546.118			0.885119			0.442559	+	0.896739i	$0.354071\pi$
$618$		0			0
$619$	292.910	+	507.336i	0.473199	+	0.819605i	0.999529	−	0.0306750i	$-0.00976569\pi$
$619$	292.910	+	507.336i	0.473199	+	0.819605i	−0.526330	+	0.850280i	$0.676432\pi$
$620$		0			0
$621$	−303.351	+	403.061i	−0.488487	+	0.649052i
$622$		0			0
$623$	1473.37	+	850.649i	2.36495	+	1.36541i
$624$		0			0
$625$	177.589	+	307.593i	0.284142	+	0.492148i
$626$		0			0
$627$	864.956	−	266.353i	1.37951	−	0.424806i
$628$		0			0
$629$	463.621	+	267.671i	0.737076	+	0.425551i
$630$		0			0
$631$	174.403	+	302.075i	0.276392	+	0.478725i	0.970485	−	0.241160i	$-0.0775279\pi$
$631$	174.403	+	302.075i	0.276392	+	0.478725i	−0.694093	+	0.719885i	$0.744195\pi$
$632$		0			0
$633$	235.572	+	51.4574i	0.372152	+	0.0812913i
$634$		0			0
$635$	−814.927	−	470.498i	−1.28335	−	0.740942i
$636$		0			0
$637$	−40.3906	−	23.3195i	−0.0634075	−	0.0366083i
$638$		0			0
$639$	−87.9795	+	191.776i	−0.137683	+	0.300119i
$640$		0			0
$641$		−	817.703i		−	1.27567i	−0.770174	−	0.637834i	$-0.779831\pi$
$641$		−	817.703i		−	1.27567i	0.770174	−	0.637834i	$-0.220169\pi$
$642$		0			0
$643$	−160.386	−	277.797i	−0.249434	−	0.432033i	0.713935	−	0.700212i	$-0.246911\pi$
$643$	−160.386	−	277.797i	−0.249434	−	0.432033i	−0.963369	+	0.268179i	$0.913578\pi$
$644$		0			0
$645$	−42.3177	+	193.730i	−0.0656088	+	0.300357i
$646$		0			0
$647$	−499.685			−0.772310			−0.386155	−	0.922434i	$-0.626197\pi$
$647$	−499.685			−0.772310			−0.386155	+	0.922434i	$0.626197\pi$
$648$		0			0
$649$	954.903	+	551.313i	1.47134	+	0.849481i
$650$		0			0
$651$	−385.154	+	422.953i	−0.591634	+	0.649698i
$652$		0			0
$653$	510.680	−	884.524i	0.782052	−	1.35455i	−0.148692	−	0.988884i	$-0.547506\pi$
$653$	510.680	−	884.524i	0.782052	−	1.35455i	0.930744	−	0.365671i	$-0.119160\pi$
$654$		0			0
$655$	132.488	−	229.475i	0.202271	−	0.350344i
$656$		0			0
$657$	541.233	+	248.297i	0.823794	+	0.377925i
$658$		0			0
$659$	−359.383	−	207.490i	−0.545346	−	0.314856i	0.201897	−	0.979407i	$-0.435289\pi$
$659$	−359.383	−	207.490i	−0.545346	−	0.314856i	−0.747243	+	0.664551i	$0.768623\pi$
$660$		0			0
$661$		−	277.158i		−	0.419301i	−0.977776	−	0.209650i	$-0.932767\pi$
$661$		−	277.158i		−	0.419301i	0.977776	−	0.209650i	$-0.0672325\pi$
$662$		0			0
$663$	−5.32161	−	16.6968i	−0.00802655	−	0.0251838i
$664$		0			0
$665$	1012.45	+	9.93934i	1.52248	+	0.0149464i
$666$		0			0
$667$	−246.676	−	142.418i	−0.369829	−	0.213521i
$668$		0			0
$669$	−263.402	+	289.252i	−0.393725	+	0.432365i
$670$		0			0
$671$	−1208.13			−1.80049
$672$		0			0
$673$	−780.615	+	450.688i	−1.15990	+	0.669670i	−0.951281	−	0.308326i	$-0.900231\pi$
$673$	−780.615	+	450.688i	−1.15990	+	0.669670i	−0.208622	+	0.977996i	$0.566898\pi$
$674$		0			0
$675$	−86.0120	−	202.295i	−0.127425	−	0.299696i
