LMFDB - Embedded newform 403.2.h.b.222.12

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:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			222.12
Character	$\chi$	$=$	403.222
Dual form			403.2.h.b.118.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.35626 q^{2} +(0.0933728 - 0.161726i) q^{3} -0.160553 q^{4} +(1.08899 + 1.88618i) q^{5} +(0.126638 - 0.219343i) q^{6} +(-1.43912 + 2.49263i) q^{7} -2.93028 q^{8} +(1.48256 + 2.56787i) q^{9} +O(q^{10})$	\(q+1.35626 q^{2} +(0.0933728 - 0.161726i) q^{3} -0.160553 q^{4} +(1.08899 + 1.88618i) q^{5} +(0.126638 - 0.219343i) q^{6} +(-1.43912 + 2.49263i) q^{7} -2.93028 q^{8} +(1.48256 + 2.56787i) q^{9} +(1.47695 + 2.55816i) q^{10} +(1.47628 + 2.55699i) q^{11} +(-0.0149913 + 0.0259657i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-1.95182 + 3.38066i) q^{14} +0.406727 q^{15} -3.65312 q^{16} +(0.832376 - 1.44172i) q^{17} +(2.01074 + 3.48271i) q^{18} +(3.39325 - 5.87729i) q^{19} +(-0.174840 - 0.302832i) q^{20} +(0.268749 + 0.465488i) q^{21} +(2.00222 + 3.46795i) q^{22} +4.72909 q^{23} +(-0.273608 + 0.473903i) q^{24} +(0.128215 - 0.222075i) q^{25} +(-0.678131 - 1.17456i) q^{26} +1.11396 q^{27} +(0.231056 - 0.400200i) q^{28} -1.93062 q^{29} +0.551628 q^{30} +(-4.88752 + 2.66686i) q^{31} +0.905970 q^{32} +0.551377 q^{33} +(1.12892 - 1.95535i) q^{34} -6.26873 q^{35} +(-0.238030 - 0.412281i) q^{36} +(-0.166256 + 0.287964i) q^{37} +(4.60214 - 7.97114i) q^{38} -0.186746 q^{39} +(-3.19103 - 5.52703i) q^{40} +(-0.561667 - 0.972836i) q^{41} +(0.364495 + 0.631323i) q^{42} +(2.62471 - 4.54613i) q^{43} +(-0.237022 - 0.410533i) q^{44} +(-3.22898 + 5.59276i) q^{45} +6.41388 q^{46} -8.43721 q^{47} +(-0.341102 + 0.590805i) q^{48} +(-0.642137 - 1.11221i) q^{49} +(0.173893 - 0.301192i) q^{50} +(-0.155443 - 0.269234i) q^{51} +(0.0802766 + 0.139043i) q^{52} +(5.94060 + 10.2894i) q^{53} +1.51082 q^{54} +(-3.21530 + 5.56906i) q^{55} +(4.21702 - 7.30410i) q^{56} +(-0.633675 - 1.09756i) q^{57} -2.61843 q^{58} +(3.23067 - 5.59568i) q^{59} -0.0653013 q^{60} +5.91690 q^{61} +(-6.62876 + 3.61696i) q^{62} -8.53435 q^{63} +8.53497 q^{64} +(1.08899 - 1.88618i) q^{65} +0.747812 q^{66} +(-5.73764 - 9.93788i) q^{67} +(-0.133641 + 0.231472i) q^{68} +(0.441568 - 0.764819i) q^{69} -8.50205 q^{70} +(-0.218153 - 0.377852i) q^{71} +(-4.34432 - 7.52458i) q^{72} +(2.33501 + 4.04435i) q^{73} +(-0.225487 + 0.390554i) q^{74} +(-0.0239436 - 0.0414715i) q^{75} +(-0.544798 + 0.943617i) q^{76} -8.49818 q^{77} -0.253276 q^{78} +(6.84557 - 11.8569i) q^{79} +(-3.97820 - 6.89044i) q^{80} +(-4.34368 + 7.52347i) q^{81} +(-0.761767 - 1.31942i) q^{82} +(-3.91140 - 6.77474i) q^{83} +(-0.0431486 - 0.0747356i) q^{84} +3.62579 q^{85} +(3.55979 - 6.16574i) q^{86} +(-0.180267 + 0.312232i) q^{87} +(-4.32591 - 7.49269i) q^{88} +4.45512 q^{89} +(-4.37935 + 7.58525i) q^{90} +2.87824 q^{91} -0.759271 q^{92} +(-0.0250597 + 1.03945i) q^{93} -11.4431 q^{94} +14.7808 q^{95} +(0.0845929 - 0.146519i) q^{96} -1.02000 q^{97} +(-0.870906 - 1.50845i) q^{98} +(-4.37736 + 7.58180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) $ 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.35626			0.959022			0.479511	−	0.877536i	$-0.340814\pi$
$2$	1.35626			0.959022			0.479511	+	0.877536i	$0.340814\pi$
$3$	0.0933728	−	0.161726i	0.0539088	−	0.0933728i	−0.837812	−	0.545959i	$-0.816165\pi$
$3$	0.0933728	−	0.161726i	0.0539088	−	0.0933728i	0.891720	+	0.452587i	$0.149499\pi$
$4$	−0.160553			−0.0802766
$5$	1.08899	+	1.88618i	0.487010	+	0.843526i	0.999888	−	0.0149354i	$-0.00475427\pi$
$5$	1.08899	+	1.88618i	0.487010	+	0.843526i	−0.512879	+	0.858461i	$0.671421\pi$
$6$	0.126638	−	0.219343i	0.0516997	−	0.0895466i
$7$	−1.43912	+	2.49263i	−0.543936	+	0.942126i	0.454737	+	0.890626i	$0.349733\pi$
$7$	−1.43912	+	2.49263i	−0.543936	+	0.942126i	−0.998673	+	0.0514996i	$0.983600\pi$
$8$	−2.93028			−1.03601
$9$	1.48256	+	2.56787i	0.494188	+	0.855958i
$10$	1.47695	+	2.55816i	0.467053	+	0.808960i
$11$	1.47628	+	2.55699i	0.445115	+	0.770962i	0.998060	−	0.0622557i	$-0.0198294\pi$
$11$	1.47628	+	2.55699i	0.445115	+	0.770962i	−0.552945	+	0.833218i	$0.686496\pi$
$12$	−0.0149913	+	0.0259657i	−0.00432762	+	0.00749565i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	−1.95182	+	3.38066i	−0.521647	+	0.903519i
$15$	0.406727			0.105016
$16$	−3.65312			−0.913279
$17$	0.832376	−	1.44172i	0.201881	−	0.349668i	−0.747254	−	0.664539i	$-0.768628\pi$
$17$	0.832376	−	1.44172i	0.201881	−	0.349668i	0.949134	+	0.314871i	$0.101961\pi$
$18$	2.01074	+	3.48271i	0.473937	+	0.820883i
$19$	3.39325	−	5.87729i	0.778465	−	1.34834i	−0.154360	−	0.988015i	$-0.549332\pi$
$19$	3.39325	−	5.87729i	0.778465	−	1.34834i	0.932826	−	0.360327i	$-0.117335\pi$
$20$	−0.174840	−	0.302832i	−0.0390955	−	0.0677154i
$21$	0.268749	+	0.465488i	0.0586459	+	0.101578i
$22$	2.00222	+	3.46795i	0.426875	+	0.739370i
$23$	4.72909			0.986083			0.493042	−	0.870006i	$-0.335885\pi$
$23$	4.72909			0.986083			0.493042	+	0.870006i	$0.335885\pi$
$24$	−0.273608	+	0.473903i	−0.0558500	+	0.0967351i
$25$	0.128215	−	0.222075i	0.0256430	−	0.0444149i
$26$	−0.678131	−	1.17456i	−0.132992	−	0.230350i
$27$	1.11396			0.214382
$28$	0.231056	−	0.400200i	0.0436654	−	0.0756307i
$29$	−1.93062			−0.358507			−0.179254	−	0.983803i	$-0.557368\pi$
$29$	−1.93062			−0.358507			−0.179254	+	0.983803i	$0.557368\pi$
$30$	0.551628			0.100713
$31$	−4.88752	+	2.66686i	−0.877825	+	0.478982i
$31$	−4.88752	+	2.66686i	−0.877825	+	0.478982i
$32$	0.905970			0.160154
$33$	0.551377			0.0959825
$34$	1.12892	−	1.95535i	0.193608	−	0.335339i
$35$	−6.26873			−1.05961
$36$	−0.238030	−	0.412281i	−0.0396717	−	0.0687134i
$37$	−0.166256	+	0.287964i	−0.0273323	+	0.0473410i	−0.879368	−	0.476143i	$-0.842035\pi$
$37$	−0.166256	+	0.287964i	−0.0273323	+	0.0473410i	0.852036	+	0.523484i	$0.175368\pi$
$38$	4.60214	−	7.97114i	0.746566	−	1.29309i
$39$	−0.186746			−0.0299032
$40$	−3.19103	−	5.52703i	−0.504547	−	0.873900i
$41$	−0.561667	−	0.972836i	−0.0877176	−	0.151931i	0.818828	−	0.574038i	$-0.194624\pi$
$41$	−0.561667	−	0.972836i	−0.0877176	−	0.151931i	−0.906546	+	0.422107i	$0.861291\pi$
$42$	0.364495	+	0.631323i	0.0562427	+	0.0974153i
$43$	2.62471	−	4.54613i	0.400264	−	0.693278i	−0.593493	−	0.804839i	$-0.702252\pi$
$43$	2.62471	−	4.54613i	0.400264	−	0.693278i	0.993758	+	0.111561i	$0.0355849\pi$
$44$	−0.237022	−	0.410533i	−0.0357323	−	0.0618902i
$45$	−3.22898	+	5.59276i	−0.481348	+	0.833720i
$46$	6.41388			0.945676
$47$	−8.43721			−1.23069			−0.615347	−	0.788256i	$-0.710984\pi$
$47$	−8.43721			−1.23069			−0.615347	+	0.788256i	$0.710984\pi$
$48$	−0.341102	+	0.590805i	−0.0492338	+	0.0852754i
$49$	−0.642137	−	1.11221i	−0.0917338	−	0.158888i
$50$	0.173893	−	0.301192i	0.0245922	−	0.0425949i
$51$	−0.155443	−	0.269234i	−0.0217663	−	0.0377003i
$52$	0.0802766	+	0.139043i	0.0111324	+	0.0192818i
$53$	5.94060	+	10.2894i	0.816004	+	1.41336i	0.908605	+	0.417657i	$0.137148\pi$
$53$	5.94060	+	10.2894i	0.816004	+	1.41336i	−0.0926012	+	0.995703i	$0.529518\pi$
$54$	1.51082			0.205597
$55$	−3.21530	+	5.56906i	−0.433551	+	0.750932i
$56$	4.21702	−	7.30410i	0.563523	−	0.976051i
$57$	−0.633675	−	1.09756i	−0.0839323	−	0.145375i
$58$	−2.61843			−0.343816
$59$	3.23067	−	5.59568i	0.420597	−	0.728495i	−0.575401	−	0.817871i	$-0.695154\pi$
$59$	3.23067	−	5.59568i	0.420597	−	0.728495i	0.995998	+	0.0893762i	$0.0284873\pi$
$60$	−0.0653013			−0.00843037
$61$	5.91690			0.757581			0.378790	−	0.925482i	$-0.376340\pi$
$61$	5.91690			0.757581			0.378790	+	0.925482i	$0.376340\pi$
$62$	−6.62876	+	3.61696i	−0.841853	+	0.459355i
$63$	−8.53435			−1.07523
$64$	8.53497			1.06687
$65$	1.08899	−	1.88618i	0.135072	−	0.233952i
$66$	0.747812			0.0920493
$67$	−5.73764	−	9.93788i	−0.700964	−	1.21411i	−0.968128	−	0.250454i	$-0.919420\pi$
$67$	−5.73764	−	9.93788i	−0.700964	−	1.21411i	0.267164	−	0.963651i	$-0.413913\pi$
$68$	−0.133641	+	0.231472i	−0.0162063	+	0.0280702i
$69$	0.441568	−	0.764819i	0.0531586	−	0.0920733i
$70$	−8.50205			−1.01619
$71$	−0.218153	−	0.377852i	−0.0258900	−	0.0448428i	0.852790	−	0.522254i	$-0.174909\pi$
$71$	−0.218153	−	0.377852i	−0.0258900	−	0.0448428i	−0.878680	+	0.477411i	$0.841575\pi$
$72$	−4.34432	−	7.52458i	−0.511983	−	0.886781i
$73$	2.33501	+	4.04435i	0.273292	+	0.473356i	0.969703	−	0.244288i	$-0.0785541\pi$
$73$	2.33501	+	4.04435i	0.273292	+	0.473356i	−0.696411	+	0.717644i	$0.745221\pi$
$74$	−0.225487	+	0.390554i	−0.0262123	+	0.0454010i
