LMFDB - Embedded newform 140.2.s.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(19,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("140.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$140 = 2^{2} \cdot 5 \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	140.s (of order $6$ , degree $2$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	140.19
Dual form			140.2.s.b.59.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38503 + 0.285823i) q^{2} +(2.24836 - 1.29809i) q^{3} +(1.83661 - 0.791746i) q^{4} +(2.07525 - 0.832668i) q^{5} +(-2.74302 + 2.44053i) q^{6} +(-2.57589 - 0.603960i) q^{7} +(-2.31746 + 1.62154i) q^{8} +(1.87009 - 3.23909i) q^{9} +(-2.63629 + 1.74642i) q^{10} +(-3.12008 + 1.80138i) q^{11} +(3.10161 - 4.16422i) q^{12} -0.818282 q^{13} +(3.74031 + 0.100253i) q^{14} +(3.58504 - 4.56601i) q^{15} +(2.74628 - 2.90826i) q^{16} +(3.69814 + 6.40537i) q^{17} +(-1.66432 + 5.02075i) q^{18} +(1.65329 - 2.86358i) q^{19} +(3.15217 - 3.17236i) q^{20} +(-6.57554 + 1.98583i) q^{21} +(3.80652 - 3.38675i) q^{22} +(-1.26758 + 2.19550i) q^{23} +(-3.10559 + 6.65408i) q^{24} +(3.61333 - 3.45599i) q^{25} +(1.13334 - 0.233884i) q^{26} -1.92166i q^{27} +(-5.20910 + 0.930214i) q^{28} -2.04334 q^{29} +(-3.66031 + 7.34874i) q^{30} +(0.955727 + 1.65537i) q^{31} +(-2.97243 + 4.81297i) q^{32} +(-4.67671 + 8.10030i) q^{33} +(-6.95283 - 7.81461i) q^{34} +(-5.84852 + 0.891498i) q^{35} +(0.870092 - 7.42959i) q^{36} +(-6.20697 - 3.58360i) q^{37} +(-1.47138 + 4.43869i) q^{38} +(-1.83980 + 1.06221i) q^{39} +(-3.45911 + 5.29477i) q^{40} +2.65824i q^{41} +(8.53972 - 4.62987i) q^{42} +2.39696 q^{43} +(-4.30413 + 5.77873i) q^{44} +(1.18382 - 8.27910i) q^{45} +(1.12810 - 3.40314i) q^{46} +(-1.15593 - 0.667376i) q^{47} +(2.39944 - 10.1037i) q^{48} +(6.27046 + 3.11147i) q^{49} +(-4.01676 + 5.81942i) q^{50} +(16.6295 + 9.60106i) q^{51} +(-1.50287 + 0.647871i) q^{52} +(1.56838 - 0.905503i) q^{53} +(0.549253 + 2.66155i) q^{54} +(-4.97499 + 6.33630i) q^{55} +(6.94888 - 2.77725i) q^{56} -8.58450i q^{57} +(2.83009 - 0.584034i) q^{58} +(-0.955727 - 1.65537i) q^{59} +(2.96920 - 11.2244i) q^{60} +(-8.46625 - 4.88799i) q^{61} +(-1.79685 - 2.01956i) q^{62} +(-6.77344 + 7.21411i) q^{63} +(2.74124 - 7.51569i) q^{64} +(-1.69814 + 0.681358i) q^{65} +(4.16213 - 12.5559i) q^{66} +(4.63112 + 8.02134i) q^{67} +(11.8635 + 8.83618i) q^{68} +6.58172i q^{69} +(7.84556 - 2.90639i) q^{70} +1.38422i q^{71} +(0.918444 + 10.5389i) q^{72} +(-3.69814 - 6.40537i) q^{73} +(9.62111 + 3.18929i) q^{74} +(3.63787 - 12.4608i) q^{75} +(0.769222 - 6.56827i) q^{76} +(9.12495 - 2.75576i) q^{77} +(2.24457 - 1.99704i) q^{78} +(-6.70979 - 3.87390i) q^{79} +(3.27760 - 8.32210i) q^{80} +(3.11579 + 5.39670i) q^{81} +(-0.759784 - 3.68173i) q^{82} -10.4973i q^{83} +(-10.5044 + 8.85335i) q^{84} +(13.0081 + 10.2134i) q^{85} +(-3.31986 + 0.685105i) q^{86} +(-4.59418 + 2.65245i) q^{87} +(4.30966 - 9.23393i) q^{88} +(-9.19133 - 5.30662i) q^{89} +(0.726733 + 11.8052i) q^{90} +(2.10781 + 0.494210i) q^{91} +(-0.589761 + 5.03589i) q^{92} +(4.29764 + 2.48125i) q^{93} +(1.79175 + 0.593945i) q^{94} +(1.04658 - 7.31930i) q^{95} +(-0.435416 + 14.6798i) q^{96} -7.32005 q^{97} +(-9.57411 - 2.51724i) q^{98} +13.4750i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q + 6 q^{4} - 6 q^{5} + 4 q^{9} - 12 q^{10} + 22 q^{14} + 18 q^{16} - 52 q^{21} - 48 q^{24} - 26 q^{25} - 18 q^{26} - 26 q^{30} - 28 q^{36} + 42 q^{40} - 26 q^{44} + 36 q^{45} - 22 q^{46} + 36 q^{50}+ \cdots + 60 q^{96}+O(q^{100})$ 32 * q + 6 * q^4 - 6 * q^5 + 4 * q^9 - 12 * q^10 + 22 * q^14 + 18 * q^16 - 52 * q^21 - 48 * q^24 - 26 * q^25 - 18 * q^26 - 26 * q^30 - 28 * q^36 + 42 * q^40 - 26 * q^44 + 36 * q^45 - 22 * q^46 + 36 * q^50 + 48 * q^54 - 16 * q^56 + 4 * q^60 + 36 * q^61 + 36 * q^64 - 4 * q^65 - 24 * q^66 + 26 * q^70 + 14 * q^74 + 72 * q^80 + 72 * q^81 + 56 * q^84 + 20 * q^85 + 8 * q^86 - 108 * q^89 + 30 * q^94 + 60 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$ .

$n$	$57$	$71$	$101$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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

)

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

$2$	−1.38503	+	0.285823i	−0.979363	+	0.202107i
$2$	−1.38503	+	0.285823i	−0.979363	+	0.202107i
$3$	2.24836	−	1.29809i	1.29809	−	0.749454i	0.318019	−	0.948084i	$-0.396983\pi$
$3$	2.24836	−	1.29809i	1.29809	−	0.749454i	0.980075	+	0.198630i	$0.0636492\pi$
$4$	1.83661	−	0.791746i	0.918305	−	0.395873i
$5$	2.07525	−	0.832668i	0.928080	−	0.372381i
$5$	2.07525	−	0.832668i	0.928080	−	0.372381i
$6$	−2.74302	+	2.44053i	−1.11983	+	0.996342i
$7$	−2.57589	−	0.603960i	−0.973597	−	0.228275i
$7$	−2.57589	−	0.603960i	−0.973597	−	0.228275i
$8$	−2.31746	+	1.62154i	−0.819346	+	0.573300i
$9$	1.87009	−	3.23909i	0.623364	−	1.07970i
$10$	−2.63629	+	1.74642i	−0.833667	+	0.552268i
$11$	−3.12008	+	1.80138i	−0.940738	+	0.543136i	−0.890192	−	0.455586i	$-0.849430\pi$
$11$	−3.12008	+	1.80138i	−0.940738	+	0.543136i	−0.0505467	+	0.998722i	$0.516096\pi$
$12$	3.10161	−	4.16422i	0.895357	−	1.20211i
$13$	−0.818282			−0.226951			−0.113475	−	0.993541i	$-0.536198\pi$
$13$	−0.818282			−0.226951			−0.113475	+	0.993541i	$0.536198\pi$
$14$	3.74031	+	0.100253i	0.999641	+	0.0267937i
$15$	3.58504	−	4.56601i	0.925652	−	1.17894i
$16$	2.74628	−	2.90826i	0.686569	−	0.727064i
$17$	3.69814	+	6.40537i	0.896931	+	1.55353i	0.831396	+	0.555680i	$0.187542\pi$
$17$	3.69814	+	6.40537i	0.896931	+	1.55353i	0.0655347	+	0.997850i	$0.479125\pi$
$18$	−1.66432	+	5.02075i	−0.392285	+	1.18340i
$19$	1.65329	−	2.86358i	0.379291	−	0.656951i	−0.611668	−	0.791114i	$-0.709501\pi$
$19$	1.65329	−	2.86358i	0.379291	−	0.656951i	0.990959	+	0.134163i	$0.0428346\pi$
$20$	3.15217	−	3.17236i	0.704846	−	0.709361i
$21$	−6.57554	+	1.98583i	−1.43490	+	0.433344i
$22$	3.80652	−	3.38675i	0.811553	−	0.722057i
$23$	−1.26758	+	2.19550i	−0.264308	+	0.457794i	−0.967382	−	0.253322i	$-0.918477\pi$
$23$	−1.26758	+	2.19550i	−0.264308	+	0.457794i	0.703074	+	0.711116i	$0.251810\pi$
$24$	−3.10559	+	6.65408i	−0.633925	+	1.35826i
$25$	3.61333	−	3.45599i	0.722665	−	0.691198i
$26$	1.13334	−	0.233884i	0.222267	−	0.0458684i
$27$		−	1.92166i		−	0.369823i
$28$	−5.20910	+	0.930214i	−0.984427	+	0.175794i
$29$	−2.04334			−0.379439			−0.189720	−	0.981838i	$-0.560758\pi$
$29$	−2.04334			−0.379439			−0.189720	+	0.981838i	$0.560758\pi$
$30$	−3.66031	+	7.34874i	−0.668278	+	1.34169i
$31$	0.955727	+	1.65537i	0.171654	+	0.297313i	0.938998	−	0.343922i	$-0.111756\pi$
$31$	0.955727	+	1.65537i	0.171654	+	0.297313i	−0.767345	+	0.641235i	$0.778422\pi$
$32$	−2.97243	+	4.81297i	−0.525456	+	0.850821i
$33$	−4.67671	+	8.10030i	−0.814111	+	1.41008i
$34$	−6.95283	−	7.81461i	−1.19240	−	1.34019i
$35$	−5.84852	+	0.891498i	−0.988581	+	0.150691i
$36$	0.870092	−	7.42959i	0.145015	−	1.23827i
$37$	−6.20697	−	3.58360i	−1.02042	−	0.589140i	−0.106195	−	0.994345i	$-0.533867\pi$
$37$	−6.20697	−	3.58360i	−1.02042	−	0.589140i	−0.914226	+	0.405206i	$0.867200\pi$
$38$	−1.47138	+	4.43869i	−0.238689	+	0.720051i
$39$	−1.83980	+	1.06221i	−0.294603	+	0.170089i
$40$	−3.45911	+	5.29477i	−0.546933	+	0.837176i
$41$			2.65824i			0.415147i	0.978219	+	0.207573i	$0.0665566\pi$
$41$			2.65824i			0.415147i	−0.978219	+	0.207573i	$0.933443\pi$
$42$	8.53972	−	4.62987i	1.31771	−	0.714405i
$43$	2.39696			0.365533			0.182766	−	0.983156i	$-0.441495\pi$
$43$	2.39696			0.365533			0.182766	+	0.983156i	$0.441495\pi$
$44$	−4.30413	+	5.77873i	−0.648872	+	0.871177i
$45$	1.18382	−	8.27910i	0.176473	−	1.23418i
$46$	1.12810	−	3.40314i	0.166330	−	0.501766i
$47$	−1.15593	−	0.667376i	−0.168610	−	0.0973468i	0.413320	−	0.910586i	$-0.364369\pi$
$47$	−1.15593	−	0.667376i	−0.168610	−	0.0973468i	−0.581930	+	0.813239i	$0.697702\pi$
$48$	2.39944	−	10.1037i	0.346330	−	1.45835i
$49$	6.27046	+	3.11147i	0.895781	+	0.444496i
$50$	−4.01676	+	5.81942i	−0.568056	+	0.822990i
$51$	16.6295	+	9.60106i	2.32860	+	1.34442i
$52$	−1.50287	+	0.647871i	−0.208410	+	0.0898436i
$53$	1.56838	−	0.905503i	0.215433	−	0.124380i	−0.388401	−	0.921491i	$-0.626972\pi$
$53$	1.56838	−	0.905503i	0.215433	−	0.124380i	0.603834	+	0.797110i	$0.293639\pi$
$54$	0.549253	+	2.66155i	0.0747439	+	0.362191i
$55$	−4.97499	+	6.33630i	−0.670827	+	0.854386i
$56$	6.94888	−	2.77725i	0.928583	−	0.371126i
$57$		−	8.58450i		−	1.13705i
$58$	2.83009	−	0.584034i	0.371609	−	0.0766874i
$59$	−0.955727	−	1.65537i	−0.124425	−	0.215510i	0.797083	−	0.603870i	$-0.206375\pi$
$59$	−0.955727	−	1.65537i	−0.124425	−	0.215510i	−0.921508	+	0.388359i	$0.873042\pi$
$60$	2.96920	−	11.2244i	0.383322	−	1.44907i
$61$	−8.46625	−	4.88799i	−1.08399	−	0.625843i	−0.152021	−	0.988377i	$-0.548578\pi$
$61$	−8.46625	−	4.88799i	−1.08399	−	0.625843i	−0.931970	+	0.362534i	$0.881912\pi$
$62$	−1.79685	−	2.01956i	−0.228200	−	0.256485i
$63$	−6.77344	+	7.21411i	−0.853374	+	0.908892i
$64$	2.74124	−	7.51569i	0.342655	−	0.939461i
