LMFDB - Embedded newform 220.3.i.a.43.18

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			43.18
Character	$\chi$	$=$	220.43
Dual form			220.3.i.a.87.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33687 - 1.48754i) q^{2} +(-2.95023 + 2.95023i) q^{3} +(-0.425555 + 3.97730i) q^{4} +(4.93806 + 0.784567i) q^{5} +(8.33266 + 0.444512i) q^{6} +(2.85360 - 2.85360i) q^{7} +(6.48530 - 4.68410i) q^{8} -8.40772i q^{9} +(-5.43447 - 8.39443i) q^{10} +(-8.62034 + 6.83299i) q^{11} +(-10.4785 - 12.9894i) q^{12} +(4.71661 - 4.71661i) q^{13} +(-8.05974 - 0.429952i) q^{14} +(-16.8831 + 12.2538i) q^{15} +(-15.6378 - 3.38511i) q^{16} +(13.9929 + 13.9929i) q^{17} +(-12.5068 + 11.2400i) q^{18} +23.9819i q^{19} +(-5.22187 + 19.3063i) q^{20} +16.8376i q^{21} +(21.6886 + 3.68829i) q^{22} +(6.43276 - 6.43276i) q^{23} +(-5.31396 + 32.9523i) q^{24} +(23.7689 + 7.74848i) q^{25} +(-13.3216 - 0.710652i) q^{26} +(-1.74735 - 1.74735i) q^{27} +(10.1353 + 12.5640i) q^{28} -41.9911 q^{29} +(40.7985 + 8.73256i) q^{30} +52.7698i q^{31} +(15.8702 + 27.7873i) q^{32} +(5.27311 - 45.5909i) q^{33} +(2.10831 - 39.5216i) q^{34} +(16.3301 - 11.8524i) q^{35} +(33.4400 + 3.57794i) q^{36} +(-40.8207 + 40.8207i) q^{37} +(35.6740 - 32.0607i) q^{38} +27.8302i q^{39} +(35.6998 - 18.0422i) q^{40} -20.9489i q^{41} +(25.0465 - 22.5096i) q^{42} +(-23.2809 - 23.2809i) q^{43} +(-23.5084 - 37.1935i) q^{44} +(6.59642 - 41.5179i) q^{45} +(-18.1688 - 0.969226i) q^{46} +(29.3122 + 29.3122i) q^{47} +(56.1220 - 36.1483i) q^{48} +32.7139i q^{49} +(-20.2498 - 45.7159i) q^{50} -82.5645 q^{51} +(16.7522 + 20.7665i) q^{52} +(8.85084 + 8.85084i) q^{53} +(-0.263274 + 4.93525i) q^{54} +(-47.9287 + 26.9785i) q^{55} +(5.13991 - 31.8730i) q^{56} +(-70.7521 - 70.7521i) q^{57} +(56.1366 + 62.4634i) q^{58} +48.6533 q^{59} +(-41.5522 - 72.3637i) q^{60} +61.5189i q^{61} +(78.4972 - 70.5464i) q^{62} +(-23.9923 - 23.9923i) q^{63} +(20.1184 - 60.7557i) q^{64} +(26.9914 - 19.5904i) q^{65} +(-74.8678 + 53.1051i) q^{66} +(-8.41788 - 8.41788i) q^{67} +(-61.6086 + 49.6991i) q^{68} +37.9563i q^{69} +(-39.4622 - 8.44653i) q^{70} -84.4988i q^{71} +(-39.3826 - 54.5266i) q^{72} +(-1.63778 + 1.63778i) q^{73} +(115.295 + 6.15047i) q^{74} +(-92.9836 + 47.2640i) q^{75} +(-95.3832 - 10.2056i) q^{76} +(-5.10039 + 44.0976i) q^{77} +(41.3985 - 37.2053i) q^{78} -40.3760i q^{79} +(-74.5646 - 28.9848i) q^{80} +85.9797 q^{81} +(-31.1623 + 28.0059i) q^{82} +(-40.8742 - 40.8742i) q^{83} +(-66.9680 - 7.16530i) q^{84} +(58.1194 + 80.0761i) q^{85} +(-3.50774 + 65.7548i) q^{86} +(123.883 - 123.883i) q^{87} +(-23.8991 + 84.6926i) q^{88} +5.36138i q^{89} +(-70.5781 + 45.6916i) q^{90} -26.9186i q^{91} +(22.8475 + 28.3225i) q^{92} +(-155.683 - 155.683i) q^{93} +(4.41647 - 82.7896i) q^{94} +(-18.8154 + 118.424i) q^{95} +(-128.800 - 35.1582i) q^{96} +(86.0209 - 86.0209i) q^{97} +(48.6633 - 43.7343i) q^{98} +(57.4499 + 72.4774i) 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 $

$2$	−1.33687	−	1.48754i	−0.668435	−	0.743770i
$2$	−1.33687	−	1.48754i	−0.668435	−	0.743770i
$3$	−2.95023	+	2.95023i	−0.983410	+	0.983410i	−0.999865	−	0.0164544i	$-0.994762\pi$
$3$	−2.95023	+	2.95023i	−0.983410	+	0.983410i	0.0164544	+	0.999865i	$0.494762\pi$
$4$	−0.425555	+	3.97730i	−0.106389	+	0.994325i
$5$	4.93806	+	0.784567i	0.987612	+	0.156913i
$5$	4.93806	+	0.784567i	0.987612	+	0.156913i
$6$	8.33266	+	0.444512i	1.38878	+	0.0740853i
$7$	2.85360	−	2.85360i	0.407657	−	0.407657i	−0.473264	−	0.880921i	$-0.656924\pi$
$7$	2.85360	−	2.85360i	0.407657	−	0.407657i	0.880921	+	0.473264i	$0.156924\pi$
$8$	6.48530	−	4.68410i	0.810663	−	0.585513i
$9$		−	8.40772i		−	0.934191i
$10$	−5.43447	−	8.39443i	−0.543447	−	0.839443i
$11$	−8.62034	+	6.83299i	−0.783667	+	0.621181i
$11$	−8.62034	+	6.83299i	−0.783667	+	0.621181i
$12$	−10.4785	−	12.9894i	−0.873205	−	1.08245i
$13$	4.71661	−	4.71661i	0.362816	−	0.362816i	−0.502033	−	0.864849i	$-0.667414\pi$
$13$	4.71661	−	4.71661i	0.362816	−	0.362816i	0.864849	+	0.502033i	$0.167414\pi$
$14$	−8.05974	−	0.429952i	−0.575695	−	0.0307109i
$15$	−16.8831	+	12.2538i	−1.12554	+	0.816918i
$16$	−15.6378	−	3.38511i	−0.977363	−	0.211570i
$17$	13.9929	+	13.9929i	0.823111	+	0.823111i	0.986553	−	0.163442i	$-0.0522598\pi$
$17$	13.9929	+	13.9929i	0.823111	+	0.823111i	−0.163442	+	0.986553i	$0.552260\pi$
$18$	−12.5068	+	11.2400i	−0.694824	+	0.624446i
$19$			23.9819i			1.26221i	0.775699	+	0.631103i	$0.217397\pi$
$19$			23.9819i			1.26221i	−0.775699	+	0.631103i	$0.782603\pi$
$20$	−5.22187	+	19.3063i	−0.261094	+	0.965313i
$21$			16.8376i			0.801788i
$22$	21.6886	+	3.68829i	0.985847	+	0.167650i
$23$	6.43276	−	6.43276i	0.279685	−	0.279685i	−0.553298	−	0.832983i	$-0.686631\pi$
$23$	6.43276	−	6.43276i	0.279685	−	0.279685i	0.832983	+	0.553298i	$0.186631\pi$
$24$	−5.31396	+	32.9523i	−0.221415	+	1.37301i
$25$	23.7689	+	7.74848i	0.950756	+	0.309939i
$26$	−13.3216	−	0.710652i	−0.512371	−	0.0273328i
$27$	−1.74735	−	1.74735i	−0.0647168	−	0.0647168i
$28$	10.1353	+	12.5640i	0.361973	+	0.448713i
$29$	−41.9911			−1.44797			−0.723984	−	0.689817i	$-0.757691\pi$
$29$	−41.9911			−1.44797			−0.723984	+	0.689817i	$0.757691\pi$
$30$	40.7985	+	8.73256i	1.35995	+	0.291085i
$31$			52.7698i			1.70225i	0.524962	+	0.851126i	$0.324080\pi$
$31$			52.7698i			1.70225i	−0.524962	+	0.851126i	$0.675920\pi$
$32$	15.8702	+	27.7873i	0.495945	+	0.868354i
$33$	5.27311	−	45.5909i	0.159791	−	1.38154i
$34$	2.10831	−	39.5216i	0.0620091	−	1.16240i
$35$	16.3301	−	11.8524i	0.466574	−	0.338640i
$36$	33.4400	+	3.57794i	0.928890	+	0.0993874i
$37$	−40.8207	+	40.8207i	−1.10326	+	1.10326i	−0.109249	+	0.994014i	$0.534844\pi$
$37$	−40.8207	+	40.8207i	−1.10326	+	1.10326i	−0.994014	+	0.109249i	$0.965156\pi$
$38$	35.6740	−	32.0607i	0.938791	−	0.843702i
$39$			27.8302i			0.713594i
$40$	35.6998	−	18.0422i	0.892496	−	0.451056i
$41$		−	20.9489i		−	0.510948i	−0.966816	−	0.255474i	$-0.917768\pi$
$41$		−	20.9489i		−	0.510948i	0.966816	−	0.255474i	$-0.0822315\pi$
$42$	25.0465	−	22.5096i	0.596346	−	0.535943i
$43$	−23.2809	−	23.2809i	−0.541416	−	0.541416i	0.382528	−	0.923944i	$-0.375054\pi$
$43$	−23.2809	−	23.2809i	−0.541416	−	0.541416i	−0.923944	+	0.382528i	$0.875054\pi$
$44$	−23.5084	−	37.1935i	−0.534282	−	0.845306i
$45$	6.59642	−	41.5179i	0.146587	−	0.922619i
$46$	−18.1688	−	0.969226i	−0.394973	−	0.0210701i
$47$	29.3122	+	29.3122i	0.623663	+	0.623663i	0.946466	−	0.322803i	$-0.104625\pi$
$47$	29.3122	+	29.3122i	0.623663	+	0.623663i	−0.322803	+	0.946466i	$0.604625\pi$
$48$	56.1220	−	36.1483i	1.16921	−	0.753089i
$49$			32.7139i			0.667632i
$50$	−20.2498	−	45.7159i	−0.404996	−	0.914319i
$51$	−82.5645			−1.61891
$52$	16.7522	+	20.7665i	0.322157	+	0.399356i
$53$	8.85084	+	8.85084i	0.166997	+	0.166997i	0.785658	−	0.618661i	$-0.212325\pi$
$53$	8.85084	+	8.85084i	0.166997	+	0.166997i	−0.618661	+	0.785658i	$0.712325\pi$