$75$	−0.0239436	−	0.0414715i	−0.00276477	−	0.00478871i
$76$	−0.544798	+	0.943617i	−0.0624926	+	0.108240i
$77$	−8.49818			−0.968457
$78$	−0.253276			−0.0286779
$79$	6.84557	−	11.8569i	0.770187	−	1.33400i	−0.167274	−	0.985910i	$-0.553496\pi$
$79$	6.84557	−	11.8569i	0.770187	−	1.33400i	0.937460	−	0.348092i	$-0.113170\pi$
$80$	−3.97820	−	6.89044i	−0.444776	−	0.770374i
$81$	−4.34368	+	7.52347i	−0.482631	+	0.835941i
$82$	−0.761767	−	1.31942i	−0.0841231	−	0.145706i
$83$	−3.91140	−	6.77474i	−0.429331	−	0.743624i	0.567483	−	0.823385i	$-0.307917\pi$
$83$	−3.91140	−	6.77474i	−0.429331	−	0.743624i	−0.996814	+	0.0797616i	$0.974584\pi$
$84$	−0.0431486	−	0.0747356i	−0.00470790	−	0.00815432i
$85$	3.62579			0.393272
$86$	3.55979	−	6.16574i	0.383862	−	0.664869i
$87$	−0.180267	+	0.312232i	−0.0193267	+	0.0334748i
$88$	−4.32591	−	7.49269i	−0.461143	−	0.798724i
$89$	4.45512			0.472242			0.236121	−	0.971724i	$-0.424124\pi$
$89$	4.45512			0.472242			0.236121	+	0.971724i	$0.424124\pi$
$90$	−4.37935	+	7.58525i	−0.461624	+	0.799556i
$91$	2.87824			0.301722
$92$	−0.759271			−0.0791594
$93$	−0.0250597	+	1.03945i	−0.00259857	+	0.107786i
$94$	−11.4431			−1.18026
$95$	14.7808			1.51648
$96$	0.0845929	−	0.146519i	0.00863373	−	0.0149541i
$97$	−1.02000			−0.103565			−0.0517826	−	0.998658i	$-0.516490\pi$
$97$	−1.02000			−0.103565			−0.0517826	+	0.998658i	$0.516490\pi$
$98$	−0.870906	−	1.50845i	−0.0879748	−	0.152377i
$99$	−4.37736	+	7.58180i	−0.439941	+	0.762000i
$100$	−0.0205853	+	0.0356548i	−0.00205853	+	0.00356548i
$101$	11.5844			1.15269			0.576347	−	0.817205i	$-0.304478\pi$
$101$	11.5844			1.15269			0.576347	+	0.817205i	$0.304478\pi$
$102$	−0.210821	−	0.365152i	−0.0208744	−	0.0361555i
$103$	−3.20893	−	5.55803i	−0.316185	−	0.547649i	0.663503	−	0.748173i	$-0.269069\pi$
$103$	−3.20893	−	5.55803i	−0.316185	−	0.547649i	−0.979689	+	0.200524i	$0.935735\pi$
$104$	1.46514	+	2.53769i	0.143669	+	0.248841i
$105$	−0.585329	+	1.01382i	−0.0571223	+	0.0989387i
$106$	8.05701	+	13.9551i	0.782566	+	1.35544i
$107$	−6.84343	+	11.8532i	−0.661580	+	1.14589i	0.318621	+	0.947882i	$0.396780\pi$
$107$	−6.84343	+	11.8532i	−0.661580	+	1.14589i	−0.980201	+	0.198007i	$0.936553\pi$
$108$	−0.178850			−0.0172099
$109$	−6.09277			−0.583582			−0.291791	−	0.956482i	$-0.594251\pi$
$109$	−6.09277			−0.583582			−0.291791	+	0.956482i	$0.594251\pi$
$110$	−4.36079	+	7.55311i	−0.415785	+	0.720160i
$111$	0.0310476	+	0.0537760i	0.00294691	+	0.00510419i
$112$	5.25727	−	9.10587i	0.496766	−	0.860424i
$113$	2.97561	+	5.15390i	0.279922	+	0.484838i	0.971365	−	0.237592i	$-0.0763582\pi$
$113$	2.97561	+	5.15390i	0.279922	+	0.484838i	−0.691443	+	0.722431i	$0.743025\pi$
$114$	−0.859429	−	1.48857i	−0.0804929	−	0.139418i
$115$	5.14992	+	8.91992i	0.480232	+	0.831786i
$116$	0.309967			0.0287798
$117$	1.48256	−	2.56787i	0.137063	−	0.237400i
$118$	4.38163	−	7.58921i	0.403362	−	0.698643i
$119$	2.39578	+	4.14961i	0.219621	+	0.380394i
$120$	−1.19182			−0.108798
$121$	1.14120	−	1.97661i	0.103745	−	0.179692i
$122$	8.02486			0.726537
$123$	−0.209778			−0.0189150
$124$	0.784707	−	0.428173i	0.0704688	−	0.0384511i
$125$	11.4484			1.02397
$126$	−11.5748			−1.03117
$127$	−3.92779	+	6.80314i	−0.348535	+	0.603681i	−0.985990	−	0.166807i	$-0.946654\pi$
$127$	−3.92779	+	6.80314i	−0.348535	+	0.603681i	0.637454	+	0.770488i	$0.279988\pi$
$128$	9.76371			0.862998
$129$	−0.490153	−	0.848970i	−0.0431556	−	0.0747476i
$130$	1.47695	−	2.55816i	0.129537	−	0.224365i
$131$	6.23032	−	10.7912i	0.544346	−	0.942835i	−0.454302	−	0.890848i	$-0.650111\pi$
$131$	6.23032	−	10.7912i	0.544346	−	0.942835i	0.998648	−	0.0519869i	$-0.0165554\pi$
$132$	−0.0885255			−0.00770515
$133$	9.76660	+	16.9162i	0.846872	+	1.46682i
$134$	−7.78174	−	13.4784i	−0.672240	−	1.16435i
$135$	1.21309	+	2.10113i	0.104406	+	0.180837i
$136$	−2.43909	+	4.22463i	−0.209150	+	0.362259i
$137$	−3.34706	−	5.79728i	−0.285959	−	0.495295i	0.686882	−	0.726769i	$-0.258979\pi$
$137$	−3.34706	−	5.79728i	−0.285959	−	0.495295i	−0.972841	+	0.231473i	$0.925645\pi$
$138$	0.598882	−	1.03729i	0.0509802	−	0.0883004i
$139$	−1.57378			−0.133486			−0.0667432	−	0.997770i	$-0.521261\pi$
$139$	−1.57378			−0.133486			−0.0667432	+	0.997770i	$0.521261\pi$
$140$	1.00647			0.0850619
$141$	−0.787806	+	1.36452i	−0.0663453	+	0.114913i
$142$	−0.295873	−	0.512466i	−0.0248291	−	0.0430052i
$143$	1.47628	−	2.55699i	0.123453	−	0.213826i
$144$	−5.41597	−	9.38074i	−0.451331	−	0.781729i
$145$	−2.10242	−	3.64150i	−0.174597	−	0.302410i
$146$	3.16688	+	5.48521i	0.262093	+	0.453959i
$147$	−0.239832			−0.0197810
$148$	0.0266929	−	0.0462335i	0.00219415	−	0.00380037i
$149$	7.20311	−	12.4762i	0.590102	−	1.02209i	−0.404116	−	0.914708i	$-0.632421\pi$
$149$	7.20311	−	12.4762i	0.590102	−	1.02209i	0.994218	−	0.107379i	$-0.0342458\pi$
$150$	−0.0324738	−	0.0562462i	−0.00265147	−	0.00459248i
$151$	−11.9734			−0.974385			−0.487193	−	0.873295i	$-0.661979\pi$
$151$	−11.9734			−0.974385			−0.487193	+	0.873295i	$0.661979\pi$
$152$	−9.94317	+	17.2221i	−0.806497	+	1.39689i
$153$	4.93620			0.399068
$154$	−11.5258			−0.928772
$155$	−10.3526	−	6.31457i	−0.831543	−	0.507199i
$156$	0.0299826			0.00240053
$157$	−9.19658			−0.733967			−0.366983	−	0.930227i	$-0.619609\pi$
$157$	−9.19658			−0.733967			−0.366983	+	0.930227i	$0.619609\pi$
$158$	9.28438	−	16.0810i	0.738626	−	1.27934i
$159$	2.21876			0.175959
$160$	0.986590	+	1.70882i	0.0779968	+	0.135094i
$161$	−6.80573	+	11.7879i	−0.536367	+	0.929014i
$162$	−5.89116	+	10.2038i	−0.462853	+	0.801686i
$163$	0.327869			0.0256807			0.0128404	−	0.999918i	$-0.495913\pi$
$163$	0.327869			0.0256807			0.0128404	+	0.999918i	$0.495913\pi$
$164$	0.0901775	+	0.156192i	0.00704168	+	0.0121965i
$165$	0.600443	+	1.04000i	0.0467444	+	0.0809637i
$166$	−5.30488	−	9.18832i	−0.411738	−	0.713152i
$167$	0.259404	−	0.449301i	0.0200733	−	0.0347680i	−0.855814	−	0.517283i	$-0.826943\pi$
$167$	0.259404	−	0.449301i	0.0200733	−	0.0347680i	0.875888	+	0.482515i	$0.160277\pi$
$168$	−0.787510	−	1.36401i	−0.0607577	−	0.105235i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	4.91752			0.377156
$171$	20.1228			1.53883
$172$	−0.421406	+	0.729896i	−0.0321319	+	0.0556541i
$173$	−3.54626	−	6.14231i	−0.269617	−	0.466991i	0.699146	−	0.714979i	$-0.253564\pi$
$173$	−3.54626	−	6.14231i	−0.269617	−	0.466991i	−0.968763	+	0.247988i	$0.920231\pi$
$174$	−0.244490	+	0.423469i	−0.0185347	+	0.0321031i
$175$	0.369033	+	0.639185i	0.0278963	+	0.0483178i
$176$	−5.39302	−	9.34099i	−0.406514	−	0.704103i
$177$	−0.603313	−	1.04497i	−0.0453478	−	0.0785446i
$178$	6.04231			0.452890
$179$	−9.91972	+	17.1815i	−0.741435	+	1.28420i	0.210408	+	0.977614i	$0.432521\pi$
$179$	−9.91972	+	17.1815i	−0.741435	+	1.28420i	−0.951842	+	0.306589i	$0.900812\pi$
$180$	0.518424	−	0.897936i	0.0386410	−	0.0669282i
$181$	6.83259	+	11.8344i	0.507862	+	0.879643i	0.999959	+	0.00910261i	$0.00289749\pi$
$181$	6.83259	+	11.8344i	0.507862	+	0.879643i	−0.492096	+	0.870541i	$0.663769\pi$
$182$	3.90365			0.289358
$183$	0.552477	−	0.956918i	0.0408403	−	0.0707374i
$184$	−13.8575			−1.02159
$185$	−0.724203			−0.0532444
$186$	−0.0339875	+	1.40977i	−0.00249208	+	0.103369i
$187$	4.91528			0.359441
$188$	1.35462			0.0987960
$189$	−1.60312	+	2.77669i	−0.116610	+	0.201975i
$190$	20.0467			1.45434
$191$	−12.0453	−	20.8630i	−0.871566	−	1.50960i	−0.860376	−	0.509660i	$-0.829771\pi$
$191$	−12.0453	−	20.8630i	−0.871566	−	1.50960i	−0.0111903	−	0.999937i	$-0.503562\pi$
$192$	0.796933	−	1.38033i	0.0575137	−	0.0996167i
$193$	−0.0996204	+	0.172548i	−0.00717083	+	0.0124202i	−0.869589	−	0.493777i	$-0.835616\pi$
$193$	−0.0996204	+	0.172548i	−0.00717083	+	0.0124202i	0.862418	+	0.506197i	$0.168949\pi$
$194$	−1.38339			−0.0993214
$195$	−0.203363	−	0.352236i	−0.0145632	−	0.0252241i
$196$	0.103097	+	0.178570i	0.00736408	+	0.0127550i
$197$	−0.331896	−	0.574860i	−0.0236466	−	0.0409571i	0.853960	−	0.520339i	$-0.174194\pi$
$197$	−0.331896	−	0.574860i	−0.0236466	−	0.0409571i	−0.877607	+	0.479382i	$0.840861\pi$
$198$	−5.93684	+	10.2829i	−0.421913	+	0.730775i
$199$	8.60620	+	14.9064i	0.610077	+	1.05668i	0.991227	+	0.132172i	$0.0421950\pi$
$199$	8.60620	+	14.9064i	0.610077	+	1.05668i	−0.381150	+	0.924513i	$0.624472\pi$
$200$	−0.375705	+	0.650740i	−0.0265664	+	0.0460143i
$201$	−2.14296			−0.151153
$202$	15.7115			1.10546
$203$	2.77840	−	4.81232i	0.195005	−	0.337759i
$204$	0.0249568	+	0.0432265i	0.00174733	+	0.00302646i
$205$	1.22330	−	2.11881i	0.0854387	−	0.147984i
