LMFDB - Embedded newform 425.2.k.a.86.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(86,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("425.86");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	425.86
Dual form			425.2.k.a.341.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.11803 - 1.53884i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.50000 - 4.61653i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(0.809017 + 2.48990i) q^{6} +2.38197 q^{7} +(-2.30902 - 7.10642i) q^{8} +(1.61803 + 1.17557i) q^{9} -5.85410 q^{10} +(1.00000 - 0.726543i) q^{11} +(3.92705 + 2.85317i) q^{12} +(-3.92705 - 2.85317i) q^{13} +(5.04508 - 3.66547i) q^{14} +(1.80902 - 1.31433i) q^{15} +(-7.97214 - 5.79210i) q^{16} +(0.309017 + 0.951057i) q^{17} +5.23607 q^{18} +(-0.572949 - 1.76336i) q^{19} +(-8.78115 + 6.37988i) q^{20} +(-0.736068 + 2.26538i) q^{21} +(1.00000 - 3.07768i) q^{22} +(1.80902 - 1.31433i) q^{23} +7.47214 q^{24} +(1.54508 + 4.75528i) q^{25} -12.7082 q^{26} +(-4.04508 + 2.93893i) q^{27} +(3.57295 - 10.9964i) q^{28} +(-2.66312 + 8.19624i) q^{29} +(1.80902 - 5.56758i) q^{30} +(1.78115 + 5.48183i) q^{31} -10.8541 q^{32} +(0.381966 + 1.17557i) q^{33} +(2.11803 + 1.53884i) q^{34} +(-4.30902 - 3.13068i) q^{35} +(7.85410 - 5.70634i) q^{36} +(6.42705 + 4.66953i) q^{37} +(-3.92705 - 2.85317i) q^{38} +(3.92705 - 2.85317i) q^{39} +(-5.16312 + 15.8904i) q^{40} +(5.23607 + 3.80423i) q^{41} +(1.92705 + 5.93085i) q^{42} -0.145898 q^{43} +(-1.85410 - 5.70634i) q^{44} +(-1.38197 - 4.25325i) q^{45} +(1.80902 - 5.56758i) q^{46} +(0.118034 - 0.363271i) q^{47} +(7.97214 - 5.79210i) q^{48} -1.32624 q^{49} +(10.5902 + 7.69421i) q^{50} -1.00000 q^{51} +(-19.0623 + 13.8496i) q^{52} +(2.54508 - 7.83297i) q^{53} +(-4.04508 + 12.4495i) q^{54} -2.76393 q^{55} +(-5.50000 - 16.9273i) q^{56} +1.85410 q^{57} +(6.97214 + 21.4580i) q^{58} +(-7.59017 - 5.51458i) q^{59} +(-3.35410 - 10.3229i) q^{60} +(4.04508 - 2.93893i) q^{61} +(12.2082 + 8.86978i) q^{62} +(3.85410 + 2.80017i) q^{63} +(-7.04508 + 5.11855i) q^{64} +(3.35410 + 10.3229i) q^{65} +(2.61803 + 1.90211i) q^{66} +(3.52786 + 10.8576i) q^{67} +4.85410 q^{68} +(0.690983 + 2.12663i) q^{69} -13.9443 q^{70} +(0.354102 - 1.08981i) q^{71} +(4.61803 - 14.2128i) q^{72} +(-7.28115 + 5.29007i) q^{73} +20.7984 q^{74} -5.00000 q^{75} -9.00000 q^{76} +(2.38197 - 1.73060i) q^{77} +(3.92705 - 12.0862i) q^{78} +(-2.80902 + 8.64527i) q^{79} +(6.80902 + 20.9560i) q^{80} +(0.309017 + 0.951057i) q^{81} +16.9443 q^{82} +(-3.69098 - 11.3597i) q^{83} +(9.35410 + 6.79615i) q^{84} +(0.690983 - 2.12663i) q^{85} +(-0.309017 + 0.224514i) q^{86} +(-6.97214 - 5.06555i) q^{87} +(-7.47214 - 5.42882i) q^{88} +(2.61803 - 1.90211i) q^{89} +(-9.47214 - 6.88191i) q^{90} +(-9.35410 - 6.79615i) q^{91} +(-3.35410 - 10.3229i) q^{92} -5.76393 q^{93} +(-0.309017 - 0.951057i) q^{94} +(-1.28115 + 3.94298i) q^{95} +(3.35410 - 10.3229i) q^{96} +(4.59017 - 14.1271i) q^{97} +(-2.80902 + 2.04087i) q^{98} +2.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + q^{3} + 6 q^{4} - 5 q^{5} + q^{6} + 14 q^{7} - 7 q^{8} + 2 q^{9} - 10 q^{10} + 4 q^{11} + 9 q^{12} - 9 q^{13} + 9 q^{14} + 5 q^{15} - 14 q^{16} - q^{17} + 12 q^{18} - 9 q^{19} - 15 q^{20}+ \cdots - 8 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + q^3 + 6 * q^4 - 5 * q^5 + q^6 + 14 * q^7 - 7 * q^8 + 2 * q^9 - 10 * q^10 + 4 * q^11 + 9 * q^12 - 9 * q^13 + 9 * q^14 + 5 * q^15 - 14 * q^16 - q^17 + 12 * q^18 - 9 * q^19 - 15 * q^20 + 6 * q^21 + 4 * q^22 + 5 * q^23 + 12 * q^24 - 5 * q^25 - 24 * q^26 - 5 * q^27 + 21 * q^28 + 5 * q^29 + 5 * q^30 - 13 * q^31 - 30 * q^32 + 6 * q^33 + 4 * q^34 - 15 * q^35 + 18 * q^36 + 19 * q^37 - 9 * q^38 + 9 * q^39 - 5 * q^40 + 12 * q^41 + q^42 - 14 * q^43 + 6 * q^44 - 10 * q^45 + 5 * q^46 - 4 * q^47 + 14 * q^48 + 26 * q^49 + 20 * q^50 - 4 * q^51 - 36 * q^52 - q^53 - 5 * q^54 - 20 * q^55 - 22 * q^56 - 6 * q^57 + 10 * q^58 - 8 * q^59 + 5 * q^61 + 22 * q^62 + 2 * q^63 - 17 * q^64 + 6 * q^66 + 32 * q^67 + 6 * q^68 + 5 * q^69 - 20 * q^70 - 12 * q^71 + 14 * q^72 - 9 * q^73 + 34 * q^74 - 20 * q^75 - 36 * q^76 + 14 * q^77 + 9 * q^78 - 9 * q^79 + 25 * q^80 - q^81 + 32 * q^82 - 17 * q^83 + 24 * q^84 + 5 * q^85 + q^86 - 10 * q^87 - 12 * q^88 + 6 * q^89 - 20 * q^90 - 24 * q^91 - 32 * q^93 + q^94 + 15 * q^95 - 4 * q^97 - 9 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	2.11803	−	1.53884i	1.49768	−	1.08813i	0.526381	−	0.850249i	$-0.323549\pi$
$2$	2.11803	−	1.53884i	1.49768	−	1.08813i	0.971295	−	0.237877i	$-0.0764514\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i	−0.999773	−	0.0213149i	$-0.993215\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i	0.821362	+	0.570408i	$0.193215\pi$
$4$	1.50000	−	4.61653i	0.750000	−	2.30826i
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$6$	0.809017	+	2.48990i	0.330280	+	1.01650i
$7$	2.38197			0.900299			0.450149	−	0.892953i	$-0.351371\pi$
$7$	2.38197			0.900299			0.450149	+	0.892953i	$0.351371\pi$
$8$	−2.30902	−	7.10642i	−0.816361	−	2.51250i
$9$	1.61803	+	1.17557i	0.539345	+	0.391857i
$10$	−5.85410			−1.85123
$11$	1.00000	−	0.726543i	0.301511	−	0.219061i	−0.426734	−	0.904377i	$-0.640336\pi$
$11$	1.00000	−	0.726543i	0.301511	−	0.219061i	0.728246	+	0.685316i	$0.240336\pi$
$12$	3.92705	+	2.85317i	1.13364	+	0.823639i
$13$	−3.92705	−	2.85317i	−1.08917	−	0.791327i	−0.109909	−	0.993942i	$-0.535056\pi$
$13$	−3.92705	−	2.85317i	−1.08917	−	0.791327i	−0.979259	+	0.202615i	$0.935056\pi$
$14$	5.04508	−	3.66547i	1.34836	−	0.979638i
$15$	1.80902	−	1.31433i	0.467086	−	0.339358i
$16$	−7.97214	−	5.79210i	−1.99303	−	1.44802i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	5.23607			1.23415
$19$	−0.572949	−	1.76336i	−0.131444	−	0.404542i	0.863576	−	0.504218i	$-0.168219\pi$
$19$	−0.572949	−	1.76336i	−0.131444	−	0.404542i	−0.995020	+	0.0996765i	$0.968219\pi$
$20$	−8.78115	+	6.37988i	−1.96353	+	1.42658i
$21$	−0.736068	+	2.26538i	−0.160623	+	0.494347i
$22$	1.00000	−	3.07768i	0.213201	−	0.656164i
$23$	1.80902	−	1.31433i	0.377206	−	0.274056i	−0.382987	−	0.923754i	$-0.625104\pi$
$23$	1.80902	−	1.31433i	0.377206	−	0.274056i	0.760193	+	0.649698i	$0.225104\pi$
$24$	7.47214			1.52524
$25$	1.54508	+	4.75528i	0.309017	+	0.951057i
$26$	−12.7082			−2.49228
$27$	−4.04508	+	2.93893i	−0.778477	+	0.565597i
$28$	3.57295	−	10.9964i	0.675224	−	2.07813i
$29$	−2.66312	+	8.19624i	−0.494529	+	1.52200i	0.323161	+	0.946344i	$0.395254\pi$
$29$	−2.66312	+	8.19624i	−0.494529	+	1.52200i	−0.817690	+	0.575659i	$0.804746\pi$
$30$	1.80902	−	5.56758i	0.330280	−	1.01650i
$31$	1.78115	+	5.48183i	0.319905	+	0.984565i	0.973688	+	0.227884i	$0.0731805\pi$
$31$	1.78115	+	5.48183i	0.319905	+	0.984565i	−0.653784	+	0.756681i	$0.726819\pi$
$32$	−10.8541			−1.91875
$33$	0.381966	+	1.17557i	0.0664917	+	0.204641i
$34$	2.11803	+	1.53884i	0.363240	+	0.263909i
$35$	−4.30902	−	3.13068i	−0.728357	−	0.529182i
$36$	7.85410	−	5.70634i	1.30902	−	0.951057i
$37$	6.42705	+	4.66953i	1.05660	+	0.767665i	0.973456	−	0.228872i	$-0.0735038\pi$
$37$	6.42705	+	4.66953i	1.05660	+	0.767665i	0.0831442	+	0.996538i	$0.473504\pi$
$38$	−3.92705	−	2.85317i	−0.637052	−	0.462845i