$65$	−1.69814	+	0.681358i	−0.210628	+	0.0845120i
$66$	4.16213	−	12.5559i	0.512323	−	1.54552i
$67$	4.63112	+	8.02134i	0.565782	+	0.979963i	0.996976	+	0.0777041i	$0.0247589\pi$
$67$	4.63112	+	8.02134i	0.565782	+	0.979963i	−0.431195	+	0.902259i	$0.641908\pi$
$68$	11.8635	+	8.83618i	1.43866	+	1.07154i
$69$			6.58172i			0.792346i
$70$	7.84556	−	2.90639i	0.937724	−	0.347380i
$71$			1.38422i			0.164277i	0.996621	+	0.0821385i	$0.0261750\pi$
$71$			1.38422i			0.164277i	−0.996621	+	0.0821385i	$0.973825\pi$
$72$	0.918444	+	10.5389i	0.108240	+	1.24202i
$73$	−3.69814	−	6.40537i	−0.432835	−	0.749692i	0.564281	−	0.825583i	$-0.309153\pi$
$73$	−3.69814	−	6.40537i	−0.432835	−	0.749692i	−0.997116	+	0.0758908i	$0.975820\pi$
$74$	9.62111	+	3.18929i	1.11843	+	0.370748i
$75$	3.63787	−	12.4608i	0.420065	−	1.43884i
$76$	0.769222	−	6.56827i	0.0882358	−	0.753433i
$77$	9.12495	−	2.75576i	1.03988	−	0.314048i
$78$	2.24457	−	1.99704i	0.254147	−	0.226121i
$79$	−6.70979	−	3.87390i	−0.754910	−	0.435848i	0.0725552	−	0.997364i	$-0.476885\pi$
$79$	−6.70979	−	3.87390i	−0.754910	−	0.435848i	−0.827465	+	0.561517i	$0.810218\pi$
$80$	3.27760	−	8.32210i	0.366447	−	0.930439i
$81$	3.11579	+	5.39670i	0.346199	+	0.599634i
$82$	−0.759784	−	3.68173i	−0.0839041	−	0.406579i
$83$		−	10.4973i		−	1.15223i	−0.817370	−	0.576113i	$-0.804569\pi$
$83$		−	10.4973i		−	1.15223i	0.817370	−	0.576113i	$-0.195431\pi$
$84$	−10.5044	+	8.85335i	−1.14613	+	0.965980i
$85$	13.0081	+	10.2134i	1.41093	+	1.10780i
$86$	−3.31986	+	0.685105i	−0.357989	+	0.0738768i
$87$	−4.59418	+	2.65245i	−0.492547	+	0.284372i
$88$	4.30966	−	9.23393i	0.459411	−	0.984341i
$89$	−9.19133	−	5.30662i	−0.974279	−	0.562500i	−0.0737410	−	0.997277i	$-0.523494\pi$
$89$	−9.19133	−	5.30662i	−0.974279	−	0.562500i	−0.900538	+	0.434777i	$0.856827\pi$
$90$	0.726733	+	11.8052i	0.0766044	+	1.24437i
$91$	2.10781	+	0.494210i	0.220958	+	0.0518073i
$92$	−0.589761	+	5.03589i	−0.0614868	+	0.525027i
$93$	4.29764	+	2.48125i	0.445645	+	0.257293i
$94$	1.79175	+	0.593945i	0.184805	+	0.0612607i
$95$	1.04658	−	7.31930i	0.107376	−	0.750944i
$96$	−0.435416	+	14.6798i	−0.0444395	+	1.49825i
$97$	−7.32005			−0.743239			−0.371619	−	0.928385i	$-0.621197\pi$
$97$	−7.32005			−0.743239			−0.371619	+	0.928385i	$0.621197\pi$
$98$	−9.57411	−	2.51724i	−0.967131	−	0.254280i
$99$			13.4750i			1.35428i
$100$	3.90001	−	9.20814i	0.390001	−	0.920814i
$101$	−5.50608	+	3.17894i	−0.547875	+	0.316316i	−0.748265	−	0.663400i	$-0.769113\pi$
$101$	−5.50608	+	3.17894i	−0.547875	+	0.316316i	0.200389	+	0.979716i	$0.435779\pi$
$102$	−25.7766	−	8.54465i	−2.55226	−	0.846047i
$103$	−0.885144	−	0.511038i	−0.0872158	−	0.0503541i	0.455758	−	0.890104i	$-0.349368\pi$
$103$	−0.885144	−	0.511038i	−0.0872158	−	0.0503541i	−0.542974	+	0.839750i	$0.682702\pi$
$104$	1.89634	−	1.32687i	0.185951	−	0.130111i
$105$	−11.9924	+	9.59634i	−1.17033	+	0.936507i
$106$	−1.91343	+	1.70243i	−0.185849	+	0.165354i
$107$	3.62578	−	6.28003i	0.350517	−	0.607114i	−0.635823	−	0.771835i	$-0.719339\pi$
$107$	3.62578	−	6.28003i	0.350517	−	0.607114i	0.986340	+	0.164721i	$0.0526724\pi$
$108$	−1.52146	−	3.52933i	−0.146403	−	0.339610i
$109$	3.98588	+	6.90375i	0.381778	+	0.661259i	0.991316	−	0.131498i	$-0.0419786\pi$
$109$	3.98588	+	6.90375i	0.381778	+	0.661259i	−0.609538	+	0.792756i	$0.708645\pi$
$110$	5.07945	−	10.1979i	0.484306	−	0.972333i
$111$	−18.6074			−1.76613
$112$	−8.83059	+	5.83272i	−0.834413	+	0.551140i
$113$		−	7.61610i		−	0.716462i	−0.933633	−	0.358231i	$-0.883380\pi$
$113$		−	7.61610i		−	0.716462i	0.933633	−	0.358231i	$-0.116620\pi$
$114$	2.45365	+	11.8898i	0.229805	+	1.11358i
$115$	−0.802408	+	5.61169i	−0.0748250	+	0.523293i
$116$	−3.75282	+	1.61781i	−0.348441	+	0.150210i
$117$	−1.53026	+	2.65049i	−0.141473	+	0.245038i
$118$	1.79685	+	2.01956i	0.165414	+	0.185916i
$119$	−5.65744	−	18.7331i	−0.518616	−	1.71726i
$120$	−0.904229	+	16.3948i	−0.0825444	+	1.49663i
$121$	0.989917	−	1.71459i	0.0899925	−	0.155872i
$122$	13.1231	+	4.35016i	1.18811	+	0.393845i
$123$	3.45064	+	5.97668i	0.311134	+	0.538899i
$124$	3.06593	+	2.28357i	0.275328	+	0.205071i
$125$	4.62086	−	10.1807i	0.413303	−	0.910594i
$126$	7.31946	−	11.9277i	0.652069	−	1.06261i
$127$	8.78136			0.779220			0.389610	−	0.920980i	$-0.372610\pi$
$127$	8.78136			0.779220			0.389610	+	0.920980i	$0.372610\pi$
$128$	−1.64855	+	11.1930i	−0.145712	+	0.989327i
$129$	5.38923	−	3.11147i	0.474495	−	0.273950i
$130$	2.15723	−	1.42907i	0.189201	−	0.125338i
$131$	−6.69467	+	11.5955i	−0.584916	+	1.01310i	0.409970	+	0.912099i	$0.365539\pi$
$131$	−6.69467	+	11.5955i	−0.584916	+	1.01310i	−0.994886	+	0.101005i	$0.967794\pi$
$132$	−2.17592	+	18.5799i	−0.189389	+	1.61717i
$133$	−5.98819	+	6.37777i	−0.519242	+	0.553023i
$134$	−8.70692	−	9.78611i	−0.752164	−	0.845391i
$135$	−1.60010	−	3.98792i	−0.137715	−	0.343225i
$136$	−18.9568	−	8.84752i	−1.62553	−	0.758668i
$137$	4.52425	−	2.61208i	0.386533	−	0.223165i	−0.294124	−	0.955767i	$-0.595028\pi$
$137$	4.52425	−	2.61208i	0.386533	−	0.223165i	0.680657	+	0.732602i	$0.261694\pi$
$138$	−1.88121	−	9.11588i	−0.160139	−	0.775995i
$139$	21.9442			1.86128			0.930641	−	0.365933i	$-0.119250\pi$
$139$	21.9442			1.86128			0.930641	+	0.365933i	$0.119250\pi$
$140$	−10.0356	+	6.26788i	−0.848165	+	0.529732i
$141$	−3.46527			−0.291828
$142$	−0.395643	−	1.91719i	−0.0332016	−	0.160887i
$143$	2.55310	−	1.47403i	0.213501	−	0.123265i
$144$	−4.28433	−	14.3342i	−0.357027	−	1.19451i
$145$	−4.24045	+	1.70143i	−0.352150	+	0.141296i
$146$	6.95283	+	7.81461i	0.575421	+	0.646742i
$147$	18.1373	−	1.14392i	1.49594	−	0.0943492i
$148$	−14.2371	−	1.66733i	−1.17028	−	0.137054i
$149$	11.9749	−	20.7411i	0.981019	−	1.69917i	0.322575	−	0.946544i	$-0.395452\pi$
$149$	11.9749	−	20.7411i	0.981019	−	1.69917i	0.658444	−	0.752630i	$-0.271215\pi$
$150$	−1.47699	+	18.2983i	−0.120596	+	1.49405i
$151$	6.06876	−	3.50380i	0.493869	−	0.285135i	−0.232309	−	0.972642i	$-0.574628\pi$
$151$	6.06876	−	3.50380i	0.493869	−	0.285135i	0.726178	+	0.687507i	$0.241295\pi$
$152$	0.811968	+	9.31711i	0.0658593	+	0.755717i
$153$	27.6635			2.23646
$154$	−11.8507	+	6.42492i	−0.954953	+	0.517735i
$155$	3.36174	+	2.63950i	0.270022	+	0.212010i
$156$	−2.53799	+	3.40751i	−0.203202	+	0.272819i
$157$	3.21277	+	5.56468i	0.256407	+	0.444110i	0.965277	−	0.261229i	$-0.0841279\pi$
$157$	3.21277	+	5.56468i	0.256407	+	0.444110i	−0.708870	+	0.705340i	$0.750795\pi$
$158$	10.4005	+	3.44765i	0.827419	+	0.274280i
$159$	2.35085	−	4.07180i	0.186435	−	0.322915i
$160$	−2.16092	+	12.4632i	−0.170836	+	0.985299i
$161$	4.59114	−	4.88982i	0.361832	−	0.385372i
$162$	−5.85796	−	6.58403i	−0.460245	−	0.517290i
$163$	9.23950	−	16.0033i	0.723693	−	1.25347i	−0.235816	−	0.971798i	$-0.575776\pi$
$163$	9.23950	−	16.0033i	0.723693	−	1.25347i	0.959510	−	0.281676i	$-0.0908903\pi$
$164$	2.10465	+	4.88214i	0.164345	+	0.381231i
$165$	−2.96048	+	20.7043i	−0.230473	+	1.61183i
$166$	3.00036	+	14.5390i	0.232873	+	1.12845i
$167$		−	1.82894i		−	0.141527i	−0.997493	−	0.0707637i	$-0.977456\pi$
$167$		−	1.82894i		−	0.141527i	0.997493	−	0.0707637i	$-0.0225436\pi$
$168$	12.0185	−	15.2646i	0.927245	−	1.17769i
$169$	−12.3304			−0.948493
$170$	−20.9358	−	10.4279i	−1.60571	−	0.799781i
$171$	−6.18361	−	10.7103i	−0.472873	−	0.819039i
$172$	4.40228	−	1.89778i	0.335671	−	0.144704i
$173$	7.62476	−	13.2065i	0.579700	−	1.00407i	−0.415814	−	0.909450i	$-0.636503\pi$
$173$	7.62476	−	13.2065i	0.579700	−	1.00407i	0.995514	−	0.0946193i	$-0.0301634\pi$
$174$	5.60494	−	4.98684i	0.424909	−	0.378051i
$175$	−11.3948	+	6.71996i	−0.861368	+	0.507981i
$176$	−3.32973	+	14.0211i	−0.250988	+	1.05688i
$177$	−4.29764	−	2.48125i	−0.323031	−	0.186502i
$178$	14.2470	+	4.72273i	1.06786	+	0.353983i
$179$	−10.8572	+	6.26844i	−0.811509	+	0.468525i	−0.847480	−	0.530828i	$-0.821881\pi$
$179$	−10.8572	+	6.26844i	−0.811509	+	0.468525i	0.0359707	+	0.999353i	$0.488548\pi$
$180$	−4.38073	−	16.1428i	−0.326520	−	1.20321i
$181$		−	8.01839i		−	0.596002i	−0.954566	−	0.298001i	$-0.903680\pi$
$181$		−	8.01839i		−	0.596002i	0.954566	−	0.298001i	$-0.0963199\pi$
$182$	−3.06063	−	0.0820350i	−0.226869	−	0.00608084i
$183$	−25.3803			−1.87616
$184$	−0.622535	−	7.14341i	−0.0458939	−	0.526619i
$185$	−15.8650	−	2.26851i	−1.16642	−	0.166784i
$186$	−6.66156	−	2.20823i	−0.488449	−	0.161915i
$187$	−23.0770	−	13.3235i	−1.68755	−	0.974310i
$188$	−2.65139	−	0.310508i	−0.193372	−	0.0226461i
$189$	−1.16060	+	4.94998i	−0.0844215	+	0.360058i
$190$	0.642483	+	10.4366i	0.0466106	+	0.757148i
$191$	5.85379	+	3.37969i	0.423565	+	0.244546i	0.696602	−	0.717458i	$-0.254695\pi$
$191$	5.85379	+	3.37969i	0.423565	+	0.244546i	−0.273036	+	0.962004i	$0.588028\pi$
$192$	−3.59276	−	20.4564i	−0.259285	−	1.47631i
$193$	−2.04384	+	1.18001i	−0.147119	+	0.0849392i	−0.571753	−	0.820426i	$-0.693736\pi$
$193$	−2.04384	+	1.18001i	−0.147119	+	0.0849392i	0.424634	+	0.905365i	$0.360403\pi$
$194$	10.1385	−	2.09224i	0.727901	−	0.150214i
