LMFDB - Embedded newform 354.2.e.b.253.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$2$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			253.1
Character	$\chi$	$=$	354.253
Dual form			354.2.e.b.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.561187 - 0.827689i) q^{2} +(-0.0541389 - 0.998533i) q^{3} +(-0.370138 - 0.928977i) q^{4} +(-2.31715 - 1.07203i) q^{5} +(-0.856857 - 0.515554i) q^{6} +(0.0770120 + 0.277372i) q^{7} +(-0.976621 - 0.214970i) q^{8} +(-0.994138 + 0.108119i) q^{9} +O(q^{10})$	\(q+(0.561187 - 0.827689i) q^{2} +(-0.0541389 - 0.998533i) q^{3} +(-0.370138 - 0.928977i) q^{4} +(-2.31715 - 1.07203i) q^{5} +(-0.856857 - 0.515554i) q^{6} +(0.0770120 + 0.277372i) q^{7} +(-0.976621 - 0.214970i) q^{8} +(-0.994138 + 0.108119i) q^{9} +(-2.18766 + 1.31627i) q^{10} +(-2.41351 - 2.28620i) q^{11} +(-0.907575 + 0.419889i) q^{12} +(-1.39566 - 0.151787i) q^{13} +(0.272796 + 0.0919157i) q^{14} +(-0.945008 + 2.37179i) q^{15} +(-0.725995 + 0.687699i) q^{16} +(0.514946 - 1.85467i) q^{17} +(-0.468408 + 0.883512i) q^{18} +(1.40611 + 1.06890i) q^{19} +(-0.138223 + 2.54938i) q^{20} +(0.272796 - 0.0919157i) q^{21} +(-3.24669 + 0.714651i) q^{22} +(-1.00267 - 1.89123i) q^{23} +(-0.161782 + 0.986827i) q^{24} +(0.983010 + 1.15729i) q^{25} +(-0.908858 + 1.06999i) q^{26} +(0.161782 + 0.986827i) q^{27} +(0.229167 - 0.174208i) q^{28} +(-0.623479 - 0.919563i) q^{29} +(1.43278 + 2.11319i) q^{30} +(0.832355 - 0.632740i) q^{31} +(0.161782 + 0.986827i) q^{32} +(-2.15218 + 2.53374i) q^{33} +(-1.24611 - 1.46703i) q^{34} +(0.118902 - 0.725272i) q^{35} +(0.468408 + 0.883512i) q^{36} +(4.55780 - 1.00325i) q^{37} +(1.67381 - 0.563972i) q^{38} +(-0.0760049 + 1.40183i) q^{39} +(2.03252 + 1.54508i) q^{40} +(2.72425 - 5.13848i) q^{41} +(0.0770120 - 0.277372i) q^{42} +(2.30538 - 2.18378i) q^{43} +(-1.23049 + 3.08831i) q^{44} +(2.41947 + 0.815216i) q^{45} +(-2.12803 - 0.231438i) q^{46} +(4.52581 - 2.09386i) q^{47} +(0.725995 + 0.687699i) q^{48} +(5.92700 - 3.56616i) q^{49} +(1.50953 - 0.164171i) q^{50} +(-1.87983 - 0.413781i) q^{51} +(0.375580 + 1.35272i) q^{52} +(-1.51146 - 0.909416i) q^{53} +(0.907575 + 0.419889i) q^{54} +(3.14160 + 7.88482i) q^{55} +(-0.0155847 - 0.287443i) q^{56} +(0.991206 - 1.46192i) q^{57} -1.11100 q^{58} +(-4.43334 - 6.27260i) q^{59} +2.55312 q^{60} +(-0.430491 + 0.634927i) q^{61} +(-0.0566049 - 1.04402i) q^{62} +(-0.106550 - 0.267420i) q^{63} +(0.907575 + 0.419889i) q^{64} +(3.07123 + 1.84790i) q^{65} +(0.889376 + 3.20324i) q^{66} +(-9.18997 - 2.02287i) q^{67} +(-1.91355 + 0.208111i) q^{68} +(-1.83417 + 1.10359i) q^{69} +(-0.533573 - 0.505428i) q^{70} +(-2.47220 + 1.14376i) q^{71} +(0.994138 + 0.108119i) q^{72} +(8.49301 + 2.86163i) q^{73} +(1.72740 - 4.33545i) q^{74} +(1.10237 - 1.04422i) q^{75} +(0.472527 - 1.70189i) q^{76} +(0.448259 - 0.845506i) q^{77} +(1.11763 + 0.849597i) q^{78} +(-0.475896 + 8.77738i) q^{79} +(2.41947 - 0.815216i) q^{80} +(0.976621 - 0.214970i) q^{81} +(-2.72425 - 5.13848i) q^{82} +(2.16274 - 13.1922i) q^{83} +(-0.186360 - 0.219400i) q^{84} +(-3.18146 + 3.74551i) q^{85} +(-0.513735 - 3.13365i) q^{86} +(-0.884460 + 0.672349i) q^{87} +(1.86562 + 2.75158i) q^{88} +(8.92466 + 13.1629i) q^{89} +(2.03252 - 1.54508i) q^{90} +(-0.0653810 - 0.398806i) q^{91} +(-1.38578 + 1.63147i) q^{92} +(-0.676875 - 0.796879i) q^{93} +(0.806759 - 4.92101i) q^{94} +(-2.11229 - 3.98419i) q^{95} +(0.976621 - 0.214970i) q^{96} +(5.15668 - 1.73749i) q^{97} +(0.374486 - 6.90699i) q^{98} +(2.64654 + 2.01185i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} + 30 q^{11} + 2 q^{12} + 5 q^{13} + 28 q^{14} + 2 q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 28 q^{21} - q^{22} - 2 q^{23} - 2 q^{24} + 64 q^{25} - 34 q^{26} + 2 q^{27} + q^{28} + 8 q^{29} - 2 q^{30} + 2 q^{32} - q^{33} + 32 q^{34} - 87 q^{35} - 2 q^{36} + 47 q^{37} + 4 q^{38} - 5 q^{39} + 2 q^{40} + 3 q^{41} + q^{42} - 61 q^{43} + q^{44} - 2 q^{45} - 27 q^{46} + 50 q^{47} + 2 q^{48} - 45 q^{49} - 6 q^{50} + 3 q^{51} - 24 q^{52} - 27 q^{53} - 2 q^{54} - 95 q^{55} - q^{56} + 4 q^{57} + 50 q^{58} - 58 q^{59} + 2 q^{60} - 74 q^{61} - 29 q^{62} + q^{63} - 2 q^{64} - 17 q^{65} + q^{66} + 4 q^{67} - 32 q^{68} + 31 q^{69} - 58 q^{70} - 47 q^{71} + 2 q^{72} + 43 q^{73} - 18 q^{74} - 6 q^{75} - 33 q^{76} - 5 q^{77} + 5 q^{78} + 19 q^{79} - 2 q^{80} - 2 q^{81} - 3 q^{82} + 47 q^{83} - q^{84} - 149 q^{85} - 55 q^{86} + 21 q^{87} + 28 q^{88} + 36 q^{89} + 2 q^{90} + 175 q^{91} - 2 q^{92} - 29 q^{93} - 21 q^{94} + 50 q^{95} - 2 q^{96} + 10 q^{97} - 13 q^{98} + q^{99}+O(q^{100}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 + 30 * q^11 + 2 * q^12 + 5 * q^13 + 28 * q^14 + 2 * q^15 - 2 * q^16 - 3 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 28 * q^21 - q^22 - 2 * q^23 - 2 * q^24 + 64 * q^25 - 34 * q^26 + 2 * q^27 + q^28 + 8 * q^29 - 2 * q^30 + 2 * q^32 - q^33 + 32 * q^34 - 87 * q^35 - 2 * q^36 + 47 * q^37 + 4 * q^38 - 5 * q^39 + 2 * q^40 + 3 * q^41 + q^42 - 61 * q^43 + q^44 - 2 * q^45 - 27 * q^46 + 50 * q^47 + 2 * q^48 - 45 * q^49 - 6 * q^50 + 3 * q^51 - 24 * q^52 - 27 * q^53 - 2 * q^54 - 95 * q^55 - q^56 + 4 * q^57 + 50 * q^58 - 58 * q^59 + 2 * q^60 - 74 * q^61 - 29 * q^62 + q^63 - 2 * q^64 - 17 * q^65 + q^66 + 4 * q^67 - 32 * q^68 + 31 * q^69 - 58 * q^70 - 47 * q^71 + 2 * q^72 + 43 * q^73 - 18 * q^74 - 6 * q^75 - 33 * q^76 - 5 * q^77 + 5 * q^78 + 19 * q^79 - 2 * q^80 - 2 * q^81 - 3 * q^82 + 47 * q^83 - q^84 - 149 * q^85 - 55 * q^86 + 21 * q^87 + 28 * q^88 + 36 * q^89 + 2 * q^90 + 175 * q^91 - 2 * q^92 - 29 * q^93 - 21 * q^94 + 50 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{20}{29}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.561187	−	0.827689i	0.396819	−	0.585265i
$2$	0.561187	−	0.827689i	0.396819	−	0.585265i
$3$	−0.0541389	−	0.998533i	−0.0312571	−	0.576504i
$3$	−0.0541389	−	0.998533i	−0.0312571	−	0.576504i
$4$	−0.370138	−	0.928977i	−0.185069	−	0.464488i
$5$	−2.31715	−	1.07203i	−1.03626	−	0.479425i	−0.173392	−	0.984853i	$-0.555473\pi$
$5$	−2.31715	−	1.07203i	−1.03626	−	0.479425i	−0.862869	+	0.505427i	$0.831335\pi$
$6$	−0.856857	−	0.515554i	−0.349810	−	0.210474i
$7$	0.0770120	+	0.277372i	0.0291078	+	0.104837i	0.976677	−	0.214714i	$-0.0688819\pi$
$7$	0.0770120	+	0.277372i	0.0291078	+	0.104837i	−0.947569	+	0.319551i	$0.896468\pi$
$8$	−0.976621	−	0.214970i	−0.345288	−	0.0760035i
$9$	−0.994138	+	0.108119i	−0.331379	+	0.0360397i
$10$	−2.18766	+	1.31627i	−0.691799	+	0.416242i
$11$	−2.41351	−	2.28620i	−0.727701	−	0.689315i	0.231248	−	0.972895i	$-0.425719\pi$
$11$	−2.41351	−	2.28620i	−0.727701	−	0.689315i	−0.958949	+	0.283580i	$0.908478\pi$
$12$	−0.907575	+	0.419889i	−0.261994	+	0.121212i
$13$	−1.39566	−	0.151787i	−0.387086	−	0.0420981i	−0.0874927	−	0.996165i	$-0.527885\pi$
$13$	−1.39566	−	0.151787i	−0.387086	−	0.0420981i	−0.299593	+	0.954067i	$0.596851\pi$
$14$	0.272796	+	0.0919157i	0.0729078	+	0.0245655i
$15$	−0.945008	+	2.37179i	−0.244000	+	0.612394i
$16$	−0.725995	+	0.687699i	−0.181499	+	0.171925i
$17$	0.514946	−	1.85467i	0.124893	−	0.449823i	−0.874487	−	0.485050i	$-0.838801\pi$
$17$	0.514946	−	1.85467i	0.124893	−	0.449823i	0.999379	+	0.0352265i	$0.0112153\pi$
$18$	−0.468408	+	0.883512i	−0.110405	+	0.208246i
$19$	1.40611	+	1.06890i	0.322585	+	0.245222i	0.753916	−	0.656971i	$-0.228163\pi$
$19$	1.40611	+	1.06890i	0.322585	+	0.245222i	−0.431331	+	0.902194i	$0.641956\pi$
$20$	−0.138223	+	2.54938i	−0.0309076	+	0.570058i
$21$	0.272796	−	0.0919157i	0.0595290	−	0.0200577i
$22$	−3.24669	+	0.714651i	−0.692197	+	0.152364i
$23$	−1.00267	−	1.89123i	−0.209071	−	0.394349i	0.756694	−	0.653769i	$-0.226813\pi$
$23$	−1.00267	−	1.89123i	−0.209071	−	0.394349i	−0.965764	+	0.259420i	$0.916468\pi$
$24$	−0.161782	+	0.986827i	−0.0330236	+	0.201435i
$25$	0.983010	+	1.15729i	0.196602	+	0.231458i
$26$	−0.908858	+	1.06999i	−0.178242	+	0.209842i
$27$	0.161782	+	0.986827i	0.0311350	+	0.189915i
$28$	0.229167	−	0.174208i	0.0433085	−	0.0329223i
$29$	−0.623479	−	0.919563i	−0.115777	−	0.170759i	0.765385	−	0.643573i	$-0.222549\pi$
$29$	−0.623479	−	0.919563i	−0.115777	−	0.170759i	−0.881162	+	0.472814i	$0.843238\pi$
$30$	1.43278	+	2.11319i	0.261588	+	0.385814i
$31$	0.832355	−	0.632740i	0.149495	−	0.113643i	−0.527753	−	0.849398i	$-0.676965\pi$
$31$	0.832355	−	0.632740i	0.149495	−	0.113643i	0.677248	+	0.735754i	$0.263172\pi$
$32$	0.161782	+	0.986827i	0.0285993	+	0.174448i
$33$	−2.15218	+	2.53374i	−0.374647	+	0.441068i
$34$	−1.24611	−	1.46703i	−0.213706	−	0.251594i
$35$	0.118902	−	0.725272i	0.0200982	−	0.122593i
$36$	0.468408	+	0.883512i	0.0780681	+	0.147252i
$37$	4.55780	−	1.00325i	0.749298	−	0.164933i	0.176126	−	0.984368i	$-0.443644\pi$
$37$	4.55780	−	1.00325i	0.749298	−	0.164933i	0.573173	+	0.819435i	$0.305712\pi$
$38$	1.67381	−	0.563972i	0.271528	−	0.0914883i
$39$	−0.0760049	+	1.40183i	−0.0121705	+	0.224472i
$40$	2.03252	+	1.54508i	0.321370	+	0.244299i
$41$	2.72425	−	5.13848i	0.425457	−	0.802496i	−0.574414	−	0.818565i	$-0.694770\pi$
$41$	2.72425	−	5.13848i	0.425457	−	0.802496i	0.999871	+	0.0160685i	$0.00511498\pi$
$42$	0.0770120	−	0.277372i	0.0118832	−	0.0427995i
$43$	2.30538	−	2.18378i	0.351568	−	0.333023i	−0.491453	−	0.870904i	$-0.663534\pi$
$43$	2.30538	−	2.18378i	0.351568	−	0.333023i	0.843020	+	0.537882i	$0.180775\pi$
$44$	−1.23049	+	3.08831i	−0.185504	+	0.465580i
$45$	2.41947	+	0.815216i	0.360674	+	0.121525i
$46$	−2.12803	−	0.231438i	−0.313762	−	0.0341236i
$47$	4.52581	−	2.09386i	0.660158	−	0.305421i	−0.0610559	−	0.998134i	$-0.519447\pi$
$47$	4.52581	−	2.09386i	0.660158	−	0.305421i	0.721213	+	0.692713i	$0.243585\pi$
$48$	0.725995	+	0.687699i	0.104788	+	0.0992609i
$49$	5.92700	−	3.56616i	0.846714	−	0.509451i
$50$	1.50953	−	0.164171i	0.213479	−	0.0232173i
$51$	−1.87983	−	0.413781i	−0.263229	−	0.0579410i
$52$	0.375580	+	1.35272i	0.0520835	+	0.187588i
$53$	−1.51146	−	0.909416i	−0.207615	−	0.124918i	0.407949	−	0.913005i	$-0.366244\pi$
$53$	−1.51146	−	0.909416i	−0.207615	−	0.124918i	−0.615564	+	0.788087i	$0.711072\pi$