$39$	3.92705	−	2.85317i	0.628831	−	0.456873i
$40$	−5.16312	+	15.8904i	−0.816361	+	2.51250i
$41$	5.23607	+	3.80423i	0.817736	+	0.594120i	0.916063	−	0.401034i	$-0.131349\pi$
$41$	5.23607	+	3.80423i	0.817736	+	0.594120i	−0.0983268	+	0.995154i	$0.531349\pi$
$42$	1.92705	+	5.93085i	0.297350	+	0.915150i
$43$	−0.145898			−0.0222492			−0.0111246	−	0.999938i	$-0.503541\pi$
$43$	−0.145898			−0.0222492			−0.0111246	+	0.999938i	$0.503541\pi$
$44$	−1.85410	−	5.70634i	−0.279516	−	0.860263i
$45$	−1.38197	−	4.25325i	−0.206011	−	0.634038i
$46$	1.80902	−	5.56758i	0.266725	−	0.820895i
$47$	0.118034	−	0.363271i	0.0172170	−	0.0529886i	−0.942079	−	0.335391i	$-0.891131\pi$
$47$	0.118034	−	0.363271i	0.0172170	−	0.0529886i	0.959296	+	0.282403i	$0.0911315\pi$
$48$	7.97214	−	5.79210i	1.15068	−	0.836017i
$49$	−1.32624			−0.189463
$50$	10.5902	+	7.69421i	1.49768	+	1.08813i
$51$	−1.00000			−0.140028
$52$	−19.0623	+	13.8496i	−2.64347	+	1.92059i
$53$	2.54508	−	7.83297i	0.349594	−	1.07594i	−0.609484	−	0.792799i	$-0.708623\pi$
$53$	2.54508	−	7.83297i	0.349594	−	1.07594i	0.959078	−	0.283142i	$-0.0913768\pi$
$54$	−4.04508	+	12.4495i	−0.550466	+	1.69416i
$55$	−2.76393			−0.372689
$56$	−5.50000	−	16.9273i	−0.734968	−	2.26200i
$57$	1.85410			0.245582
$58$	6.97214	+	21.4580i	0.915486	+	2.81758i
$59$	−7.59017	−	5.51458i	−0.988156	−	0.717937i	−0.0286395	−	0.999590i	$-0.509117\pi$
$59$	−7.59017	−	5.51458i	−0.988156	−	0.717937i	−0.959516	+	0.281652i	$0.909117\pi$
$60$	−3.35410	−	10.3229i	−0.433013	−	1.33268i
$61$	4.04508	−	2.93893i	0.517920	−	0.376291i	−0.297900	−	0.954597i	$-0.596286\pi$
$61$	4.04508	−	2.93893i	0.517920	−	0.376291i	0.815820	+	0.578306i	$0.196286\pi$
$62$	12.2082	+	8.86978i	1.55044	+	1.12646i
$63$	3.85410	+	2.80017i	0.485571	+	0.352788i
$64$	−7.04508	+	5.11855i	−0.880636	+	0.639819i
$65$	3.35410	+	10.3229i	0.416025	+	1.28039i
$66$	2.61803	+	1.90211i	0.322258	+	0.234134i
$67$	3.52786	+	10.8576i	0.430997	+	1.32647i	0.897133	+	0.441760i	$0.145646\pi$
$67$	3.52786	+	10.8576i	0.430997	+	1.32647i	−0.466136	+	0.884713i	$0.654354\pi$
$68$	4.85410			0.588646
$69$	0.690983	+	2.12663i	0.0831846	+	0.256016i
$70$	−13.9443			−1.66666
$71$	0.354102	−	1.08981i	0.0420242	−	0.129337i	−0.927843	−	0.372970i	$-0.878339\pi$
$71$	0.354102	−	1.08981i	0.0420242	−	0.129337i	0.969867	+	0.243633i	$0.0783393\pi$
$72$	4.61803	−	14.2128i	0.544241	−	1.67500i
$73$	−7.28115	+	5.29007i	−0.852194	+	0.619156i	−0.925750	−	0.378136i	$-0.876565\pi$
$73$	−7.28115	+	5.29007i	−0.852194	+	0.619156i	0.0735557	+	0.997291i	$0.476565\pi$
$74$	20.7984			2.41776
$75$	−5.00000			−0.577350
$76$	−9.00000			−1.03237
$77$	2.38197	−	1.73060i	0.271450	−	0.197220i
$78$	3.92705	−	12.0862i	0.444651	−	1.36849i
$79$	−2.80902	+	8.64527i	−0.316039	+	0.972668i	0.659286	+	0.751893i	$0.270859\pi$
$79$	−2.80902	+	8.64527i	−0.316039	+	0.972668i	−0.975325	+	0.220776i	$0.929141\pi$
$80$	6.80902	+	20.9560i	0.761271	+	2.34295i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	16.9443			1.87118
$83$	−3.69098	−	11.3597i	−0.405138	−	1.24689i	−0.920780	−	0.390082i	$-0.872447\pi$
$83$	−3.69098	−	11.3597i	−0.405138	−	1.24689i	0.515642	−	0.856804i	$-0.327553\pi$
$84$	9.35410	+	6.79615i	1.02062	+	0.741521i
$85$	0.690983	−	2.12663i	0.0749476	−	0.230665i
$86$	−0.309017	+	0.224514i	−0.0333222	+	0.0242100i
$87$	−6.97214	−	5.06555i	−0.747491	−	0.543084i
$88$	−7.47214	−	5.42882i	−0.796532	−	0.578715i
$89$	2.61803	−	1.90211i	0.277511	−	0.201624i	−0.440320	−	0.897841i	$-0.645135\pi$
$89$	2.61803	−	1.90211i	0.277511	−	0.201624i	0.717831	+	0.696217i	$0.245135\pi$
$90$	−9.47214	−	6.88191i	−0.998451	−	0.725417i
$91$	−9.35410	−	6.79615i	−0.980576	−	0.712430i
$92$	−3.35410	−	10.3229i	−0.349689	−	1.07623i
$93$	−5.76393			−0.597692
$94$	−0.309017	−	0.951057i	−0.0318727	−	0.0980940i
$95$	−1.28115	+	3.94298i	−0.131444	+	0.404542i
$96$	3.35410	−	10.3229i	0.342327	−	1.05357i
$97$	4.59017	−	14.1271i	0.466061	−	1.43439i	−0.391582	−	0.920143i	$-0.628072\pi$
$97$	4.59017	−	14.1271i	0.466061	−	1.43439i	0.857643	−	0.514245i	$-0.171928\pi$
$98$	−2.80902	+	2.04087i	−0.283754	+	0.206159i
$99$	2.47214			0.248459
$100$	24.2705			2.42705
$101$	−12.2361			−1.21753			−0.608767	−	0.793349i	$-0.708336\pi$
$101$	−12.2361			−1.21753			−0.608767	+	0.793349i	$0.708336\pi$
$102$	−2.11803	+	1.53884i	−0.209717	+	0.152368i
$103$	−4.42705	+	13.6251i	−0.436210	+	1.34252i	0.455631	+	0.890169i	$0.349414\pi$
$103$	−4.42705	+	13.6251i	−0.436210	+	1.34252i	−0.891841	+	0.452348i	$0.850586\pi$
$104$	−11.2082	+	34.4953i	−1.09905	+	3.38254i
$105$	4.30902	−	3.13068i	0.420517	−	0.305523i
$106$	−6.66312	−	20.5070i	−0.647179	−	1.99181i
$107$	−17.9443			−1.73474			−0.867369	−	0.497665i	$-0.834191\pi$
$107$	−17.9443			−1.73474			−0.867369	+	0.497665i	$0.834191\pi$
$108$	7.50000	+	23.0826i	0.721688	+	2.22113i
$109$	−6.23607	−	4.53077i	−0.597307	−	0.433969i	0.247615	−	0.968859i	$-0.420353\pi$
$109$	−6.23607	−	4.53077i	−0.597307	−	0.433969i	−0.844922	+	0.534890i	$0.820353\pi$
$110$	−5.85410	+	4.25325i	−0.558167	+	0.405532i
$111$	−6.42705	+	4.66953i	−0.610029	+	0.443212i
$112$	−18.9894	−	13.7966i	−1.79433	−	1.30365i
$113$	−6.73607	−	4.89404i	−0.633676	−	0.460393i	0.223996	−	0.974590i	$-0.428090\pi$
$113$	−6.73607	−	4.89404i	−0.633676	−	0.460393i	−0.857672	+	0.514198i	$0.828090\pi$
$114$	3.92705	−	2.85317i	0.367802	−	0.267224i
$115$	−5.00000			−0.466252
$116$	33.8435	+	24.5887i	3.14229	+	2.28300i
$117$	−3.00000	−	9.23305i	−0.277350	−	0.853596i
$118$	−24.5623			−2.26114
$119$	0.736068	+	2.26538i	0.0674752	+	0.207667i
$120$	−13.5172	−	9.82084i	−1.23395	−	0.896516i
$121$	−2.92705	+	9.00854i	−0.266096	+	0.818958i
$122$	4.04508	−	12.4495i	0.366225	−	1.12712i
$123$	−5.23607	+	3.80423i	−0.472120	+	0.343016i
$124$	27.9787			2.51256
$125$	3.45492	−	10.6331i	0.309017	−	0.951057i
$126$	12.4721			1.11111
$127$	15.7082	−	11.4127i	1.39388	−	1.01271i	0.398450	−	0.917190i	$-0.369548\pi$
$127$	15.7082	−	11.4127i	1.39388	−	1.01271i	0.995427	−	0.0955215i	$-0.0304519\pi$
$128$	−0.336881	+	1.03681i	−0.0297764	+	0.0916422i
$129$	0.0450850	−	0.138757i	0.00396951	−	0.0122169i
$130$	22.9894	+	16.7027i	2.01630	+	1.46493i
$131$	1.44427	+	4.44501i	0.126187	+	0.388362i	0.994115	−	0.108326i	$-0.0345491\pi$
$131$	1.44427	+	4.44501i	0.126187	+	0.388362i	−0.867929	+	0.496689i	$0.834549\pi$
$132$	6.00000			0.522233
$133$	−1.36475	−	4.20025i	−0.118338	−	0.364208i
$134$	24.1803	+	17.5680i	2.08886	+	1.51765i
$135$	11.1803			0.962250
$136$	6.04508	−	4.39201i	0.518362	−	0.376612i
$137$	−18.1353	−	13.1760i	−1.54940	−	1.12570i	−0.944077	−	0.329724i	$-0.893044\pi$
$137$	−18.1353	−	13.1760i	−1.54940	−	1.12570i	−0.605322	−	0.795981i	$-0.706956\pi$
$138$	4.73607	+	3.44095i	0.403161	+	0.292914i
$139$	0.190983	−	0.138757i	0.0161990	−	0.0117692i	−0.579656	−	0.814861i	$-0.696813\pi$
$139$	0.190983	−	0.138757i	0.0161990	−	0.0117692i	0.595855	+	0.803092i	$0.296813\pi$
$140$	−20.9164	+	15.1967i	−1.76776	+	1.28435i
$141$	0.309017	+	0.224514i	0.0260239	+	0.0189075i
$142$	−0.927051	−	2.85317i	−0.0777964	−	0.239433i
$143$	−6.00000			−0.501745
$144$	−6.09017	−	18.7436i	−0.507514	−	1.56197i
$145$	15.5902	−	11.3269i	1.29469	−	0.940650i
$146$	−7.28115	+	22.4091i	−0.602593	+	1.85459i
