LMFDB - Embedded newform 430.2.q.b.81.1

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:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			81.1
Character	$\chi$	$=$	430.81
Dual form			430.2.q.b.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.222521 + 0.974928i) q^{2} +(-1.77929 - 0.548838i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.365341 - 0.930874i) q^{5} +(0.931007 - 1.61255i) q^{6} +(1.00410 + 1.73915i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.385931 + 0.263123i) q^{9} +O(q^{10})$	\(q+(-0.222521 + 0.974928i) q^{2} +(-1.77929 - 0.548838i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.365341 - 0.930874i) q^{5} +(0.931007 - 1.61255i) q^{6} +(1.00410 + 1.73915i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.385931 + 0.263123i) q^{9} +(0.988831 - 0.149042i) q^{10} +(0.199068 - 0.0958662i) q^{11} +(1.36495 + 1.26649i) q^{12} +(1.92908 + 0.290761i) q^{13} +(-1.91898 + 0.591926i) q^{14} +(0.139148 + 1.85681i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-1.22957 + 3.13290i) q^{17} +(-0.342404 + 0.317704i) q^{18} +(-4.16251 + 2.83795i) q^{19} +(-0.0747301 + 0.997204i) q^{20} +(-0.832069 - 3.64553i) q^{21} +(0.0491658 + 0.215409i) q^{22} +(-0.561199 + 7.48867i) q^{23} +(-1.53847 + 1.04891i) q^{24} +(-0.733052 + 0.680173i) q^{25} +(-0.712731 + 1.81601i) q^{26} +(2.94057 + 3.68736i) q^{27} +(-0.150073 - 2.00258i) q^{28} +(-6.89648 + 2.12728i) q^{29} +(-1.84122 - 0.277519i) q^{30} +(2.10803 + 1.95597i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(-0.406815 + 0.0613175i) q^{33} +(-2.78075 - 1.89588i) q^{34} +(1.25209 - 1.57007i) q^{35} +(-0.233547 - 0.404515i) q^{36} +(-0.494716 + 0.856873i) q^{37} +(-1.84055 - 4.68965i) q^{38} +(-3.27280 - 1.57610i) q^{39} +(-0.955573 - 0.294755i) q^{40} +(0.0413326 - 0.181090i) q^{41} +3.73928 q^{42} +(0.532363 + 6.53579i) q^{43} -0.220949 q^{44} +(0.103938 - 0.455382i) q^{45} +(-7.17604 - 2.21351i) q^{46} +(4.59682 + 2.21371i) q^{47} +(-0.680270 - 1.73330i) q^{48} +(1.48358 - 2.56963i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(3.90722 - 4.89950i) q^{51} +(-1.61188 - 1.09896i) q^{52} +(-3.09247 + 0.466115i) q^{53} +(-4.24924 + 2.04633i) q^{54} +(-0.161967 - 0.150283i) q^{55} +(1.98576 + 0.299306i) q^{56} +(8.96389 - 2.76499i) q^{57} +(-0.539336 - 7.19693i) q^{58} +(-5.30630 - 6.65389i) q^{59} +(0.680270 - 1.73330i) q^{60} +(0.213073 - 0.197702i) q^{61} +(-2.37601 + 1.61993i) q^{62} +(-0.0700979 + 0.935392i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-0.434108 - 1.90195i) q^{65} +(0.0307447 - 0.410260i) q^{66} +(3.70043 - 2.52291i) q^{67} +(2.46712 - 2.28916i) q^{68} +(5.10860 - 13.0165i) q^{69} +(1.25209 + 1.57007i) q^{70} +(0.0301273 + 0.402021i) q^{71} +(0.446342 - 0.137678i) q^{72} +(8.36685 + 1.26110i) q^{73} +(-0.725304 - 0.672984i) q^{74} +(1.67762 - 0.807897i) q^{75} +(4.98163 - 0.750860i) q^{76} +(0.366609 + 0.249950i) q^{77} +(2.26485 - 2.84003i) q^{78} +(8.79305 + 15.2300i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-3.72031 - 9.47918i) q^{81} +(0.167352 + 0.0805927i) q^{82} +(-5.34845 - 1.64978i) q^{83} +(-0.832069 + 3.64553i) q^{84} +3.36555 q^{85} +(-6.49039 - 0.935335i) q^{86} +13.4384 q^{87} +(0.0491658 - 0.215409i) q^{88} +(-3.50976 - 1.08262i) q^{89} +(0.420837 + 0.202664i) q^{90} +(1.43130 + 3.64690i) q^{91} +(3.75484 - 6.50357i) q^{92} +(-2.67729 - 4.63720i) q^{93} +(-3.18110 + 3.98897i) q^{94} +(4.16251 + 2.83795i) q^{95} +(1.84122 - 0.277519i) q^{96} +(3.20309 - 1.54253i) q^{97} +(2.17508 + 2.01818i) q^{98} +(0.102051 + 0.0153817i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9}+O(q^{10}) $ 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9} - 4 q^{10} - 9 q^{11} - q^{12} - 11 q^{13} + 7 q^{14} - 6 q^{15} - 8 q^{16} - 11 q^{17} - 15 q^{18} + 31 q^{19} - 4 q^{20} + 4 q^{21} + 12 q^{22} + 4 q^{23} + 6 q^{24} + 4 q^{25} + 31 q^{26} + 44 q^{27} + 13 q^{29} + q^{30} - q^{31} - 8 q^{32} - 30 q^{33} - 25 q^{34} + 14 q^{35} - 36 q^{36} - 27 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{40} + 16 q^{41} + 4 q^{42} - 7 q^{43} - 30 q^{44} + 12 q^{45} - 52 q^{46} - 43 q^{47} - q^{48} - 23 q^{49} - 24 q^{50} - 7 q^{51} - 25 q^{52} + 73 q^{53} - 61 q^{54} + 27 q^{55} + 7 q^{56} + 136 q^{57} - 36 q^{58} + 58 q^{59} + q^{60} - 61 q^{61} + 27 q^{62} + 32 q^{63} - 8 q^{64} - q^{65} + 12 q^{66} + 39 q^{67} + 17 q^{68} - 34 q^{69} + 14 q^{70} + 60 q^{71} + 27 q^{72} + 3 q^{73} + 29 q^{74} - 12 q^{75} + 17 q^{76} - 27 q^{77} - 17 q^{78} - 2 q^{79} + 24 q^{80} - 165 q^{81} + 2 q^{82} + 74 q^{83} + 4 q^{84} - 8 q^{85} + 14 q^{86} + 88 q^{87} + 12 q^{88} + 23 q^{89} - 2 q^{90} - 39 q^{91} + 4 q^{92} - 46 q^{93} + 55 q^{94} - 31 q^{95} - q^{96} - 85 q^{97} + 33 q^{98} - 168 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9 - 4 * q^10 - 9 * q^11 - q^12 - 11 * q^13 + 7 * q^14 - 6 * q^15 - 8 * q^16 - 11 * q^17 - 15 * q^18 + 31 * q^19 - 4 * q^20 + 4 * q^21 + 12 * q^22 + 4 * q^23 + 6 * q^24 + 4 * q^25 + 31 * q^26 + 44 * q^27 + 13 * q^29 + q^30 - q^31 - 8 * q^32 - 30 * q^33 - 25 * q^34 + 14 * q^35 - 36 * q^36 - 27 * q^37 - 4 * q^38 + 4 * q^39 - 4 * q^40 + 16 * q^41 + 4 * q^42 - 7 * q^43 - 30 * q^44 + 12 * q^45 - 52 * q^46 - 43 * q^47 - q^48 - 23 * q^49 - 24 * q^50 - 7 * q^51 - 25 * q^52 + 73 * q^53 - 61 * q^54 + 27 * q^55 + 7 * q^56 + 136 * q^57 - 36 * q^58 + 58 * q^59 + q^60 - 61 * q^61 + 27 * q^62 + 32 * q^63 - 8 * q^64 - q^65 + 12 * q^66 + 39 * q^67 + 17 * q^68 - 34 * q^69 + 14 * q^70 + 60 * q^71 + 27 * q^72 + 3 * q^73 + 29 * q^74 - 12 * q^75 + 17 * q^76 - 27 * q^77 - 17 * q^78 - 2 * q^79 + 24 * q^80 - 165 * q^81 + 2 * q^82 + 74 * q^83 + 4 * q^84 - 8 * q^85 + 14 * q^86 + 88 * q^87 + 12 * q^88 + 23 * q^89 - 2 * q^90 - 39 * q^91 + 4 * q^92 - 46 * q^93 + 55 * q^94 - 31 * q^95 - q^96 - 85 * q^97 + 33 * q^98 - 168 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{2}{21}\right)$

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 $

$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$3$	−1.77929	−	0.548838i	−1.02727	−	0.316872i	−0.265083	−	0.964225i	$-0.585399\pi$
$3$	−1.77929	−	0.548838i	−1.02727	−	0.316872i	−0.762190	+	0.647354i	$0.775876\pi$
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	−0.365341	−	0.930874i	−0.163385	−	0.416299i
$5$	−0.365341	−	0.930874i	−0.163385	−	0.416299i
$6$	0.931007	−	1.61255i	0.380082	−	0.658321i
$7$	1.00410	+	1.73915i	0.379513	+	0.657336i	0.990991	−	0.133925i	$-0.0427582\pi$
$7$	1.00410	+	1.73915i	0.379513	+	0.657336i	−0.611478	+	0.791261i	$0.709425\pi$
$8$	0.623490	−	0.781831i	0.220437	−	0.276419i
$9$	0.385931	+	0.263123i	0.128644	+	0.0877077i
$10$	0.988831	−	0.149042i	0.312696	−	0.0471313i
$11$	0.199068	−	0.0958662i	0.0600213	−	0.0289047i	−0.403632	−	0.914921i	$-0.632252\pi$
$11$	0.199068	−	0.0958662i	0.0600213	−	0.0289047i	0.463654	+	0.886017i	$0.346538\pi$
$12$	1.36495	+	1.26649i	0.394028	+	0.365604i
$13$	1.92908	+	0.290761i	0.535029	+	0.0806427i	0.410999	−	0.911636i	$-0.365180\pi$
$13$	1.92908	+	0.290761i	0.535029	+	0.0806427i	0.124030	+	0.992278i	$0.460418\pi$
$14$	−1.91898	+	0.591926i	−0.512868	+	0.158199i
$15$	0.139148	+	1.85681i	0.0359280	+	0.479425i
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	−1.22957	+	3.13290i	−0.298215	+	0.759840i	0.700708	+	0.713448i	$0.252868\pi$
$17$	−1.22957	+	3.13290i	−0.298215	+	0.759840i	−0.998923	+	0.0463921i	$0.985228\pi$
$18$	−0.342404	+	0.317704i	−0.0807053	+	0.0748836i
$19$	−4.16251	+	2.83795i	−0.954945	+	0.651071i	−0.937208	−	0.348772i	$-0.886599\pi$
$19$	−4.16251	+	2.83795i	−0.954945	+	0.651071i	−0.0177378	+	0.999843i	$0.505646\pi$
$20$	−0.0747301	+	0.997204i	−0.0167102	+	0.222982i
$21$	−0.832069	−	3.64553i	−0.181572	−	0.795520i
$22$	0.0491658	+	0.215409i	0.0104822	+	0.0459254i
$23$	−0.561199	+	7.48867i	−0.117018	+	1.56150i	0.561852	+	0.827238i	$0.310089\pi$
$23$	−0.561199	+	7.48867i	−0.117018	+	1.56150i	−0.678870	+	0.734259i	$0.737530\pi$
$24$	−1.53847	+	1.04891i	−0.314038	+	0.214108i
$25$	−0.733052	+	0.680173i	−0.146610	+	0.136035i
$26$	−0.712731	+	1.81601i	−0.139778	+	0.356149i
$27$	2.94057	+	3.68736i	0.565913	+	0.709632i
$28$	−0.150073	−	2.00258i	−0.0283610	−	0.378452i
$29$	−6.89648	+	2.12728i	−1.28064	+	0.395026i	−0.859112	−	0.511787i	$-0.828984\pi$
$29$	−6.89648	+	2.12728i	−1.28064	+	0.395026i	−0.421532	+	0.906814i	$0.638507\pi$
$30$	−1.84122	−	0.277519i	−0.336159	−	0.0506677i
$31$	2.10803	+	1.95597i	0.378614	+	0.351302i	0.846408	−	0.532535i	$-0.178761\pi$
$31$	2.10803	+	1.95597i	0.378614	+	0.351302i	−0.467794	+	0.883837i	$0.654951\pi$
$32$	−0.900969	+	0.433884i	−0.159270	+	0.0767005i
$33$	−0.406815	+	0.0613175i	−0.0708174	+	0.0106740i
$34$	−2.78075	−	1.89588i	−0.476894	−	0.325141i
$35$	1.25209	−	1.57007i	0.211642	−	0.265390i
$36$	−0.233547	−	0.404515i	−0.0389245	−	0.0674191i
$37$	−0.494716	+	0.856873i	−0.0813308	+	0.140869i	−0.903822	−	0.427909i	$-0.859250\pi$
$37$	−0.494716	+	0.856873i	−0.0813308	+	0.140869i	0.822491	+	0.568778i	$0.192584\pi$
$38$	−1.84055	−	4.68965i	−0.298577	−	0.760762i
$39$	−3.27280	−	1.57610i	−0.524068	−	0.252378i
$40$	−0.955573	−	0.294755i	−0.151089	−	0.0466049i
$41$	0.0413326	−	0.181090i	0.00645507	−	0.0282815i	−0.971598	−	0.236638i	$-0.923954\pi$
$41$	0.0413326	−	0.181090i	0.00645507	−	0.0282815i	0.978053	+	0.208357i	$0.0668115\pi$
$42$	3.73928			0.576984
$43$	0.532363	+	6.53579i	0.0811846	+	0.996699i
$43$	0.532363	+	6.53579i	0.0811846	+	0.996699i
$44$	−0.220949			−0.0333093
$45$	0.103938	−	0.455382i	0.0154942	−	0.0678844i
$46$	−7.17604	−	2.21351i	−1.05805	−	0.326365i
$47$	4.59682	+	2.21371i	0.670515	+	0.322903i	0.737984	−	0.674818i	$-0.235778\pi$
$47$	4.59682	+	2.21371i	0.670515	+	0.322903i	−0.0674689	+	0.997721i	$0.521492\pi$
$48$	−0.680270	−	1.73330i	−0.0981885	−	0.250180i
$49$	1.48358	−	2.56963i	0.211940	−	0.367090i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	3.90722	−	4.89950i	0.547121	−	0.686068i
$52$	−1.61188	−	1.09896i	−0.223528	−	0.152399i