$54$	0.907575	+	0.419889i	0.123505	+	0.0571397i
$55$	3.14160	+	7.88482i	0.423613	+	1.06319i
$56$	−0.0155847	−	0.287443i	−0.00208259	−	0.0384112i
$57$	0.991206	−	1.46192i	0.131289	−	0.193636i
$58$	−1.11100			−0.145882
$59$	−4.43334	−	6.27260i	−0.577172	−	0.816623i
$59$	−4.43334	−	6.27260i	−0.577172	−	0.816623i
$60$	2.55312			0.329607
$61$	−0.430491	+	0.634927i	−0.0551187	+	0.0812940i	−0.854250	−	0.519863i	$-0.825983\pi$
$61$	−0.430491	+	0.634927i	−0.0551187	+	0.0812940i	0.799131	+	0.601157i	$0.205293\pi$
$62$	−0.0566049	−	1.04402i	−0.00718883	−	0.132590i
$63$	−0.106550	−	0.267420i	−0.0134240	−	0.0336917i
$64$	0.907575	+	0.419889i	0.113447	+	0.0524861i
$65$	3.07123	+	1.84790i	0.380939	+	0.229203i
$66$	0.889376	+	3.20324i	0.109475	+	0.394292i
$67$	−9.18997	−	2.02287i	−1.12273	−	0.247132i	−0.385459	−	0.922725i	$-0.625957\pi$
$67$	−9.18997	−	2.02287i	−1.12273	−	0.247132i	−0.737275	+	0.675593i	$0.763888\pi$
$68$	−1.91355	+	0.208111i	−0.232052	+	0.0252371i
$69$	−1.83417	+	1.10359i	−0.220809	+	0.132856i
$70$	−0.533573	−	0.505428i	−0.0637742	−	0.0604101i
$71$	−2.47220	+	1.14376i	−0.293396	+	0.135739i	−0.561066	−	0.827771i	$-0.689608\pi$
$71$	−2.47220	+	1.14376i	−0.293396	+	0.135739i	0.267670	+	0.963511i	$0.413746\pi$
$72$	0.994138	+	0.108119i	0.117160	+	0.0127419i
$73$	8.49301	+	2.86163i	0.994032	+	0.334928i	0.768878	−	0.639395i	$-0.220815\pi$
$73$	8.49301	+	2.86163i	0.994032	+	0.334928i	0.225153	+	0.974323i	$0.427712\pi$
$74$	1.72740	−	4.33545i	0.200806	−	0.503986i
$75$	1.10237	−	1.04422i	0.127291	−	0.120576i
$76$	0.472527	−	1.70189i	0.0542025	−	0.195220i
$77$	0.448259	−	0.845506i	0.0510838	−	0.0963543i
$78$	1.11763	+	0.849597i	0.126546	+	0.0961979i
$79$	−0.475896	+	8.77738i	−0.0535425	+	0.987532i	0.841137	+	0.540823i	$0.181887\pi$
$79$	−0.475896	+	8.77738i	−0.0535425	+	0.987532i	−0.894679	+	0.446710i	$0.852596\pi$
$80$	2.41947	−	0.815216i	0.270505	−	0.0911439i
$81$	0.976621	−	0.214970i	0.108513	−	0.0238856i
$82$	−2.72425	−	5.13848i	−0.300843	−	0.567451i
$83$	2.16274	−	13.1922i	0.237392	−	1.44803i	−0.551850	−	0.833944i	$-0.686078\pi$
$83$	2.16274	−	13.1922i	0.237392	−	1.44803i	0.789241	−	0.614083i	$-0.210474\pi$
$84$	−0.186360	−	0.219400i	−0.0203335	−	0.0239385i
$85$	−3.18146	+	3.74551i	−0.345078	+	0.406258i
$86$	−0.513735	−	3.13365i	−0.0553975	−	0.337910i
$87$	−0.884460	+	0.672349i	−0.0948241	+	0.0720834i
$88$	1.86562	+	2.75158i	0.198876	+	0.293320i
$89$	8.92466	+	13.1629i	0.946012	+	1.39526i	0.918404	+	0.395645i	$0.129479\pi$
$89$	8.92466	+	13.1629i	0.946012	+	1.39526i	0.0276086	+	0.999619i	$0.491211\pi$
$90$	2.03252	−	1.54508i	0.214247	−	0.162866i
$91$	−0.0653810	−	0.398806i	−0.00685379	−	0.0418062i
$92$	−1.38578	+	1.63147i	−0.144478	+	0.170093i
$93$	−0.676875	−	0.796879i	−0.0701886	−	0.0826325i
$94$	0.806759	−	4.92101i	0.0832109	−	0.507564i
$95$	−2.11229	−	3.98419i	−0.216716	−	0.408770i
$96$	0.976621	−	0.214970i	0.0996759	−	0.0219403i
$97$	5.15668	−	1.73749i	0.523582	−	0.176415i	−0.0450852	−	0.998983i	$-0.514356\pi$
$97$	5.15668	−	1.73749i	0.523582	−	0.176415i	0.568667	+	0.822568i	$0.307459\pi$
$98$	0.374486	−	6.90699i	0.0378288	−	0.697711i
$99$	2.64654	+	2.01185i	0.265988	+	0.202199i
$100$	0.711245	−	1.34155i	0.0711245	−	0.134155i
$101$	2.15451	−	7.75984i	0.214382	−	0.772133i	−0.775635	−	0.631182i	$-0.782570\pi$
$101$	2.15451	−	7.75984i	0.214382	−	0.772133i	0.990017	−	0.140951i	$-0.0450161\pi$
$102$	−1.39742	+	1.32370i	−0.138365	+	0.131066i
$103$	−4.34215	+	10.8980i	−0.427844	+	1.07381i	0.544188	+	0.838963i	$0.316838\pi$
$103$	−4.34215	+	10.8980i	−0.427844	+	1.07381i	−0.972033	+	0.234846i	$0.924542\pi$
$104$	1.33040	+	0.448263i	0.130456	+	0.0439558i
$105$	−0.730646	−	0.0794625i	−0.0713037	−	0.00775475i
$106$	−1.60093	+	0.740667i	−0.155496	+	0.0719400i
$107$	−1.99313	−	1.88799i	−0.192683	−	0.182519i	0.585276	−	0.810834i	$-0.300986\pi$
$107$	−1.99313	−	1.88799i	−0.192683	−	0.182519i	−0.777959	+	0.628315i	$0.783745\pi$
$108$	0.856857	−	0.515554i	0.0824511	−	0.0496092i
$109$	7.70020	−	0.837447i	0.737545	−	0.0802129i	0.268367	−	0.963317i	$-0.413516\pi$
$109$	7.70020	−	0.837447i	0.737545	−	0.0802129i	0.469178	+	0.883104i	$0.344550\pi$
$110$	8.28920	+	1.82459i	0.790344	+	0.173968i
$111$	−1.24853	−	4.49680i	−0.118505	−	0.426818i
$112$	−0.246659	−	0.148410i	−0.0233071	−	0.0140234i
$113$	12.7688	+	5.90748i	1.20119	+	0.555729i	0.915393	−	0.402562i	$-0.131880\pi$
$113$	12.7688	+	5.90748i	1.20119	+	0.555729i	0.285795	+	0.958291i	$0.407742\pi$
$114$	−0.653763	−	1.64082i	−0.0612305	−	0.153677i
$115$	0.295878	+	5.45715i	0.0275908	+	0.508882i
$116$	−0.623479	+	0.919563i	−0.0578886	+	0.0853793i
$117$	1.40389			0.129789
$118$	−7.67969	+	0.149324i	−0.706973	+	0.0137464i
$119$	0.554091			0.0507934
$120$	1.43278	−	2.11319i	0.130794	−	0.192907i
$121$	0.00280143	+	0.0516693i	0.000254675	+	0.00469721i
$122$	0.283936	+	0.712625i	0.0257063	+	0.0645181i
$123$	−5.27843	−	2.44206i	−0.475940	−	0.220193i
$124$	−0.895887	−	0.539037i	−0.0804530	−	0.0484070i
$125$	2.37803	+	8.56488i	0.212697	+	0.766066i
$126$	−0.281135	−	0.0618825i	−0.0250455	−	0.00551293i
$127$	−9.19836	+	1.00038i	−0.816222	+	0.0887695i	−0.506700	−	0.862123i	$-0.669135\pi$
$127$	−9.19836	+	1.00038i	−0.816222	+	0.0887695i	−0.309523	+	0.950892i	$0.600169\pi$
$128$	0.856857	−	0.515554i	0.0757362	−	0.0455690i
$129$	−2.30538	−	2.18378i	−0.202978	−	0.192271i
$130$	3.25302	−	1.50501i	0.285309	−	0.131998i
$131$	−18.7539	−	2.03961i	−1.63854	−	0.178202i	−0.758026	−	0.652224i	$-0.773836\pi$
$131$	−18.7539	−	2.03961i	−1.63854	−	0.178202i	−0.880513	+	0.474023i	$0.842801\pi$
$132$	3.15039	+	1.06149i	0.274207	+	0.0923910i
$133$	−0.188195	+	0.472335i	−0.0163186	+	0.0409566i
$134$	−6.83160	+	6.47123i	−0.590160	+	0.559029i
$135$	0.683032	−	2.46006i	0.0587861	−	0.211728i
$136$	−0.901606	+	1.70061i	−0.0773121	+	0.145826i
$137$	−3.09546	−	2.35311i	−0.264463	−	0.201039i	0.464536	−	0.885554i	$-0.346221\pi$
$137$	−3.09546	−	2.35311i	−0.264463	−	0.201039i	−0.728999	+	0.684515i	$0.760014\pi$
$138$	−0.115889	+	2.13744i	−0.00986511	+	0.181951i
$139$	4.76096	−	1.60415i	0.403819	−	0.136063i	−0.110060	−	0.993925i	$-0.535104\pi$
$139$	4.76096	−	1.60415i	0.403819	−	0.136063i	0.513880	+	0.857862i	$0.328208\pi$
$140$	−0.717771	+	0.157993i	−0.0606627	+	0.0133529i
$141$	−2.33582	−	4.40581i	−0.196711	−	0.371037i
$142$	−0.440688	+	2.68808i	−0.0369817	+	0.225578i
$143$	3.02142	+	3.55709i	0.252664	+	0.297459i
$144$	0.647386	−	0.762162i	0.0539489	−	0.0635135i
$145$	0.458898	+	2.79915i	0.0381094	+	0.232457i
$146$	7.13471	−	5.42366i	0.590472	−	0.448866i
$147$	−3.88181	−	5.72524i	−0.320166	−	0.472209i
$148$	−2.61901	−	3.86275i	−0.215281	−	0.317516i
$149$	−9.01359	+	6.85195i	−0.738422	+	0.561334i	−0.905366	−	0.424633i	$-0.860403\pi$
$149$	−9.01359	+	6.85195i	−0.738422	+	0.561334i	0.166944	+	0.985966i	$0.446610\pi$
$150$	−0.245654	−	1.49843i	−0.0200576	−	0.122346i
$151$	−13.2198	+	15.5635i	−1.07581	+	1.26654i	−0.113804	+	0.993503i	$0.536304\pi$
$151$	−13.2198	+	15.5635i	−1.07581	+	1.26654i	−0.962004	+	0.273036i	$0.911972\pi$
$152$	−1.14346	−	1.34618i	−0.0927466	−	0.109190i
$153$	−0.311403	+	1.89947i	−0.0251754	+	0.153563i
$154$	−0.448259	−	0.845506i	−0.0361217	−	0.0681328i
$155$	−2.60701	+	0.573846i	−0.209400	+	0.0460924i
$156$	1.33040	−	0.448263i	0.106517	−	0.0358898i
$157$	0.981424	−	18.1013i	0.0783262	−	1.44464i	−0.650273	−	0.759701i	$-0.725345\pi$
$157$	0.981424	−	18.1013i	0.0783262	−	1.44464i	0.728599	−	0.684940i	$-0.240172\pi$
$158$	6.99787	+	5.31965i	0.556721	+	0.423208i
$159$	−0.826254	+	1.55848i	−0.0655262	+	0.123595i
$160$	0.683032	−	2.46006i	0.0539984	−	0.194485i
$161$	0.447358	−	0.423760i	0.0352567	−	0.0333969i
$162$	0.370138	−	0.928977i	0.0290808	−	0.0729873i
$163$	−3.85638	−	1.29937i	−0.302055	−	0.101774i	0.164193	−	0.986428i	$-0.447498\pi$
$163$	−3.85638	−	1.29937i	−0.302055	−	0.101774i	−0.466248	+	0.884654i	$0.654395\pi$
$164$	−5.78188	−	0.628817i	−0.451489	−	0.0491024i
$165$	7.70317	−	3.56387i	0.599691	−	0.277447i
$166$	−9.70529	−	9.19334i	−0.753277	−	0.713542i
$167$	1.66326	−	1.00075i	0.128707	−	0.0774403i	−0.449744	−	0.893157i	$-0.648485\pi$
$167$	1.66326	−	1.00075i	0.128707	−	0.0774403i	0.578451	+	0.815717i	$0.303657\pi$
$168$	−0.286177	+	0.0311237i	−0.0220791	+	0.00240124i
$169$	−10.7712	−	2.37093i	−0.828557	−	0.182379i
$170$	1.31472	+	4.73520i	0.100834	+	0.363173i
$171$	−1.51344	−	0.910606i	−0.115736	−	0.0696358i
$172$	−2.88199	−	1.33335i	−0.219749	−	0.101667i
$173$	9.04690	+	22.7060i	0.687823	+	1.72631i	0.687371	+	0.726306i	$0.258764\pi$
$173$	9.04690	+	22.7060i	0.687823	+	1.72631i	0.000451745		1.00000i	$0.499856\pi$
$174$	0.0601484	+	1.10937i	0.00455984	+	0.0841012i
$175$	−0.245296	+	0.361785i	−0.0185426	+	0.0273484i
$176$	3.32442			0.250587
$177$	−6.02338	+	4.76643i	−0.452745	+	0.358267i
$178$	15.9032			1.19199
$179$	−7.51210	+	11.0795i	−0.561481	+	0.828122i	−0.997415	−	0.0718563i	$-0.977108\pi$
$179$	−7.51210	+	11.0795i	−0.561481	+	0.828122i	0.435934	+	0.899979i	$0.356418\pi$
$180$	−0.138223	−	2.54938i	−0.0103025	−	0.190019i
$181$	3.07073	+	7.70694i	0.228245	+	0.572852i	0.997841	−	0.0656794i	$-0.0209214\pi$
$181$	3.07073	+	7.70694i	0.228245	+	0.572852i	−0.769596	+	0.638532i	$0.779542\pi$
$182$	−0.366778	−	0.169690i	−0.0271874	−	0.0125782i
$183$	0.657302	+	0.395485i	0.0485892	+	0.0292351i
$184$	0.572667	+	2.06256i	0.0422175	+	0.152054i
$185$	−11.6366	−	2.56141i	−0.855542	−	0.188319i
$186$	−1.03942	+	0.113044i	−0.0762140	+	0.00828878i
$187$	−5.48297	+	3.29900i	−0.400955	+	0.241246i
$188$	−3.62033	−	3.42936i	−0.264039	−	0.250111i
$189$	−0.261259	+	0.120871i	−0.0190038	+	0.00879210i
$190$	−4.48306	−	0.487562i	−0.325235	−	0.0353715i
$191$	−10.3584	−	3.49016i	−0.749509	−	0.252539i	−0.0814810	−	0.996675i	$-0.525965\pi$
$191$	−10.3584	−	3.49016i	−0.749509	−	0.252539i	−0.668028	+	0.744136i	$0.732862\pi$
$192$	0.370138	−	0.928977i	0.0267124	−	0.0670431i
$193$	12.5134	−	11.8533i	0.900733	−	0.853220i	−0.0890169	−	0.996030i	$-0.528373\pi$
