LMFDB - Embedded newform 425.2.r.a.69.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(69,425)]

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([9, 0]))

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

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

chi := DirichletCharacter("425.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.r (of order $10$, 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:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.6
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.14124 + 0.695730i) q^{2} +(1.08145 + 1.48849i) q^{3} +(2.48282 - 1.80387i) q^{4} +(-0.133284 + 2.23209i) q^{5} +(-3.35124 - 2.43482i) q^{6} -4.38149i q^{7} +(-1.41458 + 1.94701i) q^{8} +(-0.119019 + 0.366304i) q^{9} +(-1.26754 - 4.87217i) q^{10} +(1.54742 + 4.76246i) q^{11} +(5.37011 + 1.74485i) q^{12} +(5.16707 + 1.67888i) q^{13} +(3.04833 + 9.38180i) q^{14} +(-3.46659 + 2.21551i) q^{15} +(-0.222341 + 0.684295i) q^{16} +(0.587785 - 0.809017i) q^{17} -0.867149i q^{18} +(2.84744 + 2.06879i) q^{19} +(3.69549 + 5.78231i) q^{20} +(6.52181 - 4.73838i) q^{21} +(-6.62677 - 9.12097i) q^{22} +(-3.72988 + 1.21191i) q^{23} -4.42791 q^{24} +(-4.96447 - 0.595005i) q^{25} -12.2320 q^{26} +(4.57553 - 1.48668i) q^{27} +(-7.90365 - 10.8784i) q^{28} +(-1.35616 + 0.985311i) q^{29} +(5.88140 - 7.15575i) q^{30} +(4.45495 + 3.23671i) q^{31} -6.43319i q^{32} +(-5.41543 + 7.45370i) q^{33} +(-0.695730 + 2.14124i) q^{34} +(9.77988 + 0.583982i) q^{35} +(0.365263 + 1.12416i) q^{36} +(-5.69639 - 1.85087i) q^{37} +(-7.53636 - 2.44871i) q^{38} +(3.08894 + 9.50678i) q^{39} +(-4.15735 - 3.41698i) q^{40} +(-1.38219 + 4.25393i) q^{41} +(-10.6681 + 14.6834i) q^{42} -2.73959i q^{43} +(12.4328 + 9.03298i) q^{44} +(-0.801761 - 0.314485i) q^{45} +(7.14340 - 5.18998i) q^{46} +(-2.75987 - 3.79863i) q^{47} +(-1.25902 + 0.409080i) q^{48} -12.1974 q^{49} +(11.0441 - 2.17989i) q^{50} +1.83988 q^{51} +(15.8574 - 5.15238i) q^{52} +(4.49551 + 6.18754i) q^{53} +(-8.76297 + 6.36667i) q^{54} +(-10.8365 + 2.81922i) q^{55} +(8.53078 + 6.19797i) q^{56} +6.47569i q^{57} +(2.21836 - 3.05331i) q^{58} +(-1.96156 + 6.03707i) q^{59} +(-4.61043 + 11.7540i) q^{60} +(-0.481029 - 1.48046i) q^{61} +(-11.7910 - 3.83112i) q^{62} +(1.60496 + 0.521482i) q^{63} +(4.03108 + 12.4064i) q^{64} +(-4.43611 + 11.3096i) q^{65} +(6.40995 - 19.7278i) q^{66} +(-6.97108 + 9.59486i) q^{67} -3.06893i q^{68} +(-5.83762 - 4.24128i) q^{69} +(-21.3473 + 5.55371i) q^{70} +(12.2357 - 8.88975i) q^{71} +(-0.544833 - 0.749898i) q^{72} +(1.39360 - 0.452808i) q^{73} +13.4850 q^{74} +(-4.48319 - 8.03305i) q^{75} +10.8015 q^{76} +(20.8666 - 6.77999i) q^{77} +(-13.2283 - 18.2072i) q^{78} +(-3.22393 + 2.34232i) q^{79} +(-1.49777 - 0.587491i) q^{80} +(8.09593 + 5.88204i) q^{81} -10.0703i q^{82} +(6.78571 - 9.33973i) q^{83} +(7.64506 - 23.5291i) q^{84} +(1.72746 + 1.41982i) q^{85} +(1.90601 + 5.86610i) q^{86} +(-2.93326 - 0.953074i) q^{87} +(-11.4615 - 3.72406i) q^{88} +(-4.22214 - 12.9944i) q^{89} +(1.93556 + 0.115577i) q^{90} +(7.35600 - 22.6394i) q^{91} +(-7.07449 + 9.73720i) q^{92} +10.1315i q^{93} +(8.55235 + 6.21364i) q^{94} +(-4.99724 + 6.08001i) q^{95} +(9.57576 - 6.95719i) q^{96} +(6.46389 + 8.89679i) q^{97} +(26.1176 - 8.48612i) q^{98} -1.92868 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) $ 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Character values

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

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	−2.14124	+	0.695730i	−1.51408	+	0.491955i	−0.944088	−	0.329693i	$-0.893055\pi$
$2$	−2.14124	+	0.695730i	−1.51408	+	0.491955i	−0.569995	+	0.821648i	$0.693055\pi$
$3$	1.08145	+	1.48849i	0.624378	+	0.859382i	0.997662	−	0.0683347i	$-0.0217686\pi$
$3$	1.08145	+	1.48849i	0.624378	+	0.859382i	−0.373285	+	0.927717i	$0.621769\pi$
$4$	2.48282	−	1.80387i	1.24141	−	0.901937i
$5$	−0.133284	+	2.23209i	−0.0596064	+	0.998222i
$5$	−0.133284	+	2.23209i	−0.0596064	+	0.998222i
$6$	−3.35124	−	2.43482i	−1.36814	−	0.994010i
$7$		−	4.38149i		−	1.65605i	−0.560694	−	0.828023i	$-0.689465\pi$
$7$		−	4.38149i		−	1.65605i	0.560694	−	0.828023i	$-0.310535\pi$
$8$	−1.41458	+	1.94701i	−0.500130	+	0.688370i
$9$	−0.119019	+	0.366304i	−0.0396731	+	0.122101i
$10$	−1.26754	−	4.87217i	−0.400832	−	1.54071i
$11$	1.54742	+	4.76246i	0.466564	+	1.43594i	0.857005	+	0.515307i	$0.172322\pi$
$11$	1.54742	+	4.76246i	0.466564	+	1.43594i	−0.390442	+	0.920628i	$0.627678\pi$
$12$	5.37011	+	1.74485i	1.55022	+	0.503696i
$13$	5.16707	+	1.67888i	1.43309	+	0.465638i	0.919735	−	0.392540i	$-0.128404\pi$
$13$	5.16707	+	1.67888i	1.43309	+	0.465638i	0.513352	+	0.858178i	$0.328404\pi$
$14$	3.04833	+	9.38180i	0.814701	+	2.50739i
$15$	−3.46659	+	2.21551i	−0.895071	+	0.572043i
$16$	−0.222341	+	0.684295i	−0.0555852	+	0.171074i
$17$	0.587785	−	0.809017i	0.142559	−	0.196215i
$17$	0.587785	−	0.809017i	0.142559	−	0.196215i
$18$		−	0.867149i		−	0.204389i
$19$	2.84744	+	2.06879i	0.653248	+	0.474612i	0.864376	−	0.502846i	$-0.167714\pi$
$19$	2.84744	+	2.06879i	0.653248	+	0.474612i	−0.211128	+	0.977458i	$0.567714\pi$
$20$	3.69549	+	5.78231i	0.826338	+	1.29296i
$21$	6.52181	−	4.73838i	1.42318	−	1.03400i
$22$	−6.62677	−	9.12097i	−1.41283	−	1.94460i
$23$	−3.72988	+	1.21191i	−0.777734	+	0.252701i	−0.670872	−	0.741573i	$-0.734080\pi$
$23$	−3.72988	+	1.21191i	−0.777734	+	0.252701i	−0.106862	+	0.994274i	$0.534080\pi$
$24$	−4.42791			−0.903843
$25$	−4.96447	−	0.595005i	−0.992894	−	0.119001i
$26$	−12.2320			−2.39889
$27$	4.57553	−	1.48668i	0.880562	−	0.286112i
$28$	−7.90365	−	10.8784i	−1.49365	−	2.05583i
$29$	−1.35616	+	0.985311i	−0.251833	+	0.182968i	−0.706539	−	0.707674i	$-0.749745\pi$
$29$	−1.35616	+	0.985311i	−0.251833	+	0.182968i	0.454706	+	0.890642i	$0.349745\pi$
$30$	5.88140	−	7.15575i	1.07379	−	1.30646i
$31$	4.45495	+	3.23671i	0.800133	+	0.581331i	0.910953	−	0.412510i	$-0.135348\pi$
$31$	4.45495	+	3.23671i	0.800133	+	0.581331i	−0.110820	+	0.993840i	$0.535348\pi$
$32$		−	6.43319i		−	1.13724i
$33$	−5.41543	+	7.45370i	−0.942705	+	1.29752i
$34$	−0.695730	+	2.14124i	−0.119317	+	0.367219i
$35$	9.77988	+	0.583982i	1.65310	+	0.0987110i
$36$	0.365263	+	1.12416i	0.0608771	+	0.187360i
$37$	−5.69639	−	1.85087i	−0.936481	−	0.304281i	−0.199271	−	0.979944i	$-0.563857\pi$
$37$	−5.69639	−	1.85087i	−0.936481	−	0.304281i	−0.737210	+	0.675663i	$0.763857\pi$
$38$	−7.53636	−	2.44871i	−1.22256	−	0.397234i
$39$	3.08894	+	9.50678i	0.494626	+	1.52230i
$40$	−4.15735	−	3.41698i	−0.657335	−	0.540272i
$41$	−1.38219	+	4.25393i	−0.215861	+	0.664352i	0.783230	+	0.621732i	$0.213571\pi$
$41$	−1.38219	+	4.25393i	−0.215861	+	0.664352i	−0.999091	+	0.0426203i	$0.986429\pi$
$42$	−10.6681	+	14.6834i	−1.64613	+	2.26570i
$43$		−	2.73959i		−	0.417783i	−0.977939	−	0.208892i	$-0.933014\pi$
$43$		−	2.73959i		−	0.417783i	0.977939	−	0.208892i	$-0.0669856\pi$
$44$	12.4328	+	9.03298i	1.87432	+	1.36177i
$45$	−0.801761	−	0.314485i	−0.119519	−	0.0468806i
$46$	7.14340	−	5.18998i	1.05324	−	0.765221i
$47$	−2.75987	−	3.79863i	−0.402568	−	0.554087i	0.558818	−	0.829290i	$-0.311255\pi$
