LMFDB - Embedded newform 220.2.r.b.51.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(51,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 7]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("220.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.r (of order $10$, degree $4$, 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:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			51.2
Root			$-0.104528 - 0.994522i$ of defining polynomial
Character	$\chi$	$=$	220.51
Dual form			220.2.r.b.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.16913 - 0.795697i) q^{2} +(0.639886 + 0.207912i) q^{3} +(0.733733 - 1.86055i) q^{4} +(0.809017 - 0.587785i) q^{5} +(0.913545 - 0.266080i) q^{6} +(0.513506 + 1.58041i) q^{7} +(-0.622602 - 2.75905i) q^{8} +(-2.06082 - 1.49728i) q^{9} +(0.478148 - 1.33093i) q^{10} +(-0.384301 + 3.29428i) q^{11} +(0.856335 - 1.03799i) q^{12} +(-0.182636 + 0.251377i) q^{13} +(1.85788 + 1.43911i) q^{14} +(0.639886 - 0.207912i) q^{15} +(-2.92327 - 2.73029i) q^{16} +(0.867017 + 1.19335i) q^{17} +(-3.60075 - 0.110720i) q^{18} +(-0.342040 + 1.05269i) q^{19} +(-0.500000 - 1.93649i) q^{20} +1.11805i q^{21} +(2.17195 + 4.15724i) q^{22} -1.98524i q^{23} +(0.175244 - 1.89493i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-0.0135055 + 0.439216i) q^{26} +(-2.19381 - 3.01952i) q^{27} +(3.31720 + 0.204195i) q^{28} +(2.12543 - 0.690593i) q^{29} +(0.582676 - 0.752232i) q^{30} +(-6.00217 + 8.26128i) q^{31} +(-5.59017 - 0.866025i) q^{32} +(-0.930829 + 2.02807i) q^{33} +(1.96320 + 0.705295i) q^{34} +(1.34437 + 0.976746i) q^{35} +(-4.29785 + 2.73566i) q^{36} +(1.52642 + 4.69784i) q^{37} +(0.437733 + 1.50289i) q^{38} +(-0.169131 + 0.122881i) q^{39} +(-2.12543 - 1.86616i) q^{40} +(4.42987 + 1.43935i) q^{41} +(0.889625 + 1.30714i) q^{42} -3.30211 q^{43} +(5.84720 + 3.13214i) q^{44} -2.54732 q^{45} +(-1.57965 - 2.32101i) q^{46} +(-4.65701 - 1.51315i) q^{47} +(-1.30290 - 2.35486i) q^{48} +(3.42912 - 2.49140i) q^{49} +(-0.395472 - 1.35779i) q^{50} +(0.306682 + 0.943869i) q^{51} +(0.333693 + 0.524247i) q^{52} +(-9.05609 - 6.57963i) q^{53} +(-4.96747 - 1.78460i) q^{54} +(1.62543 + 2.89102i) q^{55} +(4.04072 - 2.40075i) q^{56} +(-0.437733 + 0.602488i) q^{57} +(1.93540 - 2.49859i) q^{58} +(3.61728 - 1.17533i) q^{59} +(0.0826761 - 1.34309i) q^{60} +(3.54082 + 4.87352i) q^{61} +(-0.443847 + 14.4344i) q^{62} +(1.30806 - 4.02580i) q^{63} +(-7.22473 + 3.43558i) q^{64} +0.310719i q^{65} +(0.525466 + 3.11173i) q^{66} -8.88598i q^{67} +(2.85644 - 0.737529i) q^{68} +(0.412756 - 1.27033i) q^{69} +(2.34894 + 0.0722281i) q^{70} +(6.56322 + 9.03350i) q^{71} +(-2.84799 + 6.61813i) q^{72} +(4.94844 - 1.60784i) q^{73} +(5.52264 + 4.27782i) q^{74} +(0.395472 - 0.544320i) q^{75} +(1.70761 + 1.40877i) q^{76} +(-5.40365 + 1.08428i) q^{77} +(-0.0999601 + 0.278240i) q^{78} +(-9.33304 - 6.78085i) q^{79} +(-3.96980 - 0.490594i) q^{80} +(1.58550 + 4.87967i) q^{81} +(6.32439 - 1.84205i) q^{82} +(13.8102 - 10.0337i) q^{83} +(2.08018 + 0.820346i) q^{84} +(1.40286 + 0.455818i) q^{85} +(-3.86060 + 2.62748i) q^{86} +1.50361 q^{87} +(9.32837 - 0.990723i) q^{88} -10.7378 q^{89} +(-2.97815 + 2.02689i) q^{90} +(-0.491063 - 0.159556i) q^{91} +(-3.69364 - 1.45664i) q^{92} +(-5.55832 + 4.03836i) q^{93} +(-6.64866 + 1.93649i) q^{94} +(0.342040 + 1.05269i) q^{95} +(-3.39702 - 1.71642i) q^{96} +(-8.32486 - 6.04836i) q^{97} +(2.02669 - 5.64131i) q^{98} +(5.72443 - 6.21354i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{2} + 5 q^{3} - q^{4} + 2 q^{5} + q^{6} - 3 q^{7} + 5 q^{8} + 3 q^{9} - 5 q^{10} - q^{11} - 10 q^{12} + 10 q^{13} + 5 q^{14} + 5 q^{15} + 7 q^{16} - 5 q^{17} - 10 q^{18} - 11 q^{19} - 4 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 8 * q + 5 * q^2 + 5 * q^3 - q^4 + 2 * q^5 + q^6 - 3 * q^7 + 5 * q^8 + 3 * q^9 - 5 * q^10 - q^11 - 10 * q^12 + 10 * q^13 + 5 * q^14 + 5 * q^15 + 7 * q^16 - 5 * q^17 - 10 * q^18 - 11 * q^19 - 4 * q^20 + q^22 + 3 * q^24 - 2 * q^25 + 7 * q^26 - 10 * q^27 - 9 * q^28 - 5 * q^29 - 6 * q^30 + 10 * q^31 - 11 * q^33 - 14 * q^34 + 8 * q^35 - 26 * q^36 + 20 * q^37 - 5 * q^38 + 3 * q^39 + 5 * q^40 + 10 * q^41 + 29 * q^42 - 34 * q^43 + 32 * q^44 - 8 * q^45 - 10 * q^46 - 23 * q^49 - 5 * q^50 + 9 * q^51 - 5 * q^52 - 7 * q^53 - 26 * q^54 - 9 * q^55 + 15 * q^56 + 5 * q^57 + 18 * q^58 - 5 * q^59 - 10 * q^60 - 10 * q^61 - q^62 - 23 * q^63 + 11 * q^64 - 17 * q^66 - 15 * q^68 + 15 * q^69 + 15 * q^70 + 90 * q^71 + 10 * q^72 + 5 * q^73 + 35 * q^74 + 5 * q^75 - 18 * q^76 - 14 * q^77 - 21 * q^79 - 7 * q^80 - 10 * q^81 - 2 * q^82 + 19 * q^83 - 30 * q^84 - 30 * q^86 - 18 * q^87 + 43 * q^88 + 20 * q^89 - 15 * q^90 - 10 * q^91 + 25 * q^92 + 11 * q^93 + 11 * q^95 - 36 * q^96 - 44 * q^97 + 50 * q^98 - 6 * q^99

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$

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 $

$2$	1.16913	−	0.795697i	0.826700	−	0.562643i
$2$	1.16913	−	0.795697i	0.826700	−	0.562643i
$3$	0.639886	+	0.207912i	0.369439	+	0.120038i	0.487852	−	0.872927i	$-0.337781\pi$
$3$	0.639886	+	0.207912i	0.369439	+	0.120038i	−0.118413	+	0.992964i	$0.537781\pi$
$4$	0.733733	−	1.86055i	0.366866	−	0.930274i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$	0.913545	−	0.266080i	0.372953	−	0.108627i
$7$	0.513506	+	1.58041i	0.194087	+	0.597338i	0.999986	+	0.00528511i	$0.00168231\pi$
$7$	0.513506	+	1.58041i	0.194087	+	0.597338i	−0.805899	+	0.592053i	$0.798318\pi$
$8$	−0.622602	−	2.75905i	−0.220123	−	0.975472i
$9$	−2.06082	−	1.49728i	−0.686941	−	0.499092i
$10$	0.478148	−	1.33093i	0.151204	−	0.420877i
$11$	−0.384301	+	3.29428i	−0.115871	+	0.993264i
$11$	−0.384301	+	3.29428i	−0.115871	+	0.993264i
$12$	0.856335	−	1.03799i	0.247203	−	0.299641i
$13$	−0.182636	+	0.251377i	−0.0506541	+	0.0697195i	−0.833593	−	0.552380i	$-0.813720\pi$
$13$	−0.182636	+	0.251377i	−0.0506541	+	0.0697195i	0.782939	+	0.622099i	$0.213720\pi$
$14$	1.85788	+	1.43911i	0.496539	+	0.384618i
$15$	0.639886	−	0.207912i	0.165218	−	0.0536826i
$16$	−2.92327	−	2.73029i	−0.730818	−	0.682572i
$17$	0.867017	+	1.19335i	0.210283	+	0.289429i	0.901110	−	0.433591i	$-0.142754\pi$
$17$	0.867017	+	1.19335i	0.210283	+	0.289429i	−0.690827	+	0.723020i	$0.742754\pi$
$18$	−3.60075	−	0.110720i	−0.848705	−	0.0260970i
$19$	−0.342040	+	1.05269i	−0.0784693	+	0.241504i	−0.982594	−	0.185764i	$-0.940524\pi$
$19$	−0.342040	+	1.05269i	−0.0784693	+	0.241504i	0.904125	+	0.427268i	$0.140524\pi$
$20$	−0.500000	−	1.93649i	−0.111803	−	0.433013i
$21$			1.11805i			0.243977i
$22$	2.17195	+	4.15724i	0.463062	+	0.886326i
$23$		−	1.98524i		−	0.413952i	−0.978346	−	0.206976i	$-0.933638\pi$
$23$		−	1.98524i		−	0.413952i	0.978346	−	0.206976i	$-0.0663622\pi$
$24$	0.175244	−	1.89493i	0.0357716	−	0.386800i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	−0.0135055	+	0.439216i	−0.00264865	+	0.0861373i
$27$	−2.19381	−	3.01952i	−0.422198	−	0.581106i
$28$	3.31720	+	0.204195i	0.626892	+	0.0385893i
$29$	2.12543	−	0.690593i	0.394682	−	0.128240i	−0.104951	−	0.994477i	$-0.533468\pi$
$29$	2.12543	−	0.690593i	0.394682	−	0.128240i	0.499632	+	0.866238i	$0.333468\pi$
$30$	0.582676	−	0.752232i	0.106382	−	0.137338i
$31$	−6.00217	+	8.26128i	−1.07802	+	1.48377i	−0.216341	+	0.976318i	$0.569412\pi$
$31$	−6.00217	+	8.26128i	−1.07802	+	1.48377i	−0.861680	+	0.507452i	$0.830588\pi$
$32$	−5.59017	−	0.866025i	−0.988212	−	0.153093i
$33$	−0.930829	+	2.02807i	−0.162037	+	0.353041i
$34$	1.96320	+	0.705295i	0.336686	+	0.120957i
$35$	1.34437	+	0.976746i	0.227241	+	0.165100i
$36$	−4.29785	+	2.73566i	−0.716308	+	0.455943i