$54$	−0.263274	+	4.93525i	−0.00487545	+	0.0913934i
$55$	−47.9287	+	26.9785i	−0.871431	+	0.490518i
$56$	5.13991	−	31.8730i	0.0917840	−	0.569161i
$57$	−70.7521	−	70.7521i	−1.24127	−	1.24127i
$58$	56.1366	+	62.4634i	0.967873	+	1.07696i
$59$	48.6533			0.824632			0.412316	−	0.911041i	$-0.364720\pi$
$59$	48.6533			0.824632			0.412316	+	0.911041i	$0.364720\pi$
$60$	−41.5522	−	72.3637i	−0.692537	−	1.20606i
$61$			61.5189i			1.00851i	0.863556	+	0.504253i	$0.168232\pi$
$61$			61.5189i			1.00851i	−0.863556	+	0.504253i	$0.831768\pi$
$62$	78.4972	−	70.5464i	1.26608	−	1.13784i
$63$	−23.9923	−	23.9923i	−0.380830	−	0.380830i
$64$	20.1184	−	60.7557i	0.314349	−	0.949307i
$65$	26.9914	−	19.5904i	0.415252	−	0.301391i
$66$	−74.8678	+	53.1051i	−1.13436	+	0.804623i
$67$	−8.41788	−	8.41788i	−0.125640	−	0.125640i	0.641491	−	0.767131i	$-0.278316\pi$
$67$	−8.41788	−	8.41788i	−0.125640	−	0.125640i	−0.767131	+	0.641491i	$0.778316\pi$
$68$	−61.6086	+	49.6991i	−0.906009	+	0.730870i
$69$			37.9563i			0.550091i
$70$	−39.4622	−	8.44653i	−0.563745	−	0.120665i
$71$		−	84.4988i		−	1.19012i	−0.803680	−	0.595062i	$-0.797128\pi$
$71$		−	84.4988i		−	1.19012i	0.803680	−	0.595062i	$-0.202872\pi$
$72$	−39.3826	−	54.5266i	−0.546981	−	0.757315i
$73$	−1.63778	+	1.63778i	−0.0224353	+	0.0224353i	−0.718235	−	0.695800i	$-0.755050\pi$
$73$	−1.63778	+	1.63778i	−0.0224353	+	0.0224353i	0.695800	+	0.718235i	$0.255050\pi$
$74$	115.295	+	6.15047i	1.55803	+	0.0831144i
$75$	−92.9836	+	47.2640i	−1.23978	+	0.630186i
$76$	−95.3832	−	10.2056i	−1.25504	−	0.134284i
$77$	−5.10039	+	44.0976i	−0.0662388	+	0.572696i
$78$	41.3985	−	37.2053i	0.530750	−	0.476991i
$79$		−	40.3760i		−	0.511089i	−0.966797	−	0.255544i	$-0.917745\pi$
$79$		−	40.3760i		−	0.511089i	0.966797	−	0.255544i	$-0.0822547\pi$
$80$	−74.5646	−	28.9848i	−0.932058	−	0.362310i
$81$	85.9797			1.06148
$82$	−31.1623	+	28.0059i	−0.380028	+	0.341536i
$83$	−40.8742	−	40.8742i	−0.492460	−	0.492460i	0.416620	−	0.909081i	$-0.363214\pi$
$83$	−40.8742	−	40.8742i	−0.492460	−	0.492460i	−0.909081	+	0.416620i	$0.863214\pi$
$84$	−66.9680	−	7.16530i	−0.797238	−	0.0853011i
$85$	58.1194	+	80.0761i	0.683757	+	0.942071i
$86$	−3.50774	+	65.7548i	−0.0407876	+	0.764591i
$87$	123.883	−	123.883i	1.42395	−	1.42395i
$88$	−23.8991	+	84.6926i	−0.271581	+	0.962416i
$89$			5.36138i			0.0602402i	0.999546	+	0.0301201i	$0.00958898\pi$
$89$			5.36138i			0.0602402i	−0.999546	+	0.0301201i	$0.990411\pi$
$90$	−70.5781	+	45.6916i	−0.784201	+	0.507684i
$91$		−	26.9186i		−	0.295809i
$92$	22.8475	+	28.3225i	0.248343	+	0.307853i
$93$	−155.683	−	155.683i	−1.67401	−	1.67401i
$94$	4.41647	−	82.7896i	0.0469837	−	0.880741i
$95$	−18.8154	+	118.424i	−0.198057	+	1.24657i
$96$	−128.800	−	35.1582i	−1.34167	−	0.366231i
$97$	86.0209	−	86.0209i	0.886814	−	0.886814i	−0.107402	−	0.994216i	$-0.534253\pi$
$97$	86.0209	−	86.0209i	0.886814	−	0.886814i	0.994216	+	0.107402i	$0.0342531\pi$
$98$	48.6633	−	43.7343i	0.496565	−	0.446268i
$99$	57.4499	+	72.4774i	0.580302	+	0.732095i
$100$	−40.9330	+	91.2386i	−0.409330	+	0.912386i
$101$			42.9360i			0.425109i	0.977149	+	0.212555i	$0.0681783\pi$
$101$			42.9360i			0.425109i	−0.977149	+	0.212555i	$0.931822\pi$
$102$	110.378	+	122.818i	1.08214	+	1.20410i
$103$	−3.23744	+	3.23744i	−0.0314314	+	0.0314314i	−0.722648	−	0.691216i	$-0.757075\pi$
$103$	−3.23744	+	3.23744i	−0.0314314	+	0.0314314i	0.691216	+	0.722648i	$0.257075\pi$
$104$	8.49556	−	52.6817i	0.0816881	−	0.506555i
$105$	−13.2102	+	83.1449i	−0.125811	+	0.791856i
$106$	1.33356	−	24.9984i	0.0125807	−	0.235834i
$107$	136.140	−	136.140i	1.27233	−	1.27233i	0.327472	−	0.944861i	$-0.393803\pi$
$107$	136.140	−	136.140i	1.27233	−	1.27233i	0.944861	−	0.327472i	$-0.106197\pi$
$108$	7.69334	−	6.20615i	0.0712346	−	0.0574644i
$109$	9.16768			0.0841071			0.0420536	−	0.999115i	$-0.486610\pi$
$109$	9.16768			0.0841071			0.0420536	+	0.999115i	$0.486610\pi$
$110$	104.206	+	35.2292i	0.947328	+	0.320265i
$111$		−	240.861i		−	2.16992i
$112$	−54.2838	+	34.9643i	−0.484677	+	0.312181i
$113$	47.3297	+	47.3297i	0.418847	+	0.418847i	0.884806	−	0.465959i	$-0.154291\pi$
$113$	47.3297	+	47.3297i	0.418847	+	0.418847i	−0.465959	+	0.884806i	$0.654291\pi$
$114$	−10.6602	+	199.833i	−0.0935109	+	1.75292i
$115$	36.8123	−	26.7185i	0.320107	−	0.232334i
$116$	17.8695	−	167.011i	0.154047	−	1.43975i
$117$	−39.6559	−	39.6559i	−0.338940	−	0.338940i
$118$	−65.0432	−	72.3738i	−0.551213	−	0.613337i
$119$	79.8601			0.671094
$120$	−52.0940	+	158.551i	−0.434116	+	1.32126i
$121$	27.6206	−	117.805i	0.228269	−	0.973598i
$122$	91.5118	−	82.2427i	0.750097	−	0.674121i
$123$	61.8040	+	61.8040i	0.502472	+	0.502472i
$124$	−209.881	−	22.4564i	−1.69259	−	0.181100i
$125$	111.293	+	56.9108i	0.890345	+	0.455286i
$126$	−3.61492	+	67.7640i	−0.0286898	+	0.537810i
$127$	−135.590	+	135.590i	−1.06763	+	1.06763i	−0.0700935	+	0.997540i	$0.522330\pi$
$127$	−135.590	+	135.590i	−1.06763	+	1.06763i	−0.997540	+	0.0700935i	$0.977670\pi$
$128$	−117.272	+	51.2956i	−0.916189	+	0.400747i
$129$	137.368			1.06487
$130$	−65.2255	−	13.9610i	−0.501735	−	0.107392i
$131$	223.136			1.70333			0.851665	−	0.524087i	$-0.175593\pi$
$131$	223.136			1.70333			0.851665	+	0.524087i	$0.175593\pi$
$132$	179.085	+	40.3741i	1.35670	+	0.305865i
$133$	68.4347	+	68.4347i	0.514547	+	0.514547i
$134$	−1.26832	+	23.7756i	−0.00946510	+	0.177430i
$135$	−7.25762	−	9.99946i	−0.0537602	−	0.0740700i
$136$	156.292	+	25.2040i	1.14921	+	0.185323i
$137$	30.6040	−	30.6040i	0.223387	−	0.223387i	−0.586536	−	0.809923i	$-0.699509\pi$
$137$	30.6040	−	30.6040i	0.223387	−	0.223387i	0.809923	+	0.586536i	$0.199509\pi$
$138$	56.4615	−	50.7426i	0.409141	−	0.367700i
$139$			270.899i			1.94891i	0.224576	+	0.974457i	$0.427900\pi$
$139$			270.899i			1.94891i	−0.224576	+	0.974457i	$0.572100\pi$
$140$	40.1912	+	69.9935i	0.287080	+	0.499953i
$141$	−172.955			−1.22663
$142$	−125.695	+	112.964i	−0.885179	+	0.795521i
$143$	−8.43025	+	72.8873i	−0.0589528	+	0.509701i
$144$	−28.4611	+	131.478i	−0.197647	+	0.913044i
$145$	−207.354	−	32.9448i	−1.43003	−	0.227206i
$146$	4.62577	+	0.246765i	0.0316833	+	0.00169017i
$147$	−96.5137	−	96.5137i	−0.656556	−	0.656556i
$148$	−144.985	−	179.728i	−0.979627	−	1.21438i
$149$	−16.6615			−0.111822			−0.0559111	−	0.998436i	$-0.517806\pi$
$149$	−16.6615			−0.111822			−0.0559111	+	0.998436i	$0.517806\pi$
$150$	194.614	+	75.1310i	1.29743	+	0.500874i
$151$	−83.2430			−0.551278			−0.275639	−	0.961261i	$-0.588889\pi$
$151$	−83.2430			−0.551278			−0.275639	+	0.961261i	$0.588889\pi$
$152$	112.334	+	155.530i	0.739037	+	1.02322i
$153$	117.648	−	117.648i	0.768943	−	0.768943i
$154$	72.4155	−	51.3657i	0.470231	−	0.333544i
$155$	−41.4014	+	260.581i	−0.267106	+	1.68116i
$156$	−110.689	−	11.8433i	−0.709544	−	0.0759183i
$157$	25.4390	−	25.4390i	0.162032	−	0.162032i	−0.621434	−	0.783466i	$-0.713450\pi$
$157$	25.4390	−	25.4390i	0.162032	−	0.162032i	0.783466	+	0.621434i	$0.213450\pi$
