LMFDB - Embedded newform 220.3.i.a.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(43,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("220.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.i (of order $4$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.1
Character	$\chi$	$=$	220.43
Dual form			220.3.i.a.87.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.99997 + 0.0112748i) q^{2} +(3.70405 - 3.70405i) q^{3} +(3.99975 - 0.0450984i) q^{4} +(-3.59444 + 3.47563i) q^{5} +(-7.36622 + 7.44975i) q^{6} +(-1.62459 + 1.62459i) q^{7} +(-7.99886 + 0.135292i) q^{8} -18.4400i q^{9} +(7.14958 - 6.99168i) q^{10} +(5.08557 - 9.75382i) q^{11} +(14.6482 - 14.9823i) q^{12} +(13.7602 - 13.7602i) q^{13} +(3.23081 - 3.26744i) q^{14} +(-0.440067 + 26.1879i) q^{15} +(15.9959 - 0.360764i) q^{16} +(-22.0851 - 22.0851i) q^{17} +(0.207907 + 36.8794i) q^{18} -5.92820i q^{19} +(-14.2201 + 14.0637i) q^{20} +12.0351i q^{21} +(-10.0610 + 19.5647i) q^{22} +(-6.31990 + 6.31990i) q^{23} +(-29.1270 + 30.1293i) q^{24} +(0.839974 - 24.9859i) q^{25} +(-27.3649 + 27.6751i) q^{26} +(-34.9662 - 34.9662i) q^{27} +(-6.42467 + 6.57120i) q^{28} +34.0393 q^{29} +(0.584858 - 52.3799i) q^{30} +22.2160i q^{31} +(-31.9873 + 0.901868i) q^{32} +(-17.2914 - 54.9659i) q^{33} +(44.4184 + 43.9204i) q^{34} +(0.193012 - 11.4859i) q^{35} +(-0.831614 - 73.7553i) q^{36} +(8.71788 - 8.71788i) q^{37} +(0.0668392 + 11.8562i) q^{38} -101.937i q^{39} +(28.2812 - 28.2874i) q^{40} +44.8146i q^{41} +(-0.135693 - 24.0698i) q^{42} +(11.2370 + 11.2370i) q^{43} +(19.9011 - 39.2421i) q^{44} +(64.0906 + 66.2814i) q^{45} +(12.5683 - 12.7108i) q^{46} +(-6.26838 - 6.26838i) q^{47} +(57.9135 - 60.5860i) q^{48} +43.7214i q^{49} +(-1.39821 + 49.9804i) q^{50} -163.608 q^{51} +(54.4168 - 55.6579i) q^{52} +(-36.4914 - 36.4914i) q^{53} +(70.3255 + 69.5371i) q^{54} +(15.6209 + 52.7351i) q^{55} +(12.7750 - 13.2146i) q^{56} +(-21.9584 - 21.9584i) q^{57} +(-68.0775 + 0.383786i) q^{58} +8.49349 q^{59} +(-0.579124 + 104.765i) q^{60} -64.3732i q^{61} +(-0.250481 - 44.4313i) q^{62} +(29.9574 + 29.9574i) q^{63} +(63.9634 - 2.16436i) q^{64} +(-1.63481 + 97.2857i) q^{65} +(35.2020 + 109.735i) q^{66} +(50.4964 + 50.4964i) q^{67} +(-89.3306 - 87.3386i) q^{68} +46.8184i q^{69} +(-0.256517 + 22.9737i) q^{70} +57.3348i q^{71} +(2.49478 + 147.499i) q^{72} +(33.7647 - 33.7647i) q^{73} +(-17.3372 + 17.5338i) q^{74} +(-89.4377 - 95.6603i) q^{75} +(-0.267353 - 23.7113i) q^{76} +(7.58397 + 24.1079i) q^{77} +(1.14932 + 203.871i) q^{78} +91.0525i q^{79} +(-56.2425 + 56.8927i) q^{80} -93.0733 q^{81} +(-0.505275 - 89.6278i) q^{82} +(67.5635 + 67.5635i) q^{83} +(0.542764 + 48.1374i) q^{84} +(156.143 + 2.62386i) q^{85} +(-22.6004 - 22.3470i) q^{86} +(126.083 - 126.083i) q^{87} +(-39.3591 + 78.7074i) q^{88} -13.8142i q^{89} +(-128.926 - 131.838i) q^{90} +44.7093i q^{91} +(-24.9930 + 25.5630i) q^{92} +(82.2893 + 82.2893i) q^{93} +(12.6072 + 12.4659i) q^{94} +(20.6042 + 21.3086i) q^{95} +(-115.142 + 121.823i) q^{96} +(37.0639 - 37.0639i) q^{97} +(-0.492950 - 87.4415i) q^{98} +(-179.860 - 93.7779i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) $ 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.99997	+	0.0112748i	−0.999984	+	0.00563739i
$2$	−1.99997	+	0.0112748i	−0.999984	+	0.00563739i
$3$	3.70405	−	3.70405i	1.23468	−	1.23468i	0.272539	−	0.962145i	$-0.412137\pi$
$3$	3.70405	−	3.70405i	1.23468	−	1.23468i	0.962145	−	0.272539i	$-0.0878634\pi$
$4$	3.99975	−	0.0450984i	0.999936	−	0.0112746i
$5$	−3.59444	+	3.47563i	−0.718888	+	0.695126i
$5$	−3.59444	+	3.47563i	−0.718888	+	0.695126i
$6$	−7.36622	+	7.44975i	−1.22770	+	1.24162i
$7$	−1.62459	+	1.62459i	−0.232084	+	0.232084i	−0.813562	−	0.581478i	$-0.802475\pi$
$7$	−1.62459	+	1.62459i	−0.232084	+	0.232084i	0.581478	+	0.813562i	$0.302475\pi$
$8$	−7.99886	+	0.135292i	−0.999857	+	0.0169115i
$9$		−	18.4400i		−	2.04889i
$10$	7.14958	−	6.99168i	0.714958	−	0.699168i
$11$	5.08557	−	9.75382i	0.462325	−	0.886711i
$11$	5.08557	−	9.75382i	0.462325	−	0.886711i
$12$	14.6482	−	14.9823i	1.22068	−	1.24853i
$13$	13.7602	−	13.7602i	1.05848	−	1.05848i	0.0602980	−	0.998180i	$-0.480795\pi$
$13$	13.7602	−	13.7602i	1.05848	−	1.05848i	0.998180	−	0.0602980i	$-0.0192051\pi$
$14$	3.23081	−	3.26744i	0.230772	−	0.233388i
$15$	−0.440067	+	26.1879i	−0.0293378	+	1.74586i
$16$	15.9959	−	0.360764i	0.999746	−	0.0225478i
$17$	−22.0851	−	22.0851i	−1.29912	−	1.29912i	−0.928973	−	0.370148i	$-0.879307\pi$
$17$	−22.0851	−	22.0851i	−1.29912	−	1.29912i	−0.370148	−	0.928973i	$-0.620693\pi$
$18$	0.207907	+	36.8794i	0.0115504	+	2.04886i
$19$		−	5.92820i		−	0.312011i	−0.987756	−	0.156005i	$-0.950138\pi$
$19$		−	5.92820i		−	0.312011i	0.987756	−	0.156005i	$-0.0498617\pi$
$20$	−14.2201	+	14.0637i	−0.711005	+	0.703187i
$21$			12.0351i			0.573100i
$22$	−10.0610	+	19.5647i	−0.457319	+	0.889303i
$23$	−6.31990	+	6.31990i	−0.274778	+	0.274778i	−0.831020	−	0.556242i	$-0.812243\pi$
$23$	−6.31990	+	6.31990i	−0.274778	+	0.274778i	0.556242	+	0.831020i	$0.312243\pi$
$24$	−29.1270	+	30.1293i	−1.21363	+	1.25539i
$25$	0.839974	−	24.9859i	0.0335990	−	0.999435i
$26$	−27.3649	+	27.6751i	−1.05249	+	1.06443i
$27$	−34.9662	−	34.9662i	−1.29504	−	1.29504i
$28$	−6.42467	+	6.57120i	−0.229452	+	0.234686i
$29$	34.0393			1.17377			0.586884	−	0.809671i	$-0.300354\pi$
$29$	34.0393			1.17377			0.586884	+	0.809671i	$0.300354\pi$
$30$	0.584858	−	52.3799i	0.0194953	−	1.74600i
$31$			22.2160i			0.716646i	0.933598	+	0.358323i	$0.116651\pi$
$31$			22.2160i			0.716646i	−0.933598	+	0.358323i	$0.883349\pi$
$32$	−31.9873	+	0.901868i	−0.999603	+	0.0281834i
$33$	−17.2914	−	54.9659i	−0.523982	−	1.66563i
$34$	44.4184	+	43.9204i	1.30642	+	1.29178i
$35$	0.193012	−	11.4859i	0.00551464	−	0.328170i
$36$	−0.831614	−	73.7553i	−0.0231004	−	2.04876i
$37$	8.71788	−	8.71788i	0.235618	−	0.235618i	−0.579415	−	0.815033i	$-0.696719\pi$
$37$	8.71788	−	8.71788i	0.235618	−	0.235618i	0.815033	+	0.579415i	$0.196719\pi$
$38$	0.0668392	+	11.8562i	0.00175893	+	0.312006i
$39$		−	101.937i		−	2.61377i
$40$	28.2812	−	28.2874i	0.707029	−	0.707184i
$41$			44.8146i			1.09304i	0.837446	+	0.546520i	$0.184048\pi$
$41$			44.8146i			1.09304i	−0.837446	+	0.546520i	$0.815952\pi$
$42$	−0.135693	−	24.0698i	−0.00323079	−	0.573091i
$43$	11.2370	+	11.2370i	0.261326	+	0.261326i	0.825593	−	0.564267i	$-0.190841\pi$
$43$	11.2370	+	11.2370i	0.261326	+	0.261326i	−0.564267	+	0.825593i	$0.690841\pi$
$44$	19.9011	−	39.2421i	0.452298	−	0.891867i
$45$	64.0906	+	66.2814i	1.42424	+	1.47292i
$46$	12.5683	−	12.7108i	0.273225	−	0.276323i
$47$	−6.26838	−	6.26838i	−0.133370	−	0.133370i	0.637270	−	0.770640i	$-0.280063\pi$
$47$	−6.26838	−	6.26838i	−0.133370	−	0.133370i	−0.770640	+	0.637270i	$0.780063\pi$
$48$	57.9135	−	60.5860i	1.20653	−	1.26221i
$49$			43.7214i			0.892274i
$50$	−1.39821	+	49.9804i	−0.0279642	+	0.999609i
$51$	−163.608			−3.20801
$52$	54.4168	−	55.6579i	1.04648	−	1.07035i
$53$	−36.4914	−	36.4914i	−0.688518	−	0.688518i	0.273386	−	0.961904i	$-0.411856\pi$
$53$	−36.4914	−	36.4914i	−0.688518	−	0.688518i	−0.961904	+	0.273386i	$0.911856\pi$
$54$	70.3255	+	69.5371i	1.30232	+	1.28772i
$55$	15.6209	+	52.7351i	0.284016	+	0.958819i
$56$	12.7750	−	13.2146i	0.228126	−	0.235976i
$57$	−21.9584	−	21.9584i	−0.385234	−	0.385234i
$58$	−68.0775	+	0.383786i	−1.17375	+	0.00661699i
$59$	8.49349			0.143957			0.0719787	−	0.997406i	$-0.477069\pi$
$59$	8.49349			0.143957			0.0719787	+	0.997406i	$0.477069\pi$
$60$	−0.579124	+	104.765i	−0.00965207	+	1.74608i
$61$		−	64.3732i		−	1.05530i	−0.849463	−	0.527649i	$-0.823074\pi$
$61$		−	64.3732i		−	1.05530i	0.849463	−	0.527649i	$-0.176926\pi$
$62$	−0.250481	−	44.4313i	−0.00404001	−	0.716634i
$63$	29.9574	+	29.9574i	0.475514	+	0.475514i
$64$	63.9634	−	2.16436i	0.999428	−	0.0338181i
$65$	−1.63481	+	97.2857i	−0.0251509	+	1.49670i
$66$	35.2020	+	109.735i	0.533364	+	1.66265i
$67$	50.4964	+	50.4964i	0.753677	+	0.753677i	0.975164	−	0.221486i	$-0.0710908\pi$
$67$	50.4964	+	50.4964i	0.753677	+	0.753677i	−0.221486	+	0.975164i	$0.571091\pi$
$68$	−89.3306	−	87.3386i	−1.31369	−	1.28439i
$69$			46.8184i			0.678528i
$70$	−0.256517	+	22.9737i	−0.00366453	+	0.328196i
$71$			57.3348i			0.807532i	0.914862	+	0.403766i	$0.132299\pi$
$71$			57.3348i			0.807532i	−0.914862	+	0.403766i	$0.867701\pi$
$72$	2.49478	+	147.499i	0.0346497	+	2.04859i
$73$	33.7647	−	33.7647i	0.462530	−	0.462530i	−0.436954	−	0.899484i	$-0.643943\pi$
$73$	33.7647	−	33.7647i	0.462530	−	0.462530i	0.899484	+	0.436954i	$0.143943\pi$
$74$	−17.3372	+	17.5338i	−0.234286	+	0.236943i
$75$	−89.4377	−	95.6603i	−1.19250	−	1.27547i
$76$	−0.267353	−	23.7113i	−0.00351780	−	0.311991i
$77$	7.58397	+	24.1079i	0.0984931	+	0.313089i
$78$	1.14932	+	203.871i	0.0147349	+	2.61373i
