LMFDB - Embedded newform 520.2.ca.a.101.10

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			101.10
Character	$\chi$	$=$	520.101
Dual form			520.2.ca.a.381.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.683296 + 1.23819i) q^{2} +(-2.80828 + 1.62136i) q^{3} +(-1.06621 - 1.69210i) q^{4} -1.00000 q^{5} +(-0.0886625 - 4.58505i) q^{6} +(3.76770 + 2.17528i) q^{7} +(2.82367 - 0.163970i) q^{8} +(3.75763 - 6.50841i) q^{9} +O(q^{10})$	\(q+(-0.683296 + 1.23819i) q^{2} +(-2.80828 + 1.62136i) q^{3} +(-1.06621 - 1.69210i) q^{4} -1.00000 q^{5} +(-0.0886625 - 4.58505i) q^{6} +(3.76770 + 2.17528i) q^{7} +(2.82367 - 0.163970i) q^{8} +(3.75763 - 6.50841i) q^{9} +(0.683296 - 1.23819i) q^{10} +(1.73976 + 3.01336i) q^{11} +(5.73773 + 3.02316i) q^{12} +(3.51068 + 0.821651i) q^{13} +(-5.26786 + 3.17876i) q^{14} +(2.80828 - 1.62136i) q^{15} +(-1.72638 + 3.60827i) q^{16} +(-0.0871303 + 0.150914i) q^{17} +(5.49106 + 9.09982i) q^{18} +(3.52537 - 6.10612i) q^{19} +(1.06621 + 1.69210i) q^{20} -14.1077 q^{21} +(-4.91988 + 0.0951372i) q^{22} +(0.971921 + 1.68342i) q^{23} +(-7.66381 + 5.03867i) q^{24} +1.00000 q^{25} +(-3.41619 + 3.78545i) q^{26} +14.6418i q^{27} +(-0.336387 - 8.69463i) q^{28} +(2.50740 - 1.44765i) q^{29} +(0.0886625 + 4.58505i) q^{30} +4.00389i q^{31} +(-3.28809 - 4.60309i) q^{32} +(-9.77150 - 5.64158i) q^{33} +(-0.127324 - 0.211002i) q^{34} +(-3.76770 - 2.17528i) q^{35} +(-15.0193 + 0.581083i) q^{36} +(-3.07858 - 5.33225i) q^{37} +(5.15165 + 8.53736i) q^{38} +(-11.1912 + 3.38466i) q^{39} +(-2.82367 + 0.163970i) q^{40} +(-3.76751 + 2.17517i) q^{41} +(9.63973 - 17.4680i) q^{42} +(7.49255 + 4.32582i) q^{43} +(3.24393 - 6.15673i) q^{44} +(-3.75763 + 6.50841i) q^{45} +(-2.74849 + 0.0531485i) q^{46} -3.80183i q^{47} +(-1.00216 - 12.9321i) q^{48} +(5.96372 + 10.3295i) q^{49} +(-0.683296 + 1.23819i) q^{50} -0.565079i q^{51} +(-2.35283 - 6.81647i) q^{52} +6.77726i q^{53} +(-18.1292 - 10.0047i) q^{54} +(-1.73976 - 3.01336i) q^{55} +(10.9954 + 5.52449i) q^{56} +22.8636i q^{57} +(0.0791630 + 4.09380i) q^{58} +(-0.345814 + 0.598967i) q^{59} +(-5.73773 - 3.02316i) q^{60} +(-3.53499 - 2.04093i) q^{61} +(-4.95757 - 2.73584i) q^{62} +(28.3153 - 16.3478i) q^{63} +(7.94623 - 0.925995i) q^{64} +(-3.51068 - 0.821651i) q^{65} +(13.6622 - 8.24408i) q^{66} +(3.84011 + 6.65126i) q^{67} +(0.348260 - 0.0134739i) q^{68} +(-5.45886 - 3.15167i) q^{69} +(5.26786 - 3.17876i) q^{70} +(5.70744 + 3.29519i) q^{71} +(9.54313 - 18.9937i) q^{72} -5.78564i q^{73} +(8.70590 - 0.168349i) q^{74} +(-2.80828 + 1.62136i) q^{75} +(-14.0909 + 0.545166i) q^{76} +15.1379i q^{77} +(3.45604 - 16.1695i) q^{78} -4.84812 q^{79} +(1.72638 - 3.60827i) q^{80} +(-12.4667 - 21.5930i) q^{81} +(-0.118947 - 6.15117i) q^{82} -10.7720 q^{83} +(15.0418 + 23.8716i) q^{84} +(0.0871303 - 0.150914i) q^{85} +(-10.4758 + 6.32136i) q^{86} +(-4.69432 + 8.13080i) q^{87} +(5.40662 + 8.22347i) q^{88} +(-7.02896 + 4.05817i) q^{89} +(-5.49106 - 9.09982i) q^{90} +(11.4399 + 10.7325i) q^{91} +(1.81223 - 3.43946i) q^{92} +(-6.49176 - 11.2441i) q^{93} +(4.70738 + 2.59777i) q^{94} +(-3.52537 + 6.10612i) q^{95} +(16.6972 + 7.59560i) q^{96} +(4.51069 + 2.60425i) q^{97} +(-16.8648 + 0.326120i) q^{98} +26.1496 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9}+O(q^{10}) $ 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9	$ 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30} + 16 q^{34} - 21 q^{36} - 4 q^{37} - 24 q^{39} + 29 q^{42} - 24 q^{44} - 28 q^{45} - 11 q^{46} + 3 q^{48} + 20 q^{49} + 18 q^{52} - 49 q^{54} - 8 q^{55} + 61 q^{56} - 47 q^{58} + 16 q^{59} - 6 q^{60} - 2 q^{62} - 30 q^{64} + 14 q^{66} + 36 q^{67} + 33 q^{68} + 4 q^{70} - 51 q^{72} - 2 q^{74} - 48 q^{76} - 35 q^{78} + 10 q^{80} - 28 q^{81} - 21 q^{82} - 40 q^{83} - 61 q^{84} + 28 q^{86} - 36 q^{87} + 41 q^{88} + 18 q^{90} - 16 q^{91} - 18 q^{92} - 41 q^{94} - 16 q^{95} + 48 q^{96} + 24 q^{97} + 28 q^{98} + 48 q^{99}+O(q^{100}) $ 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * 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 $

$2$	−0.683296	+	1.23819i	−0.483163	+	0.875530i
$2$	−0.683296	+	1.23819i	−0.483163	+	0.875530i
$3$	−2.80828	+	1.62136i	−1.62136	+	0.936094i	−0.634807	+	0.772671i	$0.718920\pi$
$3$	−2.80828	+	1.62136i	−1.62136	+	0.936094i	−0.986556	+	0.163423i	$0.947746\pi$
$4$	−1.06621	−	1.69210i	−0.533107	−	0.846048i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.0886625	−	4.58505i	−0.0361963	−	1.87184i
$7$	3.76770	+	2.17528i	1.42406	+	0.822180i	0.996643	−	0.0818753i	$-0.0260909\pi$
$7$	3.76770	+	2.17528i	1.42406	+	0.822180i	0.427415	+	0.904055i	$0.359424\pi$
$8$	2.82367	−	0.163970i	0.998318	−	0.0579722i
$9$	3.75763	−	6.50841i	1.25254	−	2.16947i
$10$	0.683296	−	1.23819i	0.216077	−	0.391549i
$11$	1.73976	+	3.01336i	0.524559	+	0.908562i	0.999591	+	0.0285940i	$0.00910298\pi$
$11$	1.73976	+	3.01336i	0.524559	+	0.908562i	−0.475032	+	0.879968i	$0.657564\pi$
$12$	5.73773	+	3.02316i	1.65634	+	0.872712i
$13$	3.51068	+	0.821651i	0.973688	+	0.227885i
$13$	3.51068	+	0.821651i	0.973688	+	0.227885i
$14$	−5.26786	+	3.17876i	−1.40790	+	0.849559i
$15$	2.80828	−	1.62136i	0.725095	−	0.418634i
$16$	−1.72638	+	3.60827i	−0.431594	+	0.902068i
$17$	−0.0871303	+	0.150914i	−0.0211322	+	0.0366020i	−0.876398	−	0.481587i	$-0.840060\pi$
$17$	−0.0871303	+	0.150914i	−0.0211322	+	0.0366020i	0.855266	+	0.518189i	$0.173394\pi$
$18$	5.49106	+	9.09982i	1.29425	+	2.14485i
$19$	3.52537	−	6.10612i	0.808776	−	1.40084i	−0.104936	−	0.994479i	$-0.533464\pi$
$19$	3.52537	−	6.10612i	0.808776	−	1.40084i	0.913712	−	0.406362i	$-0.133203\pi$
$20$	1.06621	+	1.69210i	0.238413	+	0.378364i
$21$	−14.1077			−3.07855
$22$	−4.91988	+	0.0951372i	−1.04892	+	0.0202833i
$23$	0.971921	+	1.68342i	0.202659	+	0.351017i	0.949384	−	0.314116i	$-0.101708\pi$
$23$	0.971921	+	1.68342i	0.202659	+	0.351017i	−0.746725	+	0.665133i	$0.768375\pi$
$24$	−7.66381	+	5.03867i	−1.56437	+	1.02851i
$25$	1.00000			0.200000
$26$	−3.41619	+	3.78545i	−0.669970	+	0.742388i
$27$			14.6418i			2.81781i
$28$	−0.336387	−	8.69463i	−0.0635712	−	1.64313i
$29$	2.50740	−	1.44765i	0.465612	−	0.268821i	−0.248789	−	0.968558i	$-0.580033\pi$
$29$	2.50740	−	1.44765i	0.465612	−	0.268821i	0.714401	+	0.699736i	$0.246699\pi$
$30$	0.0886625	+	4.58505i	0.0161875	+	0.837112i
$31$			4.00389i			0.719121i	0.933122	+	0.359560i	$0.117073\pi$
$31$			4.00389i			0.719121i	−0.933122	+	0.359560i	$0.882927\pi$
$32$	−3.28809	−	4.60309i	−0.581258	−	0.813720i
$33$	−9.77150	−	5.64158i	−1.70100	−	0.982073i
$34$	−0.127324	−	0.211002i	−0.0218359	−	0.0361866i
$35$	−3.76770	−	2.17528i	−0.636858	−	0.367690i
$36$	−15.0193	+	0.581083i	−2.50322	+	0.0968471i
$37$	−3.07858	−	5.33225i	−0.506115	−	0.876616i	−0.999975	−	0.00707510i	$-0.997748\pi$
$37$	−3.07858	−	5.33225i	−0.506115	−	0.876616i	0.493860	−	0.869541i	$-0.335585\pi$
$38$	5.15165	+	8.53736i	0.835708	+	1.38494i
$39$	−11.1912	+	3.38466i	−1.79202	+	0.541980i
$40$	−2.82367	+	0.163970i	−0.446461	+	0.0259259i
$41$	−3.76751	+	2.17517i	−0.588386	+	0.339705i	−0.764459	−	0.644672i	$-0.776994\pi$
$41$	−3.76751	+	2.17517i	−0.588386	+	0.339705i	0.176073	+	0.984377i	$0.443661\pi$
$42$	9.63973	−	17.4680i	1.48744	−	2.69537i
