LMFDB - Embedded newform 520.2.ca.b.101.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(101,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("520.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.ca (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.14
Character	$\chi$	$=$	520.101
Dual form			520.2.ca.b.381.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0643054 - 1.41275i) q^{2} +(-0.756863 + 0.436975i) q^{3} +(-1.99173 + 0.181695i) q^{4} +1.00000 q^{5} +(0.666007 + 1.04116i) q^{6} +(-0.0742471 - 0.0428666i) q^{7} +(0.384769 + 2.80213i) q^{8} +(-1.11811 + 1.93662i) q^{9} +O(q^{10})$	\(q+(-0.0643054 - 1.41275i) q^{2} +(-0.756863 + 0.436975i) q^{3} +(-1.99173 + 0.181695i) q^{4} +1.00000 q^{5} +(0.666007 + 1.04116i) q^{6} +(-0.0742471 - 0.0428666i) q^{7} +(0.384769 + 2.80213i) q^{8} +(-1.11811 + 1.93662i) q^{9} +(-0.0643054 - 1.41275i) q^{10} +(-2.27673 - 3.94342i) q^{11} +(1.42807 - 1.00785i) q^{12} +(-3.32098 + 1.40396i) q^{13} +(-0.0557853 + 0.107649i) q^{14} +(-0.756863 + 0.436975i) q^{15} +(3.93397 - 0.723775i) q^{16} +(-1.52793 + 2.64646i) q^{17} +(2.80786 + 1.45507i) q^{18} +(-3.10816 + 5.38350i) q^{19} +(-1.99173 + 0.181695i) q^{20} +0.0749265 q^{21} +(-5.42466 + 3.47004i) q^{22} +(-0.442273 - 0.766039i) q^{23} +(-1.51568 - 1.95270i) q^{24} +1.00000 q^{25} +(2.19701 + 4.60143i) q^{26} -4.57619i q^{27} +(0.155669 + 0.0718883i) q^{28} +(-7.25294 + 4.18749i) q^{29} +(0.666007 + 1.04116i) q^{30} +0.361482i q^{31} +(-1.27549 - 5.51118i) q^{32} +(3.44635 + 1.98975i) q^{33} +(3.83704 + 1.98841i) q^{34} +(-0.0742471 - 0.0428666i) q^{35} +(1.87509 - 4.06037i) q^{36} +(5.44751 + 9.43537i) q^{37} +(7.80541 + 4.04487i) q^{38} +(1.90003 - 2.51379i) q^{39} +(0.384769 + 2.80213i) q^{40} +(-2.68015 + 1.54738i) q^{41} +(-0.00481818 - 0.105852i) q^{42} +(7.38455 + 4.26347i) q^{43} +(5.25114 + 7.44055i) q^{44} +(-1.11811 + 1.93662i) q^{45} +(-1.05378 + 0.674081i) q^{46} -1.90393i q^{47} +(-2.66121 + 2.26685i) q^{48} +(-3.49632 - 6.05581i) q^{49} +(-0.0643054 - 1.41275i) q^{50} -2.67068i q^{51} +(6.35939 - 3.39972i) q^{52} +7.26904i q^{53} +(-6.46501 + 0.294274i) q^{54} +(-2.27673 - 3.94342i) q^{55} +(0.0915499 - 0.224544i) q^{56} -5.43276i q^{57} +(6.38228 + 9.97732i) q^{58} +(3.94248 - 6.82858i) q^{59} +(1.42807 - 1.00785i) q^{60} +(-7.64214 - 4.41219i) q^{61} +(0.510684 - 0.0232453i) q^{62} +(0.166032 - 0.0958587i) q^{63} +(-7.70391 + 2.15635i) q^{64} +(-3.32098 + 1.40396i) q^{65} +(2.58940 - 4.99679i) q^{66} +(-2.77767 - 4.81106i) q^{67} +(2.56238 - 5.54865i) q^{68} +(0.669480 + 0.386524i) q^{69} +(-0.0557853 + 0.107649i) q^{70} +(-0.246775 - 0.142475i) q^{71} +(-5.85687 - 2.38793i) q^{72} +2.37550i q^{73} +(12.9795 - 8.30273i) q^{74} +(-0.756863 + 0.436975i) q^{75} +(5.21247 - 11.2872i) q^{76} +0.390383i q^{77} +(-3.67354 - 2.52262i) q^{78} -12.8740 q^{79} +(3.93397 - 0.723775i) q^{80} +(-1.35464 - 2.34630i) q^{81} +(2.35842 + 3.68687i) q^{82} -7.10893 q^{83} +(-0.149233 + 0.0136138i) q^{84} +(-1.52793 + 2.64646i) q^{85} +(5.54835 - 10.7067i) q^{86} +(3.65965 - 6.33871i) q^{87} +(10.1740 - 7.89702i) q^{88} +(10.3751 - 5.99007i) q^{89} +(2.80786 + 1.45507i) q^{90} +(0.306756 + 0.0381187i) q^{91} +(1.02007 + 1.44538i) q^{92} +(-0.157959 - 0.273593i) q^{93} +(-2.68978 + 0.122433i) q^{94} +(-3.10816 + 5.38350i) q^{95} +(3.37362 + 3.61385i) q^{96} +(13.3330 + 7.69782i) q^{97} +(-8.33052 + 5.32886i) q^{98} +10.1825 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9}+O(q^{10}) $ 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9	$ 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9} - 8 q^{11} + 6 q^{12} - 4 q^{14} + 14 q^{16} + 18 q^{18} - 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 22 q^{24} + 56 q^{25} - 37 q^{26} - 12 q^{28} - 13 q^{30} - 30 q^{32} - 16 q^{34} + 15 q^{36} + 4 q^{37} - 24 q^{39} - 61 q^{42} + 24 q^{44} + 28 q^{45} - 19 q^{46} - 51 q^{48} + 20 q^{49} - 64 q^{52} - 5 q^{54} - 8 q^{55} - 23 q^{56} - q^{58} - 16 q^{59} + 6 q^{60} + 10 q^{62} - 30 q^{64} + 14 q^{66} - 36 q^{67} - 51 q^{68} - 4 q^{70} - 81 q^{72} + 70 q^{74} - 60 q^{76} + 143 q^{78} + 14 q^{80} - 28 q^{81} + 21 q^{82} + 40 q^{83} + 31 q^{84} - 28 q^{86} - 36 q^{87} - 19 q^{88} + 18 q^{90} + 16 q^{91} - 18 q^{92} + 43 q^{94} - 16 q^{95} - 48 q^{96} + 24 q^{97} + 56 q^{98} - 48 q^{99}+O(q^{100}) $ 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9 - 8 * q^11 + 6 * q^12 - 4 * q^14 + 14 * q^16 + 18 * q^18 - 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 22 * q^24 + 56 * q^25 - 37 * q^26 - 12 * q^28 - 13 * q^30 - 30 * q^32 - 16 * q^34 + 15 * q^36 + 4 * q^37 - 24 * q^39 - 61 * q^42 + 24 * q^44 + 28 * q^45 - 19 * q^46 - 51 * q^48 + 20 * q^49 - 64 * q^52 - 5 * q^54 - 8 * q^55 - 23 * q^56 - q^58 - 16 * q^59 + 6 * q^60 + 10 * q^62 - 30 * q^64 + 14 * q^66 - 36 * q^67 - 51 * q^68 - 4 * q^70 - 81 * q^72 + 70 * q^74 - 60 * q^76 + 143 * q^78 + 14 * q^80 - 28 * q^81 + 21 * q^82 + 40 * q^83 + 31 * q^84 - 28 * q^86 - 36 * q^87 - 19 * q^88 + 18 * q^90 + 16 * q^91 - 18 * q^92 + 43 * q^94 - 16 * q^95 - 48 * q^96 + 24 * q^97 + 56 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.0643054	−	1.41275i	−0.0454708	−	0.998966i
$2$	−0.0643054	−	1.41275i	−0.0454708	−	0.998966i
$3$	−0.756863	+	0.436975i	−0.436975	+	0.252288i	−0.702314	−	0.711868i	$-0.747850\pi$
$3$	−0.756863	+	0.436975i	−0.436975	+	0.252288i	0.265339	+	0.964155i	$0.414516\pi$
$4$	−1.99173	+	0.181695i	−0.995865	+	0.0908476i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.666007	+	1.04116i	0.271896	+	0.425051i
$7$	−0.0742471	−	0.0428666i	−0.0280628	−	0.0162020i	0.485903	−	0.874013i	$-0.338491\pi$
$7$	−0.0742471	−	0.0428666i	−0.0280628	−	0.0162020i	−0.513966	+	0.857811i	$0.671824\pi$
$8$	0.384769	+	2.80213i	0.136036	+	0.990704i
$9$	−1.11811	+	1.93662i	−0.372702	+	0.645538i
$10$	−0.0643054	−	1.41275i	−0.0203352	−	0.446751i
$11$	−2.27673	−	3.94342i	−0.686461	−	1.18899i	−0.972975	−	0.230909i	$-0.925830\pi$
$11$	−2.27673	−	3.94342i	−0.686461	−	1.18899i	0.286514	−	0.958076i	$-0.407503\pi$
$12$	1.42807	−	1.00785i	0.412248	−	0.290943i
$13$	−3.32098	+	1.40396i	−0.921073	+	0.389389i
$13$	−3.32098	+	1.40396i	−0.921073	+	0.389389i
$14$	−0.0557853	+	0.107649i	−0.0149092	+	0.0287704i
$15$	−0.756863	+	0.436975i	−0.195421	+	0.112827i
$16$	3.93397	−	0.723775i	0.983493	−	0.180944i
$17$	−1.52793	+	2.64646i	−0.370579	+	0.641861i	−0.989655	−	0.143470i	$-0.954174\pi$
$17$	−1.52793	+	2.64646i	−0.370579	+	0.641861i	0.619076	+	0.785331i	$0.287507\pi$
$18$	2.80786	+	1.45507i	0.661818	+	0.342963i
$19$	−3.10816	+	5.38350i	−0.713061	+	1.23506i	0.250641	+	0.968080i	$0.419359\pi$
$19$	−3.10816	+	5.38350i	−0.713061	+	1.23506i	−0.963702	+	0.266979i	$0.913975\pi$
$20$	−1.99173	+	0.181695i	−0.445364	+	0.0406283i
$21$	0.0749265			0.0163503
$22$	−5.42466	+	3.47004i	−1.15654	+	0.739815i
$23$	−0.442273	−	0.766039i	−0.0922202	−	0.159730i	0.816225	−	0.577734i	$-0.196063\pi$
$23$	−0.442273	−	0.766039i	−0.0922202	−	0.159730i	−0.908445	+	0.418004i	$0.862730\pi$
$24$	−1.51568	−	1.95270i	−0.309387	−	0.398593i
$25$	1.00000			0.200000
$26$	2.19701	+	4.60143i	0.430869	+	0.902415i
$27$		−	4.57619i		−	0.880688i
$28$	0.155669	+	0.0718883i	0.0294186	+	0.0135856i
$29$	−7.25294	+	4.18749i	−1.34684	+	0.777597i	−0.987800	−	0.155727i	$-0.950228\pi$
$29$	−7.25294	+	4.18749i	−1.34684	+	0.777597i	−0.359037	+	0.933323i	$0.616895\pi$
$30$	0.666007	+	1.04116i	0.121596	+	0.190089i
$31$			0.361482i			0.0649241i	0.999473	+	0.0324621i	$0.0103348\pi$
$31$			0.361482i			0.0649241i	−0.999473	+	0.0324621i	$0.989665\pi$