$79$			91.0525i			1.15256i	0.817251	+	0.576281i	$0.195497\pi$
$79$			91.0525i			1.15256i	−0.817251	+	0.576281i	$0.804503\pi$
$80$	−56.2425	+	56.8927i	−0.703031	+	0.711159i
$81$	−93.0733			−1.14905
$82$	−0.505275	−	89.6278i	−0.00616189	−	1.09302i
$83$	67.5635	+	67.5635i	0.814019	+	0.814019i	0.985234	−	0.171215i	$-0.0547693\pi$
$83$	67.5635	+	67.5635i	0.814019	+	0.814019i	−0.171215	+	0.985234i	$0.554769\pi$
$84$	0.542764	+	48.1374i	0.00646148	+	0.573064i
$85$	156.143	+	2.62386i	1.83697	+	0.0308689i
$86$	−22.6004	−	22.3470i	−0.262795	−	0.259849i
$87$	126.083	−	126.083i	1.44923	−	1.44923i
$88$	−39.3591	+	78.7074i	−0.447263	+	0.894402i
$89$		−	13.8142i		−	0.155216i	−0.996984	−	0.0776078i	$-0.975272\pi$
$89$		−	13.8142i		−	0.155216i	0.996984	−	0.0776078i	$-0.0247282\pi$
$90$	−128.926	−	131.838i	−1.43252	−	1.46487i
$91$			44.7093i			0.491311i
$92$	−24.9930	+	25.5630i	−0.271663	+	0.277859i
$93$	82.2893	+	82.2893i	0.884831	+	0.884831i
$94$	12.6072	+	12.4659i	0.134120	+	0.132616i
$95$	20.6042	+	21.3086i	0.216887	+	0.224301i
$96$	−115.142	+	121.823i	−1.19940	+	1.26899i
$97$	37.0639	−	37.0639i	0.382102	−	0.382102i	−0.489757	−	0.871859i	$-0.662915\pi$
$97$	37.0639	−	37.0639i	0.382102	−	0.382102i	0.871859	+	0.489757i	$0.162915\pi$
$98$	−0.492950	−	87.4415i	−0.00503010	−	0.892260i
$99$	−179.860	−	93.7779i	−1.81677	−	0.947252i
$100$	2.23286	−	99.9751i	0.0223286	−	0.999751i
$101$			118.605i			1.17431i	0.809475	+	0.587155i	$0.199752\pi$
$101$			118.605i			1.17431i	−0.809475	+	0.587155i	$0.800248\pi$
$102$	327.211	−	1.84465i	3.20796	−	0.0180848i
$103$	132.061	−	132.061i	1.28215	−	1.28215i	0.342701	−	0.939445i	$-0.388658\pi$
$103$	132.061	−	132.061i	1.28215	−	1.28215i	0.939445	−	0.342701i	$-0.111342\pi$
$104$	−108.204	+	111.928i	−1.04043	+	1.07623i
$105$	−41.8296	−	43.2594i	−0.398377	−	0.411995i
$106$	73.3932	+	72.5703i	0.692388	+	0.684625i
$107$	−18.9476	+	18.9476i	−0.177080	+	0.177080i	−0.790082	−	0.613001i	$-0.789962\pi$
$107$	−18.9476	+	18.9476i	−0.177080	+	0.177080i	0.613001	+	0.790082i	$0.289962\pi$
$108$	−141.433	−	138.279i	−1.30956	−	1.28036i
$109$	−50.7151			−0.465276			−0.232638	−	0.972563i	$-0.574736\pi$
$109$	−50.7151			−0.465276			−0.232638	+	0.972563i	$0.574736\pi$
$110$	−31.8359	−	105.292i	−0.289417	−	0.957203i
$111$		−	64.5829i		−	0.581828i
$112$	−25.4007	+	26.5729i	−0.226792	+	0.237258i
$113$	−93.6330	−	93.6330i	−0.828610	−	0.828610i	0.158714	−	0.987325i	$-0.449265\pi$
$113$	−93.6330	−	93.6330i	−0.828610	−	0.828610i	−0.987325	+	0.158714i	$0.949265\pi$
$114$	44.1636	+	43.6685i	0.387400	+	0.383057i
$115$	0.750848	−	44.6821i	0.00652911	−	0.388540i
$116$	136.149	−	1.53512i	1.17369	−	0.0132338i
$117$	−253.738	−	253.738i	−2.16870	−	2.16870i
$118$	−16.9867	+	0.0957623i	−0.143955	+	0.000811545i
$119$	71.7582			0.603010
$120$	−0.0229700	−	209.533i	−0.000191417	−	1.74611i
$121$	−69.2739	−	99.2075i	−0.572512	−	0.819897i
$122$	0.725793	+	128.744i	0.00594913	+	1.05528i
$123$	165.996	+	165.996i	1.34956	+	1.34956i
$124$	1.00191	+	88.8584i	0.00807990	+	0.716600i
$125$	83.8225	+	92.7297i	0.670580	+	0.741837i
$126$	−60.2515	−	59.5760i	−0.478187	−	0.472826i
$127$	−148.955	+	148.955i	−1.17288	+	1.17288i	−0.191354	+	0.981521i	$0.561288\pi$
$127$	−148.955	+	148.955i	−1.17288	+	1.17288i	−0.981521	+	0.191354i	$0.938712\pi$
$128$	−127.900	+	5.04982i	−0.999221	+	0.0394517i
$129$	83.2450			0.645310
$130$	2.17269	−	194.587i	0.0167130	−	1.49682i
$131$	142.569			1.08832			0.544158	−	0.838983i	$-0.316849\pi$
$131$	142.569			1.08832			0.544158	+	0.838983i	$0.316849\pi$
$132$	−71.6402	−	219.070i	−0.542728	−	1.65962i
$133$	9.63088	+	9.63088i	0.0724126	+	0.0724126i
$134$	−101.560	−	100.422i	−0.757914	−	0.749417i
$135$	247.214	+	4.15423i	1.83121	+	0.0307721i
$136$	179.643	+	173.667i	1.32091	+	1.27697i
$137$	72.3548	−	72.3548i	0.528137	−	0.528137i	−0.391879	−	0.920017i	$-0.628175\pi$
$137$	72.3548	−	72.3548i	0.528137	−	0.528137i	0.920017	+	0.391879i	$0.128175\pi$
$138$	−0.527868	−	93.6354i	−0.00382513	−	0.678517i
$139$		−	29.2001i		−	0.210072i	−0.994468	−	0.105036i	$-0.966504\pi$
$139$		−	29.2001i		−	0.210072i	0.994468	−	0.105036i	$-0.0334958\pi$
$140$	0.254002	−	45.9496i	0.00181430	−	0.328211i
$141$	−46.4368			−0.329339
$142$	−0.646437	−	114.668i	−0.00455237	−	0.807519i
$143$	−64.2361	−	204.193i	−0.449203	−	1.42792i
$144$	−6.65249	−	294.965i	−0.0461979	−	2.04837i
$145$	−122.352	+	118.308i	−0.843808	+	0.815917i
$146$	−67.1476	+	67.9090i	−0.459915	+	0.465130i
$147$	161.946	+	161.946i	1.10168	+	1.10168i
$148$	34.4761	−	35.2625i	0.232947	−	0.238260i
$149$	94.1728			0.632032			0.316016	−	0.948754i	$-0.397655\pi$
$149$	94.1728			0.632032			0.316016	+	0.948754i	$0.397655\pi$
$150$	179.951	+	190.309i	1.19967	+	1.26873i
$151$	200.954			1.33082			0.665412	−	0.746477i	$-0.268256\pi$
$151$	200.954			1.33082			0.665412	+	0.746477i	$0.268256\pi$
$152$	0.802036	+	47.4188i	0.00527656	+	0.311966i
$153$	−407.248	+	407.248i	−2.66175	+	2.66175i
$154$	−15.4395	−	48.1295i	−0.100257	−	0.312529i
$155$	−77.2147	−	79.8541i	−0.498159	−	0.515188i
$156$	−4.59720	−	407.723i	−0.0294692	−	2.61361i
$157$	−54.4689	+	54.4689i	−0.346936	+	0.346936i	−0.858967	−	0.512031i	$-0.828893\pi$
$157$	−54.4689	+	54.4689i	−0.346936	+	0.346936i	0.512031	+	0.858967i	$0.328893\pi$
$158$	−1.02660	−	182.102i	−0.00649745	−	1.15254i
$159$	−270.332			−1.70020
$160$	111.842	−	114.418i	0.699011	−	0.715111i
$161$		−	20.5344i		−	0.127543i
$162$	186.144	−	1.04938i	1.14904	−	0.00647766i
$163$	−161.844	+	161.844i	−0.992906	+	0.992906i	−0.999975	−	0.00706858i	$-0.997750\pi$
$163$	−161.844	+	161.844i	−0.992906	+	0.992906i	0.00706858	+	0.999975i	$0.497750\pi$
$164$	2.02107	+	179.247i	0.0123236	+	1.09297i
$165$	253.194	+	137.473i	1.53451	+	0.833168i
$166$	−135.887	−	134.363i	−0.818595	−	0.809417i
$167$	−94.4017	+	94.4017i	−0.565279	+	0.565279i	−0.930802	−	0.365523i	$-0.880890\pi$
$167$	−94.4017	+	94.4017i	−0.565279	+	0.565279i	0.365523	+	0.930802i	$0.380890\pi$
$168$	−1.62825	−	96.2671i	−0.00969196	−	0.573018i
$169$		−	209.687i		−	1.24075i
$170$	−312.310	−	3.48716i	−1.83712	−	0.0205127i
$171$	−109.316			−0.639275
$172$	45.4520	+	44.4385i	0.264256	+	0.258363i
$173$	−68.5259	+	68.5259i	−0.396104	+	0.396104i	−0.876856	−	0.480753i	$-0.840364\pi$
$173$	−68.5259	+	68.5259i	−0.396104	+	0.396104i	0.480753	+	0.876856i	$0.340364\pi$
$174$	−250.741	+	253.584i	−1.44104	+	1.45738i
$175$	39.2271	+	41.9564i	0.224155	+	0.239751i
$176$	77.8296	−	157.856i	0.442214	−	0.896910i
$177$	31.4603	−	31.4603i	0.177742	−	0.177742i
$178$	0.155752	+	27.6279i	0.000875011	+	0.155213i
$179$	124.953			0.698060			0.349030	−	0.937112i	$-0.386511\pi$
$179$	124.953			0.698060			0.349030	+	0.937112i	$0.386511\pi$
$180$	259.335	+	262.218i	1.44075	+	1.45677i
$181$	59.7248			0.329971			0.164986	−	0.986296i	$-0.447242\pi$
$181$	59.7248			0.329971			0.164986	+	0.986296i	$0.447242\pi$
$182$	−0.504088	−	89.4173i	−0.00276972	−	0.491304i
$183$	−238.441	−	238.441i	−1.30296	−	1.30296i
$184$	49.6969	−	51.4070i	0.270092	−	0.279386i
$185$	−1.03575	+	61.6360i	−0.00559862	+	0.333168i
$186$	−165.504	−	163.648i	−0.889805	−	0.879829i
$187$	−327.729	+	103.098i	−1.75256	+	0.551329i
$188$	−25.3546	−	24.7892i	−0.134865	−	0.131858i
$189$	113.611			0.601118
$190$	−41.4481	−	42.3841i	−0.218148	−	0.223074i
$191$			58.7271i			0.307471i	0.988112	+	0.153736i	$0.0491305\pi$
$191$			58.7271i			0.307471i	−0.988112	+	0.153736i	$0.950870\pi$
$192$	228.907	−	244.941i	1.19222	−	1.27573i
$193$	102.445	−	102.445i	0.530801	−	0.530801i	−0.390009	−	0.920811i	$-0.627528\pi$
$193$	102.445	−	102.445i	0.530801	−	0.530801i	0.920811	+	0.390009i	$0.127528\pi$
$194$	−73.7087	+	74.5445i	−0.379942	+	0.384250i
$195$	354.296	+	366.407i	1.81690	+	1.87901i
$196$	1.97177	+	174.875i	0.0100600	+	0.892217i
$197$	121.540	+	121.540i	0.616956	+	0.616956i	0.944749	−	0.327793i	$-0.106305\pi$
$197$	121.540	+	121.540i	0.616956	+	0.616956i	−0.327793	+	0.944749i	$0.606305\pi$
$198$	360.772	+	185.525i	1.82208	+	0.936995i
$199$	90.5475			0.455012			0.227506	−	0.973777i	$-0.426943\pi$
$199$	90.5475			0.455012			0.227506	+	0.973777i	$0.426943\pi$
$200$	−3.33845	+	199.972i	−0.0166922	+	0.999861i
$201$	374.082			1.86111
$202$	−1.33725	−	237.207i	−0.00662004	−	1.17429i
$203$	−55.2998	+	55.2998i	−0.272413	+	0.272413i
$204$	−654.392	+	7.37848i	−3.20780	+	0.0361690i
$205$	−155.759	−	161.083i	−0.759800	−	0.785772i
$206$	−262.629	+	265.607i	−1.27490	+	1.28935i
$207$	116.539	+	116.539i	0.562990	+	0.562990i
$208$	215.143	−	225.072i	1.03434	−	1.08208i
$209$	−57.8226	−	30.1483i	−0.276663	−	0.144250i
$210$	84.1456	+	86.0459i	0.400693	+	0.409742i
$211$	−242.037			−1.14710			−0.573548	−	0.819172i	$-0.694433\pi$
