LMFDB - Embedded newform 403.2.l.c.25.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(25,403)]

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([3, 2]))

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

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

chi := DirichletCharacter("403.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.4
Character	$\chi$	$=$	403.25
Dual form			403.2.l.c.129.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42820i q^{2} +(1.37274 + 2.37765i) q^{3} -3.89617 q^{4} +(-2.09477 - 1.20941i) q^{5} +(5.77342 - 3.33328i) q^{6} +(-4.33186 + 2.50100i) q^{7} +4.60429i q^{8} +(-2.26881 + 3.92970i) q^{9} +O(q^{10})$	\(q-2.42820i q^{2} +(1.37274 + 2.37765i) q^{3} -3.89617 q^{4} +(-2.09477 - 1.20941i) q^{5} +(5.77342 - 3.33328i) q^{6} +(-4.33186 + 2.50100i) q^{7} +4.60429i q^{8} +(-2.26881 + 3.92970i) q^{9} +(-2.93671 + 5.08652i) q^{10} +(4.09276 + 2.36296i) q^{11} +(-5.34842 - 9.26373i) q^{12} +(-0.352975 + 3.58823i) q^{13} +(6.07293 + 10.5186i) q^{14} -6.64083i q^{15} +3.38782 q^{16} +(-1.24548 - 2.15724i) q^{17} +(9.54210 + 5.50914i) q^{18} +(-4.12975 + 2.38431i) q^{19} +(8.16158 + 4.71209i) q^{20} +(-11.8930 - 6.86643i) q^{21} +(5.73774 - 9.93806i) q^{22} +0.407695 q^{23} +(-10.9474 + 6.32048i) q^{24} +(0.425368 + 0.736759i) q^{25} +(8.71296 + 0.857096i) q^{26} -4.22150 q^{27} +(16.8777 - 9.74432i) q^{28} +0.937479 q^{29} -16.1253 q^{30} +(-1.51826 + 5.35676i) q^{31} +0.982276i q^{32} +12.9749i q^{33} +(-5.23821 + 3.02428i) q^{34} +12.0990 q^{35} +(8.83968 - 15.3108i) q^{36} +(2.00430 - 1.15719i) q^{37} +(5.78959 + 10.0279i) q^{38} +(-9.01610 + 4.08645i) q^{39} +(5.56850 - 9.64493i) q^{40} +(-8.68112 - 5.01205i) q^{41} +(-16.6731 + 28.8786i) q^{42} +(0.428046 + 0.741397i) q^{43} +(-15.9461 - 9.20649i) q^{44} +(9.50527 - 5.48787i) q^{45} -0.989966i q^{46} -2.40762i q^{47} +(4.65058 + 8.05504i) q^{48} +(9.00999 - 15.6058i) q^{49} +(1.78900 - 1.03288i) q^{50} +(3.41944 - 5.92264i) q^{51} +(1.37525 - 13.9804i) q^{52} +(-5.12189 + 8.87137i) q^{53} +10.2507i q^{54} +(-5.71559 - 9.89970i) q^{55} +(-11.5153 - 19.9451i) q^{56} +(-11.3381 - 6.54606i) q^{57} -2.27639i q^{58} +(9.00882 - 5.20124i) q^{59} +25.8738i q^{60} -4.35112 q^{61} +(13.0073 + 3.68664i) q^{62} -22.6972i q^{63} +9.16080 q^{64} +(5.07906 - 7.08962i) q^{65} +31.5056 q^{66} +(7.21500 + 4.16558i) q^{67} +(4.85261 + 8.40497i) q^{68} +(0.559658 + 0.969356i) q^{69} -29.3788i q^{70} +(-3.24465 - 1.87330i) q^{71} +(-18.0935 - 10.4463i) q^{72} +(5.38151 + 3.10702i) q^{73} +(-2.80988 - 4.86686i) q^{74} +(-1.16784 + 2.02275i) q^{75} +(16.0902 - 9.28968i) q^{76} -23.6390 q^{77} +(9.92272 + 21.8929i) q^{78} +(-3.94652 - 6.83557i) q^{79} +(-7.09669 - 4.09728i) q^{80} +(1.01142 + 1.75184i) q^{81} +(-12.1703 + 21.0795i) q^{82} +(3.55686 + 2.05355i) q^{83} +(46.3372 + 26.7528i) q^{84} +6.02522i q^{85} +(1.80026 - 1.03938i) q^{86} +(1.28691 + 2.22900i) q^{87} +(-10.8798 + 18.8443i) q^{88} +5.15881i q^{89} +(-13.3257 - 23.0807i) q^{90} +(-7.44513 - 16.4265i) q^{91} -1.58845 q^{92} +(-14.8207 + 3.74354i) q^{93} -5.84620 q^{94} +11.5345 q^{95} +(-2.33551 + 1.34841i) q^{96} -4.77033i q^{97} +(-37.8940 - 21.8781i) q^{98} +(-18.5714 + 10.7222i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

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 $

$2$		−	2.42820i		−	1.71700i	−0.512814	−	0.858500i	$-0.671397\pi$
$2$		−	2.42820i		−	1.71700i	0.512814	−	0.858500i	$-0.328603\pi$
$3$	1.37274	+	2.37765i	0.792550	+	1.37274i	0.924383	+	0.381465i	$0.124580\pi$
$3$	1.37274	+	2.37765i	0.792550	+	1.37274i	−0.131834	+	0.991272i	$0.542086\pi$
$4$	−3.89617			−1.94809
$5$	−2.09477	−	1.20941i	−0.936809	−	0.540867i	−0.0478502	−	0.998855i	$-0.515237\pi$
$5$	−2.09477	−	1.20941i	−0.936809	−	0.540867i	−0.888958	+	0.457988i	$0.848570\pi$
$6$	5.77342	−	3.33328i	2.35699	−	1.36081i
$7$	−4.33186	+	2.50100i	−1.63729	+	0.945289i	−0.655527	+	0.755172i	$0.727553\pi$
$7$	−4.33186	+	2.50100i	−1.63729	+	0.945289i	−0.981762	+	0.190117i	$0.939113\pi$
$8$			4.60429i			1.62786i
$9$	−2.26881	+	3.92970i	−0.756270	+	1.30990i
$10$	−2.93671	+	5.08652i	−0.928668	+	1.60850i
$11$	4.09276	+	2.36296i	1.23401	+	0.712459i	0.967864	−	0.251473i	$-0.0809149\pi$
$11$	4.09276	+	2.36296i	1.23401	+	0.712459i	0.266150	+	0.963932i	$0.414248\pi$
$12$	−5.34842	−	9.26373i	−1.54396	−	2.67421i
$13$	−0.352975	+	3.58823i	−0.0978977	+	0.995196i
$13$	−0.352975	+	3.58823i	−0.0978977	+	0.995196i
$14$	6.07293	+	10.5186i	1.62306	+	2.81122i
$15$		−	6.64083i		−	1.71466i
$16$	3.38782			0.846955
$17$	−1.24548	−	2.15724i	−0.302074	−	0.523207i	0.674532	−	0.738246i	$-0.264346\pi$
$17$	−1.24548	−	2.15724i	−0.302074	−	0.523207i	−0.976606	+	0.215039i	$0.931012\pi$
$18$	9.54210	+	5.50914i	2.24910	+	1.29852i
$19$	−4.12975	+	2.38431i	−0.947429	+	0.546998i	−0.892281	−	0.451480i	$-0.850896\pi$
$19$	−4.12975	+	2.38431i	−0.947429	+	0.546998i	−0.0551474	+	0.998478i	$0.517563\pi$
$20$	8.16158	+	4.71209i	1.82498	+	1.05366i
$21$	−11.8930	−	6.86643i	−2.59526	−	1.49838i