$47$	−2.75987	−	3.79863i	−0.402568	−	0.554087i	−0.961386	+	0.275203i	$0.911255\pi$
$48$	−1.25902	+	0.409080i	−0.181724	+	0.0590457i
$49$	−12.1974			−1.74249
$50$	11.0441	−	2.17989i	1.56187	−	0.308282i
$51$	1.83988			0.257635
$52$	15.8574	−	5.15238i	2.19902	−	0.714507i
$53$	4.49551	+	6.18754i	0.617506	+	0.849925i	0.997168	−	0.0752006i	$-0.0239597\pi$
$53$	4.49551	+	6.18754i	0.617506	+	0.849925i	−0.379662	+	0.925125i	$0.623960\pi$
$54$	−8.76297	+	6.36667i	−1.19249	+	0.866394i
$55$	−10.8365	+	2.81922i	−1.46119	+	0.380143i
$56$	8.53078	+	6.19797i	1.13997	+	0.828239i
$57$			6.47569i			0.857727i
$58$	2.21836	−	3.05331i	0.291285	−	0.400919i
$59$	−1.96156	+	6.03707i	−0.255374	+	0.785959i	0.738382	+	0.674382i	$0.235590\pi$
$59$	−1.96156	+	6.03707i	−0.255374	+	0.785959i	−0.993756	+	0.111577i	$0.964410\pi$
$60$	−4.61043	+	11.7540i	−0.595203	+	1.51744i
$61$	−0.481029	−	1.48046i	−0.0615895	−	0.189553i	0.915528	−	0.402255i	$-0.131774\pi$
$61$	−0.481029	−	1.48046i	−0.0615895	−	0.189553i	−0.977117	+	0.212702i	$0.931774\pi$
$62$	−11.7910	−	3.83112i	−1.49746	−	0.486553i
$63$	1.60496	+	0.521482i	0.202205	+	0.0657005i
$64$	4.03108	+	12.4064i	0.503885	+	1.55080i
$65$	−4.43611	+	11.3096i	−0.550231	+	1.40278i
$66$	6.40995	−	19.7278i	0.789011	−	2.42832i
$67$	−6.97108	+	9.59486i	−0.851653	+	1.17220i	0.131844	+	0.991271i	$0.457910\pi$
$67$	−6.97108	+	9.59486i	−0.851653	+	1.17220i	−0.983496	+	0.180929i	$0.942090\pi$
$68$		−	3.06893i		−	0.372163i
$69$	−5.83762	−	4.24128i	−0.702767	−	0.510590i
$70$	−21.3473	+	5.55371i	−2.55150	+	0.663796i
$71$	12.2357	−	8.88975i	1.45211	−	1.05502i	0.466777	−	0.884375i	$-0.345415\pi$
$71$	12.2357	−	8.88975i	1.45211	−	1.05502i	0.985333	−	0.170645i	$-0.0545851\pi$
$72$	−0.544833	−	0.749898i	−0.0642092	−	0.0883764i
$73$	1.39360	−	0.452808i	0.163108	−	0.0529972i	−0.226325	−	0.974052i	$-0.572671\pi$
$73$	1.39360	−	0.452808i	0.163108	−	0.0529972i	0.389433	+	0.921055i	$0.372671\pi$
$74$	13.4850			1.56760
$75$	−4.48319	−	8.03305i	−0.517674	−	0.927577i
$76$	10.8015			1.23902
$77$	20.8666	−	6.77999i	2.37798	−	0.772651i
$78$	−13.2283	−	18.2072i	−1.49781	−	2.06156i
$79$	−3.22393	+	2.34232i	−0.362721	+	0.263532i	−0.754186	−	0.656661i	$-0.771968\pi$
$79$	−3.22393	+	2.34232i	−0.362721	+	0.263532i	0.391465	+	0.920193i	$0.371968\pi$
$80$	−1.49777	−	0.587491i	−0.167456	−	0.0656835i
$81$	8.09593	+	5.88204i	0.899548	+	0.653560i
$82$		−	10.0703i		−	1.11208i
$83$	6.78571	−	9.33973i	0.744829	−	1.02517i	−0.253498	−	0.967336i	$-0.581581\pi$
$83$	6.78571	−	9.33973i	0.744829	−	1.02517i	0.998326	−	0.0578327i	$-0.0184190\pi$
$84$	7.64506	−	23.5291i	0.834144	−	2.56723i
$85$	1.72746	+	1.41982i	0.187369	+	0.154001i
$86$	1.90601	+	5.86610i	0.205531	+	0.632558i
$87$	−2.93326	−	0.953074i	−0.314478	−	0.102180i
$88$	−11.4615	−	3.72406i	−1.22180	−	0.396986i
$89$	−4.22214	−	12.9944i	−0.447546	−	1.37740i	−0.879667	−	0.475589i	$-0.842235\pi$
$89$	−4.22214	−	12.9944i	−0.447546	−	1.37740i	0.432121	−	0.901815i	$-0.357765\pi$
$90$	1.93556	+	0.115577i	0.204026	+	0.0121829i
$91$	7.35600	−	22.6394i	0.771118	−	2.37326i
$92$	−7.07449	+	9.73720i	−0.737566	+	1.01517i
$93$			10.1315i			1.05059i
$94$	8.55235	+	6.21364i	0.882107	+	0.640888i
$95$	−4.99724	+	6.08001i	−0.512706	+	0.623796i
$96$	9.57576	−	6.95719i	0.977322	−	0.710066i
$97$	6.46389	+	8.89679i	0.656309	+	0.903332i	0.999352	−	0.0359878i	$-0.0114577\pi$
$97$	6.46389	+	8.89679i	0.656309	+	0.903332i	−0.343043	+	0.939320i	$0.611458\pi$
$98$	26.1176	−	8.48612i	2.63827	−	0.857227i
$99$	−1.92868			−0.193840
$100$	−13.3992	+	7.47799i	−1.33992	+	0.747799i
$101$	−3.12700			−0.311148			−0.155574	−	0.987824i	$-0.549723\pi$
$101$	−3.12700			−0.311148			−0.155574	+	0.987824i	$0.549723\pi$
$102$	−3.93962	+	1.28006i	−0.390080	+	0.126745i
$103$	−3.18436	−	4.38290i	−0.313765	−	0.431860i	0.622786	−	0.782392i	$-0.286001\pi$
$103$	−3.18436	−	4.38290i	−0.313765	−	0.431860i	−0.936551	+	0.350532i	$0.886001\pi$
$104$	−10.5780	+	7.68539i	−1.03726	+	0.753615i
$105$	9.70724	+	15.1888i	0.947329	+	1.48228i
$106$	−13.9308	−	10.1213i	−1.35308	−	0.983071i
$107$			11.3245i			1.09478i	0.836879	+	0.547389i	$0.184378\pi$
$107$			11.3245i			1.09478i	−0.836879	+	0.547389i	$0.815622\pi$
$108$	8.67844	−	11.9448i	0.835083	−	1.14939i
$109$	2.07387	−	6.38271i	0.198640	−	0.611353i	−0.801274	−	0.598297i	$-0.795844\pi$
$109$	2.07387	−	6.38271i	0.198640	−	0.611353i	0.999915	−	0.0130554i	$-0.00415577\pi$
$110$	21.2421	−	13.5759i	2.02535	−	1.29441i
$111$	−3.40538	−	10.4807i	−0.323224	−	0.994782i
$112$	2.99823	+	0.974184i	0.283306	+	0.0920517i
$113$	−2.19227	−	0.712311i	−0.206231	−	0.0670086i	0.204080	−	0.978954i	$-0.434580\pi$
$113$	−2.19227	−	0.712311i	−0.206231	−	0.0670086i	−0.410311	+	0.911946i	$0.634580\pi$
$114$	−4.50533	−	13.8660i	−0.421963	−	1.29867i
$115$	−2.20797	−	8.48697i	−0.205894	−	0.791414i
$116$	−1.58974	+	4.89270i	−0.147603	+	0.454276i
$117$	−1.22996	+	1.69290i	−0.113710	+	0.156508i
$118$		−	14.2915i		−	1.31564i
$119$	−3.54470	−	2.57537i	−0.324942	−	0.236084i
$120$	0.590170	−	9.88350i	0.0538749	−	0.902236i
$121$	−11.3873	+	8.27337i	−1.03521	+	0.752125i
$122$	2.06000	+	2.83534i	0.186503	+	0.256700i
$123$	−7.82671	+	2.54305i	−0.705711	+	0.229299i
$124$	16.8995			1.51762
$125$	1.98979	−	11.0019i	0.177972	−	0.984036i
$126$	−3.79940			−0.338478
$127$	12.8916	−	4.18872i	1.14394	−	0.371689i	0.325083	−	0.945685i	$-0.394608\pi$
$127$	12.8916	−	4.18872i	1.14394	−	0.371689i	0.818858	+	0.573997i	$0.194608\pi$
$128$	−9.70032	−	13.3514i	−0.857396	−	1.18010i
$129$	4.07786	−	2.96274i	0.359035	−	0.260854i
$130$	1.63033	−	27.3029i	0.142989	−	2.39462i
$131$	−5.02960	−	3.65422i	−0.439438	−	0.319270i	0.345974	−	0.938244i	$-0.387549\pi$
$131$	−5.02960	−	3.65422i	−0.439438	−	0.319270i	−0.785412	+	0.618974i	$0.787549\pi$
$132$			28.2749i			2.46102i
$133$	9.06436	−	12.4760i	0.785980	−	1.08181i
$134$	8.25129	−	25.3949i	0.712803	−	2.19378i
$135$	2.70856	+	10.4112i	0.233116	+	0.896050i
$136$	0.743690	+	2.28884i	0.0637709	+	0.196267i
$137$	−12.3527	−	4.01364i	−1.05536	−	0.342908i	−0.270592	−	0.962694i	$-0.587219\pi$
$137$	−12.3527	−	4.01364i	−1.05536	−	0.342908i	−0.784771	+	0.619786i	$0.787219\pi$
$138$	15.4505	+	5.02017i	1.31523	+	0.427346i
$139$	4.28927	+	13.2010i	0.363811	+	1.11969i	0.950722	+	0.310044i	$0.100344\pi$
$139$	4.28927	+	13.2010i	0.363811	+	1.11969i	−0.586912	+	0.809651i	$0.699656\pi$
$140$	25.3351	−	16.1918i	2.14121	−	1.36845i
$141$	2.66957	−	8.21608i	0.224818	−	0.691919i
$142$	−20.0147	+	27.5478i	−1.67959	+	2.31176i
$143$			27.2059i			2.27507i
$144$	−0.224197	−	0.162889i	−0.0186831	−	0.0135741i
$145$	−2.01855	−	3.15841i	−0.167632	−	0.262292i
$146$	−2.66899	+	1.93914i	−0.220888	+	0.160484i
$147$	−13.1910	−	18.1558i	−1.08797	−	1.49746i
$148$	−17.4819	+	5.68020i	−1.43700	+	0.466910i
$149$	3.72754			0.305372			0.152686	−	0.988275i	$-0.451208\pi$
$149$	3.72754			0.305372			0.152686	+	0.988275i	$0.451208\pi$
$150$	15.1884	+	14.0816i	1.24013	+	1.14976i
$151$	3.58849			0.292027			0.146013	−	0.989283i	$-0.453356\pi$