$53$	−3.09247	+	0.466115i	−0.424784	+	0.0640258i	−0.357955	−	0.933739i	$-0.616526\pi$
$53$	−3.09247	+	0.466115i	−0.424784	+	0.0640258i	−0.0668282	+	0.997764i	$0.521288\pi$
$54$	−4.24924	+	2.04633i	−0.578249	+	0.278470i
$55$	−0.161967	−	0.150283i	−0.0218396	−	0.0202642i
$56$	1.98576	+	0.299306i	0.265359	+	0.0399964i
$57$	8.96389	−	2.76499i	1.18730	−	0.366232i
$58$	−0.539336	−	7.19693i	−0.0708182	−	0.945004i
$59$	−5.30630	−	6.65389i	−0.690822	−	0.866263i	0.305479	−	0.952199i	$-0.401183\pi$
$59$	−5.30630	−	6.65389i	−0.690822	−	0.866263i	−0.996301	+	0.0859360i	$0.972612\pi$
$60$	0.680270	−	1.73330i	0.0878225	−	0.223768i
$61$	0.213073	−	0.197702i	0.0272811	−	0.0253132i	−0.666414	−	0.745582i	$-0.732172\pi$
$61$	0.213073	−	0.197702i	0.0272811	−	0.0253132i	0.693696	+	0.720268i	$0.255981\pi$
$62$	−2.37601	+	1.61993i	−0.301753	+	0.205732i
$63$	−0.0700979	+	0.935392i	−0.00883151	+	0.117848i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	−0.434108	−	1.90195i	−0.0538445	−	0.235908i
$66$	0.0307447	−	0.410260i	0.00378441	−	0.0504995i
$67$	3.70043	−	2.52291i	0.452080	−	0.308223i	−0.315790	−	0.948829i	$-0.602269\pi$
$67$	3.70043	−	2.52291i	0.452080	−	0.308223i	0.767869	+	0.640607i	$0.221317\pi$
$68$	2.46712	−	2.28916i	0.299183	−	0.277601i
$69$	5.10860	−	13.0165i	0.615004	−	1.56700i
$70$	1.25209	+	1.57007i	0.149653	+	0.187659i
$71$	0.0301273	+	0.402021i	0.00357545	+	0.0477111i	0.998706	−	0.0508532i	$-0.0161940\pi$
$71$	0.0301273	+	0.402021i	0.00357545	+	0.0477111i	−0.995131	+	0.0985643i	$0.968575\pi$
$72$	0.446342	−	0.137678i	0.0526019	−	0.0162255i
$73$	8.36685	+	1.26110i	0.979266	+	0.147601i	0.619121	−	0.785296i	$-0.287489\pi$
$73$	8.36685	+	1.26110i	0.979266	+	0.147601i	0.360145	+	0.932896i	$0.382727\pi$
$74$	−0.725304	−	0.672984i	−0.0843149	−	0.0782328i
$75$	1.67762	−	0.807897i	0.193714	−	0.0932879i
$76$	4.98163	−	0.750860i	0.571433	−	0.0861296i
$77$	0.366609	+	0.249950i	0.0417790	+	0.0284844i
$78$	2.26485	−	2.84003i	0.256444	−	0.321570i
$79$	8.79305	+	15.2300i	0.989295	+	1.71351i	0.621024	+	0.783791i	$0.286717\pi$
$79$	8.79305	+	15.2300i	0.989295	+	1.71351i	0.368271	+	0.929718i	$0.379950\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−3.72031	−	9.47918i	−0.413367	−	1.05324i
$82$	0.167352	+	0.0805927i	0.0184810	+	0.00889997i
$83$	−5.34845	−	1.64978i	−0.587068	−	0.181087i	−0.0130300	−	0.999915i	$-0.504148\pi$
$83$	−5.34845	−	1.64978i	−0.587068	−	0.181087i	−0.574038	+	0.818829i	$0.694624\pi$
$84$	−0.832069	+	3.64553i	−0.0907862	+	0.397760i
$85$	3.36555			0.365045
$86$	−6.49039	−	0.935335i	−0.699877	−	0.100860i
$87$	13.4384			1.44074
$88$	0.0491658	−	0.215409i	0.00524109	−	0.0229627i
$89$	−3.50976	−	1.08262i	−0.372034	−	0.114757i	0.103099	−	0.994671i	$-0.467124\pi$
$89$	−3.50976	−	1.08262i	−0.372034	−	0.114757i	−0.475133	+	0.879914i	$0.657600\pi$
$90$	0.420837	+	0.202664i	0.0443601	+	0.0213627i
$91$	1.43130	+	3.64690i	0.150041	+	0.382299i
$92$	3.75484	−	6.50357i	0.391469	−	0.678044i
$93$	−2.67729	−	4.63720i	−0.277622	−	0.480855i
$94$	−3.18110	+	3.98897i	−0.328105	+	0.411431i
$95$	4.16251	+	2.83795i	0.427065	+	0.291168i
$96$	1.84122	−	0.277519i	0.187918	−	0.0283241i
$97$	3.20309	−	1.54253i	0.325225	−	0.156620i	−0.264146	−	0.964483i	$-0.585090\pi$
$97$	3.20309	−	1.54253i	0.325225	−	0.156620i	0.589371	+	0.807863i	$0.299376\pi$
$98$	2.17508	+	2.01818i	0.219716	+	0.203867i
$99$	0.102051	+	0.0153817i	0.0102565	+	0.00154592i
$100$	0.955573	−	0.294755i	0.0955573	−	0.0294755i
$101$	−0.189781	−	2.53245i	−0.0188839	−	0.251988i	−0.998654	−	0.0518627i	$-0.983484\pi$
$101$	−0.189781	−	2.53245i	−0.0188839	−	0.251988i	0.979770	−	0.200125i	$-0.0641349\pi$
$102$	3.90722	+	4.89950i	0.386873	+	0.485123i
$103$	−5.79115	+	14.7556i	−0.570619	+	1.45391i	0.296119	+	0.955151i	$0.404307\pi$
$103$	−5.79115	+	14.7556i	−0.570619	+	1.45391i	−0.866739	+	0.498763i	$0.833788\pi$
$104$	1.43009	−	1.32693i	0.140231	−	0.130116i
$105$	−3.08954	+	2.10641i	−0.301508	+	0.205565i
$106$	0.233711	−	3.11866i	0.0227000	−	0.302911i
$107$	−1.57470	−	6.89919i	−0.152232	−	0.666970i	−0.992234	−	0.124387i	$-0.960304\pi$
$107$	−1.57470	−	6.89919i	−0.152232	−	0.666970i	0.840002	−	0.542583i	$-0.182554\pi$
$108$	−1.04948	−	4.59806i	−0.100986	−	0.442448i
$109$	0.399488	−	5.33080i	0.0382640	−	0.510598i	−0.944838	−	0.327538i	$-0.893781\pi$
$109$	0.399488	−	5.33080i	0.0382640	−	0.510598i	0.983102	−	0.183059i	$-0.0586001\pi$
$110$	0.182557	−	0.124465i	0.0174061	−	0.0118673i
$111$	1.35053	−	1.25311i	0.128186	−	0.118940i
$112$	−0.733676	+	1.86938i	−0.0693258	+	0.176639i
$113$	−6.45479	−	8.09406i	−0.607216	−	0.761425i	0.379267	−	0.925287i	$-0.376176\pi$
$113$	−6.45479	−	8.09406i	−0.607216	−	0.761425i	−0.986483	+	0.163862i	$0.947605\pi$
$114$	0.701016	+	9.35441i	0.0656562	+	0.876121i
$115$	7.17604	−	2.21351i	0.669169	−	0.206411i
$116$	7.13650	+	1.07565i	0.662608	+	0.0998721i
$117$	0.667984	+	0.619798i	0.0617551	+	0.0573004i
$118$	7.66783	−	3.69263i	0.705881	−	0.339934i
$119$	−6.68319	+	1.00733i	−0.612647	+	0.0923417i
$120$	1.53847	+	1.04891i	0.140442	+	0.0957519i
$121$	−6.82795	+	8.56198i	−0.620723	+	0.778362i
$122$	0.145333	+	0.251723i	0.0131578	+	0.0227900i
$123$	−0.172932	+	0.299527i	−0.0155927	+	0.0270074i
$124$	−1.05061	−	2.67691i	−0.0943474	−	0.240393i
$125$	0.900969	+	0.433884i	0.0805851	+	0.0388077i
$126$	−0.896341	−	0.276485i	−0.0798524	−	0.0246312i
$127$	−1.16125	+	5.08775i	−0.103044	+	0.451465i	0.896913	+	0.442207i	$0.145804\pi$
$127$	−1.16125	+	5.08775i	−0.103044	+	0.451465i	−0.999957	+	0.00925836i	$0.997053\pi$
$128$	1.00000			0.0883883
$129$	2.63986	−	11.9212i	0.232427	−	1.04961i
$130$	1.95087			0.171102
$131$	−1.71341	+	7.50693i	−0.149701	+	0.655884i	0.843266	+	0.537496i	$0.180630\pi$
$131$	−1.71341	+	7.50693i	−0.149701	+	0.655884i	−0.992967	+	0.118388i	$0.962227\pi$
$132$	0.393132	+	0.121265i	0.0342178	+	0.0105548i
$133$	−9.11518	−	4.38964i	−0.790386	−	0.380630i
$134$	1.63623	+	4.16905i	0.141349	+	0.360151i
$135$	2.35815	−	4.08444i	0.202957	−	0.351533i
$136$	1.68277	+	2.91465i	0.144297	+	0.249929i
$137$	−7.41865	+	9.30269i	−0.633818	+	0.794782i	−0.990215	−	0.139552i	$-0.955434\pi$
$137$	−7.41865	+	9.30269i	−0.633818	+	0.794782i	0.356397	+	0.934335i	$0.384005\pi$
$138$	11.5534	+	7.87697i	0.983490	+	0.670532i
$139$	10.2826	−	1.54985i	0.872155	−	0.131456i	0.302311	−	0.953209i	$-0.402242\pi$
$139$	10.2826	−	1.54985i	0.872155	−	0.131456i	0.569844	+	0.821753i	$0.307004\pi$
$140$	−1.80932	+	0.871323i	−0.152915	+	0.0736402i
$141$	−6.96410	−	6.46174i	−0.586483	−	0.544177i
$142$	−0.398645	−	0.0600861i	−0.0334536	−	0.00504232i
$143$	0.411892	−	0.127052i	0.0344441	−	0.0106246i
$144$	0.0349059	+	0.465787i	0.00290883	+	0.0388156i
$145$	4.49980	+	5.64257i	0.373688	+	0.468590i
$146$	−3.09128	+	7.87646i	−0.255836	+	0.651860i
$147$	−4.05003	+	3.75787i	−0.334041	+	0.309944i
$148$	0.817507	−	0.557367i	0.0671986	−	0.0458152i
$149$	1.59385	−	21.2685i	0.130573	−	1.74238i	−0.419938	−	0.907553i	$-0.637948\pi$
$149$	1.59385	−	21.2685i	0.130573	−	1.74238i	0.550511	−	0.834828i	$-0.314433\pi$
$150$	0.414337	+	1.81533i	0.0338305	+	0.148221i
$151$	−3.54115	−	15.5148i	−0.288174	−	1.26257i	−0.887028	−	0.461716i	$-0.847234\pi$
$151$	−3.54115	−	15.5148i	−0.288174	−	1.26257i	0.598853	−	0.800859i	$-0.295623\pi$
$152$	−0.376483	+	5.02382i	−0.0305368	+	0.407485i
$153$	−1.29887	+	0.885554i	−0.105007	+	0.0715928i
$154$	−0.325261	+	0.301798i	−0.0262103	+	0.0243196i
$155$	1.05061	−	2.67691i	0.0843869	−	0.215014i
$156$	2.26485	+	2.84003i	0.181333	+	0.227385i
$157$	−0.625711	−	8.34953i	−0.0499372	−	0.666365i	−0.964865	−	0.262747i	$-0.915372\pi$
$157$	−0.625711	−	8.34953i	−0.0499372	−	0.666365i	0.914928	−	0.403618i	$-0.132248\pi$
$158$	−16.8048	+	5.18359i	−1.33692	+	0.412385i
$159$	5.75822	+	0.867912i	0.456657	+	0.0688299i
$160$	0.733052	+	0.680173i	0.0579528	+	0.0537724i
$161$	−13.5874	+	6.54335i	−1.07084	+	0.515688i
$162$	10.0694	−	1.51771i	0.791124	−	0.119243i
$163$	6.15528	+	4.19660i	0.482119	+	0.328703i	0.779871	−	0.625940i	$-0.215285\pi$
$163$	6.15528	+	4.19660i	0.482119	+	0.328703i	−0.297752	+	0.954643i	$0.596237\pi$
$164$	−0.115811	+	0.145223i	−0.00904336	+	0.0113400i
$165$	0.205705	+	0.356291i	0.0160141	+	0.0277373i
$166$	2.79855	−	4.84724i	0.217210	−	0.376219i
$167$	0.998732	+	2.54473i	0.0772842	+	0.196917i	0.964294	−	0.264833i	$-0.0853169\pi$
$167$	0.998732	+	2.54473i	0.0772842	+	0.196917i	−0.887010	+	0.461750i	$0.847222\pi$
$168$	−3.36898	−	1.62241i	−0.259922	−	0.125172i
$169$	−8.78566	−	2.71002i	−0.675820	−	0.208463i
$170$	−0.748905	+	3.28117i	−0.0574384	+	0.251654i
$171$	−2.35317			−0.179952
$172$	2.35613	−	6.11953i	0.179653	−	0.466610i
$173$	−9.40481			−0.715035			−0.357517	−	0.933906i	$-0.616377\pi$
$173$	−9.40481			−0.715035			−0.357517	+	0.933906i	$0.616377\pi$
$174$	−2.99032	+	13.1014i	−0.226695	+	0.993217i
$175$	−1.91898	−	0.591926i	−0.145061	−	0.0447454i
$176$	0.199068	+	0.0958662i	0.0150053	+	0.00722618i
$177$	5.78954	+	14.7515i	0.435168	+	1.10879i
$178$	1.83647	−	3.18086i	0.137649	−	0.238416i
$179$	−2.75866	−	4.77814i	−0.206192	−	0.357135i	0.744320	−	0.667823i	$-0.232774\pi$
$179$	−2.75866	−	4.77814i	−0.206192	−	0.357135i	−0.950512	+	0.310688i	$0.899441\pi$
$180$	−0.291228	+	0.365188i	−0.0217069	+	0.0272195i
$181$	20.5210	+	13.9910i	1.52531	+	1.03994i	0.979360	+	0.202122i	$0.0647839\pi$
$181$	20.5210	+	13.9910i	1.52531	+	1.03994i	0.545951	+	0.837817i	$0.316169\pi$
$182$	−3.87396	+	0.583905i	−0.287157	+	0.0432819i
$183$	−0.487624	+	0.234828i	−0.0360462	+	0.0173590i
$184$	5.50498	+	5.10787i	0.405832	+	0.376558i
$185$	0.978380	+	0.147467i	0.0719319	+	0.0108420i
$186$	5.11669	−	1.57829i	0.375174	−	0.115726i
$187$	0.0555704	+	0.741535i	0.00406371	+	0.0542264i
$188$	−3.18110	−	3.98897i	−0.232005	−	0.290926i
$189$	−3.46024	+	8.81655i	−0.251695	+	0.641309i
$190$	−3.69304	+	3.42664i	−0.267922	+	0.248595i
$191$	−7.99459	+	5.45062i	−0.578468	+	0.394393i	−0.816911	−	0.576763i	$-0.804315\pi$
$191$	−7.99459	+	5.45062i	−0.578468	+	0.394393i	0.238443	+	0.971157i	$0.423363\pi$