$158$	−60.0610	+	53.9775i	−0.380133	+	0.341630i
$159$	−52.2240			−0.328453
$160$	56.5671	+	149.667i	0.353545	+	0.935418i
$161$		−	36.7131i		−	0.228031i
$162$	−114.944	−	127.898i	−0.709529	−	0.789496i
$163$	86.4306	−	86.4306i	0.530249	−	0.530249i	−0.390397	−	0.920646i	$-0.627662\pi$
$163$	86.4306	−	86.4306i	0.530249	−	0.530249i	0.920646	+	0.390397i	$0.127662\pi$
$164$	83.3199	+	8.91489i	0.508048	+	0.0543591i
$165$	61.8080	−	220.994i	0.374594	−	1.33935i
$166$	−6.15853	+	115.446i	−0.0370996	+	0.695455i
$167$	201.686	−	201.686i	1.20770	−	1.20770i	0.235933	−	0.971769i	$-0.424185\pi$
$167$	201.686	−	201.686i	1.20770	−	1.20770i	0.971769	−	0.235933i	$-0.0758145\pi$
$168$	78.8688	+	109.197i	0.469457	+	0.649980i
$169$			124.507i			0.736729i
$170$	41.4183	−	193.506i	0.243637	−	1.13827i
$171$	201.633			1.17914
$172$	102.502	−	82.6878i	0.595944	−	0.480743i
$173$	−149.223	+	149.223i	−0.862562	+	0.862562i	−0.991635	−	0.129073i	$-0.958800\pi$
$173$	−149.223	+	149.223i	−0.862562	+	0.862562i	0.129073	+	0.991635i	$0.458800\pi$
$174$	−349.897	−	18.6655i	−2.01091	−	0.107273i
$175$	89.9380	−	45.7159i	0.513931	−	0.261234i
$176$	157.934	−	77.6721i	0.897350	−	0.441319i
$177$	−143.538	+	143.538i	−0.810952	+	0.810952i
$178$	7.97527	−	7.16747i	0.0448049	−	0.0402667i
$179$	−103.164			−0.576334			−0.288167	−	0.957580i	$-0.593046\pi$
$179$	−103.164			−0.576334			−0.288167	+	0.957580i	$0.593046\pi$
$180$	162.322	+	43.9040i	0.901788	+	0.243911i
$181$	−120.023			−0.663109			−0.331555	−	0.943436i	$-0.607573\pi$
$181$	−120.023			−0.663109			−0.331555	+	0.943436i	$0.607573\pi$
$182$	−40.0425	+	35.9867i	−0.220014	+	0.197729i
$183$	−181.495	−	181.495i	−0.991775	−	0.991775i
$184$	11.5867	−	71.8502i	0.0629712	−	0.390490i
$185$	−233.602	+	169.549i	−1.26271	+	0.916479i
$186$	−23.4568	+	439.713i	−0.126112	+	2.36405i
$187$	−216.237	−	25.0102i	−1.15635	−	0.133745i
$188$	−129.057	+	104.109i	−0.686474	+	0.553773i
$189$	−9.97249			−0.0527645
$190$	201.314	−	130.329i	1.05955	−	0.685942i
$191$		−	135.139i		−	0.707536i	−0.935333	−	0.353768i	$-0.884900\pi$
$191$		−	135.139i		−	0.707536i	0.935333	−	0.353768i	$-0.115100\pi$
$192$	119.889	+	238.597i	0.624424	+	1.24269i
$193$	−193.578	+	193.578i	−1.00299	+	1.00299i	−0.00299750	+	0.999996i	$0.500954\pi$
$193$	−193.578	+	193.578i	−1.00299	+	1.00299i	−0.999996	+	0.00299750i	$0.999046\pi$
$194$	−242.959	−	12.9608i	−1.25236	−	0.0668082i
$195$	−21.8346	+	137.427i	−0.111972	+	0.704754i
$196$	−130.113	−	13.9216i	−0.663842	−	0.0710284i
$197$	−43.7391	−	43.7391i	−0.222026	−	0.222026i	0.587325	−	0.809351i	$-0.300181\pi$
$197$	−43.7391	−	43.7391i	−0.222026	−	0.222026i	−0.809351	+	0.587325i	$0.800181\pi$
$198$	31.0101	−	182.352i	0.156617	−	0.920970i
$199$	259.956			1.30631			0.653156	−	0.757223i	$-0.273445\pi$
$199$	259.956			1.30631			0.653156	+	0.757223i	$0.273445\pi$
$200$	190.443	−	61.0848i	0.952216	−	0.305424i
$201$	49.6694			0.247111
$202$	63.8691	−	57.3999i	0.316184	−	0.284158i
$203$	−119.826	+	119.826i	−0.590274	+	0.590274i
$204$	35.1357	−	328.383i	0.172234	−	1.60972i
$205$	16.4358	−	103.447i	0.0801746	−	0.504619i
$206$	9.14386	+	0.487785i	0.0443877	+	0.00236789i
$207$	−54.0849	−	54.0849i	−0.261280	−	0.261280i
$208$	−89.7237	+	57.7911i	−0.431364	+	0.277842i
$209$	−163.868	−	206.732i	−0.784057	−	0.989149i
$210$	141.342	−	91.5032i	0.673056	−	0.435730i
$211$	193.253			0.915891			0.457946	−	0.888980i	$-0.348585\pi$
$211$	193.253			0.915891			0.457946	+	0.888980i	$0.348585\pi$
$212$	−38.9689	+	31.4359i	−0.183816	+	0.148283i
$213$	249.291	+	249.291i	1.17038	+	1.17038i
$214$	−384.514	−	20.5122i	−1.79680	−	0.0958513i
$215$	−96.6971	−	133.228i	−0.449754	−	0.619665i
$216$	−19.5169	−	3.14734i	−0.0903560	−	0.0145710i
$217$	150.584	+	150.584i	0.693935	+	0.693935i
$218$	−12.2560	−	13.6373i	−0.0562202	−	0.0625564i
$219$		−	9.66366i		−	0.0441263i
$220$	−86.9052	−	202.108i	−0.395024	−	0.918671i
$221$	131.998			0.597275
$222$	−358.291	+	322.000i	−1.61392	+	1.45045i
$223$	124.127	−	124.127i	0.556625	−	0.556625i	−0.371720	−	0.928345i	$-0.621232\pi$
$223$	124.127	−	124.127i	0.556625	−	0.556625i	0.928345	+	0.371720i	$0.121232\pi$
$224$	124.581	+	34.0066i	0.556166	+	0.151815i
$225$	65.1471	−	199.842i	0.289543	−	0.888188i
$226$	7.13118	−	133.679i	0.0315539	−	0.591498i
$227$	52.1429	−	52.1429i	0.229704	−	0.229704i	−0.582865	−	0.812569i	$-0.698068\pi$
$227$	52.1429	−	52.1429i	0.229704	−	0.229704i	0.812569	+	0.582865i	$0.198068\pi$
$228$	311.511	−	251.293i	1.36628	−	1.10216i
$229$		−	320.338i		−	1.39886i	−0.714702	−	0.699429i	$-0.753438\pi$
$229$		−	320.338i		−	1.39886i	0.714702	−	0.699429i	$-0.246562\pi$
$230$	−88.9581	−	19.0407i	−0.386774	−	0.0827857i
$231$	−115.051	−	145.145i	−0.498055	−	0.628335i
$232$	−272.325	+	196.690i	−1.17381	+	0.847804i
$233$	125.112	−	125.112i	0.536962	−	0.536962i	−0.385674	−	0.922635i	$-0.626031\pi$
$233$	125.112	−	125.112i	0.536962	−	0.536962i	0.922635	+	0.385674i	$0.126031\pi$
$234$	−5.97497	+	112.005i	−0.0255340	+	0.478652i
$235$	121.748	+	167.743i	0.518076	+	0.713799i
$236$	−20.7046	+	193.509i	−0.0877315	+	0.819952i
$237$	119.119	+	119.119i	0.502610	+	0.502610i
$238$	−106.763	−	118.795i	−0.448583	−	0.499140i
$239$		−	39.2846i		−	0.164371i	−0.996617	−	0.0821854i	$-0.973810\pi$
$239$		−	39.2846i		−	0.164371i	0.996617	−	0.0821854i	$-0.0261900\pi$
$240$	305.495	−	134.471i	1.27289	−	0.560295i
$241$		−	322.935i		−	1.33998i	−0.742371	−	0.669989i	$-0.766299\pi$
$241$		−	322.935i		−	1.33998i	0.742371	−	0.669989i	$-0.233701\pi$
$242$	−212.165	+	116.404i	−0.876717	+	0.481007i
$243$	−237.934	+	237.934i	−0.979151	+	0.979151i
$244$	−244.679	−	26.1796i	−1.00278	−	0.107294i
$245$	−25.6663	+	161.543i	−0.104760	+	0.659361i
$246$	9.31202	−	174.560i	0.0378537	−	0.709593i
$247$	113.113	+	113.113i	0.457948	+	0.457948i
$248$	247.179	+	342.228i	0.996690	+	1.37995i
$249$	241.177			0.968581
$250$	−64.1274	−	241.635i	−0.256510	−	0.966542i
$251$		−	315.202i		−	1.25579i	−0.778300	−	0.627893i	$-0.783918\pi$
$251$		−	315.202i		−	1.25579i	0.778300	−	0.627893i	$-0.216082\pi$
$252$	105.634	−	85.2144i	0.419184	−	0.338152i
$253$	−11.4976	+	99.4076i	−0.0454452	+	0.392916i
$254$	382.961	+	20.4293i	1.50772	+	0.0804303i
$255$	−407.708	−	64.7773i	−1.59886	−	0.254029i
$256$	233.082	+	105.872i	0.910477	+	0.413561i
$257$	188.045	−	188.045i	0.731692	−	0.731692i	−0.239263	−	0.970955i	$-0.576906\pi$
$257$	188.045	−	188.045i	0.731692	−	0.731692i	0.970955	+	0.239263i	$0.0769057\pi$
$258$	−183.643	−	204.341i	−0.711796	−	0.792018i
$259$			232.972i			0.899506i
$260$	66.4306	+	115.690i	0.255502	+	0.444960i
$261$			353.049i			1.35268i
$262$	−298.304	−	331.924i	−1.13857	−	1.26689i
$263$	−277.864	−	277.864i	−1.05652	−	1.05652i	−0.998304	−	0.0582135i	$-0.981460\pi$
$263$	−277.864	−	277.864i	−1.05652	−	1.05652i	−0.0582135	−	0.998304i	$-0.518540\pi$
$264$	−179.355	−	320.371i	−0.679374	−	1.21352i