$151$	3.58849			0.292027			0.146013	+	0.989283i	$0.453356\pi$
$152$	−8.05588	+	2.61751i	−0.653418	+	0.212308i
$153$	0.226388	+	0.311597i	0.0183024	+	0.0251911i
$154$	−39.9634	+	29.0351i	−3.22034	+	2.33972i
$155$	−7.81841	+	9.51246i	−0.627990	+	0.764059i
$156$	24.8183	+	18.0316i	1.98706	+	1.44368i
$157$		−	22.1837i		−	1.77046i	−0.465157	−	0.885228i	$-0.654002\pi$
$157$		−	22.1837i		−	1.77046i	0.465157	−	0.885228i	$-0.345998\pi$
$158$	5.27358	−	7.25846i	0.419543	−	0.577452i
$159$	−4.34843	+	13.3831i	−0.344853	+	1.06135i
$160$	14.3595	+	0.857441i	1.13522	+	0.0677867i
$161$	5.30998	+	16.3424i	0.418485	+	1.28796i
$162$	−21.4276	−	6.96225i	−1.68351	−	0.547006i
$163$	2.93896	+	0.954927i	0.230197	+	0.0747957i	0.421844	−	0.906668i	$-0.361383\pi$
$163$	2.93896	+	0.954927i	0.230197	+	0.0747957i	−0.191647	+	0.981464i	$0.561383\pi$
$164$	4.24184	+	13.0550i	0.331232	+	1.01943i
$165$	−15.9155	−	13.0812i	−1.23902	−	1.01837i
$166$	−8.03188	+	24.7196i	−0.623395	+	1.91861i
$167$	5.84400	−	8.04357i	0.452222	−	0.622430i	−0.520651	−	0.853770i	$-0.674311\pi$
$167$	5.84400	−	8.04357i	0.452222	−	0.622430i	0.972873	+	0.231339i	$0.0743107\pi$
$168$			19.4008i			1.49681i
$169$	13.3627	+	9.70859i	1.02790	+	0.746815i
$170$	−4.68671	−	1.83833i	−0.359454	−	0.140993i
$171$	−1.09671	+	0.796803i	−0.0838671	+	0.0609330i
$172$	−4.94187	−	6.80190i	−0.376814	−	0.518640i
$173$	−15.6643	+	5.08964i	−1.19093	+	0.386958i	−0.836418	−	0.548092i	$-0.815354\pi$
$173$	−15.6643	+	5.08964i	−1.19093	+	0.386958i	−0.354516	+	0.935050i	$0.615354\pi$
$174$	6.94388			0.526414
$175$	−2.60700	+	21.7518i	−0.197071	+	1.64428i
$176$	−3.60298			−0.271585
$177$	−11.1075	+	3.60904i	−0.834889	+	0.271272i
$178$	18.0812	+	24.8866i	1.35524	+	1.86533i
$179$	18.4521	−	13.4062i	1.37917	−	1.00203i	0.382217	−	0.924073i	$-0.375161\pi$
$179$	18.4521	−	13.4062i	1.37917	−	1.00203i	0.996957	−	0.0779556i	$-0.0248392\pi$
$180$	−2.55792	+	0.665467i	−0.190656	+	0.0496010i
$181$	−17.5195	−	12.7287i	−1.30222	−	0.946116i	−0.302242	−	0.953231i	$-0.597735\pi$
$181$	−17.5195	−	12.7287i	−1.30222	−	0.946116i	−0.999975	+	0.00711506i	$0.997735\pi$
$182$			53.5942i			3.97267i
$183$	1.68344	−	2.31705i	0.124443	−	0.171282i
$184$	2.91662	−	8.97645i	0.215016	−	0.661752i
$185$	4.89055	−	12.4682i	0.359561	−	0.916679i
$186$	−7.04880	−	21.6940i	−0.516843	−	1.59068i
$187$	4.76246	+	1.54742i	0.348265	+	0.113158i
$188$	−13.7045	−	4.45286i	−0.999504	−	0.324758i
$189$	−6.51387	−	20.0476i	−0.473814	−	1.45825i
$190$	6.47023	−	16.4955i	0.469400	−	1.19671i
$191$	−3.24665	+	9.99216i	−0.234919	+	0.723008i	0.762213	+	0.647327i	$0.224113\pi$
$191$	−3.24665	+	9.99216i	−0.234919	+	0.723008i	−0.997132	+	0.0756810i	$0.975887\pi$
$192$	−14.1074	+	19.4172i	−1.01811	+	1.40131i
$193$		−	14.4285i		−	1.03859i	−0.854596	−	0.519293i	$-0.826195\pi$
$193$		−	14.4285i		−	1.03859i	0.854596	−	0.519293i	$-0.173805\pi$
$194$	−20.0305	−	14.5530i	−1.43811	−	1.04484i
$195$	−21.6317	+	5.62770i	−1.54908	+	0.403008i
$196$	−30.2840	+	22.0026i	−2.16314	+	1.57162i
$197$	−1.87241	−	2.57716i	−0.133404	−	0.183615i	0.737089	−	0.675796i	$-0.236200\pi$
$197$	−1.87241	−	2.57716i	−0.133404	−	0.183615i	−0.870493	+	0.492181i	$0.836200\pi$
$198$	4.12976	−	1.34184i	0.293489	−	0.0953604i
$199$	−0.482209			−0.0341829			−0.0170914	−	0.999854i	$-0.505441\pi$
$199$	−0.482209			−0.0341829			−0.0170914	+	0.999854i	$0.505441\pi$
$200$	8.18113	−	8.82417i	0.578493	−	0.623963i
$201$	−21.8208			−1.53912
$202$	6.69564	−	2.17554i	0.471103	−	0.153071i
$203$	4.31713	+	5.94202i	0.303003	+	0.417048i
$204$	4.56809	−	3.31891i	0.319830	−	0.232370i
$205$	−9.31094	−	3.65215i	−0.650304	−	0.255077i
$206$	9.86779	+	7.16937i	0.687522	+	0.499514i
$207$		−	1.51051i		−	0.104988i
$208$	−2.29770	+	3.16251i	−0.159317	+	0.219281i
$209$	−5.44633	+	16.7621i	−0.376731	+	1.15946i
$210$	−31.3528	−	25.7693i	−2.16355	−	1.77825i
$211$	4.36987	+	13.4491i	0.300834	+	0.925873i	0.981199	+	0.192999i	$0.0618215\pi$
$211$	4.36987	+	13.4491i	0.300834	+	0.925873i	−0.680364	+	0.732874i	$0.738178\pi$
$212$	22.3231	+	7.25322i	1.53316	+	0.498153i
$213$	26.4647	+	8.59890i	1.81333	+	0.589187i
$214$	−7.87877	−	24.2484i	−0.538582	−	1.65758i
$215$	6.11501	+	0.365143i	0.417040	+	0.0249026i
$216$	−3.57789	+	11.0116i	−0.243445	+	0.749245i
$217$	14.1816	−	19.5193i	0.962710	−	1.32506i
$218$			15.1097i			1.02336i
$219$	2.18111	+	1.58467i	0.147386	+	0.107082i
$220$	−21.8195	+	26.5473i	−1.47107	+	1.78982i
$221$	4.39537	−	3.19342i	0.295665	−	0.214813i
$222$	14.5834	+	20.0724i	0.978776	+	1.34717i
$223$	23.2997	−	7.57052i	1.56026	−	0.506960i	0.603384	−	0.797451i	$-0.293819\pi$
$223$	23.2997	−	7.57052i	1.56026	−	0.506960i	0.956878	+	0.290491i	$0.0938186\pi$
$224$	−28.1869			−1.88332
$225$	0.808821	−	1.74769i	0.0539214	−	0.116513i
$226$	5.18974			0.345216
$227$	8.00915	−	2.60233i	0.531586	−	0.172723i	−0.0309110	−	0.999522i	$-0.509841\pi$
$227$	8.00915	−	2.60233i	0.531586	−	0.172723i	0.562497	+	0.826799i	$0.309841\pi$
$228$	11.6813	+	16.0780i	0.773615	+	1.06479i
$229$	23.7765	−	17.2747i	1.57120	−	1.14154i	0.645200	−	0.764013i	$-0.276774\pi$
$229$	23.7765	−	17.2747i	1.57120	−	1.14154i	0.925998	−	0.377529i	$-0.123226\pi$
$230$	10.6324	+	16.6365i	0.701081	+	1.09698i
$231$	32.6583	+	23.7276i	2.14876	+	1.56116i
$232$		−	4.03426i		−	0.264862i
$233$	−9.96020	+	13.7090i	−0.652515	+	0.898109i	−0.999205	−	0.0398703i	$-0.987306\pi$
$233$	−9.96020	+	13.7090i	−0.652515	+	0.898109i	0.346690	+	0.937980i	$0.387306\pi$
$234$	1.45584	−	4.48062i	0.0951713	−	0.292907i
$235$	8.84674	−	5.65398i	0.577098	−	0.368825i
$236$	6.01990	+	18.5274i	0.391862	+	1.20603i
$237$	−6.97307	−	2.26569i	−0.452950	−	0.147172i
$238$	9.38180	+	3.04833i	0.608132	+	0.197594i
$239$	−2.61216	−	8.03941i	−0.168967	−	0.520026i	0.830340	−	0.557257i	$-0.188146\pi$
$239$	−2.61216	−	8.03941i	−0.168967	−	0.520026i	−0.999307	+	0.0372311i	$0.988146\pi$
$240$	−0.745298	−	2.86477i	−0.0481088	−	0.184920i
$241$	2.74337	−	8.44321i	0.176716	−	0.543875i	−0.822992	−	0.568053i	$-0.807697\pi$
$241$	2.74337	−	8.44321i	0.176716	−	0.543875i	0.999708	+	0.0241779i	$0.00769681\pi$
$242$	18.6269	−	25.6377i	1.19738	−	1.64806i
$243$			3.97889i			0.255246i
$244$	−3.86487	−	2.80799i	−0.247423	−	0.179763i
$245$	1.62572	−	27.2258i	0.103864	−	1.73939i
$246$	14.9896	−	10.8906i	0.955700	−	0.694357i
$247$	11.2397	+	15.4701i	0.715163	+	0.984338i
$248$	−12.6038	+	4.09522i	−0.800341	+	0.260047i
$249$	21.2406			1.34607
$250$	3.39371	+	24.9419i	0.214637	+	1.57747i
$251$	−25.3643			−1.60098			−0.800489	−	0.599347i	$-0.795427\pi$
$251$	−25.3643			−1.60098			−0.800489	+	0.599347i	$0.795427\pi$
$252$	4.92550	−	1.60039i	0.310278	−	0.100815i
$253$	−11.5434	−	15.8881i	−0.725725	−	0.998875i
$254$	−24.6897	+	17.9381i	−1.54917	+	1.12554i
$255$	−0.245227	+	4.10678i	−0.0153567	+	0.257177i
$256$	8.95262	+	6.50446i	0.559539	+	0.406529i
$257$		−	9.60204i		−	0.598958i	−0.954103	−	0.299479i	$-0.903187\pi$
$257$		−	9.60204i		−	0.598958i	0.954103	−	0.299479i	$-0.0968129\pi$
$258$	−6.67039	+	9.18101i	−0.415280	+	0.571585i
$259$	−8.10957	+	24.9587i	−0.503904	+	1.55086i