$22$	5.73774	−	9.93806i	1.22329	−	2.11880i
$23$	0.407695			0.0850103			0.0425051	−	0.999096i	$-0.486466\pi$
$23$	0.407695			0.0850103			0.0425051	+	0.999096i	$0.486466\pi$
$24$	−10.9474	+	6.32048i	−2.23463	+	1.29016i
$25$	0.425368	+	0.736759i	0.0850736	+	0.147352i
$26$	8.71296	+	0.857096i	1.70875	+	0.168090i
$27$	−4.22150			−0.812429
$28$	16.8777	−	9.74432i	3.18958	−	1.84150i
$29$	0.937479			0.174085			0.0870427	−	0.996205i	$-0.472258\pi$
$29$	0.937479			0.174085			0.0870427	+	0.996205i	$0.472258\pi$
$30$	−16.1253			−2.94406
$31$	−1.51826	+	5.35676i	−0.272687	+	0.962103i
$31$	−1.51826	+	5.35676i	−0.272687	+	0.962103i
$32$			0.982276i			0.173643i
$33$			12.9749i			2.25864i
$34$	−5.23821	+	3.02428i	−0.898346	+	0.518660i
$35$	12.0990			2.04510
$36$	8.83968	−	15.3108i	1.47328	−	2.55180i
$37$	2.00430	−	1.15719i	0.329506	−	0.190240i	−0.326116	−	0.945330i	$-0.605740\pi$
$37$	2.00430	−	1.15719i	0.329506	−	0.190240i	0.655622	+	0.755090i	$0.272407\pi$
$38$	5.78959	+	10.0279i	0.939195	+	1.62673i
$39$	−9.01610	+	4.08645i	−1.44373	+	0.654355i
$40$	5.56850	−	9.64493i	0.880457	−	1.52500i
$41$	−8.68112	−	5.01205i	−1.35576	−	0.782751i	−0.366714	−	0.930334i	$-0.619517\pi$
$41$	−8.68112	−	5.01205i	−1.35576	−	0.782751i	−0.989050	+	0.147583i	$0.952851\pi$
$42$	−16.6731	+	28.8786i	−2.57271	+	4.45607i
$43$	0.428046	+	0.741397i	0.0652764	+	0.113062i	0.896817	−	0.442403i	$-0.145874\pi$
$43$	0.428046	+	0.741397i	0.0652764	+	0.113062i	−0.831540	+	0.555465i	$0.812540\pi$
$44$	−15.9461	−	9.20649i	−2.40397	−	1.38793i
$45$	9.50527	−	5.48787i	1.41696	−	0.818083i
$46$		−	0.989966i		−	0.145963i
$47$		−	2.40762i		−	0.351188i	−0.984463	−	0.175594i	$-0.943815\pi$
$47$		−	2.40762i		−	0.351188i	0.984463	−	0.175594i	$-0.0561846\pi$
$48$	4.65058	+	8.05504i	0.671254	+	1.16265i
$49$	9.00999	−	15.6058i	1.28714	−	2.22939i
$50$	1.78900	−	1.03288i	0.253003	−	0.146071i
$51$	3.41944	−	5.92264i	0.478817	−	0.829335i
$52$	1.37525	−	13.9804i	0.190713	−	1.93873i
$53$	−5.12189	+	8.87137i	−0.703546	+	1.21858i	0.263668	+	0.964613i	$0.415068\pi$
$53$	−5.12189	+	8.87137i	−0.703546	+	1.21858i	−0.967214	+	0.253963i	$0.918266\pi$
$54$			10.2507i			1.39494i
$55$	−5.71559	−	9.89970i	−0.770690	−	1.33487i
$56$	−11.5153	−	19.9451i	−1.53880	−	2.66528i
$57$	−11.3381	−	6.54606i	−1.50177	−	0.867047i
$58$		−	2.27639i		−	0.298905i
$59$	9.00882	−	5.20124i	1.17285	−	0.677144i	0.218499	−	0.975837i	$-0.429884\pi$
$59$	9.00882	−	5.20124i	1.17285	−	0.677144i	0.954349	+	0.298693i	$0.0965507\pi$
$60$			25.8738i			3.34030i