$676$		0			0
$677$	341.330	−	197.067i	0.504181	−	0.291089i	−0.226258	−	0.974067i	$-0.572649\pi$
$677$	341.330	−	197.067i	0.504181	−	0.291089i	0.730438	+	0.682979i	$0.239316\pi$
$678$		0			0
$679$	1622.18	−	936.568i	2.38908	−	1.37933i
$680$		0			0
$681$	108.396	+	23.6776i	0.159172	+	0.0347688i
$682$		0			0
$683$		−	591.311i		−	0.865755i	−0.901453	−	0.432878i	$-0.857498\pi$
$683$		−	591.311i		−	0.865755i	0.901453	−	0.432878i	$-0.142502\pi$
$684$		0			0
$685$	−406.361			−0.593227
$686$		0			0
$687$	452.388	−	144.185i	0.658498	−	0.209876i
$688$		0			0
$689$	3.98726	+	6.90613i	0.00578702	+	0.0100234i
$690$		0			0
$691$	−44.4269	−	76.9497i	−0.0642937	−	0.111360i	0.832087	−	0.554645i	$-0.187146\pi$
$691$	−44.4269	−	76.9497i	−0.0642937	−	0.111360i	−0.896380	+	0.443286i	$0.853813\pi$
$692$		0			0
$693$	−1685.74	−	773.350i	−2.43252	−	1.11595i
$694$		0			0
$695$	−254.018	−	439.973i	−0.365494	−	0.633054i
$696$		0			0
$697$		−	342.445i		−	0.491313i
$698$		0			0
$699$	717.306	−	228.619i	1.02619	−	0.327066i
$700$		0			0
$701$	−545.551	+	944.922i	−0.778247	+	1.34796i	0.154704	+	0.987961i	$0.450558\pi$
$701$	−545.551	+	944.922i	−0.778247	+	1.34796i	−0.932951	+	0.360003i	$0.882776\pi$
$702$		0			0
$703$	592.113	−	334.150i	0.842266	−	0.475320i
$704$		0			0
$705$	391.354	+	356.379i	0.555112	+	0.505502i
$706$		0			0
$707$	−2360.28			−3.33844
$708$		0			0
$709$	509.445	−	882.385i	0.718541	−	1.24455i	−0.243037	−	0.970017i	$-0.578144\pi$
$709$	509.445	−	882.385i	0.718541	−	1.24455i	0.961578	−	0.274532i	$-0.0885229\pi$
$710$		0			0
$711$	−1083.03	+	101.541i	−1.52326	+	0.142815i
$712$		0			0
$713$	−237.722	−	137.249i	−0.333411	−	0.192495i
$714$		0			0
$715$	−22.0449	−	12.7276i	−0.0308320	−	0.0178009i
$716$		0			0
$717$	500.237	−	159.435i	0.697681	−	0.222364i
$718$		0			0
$719$	−162.296	+	281.105i	−0.225725	+	0.390967i	−0.956537	−	0.291612i	$-0.905808\pi$
$719$	−162.296	+	281.105i	−0.225725	+	0.390967i	0.730812	+	0.682579i	$0.239142\pi$
$720$		0			0
$721$		−	1846.47i		−	2.56099i
$722$		0			0
$723$	−311.471	−	977.259i	−0.430804	−	1.35167i
$724$		0			0
$725$	107.490	−	62.0596i	0.148263	−	0.0855994i
$726$		0			0
$727$	208.135			0.286293			0.143146	−	0.989702i	$-0.454278\pi$
$727$	208.135			0.286293			0.143146	+	0.989702i	$0.454278\pi$
$728$		0			0
$729$	−201.778	−	700.519i	−0.276787	−	0.960931i
$730$		0			0
$731$	120.421	−	208.576i	0.164735	−	0.285330i
$732$		0			0
$733$	178.182	−	308.619i	0.243085	−	0.421036i	−0.718506	−	0.695521i	$-0.755174\pi$
$733$	178.182	−	308.619i	0.243085	−	0.421036i	0.961592	+	0.274484i	$0.0885072\pi$
$734$		0			0
$735$	−1087.85	−	990.625i	−1.48006	−	1.34779i
$736$		0			0
$737$	616.709	−	356.057i	0.836783	−	0.483117i
$738$		0			0
$739$	12.3234	−	21.3448i	0.0166758	−	0.0288833i	−0.857567	−	0.514372i	$-0.828025\pi$
