LMFDB - Embedded newform 403.2.h.a.118.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (of order $3$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			118.15
Character	$\chi$	$=$	403.118
Dual form			403.2.h.a.222.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.38763 q^{2} +(-0.113336 - 0.196303i) q^{3} +3.70079 q^{4} +(0.669573 - 1.15973i) q^{5} +(-0.270604 - 0.468700i) q^{6} +(-0.988047 - 1.71135i) q^{7} +4.06087 q^{8} +(1.47431 - 2.55358i) q^{9} +O(q^{10})$	\(q+2.38763 q^{2} +(-0.113336 - 0.196303i) q^{3} +3.70079 q^{4} +(0.669573 - 1.15973i) q^{5} +(-0.270604 - 0.468700i) q^{6} +(-0.988047 - 1.71135i) q^{7} +4.06087 q^{8} +(1.47431 - 2.55358i) q^{9} +(1.59869 - 2.76902i) q^{10} +(-2.83142 + 4.90416i) q^{11} +(-0.419432 - 0.726478i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-2.35909 - 4.08607i) q^{14} -0.303546 q^{15} +2.29427 q^{16} +(2.83315 + 4.90716i) q^{17} +(3.52011 - 6.09701i) q^{18} +(0.631321 + 1.09348i) q^{19} +(2.47795 - 4.29193i) q^{20} +(-0.223962 + 0.387914i) q^{21} +(-6.76038 + 11.7093i) q^{22} -6.56157 q^{23} +(-0.460241 - 0.797162i) q^{24} +(1.60334 + 2.77707i) q^{25} +(1.19382 - 2.06775i) q^{26} -1.34838 q^{27} +(-3.65656 - 6.33334i) q^{28} -0.229957 q^{29} -0.724757 q^{30} +(5.45651 - 1.10747i) q^{31} -2.64385 q^{32} +1.28360 q^{33} +(6.76452 + 11.7165i) q^{34} -2.64628 q^{35} +(5.45611 - 9.45027i) q^{36} +(2.08319 + 3.60819i) q^{37} +(1.50736 + 2.61083i) q^{38} -0.226672 q^{39} +(2.71905 - 4.70952i) q^{40} +(-2.42812 + 4.20563i) q^{41} +(-0.534740 + 0.926197i) q^{42} +(-2.75576 - 4.77312i) q^{43} +(-10.4785 + 18.1493i) q^{44} +(-1.97432 - 3.41962i) q^{45} -15.6666 q^{46} -10.2220 q^{47} +(-0.260023 - 0.450374i) q^{48} +(1.54752 - 2.68039i) q^{49} +(3.82820 + 6.63063i) q^{50} +(0.642194 - 1.11231i) q^{51} +(1.85040 - 3.20498i) q^{52} +(6.76020 - 11.7090i) q^{53} -3.21944 q^{54} +(3.79168 + 6.56738i) q^{55} +(-4.01233 - 6.94956i) q^{56} +(0.143103 - 0.247861i) q^{57} -0.549054 q^{58} +(0.304085 + 0.526691i) q^{59} -1.12336 q^{60} -0.648736 q^{61} +(13.0281 - 2.64423i) q^{62} -5.82675 q^{63} -10.9011 q^{64} +(-0.669573 - 1.15973i) q^{65} +3.06477 q^{66} +(4.20855 - 7.28942i) q^{67} +(10.4849 + 18.1604i) q^{68} +(0.743661 + 1.28806i) q^{69} -6.31834 q^{70} +(3.35565 - 5.81216i) q^{71} +(5.98697 - 10.3697i) q^{72} +(-8.36646 + 14.4911i) q^{73} +(4.97389 + 8.61503i) q^{74} +(0.363433 - 0.629484i) q^{75} +(2.33639 + 4.04674i) q^{76} +11.1903 q^{77} -0.541209 q^{78} +(-5.77172 - 9.99691i) q^{79} +(1.53618 - 2.66075i) q^{80} +(-4.27011 - 7.39605i) q^{81} +(-5.79746 + 10.0415i) q^{82} +(-2.43578 + 4.21890i) q^{83} +(-0.828838 + 1.43559i) q^{84} +7.58800 q^{85} +(-6.57975 - 11.3965i) q^{86} +(0.0260624 + 0.0451414i) q^{87} +(-11.4980 + 19.9151i) q^{88} +3.58910 q^{89} +(-4.71394 - 8.16479i) q^{90} -1.97609 q^{91} -24.2830 q^{92} +(-0.835818 - 0.945616i) q^{93} -24.4065 q^{94} +1.69086 q^{95} +(0.299643 + 0.518996i) q^{96} -0.808802 q^{97} +(3.69492 - 6.39979i) q^{98} +(8.34877 + 14.4605i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) $ 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} + 15 q^{13} + 3 q^{14} + 4 q^{15} + 22 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 10 q^{20} - 15 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 20 q^{25} - 3 q^{26} + 4 q^{27} + 13 q^{28} + 26 q^{29} + 28 q^{30} + 19 q^{31} - 74 q^{32} + 2 q^{33} - 21 q^{34} - 30 q^{35} + 37 q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{39} - 17 q^{40} + 7 q^{41} + 44 q^{42} + 15 q^{43} - 70 q^{44} + 15 q^{45} - 58 q^{46} - 24 q^{47} + 31 q^{48} - 29 q^{49} + 2 q^{50} + 25 q^{51} + 11 q^{52} + 4 q^{53} + 34 q^{54} + 13 q^{55} - 41 q^{56} + 8 q^{57} - 46 q^{58} + 27 q^{59} + 78 q^{60} + 8 q^{61} + 20 q^{62} - 112 q^{63} + 60 q^{64} - 7 q^{65} + 60 q^{66} + 29 q^{67} + 41 q^{68} - 23 q^{69} - 112 q^{70} + 29 q^{71} + 14 q^{72} - 10 q^{73} + 25 q^{74} - 18 q^{75} + 24 q^{76} - 72 q^{77} + 9 q^{79} - 11 q^{81} - 38 q^{82} - 13 q^{83} - 62 q^{84} + 108 q^{85} - 38 q^{86} - 18 q^{87} + 32 q^{88} + 6 q^{89} + 7 q^{90} + 12 q^{91} + 2 q^{92} + 37 q^{93} - 154 q^{94} - 28 q^{95} - 105 q^{96} - 84 q^{97} + 50 q^{98} + 10 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9 - 3 * q^10 - 3 * q^11 + 12 * q^12 + 15 * q^13 + 3 * q^14 + 4 * q^15 + 22 * q^16 + 4 * q^17 - 6 * q^18 + 5 * q^19 + 10 * q^20 - 15 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 20 * q^25 - 3 * q^26 + 4 * q^27 + 13 * q^28 + 26 * q^29 + 28 * q^30 + 19 * q^31 - 74 * q^32 + 2 * q^33 - 21 * q^34 - 30 * q^35 + 37 * q^36 - 4 * q^37 - 4 * q^38 - 4 * q^39 - 17 * q^40 + 7 * q^41 + 44 * q^42 + 15 * q^43 - 70 * q^44 + 15 * q^45 - 58 * q^46 - 24 * q^47 + 31 * q^48 - 29 * q^49 + 2 * q^50 + 25 * q^51 + 11 * q^52 + 4 * q^53 + 34 * q^54 + 13 * q^55 - 41 * q^56 + 8 * q^57 - 46 * q^58 + 27 * q^59 + 78 * q^60 + 8 * q^61 + 20 * q^62 - 112 * q^63 + 60 * q^64 - 7 * q^65 + 60 * q^66 + 29 * q^67 + 41 * q^68 - 23 * q^69 - 112 * q^70 + 29 * q^71 + 14 * q^72 - 10 * q^73 + 25 * q^74 - 18 * q^75 + 24 * q^76 - 72 * q^77 + 9 * q^79 - 11 * q^81 - 38 * q^82 - 13 * q^83 - 62 * q^84 + 108 * q^85 - 38 * q^86 - 18 * q^87 + 32 * q^88 + 6 * q^89 + 7 * q^90 + 12 * q^91 + 2 * q^92 + 37 * q^93 - 154 * q^94 - 28 * q^95 - 105 * q^96 - 84 * q^97 + 50 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.38763			1.68831			0.844156	−	0.536098i	$-0.180102\pi$
$2$	2.38763			1.68831			0.844156	+	0.536098i	$0.180102\pi$
$3$	−0.113336	−	0.196303i	−0.0654345	−	0.113336i	0.831452	−	0.555596i	$-0.187510\pi$
$3$	−0.113336	−	0.196303i	−0.0654345	−	0.113336i	−0.896887	+	0.442261i	$0.854177\pi$
$4$	3.70079			1.85040
$5$	0.669573	−	1.15973i	0.299442	−	0.518649i	−0.676566	−	0.736382i	$-0.736533\pi$
$5$	0.669573	−	1.15973i	0.299442	−	0.518649i	0.976008	+	0.217733i	$0.0698661\pi$
$6$	−0.270604	−	0.468700i	−0.110474	−	0.191346i
$7$	−0.988047	−	1.71135i	−0.373447	−	0.646829i	0.616646	−	0.787240i	$-0.288491\pi$
$7$	−0.988047	−	1.71135i	−0.373447	−	0.646829i	−0.990093	+	0.140411i	$0.955158\pi$
$8$	4.06087			1.43573
$9$	1.47431	−	2.55358i	0.491437	−	0.851193i
$10$	1.59869	−	2.76902i	0.505552	−	0.875641i
$11$	−2.83142	+	4.90416i	−0.853704	+	1.47866i	0.0241374	+	0.999709i	$0.492316\pi$
$11$	−2.83142	+	4.90416i	−0.853704	+	1.47866i	−0.877842	+	0.478951i	$0.841017\pi$
$12$	−0.419432	−	0.726478i	−0.121080	−	0.209716i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	−2.35909	−	4.08607i	−0.630495	−	1.09205i
$15$	−0.303546			−0.0783753
$16$	2.29427			0.573568
$17$	2.83315	+	4.90716i	0.687139	+	1.19016i	0.972759	+	0.231817i	$0.0744671\pi$
$17$	2.83315	+	4.90716i	0.687139	+	1.19016i	−0.285620	+	0.958343i	$0.592200\pi$
$18$	3.52011	−	6.09701i	0.829698	−	1.43708i
$19$	0.631321	+	1.09348i	0.144835	+	0.250862i	0.929311	−	0.369297i	$-0.120402\pi$
$19$	0.631321	+	1.09348i	0.144835	+	0.250862i	−0.784476	+	0.620159i	$0.787068\pi$
$20$	2.47795	−	4.29193i	0.554086	−	0.959706i
$21$	−0.223962	+	0.387914i	−0.0488726	+	0.0846498i
$22$	−6.76038	+	11.7093i	−1.44132	+	2.49644i
$23$	−6.56157			−1.36818			−0.684091	−	0.729396i	$-0.739801\pi$
$23$	−6.56157			−1.36818			−0.684091	+	0.729396i	$0.739801\pi$
$24$	−0.460241	−	0.797162i	−0.0939464	−	0.162720i
$25$	1.60334	+	2.77707i	0.320669	+	0.555415i
$26$	1.19382	−	2.06775i	0.234127	−	0.405519i
$27$	−1.34838			−0.259496
$28$	−3.65656	−	6.33334i	−0.691024	−	1.19689i
$29$	−0.229957			−0.0427020			−0.0213510	−	0.999772i	$-0.506797\pi$
$29$	−0.229957			−0.0427020			−0.0213510	+	0.999772i	$0.506797\pi$
$30$	−0.724757			−0.132322
$31$	5.45651	−	1.10747i	0.980018	−	0.198907i
$31$	5.45651	−	1.10747i	0.980018	−	0.198907i
$32$	−2.64385			−0.467371
$33$	1.28360			0.223447
$34$	6.76452	+	11.7165i	1.16011	+	2.00936i
$35$	−2.64628			−0.447303
$36$	5.45611	−	9.45027i	0.909352	−	1.57504i
$37$	2.08319	+	3.60819i	0.342474	+	0.593183i	0.984892	−	0.173172i	$-0.0554018\pi$
$37$	2.08319	+	3.60819i	0.342474	+	0.593183i	−0.642417	+	0.766355i	$0.722068\pi$
$38$	1.50736	+	2.61083i	0.244527	+	0.423533i
$39$	−0.226672			−0.0362965
$40$	2.71905	−	4.70952i	0.429919	−	0.744641i
$41$	−2.42812	+	4.20563i	−0.379209	+	0.656809i	−0.990947	−	0.134251i	$-0.957137\pi$
$41$	−2.42812	+	4.20563i	−0.379209	+	0.656809i	0.611739	+	0.791060i	$0.290470\pi$
$42$	−0.534740	+	0.926197i	−0.0825121	+	0.142915i
$43$	−2.75576	−	4.77312i	−0.420250	−	0.727894i	0.575714	−	0.817651i	$-0.304724\pi$
$43$	−2.75576	−	4.77312i	−0.420250	−	0.727894i	−0.995964	+	0.0897572i	$0.971391\pi$
$44$	−10.4785	+	18.1493i	−1.57969	+	2.73610i
$45$	−1.97432	−	3.41962i	−0.294314	−	0.509766i
$46$	−15.6666			−2.30992
$47$	−10.2220			−1.49104			−0.745518	−	0.666485i	$-0.767798\pi$
$47$	−10.2220			−1.49104			−0.745518	+	0.666485i	$0.767798\pi$
$48$	−0.260023	−	0.450374i	−0.0375311	−	0.0650058i
$49$	1.54752	−	2.68039i	0.221075	−	0.382913i
$50$	3.82820	+	6.63063i	0.541389	+	0.937713i