$61$	−4.35112			−0.557104			−0.278552	−	0.960421i	$-0.589854\pi$
$61$	−4.35112			−0.557104			−0.278552	+	0.960421i	$0.589854\pi$
$62$	13.0073	+	3.68664i	1.65193	+	0.468203i
$63$		−	22.6972i		−	2.85958i
$64$	9.16080			1.14510
$65$	5.07906	−	7.08962i	0.629980	−	0.879359i
$66$	31.5056			3.87808
$67$	7.21500	+	4.16558i	0.881453	+	0.508907i	0.871137	−	0.491040i	$-0.163383\pi$
$67$	7.21500	+	4.16558i	0.881453	+	0.508907i	0.0103155	+	0.999947i	$0.496716\pi$
$68$	4.85261	+	8.40497i	0.588466	+	1.01925i
$69$	0.559658	+	0.969356i	0.0673749	+	0.116697i
$70$		−	29.3788i		−	3.51144i
$71$	−3.24465	−	1.87330i	−0.385069	−	0.222320i	0.294952	−	0.955512i	$-0.404696\pi$
$71$	−3.24465	−	1.87330i	−0.385069	−	0.222320i	−0.680021	+	0.733192i	$0.738030\pi$
$72$	−18.0935	−	10.4463i	−2.13234	−	1.23111i
$73$	5.38151	+	3.10702i	0.629858	+	0.363649i	0.780697	−	0.624910i	$-0.214864\pi$
$73$	5.38151	+	3.10702i	0.629858	+	0.363649i	−0.150839	+	0.988558i	$0.548198\pi$
$74$	−2.80988	−	4.86686i	−0.326642	−	0.565761i
$75$	−1.16784	+	2.02275i	−0.134850	+	0.233567i
$76$	16.0902	−	9.28968i	1.84567	−	1.06560i
$77$	−23.6390			−2.69392
$78$	9.92272	+	21.8929i	1.12353	+	2.47889i
$79$	−3.94652	−	6.83557i	−0.444018	−	0.769062i	0.553965	−	0.832540i	$-0.313114\pi$
$79$	−3.94652	−	6.83557i	−0.444018	−	0.769062i	−0.997983	+	0.0634779i	$0.979781\pi$
$80$	−7.09669	−	4.09728i	−0.793434	−	0.458090i
$81$	1.01142	+	1.75184i	0.112380	+	0.194649i
$82$	−12.1703	+	21.0795i	−1.34398	+	2.32785i
$83$	3.55686	+	2.05355i	0.390416	+	0.225407i	0.682340	−	0.731035i	$-0.260962\pi$
$83$	3.55686	+	2.05355i	0.390416	+	0.225407i	−0.291924	+	0.956441i	$0.594296\pi$
$84$	46.3372	+	26.7528i	5.05580	+	2.91897i
$85$			6.02522i			0.653527i
$86$	1.80026	−	1.03938i	0.194127	−	0.112079i
$87$	1.28691	+	2.22900i	0.137971	+	0.238973i
$88$	−10.8798	+	18.8443i	−1.15979	+	2.00881i
$89$			5.15881i			0.546833i	0.961896	+	0.273417i	$0.0881538\pi$
$89$			5.15881i			0.546833i	−0.961896	+	0.273417i	$0.911846\pi$
$90$	−13.3257	−	23.0807i	−1.40465	−	2.43292i
$91$	−7.44513	−	16.4265i	−0.780461	−	1.72196i
$92$	−1.58845			−0.165607
$93$	−14.8207	+	3.74354i	−1.53683	+	0.388187i
$94$	−5.84620			−0.602989
$95$	11.5345			1.18341
$96$	−2.33551	+	1.34841i	−0.238367	+	0.137621i
$97$		−	4.77033i		−	0.484354i	−0.970232	−	0.242177i	$-0.922139\pi$
$97$		−	4.77033i		−	0.484354i	0.970232	−	0.242177i	$-0.0778614\pi$
$98$	−37.8940	−	21.8781i	−3.82787	−	2.21002i
$99$	−18.5714	+	10.7222i	−1.86650	+	1.07762i
$100$	−1.65731	−	2.87054i	−0.165731	−	0.287054i