$739$	12.3234	−	21.3448i	0.0166758	−	0.0288833i	0.874243	+	0.485489i	$0.161358\pi$
$740$		0			0
$741$	−21.6958	−	4.96278i	−0.0292791	−	0.00669741i
$742$		0			0
$743$	−956.068	+	551.986i	−1.28677	+	0.742915i	−0.978076	−	0.208247i	$-0.933224\pi$
$743$	−956.068	+	551.986i	−1.28677	+	0.742915i	−0.308691	+	0.951162i	$0.599891\pi$
$744$		0			0
$745$	−313.443	+	542.899i	−0.420728	+	0.728723i
$746$		0			0
$747$	955.717	−	678.093i	1.27941	−	0.907755i
$748$		0			0
$749$	85.4266	−	49.3211i	0.114054	−	0.0658493i
$750$		0			0
$751$		−	114.360i		−	0.152277i	−0.997097	−	0.0761384i	$-0.975741\pi$
$751$		−	114.360i		−	0.152277i	0.997097	−	0.0761384i	$-0.0242591\pi$
$752$		0			0
$753$	−177.286	+	811.618i	−0.235440	+	1.07785i
$754$		0			0
$755$	316.210	+	182.564i	0.418821	+	0.241806i
$756$		0			0
$757$	−463.471	+	802.756i	−0.612248	+	1.06044i	0.378613	+	0.925555i	$0.376401\pi$
$757$	−463.471	+	802.756i	−0.612248	+	1.06044i	−0.990861	+	0.134889i	$0.956932\pi$
$758$		0			0
$759$	189.923	−	869.469i	0.250228	−	1.14555i
$760$		0			0
$761$	291.762	−	505.347i	0.383393	−	0.664056i	−0.608152	−	0.793821i	$-0.708089\pi$
$761$	291.762	−	505.347i	0.383393	−	0.664056i	0.991545	+	0.129765i	$0.0414222\pi$
$762$		0			0
$763$			730.555i			0.957477i
$764$		0			0
$765$	−51.6055	−	550.423i	−0.0674582	−	0.719507i
$766$		0			0
$767$	−13.5576	−	23.4825i	−0.0176762	−	0.0306160i
$768$		0			0
$769$	890.370			1.15783			0.578914	−	0.815388i	$-0.303477\pi$
$769$	890.370			1.15783			0.578914	+	0.815388i	$0.303477\pi$
$770$		0			0
$771$	−191.438	+	210.226i	−0.248298	+	0.272667i
$772$		0			0
$773$	1247.51	−	720.250i	1.61385	−	0.931759i	0.625388	−	0.780314i	$-0.284941\pi$
$773$	1247.51	−	720.250i	1.61385	−	0.931759i	0.988466	−	0.151445i	$-0.0483928\pi$
$774$		0			0
$775$	103.589	−	59.8070i	0.133663	−	0.0771704i
$776$		0			0
$777$	−1361.19	−	297.332i	−1.75185	−	0.382667i
$778$		0			0
$779$	−374.490	−	221.142i	−0.480732	−	0.283879i
$780$		0			0
$781$		−	372.237i		−	0.476616i
$782$		0			0
$783$	378.802	−	161.059i	0.483783	−	0.205695i
$784$		0			0
$785$	−392.514	+	679.855i	−0.500018	+	0.866057i
$786$		0			0
$787$	−885.613	−	511.309i	−1.12530	−	0.649693i	−0.182553	−	0.983196i	$-0.558436\pi$
$787$	−885.613	−	511.309i	−1.12530	−	0.649693i	−0.942749	+	0.333503i	$0.891769\pi$
$788$		0			0
$789$	−232.581	−	211.795i	−0.294780	−	0.268435i
$790$		0			0
$791$		−	635.292i		−	0.803150i
$792$		0			0
$793$	25.7293	+	14.8548i	0.0324455	+	0.0187324i
$794$		0			0
$795$	76.3939	+	239.690i	0.0960929	+	0.301497i
$796$		0			0
$797$	424.917	+	245.326i	0.533146	+	0.307812i	0.742297	−	0.670071i	$-0.233737\pi$
$797$	424.917	+	245.326i	0.533146	+	0.307812i	−0.209151	+	0.977883i	$0.567070\pi$
$798$		0			0
$799$	−321.433	−	556.739i	−0.402294	−	0.696794i
$800$		0			0
