LMFDB - Embedded newform 430.2.q.d.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			31.3
Character	$\chi$	$=$	430.31
Dual form			430.2.q.d.111.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 - 0.433884i) q^{2} +(-0.206973 + 0.141112i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(-0.125250 + 0.216939i) q^{6} +(0.851274 + 1.47445i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-1.07310 + 2.73421i) q^{9} +O(q^{10})$	\(q+(0.900969 - 0.433884i) q^{2} +(-0.206973 + 0.141112i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(-0.125250 + 0.216939i) q^{6} +(0.851274 + 1.47445i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-1.07310 + 2.73421i) q^{9} +(0.955573 + 0.294755i) q^{10} +(2.65093 + 3.32417i) q^{11} +(-0.0187199 + 0.249799i) q^{12} +(1.47484 - 0.454929i) q^{13} +(1.40671 + 0.959079i) q^{14} +(-0.247702 - 0.0373351i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(1.28572 - 1.19298i) q^{17} +(0.219501 + 2.92904i) q^{18} +(-2.72203 - 6.93561i) q^{19} +(0.988831 - 0.149042i) q^{20} +(-0.384252 - 0.185046i) q^{21} +(3.83071 + 1.84477i) q^{22} +(4.12972 - 0.622454i) q^{23} +(0.0915179 + 0.233184i) q^{24} +(0.0747301 + 0.997204i) q^{25} +(1.13140 - 1.04979i) q^{26} +(-0.330951 - 1.44999i) q^{27} +(1.68353 + 0.253751i) q^{28} +(-2.14682 - 1.46368i) q^{29} +(-0.239371 + 0.0738361i) q^{30} +(0.0319532 - 0.426385i) q^{31} +(-0.623490 - 0.781831i) q^{32} +(-1.01775 - 0.313934i) q^{33} +(0.640782 - 1.63269i) q^{34} +(-0.378852 + 1.65986i) q^{35} +(1.46862 + 2.54373i) q^{36} +(-2.77507 + 4.80657i) q^{37} +(-5.46171 - 5.06773i) q^{38} +(-0.241057 + 0.302276i) q^{39} +(0.826239 - 0.563320i) q^{40} +(-2.20091 + 1.05990i) q^{41} -0.426488 q^{42} +(-1.74310 + 6.32152i) q^{43} +4.25177 q^{44} +(-2.64637 + 1.27442i) q^{45} +(3.45067 - 2.35263i) q^{46} +(3.28063 - 4.11378i) q^{47} +(0.183629 + 0.170383i) q^{48} +(2.05067 - 3.55186i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-0.0977666 + 0.428343i) q^{51} +(0.563873 - 1.43672i) q^{52} +(-4.44393 - 1.37077i) q^{53} +(-0.927304 - 1.16280i) q^{54} +(-0.317735 + 4.23988i) q^{55} +(1.62691 - 0.501835i) q^{56} +(1.54208 + 1.05137i) q^{57} +(-2.56929 - 0.387257i) q^{58} +(-2.87973 - 12.6169i) q^{59} +(-0.183629 + 0.170383i) q^{60} +(0.549920 + 7.33817i) q^{61} +(-0.156213 - 0.398024i) q^{62} +(-4.94495 + 0.745332i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(1.39057 + 0.669662i) q^{65} +(-1.05317 + 0.158740i) q^{66} +(-0.396958 - 1.01143i) q^{67} +(-0.131071 - 1.74903i) q^{68} +(-0.766903 + 0.711582i) q^{69} +(0.378852 + 1.65986i) q^{70} +(-7.14974 - 1.07765i) q^{71} +(2.42687 + 1.65461i) q^{72} +(-6.61351 + 2.04000i) q^{73} +(-0.414763 + 5.53463i) q^{74} +(-0.156184 - 0.195849i) q^{75} +(-7.11963 - 2.19612i) q^{76} +(-2.64464 + 6.73844i) q^{77} +(-0.0860322 + 0.376932i) q^{78} +(-7.10942 - 12.3139i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-6.18636 - 5.74010i) q^{81} +(-1.52308 + 1.90988i) q^{82} +(5.65700 - 3.85688i) q^{83} +(-0.384252 + 0.185046i) q^{84} +1.75393 q^{85} +(1.17233 + 6.45179i) q^{86} +0.650875 q^{87} +(3.83071 - 1.84477i) q^{88} +(-7.64302 + 5.21092i) q^{89} +(-1.83135 + 2.29643i) q^{90} +(1.92627 + 1.78731i) q^{91} +(2.08818 - 3.61684i) q^{92} +(0.0535545 + 0.0927591i) q^{93} +(1.17084 - 5.12979i) q^{94} +(2.72203 - 6.93561i) q^{95} +(0.239371 + 0.0738361i) q^{96} +(10.9090 + 13.6794i) q^{97} +(0.306493 - 4.08986i) q^{98} +(-11.9337 + 3.68105i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) $ 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9} + 5 q^{10} + 3 q^{11} - q^{12} + 13 q^{13} - 15 q^{14} + q^{15} - 10 q^{16} + 38 q^{17} + 6 q^{18} + 17 q^{19} - 5 q^{20} + 4 q^{21} + 11 q^{22} - 8 q^{23} + q^{24} + 5 q^{25} + 29 q^{26} - 16 q^{27} - 6 q^{28} - 41 q^{29} - q^{30} + 15 q^{31} + 10 q^{32} + 63 q^{33} - 10 q^{34} + 2 q^{35} - 48 q^{36} + 7 q^{37} + 25 q^{38} - 64 q^{39} + 5 q^{40} - 22 q^{41} - 60 q^{42} + 6 q^{43} - 4 q^{44} + 30 q^{45} - 20 q^{46} - 13 q^{47} - q^{48} - 93 q^{49} + 30 q^{50} + 18 q^{51} - 15 q^{52} + 71 q^{53} - 5 q^{54} - 16 q^{55} - q^{56} - 94 q^{57} - 22 q^{58} + 20 q^{59} + q^{60} + 91 q^{61} + 69 q^{62} - 50 q^{63} - 10 q^{64} + 5 q^{65} + 14 q^{66} - 26 q^{67} - 18 q^{68} - 94 q^{69} - 2 q^{70} + 20 q^{71} - 36 q^{72} - 56 q^{73} - 7 q^{74} + 2 q^{75} + 38 q^{76} + 41 q^{77} - 13 q^{78} - 46 q^{79} + 30 q^{80} + 39 q^{81} + 8 q^{82} - 115 q^{83} + 4 q^{84} + 6 q^{85} + 29 q^{86} + 20 q^{87} + 11 q^{88} + 30 q^{89} - 16 q^{90} - 53 q^{91} - 8 q^{92} + 16 q^{93} + 41 q^{94} - 17 q^{95} + q^{96} + 113 q^{97} + 2 q^{98} + 139 q^{99}+O(q^{100}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9 + 5 * q^10 + 3 * q^11 - q^12 + 13 * q^13 - 15 * q^14 + q^15 - 10 * q^16 + 38 * q^17 + 6 * q^18 + 17 * q^19 - 5 * q^20 + 4 * q^21 + 11 * q^22 - 8 * q^23 + q^24 + 5 * q^25 + 29 * q^26 - 16 * q^27 - 6 * q^28 - 41 * q^29 - q^30 + 15 * q^31 + 10 * q^32 + 63 * q^33 - 10 * q^34 + 2 * q^35 - 48 * q^36 + 7 * q^37 + 25 * q^38 - 64 * q^39 + 5 * q^40 - 22 * q^41 - 60 * q^42 + 6 * q^43 - 4 * q^44 + 30 * q^45 - 20 * q^46 - 13 * q^47 - q^48 - 93 * q^49 + 30 * q^50 + 18 * q^51 - 15 * q^52 + 71 * q^53 - 5 * q^54 - 16 * q^55 - q^56 - 94 * q^57 - 22 * q^58 + 20 * q^59 + q^60 + 91 * q^61 + 69 * q^62 - 50 * q^63 - 10 * q^64 + 5 * q^65 + 14 * q^66 - 26 * q^67 - 18 * q^68 - 94 * q^69 - 2 * q^70 + 20 * q^71 - 36 * q^72 - 56 * q^73 - 7 * q^74 + 2 * q^75 + 38 * q^76 + 41 * q^77 - 13 * q^78 - 46 * q^79 + 30 * q^80 + 39 * q^81 + 8 * q^82 - 115 * q^83 + 4 * q^84 + 6 * q^85 + 29 * q^86 + 20 * q^87 + 11 * q^88 + 30 * q^89 - 16 * q^90 - 53 * q^91 - 8 * q^92 + 16 * q^93 + 41 * q^94 - 17 * q^95 + q^96 + 113 * q^97 + 2 * q^98 + 139 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{17}{21}\right)$

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 $

$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$3$	−0.206973	+	0.141112i	−0.119496	+	0.0814708i	−0.621593	−	0.783340i	$-0.713514\pi$
$3$	−0.206973	+	0.141112i	−0.119496	+	0.0814708i	0.502097	+	0.864811i	$0.332562\pi$
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	0.733052	+	0.680173i	0.327831	+	0.304182i
$5$	0.733052	+	0.680173i	0.327831	+	0.304182i
$6$	−0.125250	+	0.216939i	−0.0511331	+	0.0885651i
$7$	0.851274	+	1.47445i	0.321751	+	0.557289i	0.980849	−	0.194767i	$-0.0623952\pi$
$7$	0.851274	+	1.47445i	0.321751	+	0.557289i	−0.659098	+	0.752057i	$0.729062\pi$
$8$	0.222521	−	0.974928i	0.0786730	−	0.344689i
$9$	−1.07310	+	2.73421i	−0.357699	+	0.911403i
$10$	0.955573	+	0.294755i	0.302179	+	0.0932098i
$11$	2.65093	+	3.32417i	0.799287	+	1.00227i	0.999745	+	0.0225719i	$0.00718546\pi$
$11$	2.65093	+	3.32417i	0.799287	+	1.00227i	−0.200458	+	0.979702i	$0.564243\pi$
$12$	−0.0187199	+	0.249799i	−0.00540396	+	0.0721109i
$13$	1.47484	−	0.454929i	0.409048	−	0.126175i	−0.0834005	−	0.996516i	$-0.526578\pi$
$13$	1.47484	−	0.454929i	0.409048	−	0.126175i	0.492449	+	0.870341i	$0.336102\pi$
$14$	1.40671	+	0.959079i	0.375959	+	0.256325i
$15$	−0.247702	−	0.0373351i	−0.0639564	−	0.00963987i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	1.28572	−	1.19298i	0.311833	−	0.289339i	−0.508693	−	0.860948i	$-0.669871\pi$
$17$	1.28572	−	1.19298i	0.311833	−	0.289339i	0.820526	+	0.571609i	$0.193681\pi$
$18$	0.219501	+	2.92904i	0.0517369	+	0.690381i
$19$	−2.72203	−	6.93561i	−0.624476	−	1.59114i	−0.795555	−	0.605881i	$-0.792821\pi$
$19$	−2.72203	−	6.93561i	−0.624476	−	1.59114i	0.171080	−	0.985257i	$-0.445274\pi$
$20$	0.988831	−	0.149042i	0.221109	−	0.0333269i
$21$	−0.384252	−	0.185046i	−0.0838507	−	0.0403804i
$22$	3.83071	+	1.84477i	0.816711	+	0.393307i
$23$	4.12972	−	0.622454i	0.861105	−	0.129791i	0.296380	−	0.955070i	$-0.404220\pi$
$23$	4.12972	−	0.622454i	0.861105	−	0.129791i	0.564725	+	0.825279i	$0.308982\pi$
$24$	0.0915179	+	0.233184i	0.0186810	+	0.0475984i
$25$	0.0747301	+	0.997204i	0.0149460	+	0.199441i
$26$	1.13140	−	1.04979i	0.221886	−	0.205880i
$27$	−0.330951	−	1.44999i	−0.0636915	−	0.279051i
$28$	1.68353	+	0.253751i	0.318157	+	0.0479545i
$29$	−2.14682	−	1.46368i	−0.398655	−	0.271798i	0.347354	−	0.937734i	$-0.387080\pi$
$29$	−2.14682	−	1.46368i	−0.398655	−	0.271798i	−0.746009	+	0.665936i	$0.768032\pi$
$30$	−0.239371	+	0.0738361i	−0.0437029	+	0.0134806i
$31$	0.0319532	−	0.426385i	0.00573896	−	0.0765810i	−0.993599	−	0.112966i	$-0.963965\pi$
$31$	0.0319532	−	0.426385i	0.00573896	−	0.0765810i	0.999338	+	0.0363845i	$0.0115841\pi$
$32$	−0.623490	−	0.781831i	−0.110218	−	0.138210i
$33$	−1.01775	−	0.313934i	−0.177167	−	0.0546489i
$34$	0.640782	−	1.63269i	0.109893	−	0.280004i
$35$	−0.378852	+	1.65986i	−0.0640377	+	0.280568i
$36$	1.46862	+	2.54373i	0.244771	+	0.423955i
$37$	−2.77507	+	4.80657i	−0.456219	+	0.790195i	−0.998757	−	0.0498362i	$-0.984130\pi$
$37$	−2.77507	+	4.80657i	−0.456219	+	0.790195i	0.542538	+	0.840031i	$0.317463\pi$
$38$	−5.46171	−	5.06773i	−0.886006	−	0.822094i
$39$	−0.241057	+	0.302276i	−0.0386000	+	0.0484028i
$40$	0.826239	−	0.563320i	0.130640	−	0.0890687i
$41$	−2.20091	+	1.05990i	−0.343724	+	0.165529i	−0.597779	−	0.801661i	$-0.703950\pi$
$41$	−2.20091	+	1.05990i	−0.343724	+	0.165529i	0.254055	+	0.967190i	$0.418236\pi$
$42$	−0.426488			−0.0658085
$43$	−1.74310	+	6.32152i	−0.265820	+	0.964023i
$43$	−1.74310	+	6.32152i	−0.265820	+	0.964023i
$44$	4.25177			0.640978
$45$	−2.64637	+	1.27442i	−0.394498	+	0.189980i
$46$	3.45067	−	2.35263i	0.508774	−	0.346876i
$47$	3.28063	−	4.11378i	0.478529	−	0.600056i	−0.482708	−	0.875781i	$-0.660347\pi$
$47$	3.28063	−	4.11378i	0.478529	−	0.600056i	0.961236	+	0.275726i	$0.0889181\pi$
$48$	0.183629	+	0.170383i	0.0265046	+	0.0245927i
$49$	2.05067	−	3.55186i	0.292952	−	0.507408i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−0.0977666	+	0.428343i	−0.0136901	+	0.0599801i
$52$	0.563873	−	1.43672i	0.0781951	−	0.199238i
$53$	−4.44393	−	1.37077i	−0.610421	−	0.188290i	−0.0258945	−	0.999665i	$-0.508243\pi$