$37$	1.52642	+	4.69784i	0.250942	+	0.772320i	0.994602	+	0.103762i	$0.0330881\pi$
$37$	1.52642	+	4.69784i	0.250942	+	0.772320i	−0.743660	+	0.668558i	$0.766912\pi$
$38$	0.437733	+	1.50289i	0.0710097	+	0.243801i
$39$	−0.169131	+	0.122881i	−0.0270826	+	0.0196766i
$40$	−2.12543	−	1.86616i	−0.336059	−	0.295066i
$41$	4.42987	+	1.43935i	0.691830	+	0.224789i	0.633767	−	0.773524i	$-0.281508\pi$
$41$	4.42987	+	1.43935i	0.691830	+	0.224789i	0.0580628	+	0.998313i	$0.481508\pi$
$42$	0.889625	+	1.30714i	0.137272	+	0.201696i
$43$	−3.30211			−0.503568			−0.251784	−	0.967784i	$-0.581017\pi$
$43$	−3.30211			−0.503568			−0.251784	+	0.967784i	$0.581017\pi$
$44$	5.84720	+	3.13214i	0.881498	+	0.472187i
$45$	−2.54732			−0.379732
$46$	−1.57965	−	2.32101i	−0.232907	−	0.342214i
$47$	−4.65701	−	1.51315i	−0.679294	−	0.220716i	−0.0510078	−	0.998698i	$-0.516243\pi$
$47$	−4.65701	−	1.51315i	−0.679294	−	0.220716i	−0.628286	+	0.777982i	$0.716243\pi$
$48$	−1.30290	−	2.35486i	−0.188058	−	0.339894i
$49$	3.42912	−	2.49140i	0.489874	−	0.355914i
$50$	−0.395472	−	1.35779i	−0.0559281	−	0.192021i
$51$	0.306682	+	0.943869i	0.0429440	+	0.132168i
$52$	0.333693	+	0.524247i	0.0462749	+	0.0726999i
$53$	−9.05609	−	6.57963i	−1.24395	−	0.903782i	−0.246095	−	0.969246i	$-0.579147\pi$
$53$	−9.05609	−	6.57963i	−1.24395	−	0.903782i	−0.997855	+	0.0654635i	$0.979147\pi$
$54$	−4.96747	−	1.78460i	−0.675986	−	0.242854i
$55$	1.62543	+	2.89102i	0.219172	+	0.389825i
$56$	4.04072	−	2.40075i	0.539963	−	0.320814i
$57$	−0.437733	+	0.602488i	−0.0579792	+	0.0798015i
$58$	1.93540	−	2.49859i	0.254130	−	0.328081i
$59$	3.61728	−	1.17533i	0.470930	−	0.153014i	−0.0639315	−	0.997954i	$-0.520364\pi$
$59$	3.61728	−	1.17533i	0.470930	−	0.153014i	0.534861	+	0.844940i	$0.320364\pi$
$60$	0.0826761	−	1.34309i	0.0106734	−	0.173392i
$61$	3.54082	+	4.87352i	0.453355	+	0.623990i	0.973114	−	0.230323i	$-0.0739782\pi$
$61$	3.54082	+	4.87352i	0.453355	+	0.623990i	−0.519759	+	0.854313i	$0.673978\pi$
$62$	−0.443847	+	14.4344i	−0.0563686	+	1.83317i
$63$	1.30806	−	4.02580i	0.164800	−	0.507203i
$64$	−7.22473	+	3.43558i	−0.903092	+	0.429448i
$65$			0.310719i			0.0385400i
$66$	0.525466	+	3.11173i	0.0646804	+	0.383028i
$67$		−	8.88598i		−	1.08560i	−0.839863	−	0.542798i	$-0.817365\pi$
$67$		−	8.88598i		−	1.08560i	0.839863	−	0.542798i	$-0.182635\pi$
$68$	2.85644	−	0.737529i	0.346394	−	0.0894385i
$69$	0.412756	−	1.27033i	0.0496899	−	0.152930i
$70$	2.34894	+	0.0722281i	0.280752	+	0.00863291i
$71$	6.56322	+	9.03350i	0.778911	+	1.07208i	0.995401	+	0.0957944i	$0.0305391\pi$
$71$	6.56322	+	9.03350i	0.778911	+	1.07208i	−0.216490	+	0.976285i	$0.569461\pi$
$72$	−2.84799	+	6.61813i	−0.335639	+	0.779954i
$73$	4.94844	−	1.60784i	0.579171	−	0.188184i	−0.00475834	−	0.999989i	$-0.501515\pi$
$73$	4.94844	−	1.60784i	0.579171	−	0.188184i	0.583929	+	0.811805i	$0.301515\pi$
$74$	5.52264	+	4.27782i	0.641994	+	0.497287i
$75$	0.395472	−	0.544320i	0.0456651	−	0.0628526i
$76$	1.70761	+	1.40877i	0.195877	+	0.161597i
$77$	−5.40365	+	1.08428i	−0.615803	+	0.123565i
$78$	−0.0999601	+	0.278240i	−0.0113182	+	0.0315045i
$79$	−9.33304	−	6.78085i	−1.05005	−	0.762905i	−0.0778272	−	0.996967i	$-0.524798\pi$
$79$	−9.33304	−	6.78085i	−1.05005	−	0.762905i	−0.972222	+	0.234062i	$0.924798\pi$
$80$	−3.96980	−	0.490594i	−0.443837	−	0.0548500i
$81$	1.58550	+	4.87967i	0.176167	+	0.542185i
$82$	6.32439	−	1.84205i	0.698412	−	0.203420i
$83$	13.8102	−	10.0337i	1.51587	−	1.10134i	0.552382	−	0.833591i	$-0.313719\pi$
$83$	13.8102	−	10.0337i	1.51587	−	1.10134i	0.963488	−	0.267753i	$-0.0862811\pi$
$84$	2.08018	+	0.820346i	0.226966	+	0.0895071i
$85$	1.40286	+	0.455818i	0.152162	+	0.0494404i
$86$	−3.86060	+	2.62748i	−0.416299	+	0.283329i
$87$	1.50361			0.161204
$88$	9.32837	−	0.990723i	0.994407	−	0.105611i
$89$	−10.7378			−1.13820			−0.569101	−	0.822268i	$-0.692709\pi$
$89$	−10.7378			−1.13820			−0.569101	+	0.822268i	$0.692709\pi$
$90$	−2.97815	+	2.02689i	−0.313924	+	0.213653i
$91$	−0.491063	−	0.159556i	−0.0514774	−	0.0167260i
$92$	−3.69364	−	1.45664i	−0.385089	−	0.151865i
$93$	−5.55832	+	4.03836i	−0.576371	+	0.418758i
$94$	−6.64866	+	1.93649i	−0.685757	+	0.199734i
$95$	0.342040	+	1.05269i	0.0350925	+	0.108004i
$96$	−3.39702	−	1.71642i	−0.346707	−	0.175181i
$97$	−8.32486	−	6.04836i	−0.845261	−	0.614118i	0.0785741	−	0.996908i	$-0.474963\pi$
$97$	−8.32486	−	6.04836i	−0.845261	−	0.614118i	−0.923835	+	0.382790i	$0.874963\pi$
$98$	2.02669	−	5.64131i	0.204726	−	0.569859i
$99$	5.72443	−	6.21354i	0.575327	−	0.624484i
$100$	−1.54275	−	1.27276i	−0.154275	−	0.127276i
$101$	11.0887	−	15.2624i	1.10337	−	1.51866i	0.272534	−	0.962146i	$-0.412138\pi$
$101$	11.0887	−	15.2624i	1.10337	−	1.51866i	0.830838	−	0.556515i	$-0.187862\pi$
$102$	1.10959	+	0.859481i	0.109865	+	0.0851013i
$103$	−0.656415	+	0.213282i	−0.0646785	+	0.0210153i	−0.341178	−	0.939999i	$-0.610826\pi$
$103$	−0.656415	+	0.213282i	−0.0646785	+	0.0210153i	0.276499	+	0.961014i	$0.410826\pi$
$104$	0.807272	+	0.347395i	0.0791595	+	0.0340648i
$105$	0.657170	+	0.904517i	0.0641333	+	0.0882719i
$106$	−15.8231	−	0.486549i	−1.53688	−	0.0472578i
$107$	5.60309	−	17.2445i	0.541671	−	1.66709i	−0.187106	−	0.982340i	$-0.559911\pi$
$107$	5.60309	−	17.2445i	0.541671	−	1.66709i	0.728777	−	0.684751i	$-0.240089\pi$
$108$	−7.22762	+	1.86616i	−0.695478	+	0.179572i
$109$			16.5020i			1.58061i	0.612715	+	0.790304i	$0.290077\pi$
$109$			16.5020i			1.58061i	−0.612715	+	0.790304i	$0.709923\pi$
$110$	4.20071	+	2.08663i	0.400522	+	0.198953i
$111$			3.32344i			0.315447i
$112$	2.81385	−	6.02198i	0.265884	−	0.569024i
$113$	3.79088	−	11.6671i	0.356616	−	1.09755i	−0.598451	−	0.801160i	$-0.704217\pi$
$113$	3.79088	−	11.6671i	0.356616	−	1.09755i	0.955067	−	0.296391i	$-0.0957833\pi$
$114$	−0.0323694	+	1.05269i	−0.00303167	+	0.0985934i
$115$	−1.16690	−	1.60610i	−0.108814	−	0.149769i
$116$	0.274614	−	4.46117i	0.0254973	−	0.414209i
$117$	0.752762	−	0.244587i	0.0695928	−	0.0226121i
$118$	3.29387	−	4.25237i	0.303225	−	0.391462i
$119$	−1.44076	+	1.98303i	−0.132074	+	0.181784i
$120$	−0.972034	−	1.63603i	−0.0887341	−	0.149349i
$121$	−10.7046	−	2.53200i	−0.973148	−	0.230181i
$122$	8.01752	+	2.88036i	0.725872	+	0.260776i
$123$	2.53536	+	1.84205i	0.228606	+	0.166092i
$124$	10.9665	+	17.2289i	0.984822	+	1.54720i
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$	−1.67402	−	5.74751i	−0.149134	−	0.512029i
$127$	−4.39547	+	3.19350i	−0.390035	+	0.283377i	−0.765470	−	0.643472i	$-0.777493\pi$
$127$	−4.39547	+	3.19350i	−0.390035	+	0.283377i	0.375435	+	0.926849i	$0.377493\pi$
$128$	−5.71297	+	9.76534i	−0.504960	+	0.863143i
$129$	−2.11298	−	0.686548i	−0.186037	−	0.0604472i
$130$	0.247238	+	0.363271i	0.0216842	+	0.0318610i
$131$	15.8761			1.38710			0.693551	−	0.720407i	$-0.256045\pi$
$131$	15.8761			1.38710			0.693551	+	0.720407i	$0.256045\pi$
$132$	3.09034	+	3.21991i	0.268979	+	0.280257i
$133$	−1.83932			−0.159489
$134$	−7.07055	−	10.3889i	−0.610803	−	0.897462i
$135$	−3.54965	−	1.15335i	−0.305506	−	0.0992648i
$136$	2.75270	−	3.13513i	0.236042	−	0.268835i
$137$	1.97155	−	1.43241i	0.168441	−	0.122379i	−0.500371	−	0.865811i	$-0.666803\pi$
$137$	1.97155	−	1.43241i	0.168441	−	0.122379i	0.668812	+	0.743432i	$0.266803\pi$
$138$	−0.528233	−	1.81361i	−0.0449662	−	0.154385i
$139$	−3.27240	−	10.0714i	−0.277562	−	0.854247i	−0.988530	−	0.151023i	$-0.951743\pi$
$139$	−3.27240	−	10.0714i	−0.277562	−	0.854247i	0.710969	−	0.703224i	$-0.248257\pi$
$140$	2.80369	−	1.78460i	0.236955	−	0.150826i
$141$	−2.66535	−	1.93649i	−0.224463	−	0.163082i
$142$	14.8612	+	5.33901i	1.24712	+	0.448039i