$32$	−1.27549	−	5.51118i	−0.225477	−	0.974249i
$33$	3.44635	+	1.98975i	0.599933	+	0.346371i
$34$	3.83704	+	1.98841i	0.658047	+	0.341009i
$35$	−0.0742471	−	0.0428666i	−0.0125500	−	0.00724577i
$36$	1.87509	−	4.06037i	0.312515	−	0.676728i
$37$	5.44751	+	9.43537i	0.895566	+	1.55117i	0.833103	+	0.553118i	$0.186562\pi$
$37$	5.44751	+	9.43537i	0.895566	+	1.55117i	0.0624631	+	0.998047i	$0.480104\pi$
$38$	7.80541	+	4.04487i	1.26620	+	0.656165i
$39$	1.90003	−	2.51379i	0.304248	−	0.402529i
$40$	0.384769	+	2.80213i	0.0608373	+	0.443056i
$41$	−2.68015	+	1.54738i	−0.418569	+	0.241661i	−0.694465	−	0.719527i	$-0.744359\pi$
$41$	−2.68015	+	1.54738i	−0.418569	+	0.241661i	0.275896	+	0.961187i	$0.411025\pi$
$42$	−0.00481818	−	0.105852i	−0.000743461	−	0.0163334i
$43$	7.38455	+	4.26347i	1.12613	+	0.650173i	0.942959	−	0.332908i	$-0.108030\pi$
$43$	7.38455	+	4.26347i	1.12613	+	0.650173i	0.183173	+	0.983081i	$0.441363\pi$
$44$	5.25114	+	7.44055i	0.791639	+	1.12171i
$45$	−1.11811	+	1.93662i	−0.166677	+	0.288694i
$46$	−1.05378	+	0.674081i	−0.155372	+	0.0993879i
$47$		−	1.90393i		−	0.277717i	−0.990312	−	0.138859i	$-0.955657\pi$
$47$		−	1.90393i		−	0.277717i	0.990312	−	0.138859i	$-0.0443434\pi$
$48$	−2.66121	+	2.26685i	−0.384112	+	0.327191i
$49$	−3.49632	−	6.05581i	−0.499475	−	0.865116i
$50$	−0.0643054	−	1.41275i	−0.00909416	−	0.199793i
$51$		−	2.67068i		−	0.373970i
$52$	6.35939	−	3.39972i	0.881889	−	0.471457i
$53$			7.26904i			0.998479i	0.866464	+	0.499240i	$0.166387\pi$
$53$			7.26904i			0.998479i	−0.866464	+	0.499240i	$0.833613\pi$
$54$	−6.46501	+	0.294274i	−0.879777	+	0.0400456i
$55$	−2.27673	−	3.94342i	−0.306995	−	0.531730i
$56$	0.0915499	−	0.224544i	0.0122339	−	0.0300059i
$57$		−	5.43276i		−	0.719587i
$58$	6.38228	+	9.97732i	0.838034	+	1.31009i
$59$	3.94248	−	6.82858i	0.513268	−	0.889005i	−0.486614	−	0.873617i	$-0.661768\pi$
$59$	3.94248	−	6.82858i	0.513268	−	0.889005i	0.999882	−	0.0153884i	$-0.00489846\pi$
$60$	1.42807	−	1.00785i	0.184363	−	0.130113i
$61$	−7.64214	−	4.41219i	−0.978475	−	0.564923i	−0.0766658	−	0.997057i	$-0.524427\pi$
$61$	−7.64214	−	4.41219i	−0.978475	−	0.564923i	−0.901809	+	0.432134i	$0.857761\pi$
$62$	0.510684	−	0.0232453i	0.0648570	−	0.00295215i
$63$	0.166032	−	0.0958587i	0.0209181	−	0.0120771i
$64$	−7.70391	+	2.15635i	−0.962988	+	0.269544i
$65$	−3.32098	+	1.40396i	−0.411916	+	0.174140i
$66$	2.58940	−	4.99679i	0.318734	−	0.615062i
$67$	−2.77767	−	4.81106i	−0.339346	−	0.587764i	0.644964	−	0.764213i	$-0.276872\pi$
$67$	−2.77767	−	4.81106i	−0.339346	−	0.587764i	−0.984310	+	0.176449i	$0.943539\pi$
$68$	2.56238	−	5.54865i	0.310735	−	0.672873i
$69$	0.669480	+	0.386524i	0.0805959	+	0.0465321i
$70$	−0.0557853	+	0.107649i	−0.00666762	+	0.0128665i
$71$	−0.246775	−	0.142475i	−0.0292868	−	0.0169087i	0.485285	−	0.874356i	$-0.338716\pi$
$71$	−0.246775	−	0.142475i	−0.0292868	−	0.0169087i	−0.514572	+	0.857447i	$0.672049\pi$
$72$	−5.85687	−	2.38793i	−0.690238	−	0.281420i
$73$			2.37550i			0.278032i	0.990290	+	0.139016i	$0.0443939\pi$
$73$			2.37550i			0.278032i	−0.990290	+	0.139016i	$0.955606\pi$
$74$	12.9795	−	8.30273i	1.50884	−	0.965172i
$75$	−0.756863	+	0.436975i	−0.0873950	+	0.0504575i
$76$	5.21247	−	11.2872i	0.597911	−	1.29473i
$77$			0.390383i			0.0444883i
$78$	−3.67354	−	2.52262i	−0.415947	−	0.285630i
$79$	−12.8740			−1.44844			−0.724218	−	0.689572i	$-0.757799\pi$
$79$	−12.8740			−1.44844			−0.724218	+	0.689572i	$0.757799\pi$
$80$	3.93397	−	0.723775i	0.439832	−	0.0809205i
$81$	−1.35464	−	2.34630i	−0.150515	−	0.260700i
$82$	2.35842	+	3.68687i	0.260443	+	0.407147i
$83$	−7.10893			−0.780307			−0.390153	−	0.920750i	$-0.627578\pi$
$83$	−7.10893			−0.780307			−0.390153	+	0.920750i	$0.627578\pi$
$84$	−0.149233	+	0.0136138i	−0.0162827	+	0.00148538i
$85$	−1.52793	+	2.64646i	−0.165728	+	0.287049i
$86$	5.54835	−	10.7067i	0.598294	−	1.15453i
$87$	3.65965	−	6.33871i	0.392356	−	0.679581i
$88$	10.1740	−	7.89702i	1.08455	−	0.841825i
$89$	10.3751	−	5.99007i	1.09976	−	0.634946i	0.163602	−	0.986526i	$-0.447689\pi$
$89$	10.3751	−	5.99007i	1.09976	−	0.634946i	0.936158	+	0.351580i	$0.114355\pi$
$90$	2.80786	+	1.45507i	0.295974	+	0.153378i
$91$	0.306756	+	0.0381187i	0.0321568	+	0.00399592i
$92$	1.02007	+	1.44538i	0.106350	+	0.150692i
$93$	−0.157959	−	0.273593i	−0.0163796	−	0.0283702i
$94$	−2.68978	+	0.122433i	−0.277430	+	0.0126280i
$95$	−3.10816	+	5.38350i	−0.318891	+	0.552335i
$96$	3.37362	+	3.61385i	0.344319	+	0.368837i
$97$	13.3330	+	7.69782i	1.35376	+	0.781595i	0.988774	−	0.149417i	$-0.0477398\pi$
$97$	13.3330	+	7.69782i	1.35376	+	0.781595i	0.364988	+	0.931012i	$0.381073\pi$
$98$	−8.33052	+	5.32886i	−0.841510	+	0.538296i
$99$	10.1825			1.02338
$100$	−1.99173	+	0.181695i	−0.199173	+	0.0181695i
$101$	−2.25454	+	1.30166i	−0.224335	+	0.129520i	−0.607956	−	0.793971i	$-0.708010\pi$
$101$	−2.25454	+	1.30166i	−0.224335	+	0.129520i	0.383621	+	0.923491i	$0.374677\pi$
$102$	−3.77300	+	0.171739i	−0.373583	+	0.0170047i
$103$	−13.1891			−1.29956			−0.649780	−	0.760122i	$-0.725139\pi$
$103$	−13.1891			−1.29956			−0.649780	+	0.760122i	$0.725139\pi$
$104$	−5.21190	−	8.76562i	−0.511069	−	0.859540i
$105$	0.0749265			0.00731208
$106$	10.2693	−	0.467439i	0.997447	−	0.0454017i
$107$	−0.686143	+	0.396145i	−0.0663320	+	0.0382968i	−0.532799	−	0.846242i	$-0.678860\pi$
$107$	−0.686143	+	0.396145i	−0.0663320	+	0.0382968i	0.466467	+	0.884538i	$0.345527\pi$
$108$	0.831471	+	9.11453i	0.0800083	+	0.877046i
$109$	−4.25841			−0.407882			−0.203941	−	0.978983i	$-0.565375\pi$
$109$	−4.25841			−0.407882			−0.203941	+	0.978983i	$0.565375\pi$
$110$	−5.42466	+	3.47004i	−0.517221	+	0.330855i
$111$	−8.24605	−	4.76086i	−0.782680	−	0.451881i
$112$	−0.323112	−	0.114898i	−0.0305312	−	0.0108568i
$113$	9.57915	−	16.5916i	0.901131	−	1.56080i	0.0751021	−	0.997176i	$-0.476072\pi$
$113$	9.57915	−	16.5916i	0.901131	−	1.56080i	0.826029	−	0.563628i	$-0.190595\pi$
$114$	−7.67514	+	0.349356i	−0.718842	+	0.0327202i
$115$	−0.442273	−	0.766039i	−0.0412421	−	0.0714335i
$116$	13.6850	−	9.65816i	1.27062	−	0.896738i
$117$	0.994264	−	8.00123i	0.0919197	−	0.739714i
$118$	−9.90061	−	5.13063i	−0.911425	−	0.472313i
$119$	0.226889	−	0.130995i	0.0207989	−	0.0120083i
$120$	−1.51568	−	1.95270i	−0.138362	−	0.178256i
$121$	−4.86703	+	8.42994i	−0.442457	+	0.766358i
$122$	−5.74189	+	11.0802i	−0.519847	+	1.00315i
$123$	1.35234	−	2.34232i	0.121936	−	0.211199i
$124$	−0.0656796	−	0.719975i	−0.00589820	−	0.0646557i
$125$	1.00000			0.0894427
$126$	−0.146101	−	0.228398i	−0.0130157	−	0.0203473i
$127$	−1.86945	−	3.23798i	−0.165887	−	0.287324i	0.771083	−	0.636734i	$-0.219715\pi$
$127$	−1.86945	−	3.23798i	−0.165887	−	0.287324i	−0.936970	+	0.349410i	$0.886382\pi$
$128$	3.54179	+	10.7450i	0.313053	+	0.949736i
$129$	−7.45212			−0.656123
$130$	2.19701	+	4.60143i	0.192690	+	0.403572i
$131$		−	14.0025i		−	1.22341i	−0.791088	−	0.611703i	$-0.790485\pi$
$131$		−	14.0025i		−	1.22341i	0.791088	−	0.611703i	$-0.209515\pi$
$132$	−7.22573	−	3.33686i	−0.628919	−	0.290437i
$133$	0.461544	−	0.266473i	0.0400209	−	0.0231061i
$134$	−6.61821	+	4.23353i	−0.571726	+	0.365721i
$135$		−	4.57619i		−	0.393856i
$136$	−8.00364	−	3.26320i	−0.686306	−	0.279817i
$137$	−0.324458	−	0.187326i	−0.0277204	−	0.0160044i	0.486076	−	0.873917i	$-0.338428\pi$
$137$	−0.324458	−	0.187326i	−0.0277204	−	0.0160044i	−0.513796	+	0.857912i	$0.671761\pi$
$138$	0.503011	−	0.970663i	0.0428192	−	0.0826284i
$139$	−5.07048	−	2.92744i	−0.430073	−	0.248302i	0.269305	−	0.963055i	$-0.413206\pi$
$139$	−5.07048	−	2.92744i	−0.430073	−	0.248302i	−0.699378	+	0.714752i	$0.746539\pi$