$192$	−0.139148	+	1.85681i	−0.0100422	+	0.134003i
$193$	−3.60599	−	15.7989i	−0.259565	−	1.13723i	−0.921718	−	0.387860i	$-0.873214\pi$
$193$	−3.60599	−	15.7989i	−0.259565	−	1.13723i	0.662153	−	0.749368i	$-0.269643\pi$
$194$	0.791098	+	3.46603i	0.0567975	+	0.248846i
$195$	−0.271460	+	3.62238i	−0.0194396	+	0.259404i
$196$	−2.45158	+	1.67146i	−0.175113	+	0.119390i
$197$	5.34139	−	4.95609i	0.380558	−	0.353107i	−0.466580	−	0.884479i	$-0.654514\pi$
$197$	5.34139	−	4.95609i	0.380558	−	0.353107i	0.847138	+	0.531373i	$0.178324\pi$
$198$	−0.0377046	+	0.0960697i	−0.00267955	+	0.00682738i
$199$	−7.69566	−	9.65006i	−0.545531	−	0.684074i	0.430279	−	0.902696i	$-0.358415\pi$
$199$	−7.69566	−	9.65006i	−0.545531	−	0.684074i	−0.975810	+	0.218622i	$0.929844\pi$
$200$	0.0747301	+	0.997204i	0.00528422	+	0.0705130i
$201$	−7.96881	+	2.45805i	−0.562076	+	0.173378i
$202$	2.51118	+	0.378500i	0.176686	+	0.0266312i
$203$	−10.6244	−	9.85799i	−0.745686	−	0.691895i
$204$	−5.64610	+	2.71902i	−0.395306	+	0.190369i
$205$	−0.183673	+	0.0276842i	−0.0128282	+	0.00193355i
$206$	−13.0970	−	8.92939i	−0.912512	−	0.622140i
$207$	−2.18703	+	2.74245i	−0.152009	+	0.190613i
$208$	0.975433	+	1.68950i	0.0676341	+	0.117146i
$209$	−0.556560	+	0.963990i	−0.0384980	+	0.0666806i
$210$	−1.36611	−	3.48080i	−0.0942708	−	0.240198i
$211$	−8.39968	−	4.04507i	−0.578258	−	0.278474i	0.121807	−	0.992554i	$-0.461131\pi$
$211$	−8.39968	−	4.04507i	−0.578258	−	0.278474i	−0.700064	+	0.714080i	$0.746845\pi$
$212$	2.98846	+	0.921818i	0.205248	+	0.0633107i
$213$	0.167039	−	0.731847i	0.0114453	−	0.0501453i
$214$	7.07662			0.483747
$215$	5.88950	−	2.88336i	0.401661	−	0.196643i
$216$	4.71631			0.320904
$217$	−1.28505	+	5.63016i	−0.0872346	+	0.382200i
$218$	5.10825	+	1.57569i	0.345974	+	0.106719i
$219$	−14.1949	−	6.83591i	−0.959203	−	0.461928i
$220$	0.0807217	+	0.205676i	0.00544226	+	0.0138666i
$221$	−3.28287	+	5.68609i	−0.220830	+	0.382488i
$222$	0.921167	+	1.59551i	0.0618247	+	0.107084i
$223$	−14.9923	+	18.7997i	−1.00396	+	1.25892i	−0.0382532	+	0.999268i	$0.512179\pi$
$223$	−14.9923	+	18.7997i	−1.00396	+	1.25892i	−0.965702	+	0.259652i	$0.916392\pi$
$224$	−1.65925	−	1.13126i	−0.110863	−	0.0755852i
$225$	−0.461876	+	0.0696167i	−0.0307918	+	0.00464111i
$226$	9.32745	−	4.49186i	0.620453	−	0.298794i
$227$	−12.9096	−	11.9784i	−0.856840	−	0.795031i	0.123501	−	0.992344i	$-0.460588\pi$
$227$	−12.9096	−	11.9784i	−0.856840	−	0.795031i	−0.980340	+	0.197313i	$0.936778\pi$
$228$	−9.27587	−	1.39811i	−0.614309	−	0.0925922i
$229$	23.3367	−	7.19841i	1.54213	−	0.475684i	0.596962	−	0.802269i	$-0.296374\pi$
$229$	23.3367	−	7.19841i	1.54213	−	0.475684i	0.945168	+	0.326585i	$0.105898\pi$
$230$	0.561199	+	7.48867i	0.0370043	+	0.493789i
$231$	−0.515122	−	0.645942i	−0.0338925	−	0.0424999i
$232$	−2.63671	+	6.71822i	−0.173108	+	0.441073i
$233$	−9.72367	+	9.02224i	−0.637019	+	0.591067i	−0.931122	−	0.364707i	$-0.881169\pi$
$233$	−9.72367	+	9.02224i	−0.637019	+	0.591067i	0.294104	+	0.955773i	$0.404979\pi$
$234$	−0.752899	+	0.513318i	−0.0492185	+	0.0335566i
$235$	0.381279	−	5.08782i	0.0248719	−	0.331893i
$236$	1.89380	+	8.29727i	0.123276	+	0.540106i
$237$	−7.28657	−	31.9245i	−0.473314	−	2.07372i
$238$	0.505077	−	6.73978i	0.0327393	−	0.436875i
$239$	−8.74304	+	5.96091i	−0.565540	+	0.385579i	−0.812073	−	0.583556i	$-0.801661\pi$
$239$	−8.74304	+	5.96091i	−0.565540	+	0.385579i	0.246533	+	0.969134i	$0.420709\pi$
$240$	−1.36495	+	1.26649i	−0.0881073	+	0.0817516i
$241$	0.167698	−	0.427288i	0.0108024	−	0.0275241i	−0.925371	−	0.379063i	$-0.876246\pi$
$241$	0.167698	−	0.427288i	0.0108024	−	0.0275241i	0.936173	+	0.351539i	$0.114342\pi$
$242$	−6.82795	−	8.56198i	−0.438917	−	0.550385i
$243$	0.359613	+	4.79870i	0.0230692	+	0.307837i
$244$	−0.277752	+	0.0856750i	−0.0177812	+	0.00548478i
$245$	−2.93401	−	0.442232i	−0.187447	−	0.0282531i
$246$	−0.253536	−	0.235247i	−0.0161649	−	0.0149988i
$247$	−8.85496	+	4.26433i	−0.563428	+	0.271333i
$248$	2.84357	−	0.428600i	0.180567	−	0.0272161i
$249$	8.61097	+	5.87086i	0.545698	+	0.372051i
$250$	−0.623490	+	0.781831i	−0.0394330	+	0.0494474i
$251$	12.6726	+	21.9496i	0.799887	+	1.38544i	0.919689	+	0.392647i	$0.128440\pi$
$251$	12.6726	+	21.9496i	0.799887	+	1.38544i	−0.119803	+	0.992798i	$0.538226\pi$
$252$	0.469007	−	0.812344i	0.0295447	−	0.0511729i
$253$	0.606194	+	1.54456i	0.0381111	+	0.0971054i
$254$	−4.70179	−	2.26426i	−0.295017	−	0.142072i
$255$	−5.98829	−	1.84714i	−0.375001	−	0.115673i
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	18.9951			1.18488			0.592441	−	0.805614i	$-0.298164\pi$
$257$	18.9951			1.18488			0.592441	+	0.805614i	$0.298164\pi$
$258$	11.0349	+	5.22640i	0.687005	+	0.325382i
$259$	−1.98697			−0.123464
$260$	−0.434108	+	1.90195i	−0.0269223	+	0.117954i
$261$	−3.22130	−	0.993639i	−0.199393	−	0.0615047i
$262$	−6.93745	−	3.34090i	−0.428597	−	0.206401i
$263$	2.80950	+	7.15850i	0.173241	+	0.441412i	0.990952	−	0.134218i	$-0.0428522\pi$
$263$	2.80950	+	7.15850i	0.173241	+	0.441412i	−0.817710	+	0.575630i	$0.804757\pi$
$264$	−0.205705	+	0.356291i	−0.0126603	+	0.0219282i
$265$	1.56370	+	2.70841i	0.0960574	+	0.166376i
$266$	6.30790	−	7.90986i	0.386762	−	0.484984i
$267$	5.65070	+	3.85258i	0.345817	+	0.235774i
$268$	−4.42862	+	0.667508i	−0.270521	+	0.0407745i
$269$	11.1487	−	5.36892i	0.679747	−	0.327349i	−0.0619548	−	0.998079i	$-0.519733\pi$
$269$	11.1487	−	5.36892i	0.679747	−	0.327349i	0.741701	+	0.670730i	$0.234019\pi$
$270$	3.45730	+	3.20790i	0.210404	+	0.195227i
$271$	8.18662	+	1.23393i	0.497302	+	0.0749562i	0.392904	−	0.919579i	$-0.371470\pi$
$271$	8.18662	+	1.23393i	0.497302	+	0.0749562i	0.104398	+	0.994536i	$0.466709\pi$
$272$	−3.21603	+	0.992013i	−0.195000	+	0.0601496i
$273$	−0.545144	−	7.27444i	−0.0329936	−	0.440269i
$274$	−7.41865	−	9.30269i	−0.448177	−	0.561996i
$275$	−0.0807217	+	0.205676i	−0.00486770	+	0.0124027i
$276$	−10.2503	+	9.51093i	−0.616998	+	0.572491i
$277$	−24.1452	+	16.4619i	−1.45074	+	0.989100i	−0.455651	+	0.890159i	$0.650593\pi$
$277$	−24.1452	+	16.4619i	−1.45074	+	0.989100i	−0.995093	+	0.0989417i	$0.968454\pi$
$278$	−0.777096	+	10.3696i	−0.0466071	+	0.621929i
$279$	0.298894	+	1.30954i	0.0178943	+	0.0784001i
$280$	−0.446865	−	1.95784i	−0.0267053	−	0.117004i
$281$	−2.09168	+	27.9115i	−0.124779	+	1.66506i	0.486524	+	0.873667i	$0.338264\pi$
$281$	−2.09168	+	27.9115i	−0.124779	+	1.66506i	−0.611304	+	0.791396i	$0.709355\pi$
$282$	7.84939	−	5.35162i	0.467424	−	0.318685i
$283$	7.24229	−	6.71986i	0.430509	−	0.399454i	−0.434933	−	0.900463i	$-0.643228\pi$
$283$	7.24229	−	6.71986i	0.430509	−	0.399454i	0.865442	+	0.501009i	$0.167037\pi$
$284$	0.147287	−	0.375280i	0.00873985	−	0.0222688i
$285$	−5.84873	−	7.33408i	−0.346449	−	0.434433i
$286$	0.0322118	+	0.429836i	0.00190472	+	0.0254168i
$287$	0.356444	−	0.109949i	0.0210402	−	0.00649006i
$288$	−0.461876	−	0.0696167i	−0.0272163	−	0.00410220i
$289$	4.15866	+	3.85867i	0.244627	+	0.226981i
$290$	−6.50239	+	3.13139i	−0.381834	+	0.183881i
$291$	−6.54582	+	0.986624i	−0.383723	+	0.0578369i
$292$	−6.99110	−	4.76645i	−0.409123	−	0.278936i
$293$	0.0641004	−	0.0803793i	0.00374478	−	0.00469581i	−0.779956	−	0.625835i	$-0.784758\pi$
$293$	0.0641004	−	0.0803793i	0.00374478	−	0.00469581i	0.783700	+	0.621139i	$0.213330\pi$
$294$	−2.76244	−	4.78469i	−0.161109	−	0.279049i
$295$	−4.25532	+	7.37044i	−0.247754	+	0.429123i
$296$	0.361480	+	0.921036i	0.0210106	+	0.0535341i
$297$	0.938866	+	0.452134i	0.0544785	+	0.0262355i
$298$	20.3806	+	6.28657i	1.18061	+	0.364171i
$299$	−3.26001	+	14.2830i	−0.188531	+	0.826010i
$300$	−1.86201			−0.107503
$301$	−10.8322	+	7.48843i	−0.624355	+	0.431626i
$302$	15.9138			0.915734
$303$	−1.05223	+	4.61011i	−0.0604489	+	0.264844i
$304$	−4.81408	−	1.48495i	−0.276107	−	0.0851676i
$305$	−0.261880	−	0.126115i	−0.0149952	−	0.00722132i
$306$	−0.574326	−	1.46336i	−0.0328320	−	0.0836546i
$307$	12.9065	−	22.3547i	0.736611	−	1.27585i	−0.217402	−	0.976082i	$-0.569758\pi$
$307$	12.9065	−	22.3547i	0.736611	−	1.27585i	0.954013	−	0.299766i	$-0.0969085\pi$
$308$	−0.221854	−	0.384263i	−0.0126413	−	0.0218954i
$309$	18.4026	−	23.0761i	1.04689	−	1.31275i
$310$	2.37601	+	1.61993i	0.134948	+	0.0920061i
$311$	32.4614	−	4.89277i	1.84072	−	0.277443i	0.865861	−	0.500284i	$-0.166771\pi$
$311$	32.4614	−	4.89277i	1.84072	−	0.277443i	0.974855	+	0.222841i	$0.0715331\pi$
$312$	−3.27280	+	1.57610i	−0.185286	+	0.0892290i
$313$	18.3940	+	17.0672i	1.03969	+	0.964693i	0.999405	−	0.0344951i	$-0.0109823\pi$
$313$	18.3940	+	17.0672i	1.03969	+	0.964693i	0.0402869	+	0.999188i	$0.487173\pi$
$314$	8.27942	+	1.24792i	0.467235	+	0.0704243i
$315$	0.896341	−	0.276485i	0.0505031	−	0.0155781i
$316$	−1.31421	−	17.5369i	−0.0739301	−	0.986529i
$317$	9.54951	+	11.9747i	0.536354	+	0.672567i	0.973991	−	0.226585i	$-0.0727561\pi$
$317$	9.54951	+	11.9747i	0.536354	+	0.672567i	−0.437637	+	0.899152i	$0.644185\pi$
$318$	−2.12748	+	5.42072i	−0.119303	+	0.303979i
$319$	−1.16893	+	1.08461i	−0.0654478	+	0.0607267i
$320$	−0.826239	+	0.563320i	−0.0461882	+	0.0314905i
$321$	−0.984700	+	13.1399i	−0.0549606	+	0.733398i
$322$	−3.35581	−	14.7028i	−0.187012	−	0.819354i
$323$	−3.77291	−	16.5302i	−0.209930	−	0.919765i
$324$	−0.760984	+	10.1546i	−0.0422769	+	0.564146i
$325$	−1.61188	+	1.09896i	−0.0894110	+	0.0609594i
$326$	−5.46106	+	5.06712i	−0.302460	+	0.280642i
$327$	−3.63655	+	9.26578i	−0.201102	+	0.512399i
$328$	−0.115811	−	0.145223i	−0.00639462	−	0.00801860i
$329$	0.765683	+	10.2173i	0.0422135	+	0.563299i
$330$	−0.393132	+	0.121265i	−0.0216412	+	0.00667543i
$331$	4.44721	+	0.670309i	0.244441	+	0.0368435i	0.270120	−	0.962827i	$-0.412937\pi$
$331$	4.44721	+	0.670309i	0.244441	+	0.0368435i	−0.0256790	+	0.999670i	$0.508175\pi$
$332$	4.10297	+	3.80700i	0.225180	+	0.208936i
$333$	−0.416389	+	0.200522i	−0.0228180	+	0.0109886i
$334$	−2.70316	+	0.407437i	−0.147911	+	0.0222939i
$335$	−3.70043	−	2.52291i	−0.202176	−	0.137841i
$336$	2.33141	−	2.92349i	0.127189	−	0.159489i