$143$	−0.757920	−	0.698260i	−0.0633805	−	0.0583914i
$144$	1.93635	+	10.0036i	0.161363	+	0.833632i
$145$	1.31359	−	1.80800i	0.109087	−	0.150146i
$146$	4.50601	−	5.81724i	0.372920	−	0.481438i
$147$	2.71224	−	0.881260i	0.223702	−	0.0726851i
$148$	9.86054	+	0.606981i	0.810531	+	0.0498935i
$149$	−1.22821	−	1.69049i	−0.100619	−	0.138490i	0.755739	−	0.654873i	$-0.227278\pi$
$149$	−1.22821	−	1.69049i	−0.100619	−	0.138490i	−0.856358	+	0.516383i	$0.827278\pi$
$150$	0.0292442	−	0.951057i	0.00238778	−	0.0776534i
$151$	−3.50536	+	10.7884i	−0.285262	+	0.877946i	0.701058	+	0.713104i	$0.252711\pi$
$151$	−3.50536	+	10.7884i	−0.285262	+	0.877946i	−0.986320	+	0.164842i	$0.947289\pi$
$152$	3.11738	+	0.288298i	0.252853	+	0.0233841i
$153$		−	3.75744i		−	0.303771i
$154$	−5.45482	+	5.56734i	−0.439562	+	0.448629i
$155$			10.2115i			0.820208i
$156$	0.104528	+	0.404837i	0.00836897	+	0.0324129i
$157$	4.86517	−	14.9735i	0.388283	−	1.19501i	−0.545788	−	0.837923i	$-0.683770\pi$
$157$	4.86517	−	14.9735i	0.388283	−	1.19501i	0.934071	−	0.357088i	$-0.116230\pi$
$158$	−16.3070	−	0.501428i	−1.29732	−	0.0398915i
$159$	−4.42689	−	6.09309i	−0.351075	−	0.483213i
$160$	−5.03158	+	2.58519i	−0.397781	+	0.204377i
$161$	3.13750	−	1.01943i	0.247269	−	0.0803427i
$162$	5.73639	+	4.44339i	0.450693	+	0.349106i
$163$	−9.01034	+	12.4017i	−0.705744	+	0.971374i	0.294134	+	0.955764i	$0.404969\pi$
$163$	−9.01034	+	12.4017i	−0.705744	+	0.971374i	−0.999878	+	0.0156093i	$0.995031\pi$
$164$	5.92833	−	7.18589i	0.462925	−	0.561124i
$165$	0.439011	+	2.18787i	0.0341770	+	0.170325i
$166$	8.16216	−	22.7195i	0.633507	−	1.76337i
$167$	−0.114153	−	0.0829373i	−0.00883346	−	0.00641788i	0.583360	−	0.812214i	$-0.301738\pi$
$167$	−0.114153	−	0.0829373i	−0.00883346	−	0.00641788i	−0.592193	+	0.805796i	$0.701738\pi$
$168$	3.08474	−	0.696098i	0.237993	−	0.0537051i
$169$	3.98739	+	12.2719i	0.306722	+	0.943993i
$170$	2.00282	−	0.583343i	0.153610	−	0.0447404i
$171$	2.28105	−	1.65728i	0.174436	−	0.126735i
$172$	−2.42287	+	6.14374i	−0.184742	+	0.468456i
$173$	10.0174	+	3.25486i	0.761612	+	0.247463i	0.663970	−	0.747759i	$-0.268870\pi$
$173$	10.0174	+	3.25486i	0.761612	+	0.247463i	0.0976417	+	0.995222i	$0.468870\pi$
$174$	1.75792	−	1.19642i	0.133268	−	0.0907004i
$175$	1.66174			0.125616
$176$	10.1178	−	8.58084i	0.762655	−	0.646805i
$177$	2.55901			0.192347
$178$	−12.5539	+	8.54401i	−0.940951	+	0.640401i
$179$	4.50894	+	1.46504i	0.337014	+	0.109502i	0.472635	−	0.881258i	$-0.343303\pi$
$179$	4.50894	+	1.46504i	0.337014	+	0.109502i	−0.135621	+	0.990761i	$0.543303\pi$
$180$	−1.86905	+	4.73941i	−0.139311	+	0.353254i
$181$	−6.42626	+	4.66895i	−0.477660	+	0.347040i	−0.800419	−	0.599441i	$-0.795390\pi$
$181$	−6.42626	+	4.66895i	−0.477660	+	0.347040i	0.322759	+	0.946481i	$0.395390\pi$
$182$	−0.701075	+	0.204195i	−0.0519671	+	0.0151360i
$183$	1.25246	+	3.85468i	0.0925845	+	0.284946i
$184$	−5.47739	+	1.23602i	−0.403799	+	0.0911205i
$185$	3.99622	+	2.90342i	0.293808	+	0.213464i
$186$	−3.28510	+	9.14411i	−0.240875	+	0.670479i
$187$	−4.26442	+	2.39760i	−0.311845	+	0.175330i
$188$	−6.23229	+	7.55433i	−0.454536	+	0.550956i
$189$	3.64553	−	5.01765i	0.265174	−	0.364980i
$190$	1.23751	+	0.958572i	0.0897785	+	0.0695421i
$191$	−8.18799	+	2.66044i	−0.592462	+	0.192503i	−0.589876	−	0.807494i	$-0.700823\pi$
$191$	−8.18799	+	2.66044i	−0.592462	+	0.192503i	−0.00258660	+	0.999997i	$0.500823\pi$
$192$	−5.33731	+	0.696277i	−0.385187	+	0.0502495i
$193$	12.7024	+	17.4833i	0.914338	+	1.25848i	0.965663	+	0.259797i	$0.0836555\pi$
$193$	12.7024	+	17.4833i	0.914338	+	1.25848i	−0.0513252	+	0.998682i	$0.516344\pi$
$194$	−14.5455	−	0.447263i	−1.04431	−	0.0321116i
$195$	−0.0646021	+	0.198825i	−0.00462626	+	0.0142382i
$196$	−2.11931	−	8.20806i	−0.151379	−	0.586290i
$197$			18.9681i			1.35142i	0.737168	+	0.675709i	$0.236162\pi$
$197$			18.9681i			1.35142i	−0.737168	+	0.675709i	$0.763838\pi$
$198$	1.74852	−	11.8193i	0.124262	−	0.839964i
$199$			14.9984i			1.06321i	0.846994	+	0.531603i	$0.178410\pi$
$199$			14.9984i			1.06321i	−0.846994	+	0.531603i	$0.821590\pi$
$200$	−2.81641	−	0.260464i	−0.199150	−	0.0184176i
$201$	1.84750	−	5.68602i	0.130313	−	0.401061i
$202$	0.819988	−	26.6670i	0.0576941	−	1.87628i
$203$	2.18284	+	3.00442i	0.153205	+	0.210869i
$204$	1.98114	+	0.121952i	0.138707	+	0.00853835i
$205$	4.42987	−	1.43935i	0.309396	−	0.100529i
$206$	−0.597727	+	0.771662i	−0.0416456	+	0.0537642i
$207$	−2.97246	+	4.09124i	−0.206600	+	0.284361i
$208$	1.22023	−	0.236194i	0.0846075	−	0.0163771i
$209$	−3.33641	−	1.53133i	−0.230785	−	0.105924i
$210$	1.48804	+	0.534591i	0.102685	+	0.0368903i
$211$	−5.86501	−	4.26118i	−0.403764	−	0.293351i	0.367309	−	0.930099i	$-0.380279\pi$
$211$	−5.86501	−	4.26118i	−0.403764	−	0.293351i	−0.771072	+	0.636748i	$0.780279\pi$
$212$	−18.8865	+	12.0216i	−1.29713	+	0.825646i
$213$	2.32155	+	7.14498i	0.159070	+	0.489566i
$214$	−7.17068	−	24.6195i	−0.490177	−	1.68295i
$215$	−2.67147	+	1.94093i	−0.182192	+	0.132371i
$216$	−6.96513	+	7.93278i	−0.473917	+	0.539758i
$217$	−16.1383	−	5.24366i	−1.09554	−	0.355963i
$218$	13.1306	+	19.2930i	0.889318	+	1.30669i
$219$	3.50073			0.236557
$220$	6.57151	−	0.902946i	0.443051	−	0.0608766i
$221$	−0.458329			−0.0308305
$222$	2.64445	+	3.88554i	0.177484	+	0.260780i
$223$	−24.9409	−	8.10377i	−1.67016	−	0.542669i	−0.687199	−	0.726469i	$-0.741160\pi$
$223$	−24.9409	−	8.10377i	−1.67016	−	0.542669i	−0.982964	+	0.183800i	$0.941160\pi$
$224$	−1.50191	−	9.27946i	−0.100351	−	0.620010i
$225$	−2.06082	+	1.49728i	−0.137388	+	0.0998184i
$226$	−4.85147	−	16.6568i	−0.322715	−	1.10799i
$227$	−0.464744	−	1.43034i	−0.0308462	−	0.0949347i	0.934448	−	0.356099i	$-0.115893\pi$
$227$	−0.464744	−	1.43034i	−0.0308462	−	0.0949347i	−0.965294	+	0.261165i	$0.915893\pi$
$228$	0.799778	+	1.25649i	0.0529666	+	0.0832130i
$229$	−5.33554	−	3.87650i	−0.352582	−	0.256166i	0.397369	−	0.917659i	$-0.369923\pi$
$229$	−5.33554	−	3.87650i	−0.352582	−	0.256166i	−0.749952	+	0.661493i	$0.769923\pi$
$230$	−2.64222	−	0.949240i	−0.174223	−	0.0625910i
$231$	−3.68316	−	0.429666i	−0.242334	−	0.0282700i
$232$	−3.22868	−	5.43420i	−0.211973	−	0.356772i
$233$	−10.8778	+	14.9720i	−0.712626	+	0.980845i	0.287111	+	0.957897i	$0.407305\pi$
$233$	−10.8778	+	14.9720i	−0.712626	+	0.980845i	−0.999737	+	0.0229478i	$0.992695\pi$
$234$	0.685460	−	0.884924i	0.0448099	−	0.0578493i
$235$	−4.65701	+	1.51315i	−0.303790	+	0.0987072i
$236$	0.467368	−	7.59249i	0.0304231	−	0.494229i
$237$	−4.56227	−	6.27942i	−0.296351	−	0.407892i
$238$	−0.106541	+	3.46483i	−0.00690600	+	0.224591i
$239$	−5.32504	+	16.3888i	−0.344448	+	1.06010i	0.617430	+	0.786626i	$0.288174\pi$
$239$	−5.32504	+	16.3888i	−0.344448	+	1.06010i	−0.961878	+	0.273478i	$0.911826\pi$
$240$	−2.43822	−	1.13929i	−0.157387	−	0.0735410i
$241$			10.1759i			0.655490i	0.944766	+	0.327745i	$0.106289\pi$
$241$			10.1759i			0.655490i	−0.944766	+	0.327745i	$0.893711\pi$
$242$	−14.5298	+	5.55740i	−0.934011	+	0.357243i
$243$			14.6491i			0.939737i
$244$	11.6654	−	3.01200i	0.746802	−	0.192824i
$245$	1.30981	−	4.03117i	0.0836805	−	0.257542i
$246$	4.42987	+	0.136215i	0.282438	+	0.00868475i
$247$	−0.202153	−	0.278240i	−0.0128627	−	0.0177040i
$248$	26.5303	+	11.4168i	1.68467	+	0.724968i
$249$	10.9231	−	3.54913i	0.692224	−	0.224917i
$250$	−1.11803	−	0.866025i	−0.0707107	−	0.0547723i
$251$	9.19424	−	12.6548i	0.580336	−	0.798763i	−0.413397	−	0.910551i	$-0.635658\pi$
$251$	9.19424	−	12.6548i	0.580336	−	0.798763i	0.993732	+	0.111788i	$0.0356577\pi$
$252$	−6.53042	−	5.38757i	−0.411378	−	0.339385i
$253$	6.53996	+	0.762932i	0.411164	+	0.0479651i