$211$	−242.037			−1.14710			−0.573548	+	0.819172i	$0.694433\pi$
$212$	−147.602	−	144.311i	−0.696237	−	0.680711i
$213$	212.371	+	212.371i	0.997047	+	0.997047i
$214$	37.6809	−	38.1082i	0.176079	−	0.178076i
$215$	−79.4466	−	1.33504i	−0.369519	−	0.00620948i
$216$	284.420	+	274.959i	1.31676	+	1.27296i
$217$	−36.0918	−	36.0918i	−0.166322	−	0.166322i
$218$	101.429	−	0.571802i	0.465269	−	0.00262294i
$219$		−	250.132i		−	1.14216i
$220$	64.8579	+	210.222i	0.294809	+	0.955556i
$221$	−607.790			−2.75018
$222$	0.728159	+	129.164i	0.00327999	+	0.581819i
$223$	−9.03062	+	9.03062i	−0.0404961	+	0.0404961i	−0.727065	−	0.686569i	$-0.759116\pi$
$223$	−9.03062	+	9.03062i	−0.0404961	+	0.0404961i	0.686569	+	0.727065i	$0.259116\pi$
$224$	50.5010	−	53.4313i	0.225451	−	0.238533i
$225$	−460.739	−	15.4891i	−2.04773	−	0.0688405i
$226$	188.319	+	186.207i	0.833269	+	0.823926i
$227$	66.4954	−	66.4954i	0.292931	−	0.292931i	−0.545306	−	0.838237i	$-0.683586\pi$
$227$	66.4954	−	66.4954i	0.292931	−	0.292931i	0.838237	+	0.545306i	$0.183586\pi$
$228$	−88.8182	−	86.8376i	−0.389553	−	0.380867i
$229$			129.901i			0.567254i	0.958935	+	0.283627i	$0.0915378\pi$
$229$			129.901i			0.567254i	−0.958935	+	0.283627i	$0.908462\pi$
$230$	−0.997891	+	89.3713i	−0.00433866	+	0.388571i
$231$	117.388	+	61.2054i	0.508174	+	0.264958i
$232$	−272.275	+	4.60523i	−1.17360	+	0.0198501i
$233$	121.518	−	121.518i	0.521537	−	0.521537i	−0.396498	−	0.918035i	$-0.629775\pi$
$233$	121.518	−	121.518i	0.521537	−	0.521537i	0.918035	+	0.396498i	$0.129775\pi$
$234$	510.329	+	504.608i	2.18089	+	2.15644i
$235$	44.3179	+	0.744728i	0.188587	+	0.00316905i
$236$	33.9718	−	0.383043i	0.143948	−	0.00162306i
$237$	337.263	+	337.263i	1.42305	+	1.42305i
$238$	−143.514	+	0.809058i	−0.603000	+	0.00339940i
$239$		−	60.6306i		−	0.253685i	−0.991923	−	0.126842i	$-0.959516\pi$
$239$		−	60.6306i		−	0.253685i	0.991923	−	0.126842i	$-0.0404842\pi$
$240$	2.40838	+	419.059i	0.0100349	+	1.74608i
$241$		−	124.194i		−	0.515328i	−0.966235	−	0.257664i	$-0.917047\pi$
$241$		−	124.194i		−	0.515328i	0.966235	−	0.257664i	$-0.0829528\pi$
$242$	139.664	+	197.631i	0.577125	+	0.816656i
$243$	−30.0525	+	30.0525i	−0.123673	+	0.123673i
$244$	−2.90313	−	257.476i	−0.0118981	−	1.05523i
$245$	−151.960	−	157.154i	−0.620243	−	0.641445i
$246$	−333.857	−	330.114i	−1.35714	−	1.34193i
$247$	−81.5734	−	81.5734i	−0.330257	−	0.330257i
$248$	−3.00564	−	177.703i	−0.0121195	−	0.716543i
$249$	500.518			2.01011
$250$	−168.688	−	184.511i	−0.674751	−	0.738045i
$251$		−	380.561i		−	1.51618i	−0.652150	−	0.758090i	$-0.726133\pi$
$251$		−	380.561i		−	1.51618i	0.652150	−	0.758090i	$-0.273867\pi$
$252$	121.173	+	118.471i	0.480845	+	0.470122i
$253$	29.5028	+	93.7834i	0.116612	+	0.370685i
$254$	296.226	−	299.585i	1.16624	−	1.17947i
$255$	588.080	−	568.642i	2.30620	−	2.22997i
$256$	255.740	−	11.5415i	0.998983	−	0.0450841i
$257$	−57.6263	+	57.6263i	−0.224227	+	0.224227i	−0.810276	−	0.586049i	$-0.800683\pi$
$257$	−57.6263	+	57.6263i	−0.224227	+	0.224227i	0.586049	+	0.810276i	$0.300683\pi$
$258$	−166.487	+	0.938570i	−0.645300	+	0.00363787i
$259$			28.3259i			0.109366i
$260$	−2.15140	+	389.192i	−0.00827460	+	1.49689i
$261$		−	627.684i		−	2.40492i
$262$	−285.134	+	1.60744i	−1.08830	+	0.00613527i
$263$	80.2515	+	80.2515i	0.305139	+	0.305139i	0.843020	−	0.537882i	$-0.180775\pi$
$263$	80.2515	+	80.2515i	0.305139	+	0.305139i	−0.537882	+	0.843020i	$0.680775\pi$
$264$	145.748	+	437.325i	0.552076	+	1.65653i
$265$	257.997	+	4.33544i	0.973574	+	0.0163601i
$266$	−19.3700	−	19.1529i	−0.0728197	−	0.0720033i
$267$	−51.1684	−	51.1684i	−0.191642	−	0.191642i
$268$	204.250	+	199.695i	0.762127	+	0.745132i
$269$		−	300.863i		−	1.11845i	−0.829016	−	0.559225i	$-0.811099\pi$
$269$		−	300.863i		−	1.11845i	0.829016	−	0.559225i	$-0.188901\pi$
$270$	−494.466	−	5.52105i	−1.83136	−	0.0204483i
$271$	−113.311			−0.418122			−0.209061	−	0.977903i	$-0.567041\pi$
$271$	−113.311			−0.418122			−0.209061	+	0.977903i	$0.567041\pi$
$272$	−361.239	−	345.304i	−1.32808	−	1.26950i
$273$	165.606	+	165.606i	0.606614	+	0.606614i
$274$	−143.892	+	145.523i	−0.525152	+	0.531106i
$275$	−239.436	−	135.260i	−0.870676	−	0.491856i
$276$	2.11144	+	187.262i	0.00765014	+	0.678485i
$277$	−92.5588	−	92.5588i	−0.334147	−	0.334147i	0.520012	−	0.854159i	$-0.325928\pi$
$277$	−92.5588	−	92.5588i	−0.334147	−	0.334147i	−0.854159	+	0.520012i	$0.825928\pi$
$278$	0.329224	+	58.3992i	0.00118426	+	0.210069i
$279$	409.663			1.46833
$280$	0.0100746	+	91.9005i	3.59806e−5	+	0.328216i
$281$		−	401.370i		−	1.42836i	−0.699960	−	0.714182i	$-0.746799\pi$
$281$		−	401.370i		−	1.42836i	0.699960	−	0.714182i	$-0.253201\pi$
$282$	92.8721	−	0.523565i	0.329334	−	0.00185661i
$283$	−226.496	−	226.496i	−0.800340	−	0.800340i	0.182808	−	0.983149i	$-0.441481\pi$
$283$	−226.496	−	226.496i	−0.800340	−	0.800340i	−0.983149	+	0.182808i	$0.941481\pi$
$284$	2.58571	+	229.324i	0.00910460	+	0.807481i
$285$	155.247	+	2.60881i	0.544727	+	0.00915371i
$286$	130.772	+	407.656i	0.457246	+	1.42537i
$287$	−72.8052	−	72.8052i	−0.253677	−	0.253677i
$288$	16.6304	+	589.845i	0.0577446	+	2.04807i
$289$			686.499i			2.37543i
$290$	243.366	−	237.992i	0.839195	−	0.820661i
$291$		−	274.573i		−	0.943550i
$292$	133.527	−	136.573i	0.457286	−	0.467715i
$293$	−101.907	+	101.907i	−0.347807	+	0.347807i	−0.859292	−	0.511485i	$-0.829096\pi$
$293$	−101.907	+	101.907i	−0.347807	+	0.347807i	0.511485	+	0.859292i	$0.329096\pi$
$294$	−325.714	−	322.062i	−1.10787	−	1.09545i
$295$	−30.5293	+	29.5202i	−0.103489	+	0.100069i
$296$	−68.5536	+	70.9125i	−0.231600	+	0.239569i
$297$	−518.877	+	163.231i	−1.74706	+	0.549599i
$298$	−188.343	+	1.06178i	−0.632022	+	0.00356301i
$299$			173.926i			0.581693i
$300$	−362.042	−	378.583i	−1.20681	−	1.26194i
$301$	−36.5110			−0.121299
$302$	−401.902	+	2.26572i	−1.33080	+	0.00750237i
$303$	439.320	+	439.320i	1.44990	+	1.44990i
$304$	−2.13868	−	94.8271i	−0.00703515	−	0.311931i
$305$	223.737	+	231.385i	0.733565	+	0.758641i
$306$	809.892	−	819.075i	2.64671	−	2.67672i
$307$	−222.367	+	222.367i	−0.724322	+	0.724322i	−0.969483	−	0.245161i	$-0.921159\pi$
$307$	−222.367	+	222.367i	−0.724322	+	0.724322i	0.245161	+	0.969483i	$0.421159\pi$
$308$	31.4212	+	96.0834i	0.102017	+	0.311959i
$309$		−	978.321i		−	3.16609i
$310$	155.327	+	158.835i	0.501056	+	0.512371i
$311$			431.545i			1.38761i	0.720165	+	0.693803i	$0.244066\pi$
$311$			431.545i			1.38761i	−0.720165	+	0.693803i	$0.755934\pi$
$312$	13.7912	+	815.380i	0.0442027	+	2.61340i
$313$	−193.849	−	193.849i	−0.619327	−	0.619327i	0.326032	−	0.945359i	$-0.394288\pi$
$313$	−193.849	−	193.849i	−0.619327	−	0.619327i	−0.945359	+	0.326032i	$0.894288\pi$
$314$	108.322	−	109.550i	0.344974	−	0.348886i
$315$	−211.801	−	3.55915i	−0.672383	−	0.0112989i
$316$	4.10632	+	364.187i	0.0129947	+	1.15249i
$317$	−231.515	+	231.515i	−0.730333	+	0.730333i	−0.970686	−	0.240353i	$-0.922737\pi$
$317$	−231.515	+	231.515i	−0.730333	+	0.730333i	0.240353	+	0.970686i	$0.422737\pi$
$318$	540.656	−	3.04794i	1.70018	−	0.00958471i
$319$	173.109	−	332.013i	0.542662	−	1.04079i
$320$	−222.390	+	230.093i	−0.694969	+	0.719040i
$321$			140.366i			0.437276i
$322$	0.231521	+	41.0682i	0.000719011	+	0.127541i
$323$	−130.925	+	130.925i	−0.405340	+	0.405340i
$324$	−372.270	+	4.19746i	−1.14898	+	0.0129551i
$325$	−332.253	−	355.369i	−1.02232	−	1.09344i
$326$	321.858	−	325.507i	0.987293	−	0.998488i
$327$	−187.851	+	187.851i	−0.574469	+	0.574469i
$328$	−6.06304	−	358.466i	−0.0184849	−	1.09288i
$329$	20.3671			0.0619060
$330$	−507.930	−	272.087i	−1.53918	−	0.824505i
$331$			516.607i			1.56075i	0.625314	+	0.780373i	$0.284971\pi$
$331$			516.607i			1.56075i	−0.625314	+	0.780373i	$0.715029\pi$
$332$	273.284	+	267.190i	0.823145	+	0.804789i
$333$	−160.758	−	160.758i	−0.482756	−	0.482756i
$334$	187.736	−	189.865i	0.562084	−	0.568457i
$335$	−357.013	−	5.99932i	−1.06571	−	0.0179084i
$336$	4.34184	+	192.513i	0.0129221	+	0.572955i
$337$	91.3868	+	91.3868i	0.271177	+	0.271177i	0.829574	−	0.558397i	$-0.188583\pi$
$337$	91.3868	+	91.3868i	0.271177	+	0.271177i	−0.558397	+	0.829574i	$0.688583\pi$
$338$	2.36418	+	419.368i	0.00699461	+	1.24073i
$339$	−693.643			−2.04614
$340$	624.650	+	3.45297i	1.83721	+	0.0101558i
$341$	216.691	+	112.981i	0.635457	+	0.331323i
$342$	218.629	−	1.23251i	0.639265	−	0.00360384i
$343$	−150.634	−	150.634i	−0.439166	−	0.439166i
$344$	−91.4036	−	88.3631i	−0.265708	−	0.256869i
$345$	−162.724	−	168.286i	−0.471663	−	0.487786i
$346$	136.277	−	137.822i	0.393864	−	0.398330i
$347$	238.516	−	238.516i	0.687366	−	0.687366i	−0.274283	−	0.961649i	$-0.588441\pi$
$347$	238.516	−	238.516i	0.687366	−	0.687366i	0.961649	+	0.274283i	$0.0884405\pi$
$348$	498.615	−	509.987i	1.43280	−	1.46548i
$349$	93.8343			0.268866			0.134433	−	0.990923i	$-0.457079\pi$