$51$	0.642194	−	1.11231i	0.0899252	−	0.155755i
$52$	1.85040	−	3.20498i	0.256604	−	0.444451i
$53$	6.76020	−	11.7090i	0.928585	−	1.60836i	0.142892	−	0.989738i	$-0.454360\pi$
$53$	6.76020	−	11.7090i	0.928585	−	1.60836i	0.785692	−	0.618617i	$-0.212307\pi$
$54$	−3.21944			−0.438111
$55$	3.79168	+	6.56738i	0.511270	+	0.885546i
$56$	−4.01233	−	6.94956i	−0.536170	−	0.928673i
$57$	0.143103	−	0.247861i	0.0189544	−	0.0328300i
$58$	−0.549054			−0.0720943
$59$	0.304085	+	0.526691i	0.0395885	+	0.0685693i	0.885141	−	0.465323i	$-0.154062\pi$
$59$	0.304085	+	0.526691i	0.0395885	+	0.0685693i	−0.845552	+	0.533893i	$0.820729\pi$
$60$	−1.12336			−0.145025
$61$	−0.648736			−0.0830621			−0.0415310	−	0.999137i	$-0.513224\pi$
$61$	−0.648736			−0.0830621			−0.0415310	+	0.999137i	$0.513224\pi$
$62$	13.0281	−	2.64423i	1.65458	−	0.335818i
$63$	−5.82675			−0.734102
$64$	−10.9011			−1.36264
$65$	−0.669573	−	1.15973i	−0.0830503	−	0.143847i
$66$	3.06477			0.377248
$67$	4.20855	−	7.28942i	0.514156	−	0.890545i	−0.485709	−	0.874121i	$-0.661439\pi$
$67$	4.20855	−	7.28942i	0.514156	−	0.890545i	0.999865	−	0.0164239i	$-0.00522814\pi$
$68$	10.4849	+	18.1604i	1.27148	+	2.20227i
$69$	0.743661	+	1.28806i	0.0895263	+	0.155064i
$70$	−6.31834			−0.755187
$71$	3.35565	−	5.81216i	0.398242	−	0.689776i	−0.595267	−	0.803528i	$-0.702954\pi$
$71$	3.35565	−	5.81216i	0.398242	−	0.689776i	0.993509	+	0.113752i	$0.0362870\pi$
$72$	5.98697	−	10.3697i	0.705572	−	1.22209i
$73$	−8.36646	+	14.4911i	−0.979220	+	1.69606i	−0.313978	+	0.949430i	$0.601662\pi$
$73$	−8.36646	+	14.4911i	−0.979220	+	1.69606i	−0.665242	+	0.746628i	$0.731672\pi$
$74$	4.97389	+	8.61503i	0.578203	+	1.00148i
$75$	0.363433	−	0.629484i	0.0419656	−	0.0726865i
$76$	2.33639	+	4.04674i	0.268002	+	0.464193i
$77$	11.1903			1.27525
$78$	−0.541209			−0.0612798
$79$	−5.77172	−	9.99691i	−0.649369	−	1.12474i	−0.983274	−	0.182134i	$-0.941700\pi$
$79$	−5.77172	−	9.99691i	−0.649369	−	1.12474i	0.333904	−	0.942607i	$-0.391634\pi$
$80$	1.53618	−	2.66075i	0.171751	−	0.297481i
$81$	−4.27011	−	7.39605i	−0.474457	−	0.821783i
$82$	−5.79746	+	10.0415i	−0.640223	+	1.10890i
$83$	−2.43578	+	4.21890i	−0.267362	+	0.463084i	−0.968180	−	0.250256i	$-0.919485\pi$
$83$	−2.43578	+	4.21890i	−0.267362	+	0.463084i	0.700818	+	0.713340i	$0.252819\pi$
$84$	−0.828838	+	1.43559i	−0.0904336	+	0.156636i
$85$	7.58800			0.823034
$86$	−6.57975	−	11.3965i	−0.709513	−	1.22891i
$87$	0.0260624	+	0.0451414i	0.00279418	+	0.00483966i
$88$	−11.4980	+	19.9151i	−1.22569	+	2.12296i
$89$	3.58910			0.380444			0.190222	−	0.981741i	$-0.439079\pi$
$89$	3.58910			0.380444			0.190222	+	0.981741i	$0.439079\pi$
$90$	−4.71394	−	8.16479i	−0.496893	−	0.860644i
$91$	−1.97609			−0.207151
$92$	−24.2830			−2.53168
$93$	−0.835818	−	0.945616i	−0.0866703	−	0.0980558i
$94$	−24.4065			−2.51733
$95$	1.69086			0.173479
$96$	0.299643	+	0.518996i	0.0305821	+	0.0529698i
$97$	−0.808802			−0.0821215			−0.0410607	−	0.999157i	$-0.513074\pi$
$97$	−0.808802			−0.0821215			−0.0410607	+	0.999157i	$0.513074\pi$
$98$	3.69492	−	6.39979i	0.373243	−	0.646476i
$99$	8.34877	+	14.4605i	0.839083	+	1.45333i
$100$	5.93364	+	10.2774i	0.593364	+	1.02774i
$101$	−13.9412			−1.38720			−0.693599	−	0.720361i	$-0.743976\pi$
$101$	−13.9412			−1.38720			−0.693599	+	0.720361i	$0.743976\pi$
$102$	1.53332	−	2.65579i	0.151822	−	0.262963i
$103$	−0.343618	+	0.595164i	−0.0338577	+	0.0586433i	−0.882458	−	0.470392i	$-0.844113\pi$
$103$	−0.343618	+	0.595164i	−0.0338577	+	0.0586433i	0.848600	+	0.529035i	$0.177446\pi$
$104$	2.03043	−	3.51681i	0.199100	−	0.344852i
$105$	0.299918	+	0.519474i	0.0292690	+	0.0506954i
$106$	16.1409	−	27.9568i	1.56774	−	2.71541i
$107$	10.0192	+	17.3538i	0.968592	+	1.67765i	0.699638	+	0.714498i	$0.253345\pi$
$107$	10.0192	+	17.3538i	0.968592	+	1.67765i	0.268955	+	0.963153i	$0.413322\pi$
$108$	−4.99009			−0.480171
$109$	13.0263			1.24770			0.623848	−	0.781546i	$-0.285569\pi$
$109$	13.0263			1.24770			0.623848	+	0.781546i	$0.285569\pi$
$110$	9.05314	+	15.6805i	0.863183	+	1.49508i
$111$	0.472200	−	0.817874i	0.0448192	−	0.0776292i
$112$	−2.26685	−	3.92630i	−0.214197	−	0.371001i
$113$	1.96320	−	3.40035i	0.184682	−	0.319878i	−0.758787	−	0.651338i	$-0.774208\pi$
$113$	1.96320	−	3.40035i	0.184682	−	0.319878i	0.943469	+	0.331460i	$0.107541\pi$
$114$	0.341677	−	0.591801i	0.0320009	−	0.0554273i
$115$	−4.39345	+	7.60968i	−0.409691	+	0.709606i
$116$	−0.851024			−0.0790156
$117$	−1.47431	−	2.55358i	−0.136300	−	0.236079i
$118$	0.726044	+	1.25754i	0.0668377	+	0.115766i
$119$	5.59857	−	9.69701i	0.513220	−	0.888923i
$120$	−1.23266			−0.112526
$121$	−10.5338	−	18.2452i	−0.957622	−	1.65865i
$122$	−1.54894			−0.140235
$123$	1.10077			0.0992533
$124$	20.1934	−	4.09851i	1.81342	−	0.368057i
$125$	10.9900			0.982971
$126$	−13.9121			−1.23939
$127$	−5.12884	−	8.88342i	−0.455111	−	0.788276i	0.543583	−	0.839355i	$-0.317067\pi$
$127$	−5.12884	−	8.88342i	−0.455111	−	0.788276i	−0.998695	+	0.0510793i	$0.983734\pi$
$128$	−20.7401			−1.83318
$129$	−0.624653	+	1.08193i	−0.0549976	+	0.0952587i
$130$	−1.59869	−	2.76902i	−0.140215	−	0.242859i
$131$	7.40081	+	12.8186i	0.646612	+	1.11996i	0.983927	+	0.178573i	$0.0571479\pi$
$131$	7.40081	+	12.8186i	0.646612	+	1.11996i	−0.337315	+	0.941392i	$0.609519\pi$
$132$	4.75035			0.413465
$133$	1.24755	−	2.16082i	0.108176	−	0.187367i
$134$	10.0485	−	17.4045i	0.868056	−	1.50352i
$135$	−0.902841	+	1.56377i	−0.0777042	+	0.134588i
$136$	11.5050	+	19.9273i	0.986548	+	1.70875i
$137$	7.18157	−	12.4388i	0.613563	−	1.06272i	−0.377072	−	0.926184i	$-0.623069\pi$
$137$	7.18157	−	12.4388i	0.613563	−	1.06272i	0.990635	−	0.136538i	$-0.0435977\pi$
$138$	1.77559	+	3.07541i	0.151148	+	0.261796i
$139$	19.3624			1.64230			0.821150	−	0.570713i	$-0.193333\pi$
$139$	19.3624			1.64230			0.821150	+	0.570713i	$0.193333\pi$
$140$	−9.79333			−0.827687
$141$	1.15852	+	2.00662i	0.0975652	+	0.168988i
$142$	8.01206	−	13.8773i	0.672357	−	1.16456i
$143$	2.83142	+	4.90416i	0.236775	+	0.410106i
$144$	3.38247	−	5.85861i	0.281873	−	0.488217i
$145$	−0.153973	+	0.266689i	−0.0127868	+	0.0221473i
$146$	−19.9760	+	34.5995i	−1.65323	+	2.86347i
$147$	−0.701560			−0.0578637
$148$	7.70945	+	13.3532i	0.633713	+	1.09762i
$149$	−4.10175	−	7.10444i	−0.336029	−	0.582019i	0.647653	−	0.761935i	$-0.275751\pi$
$149$	−4.10175	−	7.10444i	−0.336029	−	0.582019i	−0.983682	+	0.179917i	$0.942417\pi$
$150$	0.867744	−	1.50298i	0.0708510	−	0.122717i
$151$	10.1638			0.827122			0.413561	−	0.910476i	$-0.364285\pi$
$151$	10.1638			0.827122			0.413561	+	0.910476i	$0.364285\pi$
$152$	2.56371	+	4.44048i	0.207944	+	0.360170i
$153$	16.7078			1.35074
$154$	26.7183			2.15302
$155$	2.36916	−	7.06963i	0.190296	−	0.567847i
$156$	−0.838864			−0.0671629
$157$	−5.81082			−0.463754			−0.231877	−	0.972745i	$-0.574487\pi$
$157$	−5.81082			−0.463754			−0.231877	+	0.972745i	$0.574487\pi$
$158$	−13.7808	−	23.8690i	−1.09634	−	1.89891i
$159$	−3.06469			−0.243046
$160$	−1.77025	+	3.06616i	−0.139950	+	0.242401i
$161$	6.48314	+	11.2291i	0.510943	+	0.884980i
$162$	−10.1955	−	17.6590i	−0.801031	−	1.38743i
$163$	−5.15359			−0.403660			−0.201830	−	0.979421i	$-0.564689\pi$
$163$	−5.15359			−0.403660			−0.201830	+	0.979421i	$0.564689\pi$
$164$	−8.98597	+	15.5642i	−0.701686	+	1.21536i
$165$	0.859466	−	1.48864i	0.0669094	−	0.115890i
$166$	−5.81576	+	10.0732i	−0.451390	+	0.781831i
$167$	−5.83045	−	10.0986i	−0.451174	−	0.781456i	0.547286	−	0.836946i	$-0.315661\pi$
$167$	−5.83045	−	10.0986i	−0.451174	−	0.781456i	−0.998459	+	0.0554902i	$0.982328\pi$
$168$	−0.909481	+	1.57527i	−0.0701680	+	0.121534i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	18.1173			1.38954
$171$	3.72305			0.284709
$172$	−10.1985	−	17.6643i	−0.777628	−	1.34689i
$173$	6.12137	−	10.6025i	0.465399	−	0.806094i	−0.533821	−	0.845598i	$-0.679244\pi$
$173$	6.12137	−	10.6025i	0.465399	−	0.806094i	0.999219	+	0.0395034i	$0.0125776\pi$
$174$	0.0622274	+	0.107781i	0.00471745	+	0.00817086i
$175$	3.16836	−	5.48776i	0.239506	−	0.414836i
$176$	−6.49604	+	11.2515i	−0.489658	+	0.848112i
$177$	0.0689275	−	0.119386i	0.00518091	−	0.00897359i
$178$	8.56945			0.642308
$179$	−2.20774	−	3.82392i	−0.165014	−	0.285813i	0.771646	−	0.636052i	$-0.219434\pi$
$179$	−2.20774	−	3.82392i	−0.165014	−	0.285813i	−0.936660	+	0.350239i	$0.886100\pi$
$180$	−7.30653	−	12.6553i	−0.544597	−	0.943269i
$181$	2.93442	−	5.08256i	0.218113	−	0.377784i	−0.736118	−	0.676854i	$-0.763343\pi$
$181$	2.93442	−	5.08256i	0.218113	−	0.377784i	0.954231	+	0.299070i	$0.0966764\pi$
$182$	−4.71819			−0.349735
$183$	0.0735250	+	0.127349i	0.00543512	+	0.00941391i
$184$	−26.6457			−1.96434
$185$	5.57939			0.410205
$186$	−1.99563	−	2.25778i	−0.146326	−	0.165549i
$187$	−32.0873			−2.34646
$188$	−37.8296			−2.75901
$189$	1.33227	+	2.30755i	0.0969081	+	0.167850i
$190$	4.03716			0.292886
$191$	−5.59655	+	9.69350i	−0.404952	+	0.701397i	−0.994316	−	0.106470i	$-0.966045\pi$