$43$	7.49255	+	4.32582i	1.14260	+	0.659682i	0.947074	−	0.321016i	$-0.104024\pi$
$43$	7.49255	+	4.32582i	1.14260	+	0.659682i	0.195529	+	0.980698i	$0.437358\pi$
$44$	3.24393	−	6.15673i	0.489041	−	0.928163i
$45$	−3.75763	+	6.50841i	−0.560155	+	0.970217i
$46$	−2.74849	+	0.0531485i	−0.405243	+	0.00783631i
$47$		−	3.80183i		−	0.554554i	−0.960790	−	0.277277i	$-0.910568\pi$
$47$		−	3.80183i		−	0.554554i	0.960790	−	0.277277i	$-0.0894320\pi$
$48$	−1.00216	−	12.9321i	−0.144650	−	1.86659i
$49$	5.96372	+	10.3295i	0.851960	+	1.47564i
$50$	−0.683296	+	1.23819i	−0.0966326	+	0.175106i
$51$		−	0.565079i		−	0.0791269i
$52$	−2.35283	−	6.81647i	−0.326278	−	0.945274i
$53$			6.77726i			0.930928i	0.885067	+	0.465464i	$0.154112\pi$
$53$			6.77726i			0.930928i	−0.885067	+	0.465464i	$0.845888\pi$
$54$	−18.1292	−	10.0047i	−2.46708	−	1.36146i
$55$	−1.73976	−	3.01336i	−0.234590	−	0.406321i
$56$	10.9954	+	5.52449i	1.46933	+	0.738242i
$57$			22.8636i			3.02836i
$58$	0.0791630	+	4.09380i	0.0103946	+	0.537542i
$59$	−0.345814	+	0.598967i	−0.0450211	+	0.0779789i	−0.887658	−	0.460504i	$-0.847669\pi$
$59$	−0.345814	+	0.598967i	−0.0450211	+	0.0779789i	0.842637	+	0.538482i	$0.181002\pi$
$60$	−5.73773	−	3.02316i	−0.740738	−	0.390289i
$61$	−3.53499	−	2.04093i	−0.452609	−	0.261314i	0.256322	−	0.966591i	$-0.417489\pi$
$61$	−3.53499	−	2.04093i	−0.452609	−	0.261314i	−0.708932	+	0.705277i	$0.750822\pi$
$62$	−4.95757	−	2.73584i	−0.629612	−	0.347452i
$63$	28.3153	−	16.3478i	3.56739	−	2.05963i
$64$	7.94623	−	0.925995i	0.993278	−	0.115749i
$65$	−3.51068	−	0.821651i	−0.435447	−	0.101913i
$66$	13.6622	−	8.24408i	1.68169	−	1.01478i
$67$	3.84011	+	6.65126i	0.469144	+	0.812580i	0.999378	−	0.0352707i	$-0.0112294\pi$
$67$	3.84011	+	6.65126i	0.469144	+	0.812580i	−0.530234	+	0.847851i	$0.677896\pi$
$68$	0.348260	−	0.0134739i	0.0422328	−	0.00163395i
$69$	−5.45886	−	3.15167i	−0.657169	−	0.379417i
$70$	5.26786	−	3.17876i	0.629630	−	0.379934i
$71$	5.70744	+	3.29519i	0.677349	+	0.391067i	0.798855	−	0.601523i	$-0.205439\pi$
$71$	5.70744	+	3.29519i	0.677349	+	0.391067i	−0.121507	+	0.992591i	$0.538773\pi$
$72$	9.54313	−	18.9937i	1.12467	−	2.23843i
$73$		−	5.78564i		−	0.677157i	−0.940938	−	0.338579i	$-0.890054\pi$
$73$		−	5.78564i		−	0.677157i	0.940938	−	0.338579i	$-0.109946\pi$
$74$	8.70590	−	0.168349i	1.01204	−	0.0195701i
$75$	−2.80828	+	1.62136i	−0.324273	+	0.187219i
$76$	−14.0909	+	0.545166i	−1.61634	+	0.0625348i
$77$			15.1379i			1.72513i
$78$	3.45604	−	16.1695i	0.391320	−	1.83084i
$79$	−4.84812			−0.545456			−0.272728	−	0.962091i	$-0.587926\pi$
$79$	−4.84812			−0.545456			−0.272728	+	0.962091i	$0.587926\pi$
$80$	1.72638	−	3.60827i	0.193015	−	0.403417i
$81$	−12.4667	−	21.5930i	−1.38519	−	2.39922i
$82$	−0.118947	−	6.15117i	−0.0131355	−	0.679283i
$83$	−10.7720			−1.18238			−0.591189	−	0.806533i	$-0.701341\pi$
$83$	−10.7720			−1.18238			−0.591189	+	0.806533i	$0.701341\pi$
$84$	15.0418	+	23.8716i	1.64120	+	2.60460i
$85$	0.0871303	−	0.150914i	0.00945060	−	0.0163689i
$86$	−10.4758	+	6.32136i	−1.12963	+	0.681649i
$87$	−4.69432	+	8.13080i	−0.503284	+	0.871713i
$88$	5.40662	+	8.22347i	0.576348	+	0.876624i
$89$	−7.02896	+	4.05817i	−0.745068	+	0.430165i	−0.823909	−	0.566722i	$-0.808211\pi$
$89$	−7.02896	+	4.05817i	−0.745068	+	0.430165i	0.0788410	+	0.996887i	$0.474878\pi$
$90$	−5.49106	−	9.09982i	−0.578808	−	0.959206i
$91$	11.4399	+	10.7325i	1.19923	+	1.12507i
$92$	1.81223	−	3.43946i	0.188938	−	0.358589i
$93$	−6.49176	−	11.2441i	−0.673165	−	1.16596i
$94$	4.70738	+	2.59777i	0.485529	+	0.267940i
$95$	−3.52537	+	6.10612i	−0.361696	+	0.626475i
$96$	16.6972	+	7.59560i	1.70415	+	0.775223i
$97$	4.51069	+	2.60425i	0.457991	+	0.264421i	0.711199	−	0.702991i	$-0.248152\pi$
$97$	4.51069	+	2.60425i	0.457991	+	0.264421i	−0.253208	+	0.967412i	$0.581486\pi$
$98$	−16.8648	+	0.326120i	−1.70360	+	0.0329431i
$99$	26.1496			2.62813
$100$	−1.06621	−	1.69210i	−0.106621	−	0.169210i
$101$	8.61732	−	4.97521i	0.857456	−	0.495052i	−0.00570385	−	0.999984i	$-0.501816\pi$
$101$	8.61732	−	4.97521i	0.857456	−	0.495052i	0.863159	+	0.504932i	$0.168482\pi$
$102$	0.699673	+	0.386116i	0.0692780	+	0.0382312i
$103$	4.46886			0.440330			0.220165	−	0.975463i	$-0.429340\pi$
$103$	4.46886			0.440330			0.220165	+	0.975463i	$0.429340\pi$
$104$	10.0477	+	1.74442i	0.985261	+	0.171055i
$105$	14.1077			1.37677
$106$	−8.39151	−	4.63087i	−0.815055	−	0.449790i
$107$	−8.53297	+	4.92651i	−0.824914	+	0.476264i	−0.852108	−	0.523366i	$-0.824676\pi$
$107$	−8.53297	+	4.92651i	−0.824914	+	0.476264i	0.0271944	+	0.999630i	$0.491343\pi$
$108$	24.7753	−	15.6113i	2.38400	−	1.50219i
$109$	9.16126			0.877490			0.438745	−	0.898612i	$-0.355423\pi$
$109$	9.16126			0.877490			0.438745	+	0.898612i	$0.355423\pi$
$110$	4.91988	−	0.0951372i	0.469092	−	0.00907097i
$111$	17.2910	+	9.98297i	1.64119	+	0.947542i
$112$	−14.3535	+	9.83954i	−1.35628	+	0.929749i
$113$	−4.01133	+	6.94783i	−0.377354	+	0.653597i	−0.990676	−	0.136236i	$-0.956499\pi$
$113$	−4.01133	+	6.94783i	−0.377354	+	0.653597i	0.613322	+	0.789833i	$0.289833\pi$
$114$	−28.3094	−	15.6226i	−2.65142	−	1.46319i
$115$	−0.971921	−	1.68342i	−0.0906321	−	0.156979i
$116$	−5.12298	−	2.69926i	−0.475657	−	0.250620i
$117$	18.5395	−	19.7615i	1.71398	−	1.82695i
$118$	−0.505340	−	0.837454i	−0.0465203	−	0.0770939i
$119$	−0.656562	+	0.379066i	−0.0601869	+	0.0347489i
$120$	7.66381	−	5.03867i	0.699607	−	0.459965i
$121$	−0.553559	+	0.958792i	−0.0503235	+	0.0871629i
$122$	4.94249	−	2.98242i	0.447472	−	0.270016i
$123$	7.05349	−	12.2170i	0.635992	−	1.10157i
$124$	6.77497	−	4.26901i	0.608410	−	0.383368i
$125$	−1.00000			−0.0894427
$126$	0.893964	+	46.2300i	0.0796407	+	4.11850i
$127$	1.31236	+	2.27308i	0.116453	+	0.201703i	0.918360	−	0.395747i	$-0.129514\pi$
$127$	1.31236	+	2.27308i	0.116453	+	0.201703i	−0.801906	+	0.597450i	$0.796181\pi$
$128$	−4.28307	+	10.4716i	−0.378573	+	0.925571i
$129$	−28.0549			−2.47010
$130$	3.41619	−	3.78545i	0.299620	−	0.332006i
$131$			11.7817i			1.02937i	0.857380	+	0.514685i	$0.172091\pi$
$131$			11.7817i			1.02937i	−0.857380	+	0.514685i	$0.827909\pi$
$132$	0.872417	+	22.5494i	0.0759342	+	1.96268i
$133$	26.5651	−	15.3374i	2.30349	−	1.32992i
$134$	−10.8594	+	0.209992i	−0.938112	+	0.0181406i
$135$		−	14.6418i		−	1.26016i
$136$	−0.221282	+	0.440418i	−0.0189748	+	0.0377655i
$137$	−7.08319	−	4.08948i	−0.605158	−	0.349388i	0.165910	−	0.986141i	$-0.446944\pi$
$137$	−7.08319	−	4.08948i	−0.605158	−	0.349388i	−0.771068	+	0.636753i	$0.780277\pi$
$138$	7.63237	−	4.60556i	0.649711	−	0.392051i
$139$	−17.7361	−	10.2400i	−1.50436	−	0.868542i	−0.999987	−	0.00505590i	$-0.998391\pi$
$139$	−17.7361	−	10.2400i	−1.50436	−	0.868542i	−0.504372	−	0.863486i	$-0.668276\pi$
$140$	0.336387	+	8.69463i	0.0284299	+	0.734831i
$141$	6.16415	+	10.6766i	0.519115	+	0.899133i
$142$	−7.97993	+	4.81529i	−0.669661	+	0.404090i
$143$	3.63183	+	12.0084i	0.303709	+	1.00420i
$144$	16.9970	+	24.7945i	1.41642	+	2.06621i
$145$	−2.50740	+	1.44765i	−0.208228	+	0.120221i
$146$	7.16370	+	3.95330i	0.592872	+	0.327177i
$147$	−33.4956	−	19.3387i	−2.76267	−	1.59503i
$148$	−5.74026	+	10.8946i	−0.471846	+	0.895528i
$149$	9.69588	−	16.7937i	0.794317	−	1.37580i	−0.128955	−	0.991650i	$-0.541162\pi$
$149$	9.69588	−	16.7937i	0.794317	−	1.37580i	0.923272	−	0.384147i	$-0.125504\pi$