$193$	12.5134	−	11.8533i	0.900733	−	0.853220i	0.989750	+	0.142810i	$0.0456139\pi$
$194$	1.45576	−	5.24318i	0.104518	−	0.376439i
$195$	1.67891	−	3.16677i	0.120230	−	0.226777i
$196$	−5.50668	−	4.18607i	−0.393334	−	0.299005i
$197$	−0.699667	+	12.9046i	−0.0498492	+	0.919414i	0.861494	+	0.507767i	$0.169529\pi$
$197$	−0.699667	+	12.9046i	−0.0498492	+	0.919414i	−0.911343	+	0.411647i	$0.864954\pi$
$198$	3.15039	−	1.06149i	0.223889	−	0.0754369i
$199$	12.7498	−	2.80644i	0.903809	−	0.198944i	0.261333	−	0.965249i	$-0.415838\pi$
$199$	12.7498	−	2.80644i	0.903809	−	0.198944i	0.642477	+	0.766305i	$0.277907\pi$
$200$	−0.711245	−	1.34155i	−0.0502926	−	0.0948619i
$201$	−1.52236	+	9.28601i	−0.107379	+	0.654985i
$202$	−5.21365	−	6.13799i	−0.366831	−	0.431867i
$203$	0.207046	−	0.243753i	0.0145318	−	0.0171081i
$204$	0.311403	+	1.89947i	0.0218026	+	0.132990i
$205$	−11.8211	+	8.98616i	−0.825621	+	0.627621i
$206$	6.58337	+	9.70975i	0.458685	+	0.676510i
$207$	1.20127	+	1.77174i	0.0834939	+	0.123144i
$208$	1.11763	−	0.849597i	0.0774934	−	0.0589089i
$209$	−0.949953	−	5.79446i	−0.0657096	−	0.400811i
$210$	−0.475799	+	0.560154i	−0.0328333	+	0.0386543i
$211$	−17.1556	−	20.1971i	−1.18104	−	1.39043i	−0.902880	−	0.429892i	$-0.858551\pi$
$211$	−17.1556	−	20.1971i	−1.18104	−	1.39043i	−0.278160	−	0.960535i	$-0.589724\pi$
$212$	−0.285377	+	1.74072i	−0.0195998	+	0.119553i
$213$	1.27593	+	2.40665i	0.0874250	+	0.164901i
$214$	−2.68119	+	0.590174i	−0.183282	+	0.0403434i
$215$	−7.68299	+	2.58870i	−0.523975	+	0.176548i
$216$	0.0541389	−	0.998533i	0.00368369	−	0.0679416i
$217$	0.239606	+	0.182144i	0.0162655	+	0.0123647i
$218$	3.62811	−	6.84333i	0.245726	−	0.463489i
$219$	2.39763	−	8.63548i	0.162017	−	0.583532i
$220$	6.16199	−	5.83694i	0.415441	−	0.393527i
$221$	−1.00020	+	2.51032i	−0.0672810	+	0.168862i
$222$	−4.42261	−	1.49015i	−0.296826	−	0.100012i
$223$	14.8761	+	1.61788i	0.996179	+	0.108341i	0.591659	−	0.806188i	$-0.298473\pi$
$223$	14.8761	+	1.61788i	0.996179	+	0.108341i	0.404520	+	0.914529i	$0.367439\pi$
$224$	−0.261259	+	0.120871i	−0.0174561	+	0.00807606i
$225$	−1.10237	−	1.04422i	−0.0734915	−	0.0696148i
$226$	12.0552	−	7.25340i	0.801903	−	0.482489i
$227$	7.90617	−	0.859848i	0.524751	−	0.0570701i	0.158090	−	0.987425i	$-0.449466\pi$
$227$	7.90617	−	0.859848i	0.524751	−	0.0570701i	0.366661	+	0.930355i	$0.380501\pi$
$228$	−1.72497	−	0.379695i	−0.114239	−	0.0251459i
$229$	−5.42661	−	19.5449i	−0.358601	−	1.29156i	−0.894419	−	0.447229i	$-0.852411\pi$
$229$	−5.42661	−	19.5449i	−0.358601	−	1.29156i	0.535819	−	0.844333i	$-0.320003\pi$
$230$	4.68287	+	2.81759i	0.308779	+	0.185786i
$231$	−0.868534	−	0.401827i	−0.0571454	−	0.0264383i
$232$	0.411224	+	1.03209i	0.0269982	+	0.0677603i
$233$	0.578695	+	10.6734i	0.0379116	+	0.699238i	0.954282	+	0.298907i	$0.0966221\pi$
$233$	0.578695	+	10.6734i	0.0379116	+	0.699238i	−0.916371	+	0.400331i	$0.868895\pi$
$234$	0.787844	−	1.16198i	0.0515029	−	0.0759612i
$235$	−12.7317			−0.830522
$236$	−4.18615	+	6.44020i	−0.272495	+	0.419221i
$237$	8.79027			0.570990
$238$	0.310949	−	0.458615i	0.0201558	−	0.0297276i
$239$	0.942496	+	17.3833i	0.0609650	+	1.12443i	0.855698	+	0.517475i	$0.173128\pi$
$239$	0.942496	+	17.3833i	0.0609650	+	1.12443i	−0.794733	+	0.606959i	$0.792389\pi$
$240$	−0.945008	−	2.37179i	−0.0610000	−	0.153098i
$241$	0.428330	+	0.198166i	0.0275911	+	0.0127650i	0.433636	−	0.901088i	$-0.357230\pi$
$241$	0.428330	+	0.198166i	0.0275911	+	0.0127650i	−0.406045	+	0.913853i	$0.633092\pi$
$242$	0.0443382	+	0.0266774i	0.00285017	+	0.00171489i
$243$	−0.267528	−	0.963550i	−0.0171620	−	0.0618118i
$244$	0.749173	+	0.164906i	0.0479609	+	0.0105570i
$245$	−17.5568	+	1.90941i	−1.12166	+	0.121988i
$246$	−4.98346	+	2.99845i	−0.317734	+	0.191174i
$247$	−1.80021	−	1.70525i	−0.114544	−	0.108502i
$248$	−0.948916	+	0.439015i	−0.0602562	+	0.0278775i
$249$	−13.2899	−	1.44536i	−0.842213	−	0.0915961i
$250$	8.42357	+	2.83823i	0.532753	+	0.179506i
$251$	6.25889	−	15.7086i	0.395058	−	0.991520i	−0.588105	−	0.808785i	$-0.700126\pi$
$251$	6.25889	−	15.7086i	0.395058	−	0.991520i	0.983162	−	0.182735i	$-0.0584951\pi$
$252$	−0.208989	+	0.197965i	−0.0131650	+	0.0124706i
$253$	−1.90378	+	6.85680i	−0.119690	+	0.431084i
$254$	−4.33400	+	8.17478i	−0.271939	+	0.512931i
$255$	3.91226	+	2.97402i	0.244995	+	0.186240i
$256$	0.0541389	−	0.998533i	0.00338368	−	0.0624083i
$257$	−4.24217	+	1.42936i	−0.264620	+	0.0891607i	−0.448484	−	0.893791i	$-0.648036\pi$
$257$	−4.24217	+	1.42936i	−0.264620	+	0.0891607i	0.183864	+	0.982952i	$0.441139\pi$
$258$	−3.10124	+	0.682634i	−0.193075	+	0.0424990i
$259$	0.629279	+	1.18695i	0.0391015	+	0.0737532i
$260$	0.579874	−	3.53708i	0.0359623	−	0.219360i
$261$	0.719247	+	0.846763i	0.0445202	+	0.0524133i
$262$	−12.2126	+	14.3778i	−0.754499	+	0.888265i
$263$	−0.334567	−	2.04077i	−0.0206303	−	0.125839i	0.974503	−	0.224372i	$-0.0720332\pi$
$263$	−0.334567	−	2.04077i	−0.0206303	−	0.125839i	−0.995134	+	0.0985332i	$0.968585\pi$
$264$	2.64654	−	2.01185i	0.162884	−	0.123821i
$265$	2.52736	+	3.72758i	0.155255	+	0.228984i
$266$	0.285334	+	0.420836i	0.0174949	+	0.0258031i
$267$	12.6604	−	9.62420i	0.774805	−	0.588991i
$268$	1.52236	+	9.28601i	0.0929932	+	0.567233i
$269$	−8.35465	+	9.83585i	−0.509392	+	0.599702i	−0.955396	−	0.295329i	$-0.904571\pi$
$269$	−8.35465	+	9.83585i	−0.509392	+	0.599702i	0.446004	+	0.895031i	$0.352847\pi$
$270$	−1.65286	−	1.94589i	−0.100590	−	0.118423i
$271$	3.58227	−	21.8509i	0.217607	−	1.32735i	−0.621514	−	0.783403i	$-0.713482\pi$
$271$	3.58227	−	21.8509i	0.217607	−	1.32735i	0.839122	−	0.543944i	$-0.183070\pi$
$272$	0.901606	+	1.70061i	0.0546679	+	0.103115i
$273$	−0.394682	+	0.0868760i	−0.0238872	+	0.00525797i
$274$	−3.68477	+	1.24154i	−0.222605	+	0.0750044i
$275$	0.273287	−	5.04049i	0.0164798	−	0.303953i
$276$	1.70410	+	1.29543i	0.102575	+	0.0779755i
$277$	7.77218	−	14.6599i	0.466985	−	0.880827i	−0.532425	−	0.846477i	$-0.678719\pi$
$277$	7.77218	−	14.6599i	0.466985	−	0.880827i	0.999410	−	0.0343500i	$-0.0109361\pi$
$278$	1.34405	−	4.84082i	0.0806107	−	0.290333i
$279$	−0.759065	+	0.719024i	−0.0454440	+	0.0430469i
$280$	−0.272035	+	0.682755i	−0.0162572	+	0.0408024i
$281$	−17.1323	−	5.77253i	−1.02203	−	0.344360i	−0.242112	−	0.970248i	$-0.577840\pi$
$281$	−17.1323	−	5.77253i	−1.02203	−	0.344360i	−0.779913	+	0.625888i	$0.784737\pi$
$282$	−4.95747	−	0.539158i	−0.295213	−	0.0321064i
$283$	23.1976	−	10.7323i	1.37895	−	0.637971i	0.416429	−	0.909168i	$-0.363282\pi$
$283$	23.1976	−	10.7323i	1.37895	−	0.637971i	0.962524	+	0.271197i	$0.0874195\pi$
$284$	1.97758	+	1.87327i	0.117348	+	0.111158i
$285$	−3.86399	+	2.32489i	−0.228883	+	0.137714i
$286$	4.63975	−	0.504603i	0.274354	−	0.0298378i
$287$	1.63507	+	0.359907i	0.0965153	+	0.0212446i
$288$	−0.267528	−	0.963550i	−0.0157643	−	0.0567777i
$289$	11.3919	+	6.85431i	0.670114	+	0.403194i
$290$	2.57436	+	1.19102i	0.151171	+	0.0699393i
$291$	−2.01412	−	5.05505i	−0.118070	−	0.296332i
$292$	−0.485201	−	8.94901i	−0.0283942	−	0.523701i
$293$	5.15995	−	7.61036i	0.301448	−	0.444602i	−0.646554	−	0.762868i	$-0.723790\pi$
$293$	5.15995	−	7.61036i	0.301448	−	0.444602i	0.948001	+	0.318267i	$0.103101\pi$
$294$	−6.91713			−0.403415
$295$	3.54831	+	19.2872i	0.206591	+	1.12295i
$296$	−4.66691			−0.271259
$297$	1.86562	−	2.75158i	0.108254	−	0.159663i
$298$	0.612976	+	11.3057i	0.0355087	+	0.654920i
$299$	1.11232	+	2.79170i	0.0643269	+	0.161448i
$300$	−1.37809	−	0.637572i	−0.0795640	−	0.0368102i
$301$	0.783261	+	0.471273i	0.0451464	+	0.0271637i
$302$	5.46298	+	19.6759i	0.314359	+	1.13222i
$303$	−7.86510	−	1.73124i	−0.451838	−	0.0994572i
$304$	−1.75591	+	0.190967i	−0.100709	+	0.0109527i
$305$	1.67817	−	1.00972i	0.0960918	−	0.0578165i
$306$	1.39742	+	1.32370i	0.0798850	+	0.0756711i
$307$	16.9121	−	7.82436i	0.965223	−	0.446560i	0.127009	−	0.991902i	$-0.459462\pi$
$307$	16.9121	−	7.82436i	0.965223	−	0.446560i	0.838214	+	0.545342i	$0.183600\pi$
$308$	−0.951373	−	0.103468i	−0.0542095	−	0.00589564i
$309$	11.1171	+	3.74577i	0.632428	+	0.213090i
$310$	−0.988053	+	2.47983i	−0.0561176	+	0.140845i
$311$	3.31888	−	3.14381i	0.188196	−	0.178269i	−0.587800	−	0.809006i	$-0.700006\pi$
$311$	3.31888	−	3.14381i	0.188196	−	0.178269i	0.775997	+	0.630737i	$0.217247\pi$
$312$	0.375580	−	1.35272i	0.0212630	−	0.0765825i
$313$	0.678633	−	1.28004i	0.0383586	−	0.0723520i	−0.863592	−	0.504192i	$-0.831791\pi$
$313$	0.678633	−	1.28004i	0.0383586	−	0.0723520i	0.901950	+	0.431840i	$0.142135\pi$
$314$	−14.4315	−	10.9705i	−0.814416	−	0.619103i
$315$	−0.0397896	+	0.733876i	−0.00224189	+	0.0413492i
$316$	8.33013	−	2.80675i	0.468606	−	0.157892i
$317$	30.4826	−	6.70973i	1.71207	−	0.376856i	0.752561	−	0.658522i	$-0.228818\pi$
$317$	30.4826	−	6.70973i	1.71207	−	0.376856i	0.959512	+	0.281666i	$0.0908871\pi$
$318$	0.826254	+	1.55848i	0.0463340	+	0.0873952i
$319$	−0.597530	+	3.64477i	−0.0334553	+	0.204068i
$320$	−1.65286	−	1.94589i	−0.0923974	−	0.108779i
$321$	−1.77732	+	2.09242i	−0.0992001	+	0.116787i
$322$	−0.0996899	−	0.608081i	−0.00555550	−	0.0338870i
$323$	2.70653	−	2.05745i	0.150595	−	0.114480i
$324$	−0.561187	−	0.827689i	−0.0311771	−	0.0459827i
$325$	−1.19628	−	1.76439i	−0.0663579	−	0.0978706i
$326$	−3.23962	+	2.46270i	−0.179426	+	0.136396i
$327$	−1.25310	−	7.64357i	−0.0692965	−	0.422690i
$328$	−3.76518	+	4.43271i	−0.207897	+	0.244756i
$329$	0.929322	+	1.09408i	0.0512352	+	0.0603187i
$330$	1.37315	−	8.37583i	0.0755893	−	0.461074i
$331$	6.96616	+	13.1396i	0.382895	+	0.722216i	0.997794	−	0.0663897i	$-0.0211480\pi$
$331$	6.96616	+	13.1396i	0.382895	+	0.722216i	−0.614899	+	0.788606i	$0.710803\pi$
$332$	−13.0557	+	2.87378i	−0.716525	+	0.157719i
$333$	−4.42261	+	1.49015i	−0.242358	+	0.0816598i
$334$	0.105090	−	1.93827i	0.00575026	−	0.106057i
$335$	19.1260	+	14.5392i	1.04496	+	0.794361i
$336$	−0.134838	+	0.254332i	−0.00735604	+	0.0138750i
$337$	7.40602	−	26.6741i	0.403432	−	1.45303i	−0.431218	−	0.902248i	$-0.641916\pi$
$337$	7.40602	−	26.6741i	0.403432	−	1.45303i	0.834650	−	0.550781i	$-0.185670\pi$