$147$	0.409830	−	1.26133i	0.0338022	−	0.104033i
$148$	31.1976	−	22.6664i	2.56442	−	1.86316i
$149$	7.18034			0.588236			0.294118	−	0.955769i	$-0.404974\pi$
$149$	7.18034			0.588236			0.294118	+	0.955769i	$0.404974\pi$
$150$	−10.5902	+	7.69421i	−0.864684	+	0.628230i
$151$	17.8541			1.45295			0.726473	−	0.687195i	$-0.241158\pi$
$151$	17.8541			1.45295			0.726473	+	0.687195i	$0.241158\pi$
$152$	−11.2082	+	8.14324i	−0.909105	+	0.660504i
$153$	−0.618034	+	1.90211i	−0.0499651	+	0.153777i
$154$	2.38197	−	7.33094i	0.191944	−	0.590744i
$155$	3.98278	−	12.2577i	0.319905	−	0.984565i
$156$	−7.28115	−	22.4091i	−0.582959	−	1.79416i
$157$	21.0000			1.67598			0.837991	−	0.545684i	$-0.183730\pi$
$157$	21.0000			1.67598			0.837991	+	0.545684i	$0.183730\pi$
$158$	7.35410	+	22.6336i	0.585061	+	1.80063i
$159$	6.66312	+	4.84104i	0.528420	+	0.383919i
$160$	19.6353	+	14.2658i	1.55230	+	1.12781i
$161$	4.30902	−	3.13068i	0.339598	−	0.246732i
$162$	2.11803	+	1.53884i	0.166408	+	0.120903i
$163$	−15.8992	−	11.5514i	−1.24532	−	0.904778i	−0.247380	−	0.968919i	$-0.579569\pi$
$163$	−15.8992	−	11.5514i	−1.24532	−	0.904778i	−0.997941	+	0.0641404i	$0.979569\pi$
$164$	25.4164	−	18.4661i	1.98469	−	1.44196i
$165$	0.854102	−	2.62866i	0.0664917	−	0.204641i
$166$	−25.2984	−	18.3803i	−1.96353	−	1.42659i
$167$	−2.75329	−	8.47375i	−0.213056	−	0.655719i	−0.999286	−	0.0377847i	$-0.987970\pi$
$167$	−2.75329	−	8.47375i	−0.213056	−	0.655719i	0.786230	−	0.617934i	$-0.212030\pi$
$168$	17.7984			1.37317
$169$	3.26393	+	10.0453i	0.251072	+	0.772719i
$170$	−1.80902	−	5.56758i	−0.138745	−	0.427014i
$171$	1.14590	−	3.52671i	0.0876290	−	0.269694i
$172$	−0.218847	+	0.673542i	−0.0166869	+	0.0513571i
$173$	1.42705	−	1.03681i	0.108497	−	0.0788275i	−0.532214	−	0.846610i	$-0.678640\pi$
$173$	1.42705	−	1.03681i	0.108497	−	0.0788275i	0.640711	+	0.767782i	$0.278640\pi$
$174$	−22.5623			−1.71044
$175$	3.68034	+	11.3269i	0.278208	+	0.856235i
$176$	−12.1803			−0.918128
$177$	7.59017	−	5.51458i	0.570512	−	0.414501i
$178$	2.61803	−	8.05748i	0.196230	−	0.603934i
$179$	−6.72542	+	20.6987i	−0.502682	+	1.54710i	0.301951	+	0.953323i	$0.402362\pi$
$179$	−6.72542	+	20.6987i	−0.502682	+	1.54710i	−0.804633	+	0.593772i	$0.797638\pi$
$180$	−21.7082			−1.61803
$181$	6.61803	+	20.3682i	0.491915	+	1.51396i	0.821710	+	0.569905i	$0.193020\pi$
$181$	6.61803	+	20.3682i	0.491915	+	1.51396i	−0.329796	+	0.944052i	$0.606980\pi$
$182$	−30.2705			−2.24380
$183$	1.54508	+	4.75528i	0.114216	+	0.351521i
$184$	−13.5172	−	9.82084i	−0.996503	−	0.724002i
$185$	−5.48936	−	16.8945i	−0.403586	−	1.24211i
$186$	−12.2082	+	8.86978i	−0.895149	+	0.650364i
$187$	1.00000	+	0.726543i	0.0731272	+	0.0531301i
$188$	−1.50000	−	1.08981i	−0.109399	−	0.0794828i
$189$	−9.63525	+	7.00042i	−0.700862	+	0.509206i
$190$	3.35410	+	10.3229i	0.243332	+	0.748899i
$191$	−8.61803	−	6.26137i	−0.623579	−	0.453057i	0.230591	−	0.973051i	$-0.425934\pi$
$191$	−8.61803	−	6.26137i	−0.623579	−	0.453057i	−0.854170	+	0.519994i	$0.825934\pi$
$192$	−2.69098	−	8.28199i	−0.194205	−	0.597701i
$193$	5.05573			0.363919			0.181960	−	0.983306i	$-0.441756\pi$
$193$	5.05573			0.363919			0.181960	+	0.983306i	$0.441756\pi$
$194$	−12.0172	−	36.9852i	−0.862786	−	2.65538i
$195$	−10.8541			−0.777278
$196$	−1.98936	+	6.12261i	−0.142097	+	0.437329i
$197$	6.23607	−	19.1926i	0.444301	−	1.36742i	−0.438947	−	0.898513i	$-0.644648\pi$
$197$	6.23607	−	19.1926i	0.444301	−	1.36742i	0.883248	−	0.468906i	$-0.155352\pi$
$198$	5.23607	−	3.80423i	0.372111	−	0.270355i
$199$	−5.32624			−0.377567			−0.188783	−	0.982019i	$-0.560454\pi$
$199$	−5.32624			−0.377567			−0.188783	+	0.982019i	$0.560454\pi$
$200$	30.2254	−	21.9601i	2.13726	−	1.55281i
$201$	−11.4164			−0.805251
$202$	−25.9164	+	18.8294i	−1.82347	+	1.32483i
$203$	−6.34346	+	19.5232i	−0.445224	+	1.37026i
$204$	−1.50000	+	4.61653i	−0.105021	+	0.323221i
$205$	−4.47214	−	13.7638i	−0.312348	−	0.961307i
$206$	11.5902	+	35.6709i	0.807525	+	2.48531i
$207$	4.47214			0.310835
$208$	14.7812	+	45.4917i	1.02489	+	3.15428i
$209$	−1.85410	−	1.34708i	−0.128251	−	0.0931797i
$210$	4.30902	−	13.2618i	0.297350	−	0.915150i
$211$	−0.954915	+	0.693786i	−0.0657391	+	0.0477622i	−0.620169	−	0.784468i	$-0.712936\pi$
$211$	−0.954915	+	0.693786i	−0.0657391	+	0.0477622i	0.554430	+	0.832230i	$0.312936\pi$
$212$	−32.3435	−	23.4989i	−2.22136	−	1.61391i
$213$	0.927051	+	0.673542i	0.0635205	+	0.0461503i
$214$	−38.0066	+	27.6134i	−2.59808	+	1.88761i
$215$	0.263932	+	0.191758i	0.0180000	+	0.0130778i
$216$	30.2254	+	21.9601i	2.05658	+	1.49419i
$217$	4.24265	+	13.0575i	0.288010	+	0.886402i
$218$	−20.1803			−1.36679
$219$	−2.78115	−	8.55951i	−0.187933	−	0.578398i
$220$	−4.14590	+	12.7598i	−0.279516	+	0.860263i
$221$	1.50000	−	4.61653i	0.100901	−	0.310541i
$222$	−6.42705	+	19.7804i	−0.431355	+	1.32758i
$223$	3.00000	−	2.17963i	0.200895	−	0.145959i	−0.482790	−	0.875736i	$-0.660376\pi$
$223$	3.00000	−	2.17963i	0.200895	−	0.145959i	0.683685	+	0.729778i	$0.260376\pi$
$224$	−25.8541			−1.72745
$225$	−3.09017	+	9.51057i	−0.206011	+	0.634038i
$226$	−21.7984			−1.45001
$227$	−10.8541	+	7.88597i	−0.720412	+	0.523410i	−0.886516	−	0.462698i	$-0.846881\pi$
$227$	−10.8541	+	7.88597i	−0.720412	+	0.523410i	0.166104	+	0.986108i	$0.446881\pi$
$228$	2.78115	−	8.55951i	0.184186	−	0.566867i
$229$	1.85410	−	5.70634i	0.122523	−	0.377086i	−0.870919	−	0.491426i	$-0.836476\pi$
$229$	1.85410	−	5.70634i	0.122523	−	0.377086i	0.993442	+	0.114341i	$0.0364756\pi$
$230$	−10.5902	+	7.69421i	−0.698295	+	0.507341i
$231$	0.909830	+	2.80017i	0.0598624	+	0.184238i
$232$	64.3951			4.22775
$233$	−4.38197	−	13.4863i	−0.287072	−	0.883517i	−0.985770	−	0.168100i	$-0.946237\pi$
$233$	−4.38197	−	13.4863i	−0.287072	−	0.883517i	0.698698	−	0.715417i	$-0.253763\pi$
$234$	−20.5623	−	14.9394i	−1.34420	−	0.976618i
$235$	−0.690983	+	0.502029i	−0.0450748	+	0.0327487i
$236$	−36.8435	+	26.7683i	−2.39830	+	1.74247i
$237$	−7.35410	−	5.34307i	−0.477700	−	0.347070i
$238$	5.04508	+	3.66547i	0.327024	+	0.237597i
$239$	6.04508	−	4.39201i	0.391024	−	0.284096i	−0.374851	−	0.927085i	$-0.622306\pi$
$239$	6.04508	−	4.39201i	0.391024	−	0.284096i	0.765875	+	0.642989i	$0.222306\pi$
$240$	−22.0344			−1.42232
$241$	−7.42705	−	5.39607i	−0.478418	−	0.347591i	0.322295	−	0.946639i	$-0.395546\pi$
$241$	−7.42705	−	5.39607i	−0.478418	−	0.347591i	−0.800713	+	0.599048i	$0.795546\pi$
$242$	7.66312	+	23.5847i	0.492604	+	1.51608i
$243$	−16.0000			−1.02640
$244$	−7.50000	−	23.0826i	−0.480138	−	1.47771i
$245$	2.39919	+	1.74311i	0.153278	+	0.111363i
$246$	−5.23607	+	16.1150i	−0.333840	+	1.02745i
$247$	−2.78115	+	8.55951i	−0.176961	+	0.544628i
$248$	34.8435	−	25.3153i	2.21256	−	1.60752i
$249$	11.9443			0.756937
$250$	−9.04508	−	27.8379i	−0.572061	−	1.76062i
$251$	7.65248			0.483020			0.241510	−	0.970398i	$-0.422357\pi$
$251$	7.65248			0.483020			0.241510	+	0.970398i	$0.422357\pi$
$252$	18.7082	−	13.5923i	1.17851	−	0.856235i
$253$	0.854102	−	2.62866i	0.0536969	−	0.165262i
$254$	15.7082	−	48.3449i	0.985620	−	3.03343i
$255$	1.80902	+	1.31433i	0.113285	+	0.0823064i
$256$	−4.50000	−	13.8496i	−0.281250	−	0.865598i
$257$	−1.85410			−0.115656			−0.0578279	−	0.998327i	$-0.518417\pi$