$206$	−4.35215	−	7.53815i	−0.303229	−	0.525208i
$207$	7.01117	+	12.1437i	0.487310	+	0.844046i
$208$	1.82656	+	3.16369i	0.126649	+	0.219363i
$209$	20.0376			1.38603
$210$	−0.793860	+	1.37501i	−0.0547815	+	0.0948844i
$211$	−9.17204	+	15.8864i	−0.631429	+	1.09367i	0.355830	+	0.934551i	$0.384198\pi$
$211$	−9.17204	+	15.8864i	−0.631429	+	1.09367i	−0.987260	+	0.159117i	$0.949135\pi$
$212$	−0.953782	−	1.65200i	−0.0655060	−	0.113460i
$213$	−0.0814782			−0.00558280
$214$	−9.28149	+	16.0760i	−0.634469	+	1.09893i
$215$	11.4331			0.779731
$216$	−3.26421			−0.222102
$217$	0.386236	−	16.0207i	0.0262194	−	1.08756i
$218$	−8.26340			−0.559668
$219$	0.872105			0.0589314
$220$	0.516227	−	0.894131i	0.0348040	−	0.0602823i
$221$	−1.66475			−0.111983
$222$	0.0421086	+	0.0729343i	0.00282615	+	0.00489503i
$223$	−6.51339	+	11.2815i	−0.436169	+	0.755467i	−0.997390	−	0.0721990i	$-0.976998\pi$
$223$	−6.51339	+	11.2815i	−0.436169	+	0.755467i	0.561221	+	0.827666i	$0.310332\pi$
$224$	−1.30380	+	2.25825i	−0.0871138	+	0.150886i
$225$	0.760347			0.0506898
$226$	4.03570	+	6.99004i	0.268451	+	0.464971i
$227$	−11.1974	−	19.3944i	−0.743195	−	1.28725i	−0.951033	−	0.309088i	$-0.899976\pi$
$227$	−11.1974	−	19.3944i	−0.743195	−	1.28725i	0.207838	−	0.978163i	$-0.433357\pi$
$228$	0.101739	+	0.176216i	0.00673780	+	0.0116702i
$229$	−13.0652	+	22.6296i	−0.863374	+	1.49541i	0.00527771	+	0.999986i	$0.498320\pi$
$229$	−13.0652	+	22.6296i	−0.863374	+	1.49541i	−0.868652	+	0.495422i	$0.835013\pi$
$230$	6.98464	+	12.0977i	0.460553	+	0.797702i
$231$	−0.793499	+	1.37438i	−0.0522084	+	0.0904276i
$232$	5.65725			0.371417
$233$	10.7839			0.706474			0.353237	−	0.935534i	$-0.385081\pi$
$233$	10.7839			0.706474			0.353237	+	0.935534i	$0.385081\pi$
$234$	2.01074	−	3.48271i	0.131446	−	0.227672i
$235$	−9.18802	−	15.9141i	−0.599360	−	1.03812i
$236$	−0.518694	+	0.898404i	−0.0337641	+	0.0584811i
$237$	−1.27838	−	2.21422i	−0.0830397	−	0.143829i
$238$	3.24930	+	5.62796i	0.210621	+	0.364806i
$239$	11.0239	+	19.0939i	0.713075	+	1.23508i	0.963697	+	0.266998i	$0.0860316\pi$
$239$	11.0239	+	19.0939i	0.713075	+	1.23508i	−0.250622	+	0.968085i	$0.580635\pi$
$240$	−1.48582			−0.0959093
$241$	−4.49832	+	7.79132i	−0.289762	+	0.501883i	−0.973753	−	0.227608i	$-0.926910\pi$
$241$	−4.49832	+	7.79132i	−0.289762	+	0.501883i	0.683991	+	0.729491i	$0.260243\pi$
$242$	1.54776	−	2.68080i	0.0994938	−	0.172328i
$243$	2.48210	+	4.29913i	0.159227	+	0.275789i
$244$	−0.949977			−0.0608160
$245$	1.39856	−	2.42237i	0.0893505	−	0.154760i
$246$	−0.284513			−0.0181399
$247$	−6.78650			−0.431815
$248$	14.3218	−	7.81464i	0.909434	−	0.496230i
$249$	−1.46087			−0.0925790
$250$	15.5270			0.982013
$251$	14.4953	−	25.1067i	0.914937	−	1.58472i	0.107944	−	0.994157i	$-0.465573\pi$
$251$	14.4953	−	25.1067i	0.914937	−	1.58472i	0.806993	−	0.590561i	$-0.201093\pi$
$252$	1.37022			0.0863156
$253$	6.98146	+	12.0922i	0.438921	+	0.760233i
$254$	−5.32712	+	9.22684i	−0.334253	+	0.578943i
$255$	0.338550	−	0.586385i	0.0212008	−	0.0367209i
$256$	−3.82778			−0.239236
$257$	−8.68613	−	15.0448i	−0.541826	−	0.938470i	−0.998799	−	0.0489898i	$-0.984400\pi$
$257$	−8.68613	−	15.0448i	−0.541826	−	0.938470i	0.456973	−	0.889480i	$-0.348934\pi$
$258$	−0.664776	−	1.15143i	−0.0413871	−	0.0716846i
$259$	−0.478525	−	0.828830i	−0.0297341	−	0.0515010i
$260$	−0.174840	+	0.302832i	−0.0108431	+	0.0187809i
$261$	−2.86227	−	4.95759i	−0.177170	−	0.306867i
$262$	8.44995	−	14.6357i	0.522040	−	0.904199i
$263$	−7.59299			−0.468204			−0.234102	−	0.972212i	$-0.575215\pi$
$263$	−7.59299			−0.468204			−0.234102	+	0.972212i	$0.575215\pi$
$264$	−1.61569			−0.0994387
$265$	−12.9385	+	22.4101i	−0.794804	+	1.37664i
$266$	13.2461	+	22.9429i	0.812169	+	1.40672i
$267$	0.415987	−	0.720511i	0.0254580	−	0.0440945i
$268$	0.921197	+	1.59556i	0.0562710	+	0.0974643i
$269$	−12.7968	−	22.1646i	−0.780232	−	1.35140i	−0.931807	−	0.362955i	$-0.881768\pi$
$269$	−12.7968	−	22.1646i	−0.780232	−	1.35140i	0.151575	−	0.988446i	$-0.451565\pi$
$270$	1.64527	+	2.84968i	0.100128	+	0.173426i
$271$	−16.6475			−1.01127			−0.505633	−	0.862749i	$-0.668741\pi$
$271$	−16.6475			−1.01127			−0.505633	+	0.862749i	$0.668741\pi$
$272$	−3.04077	+	5.26676i	−0.184373	+	0.319344i
$273$	0.268749	−	0.465488i	0.0162655	−	0.0281726i
$274$	−4.53949	−	7.86263i	−0.274241	−	0.474999i
$275$	0.757124			0.0456563
$276$	−0.0708952	+	0.122794i	−0.00426739	+	0.00739134i
$277$	−7.37235			−0.442961			−0.221481	−	0.975165i	$-0.571089\pi$
$277$	−7.37235			−0.442961			−0.221481	+	0.975165i	$0.571089\pi$
$278$	−2.13446			−0.128016
$279$	−14.0942	−	8.59675i	−0.843799	−	0.514674i
$280$	18.3691			1.09777
$281$	15.1665			0.904757			0.452379	−	0.891826i	$-0.350576\pi$
$281$	15.1665			0.904757			0.452379	+	0.891826i	$0.350576\pi$
$282$	−1.06847	+	1.85065i	−0.0636266	+	0.110204i
$283$	20.4765			1.21720			0.608602	−	0.793476i	$-0.291731\pi$
$283$	20.4765			1.21720			0.608602	+	0.793476i	$0.291731\pi$
$284$	0.0350252	+	0.0606654i	0.00207836	+	0.00359983i
$285$	1.38013	−	2.39045i	0.0817517	−	0.141598i
$286$	2.00222	−	3.46795i	0.118394	−	0.205064i
$287$	3.23323			0.190851
$288$	1.34316	+	2.32642i	0.0791463	+	0.137085i
$289$	7.11430	+	12.3223i	0.418488	+	0.724843i
$290$	−2.85143	−	4.93883i	−0.167442	−	0.290018i
$291$	−0.0952402	+	0.164961i	−0.00558308	+	0.00967018i
$292$	−0.374893	−	0.649334i	−0.0219390	−	0.0379994i
$293$	−8.59044	+	14.8791i	−0.501859	+	0.869245i	0.498139	+	0.867097i	$0.334017\pi$
$293$	−8.59044	+	14.8791i	−0.501859	+	0.869245i	−0.999998	+	0.00214776i	$0.999316\pi$
$294$	−0.325276			−0.0189705
$295$	14.0726			0.819339
$296$	0.487176	−	0.843814i	0.0283165	−	0.0490457i
$297$	1.64452	+	2.84839i	0.0954246	+	0.165280i
$298$	9.76931	−	16.9209i	0.565921	−	0.980204i
$299$	−2.36454	−	4.09551i	−0.136745	−	0.236850i
$300$	0.00384422	+	0.00665838i	0.000221946	+	0.000384422i
$301$	7.55455	+	13.0849i	0.435437	+	0.754199i
$302$	−16.2391			−0.934457
$303$	1.08167	−	1.87351i	0.0621403	−	0.107630i
$304$	−12.3959	+	21.4704i	−0.710956	+	1.23141i
$305$	6.44342	+	11.1603i	0.368949	+	0.639039i
$306$	6.69478			0.382715
$307$	13.7596	−	23.8323i	0.785301	−	1.36018i	−0.143518	−	0.989648i	$-0.545841\pi$
$307$	13.7596	−	23.8323i	0.785301	−	1.36018i	0.928819	−	0.370534i	$-0.120825\pi$
$308$	1.36441			0.0777445
$309$	−1.19851			−0.0681807
$310$	−14.0409	−	8.56421i	−0.797468	−	0.486415i
$311$	24.0241			1.36228			0.681140	−	0.732154i	$-0.261485\pi$
$311$	24.0241			1.36228			0.681140	+	0.732154i	$0.261485\pi$
$312$	0.547216			0.0309800
$313$	−5.24145	+	9.07846i	−0.296264	+	0.513145i	−0.975278	−	0.220981i	$-0.929074\pi$
$313$	−5.24145	+	9.07846i	−0.296264	+	0.513145i	0.679014	+	0.734125i	$0.262408\pi$
$314$	−12.4730			−0.703890
$315$	−9.29379	−	16.0973i	−0.523646	−	0.906981i
$316$	−1.09908	+	1.90366i	−0.0618280	+	0.107089i
$317$	−15.8580	+	27.4669i	−0.890676	+	1.54270i	−0.0516094	+	0.998667i	$0.516435\pi$
$317$	−15.8580	+	27.4669i	−0.890676	+	1.54270i	−0.839067	+	0.544029i	$0.816898\pi$
$318$	3.00922			0.168749
$319$	−2.85014	−	4.93658i	−0.159577	−	0.276395i
$320$	9.29447	+	16.0985i	0.519576	+	0.899933i
$321$	1.27798	+	2.21353i	0.0713299	+	0.123547i
$322$	−9.23035	+	15.9874i	−0.514387	+	0.890945i
$323$	−5.64892	−	9.78422i	−0.314314	−	0.544409i
$324$	0.697391	−	1.20792i	0.0387440	−	0.0671065i
$325$	−0.256430			−0.0142242
$326$	0.444677			0.0246284
$327$	−0.568899	+	0.985362i	−0.0314602	+	0.0544907i
$328$	1.64584	+	2.85068i	0.0908763	+	0.157402i
$329$	12.1422	−	21.0309i	0.669420	−	1.15947i
$330$	0.814358	+	1.41051i	0.0448289	+	0.0776460i
$331$	−4.08321	−	7.07233i	−0.224433	−	0.388730i	0.731716	−	0.681610i	$-0.238720\pi$
$331$	−4.08321	−	7.07233i	−0.224433	−	0.388730i	−0.956149	+	0.292880i	$0.905386\pi$
$332$	0.627987	+	1.08771i	0.0344653	+	0.0596956i
$333$	−0.985940			−0.0540292
$334$	0.351820	−	0.609370i	0.0192507	−	0.0333433i
$335$	12.4964	−	21.6444i	0.682753	−	1.18256i
$336$	−0.981773	−	1.70048i	−0.0535601	−	0.0927688i
$337$	−19.9688			−1.08777			−0.543884	−	0.839160i	$-0.683047\pi$
$337$	−19.9688			−1.08777			−0.543884	+	0.839160i	$0.683047\pi$
$338$	−0.678131	+	1.17456i	−0.0368855	+	0.0638875i
$339$	1.11136			0.0603609
$340$	−0.582132			−0.0315705
$341$	−14.0345	−	8.56032i	−0.760010	−	0.463567i
$342$	27.2918			1.47577
$343$	−16.4512			−0.888283
$344$	−7.69113	+	13.3214i	−0.414678	+	0.718243i
$345$	1.92345			0.103555
$346$	−4.80966	−	8.33058i	−0.258569	−	0.447855i