$140$	0.155669	+	0.0718883i	0.0131564	+	0.00607567i
$141$	0.831972	+	1.44102i	0.0700647	+	0.121356i
$142$	−0.185413	+	0.357793i	−0.0155595	+	0.0300253i
$143$	13.0974	+	9.89955i	1.09526	+	0.827842i
$144$	−2.99692	+	8.42785i	−0.249744	+	0.702321i
$145$	−7.25294	+	4.18749i	−0.602324	+	0.347752i
$146$	3.35600	−	0.152758i	0.277744	−	0.0126423i
$147$	5.29248	+	3.05561i	0.436516	+	0.252023i
$148$	−12.5643	−	17.8029i	−1.03278	−	1.46339i
$149$	−4.97790	+	8.62197i	−0.407805	+	0.706339i	−0.994644	−	0.103365i	$-0.967039\pi$
$149$	−4.97790	+	8.62197i	−0.407805	+	0.706339i	0.586838	+	0.809704i	$0.300372\pi$
$150$	0.666007	+	1.04116i	0.0543793	+	0.0850103i
$151$			10.9163i			0.888355i	0.895939	+	0.444177i	$0.146504\pi$
$151$			10.9163i			0.888355i	−0.895939	+	0.444177i	$0.853496\pi$
$152$	−16.2812	−	6.63809i	−1.32058	−	0.538420i
$153$	−3.41678	−	5.91804i	−0.276231	−	0.478445i
$154$	0.551514	−	0.0251037i	0.0444422	−	0.00202292i
$155$			0.361482i			0.0290350i
$156$	−3.32760	+	5.35202i	−0.266421	+	0.428505i
$157$			12.2036i			0.973956i	0.873414	+	0.486978i	$0.161901\pi$
$157$			12.2036i			0.973956i	−0.873414	+	0.486978i	$0.838099\pi$
$158$	0.827866	+	18.1877i	0.0658615	+	1.44694i
$159$	−3.17639	−	5.50167i	−0.251904	−	0.436311i
$160$	−1.27549	−	5.51118i	−0.100836	−	0.435697i
$161$			0.0758348i			0.00597662i
$162$	−3.22762	+	2.06464i	−0.253586	+	0.162214i
$163$	−9.93436	+	17.2068i	−0.778119	+	1.34774i	0.154906	+	0.987929i	$0.450493\pi$
$163$	−9.93436	+	17.2068i	−0.778119	+	1.34774i	−0.933025	+	0.359812i	$0.882841\pi$
$164$	5.05698	−	3.56894i	0.394884	−	0.278687i
$165$	3.44635	+	1.98975i	0.268298	+	0.154902i
$166$	0.457143	+	10.0431i	0.0354812	+	0.779499i
$167$	21.1948	−	12.2369i	1.64011	−	0.946916i	0.659313	−	0.751869i	$-0.270847\pi$
$167$	21.1948	−	12.2369i	1.64011	−	0.946916i	0.980794	−	0.195047i	$-0.0624860\pi$
$168$	0.0288294	+	0.209954i	0.00222424	+	0.0161983i
$169$	9.05777	−	9.32506i	0.696752	−	0.717312i
$170$	3.83704	+	1.98841i	0.294288	+	0.152504i
$171$	−6.95051	−	12.0386i	−0.531519	−	0.920617i
$172$	−15.4827	−	7.14994i	−1.18054	−	0.545178i
$173$	15.9570	+	9.21276i	1.21319	+	0.700433i	0.963452	−	0.267882i	$-0.0863236\pi$
$173$	15.9570	+	9.21276i	1.21319	+	0.700433i	0.249734	+	0.968315i	$0.419657\pi$
$174$	−9.19035	−	4.76257i	−0.696719	−	0.361049i
$175$	−0.0742471	−	0.0428666i	−0.00561255	−	0.00324041i
$176$	−11.8108	−	13.8655i	−0.890269	−	1.04515i
$177$			6.89107i			0.517964i
$178$	−9.12966	−	14.2723i	−0.684297	−	1.06975i
$179$	21.6069	−	12.4748i	1.61498	−	0.932409i	0.626786	−	0.779191i	$-0.284370\pi$
$179$	21.6069	−	12.4748i	1.61498	−	0.932409i	0.988193	−	0.153217i	$-0.0489635\pi$
$180$	1.87509	−	4.06037i	0.139761	−	0.302642i
$181$		−	10.9187i		−	0.811581i	−0.913966	−	0.405791i	$-0.866996\pi$
$181$		−	10.9187i		−	0.811581i	0.913966	−	0.405791i	$-0.133004\pi$
$182$	0.0341261	−	0.435821i	0.00252959	−	0.0323052i
$183$	7.71207			0.570093
$184$	1.97637	−	1.53405i	0.145700	−	0.113092i
$185$	5.44751	+	9.43537i	0.400509	+	0.693702i
$186$	−0.376361	+	0.240750i	−0.0275961	+	0.0176526i
$187$	13.9148			1.01755
$188$	0.345935	+	3.79212i	0.0252299	+	0.276569i
$189$	−0.196165	+	0.339769i	−0.0142689	+	0.0247145i
$190$	7.80541	+	4.04487i	0.566264	+	0.293446i
$191$	−11.1046	+	19.2338i	−0.803502	+	1.39171i	0.113796	+	0.993504i	$0.463699\pi$
$191$	−11.1046	+	19.2338i	−0.803502	+	1.39171i	−0.917298	+	0.398202i	$0.869634\pi$
$192$	4.88853	−	4.99848i	0.352799	−	0.360734i
$193$	−9.75842	+	5.63403i	−0.702427	+	0.405546i	−0.808251	−	0.588839i	$-0.799585\pi$
$193$	−9.75842	+	5.63403i	−0.702427	+	0.405546i	0.105824	+	0.994385i	$0.466252\pi$
$194$	10.0177	−	19.3312i	0.719230	−	1.38790i
$195$	1.90003	−	2.51379i	0.136064	−	0.180016i
$196$	8.06405	+	11.4263i	0.576003	+	0.816163i
$197$	−5.69577	−	9.86537i	−0.405807	−	0.702879i	0.588608	−	0.808419i	$-0.299676\pi$
$197$	−5.69577	−	9.86537i	−0.405807	−	0.702879i	−0.994415	+	0.105540i	$0.966343\pi$
$198$	−0.654791	−	14.3854i	−0.0465340	−	1.02232i
$199$	1.03961	−	1.80067i	0.0736963	−	0.127646i	−0.826822	−	0.562463i	$-0.809854\pi$
$199$	1.03961	−	1.80067i	0.0736963	−	0.127646i	0.900519	+	0.434817i	$0.143187\pi$
$200$	0.384769	+	2.80213i	0.0272073	+	0.198141i
$201$	4.20463	+	2.42754i	0.296572	+	0.171226i
$202$	1.98390	+	3.10139i	0.139586	+	0.218213i
$203$	0.718012			0.0503946
$204$	0.485249	+	5.31927i	0.0339742	+	0.372423i
$205$	−2.68015	+	1.54738i	−0.187190	+	0.108074i
$206$	0.848131	+	18.6329i	0.0590921	+	1.29822i
$207$	1.97803			0.137483
$208$	−12.0485	+	7.92680i	−0.835412	+	0.549624i
$209$	28.3058			1.95796
$210$	−0.00481818	−	0.105852i	−0.000332486	−	0.00730451i
$211$	4.26241	−	2.46090i	0.293436	−	0.169415i	−0.346054	−	0.938215i	$-0.612479\pi$
$211$	4.26241	−	2.46090i	0.293436	−	0.169415i	0.639490	+	0.768799i	$0.279145\pi$
$212$	−1.32075	−	14.4780i	−0.0907094	−	0.994350i
$213$	0.249033			0.0170635
$214$	0.603777	+	0.943875i	0.0412733	+	0.0645220i
$215$	7.38455	+	4.26347i	0.503622	+	0.290766i
$216$	12.8231	−	1.76078i	0.872501	−	0.119806i
$217$	0.0154955	−	0.0268390i	0.00105190	−	0.00182195i
$218$	0.273839	+	6.01607i	0.0185467	+	0.407460i
$219$	−1.03804	−	1.79793i	−0.0701440	−	0.121493i
$220$	5.25114	+	7.44055i	0.354032	+	0.501642i
$221$	1.35870	−	10.9340i	0.0913961	−	0.735500i
$222$	−6.19564	+	11.9558i	−0.415824	+	0.802418i
$223$	−10.1721	+	5.87285i	−0.681173	+	0.393275i	−0.800297	−	0.599604i	$-0.795325\pi$
$223$	−10.1721	+	5.87285i	−0.681173	+	0.393275i	0.119124	+	0.992879i	$0.461991\pi$
$224$	−0.141544	+	0.463865i	−0.00945731	+	0.0309933i
$225$	−1.11811	+	1.93662i	−0.0745404	+	0.129108i
$226$	−24.0558	−	12.4660i	−1.60016	−	0.829228i
$227$	−4.94780	+	8.56984i	−0.328397	+	0.568800i	−0.982194	−	0.187870i	$-0.939842\pi$
$227$	−4.94780	+	8.56984i	−0.328397	+	0.568800i	0.653797	+	0.756670i	$0.273175\pi$
$228$	0.987106	+	10.8206i	0.0653727	+	0.716611i
$229$	−8.79054			−0.580895			−0.290448	−	0.956891i	$-0.593804\pi$
$229$	−8.79054			−0.580895			−0.290448	+	0.956891i	$0.593804\pi$
$230$	−1.05378	+	0.674081i	−0.0694843	+	0.0444476i
$231$	−0.170588	−	0.295466i	−0.0112238	−	0.0194403i
$232$	−14.5246	−	18.7125i	−0.953587	−	1.22853i
$233$	4.23373			0.277361			0.138681	−	0.990337i	$-0.455714\pi$
$233$	4.23373			0.277361			0.138681	+	0.990337i	$0.455714\pi$
$234$	−11.3677	−	0.890124i	−0.743129	−	0.0581893i
$235$		−	1.90393i		−	0.124199i
$236$	−6.61164	+	14.3170i	−0.430381	+	0.931958i
$237$	9.74384	−	5.62561i	0.632930	−	0.365422i
$238$	−0.199653	−	0.312114i	−0.0129416	−	0.0202314i
$239$			25.8561i			1.67249i	0.548356	+	0.836245i	$0.315254\pi$
$239$			25.8561i			1.67249i	−0.548356	+	0.836245i	$0.684746\pi$
$240$	−2.66121	+	2.26685i	−0.171780	+	0.146324i
$241$	−8.68380	−	5.01359i	−0.559373	−	0.322954i	0.193521	−	0.981096i	$-0.438009\pi$
$241$	−8.68380	−	5.01359i	−0.559373	−	0.322954i	−0.752894	+	0.658142i	$0.771343\pi$
$242$	12.2224	+	6.33381i	0.785684	+	0.407153i
$243$	13.9398	+	8.04817i	0.894241	+	0.516290i
$244$	16.0227	+	7.39935i	1.02575	+	0.473695i
$245$	−3.49632	−	6.05581i	−0.223372	−	0.386892i
$246$	−3.39607	−	1.75989i	−0.216526	−	0.112207i
$247$	2.76390	−	22.2422i	0.175863	−	1.41524i
$248$	−1.01292	+	0.139087i	−0.0643206	+	0.00883204i
$249$	5.38049	−	3.10643i	0.340975	−	0.196862i
$250$	−0.0643054	−	1.41275i	−0.00406703	−	0.0893502i
$251$	4.01319	+	2.31702i	0.253311	+	0.146249i	0.621279	−	0.783589i	$-0.286613\pi$
$251$	4.01319	+	2.31702i	0.253311	+	0.146249i	−0.367969	+	0.929838i	$0.619947\pi$
$252$	−0.313274	+	0.221092i	−0.0197344	+	0.0139275i
$253$	−2.01387	+	3.48813i	−0.126611	+	0.219297i
$254$	−4.45424	+	2.84928i	−0.279484	+	0.178780i