$195$	−2.93357	+	3.73628i	−0.210077	+	0.267561i
$196$	13.9799	+	0.749953i	0.998564	+	0.0535681i
$197$			20.3205i			1.44777i	0.689918	+	0.723887i	$0.257647\pi$
$197$			20.3205i			1.44777i	−0.689918	+	0.723887i	$0.742353\pi$
$198$	−3.85145	−	18.6632i	−0.273711	−	1.32634i
$199$	5.72909	+	9.92308i	0.406125	+	0.703429i	0.994452	−	0.105195i	$-0.0335465\pi$
$199$	5.72909	+	9.92308i	0.406125	+	0.703429i	−0.588327	+	0.808623i	$0.700213\pi$
$200$	−2.76973	+	13.8683i	−0.195849	+	0.980634i
$201$	20.8249	+	12.0233i	1.46888	+	0.848056i
$202$	6.71746	−	5.97668i	0.472639	−	0.420518i
$203$	5.26343	+	1.23410i	0.369421	+	0.0866166i
$204$	38.1436	+	4.46706i	2.67058	+	0.312757i
$205$	2.21343	+	5.51650i	0.154593	+	0.385289i
$206$	1.37202	+	0.454808i	0.0955929	+	0.0316880i
$207$	4.74097	+	8.21159i	0.329520	+	0.570745i
$208$	−2.24723	+	2.37978i	−0.155817	+	0.165008i
$209$			11.9128i			0.824026i
$210$	13.8669	−	16.7189i	0.956908	−	1.15371i
$211$		−	22.0647i		−	1.51900i	−0.650510	−	0.759498i	$-0.725445\pi$
$211$		−	22.0647i		−	1.51900i	0.650510	−	0.759498i	$-0.274555\pi$
$212$	2.16357	−	2.90481i	0.148595	−	0.199503i
$213$	1.79685	+	3.11224i	0.123118	+	0.213247i
$214$	−3.22683	+	9.73436i	−0.220582	+	0.665427i
$215$	4.97429	−	1.99587i	0.339243	−	0.136117i
$216$	3.11603	+	4.45336i	0.212019	+	0.303013i
$217$	−1.46208	−	4.84127i	−0.0992522	−	0.328647i
$218$	−7.49381	−	8.42263i	−0.507545	−	0.570453i
$219$	−16.6295	−	9.60106i	−1.12372	−	0.648780i
$220$	−4.12038	+	15.5762i	−0.277796	+	1.05015i
$221$	−3.02612	−	5.24140i	−0.203559	−	0.352575i
$222$	25.7718	−	5.31841i	1.72969	−	0.356948i
$223$			23.5776i			1.57887i	0.613833	+	0.789436i	$0.289627\pi$
$223$			23.5776i			1.57887i	−0.613833	+	0.789436i	$0.710373\pi$
$224$	10.5635	−	10.6025i	0.705804	−	0.708408i
$225$	−4.43703	−	18.1669i	−0.295802	−	1.21113i
$226$	2.17685	+	10.5485i	0.144802	+	0.701677i
$227$	−18.1231	+	10.4634i	−1.20287	+	0.694478i	−0.961192	−	0.275879i	$-0.911031\pi$
$227$	−18.1231	+	10.4634i	−1.20287	+	0.694478i	−0.241678	+	0.970356i	$0.577698\pi$
$228$	−6.79674	−	15.7664i	−0.450125	−	1.04415i
$229$	4.48735	+	2.59077i	0.296533	+	0.171203i	0.640884	−	0.767638i	$-0.278568\pi$
$229$	4.48735	+	2.59077i	0.296533	+	0.171203i	−0.344352	+	0.938841i	$0.611901\pi$
$230$	−0.492590	−	8.00170i	−0.0324804	−	0.527617i
$231$	16.9390	−	18.0410i	1.11450	−	1.18701i
$232$	4.73536	−	3.31335i	0.310892	−	0.217532i
$233$	−17.9868	−	10.3847i	−1.17836	−	0.680324i	−0.222722	−	0.974882i	$-0.571494\pi$
$233$	−17.9868	−	10.3847i	−1.17836	−	0.680324i	−0.955634	+	0.294558i	$0.904828\pi$
$234$	1.36189	−	4.10839i	0.0890294	−	0.268574i
$235$	−2.95455	−	0.422467i	−0.192733	−	0.0275587i
$236$	−3.06593	−	2.28357i	−0.199575	−	0.148648i
$237$	−20.1147			−1.30659
$238$	13.1901	+	24.3288i	0.854984	+	1.57700i
$239$			21.1286i			1.36670i	0.730092	+	0.683349i	$0.239477\pi$
$239$			21.1286i			1.36670i	−0.730092	+	0.683349i	$0.760523\pi$
$240$	−3.43363	−	22.9657i	−0.221640	−	1.48243i
$241$	1.57448	−	0.909029i	0.101421	−	0.0585557i	−0.448431	−	0.893817i	$-0.648017\pi$
$241$	1.57448	−	0.909029i	0.101421	−	0.0585557i	0.549853	+	0.835262i	$0.314684\pi$
$242$	−0.880996	+	2.65769i	−0.0566326	+	0.170843i
$243$	19.0035	+	10.9716i	1.21907	+	0.703832i
$244$	−19.4192	−	2.27422i	−1.24319	−	0.145592i
$245$	15.6036	+	1.23587i	0.996878	+	0.0789568i
$246$	−6.48750	−	7.29160i	−0.413628	−	0.464896i
$247$	−1.35286	+	2.34322i	−0.0860803	+	0.149095i
$248$	−4.89910	−	2.28650i	−0.311093	−	0.145193i
$249$	−13.6264	−	23.6017i	−0.863540	−	1.49570i
$250$	−3.49014	+	15.4214i	−0.220736	+	0.975334i
$251$	14.0187			0.884856			0.442428	−	0.896804i	$-0.354117\pi$
$251$	14.0187			0.884856			0.442428	+	0.896804i	$0.354117\pi$
$252$	−6.72844	+	18.6123i	−0.423852	+	1.17247i
$253$		−	9.13352i		−	0.574220i
$254$	−12.1624	+	2.50991i	−0.763140	+	0.157486i
$255$	42.5049	+	6.07773i	2.66176	+	0.380602i
$256$	−0.915918	−	15.9738i	−0.0572449	−	0.998360i
$257$	−8.93624	+	15.4780i	−0.557427	+	0.965492i	0.440283	+	0.897859i	$0.354878\pi$
$257$	−8.93624	+	15.4780i	−0.557427	+	0.965492i	−0.997710	+	0.0676333i	$0.978455\pi$
$258$	−6.57491	+	5.84985i	−0.409336	+	0.364196i
$259$	13.8242	+	12.9797i	0.858991	+	0.806521i
$260$	−2.57936	+	2.59588i	−0.159965	+	0.160990i
$261$	−3.82124	+	6.61858i	−0.236529	+	0.409680i
$262$	5.95805	−	17.9736i	0.368090	−	1.11041i
$263$	−10.9482	−	18.9629i	−0.675097	−	1.16930i	−0.976440	−	0.215787i	$-0.930768\pi$
$263$	−10.9482	−	18.9629i	−0.675097	−	1.16930i	0.301343	−	0.953516i	$-0.402565\pi$
$264$	−2.29684	−	26.3556i	−0.141361	−	1.62207i
$265$	2.50079	−	3.18508i	0.153622	−	0.195658i
$266$	6.47091	−	10.5450i	0.396757	−	0.646553i
$267$	−27.5539			−1.68627
$268$	14.8564	+	11.0654i	0.907501	+	0.675928i
$269$	2.49661	−	1.44142i	0.152221	−	0.0878847i	−0.421955	−	0.906617i	$-0.638656\pi$
$269$	2.49661	−	1.44142i	0.152221	−	0.0878847i	0.574176	+	0.818732i	$0.305323\pi$
$270$	3.35603	+	5.06604i	0.204241	+	0.308309i
$271$	−8.47793	+	14.6842i	−0.514997	+	0.892002i	0.484851	+	0.874597i	$0.338874\pi$
$271$	−8.47793	+	14.6842i	−0.514997	+	0.892002i	−0.999849	+	0.0174049i	$0.994460\pi$
$272$	28.7846	+	6.83578i	1.74532	+	0.414480i
$273$	5.38065	−	1.62497i	0.325652	−	0.0983476i
$274$	−5.51963	+	4.91094i	−0.333453	+	0.296681i
$275$	−5.04831	+	17.2919i	−0.304425	+	1.04274i
$276$	5.21105	+	12.0881i	0.313668	+	0.727616i
$277$	23.2541	−	13.4258i	1.39720	−	0.806677i	0.403106	−	0.915153i	$-0.367931\pi$
$277$	23.2541	−	13.4258i	1.39720	−	0.806677i	0.994099	+	0.108477i	$0.0345973\pi$
$278$	−30.3933	+	6.27215i	−1.82287	+	0.376179i
$279$	7.14919			0.428011
$280$	12.1081	−	11.5496i	0.723599	−	0.690221i
$281$	24.9497			1.48838			0.744188	−	0.667971i	$-0.232837\pi$
$281$	24.9497			1.48838			0.744188	+	0.667971i	$0.232837\pi$
$282$	4.79950	−	0.990452i	0.285806	−	0.0589806i
$283$	8.52014	−	4.91910i	0.506470	−	0.292410i	−0.224912	−	0.974379i	$-0.572209\pi$
$283$	8.52014	−	4.91910i	0.506470	−	0.292410i	0.731381	+	0.681969i	$0.238876\pi$
$284$	1.09595	+	2.54228i	0.0650328	+	0.150857i
$285$	−7.14804	−	17.8150i	−0.423414	−	1.05527i
$286$	−3.11481	+	2.77132i	−0.184183	+	0.163871i
$287$	1.60547	−	6.84733i	0.0947678	−	0.404185i
$288$	10.0309	+	18.6287i	0.591079	+	1.09770i
$289$	−18.8525	+	32.6535i	−1.10897	+	1.92079i
$290$	5.38684	−	3.56854i	0.316326	−	0.209552i
$291$	−16.4581	+	9.50211i	−0.964793	+	0.557024i
$292$	−11.8635	−	8.83618i	−0.694257	−	0.517098i
$293$	−23.4039			−1.36727			−0.683636	−	0.729823i	$-0.739602\pi$
$293$	−23.4039			−1.36727			−0.683636	+	0.729823i	$0.739602\pi$
$294$	−24.7937	+	6.76841i	−1.44600	+	0.394742i
$295$	−3.36174	−	2.63950i	−0.195728	−	0.153678i
$296$	20.1953	−	1.75999i	1.17383	−	0.102297i
$297$	3.46163	+	5.99571i	0.200864	+	0.347907i
$298$	−10.6573	+	32.1497i	−0.617358	+	1.86238i
$299$	1.03723	−	1.79654i	0.0599848	−	0.103897i
$300$	−3.18439	−	25.7658i	−0.183851	−	1.48759i
$301$	−6.17431	−	1.44767i	−0.355881	−	0.0834421i
$302$	−7.40395	+	6.58746i	−0.426049	+	0.379066i
$303$	−8.25311	+	14.2948i	−0.474129	+	0.821215i
$304$	−3.78764	−	12.6724i	−0.217236	−	0.726811i
$305$	−21.6397	−	3.09423i	−1.23908	−	0.177175i
$306$	−38.3147	+	7.90685i	−2.19031	+	0.452004i
$307$			2.18529i			0.124721i	0.998054	+	0.0623606i	$0.0198629\pi$
$307$			2.18529i			0.124721i	−0.998054	+	0.0623606i	$0.980137\pi$
$308$	14.5771	−	12.2859i	0.830608	−	0.700053i
$309$	−2.65350			−0.150952
$310$	−5.41054	−	2.69492i	−0.307298	−	0.153061i
$311$	−14.4501	−	25.0282i	−0.819388	−	1.41922i	−0.906134	−	0.422991i	$-0.860980\pi$
$311$	−14.4501	−	25.0282i	−0.819388	−	1.41922i	0.0867457	−	0.996230i	$-0.472353\pi$
$312$	2.54125	−	5.44492i	0.143870	−	0.308258i
$313$	−3.17652	+	5.50189i	−0.179548	+	0.310985i	−0.941726	−	0.336382i	$-0.890797\pi$
$313$	−3.17652	+	5.50189i	−0.179548	+	0.310985i	0.762178	+	0.647367i	$0.224130\pi$
$314$	−6.04030	−	6.78897i	−0.340874	−	0.383124i
$315$	−8.04963	+	20.6111i	−0.453545	+	1.16130i
$316$	−15.3904	−	1.80240i	−0.865778	−	0.101393i
$317$	16.2839	+	9.40153i	0.914597	+	0.528043i	0.881907	−	0.471423i	$-0.156259\pi$
$317$	16.2839	+	9.40153i	0.914597	+	0.528043i	0.0326894	+	0.999466i	$0.489593\pi$
$318$	−2.09219	+	6.31149i	−0.117324	+	0.353931i
$319$	6.37538	−	3.68083i	0.356953	−	0.206087i
$320$	−0.569312	−	17.8795i	−0.0318255	−	0.999493i
$321$		−	18.8264i		−	1.05079i
$322$	−4.96124	+	8.08480i	−0.276479	+	0.450548i
$323$	24.4564			1.36079
$324$	9.99530	+	7.44473i	0.555295	+	0.413596i
$325$	−2.95672	+	2.82798i	−0.164009	+	0.156868i
$326$	−8.22287	+	24.8059i	−0.455423	+	1.37387i
$327$	17.9234	+	10.3481i	0.991167	+	0.572250i
$328$	−4.31042	−	6.16035i	−0.238003	−	0.340149i
$329$	2.57448	+	2.41723i	0.141936	+	0.133266i
$330$	−1.81741	−	29.5222i	−0.100045	−	1.62514i
$331$	−11.3353	−	6.54441i	−0.623042	−	0.359713i	0.155010	−	0.987913i	$-0.450459\pi$
$331$	−11.3353	−	6.54441i	−0.623042	−	0.359713i	−0.778052	+	0.628199i	$0.783792\pi$
$332$	−8.31117	−	19.2794i	−0.456135	−	1.05809i
