LMFDB - Embedded newform 220.3.i.a.87.58

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			87.58
Character	$\chi$	$=$	220.87
Dual form			220.3.i.a.43.58

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73178 + 1.00047i) q^{2} +(1.22071 + 1.22071i) q^{3} +(1.99810 + 3.46520i) q^{4} +(4.48571 + 2.20872i) q^{5} +(0.892710 + 3.33529i) q^{6} +(3.81872 + 3.81872i) q^{7} +(-0.00657265 + 8.00000i) q^{8} -6.01972i q^{9} +(5.55847 + 8.31284i) q^{10} +(-7.54107 - 8.00826i) q^{11} +(-1.79090 + 6.66912i) q^{12} +(-17.0270 - 17.0270i) q^{13} +(2.79264 + 10.4337i) q^{14} +(2.77954 + 8.17197i) q^{15} +(-8.01517 + 13.8476i) q^{16} +(7.50031 - 7.50031i) q^{17} +(6.02258 - 10.4248i) q^{18} +12.1979i q^{19} +(1.30925 + 19.9571i) q^{20} +9.32312i q^{21} +(-5.04739 - 21.4132i) q^{22} +(20.1933 + 20.1933i) q^{23} +(-9.77372 + 9.75767i) q^{24} +(15.2431 + 19.8153i) q^{25} +(-12.4519 - 46.5220i) q^{26} +(18.3348 - 18.3348i) q^{27} +(-5.60242 + 20.8628i) q^{28} -29.2106 q^{29} +(-3.36230 + 16.9329i) q^{30} -11.9603i q^{31} +(-27.7347 + 15.9620i) q^{32} +(0.570308 - 18.9813i) q^{33} +(20.4927 - 5.48500i) q^{34} +(8.69517 + 25.5641i) q^{35} +(20.8595 - 12.0280i) q^{36} +(-14.8278 - 14.8278i) q^{37} +(-12.2037 + 21.1241i) q^{38} -41.5701i q^{39} +(-17.6992 + 35.8711i) q^{40} -23.1736i q^{41} +(-9.32754 + 16.1456i) q^{42} +(21.2346 - 21.2346i) q^{43} +(12.6824 - 42.1326i) q^{44} +(13.2959 - 27.0027i) q^{45} +(14.7674 + 55.1731i) q^{46} +(-55.8217 + 55.8217i) q^{47} +(-26.6882 + 7.11976i) q^{48} -19.8347i q^{49} +(6.57292 + 49.5661i) q^{50} +18.3114 q^{51} +(24.9802 - 93.0236i) q^{52} +(62.0677 - 62.0677i) q^{53} +(50.0952 - 13.4083i) q^{54} +(-16.1390 - 52.5788i) q^{55} +(-30.5749 + 30.5247i) q^{56} +(-14.8901 + 14.8901i) q^{57} +(-50.5863 - 29.2245i) q^{58} +12.4952 q^{59} +(-22.7637 + 25.9601i) q^{60} +33.9624i q^{61} +(11.9659 - 20.7125i) q^{62} +(22.9876 - 22.9876i) q^{63} +(-63.9999 - 0.105162i) q^{64} +(-38.7702 - 113.986i) q^{65} +(19.9779 - 32.3007i) q^{66} +(-37.9793 + 37.9793i) q^{67} +(40.9764 + 11.0037i) q^{68} +49.3004i q^{69} +(-10.5182 + 52.9707i) q^{70} +11.1299i q^{71} +(48.1578 + 0.0395656i) q^{72} +(34.2833 + 34.2833i) q^{73} +(-10.8436 - 40.5134i) q^{74} +(-5.58138 + 42.7963i) q^{75} +(-42.2682 + 24.3727i) q^{76} +(1.78408 - 59.3786i) q^{77} +(41.5899 - 71.9902i) q^{78} +93.2636i q^{79} +(-66.5393 + 44.4131i) q^{80} -9.41456 q^{81} +(23.1846 - 40.1315i) q^{82} +(75.9544 - 75.9544i) q^{83} +(-32.3064 + 18.6285i) q^{84} +(50.2103 - 17.0781i) q^{85} +(58.0183 - 15.5289i) q^{86} +(-35.6578 - 35.6578i) q^{87} +(64.1156 - 60.2759i) q^{88} +82.3572i q^{89} +(50.0410 - 33.4605i) q^{90} -130.043i q^{91} +(-29.6254 + 110.322i) q^{92} +(14.6001 - 14.6001i) q^{93} +(-152.519 + 40.8225i) q^{94} +(-26.9418 + 54.7162i) q^{95} +(-53.3411 - 14.3710i) q^{96} +(-2.25877 - 2.25877i) q^{97} +(19.8441 - 34.3493i) q^{98} +(-48.2075 + 45.3951i) 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 $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.73178	+	1.00047i	0.865888	+	0.500237i
$2$	1.73178	+	1.00047i	0.865888	+	0.500237i
$3$	1.22071	+	1.22071i	0.406904	+	0.406904i	0.880658	−	0.473753i	$-0.157101\pi$
$3$	1.22071	+	1.22071i	0.406904	+	0.406904i	−0.473753	+	0.880658i	$0.657101\pi$
$4$	1.99810	+	3.46520i	0.499526	+	0.866299i
$5$	4.48571	+	2.20872i	0.897141	+	0.441744i
$5$	4.48571	+	2.20872i	0.897141	+	0.441744i
$6$	0.892710	+	3.33529i	0.148785	+	0.555882i
$7$	3.81872	+	3.81872i	0.545532	+	0.545532i	0.925145	−	0.379614i	$-0.123943\pi$
$7$	3.81872	+	3.81872i	0.545532	+	0.545532i	−0.379614	+	0.925145i	$0.623943\pi$
$8$	−0.00657265	+	8.00000i	−0.000821582	+	1.00000i
$9$		−	6.01972i		−	0.668858i
$10$	5.55847	+	8.31284i	0.555847	+	0.831284i
$11$	−7.54107	−	8.00826i	−0.685552	−	0.728024i
$11$	−7.54107	−	8.00826i	−0.685552	−	0.728024i
$12$	−1.79090	+	6.66912i	−0.149242	+	0.555760i
$13$	−17.0270	−	17.0270i	−1.30977	−	1.30977i	−0.921579	−	0.388190i	$-0.873100\pi$
$13$	−17.0270	−	17.0270i	−1.30977	−	1.30977i	−0.388190	−	0.921579i	$-0.626900\pi$
$14$	2.79264	+	10.4337i	0.199474	+	0.745265i
$15$	2.77954	+	8.17197i	0.185303	+	0.544798i
$16$	−8.01517	+	13.8476i	−0.500948	+	0.865477i
$17$	7.50031	−	7.50031i	0.441195	−	0.441195i	−0.451219	−	0.892413i	$-0.649011\pi$
$17$	7.50031	−	7.50031i	0.441195	−	0.441195i	0.892413	+	0.451219i	$0.149011\pi$
$18$	6.02258	−	10.4248i	0.334588	−	0.579156i
$19$			12.1979i			0.641995i	0.947080	+	0.320998i	$0.104018\pi$
$19$			12.1979i			0.641995i	−0.947080	+	0.320998i	$0.895982\pi$
$20$	1.30925	+	19.9571i	0.0654624	+	0.997855i
$21$			9.32312i			0.443958i
$22$	−5.04739	−	21.4132i	−0.229427	−	0.973326i
$23$	20.1933	+	20.1933i	0.877968	+	0.877968i	0.993324	−	0.115356i	$-0.0368008\pi$
$23$	20.1933	+	20.1933i	0.877968	+	0.877968i	−0.115356	+	0.993324i	$0.536801\pi$
$24$	−9.77372	+	9.75767i	−0.407238	+	0.406570i
$25$	15.2431	+	19.8153i	0.609724	+	0.792614i
$26$	−12.4519	−	46.5220i	−0.478919	−	1.78931i
$27$	18.3348	−	18.3348i	0.679065	−	0.679065i
$28$	−5.60242	+	20.8628i	−0.200087	+	0.745101i
$29$	−29.2106			−1.00726			−0.503632	−	0.863919i	$-0.668003\pi$
$29$	−29.2106			−1.00726			−0.503632	+	0.863919i	$0.668003\pi$
$30$	−3.36230	+	16.9329i	−0.112077	+	0.564430i
$31$		−	11.9603i		−	0.385815i	−0.981217	−	0.192908i	$-0.938208\pi$
$31$		−	11.9603i		−	0.385815i	0.981217	−	0.192908i	$-0.0617918\pi$
$32$	−27.7347	+	15.9620i	−0.866709	+	0.498814i
$33$	0.570308	−	18.9813i	0.0172821	−	0.575190i
$34$	20.4927	−	5.48500i	0.602727	−	0.161323i
$35$	8.69517	+	25.5641i	0.248433	+	0.730404i
$36$	20.8595	−	12.0280i	0.579431	−	0.334112i
$37$	−14.8278	−	14.8278i	−0.400752	−	0.400752i	0.477746	−	0.878498i	$-0.341454\pi$
$37$	−14.8278	−	14.8278i	−0.400752	−	0.400752i	−0.878498	+	0.477746i	$0.841454\pi$
$38$	−12.2037	+	21.1241i	−0.321150	+	0.555896i
$39$		−	41.5701i		−	1.06590i
$40$	−17.6992	+	35.8711i	−0.442481	+	0.896778i
$41$		−	23.1736i		−	0.565210i	−0.959236	−	0.282605i	$-0.908801\pi$
$41$		−	23.1736i		−	0.565210i	0.959236	−	0.282605i	$-0.0911986\pi$
$42$	−9.32754	+	16.1456i	−0.222084	+	0.384418i
$43$	21.2346	−	21.2346i	0.493829	−	0.493829i	−0.415682	−	0.909510i	$-0.636457\pi$
$43$	21.2346	−	21.2346i	0.493829	−	0.493829i	0.909510	+	0.415682i	$0.136457\pi$
$44$	12.6824	−	42.1326i	0.288236	−	0.957559i
$45$	13.2959	−	27.0027i	0.295464	−	0.600060i
$46$	14.7674	+	55.1731i	0.321030	+	1.19942i
$47$	−55.8217	+	55.8217i	−1.18770	+	1.18770i	−0.209993	+	0.977703i	$0.567344\pi$
$47$	−55.8217	+	55.8217i	−1.18770	+	1.18770i	−0.977703	+	0.209993i	$0.932656\pi$
$48$	−26.6882	+	7.11976i	−0.556004	+	0.148328i
$49$		−	19.8347i		−	0.404791i
$50$	6.57292	+	49.5661i	0.131458	+	0.991322i
$51$	18.3114			0.359048
$52$	24.9802	−	93.0236i	0.480389	−	1.78892i
$53$	62.0677	−	62.0677i	1.17109	−	1.17109i	0.189139	−	0.981950i	$-0.439430\pi$
$53$	62.0677	−	62.0677i	1.17109	−	1.17109i	0.981950	−	0.189139i	$-0.0605697\pi$
$54$	50.0952	−	13.4083i	0.927688	−	0.248301i
$55$	−16.1390	−	52.5788i	−0.293436	−	0.955979i
$56$	−30.5749	+	30.5247i	−0.545980	+	0.545083i
$57$	−14.8901	+	14.8901i	−0.261231	+	0.261231i
$58$	−50.5863	−	29.2245i	−0.872177	−	0.503870i
$59$	12.4952			0.211782			0.105891	−	0.994378i	$-0.466230\pi$
$59$	12.4952			0.211782			0.105891	+	0.994378i	$0.466230\pi$
$60$	−22.7637	+	25.9601i	−0.379394	+	0.432668i
$61$			33.9624i			0.556760i	0.960471	+	0.278380i	$0.0897975\pi$
$61$			33.9624i			0.556760i	−0.960471	+	0.278380i	$0.910203\pi$
$62$	11.9659	−	20.7125i	0.192999	−	0.334073i
$63$	22.9876	−	22.9876i	0.364883	−	0.364883i
$64$	−63.9999	−	0.105162i	−0.999999	−	0.00164316i
$65$	−38.7702	−	113.986i	−0.596465	−	1.75363i
$66$	19.9779	−	32.3007i	0.302696	−	0.489405i
$67$	−37.9793	+	37.9793i	−0.566856	+	0.566856i	−0.931246	−	0.364390i	$-0.881277\pi$
$67$	−37.9793	+	37.9793i	−0.566856	+	0.566856i	0.364390	+	0.931246i	$0.381277\pi$
$68$	40.9764	+	11.0037i	0.602595	+	0.161819i
$69$			49.3004i			0.714498i
$70$	−10.5182	+	52.9707i	−0.150260	+	0.756724i
$71$			11.1299i			0.156759i	0.996924	+	0.0783795i	$0.0249746\pi$
$71$			11.1299i			0.156759i	−0.996924	+	0.0783795i	$0.975025\pi$
$72$	48.1578	+	0.0395656i	0.668858	+	0.000549522i
$73$	34.2833	+	34.2833i	0.469635	+	0.469635i	0.901796	−	0.432161i	$-0.142249\pi$
$73$	34.2833	+	34.2833i	0.469635	+	0.469635i	−0.432161	+	0.901796i	$0.642249\pi$
$74$	−10.8436	−	40.5134i	−0.146536	−	0.547478i
$75$	−5.58138	+	42.7963i	−0.0744184	+	0.570617i
$76$	−42.2682	+	24.3727i	−0.556160	+	0.320693i
$77$	1.78408	−	59.3786i	0.0231699	−	0.771150i
$78$	41.5899	−	71.9902i	0.533203	−	0.922952i
$79$			93.2636i			1.18055i	0.807202	+	0.590276i	$0.200981\pi$
$79$			93.2636i			1.18055i	−0.807202	+	0.590276i	$0.799019\pi$