$191$	−5.59655	+	9.69350i	−0.404952	+	0.701397i	0.589364	+	0.807868i	$0.299378\pi$
$192$	1.23548	+	2.13992i	0.0891633	+	0.154435i
$193$	1.61873	+	2.80373i	0.116519	+	0.201817i	0.918386	−	0.395686i	$-0.129493\pi$
$193$	1.61873	+	2.80373i	0.116519	+	0.201817i	−0.801867	+	0.597503i	$0.796160\pi$
$194$	−1.93112			−0.138647
$195$	−0.151773	+	0.262879i	−0.0108687	+	0.0188251i
$196$	5.72706	−	9.91957i	0.409076	−	0.708541i
$197$	−9.28060	+	16.0745i	−0.661216	+	1.14526i	0.319081	+	0.947727i	$0.396626\pi$
$197$	−9.28060	+	16.0745i	−0.661216	+	1.14526i	−0.980297	+	0.197532i	$0.936708\pi$
$198$	19.9338	+	34.5264i	1.41663	+	2.45368i
$199$	1.84117	−	3.18900i	0.130517	−	0.226062i	−0.793359	−	0.608754i	$-0.791670\pi$
$199$	1.84117	−	3.18900i	0.130517	−	0.226062i	0.923876	+	0.382692i	$0.125003\pi$
$200$	6.51096	+	11.2773i	0.460395	+	0.797427i
$201$	−1.90792			−0.134574
$202$	−33.2864			−2.34202
$203$	0.227209	+	0.393537i	0.0159469	+	0.0276209i
$204$	2.37663	−	4.11644i	0.166397	−	0.288208i
$205$	3.25161	+	5.63195i	0.227102	+	0.393353i
$206$	−0.820434	+	1.42103i	−0.0571624	+	0.0990081i
$207$	−9.67379	+	16.7555i	−0.672375	+	1.16459i
$208$	1.14714	−	1.98690i	0.0795396	−	0.137767i
$209$	−7.15014			−0.494585
$210$	0.716095	+	1.24031i	0.0494152	+	0.0855897i
$211$	−6.00178	−	10.3954i	−0.413180	−	0.715648i	0.582056	−	0.813149i	$-0.302249\pi$
$211$	−6.00178	−	10.3954i	−0.413180	−	0.715648i	−0.995235	+	0.0975006i	$0.968915\pi$
$212$	25.0181	−	43.3326i	1.71825	−	2.97609i
$213$	−1.52126			−0.104235
$214$	23.9222	+	41.4344i	1.63529	+	2.83240i
$215$	−7.38074			−0.503362
$216$	−5.47560			−0.372568
$217$	−7.28656	−	8.24376i	−0.494644	−	0.559623i
$218$	31.1021			2.10650
$219$	3.79288			0.256299
$220$	14.0322	+	24.3045i	0.946052	+	1.63861i
$221$	5.66630			0.381156
$222$	1.12744	−	1.95278i	0.0756688	−	0.131062i
$223$	11.3856	+	19.7205i	0.762439	+	1.32058i	0.941590	+	0.336762i	$0.109332\pi$
$223$	11.3856	+	19.7205i	0.762439	+	1.32058i	−0.179150	+	0.983822i	$0.557335\pi$
$224$	2.61225	+	4.52454i	0.174538	+	0.302309i
$225$	9.45531			0.630354
$226$	4.68739	−	8.11880i	0.311800	−	0.540054i
$227$	8.57891	−	14.8591i	0.569402	−	0.986234i	−0.427223	−	0.904146i	$-0.640508\pi$
$227$	8.57891	−	14.8591i	0.569402	−	0.986234i	0.996625	−	0.0820875i	$-0.0261587\pi$
$228$	0.529593	−	0.917282i	0.0350732	−	0.0607485i
$229$	−1.97253	−	3.41653i	−0.130349	−	0.225770i	0.793462	−	0.608619i	$-0.208276\pi$
$229$	−1.97253	−	3.41653i	−0.130349	−	0.225770i	−0.923811	+	0.382849i	$0.874943\pi$
$230$	−10.4899	+	18.1691i	−0.691687	+	1.19804i
$231$	−1.26826	−	2.19669i	−0.0834455	−	0.144532i
$232$	−0.933825			−0.0613086
$233$	−8.18105			−0.535958			−0.267979	−	0.963425i	$-0.586356\pi$
$233$	−8.18105			−0.535958			−0.267979	+	0.963425i	$0.586356\pi$
$234$	−3.52011	−	6.09701i	−0.230117	−	0.398574i
$235$	−6.84439	+	11.8548i	−0.446479	+	0.773324i
$236$	1.12536	+	1.94917i	0.0732544	+	0.126880i
$237$	−1.30829	+	2.26602i	−0.0849823	+	0.147194i
$238$	13.3673	−	23.1529i	0.866475	−	1.50078i
$239$	−5.92090	+	10.2553i	−0.382991	+	0.663360i	−0.991488	−	0.130196i	$-0.958439\pi$
$239$	−5.92090	+	10.2553i	−0.382991	+	0.663360i	0.608497	+	0.793556i	$0.291773\pi$
$240$	−0.696418			−0.0449536
$241$	9.55271	+	16.5458i	0.615344	+	1.06581i	0.990324	+	0.138775i	$0.0443164\pi$
$241$	9.55271	+	16.5458i	0.615344	+	1.06581i	−0.374980	+	0.927033i	$0.622350\pi$
$242$	−25.1510	−	43.5627i	−1.61676	−	2.80032i
$243$	−2.99049	+	5.17968i	−0.191840	+	0.332276i
$244$	−2.40083			−0.153698
$245$	−2.07236	−	3.58943i	−0.132398	−	0.229321i
$246$	2.62824			0.167570
$247$	1.26264			0.0803400
$248$	22.1582	−	4.49728i	1.40704	−	0.285578i
$249$	1.10425			0.0699787
$250$	26.2400			1.65956
$251$	1.82925	+	3.16836i	0.115461	+	0.199985i	0.917964	−	0.396663i	$-0.129832\pi$
$251$	1.82925	+	3.16836i	0.115461	+	0.199985i	−0.802503	+	0.596649i	$0.796499\pi$
$252$	−21.5636			−1.35838
$253$	18.5785	−	32.1790i	1.16802	−	2.02308i
$254$	−12.2458	−	21.2103i	−0.768370	−	1.33086i
$255$	−0.859992	−	1.48955i	−0.0538548	−	0.0932792i
$256$	−27.7176			−1.73235
$257$	1.44408	−	2.50122i	0.0900794	−	0.156022i	−0.817465	−	0.575978i	$-0.804621\pi$
$257$	1.44408	−	2.50122i	0.0900794	−	0.156022i	0.907544	+	0.419956i	$0.137955\pi$
$258$	−1.49144	+	2.58325i	−0.0928531	+	0.160826i
$259$	4.11658	−	7.13012i	0.255792	−	0.443044i
$260$	−2.47795	−	4.29193i	−0.153676	−	0.266174i
$261$	−0.339028	+	0.587214i	−0.0209853	+	0.0363476i
$262$	17.6704	+	30.6061i	1.09168	+	1.89085i
$263$	−10.1145			−0.623687			−0.311843	−	0.950134i	$-0.600946\pi$
$263$	−10.1145			−0.623687			−0.311843	+	0.950134i	$0.600946\pi$
$264$	5.21254			0.320810
$265$	−9.05289	−	15.6801i	−0.556115	−	0.963219i
$266$	2.97869	−	5.15925i	0.182635	−	0.316334i
$267$	−0.406773	−	0.704552i	−0.0248941	−	0.0431179i
$268$	15.5750	−	26.9766i	0.951392	−	1.64786i
$269$	3.33019	−	5.76806i	0.203045	−	0.351685i	−0.746463	−	0.665427i	$-0.768249\pi$
$269$	3.33019	−	5.76806i	0.203045	−	0.351685i	0.949508	+	0.313742i	$0.101583\pi$
$270$	−2.15565	+	3.73370i	−0.131189	+	0.227226i
$271$	−1.29433			−0.0786251			−0.0393125	−	0.999227i	$-0.512517\pi$
$271$	−1.29433			−0.0786251			−0.0393125	+	0.999227i	$0.512517\pi$
$272$	6.50001	+	11.2584i	0.394121	+	0.682638i
$273$	0.223962	+	0.387914i	0.0135548	+	0.0234776i
$274$	17.1470	−	29.6994i	1.03589	−	1.79421i
$275$	−18.1589			−1.09503
$276$	2.75213	+	4.76684i	0.165659	+	0.286930i
$277$	−15.0525			−0.904419			−0.452209	−	0.891912i	$-0.649364\pi$
$277$	−15.0525			−0.904419			−0.452209	+	0.891912i	$0.649364\pi$
$278$	46.2304			2.77271
$279$	5.21658	−	15.5664i	0.312308	−	0.931935i
$280$	−10.7462			−0.642207
$281$	1.50804			0.0899622			0.0449811	−	0.998988i	$-0.485677\pi$
$281$	1.50804			0.0899622			0.0449811	+	0.998988i	$0.485677\pi$
$282$	2.76613	+	4.79107i	0.164720	+	0.285304i
$283$	14.5307			0.863760			0.431880	−	0.901931i	$-0.357850\pi$
$283$	14.5307			0.863760			0.431880	+	0.901931i	$0.357850\pi$
$284$	12.4186	−	21.5096i	0.736906	−	1.27636i
$285$	−0.191635	−	0.331922i	−0.0113515	−	0.0196614i
$286$	6.76038	+	11.7093i	0.399750	+	0.692387i
$287$	9.59640			0.566457
$288$	−3.89785	+	6.75128i	−0.229683	+	0.397823i
$289$	−7.55345	+	13.0830i	−0.444321	+	0.769586i
$290$	−0.367631	+	0.636756i	−0.0215881	+	0.0373916i
$291$	0.0916663	+	0.158771i	0.00537357	+	0.00930730i
$292$	−30.9625	+	53.6286i	−1.81194	+	3.13838i
$293$	8.82615	+	15.2873i	0.515629	+	0.893096i	0.999835	+	0.0181422i	$0.00577515\pi$
$293$	8.82615	+	15.2873i	0.515629	+	0.893096i	−0.484206	+	0.874954i	$0.660892\pi$
$294$	−1.67507			−0.0976919
$295$	0.814429			0.0474179
$296$	8.45955	+	14.6524i	0.491701	+	0.851652i
$297$	3.81784	−	6.61269i	0.221533	−	0.383707i
$298$	−9.79348	−	16.9628i	−0.567321	−	0.982629i
$299$	−3.28079	+	5.68249i	−0.189733	+	0.328627i
$300$	1.34499	−	2.32959i	0.0776529	−	0.134499i
$301$	−5.44565	+	9.43214i	−0.313882	+	0.543659i
$302$	24.2675			1.39644
$303$	1.58003	+	2.73670i	0.0907706	+	0.157219i
$304$	1.44842	+	2.50874i	0.0830728	+	0.143886i
$305$	−0.434376	+	0.752361i	−0.0248723	+	0.0430801i
$306$	39.8920			2.28047
$307$	−14.4702	−	25.0632i	−0.825859	−	1.43043i	−0.901261	−	0.433276i	$-0.857357\pi$
$307$	−14.4702	−	25.0632i	−0.825859	−	1.43043i	0.0754022	−	0.997153i	$-0.475976\pi$
$308$	41.4130			2.35972
$309$	0.155777			0.00886184
$310$	5.65669	−	16.8797i	0.321278	−	0.958702i
$311$	8.51095			0.482611			0.241306	−	0.970449i	$-0.422424\pi$
$311$	8.51095			0.482611			0.241306	+	0.970449i	$0.422424\pi$
$312$	−0.920483			−0.0521121
$313$	−1.23119	−	2.13249i	−0.0695910	−	0.120535i	0.829130	−	0.559055i	$-0.188836\pi$
$313$	−1.23119	−	2.13249i	−0.0695910	−	0.120535i	−0.898721	+	0.438520i	$0.855503\pi$
$314$	−13.8741			−0.782961
$315$	−3.90144	+	6.75749i	−0.219821	+	0.380741i
$316$	−21.3599	−	36.9965i	−1.20159	−	2.08122i
$317$	6.52409	+	11.3001i	0.366430	+	0.634675i	0.989004	−	0.147886i	$-0.0472468\pi$
$317$	6.52409	+	11.3001i	0.366430	+	0.634675i	−0.622575	+	0.782560i	$0.713913\pi$
$318$	−7.31735			−0.410337
$319$	0.651105	−	1.12775i	0.0364549	−	0.0631417i
$320$	−7.29907	+	12.6424i	−0.408030	+	0.706730i
$321$	2.27107	−	3.93360i	0.126759	−	0.219552i
$322$	15.4794	+	26.8111i	0.862632	+	1.49412i
$323$	−3.57725	+	6.19598i	−0.199044	+	0.344754i
$324$	−15.8028	−	27.3712i	−0.877933	−	1.52062i
$325$	3.20669			0.177875
$326$	−12.3049			−0.681504
$327$	−1.47635	−	2.55711i	−0.0816423	−	0.141409i
$328$	−9.86027	+	17.0785i	−0.544443	+	0.943002i
$329$	10.0999	+	17.4935i	0.556823	+	0.964445i
$330$	2.05209	−	3.55432i	0.112964	−	0.195659i
$331$	2.54744	−	4.41229i	0.140020	−	0.242521i	−0.787484	−	0.616335i	$-0.788617\pi$
$331$	2.54744	−	4.41229i	0.140020	−	0.242521i	0.927504	+	0.373814i	$0.121950\pi$
$332$	−9.01432	+	15.6133i	−0.494725	+	0.856889i
$333$	12.2851			0.673217
$334$	−13.9210	−	24.1118i	−0.761722	−	1.31934i
$335$	−5.63586	−	9.76160i	−0.307920	−	0.533333i