$260$	9.38705	+	36.0819i	0.582160	+	2.23770i
$261$	−0.199514	−	0.614040i	−0.0123496	−	0.0380081i
$262$	13.3119	+	4.32530i	0.822412	+	0.267218i
$263$	−27.2554	−	8.85582i	−1.68064	−	0.546073i	−0.695605	−	0.718425i	$-0.744864\pi$
$263$	−27.2554	−	8.85582i	−1.68064	−	0.546073i	−0.985036	+	0.172351i	$0.944864\pi$
$264$	−6.85182	−	21.0877i	−0.421700	−	1.29786i
$265$	−14.4104	+	9.20970i	−0.885221	+	0.565747i
$266$	−10.7290	+	33.0205i	−0.657837	+	2.02461i
$267$	14.7760	−	20.3375i	0.904279	−	1.24463i
$268$			36.3973i			2.22332i
$269$	1.19700	+	0.869674i	0.0729826	+	0.0530250i	0.623678	−	0.781681i	$-0.285638\pi$
$269$	1.19700	+	0.869674i	0.0729826	+	0.0530250i	−0.550696	+	0.834706i	$0.685638\pi$
$270$	−13.0430	−	20.4083i	−0.793773	−	1.24201i
$271$	17.0860	−	12.4137i	1.03790	−	0.754079i	0.0680265	−	0.997684i	$-0.478330\pi$
$271$	17.0860	−	12.4137i	1.03790	−	0.754079i	0.969875	+	0.243604i	$0.0783298\pi$
$272$	0.422917	+	0.582096i	0.0256431	+	0.0352947i
$273$	41.6538	−	13.5342i	2.52101	−	0.819124i
$274$	29.2425			1.76660
$275$	−4.84842	−	24.5638i	−0.292371	−	1.48125i
$276$	−22.1445			−1.33294
$277$	−0.322393	+	0.104752i	−0.0193707	+	0.00629393i	−0.318686	−	0.947860i	$-0.603242\pi$
$277$	−0.322393	+	0.104752i	−0.0193707	+	0.00629393i	0.299316	+	0.954154i	$0.403242\pi$
$278$	−18.3687	−	25.2823i	−1.10168	−	1.51633i
$279$	−1.71585	+	1.24663i	−0.102725	+	0.0746341i
$280$	−14.9715	+	18.2154i	−0.894716	+	1.08858i
$281$	1.02639	+	0.745717i	0.0612294	+	0.0444858i	0.617979	−	0.786195i	$-0.287952\pi$
$281$	1.02639	+	0.745717i	0.0612294	+	0.0444858i	−0.556750	+	0.830680i	$0.687952\pi$
$282$			19.4499i			1.15822i
$283$	1.19086	−	1.63908i	0.0707893	−	0.0974331i	−0.772154	−	0.635435i	$-0.780821\pi$
$283$	1.19086	−	1.63908i	0.0707893	−	0.0974331i	0.842944	+	0.538002i	$0.180821\pi$
$284$	14.3430	−	44.1433i	0.851102	−	2.61942i
$285$	−14.4543	−	0.863107i	−0.856201	−	0.0511260i
$286$	−18.9279	−	58.2542i	−1.11923	−	3.44464i
$287$	18.6385	+	6.05603i	1.10020	+	0.357476i
$288$	2.35650	+	0.765674i	0.138858	+	0.0451178i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	6.51960	+	5.35854i	0.382844	+	0.314664i
$291$	−6.25241	+	19.2429i	−0.366523	+	1.12804i
$292$	2.64325	−	3.63812i	0.154684	−	0.212905i
$293$			1.82547i			0.106645i	0.998577	+	0.0533227i	$0.0169812\pi$
$293$			1.82547i			0.106645i	−0.998577	+	0.0533227i	$0.983019\pi$
$294$	40.8765	+	29.6985i	2.38397	+	1.73205i
$295$	−13.2138	−	5.18303i	−0.769340	−	0.301768i
$296$	11.6617	−	8.47270i	0.677821	−	0.492466i
$297$	14.1605	+	19.4903i	0.821676	+	1.13094i
$298$	−7.98155	+	2.59336i	−0.462359	+	0.150229i
$299$	−21.3072			−1.23223
$300$	−25.6216	−	11.8575i	−1.47926	−	0.684594i
$301$	−12.0035			−0.691868
$302$	−7.68380	+	2.49662i	−0.442153	+	0.143664i
$303$	−3.38170	−	4.65451i	−0.194274	−	0.267395i
$304$	−2.04876	+	1.48851i	−0.117505	+	0.0853721i
$305$	3.36863	−	0.876381i	0.192887	−	0.0501814i
$306$	−0.701538	−	0.509697i	−0.0401043	−	0.0291375i
$307$			19.7199i			1.12548i	0.826635	+	0.562738i	$0.190252\pi$
$307$			19.7199i			1.12548i	−0.826635	+	0.562738i	$0.809748\pi$
$308$	39.5779	−	54.4743i	2.25516	−	3.10396i
$309$	3.08018	−	9.47981i	0.175225	−	0.539287i
$310$	10.1230	−	25.8079i	0.574946	−	1.46579i
$311$	−2.78338	−	8.56636i	−0.157831	−	0.485754i	0.840606	−	0.541647i	$-0.182199\pi$
$311$	−2.78338	−	8.56636i	−0.157831	−	0.485754i	−0.998437	+	0.0558937i	$0.982199\pi$
$312$	−22.8793	−	7.43394i	−1.29529	−	0.420864i
$313$	−13.7844	−	4.47883i	−0.779141	−	0.253158i	−0.107668	−	0.994187i	$-0.534338\pi$
$313$	−13.7844	−	4.47883i	−0.779141	−	0.253158i	−0.671473	+	0.741029i	$0.734338\pi$
$314$	15.4339	+	47.5007i	0.870985	+	2.68062i
$315$	−1.37791	+	3.51290i	−0.0776365	+	0.197930i
$316$	−3.77919	+	11.6311i	−0.212596	+	0.654303i
$317$	−2.05597	+	2.82980i	−0.115475	+	0.158937i	−0.862842	−	0.505474i	$-0.831318\pi$
$317$	−2.05597	+	2.82980i	−0.115475	+	0.158937i	0.747367	+	0.664411i	$0.231318\pi$
$318$		−	31.6817i		−	1.77662i
$319$	−6.79106	−	4.93399i	−0.380226	−	0.276250i
$320$	−28.2295	+	7.34417i	−1.57808	+	0.410551i
$321$	−16.8564	+	12.2469i	−0.940832	+	0.683554i
$322$	−22.7398	−	31.2987i	−1.26724	−	1.74421i
$323$	3.34737	−	1.08763i	0.186252	−	0.0605171i
$324$	30.7112			1.70618
$325$	−24.6528	−	11.4092i	−1.36749	−	0.632868i
$326$	−6.95739			−0.385334
$327$	11.7434	−	3.81567i	0.649412	−	0.211007i
$328$	−6.32721	−	8.70865i	−0.349362	−	0.480855i
$329$	−16.6436	+	12.0923i	−0.917594	+	0.666671i
$330$	43.1799	+	16.9370i	2.37698	+	0.932351i
$331$	−23.9396	−	17.3931i	−1.31584	−	0.956014i	−0.999974	−	0.00720969i	$-0.997705\pi$
$331$	−23.9396	−	17.3931i	−1.31584	−	0.956014i	−0.315866	−	0.948804i	$-0.602295\pi$
$332$		−	35.4294i		−	1.94444i
$333$	1.35596	−	1.86632i	0.0743063	−	0.102274i
$334$	−6.91723	+	21.2890i	−0.378494	+	1.16488i
$335$	−20.4875	−	16.8389i	−1.11935	−	0.920009i
$336$	1.79238	+	5.51638i	0.0977823	+	0.300943i
$337$	−21.7116	−	7.05453i	−1.18271	−	0.384285i	−0.349335	−	0.936998i	$-0.613593\pi$
$337$	−21.7116	−	7.05453i	−1.18271	−	0.384285i	−0.833372	+	0.552713i	$0.813593\pi$
$338$	−35.3673	−	11.4915i	−1.92373	−	0.625057i
$339$	−1.31057	−	4.03351i	−0.0711802	−	0.219070i
$340$	6.85014	+	0.409040i	0.371501	+	0.0221833i
$341$	−8.52104	+	26.2251i	−0.461440	+	1.42017i
$342$	1.79395	−	2.46915i	0.0970055	−	0.133517i
$343$			22.7725i			1.22960i
$344$	5.33399	+	3.87537i	0.287589	+	0.208946i
$345$	10.2450	−	12.4648i	0.551571	−	0.671083i
$346$	29.9999	−	21.7962i	1.61281	−	1.17177i
$347$	−13.9980	−	19.2666i	−0.751453	−	1.03429i	−0.997877	−	0.0651248i	$-0.979255\pi$
$347$	−13.9980	−	19.2666i	−0.751453	−	1.03429i	0.246424	−	0.969162i	$-0.420745\pi$
$348$	−9.00198	+	2.92492i	−0.482557	+	0.156792i
$349$	−3.74351			−0.200385			−0.100193	−	0.994968i	$-0.531946\pi$
$349$	−3.74351			−0.200385			−0.100193	+	0.994968i	$0.531946\pi$
$350$	−9.55114	−	48.3894i	−0.510530	−	2.58652i
$351$	26.1380			1.39515
$352$	30.6378	−	9.95482i	1.63300	−	0.530594i
$353$	−16.0607	−	22.1057i	−0.854826	−	1.17657i	−0.982779	−	0.184787i	$-0.940840\pi$
$353$	−16.0607	−	22.1057i	−0.854826	−	1.17657i	0.127952	−	0.991780i	$-0.459160\pi$
$354$	21.2728	−	15.4556i	1.13064	−	0.821456i
$355$	18.2119	+	28.4961i	0.966589	+	1.51241i
$356$	−33.9231	−	24.6466i	−1.79792	−	1.30627i
$357$		−	8.06141i		−	0.426655i
$358$	−30.1832	+	41.5436i	−1.59523	+	2.19565i
$359$	−2.56176	+	7.88427i	−0.135204	+	0.416116i	−0.995622	−	0.0934739i	$-0.970203\pi$
$359$	−2.56176	+	7.88427i	−0.135204	+	0.416116i	0.860417	+	0.509590i	$0.170203\pi$
$360$	1.74646	−	1.11617i	0.0920465	−	0.0588272i
$361$	−2.04328	−	6.28858i	−0.107541	−	0.330978i
$362$	46.3692	+	15.0663i	2.43711	+	0.791866i
$363$	−24.6297	−	8.00268i	−1.29273	−	0.420032i
$364$	−22.5751	−	69.4790i	−1.18326	−	3.64169i
$365$	0.824964	+	3.17099i	0.0431806	+	0.165977i
$366$	−1.99260	+	6.13258i	−0.104155	+	0.320555i
$367$	−17.7309	+	24.4044i	−0.925543	+	1.27390i	0.0360292	+	0.999351i	$0.488529\pi$
$367$	−17.7309	+	24.4044i	−0.925543	+	1.27390i	−0.961573	+	0.274551i	$0.911471\pi$
$368$		−	2.82180i		−	0.147096i
$369$	−1.39372	−	1.01260i	−0.0725544	−	0.0527138i