$347$	−7.61368	+	13.1873i	−0.408724	+	0.707930i	−0.994747	−	0.102364i	$-0.967359\pi$
$347$	−7.61368	+	13.1873i	−0.408724	+	0.707930i	0.586023	+	0.810294i	$0.300693\pi$
$348$	0.0289425	−	0.0501299i	0.00155148	−	0.00268725i
$349$	−26.7180			−1.43018			−0.715092	−	0.699030i	$-0.753615\pi$
$349$	−26.7180			−1.43018			−0.715092	+	0.699030i	$0.753615\pi$
$350$	0.500506	+	0.866902i	0.0267532	+	0.0463379i
$351$	−0.556980	−	0.964718i	−0.0297294	−	0.0514929i
$352$	1.33747	+	2.31656i	0.0712871	+	0.123473i
$353$	9.27936	−	16.0723i	0.493891	−	0.855443i	−0.506085	−	0.862484i	$-0.668908\pi$
$353$	9.27936	−	16.0723i	0.493891	−	0.855443i	0.999975	+	0.00704033i	$0.00224102\pi$
$354$	−0.818250	−	1.41725i	−0.0434895	−	0.0753260i
$355$	0.475132	−	0.822952i	0.0252174	−	0.0436778i
$356$	−0.715284			−0.0379100
$357$	0.894802			0.0473579
$358$	−13.4537	+	23.3026i	−0.711052	+	1.23158i
$359$	−6.03482	−	10.4526i	−0.318505	−	0.551668i	0.661671	−	0.749794i	$-0.269848\pi$
$359$	−6.03482	−	10.4526i	−0.318505	−	0.551668i	−0.980176	+	0.198127i	$0.936514\pi$
$360$	9.46181	−	16.3883i	0.498681	−	0.863742i
$361$	−13.5283	−	23.4317i	−0.712017	−	1.23325i
$362$	9.26678	+	16.0505i	0.487051	+	0.843597i
$363$	−0.213113	−	0.369123i	−0.0111855	−	0.0193739i
$364$	−0.462111			−0.0242212
$365$	−5.08559	+	8.80850i	−0.266192	+	0.461058i
$366$	0.749304	−	1.29783i	0.0391667	−	0.0678388i
$367$	−17.9960	−	31.1699i	−0.939382	−	1.62706i	−0.766628	−	0.642092i	$-0.778067\pi$
$367$	−17.9960	−	31.1699i	−0.939382	−	1.62706i	−0.172754	−	0.984965i	$-0.555267\pi$
$368$	−17.2759			−0.900569
$369$	1.66541	−	2.88458i	0.0866979	−	0.150165i
$370$	−0.982208			−0.0510626
$371$	−34.1969			−1.77542
$372$	0.00402341	−	0.166888i	0.000208604	−	0.00865272i
$373$	31.3883			1.62523			0.812613	−	0.582803i	$-0.198044\pi$
$373$	31.3883			1.62523			0.812613	+	0.582803i	$0.198044\pi$
$374$	6.66641			0.344712
$375$	1.06897	−	1.85150i	0.0552012	−	0.0956112i
$376$	24.7234			1.27501
$377$	0.965310	+	1.67197i	0.0497160	+	0.0861106i
$378$	−2.17426	+	3.76592i	−0.111832	+	0.193698i
$379$	−13.8879	+	24.0546i	−0.713375	+	1.23560i	0.250208	+	0.968192i	$0.419501\pi$
$379$	−13.8879	+	24.0546i	−0.713375	+	1.23560i	−0.963583	+	0.267409i	$0.913832\pi$
$380$	−2.37311			−0.121738
$381$	0.733498	+	1.27046i	0.0375782	+	0.0650874i
$382$	−16.3366	−	28.2958i	−0.835851	−	1.44774i
$383$	−5.60038	−	9.70015i	−0.286166	−	0.495654i	0.686725	−	0.726917i	$-0.259048\pi$
$383$	−5.60038	−	9.70015i	−0.286166	−	0.495654i	−0.972891	+	0.231263i	$0.925714\pi$
$384$	0.911665	−	1.57905i	0.0465232	−	0.0805805i
$385$	−9.25441	−	16.0291i	−0.471648	−	0.816919i
$386$	−0.135111	+	0.234020i	−0.00687699	+	0.0119113i
$387$	15.5652			0.791223
$388$	0.163764			0.00831387
$389$	17.3718	−	30.0888i	0.880784	−	1.52556i	0.0303128	−	0.999540i	$-0.490350\pi$
$389$	17.3718	−	30.0888i	0.880784	−	1.52556i	0.850471	−	0.526022i	$-0.176317\pi$
$390$	−0.275814	−	0.477724i	−0.0139664	−	0.0241905i
$391$	3.93638	−	6.81801i	0.199071	−	0.344802i
$392$	1.88164	+	3.25909i	0.0950371	+	0.164609i
$393$	−1.16349	−	2.01522i	−0.0586901	−	0.101654i
$394$	−0.450138	−	0.779661i	−0.0226776	−	0.0392788i
$395$	29.8189			1.50035
$396$	0.702799	−	1.21728i	0.0353170	−	0.0611708i
$397$	−3.55656	+	6.16015i	−0.178499	+	0.309169i	−0.941367	−	0.337386i	$-0.890457\pi$
$397$	−3.55656	+	6.16015i	−0.178499	+	0.309169i	0.762868	+	0.646555i	$0.223791\pi$
$398$	11.6723	+	20.2170i	0.585078	+	1.01338i
$399$	3.64774			0.182615
$400$	−0.468384	+	0.811265i	−0.0234192	+	0.0405632i
$401$	8.14388			0.406686			0.203343	−	0.979108i	$-0.434819\pi$
$401$	8.14388			0.406686			0.203343	+	0.979108i	$0.434819\pi$
$402$	−2.90641			−0.144959
$403$	4.75333	+	2.89929i	0.236780	+	0.144424i
$404$	−1.85992			−0.0925344
$405$	−18.9208			−0.940183
$406$	3.76823	−	6.52677i	0.187014	−	0.323918i
$407$	−0.981762			−0.0486641
$408$	0.455490	+	0.788931i	0.0225501	+	0.0390579i
$409$	13.7112	−	23.7485i	0.677975	−	1.17429i	−0.297615	−	0.954686i	$-0.596191\pi$
$409$	13.7112	−	23.7485i	0.677975	−	1.17429i	0.975590	−	0.219601i	$-0.0704756\pi$
$410$	1.65911	−	2.87366i	0.0819376	−	0.141920i
$411$	−1.25010			−0.0616628
$412$	0.515204	+	0.892360i	0.0253823	+	0.0439634i
$413$	9.29864	+	16.1057i	0.457556	+	0.792510i
$414$	9.50899	+	16.4700i	0.467341	+	0.809459i
$415$	8.51892	−	14.7552i	0.418177	−	0.724304i
$416$	−0.452985	−	0.784593i	−0.0222094	−	0.0384678i
$417$	−0.146948	+	0.254522i	−0.00719610	+	0.0124640i
$418$	27.1762			1.32923
$419$	−9.57344			−0.467693			−0.233847	−	0.972273i	$-0.575131\pi$
$419$	−9.57344			−0.467693			−0.233847	+	0.972273i	$0.575131\pi$
$420$	0.0939765	−	0.162772i	0.00458558	−	0.00794247i
$421$	−11.7265	−	20.3108i	−0.571513	−	0.989890i	−0.996411	−	0.0846482i	$-0.973023\pi$
$421$	−11.7265	−	20.3108i	−0.571513	−	0.989890i	0.424898	−	0.905241i	$-0.360310\pi$
$422$	−12.4397	+	21.5462i	−0.605555	+	1.04885i
$423$	−12.5087	−	21.6657i	−0.608194	−	1.05342i
$424$	−17.4076	−	30.1508i	−0.845387	−	1.46425i
$425$	−0.213446	−	0.369699i	−0.0103537	−	0.0179331i
$426$	−0.110506			−0.00535402
$427$	−8.51513	+	14.7486i	−0.412076	+	0.713736i
$428$	1.09874	−	1.90307i	0.0531094	−	0.0919881i
$429$	−0.275689	−	0.477507i	−0.0133104	−	0.0230542i
$430$	15.5063			0.747779
$431$	10.4062	−	18.0241i	0.501251	−	0.868192i	−0.498748	−	0.866747i	$-0.666207\pi$
$431$	10.4062	−	18.0241i	0.501251	−	0.868192i	0.999999	−	0.00144499i	$-0.000459954\pi$
$432$	−4.06943			−0.195790
$433$	−30.7389			−1.47722			−0.738609	−	0.674134i	$-0.764517\pi$
$433$	−30.7389			−1.47722			−0.738609	+	0.674134i	$0.764517\pi$
$434$	0.523837	−	21.7283i	0.0251450	−	1.04299i
$435$	−0.785235			−0.0376492
$436$	0.978215			0.0468480
$437$	16.0470	−	27.7942i	0.767632	−	1.32958i
$438$	1.18280			0.0565165
$439$	−0.576157	−	0.997933i	−0.0274985	−	0.0476287i	0.851949	−	0.523625i	$-0.175421\pi$
$439$	−0.576157	−	0.997933i	−0.0274985	−	0.0476287i	−0.879447	+	0.475997i	$0.842087\pi$
$440$	9.42171	−	16.3189i	0.449163	−	0.777972i
$441$	1.90402	−	3.29785i	0.0906675	−	0.157041i
$442$	−2.25784			−0.107394
$443$	−9.80273	−	16.9788i	−0.465742	−	0.806689i	0.533493	−	0.845805i	$-0.320879\pi$
$443$	−9.80273	−	16.9788i	−0.465742	−	0.806689i	−0.999235	+	0.0391161i	$0.987546\pi$
$444$	−0.00498479	−	0.00863391i	−0.000236568	−	0.000409747i
$445$	4.85157	+	8.40316i	0.229986	+	0.398348i
$446$	−8.83387	+	15.3007i	−0.418296	+	0.724509i
$447$	−1.34515	−	2.32987i	−0.0636234	−	0.110199i
$448$	−12.2828	+	21.2745i	−0.580310	+	1.00513i
$449$	−2.59800			−0.122607			−0.0613035	−	0.998119i	$-0.519526\pi$
$449$	−2.59800			−0.122607			−0.0613035	+	0.998119i	$0.519526\pi$
$450$	1.03123			0.0486126
$451$	1.65835	−	2.87236i	0.0780889	−	0.135254i
$452$	−0.477743	−	0.827476i	−0.0224712	−	0.0389212i
$453$	−1.11799	+	1.93642i	−0.0525279	+	0.0909811i
$454$	−15.1866	−	26.3039i	−0.712740	−	1.23450i
$455$	3.13437	+	5.42888i	0.146941	+	0.254510i
$456$	1.85684	+	3.21615i	0.0869546	+	0.150610i
$457$	−36.8522			−1.72387			−0.861936	−	0.507018i	$-0.830748\pi$
$457$	−36.8522			−1.72387			−0.861936	+	0.507018i	$0.830748\pi$
$458$	−17.7199	+	30.6917i	−0.827995	+	1.43413i
$459$	0.927234	−	1.60602i	0.0432796	−	0.0749624i
$460$	−0.826836	−	1.43212i	−0.0385514	−	0.0667730i
$461$	31.8251			1.48224			0.741121	−	0.671371i	$-0.234294\pi$
$461$	31.8251			1.48224			0.741121	+	0.671371i	$0.234294\pi$
$462$	−1.07619	+	1.86402i	−0.0500690	+	0.0867220i
$463$	−6.89236			−0.320315			−0.160158	−	0.987091i	$-0.551200\pi$
$463$	−6.89236			−0.320315			−0.160158	+	0.987091i	$0.551200\pi$
$464$	7.05278			0.327417
$465$	−1.98789	+	1.08468i	−0.0921860	+	0.0503010i
$466$	14.6257			0.677524
$467$	−32.8087			−1.51821			−0.759104	−	0.650970i	$-0.774362\pi$
$467$	−32.8087			−1.51821			−0.759104	+	0.650970i	$0.774362\pi$
$468$	−0.238030	+	0.412281i	−0.0110030	+	0.0190577i
$469$	33.0286			1.52512
$470$	−12.4614	−	21.5837i	−0.574800	−	0.995582i
$471$	−0.858710	+	1.48733i	−0.0395673	+	0.0685325i
$472$	−9.46674	+	16.3969i	−0.435742	+	0.754728i
$473$	15.4992			0.712655
$474$	−1.73382	−	3.00306i	−0.0796369	−	0.137935i
$475$	−0.870131	−	1.50711i	−0.0399244	−	0.0691510i
$476$	−0.384650	−	0.666234i	−0.0176304	−	0.0305368i
$477$	−17.6146	+	30.5094i	−0.806518	+	1.39693i
$478$	14.9513	+	25.8964i	0.683855	+	1.18447i
$479$	−9.12652	+	15.8076i	−0.417001	+	0.722267i	−0.995636	−	0.0933193i	$-0.970252\pi$
$479$	−9.12652	+	15.8076i	−0.417001	+	0.722267i	0.578635	+	0.815587i	$0.303586\pi$
$480$	0.368482			0.0168188
$481$	0.332512			0.0151612