$338$	−8.00708	+	7.58471i	−0.435528	+	0.412554i
$339$	5.20753	−	13.0699i	0.282834	−	0.709860i
$340$	4.65707	+	1.56915i	0.252565	+	0.0850991i
$341$	−3.45547	−	0.375805i	−0.187124	−	0.0203510i
$342$	−1.60302	+	0.741636i	−0.0866814	+	0.0401031i
$343$	2.90852	+	2.75510i	0.157045	+	0.148761i
$344$	−2.72093	+	1.63713i	−0.146703	+	0.0882682i
$345$	5.43313	−	0.590889i	0.292510	−	0.0318124i
$346$	23.8705	+	5.25430i	1.28329	+	0.282473i
$347$	2.35898	+	8.49627i	0.126636	+	0.456103i	0.999492	−	0.0318756i	$-0.0101480\pi$
$347$	2.35898	+	8.49627i	0.126636	+	0.456103i	−0.872855	+	0.487979i	$0.837734\pi$
$348$	0.951969	+	0.572781i	0.0510309	+	0.0307043i
$349$	9.95807	+	4.60709i	0.533043	+	0.246612i	0.667897	−	0.744253i	$-0.267195\pi$
$349$	9.95807	+	4.60709i	0.533043	+	0.246612i	−0.134854	+	0.990865i	$0.543057\pi$
$350$	0.161788	+	0.406058i	0.00864794	+	0.0217047i
$351$	−0.0760049	−	1.40183i	−0.00405684	−	0.0748241i
$352$	1.86562	−	2.75158i	0.0994379	−	0.146660i
$353$	33.7444			1.79604			0.898018	−	0.439959i	$-0.145007\pi$
$353$	33.7444			1.79604			0.898018	+	0.439959i	$0.145007\pi$
$354$	0.564876	+	7.66035i	0.0300228	+	0.407143i
$355$	6.95460			0.369112
$356$	8.92466	−	13.1629i	0.473006	−	0.697632i
$357$	−0.0299979	−	0.553278i	−0.00158766	−	0.0292826i
$358$	4.95470	+	12.4354i	0.261864	+	0.657230i
$359$	11.8585	+	5.48632i	0.625866	+	0.289557i	0.707073	−	0.707141i	$-0.250015\pi$
$359$	11.8585	+	5.48632i	0.625866	+	0.289557i	−0.0812065	+	0.996697i	$0.525877\pi$
$360$	−2.18766	−	1.31627i	−0.115300	−	0.0693736i
$361$	−4.24843	−	15.3015i	−0.223602	−	0.805340i
$362$	8.10220	+	1.78343i	0.425842	+	0.0937350i
$363$	0.0514418	−	0.00559464i	0.00270000	−	0.000293642i
$364$	−0.346282	+	0.208351i	−0.0181501	+	0.0109205i
$365$	−16.6118	−	15.7356i	−0.869503	−	0.823637i
$366$	0.696208	−	0.322100i	0.0363914	−	0.0168364i
$367$	−15.9787	−	1.73779i	−0.834081	−	0.0907118i	−0.318895	−	0.947790i	$-0.603312\pi$
$367$	−15.9787	−	1.73779i	−0.834081	−	0.0907118i	−0.515186	+	0.857078i	$0.672277\pi$
$368$	2.02853	+	0.683491i	0.105744	+	0.0356295i
$369$	−2.15271	+	5.40290i	−0.112066	+	0.281264i
$370$	−8.65038	+	8.19407i	−0.449712	+	0.425990i
$371$	0.135846	−	0.489273i	0.00705278	−	0.0254018i
$372$	−0.489744	+	0.923756i	−0.0253921	+	0.0478945i
$373$	−1.63736	−	1.24469i	−0.0847793	−	0.0644475i	0.561926	−	0.827187i	$-0.310061\pi$
$373$	−1.63736	−	1.24469i	−0.0847793	−	0.0644475i	−0.646705	+	0.762740i	$0.723854\pi$
$374$	−0.346431	+	6.38955i	−0.0179135	+	0.330396i
$375$	8.42357	−	2.83823i	0.434991	−	0.146566i
$376$	−4.87012	+	1.07199i	−0.251157	+	0.0552839i
$377$	0.730586	+	1.37803i	0.0376271	+	0.0709722i
$378$	−0.0465714	+	0.284073i	−0.00239537	+	0.0146111i
$379$	−2.57117	−	3.02702i	−0.132072	−	0.155487i	0.692150	−	0.721753i	$-0.256663\pi$
$379$	−2.57117	−	3.02702i	−0.132072	−	0.155487i	−0.824223	+	0.566266i	$0.808388\pi$
$380$	−2.91939	+	3.43697i	−0.149761	+	0.176313i
$381$	1.49690	+	9.13071i	0.0766887	+	0.467780i
$382$	−8.70178	+	6.61492i	−0.445222	+	0.338449i
$383$	18.7150	+	27.6026i	0.956293	+	1.41043i	0.911440	+	0.411432i	$0.134971\pi$
$383$	18.7150	+	27.6026i	0.956293	+	1.41043i	0.0448524	+	0.998994i	$0.485718\pi$
$384$	−0.561187	−	0.827689i	−0.0286380	−	0.0422378i
$385$	−1.94509	+	1.47862i	−0.0991309	+	0.0753574i
$386$	−2.78850	−	17.0091i	−0.141931	−	0.865741i
$387$	−2.05576	+	2.42023i	−0.104500	+	0.123027i
$388$	−3.52277	−	4.14733i	−0.178842	−	0.210549i
$389$	−1.51627	+	9.24887i	−0.0768782	+	0.468936i	0.920128	+	0.391617i	$0.128084\pi$
$389$	−1.51627	+	9.24887i	−0.0768782	+	0.468936i	−0.997006	+	0.0773190i	$0.975364\pi$
$390$	−1.67891	−	3.16677i	−0.0850151	−	0.160356i
$391$	−4.02393	+	0.885733i	−0.203499	+	0.0447935i
$392$	−6.55504	+	2.20865i	−0.331080	+	0.111554i
$393$	−1.02130	+	18.8368i	−0.0515180	+	0.950193i
$394$	10.2883	+	7.82100i	0.518319	+	0.394016i
$395$	10.5123	−	19.8283i	0.528932	−	0.997672i
$396$	0.889376	−	3.20324i	0.0446928	−	0.160969i
$397$	−10.7905	+	10.2213i	−0.541559	+	0.512992i	−0.908855	−	0.417112i	$-0.863042\pi$
$397$	−10.7905	+	10.2213i	−0.541559	+	0.512992i	0.367296	+	0.930104i	$0.380284\pi$
$398$	4.83216	−	12.1278i	0.242214	−	0.607912i
$399$	0.481831	+	0.162348i	0.0241217	+	0.00812755i
$400$	−1.50953	−	0.164171i	−0.0754764	−	0.00820855i
$401$	28.0445	−	12.9748i	1.40047	−	0.647928i	0.433115	−	0.901338i	$-0.357414\pi$
$401$	28.0445	−	12.9748i	1.40047	−	0.647928i	0.967359	+	0.253410i	$0.0815522\pi$
$402$	6.83160	+	6.47123i	0.340729	+	0.322756i
$403$	−1.25772	+	0.756748i	−0.0626517	+	0.0376963i
$404$	−8.00618	+	0.870724i	−0.398322	+	0.0433202i
$405$	−2.49343	−	0.548846i	−0.123900	−	0.0272724i
$406$	−0.0855604	−	0.308161i	−0.00424629	−	0.0152938i
$407$	−13.2939	−	7.99870i	−0.658956	−	0.396481i
$408$	1.74693	+	0.808215i	0.0864858	+	0.0400126i
$409$	−1.16723	−	2.92954i	−0.0577160	−	0.144856i	0.897291	−	0.441440i	$-0.145532\pi$
$409$	−1.16723	−	2.92954i	−0.0577160	−	0.144856i	−0.955007	+	0.296583i	$0.904153\pi$
$410$	0.803903	+	14.8271i	0.0397019	+	0.732259i
$411$	−2.18207	+	3.21831i	−0.107634	+	0.158748i
$412$	11.7312			0.577952
$413$	1.39842	−	1.71275i	0.0688120	−	0.0842790i
$414$	2.14058			0.105204
$415$	−19.1538	+	28.2497i	−0.940221	+	1.38672i
$416$	−0.0760049	−	1.40183i	−0.00372645	−	0.0687303i
$417$	−1.85955	−	4.66713i	−0.0910628	−	0.228550i
$418$	−5.32911	−	2.46551i	−0.260655	−	0.120592i
$419$	17.9628	+	10.8079i	0.877541	+	0.527999i	0.881602	−	0.471993i	$-0.156465\pi$
$419$	17.9628	+	10.8079i	0.877541	+	0.527999i	−0.00406133	+	0.999992i	$0.501293\pi$
$420$	0.196621	+	0.708165i	0.00959412	+	0.0345549i
$421$	−9.57544	−	2.10771i	−0.466679	−	0.102724i	−0.0245948	−	0.999698i	$-0.507830\pi$
$421$	−9.57544	−	2.10771i	−0.466679	−	0.102724i	−0.442084	+	0.896974i	$0.645761\pi$
$422$	−26.3444	+	2.86513i	−1.28243	+	0.139472i
$423$	−4.27289	+	2.57092i	−0.207755	+	0.125002i
$424$	1.28063	+	1.21307i	0.0621927	+	0.0589121i
$425$	2.65258	−	1.22722i	0.128669	−	0.0595287i
$426$	2.70799	+	0.294512i	0.131203	+	0.0142691i
$427$	−0.209264	−	0.0705093i	−0.0101270	−	0.00341218i
$428$	−1.01617	+	2.55039i	−0.0491183	+	0.123278i
$429$	3.38830	−	3.20957i	0.163589	−	0.154959i
$430$	−2.16896	+	7.81187i	−0.104596	+	0.376722i
$431$	2.83362	−	5.34478i	0.136491	−	0.257449i	−0.805839	−	0.592135i	$-0.798285\pi$
$431$	2.83362	−	5.34478i	0.136491	−	0.257449i	0.942330	+	0.334686i	$0.108630\pi$
$432$	−0.796093	−	0.605174i	−0.0383020	−	0.0291165i
$433$	0.168043	−	3.09937i	0.00807563	−	0.148946i	−0.991715	−	0.128461i	$-0.958996\pi$
$433$	0.168043	−	3.09937i	0.00807563	−	0.148946i	0.999790	−	0.0204850i	$-0.00652104\pi$
$434$	0.285222	−	0.0961025i	0.0136911	−	0.00461307i
$435$	2.77020	−	0.609768i	0.132821	−	0.0292361i
$436$	−3.62811	−	6.84333i	−0.173755	−	0.327736i
$437$	0.611672	−	3.73104i	0.0292603	−	0.178480i
$438$	−5.80197	−	6.83061i	−0.277229	−	0.326379i
$439$	−6.28982	+	7.40495i	−0.300197	+	0.353419i	−0.891492	−	0.453036i	$-0.850341\pi$
$439$	−6.28982	+	7.40495i	−0.300197	+	0.353419i	0.591295	+	0.806455i	$0.298617\pi$
$440$	−1.37315	−	8.37583i	−0.0654622	−	0.399302i
$441$	−5.50668	+	4.18607i	−0.262223	+	0.199337i
$442$	1.51646	+	2.23662i	0.0721308	+	0.106385i
$443$	10.6849	+	15.7591i	0.507657	+	0.748738i	0.992013	−	0.126133i	$-0.0402565\pi$
$443$	10.6849	+	15.7591i	0.507657	+	0.748738i	−0.484356	+	0.874871i	$0.660946\pi$
$444$	−3.71530	+	2.82430i	−0.176320	+	0.134035i
$445$	−6.56880	−	40.0679i	−0.311391	−	1.89940i
$446$	9.68739	−	11.4049i	0.458711	−	0.540037i
$447$	7.32989	+	8.62941i	0.346692	+	0.408157i
$448$	−0.0465714	+	0.284073i	−0.00220029	+	0.0134212i
$449$	−17.3944	−	32.8093i	−0.820892	−	1.54837i	−0.836162	−	0.548483i	$-0.815206\pi$
$449$	−17.3944	−	32.8093i	−0.820892	−	1.54837i	0.0152703	−	0.999883i	$-0.495139\pi$
$450$	−1.48293	+	0.326417i	−0.0699059	+	0.0153875i
$451$	−18.3226	+	6.17361i	−0.862778	+	0.290704i
$452$	0.761688	−	14.0485i	0.0358268	−	0.660786i
$453$	16.2564	+	12.3578i	0.763791	+	0.580619i
$454$	3.72515	−	7.02639i	0.174830	−	0.329765i
$455$	−0.276034	+	0.994184i	−0.0129407	+	0.0466081i
$456$	−1.28230	+	1.21466i	−0.0600493	+	0.0568817i
$457$	−8.08239	+	20.2853i	−0.378078	+	0.948905i	0.609643	+	0.792676i	$0.291313\pi$
$457$	−8.08239	+	20.2853i	−0.378078	+	0.948905i	−0.987721	+	0.156228i	$0.950066\pi$
$458$	−19.2224	−	6.47679i	−0.898205	−	0.302641i
$459$	1.91355	+	0.208111i	0.0893167	+	0.00971377i
$460$	4.96005	−	2.29476i	0.231264	−	0.106994i
$461$	−8.18331	−	7.75164i	−0.381135	−	0.361030i	0.473018	−	0.881053i	$-0.343165\pi$
$461$	−8.18331	−	7.75164i	−0.381135	−	0.361030i	−0.854152	+	0.520023i	$0.825923\pi$
$462$	−0.819998	+	0.493376i	−0.0381497	+	0.0229539i
$463$	−10.9754	+	1.19364i	−0.510068	+	0.0554733i	−0.359535	−	0.933132i	$-0.617065\pi$
$463$	−10.9754	+	1.19364i	−0.510068	+	0.0554733i	−0.150533	+	0.988605i	$0.548099\pi$
$464$	1.08503	+	0.238832i	0.0503711	+	0.0110875i
$465$	0.714144	+	2.57212i	0.0331177	+	0.119279i
$466$	9.15902	+	5.51080i	0.424283	+	0.255283i
$467$	19.6688	+	9.09973i	0.910161	+	0.421085i	0.818369	−	0.574693i	$-0.194878\pi$
$467$	19.6688	+	9.09973i	0.910161	+	0.421085i	0.0917921	+	0.995778i	$0.470740\pi$
$468$	−0.519632	−	1.30418i	−0.0240200	−	0.0602857i
$469$	−0.146652	−	2.70483i	−0.00677174	−	0.124897i
$470$	−7.14485	+	10.5379i	−0.329567	+	0.486075i
$471$	−18.1279			−0.835289
$472$	2.98127	+	7.07899i	0.137224	+	0.325837i
$473$	−10.5566			−0.485394
$474$	4.93299	−	7.27561i	0.226580	−	0.334180i
$475$	0.145198	+	2.67802i	0.00666214	+	0.122876i
$476$	−0.205090	−	0.514737i	−0.00940029	−	0.0235930i
$477$	1.60093	+	0.740667i	0.0733014	+	0.0339128i
$478$	14.9169	+	8.97520i	0.682283	+	0.410516i
$479$	−0.940844	−	3.38861i	−0.0429882	−	0.154830i	0.938941	−	0.344078i	$-0.111809\pi$
$479$	−0.940844	−	3.38861i	−0.0429882	−	0.154830i	−0.981929	+	0.189249i	$0.939395\pi$
$480$	−2.49343	−	0.548846i	−0.113809	−	0.0250513i
$481$	−6.51341	+	0.708376i	−0.296986	+	0.0322992i
$482$	0.404393	−	0.243315i	0.0184196	−	0.0110827i
$483$	−0.447358	−	0.423760i	−0.0203555	−	0.0192817i