$333$	−23.2152	+	13.4033i	−1.27219	+	0.734497i
$334$	0.522752	+	2.53313i	0.0286037	+	0.138607i
$335$	16.2899	+	12.7901i	0.890010	+	0.698798i
$336$	−12.2830	+	24.5770i	−0.670091	+	1.34079i
$337$			11.7319i			0.639079i	0.947573	+	0.319539i	$0.103528\pi$
$337$			11.7319i			0.639079i	−0.947573	+	0.319539i	$0.896472\pi$
$338$	17.0780	−	3.52431i	0.928920	−	0.191697i
$339$	−9.88640	−	17.1238i	−0.536956	−	0.930035i
$340$	31.9773	+	8.45895i	1.73421	+	0.458751i
$341$	−5.96388	−	3.44325i	−0.322962	−	0.186462i
$342$	11.6257	+	13.0667i	0.628648	+	0.706566i
$343$	−14.2729	−	11.8019i	−0.770661	−	0.637245i
$344$	−5.55485	+	3.88675i	−0.299498	+	0.209560i
$345$	5.48039	+	13.6587i	0.295054	+	0.735361i
$346$	−6.78580	+	20.4707i	−0.364807	+	1.10051i
$347$	−2.20585	−	3.82065i	−0.118416	−	0.205103i	0.800724	−	0.599034i	$-0.204448\pi$
$347$	−2.20585	−	3.82065i	−0.118416	−	0.205103i	−0.919140	+	0.393930i	$0.871115\pi$
$348$	−6.33765	+	8.50894i	−0.339734	+	0.456127i
$349$			18.3479i			0.982142i	0.871120	+	0.491071i	$0.163394\pi$
$349$			18.3479i			0.982142i	−0.871120	+	0.491071i	$0.836606\pi$
$350$	13.8614	−	12.5642i	0.740926	−	0.671587i
$351$			1.57246i			0.0839316i
$352$	0.604231	−	20.3713i	0.0322056	−	1.08579i
$353$	5.87406	+	10.1742i	0.312645	+	0.541516i	0.978934	−	0.204177i	$-0.0654518\pi$
$353$	5.87406	+	10.1742i	0.312645	+	0.541516i	−0.666289	+	0.745693i	$0.732118\pi$
$354$	6.66156	+	2.20823i	0.354058	+	0.117366i
$355$	1.15260	+	2.87261i	0.0611736	+	0.152462i
$356$	−21.0824	−	2.46899i	−1.11736	−	0.130856i
$357$	−37.0373	−	34.7749i	−1.96022	−	1.84048i
$358$	13.2459	−	11.7852i	0.700070	−	0.622868i
$359$	−0.171388	−	0.0989510i	−0.00904552	−	0.00522243i	0.495470	−	0.868625i	$-0.334996\pi$
$359$	−0.171388	−	0.0989510i	−0.00904552	−	0.00522243i	−0.504516	+	0.863402i	$0.668329\pi$
$360$	10.6814	+	21.1061i	0.562959	+	1.11239i
$361$	4.03326	+	6.98581i	0.212277	+	0.367674i
$362$	2.29184	+	11.1057i	0.120456	+	0.583703i
$363$		−	5.14002i		−	0.269781i
$364$	4.26251	−	0.761178i	0.223416	−	0.0398966i
$365$	−13.0081	−	10.2134i	−0.680876	−	0.534595i
$366$	35.1524	−	7.25426i	1.83745	−	0.379186i
$367$	6.51964	−	3.76412i	0.340323	−	0.196485i	−0.320092	−	0.947386i	$-0.603714\pi$
$367$	6.51964	−	3.76412i	0.340323	−	0.196485i	0.660415	+	0.750901i	$0.270381\pi$
$368$	2.90398	+	9.71590i	0.151380	+	0.506476i
$369$	8.61028	+	4.97115i	0.448233	+	0.258787i
$370$	22.6218	−	1.39262i	1.17605	−	0.0723987i
$371$	−4.58686	+	1.38524i	−0.238138	+	0.0719182i
$372$	9.85761	+	1.15444i	0.511093	+	0.0598550i
$373$	26.9674	+	15.5696i	1.39632	+	0.806164i	0.994005	−	0.109339i	$-0.0348734\pi$
$373$	26.9674	+	15.5696i	1.39632	+	0.806164i	0.402312	+	0.915503i	$0.368207\pi$
$374$	35.7704	+	11.8575i	1.84964	+	0.613137i
$375$	−2.82618	−	28.8883i	−0.145943	−	1.49179i
$376$	3.76100	−	0.327763i	0.193959	−	0.0169031i
$377$	1.67203			0.0861140
$378$	0.192651	−	7.18760i	0.00990891	−	0.369690i
$379$		−	16.3396i		−	0.839307i	−0.907684	−	0.419654i	$-0.862152\pi$
$379$		−	16.3396i		−	0.839307i	0.907684	−	0.419654i	$-0.137848\pi$
$380$	−3.87287	−	14.2713i	−0.198674	−	0.732103i
$381$	19.7437	−	11.3990i	1.01150	−	0.583990i
$382$	−9.07366	−	3.00782i	−0.464249	−	0.153893i
$383$	−7.66318	−	4.42434i	−0.391570	−	0.226073i	0.291270	−	0.956641i	$-0.405922\pi$
$383$	−7.66318	−	4.42434i	−0.391570	−	0.226073i	−0.682840	+	0.730568i	$0.739256\pi$
$384$	10.8230	+	27.3058i	0.552307	+	1.39344i
$385$	16.6419	−	13.3169i	0.848151	−	0.678694i
$386$	2.49351	−	2.21853i	0.126916	−	0.112920i
$387$	4.48253	−	7.76397i	0.227860	−	0.394665i
$388$	−13.4441	+	5.79562i	−0.682520	+	0.294228i
$389$	−4.67264	−	8.09325i	−0.236912	−	0.410344i	0.722915	−	0.690937i	$-0.242802\pi$
$389$	−4.67264	−	8.09325i	−0.236912	−	0.410344i	−0.959827	+	0.280594i	$0.909469\pi$
$390$	2.99517	−	6.01334i	0.151666	−	0.304498i
$391$	−18.7507			−0.948263
$392$	−19.5769	+	2.95707i	−0.988784	+	0.149354i
$393$			34.7612i			1.75347i
$394$	−5.80806	−	28.1445i	−0.292606	−	1.41790i
$395$	−17.1502	−	2.45228i	−0.862918	−	0.123388i
$396$	10.6687	+	24.7483i	0.536125	+	1.24365i
$397$	10.1513	−	17.5826i	0.509480	−	0.882446i	−0.490459	−	0.871464i	$-0.663171\pi$
$397$	10.1513	−	17.5826i	0.509480	−	0.882446i	0.999940	−	0.0109817i	$-0.00349564\pi$
$398$	−10.7712	−	12.1063i	−0.539912	−	0.606831i
$399$	−5.18470	+	22.1128i	−0.259559	+	1.10702i
$400$	−0.127710	−	19.9996i	−0.00638551	−	0.999980i
$401$	5.54334	−	9.60135i	0.276821	−	0.479469i	−0.693772	−	0.720195i	$-0.744052\pi$
$401$	5.54334	−	9.60135i	0.276821	−	0.479469i	0.970593	+	0.240726i	$0.0773857\pi$
$402$	−32.2796	−	10.7003i	−1.60996	−	0.533684i
$403$	−0.782054	−	1.35456i	−0.0389569	−	0.0674753i
$404$	−7.59561	+	10.1979i	−0.377896	+	0.507363i
$405$	10.9597	+	8.60509i	0.544592	+	0.427590i
$406$	−7.64274	−	0.204851i	−0.379303	−	0.0101666i
$407$	25.8216			1.27993
$408$	−54.1067	+	4.71530i	−2.67868	+	0.233442i
$409$	5.09812	−	2.94340i	0.252086	−	0.145542i	−0.368633	−	0.929575i	$-0.620174\pi$
$409$	5.09812	−	2.94340i	0.252086	−	0.145542i	0.620719	+	0.784033i	$0.286841\pi$
$410$	−4.64241	−	7.00787i	−0.229272	−	0.346094i
$411$	6.78145	−	11.7458i	0.334504	−	0.579378i
$412$	−2.03028	−	0.237769i	−0.100025	−	0.0117140i
$413$	1.46208	+	4.84127i	0.0719441	+	0.238223i
$414$	−8.91343	−	10.0182i	−0.438071	−	0.492369i
$415$	−8.74075	−	21.7845i	−0.429066	−	1.06936i
$416$	2.43229	−	3.93837i	0.119253	−	0.193094i
$417$	49.3385	−	28.4856i	2.41612	−	1.39495i
$418$	−3.40495	−	16.4996i	−0.166542	−	0.807020i
$419$	−16.7262			−0.817126			−0.408563	−	0.912730i	$-0.633970\pi$
$419$	−16.7262			−0.817126			−0.408563	+	0.912730i	$0.633970\pi$
$420$	−14.4274	+	27.1196i	−0.703987	+	1.32330i
$421$	−1.18823			−0.0579109			−0.0289555	−	0.999581i	$-0.509218\pi$
$421$	−1.18823			−0.0579109			−0.0289555	+	0.999581i	$0.509218\pi$
$422$	6.30659	+	30.5602i	0.307000	+	1.48765i
$423$	−4.32339	+	2.49611i	−0.210210	+	0.121365i
$424$	−2.16635	+	4.64165i	−0.105207	+	0.225418i
$425$	35.4995	+	10.3639i	1.72198	+	0.502725i
$426$	−3.37824	−	3.79696i	−0.163676	−	0.183963i
$427$	18.8560	+	17.7042i	0.912506	+	0.856767i
$428$	1.68696	−	14.4047i	0.0815421	−	0.696276i
$429$	3.82687	−	6.62833i	0.184763	−	0.320019i
$430$	−6.31907	+	4.18610i	−0.304732	+	0.201872i
$431$	20.8669	−	12.0475i	1.00512	−	0.580307i	0.0953622	−	0.995443i	$-0.469599\pi$
$431$	20.8669	−	12.0475i	1.00512	−	0.580307i	0.909760	+	0.415135i	$0.136266\pi$
$432$	−5.58867	−	5.27740i	−0.268885	−	0.253909i
$433$	−14.9805			−0.719916			−0.359958	−	0.932968i	$-0.617209\pi$
$433$	−14.9805			−0.719916			−0.359958	+	0.932968i	$0.617209\pi$
$434$	3.40876	+	6.28741i	0.163626	+	0.301805i
$435$	−7.32546	+	9.32992i	−0.351229	+	0.447335i
$436$	12.7865	+	9.52369i	0.612363	+	0.456102i
$437$	4.19134	+	7.25962i	0.200499	+	0.347275i
$438$	25.7766	+	8.54465i	1.23165	+	0.408279i
$439$	−8.66266	+	15.0042i	−0.413446	+	0.716110i	−0.995264	−	0.0972091i	$-0.969008\pi$
$439$	−8.66266	+	15.0042i	−0.413446	+	0.716110i	0.581818	+	0.813319i	$0.302342\pi$
$440$	1.25481	−	22.7512i	0.0598206	−	1.08462i
$441$	21.8047	−	14.4919i	1.03832	−	0.690090i
$442$	5.68938	+	6.39456i	0.270616	+	0.304158i
$443$	−12.6162	+	21.8520i	−0.599416	+	1.03822i	0.393492	+	0.919328i	$0.371267\pi$
$443$	−12.6162	+	21.8520i	−0.599416	+	1.03822i	−0.992907	+	0.118890i	$0.962066\pi$
$444$	−34.1745	+	14.7323i	−1.62185	+	0.699164i
$445$	−23.4930	−	3.35923i	−1.11367	−	0.159243i
$446$	−6.73901	−	32.6556i	−0.319101	−	1.54629i
$447$		−	62.1779i		−	2.94091i
$448$	−11.6003	+	17.7040i	−0.548064	+	0.836436i
$449$	7.06145			0.333251			0.166625	−	0.986020i	$-0.446713\pi$
$449$	7.06145			0.333251			0.166625	+	0.986020i	$0.446713\pi$
$450$	11.3379	+	23.8935i	0.534475	+	1.12635i
$451$	−4.78848	−	8.29390i	−0.225481	−	0.390544i
$452$	−6.03001	−	13.9878i	−0.283628	−	0.657931i
$453$	9.09653	−	15.7556i	0.427392	−	0.740265i
$454$	22.1103	−	19.6720i	1.03769	−	0.923255i
$455$	4.78574	−	0.729497i	0.224359	−	0.0341993i
$456$	13.9201	+	19.8942i	0.651867	+	0.931633i
$457$	−16.3519	−	9.44078i	−0.764910	−	0.441621i	0.0661459	−	0.997810i	$-0.478930\pi$
$457$	−16.3519	−	9.44078i	−0.764910	−	0.441621i	−0.831056	+	0.556189i	$0.812263\pi$
$458$	−6.95562	−	2.30571i	−0.325015	−	0.107739i
$459$	12.3089	−	7.10656i	0.574531	−	0.331706i
$460$	2.96932	+	10.9418i	0.138445	+	0.510164i
$461$			34.6087i			1.61189i	0.591992	+	0.805944i	$0.298342\pi$
$461$			34.6087i			1.61189i	−0.591992	+	0.805944i	$0.701658\pi$
$462$	−18.3044	+	29.8288i	−0.851600	+	1.38776i
$463$	15.0235			0.698202			0.349101	−	0.937085i	$-0.386487\pi$
$463$	15.0235			0.698202			0.349101	+	0.937085i	$0.386487\pi$
$464$	−5.61159	+	5.94257i	−0.260511	+	0.275877i
$465$	10.9847	+	1.57069i	0.509405	+	0.0728392i
$466$	27.8804	+	9.24206i	1.29154	+	0.428130i
$467$	22.0309	+	12.7195i	1.01947	+	0.588590i	0.913950	−	0.405828i	$-0.133017\pi$
$467$	22.0309	+	12.7195i	1.01947	+	0.588590i	0.105518	+	0.994417i	$0.466350\pi$