$101$	−1.53159			−0.152399			−0.0761997	−	0.997093i	$-0.524279\pi$
$101$	−1.53159			−0.152399			−0.0761997	+	0.997093i	$0.524279\pi$
$102$	−14.3814	−	8.30309i	−1.42397	−	0.822128i
$103$	0.670292	−	1.16098i	0.0660458	−	0.114395i	−0.831112	−	0.556106i	$-0.812295\pi$
$103$	0.670292	−	1.16098i	0.0660458	−	0.114395i	0.897157	+	0.441711i	$0.145628\pi$
$104$	−16.5213	−	1.62520i	−1.62004	−	0.159364i
$105$	16.6087	+	28.7671i	1.62084	+	2.80738i
$106$	21.5415	+	12.4370i	2.09230	+	1.20799i
$107$	8.91378	+	15.4391i	0.861728	+	1.49256i	0.870260	+	0.492593i	$0.163951\pi$
$107$	8.91378	+	15.4391i	0.861728	+	1.49256i	−0.00853215	+	0.999964i	$0.502716\pi$
$108$	16.4477			1.58268
$109$			14.6311i			1.40140i	0.713454	+	0.700702i	$0.247130\pi$
$109$			14.6311i			1.40140i	−0.713454	+	0.700702i	$0.752870\pi$
$110$	−24.0385	+	13.8786i	−2.29198	+	1.32327i
$111$	5.50276	+	3.17702i	0.522299	+	0.301550i
$112$	−14.6755	+	8.47293i	−1.38671	+	0.800617i
$113$	−0.911585	+	1.57891i	−0.0857547	+	0.148532i	−0.905713	−	0.423892i	$-0.860663\pi$
$113$	−0.911585	+	1.57891i	−0.0857547	+	0.148532i	0.819958	+	0.572424i	$0.193997\pi$
$114$	−15.8952	+	27.5312i	−1.48872	+	2.57854i
$115$	−0.854026	−	0.493072i	−0.0796384	−	0.0459792i
$116$	−3.65258			−0.339133
$117$	−13.2998	−	9.52811i	−1.22957	−	0.880874i
$118$	−12.6297	−	21.8752i	−1.16266	−	2.01378i
$119$	10.7905	+	6.22990i	0.989164	+	0.571094i
$120$	30.5763			2.79123
$121$	5.66714	+	9.81578i	0.515195	+	0.892343i
$122$			10.5654i			0.956547i
$123$		−	27.5209i		−	2.48148i
$124$	5.91539	−	20.8709i	0.531218	−	1.87426i
$125$			10.0364i			0.897680i
$126$	−55.1134			−4.90989
$127$	7.21809	+	12.5021i	0.640502	+	1.10938i	0.985321	+	0.170713i	$0.0546071\pi$
$127$	7.21809	+	12.5021i	0.640502	+	1.10938i	−0.344819	+	0.938669i	$0.612060\pi$
$128$		−	20.2797i		−	1.79249i
$129$	−1.17519	+	2.03549i	−0.103470	+	0.179215i
$130$	−17.2150	−	12.3330i	−1.50986	−	1.08168i
$131$	0.938752	+	1.62597i	0.0820191	+	0.142061i	0.904117	−	0.427285i	$-0.140530\pi$
$131$	0.938752	+	1.62597i	0.0820191	+	0.142061i	−0.822098	+	0.569346i	$0.807196\pi$
$132$		−	50.5524i		−	4.40002i
$133$	11.9263	−	20.6570i	1.03414	−	1.79119i
$134$	10.1149	−	17.5195i	0.873793	−	1.51345i
$135$	8.84307	+	5.10555i	0.761090	+	0.439416i
$136$	9.93256	−	5.73457i	0.851710	−	0.491735i
$137$	3.83919	+	2.21656i	0.328004	+	0.189373i	0.654955	−	0.755668i	$-0.272688\pi$
$137$	3.83919	+	2.21656i	0.328004	+	0.189373i	−0.326951	+	0.945041i	$0.606021\pi$
$138$	2.35379	−	1.35896i	0.200368	−	0.115683i