$349$	93.8343			0.268866			0.134433	+	0.990923i	$0.457079\pi$
$350$	−78.9261	−	83.4691i	−0.225503	−	0.238483i
$351$	−962.285			−2.74155
$352$	−153.877	+	316.585i	−0.437151	+	0.899388i
$353$	383.433	+	383.433i	1.08621	+	1.08621i	0.995915	+	0.0902984i	$0.0287821\pi$
$353$	383.433	+	383.433i	1.08621	+	1.08621i	0.0902984	+	0.995915i	$0.471218\pi$
$354$	−62.5649	+	63.2744i	−0.176737	+	0.178741i
$355$	−199.275	−	206.086i	−0.561337	−	0.580525i
$356$	−0.622998	−	55.2532i	−0.00174999	−	0.155206i
$357$	265.796	−	265.796i	0.744527	−	0.744527i
$358$	−249.901	+	1.40881i	−0.698049	+	0.00393524i
$359$			57.3533i			0.159759i	0.996805	+	0.0798793i	$0.0254535\pi$
$359$			57.3533i			0.159759i	−0.996805	+	0.0798793i	$0.974547\pi$
$360$	−521.619	−	521.505i	−1.44894	−	1.44862i
$361$	325.856			0.902649
$362$	−119.448	+	0.673384i	−0.329966	+	0.00186018i
$363$	−624.064	−	110.875i	−1.71918	−	0.305442i
$364$	2.01632	+	178.826i	0.00553934	+	0.491280i
$365$	−4.01148	+	238.719i	−0.0109904	+	0.654024i
$366$	479.564	+	474.187i	1.31028	+	1.29559i
$367$	391.149	+	391.149i	1.06580	+	1.06580i	0.997677	+	0.0681232i	$0.0217011\pi$
$367$	391.149	+	391.149i	1.06580	+	1.06580i	0.0681232	+	0.997677i	$0.478299\pi$
$368$	−98.8127	+	103.373i	−0.268513	+	0.280904i
$369$	826.381			2.23951
$370$	1.37652	−	123.282i	0.00372034	−	0.333194i
$371$	118.567			0.319588
$372$	332.847	+	325.425i	0.894751	+	0.874798i
$373$	−237.138	+	237.138i	−0.635758	+	0.635758i	−0.949506	−	0.313748i	$-0.898415\pi$
$373$	−237.138	+	237.138i	−0.635758	+	0.635758i	0.313748	+	0.949506i	$0.398415\pi$
$374$	654.285	−	209.889i	1.74942	−	0.561200i
$375$	653.958	+	32.9926i	1.74389	+	0.0879803i
$376$	50.9879	+	49.2918i	0.135606	+	0.131095i
$377$	468.388	−	468.388i	1.24241	−	1.24241i
$378$	−227.219	+	1.28094i	−0.601108	+	0.00338874i
$379$	113.361			0.299106			0.149553	−	0.988754i	$-0.452217\pi$
$379$	113.361			0.299106			0.149553	+	0.988754i	$0.452217\pi$
$380$	83.3727	+	84.2996i	0.219402	+	0.221841i
$381$			1103.48i			2.89626i
$382$	−0.662135	−	117.452i	−0.00173334	−	0.307467i
$383$	320.539	−	320.539i	0.836916	−	0.836916i	−0.151535	−	0.988452i	$-0.548422\pi$
$383$	320.539	−	320.539i	0.836916	−	0.836916i	0.988452	+	0.151535i	$0.0484218\pi$
$384$	−455.045	+	492.454i	−1.18501	+	1.28243i
$385$	−111.050	−	60.2952i	−0.288442	−	0.156611i
$386$	−203.731	+	206.041i	−0.527801	+	0.533785i
$387$	207.211	−	207.211i	0.535428	−	0.535428i
$388$	146.575	−	149.918i	0.377770	−	0.386386i
$389$		−	347.708i		−	0.893851i	−0.894571	−	0.446925i	$-0.852519\pi$
$389$		−	347.708i		−	0.893851i	0.894571	−	0.446925i	$-0.147481\pi$
$390$	−712.712	−	728.807i	−1.82747	−	1.86874i
$391$	279.151			0.713940
$392$	−5.91515	−	349.721i	−0.0150897	−	0.892147i
$393$	528.084	−	528.084i	1.34373	−	1.34373i
$394$	−244.447	−	241.707i	−0.620424	−	0.613468i
$395$	−316.465	−	327.282i	−0.801177	−	0.828563i
$396$	−723.625	−	366.976i	−1.82734	−	0.926708i
$397$	−541.110	+	541.110i	−1.36300	+	1.36300i	−0.492926	+	0.870071i	$0.664073\pi$
$397$	−541.110	+	541.110i	−1.36300	+	1.36300i	−0.870071	+	0.492926i	$0.835927\pi$
$398$	−181.092	+	1.02090i	−0.455005	+	0.00256508i
$399$	71.3465			0.178813
$400$	4.42215	−	399.976i	0.0110554	−	0.999939i
$401$	14.6203			0.0364596			0.0182298	−	0.999834i	$-0.494197\pi$
$401$	14.6203			0.0364596			0.0182298	+	0.999834i	$0.494197\pi$
$402$	−748.153	+	4.21770i	−1.86108	+	0.0104918i
$403$	305.697	+	305.697i	0.758554	+	0.758554i
$404$	5.34891	+	474.391i	0.0132399	+	1.17423i
$405$	334.546	−	323.489i	0.826040	−	0.798737i
$406$	109.974	−	111.221i	0.270873	−	0.273944i
$407$	−40.6972	−	129.368i	−0.0999931	−	0.317858i
$408$	1308.68	−	22.1348i	3.20755	−	0.0542521i
$409$	−626.095			−1.53080			−0.765398	−	0.643558i	$-0.777458\pi$
$409$	−626.095			−1.53080			−0.765398	+	0.643558i	$0.777458\pi$
$410$	313.329	+	320.405i	0.764218	+	0.781477i
$411$		−	536.012i		−	1.30417i
$412$	522.255	−	534.166i	1.26761	−	1.29652i
$413$	−13.7984	+	13.7984i	−0.0334102	+	0.0334102i
$414$	−234.388	−	231.760i	−0.566154	−	0.559807i
$415$	−477.679	−	8.02702i	−1.15103	−	0.0193422i
$416$	−427.742	+	452.562i	−1.02823	+	1.08789i
$417$	−108.159	−	108.159i	−0.259373	−	0.259373i
$418$	115.983	+	59.6437i	0.277472	+	0.142688i
$419$	−318.953			−0.761225			−0.380612	−	0.924735i	$-0.624287\pi$
$419$	−318.953			−0.761225			−0.380612	+	0.924735i	$0.624287\pi$
$420$	−169.259	−	171.140i	−0.402997	−	0.407477i
$421$	−106.730			−0.253515			−0.126758	−	0.991934i	$-0.540457\pi$
$421$	−106.730			−0.253515			−0.126758	+	0.991934i	$0.540457\pi$
$422$	484.067	−	2.72892i	1.14708	−	0.00646663i
$423$	−115.589	+	115.589i	−0.273260	+	0.273260i
$424$	296.827	+	286.953i	0.700063	+	0.676775i
$425$	−570.365	+	533.264i	−1.34204	+	1.25474i
$426$	−427.130	−	422.341i	−1.00265	−	0.991410i
$427$	104.580	+	104.580i	0.244918	+	0.244918i
$428$	−74.9310	+	76.6400i	−0.175072	+	0.179066i
$429$	−994.276	−	518.409i	−2.31766	−	1.20841i
$430$	158.906	+	1.77429i	0.369548	+	0.00412626i
$431$	7.13997			0.0165661			0.00828303	−	0.999966i	$-0.497363\pi$
$431$	7.13997			0.0165661			0.00828303	+	0.999966i	$0.497363\pi$
$432$	−571.932	−	546.703i	−1.32392	−	1.26552i
$433$	−218.819	−	218.819i	−0.505355	−	0.505355i	0.407742	−	0.913097i	$-0.366316\pi$
$433$	−218.819	−	218.819i	−0.505355	−	0.505355i	−0.913097	+	0.407742i	$0.866316\pi$
$434$	72.5895	+	71.7756i	0.167257	+	0.165382i
$435$	−14.9796	+	891.418i	−0.0344358	+	2.04924i
$436$	−202.847	+	2.28717i	−0.465246	+	0.00524580i
$437$	37.4656	+	37.4656i	0.0857337	+	0.0857337i
$438$	2.82019	+	500.256i	0.00643878	+	1.14214i
$439$		−	735.002i		−	1.67426i	−0.547001	−	0.837132i	$-0.684231\pi$
$439$		−	735.002i		−	1.67426i	0.547001	−	0.837132i	$-0.315769\pi$
$440$	−132.084	−	419.707i	−0.300191	−	0.953879i
$441$	806.223			1.82817
$442$	1215.56	−	6.85271i	2.75014	−	0.0155039i
$443$	528.261	−	528.261i	1.19246	−	1.19246i	0.216089	−	0.976374i	$-0.430670\pi$
$443$	528.261	−	528.261i	1.19246	−	1.19246i	0.976374	−	0.216089i	$-0.0693301\pi$
$444$	−2.91259	−	258.315i	−0.00655988	−	0.581791i
$445$	48.0130	+	49.6542i	0.107894	+	0.111583i
$446$	17.9591	−	18.1628i	0.0402671	−	0.0407237i
$447$	348.821	−	348.821i	0.780360	−	0.780360i
$448$	−100.398	+	107.430i	−0.224102	+	0.239800i
$449$			232.808i			0.518503i	0.965810	+	0.259251i	$0.0834758\pi$
$449$			232.808i			0.518503i	−0.965810	+	0.259251i	$0.916524\pi$
$450$	921.639	+	25.7830i	2.04809	+	0.0572955i
$451$	437.113	+	227.908i	0.969209	+	0.505339i
$452$	−378.731	−	370.285i	−0.837900	−	0.819216i
$453$	744.345	−	744.345i	1.64315	−	1.64315i
$454$	−132.239	+	133.738i	−0.291275	+	0.294578i
$455$	−155.393	−	160.705i	−0.341524	−	0.353198i
$456$	178.613	+	172.671i	0.391694	+	0.378665i
$457$	−39.6097	−	39.6097i	−0.0866733	−	0.0866733i	0.662441	−	0.749114i	$-0.269521\pi$
$457$	−39.6097	−	39.6097i	−0.0866733	−	0.0866733i	−0.749114	+	0.662441i	$0.769521\pi$
$458$	−1.46461	−	259.798i	−0.00319783	−	0.567245i
$459$			1544.46i			3.36484i
$460$	0.988109	−	178.751i	0.00214806	−	0.388589i
$461$		−	791.088i		−	1.71603i	−0.513628	−	0.858013i	$-0.671699\pi$
$461$		−	791.088i		−	1.71603i	0.513628	−	0.858013i	$-0.328301\pi$
$462$	−235.463	−	121.085i	−0.509660	−	0.262089i
$463$	186.630	−	186.630i	0.403089	−	0.403089i	−0.476231	−	0.879320i	$-0.657997\pi$
$463$	186.630	−	186.630i	0.403089	−	0.403089i	0.879320	+	0.476231i	$0.157997\pi$
$464$	544.490	−	12.2802i	1.17347	−	0.0264659i
$465$	−581.791	−	9.77654i	−1.25116	−	0.0210248i
$466$	−241.662	+	244.402i	−0.518588	+	0.524469i
$467$	253.257	+	253.257i	0.542306	+	0.542306i	0.924204	−	0.381898i	$-0.124729\pi$
$467$	253.257	+	253.257i	0.542306	+	0.542306i	−0.381898	+	0.924204i	$0.624729\pi$
$468$	−1026.33	−	1003.45i	−2.19302	−	2.14411i
$469$	−164.072			−0.349833
$470$	−88.6428	−	0.989757i	−0.188602	−	0.00210587i
$471$			403.511i			0.856712i
$472$	−67.9382	+	1.14910i	−0.143937	+	0.00243453i
$473$	166.751	−	52.4572i	0.352538	−	0.110903i
$474$	−678.318	−	670.713i	−1.43105	−	1.41501i
$475$	−148.121	−	4.97954i	−0.311834	−	0.0104832i
$476$	287.014	−	3.23618i	0.602972	−	0.00679870i
$477$	−672.902	+	672.902i	−1.41070	+	1.41070i
$478$	0.683597	+	121.259i	0.00143012	+	0.253680i
$479$		−	406.686i		−	0.849031i	−0.905421	−	0.424516i	$-0.860444\pi$
$479$		−	406.686i		−	0.849031i	0.905421	−	0.424516i	$-0.139556\pi$
$480$	−9.54147	−	838.077i	−0.0198781	−	1.74599i
$481$		−	239.920i		−	0.498794i
$482$	1.40026	+	248.384i	0.00290511	+	0.515320i
$483$	−76.0606	−	76.0606i	−0.157475	−	0.157475i
$484$	−281.552	−	393.681i	−0.581719	−	0.813390i
$485$	−4.40345	+	262.044i	−0.00907928	+	0.540298i
$486$	59.7652	−	60.4429i	0.122974	−	0.124368i
$487$	−94.0358	−	94.0358i	−0.193092	−	0.193092i	0.603939	−	0.797031i	$-0.293597\pi$