$265$	36.7619	+	50.6501i	0.138724	+	0.191132i
$266$	10.3111	−	193.288i	0.0387634	−	0.726646i
$267$	−15.8173	−	15.8173i	−0.0592408	−	0.0592408i
$268$	37.0627	−	29.8982i	0.138294	−	0.111560i
$269$		−	181.174i		−	0.673510i	−0.941592	−	0.336755i	$-0.890671\pi$
$269$		−	181.174i		−	0.673510i	0.941592	−	0.336755i	$-0.109329\pi$
$270$	−5.17209	+	24.1640i	−0.0191559	+	0.0894963i
$271$	−102.599			−0.378594			−0.189297	−	0.981920i	$-0.560621\pi$
$271$	−102.599			−0.378594			−0.189297	+	0.981920i	$0.560621\pi$
$272$	−171.450	−	266.185i	−0.630333	−	0.978623i
$273$	79.4161	+	79.4161i	0.290902	+	0.290902i
$274$	−86.4384	−	4.61112i	−0.315469	−	0.0168289i
$275$	−257.841	+	95.6181i	−0.937605	+	0.347702i
$276$	−150.963	−	16.1525i	−0.546969	−	0.0585234i
$277$	189.335	+	189.335i	0.683521	+	0.683521i	0.960792	−	0.277271i	$-0.0894298\pi$
$277$	189.335	+	189.335i	0.683521	+	0.683521i	−0.277271	+	0.960792i	$0.589430\pi$
$278$	402.973	−	362.157i	1.44954	−	1.30272i
$279$	443.674			1.59023
$280$	50.3877	−	153.358i	0.179956	−	0.547708i
$281$		−	86.3451i		−	0.307278i	−0.988127	−	0.153639i	$-0.950901\pi$
$281$		−	86.3451i		−	0.307278i	0.988127	−	0.153639i	$-0.0490993\pi$
$282$	231.219	+	257.278i	0.819925	+	0.912334i
$283$	160.770	+	160.770i	0.568094	+	0.568094i	0.931594	−	0.363500i	$-0.118418\pi$
$283$	160.770	+	160.770i	0.568094	+	0.568094i	−0.363500	+	0.931594i	$0.618418\pi$
$284$	336.077	+	35.9588i	1.18337	+	0.126616i
$285$	−293.869	−	404.888i	−1.03112	−	1.42066i
$286$	119.693	−	84.9005i	0.418507	−	0.296855i
$287$	−59.7797	−	59.7797i	−0.208292	−	0.208292i
$288$	233.628	−	133.432i	0.811209	−	0.463307i
$289$			102.601i			0.355022i
$290$	228.199	+	352.491i	0.786894	+	1.21549i
$291$			507.563i			1.74420i
$292$	−5.81698	−	7.21091i	−0.0199212	−	0.0246949i
$293$	5.51757	−	5.51757i	0.0188313	−	0.0188313i	−0.697628	−	0.716460i	$-0.745761\pi$
$293$	5.51757	−	5.51757i	0.0188313	−	0.0188313i	0.716460	+	0.697628i	$0.245761\pi$
$294$	−14.5417	+	272.594i	−0.0494617	+	0.927192i
$295$	240.253	+	38.1718i	0.814417	+	0.129396i
$296$	−73.5264	+	455.943i	−0.248400	+	1.54035i
$297$	27.0024	+	3.12314i	0.0909173	+	0.0105156i
$298$	22.2743	+	24.7847i	0.0747459	+	0.0831700i
$299$		−	60.6817i		−	0.202949i
$300$	−148.413	−	389.937i	−0.494711	−	1.29979i
$301$	−132.869			−0.441424
$302$	111.285	+	123.827i	0.368494	+	0.410024i
$303$	−126.671	−	126.671i	−0.418057	−	0.418057i
$304$	81.1815	−	375.024i	0.267044	−	1.23363i
$305$	−48.2657	+	303.784i	−0.158248	+	0.996013i
$306$	−332.287	−	17.7261i	−1.08591	−	0.0579284i
$307$	−246.073	+	246.073i	−0.801541	+	0.801541i	−0.983336	−	0.181796i	$-0.941809\pi$
$307$	−246.073	+	246.073i	−0.801541	+	0.801541i	0.181796	+	0.983336i	$0.441809\pi$
$308$	−173.219	−	39.0517i	−0.562399	−	0.126791i
$309$		−	19.1024i		−	0.0618200i
$310$	442.972	−	286.776i	1.42894	−	0.925084i
$311$			415.341i			1.33550i	0.744385	+	0.667750i	$0.232743\pi$
$311$			415.341i			1.33550i	−0.744385	+	0.667750i	$0.767257\pi$
$312$	130.359	+	180.487i	0.417818	+	0.578484i
$313$	−124.153	−	124.153i	−0.396656	−	0.396656i	0.480396	−	0.877052i	$-0.340493\pi$
$313$	−124.153	−	124.153i	−0.396656	−	0.396656i	−0.877052	+	0.480396i	$0.840493\pi$
$314$	−71.8502	−	3.83290i	−0.228822	−	0.0122067i
$315$	−99.6518	−	137.299i	−0.316355	−	0.435869i
$316$	160.587	+	17.1822i	0.508188	+	0.0543741i
$317$	173.038	−	173.038i	0.545861	−	0.545861i	−0.379380	−	0.925241i	$-0.623863\pi$
$317$	173.038	−	173.038i	0.545861	−	0.545861i	0.925241	+	0.379380i	$0.123863\pi$
$318$	69.8168	+	77.6854i	0.219550	+	0.244294i
$319$	361.977	−	286.924i	1.13473	−	0.899450i
$320$	147.013	−	284.231i	0.459414	−	0.888222i
$321$			803.286i			2.50245i
$322$	−54.6122	+	49.0806i	−0.169603	+	0.152424i
$323$	−335.576	+	335.576i	−1.03893	+	1.03893i
$324$	−36.5891	+	341.967i	−0.112929	+	1.05545i
$325$	148.655	−	75.5621i	0.457401	−	0.232499i
$326$	−244.116	−	13.0225i	−0.748821	−	0.0399464i
$327$	−27.0468	+	27.0468i	−0.0827118	+	0.0827118i
$328$	−98.1267	−	135.860i	−0.299167	−	0.414207i
$329$	167.290			0.508481
$330$	−411.366	+	203.498i	−1.24656	+	0.616660i
$331$			178.943i			0.540613i	0.962774	+	0.270306i	$0.0871250\pi$
$331$			178.943i			0.540613i	−0.962774	+	0.270306i	$0.912875\pi$
$332$	179.963	−	145.175i	0.542058	−	0.437273i
$333$	343.209	+	343.209i	1.03066	+	1.03066i
$334$	−569.645	−	30.3881i	−1.70552	−	0.0909824i
$335$	−34.9636	−	48.1724i	−0.104369	−	0.143798i
$336$	56.9970	−	263.302i	0.169634	−	0.783638i
$337$	−198.832	−	198.832i	−0.590007	−	0.590007i	0.347626	−	0.937633i	$-0.386988\pi$
$337$	−198.832	−	198.832i	−0.590007	−	0.590007i	−0.937633	+	0.347626i	$0.886988\pi$
$338$	185.210	−	166.450i	0.547957	−	0.492456i
$339$	−279.267			−0.823797
$340$	−343.219	+	197.081i	−1.00947	+	0.579651i
$341$	−360.575	−	454.894i	−1.05741	−	1.33400i
$342$	−269.557	−	299.938i	−0.788180	−	0.877010i
$343$	233.179	+	233.179i	0.679822	+	0.679822i
$344$	−260.034	−	41.9336i	−0.755912	−	0.121900i
$345$	−29.7792	+	187.430i	−0.0863166	+	0.543277i
$346$	421.468	+	22.4835i	1.21811	+	0.0649812i
$347$	−142.195	+	142.195i	−0.409783	+	0.409783i	−0.881663	−	0.471880i	$-0.843576\pi$
$347$	−142.195	+	142.195i	−0.409783	+	0.409783i	0.471880	+	0.881663i	$0.343576\pi$
$348$	440.002	+	545.440i	1.26437	+	1.56736i
$349$	−474.609			−1.35991			−0.679956	−	0.733253i	$-0.738001\pi$
$349$	−474.609			−1.35991			−0.679956	+	0.733253i	$0.738001\pi$
$350$	−188.240	−	72.6702i	−0.537828	−	0.207629i
$351$	−16.4832			−0.0469606
$352$	−326.677	−	131.095i	−0.928060	−	0.372430i
$353$	−369.364	−	369.364i	−1.04636	−	1.04636i	−0.998872	−	0.0474863i	$-0.984879\pi$
$353$	−369.364	−	369.364i	−1.04636	−	1.04636i	−0.0474863	−	0.998872i	$-0.515121\pi$
$354$	405.412	+	21.6270i	1.14523	+	0.0610931i
$355$	66.2949	−	417.260i	0.186746	−	1.17538i
$356$	−21.3238	−	2.28156i	−0.0598983	−	0.00640887i
$357$	−235.606	+	235.606i	−0.659960	+	0.659960i
$358$	137.917	+	153.460i	0.385242	+	0.428660i
$359$		−	65.7181i		−	0.183059i	−0.995802	−	0.0915294i	$-0.970824\pi$
$359$		−	65.7181i		−	0.183059i	0.995802	−	0.0915294i	$-0.0291755\pi$
$360$	−151.694	−	300.154i	−0.421373	−	0.833762i
$361$	−214.131			−0.593162
$362$	160.455	+	178.539i	0.443246	+	0.493201i
$363$	266.066	+	429.040i	0.732964	+	1.18193i
$364$	107.063	+	11.4553i	0.294130	+	0.0314707i
$365$	−9.37241	+	6.80251i	−0.0256778	+	0.0186370i
$366$	−27.3459	+	512.616i	−0.0747155	+	1.40059i
$367$	−296.069	−	296.069i	−0.806728	−	0.806728i	0.177409	−	0.984137i	$-0.443229\pi$
$367$	−296.069	−	296.069i	−0.806728	−	0.806728i	−0.984137	+	0.177409i	$0.943229\pi$
$368$	−122.370	+	78.8187i	−0.332527	+	0.214181i
$369$	−176.132			−0.477323
$370$	564.506	+	120.828i	1.52569	+	0.326561i
$371$	50.5135			0.136155
$372$	685.450	−	552.946i	1.84261	−	1.48642i
$373$	397.167	−	397.167i	1.06479	−	1.06479i	0.0670417	−	0.997750i	$-0.478644\pi$
$373$	397.167	−	397.167i	1.06479	−	1.06479i	0.997750	−	0.0670417i	$-0.0213560\pi$