$484$	0.0469626	−	0.0217272i	0.00213467	−	0.000987601i
$485$	−13.8114	−	1.50208i	−0.627145	−	0.0682061i
$486$	−0.947653	−	0.319302i	−0.0429864	−	0.0144838i
$487$	13.3357	−	33.4701i	0.604299	−	1.51668i	−0.234434	−	0.972132i	$-0.575324\pi$
$487$	13.3357	−	33.4701i	0.604299	−	1.51668i	0.838733	−	0.544543i	$-0.183297\pi$
$488$	0.556917	−	0.527540i	0.0252104	−	0.0238806i
$489$	−1.08868	+	3.92107i	−0.0492318	+	0.177317i
$490$	−8.27222	+	15.6031i	−0.373701	+	0.704875i
$491$	−24.5906	−	18.6933i	−1.10976	−	0.843617i	−0.120929	−	0.992661i	$-0.538587\pi$
$491$	−24.5906	−	18.6933i	−1.10976	−	0.843617i	−0.988831	+	0.149044i	$0.952380\pi$
$492$	−0.314870	+	5.80744i	−0.0141955	+	0.261820i
$493$	−2.02654	+	0.682822i	−0.0912709	+	0.0307528i
$494$	−2.42167	+	0.533049i	−0.108956	+	0.0239830i
$495$	−3.97568	−	7.49893i	−0.178694	−	0.337052i
$496$	−0.169151	+	1.03178i	−0.00759511	+	0.0463281i
$497$	−0.507637	−	0.597636i	−0.0227706	−	0.0268076i
$498$	−8.65443	+	10.1888i	−0.387814	+	0.456570i
$499$	1.72061	+	10.4952i	0.0770250	+	0.469832i	0.996970	+	0.0777847i	$0.0247847\pi$
$499$	1.72061	+	10.4952i	0.0770250	+	0.469832i	−0.919945	+	0.392047i	$0.871767\pi$
$500$	7.07637	−	5.37932i	0.316465	−	0.240570i
$501$	−1.08933	−	1.60664i	−0.0486676	−	0.0717794i
$502$	−9.48945	−	13.9959i	−0.423535	−	0.624667i
$503$	−2.56829	+	1.95236i	−0.114514	+	0.0870515i	−0.660864	−	0.750506i	$-0.729810\pi$
$503$	−2.56829	+	1.95236i	−0.114514	+	0.0870515i	0.546350	+	0.837557i	$0.316017\pi$
$504$	0.0465714	+	0.284073i	0.00207445	+	0.0126536i
$505$	−13.3111	+	15.6710i	−0.592336	+	0.697351i
$506$	4.60692	+	5.42369i	0.204803	+	0.241112i
$507$	−1.78431	+	10.8838i	−0.0792440	+	0.483367i
$508$	4.33400	+	8.17478i	0.192290	+	0.362697i
$509$	−22.9184	+	5.04472i	−1.01584	+	0.223603i	−0.691530	−	0.722347i	$-0.743063\pi$
$509$	−22.9184	+	5.04472i	−1.01584	+	0.223603i	−0.324310	+	0.945951i	$0.605132\pi$
$510$	4.65707	−	1.56915i	0.206219	−	0.0694832i
$511$	−0.139672	+	2.57611i	−0.00617874	+	0.113960i
$512$	−0.796093	−	0.605174i	−0.0351827	−	0.0267452i
$513$	−0.827335	+	1.56052i	−0.0365277	+	0.0688986i
$514$	−1.19759	+	4.31334i	−0.0528235	+	0.190253i
$515$	21.7443	−	20.5973i	0.958170	−	0.907627i
$516$	−1.17537	+	2.94995i	−0.0517426	+	0.129864i
$517$	−15.7101	−	5.29335i	−0.690929	−	0.232801i
$518$	1.33557	+	0.145251i	0.0586814	+	0.00638198i
$519$	22.1829	−	10.2629i	0.973722	−	0.450492i
$520$	−2.60218	−	2.46492i	−0.114113	−	0.108094i
$521$	−2.01527	+	1.21255i	−0.0882907	+	0.0531228i	−0.559015	−	0.829158i	$-0.688820\pi$
$521$	−2.01527	+	1.21255i	−0.0882907	+	0.0531228i	0.470724	+	0.882281i	$0.343993\pi$
$522$	1.10449	−	0.120120i	0.0483421	−	0.00525752i
$523$	−42.0526	−	9.25647i	−1.83883	−	0.404757i	−0.846923	−	0.531715i	$-0.821548\pi$
$523$	−42.0526	−	9.25647i	−1.83883	−	0.404757i	−0.991908	+	0.126958i	$0.959479\pi$
$524$	5.04679	+	18.1769i	0.220470	+	0.794062i
$525$	0.374534	+	0.225350i	0.0163460	+	0.00983507i
$526$	−1.87688	−	0.868337i	−0.0818358	−	0.0378613i
$527$	−0.744905	−	1.86957i	−0.0324486	−	0.0814398i
$528$	−0.179980	−	3.31954i	−0.00783264	−	0.144464i
$529$	10.3359	−	15.2443i	0.449386	−	0.662795i
$530$	4.50360			0.195624
$531$	5.08554	+	5.75650i	0.220694	+	0.249811i
$532$	0.508446			0.0220439
$533$	−4.58208	+	6.75806i	−0.198472	+	0.292724i
$534$	−0.860981	−	15.8799i	−0.0372583	−	0.687189i
$535$	2.59440	+	6.51144i	0.112166	+	0.281514i
$536$	8.54026	+	3.95114i	0.368883	+	0.170663i
$537$	11.4700	+	6.90125i	0.494966	+	0.297811i
$538$	3.45251	+	12.4348i	0.148848	+	0.536102i
$539$	−22.4578	−	4.94334i	−0.967326	−	0.212925i
$540$	−2.53815	+	0.276041i	−0.109225	+	0.0118789i
$541$	−8.50907	+	5.11974i	−0.365833	+	0.220115i	−0.686586	−	0.727048i	$-0.740892\pi$
$541$	−8.50907	+	5.11974i	−0.365833	+	0.220115i	0.320753	+	0.947163i	$0.396064\pi$
$542$	−16.0754	−	15.2274i	−0.690498	−	0.654075i
$543$	7.52939	−	3.48347i	0.323117	−	0.149490i
$544$	1.91355	+	0.208111i	0.0820426	+	0.00892267i
$545$	−18.7403	−	6.31434i	−0.802745	−	0.270476i
$546$	−0.149584	+	0.375427i	−0.00640160	+	0.0160668i
$547$	−9.05874	+	8.58090i	−0.387324	+	0.366893i	−0.856442	−	0.516243i	$-0.827330\pi$
$547$	−9.05874	+	8.58090i	−0.387324	+	0.366893i	0.469119	+	0.883135i	$0.344572\pi$
$548$	−1.04023	+	3.74658i	−0.0444366	+	0.160046i
$549$	0.359320	−	0.677749i	0.0153354	−	0.0289256i
$550$	−4.01859	−	3.05485i	−0.171353	−	0.130259i
$551$	0.106238	−	1.95945i	0.00452590	−	0.0834752i
$552$	2.02853	−	0.683491i	0.0863400	−	0.0290913i
$553$	−2.47125	+	0.543964i	−0.105088	+	0.0231317i
$554$	−7.77218	−	14.6599i	−0.330208	−	0.622839i
$555$	−1.92766	+	11.7582i	−0.0818248	+	0.499109i
$556$	−3.25243	−	3.82906i	−0.137934	−	0.162388i
$557$	21.2938	−	25.0690i	0.902248	−	1.06221i	−0.0955194	−	0.995428i	$-0.530451\pi$
$557$	21.2938	−	25.0690i	0.902248	−	1.06221i	0.997768	−	0.0667811i	$-0.0212729\pi$
$558$	0.169151	+	1.03178i	0.00716074	+	0.0436786i
$559$	−3.54900	+	2.69788i	−0.150107	+	0.114108i
$560$	0.412447	+	0.608313i	0.0174291	+	0.0257059i
$561$	3.59100	+	5.29633i	0.151612	+	0.223611i
$562$	−14.3923	+	10.9407i	−0.607101	+	0.461506i
$563$	−2.59547	−	15.8316i	−0.109386	−	0.667224i	−0.983418	−	0.181356i	$-0.941952\pi$
$563$	−2.59547	−	15.8316i	−0.109386	−	0.667224i	0.874032	−	0.485869i	$-0.161497\pi$
$564$	−3.22833	+	3.80068i	−0.135937	+	0.160037i
$565$	−23.2543	−	27.3770i	−0.978314	−	1.15176i
$566$	4.13514	−	25.2232i	0.173813	−	1.06021i
$567$	0.134838	+	0.254332i	0.00566268	+	0.0106809i
$568$	2.66028	−	0.585571i	0.111623	−	0.0245700i
$569$	−15.5541	+	5.24079i	−0.652062	+	0.219705i	−0.625841	−	0.779951i	$-0.715244\pi$
$569$	−15.5541	+	5.24079i	−0.652062	+	0.219705i	−0.0262215	+	0.999656i	$0.508348\pi$
$570$	−0.244139	+	4.50288i	−0.0102259	+	0.188605i
$571$	1.84460	+	1.40223i	0.0771942	+	0.0586815i	0.643060	−	0.765816i	$-0.277665\pi$
$571$	1.84460	+	1.40223i	0.0771942	+	0.0586815i	−0.565865	+	0.824498i	$0.691458\pi$
$572$	2.18611	−	4.12345i	0.0914059	−	0.172410i
$573$	−2.92425	+	10.5322i	−0.122162	+	0.439988i
$574$	1.21547	−	1.15136i	0.0507328	−	0.0480567i
$575$	1.20307	−	3.01947i	0.0501714	−	0.125921i
$576$	−0.947653	−	0.319302i	−0.0394855	−	0.0133042i
$577$	13.0879	+	1.42339i	0.544856	+	0.0592566i	0.376408	−	0.926454i	$-0.377159\pi$
$577$	13.0879	+	1.42339i	0.544856	+	0.0592566i	0.168448	+	0.985711i	$0.446125\pi$
$578$	12.0662	−	5.58244i	0.501890	−	0.232199i
$579$	−12.5134	−	11.8533i	−0.520039	−	0.492607i
$580$	2.43049	−	1.46238i	0.100921	−	0.0607220i
$581$	3.82569	−	0.416069i	0.158717	−	0.0172615i
$582$	−5.31431	−	1.16977i	−0.220285	−	0.0484884i
$583$	1.56882	+	5.65039i	0.0649740	+	0.234015i
$584$	−7.67928	−	4.62047i	−0.317771	−	0.191196i
$585$	−3.25302	−	1.50501i	−0.134496	−	0.0622244i
$586$	−3.40331	−	8.54167i	−0.140590	−	0.352853i
$587$	−2.18725	−	40.3414i	−0.0902774	−	1.66507i	−0.596460	−	0.802643i	$-0.703426\pi$
$587$	−2.18725	−	40.3414i	−0.0902774	−	1.66507i	0.506182	−	0.862426i	$-0.331056\pi$
$588$	−3.88181	+	5.72524i	−0.160083	+	0.236105i
$589$	1.84672			0.0760928
$590$	17.9551	+	7.88684i	0.739199	+	0.324696i
$591$	12.9235			0.531604
$592$	−2.61901	+	3.86275i	−0.107641	+	0.158758i
$593$	−0.358508	−	6.61228i	−0.0147221	−	0.271534i	−0.996622	−	0.0821308i	$-0.973827\pi$
$593$	−0.358508	−	6.61228i	−0.0147221	−	0.271534i	0.981899	−	0.189403i	$-0.0606553\pi$
$594$	−1.23049	−	3.08831i	−0.0504878	−	0.126715i
$595$	−1.28391	−	0.594001i	−0.0526352	−	0.0243517i
$596$	9.70157	+	5.83724i	0.397392	+	0.239103i
$597$	−3.49259	−	12.5792i	−0.142942	−	0.514831i
$598$	2.93488	+	0.646016i	0.120016	+	0.0264176i
$599$	−42.2194	+	4.59164i	−1.72504	+	0.187609i	−0.916282	−	0.400533i	$-0.868825\pi$
$599$	−42.2194	+	4.59164i	−1.72504	+	0.187609i	−0.808757	+	0.588142i	$0.799859\pi$
$600$	−1.30108	+	0.782832i	−0.0531162	+	0.0319590i
$601$	−10.9665	−	10.3880i	−0.447331	−	0.423735i	0.430584	−	0.902550i	$-0.358308\pi$
$601$	−10.9665	−	10.3880i	−0.447331	−	0.423735i	−0.877915	+	0.478816i	$0.841066\pi$
$602$	0.829623	−	0.383824i	0.0338129	−	0.0156435i
$603$	9.35481	+	1.01740i	0.380957	+	0.0414316i
$604$	19.3513	+	6.52020i	0.787392	+	0.265303i
$605$	0.0488996	−	0.122729i	0.00198805	−	0.00498963i
$606$	−5.84672	+	5.53831i	−0.237507	+	0.224978i
$607$	−9.94268	+	35.8103i	−0.403561	+	1.45350i	0.430885	+	0.902407i	$0.358201\pi$
$607$	−9.94268	+	35.8103i	−0.403561	+	1.45350i	−0.834446	+	0.551089i	$0.814212\pi$
$608$	−0.827335	+	1.56052i	−0.0335528	+	0.0632874i
$609$	−0.254605	−	0.193546i	−0.0103171	−	0.00784287i
$610$	0.106032	−	1.95565i	0.00429311	−	0.0791818i
$611$	−6.63431	+	2.23536i	−0.268395	+	0.0904329i
$612$	1.87983	−	0.413781i	0.0759875	−	0.0167261i
$613$	7.76041	+	14.6377i	0.313440	+	0.591211i	0.989313	−	0.145807i	$-0.0465780\pi$
$613$	7.76041	+	14.6377i	0.313440	+	0.591211i	−0.675873	+	0.737018i	$0.736233\pi$
$614$	3.01470	−	18.3889i	0.121663	−	0.742114i
$615$	9.61297	+	11.3173i	0.387632	+	0.456356i
$616$	−0.619538	+	0.729376i	−0.0249619	+	0.0293874i
$617$	4.06581	+	24.8004i	0.163684	+	0.998425i	0.933084	+	0.359659i	$0.117107\pi$
$617$	4.06581	+	24.8004i	0.163684	+	0.998425i	−0.769400	+	0.638767i	$0.779445\pi$
$618$	9.33909	−	7.09939i	0.375673	−	0.285579i
$619$	24.8969	+	36.7201i	1.00069	+	1.47591i	0.875170	+	0.483815i	$0.160749\pi$
$619$	24.8969	+	36.7201i	1.00069	+	1.47591i	0.125519	+	0.992091i	$0.459940\pi$
$620$	1.49804	+	2.20945i	0.0601628	+	0.0887335i
$621$	1.70410	−	1.29543i	0.0683833	−	0.0519836i
$622$	−0.739583	−	4.51126i	−0.0296546	−	0.180885i
$623$	−2.96371	+	3.48915i	−0.118739	+	0.139790i
$624$	−0.908858	−	1.06999i	−0.0363834	−	0.0428339i
$625$	4.89981	−	29.8875i	0.195993	−	1.19550i
$626$	−0.678633	−	1.28004i	−0.0271236	−	0.0511606i
$627$	−5.73453	+	1.26227i	−0.229015	+	0.0504100i
$628$	−17.1789	+	5.78826i	−0.685515	+	0.230977i
$629$	0.486330	−	8.96984i	0.0193913	−	0.357651i
$630$	0.585092	+	0.444775i	0.0233106	+	0.0177203i
$631$	−1.42343	+	2.68486i	−0.0566657	+	0.106883i	−0.910227	−	0.414109i	$-0.864093\pi$
$631$	−1.42343	+	2.68486i	−0.0566657	+	0.106883i	0.853561	+	0.520992i	$0.174438\pi$