$257$	−1.85410			−0.115656			−0.0578279	+	0.998327i	$0.518417\pi$
$258$	−0.118034	−	0.363271i	−0.00734848	−	0.0226163i
$259$	15.3090	+	11.1227i	0.951256	+	0.691128i
$260$	52.6869			3.26750
$261$	−13.9443	+	10.1311i	−0.863129	+	0.627100i
$262$	9.89919	+	7.19218i	0.611574	+	0.444334i
$263$	−7.78115	−	5.65334i	−0.479806	−	0.348600i	0.321444	−	0.946928i	$-0.395832\pi$
$263$	−7.78115	−	5.65334i	−0.479806	−	0.348600i	−0.801251	+	0.598329i	$0.795832\pi$
$264$	7.47214	−	5.42882i	0.459878	−	0.334121i
$265$	−14.8992	+	10.8249i	−0.915250	+	0.664968i
$266$	−9.35410	−	6.79615i	−0.573537	−	0.416699i
$267$	1.00000	+	3.07768i	0.0611990	+	0.188351i
$268$	55.4164			3.38510
$269$	4.14590	+	12.7598i	0.252780	+	0.777976i	0.994259	+	0.107000i	$0.0341246\pi$
$269$	4.14590	+	12.7598i	0.252780	+	0.777976i	−0.741479	+	0.670976i	$0.765875\pi$
$270$	23.6803	−	17.2048i	1.44114	−	1.04705i
$271$	6.14590	−	18.9151i	0.373337	−	1.14901i	−0.571257	−	0.820771i	$-0.693544\pi$
$271$	6.14590	−	18.9151i	0.373337	−	1.14901i	0.944594	−	0.328241i	$-0.106456\pi$
$272$	3.04508	−	9.37181i	0.184635	−	0.568249i
$273$	9.35410	−	6.79615i	0.566136	−	0.411322i
$274$	−58.6869			−3.54541
$275$	5.00000	+	3.63271i	0.301511	+	0.219061i
$276$	10.8541			0.653340
$277$	17.9894	−	13.0700i	1.08088	−	0.785302i	0.103040	−	0.994677i	$-0.467143\pi$
$277$	17.9894	−	13.0700i	1.08088	−	0.785302i	0.977835	+	0.209375i	$0.0671429\pi$
$278$	0.190983	−	0.587785i	0.0114544	−	0.0352530i
$279$	−3.56231	+	10.9637i	−0.213270	+	0.656377i
$280$	−12.2984	+	37.8505i	−0.734968	+	2.26200i
$281$	3.57295	+	10.9964i	0.213144	+	0.655991i	0.999280	+	0.0379369i	$0.0120786\pi$
$281$	3.57295	+	10.9964i	0.213144	+	0.655991i	−0.786136	+	0.618054i	$0.787921\pi$
$282$	1.00000			0.0595491
$283$	4.35410	+	13.4005i	0.258824	+	0.796580i	0.993052	+	0.117676i	$0.0375445\pi$
$283$	4.35410	+	13.4005i	0.258824	+	0.796580i	−0.734228	+	0.678904i	$0.762455\pi$
$284$	−4.50000	−	3.26944i	−0.267026	−	0.194006i
$285$	−3.35410	−	2.43690i	−0.198680	−	0.144349i
$286$	−12.7082	+	9.23305i	−0.751452	+	0.545962i
$287$	12.4721	+	9.06154i	0.736207	+	0.534886i
$288$	−17.5623	−	12.7598i	−1.03487	−	0.751876i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	15.5902	−	47.9816i	0.915486	−	2.81758i
$291$	12.0172	+	8.73102i	0.704462	+	0.511822i
$292$	13.5000	+	41.5487i	0.790028	+	2.43146i
$293$	14.9443			0.873054			0.436527	−	0.899691i	$-0.356208\pi$
$293$	14.9443			0.873054			0.436527	+	0.899691i	$0.356208\pi$
$294$	−1.07295	−	3.30220i	−0.0625757	−	0.192588i
$295$	6.48278	+	19.9519i	0.377442	+	1.16165i
$296$	18.3435	−	56.4554i	1.06619	−	3.28140i
$297$	−1.90983	+	5.87785i	−0.110820	+	0.341068i
$298$	15.2082	−	11.0494i	0.880988	−	0.640075i
$299$	−10.8541			−0.627709
$300$	−7.50000	+	23.0826i	−0.433013	+	1.33268i
$301$	−0.347524			−0.0200310
$302$	37.8156	−	27.4746i	2.17604	−	1.58099i
$303$	3.78115	−	11.6372i	0.217222	−	0.668539i
$304$	−5.64590	+	17.3763i	−0.323814	+	0.996598i
$305$	−11.1803			−0.640184
$306$	1.61803	+	4.97980i	0.0924968	+	0.284676i
$307$	−18.9443			−1.08121			−0.540603	−	0.841278i	$-0.681804\pi$
$307$	−18.9443			−1.08121			−0.540603	+	0.841278i	$0.681804\pi$
$308$	−4.41641	−	13.5923i	−0.251648	−	0.774494i
$309$	−11.5902	−	8.42075i	−0.659342	−	0.479040i
$310$	−10.4271	−	32.0912i	−0.592217	−	1.82266i
$311$	−28.3435	+	20.5927i	−1.60721	+	1.16771i	−0.735731	+	0.677274i	$0.763161\pi$
$311$	−28.3435	+	20.5927i	−1.60721	+	1.16771i	−0.871479	+	0.490433i	$0.836839\pi$
$312$	−29.3435	−	21.3193i	−1.66125	−	1.20697i
$313$	10.8541	+	7.88597i	0.613510	+	0.445741i	0.850649	−	0.525735i	$-0.176210\pi$
$313$	10.8541	+	7.88597i	0.613510	+	0.445741i	−0.237138	+	0.971476i	$0.576210\pi$
$314$	44.4787	−	32.3157i	2.51008	−	1.82368i
$315$	−3.29180	−	10.1311i	−0.185472	−	0.570823i
$316$	35.6976	+	25.9358i	2.00814	+	1.45900i
$317$	−8.30902	−	25.5725i	−0.466681	−	1.43630i	−0.856856	−	0.515555i	$-0.827586\pi$
$317$	−8.30902	−	25.5725i	−0.466681	−	1.43630i	0.390175	−	0.920741i	$-0.372414\pi$
$318$	21.5623			1.20915
$319$	3.29180	+	10.1311i	0.184305	+	0.567233i
$320$	19.4721			1.08853
$321$	5.54508	−	17.0660i	0.309496	−	0.952532i
$322$	4.30902	−	13.2618i	0.240132	−	0.739051i
$323$	1.50000	−	1.08981i	0.0834622	−	0.0606389i
$324$	4.85410			0.269672
$325$	7.50000	−	23.0826i	0.416025	−	1.28039i
$326$	−51.4508			−2.84960
$327$	6.23607	−	4.53077i	0.344855	−	0.250552i
$328$	14.9443	−	45.9937i	0.825159	−	2.53958i
$329$	0.281153	−	0.865300i	0.0155005	−	0.0477055i
$330$	−2.23607	−	6.88191i	−0.123091	−	0.378837i
$331$	2.90983	+	8.95554i	0.159939	+	0.492241i	0.998628	−	0.0523698i	$-0.0166775\pi$
$331$	2.90983	+	8.95554i	0.159939	+	0.492241i	−0.838689	+	0.544611i	$0.816677\pi$
$332$	−57.9787			−3.18200
$333$	4.90983	+	15.1109i	0.269057	+	0.828072i
$334$	−18.8713	−	13.7108i	−1.03259	−	0.750223i
$335$	7.88854	−	24.2784i	0.430997	−	1.32647i
$336$	18.9894	−	13.7966i	1.03595	−	0.752665i
$337$	−1.07295	−	0.779543i	−0.0584473	−	0.0424644i	0.558178	−	0.829721i	$-0.311501\pi$
$337$	−1.07295	−	0.779543i	−0.0584473	−	0.0424644i	−0.616625	+	0.787257i	$0.711501\pi$
$338$	22.3713	+	16.2537i	1.21684	+	0.884086i
$339$	6.73607	−	4.89404i	0.365853	−	0.265808i
$340$	−8.78115	−	6.37988i	−0.476225	−	0.345998i
$341$	5.76393	+	4.18774i	0.312134	+	0.226779i
$342$	−3.00000	−	9.23305i	−0.162221	−	0.499266i
$343$	−19.8328			−1.07087
$344$	0.336881	+	1.03681i	0.0181634	+	0.0559012i
$345$	1.54508	−	4.75528i	0.0831846	−	0.256016i
$346$	1.42705	−	4.39201i	0.0767187	−	0.236116i
$347$	−6.19098	+	19.0539i	−0.332349	+	1.02287i	0.635664	+	0.771966i	$0.280727\pi$
$347$	−6.19098	+	19.0539i	−0.332349	+	1.02287i	−0.968013	+	0.250900i	$0.919273\pi$
$348$	−33.8435	+	24.5887i	−1.81420	+	1.31809i
$349$	−6.00000			−0.321173			−0.160586	−	0.987022i	$-0.551338\pi$
$349$	−6.00000			−0.321173			−0.160586	+	0.987022i	$0.551338\pi$
$350$	25.2254	+	18.3273i	1.34836	+	0.979638i
$351$	24.2705			1.29546
$352$	−10.8541	+	7.88597i	−0.578526	+	0.420323i
$353$	−6.79180	+	20.9030i	−0.361491	+	1.11255i	0.590659	+	0.806922i	$0.298868\pi$
$353$	−6.79180	+	20.9030i	−0.361491	+	1.11255i	−0.952149	+	0.305633i	$0.901132\pi$
$354$	7.59017	−	23.3601i	0.403413	−	1.24158i
$355$	−2.07295	+	1.50609i	−0.110021	+	0.0799347i
$356$	−4.85410	−	14.9394i	−0.257267	−	0.791786i
$357$	−2.38197			−0.126067
$358$	17.6074	+	54.1900i	0.930580	+	2.86403i
$359$	8.25329	+	5.99637i	0.435592	+	0.316476i	0.783881	−	0.620911i	$-0.213237\pi$
$359$	8.25329	+	5.99637i	0.435592	+	0.316476i	−0.348289	+	0.937387i	$0.613237\pi$
$360$	−27.0344	+	19.6417i	−1.42484	+	1.03521i
$361$	12.5902	−	9.14729i	0.662641	−	0.481437i
$362$	45.3607	+	32.9565i	2.38410	+	1.73215i
$363$	−7.66312	−	5.56758i	−0.402209	−	0.292222i
$364$	−45.4058	+	32.9892i	−2.37991	+	1.72910i
$365$	20.1246			1.05337
$366$	10.5902	+	7.69421i	0.553557	+	0.402183i
$367$	8.38854	+	25.8173i	0.437878	+	1.34765i	0.890108	+	0.455750i	$0.150629\pi$
$367$	8.38854	+	25.8173i	0.437878	+	1.34765i	−0.452230	+	0.891902i	$0.649371\pi$
$368$	−22.0344			−1.14862
$369$	4.00000	+	12.3107i	0.208232	+	0.640871i
$370$	−37.6246	−	27.3359i	−1.95601	−	1.42112i
$371$	6.06231	−	18.6579i	0.314739	−	0.968668i
