LMFDB - Embedded newform 220.3.i.a.43.4

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			43.4
Character	$\chi$	$=$	220.43
Dual form			220.3.i.a.87.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.97634 - 0.306706i) q^{2} +(-0.409452 + 0.409452i) q^{3} +(3.81186 + 1.21231i) q^{4} +(4.83179 + 1.28601i) q^{5} +(0.934798 - 0.683636i) q^{6} +(5.71256 - 5.71256i) q^{7} +(-7.16172 - 3.56507i) q^{8} +8.66470i q^{9} +(-9.15485 - 4.02353i) q^{10} +(4.85945 - 9.86842i) q^{11} +(-2.05716 + 1.06439i) q^{12} +(-5.84564 + 5.84564i) q^{13} +(-13.0421 + 9.53790i) q^{14} +(-2.50494 + 1.45183i) q^{15} +(13.0606 + 9.24234i) q^{16} +(-3.24226 - 3.24226i) q^{17} +(2.65752 - 17.1244i) q^{18} +8.60845i q^{19} +(16.8591 + 10.7597i) q^{20} +4.67804i q^{21} +(-12.6306 + 18.0130i) q^{22} +(19.1843 - 19.1843i) q^{23} +(4.39210 - 1.47266i) q^{24} +(21.6924 + 12.4274i) q^{25} +(13.3459 - 9.76009i) q^{26} +(-7.23284 - 7.23284i) q^{27} +(28.7009 - 14.8501i) q^{28} +43.1511 q^{29} +(5.39591 - 2.10103i) q^{30} +18.8814i q^{31} +(-22.9775 - 22.2718i) q^{32} +(2.05093 + 6.03035i) q^{33} +(5.41339 + 7.40223i) q^{34} +(34.9483 - 20.2555i) q^{35} +(-10.5043 + 33.0286i) q^{36} +(34.1716 - 34.1716i) q^{37} +(2.64026 - 17.0133i) q^{38} -4.78701i q^{39} +(-30.0192 - 26.4357i) q^{40} +24.9595i q^{41} +(1.43478 - 9.24540i) q^{42} +(24.3874 + 24.3874i) q^{43} +(30.4872 - 31.7259i) q^{44} +(-11.1428 + 41.8660i) q^{45} +(-43.7987 + 32.0308i) q^{46} +(-1.45945 - 1.45945i) q^{47} +(-9.13198 + 1.56339i) q^{48} -16.2667i q^{49} +(-39.0600 - 31.2140i) q^{50} +2.65510 q^{51} +(-29.3695 + 15.1960i) q^{52} +(-45.7272 - 45.7272i) q^{53} +(12.0762 + 16.5129i) q^{54} +(36.1707 - 41.4329i) q^{55} +(-61.2775 + 20.5461i) q^{56} +(-3.52474 - 3.52474i) q^{57} +(-85.2814 - 13.2347i) q^{58} -43.3211 q^{59} +(-11.3086 + 2.49739i) q^{60} +108.835i q^{61} +(5.79104 - 37.3161i) q^{62} +(49.4976 + 49.4976i) q^{63} +(38.5806 + 51.0641i) q^{64} +(-35.7624 + 20.7274i) q^{65} +(-2.20380 - 12.5471i) q^{66} +(6.63930 + 6.63930i) q^{67} +(-8.42841 - 16.2897i) q^{68} +15.7101i q^{69} +(-75.2823 + 29.3130i) q^{70} -19.9354i q^{71} +(30.8902 - 62.0542i) q^{72} +(-25.1503 + 25.1503i) q^{73} +(-78.0154 + 57.0541i) q^{74} +(-13.9704 + 3.79356i) q^{75} +(-10.4361 + 32.8142i) q^{76} +(-28.6141 - 84.1339i) q^{77} +(-1.46821 + 9.46078i) q^{78} -122.741i q^{79} +(51.2203 + 61.4530i) q^{80} -72.0593 q^{81} +(7.65523 - 49.3286i) q^{82} +(-56.7102 - 56.7102i) q^{83} +(-5.67124 + 17.8320i) q^{84} +(-11.4963 - 19.8355i) q^{85} +(-40.7182 - 55.6777i) q^{86} +(-17.6683 + 17.6683i) q^{87} +(-69.9836 + 53.3507i) q^{88} -51.9183i q^{89} +(34.8626 - 79.3240i) q^{90} +66.7871i q^{91} +(96.3854 - 49.8706i) q^{92} +(-7.73102 - 7.73102i) q^{93} +(2.43675 + 3.33200i) q^{94} +(-11.0705 + 41.5942i) q^{95} +(18.5274 - 0.288965i) q^{96} +(-41.3583 + 41.3583i) q^{97} +(-4.98910 + 32.1486i) q^{98} +(85.5069 + 42.1057i) 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 $

$2$	−1.97634	−	0.306706i	−0.988171	−	0.153353i
$2$	−1.97634	−	0.306706i	−0.988171	−	0.153353i
$3$	−0.409452	+	0.409452i	−0.136484	+	0.136484i	−0.772048	−	0.635564i	$-0.780768\pi$
$3$	−0.409452	+	0.409452i	−0.136484	+	0.136484i	0.635564	+	0.772048i	$0.280768\pi$
$4$	3.81186	+	1.21231i	0.952966	+	0.303078i
$5$	4.83179	+	1.28601i	0.966358	+	0.257201i
$5$	4.83179	+	1.28601i	0.966358	+	0.257201i
$6$	0.934798	−	0.683636i	0.155800	−	0.113939i
$7$	5.71256	−	5.71256i	0.816080	−	0.816080i	−0.169457	−	0.985538i	$-0.554202\pi$
$7$	5.71256	−	5.71256i	0.816080	−	0.816080i	0.985538	+	0.169457i	$0.0542015\pi$
$8$	−7.16172	−	3.56507i	−0.895216	−	0.445633i
$9$			8.66470i			0.962744i
$10$	−9.15485	−	4.02353i	−0.915485	−	0.402353i
$11$	4.85945	−	9.86842i	0.441768	−	0.897129i
$11$	4.85945	−	9.86842i	0.441768	−	0.897129i
$12$	−2.05716	+	1.06439i	−0.171430	+	0.0886992i
$13$	−5.84564	+	5.84564i	−0.449665	+	0.449665i	−0.895243	−	0.445578i	$-0.852998\pi$
$13$	−5.84564	+	5.84564i	−0.449665	+	0.449665i	0.445578	+	0.895243i	$0.352998\pi$
$14$	−13.0421	+	9.53790i	−0.931576	+	0.681279i
$15$	−2.50494	+	1.45183i	−0.166996	+	0.0967885i
$16$	13.0606	+	9.24234i	0.816287	+	0.577646i
$17$	−3.24226	−	3.24226i	−0.190721	−	0.190721i	0.605287	−	0.796008i	$-0.293059\pi$
$17$	−3.24226	−	3.24226i	−0.190721	−	0.190721i	−0.796008	+	0.605287i	$0.793059\pi$
$18$	2.65752	−	17.1244i	0.147640	−	0.951356i
$19$			8.60845i			0.453076i	0.974002	+	0.226538i	$0.0727408\pi$
$19$			8.60845i			0.453076i	−0.974002	+	0.226538i	$0.927259\pi$
$20$	16.8591	+	10.7597i	0.842954	+	0.537986i
$21$			4.67804i			0.222764i
$22$	−12.6306	+	18.0130i	−0.574120	+	0.818771i
$23$	19.1843	−	19.1843i	0.834101	−	0.834101i	−0.153974	−	0.988075i	$-0.549207\pi$
$23$	19.1843	−	19.1843i	0.834101	−	0.834101i	0.988075	+	0.153974i	$0.0492072\pi$
$24$	4.39210	−	1.47266i	0.183004	−	0.0613607i
$25$	21.6924	+	12.4274i	0.867695	+	0.497097i
$26$	13.3459	−	9.76009i	0.513303	−	0.375388i
$27$	−7.23284	−	7.23284i	−0.267883	−	0.267883i
$28$	28.7009	−	14.8501i	1.02503	−	0.530360i
$29$	43.1511			1.48797			0.743985	−	0.668197i	$-0.232934\pi$
$29$	43.1511			1.48797			0.743985	+	0.668197i	$0.232934\pi$
$30$	5.39591	−	2.10103i	0.179864	−	0.0700343i
$31$			18.8814i			0.609077i	0.952500	+	0.304539i	$0.0985022\pi$
$31$			18.8814i			0.609077i	−0.952500	+	0.304539i	$0.901498\pi$
$32$	−22.9775	−	22.2718i	−0.718048	−	0.695994i
$33$	2.05093	+	6.03035i	0.0621495	+	0.182738i
$34$	5.41339	+	7.40223i	0.159217	+	0.217713i
$35$	34.9483	−	20.2555i	0.998522	−	0.578729i
$36$	−10.5043	+	33.0286i	−0.291787	+	0.917462i
$37$	34.1716	−	34.1716i	0.923556	−	0.923556i	−0.0737227	−	0.997279i	$-0.523488\pi$
$37$	34.1716	−	34.1716i	0.923556	−	0.923556i	0.997279	+	0.0737227i	$0.0234880\pi$
$38$	2.64026	−	17.0133i	0.0694806	−	0.447717i
$39$		−	4.78701i		−	0.122744i
$40$	−30.0192	−	26.4357i	−0.750481	−	0.660892i
$41$			24.9595i			0.608769i	0.952549	+	0.304384i	$0.0984507\pi$
$41$			24.9595i			0.608769i	−0.952549	+	0.304384i	$0.901549\pi$
$42$	1.43478	−	9.24540i	0.0341615	−	0.220129i
$43$	24.3874	+	24.3874i	0.567150	+	0.567150i	0.931329	−	0.364179i	$-0.118650\pi$
$43$	24.3874	+	24.3874i	0.567150	+	0.567150i	−0.364179	+	0.931329i	$0.618650\pi$
$44$	30.4872	−	31.7259i	0.692890	−	0.721043i
$45$	−11.1428	+	41.8660i	−0.247619	+	0.930356i
$46$	−43.7987	+	32.0308i	−0.952147	+	0.696323i
$47$	−1.45945	−	1.45945i	−0.0310521	−	0.0310521i	0.691410	−	0.722462i	$-0.256990\pi$
$47$	−1.45945	−	1.45945i	−0.0310521	−	0.0310521i	−0.722462	+	0.691410i	$0.756990\pi$
$48$	−9.13198	+	1.56339i	−0.190249	+	0.0325707i
$49$		−	16.2667i		−	0.331974i
$50$	−39.0600	−	31.2140i	−0.781200	−	0.624280i
$51$	2.65510			0.0520607
$52$	−29.3695	+	15.1960i	−0.564798	+	0.292231i
$53$	−45.7272	−	45.7272i	−0.862777	−	0.862777i	0.128883	−	0.991660i	$-0.458861\pi$
$53$	−45.7272	−	45.7272i	−0.862777	−	0.862777i	−0.991660	+	0.128883i	$0.958861\pi$