$632$	2.35165	−	8.46987i	0.0935435	−	0.336913i
$633$	−19.2387	+	18.2239i	−0.764670	+	0.724334i
$634$	11.5529	−	28.9955i	0.458823	−	1.15156i
$635$	22.3864	+	7.54286i	0.888378	+	0.299329i
$636$	1.75362	+	0.190718i	0.0695355	+	0.00756244i
$637$	−8.81335	+	4.07749i	−0.349198	+	0.161556i
$638$	2.68141	+	2.53997i	0.106158	+	0.100558i
$639$	2.33404	−	1.40435i	0.0923334	−	0.0555551i
$640$	−2.53815	+	0.276041i	−0.100329	+	0.0109115i
$641$	−14.5675	−	3.20655i	−0.575382	−	0.126651i	−0.0822594	−	0.996611i	$-0.526214\pi$
$641$	−14.5675	−	3.20655i	−0.575382	−	0.126651i	−0.493123	+	0.869960i	$0.664145\pi$
$642$	0.734464	+	2.64530i	0.0289870	+	0.104402i
$643$	14.9490	+	8.99449i	0.589529	+	0.354708i	0.778853	−	0.627207i	$-0.215802\pi$
$643$	14.9490	+	8.99449i	0.589529	+	0.354708i	−0.189324	+	0.981915i	$0.560630\pi$
$644$	−0.559247	−	0.258735i	−0.0220374	−	0.0101956i
$645$	3.00085	+	7.53157i	0.118158	+	0.296555i
$646$	−0.184059	−	3.39478i	−0.00724172	−	0.133566i
$647$	6.80237	−	10.0327i	0.267429	−	0.394428i	−0.670136	−	0.742238i	$-0.733764\pi$
$647$	6.80237	−	10.0327i	0.267429	−	0.394428i	0.937565	+	0.347810i	$0.113075\pi$
$648$	−1.00000			−0.0392837
$649$	−3.64050	+	25.2745i	−0.142902	+	0.992110i
$650$	−2.13170			−0.0836123
$651$	0.168905	−	0.249116i	0.00661989	−	0.00976361i
$652$	0.220313	+	4.06343i	0.00862812	+	0.159136i
$653$	−3.95676	−	9.93071i	−0.154840	−	0.388619i	0.831008	−	0.556260i	$-0.187764\pi$
$653$	−3.95676	−	9.93071i	−0.154840	−	0.388619i	−0.985848	+	0.167642i	$0.946385\pi$
$654$	−7.02972	−	3.25229i	−0.274884	−	0.127175i
$655$	41.2692	+	24.8308i	1.61252	+	0.970221i
$656$	1.55594	+	5.60398i	0.0607492	+	0.218799i
$657$	−8.75262	−	1.92660i	−0.341472	−	0.0751637i
$658$	1.42708	−	0.155205i	0.0556335	−	0.00605051i
$659$	−20.7927	+	12.5106i	−0.809970	+	0.487343i	−0.859320	−	0.511439i	$-0.829113\pi$
$659$	−20.7927	+	12.5106i	−0.809970	+	0.487343i	0.0493495	+	0.998782i	$0.484285\pi$
$660$	−6.16199	−	5.83694i	−0.239855	−	0.227203i
$661$	−1.24254	+	0.574859i	−0.0483291	+	0.0223594i	−0.443905	−	0.896074i	$-0.646407\pi$
$661$	−1.24254	+	0.574859i	−0.0483291	+	0.0223594i	0.395576	+	0.918433i	$0.370545\pi$
$662$	14.7848	+	1.60794i	0.574628	+	0.0624945i
$663$	2.56079	+	0.862831i	0.0994528	+	0.0335096i
$664$	−4.94810	+	12.4188i	−0.192024	+	0.481943i
$665$	0.942433	−	0.892720i	0.0365460	−	0.0346182i
$666$	−1.24853	+	4.49680i	−0.0483796	+	0.174248i
$667$	−1.11396	+	2.10116i	−0.0431329	+	0.0813572i
$668$	−1.54531	−	1.17471i	−0.0597898	−	0.0454510i
$669$	0.810126	−	14.9419i	0.0313213	−	0.577687i
$670$	22.7672	−	7.67116i	0.879573	−	0.296363i
$671$	2.49056	−	0.548215i	0.0961472	−	0.0211636i
$672$	0.134838	+	0.254332i	0.00520150	+	0.00981108i
$673$	−4.58029	+	27.9385i	−0.176557	+	1.07695i	0.738686	+	0.674050i	$0.235447\pi$
$673$	−4.58029	+	27.9385i	−0.176557	+	1.07695i	−0.915243	+	0.402902i	$0.868002\pi$
$674$	−17.9217	−	21.0990i	−0.690317	−	0.812704i
$675$	−0.983010	+	1.15729i	−0.0378361	+	0.0445441i
$676$	1.78431	+	10.8838i	0.0686273	+	0.418608i
$677$	−5.98062	+	4.54635i	−0.229854	+	0.174730i	−0.713762	−	0.700389i	$-0.753010\pi$
$677$	−5.98062	+	4.54635i	−0.229854	+	0.174730i	0.483908	+	0.875119i	$0.339217\pi$
$678$	−7.89542	−	11.6449i	−0.303222	−	0.447219i
$679$	0.879057	+	1.29651i	0.0337351	+	0.0497556i
$680$	3.91226	−	2.97402i	0.150028	−	0.114049i
$681$	−1.28662	−	7.84802i	−0.0493033	−	0.300737i
$682$	−2.25021	+	2.64916i	−0.0861651	+	0.101441i
$683$	23.1664	+	27.2736i	0.886438	+	1.04360i	0.998753	+	0.0499234i	$0.0158977\pi$
$683$	23.1664	+	27.2736i	0.886438	+	1.04360i	−0.112315	+	0.993673i	$0.535826\pi$
$684$	−0.285750	+	1.74300i	−0.0109259	+	0.0666453i
$685$	4.65004	+	8.77091i	0.177669	+	0.335119i
$686$	3.91259	−	0.861226i	0.149383	−	0.0328818i
$687$	−19.2224	+	6.47679i	−0.733381	+	0.247105i
$688$	−0.171917	+	3.17082i	−0.00655427	+	0.120886i
$689$	1.97145	+	1.49865i	0.0751061	+	0.0570942i
$690$	2.55993	−	4.82854i	0.0974549	−	0.183819i
$691$	2.71509	−	9.77888i	0.103287	−	0.372006i	−0.893783	−	0.448500i	$-0.851959\pi$
$691$	2.71509	−	9.77888i	0.103287	−	0.372006i	0.997070	+	0.0764933i	$0.0243724\pi$
$692$	17.7448	−	16.8087i	0.674554	−	0.638972i
$693$	−0.354216	+	0.889015i	−0.0134555	+	0.0337709i
$694$	8.35609	+	2.81550i	0.317193	+	0.106875i
$695$	−12.7516	−	1.38682i	−0.483694	−	0.0526049i
$696$	1.00832	−	0.466497i	0.0382202	−	0.0176825i
$697$	−8.12734	−	7.69863i	−0.307845	−	0.291606i
$698$	9.40158	−	5.65674i	0.355855	−	0.214111i
$699$	10.6264	−	1.15569i	0.401928	−	0.0437123i
$700$	0.426883	+	0.0939641i	0.0161347	+	0.00355151i
$701$	7.22399	+	26.0184i	0.272846	+	0.982703i	0.965279	+	0.261221i	$0.0841251\pi$
$701$	7.22399	+	26.0184i	0.272846	+	0.982703i	−0.692433	+	0.721482i	$0.743461\pi$
$702$	−1.20293	−	0.723780i	−0.0454017	−	0.0273173i
$703$	7.48116	+	3.46115i	0.282157	+	0.130540i
$704$	−1.23049	−	3.08831i	−0.0463760	−	0.116395i
$705$	0.689278	+	12.7130i	0.0259597	+	0.478799i
$706$	18.9369	−	27.9299i	0.712701	−	1.05116i
$707$	2.31829			0.0871882
$708$	6.65739	+	3.83135i	0.250200	+	0.143991i
$709$	13.1464			0.493724			0.246862	−	0.969051i	$-0.420601\pi$
$709$	13.1464			0.493724			0.246862	+	0.969051i	$0.420601\pi$
$710$	3.90283	−	5.75625i	0.146471	−	0.216028i
$711$	−0.475896	−	8.77738i	−0.0178475	−	0.329177i
$712$	−5.88638	−	14.7737i	−0.220601	−	0.553667i
$713$	−2.03123	−	0.939748i	−0.0760703	−	0.0351938i
$714$	−0.474777	−	0.285664i	−0.0177681	−	0.0106907i
$715$	−3.18778	−	11.4814i	−0.119216	−	0.429379i
$716$	13.0731	+	2.87761i	0.488566	+	0.107541i
$717$	17.3068	−	1.88223i	0.646334	−	0.0702931i
$718$	11.1958	−	6.73628i	0.417823	−	0.251396i
$719$	29.8330	+	28.2594i	1.11258	+	1.05390i	0.998170	+	0.0604629i	$0.0192577\pi$
$719$	29.8330	+	28.2594i	1.11258	+	1.05390i	0.114414	+	0.993433i	$0.463501\pi$
$720$	−2.31715	+	1.07203i	−0.0863551	+	0.0399521i
$721$	−3.35719	−	0.365117i	−0.125028	−	0.0135977i
$722$	−15.0490	−	5.07060i	−0.560066	−	0.188708i
$723$	0.174686	−	0.438430i	0.00649666	−	0.0163054i
$724$	6.02297	−	5.70526i	0.223842	−	0.212034i
$725$	0.451314	−	1.62548i	0.0167614	−	0.0603690i
$726$	0.0242379	−	0.0457175i	0.000899552	−	0.00169673i
$727$	20.0982	+	15.2783i	0.745403	+	0.566640i	0.907459	−	0.420141i	$-0.138019\pi$
$727$	20.0982	+	15.2783i	0.745403	+	0.566640i	−0.162056	+	0.986782i	$0.551813\pi$
$728$	−0.0218792	+	0.403537i	−0.000810895	+	0.0149561i
$729$	−0.947653	+	0.319302i	−0.0350983	+	0.0118260i
$730$	−22.3465	+	4.91884i	−0.827081	+	0.182054i
$731$	−2.86303	−	5.40025i	−0.105893	−	0.199736i
$732$	0.124104	−	0.757002i	0.00458702	−	0.0279796i
$733$	13.2092	+	15.5511i	0.487895	+	0.574394i	0.949928	−	0.312468i	$-0.101156\pi$
$733$	13.2092	+	15.5511i	0.487895	+	0.574394i	−0.462033	+	0.886862i	$0.652880\pi$
$734$	−10.4054	+	12.2502i	−0.384070	+	0.452162i
$735$	2.85712	+	17.4276i	0.105386	+	0.642828i
$736$	1.70410	−	1.29543i	0.0628141	−	0.0477500i
$737$	17.5554	+	25.8923i	0.646663	+	0.953756i
$738$	3.26385	+	4.81382i	0.120144	+	0.177199i
$739$	10.3034	−	7.83245i	0.379017	−	0.288121i	−0.398269	−	0.917269i	$-0.630389\pi$
$739$	10.3034	−	7.83245i	0.379017	−	0.288121i	0.777286	+	0.629147i	$0.216596\pi$
$740$	1.92766	+	11.7582i	0.0708623	+	0.432241i
$741$	−1.60529	+	1.88989i	−0.0589716	+	0.0694268i
$742$	−0.328731	−	0.387012i	−0.0120681	−	0.0142077i
$743$	2.79422	−	17.0440i	0.102510	−	0.625282i	−0.884738	−	0.466089i	$-0.845663\pi$
$743$	2.79422	−	17.0440i	0.102510	−	0.625282i	0.987247	−	0.159193i	$-0.0508892\pi$
$744$	0.489744	+	0.923756i	0.0179549	+	0.0338665i
$745$	28.2313	−	6.21418i	1.03432	−	0.227670i
$746$	−1.94908	+	0.656722i	−0.0713609	+	0.0240443i
$747$	−0.723743	+	13.3487i	−0.0264804	+	0.488402i
$748$	5.09415	+	3.87247i	0.186260	+	0.141592i
$749$	0.370181	−	0.698236i	0.0135261	−	0.0255130i
$750$	2.37803	−	8.56488i	0.0868332	−	0.312745i
$751$	−2.77665	+	2.63018i	−0.101321	+	0.0959768i	−0.736684	−	0.676237i	$-0.763609\pi$
$751$	−2.77665	+	2.63018i	−0.101321	+	0.0959768i	0.635362	+	0.772214i	$0.280851\pi$
$752$	−1.84577	+	4.63253i	−0.0673083	+	0.168931i
$753$	−16.0244	−	5.39926i	−0.583963	−	0.196760i
$754$	1.55058	+	0.168635i	0.0564687	+	0.00614134i
$755$	47.3167	−	21.8910i	1.72203	−	0.796696i
$756$	0.208989	+	0.197965i	0.00760084	+	0.00719990i
$757$	−28.3731	+	17.0715i	−1.03124	+	0.620475i	−0.927381	−	0.374117i	$-0.877946\pi$
$757$	−28.3731	+	17.0715i	−1.03124	+	0.620475i	−0.103856	+	0.994592i	$0.533118\pi$
$758$	−3.94834	+	0.429408i	−0.143410	+	0.0155968i
$759$	6.94982	+	1.52977i	0.252262	+	0.0555271i
$760$	1.20642	+	4.34512i	0.0437614	+	0.157614i
$761$	−38.1740	−	22.9685i	−1.38381	−	0.832609i	−0.387788	−	0.921749i	$-0.626761\pi$
$761$	−38.1740	−	22.9685i	−1.38381	−	0.832609i	−0.996019	+	0.0891398i	$0.971588\pi$
$762$	8.39743	+	3.88507i	0.304207	+	0.140741i
$763$	0.825292	+	2.07133i	0.0298776	+	0.0749871i
$764$	0.591771	+	10.9146i	0.0214095	+	0.394876i
$765$	2.75785	−	4.06753i	0.0997104	−	0.147062i
$766$	33.3490			1.20495
$767$	5.23533	+	9.42733i	0.189037	+	0.340401i
$768$	−1.00000			−0.0360844
$769$	12.1335	−	17.8956i	0.437547	−	0.645333i	−0.543431	−	0.839454i	$-0.682875\pi$
$769$	12.1335	−	17.8956i	0.437547	−	0.645333i	0.980978	+	0.194121i	$0.0621853\pi$
$770$	0.132277	+	2.43971i	0.00476694	+	0.0879211i
$771$	1.65693	+	4.15857i	0.0596727	+	0.149767i
$772$	−15.6431	−	7.23728i	−0.563009	−	0.260475i
$773$	35.8497	+	21.5701i	1.28943	+	0.775821i	0.984302	−	0.176492i	$-0.0564748\pi$
$773$	35.8497	+	21.5701i	1.28943	+	0.775821i	0.305123	+	0.952313i	$0.401302\pi$
$774$	0.849531	+	3.05973i	0.0305358	+	0.109980i
$775$	1.55048	+	0.341286i	0.0556947	+	0.0122593i
$776$	−5.40963	+	0.588333i	−0.194194	+	0.0211199i
$777$	1.15114	−	0.692616i	0.0412968	−	0.0248475i
$778$	6.80427	+	6.44535i	0.243945	+	0.231077i
$779$	9.32313	−	4.31334i	0.334036	−	0.154541i
$780$	−3.56328	−	0.387530i	−0.127586	−	0.0138758i
$781$	8.58155	+	2.89146i	0.307072	+	0.103465i
$782$	−1.52506	+	3.82762i	−0.0545362	+	0.136876i
$783$	0.806582	−	0.764035i	0.0288249	−	0.0273044i