$150$	−0.0886625	−	4.58505i	−0.00723926	−	0.374368i
$151$		−	20.1283i		−	1.63802i	−0.573783	−	0.819008i	$-0.694525\pi$
$151$		−	20.1283i		−	1.63802i	0.573783	−	0.819008i	$-0.305475\pi$
$152$	8.95327	−	17.8197i	0.726206	−	1.44537i
$153$	0.654807	+	1.13416i	0.0529380	+	0.0916913i
$154$	−18.7436	−	10.3437i	−1.51040	−	0.833518i
$155$		−	4.00389i		−	0.321600i
$156$	17.6594	+	15.3278i	1.41388	+	1.22720i
$157$			2.26965i			0.181138i	0.995890	+	0.0905691i	$0.0288686\pi$
$157$			2.26965i			0.181138i	−0.995890	+	0.0905691i	$0.971131\pi$
$158$	3.31270	−	6.00288i	0.263544	−	0.477563i
$159$	−10.9884	−	19.0324i	−0.871436	−	1.50937i
$160$	3.28809	+	4.60309i	0.259946	+	0.363906i
$161$			8.45682i			0.666490i
$162$	35.2546	−	0.681729i	2.76986	−	0.0535617i
$163$	−8.50577	+	14.7324i	−0.666223	+	1.15393i	0.312729	+	0.949842i	$0.398757\pi$
$163$	−8.50577	+	14.7324i	−0.666223	+	1.15393i	−0.978952	+	0.204090i	$0.934577\pi$
$164$	7.69757	+	4.05579i	0.601080	+	0.316704i
$165$	9.77150	+	5.64158i	0.760710	+	0.439196i
$166$	7.36045	−	13.3377i	0.571282	−	1.03521i
$167$	−10.5757	+	6.10587i	−0.818370	+	0.472486i	−0.849854	−	0.527018i	$-0.823310\pi$
$167$	−10.5757	+	6.10587i	−0.818370	+	0.472486i	0.0314839	+	0.999504i	$0.489977\pi$
$168$	−39.8355	+	2.31324i	−3.07337	+	0.178470i
$169$	11.6498	+	5.76911i	0.896137	+	0.443778i
$170$	0.127324	+	0.211002i	0.00976531	+	0.0161831i
$171$	−26.4941	−	45.8892i	−2.02606	−	3.50923i
$172$	−0.668948	−	17.2904i	−0.0510068	−	1.31838i
$173$	−6.51681	−	3.76248i	−0.495464	−	0.286056i	0.231374	−	0.972865i	$-0.425678\pi$
$173$	−6.51681	−	3.76248i	−0.495464	−	0.286056i	−0.726838	+	0.686809i	$0.759011\pi$
$174$	−6.85984	−	11.3682i	−0.520043	−	0.861820i
$175$	3.76770	+	2.17528i	0.284812	+	0.164436i
$176$	−13.8765	+	1.07535i	−1.04598	+	0.0810574i
$177$		−	2.24276i		−	0.168576i
$178$	−0.221917	−	11.4761i	−0.0166334	−	0.860170i
$179$	8.81127	−	5.08719i	0.658585	−	0.380234i	−0.133152	−	0.991096i	$-0.542510\pi$
$179$	8.81127	−	5.08719i	0.658585	−	0.380234i	0.791738	+	0.610861i	$0.209177\pi$
$180$	15.0193	−	0.581083i	1.11947	−	0.0433114i
$181$		−	22.5150i		−	1.67352i	−0.547567	−	0.836762i	$-0.684446\pi$
$181$		−	22.5150i		−	1.67352i	0.547567	−	0.836762i	$-0.315554\pi$
$182$	−21.1056	+	6.83126i	−1.56445	+	0.506367i
$183$	13.2363			0.978458
$184$	3.02041	+	4.59405i	0.222668	+	0.338678i
$185$	3.07858	+	5.33225i	0.226341	+	0.392035i
$186$	18.3580	−	0.354995i	1.34608	−	0.0260295i
$187$	−0.606344			−0.0443403
$188$	−6.43306	+	4.05356i	−0.469179	+	0.295637i
$189$	−31.8500	+	55.1658i	−2.31675	+	4.01272i
$190$	−5.15165	−	8.53736i	−0.373740	−	0.619365i
$191$	5.11767	−	8.86407i	0.370302	−	0.641382i	−0.619310	−	0.785147i	$-0.712588\pi$
$191$	5.11767	−	8.86407i	0.370302	−	0.641382i	0.989612	+	0.143765i	$0.0459209\pi$
$192$	−20.8139	+	15.4842i	−1.50211	+	1.11747i
$193$	13.2572	−	7.65407i	0.954277	−	0.550952i	0.0598699	−	0.998206i	$-0.480931\pi$
$193$	13.2572	−	7.65407i	0.954277	−	0.550952i	0.894407	+	0.447254i	$0.147598\pi$
$194$	−6.30668	+	3.80560i	−0.452793	+	0.273226i
$195$	11.1912	−	3.38466i	0.801417	−	0.242381i
$196$	11.1199	−	21.1046i	0.794275	−	1.50747i
$197$	4.35638	+	7.54548i	0.310379	+	0.537593i	0.978445	−	0.206510i	$-0.0662106\pi$
$197$	4.35638	+	7.54548i	0.310379	+	0.537593i	−0.668065	+	0.744103i	$0.732877\pi$
$198$	−17.8679	+	32.3781i	−1.26982	+	2.30101i
$199$	−5.74530	+	9.95116i	−0.407274	+	0.705419i	−0.994583	−	0.103944i	$-0.966854\pi$
$199$	−5.74530	+	9.95116i	−0.407274	+	0.705419i	0.587309	+	0.809362i	$0.300187\pi$
$200$	2.82367	−	0.163970i	0.199664	−	0.0115944i
$201$	−21.5682	−	12.4524i	−1.52130	−	0.878325i
$202$	0.272064	+	14.0694i	0.0191424	+	0.989919i
$203$	12.5962			0.884078
$204$	−0.956168	+	0.602495i	−0.0669451	+	0.0421831i
$205$	3.76751	−	2.17517i	0.263134	−	0.151921i
$206$	−3.05355	+	5.53329i	−0.212751	+	0.385522i
$207$	14.6085			1.01536
$208$	−9.02550	+	11.2490i	−0.625806	+	0.779979i
$209$	24.5333			1.69700
$210$	−9.63973	+	17.4680i	−0.665205	+	1.20540i
$211$	−2.97267	+	1.71627i	−0.204647	+	0.118153i	−0.598821	−	0.800883i	$-0.704364\pi$
$211$	−2.97267	+	1.71627i	−0.204647	+	0.118153i	0.394174	+	0.919036i	$0.371031\pi$
$212$	11.4678	−	7.22600i	0.787609	−	0.496284i
$213$	−21.3708			−1.46430
$214$	−0.269401	−	13.9317i	−0.0184159	−	0.952350i
$215$	−7.49255	−	4.32582i	−0.510987	−	0.295019i
$216$	2.40081	+	41.3435i	0.163355	+	2.81307i
$217$	−8.70961	+	15.0855i	−0.591247	+	1.02407i
$218$	−6.25985	+	11.3434i	−0.423971	+	0.768269i
$219$	9.38061	+	16.2477i	0.633883	+	1.09792i
$220$	−3.24393	+	6.15673i	−0.218706	+	0.415087i
$221$	−0.429885	+	0.458221i	−0.0289172	+	0.0308232i
$222$	−24.1757	+	14.5882i	−1.62256	+	0.979095i
$223$	−21.3931	+	12.3513i	−1.43259	+	0.827106i	−0.997318	−	0.0731926i	$-0.976681\pi$
$223$	−21.3931	+	12.3513i	−1.43259	+	0.827106i	−0.435272	+	0.900299i	$0.643348\pi$
$224$	−2.37551	−	24.4956i	−0.158720	−	1.63668i
$225$	3.75763	−	6.50841i	0.250509	−	0.433894i
$226$	−5.86179	−	9.71420i	−0.389920	−	0.646179i
$227$	−10.8312	+	18.7601i	−0.718889	+	1.24515i	0.242551	+	0.970139i	$0.422016\pi$
$227$	−10.8312	+	18.7601i	−0.718889	+	1.24515i	−0.961440	+	0.275014i	$0.911318\pi$
$228$	38.6875	−	24.3775i	2.56214	−	1.61444i
$229$	−9.85088			−0.650964			−0.325482	−	0.945548i	$-0.605527\pi$
$229$	−9.85088			−0.650964			−0.325482	+	0.945548i	$0.605527\pi$
$230$	2.74849	−	0.0531485i	0.181230	−	0.00350451i
$231$	−24.5441	−	42.5116i	−1.61488	−	2.79706i
$232$	6.84269	−	4.49881i	0.449245	−	0.295362i
$233$	1.91774			0.125636			0.0628178	−	0.998025i	$-0.479991\pi$
$233$	1.91774			0.125636			0.0628178	+	0.998025i	$0.479991\pi$
$234$	11.8005	+	36.4583i	0.771421	+	2.38335i
$235$			3.80183i			0.248004i
$236$	1.38222	−	0.0534769i	0.0899749	−	0.00348105i
$237$	13.6149	−	7.86056i	0.884382	−	0.510598i
$238$	−0.0207288	−	1.07196i	−0.00134365	−	0.0694849i
$239$		−	1.29795i		−	0.0839574i	−0.999119	−	0.0419787i	$-0.986634\pi$
$239$		−	1.29795i		−	0.0839574i	0.999119	−	0.0419787i	$-0.0133662\pi$
$240$	1.00216	+	12.9321i	0.0646894	+	0.834765i
$241$	13.7951	+	7.96463i	0.888623	+	0.513047i	0.873492	−	0.486839i	$-0.161850\pi$
$241$	13.7951	+	7.96463i	0.888623	+	0.513047i	0.0151311	+	0.999886i	$0.495183\pi$
$242$	−0.808919	−	1.34055i	−0.0519993	−	0.0861737i
$243$	31.9797	+	18.4635i	2.05150	+	1.18443i
$244$	0.315610	+	8.15761i	0.0202049	+	0.522237i
$245$	−5.96372	−	10.3295i	−0.381008	−	0.659926i
$246$	10.3073	+	17.0814i	0.657170	+	1.08907i
$247$	17.3936	−	18.5400i	1.10673	−	1.17967i
$248$	0.656519	+	11.3057i	0.0416890	+	0.717911i
$249$	30.2508	−	17.4653i	1.91706	−	1.10682i
$250$	0.683296	−	1.23819i	0.0432154	−	0.0783098i
$251$	4.91353	+	2.83683i	0.310140	+	0.179059i	0.646989	−	0.762499i	$-0.276028\pi$
$251$	4.91353	+	2.83683i	0.310140	+	0.179059i	−0.336849	+	0.941559i	$0.609361\pi$
$252$	−57.8523	−	30.4819i	−3.64435	−	1.92018i
$253$	−3.38183	+	5.85749i	−0.212614	+	0.368257i
$254$	−3.71123	+	0.0717651i	−0.232863	+	0.00450294i
$255$			0.565079i			0.0353866i
$256$	−10.0392	−	12.4585i	−0.627453	−	0.778654i
$257$	−5.37143	−	9.30358i	−0.335060	−	0.580342i	0.648436	−	0.761269i	$-0.275423\pi$
$257$	−5.37143	−	9.30358i	−0.335060	−	0.580342i	−0.983496	+	0.180927i	$0.942090\pi$
$258$	19.1698	−	34.7372i	1.19346	−	2.16265i