$54$	12.0762	+	16.5129i	0.223634	+	0.305795i
$55$	36.1707	−	41.4329i	0.657649	−	0.753325i
$56$	−61.2775	+	20.5461i	−1.09424	+	0.366895i
$57$	−3.52474	−	3.52474i	−0.0618376	−	0.0618376i
$58$	−85.2814	−	13.2347i	−1.47037	−	0.228185i
$59$	−43.3211			−0.734255			−0.367128	−	0.930171i	$-0.619659\pi$
$59$	−43.3211			−0.734255			−0.367128	+	0.930171i	$0.619659\pi$
$60$	−11.3086	+	2.49739i	−0.188476	+	0.0416232i
$61$			108.835i			1.78417i	0.451864	+	0.892087i	$0.350759\pi$
$61$			108.835i			1.78417i	−0.451864	+	0.892087i	$0.649241\pi$
$62$	5.79104	−	37.3161i	0.0934038	−	0.601873i
$63$	49.4976	+	49.4976i	0.785677	+	0.785677i
$64$	38.5806	+	51.0641i	0.602822	+	0.797876i
$65$	−35.7624	+	20.7274i	−0.550191	+	0.318883i
$66$	−2.20380	−	12.5471i	−0.0333909	−	0.190107i
$67$	6.63930	+	6.63930i	0.0990941	+	0.0990941i	0.754916	−	0.655822i	$-0.227678\pi$
$67$	6.63930	+	6.63930i	0.0990941	+	0.0990941i	−0.655822	+	0.754916i	$0.727678\pi$
$68$	−8.42841	−	16.2897i	−0.123947	−	0.239554i
$69$			15.7101i			0.227683i
$70$	−75.2823	+	29.3130i	−1.07546	+	0.418757i
$71$		−	19.9354i		−	0.280781i	−0.990096	−	0.140390i	$-0.955164\pi$
$71$		−	19.9354i		−	0.280781i	0.990096	−	0.140390i	$-0.0448358\pi$
$72$	30.8902	−	62.0542i	0.429031	−	0.861864i
$73$	−25.1503	+	25.1503i	−0.344524	+	0.344524i	−0.858065	−	0.513541i	$-0.828333\pi$
$73$	−25.1503	+	25.1503i	−0.344524	+	0.344524i	0.513541	+	0.858065i	$0.328333\pi$
$74$	−78.0154	+	57.0541i	−1.05426	+	0.771002i
$75$	−13.9704	+	3.79356i	−0.186272	+	0.0505808i
$76$	−10.4361	+	32.8142i	−0.137318	+	0.431766i
$77$	−28.6141	−	84.1339i	−0.371611	−	1.09265i
$78$	−1.46821	+	9.46078i	−0.0188232	+	0.121292i
$79$		−	122.741i		−	1.55369i	−0.629695	−	0.776843i	$-0.716820\pi$
$79$		−	122.741i		−	1.55369i	0.629695	−	0.776843i	$-0.283180\pi$
$80$	51.2203	+	61.4530i	0.640254	+	0.768163i
$81$	−72.0593			−0.889621
$82$	7.65523	−	49.3286i	0.0933565	−	0.601568i
$83$	−56.7102	−	56.7102i	−0.683255	−	0.683255i	0.277477	−	0.960732i	$-0.410502\pi$
$83$	−56.7102	−	56.7102i	−0.683255	−	0.683255i	−0.960732	+	0.277477i	$0.910502\pi$
$84$	−5.67124	+	17.8320i	−0.0675148	+	0.212286i
$85$	−11.4963	−	19.8355i	−0.135251	−	0.233358i
$86$	−40.7182	−	55.6777i	−0.473467	−	0.647416i
$87$	−17.6683	+	17.6683i	−0.203084	+	0.203084i
$88$	−69.9836	+	53.3507i	−0.795268	+	0.606257i
$89$		−	51.9183i		−	0.583351i	−0.956517	−	0.291676i	$-0.905787\pi$
$89$		−	51.9183i		−	0.583351i	0.956517	−	0.291676i	$-0.0942128\pi$
$90$	34.8626	−	79.3240i	0.387363	−	0.881378i
$91$			66.7871i			0.733925i
$92$	96.3854	−	49.8706i	1.04767	−	0.542072i
$93$	−7.73102	−	7.73102i	−0.0831292	−	0.0831292i
$94$	2.43675	+	3.33200i	0.0259229	+	0.0354468i
$95$	−11.0705	+	41.5942i	−0.116532	+	0.437834i
$96$	18.5274	−	0.288965i	0.192994	−	0.00301005i
$97$	−41.3583	+	41.3583i	−0.426374	+	0.426374i	−0.887391	−	0.461017i	$-0.847485\pi$
$97$	−41.3583	+	41.3583i	−0.426374	+	0.426374i	0.461017	+	0.887391i	$0.347485\pi$
$98$	−4.98910	+	32.1486i	−0.0509092	+	0.328047i
$99$	85.5069	+	42.1057i	0.863706	+	0.425310i
$100$	67.6225	+	73.6695i	0.676225	+	0.736695i
$101$		−	136.857i		−	1.35502i	−0.735513	−	0.677511i	$-0.763059\pi$
$101$		−	136.857i		−	1.35502i	0.735513	−	0.677511i	$-0.236941\pi$
$102$	−5.24738	−	0.814334i	−0.0514449	−	0.00798366i
$103$	−118.433	+	118.433i	−1.14983	+	1.14983i	−0.163245	+	0.986586i	$0.552196\pi$
$103$	−118.433	+	118.433i	−1.14983	+	1.14983i	−0.986586	+	0.163245i	$0.947804\pi$
$104$	62.7050	−	21.0248i	0.602932	−	0.202161i
$105$	−6.01598	+	22.6033i	−0.0572950	+	0.215269i
$106$	76.3478	+	104.397i	0.720262	+	0.984881i
$107$	−58.5150	+	58.5150i	−0.546869	+	0.546869i	−0.925534	−	0.378665i	$-0.876383\pi$
$107$	−58.5150	+	58.5150i	−0.546869	+	0.546869i	0.378665	+	0.925534i	$0.376383\pi$
$108$	−18.8021	−	36.3391i	−0.174094	−	0.336473i
$109$	132.225			1.21307			0.606536	−	0.795056i	$-0.292559\pi$
$109$	132.225			1.21307			0.606536	+	0.795056i	$0.292559\pi$
$110$	−84.1934	+	70.7918i	−0.765394	+	0.643562i
$111$			27.9832i			0.252101i
$112$	127.407	−	21.8120i	1.13756	−	0.194750i
$113$	5.11251	+	5.11251i	0.0452434	+	0.0452434i	0.729367	−	0.684123i	$-0.239815\pi$
$113$	5.11251	+	5.11251i	0.0452434	+	0.0452434i	−0.684123	+	0.729367i	$0.739815\pi$
$114$	5.88504	+	8.04717i	0.0516232	+	0.0705892i
$115$	117.366	−	68.0235i	1.02057	−	0.591508i
$116$	164.486	+	52.3126i	1.41798	+	0.450971i
$117$	−50.6507	−	50.6507i	−0.432912	−	0.432912i
$118$	85.6173	+	13.2868i	0.725570	+	0.112600i
$119$	−37.0432			−0.311287
$120$	23.1156	−	1.46730i	0.192630	−	0.0122275i
$121$	−73.7715	−	95.9102i	−0.609682	−	0.792646i
$122$	33.3802	−	215.094i	0.273608	−	1.76307i
$123$	−10.2197	−	10.2197i	−0.0830871	−	0.0830871i
$124$	−22.8902	+	71.9733i	−0.184598	+	0.580430i
$125$	88.8313	+	87.9432i	0.710650	+	0.703545i
$126$	−82.6431	−	113.005i	−0.655897	−	0.896869i
$127$	−130.053	+	130.053i	−1.02404	+	1.02404i	−0.0243349	+	0.999704i	$0.507747\pi$
$127$	−130.053	+	130.053i	−1.02404	+	1.02404i	−0.999704	+	0.0243349i	$0.992253\pi$
$128$	−60.5868	−	112.753i	−0.473335	−	0.880883i
$129$	−19.9710			−0.154814
$130$	77.0360	−	29.9959i	0.592585	−	0.230737i
$131$	−60.5454			−0.462178			−0.231089	−	0.972933i	$-0.574229\pi$
$131$	−60.5454			−0.462178			−0.231089	+	0.972933i	$0.574229\pi$
$132$	0.507202	+	25.4732i	0.00384244	+	0.192979i
$133$	49.1763	+	49.1763i	0.369747	+	0.369747i
$134$	−11.0852	−	15.1579i	−0.0827255	−	0.113118i
$135$	−25.6461	−	44.2490i	−0.189971	−	0.327771i
$136$	11.6613	+	34.7790i	0.0857447	+	0.255728i
$137$	56.3745	−	56.3745i	0.411493	−	0.411493i	−0.470766	−	0.882258i	$-0.656022\pi$
$137$	56.3745	−	56.3745i	0.411493	−	0.411493i	0.882258	+	0.470766i	$0.156022\pi$
$138$	4.81838	−	31.0486i	0.0349158	−	0.224990i
$139$		−	215.606i		−	1.55112i	−0.631272	−	0.775561i	$-0.717467\pi$
$139$		−	215.606i		−	1.55112i	0.631272	−	0.775561i	$-0.282533\pi$
$140$	157.774	−	34.8430i	1.12696	−	0.248878i
$141$	1.19515			0.00847623
$142$	−6.11432	+	39.3993i	−0.0430586	+	0.277460i
$143$	29.2807	+	86.0938i	0.204760	+	0.602055i
$144$	−80.0821	+	113.166i	−0.556126	+	0.785876i
$145$	208.497	+	55.4926i	1.43791	+	0.382707i
$146$	57.4193	−	41.9918i	0.393283	−	0.287615i
$147$	6.66043	+	6.66043i	0.0453091	+	0.0453091i
$148$	171.684	−	88.8307i	1.16003	−	0.600208i
$149$	72.0890			0.483819			0.241909	−	0.970299i	$-0.422226\pi$
$149$	72.0890			0.483819			0.241909	+	0.970299i	$0.422226\pi$
$150$	28.7738	−	3.21256i	0.191825	−	0.0214171i
$151$	−218.192			−1.44498			−0.722491	−	0.691381i	$-0.757003\pi$
$151$	−218.192			−1.44498			−0.722491	+	0.691381i	$0.757003\pi$
$152$	30.6897	−	61.6514i	0.201906	−	0.405601i
$153$	28.0932	−	28.0932i	0.183616	−	0.183616i
$154$	30.7468	+	175.053i	0.199655	+	1.13671i
$155$	−24.2816	+	91.2309i	−0.156655	+	0.588586i
$156$	5.80336	−	18.2474i	0.0372010	−	0.116971i
$157$	−31.1663	+	31.1663i	−0.198511	+	0.198511i	−0.799362	−	0.600850i	$-0.794829\pi$
$157$	−31.1663	+	31.1663i	−0.198511	+	0.198511i	0.600850	+	0.799362i	$0.294829\pi$