$784$	−1.85053	+	6.66500i	−0.0660903	+	0.238036i
$785$	−21.6792	+	40.8913i	−0.773764	+	1.45947i
$786$	15.0179	+	11.4163i	0.535671	+	0.407207i
$787$	0.966664	−	17.8291i	0.0344578	−	0.635537i	−0.929392	−	0.369093i	$-0.879668\pi$
$787$	0.966664	−	17.8291i	0.0344578	−	0.635537i	0.963850	−	0.266444i	$-0.0858489\pi$
$788$	12.2470	−	4.12651i	0.436283	−	0.147001i
$789$	−2.01966	+	0.444562i	−0.0719020	+	0.0158268i
$790$	−10.5123	−	19.8283i	−0.374011	−	0.705461i
$791$	−0.655219	+	3.99666i	−0.0232969	+	0.142105i
$792$	−2.15218	−	2.53374i	−0.0764744	−	0.0900327i
$793$	0.697192	−	0.820798i	0.0247580	−	0.0291474i
$794$	2.40457	+	14.6672i	0.0853350	+	0.520521i
$795$	3.58529	−	2.72546i	0.127157	−	0.0966623i
$796$	−7.32631	−	10.8055i	−0.259674	−	0.382991i
$797$	15.4588	+	22.8001i	0.547580	+	0.807620i	0.996290	−	0.0860573i	$-0.0274268\pi$
$797$	15.4588	+	22.8001i	0.547580	+	0.807620i	−0.448710	+	0.893677i	$0.648116\pi$
$798$	0.404771	−	0.307699i	0.0143287	−	0.0108924i
$799$	−1.55287	−	9.47211i	−0.0549367	−	0.335099i
$800$	−0.983010	+	1.15729i	−0.0347546	+	0.0409163i
$801$	−10.2955	−	12.1208i	−0.363774	−	0.428268i
$802$	4.99913	−	30.4934i	0.176526	−	1.07676i
$803$	−13.9557	−	26.3233i	−0.492487	−	0.928929i
$804$	9.18997	−	2.02287i	0.324105	−	0.0713410i
$805$	−1.49088	+	0.502335i	−0.0525465	+	0.0177050i
$806$	−0.0794670	+	1.46568i	−0.00279910	+	0.0516264i
$807$	10.2737	+	7.80989i	0.361653	+	0.274921i
$808$	−3.77227	+	7.11526i	−0.132708	+	0.250314i
$809$	−3.65903	+	13.1786i	−0.128645	+	0.463336i	−0.999608	−	0.0280125i	$-0.991082\pi$
$809$	−3.65903	+	13.1786i	−0.128645	+	0.463336i	0.870963	+	0.491349i	$0.163496\pi$
$810$	−1.85355	+	1.75578i	−0.0651273	+	0.0616918i
$811$	−6.38093	+	16.0149i	−0.224065	+	0.562360i	−0.997434	−	0.0715959i	$-0.977191\pi$
$811$	−6.38093	+	16.0149i	−0.224065	+	0.562360i	0.773369	+	0.633956i	$0.218570\pi$
$812$	−0.303077	−	0.102118i	−0.0106359	−	0.00358365i
$813$	−22.0128	−	2.39403i	−0.772022	−	0.0839624i
$814$	−14.0808	+	6.51448i	−0.493532	+	0.228332i
$815$	7.54286	+	7.14497i	0.264215	+	0.250278i
$816$	1.64930	−	0.992353i	0.0577372	−	0.0347393i
$817$	5.57587	−	0.606412i	0.195075	−	0.0212157i
$818$	−3.07978	−	0.677911i	−0.107682	−	0.0237026i
$819$	0.108116	+	0.389399i	0.00377789	+	0.0136067i
$820$	12.7234	+	7.65540i	0.444320	+	0.267338i
$821$	7.67966	+	3.55299i	0.268022	+	0.124000i	0.549297	−	0.835627i	$-0.314895\pi$
$821$	7.67966	+	3.55299i	0.268022	+	0.124000i	−0.281276	+	0.959627i	$0.590757\pi$
$822$	1.43921	+	3.61215i	0.0501983	+	0.125988i
$823$	−2.07168	−	38.2098i	−0.0722141	−	1.33191i	−0.780132	−	0.625615i	$-0.784848\pi$
$823$	−2.07168	−	38.2098i	−0.0722141	−	1.33191i	0.707918	−	0.706295i	$-0.249635\pi$
$824$	6.58337	−	9.70975i	0.229343	−	0.338255i
$825$	−5.04789			−0.175745
$826$	−0.632847	−	2.11863i	−0.0220196	−	0.0737167i
$827$	−5.80283			−0.201784			−0.100892	−	0.994897i	$-0.532170\pi$
$827$	−5.80283			−0.201784			−0.100892	+	0.994897i	$0.532170\pi$
$828$	1.20127	−	1.77174i	0.0417469	−	0.0615721i
$829$	−2.89682	−	53.4288i	−0.100611	−	1.85566i	−0.419361	−	0.907819i	$-0.637746\pi$
$829$	−2.89682	−	53.4288i	−0.100611	−	1.85566i	0.318750	−	0.947839i	$-0.396737\pi$
$830$	12.6331	+	31.7067i	0.438501	+	1.10056i
$831$	−15.0592	−	6.96711i	−0.522397	−	0.241686i
$832$	−1.20293	−	0.723780i	−0.0417041	−	0.0250925i
$833$	−3.56195	−	12.8290i	−0.123414	−	0.444498i
$834$	−4.90649	−	1.08000i	−0.169898	−	0.0373973i
$835$	−4.92685	+	0.535827i	−0.170501	+	0.0185431i
$836$	−5.03130	+	3.02723i	−0.174011	+	0.104699i
$837$	0.759065	+	0.719024i	0.0262371	+	0.0248531i
$838$	19.0261	−	8.80239i	0.657244	−	0.304074i
$839$	−13.1394	−	1.42899i	−0.453621	−	0.0493343i	−0.121543	−	0.992586i	$-0.538784\pi$
$839$	−13.1394	−	1.42899i	−0.453621	−	0.0493343i	−0.332078	+	0.943252i	$0.607750\pi$
$840$	0.696482	+	0.234672i	0.0240309	+	0.00809695i
$841$	10.2771	−	25.7937i	0.354384	−	0.889437i
$842$	−7.11815	+	6.74267i	−0.245308	+	0.232368i
$843$	−4.83654	+	17.4197i	−0.166579	+	0.599965i
$844$	−12.4127	+	23.4129i	−0.427263	+	0.805904i
$845$	22.4169	+	17.0409i	0.771164	+	0.586224i
$846$	−0.269975	+	4.97939i	−0.00928193	+	0.171195i
$847$	−0.0141159	+	0.00475619i	−0.000485027	+	0.000163425i
$848$	1.72272	−	0.379199i	0.0591584	−	0.0130218i
$849$	−11.9725	−	22.5825i	−0.410895	−	0.775030i
$850$	0.472843	−	2.88421i	0.0162184	−	0.0989277i
$851$	−6.46733	−	7.61393i	−0.221697	−	0.261002i
$852$	1.76345	−	2.07610i	0.0604149	−	0.0711260i
$853$	−0.339335	−	2.06985i	−0.0116186	−	0.0708704i	0.980381	−	0.197113i	$-0.0631565\pi$
$853$	−0.339335	−	2.06985i	−0.0116186	−	0.0708704i	−0.991999	+	0.126242i	$0.959708\pi$
$854$	−0.175796	+	0.133637i	−0.00601562	+	0.00457295i
$855$	2.53067	+	3.73246i	0.0865471	+	0.127647i
$856$	1.54067	+	2.27231i	0.0526589	+	0.0776661i
$857$	−36.3098	+	27.6020i	−1.24032	+	0.942866i	−0.999615	−	0.0277325i	$-0.991171\pi$
$857$	−36.3098	+	27.6020i	−1.24032	+	0.942866i	−0.240704	+	0.970599i	$0.577378\pi$
$858$	−0.755054	−	4.60562i	−0.0257771	−	0.157233i
$859$	12.5268	−	14.7477i	0.427410	−	0.503186i	−0.505734	−	0.862690i	$-0.668778\pi$
$859$	12.5268	−	14.7477i	0.427410	−	0.503186i	0.933144	+	0.359504i	$0.117054\pi$
$860$	5.24861	+	6.17914i	0.178976	+	0.210707i
$861$	0.270858	−	1.65216i	0.00923081	−	0.0563055i
$862$	−2.83362	−	5.34478i	−0.0965136	−	0.182044i
$863$	−10.4450	+	2.29913i	−0.355554	+	0.0782632i	−0.389156	−	0.921172i	$-0.627233\pi$
$863$	−10.4450	+	2.29913i	−0.355554	+	0.0782632i	0.0336021	+	0.999435i	$0.489302\pi$
$864$	−0.947653	+	0.319302i	−0.0322398	+	0.0108629i
$865$	3.37845	−	62.3118i	0.114871	−	2.11866i
$866$	−2.47101	−	1.87841i	−0.0839684	−	0.0638311i
$867$	6.22751	−	11.7463i	0.211497	−	0.398926i
$868$	0.0805199	−	0.290007i	0.00273302	−	0.00984346i
$869$	21.2154	−	20.0963i	0.719684	−	0.681721i
$870$	1.04990	−	2.63506i	0.0355951	−	0.0893369i
$871$	12.5190	+	4.21815i	0.424191	+	0.142926i
$872$	−7.70020	−	0.837447i	−0.260762	−	0.0283595i
$873$	−4.93860	+	2.28484i	−0.167146	+	0.0773301i
$874$	−2.74487	−	2.60008i	−0.0928468	−	0.0879491i
$875$	−2.19252	+	1.31920i	−0.0741208	+	0.0445970i
$876$	−8.90961	+	0.968979i	−0.301028	+	0.0327388i
$877$	−50.3915	−	11.0920i	−1.70160	−	0.374551i	−0.745253	−	0.666781i	$-0.767672\pi$
$877$	−50.3915	−	11.0920i	−1.70160	−	0.374551i	−0.956348	+	0.292231i	$0.905603\pi$
$878$	2.59923	+	9.36158i	0.0877198	+	0.315938i
$879$	−7.87855	−	4.74037i	−0.265737	−	0.159889i
$880$	−7.70317	−	3.56387i	−0.259674	−	0.120138i
$881$	7.06107	+	17.7220i	0.237894	+	0.597068i	0.998649	−	0.0519712i	$-0.0165504\pi$
$881$	7.06107	+	17.7220i	0.237894	+	0.597068i	−0.760755	+	0.649039i	$0.775171\pi$
$882$	0.374486	+	6.90699i	0.0126096	+	0.232570i
$883$	9.91350	−	14.6213i	0.333616	−	0.492047i	−0.623471	−	0.781846i	$-0.714278\pi$
$883$	9.91350	−	14.6213i	0.333616	−	0.492047i	0.957087	+	0.289799i	$0.0935886\pi$
$884$	2.70224			0.0908863
$885$	19.0668	−	4.58730i	0.640924	−	0.154200i
$886$	19.0399			0.639658
$887$	−10.8869	+	16.0569i	−0.365546	+	0.539139i	−0.965333	−	0.261020i	$-0.915941\pi$
$887$	−10.8869	+	16.0569i	−0.365546	+	0.539139i	0.599788	+	0.800159i	$0.295252\pi$
$888$	0.252662	+	4.66007i	0.00847877	+	0.156382i
$889$	−0.985862	−	2.47433i	−0.0330648	−	0.0829863i
$890$	−36.8501	−	17.0487i	−1.23522	−	0.571472i
$891$	−2.84855	−	1.71392i	−0.0954300	−	0.0574183i
$892$	−4.00325	−	14.4184i	−0.134039	−	0.482764i
$893$	8.60193	+	1.89343i	0.287853	+	0.0633612i
$894$	11.2559	−	1.22415i	0.376454	−	0.0409418i
$895$	29.2842	−	17.6197i	0.978864	−	0.588963i
$896$	0.208989	+	0.197965i	0.00698182	+	0.00661353i
$897$	2.72739	−	1.26182i	0.0910649	−	0.0421311i
$898$	−36.9174	−	4.01501i	−1.23195	−	0.133983i
$899$	−1.10080	−	0.370903i	−0.0367137	−	0.0123703i
$900$	−0.562028	+	1.41058i	−0.0187343	+	0.0470195i
$901$	−2.46499	+	2.33496i	−0.0821207	+	0.0777888i
$902$	−5.17259	+	18.6300i	−0.172228	+	0.620310i
$903$	0.428176	−	0.807626i	0.0142488	−	0.0268761i
$904$	−11.2003	−	8.51428i	−0.372518	−	0.283181i
$905$	1.14672	−	21.1500i	0.0381183	−	0.703051i
$906$	19.3513	−	6.52020i	0.642903	−	0.216619i
$907$	2.68471	−	0.590948i	0.0891442	−	0.0196221i	−0.170174	−	0.985414i	$-0.554433\pi$
$907$	2.68471	−	0.590948i	0.0891442	−	0.0196221i	0.259319	+	0.965792i	$0.416502\pi$
$908$	−3.72515	−	7.02639i	−0.123624	−	0.233179i
$909$	−1.30289	+	7.94730i	−0.0432142	+	0.263595i
$910$	0.667969	+	0.786393i	0.0221429	+	0.0260687i
$911$	16.7212	−	19.6857i	0.553998	−	0.652217i	−0.411872	−	0.911242i	$-0.635125\pi$
$911$	16.7212	−	19.6857i	0.553998	−	0.652217i	0.965871	+	0.259024i	$0.0834009\pi$
$912$	0.285750	+	1.74300i	0.00946214	+	0.0577165i
$913$	−35.3797	+	26.8949i	−1.17090	+	0.890093i
$914$	12.2542	+	18.0735i	0.405332	+	0.597819i
$915$	−1.09910	−	1.62105i	−0.0363350	−	0.0535901i
$916$	−16.1481	+	12.2755i	−0.533550	+	0.405594i
$917$	−0.878546	−	5.35889i	−0.0290122	−	0.176966i
$918$	1.24611	−	1.46703i	0.0411277	−	0.0484193i
$919$	−7.33669	−	8.63742i	−0.242015	−	0.284922i	0.627722	−	0.778438i	$-0.283987\pi$
$919$	−7.33669	−	8.63742i	−0.242015	−	0.284922i	−0.869737	+	0.493516i	$0.835712\pi$
$920$	0.884166	−	5.39317i	0.0291501	−	0.177808i
$921$	−8.72848	−	16.4637i	−0.287613	−	0.542496i
$922$	−11.0083	+	2.42311i	−0.362540	+	0.0798010i
$923$	3.62395	−	1.22105i	0.119284	−	0.0401914i
$924$	−0.0518100	+	0.955579i	−0.00170442	+	0.0314363i
$925$	5.64141	+	4.28849i	0.185488	+	0.141005i
$926$	−5.17126	+	9.75404i	−0.169938	+	0.320538i
$927$	3.13842	−	11.3036i	0.103079	−	0.371257i
$928$	0.806582	−	0.764035i	0.0264773	−	0.0250807i
$929$	−5.28116	+	13.2547i	−0.173269	+	0.434873i	−0.989806	−	0.142420i	$-0.954512\pi$
$929$	−5.28116	+	13.2547i	−0.173269	+	0.434873i	0.816537	+	0.577293i	$0.195891\pi$
$930$	2.52968	+	0.852349i	0.0829515	+	0.0279496i
$931$	12.1459	+	1.32095i	0.398065	+	0.0432922i
$932$	9.70115	−	4.48823i	0.317772	−	0.147017i
$933$	−3.31888	−	3.14381i	−0.108655	−	0.102924i
$934$	18.5696	−	11.1730i	0.607616	−	0.365590i
$935$	16.2415	−	1.76637i	0.531153	−	0.0577664i
$936$	−1.37107	−	0.301794i	−0.0448147	−	0.00986446i