$53$	−4.44393	−	1.37077i	−0.610421	−	0.188290i	−0.584526	+	0.811375i	$0.698720\pi$
$54$	−0.927304	−	1.16280i	−0.126190	−	0.158237i
$55$	−0.317735	+	4.23988i	−0.0428434	+	0.571705i
$56$	1.62691	−	0.501835i	0.217405	−	0.0670605i
$57$	1.54208	+	1.05137i	0.204254	+	0.139258i
$58$	−2.56929	−	0.387257i	−0.337364	−	0.0508494i
$59$	−2.87973	−	12.6169i	−0.374909	−	1.64258i	−0.712778	−	0.701390i	$-0.752563\pi$
$59$	−2.87973	−	12.6169i	−0.374909	−	1.64258i	0.337869	−	0.941193i	$-0.390294\pi$
$60$	−0.183629	+	0.170383i	−0.0237065	+	0.0219964i
$61$	0.549920	+	7.33817i	0.0704100	+	0.939557i	0.914821	+	0.403860i	$0.132332\pi$
$61$	0.549920	+	7.33817i	0.0704100	+	0.939557i	−0.844411	+	0.535696i	$0.820049\pi$
$62$	−0.156213	−	0.398024i	−0.0198390	−	0.0505491i
$63$	−4.94495	+	0.745332i	−0.623005	+	0.0939029i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	1.39057	+	0.669662i	0.172479	+	0.0830614i
$66$	−1.05317	+	0.158740i	−0.129636	+	0.0195396i
$67$	−0.396958	−	1.01143i	−0.0484961	−	0.123566i	0.904573	−	0.426319i	$-0.140190\pi$
$67$	−0.396958	−	1.01143i	−0.0484961	−	0.123566i	−0.953069	+	0.302752i	$0.902094\pi$
$68$	−0.131071	−	1.74903i	−0.0158947	−	0.212100i
$69$	−0.766903	+	0.711582i	−0.0923243	+	0.0856644i
$70$	0.378852	+	1.65986i	0.0452815	+	0.198391i
$71$	−7.14974	−	1.07765i	−0.848518	−	0.127894i	−0.289632	−	0.957138i	$-0.593533\pi$
$71$	−7.14974	−	1.07765i	−0.848518	−	0.127894i	−0.558886	+	0.829244i	$0.688771\pi$
$72$	2.42687	+	1.65461i	0.286009	+	0.194998i
$73$	−6.61351	+	2.04000i	−0.774053	+	0.238764i	−0.656524	−	0.754306i	$-0.727974\pi$
$73$	−6.61351	+	2.04000i	−0.774053	+	0.238764i	−0.117530	+	0.993069i	$0.537498\pi$
$74$	−0.414763	+	5.53463i	−0.0482152	+	0.643387i
$75$	−0.156184	−	0.195849i	−0.0180346	−	0.0226147i
$76$	−7.11963	−	2.19612i	−0.816678	−	0.251912i
$77$	−2.64464	+	6.73844i	−0.301385	+	0.767917i
$78$	−0.0860322	+	0.376932i	−0.00974123	+	0.0426791i
$79$	−7.10942	−	12.3139i	−0.799872	−	1.38542i	−0.919699	−	0.392624i	$-0.871567\pi$
$79$	−7.10942	−	12.3139i	−0.799872	−	1.38542i	0.119827	−	0.992795i	$-0.461766\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−6.18636	−	5.74010i	−0.687373	−	0.637789i
$82$	−1.52308	+	1.90988i	−0.168196	+	0.210911i
$83$	5.65700	−	3.85688i	0.620937	−	0.423348i	−0.211570	−	0.977363i	$-0.567858\pi$
$83$	5.65700	−	3.85688i	0.620937	−	0.423348i	0.832506	+	0.554015i	$0.186905\pi$
$84$	−0.384252	+	0.185046i	−0.0419254	+	0.0201902i
$85$	1.75393			0.190240
$86$	1.17233	+	6.45179i	0.126415	+	0.695715i
$87$	0.650875			0.0697812
$88$	3.83071	−	1.84477i	0.408355	−	0.196654i
$89$	−7.64302	+	5.21092i	−0.810159	+	0.552357i	−0.896053	−	0.443947i	$-0.853578\pi$
$89$	−7.64302	+	5.21092i	−0.810159	+	0.552357i	0.0858942	+	0.996304i	$0.472625\pi$
$90$	−1.83135	+	2.29643i	−0.193041	+	0.242065i
$91$	1.92627	+	1.78731i	0.201928	+	0.187361i
$92$	2.08818	−	3.61684i	0.217708	−	0.377081i
$93$	0.0535545	+	0.0927591i	0.00555334	+	0.00961867i
$94$	1.17084	−	5.12979i	0.120763	−	0.529098i
$95$	2.72203	−	6.93561i	0.279274	−	0.711579i
$96$	0.239371	+	0.0738361i	0.0244307	+	0.00753587i
$97$	10.9090	+	13.6794i	1.10764	+	1.38893i	0.912952	+	0.408066i	$0.133797\pi$
$97$	10.9090	+	13.6794i	1.10764	+	1.38893i	0.194684	+	0.980866i	$0.437632\pi$
$98$	0.306493	−	4.08986i	0.0309605	−	0.413139i
$99$	−11.9337	+	3.68105i	−1.19938	+	0.369960i
$100$	0.826239	+	0.563320i	0.0826239	+	0.0563320i
$101$	−2.88186	−	0.434371i	−0.286756	−	0.0432215i	0.00408924	−	0.999992i	$-0.498698\pi$
$101$	−2.88186	−	0.434371i	−0.286756	−	0.0432215i	−0.290845	+	0.956770i	$0.593936\pi$
$102$	0.0977666	+	0.428343i	0.00968034	+	0.0424123i
$103$	4.95309	−	4.59580i	0.488043	−	0.452838i	−0.397359	−	0.917663i	$-0.630073\pi$
$103$	4.95309	−	4.59580i	0.488043	−	0.452838i	0.885402	+	0.464825i	$0.153883\pi$
$104$	−0.115340	−	1.53910i	−0.0113100	−	0.150921i
$105$	−0.155813	−	0.397006i	−0.0152058	−	0.0387438i
$106$	−4.59860	+	0.693127i	−0.446655	+	0.0673224i
$107$	3.07089	+	1.47886i	0.296874	+	0.142967i	0.576392	−	0.817174i	$-0.304460\pi$
$107$	3.07089	+	1.47886i	0.296874	+	0.142967i	−0.279518	+	0.960141i	$0.590175\pi$
$108$	−1.33999	−	0.645307i	−0.128941	−	0.0620947i
$109$	−7.67497	+	1.15682i	−0.735129	+	0.110803i	−0.505927	−	0.862576i	$-0.668850\pi$
$109$	−7.67497	+	1.15682i	−0.735129	+	0.110803i	−0.229201	+	0.973379i	$0.573611\pi$
$110$	1.55335	+	3.95786i	0.148106	+	0.377367i
$111$	−0.103898	−	1.38642i	−0.00986157	−	0.131593i
$112$	1.24806	−	1.15803i	0.117930	−	0.109423i
$113$	−1.87193	−	8.20147i	−0.176097	−	0.771530i	−0.983409	−	0.181405i	$-0.941936\pi$
$113$	−1.87193	−	8.20147i	−0.176097	−	0.771530i	0.807312	−	0.590125i	$-0.200922\pi$
$114$	1.84554	+	0.278170i	0.172851	+	0.0260530i
$115$	3.45067	+	2.35263i	0.321777	+	0.219384i
$116$	−2.48287	+	0.765864i	−0.230529	+	0.0711087i
$117$	−0.338781	+	4.52072i	−0.0313203	+	0.417940i
$118$	−8.06882	−	10.1180i	−0.742795	−	0.931436i
$119$	2.85348	+	0.880183i	0.261578	+	0.0806862i
$120$	−0.0915179	+	0.233184i	−0.00835440	+	0.0212867i
$121$	−1.57490	+	6.90009i	−0.143173	+	0.627281i
$122$	3.67937	+	6.37286i	0.333115	+	0.576972i
$123$	0.305964	−	0.529944i	0.0275878	−	0.0477835i
$124$	−0.313439	−	0.290829i	−0.0281476	−	0.0261172i
$125$	−0.623490	+	0.781831i	−0.0557666	+	0.0699291i
$126$	−4.13186	+	2.81705i	−0.368095	+	0.250963i
$127$	0.883186	−	0.425320i	0.0783701	−	0.0377411i	−0.394288	−	0.918987i	$-0.629009\pi$
$127$	0.883186	−	0.425320i	0.0783701	−	0.0377411i	0.472658	+	0.881246i	$0.343295\pi$
$128$	−1.00000			−0.0883883
$129$	−0.531266	−	1.55435i	−0.0467754	−	0.136853i
$130$	1.54341			0.135366
$131$	17.6443	−	8.49704i	1.54159	−	0.742390i	0.546141	−	0.837693i	$-0.316096\pi$
$131$	17.6443	−	8.49704i	1.54159	−	0.742390i	0.995448	+	0.0953031i	$0.0303820\pi$
$132$	−0.880000	+	0.599974i	−0.0765942	+	0.0522210i
$133$	7.90901	−	9.91759i	0.685799	−	0.859964i
$134$	−0.796491	−	0.739036i	−0.0688063	−	0.0638430i
$135$	0.743640	−	1.28802i	0.0640024	−	0.110855i
$136$	−0.876965	−	1.51895i	−0.0751991	−	0.130249i
$137$	−0.543368	+	2.38065i	−0.0464230	+	0.203393i	−0.992821	−	0.119611i	$-0.961835\pi$
$137$	−0.543368	+	2.38065i	−0.0464230	+	0.203393i	0.946398	+	0.323003i	$0.104692\pi$
$138$	−0.382212	+	0.973860i	−0.0325360	+	0.0829004i
$139$	−4.10942	−	1.26759i	−0.348557	−	0.107515i	0.115533	−	0.993304i	$-0.463142\pi$
$139$	−4.10942	−	1.26759i	−0.348557	−	0.107515i	−0.464090	+	0.885788i	$0.653618\pi$
$140$	1.06152	+	1.33110i	0.0897149	+	0.112499i
$141$	−0.0984987	+	1.31437i	−0.00829509	+	0.110690i
$142$	−6.90927	+	2.13123i	−0.579813	+	0.178849i
$143$	5.42198	+	3.69664i	0.453409	+	0.309129i
$144$	2.90444	+	0.437774i	0.242037	+	0.0364812i
$145$	−0.578178	−	2.53316i	−0.0480150	−	0.210368i
$146$	−5.07345	+	4.70747i	−0.419882	+	0.389593i
$147$	0.0767765	+	1.02451i	0.00633242	+	0.0845002i
$148$	2.02770	+	5.16649i	0.166676	+	0.424683i
$149$	8.41979	−	1.26908i	0.689776	−	0.103967i	0.205205	−	0.978719i	$-0.434214\pi$
$149$	8.41979	−	1.26908i	0.689776	−	0.103967i	0.484571	+	0.874752i	$0.338976\pi$
$150$	−0.225693	−	0.108688i	−0.0184277	−	0.00887432i
$151$	−1.88019	−	0.905453i	−0.153008	−	0.0736847i	0.355813	−	0.934557i	$-0.384204\pi$
$151$	−1.88019	−	0.905453i	−0.153008	−	0.0736847i	−0.508821	+	0.860873i	$0.669918\pi$
$152$	−7.36743	+	1.11046i	−0.597577	+	0.0900703i
$153$	1.88214	+	4.79561i	0.152162	+	0.387702i
$154$	0.540959	+	7.21860i	0.0435917	+	0.581691i
$155$	0.313439	−	0.290829i	0.0251760	−	0.0233599i
$156$	0.0860322	+	0.376932i	0.00688809	+	0.0301787i
$157$	−1.67213	−	0.252034i	−0.133451	−	0.0201145i	0.0819772	−	0.996634i	$-0.473877\pi$
$157$	−1.67213	−	0.252034i	−0.133451	−	0.0201145i	−0.215428	+	0.976520i	$0.569115\pi$
$158$	−11.7481	−	8.00975i	−0.934633	−	0.637222i
$159$	1.11320	−	0.343378i	0.0882828	−	0.0272316i
$160$	0.0747301	−	0.997204i	0.00590793	−	0.0788359i
$161$	4.43330	+	5.55918i	0.349393	+	0.438124i
$162$	−8.06426	−	2.48749i	−0.633588	−	0.195436i
$163$	−2.34955	+	5.98655i	−0.184031	+	0.468903i	−0.992881	−	0.119112i	$-0.961995\pi$
$163$	−2.34955	+	5.98655i	−0.184031	+	0.468903i	0.808850	+	0.588015i	$0.200090\pi$
$164$	−0.543580	+	2.38158i	−0.0424464	+	0.185970i
$165$	−0.532534	−	0.922376i	−0.0414577	−	0.0718068i
$166$	3.42335	−	5.92941i	0.265703	−	0.460212i
$167$	11.3252	+	10.5083i	0.876372	+	0.813154i	0.983466	−	0.181095i	$-0.0579641\pi$
$167$	11.3252	+	10.5083i	0.876372	+	0.813154i	−0.107094	+	0.994249i	$0.534155\pi$
$168$	−0.265911	+	0.333442i	−0.0205155	+	0.0257256i
$169$	−8.77290	+	5.98126i	−0.674838	+	0.460097i
$170$	1.58024	−	0.761002i	0.121199	−	0.0583662i
$171$	21.8844			1.67354
$172$	3.85556	+	5.30421i	0.293984	+	0.404442i
$173$	−3.55103			−0.269979			−0.134990	−	0.990847i	$-0.543100\pi$
$173$	−3.55103			−0.269979			−0.134990	+	0.990847i	$0.543100\pi$
$174$	0.586418	−	0.282404i	0.0444563	−	0.0214090i
$175$	−1.40671	+	0.959079i	−0.106337	+	0.0724996i
$176$	2.65093	−	3.32417i	0.199822	−	0.250569i
$177$	2.37642	+	2.20499i	0.178623	+	0.165737i
$178$	−4.62519	+	8.01106i	−0.346673	+	0.600455i
$179$	−10.1463	−	17.5739i	−0.758370	−	1.31354i	−0.943681	−	0.330855i	$-0.892663\pi$
$179$	−10.1463	−	17.5739i	−0.758370	−	1.31354i	0.185312	−	0.982680i	$-0.440671\pi$
$180$	−0.653600	+	2.86361i	−0.0487164	+	0.213441i
$181$	1.58121	−	4.02886i	0.117530	−	0.299463i	−0.859987	−	0.510315i	$-0.829529\pi$
$181$	1.58121	−	4.02886i	0.117530	−	0.299463i	0.977518	+	0.210853i	$0.0676240\pi$
$182$	2.51099	+	0.774539i	0.186127	+	0.0574126i
$183$	−1.14932	−	1.44120i	−0.0849602	−	0.106537i
$184$	0.312100	−	4.16468i	0.0230083	−	0.307025i
$185$	−5.30357	+	1.63593i	−0.389926	+	0.120276i
$186$	0.0884976	+	0.0603366i	0.00648896	+	0.00442410i
$187$	7.37401	+	1.11145i	0.539241	+	0.0812775i
$188$	−1.17084	−	5.12979i	−0.0853924	−	0.374129i
$189$	1.85621	−	1.72231i	0.135019	−	0.125280i
$190$	−0.556787	−	7.42981i	−0.0403936	−	0.539015i
$191$	−5.77163	−	14.7059i	−0.417621	−	1.06408i	−0.972655	−	0.232253i	$-0.925390\pi$
$191$	−5.77163	−	14.7059i	−0.417621	−	1.06408i	0.555035	−	0.831827i	$-0.312705\pi$