$801$	−682.674	−	962.173i	−0.852277	−	1.20122i
$802$		0			0
$803$	−1050.53			−1.30826
$804$		0			0
$805$	497.821	−	862.251i	0.618411	−	1.07112i
$806$		0			0
$807$	−129.250	−	405.530i	−0.160161	−	0.502515i
$808$		0			0
$809$	654.603			0.809151			0.404575	−	0.914505i	$-0.367419\pi$
$809$	654.603			0.809151			0.404575	+	0.914505i	$0.367419\pi$
$810$		0			0
$811$	−231.770	+	133.812i	−0.285783	+	0.164997i	−0.636038	−	0.771657i	$-0.719428\pi$
$811$	−231.770	+	133.812i	−0.285783	+	0.164997i	0.350256	+	0.936654i	$0.386095\pi$
$812$		0			0
$813$	278.861	−	88.8783i	0.343002	−	0.109321i
$814$		0			0
$815$	−28.6471	−	49.6183i	−0.0351499	−	0.0608813i
$816$		0			0
$817$	−150.329	−	266.383i	−0.184001	−	0.326050i
$818$		0			0
$819$	26.3919	+	37.1973i	0.0322246	+	0.0454179i
$820$		0			0
$821$	390.814	−	676.909i	0.476022	−	0.824494i	−0.523601	−	0.851964i	$-0.675412\pi$
$821$	390.814	−	676.909i	0.476022	−	0.824494i	0.999623	+	0.0274699i	$0.00874504\pi$
$822$		0			0
$823$	23.6833			0.0287767			0.0143884	−	0.999896i	$-0.495420\pi$
$823$	23.6833			0.0287767			0.0143884	+	0.999896i	$0.495420\pi$
$824$		0			0
$825$	286.736	+	261.110i	0.347559	+	0.316498i
$826$		0			0
$827$	215.842	−	124.616i	0.260994	−	0.150685i	−0.363794	−	0.931479i	$-0.618519\pi$
$827$	215.842	−	124.616i	0.260994	−	0.150685i	0.624788	+	0.780794i	$0.285185\pi$
$828$		0			0
$829$		−	1194.32i		−	1.44068i	−0.693622	−	0.720339i	$-0.743986\pi$
$829$		−	1194.32i		−	1.44068i	0.693622	−	0.720339i	$-0.256014\pi$
$830$		0			0
$831$	109.021	−	499.096i	0.131192	−	0.600597i
$832$		0			0
$833$	893.487	+	1547.57i	1.07261	+	1.85782i
$834$		0			0
$835$	−848.685	+	489.989i	−1.01639	+	0.586813i
$836$		0			0
$837$	365.053	−	155.214i	0.436144	−	0.185440i
$838$		0			0
$839$			545.157i			0.649770i	0.945754	+	0.324885i	$0.105326\pi$
$839$			545.157i			0.649770i	−0.945754	+	0.324885i	$0.894674\pi$
$840$		0			0
$841$	−304.292	−	527.049i	−0.361822	−	0.626694i
$842$		0			0
$843$	446.495	+	1400.90i	0.529650	+	1.66181i
$844$		0			0
$845$	−346.636	−	600.391i	−0.410220	−	0.710522i
$846$		0			0
$847$	1701.58			2.00895
$848$		0			0
$849$	279.940	−	1281.56i	0.329729	−	1.50950i
$850$		0			0
$851$		−	668.574i		−	0.785634i
$852$		0			0
$853$	888.831			1.04201			0.521003	−	0.853555i	$-0.325558\pi$
$853$	888.831			1.04201			0.521003	+	0.853555i	$0.325558\pi$
$854$		0			0
$855$	−635.255	−	299.014i	−0.742989	−	0.349724i
$856$		0			0
$857$			181.233i			0.211474i	0.994394	+	0.105737i	$0.0337202\pi$
$857$			181.233i			0.211474i	−0.994394	+	0.105737i	$0.966280\pi$
$858$		0			0
$859$	1255.94			1.46210			0.731048	−	0.682326i	$-0.239032\pi$
$859$	1255.94			1.46210			0.731048	+	0.682326i	$0.239032\pi$
$860$		0			0
$861$	270.644	+	849.160i	0.314336	+	0.986248i
$862$		0			0