$259$		−	26.7871i		−	1.66447i
$260$	2.35283	+	6.81647i	0.145916	+	0.422739i
$261$		−	21.7589i		−	1.34684i
$262$	−14.5879	−	8.05036i	−0.901244	−	0.497353i
$263$	−0.121811	−	0.210982i	−0.00751117	−	0.0130097i	0.862245	−	0.506491i	$-0.169058\pi$
$263$	−0.121811	−	0.210982i	−0.00751117	−	0.0130097i	−0.869757	+	0.493481i	$0.835724\pi$
$264$	−28.5165	−	14.3277i	−1.75507	−	0.881810i
$265$		−	6.77726i		−	0.416323i
$266$	0.838708	+	43.3725i	0.0514245	+	2.65934i
$267$	13.1595	−	22.7930i	0.805350	−	1.39491i
$268$	7.16019	−	13.5895i	0.437378	−	0.830110i
$269$	−11.6318	−	6.71561i	−0.709202	−	0.409458i	0.101564	−	0.994829i	$-0.467615\pi$
$269$	−11.6318	−	6.71561i	−0.709202	−	0.409458i	−0.810765	+	0.585371i	$0.800949\pi$
$270$	18.1292	+	10.0047i	1.10331	+	0.608864i
$271$	−8.02102	+	4.63094i	−0.487242	+	0.281309i	−0.723430	−	0.690398i	$-0.757435\pi$
$271$	−8.02102	+	4.63094i	−0.487242	+	0.281309i	0.236187	+	0.971708i	$0.424102\pi$
$272$	−0.394119	−	0.574924i	−0.0238970	−	0.0348599i
$273$	−49.5276	−	11.5916i	−2.99755	−	0.701556i
$274$	9.90346	−	5.97599i	0.598290	−	0.361023i
$275$	1.73976	+	3.01336i	0.104912	+	0.181712i
$276$	0.487377	+	12.5973i	0.0293366	+	0.758266i
$277$	7.82314	+	4.51669i	0.470047	+	0.271382i	0.716259	−	0.697834i	$-0.245853\pi$
$277$	7.82314	+	4.51669i	0.470047	+	0.271382i	−0.246213	+	0.969216i	$0.579186\pi$
$278$	24.7980	−	14.9637i	1.48729	−	0.897465i
$279$	26.0590	+	15.0452i	1.56011	+	0.900730i
$280$	−10.9954	−	5.52449i	−0.657103	−	0.330152i
$281$			26.5298i			1.58263i	0.611407	+	0.791316i	$0.290604\pi$
$281$			26.5298i			1.58263i	−0.611407	+	0.791316i	$0.709396\pi$
$282$	−17.4316	+	0.337080i	−1.03804	+	0.0200728i
$283$	−7.95167	+	4.59090i	−0.472678	+	0.272901i	−0.717360	−	0.696703i	$-0.754650\pi$
$283$	−7.95167	+	4.59090i	−0.472678	+	0.272901i	0.244682	+	0.969603i	$0.421316\pi$
$284$	−0.509571	−	13.1709i	−0.0302375	−	0.781550i
$285$		−	22.8636i		−	1.35432i
$286$	−17.3503	−	3.70842i	−1.02594	−	0.219284i
$287$	−18.9265			−1.11719
$288$	−42.3143	+	4.10350i	−2.49339	+	0.241801i
$289$	8.48482	+	14.6961i	0.499107	+	0.864478i
$290$	−0.0791630	−	4.09380i	−0.00464861	−	0.240396i
$291$	−16.8897			−0.990092
$292$	−9.78985	+	6.16872i	−0.572908	+	0.360997i
$293$	9.79438	−	16.9644i	0.572194	−	0.991069i	−0.424146	−	0.905594i	$-0.639426\pi$
$293$	9.79438	−	16.9644i	0.572194	−	0.991069i	0.996340	−	0.0854753i	$-0.0272409\pi$
$294$	46.8324	−	28.2598i	2.73132	−	1.64814i
$295$	0.345814	−	0.598967i	0.0201341	−	0.0348732i
$296$	−9.56721	−	14.5517i	−0.556083	−	0.845802i
$297$	−44.1209	+	25.4732i	−2.56016	+	1.47811i
$298$	14.1687	+	23.4804i	0.820768	+	1.36018i
$299$	2.02892	+	6.70852i	0.117336	+	0.387964i
$300$	5.73773	+	3.02316i	0.331268	+	0.174542i
$301$	18.8198	+	32.5968i	1.08475	+	1.87885i
$302$	24.9226	+	13.7536i	1.43413	+	0.791428i
$303$	−16.1332	+	27.9436i	−0.926831	+	1.60532i
$304$	15.9464	+	23.2620i	0.914591	+	1.33417i
$305$	3.53499	+	2.04093i	0.202413	+	0.116863i
$306$	−1.85173	+	0.0358074i	−0.105856	+	0.00204697i
$307$	−4.40198			−0.251234			−0.125617	−	0.992079i	$-0.540091\pi$
$307$	−4.40198			−0.251234			−0.125617	+	0.992079i	$0.540091\pi$
$308$	25.6148	−	16.1403i	1.45954	−	0.919677i
$309$	−12.5498	+	7.24565i	−0.713935	+	0.412190i
$310$	4.95757	+	2.73584i	0.281571	+	0.155385i
$311$	18.3297			1.03938			0.519691	−	0.854354i	$-0.326047\pi$
$311$	18.3297			1.03938			0.519691	+	0.854354i	$0.326047\pi$
$312$	−31.0452	+	11.3922i	−1.75759	+	0.644956i
$313$	5.44772			0.307923			0.153962	−	0.988077i	$-0.450797\pi$
$313$	5.44772			0.307923			0.153962	+	0.988077i	$0.450797\pi$
$314$	−2.81026	−	1.55085i	−0.158592	−	0.0875193i
$315$	−28.3153	+	16.3478i	−1.59539	+	0.921097i
$316$	5.16913	+	8.20348i	0.290786	+	0.461482i
$317$	10.1490			0.570023			0.285011	−	0.958524i	$-0.408003\pi$
$317$	10.1490			0.570023			0.285011	+	0.958524i	$0.408003\pi$
$318$	31.0740	−	0.600888i	1.74255	−	0.0336961i
$319$	8.72456	+	5.03713i	0.488482	+	0.282025i
$320$	−7.94623	+	0.925995i	−0.444208	+	0.0517647i
$321$	15.9753	−	27.6701i	0.891656	−	1.54439i
$322$	−10.4711	−	5.77851i	−0.583533	−	0.322024i
$323$	0.614333	+	1.06406i	0.0341824	+	0.0592057i
$324$	−23.2452	+	44.1176i	−1.29140	+	2.45098i
$325$	3.51068	+	0.821651i	0.194738	+	0.0455770i
$326$	−12.4295	−	20.5983i	−0.688408	−	1.14084i
$327$	−25.7274	+	14.8537i	−1.42273	+	0.821413i
$328$	−10.2815	+	6.75973i	−0.567703	+	0.373244i
$329$	8.27006	−	14.3242i	0.455943	−	0.789717i
$330$	−13.6622	+	8.24408i	−0.752077	+	0.453821i
$331$	−4.16389	+	7.21207i	−0.228868	+	0.396411i	−0.957473	−	0.288523i	$-0.906836\pi$
$331$	−4.16389	+	7.21207i	−0.228868	+	0.396411i	0.728605	+	0.684934i	$0.240169\pi$
$332$	11.4852	+	18.2272i	0.630334	+	1.00035i
$333$	−46.2726			−2.53572
$334$	−0.333893	−	17.2668i	−0.0182698	−	0.944796i
$335$	−3.84011	−	6.65126i	−0.209807	−	0.363397i
$336$	24.3552	−	50.9044i	1.32868	−	2.77706i
$337$	−0.369183			−0.0201107			−0.0100553	−	0.999949i	$-0.503201\pi$
$337$	−0.369183			−0.0201107			−0.0100553	+	0.999949i	$0.503201\pi$
$338$	−15.1035	+	10.4826i	−0.821521	+	0.570178i
$339$		−	26.0153i		−	1.41296i
$340$	−0.348260	+	0.0134739i	−0.0188871	+	0.000730724i
$341$	−12.0652	+	6.96583i	−0.653366	+	0.377221i
$342$	74.9227	−	1.44880i	4.05135	−	0.0783423i
$343$			21.4372i			1.15750i
$344$	21.8658	+	10.9861i	1.17892	+	0.592333i
$345$	5.45886	+	3.15167i	0.293895	+	0.169680i
$346$	9.11157	−	5.49814i	0.489841	−	0.295582i
$347$	27.7146	+	16.0010i	1.48780	+	0.858981i	0.999903	−	0.0139210i	$-0.00443134\pi$
$347$	27.7146	+	16.0010i	1.48780	+	0.858981i	0.487896	+	0.872902i	$0.337765\pi$
$348$	18.7632	−	0.725933i	1.00582	−	0.0389141i
$349$	11.0620	+	19.1600i	0.592138	+	1.02561i	0.993944	+	0.109888i	$0.0350493\pi$
$349$	11.0620	+	19.1600i	0.592138	+	1.02561i	−0.401806	+	0.915725i	$0.631617\pi$
$350$	−5.26786	+	3.17876i	−0.281579	+	0.169912i
$351$	−12.0304	+	51.4026i	−0.642137	+	2.74367i
$352$	8.15028	−	17.9165i	0.434411	−	0.954952i
$353$	6.93899	−	4.00623i	0.369325	−	0.213230i	−0.303838	−	0.952724i	$-0.598268\pi$
$353$	6.93899	−	4.00623i	0.369325	−	0.213230i	0.673164	+	0.739494i	$0.264935\pi$
$354$	2.77695	+	1.53247i	0.147593	+	0.0814497i
$355$	−5.70744	−	3.29519i	−0.302920	−	0.174891i
$356$	14.3612	+	7.56679i	0.761141	+	0.401039i
$357$	1.22921	−	2.12905i	0.0650565	−	0.112681i
$358$	0.278188	+	14.3861i	0.0147027	+	0.760327i
$359$		−	18.2254i		−	0.961902i	−0.876748	−	0.480951i	$-0.840292\pi$
$359$		−	18.2254i		−	0.961902i	0.876748	−	0.480951i	$-0.159708\pi$
$360$	−9.54313	+	18.9937i	−0.502967	+	1.00106i
$361$	−15.3565	−	26.5982i	−0.808237	−	1.39991i
$362$	27.8777	+	15.3844i	1.46522	+	0.808585i
$363$		−	3.59008i		−	0.188430i
$364$	5.96300	−	30.8005i	0.312546	−	1.61438i
$365$			5.78564i			0.302834i
$366$	−9.04433	+	16.3891i	−0.472755	+	0.856670i
$367$	−8.30557	−	14.3857i	−0.433547	−	0.750926i	0.563629	−	0.826028i	$-0.309405\pi$
$367$	−8.30557	−	14.3857i	−0.433547	−	0.750926i	−0.997176	+	0.0751024i	$0.976072\pi$
$368$	−7.75212	+	0.600744i	−0.404107	+	0.0313160i
$369$			32.6940i			1.70198i
$370$	−8.70590	+	0.168349i	−0.452598	+	0.00875203i
$371$	−14.7425	+	25.5347i	−0.765390	+	1.32569i
$372$	−12.1044	+	22.9733i	−0.627585	+	1.19111i
$373$	−16.9366	−	9.77836i	−0.876945	−	0.506304i	−0.00729516	−	0.999973i	$-0.502322\pi$