$192$	0.247702	−	0.0373351i	0.0178764	−	0.00269443i
$193$	23.0296	+	11.0905i	1.65771	+	0.798309i	0.998943	+	0.0459587i	$0.0146343\pi$
$193$	23.0296	+	11.0905i	1.65771	+	0.798309i	0.658763	+	0.752351i	$0.271080\pi$
$194$	15.7639	+	7.59149i	1.13178	+	0.545037i
$195$	−0.382307	+	0.0576235i	−0.0273776	+	0.00412650i
$196$	−1.49839	−	3.81782i	−0.107028	−	0.272702i
$197$	−1.60526	−	21.4207i	−0.114370	−	1.52616i	−0.699152	−	0.714973i	$-0.746439\pi$
$197$	−1.60526	−	21.4207i	−0.114370	−	1.52616i	0.584782	−	0.811191i	$-0.301180\pi$
$198$	−9.15472	+	8.49434i	−0.650598	+	0.603667i
$199$	5.41872	+	23.7410i	0.384123	+	1.68295i	0.684404	+	0.729103i	$0.260062\pi$
$199$	5.41872	+	23.7410i	0.384123	+	1.68295i	−0.300281	+	0.953851i	$0.597081\pi$
$200$	0.988831	+	0.149042i	0.0699209	+	0.0105389i
$201$	0.224884	+	0.153324i	0.0158621	+	0.0108146i
$202$	−2.78493	+	0.859038i	−0.195947	+	0.0604417i
$203$	0.330586	−	4.41137i	0.0232026	−	0.309617i
$204$	0.273936	+	0.343505i	0.0191794	+	0.0240501i
$205$	−2.33430	−	0.720035i	−0.163034	−	0.0502894i
$206$	2.46854	−	6.28974i	0.171991	−	0.438227i
$207$	−2.72967	+	11.9595i	−0.189725	+	0.831240i
$208$	−0.771707	−	1.33664i	−0.0535083	−	0.0926790i
$209$	15.8392	−	27.4343i	1.09562	−	1.89767i
$210$	−0.312638	−	0.290085i	−0.0215741	−	0.0200178i
$211$	0.186025	−	0.233268i	0.0128065	−	0.0160588i	−0.775387	−	0.631486i	$-0.782445\pi$
$211$	0.186025	−	0.233268i	0.0128065	−	0.0160588i	0.788193	+	0.615428i	$0.211017\pi$
$212$	−3.84246	+	2.61974i	−0.263901	+	0.179925i
$213$	1.63187	−	0.785867i	0.111814	−	0.0538467i
$214$	3.40843			0.232995
$215$	−5.57751	+	3.44839i	−0.380383	+	0.235179i
$216$	−1.48728			−0.101197
$217$	0.655884	−	0.315857i	0.0445243	−	0.0214418i
$218$	−6.41298	+	4.37230i	−0.434342	+	0.296129i
$219$	1.08095	−	1.35547i	0.0730438	−	0.0915940i
$220$	3.11677	+	2.89194i	0.210132	+	0.194974i
$221$	1.35352	−	2.34437i	0.0910476	−	0.157699i
$222$	−0.695156	−	1.20404i	−0.0466558	−	0.0808102i
$223$	4.18679	−	18.3435i	0.280368	−	1.22837i	−0.616954	−	0.786999i	$-0.711634\pi$
$223$	4.18679	−	18.3435i	0.280368	−	1.22837i	0.897323	−	0.441375i	$-0.145509\pi$
$224$	0.622010	−	1.58486i	0.0415598	−	0.105893i
$225$	−2.80676	−	0.865770i	−0.187117	−	0.0577180i
$226$	−5.24504	−	6.57707i	−0.348895	−	0.437500i
$227$	0.318319	−	4.24767i	0.0211276	−	0.281928i	−0.976626	−	0.214943i	$-0.931043\pi$
$227$	0.318319	−	4.24767i	0.0211276	−	0.281928i	0.997754	−	0.0669841i	$-0.0213377\pi$
$228$	1.78347	−	0.550127i	0.118113	−	0.0364330i
$229$	−13.2328	−	9.02197i	−0.874448	−	0.596189i	0.0407603	−	0.999169i	$-0.487022\pi$
$229$	−13.2328	−	9.02197i	−0.874448	−	0.596189i	−0.915209	+	0.402980i	$0.867974\pi$
$230$	4.12972	+	0.622454i	0.272305	+	0.0410434i
$231$	−0.403503	−	1.76786i	−0.0265486	−	0.116317i
$232$	−1.90469	+	1.76730i	−0.125049	+	0.116029i
$233$	1.39156	+	18.5690i	0.0911638	+	1.21650i	0.835803	+	0.549029i	$0.185002\pi$
$233$	1.39156	+	18.5690i	0.0911638	+	1.21650i	−0.744639	+	0.667467i	$0.767378\pi$
$234$	1.65623	+	4.22002i	0.108271	+	0.275871i
$235$	5.20295	−	0.784218i	0.339403	−	0.0511568i
$236$	−11.6598	−	5.61506i	−0.758987	−	0.365509i
$237$	3.20908	+	1.54541i	0.208452	+	0.100385i
$238$	2.95280	−	0.445062i	0.191401	−	0.0288491i
$239$	5.92465	+	15.0958i	0.383234	+	0.976464i	0.984180	+	0.177174i	$0.0566955\pi$
$239$	5.92465	+	15.0958i	0.383234	+	0.976464i	−0.600946	+	0.799290i	$0.705209\pi$
$240$	0.0187199	+	0.249799i	0.00120836	+	0.0161245i
$241$	−18.9285	+	17.5631i	−1.21929	+	1.13134i	−0.231954	+	0.972727i	$0.574512\pi$
$241$	−18.9285	+	17.5631i	−1.21929	+	1.13134i	−0.987341	+	0.158613i	$0.949298\pi$
$242$	1.57490	+	6.90009i	0.101238	+	0.443555i
$243$	6.50241	+	0.980080i	0.417130	+	0.0628722i
$244$	6.08008	+	4.14533i	0.389237	+	0.265378i
$245$	3.91912	−	1.20889i	0.250384	−	0.0772331i
$246$	0.0457294	−	0.610216i	0.00291560	−	0.0389060i
$247$	−7.16978	−	8.99062i	−0.456202	−	0.572059i
$248$	−0.408585	−	0.126032i	−0.0259451	−	0.00800302i
$249$	−0.626595	+	1.59654i	−0.0397088	+	0.101176i
$250$	−0.222521	+	0.974928i	−0.0140735	+	0.0616599i
$251$	−8.03813	−	13.9224i	−0.507362	−	0.878777i	−0.999964	−	0.00852184i	$-0.997287\pi$
$251$	−8.03813	−	13.9224i	−0.507362	−	0.878777i	0.492602	−	0.870255i	$-0.336046\pi$
$252$	−2.50040	+	4.33083i	−0.157511	+	0.272816i
$253$	13.0167	+	12.0778i	0.818356	+	0.759323i
$254$	0.611184	−	0.766401i	0.0383491	−	0.0480882i
$255$	−0.363016	+	0.247500i	−0.0227329	+	0.0154990i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	21.9160			1.36708			0.683541	−	0.729912i	$-0.260439\pi$
$257$	21.9160			1.36708			0.683541	+	0.729912i	$0.260439\pi$
$258$	−1.15306	−	1.16992i	−0.0717865	−	0.0728358i
$259$	−9.44939			−0.587156
$260$	1.39057	−	0.669662i	0.0862394	−	0.0415307i
$261$	6.30575	−	4.29919i	0.390316	−	0.266113i
$262$	12.2102	−	15.3111i	0.754351	−	0.945926i
$263$	−6.86717	−	6.37180i	−0.423448	−	0.392902i	0.439461	−	0.898262i	$-0.355169\pi$
$263$	−6.86717	−	6.37180i	−0.423448	−	0.392902i	−0.862909	+	0.505360i	$0.831360\pi$
$264$	−0.532534	+	0.922376i	−0.0327752	+	0.0567683i
$265$	−2.32527	−	4.02749i	−0.142840	−	0.247406i
$266$	2.82269	−	12.3670i	0.173071	−	0.758271i
$267$	0.846575	−	2.15704i	0.0518095	−	0.132009i
$268$	−1.03827	−	0.320264i	−0.0634224	−	0.0195632i
$269$	7.17421	+	8.99617i	0.437419	+	0.548506i	0.950861	−	0.309618i	$-0.100201\pi$
$269$	7.17421	+	8.99617i	0.437419	+	0.548506i	−0.513442	+	0.858124i	$0.671630\pi$
$270$	0.111145	−	1.48312i	0.00676404	−	0.0902599i
$271$	26.1961	−	8.08043i	1.59130	−	0.490851i	0.632411	−	0.774633i	$-0.282065\pi$
$271$	26.1961	−	8.08043i	1.59130	−	0.490851i	0.958889	+	0.283782i	$0.0915892\pi$
$272$	−1.44916	−	0.988024i	−0.0878685	−	0.0599077i
$273$	−0.650895	−	0.0981067i	−0.0393940	−	0.00593769i
$274$	0.543368	+	2.38065i	0.0328260	+	0.143820i
$275$	−3.11677	+	2.89194i	−0.187948	+	0.174390i
$276$	0.0781810	+	1.04325i	0.00470594	+	0.0627964i
$277$	8.56474	+	21.8226i	0.514605	+	1.31119i	0.918150	+	0.396233i	$0.129683\pi$
$277$	8.56474	+	21.8226i	0.514605	+	1.31119i	−0.403544	+	0.914960i	$0.632222\pi$
$278$	−4.25245	+	0.640953i	−0.255045	+	0.0384418i
$279$	1.13154	+	0.544920i	0.0677434	+	0.0326235i
$280$	1.53394	+	0.738708i	0.0916706	+	0.0441462i
$281$	5.06968	−	0.764132i	0.302432	−	0.0455843i	0.00392679	−	0.999992i	$-0.498750\pi$
$281$	5.06968	−	0.764132i	0.302432	−	0.0455843i	0.298505	+	0.954408i	$0.403512\pi$
$282$	0.481541	+	1.22695i	0.0286754	+	0.0730636i
$283$	1.36359	+	18.1958i	0.0810570	+	1.08163i	0.878344	+	0.478030i	$0.158649\pi$
$283$	1.36359	+	18.1958i	0.0810570	+	1.08163i	−0.797287	+	0.603601i	$0.793732\pi$
$284$	−5.30033	+	4.91799i	−0.314517	+	0.291829i
$285$	0.415310	+	1.81959i	0.0246008	+	0.107783i
$286$	6.48895	+	0.978051i	0.383699	+	0.0578334i
$287$	−3.43635	−	2.34286i	−0.202841	−	0.138295i
$288$	2.80676	−	0.865770i	0.165390	−	0.0510160i
$289$	−1.04052	+	13.8848i	−0.0612072	+	0.816753i
$290$	−1.62002	−	2.03144i	−0.0951307	−	0.119290i
$291$	−4.18818	−	1.29188i	−0.245515	−	0.0757314i
$292$	−2.52852	+	6.44257i	−0.147971	+	0.377023i
$293$	1.81125	−	7.93561i	0.105814	−	0.463603i	−0.894063	−	0.447941i	$-0.852157\pi$
$293$	1.81125	−	7.93561i	0.105814	−	0.463603i	0.999877	−	0.0156618i	$-0.00498551\pi$
$294$	0.513692	+	0.889740i	0.0299591	+	0.0518907i
$295$	6.47069	−	11.2076i	0.376738	−	0.652530i
$296$	4.06855	+	3.77506i	0.236479	+	0.219421i
$297$	3.94268	−	4.94397i	0.228778	−	0.286878i
$298$	7.03534	−	4.79661i	0.407546	−	0.277860i
$299$	5.80752	−	2.79675i	0.335857	−	0.161740i
$300$	−0.250500			−0.0144626
$301$	−10.8046	+	2.81123i	−0.622767	+	0.162037i
$302$	−2.08686			−0.120085
$303$	0.657761	−	0.316761i	0.0377874	−	0.0181975i
$304$	−6.15601	+	4.19710i	−0.353072	+	0.240720i
$305$	−4.58811	+	5.75330i	−0.262714	+	0.329433i
$306$	3.77648	+	3.50407i	0.215887	+	0.200314i
$307$	−3.91766	+	6.78559i	−0.223593	+	0.387274i	−0.955896	−	0.293704i	$-0.905112\pi$
$307$	−3.91766	+	6.78559i	−0.223593	+	0.387274i	0.732304	+	0.680978i	$0.238445\pi$
$308$	3.61942	+	6.26902i	0.206236	+	0.357210i
$309$	−0.376635	+	1.65014i	−0.0214260	+	0.0938734i
$310$	0.156213	−	0.398024i	0.00887229	−	0.0226062i
$311$	21.5885	+	6.65916i	1.22417	+	0.377607i	0.838434	−	0.545003i	$-0.183471\pi$
$311$	21.5885	+	6.65916i	1.22417	+	0.377607i	0.385736	+	0.922609i	$0.373948\pi$
$312$	0.241057	+	0.302276i	0.0136472	+	0.0171130i
$313$	−1.81925	+	24.2762i	−0.102830	+	1.37217i	0.672258	+	0.740317i	$0.265325\pi$
$313$	−1.81925	+	24.2762i	−0.102830	+	1.37217i	−0.775088	+	0.631853i	$0.782295\pi$
$314$	−1.61589	+	0.498437i	−0.0911901	+	0.0281284i
$315$	−4.13186	−	2.81705i	−0.232804	−	0.158723i
$316$	−14.0600	−	2.11921i	−0.790938	−	0.119215i
$317$	−5.87549	−	25.7422i	−0.330000	−	1.44583i	−0.819126	−	0.573613i	$-0.805541\pi$
$317$	−5.87549	−	25.7422i	−0.330000	−	1.44583i	0.489126	−	0.872213i	$-0.337316\pi$
$318$	0.853976	−	0.792374i	0.0478886	−	0.0444341i
$319$	−0.825573	−	11.0165i	−0.0462232	−	0.616806i
$320$	−0.365341	−	0.930874i	−0.0204232	−	0.0520374i
$321$	−0.844274	+	0.127254i	−0.0471228	+	0.00710262i
$322$	6.40630	+	3.08511i	0.357009	+	0.171926i
$323$	−11.7738	−	5.66995i	−0.655111	−	0.315485i
$324$	−8.34493	+	1.25780i	−0.463607	+	0.0698775i
$325$	0.563873	+	1.43672i	0.0312780	+	0.0796951i
$326$	0.480598	+	6.41313i	0.0266178	+	0.355190i
$327$	1.42527	−	1.32246i	0.0788175	−	0.0731320i
$328$	0.543580	+	2.38158i	0.0300142	+	0.131501i
$329$	8.85826	+	1.33517i	0.488372	+	0.0736102i
$330$	−0.880000	−	0.599974i	−0.0484424	−	0.0330275i
$331$	−5.77399	+	1.78104i	−0.317367	+	0.0978948i	−0.449346	−	0.893358i	$-0.648343\pi$
$331$	−5.77399	+	1.78104i	−0.317367	+	0.0978948i	0.131979	+	0.991253i	$0.457867\pi$
$332$	0.511654	−	6.82755i	0.0280807	−	0.374710i
$333$	−10.1642	−	12.7455i	−0.556997	−	0.698452i
$334$	14.7630	+	4.55379i	0.807797	+	0.249172i
$335$	0.396958	−	1.01143i	0.0216881	−	0.0552605i
$336$	−0.0949025	+	0.415795i	−0.00517735	+	0.0226835i
$337$	2.45943	+	4.25986i	0.133974	+	0.232049i	0.925205	−	0.379468i	$-0.123893\pi$