$158$	−37.6455	+	242.579i	−0.238262	+	1.53531i
$159$	37.4461			0.235510
$160$	−82.3810	−	137.162i	−0.514881	−	0.857262i
$161$		−	219.183i		−	1.36139i
$162$	142.414	+	22.1010i	0.879098	+	0.136426i
$163$	183.074	−	183.074i	1.12316	−	1.12316i	0.131891	−	0.991264i	$-0.457895\pi$
$163$	183.074	−	183.074i	1.12316	−	1.12316i	0.991264	−	0.131891i	$-0.0421049\pi$
$164$	−30.2587	+	95.1422i	−0.184504	+	0.580136i
$165$	2.15461	+	31.7749i	0.0130583	+	0.192575i
$166$	94.6854	+	129.472i	0.570394	+	0.779952i
$167$	18.1541	−	18.1541i	0.108707	−	0.108707i	−0.650661	−	0.759368i	$-0.725508\pi$
$167$	18.1541	−	18.1541i	0.108707	−	0.108707i	0.759368	+	0.650661i	$0.225508\pi$
$168$	16.6775	−	33.5028i	0.0992709	−	0.199421i
$169$			100.657i			0.595604i
$170$	16.6371	+	42.7277i	0.0978651	+	0.251339i
$171$	−74.5896			−0.436197
$172$	63.3964	+	122.527i	0.368584	+	0.712365i
$173$	−119.355	+	119.355i	−0.689916	+	0.689916i	−0.962213	−	0.272297i	$-0.912217\pi$
$173$	−119.355	+	119.355i	−0.689916	+	0.689916i	0.272297	+	0.962213i	$0.412217\pi$
$174$	40.3376	−	29.4996i	0.231825	−	0.169538i
$175$	194.911	−	52.9267i	1.11378	−	0.302438i
$176$	154.675	−	83.9748i	0.878833	−	0.477130i
$177$	17.7379	−	17.7379i	0.100214	−	0.100214i
$178$	−15.9236	+	102.608i	−0.0894587	+	0.576451i
$179$	−82.2861			−0.459699			−0.229849	−	0.973226i	$-0.573823\pi$
$179$	−82.2861			−0.459699			−0.229849	+	0.973226i	$0.573823\pi$
$180$	−93.2297	+	146.079i	−0.517943	+	0.811549i
$181$	−202.957			−1.12131			−0.560654	−	0.828050i	$-0.689450\pi$
$181$	−202.957			−1.12131			−0.560654	+	0.828050i	$0.689450\pi$
$182$	20.4840	−	131.994i	0.112550	−	0.725243i
$183$	−44.5625	−	44.5625i	−0.243511	−	0.243511i
$184$	−205.786	+	68.9994i	−1.11840	+	0.374997i
$185$	209.055	−	121.165i	1.13003	−	0.654946i
$186$	12.9080	+	17.6503i	0.0693978	+	0.0948940i
$187$	−47.7515	+	16.2404i	−0.255356	+	0.0868469i
$188$	−3.79391	−	7.33253i	−0.0201804	−	0.0390028i
$189$	−82.6361			−0.437228
$190$	34.6363	−	78.8091i	0.182296	−	0.414784i
$191$			289.533i			1.51588i	0.652323	+	0.757941i	$0.273795\pi$
$191$			289.533i			1.51588i	−0.652323	+	0.757941i	$0.726205\pi$
$192$	−36.7052	−	5.11138i	−0.191173	−	0.0266218i
$193$	14.1389	−	14.1389i	0.0732586	−	0.0732586i	−0.669528	−	0.742787i	$-0.733504\pi$
$193$	14.1389	−	14.1389i	0.0732586	−	0.0732586i	0.742787	+	0.669528i	$0.233504\pi$
$194$	94.4229	−	69.0533i	0.486716	−	0.355945i
$195$	6.15613	−	23.1298i	0.0315699	−	0.118615i
$196$	19.7203	−	62.0065i	0.100614	−	0.316360i
$197$	−262.463	−	262.463i	−1.33230	−	1.33230i	−0.903311	−	0.428987i	$-0.858871\pi$
$197$	−262.463	−	262.463i	−1.33230	−	1.33230i	−0.428987	−	0.903311i	$-0.641129\pi$
$198$	−156.077	−	109.441i	−0.788267	−	0.552731i
$199$	−296.932			−1.49212			−0.746061	−	0.665878i	$-0.768057\pi$
$199$	−296.932			−1.49212			−0.746061	+	0.665878i	$0.768057\pi$
$200$	−111.050	−	166.337i	−0.555251	−	0.831683i
$201$	−5.43695			−0.0270495
$202$	−41.9749	+	270.477i	−0.207797	+	1.33899i
$203$	246.503	−	246.503i	1.21430	−	1.21430i
$204$	10.1209	+	3.21881i	0.0496121	+	0.0157785i
$205$	−32.0981	+	120.599i	−0.156576	+	0.588288i
$206$	270.387	−	197.739i	1.31256	−	0.959900i
$207$	166.226	+	166.226i	0.803026	+	0.803026i
$208$	−130.375	+	22.3201i	−0.626802	+	0.107308i
$209$	84.9518	+	41.8323i	0.406468	+	0.200155i
$210$	18.8222	−	42.8267i	0.0896295	−	0.203937i
$211$	−141.414			−0.670210			−0.335105	−	0.942181i	$-0.608772\pi$
$211$	−141.414			−0.670210			−0.335105	+	0.942181i	$0.608772\pi$
$212$	−118.870	−	229.741i	−0.560708	−	1.08369i
$213$	8.16260	+	8.16260i	0.0383221	+	0.0383221i
$214$	133.593	−	97.6988i	0.624265	−	0.456537i
$215$	86.4726	+	149.197i	0.402198	+	0.693941i
$216$	26.0140	+	77.5852i	0.120435	+	0.359191i
$217$	107.861	+	107.861i	0.497056	+	0.497056i
$218$	−261.322	−	40.5542i	−1.19872	−	0.186028i
$219$		−	20.5956i		−	0.0940440i
$220$	188.107	−	114.086i	0.855033	−	0.518574i
$221$	37.9061			0.171521
$222$	8.58262	−	55.3044i	0.0386605	−	0.249119i
$223$	−306.011	+	306.011i	−1.37224	+	1.37224i	−0.515137	+	0.857108i	$0.672259\pi$
$223$	−306.011	+	306.011i	−1.37224	+	1.37224i	−0.857108	+	0.515137i	$0.827741\pi$
$224$	−258.490	+	4.03156i	−1.15397	+	0.0179980i
$225$	−107.680	+	187.958i	−0.478577	+	0.835369i
$226$	−8.53603	−	11.6721i	−0.0377701	−	0.0516465i
$227$	−112.010	+	112.010i	−0.493435	+	0.493435i	−0.909387	−	0.415951i	$-0.863449\pi$
$227$	−112.010	+	112.010i	−0.493435	+	0.493435i	0.415951	+	0.909387i	$0.363449\pi$
$228$	−9.16275	−	17.7089i	−0.0401875	−	0.0776708i
$229$			77.6468i			0.339069i	0.985524	+	0.169534i	$0.0542264\pi$
$229$			77.6468i			0.339069i	−0.985524	+	0.169534i	$0.945774\pi$
$230$	−252.818	+	98.4409i	−1.09921	+	0.428004i
$231$	46.1648	+	22.7327i	0.199848	+	0.0984098i
$232$	−309.036	−	153.837i	−1.33205	−	0.663089i
$233$	−248.570	+	248.570i	−1.06682	+	1.06682i	−0.0692218	+	0.997601i	$0.522052\pi$
$233$	−248.570	+	248.570i	−1.06682	+	1.06682i	−0.997601	+	0.0692218i	$0.977948\pi$
$234$	84.5683	+	115.638i	0.361403	+	0.494180i
$235$	−5.17489	−	8.92861i	−0.0220208	−	0.0379941i
$236$	−165.134	−	52.5187i	−0.699720	−	0.222537i
$237$	50.2566	+	50.2566i	0.212053	+	0.212053i
$238$	73.2100	+	11.3614i	0.307605	+	0.0477368i
$239$		−	3.52915i		−	0.0147663i	−0.999973	−	0.00738315i	$-0.997650\pi$
$239$		−	3.52915i		−	0.0147663i	0.999973	−	0.00738315i	$-0.00235015\pi$
$240$	−46.1343	−	4.18979i	−0.192226	−	0.0174575i
$241$		−	297.959i		−	1.23634i	−0.786043	−	0.618172i	$-0.787874\pi$
$241$		−	297.959i		−	1.23634i	0.786043	−	0.618172i	$-0.212126\pi$
$242$	116.382	+	212.178i	0.480916	+	0.876767i
$243$	94.6004	−	94.6004i	0.389302	−	0.389302i
$244$	−131.942	+	414.863i	−0.540744	+	1.70026i
$245$	20.9191	−	78.5973i	0.0853840	−	0.320805i
$246$	17.0632	+	23.3321i	0.0693627	+	0.0948460i
$247$	−50.3219	−	50.3219i	−0.203732	−	0.203732i
$248$	67.3134	−	135.223i	0.271425	−	0.545255i
$249$	46.4401			0.186507
$250$	−148.588	−	201.051i	−0.594354	−	0.804204i
$251$		−	471.623i		−	1.87898i	−0.342581	−	0.939488i	$-0.611301\pi$
$251$		−	471.623i		−	1.87898i	0.342581	−	0.939488i	$-0.388699\pi$
$252$	128.672	+	248.685i	0.510601	+	0.986844i
$253$	−96.0937	−	282.544i	−0.379817	−	1.11678i
$254$	296.917	−	217.141i	1.16897	−	0.854886i
$255$	12.8289	+	3.41447i	0.0503093	+	0.0133901i
$256$	85.1583	+	241.421i	0.332650	+	0.943050i
$257$	−29.9858	+	29.9858i	−0.116676	+	0.116676i	−0.763034	−	0.646358i	$-0.776291\pi$
$257$	−29.9858	+	29.9858i	−0.116676	+	0.116676i	0.646358	+	0.763034i	$0.276291\pi$
$258$	39.4695	+	6.12522i	0.152982	+	0.0237411i
$259$		−	390.414i		−	1.50739i
$260$	−161.450	+	35.6547i	−0.620960	+	0.137133i
$261$			373.891i			1.43253i
$262$	119.658	+	18.5696i	0.456711	+	0.0708764i
$263$	282.981	+	282.981i	1.07597	+	1.07597i	0.996866	+	0.0791063i	$0.0252066\pi$
$263$	282.981	+	282.981i	1.07597	+	1.07597i	0.0791063	+	0.996866i	$0.474793\pi$