$863$			267.394i			0.309843i	0.987927	+	0.154921i	$0.0495124\pi$
$863$			267.394i			0.309843i	−0.987927	+	0.154921i	$0.950488\pi$
$864$		0			0
$865$	−503.383	+	290.628i	−0.581945	+	0.335986i
$866$		0			0
$867$	41.7319	−	191.049i	0.0481336	−	0.220356i
$868$		0			0
$869$	1661.97	−	959.537i	1.91251	−	1.10419i
$870$		0			0
$871$	−17.5119			−0.0201056
$872$		0			0
$873$	−1293.24	+	121.250i	−1.48138	+	0.138888i
$874$		0			0
$875$	883.045	+	1529.48i	1.00919	+	1.74797i
$876$		0			0
$877$	−1082.85	+	625.186i	−1.23472	+	0.712869i	−0.968011	−	0.250907i	$-0.919271\pi$
$877$	−1082.85	+	625.186i	−1.23472	+	0.712869i	−0.266714	+	0.963776i	$0.585938\pi$
$878$		0			0
$879$	−244.981	−	768.643i	−0.278705	−	0.874452i
$880$		0			0
$881$	596.782			0.677392			0.338696	−	0.940896i	$-0.390014\pi$
$881$	596.782			0.677392			0.338696	+	0.940896i	$0.390014\pi$
$882$		0			0
$883$	438.181	+	758.951i	0.496241	+	0.859514i	0.999991	−	0.00433543i	$-0.00138001\pi$
$883$	438.181	+	758.951i	0.496241	+	0.859514i	−0.503750	+	0.863850i	$0.668047\pi$
$884$		0			0
$885$	−259.757	−	815.002i	−0.293511	−	0.920907i
$886$		0			0
$887$		−	1133.01i		−	1.27735i	−0.769478	−	0.638673i	$-0.779484\pi$
$887$		−	1133.01i		−	1.27735i	0.769478	−	0.638673i	$-0.220516\pi$
$888$		0			0
$889$	−2575.97	−	1487.24i	−2.89760	−	1.67293i
$890$		0			0
$891$	838.878	+	974.860i	0.941501	+	1.09412i
$892$		0			0
$893$	−816.410	−	8.01481i	−0.914233	−	0.00897515i
$894$		0			0
$895$	−901.544	+	520.507i	−1.00731	+	0.581572i
$896$		0			0
$897$	−14.7355	+	16.1817i	−0.0164276	+	0.0180398i
$898$		0			0
$899$	111.990	+	193.972i	0.124572	+	0.215765i
$900$		0			0
$901$		−	305.544i		−	0.339116i
$902$		0			0
$903$	−133.765	+	612.378i	−0.148134	+	0.678160i
$904$		0			0
$905$	821.460	+	474.270i	0.907691	+	0.524056i
$906$		0			0
$907$		−	410.807i		−	0.452930i	−0.974019	−	0.226465i	$-0.927283\pi$
$907$		−	410.807i		−	0.452930i	0.974019	−	0.226465i	$-0.0727168\pi$
$908$		0			0
$909$	1487.64	+	682.473i	1.63657	+	0.750796i
$910$		0			0
$911$	822.448	−	474.840i	0.902797	−	0.521230i	0.0246902	−	0.999695i	$-0.492140\pi$
$911$	822.448	−	474.840i	0.902797	−	0.521230i	0.878107	+	0.478465i	$0.158807\pi$
$912$		0			0
$913$	−1033.68	+	1790.39i	−1.13218	+	1.96100i
$914$		0			0
$915$	692.971	+	631.040i	0.757345	+	0.689661i
$916$		0			0
$917$	418.791	−	725.367i	0.456697	−	0.791022i
$918$		0			0
$919$	943.523			1.02668			0.513342	−	0.858184i	$-0.328407\pi$
$919$	943.523			1.02668			0.513342	+	0.858184i	$0.328407\pi$
$920$		0			0
$921$	−233.986	−	734.143i	−0.254056	−	0.797115i
$922$		0			0
$923$	−4.57693	+	7.92747i	−0.00495875	+	0.00858881i
$924$		0			0
$925$	252.304	+	145.668i	0.272761	+	0.157478i
$926$		0			0
$927$	−533.907	+	1163.80i	−0.575952	+	1.25545i
$928$		0			0
$929$	−162.170			−0.174564			−0.0872819	−	0.996184i	$-0.527818\pi$