$255$		−	2.67068i		−	0.167244i
$256$	14.9523	−	5.69462i	0.934519	−	0.355914i
$257$	8.44614	+	14.6291i	0.526856	+	0.912541i	0.999510	+	0.0312931i	$0.00996254\pi$
$257$	8.44614	+	14.6291i	0.526856	+	0.912541i	−0.472654	+	0.881248i	$0.656704\pi$
$258$	0.479212	+	10.5280i	0.0298344	+	0.655444i
$259$		−	0.934065i		−	0.0580400i
$260$	6.35939	−	3.39972i	0.394393	−	0.210842i
$261$		−	18.7282i		−	1.15925i
$262$	−19.7821	+	0.900438i	−1.22214	+	0.0556292i
$263$	0.455144	+	0.788333i	0.0280654	+	0.0486107i	0.879717	−	0.475498i	$-0.157732\pi$
$263$	0.455144	+	0.788333i	0.0280654	+	0.0486107i	−0.851652	+	0.524108i	$0.824399\pi$
$264$	−4.24950	+	10.4227i	−0.261539	+	0.641475i
$265$			7.26904i			0.446534i
$266$	−0.406139	−	0.634911i	−0.0249020	−	0.0389289i
$267$	−5.23503	+	9.06733i	−0.320378	+	0.554912i
$268$	6.40651	+	9.07764i	0.391340	+	0.554505i
$269$	16.7083	+	9.64653i	1.01872	+	0.588159i	0.913733	−	0.406314i	$-0.133186\pi$
$269$	16.7083	+	9.64653i	1.01872	+	0.588159i	0.104988	+	0.994473i	$0.466520\pi$
$270$	−6.46501	+	0.294274i	−0.393448	+	0.0179089i
$271$	0.699374	−	0.403784i	0.0424840	−	0.0245281i	−0.478608	−	0.878029i	$-0.658858\pi$
$271$	0.699374	−	0.403784i	0.0424840	−	0.0245281i	0.521092	+	0.853501i	$0.325525\pi$
$272$	−4.09541	+	11.5170i	−0.248321	+	0.698320i
$273$	−0.248829	+	0.105194i	−0.0150598	+	0.00636664i
$274$	−0.243781	+	0.470425i	−0.0147273	+	0.0284194i
$275$	−2.27673	−	3.94342i	−0.137292	−	0.237797i
$276$	−1.40365	−	0.648211i	−0.0844899	−	0.0390177i
$277$	25.1286	+	14.5080i	1.50983	+	0.871701i	0.999934	+	0.0114653i	$0.00364961\pi$
$277$	25.1286	+	14.5080i	1.50983	+	0.871701i	0.509896	+	0.860236i	$0.329684\pi$
$278$	−3.80969	+	7.35158i	−0.228490	+	0.440918i
$279$	−0.700052	−	0.404175i	−0.0419110	−	0.0241973i
$280$	0.0915499	−	0.224544i	0.00547115	−	0.0134191i
$281$			21.6992i			1.29447i	0.762293	+	0.647233i	$0.224074\pi$
$281$			21.6992i			1.29447i	−0.762293	+	0.647233i	$0.775926\pi$
$282$	1.98230	−	1.26803i	0.118044	−	0.0755103i
$283$	16.5669	−	9.56493i	0.984803	−	0.568576i	0.0810860	−	0.996707i	$-0.474161\pi$
$283$	16.5669	−	9.56493i	0.984803	−	0.568576i	0.903717	+	0.428131i	$0.140828\pi$
$284$	0.517396	+	0.238935i	0.0307018	+	0.0141782i
$285$		−	5.43276i		−	0.321809i
$286$	13.1434	−	19.1399i	0.777183	−	1.13177i
$287$	0.265324			0.0156616
$288$	12.0992	+	3.69195i	0.712951	+	0.217550i
$289$	3.83083	+	6.63520i	0.225343	+	0.390306i
$290$	6.38228	+	9.97732i	0.374780	+	0.585888i
$291$	−13.4550			−0.788747
$292$	−0.431617	−	4.73136i	−0.0252585	−	0.276882i
$293$	8.51380	−	14.7463i	0.497381	−	0.861490i	−0.502614	−	0.864511i	$-0.667628\pi$
$293$	8.51380	−	14.7463i	0.497381	−	0.861490i	0.999995	+	0.00302101i	$0.000961620\pi$
$294$	3.97649	−	7.67345i	0.231913	−	0.447525i
$295$	3.94248	−	6.82858i	0.229540	−	0.397575i
$296$	−24.3431	+	18.8951i	−1.41492	+	1.09826i
$297$	−18.0458	+	10.4188i	−1.04712	+	0.604558i
$298$	12.5008	+	6.47809i	0.724152	+	0.375266i
$299$	2.54427	+	1.92306i	0.147139	+	0.111214i
$300$	1.42807	−	1.00785i	0.0824497	−	0.0581885i
$301$	−0.365521	−	0.633100i	−0.0210683	−	0.0364913i
$302$	15.4220	−	0.701977i	0.887436	−	0.0403942i
$303$	1.13758	−	1.97035i	0.0653525	−	0.113194i
$304$	−8.33099	+	23.4281i	−0.477815	+	1.34370i
$305$	−7.64214	−	4.41219i	−0.437587	−	0.252641i
$306$	−8.14100	+	5.20763i	−0.465390	+	0.297700i
$307$	1.51638			0.0865444			0.0432722	−	0.999063i	$-0.486222\pi$
$307$	1.51638			0.0865444			0.0432722	+	0.999063i	$0.486222\pi$
$308$	−0.0709307	−	0.777537i	−0.00404165	−	0.0443043i
$309$	9.98234	−	5.76331i	0.567876	−	0.327863i
$310$	0.510684	−	0.0232453i	0.0290049	−	0.00132024i
$311$	−19.9984			−1.13401			−0.567003	−	0.823716i	$-0.691897\pi$
$311$	−19.9984			−1.13401			−0.567003	+	0.823716i	$0.691897\pi$
$312$	7.77506	+	4.35690i	0.440176	+	0.246661i
$313$	−20.3211			−1.14861			−0.574307	−	0.818640i	$-0.694728\pi$
$313$	−20.3211			−1.14861			−0.574307	+	0.818640i	$0.694728\pi$
$314$	17.2407	−	0.784760i	0.972948	−	0.0442865i
$315$	0.166032	−	0.0958587i	0.00935485	−	0.00540102i
$316$	25.6415	−	2.33914i	1.44245	−	0.131587i
$317$	8.94280			0.502278			0.251139	−	0.967951i	$-0.419195\pi$
$317$	8.94280			0.502278			0.251139	+	0.967951i	$0.419195\pi$
$318$	−7.56823	+	4.84123i	−0.424405	+	0.271483i
$319$	33.0260	+	19.0676i	1.84910	+	1.06758i
$320$	−7.70391	+	2.15635i	−0.430661	+	0.120544i
$321$	0.346211	−	0.599655i	0.0193236	−	0.0334695i
$322$	0.107136	−	0.00487659i	0.00597044	−	0.000271762i
$323$	−9.49814	−	16.4513i	−0.528491	−	0.915372i
$324$	3.12438	+	4.42706i	0.173577	+	0.245948i
$325$	−3.32098	+	1.40396i	−0.184215	+	0.0778779i
$326$	24.9478	+	12.9283i	1.38173	+	0.716031i
$327$	3.22303	−	1.86082i	0.178234	−	0.102904i
$328$	−5.36721	−	6.91475i	−0.296355	−	0.381803i
$329$	−0.0816151	+	0.141361i	−0.00449959	+	0.00779351i
$330$	2.58940	−	4.99679i	0.142542	−	0.275064i
$331$	−15.2247	+	26.3700i	−0.836827	+	1.44943i	0.0557078	+	0.998447i	$0.482258\pi$
$331$	−15.2247	+	26.3700i	−0.836827	+	1.44943i	−0.892534	+	0.450979i	$0.851075\pi$
$332$	14.1591	−	1.29166i	0.777080	−	0.0708889i
$333$	−24.3636			−1.33512
$334$	−18.6506	−	29.1561i	−1.02051	−	1.59535i
$335$	−2.77767	−	4.81106i	−0.151760	−	0.262856i
$336$	0.294759	−	0.0542299i	0.0160804	−	0.00295849i
$337$	−24.7866			−1.35021			−0.675106	−	0.737721i	$-0.735902\pi$
$337$	−24.7866			−1.35021			−0.675106	+	0.737721i	$0.735902\pi$
$338$	−13.7565	−	12.1967i	−0.748252	−	0.663414i
$339$			16.7434i			0.909377i
$340$	2.56238	−	5.54865i	0.138965	−	0.300918i
$341$	1.42548	−	0.822999i	0.0771938	−	0.0445679i
$342$	−16.5606	+	10.5935i	−0.895496	+	0.572830i
$343$			1.19963i			0.0647741i
$344$	−9.10547	+	22.3329i	−0.490934	+	1.20411i
$345$	0.669480	+	0.386524i	0.0360436	+	0.0208098i
$346$	11.9892	−	23.1356i	0.644544	−	1.24378i
$347$	−24.7946	−	14.3152i	−1.33104	−	0.768478i	−0.345583	−	0.938388i	$-0.612319\pi$
$347$	−24.7946	−	14.3152i	−1.33104	−	0.768478i	−0.985459	+	0.169911i	$0.945652\pi$
$348$	−6.13733	+	13.2899i	−0.328995	+	0.712415i
$349$	−6.20443	−	10.7464i	−0.332115	−	0.575241i	0.650811	−	0.759240i	$-0.274429\pi$
$349$	−6.20443	−	10.7464i	−0.332115	−	0.575241i	−0.982926	+	0.183999i	$0.941096\pi$
$350$	−0.0557853	+	0.107649i	−0.00298185	+	0.00575409i
$351$	6.42480	+	15.1974i	0.342931	+	0.811178i
$352$	−18.8289	+	17.5773i	−1.00359	+	0.936872i
$353$	−4.14246	+	2.39165i	−0.220481	+	0.127295i	−0.606173	−	0.795333i	$-0.707296\pi$
$353$	−4.14246	+	2.39165i	−0.220481	+	0.127295i	0.385692	+	0.922628i	$0.373963\pi$
$354$	9.73536	−	0.443133i	0.517429	−	0.0235523i
$355$	−0.246775	−	0.142475i	−0.0130974	−	0.00756181i
$356$	−19.5760	+	13.8157i	−1.03753	+	0.732231i
$357$	−0.114483	+	0.198290i	−0.00605907	+	0.0104946i
$358$	−19.0132	−	29.7230i	−1.00488	−	1.57091i
$359$			25.7775i			1.36049i	0.732987	+	0.680243i	$0.238126\pi$
$359$			25.7775i			1.36049i	−0.732987	+	0.680243i	$0.761874\pi$
$360$	−5.85687	−	2.38793i	−0.308684	−	0.125855i
$361$	−9.82135	−	17.0111i	−0.516913	−	0.895320i
$362$	−15.4254	+	0.702132i	−0.810742	+	0.0369032i
$363$		−	8.50708i		−	0.446506i
$364$	−0.617901	−	0.0201860i	−0.0323868	−	0.00105804i
$365$			2.37550i			0.124340i
$366$	−0.495928	−	10.8952i	−0.0259226	−	0.569503i
$367$	4.48045	+	7.76036i	0.233877	+	0.405088i	0.958946	−	0.283589i	$-0.0915252\pi$
$367$	4.48045	+	7.76036i	0.233877	+	0.405088i	−0.725068	+	0.688677i	$0.758192\pi$
$368$	−2.29433	−	2.69347i	−0.119600	−	0.140407i
$369$		−	6.92055i		−	0.360270i
$370$	12.9795	−	8.30273i	0.674773	−	0.431638i
$371$	0.311599	−	0.539705i	0.0161774	−	0.0280201i
$372$	0.364322	+	0.516222i	0.0188892	+	0.0267649i