$337$	2.45943	+	4.25986i	0.133974	+	0.232049i	−0.791231	+	0.611517i	$0.790560\pi$
$338$	−5.30894	+	9.19535i	−0.288768	+	0.500161i
$339$	1.54476	+	1.43333i	0.0839000	+	0.0778478i
$340$	1.09356	−	1.37128i	0.0593065	−	0.0743680i
$341$	1.50208	−	1.02410i	0.0813423	−	0.0554582i
$342$	19.7172	−	9.49529i	1.06618	−	0.513446i
$343$	18.9005			1.02053
$344$	5.77515	+	3.10607i	0.311375	+	0.167468i
$345$	−1.04618			−0.0563243
$346$	−3.19936	+	1.54073i	−0.171999	+	0.0828303i
$347$	−16.4693	+	11.2286i	−0.884117	+	0.602781i	−0.917972	−	0.396646i	$-0.870174\pi$
$347$	−16.4693	+	11.2286i	−0.884117	+	0.602781i	0.0338547	+	0.999427i	$0.489222\pi$
$348$	0.405814	−	0.508875i	0.0217539	−	0.0272786i
$349$	−14.4128	−	13.3731i	−0.771499	−	0.715847i	0.192633	−	0.981271i	$-0.438297\pi$
$349$	−14.4128	−	13.3731i	−0.771499	−	0.715847i	−0.964132	+	0.265424i	$0.914488\pi$
$350$	−0.851274	+	1.47445i	−0.0455025	+	0.0788126i
$351$	−1.14774	−	1.98795i	−0.0612621	−	0.106109i
$352$	0.946108	−	4.14517i	0.0504277	−	0.220938i
$353$	−7.24255	+	18.4537i	−0.385482	+	0.982192i	0.598050	+	0.801459i	$0.295942\pi$
$353$	−7.24255	+	18.4537i	−0.385482	+	0.982192i	−0.983532	+	0.180733i	$0.942153\pi$
$354$	3.09779	+	0.955542i	0.164646	+	0.0507865i
$355$	−4.50814	−	5.65303i	−0.239267	−	0.300032i
$356$	−0.691282	+	9.22451i	−0.0366379	+	0.488898i
$357$	−0.714797	+	0.220486i	−0.0378311	+	0.0116693i
$358$	−16.7665	−	11.4312i	−0.886139	−	0.604159i
$359$	20.5105	+	3.09146i	1.08250	+	0.163161i	0.665984	−	0.745966i	$-0.268012\pi$
$359$	20.5105	+	3.09146i	1.08250	+	0.163161i	0.416519	+	0.909127i	$0.363250\pi$
$360$	0.653600	+	2.86361i	0.0344477	+	0.150925i
$361$	−26.7653	+	24.8345i	−1.40870	+	1.30708i
$362$	−0.323435	−	4.31594i	−0.0169994	−	0.226841i
$363$	−0.647722	−	1.65037i	−0.0339966	−	0.0866218i
$364$	2.59839	−	0.391644i	0.136192	−	0.0205277i
$365$	−6.23560	−	3.00291i	−0.326386	−	0.157179i
$366$	−1.66082	−	0.799806i	−0.0868122	−	0.0418065i
$367$	−23.4236	+	3.53054i	−1.22270	+	0.184293i	−0.728495	−	0.685051i	$-0.759780\pi$
$367$	−23.4236	+	3.53054i	−1.22270	+	0.184293i	−0.494207	+	0.869344i	$0.664542\pi$
$368$	−1.52580	−	3.88767i	−0.0795376	−	0.202659i
$369$	−0.536202	−	7.15512i	−0.0279136	−	0.372481i
$370$	−4.06855	+	3.77506i	−0.211514	+	0.196256i
$371$	−1.76187	−	7.71925i	−0.0914716	−	0.400763i
$372$	0.105913	+	0.0159638i	0.00549131	+	0.000827682i
$373$	−18.3890	−	12.5374i	−0.952149	−	0.649164i	−0.0156659	−	0.999877i	$-0.504987\pi$
$373$	−18.3890	−	12.5374i	−0.952149	−	0.649164i	−0.936483	+	0.350713i	$0.885939\pi$
$374$	7.12600	−	2.19808i	0.368477	−	0.113660i
$375$	0.0187199	−	0.249799i	0.000966690	−	0.0128996i
$376$	−3.28063	−	4.11378i	−0.169185	−	0.212152i
$377$	−3.83210	−	1.18205i	−0.197363	−	0.0608785i
$378$	0.925104	−	2.35713i	0.0475822	−	0.121237i
$379$	−4.56856	+	20.0162i	−0.234671	+	1.02816i	0.711039	+	0.703152i	$0.248225\pi$
$379$	−4.56856	+	20.0162i	−0.234671	+	1.02816i	−0.945711	+	0.325010i	$0.894632\pi$
$380$	−3.72532	−	6.45245i	−0.191105	−	0.331004i
$381$	−0.122778	+	0.212658i	−0.00629010	+	0.0108948i
$382$	−11.5807	−	10.7453i	−0.592520	−	0.549778i
$383$	−13.0722	+	16.3921i	−0.667960	+	0.837595i	−0.994184	−	0.107698i	$-0.965652\pi$
$383$	−13.0722	+	16.3921i	−0.667960	+	0.837595i	0.326224	+	0.945292i	$0.394224\pi$
$384$	0.206973	−	0.141112i	0.0105620	−	0.00720107i
$385$	−6.52197	+	3.14081i	−0.332390	+	0.160071i
$386$	25.5609			1.30102
$387$	−15.4138	−	11.5496i	−0.783529	−	0.587099i
$388$	17.4966			0.888255
$389$	−7.79870	+	3.75566i	−0.395410	+	0.190419i	−0.621014	−	0.783800i	$-0.713279\pi$
$389$	−7.79870	+	3.75566i	−0.395410	+	0.190419i	0.225604	+	0.974219i	$0.427565\pi$
$390$	−0.319445	+	0.217794i	−0.0161757	+	0.0110284i
$391$	4.56709	−	5.72695i	0.230968	−	0.289624i
$392$	−3.00649	−	2.78961i	−0.151851	−	0.140897i
$393$	−2.45286	+	4.24847i	−0.123730	+	0.214307i
$394$	−10.7404	−	18.6029i	−0.541093	−	0.937201i
$395$	3.16399	−	13.8623i	0.159197	−	0.697490i
$396$	−4.56256	+	11.6252i	−0.229277	+	0.584190i
$397$	−20.0923	−	6.19767i	−1.00841	−	0.311052i	−0.253819	−	0.967252i	$-0.581687\pi$
$397$	−20.0923	−	6.19767i	−1.00841	−	0.311052i	−0.754587	+	0.656200i	$0.772163\pi$
$398$	15.1829	+	19.0388i	0.761051	+	0.954328i
$399$	−0.237463	+	3.16872i	−0.0118880	+	0.158635i
$400$	0.955573	−	0.294755i	0.0477786	−	0.0147378i
$401$	−9.33650	−	6.36552i	−0.466242	−	0.317879i	0.307312	−	0.951609i	$-0.400571\pi$
$401$	−9.33650	−	6.36552i	−0.466242	−	0.317879i	−0.773554	+	0.633730i	$0.781523\pi$
$402$	0.269138	+	0.0405661i	0.0134234	+	0.00202325i
$403$	−0.146849	−	0.643388i	−0.00731508	−	0.0320495i
$404$	−2.13642	+	1.98230i	−0.106291	+	0.0986233i
$405$	−0.630661	−	8.41559i	−0.0313378	−	0.418174i
$406$	−1.61617	−	4.11794i	−0.0802093	−	0.204370i
$407$	−23.3344	+	3.51709i	−1.15664	+	0.174336i
$408$	0.395849	+	0.190631i	0.0195974	+	0.00943763i
$409$	10.3812	+	4.99933i	0.513318	+	0.247201i	0.672565	−	0.740038i	$-0.265192\pi$
$409$	10.3812	+	4.99933i	0.513318	+	0.247201i	−0.159247	+	0.987239i	$0.550907\pi$
$410$	−2.41554	+	0.364084i	−0.119295	+	0.0179808i
$411$	−0.223475	−	0.569405i	−0.0110232	−	0.0280867i
$412$	−0.504937	−	6.73792i	−0.0248765	−	0.331953i
$413$	16.1516	−	14.9865i	0.794766	−	0.737436i
$414$	2.72967	+	11.9595i	0.134156	+	0.587775i
$415$	6.77022	+	1.02045i	0.332337	+	0.0500918i
$416$	−1.27523	−	0.869436i	−0.0625232	−	0.0426276i
$417$	1.02941	−	0.317531i	0.0504104	−	0.0155495i
$418$	2.36733	−	31.5898i	0.115790	−	1.54511i
$419$	−8.99376	−	11.2778i	−0.439374	−	0.550957i	0.512004	−	0.858983i	$-0.328903\pi$
$419$	−8.99376	−	11.2778i	−0.439374	−	0.550957i	−0.951378	+	0.308026i	$0.900332\pi$
$420$	−0.407540	−	0.125709i	−0.0198859	−	0.00613400i
$421$	−9.98523	+	25.4420i	−0.486650	+	1.23996i	0.451043	+	0.892502i	$0.351052\pi$
$421$	−9.98523	+	25.4420i	−0.486650	+	1.23996i	−0.937694	+	0.347463i	$0.887043\pi$
$422$	0.0663916	−	0.290880i	0.00323189	−	0.0141598i
$423$	7.72749	+	13.3844i	0.375723	+	0.650772i
$424$	−2.32527	+	4.02749i	−0.112925	+	0.195592i
$425$	1.28572	+	1.19298i	0.0623666	+	0.0578678i
$426$	1.12929	−	1.41608i	0.0547143	−	0.0686095i
$427$	−10.3516	+	7.05762i	−0.500950	+	0.341542i
$428$	3.07089	−	1.47886i	0.148437	−	0.0714834i
$429$	−1.64384			−0.0793654
$430$	−3.52896	+	5.52688i	−0.170181	+	0.266530i
$431$	−7.60455			−0.366298			−0.183149	−	0.983085i	$-0.558629\pi$
$431$	−7.60455			−0.366298			−0.183149	+	0.983085i	$0.558629\pi$
$432$	−1.33999	+	0.645307i	−0.0644705	+	0.0310473i
$433$	30.3829	−	20.7147i	1.46011	−	0.995486i	0.466271	−	0.884642i	$-0.345597\pi$
$433$	30.3829	−	20.7147i	1.46011	−	0.995486i	0.993838	−	0.110844i	$-0.0353553\pi$
$434$	0.453886	−	0.569155i	0.0217872	−	0.0273203i
$435$	0.477125	+	0.442708i	0.0228764	+	0.0212262i
$436$	−3.88083	+	6.72179i	−0.185858	+	0.321916i
$437$	−15.5583	−	26.9478i	−0.744254	−	1.28909i
$438$	0.385786	−	1.69024i	0.0184336	−	0.0807628i
$439$	−4.60186	+	11.7254i	−0.219635	+	0.559621i	−0.997642	−	0.0686350i	$-0.978136\pi$
$439$	−4.60186	+	11.7254i	−0.219635	+	0.559621i	0.778007	+	0.628256i	$0.216231\pi$
$440$	4.06288	+	1.25323i	0.193690	+	0.0597454i
$441$	7.51096	+	9.41844i	0.357665	+	0.448497i
$442$	0.202297	−	2.69947i	0.00962230	−	0.128401i
$443$	25.0998	−	7.74227i	1.19253	−	0.367846i	0.365932	−	0.930642i	$-0.380750\pi$
$443$	25.0998	−	7.74227i	1.19253	−	0.367846i	0.826596	+	0.562796i	$0.190274\pi$
$444$	−1.14873	−	0.783190i	−0.0545163	−	0.0371686i
$445$	−9.14706	−	1.37870i	−0.433612	−	0.0653565i
$446$	−4.18679	−	18.3435i	−0.198250	−	0.868592i
$447$	−1.56358	+	1.45079i	−0.0739550	+	0.0686202i
$448$	−0.127232	−	1.69779i	−0.00601112	−	0.0802129i
$449$	6.51378	+	16.5968i	0.307404	+	0.783253i	0.998187	+	0.0601908i	$0.0191709\pi$
$449$	6.51378	+	16.5968i	0.307404	+	0.783253i	−0.690783	+	0.723062i	$0.742734\pi$
$450$	−2.90444	+	0.437774i	−0.136917	+	0.0206369i
$451$	−9.35776	−	4.50646i	−0.440640	−	0.212201i
$452$	−7.57930	−	3.65000i	−0.356500	−	0.171682i
$453$	0.516919	−	0.0779129i	0.0242870	−	0.00366067i
$454$	−1.55620	−	3.96513i	−0.0730360	−	0.186093i
$455$	0.196371	+	2.62039i	0.00920601	+	0.122846i
$456$	1.36816	−	1.26946i	0.0640698	−	0.0594481i
$457$	−6.94425	−	30.4247i	−0.324838	−	1.42321i	−0.828830	−	0.559501i	$-0.810993\pi$
$457$	−6.94425	−	30.4247i	−0.324838	−	1.42321i	0.503991	−	0.863709i	$-0.331864\pi$
$458$	−15.8368	−	2.38702i	−0.740007	−	0.111538i
$459$	−2.15531	−	1.46947i	−0.100601	−	0.0685889i
$460$	3.99082	−	1.23100i	0.186073	−	0.0573959i
$461$	2.82234	−	37.6614i	0.131449	−	1.75407i	−0.408856	−	0.912599i	$-0.634072\pi$
$461$	2.82234	−	37.6614i	0.131449	−	1.75407i	0.540305	−	0.841469i	$-0.318309\pi$
$462$	−1.13059	−	1.41772i	−0.0525999	−	0.0659582i
$463$	−22.6555	−	6.98831i	−1.05289	−	0.324774i	−0.280456	−	0.959867i	$-0.590486\pi$
$463$	−22.6555	−	6.98831i	−1.05289	−	0.324774i	−0.772436	+	0.635093i	$0.780962\pi$
$464$	−0.949268	+	2.41870i	−0.0440687	+	0.112285i
$465$	−0.0238340	+	0.104423i	−0.00110527	+	0.00484252i
$466$	9.31054	+	16.1263i	0.431302	+	0.747038i
$467$	1.70347	−	2.95050i	0.0788273	−	0.136533i	−0.823917	−	0.566711i	$-0.808216\pi$
$467$	1.70347	−	2.95050i	0.0788273	−	0.136533i	0.902744	+	0.430178i	$0.141549\pi$
$468$	3.32321	+	3.08349i	0.153616	+	0.142534i
$469$	1.15339	−	1.44630i	0.0532584	−	0.0667839i
$470$	4.34743	−	2.96403i	0.200532	−	0.136721i
$471$	0.381651	−	0.183793i	0.0175855	−	0.00846875i
$472$	−12.9414			−0.595675
$473$	−25.6346	+	10.9636i	−1.17868	+	0.504106i
$474$	3.56182			0.163600
$475$	6.71280	−	3.23271i	0.308004	−	0.148327i
$476$	2.46727	−	1.68216i	0.113087	−	0.0771015i
$477$	8.51674	−	10.6797i	0.389955	−	0.488988i
$478$	11.8877	+	11.0302i	0.543732	+	0.504510i
$479$	−5.47624	+	9.48513i	−0.250216	+	0.433386i	−0.963585	−	0.267402i	$-0.913835\pi$
$479$	−5.47624	+	9.48513i	−0.250216	+	0.433386i	0.713369	+	0.700788i	$0.247168\pi$
$480$	0.125250	+	0.216939i	0.00571685	+	0.00990188i
$481$	−1.90615	+	8.35141i	−0.0869131	+	0.380791i
$482$	−9.43368	+	24.0366i	−0.429692	+	1.09484i