$929$	−162.170			−0.174564			−0.0872819	+	0.996184i	$0.527818\pi$
$930$		0			0
$931$	2269.37	+	22.2787i	2.43757	+	0.0239299i
$932$		0			0
$933$	−443.926	+	141.488i	−0.475804	+	0.151648i
$934$		0			0
$935$	487.659	+	844.649i	0.521560	+	0.903368i
$936$		0			0
$937$	−118.230	−	204.780i	−0.126179	−	0.218548i	0.796014	−	0.605278i	$-0.206938\pi$
$937$	−118.230	−	204.780i	−0.126179	−	0.218548i	−0.922193	+	0.386730i	$0.873605\pi$
$938$		0			0
$939$	474.077	−	151.098i	0.504874	−	0.160913i
$940$		0			0
$941$		−	193.356i		−	0.205479i	−0.994708	−	0.102740i	$-0.967239\pi$
$941$		−	193.356i		−	0.205479i	0.994708	−	0.102740i	$-0.0327608\pi$
$942$		0			0
$943$	−370.373	+	213.835i	−0.392760	+	0.226760i
$944$		0			0
$945$	562.980	+	1324.10i	0.595746	+	1.40116i
$946$		0			0
$947$	409.213			0.432115			0.216058	−	0.976381i	$-0.430680\pi$
$947$	409.213			0.432115			0.216058	+	0.976381i	$0.430680\pi$
$948$		0			0
$949$	22.3730	+	12.9170i	0.0235753	+	0.0136112i
$950$		0			0
$951$	253.085	+	794.070i	0.266126	+	0.834984i
$952$		0			0
$953$	−1046.85	−	604.399i	−1.09848	−	0.634207i	−0.162658	−	0.986683i	$-0.552007\pi$
$953$	−1046.85	−	604.399i	−1.09848	−	0.634207i	−0.935821	+	0.352476i	$0.885340\pi$
$954$		0			0
$955$	−554.598	+	960.593i	−0.580731	+	1.00586i
$956$		0			0
$957$	−488.935	+	536.920i	−0.510904	+	0.561045i
$958$		0			0
$959$	−1284.50			−1.33941
$960$		0			0
$961$	−372.575	−	645.319i	−0.387695	−	0.671507i
$962$		0			0
$963$	−68.1042	+	6.38519i	−0.0707209	+	0.00663052i
$964$		0			0
$965$	−88.9184	−	51.3371i	−0.0921434	−	0.0531990i
$966$		0			0
$967$	−589.929	−	1021.79i	−0.610061	−	1.05666i	−0.991230	−	0.132151i	$-0.957812\pi$
$967$	−589.929	−	1021.79i	−0.610061	−	1.05666i	0.381169	−	0.924505i	$-0.375522\pi$
$968$		0			0
$969$	624.832	+	580.312i	0.644821	+	0.598877i
$970$		0			0
$971$	927.828	+	535.682i	0.955538	+	0.551680i	0.894797	−	0.446473i	$-0.147320\pi$
$971$	927.828	+	535.682i	0.955538	+	0.551680i	0.0607413	+	0.998154i	$0.480654\pi$
$972$		0			0
$973$	−802.947	−	1390.74i	−0.825228	−	1.42934i
$974$		0			0
$975$	−2.89603	−	9.08646i	−0.00297029	−	0.00931945i
$976$		0			0
$977$	489.309	+	282.503i	0.500828	+	0.289153i	0.729055	−	0.684455i	$-0.239960\pi$
$977$	489.309	+	282.503i	0.500828	+	0.289153i	−0.228228	+	0.973608i	$0.573293\pi$
$978$		0			0
$979$	1802.48	+	1040.66i	1.84115	+	1.06299i
$980$		0			0
$981$	211.240	−	460.457i	0.215331	−	0.469375i
$982$		0			0
$983$			425.809i			0.433173i	0.976263	+	0.216586i	$0.0694923\pi$
$983$			425.809i			0.433173i	−0.976263	+	0.216586i	$0.930508\pi$
$984$		0			0
$985$	−500.783	−	867.382i	−0.508409	−	0.880591i
$986$		0			0
$987$	1237.06	+	1126.51i	1.25336	+	1.14134i
$988$		0			0
$989$	−300.782			−0.304127
$990$		0			0
$991$	−618.826	−	357.279i	−0.624446	−	0.360524i	0.154152	−	0.988047i	$-0.450735\pi$