$373$	−4.30847	−	2.48749i	−0.223084	−	0.128798i	0.384293	−	0.923211i	$-0.374445\pi$
$373$	−4.30847	−	2.48749i	−0.223084	−	0.128798i	−0.607377	+	0.794413i	$0.707778\pi$
$374$	−0.894797	−	19.6581i	−0.0462689	−	1.01650i
$375$	−0.756863	+	0.436975i	−0.0390842	+	0.0225653i
$376$	5.33508	−	0.732575i	0.275136	−	0.0377796i
$377$	18.2078	−	24.0894i	0.937747	−	1.24067i
$378$	0.492623	+	0.255284i	0.0253378	+	0.0131304i
$379$	9.66780	+	16.7451i	0.496602	+	0.860139i	0.999992	−	0.00391972i	$-0.00124769\pi$
$379$	9.66780	+	16.7451i	0.496602	+	0.860139i	−0.503391	+	0.864059i	$0.667914\pi$
$380$	5.21247	−	11.2872i	0.267394	−	0.579021i
$381$	2.82983	+	1.63380i	0.144977	+	0.0837023i
$382$	27.8866	+	14.4512i	1.42680	+	0.739389i
$383$	−8.59222	−	4.96072i	−0.439042	−	0.253481i	0.264149	−	0.964482i	$-0.414909\pi$
$383$	−8.59222	−	4.96072i	−0.439042	−	0.253481i	−0.703191	+	0.711001i	$0.748242\pi$
$384$	−7.37596	−	6.58485i	−0.376403	−	0.336032i
$385$			0.390383i			0.0198958i
$386$	8.58700	+	13.4239i	0.437067	+	0.683260i
$387$	−16.5134	+	9.53402i	−0.839423	+	0.484641i
$388$	−27.9544	−	12.9094i	−1.41917	−	0.655377i
$389$		−	26.5193i		−	1.34458i	−0.740287	−	0.672291i	$-0.765310\pi$
$389$		−	26.5193i		−	1.34458i	0.740287	−	0.672291i	$-0.234690\pi$
$390$	−3.67354	−	2.52262i	−0.186017	−	0.127738i
$391$	2.70305			0.136699
$392$	15.6239	−	12.1273i	0.789127	−	0.612519i
$393$	6.11875	+	10.5980i	0.308650	+	0.534598i
$394$	−13.5710	+	8.68111i	−0.683699	+	0.437348i
$395$	−12.8740			−0.647760
$396$	−20.2808	+	1.85011i	−1.01915	+	0.0929716i
$397$	−2.18812	+	3.78994i	−0.109819	+	0.190211i	−0.915697	−	0.401870i	$-0.868360\pi$
$397$	−2.18812	+	3.78994i	−0.109819	+	0.190211i	0.805878	+	0.592082i	$0.201694\pi$
$398$	−2.61074	−	1.35292i	−0.130865	−	0.0678160i
$399$	−0.232884	+	0.403366i	−0.0116588	+	0.0201936i
$400$	3.93397	−	0.723775i	0.196699	−	0.0361888i
$401$	−6.25613	+	3.61198i	−0.312416	+	0.180373i	−0.648007	−	0.761634i	$-0.724397\pi$
$401$	−6.25613	+	3.61198i	−0.312416	+	0.180373i	0.335591	+	0.942008i	$0.391064\pi$
$402$	3.15913	−	6.09619i	0.157563	−	0.304051i
$403$	−0.507508	−	1.20047i	−0.0252808	−	0.0597999i
$404$	4.25392	−	3.00219i	0.211641	−	0.149364i
$405$	−1.35464	−	2.34630i	−0.0673124	−	0.116588i
$406$	−0.0461721	−	1.01437i	−0.00229148	−	0.0503425i
$407$	24.8051	−	42.9636i	1.22954	−	2.12963i
$408$	7.48360	−	1.02759i	0.370493	−	0.0508735i
$409$	−14.3919	−	8.30916i	−0.711633	−	0.410862i	0.100032	−	0.994984i	$-0.468105\pi$
$409$	−14.3919	−	8.30916i	−0.711633	−	0.410862i	−0.811665	+	0.584123i	$0.801439\pi$
$410$	2.35842	+	3.68687i	0.116474	+	0.182082i
$411$	0.327428			0.0161508
$412$	26.2691	−	2.39639i	1.29419	−	0.118062i
$413$	−0.585435	+	0.338001i	−0.0288074	+	0.0166320i
$414$	−0.127198	−	2.79446i	−0.00625144	−	0.137340i
$415$	−7.10893			−0.348964
$416$	11.9734	+	16.5118i	0.587043	+	0.809556i
$417$	5.11688			0.250575
$418$	−1.82022	−	39.9891i	−0.0890298	−	1.95593i
$419$	−21.7622	+	12.5644i	−1.06315	+	0.613812i	−0.926303	−	0.376780i	$-0.877031\pi$
$419$	−21.7622	+	12.5644i	−1.06315	+	0.613812i	−0.136850	+	0.990592i	$0.543698\pi$
$420$	−0.149233	+	0.0136138i	−0.00728184	+	0.000664284i
$421$	2.23994			0.109168			0.0545840	−	0.998509i	$-0.482617\pi$
$421$	2.23994			0.109168			0.0545840	+	0.998509i	$0.482617\pi$
$422$	−3.75074	−	5.86347i	−0.182583	−	0.285429i
$423$	3.68719	+	2.12880i	0.179277	+	0.103506i
$424$	−20.3688	+	2.79690i	−0.989197	+	0.135830i
$425$	−1.52793	+	2.64646i	−0.0741157	+	0.128372i
$426$	−0.0160142	−	0.351822i	−0.000775889	−	0.0170458i
$427$	0.378271	+	0.655184i	0.0183058	+	0.0317066i
$428$	1.29463	−	0.913683i	0.0625785	−	0.0441645i
$429$	−14.2388	−	1.76937i	−0.687455	−	0.0854258i
$430$	5.54835	−	10.7067i	0.267565	−	0.516322i
$431$	−0.874768	+	0.505047i	−0.0421361	+	0.0243273i	−0.520920	−	0.853605i	$-0.674411\pi$
$431$	−0.874768	+	0.505047i	−0.0421361	+	0.0243273i	0.478784	+	0.877933i	$0.341078\pi$
$432$	−3.31213	−	18.0026i	−0.159355	−	0.866151i
$433$	9.73629	−	16.8637i	0.467896	−	0.810420i	−0.531431	−	0.847102i	$-0.678345\pi$
$433$	9.73629	−	16.8637i	0.467896	−	0.810420i	0.999327	+	0.0366819i	$0.0116788\pi$
$434$	−0.0389133	−	0.0201654i	−0.00186790	−	0.000967970i
$435$	3.65965	−	6.33871i	0.175467	−	0.303918i
$436$	8.48160	−	0.773732i	0.406195	−	0.0370550i
$437$	5.49862			0.263035
$438$	−2.47328	+	1.58210i	−0.118178	+	0.0755958i
$439$	−4.46944	−	7.74129i	−0.213315	−	0.369472i	0.739435	−	0.673228i	$-0.235093\pi$
$439$	−4.46944	−	7.74129i	−0.213315	−	0.369472i	−0.952750	+	0.303756i	$0.901759\pi$
$440$	10.1740	−	7.89702i	0.485025	−	0.376475i
$441$	15.6370			0.744621
$442$	−15.5344	−	1.21639i	−0.738895	−	0.0578578i
$443$			27.0696i			1.28612i	0.765817	+	0.643058i	$0.222335\pi$
$443$			27.0696i			1.28612i	−0.765817	+	0.643058i	$0.777665\pi$
$444$	17.2889	+	7.98407i	0.820496	+	0.378907i
$445$	10.3751	−	5.99007i	0.491827	−	0.283957i
$446$	8.95100	+	13.9930i	0.423842	+	0.662586i
$447$		−	8.70087i		−	0.411537i
$448$	0.664428	+	0.170137i	0.0313913	+	0.00803824i
$449$	−9.74642	−	5.62710i	−0.459962	−	0.265559i	0.252066	−	0.967710i	$-0.418890\pi$
$449$	−9.74642	−	5.62710i	−0.459962	−	0.265559i	−0.712028	+	0.702151i	$0.752223\pi$
$450$	2.80786	+	1.45507i	0.132364	+	0.0685926i
$451$	12.2040	+	7.04596i	0.574662	+	0.331781i
$452$	−16.0645	+	34.7864i	−0.755609	+	1.63622i
$453$	−4.77015	−	8.26214i	−0.224121	−	0.388189i
$454$	12.4252	+	6.43892i	0.583145	+	0.302194i
$455$	0.306756	+	0.0381187i	0.0143809	+	0.00178703i
$456$	15.2233	−	2.09036i	0.712897	−	0.0978900i
$457$	−12.2608	+	7.07878i	−0.573537	+	0.331132i	−0.758561	−	0.651602i	$-0.774097\pi$
$457$	−12.2608	+	7.07878i	−0.573537	+	0.331132i	0.185024	+	0.982734i	$0.440764\pi$
$458$	0.565280	+	12.4188i	0.0264138	+	0.580295i
$459$	12.1107	+	6.99212i	0.565279	+	0.326364i
$460$	1.02007	+	1.44538i	0.0475611	+	0.0673913i
$461$	−16.4155	+	28.4325i	−0.764547	+	1.32423i	0.175939	+	0.984401i	$0.443704\pi$
$461$	−16.4155	+	28.4325i	−0.764547	+	1.32423i	−0.940486	+	0.339833i	$0.889629\pi$
$462$	−0.406451	+	0.259998i	−0.0189098	+	0.0120962i
$463$			13.2835i			0.617335i	0.951170	+	0.308667i	$0.0998830\pi$
$463$			13.2835i			0.617335i	−0.951170	+	0.308667i	$0.900117\pi$
$464$	−25.5021	+	21.7230i	−1.18390	+	1.00846i
$465$	−0.157959	−	0.273593i	−0.00732516	−	0.0126876i
$466$	−0.272252	−	5.98121i	−0.0126118	−	0.277074i
$467$		−	12.1506i		−	0.562262i	−0.959669	−	0.281131i	$-0.909290\pi$
$467$		−	12.1506i		−	0.562262i	0.959669	−	0.281131i	$-0.0907096\pi$
$468$	−0.526520	+	16.1169i	−0.0243384	+	0.745006i
$469$			0.476276i			0.0219924i
$470$	−2.68978	+	0.122433i	−0.124070	+	0.00564743i
$471$	−5.33268	−	9.23648i	−0.245717	−	0.425594i
$472$	20.6515	+	8.41994i	0.950564	+	0.387559i
$473$		−	38.8271i		−	1.78527i
$474$	−8.57416	−	13.4039i	−0.393824	−	0.615659i
$475$	−3.10816	+	5.38350i	−0.142612	+	0.247012i
$476$	−0.428101	+	0.302130i	−0.0196220	+	0.0138481i
$477$	−14.0773	−	8.12755i	−0.644557	−	0.372135i
$478$	36.5282	−	1.66269i	1.67076	−	0.0760494i
$479$	15.2490	−	8.80400i	0.696743	−	0.402265i	−0.109390	−	0.993999i	$-0.534890\pi$
$479$	15.2490	−	8.80400i	0.696743	−	0.402265i	0.806133	+	0.591734i	$0.201556\pi$
$480$	3.37362	+	3.61385i	0.153984	+	0.164949i
$481$	−31.3380	−	23.6865i	−1.42889	−	1.08001i
$482$	−6.52454	+	12.5904i	−0.297185	+	0.573479i
$483$	−0.0331379	−	0.0573966i	−0.00150783	−	0.00261163i
$484$	8.16213	−	17.6745i	0.371006	−	0.803385i
$485$	13.3330	+	7.69782i	0.605421	+	0.349540i
$486$	10.4736	−	20.2111i	0.475094	−	0.916792i
$487$	−12.1147	−	6.99445i	−0.548971	−	0.316949i	0.199736	−	0.979850i	$-0.435992\pi$