$483$	−1.70204	−	0.525008i	−0.0774453	−	0.0238887i
$484$	4.41278	+	5.53345i	0.200581	+	0.251520i
$485$	−1.30752	+	17.4477i	−0.0593715	+	0.792258i
$486$	6.28371	−	1.93827i	0.285035	−	0.0879216i
$487$	−31.8647	−	21.7250i	−1.44393	−	0.984454i	−0.995902	−	0.0904336i	$-0.971175\pi$
$487$	−31.8647	−	21.7250i	−1.44393	−	0.984454i	−0.448026	−	0.894020i	$-0.647873\pi$
$488$	7.27656	+	1.09676i	0.329394	+	0.0496482i
$489$	−0.358480	−	1.57060i	−0.0162110	−	0.0710250i
$490$	3.00649	−	2.78961i	0.135819	−	0.126022i
$491$	1.89961	+	25.3485i	0.0857282	+	1.14396i	0.859719	+	0.510767i	$0.170638\pi$
$491$	1.89961	+	25.3485i	0.0857282	+	1.14396i	−0.773991	+	0.633196i	$0.781743\pi$
$492$	−0.223562	−	0.569627i	−0.0100790	−	0.0256808i
$493$	−4.50635	+	0.679222i	−0.202956	+	0.0305906i
$494$	−10.3606	−	4.98942i	−0.466147	−	0.224484i
$495$	−11.2518	−	5.41856i	−0.505729	−	0.243546i
$496$	−0.422805	+	0.0637276i	−0.0189845	+	0.00286145i
$497$	−4.49745	−	11.4593i	−0.201738	−	0.514020i
$498$	0.128169	+	1.71030i	0.00574340	+	0.0766404i
$499$	−10.0564	+	9.33102i	−0.450188	+	0.417714i	−0.872407	−	0.488780i	$-0.837442\pi$
$499$	−10.0564	+	9.33102i	−0.450188	+	0.417714i	0.422219	+	0.906494i	$0.361251\pi$
$500$	0.222521	+	0.974928i	0.00995144	+	0.0436001i
$501$	−3.82685	−	0.576805i	−0.170971	−	0.0257697i
$502$	−13.2828	−	9.05607i	−0.592841	−	0.404192i
$503$	−24.7606	+	7.63764i	−1.10402	+	0.340545i	−0.792610	−	0.609730i	$-0.791278\pi$
$503$	−24.7606	+	7.63764i	−1.10402	+	0.340545i	−0.311412	+	0.950275i	$0.600802\pi$
$504$	−0.373711	+	4.98682i	−0.0166464	+	0.222131i
$505$	−1.81711	−	2.27858i	−0.0808602	−	0.101395i
$506$	16.9680	+	5.23395i	0.754321	+	0.232677i
$507$	0.971725	−	2.47592i	0.0431558	−	0.109959i
$508$	0.218129	−	0.955686i	0.00967791	−	0.0424017i
$509$	6.35002	+	10.9986i	0.281460	+	0.487502i	0.971744	−	0.236035i	$-0.0758481\pi$
$509$	6.35002	+	10.9986i	0.281460	+	0.487502i	−0.690285	+	0.723538i	$0.742515\pi$
$510$	−0.219680	+	0.380496i	−0.00972757	+	0.0168487i
$511$	−8.63778	−	8.01469i	−0.382113	−	0.354549i
$512$	−0.623490	+	0.781831i	−0.0275546	+	0.0345524i
$513$	−9.15571	+	6.24226i	−0.404235	+	0.275603i
$514$	19.7456	−	9.50900i	0.870943	−	0.419424i
$515$	6.75681			0.297741
$516$	−1.54648	−	0.553763i	−0.0680800	−	0.0243781i
$517$	22.3716			0.983902
$518$	−8.51360	+	4.09994i	−0.374066	+	0.180141i
$519$	0.734965	−	0.501091i	0.0322614	−	0.0219954i
$520$	0.962303	−	1.20669i	0.0421998	−	0.0529169i
$521$	7.87754	+	7.30929i	0.345121	+	0.320226i	0.833619	−	0.552339i	$-0.186265\pi$
$521$	7.87754	+	7.30929i	0.345121	+	0.320226i	−0.488498	+	0.872565i	$0.662455\pi$
$522$	3.81594	−	6.60940i	0.167019	−	0.289285i
$523$	1.45637	+	2.52251i	0.0636827	+	0.110302i	0.896109	−	0.443834i	$-0.146382\pi$
$523$	1.45637	+	2.52251i	0.0636827	+	0.110302i	−0.832426	+	0.554136i	$0.813049\pi$
$524$	4.35778	−	19.0927i	0.190371	−	0.834068i
$525$	0.155813	−	0.397006i	0.00680026	−	0.0173268i
$526$	−8.95172	−	2.76124i	−0.390314	−	0.120396i
$527$	−0.467584	−	0.586332i	−0.0203683	−	0.0255410i
$528$	−0.0795926	+	1.06209i	−0.00346382	+	0.0462215i
$529$	−5.31107	+	1.63825i	−0.230916	+	0.0712282i
$530$	−3.84246	−	2.61974i	−0.166906	−	0.113794i
$531$	37.5875	+	5.66541i	1.63116	+	0.245858i
$532$	−2.82269	−	12.3670i	−0.122379	−	0.536179i
$533$	−2.76382	+	2.56445i	−0.119714	+	0.111079i
$534$	−0.173166	−	2.31074i	−0.00749362	−	0.0999955i
$535$	1.24524	+	3.17281i	0.0538363	+	0.137173i
$536$	−1.07441	+	0.161941i	−0.0464072	+	0.00699477i
$537$	4.57989	+	2.20556i	0.197637	+	0.0951768i
$538$	10.3670	+	4.99250i	0.446954	+	0.215242i
$539$	17.2432	−	2.59899i	0.742715	−	0.111946i
$540$	−0.543364	−	1.38447i	−0.0233827	−	0.0595781i
$541$	−0.223763	−	2.98591i	−0.00962034	−	0.128374i	0.990326	−	0.138762i	$-0.0443124\pi$
$541$	−0.223763	−	2.98591i	−0.00962034	−	0.128374i	−0.999946	+	0.0103879i	$0.996693\pi$
$542$	20.0959	−	18.6463i	0.863193	−	0.800926i
$543$	0.241251	+	1.05699i	0.0103531	+	0.0453598i
$544$	−1.73434	−	0.261410i	−0.0743592	−	0.0112078i
$545$	−6.41298	−	4.37230i	−0.274702	−	0.187289i
$546$	−0.629003	+	0.194022i	−0.0269189	+	0.00830337i
$547$	−1.63619	+	21.8334i	−0.0699583	+	0.933529i	0.846239	+	0.532803i	$0.178861\pi$
$547$	−1.63619	+	21.8334i	−0.0699583	+	0.933529i	−0.916198	+	0.400726i	$0.868758\pi$
$548$	1.52248	+	1.90913i	0.0650372	+	0.0815541i
$549$	−20.6542	−	6.37098i	−0.881500	−	0.271907i
$550$	−1.55335	+	3.95786i	−0.0662349	+	0.168764i
$551$	−4.30780	+	18.8737i	−0.183518	+	0.804046i
$552$	0.523089	+	0.906017i	0.0222641	+	0.0385626i
$553$	12.1041	−	20.9649i	0.514719	−	0.891520i
$554$	17.1850	+	15.9454i	0.730122	+	0.677455i
$555$	0.866845	−	1.08699i	0.0367955	−	0.0461401i
$556$	−3.55322	+	2.42255i	−0.150690	+	0.102739i
$557$	18.8998	−	9.10166i	0.800810	−	0.385650i	0.0117228	−	0.999931i	$-0.496268\pi$
$557$	18.8998	−	9.10166i	0.800810	−	0.385650i	0.789087	+	0.614282i	$0.210554\pi$
$558$	1.25591			0.0531670
$559$	0.305046	+	10.1162i	0.0129021	+	0.427872i
$560$	1.70255			0.0719457
$561$	−1.68306	+	0.810518i	−0.0710588	+	0.0342201i
$562$	4.23608	−	2.88811i	0.178688	−	0.121828i
$563$	−15.8312	+	19.8517i	−0.667206	+	0.836650i	−0.994106	−	0.108409i	$-0.965424\pi$
$563$	−15.8312	+	19.8517i	−0.667206	+	0.836650i	0.326900	+	0.945059i	$0.393996\pi$
$564$	0.966206	+	0.896508i	0.0406846	+	0.0377498i
$565$	4.20619	−	7.28534i	0.176956	−	0.306497i
$566$	9.12344	+	15.8023i	0.383487	+	0.664218i
$567$	3.19721	−	14.0079i	0.134270	−	0.588275i
$568$	−2.64160	+	6.73068i	−0.110839	+	0.282413i
$569$	41.3916	+	12.7676i	1.73523	+	0.535246i	0.991138	−	0.132836i	$-0.0424083\pi$
$569$	41.3916	+	12.7676i	1.73523	+	0.535246i	0.744088	+	0.668082i	$0.232885\pi$
$570$	1.16367	+	1.45920i	0.0487409	+	0.0611191i
$571$	−1.81631	+	24.2370i	−0.0760104	+	1.01429i	0.820610	+	0.571489i	$0.193634\pi$
$571$	−1.81631	+	24.2370i	−0.0760104	+	1.01429i	−0.896620	+	0.442800i	$0.853985\pi$
$572$	6.27070	−	1.93425i	0.262191	−	0.0808753i
$573$	3.26974	+	2.22927i	0.136595	+	0.0931291i
$574$	−4.11257	−	0.619870i	−0.171655	−	0.0258729i
$575$	0.929328	+	4.07165i	0.0387557	+	0.169800i
$576$	2.15316	−	1.99784i	0.0897149	−	0.0832432i
$577$	1.44945	+	19.3416i	0.0603414	+	0.805200i	0.942491	+	0.334231i	$0.108477\pi$
$577$	1.44945	+	19.3416i	0.0603414	+	0.805200i	−0.882150	+	0.470969i	$0.843904\pi$
$578$	5.08691	+	12.9612i	0.211588	+	0.539116i
$579$	−6.33149	+	0.954319i	−0.263128	+	0.0396601i
$580$	−2.34099	−	1.12736i	−0.0972045	−	0.0468112i
$581$	10.5024	+	5.05770i	0.435714	+	0.209829i
$582$	−4.33394	+	0.653237i	−0.179648	+	0.0270775i
$583$	−7.22390	−	18.4062i	−0.299183	−	0.762306i
$584$	0.517207	+	6.90164i	0.0214022	+	0.285592i
$585$	−3.32321	+	3.08349i	−0.137398	+	0.127487i
$586$	−1.81125	−	7.93561i	−0.0748221	−	0.327817i
$587$	29.5717	+	4.45721i	1.22055	+	0.183969i	0.727547	−	0.686057i	$-0.240660\pi$
$587$	29.5717	+	4.45721i	1.22055	+	0.183969i	0.493006	+	0.870026i	$0.335898\pi$
$588$	0.848864	+	0.578746i	0.0350066	+	0.0238671i
$589$	−3.04422	+	0.939017i	−0.125435	+	0.0386915i
$590$	0.967111	−	12.9052i	0.0398153	−	0.531299i
$591$	3.35496	+	4.20698i	0.138005	+	0.173052i
$592$	5.30357	+	1.63593i	0.217975	+	0.0672365i
$593$	−3.58635	+	9.13787i	−0.147274	+	0.375247i	−0.985406	−	0.170219i	$-0.945552\pi$
$593$	−3.58635	+	9.13787i	−0.147274	+	0.375247i	0.838132	+	0.545467i	$0.183648\pi$
$594$	1.40713	−	6.16503i	0.0577351	−	0.252954i
$595$	1.49307	+	2.58608i	0.0612101	+	0.106019i
$596$	4.25745	−	7.37411i	0.174392	−	0.302055i
$597$	−4.47166	−	4.14909i	−0.183013	−	0.169811i
$598$	4.01893	−	5.03957i	0.164346	−	0.206084i
$599$	−18.9721	+	12.9349i	−0.775177	+	0.528507i	−0.885082	−	0.465435i	$-0.845898\pi$
$599$	−18.9721	+	12.9349i	−0.775177	+	0.528507i	0.109905	+	0.993942i	$0.464945\pi$
$600$	−0.225693	+	0.108688i	−0.00921386	+	0.00443716i
$601$	15.6069			0.636619			0.318309	−	0.947987i	$-0.396885\pi$
$601$	15.6069			0.636619			0.318309	+	0.947987i	$0.396885\pi$
$602$	−8.51487	+	7.22078i	−0.347040	+	0.294297i
$603$	3.19144			0.129966
$604$	−1.88019	+	0.905453i	−0.0765040	+	0.0368424i
$605$	−5.84774	+	3.98692i	−0.237744	+	0.162091i
$606$	0.455185	−	0.570784i	0.0184906	−	0.0231865i
$607$	−11.1319	−	10.3289i	−0.451831	−	0.419238i	0.421151	−	0.906991i	$-0.361626\pi$
$607$	−11.1319	−	10.3289i	−0.451831	−	0.419238i	−0.872982	+	0.487753i	$0.837817\pi$
$608$	−3.72532	+	6.45245i	−0.151082	+	0.261681i
$609$	0.554073	+	0.959683i	0.0224522	+	0.0388883i
$610$	−1.63748	+	7.17425i	−0.0662995	+	0.290477i
$611$	2.96694	−	7.55964i	0.120029	−	0.305830i
$612$	4.92285	+	1.51850i	0.198995	+	0.0613817i
$613$	28.6871	+	35.9725i	1.15866	+	1.45292i	0.868327	+	0.495993i	$0.165196\pi$
$613$	28.6871	+	35.9725i	1.15866	+	1.45292i	0.290336	+	0.956925i	$0.406233\pi$
$614$	−0.585534	+	7.81341i	−0.0236302	+	0.315324i
$615$	0.584741	−	0.180369i	0.0235790	−	0.00727317i
$616$	5.98101	+	4.07778i	0.240982	+	0.164299i
$617$	33.4520	+	5.04208i	1.34673	+	0.202986i	0.782509	−	0.622640i	$-0.213940\pi$
$617$	33.4520	+	5.04208i	1.34673	+	0.202986i	0.564218	+	0.825626i	$0.309178\pi$
$618$	0.376635	+	1.65014i	0.0151505	+	0.0663785i
$619$	12.0551	−	11.1855i	0.484535	−	0.449582i	−0.399686	−	0.916652i	$-0.630881\pi$
$619$	12.0551	−	11.1855i	0.484535	−	0.449582i	0.884220	+	0.467070i	$0.154690\pi$
$620$	−0.0319532	−	0.426385i	−0.00128327	−	0.0171240i
$621$	−2.26929	−	5.78205i	−0.0910633	−	0.232026i
$622$	22.3398	−	3.36719i	0.895746	−	0.135012i
$623$	−14.1895	−	6.83332i	−0.568492	−	0.273771i
$624$	0.348337	+	0.167750i	0.0139446	+	0.00671539i
$625$	−0.988831	+	0.149042i	−0.0395532	+	0.00596169i
$626$	8.89395	+	22.6614i	0.355474	+	0.905732i
$627$	0.593016	+	7.91325i	0.0236828	+	0.316025i
$628$	−1.23961	+	1.15019i	−0.0494657	+	0.0458974i
$629$	2.16615	+	9.49050i	0.0863699	+	0.378411i
$630$	−4.94495	−	0.745332i	−0.197012	−	0.0296947i
$631$	6.90493	+	4.70770i	0.274881	+	0.187411i	0.692912	−	0.721022i	$-0.256327\pi$
$631$	6.90493	+	4.70770i	0.274881	+	0.187411i	−0.418031	+	0.908433i	$0.637280\pi$
$632$	−13.5871	+	4.19107i	−0.540467	+	0.166712i