$468$	−0.711981	+	6.07950i	−0.0329113	+	0.281025i
$469$	−7.08472	−	23.4591i	−0.327142	−	1.08324i
$470$	4.21288	−	0.259348i	0.194326	−	0.0119628i
$471$	14.4470	+	8.34096i	0.665681	+	0.384331i
$472$	4.89910	+	2.28650i	0.225499	+	0.105245i
$473$	−7.47869	+	4.31782i	−0.343871	+	0.198534i
$474$	27.8595	−	5.74925i	1.27963	−	0.264072i
$475$	−3.92264	−	16.0608i	−0.179983	−	0.736921i
$476$	−25.2223	−	29.9261i	−1.15606	−	1.37166i
$477$		−	6.77350i		−	0.310137i
$478$	−6.03905	−	29.2638i	−0.276220	−	1.33849i
$479$	10.2844	+	17.8131i	0.469905	+	0.813900i	0.999408	−	0.0344084i	$-0.0109547\pi$
$479$	10.2844	+	17.8131i	0.469905	+	0.813900i	−0.529502	+	0.848308i	$0.677621\pi$
$480$	11.3198	+	30.8268i	0.516676	+	1.40704i
$481$	5.07906	+	2.93239i	0.231585	+	0.133706i
$482$	−1.92089	+	1.70906i	−0.0874939	+	0.0778453i
$483$	3.97510	−	16.9538i	0.180873	−	0.771426i
$484$	0.460576	−	3.93279i	0.0209353	−	0.178763i
$485$	−15.1909	+	6.09518i	−0.689785	+	0.276768i
$486$	−29.4563	−	9.76443i	−1.33616	−	0.442924i
$487$	14.5295	+	25.1658i	0.658394	+	1.14037i	0.981031	+	0.193849i	$0.0620971\pi$
$487$	14.5295	+	25.1658i	0.658394	+	1.14037i	−0.322638	+	0.946522i	$0.604570\pi$
$488$	27.5462	−	2.40060i	1.24696	−	0.108670i
$489$		−	47.9749i		−	2.16950i
$490$	−21.9647	+	2.74815i	−0.992264	+	0.124149i
$491$		−	9.51815i		−	0.429548i	−0.976664	−	0.214774i	$-0.931098\pi$
$491$		−	9.51815i		−	0.429548i	0.976664	−	0.214774i	$-0.0689015\pi$
$492$	11.0695	+	8.24481i	0.499051	+	0.371705i
$493$	−7.55657	−	13.0884i	−0.340331	−	0.589470i
$494$	1.20400	−	3.63210i	0.0541706	−	0.163416i
$495$	11.2202	+	27.9639i	0.504309	+	1.25688i
$496$	7.43893	+	1.76660i	0.334018	+	0.0793226i
$497$	0.836015	−	3.56561i	0.0375004	−	0.159940i
$498$	25.6189	+	28.7943i	1.14801	+	1.29030i
$499$	17.4855	+	10.0953i	0.782760	+	0.451927i	0.837407	−	0.546579i	$-0.184070\pi$
$499$	17.4855	+	10.0953i	0.782760	+	0.451927i	−0.0546477	+	0.998506i	$0.517404\pi$
$500$	0.426164	−	22.3566i	0.0190586	−	0.999818i
$501$	−2.37413	−	4.11211i	−0.106068	−	0.183716i
$502$	−19.4164	+	4.00688i	−0.866595	+	0.178836i
$503$			13.3134i			0.593616i	0.954937	+	0.296808i	$0.0959221\pi$
$503$			13.3134i			0.593616i	−0.954937	+	0.296808i	$0.904078\pi$
$504$	3.99925	−	27.7018i	0.178141	−	1.23394i
$505$	−8.77949	+	11.1818i	−0.390682	+	0.497585i
$506$	2.61057	+	12.6502i	0.116054	+	0.562370i
$507$	−27.7233	+	16.0060i	−1.23123	+	0.710853i
$508$	16.1279	−	6.95261i	0.715562	−	0.308472i
$509$	12.4294	+	7.17613i	0.550925	+	0.318077i	0.749495	−	0.662010i	$-0.230296\pi$
$509$	12.4294	+	7.17613i	0.550925	+	0.318077i	−0.198570	+	0.980087i	$0.563630\pi$
$510$	−60.6077	+	3.73105i	−2.68376	+	0.165214i
$511$	5.65744	+	18.7331i	0.250270	+	0.828703i
$512$	5.83424	+	21.8623i	0.257839	+	0.966188i
$513$	−5.50282	−	3.17706i	−0.242956	−	0.140270i
$514$	7.95298	−	23.9917i	0.350791	−	1.05823i
$515$	−2.26242	−	0.323500i	−0.0996941	−	0.0142551i
$516$	7.43442	−	9.98147i	0.327282	−	0.439410i
$517$	4.80879			0.211490
$518$	−22.8568	−	14.0260i	−1.00427	−	0.616269i
$519$		−	39.5906i		−	1.73783i
$520$	2.83053	−	4.33262i	0.124127	−	0.189998i
$521$	−31.9571	+	18.4505i	−1.40007	+	0.808330i	−0.994399	−	0.105690i	$-0.966295\pi$
$521$	−31.9571	+	18.4505i	−1.40007	+	0.808330i	−0.405669	+	0.914020i	$0.632961\pi$
$522$	3.40079	−	10.2591i	0.148848	−	0.449030i
$523$	−15.7185	−	9.07509i	−0.687323	−	0.396826i	0.115285	−	0.993332i	$-0.463222\pi$
$523$	−15.7185	−	9.07509i	−0.687323	−	0.396826i	−0.802608	+	0.596506i	$0.796555\pi$
$524$	−3.11481	+	26.5969i	−0.136071	+	1.16189i
$525$	−16.8966	+	29.9005i	−0.737427	+	1.30496i
$526$	20.5837	+	23.1349i	0.897490	+	1.00873i
$527$	−7.06883	+	12.2436i	−0.307923	+	0.533338i
$528$	10.7142	+	35.8467i	0.466276	+	1.56003i
$529$	8.28651	+	14.3526i	0.360283	+	0.624028i
$530$	−2.55330	+	5.12622i	−0.110908	+	0.222669i
$531$	−7.14919			−0.310248
$532$	−5.94841	+	16.4546i	−0.257896	+	0.713397i
$533$		−	2.17519i		−	0.0942178i
$534$	38.1630	−	7.87554i	1.65147	−	0.340808i
$535$	2.29521	−	16.0517i	0.0992307	−	0.693976i
$536$	−23.7393	−	11.0796i	−1.02538	−	0.478566i
$537$	−16.2740	+	28.1874i	−0.702276	+	1.21638i
$538$	−3.04588	+	2.70999i	−0.131317	+	0.116836i
$539$	−25.1693	+	1.58743i	−1.08412	+	0.0683756i
$540$	−6.09618	−	6.05738i	−0.262338	−	0.260668i
$541$	9.37629	−	16.2402i	0.403118	−	0.698221i	−0.590982	−	0.806685i	$-0.701260\pi$
$541$	9.37629	−	16.2402i	0.403118	−	0.698221i	0.994100	+	0.108463i	$0.0345930\pi$
$542$	7.54509	−	22.7612i	0.324090	−	0.977678i
$543$	−10.4086	−	18.0283i	−0.446677	−	0.773667i
$544$	−41.8213	−	1.24046i	−1.79307	−	0.0531842i
$545$	14.0202	+	11.0081i	0.600561	+	0.471535i
$546$	−6.98790	+	3.78854i	−0.299055	+	0.162135i
$547$	−34.1580			−1.46049			−0.730246	−	0.683185i	$-0.760594\pi$
$547$	−34.1580			−1.46049			−0.730246	+	0.683185i	$0.760594\pi$
$548$	6.24119	−	8.37943i	0.266610	−	0.357952i
$549$	−31.6653	+	18.2820i	−1.35144	+	0.780256i
$550$	2.04964	−	25.3927i	0.0873968	−	1.08275i
$551$	−3.37824	+	5.85128i	−0.143918	+	0.249273i
$552$	−10.6725	−	15.2529i	−0.454252	−	0.649206i
$553$	14.9440	+	14.0312i	0.635485	+	0.596667i
$554$	−28.3702	+	25.2416i	−1.20534	+	1.07241i
$555$	−38.6150	+	15.4938i	−1.63911	+	0.657674i
$556$	40.3029	−	17.3742i	1.70923	−	0.736831i
$557$	−35.0192	+	20.2183i	−1.48381	+	0.856679i	−0.999831	−	0.0184005i	$-0.994143\pi$
$557$	−35.0192	+	20.2183i	−1.48381	+	0.856679i	−0.483980	+	0.875079i	$0.660809\pi$
$558$	−9.90183	+	2.04340i	−0.419178	+	0.0865041i
$559$	−1.96139			−0.0829579
$560$	−13.4690	+	19.4573i	−0.569168	+	0.822221i
$561$	−69.1805			−2.92080
$562$	−34.5561	+	7.13120i	−1.45766	+	0.300811i
$563$	0.276201	−	0.159465i	0.0116405	−	0.00672065i	−0.494168	−	0.869366i	$-0.664527\pi$
$563$	0.276201	−	0.159465i	0.0116405	−	0.00672065i	0.505809	+	0.862646i	$0.331194\pi$
$564$	−6.36435	+	2.74361i	−0.267987	+	0.115527i
$565$	−6.34168	−	15.8053i	−0.266797	−	0.664934i
$566$	−10.3946	+	9.24835i	−0.436920	+	0.388737i
$567$	−4.76655	−	15.7831i	−0.200176	−	0.662830i
$568$	−2.24457	−	3.20788i	−0.0941800	−	0.134600i
$569$	−15.3058	+	26.5104i	−0.641651	+	1.11137i	0.343413	+	0.939184i	$0.388417\pi$
$569$	−15.3058	+	26.5104i	−0.641651	+	1.11137i	−0.985064	+	0.172188i	$0.944916\pi$
$570$	14.9922	+	22.6312i	0.627953	+	0.947917i
$571$	7.35081	−	4.24399i	0.307622	−	0.177606i	−0.338240	−	0.941060i	$-0.609832\pi$
$571$	7.35081	−	4.24399i	0.307622	−	0.177606i	0.645862	+	0.763454i	$0.276498\pi$
$572$	3.52200	−	4.72864i	0.147262	−	0.197714i
$573$	17.5486			0.733103
$574$	−0.266495	+	9.94264i	−0.0111233	+	0.414998i
$575$	3.00748	+	12.3138i	0.125421	+	0.513521i
$576$	−19.2177	−	22.9342i	−0.800735	−	0.955591i
$577$	1.68251	+	2.91419i	0.0700438	+	0.121319i	0.898920	−	0.438112i	$-0.144353\pi$
$577$	1.68251	+	2.91419i	0.0700438	+	0.121319i	−0.828876	+	0.559432i	$0.811019\pi$
$578$	16.7781	−	50.6145i	0.697879	−	2.10529i
$579$	−3.06354	+	5.30620i	−0.127316	+	0.220518i
$580$	−6.44095	+	6.48221i	−0.267446	+	0.269159i
$581$	−6.33993	+	27.0399i	−0.263025	+	1.12180i
$582$	20.0791	−	17.8648i	0.832305	−	0.740520i
$583$	−3.26230	+	5.65048i	−0.135111	+	0.234019i
$584$	18.9568	+	8.84752i	0.784439	+	0.366113i
$585$	−0.968697	+	6.77464i	−0.0400507	+	0.280097i
$586$	32.4151	−	6.68938i	1.33906	−	0.276336i
$587$			2.02359i			0.0835225i	0.999128	+	0.0417613i	$0.0132969\pi$
$587$			2.02359i			0.0835225i	−0.999128	+	0.0417613i	$0.986703\pi$
$588$	32.4054	−	16.4610i	1.33638	−	0.678842i
$589$	6.32038			0.260427
$590$	5.41054	+	2.69492i	0.222748	+	0.110948i
$591$	26.3779	+	45.6878i	1.08504	+	1.87935i
$592$	−27.4681	+	8.20992i	−1.12893	+	0.337426i
$593$	13.4129	−	23.2318i	0.550802	−	0.954016i	−0.447415	−	0.894326i	$-0.647655\pi$
$593$	13.4129	−	23.2318i	0.550802	−	0.954016i	0.998217	−	0.0596901i	$-0.0190113\pi$
$594$	−6.50817	−	7.31483i	−0.267033	−	0.300131i
$595$	−27.3390	−	34.1651i	−1.12079	−	1.40063i
$596$	5.57151	−	47.5743i	0.228218	−	1.94872i
$597$	25.7622	+	14.8738i	1.05438	+	0.608744i
$598$	−0.923107	+	2.78473i	−0.0377487	+	0.113876i
$599$	32.0964	−	18.5309i	1.31143	−	0.757152i	0.329093	−	0.944297i	$-0.393257\pi$
$599$	32.0964	−	18.5309i	1.31143	−	0.757152i	0.982332	+	0.187146i	$0.0599237\pi$
$600$	11.7749	+	34.7763i	0.480710	+	1.41973i
$601$			1.27911i			0.0521761i	0.999660	+	0.0260880i	$0.00830503\pi$
$601$			1.27911i			0.0521761i	−0.999660	+	0.0260880i	$0.991695\pi$
$602$	8.96537	+	0.240301i	0.365401	+	0.00979396i
$603$	34.6425			1.41075
$604$	8.37184	−	11.2400i	0.340645	−	0.457351i
$605$	0.626644	−	4.38247i	0.0254767	−	0.178173i
$606$	7.34501	−	22.1576i	0.298371	−	0.900093i
$607$	−19.5800	−	11.3045i	−0.794727	−	0.458836i	0.0468970	−	0.998900i	$-0.485067\pi$
$607$	−19.5800	−	11.3045i	−0.794727	−	0.458836i	−0.841624	+	0.540064i	$0.818400\pi$
$608$	8.86805	+	16.4690i	0.359647	+	0.667907i
$609$	13.4361	−	4.05773i	0.544458	−	0.164428i
$610$	30.8560	−	1.89951i	1.24932	−	0.0769091i
$611$	0.945877	+	0.546102i	0.0382661	+	0.0220929i