$80$	−66.5393	+	44.4131i	−0.831741	+	0.555164i
$81$	−9.41456			−0.116229
$82$	23.1846	−	40.1315i	0.282739	−	0.489409i
$83$	75.9544	−	75.9544i	0.915113	−	0.915113i	−0.0815558	−	0.996669i	$-0.525989\pi$
$83$	75.9544	−	75.9544i	0.915113	−	0.915113i	0.996669	+	0.0815558i	$0.0259889\pi$
$84$	−32.3064	+	18.6285i	−0.384601	+	0.221768i
$85$	50.2103	−	17.0781i	0.590709	−	0.200919i
$86$	58.0183	−	15.5289i	0.674632	−	0.180569i
$87$	−35.6578	−	35.6578i	−0.409860	−	0.409860i
$88$	64.1156	−	60.2759i	0.728587	−	0.684953i
$89$			82.3572i			0.925362i	0.886525	+	0.462681i	$0.153112\pi$
$89$			82.3572i			0.925362i	−0.886525	+	0.462681i	$0.846888\pi$
$90$	50.0410	−	33.4605i	0.556011	−	0.371783i
$91$		−	130.043i		−	1.42904i
$92$	−29.6254	+	110.322i	−0.322016	+	1.19915i
$93$	14.6001	−	14.6001i	0.156990	−	0.156990i
$94$	−152.519	+	40.8225i	−1.62254	+	0.434282i
$95$	−26.9418	+	54.7162i	−0.283598	+	0.575960i
$96$	−53.3411	−	14.3710i	−0.555637	−	0.149698i
$97$	−2.25877	−	2.25877i	−0.0232862	−	0.0232862i	0.695368	−	0.718654i	$-0.255241\pi$
$97$	−2.25877	−	2.25877i	−0.0232862	−	0.0232862i	−0.718654	+	0.695368i	$0.755241\pi$
$98$	19.8441	−	34.3493i	0.202491	−	0.350503i
$99$	−48.2075	+	45.3951i	−0.486945	+	0.458537i
$100$	−38.2068	+	92.4134i	−0.382068	+	0.924134i
$101$			58.0996i			0.575244i	0.957744	+	0.287622i	$0.0928646\pi$
$101$			58.0996i			0.575244i	−0.957744	+	0.287622i	$0.907135\pi$
$102$	31.7113	+	18.3201i	0.310895	+	0.179609i
$103$	−117.785	−	117.785i	−1.14354	−	1.14354i	−0.987798	−	0.155742i	$-0.950223\pi$
$103$	−117.785	−	117.785i	−1.14354	−	1.14354i	−0.155742	−	0.987798i	$-0.549777\pi$
$104$	136.328	−	136.104i	1.31085	−	1.30869i
$105$	−20.5922	+	41.8208i	−0.196116	+	0.398293i
$106$	169.585	−	45.3903i	1.59986	−	0.428210i
$107$	−104.926	−	104.926i	−0.980620	−	0.980620i	0.0191957	−	0.999816i	$-0.493889\pi$
$107$	−104.926	−	104.926i	−0.980620	−	0.980620i	−0.999816	+	0.0191957i	$0.993889\pi$
$108$	100.168	+	26.8988i	0.927484	+	0.249063i
$109$	184.321			1.69102			0.845510	−	0.533959i	$-0.179296\pi$
$109$	184.321			1.69102			0.845510	+	0.533959i	$0.179296\pi$
$110$	24.6546	−	107.201i	0.224133	−	0.974559i
$111$		−	36.2010i		−	0.326135i
$112$	−83.4880	+	22.2725i	−0.745428	+	0.198862i
$113$	−50.9267	+	50.9267i	−0.450678	+	0.450678i	−0.895580	−	0.444901i	$-0.853239\pi$
$113$	−50.9267	+	50.9267i	−0.450678	+	0.450678i	0.444901	+	0.895580i	$0.353239\pi$
$114$	−40.6836	+	10.8892i	−0.356874	+	0.0955193i
$115$	45.9798	+	135.182i	0.399824	+	1.17550i
$116$	−58.3658	−	101.221i	−0.503154	−	0.872591i
$117$	−102.498	+	102.498i	−0.876050	+	0.876050i
$118$	21.6388	+	12.5011i	0.183380	+	0.105941i
$119$	57.2832			0.481371
$120$	−65.3940	+	22.1826i	−0.544950	+	0.184855i
$121$	−7.26454	+	120.782i	−0.0600375	+	0.998196i
$122$	−33.9785	+	58.8152i	−0.278512	+	0.482092i
$123$	28.2883	−	28.2883i	0.229986	−	0.229986i
$124$	41.4447	−	23.8978i	0.334231	−	0.192725i
$125$	24.6095	+	122.554i	0.196876	+	0.980428i
$126$	62.8080	−	16.8109i	0.498476	−	0.133420i
$127$	9.46661	+	9.46661i	0.0745402	+	0.0745402i	0.743394	−	0.668854i	$-0.233215\pi$
$127$	9.46661	+	9.46661i	0.0745402	+	0.0745402i	−0.668854	+	0.743394i	$0.733215\pi$
$128$	−110.728	−	64.2124i	−0.865065	−	0.501659i
$129$	51.8428			0.401882
$130$	46.8987	−	236.187i	0.360759	−	1.81682i
$131$	−119.794			−0.914456			−0.457228	−	0.889350i	$-0.651158\pi$
$131$	−119.794			−0.914456			−0.457228	+	0.889350i	$0.651158\pi$
$132$	66.9133	−	35.9503i	0.506919	−	0.272351i
$133$	−46.5804	+	46.5804i	−0.350229	+	0.350229i
$134$	−103.769	+	27.7744i	−0.774396	+	0.207272i
$135$	122.741	−	41.7480i	0.909190	−	0.309244i
$136$	59.9532	+	60.0518i	0.440832	+	0.441557i
$137$	−182.709	−	182.709i	−1.33364	−	1.33364i	−0.902086	−	0.431556i	$-0.857965\pi$
$137$	−182.709	−	182.709i	−1.33364	−	1.33364i	−0.431556	−	0.902086i	$-0.642035\pi$
$138$	−49.3237	+	85.3772i	−0.357418	+	0.618675i
$139$			87.1786i			0.627184i	0.949558	+	0.313592i	$0.101532\pi$
$139$			87.1786i			0.627184i	−0.949558	+	0.313592i	$0.898468\pi$
$140$	−71.2110	+	81.2103i	−0.508650	+	0.580073i
$141$	−136.284			−0.966556
$142$	−11.1352	+	19.2745i	−0.0784167	+	0.135736i
$143$	−7.95490	+	264.759i	−0.0556287	+	1.85146i
$144$	83.3589	+	48.2491i	0.578881	+	0.335063i
$145$	−131.030	−	64.5181i	−0.903657	−	0.444953i
$146$	25.0715	+	93.6707i	0.171723	+	0.641580i
$147$	24.2125	−	24.2125i	0.164711	−	0.164711i
$148$	21.7538	−	81.0089i	0.146985	−	0.547357i
$149$	34.0643			0.228619			0.114310	−	0.993445i	$-0.463534\pi$
$149$	34.0643			0.228619			0.114310	+	0.993445i	$0.463534\pi$
$150$	−52.4823	+	68.5296i	−0.349882	+	0.456864i
$151$	173.276			1.14752			0.573762	−	0.819022i	$-0.305484\pi$
$151$	173.276			1.14752			0.573762	+	0.819022i	$0.305484\pi$
$152$	−97.5833	−	0.0801726i	−0.641995	−	0.000527452i
$153$	−45.1498	−	45.1498i	−0.295097	−	0.295097i
$154$	62.4964	−	101.045i	0.405820	−	0.656140i
$155$	26.4169	−	53.6503i	0.170432	−	0.346131i
$156$	144.049	−	83.0614i	0.923389	−	0.532445i
$157$	25.3500	+	25.3500i	0.161465	+	0.161465i	0.783215	−	0.621751i	$-0.213578\pi$
$157$	25.3500	+	25.3500i	0.161465	+	0.161465i	−0.621751	+	0.783215i	$0.713578\pi$
$158$	−93.3078	+	161.512i	−0.590556	+	1.02223i
$159$	151.534			0.953042
$160$	−159.665	+	10.3428i	−0.997908	+	0.0646425i
$161$			154.225i			0.957919i
$162$	−16.3039	−	9.41903i	−0.100642	−	0.0581422i
$163$	−52.4419	−	52.4419i	−0.321729	−	0.321729i	0.527701	−	0.849430i	$-0.323054\pi$
$163$	−52.4419	−	52.4419i	−0.321729	−	0.321729i	−0.849430	+	0.527701i	$0.823054\pi$
$164$	80.3011	−	46.3033i	0.489641	−	0.282337i
$165$	44.4825	−	83.8847i	0.269591	−	0.508392i
$166$	207.526	−	55.5456i	1.25016	−	0.334612i
$167$	107.739	+	107.739i	0.645144	+	0.645144i	0.951816	−	0.306671i	$-0.0992152\pi$
$167$	107.739	+	107.739i	0.645144	+	0.645144i	−0.306671	+	0.951816i	$0.599215\pi$
$168$	−74.5849	−	0.0612776i	−0.443958	−	0.000364748i
$169$			410.838i			2.43099i
$170$	104.039	+	20.6586i	0.611995	+	0.121521i
$171$	73.4280			0.429404
$172$	116.011	+	31.1532i	0.674483	+	0.181123i
$173$	20.6428	+	20.6428i	0.119322	+	0.119322i	0.764247	−	0.644924i	$-0.223111\pi$
$173$	20.6428	+	20.6428i	0.119322	+	0.119322i	−0.644924	+	0.764247i	$0.723111\pi$
$174$	−26.0766	−	97.4260i	−0.149866	−	0.559920i
$175$	−17.4601	+	133.878i	−0.0997719	+	0.765020i
$176$	171.338	−	40.2384i	0.973514	−	0.228627i
$177$	15.2530	+	15.2530i	0.0861751	+	0.0861751i
$178$	−82.3963	+	142.624i	−0.462900	+	0.801260i
$179$	−321.360			−1.79531			−0.897655	−	0.440700i	$-0.854730\pi$
$179$	−321.360			−1.79531			−0.897655	+	0.440700i	$0.854730\pi$
$180$	120.136	−	7.88131i	0.667423	−	0.0437850i
$181$	164.845			0.910745			0.455372	−	0.890301i	$-0.349506\pi$
$181$	164.845			0.910745			0.455372	+	0.890301i	$0.349506\pi$
$182$	130.104	−	225.205i	0.714860	−	1.23739i
$183$	−41.4583	+	41.4583i	−0.226548	+	0.226548i
$184$	−161.679	+	161.413i	−0.878689	+	0.877247i
$185$	−33.7628	−	99.2638i	−0.182501	−	0.536561i
$186$	39.8910	−	10.6771i	0.214468	−	0.0574035i
$187$	−116.625	−	3.50409i	−0.623662	−	0.0187385i
$188$	−304.971	−	81.8957i	−1.62218	−	0.435615i
$189$	140.031			0.740903
$190$	−101.399	+	67.8018i	−0.533681	+	0.356851i
$191$			215.308i			1.12727i	0.826025	+	0.563633i	$0.190597\pi$
$191$			215.308i			1.12727i	−0.826025	+	0.563633i	$0.809403\pi$
$192$	−77.9971	−	78.2539i	−0.406235	−	0.407572i
$193$	112.293	+	112.293i	0.581830	+	0.581830i	0.935406	−	0.353576i	$-0.115034\pi$
$193$	112.293	+	112.293i	0.581830	+	0.581830i	−0.353576	+	0.935406i	$0.615034\pi$
$194$	−1.65184	−	6.17152i	−0.00851465	−	0.0318119i
$195$	91.8168	−	186.471i	0.470856	−	0.956264i
$196$	68.7313	−	39.6318i	0.350670	−	0.202203i
$197$	−94.5590	+	94.5590i	−0.479995	+	0.479995i	−0.905130	−	0.425135i	$-0.860227\pi$
$197$	−94.5590	+	94.5590i	−0.479995	+	0.479995i	0.425135	+	0.905130i	$0.360227\pi$
$198$	−128.901	+	30.3839i	−0.651017	+	0.153454i
$199$	4.28315			0.0215234			0.0107617	−	0.999942i	$-0.496574\pi$
$199$	4.28315			0.0215234			0.0107617	+	0.999942i	$0.496574\pi$
$200$	−158.623	+	121.815i	−0.793114	+	0.609073i
$201$	−92.7237			−0.461312
$202$	−58.1272	+	100.616i	−0.287758	+	0.498097i
$203$	−111.547	−	111.547i	−0.549494	−	0.549494i
$204$	36.5881	+	63.4527i	0.179354	+	0.311043i
$205$	51.1840	−	103.950i	0.249678	−	0.507073i
$206$	−86.1361	−	321.817i	−0.418137	−	1.56222i
$207$	121.558	−	121.558i	0.587236	−	0.587236i
$208$	372.258	−	99.3093i	1.78970	−	0.477449i
$209$	97.6841	−	91.9853i	0.467388	−	0.440121i
$210$	−77.5016	+	51.8223i	−0.369055	+	0.246773i
$211$	−45.8243			−0.217177			−0.108588	−	0.994087i	$-0.534633\pi$
$211$	−45.8243			−0.217177			−0.108588	+	0.994087i	$0.534633\pi$
$212$	339.095	+	91.0592i	1.59950	+	0.429525i
$213$	−13.5864	+	13.5864i	−0.0637859	+	0.0637859i