$264$	6.81039	−	50.4994i	0.0257969	−	0.191286i
$265$	−162.139	−	279.749i	−0.611844	−	1.05566i
$266$	−82.1066	−	112.272i	−0.308671	−	0.422075i
$267$	21.2580	+	21.2580i	0.0796181	+	0.0796181i
$268$	17.2592	+	33.3570i	0.0644000	+	0.124466i
$269$		−	319.121i		−	1.18632i	−0.805084	−	0.593161i	$-0.797880\pi$
$269$		−	319.121i		−	1.18632i	0.805084	−	0.593161i	$-0.202120\pi$
$270$	37.1140	+	95.3171i	0.137459	+	0.353026i
$271$	501.057			1.84892			0.924458	−	0.381283i	$-0.124518\pi$
$271$	501.057			1.84892			0.924458	+	0.381283i	$0.124518\pi$
$272$	−12.3798	−	72.3118i	−0.0455138	−	0.265852i
$273$	−27.3461	−	27.3461i	−0.100169	−	0.100169i
$274$	−128.706	+	94.1249i	−0.469729	+	0.343522i
$275$	228.052	−	153.679i	0.829280	−	0.558833i
$276$	−19.0456	+	59.8848i	−0.0690057	+	0.216974i
$277$	220.118	+	220.118i	0.794650	+	0.794650i	0.982246	−	0.187596i	$-0.0600695\pi$
$277$	220.118	+	220.118i	0.794650	+	0.794650i	−0.187596	+	0.982246i	$0.560070\pi$
$278$	−66.1277	+	426.112i	−0.237869	+	1.53278i
$279$	−163.602			−0.586386
$280$	−322.502	+	20.4714i	−1.15179	+	0.0731122i
$281$			219.144i			0.779872i	0.920842	+	0.389936i	$0.127503\pi$
$281$			219.144i			0.779872i	−0.920842	+	0.389936i	$0.872497\pi$
$282$	−2.36202	−	0.366559i	−0.00837597	−	0.00129986i
$283$	−132.490	−	132.490i	−0.468161	−	0.468161i	0.433157	−	0.901318i	$-0.357399\pi$
$283$	−132.490	−	132.490i	−0.468161	−	0.468161i	−0.901318	+	0.433157i	$0.857399\pi$
$284$	24.1680	−	75.9912i	0.0850986	−	0.267575i
$285$	−12.4980	−	21.5637i	−0.0438526	−	0.0756620i
$286$	−31.4631	−	179.131i	−0.110011	−	0.626334i
$287$	142.583	+	142.583i	0.496804	+	0.496804i
$288$	192.978	−	199.093i	0.670064	−	0.691297i
$289$		−	267.976i		−	0.927251i
$290$	−395.042	−	173.620i	−1.36221	−	0.598688i
$291$		−	33.8684i		−	0.116386i
$292$	−126.359	+	65.3793i	−0.432737	+	0.223902i
$293$	122.524	−	122.524i	0.418171	−	0.418171i	−0.466402	−	0.884573i	$-0.654450\pi$
$293$	122.524	−	122.524i	0.418171	−	0.418171i	0.884573	+	0.466402i	$0.154450\pi$
$294$	−11.1205	−	15.2061i	−0.0378248	−	0.0517214i
$295$	−209.318	−	55.7111i	−0.709554	−	0.188851i
$296$	−366.551	+	122.903i	−1.23835	+	0.415214i
$297$	−106.524	+	36.2291i	−0.358668	+	0.121984i
$298$	−142.473	−	22.1101i	−0.478096	−	0.0741951i
$299$			224.289i			0.750131i
$300$	−57.8523	−	2.47599i	−0.192841	−	0.00825330i
$301$	278.630			0.925680
$302$	431.223	+	66.9209i	1.42789	+	0.221592i
$303$	56.0364	+	56.0364i	0.184939	+	0.184939i
$304$	−79.5622	+	112.431i	−0.261718	+	0.369840i
$305$	−139.962	+	525.866i	−0.458891	+	1.72415i
$306$	−64.1381	+	46.9054i	−0.209602	+	0.153286i
$307$	347.093	−	347.093i	1.13059	−	1.13059i	0.140517	−	0.990078i	$-0.455124\pi$
$307$	347.093	−	347.093i	1.13059	−	1.13059i	0.990078	−	0.140517i	$-0.0448763\pi$
$308$	−7.07635	−	355.396i	−0.0229751	−	1.15388i
$309$		−	96.9848i		−	0.313867i
$310$	75.9698	−	172.856i	0.245064	−	0.557601i
$311$			288.132i			0.926470i	0.886235	+	0.463235i	$0.153311\pi$
$311$			288.132i			0.926470i	−0.886235	+	0.463235i	$0.846689\pi$
$312$	−17.0660	+	34.2833i	−0.0546988	+	0.109882i
$313$	165.999	+	165.999i	0.530348	+	0.530348i	0.920676	−	0.390328i	$-0.127638\pi$
$313$	165.999	+	165.999i	0.530348	+	0.530348i	−0.390328	+	0.920676i	$0.627638\pi$
$314$	71.1542	−	52.0364i	0.226606	−	0.165721i
$315$	175.508	+	302.816i	0.557168	+	0.961322i
$316$	148.801	−	467.872i	0.470888	−	1.48061i
$317$	−173.748	+	173.748i	−0.548100	+	0.548100i	−0.925891	−	0.377791i	$-0.876684\pi$
$317$	−173.748	+	173.748i	−0.548100	+	0.548100i	0.377791	+	0.925891i	$0.376684\pi$
$318$	−74.0064	−	11.4850i	−0.232725	−	0.0361162i
$319$	209.691	−	425.833i	0.657337	−	1.33490i
$320$	120.745	+	296.346i	0.377327	+	0.926080i
$321$		−	47.9182i		−	0.149278i
$322$	−67.2248	+	433.181i	−0.208773	+	1.34528i
$323$	27.9108	−	27.9108i	0.0864112	−	0.0864112i
$324$	−274.680	−	87.3584i	−0.847778	−	0.269625i
$325$	−199.452	+	54.1597i	−0.613699	+	0.166645i
$326$	−417.968	+	305.668i	−1.28211	+	0.937631i
$327$	−54.1397	+	54.1397i	−0.165565	+	0.165565i
$328$	88.9823	−	178.753i	0.271288	−	0.544979i
$329$	−16.6744			−0.0506820
$330$	5.48730	−	63.4589i	0.0166282	−	0.192300i
$331$		−	208.576i		−	0.630139i	−0.949069	−	0.315070i	$-0.897972\pi$
$331$		−	208.576i		−	0.630139i	0.949069	−	0.315070i	$-0.102028\pi$
$332$	−147.421	−	284.922i	−0.444039	−	0.858198i
$333$	296.086	+	296.086i	0.889148	+	0.889148i
$334$	−41.4468	+	30.3108i	−0.124092	+	0.0907510i
$335$	23.5415	+	40.6179i	0.0702732	+	0.121247i
$336$	−43.2360	+	61.0979i	−0.128679	+	0.181839i
$337$	−149.331	−	149.331i	−0.443118	−	0.443118i	0.449941	−	0.893058i	$-0.351445\pi$
$337$	−149.331	−	149.331i	−0.443118	−	0.443118i	−0.893058	+	0.449941i	$0.851445\pi$
$338$	30.8721	−	198.933i	0.0913376	−	0.588558i
$339$	−4.18665			−0.0123500
$340$	−19.7757	−	89.5472i	−0.0581638	−	0.263374i
$341$	186.330	+	91.7531i	0.546421	+	0.269071i
$342$	147.415	+	22.8771i	0.431037	+	0.0668921i
$343$	186.991	+	186.991i	0.545163	+	0.545163i
$344$	−87.7133	−	261.599i	−0.254980	−	0.760462i
$345$	−20.2033	+	75.9079i	−0.0585602	+	0.220023i
$346$	272.494	−	199.280i	0.787556	−	0.575955i
$347$	−26.2543	+	26.2543i	−0.0756607	+	0.0756607i	−0.743924	−	0.668264i	$-0.767038\pi$
$347$	−26.2543	+	26.2543i	−0.0756607	+	0.0756607i	0.668264	+	0.743924i	$0.267038\pi$
$348$	−88.7686	+	45.9296i	−0.255082	+	0.131982i
$349$	485.924			1.39233			0.696167	−	0.717880i	$-0.254887\pi$
$349$	485.924			1.39233			0.696167	+	0.717880i	$0.254887\pi$
$350$	−401.445	+	44.8208i	−1.14698	+	0.128059i
$351$	84.5612			0.240915
$352$	−331.446	+	118.523i	−0.941607	+	0.336714i
$353$	315.455	+	315.455i	0.893640	+	0.893640i	0.994864	−	0.101224i	$-0.0322759\pi$
$353$	315.455	+	315.455i	0.893640	+	0.893640i	−0.101224	+	0.994864i	$0.532276\pi$
$354$	−40.4965	+	29.6158i	−0.114397	+	0.0836605i
$355$	25.6371	−	96.3239i	0.0722172	−	0.271335i
$356$	62.9412	−	197.905i	0.176801	−	0.555914i
$357$	15.1674	−	15.1674i	0.0424857	−	0.0424857i
$358$	162.626	+	25.2377i	0.454261	+	0.0704962i
$359$			233.875i			0.651463i	0.945462	+	0.325731i	$0.105611\pi$
$359$			233.875i			0.651463i	−0.945462	+	0.325731i	$0.894389\pi$
$360$	229.057	−	260.108i	0.636270	−	0.722522i
$361$	286.895			0.794722
$362$	401.112	+	62.2480i	1.10804	+	0.171956i
$363$	69.4765	+	9.06471i	0.191395	+	0.0249717i
$364$	−80.9669	+	254.583i	−0.222437	+	0.699405i
$365$	−153.864	+	89.1774i	−0.421546	+	0.244322i
$366$	74.4032	+	101.738i	0.203287	+	0.277974i
$367$	−221.548	−	221.548i	−0.603672	−	0.603672i	0.337613	−	0.941285i	$-0.390381\pi$
$367$	−221.548	−	221.548i	−0.603672	−	0.603672i	−0.941285	+	0.337613i	$0.890381\pi$
$368$	427.867	−	73.2506i	1.16268	−	0.199051i
$369$	−216.267			−0.586088
$370$	−450.326	+	175.345i	−1.21710	+	0.473906i
$371$	−522.439			−1.40819
$372$	−20.0972	−	38.8420i	−0.0540246	−	0.104414i
$373$	374.690	−	374.690i	1.00453	−	1.00453i	0.00454024	−	0.999990i	$-0.498555\pi$
$373$	374.690	−	374.690i	1.00453	−	1.00453i	0.999990	−	0.00454024i	$-0.00144521\pi$