$374$	251.877	+	355.096i	0.673467	+	0.949455i
$375$	−496.240	+	160.441i	−1.32331	+	0.427842i
$376$	327.400	+	52.7971i	0.870744	+	0.140418i
$377$	−198.055	+	198.055i	−0.525346	+	0.525346i
$378$	13.3319	+	14.8345i	0.0352697	+	0.0392447i
$379$	−33.0684			−0.0872516			−0.0436258	−	0.999048i	$-0.513891\pi$
$379$	−33.0684			−0.0872516			−0.0436258	+	0.999048i	$0.513891\pi$
$380$	−463.001	−	125.230i	−1.21842	−	0.329554i
$381$		−	800.041i		−	2.09984i
$382$	−201.025	+	180.664i	−0.526244	+	0.472942i
$383$	−193.694	+	193.694i	−0.505728	+	0.505728i	−0.913212	−	0.407484i	$-0.866406\pi$
$383$	−193.694	+	193.694i	−0.505728	+	0.505728i	0.407484	+	0.913212i	$0.366406\pi$
$384$	194.646	−	497.314i	0.506891	−	1.29509i
$385$	−59.7836	+	213.755i	−0.155282	+	0.555208i
$386$	546.743	+	29.1664i	1.41643	+	0.0755606i
$387$	−195.739	+	195.739i	−0.505786	+	0.505786i
$388$	305.524	+	378.738i	0.787434	+	0.976128i
$389$			450.342i			1.15769i	0.815437	+	0.578845i	$0.196497\pi$
$389$			450.342i			1.15769i	−0.815437	+	0.578845i	$0.803503\pi$
$390$	233.618	−	151.242i	0.599022	−	0.387801i
$391$	180.026			0.460424
$392$	153.236	+	212.160i	0.390907	+	0.541224i
$393$	−658.303	+	658.303i	−1.67507	+	1.67507i
$394$	−6.59018	+	123.537i	−0.0167264	+	0.313546i
$395$	31.6777	−	199.379i	0.0801967	−	0.504758i
$396$	−312.712	+	197.652i	−0.789678	+	0.499122i
$397$	39.0747	−	39.0747i	0.0984250	−	0.0984250i	−0.656180	−	0.754605i	$-0.727829\pi$
$397$	39.0747	−	39.0747i	0.0984250	−	0.0984250i	0.754605	+	0.656180i	$0.227829\pi$
$398$	−347.528	−	386.695i	−0.873185	−	0.971596i
$399$	−403.796			−1.01202
$400$	−345.464	−	201.630i	−0.863660	−	0.504074i
$401$	166.655			0.415598			0.207799	−	0.978172i	$-0.433370\pi$
$401$	166.655			0.415598			0.207799	+	0.978172i	$0.433370\pi$
$402$	−66.4015	−	73.8852i	−0.165178	−	0.183794i
$403$	248.894	+	248.894i	0.617604	+	0.617604i
$404$	−170.769	−	18.2716i	−0.422697	−	0.0452268i
$405$	424.573	+	67.4568i	1.04833	+	0.166560i
$406$	338.437	+	18.0542i	0.833589	+	0.0444684i
$407$	72.9611	−	630.816i	0.179266	−	1.54992i
$408$	−535.456	+	386.740i	−1.31239	+	0.947893i
$409$	783.414			1.91544			0.957719	−	0.287705i	$-0.0928921\pi$
$409$	783.414			1.91544			0.957719	+	0.287705i	$0.0928921\pi$
$410$	−175.854	+	113.846i	−0.428912	+	0.277673i
$411$			180.578i			0.439362i
$412$	−11.4986	−	14.2540i	−0.0279091	−	0.0345970i
$413$	138.837	−	138.837i	0.336167	−	0.336167i
$414$	−8.14898	+	152.758i	−0.0196835	+	0.368981i
$415$	−169.771	−	233.908i	−0.409086	−	0.563634i
$416$	205.916	+	56.2083i	0.494989	+	0.135116i
$417$	−799.214	−	799.214i	−1.91658	−	1.91658i
$418$	−88.4522	+	520.134i	−0.211608	+	1.24434i
$419$	612.469			1.46174			0.730870	−	0.682517i	$-0.239115\pi$
$419$	612.469			1.46174			0.730870	+	0.682517i	$0.239115\pi$
$420$	−325.070	−	87.9235i	−0.773977	−	0.209342i
$421$	813.501			1.93231			0.966153	−	0.257968i	$-0.0830529\pi$
$421$	813.501			1.93231			0.966153	+	0.257968i	$0.0830529\pi$
$422$	−258.354	−	287.472i	−0.612214	−	0.681213i
$423$	246.449	−	246.449i	0.582621	−	0.582621i
$424$	98.8586	+	15.9421i	0.233157	+	0.0375994i
$425$	224.172	+	441.019i	0.527463	+	1.03769i
$426$	37.5607	−	704.100i	0.0881707	−	1.65282i
$427$	175.550	+	175.550i	0.411124	+	0.411124i
$428$	483.533	+	599.403i	1.12975	+	1.40047i
$429$	−190.163	−	239.906i	−0.443271	−	0.559220i
$430$	−68.9105	+	321.949i	−0.160257	+	0.748720i
$431$	−480.808			−1.11556			−0.557782	−	0.829987i	$-0.688348\pi$
$431$	−480.808			−1.11556			−0.557782	+	0.829987i	$0.688348\pi$
$432$	21.4098	+	33.2398i	0.0495597	+	0.0769439i
$433$	−332.664	−	332.664i	−0.768276	−	0.768276i	0.209527	−	0.977803i	$-0.432808\pi$
$433$	−332.664	−	332.664i	−0.768276	−	0.768276i	−0.977803	+	0.209527i	$0.932808\pi$
$434$	22.6885	−	425.311i	0.0522776	−	0.979979i
$435$	708.938	−	514.549i	1.62974	−	1.18287i
$436$	−3.90135	+	36.4626i	−0.00894804	+	0.0836298i
$437$	154.270	+	154.270i	0.353020	+	0.353020i
$438$	−14.3751	+	12.9191i	−0.0328198	+	0.0294956i
$439$			744.953i			1.69693i	0.529249	+	0.848466i	$0.322474\pi$
$439$			744.953i			1.69693i	−0.529249	+	0.848466i	$0.677526\pi$
$440$	−184.462	+	399.467i	−0.419233	+	0.907879i
$441$	275.050			0.623696
$442$	−176.464	−	196.352i	−0.399240	−	0.444236i
$443$	191.340	−	191.340i	0.431919	−	0.431919i	−0.457361	−	0.889281i	$-0.651205\pi$
$443$	191.340	−	191.340i	0.431919	−	0.431919i	0.889281	+	0.457361i	$0.151205\pi$
$444$	957.977	+	102.500i	2.15761	+	0.230855i
$445$	−4.20636	+	26.4748i	−0.00945249	+	0.0594940i
$446$	−350.587	−	18.7023i	−0.786069	−	0.0419334i
$447$	49.1553	−	49.1553i	0.109967	−	0.109967i
$448$	−115.963	−	230.782i	−0.258845	−	0.515138i
$449$			525.098i			1.16948i	0.811220	+	0.584742i	$0.198804\pi$
$449$			525.098i			1.16948i	−0.811220	+	0.584742i	$0.801196\pi$
$450$	−384.367	+	170.255i	−0.854149	+	0.378343i
$451$	143.143	+	180.586i	0.317391	+	0.400413i
$452$	−208.386	+	168.103i	−0.461031	+	0.371909i
$453$	245.586	−	245.586i	0.542133	−	0.542133i
$454$	−147.273	−	7.85638i	−0.324390	−	0.0173048i
$455$	21.1195	−	132.926i	0.0464164	−	0.292145i
$456$	−790.259	−	127.439i	−1.73303	−	0.279471i
$457$	487.268	+	487.268i	1.06623	+	1.06623i	0.997645	+	0.0685878i	$0.0218493\pi$
$457$	487.268	+	487.268i	1.06623	+	1.06623i	0.0685878	+	0.997645i	$0.478151\pi$
$458$	−476.516	+	428.251i	−1.04043	+	0.935046i
$459$		−	48.9010i		−	0.106538i
$460$	90.6016	+	157.784i	0.196960	+	0.343008i
$461$		−	45.5227i		−	0.0987477i	−0.998780	−	0.0493739i	$-0.984277\pi$
$461$		−	45.5227i		−	0.0987477i	0.998780	−	0.0493739i	$-0.0157226\pi$
$462$	−62.1018	+	365.183i	−0.134419	+	0.790440i
$463$	500.542	−	500.542i	1.08108	−	1.08108i	0.0846757	−	0.996409i	$-0.473015\pi$
$463$	500.542	−	500.542i	1.08108	−	1.08108i	0.996409	−	0.0846757i	$-0.0269854\pi$
$464$	656.648	+	142.145i	1.41519	+	0.306346i
$465$	−646.629	−	890.916i	−1.39060	−	1.91595i
$466$	−353.368	−	18.8507i	−0.758300	−	0.0404521i
$467$	−319.616	−	319.616i	−0.684403	−	0.684403i	0.276586	−	0.960989i	$-0.410797\pi$
$467$	−319.616	−	319.616i	−0.684403	−	0.684403i	−0.960989	+	0.276586i	$0.910797\pi$
$468$	174.599	−	140.848i	0.373075	−	0.300957i
$469$	−48.0425			−0.102436
$470$	86.7628	−	405.355i	0.184602	−	0.862458i
$471$			150.102i			0.318687i
$472$	315.531	−	227.897i	0.668499	−	0.482833i
$473$	359.767	+	41.6112i	0.760608	+	0.0879730i
$474$	17.9476	−	336.440i	0.0378642	−	0.709789i
$475$	−185.823	+	570.024i	−0.391207	+	1.20005i
$476$	−33.9848	+	317.628i	−0.0713967	+	0.667285i
$477$	74.4154	−	74.4154i	0.156007	−	0.156007i
$478$	−58.4375	+	52.5185i	−0.122254	+	0.109871i
$479$			353.953i			0.738942i	0.929242	+	0.369471i	$0.120461\pi$
$479$			353.953i			0.738942i	−0.929242	+	0.369471i	$0.879539\pi$
$480$	−608.438	−	274.666i	−1.26758	−	0.572220i
$481$			385.071i			0.800563i
$482$	−480.379	+	431.722i	−0.996636	+	0.895689i
$483$	108.312	+	108.312i	0.224248	+	0.224248i