$337$	−5.63095	−	9.75309i	−0.306737	−	0.531284i	0.670909	−	0.741539i	$-0.265904\pi$
$337$	−5.63095	−	9.75309i	−0.306737	−	0.531284i	−0.977647	+	0.210255i	$0.932571\pi$
$338$	4.59706	−	7.96235i	0.250047	−	0.433095i
$339$	7.04262	+	17.9443i	0.382503	+	0.974601i
$340$	−3.03226	−	1.46026i	−0.164447	−	0.0791936i
$341$	0.607153	+	0.187282i	0.0328792	+	0.0101419i
$342$	0.523630	−	2.29417i	0.0283147	−	0.124055i
$343$	20.0160			1.08076
$344$	5.44181	+	3.65878i	0.293403	+	0.197268i
$345$	−13.9831			−0.752825
$346$	2.09277	−	9.16902i	0.112508	−	0.492929i
$347$	−27.8849	−	8.60136i	−1.49694	−	0.461745i	−0.565226	−	0.824936i	$-0.691211\pi$
$347$	−27.8849	−	8.60136i	−1.49694	−	0.461745i	−0.931715	+	0.363191i	$0.881687\pi$
$348$	−12.1075	−	5.83069i	−0.649033	−	0.312558i
$349$	2.50374	+	6.37943i	0.134022	+	0.341483i	0.982092	−	0.188401i	$-0.0603306\pi$
$349$	2.50374	+	6.37943i	0.134022	+	0.341483i	−0.848070	+	0.529884i	$0.822235\pi$
$350$	1.00410	−	1.73915i	0.0536713	−	0.0929613i
$351$	4.60044	+	7.96819i	0.245553	+	0.425311i
$352$	−0.137759	+	0.172745i	−0.00734260	+	0.00920733i
$353$	19.9854	+	13.6258i	1.06371	+	0.725227i	0.962949	−	0.269683i	$-0.0869189\pi$
$353$	19.9854	+	13.6258i	1.06371	+	0.725227i	0.100764	+	0.994910i	$0.467871\pi$
$354$	−15.6699	+	2.36186i	−0.832848	+	0.125532i
$355$	0.363224	−	0.174919i	0.0192779	−	0.00928376i
$356$	2.69246	+	2.49823i	0.142700	+	0.132406i
$357$	12.4442	+	1.87566i	0.658616	+	0.0992704i
$358$	5.27221	−	1.62626i	0.278645	−	0.0859505i
$359$	−1.09349	−	14.5916i	−0.0577123	−	0.770117i	−0.948718	−	0.316124i	$-0.897618\pi$
$359$	−1.09349	−	14.5916i	−0.0577123	−	0.770117i	0.891005	−	0.453993i	$-0.150001\pi$
$360$	−0.291228	−	0.365188i	−0.0153491	−	0.0192471i
$361$	2.33104	−	5.93940i	0.122687	−	0.312600i
$362$	−18.2065	+	16.8932i	−0.956913	+	0.887886i
$363$	16.8480	−	11.4868i	0.884293	−	0.602901i
$364$	0.292771	−	3.90676i	0.0153454	−	0.204770i
$365$	−1.88283	−	8.24921i	−0.0985518	−	0.431784i
$366$	−0.120433	−	0.527653i	−0.00629515	−	0.0275808i
$367$	2.35564	−	31.4339i	0.122964	−	1.64084i	−0.505378	−	0.862898i	$-0.668647\pi$
$367$	2.35564	−	31.4339i	0.122964	−	1.64084i	0.628342	−	0.777937i	$-0.283734\pi$
$368$	−6.20478	+	4.23035i	−0.323447	+	0.220522i
$369$	0.0636005	−	0.0590127i	0.00331091	−	0.00307208i
$370$	−0.361480	+	0.921036i	−0.0187924	+	0.0478824i
$371$	−3.91578	−	4.91024i	−0.203297	−	0.254927i
$372$	0.400148	+	5.33960i	0.0207467	+	0.276846i
$373$	12.5676	−	3.87659i	0.650726	−	0.200722i	0.0482201	−	0.998837i	$-0.484645\pi$
$373$	12.5676	−	3.87659i	0.650726	−	0.200722i	0.602506	+	0.798114i	$0.294169\pi$
$374$	−0.735309	−	0.110830i	−0.0380219	−	0.00573088i
$375$	−1.36495	−	1.26649i	−0.0704858	−	0.0654013i
$376$	4.59682	−	2.21371i	0.237063	−	0.114163i
$377$	−13.9224	+	2.09846i	−0.717038	+	0.108076i
$378$	−7.82552	−	5.33535i	−0.402501	−	0.274421i
$379$	−10.7265	+	13.4507i	−0.550986	+	0.690914i	−0.976863	−	0.213867i	$-0.931394\pi$
$379$	−10.7265	+	13.4507i	−0.550986	+	0.690914i	0.425877	+	0.904781i	$0.359966\pi$
$380$	−2.51895	−	4.36295i	−0.129219	−	0.223815i
$381$	4.85855	−	8.41525i	0.248911	−	0.431126i
$382$	−3.53500	−	9.00703i	−0.180866	−	0.460840i
$383$	−11.5462	−	5.56038i	−0.589985	−	0.284122i	0.114975	−	0.993368i	$-0.463321\pi$
$383$	−11.5462	−	5.56038i	−0.589985	−	0.284122i	−0.704961	+	0.709246i	$0.749035\pi$
$384$	−1.77929	−	0.548838i	−0.0907990	−	0.0280078i
$385$	0.0987344	−	0.432584i	0.00503197	−	0.0220465i
$386$	16.2052			0.824822
$387$	−1.51426	+	2.66244i	−0.0769743	+	0.135339i
$388$	−3.55516			−0.180486
$389$	−0.950949	+	4.16638i	−0.0482150	+	0.211244i	−0.993297	−	0.115589i	$-0.963124\pi$
$389$	−0.950949	+	4.16638i	−0.0482150	+	0.211244i	0.945082	+	0.326833i	$0.105982\pi$
$390$	−3.47115	−	1.07071i	−0.175769	−	0.0542175i
$391$	−22.7712	−	10.9661i	−1.15159	−	0.554577i
$392$	−1.08402	−	2.76205i	−0.0547515	−	0.139504i
$393$	7.16874	−	12.4166i	0.361615	−	0.626335i
$394$	3.64326	+	6.31030i	0.183545	+	0.317909i
$395$	10.9648	−	13.7494i	0.551697	−	0.691806i
$396$	−0.0852710	−	0.0581368i	−0.00428503	−	0.00292148i
$397$	22.6733	−	3.41745i	1.13794	−	0.171517i	0.447072	−	0.894498i	$-0.352467\pi$
$397$	22.6733	−	3.41745i	1.13794	−	0.171517i	0.690868	+	0.722981i	$0.257229\pi$
$398$	11.1206	−	5.35538i	0.557423	−	0.268441i
$399$	13.8093	+	12.8132i	0.691332	+	0.641462i
$400$	−0.988831	−	0.149042i	−0.0494415	−	0.00745211i
$401$	17.9850	−	5.54763i	0.898126	−	0.277035i	0.188883	−	0.982000i	$-0.439513\pi$
$401$	17.9850	−	5.54763i	0.898126	−	0.277035i	0.709243	+	0.704964i	$0.249037\pi$
$402$	−0.623197	−	8.31598i	−0.0310822	−	0.414763i
$403$	3.49783	+	4.38614i	0.174239	+	0.218489i
$404$	−0.927801	+	2.36400i	−0.0461598	+	0.117613i
$405$	−7.46474	+	6.92627i	−0.370926	+	0.344169i
$406$	11.9750	−	8.16440i	0.594308	−	0.405193i
$407$	−0.0163370	+	0.218003i	−0.000809797	+	0.0108060i
$408$	−1.39447	−	6.10958i	−0.0690366	−	0.302469i
$409$	−0.925663	−	4.05559i	−0.0457711	−	0.200536i	0.946873	−	0.321609i	$-0.104224\pi$
$409$	−0.925663	−	4.05559i	−0.0457711	−	0.200536i	−0.992644	+	0.121073i	$0.961367\pi$
$410$	0.0138809	−	0.185228i	0.000685529	−	0.00914775i
$411$	18.3056	−	12.4805i	0.902948	−	0.615619i
$412$	11.6199	−	10.7817i	0.572470	−	0.531174i
$413$	6.24405	−	15.9096i	0.307250	−	0.782860i
$414$	−2.18703	−	2.74245i	−0.107487	−	0.134784i
$415$	0.418272	+	5.58146i	0.0205322	+	0.273983i
$416$	−1.86419	+	0.575028i	−0.0913996	+	0.0281930i
$417$	−19.1463	−	2.88583i	−0.937596	−	0.141320i
$418$	−0.815974	−	0.757113i	−0.0399106	−	0.0370316i
$419$	17.4995	−	8.42731i	0.854906	−	0.411701i	0.0455096	−	0.998964i	$-0.485509\pi$
$419$	17.4995	−	8.42731i	0.854906	−	0.411701i	0.809396	+	0.587263i	$0.199795\pi$
$420$	3.69752	−	0.557311i	0.180420	−	0.0271940i
$421$	−22.7708	−	15.5249i	−1.10978	−	0.756636i	−0.137512	−	0.990500i	$-0.543911\pi$
$421$	−22.7708	−	15.5249i	−1.10978	−	0.756636i	−0.972269	+	0.233864i	$0.924863\pi$
$422$	5.81276	−	7.28897i	0.282961	−	0.354821i
$423$	1.19158	+	2.06387i	0.0579364	+	0.100349i
$424$	−1.56370	+	2.70841i	−0.0759400	+	0.131532i
$425$	−1.22957	−	3.13290i	−0.0596431	−	0.151968i
$426$	0.676328	+	0.325702i	0.0327682	+	0.0157803i
$427$	0.557779	+	0.172052i	0.0269928	+	0.00832619i
$428$	−1.57470	+	6.89919i	−0.0761158	+	0.333485i
$429$	−0.802605			−0.0387501
$430$	1.50053	+	6.38345i	0.0723618	+	0.307837i
$431$	15.9159			0.766643			0.383322	−	0.923615i	$-0.374780\pi$
$431$	15.9159			0.766643			0.383322	+	0.923615i	$0.374780\pi$
$432$	−1.04948	+	4.59806i	−0.0504930	+	0.221224i
$433$	27.6313	+	8.52313i	1.32788	+	0.409596i	0.875925	−	0.482447i	$-0.160252\pi$
$433$	27.6313	+	8.52313i	1.32788	+	0.409596i	0.451951	+	0.892043i	$0.350728\pi$
$434$	−5.20305	−	2.50566i	−0.249754	−	0.120275i
$435$	−4.90958	−	12.5094i	−0.235397	−	0.599781i
$436$	−2.67287	+	4.62955i	−0.128007	+	0.221715i
$437$	−18.9165	−	32.7643i	−0.904899	−	1.56733i
$438$	9.82318	−	12.3179i	0.469370	−	0.588571i
$439$	−8.23353	−	5.61353i	−0.392965	−	0.267919i	0.350678	−	0.936496i	$-0.385951\pi$
$439$	−8.23353	−	5.61353i	−0.392965	−	0.267919i	−0.743643	+	0.668577i	$0.766904\pi$
$440$	−0.218481	+	0.0329307i	−0.0104157	+	0.00156991i
$441$	1.24869	−	0.601336i	0.0594613	−	0.0286351i
$442$	−4.81302	−	4.46583i	−0.228932	−	0.212418i
$443$	−0.965216	−	0.145483i	−0.0458588	−	0.00691210i	0.126073	−	0.992021i	$-0.459763\pi$
$443$	−0.965216	−	0.145483i	−0.0458588	−	0.00691210i	−0.171932	+	0.985109i	$0.555001\pi$
$444$	−1.76048	+	0.543038i	−0.0835489	+	0.0257714i
$445$	0.274479	+	3.66267i	0.0130116	+	0.173627i
$446$	−14.9923	−	18.7997i	−0.709904	−	0.890191i
$447$	−14.5089	+	36.9680i	−0.686246	+	1.74853i
$448$	1.47211	−	1.36592i	0.0695507	−	0.0645336i
$449$	6.84893	−	4.66952i	0.323221	−	0.220368i	−0.390828	−	0.920464i	$-0.627811\pi$
$449$	6.84893	−	4.66952i	0.323221	−	0.220368i	0.714050	+	0.700095i	$0.246859\pi$
$450$	0.0349059	−	0.465787i	0.00164548	−	0.0219574i
$451$	−0.00913240	−	0.0400117i	−0.000430028	−	0.00188408i
$452$	2.30369	+	10.0931i	0.108356	+	0.474741i
$453$	−2.21438	+	29.5488i	−0.104040	+	1.38832i
$454$	14.5507	−	9.92049i	0.682897	−	0.465592i
$455$	2.87189	−	2.66472i	0.134636	−	0.124924i
$456$	3.42713	−	8.73219i	0.160490	−	0.408922i
$457$	−6.43579	−	8.07022i	−0.301054	−	0.377509i	0.608178	−	0.793801i	$-0.291901\pi$
$457$	−6.43579	−	8.07022i	−0.301054	−	0.377509i	−0.909231	+	0.416292i	$0.863329\pi$
$458$	1.82503	+	24.3534i	0.0852782	+	1.13796i
$459$	−15.1678	+	4.67864i	−0.707971	+	0.218380i
$460$	−7.42580	−	1.11926i	−0.346230	−	0.0521857i
$461$	−7.65698	−	7.10464i	−0.356621	−	0.330896i	0.481433	−	0.876483i	$-0.340116\pi$
$461$	−7.65698	−	7.10464i	−0.356621	−	0.330896i	−0.838054	+	0.545587i	$0.816307\pi$
$462$	0.744372	−	0.358471i	0.0346313	−	0.0166776i
$463$	2.61167	−	0.393646i	0.121375	−	0.0182943i	−0.0880739	−	0.996114i	$-0.528071\pi$
$463$	2.61167	−	0.393646i	0.121375	−	0.0182943i	0.209449	+	0.977820i	$0.432833\pi$
$464$	−5.96306	−	4.06554i	−0.276828	−	0.188738i
$465$	−3.33852	+	4.18638i	−0.154820	+	0.194139i
$466$	−6.63232	−	11.4875i	−0.307236	−	0.532149i
$467$	−14.9122	+	25.8286i	−0.690053	+	1.19521i	0.281768	+	0.959483i	$0.409079\pi$
$467$	−14.9122	+	25.8286i	−0.690053	+	1.19521i	−0.971820	+	0.235723i	$0.924254\pi$
$468$	−0.332912	−	0.848246i	−0.0153889	−	0.0392102i
$469$	8.10331	+	3.90235i	0.374176	+	0.180194i
$470$	4.87541	+	1.50387i	0.224886	+	0.0693681i
$471$	−3.46922	+	15.1996i	−0.159853	+	0.700363i
$472$	−8.51065			−0.391734
$473$	0.732538	+	1.25003i	0.0336821	+	0.0574766i
$474$	32.7455			1.50405
$475$	1.12104	−	4.91159i	0.0514368	−	0.225359i
$476$	6.45841	+	1.99216i	0.296021	+	0.0913103i
$477$	−1.31613	−	0.633813i	−0.0602612	−	0.0290203i
$478$	−3.86594	−	9.85026i	−0.176824	−	0.450541i
$479$	14.8284	−	25.6835i	0.677526	−	1.17351i	−0.298197	−	0.954504i	$-0.596385\pi$
$479$	14.8284	−	25.6835i	0.677526	−	1.17351i	0.975724	−	0.219006i	$-0.0702813\pi$
$480$	−0.931007	−	1.61255i	−0.0424944	−	0.0736025i
$481$	−1.20349	+	1.50913i	−0.0548744	+	0.0688103i
$482$	0.379259	+	0.258574i	0.0172748	+	0.0117777i