$487$	−94.0358	−	94.0358i	−0.193092	−	0.193092i	−0.797031	+	0.603939i	$0.793597\pi$
$488$	8.70915	+	514.912i	0.0178466	+	1.05515i
$489$			1198.96i			2.45185i
$490$	305.686	+	312.590i	0.623849	+	0.637938i
$491$	741.561			1.51031			0.755153	−	0.655548i	$-0.227562\pi$
$491$	741.561			1.51031			0.755153	+	0.655548i	$0.227562\pi$
$492$	671.426	+	656.454i	1.36469	+	1.33426i
$493$	−751.760	−	751.760i	−1.52487	−	1.52487i
$494$	164.064	+	162.224i	0.332113	+	0.328389i
$495$	972.434	−	288.049i	1.96451	−	0.581918i
$496$	8.01475	+	355.366i	0.0161588	+	0.716463i
$497$	−93.1453	−	93.1453i	−0.187415	−	0.187415i
$498$	−1001.02	+	5.64323i	−2.01008	+	0.0113318i
$499$	−927.581			−1.85888			−0.929440	−	0.368973i	$-0.879709\pi$
$499$	−927.581			−1.85888			−0.929440	+	0.368973i	$0.879709\pi$
$500$	339.451	+	367.115i	0.678901	+	0.734230i
$501$			699.337i			1.39588i
$502$	4.29074	+	761.110i	0.00854730	+	1.51616i
$503$	664.811	+	664.811i	1.32169	+	1.32169i	0.912407	+	0.409285i	$0.134222\pi$
$503$	664.811	+	664.811i	1.32169	+	1.32169i	0.409285	+	0.912407i	$0.365778\pi$
$504$	−243.678	−	235.572i	−0.483487	−	0.467404i
$505$	−412.228	−	426.319i	−0.816293	−	0.844197i
$506$	−60.0621	−	187.231i	−0.118700	−	0.370022i
$507$	−776.692	−	776.692i	−1.53194	−	1.53194i
$508$	−589.065	+	602.500i	−1.15958	+	1.18602i
$509$			306.657i			0.602469i	0.953550	+	0.301234i	$0.0973987\pi$
$509$			306.657i			0.602469i	−0.953550	+	0.301234i	$0.902601\pi$
$510$	−1169.73	+	1143.90i	−2.29359	+	2.24294i
$511$			109.707i			0.214691i
$512$	−511.341	+	25.9661i	−0.998713	+	0.0507150i
$513$	−207.287	+	207.287i	−0.404068	+	0.404068i
$514$	114.601	−	115.901i	0.222959	−	0.225487i
$515$	−15.6898	+	933.680i	−0.0304656	+	1.81297i
$516$	332.959	−	3.75422i	0.645269	−	0.00727562i
$517$	−93.0189	+	29.2623i	−0.179921	+	0.0566003i
$518$	−0.319368	−	56.6509i	−0.000616541	−	0.109365i
$519$			507.647i			0.978126i
$520$	−0.0853315	−	778.396i	−0.000164099	−	1.49691i
$521$	314.557			0.603756			0.301878	−	0.953347i	$-0.402386\pi$
$521$	314.557			0.603756			0.301878	+	0.953347i	$0.402386\pi$
$522$	7.07700	+	1255.35i	0.0135575	+	2.40488i
$523$	634.181	+	634.181i	1.21258	+	1.21258i	0.970174	+	0.242410i	$0.0779378\pi$
$523$	634.181	+	634.181i	1.21258	+	1.21258i	0.242410	+	0.970174i	$0.422062\pi$
$524$	570.241	−	6.42966i	1.08825	−	0.0122703i
$525$	300.708	+	10.1092i	0.572777	+	0.0192556i
$526$	−161.405	−	159.596i	−0.306854	−	0.303414i
$527$	490.642	−	490.642i	0.931009	−	0.931009i
$528$	−296.422	−	872.992i	−0.561405	−	1.65339i
$529$			449.118i			0.848994i
$530$	−516.035	−	5.76188i	−0.973651	−	0.0108715i
$531$		−	156.620i		−	0.294953i
$532$	38.9554	+	38.0867i	0.0732245	+	0.0715916i
$533$	616.659	+	616.659i	1.15696	+	1.15696i
$534$	102.912	+	101.758i	0.192719	+	0.190559i
$535$	2.25111	−	133.961i	0.00420768	−	0.250394i
$536$	−410.745	−	397.082i	−0.766315	−	0.740824i
$537$	462.831	−	462.831i	0.861883	−	0.861883i
$538$	3.39216	+	601.716i	0.00630514	+	1.11843i
$539$	426.451	+	222.349i	0.791189	+	0.412520i
$540$	988.979	+	5.46693i	1.83144	+	0.0101239i
$541$		−	102.636i		−	0.189716i	−0.995491	−	0.0948580i	$-0.969760\pi$
$541$		−	102.636i		−	0.189716i	0.995491	−	0.0948580i	$-0.0302397\pi$
$542$	226.619	−	1.27756i	0.418115	−	0.00235712i
$543$	221.224	−	221.224i	0.407410	−	0.407410i
$544$	726.359	+	686.523i	1.33522	+	1.26199i
$545$	182.292	−	176.267i	0.334481	−	0.323426i
$546$	−333.073	−	329.339i	−0.610024	−	0.603185i
$547$	−30.2457	+	30.2457i	−0.0552938	+	0.0552938i	−0.734213	−	0.678919i	$-0.762449\pi$
$547$	−30.2457	+	30.2457i	−0.0552938	+	0.0552938i	0.678919	+	0.734213i	$0.262449\pi$
$548$	286.138	−	292.664i	0.522149	−	0.534058i
$549$	−1187.04			−2.16219
$550$	480.389	+	267.817i	0.873435	+	0.486940i
$551$		−	201.792i		−	0.366228i
$552$	−6.33415	−	374.494i	−0.0114749	−	0.678431i
$553$	−147.923	−	147.923i	−0.267491	−	0.267491i
$554$	186.158	+	184.071i	0.336026	+	0.332258i
$555$	224.467	+	232.139i	0.404444	+	0.418269i
$556$	−1.31688	−	116.793i	−0.00236848	−	0.210059i
$557$	200.019	+	200.019i	0.359100	+	0.359100i	0.863481	−	0.504381i	$-0.168279\pi$
$557$	200.019	+	200.019i	0.359100	+	0.359100i	−0.504381	+	0.863481i	$0.668279\pi$
$558$	−819.313	+	4.61886i	−1.46830	+	0.00827753i
$559$	309.248			0.553216
$560$	−1.05631	−	183.798i	−0.00188626	−	0.328211i
$561$	−832.042	+	1595.81i	−1.48314	+	2.84457i
$562$	4.52536	+	802.727i	0.00805224	+	1.42834i
$563$	−392.703	−	392.703i	−0.697519	−	0.697519i	0.266356	−	0.963875i	$-0.414180\pi$
$563$	−392.703	−	392.703i	−0.697519	−	0.697519i	−0.963875	+	0.266356i	$0.914180\pi$
$564$	−185.735	+	2.09423i	−0.329318	+	0.00371317i
$565$	661.992	+	11.1243i	1.17167	+	0.0196889i
$566$	455.539	+	450.432i	0.804840	+	0.795816i
$567$	151.206	−	151.206i	0.266677	−	0.266677i
$568$	−7.75692	−	458.613i	−0.0136565	−	0.807416i
$569$	152.775			0.268497			0.134248	−	0.990948i	$-0.457138\pi$
$569$	152.775			0.268497			0.134248	+	0.990948i	$0.457138\pi$
$570$	−310.519	−	3.46715i	−0.544770	−	0.00608273i
$571$	−1125.27			−1.97070			−0.985351	−	0.170541i	$-0.945449\pi$
$571$	−1125.27			−1.97070			−0.985351	+	0.170541i	$0.945449\pi$
$572$	−266.137	−	813.824i	−0.465274	−	1.42277i
$573$	217.528	+	217.528i	0.379630	+	0.379630i
$574$	146.429	+	144.787i	0.255103	+	0.252243i
$575$	152.600	+	163.217i	0.265391	+	0.283855i
$576$	−39.9107	−	1179.48i	−0.0692895	−	2.04772i
$577$	−105.873	+	105.873i	−0.183489	+	0.183489i	−0.792874	−	0.609385i	$-0.791416\pi$
$577$	−105.873	+	105.873i	−0.183489	+	0.183489i	0.609385	+	0.792874i	$0.291416\pi$
$578$	−7.74013	−	1372.98i	−0.0133912	−	2.37539i
$579$		−	758.921i		−	1.31074i
$580$	−484.042	+	478.720i	−0.834555	+	0.825379i
$581$	−219.526			−0.377841
$582$	3.09575	+	549.137i	0.00531916	+	0.943535i
$583$	−541.511	+	170.351i	−0.928835	+	0.292197i
$584$	−265.511	+	274.647i	−0.454642	+	0.470286i
$585$	1793.95	+	30.1459i	3.06658	+	0.0515314i
$586$	202.663	−	204.961i	0.345841	−	0.349762i
$587$	−115.724	−	115.724i	−0.197145	−	0.197145i	0.601630	−	0.798775i	$-0.294518\pi$
$587$	−115.724	−	115.724i	−0.197145	−	0.197145i	−0.798775	+	0.601630i	$0.794518\pi$
$588$	655.048	+	640.441i	1.11403	+	1.08919i
$589$	131.701			0.223601
$590$	60.7249	−	59.3838i	0.102923	−	0.100650i
$591$	900.383			1.52349
$592$	136.306	−	142.596i	0.230246	−	0.240871i
$593$	−305.757	+	305.757i	−0.515611	+	0.515611i	−0.916240	−	0.400629i	$-0.868792\pi$
$593$	−305.757	+	305.757i	−0.515611	+	0.515611i	0.400629	+	0.916240i	$0.368792\pi$
$594$	1035.90	−	332.307i	1.74394	−	0.559439i
$595$	−257.930	+	249.405i	−0.433496	+	0.419168i
$596$	376.667	−	4.24704i	0.631992	−	0.00712591i
$597$	335.392	−	335.392i	0.561796	−	0.561796i
$598$	−1.96098	−	347.847i	−0.00327923	−	0.581684i
$599$	159.646			0.266521			0.133261	−	0.991081i	$-0.457455\pi$
$599$	159.646			0.266521			0.133261	+	0.991081i	$0.457455\pi$
$600$	728.341	+	753.073i	1.21390	+	1.25512i
$601$		−	721.536i		−	1.20056i	−0.799790	−	0.600279i	$-0.795056\pi$
$601$		−	721.536i		−	1.20056i	0.799790	−	0.600279i	$-0.204944\pi$
$602$	73.0209	−	0.411654i	0.121297	−	0.000683811i
$603$	931.153	−	931.153i	1.54420	−	1.54420i
$604$	803.766	−	9.06272i	1.33074	−	0.0150045i
$605$	593.809	+	115.825i	0.981503	+	0.191446i
$606$	−883.579	−	873.673i	−1.45805	−	1.44170i
$607$	−633.148	+	633.148i	−1.04308	+	1.04308i	−0.0440488	+	0.999029i	$0.514026\pi$
$607$	−633.148	+	633.148i	−1.04308	+	1.04308i	−0.999029	+	0.0440488i	$0.985974\pi$
$608$	5.34646	+	189.627i	0.00879351	+	0.311887i
$609$			409.666i			0.672687i
$610$	−450.076	−	460.241i	−0.737830	−	0.754493i
$611$	−172.509			−0.282338
$612$	−1610.52	+	1647.26i	−2.63157	+	2.69159i
$613$	380.705	−	380.705i	0.621052	−	0.621052i	−0.324749	−	0.945800i	$-0.605280\pi$
$613$	380.705	−	380.705i	0.621052	−	0.621052i	0.945800	+	0.324749i	$0.105280\pi$
$614$	442.219	−	447.234i	0.720227	−	0.728394i
$615$	−1173.60	−	19.7214i	−1.90829	−	0.0320674i
$616$	−63.9247	−	191.809i	−0.103774	−	0.311379i
$617$	138.695	−	138.695i	0.224789	−	0.224789i	−0.585723	−	0.810512i	$-0.699189\pi$
$617$	138.695	−	138.695i	0.224789	−	0.224789i	0.810512	+	0.585723i	$0.199189\pi$
$618$	11.0304	+	1956.61i	0.0178485	+	3.16604i
$619$	434.682			0.702233			0.351116	−	0.936332i	$-0.385802\pi$
$619$	434.682			0.702233			0.351116	+	0.936332i	$0.385802\pi$
$620$	−312.440	−	315.914i	−0.503936	−	0.509538i
$621$	441.966			0.711700
$622$	−4.86558	−	863.077i	−0.00782248	−	1.38758i
$623$	22.4423	+	22.4423i	0.0360230	+	0.0360230i
$624$	−36.7753	−	1630.58i	−0.0589347	−	2.61311i
$625$	−623.589	−	41.9750i	−0.997742	−	0.0671600i
$626$	389.878	+	385.507i	0.622809	+	0.615826i
$627$	−325.849	+	102.507i	−0.519695	+	0.163488i
$628$	−215.405	+	220.318i	−0.343002	+	0.350825i
$629$	−385.070			−0.612193
$630$	423.635	+	4.73017i	0.672436	+	0.00750821i