$370$	−1.79734	+	30.0998i	−0.0934392	+	1.56482i
$371$	27.1106	−	19.6970i	1.40751	−	1.02262i
$372$	18.2760	+	25.1547i	0.947566	+	1.30421i
$373$	20.8676	−	6.78030i	1.08048	−	0.351070i	0.285921	−	0.958253i	$-0.407700\pi$
$373$	20.8676	−	6.78030i	1.08048	−	0.351070i	0.794562	+	0.607183i	$0.207700\pi$
$374$	−11.2741			−0.582972
$375$	18.5280	−	8.93620i	0.956784	−	0.461464i
$376$	11.3000			0.582753
$377$	−8.66162	+	2.81433i	−0.446096	+	0.144945i
$378$	27.8955	+	38.3948i	1.43479	+	1.97482i
$379$	−0.981148	+	0.712845i	−0.0503982	+	0.0366164i	−0.612699	−	0.790316i	$-0.709916\pi$
$379$	−0.981148	+	0.712845i	−0.0503982	+	0.0366164i	0.562301	+	0.826933i	$0.309916\pi$
$380$	−1.43967	+	24.1100i	−0.0738535	+	1.23682i
$381$	20.1765	+	14.6591i	1.03367	+	0.751008i
$382$		−	23.6544i		−	1.21026i
$383$	−2.30108	+	3.16717i	−0.117580	+	0.161835i	−0.863750	−	0.503920i	$-0.831890\pi$
$383$	−2.30108	+	3.16717i	−0.117580	+	0.161835i	0.746170	+	0.665755i	$0.231890\pi$
$384$	9.38295	−	28.8777i	0.478821	−	1.47366i
$385$	12.3524	+	47.4799i	0.629535	+	2.41980i
$386$	10.0383	+	30.8949i	0.510938	+	1.57251i
$387$	1.00352	+	0.326064i	0.0510119	+	0.0165748i
$388$	32.0974	+	10.4291i	1.62950	+	0.529456i
$389$	−2.16043	−	6.64913i	−0.109538	−	0.337124i	0.881230	−	0.472687i	$-0.156716\pi$
$389$	−2.16043	−	6.64913i	−0.109538	−	0.337124i	−0.990769	+	0.135563i	$0.956716\pi$
$390$	42.4033	−	27.1001i	2.14717	−	1.37227i
$391$	−1.21191	+	3.72988i	−0.0612890	+	0.188628i
$392$	17.2543	−	23.7485i	0.871472	−	1.19948i
$393$		−	11.4384i		−	0.576990i
$394$	5.80229	+	4.21561i	0.292315	+	0.212379i
$395$	−4.79859	−	7.50831i	−0.241443	−	0.377784i
$396$	−4.78856	+	3.47910i	−0.240634	+	0.174831i
$397$	−4.79924	−	6.60559i	−0.240867	−	0.331525i	0.671420	−	0.741077i	$-0.265685\pi$
$397$	−4.79924	−	6.60559i	−0.240867	−	0.331525i	−0.912287	+	0.409552i	$0.865685\pi$
$398$	1.03252	−	0.335487i	0.0517557	−	0.0168165i
$399$	28.3732			1.42044
$400$	1.51096	−	3.26487i	0.0755482	−	0.163243i
$401$	−2.43570			−0.121633			−0.0608165	−	0.998149i	$-0.519370\pi$
$401$	−2.43570			−0.121633			−0.0608165	+	0.998149i	$0.519370\pi$
$402$	46.7235	−	15.1814i	2.33035	−	0.757178i
$403$	17.5850	+	24.2036i	0.875970	+	1.20567i
$404$	−7.76377	+	5.64071i	−0.386262	+	0.280636i
$405$	−14.2083	+	17.2869i	−0.706017	+	0.858992i
$406$	−13.3780	−	9.71971i	−0.663941	−	0.482381i
$407$		−	29.9929i		−	1.48669i
$408$	−2.60266	+	3.58225i	−0.128851	+	0.177348i
$409$	10.2770	−	31.6295i	0.508167	−	1.56398i	−0.287213	−	0.957867i	$-0.592729\pi$
$409$	10.2770	−	31.6295i	0.508167	−	1.56398i	0.795380	−	0.606111i	$-0.207271\pi$
$410$	22.4778	+	1.34221i	1.11010	+	0.0662870i
$411$	−7.38460	−	22.7275i	−0.364256	−	1.12106i
$412$	−15.8124	−	5.13776i	−0.779021	−	0.253119i
$413$	26.4513	+	8.59456i	1.30158	+	0.422911i
$414$	1.05091	+	3.23436i	0.0516493	+	0.158960i
$415$	19.9427	+	16.3912i	0.978949	+	0.804611i
$416$	10.8006	−	33.2407i	0.529541	−	1.62976i
$417$	−15.0110	+	20.6608i	−0.735090	+	1.01176i
$418$		−	39.6808i		−	1.94085i
$419$	14.3456	+	10.4227i	0.700826	+	0.509180i	0.880201	−	0.474601i	$-0.157408\pi$
$419$	14.3456	+	10.4227i	0.700826	+	0.509180i	−0.179375	+	0.983781i	$0.557408\pi$
$420$	51.5001	+	20.2005i	2.51295	+	0.985685i
$421$	−9.06728	+	6.58776i	−0.441912	+	0.321068i	−0.786394	−	0.617725i	$-0.788054\pi$
$421$	−9.06728	+	6.58776i	−0.441912	+	0.321068i	0.344482	+	0.938793i	$0.388054\pi$
$422$	−18.7139	−	25.7574i	−0.910977	−	1.25385i
$423$	1.71993	−	0.558839i	0.0836259	−	0.0271717i
$424$	−18.4065			−0.893896
$425$	−3.39941	+	3.66661i	−0.164896	+	0.177857i
$426$	−62.6496			−3.03539
$427$	−6.48660	+	2.10762i	−0.313909	+	0.101995i
$428$	20.4279	+	28.1166i	0.987420	+	1.35907i
$429$	−40.4958	+	29.4219i	−1.95515	+	1.42050i
$430$	−13.3477	+	3.47254i	−0.643684	+	0.167461i
$431$	23.0408	+	16.7401i	1.10983	+	0.806342i	0.982638	−	0.185535i	$-0.0594019\pi$
$431$	23.0408	+	16.7401i	1.10983	+	0.806342i	0.127197	+	0.991877i	$0.459402\pi$
$432$			3.46156i			0.166544i
$433$	−12.6541	+	17.4169i	−0.608118	+	0.837002i	−0.996421	−	0.0845295i	$-0.973061\pi$
$433$	−12.6541	+	17.4169i	−0.608118	+	0.837002i	0.388303	+	0.921532i	$0.373061\pi$
$434$	−16.7860	+	51.6620i	−0.805754	+	2.47986i
$435$	2.51830	−	6.42027i	0.120743	−	0.307829i
$436$	−6.36456	−	19.5881i	−0.304807	−	0.938100i
$437$	−13.1278	−	4.26548i	−0.627988	−	0.204046i
$438$	−5.77279	−	1.87569i	−0.275834	−	0.0896240i
$439$	−3.09157	−	9.51486i	−0.147552	−	0.454120i	0.849778	−	0.527141i	$-0.176736\pi$
$439$	−3.09157	−	9.51486i	−0.147552	−	0.454120i	−0.997330	+	0.0730212i	$0.976736\pi$
$440$	9.84008	−	25.0867i	0.469107	−	1.19596i
$441$	1.45173	−	4.46797i	0.0691300	−	0.212760i
$442$	−7.18977	+	9.89587i	−0.341982	+	0.470698i
$443$			12.6152i			0.599368i	0.954039	+	0.299684i	$0.0968812\pi$
$443$			12.6152i			0.599368i	−0.954039	+	0.299684i	$0.903119\pi$
$444$	−27.3608	−	19.8788i	−1.29848	−	0.943404i
$445$	29.5675	−	7.69226i	1.40163	−	0.364648i
$446$	−44.6231	+	32.4206i	−2.11296	+	1.53516i
$447$	4.03116	+	5.54842i	0.190668	+	0.262431i
$448$	54.3584	−	17.6621i	2.56819	−	0.834457i
$449$	−7.92591			−0.374047			−0.187024	−	0.982355i	$-0.559884\pi$
$449$	−7.92591			−0.374047			−0.187024	+	0.982355i	$0.559884\pi$
$450$	−0.515957	+	4.30493i	−0.0243225	+	0.202937i
$451$	−22.3980			−1.05468
$452$	−6.72792	+	2.18604i	−0.316455	+	0.102822i
$453$	3.88078	+	5.34144i	0.182335	+	0.250963i
$454$	−15.3390	+	11.1444i	−0.719893	+	0.523033i
$455$	49.5529	+	19.4368i	2.32308	+	0.911209i
$456$	−12.6082	−	9.16040i	−0.590433	−	0.428975i
$457$		−	2.90103i		−	0.135704i	−0.997695	−	0.0678522i	$-0.978385\pi$
$457$		−	2.90103i		−	0.135704i	0.997695	−	0.0678522i	$-0.0216146\pi$
$458$	−38.8927	+	53.5312i	−1.81734	+	2.50135i
$459$	1.48668	−	4.57553i	0.0693923	−	0.213568i
$460$	−20.7914	−	17.0887i	−0.969404	−	0.796766i
$461$	0.185099	+	0.569675i	0.00862091	+	0.0265324i	0.955274	−	0.295721i	$-0.0955598\pi$
$461$	0.185099	+	0.569675i	0.00862091	+	0.0265324i	−0.946654	+	0.322253i	$0.895560\pi$
$462$	−86.4371	−	28.0851i	−4.02142	−	1.30664i
$463$	19.3206	+	6.27765i	0.897906	+	0.291747i	0.721372	−	0.692547i	$-0.243512\pi$
$463$	19.3206	+	6.27765i	0.897906	+	0.291747i	0.176533	+	0.984295i	$0.443512\pi$
$464$	−0.372713	−	1.14709i	−0.0173027	−	0.0532524i
$465$	−22.6145	−	1.35037i	−1.04872	−	0.0626219i
$466$	11.7894	−	36.2839i	0.546132	−	1.68082i
$467$	−2.12490	+	2.92467i	−0.0983285	+	0.135338i	−0.855346	−	0.518057i	$-0.826656\pi$
$467$	−2.12490	+	2.92467i	−0.0983285	+	0.135338i	0.757018	+	0.653394i	$0.226656\pi$
$468$			6.42186i			0.296851i
$469$	42.0398	+	30.5437i	1.94122	+	1.41038i
$470$	−15.0093	+	18.2614i	−0.692328	+	0.842338i
$471$	33.0204	−	23.9907i	1.52150	−	1.10543i
$472$	−8.97941	−	12.3591i	−0.413311	−	0.568873i
$473$	13.0472	−	4.23928i	0.599909	−	0.194922i
$474$	16.5073			0.758205
$475$	−12.9051	−	11.9647i	−0.592126	−	0.548977i
$476$	−13.4465			−0.616319
$477$	−2.80158	+	0.910287i	−0.128275	+	0.0416792i
$478$	11.1865	+	15.3969i	0.511659	+	0.704238i
$479$	11.6698	−	8.47864i	0.533209	−	0.387399i	−0.288348	−	0.957526i	$-0.593106\pi$