$633$	−0.00558528	+	0.0745304i	−0.000221995	+	0.00296232i
$634$	−16.4628	−	20.6436i	−0.653820	−	0.819864i
$635$	0.936713	+	0.288938i	0.0371723	+	0.0114661i
$636$	0.425608	−	1.08443i	0.0168764	−	0.0430005i
$637$	1.40857	−	6.17135i	0.0558096	−	0.244518i
$638$	−5.52370	−	9.56733i	−0.218685	−	0.378774i
$639$	10.6189	−	18.3925i	0.420077	−	0.727595i
$640$	−0.733052	−	0.680173i	−0.0289764	−	0.0268862i
$641$	−19.0674	+	23.9097i	−0.753115	+	0.944376i	−0.999694	−	0.0247463i	$-0.992122\pi$
$641$	−19.0674	+	23.9097i	−0.753115	+	0.944376i	0.246579	+	0.969123i	$0.420694\pi$
$642$	−0.705451	+	0.480968i	−0.0278419	+	0.0189823i
$643$	15.6085	−	7.51668i	0.615541	−	0.296429i	−0.100013	−	0.994986i	$-0.531889\pi$
$643$	15.6085	−	7.51668i	0.615541	−	0.296429i	0.715554	+	0.698557i	$0.246174\pi$
$644$	7.11045			0.280191
$645$	0.667783	−	1.50077i	0.0262939	−	0.0590929i
$646$	−13.0679			−0.514150
$647$	24.7594	−	11.9235i	0.973394	−	0.468762i	0.121566	−	0.992583i	$-0.461208\pi$
$647$	24.7594	−	11.9235i	0.973394	−	0.468762i	0.851828	+	0.523821i	$0.175494\pi$
$648$	−6.97278	+	4.75396i	−0.273917	+	0.186753i
$649$	34.3068	−	43.0193i	1.34666	−	1.68866i
$650$	1.13140	+	1.04979i	0.0443773	+	0.0411761i
$651$	−0.0911790	+	0.157927i	−0.00357359	+	0.00618963i
$652$	3.21556	+	5.56951i	0.125931	+	0.218119i
$653$	10.3514	−	45.3524i	0.405082	−	1.77478i	−0.201223	−	0.979545i	$-0.564492\pi$
$653$	10.3514	−	45.3524i	0.405082	−	1.77478i	0.606304	−	0.795233i	$-0.292651\pi$
$654$	0.710331	−	1.80989i	0.0277761	−	0.0707724i
$655$	18.7136	+	5.77239i	0.731202	+	0.225546i
$656$	1.52308	+	1.90988i	0.0594661	+	0.0745682i
$657$	1.51916	−	20.2718i	0.0592683	−	0.790880i
$658$	8.56033	−	2.64051i	0.333716	−	0.102938i
$659$	20.7443	+	14.1433i	0.808085	+	0.550943i	0.895413	−	0.445237i	$-0.146880\pi$
$659$	20.7443	+	14.1433i	0.808085	+	0.550943i	−0.0873280	+	0.996180i	$0.527833\pi$
$660$	−1.05317	−	0.158740i	−0.0409947	−	0.00617895i
$661$	−9.52131	−	41.7156i	−0.370336	−	1.62255i	−0.725834	−	0.687870i	$-0.758546\pi$
$661$	−9.52131	−	41.7156i	−0.370336	−	1.62255i	0.355498	−	0.934677i	$-0.384311\pi$
$662$	−4.42942	+	4.10990i	−0.172154	+	0.159736i
$663$	0.0506755	+	0.676217i	0.00196807	+	0.0262621i
$664$	−2.50138	−	6.37341i	−0.0970723	−	0.247336i
$665$	12.5434	−	1.89061i	0.486412	−	0.0733148i
$666$	−14.6877	−	7.07325i	−0.569139	−	0.274083i
$667$	−9.77684	−	4.70828i	−0.378561	−	0.182305i
$668$	15.2768	−	2.30261i	0.591079	−	0.0890908i
$669$	1.72193	+	4.38742i	0.0665738	+	0.169627i
$670$	−0.0811973	−	1.08350i	−0.00313693	−	0.0418594i
$671$	−22.9355	+	21.2810i	−0.885416	+	0.821546i
$672$	0.0949025	+	0.415795i	0.00366094	+	0.0160396i
$673$	35.8431	+	5.40248i	1.38165	+	0.208250i	0.797463	−	0.603368i	$-0.206175\pi$
$673$	35.8431	+	5.40248i	1.38165	+	0.208250i	0.584188	+	0.811618i	$0.301413\pi$
$674$	4.06415	+	2.77089i	0.156545	+	0.106731i
$675$	1.42120	−	0.438384i	0.0547022	−	0.0168734i
$676$	−0.793475	+	10.5882i	−0.0305183	+	0.407238i
$677$	−28.4511	−	35.6766i	−1.09347	−	1.37116i	−0.922550	−	0.385878i	$-0.873899\pi$
$677$	−28.4511	−	35.6766i	−1.09347	−	1.37116i	−0.170916	−	0.985286i	$-0.554673\pi$
$678$	2.01368	+	0.621138i	0.0773349	+	0.0238547i
$679$	−10.8831	+	27.7296i	−0.417654	+	1.06416i
$680$	0.390286	−	1.70995i	0.0149668	−	0.0655738i
$681$	0.533512	+	0.924070i	0.0204442	+	0.0354104i
$682$	0.908988	−	1.57441i	0.0348069	−	0.0602874i
$683$	3.47650	+	3.22572i	0.133025	+	0.123429i	0.743879	−	0.668314i	$-0.232984\pi$
$683$	3.47650	+	3.22572i	0.133025	+	0.123429i	−0.610855	+	0.791743i	$0.709174\pi$
$684$	13.6447	−	17.1099i	0.521718	−	0.654214i
$685$	−2.01757	+	1.37556i	−0.0770874	+	0.0525573i
$686$	17.0288	−	8.20064i	0.650163	−	0.313102i
$687$	4.01193			0.153065
$688$	6.55090	+	0.292725i	0.249751	+	0.0111600i
$689$	−7.17771			−0.273449
$690$	−0.942574	+	0.453920i	−0.0358832	+	0.0172804i
$691$	6.87753	−	4.68902i	0.261633	−	0.178379i	−0.425398	−	0.905006i	$-0.639866\pi$
$691$	6.87753	−	4.68902i	0.261633	−	0.178379i	0.687031	+	0.726628i	$0.258913\pi$
$692$	−2.21403	+	2.77630i	−0.0841647	+	0.105539i
$693$	−15.5864	−	14.4620i	−0.592077	−	0.549367i
$694$	−9.96641	+	17.2623i	−0.378320	+	0.655269i
$695$	−2.15024	−	3.72432i	−0.0815632	−	0.141272i
$696$	0.144833	−	0.634557i	0.00548990	−	0.0240528i
$697$	−1.56532	+	3.98837i	−0.0592907	+	0.151070i
$698$	−18.7879	−	5.79529i	−0.711131	−	0.219355i
$699$	−2.90832	−	3.64691i	−0.110003	−	0.137939i
$700$	−0.127232	+	1.69779i	−0.00480890	+	0.0641703i
$701$	−25.5277	+	7.87425i	−0.964167	+	0.297406i	−0.736579	−	0.676351i	$-0.763560\pi$
$701$	−25.5277	+	7.87425i	−0.964167	+	0.297406i	−0.227588	+	0.973758i	$0.573084\pi$
$702$	−1.89662	−	1.29310i	−0.0715834	−	0.0488047i
$703$	40.8903	+	6.16322i	1.54221	+	0.232450i
$704$	−0.946108	−	4.14517i	−0.0356578	−	0.156227i
$705$	−0.966206	+	0.896508i	−0.0363894	+	0.0337644i
$706$	1.48145	+	19.7686i	0.0557553	+	0.744002i
$707$	−1.81279	−	4.61893i	−0.0681772	−	0.173713i
$708$	3.20561	−	0.483167i	0.120474	−	0.0181585i
$709$	32.9658	+	15.8755i	1.23806	+	0.596218i	0.934285	−	0.356527i	$-0.116039\pi$
$709$	32.9658	+	15.8755i	1.23806	+	0.596218i	0.303773	+	0.952744i	$0.401753\pi$
$710$	−6.51446	−	3.13720i	−0.244483	−	0.117737i
$711$	41.2978	−	6.22464i	1.54879	−	0.233442i
$712$	3.37954	+	8.61093i	0.126654	+	0.322708i
$713$	−0.133448	−	1.78074i	−0.00499767	−	0.0666892i
$714$	−0.548345	+	0.508789i	−0.0205213	+	0.0190410i
$715$	1.46024	+	6.39771i	0.0546097	+	0.239261i
$716$	−20.0659	−	3.02445i	−0.749900	−	0.113029i
$717$	−3.35643	−	2.28837i	−0.125348	−	0.0854609i
$718$	19.8207	−	6.11387i	0.739701	−	0.228168i
$719$	0.136546	−	1.82208i	0.00509231	−	0.0679522i	−0.994079	−	0.108663i	$-0.965343\pi$
$719$	0.136546	−	1.82208i	0.00509231	−	0.0679522i	0.999171	+	0.0407106i	$0.0129622\pi$
$720$	1.83135	+	2.29643i	0.0682502	+	0.0855831i
$721$	10.9927	+	3.39080i	0.409390	+	0.126280i
$722$	−13.3394	+	33.9882i	−0.496440	+	1.26491i
$723$	1.43933	−	6.30612i	0.0535293	−	0.234527i
$724$	−2.16402	−	3.74819i	−0.0804251	−	0.139300i
$725$	1.29915	−	2.25020i	0.0482493	−	0.0835703i
$726$	−1.29964	−	1.20589i	−0.0482343	−	0.0447549i
$727$	−12.7771	+	16.0220i	−0.473876	+	0.594222i	−0.960115	−	0.279604i	$-0.909797\pi$
$727$	−12.7771	+	16.0220i	−0.473876	+	0.594222i	0.486240	+	0.873826i	$0.338368\pi$
$728$	2.17114	−	1.48026i	0.0804677	−	0.0548619i
$729$	21.3262	−	10.2702i	0.789860	−	0.380376i
$730$	−6.92099			−0.256158
$731$	5.30028	+	10.2072i	0.196038	+	0.377526i
$732$	−1.84337			−0.0681328
$733$	15.3441	−	7.38931i	0.566746	−	0.272930i	−0.128492	−	0.991711i	$-0.541014\pi$
$733$	15.3441	−	7.38931i	0.566746	−	0.272930i	0.695237	+	0.718780i	$0.255299\pi$
$734$	−19.5721	+	13.3440i	−0.722419	+	0.492537i
$735$	−0.640563	+	0.803241i	−0.0236275	+	0.0296280i
$736$	−3.06149	−	2.84065i	−0.112848	−	0.104708i
$737$	2.30986	−	4.00080i	0.0850848	−	0.147371i
$738$	−3.58759	−	6.21389i	−0.132061	−	0.228737i
$739$	−8.50755	+	37.2740i	−0.312955	+	1.37115i	0.536684	+	0.843783i	$0.319677\pi$
$739$	−8.50755	+	37.2740i	−0.312955	+	1.37115i	−0.849640	+	0.527364i	$0.823180\pi$
$740$	−2.02770	+	5.16649i	−0.0745396	+	0.189924i
$741$	2.75263	+	0.849074i	0.101120	+	0.0311915i
$742$	−4.93664	−	6.19036i	−0.181230	−	0.227255i
$743$	−2.48508	+	33.1611i	−0.0911687	+	1.21656i	0.744612	+	0.667498i	$0.232635\pi$
$743$	−2.48508	+	33.1611i	−0.0911687	+	1.21656i	−0.835780	+	0.549064i	$0.814984\pi$
$744$	0.102350	−	0.0315709i	0.00375235	−	0.00115745i
$745$	7.03534	+	4.79661i	0.257755	+	0.175734i
$746$	−22.0078	−	3.31713i	−0.805761	−	0.121449i
$747$	4.47500	+	19.6062i	0.163732	+	0.717355i
$748$	5.46659	−	5.07226i	0.199878	−	0.185460i
$749$	0.433659	+	5.78678i	0.0158456	+	0.211444i
$750$	−0.0915179	−	0.233184i	−0.00334176	−	0.00851467i
$751$	−4.82763	+	0.727647i	−0.176163	+	0.0265522i	−0.236531	−	0.971624i	$-0.576011\pi$
$751$	−4.82763	+	0.727647i	−0.176163	+	0.0265522i	0.0603685	+	0.998176i	$0.480772\pi$
$752$	−4.74064	−	2.28297i	−0.172873	−	0.0832515i
$753$	3.62829	+	1.74729i	0.132222	+	0.0636749i
$754$	−3.96547	+	0.597699i	−0.144414	+	0.0217669i
$755$	−0.762415	−	1.94260i	−0.0277471	−	0.0706985i
$756$	−0.189229	−	2.52508i	−0.00688219	−	0.0918364i
$757$	−29.6333	+	27.4957i	−1.07704	+	0.999347i	−0.0770421	+	0.997028i	$0.524548\pi$
$757$	−29.6333	+	27.4957i	−1.07704	+	0.999347i	−0.999997	+	0.00231866i	$0.999262\pi$
$758$	4.56856	+	20.0162i	0.165938	+	0.727021i
$759$	−4.39843	−	0.662956i	−0.159653	−	0.0240638i
$760$	−6.15601	−	4.19710i	−0.223302	−	0.152245i
$761$	2.04118	−	0.629620i	0.0739926	−	0.0228237i	−0.257538	−	0.966268i	$-0.582911\pi$
$761$	2.04118	−	0.629620i	0.0739926	−	0.0228237i	0.331530	+	0.943445i	$0.392435\pi$
$762$	−0.0183504	+	0.244869i	−0.000664765	+	0.00887067i
$763$	−8.23916	−	10.3316i	−0.298278	−	0.374028i
$764$	−15.0961	−	4.65652i	−0.546157	−	0.168467i
$765$	−1.88214	+	4.79561i	−0.0680488	+	0.173386i
$766$	−4.66542	+	20.4406i	−0.168569	+	0.738547i
$767$	−9.98696	−	17.2979i	−0.360608	−	0.624592i
$768$	0.125250	−	0.216939i	0.00451957	−	0.00782812i
$769$	2.33173	+	2.16353i	0.0840843	+	0.0780188i	0.721095	−	0.692836i	$-0.243639\pi$
$769$	2.33173	+	2.16353i	0.0840843	+	0.0780188i	−0.637011	+	0.770855i	$0.719829\pi$
$770$	−4.51334	+	5.65955i	−0.162650	+	0.203956i
$771$	−4.53601	+	3.09260i	−0.163361	+	0.111377i
$772$	23.0296	−	11.0905i	0.828853	−	0.399155i
$773$	−38.8672			−1.39796			−0.698978	−	0.715143i	$-0.746362\pi$
$773$	−38.8672			−1.39796			−0.698978	+	0.715143i	$0.746362\pi$
$774$	−18.8986	−	3.71802i	−0.679295	−	0.133641i
$775$	0.427581			0.0153592
$776$	15.7639	−	7.59149i	0.565891	−	0.272519i
$777$	1.95577	−	1.33342i	0.0701627	−	0.0478361i
$778$	−5.39687	+	6.76746i	−0.193487	+	0.242625i
$779$	13.3420	+	12.3796i	0.478027	+	0.443544i
$780$	−0.193313	+	0.334827i	−0.00692170	+	0.0119887i
$781$	−15.3712	−	26.6237i	−0.550025	−	0.952672i
$782$	1.62998	−	7.14139i	0.0582878	−	0.255376i
$783$	−1.41183	+	3.59728i	−0.0504546	+	0.128556i
$784$	−3.91912	−	1.20889i	−0.139969	−	0.0431746i