$254$	−2.59782	+	7.23108i	−0.163002	+	0.453718i
$255$	0.802903	+	0.583343i	0.0502798	+	0.0365304i
$256$	1.09104	+	15.9628i	0.0681903	+	0.997672i
$257$	4.47496	+	13.7725i	0.279140	+	0.859105i	0.988094	+	0.153851i	$0.0491674\pi$
$257$	4.47496	+	13.7725i	0.279140	+	0.859105i	−0.708954	+	0.705255i	$0.750833\pi$
$258$	−3.01663	+	0.878625i	−0.187807	+	0.0547008i
$259$	−6.64068	+	4.82473i	−0.412632	+	0.299794i
$260$	0.578108	+	0.227985i	0.0358527	+	0.0141390i
$261$	−5.41414	−	1.75916i	−0.335127	−	0.108889i
$262$	18.5612	−	12.6326i	1.14672	−	0.780443i
$263$	−16.8446			−1.03868			−0.519341	−	0.854567i	$-0.673823\pi$
$263$	−16.8446			−1.03868			−0.519341	+	0.854567i	$0.673823\pi$
$264$	6.17508	+	1.30553i	0.380050	+	0.0803496i
$265$	−11.1939			−0.687638
$266$	−2.15040	+	1.46354i	−0.131850	+	0.0897354i
$267$	−6.87095	−	2.23251i	−0.420496	−	0.136627i
$268$	−16.5328	−	6.51994i	−1.00990	−	0.398269i
$269$	11.8003	−	8.57345i	0.719479	−	0.522732i	−0.166738	−	0.986001i	$-0.553324\pi$
$269$	11.8003	−	8.57345i	0.719479	−	0.522732i	0.886218	+	0.463269i	$0.153324\pi$
$270$	−5.06773	+	1.47603i	−0.308412	+	0.0898283i
$271$	1.87439	+	5.76877i	0.113861	+	0.350428i	0.991708	−	0.128514i	$-0.0410206\pi$
$271$	1.87439	+	5.76877i	0.113861	+	0.350428i	−0.877847	+	0.478942i	$0.841021\pi$
$272$	0.723654	−	5.85569i	0.0438780	−	0.355053i
$273$	−0.281051	−	0.204195i	−0.0170100	−	0.0123585i
$274$	1.16523	−	3.24343i	0.0703940	−	0.195943i
$275$	3.01430	+	1.38348i	0.181769	+	0.0834271i
$276$	−2.06066	−	1.70003i	−0.124037	−	0.102330i
$277$	−5.19309	+	7.14768i	−0.312023	+	0.429462i	−0.936011	−	0.351972i	$-0.885511\pi$
$277$	−5.19309	+	7.14768i	−0.312023	+	0.429462i	0.623988	+	0.781434i	$0.285511\pi$
$278$	−11.8397	−	9.17096i	−0.710096	−	0.550038i
$279$	24.7388	−	8.03813i	1.48107	−	0.481230i
$280$	1.85788	−	4.31732i	0.111030	−	0.258009i
$281$	5.03966	+	6.93650i	0.300641	+	0.413797i	0.932434	−	0.361340i	$-0.117681\pi$
$281$	5.03966	+	6.93650i	0.300641	+	0.413797i	−0.631793	+	0.775137i	$0.717681\pi$
$282$	−4.65701	−	0.143199i	−0.277321	−	0.00852738i
$283$	−5.97118	+	18.3774i	−0.354950	+	1.09242i	0.601089	+	0.799182i	$0.294734\pi$
$283$	−5.97118	+	18.3774i	−0.354950	+	1.09242i	−0.956039	+	0.293241i	$0.905266\pi$
$284$	21.6229	−	5.58301i	1.28308	−	0.331291i
$285$			0.744716i			0.0441132i
$286$	−1.44171	−	0.213282i	−0.0852502	−	0.0126116i
$287$			7.74012i			0.456885i
$288$	10.2237	+	10.1548i	0.602436	+	0.598375i
$289$	4.58093	−	14.0987i	0.269467	−	0.829333i
$290$	0.0971366	−	3.15900i	0.00570406	−	0.185503i
$291$	−4.06944	−	5.60110i	−0.238555	−	0.328342i
$292$	0.639359	−	10.3865i	0.0374157	−	0.607826i
$293$	10.5732	−	3.43543i	0.617691	−	0.200700i	0.0165764	−	0.999863i	$-0.494723\pi$
$293$	10.5732	−	3.43543i	0.617691	−	0.200700i	0.601115	+	0.799162i	$0.294723\pi$
$294$	2.46974	−	3.18843i	0.144038	−	0.185953i
$295$	2.23560	−	3.07704i	0.130162	−	0.179152i
$296$	12.0112	−	7.13636i	0.698139	−	0.414793i
$297$	10.7902	−	6.06662i	0.626112	−	0.352021i
$298$	−2.78105	−	0.999115i	−0.161102	−	0.0578772i
$299$	0.499045	+	0.362577i	0.0288605	+	0.0209684i
$300$	−0.722562	−	1.13518i	−0.0417172	−	0.0655396i
$301$	−1.69565	−	5.21868i	−0.0977358	−	0.300800i
$302$	4.48606	+	15.4022i	0.258144	+	0.886299i
$303$	10.2688	−	7.46069i	0.589925	−	0.428606i
$304$	3.87402	−	2.14343i	0.222190	−	0.122934i
$305$	5.72916	+	1.86152i	0.328051	+	0.106590i
$306$	−2.98978	−	4.39294i	−0.170915	−	0.251128i
$307$	29.1089			1.66133			0.830666	−	0.556771i	$-0.187960\pi$
$307$	29.1089			1.66133			0.830666	+	0.556771i	$0.187960\pi$
$308$	−1.94748	+	10.8493i	−0.110968	+	0.618198i
$309$	−0.464375			−0.0264174
$310$	8.12526	+	11.9386i	0.461484	+	0.678066i
$311$	10.8418	+	3.52272i	0.614783	+	0.199755i	0.599823	−	0.800133i	$-0.295238\pi$
$311$	10.8418	+	3.52272i	0.614783	+	0.199755i	0.0149602	+	0.999888i	$0.495238\pi$
$312$	0.444335	+	0.390134i	0.0251555	+	0.0220870i
$313$	−2.55294	+	1.85482i	−0.144301	+	0.104841i	−0.657594	−	0.753373i	$-0.728426\pi$
$313$	−2.55294	+	1.85482i	−0.144301	+	0.104841i	0.513293	+	0.858214i	$0.328426\pi$
$314$	−6.22631	−	21.3771i	−0.351371	−	1.20638i
$315$	−1.30806	−	4.02580i	−0.0737009	−	0.226828i
$316$	−19.4640	+	12.3892i	−1.09494	+	0.696949i
$317$	−11.4737	−	8.33612i	−0.644426	−	0.468203i	0.216942	−	0.976185i	$-0.430392\pi$
$317$	−11.4737	−	8.33612i	−0.644426	−	0.468203i	−0.861368	+	0.507982i	$0.830392\pi$
$318$	−10.0239	−	3.60115i	−0.562110	−	0.201943i
$319$	1.45821	+	7.26715i	0.0816438	+	0.406882i
$320$	−3.82555	+	7.02604i	−0.213855	+	0.392767i
$321$	7.17068	−	9.86959i	0.400228	−	0.550867i
$322$	2.85698	−	3.68835i	0.159213	−	0.205544i
$323$	−1.55278	+	0.504528i	−0.0863989	+	0.0280727i
$324$	10.2422	+	0.630474i	0.569010	+	0.0350263i
$325$	0.182636	+	0.251377i	0.0101308	+	0.0139439i
$326$	−0.666294	+	21.6687i	−0.0369026	+	1.20012i
$327$	−3.43097	+	10.5594i	−0.189733	+	0.583938i
$328$	1.21320	−	13.1184i	0.0669878	−	0.724342i
$329$		−	8.13698i		−	0.448606i
$330$	2.25414	+	2.20858i	0.124086	+	0.121579i
$331$		−	35.8167i		−	1.96866i	−0.176330	−	0.984331i	$-0.556422\pi$
$331$		−	35.8167i		−	1.96866i	0.176330	−	0.984331i	$-0.443578\pi$
$332$	−8.53519	−	33.0567i	−0.468430	−	1.81422i
$333$	3.88828	−	11.9669i	0.213076	−	0.655782i
$334$	−0.199453	−	0.00613303i	−0.0109136	−	0.000335584i
$335$	−5.22305	−	7.18891i	−0.285366	−	0.392772i
$336$	3.05259	−	3.26835i	0.166532	−	0.178303i
$337$	17.6895	−	5.74766i	0.963607	−	0.313095i	0.215375	−	0.976531i	$-0.430903\pi$
$337$	17.6895	−	5.74766i	0.963607	−	0.313095i	0.748233	+	0.663437i	$0.230903\pi$
$338$	14.4265	+	11.1747i	0.784698	+	0.607825i
$339$	4.85147	−	6.67747i	0.263495	−	0.362670i
$340$	1.87740	−	2.27565i	0.101816	−	0.123414i
$341$	−24.9084	−	22.9477i	−1.34886	−	1.24269i
$342$	1.34815	−	3.75260i	0.0728998	−	0.202918i
$343$	15.1089	+	10.9773i	0.815805	+	0.592717i
$344$	2.05590	+	9.11070i	0.110847	+	0.491216i
$345$	−0.412756	−	1.27033i	−0.0222220	−	0.0683923i
$346$	14.3016	−	4.16549i	0.768858	−	0.223938i
$347$	−4.32788	+	3.14439i	−0.232333	+	0.168800i	−0.697861	−	0.716234i	$-0.745865\pi$
$347$	−4.32788	+	3.14439i	−0.232333	+	0.168800i	0.465528	+	0.885033i	$0.345865\pi$
$348$	1.10325	−	2.79754i	0.0591404	−	0.149964i
$349$	−18.0694	−	5.87111i	−0.967234	−	0.314274i	−0.217535	−	0.976052i	$-0.569802\pi$
$349$	−18.0694	−	5.87111i	−0.967234	−	0.314274i	−0.749699	+	0.661779i	$0.769802\pi$
$350$	1.94279	−	1.32224i	0.103846	−	0.0706767i
$351$	1.15971			0.0619005
$352$	5.00124	−	18.0828i	0.266567	−	0.963816i
$353$	−30.9248			−1.64596			−0.822979	−	0.568071i	$-0.807690\pi$
$353$	−30.9248			−1.64596			−0.822979	+	0.568071i	$0.807690\pi$
$354$	2.99182	−	2.03620i	0.159013	−	0.108223i
$355$	10.6195	+	3.45049i	0.563625	+	0.183133i
$356$	−7.87865	+	19.9781i	−0.417568	+	1.05884i
$357$	−1.33422	+	0.969364i	−0.0706142	+	0.0513042i
$358$	6.43727	−	1.87492i	0.340220	−	0.0990927i
$359$	−2.53477	−	7.80121i	−0.133780	−	0.411732i	0.861618	−	0.507557i	$-0.169451\pi$
$359$	−2.53477	−	7.80121i	−0.133780	−	0.411732i	−0.995398	+	0.0958245i	$0.969451\pi$
$360$	1.58597	+	7.02818i	0.0835878	+	0.370418i
$361$	14.3802	+	10.4478i	0.756850	+	0.549884i
$362$	−3.79807	+	10.5720i	−0.199622	+	0.555650i
$363$	−6.32331	−	3.84581i	−0.331888	−	0.201852i
$364$	−0.657170	+	0.796574i	−0.0344451	+	0.0417518i
$365$	3.05830	−	4.20939i	0.160079	−	0.220330i
$366$	4.53144	+	3.51004i	0.236862	+	0.183473i
$367$	11.3059	−	3.67351i	0.590163	−	0.191756i	0.00131453	−	0.999999i	$-0.499582\pi$
$367$	11.3059	−	3.67351i	0.590163	−	0.191756i	0.588848	+	0.808244i	$0.299582\pi$
$368$	−5.42029	+	5.80341i	−0.282552	+	0.302524i