$631$		−	20.0839i		−	0.0318287i	−0.999873	−	0.0159144i	$-0.994934\pi$
$631$		−	20.0839i		−	0.0318287i	0.999873	−	0.0159144i	$-0.00506591\pi$
$632$	−12.3186	−	728.316i	−0.0194915	−	1.15240i
$633$	−896.518	+	896.518i	−1.41630	+	1.41630i
$634$	460.413	−	465.634i	0.726204	−	0.734438i
$635$	17.6969	−	1053.12i	0.0278692	−	1.65846i
$636$	−1081.26	+	12.1916i	−1.70010	+	0.0191691i
$637$	601.617	+	601.617i	0.944453	+	0.944453i
$638$	−342.470	+	665.967i	−0.536786	+	1.04384i
$639$	1057.25			1.65454
$640$	442.179	−	462.686i	0.690904	−	0.722946i
$641$	177.219			0.276473			0.138237	−	0.990399i	$-0.455857\pi$
$641$	177.219			0.276473			0.138237	+	0.990399i	$0.455857\pi$
$642$	−1.58259	−	280.727i	−0.00246510	−	0.437269i
$643$	605.787	−	605.787i	0.942127	−	0.942127i	−0.0562879	−	0.998415i	$-0.517926\pi$
$643$	605.787	−	605.787i	0.942127	−	0.942127i	0.998415	+	0.0562879i	$0.0179265\pi$
$644$	−0.926071	−	82.1326i	−0.00143800	−	0.127535i
$645$	−299.219	+	289.329i	−0.463906	+	0.448572i
$646$	260.369	−	263.321i	0.403048	−	0.407618i
$647$	−315.852	−	315.852i	−0.488180	−	0.488180i	0.419552	−	0.907731i	$-0.362187\pi$
$647$	−315.852	−	315.852i	−0.488180	−	0.488180i	−0.907731	+	0.419552i	$0.862187\pi$
$648$	744.480	−	12.5920i	1.14889	−	0.0194322i
$649$	43.1943	−	82.8440i	0.0665551	−	0.127649i
$650$	668.502	+	706.982i	1.02846	+	1.08766i
$651$	−267.372			−0.410710
$652$	−640.035	+	654.633i	−0.981649	+	1.00404i
$653$	332.094	+	332.094i	0.508567	+	0.508567i	0.914086	−	0.405520i	$-0.132909\pi$
$653$	332.094	+	332.094i	0.508567	+	0.508567i	−0.405520	+	0.914086i	$0.632909\pi$
$654$	373.579	−	377.814i	0.571221	−	0.577698i
$655$	−512.457	+	495.519i	−0.782377	+	0.756517i
$656$	16.1675	+	716.851i	0.0246456	+	1.09276i
$657$	−622.620	−	622.620i	−0.947672	−	0.947672i
$658$	−40.7335	+	0.229634i	−0.0619050	+	0.000348988i
$659$			337.270i			0.511790i	0.966705	+	0.255895i	$0.0823702\pi$
$659$			337.270i			0.511790i	−0.966705	+	0.255895i	$0.917630\pi$
$660$	1018.91	+	538.438i	1.54381	+	0.815814i
$661$	−800.999			−1.21180			−0.605899	−	0.795541i	$-0.707187\pi$
$661$	−800.999			−1.21180			−0.605899	+	0.795541i	$0.707187\pi$
$662$	−5.82463	−	1033.20i	−0.00879854	−	1.56072i
$663$	−2251.29	+	2251.29i	−3.39561	+	3.39561i
$664$	−549.572	−	531.290i	−0.827668	−	0.800136i
$665$	−68.0910	−	1.14422i	−0.102392	−	0.00172063i
$666$	323.323	+	319.698i	0.485469	+	0.480026i
$667$	−215.125	+	215.125i	−0.322526	+	0.322526i
$668$	−373.325	+	381.840i	−0.558870	+	0.571617i
$669$			66.8998i			0.0999997i
$670$	714.082	+	7.97322i	1.06579	+	0.0119003i
$671$	−627.884	−	327.374i	−0.935744	−	0.487890i
$672$	−10.8541	−	384.970i	−0.0161519	−	0.572873i
$673$	−197.870	+	197.870i	−0.294012	+	0.294012i	−0.838663	−	0.544651i	$-0.816662\pi$
$673$	−197.870	+	197.870i	−0.294012	+	0.294012i	0.544651	+	0.838663i	$0.316662\pi$
$674$	−183.801	−	181.740i	−0.272702	−	0.269644i
$675$	−903.032	+	844.291i	−1.33783	+	1.25080i
$676$	−9.45656	−	838.696i	−0.0139890	−	1.24067i
$677$	322.660	+	322.660i	0.476602	+	0.476602i	0.904043	−	0.427441i	$-0.140585\pi$
$677$	322.660	+	322.660i	0.476602	+	0.476602i	−0.427441	+	0.904043i	$0.640585\pi$
$678$	1387.26	−	7.82067i	2.04611	−	0.0115349i
$679$			120.427i			0.177359i
$680$	−1249.32	+	0.136956i	−1.83723	+	0.000201406i
$681$		−	492.605i		−	0.723355i
$682$	−434.649	−	223.516i	−0.637315	−	0.327735i
$683$	−727.235	+	727.235i	−1.06477	+	1.06477i	−0.0670137	+	0.997752i	$0.521347\pi$
$683$	−727.235	+	727.235i	−1.06477	+	1.06477i	−0.997752	+	0.0670137i	$0.978653\pi$
$684$	−437.236	+	4.92998i	−0.639234	+	0.00720757i
$685$	−8.59626	+	511.554i	−0.0125493	+	0.746794i
$686$	302.962	+	299.565i	0.441635	+	0.436684i
$687$	481.161	+	481.161i	0.700379	+	0.700379i
$688$	183.801	+	175.693i	0.267152	+	0.255367i
$689$	−1004.26			−1.45756
$690$	327.340	+	334.732i	0.474405	+	0.485119i
$691$		−	778.221i		−	1.12622i	−0.826381	−	0.563112i	$-0.809604\pi$
$691$		−	778.221i		−	1.12622i	0.826381	−	0.563112i	$-0.190396\pi$
$692$	−270.996	+	277.177i	−0.391613	+	0.400544i
$693$	444.549	−	139.848i	0.641485	−	0.201801i
$694$	−474.335	+	479.714i	−0.683480	+	0.691230i
$695$	101.489	+	104.958i	0.146027	+	0.151018i
$696$	−991.464	+	1025.58i	−1.42452	+	1.47353i
$697$	989.733	−	989.733i	1.41999	−	1.41999i
$698$	−187.666	+	1.05796i	−0.268862	+	0.00151570i
$699$		−	900.218i		−	1.28787i
$700$	158.791	+	166.046i	0.226844	+	0.237208i
$701$			290.062i			0.413783i	0.978364	+	0.206892i	$0.0663348\pi$
$701$			290.062i			0.413783i	−0.978364	+	0.206892i	$0.933665\pi$
$702$	1924.54	−	10.8496i	2.74151	−	0.0154552i
$703$	−51.6814	−	51.6814i	−0.0735154	−	0.0735154i
$704$	304.180	−	634.894i	0.432073	−	0.901838i
$705$	166.914	−	161.397i	0.236758	−	0.228932i
$706$	−771.177	−	762.531i	−1.09232	−	1.08007i
$707$	−192.685	−	192.685i	−0.272538	−	0.272538i
$708$	124.414	−	127.252i	0.175727	−	0.179735i
$709$		−	68.4706i		−	0.0965735i	−0.998834	−	0.0482867i	$-0.984624\pi$
$709$		−	68.4706i		−	0.0965735i	0.998834	−	0.0482867i	$-0.0153761\pi$
$710$	400.866	+	409.919i	0.564600	+	0.577351i
$711$	1679.01			2.36147
$712$	1.86894	+	110.498i	0.00262492	+	0.155193i
$713$	−140.403	−	140.403i	−0.196919	−	0.196919i
$714$	−528.587	+	534.580i	−0.740317	+	0.748712i
$715$	940.593	+	510.699i	1.31551	+	0.714265i
$716$	499.779	−	5.63517i	0.698015	−	0.00787035i
$717$	−224.579	−	224.579i	−0.313220	−	0.313220i
$718$	−0.646646	−	114.705i	−0.000900621	−	0.159756i
$719$	113.225			0.157476			0.0787380	−	0.996895i	$-0.474911\pi$
$719$	113.225			0.157476			0.0787380	+	0.996895i	$0.474911\pi$
$720$	1049.10	+	1037.11i	1.45708	+	1.44043i
$721$			429.089i			0.595131i
$722$	−651.702	+	3.67396i	−0.902635	+	0.00508859i
$723$	−460.021	−	460.021i	−0.636267	−	0.636267i
$724$	238.884	−	2.69349i	0.329950	−	0.00372029i
$725$	28.5921	−	850.502i	0.0394374	−	1.17311i
$726$	1249.36	+	214.711i	1.72088	+	0.295746i
$727$	245.971	+	245.971i	0.338337	+	0.338337i	0.855741	−	0.517404i	$-0.173102\pi$
$727$	245.971	+	245.971i	0.338337	+	0.338337i	−0.517404	+	0.855741i	$0.673102\pi$
$728$	−6.04880	−	357.624i	−0.00830879	−	0.491241i
$729$		−	615.028i		−	0.843660i
$730$	5.33133	−	477.475i	0.00730320	−	0.654075i
$731$		−	496.341i		−	0.678989i
$732$	−964.459	−	942.952i	−1.31757	−	1.28819i
$733$	246.021	−	246.021i	0.335635	−	0.335635i	−0.519087	−	0.854722i	$-0.673728\pi$
$733$	246.021	−	246.021i	0.335635	−	0.335635i	0.854722	+	0.519087i	$0.173728\pi$
$734$	−786.695	−	777.875i	−1.07179	−	1.05977i
$735$	−1144.97	−	19.2404i	−1.55779	−	0.0261774i
$736$	196.457	−	207.856i	0.266925	−	0.282413i
$737$	749.336	−	235.730i	1.01674	−	0.319850i
$738$	−1652.74	+	9.31727i	−2.23948	+	0.0126250i
$739$			886.339i			1.19938i	0.800234	+	0.599688i	$0.204709\pi$
$739$			886.339i			1.19938i	−0.800234	+	0.599688i	$0.795291\pi$
$740$	−1.36303	+	246.575i	−0.00184193	+	0.333210i
$741$	−604.304			−0.815525
$742$	−237.130	+	1.33682i	−0.319583	+	0.00180164i
$743$	149.673	+	149.673i	0.201444	+	0.201444i	0.800618	−	0.599175i	$-0.204505\pi$
$743$	149.673	+	149.673i	0.201444	+	0.201444i	−0.599175	+	0.800618i	$0.704505\pi$
$744$	−669.353	−	647.087i	−0.899668	−	0.869740i
$745$	−338.498	+	327.310i	−0.454360	+	0.439342i
$746$	471.594	−	476.941i	0.632164	−	0.639332i
$747$	1245.87	−	1245.87i	1.66783	−	1.66783i
$748$	−1306.18	+	427.148i	−1.74623	+	0.571053i
$749$		−	61.5640i		−	0.0821949i
$750$	−1308.27	−	58.6110i	−1.74436	−	0.0781479i
$751$		−	836.006i		−	1.11319i	−0.830784	−	0.556595i	$-0.812108\pi$
$751$		−	836.006i		−	1.11319i	0.830784	−	0.556595i	$-0.187892\pi$
$752$	−102.530	−	98.0072i	−0.136343	−	0.130329i
$753$	−1409.62	−	1409.62i	−1.87200	−	1.87200i
$754$	−931.480	+	942.042i	−1.23539	+	1.24939i
$755$	−722.318	+	698.443i	−0.956712	+	0.925090i
$756$	454.416	−	5.12369i	0.601080	−	0.00677737i
$757$	−556.320	+	556.320i	−0.734902	+	0.734902i	−0.971586	−	0.236685i	$-0.923939\pi$
$757$	−556.320	+	556.320i	−0.734902	+	0.734902i	0.236685	+	0.971586i	$0.423939\pi$
$758$	−226.719	+	1.27812i	−0.299101	+	0.00168618i
$759$	456.659	+	238.099i	0.601658	+	0.313700i
$760$	−167.693	−	167.656i	−0.220649	−	0.220601i
$761$		−	977.034i		−	1.28388i	−0.766754	−	0.641941i	$-0.778129\pi$
$761$		−	977.034i		−	1.28388i	0.766754	−	0.641941i	$-0.221871\pi$
$762$	−12.4414	−	2206.92i	−0.0163274	−	2.89621i
$763$	82.3910	−	82.3910i	0.107983	−	0.107983i
$764$	2.64850	+	234.893i	0.00346662	+	0.307452i
$765$	48.3839	−	2879.27i	0.0632470	−	3.76376i
$766$	−637.454	+	644.682i	−0.832185	+	0.841621i
$767$	116.872	−	116.872i	0.152376	−	0.152376i
$768$	904.523	−	990.023i	1.17776	−	1.28909i
$769$	1509.11			1.96243			0.981216	−	0.192911i	$-0.0617930\pi$
$769$	1509.11			1.96243			0.981216	+	0.192911i	$0.0617930\pi$
$770$	222.777	+	119.336i	0.289320	+	0.154982i
$771$			426.902i			0.553699i