$374$	99.3544	−	17.4509i	0.265654	−	0.0466601i
$375$	−72.3806	+	0.363646i	−0.193015	+	0.000969724i
$376$	5.24914	+	15.6552i	0.0139605	+	0.0416362i
$377$	−252.246	+	252.246i	−0.669087	+	0.669087i
$378$	163.317	+	25.3450i	0.432056	+	0.0670502i
$379$	3.86152			0.0101887			0.00509435	−	0.999987i	$-0.498378\pi$
$379$	3.86152			0.0101887			0.00509435	+	0.999987i	$0.498378\pi$
$380$	−92.6245	+	145.131i	−0.243749	+	0.381922i
$381$		−	106.501i		−	0.279530i
$382$	88.8017	−	572.217i	0.232465	−	1.49795i
$383$	−56.6369	+	56.6369i	−0.147877	+	0.147877i	−0.777169	−	0.629292i	$-0.783345\pi$
$383$	−56.6369	+	56.6369i	−0.147877	+	0.147877i	0.629292	+	0.777169i	$0.283345\pi$
$384$	70.9743	+	21.3595i	0.184829	+	0.0556238i
$385$	−30.0606	−	443.315i	−0.0780794	−	1.15147i
$386$	−32.2798	+	23.6068i	−0.0836265	+	0.0611576i
$387$	−211.310	+	211.310i	−0.546020	+	0.546020i
$388$	−207.791	+	107.513i	−0.535544	+	0.277095i
$389$		−	35.7773i		−	0.0919726i	−0.998942	−	0.0459863i	$-0.985357\pi$
$389$		−	35.7773i		−	0.0919726i	0.998942	−	0.0459863i	$-0.0146431\pi$
$390$	−19.2607	+	43.8244i	−0.0493864	+	0.112370i
$391$	−124.401			−0.318161
$392$	−57.9919	+	116.498i	−0.147939	+	0.297188i
$393$	24.7904	−	24.7904i	0.0630799	−	0.0630799i
$394$	438.217	+	599.215i	1.11223	+	1.52085i
$395$	157.846	−	593.059i	0.399610	−	1.50142i
$396$	274.895	+	264.162i	0.694180	+	0.667076i
$397$	−415.625	+	415.625i	−1.04691	+	1.04691i	−0.0480699	+	0.998844i	$0.515307\pi$
$397$	−415.625	+	415.625i	−1.04691	+	1.04691i	−0.998844	+	0.0480699i	$0.984693\pi$
$398$	586.840	+	91.0709i	1.47447	+	0.228821i
$399$	−40.2706			−0.100929
$400$	168.457	+	362.798i	0.421143	+	0.906994i
$401$	53.4611			0.133320			0.0666598	−	0.997776i	$-0.478766\pi$
$401$	53.4611			0.133320			0.0666598	+	0.997776i	$0.478766\pi$
$402$	10.7453	+	1.66754i	0.0267295	+	0.00414812i
$403$	−110.374	−	110.374i	−0.273880	−	0.273880i
$404$	165.914	−	521.681i	0.410678	−	1.29129i
$405$	−348.175	−	92.6686i	−0.859692	−	0.228811i
$406$	−562.779	+	411.571i	−1.38616	+	1.01372i
$407$	−171.165	−	503.275i	−0.420552	−	1.23655i
$408$	−19.0151	−	9.46559i	−0.0466055	−	0.0232000i
$409$	−58.7179			−0.143565			−0.0717823	−	0.997420i	$-0.522869\pi$
$409$	−58.7179			−0.143565			−0.0717823	+	0.997420i	$0.522869\pi$
$410$	100.425	−	228.501i	0.244940	−	0.557318i
$411$			46.1653i			0.112324i
$412$	−595.026	+	307.871i	−1.44424	+	0.747260i
$413$	−247.474	+	247.474i	−0.599211	+	0.599211i
$414$	−277.538	−	379.503i	−0.670381	−	0.916674i
$415$	−201.082	−	346.941i	−0.484535	−	0.836003i
$416$	264.511	−	4.12548i	0.635844	−	0.00991702i
$417$	88.2803	+	88.2803i	0.211703	+	0.211703i
$418$	−155.064	−	108.730i	−0.370966	−	0.260120i
$419$	403.360			0.962673			0.481337	−	0.876536i	$-0.340152\pi$
$419$	403.360			0.962673			0.481337	+	0.876536i	$0.340152\pi$
$420$	−50.3343	+	78.8674i	−0.119844	+	0.187779i
$421$	298.522			0.709079			0.354539	−	0.935041i	$-0.384638\pi$
$421$	298.522			0.709079			0.354539	+	0.935041i	$0.384638\pi$
$422$	279.483	+	43.3726i	0.662282	+	0.102779i
$423$	12.6457	−	12.6457i	0.0298953	−	0.0298953i
$424$	164.465	+	490.506i	0.387889	+	1.15685i
$425$	−30.0394	−	110.625i	−0.0706809	−	0.260294i
$426$	−13.6286	−	18.6356i	−0.0319920	−	0.0437456i
$427$	621.724	+	621.724i	1.45603	+	1.45603i
$428$	−293.990	+	152.113i	−0.686892	+	0.355404i
$429$	−47.2403	−	23.2622i	−0.110117	−	0.0542244i
$430$	−125.140	−	321.387i	−0.291023	−	0.747411i
$431$	−415.527			−0.964101			−0.482050	−	0.876143i	$-0.660108\pi$
$431$	−415.527			−0.964101			−0.482050	+	0.876143i	$0.660108\pi$
$432$	−27.6168	−	161.314i	−0.0639279	−	0.373411i
$433$	−156.674	−	156.674i	−0.361833	−	0.361833i	0.502654	−	0.864488i	$-0.332357\pi$
$433$	−156.674	−	156.674i	−0.361833	−	0.361833i	−0.864488	+	0.502654i	$0.832357\pi$
$434$	−180.089	−	246.252i	−0.414951	−	0.567401i
$435$	−108.091	+	62.6480i	−0.248485	+	0.144018i
$436$	504.023	+	160.298i	1.15602	+	0.367656i
$437$	165.147	+	165.147i	0.377911	+	0.377911i
$438$	−6.31681	+	40.7040i	−0.0144219	+	0.0929316i
$439$			432.686i			0.985617i	0.870138	+	0.492809i	$0.164030\pi$
$439$			432.686i			0.985617i	−0.870138	+	0.492809i	$0.835970\pi$
$440$	−406.755	+	167.780i	−0.924444	+	0.381318i
$441$	140.946			0.319606
$442$	−74.9155	−	11.6260i	−0.169492	−	0.0263033i
$443$	212.241	−	212.241i	0.479099	−	0.479099i	−0.425745	−	0.904843i	$-0.639988\pi$
$443$	212.241	−	212.241i	0.479099	−	0.479099i	0.904843	+	0.425745i	$0.139988\pi$
$444$	−33.9244	+	106.668i	−0.0764063	+	0.240244i
$445$	66.7672	−	250.858i	0.150039	−	0.563726i
$446$	698.637	−	510.927i	1.56645	−	1.14558i
$447$	−29.5170	+	29.5170i	−0.0660335	+	0.0660335i
$448$	512.101	+	71.3126i	1.14308	+	0.159180i
$449$		−	121.061i		−	0.269624i	−0.990871	−	0.134812i	$-0.956957\pi$
$449$		−	121.061i		−	0.269624i	0.990871	−	0.134812i	$-0.0430431\pi$
$450$	270.460	−	338.443i	0.601022	−	0.752096i
$451$	246.311	+	121.289i	0.546144	+	0.268935i
$452$	13.2902	+	25.6861i	0.0294031	+	0.0568277i
$453$	89.3392	−	89.3392i	0.197217	−	0.197217i
$454$	255.724	−	187.016i	0.563269	−	0.411929i
$455$	−85.8886	+	322.701i	−0.188766	+	0.709234i
$456$	12.6773	+	37.8092i	0.0278011	+	0.0829149i
$457$	199.697	+	199.697i	0.436973	+	0.436973i	0.890992	−	0.454019i	$-0.150010\pi$
$457$	199.697	+	199.697i	0.436973	+	0.436973i	−0.454019	+	0.890992i	$0.650010\pi$
$458$	23.8147	−	153.457i	0.0519972	−	0.335058i
$459$			46.9015i			0.102182i
$460$	529.848	−	117.012i	1.15184	−	0.254374i
$461$		−	752.016i		−	1.63127i	−0.578567	−	0.815635i	$-0.696388\pi$
$461$		−	752.016i		−	1.63127i	0.578567	−	0.815635i	$-0.303612\pi$
$462$	−84.2653	−	59.0866i	−0.182392	−	0.127893i
$463$	−54.6196	+	54.6196i	−0.117969	+	0.117969i	−0.763627	−	0.645658i	$-0.776583\pi$
$463$	−54.6196	+	54.6196i	−0.117969	+	0.117969i	0.645658	+	0.763627i	$0.276583\pi$
$464$	563.579	+	398.817i	1.21461	+	0.859520i
$465$	−27.4125	−	47.2968i	−0.0589517	−	0.101714i
$466$	567.497	−	415.021i	1.21780	−	0.890604i
$467$	−106.562	−	106.562i	−0.228183	−	0.228183i	0.583750	−	0.811933i	$-0.301585\pi$
$467$	−106.562	−	106.562i	−0.228183	−	0.228183i	−0.811933	+	0.583750i	$0.801585\pi$
$468$	−131.669	−	254.478i	−0.281344	−	0.543756i
$469$	75.8548			0.161737
$470$	7.48890	+	19.2332i	0.0159338	+	0.0409216i
$471$		−	25.5222i		−	0.0541872i
$472$	310.254	+	154.443i	0.657317	+	0.327209i
$473$	359.175	−	122.156i	0.759356	−	0.258258i
$474$	−83.9102	−	114.738i	−0.177026	−	0.242064i
$475$	−106.981	+	186.738i	−0.225223	+	0.393132i
$476$	−141.204	−	44.9079i	−0.296646	−	0.0943444i
$477$	396.212	−	396.212i	0.830633	−	0.830633i
$478$	−1.08241	+	6.97480i	−0.00226446	+	0.0145916i
$479$			395.692i			0.826080i	0.910713	+	0.413040i	$0.135533\pi$
$479$			395.692i			0.826080i	−0.910713	+	0.413040i	$0.864467\pi$
$480$	89.8922	+	22.4301i	0.187275	+	0.0467295i
$481$			399.509i			0.830581i
$482$	−91.3858	+	588.869i	−0.189597	+	1.22172i