$369$	−6.97408	−	9.59900i	−0.363056	−	0.499704i
$370$	6.98235	+	0.214702i	0.362995	+	0.0111618i
$371$	5.74815	−	17.6910i	0.298429	−	0.918471i
$372$	3.43523	+	13.3046i	0.178109	+	0.689811i
$373$		−	0.743922i		−	0.0385188i	−0.999815	−	0.0192594i	$-0.993869\pi$
$373$		−	0.743922i		−	0.0385188i	0.999815	−	0.0192594i	$-0.00613084\pi$
$374$	−3.07790	+	6.19629i	−0.159155	+	0.320403i
$375$		−	0.672816i		−	0.0347441i
$376$	−1.27540	+	13.7910i	−0.0657739	+	0.711217i
$377$	−0.214580	+	0.660410i	−0.0110515	+	0.0340129i
$378$	0.269579	−	8.76702i	0.0138656	−	0.450927i
$379$	−8.25467	−	11.3616i	−0.424014	−	0.583605i	0.542552	−	0.840022i	$-0.317458\pi$
$379$	−8.25467	−	11.3616i	−0.424014	−	0.583605i	−0.966566	+	0.256417i	$0.917458\pi$
$380$	2.20955	+	0.136012i	0.113347	+	0.00697727i
$381$	−3.47657	+	1.12961i	−0.178110	+	0.0578714i
$382$	−7.45593	+	9.62556i	−0.381479	+	0.492487i
$383$	18.1676	−	25.0056i	0.928322	−	1.27773i	−0.0321882	−	0.999482i	$-0.510248\pi$
$383$	18.1676	−	25.0056i	0.928322	−	1.27773i	0.960510	−	0.278244i	$-0.0897524\pi$
$384$	−5.68598	+	5.06092i	−0.290162	+	0.258264i
$385$	−3.73432	+	4.05339i	−0.190319	+	0.206580i
$386$	28.7622	+	10.3331i	1.46396	+	0.525939i
$387$	6.80507	+	4.94418i	0.345921	+	0.251327i
$388$	−17.3615	+	11.0509i	−0.881396	+	0.561025i
$389$	4.72653	+	14.5468i	0.239644	+	0.737550i	0.996471	+	0.0839343i	$0.0267486\pi$
$389$	4.72653	+	14.5468i	0.239644	+	0.737550i	−0.756827	+	0.653615i	$0.773251\pi$
$390$	0.0826761	+	0.283856i	0.00418647	+	0.0143736i
$391$	2.36909	−	1.72124i	0.119810	−	0.0870469i
$392$	−9.00888	−	7.90996i	−0.455017	−	0.399514i
$393$	10.1589	+	3.30083i	0.512449	+	0.166505i
$394$	15.0928	+	22.1761i	0.760366	+	1.11722i
$395$	−11.5363			−0.580453
$396$	−7.36037	−	15.2096i	−0.369873	−	0.764314i
$397$	30.1221			1.51178			0.755892	−	0.654696i	$-0.227203\pi$
$397$	30.1221			1.51178			0.755892	+	0.654696i	$0.227203\pi$
$398$	11.9342	+	17.5350i	0.598205	+	0.878953i
$399$	−1.17695	−	0.382416i	−0.0589214	−	0.0191447i
$400$	−3.50000	+	1.93649i	−0.175000	+	0.0968246i
$401$	−15.7563	+	11.4476i	−0.786834	+	0.571668i	−0.907022	−	0.421083i	$-0.861650\pi$
$401$	−15.7563	+	11.4476i	−0.786834	+	0.571668i	0.120188	+	0.992751i	$0.461650\pi$
$402$	−2.36438	−	8.11775i	−0.117925	−	0.404877i
$403$	−0.980483	−	3.01762i	−0.0488413	−	0.150318i
$404$	−20.2602	−	31.8296i	−1.00798	−	1.58358i
$405$	4.15089	+	3.01580i	0.206259	+	0.149856i
$406$	4.94262	+	1.77568i	0.245298	+	0.0881254i
$407$	−16.0626	+	3.22308i	−0.796195	+	0.159762i
$408$	2.41324	−	1.43381i	0.119473	−	0.0709840i
$409$	−13.4445	+	18.5047i	−0.664786	+	0.915000i	−0.999628	−	0.0272745i	$-0.991317\pi$
$409$	−13.4445	+	18.5047i	−0.664786	+	0.915000i	0.334842	+	0.942274i	$0.391317\pi$
$410$	4.03381	−	5.20763i	0.199216	−	0.257186i
$411$	1.55938	−	0.506673i	0.0769186	−	0.0249924i
$412$	−0.0848116	+	1.37778i	−0.00417837	+	0.0678785i
$413$	3.71499	+	5.11324i	0.182802	+	0.251606i
$414$	−0.219807	+	7.14837i	−0.0108029	+	0.351323i
$415$	5.27504	−	16.2349i	0.258941	−	0.796940i
$416$	1.23867	−	1.24707i	0.0607306	−	0.0611428i
$417$		−	7.12493i		−	0.348910i
$418$	−5.11918	+	0.864454i	−0.250387	+	0.0422818i
$419$			9.82290i			0.479880i	0.970788	+	0.239940i	$0.0771278\pi$
$419$			9.82290i			0.479880i	−0.970788	+	0.239940i	$0.922872\pi$
$420$	2.16508	−	0.559023i	0.105645	−	0.0272775i
$421$	−6.25831	+	19.2611i	−0.305011	+	0.938728i	0.674662	+	0.738127i	$0.264289\pi$
$421$	−6.25831	+	19.2611i	−0.305011	+	0.938728i	−0.979673	+	0.200601i	$0.935711\pi$
$422$	−10.2476	−	0.315104i	−0.498843	−	0.0153390i
$423$	7.33166	+	10.0912i	0.356477	+	0.490649i
$424$	−12.5152	+	29.0827i	−0.607792	+	1.41238i
$425$	1.40286	−	0.455818i	0.0680489	−	0.0221104i
$426$	8.39943	+	6.50617i	0.406954	+	0.315225i
$427$	−5.88392	+	8.09851i	−0.284743	+	0.391915i
$428$	−27.9731	−	23.0777i	−1.35213	−	1.11550i
$429$	−0.339807	−	0.604388i	−0.0164060	−	0.0291801i
$430$	−1.57890	+	4.39488i	−0.0761412	+	0.211940i
$431$	−26.6495	−	19.3620i	−1.28366	−	0.932636i	−0.284006	−	0.958822i	$-0.591664\pi$
$431$	−26.6495	−	19.3620i	−1.28366	−	0.932636i	−0.999657	+	0.0261864i	$0.991664\pi$
$432$	−1.83106	+	14.8166i	−0.0880967	+	0.712864i
$433$	−6.41735	−	19.7506i	−0.308398	−	0.949151i	−0.978387	−	0.206781i	$-0.933701\pi$
$433$	−6.41735	−	19.7506i	−0.308398	−	0.949151i	0.669989	−	0.742371i	$-0.266299\pi$
$434$	−23.0402	+	6.71070i	−1.10596	+	0.322124i
$435$	1.21645	−	0.883802i	0.0583243	−	0.0423751i
$436$	30.7028	+	12.1081i	1.47040	+	0.579872i
$437$	2.08985	+	0.679032i	0.0999709	+	0.0324825i
$438$	4.09281	−	2.78552i	0.195562	−	0.133097i
$439$	3.65495			0.174441			0.0872207	−	0.996189i	$-0.472201\pi$
$439$	3.65495			0.174441			0.0872207	+	0.996189i	$0.472201\pi$
$440$	6.96448	−	6.28459i	0.332018	−	0.299606i
$441$	−10.7971			−0.514149
$442$	−0.535846	+	0.364691i	−0.0254876	+	0.0173466i
$443$	−2.93134	−	0.952450i	−0.139272	−	0.0452523i	0.238551	−	0.971130i	$-0.423327\pi$
$443$	−2.93134	−	0.952450i	−0.139272	−	0.0452523i	−0.377824	+	0.925878i	$0.623327\pi$
$444$	6.18343	+	2.43852i	0.293452	+	0.115727i
$445$	−8.68704	+	6.31150i	−0.411805	+	0.299194i
$446$	−35.6073	+	10.3710i	−1.68605	+	0.491081i
$447$	−0.434443	−	1.33708i	−0.0205484	−	0.0632416i
$448$	−9.13956	−	9.65383i	−0.431804	−	0.456101i
$449$	1.20449	+	0.875112i	0.0568433	+	0.0412991i	0.615844	−	0.787868i	$-0.288815\pi$
$449$	1.20449	+	0.875112i	0.0568433	+	0.0412991i	−0.559001	+	0.829167i	$0.688815\pi$
$450$	−1.21799	+	3.39030i	−0.0574168	+	0.159820i
$451$	−6.44405	+	14.0401i	−0.303438	+	0.661124i
$452$	−18.9258	−	15.6137i	−0.890193	−	0.734405i
$453$	−4.48606	+	6.17453i	−0.210774	+	0.290105i
$454$	−1.68146	−	1.30245i	−0.0789148	−	0.0611272i
$455$	−0.491063	+	0.159556i	−0.0230214	+	0.00748010i
$456$	1.93483	+	0.832618i	0.0906067	+	0.0389909i
$457$	−5.86507	−	8.07258i	−0.274357	−	0.377619i	0.649498	−	0.760363i	$-0.274979\pi$
$457$	−5.86507	−	8.07258i	−0.274357	−	0.377619i	−0.923854	+	0.382744i	$0.874979\pi$
$458$	−9.32246	−	0.286658i	−0.435610	−	0.0133947i
$459$	1.70126	−	5.23594i	0.0794081	−	0.244393i
$460$	−3.84441	+	0.992622i	−0.179247	+	0.0462813i
$461$			19.5207i			0.909168i	0.890704	+	0.454584i	$0.150212\pi$
$461$			19.5207i			0.909168i	−0.890704	+	0.454584i	$0.849788\pi$
$462$	−4.64798	+	2.42834i	−0.216243	+	0.112977i
$463$		−	5.16101i		−	0.239852i	−0.992783	−	0.119926i	$-0.961734\pi$
$463$		−	5.16101i		−	0.239852i	0.992783	−	0.119926i	$-0.0382658\pi$
$464$	−8.09872	−	3.78424i	−0.375973	−	0.175679i
$465$	−2.12309	+	6.53420i	−0.0984560	+	0.303016i
$466$	−0.804386	+	26.1596i	−0.0372624	+	1.21182i
$467$	1.67953	+	2.31168i	0.0777195	+	0.106972i	0.846107	−	0.533013i	$-0.178940\pi$
$467$	1.67953	+	2.31168i	0.0777195	+	0.106972i	−0.768387	+	0.639985i	$0.778940\pi$
$468$	0.0972600	−	1.58001i	0.00449585	−	0.0730360i
$469$	14.0435	−	4.56300i	0.648467	−	0.210700i
$470$	−4.24064	+	5.47464i	−0.195606	+	0.252526i
$471$	6.22631	−	8.56978i	0.286893	−	0.394875i
$472$	−5.49491	−	9.24850i	−0.252924	−	0.425697i
$473$	1.26901	−	10.8781i	0.0583490	−	0.500176i
$474$	−10.3304	−	3.71128i	−0.474491	−	0.170465i
$475$	0.895472	+	0.650598i	0.0410871	+	0.0298515i
$476$	2.63239	+	4.13561i	0.120656	+	0.189555i
$477$	8.81148	+	27.1189i	0.403450	+	1.24169i
$478$	6.81485	+	23.3978i	0.311704	+	1.07019i
$479$	−25.1392	+	18.2647i	−1.14864	+	0.834536i	−0.988300	−	0.152525i	$-0.951259\pi$
$479$	−25.1392	+	18.2647i	−1.14864	+	0.834536i	−0.160341	+	0.987062i	$0.551259\pi$
$480$	−3.75713	+	0.608104i	−0.171489	+	0.0277560i
$481$	−1.45971	−	0.474288i	−0.0665570	−	0.0216257i
$482$	8.09697	+	11.8970i	0.368807	+	0.541894i