$772$	405.133	−	414.373i	0.524783	−	0.536752i
$773$	−24.1418	−	24.1418i	−0.0312312	−	0.0312312i	0.691319	−	0.722550i	$-0.257030\pi$
$773$	−24.1418	−	24.1418i	−0.0312312	−	0.0312312i	−0.722550	+	0.691319i	$0.757030\pi$
$774$	−412.078	+	416.751i	−0.532401	+	0.538438i
$775$	555.087	+	18.6609i	0.716241	+	0.0240785i
$776$	−291.454	+	301.483i	−0.375585	+	0.388509i
$777$	104.921	+	104.921i	0.135033	+	0.135033i
$778$	3.92033	+	695.405i	0.00503899	+	0.893837i
$779$	265.670			0.341040
$780$	1433.62	+	1449.56i	1.83797	+	1.85840i
$781$	559.233	+	291.580i	0.716047	+	0.373342i
$782$	−558.292	+	3.14736i	−0.713929	+	0.00402476i
$783$	−1190.22	−	1190.22i	−1.52008	−	1.52008i
$784$	15.7731	+	699.365i	0.0201188	+	0.892047i
$785$	6.47129	−	385.099i	0.00824368	−	0.490572i
$786$	−1050.20	+	1062.11i	−1.33613	+	1.35128i
$787$	857.123	−	857.123i	1.08910	−	1.08910i	0.0934806	−	0.995621i	$-0.470201\pi$
$787$	857.123	−	857.123i	1.08910	−	1.08910i	0.995621	−	0.0934806i	$-0.0297993\pi$
$788$	491.612	+	480.649i	0.623873	+	0.609961i
$789$	594.511			0.753500
$790$	636.610	+	650.986i	0.805835	+	0.824034i
$791$	304.230			0.384614
$792$	1451.36	+	725.782i	1.83253	+	0.916392i
$793$	−885.789	−	885.789i	−1.11701	−	1.11701i
$794$	1076.10	−	1088.30i	1.35529	−	1.37066i
$795$	971.693	−	939.576i	1.22226	−	1.18186i
$796$	362.167	−	4.08355i	0.454983	−	0.00513008i
$797$	674.477	−	674.477i	0.846269	−	0.846269i	−0.143396	−	0.989665i	$-0.545802\pi$
$797$	674.477	−	674.477i	0.846269	−	0.846269i	0.989665	+	0.143396i	$0.0458023\pi$
$798$	−142.691	+	0.804417i	−0.178811	+	0.00100804i
$799$			276.875i			0.346527i
$800$	−4.33452	+	799.988i	−0.00541815	+	0.999985i
$801$	−254.733			−0.318019
$802$	−29.2401	+	0.164841i	−0.0364590	+	0.000205537i
$803$	−157.622	−	501.047i	−0.196291	−	0.623969i
$804$	1496.23	−	16.8705i	1.86099	−	0.0209832i
$805$	71.3702	+	73.8098i	0.0886586	+	0.0916892i
$806$	−614.831	−	607.938i	−0.762818	−	0.754266i
$807$	−1114.41	−	1114.41i	−1.38093	−	1.38093i
$808$	−16.0463	−	948.706i	−0.0198593	−	1.17414i
$809$	68.6077			0.0848055			0.0424028	−	0.999101i	$-0.486499\pi$
$809$	68.6077			0.0848055			0.0424028	+	0.999101i	$0.486499\pi$
$810$	−665.435	+	650.739i	−0.821524	+	0.803381i
$811$	464.005			0.572139			0.286070	−	0.958209i	$-0.407651\pi$
$811$	464.005			0.572139			0.286070	+	0.958209i	$0.407651\pi$
$812$	−218.691	+	223.679i	−0.269324	+	0.275467i
$813$	−419.710	+	419.710i	−0.516249	+	0.516249i
$814$	82.8517	+	258.273i	0.101783	+	0.317289i
$815$	19.2282	−	1144.25i	0.0235929	−	1.40398i
$816$	−2617.07	+	59.0241i	−3.20719	+	0.0723334i
$817$	66.6154	−	66.6154i	0.0815366	−	0.0815366i
$818$	1252.17	−	7.05909i	1.53077	−	0.00862969i
$819$	824.440			1.00664
$820$	−630.261	−	637.268i	−0.768611	−	0.777156i
$821$		−	453.370i		−	0.552217i	−0.961127	−	0.276108i	$-0.910955\pi$
$821$		−	453.370i		−	0.552217i	0.961127	−	0.276108i	$-0.0890449\pi$
$822$	6.04342	+	1072.01i	0.00735209	+	1.30414i
$823$	−185.347	+	185.347i	−0.225209	+	0.225209i	−0.810688	−	0.585479i	$-0.800907\pi$
$823$	−185.347	+	185.347i	−0.225209	+	0.225209i	0.585479	+	0.810688i	$0.300907\pi$
$824$	−1038.47	+	1074.20i	−1.26028	+	1.30365i
$825$	−1387.89	+	385.872i	−1.68230	+	0.467723i
$826$	27.4408	−	27.7520i	0.0332213	−	0.0335980i
$827$	−757.186	+	757.186i	−0.915582	+	0.915582i	−0.996704	−	0.0811220i	$-0.974150\pi$
$827$	−757.186	+	757.186i	−0.915582	+	0.915582i	0.0811220	+	0.996704i	$0.474150\pi$
$828$	471.381	+	460.870i	0.569301	+	0.556606i
$829$			941.265i			1.13542i	0.823228	+	0.567711i	$0.192171\pi$
$829$			941.265i			1.13542i	−0.823228	+	0.567711i	$0.807829\pi$
$830$	955.433	+	10.6681i	1.15112	+	0.0128531i
$831$	−685.685			−0.825133
$832$	850.368	−	909.932i	1.02208	−	1.09367i
$833$	965.590	−	965.590i	1.15917	−	1.15917i
$834$	217.533	+	215.094i	0.260831	+	0.257907i
$835$	11.2156	−	667.426i	0.0134318	−	0.799313i
$836$	−232.635	−	117.978i	−0.278272	−	0.141122i
$837$	776.810	−	776.810i	0.928088	−	0.928088i
$838$	637.896	−	3.59613i	0.761213	−	0.00429132i
$839$	−1309.36			−1.56062			−0.780308	−	0.625396i	$-0.784938\pi$
$839$	−1309.36			−1.56062			−0.780308	+	0.625396i	$0.784938\pi$
$840$	340.442	+	340.367i	0.405288	+	0.405199i
$841$	317.673			0.377733
$842$	213.457	−	1.20336i	0.253511	−	0.00142917i
$843$	−1486.70	−	1486.70i	−1.76358	−	1.76358i
$844$	−968.087	+	10.9155i	−1.14702	+	0.0129331i
$845$	728.796	+	753.708i	0.862480	+	0.891962i
$846$	229.871	−	232.477i	0.271715	−	0.274796i
$847$	273.713	+	48.6297i	0.323155	+	0.0574140i
$848$	−596.879	−	570.550i	−0.703867	−	0.672818i
$849$	−1677.91			−1.97633
$850$	1134.70	−	1072.94i	1.33494	−	1.26228i
$851$			110.192i			0.129486i
$852$	859.007	+	839.852i	1.00822	+	0.985742i
$853$	−84.1524	+	84.1524i	−0.0986546	+	0.0986546i	−0.754711	−	0.656057i	$-0.772223\pi$
$853$	−84.1524	+	84.1524i	−0.0986546	+	0.0986546i	0.656057	+	0.754711i	$0.272223\pi$
$854$	−210.335	−	207.977i	−0.246294	−	0.243533i
$855$	392.930	−	379.942i	0.459567	−	0.444377i
$856$	148.996	−	154.122i	0.174060	−	0.180050i
$857$	110.641	+	110.641i	0.129102	+	0.129102i	0.768705	−	0.639603i	$-0.220901\pi$
$857$	110.641	+	110.641i	0.129102	+	0.129102i	−0.639603	+	0.768705i	$0.720901\pi$
$858$	1994.37	+	1025.59i	2.32444	+	1.19533i
$859$	−960.357			−1.11799			−0.558997	−	0.829169i	$-0.688814\pi$
$859$	−960.357			−1.11799			−0.558997	+	0.829169i	$0.688814\pi$
$860$	−317.826	−	1.75690i	−0.369565	−	0.00204290i
$861$	−539.348			−0.626421
$862$	−14.2797	+	0.0805016i	−0.0165658	+	9.33893e-5i
$863$	−350.117	+	350.117i	−0.405697	+	0.405697i	−0.880235	−	0.474538i	$-0.842615\pi$
$863$	−350.117	+	350.117i	−0.405697	+	0.405697i	0.474538	+	0.880235i	$0.342615\pi$
$864$	1150.01	+	1086.94i	1.33103	+	1.25803i
$865$	8.14136	−	484.483i	0.00941198	−	0.560096i
$866$	440.097	+	435.163i	0.508196	+	0.502498i
$867$	2542.83	+	2542.83i	2.93290	+	2.93290i
$868$	−145.986	−	142.731i	−0.168187	−	0.164436i
$869$	888.109	+	463.054i	1.02199	+	0.532858i
$870$	19.9081	−	1782.98i	0.0228829	−	2.04940i
$871$	1389.68			1.59550
$872$	405.663	−	6.86133i	0.465209	−	0.00786849i
$873$	−683.458	−	683.458i	−0.782884	−	0.782884i
$874$	−75.3525	−	74.5076i	−0.0862157	−	0.0852490i
$875$	−286.824	−	14.4705i	−0.327799	−	0.0165377i
$876$	−11.2806	−	1000.47i	−0.0128774	−	1.14208i
$877$	682.311	+	682.311i	0.778006	+	0.778006i	0.979492	−	0.201485i	$-0.0645768\pi$
$877$	682.311	+	682.311i	0.778006	+	0.778006i	−0.201485	+	0.979492i	$0.564577\pi$
$878$	8.28699	+	1469.98i	0.00943848	+	1.67424i
$879$			754.941i			0.858863i
$880$	268.896	+	837.911i	0.305563	+	0.952172i
$881$	−864.371			−0.981124			−0.490562	−	0.871406i	$-0.663209\pi$
$881$	−864.371			−0.981124			−0.490562	+	0.871406i	$0.663209\pi$
$882$	−1612.42	+	9.08999i	−1.82814	+	0.0103061i
$883$	726.979	−	726.979i	0.823306	−	0.823306i	−0.163274	−	0.986581i	$-0.552206\pi$
$883$	726.979	−	726.979i	0.823306	−	0.823306i	0.986581	+	0.163274i	$0.0522056\pi$
$884$	−2431.01	+	27.4104i	−2.75001	+	0.0310072i
$885$	−3.73771	+	222.427i	−0.00422340	+	0.251330i
$886$	−1050.55	+	1062.46i	−1.18572	+	1.19917i
$887$	−987.287	+	987.287i	−1.11306	+	1.11306i	−0.120329	+	0.992734i	$0.538395\pi$
$887$	−987.287	+	987.287i	−1.11306	+	1.11306i	−0.992734	+	0.120329i	$0.961605\pi$
$888$	8.73753	+	516.590i	0.00983957	+	0.581745i
$889$		−	483.981i		−	0.544411i
$890$	−96.5843	−	98.7656i	−0.108522	−	0.110973i
$891$	−473.331	+	907.820i	−0.531236	+	1.01888i
$892$	−35.7129	+	36.5275i	−0.0400369	+	0.0409501i
$893$	−37.1602	+	37.1602i	−0.0416128	+	0.0416128i
$894$	−693.697	+	701.563i	−0.775948	+	0.784746i
$895$	−449.135	+	434.289i	−0.501827	+	0.485240i
$896$	199.581	−	215.989i	0.222747	−	0.241059i
$897$	644.232	+	644.232i	0.718207	+	0.718207i
$898$	−2.62486	−	465.608i	−0.00292300	−	0.518494i
$899$			756.217i			0.841176i
$900$	−1843.54	−	41.1739i	−2.04838	−	0.0457488i
$901$			1611.83i			1.78894i
$902$	−876.783	−	450.880i	−0.972043	−	0.499867i
$903$	−135.239	+	135.239i	−0.149766	+	0.149766i
$904$	761.625	+	736.289i	0.842505	+	0.814479i
$905$	−214.677	+	207.581i	−0.237212	+	0.229372i
$906$	−1480.27	+	1497.06i	−1.63386	+	1.65238i
$907$	−337.668	−	337.668i	−0.372291	−	0.372291i	0.496020	−	0.868311i	$-0.334794\pi$
$907$	−337.668	−	337.668i	−0.372291	−	0.372291i	−0.868311	+	0.496020i	$0.834794\pi$
$908$	262.966	−	268.964i	0.289610	−	0.296215i
$909$	2187.08			2.40603
$910$	312.593	+	319.653i	0.343509	+	0.351267i
$911$			77.6555i			0.0852421i	0.999091	+	0.0426210i	$0.0135708\pi$
$911$			77.6555i			0.0852421i	−0.999091	+	0.0426210i	$0.986429\pi$
$912$	−359.166	−	343.323i	−0.393823	−	0.376450i
$913$	1002.60	−	315.403i	1.09814	−	0.345458i
$914$	79.6647	+	78.7715i	0.0871605	+	0.0861833i
$915$	1685.80	+	28.3285i	1.84240	+	0.0309601i
$916$	5.85834	+	519.572i	0.00639556	+	0.567218i