$372$	−8.64590	+	26.6093i	−0.448269	+	1.37963i
$373$	−16.0623	+	11.6699i	−0.831675	+	0.604247i	−0.920033	−	0.391842i	$-0.871838\pi$
$373$	−16.0623	+	11.6699i	−0.831675	+	0.604247i	0.0883579	+	0.996089i	$0.471838\pi$
$374$	3.23607			0.167333
$375$	9.04508	+	6.57164i	0.467086	+	0.339358i
$376$	−2.85410			−0.147189
$377$	33.8435	−	24.5887i	1.74303	−	1.26638i
$378$	−9.63525	+	29.6543i	−0.495584	+	1.52525i
$379$	−3.98278	+	12.2577i	−0.204582	+	0.629637i	0.795149	+	0.606415i	$0.207393\pi$
$379$	−3.98278	+	12.2577i	−0.204582	+	0.629637i	−0.999730	+	0.0232230i	$0.992607\pi$
$380$	16.2812	+	11.8290i	0.835206	+	0.606812i
$381$	6.00000	+	18.4661i	0.307389	+	0.946047i
$382$	−27.8885			−1.42690
$383$	7.87132	+	24.2254i	0.402206	+	1.23786i	0.923206	+	0.384306i	$0.125559\pi$
$383$	7.87132	+	24.2254i	0.402206	+	1.23786i	−0.521000	+	0.853557i	$0.674441\pi$
$384$	−0.881966	−	0.640786i	−0.0450076	−	0.0327000i
$385$	−6.58359			−0.335531
$386$	10.7082	−	7.77997i	0.545033	−	0.395990i
$387$	−0.236068	−	0.171513i	−0.0120000	−	0.00871852i
$388$	−58.3328	−	42.3813i	−2.96140	−	2.15158i
$389$	17.2812	−	12.5555i	0.876189	−	0.636589i	−0.0560513	−	0.998428i	$-0.517851\pi$
$389$	17.2812	−	12.5555i	0.876189	−	0.636589i	0.932241	+	0.361839i	$0.117851\pi$
$390$	−22.9894	+	16.7027i	−1.16411	+	0.845776i
$391$	1.80902	+	1.31433i	0.0914859	+	0.0664684i
$392$	3.06231	+	9.42481i	0.154670	+	0.476025i
$393$	−4.67376			−0.235760
$394$	−16.3262	−	50.2470i	−0.822504	−	2.53141i
$395$	16.4443	−	11.9475i	0.827401	−	0.601142i
$396$	3.70820	−	11.4127i	0.186344	−	0.573509i
$397$	5.28115	−	16.2537i	0.265053	−	0.815751i	−0.726628	−	0.687032i	$-0.758913\pi$
$397$	5.28115	−	16.2537i	0.265053	−	0.815751i	0.991681	−	0.128719i	$-0.0410866\pi$
$398$	−11.2812	+	8.19624i	−0.565473	+	0.410840i
$399$	4.41641			0.221097
$400$	15.2254	−	46.8590i	0.761271	−	2.34295i
$401$	8.23607			0.411290			0.205645	−	0.978627i	$-0.434071\pi$
$401$	8.23607			0.411290			0.205645	+	0.978627i	$0.434071\pi$
$402$	−24.1803	+	17.5680i	−1.20601	+	0.876214i
$403$	8.64590	−	26.6093i	0.430683	−	1.32551i
$404$	−18.3541	+	56.4881i	−0.913151	+	2.81039i
$405$	0.690983	−	2.12663i	0.0343352	−	0.105673i
$406$	16.6074	+	51.1123i	0.824211	+	2.53666i
$407$	9.81966			0.486742
$408$	2.30902	+	7.10642i	0.114313	+	0.351820i
$409$	21.1353	+	15.3557i	1.04507	+	0.759289i	0.971269	−	0.237984i	$-0.0764867\pi$
$409$	21.1353	+	15.3557i	1.04507	+	0.759289i	0.0738021	+	0.997273i	$0.476487\pi$
$410$	−30.6525	−	22.2703i	−1.51382	−	1.09985i
$411$	18.1353	−	13.1760i	0.894546	−	0.649926i
$412$	56.2599	+	40.8752i	2.77172	+	2.01378i
$413$	−18.0795	−	13.1355i	−0.889635	−	0.646358i
$414$	9.47214	−	6.88191i	0.465530	−	0.338227i
$415$	−8.25329	+	25.4010i	−0.405138	+	1.24689i
$416$	42.6246	+	30.9686i	2.08984	+	1.51836i
$417$	0.0729490	+	0.224514i	0.00357233	+	0.0109945i
$418$	−6.00000			−0.293470
$419$	1.96149	+	6.03685i	0.0958252	+	0.294920i	0.987468	−	0.157820i	$-0.0504466\pi$
$419$	1.96149	+	6.03685i	0.0958252	+	0.294920i	−0.891643	+	0.452740i	$0.850447\pi$
$420$	−7.98936	−	24.5887i	−0.389841	−	1.19981i
$421$	2.23607	−	6.88191i	0.108979	−	0.335404i	−0.881664	−	0.471877i	$-0.843577\pi$
$421$	2.23607	−	6.88191i	0.108979	−	0.335404i	0.990644	+	0.136473i	$0.0435767\pi$
$422$	−0.954915	+	2.93893i	−0.0464845	+	0.143065i
$423$	0.618034	−	0.449028i	0.0300498	−	0.0218325i
$424$	−61.5410			−2.98870
$425$	−4.04508	+	2.93893i	−0.196215	+	0.142559i
$426$	3.00000			0.145350
$427$	9.63525	−	7.00042i	0.466283	−	0.338774i
$428$	−26.9164	+	82.8402i	−1.30105	+	4.00423i
$429$	1.85410	−	5.70634i	0.0895169	−	0.275505i
$430$	0.854102			0.0411885
$431$	4.12868	+	12.7068i	0.198871	+	0.612063i	0.999910	+	0.0134499i	$0.00428136\pi$
$431$	4.12868	+	12.7068i	0.198871	+	0.612063i	−0.801038	+	0.598613i	$0.795719\pi$
$432$	49.2705			2.37053
$433$	−3.57295	−	10.9964i	−0.171705	−	0.528454i	0.827763	−	0.561078i	$-0.189613\pi$
$433$	−3.57295	−	10.9964i	−0.171705	−	0.528454i	−0.999468	+	0.0326248i	$0.989613\pi$
$434$	29.0795	+	21.1275i	1.39586	+	1.01415i
$435$	5.95492	+	18.3273i	0.285516	+	0.878729i
$436$	−30.2705	+	21.9928i	−1.44969	+	1.05326i
$437$	−3.35410	−	2.43690i	−0.160448	−	0.116573i
$438$	−19.0623	−	13.8496i	−0.910832	−	0.661758i
$439$	−5.92705	+	4.30625i	−0.282883	+	0.205526i	−0.720174	−	0.693794i	$-0.755938\pi$
$439$	−5.92705	+	4.30625i	−0.282883	+	0.205526i	0.437291	+	0.899320i	$0.355938\pi$
$440$	6.38197	+	19.6417i	0.304248	+	0.936380i
$441$	−2.14590	−	1.55909i	−0.102186	−	0.0742422i
$442$	−3.92705	−	12.0862i	−0.186791	−	0.574883i
$443$	−3.47214			−0.164966			−0.0824831	−	0.996592i	$-0.526285\pi$
$443$	−3.47214			−0.164966			−0.0824831	+	0.996592i	$0.526285\pi$
$444$	11.9164	+	36.6749i	0.565528	+	1.74052i
$445$	−7.23607			−0.343023
$446$	3.00000	−	9.23305i	0.142054	−	0.437198i
$447$	−2.21885	+	6.82891i	−0.104948	+	0.322996i
$448$	−16.7812	+	12.1922i	−0.792835	+	0.576028i
$449$	−10.9098			−0.514867			−0.257433	−	0.966296i	$-0.582877\pi$
$449$	−10.9098			−0.514867			−0.257433	+	0.966296i	$0.582877\pi$
$450$	8.09017	+	24.8990i	0.381374	+	1.17375i
$451$	8.00000			0.376705
$452$	−32.6976	+	23.7562i	−1.53796	+	1.11740i
$453$	−5.51722	+	16.9803i	−0.259222	+	0.797802i
$454$	−10.8541	+	33.4055i	−0.509408	+	1.56780i
$455$	7.98936	+	24.5887i	0.374547	+	1.15274i
$456$	−4.28115	−	13.1760i	−0.200483	−	0.617024i
$457$	−28.8328			−1.34874			−0.674371	−	0.738393i	$-0.735585\pi$
$457$	−28.8328			−1.34874			−0.674371	+	0.738393i	$0.735585\pi$
$458$	−4.85410	−	14.9394i	−0.226817	−	0.698072i
$459$	−4.04508	−	2.93893i	−0.188808	−	0.137177i
$460$	−7.50000	+	23.0826i	−0.349689	+	1.07623i
$461$	10.8992	−	7.91872i	0.507626	−	0.368812i	−0.304296	−	0.952577i	$-0.598421\pi$
$461$	10.8992	−	7.91872i	0.507626	−	0.368812i	0.811922	+	0.583766i	$0.198421\pi$
$462$	6.23607	+	4.53077i	0.290128	+	0.210790i
$463$	−21.5172	−	15.6332i	−0.999990	−	0.726535i	−0.0379040	−	0.999281i	$-0.512068\pi$
$463$	−21.5172	−	15.6332i	−0.999990	−	0.726535i	−0.962086	+	0.272746i	$0.912068\pi$
$464$	68.7041	−	49.9165i	3.18951	−	2.31731i
$465$	10.4271	+	7.57570i	0.483543	+	0.351314i
$466$	−30.0344	−	21.8213i	−1.39132	−	1.01085i
$467$	−1.88197	−	5.79210i	−0.0870870	−	0.268026i	0.898024	−	0.439947i	$-0.145003\pi$
$467$	−1.88197	−	5.79210i	−0.0870870	−	0.268026i	−0.985111	+	0.171921i	$0.945003\pi$
$468$	−47.1246			−2.17834
$469$	8.40325	+	25.8626i	0.388026	+	1.19422i
$470$	−0.690983	+	2.12663i	−0.0318727	+	0.0980940i
$471$	−6.48936	+	19.9722i	−0.299014	+	0.920270i
$472$	−21.6631	+	66.6722i	−0.997126	+	3.06884i
$473$	−0.145898	+	0.106001i	−0.00670840	+	0.00487394i
$474$	−23.7984			−1.09310
$475$	7.50000	−	5.44907i	0.344124	−	0.250020i
$476$	11.5623			0.529957
$477$	13.3262	−	9.68208i	0.610167	−	0.443312i
$478$	6.04508	−	18.6049i	0.276496	−	0.850966i
$479$	9.28115	−	28.5645i	0.424067	−	1.30514i	−0.479818	−	0.877368i	$-0.659297\pi$
$479$	9.28115	−	28.5645i	0.424067	−	1.30514i	0.903885	−	0.427775i	$-0.140703\pi$
$480$	−19.6353	+	14.2658i	−0.896223	+	0.651144i
$481$	−11.9164	−	36.6749i	−0.543341	−	1.67223i
$482$	−24.0344			−1.09474
$483$	1.64590	+	5.06555i	0.0748910	+	0.230491i
$484$	37.1976	+	27.0256i	1.69080	+	1.22844i