$139$	0.397788			0.0337399			0.0168700	−	0.999858i	$-0.494630\pi$
$139$	0.397788			0.0337399			0.0168700	+	0.999858i	$0.494630\pi$
$140$	−47.1397			−3.98403
$141$	5.72448	−	3.30503i	0.482088	−	0.278334i
$142$	−4.54875	+	7.87867i	−0.381723	+	0.661163i
$143$	−9.92349	+	13.8517i	−0.829844	+	1.15834i
$144$	−7.68632	+	13.3131i	−0.640527	+	1.10942i
$145$	−1.96380	−	1.13380i	−0.163085	−	0.0941570i
$146$	7.54447	−	13.0674i	0.624385	−	1.08147i
$147$	49.4734			4.08049
$148$	−7.80912	+	4.50860i	−0.641906	+	0.370604i
$149$	3.07431	−	1.77496i	0.251857	−	0.145410i	−0.368757	−	0.929526i	$-0.620217\pi$
$149$	3.07431	−	1.77496i	0.251857	−	0.145410i	0.620614	+	0.784116i	$0.286883\pi$
$150$	4.91165	+	2.83574i	0.401035	+	0.231538i
$151$		−	17.6023i		−	1.43245i	−0.697869	−	0.716226i	$-0.745868\pi$
$151$		−	17.6023i		−	1.43245i	0.697869	−	0.716226i	$-0.254132\pi$
$152$	−10.9781	−	19.0146i	−0.890439	−	1.54228i
$153$	11.3031			0.913798
$154$			57.4004i			4.62545i
$155$	9.65894	−	9.38497i	0.775825	−	0.753819i
$156$	35.1283	−	15.9215i	2.81251	−	1.27474i
$157$	−21.9248			−1.74979			−0.874894	−	0.484314i	$-0.839069\pi$
$157$	−21.9248			−1.74979			−0.874894	+	0.484314i	$0.839069\pi$
$158$	−16.5982	+	9.58295i	−1.32048	+	0.762379i
$159$	−28.1240			−2.23038
$160$	1.18798	−	2.05764i	0.0939180	−	0.162671i
$161$	−1.76608	+	1.01964i	−0.139186	+	0.0803593i
$162$	4.25382	−	2.45594i	0.334211	−	0.192957i
$163$			9.82664i			0.769682i	0.922983	+	0.384841i	$0.125744\pi$
$163$			9.82664i			0.769682i	−0.922983	+	0.384841i	$0.874256\pi$
$164$	33.8232	+	19.5278i	2.64115	+	1.52487i
$165$	15.6920	−	27.1794i	1.22162	−	2.11591i
$166$	4.98645	−	8.63678i	0.387023	−	0.670344i
$167$	−9.93681	+	5.73702i	−0.768933	+	0.443944i	−0.832494	−	0.554034i	$-0.813088\pi$
$167$	−9.93681	+	5.73702i	−0.768933	+	0.443944i	0.0635605	+	0.997978i	$0.479754\pi$
$168$	31.6150	−	54.7589i	2.43915	−	4.22474i
$169$	−12.7508	−	2.53311i	−0.980832	−	0.194855i
$170$	14.6305			1.12210
$171$		−	21.6382i		−	1.65471i
$172$	−1.66774	−	2.88861i	−0.127164	−	0.220255i
$173$	−9.01550	+	15.6153i	−0.685436	+	1.18721i	0.287863	+	0.957671i	$0.407055\pi$
$173$	−9.01550	+	15.6153i	−0.685436	+	1.18721i	−0.973300	+	0.229539i	$0.926278\pi$
$174$	5.41246	−	3.12488i	0.410317	−	0.236897i
$175$	−3.68527	−	2.12769i	−0.278580	−	0.160838i
$176$	13.8655	+	8.00527i	1.04515	+	0.603420i
$177$	24.7335	+	14.2799i	1.85908	+	1.07334i
$178$	12.5267			0.938912
$179$	3.90043	+	6.75574i	0.291531	+	0.504947i	0.974172	−	0.225807i	$-0.0725019\pi$
$179$	3.90043	+	6.75574i	0.291531	+	0.504947i	−0.682641	+	0.730754i	$0.739169\pi$