$483$	27.7672	−	4.18523i	1.26345	−	0.190434i
$484$	9.86667	−	4.75154i	0.448485	−	0.215979i
$485$	−2.60612	−	2.41812i	−0.118338	−	0.109801i
$486$	−4.75841	−	0.717215i	−0.215846	−	0.0325335i
$487$	−20.7147	+	6.38963i	−0.938671	+	0.289542i	−0.726088	−	0.687601i	$-0.758664\pi$
$487$	−20.7147	+	6.38963i	−0.938671	+	0.289542i	−0.212583	+	0.977143i	$0.568187\pi$
$488$	−0.0217214	−	0.289852i	−0.000983283	−	0.0131210i
$489$	−8.64877	−	10.8452i	−0.391111	−	0.490438i
$490$	1.08402	−	2.76205i	0.0489712	−	0.124777i
$491$	10.3626	−	9.61507i	0.467657	−	0.433922i	−0.410813	−	0.911720i	$-0.634755\pi$
$491$	10.3626	−	9.61507i	0.467657	−	0.433922i	0.878470	+	0.477797i	$0.158565\pi$
$492$	0.285766	−	0.194832i	0.0128833	−	0.00878370i
$493$	1.81516	−	24.2216i	0.0817507	−	1.09089i
$494$	−2.18700	−	9.58185i	−0.0983976	−	0.431108i
$495$	−0.0229650	−	0.100616i	−0.00103220	−	0.00452237i
$496$	−0.214901	+	2.86765i	−0.00964933	+	0.128761i
$497$	−0.668923	+	0.456064i	−0.0300053	+	0.0204573i
$498$	−7.63979	+	7.08869i	−0.342347	+	0.317652i
$499$	−0.344127	+	0.876821i	−0.0154052	+	0.0392519i	−0.938369	−	0.345634i	$-0.887664\pi$
$499$	−0.344127	+	0.876821i	−0.0154052	+	0.0392519i	0.922964	+	0.384886i	$0.125759\pi$
$500$	−0.623490	−	0.781831i	−0.0278833	−	0.0349646i
$501$	−0.380390	−	5.07595i	−0.0169946	−	0.226777i
$502$	−24.2192	+	7.47062i	−1.08095	+	0.333430i
$503$	−28.6119	−	4.31255i	−1.27574	−	0.192287i	−0.523984	−	0.851728i	$-0.675555\pi$
$503$	−28.6119	−	4.31255i	−1.27574	−	0.192287i	−0.751756	+	0.659441i	$0.770793\pi$
$504$	0.687613	+	0.638012i	0.0306287	+	0.0284193i
$505$	−2.28805	+	1.10187i	−0.101817	+	0.0490325i
$506$	−1.64072	+	0.247299i	−0.0729390	+	0.0109938i
$507$	14.1449	+	9.64380i	0.628195	+	0.428296i
$508$	3.25374	−	4.08006i	0.144361	−	0.181023i
$509$	19.2356	+	33.3170i	0.852601	+	1.47675i	0.878853	+	0.477093i	$0.158310\pi$
$509$	19.2356	+	33.3170i	0.852601	+	1.47675i	−0.0262513	+	0.999655i	$0.508357\pi$
$510$	3.13335	−	5.42712i	0.138747	−	0.240317i
$511$	6.20789	+	15.8175i	0.274621	+	0.699723i
$512$	−0.900969	−	0.433884i	−0.0398176	−	0.0191751i
$513$	−22.7047	−	7.00347i	−1.00244	−	0.309211i
$514$	−4.22681	+	18.5189i	−0.186437	+	0.816832i
$515$	15.8514			0.698494
$516$	−7.55087	+	9.59528i	−0.332409	+	0.422409i
$517$	1.12730			0.0495786
$518$	0.442143	−	1.93715i	0.0194266	−	0.0851136i
$519$	16.7339	+	5.16172i	0.734536	+	0.226574i
$520$	−1.75767	−	0.846449i	−0.0770789	−	0.0371192i
$521$	5.79039	+	14.7537i	0.253682	+	0.646370i	0.999811	−	0.0194305i	$-0.00618532\pi$
$521$	5.79039	+	14.7537i	0.253682	+	0.646370i	−0.746130	+	0.665801i	$0.768090\pi$
$522$	1.68553	−	2.91943i	0.0737738	−	0.127780i
$523$	14.2415	+	24.6671i	0.622739	+	1.07862i	0.988973	+	0.148093i	$0.0473134\pi$
$523$	14.2415	+	24.6671i	0.622739	+	1.07862i	−0.366235	+	0.930523i	$0.619353\pi$
$524$	4.80086	−	6.02009i	0.209727	−	0.262989i
$525$	3.08954	+	2.10641i	0.134839	+	0.0919314i
$526$	−7.60420	+	1.14615i	−0.331559	+	0.0499744i
$527$	−8.71983	+	4.19925i	−0.379842	+	0.182922i
$528$	−0.301585	−	0.279830i	−0.0131248	−	0.0121780i
$529$	−33.0222	−	4.97729i	−1.43575	−	0.216404i
$530$	−2.98846	+	0.921818i	−0.129810	+	0.0400412i
$531$	−0.297072	−	3.96415i	−0.0128918	−	0.172030i
$532$	6.30790	+	7.90986i	0.273482	+	0.342936i
$533$	0.132388	−	0.337319i	0.00573435	−	0.0146109i
$534$	−5.01339	+	4.65175i	−0.216951	+	0.201301i
$535$	−5.84697	+	3.98640i	−0.252787	+	0.172347i
$536$	0.334690	−	4.46612i	0.0144564	−	0.192907i
$537$	2.28603	+	10.0158i	0.0986495	+	0.432212i
$538$	2.75349	+	12.0638i	0.118712	+	0.520109i
$539$	0.0489923	−	0.653757i	0.00211025	−	0.0281593i
$540$	−3.89679	+	2.65679i	−0.167691	+	0.114330i
$541$	−0.452731	+	0.420073i	−0.0194644	+	0.0180603i	−0.689845	−	0.723957i	$-0.742321\pi$
$541$	−0.452731	+	0.420073i	−0.0194644	+	0.0180603i	0.670381	+	0.742017i	$0.266131\pi$
$542$	−3.02469	+	7.70679i	−0.129922	+	0.331035i
$543$	−28.8340	−	36.1566i	−1.23738	−	1.55163i
$544$	−0.251508	−	3.35614i	−0.0107833	−	0.143893i
$545$	−5.10825	+	1.57569i	−0.218813	+	0.0674950i
$546$	7.21336	+	1.08724i	0.308703	+	0.0465296i
$547$	−13.9446	−	12.9387i	−0.596228	−	0.553218i	0.323274	−	0.946306i	$-0.395217\pi$
$547$	−13.9446	−	12.9387i	−0.596228	−	0.553218i	−0.919501	+	0.393087i	$0.871407\pi$
$548$	10.7203	−	5.16260i	0.457947	−	0.220535i
$549$	0.134251	−	0.0202351i	0.00572971	−	0.000863615i
$550$	−0.182557	−	0.124465i	−0.00778424	−	0.00530720i
$551$	22.6695	−	28.4267i	0.965755	−	1.21102i
$552$	−6.99156	−	12.1097i	−0.297580	−	0.515424i
$553$	−17.6582	+	30.5848i	−0.750901	+	1.30060i
$554$	−10.6764	−	27.2029i	−0.453595	−	1.15574i
$555$	−1.65989	−	0.799359i	−0.0704582	−	0.0339309i
$556$	−9.93672	−	3.06507i	−0.421411	−	0.129988i
$557$	−7.13072	+	31.2417i	−0.302138	+	1.32375i	0.564754	+	0.825259i	$0.308971\pi$
$557$	−7.13072	+	31.2417i	−0.302138	+	1.32375i	−0.866892	+	0.498496i	$0.833886\pi$
$558$	−1.34322			−0.0568629
$559$	−0.873387	+	12.7628i	−0.0369403	+	0.539810i
$560$	2.00819			0.0848617
$561$	0.308107	−	1.34991i	0.0130083	−	0.0569930i
$562$	−26.7463	−	8.25014i	−1.12822	−	0.348011i
$563$	−13.2879	−	6.39913i	−0.560019	−	0.269691i	0.132388	−	0.991198i	$-0.457735\pi$
$563$	−13.2879	−	6.39913i	−0.560019	−	0.269691i	−0.692407	+	0.721507i	$0.743450\pi$
$564$	3.47079	+	8.84344i	0.146147	+	0.372376i
$565$	−5.17634	+	8.96569i	−0.217770	+	0.377189i
$566$	4.93982	+	8.55602i	0.207636	+	0.359636i
$567$	12.7501	−	15.9882i	0.535456	−	0.671441i
$568$	0.333097	+	0.227101i	0.0139764	+	0.00952897i
$569$	14.7228	−	2.21911i	0.617214	−	0.0930300i	0.167009	−	0.985955i	$-0.446589\pi$
$569$	14.7228	−	2.21911i	0.617214	−	0.0930300i	0.450205	+	0.892925i	$0.351351\pi$
$570$	8.45167	−	4.07011i	0.354001	−	0.170478i
$571$	−11.4206	−	10.5967i	−0.477936	−	0.443460i	0.404049	−	0.914737i	$-0.367603\pi$
$571$	−11.4206	−	10.5967i	−0.477936	−	0.443460i	−0.881985	+	0.471277i	$0.843793\pi$
$572$	−0.426227	−	0.0642434i	−0.0178215	−	0.00268615i
$573$	17.2162	−	5.31050i	0.719217	−	0.221849i
$574$	0.0278756	+	0.371973i	0.00116350	+	0.0155259i
$575$	−4.68220	−	5.87130i	−0.195261	−	0.244850i
$576$	0.170648	−	0.434805i	0.00711035	−	0.0181169i
$577$	−14.9573	+	13.8784i	−0.622682	+	0.577765i	−0.927119	−	0.374768i	$-0.877722\pi$
$577$	−14.9573	+	13.8784i	−0.622682	+	0.577765i	0.304436	+	0.952533i	$0.401532\pi$
$578$	−4.68731	+	3.19576i	−0.194967	+	0.132926i
$579$	−2.25493	+	30.0899i	−0.0937115	+	1.25049i
$580$	−1.60596	−	7.03617i	−0.0666838	−	0.292161i
$581$	−2.50115	−	10.9583i	−0.103765	−	0.454626i
$582$	0.494695	−	6.60125i	0.0205058	−	0.273631i
$583$	−0.570928	+	0.389252i	−0.0236454	+	0.0161212i
$584$	6.20261	−	5.75518i	0.256666	−	0.238151i
$585$	0.332912	−	0.848246i	0.0137642	−	0.0350707i
$586$	0.0641004	+	0.0803793i	0.00264796	+	0.00332044i
$587$	3.49246	+	46.6037i	0.144149	+	1.92354i	0.335540	+	0.942026i	$0.391081\pi$
$587$	3.49246	+	46.6037i	0.144149	+	1.92354i	−0.191391	+	0.981514i	$0.561300\pi$
$588$	5.27943	−	1.62849i	0.217720	−	0.0671577i
$589$	−14.3256	−	2.15924i	−0.590278	−	0.0889700i
$590$	−6.23874	−	5.78871i	−0.256845	−	0.238317i
$591$	−12.2240	+	5.88675i	−0.502827	+	0.242149i
$592$	−0.978380	+	0.147467i	−0.0402112	+	0.00606086i
$593$	12.1110	+	8.25715i	0.497340	+	0.339081i	0.785872	−	0.618390i	$-0.212215\pi$
$593$	12.1110	+	8.25715i	0.497340	+	0.339081i	−0.288532	+	0.957470i	$0.593167\pi$
$594$	−0.649716	+	0.814718i	−0.0266582	+	0.0334283i
$595$	3.37934	+	5.85319i	0.138539	+	0.239957i
$596$	−10.6641	+	18.4707i	−0.436817	+	0.756588i
$597$	8.39649	+	21.3939i	0.343646	+	0.875595i
$598$	−13.1995	−	6.35655i	−0.539768	−	0.259939i
$599$	19.2642	+	5.94222i	0.787115	+	0.242793i	0.662153	−	0.749369i	$-0.269643\pi$
$599$	19.2642	+	5.94222i	0.787115	+	0.242793i	0.124962	+	0.992162i	$0.460119\pi$
$600$	0.414337	−	1.81533i	0.0169152	−	0.0741105i
$601$	−10.0428			−0.409655			−0.204827	−	0.978798i	$-0.565663\pi$
$601$	−10.0428			−0.409655			−0.204827	+	0.978798i	$0.565663\pi$
$602$	−4.89030	−	12.2269i	−0.199314	−	0.498332i
$603$	2.09195			0.0851906
$604$	−3.54115	+	15.5148i	−0.144087	+	0.631287i
$605$	10.4647	+	3.22792i	0.425449	+	0.131234i
$606$	−4.26039	−	2.05169i	−0.173066	−	0.0833444i
$607$	10.0542	+	25.6177i	0.408087	+	1.03979i	0.976207	+	0.216842i	$0.0695758\pi$
$607$	10.0542	+	25.6177i	0.408087	+	1.03979i	−0.568120	+	0.822946i	$0.692329\pi$
$608$	2.51895	−	4.36295i	0.102157	−	0.176941i
$609$	13.4934	+	23.3713i	0.546781	+	0.947052i
$610$	0.181227	−	0.227251i	0.00733766	−	0.00920113i
$611$	8.22395	+	5.60699i	0.332705	+	0.226835i
$612$	1.55447	−	0.234298i	0.0628357	−	0.00947095i
$613$	20.8563	−	10.0439i	0.842377	−	0.405668i	0.0376348	−	0.999292i	$-0.488018\pi$
$613$	20.8563	−	10.0439i	0.842377	−	0.405668i	0.804743	+	0.593624i	$0.202303\pi$
$614$	18.9222	+	17.5573i	0.763639	+	0.708553i
$615$	0.342001	+	0.0515483i	0.0137908	+	0.00207863i
$616$	0.423996	−	0.130785i	0.0170833	−	0.00526949i
$617$	−1.15168	−	15.3682i	−0.0463651	−	0.618699i	−0.971190	−	0.238306i	$-0.923408\pi$
$617$	−1.15168	−	15.3682i	−0.0463651	−	0.618699i	0.924825	−	0.380393i	$-0.124211\pi$
$618$	18.4026	+	23.0761i	0.740260	+	0.928257i
$619$	−8.90501	+	22.6896i	−0.357922	+	0.911972i	0.632582	+	0.774493i	$0.281995\pi$
$619$	−8.90501	+	22.6896i	−0.357922	+	0.911972i	−0.990505	+	0.137478i	$0.956100\pi$
$620$	−2.10803	+	1.95597i	−0.0846606	+	0.0785535i
$621$	−29.2637	+	19.9516i	−1.17431	+	0.800631i
$622$	−2.45324	+	32.7362i	−0.0983661	+	1.31260i
$623$	−1.64131	−	7.19105i	−0.0657577	−	0.288103i
$624$	−0.808316	−	3.54146i	−0.0323585	−	0.141772i
$625$	0.0747301	−	0.997204i	0.00298920	−	0.0398882i
$626$	−20.7323	+	14.1350i	−0.828630	+	0.564950i
$627$	1.51935	−	1.40976i	0.0606772	−	0.0563002i
$628$	−3.05898	+	7.79415i	−0.122067	+	0.311021i
$629$	−2.07621	−	2.60348i	−0.0827839	−	0.103808i
$630$	0.0700979	+	0.935392i	0.00279277	+	0.0372669i
$631$	46.0873	−	14.2161i	1.83471	−	0.565932i	0.834826	−	0.550515i	$-0.185568\pi$
$631$	46.0873	−	14.2161i	1.83471	−	0.565932i	0.999881	−	0.0154174i	$-0.00490771\pi$