$485$	−26.8713	+	19.5232i	−1.22016	+	0.886501i
$486$	−33.8885	+	24.6215i	−1.53722	+	1.11685i
$487$	3.57295	+	2.59590i	0.161906	+	0.117631i	0.665788	−	0.746141i	$-0.268095\pi$
$487$	3.57295	+	2.59590i	0.161906	+	0.117631i	−0.503882	+	0.863772i	$0.668095\pi$
$488$	−30.2254	−	21.9601i	−1.36824	−	0.994085i
$489$	15.8992	−	11.5514i	0.718986	−	0.522374i
$490$	7.76393			0.350739
$491$	3.19098	+	2.31838i	0.144007	+	0.104627i	0.657456	−	0.753493i	$-0.271632\pi$
$491$	3.19098	+	2.31838i	0.144007	+	0.104627i	−0.513449	+	0.858120i	$0.671632\pi$
$492$	9.70820	+	29.8788i	0.437680	+	1.34704i
$493$	−8.61803			−0.388137
$494$	7.28115	+	22.4091i	0.327595	+	1.00823i
$495$	−4.47214	−	3.24920i	−0.201008	−	0.146041i
$496$	17.5517	−	54.0185i	0.788093	−	2.42550i
$497$	0.843459	−	2.59590i	0.0378343	−	0.116442i
$498$	25.2984	−	18.3803i	1.13365	−	0.823643i
$499$	−6.67376			−0.298759			−0.149379	−	0.988780i	$-0.547728\pi$
$499$	−6.67376			−0.298759			−0.149379	+	0.988780i	$0.547728\pi$
$500$	−43.9058	−	31.8994i	−1.96353	−	1.42658i
$501$	8.90983			0.398062
$502$	16.2082	−	11.7759i	0.723408	−	0.525586i
$503$	2.43769	−	7.50245i	0.108691	−	0.334518i	−0.881888	−	0.471460i	$-0.843727\pi$
$503$	2.43769	−	7.50245i	0.108691	−	0.334518i	0.990579	+	0.136942i	$0.0437273\pi$
$504$	11.0000	−	33.8545i	0.489979	−	1.50800i
$505$	22.1353	+	16.0822i	0.985006	+	0.715649i
$506$	−2.23607	−	6.88191i	−0.0994053	−	0.305938i
$507$	−10.5623			−0.469088
$508$	−29.1246	−	89.6363i	−1.29220	−	3.97697i
$509$	14.6353	+	10.6331i	0.648696	+	0.471305i	0.862827	−	0.505500i	$-0.168692\pi$
$509$	14.6353	+	10.6331i	0.648696	+	0.471305i	−0.214131	+	0.976805i	$0.568692\pi$
$510$	5.85410			0.259224
$511$	−17.3435	+	12.6008i	−0.767229	+	0.557425i
$512$	−32.6074	−	23.6907i	−1.44106	−	1.04699i
$513$	7.50000	+	5.44907i	0.331133	+	0.240582i
$514$	−3.92705	+	2.85317i	−0.173215	+	0.125848i
$515$	25.9164	−	18.8294i	1.14201	−	0.829721i
$516$	−0.572949	−	0.416272i	−0.0252227	−	0.0183253i
$517$	−0.145898	−	0.449028i	−0.00641659	−	0.0197482i
$518$	49.5410			2.17671
$519$	0.545085	+	1.67760i	0.0239266	+	0.0736384i
$520$	65.6140	−	47.6713i	2.87736	−	2.09053i
$521$	10.3992	−	32.0054i	0.455597	−	1.40218i	−0.414837	−	0.909896i	$-0.636161\pi$
$521$	10.3992	−	32.0054i	0.455597	−	1.40218i	0.870433	−	0.492286i	$-0.163839\pi$
$522$	−13.9443	+	42.9161i	−0.610324	+	1.87838i
$523$	15.5902	−	11.3269i	0.681711	−	0.495292i	−0.192214	−	0.981353i	$-0.561567\pi$
$523$	15.5902	−	11.3269i	0.681711	−	0.495292i	0.873925	+	0.486061i	$0.161567\pi$
$524$	22.6869			0.991083
$525$	−11.9098			−0.519788
$526$	−25.1803			−1.09791
$527$	−4.66312	+	3.38795i	−0.203129	+	0.147582i
$528$	3.76393	−	11.5842i	0.163804	−	0.504137i
$529$	−5.56231	+	17.1190i	−0.241839	+	0.744305i
$530$	−14.8992	+	45.8550i	−0.647179	+	1.99181i
$531$	−5.79837	−	17.8456i	−0.251628	−	0.774431i
$532$	−21.4377			−0.929442
$533$	−9.70820	−	29.8788i	−0.420509	−	1.29419i
$534$	6.85410	+	4.97980i	0.296606	+	0.215497i
$535$	32.4615	+	23.5847i	1.40343	+	1.01965i
$536$	69.0132	−	50.1410i	2.98091	−	2.16576i
$537$	−17.6074	−	12.7925i	−0.759815	−	0.552038i
$538$	28.4164	+	20.6457i	1.22512	+	0.890101i
$539$	−1.32624	+	0.963568i	−0.0571251	+	0.0415038i
$540$	16.7705	−	51.6143i	0.721688	−	2.22113i
$541$	−23.3262	−	16.9475i	−1.00287	−	0.728630i	−0.0401709	−	0.999193i	$-0.512790\pi$
$541$	−23.3262	−	16.9475i	−1.00287	−	0.728630i	−0.962702	+	0.270563i	$0.912790\pi$
$542$	−16.0902	−	49.5205i	−0.691132	−	2.12709i
$543$	−21.4164			−0.919066
$544$	−3.35410	−	10.3229i	−0.143806	−	0.442589i
$545$	5.32624	+	16.3925i	0.228151	+	0.702176i
$546$	9.35410	−	28.7890i	0.400319	−	1.23205i
$547$	4.51064	−	13.8823i	0.192861	−	0.593566i	−0.807134	−	0.590369i	$-0.798982\pi$
$547$	4.51064	−	13.8823i	0.192861	−	0.593566i	0.999995	−	0.00319699i	$-0.00101764\pi$
$548$	−88.0304	+	63.9578i	−3.76047	+	2.73214i
$549$	10.0000			0.426790
$550$	16.1803			0.689932
$551$	15.9787			0.680716
$552$	13.5172	−	9.82084i	0.575331	−	0.418003i
$553$	−6.69098	+	20.5927i	−0.284530	+	0.875692i
$554$	17.9894	−	55.3655i	0.764295	−	2.35226i
$555$	17.7639			0.754037
$556$	−0.354102	−	1.08981i	−0.0150173	−	0.0462184i
$557$	−8.83282			−0.374258			−0.187129	−	0.982335i	$-0.559918\pi$
$557$	−8.83282			−0.374258			−0.187129	+	0.982335i	$0.559918\pi$
$558$	9.32624	+	28.7032i	0.394811	+	1.21510i
$559$	0.572949	+	0.416272i	0.0242332	+	0.0176064i
$560$	16.2188	+	49.9165i	0.685371	+	2.10936i
$561$	−1.00000	+	0.726543i	−0.0422200	+	0.0306746i
$562$	24.4894	+	17.7926i	1.03302	+	0.750534i
$563$	13.6353	+	9.90659i	0.574657	+	0.417513i	0.836794	−	0.547518i	$-0.184427\pi$
$563$	13.6353	+	9.90659i	0.574657	+	0.417513i	−0.262137	+	0.965031i	$0.584427\pi$
$564$	1.50000	−	1.08981i	0.0631614	−	0.0458894i
$565$	5.75329	+	17.7068i	0.242043	+	0.744931i
$566$	29.8435	+	21.6825i	1.25441	+	0.911385i
$567$	0.736068	+	2.26538i	0.0309119	+	0.0951372i
$568$	−8.56231			−0.359266
$569$	−6.27458	−	19.3112i	−0.263044	−	0.809566i	−0.992138	−	0.125152i	$-0.960058\pi$
$569$	−6.27458	−	19.3112i	−0.263044	−	0.809566i	0.729094	−	0.684414i	$-0.239942\pi$
$570$	−10.8541			−0.454628
$571$	−11.7812	+	36.2587i	−0.493026	+	1.51738i	0.326985	+	0.945030i	$0.393967\pi$
$571$	−11.7812	+	36.2587i	−0.493026	+	1.51738i	−0.820011	+	0.572348i	$0.806033\pi$
$572$	−9.00000	+	27.6992i	−0.376309	+	1.15816i
$573$	8.61803	−	6.26137i	0.360024	−	0.261572i
$574$	40.3607			1.68462
$575$	9.04508	+	6.57164i	0.377206	+	0.274056i
$576$	−17.4164			−0.725684
$577$	−25.6525	+	18.6376i	−1.06793	+	0.775894i	−0.975538	−	0.219829i	$-0.929450\pi$
$577$	−25.6525	+	18.6376i	−1.06793	+	0.775894i	−0.0923881	+	0.995723i	$0.529450\pi$
$578$	−0.809017	+	2.48990i	−0.0336507	+	0.103566i
$579$	−1.56231	+	4.80828i	−0.0649272	+	0.199825i
$580$	−28.9058	−	88.9628i	−1.20025	−	3.69398i
$581$	−8.79180	−	27.0584i	−0.364745	−	1.12257i
$582$	38.8885			1.61198
$583$	−3.14590	−	9.68208i	−0.130290	−	0.400991i
$584$	54.4058	+	39.5281i	2.25133	+	1.63568i
$585$	−6.70820	+	20.6457i	−0.277350	+	0.853596i
$586$	31.6525	−	22.9969i	1.30755	−	0.949992i
$587$	18.5172	+	13.4535i	0.764288	+	0.555287i	0.900222	−	0.435430i	$-0.143404\pi$
$587$	18.5172	+	13.4535i	0.764288	+	0.555287i	−0.135935	+	0.990718i	$0.543404\pi$
$588$	−5.20820	−	3.78398i	−0.214783	−	0.156049i
$589$	8.64590	−	6.28161i	0.356248	−	0.258829i
$590$	44.4336	+	32.2829i	1.82930	+	1.32907i
$591$	16.3262	+	11.8617i	0.671572	+	0.487925i
$592$	−24.1910	−	74.4522i	−0.994243	−	3.05997i
$593$	25.9098			1.06399			0.531995	−	0.846748i	$-0.321443\pi$
$593$	25.9098			1.06399			0.531995	+	0.846748i	$0.321443\pi$
$594$	5.00000	+	15.3884i	0.205152	+	0.631394i
$595$	1.64590	−	5.06555i	0.0674752	−	0.207667i
$596$	10.7705	−	33.1482i	0.441177	−	1.35780i
$597$	1.64590	−	5.06555i	0.0673621	−	0.207319i
$598$	−22.9894	+	16.7027i	−0.940105	+	0.683026i
$599$	−35.1803			−1.43743			−0.718715	−	0.695305i	$-0.755269\pi$
$599$	−35.1803			−1.43743			−0.718715	+	0.695305i	$0.755269\pi$
$600$	11.5451	+	35.5321i	0.471326	+	1.45059i
$601$	21.1459			0.862559			0.431280	−	0.902218i	$-0.358062\pi$
$601$	21.1459			0.862559			0.431280	+	0.902218i	$0.358062\pi$
$602$	−0.736068	+	0.534785i	−0.0299999	+	0.0217962i