$214$	−76.7329	−	286.685i	−0.358565	−	1.33965i
$215$	142.154	−	48.3509i	0.661180	−	0.224888i
$216$	146.558	+	146.799i	0.678507	+	0.679623i
$217$	45.6729	−	45.6729i	0.210474	−	0.210474i
$218$	319.203	+	184.409i	1.46423	+	0.845911i
$219$			83.7002i			0.382193i
$220$	149.949	−	160.983i	0.681584	−	0.731739i
$221$	−255.416			−1.15573
$222$	36.2182	−	62.6921i	0.163145	−	0.282397i
$223$	198.915	+	198.915i	0.891997	+	0.891997i	0.994711	−	0.102714i	$-0.0327526\pi$
$223$	198.915	+	198.915i	0.891997	+	0.891997i	−0.102714	+	0.994711i	$0.532753\pi$
$224$	−166.866	−	44.9565i	−0.744936	−	0.200699i
$225$	119.283	−	91.7593i	0.530146	−	0.407819i
$226$	−139.144	+	37.2428i	−0.615683	+	0.164791i
$227$	−176.483	−	176.483i	−0.777459	−	0.777459i	0.201939	−	0.979398i	$-0.435276\pi$
$227$	−176.483	−	176.483i	−0.777459	−	0.777459i	−0.979398	+	0.201939i	$0.935276\pi$
$228$	−81.3493	−	21.8452i	−0.356795	−	0.0958124i
$229$			216.745i			0.946483i	0.880933	+	0.473242i	$0.156916\pi$
$229$			216.745i			0.946483i	−0.880933	+	0.473242i	$0.843084\pi$
$230$	−55.6198	+	280.107i	−0.241825	+	1.21786i
$231$	74.6620	−	70.3063i	0.323212	−	0.304356i
$232$	0.191991	−	233.685i	0.000827549	−	1.00726i
$233$	−36.9257	−	36.9257i	−0.158480	−	0.158480i	0.623413	−	0.781893i	$-0.285746\pi$
$233$	−36.9257	−	36.9257i	−0.158480	−	0.158480i	−0.781893	+	0.623413i	$0.785746\pi$
$234$	−280.050	+	74.9569i	−1.19679	+	0.320329i
$235$	−373.694	+	127.105i	−1.59019	+	0.540873i
$236$	24.9666	+	43.2982i	0.105791	+	0.183467i
$237$	−113.848	+	113.848i	−0.480371	+	0.480371i
$238$	99.2017	+	57.3104i	0.416814	+	0.240800i
$239$		−	77.4780i		−	0.324176i	−0.986776	−	0.162088i	$-0.948177\pi$
$239$		−	77.4780i		−	0.324176i	0.986776	−	0.162088i	$-0.0518228\pi$
$240$	−135.441	−	27.0096i	−0.564337	−	0.112540i
$241$		−	384.201i		−	1.59420i	−0.603850	−	0.797098i	$-0.706367\pi$
$241$		−	384.201i		−	1.59420i	0.603850	−	0.797098i	$-0.293633\pi$
$242$	−133.420	+	201.899i	−0.551321	+	0.834293i
$243$	−176.505	−	176.505i	−0.726359	−	0.726359i
$244$	−117.686	+	67.8603i	−0.482321	+	0.278116i
$245$	43.8094	−	88.9728i	0.178814	−	0.363154i
$246$	77.2908	−	20.6873i	0.314190	−	0.0840948i
$247$	207.694	−	207.694i	0.840866	−	0.840866i
$248$	95.6821	+	0.0786107i	0.385815	+	0.000316979i
$249$	185.437			0.744726
$250$	−79.9934	+	236.857i	−0.319974	+	0.947426i
$251$			71.4560i			0.284685i	0.989817	+	0.142343i	$0.0454635\pi$
$251$			71.4560i			0.284685i	−0.989817	+	0.142343i	$0.954537\pi$
$252$	125.588	+	33.7250i	0.498366	+	0.133830i
$253$	9.43416	−	313.992i	0.0372892	−	1.24107i
$254$	6.92295	+	25.8651i	0.0272557	+	0.101831i
$255$	82.1397	+	40.4449i	0.322117	+	0.158607i
$256$	−127.514	−	221.982i	−0.498101	−	0.867119i
$257$	−80.4439	−	80.4439i	−0.313011	−	0.313011i	0.533064	−	0.846075i	$-0.321041\pi$
$257$	−80.4439	−	80.4439i	−0.313011	−	0.313011i	−0.846075	+	0.533064i	$0.821041\pi$
$258$	89.7801	+	51.8673i	0.347985	+	0.201036i
$259$		−	113.247i		−	0.437246i
$260$	317.517	−	362.102i	1.22122	−	1.39270i
$261$			175.840i			0.673716i
$262$	−207.456	−	119.851i	−0.791817	−	0.457445i
$263$	−306.069	+	306.069i	−1.16376	+	1.16376i	−0.180116	+	0.983645i	$0.557647\pi$
$263$	−306.069	+	306.069i	−1.16376	+	1.16376i	−0.983645	+	0.180116i	$0.942353\pi$
$264$	151.846	+	4.68722i	0.575175	+	0.0177546i
$265$	415.508	−	141.327i	1.56795	−	0.533311i
$266$	−127.269	+	34.0644i	−0.478456	+	0.128062i
$267$	−100.534	+	100.534i	−0.376534	+	0.376534i
$268$	−207.492	−	55.7193i	−0.774226	−	0.207908i
$269$		−	203.022i		−	0.754730i	−0.926065	−	0.377365i	$-0.876830\pi$
$269$		−	203.022i		−	0.754730i	0.926065	−	0.377365i	$-0.123170\pi$
$270$	254.327	+	50.5007i	0.941953	+	0.187040i
$271$	−251.162			−0.926795			−0.463398	−	0.886150i	$-0.653370\pi$
$271$	−251.162			−0.926795			−0.463398	+	0.886150i	$0.653370\pi$
$272$	43.7453	+	163.978i	0.160828	+	0.602860i
$273$	158.745	−	158.745i	0.581483	−	0.581483i
$274$	−133.616	−	499.207i	−0.487648	−	1.82192i
$275$	43.7371	−	271.500i	0.159044	−	0.987271i
$276$	−170.835	+	98.5072i	−0.618969	+	0.356910i
$277$	32.9708	−	32.9708i	0.119028	−	0.119028i	−0.645084	−	0.764112i	$-0.723178\pi$
$277$	32.9708	−	32.9708i	0.119028	−	0.119028i	0.764112	+	0.645084i	$0.223178\pi$
$278$	−87.2199	+	150.974i	−0.313741	+	0.543071i
$279$	−71.9975			−0.258056
$280$	−204.570	+	69.3933i	−0.730608	+	0.247833i
$281$			123.056i			0.437923i	0.975734	+	0.218961i	$0.0702669\pi$
$281$			123.056i			0.437923i	−0.975734	+	0.218961i	$0.929733\pi$
$282$	−236.014	−	136.349i	−0.836930	−	0.483507i
$283$	370.554	−	370.554i	1.30938	−	1.30938i	0.387512	−	0.921865i	$-0.373335\pi$
$283$	370.554	−	370.554i	1.30938	−	1.30938i	0.921865	−	0.387512i	$-0.126665\pi$
$284$	−38.5672	+	22.2387i	−0.135800	+	0.0783051i
$285$	−99.6809	+	33.9046i	−0.349758	+	0.118964i
$286$	−278.660	+	450.544i	−0.974336	+	1.57533i
$287$	88.4936	−	88.4936i	0.308340	−	0.308340i
$288$	96.0870	+	166.955i	0.333636	+	0.579705i
$289$			176.491i			0.610694i
$290$	−162.366	−	242.823i	−0.559884	−	0.837322i
$291$		−	5.51461i		−	0.0189505i
$292$	−50.2969	+	187.300i	−0.172250	+	0.641439i
$293$	−392.259	−	392.259i	−1.33877	−	1.33877i	−0.897254	−	0.441516i	$-0.854441\pi$
$293$	−392.259	−	392.259i	−1.33877	−	1.33877i	−0.441516	−	0.897254i	$-0.645559\pi$
$294$	66.1547	−	17.7067i	0.225016	−	0.0602268i
$295$	56.0496	+	27.5983i	0.189999	+	0.0935536i
$296$	118.720	−	118.525i	0.401081	−	0.400423i
$297$	−285.093	−	8.56587i	−0.959910	−	0.0288413i
$298$	58.9917	+	34.0804i	0.197959	+	0.114364i
$299$		−	687.662i		−	2.29987i
$300$	−159.450	+	66.1708i	−0.531499	+	0.220569i
$301$	162.178			0.538798
$302$	300.075	+	173.358i	0.993627	+	0.574034i
$303$	−70.9229	+	70.9229i	−0.234069	+	0.234069i
$304$	−168.912	−	97.7684i	−0.555632	−	0.321607i
$305$	−75.0134	+	152.345i	−0.245945	+	0.499492i
$306$	−33.0182	−	123.361i	−0.107902	−	0.403139i
$307$	156.629	+	156.629i	0.510192	+	0.510192i	0.914585	−	0.404393i	$-0.132517\pi$
$307$	156.629	+	156.629i	0.510192	+	0.510192i	−0.404393	+	0.914585i	$0.632517\pi$
$308$	209.323	−	112.462i	0.679621	−	0.365137i
$309$		−	287.562i		−	0.930622i
$310$	99.4239	−	66.4808i	0.320722	−	0.214454i
$311$		−	82.1856i		−	0.264262i	−0.991232	−	0.132131i	$-0.957818\pi$
$311$		−	82.1856i		−	0.264262i	0.991232	−	0.132131i	$-0.0421820\pi$
$312$	332.561	+	0.273226i	1.06590	+	0.000875725i
$313$	217.002	−	217.002i	0.693296	−	0.693296i	−0.269660	−	0.962956i	$-0.586911\pi$
$313$	217.002	−	217.002i	0.693296	−	0.693296i	0.962956	+	0.269660i	$0.0869112\pi$
$314$	18.5385	+	69.2624i	0.0590398	+	0.220581i
$315$	153.889	−	52.3425i	0.488537	−	0.166167i
$316$	−323.177	+	186.350i	−1.02271	+	0.589716i
$317$	−41.1916	−	41.1916i	−0.129942	−	0.129942i	0.639145	−	0.769087i	$-0.279289\pi$
$317$	−41.1916	−	41.1916i	−0.129942	−	0.129942i	−0.769087	+	0.639145i	$0.779289\pi$
$318$	262.423	+	151.606i	0.825228	+	0.476747i
$319$	220.279	+	233.926i	0.690531	+	0.733312i
$320$	−286.852	−	141.830i	−0.896414	−	0.443218i
$321$		−	256.170i		−	0.798037i
$322$	−154.298	+	267.083i	−0.479187	+	0.829451i
$323$	91.4881	+	91.4881i	0.283245	+	0.283245i
$324$	−18.8113	−	32.6233i	−0.0580594	−	0.100689i
$325$	77.8514	−	596.940i	0.239543	−	1.83674i
$326$	−38.3509	−	143.284i	−0.117641	−	0.439523i
$327$	225.003	+	225.003i	0.688083	+	0.688083i
$328$	185.389	+	0.152312i	0.565210	+	0.000464366i
$329$	−426.335			−1.29585
$330$	160.958	−	100.766i	0.487752	−	0.305351i
$331$			263.642i			0.796503i	0.917276	+	0.398251i	$0.130383\pi$
$331$			263.642i			0.796503i	−0.917276	+	0.398251i	$0.869617\pi$
$332$	414.961	+	111.432i	1.24988	+	0.335639i
$333$	−89.2594	+	89.2594i	−0.268046	+	0.268046i
$334$	78.7899	+	294.370i	0.235898	+	0.881348i
$335$	−254.250	+	86.4784i	−0.758955	+	0.258144i
$336$	−129.103	−	74.7264i	−0.384236	−	0.222400i
$337$	71.2005	−	71.2005i	0.211278	−	0.211278i	−0.593532	−	0.804810i	$-0.702267\pi$
$337$	71.2005	−	71.2005i	0.211278	−	0.211278i	0.804810	+	0.593532i	$0.202267\pi$
$338$	−411.033	+	711.479i	−1.21607	+	2.10497i
$339$	−124.334			−0.366766
$340$	159.504	+	139.865i	0.469130	+	0.411367i
$341$	−95.7810	+	90.1932i	−0.280883	+	0.264496i
$342$	127.161	+	73.4629i	0.371816	+	0.214804i
$343$	262.861	−	262.861i	0.766358	−	0.766358i
$344$	169.737	+	170.017i	0.493423	+	0.494234i
$345$	−108.891	+	221.147i	−0.315625	+	0.641005i
$346$	15.0961	+	56.4012i	0.0436304	+	0.163009i
$347$	129.961	+	129.961i	0.374528	+	0.374528i	0.869123	−	0.494595i	$-0.164684\pi$
$347$	129.961	+	129.961i	0.374528	+	0.374528i	−0.494595	+	0.869123i	$0.664684\pi$
$348$	52.3133	−	194.809i	0.150326	−	0.559796i
$349$	162.716			0.466234			0.233117	−	0.972449i	$-0.425107\pi$
$349$	162.716			0.466234			0.233117	+	0.972449i	$0.425107\pi$
$350$	−164.179	+	214.379i	−0.469083	+	0.612512i