$917$	−231.616	+	231.616i	−0.252581	+	0.252581i
$918$	−17.4135	−	3088.87i	−0.0189689	−	3.36479i
$919$			206.054i			0.224216i	0.993696	+	0.112108i	$0.0357603\pi$
$919$			206.054i			0.224216i	−0.993696	+	0.112108i	$0.964240\pi$
$920$	0.0391917	+	357.507i	4.25996e−5	+	0.388595i
$921$			1647.32i			1.78862i
$922$	8.91935	+	1582.15i	0.00967391	+	1.71600i
$923$	788.939	+	788.939i	0.854755	+	0.854755i
$924$	472.283	+	239.512i	0.511129	+	0.259212i
$925$	−210.501	−	225.147i	−0.227569	−	0.243402i
$926$	−371.150	+	375.359i	−0.400810	+	0.405355i
$927$	−2435.20	−	2435.20i	−2.62697	−	2.62697i
$928$	−1088.82	+	30.6989i	−1.17330	+	0.0330808i
$929$		−	148.983i		−	0.160369i	−0.996780	−	0.0801845i	$-0.974449\pi$
$929$		−	148.983i		−	0.160369i	0.996780	−	0.0801845i	$-0.0255509\pi$
$930$	1163.67	+	12.9932i	1.25126	+	0.0139712i
$931$	259.190			0.278399
$932$	480.561	−	491.522i	0.515624	−	0.527384i
$933$	1598.47	+	1598.47i	1.71325	+	1.71325i
$934$	−509.362	−	503.651i	−0.545355	−	0.539241i
$935$	819.668	−	1509.65i	0.876651	−	1.61459i
$936$	2063.94	+	1995.29i	2.20507	+	2.13172i
$937$	268.109	+	268.109i	0.286135	+	0.286135i	0.835550	−	0.549415i	$-0.185149\pi$
$937$	268.109	+	268.109i	0.286135	+	0.286135i	−0.549415	+	0.835550i	$0.685149\pi$
$938$	328.138	−	1.84987i	0.349827	−	0.00197214i
$939$	−1436.06			−1.52935
$940$	177.294	+	0.980055i	0.188610	+	0.00104261i
$941$		−	918.269i		−	0.975843i	−0.872887	−	0.487922i	$-0.837755\pi$
$941$		−	918.269i		−	0.975843i	0.872887	−	0.487922i	$-0.162245\pi$
$942$	−4.54950	−	807.010i	−0.00482962	−	0.856698i
$943$	−283.224	−	283.224i	−0.300343	−	0.300343i
$944$	135.861	−	3.06415i	0.143921	−	0.00324592i
$945$	−408.369	+	394.871i	−0.432136	+	0.417853i
$946$	−332.904	+	106.793i	−0.351907	+	0.112889i
$947$	1054.63	+	1054.63i	1.11366	+	1.11366i	0.992652	+	0.121004i	$0.0386113\pi$
$947$	1054.63	+	1054.63i	1.11366	+	1.11366i	0.121004	+	0.992652i	$0.461389\pi$
$948$	1364.18	+	1333.76i	1.43900	+	1.40692i
$949$		−	929.219i		−	0.979156i
$950$	296.294	+	8.28888i	0.311889	+	0.00872513i
$951$			1715.09i			1.80346i
$952$	−573.983	+	9.70828i	−0.602924	+	0.0101978i
$953$	−1079.46	+	1079.46i	−1.13269	+	1.13269i	−0.142967	+	0.989727i	$0.545664\pi$
$953$	−1079.46	+	1079.46i	−1.13269	+	1.13269i	−0.989727	+	0.142967i	$0.954336\pi$
$954$	1338.20	−	1353.37i	1.40272	−	1.41863i
$955$	−204.114	−	211.091i	−0.213732	−	0.221037i
$956$	−2.73434	−	242.507i	−0.00286019	−	0.253668i
$957$	−588.588	−	1871.00i	−0.615034	−	1.95507i
$958$	4.58530	+	813.359i	0.00478632	+	0.849018i
$959$			235.093i			0.245144i
$960$	28.5318	+	1676.02i	0.0297206	+	1.74585i
$961$	467.449			0.486419
$962$	2.70504	+	479.832i	0.00281190	+	0.498786i
$963$	349.393	+	349.393i	0.362818	+	0.362818i
$964$	−5.60096	−	496.745i	−0.00581012	−	0.515295i
$965$	−12.1711	+	724.291i	−0.0126126	+	0.750561i
$966$	152.976	+	151.261i	0.158361	+	0.156585i
$967$	−619.752	+	619.752i	−0.640902	+	0.640902i	−0.950777	−	0.309875i	$-0.899713\pi$
$967$	−619.752	+	619.752i	−0.640902	+	0.640902i	0.309875	+	0.950777i	$0.399713\pi$
$968$	567.534	+	784.174i	0.586295	+	0.810097i
$969$			969.903i			1.00093i
$970$	5.85227	−	524.130i	0.00603327	−	0.540340i
$971$			1583.36i			1.63064i	0.579008	+	0.815322i	$0.303440\pi$
$971$			1583.36i			1.63064i	−0.579008	+	0.815322i	$0.696560\pi$
$972$	−118.847	+	121.558i	−0.122271	+	0.125059i
$973$	47.4380	+	47.4380i	0.0487544	+	0.0487544i
$974$	189.129	+	187.008i	0.194178	+	0.192000i
$975$	−2546.99	−	85.6245i	−2.61230	−	0.0878200i
$976$	−23.2235	−	1029.71i	−0.0237946	−	1.05503i
$977$	704.972	−	704.972i	0.721568	−	0.721568i	−0.247356	−	0.968925i	$-0.579562\pi$
$977$	704.972	−	704.972i	0.721568	−	0.721568i	0.968925	+	0.247356i	$0.0795618\pi$
$978$	−13.5180	−	2397.87i	−0.0138220	−	2.45181i
$979$	−134.741	−	70.2530i	−0.137631	−	0.0717600i
$980$	−614.887	−	621.723i	−0.627436	−	0.634411i
$981$			935.185i			0.953298i
$982$	−1483.10	+	8.36093i	−1.51028	+	0.00851419i
$983$	608.596	−	608.596i	0.619121	−	0.619121i	−0.326185	−	0.945306i	$-0.605763\pi$
$983$	608.596	−	608.596i	0.619121	−	0.619121i	0.945306	+	0.326185i	$0.105763\pi$
$984$	−1350.23	−	1305.32i	−1.37219	−	1.32654i
$985$	−859.299	−	14.4398i	−0.872385	−	0.0146597i
$986$	1511.97	+	1495.02i	1.53344	+	1.51625i
$987$	75.4406	−	75.4406i	0.0764343	−	0.0764343i
$988$	−329.952	−	322.594i	−0.333959	−	0.326512i
$989$	−142.034			−0.143613
$990$	−1941.59	+	587.053i	−1.96120	+	0.592983i
$991$		−	1202.88i		−	1.21380i	−0.794776	−	0.606902i	$-0.792412\pi$
$991$		−	1202.88i		−	1.21380i	0.794776	−	0.606902i	$-0.207588\pi$
$992$	−20.0359	−	710.630i	−0.0201975	−	0.716361i
$993$	1913.54	+	1913.54i	1.92703	+	1.92703i
$994$	187.338	+	185.237i	0.188469	+	0.186356i
$995$	−325.467	+	314.710i	−0.327103	+	0.316291i
$996$	2001.94	−	22.5726i	2.00998	−	0.0226632i
$997$	−524.498	−	524.498i	−0.526076	−	0.526076i	0.393324	−	0.919400i	$-0.371325\pi$
$997$	−524.498	−	524.498i	−0.526076	−	0.526076i	−0.919400	+	0.393324i	$0.871325\pi$
$998$	1855.13	−	10.4583i	1.85885	−	0.0104792i
$999$	−609.662			−0.610273

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.i.a.43.1	✓	136
4.3	odd	2	inner	220.3.i.a.43.35	yes	136
5.2	odd	4	inner	220.3.i.a.87.34	yes	136
11.10	odd	2	inner	220.3.i.a.43.68	yes	136
20.7	even	4	inner	220.3.i.a.87.68	yes	136
44.43	even	2	inner	220.3.i.a.43.34	yes	136
55.32	even	4	inner	220.3.i.a.87.35	yes	136
220.87	odd	4	inner	220.3.i.a.87.1	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.i.a.43.1	✓	136	1.1	even	1	trivial
220.3.i.a.43.34	yes	136	44.43	even	2	inner
220.3.i.a.43.35	yes	136	4.3	odd	2	inner
220.3.i.a.43.68	yes	136	11.10	odd	2	inner
220.3.i.a.87.1	yes	136	220.87	odd	4	inner
220.3.i.a.87.34	yes	136	5.2	odd	4	inner
220.3.i.a.87.35	yes	136	55.32	even	4	inner
220.3.i.a.87.68	yes	136	20.7	even	4	inner

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99997 + 0.0112748i) q^{2} +(3.70405 - 3.70405i) q^{3} +(3.99975 - 0.0450984i) q^{4} +(-3.59444 + 3.47563i) q^{5} +(-7.36622 + 7.44975i) q^{6} +(-1.62459 + 1.62459i) q^{7} +(-7.99886 + 0.135292i) q^{8} -18.4400i q^{9} +(7.14958 - 6.99168i) q^{10} +(5.08557 - 9.75382i) q^{11} +(14.6482 - 14.9823i) q^{12} +(13.7602 - 13.7602i) q^{13} +(3.23081 - 3.26744i) q^{14} +(-0.440067 + 26.1879i) q^{15} +(15.9959 - 0.360764i) q^{16} +(-22.0851 - 22.0851i) q^{17} +(0.207907 + 36.8794i) q^{18} -5.92820i q^{19} +(-14.2201 + 14.0637i) q^{20} +12.0351i q^{21} +(-10.0610 + 19.5647i) q^{22} +(-6.31990 + 6.31990i) q^{23} +(-29.1270 + 30.1293i) q^{24} +(0.839974 - 24.9859i) q^{25} +(-27.3649 + 27.6751i) q^{26} +(-34.9662 - 34.9662i) q^{27} +(-6.42467 + 6.57120i) q^{28} +34.0393 q^{29} +(0.584858 - 52.3799i) q^{30} +22.2160i q^{31} +(-31.9873 + 0.901868i) q^{32} +(-17.2914 - 54.9659i) q^{33} +(44.4184 + 43.9204i) q^{34} +(0.193012 - 11.4859i) q^{35} +(-0.831614 - 73.7553i) q^{36} +(8.71788 - 8.71788i) q^{37} +(0.0668392 + 11.8562i) q^{38} -101.937i q^{39} +(28.2812 - 28.2874i) q^{40} +44.8146i q^{41} +(-0.135693 - 24.0698i) q^{42} +(11.2370 + 11.2370i) q^{43} +(19.9011 - 39.2421i) q^{44} +(64.0906 + 66.2814i) q^{45} +(12.5683 - 12.7108i) q^{46} +(-6.26838 - 6.26838i) q^{47} +(57.9135 - 60.5860i) q^{48} +43.7214i q^{49} +(-1.39821 + 49.9804i) q^{50} -163.608 q^{51} +(54.4168 - 55.6579i) q^{52} +(-36.4914 - 36.4914i) q^{53} +(70.3255 + 69.5371i) q^{54} +(15.6209 + 52.7351i) q^{55} +(12.7750 - 13.2146i) q^{56} +(-21.9584 - 21.9584i) q^{57} +(-68.0775 + 0.383786i) q^{58} +8.49349 q^{59} +(-0.579124 + 104.765i) q^{60} -64.3732i q^{61} +(-0.250481 - 44.4313i) q^{62} +(29.9574 + 29.9574i) q^{63} +(63.9634 - 2.16436i) q^{64} +(-1.63481 + 97.2857i) q^{65} +(35.2020 + 109.735i) q^{66} +(50.4964 + 50.4964i) q^{67} +(-89.3306 - 87.3386i) q^{68} +46.8184i q^{69} +(-0.256517 + 22.9737i) q^{70} +57.3348i q^{71} +(2.49478 + 147.499i) q^{72} +(33.7647 - 33.7647i) q^{73} +(-17.3372 + 17.5338i) q^{74} +(-89.4377 - 95.6603i) q^{75} +(-0.267353 - 23.7113i) q^{76} +(7.58397 + 24.1079i) q^{77} +(1.14932 + 203.871i) q^{78} +91.0525i q^{79} +(-56.2425 + 56.8927i) q^{80} -93.0733 q^{81} +(-0.505275 - 89.6278i) q^{82} +(67.5635 + 67.5635i) q^{83} +(0.542764 + 48.1374i) q^{84} +(156.143 + 2.62386i) q^{85} +(-22.6004 - 22.3470i) q^{86} +(126.083 - 126.083i) q^{87} +(-39.3591 + 78.7074i) q^{88} -13.8142i q^{89} +(-128.926 - 131.838i) q^{90} +44.7093i q^{91} +(-24.9930 + 25.5630i) q^{92} +(82.2893 + 82.2893i) q^{93} +(12.6072 + 12.4659i) q^{94} +(20.6042 + 21.3086i) q^{95} +(-115.142 + 121.823i) q^{96} +(37.0639 - 37.0639i) q^{97} +(-0.492950 - 87.4415i) q^{98} +(-179.860 - 93.7779i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) \) 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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