$483$	2.21959			0.100995
$484$	−12.5652	+	18.0587i	−0.571147	+	0.820848i
$485$	−10.2901			−0.467249
$486$	11.6562	+	17.1267i	0.528736	+	0.776881i
$487$	29.6282	+	9.62678i	1.34258	+	0.436231i	0.890190	−	0.455589i	$-0.150571\pi$
$487$	29.6282	+	9.62678i	1.34258	+	0.436231i	0.452391	+	0.891820i	$0.350571\pi$
$488$	11.2418	−	12.8036i	0.508891	−	0.579590i
$489$	−8.34404	+	6.06230i	−0.377331	+	0.274147i
$490$	−1.67626	−	5.75517i	−0.0757255	−	0.259992i
$491$	−8.44831	−	26.0012i	−0.381267	−	1.17342i	−0.939152	−	0.343501i	$-0.888387\pi$
$491$	−8.44831	−	26.0012i	−0.381267	−	1.17342i	0.557885	−	0.829918i	$-0.311613\pi$
$492$	5.28749	−	3.36558i	0.238378	−	0.151732i
$493$	2.66690	+	1.93761i	0.120111	+	0.0872658i
$494$	−0.457738	−	0.164446i	−0.0205946	−	0.00739879i
$495$	0.978938	−	8.39159i	0.0440000	−	0.377174i
$496$	40.1017	−	7.76231i	1.80062	−	0.348538i
$497$	−10.9064	+	15.0113i	−0.489217	+	0.673350i
$498$	9.94651	−	12.8409i	0.445714	−	0.575414i
$499$	−8.59428	+	2.79245i	−0.384733	+	0.125007i	−0.494996	−	0.868895i	$-0.664831\pi$
$499$	−8.59428	+	2.79245i	−0.384733	+	0.125007i	0.110263	+	0.993902i	$0.464831\pi$
$500$	−1.99622	−	0.122881i	−0.0892737	−	0.00549539i
$501$	−0.0558016	−	0.0768043i	−0.00249303	−	0.00343136i
$502$	0.679893	−	22.1109i	0.0303451	−	0.986859i
$503$	12.6723	−	39.0014i	0.565031	−	1.73899i	−0.102830	−	0.994699i	$-0.532790\pi$
$503$	12.6723	−	39.0014i	0.565031	−	1.73899i	0.667860	−	0.744287i	$-0.267210\pi$
$504$	−11.9218	−	1.10254i	−0.531039	−	0.0491109i
$505$		−	18.8653i		−	0.839495i
$506$	8.25313	−	4.31186i	0.366896	−	0.191686i
$507$			8.68165i			0.385566i
$508$	2.71655	+	10.5212i	0.120527	+	0.466801i
$509$	−9.13304	+	28.1086i	−0.404815	+	1.24589i	0.516235	+	0.856447i	$0.327333\pi$
$509$	−9.13304	+	28.1086i	−0.404815	+	1.24589i	−0.921050	+	0.389445i	$0.872667\pi$
$510$	1.40286	+	0.0431369i	0.0621198	+	0.00191013i
$511$	5.08210	+	6.99491i	0.224819	+	0.309437i
$512$	13.9771	+	17.7944i	0.617706	+	0.786409i
$513$	3.92898	−	1.27660i	0.173469	−	0.0563634i
$514$	16.1906	+	12.5412i	0.714135	+	0.553166i
$515$	−0.405687	+	0.558380i	−0.0178767	+	0.0246052i
$516$	−2.82772	+	3.42755i	−0.124483	+	0.150890i
$517$	6.77445	−	14.7600i	0.297940	−	0.649144i
$518$	−3.92479	+	10.9247i	−0.172445	+	0.480004i
$519$	5.73330	+	4.16549i	0.251664	+	0.182845i
$520$	0.857290	−	0.193454i	0.0375947	−	0.00848354i
$521$	−9.13149	−	28.1038i	−0.400058	−	1.23125i	−0.924952	−	0.380084i	$-0.875895\pi$
$521$	−9.13149	−	28.1038i	−0.400058	−	1.23125i	0.524894	−	0.851167i	$-0.324105\pi$
$522$	−7.72959	+	2.25132i	−0.338315	+	0.0985378i
$523$	−10.6513	+	7.73863i	−0.465750	+	0.338387i	−0.795782	−	0.605583i	$-0.792940\pi$
$523$	−10.6513	+	7.73863i	−0.465750	+	0.338387i	0.330033	+	0.943969i	$0.392940\pi$
$524$	11.6488	−	29.5383i	0.508881	−	1.29038i
$525$	1.06332	+	0.345495i	0.0464073	+	0.0150786i
$526$	−19.6935	+	13.4032i	−0.858679	+	0.584407i
$527$	−15.0626			−0.656135
$528$	8.25828	−	3.38716i	0.359395	−	0.147407i
$529$	19.0588			0.828644
$530$	−13.0872	+	8.90699i	−0.568471	+	0.386895i
$531$	−9.21436	−	2.99393i	−0.399869	−	0.129925i
$532$	−1.34957	+	3.42214i	−0.0585112	+	0.148369i
$533$	−1.17088	+	0.850691i	−0.0507163	+	0.0368475i
$534$	−9.80944	+	2.85710i	−0.424496	+	0.123639i
$535$	−5.60309	−	17.2445i	−0.242242	−	0.745546i
$536$	−24.5169	+	5.53244i	−1.05897	+	0.238965i
$537$	2.58061	+	1.87492i	0.111361	+	0.0809088i
$538$	6.97427	−	19.4130i	0.300682	−	0.836953i
$539$	6.88957	+	12.2539i	0.296755	+	0.527815i
$540$	−4.75036	+	5.75805i	−0.204423	+	0.247787i
$541$	20.9681	−	28.8601i	0.901488	−	1.24079i	−0.0685034	−	0.997651i	$-0.521822\pi$
$541$	20.9681	−	28.8601i	0.901488	−	1.24079i	0.969991	−	0.243140i	$-0.0781776\pi$
$542$	6.78160	+	5.25300i	0.291295	+	0.225636i
$543$	−5.08281	+	1.65150i	−0.218124	+	0.0708728i
$544$	−3.81331	−	7.42187i	−0.163494	−	0.318210i
$545$	9.69965	+	13.3504i	0.415487	+	0.571869i
$546$	−0.491063	−	0.0150998i	−0.0210156	−	0.000646211i
$547$	−10.1850	+	31.3463i	−0.435481	+	1.34027i	0.457112	+	0.889409i	$0.348884\pi$
$547$	−10.1850	+	31.3463i	−0.435481	+	1.34027i	−0.892593	+	0.450864i	$0.851116\pi$
$548$	−1.21848	−	4.71916i	−0.0520510	−	0.201593i
$549$		−	15.3450i		−	0.654911i
$550$	4.62494	−	0.780994i	0.197208	−	0.0333017i
$551$			2.47362i			0.105380i
$552$	−3.76189	−	0.347903i	−0.160117	−	0.0148077i
$553$	5.92394	−	18.2320i	0.251912	−	0.775304i
$554$	−0.384017	+	12.4887i	−0.0163153	+	0.530594i
$555$	1.95347	+	2.68872i	0.0829203	+	0.114130i
$556$	−21.1394	−	1.30127i	−0.896511	−	0.0551862i
$557$	−8.39704	+	2.72836i	−0.355794	+	0.115604i	−0.481460	−	0.876468i	$-0.659893\pi$
$557$	−8.39704	+	2.72836i	−0.355794	+	0.115604i	0.125666	+	0.992073i	$0.459893\pi$
$558$	22.5270	−	29.0822i	0.953644	−	1.23115i
$559$	0.603085	−	0.830076i	0.0255078	−	0.0351085i
$560$	−1.26318	−	6.52583i	−0.0533790	−	0.275766i
$561$	−3.22723	+	0.647567i	−0.136254	+	0.0273403i
$562$	11.4114	+	4.09963i	0.481360	+	0.172932i
$563$	19.9609	+	14.5024i	0.841250	+	0.611204i	0.922720	−	0.385472i	$-0.125961\pi$
$563$	19.9609	+	14.5024i	0.841250	+	0.611204i	−0.0814697	+	0.996676i	$0.525961\pi$
$564$	−5.55859	+	3.53815i	−0.234059	+	0.148983i
$565$	−3.79088	−	11.6671i	−0.159484	−	0.490840i
$566$	7.64175	+	26.2368i	0.321207	+	1.10282i
$567$	−6.89770	+	5.01147i	−0.289676	+	0.210462i
$568$	20.8376	−	23.7325i	0.874327	−	0.995796i
$569$	35.4388	+	11.5147i	1.48567	+	0.482723i	0.935801	−	0.352528i	$-0.114678\pi$
$569$	35.4388	+	11.5147i	1.48567	+	0.482723i	0.549869	+	0.835251i	$0.314678\pi$
$570$	0.592568	+	0.870670i	0.0248200	+	0.0364684i
$571$	−20.0777			−0.840228			−0.420114	−	0.907471i	$-0.638010\pi$
$571$	−20.0777			−0.840228			−0.420114	+	0.907471i	$0.638010\pi$
$572$	−1.85526	+	0.897811i	−0.0775722	+	0.0375393i
$573$	−5.79252			−0.241986
$574$	6.15879	+	9.04921i	0.257063	+	0.377707i
$575$	−1.88808	−	0.613474i	−0.0787384	−	0.0255836i
$576$	20.0329	+	3.73729i	0.834705	+	0.155720i
$577$	10.5306	−	7.65092i	0.438394	−	0.318512i	−0.346602	−	0.938012i	$-0.612665\pi$
$577$	10.5306	−	7.65092i	0.438394	−	0.318512i	0.784997	+	0.619500i	$0.212665\pi$
$578$	−5.86255	−	20.1282i	−0.243850	−	0.837223i
$579$	4.49310	+	13.8283i	0.186727	+	0.574686i
$580$	−2.40004	−	3.77057i	−0.0996562	−	0.156565i
$581$	22.9490	+	16.6734i	0.952085	+	0.691730i
$582$	−9.21448	−	3.31038i	−0.381953	−	0.137220i
$583$	25.1555	−	27.3048i	1.04183	−	1.13085i
$584$	−7.51703	−	12.6519i	−0.311057	−	0.523541i
$585$	0.465232	−	0.640337i	0.0192350	−	0.0264747i
$586$	9.62786	−	12.4295i	0.397723	−	0.513458i
$587$	−7.89054	+	2.56379i	−0.325677	+	0.105819i	−0.467292	−	0.884103i	$-0.654770\pi$
$587$	−7.89054	+	2.56379i	−0.325677	+	0.105819i	0.141615	+	0.989922i	$0.454770\pi$
$588$	0.350433	−	5.69286i	0.0144516	−	0.234769i
$589$	−6.64358	−	9.14411i	−0.273744	−	0.376776i
$590$	0.165318	−	5.37632i	0.00680602	−	0.221340i
$591$	−3.94368	+	12.1374i	−0.162221	+	0.499266i
$592$	8.36432	−	17.9006i	0.343771	−	0.735712i
$593$		−	30.8668i		−	1.26755i	−0.773519	−	0.633773i	$-0.781505\pi$
$593$		−	30.8668i		−	1.26755i	0.773519	−	0.633773i	$-0.218495\pi$
$594$	7.78799	−	15.6784i	0.319545	−	0.643293i
$595$			2.45116i			0.100488i
$596$	−4.04640	+	1.04478i	−0.165747	+	0.0427957i
$597$	−3.11834	+	9.59725i	−0.127625	+	0.392789i
$598$	0.871950	+	0.0268118i	0.0356567	+	0.00109641i
$599$	22.6749	+	31.2093i	0.926469	+	1.27518i	0.961221	+	0.275780i	$0.0889361\pi$
$599$	22.6749	+	31.2093i	0.926469	+	1.27518i	−0.0347513	+	0.999396i	$0.511064\pi$
$600$	−1.74803	−	0.752232i	−0.0713630	−	0.0307097i
$601$	5.00956	−	1.62770i	0.204344	−	0.0663954i	−0.205057	−	0.978750i	$-0.565738\pi$