$785$	−1.05433	−	1.32209i	−0.0376308	−	0.0471875i
$786$	−0.366604	+	4.89199i	−0.0130763	+	0.174492i
$787$	−19.5181	+	6.02055i	−0.695746	+	0.214609i	−0.622402	−	0.782697i	$-0.713843\pi$
$787$	−19.5181	+	6.02055i	−0.695746	+	0.214609i	−0.0733438	+	0.997307i	$0.523367\pi$
$788$	−17.7483	−	12.1006i	−0.632256	−	0.431065i
$789$	2.32045	+	0.349752i	0.0826102	+	0.0124515i
$790$	−3.16399	−	13.8623i	−0.112570	−	0.493200i
$791$	10.4991	−	9.74177i	0.373306	−	0.346377i
$792$	0.933267	+	12.4536i	0.0331622	+	0.442519i
$793$	4.14940	+	10.5725i	0.147349	+	0.375440i
$794$	−20.7916	+	3.13384i	−0.737868	+	0.111216i
$795$	1.04959	+	0.505457i	0.0372252	+	0.0179267i
$796$	21.9400	+	10.5657i	0.777641	+	0.374492i
$797$	15.2698	−	2.30156i	0.540885	−	0.0815253i	0.127083	−	0.991892i	$-0.459439\pi$
$797$	15.2698	−	2.30156i	0.540885	−	0.0815253i	0.413802	+	0.910367i	$0.364200\pi$
$798$	1.16091	+	2.95795i	0.0410958	+	0.104710i
$799$	−0.689660	−	9.20288i	−0.0243984	−	0.325574i
$800$	0.733052	−	0.680173i	0.0259173	−	0.0240477i
$801$	−6.04604	−	26.4894i	−0.213626	−	0.935959i
$802$	−11.1738	−	1.68418i	−0.394560	−	0.0594704i
$803$	−24.3133	−	16.5765i	−0.857997	−	0.584973i
$804$	0.260086	−	0.0802260i	0.00917254	−	0.00282935i
$805$	−0.531365	+	7.09057i	−0.0187282	+	0.249910i
$806$	−0.411462	−	0.515958i	−0.0144931	−	0.0181738i
$807$	−2.75433	−	0.849598i	−0.0969570	−	0.0299073i
$808$	−1.06475	+	2.71295i	−0.0374579	+	0.0954413i
$809$	7.28332	−	31.9103i	0.256068	−	1.12191i	−0.669347	−	0.742950i	$-0.733426\pi$
$809$	7.28332	−	31.9103i	0.256068	−	1.12191i	0.925415	−	0.378956i	$-0.123717\pi$
$810$	−4.21959	−	7.30855i	−0.148261	−	0.256796i
$811$	19.6014	−	33.9506i	0.688299	−	1.19217i	−0.284089	−	0.958798i	$-0.591691\pi$
$811$	19.6014	−	33.9506i	0.688299	−	1.19217i	0.972388	−	0.233370i	$-0.0749754\pi$
$812$	−3.24283	−	3.00891i	−0.113801	−	0.105592i
$813$	−4.28164	+	5.36900i	−0.150164	+	0.188299i
$814$	−19.4975	+	13.2932i	−0.683388	+	0.465926i
$815$	−5.79423	+	2.79035i	−0.202963	+	0.0977418i
$816$	0.439359			0.0153806
$817$	48.5884	−	5.11789i	1.69989	−	0.179052i
$818$	11.5223			0.402867
$819$	−6.95396	+	3.34885i	−0.242991	+	0.117018i
$820$	−2.01836	+	1.37609i	−0.0704841	+	0.0480552i
$821$	−16.5318	+	20.7302i	−0.576962	+	0.723488i	−0.981591	−	0.190993i	$-0.938829\pi$
$821$	−16.5318	+	20.7302i	−0.576962	+	0.723488i	0.404629	+	0.914481i	$0.367401\pi$
$822$	−0.448399	−	0.416054i	−0.0156397	−	0.0145115i
$823$	10.1426	−	17.5674i	0.353547	−	0.612361i	−0.633321	−	0.773889i	$-0.718309\pi$
$823$	10.1426	−	17.5674i	0.353547	−	0.612361i	0.986868	+	0.161528i	$0.0516421\pi$
$824$	−3.37841	−	5.85157i	−0.117692	−	0.203849i
$825$	0.237000	−	1.03836i	0.00825128	−	0.0361512i
$826$	8.04967	−	20.5102i	0.280084	−	0.713642i
$827$	14.2931	+	4.40885i	0.497021	+	0.153311i	0.533123	−	0.846037i	$-0.321018\pi$
$827$	14.2931	+	4.40885i	0.497021	+	0.153311i	−0.0361026	+	0.999348i	$0.511494\pi$
$828$	7.64836	+	9.59074i	0.265799	+	0.333301i
$829$	0.160168	−	2.13729i	0.00556286	−	0.0742312i	−0.993731	−	0.111794i	$-0.964340\pi$
$829$	0.160168	−	2.13729i	0.00556286	−	0.0742312i	0.999294	+	0.0375627i	$0.0119594\pi$
$830$	6.54251	−	2.01810i	0.227094	−	0.0700492i
$831$	−4.85209	−	3.30810i	−0.168317	−	0.114757i
$832$	−1.52618	−	0.230034i	−0.0529106	−	0.00797499i
$833$	−1.60069	−	7.01309i	−0.0554607	−	0.242989i
$834$	0.789694	−	0.732729i	0.0273449	−	0.0253723i
$835$	1.15454	+	15.4062i	0.0399544	+	0.533154i
$836$	−11.5734	−	29.4886i	−0.400275	−	1.01989i
$837$	−0.628830	+	0.0947808i	−0.0217355	+	0.00327610i
$838$	−12.9964	−	6.25872i	−0.448952	−	0.216204i
$839$	−22.8839	−	11.0203i	−0.790040	−	0.380463i	−0.00506252	−	0.999987i	$-0.501611\pi$
$839$	−22.8839	−	11.0203i	−0.790040	−	0.380463i	−0.784978	+	0.619524i	$0.787326\pi$
$840$	−0.421724	+	0.0635647i	−0.0145509	+	0.00219319i
$841$	−8.12840	−	20.7108i	−0.280290	−	0.714166i
$842$	2.04247	+	27.2548i	0.0703881	+	0.939264i
$843$	−0.941458	+	0.873546i	−0.0324255	+	0.0300865i
$844$	−0.0663916	−	0.290880i	−0.00228529	−	0.0100125i
$845$	−10.4993	−	1.58251i	−0.361186	−	0.0544401i
$846$	12.7695	+	8.70610i	0.439025	+	0.299322i
$847$	−11.5145	+	3.55176i	−0.395643	+	0.122040i
$848$	−0.347535	+	4.63754i	−0.0119344	+	0.159254i
$849$	−2.84987	−	3.57363i	−0.0978073	−	0.122647i
$850$	1.67601	+	0.516980i	0.0574866	+	0.0177323i
$851$	−8.46839	+	21.5771i	−0.290293	+	0.739654i
$852$	0.403039	−	1.76583i	0.0138079	−	0.0604963i
$853$	−10.1128	−	17.5159i	−0.346256	−	0.599734i	0.639325	−	0.768937i	$-0.279214\pi$
$853$	−10.1128	−	17.5159i	−0.346256	−	0.599734i	−0.985581	+	0.169203i	$0.945881\pi$
$854$	−6.26431	+	10.8501i	−0.214360	+	0.371283i
$855$	16.0424	+	14.8852i	0.548639	+	0.509062i
$856$	2.12512	−	2.66481i	0.0726351	−	0.0910815i
$857$	−35.6214	+	24.2863i	−1.21680	+	0.829603i	−0.989544	−	0.144231i	$-0.953929\pi$
$857$	−35.6214	+	24.2863i	−1.21680	+	0.829603i	−0.227261	+	0.973834i	$0.572977\pi$
$858$	−1.48105	+	0.713236i	−0.0505622	+	0.0243495i
$859$	38.4730			1.31268			0.656341	−	0.754464i	$-0.272103\pi$
$859$	38.4730			1.31268			0.656341	+	0.754464i	$0.272103\pi$
$860$	−0.781456	+	6.51071i	−0.0266474	+	0.222013i
$861$	1.04183			0.0355056
$862$	−6.85147	+	3.29949i	−0.233362	+	0.112381i
$863$	−18.3329	+	12.4992i	−0.624060	+	0.425477i	−0.833635	−	0.552316i	$-0.813744\pi$
$863$	−18.3329	+	12.4992i	−0.624060	+	0.425477i	0.209575	+	0.977793i	$0.432792\pi$
$864$	−0.927304	+	1.16280i	−0.0315475	+	0.0395593i
$865$	−2.60309	−	2.41531i	−0.0885076	−	0.0821230i
$866$	18.3863	−	31.8460i	0.624791	−	1.08217i
$867$	−1.74395	−	3.02060i	−0.0592275	−	0.102585i
$868$	0.161990	−	0.709725i	0.00549830	−	0.0240896i
$869$	22.0868	−	56.2761i	0.749242	−	1.90904i
$870$	0.621959	+	0.191849i	0.0210864	+	0.00650429i
$871$	−1.04558	−	1.31112i	−0.0354282	−	0.0444255i
$872$	−0.580030	+	7.73996i	−0.0196423	+	0.262108i
$873$	−49.1087	+	15.1480i	−1.66208	+	0.512683i
$874$	−25.7097	−	17.5286i	−0.869645	−	0.592914i
$875$	−1.68353	−	0.253751i	−0.0569137	−	0.00857837i
$876$	−0.385786	−	1.69024i	−0.0130345	−	0.0571079i
$877$	37.3930	−	34.6956i	1.26267	−	1.17159i	0.285677	−	0.958326i	$-0.407781\pi$
$877$	37.3930	−	34.6956i	1.26267	−	1.17159i	0.976995	−	0.213263i	$-0.0684091\pi$
$878$	0.941306	+	12.5609i	0.0317675	+	0.423908i
$879$	0.744927	+	1.89804i	0.0251258	+	0.0640194i
$880$	4.20428	−	0.633693i	0.141726	−	0.0213618i
$881$	−13.3888	−	6.44771i	−0.451080	−	0.217229i	0.194529	−	0.980897i	$-0.437682\pi$
$881$	−13.3888	−	6.44771i	−0.451080	−	0.217229i	−0.645609	+	0.763668i	$0.723396\pi$
$882$	10.8536	+	5.22684i	0.365461	+	0.175997i
$883$	−22.7461	+	3.42842i	−0.765467	+	0.115376i	−0.520159	−	0.854069i	$-0.674127\pi$
$883$	−22.7461	+	3.42842i	−0.765467	+	0.115376i	−0.245308	+	0.969445i	$0.578889\pi$
$884$	−0.988993	−	2.51991i	−0.0332634	−	0.0847538i
$885$	0.242261	+	3.23275i	0.00814352	+	0.108668i
$886$	19.2549	−	17.8659i	0.646881	−	0.600218i
$887$	8.39168	+	36.7663i	0.281765	+	1.23449i	0.895529	+	0.445003i	$0.146797\pi$
$887$	8.39168	+	36.7663i	0.281765	+	1.23449i	−0.613764	+	0.789489i	$0.710345\pi$
$888$	−1.37478	−	0.207215i	−0.0461347	−	0.00695368i
$889$	1.37895	+	0.940150i	0.0462484	+	0.0315316i
$890$	−8.83941	+	2.72660i	−0.296298	+	0.0913957i
$891$	2.68143	−	35.7811i	0.0898311	−	1.19871i
$892$	−11.7311	−	14.7104i	−0.392787	−	0.492540i
$893$	−37.4615	−	11.5553i	−1.25360	−	0.386685i
$894$	−0.779265	+	1.98553i	−0.0260625	+	0.0664062i
$895$	4.51553	−	19.7838i	0.150937	−	0.661300i
$896$	−0.851274	−	1.47445i	−0.0284391	−	0.0492579i
$897$	−0.807343	+	1.39836i	−0.0269564	+	0.0466899i
$898$	13.0698	+	12.1270i	0.436145	+	0.404684i
$899$	−0.692688	+	0.868604i	−0.0231025	+	0.0289696i
$900$	−2.42687	+	1.65461i	−0.0808957	+	0.0551537i
$901$	−7.34895	+	3.53907i	−0.244829	+	0.117903i
$902$	−10.3863			−0.345827
$903$	1.83956	−	2.10650i	0.0612168	−	0.0701001i
$904$	−8.41239			−0.279792
$905$	3.89943	−	1.87787i	0.129621	−	0.0624224i
$906$	0.431922	−	0.294480i	0.0143497	−	0.00978343i
$907$	8.98167	−	11.2627i	0.298232	−	0.373971i	−0.610026	−	0.792381i	$-0.708841\pi$
$907$	8.98167	−	11.2627i	0.298232	−	0.373971i	0.908258	+	0.418410i	$0.137413\pi$
$908$	−3.12249	−	2.89725i	−0.103624	−	0.0961486i
$909$	4.28018	−	7.41349i	0.141965	−	0.245890i
$910$	1.31387	+	2.27569i	0.0435543	+	0.0754383i
$911$	−3.83170	+	16.7878i	−0.126950	+	0.556204i	0.870947	+	0.491378i	$0.163506\pi$
$911$	−3.83170	+	16.7878i	−0.126950	+	0.556204i	−0.997897	+	0.0648264i	$0.979351\pi$
$912$	0.681867	−	1.73737i	0.0225789	−	0.0575300i
$913$	27.8173	+	8.58049i	0.920617	+	0.283973i
$914$	−19.4574	−	24.3988i	−0.643592	−	0.807039i
$915$	0.137755	−	1.83821i	0.00455404	−	0.0607694i
$916$	−15.3042	+	4.72072i	−0.505664	+	0.155977i
$917$	27.5486	+	18.7823i	0.909734	+	0.620246i
$918$	−2.57945	−	0.388789i	−0.0851345	−	0.0128320i
$919$	−0.723011	−	3.16772i	−0.0238499	−	0.104493i	0.961602	−	0.274448i	$-0.0884951\pi$
$919$	−0.723011	−	3.16772i	−0.0238499	−	0.104493i	−0.985452	+	0.169954i	$0.945638\pi$
$920$	3.06149	−	2.84065i	0.100934	−	0.0936534i
$921$	−0.146676	−	1.95726i	−0.00483315	−	0.0644939i
$922$	−13.7979	−	35.1564i	−0.454408	−	1.15781i
$923$	−11.0350	+	1.66326i	−0.363222	+	0.0547469i
$924$	−1.63375	−	0.786773i	−0.0537465	−	0.0258829i
$925$	−5.00051	−	2.40812i	−0.164416	−	0.0791785i
$926$	−23.4440	+	3.53362i	−0.770419	+	0.116122i
$927$	7.25072	+	18.4745i	0.238145	+	0.606783i
$928$	0.194172	+	2.59104i	0.00637400	+	0.0850551i
$929$	−18.8575	+	17.4972i	−0.618694	+	0.574065i	−0.925989	−	0.377550i	$-0.876767\pi$
$929$	−18.8575	+	17.4972i	−0.618694	+	0.574065i	0.307295	+	0.951614i	$0.400576\pi$
$930$	0.0238340	+	0.104423i	0.000781547	+	0.00342418i
$931$	−30.2163	−	4.55437i	−0.990298	−	0.149263i
$932$	15.3855	+	10.4896i	0.503967	+	0.343599i
$933$	−5.40791	+	1.66812i	−0.177047	+	0.0546118i
$934$	0.254601	−	3.39742i	0.00833081	−	0.111167i
$935$	4.64955	+	5.83036i	0.152057	+	0.190673i
$936$	4.33199	+	1.33624i	0.141595	+	0.0436764i
$937$	−8.72271	+	22.2251i	−0.284959	+	0.726062i	0.714687	+	0.699444i	$0.246569\pi$