$484$	456.793	+	159.988i	0.943787	+	0.330553i
$485$	492.266	−	357.288i	1.01498	−	0.736675i
$486$	672.023	+	35.8495i	1.38276	+	0.0737645i
$487$	547.477	+	547.477i	1.12418	+	1.12418i	0.991106	+	0.133076i	$0.0424855\pi$
$487$	547.477	+	547.477i	1.12418	+	1.12418i	0.133076	+	0.991106i	$0.457514\pi$
$488$	288.161	+	398.969i	0.590493	+	0.817558i
$489$			509.980i			1.04290i
$490$	274.615	−	177.783i	0.560439	−	0.362823i
$491$	741.586			1.51036			0.755180	−	0.655518i	$-0.227550\pi$
$491$	741.586			1.51036			0.755180	+	0.655518i	$0.227550\pi$
$492$	−272.114	+	219.512i	−0.553077	+	0.446163i
$493$	−587.576	−	587.576i	−1.19184	−	1.19184i
$494$	17.0428	−	319.478i	0.0344996	−	0.646717i
$495$	226.828	+	402.971i	0.458238	+	0.814084i
$496$	178.632	−	825.204i	0.360145	−	1.66372i
$497$	−241.126	−	241.126i	−0.485162	−	0.485162i
$498$	−322.422	−	358.760i	−0.647434	−	0.720402i
$499$	−114.519			−0.229497			−0.114749	−	0.993395i	$-0.536606\pi$
$499$	−114.519			−0.229497			−0.114749	+	0.993395i	$0.536606\pi$
$500$	−273.712	+	418.427i	−0.547425	+	0.836855i
$501$			1190.04i			2.37533i
$502$	−468.876	+	421.385i	−0.934016	+	0.839412i
$503$	4.53874	+	4.53874i	0.00902333	+	0.00902333i	0.711604	−	0.702581i	$-0.247969\pi$
$503$	4.53874	+	4.53874i	0.00902333	+	0.00902333i	−0.702581	+	0.711604i	$0.747969\pi$
$504$	−267.979	−	43.2149i	−0.531705	−	0.0857439i
$505$	−33.6862	+	212.021i	−0.0667053	+	0.419843i
$506$	163.244	−	115.792i	0.322616	−	0.228838i
$507$	−367.325	−	367.325i	−0.724507	−	0.724507i
$508$	−481.579	−	596.981i	−0.947991	−	1.17516i
$509$		−	506.523i		−	0.995135i	−0.867425	−	0.497567i	$-0.834227\pi$
$509$		−	506.523i		−	0.995135i	0.867425	−	0.497567i	$-0.165773\pi$
$510$	448.694	+	693.082i	0.879793	+	1.35898i
$511$			9.34714i			0.0182919i
$512$	−154.112	−	488.255i	−0.301000	−	0.953624i
$513$	41.9049	−	41.9049i	0.0816859	−	0.0816859i
$514$	−531.116	−	28.3328i	−1.03330	−	0.0551221i
$515$	−18.5267	+	13.4467i	−0.0359741	+	0.0261101i
$516$	−58.4576	+	546.354i	−0.113290	+	1.05883i
$517$	−452.971	−	52.3912i	−0.876152	−	0.101337i
$518$	346.555	−	311.453i	0.669026	−	0.601261i
$519$		−	880.486i		−	1.69650i
$520$	83.2839	−	253.480i	0.160161	−	0.487462i
$521$	−96.1043			−0.184461			−0.0922306	−	0.995738i	$-0.529400\pi$
$521$	−96.1043			−0.184461			−0.0922306	+	0.995738i	$0.529400\pi$
$522$	525.175	−	471.981i	1.00608	−	0.904178i
$523$	−676.382	−	676.382i	−1.29327	−	1.29327i	−0.932750	−	0.360524i	$-0.882598\pi$
$523$	−676.382	−	676.382i	−1.29327	−	1.29327i	−0.360524	−	0.932750i	$-0.617402\pi$
$524$	−94.9566	+	887.479i	−0.181215	+	1.69366i
$525$	−130.465	+	400.210i	−0.248506	+	0.762305i
$526$	−41.8658	+	784.803i	−0.0795929	+	1.49202i
$527$	−738.401	+	738.401i	−1.40114	+	1.40114i
$528$	−236.790	+	695.091i	−0.448466	+	1.31646i
$529$			446.239i			0.843552i
$530$	26.1981	−	122.397i	0.0494304	−	0.230939i
$531$		−	409.063i		−	0.770364i
$532$	−301.308	+	243.063i	−0.566368	+	0.456885i
$533$	−98.8076	−	98.8076i	−0.185380	−	0.185380i
$534$	−2.38320	+	44.6746i	−0.00446291	+	0.0836602i
$535$	779.076	−	565.455i	1.45622	−	1.05693i
$536$	−94.0228	−	15.1623i	−0.175416	−	0.0282879i
$537$	304.357	−	304.357i	0.566773	−	0.566773i
$538$	−269.504	+	242.206i	−0.500937	+	0.450198i
$539$	−223.534	−	282.005i	−0.414720	−	0.523201i
$540$	42.8593	−	24.6104i	0.0793691	−	0.0455749i
$541$			80.2693i			0.148372i	0.997244	+	0.0741861i	$0.0236359\pi$
$541$			80.2693i			0.148372i	−0.997244	+	0.0741861i	$0.976364\pi$
$542$	137.162	+	152.620i	0.253066	+	0.281587i
$543$	354.095	−	354.095i	0.652109	−	0.652109i
$544$	−166.755	+	610.895i	−0.306534	+	1.12297i
$545$	45.2706	+	7.19266i	0.0830652	+	0.0131975i
$546$	11.9656	−	224.304i	0.0219151	−	0.410813i
$547$	−104.234	+	104.234i	−0.190555	+	0.190555i	−0.795936	−	0.605381i	$-0.793021\pi$
$547$	−104.234	+	104.234i	−0.190555	+	0.190555i	0.605381	+	0.795936i	$0.293021\pi$
$548$	108.698	+	134.745i	0.198353	+	0.245885i
$549$	517.233			0.942138
$550$	486.936	+	255.720i	0.885339	+	0.464946i
$551$		−	1007.03i		−	1.82763i
$552$	177.791	+	246.158i	0.322085	+	0.445938i
$553$	−115.217	−	115.217i	−0.208349	−	0.208349i
$554$	28.5272	−	534.761i	0.0514931	−	0.965273i
$555$	188.972	−	1189.39i	0.340490	−	2.14304i
$556$	−1077.45	−	115.282i	−1.93785	−	0.207342i
$557$	269.311	+	269.311i	0.483503	+	0.483503i	0.906249	−	0.422745i	$-0.138934\pi$
$557$	269.311	+	269.311i	0.483503	+	0.483503i	−0.422745	+	0.906249i	$0.638934\pi$
$558$	−593.134	−	659.983i	−1.06297	−	1.18277i
$559$	−219.614			−0.392869
$560$	−295.489	+	130.066i	−0.527658	+	0.232262i
$561$	711.734	−	564.162i	1.26869	−	1.00564i
$562$	−128.442	+	115.432i	−0.228544	+	0.205395i
$563$	441.086	+	441.086i	0.783457	+	0.783457i	0.980412	−	0.196956i	$-0.0631055\pi$
$563$	441.086	+	441.086i	0.783457	+	0.783457i	−0.196956	+	0.980412i	$0.563105\pi$
$564$	73.6019	−	687.895i	0.130500	−	1.21967i
$565$	196.584	+	270.850i	0.347936	+	0.479381i
$566$	24.2233	−	454.082i	0.0427974	−	0.802265i
$567$	245.352	−	245.352i	0.432719	−	0.432719i
$568$	−395.801	−	548.000i	−0.696833	−	0.964789i
$569$	211.547			0.371787			0.185894	−	0.982570i	$-0.440482\pi$
$569$	211.547			0.371787			0.185894	+	0.982570i	$0.440482\pi$
$570$	−209.423	+	978.425i	−0.367409	+	1.71653i
$571$	−429.918			−0.752922			−0.376461	−	0.926432i	$-0.622859\pi$
$571$	−429.918			−0.752922			−0.376461	+	0.926432i	$0.622859\pi$
$572$	−286.307	−	64.5471i	−0.500537	−	0.112845i
$573$	398.692	+	398.692i	0.695798	+	0.695798i
$574$	−9.00701	+	168.842i	−0.0156917	+	0.294151i
$575$	202.744	−	103.056i	0.352598	−	0.179227i
$576$	−510.817	−	169.150i	−0.886835	−	0.293662i
$577$	157.849	−	157.849i	0.273569	−	0.273569i	−0.556966	−	0.830535i	$-0.688035\pi$
$577$	157.849	−	157.849i	0.273569	−	0.273569i	0.830535	+	0.556966i	$0.188035\pi$
$578$	152.624	−	137.165i	0.264055	−	0.237309i
$579$		−	1142.20i		−	1.97271i
$580$	219.272	−	810.691i	0.378055	−	1.39774i
$581$	−233.277			−0.401510
$582$	755.021	−	678.546i	1.29729	−	1.16589i
$583$	−136.775	−	15.8196i	−0.234605	−	0.0271348i
$584$	−2.94997	+	18.2930i	−0.00505132	+	0.0313237i
$585$	−164.711	−	226.936i	−0.281557	−	0.387925i
$586$	−15.5839	−	0.831333i	−0.0265936	−	0.00141866i
$587$	127.820	+	127.820i	0.217752	+	0.217752i	0.807550	−	0.589799i	$-0.200793\pi$
$587$	127.820	+	127.820i	0.217752	+	0.217752i	−0.589799	+	0.807550i	$0.700793\pi$
$588$	424.936	−	342.792i	0.722680	−	0.582979i
$589$	−1265.52			−2.14859
$590$	−264.405	−	408.417i	−0.448144	−	0.692232i
$591$	258.081			0.436685
$592$	776.530	−	500.164i	1.31171	−	0.844871i
$593$	284.588	−	284.588i	0.479912	−	0.479912i	−0.425191	−	0.905104i	$-0.639793\pi$
$593$	284.588	−	284.588i	0.479912	−	0.479912i	0.905104	+	0.425191i	$0.139793\pi$
$594$	−31.4530	−	44.3424i	−0.0529511	−	0.0746506i
$595$	394.354	+	62.6556i	0.662780	+	0.105304i
$596$	7.09038	−	66.2678i	0.0118966	−	0.111188i
$597$	−766.931	+	766.931i	−1.28464	+	1.28464i