$479$	11.6698	−	8.47864i	0.533209	−	0.387399i	0.821557	+	0.570127i	$0.193106\pi$
$480$	14.2528	+	22.3013i	0.650549	+	1.01791i
$481$	−26.3263	−	19.1272i	−1.20037	−	0.872123i
$482$			19.9876i			0.910408i
$483$	−18.5831	+	25.5774i	−0.845560	+	1.16381i
$484$	−13.3485	+	41.0826i	−0.606752	+	1.86739i
$485$	−20.7200	+	13.2422i	−0.940846	+	0.601298i
$486$	−2.76824	−	8.51975i	−0.125570	−	0.386464i
$487$	−20.1418	−	6.54447i	−0.912713	−	0.296558i	−0.185239	−	0.982694i	$-0.559306\pi$
$487$	−20.1418	−	6.54447i	−0.912713	−	0.296558i	−0.727474	+	0.686135i	$0.759306\pi$
$488$	3.56291	+	1.15766i	0.161285	+	0.0524048i
$489$	1.75695	+	5.40734i	0.0794521	+	0.244528i
$490$	15.4607	+	59.4279i	0.698445	+	2.68468i
$491$	−2.91084	+	8.95863i	−0.131364	+	0.404297i	−0.995007	−	0.0998073i	$-0.968177\pi$
$491$	−2.91084	+	8.95863i	−0.131364	+	0.404297i	0.863643	+	0.504105i	$0.168177\pi$
$492$	−14.8450	+	20.4324i	−0.669263	+	0.921162i
$493$			1.67631i			0.0754973i
$494$	−34.8298	−	25.3053i	−1.56707	−	1.13854i
$495$	0.257062	−	4.30499i	0.0115541	−	0.193495i
$496$	−3.20538	+	2.32885i	−0.143926	+	0.104568i
$497$	−38.9503	−	53.6105i	−1.74716	−	2.40476i
$498$	−45.4811	+	14.7777i	−2.03806	+	0.662204i
$499$	0.395435			0.0177021			0.00885106	−	0.999961i	$-0.497183\pi$
$499$	0.395435			0.0177021			0.00885106	+	0.999961i	$0.497183\pi$
$500$	−14.9057	−	30.9049i	−0.666602	−	1.38211i
$501$	18.2928			0.817263
$502$	54.3109	−	17.6467i	2.42401	−	0.787610i
$503$	16.2835	+	22.4123i	0.726044	+	0.999314i	0.999301	+	0.0373726i	$0.0118988\pi$
$503$	16.2835	+	22.4123i	0.726044	+	0.999314i	−0.273258	+	0.961941i	$0.588101\pi$
$504$	−3.28567	+	2.38718i	−0.146355	+	0.106333i
$505$	0.416779	−	6.97974i	0.0185464	−	0.310594i
$506$	35.7709	+	25.9891i	1.59021	+	1.15535i
$507$			30.3897i			1.34966i
$508$	24.4515	−	33.6546i	1.08486	−	1.49318i
$509$	1.90483	−	5.86246i	0.0844301	−	0.259849i	−0.899925	−	0.436044i	$-0.856379\pi$
$509$	1.90483	−	5.86246i	0.0844301	−	0.259849i	0.984355	+	0.176195i	$0.0563790\pi$
$510$	−2.33212	−	8.96420i	−0.103268	−	0.396941i
$511$	−1.98397	−	6.10604i	−0.0877658	−	0.270115i
$512$	7.69589	+	2.50054i	0.340113	+	0.110510i
$513$	16.1042	+	5.23256i	0.711017	+	0.231023i
$514$	6.68042	+	20.5602i	0.294661	+	0.906873i
$515$	10.2075	−	6.52362i	0.449794	−	0.287465i
$516$	4.78018	−	14.7119i	0.210436	−	0.647655i
$517$	13.8202	−	19.0218i	0.607810	−	0.836578i
$518$		−	59.0845i		−	2.59602i
$519$	−24.5161	−	17.8120i	−1.07614	−	0.781859i
$520$	−15.7446	−	24.6355i	−0.690447	−	1.08034i
$521$	25.9163	−	18.8293i	1.13542	−	0.824928i	0.148942	−	0.988846i	$-0.452413\pi$
$521$	25.9163	−	18.8293i	1.13542	−	0.824928i	0.986474	+	0.163918i	$0.0524133\pi$
$522$	0.854412	+	1.17600i	0.0373966	+	0.0514720i
$523$	−35.2793	+	11.4629i	−1.54266	+	0.501239i	−0.952108	−	0.305763i	$-0.901088\pi$
$523$	−35.2793	+	11.4629i	−1.54266	+	0.501239i	−0.590548	+	0.807002i	$0.701088\pi$
$524$	−19.0793			−0.833485
$525$	−35.1967	+	19.6430i	−1.53611	+	0.857292i
$526$	64.5215			2.81327
$527$	5.23711	−	1.70164i	0.228132	−	0.0741246i
$528$	−3.89646	−	5.36301i	−0.169571	−	0.233395i
$529$	−6.16410	+	4.47848i	−0.268005	+	0.194717i
$530$	24.4485	−	29.7459i	1.06198	−	1.29208i
$531$	−1.97794	−	1.43706i	−0.0858352	−	0.0623629i
$532$		−	47.3267i		−	2.05187i
$533$	−14.2837	+	19.6598i	−0.618695	+	0.851561i
$534$	−17.4896	+	53.8275i	−0.756850	+	2.32934i
$535$	−25.2772	−	1.50937i	−1.09283	−	0.0652558i
$536$	−8.82009	−	27.1454i	−0.380970	−	1.17250i
$537$	39.9102	+	12.9676i	1.72225	+	0.559593i
$538$	−3.16813	−	1.02939i	−0.136588	−	0.0443800i
$539$	−18.8745	−	58.0898i	−0.812982	−	2.50210i
$540$	25.5053	+	20.9631i	1.09757	+	0.902109i
$541$	−7.54380	+	23.2174i	−0.324333	+	0.998196i	0.647407	+	0.762144i	$0.275853\pi$
$541$	−7.54380	+	23.2174i	−0.324333	+	0.998196i	−0.971741	+	0.236051i	$0.924147\pi$
$542$	−27.9486	+	38.4679i	−1.20050	+	1.65234i
$543$		−	39.8432i		−	1.70984i
$544$	−5.20456	−	3.78133i	−0.223144	−	0.162123i
$545$	13.9704	+	5.47978i	0.598425	+	0.234728i
$546$	−79.7746	+	57.9596i	−3.41404	+	2.48044i
$547$	8.00837	+	11.0226i	0.342413	+	0.471291i	0.945144	−	0.326653i	$-0.105921\pi$
$547$	8.00837	+	11.0226i	0.342413	+	0.471291i	−0.602731	+	0.797944i	$0.705921\pi$
$548$	−37.9096	+	12.3176i	−1.61942	+	0.526181i
$549$	0.599549			0.0255881
$550$	27.4714	+	49.2237i	1.17138	+	2.09891i
$551$	−5.90000			−0.251348
$552$	16.5156	−	5.36624i	0.702950	−	0.228402i
$553$	10.2629	+	14.1256i	0.436421	+	0.600683i
$554$	0.617441	−	0.448597i	0.0262326	−	0.0190591i
$555$	23.8477	−	6.20421i	1.01228	−	0.263354i
$556$	34.4624	+	25.0384i	1.46153	+	1.06187i
$557$			9.29003i			0.393631i	0.980441	+	0.196816i	$0.0630600\pi$
$557$			9.29003i			0.393631i	−0.980441	+	0.196816i	$0.936940\pi$
$558$	2.80671	−	3.86311i	0.118818	−	0.163538i
$559$	4.59944	−	14.1556i	0.194536	−	0.598719i
$560$	−2.57408	+	6.56248i	−0.108775	+	0.277315i
$561$	2.84706	+	8.76235i	0.120203	+	0.369947i
$562$	−2.71657	−	0.882666i	−0.114591	−	0.0372330i
$563$	1.91463	+	0.622102i	0.0806922	+	0.0262185i	0.349085	−	0.937091i	$-0.386492\pi$
$563$	1.91463	+	0.622102i	0.0806922	+	0.0262185i	−0.268393	+	0.963310i	$0.586492\pi$
$564$	−8.19273	−	25.2146i	−0.344976	−	1.06173i
$565$	1.88214	−	4.79840i	0.0791821	−	0.201870i
$566$	−1.40956	+	4.33817i	−0.0592481	+	0.182347i
$567$	25.7721	−	35.4722i	1.08233	−	1.48969i
$568$			36.3982i			1.52724i
$569$	−33.6342	−	24.4366i	−1.41002	−	1.02444i	−0.993320	−	0.115392i	$-0.963187\pi$
$569$	−33.6342	−	24.4366i	−1.41002	−	1.02444i	−0.416697	−	0.909045i	$-0.636813\pi$
$570$	31.5507	−	8.20820i	1.32151	−	0.343804i
$571$	20.1781	−	14.6603i	0.844428	−	0.613513i	−0.0791764	−	0.996861i	$-0.525229\pi$
$571$	20.1781	−	14.6603i	0.844428	−	0.613513i	0.923604	+	0.383348i	$0.125229\pi$
$572$	49.0760	+	67.5473i	2.05197	+	2.82429i
$573$	−18.3844	+	5.97345i	−0.768018	+	0.249544i
$574$	−44.1229			−1.84165
$575$	19.2380	−	3.79721i	0.802279	−	0.158354i
$576$	−5.02428			−0.209345
$577$	−30.8847	+	10.0350i	−1.28575	+	0.417764i	−0.870600	−	0.491991i	$-0.836269\pi$
$577$	−30.8847	+	10.0350i	−1.28575	+	0.417764i	−0.415145	+	0.909755i	$0.636269\pi$
$578$	1.32336	+	1.82144i	0.0550444	+	0.0757621i
$579$	21.4767	−	15.6038i	0.892543	−	0.648470i
$580$	−10.7091	−	4.20055i	−0.444670	−	0.174419i
$581$	−40.9219	−	29.7315i	−1.69773	−	1.23347i
$582$		−	45.5536i		−	1.88826i
$583$	−22.5115	+	30.9844i	−0.932331	+	1.28324i
$584$	−1.08974	+	3.35388i	−0.0450938	+	0.138785i
$585$	−3.61477	−	2.97103i	−0.149452	−	0.122837i
$586$	−1.27004	−	3.90877i	−0.0524647	−	0.161470i
$587$	39.4884	+	12.8306i	1.62986	+	0.529574i	0.974239	−	0.225517i	$-0.0724071\pi$
$587$	39.4884	+	12.8306i	1.62986	+	0.529574i	0.655621	+	0.755090i	$0.272407\pi$
$588$	−65.5016	−	21.2827i	−2.70124	−	0.877686i
$589$	5.98914	+	18.4327i	0.246778	+	0.759506i
$590$	31.9000	+	1.90483i	1.31330	+	0.0784206i
$591$	1.81115	−	5.57415i	0.0745008	−	0.229290i
$592$	2.53308	−	3.48649i	0.104109	−	0.143294i
$593$		−	23.1063i		−	0.948862i	−0.880293	−	0.474431i	$-0.842654\pi$
$593$		−	23.1063i		−	0.948862i	0.880293	−	0.474431i	$-0.157346\pi$
$594$	−43.8810	−	31.8814i	−1.80046	−	1.30811i