$336$	−0.513831	+	0.889981i	−0.0280318	+	0.0485524i
$337$	−29.0973			−1.58503			−0.792517	−	0.609850i	$-0.791230\pi$
$337$	−29.0973			−1.58503			−0.792517	+	0.609850i	$0.791230\pi$
$338$	−1.19382	−	2.06775i	−0.0649351	−	0.112471i
$339$	−0.890001			−0.0483382
$340$	28.0816			1.52294
$341$	−10.0185	+	29.8953i	−0.542530	+	1.61892i
$342$	8.88929			0.480678
$343$	−19.9488			−1.07713
$344$	−11.1908	−	19.3830i	−0.603366	−	1.04506i
$345$	1.99174			0.107232
$346$	14.6156	−	25.3149i	0.785738	−	1.36094i
$347$	−7.47184	−	12.9416i	−0.401109	−	0.694742i	0.592751	−	0.805386i	$-0.298042\pi$
$347$	−7.47184	−	12.9416i	−0.401109	−	0.694742i	−0.993860	+	0.110644i	$0.964709\pi$
$348$	0.0964515	+	0.167059i	0.00517034	+	0.00895529i
$349$	17.2669			0.924276			0.462138	−	0.886808i	$-0.347082\pi$
$349$	17.2669			0.924276			0.462138	+	0.886808i	$0.347082\pi$
$350$	7.56488	−	13.1028i	0.404360	−	0.700372i
$351$	−0.674192	+	1.16773i	−0.0359857	+	0.0623290i
$352$	7.48584	−	12.9658i	0.398996	−	0.691082i
$353$	16.4011	+	28.4075i	0.872941	+	1.51198i	0.858940	+	0.512077i	$0.171124\pi$
$353$	16.4011	+	28.4075i	0.872941	+	1.51198i	0.0140015	+	0.999902i	$0.495543\pi$
$354$	0.164574	−	0.285050i	0.00874698	−	0.0151502i
$355$	−4.49370	−	7.78333i	−0.238501	−	0.413096i
$356$	13.2825			0.703971
$357$	−2.53807			−0.134329
$358$	−5.27127	−	9.13011i	−0.278595	−	0.482542i
$359$	−12.6964	+	21.9908i	−0.670091	+	1.16063i	0.307787	+	0.951455i	$0.400411\pi$
$359$	−12.6964	+	21.9908i	−0.670091	+	1.16063i	−0.977878	+	0.209176i	$0.932922\pi$
$360$	−8.01743	−	13.8866i	−0.422556	−	0.731888i
$361$	8.70287	−	15.0738i	0.458046	−	0.793358i
$362$	7.00631	−	12.1353i	0.368243	−	0.637816i
$363$	−2.38772	+	4.13566i	−0.125323	+	0.217066i
$364$	−7.31311			−0.383311
$365$	11.2039	+	19.4057i	0.586439	+	1.01574i
$366$	0.175551	+	0.304063i	0.00917618	+	0.0158936i
$367$	−4.07806	+	7.06341i	−0.212873	+	0.368707i	−0.952613	−	0.304186i	$-0.901615\pi$
$367$	−4.07806	+	7.06341i	−0.212873	+	0.368707i	0.739739	+	0.672893i	$0.234949\pi$
$368$	−15.0540			−0.784746
$369$	7.15961	+	12.4008i	0.372714	+	0.645560i
$370$	13.3215			0.692553
$371$	−26.7176			−1.38711
$372$	−3.09319	−	3.49953i	−0.160374	−	0.181442i
$373$	13.7501			0.711954			0.355977	−	0.934495i	$-0.384148\pi$
$373$	13.7501			0.711954			0.355977	+	0.934495i	$0.384148\pi$
$374$	−76.6127			−3.96155
$375$	−1.24556	−	2.15736i	−0.0643202	−	0.111406i
$376$	−41.5103			−2.14073
$377$	−0.114979	+	0.199149i	−0.00592170	+	0.0102567i
$378$	3.18096	+	5.50959i	0.163611	+	0.283383i
$379$	15.8326	+	27.4229i	0.813267	+	1.40862i	0.910565	+	0.413365i	$0.135647\pi$
$379$	15.8326	+	27.4229i	0.813267	+	1.40862i	−0.0972978	+	0.995255i	$0.531020\pi$
$380$	6.25753			0.321005
$381$	−1.16256	+	2.01362i	−0.0595599	+	0.103161i
$382$	−13.3625	+	23.1445i	−0.683685	+	1.18418i
$383$	−15.7920	+	27.3525i	−0.806931	+	1.39765i	0.108048	+	0.994146i	$0.465540\pi$
$383$	−15.7920	+	27.3525i	−0.806931	+	1.39765i	−0.914980	+	0.403500i	$0.867793\pi$
$384$	2.35060	+	4.07135i	0.119953	+	0.207765i
$385$	7.49272	−	12.9778i	0.381864	−	0.661409i
$386$	3.86494	+	6.69428i	0.196720	+	0.340730i
$387$	−16.2514			−0.826105
$388$	−2.99321			−0.151957
$389$	4.25042	+	7.36194i	0.215505	+	0.373265i	0.953429	−	0.301619i	$-0.0975270\pi$
$389$	4.25042	+	7.36194i	0.215505	+	0.373265i	−0.737924	+	0.674884i	$0.764194\pi$
$390$	−0.362379	+	0.627658i	−0.0183498	+	0.0317827i
$391$	−18.5899	−	32.1987i	−0.940132	−	1.62836i
$392$	6.28429	−	10.8847i	0.317404	−	0.549761i
$393$	1.67755	−	2.90561i	0.0846214	−	0.146569i
$394$	−22.1587	+	38.3799i	−1.11634	+	1.93355i
$395$	−15.4584			−0.777794
$396$	30.8971	+	53.5153i	1.55264	+	2.68924i
$397$	−12.0722	−	20.9096i	−0.605885	−	1.04942i	−0.991911	−	0.126936i	$-0.959486\pi$
$397$	−12.0722	−	20.9096i	−0.605885	−	1.04942i	0.386026	−	0.922488i	$-0.373847\pi$
$398$	4.39604	−	7.61416i	0.220354	−	0.381663i
$399$	−0.565569			−0.0283139
$400$	3.67851	+	6.37137i	0.183925	+	0.318568i
$401$	−22.8040			−1.13878			−0.569388	−	0.822069i	$-0.692820\pi$
$401$	−22.8040			−1.13878			−0.569388	+	0.822069i	$0.692820\pi$
$402$	−4.55541			−0.227203
$403$	1.76916	−	5.27921i	0.0881281	−	0.262976i
$404$	−51.5934			−2.56687
$405$	−11.4366			−0.568289
$406$	0.542491	+	0.939622i	0.0269234	+	0.0466327i
$407$	−23.5935			−1.16949
$408$	2.60786	−	4.51695i	0.129109	−	0.223622i
$409$	−11.7894	−	20.4198i	−0.582948	−	1.00970i	−0.995128	−	0.0985935i	$-0.968566\pi$
$409$	−11.7894	−	20.4198i	−0.582948	−	1.00970i	0.412179	−	0.911103i	$-0.364768\pi$
$410$	7.76365	+	13.4470i	0.383419	+	0.664102i
$411$	−3.25572			−0.160593
$412$	−1.27166	+	2.20258i	−0.0626501	+	0.108513i
$413$	0.600901	−	1.04079i	0.0295684	−	0.0512140i
$414$	−23.0975	+	40.0060i	−1.13518	+	1.96619i
$415$	3.26187	+	5.64972i	0.160119	+	0.277334i
$416$	−1.32192	+	2.28964i	−0.0648127	+	0.112259i
$417$	−2.19446	−	3.80091i	−0.107463	−	0.186131i
$418$	−17.0719			−0.835014
$419$	21.7094			1.06058			0.530288	−	0.847818i	$-0.322084\pi$
$419$	21.7094			1.06058			0.530288	+	0.847818i	$0.322084\pi$
$420$	1.10993	+	1.92246i	0.0541593	+	0.0938066i
$421$	10.9757	−	19.0105i	0.534924	−	0.926515i	−0.464243	−	0.885708i	$-0.653674\pi$
$421$	10.9757	−	19.0105i	0.534924	−	0.926515i	0.999167	−	0.0408072i	$-0.0129929\pi$
$422$	−14.3301	−	24.8204i	−0.697576	−	1.20824i
$423$	−15.0704	+	26.1028i	−0.732750	+	1.26916i
$424$	27.4523	−	47.5487i	1.33320	−	2.30917i
$425$	−9.08502	+	15.7357i	−0.440688	+	0.763295i
$426$	−3.63221			−0.175981
$427$	0.640982	+	1.11021i	0.0310193	+	0.0537270i
$428$	37.0789	+	64.2226i	1.79228	+	3.10432i
$429$	0.641802	−	1.11163i	0.0309865	−	0.0536702i
$430$	−17.6225			−0.849832
$431$	−1.29329	−	2.24005i	−0.0622957	−	0.107899i	0.833195	−	0.552979i	$-0.186509\pi$
$431$	−1.29329	−	2.24005i	−0.0622957	−	0.107899i	−0.895491	+	0.445079i	$0.853176\pi$
$432$	−3.09356			−0.148839
$433$	−18.0386			−0.866879			−0.433439	−	0.901183i	$-0.642700\pi$
$433$	−18.0386			−0.866879			−0.433439	+	0.901183i	$0.642700\pi$
$434$	−17.3976	−	19.6831i	−0.835113	−	0.944818i
$435$	0.0698027			0.00334678
$436$	48.2077			2.30873
$437$	−4.14246	−	7.17495i	−0.198161	−	0.343225i
$438$	9.05600			0.432712
$439$	−9.36869	+	16.2270i	−0.447143	+	0.774475i	−0.998199	−	0.0599939i	$-0.980892\pi$
$439$	−9.36869	+	16.2270i	−0.447143	+	0.774475i	0.551056	+	0.834469i	$0.314225\pi$
$440$	15.3975	+	26.6693i	0.734047	+	1.27141i
$441$	−4.56306	−	7.90345i	−0.217289	−	0.376355i
$442$	13.5290			0.643510
$443$	−14.6730	+	25.4143i	−0.697134	+	1.20747i	0.272323	+	0.962206i	$0.412208\pi$
$443$	−14.6730	+	25.4143i	−0.697134	+	1.20747i	−0.969456	+	0.245265i	$0.921125\pi$
$444$	1.74751	−	3.02678i	0.0829333	−	0.143645i
$445$	2.40316	−	4.16240i	0.113921	−	0.197317i
$446$	27.1848	+	47.0854i	1.28724	+	2.22956i
$447$	−0.929751	+	1.61038i	−0.0439757	+	0.0761682i
$448$	10.7708	+	18.6556i	0.508872	+	0.881392i
$449$	−15.3807			−0.725861			−0.362931	−	0.931816i	$-0.618224\pi$
$449$	−15.3807			−0.725861			−0.362931	+	0.931816i	$0.618224\pi$
$450$	22.5758			1.06423
$451$	−13.7500	−	23.8158i	−0.647464	−	1.12144i
$452$	7.26537	−	12.5840i	0.341734	−	0.591902i
$453$	−1.15193	−	1.99520i	−0.0541223	−	0.0937425i
$454$	20.4833	−	35.4781i	0.961329	−	1.66507i
$455$	−1.32314	+	2.29175i	−0.0620297	+	0.107439i
$456$	0.581121	−	1.00653i	0.0272135	−	0.0471351i
$457$	−18.4099			−0.861177			−0.430589	−	0.902548i	$-0.641694\pi$
$457$	−18.4099			−0.861177			−0.430589	+	0.902548i	$0.641694\pi$
$458$	−4.70968	−	8.15741i	−0.220069	−	0.381171i
$459$	−3.82017	−	6.61673i	−0.178310	−	0.308842i
$460$	−16.2592	+	28.1618i	−0.758091	+	1.31305i
$461$	−9.43473			−0.439419			−0.219710	−	0.975565i	$-0.570511\pi$
$461$	−9.43473			−0.439419			−0.219710	+	0.975565i	$0.570511\pi$
$462$	−3.02814	−	5.24490i	−0.140882	−	0.244015i
$463$	−11.1887			−0.519981			−0.259990	−	0.965611i	$-0.583719\pi$
$463$	−11.1887			−0.519981			−0.259990	+	0.965611i	$0.583719\pi$
$464$	−0.527585			−0.0244925
$465$	−1.65630	+	0.336168i	−0.0768093	+	0.0155894i
$466$	−19.5333			−0.904865
$467$	9.97623			0.461645			0.230822	−	0.972996i	$-0.425858\pi$
$467$	9.97623			0.461645			0.230822	+	0.972996i	$0.425858\pi$
$468$	−5.45611	−	9.45027i	−0.252209	−	0.436839i
$469$	−16.6330			−0.768040
$470$	−16.3419	+	28.3050i	−0.753796	+	1.30561i
$471$	0.658574	+	1.14068i	0.0303455	+	0.0525599i
$472$	1.23485	+	2.13882i	0.0568385	+	0.0984472i
$473$	31.2109			1.43508
$474$	−3.12371	+	5.41042i	−0.143477	+	0.248509i
$475$	−2.02445	+	3.50645i	−0.0928882	+	0.160887i
$476$	20.7191	−	35.8866i	0.949660	−	1.64486i
$477$	−19.9333	−	34.5254i	−0.912681	−	1.58081i
$478$	−14.1369	+	24.4859i	−0.646608	+	1.11996i
$479$	10.8334	+	18.7640i	0.494992	+	0.857351i	0.999983	−	0.00577337i	$-0.00183773\pi$
$479$	10.8334	+	18.7640i	0.494992	+	0.857351i	−0.504992	+	0.863124i	$0.668504\pi$
$480$	0.802530			0.0366303
$481$	4.16638			0.189970
$482$	22.8084	+	39.5053i	1.03889	+	1.79942i