$487$	−12.1147	−	6.99445i	−0.548971	−	0.316949i	−0.748707	+	0.662901i	$0.769325\pi$
$488$	9.42309	−	23.1120i	0.426563	−	1.04623i
$489$		−	17.3643i		−	0.785239i
$490$	−8.33052	+	5.32886i	−0.376335	+	0.240733i
$491$	15.1321	−	8.73650i	0.682900	−	0.394273i	−0.118047	−	0.993008i	$-0.537663\pi$
$491$	15.1321	−	8.73650i	0.682900	−	0.394273i	0.800947	+	0.598735i	$0.204330\pi$
$492$	−2.26790	+	4.91097i	−0.102245	+	0.221404i
$493$		−	25.5928i		−	1.15264i
$494$	−31.6004	−	2.47441i	−1.42177	−	0.111329i
$495$	10.1825			0.457670
$496$	0.261632	+	1.42206i	0.0117476	+	0.0638525i
$497$	0.0122149	+	0.0211568i	0.000547912	+	0.000949011i
$498$	−4.73460	−	7.40153i	−0.212163	−	0.331670i
$499$	27.4989			1.23102			0.615509	−	0.788130i	$-0.288950\pi$
$499$	27.4989			1.23102			0.615509	+	0.788130i	$0.288950\pi$
$500$	−1.99173	+	0.181695i	−0.0890729	+	0.00812565i
$501$	−10.6944	+	18.5232i	−0.477791	+	0.827558i
$502$	3.01530	−	5.81864i	0.134579	−	0.259699i
$503$	−1.38755	+	2.40330i	−0.0618676	+	0.107158i	−0.895300	−	0.445463i	$-0.853039\pi$
$503$	−1.38755	+	2.40330i	−0.0618676	+	0.107158i	0.833433	+	0.552621i	$0.186372\pi$
$504$	0.332493	+	0.428361i	0.0148104	+	0.0190807i
$505$	−2.25454	+	1.30166i	−0.100326	+	0.0579230i
$506$	5.05736	+	2.62080i	0.224827	+	0.116509i
$507$	−2.78067	+	11.0158i	−0.123494	+	0.489230i
$508$	4.31176	+	6.10951i	0.191303	+	0.271066i
$509$	−2.21856	−	3.84266i	−0.0983359	−	0.170323i	0.812660	−	0.582738i	$-0.198019\pi$
$509$	−2.21856	−	3.84266i	−0.0983359	−	0.170323i	−0.910996	+	0.412415i	$0.864685\pi$
$510$	−3.77300	+	0.171739i	−0.167071	+	0.00760473i
$511$	0.101830	−	0.176374i	0.00450468	−	0.00780234i
$512$	−9.00660	−	20.7577i	−0.398039	−	0.917368i
$513$	24.6359	+	14.2235i	1.08770	+	0.627985i
$514$	20.1242	−	12.8730i	0.887641	−	0.567805i
$515$	−13.1891			−0.581181
$516$	14.8426	−	1.35401i	0.653409	−	0.0596071i
$517$	−7.50801	+	4.33475i	−0.330202	+	0.190642i
$518$	−1.31960	+	0.0600654i	−0.0579799	+	0.00263912i
$519$	−16.1030			−0.706843
$520$	−5.21190	−	8.76562i	−0.228557	−	0.384398i
$521$	−12.5748			−0.550911			−0.275455	−	0.961314i	$-0.588829\pi$
$521$	−12.5748			−0.550911			−0.275455	+	0.961314i	$0.588829\pi$
$522$	−26.4583	+	1.20433i	−1.15805	+	0.0527119i
$523$	−17.4083	+	10.0507i	−0.761211	+	0.439485i	−0.829730	−	0.558165i	$-0.811506\pi$
$523$	−17.4083	+	10.0507i	−0.761211	+	0.439485i	0.0685196	+	0.997650i	$0.478172\pi$
$524$	2.54419	+	27.8892i	0.111143	+	1.21835i
$525$	0.0749265			0.00327006
$526$	1.08445	−	0.693700i	0.0472843	−	0.0302467i
$527$	−0.956648	−	0.552321i	−0.0416723	−	0.0240595i
$528$	14.9980	+	5.33325i	0.652704	+	0.232100i
$529$	11.1088	−	19.2410i	0.482991	−	0.836565i
$530$	10.2693	−	0.467439i	0.446072	−	0.0203042i
$531$	8.81622	+	15.2701i	0.382591	+	0.662668i
$532$	−0.870854	+	0.614601i	−0.0377563	+	0.0266464i
$533$	6.72824	−	8.90165i	0.291432	−	0.385573i
$534$	13.1465	+	6.81271i	0.568906	+	0.294815i
$535$	−0.686143	+	0.396145i	−0.0296646	+	0.0171268i
$536$	12.4125	−	9.63454i	0.536137	−	0.416149i
$537$	−10.9023	+	18.8834i	−0.470470	+	0.814879i
$538$	12.5537	−	24.2250i	0.541229	−	1.04441i
$539$	−15.9204	+	27.5749i	−0.685740	+	1.18774i
$540$	0.831471	+	9.11453i	0.0357808	+	0.392227i
$541$	9.45913			0.406680			0.203340	−	0.979108i	$-0.434820\pi$
$541$	9.45913			0.406680			0.203340	+	0.979108i	$0.434820\pi$
$542$	−0.615420	−	0.962076i	−0.0264345	−	0.0413247i
$543$	4.77120	+	8.26397i	0.204752	+	0.354641i
$544$	16.5340	+	5.04519i	0.708889	+	0.216311i
$545$	−4.25841			−0.182410
$546$	0.164614	+	0.344769i	0.00704483	+	0.0147548i
$547$			29.6756i			1.26884i	0.772990	+	0.634418i	$0.218760\pi$
$547$			29.6756i			1.26884i	−0.772990	+	0.634418i	$0.781240\pi$
$548$	0.680270	+	0.314151i	0.0290597	+	0.0134198i
$549$	17.0894	−	9.86659i	0.729359	−	0.421096i
$550$	−5.42466	+	3.47004i	−0.231308	+	0.147963i
$551$		−	52.0616i		−	2.21790i
$552$	−0.825498	+	2.02469i	−0.0351355	+	0.0861767i
$553$	0.955855	+	0.551863i	0.0406471	+	0.0234676i
$554$	18.8803	−	36.4334i	0.802146	−	1.54791i
$555$	−8.24605	−	4.76086i	−0.350025	−	0.202087i
$556$	10.6309	+	4.90939i	0.450852	+	0.208205i
$557$	20.2892	+	35.1420i	0.859682	+	1.48901i	0.872232	+	0.489092i	$0.162672\pi$
$557$	20.2892	+	35.1420i	0.859682	+	1.48901i	−0.0125505	+	0.999921i	$0.503995\pi$
$558$	−0.525982	+	1.01499i	−0.0222666	+	0.0429679i
$559$	−30.5097	−	3.79125i	−1.29042	−	0.160353i
$560$	−0.323112	−	0.114898i	−0.0136540	−	0.00485532i
$561$	−10.5316	+	6.08042i	−0.444644	+	0.256716i
$562$	30.6555	−	1.39538i	1.29313	−	0.0588604i
$563$	−9.61963	−	5.55390i	−0.405419	−	0.234069i	0.283400	−	0.959002i	$-0.408537\pi$
$563$	−9.61963	−	5.55390i	−0.405419	−	0.234069i	−0.688820	+	0.724933i	$0.741871\pi$
$564$	−1.91889	−	2.71895i	−0.0807998	−	0.114489i
$565$	9.57915	−	16.5916i	0.402998	−	0.698013i
$566$	−14.5782	−	22.7899i	−0.612768	−	0.957930i
$567$			0.232274i			0.00975460i
$568$	0.304284	−	0.746316i	0.0127675	−	0.0313147i
$569$	−7.45431	−	12.9112i	−0.312501	−	0.541268i	0.666402	−	0.745592i	$-0.267833\pi$
$569$	−7.45431	−	12.9112i	−0.312501	−	0.541268i	−0.978903	+	0.204325i	$0.934500\pi$
$570$	−7.67514	+	0.349356i	−0.321476	+	0.0146329i
$571$			35.4496i			1.48352i	0.670666	+	0.741759i	$0.266008\pi$
$571$			35.4496i			1.48352i	−0.670666	+	0.741759i	$0.733992\pi$
$572$	−27.8852	−	17.3375i	−1.16594	−	0.724917i
$573$		−	19.4098i		−	0.810855i
$574$	−0.0170618	−	0.374837i	−0.000712145	−	0.0156454i
$575$	−0.442273	−	0.766039i	−0.0184440	−	0.0319460i
$576$	4.43776	−	17.3305i	0.184907	−	0.722105i
$577$			26.8210i			1.11657i	0.829648	+	0.558287i	$0.188541\pi$
$577$			26.8210i			1.11657i	−0.829648	+	0.558287i	$0.811459\pi$
$578$	9.12754	−	5.83869i	0.379656	−	0.242858i
$579$	4.92386	−	8.52838i	0.204629	−	0.354427i
$580$	13.6850	−	9.65816i	0.568241	−	0.401033i
$581$	0.527817	+	0.304735i	0.0218975	+	0.0126426i
$582$	0.865231	+	19.0086i	0.0358650	+	0.787931i
$583$	28.6649	−	16.5497i	1.18718	−	0.685417i
$584$	−6.65648	+	0.914020i	−0.275447	+	0.0378224i
$585$	0.994264	−	8.00123i	0.0411078	−	0.330810i
$586$	−21.3804	−	11.0796i	−0.883215	−	0.457694i
$587$	−15.9431	−	27.6143i	−0.658043	−	1.13976i	−0.981122	−	0.193391i	$-0.938051\pi$
$587$	−15.9431	−	27.6143i	−0.658043	−	1.13976i	0.323079	−	0.946372i	$-0.395282\pi$
$588$	−11.0964	−	5.12434i	−0.457607	−	0.211324i
$589$	−1.94604	−	1.12355i	−0.0801851	−	0.0462949i
$590$	−9.90061	−	5.13063i	−0.407601	−	0.211225i
$591$	8.62184	+	4.97782i	0.354655	+	0.204760i
$592$	28.2595	+	33.1757i	1.16146	+	1.36351i
$593$		−	9.27008i		−	0.380677i	−0.981719	−	0.190338i	$-0.939042\pi$
$593$		−	9.27008i		−	0.380677i	0.981719	−	0.190338i	$-0.0609585\pi$
$594$	15.8796	+	24.8243i	0.651546	+	1.01855i
$595$	0.226889	−	0.130995i	0.00930155	−	0.00537025i
$596$	8.34806	−	18.0771i	0.341950	−	0.740467i
$597$			1.81714i			0.0743707i
$598$	2.55320	−	3.71808i	0.104408	−	0.152044i
$599$	−14.8455			−0.606572			−0.303286	−	0.952900i	$-0.598084\pi$
$599$	−14.8455			−0.606572			−0.303286	+	0.952900i	$0.598084\pi$
$600$	−1.51568	−	1.95270i	−0.0618774	−	0.0797185i
$601$	22.3119	+	38.6453i	0.910121	+	1.57638i	0.813891	+	0.581017i	$0.197345\pi$
$601$	22.3119	+	38.6453i	0.910121	+	1.57638i	0.0962298	+	0.995359i	$0.469322\pi$
$602$	−0.870908	+	0.557101i	−0.0354956	+	0.0227058i
$603$	12.4229			0.505899
$604$	−1.98344	−	21.7423i	−0.0807049	−	0.884681i
$605$	−4.86703	+	8.42994i	−0.197873	+	0.342726i
$606$	−2.85677	−	1.48042i	−0.116048	−	0.0601379i
$607$	−5.30922	+	9.19583i	−0.215494	+	0.373247i	−0.953425	−	0.301629i	$-0.902470\pi$
$607$	−5.30922	+	9.19583i	−0.215494	+	0.373247i	0.737931	+	0.674876i	$0.235803\pi$