$595$	6.22092	−	7.56884i	0.255033	−	0.310292i
$596$	9.25482	−	6.72402i	0.379092	−	0.275427i
$597$	−0.521487	−	0.717765i	−0.0213430	−	0.0293762i
$598$	45.6238	−	14.8241i	1.86570	−	0.606201i
$599$	−17.1616			−0.701204			−0.350602	−	0.936525i	$-0.614023\pi$
$599$	−17.1616			−0.701204			−0.350602	+	0.936525i	$0.614023\pi$
$600$	21.9822	+	2.63463i	0.897421	+	0.107558i
$601$	14.5591			0.593876			0.296938	−	0.954897i	$-0.404034\pi$
$601$	14.5591			0.593876			0.296938	+	0.954897i	$0.404034\pi$
$602$	25.7023	−	8.35117i	1.04755	−	0.340368i
$603$	−2.68494	−	3.69551i	−0.109339	−	0.150493i
$604$	8.90956	−	6.47318i	0.362525	−	0.263390i
$605$	−16.9492	−	26.5203i	−0.689082	−	1.07820i
$606$	10.4793	+	7.61366i	0.425693	+	0.309284i
$607$			15.0544i			0.611039i	0.952186	+	0.305520i	$0.0988302\pi$
$607$			15.0544i			0.611039i	−0.952186	+	0.305520i	$0.901170\pi$
$608$	13.3089	−	18.3181i	0.539747	−	0.742898i
$609$	−4.17588	+	12.8520i	−0.169215	+	0.520791i
$610$	−6.60331	+	4.22019i	−0.267360	+	0.170871i
$611$	−7.88296	−	24.2613i	−0.318911	−	0.981506i
$612$	1.12416	+	0.365263i	0.0454416	+	0.0147649i
$613$	26.4289	+	8.58727i	1.06745	+	0.346837i	0.789495	−	0.613757i	$-0.210342\pi$
$613$	26.4289	+	8.58727i	1.06745	+	0.346837i	0.277958	+	0.960593i	$0.410342\pi$
$614$	−13.7197	−	42.2250i	−0.553684	−	1.70406i
$615$	−4.63315	−	17.8089i	−0.186827	−	0.718124i
$616$	−16.3169	+	50.2183i	−0.657427	+	2.02335i
$617$	−1.26046	+	1.73488i	−0.0507444	+	0.0698437i	−0.833635	−	0.552316i	$-0.813744\pi$
$617$	−1.26046	+	1.73488i	−0.0507444	+	0.0698437i	0.782891	+	0.622159i	$0.213744\pi$
$618$			22.4415i			0.902729i
$619$	26.1997	+	19.0352i	1.05306	+	0.765090i	0.972791	−	0.231684i	$-0.0744235\pi$
$619$	26.1997	+	19.0352i	1.05306	+	0.765090i	0.0802645	+	0.996774i	$0.474424\pi$
$620$	−2.25243	+	37.7212i	−0.0904597	+	1.51492i
$621$	−15.2645	+	11.0903i	−0.612542	+	0.445038i
$622$	11.9197	+	16.4061i	0.477938	+	0.657826i
$623$	−56.9349	+	18.4993i	−2.28105	+	0.741157i
$624$	−7.19224			−0.287920
$625$	24.2919	+	5.90776i	0.971678	+	0.236311i
$626$	32.6318			1.30423
$627$	−30.8402	+	10.0206i	−1.23164	+	0.400184i
$628$	−40.0167	−	55.0783i	−1.59684	−	2.19786i
$629$	−4.84564	+	3.52057i	−0.193208	+	0.140374i
$630$	0.506400	−	8.48061i	0.0201754	−	0.337876i
$631$	−21.8137	−	15.8486i	−0.868391	−	0.630923i	0.0617637	−	0.998091i	$-0.480327\pi$
$631$	−21.8137	−	15.8486i	−0.868391	−	0.630923i	−0.930155	+	0.367168i	$0.880327\pi$
$632$		−	9.59043i		−	0.381487i
$633$	−15.2931	+	21.0491i	−0.607845	+	0.836626i
$634$	2.43354	−	7.48966i	0.0966482	−	0.297453i
$635$	7.63137	+	29.3334i	0.302842	+	1.16406i
$636$	13.3450	+	41.0718i	0.529165	+	1.62860i
$637$	−63.0250	−	20.4781i	−2.49714	−	0.811370i
$638$	17.9740	+	5.84010i	0.711597	+	0.231212i
$639$	1.80007	+	5.54004i	0.0712095	+	0.219160i
$640$	31.0943	−	19.8725i	1.22911	−	0.785529i
$641$	−7.57249	+	23.3057i	−0.299095	+	0.920521i	0.682719	+	0.730681i	$0.260797\pi$
$641$	−7.57249	+	23.3057i	−0.299095	+	0.920521i	−0.981815	+	0.189841i	$0.939203\pi$
$642$	27.5730	−	37.9510i	1.08822	−	1.49781i
$643$			23.3381i			0.920366i	0.887824	+	0.460183i	$0.152216\pi$
$643$			23.3381i			0.920366i	−0.887824	+	0.460183i	$0.847784\pi$
$644$	42.6634	+	30.9968i	1.68117	+	1.22144i
$645$	6.06959	+	9.49704i	0.238990	+	0.373946i
$646$	−6.41081	+	4.65773i	−0.252230	+	0.183256i
$647$	−1.58787	−	2.18551i	−0.0624254	−	0.0859212i	0.776663	−	0.629917i	$-0.216911\pi$
$647$	−1.58787	−	2.18551i	−0.0624254	−	0.0859212i	−0.839088	+	0.543995i	$0.816911\pi$
$648$	−22.9047	+	7.44219i	−0.899782	+	0.292357i
$649$	−31.7866			−1.24773
$650$	60.7252	+	7.27807i	2.38184	+	0.285470i
$651$	44.3911			1.73983
$652$	9.01949	−	2.93061i	0.353230	−	0.114772i
$653$	−14.3742	−	19.7844i	−0.562507	−	0.774225i	0.429135	−	0.903240i	$-0.358818\pi$
$653$	−14.3742	−	19.7844i	−0.562507	−	0.774225i	−0.991643	+	0.129015i	$0.958818\pi$
$654$	−22.4907	+	16.3405i	−0.879458	+	0.638963i
$655$	8.82691	−	10.7395i	0.344896	−	0.419626i
$656$	−2.60363	−	1.89164i	−0.101654	−	0.0738563i
$657$			0.564374i			0.0220183i
$658$	27.2250	−	37.4720i	1.06134	−	1.46081i
$659$	11.7408	−	36.1345i	0.457358	−	1.40760i	−0.410987	−	0.911641i	$-0.634816\pi$
$659$	11.7408	−	36.1345i	0.457358	−	1.40760i	0.868345	−	0.495961i	$-0.165184\pi$
$660$	−63.1123	−	3.76860i	−2.45664	−	0.146692i
$661$	−7.80826	−	24.0314i	−0.303706	−	0.934712i	−0.980157	−	0.198224i	$-0.936483\pi$
$661$	−7.80826	−	24.0314i	−0.303706	−	0.934712i	0.676451	−	0.736488i	$-0.263517\pi$
$662$	63.3613	+	20.5873i	2.46261	+	0.800149i
$663$	9.50678	+	3.08894i	0.369213	+	0.119965i
$664$	8.58556	+	26.4236i	0.333184	+	1.02544i
$665$	26.6395	+	21.8953i	1.03304	+	0.849065i
$666$	−1.60498	+	4.93962i	−0.0621917	+	0.191406i
$667$	3.86422	−	5.31865i	0.149623	−	0.205939i
$668$		−	30.5126i		−	1.18057i
$669$	36.4662	+	26.4942i	1.40986	+	1.02433i
$670$	55.5839	+	21.8024i	2.14739	+	0.842299i
$671$	6.30626	−	4.58176i	0.243450	−	0.176877i
$672$	−30.4829	−	41.9561i	−1.17590	−	1.61849i
$673$	−37.3431	+	12.1335i	−1.43947	+	0.467713i	−0.921733	−	0.387825i	$-0.873226\pi$
$673$	−37.3431	+	12.1335i	−1.43947	+	0.467713i	−0.517740	+	0.855538i	$0.673226\pi$
$674$	51.3977			1.97977
$675$	−23.5997	+	4.65812i	−0.908352	+	0.179291i
$676$	50.6903			1.94963
$677$	−6.88202	+	2.23610i	−0.264498	+	0.0859405i	−0.438264	−	0.898846i	$-0.644406\pi$
$677$	−6.88202	+	2.23610i	−0.264498	+	0.0859405i	0.173766	+	0.984787i	$0.444406\pi$
$678$	5.61246	+	7.72489i	0.215545	+	0.296673i
$679$	38.9812	−	28.3215i	1.49596	−	1.08688i
$680$	−5.20803	+	1.35492i	−0.199719	+	0.0519587i
$681$	12.5351	+	9.10726i	0.480345	+	0.348991i
$682$		−	62.0824i		−	2.37726i
$683$	5.92945	−	8.16118i	0.226884	−	0.312279i	−0.680365	−	0.732874i	$-0.738179\pi$
$683$	5.92945	−	8.16118i	0.226884	−	0.312279i	0.907249	+	0.420595i	$0.138179\pi$
$684$	−1.28559	+	3.95664i	−0.0491557	+	0.151286i
$685$	10.6052	−	27.0374i	0.405205	−	1.03305i
$686$	−15.8435	−	48.7613i	−0.604908	−	1.86171i
$687$	51.4265	+	16.7095i	1.96204	+	0.637506i
$688$	1.87468	+	0.609122i	0.0714717	+	0.0232226i
$689$	12.8405	+	39.5189i	0.489183	+	1.50555i
$690$	−13.2648	+	33.8178i	−0.504982	+	1.28742i
$691$	3.15240	−	9.70209i	0.119923	−	0.369085i	−0.873019	−	0.487686i	$-0.837841\pi$
$691$	3.15240	−	9.70209i	0.119923	−	0.369085i	0.992942	+	0.118601i	$0.0378411\pi$
$692$	−29.7106	+	40.8931i	−1.12943	+	1.55452i
$693$			8.45049i			0.321007i
$694$	43.3775	+	31.5156i	1.64659	+	1.19631i
$695$	−30.0376	+	7.81455i	−1.13939	+	0.296423i
$696$	6.00497	−	4.36287i	0.227618	−	0.165374i
$697$	2.62907	+	3.61861i	0.0995832	+	0.137065i
$698$	8.01573	−	2.60447i	0.303400	−	0.0985806i
$699$	−31.1773			−1.17923
$700$	32.7647	+	58.7084i	1.23839	+	2.21897i
$701$	20.7358			0.783181			0.391591	−	0.920140i	$-0.371925\pi$
$701$	20.7358			0.783181			0.391591	+	0.920140i	$0.371925\pi$
$702$	−55.9677	+	18.1850i	−2.11237	+	0.686349i
$703$	−12.3911	−	17.0549i	−0.467339	−	0.643236i
$704$	−52.8471	+	38.3957i	−1.99175	+	1.44709i
$705$	17.9832	+	7.05379i	0.677288	+	0.265661i
$706$	49.7694	+	36.1596i	1.87310	+	1.36088i
$707$			13.7009i			0.515275i