$180$	−37.0342	+	21.3817i	−2.76036	+	1.59370i
$181$	6.41028	−	11.1029i	0.476472	−	0.825274i	−0.523164	−	0.852232i	$-0.675249\pi$
$181$	6.41028	−	11.1029i	0.476472	−	0.825274i	0.999637	+	0.0269575i	$0.00858188\pi$
$182$	−39.8869	+	18.0783i	−2.95661	+	1.34005i
$183$	−5.97294	−	10.3454i	−0.441533	−	0.764757i
$184$			1.87715i			0.138385i
$185$	−5.59807			−0.411578
$186$	9.09007	+	35.9876i	0.666517	+	2.63874i
$187$		−	11.7721i		−	0.860860i
$188$			9.38051i			0.684144i
$189$	18.2869	−	10.5580i	1.33018	−	0.767979i
$190$		−	28.0081i		−	2.03192i
$191$	6.13544	−	10.6269i	0.443945	−	0.768935i	−0.554033	−	0.832495i	$-0.686912\pi$
$191$	6.13544	−	10.6269i	0.443945	−	0.768935i	0.997978	+	0.0635596i	$0.0202453\pi$
$192$	12.5754	+	21.7812i	0.907549	+	1.57192i
$193$	5.52012	−	3.18704i	0.397347	−	0.229408i	−0.287992	−	0.957633i	$-0.592988\pi$
$193$	5.52012	−	3.18704i	0.397347	−	0.229408i	0.685339	+	0.728224i	$0.259654\pi$
$194$	−11.5833			−0.831635
$195$	23.8288	+	2.34405i	1.70642	+	0.167861i
$196$	−35.1045	+	60.8027i	−2.50746	+	4.34305i
$197$	16.8766	+	9.74371i	1.20241	+	0.694211i	0.961090	−	0.276235i	$-0.0890869\pi$
$197$	16.8766	+	9.74371i	1.20241	+	0.694211i	0.241318	+	0.970446i	$0.422420\pi$
$198$	26.0357	+	45.0952i	1.85028	+	3.20478i
$199$	−2.10359	+	3.64353i	−0.149120	+	0.258283i	−0.930902	−	0.365268i	$-0.880977\pi$
$199$	−2.10359	+	3.64353i	−0.149120	+	0.258283i	0.781783	+	0.623551i	$0.214311\pi$
$200$	−3.39226	+	1.95852i	−0.239869	+	0.138488i
$201$			22.8730i			1.61334i
$202$			3.71902i			0.261670i
$203$	−4.06102	+	2.34463i	−0.285028	+	0.164561i
$204$	−13.3227	+	23.0756i	−0.932777	+	1.61562i
$205$	12.1233	+	20.9982i	0.846728	+	1.46658i
$206$	−2.81910	−	1.62761i	−0.196416	−	0.113401i
$207$	−0.924983	+	1.60212i	−0.0642908	+	0.111355i
$208$	−1.19582	+	12.1563i	−0.0829149	+	0.842886i
$209$	−22.5361			−1.55885
$210$	69.8525	−	40.3293i	4.82028	−	2.78299i
$211$	13.7870	+	23.8797i	0.949134	+	1.64395i	0.747255	+	0.664538i	$0.231371\pi$
$211$	13.7870	+	23.8797i	0.949134	+	1.64395i	0.201879	+	0.979410i	$0.435295\pi$
$212$	19.9558	−	34.5644i	1.37057	−	2.37389i
$213$		−	10.2862i		−	0.704798i
$214$	37.4893	−	21.6445i	2.56272	−	1.47959i
$215$		−	2.07074i		−	0.141223i
$216$		−	19.4370i		−	1.32252i
$217$	−6.82038	−	27.0019i	−0.462998	−	1.83301i
$218$	35.5273			2.40621
$219$			17.0605i			1.15284i
$220$	22.2689	+	38.5709i	1.50137	+	2.60045i
$221$	8.18030	−	3.70763i	0.550266	−	0.249402i
$222$	7.71446	−	13.3618i	0.517761	−	0.896788i