$351$	−624.372			−1.77884
$352$	336.977	+	101.736i	0.957322	+	0.289022i
$353$	−156.532	+	156.532i	−0.443433	+	0.443433i	−0.893164	−	0.449731i	$-0.851520\pi$
$353$	−156.532	+	156.532i	−0.443433	+	0.443433i	0.449731	+	0.893164i	$0.351520\pi$
$354$	11.1546	+	41.6750i	0.0315100	+	0.117726i
$355$	−24.5828	+	49.9254i	−0.0692474	+	0.140635i
$356$	−285.384	+	164.558i	−0.801640	+	0.462242i
$357$	69.9263	+	69.9263i	0.195872	+	0.195872i
$358$	−556.524	−	321.513i	−1.55454	−	0.898080i
$359$			526.944i			1.46781i	0.679252	+	0.733905i	$0.262304\pi$
$359$			526.944i			1.46781i	−0.679252	+	0.733905i	$0.737696\pi$
$360$	215.934	+	106.545i	0.599817	+	0.295957i
$361$	212.211			0.587842
$362$	285.474	+	164.923i	0.788603	+	0.455588i
$363$	−156.308	+	138.572i	−0.430600	+	0.381741i
$364$	450.624	−	259.839i	1.23798	−	0.713843i
$365$	78.0627	+	229.507i	0.213870	+	0.628787i
$366$	−113.274	+	30.3185i	−0.309493	+	0.0828376i
$367$	195.297	−	195.297i	0.532145	−	0.532145i	−0.389065	−	0.921210i	$-0.627202\pi$
$367$	195.297	−	195.297i	0.532145	−	0.532145i	0.921210	+	0.389065i	$0.127202\pi$
$368$	−441.482	+	117.776i	−1.19968	+	0.320045i
$369$	−139.499			−0.378045
$370$	40.8414	−	205.682i	0.110382	−	0.555896i
$371$	474.039			1.27773
$372$	79.7644	+	21.4196i	0.214421	+	0.0575797i
$373$	139.231	+	139.231i	0.373274	+	0.373274i	0.868668	−	0.495394i	$-0.164976\pi$
$373$	139.231	+	139.231i	0.373274	+	0.373274i	−0.495394	+	0.868668i	$0.664976\pi$
$374$	−198.462	−	122.748i	−0.530648	−	0.328204i
$375$	−119.561	+	179.644i	−0.318831	+	0.479050i
$376$	−446.206	−	446.940i	−1.18672	−	1.18867i
$377$	497.369	+	497.369i	1.31928	+	1.31928i
$378$	242.502	+	140.097i	0.641539	+	0.370627i
$379$	−121.053			−0.319402			−0.159701	−	0.987165i	$-0.551053\pi$
$379$	−121.053			−0.319402			−0.159701	+	0.987165i	$0.551053\pi$
$380$	−243.435	+	15.9701i	−0.640618	+	0.0420265i
$381$			23.1120i			0.0606614i
$382$	−215.410	+	372.865i	−0.563901	+	0.976087i
$383$	430.859	+	430.859i	1.12496	+	1.12496i	0.990985	+	0.133974i	$0.0427739\pi$
$383$	430.859	+	430.859i	1.12496	+	1.12496i	0.133974	+	0.990985i	$0.457226\pi$
$384$	−56.7826	−	213.552i	−0.147871	−	0.556126i
$385$	139.154	−	262.414i	0.361438	−	0.681595i
$386$	82.1204	+	306.813i	0.212747	+	0.794853i
$387$	−127.827	−	127.827i	−0.330301	−	0.330301i
$388$	3.31382	−	12.3403i	0.00854078	−	0.0318049i
$389$			45.9252i			0.118060i	0.998256	+	0.0590299i	$0.0188007\pi$
$389$			45.9252i			0.118060i	−0.998256	+	0.0590299i	$0.981199\pi$
$390$	345.566	−	231.067i	0.886067	−	0.592478i
$391$	302.912			0.774710
$392$	158.678	+	0.130367i	0.404790	+	0.000332569i
$393$	−146.234	−	146.234i	−0.372096	−	0.372096i
$394$	−258.359	+	69.1513i	−0.655734	+	0.175511i
$395$	−205.993	+	418.353i	−0.521502	+	1.05912i
$396$	−253.627	−	76.3444i	−0.640471	−	0.192789i
$397$	189.606	+	189.606i	0.477598	+	0.477598i	0.904363	−	0.426765i	$-0.140347\pi$
$397$	189.606	+	189.606i	0.477598	+	0.477598i	−0.426765	+	0.904363i	$0.640347\pi$
$398$	7.41746	+	4.28518i	0.0186368	+	0.0107668i
$399$	−113.723			−0.285019
$400$	−396.572	+	52.2576i	−0.991429	+	0.130644i
$401$	−335.445			−0.836521			−0.418260	−	0.908327i	$-0.637360\pi$
$401$	−335.445			−0.836521			−0.418260	+	0.908327i	$0.637360\pi$
$402$	−160.577	−	92.7677i	−0.399445	−	0.230765i
$403$	−203.648	+	203.648i	−0.505329	+	0.505329i
$404$	−201.327	+	116.089i	−0.498333	+	0.287349i
$405$	−42.2310	−	20.7941i	−0.104274	−	0.0513436i
$406$	−81.5748	−	304.775i	−0.200923	−	0.750678i
$407$	−6.92746	+	230.563i	−0.0170208	+	0.566494i
$408$	−0.120355	+	146.491i	−0.000294987	+	0.359048i
$409$	518.858			1.26860			0.634300	−	0.773087i	$-0.281288\pi$
$409$	518.858			1.26860			0.634300	+	0.773087i	$0.281288\pi$
$410$	192.639	−	128.810i	0.469850	−	0.314171i
$411$		−	446.070i		−	1.08533i
$412$	172.801	−	643.492i	0.419420	−	1.56187i
$413$	47.7155	+	47.7155i	0.115534	+	0.115534i
$414$	332.127	−	88.8956i	0.802238	−	0.214724i
$415$	508.471	−	172.947i	1.22523	−	0.416740i
$416$	744.024	+	200.453i	1.78852	+	0.481858i
$417$	−106.420	+	106.420i	−0.255204	+	0.255204i
$418$	261.196	−	61.5676i	0.624871	−	0.147291i
$419$	520.164			1.24144			0.620721	−	0.784031i	$-0.286840\pi$
$419$	520.164			1.24144			0.620721	+	0.784031i	$0.286840\pi$
$420$	−186.062	+	12.2063i	−0.443006	+	0.0290626i
$421$	−352.410			−0.837078			−0.418539	−	0.908199i	$-0.637458\pi$
$421$	−352.410			−0.837078			−0.418539	+	0.908199i	$0.637458\pi$
$422$	−79.3575	−	45.8460i	−0.188051	−	0.108640i
$423$	336.031	+	336.031i	0.794400	+	0.794400i
$424$	496.134	+	496.950i	1.17013	+	1.17205i
$425$	262.949	+	34.2932i	0.618704	+	0.0806898i
$426$	−37.1214	+	9.93576i	−0.0871395	+	0.0233234i
$427$	−129.693	+	129.693i	−0.303730	+	0.303730i
$428$	153.937	−	573.244i	0.359665	−	1.33936i
$429$	−332.905	+	313.483i	−0.776002	+	0.730730i
$430$	294.552	+	58.4881i	0.685005	+	0.136019i
$431$	−527.215			−1.22324			−0.611618	−	0.791153i	$-0.709481\pi$
$431$	−527.215			−1.22324			−0.611618	+	0.791153i	$0.709481\pi$
$432$	106.937	+	400.849i	0.247539	+	0.927892i
$433$	111.830	−	111.830i	0.258267	−	0.258267i	−0.566082	−	0.824349i	$-0.691541\pi$
$433$	111.830	−	111.830i	0.258267	−	0.258267i	0.824349	+	0.566082i	$0.191541\pi$
$434$	124.790	−	33.4007i	0.287534	−	0.0769602i
$435$	−81.1922	−	238.708i	−0.186649	−	0.548755i
$436$	368.293	+	638.709i	0.844708	+	1.46493i
$437$	−246.316	+	246.316i	−0.563652	+	0.563652i
$438$	−83.7399	+	144.950i	−0.191187	+	0.330936i
$439$			409.254i			0.932241i	0.884721	+	0.466120i	$0.154349\pi$
$439$			409.254i			0.932241i	−0.884721	+	0.466120i	$0.845651\pi$
$440$	420.737	−	128.766i	0.956219	−	0.292651i
$441$	−119.400			−0.270747
$442$	−442.323	−	255.537i	−1.00073	−	0.578137i
$443$	−289.194	−	289.194i	−0.652807	−	0.652807i	0.300861	−	0.953668i	$-0.402726\pi$
$443$	−289.194	−	289.194i	−0.652807	−	0.652807i	−0.953668	+	0.300861i	$0.902726\pi$
$444$	125.444	−	72.3334i	0.282531	−	0.162913i
$445$	−181.904	+	369.430i	−0.408773	+	0.830180i
$446$	145.467	+	543.487i	0.326160	+	1.21858i
$447$	41.5827	+	41.5827i	0.0930261	+	0.0930261i
$448$	−243.996	−	244.799i	−0.544634	−	0.546427i
$449$		−	357.561i		−	0.796350i	−0.917309	−	0.398175i	$-0.869644\pi$
$449$		−	357.561i		−	0.796350i	0.917309	−	0.398175i	$-0.130356\pi$
$450$	298.374	−	39.5672i	0.663054	−	0.0879270i
$451$	−185.580	+	174.754i	−0.411487	+	0.387481i
$452$	−278.228	−	74.7142i	−0.615548	−	0.165297i
$453$	211.520	+	211.520i	0.466932	+	0.466932i
$454$	−129.063	−	482.196i	−0.284279	−	1.06211i
$455$	287.228	−	583.333i	0.631271	−	1.28205i
$456$	−119.023	−	119.219i	−0.261016	−	0.261445i
$457$	−52.4029	+	52.4029i	−0.114667	+	0.114667i	−0.762112	−	0.647445i	$-0.775838\pi$
$457$	−52.4029	+	52.4029i	−0.114667	+	0.114667i	0.647445	+	0.762112i	$0.275838\pi$
$458$	−216.847	+	375.353i	−0.473466	+	0.819549i
$459$		−	275.033i		−	0.599200i
$460$	−376.561	+	429.437i	−0.818611	+	0.933559i
$461$		−	78.9775i		−	0.171318i	−0.996325	−	0.0856589i	$-0.972700\pi$
$461$		−	78.9775i		−	0.171318i	0.996325	−	0.0856589i	$-0.0272995\pi$
$462$	199.638	−	47.0574i	0.432116	−	0.101856i
$463$	−140.726	−	140.726i	−0.303943	−	0.303943i	0.538611	−	0.842554i	$-0.318949\pi$
$463$	−140.726	−	140.726i	−0.303943	−	0.303943i	−0.842554	+	0.538611i	$0.818949\pi$
$464$	234.128	−	404.498i	0.504587	−	0.871763i
$465$	97.7390	−	33.2441i	0.210191	−	0.0714927i
$466$	−27.0039	−	100.890i	−0.0579483	−	0.216503i
$467$	137.005	−	137.005i	0.293373	−	0.293373i	−0.545038	−	0.838411i	$-0.683485\pi$
$467$	137.005	−	137.005i	0.293373	−	0.293373i	0.838411	+	0.545038i	$0.183485\pi$
$468$	−559.976	−	150.374i	−1.19653	−	0.321312i
$469$	−290.065			−0.618476
$470$	−774.320	−	153.754i	−1.64749	−	0.327135i
$471$			61.8900i			0.131401i
$472$	−0.0821263	+	99.9612i	−0.000173996	+	0.211782i
$473$	−330.184	−	9.92067i	−0.698064	−	0.0209739i
$474$	−311.061	+	83.2573i	−0.656247	+	0.175648i
$475$	−241.706	+	185.934i	−0.508854	+	0.391440i
$476$	114.458	+	198.497i	0.240457	+	0.417012i
$477$	−373.631	−	373.631i	−0.783293	−	0.783293i
$478$	77.5148	−	134.175i	0.162165	−	0.280700i
$479$		−	716.300i		−	1.49541i	−0.664032	−	0.747704i	$-0.731156\pi$
$479$		−	716.300i		−	1.49541i	0.664032	−	0.747704i	$-0.268844\pi$
$480$	−207.531	−	182.280i	−0.432356	−	0.379750i
$481$			504.947i			1.04979i
$482$	384.383	−	665.351i	0.797476	−	1.38040i
$483$	−188.264	+	188.264i	−0.389781	+	0.389781i
$484$	−433.048	+	216.161i	−0.894727	+	0.446614i
$485$	−5.14318	−	15.1211i	−0.0106045	−	0.0311776i
$486$	−129.079	−	482.257i	−0.265594	−	0.992298i
$487$	365.486	−	365.486i	0.750484	−	0.750484i	−0.224086	−	0.974569i	$-0.571940\pi$
$487$	365.486	−	365.486i	0.750484	−	0.750484i	0.974569	+	0.224086i	$0.0719396\pi$
$488$	−271.699	−	0.223223i	−0.556760	−	0.000457424i