$483$	1.46954	−	2.54533i	0.0668666	−	0.115816i
$484$	−38.9836	−	67.5215i	−1.77198	−	3.06916i
$485$	−0.541552	+	0.937996i	−0.0245906	+	0.0425922i
$486$	−7.14019	+	12.3672i	−0.323885	+	0.560986i
$487$	9.43854	−	16.3480i	0.427701	−	0.740800i	−0.568967	−	0.822360i	$-0.692657\pi$
$487$	9.43854	−	16.3480i	0.427701	−	0.740800i	0.996668	+	0.0815599i	$0.0259902\pi$
$488$	−2.63443			−0.119255
$489$	0.584086	+	1.01167i	0.0264133	+	0.0457491i
$490$	−4.94804	−	8.57025i	−0.223530	−	0.387165i
$491$	−12.0463	+	20.8648i	−0.543642	+	0.941615i	0.455049	+	0.890466i	$0.349622\pi$
$491$	−12.0463	+	20.8648i	−0.543642	+	0.941615i	−0.998691	+	0.0511491i	$0.983712\pi$
$492$	4.07373			0.183658
$493$	−0.651503	−	1.12844i	−0.0293422	−	0.0508222i
$494$	3.01473			0.135639
$495$	22.3604			1.00503
$496$	12.5187	−	2.54084i	0.562107	−	0.114087i
$497$	−13.2622			−0.594889
$498$	2.63653			0.118146
$499$	−2.06399	−	3.57494i	−0.0923971	−	0.160036i	0.816122	−	0.577879i	$-0.196120\pi$
$499$	−2.06399	−	3.57494i	−0.0923971	−	0.160036i	−0.908519	+	0.417843i	$0.862786\pi$
$500$	40.6715			1.81889
$501$	−1.32160	+	2.28907i	−0.0590446	+	0.102268i
$502$	4.36759	+	7.56488i	0.194935	+	0.337637i
$503$	−8.47288	−	14.6755i	−0.377787	−	0.654347i	0.612953	−	0.790120i	$-0.289982\pi$
$503$	−8.47288	−	14.6755i	−0.377787	−	0.654347i	−0.990740	+	0.135773i	$0.956648\pi$
$504$	−23.6617			−1.05397
$505$	−9.33463	+	16.1681i	−0.415386	+	0.719469i
$506$	44.3588	−	76.8316i	1.97199	−	3.41558i
$507$	−0.113336	+	0.196303i	−0.00503342	+	0.00871814i
$508$	−18.9808	−	32.8757i	−0.842136	−	1.45862i
$509$	−3.30485	+	5.72416i	−0.146485	+	0.253719i	−0.929926	−	0.367747i	$-0.880129\pi$
$509$	−3.30485	+	5.72416i	−0.146485	+	0.253719i	0.783441	+	0.621466i	$0.213463\pi$
$510$	−2.05334	−	3.55650i	−0.0909236	−	0.157484i
$511$	33.0658			1.46275
$512$	−24.6992			−1.09156
$513$	−0.851263	−	1.47443i	−0.0375842	−	0.0650977i
$514$	3.44794	−	5.97200i	0.152082	−	0.263414i
$515$	0.460155	+	0.797012i	0.0202768	+	0.0351205i
$516$	−2.31171	+	4.00400i	−0.101767	+	0.176266i
$517$	28.9428	−	50.1305i	1.27290	−	2.20473i
$518$	9.82888	−	17.0241i	0.431856	−	0.747997i
$519$	−2.77508			−0.121812
$520$	−2.71905	−	4.70952i	−0.119238	−	0.206526i
$521$	5.41865	+	9.38538i	0.237395	+	0.411181i	0.959966	−	0.280116i	$-0.0903729\pi$
$521$	5.41865	+	9.38538i	0.237395	+	0.411181i	−0.722571	+	0.691297i	$0.757040\pi$
$522$	−0.809475	+	1.40205i	−0.0354298	+	0.0613662i
$523$	17.8796			0.781821			0.390911	−	0.920429i	$-0.372160\pi$
$523$	17.8796			0.781821			0.390911	+	0.920429i	$0.372160\pi$
$524$	27.3889	+	47.4389i	1.19649	+	2.07238i
$525$	−1.43635			−0.0626877
$526$	−24.1497			−1.05298
$527$	20.8936	+	23.6383i	0.910141	+	1.02970i
$528$	2.94494			0.128162
$529$	20.0542			0.871923
$530$	−21.6150	−	37.4382i	−0.938895	−	1.62621i
$531$	1.79326			0.0778210
$532$	4.61693	−	7.99675i	0.200169	−	0.346703i
$533$	2.42812	+	4.20563i	0.105174	+	0.182166i
$534$	−0.971226	−	1.68221i	−0.0420290	−	0.0727964i
$535$	26.8343			1.16015
$536$	17.0904	−	29.6014i	0.738191	−	1.27858i
$537$	−0.500432	+	0.866774i	−0.0215952	+	0.0374040i
$538$	7.95128	−	13.7720i	0.342804	−	0.593754i
$539$	8.76337	+	15.1786i	0.377465	+	0.653789i
$540$	−3.34123	+	5.78717i	−0.143783	+	0.249040i
$541$	13.3762	+	23.1682i	0.575086	+	0.996079i	0.996032	+	0.0889930i	$0.0283649\pi$
$541$	13.3762	+	23.1682i	0.575086	+	0.996079i	−0.420946	+	0.907086i	$0.638302\pi$
$542$	−3.09039			−0.132744
$543$	−1.33030			−0.0570885
$544$	−7.49041	−	12.9738i	−0.321149	−	0.556246i
$545$	8.72207	−	15.1071i	0.373613	−	0.647116i
$546$	0.534740	+	0.926197i	0.0228848	+	0.0396376i
$547$	0.745297	−	1.29089i	0.0318666	−	0.0551946i	−0.849652	−	0.527343i	$-0.823188\pi$
$547$	0.745297	−	1.29089i	0.0318666	−	0.0551946i	0.881519	+	0.472149i	$0.156521\pi$
$548$	26.5775	−	46.0336i	1.13533	−	1.96646i
$549$	−0.956437	+	1.65660i	−0.0408197	+	0.0707019i
$550$	−43.3569			−1.84874
$551$	−0.145177	−	0.251454i	−0.00618475	−	0.0107123i
$552$	3.01991	+	5.23063i	0.128536	+	0.222631i
$553$	−11.4055	+	19.7549i	−0.485010	+	0.840062i
$554$	−35.9399			−1.52694
$555$	−0.632344	−	1.09525i	−0.0268415	−	0.0464909i
$556$	71.6563			3.03890
$557$	38.3972			1.62694			0.813471	−	0.581606i	$-0.197575\pi$
$557$	38.3972			1.62694			0.813471	+	0.581606i	$0.197575\pi$
$558$	12.4553	−	37.1668i	0.527274	−	1.57340i
$559$	−5.51152			−0.233113
$560$	−6.07129			−0.256559
$561$	3.63664	+	6.29884i	0.153539	+	0.265937i
$562$	3.60065			0.151884
$563$	5.96487	−	10.3315i	0.251389	−	0.435419i	−0.712519	−	0.701652i	$-0.752446\pi$
$563$	5.96487	−	10.3315i	0.251389	−	0.435419i	0.963909	+	0.266234i	$0.0857793\pi$
$564$	4.28745	+	7.42608i	0.180534	+	0.312694i
$565$	−2.62900	−	4.55357i	−0.110603	−	0.191570i
$566$	34.6940			1.45830
$567$	−8.43814	+	14.6153i	−0.354369	+	0.613785i
$568$	13.6268	−	23.6024i	0.571770	−	0.990334i
$569$	16.0122	−	27.7339i	0.671265	−	1.16267i	−0.306281	−	0.951941i	$-0.599085\pi$
$569$	16.0122	−	27.7339i	0.671265	−	1.16267i	0.977546	−	0.210724i	$-0.0675821\pi$
$570$	−0.457555	−	0.792508i	−0.0191649	−	0.0331945i
$571$	6.40826	−	11.0994i	0.268177	−	0.464497i	−0.700214	−	0.713933i	$-0.746912\pi$
$571$	6.40826	−	11.0994i	0.268177	−	0.464497i	0.968391	+	0.249436i	$0.0802454\pi$
$572$	10.4785	+	18.1493i	0.438127	+	0.758859i
$573$	2.53716			0.105991
$574$	22.9127			0.956356
$575$	−10.5205	−	18.2220i	−0.438733	−	0.759909i
$576$	−16.0716	+	27.8368i	−0.669649	+	1.15987i
$577$	20.9874	+	36.3513i	0.873718	+	1.51332i	0.858122	+	0.513445i	$0.171631\pi$
$577$	20.9874	+	36.3513i	0.873718	+	1.51332i	0.0155955	+	0.999878i	$0.495036\pi$
$578$	−18.0349	+	31.2373i	−0.750152	+	1.29930i
$579$	0.366921	−	0.635526i	0.0152487	−	0.0264116i
$580$	−0.569823	+	0.986962i	−0.0236606	+	0.0409813i
$581$	9.62668			0.399382
$582$	0.218865	+	0.379086i	0.00907226	+	0.0157136i
$583$	38.2819	+	66.3062i	1.58547	+	2.74612i
$584$	−33.9751	+	58.8465i	−1.40590	+	2.43509i
$585$	−3.94863			−0.163256
$586$	21.0736	+	36.5006i	0.870543	+	1.50782i
$587$	−42.3389			−1.74751			−0.873756	−	0.486365i	$-0.838323\pi$
$587$	−42.3389			−1.74751			−0.873756	+	0.486365i	$0.838323\pi$
$588$	−2.59633			−0.107071
$589$	4.65581	+	5.26742i	0.191839	+	0.217040i
$590$	1.94456			0.0800561
$591$	4.20730			0.173065
$592$	4.77940	+	8.27817i	0.196432	+	0.340231i
$593$	−13.4101			−0.550687			−0.275344	−	0.961346i	$-0.588792\pi$
$593$	−13.4101			−0.550687			−0.275344	+	0.961346i	$0.588792\pi$
$594$	9.11559	−	15.7887i	0.374017	−	0.647817i
$595$	−7.49730	−	12.9857i	−0.307359	−	0.532362i
$596$	−15.1797	−	26.2921i	−0.621786	−	1.07696i
$597$	−0.834682			−0.0341613
$598$	−7.83331	+	13.5677i	−0.320328	+	0.554824i
$599$	12.8017	−	22.1732i	0.523063	−	0.905972i	−0.476577	−	0.879133i	$-0.658123\pi$
$599$	12.8017	−	22.1732i	0.523063	−	0.905972i	0.999640	−	0.0268388i	$-0.00854408\pi$
$600$	1.47585	−	2.55625i	0.0602514	−	0.104358i
$601$	−16.1342	−	27.9452i	−0.658126	−	1.13991i	−0.981100	−	0.193500i	$-0.938016\pi$
$601$	−16.1342	−	27.9452i	−0.658126	−	1.13991i	0.322974	−	0.946408i	$-0.395317\pi$
$602$	−13.0022	+	22.5205i	−0.529930	+	0.917866i
$603$	−12.4094	−	21.4937i	−0.505350	−	0.875292i
$604$	37.6143			1.53050
$605$	−28.2127			−1.14701
$606$	3.77254	+	6.53423i	0.153249	+	0.265435i
$607$	0.338294	−	0.585943i	0.0137309	−	0.0237827i	−0.859078	−	0.511844i	$-0.828963\pi$
$607$	0.338294	−	0.585943i	0.0137309	−	0.0237827i	0.872809	+	0.488062i	$0.162296\pi$
$608$	−1.66912	−	2.89100i	−0.0676917	−	0.117245i
$609$	0.0515018	−	0.0892037i	0.00208696	−	0.00361472i
$610$	−1.03713	+	1.79636i	−0.0419922	+	0.0727326i
$611$	−5.11102	+	8.85254i	−0.206770	+	0.358135i
$612$	61.8319			2.49941
$613$	−9.77989	−	16.9393i	−0.395006	−	0.684170i	0.598096	−	0.801424i	$-0.295924\pi$
$613$	−9.77989	−	16.9393i	−0.395006	−	0.684170i	−0.993102	+	0.117254i	$0.962591\pi$
$614$	−34.5496	−	59.8416i	−1.39431	−	2.41501i
$615$	0.737047	−	1.27660i	0.0297206	−	0.0514776i
$616$	45.4423			1.83092
$617$	−10.4710	−	18.1362i	−0.421545	−	0.730137i	0.574546	−	0.818472i	$-0.305179\pi$
$617$	−10.4710	−	18.1362i	−0.421545	−	0.730137i	−0.996091	+	0.0883351i	$0.971845\pi$
$618$	0.371938			0.0149615
$619$	19.4282			0.780887			0.390444	−	0.920627i	$-0.372322\pi$
$619$	19.4282			0.780887			0.390444	+	0.920627i	$0.372322\pi$
$620$	8.76777	−	26.1632i	0.352122	−	1.05074i
$621$	8.84751			0.355039
$622$	20.3210			0.814798
$623$	−3.54620	−	6.14220i	−0.142076	−	0.246082i
$624$	−0.520047			−0.0208185
$625$	−0.658147	+	1.13994i	−0.0263259	+	0.0455977i
$626$	−2.93963	−	5.09159i	−0.117491	−	0.203501i
$627$	0.810367	+	1.40360i	0.0323629	+	0.0560542i
$628$	−21.5046			−0.858128
$629$	−11.8040	+	20.4451i	−0.470655	+	0.815198i
$630$	−9.31520	+	16.1344i	−0.371126	+	0.642810i
$631$	2.58177	−	4.47176i	0.102779	−	0.178018i	−0.810050	−	0.586361i	$-0.800560\pi$
$631$	2.58177	−	4.47176i	0.102779	−	0.178018i	0.912828	+	0.408343i	$0.133893\pi$