$612$	50.8070	−	21.9024i	2.05375	−	0.885353i
$613$	−2.61492	+	1.50973i	−0.105616	+	0.0609773i	−0.551877	−	0.833925i	$-0.686088\pi$
$613$	−2.61492	+	1.50973i	−0.105616	+	0.0609773i	0.446262	+	0.894903i	$0.352755\pi$
$614$	−0.624606	−	3.02669i	−0.0252071	−	0.122147i
$615$	12.1375	+	9.52987i	0.489432	+	0.384281i
$616$	−16.6781	+	21.1828i	−0.671982	+	0.853479i
$617$		−	14.3344i		−	0.577081i	−0.957468	−	0.288540i	$-0.906830\pi$
$617$		−	14.3344i		−	0.577081i	0.957468	−	0.288540i	$-0.0931700\pi$
$618$	3.67517	−	0.758431i	0.147837	−	0.0305086i
$619$	10.8987	+	18.8771i	0.438055	+	0.758733i	0.997539	−	0.0701078i	$-0.0223343\pi$
$619$	10.8987	+	18.8771i	0.438055	+	0.758733i	−0.559485	+	0.828841i	$0.689001\pi$
$620$	8.26403	+	2.18608i	0.331891	+	0.0877952i
$621$	4.21901	+	2.43584i	0.169303	+	0.0977471i
$622$	27.1674	+	30.5347i	1.08931	+	1.22433i
$623$	20.4709	+	19.2205i	0.820150	+	0.770052i
$624$	−1.96342	+	8.26771i	−0.0785997	+	0.330973i
$625$	1.11226	−	24.9752i	0.0444904	−	0.999010i
$626$	2.82701	−	8.52821i	0.112990	−	0.340856i
$627$	15.4639	+	26.7843i	0.617570	+	1.06966i
$628$	10.3064	+	7.67646i	0.411271	+	0.306324i
$629$		−	53.0106i		−	2.11367i
$630$	5.25785	−	30.8477i	0.209478	−	1.22900i
$631$			15.1512i			0.603160i	0.953441	+	0.301580i	$0.0975140\pi$
$631$			15.1512i			0.603160i	−0.953441	+	0.301580i	$0.902486\pi$
$632$	21.8313	−	1.90256i	0.868404	−	0.0756797i
$633$	−28.6420	−	49.6094i	−1.13842	−	1.97180i
$634$	−25.2409	−	8.36708i	−1.00244	−	0.332299i
$635$	18.2235	−	7.31196i	0.723179	−	0.290166i
$636$	1.09378	−	9.33959i	0.0433710	−	0.370339i
$637$	−5.13101	−	2.54606i	−0.203298	−	0.100879i
$638$	−7.77803	+	6.92029i	−0.307935	+	0.273977i
$639$	4.48363	+	2.58863i	0.177370	+	0.102404i
$640$	5.89888	+	24.6009i	0.233174	+	0.972435i
$641$	−14.9960	−	25.9739i	−0.592308	−	1.02591i	−0.993921	−	0.110098i	$-0.964884\pi$
$641$	−14.9960	−	25.9739i	−0.592308	−	1.02591i	0.401613	−	0.915809i	$-0.368450\pi$
$642$	5.38101	+	26.0751i	0.212372	+	1.02910i
$643$			1.63196i			0.0643583i	0.999482	+	0.0321792i	$0.0102447\pi$
$643$			1.63196i			0.0643583i	−0.999482	+	0.0321792i	$0.989755\pi$
$644$	4.56063	−	12.6157i	0.179714	−	0.497129i
$645$	8.59318	−	10.9445i	0.338356	−	0.430940i
$646$	−33.8728	+	6.99020i	−1.33271	+	0.275026i
$647$	−28.3765	+	16.3832i	−1.11560	+	0.644090i	−0.940273	−	0.340421i	$-0.889430\pi$
$647$	−28.3765	+	16.3832i	−1.11560	+	0.644090i	−0.175323	+	0.984511i	$0.556097\pi$
$648$	−15.9717	−	7.45428i	−0.627426	−	0.292832i
$649$	5.96388	+	3.44325i	0.234103	+	0.135159i
$650$	3.28684	−	4.76193i	0.128921	−	0.186778i
$651$	−9.57170	−	8.98703i	−0.375145	−	0.352229i
$652$	4.29883	−	36.7071i	0.168355	−	1.43756i
$653$	19.5109	+	11.2646i	0.763521	+	0.440819i	0.830558	−	0.556932i	$-0.188021\pi$
$653$	19.5109	+	11.2646i	0.763521	+	0.440819i	−0.0670377	+	0.997750i	$0.521355\pi$
$654$	−27.7822	−	9.20948i	−1.08637	−	0.360119i
$655$	−4.23790	+	29.6380i	−0.165589	+	1.15805i
$656$	7.73083	+	7.30025i	0.301838	+	0.285027i
$657$	−27.6635			−1.07925
$658$	−4.25663	−	2.61208i	−0.165941	−	0.101830i
$659$		−	19.2525i		−	0.749969i	−0.927031	−	0.374985i	$-0.877648\pi$
$659$		−	19.2525i		−	0.749969i	0.927031	−	0.374985i	$-0.122352\pi$
$660$	10.9553	+	40.3697i	0.426434	+	1.57139i
$661$	30.1079	−	17.3828i	1.17106	−	0.676113i	0.217132	−	0.976142i	$-0.430330\pi$
$661$	30.1079	−	17.3828i	1.17106	−	0.676113i	0.953930	+	0.300030i	$0.0969966\pi$
$662$	17.5702	+	5.82433i	0.682885	+	0.226369i
$663$	−13.6077	−	7.85638i	−0.528477	−	0.305117i
$664$	17.0217	+	24.3270i	0.660570	+	0.944071i
$665$	−7.11643	+	18.2216i	−0.275963	+	0.706605i
$666$	28.3228	−	25.1994i	1.09749	−	0.976458i
$667$	2.59009	−	4.48617i	0.100289	−	0.173705i
$668$	−1.44805	−	3.35904i	−0.0560268	−	0.129965i
$669$	30.6059	+	53.0110i	1.18329	+	2.04952i
$670$	−26.2176	−	13.0587i	−1.01288	−	0.504500i
$671$	35.2205			1.35967
$672$	9.98759	−	37.5506i	0.385280	−	1.44855i
$673$		−	42.6368i		−	1.64353i	−0.569827	−	0.821764i	$-0.692990\pi$
$673$		−	42.6368i		−	1.64353i	0.569827	−	0.821764i	$-0.307010\pi$
$674$	−3.35325	−	16.2491i	−0.129162	−	0.625890i
$675$	−6.64123	−	6.94357i	−0.255621	−	0.267258i
$676$	−22.6462	+	9.76255i	−0.871007	+	0.375483i
$677$	−0.892648	+	1.54611i	−0.0343073	+	0.0594219i	−0.882669	−	0.469995i	$-0.844256\pi$
$677$	−0.892648	+	1.54611i	−0.0343073	+	0.0594219i	0.848362	+	0.529417i	$0.177589\pi$
$678$	18.5873	+	20.8911i	0.713842	+	0.802319i
$679$	18.8557	+	4.42102i	0.723615	+	0.169663i
$680$	−46.7072	−	2.57606i	−1.79114	−	0.0987874i
$681$	−27.1648	+	47.0509i	−1.04096	+	1.80299i
$682$	9.24431	+	3.06439i	0.353983	+	0.117341i
$683$	4.30263	+	7.45237i	0.164636	+	0.285157i	0.936526	−	0.350599i	$-0.114022\pi$
$683$	4.30263	+	7.45237i	0.164636	+	0.285157i	−0.771890	+	0.635756i	$0.780689\pi$
$684$	−19.8367	−	14.7749i	−0.758477	−	0.564931i
$685$	7.21396	−	9.18792i	0.275631	−	0.351052i
$686$	23.1416	+	12.2665i	0.883549	+	0.468338i
$687$	13.4523			0.513236
$688$	6.58271	−	6.97097i	0.250963	−	0.265766i
$689$	−1.28338	+	0.740957i	−0.0488927	+	0.0282282i
$690$	−11.4945	−	17.3513i	−0.437587	−	0.660553i
$691$	−20.1511	+	34.9027i	−0.766583	+	1.32776i	0.172822	+	0.984953i	$0.444711\pi$
$691$	−20.1511	+	34.9027i	−0.766583	+	1.32776i	−0.939405	+	0.342808i	$0.888622\pi$
$692$	3.54755	−	30.2920i	0.134858	−	1.15153i
$693$	8.13834	−	34.7101i	0.309150	−	1.31853i
$694$	4.14720	+	4.66123i	0.157426	+	0.176938i
$695$	45.5397	−	18.2722i	1.72742	−	0.693105i
$696$	6.34578	−	13.5966i	0.240536	−	0.515377i
$697$	−17.0270	+	9.83053i	−0.644943	+	0.372358i
$698$	−5.24425	−	25.4124i	−0.198498	−	0.961874i
$699$	−53.9212			−2.03949
$700$	−15.6074	+	21.3638i	−0.589903	+	0.807474i
$701$	37.3051			1.40899			0.704497	−	0.709707i	$-0.251172\pi$
$701$	37.3051			1.40899			0.704497	+	0.709707i	$0.251172\pi$
$702$	−0.449444	−	2.17790i	−0.0169632	−	0.0821995i
$703$	−20.5239	+	11.8495i	−0.774072	+	0.446911i
$704$	4.98570	+	28.3875i	0.187906	+	1.06990i
$705$	−7.19130	+	2.88542i	−0.270840	+	0.108671i
$706$	−11.0438	−	12.4126i	−0.415637	−	0.467154i
$707$	16.1030	−	4.86315i	0.605617	−	0.182898i
$708$	−9.85761	−	1.15444i	−0.370472	−	0.0433866i
$709$	4.02866	−	6.97784i	0.151299	−	0.262058i	−0.780406	−	0.625273i	$-0.784988\pi$
$709$	4.02866	−	6.97784i	0.151299	−	0.262058i	0.931705	+	0.363215i	$0.118321\pi$
$710$	−2.41744	−	3.64921i	−0.0907249	−	0.136952i
$711$	−25.0958	+	14.4891i	−0.941168	+	0.543383i
$712$	29.9054	−	2.60620i	1.12075	−	0.0976714i
$713$	−4.84582			−0.181477
$714$	61.2371	+	37.5782i	2.29174	+	1.40633i
$715$	4.07095	−	5.18488i	0.152245	−	0.193903i
$716$	−14.9775	+	20.1089i	−0.559737	+	0.751503i
$717$	27.4269	+	47.5049i	1.02428	+	1.77410i
$718$	0.265660	+	0.0880634i	0.00991434	+	0.00328650i
$719$	5.87241	−	10.1713i	0.219004	−	0.379326i	−0.735500	−	0.677525i	$-0.763053\pi$
$719$	5.87241	−	10.1713i	0.219004	−	0.379326i	0.954504	+	0.298199i	$0.0963859\pi$
$720$	−20.8267	−	26.1795i	−0.776164	−	0.975654i
$721$	1.97139	+	1.85097i	0.0734184	+	0.0689338i
$722$	−7.58289	−	8.52275i	−0.282206	−	0.317184i
$723$	2.36001	−	4.08766i	0.0877697	−	0.152022i
$724$	−6.34853	−	14.7267i	−0.235941	−	0.547312i
$725$	−7.38326	+	7.06177i	−0.274208	+	0.262268i
$726$	1.46913	+	7.11908i	0.0545247	+	0.264214i
$727$		−	33.3549i		−	1.23706i	−0.785760	−	0.618532i	$-0.787728\pi$
$727$		−	33.3549i		−	1.23706i	0.785760	−	0.618532i	$-0.212272\pi$
$728$	−5.68614	+	2.27258i	−0.210742	+	0.0842273i
$729$	38.2742			1.41756
$730$	20.9358	+	10.4279i	0.774870	+	0.385953i
$731$	8.86429	+	15.3534i	0.327857	+	0.567866i
$732$	−46.6137	+	20.0947i	−1.72289	+	0.742722i
$733$	−5.75003	+	9.95934i	−0.212382	+	0.367856i	−0.952460	−	0.304665i	$-0.901455\pi$
$733$	−5.75003	+	9.95934i	−0.212382	+	0.367856i	0.740077	+	0.672522i	$0.234789\pi$
$734$	−7.95403	+	7.07688i	−0.293588	+	0.261212i
$735$	36.6869	−	17.4763i	1.35322	−	0.644621i
$736$	−6.79912	−	12.6268i	−0.250619	−	0.465429i
$737$	−28.8989	−	16.6848i	−1.06451	−	0.614593i
$738$	−13.3463	−	4.42417i	−0.491286	−	0.162856i
$739$	−9.70301	+	5.60203i	−0.356931	+	0.206074i	−0.667734	−	0.744400i	$-0.732735\pi$
$739$	−9.70301	+	5.60203i	−0.356931	+	0.206074i	0.310803	+	0.950474i	$0.399402\pi$
$740$	−30.9339	+	8.39465i	−1.13715	+	0.308593i
$741$			7.02455i			0.258053i
$742$	5.95700	−	3.22963i	0.218688	−	0.118564i
$743$	−43.7950			−1.60668			−0.803341	−	0.595520i	$-0.796946\pi$
$743$	−43.7950			−1.60668			−0.803341	+	0.595520i	$0.796946\pi$
$744$	−13.9830	+	1.21859i	−0.512643	+	0.0446759i
$745$	7.58040	−	53.0140i	0.277724	−	1.94228i
$746$	−41.8007	−	13.8565i	−1.53043	−	0.507322i
$747$	−34.0017	−	19.6309i	−1.24406	−	0.718256i
$748$	−52.9322	−	6.19898i	−1.93539	−	0.226657i
$749$	−13.1325	+	13.9869i	−0.479852	+	0.511069i
$750$	12.1713	+	39.2034i	0.444432	+	1.43151i
$751$	−44.5322	−	25.7107i	−1.62500	−	0.938196i	−0.985554	−	0.169364i	$-0.945829\pi$
$751$	−44.5322	−	25.7107i	−1.62500	−	0.938196i	−0.639450	−	0.768832i	$-0.720838\pi$