$489$		−	128.033i		−	0.261826i
$490$	164.883	−	110.251i	0.336496	−	0.225002i
$491$	−149.770			−0.305030			−0.152515	−	0.988301i	$-0.548737\pi$
$491$	−149.770			−0.305030			−0.152515	+	0.988301i	$0.548737\pi$
$492$	154.548	+	41.5016i	0.314121	+	0.0843529i
$493$	−219.089	+	219.089i	−0.444399	+	0.444399i
$494$	567.472	−	151.887i	1.14873	−	0.307464i
$495$	−316.510	+	97.1523i	−0.639414	+	0.196267i
$496$	165.621	+	95.8637i	0.333914	+	0.193273i
$497$	−42.5019	+	42.5019i	−0.0855170	+	0.0855170i
$498$	321.135	+	185.525i	0.644850	+	0.372540i
$499$	−288.828			−0.578815			−0.289407	−	0.957206i	$-0.593458\pi$
$499$	−288.828			−0.578815			−0.289407	+	0.957206i	$0.593458\pi$
$500$	−375.500	+	330.151i	−0.750999	+	0.660303i
$501$			263.037i			0.525024i
$502$	−71.4899	+	123.746i	−0.142410	+	0.246506i
$503$	339.191	−	339.191i	0.674336	−	0.674336i	−0.284376	−	0.958713i	$-0.591787\pi$
$503$	339.191	−	339.191i	0.674336	−	0.674336i	0.958713	+	0.284376i	$0.0917865\pi$
$504$	183.750	+	184.052i	0.364583	+	0.365183i
$505$	−128.326	+	260.618i	−0.254111	+	0.516075i
$506$	330.479	−	534.325i	0.653120	−	1.05598i
$507$	−501.515	+	501.515i	−0.989181	+	0.989181i
$508$	−13.8884	+	51.7189i	−0.0273394	+	0.101809i
$509$		−	763.452i		−	1.49991i	−0.661491	−	0.749953i	$-0.730076\pi$
$509$		−	763.452i		−	1.49991i	0.661491	−	0.749953i	$-0.269924\pi$
$510$	101.784	+	152.220i	0.199576	+	0.298471i
$511$			261.837i			0.512401i
$512$	1.26195	−	511.998i	0.00246474	−	0.999997i
$513$	223.646	+	223.646i	0.435957	+	0.435957i
$514$	−58.8288	−	219.793i	−0.114453	−	0.427613i
$515$	−268.194	−	788.500i	−0.520764	−	1.53107i
$516$	103.587	+	179.645i	0.200750	+	0.348150i
$517$	867.990	+	26.0795i	1.67890	+	0.0504439i
$518$	113.300	−	196.118i	0.218727	−	0.378606i
$519$			50.3978i			0.0971055i
$520$	912.143	−	309.413i	1.75412	−	0.595024i
$521$	197.199			0.378501			0.189251	−	0.981929i	$-0.439394\pi$
$521$	197.199			0.378501			0.189251	+	0.981929i	$0.439394\pi$
$522$	−175.923	+	304.515i	−0.337018	+	0.583363i
$523$	178.216	−	178.216i	0.340757	−	0.340757i	−0.515895	−	0.856652i	$-0.672541\pi$
$523$	178.216	−	178.216i	0.340757	−	0.340757i	0.856652	+	0.515895i	$0.172541\pi$
$524$	−239.360	−	415.109i	−0.456794	−	0.792192i
$525$	−184.741	+	142.113i	−0.351887	+	0.270692i
$526$	−836.258	+	223.829i	−1.58984	+	0.425531i
$527$	−89.7057	−	89.7057i	−0.170220	−	0.170220i
$528$	258.274	+	160.036i	0.489156	+	0.303098i
$529$			286.536i			0.541657i
$530$	860.961	+	170.958i	1.62446	+	0.322562i
$531$		−	75.2174i		−	0.141652i
$532$	−254.483	−	68.3379i	−0.478351	−	0.128455i
$533$	−394.577	+	394.577i	−0.740295	+	0.740295i
$534$	−274.685	+	73.5211i	−0.514392	+	0.137680i
$535$	−238.916	−	702.422i	−0.446571	−	1.31294i
$536$	−303.585	−	304.084i	−0.566390	−	0.567321i
$537$	−392.289	−	392.289i	−0.730519	−	0.730519i
$538$	203.119	−	351.590i	0.377544	−	0.653512i
$539$	−158.842	+	149.575i	−0.294697	+	0.277505i
$540$	389.913	+	341.904i	0.722062	+	0.633155i
$541$		−	82.1696i		−	0.151885i	−0.997112	−	0.0759423i	$-0.975804\pi$
$541$		−	82.1696i		−	0.151885i	0.997112	−	0.0759423i	$-0.0241965\pi$
$542$	−434.956	−	251.281i	−0.802501	−	0.463618i
$543$	201.228	+	201.228i	0.370586	+	0.370586i
$544$	−88.2986	+	327.739i	−0.162314	+	0.602461i
$545$	826.811	+	407.114i	1.51708	+	0.746998i
$546$	433.731	−	116.090i	0.794379	−	0.212620i
$547$	−81.5062	−	81.5062i	−0.149006	−	0.149006i	0.628668	−	0.777674i	$-0.283600\pi$
$547$	−81.5062	−	81.5062i	−0.149006	−	0.149006i	−0.777674	+	0.628668i	$0.783600\pi$
$548$	268.051	−	998.194i	0.489145	−	1.82152i
$549$	204.444			0.372393
$550$	347.371	−	426.419i	0.631584	−	0.775307i
$551$		−	356.309i		−	0.646658i
$552$	−394.403	−	0.324034i	−0.714498	−	0.000587018i
$553$	−356.148	+	356.148i	−0.644028	+	0.644028i
$554$	90.0845	−	24.1116i	0.162607	−	0.0435228i
$555$	79.9580	−	162.387i	0.144068	−	0.292590i
$556$	−302.091	+	174.192i	−0.543329	+	0.313294i
$557$	751.060	−	751.060i	1.34840	−	1.34840i	0.461005	−	0.887398i	$-0.347489\pi$
$557$	751.060	−	751.060i	1.34840	−	1.34840i	0.887398	−	0.461005i	$-0.152511\pi$
$558$	−124.684	−	72.0317i	−0.223447	−	0.129089i
$559$	−723.124			−1.29360
$560$	−423.696	−	84.4935i	−0.756600	−	0.150881i
$561$	−138.088	−	146.643i	−0.246146	−	0.261395i
$562$	−123.115	+	213.106i	−0.219065	+	0.379192i
$563$	213.567	−	213.567i	0.379337	−	0.379337i	−0.491526	−	0.870863i	$-0.663561\pi$
$563$	213.567	−	213.567i	0.379337	−	0.379337i	0.870863	+	0.491526i	$0.163561\pi$
$564$	−272.310	−	472.252i	−0.482820	−	0.837327i
$565$	−340.925	+	115.959i	−0.603407	+	0.205238i
$566$	1012.45	−	270.987i	1.78877	−	0.478775i
$567$	−35.9516	−	35.9516i	−0.0634067	−	0.0634067i
$568$	−89.0391	−	0.0731529i	−0.156759	−	0.000128790i
$569$	395.306			0.694737			0.347369	−	0.937729i	$-0.387075\pi$
$569$	395.306			0.694737			0.347369	+	0.937729i	$0.387075\pi$
$570$	−206.546	−	41.0130i	−0.362361	−	0.0719526i
$571$	−551.953			−0.966643			−0.483322	−	0.875443i	$-0.660570\pi$
$571$	−551.953			−0.966643			−0.483322	+	0.875443i	$0.660570\pi$
$572$	−933.335	+	501.449i	−1.63170	+	0.876660i
$573$	−262.829	+	262.829i	−0.458689	+	0.458689i
$574$	241.787	−	64.7156i	0.421231	−	0.112745i
$575$	−92.3283	+	707.945i	−0.160571	+	1.23121i
$576$	−0.633049	+	385.262i	−0.00109904	+	0.668857i
$577$	−133.865	−	133.865i	−0.232002	−	0.232002i	0.581526	−	0.813528i	$-0.302456\pi$
$577$	−133.865	−	133.865i	−0.232002	−	0.232002i	−0.813528	+	0.581526i	$0.802456\pi$
$578$	−176.574	+	305.643i	−0.305492	+	0.528793i
$579$			274.156i			0.473498i
$580$	−38.2440	−	582.959i	−0.0659378	−	1.00510i
$581$	580.097			0.998446
$582$	5.51722	−	9.55007i	0.00947976	−	0.0164091i
$583$	−965.112	−	28.9976i	−1.65542	−	0.0497386i
$584$	−274.492	+	274.041i	−0.470021	+	0.469249i
$585$	−686.164	+	233.386i	−1.17293	+	0.398950i
$586$	−286.860	−	1071.75i	−0.489523	−	1.82893i
$587$	−445.693	+	445.693i	−0.759272	+	0.759272i	−0.976190	−	0.216918i	$-0.930400\pi$
$587$	−445.693	+	445.693i	−0.759272	+	0.759272i	0.216918	+	0.976190i	$0.430400\pi$
$588$	132.280	+	35.5220i	0.224966	+	0.0604116i
$589$	145.890			0.247692
$590$	69.4540	+	103.870i	0.117719	+	0.176051i
$591$	−230.859			−0.390624
$592$	324.178	−	86.4827i	0.547598	−	0.146086i
$593$	702.062	+	702.062i	1.18392	+	1.18392i	0.978721	+	0.205195i	$0.0657829\pi$
$593$	702.062	+	702.062i	1.18392	+	1.18392i	0.205195	+	0.978721i	$0.434217\pi$
$594$	−485.148	−	300.063i	−0.816748	−	0.505156i
$595$	256.955	+	126.523i	0.431858	+	0.212643i
$596$	68.0639	+	118.039i	0.114201	+	0.198053i
$597$	5.22849	+	5.22849i	0.00875795	+	0.00875795i
$598$	687.988	−	1190.88i	1.15048	−	1.99143i
$599$	−127.836			−0.213415			−0.106708	−	0.994290i	$-0.534031\pi$
$599$	−127.836			−0.213415			−0.106708	+	0.994290i	$0.534031\pi$
$600$	−342.333	−	44.9323i	−0.570556	−	0.0748872i
$601$		−	660.027i		−	1.09821i	−0.835752	−	0.549107i	$-0.814968\pi$
$601$		−	660.027i		−	1.09821i	0.835752	−	0.549107i	$-0.185032\pi$
$602$	280.857	+	162.255i	0.466539	+	0.269527i
$603$	228.625	+	228.625i	0.379146	+	0.379146i
$604$	346.223	+	600.436i	0.573217	+	0.994099i
$605$	−299.360	+	525.746i	−0.494809	+	0.869002i
$606$	−193.779	+	51.8661i	−0.319768	+	0.0855877i
$607$	605.035	+	605.035i	0.996763	+	0.996763i	0.999995	−	0.00323225i	$-0.00102886\pi$
$607$	605.035	+	605.035i	0.996763	+	0.996763i	−0.00323225	+	0.999995i	$0.501029\pi$
$608$	−194.704	−	338.305i	−0.320236	−	0.556423i
$609$		−	272.334i		−	0.447183i
$610$	−282.324	+	188.779i	−0.462826	+	0.309474i
$611$	1900.95			3.11121
$612$	66.2390	−	246.667i	0.108234	−	0.403050i
$613$	523.218	+	523.218i	0.853536	+	0.853536i	0.990567	−	0.137031i	$-0.0437559\pi$
$613$	523.218	+	523.218i	0.853536	+	0.853536i	−0.137031	+	0.990567i	$0.543756\pi$
$614$	114.543	+	427.949i	0.186552	+	0.696986i
$615$	189.374	−	64.4121i	0.307925	−	0.104735i
$616$	475.017	+	14.6629i	0.771131	+	0.0238034i
$617$	274.281	+	274.281i	0.444539	+	0.444539i	0.893534	−	0.448995i	$-0.148218\pi$
$617$	274.281	+	274.281i	0.444539	+	0.444539i	−0.448995	+	0.893534i	$0.648218\pi$
$618$	287.699	−	497.993i	0.465532	−	0.805815i
$619$	760.653			1.22884			0.614421	−	0.788978i	$-0.289390\pi$
$619$	760.653			1.22884			0.614421	+	0.788978i	$0.289390\pi$
$620$	238.692	−	15.6590i	0.384988	−	0.0252564i
$621$	740.478			1.19240
$622$	82.2246	−	142.327i	0.132194	−	0.228822i
$623$	−314.499	+	314.499i	−0.504814	+	0.504814i
$624$	575.648	+	333.192i	0.922513	+	0.533961i
$625$	−160.295	+	604.095i	−0.256473	+	0.966552i
$626$	592.903	−	158.694i	0.947129	−	0.253505i
$627$	231.532	+	6.95657i	0.369269	+	0.0110950i
$628$	−37.1908	+	138.494i	−0.0592210	+	0.220532i
$629$	−222.427			−0.353620
$630$	318.869	+	63.3165i	0.506141	+	0.100502i
$631$			1043.71i			1.65405i	0.562163	+	0.827026i	$0.309969\pi$