$608$	33.6339	+	10.2631i	1.36403	+	0.416222i
$609$	−0.543437	+	0.313754i	−0.0220212	+	0.0127139i
$610$	−5.74189	+	11.0802i	−0.232482	+	0.448623i
$611$	2.67305	+	6.32292i	0.108140	+	0.255798i
$612$	7.88059	+	11.1663i	0.318554	+	0.451372i
$613$	0.229598	+	0.397675i	0.00927337	+	0.0160619i	0.870625	−	0.491948i	$-0.163715\pi$
$613$	0.229598	+	0.397675i	0.00927337	+	0.0160619i	−0.861351	+	0.508009i	$0.830381\pi$
$614$	−0.0975115	−	2.14227i	−0.00393524	−	0.0864549i
$615$	1.35234	−	2.34232i	0.0545315	−	0.0944513i
$616$	−1.09391	+	0.150207i	−0.0440747	+	0.00605202i
$617$	14.5888	+	8.42284i	0.587323	+	0.339091i	0.764038	−	0.645171i	$-0.223214\pi$
$617$	14.5888	+	8.42284i	0.587323	+	0.339091i	−0.176716	+	0.984262i	$0.556547\pi$
$618$	−8.78404	−	13.7320i	−0.353346	−	0.552380i
$619$	−17.9722			−0.722364			−0.361182	−	0.932495i	$-0.617627\pi$
$619$	−17.9722			−0.722364			−0.361182	+	0.932495i	$0.617627\pi$
$620$	−0.0656796	−	0.719975i	−0.00263775	−	0.0289149i
$621$	−3.50554	+	2.02392i	−0.140672	+	0.0812172i
$622$	1.28601	+	28.2528i	0.0515642	+	1.13283i
$623$	−1.02710			−0.0411497
$624$	5.65524	−	11.2644i	0.226391	−	0.450936i
$625$	1.00000			0.0400000
$626$	1.30675	+	28.7086i	0.0522284	+	1.14743i
$627$	−21.4236	+	12.3689i	−0.855578	+	0.493968i
$628$	−2.21734	−	24.3063i	−0.0884815	−	0.969928i
$629$	−33.2938			−1.32751
$630$	−0.146101	−	0.228398i	−0.00582081	−	0.00909958i
$631$	27.5020	+	15.8783i	1.09484	+	0.632105i	0.934860	−	0.355015i	$-0.115524\pi$
$631$	27.5020	+	15.8783i	1.09484	+	0.632105i	0.159978	+	0.987121i	$0.448858\pi$
$632$	−4.95350	−	36.0746i	−0.197040	−	1.43497i
$633$	−2.15071	+	3.72513i	−0.0854829	+	0.148061i
$634$	−0.575071	−	12.6340i	−0.0228390	−	0.501758i
$635$	−1.86945	−	3.23798i	−0.0741867	−	0.128495i
$636$	7.32614	+	10.3807i	0.290500	+	0.411622i
$637$	20.1134	+	15.2025i	0.796920	+	0.602345i
$638$	24.8140	−	47.8837i	0.982395	−	1.89573i
$639$	0.551840	−	0.318605i	0.0218305	−	0.0126038i
$640$	3.54179	+	10.7450i	0.140001	+	0.424735i
$641$	19.3471	−	33.5101i	0.764163	−	1.32357i	−0.176525	−	0.984296i	$-0.556486\pi$
$641$	19.3471	−	33.5101i	0.764163	−	1.32357i	0.940688	−	0.339273i	$-0.110181\pi$
$642$	−0.869427	−	0.450549i	−0.0343135	−	0.0177817i
$643$	−4.32632	+	7.49341i	−0.170614	+	0.295511i	−0.938635	−	0.344913i	$-0.887908\pi$
$643$	−4.32632	+	7.49341i	−0.170614	+	0.295511i	0.768021	+	0.640425i	$0.221242\pi$
$644$	−0.0137788	−	0.151042i	−0.000542961	−	0.00595191i
$645$	−7.45212			−0.293427
$646$	−22.6307	+	14.4764i	−0.890395	+	0.569567i
$647$	−3.23005	−	5.59461i	−0.126986	−	0.219947i	0.795521	−	0.605926i	$-0.207197\pi$
$647$	−3.23005	−	5.59461i	−0.126986	−	0.219947i	−0.922508	+	0.385979i	$0.873864\pi$
$648$	6.05342	−	4.69865i	0.237801	−	0.184580i
$649$	−35.9039			−1.40935
$650$	2.19701	+	4.60143i	0.0861737	+	0.180483i
$651$			0.0270846i			0.00106153i
$652$	16.6602	−	36.0763i	0.652462	−	1.41286i
$653$	8.91032	−	5.14438i	0.348688	−	0.201315i	−0.315419	−	0.948952i	$-0.602145\pi$
$653$	8.91032	−	5.14438i	0.348688	−	0.201315i	0.664107	+	0.747637i	$0.268812\pi$
$654$	−2.83613	−	4.43368i	−0.110902	−	0.173371i
$655$		−	14.0025i		−	0.547123i
$656$	−9.42367	+	8.02719i	−0.367933	+	0.313409i
$657$	−4.60044	−	2.65606i	−0.179480	−	0.103623i
$658$	0.204957	+	0.106211i	0.00799005	+	0.00414055i
$659$	−13.1886	−	7.61444i	−0.513755	−	0.296616i	0.220621	−	0.975360i	$-0.429192\pi$
$659$	−13.1886	−	7.61444i	−0.513755	−	0.296616i	−0.734376	+	0.678743i	$0.762525\pi$
$660$	−7.22573	−	3.33686i	−0.281261	−	0.129887i
$661$	−0.728643	−	1.26205i	−0.0283409	−	0.0490879i	0.851507	−	0.524343i	$-0.175689\pi$
$661$	−0.728643	−	1.26205i	−0.0283409	−	0.0490879i	−0.879848	+	0.475255i	$0.842356\pi$
$662$	38.2333	+	19.8130i	1.48598	+	0.770054i
$663$	3.74953	+	8.86926i	0.145620	+	0.344453i
$664$	−2.73530	−	19.9202i	−0.106150	−	0.773053i
$665$	0.461544	−	0.266473i	0.0178979	−	0.0103334i
$666$	1.56671	+	34.4197i	0.0607088	+	1.33374i
$667$	6.41555	+	3.70402i	0.248411	+	0.143420i
$668$	−39.9910	+	28.2235i	−1.54730	+	1.09200i
$669$	5.13258	−	8.88989i	0.198437	−	0.343703i
$670$	−6.61821	+	4.23353i	−0.255684	+	0.163555i
$671$			40.1815i			1.55119i
$672$	−0.0955680	−	0.412934i	−0.00368661	−	0.0159293i
$673$	1.68543	+	2.91925i	0.0649685	+	0.112529i	0.896680	−	0.442679i	$-0.145972\pi$
$673$	1.68543	+	2.91925i	0.0649685	+	0.112529i	−0.831712	+	0.555208i	$0.812639\pi$
$674$	1.59391	+	35.0173i	0.0613952	+	1.34881i
$675$		−	4.57619i		−	0.176138i
$676$	−16.3463	+	20.2188i	−0.628704	+	0.777644i
$677$			2.79883i			0.107568i	0.998553	+	0.0537838i	$0.0171282\pi$
$677$			2.79883i			0.107568i	−0.998553	+	0.0537838i	$0.982872\pi$
$678$	23.6543	−	1.07669i	0.908436	−	0.0413501i
$679$	−0.659958	−	1.14308i	−0.0253269	−	0.0438674i
$680$	−8.00364	−	3.26320i	−0.306925	−	0.125138i
$681$		−	8.64827i		−	0.331402i
$682$	−1.25436	−	1.96092i	−0.0480318	−	0.0750874i
$683$	23.4208	−	40.5661i	0.896174	−	1.55222i	0.0638289	−	0.997961i	$-0.479669\pi$
$683$	23.4208	−	40.5661i	0.896174	−	1.55222i	0.832345	−	0.554258i	$-0.186998\pi$
$684$	16.0309	+	22.7148i	0.612956	+	0.868523i
$685$	−0.324458	−	0.187326i	−0.0123969	−	0.00715736i
$686$	1.69478	−	0.0771430i	0.0647071	−	0.00294533i
$687$	6.65324	−	3.84125i	0.253837	−	0.146553i
$688$	32.1364	+	11.4276i	1.22519	+	0.435674i
$689$	−10.2055	−	24.1403i	−0.388797	−	0.919673i
$690$	0.503011	−	0.970663i	0.0191493	−	0.0369525i
$691$	−20.8294	−	36.0776i	−0.792388	−	1.37246i	−0.924484	−	0.381220i	$-0.875504\pi$
$691$	−20.8294	−	36.0776i	−0.792388	−	1.37246i	0.132096	−	0.991237i	$-0.457829\pi$
$692$	−33.4559	−	15.4500i	−1.27180	−	0.587322i
$693$	−0.756022	−	0.436489i	−0.0287189	−	0.0165809i
$694$	−18.6293	+	35.9491i	−0.707159	+	1.36461i
$695$	−5.07048	−	2.92744i	−0.192334	−	0.111044i
$696$	19.1700	+	7.81590i	0.726638	+	0.296261i
$697$		−	9.45720i		−	0.358217i
$698$	−14.7830	+	9.45636i	−0.559544	+	0.357928i
$699$	−3.20436	+	1.85004i	−0.121200	+	0.0699748i
$700$	0.155669	+	0.0718883i	0.00588372	+	0.00271712i
$701$		−	31.2373i		−	1.17982i	−0.807470	−	0.589909i	$-0.799164\pi$
$701$		−	31.2373i		−	1.17982i	0.807470	−	0.589909i	$-0.200836\pi$
$702$	21.0570	−	10.0539i	0.794746	−	0.379461i
$703$	−67.7271			−2.55437
$704$	26.0431	+	25.4703i	0.981537	+	0.959948i
$705$	0.831972	+	1.44102i	0.0313339	+	0.0542718i
$706$	3.64519	+	5.69847i	0.137188	+	0.214465i
$707$	0.223190			0.00839393
$708$	−1.25207	−	13.7251i	−0.0470558	−	0.515823i
$709$	−9.77477	+	16.9304i	−0.367099	+	0.635835i	−0.989111	−	0.147174i	$-0.952982\pi$
$709$	−9.77477	+	16.9304i	−0.367099	+	0.635835i	0.622011	+	0.783008i	$0.286316\pi$
$710$	−0.185413	+	0.357793i	−0.00695844	+	0.0134277i
$711$	14.3945	−	24.9319i	0.539834	−	0.935021i
$712$	20.7770	+	26.7677i	0.778651	+	1.00316i
$713$	0.276909	−	0.159874i	0.0103703	−	0.00598732i
$714$	0.287496	+	0.148984i	0.0107593	+	0.00557560i
$715$	13.0974	+	9.89955i	0.489815	+	0.370222i
$716$	−40.7686	+	28.7723i	−1.52359	+	1.07527i
$717$	−11.2985	−	19.5695i	−0.421949	−	0.730836i
$718$	36.4172	−	1.65763i	1.35908	−	0.0618624i
$719$	−21.1163	+	36.5745i	−0.787506	+	1.36400i	0.139985	+	0.990154i	$0.455295\pi$
$719$	−21.1163	+	36.5745i	−0.787506	+	1.36400i	−0.927491	+	0.373846i	$0.878039\pi$
$720$	−2.99692	+	8.42785i	−0.111689	+	0.314087i
$721$	0.979252	+	0.565371i	0.0364692	+	0.0210555i
$722$	−23.4009	+	14.9690i	−0.870890	+	0.557090i
$723$	8.76326			0.325909
$724$	1.98388	+	21.7471i	0.0737302	+	0.808225i
$725$	−7.25294	+	4.18749i	−0.269367	+	0.155519i
$726$	−12.0184	+	0.547052i	−0.446044	+	0.0203030i
$727$	20.5563			0.762390			0.381195	−	0.924495i	$-0.375513\pi$
$727$	20.5563			0.762390			0.381195	+	0.924495i	$0.375513\pi$