$373$	−16.9366	−	9.77836i	−0.876945	−	0.506304i	−0.869650	+	0.493669i	$0.835655\pi$
$374$	0.414313	−	0.750768i	0.0214236	−	0.0388213i
$375$	2.80828	−	1.62136i	0.145019	−	0.0837268i
$376$	−0.623386	−	10.7351i	−0.0321487	−	0.553621i
$377$	9.99214	−	3.02202i	0.514621	−	0.155642i
$378$	−46.5426	−	77.1309i	−2.39390	−	3.96718i
$379$	17.7727	+	30.7833i	0.912923	+	1.58123i	0.809913	+	0.586550i	$0.199514\pi$
$379$	17.7727	+	30.7833i	0.912923	+	1.58123i	0.103010	+	0.994680i	$0.467153\pi$
$380$	14.0909	−	0.545166i	0.722850	−	0.0279664i
$381$	−7.37097	−	4.25563i	−0.377626	−	0.218023i
$382$	7.47849	+	12.3934i	0.382633	+	0.634102i
$383$	−8.45235	−	4.87996i	−0.431895	−	0.249355i	0.268259	−	0.963347i	$-0.413552\pi$
$383$	−8.45235	−	4.87996i	−0.431895	−	0.249355i	−0.700153	+	0.713992i	$0.746885\pi$
$384$	−4.95026	−	36.3517i	−0.252617	−	1.85507i
$385$		−	15.1379i		−	0.771500i
$386$	0.418555	+	21.6449i	0.0213039	+	1.10170i
$387$	56.3085	−	32.5097i	2.86232	−	1.65256i
$388$	−0.402722	−	10.4092i	−0.0204451	−	0.528447i
$389$		−	6.49427i		−	0.329273i	−0.986354	−	0.164636i	$-0.947355\pi$
$389$		−	6.49427i		−	0.329273i	0.986354	−	0.164636i	$-0.0526450\pi$
$390$	−3.45604	+	16.1695i	−0.175004	+	0.818774i
$391$	−0.338735			−0.0171306
$392$	18.5333	+	28.1891i	0.936074	+	1.42377i
$393$	−19.1024	−	33.0862i	−0.963586	−	1.66898i
$394$	−12.3194	+	0.238224i	−0.620643	+	0.0120016i
$395$	4.84812			0.243935
$396$	−27.8810	−	44.2476i	−1.40108	−	2.22353i
$397$	4.89890	−	8.48514i	0.245869	−	0.425857i	−0.716507	−	0.697580i	$-0.754260\pi$
$397$	4.89890	−	8.48514i	0.245869	−	0.425857i	0.962375	+	0.271723i	$0.0875935\pi$
$398$	−8.39565	−	13.9133i	−0.420836	−	0.697413i
$399$	−49.7349	+	86.1434i	−2.48986	+	4.31256i
$400$	−1.72638	+	3.60827i	−0.0863188	+	0.180414i
$401$	−29.1996	+	16.8584i	−1.45816	+	0.841867i	−0.998921	−	0.0464469i	$-0.985210\pi$
$401$	−29.1996	+	16.8584i	−1.45816	+	0.841867i	−0.459236	+	0.888314i	$0.651877\pi$
$402$	30.1559	−	18.1968i	1.50404	−	0.907573i
$403$	−3.28980	+	14.0564i	−0.163877	+	0.700199i
$404$	−17.6064	−	9.27669i	−0.875953	−	0.461533i
$405$	12.4667	+	21.5930i	0.619476	+	1.07296i
$406$	−8.60691	+	15.5964i	−0.427154	+	0.774037i
$407$	10.7120	−	18.5537i	0.530974	−	0.919673i
$408$	−0.0926560	−	1.59560i	−0.00458716	−	0.0789938i
$409$	−28.7701	−	16.6104i	−1.42259	−	0.821332i	−0.426070	−	0.904690i	$-0.640102\pi$
$409$	−28.7701	−	16.6104i	−1.42259	−	0.821332i	−0.996520	+	0.0833579i	$0.973436\pi$
$410$	0.118947	+	6.15117i	0.00587438	+	0.303785i
$411$	26.5221			1.30824
$412$	−4.76476	−	7.56174i	−0.234743	−	0.372540i
$413$	−2.60585	+	1.50449i	−0.128225	+	0.0740309i
$414$	−9.98192	+	18.0880i	−0.490584	+	0.888979i
$415$	10.7720			0.528776
$416$	−7.76130	−	18.8617i	−0.380529	−	0.924769i
$417$	66.4108			3.25215
$418$	−16.7635	+	30.3768i	−0.819929	+	1.48578i
$419$	27.1497	−	15.6749i	1.32635	−	0.765767i	0.341615	−	0.939840i	$-0.389026\pi$
$419$	27.1497	−	15.6749i	1.32635	−	0.765767i	0.984733	+	0.174073i	$0.0556928\pi$
$420$	−15.0418	−	23.8716i	−0.733966	−	1.16481i
$421$	−13.4850			−0.657220			−0.328610	−	0.944466i	$-0.606580\pi$
$421$	−13.4850			−0.657220			−0.328610	+	0.944466i	$0.606580\pi$
$422$	−0.0938524	−	4.85344i	−0.00456866	−	0.236262i
$423$	−24.7439	−	14.2859i	−1.20309	−	0.694603i
$424$	1.11127	+	19.1367i	0.0539679	+	0.929362i
$425$	−0.0871303	+	0.150914i	−0.00422644	+	0.00732041i
$426$	14.6026	−	26.4611i	0.707497	−	1.28204i
$427$	−8.87920	−	15.3792i	−0.429694	−	0.744253i
$428$	17.4341	+	9.18589i	0.842709	+	0.444017i
$429$	−29.6692	−	27.8345i	−1.43244	−	1.34386i
$430$	10.4758	−	6.32136i	0.505188	−	0.304843i
$431$	8.88410	−	5.12924i	0.427932	−	0.247067i	−0.270533	−	0.962711i	$-0.587200\pi$
$431$	8.88410	−	5.12924i	0.427932	−	0.247067i	0.698465	+	0.715644i	$0.253867\pi$
$432$	−52.8315	−	25.2772i	−2.54186	−	1.21615i
$433$	5.96184	−	10.3262i	0.286508	−	0.496246i	−0.686466	−	0.727162i	$-0.740839\pi$
$433$	5.96184	−	10.3262i	0.286508	−	0.496246i	0.972974	+	0.230916i	$0.0741723\pi$
$434$	−12.7274	−	21.0920i	−0.610935	−	1.01245i
$435$	4.69432	−	8.13080i	0.225075	−	0.389842i
$436$	−9.76787	−	15.5017i	−0.467796	−	0.742399i
$437$	13.7055			0.655624
$438$	−26.5274	+	0.512969i	−1.26753	+	0.0245106i
$439$	0.238520	+	0.413129i	0.0113839	+	0.0197176i	0.871661	−	0.490109i	$-0.163043\pi$
$439$	0.238520	+	0.413129i	0.0113839	+	0.0197176i	−0.860277	+	0.509826i	$0.829710\pi$
$440$	−5.40662	−	8.22347i	−0.257751	−	0.392038i
$441$	89.6379			4.26847
$442$	−0.273624	−	0.845378i	−0.0130150	−	0.0402106i
$443$		−	34.3454i		−	1.63180i	−0.578194	−	0.815900i	$-0.696242\pi$
$443$		−	34.3454i		−	1.63180i	0.578194	−	0.815900i	$-0.303758\pi$
$444$	−1.54377	−	39.9020i	−0.0732642	−	1.89367i
$445$	7.02896	−	4.05817i	0.333205	−	0.192376i
$446$	−0.675419	−	34.9283i	−0.0319820	−	1.65390i
$447$			62.8821i			2.97422i
$448$	31.9533	+	13.7964i	1.50965	+	0.651820i
$449$	−10.3848	−	5.99567i	−0.490089	−	0.282953i	0.234522	−	0.972111i	$-0.424647\pi$
$449$	−10.3848	−	5.99567i	−0.490089	−	0.282953i	−0.724611	+	0.689158i	$0.757981\pi$
$450$	5.49106	+	9.09982i	0.258851	+	0.428970i
$451$	−13.1092	−	7.56858i	−0.617286	−	0.356390i
$452$	16.0333	−	0.620315i	0.754144	−	0.0291772i
$453$	32.6352	+	56.5259i	1.53334	+	2.65582i
$454$	−15.8276	−	26.2297i	−0.742828	−	1.23102i
$455$	−11.4399	−	10.7325i	−0.536310	−	0.503146i
$456$	3.74895	+	64.5594i	0.175561	+	3.02327i
$457$	22.3688	−	12.9147i	1.04637	−	0.604122i	0.124740	−	0.992190i	$-0.460190\pi$
$457$	22.3688	−	12.9147i	1.04637	−	0.604122i	0.921631	+	0.388067i	$0.126857\pi$
$458$	6.73106	−	12.1972i	0.314522	−	0.569939i
$459$	−2.20965	−	1.27574i	−0.103138	−	0.0595465i
$460$	−1.81223	+	3.43946i	−0.0844955	+	0.160366i
$461$	−11.1354	+	19.2872i	−0.518629	+	0.898292i	0.481136	+	0.876646i	$0.340224\pi$
$461$	−11.1354	+	19.2872i	−0.518629	+	0.898292i	−0.999766	+	0.0216466i	$0.993109\pi$
$462$	69.4081	−	1.34217i	3.22916	−	0.0624432i
$463$		−	36.3456i		−	1.68912i	−0.535457	−	0.844562i	$-0.679861\pi$
$463$		−	36.3456i		−	1.68912i	0.535457	−	0.844562i	$-0.320139\pi$
$464$	0.894790	+	11.5466i	0.0415396	+	0.536035i
$465$	6.49176	+	11.2441i	0.301048	+	0.521431i
$466$	−1.31039	+	2.37453i	−0.0607025	+	0.109998i
$467$		−	4.47887i		−	0.207258i	−0.994616	−	0.103629i	$-0.966955\pi$
$467$		−	4.47887i		−	0.207258i	0.994616	−	0.103629i	$-0.0330454\pi$
$468$	−53.2054	−	10.3006i	−2.45942	−	0.476146i
$469$			33.4133i			1.54288i
$470$	−4.70738	−	2.59777i	−0.217135	−	0.119826i
$471$	−3.67993	−	6.37383i	−0.169562	−	0.293691i
$472$	−0.878251	+	1.74799i	−0.0404248	+	0.0804577i
$473$			30.1037i			1.38417i
$474$	0.429846	+	22.2289i	0.0197435	+	1.02101i
$475$	3.52537	−	6.10612i	0.161755	−	0.280168i
$476$	1.34145	+	0.706800i	0.0614853	+	0.0323961i
$477$	44.1092	+	25.4664i	2.01962	+	1.16603i
$478$	1.60711	+	0.886884i	0.0735073	+	0.0405651i
$479$	25.4604	−	14.6996i	1.16332	−	0.671641i	0.211219	−	0.977439i	$-0.432257\pi$
$479$	25.4604	−	14.6996i	1.16332	−	0.671641i	0.952096	+	0.305798i	$0.0989232\pi$
$480$	−16.6972	−	7.59560i	−0.762118	−	0.346690i
$481$	−6.42665	−	21.2493i	−0.293030	−	0.968887i
$482$	−19.2879	+	11.6388i	−0.878538	+	0.530131i
$483$	−13.7116	−	23.7491i	−0.623898	−	1.08062i
$484$	2.21258	−	0.0856027i	0.100572	−	0.00389103i