$482$	−6.10090	+	10.5671i	−0.277888	+	0.481317i
$483$	1.27094	+	2.20133i	0.0578298	+	0.100164i
$484$	−0.183223	+	0.317351i	−0.00832831	+	0.0144250i
$485$	−1.11077	−	1.92390i	−0.0504373	−	0.0873600i
$486$	3.36638	+	5.83075i	0.152702	+	0.264488i
$487$	8.01984	+	13.8908i	0.363414	+	0.629451i	0.988520	−	0.151088i	$-0.0482778\pi$
$487$	8.01984	+	13.8908i	0.363414	+	0.629451i	−0.625106	+	0.780539i	$0.714944\pi$
$488$	−17.3381			−0.784861
$489$	0.0306141	−	0.0530251i	0.00138442	−	0.00239788i
$490$	1.89681	−	3.28537i	0.0856891	−	0.148418i
$491$	−6.84390	−	11.8540i	−0.308861	−	0.534962i	0.669253	−	0.743035i	$-0.266614\pi$
$491$	−6.84390	−	11.8540i	−0.308861	−	0.534962i	−0.978113	+	0.208072i	$0.933281\pi$
$492$	0.0336805			0.00151843
$493$	−1.60700	+	2.78341i	−0.0723757	+	0.125358i
$494$	−9.20428			−0.414120
$495$	−19.0675			−0.857022
$496$	17.8547	−	9.74235i	0.801699	−	0.437444i
$497$	1.25579			0.0563301
$498$	−1.98132			−0.0887853
$499$	−3.55686	+	6.16065i	−0.159227	+	0.275789i	−0.934590	−	0.355727i	$-0.884233\pi$
$499$	−3.55686	+	6.16065i	−0.159227	+	0.275789i	0.775363	+	0.631515i	$0.217567\pi$
$500$	−1.83807			−0.0822011
$501$	−0.0484426	−	0.0839050i	−0.00216426	−	0.00374860i
$502$	19.6595	−	34.0512i	0.877445	−	1.51978i
$503$	18.5050	−	32.0516i	0.825097	−	1.42911i	−0.0767478	−	0.997051i	$-0.524454\pi$
$503$	18.5050	−	32.0516i	0.825097	−	1.42911i	0.901845	−	0.432060i	$-0.142213\pi$
$504$	25.0080			1.11394
$505$	12.6153	+	21.8503i	0.561373	+	0.972327i
$506$	9.46869	+	16.4002i	0.420934	+	0.729080i
$507$	0.0933728	+	0.161726i	0.00414683	+	0.00718252i
$508$	0.630620	−	1.09227i	0.0279792	−	0.0484615i
$509$	15.0910	+	26.1384i	0.668896	+	1.15856i	0.978213	+	0.207603i	$0.0665663\pi$
$509$	15.0910	+	26.1384i	0.668896	+	1.15856i	−0.309317	+	0.950959i	$0.600100\pi$
$510$	0.459162	−	0.795292i	0.0203320	−	0.0352161i
$511$	−13.4414			−0.594614
$512$	−24.7189			−1.09243
$513$	3.77995	−	6.54707i	0.166889	−	0.289060i
$514$	−11.7807	−	20.4047i	−0.519623	−	0.900014i
$515$	6.98897	−	12.1052i	0.307971	−	0.533421i
$516$	0.0786957	+	0.136305i	0.00346438	+	0.00600049i
$517$	−12.4557	−	21.5739i	−0.547801	−	0.948818i
$518$	−0.649005	−	1.12411i	−0.0285157	−	0.0493906i
$519$	−1.32450			−0.0581390
$520$	−3.19103	+	5.52703i	−0.139936	+	0.242376i
$521$	1.91968	−	3.32498i	0.0841025	−	0.145670i	−0.820906	−	0.571063i	$-0.806531\pi$
$521$	1.91968	−	3.32498i	0.0841025	−	0.145670i	0.905008	+	0.425394i	$0.139864\pi$
$522$	−3.88198	−	6.72379i	−0.169910	−	0.294292i
$523$	38.3566			1.67722			0.838609	−	0.544734i	$-0.183370\pi$
$523$	38.3566			1.67722			0.838609	+	0.544734i	$0.183370\pi$
$524$	−1.00030	+	1.73257i	−0.0436983	+	0.0756876i
$525$	0.137831			0.00601543
$526$	−10.2981			−0.449018
$527$	−0.223396	+	9.26625i	−0.00973127	+	0.403644i
$528$	−2.01425			−0.0876588
$529$	−0.635718			−0.0276399
$530$	−17.5479	+	30.3939i	−0.762234	+	1.32023i
$531$	19.1587			0.831415
$532$	−1.56806	−	2.71596i	−0.0679840	−	0.117752i
$533$	−0.561667	+	0.972836i	−0.0243285	+	0.0421382i
$534$	0.564187	−	0.977201i	0.0244148	−	0.0422876i
$535$	−29.8096			−1.28878
$536$	16.8129	+	29.1207i	0.726205	+	1.25782i
$537$	1.85246	+	3.20856i	0.0799397	+	0.138460i
$538$	−17.3557	−	30.0610i	−0.748259	−	1.29602i
$539$	1.89595	−	3.28388i	0.0816642	−	0.141447i
$540$	−0.194765	−	0.337344i	−0.00838137	−	0.0145170i
$541$	−12.8613	+	22.2765i	−0.552952	+	0.957741i	0.445108	+	0.895477i	$0.353165\pi$
$541$	−12.8613	+	22.2765i	−0.552952	+	0.957741i	−0.998060	+	0.0622638i	$0.980168\pi$
$542$	−22.5784			−0.969826
$543$	2.55191			0.109513
$544$	0.754108	−	1.30615i	0.0323321	−	0.0560008i
$545$	−6.63495	−	11.4921i	−0.284210	−	0.492266i
$546$	0.364495	−	0.631323i	0.0155989	−	0.0270181i
$547$	2.50748	+	4.34309i	0.107212	+	0.185697i	0.914640	−	0.404270i	$-0.132474\pi$
$547$	2.50748	+	4.34309i	0.107212	+	0.185697i	−0.807428	+	0.589967i	$0.799141\pi$
$548$	0.537382	+	0.930773i	0.0229558	+	0.0397606i
$549$	8.77217	+	15.1938i	0.374387	+	0.648457i
$550$	1.02686			0.0437854
$551$	−6.55108	+	11.3468i	−0.279085	+	0.483390i
$552$	−1.29392	+	2.24113i	−0.0550728	+	0.0953888i
$553$	19.7032	+	34.1269i	0.837865	+	1.45123i
$554$	−9.99883			−0.424810
$555$	−0.0676208	+	0.117123i	−0.00287034	+	0.00497158i
$556$	0.252676			0.0107158
$557$	0.0641080			0.00271634			0.00135817	−	0.999999i	$-0.499568\pi$
$557$	0.0641080			0.00271634			0.00135817	+	0.999999i	$0.499568\pi$
$558$	−19.1155	−	11.6594i	−0.809222	−	0.493584i
$559$	−5.24942			−0.222027
$560$	22.9004			0.967719
$561$	0.458953	−	0.794930i	0.0193770	−	0.0335620i
$562$	20.5697			0.867682
$563$	3.22100	+	5.57894i	0.135749	+	0.235124i	0.925883	−	0.377809i	$-0.123323\pi$
$563$	3.22100	+	5.57894i	0.135749	+	0.235124i	−0.790134	+	0.612934i	$0.789989\pi$
$564$	0.126485	−	0.219078i	0.00532597	−	0.00922486i
$565$	−6.48079	+	11.2251i	−0.272649	+	0.472242i
$566$	27.7715			1.16732
$567$	−12.5021	−	21.6544i	−0.525041	−	0.909397i
$568$	0.639249	+	1.10721i	0.0268223	+	0.0464575i
$569$	6.00352	+	10.3984i	0.251680	+	0.435923i	0.963989	−	0.265943i	$-0.0856835\pi$
$569$	6.00352	+	10.3984i	0.251680	+	0.435923i	−0.712308	+	0.701867i	$0.752350\pi$
$570$	1.87181	−	3.24208i	0.0784017	−	0.135796i
$571$	18.8128	+	32.5848i	0.787293	+	1.36363i	0.927620	+	0.373526i	$0.121851\pi$
$571$	18.8128	+	32.5848i	0.787293	+	1.36363i	−0.140327	+	0.990105i	$0.544815\pi$
$572$	−0.237022	+	0.410533i	−0.00991037	+	0.0171653i
$573$	−4.49881			−0.187940
$574$	4.38510			0.183031
$575$	0.606340	−	1.05021i	0.0252861	−	0.0437968i
$576$	12.6536	+	21.9167i	0.527234	+	0.913197i
$577$	−4.10675	+	7.11310i	−0.170966	+	0.296122i	−0.938758	−	0.344577i	$-0.888022\pi$
$577$	−4.10675	+	7.11310i	−0.170966	+	0.296122i	0.767792	+	0.640700i	$0.221356\pi$
$578$	9.64886	+	16.7123i	0.401340	+	0.695140i
$579$	0.0186037	+	0.0322225i	0.000773142	+	0.00133912i
$580$	0.337550	+	0.584655i	0.0140160	+	0.0242765i
$581$	22.5159			0.934116
$582$	−0.129171	+	0.223730i	−0.00535430	+	0.00927391i
$583$	−17.5400	+	30.3801i	−0.726431	+	1.25822i
$584$	−6.84222	−	11.8511i	−0.283133	−	0.490401i
$585$	6.45797			0.267004
$586$	−11.6509	+	20.1799i	−0.481294	+	0.833625i
$587$	8.54422			0.352658			0.176329	−	0.984331i	$-0.443578\pi$
$587$	8.54422			0.352658			0.176329	+	0.984331i	$0.443578\pi$
$588$	0.0385059			0.00158796
$589$	−0.910692	+	37.7747i	−0.0375244	+	1.55648i
$590$	19.0862			0.785764
$591$	−0.123960			−0.00509904
$592$	0.607353	−	1.05197i	0.0249620	−	0.0432355i
$593$	20.7398			0.851681			0.425840	−	0.904798i	$-0.359978\pi$
$593$	20.7398			0.851681			0.425840	+	0.904798i	$0.359978\pi$
$594$	2.23040	+	3.86316i	0.0915143	+	0.158507i
$595$	−5.21794	+	9.03774i	−0.213915	+	0.370511i
$596$	−1.15648	+	2.00309i	−0.0473714	+	0.0820497i
$597$	3.21434			0.131554
$598$	−3.20694	−	5.55459i	−0.131142	−	0.227144i
$599$	−3.84848	−	6.66576i	−0.157245	−	0.272356i	0.776630	−	0.629958i	$-0.216928\pi$
$599$	−3.84848	−	6.66576i	−0.157245	−	0.272356i	−0.933874	+	0.357602i	$0.883594\pi$
$600$	0.0701613	+	0.121523i	0.00286432	+	0.00496115i
$601$	23.1095	−	40.0269i	0.942658	−	1.63273i	0.182285	−	0.983246i	$-0.441651\pi$
$601$	23.1095	−	40.0269i	0.942658	−	1.63273i	0.760374	−	0.649486i	$-0.225016\pi$
$602$	10.2459	+	17.7465i	0.417594	+	0.723293i
$603$	17.0128	−	29.4671i	0.692816	−	1.19999i
$604$	1.92238			0.0782204
$605$	4.97099			0.202099
$606$	1.46703	−	2.54097i	0.0595940	−	0.103220i
$607$	−3.63460	−	6.29531i	−0.147524	−	0.255519i	0.782788	−	0.622289i	$-0.213797\pi$
$607$	−3.63460	−	6.29531i	−0.147524	−	0.255519i	−0.930312	+	0.366770i	$0.880464\pi$
$608$	3.07419	−	5.32464i	0.124675	−	0.215943i
$609$	−0.518853	−	0.898680i	−0.0210250	−	0.0364163i
$610$	8.73897	+	15.1363i	0.353830	+	0.612852i
$611$	4.21861	+	7.30684i	0.170667	+	0.295603i
$612$	−0.792523			−0.0320358
$613$	−21.2675	+	36.8364i	−0.858985	+	1.48781i	0.0139125	+	0.999903i	$0.495571\pi$
$613$	−21.2675	+	36.8364i	−0.858985	+	1.48781i	−0.872898	+	0.487903i	$0.837762\pi$
$614$	18.6616	−	32.3229i	0.753121	−	1.30444i
$615$	−0.228445	−	0.395678i	−0.00921179	−	0.0159553i
$616$	24.9020			1.00333
$617$	−0.984131	+	1.70456i	−0.0396196	+	0.0686232i	−0.885155	−	0.465296i	$-0.845948\pi$
$617$	−0.984131	+	1.70456i	−0.0396196	+	0.0686232i	0.845536	+	0.533919i	$0.179281\pi$
$618$	−1.62549			−0.0653868
$619$	43.9663			1.76716			0.883578	−	0.468285i	$-0.155128\pi$
$619$	43.9663			1.76716			0.883578	+	0.468285i	$0.155128\pi$
$620$	1.66215	+	1.01383i	0.0667535	+	0.0407162i