$603$	−7.05573	+	21.7153i	−0.287331	+	0.884315i
$604$	26.7812	−	82.4239i	1.08971	−	3.35378i
$605$	17.1353	−	12.4495i	0.696647	−	0.506144i
$606$	−9.89919	−	30.4666i	−0.402127	−	1.23762i
$607$	−28.3820			−1.15199			−0.575994	−	0.817454i	$-0.695385\pi$
$607$	−28.3820			−1.15199			−0.575994	+	0.817454i	$0.695385\pi$
$608$	6.21885	+	19.1396i	0.252208	+	0.776215i
$609$	−16.6074	−	12.0660i	−0.672965	−	0.488938i
$610$	−23.6803	+	17.2048i	−0.958789	+	0.696601i
$611$	−1.50000	+	1.08981i	−0.0606835	+	0.0440891i
$612$	7.85410	+	5.70634i	0.317483	+	0.230665i
$613$	17.1074	+	12.4292i	0.690961	+	0.502013i	0.876976	−	0.480534i	$-0.159557\pi$
$613$	17.1074	+	12.4292i	0.690961	+	0.502013i	−0.186015	+	0.982547i	$0.559557\pi$
$614$	−40.1246	+	29.1522i	−1.61930	+	1.17649i
$615$	14.4721			0.583573
$616$	−17.7984	−	12.9313i	−0.717117	−	0.521016i
$617$	13.6008	+	41.8590i	0.547548	+	1.68518i	0.714853	+	0.699275i	$0.246494\pi$
$617$	13.6008	+	41.8590i	0.547548	+	1.68518i	−0.167305	+	0.985905i	$0.553506\pi$
$618$	−37.5066			−1.50874
$619$	5.34346	+	16.4455i	0.214772	+	0.660999i	0.999170	+	0.0407416i	$0.0129720\pi$
$619$	5.34346	+	16.4455i	0.214772	+	0.660999i	−0.784398	+	0.620258i	$0.787028\pi$
$620$	−50.6140	−	36.7732i	−2.03271	−	1.47685i
$621$	−3.45492	+	10.6331i	−0.138641	+	0.426693i
$622$	−28.3435	+	87.2322i	−1.13647	+	3.49769i
$623$	6.23607	−	4.53077i	0.249843	−	0.181521i
$624$	−47.8328			−1.91485
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$	35.1246			1.40386
$627$	1.85410	−	1.34708i	0.0740457	−	0.0537974i
$628$	31.5000	−	96.9470i	1.25699	−	3.86861i
$629$	−2.45492	+	7.55545i	−0.0978839	+	0.301256i
$630$	−22.5623	−	16.3925i	−0.898904	−	0.653092i
$631$	−8.69098	−	26.7481i	−0.345983	−	1.06482i	−0.961056	−	0.276355i	$-0.910874\pi$
$631$	−8.69098	−	26.7481i	−0.345983	−	1.06482i	0.615073	−	0.788470i	$-0.289126\pi$
$632$	67.9230			2.70183
$633$	−0.364745	−	1.12257i	−0.0144973	−	0.0446181i
$634$	−56.9508	−	41.3772i	−2.26181	−	1.64330i
$635$	−43.4164			−1.72293
$636$	32.3435	−	23.4989i	1.28250	−	0.931792i
$637$	5.20820	+	3.78398i	0.206357	+	0.149927i
$638$	22.5623	+	16.3925i	0.893250	+	0.648984i
$639$	1.85410	−	1.34708i	0.0733471	−	0.0532898i
$640$	1.97214	−	1.43284i	0.0779555	−	0.0566380i
$641$	−0.781153	−	0.567541i	−0.0308537	−	0.0224165i	0.572252	−	0.820078i	$-0.306070\pi$
$641$	−0.781153	−	0.567541i	−0.0308537	−	0.0224165i	−0.603105	+	0.797662i	$0.706070\pi$
$642$	−14.5172	−	44.6794i	−0.572949	−	1.76336i
$643$	7.70820			0.303982			0.151991	−	0.988382i	$-0.451432\pi$
$643$	7.70820			0.303982			0.151991	+	0.988382i	$0.451432\pi$
$644$	−7.98936	−	24.5887i	−0.314825	−	0.968931i
$645$	−0.263932	+	0.191758i	−0.0103923	+	0.00755046i
$646$	1.50000	−	4.61653i	0.0590167	−	0.181635i
$647$	13.4721	−	41.4630i	0.529644	−	1.63008i	−0.225301	−	0.974289i	$-0.572336\pi$
$647$	13.4721	−	41.4630i	0.529644	−	1.63008i	0.754945	−	0.655788i	$-0.227664\pi$
$648$	6.04508	−	4.39201i	0.237473	−	0.172534i
$649$	−11.5967			−0.455212
$650$	−19.6353	−	60.4311i	−0.770158	−	2.37030i
$651$	−13.7295			−0.538101
$652$	−77.1763	+	56.0718i	−3.02246	+	2.19594i
$653$	10.1180	−	31.1401i	0.395949	−	1.21861i	−0.532271	−	0.846574i	$-0.678661\pi$
$653$	10.1180	−	31.1401i	0.395949	−	1.21861i	0.928220	−	0.372032i	$-0.121339\pi$
$654$	6.23607	−	19.1926i	0.243850	−	0.750492i
$655$	3.22949	−	9.93935i	0.126187	−	0.388362i
$656$	−19.7082	−	60.6556i	−0.769476	−	2.36820i
$657$	−18.0000			−0.702247
$658$	−0.736068	−	2.26538i	−0.0286949	−	0.0883139i
$659$	−34.3607	−	24.9645i	−1.33850	−	0.972479i	−0.999498	−	0.0316939i	$-0.989910\pi$
$659$	−34.3607	−	24.9645i	−1.33850	−	0.972479i	−0.339004	−	0.940785i	$-0.610090\pi$
$660$	−10.8541	−	7.88597i	−0.422495	−	0.306961i
$661$	10.2639	−	7.45718i	0.399221	−	0.290051i	−0.370003	−	0.929031i	$-0.620643\pi$
$661$	10.2639	−	7.45718i	0.399221	−	0.290051i	0.769223	+	0.638980i	$0.220643\pi$
$662$	19.9443	+	14.4904i	0.775156	+	0.563184i
$663$	3.92705	+	2.85317i	0.152514	+	0.110808i
$664$	−72.2041	+	52.4594i	−2.80206	+	2.03582i
$665$	−3.05166	+	9.39205i	−0.118338	+	0.364208i
$666$	33.6525	+	24.4500i	1.30401	+	0.947417i
$667$	5.95492	+	18.3273i	0.230575	+	0.709638i
$668$	−43.2492			−1.67336
$669$	1.14590	+	3.52671i	0.0443030	+	0.136351i
$670$	−20.6525	−	63.5618i	−0.797875	−	2.45561i
$671$	1.90983	−	5.87785i	0.0737282	−	0.226912i
$672$	7.98936	−	24.5887i	0.308196	−	0.948530i
$673$	20.4164	−	14.8334i	0.786995	−	0.571785i	−0.120075	−	0.992765i	$-0.538314\pi$
$673$	20.4164	−	14.8334i	0.786995	−	0.571785i	0.907070	+	0.420980i	$0.138314\pi$
$674$	−3.47214			−0.133742
$675$	−20.2254	−	14.6946i	−0.778477	−	0.565597i
$676$	51.2705			1.97194
$677$	−4.25329	+	3.09020i	−0.163467	+	0.118766i	−0.666511	−	0.745495i	$-0.732213\pi$
$677$	−4.25329	+	3.09020i	−0.163467	+	0.118766i	0.503044	+	0.864261i	$0.332213\pi$
$678$	6.73607	−	20.7315i	0.258697	−	0.796188i
$679$	10.9336	−	33.6502i	0.419594	−	1.29138i
$680$	−16.7082			−0.640730
$681$	−4.14590	−	12.7598i	−0.158871	−	0.488955i
$682$	18.6525			0.714240
$683$	−11.2877	−	34.7401i	−0.431913	−	1.32929i	−0.896217	−	0.443616i	$-0.853696\pi$
$683$	−11.2877	−	34.7401i	−0.431913	−	1.32929i	0.464304	−	0.885676i	$-0.346304\pi$
$684$	−14.5623	−	10.5801i	−0.556804	−	0.404542i
$685$	15.4894	+	47.6713i	0.591818	+	1.82143i
$686$	−42.0066	+	30.5196i	−1.60382	+	1.16524i
$687$	4.85410	+	3.52671i	0.185196	+	0.134552i
$688$	1.16312	+	0.845055i	0.0443435	+	0.0322174i
$689$	−32.3435	+	23.4989i	−1.23219	+	0.895237i
$690$	−4.04508	−	12.4495i	−0.153994	−	0.473944i
$691$	−31.7705	−	23.0826i	−1.20861	−	0.878104i	−0.213504	−	0.976942i	$-0.568488\pi$
$691$	−31.7705	−	23.0826i	−1.20861	−	0.878104i	−0.995104	+	0.0988378i	$0.968488\pi$
$692$	−2.64590	−	8.14324i	−0.100582	−	0.309559i
$693$	5.88854			0.223687
$694$	16.2082	+	49.8837i	0.615255	+	1.89356i
$695$	−0.527864			−0.0200230
$696$	−19.8992	+	61.2434i	−0.754277	+	2.32143i
$697$	−2.00000	+	6.15537i	−0.0757554	+	0.233151i
$698$	−12.7082	+	9.23305i	−0.481013	+	0.349476i
$699$	14.1803			0.536350
$700$	57.8115			2.18507
$701$	−2.36068			−0.0891616			−0.0445808	−	0.999006i	$-0.514195\pi$
$701$	−2.36068			−0.0891616			−0.0445808	+	0.999006i	$0.514195\pi$
$702$	51.4058	−	37.3485i	1.94019	−	1.40963i
$703$	4.55166	−	14.0086i	0.171669	−	0.528344i
$704$	−3.32624	+	10.2371i	−0.125362	+	0.385826i
$705$	−0.263932	−	0.812299i	−0.00994026	−	0.0305930i
$706$	17.7812	+	54.7248i	0.669203	+	2.05959i
$707$	−29.1459			−1.09614
$708$	−14.0729	−	43.3121i	−0.528894	−	1.62777i
$709$	8.89919	+	6.46564i	0.334216	+	0.242822i	0.742217	−	0.670159i	$-0.233774\pi$
$709$	8.89919	+	6.46564i	0.334216	+	0.242822i	−0.408001	+	0.912981i	$0.633774\pi$
$710$	−2.07295	+	6.37988i	−0.0777964	+	0.239433i
$711$	−14.7082	+	10.6861i	−0.551601	+	0.400761i
$712$	−19.5623	−	14.2128i	−0.733128	−	0.532649i
$713$	10.4271	+	7.57570i	0.390496	+	0.283712i
$714$	−5.04508	+	3.66547i	−0.188808	+	0.137177i
$715$	10.8541	+	7.88597i	0.405920	+	0.294918i
$716$	85.4681	+	62.0962i	3.19409	+	2.32064i
$717$	2.30902	+	7.10642i	0.0862318	+	0.265394i
$718$	26.7082			0.996741
$719$	−6.25329	−	19.2456i	−0.233208	−	0.717741i	−0.997354	−	0.0726977i	$-0.976839\pi$
$719$	−6.25329	−	19.2456i	−0.233208	−	0.717741i	0.764146	−	0.645044i	$-0.223161\pi$