$598$	−90.2664	+	81.1235i	−0.150947	+	0.135658i
$599$	−495.013			−0.826399			−0.413200	−	0.910640i	$-0.635589\pi$
$599$	−495.013			−0.826399			−0.413200	+	0.910640i	$0.635589\pi$
$600$	−381.637	+	742.066i	−0.636062	+	1.23678i
$601$		−	1143.04i		−	1.90190i	−0.309341	−	0.950951i	$-0.600109\pi$
$601$		−	1143.04i		−	1.90190i	0.309341	−	0.950951i	$-0.399891\pi$
$602$	177.628	+	197.648i	0.295064	+	0.328318i
$603$	−70.7752	+	70.7752i	−0.117372	+	0.117372i
$604$	35.4244	−	331.082i	0.0586497	−	0.548149i
$605$	228.818	−	560.060i	0.378212	−	0.925719i
$606$	−19.0856	+	357.772i	−0.0314943	+	0.590382i
$607$	244.186	−	244.186i	0.402283	−	0.402283i	−0.476754	−	0.879037i	$-0.658187\pi$
$607$	244.186	−	244.186i	0.402283	−	0.402283i	0.879037	+	0.476754i	$0.158187\pi$
$608$	−666.393	+	380.598i	−1.09604	+	0.625984i
$609$		−	707.027i		−	1.16096i
$610$	516.416	−	334.323i	0.846583	−	0.548070i
$611$	276.508			0.452550
$612$	417.856	+	517.988i	0.682772	+	0.846386i
$613$	608.066	−	608.066i	0.991951	−	0.991951i	−0.00801702	−	0.999968i	$-0.502552\pi$
$613$	608.066	−	608.066i	0.991951	−	0.991951i	0.999968	+	0.00801702i	$0.00255192\pi$
$614$	695.011	+	37.0759i	1.13194	+	0.0603841i
$615$	256.703	+	353.681i	0.417403	+	0.575092i
$616$	173.480	+	309.877i	0.281624	+	0.503047i
$617$	−282.421	+	282.421i	−0.457732	+	0.457732i	−0.897910	−	0.440178i	$-0.854915\pi$
$617$	−282.421	+	282.421i	−0.457732	+	0.457732i	0.440178	+	0.897910i	$0.354915\pi$
$618$	−28.4156	+	25.5374i	−0.0459799	+	0.0413227i
$619$	−568.021			−0.917642			−0.458821	−	0.888529i	$-0.651728\pi$
$619$	−568.021			−0.917642			−0.458821	+	0.888529i	$0.651728\pi$
$620$	−1018.79	−	275.557i	−1.64321	−	0.444447i
$621$	−22.4806			−0.0362007
$622$	617.836	−	555.257i	0.993306	−	0.892696i
$623$	15.2992	+	15.2992i	0.0245573	+	0.0245573i
$624$	94.2083	−	435.203i	0.150975	−	0.697440i
$625$	504.922	+	368.346i	0.807875	+	0.589353i
$626$	−18.7062	+	350.660i	−0.0298821	+	0.560159i
$627$	1093.36	+	126.459i	1.74379	+	0.201689i
$628$	90.3528	+	112.004i	0.143874	+	0.178351i
$629$	−1142.40			−1.81621
$630$	−71.0161	+	331.787i	−0.112724	+	0.526646i
$631$		−	27.8174i		−	0.0440847i	−0.999757	−	0.0220423i	$-0.992983\pi$
$631$		−	27.8174i		−	0.0440847i	0.999757	−	0.0220423i	$-0.00701686\pi$
$632$	−189.125	−	261.851i	−0.299249	−	0.414321i
$633$	−570.141	+	570.141i	−0.900697	+	0.900697i
$634$	−488.730	−	26.0717i	−0.770868	−	0.0411225i
$635$	−775.928	+	563.170i	−1.22193	+	0.886882i
$636$	22.2242	−	207.711i	0.0349437	−	0.326589i
$637$	154.299	+	154.299i	0.242227	+	0.242227i
$638$	−910.729	−	154.875i	−1.42747	−	0.242751i
$639$	−710.442			−1.11180
$640$	−619.342	+	161.293i	−0.967722	+	0.252020i
$641$	−686.709			−1.07131			−0.535654	−	0.844438i	$-0.679935\pi$
$641$	−686.709			−1.07131			−0.535654	+	0.844438i	$0.679935\pi$
$642$	1194.92	−	1073.89i	1.86125	−	1.67273i
$643$	360.493	−	360.493i	0.560642	−	0.560642i	−0.368848	−	0.929490i	$-0.620248\pi$
$643$	360.493	−	360.493i	0.560642	−	0.560642i	0.929490	+	0.368848i	$0.120248\pi$
$644$	146.019	+	15.6234i	0.226737	+	0.0242600i
$645$	678.332	+	107.774i	1.05168	+	0.167092i
$646$	947.804	+	50.5613i	1.46719	+	0.0782682i
$647$	215.063	+	215.063i	0.332400	+	0.332400i	0.853497	−	0.521098i	$-0.174477\pi$
$647$	215.063	+	215.063i	0.332400	+	0.332400i	−0.521098	+	0.853497i	$0.674477\pi$
$648$	557.605	−	402.738i	0.860501	−	0.621509i
$649$	−419.408	+	332.447i	−0.646237	+	0.512246i
$650$	−311.134	−	120.114i	−0.478668	−	0.184791i
$651$	−888.514			−1.36485
$652$	306.979	+	380.541i	0.470827	+	0.583652i
$653$	−621.487	−	621.487i	−0.951742	−	0.951742i	0.0471461	−	0.998888i	$-0.484987\pi$
$653$	−621.487	−	621.487i	−0.951742	−	0.951742i	−0.998888	+	0.0471461i	$0.984987\pi$
$654$	76.3912	+	4.07514i	0.116806	+	0.00623110i
$655$	1101.86	+	175.065i	1.68223	+	0.267275i
$656$	−70.9143	+	327.594i	−0.108101	+	0.499382i
$657$	13.7700	+	13.7700i	0.0209589	+	0.0209589i
$658$	−223.646	−	248.851i	−0.339887	−	0.378193i
$659$		−	2.90418i		−	0.00440694i	−0.999998	−	0.00220347i	$-0.999299\pi$
$659$		−	2.90418i		−	0.00440694i	0.999998	−	0.00220347i	$-0.000701387\pi$
$660$	852.654	+	339.874i	1.29190	+	0.514960i
$661$	−881.200			−1.33313			−0.666566	−	0.745446i	$-0.732237\pi$
$661$	−881.200			−1.33313			−0.666566	+	0.745446i	$0.732237\pi$
$662$	266.185	−	239.223i	0.402092	−	0.361365i
$663$	−389.424	+	389.424i	−0.587367	+	0.587367i
$664$	−456.541	−	73.6227i	−0.687561	−	0.110878i
$665$	284.243	+	391.626i	0.427433	+	0.588912i
$666$	51.7114	−	969.364i	0.0776448	−	1.45550i
$667$	−270.119	+	270.119i	−0.404975	+	0.404975i
$668$	716.338	+	887.995i	1.07236	+	1.32933i
$669$			732.409i			1.09478i
$670$	−24.9166	+	116.410i	−0.0371889	+	0.173746i
$671$	−420.358	−	530.314i	−0.626464	−	0.790333i
$672$	−467.871	+	267.216i	−0.696236	+	0.397642i
$673$	200.228	−	200.228i	0.297516	−	0.297516i	−0.542524	−	0.840040i	$-0.682531\pi$
$673$	200.228	−	200.228i	0.297516	−	0.297516i	0.840040	+	0.542524i	$0.182531\pi$
$674$	−29.9581	+	561.585i	−0.0444482	+	0.833211i
$675$	−27.9934	−	55.0720i	−0.0414716	−	0.0815882i
$676$	−495.202	−	52.9846i	−0.732548	−	0.0783796i
$677$	434.262	+	434.262i	0.641450	+	0.641450i	0.950912	−	0.309462i	$-0.100149\pi$
$677$	434.262	+	434.262i	0.641450	+	0.641450i	−0.309462	+	0.950912i	$0.600149\pi$
$678$	373.344	+	415.421i	0.550655	+	0.612716i
$679$		−	490.939i		−	0.723032i
$680$	752.006	+	247.081i	1.10589	+	0.363354i
$681$			307.667i			0.451787i
$682$	−194.630	+	1144.50i	−0.285382	+	1.67816i
$683$	−558.733	+	558.733i	−0.818057	+	0.818057i	−0.985826	−	0.167770i	$-0.946344\pi$
$683$	−558.733	+	558.733i	−0.818057	+	0.818057i	0.167770	+	0.985826i	$0.446344\pi$
$684$	−85.8059	+	801.955i	−0.125447	+	1.17245i
$685$	175.136	−	127.114i	0.255672	−	0.185567i
$686$	35.1331	−	658.593i	0.0512144	−	0.960048i
$687$	945.072	+	945.072i	1.37565	+	1.37565i
$688$	285.254	+	442.871i	0.414613	+	0.643707i
$689$	83.4919			0.121178
$690$	318.621	−	206.272i	0.461770	−	0.298946i
$691$			999.806i			1.44690i	0.690378	+	0.723449i	$0.257444\pi$
$691$			999.806i			1.44690i	−0.690378	+	0.723449i	$0.742556\pi$
$692$	−530.003	−	657.008i	−0.765900	−	0.949433i
$693$	370.760	+	42.8827i	0.535008	+	0.0618798i
$694$	401.617	+	21.4245i	0.578698	+	0.0308711i
$695$	−212.538	+	1337.72i	−0.305811	+	1.92477i
$696$	223.139	−	1383.70i	0.320602	−	1.98808i
$697$	293.135	−	293.135i	0.420567	−	0.420567i
$698$	634.491	+	706.000i	0.909013	+	1.01146i
$699$			738.219i			1.05611i
$700$	143.552	+	377.165i	0.205075	+	0.538807i
$701$			1014.39i			1.44706i	0.690294	+	0.723529i	$0.257481\pi$
$701$			1014.39i			1.44706i	−0.690294	+	0.723529i	$0.742519\pi$
$702$	22.0359	+	24.5194i	0.0313901	+	0.0349279i
$703$	−978.959	−	978.959i	−1.39254	−	1.39254i
$704$	241.716	+	661.203i	0.343346	+	0.939209i
$705$	−854.064	−	135.695i	−1.21144	−	0.192475i
$706$	−55.6522	+	1043.24i	−0.0788275	+	1.47767i
$707$	122.522	+	122.522i	0.173299	+	0.173299i