$485$	−4.51069	−	2.60425i	−0.204820	−	0.118253i
$486$	−44.7128	+	26.9808i	−2.02822	+	1.22387i
$487$	−17.3765	−	10.0323i	−0.787404	−	0.454608i	0.0516439	−	0.998666i	$-0.483554\pi$
$487$	−17.3765	−	10.0323i	−0.787404	−	0.454608i	−0.839048	+	0.544058i	$0.816887\pi$
$488$	−10.3163	−	5.18328i	−0.466997	−	0.234636i
$489$		−	55.1637i		−	2.49459i
$490$	16.8648	−	0.326120i	0.761874	−	0.0147326i
$491$	4.61110	−	2.66222i	0.208096	−	0.120144i	−0.392330	−	0.919824i	$-0.628331\pi$
$491$	4.61110	−	2.66222i	0.208096	−	0.120144i	0.600426	+	0.799680i	$0.294998\pi$
$492$	−28.1929	+	1.09076i	−1.27103	+	0.0491751i
$493$			0.504535i			0.0227231i
$494$	11.0711	+	34.2048i	0.498112	+	1.53895i
$495$	−26.1496			−1.17534
$496$	−14.4471	−	6.91223i	−0.648696	−	0.310368i
$497$	14.3360	+	24.8306i	0.643056	+	1.11381i
$498$	0.955071	+	49.3901i	0.0427978	+	2.21322i
$499$	18.2983			0.819146			0.409573	−	0.912277i	$-0.365678\pi$
$499$	18.2983			0.819146			0.409573	+	0.912277i	$0.365678\pi$
$500$	1.06621	+	1.69210i	0.0476825	+	0.0756728i
$501$	19.7997	−	34.2940i	0.884583	−	1.53214i
$502$	−6.86992	+	4.14548i	−0.306620	+	0.185022i
$503$	21.0061	−	36.3836i	0.936615	−	1.62227i	0.164888	−	0.986312i	$-0.447274\pi$
$503$	21.0061	−	36.3836i	0.936615	−	1.62227i	0.771728	−	0.635953i	$-0.219393\pi$
$504$	77.2725	−	50.8038i	3.44199	−	2.26298i
$505$	−8.61732	+	4.97521i	−0.383466	+	0.221394i
$506$	−4.94189	−	8.18973i	−0.219694	−	0.364078i
$507$	−42.0697	+	2.68723i	−1.86838	+	0.119344i
$508$	2.44701	−	4.64423i	0.108568	−	0.206054i
$509$	2.11106	+	3.65646i	0.0935709	+	0.162070i	0.909011	−	0.416771i	$-0.136838\pi$
$509$	2.11106	+	3.65646i	0.0935709	+	0.162070i	−0.815440	+	0.578841i	$0.803505\pi$
$510$	−0.699673	−	0.386116i	−0.0309821	−	0.0170975i
$511$	12.5854	−	21.7986i	0.556745	−	0.964311i
$512$	22.2857	−	3.91765i	0.984898	−	0.173137i
$513$	89.4045	+	51.6177i	3.94730	+	2.27898i
$514$	15.1899	−	0.293731i	0.669996	−	0.0129559i
$515$	−4.46886			−0.196922
$516$	29.9125	+	47.4716i	1.31683	+	2.08982i
$517$	11.4563	−	6.61429i	0.503847	−	0.290896i
$518$	33.1674	+	18.3035i	1.45729	+	0.804210i
$519$	24.4014			1.07110
$520$	−10.0477	−	1.74442i	−0.440622	−	0.0764981i
$521$	40.6898			1.78265			0.891326	−	0.453363i	$-0.149776\pi$
$521$	40.6898			1.78265			0.891326	+	0.453363i	$0.149776\pi$
$522$	26.9416	+	14.8678i	1.17920	+	0.650744i
$523$	−9.14346	+	5.27898i	−0.399816	+	0.230834i	−0.686404	−	0.727220i	$-0.740812\pi$
$523$	−9.14346	+	5.27898i	−0.399816	+	0.230834i	0.286589	+	0.958054i	$0.407479\pi$
$524$	19.9357	−	12.5618i	0.870895	−	0.548764i
$525$	−14.1077			−0.615710
$526$	0.344469	−	0.00666109i	0.0150195	−	0.000290437i
$527$	−0.604244	−	0.348860i	−0.0263213	−	0.0151966i
$528$	37.2256	−	25.5187i	1.62004	−	1.11056i
$529$	9.61074	−	16.6463i	0.417858	−	0.723752i
$530$	8.39151	+	4.63087i	0.364504	+	0.201152i
$531$	2.59888	+	4.50140i	0.112782	+	0.195344i
$532$	−54.2764	−	28.5978i	−2.35318	−	1.23987i
$533$	−15.0138	+	4.54076i	−0.650318	+	0.196682i
$534$	19.2301	+	31.8683i	0.832169	+	1.37908i
$535$	8.53297	−	4.92651i	0.368913	−	0.212992i
$536$	11.9338	+	18.1513i	0.515462	+	0.784017i
$537$	−16.4964	+	28.5725i	−0.711870	+	1.23300i
$538$	16.2631	−	9.81357i	0.701153	−	0.423093i
$539$	−20.7509	+	35.9417i	−0.893806	+	1.54812i
$540$	−24.7753	+	15.6113i	−1.06616	+	0.671802i
$541$	2.55153			0.109699			0.0548495	−	0.998495i	$-0.482532\pi$
$541$	2.55153			0.109699			0.0548495	+	0.998495i	$0.482532\pi$
$542$	−0.253238	−	13.0958i	−0.0108775	−	0.562514i
$543$	36.5049	+	63.2284i	1.56658	+	2.71339i
$544$	0.981163	−	0.0951501i	0.0420670	−	0.00407953i
$545$	−9.16126			−0.392425
$546$	48.1946	−	53.4040i	2.06254	−	2.28548i
$547$			12.6446i			0.540645i	0.962770	+	0.270323i	$0.0871304\pi$
$547$			12.6446i			0.540645i	−0.962770	+	0.270323i	$0.912870\pi$
$548$	0.632400	+	16.3457i	0.0270148	+	0.698254i
$549$	−26.5664	+	15.3381i	−1.13383	+	0.654615i
$550$	−4.91988	+	0.0951372i	−0.209784	+	0.00405666i
$551$		−	20.4140i		−	0.869665i
$552$	−15.9308	−	8.00419i	−0.678059	−	0.340681i
$553$	−18.2663	−	10.5460i	−0.776761	−	0.448463i
$554$	−10.9380	+	6.60027i	−0.464712	+	0.280419i
$555$	−17.2910	−	9.98297i	−0.733963	−	0.423754i
$556$	1.58351	+	40.9292i	0.0671560	+	1.73579i
$557$	−12.2626	−	21.2394i	−0.519583	−	0.899944i	−0.999741	−	0.0227621i	$-0.992754\pi$
$557$	−12.2626	−	21.2394i	−0.519583	−	0.899944i	0.480158	−	0.877182i	$-0.340579\pi$
$558$	−36.4347	+	21.9856i	−1.54240	+	0.930725i
$559$	22.7496	+	21.3428i	0.962207	+	0.902706i
$560$	14.3535	−	9.83954i	0.606546	−	0.415796i
$561$	1.70279	−	0.983104i	0.0718917	−	0.0415067i
$562$	−32.8488	−	18.1277i	−1.38564	−	0.764669i
$563$	−36.7348	−	21.2089i	−1.54819	−	0.893847i	−0.998280	−	0.0586214i	$-0.981330\pi$
$563$	−36.7348	−	21.2089i	−1.54819	−	0.893847i	−0.549908	−	0.835225i	$-0.685337\pi$
$564$	11.4936	−	21.8139i	0.483966	−	0.918530i
$565$	4.01133	−	6.94783i	0.168758	−	0.292297i
$566$	−0.251049	−	12.9826i	−0.0105524	−	0.545700i
$567$		−	108.475i		−	4.55551i
$568$	16.6562	+	8.36869i	0.698880	+	0.351142i
$569$	−0.0235241	−	0.0407450i	−0.000986182	−	0.00170812i	0.865532	−	0.500854i	$-0.166981\pi$
$569$	−0.0235241	−	0.0407450i	−0.000986182	−	0.00170812i	−0.866518	+	0.499146i	$0.833647\pi$
$570$	28.3094	+	15.6226i	1.18575	+	0.654360i
$571$			22.2621i			0.931641i	0.884879	+	0.465821i	$0.154241\pi$
$571$			22.2621i			0.931641i	−0.884879	+	0.465821i	$0.845759\pi$
$572$	16.4471	−	18.9490i	0.687688	−	0.792296i
$573$			33.1904i			1.38655i
$574$	12.9324	−	23.4345i	0.539787	−	0.978138i
$575$	0.971921	+	1.68342i	0.0405319	+	0.0702033i
$576$	23.8323	−	55.1969i	0.993011	−	2.29987i
$577$		−	42.4031i		−	1.76527i	−0.470063	−	0.882633i	$-0.655769\pi$
$577$		−	42.4031i		−	1.76527i	0.470063	−	0.882633i	$-0.344231\pi$
$578$	−23.9942	+	0.463983i	−0.998027	+	0.0192992i
$579$	−24.8200	+	42.9896i	−1.03149	+	1.78659i
$580$	5.12298	+	2.69926i	0.212720	+	0.112081i
$581$	−40.5856	−	23.4321i	−1.68378	−	0.972128i
$582$	11.5407	−	20.9126i	0.478376	−	0.866856i
$583$	−20.4223	+	11.7908i	−0.845806	+	0.488326i
$584$	−0.948671	−	16.3367i	−0.0392563	−	0.676019i
$585$	−18.5395	+	19.7615i	−0.766514	+	0.817038i
$586$	14.3126	+	23.7190i	0.591248	+	0.979821i
$587$	−14.6618	−	25.3949i	−0.605155	−	1.04816i	−0.992027	−	0.126026i	$-0.959778\pi$
$587$	−14.6618	−	25.3949i	−0.605155	−	1.04816i	0.386871	−	0.922134i	$-0.373556\pi$
$588$	2.99055	+	77.2970i	0.123328	+	3.18768i
$589$	24.4483	+	14.1152i	1.00737	+	0.581607i
$590$	0.505340	+	0.837454i	0.0208045	+	0.0344774i
$591$	−24.4679	−	14.1266i	−1.00648	−	0.581089i
$592$	24.5550	−	1.90287i	1.00920	−	0.0782074i
$593$			33.7161i			1.38456i	0.721631	+	0.692278i	$0.243393\pi$
$593$			33.7161i			1.38456i	−0.721631	+	0.692278i	$0.756607\pi$
$594$	−1.39298	−	72.0357i	−0.0571545	−	2.95566i
$595$	0.656562	−	0.379066i	0.0269164	−	0.0155402i
$596$	−38.7545	+	1.49938i	−1.58745	+	0.0614168i
$597$		−	37.2609i		−	1.52499i
$598$	−9.69276	−	2.07171i	−0.396366	−	0.0847187i
$599$	−42.5949			−1.74038			−0.870190	−	0.492717i	$-0.836004\pi$
$599$	−42.5949			−1.74038			−0.870190	+	0.492717i	$0.836004\pi$
$600$	−7.66381	+	5.03867i	−0.312874	+	0.205703i
$601$	0.772803	+	1.33853i	0.0315233	+	0.0545999i	0.881357	−	0.472452i	$-0.156631\pi$
$601$	0.772803	+	1.33853i	0.0315233	+	0.0545999i	−0.849833	+	0.527051i	$0.823297\pi$