$632$	−23.4382	−	40.5961i	−0.932321	−	1.61483i
$633$	−1.36043	+	2.35634i	−0.0540724	+	0.0936561i
$634$	15.5771	+	26.9804i	0.618647	+	1.07153i
$635$	−13.7365			−0.545118
$636$	−11.3418			−0.449731
$637$	−1.54752	−	2.68039i	−0.0613151	−	0.106201i
$638$	1.55460	−	2.69265i	0.0615472	−	0.106603i
$639$	−9.89454	−	17.1378i	−0.391422	−	0.677963i
$640$	−13.8870	+	24.0530i	−0.548932	+	0.950778i
$641$	−8.80031	+	15.2426i	−0.347591	+	0.602046i	−0.985821	−	0.167800i	$-0.946334\pi$
$641$	−8.80031	+	15.2426i	−0.347591	+	0.602046i	0.638230	+	0.769846i	$0.279667\pi$
$642$	5.42247	−	9.39200i	0.214008	−	0.370673i
$643$	−14.5332			−0.573134			−0.286567	−	0.958060i	$-0.592514\pi$
$643$	−14.5332			−0.573134			−0.286567	+	0.958060i	$0.592514\pi$
$644$	23.9928	+	41.5567i	0.945447	+	1.63756i
$645$	0.836502	+	1.44886i	0.0329372	+	0.0570489i
$646$	−8.54117	+	14.7937i	−0.336048	+	0.582052i
$647$	30.4360			1.19656			0.598281	−	0.801287i	$-0.295851\pi$
$647$	30.4360			1.19656			0.598281	+	0.801287i	$0.295851\pi$
$648$	−17.3403	−	30.0344i	−0.681193	−	1.17986i
$649$	−3.44397			−0.135188
$650$	7.65640			0.300309
$651$	−0.792450	+	2.36469i	−0.0310586	+	0.0926795i
$652$	−19.0723			−0.746931
$653$	13.9303			0.545136			0.272568	−	0.962136i	$-0.412127\pi$
$653$	13.9303			0.545136			0.272568	+	0.962136i	$0.412127\pi$
$654$	−3.52498	−	6.10544i	−0.137838	−	0.238742i
$655$	19.8215			0.774491
$656$	−5.57077	+	9.64886i	−0.217502	+	0.376725i
$657$	24.6695	+	42.7288i	0.962449	+	1.66701i
$658$	24.1147	+	41.7680i	0.940090	+	1.62828i
$659$	41.6607			1.62287			0.811436	−	0.584441i	$-0.198686\pi$
$659$	41.6607			1.62287			0.811436	+	0.584441i	$0.198686\pi$
$660$	3.18071	−	5.50914i	0.123809	−	0.214443i
$661$	−18.7072	+	32.4019i	−0.727627	+	1.26029i	0.230256	+	0.973130i	$0.426043\pi$
$661$	−18.7072	+	32.4019i	−0.727627	+	1.26029i	−0.957884	+	0.287157i	$0.907290\pi$
$662$	6.08235	−	10.5349i	0.236397	−	0.409452i
$663$	−0.642194	−	1.11231i	−0.0249408	−	0.0431987i
$664$	−9.89139	+	17.1324i	−0.383860	+	0.664865i
$665$	−1.67065	−	2.89366i	−0.0647851	−	0.112211i
$666$	29.3322			1.13660
$667$	1.50888			0.0584241
$668$	−21.5773	−	37.3729i	−0.834850	−	1.44600i
$669$	2.58080	−	4.47008i	0.0997796	−	0.172823i
$670$	−13.4564	−	23.3071i	−0.519865	−	0.900432i
$671$	1.83684	−	3.18150i	0.0709105	−	0.122821i
$672$	0.592122	−	1.02559i	0.0228416	−	0.0395628i
$673$	18.3798	−	31.8347i	0.708488	−	1.22714i	−0.256929	−	0.966430i	$-0.582711\pi$
$673$	18.3798	−	31.8347i	0.708488	−	1.22714i	0.965418	−	0.260708i	$-0.0839559\pi$
$674$	−69.4738			−2.67603
$675$	−2.16192	−	3.74456i	−0.0832124	−	0.144128i
$676$	−1.85040	−	3.20498i	−0.0711691	−	0.123268i
$677$	19.0553	−	33.0047i	0.732354	−	1.26847i	−0.223521	−	0.974699i	$-0.571755\pi$
$677$	19.0553	−	33.0047i	0.732354	−	1.26847i	0.955875	−	0.293775i	$-0.0949116\pi$
$678$	−2.12500			−0.0816100
$679$	0.799135	+	1.38414i	0.0306680	+	0.0531185i
$680$	30.8138			1.18166
$681$	−3.88919			−0.149034
$682$	−23.9204	+	71.3790i	−0.915959	+	2.73324i
$683$	−17.4875			−0.669140			−0.334570	−	0.942371i	$-0.608591\pi$
$683$	−17.4875			−0.669140			−0.334570	+	0.942371i	$0.608591\pi$
$684$	13.7782			0.526824
$685$	−9.61717	−	16.6574i	−0.367453	−	0.636448i
$686$	−47.6304			−1.81854
$687$	−0.447117	+	0.774430i	−0.0170586	+	0.0295463i
$688$	−6.32247	−	10.9508i	−0.241042	−	0.417497i
$689$	−6.76020	−	11.7090i	−0.257543	−	0.446078i
$690$	4.75555			0.181041
$691$	14.6316	−	25.3426i	0.556611	−	0.964078i	−0.441165	−	0.897426i	$-0.645435\pi$
$691$	14.6316	−	25.3426i	0.556611	−	0.964078i	0.997776	−	0.0666526i	$-0.0212319\pi$
$692$	22.6539	−	39.2377i	0.861172	−	1.49159i
$693$	16.4980	−	28.5753i	0.626706	−	1.08549i
$694$	−17.8400	−	30.8998i	−0.677198	−	1.17294i
$695$	12.9646	−	22.4553i	0.491774	−	0.851777i
$696$	0.105836	+	0.183313i	0.00401170	+	0.00694846i
$697$	−27.5169			−1.04228
$698$	41.2270			1.56047
$699$	0.927206	+	1.60597i	0.0350701	+	0.0607433i
$700$	11.7254	−	20.3091i	0.443180	−	0.767610i
$701$	−0.588030	−	1.01850i	−0.0222096	−	0.0384681i	0.854707	−	0.519111i	$-0.173737\pi$
$701$	−0.588030	−	1.01850i	−0.0222096	−	0.0384681i	−0.876917	+	0.480643i	$0.840403\pi$
$702$	−1.60972	+	2.78812i	−0.0607550	+	0.105231i
$703$	−2.63032	+	4.55585i	−0.0992045	+	0.171827i
$704$	30.8655	−	53.4606i	1.16329	−	2.01487i
$705$	3.10286			0.116860
$706$	39.1598	+	67.8267i	1.47380	+	2.55269i
$707$	13.7745	+	23.8582i	0.518045	+	0.897280i
$708$	0.255086	−	0.441822i	0.00958673	−	0.0166047i
$709$	−3.48828			−0.131005			−0.0655026	−	0.997852i	$-0.520865\pi$
$709$	−3.48828			−0.131005			−0.0655026	+	0.997852i	$0.520865\pi$
$710$	−10.7293	−	18.5837i	−0.402664	−	0.697435i
$711$	−34.0372			−1.27650
$712$	14.5748			0.546216
$713$	−35.8033	+	7.26674i	−1.34084	+	0.272142i
$714$	−6.05999			−0.226789
$715$	7.58336			0.283602
$716$	−8.17039	−	14.1515i	−0.305342	−	0.528867i
$717$	2.68420			0.100243
$718$	−30.3144	+	52.5060i	−1.13132	+	1.95951i
$719$	−3.08569	−	5.34457i	−0.115077	−	0.199319i	0.802734	−	0.596338i	$-0.203378\pi$
$719$	−3.08569	−	5.34457i	−0.115077	−	0.199319i	−0.917810	+	0.397019i	$0.870045\pi$
$720$	−4.52962	−	7.84553i	−0.168809	−	0.292386i
$721$	1.35804			0.0505762
$722$	20.7793	−	35.9907i	0.773324	−	1.33944i
$723$	2.16533	−	3.75046i	0.0805295	−	0.139481i
$724$	10.8597	−	18.8095i	0.403596	−	0.699049i
$725$	−0.368701	−	0.638608i	−0.0136932	−	0.0237173i
$726$	−5.70101	+	9.87444i	−0.211584	+	0.366475i
$727$	−4.48247	−	7.76387i	−0.166246	−	0.287946i	0.770851	−	0.637015i	$-0.219831\pi$
$727$	−4.48247	−	7.76387i	−0.166246	−	0.287946i	−0.937097	+	0.349069i	$0.886498\pi$
$728$	−8.02466			−0.297414
$729$	−24.2649			−0.898702
$730$	26.7508	+	46.3338i	0.990092	+	1.71489i
$731$	15.6150	−	27.0459i	0.577540	−	1.00033i
$732$	0.272101	+	0.471292i	0.0100571	+	0.0174195i
$733$	19.7237	−	34.1625i	0.728513	−	1.26182i	−0.228999	−	0.973427i	$-0.573545\pi$
$733$	19.7237	−	34.1625i	0.728513	−	1.26182i	0.957512	−	0.288395i	$-0.0931215\pi$
$734$	−9.73691	+	16.8648i	−0.359396	+	0.622492i
$735$	−0.469745	+	0.813623i	−0.0173268	+	0.0300109i
$736$	17.3478			0.639448
$737$	23.8323	+	41.2788i	0.877875	+	1.52052i
$738$	17.0945	+	29.6086i	0.629258	+	1.08991i
$739$	−25.2122	+	43.6688i	−0.927445	+	1.60638i	−0.139865	+	0.990171i	$0.544667\pi$
$739$	−25.2122	+	43.6688i	−0.927445	+	1.60638i	−0.787581	+	0.616212i	$0.788667\pi$
$740$	20.6481			0.759041
$741$	−0.143103	−	0.247861i	−0.00525701	−	0.00910540i
$742$	−63.7918			−2.34187
$743$	52.9648			1.94309			0.971546	−	0.236852i	$-0.0761156\pi$
$743$	52.9648			1.94309			0.971546	+	0.236852i	$0.0761156\pi$
$744$	−3.39414	−	3.84002i	−0.124435	−	0.140782i
$745$	−10.9857			−0.402484
$746$	32.8302			1.20200
$747$	7.18220	+	12.4399i	0.262783	+	0.455153i
$748$	−118.748			−4.34187
$749$	19.7989	−	34.2927i	0.723435	−	1.25303i
$750$	−2.97393	−	5.15100i	−0.108593	−	0.188088i
$751$	9.70514	+	16.8098i	0.354145	+	0.613398i	0.986971	−	0.160896i	$-0.0514384\pi$
$751$	9.70514	+	16.8098i	0.354145	+	0.613398i	−0.632826	+	0.774294i	$0.718105\pi$
$752$	−23.4521			−0.855211
$753$	0.414640	−	0.718177i	0.0151103	−	0.0261718i
$754$	−0.274527	+	0.475494i	−0.00999768	+	0.0173165i
$755$	6.80543	−	11.7874i	0.247675	−	0.428986i
$756$	4.93044	+	8.53977i	0.179318	+	0.310589i
$757$	25.6947	−	44.5045i	0.933889	−	1.61754i	0.157286	−	0.987553i	$-0.449726\pi$
$757$	25.6947	−	44.5045i	0.933889	−	1.61754i	0.776603	−	0.629990i	$-0.216941\pi$
$758$	37.8025	+	65.4759i	1.37305	+	2.37819i
$759$	−8.42246			−0.305716
$760$	6.86637			0.249069
$761$	15.8896	+	27.5216i	0.575997	+	0.997657i	0.995932	+	0.0901025i	$0.0287195\pi$
$761$	15.8896	+	27.5216i	0.575997	+	0.997657i	−0.419935	+	0.907554i	$0.637947\pi$
$762$	−2.77577	+	4.80778i	−0.100556	+	0.174168i
$763$	−12.8706	−	22.2926i	−0.465948	−	0.807045i
$764$	−20.7116	+	35.8736i	−0.749321	+	1.29786i
$765$	11.1871	−	19.3766i	0.404469	−	0.700561i
$766$	−37.7054	+	65.3077i	−1.36235	+	2.35966i
$767$	0.608170			0.0219598
$768$	3.14139	+	5.44105i	0.113355	+	0.196337i
$769$	18.4184	+	31.9016i	0.664185	+	1.15040i	0.979506	+	0.201417i	$0.0645546\pi$
$769$	18.4184	+	31.9016i	0.664185	+	1.15040i	−0.315321	+	0.948985i	$0.602112\pi$
$770$	17.8899	−	30.9862i	0.644706	−	1.11666i
$771$	−0.654665			−0.0235772
$772$	5.99060	+	10.3760i	0.215606	+	0.373441i
$773$	−1.44035			−0.0518057			−0.0259028	−	0.999664i	$-0.508246\pi$
$773$	−1.44035			−0.0518057			−0.0259028	+	0.999664i	$0.508246\pi$
$774$	−38.8024			−1.39472
$775$	11.8242	+	13.3775i	0.424737	+	0.480533i
$776$	−3.28444			−0.117904
$777$	−1.86622			−0.0669504
$778$	10.1484	+	17.5776i	0.363839	+	0.630188i
$779$	−6.13170			−0.219691
$780$	−0.561681	+	0.972860i	−0.0201114	+	0.0348340i
$781$	19.0025	+	32.9133i	0.679963	+	1.17773i
$782$	−44.3859	−	76.8786i	−1.58724	−	2.74917i
$783$	0.310071			0.0110810
$784$	3.55044	−	6.14955i	0.126802	−	0.219627i
$785$	−3.89077	+	6.73901i	−0.138867	+	0.240525i
$786$	4.00538	−	6.93753i	0.142867	−	0.247453i