$632$	17.3897	+	2.62107i	0.691724	+	0.104261i
$633$	12.7254	+	11.8074i	0.505788	+	0.469303i
$634$	−13.7994	+	6.64546i	−0.548046	+	0.263925i
$635$	5.16031	−	0.777791i	0.204780	−	0.0308657i
$636$	−4.81141	−	3.28036i	−0.190785	−	0.130075i
$637$	3.60908	−	4.52565i	0.142997	−	0.179313i
$638$	−0.797307	−	1.38098i	−0.0315657	−	0.0546734i
$639$	−0.0941540	+	0.163079i	−0.00372467	+	0.00645132i
$640$	−0.365341	−	0.930874i	−0.0144414	−	0.0367960i
$641$	−17.9736	−	8.65562i	−0.709914	−	0.341876i	0.0438353	−	0.999039i	$-0.486042\pi$
$641$	−17.9736	−	8.65562i	−0.709914	−	0.341876i	−0.753749	+	0.657162i	$0.771757\pi$
$642$	−12.5913	−	3.88392i	−0.496941	−	0.153286i
$643$	−8.96466	+	39.2767i	−0.353532	+	1.54892i	0.415428	+	0.909626i	$0.363632\pi$
$643$	−8.96466	+	39.2767i	−0.353532	+	1.54892i	−0.768960	+	0.639297i	$0.779225\pi$
$644$	15.0809			0.594270
$645$	−12.0616	+	1.89794i	−0.474926	+	0.0747314i
$646$	16.9553			0.667098
$647$	4.66842	−	20.4537i	0.183535	−	0.804118i	−0.796395	−	0.604776i	$-0.793263\pi$
$647$	4.66842	−	20.4537i	0.183535	−	0.804118i	0.979930	−	0.199342i	$-0.0638803\pi$
$648$	−9.73070	−	3.00152i	−0.382258	−	0.117911i
$649$	−1.69420	−	0.815883i	−0.0665031	−	0.0320262i
$650$	−0.712731	−	1.81601i	−0.0279556	−	0.0712297i
$651$	5.37651	−	9.31240i	0.210722	−	0.364982i
$652$	−3.72488	−	6.45168i	−0.145878	−	0.252667i
$653$	−20.2375	+	25.3770i	−0.791955	+	0.993081i	0.207933	+	0.978143i	$0.433326\pi$
$653$	−20.2375	+	25.3770i	−0.791955	+	0.993081i	−0.999888	+	0.0149375i	$0.995245\pi$
$654$	−8.22426	−	5.60720i	−0.321594	−	0.219259i
$655$	7.61398	−	1.14762i	0.297503	−	0.0448413i
$656$	0.167352	−	0.0805927i	0.00653402	−	0.00314662i
$657$	2.89720	+	2.68821i	0.113031	+	0.104877i
$658$	−10.1315	−	1.52708i	−0.394968	−	0.0595319i
$659$	24.9914	−	7.70883i	0.973527	−	0.300293i	0.233117	−	0.972449i	$-0.425107\pi$
$659$	24.9914	−	7.70883i	0.973527	−	0.300293i	0.740410	+	0.672155i	$0.234631\pi$
$660$	−0.0307447	−	0.410260i	−0.00119674	−	0.0159693i
$661$	−21.9542	−	27.5297i	−0.853921	−	1.07078i	−0.996712	−	0.0810297i	$-0.974179\pi$
$661$	−21.9542	−	27.5297i	−0.853921	−	1.07078i	0.142791	−	0.989753i	$-0.454392\pi$
$662$	−1.64310	+	4.18655i	−0.0638609	+	0.162715i
$663$	8.96191	−	8.31544i	0.348052	−	0.322945i
$664$	−4.62455	+	3.15296i	−0.179467	+	0.122359i
$665$	−0.756051	+	10.0888i	−0.0293184	+	0.391227i
$666$	−0.102840	−	0.450570i	−0.00398495	−	0.0174592i
$667$	−12.0602	−	52.8393i	−0.466974	−	2.04595i
$668$	0.204290	−	2.72605i	0.00790420	−	0.105474i
$669$	36.9935	−	25.2218i	1.43025	−	0.975130i
$670$	3.28308	−	3.04625i	0.126836	−	0.117687i
$671$	0.0234630	−	0.0597827i	0.000905779	−	0.00230789i
$672$	2.33141	+	2.92349i	0.0899359	+	0.112776i
$673$	1.88816	+	25.1958i	0.0727833	+	0.971226i	0.907366	+	0.420342i	$0.138090\pi$
$673$	1.88816	+	25.1958i	0.0727833	+	0.971226i	−0.834582	+	0.550883i	$0.814291\pi$
$674$	10.7616	−	3.31950i	0.414520	−	0.127862i
$675$	−4.66363	−	0.702929i	−0.179503	−	0.0270557i
$676$	6.73977	+	6.25359i	0.259222	+	0.240523i
$677$	28.9029	−	13.9189i	1.11083	−	0.534947i	0.213782	−	0.976881i	$-0.431422\pi$
$677$	28.9029	−	13.9189i	1.11083	−	0.534947i	0.897048	+	0.441934i	$0.145707\pi$
$678$	−19.0615	+	2.87306i	−0.732054	+	0.110339i
$679$	5.89890	+	4.02180i	0.226379	+	0.154342i
$680$	2.09839	−	2.63129i	0.0804694	−	0.100905i
$681$	16.3957	+	28.3982i	0.628285	+	1.08822i
$682$	−0.317691	+	0.550256i	−0.0121650	+	0.0210704i
$683$	5.11361	+	13.0293i	0.195667	+	0.498551i	0.994710	−	0.102723i	$-0.0327554\pi$
$683$	5.11361	+	13.0293i	0.195667	+	0.498551i	−0.799043	+	0.601274i	$0.794660\pi$
$684$	2.12013	+	1.02100i	0.0810654	+	0.0390390i
$685$	11.3700	+	3.50717i	0.434424	+	0.134002i
$686$	−4.45398	+	19.5141i	−0.170054	+	0.745053i
$687$	−45.4734			−1.73492
$688$	−4.77797	+	4.49122i	−0.182158	+	0.171226i
$689$	−6.10114			−0.232435
$690$	3.11153	−	13.6325i	0.118454	−	0.518981i
$691$	−21.2430	−	6.55259i	−0.808121	−	0.249272i	−0.136953	−	0.990578i	$-0.543731\pi$
$691$	−21.2430	−	6.55259i	−0.808121	−	0.249272i	−0.671168	+	0.741305i	$0.734207\pi$
$692$	8.47344	+	4.08060i	0.322112	+	0.155121i
$693$	0.0757181	+	0.192927i	0.00287629	+	0.00732868i
$694$	14.5907	−	25.2718i	0.553855	−	0.959304i
$695$	−5.19935	−	9.00554i	−0.197223	−	0.341600i
$696$	8.37868	−	10.5065i	0.317593	−	0.398249i
$697$	0.516516	+	0.352155i	0.0195644	+	0.0133388i
$698$	−6.77662	+	1.02141i	−0.256499	+	0.0386610i
$699$	22.2530	−	10.7165i	0.841684	−	0.405334i
$700$	1.47211	+	1.36592i	0.0556406	+	0.0516269i
$701$	−11.1155	−	1.67539i	−0.419826	−	0.0632787i	−0.0642679	−	0.997933i	$-0.520471\pi$
$701$	−11.1155	−	1.67539i	−0.419826	−	0.0632787i	−0.355558	+	0.934654i	$0.615709\pi$
$702$	−8.79211	+	2.71201i	−0.331837	+	0.102358i
$703$	−0.372504	−	4.97072i	−0.0140493	−	0.187474i
$704$	−0.137759	−	0.172745i	−0.00519200	−	0.00651057i
$705$	−3.47079	+	8.84344i	−0.130718	+	0.333063i
$706$	−17.7313	+	16.4523i	−0.667327	+	0.619189i
$707$	4.21374	−	2.87288i	0.158474	−	0.108046i
$708$	1.18424	−	15.8026i	0.0445066	−	0.593899i
$709$	−2.75931	−	12.0893i	−0.103628	−	0.454024i	−0.999944	−	0.0106077i	$-0.996623\pi$
$709$	−2.75931	−	12.0893i	−0.103628	−	0.454024i	0.896316	−	0.443417i	$-0.146234\pi$
$710$	0.0897089	+	0.393040i	0.00336672	+	0.0147505i
$711$	−0.613859	+	8.19138i	−0.0230215	+	0.307201i
$712$	−3.03473	+	2.06904i	−0.113731	+	0.0775406i
$713$	−15.8306	+	14.6887i	−0.592861	+	0.550095i
$714$	−4.59772	+	11.7148i	−0.172066	+	0.438416i
$715$	−0.268750	−	0.337002i	−0.0100507	−	0.0126032i
$716$	0.412310	+	5.50190i	0.0154088	+	0.205616i
$717$	18.8280	−	5.80766i	0.703144	−	0.216891i
$718$	14.4691	+	2.18087i	0.539983	+	0.0813893i
$719$	−26.1335	−	24.2483i	−0.974614	−	0.904310i	0.0208179	−	0.999783i	$-0.493373\pi$
$719$	−26.1335	−	24.2483i	−0.974614	−	0.904310i	−0.995432	+	0.0954736i	$0.969563\pi$
$720$	0.420837	−	0.202664i	0.0156837	−	0.00755285i
$721$	−31.4771	+	4.74440i	−1.17227	+	0.176691i
$722$	5.27179	+	3.59424i	0.196196	+	0.133764i
$723$	−0.532896	+	0.668230i	−0.0198186	+	0.0248517i
$724$	−12.4183	−	21.5091i	−0.461522	−	0.799380i
$725$	3.60856	−	6.25020i	0.134018	−	0.232127i
$726$	7.44976	+	18.9817i	0.276486	+	0.704476i
$727$	31.9852	+	15.4032i	1.18626	+	0.571275i	0.919730	−	0.392551i	$-0.128407\pi$
$727$	31.9852	+	15.4032i	1.18626	+	0.571275i	0.266534	+	0.963826i	$0.414122\pi$
$728$	3.74366	+	1.15477i	0.138749	+	0.0427985i
$729$	−4.80401	+	21.0477i	−0.177926	+	0.779545i
$730$	8.46136			0.313169
$731$	−21.1306	−	6.36840i	−0.781543	−	0.235544i
$732$	0.541222			0.0200042
$733$	0.0601848	−	0.263687i	0.00222297	−	0.00973949i	−0.973804	−	0.227388i	$-0.926981\pi$
$733$	0.0601848	−	0.263687i	0.00222297	−	0.00973949i	0.976027	+	0.217648i	$0.0698386\pi$
$734$	30.1216	+	9.29128i	1.11181	+	0.342947i
$735$	4.97775	+	2.39716i	0.183607	+	0.0884205i
$736$	−2.74359	−	6.99056i	−0.101130	−	0.257675i
$737$	0.494776	−	0.856977i	0.0182253	−	0.0315672i
$738$	0.0433807	+	0.0751375i	0.00159686	+	0.00276585i
$739$	−25.8367	+	32.3982i	−0.950420	+	1.19179i	0.0309228	+	0.999522i	$0.490155\pi$
$739$	−25.8367	+	32.3982i	−0.950420	+	1.19179i	−0.981343	+	0.192267i	$0.938416\pi$
$740$	−0.817507	−	0.557367i	−0.0300521	−	0.0204892i
$741$	18.0960	−	2.72753i	0.664772	−	0.100198i
$742$	5.65847	−	2.72498i	0.207729	−	0.100037i
$743$	−28.0229	−	26.0014i	−1.02806	−	0.953900i	−0.0291031	−	0.999576i	$-0.509265\pi$
$743$	−28.0229	−	26.0014i	−1.02806	−	0.953900i	−0.998956	+	0.0456767i	$0.985456\pi$
$744$	−5.29477	−	0.798058i	−0.194116	−	0.0292582i
$745$	−20.3806	+	6.28657i	−0.746686	+	0.230322i
$746$	0.982844	+	13.1151i	0.0359845	+	0.480179i
$747$	−1.63004	−	2.04400i	−0.0596399	−	0.0747860i
$748$	0.271673	−	0.692211i	0.00993335	−	0.0253098i
$749$	10.4176	−	9.66608i	0.380649	−	0.353191i
$750$	1.53847	−	1.04891i	0.0561769	−	0.0383008i
$751$	0.237226	−	3.16557i	0.00865652	−	0.115513i	−0.991202	−	0.132361i	$-0.957744\pi$
$751$	0.237226	−	3.16557i	0.00865652	−	0.115513i	0.999858	+	0.0168481i	$0.00536316\pi$
$752$	1.13532	+	4.97416i	0.0414009	+	0.181389i
$753$	−10.5014	−	46.0098i	−0.382694	−	1.67669i
$754$	1.05217	−	14.0402i	0.0383178	−	0.511316i
$755$	−13.1486	+	8.96454i	−0.478525	+	0.326253i
$756$	6.94292	−	6.44209i	0.252512	−	0.234297i
$757$	7.72783	−	19.6902i	0.280873	−	0.715652i	−0.718916	−	0.695097i	$-0.755361\pi$
$757$	7.72783	−	19.6902i	0.280873	−	0.715652i	0.999789	−	0.0205552i	$-0.00654338\pi$
$758$	−10.7265	−	13.4507i	−0.389606	−	0.488550i
$759$	−0.230883	−	3.08091i	−0.00838051	−	0.111830i
$760$	4.81408	−	1.48495i	0.174625	−	0.0538647i
$761$	5.00691	+	0.754671i	0.181500	+	0.0273568i	0.239164	−	0.970979i	$-0.423127\pi$
$761$	5.00691	+	0.754671i	0.181500	+	0.0273568i	−0.0576630	+	0.998336i	$0.518365\pi$
$762$	7.12313	+	6.60930i	0.258044	+	0.239430i
$763$	9.67217	−	4.65787i	0.350156	−	0.168626i
$764$	9.56782	−	1.44212i	0.346151	−	0.0521739i
$765$	1.29887	+	0.885554i	0.0469607	+	0.0320173i
$766$	7.99025	−	10.0195i	0.288699	−	0.362018i
$767$	−8.30156	−	14.3787i	−0.299752	−	0.519186i
$768$	0.931007	−	1.61255i	0.0335948	−	0.0581879i
$769$	5.73491	+	14.6123i	0.206806	+	0.526934i	0.996214	−	0.0869356i	$-0.0277075\pi$
$769$	5.73491	+	14.6123i	0.206806	+	0.526934i	−0.789408	+	0.613869i	$0.789612\pi$
$770$	0.399768	+	0.192518i	0.0144066	+	0.00693786i
$771$	−33.7978	−	10.4252i	−1.21720	−	0.375456i
$772$	−3.60599	+	15.7989i	−0.129782	+	0.568614i
$773$	−14.4332			−0.519127			−0.259564	−	0.965726i	$-0.583579\pi$
$773$	−14.4332			−0.519127			−0.259564	+	0.965726i	$0.583579\pi$
$774$	−2.25873	−	2.06875i	−0.0811885	−	0.0743595i
$775$	−2.87569			−0.103298
$776$	0.791098	−	3.46603i	0.0283988	−	0.124423i
$777$	3.53540	+	1.09052i	0.126832	+	0.0391224i
$778$	−3.85032	−	1.85421i	−0.138040	−	0.0664768i
$779$	0.341877	+	0.871090i	0.0122490	+	0.0312100i
$780$	1.81627	−	3.14587i	0.0650328	−	0.112640i
$781$	0.0445376	+	0.0771414i	0.00159368	+	0.00276034i
$782$	15.7582	−	19.7601i	0.563512	−	0.706621i
$783$	−28.1236	−	19.1744i	−1.00506	−	0.685235i
$784$	2.93401	−	0.442232i	0.104786	−	0.0157940i