$621$	5.26802			0.211398
$622$	32.5829			1.30646
$623$	−6.41146	+	11.1050i	−0.256870	+	0.444911i
$624$	0.682203			0.0273100
$625$	11.8260	+	20.4833i	0.473042	+	0.819333i
$626$	−7.10878	+	12.3128i	−0.284124	+	0.492117i
$627$	1.87096	−	3.24060i	0.0747191	−	0.129417i
$628$	1.47654			0.0589204
$629$	0.276775	+	0.479388i	0.0110357	+	0.0191145i
$630$	−12.6048	−	21.8322i	−0.502188	−	0.869815i
$631$	15.7299	+	27.2450i	0.626197	+	1.08461i	0.988308	+	0.152470i	$0.0487228\pi$
$631$	15.7299	+	27.2450i	0.626197	+	1.08461i	−0.362111	+	0.932135i	$0.617944\pi$
$632$	−20.0594	+	34.7439i	−0.797920	+	1.38204i
$633$	1.71284	+	2.96672i	0.0680792	+	0.117917i
$634$	−21.5077	+	37.2523i	−0.854178	+	1.47948i
$635$	−17.1093			−0.678960
$636$	−0.356229			−0.0141254
$637$	−0.642137	+	1.11221i	−0.0254424	+	0.0440675i
$638$	−3.86553	−	6.69530i	−0.153038	−	0.265069i
$639$	0.646851	−	1.12038i	0.0255890	−	0.0443215i
$640$	10.6326	+	18.4161i	0.420289	+	0.727961i
$641$	1.03194	+	1.78737i	0.0407592	+	0.0705971i	0.885685	−	0.464286i	$-0.153689\pi$
$641$	1.03194	+	1.78737i	0.0407592	+	0.0705971i	−0.844926	+	0.534883i	$0.820356\pi$
$642$	1.73328	+	3.00212i	0.0684070	+	0.118484i
$643$	−15.7954			−0.622910			−0.311455	−	0.950261i	$-0.600816\pi$
$643$	−15.7954			−0.622910			−0.311455	+	0.950261i	$0.600816\pi$
$644$	1.09268	−	1.89258i	0.0430577	−	0.0745781i
$645$	1.06754	−	1.84903i	0.0420344	−	0.0728056i
$646$	−7.66142	−	13.2700i	−0.301435	−	0.522100i
$647$	9.03423			0.355172			0.177586	−	0.984105i	$-0.443171\pi$
$647$	9.03423			0.355172			0.177586	+	0.984105i	$0.443171\pi$
$648$	12.7282	−	22.0458i	0.500010	−	0.866042i
$649$	19.0775			0.748856
$650$	−0.347786			−0.0136413
$651$	−2.55491	−	1.55836i	−0.100135	−	0.0610771i
$652$	−0.0526405			−0.00206156
$653$	−2.31286			−0.0905092			−0.0452546	−	0.998975i	$-0.514410\pi$
$653$	−2.31286			−0.0905092			−0.0452546	+	0.998975i	$0.514410\pi$
$654$	−0.771576	+	1.33641i	−0.0301710	+	0.0522577i
$655$	27.1390			1.06041
$656$	2.05183	+	3.55388i	0.0801107	+	0.138756i
$657$	−6.92360	+	11.9920i	−0.270115	+	0.467853i
$658$	16.4680	−	28.5234i	0.641988	−	1.11196i
$659$	−13.3775			−0.521113			−0.260557	−	0.965459i	$-0.583906\pi$
$659$	−13.3775			−0.521113			−0.260557	+	0.965459i	$0.583906\pi$
$660$	−0.0964031	−	0.166975i	−0.00375248	−	0.00649949i
$661$	−8.35346	−	14.4686i	−0.324912	−	0.562764i	0.656582	−	0.754254i	$-0.272001\pi$
$661$	−8.35346	−	14.4686i	−0.324912	−	0.562764i	−0.981495	+	0.191490i	$0.938668\pi$
$662$	−5.53790	−	9.59193i	−0.215237	−	0.372801i
$663$	−0.155443	+	0.269234i	−0.00603689	+	0.0104562i
$664$	11.4615	+	19.8518i	0.444791	+	0.770401i
$665$	−21.2714	+	36.8431i	−0.824869	+	1.42872i
$666$	−1.33719			−0.0518152
$667$	−9.13008			−0.353518
$668$	−0.0416482	+	0.0721368i	−0.00161142	+	0.00279106i
$669$	1.21635	+	2.10677i	0.0470267	+	0.0814526i
$670$	16.9484	−	29.3555i	0.654775	−	1.13410i
$671$	8.73499	+	15.1295i	0.337211	+	0.584066i
$672$	0.243479	+	0.421718i	0.00939240	+	0.0162681i
$673$	−25.4022	−	43.9979i	−0.979182	−	1.69599i	−0.665380	−	0.746505i	$-0.731730\pi$
$673$	−25.4022	−	43.9979i	−0.979182	−	1.69599i	−0.313803	−	0.949488i	$-0.601603\pi$
$674$	−27.0829			−1.04319
$675$	0.142826	−	0.247383i	0.00549739	−	0.00952176i
$676$	0.0802766	−	0.139043i	0.00308756	−	0.00534782i
$677$	11.8003	+	20.4387i	0.453523	+	0.785524i	0.998602	−	0.0528604i	$-0.0168338\pi$
$677$	11.8003	+	20.4387i	0.453523	+	0.785524i	−0.545079	+	0.838384i	$0.683500\pi$
$678$	1.50730			0.0578875
$679$	1.46790	−	2.54248i	0.0563329	−	0.0975715i
$680$	−10.6246			−0.407433
$681$	−4.18212			−0.160259
$682$	−19.0344	−	11.6100i	−0.728866	−	0.444571i
$683$	−46.6744			−1.78594			−0.892972	−	0.450111i	$-0.851384\pi$
$683$	−46.6744			−1.78594			−0.892972	+	0.450111i	$0.851384\pi$
$684$	−3.23079			−0.123532
$685$	7.28981	−	12.6263i	0.278530	−	0.482427i
$686$	−22.3122			−0.851883
$687$	2.43987	+	4.22598i	0.0930870	+	0.161231i
$688$	−9.58837	+	16.6075i	−0.365553	+	0.633157i
$689$	5.94060	−	10.2894i	0.226319	−	0.391996i
$690$	2.60870			0.0993115
$691$	−3.43710	−	5.95323i	−0.130753	−	0.226471i	0.793214	−	0.608943i	$-0.208406\pi$
$691$	−3.43710	−	5.95323i	−0.130753	−	0.226471i	−0.923967	+	0.382472i	$0.875073\pi$
$692$	0.569364	+	0.986168i	0.0216440	+	0.0374885i
$693$	−12.5991	−	21.8223i	−0.478600	−	0.828959i
$694$	−10.3261	+	17.8854i	−0.391975	+	0.678921i
$695$	−1.71383	−	2.96844i	−0.0650092	−	0.112599i
$696$	0.528233	−	0.914927i	0.0200226	−	0.0346802i
$697$	−1.87007			−0.0708340
$698$	−36.2367			−1.37158
$699$	1.00692	−	1.74403i	0.0380851	−	0.0659654i
$700$	−0.0592495	−	0.102623i	−0.00223942	−	0.00387879i
$701$	−21.7566	+	37.6835i	−0.821736	+	1.42329i	0.0826530	+	0.996578i	$0.473661\pi$
$701$	−21.7566	+	37.6835i	−0.821736	+	1.42329i	−0.904389	+	0.426710i	$0.859673\pi$
$702$	−0.755411	−	1.30841i	−0.0285112	−	0.0493828i
$703$	1.12830	+	1.95427i	0.0425545	+	0.0737066i
$704$	12.6000	+	21.8238i	0.474880	+	0.822517i
$705$	−3.43164			−0.129243
$706$	12.5852	−	21.7983i	0.473652	−	0.820389i
$707$	−16.6714	+	28.8757i	−0.626992	+	1.08598i
$708$	0.0968638	+	0.167773i	0.00364036	+	0.00630530i
$709$	9.78000			0.367296			0.183648	−	0.982992i	$-0.441209\pi$
$709$	9.78000			0.367296			0.183648	+	0.982992i	$0.441209\pi$
$710$	0.644403	−	1.11614i	0.0241840	−	0.0418879i
$711$	40.5959			1.52247
$712$	−13.0547			−0.489247
$713$	−23.1135	+	12.6118i	−0.865608	+	0.472316i
$714$	1.21359			0.0454173
$715$	6.43060			0.240491
$716$	1.59264	−	2.75854i	0.0595199	−	0.103091i
$717$	4.11732			0.153764
$718$	−8.18479	−	14.1765i	−0.305454	−	0.529061i
$719$	−11.4743	+	19.8740i	−0.427918	+	0.741175i	−0.996688	−	0.0813213i	$-0.974086\pi$
$719$	−11.4743	+	19.8740i	−0.427918	+	0.741175i	0.568770	+	0.822496i	$0.307419\pi$
$720$	11.7959	−	20.4310i	0.439605	−	0.761419i
$721$	18.4722			0.687939
$722$	−18.3480	−	31.7796i	−0.682840	−	1.18271i
$723$	0.840041	+	1.45499i	0.0312415	+	0.0541118i
$724$	−1.09699	−	1.90005i	−0.0407695	−	0.0706148i
$725$	−0.247534	+	0.428742i	−0.00919319	+	0.0159231i
$726$	−0.289037	−	0.500628i	−0.0107272	−	0.0185800i
$727$	−11.3168	+	19.6013i	−0.419717	+	0.726972i	−0.995911	−	0.0903416i	$-0.971204\pi$
$727$	−11.3168	+	19.6013i	−0.419717	+	0.726972i	0.576194	+	0.817313i	$0.304537\pi$
$728$	−8.43404			−0.312586
$729$	−25.1350			−0.930926
$730$	−6.89739	+	11.9466i	−0.255284	+	0.442165i
$731$	−4.36949	−	7.56818i	−0.161611	−	0.279919i
$732$	−0.0887020	+	0.153636i	−0.00327852	+	0.00567856i
$733$	−3.75883	−	6.51048i	−0.138835	−	0.240470i	0.788221	−	0.615393i	$-0.211003\pi$
$733$	−3.75883	−	6.51048i	−0.138835	−	0.240470i	−0.927056	+	0.374923i	$0.877669\pi$
$734$	−24.4072	−	42.2746i	−0.900888	−	1.56038i
$735$	−0.261174	−	0.452367i	−0.00963356	−	0.0166858i
$736$	4.28441			0.157926
$737$	16.9407	−	29.3422i	0.624019	−	1.08083i
$738$	2.25874	−	3.91225i	0.0831452	−	0.144012i
$739$	17.6005	+	30.4849i	0.647445	+	1.12141i	0.983731	+	0.179647i	$0.0574956\pi$
$739$	17.6005	+	30.4849i	0.647445	+	1.12141i	−0.336287	+	0.941760i	$0.609171\pi$
$740$	0.116273			0.00427428
$741$	−0.633675	+	1.09756i	−0.0232786	+	0.0403198i
$742$	−46.3800			−1.70266
$743$	17.9335			0.657915			0.328957	−	0.944345i	$-0.393303\pi$
$743$	17.9335			0.657915			0.328957	+	0.944345i	$0.393303\pi$
$744$	0.0734318	−	3.04589i	0.00269214	−	0.111668i
$745$	31.3764			1.14954
$746$	42.5708			1.55863
$747$	11.5978	−	20.0879i	0.424341	−	0.734979i
$748$	−0.789164			−0.0288547
$749$	−19.6970	−	34.1163i	−0.719714	−	1.24658i
$750$	1.44980	−	2.51112i	0.0529391	−	0.0916933i
$751$	15.0065	−	25.9921i	0.547596	−	0.948465i	−0.450842	−	0.892604i	$-0.648876\pi$
$751$	15.0065	−	25.9921i	0.547596	−	0.948465i	0.998439	−	0.0558611i	$-0.0177904\pi$
$752$	30.8221			1.12397
$753$	−2.70694	−	4.68856i	−0.0986463	−	0.170860i
$754$	1.30921	+	2.26762i	0.0476787	+	0.0825820i
$755$	−13.0389	−	22.5841i	−0.474535	−	0.821919i
$756$	0.257387	−	0.445807i	0.00936107	−	0.0162138i
$757$	−0.495280	−	0.857850i	−0.0180012	−	0.0311791i	0.856884	−	0.515509i	$-0.172397\pi$
$757$	−0.495280	−	0.857850i	−0.0180012	−	0.0311791i	−0.874886	+	0.484329i	$0.839064\pi$
$758$	−18.8357	+	32.6243i	−0.684142	+	1.18497i
$759$	2.60751			0.0946467
$760$	−43.3119			−1.57109
$761$	−21.9233	+	37.9723i	−0.794720	+	1.37650i	0.128296	+	0.991736i	$0.459049\pi$
$761$	−21.9233	+	37.9723i	−0.794720	+	1.37650i	−0.923017	+	0.384760i	$0.874284\pi$
$762$	0.994816	+	1.72307i	0.0360384	+	0.0624203i
$763$	8.76823	−	15.1870i	0.317431	−	0.549807i