$787$	12.4460	+	21.5572i	0.443653	+	0.768430i	0.997957	−	0.0638844i	$-0.0203489\pi$
$787$	12.4460	+	21.5572i	0.443653	+	0.768430i	−0.554304	+	0.832314i	$0.687016\pi$
$788$	−34.3456	+	59.4883i	−1.22351	+	2.11918i
$789$	1.14633	+	1.98551i	0.0408106	+	0.0706860i
$790$	−36.9089			−1.31316
$791$	−7.75892			−0.275875
$792$	33.9032	+	58.7221i	1.20470	+	2.08660i
$793$	−0.324368	+	0.561821i	−0.0115186	+	0.0199509i
$794$	−28.8239	−	49.9245i	−1.02292	−	1.77175i
$795$	−2.05203	+	3.55423i	−0.0727781	+	0.126055i
$796$	6.81379	−	11.8018i	0.241508	−	0.418305i
$797$	−10.2389	+	17.7343i	−0.362680	+	0.628180i	−0.988401	−	0.151867i	$-0.951472\pi$
$797$	−10.2389	+	17.7343i	−0.362680	+	0.628180i	0.625721	+	0.780047i	$0.284805\pi$
$798$	−1.35037			−0.0478026
$799$	−28.9605	−	50.1611i	−1.02455	−	1.77457i
$800$	−4.23900	−	7.34216i	−0.149871	−	0.259585i
$801$	5.29145	−	9.16505i	0.186964	−	0.323831i
$802$	−54.4475			−1.92261
$803$	−47.3779	−	82.0609i	−1.67193	−	2.89586i
$804$	−7.06080			−0.249015
$805$	17.3638			0.611992
$806$	4.22410	−	12.6048i	0.148788	−	0.443986i
$807$	−1.50972			−0.0531447
$808$	−56.6132			−1.99165
$809$	25.3862	+	43.9702i	0.892532	+	1.54591i	0.836829	+	0.547464i	$0.184407\pi$
$809$	25.3862	+	43.9702i	0.892532	+	1.54591i	0.0557029	+	0.998447i	$0.482260\pi$
$810$	−27.3064			−0.959449
$811$	−0.701719	+	1.21541i	−0.0246407	+	0.0426789i	−0.878083	−	0.478509i	$-0.841177\pi$
$811$	−0.701719	+	1.21541i	−0.0246407	+	0.0426789i	0.853442	+	0.521188i	$0.174511\pi$
$812$	0.840852	+	1.45640i	0.0295081	+	0.0511096i
$813$	0.146694	+	0.254082i	0.00514479	+	0.00891104i
$814$	−56.3326			−1.97446
$815$	−3.45070	+	5.97679i	−0.120873	+	0.209358i
$816$	1.47337	−	2.55195i	0.0515782	−	0.0893361i
$817$	3.47954	−	6.02675i	0.121734	−	0.210849i
$818$	−28.1488	−	48.7551i	−0.984198	−	1.70468i
$819$	−2.91338	+	5.04612i	−0.101802	+	0.176326i
$820$	12.0335	+	20.8427i	0.420229	+	0.727858i
$821$	−26.7602			−0.933939			−0.466970	−	0.884273i	$-0.654654\pi$
$821$	−26.7602			−0.933939			−0.466970	+	0.884273i	$0.654654\pi$
$822$	−7.77346			−0.271130
$823$	2.08858	+	3.61753i	0.0728033	+	0.126099i	0.900129	−	0.435624i	$-0.143472\pi$
$823$	2.08858	+	3.61753i	0.0728033	+	0.126099i	−0.827326	+	0.561723i	$0.810139\pi$
$824$	−1.39539	+	2.41688i	−0.0486106	+	0.0841961i
$825$	2.05806	+	3.56466i	0.0716524	+	0.124106i
$826$	1.43473	−	2.48503i	0.0499207	−	0.0864652i
$827$	7.58693	−	13.1410i	0.263823	−	0.456956i	−0.703431	−	0.710763i	$-0.748350\pi$
$827$	7.58693	−	13.1410i	0.263823	−	0.456956i	0.967255	+	0.253808i	$0.0816830\pi$
$828$	−35.8007	+	62.0086i	−1.24416	+	2.15495i
$829$	32.8429			1.14068			0.570341	−	0.821408i	$-0.306811\pi$
$829$	32.8429			1.14068			0.570341	+	0.821408i	$0.306811\pi$
$830$	7.78814	+	13.4895i	0.270330	+	0.468226i
$831$	1.70599	+	2.95486i	0.0591801	+	0.102503i
$832$	−5.45054	+	9.44062i	−0.188964	+	0.327294i
$833$	17.5375			0.607637
$834$	−5.23956	−	9.07518i	−0.181431	−	0.314248i
$835$	−15.6156			−0.540402
$836$	−26.4612			−0.915178
$837$	−7.35747	+	1.49329i	−0.254311	+	0.0516158i
$838$	51.8342			1.79058
$839$	52.3969			1.80894			0.904472	−	0.426534i	$-0.140266\pi$
$839$	52.3969			1.80894			0.904472	+	0.426534i	$0.140266\pi$
$840$	1.21793	+	2.10951i	0.0420225	+	0.0727851i
$841$	−28.9471			−0.998177
$842$	26.2060	−	45.3901i	0.903118	−	1.56425i
$843$	−0.170915	−	0.296034i	−0.00588663	−	0.0101959i
$844$	−22.2113	−	38.4712i	−0.764546	−	1.32423i
$845$	−1.33915			−0.0460680
$846$	−35.9827	+	62.3238i	−1.23711	+	2.14274i
$847$	−20.8159	+	36.0542i	−0.715242	+	1.23884i
$848$	15.5097	−	26.8637i	0.532607	−	0.922502i
$849$	−1.64685	−	2.85242i	−0.0565197	−	0.0978949i
$850$	−21.6917	+	37.5711i	−0.744019	+	1.28868i
$851$	−13.6690	−	23.6754i	−0.468567	−	0.811582i
$852$	−5.62987			−0.192876
$853$	−18.3582			−0.628572			−0.314286	−	0.949328i	$-0.601765\pi$
$853$	−18.3582			−0.628572			−0.314286	+	0.949328i	$0.601765\pi$
$854$	1.53043	+	2.65078i	0.0523702	+	0.0907078i
$855$	2.49286	−	4.31775i	0.0852539	−	0.147664i
$856$	40.6866	+	70.4713i	1.39064	+	2.40866i
$857$	−5.98564	+	10.3674i	−0.204466	+	0.354145i	−0.949962	−	0.312365i	$-0.898879\pi$
$857$	−5.98564	+	10.3674i	−0.204466	+	0.354145i	0.745497	+	0.666509i	$0.232212\pi$
$858$	1.53239	−	2.65417i	0.0523148	−	0.0906120i
$859$	−8.17757	+	14.1640i	−0.279015	+	0.483268i	−0.971140	−	0.238509i	$-0.923341\pi$
$859$	−8.17757	+	14.1640i	−0.279015	+	0.483268i	0.692125	+	0.721777i	$0.256675\pi$
$860$	−27.3146			−0.931419
$861$	−1.08762	−	1.88380i	−0.0370658	−	0.0641999i
$862$	−3.08791	−	5.34842i	−0.105175	−	0.182168i
$863$	12.3645	−	21.4159i	0.420891	−	0.729004i	−0.575136	−	0.818058i	$-0.695051\pi$
$863$	12.3645	−	21.4159i	0.420891	−	0.729004i	0.996027	+	0.0890535i	$0.0283842\pi$
$864$	3.56492			0.121281
$865$	−8.19740	−	14.1983i	−0.278720	−	0.482757i
$866$	−43.0695			−1.46356
$867$	3.42431			0.116296
$868$	−26.9660	−	30.5084i	−0.915287	−	1.03552i
$869$	65.3686			2.21748
$870$	0.166663			0.00565041
$871$	−4.20855	−	7.28942i	−0.142601	−	0.246993i
$872$	52.8981			1.79136
$873$	−1.19243	+	2.06534i	−0.0403575	+	0.0699012i
$874$	−9.89068	−	17.1312i	−0.334557	−	0.579470i
$875$	−10.8586	−	18.8076i	−0.367088	−	0.635814i
$876$	14.0366			0.474254
$877$	−7.52890	+	13.0404i	−0.254233	+	0.440344i	−0.964687	−	0.263399i	$-0.915156\pi$
$877$	−7.52890	+	13.0404i	−0.254233	+	0.440344i	0.710454	+	0.703744i	$0.248490\pi$
$878$	−22.3690	+	38.7442i	−0.754917	+	1.30755i
$879$	2.00064	−	3.46521i	0.0674798	−	0.116879i
$880$	8.69915	+	15.0674i	0.293248	+	0.507921i
$881$	−17.0080	+	29.4587i	−0.573014	+	0.992489i	0.423241	+	0.906017i	$0.360893\pi$
$881$	−17.0080	+	29.4587i	−0.573014	+	0.992489i	−0.996254	+	0.0864716i	$0.972441\pi$
$882$	−10.8949	−	18.8705i	−0.366851	−	0.635404i
$883$	5.24023			0.176348			0.0881739	−	0.996105i	$-0.471897\pi$
$883$	5.24023			0.176348			0.0881739	+	0.996105i	$0.471897\pi$
$884$	20.9698			0.705290
$885$	−0.0923039	−	0.159875i	−0.00310276	−	0.00537414i
$886$	−35.0337	+	60.6801i	−1.17698	+	2.03859i
$887$	4.55019	+	7.88117i	0.152781	+	0.264624i	0.932249	−	0.361818i	$-0.117844\pi$
$887$	4.55019	+	7.88117i	0.152781	+	0.264624i	−0.779468	+	0.626442i	$0.784511\pi$
$888$	1.91754	−	3.32128i	0.0643484	−	0.111455i
$889$	−10.1351	+	17.5545i	−0.339920	+	0.588758i
$890$	5.73787	−	9.93829i	0.192334	−	0.333132i
$891$	48.3618			1.62018
$892$	42.1359	+	72.9815i	1.41081	+	2.44360i
$893$	−6.45339	−	11.1776i	−0.215954	−	0.374044i
$894$	−2.21990	+	3.84499i	−0.0742447	+	0.128596i
$895$	−5.91297			−0.197649
$896$	20.4922	+	35.4935i	0.684596	+	1.18576i
$897$	1.48732			0.0496602
$898$	−36.7235			−1.22548
$899$	−1.25476	+	0.254671i	−0.0418487	+	0.00849374i
$900$	34.9921			1.16640
$901$	76.6105			2.55227
$902$	−32.8301	−	56.8633i	−1.09312	−	1.89334i
$903$	2.46875			0.0821548
$904$	7.97227	−	13.8084i	0.265154	−	0.459260i
$905$	−3.92961	−	6.80629i	−0.130625	−	0.226249i
$906$	−2.75038	−	4.76380i	−0.0913752	−	0.158267i
$907$	29.3441			0.974355			0.487178	−	0.873303i	$-0.338026\pi$
$907$	29.3441			0.974355			0.487178	+	0.873303i	$0.338026\pi$
$908$	31.7488	−	54.9905i	1.05362	−	1.82492i
$909$	−20.5536	+	35.5999i	−0.681720	+	1.18077i
$910$	−3.15917	+	5.47185i	−0.104726	+	0.181390i
$911$	−16.8743	−	29.2272i	−0.559072	−	0.968341i	−0.997574	−	0.0696107i	$-0.977824\pi$
$911$	−16.8743	−	29.2272i	−0.559072	−	0.968341i	0.438503	−	0.898730i	$-0.355509\pi$
$912$	0.328317	−	0.568661i	0.0108716	−	0.0188302i
$913$	−13.7934	−	23.8909i	−0.456496	−	0.790674i
$914$	−43.9560			−1.45394
$915$	0.196921			0.00651002
$916$	−7.29993	−	12.6439i	−0.241197	−	0.417765i
$917$	14.6247	−	25.3307i	0.482950	−	0.836494i
$918$	−9.12116	−	15.7983i	−0.301043	−	0.521422i
$919$	17.3991	−	30.1361i	0.573942	−	0.994097i	−0.422214	−	0.906496i	$-0.638747\pi$
$919$	17.3991	−	30.1361i	0.573942	−	0.994097i	0.996156	−	0.0876006i	$-0.0279199\pi$
$920$	−17.8412	+	30.9019i	−0.588207	+	1.01881i
$921$	−3.27999	+	5.68110i	−0.108079	+	0.187199i
$922$	−22.5267			−0.741876
$923$	−3.35565	−	5.81216i	−0.110453	−	0.191309i
$924$	−4.69357	−	8.12950i	−0.154407	−	0.267441i
$925$	−6.68014	+	11.5703i	−0.219642	+	0.380430i
$926$	−26.7144			−0.877890
$927$	1.01320	+	1.75491i	0.0332778	+	0.0576389i
$928$	0.607972			0.0199577
$929$	29.4196			0.965226			0.482613	−	0.875834i	$-0.339688\pi$
$929$	29.4196			0.965226			0.482613	+	0.875834i	$0.339688\pi$
$930$	−3.95465	+	0.802646i	−0.129678	+	0.0263198i
$931$	3.90794			0.128078
$932$	−30.2764			−0.991735
$933$	−0.964595	−	1.67073i	−0.0315794	−	0.0546972i
$934$	23.8196			0.779400
$935$	−21.4848	+	37.2127i	−0.702627	+	1.21699i
$936$	−5.98697	−	10.3697i	−0.195690	−	0.338946i
$937$	−23.7594	−	41.1525i	−0.776187	−	1.34439i	−0.934125	−	0.356946i	$-0.883818\pi$
$937$	−23.7594	−	41.1525i	−0.776187	−	1.34439i	0.157938	−	0.987449i	$-0.449515\pi$
$938$	−39.7135			−1.29669
$939$	−0.279076	+	0.483374i	−0.00910730	+	0.0157743i