$483$	89.7449	+	89.7449i	0.185807	+	0.185807i
$484$	−164.934	−	455.031i	−0.340772	−	0.940146i
$485$	−253.021	+	146.647i	−0.521693	+	0.302366i
$486$	−215.977	+	157.948i	−0.444398	+	0.324996i
$487$	−191.487	−	191.487i	−0.393197	−	0.393197i	0.482629	−	0.875825i	$-0.339682\pi$
$487$	−191.487	−	191.487i	−0.393197	−	0.393197i	−0.875825	+	0.482629i	$0.839682\pi$
$488$	388.003	−	779.443i	0.795087	−	1.59722i
$489$			149.920i			0.306585i
$490$	−65.4495	+	148.919i	−0.133570	+	0.303917i
$491$	347.979			0.708714			0.354357	−	0.935110i	$-0.384700\pi$
$491$	347.979			0.708714			0.354357	+	0.935110i	$0.384700\pi$
$492$	−26.5667	−	51.3456i	−0.0539973	−	0.104361i
$493$	−139.907	−	139.907i	−0.283787	−	0.283787i
$494$	84.0193	+	114.887i	0.170080	+	0.232566i
$495$	359.003	+	313.408i	0.725259	+	0.633147i
$496$	−174.508	+	246.602i	−0.351831	+	0.497182i
$497$	−113.882	−	113.882i	−0.229140	−	0.229140i
$498$	−91.7816	−	14.2435i	−0.184300	−	0.0286014i
$499$	−278.582			−0.558280			−0.279140	−	0.960250i	$-0.590049\pi$
$499$	−278.582			−0.558280			−0.279140	+	0.960250i	$0.590049\pi$
$500$	231.998	+	442.919i	0.463996	+	0.885837i
$501$			14.8665i			0.0296736i
$502$	−144.650	+	932.089i	−0.288147	+	1.85675i
$503$	−386.161	−	386.161i	−0.767716	−	0.767716i	0.209988	−	0.977704i	$-0.432657\pi$
$503$	−386.161	−	386.161i	−0.767716	−	0.767716i	−0.977704	+	0.209988i	$0.932657\pi$
$504$	−178.026	−	530.951i	−0.353226	−	1.05347i
$505$	175.999	−	661.265i	0.348513	−	1.30944i
$506$	103.256	+	587.877i	0.204064	+	1.16181i
$507$	−41.2142	−	41.2142i	−0.0812903	−	0.0812903i
$508$	−653.409	+	338.079i	−1.28624	+	0.665510i
$509$			581.387i			1.14221i	0.820876	+	0.571107i	$0.193486\pi$
$509$			581.387i			1.14221i	−0.820876	+	0.571107i	$0.806514\pi$
$510$	−24.3070	−	10.6828i	−0.0476608	−	0.0209468i
$511$			287.345i			0.562319i
$512$	−94.2567	−	503.249i	−0.184095	−	0.982908i
$513$	62.2636	−	62.2636i	0.121371	−	0.121371i
$514$	68.4590	−	50.0653i	0.133189	−	0.0974034i
$515$	−724.546	+	419.936i	−1.40689	+	0.815410i
$516$	−76.1266	−	24.2111i	−0.147532	−	0.0469207i
$517$	−21.4946	+	7.31035i	−0.0415756	+	0.0141399i
$518$	−119.742	+	771.593i	−0.231163	+	1.48956i
$519$		−	97.7406i		−	0.188325i
$520$	330.015	−	20.9483i	0.634644	−	0.0402852i
$521$	−824.656			−1.58283			−0.791417	−	0.611277i	$-0.790656\pi$
$521$	−824.656			−1.58283			−0.791417	+	0.611277i	$0.790656\pi$
$522$	114.675	−	738.938i	0.219683	−	1.41559i
$523$	−633.360	−	633.360i	−1.21101	−	1.21101i	−0.970694	−	0.240320i	$-0.922748\pi$
$523$	−633.360	−	633.360i	−1.21101	−	1.21101i	−0.240320	−	0.970694i	$-0.577252\pi$
$524$	−230.791	−	73.3999i	−0.440440	−	0.140076i
$525$	−58.1359	+	101.478i	−0.110735	+	0.193291i
$526$	−472.475	−	646.059i	−0.898242	−	1.22825i
$527$	61.2183	−	61.2183i	0.116164	−	0.116164i
$528$	−28.9482	+	97.7154i	−0.0548261	+	0.185067i
$529$		−	207.076i		−	0.391448i
$530$	234.641	+	602.610i	0.442718	+	1.13700i
$531$		−	375.364i		−	0.706900i
$532$	127.836	+	247.070i	0.240294	+	0.464418i
$533$	−145.904	−	145.904i	−0.273742	−	0.273742i
$534$	−35.4932	−	48.5331i	−0.0664666	−	0.0908860i
$535$	−357.983	+	207.482i	−0.669127	+	0.387816i
$536$	−23.8793	−	71.2184i	−0.0445509	−	0.132870i
$537$	33.6922	−	33.6922i	0.0627415	−	0.0627415i
$538$	−97.8763	+	630.692i	−0.181926	+	1.17229i
$539$	−160.527	−	79.0472i	−0.297823	−	0.146655i
$540$	−44.1157	−	199.762i	−0.0816958	−	0.369930i
$541$			243.388i			0.449885i	0.974372	+	0.224942i	$0.0722194\pi$
$541$			243.388i			0.449885i	−0.974372	+	0.224942i	$0.927781\pi$
$542$	−990.259	−	153.677i	−1.82705	−	0.283537i
$543$	83.1009	−	83.1009i	0.153040	−	0.153040i
$544$	2.28818	+	146.710i	0.00420621	+	0.269687i
$545$	638.882	+	170.042i	1.17226	+	0.312003i
$546$	45.6581	+	62.4325i	0.0836228	+	0.114345i
$547$	3.14622	−	3.14622i	0.00575177	−	0.00575177i	−0.704225	−	0.709977i	$-0.748705\pi$
$547$	3.14622	−	3.14622i	0.00575177	−	0.00575177i	0.709977	+	0.704225i	$0.248705\pi$
$548$	283.235	−	146.548i	0.516853	−	0.267424i
$549$	−943.019			−1.71770
$550$	−497.843	+	233.778i	−0.905170	+	0.425051i
$551$			371.464i			0.674164i
$552$	56.0076	−	112.511i	0.101463	−	0.203825i
$553$	−701.166	−	701.166i	−1.26793	−	1.26793i
$554$	−367.517	−	502.541i	−0.663389	−	0.907113i
$555$	−35.9866	+	135.209i	−0.0648407	+	0.243620i
$556$	261.382	−	821.861i	0.470112	−	1.47817i
$557$	−327.259	−	327.259i	−0.587539	−	0.587539i	0.349425	−	0.936964i	$-0.386377\pi$
$557$	−327.259	−	327.259i	−0.587539	−	0.587539i	−0.936964	+	0.349425i	$0.886377\pi$
$558$	323.333	+	50.1776i	0.579449	+	0.0899240i
$559$	−285.120			−0.510054
$560$	643.654	+	58.4549i	1.14938	+	0.104384i
$561$	12.9023	−	26.2016i	0.0229987	−	0.0467052i
$562$	67.2128	−	433.104i	0.119596	−	0.770647i
$563$	313.787	+	313.787i	0.557347	+	0.557347i	0.928551	−	0.371204i	$-0.121055\pi$
$563$	313.787	+	313.787i	0.557347	+	0.557347i	−0.371204	+	0.928551i	$0.621055\pi$
$564$	4.55574	+	1.44889i	0.00807756	+	0.00256896i
$565$	18.1279	+	31.2773i	0.0320847	+	0.0553580i
$566$	221.209	+	302.480i	0.390829	+	0.534417i
$567$	−411.643	+	411.643i	−0.726002	+	0.726002i
$568$	−71.0712	+	142.772i	−0.125125	+	0.251359i
$569$	71.5070			0.125671			0.0628356	−	0.998024i	$-0.479986\pi$
$569$	71.5070			0.125671			0.0628356	+	0.998024i	$0.479986\pi$
$570$	18.0866	+	46.4504i	0.0317309	+	0.0814919i
$571$	−368.763			−0.645820			−0.322910	−	0.946430i	$-0.604661\pi$
$571$	−368.763			−0.645820			−0.322910	+	0.946430i	$0.604661\pi$
$572$	7.24119	+	363.675i	0.0126594	+	0.635796i
$573$	−118.550	−	118.550i	−0.206894	−	0.206894i
$574$	−238.061	−	325.523i	−0.414741	−	0.567114i
$575$	654.565	−	177.742i	1.13837	−	0.309117i
$576$	−442.455	+	334.289i	−0.768150	+	0.580363i
$577$	104.454	−	104.454i	0.181029	−	0.181029i	−0.610775	−	0.791804i	$-0.709142\pi$
$577$	104.454	−	104.454i	0.181029	−	0.181029i	0.791804	+	0.610775i	$0.209142\pi$
$578$	−82.1897	+	529.612i	−0.142197	+	0.916283i
$579$			11.5784i			0.0199972i
$580$	727.488	+	464.294i	1.25429	+	0.800506i
$581$	−647.920			−1.11518
$582$	−10.3877	+	66.9356i	−0.0178482	+	0.115010i
$583$	−673.464	+	229.046i	−1.15517	+	0.392875i
$584$	269.782	−	90.4568i	0.461955	−	0.154892i
$585$	−179.596	−	309.871i	−0.307003	−	0.529693i
$586$	−279.728	+	204.571i	−0.477352	+	0.349097i
$587$	650.785	+	650.785i	1.10866	+	1.10866i	0.993326	+	0.115337i	$0.0367947\pi$
$587$	650.785	+	650.785i	1.10866	+	1.10866i	0.115337	+	0.993326i	$0.463205\pi$
$588$	17.3141	+	33.4632i	0.0294458	+	0.0569102i
$589$	−162.540			−0.275958
$590$	396.598	+	174.303i	0.672200	+	0.295430i
$591$	214.932			0.363674
$592$	762.126	−	130.476i	1.28738	−	0.220398i
$593$	−238.338	+	238.338i	−0.401919	+	0.401919i	−0.878909	−	0.476990i	$-0.841728\pi$
$593$	−238.338	+	238.338i	−0.401919	+	0.401919i	0.476990	+	0.878909i	$0.341728\pi$
$594$	221.640	−	38.9295i	0.373132	−	0.0655378i
$595$	−178.985	−	47.6377i	−0.300815	−	0.0800634i
$596$	274.793	+	87.3944i	0.461063	+	0.146635i