$601$	5.00956	−	1.62770i	0.204344	−	0.0663954i	0.409401	+	0.912355i	$0.365738\pi$
$602$	−6.13493	−	4.75210i	−0.250041	−	0.193681i
$603$	−13.3048	+	18.3124i	−0.541812	+	0.745740i
$604$	17.5003	+	14.4377i	0.712077	+	0.587461i
$605$	−10.1485	+	4.24359i	−0.412595	+	0.172527i
$606$	6.06907	−	16.8933i	0.246539	−	0.686245i
$607$	23.2323	+	16.8792i	0.942969	+	0.685107i	0.949134	−	0.314874i	$-0.101962\pi$
$607$	23.2323	+	16.8792i	0.942969	+	0.685107i	−0.00616432	+	0.999981i	$0.501962\pi$
$608$	2.82372	−	5.58850i	0.114517	−	0.226644i
$609$	0.772114	+	2.37632i	0.0312876	+	0.0962934i
$610$	8.17935	−	2.38232i	0.331172	−	0.0964573i
$611$	1.23091	−	0.894308i	0.0497973	−	0.0361798i
$612$	−6.99090	−	2.75696i	−0.282590	−	0.111443i
$613$	−11.6976	−	3.80079i	−0.472462	−	0.153512i	0.0631014	−	0.998007i	$-0.479901\pi$
$613$	−11.6976	−	3.80079i	−0.472462	−	0.153512i	−0.535564	+	0.844495i	$0.679901\pi$
$614$	34.0321	−	23.1619i	1.37342	−	0.934737i
$615$	3.13387			0.126370
$616$	6.35591	+	14.2339i	0.256087	+	0.573499i
$617$	4.39688			0.177012			0.0885058	−	0.996076i	$-0.471791\pi$
$617$	4.39688			0.177012			0.0885058	+	0.996076i	$0.471791\pi$
$618$	−0.542915	+	0.369502i	−0.0218392	+	0.0148635i
$619$	−3.59330	−	1.16753i	−0.144427	−	0.0469271i	0.235912	−	0.971775i	$-0.424192\pi$
$619$	−3.59330	−	1.16753i	−0.144427	−	0.0469271i	−0.380338	+	0.924847i	$0.624192\pi$
$620$	18.9990	+	7.49251i	0.763017	+	0.300907i
$621$	−5.99448	+	4.35524i	−0.240550	+	0.174770i
$622$	15.4785	−	4.50828i	0.620632	−	0.180766i
$623$	−5.51390	−	16.9701i	−0.220910	−	0.679891i
$624$	0.829914	+	0.102562i	0.0332232	+	0.00410577i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−1.50885	+	4.19990i	−0.0603057	+	0.167862i
$627$	−1.81655	−	1.67355i	−0.0725458	−	0.0668353i
$628$	−24.2891	−	20.0384i	−0.969240	−	0.799619i
$629$	−4.28272	+	5.89466i	−0.170763	+	0.235035i
$630$	−4.73261	−	3.66587i	−0.188552	−	0.146052i
$631$	−0.297436	+	0.0966427i	−0.0118407	+	0.00384729i	−0.314931	−	0.949114i	$-0.601982\pi$
$631$	−0.297436	+	0.0966427i	−0.0118407	+	0.00384729i	0.303091	+	0.952962i	$0.401982\pi$
$632$	−12.8979	+	29.9721i	−0.513053	+	1.19223i
$633$	−2.86699	−	3.94607i	−0.113953	−	0.156842i
$634$	−20.0473	−	0.616437i	−0.796178	−	0.0244818i
$635$	−1.67892	+	5.16719i	−0.0666259	+	0.205054i
$636$	−14.5846	+	3.76573i	−0.578318	+	0.149321i
$637$			1.31702i			0.0521823i
$638$	7.48728	+	7.33596i	0.296424	+	0.290434i
$639$		−	28.4434i		−	1.12520i
$640$	1.11803	+	11.2583i	0.0441942	+	0.445025i
$641$	−10.9010	+	33.5499i	−0.430564	+	1.32514i	0.467000	+	0.884257i	$0.345335\pi$
$641$	−10.9010	+	33.5499i	−0.430564	+	1.32514i	−0.897564	+	0.440883i	$0.854665\pi$
$642$	0.530255	−	17.2445i	0.0209275	−	0.680587i
$643$	19.3630	+	26.6509i	0.763603	+	1.05101i	0.996906	+	0.0786050i	$0.0250466\pi$
$643$	19.3630	+	26.6509i	0.763603	+	1.05101i	−0.233303	+	0.972404i	$0.574953\pi$
$644$	0.405378	−	6.58545i	0.0159741	−	0.259503i
$645$	−2.11298	+	0.686548i	−0.0831984	+	0.0270328i
$646$	−1.41395	+	1.82540i	−0.0556311	+	0.0718194i
$647$	−19.4162	+	26.7240i	−0.763328	+	1.05063i	0.233602	+	0.972332i	$0.424949\pi$
$647$	−19.4162	+	26.7240i	−0.763328	+	1.05063i	−0.996930	+	0.0782983i	$0.975051\pi$
$648$	12.4761	−	7.41257i	0.490108	−	0.291193i
$649$	2.48173	+	12.3680i	0.0974165	+	0.485487i
$650$	0.413545	+	0.148570i	0.0162206	+	0.00582738i
$651$	−9.23648	−	6.71070i	−0.362006	−	0.263013i
$652$	16.4627	+	25.8637i	0.644729	+	1.01290i
$653$	−5.59970	−	17.2341i	−0.219133	−	0.674422i	−0.998834	−	0.0482705i	$-0.984629\pi$
$653$	−5.59970	−	17.2341i	−0.219133	−	0.674422i	0.779701	−	0.626152i	$-0.215371\pi$
$654$	4.39086	+	15.0754i	0.171696	+	0.589493i
$655$	12.8440	−	9.33174i	0.501858	−	0.364621i
$656$	−9.01988	−	16.3025i	−0.352167	−	0.636504i
$657$	−12.6052	−	4.09569i	−0.491777	−	0.159788i
$658$	−6.47457	−	9.51319i	−0.252405	−	0.370863i
$659$	−24.5400			−0.955944			−0.477972	−	0.878375i	$-0.658628\pi$
$659$	−24.5400			−0.955944			−0.477972	+	0.878375i	$0.658628\pi$
$660$	4.39275	+	0.788510i	0.170988	+	0.0306927i
$661$	30.6751			1.19312			0.596561	−	0.802567i	$-0.296533\pi$
$661$	30.6751			1.19312			0.596561	+	0.802567i	$0.296533\pi$
$662$	−28.4992	−	41.8744i	−1.10765	−	1.62749i
$663$	−0.293278	−	0.0952919i	−0.0113900	−	0.00370083i
$664$	−36.2818	−	31.8561i	−1.40801	−	1.23626i
$665$	−1.48804	+	1.08112i	−0.0577037	+	0.0419242i
$666$	−4.97611	−	17.0848i	−0.192821	−	0.662021i
$667$	−1.37100	−	4.21949i	−0.0530852	−	0.163379i
$668$	−0.238067	+	0.151534i	−0.00921109	+	0.00586303i
$669$	−14.2744	−	10.3710i	−0.551882	−	0.400966i
$670$	−11.8266	−	4.24881i	−0.456902	−	0.164146i
$671$	−17.4155	+	9.79156i	−0.672318	+	0.377999i
$672$	0.968255	−	6.25006i	0.0373513	−	0.241101i
$673$	−25.8084	+	35.5222i	−0.994840	+	1.36928i	−0.0664020	+	0.997793i	$0.521152\pi$
$673$	−25.8084	+	35.5222i	−0.994840	+	1.36928i	−0.928438	+	0.371487i	$0.878848\pi$
$674$	16.1079	−	20.7952i	0.620454	−	0.801002i
$675$	−3.54965	+	1.15335i	−0.136626	+	0.0443926i
$676$	25.7582	+	1.58558i	0.990698	+	0.0609840i
$677$	−18.9404	−	26.0693i	−0.727941	−	1.00192i	−0.999223	−	0.0394243i	$-0.987448\pi$
$677$	−18.9404	−	26.0693i	−0.727941	−	1.00192i	0.271282	−	0.962500i	$-0.412552\pi$
$678$	0.358755	−	11.6671i	0.0137779	−	0.448073i
$679$	5.28402	−	16.2625i	0.202782	−	0.624099i
$680$	0.384199	−	4.15437i	0.0147334	−	0.159313i
$681$		−	1.01188i		−	0.0387752i
$682$	−47.3805	−	7.00932i	−1.81429	−	0.268401i
$683$			17.8326i			0.682344i	0.940001	+	0.341172i	$0.110824\pi$
$683$			17.8326i			0.682344i	−0.940001	+	0.341172i	$0.889176\pi$
$684$	−1.40977	−	5.46000i	−0.0539038	−	0.208768i
$685$	0.753063	−	2.31769i	0.0287731	−	0.0885544i
$686$	26.3989	+	0.811745i	1.00791	+	0.0309926i
$687$	−2.60817	−	3.58984i	−0.0995079	−	0.136961i
$688$	9.65298	+	9.01572i	0.368016	+	0.343721i
$689$	3.30794	−	1.07481i	0.126022	−	0.0409472i
$690$	−1.49336	−	1.15675i	−0.0568514	−	0.0440369i
$691$	13.9772	−	19.2380i	0.531718	−	0.731847i	−0.455673	−	0.890147i	$-0.650601\pi$
$691$	13.9772	−	19.2380i	0.531718	−	0.731847i	0.987391	+	0.158300i	$0.0506014\pi$
$692$	13.4060	−	16.2497i	0.509618	−	0.617722i
$693$	12.7594	+	5.85625i	0.484691	+	0.222460i
$694$	−2.55788	+	7.11988i	−0.0970957	+	0.270267i
$695$	−8.56726	−	6.22448i	−0.324975	−	0.236108i
$696$	−0.936153	−	4.14855i	−0.0354848	−	0.157250i
$697$	2.12313	+	6.53432i	0.0804193	+	0.247505i
$698$	−25.7972	+	7.51369i	−0.976437	+	0.284397i
$699$	−10.0734	+	7.31873i	−0.381010	+	0.276820i
$700$	1.21927	−	3.09174i	0.0460842	−	0.116857i
$701$	5.20485	+	1.69116i	0.196585	+	0.0638742i	0.405655	−	0.914026i	$-0.367044\pi$
$701$	5.20485	+	1.69116i	0.196585	+	0.0638742i	−0.209070	+	0.977901i	$0.567044\pi$
$702$	1.35585	−	0.922774i	0.0511731	−	0.0348279i
$703$	−5.46747			−0.206209
$704$	−8.54132	−	25.1206i	−0.321913	−	0.946769i
$705$	−3.29456			−0.124080
$706$	−36.1551	+	24.6067i	−1.36071	+	0.926087i
$707$	29.8149	+	9.68744i	1.12130	+	0.364334i
$708$	1.87763	−	4.76116i	0.0705657	−	0.178935i
$709$	−3.56188	+	2.58786i	−0.133769	+	0.0971890i	−0.652658	−	0.757653i	$-0.726346\pi$
$709$	−3.56188	+	2.58786i	−0.133769	+	0.0971890i	0.518888	+	0.854842i	$0.326346\pi$
$710$	15.1611	−	4.41584i	0.568988	−	0.165724i
$711$	9.08094	+	27.9483i	0.340562	+	1.04814i
$712$	6.68536	+	29.6261i	0.250545	+	1.11028i
$713$	16.4007	+	11.9158i	0.614209	+	0.446249i
$714$	−0.788552	+	2.19494i	−0.0295108	+	0.0821437i
$715$	−1.02360	−	0.119410i	−0.0382804	−	0.00446567i
$716$	6.03414	−	7.31414i	0.225506	−	0.273342i
$717$	−6.81485	+	9.37983i	−0.254505	+	0.350296i
$718$	−9.17088	−	7.10373i	−0.342254	−	0.265109i