$752$	−5.11541	+	1.52894i	−0.186540	+	0.0557547i
$753$	31.5192	−	18.1976i	1.14862	−	0.663159i
$754$	−2.31581	+	0.477905i	−0.0843369	+	0.0174043i
$755$	9.67670	−	12.3245i	0.352171	−	0.448536i
$756$	1.78755	+	10.0101i	0.0650126	+	0.364064i
$757$			18.1453i			0.659502i	0.944068	+	0.329751i	$0.106965\pi$
$757$			18.1453i			0.659502i	−0.944068	+	0.329751i	$0.893035\pi$
$758$	4.67022	+	22.6308i	0.169630	+	0.821987i
$759$	−11.8562	−	20.5355i	−0.430352	−	0.745391i
$760$	9.44310	+	18.6592i	0.342537	+	0.676842i
$761$	−28.4860	−	16.4464i	−1.03262	−	0.596181i	−0.114883	−	0.993379i	$-0.536649\pi$
$761$	−28.4860	−	16.4464i	−1.03262	−	0.596181i	−0.917733	+	0.397198i	$0.869983\pi$
$762$	−24.0875	+	21.4312i	−0.872598	+	0.776370i
$763$	−6.09762	−	20.1906i	−0.220749	−	0.730950i
$764$	13.4270	+	1.57246i	0.485771	+	0.0568895i
$765$	57.4086	−	23.0345i	2.07561	−	0.832814i
$766$	11.8783	+	3.93753i	0.429181	+	0.142269i
$767$	0.782054	+	1.35456i	0.0282383	+	0.0489102i
$768$	−22.7948	−	34.7259i	−0.822535	−	1.25306i
$769$			20.8502i			0.751876i	0.926645	+	0.375938i	$0.122679\pi$
$769$			20.8502i			0.751876i	−0.926645	+	0.375938i	$0.877321\pi$
$770$	−19.2433	+	23.2010i	−0.693479	+	0.836105i
$771$			46.4003i			1.67107i
$772$	−2.81947	+	3.78543i	−0.101475	+	0.136241i
$773$	4.34380	+	7.52368i	0.156236	+	0.270608i	0.933508	−	0.358556i	$-0.116731\pi$
$773$	4.34380	+	7.52368i	0.156236	+	0.270608i	−0.777273	+	0.629164i	$0.783397\pi$
$774$	−3.98932	+	12.0345i	−0.143393	+	0.432572i
$775$	9.17429	+	2.67840i	0.329550	+	0.0962110i
$776$	16.9639	−	11.8697i	0.608970	−	0.426099i
$777$	47.9306	+	11.2381i	1.71950	+	0.403165i
$778$	8.78497	+	9.87384i	0.314957	+	0.353994i
$779$	7.61208	+	4.39484i	0.272731	+	0.157461i
$780$	−2.42964	+	9.18474i	−0.0869951	+	0.328867i
$781$	−2.49351	−	4.31888i	−0.0892247	−	0.154542i
$782$	25.9703	−	5.35937i	0.928694	−	0.191651i
$783$			3.92660i			0.140325i
$784$	26.2694	−	9.69115i	0.938193	−	0.346113i
$785$	11.3008	+	8.87294i	0.403344	+	0.316689i
$786$	−9.93555	−	48.1453i	−0.354389	−	1.71729i
$787$	32.2270	−	18.6062i	1.14877	−	0.663241i	0.200180	−	0.979759i	$-0.435847\pi$
$787$	32.2270	−	18.6062i	1.14877	−	0.663241i	0.948586	+	0.316518i	$0.102514\pi$
$788$	16.0887	+	37.3208i	0.573135	+	1.32950i
$789$	−49.2312	−	28.4237i	−1.75268	−	1.01191i
$790$	24.4544	−	1.50543i	0.870048	−	0.0535608i
$791$	−4.59982	+	19.6183i	−0.163551	+	0.697545i
$792$	−21.8501	−	31.2277i	−0.776411	−	1.10963i
$793$	6.92778	+	3.99976i	0.246013	+	0.142036i
$794$	−9.03437	+	27.2539i	−0.320618	+	0.967205i
$795$	1.48815	−	10.4075i	0.0527793	−	0.369115i
$796$	18.3787	+	13.6889i	0.651415	+	0.485189i
$797$	−21.3900			−0.757671			−0.378835	−	0.925464i	$-0.623675\pi$
$797$	−21.3900			−0.757671			−0.378835	+	0.925464i	$0.623675\pi$
$798$	0.860619	−	32.1087i	0.0304656	−	1.13664i
$799$		−	9.87221i		−	0.349254i
$800$	5.89322	+	27.6635i	0.208357	+	0.978053i
$801$	−34.3773	+	19.8477i	−1.21466	+	0.701285i
$802$	−4.93341	+	14.8826i	−0.174205	+	0.525522i
$803$	23.0770	+	13.3235i	0.814368	+	0.470176i
$804$	47.7666	+	5.59403i	1.68460	+	0.197286i
$805$	5.45616	−	13.9705i	0.192304	−	0.492396i
$806$	1.47033	+	1.65257i	0.0517902	+	0.0582094i
$807$	3.74219	−	6.48166i	0.131731	−	0.228165i
$808$	7.60536	−	16.2954i	0.267556	−	0.573269i
$809$	−12.1707	−	21.0803i	−0.427900	−	0.741144i	0.568787	−	0.822485i	$-0.307413\pi$
$809$	−12.1707	−	21.0803i	−0.427900	−	0.741144i	−0.996686	+	0.0813411i	$0.974080\pi$
$810$	−17.6390	−	8.78577i	−0.619773	−	0.308700i
$811$	31.3778			1.10183			0.550913	−	0.834563i	$-0.314280\pi$
$811$	31.3778			1.10183			0.550913	+	0.834563i	$0.314280\pi$
$812$	10.6440	−	1.90075i	0.373530	−	0.0667031i
$813$			44.0206i			1.54387i
$814$	−35.7637	+	7.38041i	−1.25352	+	0.258683i
$815$	5.84884	−	40.9042i	0.204876	−	1.43281i
$816$	73.5917	−	21.9958i	2.57622	−	0.770006i
$817$	3.96287	−	6.86389i	0.138643	−	0.240137i
$818$	−6.21976	+	5.53386i	−0.217469	+	0.193487i
$819$	5.54259	−	5.90317i	0.193674	−	0.206274i
$820$	8.43287	+	8.37920i	0.294489	+	0.292614i
$821$	−0.0785681	+	0.136084i	−0.00274204	+	0.00474936i	−0.867393	−	0.497623i	$-0.834206\pi$
$821$	−0.0785681	+	0.136084i	−0.00274204	+	0.00474936i	0.864651	+	0.502373i	$0.167539\pi$
$822$	−6.03528	+	18.2066i	−0.210505	+	0.635027i
$823$	9.34753	+	16.1904i	0.325835	+	0.564362i	0.981681	−	0.190532i	$-0.0610214\pi$
$823$	9.34753	+	16.1904i	0.325835	+	0.564362i	−0.655846	+	0.754894i	$0.727688\pi$
$824$	2.87995	−	0.250982i	0.100328	−	0.00874338i
$825$	11.0961	+	45.4317i	0.386316	+	1.58173i
$826$	−3.40876	−	6.28741i	−0.118606	−	0.218767i
$827$	−35.2960			−1.22736			−0.613681	−	0.789554i	$-0.710312\pi$
$827$	−35.2960			−1.22736			−0.613681	+	0.789554i	$0.710312\pi$
$828$	15.2088	+	11.3279i	0.528542	+	0.393670i
$829$	−14.2590	+	8.23245i	−0.495237	+	0.285925i	−0.726744	−	0.686908i	$-0.758967\pi$
$829$	−14.2590	+	8.23245i	−0.495237	+	0.285925i	0.231508	+	0.972833i	$0.425634\pi$
$830$	18.3327	+	27.6738i	0.636337	+	0.960572i
$831$	34.8558	−	60.3720i	1.20913	−	2.09428i
$832$	−2.24311	+	6.14996i	−0.0777659	+	0.213211i
$833$	3.25893	+	51.6713i	0.112915	+	1.79030i
$834$	−60.1934	+	53.5555i	−2.08433	+	1.85447i
$835$	−1.52290	−	3.79550i	−0.0527020	−	0.131349i
$836$	9.43191	+	21.8792i	0.326209	+	0.756707i
$837$	3.18105	−	1.83658i	0.109953	−	0.0634814i
$838$	23.1662	−	4.78072i	0.800264	−	0.165147i
$839$	−54.8000			−1.89191			−0.945953	−	0.324303i	$-0.894870\pi$
$839$	−54.8000			−1.89191			−0.945953	+	0.324303i	$0.894870\pi$
$840$	12.2310	−	41.6852i	0.422010	−	1.43828i
$841$	−24.8248			−0.856026
$842$	1.64574	−	0.339624i	0.0567158	−	0.0117042i
$843$	56.0960	−	32.3871i	1.93205	−	1.11547i
$844$	−17.4696	−	40.5243i	−0.601329	−	1.39490i
$845$	−25.5887	+	10.2671i	−0.880278	+	0.353201i
$846$	5.27458	−	4.69291i	0.181344	−	0.161346i
$847$	−3.58546	+	3.81872i	−0.123198	+	0.131213i
$848$	1.67376	−	7.04801i	0.0574773	−	0.242030i
$849$	12.7709	−	22.1199i	0.438297	−	0.759152i
$850$	−52.1301	−	4.20781i	−1.78805	−	0.144327i
$851$	15.7356	−	9.08496i	0.539410	−	0.311428i
$852$	5.76422	+	4.29332i	0.197479	+	0.147087i
$853$	38.9225			1.33268			0.666340	−	0.745648i	$-0.267860\pi$
$853$	38.9225			1.33268			0.666340	+	0.745648i	$0.267860\pi$
$854$	−31.1764	−	19.1314i	−1.06683	−	0.654662i
$855$	−21.7507	−	17.0777i	−0.743858	−	0.584046i
$856$	1.78070	+	20.4331i	0.0608631	+	0.698388i
$857$	14.6766	+	25.4206i	0.501342	+	0.868350i	0.999999	+	0.00155047i	$0.000493529\pi$
$857$	14.6766	+	25.4206i	0.501342	+	0.868350i	−0.498657	+	0.866800i	$0.666173\pi$
$858$	−3.40580	+	10.2742i	−0.116272	+	0.350757i
$859$	23.6874	−	41.0277i	0.808202	−	1.39985i	−0.105905	−	0.994376i	$-0.533774\pi$
$859$	23.6874	−	41.0277i	0.808202	−	1.39985i	0.914108	−	0.405471i	$-0.132893\pi$
$860$	7.55561	−	7.60401i	0.257644	−	0.259294i
$861$	−5.27880	−	17.4793i	−0.179901	−	0.595694i
$862$	−25.4578	+	22.6504i	−0.867095	+	0.771474i
$863$	11.8505	−	20.5257i	0.403397	−	0.698704i	−0.590737	−	0.806865i	$-0.701163\pi$
$863$	11.8505	−	20.5257i	0.403397	−	0.698704i	0.994133	+	0.108161i	$0.0344961\pi$
$864$	9.24887	+	5.71198i	0.314653	+	0.194326i
$865$	4.82667	−	33.7556i	0.164112	−	1.14773i
$866$	20.7484	−	4.28176i	0.705060	−	0.145500i
$867$			97.8892i			3.32449i
$868$	−6.51832	−	7.73394i	−0.221246	−	0.262507i
$869$	27.9134			0.946897
$870$	7.47926	−	15.0160i	0.253571	−	0.509090i
$871$	−3.78957	−	6.56372i	−0.128405	−	0.222403i
$872$	−20.4318	−	9.53591i	−0.691908	−	0.322927i
$873$	−13.6892	+	23.7103i	−0.463308	+	0.802474i
$874$	−7.88009	−	8.85680i	−0.266548	−	0.299586i
$875$	−18.0516	+	23.4337i	−0.610256	+	0.792204i
$876$	−38.1436	−	4.46706i	−1.28875	−	0.150928i
$877$	−28.7555	−	16.6020i	−0.971004	−	0.560610i	−0.0714621	−	0.997443i	$-0.522766\pi$
$877$	−28.7555	−	16.6020i	−0.971004	−	0.560610i	−0.899542	+	0.436834i	$0.856100\pi$
$878$	7.70951	−	23.2572i	0.260183	−	0.784893i
$879$	−52.6205	+	30.3805i	−1.77485	+	1.02471i
$880$	4.76488	+	31.8698i	0.160624	+	1.07433i
$881$		−	19.2043i		−	0.647008i	−0.946227	−	0.323504i	$-0.895139\pi$
$881$		−	19.2043i		−	0.647008i	0.946227	−	0.323504i	$-0.104861\pi$
$882$	−26.0580	+	26.3040i	−0.877420	+	0.885700i
$883$	8.57526			0.288581			0.144290	−	0.989535i	$-0.453910\pi$
$883$	8.57526			0.288581			0.144290	+	0.989535i	$0.453910\pi$
$884$	−9.70767	−	7.23049i	−0.326504	−	0.243188i
$885$	−10.9847	−	1.57069i	−0.369248	−	0.0527983i
$886$	11.2281	−	33.8716i	0.377214	−	1.13794i
$887$	12.7746	+	7.37543i	0.428930	+	0.247643i	0.698891	−	0.715229i	$-0.253677\pi$
$887$	12.7746	+	7.37543i	0.428930	+	0.247643i	−0.269961	+	0.962871i	$0.587011\pi$
$888$	43.1219	−	30.1725i	1.44707	−	1.01252i
$889$	−22.6199	−	5.30359i	−0.758646	−	0.177877i
$890$	33.4986	−	2.06220i	1.12287	−	0.0691250i
$891$	−19.4430	−	11.2254i	−0.651365	−	0.376066i
$892$	18.6674	+	43.3028i	0.625032	+	1.44989i
$893$	−3.82218	+	2.20673i	−0.127904	+	0.0738455i
$894$	17.7719	+	86.1182i	0.594380	+	2.88022i
$895$	−17.3120	+	22.0491i	−0.578676	+	0.737019i