$631$			1043.71i			1.65405i	−0.562163	+	0.827026i	$0.690031\pi$
$632$	−746.108	−	0.612989i	−1.18055	−	0.000969919i
$633$	−55.9383	−	55.9383i	−0.0883701	−	0.0883701i
$634$	−30.1235	−	112.546i	−0.0475134	−	0.177517i
$635$	21.5553	+	63.3735i	0.0339454	+	0.0998008i
$636$	302.780	+	525.094i	0.476069	+	0.825620i
$637$	−337.726	+	337.726i	−0.530182	+	0.530182i
$638$	147.437	+	625.492i	0.231093	+	0.980395i
$639$	66.9988			0.104850
$640$	−354.868	−	532.606i	−0.554481	−	0.832197i
$641$	226.825			0.353861			0.176930	−	0.984223i	$-0.443383\pi$
$641$	226.825			0.353861			0.176930	+	0.984223i	$0.443383\pi$
$642$	256.291	−	443.629i	0.399208	−	0.691011i
$643$	−345.770	−	345.770i	−0.537746	−	0.537746i	0.385121	−	0.922866i	$-0.374160\pi$
$643$	−345.770	−	345.770i	−0.537746	−	0.537746i	−0.922866	+	0.385121i	$0.874160\pi$
$644$	−534.420	+	308.157i	−0.829844	+	0.478505i
$645$	232.551	+	114.506i	0.360545	+	0.177529i
$646$	66.9055	+	249.968i	0.103569	+	0.386948i
$647$	221.274	−	221.274i	0.342000	−	0.342000i	−0.515118	−	0.857119i	$-0.672252\pi$
$647$	221.274	−	221.274i	0.342000	−	0.342000i	0.857119	+	0.515118i	$0.172252\pi$
$648$	0.0618787	−	75.3165i	9.54918e−5	−	0.116229i
$649$	−94.2268	−	100.064i	−0.145188	−	0.154183i
$650$	732.045	−	955.879i	1.12622	−	1.47058i
$651$	111.507			0.171286
$652$	76.9372	−	286.506i	0.118002	−	0.439426i
$653$	624.289	−	624.289i	0.956033	−	0.956033i	−0.0430405	−	0.999073i	$-0.513704\pi$
$653$	624.289	−	624.289i	0.956033	−	0.956033i	0.999073	+	0.0430405i	$0.0137045\pi$
$654$	164.545	+	614.765i	0.251598	+	0.940008i
$655$	−537.359	−	264.591i	−0.820396	−	0.403955i
$656$	320.900	+	185.741i	0.489177	+	0.283141i
$657$	206.376	−	206.376i	0.314119	−	0.314119i
$658$	−738.317	−	426.537i	−1.12206	−	0.648233i
$659$		−	108.163i		−	0.164132i	−0.996627	−	0.0820659i	$-0.973848\pi$
$659$		−	108.163i		−	0.164132i	0.996627	−	0.0820659i	$-0.0261518\pi$
$660$	379.558	−	13.4695i	0.575087	−	0.0204083i
$661$	57.1206			0.0864154			0.0432077	−	0.999066i	$-0.486242\pi$
$661$	57.1206			0.0864154			0.0432077	+	0.999066i	$0.486242\pi$
$662$	−263.768	+	456.570i	−0.398440	+	0.689683i
$663$	−311.789	−	311.789i	−0.470270	−	0.470270i
$664$	607.136	+	608.134i	0.914361	+	0.915864i
$665$	−311.829	+	106.063i	−0.468916	+	0.159493i
$666$	−243.879	+	65.2757i	−0.366185	+	0.0980115i
$667$	−589.858	−	589.858i	−0.884345	−	0.884345i
$668$	−158.063	+	588.611i	−0.236622	+	0.881154i
$669$			485.637i			0.725915i
$670$	−526.824	−	104.609i	−0.786304	−	0.156133i
$671$	271.980	−	256.113i	0.405335	−	0.381688i
$672$	−148.816	−	258.574i	−0.221452	−	0.384783i
$673$	−250.393	−	250.393i	−0.372055	−	0.372055i	0.496170	−	0.868225i	$-0.334739\pi$
$673$	−250.393	−	250.393i	−0.372055	−	0.372055i	−0.868225	+	0.496170i	$0.834739\pi$
$674$	194.538	−	52.0691i	0.288632	−	0.0772539i
$675$	642.788	+	83.8308i	0.952279	+	0.124194i
$676$	−1423.63	+	820.896i	−2.10597	+	1.21434i
$677$	−266.578	+	266.578i	−0.393764	+	0.393764i	−0.876027	−	0.482262i	$-0.839815\pi$
$677$	−266.578	+	266.578i	−0.393764	+	0.393764i	0.482262	+	0.876027i	$0.339815\pi$
$678$	−215.318	−	124.393i	−0.317578	−	0.183470i
$679$		−	17.2512i		−	0.0254068i
$680$	136.295	+	401.794i	0.200433	+	0.590874i
$681$		−	430.870i		−	0.632702i
$682$	−256.107	+	60.3681i	−0.375524	+	0.0885163i
$683$	−110.070	−	110.070i	−0.161157	−	0.161157i	0.621922	−	0.783079i	$-0.286352\pi$
$683$	−110.070	−	110.070i	−0.161157	−	0.161157i	−0.783079	+	0.621922i	$0.786352\pi$
$684$	146.717	+	254.443i	0.214498	+	0.371992i
$685$	−416.026	−	1223.13i	−0.607337	−	1.78559i
$686$	718.201	−	192.231i	1.04694	−	0.280220i
$687$	−264.583	+	264.583i	−0.385128	+	0.385128i
$688$	123.850	+	464.249i	0.180015	+	0.674780i
$689$	−2113.66			−3.06771
$690$	−409.826	+	274.035i	−0.593951	+	0.397152i
$691$		−	403.102i		−	0.583360i	−0.956516	−	0.291680i	$-0.905786\pi$
$691$		−	403.102i		−	0.583360i	0.956516	−	0.291680i	$-0.0942142\pi$
$692$	−30.2849	+	112.778i	−0.0437643	+	0.162973i
$693$	−357.442	−	10.7397i	−0.515790	−	0.0154974i
$694$	95.0410	+	355.087i	0.136947	+	0.511653i
$695$	−192.553	+	391.057i	−0.277055	+	0.562672i
$696$	285.496	−	285.028i	0.410196	−	0.409523i
$697$	−173.809	−	173.809i	−0.249368	−	0.249368i
$698$	281.787	+	162.793i	0.403707	+	0.233228i
$699$		−	90.1514i		−	0.128972i
$700$	−498.802	+	207.000i	−0.712574	+	0.295715i
$701$		−	1212.30i		−	1.72939i	−0.502299	−	0.864694i	$-0.667512\pi$
$701$		−	1212.30i		−	1.72939i	0.502299	−	0.864694i	$-0.332488\pi$
$702$	−1081.27	−	624.668i	−1.54028	−	0.889841i
$703$	180.869	−	180.869i	0.257281	−	0.257281i
$704$	481.786	+	513.321i	0.684355	+	0.729149i
$705$	−611.332	−	301.014i	−0.867137	−	0.426971i
$706$	−427.685	+	114.472i	−0.605786	+	0.162142i
$707$	−221.866	+	221.866i	−0.313814	+	0.313814i
$708$	−22.3776	+	83.3317i	−0.0316067	+	0.117700i
$709$			757.535i			1.06846i	0.845341	+	0.534228i	$0.179398\pi$
$709$			757.535i			1.06846i	−0.845341	+	0.534228i	$0.820602\pi$
$710$	−92.5210	+	61.8652i	−0.130311	+	0.0871341i
$711$	561.421			0.789621
$712$	−658.857	−	0.541305i	−0.925362	−	0.000760260i
$713$	241.517	−	241.517i	0.338734	−	0.338734i
$714$	51.1373	+	191.056i	0.0716208	+	0.267586i
$715$	−620.461	+	1170.06i	−0.867778	+	1.63645i
$716$	−642.111	−	1113.58i	−0.896803	−	1.55527i
$717$	94.5784	−	94.5784i	0.131908	−	0.131908i
$718$	−527.194	+	912.549i	−0.734253	+	1.27096i
$719$	371.694			0.516959			0.258480	−	0.966017i	$-0.416779\pi$
$719$	371.694			0.516959			0.258480	+	0.966017i	$0.416779\pi$
$720$	267.355	+	400.548i	0.371326	+	0.556317i
$721$		−	899.573i		−	1.24767i
$722$	367.502	+	212.312i	0.509006	+	0.294060i
$723$	468.999	−	468.999i	0.648685	−	0.648685i
$724$	329.377	+	571.220i	0.454940	+	0.788977i
$725$	−445.261	−	578.819i	−0.614153	−	0.798370i
$726$	−409.328	+	83.5937i	−0.563812	+	0.115143i
$727$	299.214	−	299.214i	0.411573	−	0.411573i	−0.470713	−	0.882286i	$-0.656003\pi$
$727$	299.214	−	299.214i	0.411573	−	0.411573i	0.882286	+	0.470713i	$0.156003\pi$
$728$	1040.34	+	0.854726i	1.42904	+	0.00117407i
$729$		−	346.193i		−	0.474888i
$730$	−94.4291	+	475.555i	−0.129355	+	0.651445i
$731$		−	318.533i		−	0.435749i
$732$	−226.499	−	60.8232i	−0.309425	−	0.0830918i
$733$	390.495	+	390.495i	0.532735	+	0.532735i	0.921385	−	0.388650i	$-0.127059\pi$
$733$	390.495	+	390.495i	0.532735	+	0.532735i	−0.388650	+	0.921385i	$0.627059\pi$
$734$	533.601	−	142.821i	0.726977	−	0.194580i
$735$	162.089	−	55.1315i	0.220529	−	0.0750089i
$736$	−882.380	−	237.728i	−1.19889	−	0.323001i
$737$	590.553	+	17.7437i	0.801294	+	0.0240756i
$738$	−241.581	−	139.565i	−0.327345	−	0.189112i
$739$			623.945i			0.844310i	0.906524	+	0.422155i	$0.138726\pi$
$739$			623.945i			0.844310i	−0.906524	+	0.422155i	$0.861274\pi$
$740$	276.507	−	315.334i	0.373658	−	0.426127i
$741$	507.069			0.684304
$742$	820.929	+	474.264i	1.10637	+	0.639169i
$743$	109.679	−	109.679i	0.147617	−	0.147617i	−0.629436	−	0.777053i	$-0.716714\pi$
$743$	109.679	−	109.679i	0.147617	−	0.147617i	0.777053	+	0.629436i	$0.216714\pi$
$744$	116.704	+	116.896i	0.156861	+	0.157119i
$745$	152.802	+	75.2385i	0.205104	+	0.100991i
$746$	101.820	+	380.415i	0.136488	+	0.509939i
$747$	−457.224	−	457.224i	−0.612081	−	0.612081i
$748$	−220.886	−	411.129i	−0.295302	−	0.549638i
$749$		−	801.369i		−	1.06992i
$750$	−386.783	+	191.485i	−0.515710	+	0.255313i
$751$			167.466i			0.222990i	0.993765	+	0.111495i	$0.0355639\pi$
$751$			167.466i			0.222990i	−0.993765	+	0.111495i	$0.964436\pi$
$752$	−325.578	−	1220.42i	−0.432949	−	1.62290i
$753$	−87.2272	+	87.2272i	−0.115840	+	0.115840i
$754$	363.728	+	1358.94i	0.482397	+	1.80231i
$755$	777.265	+	382.718i	1.02949	+	0.506912i
$756$	279.796	+	485.234i	0.370100	+	0.641844i
$757$	−43.2145	−	43.2145i	−0.0570865	−	0.0570865i	0.677987	−	0.735074i	$-0.262852\pi$
$757$	−43.2145	−	43.2145i	−0.0570865	−	0.0570865i	−0.735074	+	0.677987i	$0.762852\pi$
$758$	−209.638	−	121.111i	−0.276567	−	0.159777i
$759$	394.810	−	371.777i	0.520172	−	0.489825i
$760$	−437.553	−	215.894i	−0.575727	−	0.284071i
$761$			717.901i			0.943365i	0.881768	+	0.471683i	$0.156353\pi$
$761$			717.901i			0.943365i	−0.881768	+	0.471683i	$0.843647\pi$
$762$	−23.1230	+	40.0248i	−0.0303451	+	0.0525260i
$763$	703.871	+	703.871i	0.922505	+	0.922505i
$764$	−746.084	+	430.207i	−0.976550	+	0.563098i
$765$	−102.805	−	302.252i	−0.134386	−	0.395101i
$766$	315.089	+	1177.22i	0.411343	+	1.53684i
$767$	−212.755	−	212.755i	−0.277386	−	0.277386i
$768$	115.319	−	426.635i	0.150155	−	0.555514i
$769$	−724.758			−0.942468			−0.471234	−	0.882008i	$-0.656191\pi$
$769$	−724.758			−0.942468			−0.471234	+	0.882008i	$0.656191\pi$
$770$	503.522	−	315.223i	0.653924	−	0.409381i
$771$		−	196.398i		−	0.254731i