$719$	−5.62130	+	1.82647i	−0.209639	+	0.0681159i	−0.411954	−	0.911205i	$-0.635154\pi$
$719$	−5.62130	+	1.82647i	−0.209639	+	0.0681159i	0.202315	+	0.979321i	$0.435154\pi$
$720$	7.44651	+	6.95491i	0.277515	+	0.259194i
$721$	−0.674145	−	0.927882i	−0.0251065	−	0.0345561i
$722$	25.1256	+	0.772591i	0.935077	+	0.0287528i
$723$	−2.11570	+	6.51145i	−0.0786837	+	0.242163i
$724$	3.97165	+	15.3821i	0.147605	+	0.571672i
$725$		−	2.23480i		−	0.0829986i
$726$	−10.4529	+	0.535191i	−0.387943	+	0.0198628i
$727$		−	24.1614i		−	0.896096i	−0.894010	−	0.448048i	$-0.852119\pi$
$727$		−	24.1614i		−	0.896096i	0.894010	−	0.448048i	$-0.147881\pi$
$728$	−0.134486	+	1.45421i	−0.00498440	+	0.0538965i
$729$	1.71079	−	5.26527i	0.0633625	−	0.195010i
$730$	0.226154	−	7.35481i	0.00837035	−	0.272214i
$731$	−2.86299	−	3.94057i	−0.105891	−	0.145747i
$732$	8.09078	+	0.498041i	0.299044	+	0.0184081i
$733$	−6.81624	+	2.21473i	−0.251764	+	0.0818030i	−0.432180	−	0.901787i	$-0.642255\pi$
$733$	−6.81624	+	2.21473i	−0.251764	+	0.0818030i	0.180416	+	0.983590i	$0.442255\pi$
$734$	10.2951	−	13.2909i	0.379998	−	0.490575i
$735$	1.67626	−	2.30717i	0.0618296	−	0.0851012i
$736$	−1.71927	+	11.0979i	−0.0633732	+	0.409072i
$737$	29.2730	+	3.41489i	1.07828	+	0.125789i
$738$	−15.7915	−	5.67323i	−0.581293	−	0.208834i
$739$	20.3029	+	14.7510i	0.746856	+	0.542623i	0.894851	−	0.446366i	$-0.147282\pi$
$739$	20.3029	+	14.7510i	0.746856	+	0.542623i	−0.147995	+	0.988988i	$0.547282\pi$
$740$	8.33412	−	5.30482i	0.306368	−	0.195009i
$741$	−0.0715058	−	0.220072i	−0.00262683	−	0.00808455i
$742$	−7.35633	−	25.2569i	−0.270059	−	0.927209i
$743$	15.7058	−	11.4109i	0.576188	−	0.418625i	−0.261160	−	0.965296i	$-0.584105\pi$
$743$	15.7058	−	11.4109i	0.576188	−	0.418625i	0.837348	+	0.546670i	$0.184105\pi$
$744$	14.6027	+	12.8214i	0.535360	+	0.470056i
$745$	−1.98728	−	0.645708i	−0.0728085	−	0.0236569i
$746$	−0.591936	−	0.869742i	−0.0216723	−	0.0318435i
$747$	−43.4837			−1.59099
$748$	1.33190	+	9.69335i	0.0486990	+	0.354424i
$749$	30.1306			1.10095
$750$	−0.535358	−	0.786610i	−0.0195485	−	0.0287229i
$751$	9.61376	+	3.12370i	0.350811	+	0.113985i	0.479121	−	0.877749i	$-0.340955\pi$
$751$	9.61376	+	3.12370i	0.350811	+	0.113985i	−0.128310	+	0.991734i	$0.540955\pi$
$752$	9.48235	+	17.1383i	0.345786	+	0.624971i
$753$	8.51435	−	6.18604i	0.310280	−	0.225432i
$754$	0.274614	+	0.942847i	0.0100009	+	0.0343365i
$755$	3.50536	+	10.7884i	0.127573	+	0.392629i
$756$	−6.66072	−	10.4643i	−0.242248	−	0.380583i
$757$	−0.177580	−	0.129019i	−0.00645424	−	0.00468928i	0.584553	−	0.811355i	$-0.301270\pi$
$757$	−0.177580	−	0.129019i	−0.00645424	−	0.00468928i	−0.591008	+	0.806666i	$0.701270\pi$
$758$	−18.6912	−	6.71495i	−0.678893	−	0.243898i
$759$	4.02621	+	1.84792i	0.146142	+	0.0670754i
$760$	2.69147	−	1.59911i	0.0976299	−	0.0580059i
$761$	20.0675	−	27.6206i	0.727448	−	1.00125i	−0.271796	−	0.962355i	$-0.587618\pi$
$761$	20.0675	−	27.6206i	0.727448	−	1.00125i	0.999243	−	0.0388909i	$-0.0123825\pi$
$762$	−3.16574	+	4.08695i	−0.114683	+	0.148055i
$763$	−26.0799	+	8.47389i	−0.944157	+	0.306775i
$764$	−1.05792	+	17.1862i	−0.0382743	+	0.621775i
$765$	−2.20857	−	3.03983i	−0.0798510	−	0.109905i
$766$	1.34345	−	43.6907i	0.0485410	−	1.57861i
$767$	−0.365196	+	1.12396i

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16913 - 0.795697i) q^{2} +(0.639886 + 0.207912i) q^{3} +(0.733733 - 1.86055i) q^{4} +(0.809017 - 0.587785i) q^{5} +(0.913545 - 0.266080i) q^{6} +(0.513506 + 1.58041i) q^{7} +(-0.622602 - 2.75905i) q^{8} +(-2.06082 - 1.49728i) q^{9} +(0.478148 - 1.33093i) q^{10} +(-0.384301 + 3.29428i) q^{11} +(0.856335 - 1.03799i) q^{12} +(-0.182636 + 0.251377i) q^{13} +(1.85788 + 1.43911i) q^{14} +(0.639886 - 0.207912i) q^{15} +(-2.92327 - 2.73029i) q^{16} +(0.867017 + 1.19335i) q^{17} +(-3.60075 - 0.110720i) q^{18} +(-0.342040 + 1.05269i) q^{19} +(-0.500000 - 1.93649i) q^{20} +1.11805i q^{21} +(2.17195 + 4.15724i) q^{22} -1.98524i q^{23} +(0.175244 - 1.89493i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-0.0135055 + 0.439216i) q^{26} +(-2.19381 - 3.01952i) q^{27} +(3.31720 + 0.204195i) q^{28} +(2.12543 - 0.690593i) q^{29} +(0.582676 - 0.752232i) q^{30} +(-6.00217 + 8.26128i) q^{31} +(-5.59017 - 0.866025i) q^{32} +(-0.930829 + 2.02807i) q^{33} +(1.96320 + 0.705295i) q^{34} +(1.34437 + 0.976746i) q^{35} +(-4.29785 + 2.73566i) q^{36} +(1.52642 + 4.69784i) q^{37} +(0.437733 + 1.50289i) q^{38} +(-0.169131 + 0.122881i) q^{39} +(-2.12543 - 1.86616i) q^{40} +(4.42987 + 1.43935i) q^{41} +(0.889625 + 1.30714i) q^{42} -3.30211 q^{43} +(5.84720 + 3.13214i) q^{44} -2.54732 q^{45} +(-1.57965 - 2.32101i) q^{46} +(-4.65701 - 1.51315i) q^{47} +(-1.30290 - 2.35486i) q^{48} +(3.42912 - 2.49140i) q^{49} +(-0.395472 - 1.35779i) q^{50} +(0.306682 + 0.943869i) q^{51} +(0.333693 + 0.524247i) q^{52} +(-9.05609 - 6.57963i) q^{53} +(-4.96747 - 1.78460i) q^{54} +(1.62543 + 2.89102i) q^{55} +(4.04072 - 2.40075i) q^{56} +(-0.437733 + 0.602488i) q^{57} +(1.93540 - 2.49859i) q^{58} +(3.61728 - 1.17533i) q^{59} +(0.0826761 - 1.34309i) q^{60} +(3.54082 + 4.87352i) q^{61} +(-0.443847 + 14.4344i) q^{62} +(1.30806 - 4.02580i) q^{63} +(-7.22473 + 3.43558i) q^{64} +0.310719i q^{65} +(0.525466 + 3.11173i) q^{66} -8.88598i q^{67} +(2.85644 - 0.737529i) q^{68} +(0.412756 - 1.27033i) q^{69} +(2.34894 + 0.0722281i) q^{70} +(6.56322 + 9.03350i) q^{71} +(-2.84799 + 6.61813i) q^{72} +(4.94844 - 1.60784i) q^{73} +(5.52264 + 4.27782i) q^{74} +(0.395472 - 0.544320i) q^{75} +(1.70761 + 1.40877i) q^{76} +(-5.40365 + 1.08428i) q^{77} +(-0.0999601 + 0.278240i) q^{78} +(-9.33304 - 6.78085i) q^{79} +(-3.96980 - 0.490594i) q^{80} +(1.58550 + 4.87967i) q^{81} +(6.32439 - 1.84205i) q^{82} +(13.8102 - 10.0337i) q^{83} +(2.08018 + 0.820346i) q^{84} +(1.40286 + 0.455818i) q^{85} +(-3.86060 + 2.62748i) q^{86} +1.50361 q^{87} +(9.32837 - 0.990723i) q^{88} -10.7378 q^{89} +(-2.97815 + 2.02689i) q^{90} +(-0.491063 - 0.159556i) q^{91} +(-3.69364 - 1.45664i) q^{92} +(-5.55832 + 4.03836i) q^{93} +(-6.64866 + 1.93649i) q^{94} +(0.342040 + 1.05269i) q^{95} +(-3.39702 - 1.71642i) q^{96} +(-8.32486 - 6.04836i) q^{97} +(2.02669 - 5.64131i) q^{98} +(5.72443 - 6.21354i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{2} + 5 q^{3} - q^{4} + 2 q^{5} + q^{6} - 3 q^{7} + 5 q^{8} + 3 q^{9} - 5 q^{10} - q^{11} - 10 q^{12} + 10 q^{13} + 5 q^{14} + 5 q^{15} + 7 q^{16} - 5 q^{17} - 10 q^{18} - 11 q^{19} - 4 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 8 * q + 5 * q^2 + 5 * q^3 - q^4 + 2 * q^5 + q^6 - 3 * q^7 + 5 * q^8 + 3 * q^9 - 5 * q^10 - q^11 - 10 * q^12 + 10 * q^13 + 5 * q^14 + 5 * q^15 + 7 * q^16 - 5 * q^17 - 10 * q^18 - 11 * q^19 - 4 * q^20 + q^22 + 3 * q^24 - 2 * q^25 + 7 * q^26 - 10 * q^27 - 9 * q^28 - 5 * q^29 - 6 * q^30 + 10 * q^31 - 11 * q^33 - 14 * q^34 + 8 * q^35 - 26 * q^36 + 20 * q^37 - 5 * q^38 + 3 * q^39 + 5 * q^40 + 10 * q^41 + 29 * q^42 - 34 * q^43 + 32 * q^44 - 8 * q^45 - 10 * q^46 - 23 * q^49 - 5 * q^50 + 9 * q^51 - 5 * q^52 - 7 * q^53 - 26 * q^54 - 9 * q^55 + 15 * q^56 + 5 * q^57 + 18 * q^58 - 5 * q^59 - 10 * q^60 - 10 * q^61 - q^62 - 23 * q^63 + 11 * q^64 - 17 * q^66 - 15 * q^68 + 15 * q^69 + 15 * q^70 + 90 * q^71 + 10 * q^72 + 5 * q^73 + 35 * q^74 + 5 * q^75 - 18 * q^76 - 14 * q^77 - 21 * q^79 - 7 * q^80 - 10 * q^81 - 2 * q^82 + 19 * q^83 - 30 * q^84 - 30 * q^86 - 18 * q^87 + 43 * q^88 + 20 * q^89 - 15 * q^90 - 10 * q^91 + 25 * q^92 + 11 * q^93 + 11 * q^95 - 36 * q^96 - 44 * q^97 + 50 * q^98 - 6 * q^99

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