$728$	0.0112165	+	0.874238i	0.000415713	+	0.0324014i
$729$	−5.93958			−0.219985
$730$	3.35600	−	0.152758i	0.124211	−	0.00565382i
$731$	−22.5662	+	13.0286i	−0.834641	+	0.481880i
$732$	−15.3604	+	1.40125i	−0.567735	+	0.0517915i
$733$	−29.3314			−1.08338			−0.541689	−	0.840579i	$-0.682215\pi$
$733$	−29.3314			−1.08338			−0.541689	+	0.840579i	$0.682215\pi$
$734$	10.6753	−	6.82879i	0.394034	−	0.252055i
$735$	5.29248	+	3.05561i	0.195216	+	0.112708i
$736$	−3.65766	+	3.41452i	−0.134823	+	0.125861i
$737$	−12.6480	+	21.9070i	−0.465895	+	0.806955i
$738$	−9.77702	+	0.445029i	−0.359897	+	0.0163817i
$739$	22.5437	+	39.0468i	0.829282	+	1.43636i	0.898603	+	0.438764i	$0.144583\pi$
$739$	22.5437	+	39.0468i	0.829282	+	1.43636i	−0.0693208	+	0.997594i	$0.522083\pi$
$740$	−12.5643	−	17.8029i	−0.461874	−	0.654448i
$741$	7.62740	+	18.0421i	0.280199	+	0.662792i
$742$	−0.782506	−	0.405505i	−0.0287267	−	0.0148866i
$743$	−12.6235	+	7.28818i	−0.463111	+	0.267377i	−0.713352	−	0.700806i	$-0.752824\pi$
$743$	−12.6235	+	7.28818i	−0.463111	+	0.267377i	0.250240	+	0.968184i	$0.419490\pi$
$744$	0.705865	−	0.547892i	0.0258783	−	0.0200867i
$745$	−4.97790	+	8.62197i	−0.182376	+	0.315885i
$746$	−3.23715	+	6.24675i	−0.118521	+	0.228710i
$747$	7.94853	−	13.7673i	0.290822	−	0.503718i
$748$	−27.7145	+	2.52825i	−1.01334	+	0.0924420i
$749$	0.0679255			0.00248194
$750$	0.666007	+	1.04116i	0.0243192	+	0.0380178i
$751$	10.4721	+	18.1383i	0.382134	+	0.661875i	0.991367	−	0.131116i	$-0.0418559\pi$
$751$	10.4721	+	18.1383i	0.382134	+	0.661875i	−0.609233	+	0.792991i	$0.708523\pi$
$752$	−1.37802	−	7.49002i	−0.0502512	−	0.273133i
$753$	−4.04992			−0.147587
$754$	−35.2032	−	24.1739i	−1.28202	−	0.880363i
$755$			10.9163i			0.397284i
$756$	0.328974	−	0.712369i	0.0119647	−	0.0259086i
$757$	8.14420	−	4.70205i	0.296006	−	0.170899i	−0.344641	−	0.938734i	$-0.611999\pi$
$757$	8.14420	−	4.70205i	0.296006	−	0.170899i	0.640647	+	0.767835i	$0.278666\pi$
$758$	23.0350	−	14.7350i	0.836669	−	0.535199i
$759$		−	3.52005i		−	0.127770i
$760$	−16.2812	−	6.63809i	−0.590581	−	0.240789i
$761$	9.47857	+	5.47245i	0.343598	+	0.198376i	0.661862	−	0.749626i	$-0.269767\pi$
$761$	9.47857	+	5.47245i	0.343598	+	0.198376i	−0.318264	+	0.948002i	$0.603100\pi$
$762$	2.12618	−	4.10291i	0.0770235	−	0.148633i
$763$	0.316174	+	0.182543i	0.0114463	+	0.00660851i
$764$	18.6227	−	40.3261i	0.673746	−	1.45895i
$765$	−3.41678	−	5.91804i	−0.123534	−	0.213967i
$766$	−6.45574	+	12.4577i	−0.233255	+	0.450114i
$767$	−3.50581	+	28.2127i	−0.126588	+	1.01870i
$768$	−8.82844	+	10.8438i	−0.318569	+	0.391293i
$769$	27.0299

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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.ca (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0643054 - 1.41275i) q^{2} +(-0.756863 + 0.436975i) q^{3} +(-1.99173 + 0.181695i) q^{4} +1.00000 q^{5} +(0.666007 + 1.04116i) q^{6} +(-0.0742471 - 0.0428666i) q^{7} +(0.384769 + 2.80213i) q^{8} +(-1.11811 + 1.93662i) q^{9} +O(q^{10})\)	\(q+(-0.0643054 - 1.41275i) q^{2} +(-0.756863 + 0.436975i) q^{3} +(-1.99173 + 0.181695i) q^{4} +1.00000 q^{5} +(0.666007 + 1.04116i) q^{6} +(-0.0742471 - 0.0428666i) q^{7} +(0.384769 + 2.80213i) q^{8} +(-1.11811 + 1.93662i) q^{9} +(-0.0643054 - 1.41275i) q^{10} +(-2.27673 - 3.94342i) q^{11} +(1.42807 - 1.00785i) q^{12} +(-3.32098 + 1.40396i) q^{13} +(-0.0557853 + 0.107649i) q^{14} +(-0.756863 + 0.436975i) q^{15} +(3.93397 - 0.723775i) q^{16} +(-1.52793 + 2.64646i) q^{17} +(2.80786 + 1.45507i) q^{18} +(-3.10816 + 5.38350i) q^{19} +(-1.99173 + 0.181695i) q^{20} +0.0749265 q^{21} +(-5.42466 + 3.47004i) q^{22} +(-0.442273 - 0.766039i) q^{23} +(-1.51568 - 1.95270i) q^{24} +1.00000 q^{25} +(2.19701 + 4.60143i) q^{26} -4.57619i q^{27} +(0.155669 + 0.0718883i) q^{28} +(-7.25294 + 4.18749i) q^{29} +(0.666007 + 1.04116i) q^{30} +0.361482i q^{31} +(-1.27549 - 5.51118i) q^{32} +(3.44635 + 1.98975i) q^{33} +(3.83704 + 1.98841i) q^{34} +(-0.0742471 - 0.0428666i) q^{35} +(1.87509 - 4.06037i) q^{36} +(5.44751 + 9.43537i) q^{37} +(7.80541 + 4.04487i) q^{38} +(1.90003 - 2.51379i) q^{39} +(0.384769 + 2.80213i) q^{40} +(-2.68015 + 1.54738i) q^{41} +(-0.00481818 - 0.105852i) q^{42} +(7.38455 + 4.26347i) q^{43} +(5.25114 + 7.44055i) q^{44} +(-1.11811 + 1.93662i) q^{45} +(-1.05378 + 0.674081i) q^{46} -1.90393i q^{47} +(-2.66121 + 2.26685i) q^{48} +(-3.49632 - 6.05581i) q^{49} +(-0.0643054 - 1.41275i) q^{50} -2.67068i q^{51} +(6.35939 - 3.39972i) q^{52} +7.26904i q^{53} +(-6.46501 + 0.294274i) q^{54} +(-2.27673 - 3.94342i) q^{55} +(0.0915499 - 0.224544i) q^{56} -5.43276i q^{57} +(6.38228 + 9.97732i) q^{58} +(3.94248 - 6.82858i) q^{59} +(1.42807 - 1.00785i) q^{60} +(-7.64214 - 4.41219i) q^{61} +(0.510684 - 0.0232453i) q^{62} +(0.166032 - 0.0958587i) q^{63} +(-7.70391 + 2.15635i) q^{64} +(-3.32098 + 1.40396i) q^{65} +(2.58940 - 4.99679i) q^{66} +(-2.77767 - 4.81106i) q^{67} +(2.56238 - 5.54865i) q^{68} +(0.669480 + 0.386524i) q^{69} +(-0.0557853 + 0.107649i) q^{70} +(-0.246775 - 0.142475i) q^{71} +(-5.85687 - 2.38793i) q^{72} +2.37550i q^{73} +(12.9795 - 8.30273i) q^{74} +(-0.756863 + 0.436975i) q^{75} +(5.21247 - 11.2872i) q^{76} +0.390383i q^{77} +(-3.67354 - 2.52262i) q^{78} -12.8740 q^{79} +(3.93397 - 0.723775i) q^{80} +(-1.35464 - 2.34630i) q^{81} +(2.35842 + 3.68687i) q^{82} -7.10893 q^{83} +(-0.149233 + 0.0136138i) q^{84} +(-1.52793 + 2.64646i) q^{85} +(5.54835 - 10.7067i) q^{86} +(3.65965 - 6.33871i) q^{87} +(10.1740 - 7.89702i) q^{88} +(10.3751 - 5.99007i) q^{89} +(2.80786 + 1.45507i) q^{90} +(0.306756 + 0.0381187i) q^{91} +(1.02007 + 1.44538i) q^{92} +(-0.157959 - 0.273593i) q^{93} +(-2.68978 + 0.122433i) q^{94} +(-3.10816 + 5.38350i) q^{95} +(3.37362 + 3.61385i) q^{96} +(13.3330 + 7.69782i) q^{97} +(-8.33052 + 5.32886i) q^{98} +10.1825 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9}+O(q^{10}) \) 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9	\( 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9} - 8 q^{11} + 6 q^{12} - 4 q^{14} + 14 q^{16} + 18 q^{18} - 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 22 q^{24} + 56 q^{25} - 37 q^{26} - 12 q^{28} - 13 q^{30} - 30 q^{32} - 16 q^{34} + 15 q^{36} + 4 q^{37} - 24 q^{39} - 61 q^{42} + 24 q^{44} + 28 q^{45} - 19 q^{46} - 51 q^{48} + 20 q^{49} - 64 q^{52} - 5 q^{54} - 8 q^{55} - 23 q^{56} - q^{58} - 16 q^{59} + 6 q^{60} + 10 q^{62} - 30 q^{64} + 14 q^{66} - 36 q^{67} - 51 q^{68} - 4 q^{70} - 81 q^{72} + 70 q^{74} - 60 q^{76} + 143 q^{78} + 14 q^{80} - 28 q^{81} + 21 q^{82} + 40 q^{83} + 31 q^{84} - 28 q^{86} - 36 q^{87} - 19 q^{88} + 18 q^{90} + 16 q^{91} - 18 q^{92} + 43 q^{94} - 16 q^{95} - 48 q^{96} + 24 q^{97} + 56 q^{98} - 48 q^{99}+O(q^{100}) \) 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9 - 8 * q^11 + 6 * q^12 - 4 * q^14 + 14 * q^16 + 18 * q^18 - 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 22 * q^24 + 56 * q^25 - 37 * q^26 - 12 * q^28 - 13 * q^30 - 30 * q^32 - 16 * q^34 + 15 * q^36 + 4 * q^37 - 24 * q^39 - 61 * q^42 + 24 * q^44 + 28 * q^45 - 19 * q^46 - 51 * q^48 + 20 * q^49 - 64 * q^52 - 5 * q^54 - 8 * q^55 - 23 * q^56 - q^58 - 16 * q^59 + 6 * q^60 + 10 * q^62 - 30 * q^64 + 14 * q^66 - 36 * q^67 - 51 * q^68 - 4 * q^70 - 81 * q^72 + 70 * q^74 - 60 * q^76 + 143 * q^78 + 14 * q^80 - 28 * q^81 + 21 * q^82 + 40 * q^83 + 31 * q^84 - 28 * q^86 - 36 * q^87 - 19 * q^88 + 18 * q^90 + 16 * q^91 - 18 * q^92 + 43 * q^94 - 16 * q^95 - 48 * q^96 + 24 * q^97 + 56 * q^98 - 48 * q^99

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