$764$	1.93391	+	3.34963i	0.0699664	+	0.121185i
$765$	5.37546	+	9.31056i	0.194350	+	0.336624i
$766$	−7.59559	−	13.1559i	−0.274440	−	0.475343i
$767$	−6.46133			−0.233305
$768$	−0.357411	+	0.619053i	−0.0128969	+	0.0223382i
$769$	20.8735	−	36.1540i	0.752719	−	1.30375i	−0.193781	−	0.981045i	$-0.562075\pi$
$769$	20.8735	−	36.1540i	0.752719	−	1.30375i	0.946500	−	0.322703i	$-0.104591\pi$
$770$	−12.5514	−	21.7397i	−0.452321	−	0.783443i
$771$	−3.24419			−0.116837
$772$	0.0159944	−	0.0277031i	0.000575650	−	0.000997055i
$773$	18.5813			0.668322			0.334161	−	0.942516i	$-0.391547\pi$
$773$	18.5813			0.668322			0.334161	+	0.942516i	$0.391547\pi$
$774$	21.1105			0.758800
$775$	−0.0344107	+	1.42733i	−0.00123607	+	0.0512711i
$776$	2.98888			0.107295
$777$	−0.178725			−0.00641172
$778$	23.5607	−	40.8083i	0.844691	−	1.46305i
$779$	−7.62351			−0.273141
$780$	0.0326507	+	0.0565526i	0.00116908	+	0.00202491i
$781$	0.644110	−	1.11563i	0.0230481	−	0.0399204i
$782$	5.33876	−	9.24701i	0.190914	−	0.330672i
$783$	−2.15064			−0.0768574
$784$	2.34580	+	4.06305i	0.0837786	+	0.145109i
$785$	−10.0150	−	17.3464i	−0.357449	−	0.619120i
$786$	−1.57799	−	2.73316i	−0.0562851	−	0.0974886i
$787$	3.71349	−	6.43195i	0.132372	−	0.229274i	−0.792219	−	0.610237i	$-0.791074\pi$
$787$	3.71349	−	6.43195i	0.132372	−	0.229274i	0.924590	+	0.380963i	$0.124407\pi$
$788$	0.0532870	+	0.0922957i	0.00189827	+	0.00328790i
$789$	−0.708978	+	1.22799i	−0.0252403	+	0.0437175i
$790$	40.4423			1.43887
$791$	−17.1290			−0.609038
$792$	12.8269	−	22.2168i	0.455783	−	0.789439i
$793$	−2.95845	−	5.12418i	−0.105058	−	0.181965i
$794$	−4.82363	+	8.35478i	−0.171184	+	0.296500i
$795$	2.41620	+	4.18498i	0.0856938	+	0.148426i
$796$	−1.38175	−	2.39327i	−0.0489750	−	0.0848271i
$797$	−4.06670	−	7.04374i	−0.144050	−	0.249502i	0.784968	−	0.619536i	$-0.212679\pi$
$797$	−4.06670	−	7.04374i	−0.144050	−	0.249502i	−0.929018	+	0.370034i	$0.879346\pi$
$798$	4.94729			0.175132
$799$	−7.02293	+	12.1641i	−0.248454	+	0.430334i
$800$	0.116159	−	0.201193i	0.00410684	−	0.00711325i
$801$	6.60500	+	11.4402i	0.233376	+	0.404219i
$802$	11.0452			0.390021
$803$	−6.89425	+	11.9412i	−0.243293	+	0.421396i
$804$	0.344059			0.0121340
$805$	−29.6454			−1.04486
$806$	6.44676	+	3.93219i	0.227077	+	0.138506i
$807$	−4.77947			−0.168245
$808$	−33.9456			−1.19420
$809$	16.8619	−	29.2057i	0.592833	−	1.02682i	−0.401016	−	0.916071i	$-0.631343\pi$
$809$	16.8619	−	29.2057i	0.592833	−	1.02682i	0.993849	−	0.110746i	$-0.0353239\pi$
$810$	−25.6616			−0.901657
$811$	7.30735	+	12.6567i	0.256596	+	0.444437i	0.965328	−	0.261041i	$-0.0840658\pi$
$811$	7.30735	+	12.6567i	0.256596	+	0.444437i	−0.708732	+	0.705478i	$0.750732\pi$
$812$	−0.446081	+	0.772634i	−0.0156544	+	0.0271141i
$813$	−1.55443	+	2.69235i	−0.0545161	+	0.0944247i
$814$	−1.33153			−0.0466700
$815$	0.357045	+	0.618421i	0.0125068	+	0.0216623i
$816$	0.567850	+	0.983544i	0.0198787	+	0.0344309i
$817$	−17.8126	−	30.8523i	−0.623184	−	1.07939i
$818$	18.5960	−	32.2092i	0.650193	−	1.12617i
$819$	4.26717	+	7.39096i	0.149107	+	0.258261i
$820$	−0.196404	+	0.340182i	−0.00685873	+	0.0118797i
$821$	30.7838			1.07436			0.537181	−	0.843467i	$-0.319489\pi$
$821$	30.7838			1.07436			0.537181	+	0.843467i	$0.319489\pi$
$822$	−1.69546			−0.0591360
$823$	15.8659	−	27.4806i	0.553052	−	0.957914i	−0.445000	−	0.895531i	$-0.646796\pi$
$823$	15.8659	−	27.4806i	0.553052	−	0.957914i	0.998052	−	0.0623839i	$-0.0198703\pi$
$824$	9.40305	+	16.2866i	0.327571	+	0.567369i
$825$	0.0706948	−	0.122447i	0.00246128	−	0.00426306i
$826$	12.6114	+	21.8436i	0.438806	+	0.760035i
$827$	24.5922	+	42.5950i	0.855155	+	1.48117i	0.876501	+	0.481400i	$0.159872\pi$
$827$	24.5922	+	42.5950i	0.855155	+	1.48117i	−0.0213454	+	0.999772i	$0.506795\pi$
$828$	−1.12567	−	1.94971i	−0.0391196	−	0.0677572i
$829$	−11.2329			−0.390134			−0.195067	−	0.980790i	$-0.562492\pi$
$829$	−11.2329			−0.390134			−0.195067	+	0.980790i	$0.562492\pi$
$830$	11.5539	−	20.0119i	0.401041	−	0.694624i
$831$	−0.688377	+	1.19230i	−0.0238795	+	0.0413605i
$832$	−4.26748	−	7.39150i	−0.147948	−	0.256254i
$833$	−2.13800			−0.0740772
$834$	−0.199301	+	0.345199i	−0.00690121	+	0.0119533i
$835$	1.12995			0.0391036
$836$	−3.21710			−0.111266
$837$	−5.44451	+	2.97078i	−0.188190	+	0.102685i
$838$	−12.9841			−0.448528
$839$	8.02194			0.276948			0.138474	−	0.990366i	$-0.455780\pi$
$839$	8.02194			0.276948			0.138474	+	0.990366i	$0.455780\pi$
$840$	1.71518	−	2.97077i	0.0591792	−	0.102501i
$841$	−25.2727			−0.871473
$842$	−15.9042	−	27.5468i	−0.548094	−	0.949326i
$843$	1.41614	−	2.45282i	0.0487744	−	0.0844797i
$844$	1.47260	−	2.55062i	0.0506890	−	0.0877960i
$845$	−2.17797			−0.0749246
$846$	−16.9651	−	29.3844i	−0.583271	−	1.01026i
$847$	3.28464	+	5.68916i	0.112861	+	0.195482i
$848$	−21.7017	−	37.5884i	−0.745239	−	1.29079i
$849$	1.91195	−	3.31159i	0.0656180	−	0.113654i
$850$	−0.289489	−	0.501409i	−0.00992938	−	0.0171982i
$851$	−0.786240	+	1.36181i	−0.0269519	+	0.0466821i
$852$	0.0130816			0.000448168
$853$	7.75186			0.265419			0.132709	−	0.991155i	$-0.457632\pi$
$853$	7.75186			0.265419			0.132709	+	0.991155i	$0.457632\pi$
$854$	−11.5487	+	20.0030i	−0.395190	+	0.684489i
$855$	21.9135	+	37.9553i	0.749426	+	1.29804i
$856$	20.0531	−	34.7331i	0.685402	−	1.18715i
$857$	−5.72343	−	9.91327i	−0.195509	−	0.338631i	0.751558	−	0.659666i	$-0.229302\pi$
$857$	−5.72343	−	9.91327i	−0.195509	−	0.338631i	−0.947067	+	0.321036i	$0.895969\pi$
$858$	−0.373906	−	0.647624i	−0.0127649	−	0.0221095i
$859$	26.3748	+	45.6825i	0.899898	+	1.55867i	0.827624	+	0.561283i	$0.189692\pi$
$859$	26.3748	+	45.6825i	0.899898	+	1.55867i	0.0722740	+	0.997385i	$0.476974\pi$
$860$	−1.83562			−0.0625942
$861$	0.301895	−	0.522898i	0.0102886	−	0.0178203i
$862$	14.1136	−	24.4454i	0.480711	−	0.832615i
$863$	−25.6469	−	44.4217i	−0.873030	−	1.51213i	−0.858847	−	0.512233i	$-0.828819\pi$
$863$	−25.6469	−	44.4217i	−0.873030	−	1.51213i	−0.0141833	−	0.999899i	$-0.504515\pi$
$864$	1.00922			0.0343342
$865$	7.72367	−	13.3778i	0.262613	−	0.454859i
$866$	−41.6900			−1.41669
$867$	2.65713			0.0902408
$868$	−0.0620114	+	2.57218i	−0.00210480	+	0.0873054i
$869$	40.4239			1.37129
$870$	−1.06498			−0.0361064
$871$	−5.73764	+	9.93788i	−0.194412	+	0.336732i
$872$	17.8535			0.604596
$873$	−1.51221	−	2.61923i	−0.0511807	−	0.0886475i
$874$	21.7639	−	37.6962i	0.736176	−	1.27509i
$875$	−16.4756	+	28.5365i	−0.556976	+	0.964711i
$876$	−0.140019			−0.00473082
$877$	−9.24890	−	16.0196i	−0.312313	−	0.540942i	0.666549	−	0.745461i	$-0.267771\pi$
$877$	−9.24890	−	16.0196i	−0.312313	−	0.540942i	−0.978863	+	0.204518i	$0.934437\pi$
$878$	−0.781419	−	1.35346i	−0.0263716	−	0.0456770i
$879$	1.60423	+	2.77860i	0.0541092	+	0.0937199i
$880$	11.7459	−	20.3444i	0.395953	−	0.685810i
$881$	−5.05594	−	8.75714i	−0.170339	−	0.295036i	0.768199	−	0.640211i	$-0.221153\pi$
$881$	−5.05594	−	8.75714i	−0.170339	−	0.295036i	−0.938538	+	0.345175i	$0.887820\pi$
$882$	2.58235	−	4.47275i	0.0869521	−	0.150605i
$883$	2.26844			0.0763390			0.0381695	−	0.999271i	$-0.487847\pi$
$883$	2.26844			0.0763390			0.0381695	+	0.999271i	$0.487847\pi$
$884$	0.267281			0.00898964
$885$	1.31400	−	2.27591i	0.0441696	−	0.0765040i
$886$	−13.2951	−	23.0277i	−0.446657	−	0.773632i
$887$	−7.54541	+	13.0690i	−0.253350	+	0.438815i	−0.964446	−	0.264280i	$-0.914866\pi$
$887$	−7.54541	+	13.0690i	−0.253350	+	0.438815i	0.711096	+	0.703095i	$0.248199\pi$
$888$	−0.0909780	−	0.157578i	−0.00305302	−	0.00528799i
$889$	−11.3051	−	19.5811i	−0.379162	−	0.656728i
$890$	6.58000	+	11.3969i	0.220562	+	0.382025i
$891$	−25.6499			−0.859305
$892$	1.04575	−	1.81129i	0.0350142	−	0.0606463i
$893$	−28.6296	+	49.5879i	−0.958053	+	1.65940i
$894$	−1.82437	−	3.15991i	−0.0610162	−	0.105683i
$895$	−43.2098			−1.44434
$896$	−14.0512	+	24.3373i	−0.469416	+	0.813053i
$897$	−0.883136			−0.0294871
$898$	−3.52356			−0.117583
$899$	9.43595	−	5.14869i	0.314706	−	0.171719i
$900$	−0.122076			−0.00406921
$901$	19.7792			0.658942
$902$	2.24916	−	3.89567i	0.0748890	−	0.129711i
$903$	2.82156			0.0938955
$904$	−8.71935	−	15.1024i	−0.290001	−	0.502297i
$905$	−14.8812	+	25.7750i	−0.494668	+	0.856790i
$906$	−1.51629	+	2.62630i	−0.0503755	+	0.0872528i
$907$	−17.0425			−0.565888			−0.282944	−	0.959136i	$-0.591311\pi$
$907$	−17.0425			−0.565888			−0.282944	+	0.959136i	$0.591311\pi$
$908$	1.79777	+	3.11383i	0.0596612	+	0.103336i
$909$	17.1746	+	29.7474i	0.569647	+	0.986658i
$910$	4.25102	+	7.36299i	0.140920	+	0.244081i