$772$	−164.745	+	613.492i	−0.213400	+	0.794678i
$773$	418.517	−	418.517i	0.541420	−	0.541420i	−0.382525	−	0.923945i	$-0.624946\pi$
$773$	418.517	−	418.517i	0.541420	−	0.541420i	0.923945	+	0.382525i	$0.124946\pi$
$774$	−93.4799	−	349.254i	−0.120775	−	0.451233i
$775$	236.997	−	182.312i	0.305802	−	0.235241i
$776$	18.0850	−	18.0553i	0.0233054	−	0.0232671i
$777$	138.242	−	138.242i	0.177917	−	0.177917i
$778$	−45.9470	+	79.5323i	−0.0590579	+	0.102227i
$779$	282.670			0.362862
$780$	829.620	−	54.4256i	1.06361	−	0.0697764i
$781$	89.1311	−	83.9313i	0.114124	−	0.107466i
$782$	524.575	+	303.055i	0.670812	+	0.387539i
$783$	−535.570	+	535.570i	−0.683997	+	0.683997i
$784$	274.664	+	158.979i	0.350337	+	0.202779i
$785$	57.7215	+	169.703i	0.0735305	+	0.216183i
$786$	−106.941	−	399.547i	−0.136057	−	0.508330i
$787$	−157.467	−	157.467i	−0.200085	−	0.200085i	0.599951	−	0.800037i	$-0.295187\pi$
$787$	−157.467	−	157.467i	−0.200085	−	0.200085i	−0.800037	+	0.599951i	$0.795187\pi$
$788$	−516.604	−	138.727i	−0.655589	−	0.176049i
$789$	−747.245			−0.947079
$790$	−775.285	+	518.403i	−0.981374	+	0.656206i
$791$	−388.949			−0.491719
$792$	−362.844	−	385.958i	−0.458137	−	0.487321i
$793$	578.277	−	578.277i	0.729227	−	0.729227i
$794$	138.660	+	518.052i	0.174634	+	0.652458i
$795$	679.736	+	334.696i	0.855013	+	0.421001i
$796$	8.55817	+	14.8420i	0.0107515	+	0.0186457i
$797$	761.763	+	761.763i	0.955788	+	0.955788i	0.999063	−	0.0432753i	$-0.0137793\pi$
$797$	761.763	+	761.763i	0.955788	+	0.955788i	−0.0432753	+	0.999063i	$0.513779\pi$
$798$	−196.942	−	113.777i	−0.246795	−	0.142577i
$799$			837.360i			1.04801i
$800$	−739.056	−	306.261i	−0.923820	−	0.382827i
$801$	495.768			0.618936
$802$	−580.916	−	335.604i	−0.724334	−	0.418459i
$803$	16.0169	−	533.083i	0.0199464	−	0.663864i
$804$	−185.271	−	321.306i	−0.230437	−	0.399634i
$805$	−340.640	+	691.808i	−0.423155	+	0.859388i
$806$	−556.416	+	148.928i	−0.690343	+	0.184774i
$807$	247.832	−	247.832i	0.307103	−	0.307103i
$808$	−464.797	−	0.381869i	−0.575244	−	0.000472610i
$809$	−1222.82			−1.51152			−0.755761	−	0.654847i	$-0.772733\pi$
$809$	−1222.82			−1.51152			−0.755761	+	0.654847i	$0.772733\pi$
$810$	−52.3306	−	78.2618i	−0.0646057	−	0.0966195i
$811$	−464.051			−0.572196			−0.286098	−	0.958200i	$-0.592358\pi$
$811$	−464.051			−0.572196			−0.286098	+	0.958200i	$0.592358\pi$
$812$	163.650	−	609.416i	0.201540	−	0.750512i
$813$	−306.596	−	306.596i	−0.377117	−	0.377117i
$814$	−242.669	+	392.353i	−0.298119	+	0.482006i
$815$	−119.409	−	351.068i	−0.146515	−	0.430759i
$816$	−146.769	+	253.570i	−0.179864	+	0.310748i
$817$	259.018	+	259.018i	0.317036	+	0.317036i
$818$	898.545	+	519.104i	1.09847	+	0.634601i
$819$	−782.821			−0.955826
$820$	462.478	−	30.3400i	0.563998	−	0.0370000i
$821$			1111.10i			1.35335i	0.736284	+	0.676673i	$0.236579\pi$
$821$			1111.10i			1.35335i	−0.736284	+	0.676673i	$0.763421\pi$
$822$	446.282	−	772.494i	0.542922	−	0.939774i
$823$	−443.184	−	443.184i	−0.538498	−	0.538498i	0.384590	−	0.923088i	$-0.374343\pi$
$823$	−443.184	−	443.184i	−0.538498	−	0.538498i	−0.923088	+	0.384590i	$0.874343\pi$
$824$	943.050	−	941.502i	1.14448	−	1.14260i
$825$	384.813	−	278.033i	0.466441	−	0.337009i
$826$	34.8945	+	130.371i	0.0422451	+	0.157834i
$827$	−150.631	−	150.631i	−0.182141	−	0.182141i	0.610147	−	0.792288i	$-0.291110\pi$
$827$	−150.631	−	150.631i	−0.182141	−	0.182141i	−0.792288	+	0.610147i	$0.791110\pi$
$828$	664.107	+	178.337i	0.802062	+	0.215383i
$829$		−	1189.01i		−	1.43427i	−0.696937	−	0.717133i	$-0.745454\pi$
$829$		−	1189.01i		−	1.43427i	0.696937	−	0.717133i	$-0.254546\pi$
$830$	1053.59	+	209.207i	1.26938	+	0.252056i
$831$	80.4957			0.0968661
$832$	1087.94	+	1091.52i	1.30762	+	1.31192i
$833$	−148.767	−	148.767i	−0.178591	−	0.178591i
$834$	−290.766	+	77.8252i	−0.348640	+	0.0933156i
$835$	245.320	+	721.252i	0.293797	+	0.863774i
$836$	513.930	+	154.698i	0.614749	+	0.185046i
$837$	−219.289	−	219.289i	−0.261994	−	0.261994i
$838$	900.809	+	520.411i	1.07495	+	0.621016i
$839$	1406.47			1.67636			0.838181	−	0.545393i	$-0.183620\pi$
$839$	1406.47			1.67636			0.838181	+	0.545393i	$0.183620\pi$
$840$	−334.431	−	165.012i	−0.398132	−	0.196443i
$841$	12.2609			0.0145790
$842$	−610.295	−	352.577i	−0.724816	−	0.418737i
$843$	−150.216	+	150.216i	−0.178193	+	0.178193i
$844$	−91.5617	−	158.790i	−0.108485	−	0.188140i
$845$	−907.426	+	1842.90i	−1.07388	+	2.18094i
$846$	245.740	+	918.121i	0.290473	+	1.08525i
$847$	−488.973	+	433.490i	−0.577300	+	0.511795i
$848$	362.008	+	1356.98i	0.426896	+	1.60021i
$849$	904.679			1.06558
$850$	421.060	+	322.462i	0.495365	+	0.379367i
$851$		−	598.845i		−	0.703696i
$852$	−74.2265	−	19.9325i	−0.0871203	−	0.0233950i
$853$	453.619	+	453.619i	0.531792	+	0.531792i	0.921105	−	0.389313i	$-0.127288\pi$
$853$	453.619	+	453.619i	0.531792	+	0.531792i	−0.389313	+	0.921105i	$0.627288\pi$
$854$	−354.353	+	94.8447i	−0.414934	+	0.111059i
$855$	329.377	+	162.182i	0.385236	+	0.189687i
$856$	840.100	−	838.721i	0.981425	−	0.979814i
$857$	783.087	−	783.087i	0.913754	−	0.913754i	−0.0828113	−	0.996565i	$-0.526390\pi$
$857$	783.087	−	783.087i	0.913754	−	0.913754i	0.996565	+	0.0828113i	$0.0263899\pi$
$858$	−890.149	+	209.821i	−1.03747	+	0.244546i
$859$	472.093			0.549585			0.274792	−	0.961504i	$-0.411391\pi$
$859$	472.093			0.549585			0.274792	+	0.961504i	$0.411391\pi$
$860$	451.583	+	395.980i	0.525097	+	0.460442i
$861$	216.050			0.250930
$862$	−913.019	−	527.465i	−1.05919	−	0.611908i
$863$	57.4206	+	57.4206i	0.0665360	+	0.0665360i	0.739592	−	0.673056i	$-0.235019\pi$
$863$	57.4206	+	57.4206i	0.0665360	+	0.0665360i	−0.673056	+	0.739592i	$0.735019\pi$
$864$	−215.849	+	801.169i	−0.249825	+	0.927279i
$865$	47.0033	+	138.191i	0.0543390	+	0.159759i
$866$	305.547	−	81.7813i	0.352825	−	0.0944357i
$867$	−215.444	+	215.444i	−0.248494	+	0.248494i
$868$	249.525	+	67.0065i	0.287471	+	0.0771964i
$869$	746.879	−	703.307i	0.859470	−	0.809329i
$870$	98.2148	−	494.620i	0.112891	−	0.568529i
$871$	1293.35			1.48490
$872$	−1.21148	+	1474.57i	−0.00138931	+	1.69102i
$873$	−13.5971	+	13.5971i	−0.0155752	+	0.0155752i
$874$	−672.996	+	180.131i	−0.770019	+	0.206100i
$875$	−374.021	+	561.975i	−0.427452	+	0.642257i
$876$	−290.038	+	167.242i	−0.331093	+	0.190915i
$877$	844.684	−	844.684i	0.963152	−	0.963152i	−0.0361927	−	0.999345i	$-0.511523\pi$
$877$	844.684	−	844.684i	0.963152	−	0.963152i	0.999345	+	0.0361927i	$0.0115230\pi$
$878$	−409.448	+	708.736i	−0.466342	+	0.807217i
$879$		−	957.672i		−	1.08950i
$880$	857.449	+	197.941i	0.974374	+	0.224933i
$881$	−75.9756			−0.0862379			−0.0431189	−	0.999070i	$-0.513729\pi$
$881$	−75.9756			−0.0862379			−0.0431189	+	0.999070i	$0.513729\pi$
$882$	−206.774	−	119.456i	−0.234437	−	0.135438i
$883$	−729.780	−	729.780i	−0.826478	−	0.826478i	0.160550	−	0.987028i	$-0.448673\pi$
$883$	−729.780	−	729.780i	−0.826478	−	0.826478i	−0.987028	+	0.160550i	$0.948673\pi$
$884$	−510.347	−	885.065i	−0.577315	−	1.00121i
$885$	34.7308	+	102.110i	0.0392439	+	0.115379i
$886$	−211.488	−	790.150i	−0.238700	−	0.891817i
$887$	−107.883	−	107.883i	−0.121627	−	0.121627i	0.643673	−	0.765300i	$-0.277410\pi$
$887$	−107.883	−	107.883i	−0.121627	−	0.121627i	−0.765300	+	0.643673i	$0.777410\pi$
$888$	289.608	+	0.237937i	0.326135	+	0.000267947i
$889$			72.3007i			0.0813281i
$890$	−684.623	+	457.780i	−0.769239	+	0.514360i
$891$	70.9959	+	75.3943i	0.0796811	+	0.0846176i
$892$	−291.828	+	1086.73i	−0.327161	+	1.21831i
$893$	−680.908	−	680.908i	−0.762495	−	0.762495i
$894$	30.4095	+	113.614i	0.0340151	+	0.127085i
$895$	−1441.53	−	709.795i	−1.61065	−	0.793067i
$896$	−177.632	−	668.050i	−0.198249	−	0.745591i
$897$	839.437	−	839.437i	0.935828	−	0.935828i
$898$	357.731	−	619.217i	0.398364	−	0.689551i
$899$			349.367i			0.388617i
$900$	556.303	+	229.994i	0.618115	+	0.255549i
$901$		−	931.055i		−	1.03336i
$902$	−496.221	+	116.966i	−0.550134	+	0.129674i
$903$	197.973	+	197.973i	0.219239	+	0.219239i
$904$	−407.078	−	407.748i	−0.450308	−	0.451048i
$905$	739.445	+	364.096i	0.817067	+	0.402316i
$906$	154.685	+	577.926i	0.170734	+	0.637888i
$907$	−1025.92	+	1025.92i	−1.13111	+	1.13111i	−0.141118	+	0.989993i	$0.545070\pi$
$907$	−1025.92	+	1025.92i	−1.13111	+	1.13111i	−0.989993	+	0.141118i	$0.954930\pi$
$908$	258.917	−	964.180i	0.285151	−	1.06187i
$909$	349.744			0.384756
$910$	1081.03	−	722.839i	1.18794	−	0.794329i
$911$			1056.66i			1.15989i	0.814655	+	0.579946i	$0.196926\pi$
$911$			1056.66i			1.15989i	−0.814655	+	0.579946i	$0.803074\pi$
$912$	−86.8462	−	325.540i	−0.0952260	−	0.356952i
$913$	−1181.04	−	35.4854i	−1.29358	−	0.0388668i
$914$	−143.178	+	38.3224i	−0.156650	+	0.0419282i
$915$	−277.539	+	94.3999i	−0.303322	+	0.103169i