$602$	−53.2205	+	1.02914i	−2.16910	+	0.0419446i
$603$	57.7188			2.35049
$604$	−34.0590	+	21.4610i	−1.38584	+	0.873237i
$605$	0.553559	−	0.958792i	0.0225054	−	0.0389804i
$606$	−23.5756	−	39.0697i	−0.957694	−	1.58710i
$607$	−7.08488	+	12.2714i	−0.287566	+	0.498079i	−0.973228	−	0.229841i	$-0.926179\pi$
$607$	−7.08488	+	12.2714i	−0.287566	+	0.498079i	0.685662	+	0.727920i	$0.259513\pi$
$608$	−39.6988	+	3.84986i	−1.61000	+	0.156133i
$609$	−35.3736	+	20.4230i	−1.43341	+	0.827580i
$610$	−4.94249	+	2.98242i	−0.200116	+	0.120755i
$611$	3.12378	−	13.3470i	0.126375	−	0.539963i
$612$	1.22094	−	2.31725i	0.0493536	−	0.0936694i
$613$	−5.97094	−	10.3420i	−0.241164	−	0.417709i	0.719882	−	0.694096i	$-0.244196\pi$
$613$	−5.97094	−	10.3420i	−0.241164	−	0.417709i	−0.961046	+	0.276388i	$0.910863\pi$
$614$	3.00785	−	5.45047i	0.121387	−	0.219963i
$615$	−7.05349	+	12.2170i	−0.284424	+	0.492637i
$616$	2.48217	+	42.7445i	0.100009	+	1.72223i
$617$	−4.56663	−	2.63655i	−0.183846	−	0.106143i	0.405253	−	0.914205i	$-0.367184\pi$
$617$	−4.56663	−	2.63655i	−0.183846	−	0.106143i	−0.589098	+	0.808061i	$0.700517\pi$
$618$	−0.396220	−	20.4900i	−0.0159383	−	0.824227i
$619$	−10.0988			−0.405904			−0.202952	−	0.979189i	$-0.565054\pi$
$619$	−10.0988			−0.405904			−0.202952	+	0.979189i	$0.565054\pi$
$620$	−6.77497	+	4.26901i	−0.272089	+	0.171447i
$621$	−24.6482	+	14.2306i	−0.989098	+	0.571056i
$622$	−12.5246	+	22.6956i	−0.502191	+	0.910011i
$623$	−35.3107			−1.41469
$624$	7.10741	−	46.2240i	0.284524	−	1.85044i
$625$	1.00000			0.0400000
$626$	−3.72240	+	6.74530i	−0.148777	+	0.269596i
$627$	−68.8963	+	39.7773i	−2.75146	+	1.58855i
$628$	3.84047	−	2.41994i	0.153252	−	0.0965660i
$629$	1.07295			0.0427812
$630$	−0.893964	−	46.2300i	−0.0356164	−	1.84185i
$631$	33.0021	+	19.0538i	1.31379	+	0.758518i	0.982722	−	0.185088i	$-0.0592569\pi$
$631$	33.0021	+	19.0538i	1.31379	+	0.758518i	0.331070	+	0.943606i	$0.392590\pi$
$632$	−13.6895	+	0.794947i	−0.544539	+	0.0316213i
$633$	5.56539	−	9.63954i	0.221205	−	0.383137i
$634$	−6.93475	+	12.5663i	−0.275414	+	0.499072i
$635$	−1.31236	−	2.27308i	−0.0520795	−	0.0902043i
$636$	−20.4888	+	38.8861i	−0.812432	+	1.54193i
$637$	12.4495	+	41.1636i	0.493268	+	1.63096i
$638$	−12.1984	+	7.36079i	−0.482938	+	0.291416i
$639$	42.8929	−	24.7643i	1.69682	−	0.979659i
$640$	4.28307	−	10.4716i	0.169303	−	0.413928i
$641$	−10.0031	+	17.3259i	−0.395100	+	0.684334i	−0.993114	−	0.117152i	$-0.962624\pi$
$641$	−10.0031	+	17.3259i	−0.395100	+	0.684334i	0.598014	+	0.801486i	$0.295957\pi$
$642$	23.3449	+	38.6873i	0.921348	+	1.52687i
$643$	−2.97322	+	5.14977i	−0.117252	+	0.203087i	−0.918678	−	0.395008i	$-0.870742\pi$
$643$	−2.97322	+	5.14977i	−0.117252	+	0.203087i	0.801426	+	0.598095i	$0.204075\pi$
$644$	14.3097	−	9.01677i	0.563883	−	0.355311i
$645$	28.0549			1.10466
$646$	−1.73727	+	0.0335942i	−0.0683521	+	0.00132174i
$647$	4.06180	+	7.03525i	0.159686	+	0.276584i	0.934755	−	0.355292i	$-0.115619\pi$
$647$	4.06180	+	7.03525i	0.159686	+	0.276584i	−0.775070	+	0.631876i	$0.782285\pi$
$648$	−38.7425	−	58.9273i	−1.52195	−	2.31488i
$649$	−2.40654			−0.0944649
$650$	−3.41619	+	3.78545i	−0.133994	+	0.148478i
$651$		−	56.4857i		−	2.21385i
$652$	33.9976	−	1.31534i	1.33145	−	0.0515126i
$653$	−9.19313	+	5.30766i	−0.359755	+	0.207705i	−0.668973	−	0.743286i	$-0.733266\pi$
$653$	−9.19313	+	5.30766i	−0.359755	+	0.207705i	0.309218	+	0.950991i	$0.399933\pi$
$654$	−0.812261	−	42.0048i	−0.0317619	−	1.64252i
$655$		−	11.7817i		−	0.460348i
$656$	−1.34447	−	17.3494i	−0.0524929	−	0.677379i
$657$	−37.6553	−	21.7403i	−1.46907	−	0.848170i
$658$	12.0851	+	20.0275i	0.471126	+	0.780754i
$659$	−24.8204	−	14.3301i	−0.966866	−	0.558220i	−0.0685868	−	0.997645i	$-0.521849\pi$
$659$	−24.8204	−	14.3301i	−0.966866	−	0.558220i	−0.898279	+	0.439425i	$0.855182\pi$
$660$	−0.872417	−	22.5494i	−0.0339588	−	0.877736i
$661$	18.3673	+	31.8131i	0.714404	+	1.23738i	0.963189	+	0.268826i	$0.0866356\pi$
$661$	18.3673	+	31.8131i	0.714404	+	1.23738i	−0.248785	+	0.968559i	$0.580031\pi$
$662$	−6.08472	−	10.0837i	−0.236489	−	0.391912i
$663$	0.464298	−	1.98381i	0.0180318	−	0.0770449i
$664$	−30.4165	+	1.76628i	−1.18039	+	0.0685451i
$665$	−26.5651	+	15.3374i	−1.03015	+	0.594758i
$666$	31.6179	−	57.2942i	1.22517	−	2.22010i
$667$	4.87398	+	2.81400i	0.188721	+	0.108958i
$668$	21.6076	+	11.3849i	0.836025	+	0.440495i
$669$	40.0520	−	69.3721i	1.54850	−	2.68208i
$670$	10.8594	−	0.209992i	0.419536	−	0.00811270i
$671$		−	14.2029i		−	0.548298i
$672$	46.3874	+	64.9391i	1.78943	+	2.50508i
$673$	19.3088	+	33.4439i	0.744300	+	1.28917i	0.950521	+	0.310661i	$0.100550\pi$
$673$	19.3088	+	33.4439i	0.744300	+	1.28917i	−0.206221	+	0.978506i	$0.566116\pi$
$674$	0.252261	−	0.457117i	0.00971673	−	0.0176075i
$675$			14.6418i			0.563562i
$676$	−2.65927	−	25.8636i	−0.102280	−	0.994756i
$677$		−	45.0730i		−	1.73230i	−0.499786	−	0.866149i	$-0.666588\pi$
$677$		−	45.0730i		−	1.73230i	0.499786	−	0.866149i	$-0.333412\pi$
$678$	32.2118	+	17.7761i	1.23709	+	0.682689i
$679$	11.3299	+	19.6240i	0.434804	+	0.753102i
$680$	0.221282	−	0.440418i	0.00848577	−	0.0168893i
$681$		−	70.2449i		−	2.69179i
$682$	−0.380919	−	19.6987i	−0.0145861	−	0.754301i
$683$	16.7294	−	28.9762i	0.640133	−	1.10874i	−0.345270	−	0.938503i	$-0.612213\pi$
$683$	16.7294	−	28.9762i	0.640133	−	1.10874i	0.985403	−	0.170239i	$-0.0544540\pi$
$684$	−49.4005	+	93.7582i	−1.88887	+	3.58494i
$685$	7.08319	+	4.08948i	0.270635	+	0.156251i
$686$	−26.5432	−	14.6479i	−1.01343	−	0.559261i
$687$	27.6640	−	15.9718i	1.05545	−	0.609364i
$688$	−28.5437	+	19.5671i	−1.08822	+	0.745990i
$689$	−5.56854	+	23.7928i	−0.212144	+	0.906433i
$690$	−7.63237	+	4.60556i	−0.290559	+	0.175331i
$691$	19.4451	+	33.6799i	0.739727	+	1.28124i	0.952618	+	0.304169i	$0.0983787\pi$
$691$	19.4451	+	33.6799i	0.739727	+	1.28124i	−0.212891	+	0.977076i	$0.568288\pi$
$692$	0.581833	+	15.0387i	0.0221180	+	0.571685i
$693$	98.5239	+	56.8828i	3.74261	+	2.16080i
$694$	−38.7496	+	23.3824i	−1.47091	+	0.887585i
$695$	17.7361	+	10.2400i	0.672770	+	0.388424i
$696$	−11.9220	+	23.7284i	−0.451902	+	0.899424i
$697$		−	0.758094i		−	0.0287148i
$698$	−31.2824	+	0.604916i	−1.18405	+	0.0228964i
$699$	−5.38557	+	3.10936i	−0.203701	+	0.117607i
$700$	−0.336387	−	8.69463i	−0.0127142	−	0.328626i
$701$		−	2.82374i		−	0.106651i	−0.998577	−	0.0533256i	$-0.983018\pi$
$701$		−	2.82374i		−	0.106651i	0.998577	−	0.0533256i	$-0.0169821\pi$
$702$	−55.4257	−	50.0191i	−2.09191	−	1.88785i
$703$	−43.4125			−1.63733
$704$	16.6149	+	22.3338i	0.626198	+	0.841738i
$705$	−6.16415	−	10.6766i	−0.232155	−	0.402105i
$706$	0.219076	+	11.3292i	0.00824504	+	0.426380i
$707$	43.2900			1.62809
$708$	−3.79496	+	2.39126i	−0.142623	+	0.0898690i
$709$	11.1522	−	19.3162i	0.418830	−	0.725434i	−0.576992	−	0.816749i	$-0.695774\pi$
$709$	11.1522	−	19.3162i	0.418830	−	0.725434i	0.995822	+	0.0913154i	$0.0291071\pi$
$710$	7.97993	−	4.81529i	0.299482	−	0.180715i
$711$	−18.2175	+	31.5536i	−0.683208	+	1.18335i
$712$	−19.1820	+	12.6115i	−0.718877	+	0.472635i
$713$	−6.74022	+	3.89147i	−0.252423	+	0.145737i
$714$	1.79625	+	2.97676i	0.0672229	+	0.111402i
$715$	−3.63183	−	12.0084i	−0.135823	−	0.449090i
$716$	−18.0027	−	9.48548i	−0.672793	−	0.354489i