$720$	−13.6180	+	41.9120i	−0.507514	+	1.56197i
$721$	−10.5451	+	32.4544i	−0.392719	+	1.20867i
$722$	12.5902	−	38.7486i	0.468558	−	1.44207i
$723$	7.42705	−	5.39607i	0.276215	−	0.200682i
$724$	103.957			3.86355
$725$	−43.0902			−1.60033
$726$	−24.7984			−0.920354
$727$	−6.20820	+	4.51052i	−0.230250	+	0.167286i	−0.696928	−	0.717141i	$-0.745450\pi$
$727$	−6.20820	+	4.51052i	−0.230250	+	0.167286i	0.466679	+	0.884427i	$0.345450\pi$
$728$	−26.6976	+	82.1666i	−0.989477	+	3.04530i
$729$	4.01722	−	12.3637i	0.148786	−	0.457916i
$730$	42.6246	−	30.9686i	1.57761	−	1.14620i
$731$	−0.0450850	−	0.138757i	−0.00166753	−	0.00513212i
$732$	24.2705			0.897064
$733$	11.0795	+	34.0993i	0.409232	+	1.25949i	0.917310	+	0.398175i	$0.130356\pi$
$733$	11.0795	+	34.0993i	0.409232	+	1.25949i	−0.508078	+	0.861311i	$0.669644\pi$
$734$	57.4959	+	41.7732i	2.12221	+	1.54188i
$735$	−2.39919	+	1.74311i	−0.0884953	+	0.0642956i
$736$	−19.6353	+	14.2658i	−0.723765	+	0.525846i
$737$	11.4164	+	8.29451i	0.420529	+	0.305532i
$738$	27.4164	+	19.9192i	1.00921	+	0.733235i
$739$	30.6246	−	22.2501i	1.12654	−	0.818483i	0.141356	−	0.989959i	$-0.454854\pi$
$739$	30.6246	−	22.2501i	1.12654	−	0.818483i	0.985188	+	0.171476i	$0.0548537\pi$
$740$	−86.2279			−3.16980
$741$	−7.28115	−	5.29007i	−0.267480	−	0.194335i
$742$	−15.8713	−	48.8469i	−0.582655	−	1.79323i
$743$	6.00000			0.220119			0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000			0.220119			0.110059	+	0.993925i	$0.464896\pi$
$744$	13.3090	+	40.9609i	0.487932	+	1.50170i
$745$	−12.9894	−	9.43732i	−0.475893	−	0.345757i
$746$	−16.0623	+	49.4347i	−0.588083	+	1.80993i
$747$	7.38197	−	22.7194i	0.270092	−	0.831258i
$748$	4.85410	−	3.52671i	0.177484	−	0.128949i
$749$	−42.7426			−1.56178
$750$	29.2705			1.06881
$751$	17.4721			0.637567			0.318784	−	0.947828i	$-0.396726\pi$
$751$	17.4721			0.637567			0.318784	+	0.947828i	$0.396726\pi$
$752$	−3.04508	+	2.21238i	−0.111043	+	0.0806773i
$753$	−2.36475	+	7.27794i	−0.0861761	+	0.265223i
$754$	33.8435	−	104.159i	1.23251	−	3.79326i
$755$	−32.2984	−	23.4661i	−1.17546	−	0.854020i
$756$	17.8647	+	54.9820i	0.649734	+	1.99968i
$757$	15.3607			0.558293			0.279147	−	0.960248i	$-0.409948\pi$
$757$	15.3607			0.558293			0.279147	+	0.960248i	$0.409948\pi$
$758$	10.4271	+	32.0912i	0.378728	+	1.16560i
$759$	2.23607	+	1.62460i	0.0811641	+	0.0589692i
$760$	30.9787			1.12372
$761$	16.5902	−	12.0535i	0.601393	−	0.436938i	−0.244980	−	0.969528i	$-0.578781\pi$
$761$	16.5902	−	12.0535i	0.601393	−	0.436938i	0.846373	+	0.532590i	$0.178781\pi$
$762$	41.1246	+	29.8788i	1.48979	+	1.08239i
$763$	−14.8541	−	10.7921i	−0.537755	−	0.390702i
$764$	−41.8328	+	30.3933i	−1.51346	+	1.09959i
$765$	3.61803	−	2.62866i	0.130810	−	0.0950392i
$766$	53.9508	+	39.1976i	1.94932	+	1.41627i
$767$	14.0729	+	43.3121i	0.508145	+	1.56391i
$768$	14.5623			0.525472
$769$	−1.14590	−	3.52671i	−0.0413221	−	0.127176i	0.928267	−	0.371914i	$-0.121298\pi$

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.11803 - 1.53884i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.50000 - 4.61653i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(0.809017 + 2.48990i) q^{6} +2.38197 q^{7} +(-2.30902 - 7.10642i) q^{8} +(1.61803 + 1.17557i) q^{9} -5.85410 q^{10} +(1.00000 - 0.726543i) q^{11} +(3.92705 + 2.85317i) q^{12} +(-3.92705 - 2.85317i) q^{13} +(5.04508 - 3.66547i) q^{14} +(1.80902 - 1.31433i) q^{15} +(-7.97214 - 5.79210i) q^{16} +(0.309017 + 0.951057i) q^{17} +5.23607 q^{18} +(-0.572949 - 1.76336i) q^{19} +(-8.78115 + 6.37988i) q^{20} +(-0.736068 + 2.26538i) q^{21} +(1.00000 - 3.07768i) q^{22} +(1.80902 - 1.31433i) q^{23} +7.47214 q^{24} +(1.54508 + 4.75528i) q^{25} -12.7082 q^{26} +(-4.04508 + 2.93893i) q^{27} +(3.57295 - 10.9964i) q^{28} +(-2.66312 + 8.19624i) q^{29} +(1.80902 - 5.56758i) q^{30} +(1.78115 + 5.48183i) q^{31} -10.8541 q^{32} +(0.381966 + 1.17557i) q^{33} +(2.11803 + 1.53884i) q^{34} +(-4.30902 - 3.13068i) q^{35} +(7.85410 - 5.70634i) q^{36} +(6.42705 + 4.66953i) q^{37} +(-3.92705 - 2.85317i) q^{38} +(3.92705 - 2.85317i) q^{39} +(-5.16312 + 15.8904i) q^{40} +(5.23607 + 3.80423i) q^{41} +(1.92705 + 5.93085i) q^{42} -0.145898 q^{43} +(-1.85410 - 5.70634i) q^{44} +(-1.38197 - 4.25325i) q^{45} +(1.80902 - 5.56758i) q^{46} +(0.118034 - 0.363271i) q^{47} +(7.97214 - 5.79210i) q^{48} -1.32624 q^{49} +(10.5902 + 7.69421i) q^{50} -1.00000 q^{51} +(-19.0623 + 13.8496i) q^{52} +(2.54508 - 7.83297i) q^{53} +(-4.04508 + 12.4495i) q^{54} -2.76393 q^{55} +(-5.50000 - 16.9273i) q^{56} +1.85410 q^{57} +(6.97214 + 21.4580i) q^{58} +(-7.59017 - 5.51458i) q^{59} +(-3.35410 - 10.3229i) q^{60} +(4.04508 - 2.93893i) q^{61} +(12.2082 + 8.86978i) q^{62} +(3.85410 + 2.80017i) q^{63} +(-7.04508 + 5.11855i) q^{64} +(3.35410 + 10.3229i) q^{65} +(2.61803 + 1.90211i) q^{66} +(3.52786 + 10.8576i) q^{67} +4.85410 q^{68} +(0.690983 + 2.12663i) q^{69} -13.9443 q^{70} +(0.354102 - 1.08981i) q^{71} +(4.61803 - 14.2128i) q^{72} +(-7.28115 + 5.29007i) q^{73} +20.7984 q^{74} -5.00000 q^{75} -9.00000 q^{76} +(2.38197 - 1.73060i) q^{77} +(3.92705 - 12.0862i) q^{78} +(-2.80902 + 8.64527i) q^{79} +(6.80902 + 20.9560i) q^{80} +(0.309017 + 0.951057i) q^{81} +16.9443 q^{82} +(-3.69098 - 11.3597i) q^{83} +(9.35410 + 6.79615i) q^{84} +(0.690983 - 2.12663i) q^{85} +(-0.309017 + 0.224514i) q^{86} +(-6.97214 - 5.06555i) q^{87} +(-7.47214 - 5.42882i) q^{88} +(2.61803 - 1.90211i) q^{89} +(-9.47214 - 6.88191i) q^{90} +(-9.35410 - 6.79615i) q^{91} +(-3.35410 - 10.3229i) q^{92} -5.76393 q^{93} +(-0.309017 - 0.951057i) q^{94} +(-1.28115 + 3.94298i) q^{95} +(3.35410 - 10.3229i) q^{96} +(4.59017 - 14.1271i) q^{97} +(-2.80902 + 2.04087i) q^{98} +2.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + q^{3} + 6 q^{4} - 5 q^{5} + q^{6} + 14 q^{7} - 7 q^{8} + 2 q^{9} - 10 q^{10} + 4 q^{11} + 9 q^{12} - 9 q^{13} + 9 q^{14} + 5 q^{15} - 14 q^{16} - q^{17} + 12 q^{18} - 9 q^{19} - 15 q^{20}+ \cdots - 8 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + q^3 + 6 * q^4 - 5 * q^5 + q^6 + 14 * q^7 - 7 * q^8 + 2 * q^9 - 10 * q^10 + 4 * q^11 + 9 * q^12 - 9 * q^13 + 9 * q^14 + 5 * q^15 - 14 * q^16 - q^17 + 12 * q^18 - 9 * q^19 - 15 * q^20 + 6 * q^21 + 4 * q^22 + 5 * q^23 + 12 * q^24 - 5 * q^25 - 24 * q^26 - 5 * q^27 + 21 * q^28 + 5 * q^29 + 5 * q^30 - 13 * q^31 - 30 * q^32 + 6 * q^33 + 4 * q^34 - 15 * q^35 + 18 * q^36 + 19 * q^37 - 9 * q^38 + 9 * q^39 - 5 * q^40 + 12 * q^41 + q^42 - 14 * q^43 + 6 * q^44 - 10 * q^45 + 5 * q^46 - 4 * q^47 + 14 * q^48 + 26 * q^49 + 20 * q^50 - 4 * q^51 - 36 * q^52 - q^53 - 5 * q^54 - 20 * q^55 - 22 * q^56 - 6 * q^57 + 10 * q^58 - 8 * q^59 + 5 * q^61 + 22 * q^62 + 2 * q^63 - 17 * q^64 + 6 * q^66 + 32 * q^67 + 6 * q^68 + 5 * q^69 - 20 * q^70 - 12 * q^71 + 14 * q^72 - 9 * q^73 + 34 * q^74 - 20 * q^75 - 36 * q^76 + 14 * q^77 + 9 * q^78 - 9 * q^79 + 25 * q^80 - q^81 + 32 * q^82 - 17 * q^83 + 24 * q^84 + 5 * q^85 + q^86 - 10 * q^87 - 12 * q^88 + 6 * q^89 - 20 * q^90 - 24 * q^91 - 32 * q^93 + q^94 + 15 * q^95 - 4 * q^97 - 9 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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