$916$	−751.063	+	433.078i	−0.819937	+	0.472792i
$917$	−457.459	−	457.459i	−0.498865	−	0.498865i
$918$	275.163	−	476.295i	0.299742	−	0.518840i
$919$		−	1251.77i		−	1.36210i	−0.732235	−	0.681052i	$-0.761523\pi$
$919$		−	1251.77i		−	1.36210i	0.732235	−	0.681052i	$-0.238477\pi$
$920$	−1081.76	+	366.950i	−1.17583	+	0.398858i
$921$			382.398i			0.415198i
$922$	79.0150	−	136.771i	0.0856995	−	0.148342i
$923$	189.509	−	189.509i	0.205318	−	0.205318i
$924$	392.807	+	118.239i	0.425116	+	0.127965i
$925$	67.7963	−	519.841i	0.0732933	−	0.561990i
$926$	−102.913	−	384.498i	−0.111137	−	0.415224i
$927$	−709.030	+	709.030i	−0.764866	+	0.764866i
$928$	810.148	−	466.261i	0.873004	−	0.502437i
$929$			129.701i			0.139614i	0.997561	+	0.0698068i	$0.0222383\pi$
$929$			129.701i			0.139614i	−0.997561	+	0.0698068i	$0.977762\pi$
$930$	202.522	+	40.2140i	0.217766	+	0.0432408i
$931$	241.942			0.259874
$932$	54.1735	−	201.736i	0.0581261	−	0.216455i
$933$	100.325	−	100.325i	0.107529	−	0.107529i
$934$	374.333	−	100.192i	0.400785	−	0.107272i
$935$	−515.405	−	273.310i	−0.551235	−	0.292310i
$936$	−819.309	−	820.656i	−0.875330	−	0.876769i
$937$	−419.471	+	419.471i	−0.447674	+	0.447674i	−0.894581	−	0.446907i	$-0.852526\pi$
$937$	−419.471	+	419.471i	−0.447674	+	0.447674i	0.446907	+	0.894581i	$0.352526\pi$
$938$	−502.328	−	290.203i	−0.535531	−	0.309384i
$939$	529.793			0.564210
$940$	−1187.12	−	1040.95i	−1.26290	−	1.10740i
$941$			1347.04i			1.43150i	0.698355	+	0.715751i	$0.253916\pi$
$941$			1347.04i			1.43150i	−0.698355	+	0.715751i	$0.746084\pi$
$942$	−61.9194	+	107.180i	−0.0657318	+	0.113779i
$943$	467.951	−	467.951i	0.496237	−	0.496237i
$944$	−100.151	+	173.028i	−0.106092	+	0.183293i
$945$	628.136	+	309.289i	0.664695	+	0.327290i
$946$	−561.880	−	347.521i	−0.593954	−	0.367359i
$947$	−152.173	+	152.173i	−0.160689	+	0.160689i	−0.782872	−	0.622183i	$-0.786246\pi$
$947$	−152.173	+	152.173i	−0.160689	+	0.160689i	0.622183	+	0.782872i	$0.286246\pi$
$948$	−621.986	−	167.026i	−0.656103	−	0.176187i
$949$		−	1167.49i		−	1.23023i
$950$	−604.603	+	80.1759i	−0.636424	+	0.0843957i
$951$		−	100.566i		−	0.105748i
$952$	−0.376503	+	458.265i	−0.000395486	+	0.481371i
$953$	−607.043	−	607.043i	−0.636982	−	0.636982i	0.312828	−	0.949810i	$-0.398724\pi$
$953$	−607.043	−	607.043i	−0.636982	−	0.636982i	−0.949810	+	0.312828i	$0.898724\pi$
$954$	−273.237	−	1020.85i	−0.286412	−	1.07008i
$955$	−475.555	+	965.808i	−0.497963	+	1.01132i
$956$	268.477	−	154.809i	0.280833	−	0.161934i
$957$	−16.6591	+	554.455i	−0.0174076	+	0.579367i
$958$	716.640	−	1240.47i	0.748059	−	1.29486i
$959$		−	1395.43i		−	1.45509i
$960$	−177.031	−	523.298i	−0.184407	−	0.545102i
$961$	817.952			0.851147
$962$	−505.187	+	874.456i	−0.525142	+	0.908998i
$963$	−631.627	+	631.627i	−0.655896	+	0.655896i
$964$	1331.33	−	767.673i	1.38105	−	0.796342i
$965$	255.690	+	751.739i	0.264964	+	0.779004i
$966$	−514.385	+	137.678i	−0.532490	+	0.142524i
$967$	448.623	+	448.623i	0.463933	+	0.463933i	0.899942	−	0.436009i	$-0.143609\pi$
$967$	448.623	+	448.623i	0.463933	+	0.463933i	−0.436009	+	0.899942i	$0.643609\pi$
$968$	−966.206	−	58.9102i	−0.998146	−	0.0608576i
$969$			223.361i			0.230507i
$970$	6.22148	−	31.3321i	0.00641390	−	0.0323011i
$971$		−	701.291i		−	0.722235i	−0.932520	−	0.361118i	$-0.882395\pi$
$971$		−	701.291i		−	0.722235i	0.932520	−	0.361118i	$-0.117605\pi$
$972$	258.950	−	964.301i	0.266409	−	0.992080i
$973$	−332.911	+	332.911i	−0.342149	+	0.342149i
$974$	998.598	−	267.280i	1.02525	−	0.274415i
$975$	823.727	−	633.658i	0.844848	−	0.649906i
$976$	−470.298	−	272.214i	−0.481863	−	0.278908i
$977$	−1130.83	−	1130.83i	−1.15745	−	1.15745i	−0.985021	−	0.172433i	$-0.944837\pi$
$977$	−1130.83	−	1130.83i	−1.15745	−	1.15745i	−0.172433	−	0.985021i	$-0.555163\pi$
$978$	128.094	−	221.724i	0.130975	−	0.226712i
$979$	659.538	−	621.061i	0.673686	−	0.634383i
$980$	395.844	−	25.9686i	0.403922	−	0.0264986i
$981$		−	1109.56i		−	1.13105i
$982$	−259.368	−	149.841i	−0.264122	−	0.152587i
$983$	−351.794	−	351.794i	−0.357878	−	0.357878i	0.505152	−	0.863030i	$-0.331436\pi$
$983$	−351.794	−	351.794i	−0.357878	−	0.357878i	−0.863030	+	0.505152i	$0.831436\pi$
$984$	226.121	+	226.492i	0.229797	+	0.230175i
$985$	−633.018	+	215.309i	−0.642658	+	0.218588i
$986$	−598.606	+	160.220i	−0.607105	+	0.162495i
$987$	−520.432	−	520.432i	−0.527287	−	0.527287i
$988$	1134.69	+	304.706i	1.14848	+	0.308407i
$989$	857.593			0.867132
$990$	−645.323	−	148.414i	−0.651841	−	0.149913i
$991$			288.167i			0.290784i	0.989374	+	0.145392i	$0.0464443\pi$
$991$			288.167i			0.290784i	−0.989374	+	0.145392i	$0.953556\pi$
$992$	190.910	+	331.714i	0.192450	+	0.334390i
$993$	−321.832	+	321.832i	−0.324100	+	0.324100i
$994$	−116.126	+	31.0818i	−0.116827	+	0.0312694i
$995$	19.2130	+	9.46028i	0.0193095	+	0.00950782i
$996$	370.522	+	642.575i	0.372010	+	0.645156i
$997$	−921.234	+	921.234i	−0.924006	+	0.924006i	−0.997310	−	0.0733035i	$-0.976646\pi$
$997$	−921.234	+	921.234i	−0.924006	+	0.924006i	0.0733035	+	0.997310i	$0.476646\pi$
$998$	−500.186	−	288.965i	−0.501189	−	0.289545i
$999$	−543.730			−0.544274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.i.a.87.58	yes	136
4.3	odd	2	inner	220.3.i.a.87.24	yes	136
5.3	odd	4	inner	220.3.i.a.43.45	yes	136
11.10	odd	2	inner	220.3.i.a.87.11	yes	136
20.3	even	4	inner	220.3.i.a.43.11	✓	136
44.43	even	2	inner	220.3.i.a.87.45	yes	136
55.43	even	4	inner	220.3.i.a.43.24	yes	136
220.43	odd	4	inner	220.3.i.a.43.58	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.i.a.43.11	✓	136	20.3	even	4	inner
220.3.i.a.43.24	yes	136	55.43	even	4	inner
220.3.i.a.43.45	yes	136	5.3	odd	4	inner
220.3.i.a.43.58	yes	136	220.43	odd	4	inner
220.3.i.a.87.11	yes	136	11.10	odd	2	inner
220.3.i.a.87.24	yes	136	4.3	odd	2	inner
220.3.i.a.87.45	yes	136	44.43	even	2	inner
220.3.i.a.87.58	yes	136	1.1	even	1	trivial

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+(1.73178 + 1.00047i) q^{2} +(1.22071 + 1.22071i) q^{3} +(1.99810 + 3.46520i) q^{4} +(4.48571 + 2.20872i) q^{5} +(0.892710 + 3.33529i) q^{6} +(3.81872 + 3.81872i) q^{7} +(-0.00657265 + 8.00000i) q^{8} -6.01972i q^{9} +(5.55847 + 8.31284i) q^{10} +(-7.54107 - 8.00826i) q^{11} +(-1.79090 + 6.66912i) q^{12} +(-17.0270 - 17.0270i) q^{13} +(2.79264 + 10.4337i) q^{14} +(2.77954 + 8.17197i) q^{15} +(-8.01517 + 13.8476i) q^{16} +(7.50031 - 7.50031i) q^{17} +(6.02258 - 10.4248i) q^{18} +12.1979i q^{19} +(1.30925 + 19.9571i) q^{20} +9.32312i q^{21} +(-5.04739 - 21.4132i) q^{22} +(20.1933 + 20.1933i) q^{23} +(-9.77372 + 9.75767i) q^{24} +(15.2431 + 19.8153i) q^{25} +(-12.4519 - 46.5220i) q^{26} +(18.3348 - 18.3348i) q^{27} +(-5.60242 + 20.8628i) q^{28} -29.2106 q^{29} +(-3.36230 + 16.9329i) q^{30} -11.9603i q^{31} +(-27.7347 + 15.9620i) q^{32} +(0.570308 - 18.9813i) q^{33} +(20.4927 - 5.48500i) q^{34} +(8.69517 + 25.5641i) q^{35} +(20.8595 - 12.0280i) q^{36} +(-14.8278 - 14.8278i) q^{37} +(-12.2037 + 21.1241i) q^{38} -41.5701i q^{39} +(-17.6992 + 35.8711i) q^{40} -23.1736i q^{41} +(-9.32754 + 16.1456i) q^{42} +(21.2346 - 21.2346i) q^{43} +(12.6824 - 42.1326i) q^{44} +(13.2959 - 27.0027i) q^{45} +(14.7674 + 55.1731i) q^{46} +(-55.8217 + 55.8217i) q^{47} +(-26.6882 + 7.11976i) q^{48} -19.8347i q^{49} +(6.57292 + 49.5661i) q^{50} +18.3114 q^{51} +(24.9802 - 93.0236i) q^{52} +(62.0677 - 62.0677i) q^{53} +(50.0952 - 13.4083i) q^{54} +(-16.1390 - 52.5788i) q^{55} +(-30.5749 + 30.5247i) q^{56} +(-14.8901 + 14.8901i) q^{57} +(-50.5863 - 29.2245i) q^{58} +12.4952 q^{59} +(-22.7637 + 25.9601i) q^{60} +33.9624i q^{61} +(11.9659 - 20.7125i) q^{62} +(22.9876 - 22.9876i) q^{63} +(-63.9999 - 0.105162i) q^{64} +(-38.7702 - 113.986i) q^{65} +(19.9779 - 32.3007i) q^{66} +(-37.9793 + 37.9793i) q^{67} +(40.9764 + 11.0037i) q^{68} +49.3004i q^{69} +(-10.5182 + 52.9707i) q^{70} +11.1299i q^{71} +(48.1578 + 0.0395656i) q^{72} +(34.2833 + 34.2833i) q^{73} +(-10.8436 - 40.5134i) q^{74} +(-5.58138 + 42.7963i) q^{75} +(-42.2682 + 24.3727i) q^{76} +(1.78408 - 59.3786i) q^{77} +(41.5899 - 71.9902i) q^{78} +93.2636i q^{79} +(-66.5393 + 44.4131i) q^{80} -9.41456 q^{81} +(23.1846 - 40.1315i) q^{82} +(75.9544 - 75.9544i) q^{83} +(-32.3064 + 18.6285i) q^{84} +(50.2103 - 17.0781i) q^{85} +(58.0183 - 15.5289i) q^{86} +(-35.6578 - 35.6578i) q^{87} +(64.1156 - 60.2759i) q^{88} +82.3572i q^{89} +(50.0410 - 33.4605i) q^{90} -130.043i q^{91} +(-29.6254 + 110.322i) q^{92} +(14.6001 - 14.6001i) q^{93} +(-152.519 + 40.8225i) q^{94} +(-26.9418 + 54.7162i) q^{95} +(-53.3411 - 14.3710i) q^{96} +(-2.25877 - 2.25877i) q^{97} +(19.8441 - 34.3493i) q^{98} +(-48.2075 + 45.3951i) 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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