$937$	3.02225	+	10.8852i	0.0987327	+	0.355603i	0.996370	−	0.0851326i	$-0.0271314\pi$
$937$	3.02225	+	10.8852i	0.0987327	+	0.355603i	−0.897637	+	0.440736i	$0.854718\pi$
$938$	−2.32106	−	1.39653i	−0.0757852	−	0.0455984i
$939$	−1.31490	−	0.608338i	−0.0429102	−	0.0198524i
$940$	4.71248	+	11.8274i	0.153704	+	0.385768i
$941$	0.0354689	+	0.654186i	0.00115625	+	0.0213258i	0.999055	−	0.0434729i	$-0.0138422\pi$
$941$	0.0354689	+	0.654186i	0.00115625	+	0.0213258i	−0.997898	+	0.0647987i	$0.979359\pi$
$942$	−10.1731	+	15.0043i	−0.331459	+	0.488865i
$943$	−12.4496			−0.405414
$944$	7.53225	+	1.50507i	0.245154	+	0.0489860i
$945$	0.734954			0.0239081
$946$	−5.92424	+	8.73760i	−0.192614	+	0.284084i
$947$	−1.83704	−	33.8822i	−0.0596957	−	1.10102i	−0.862918	−	0.505343i	$-0.831366\pi$
$947$	−1.83704	−	33.8822i	−0.0596957	−	1.10102i	0.803223	−	0.595679i	$-0.203117\pi$
$948$	−3.25362	−	8.16596i	−0.105673	−	0.265218i
$949$	−11.4190	−	5.28298i	−0.370676	−	0.171493i
$950$	2.29805	+	1.38269i	0.0745585	+	0.0448604i
$951$	−8.35018	−	30.0746i	−0.270773	−	0.975237i
$952$	−0.541136	−	0.119113i	−0.0175383	−	0.00386048i
$953$	−15.6596	+	1.70309i	−0.507265	+	0.0551684i	−0.358174	−	0.933655i	$-0.616600\pi$
$953$	−15.6596	+	1.70309i	−0.507265	+	0.0551684i	−0.149092	+	0.988823i	$0.547635\pi$
$954$	1.51146	−	0.909416i	0.0489354	−	0.0294434i
$955$	20.2605	+	19.1917i	0.655614	+	0.621030i
$956$	15.7998	−	7.30979i	0.511004	−	0.236415i
$957$	3.67178	+	0.399330i	0.118692	+	0.0129085i
$958$	−3.33271	−	1.12292i	−0.107675	−	0.0362799i
$959$	0.414299	−	1.03981i	0.0133784	−	0.0335773i
$960$	−1.85355	+	1.75578i	−0.0598232	+	0.0566676i
$961$	−8.00092	+	28.8167i	−0.258094	+	0.929572i
$962$	−3.06893	+	5.78861i	−0.0989462	+	0.186632i
$963$	2.18557	+	1.66143i	0.0704290	+	0.0535388i
$964$	0.0255508	−	0.471257i	0.000822936	−	0.0151782i
$965$	−41.7025	+	14.0512i	−1.34245	+	0.452324i
$966$	−0.601792	+	0.132465i	−0.0193624	+	0.00426198i
$967$	19.9827	+	37.6913i	0.642599	+	1.21207i	0.964195	+	0.265193i	$0.0854357\pi$
$967$	19.9827	+	37.6913i	0.642599	+	1.21207i	−0.321596	+	0.946877i	$0.604219\pi$
$968$	0.00837144	−	0.0510635i	0.000269068	−	0.00164124i
$969$	−2.20096	−	2.59117i	−0.0707050	−	0.0832404i
$970$	−8.99406	+	10.5886i	−0.288782	+	0.339980i
$971$	3.47857	+	21.2184i	0.111633	+	0.680929i	0.982051	+	0.188616i	$0.0604002\pi$
$971$	3.47857	+	21.2184i	0.111633	+	0.680929i	−0.870418	+	0.492313i	$0.836152\pi$
$972$	−0.796093	+	0.605174i	−0.0255347	+	0.0194110i
$973$	0.811599	+	1.19702i	0.0260187	+	0.0383747i
$974$	−20.2190	−	29.8208i	−0.647859	−	0.955521i
$975$	−1.69703	+	1.29005i	−0.0543486	+	0.0413147i
$976$	−0.124104	−	0.757002i	−0.00397248	−	0.0242311i
$977$	15.4088	−	18.1407i	0.492972	−	0.580372i	−0.458271	−	0.888812i	$-0.651531\pi$
$977$	15.4088	−	18.1407i	0.492972	−	0.580372i	0.951244	+	0.308440i	$0.0998070\pi$
$978$	2.63447	+	3.10154i	0.0842412	+	0.0991764i
$979$	8.55322	−	52.1723i	0.273362	−	1.66744i
$980$	8.27222	+	15.6031i	0.264247	+	0.498422i
$981$	−7.56451	+	1.66508i	−0.241516	+	0.0531618i
$982$	−29.2722	+	9.86295i	−0.934113	+	0.314739i
$983$	1.07184	−	19.7689i	0.0341863	−	0.630529i	−0.930365	−	0.366634i	$-0.880510\pi$
$983$	1.07184	−	19.7689i	0.0341863	−	0.630529i	0.964552	−	0.263895i	$-0.0850071\pi$
$984$	4.63006	+	3.51968i	0.147601	+	0.112203i
$985$	15.4553	−	29.1518i	0.492447	−	0.928854i
$986$	−0.572106	+	2.06054i	−0.0182196	+	0.0656209i
$987$	1.04216	−	0.987191i	0.0331725	−	0.0314226i
$988$	−0.917810	+	2.30353i	−0.0291994	+	0.0732850i
$989$	−6.44156	−	2.17041i	−0.204830	−	0.0690151i
$990$	−8.43788	−	0.917675i	−0.268174	−	0.0291656i
$991$	−19.2096	+	8.88729i	−0.610212	+	0.282314i	−0.700557	−	0.713596i	$-0.747065\pi$
$991$	−19.2096	+	8.88729i	−0.610212	+	0.282314i	0.0903452	+	0.995911i	$0.471203\pi$
$992$	0.759065	+	0.719024i	0.0241003	+	0.0228290i
$993$	12.7432	−	7.66731i	0.404392	−	0.243315i
$994$	−0.779536	+	0.0847796i	−0.0247254	+	0.00268905i
$995$	−32.5518	−	7.16519i	−1.03196	−	0.227152i
$996$	3.57639	+	12.8810i	0.113322	+	0.408150i
$997$	27.5375	+	16.5688i	0.872121	+	0.524738i	0.879861	−	0.475232i	$-0.157636\pi$
$997$	27.5375	+	16.5688i	0.872121	+	0.524738i	−0.00773911	+	0.999970i	$0.502463\pi$
$998$	9.65238	+	4.46567i	0.305541	+	0.141358i
$999$	1.72740	+	4.33545i	0.0546526	+	0.137168i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.b.253.1	yes	56
59.7	even	29	inner	354.2.e.b.7.1	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.b.7.1	✓	56	59.7	even	29	inner
354.2.e.b.253.1	yes	56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.561187 - 0.827689i) q^{2} +(-0.0541389 - 0.998533i) q^{3} +(-0.370138 - 0.928977i) q^{4} +(-2.31715 - 1.07203i) q^{5} +(-0.856857 - 0.515554i) q^{6} +(0.0770120 + 0.277372i) q^{7} +(-0.976621 - 0.214970i) q^{8} +(-0.994138 + 0.108119i) q^{9} +O(q^{10})\)	\(q+(0.561187 - 0.827689i) q^{2} +(-0.0541389 - 0.998533i) q^{3} +(-0.370138 - 0.928977i) q^{4} +(-2.31715 - 1.07203i) q^{5} +(-0.856857 - 0.515554i) q^{6} +(0.0770120 + 0.277372i) q^{7} +(-0.976621 - 0.214970i) q^{8} +(-0.994138 + 0.108119i) q^{9} +(-2.18766 + 1.31627i) q^{10} +(-2.41351 - 2.28620i) q^{11} +(-0.907575 + 0.419889i) q^{12} +(-1.39566 - 0.151787i) q^{13} +(0.272796 + 0.0919157i) q^{14} +(-0.945008 + 2.37179i) q^{15} +(-0.725995 + 0.687699i) q^{16} +(0.514946 - 1.85467i) q^{17} +(-0.468408 + 0.883512i) q^{18} +(1.40611 + 1.06890i) q^{19} +(-0.138223 + 2.54938i) q^{20} +(0.272796 - 0.0919157i) q^{21} +(-3.24669 + 0.714651i) q^{22} +(-1.00267 - 1.89123i) q^{23} +(-0.161782 + 0.986827i) q^{24} +(0.983010 + 1.15729i) q^{25} +(-0.908858 + 1.06999i) q^{26} +(0.161782 + 0.986827i) q^{27} +(0.229167 - 0.174208i) q^{28} +(-0.623479 - 0.919563i) q^{29} +(1.43278 + 2.11319i) q^{30} +(0.832355 - 0.632740i) q^{31} +(0.161782 + 0.986827i) q^{32} +(-2.15218 + 2.53374i) q^{33} +(-1.24611 - 1.46703i) q^{34} +(0.118902 - 0.725272i) q^{35} +(0.468408 + 0.883512i) q^{36} +(4.55780 - 1.00325i) q^{37} +(1.67381 - 0.563972i) q^{38} +(-0.0760049 + 1.40183i) q^{39} +(2.03252 + 1.54508i) q^{40} +(2.72425 - 5.13848i) q^{41} +(0.0770120 - 0.277372i) q^{42} +(2.30538 - 2.18378i) q^{43} +(-1.23049 + 3.08831i) q^{44} +(2.41947 + 0.815216i) q^{45} +(-2.12803 - 0.231438i) q^{46} +(4.52581 - 2.09386i) q^{47} +(0.725995 + 0.687699i) q^{48} +(5.92700 - 3.56616i) q^{49} +(1.50953 - 0.164171i) q^{50} +(-1.87983 - 0.413781i) q^{51} +(0.375580 + 1.35272i) q^{52} +(-1.51146 - 0.909416i) q^{53} +(0.907575 + 0.419889i) q^{54} +(3.14160 + 7.88482i) q^{55} +(-0.0155847 - 0.287443i) q^{56} +(0.991206 - 1.46192i) q^{57} -1.11100 q^{58} +(-4.43334 - 6.27260i) q^{59} +2.55312 q^{60} +(-0.430491 + 0.634927i) q^{61} +(-0.0566049 - 1.04402i) q^{62} +(-0.106550 - 0.267420i) q^{63} +(0.907575 + 0.419889i) q^{64} +(3.07123 + 1.84790i) q^{65} +(0.889376 + 3.20324i) q^{66} +(-9.18997 - 2.02287i) q^{67} +(-1.91355 + 0.208111i) q^{68} +(-1.83417 + 1.10359i) q^{69} +(-0.533573 - 0.505428i) q^{70} +(-2.47220 + 1.14376i) q^{71} +(0.994138 + 0.108119i) q^{72} +(8.49301 + 2.86163i) q^{73} +(1.72740 - 4.33545i) q^{74} +(1.10237 - 1.04422i) q^{75} +(0.472527 - 1.70189i) q^{76} +(0.448259 - 0.845506i) q^{77} +(1.11763 + 0.849597i) q^{78} +(-0.475896 + 8.77738i) q^{79} +(2.41947 - 0.815216i) q^{80} +(0.976621 - 0.214970i) q^{81} +(-2.72425 - 5.13848i) q^{82} +(2.16274 - 13.1922i) q^{83} +(-0.186360 - 0.219400i) q^{84} +(-3.18146 + 3.74551i) q^{85} +(-0.513735 - 3.13365i) q^{86} +(-0.884460 + 0.672349i) q^{87} +(1.86562 + 2.75158i) q^{88} +(8.92466 + 13.1629i) q^{89} +(2.03252 - 1.54508i) q^{90} +(-0.0653810 - 0.398806i) q^{91} +(-1.38578 + 1.63147i) q^{92} +(-0.676875 - 0.796879i) q^{93} +(0.806759 - 4.92101i) q^{94} +(-2.11229 - 3.98419i) q^{95} +(0.976621 - 0.214970i) q^{96} +(5.15668 - 1.73749i) q^{97} +(0.374486 - 6.90699i) q^{98} +(2.64654 + 2.01185i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} + 30 q^{11} + 2 q^{12} + 5 q^{13} + 28 q^{14} + 2 q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 28 q^{21} - q^{22} - 2 q^{23} - 2 q^{24} + 64 q^{25} - 34 q^{26} + 2 q^{27} + q^{28} + 8 q^{29} - 2 q^{30} + 2 q^{32} - q^{33} + 32 q^{34} - 87 q^{35} - 2 q^{36} + 47 q^{37} + 4 q^{38} - 5 q^{39} + 2 q^{40} + 3 q^{41} + q^{42} - 61 q^{43} + q^{44} - 2 q^{45} - 27 q^{46} + 50 q^{47} + 2 q^{48} - 45 q^{49} - 6 q^{50} + 3 q^{51} - 24 q^{52} - 27 q^{53} - 2 q^{54} - 95 q^{55} - q^{56} + 4 q^{57} + 50 q^{58} - 58 q^{59} + 2 q^{60} - 74 q^{61} - 29 q^{62} + q^{63} - 2 q^{64} - 17 q^{65} + q^{66} + 4 q^{67} - 32 q^{68} + 31 q^{69} - 58 q^{70} - 47 q^{71} + 2 q^{72} + 43 q^{73} - 18 q^{74} - 6 q^{75} - 33 q^{76} - 5 q^{77} + 5 q^{78} + 19 q^{79} - 2 q^{80} - 2 q^{81} - 3 q^{82} + 47 q^{83} - q^{84} - 149 q^{85} - 55 q^{86} + 21 q^{87} + 28 q^{88} + 36 q^{89} + 2 q^{90} + 175 q^{91} - 2 q^{92} - 29 q^{93} - 21 q^{94} + 50 q^{95} - 2 q^{96} + 10 q^{97} - 13 q^{98} + q^{99}+O(q^{100}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 + 30 * q^11 + 2 * q^12 + 5 * q^13 + 28 * q^14 + 2 * q^15 - 2 * q^16 - 3 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 28 * q^21 - q^22 - 2 * q^23 - 2 * q^24 + 64 * q^25 - 34 * q^26 + 2 * q^27 + q^28 + 8 * q^29 - 2 * q^30 + 2 * q^32 - q^33 + 32 * q^34 - 87 * q^35 - 2 * q^36 + 47 * q^37 + 4 * q^38 - 5 * q^39 + 2 * q^40 + 3 * q^41 + q^42 - 61 * q^43 + q^44 - 2 * q^45 - 27 * q^46 + 50 * q^47 + 2 * q^48 - 45 * q^49 - 6 * q^50 + 3 * q^51 - 24 * q^52 - 27 * q^53 - 2 * q^54 - 95 * q^55 - q^56 + 4 * q^57 + 50 * q^58 - 58 * q^59 + 2 * q^60 - 74 * q^61 - 29 * q^62 + q^63 - 2 * q^64 - 17 * q^65 + q^66 + 4 * q^67 - 32 * q^68 + 31 * q^69 - 58 * q^70 - 47 * q^71 + 2 * q^72 + 43 * q^73 - 18 * q^74 - 6 * q^75 - 33 * q^76 - 5 * q^77 + 5 * q^78 + 19 * q^79 - 2 * q^80 - 2 * q^81 - 3 * q^82 + 47 * q^83 - q^84 - 149 * q^85 - 55 * q^86 + 21 * q^87 + 28 * q^88 + 36 * q^89 + 2 * q^90 + 175 * q^91 - 2 * q^92 - 29 * q^93 - 21 * q^94 + 50 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + q^99

Introduction

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