$708$	−509.812	−	631.979i	−0.720073	−	0.892625i
$709$		−	492.819i		−	0.695091i	−0.937663	−	0.347545i	$-0.887015\pi$
$709$		−	492.819i		−	0.695091i	0.937663	−	0.347545i	$-0.112985\pi$
$710$	−709.319	+	459.206i	−0.999041	+	0.646770i
$711$	−339.470			−0.477455
$712$	25.1132	+	34.7702i	0.0352714	+	0.0488345i
$713$	339.456	+	339.456i	0.476095	+	0.476095i
$714$	665.448	+	35.4988i	0.932000	+	0.0497182i
$715$	−98.8140	+	353.308i	−0.138201	+	0.494137i
$716$	43.9018	−	410.313i	0.0613154	−	0.573063i
$717$	115.899	+	115.899i	0.161644	+	0.161644i
$718$	−97.7583	+	87.8566i	−0.136154	+	0.122363i
$719$	−826.112			−1.14897			−0.574487	−	0.818514i	$-0.694798\pi$
$719$	−826.112			−1.14897			−0.574487	+	0.818514i	$0.694798\pi$
$720$	−243.696	+	626.919i	−0.338467	+	0.870720i
$721$			18.4767i			0.0256265i
$722$	286.266	+	318.529i	0.396490	+	0.441176i
$723$	952.732	+	952.732i	1.31775	+	1.31775i
$724$	51.0763	−	477.367i	0.0705473	−	0.659346i
$725$	−998.082	−	325.367i	−1.37666	−	0.448782i
$726$	282.519	−	969.355i	0.389144	−	1.33520i
$727$	658.233	+	658.233i	0.905409	+	0.905409i	0.995898	−	0.0904881i	$-0.0288427\pi$
$727$	658.233	+	658.233i	0.905409	+	0.905409i	−0.0904881	+	0.995898i	$0.528843\pi$
$728$	−126.090	−	174.575i	−0.173200	−	0.239801i
$729$		−	630.102i		−	0.864337i
$730$	22.6487	+	4.84776i	0.0310256	+	0.00664077i
$731$		−	651.534i		−	0.891291i
$732$	799.095	−	644.623i	1.09166	−	0.880633i
$733$	−857.313	+	857.313i	−1.16959	+	1.16959i	−0.187289	+	0.982305i	$0.559970\pi$
$733$	−857.313	+	857.313i	−1.16959	+	1.16959i	−0.982305	+	0.187289i	$0.940030\pi$
$734$	−44.6088	+	836.222i	−0.0607750	+	1.13927i
$735$	−400.869	−	552.312i	−0.545400	−	0.751445i
$736$	280.839	+	76.6599i	0.381574	+	0.104158i
$737$	130.084	+	15.0457i	0.176505	+	0.0204148i
$738$	235.466	+	262.004i	0.319060	+	0.355019i
$739$		−	10.2097i		−	0.0138155i	−0.999976	−	0.00690775i	$-0.997801\pi$
$739$		−	10.2097i		−	0.0138155i	0.999976	−	0.00690775i	$-0.00219882\pi$
$740$	−574.935	−	1001.26i	−0.776940	−	1.35305i
$741$	−667.420			−0.900702
$742$	−67.5300	−	75.1409i	−0.0910108	−	0.101268i
$743$	−329.686	−	329.686i	−0.443723	−	0.443723i	0.449538	−	0.893261i	$-0.351589\pi$
$743$	−329.686	−	329.686i	−0.443723	−	0.443723i	−0.893261	+	0.449538i	$0.851589\pi$
$744$	−1738.89	−	280.417i	−2.33721	−	0.376904i
$745$	−82.2755	−	13.0721i	−0.110437	−	0.0175464i
$746$	−1121.76	−	59.8413i	−1.50370	−	0.0802162i
$747$	−343.659	+	343.659i	−0.460052	+	0.460052i
$748$	191.494	−	849.394i	0.256007	−	1.13555i
$749$		−	776.976i		−	1.03735i
$750$	902.071	+	523.689i	1.20276	+	0.698253i
$751$			967.225i			1.28792i	0.765061	+	0.643958i	$0.222709\pi$
$751$			967.225i			1.28792i	−0.765061	+	0.643958i	$0.777291\pi$
$752$	−359.153	−	557.603i	−0.477597	−	0.741493i
$753$	929.919	+	929.919i	1.23495	+	1.23495i
$754$	559.390	+	29.8410i	0.741896	+	0.0395770i
$755$	−411.059	−	65.3097i	−0.544449	−	0.0865029i
$756$	4.24384	−	39.6636i	0.00561354	−	0.0524651i
$757$	177.197	−	177.197i	0.234078	−	0.234078i	−0.580315	−	0.814392i	$-0.697070\pi$
$757$	177.197	−	177.197i	0.234078	−	0.234078i	0.814392	+	0.580315i	$0.197070\pi$
$758$	44.2081	+	49.1905i	0.0583220	+	0.0648951i
$759$	−259.355	−	327.196i	−0.341706	−	0.431088i
$760$	432.687	+	856.150i	0.569325	+	1.12651i
$761$		−	446.102i		−	0.586206i	−0.956081	−	0.293103i	$-0.905312\pi$
$761$		−	446.102i		−	0.586206i	0.956081	−	0.293103i	$-0.0946878\pi$
$762$	−1190.09	+	1069.55i	−1.56180	+	1.40361i
$763$	26.1609	−	26.1609i	0.0342869	−	0.0342869i
$764$	537.489	+	57.5091i	0.703520	+	0.0752737i
$765$	673.257	−	488.651i	0.880075	−	0.638760i
$766$	547.071	+	29.1839i	0.714192	+	0.0380991i
$767$	229.479	−	229.479i	0.299190	−	0.299190i
$768$	−999.991	+	375.300i	−1.30207	+	0.488672i
$769$	1010.16			1.31360			0.656800	−	0.754065i	$-0.271910\pi$
$769$	1010.16			1.31360			0.656800	+	0.754065i	$0.271910\pi$
$770$	397.892	−	196.832i	0.516743	−	0.255626i
$771$			1109.55i			1.43911i
$772$	−687.538	−	852.294i	−0.890594	−	1.10401i

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+(-1.33687 - 1.48754i) q^{2} +(-2.95023 + 2.95023i) q^{3} +(-0.425555 + 3.97730i) q^{4} +(4.93806 + 0.784567i) q^{5} +(8.33266 + 0.444512i) q^{6} +(2.85360 - 2.85360i) q^{7} +(6.48530 - 4.68410i) q^{8} -8.40772i q^{9} +(-5.43447 - 8.39443i) q^{10} +(-8.62034 + 6.83299i) q^{11} +(-10.4785 - 12.9894i) q^{12} +(4.71661 - 4.71661i) q^{13} +(-8.05974 - 0.429952i) q^{14} +(-16.8831 + 12.2538i) q^{15} +(-15.6378 - 3.38511i) q^{16} +(13.9929 + 13.9929i) q^{17} +(-12.5068 + 11.2400i) q^{18} +23.9819i q^{19} +(-5.22187 + 19.3063i) q^{20} +16.8376i q^{21} +(21.6886 + 3.68829i) q^{22} +(6.43276 - 6.43276i) q^{23} +(-5.31396 + 32.9523i) q^{24} +(23.7689 + 7.74848i) q^{25} +(-13.3216 - 0.710652i) q^{26} +(-1.74735 - 1.74735i) q^{27} +(10.1353 + 12.5640i) q^{28} -41.9911 q^{29} +(40.7985 + 8.73256i) q^{30} +52.7698i q^{31} +(15.8702 + 27.7873i) q^{32} +(5.27311 - 45.5909i) q^{33} +(2.10831 - 39.5216i) q^{34} +(16.3301 - 11.8524i) q^{35} +(33.4400 + 3.57794i) q^{36} +(-40.8207 + 40.8207i) q^{37} +(35.6740 - 32.0607i) q^{38} +27.8302i q^{39} +(35.6998 - 18.0422i) q^{40} -20.9489i q^{41} +(25.0465 - 22.5096i) q^{42} +(-23.2809 - 23.2809i) q^{43} +(-23.5084 - 37.1935i) q^{44} +(6.59642 - 41.5179i) q^{45} +(-18.1688 - 0.969226i) q^{46} +(29.3122 + 29.3122i) q^{47} +(56.1220 - 36.1483i) q^{48} +32.7139i q^{49} +(-20.2498 - 45.7159i) q^{50} -82.5645 q^{51} +(16.7522 + 20.7665i) q^{52} +(8.85084 + 8.85084i) q^{53} +(-0.263274 + 4.93525i) q^{54} +(-47.9287 + 26.9785i) q^{55} +(5.13991 - 31.8730i) q^{56} +(-70.7521 - 70.7521i) q^{57} +(56.1366 + 62.4634i) q^{58} +48.6533 q^{59} +(-41.5522 - 72.3637i) q^{60} +61.5189i q^{61} +(78.4972 - 70.5464i) q^{62} +(-23.9923 - 23.9923i) q^{63} +(20.1184 - 60.7557i) q^{64} +(26.9914 - 19.5904i) q^{65} +(-74.8678 + 53.1051i) q^{66} +(-8.41788 - 8.41788i) q^{67} +(-61.6086 + 49.6991i) q^{68} +37.9563i q^{69} +(-39.4622 - 8.44653i) q^{70} -84.4988i q^{71} +(-39.3826 - 54.5266i) q^{72} +(-1.63778 + 1.63778i) q^{73} +(115.295 + 6.15047i) q^{74} +(-92.9836 + 47.2640i) q^{75} +(-95.3832 - 10.2056i) q^{76} +(-5.10039 + 44.0976i) q^{77} +(41.3985 - 37.2053i) q^{78} -40.3760i q^{79} +(-74.5646 - 28.9848i) q^{80} +85.9797 q^{81} +(-31.1623 + 28.0059i) q^{82} +(-40.8742 - 40.8742i) q^{83} +(-66.9680 - 7.16530i) q^{84} +(58.1194 + 80.0761i) q^{85} +(-3.50774 + 65.7548i) q^{86} +(123.883 - 123.883i) q^{87} +(-23.8991 + 84.6926i) q^{88} +5.36138i q^{89} +(-70.5781 + 45.6916i) q^{90} -26.9186i q^{91} +(22.8475 + 28.3225i) q^{92} +(-155.683 - 155.683i) q^{93} +(4.41647 - 82.7896i) q^{94} +(-18.8154 + 118.424i) q^{95} +(-128.800 - 35.1582i) q^{96} +(86.0209 - 86.0209i) q^{97} +(48.6633 - 43.7343i) q^{98} +(57.4499 + 72.4774i) 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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