$717$	2.10445	+	3.64501i	0.0785921	+	0.136125i
$718$	22.5665	+	12.4534i	0.842174	+	0.464755i
$719$	8.58578	−	14.8710i	0.320196	−	0.554595i	−0.660333	−	0.750973i	$-0.729585\pi$
$719$	8.58578	−	14.8710i	0.320196	−	0.554595i	0.980528	+	0.196378i	$0.0629180\pi$
$720$	−16.9970	−	24.7945i	−0.633442	−	0.924038i
$721$	16.8373	+	9.72104i	0.627055	+	0.362031i
$722$	43.4266	−	0.839754i	1.61617	−	0.0312524i
$723$	−51.6542			−1.92104
$724$	−38.0975	+	24.0058i	−1.41588	+	0.892167i
$725$	2.50740	−	1.44765i	0.0931224	−	0.0537642i
$726$	4.44519	+	2.45309i	0.164976	+	0.0910426i
$727$	−33.5503			−1.24431			−0.622156	−	0.782894i	$-0.713743\pi$
$727$	−33.5503			−1.24431			−0.622156	+	0.782894i	$0.713743\pi$
$728$	34.0623	+	28.4292i	1.26243	+	1.05365i
$729$	−44.9437			−1.66458
$730$	−7.16370	−	3.95330i	−0.265140	−	0.146318i
$731$	−1.30565	+	0.753820i	−0.0482914	+	0.0278810i
$732$	−14.1128	−	22.3972i	−0.521623	−	0.827823i
$733$	34.1152			1.26007			0.630037	−	0.776565i	$-0.283040\pi$
$733$	34.1152			1.26007			0.630037	+	0.776565i	$0.283040\pi$
$734$	23.4873	−	0.454181i	0.866932	−	0.0167641i
$735$	33.4956	+	19.3387i	1.23551	+	0.713319i
$736$	4.55316	−	10.0091i	0.167832	−	0.368939i
$737$	−13.3618	+	23.1432i	−0.492187	+	0.852492i
$738$	−40.4813	−	22.3397i	−1.49014	−	0.822335i
$739$	−11.0468	−	19.1336i	−0.406362	−	0.703840i	0.588117	−	0.808776i	$-0.299870\pi$
$739$	−11.0468	−	19.1336i	−0.406362	−	0.703840i	−0.994479	+	0.104936i	$0.966536\pi$
$740$	5.74026	−	10.8946i	0.211016	−	0.400492i
$741$	−18.7859	+	80.2669i	−0.690118	+	2.94868i
$742$	−21.5433	−	35.7017i	−0.790878	−	1.31065i
$743$	17.5782	−	10.1488i	0.644881	−	0.372322i	−0.141611	−	0.989922i	$-0.545228\pi$
$743$	17.5782	−	10.1488i	0.644881	−	0.372322i	0.786492	+	0.617600i	$0.211895\pi$
$744$	−20.1743	−	30.6851i	−0.739625	−	1.12497i
$745$	−9.69588	+	16.7937i	−0.355229	+	0.615275i
$746$	23.6802	−	14.2892i	0.866992	−	0.523164i
$747$	−40.4772	+	70.1085i	−1.48098	+	2.56514i
$748$	0.646493	+	1.02599i	0.0236381	+	0.0375140i
$749$	−42.8663			−1.56630
$750$	0.0886625	+	4.58505i	0.00323750	+	0.167422i
$751$	1.69292	+	2.93223i	0.0617756	+	0.106999i	0.895259	−	0.445546i	$-0.146990\pi$
$751$	1.69292	+	2.93223i	0.0617756	+	0.106999i	−0.833484	+	0.552544i	$0.813657\pi$
$752$	13.7180	+	6.56339i	0.500245	+	0.239342i
$753$	−18.3981			−0.670465
$754$	−3.08576	+	14.4371i	−0.112377	+	0.525767i
$755$			20.1283i			0.732543i
$756$	127.305	−	4.92531i	4.63003	−	0.179132i
$757$	−14.7103	+	8.49301i	−0.534656	+	0.308684i	−0.742910	−	0.669391i	$-0.766555\pi$
$757$	−14.7103	+	8.49301i	−0.534656	+	0.308684i	0.208254	+	0.978075i	$0.433222\pi$
$758$	−50.2595	+	0.971883i	−1.82551	+	0.0353004i
$759$		−	21.9327i		−	0.796105i
$760$	−8.95327	+	17.8197i	−0.324769	+	0.646390i
$761$	−19.4843	−	11.2493i	−0.706307	−	0.407787i	0.103385	−	0.994641i	$-0.467033\pi$
$761$	−19.4843	−	11.2493i	−0.706307	−	0.407787i	−0.809692	+	0.586855i	$0.800366\pi$
$762$	10.3058	−	6.21878i	0.373340	−	0.225283i
$763$	34.5169	+	19.9284i	1.24960	+	0.721455i
$764$	−20.4554	+	0.791400i	−0.740050	+	0.0286319i
$765$	−0.654807	−	1.13416i	−0.0236746	−	0.0410056i
$766$	11.8178	−	7.13113i	0.426993	−	0.257658i
$767$	−1.70618	+	1.81864i	−0.0616067	+	0.0656675i
$768$	48.3927	+	18.7096i	1.74622	+	0.675126i
$769$	−17.2432	+	9.95537i

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)

\(f(q)\)	\(=\)	\(q+(-0.683296 + 1.23819i) q^{2} +(-2.80828 + 1.62136i) q^{3} +(-1.06621 - 1.69210i) q^{4} -1.00000 q^{5} +(-0.0886625 - 4.58505i) q^{6} +(3.76770 + 2.17528i) q^{7} +(2.82367 - 0.163970i) q^{8} +(3.75763 - 6.50841i) q^{9} +O(q^{10})\)	\(q+(-0.683296 + 1.23819i) q^{2} +(-2.80828 + 1.62136i) q^{3} +(-1.06621 - 1.69210i) q^{4} -1.00000 q^{5} +(-0.0886625 - 4.58505i) q^{6} +(3.76770 + 2.17528i) q^{7} +(2.82367 - 0.163970i) q^{8} +(3.75763 - 6.50841i) q^{9} +(0.683296 - 1.23819i) q^{10} +(1.73976 + 3.01336i) q^{11} +(5.73773 + 3.02316i) q^{12} +(3.51068 + 0.821651i) q^{13} +(-5.26786 + 3.17876i) q^{14} +(2.80828 - 1.62136i) q^{15} +(-1.72638 + 3.60827i) q^{16} +(-0.0871303 + 0.150914i) q^{17} +(5.49106 + 9.09982i) q^{18} +(3.52537 - 6.10612i) q^{19} +(1.06621 + 1.69210i) q^{20} -14.1077 q^{21} +(-4.91988 + 0.0951372i) q^{22} +(0.971921 + 1.68342i) q^{23} +(-7.66381 + 5.03867i) q^{24} +1.00000 q^{25} +(-3.41619 + 3.78545i) q^{26} +14.6418i q^{27} +(-0.336387 - 8.69463i) q^{28} +(2.50740 - 1.44765i) q^{29} +(0.0886625 + 4.58505i) q^{30} +4.00389i q^{31} +(-3.28809 - 4.60309i) q^{32} +(-9.77150 - 5.64158i) q^{33} +(-0.127324 - 0.211002i) q^{34} +(-3.76770 - 2.17528i) q^{35} +(-15.0193 + 0.581083i) q^{36} +(-3.07858 - 5.33225i) q^{37} +(5.15165 + 8.53736i) q^{38} +(-11.1912 + 3.38466i) q^{39} +(-2.82367 + 0.163970i) q^{40} +(-3.76751 + 2.17517i) q^{41} +(9.63973 - 17.4680i) q^{42} +(7.49255 + 4.32582i) q^{43} +(3.24393 - 6.15673i) q^{44} +(-3.75763 + 6.50841i) q^{45} +(-2.74849 + 0.0531485i) q^{46} -3.80183i q^{47} +(-1.00216 - 12.9321i) q^{48} +(5.96372 + 10.3295i) q^{49} +(-0.683296 + 1.23819i) q^{50} -0.565079i q^{51} +(-2.35283 - 6.81647i) q^{52} +6.77726i q^{53} +(-18.1292 - 10.0047i) q^{54} +(-1.73976 - 3.01336i) q^{55} +(10.9954 + 5.52449i) q^{56} +22.8636i q^{57} +(0.0791630 + 4.09380i) q^{58} +(-0.345814 + 0.598967i) q^{59} +(-5.73773 - 3.02316i) q^{60} +(-3.53499 - 2.04093i) q^{61} +(-4.95757 - 2.73584i) q^{62} +(28.3153 - 16.3478i) q^{63} +(7.94623 - 0.925995i) q^{64} +(-3.51068 - 0.821651i) q^{65} +(13.6622 - 8.24408i) q^{66} +(3.84011 + 6.65126i) q^{67} +(0.348260 - 0.0134739i) q^{68} +(-5.45886 - 3.15167i) q^{69} +(5.26786 - 3.17876i) q^{70} +(5.70744 + 3.29519i) q^{71} +(9.54313 - 18.9937i) q^{72} -5.78564i q^{73} +(8.70590 - 0.168349i) q^{74} +(-2.80828 + 1.62136i) q^{75} +(-14.0909 + 0.545166i) q^{76} +15.1379i q^{77} +(3.45604 - 16.1695i) q^{78} -4.84812 q^{79} +(1.72638 - 3.60827i) q^{80} +(-12.4667 - 21.5930i) q^{81} +(-0.118947 - 6.15117i) q^{82} -10.7720 q^{83} +(15.0418 + 23.8716i) q^{84} +(0.0871303 - 0.150914i) q^{85} +(-10.4758 + 6.32136i) q^{86} +(-4.69432 + 8.13080i) q^{87} +(5.40662 + 8.22347i) q^{88} +(-7.02896 + 4.05817i) q^{89} +(-5.49106 - 9.09982i) q^{90} +(11.4399 + 10.7325i) q^{91} +(1.81223 - 3.43946i) q^{92} +(-6.49176 - 11.2441i) q^{93} +(4.70738 + 2.59777i) q^{94} +(-3.52537 + 6.10612i) q^{95} +(16.6972 + 7.59560i) q^{96} +(4.51069 + 2.60425i) q^{97} +(-16.8648 + 0.326120i) q^{98} +26.1496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9}+O(q^{10}) \) 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9	\( 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30} + 16 q^{34} - 21 q^{36} - 4 q^{37} - 24 q^{39} + 29 q^{42} - 24 q^{44} - 28 q^{45} - 11 q^{46} + 3 q^{48} + 20 q^{49} + 18 q^{52} - 49 q^{54} - 8 q^{55} + 61 q^{56} - 47 q^{58} + 16 q^{59} - 6 q^{60} - 2 q^{62} - 30 q^{64} + 14 q^{66} + 36 q^{67} + 33 q^{68} + 4 q^{70} - 51 q^{72} - 2 q^{74} - 48 q^{76} - 35 q^{78} + 10 q^{80} - 28 q^{81} - 21 q^{82} - 40 q^{83} - 61 q^{84} + 28 q^{86} - 36 q^{87} + 41 q^{88} + 18 q^{90} - 16 q^{91} - 18 q^{92} - 41 q^{94} - 16 q^{95} + 48 q^{96} + 24 q^{97} + 28 q^{98} + 48 q^{99}+O(q^{100}) \) 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * q^98 + 48 * q^99

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