$991$	−618.826	−	357.279i	−0.624446	−	0.360524i	−0.778598	+	0.627523i	$0.784069\pi$
$992$		0			0
$993$	782.141	+	170.848i	0.787655	+	0.172052i
$994$		0			0
$995$	−354.417	+	613.869i	−0.356198	+	0.616954i
$996$		0			0
$997$	204.374	−	353.986i	0.204989	−	0.355051i	−0.745140	−	0.666908i	$-0.767618\pi$
$997$	204.374	−	353.986i	0.204989	−	0.355051i	0.950129	+	0.311857i	$0.100951\pi$
$998$		0			0
$999$	771.960	+	580.990i	0.772733	+	0.581572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.10	✓	80
3.2	odd	2		2052.3.s.a.901.29		80
9.2	odd	6		2052.3.bl.a.1585.12		80
9.7	even	3		684.3.bl.a.673.4	yes	80
19.12	odd	6		684.3.bl.a.373.4	yes	80
57.50	even	6		2052.3.bl.a.145.12		80
171.88	odd	6	inner	684.3.s.a.601.10	yes	80
171.164	even	6		2052.3.s.a.829.29		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.10	✓	80	1.1	even	1	trivial
684.3.s.a.601.10	yes	80	171.88	odd	6	inner
684.3.bl.a.373.4	yes	80	19.12	odd	6
684.3.bl.a.673.4	yes	80	9.7	even	3
2052.3.s.a.829.29		80	171.164	even	6
2052.3.s.a.901.29		80	3.2	odd	2
2052.3.bl.a.145.12		80	57.50	even	6
2052.3.bl.a.1585.12		80	9.2	odd	6

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.21812 - 2.01989i) q^{3} +(-2.05295 - 3.55582i) q^{5} +(-6.48935 - 11.2399i) q^{7} +(0.840121 + 8.96070i) q^{9} +O(q^{10})\)	\(q+(-2.21812 - 2.01989i) q^{3} +(-2.05295 - 3.55582i) q^{5} +(-6.48935 - 11.2399i) q^{7} +(0.840121 + 8.96070i) q^{9} +(-7.93892 - 13.7506i) q^{11} +0.390460i q^{13} +(-2.62865 + 12.0340i) q^{15} +(7.48023 - 12.9561i) q^{17} +(-9.33801 - 16.5469i) q^{19} +(-8.30912 + 38.0391i) q^{21} -18.6837 q^{23} +(4.07076 - 7.05077i) q^{25} +(16.2361 - 21.5729i) q^{27} +(13.2027 + 7.62259i) q^{29} +(12.7235 + 7.34592i) q^{31} +(-10.1652 + 46.5363i) q^{33} +(-26.6447 + 46.1499i) q^{35} +35.7838i q^{37} +(0.788684 - 0.866087i) q^{39} +(19.8233 - 11.4450i) q^{41} +16.0986 q^{43} +(30.1379 - 21.3832i) q^{45} +(21.4855 - 37.2140i) q^{47} +(-59.7232 + 103.444i) q^{49} +(-42.7620 + 13.6291i) q^{51} +(17.6872 - 10.2117i) q^{53} +(-32.5965 + 56.4588i) q^{55} +(-12.7101 + 55.5649i) q^{57} +(-60.1406 + 34.7222i) q^{59} +(38.0444 - 65.8948i) q^{61} +(95.2654 - 67.5920i) q^{63} +(1.38840 - 0.801596i) q^{65} +44.8495i q^{67} +(41.4427 + 37.7389i) q^{69} +(20.3029 + 11.7219i) q^{71} +(33.0816 - 57.2991i) q^{73} +(-23.2712 + 7.41698i) q^{75} +(-103.037 + 178.465i) q^{77} +120.865i q^{79} +(-79.5884 + 15.0562i) q^{81} +(-65.1021 - 112.760i) q^{83} -61.4263 q^{85} +(-13.8885 - 43.5758i) q^{87} +(-113.522 + 65.5419i) q^{89} +(4.38872 - 2.53383i) q^{91} +(-13.3844 - 41.9942i) q^{93} +(-39.6675 + 67.1744i) q^{95} +144.324i q^{97} +(116.546 - 82.6905i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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