$911$	−19.4661	+	33.7163i	−0.644942	+	1.11707i	0.339373	+	0.940652i	$0.389785\pi$
$911$	−19.4661	+	33.7163i	−0.644942	+	1.11707i	−0.984315	+	0.176420i	$0.943548\pi$
$912$	2.31489	+	4.00950i	0.0766536	+	0.132768i
$913$	11.5486	−	20.0028i	0.382204	−	0.661996i
$914$	−49.9812			−1.65323
$915$	2.40656			0.0795584
$916$	2.09766	−	3.63326i	0.0693088	−	0.120046i
$917$	17.9324	+	31.0598i	0.592179	+	1.02568i
$918$	1.25757	−	2.17818i	0.0415061	−	0.0718906i
$919$	−2.39834	−	4.15404i	−0.0791138	−	0.137029i	0.823754	−	0.566947i	$-0.191876\pi$
$919$	−2.39834	−	4.15404i	−0.0791138	−	0.137029i	−0.902868	+	0.429918i	$0.858542\pi$
$920$	−15.0907	−	26.1378i	−0.497525	−	0.861738i
$921$	−2.56954	−	4.45058i	−0.0846693	−	0.146652i
$922$	43.1632			1.42150
$923$	−0.218153	+	0.377852i	−0.00718059	+	0.0124372i
$924$	0.127399	−	0.220661i	0.00419111	−	0.00725922i
$925$	0.0426330	+	0.0738425i	0.00140176	+	0.00242793i
$926$	−9.34785			−0.307189
$927$	9.51488	−	16.4803i	0.312510	−	0.541283i
$928$	−1.74908			−0.0574165
$929$	0.443552			0.0145525			0.00727624	−	0.999974i	$-0.497684\pi$
$929$	0.443552			0.0145525			0.00727624	+	0.999974i	$0.497684\pi$
$930$	−2.69609	+	1.47112i	−0.0884084	+	0.0482398i
$931$	−8.71573			−0.285646
$932$	−1.73138			−0.0567133
$933$	2.24319	−	3.88532i	0.0734388	−	0.127200i
$934$	−44.4972			−1.45599
$935$	5.35267	+	9.27110i	0.175051	+	0.303198i
$936$	−4.34432	+	7.52458i	−0.141999	+	0.245949i
$937$	11.3458	−	19.6514i	0.370650	−	0.641984i	−0.619016	−	0.785378i	$-0.712468\pi$
$937$	11.3458	−	19.6514i	0.370650	−	0.641984i	0.989666	+	0.143394i	$0.0458017\pi$
$938$	44.7955			1.46262
$939$	0.978818	+	1.69536i	0.0319425	+	0.0553261i
$940$	1.47517	+	2.55506i	0.0481146	+	0.0833370i
$941$	1.12487	+	1.94834i	0.0366698	+	0.0635140i	0.883778	−	0.467907i	$-0.154992\pi$
$941$	1.12487	+	1.94834i	0.0366698	+	0.0635140i	−0.847108	+	0.531421i	$0.821658\pi$
$942$	−1.16464	+	2.01721i	−0.0379459	+	0.0657242i
$943$	−2.65617	−	4.60063i	−0.0864969	−	0.149817i
$944$	−11.8020	+	20.4417i	−0.384122	+	0.665319i
$945$	−6.98313			−0.227161
$946$	21.0210			0.683452
$947$	−4.96238	+	8.59509i	−0.161256	+	0.279303i	−0.935319	−	0.353805i	$-0.884888\pi$
$947$	−4.96238	+	8.59509i	−0.161256	+	0.279303i	0.774064	+	0.633108i	$0.218221\pi$
$948$	0.205248	+	0.355500i	0.00666615	+	0.0115461i
$949$	2.33501	−	4.04435i	0.0757976	−	0.131285i
$950$	−1.18013	−	2.04404i	−0.0382883	−	0.0663173i
$951$	2.96142	+	5.12933i	0.0960306	+	0.166330i
$952$	−7.02029	−	12.1595i	−0.227529	−	0.394092i
$953$	−35.1157			−1.13751			−0.568754	−	0.822507i	$-0.692575\pi$
$953$	−35.1157			−1.13751			−0.568754	+	0.822507i	$0.692575\pi$
$954$	−23.8900	+	41.3788i	−0.773469	+	1.33969i
$955$	26.2343	−	45.4392i	0.848923	−	1.47038i
$956$	−1.76992	−	3.06559i	−0.0572433	−	0.0991483i
$957$	−1.06450			−0.0344104
$958$	−12.3779	+	21.4392i	−0.399913	+	0.692670i
$959$	19.2673			0.622174
$960$	3.47140			0.112039
$961$	16.7757	−	26.0687i	0.541152	−	0.840925i
$962$	0.450973			0.0145400
$963$	−40.5833			−1.30778
$964$	0.722220	−	1.25092i	0.0232611	−	0.0402895i
$965$	−0.433941			−0.0139691
$966$	1.72373	+	2.98558i	0.0554600	+	0.0960596i
$967$	11.0599	−	19.1563i	0.355661	−	0.616024i	−0.631570	−	0.775319i	$-0.717589\pi$
$967$	11.0599	−	19.1563i	0.355661	−	0.616024i	0.987231	+	0.159296i	$0.0509223\pi$
$968$	−3.34402	+	5.79201i	−0.107481	+	0.186162i
$969$	−2.10982			−0.0677773
$970$	−1.50649	−	2.60932i	−0.0483705	−	0.0837801i
$971$	1.32880	+	2.30156i	0.0426434	+	0.0738605i	0.886559	−	0.462615i	$-0.153089\pi$
$971$	1.32880	+	2.30156i	0.0426434	+	0.0738605i	−0.843916	+	0.536475i	$0.819755\pi$
$972$	−0.398510	−	0.690239i	−0.0127822	−	0.0221394i
$973$	2.26486	−	3.92286i	0.0726082	−	0.125761i
$974$	10.8770	+	18.8395i	0.348522	+	0.603658i
$975$	−0.0239436	+	0.0414715i	−0.000766808	+	0.00132815i
$976$	−21.6151			−0.691883
$977$	9.75901			0.312218			0.156109	−	0.987740i	$-0.450105\pi$
$977$	9.75901			0.312218			0.156109	+	0.987740i	$0.450105\pi$
$978$	0.0415207	−	0.0719160i	0.00132769	−	0.00229962i
$979$	6.57700	+	11.3917i	0.210202	+	0.364080i
$980$	−0.224543	+	0.388920i	−0.00717276	+	0.0124236i
$981$	−9.03292	−	15.6455i	−0.288399	−	0.499522i
$982$	−9.28212	−	16.0771i	−0.296204	−	0.513041i
$983$	4.30061	+	7.44888i	0.137168	+	0.237582i	0.926424	−	0.376483i	$-0.122867\pi$
$983$	4.30061	+	7.44888i	0.137168	+	0.237582i	−0.789255	+	0.614065i	$0.789533\pi$
$984$	0.614706			0.0195961
$985$	0.722860	−	1.25203i	0.0230322	−	0.0398930i
$986$	−2.17952	+	3.77503i	−0.0694099	+	0.120221i
$987$	−2.26750	−	3.92742i	−0.0721752	−	0.125011i
$988$	1.08960			0.0346647
$989$	12.4125	−	21.4991i	0.394694	−	0.683630i
$990$	−25.8606			−0.821903
$991$	41.2017			1.30882			0.654408	−	0.756142i	$-0.272918\pi$
$991$	41.2017			1.30882			0.654408	+	0.756142i	$0.272918\pi$
$992$	−4.42795	+	2.41610i	−0.140587	+	0.0767111i
$993$	−1.52504			−0.0483958
$994$	1.70319			0.0540218
$995$	−18.7441	+	32.4657i	−0.594227	+	1.02923i
$996$	0.234548			0.00743193
$997$	6.51742	+	11.2885i	0.206409	+	0.357511i	0.950581	−	0.310478i	$-0.100489\pi$
$997$	6.51742	+	11.2885i	0.206409	+	0.357511i	−0.744172	+	0.667988i	$0.767156\pi$
$998$	−4.82403	+	8.35546i	−0.152702	+	0.264488i
$999$	−0.185203	+	0.320780i	−0.00585955	+	0.0101490i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.b.222.12	yes	34
31.25	even	3	inner	403.2.h.b.118.12	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.b.118.12	✓	34	31.25	even	3	inner
403.2.h.b.222.12	yes	34	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+1.35626 q^{2} +(0.0933728 - 0.161726i) q^{3} -0.160553 q^{4} +(1.08899 + 1.88618i) q^{5} +(0.126638 - 0.219343i) q^{6} +(-1.43912 + 2.49263i) q^{7} -2.93028 q^{8} +(1.48256 + 2.56787i) q^{9} +O(q^{10})\)	\(q+1.35626 q^{2} +(0.0933728 - 0.161726i) q^{3} -0.160553 q^{4} +(1.08899 + 1.88618i) q^{5} +(0.126638 - 0.219343i) q^{6} +(-1.43912 + 2.49263i) q^{7} -2.93028 q^{8} +(1.48256 + 2.56787i) q^{9} +(1.47695 + 2.55816i) q^{10} +(1.47628 + 2.55699i) q^{11} +(-0.0149913 + 0.0259657i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-1.95182 + 3.38066i) q^{14} +0.406727 q^{15} -3.65312 q^{16} +(0.832376 - 1.44172i) q^{17} +(2.01074 + 3.48271i) q^{18} +(3.39325 - 5.87729i) q^{19} +(-0.174840 - 0.302832i) q^{20} +(0.268749 + 0.465488i) q^{21} +(2.00222 + 3.46795i) q^{22} +4.72909 q^{23} +(-0.273608 + 0.473903i) q^{24} +(0.128215 - 0.222075i) q^{25} +(-0.678131 - 1.17456i) q^{26} +1.11396 q^{27} +(0.231056 - 0.400200i) q^{28} -1.93062 q^{29} +0.551628 q^{30} +(-4.88752 + 2.66686i) q^{31} +0.905970 q^{32} +0.551377 q^{33} +(1.12892 - 1.95535i) q^{34} -6.26873 q^{35} +(-0.238030 - 0.412281i) q^{36} +(-0.166256 + 0.287964i) q^{37} +(4.60214 - 7.97114i) q^{38} -0.186746 q^{39} +(-3.19103 - 5.52703i) q^{40} +(-0.561667 - 0.972836i) q^{41} +(0.364495 + 0.631323i) q^{42} +(2.62471 - 4.54613i) q^{43} +(-0.237022 - 0.410533i) q^{44} +(-3.22898 + 5.59276i) q^{45} +6.41388 q^{46} -8.43721 q^{47} +(-0.341102 + 0.590805i) q^{48} +(-0.642137 - 1.11221i) q^{49} +(0.173893 - 0.301192i) q^{50} +(-0.155443 - 0.269234i) q^{51} +(0.0802766 + 0.139043i) q^{52} +(5.94060 + 10.2894i) q^{53} +1.51082 q^{54} +(-3.21530 + 5.56906i) q^{55} +(4.21702 - 7.30410i) q^{56} +(-0.633675 - 1.09756i) q^{57} -2.61843 q^{58} +(3.23067 - 5.59568i) q^{59} -0.0653013 q^{60} +5.91690 q^{61} +(-6.62876 + 3.61696i) q^{62} -8.53435 q^{63} +8.53497 q^{64} +(1.08899 - 1.88618i) q^{65} +0.747812 q^{66} +(-5.73764 - 9.93788i) q^{67} +(-0.133641 + 0.231472i) q^{68} +(0.441568 - 0.764819i) q^{69} -8.50205 q^{70} +(-0.218153 - 0.377852i) q^{71} +(-4.34432 - 7.52458i) q^{72} +(2.33501 + 4.04435i) q^{73} +(-0.225487 + 0.390554i) q^{74} +(-0.0239436 - 0.0414715i) q^{75} +(-0.544798 + 0.943617i) q^{76} -8.49818 q^{77} -0.253276 q^{78} +(6.84557 - 11.8569i) q^{79} +(-3.97820 - 6.89044i) q^{80} +(-4.34368 + 7.52347i) q^{81} +(-0.761767 - 1.31942i) q^{82} +(-3.91140 - 6.77474i) q^{83} +(-0.0431486 - 0.0747356i) q^{84} +3.62579 q^{85} +(3.55979 - 6.16574i) q^{86} +(-0.180267 + 0.312232i) q^{87} +(-4.32591 - 7.49269i) q^{88} +4.45512 q^{89} +(-4.37935 + 7.58525i) q^{90} +2.87824 q^{91} -0.759271 q^{92} +(-0.0250597 + 1.03945i) q^{93} -11.4431 q^{94} +14.7808 q^{95} +(0.0845929 - 0.146519i) q^{96} -1.02000 q^{97} +(-0.870906 - 1.50845i) q^{98} +(-4.37736 + 7.58180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Introduction

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