$785$	−7.54376	+	3.63288i	−0.269248	+	0.129663i
$786$	10.5101	+	9.75196i	0.374883	+	0.347841i
$787$	−34.0331	−	5.12966i	−1.21315	−	0.182853i	−0.488868	−	0.872358i	$-0.662590\pi$
$787$	−34.0331	−	5.12966i	−1.21315	−	0.182853i	−0.724281	+	0.689505i	$0.757828\pi$
$788$	−6.96279	+	2.14774i	−0.248039	+	0.0765100i
$789$	−1.07006	−	14.2790i	−0.0380953	−	0.508346i
$790$	10.9648	+	13.7494i	0.390108	+	0.489180i
$791$	7.59552	−	19.3531i	0.270065	−	0.688116i
$792$	0.0756538	−	0.0701964i	0.00268824	−	0.00249432i
$793$	0.468517	−	0.319430i	0.0166375	−	0.0113433i
$794$	−1.71352	+	22.8653i	−0.0608104	+	0.811459i
$795$	−1.29580	−	5.67726i	−0.0459572	−	0.201352i
$796$	2.74655	+	12.0334i	0.0973489	+	0.426513i
$797$	3.27912	−	43.7568i	0.116152	−	1.54995i	−0.569485	−	0.822002i	$-0.692857\pi$
$797$	3.27912	−	43.7568i	0.116152	−	1.54995i	0.685637	−	0.727944i	$-0.259524\pi$
$798$	−15.5648	+	10.6119i	−0.550988	+	0.375657i
$799$	−12.5875	+	11.6795i	−0.445313	+	0.413190i
$800$	0.365341	−	0.930874i	0.0129168	−	0.0329114i
$801$	−1.06966	−	1.34132i	−0.0377947	−	0.0473930i
$802$	1.40650	+	18.7685i	0.0496654	+	0.662739i
$803$	1.78647	−	0.551053i	0.0630432	−	0.0194462i
$804$	8.24616	+	1.24291i	0.290819	+	0.0438340i
$805$	11.0551	+	10.2576i	0.389640	+	0.361533i
$806$	−5.05451	+	2.43413i	−0.178038	+	0.0857384i
$807$	−22.7834	+	3.43404i	−0.802013	+	0.120884i
$808$	−2.09827	−	1.43058i	−0.0738170	−	0.0503276i
$809$	−13.9871	+	17.5393i	−0.491760	+	0.616648i	−0.964349	−	0.264635i	$-0.914748\pi$
$809$	−13.9871	+	17.5393i	−0.491760	+	0.616648i	0.472588	+	0.881283i	$0.343320\pi$
$810$	−5.09155	−	8.81883i	−0.178899	−	0.309862i
$811$	11.6902	−	20.2479i	0.410497	−	0.711002i	−0.584447	−	0.811432i	$-0.698689\pi$
$811$	11.6902	−	20.2479i	0.410497	−	0.711002i	0.994944	+	0.100430i	$0.0320219\pi$
$812$	5.29502	+	13.4915i	0.185819	+	0.473459i
$813$	−13.8891	−	6.68866i	−0.487113	−	0.234581i
$814$	−0.208901	−	0.0644376i	−0.00732199	−	0.00225854i
$815$	1.65773	−	7.26298i	0.0580677	−	0.254411i
$816$	6.26670			0.219378
$817$	−20.7642	−	25.6945i	−0.726448	−	0.898936i
$818$	4.15989			0.145447
$819$	−0.407200	+	1.78406i	−0.0142287	+	0.0623401i
$820$	0.177495	+	0.0547499i	0.00619839	+	0.00191195i
$821$	28.6675	+	13.8055i	1.00050	+	0.481816i	0.861109	−	0.508421i	$-0.169771\pi$
$821$	28.6675	+	13.8055i	1.00050	+	0.481816i	0.139393	+	0.990237i	$0.455485\pi$
$822$	8.09425	+	20.6238i	0.282319	+	0.719338i
$823$	−11.4164	+	19.7739i	−0.397952	+	0.689273i	−0.993473	−	0.114066i	$-0.963612\pi$
$823$	−11.4164	+	19.7739i	−0.397952	+	0.689273i	0.595521	+	0.803340i	$0.296946\pi$
$824$	7.92568	+	13.7277i	0.276104	+	0.478226i
$825$	0.256510	−	0.321653i	0.00893053	−	0.0111985i
$826$	14.1213	+	9.62772i	0.491342	+	0.334991i
$827$	9.36127	−	1.41098i	0.325523	−	0.0490647i	0.0157522	−	0.999876i	$-0.494986\pi$
$827$	9.36127	−	1.41098i	0.325523	−	0.0490647i	0.309771	+	0.950811i	$0.399748\pi$
$828$	3.16035	−	1.52194i	0.109830	−	0.0528912i
$829$	23.3740	+	21.6879i	0.811811	+	0.753251i	0.972287	−	0.233789i	$-0.0751125\pi$
$829$	23.3740	+	21.6879i	0.811811	+	0.753251i	−0.160476	+	0.987040i	$0.551303\pi$
$830$	−5.53459	−	0.834206i	−0.192109	−	0.0289557i
$831$	51.9962	−	16.0387i	1.80373	−	0.556376i
$832$	−0.145788	−	1.94541i	−0.00505430	−	0.0674450i
$833$	6.22624	+	7.80746i	0.215726	+	0.270512i
$834$	7.07392	−	18.0241i	0.244950	−	0.624122i
$835$	2.00394	−	1.85939i	0.0693493	−	0.0643467i
$836$	0.919702	−	0.627042i	0.0318086	−	0.0216867i
$837$	−1.01354	+	13.5247i	−0.0350330	+	0.467483i
$838$	4.32202	+	18.9360i	0.149302	+	0.654133i
$839$	−0.363109	−	1.59089i	−0.0125359	−	0.0549235i	0.968273	−	0.249894i	$-0.0803959\pi$
$839$	−0.363109	−	1.59089i	−0.0125359	−	0.0549235i	−0.980809	+	0.194971i	$0.937539\pi$
$840$	−0.279437	+	3.72883i	−0.00964150	+	0.128657i
$841$	19.0752	−	13.0052i	0.657764	−	0.448456i
$842$	20.2026	−	18.7453i	0.696228	−	0.646005i
$843$	19.0406	−	48.5147i	0.655794	−	1.67094i
$844$	5.81276	+	7.28897i	0.200083	+	0.250897i
$845$	0.687078	+	9.16842i	0.0236362	+	0.315403i
$846$	−2.27727	+	0.702446i	−0.0782943	+	0.0241506i
$847$	−21.7465	−	3.27775i	−0.747217	−	0.112625i
$848$	−2.29255	−	2.12717i	−0.0787264	−	0.0730474i
$849$	−16.5742	+	7.98173i	−0.568826	+	0.273932i
$850$	3.32796	−	0.501609i	0.114148	−	0.0172051i
$851$	−6.13921	−	4.18564i	−0.210449	−	0.143482i
$852$	−0.468033	+	0.586895i	−0.0160346	+	0.0201067i
$853$	−16.8981	−	29.2683i	−0.578579	−	1.00213i	−0.995643	−	0.0932513i	$-0.970274\pi$
$853$	−16.8981	−	29.2683i	−0.578579	−	1.00213i	0.417063	−	0.908877i	$-0.363059\pi$
$854$	−0.291856	+	0.505509i	−0.00998711	+	0.0172982i
$855$	0.859710	+	2.19051i	0.0294015	+	0.0749137i
$856$	−6.37581	−	3.07043i	−0.217921	−	0.104945i
$857$	24.9073	+	7.68290i	0.850819	+	0.262443i	0.689344	−	0.724434i	$-0.257899\pi$
$857$	24.9073	+	7.68290i	0.850819	+	0.262443i	0.161475	+	0.986877i	$0.448375\pi$
$858$	0.178596	−	0.782482i	0.00609718	−	0.0267135i
$859$	−43.7958			−1.49429			−0.747147	−	0.664659i	$-0.768577\pi$
$859$	−43.7958			−1.49429			−0.747147	+	0.664659i	$0.768577\pi$
$860$	−6.55730	+	0.0424542i	−0.223602	+	0.00144768i
$861$	−0.694562			−0.0236706
$862$	−3.54163	+	15.5169i	−0.120628	+	0.528507i
$863$	30.4694	+	9.39857i	1.03719	+	0.319931i	0.766167	−	0.642641i	$-0.222161\pi$
$863$	30.4694	+	9.39857i	1.03719	+	0.319931i	0.271024	+	0.962573i	$0.412638\pi$
$864$	−4.24924	−	2.04633i	−0.144562	−	0.0696175i
$865$	3.43596	+	8.75469i	0.116826	+	0.297669i
$866$	−14.4580	+	25.0420i	−0.491302	+	0.850961i
$867$	−5.28167	−	9.14812i	−0.179375	−	0.310686i
$868$	3.60062	−	4.51504i	0.122213	−	0.153250i
$869$	3.21046	+	2.18885i	0.108907	+	0.0742518i
$870$	13.2883	−	2.00288i	0.450514	−	0.0679041i
$871$	7.87198	−	3.79094i	0.266732	−	0.128451i
$872$	−3.91871	−	3.63603i	−0.132704	−	0.123132i
$873$	1.64205	+	0.247499i	0.0555748	+	0.00837656i
$874$	36.1522	−	11.1515i	1.22287	−	0.377204i
$875$	0.150073	+	2.00258i	0.00507338	+	0.0676995i
$876$	9.82318	+	12.3179i	0.331895	+	0.416183i
$877$	−2.07218	+	5.27983i	−0.0699726	+	0.178287i	−0.961582	−	0.274518i	$-0.911482\pi$
$877$	−2.07218	+	5.27983i	−0.0699726	+	0.178287i	0.891609	+	0.452806i	$0.149577\pi$
$878$	7.30492	−	6.77797i	0.246529	−	0.228745i
$879$	−0.158168	+	0.107837i	−0.00533489	+	0.00363726i
$880$	0.0165115	−	0.220331i	0.000556604	−	0.00742736i
$881$	−0.717816	−	3.14496i	−0.0241838	−	0.105956i	0.961396	−	0.275170i	$-0.0887342\pi$
$881$	−0.717816	−	3.14496i	−0.0241838	−	0.105956i	−0.985579	+	0.169214i	$0.945877\pi$
$882$	0.308400	+	1.35119i	0.0103844	+	0.0454970i
$883$	−2.64162	+	35.2499i	−0.0888975	+	1.18625i	0.757184	+	0.653202i	$0.226575\pi$
$883$	−2.64162	+	35.2499i	−0.0888975	+	1.18625i	−0.846082	+	0.533053i	$0.821044\pi$
$884$	5.42486	−	3.69861i	0.182458	−	0.124398i
$885$	11.6166	−	10.7787i	0.390489	−	0.362320i
$886$	0.356616	−	0.908643i	0.0119808	−	0.0305265i
$887$	−8.88877	−	11.1462i	−0.298456	−	0.374252i	0.609880	−	0.792494i	$-0.291218\pi$
$887$	−8.88877	−	11.1462i	−0.298456	−	0.374252i	−0.908335	+	0.418242i	$0.862646\pi$
$888$	−0.137678	−	1.83718i	−0.00462016	−	0.0616518i
$889$	−10.0144	+	3.08902i	−0.335871	+	0.103602i
$890$	−3.63192	−	0.547423i	−0.121742	−	0.0183497i
$891$	−1.64933	−	1.53035i	−0.0552545	−	0.0512687i
$892$	21.6644	−	10.4330i	0.725379	−	0.349324i
$893$	−25.4167	+	3.83095i	−0.850538	+	0.128198i
$894$	−32.8126	−	22.3712i	−1.09742	−	0.748206i
$895$	−3.44000	+	4.31362i	−0.114986	+	0.144188i
$896$	1.00410	+	1.73915i	0.0335445	+	0.0581008i
$897$	13.6396	−	23.6244i	0.455412	−	0.788797i
$898$	3.02842	+	7.71628i	0.101060	+	0.257496i
$899$	−18.6989	−	9.00491i	−0.623643	−	0.300330i
$900$	0.446342	+	0.137678i	0.0148781	+	0.00458927i
$901$	2.34213	−	10.2615i	0.0780276	−	0.341861i
$902$	0.0410407			0.00136650
$903$	23.3835	−	7.37898i	0.778154	−	0.245557i
$904$	−10.3527			−0.344325
$905$	5.52666	−	24.2139i	0.183713	−	0.804897i
$906$	−28.3152	−	8.73408i	−0.940709	−	0.290170i
$907$	27.5907	+	13.2870i	0.916135	+	0.441187i	0.831690	−	0.555241i	$-0.187374\pi$
$907$	27.5907	+	13.2870i	0.916135	+	0.441187i	0.0844451	+	0.996428i	$0.473088\pi$
$908$	6.43393	+	16.3934i	0.213517	+	0.544034i
$909$	0.593103	−	1.02728i	0.0196720	−	0.0340729i
$910$	1.95886	+	3.39284i	0.0649355	+	0.112472i
$911$	15.8412	−	19.8643i	0.524844	−	0.658133i	−0.446786	−	0.894641i	$-0.647431\pi$
$911$	15.8412	−	19.8643i	0.524844	−	0.658133i	0.971630	+	0.236508i	$0.0760028\pi$
$912$	7.75065	+	5.28430i	0.256650	+	0.174981i
$913$	−1.22286	+	0.184317i	−0.0404709	+	0.00610000i
$914$	9.29998	−	4.47864i	0.307616	−	0.148140i
$915$	0.396744	+	0.368125i	0.0131160	+	0.0121698i
$916$	−24.1489	−	3.63986i	−0.797902	−	0.120264i
$917$	−14.7761	+	4.55782i	−0.487949	+	0.150512i
$918$	−1.18619	−	15.8286i	−0.0391500	−	0.522421i
$919$	−27.2255	−	34.1397i	−0.898086	−	1.12616i	−0.991444	−	0.130531i	$-0.958332\pi$
$919$	−27.2255	−	34.1397i	−0.898086	−	1.12616i	0.0933585	−	0.995633i	$-0.470240\pi$
$920$	2.74359	−	6.99056i	0.0904535	−	0.230472i
$921$	−35.2334	+	32.6918i	−1.16098	+	1.07723i
$922$	8.63035	−	5.88407i	0.284226	−	0.193782i
$923$	−0.0587743	+	0.784289i	−0.00193458	+	0.0258152i
$924$	0.183845	+	0.805477i	0.00604805	+	0.0264982i
$925$	−0.220169	−	0.964624i	−0.00723912	−	0.0317166i
$926$	−0.197375	+	2.63379i	−0.00648615	+	0.0865516i
$927$	−6.11753	+	4.17086i	−0.200926	+	0.136989i
$928$	5.29052	−	4.90888i	0.173670	−	0.161142i
$929$	−7.14604	+	18.2078i	−0.234454	+	0.597379i	−0.998879	−	0.0473333i	$-0.984928\pi$
$929$	−7.14604	+	18.2078i	−0.234454	+	0.597379i	0.764425	+	0.644713i	$0.223023\pi$
$930$	−3.33852	−	4.18638i	−0.109474	−	0.137277i
$931$	1.11708	+	14.9064i	0.0366109	+	0.488539i
$932$	12.6753	−	3.90982i	0.415194	−	0.128070i
$933$	−60.4435	−	9.11040i	−1.97883	−	0.298261i
$934$	−21.8628	−	20.2857i	−0.715372	−	0.663768i
$935$	0.669974	−	0.322642i	0.0219105	−	0.0105515i
$936$	0.901059	−	0.135813i	0.0294520	−	0.00443918i
$937$	42.4711	+	28.9563i	1.38747	+	0.945962i	0.999707	+	0.0242032i	$0.00770487\pi$
$937$	42.4711	+	28.9563i	1.38747	+	0.945962i	0.387764	+	0.921759i	$0.373248\pi$