$708$	−21.0676	+	28.9971i	−0.791769	+	1.08978i
$709$	−4.87602	+	15.0069i	−0.183123	+	0.563594i	−0.999911	−	0.0133435i	$-0.995753\pi$
$709$	−4.87602	+	15.0069i	−0.183123	+	0.563594i	0.816788	+	0.576938i	$0.195753\pi$
$710$	−58.8216	−	48.3462i	−2.20754	−	1.81440i
$711$	−0.474292	−	1.45972i	−0.0177873	−	0.0547438i
$712$	31.2728	+	10.1611i	1.17200	+	0.380805i
$713$	−20.5390	−	6.67354i	−0.769193	−	0.249926i
$714$	5.60856	+	17.2614i	0.209895	+	0.645991i
$715$	−60.7260	−	3.62611i	−2.27102	−	0.135609i
$716$	21.6301	−	66.5705i	0.808353	−	2.48786i
$717$	9.14167	−	12.5824i	0.341402	−	0.469900i
$718$		−	18.6644i		−	0.696549i
$719$	38.4531	+	27.9378i	1.43406	+	1.04190i	0.989243	+	0.146281i	$0.0467304\pi$
$719$	38.4531	+	27.9378i	1.43406	+	1.04190i	0.444814	+	0.895623i	$0.353270\pi$
$720$	0.393464	−	0.478718i	0.0146636	−	0.0178408i
$721$	−19.2036	+	13.9522i	−0.715180	+	0.519609i
$722$	8.75031	+	12.0438i	0.325653	+	0.448223i
$723$	15.5345	−	5.04746i	0.577734	−	0.187717i
$724$	−66.4588			−2.46992
$725$	7.31891	−	4.08463i	0.271817	−	0.151699i
$726$	58.3058			2.16393
$727$	−17.0668	+	5.54534i	−0.632973	+	0.205665i	−0.607892	−	0.794020i	$-0.707985\pi$
$727$	−17.0668	+	5.54534i	−0.632973	+	0.205665i	−0.0250815	+	0.999685i	$0.507985\pi$
$728$	33.6734	+	46.3475i	1.24802	+	1.71775i
$729$	18.3652	−	13.3431i	0.680194	−	0.494190i
$730$	−3.97260	−	6.21590i	−0.147033	−	0.230061i
$731$	−2.21637	−	1.61029i	−0.0819755	−	0.0595587i
$732$		−	8.78954i		−	0.324871i
$733$	9.44638	−	13.0018i	0.348910	−	0.480233i	−0.598107	−	0.801416i	$-0.704080\pi$
$733$	9.44638	−	13.0018i	0.348910	−	0.480233i	0.947017	+	0.321183i	$0.104080\pi$
$734$	20.9871	−	64.5916i	0.774647	−	2.38412i
$735$	42.2836	−	27.0236i	1.55965	−	0.996779i
$736$	7.79646	+	23.9950i	0.287381	+	0.884468i
$737$	−56.4823	−	18.3522i	−2.08055	−	0.676012i
$738$	3.68879	+	1.19856i	0.135786	+	0.0441196i
$739$	−2.52011	−	7.75611i	−0.0927038	−	0.285313i	0.893945	−	0.448177i	$-0.147927\pi$
$739$	−2.52011	−	7.75611i	−0.0927038	−	0.285313i	−0.986648	+	0.162864i	$0.947927\pi$
$740$	−10.3487	−	39.7782i	−0.380425	−	1.46228i
$741$	−10.8719	+	33.4603i	−0.399390	+	1.22920i
$742$	−44.3465	+	61.0377i	−1.62801	+	2.24076i
$743$		−	4.63794i		−	0.170149i	−0.996375	−	0.0850747i	$-0.972887\pi$
$743$		−	4.63794i		−	0.170149i	0.996375	−	0.0850747i	$-0.0271129\pi$
$744$	−19.7261	−	14.3319i	−0.723195	−	0.525432i
$745$	−0.496822	+	8.32022i	−0.0182021	+	0.304829i
$746$	−39.9652	+	29.0364i	−1.46323	+	1.06310i
$747$	2.61355	+	3.59724i	0.0956248	+	0.131616i
$748$	14.6157	−	4.74892i	0.534402	−	0.173638i
$749$	49.6180			1.81300
$750$	−33.4558	+	32.0250i	−1.22163	+	1.16939i
$751$	25.2490			0.921347			0.460674	−	0.887570i	$-0.347608\pi$
$751$	25.2490			0.921347			0.460674	+	0.887570i	$0.347608\pi$
$752$	3.21301	−	1.04397i	0.117167	−	0.0380697i
$753$	−27.4303	−	37.7546i	−0.999615	−	1.37585i
$754$	16.5886	−	12.0523i	0.604120	−	0.438919i
$755$	−0.478288	+	8.00983i	−0.0174067	+	0.291508i
$756$	−52.3362	−	38.0245i	−1.90345	−	1.38294i
$757$		−	38.2681i		−	1.39088i	−0.718586	−	0.695438i	$-0.755210\pi$
$757$		−	38.2681i		−	1.39088i	0.718586	−	0.695438i	$-0.244790\pi$
$758$	1.60492	−	2.20898i	0.0582934	−	0.0802339i
$759$	11.1657	−	34.3644i	0.405289	−	1.24735i
$760$	−4.76881	−	18.3303i	−0.172983	−	0.664911i
$761$	3.29603	+	10.1441i	0.119481	+	0.367725i	0.992855	−	0.119325i	$-0.0380730\pi$
$761$	3.29603	+	10.1441i	0.119481	+	0.367725i	−0.873374	+	0.487050i	$0.838073\pi$
$762$	−53.4014	−	17.3512i	−1.93453	−	0.628567i
$763$	−27.9658	−	9.08662i	−1.01243	−	0.328958i
$764$	9.96376	+	30.6653i	0.360476	+	1.10943i
$765$	−0.725687	+	0.463789i	−0.0262373	+	0.0167683i
$766$	2.72367	−	8.38259i	0.0984102	−	0.302875i
$767$	−20.2710	+	27.9007i	−0.731945	+	1.00744i
$768$			20.3602i			0.734685i
$769$	−14.9540	−	10.8647i	−0.539253	−	0.391791i	0.284554	−	0.958660i	$-0.408154\pi$
$769$	−14.9540	−	10.8647i	−0.539253	−	0.391791i	−0.823808	+	0.566869i	$0.808154\pi$
$770$	−59.4825	−	93.0719i	−2.14360	−	3.35408i
$771$	14.2926	−	10.3842i	0.514734	−	0.373976i

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.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.14124 + 0.695730i) q^{2} +(1.08145 + 1.48849i) q^{3} +(2.48282 - 1.80387i) q^{4} +(-0.133284 + 2.23209i) q^{5} +(-3.35124 - 2.43482i) q^{6} -4.38149i q^{7} +(-1.41458 + 1.94701i) q^{8} +(-0.119019 + 0.366304i) q^{9} +(-1.26754 - 4.87217i) q^{10} +(1.54742 + 4.76246i) q^{11} +(5.37011 + 1.74485i) q^{12} +(5.16707 + 1.67888i) q^{13} +(3.04833 + 9.38180i) q^{14} +(-3.46659 + 2.21551i) q^{15} +(-0.222341 + 0.684295i) q^{16} +(0.587785 - 0.809017i) q^{17} -0.867149i q^{18} +(2.84744 + 2.06879i) q^{19} +(3.69549 + 5.78231i) q^{20} +(6.52181 - 4.73838i) q^{21} +(-6.62677 - 9.12097i) q^{22} +(-3.72988 + 1.21191i) q^{23} -4.42791 q^{24} +(-4.96447 - 0.595005i) q^{25} -12.2320 q^{26} +(4.57553 - 1.48668i) q^{27} +(-7.90365 - 10.8784i) q^{28} +(-1.35616 + 0.985311i) q^{29} +(5.88140 - 7.15575i) q^{30} +(4.45495 + 3.23671i) q^{31} -6.43319i q^{32} +(-5.41543 + 7.45370i) q^{33} +(-0.695730 + 2.14124i) q^{34} +(9.77988 + 0.583982i) q^{35} +(0.365263 + 1.12416i) q^{36} +(-5.69639 - 1.85087i) q^{37} +(-7.53636 - 2.44871i) q^{38} +(3.08894 + 9.50678i) q^{39} +(-4.15735 - 3.41698i) q^{40} +(-1.38219 + 4.25393i) q^{41} +(-10.6681 + 14.6834i) q^{42} -2.73959i q^{43} +(12.4328 + 9.03298i) q^{44} +(-0.801761 - 0.314485i) q^{45} +(7.14340 - 5.18998i) q^{46} +(-2.75987 - 3.79863i) q^{47} +(-1.25902 + 0.409080i) q^{48} -12.1974 q^{49} +(11.0441 - 2.17989i) q^{50} +1.83988 q^{51} +(15.8574 - 5.15238i) q^{52} +(4.49551 + 6.18754i) q^{53} +(-8.76297 + 6.36667i) q^{54} +(-10.8365 + 2.81922i) q^{55} +(8.53078 + 6.19797i) q^{56} +6.47569i q^{57} +(2.21836 - 3.05331i) q^{58} +(-1.96156 + 6.03707i) q^{59} +(-4.61043 + 11.7540i) q^{60} +(-0.481029 - 1.48046i) q^{61} +(-11.7910 - 3.83112i) q^{62} +(1.60496 + 0.521482i) q^{63} +(4.03108 + 12.4064i) q^{64} +(-4.43611 + 11.3096i) q^{65} +(6.40995 - 19.7278i) q^{66} +(-6.97108 + 9.59486i) q^{67} -3.06893i q^{68} +(-5.83762 - 4.24128i) q^{69} +(-21.3473 + 5.55371i) q^{70} +(12.2357 - 8.88975i) q^{71} +(-0.544833 - 0.749898i) q^{72} +(1.39360 - 0.452808i) q^{73} +13.4850 q^{74} +(-4.48319 - 8.03305i) q^{75} +10.8015 q^{76} +(20.8666 - 6.77999i) q^{77} +(-13.2283 - 18.2072i) q^{78} +(-3.22393 + 2.34232i) q^{79} +(-1.49777 - 0.587491i) q^{80} +(8.09593 + 5.88204i) q^{81} -10.0703i q^{82} +(6.78571 - 9.33973i) q^{83} +(7.64506 - 23.5291i) q^{84} +(1.72746 + 1.41982i) q^{85} +(1.90601 + 5.86610i) q^{86} +(-2.93326 - 0.953074i) q^{87} +(-11.4615 - 3.72406i) q^{88} +(-4.22214 - 12.9944i) q^{89} +(1.93556 + 0.115577i) q^{90} +(7.35600 - 22.6394i) q^{91} +(-7.07449 + 9.73720i) q^{92} +10.1315i q^{93} +(8.55235 + 6.21364i) q^{94} +(-4.99724 + 6.08001i) q^{95} +(9.57576 - 6.95719i) q^{96} +(6.46389 + 8.89679i) q^{97} +(26.1176 - 8.48612i) q^{98} -1.92868 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) \) 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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