$940$	−25.3297	+	43.8723i	−0.826163	+	1.43096i
$941$	−26.2507	+	45.4675i	−0.855747	+	1.48220i	0.0202030	+	0.999796i	$0.493569\pi$
$941$	−26.2507	+	45.4675i	−0.855747	+	1.48220i	−0.875950	+	0.482402i	$0.839765\pi$
$942$	1.57243	+	2.72353i	0.0512326	+	0.0887375i
$943$	15.9323	−	27.5955i	0.518827	−	0.898634i
$944$	0.697654	+	1.20837i	0.0227067	+	0.0393292i
$945$	3.56820			0.116074
$946$	74.5201			2.42286
$947$	−8.69286	−	15.0565i	−0.282480	−	0.489270i	0.689515	−	0.724271i	$-0.257824\pi$
$947$	−8.69286	−	15.0565i	−0.282480	−	0.489270i	−0.971995	+	0.235002i	$0.924490\pi$
$948$	−4.84169	+	8.38605i	−0.157251	+	0.272366i
$949$	8.36646	+	14.4911i	0.271587	+	0.470402i
$950$	−4.83365	+	8.37212i	−0.156824	+	0.271627i
$951$	1.47883	−	2.56140i	0.0479542	−	0.0830592i
$952$	22.7350	−	39.3782i	0.736847	−	1.27626i
$953$	0.565349			0.0183135			0.00915673	−	0.999958i	$-0.497085\pi$
$953$	0.565349			0.0183135			0.00915673	+	0.999958i	$0.497085\pi$
$954$	−47.5933	−	82.4340i	−1.54089	−	2.66890i
$955$	7.49459	+	12.9810i	0.242519	+	0.420056i
$956$	−21.9120	+	37.9527i	−0.708685	+	1.22748i
$957$	−0.295174			−0.00954162
$958$	25.8662	+	44.8016i	0.835700	+	1.44748i
$959$	−28.3829			−0.916533
$960$	3.30898			0.106797
$961$	28.5470	−	12.0858i	0.920872	−	0.389866i
$962$	9.94778			0.320729
$963$	59.0856			1.90401
$964$	35.3526	+	61.2325i	1.13863	+	1.97217i
$965$	4.33544			0.139563
$966$	3.50873	−	6.07731i	0.112892	−	0.195534i
$967$	6.32366	+	10.9529i	0.203355	+	0.352222i	0.949607	−	0.313442i	$-0.101482\pi$
$967$	6.32366	+	10.9529i	0.203355	+	0.352222i	−0.746252	+	0.665663i	$0.768149\pi$
$968$	−42.7765	−	74.0911i	−1.37489	−	2.38138i
$969$	1.62172			0.0520973
$970$	−1.29303	+	2.23959i	−0.0415166	+	0.0719089i
$971$	28.3018	−	49.0201i	0.908247	−	1.57313i	0.0917481	−	0.995782i	$-0.470755\pi$
$971$	28.3018	−	49.0201i	0.908247	−	1.57313i	0.816499	−	0.577347i	$-0.195912\pi$
$972$	−11.0672	+	19.1689i	−0.354980	+	0.614843i
$973$	−19.1310	−	33.1359i	−0.613312	−	1.06229i
$974$	22.5358	−	39.0331i	0.722093	−	1.25070i
$975$	−0.363433	−	0.629484i	−0.0116392	−	0.0201596i
$976$	−1.48838			−0.0476418
$977$	−10.3468			−0.331024			−0.165512	−	0.986208i	$-0.552928\pi$
$977$	−10.3468			−0.331024			−0.165512	+	0.986208i	$0.552928\pi$
$978$	1.39458	+	2.41549i	0.0445938	+	0.0772388i
$979$	−10.1622	+	17.6015i	−0.324787	+	0.562547i
$980$	−7.66937	−	13.2837i	−0.244989	−	0.424334i
$981$	19.2048	−	33.2638i	0.613163	−	1.06203i
$982$	−28.7621	+	49.8175i	−0.917837	+	1.58974i
$983$	−2.73189	+	4.73177i	−0.0871337	+	0.150920i	−0.906298	−	0.422638i	$-0.861104\pi$
$983$	−2.73189	+	4.73177i	−0.0871337	+	0.150920i	0.819165	+	0.573558i	$0.194437\pi$
$984$	4.47009			0.142501
$985$	12.4281	+	21.5261i	0.395992	+	0.685878i
$986$	−1.55555	−	2.69429i	−0.0495388	−	0.0858037i
$987$	2.28935	−	3.96527i	0.0728708	−	0.126216i
$988$	4.67278			0.148661
$989$	18.0821	+	31.3192i	0.574978	+	0.995892i
$990$	53.3885			1.69680
$991$	−26.5594			−0.843687			−0.421844	−	0.906669i	$-0.638617\pi$
$991$	−26.5594			−0.843687			−0.421844	+	0.906669i	$0.638617\pi$
$992$	−14.4262	+	2.92798i	−0.458032	+	0.0929635i
$993$	−1.15486			−0.0366485
$994$	−31.6652			−1.00436
$995$	−2.46560	−	4.27054i	−0.0781646	−	0.135385i
$996$	4.08658			0.129488
$997$	−28.4739	+	49.3183i	−0.901778	+	1.56193i	−0.0765935	+	0.997062i	$0.524404\pi$
$997$	−28.4739	+	49.3183i	−0.901778	+	1.56193i	−0.825185	+	0.564863i	$0.808929\pi$
$998$	−4.92806	−	8.53565i	−0.155995	−	0.270191i
$999$	−2.80894	−	4.86522i	−0.0888708	−	0.153929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.a.118.15	✓	30
31.5	even	3	inner	403.2.h.a.222.15	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.a.118.15	✓	30	1.1	even	1	trivial
403.2.h.a.222.15	yes	30	31.5	even	3	inner

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.38763 q^{2} +(-0.113336 - 0.196303i) q^{3} +3.70079 q^{4} +(0.669573 - 1.15973i) q^{5} +(-0.270604 - 0.468700i) q^{6} +(-0.988047 - 1.71135i) q^{7} +4.06087 q^{8} +(1.47431 - 2.55358i) q^{9} +O(q^{10})\)	\(q+2.38763 q^{2} +(-0.113336 - 0.196303i) q^{3} +3.70079 q^{4} +(0.669573 - 1.15973i) q^{5} +(-0.270604 - 0.468700i) q^{6} +(-0.988047 - 1.71135i) q^{7} +4.06087 q^{8} +(1.47431 - 2.55358i) q^{9} +(1.59869 - 2.76902i) q^{10} +(-2.83142 + 4.90416i) q^{11} +(-0.419432 - 0.726478i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-2.35909 - 4.08607i) q^{14} -0.303546 q^{15} +2.29427 q^{16} +(2.83315 + 4.90716i) q^{17} +(3.52011 - 6.09701i) q^{18} +(0.631321 + 1.09348i) q^{19} +(2.47795 - 4.29193i) q^{20} +(-0.223962 + 0.387914i) q^{21} +(-6.76038 + 11.7093i) q^{22} -6.56157 q^{23} +(-0.460241 - 0.797162i) q^{24} +(1.60334 + 2.77707i) q^{25} +(1.19382 - 2.06775i) q^{26} -1.34838 q^{27} +(-3.65656 - 6.33334i) q^{28} -0.229957 q^{29} -0.724757 q^{30} +(5.45651 - 1.10747i) q^{31} -2.64385 q^{32} +1.28360 q^{33} +(6.76452 + 11.7165i) q^{34} -2.64628 q^{35} +(5.45611 - 9.45027i) q^{36} +(2.08319 + 3.60819i) q^{37} +(1.50736 + 2.61083i) q^{38} -0.226672 q^{39} +(2.71905 - 4.70952i) q^{40} +(-2.42812 + 4.20563i) q^{41} +(-0.534740 + 0.926197i) q^{42} +(-2.75576 - 4.77312i) q^{43} +(-10.4785 + 18.1493i) q^{44} +(-1.97432 - 3.41962i) q^{45} -15.6666 q^{46} -10.2220 q^{47} +(-0.260023 - 0.450374i) q^{48} +(1.54752 - 2.68039i) q^{49} +(3.82820 + 6.63063i) q^{50} +(0.642194 - 1.11231i) q^{51} +(1.85040 - 3.20498i) q^{52} +(6.76020 - 11.7090i) q^{53} -3.21944 q^{54} +(3.79168 + 6.56738i) q^{55} +(-4.01233 - 6.94956i) q^{56} +(0.143103 - 0.247861i) q^{57} -0.549054 q^{58} +(0.304085 + 0.526691i) q^{59} -1.12336 q^{60} -0.648736 q^{61} +(13.0281 - 2.64423i) q^{62} -5.82675 q^{63} -10.9011 q^{64} +(-0.669573 - 1.15973i) q^{65} +3.06477 q^{66} +(4.20855 - 7.28942i) q^{67} +(10.4849 + 18.1604i) q^{68} +(0.743661 + 1.28806i) q^{69} -6.31834 q^{70} +(3.35565 - 5.81216i) q^{71} +(5.98697 - 10.3697i) q^{72} +(-8.36646 + 14.4911i) q^{73} +(4.97389 + 8.61503i) q^{74} +(0.363433 - 0.629484i) q^{75} +(2.33639 + 4.04674i) q^{76} +11.1903 q^{77} -0.541209 q^{78} +(-5.77172 - 9.99691i) q^{79} +(1.53618 - 2.66075i) q^{80} +(-4.27011 - 7.39605i) q^{81} +(-5.79746 + 10.0415i) q^{82} +(-2.43578 + 4.21890i) q^{83} +(-0.828838 + 1.43559i) q^{84} +7.58800 q^{85} +(-6.57975 - 11.3965i) q^{86} +(0.0260624 + 0.0451414i) q^{87} +(-11.4980 + 19.9151i) q^{88} +3.58910 q^{89} +(-4.71394 - 8.16479i) q^{90} -1.97609 q^{91} -24.2830 q^{92} +(-0.835818 - 0.945616i) q^{93} -24.4065 q^{94} +1.69086 q^{95} +(0.299643 + 0.518996i) q^{96} -0.808802 q^{97} +(3.69492 - 6.39979i) q^{98} +(8.34877 + 14.4605i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} + 15 q^{13} + 3 q^{14} + 4 q^{15} + 22 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 10 q^{20} - 15 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 20 q^{25} - 3 q^{26} + 4 q^{27} + 13 q^{28} + 26 q^{29} + 28 q^{30} + 19 q^{31} - 74 q^{32} + 2 q^{33} - 21 q^{34} - 30 q^{35} + 37 q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{39} - 17 q^{40} + 7 q^{41} + 44 q^{42} + 15 q^{43} - 70 q^{44} + 15 q^{45} - 58 q^{46} - 24 q^{47} + 31 q^{48} - 29 q^{49} + 2 q^{50} + 25 q^{51} + 11 q^{52} + 4 q^{53} + 34 q^{54} + 13 q^{55} - 41 q^{56} + 8 q^{57} - 46 q^{58} + 27 q^{59} + 78 q^{60} + 8 q^{61} + 20 q^{62} - 112 q^{63} + 60 q^{64} - 7 q^{65} + 60 q^{66} + 29 q^{67} + 41 q^{68} - 23 q^{69} - 112 q^{70} + 29 q^{71} + 14 q^{72} - 10 q^{73} + 25 q^{74} - 18 q^{75} + 24 q^{76} - 72 q^{77} + 9 q^{79} - 11 q^{81} - 38 q^{82} - 13 q^{83} - 62 q^{84} + 108 q^{85} - 38 q^{86} - 18 q^{87} + 32 q^{88} + 6 q^{89} + 7 q^{90} + 12 q^{91} + 2 q^{92} + 37 q^{93} - 154 q^{94} - 28 q^{95} - 105 q^{96} - 84 q^{97} + 50 q^{98} + 10 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9 - 3 * q^10 - 3 * q^11 + 12 * q^12 + 15 * q^13 + 3 * q^14 + 4 * q^15 + 22 * q^16 + 4 * q^17 - 6 * q^18 + 5 * q^19 + 10 * q^20 - 15 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 20 * q^25 - 3 * q^26 + 4 * q^27 + 13 * q^28 + 26 * q^29 + 28 * q^30 + 19 * q^31 - 74 * q^32 + 2 * q^33 - 21 * q^34 - 30 * q^35 + 37 * q^36 - 4 * q^37 - 4 * q^38 - 4 * q^39 - 17 * q^40 + 7 * q^41 + 44 * q^42 + 15 * q^43 - 70 * q^44 + 15 * q^45 - 58 * q^46 - 24 * q^47 + 31 * q^48 - 29 * q^49 + 2 * q^50 + 25 * q^51 + 11 * q^52 + 4 * q^53 + 34 * q^54 + 13 * q^55 - 41 * q^56 + 8 * q^57 - 46 * q^58 + 27 * q^59 + 78 * q^60 + 8 * q^61 + 20 * q^62 - 112 * q^63 + 60 * q^64 - 7 * q^65 + 60 * q^66 + 29 * q^67 + 41 * q^68 - 23 * q^69 - 112 * q^70 + 29 * q^71 + 14 * q^72 - 10 * q^73 + 25 * q^74 - 18 * q^75 + 24 * q^76 - 72 * q^77 + 9 * q^79 - 11 * q^81 - 38 * q^82 - 13 * q^83 - 62 * q^84 + 108 * q^85 - 38 * q^86 - 18 * q^87 + 32 * q^88 + 6 * q^89 + 7 * q^90 + 12 * q^91 + 2 * q^92 + 37 * q^93 - 154 * q^94 - 28 * q^95 - 105 * q^96 - 84 * q^97 + 50 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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