$938$	−5.60766	+	7.03179i	−0.183097	+	0.229596i
$939$	−23.3612	−	40.4628i	−0.762363	−	1.32045i
$940$	−2.55104	+	4.41853i	−0.0832058	+	0.144117i
$941$	13.0202	+	33.1749i	0.424446	+	1.08147i	0.969938	+	0.243354i	$0.0782476\pi$
$941$	13.0202	+	33.1749i	0.424446	+	1.08147i	−0.545492	+	0.838116i	$0.683657\pi$
$942$	−14.0466	−	6.76448i	−0.457662	−	0.220399i
$943$	1.33293	+	0.411154i	0.0434061	+	0.0133890i
$944$	1.89380	−	8.29727i	0.0616378	−	0.270053i
$945$	9.47126			0.308100
$946$	−1.38170	+	0.436013i	−0.0449228	+	0.0141760i
$947$	4.67517			0.151923			0.0759613	−	0.997111i	$-0.475797\pi$
$947$	4.67517			0.151923			0.0759613	+	0.997111i	$0.475797\pi$
$948$	−7.28657	+	31.9245i	−0.236657	+	1.03686i
$949$	15.7736	+	4.86551i	0.512033	+	0.157941i
$950$	4.53899	+	2.18586i	0.147264	+	0.0709188i
$951$	−10.4192	−	26.5476i	−0.337865	−	0.860865i
$952$	−3.37934	+	5.85319i	−0.109525	+	0.189703i
$953$	3.10964	+	5.38606i	0.100731	+	0.174472i	0.911986	−	0.410221i	$-0.134548\pi$
$953$	3.10964	+	5.38606i	0.100731	+	0.174472i	−0.811255	+	0.584693i	$0.801215\pi$
$954$	0.910787	−	1.14209i	0.0294878	−	0.0369766i
$955$	7.99459	+	5.45062i	0.258699	+	0.176378i
$956$	10.4635	−	1.57713i	0.338415	−	0.0510079i
$957$	2.67515	−	1.28828i	0.0864753	−	0.0416443i
$958$	21.7400	+	20.1717i	0.702386	+	0.651719i
$959$	−23.6278	−	3.56132i	−0.762981	−	0.115001i
$960$	1.77929	−	0.548838i	0.0574263	−	0.0177137i
$961$	−1.69864	−	22.6668i	−0.0547950	−	0.731188i
$962$	−1.20349	−	1.50913i	−0.0388021	−	0.0486562i
$963$	1.20761	−	3.07695i	0.0389148	−	0.0991533i
$964$	−0.336484	+	0.312212i	−0.0108374	+	0.0100557i
$965$	−13.3893	+	9.12870i	−0.431018	+	0.293863i
$966$	−2.09848	+	28.0023i	−0.0675175	+	0.900959i
$967$	0.283588	+	1.24248i	0.00911958	+	0.0399555i	0.979283	−	0.202496i	$-0.0649055\pi$
$967$	0.283588	+	1.24248i	0.00911958	+	0.0399555i	−0.970163	+	0.242452i	$0.922048\pi$
$968$	2.43687	+	10.6766i	0.0783239	+	0.343159i
$969$	−2.35930	+	31.4827i	−0.0757918	+	1.01137i
$970$	2.93741	−	2.00269i	0.0943146	−	0.0643026i
$971$	25.9694	−	24.0961i	0.833399	−	0.773281i	−0.142893	−	0.989738i	$-0.545641\pi$
$971$	25.9694	−	24.0961i	0.833399	−	0.773281i	0.976292	+	0.216457i	$0.0694501\pi$
$972$	1.75808	−	4.47951i	0.0563904	−	0.143680i
$973$	13.0201	+	16.3267i	0.417405	+	0.523410i
$974$	−1.61998	−	21.6171i	−0.0519075	−	0.692658i
$975$	3.47115	−	1.07071i	0.111166	−	0.0342901i
$976$	0.287419	+	0.0433214i	0.00920005	+	0.00138668i
$977$	42.5556	+	39.4858i	1.36147	+	1.26326i	0.933080	+	0.359670i	$0.117111\pi$
$977$	42.5556	+	39.4858i	1.36147	+	1.26326i	0.428393	+	0.903592i	$0.359080\pi$
$978$	12.4978	−	6.01864i	0.399637	−	0.192455i
$979$	−0.802468	+	0.120953i	−0.0256470	+	0.00386566i
$980$	2.45158	+	1.67146i	0.0783128	+	0.0533928i
$981$	1.55683	−	1.95220i	0.0497058	−	0.0623291i
$982$	7.06811	+	12.2423i	0.225552	+	0.390668i
$983$	18.2686	−	31.6421i	0.582677	−	1.00923i	−0.412484	−	0.910965i	$-0.635339\pi$
$983$	18.2686	−	31.6421i	0.582677	−	1.00923i	0.995161	−	0.0982606i	$-0.0313279\pi$
$984$	0.126358	+	0.321955i	0.00402815	+	0.0102636i
$985$	−6.56492	−	3.16150i	−0.209176	−	0.100734i
$986$	23.2104	+	7.15947i	0.739171	+	0.228004i
$987$	4.24529	−	18.5998i	0.135129	−	0.592039i
$988$	9.82827			0.312679
$989$	−49.2432	+	0.318817i	−1.56584	+	0.0101378i
$990$	0.103204			0.00328003
$991$	12.2509	−	53.6746i	0.389162	−	1.70503i	−0.278393	−	0.960467i	$-0.589802\pi$
$991$	12.2509	−	53.6746i	0.389162	−	1.70503i	0.667554	−	0.744561i	$-0.267341\pi$
$992$	−2.74793	−	0.847625i	−0.0872469	−	0.0269121i
$993$	−7.54498	−	3.63347i	−0.239433	−	0.115305i
$994$	−0.295780	−	0.753635i	−0.00938158	−	0.0239039i
$995$	−6.17144	+	10.6893i	−0.195648	+	0.338872i
$996$	−5.21095	−	9.02562i	−0.165115	−	0.285988i
$997$	36.3880	−	45.6291i	1.15242	−	1.44509i	0.277561	−	0.960708i	$-0.410474\pi$
$997$	36.3880	−	45.6291i	1.15242	−	1.44509i	0.874858	−	0.484380i	$-0.160955\pi$
$998$	−0.778262	−	0.530610i	−0.0246354	−	0.0167962i
$999$	−4.61434	+	0.695500i	−0.145991	+	0.0220046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.b.81.1	✓	48
43.17	even	21	inner	430.2.q.b.361.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.b.81.1	✓	48	1.1	even	1	trivial
430.2.q.b.361.1	yes	48	43.17	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)

\(f(q)\)	\(=\)	\(q+(-0.222521 + 0.974928i) q^{2} +(-1.77929 - 0.548838i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.365341 - 0.930874i) q^{5} +(0.931007 - 1.61255i) q^{6} +(1.00410 + 1.73915i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.385931 + 0.263123i) q^{9} +O(q^{10})\)	\(q+(-0.222521 + 0.974928i) q^{2} +(-1.77929 - 0.548838i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.365341 - 0.930874i) q^{5} +(0.931007 - 1.61255i) q^{6} +(1.00410 + 1.73915i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.385931 + 0.263123i) q^{9} +(0.988831 - 0.149042i) q^{10} +(0.199068 - 0.0958662i) q^{11} +(1.36495 + 1.26649i) q^{12} +(1.92908 + 0.290761i) q^{13} +(-1.91898 + 0.591926i) q^{14} +(0.139148 + 1.85681i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-1.22957 + 3.13290i) q^{17} +(-0.342404 + 0.317704i) q^{18} +(-4.16251 + 2.83795i) q^{19} +(-0.0747301 + 0.997204i) q^{20} +(-0.832069 - 3.64553i) q^{21} +(0.0491658 + 0.215409i) q^{22} +(-0.561199 + 7.48867i) q^{23} +(-1.53847 + 1.04891i) q^{24} +(-0.733052 + 0.680173i) q^{25} +(-0.712731 + 1.81601i) q^{26} +(2.94057 + 3.68736i) q^{27} +(-0.150073 - 2.00258i) q^{28} +(-6.89648 + 2.12728i) q^{29} +(-1.84122 - 0.277519i) q^{30} +(2.10803 + 1.95597i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(-0.406815 + 0.0613175i) q^{33} +(-2.78075 - 1.89588i) q^{34} +(1.25209 - 1.57007i) q^{35} +(-0.233547 - 0.404515i) q^{36} +(-0.494716 + 0.856873i) q^{37} +(-1.84055 - 4.68965i) q^{38} +(-3.27280 - 1.57610i) q^{39} +(-0.955573 - 0.294755i) q^{40} +(0.0413326 - 0.181090i) q^{41} +3.73928 q^{42} +(0.532363 + 6.53579i) q^{43} -0.220949 q^{44} +(0.103938 - 0.455382i) q^{45} +(-7.17604 - 2.21351i) q^{46} +(4.59682 + 2.21371i) q^{47} +(-0.680270 - 1.73330i) q^{48} +(1.48358 - 2.56963i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(3.90722 - 4.89950i) q^{51} +(-1.61188 - 1.09896i) q^{52} +(-3.09247 + 0.466115i) q^{53} +(-4.24924 + 2.04633i) q^{54} +(-0.161967 - 0.150283i) q^{55} +(1.98576 + 0.299306i) q^{56} +(8.96389 - 2.76499i) q^{57} +(-0.539336 - 7.19693i) q^{58} +(-5.30630 - 6.65389i) q^{59} +(0.680270 - 1.73330i) q^{60} +(0.213073 - 0.197702i) q^{61} +(-2.37601 + 1.61993i) q^{62} +(-0.0700979 + 0.935392i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-0.434108 - 1.90195i) q^{65} +(0.0307447 - 0.410260i) q^{66} +(3.70043 - 2.52291i) q^{67} +(2.46712 - 2.28916i) q^{68} +(5.10860 - 13.0165i) q^{69} +(1.25209 + 1.57007i) q^{70} +(0.0301273 + 0.402021i) q^{71} +(0.446342 - 0.137678i) q^{72} +(8.36685 + 1.26110i) q^{73} +(-0.725304 - 0.672984i) q^{74} +(1.67762 - 0.807897i) q^{75} +(4.98163 - 0.750860i) q^{76} +(0.366609 + 0.249950i) q^{77} +(2.26485 - 2.84003i) q^{78} +(8.79305 + 15.2300i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-3.72031 - 9.47918i) q^{81} +(0.167352 + 0.0805927i) q^{82} +(-5.34845 - 1.64978i) q^{83} +(-0.832069 + 3.64553i) q^{84} +3.36555 q^{85} +(-6.49039 - 0.935335i) q^{86} +13.4384 q^{87} +(0.0491658 - 0.215409i) q^{88} +(-3.50976 - 1.08262i) q^{89} +(0.420837 + 0.202664i) q^{90} +(1.43130 + 3.64690i) q^{91} +(3.75484 - 6.50357i) q^{92} +(-2.67729 - 4.63720i) q^{93} +(-3.18110 + 3.98897i) q^{94} +(4.16251 + 2.83795i) q^{95} +(1.84122 - 0.277519i) q^{96} +(3.20309 - 1.54253i) q^{97} +(2.17508 + 2.01818i) q^{98} +(0.102051 + 0.0153817i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9}+O(q^{10}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9} - 4 q^{10} - 9 q^{11} - q^{12} - 11 q^{13} + 7 q^{14} - 6 q^{15} - 8 q^{16} - 11 q^{17} - 15 q^{18} + 31 q^{19} - 4 q^{20} + 4 q^{21} + 12 q^{22} + 4 q^{23} + 6 q^{24} + 4 q^{25} + 31 q^{26} + 44 q^{27} + 13 q^{29} + q^{30} - q^{31} - 8 q^{32} - 30 q^{33} - 25 q^{34} + 14 q^{35} - 36 q^{36} - 27 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{40} + 16 q^{41} + 4 q^{42} - 7 q^{43} - 30 q^{44} + 12 q^{45} - 52 q^{46} - 43 q^{47} - q^{48} - 23 q^{49} - 24 q^{50} - 7 q^{51} - 25 q^{52} + 73 q^{53} - 61 q^{54} + 27 q^{55} + 7 q^{56} + 136 q^{57} - 36 q^{58} + 58 q^{59} + q^{60} - 61 q^{61} + 27 q^{62} + 32 q^{63} - 8 q^{64} - q^{65} + 12 q^{66} + 39 q^{67} + 17 q^{68} - 34 q^{69} + 14 q^{70} + 60 q^{71} + 27 q^{72} + 3 q^{73} + 29 q^{74} - 12 q^{75} + 17 q^{76} - 27 q^{77} - 17 q^{78} - 2 q^{79} + 24 q^{80} - 165 q^{81} + 2 q^{82} + 74 q^{83} + 4 q^{84} - 8 q^{85} + 14 q^{86} + 88 q^{87} + 12 q^{88} + 23 q^{89} - 2 q^{90} - 39 q^{91} + 4 q^{92} - 46 q^{93} + 55 q^{94} - 31 q^{95} - q^{96} - 85 q^{97} + 33 q^{98} - 168 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9 - 4 * q^10 - 9 * q^11 - q^12 - 11 * q^13 + 7 * q^14 - 6 * q^15 - 8 * q^16 - 11 * q^17 - 15 * q^18 + 31 * q^19 - 4 * q^20 + 4 * q^21 + 12 * q^22 + 4 * q^23 + 6 * q^24 + 4 * q^25 + 31 * q^26 + 44 * q^27 + 13 * q^29 + q^30 - q^31 - 8 * q^32 - 30 * q^33 - 25 * q^34 + 14 * q^35 - 36 * q^36 - 27 * q^37 - 4 * q^38 + 4 * q^39 - 4 * q^40 + 16 * q^41 + 4 * q^42 - 7 * q^43 - 30 * q^44 + 12 * q^45 - 52 * q^46 - 43 * q^47 - q^48 - 23 * q^49 - 24 * q^50 - 7 * q^51 - 25 * q^52 + 73 * q^53 - 61 * q^54 + 27 * q^55 + 7 * q^56 + 136 * q^57 - 36 * q^58 + 58 * q^59 + q^60 - 61 * q^61 + 27 * q^62 + 32 * q^63 - 8 * q^64 - q^65 + 12 * q^66 + 39 * q^67 + 17 * q^68 - 34 * q^69 + 14 * q^70 + 60 * q^71 + 27 * q^72 + 3 * q^73 + 29 * q^74 - 12 * q^75 + 17 * q^76 - 27 * q^77 - 17 * q^78 - 2 * q^79 + 24 * q^80 - 165 * q^81 + 2 * q^82 + 74 * q^83 + 4 * q^84 - 8 * q^85 + 14 * q^86 + 88 * q^87 + 12 * q^88 + 23 * q^89 - 2 * q^90 - 39 * q^91 + 4 * q^92 - 46 * q^93 + 55 * q^94 - 31 * q^95 - q^96 - 85 * q^97 + 33 * q^98 - 168 * q^99

Introduction

L-functions

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