$896$	11.0066	−	27.8362i	0.367704	−	0.929943i
$897$		−	5.38571i		−	0.179824i
$898$	−9.78032	+	2.01832i	−0.326373	+	0.0673524i
$899$	−1.95288	−	3.38248i	−0.0651321	−	0.112812i
$900$	−22.5327	−	29.8526i	−0.751089	−	0.995086i
$901$	11.6002	+	6.69736i	0.386457	+	0.223121i
$902$	9.00277	+	10.1186i	0.299760	+	0.336914i
$903$	−15.7613	+	4.75995i	−0.524503	+	0.158401i
$904$	12.3498	+	17.6500i	0.410747	+	0.587030i
$905$	−6.67666	−	16.6402i	−0.221940	−	0.553138i
$906$	−8.09563	+	24.4220i	−0.268959	+	0.811367i
$907$	−23.7946	−	41.2134i	−0.790085	−	1.36847i	−0.925914	−	0.377736i	$-0.876703\pi$
$907$	−23.7946	−	41.2134i	−0.790085	−	1.36847i	0.135828	−	0.990732i	$-0.456631\pi$
$908$	−25.0007	+	33.5660i	−0.829678	+	1.11393i
$909$			23.7796i			0.788720i
$910$	−6.41989	+	2.37825i	−0.212817	+	0.0788382i
$911$			34.7074i			1.14991i	0.818186	+	0.574954i	$0.194980\pi$
$911$			34.7074i			1.14991i	−0.818186	+	0.574954i	$0.805020\pi$
$912$	−24.9659	−	23.5754i	−0.826705	−	0.780660i
$913$	18.9095	+	32.7523i	0.625814	+	1.08394i
$914$	25.3463	+	8.40200i	0.838380	+	0.277914i
$915$	−52.6704	+	21.1333i	−1.74123	+	0.698647i
$916$	10.2928	+	1.20540i	0.340082	+	0.0398276i
$917$	24.2480	−	25.8255i	0.800739	−	0.852833i
$918$	−15.0170	+	13.3610i	−0.495635	+	0.440977i
$919$	44.9270	+	25.9386i	1.48200	+	0.855635i	0.999792	−	0.0204194i	$-0.00650013\pi$
$919$	44.9270	+	25.9386i	1.48200	+	0.855635i	0.482212	+	0.876055i	$0.339833\pi$
$920$	−7.24001	−	14.3060i	−0.238696	−	0.471655i
$921$	2.83671	+	4.91333i	0.0934729	+	0.161900i
$922$	−9.89195	−	47.9340i	−0.325774	−	1.57862i
$923$		−	1.13269i		−	0.0372828i
$924$	16.8264	−	46.5456i	0.553549	−	1.53124i
$925$	−34.8127	+	8.50253i	−1.14463	+	0.279562i
$926$	−20.8080	+	4.29406i	−0.683794	+	0.141112i
$927$	−3.31060	+	1.91138i	−0.108734	+	0.0627778i
$928$	6.07369	−	9.83454i	0.199379	−	0.322835i
$929$	37.9198	+	21.8930i	1.24411	+	0.718286i	0.969928	−	0.243393i	$-0.0782603\pi$
$929$	37.9198	+	21.8930i	1.24411	+	0.718286i	0.274180	+	0.961678i	$0.411594\pi$
$930$	−15.6631	+	0.964232i	−0.513614	+	0.0316184i
$931$	19.2769	−	12.8118i	0.631774	−	0.419891i
$932$	−41.2568	−	4.83166i	−1.35141	−	0.158266i
$933$	−64.9780	−	37.5151i	−2.12728	−	1.22819i
$934$	−34.1489	−	11.3200i	−1.11739	−	0.370402i
$935$	−58.9845	−	8.43412i	−1.92900	−	0.275825i
$936$	−0.751546	−	8.62379i	−0.0245651	−	0.281877i
$937$	14.2224			0.464624			0.232312	−	0.972641i	$-0.425371\pi$
$937$	14.2224			0.464624			0.232312	+	0.972641i	$0.425371\pi$
$938$	16.5177	+	30.4666i	0.539322	+	0.994771i
$939$			16.4937i			0.538251i
$940$	−5.76084	+	1.56334i	−0.187898	+	0.0509906i
$941$	4.80070	−	2.77169i	0.156498	−	0.0903544i	−0.419706	−	0.907660i	$-0.637867\pi$
$941$	4.80070	−	2.77169i	0.156498	−	0.0903544i	0.576204	+	0.817306i	$0.304533\pi$
$942$	−22.3935	−	7.42320i	−0.729619	−	0.241861i
$943$	−5.83617	−	3.36951i	−0.190052	−	0.109726i
$944$	−7.43893	−	1.76660i	−0.242116	−	0.0574979i
$945$	1.71315	+	11.2389i	0.0557289	+	0.365600i
$946$	9.12407	−	8.11789i	0.296649	−	0.263935i
$947$	29.7881	−	51.5945i	0.967983	−	1.67660i	0.266607	−	0.963805i	$-0.414098\pi$
$947$	29.7881	−	51.5945i	0.967983	−	1.67660i	0.701377	−	0.712791i	$-0.252569\pi$
$948$	−36.9429	+	15.9257i	−1.19985	+	0.517244i
$949$	3.02612	+	5.24140i	0.0982321	+	0.170143i
$950$	10.0235	+	21.1235i	0.325206	+	0.685338i
$951$	48.8163			1.58298
$952$	43.4872	+	34.2394i	1.40943	+	1.10971i
$953$		−	12.2577i		−	0.397065i	−0.980094	−	0.198532i	$-0.936383\pi$
$953$		−	12.2577i		−	0.397065i	0.980094	−	0.198532i	$-0.0636175\pi$
$954$	1.93602	+	9.38149i	0.0626809	+	0.303737i
$955$	14.9622	+	2.13943i	0.484167	+	0.0692304i
$956$	16.7285	+	38.8051i	0.541039	+	1.25505i
$957$	9.55612	−	16.5517i	0.308906	−	0.535040i
$958$	−19.3355	−	21.7321i	−0.624703	−	0.702133i
$959$	−13.2316	+	3.99597i	−0.427270	+	0.129037i
$960$	−24.4893	−	39.4606i	−0.790387	−	1.27358i
$961$	13.6732	−	23.6826i	0.441070	−	0.763956i
$962$	−7.87279	−	2.60974i	−0.253829	−	0.0841414i
$963$	−13.5611	−	23.4885i	−0.437000	−	0.756906i
$964$	2.17200	−	2.91612i	0.0699553	−	0.0939220i
$965$	−3.25893	+	4.15067i	−0.104909	+	0.133615i
$966$	−0.659836	+	24.6177i	−0.0212299	+	0.792062i
$967$	53.4551			1.71900			0.859499	−	0.511137i	$-0.170775\pi$
$967$	53.4551			1.71900			0.859499	+	0.511137i	$0.170775\pi$
$968$	0.486170	+	5.57867i	0.0156261	+	0.179305i
$969$	54.9869	−	31.7467i	1.76643	−	1.01985i
$970$	19.2978	−	12.7839i	0.619614	−	0.410467i
$971$	11.1284	−	19.2749i	0.357126	−	0.618561i	−0.630353	−	0.776308i	$-0.717090\pi$
$971$	11.1284	−	19.2749i	0.357126	−	0.618561i	0.987479	+	0.157748i	$0.0504232\pi$
$972$	43.5887	+	5.10475i	1.39811	+	0.163735i
$973$	−56.5259	−	13.2534i	−1.81214	−	0.424885i
$974$	−27.3167	−	30.7025i	−0.875284	−	0.983772i
$975$	−2.97681	+	10.1964i	−0.0953341	+	0.326547i
$976$	−37.4662	+	11.1982i	−1.19926	+	0.358447i
$977$	27.5351	−	15.8974i	0.880926	−	0.508603i	0.00996251	−	0.999950i	$-0.496829\pi$
$977$	27.5351	−	15.8974i	0.880926	−	0.508603i	0.870964	+	0.491347i	$0.163495\pi$
$978$	13.7123	+	66.4466i	0.438472	+	2.12473i
$979$	38.2369			1.22206
$980$	29.6362	−	10.0843i	0.946695	−	0.322130i
$981$	29.8158			0.951947
$982$	2.72051	+	13.1829i	0.0868148	+	0.420684i
$983$	−17.8275	+	10.2927i	−0.568609	+	0.328287i	−0.756594	−	0.653885i	$-0.773138\pi$
$983$	−17.8275	+	10.2927i	−0.568609	+	0.328287i	0.187985	+	0.982172i	$0.439805\pi$
$984$	−17.6881	−	8.25538i	−0.563877	−	0.263172i
$985$	16.9202	+	42.1701i	0.539123	+	1.34365i
$986$	14.2070	+	15.9679i	0.452444	+	0.508522i
$987$	8.92616	+	2.09288i	0.284123	+	0.0666172i
$988$	−0.629440	+	5.37470i	−0.0200252	+	0.170992i
$989$	−3.03832	+	5.26253i	−0.0966131	+	0.167339i
$990$	−23.5330	−	35.5239i	−0.747928	−	1.12902i
$991$	−32.2836	+	18.6390i	−1.02552	+	0.592086i	−0.915699	−	0.401865i	$-0.868362\pi$
$991$	−32.2836	+	18.6390i	−1.02552	+	0.592086i	−0.109824	+	0.993951i	$0.535029\pi$
$992$	−10.8081	−	0.320577i	−0.343156	−	0.0101783i
$993$	−33.9810			−1.07836
$994$	−0.138772	+	5.17743i	−0.00440158	+	0.164218i
$995$	20.1519	+	15.8224i	0.638859	+	0.501605i
$996$	−43.7130	−	32.5584i	−1.38510	−	1.03165i
$997$	−6.32111	−	10.9485i	−0.200191	−	0.346742i	0.748399	−	0.663249i	$-0.230823\pi$
$997$	−6.32111	−	10.9485i	−0.200191	−	0.346742i	−0.948590	+	0.316508i	$0.897490\pi$
$998$	−27.1034	−	8.98449i	−0.857944	−	0.284399i
$999$	−6.88644	+	11.9277i	−0.217877	+	0.377375i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.s.b.19.2	✓	32
4.3	odd	2	inner	140.2.s.b.19.7	yes	32
5.2	odd	4		700.2.p.e.551.7		32
5.3	odd	4		700.2.p.e.551.10		32
5.4	even	2	inner	140.2.s.b.19.15	yes	32
7.2	even	3		980.2.c.d.979.28		32
7.3	odd	6	inner	140.2.s.b.59.10	yes	32
7.4	even	3		980.2.s.e.619.10		32
7.5	odd	6		980.2.c.d.979.27		32
7.6	odd	2		980.2.s.e.19.2		32
20.3	even	4		700.2.p.e.551.2		32
20.7	even	4		700.2.p.e.551.15		32
20.19	odd	2	inner	140.2.s.b.19.10	yes	32
28.3	even	6	inner	140.2.s.b.59.15	yes	32
28.11	odd	6		980.2.s.e.619.15		32
28.19	even	6		980.2.c.d.979.8		32
28.23	odd	6		980.2.c.d.979.7		32
28.27	even	2		980.2.s.e.19.7		32
35.3	even	12		700.2.p.e.451.2		32
35.4	even	6		980.2.s.e.619.7		32
35.9	even	6		980.2.c.d.979.5		32
35.17	even	12		700.2.p.e.451.15		32
35.19	odd	6		980.2.c.d.979.6		32
35.24	odd	6	inner	140.2.s.b.59.7	yes	32
35.34	odd	2		980.2.s.e.19.15		32
140.3	odd	12		700.2.p.e.451.10		32
140.19	even	6		980.2.c.d.979.25		32
140.39	odd	6		980.2.s.e.619.2		32
140.59	even	6	inner	140.2.s.b.59.2	yes	32
140.79	odd	6		980.2.c.d.979.26		32
140.87	odd	12		700.2.p.e.451.7		32
140.139	even	2		980.2.s.e.19.10		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.s.b.19.2	✓	32	1.1	even	1	trivial
140.2.s.b.19.7	yes	32	4.3	odd	2	inner
140.2.s.b.19.10	yes	32	20.19	odd	2	inner
140.2.s.b.19.15	yes	32	5.4	even	2	inner
140.2.s.b.59.2	yes	32	140.59	even	6	inner
140.2.s.b.59.7	yes	32	35.24	odd	6	inner
140.2.s.b.59.10	yes	32	7.3	odd	6	inner
140.2.s.b.59.15	yes	32	28.3	even	6	inner
700.2.p.e.451.2		32	35.3	even	12
700.2.p.e.451.7		32	140.87	odd	12
700.2.p.e.451.10		32	140.3	odd	12
700.2.p.e.451.15		32	35.17	even	12
700.2.p.e.551.2		32	20.3	even	4
700.2.p.e.551.7		32	5.2	odd	4
700.2.p.e.551.10		32	5.3	odd	4
700.2.p.e.551.15		32	20.7	even	4
980.2.c.d.979.5		32	35.9	even	6
980.2.c.d.979.6		32	35.19	odd	6
980.2.c.d.979.7		32	28.23	odd	6
980.2.c.d.979.8		32	28.19	even	6
980.2.c.d.979.25		32	140.19	even	6
980.2.c.d.979.26		32	140.79	odd	6
980.2.c.d.979.27		32	7.5	odd	6
980.2.c.d.979.28		32	7.2	even	3
980.2.s.e.19.2		32	7.6	odd	2
980.2.s.e.19.7		32	28.27	even	2
980.2.s.e.19.10		32	140.139	even	2
980.2.s.e.19.15		32	35.34	odd	2
980.2.s.e.619.2		32	140.39	odd	6
980.2.s.e.619.7		32	35.4	even	6
980.2.s.e.619.10		32	7.4	even	3
980.2.s.e.619.15		32	28.11	odd	6

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	140.2.s.b.19.2

Level	$140$
Weight	$2$
Character	140.19
Analytic conductor	$1.118$
Analytic rank	$0$
Dimension	$32$
Inner twists	$8$