$597$	121.579	−	121.579i	0.203651	−	0.203651i
$598$	68.7909	−	443.272i	0.115035	−	0.741258i
$599$	−154.795			−0.258422			−0.129211	−	0.991617i	$-0.541244\pi$
$599$	−154.795			−0.258422			−0.129211	+	0.991617i	$0.541244\pi$
$600$	113.576	+	22.6370i	0.189294	+	0.0377284i
$601$		−	77.7110i		−	0.129303i	−0.997908	−	0.0646514i	$-0.979406\pi$
$601$		−	77.7110i		−	0.129303i	0.997908	−	0.0646514i	$-0.0205936\pi$
$602$	−550.668	−	85.4574i	−0.914730	−	0.141956i
$603$	−57.5275	+	57.5275i	−0.0954022	+	0.0954022i
$604$	−831.719	−	264.517i	−1.37702	−	0.437942i
$605$	−233.107	−	558.288i	−0.385302	−	0.922791i
$606$	−93.5605	−	127.934i	−0.154390	−	0.211112i
$607$	177.528	−	177.528i	0.292467	−	0.292467i	−0.545587	−	0.838054i	$-0.683693\pi$
$607$	177.528	−	177.528i	0.292467	−	0.292467i	0.838054	+	0.545587i	$0.183693\pi$
$608$	191.726	−	197.801i	0.315338	−	0.325331i
$609$			201.862i			0.331465i
$610$	437.899	−	996.364i	0.717867	−	1.63338i
$611$	17.0628			0.0279261
$612$	141.145	−	73.0296i	0.230629	−	0.119329i
$613$	−828.826	+	828.826i	−1.35208	+	1.35208i	−0.468750	+	0.883331i	$0.655295\pi$
$613$	−828.826	+	828.826i	−1.35208	+	1.35208i	−0.883331	+	0.468750i	$0.844705\pi$
$614$	−792.429	+	579.519i	−1.29060	+	0.943841i
$615$	−36.2369	−	62.5221i	−0.0589218	−	0.101662i
$616$	−95.0168	+	704.555i	−0.154248	+	1.14376i
$617$	530.940	−	530.940i	0.860518	−	0.860518i	−0.130880	−	0.991398i	$-0.541780\pi$
$617$	530.940	−	530.940i	0.860518	−	0.860518i	0.991398	+	0.130880i	$0.0417803\pi$
$618$	−29.7458	+	191.675i	−0.0481324	+	0.310154i
$619$	833.885			1.34715			0.673574	−	0.739120i	$-0.264758\pi$
$619$	833.885			1.34715			0.673574	+	0.739120i	$0.264758\pi$
$620$	−203.158	+	318.323i	−0.327675	+	0.513424i
$621$	−277.514			−0.446883
$622$	88.3719	−	569.448i	0.142077	−	0.915512i
$623$	−296.586	−	296.586i	−0.476061	−	0.476061i
$624$	44.2432	−	62.5213i	0.0709026	−	0.100194i
$625$	316.119	+	539.160i	0.505790	+	0.862657i
$626$	−277.158	−	378.983i	−0.442744	−	0.605405i
$627$	−51.9120	+	17.6554i	−0.0827942	+	0.0281585i
$628$	−156.585	+	81.0183i	−0.249339	+	0.129010i
$629$	−221.586			−0.352283
$630$	−253.988	−	652.298i	−0.403156	−	1.03539i
$631$		−	1069.68i		−	1.69522i	−0.530618	−	0.847611i	$-0.678040\pi$
$631$		−	1069.68i		−	1.69522i	0.530618	−	0.847611i	$-0.321960\pi$
$632$	−437.580	+	879.038i	−0.692374	+	1.39088i
$633$	57.9023	−	57.9023i	0.0914729	−	0.0914729i
$634$	396.675	−	290.096i	0.625670	−	0.457564i
$635$	−795.637	+	461.140i	−1.25297	+	0.726204i
$636$	142.740	+	45.3964i	0.224433	+	0.0713780i
$637$	95.0893	+	95.0893i	0.149277	+	0.149277i
$638$	−545.026	+	777.279i	−0.854273	+	1.21831i
$639$	172.735			0.270320
$640$	−147.742	−	622.714i	−0.230847	−	0.972990i
$641$	−136.206			−0.212490			−0.106245	−	0.994340i	$-0.533883\pi$
$641$	−136.206			−0.212490			−0.106245	+	0.994340i	$0.533883\pi$
$642$	−14.6968	+	94.7027i	−0.0228922	+	0.147512i
$643$	−336.492	+	336.492i	−0.523316	+	0.523316i	−0.918571	−	0.395255i	$-0.870656\pi$
$643$	−336.492	+	336.492i	−0.523316	+	0.523316i	0.395255	+	0.918571i	$0.370656\pi$
$644$	265.719	−	835.496i	0.412606	−	1.29735i
$645$	−96.4955	−	25.6828i	−0.149605	−	0.0398182i
$646$	−63.7217	+	46.6009i	−0.0986405	+	0.0721376i
$647$	−74.0333	−	74.0333i	−0.114425	−	0.114425i	0.647576	−	0.762001i	$-0.275783\pi$
$647$	−74.0333	−	74.0333i	−0.114425	−	0.114425i	−0.762001	+	0.647576i	$0.775783\pi$
$648$	516.069	+	256.896i	0.796402	+	0.396445i
$649$	−210.517	+	427.511i	−0.324371	+	0.658722i
$650$	410.797	−	45.8649i	0.631995	−	0.0705614i
$651$	−88.3278			−0.135680
$652$	919.797	−	475.911i	1.41073	−	0.729925i
$653$	125.770	+	125.770i	0.192604	+	0.192604i	0.796820	−	0.604216i	$-0.206514\pi$
$653$	125.770	+	125.770i	0.192604	+	0.192604i	−0.604216	+	0.796820i	$0.706514\pi$
$654$	123.604	−	90.3936i	0.188996	−	0.138217i
$655$	−292.542	−	77.8617i	−0.446630	−	0.118873i
$656$	−230.684	+	325.986i	−0.351653	+	0.496930i
$657$	−217.919	−	217.919i	−0.331689	−	0.331689i
$658$	32.9543	+	5.11414i	0.0500825	+	0.00777224i
$659$			686.144i			1.04119i	0.853804	+	0.520595i	$0.174290\pi$
$659$			686.144i			1.04119i	−0.853804	+	0.520595i	$0.825710\pi$
$660$	−30.3080	+	123.734i	−0.0459213	+	0.187475i
$661$	600.757			0.908861			0.454431	−	0.890782i	$-0.349843\pi$
$661$	600.757			0.908861			0.454431	+	0.890782i	$0.349843\pi$
$662$	−63.9715	+	412.218i	−0.0966337	+	0.622685i
$663$	−15.5207	+	15.5207i	−0.0234098	+	0.0234098i
$664$	203.967	+	608.318i	0.307179	+	0.916142i
$665$	174.369	+	300.851i	0.262208	+	0.452407i
$666$	−494.357	−	675.980i	−0.742277	−	1.01498i
$667$	827.825	−	827.825i	1.24112	−	1.24112i
$668$	91.2096	−	47.1926i	0.136541	−	0.0706476i
$669$		−	250.593i		−	0.374579i
$670$	−34.0684	−	87.4952i	−0.0508483	−	0.130590i
$671$	1074.03	+	528.876i	1.60063	+	0.788191i
$672$	104.188	−	107.490i	0.155042	−	0.159955i
$673$	396.755	−	396.755i	0.589532	−	0.589532i	−0.347972	−	0.937505i	$-0.613130\pi$
$673$	396.755	−	396.755i	0.589532	−	0.589532i	0.937505	+	0.347972i	$0.113130\pi$
$674$	249.328	+	340.929i	0.369923	+	0.505829i
$675$	−67.0120	−	246.783i	−0.0992771	−	0.365605i
$676$	−122.028	+	383.691i	−0.180514	+	0.567590i
$677$	809.653	+	809.653i	1.19594	+	1.19594i	0.975371	+	0.220571i	$0.0707920\pi$
$677$	809.653	+	809.653i	1.19594	+	1.19594i	0.220571	+	0.975371i	$0.429208\pi$
$678$	8.27426	+	1.28407i	0.0122039	+	0.00189391i
$679$			472.523i			0.695910i
$680$	11.6189	+	183.041i	0.0170866	+	0.269178i
$681$		−	91.7253i		−	0.134692i
$682$	−340.110	−	238.484i	−0.498695	−	0.349683i
$683$	−247.548	+	247.548i	−0.362443	+	0.362443i	−0.864711	−	0.502269i	$-0.832499\pi$
$683$	−247.548	+	247.548i	−0.362443	+	0.362443i	0.502269	+	0.864711i	$0.332499\pi$
$684$	−284.325	−	90.4260i	−0.415680	−	0.132202i
$685$	344.888	−	199.892i	0.503486	−	0.291813i
$686$	−312.207	−	426.909i	−0.455112	−	0.622317i
$687$	−31.7926	−	31.7926i	−0.0462774	−	0.0462774i
$688$	93.1175	+	543.912i	0.135345	+	0.790569i
$689$	534.609			0.775920
$690$	63.2100	−	143.824i	0.0916087	−	0.208440i
$691$		−	709.600i		−	1.02692i	−0.858114	−	0.513459i	$-0.828364\pi$
$691$		−	709.600i		−	1.02692i	0.858114	−	0.513459i	$-0.171636\pi$
$692$	−599.663	+	310.270i	−0.866565	+	0.448368i
$693$	728.995	−	247.932i	1.05194	−	0.357767i
$694$	59.9398	−	43.8351i	0.0863686	−	0.0631630i
$695$	277.271	−	1041.76i	0.398950	−	1.49894i
$696$	189.524	−	63.5468i	0.272305	−	0.0913029i
$697$	80.9251	−	80.9251i	0.116105	−	0.116105i
$698$	−960.353	−	149.036i	−1.37586	−	0.213519i
$699$		−	203.555i		−	0.291208i
$700$	807.139	+	34.5443i	1.15306	+	0.0493490i
$701$		−	467.864i		−	0.667424i	−0.942675	−	0.333712i	$-0.891699\pi$
$701$		−	467.864i		−	0.667424i	0.942675	−	0.333712i	$-0.108301\pi$
$702$	−167.122	−	25.9354i	−0.238065	−	0.0369450i
$703$	294.164	+	294.164i	0.418441	+	0.418441i
$704$	691.402	−	132.586i	0.982105	−	0.188333i
$705$	5.77471	+	1.53697i	0.00819107	+	0.00218010i
$706$	−526.695	−	720.199i	−0.746027	−	1.02011i