$937$	−8.72271	+	22.2251i	−0.284959	+	0.726062i	−0.999646	+	0.0266182i	$0.991526\pi$
$938$	0.411639	−	1.80351i	0.0134405	−	0.0588866i
$939$	−3.04911	−	5.28122i	−0.0995041	−	0.172346i
$940$	2.63086	−	4.55678i	0.0858091	−	0.148626i
$941$	−18.4989	−	17.1645i	−0.603047	−	0.559546i	0.318446	−	0.947941i	$-0.396839\pi$
$941$	−18.4989	−	17.1645i	−0.603047	−	0.559546i	−0.921493	+	0.388395i	$0.873029\pi$
$942$	0.264111	−	0.331184i	0.00860519	−	0.0107906i
$943$	−8.42939	+	5.74706i	−0.274499	+	0.187150i
$944$	−11.6598	+	5.61506i	−0.379494	+	0.182755i
$945$	2.53216			0.0823713
$946$	−18.3391	+	21.0003i	−0.596255	+	0.682779i
$947$	7.58771			0.246567			0.123284	−	0.992371i	$-0.460657\pi$
$947$	7.58771			0.246567			0.123284	+	0.992371i	$0.460657\pi$
$948$	3.20908	−	1.54541i	0.104226	−	0.0501927i
$949$	−8.82585	+	6.01736i	−0.286499	+	0.195332i
$950$	4.64540	−	5.82515i	0.150717	−	0.188993i
$951$	4.84859	+	4.49883i	0.157226	+	0.145885i
$952$	1.49307	−	2.58608i	0.0483908	−	0.0838153i
$953$	−9.35935	−	16.2109i	−0.303179	−	0.525122i	0.673675	−	0.739028i	$-0.264715\pi$
$953$	−9.35935	−	16.2109i	−0.303179	−	0.525122i	−0.976854	+	0.213906i	$0.931381\pi$
$954$	3.03959	−	13.3173i	0.0984104	−	0.431164i
$955$	5.77163	−	14.7059i	0.186766	−	0.475871i
$956$	15.4963	+	4.77998i	0.501186	+	0.154595i
$957$	1.72543	+	2.16362i	0.0557752	+	0.0699399i
$958$	−0.818480	+	10.9219i	−0.0264439	+	0.352869i
$959$	−3.97270	+	1.22542i	−0.128285	+	0.0395707i
$960$	0.206973	+	0.141112i	0.00668001	+	0.00455436i
$961$	30.4730	+	4.59306i	0.982999	+	0.148163i
$962$	1.90615	+	8.35141i	0.0614569	+	0.269260i
$963$	−7.33887	+	6.80948i	−0.236492	+	0.219432i
$964$	1.92965	+	25.7494i	0.0621498	+	0.829331i
$965$	9.33845	+	23.7940i	0.300615	+	0.765956i
$966$	−1.76127	+	0.265469i	−0.0566680	+	0.00854133i
$967$	−35.0861	−	16.8966i	−1.12829	−	0.543357i	−0.225848	−	0.974163i	$-0.572515\pi$
$967$	−35.0861	−	16.8966i	−1.12829	−	0.543357i	−0.902445	+	0.430805i	$0.858230\pi$
$968$	6.37665	+	3.07083i	0.204953	+	0.0987002i
$969$	3.23695	−	0.487891i	0.103986	−	0.0156733i
$970$	6.39223	+	16.2871i	0.205242	+	0.522948i
$971$	−0.455717	−	6.08112i	−0.0146246	−	0.195152i	−0.999731	−	0.0232047i	$-0.992613\pi$
$971$	−0.455717	−	6.08112i	−0.0146246	−	0.195152i	0.985106	−	0.171948i	$-0.0550060\pi$
$972$	4.82044	−	4.47272i	0.154616	−	0.143462i
$973$	−1.62925	−	7.13820i	−0.0522312	−	0.228840i
$974$	−38.1353	−	5.74797i	−1.22193	−	0.184177i
$975$	−0.319445	−	0.217794i	−0.0102304	−	0.00697498i
$976$	7.03182	−	2.16903i	0.225083	−	0.0694289i
$977$	−3.22562	+	43.0429i	−0.103197	+	1.37707i	0.669746	+	0.742590i	$0.266403\pi$
$977$	−3.22562	+	43.0429i	−0.103197	+	1.37707i	−0.772943	+	0.634475i	$0.781216\pi$
$978$	−1.00444	−	1.25952i	−0.0321184	−	0.0402752i
$979$	−37.5831	−	11.5929i	−1.20116	−	0.370509i
$980$	1.49839	−	3.81782i	0.0478642	−	0.121956i
$981$	5.07302	−	22.2263i	0.161969	−	0.709632i
$982$	12.7098	+	22.0140i	0.405586	+	0.702496i
$983$	9.29809	−	16.1048i	0.296563	−	0.513662i	−0.678784	−	0.734338i	$-0.737493\pi$
$983$	9.29809	−	16.1048i	0.296563	−	0.513662i	0.975347	+	0.220675i	$0.0708261\pi$
$984$	−0.448574	−	0.416216i	−0.0143000	−	0.0132685i
$985$	13.3931	−	16.7944i	0.426738	−	0.535113i
$986$	−3.76537	+	2.56719i	−0.119914	+	0.0817559i
$987$	−2.02183	+	0.973660i	−0.0643555	+	0.0309920i
$988$	−11.4994			−0.365846
$989$	−3.26364	+	27.1911i	−0.103778	+	0.864626i
$990$	−12.4885			−0.396911
$991$	16.8180	−	8.09913i	0.534242	−	0.257277i	−0.147255	−	0.989099i	$-0.547044\pi$
$991$	16.8180	−	8.09913i	0.534242	−	0.257277i	0.681497	+	0.731821i	$0.261329\pi$
$992$	−0.353284	+	0.240865i	−0.0112168	+	0.00764747i
$993$	0.943733	−	1.18340i	0.0299485	−	0.0375542i
$994$	−9.02407	−	8.37311i	−0.286226	−	0.265579i
$995$	−12.1758	+	21.0890i	−0.385998	+	0.668567i
$996$	0.857548	+	1.48532i	0.0271724	+	0.0470641i
$997$	−1.57998	+	6.92236i	−0.0500386	+	0.219233i	−0.993765	−	0.111493i	$-0.964437\pi$
$997$	−1.57998	+	6.92236i	−0.0500386	+	0.219233i	0.943727	+	0.330727i	$0.107294\pi$
$998$	−5.01197	+	12.7703i	−0.158651	+	0.404236i
$999$	7.88789	+	2.43309i	0.249562	+	0.0769797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.d.31.3	✓	60
43.25	even	21	inner	430.2.q.d.111.3	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.d.31.3	✓	60	1.1	even	1	trivial
430.2.q.d.111.3	yes	60	43.25	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.900969 - 0.433884i) q^{2} +(-0.206973 + 0.141112i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(-0.125250 + 0.216939i) q^{6} +(0.851274 + 1.47445i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-1.07310 + 2.73421i) q^{9} +O(q^{10})\)	\(q+(0.900969 - 0.433884i) q^{2} +(-0.206973 + 0.141112i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(-0.125250 + 0.216939i) q^{6} +(0.851274 + 1.47445i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-1.07310 + 2.73421i) q^{9} +(0.955573 + 0.294755i) q^{10} +(2.65093 + 3.32417i) q^{11} +(-0.0187199 + 0.249799i) q^{12} +(1.47484 - 0.454929i) q^{13} +(1.40671 + 0.959079i) q^{14} +(-0.247702 - 0.0373351i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(1.28572 - 1.19298i) q^{17} +(0.219501 + 2.92904i) q^{18} +(-2.72203 - 6.93561i) q^{19} +(0.988831 - 0.149042i) q^{20} +(-0.384252 - 0.185046i) q^{21} +(3.83071 + 1.84477i) q^{22} +(4.12972 - 0.622454i) q^{23} +(0.0915179 + 0.233184i) q^{24} +(0.0747301 + 0.997204i) q^{25} +(1.13140 - 1.04979i) q^{26} +(-0.330951 - 1.44999i) q^{27} +(1.68353 + 0.253751i) q^{28} +(-2.14682 - 1.46368i) q^{29} +(-0.239371 + 0.0738361i) q^{30} +(0.0319532 - 0.426385i) q^{31} +(-0.623490 - 0.781831i) q^{32} +(-1.01775 - 0.313934i) q^{33} +(0.640782 - 1.63269i) q^{34} +(-0.378852 + 1.65986i) q^{35} +(1.46862 + 2.54373i) q^{36} +(-2.77507 + 4.80657i) q^{37} +(-5.46171 - 5.06773i) q^{38} +(-0.241057 + 0.302276i) q^{39} +(0.826239 - 0.563320i) q^{40} +(-2.20091 + 1.05990i) q^{41} -0.426488 q^{42} +(-1.74310 + 6.32152i) q^{43} +4.25177 q^{44} +(-2.64637 + 1.27442i) q^{45} +(3.45067 - 2.35263i) q^{46} +(3.28063 - 4.11378i) q^{47} +(0.183629 + 0.170383i) q^{48} +(2.05067 - 3.55186i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-0.0977666 + 0.428343i) q^{51} +(0.563873 - 1.43672i) q^{52} +(-4.44393 - 1.37077i) q^{53} +(-0.927304 - 1.16280i) q^{54} +(-0.317735 + 4.23988i) q^{55} +(1.62691 - 0.501835i) q^{56} +(1.54208 + 1.05137i) q^{57} +(-2.56929 - 0.387257i) q^{58} +(-2.87973 - 12.6169i) q^{59} +(-0.183629 + 0.170383i) q^{60} +(0.549920 + 7.33817i) q^{61} +(-0.156213 - 0.398024i) q^{62} +(-4.94495 + 0.745332i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(1.39057 + 0.669662i) q^{65} +(-1.05317 + 0.158740i) q^{66} +(-0.396958 - 1.01143i) q^{67} +(-0.131071 - 1.74903i) q^{68} +(-0.766903 + 0.711582i) q^{69} +(0.378852 + 1.65986i) q^{70} +(-7.14974 - 1.07765i) q^{71} +(2.42687 + 1.65461i) q^{72} +(-6.61351 + 2.04000i) q^{73} +(-0.414763 + 5.53463i) q^{74} +(-0.156184 - 0.195849i) q^{75} +(-7.11963 - 2.19612i) q^{76} +(-2.64464 + 6.73844i) q^{77} +(-0.0860322 + 0.376932i) q^{78} +(-7.10942 - 12.3139i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-6.18636 - 5.74010i) q^{81} +(-1.52308 + 1.90988i) q^{82} +(5.65700 - 3.85688i) q^{83} +(-0.384252 + 0.185046i) q^{84} +1.75393 q^{85} +(1.17233 + 6.45179i) q^{86} +0.650875 q^{87} +(3.83071 - 1.84477i) q^{88} +(-7.64302 + 5.21092i) q^{89} +(-1.83135 + 2.29643i) q^{90} +(1.92627 + 1.78731i) q^{91} +(2.08818 - 3.61684i) q^{92} +(0.0535545 + 0.0927591i) q^{93} +(1.17084 - 5.12979i) q^{94} +(2.72203 - 6.93561i) q^{95} +(0.239371 + 0.0738361i) q^{96} +(10.9090 + 13.6794i) q^{97} +(0.306493 - 4.08986i) q^{98} +(-11.9337 + 3.68105i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9} + 5 q^{10} + 3 q^{11} - q^{12} + 13 q^{13} - 15 q^{14} + q^{15} - 10 q^{16} + 38 q^{17} + 6 q^{18} + 17 q^{19} - 5 q^{20} + 4 q^{21} + 11 q^{22} - 8 q^{23} + q^{24} + 5 q^{25} + 29 q^{26} - 16 q^{27} - 6 q^{28} - 41 q^{29} - q^{30} + 15 q^{31} + 10 q^{32} + 63 q^{33} - 10 q^{34} + 2 q^{35} - 48 q^{36} + 7 q^{37} + 25 q^{38} - 64 q^{39} + 5 q^{40} - 22 q^{41} - 60 q^{42} + 6 q^{43} - 4 q^{44} + 30 q^{45} - 20 q^{46} - 13 q^{47} - q^{48} - 93 q^{49} + 30 q^{50} + 18 q^{51} - 15 q^{52} + 71 q^{53} - 5 q^{54} - 16 q^{55} - q^{56} - 94 q^{57} - 22 q^{58} + 20 q^{59} + q^{60} + 91 q^{61} + 69 q^{62} - 50 q^{63} - 10 q^{64} + 5 q^{65} + 14 q^{66} - 26 q^{67} - 18 q^{68} - 94 q^{69} - 2 q^{70} + 20 q^{71} - 36 q^{72} - 56 q^{73} - 7 q^{74} + 2 q^{75} + 38 q^{76} + 41 q^{77} - 13 q^{78} - 46 q^{79} + 30 q^{80} + 39 q^{81} + 8 q^{82} - 115 q^{83} + 4 q^{84} + 6 q^{85} + 29 q^{86} + 20 q^{87} + 11 q^{88} + 30 q^{89} - 16 q^{90} - 53 q^{91} - 8 q^{92} + 16 q^{93} + 41 q^{94} - 17 q^{95} + q^{96} + 113 q^{97} + 2 q^{98} + 139 q^{99}+O(q^{100}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9 + 5 * q^10 + 3 * q^11 - q^12 + 13 * q^13 - 15 * q^14 + q^15 - 10 * q^16 + 38 * q^17 + 6 * q^18 + 17 * q^19 - 5 * q^20 + 4 * q^21 + 11 * q^22 - 8 * q^23 + q^24 + 5 * q^25 + 29 * q^26 - 16 * q^27 - 6 * q^28 - 41 * q^29 - q^30 + 15 * q^31 + 10 * q^32 + 63 * q^33 - 10 * q^34 + 2 * q^35 - 48 * q^36 + 7 * q^37 + 25 * q^38 - 64 * q^39 + 5 * q^40 - 22 * q^41 - 60 * q^42 + 6 * q^43 - 4 * q^44 + 30 * q^45 - 20 * q^46 - 13 * q^47 - q^48 - 93 * q^49 + 30 * q^50 + 18 * q^51 - 15 * q^52 + 71 * q^53 - 5 * q^54 - 16 * q^55 - q^56 - 94 * q^57 - 22 * q^58 + 20 * q^59 + q^60 + 91 * q^61 + 69 * q^62 - 50 * q^63 - 10 * q^64 + 5 * q^65 + 14 * q^66 - 26 * q^67 - 18 * q^68 - 94 * q^69 - 2 * q^70 + 20 * q^71 - 36 * q^72 - 56 * q^73 - 7 * q^74 + 2 * q^75 + 38 * q^76 + 41 * q^77 - 13 * q^78 - 46 * q^79 + 30 * q^80 + 39 * q^81 + 8 * q^82 - 115 * q^83 + 4 * q^84 + 6 * q^85 + 29 * q^86 + 20 * q^87 + 11 * q^88 + 30 * q^89 - 16 * q^90 - 53 * q^91 - 8 * q^92 + 16 * q^93 + 41 * q^94 - 17 * q^95 + q^96 + 113 * q^97 + 2 * q^98 + 139 * q^99

Introduction

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