$707$	−781.805	−	781.805i	−1.10581	−	1.10581i
$708$	89.1183	−	46.1105i	0.125873	−	0.0651279i
$709$			798.950i			1.12687i	0.826161	+	0.563435i	$0.190520\pi$
$709$			798.950i			1.12687i	−0.826161	+	0.563435i	$0.809480\pi$
$710$	−80.2108	+	182.506i	−0.112973	+	0.257051i
$711$	1063.51			1.49580
$712$	−185.092	+	371.824i	−0.259961	+	0.522225i
$713$	362.227	+	362.227i	0.508032	+	0.508032i
$714$	−34.6279	+	25.3240i	−0.0484985	+	0.0354678i
$715$	30.7608	+	453.642i	0.0430222	+	0.634465i
$716$	−313.663	−	99.7565i	−0.438077	−	0.139325i
$717$	1.44501	+	1.44501i	0.00201536	+	0.00201536i
$718$	71.7309	−	462.218i	0.0999038	−	0.643757i
$719$	1250.29			1.73893			0.869464	−	0.493997i	$-0.164465\pi$
$719$	1250.29			1.73893			0.869464	+	0.493997i	$0.164465\pi$
$720$	−532.472	+	443.809i	−0.739545	+	0.616401i
$721$			1353.11i			1.87671i
$722$	−567.002	−	87.9923i	−0.785321	−	0.121873i
$723$	122.000	+	122.000i	0.168741	+	0.168741i
$724$	−773.643	−	246.047i	−1.06857	−	0.339844i
$725$	936.050	+	536.257i	1.29110	+	0.739664i
$726$	−134.529	−	39.2238i	−0.185302	−	0.0540273i
$727$	−716.466	−	716.466i	−0.985510	−	0.985510i	0.0143862	−	0.999897i	$-0.495421\pi$
$727$	−716.466	−	716.466i	−0.985510	−	0.985510i	−0.999897	+	0.0143862i	$0.995421\pi$
$728$	238.101	−	478.311i	0.327061	−	0.657021i
$729$		−	571.065i		−	0.783354i
$730$	331.439	−	129.054i	0.454027	−	0.176786i
$731$		−	158.141i		−	0.216335i
$732$	−115.842	−	223.890i	−0.158255	−	0.305861i
$733$	−151.891	+	151.891i	−0.207218	+	0.207218i	−0.803084	−	0.595866i	$-0.796809\pi$
$733$	−151.891	+	151.891i	−0.207218	+	0.207218i	0.595866	+	0.803084i	$0.296809\pi$
$734$	369.904	+	505.804i	0.503957	+	0.689107i
$735$	23.6165	+	40.7472i	0.0321312	+	0.0554383i
$736$	−868.078	+	13.5391i	−1.17945	+	0.0183955i
$737$	97.7828	−	33.2561i	0.132677	−	0.0451236i
$738$	427.417	+	66.3303i	0.579156	+	0.0898785i
$739$			552.234i			0.747272i	0.927575	+	0.373636i	$0.121889\pi$
$739$			552.234i			0.747272i	−0.927575	+	0.373636i	$0.878111\pi$
$740$	943.778	−	208.425i	1.27538	−	0.281655i
$741$	41.2088			0.0556124
$742$	1032.52	+	160.235i	1.39153	+	0.215950i
$743$	380.861	+	380.861i	0.512599	+	0.512599i	0.915322	−	0.402723i	$-0.131936\pi$
$743$	380.861	+	380.861i	0.512599	+	0.512599i	−0.402723	+	0.915322i	$0.631936\pi$
$744$	27.8058	+	82.9290i	0.0373734	+	0.111464i
$745$	348.319	+	92.7068i	0.467542	+	0.124439i
$746$	−855.435	+	625.596i	−1.14670	+	0.838600i
$747$	491.376	−	491.376i	0.657800	−	0.657800i
$748$	−201.711	+	4.01629i	−0.269667	+	0.00536938i
$749$			668.541i			0.892579i
$750$	143.160	+	21.4809i	0.190881	+	0.0286412i
$751$			835.186i			1.11210i	0.831149	+	0.556049i	$0.187683\pi$
$751$			835.186i			1.11210i	−0.831149	+	0.556049i	$0.812317\pi$
$752$	−5.57255	−	32.5500i	−0.00741031	−	0.0432846i
$753$	193.107	+	193.107i	0.256450	+	0.256450i
$754$	575.890	−	421.159i	0.763779	−	0.558566i
$755$	−1054.26	−	280.596i	−1.39637	−	0.371651i
$756$	−314.997	−	100.181i	−0.416663	−	0.132514i
$757$	1004.56	−	1004.56i	1.32703	−	1.32703i	0.419074	−	0.907952i	$-0.362355\pi$
$757$	1004.56	−	1004.56i	1.32703	−	1.32703i	0.907952	−	0.419074i	$-0.137645\pi$
$758$	−7.63169	−	1.18435i	−0.0100682	−	0.00156247i
$759$	155.034	+	76.3424i	0.204261	+	0.100583i
$760$	227.570	−	258.419i	0.299434	−	0.340025i
$761$			499.749i			0.656701i	0.944556	+	0.328350i	$0.106493\pi$
$761$			499.749i			0.656701i	−0.944556	+	0.328350i	$0.893507\pi$
$762$	−32.6644	+	210.482i	−0.0428667	+	0.276223i
$763$	755.342	−	755.342i	0.989964	−	0.989964i
$764$	−351.005	+	1103.66i	−0.459431	+	1.44458i
$765$	171.868	−	99.6123i	0.224664	−	0.130212i
$766$	129.305	−	94.5631i	0.168805	−	0.123451i
$767$	253.239	−	253.239i	0.330169	−	0.330169i
$768$	−133.718	−	63.9820i	−0.174113	−	0.0833099i
$769$	120.210			0.156320			0.0781598	−	0.996941i	$-0.475096\pi$
$769$	120.210			0.156320			0.0781598	+	0.996941i	$0.475096\pi$
$770$	−76.5574	+	885.362i	−0.0994252	+	1.14982i
$771$		−	24.5554i		−	0.0318488i
$772$	71.0363	−	36.7548i	0.0920160	−	0.0476098i

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+(-1.97634 - 0.306706i) q^{2} +(-0.409452 + 0.409452i) q^{3} +(3.81186 + 1.21231i) q^{4} +(4.83179 + 1.28601i) q^{5} +(0.934798 - 0.683636i) q^{6} +(5.71256 - 5.71256i) q^{7} +(-7.16172 - 3.56507i) q^{8} +8.66470i q^{9} +(-9.15485 - 4.02353i) q^{10} +(4.85945 - 9.86842i) q^{11} +(-2.05716 + 1.06439i) q^{12} +(-5.84564 + 5.84564i) q^{13} +(-13.0421 + 9.53790i) q^{14} +(-2.50494 + 1.45183i) q^{15} +(13.0606 + 9.24234i) q^{16} +(-3.24226 - 3.24226i) q^{17} +(2.65752 - 17.1244i) q^{18} +8.60845i q^{19} +(16.8591 + 10.7597i) q^{20} +4.67804i q^{21} +(-12.6306 + 18.0130i) q^{22} +(19.1843 - 19.1843i) q^{23} +(4.39210 - 1.47266i) q^{24} +(21.6924 + 12.4274i) q^{25} +(13.3459 - 9.76009i) q^{26} +(-7.23284 - 7.23284i) q^{27} +(28.7009 - 14.8501i) q^{28} +43.1511 q^{29} +(5.39591 - 2.10103i) q^{30} +18.8814i q^{31} +(-22.9775 - 22.2718i) q^{32} +(2.05093 + 6.03035i) q^{33} +(5.41339 + 7.40223i) q^{34} +(34.9483 - 20.2555i) q^{35} +(-10.5043 + 33.0286i) q^{36} +(34.1716 - 34.1716i) q^{37} +(2.64026 - 17.0133i) q^{38} -4.78701i q^{39} +(-30.0192 - 26.4357i) q^{40} +24.9595i q^{41} +(1.43478 - 9.24540i) q^{42} +(24.3874 + 24.3874i) q^{43} +(30.4872 - 31.7259i) q^{44} +(-11.1428 + 41.8660i) q^{45} +(-43.7987 + 32.0308i) q^{46} +(-1.45945 - 1.45945i) q^{47} +(-9.13198 + 1.56339i) q^{48} -16.2667i q^{49} +(-39.0600 - 31.2140i) q^{50} +2.65510 q^{51} +(-29.3695 + 15.1960i) q^{52} +(-45.7272 - 45.7272i) q^{53} +(12.0762 + 16.5129i) q^{54} +(36.1707 - 41.4329i) q^{55} +(-61.2775 + 20.5461i) q^{56} +(-3.52474 - 3.52474i) q^{57} +(-85.2814 - 13.2347i) q^{58} -43.3211 q^{59} +(-11.3086 + 2.49739i) q^{60} +108.835i q^{61} +(5.79104 - 37.3161i) q^{62} +(49.4976 + 49.4976i) q^{63} +(38.5806 + 51.0641i) q^{64} +(-35.7624 + 20.7274i) q^{65} +(-2.20380 - 12.5471i) q^{66} +(6.63930 + 6.63930i) q^{67} +(-8.42841 - 16.2897i) q^{68} +15.7101i q^{69} +(-75.2823 + 29.3130i) q^{70} -19.9354i q^{71} +(30.8902 - 62.0542i) q^{72} +(-25.1503 + 25.1503i) q^{73} +(-78.0154 + 57.0541i) q^{74} +(-13.9704 + 3.79356i) q^{75} +(-10.4361 + 32.8142i) q^{76} +(-28.6141 - 84.1339i) q^{77} +(-1.46821 + 9.46078i) q^{78} -122.741i q^{79} +(51.2203 + 61.4530i) q^{80} -72.0593 q^{81} +(7.65523 - 49.3286i) q^{82} +(-56.7102 - 56.7102i) q^{83} +(-5.67124 + 17.8320i) q^{84} +(-11.4963 - 19.8355i) q^{85} +(-40.7182 - 55.6777i) q^{86} +(-17.6683 + 17.6683i) q^{87} +(-69.9836 + 53.3507i) q^{88} -51.9183i q^{89} +(34.8626 - 79.3240i) q^{90} +66.7871i q^{91} +(96.3854 - 49.8706i) q^{92} +(-7.73102 - 7.73102i) q^{93} +(2.43675 + 3.33200i) q^{94} +(-11.0705 + 41.5942i) q^{95} +(18.5274 - 0.288965i) q^{96} +(-41.3583 + 41.3583i) q^{97} +(-4.98910 + 32.1486i) q^{98} +(85.5069 + 42.1057i) 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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