$223$	8.65223	−	4.99537i	0.579396	−	0.334514i	−0.181497	−	0.983391i	$-0.558094\pi$
$223$	8.65223	−	4.99537i	0.579396	−	0.334514i	0.760893	+	0.648877i	$0.224761\pi$
$224$	−2.45667	−	4.25508i	−0.164143	−	0.284304i
$225$	−3.86032			−0.257355
$226$	3.83392	+	2.21351i	0.255028	+	0.147241i
$227$	10.3967	+	6.00255i	0.690054	+	0.398403i	0.803632	−	0.595126i	$-0.202898\pi$
$227$	10.3967	+	6.00255i	0.690054	+	0.398403i	−0.113578	+	0.993529i	$0.536231\pi$
$228$	44.1752	+	25.5046i	2.92558	+	1.68908i
$229$	−1.63833	+	0.945893i	−0.108264	+	0.0625064i	−0.553154	−	0.833079i	$-0.686576\pi$
$229$	−1.63833	+	0.945893i	−0.108264	+	0.0625064i	0.444890	+	0.895585i	$0.353243\pi$
$230$	−1.19728	+	2.07375i	−0.0789463	+	0.136739i
$231$	−32.4501	−	56.2053i	−2.13506	−	3.69804i
$232$			4.31643i			0.283387i
$233$	−4.13757			−0.271061			−0.135531	−	0.990773i	$-0.543274\pi$
$233$	−4.13757			−0.271061			−0.135531	+	0.990773i	$0.543274\pi$
$234$	−23.1362	+	32.2947i	−1.51246	+	2.11117i
$235$	−2.91181	+	5.04341i	−0.189946	+	0.328996i
$236$	−35.0999	+	20.2649i	−2.28481	+	1.31914i
$237$	10.8351	−	18.7669i	0.703813	−	1.21904i
$238$	15.1275	−	26.2015i	0.980568	−	1.69839i
$239$	−23.3278	−	13.4683i	−1.50895	−	0.871193i	−0.999946	−	0.0104299i	$-0.996680\pi$
$239$	−23.3278	−	13.4683i	−1.50895	−	0.871193i	−0.509005	−	0.860763i	$-0.669987\pi$
$240$		−	22.4979i		−	1.45224i
$241$	−12.3153	+	7.11025i	−0.793299	+	0.458011i	−0.841123	−	0.540845i	$-0.818105\pi$
$241$	−12.3153	+	7.11025i	−0.793299	+	0.458011i	0.0478239	+	0.998856i	$0.484771\pi$
$242$	23.8347	−	13.7610i	1.53215	−	0.884589i
$243$	−9.10909	+	15.7774i	−0.584348	+	1.01212i
$244$	16.9527			1.08529
$245$	−37.7477	+	21.7936i	−2.41161	+	1.39234i
$246$	−66.8263			−4.26069
$247$	−7.09776	−	15.6601i	−0.451620	−	0.996428i
$248$	−24.6641	−	6.99050i	−1.56617	−	0.443897i
$249$			11.2760i			0.714584i
$250$	24.3703			1.54132
$251$	−5.04804	−	8.74345i	−0.318629	−	0.551882i	0.661573	−	0.749881i	$-0.269889\pi$
$251$	−5.04804	−	8.74345i	−0.318629	−	0.551882i	−0.980202	+	0.197999i	$0.936556\pi$
$252$			88.4321i			5.57070i
$253$	1.66860	+	0.963366i	0.104904	+	0.0605663i
$254$	30.3577	−	17.5270i	1.90481	−	1.09974i
$255$	−14.3259	+	8.27104i	−0.897120	+	0.517952i
$256$	−30.9217			−1.93261
$257$	3.15610	−	5.46653i	0.196872	−	0.340993i	−0.750640	−	0.660711i	$-0.770255\pi$
$257$	3.15610	−	5.46653i	0.196872	−	0.340993i	0.947513	+	0.319718i	$0.103588\pi$
$258$	4.94257	+	2.85360i	0.307711	+	0.177657i
$259$	−5.78824	+	10.0255i	−0.359664	+	0.622956i
$260$	−19.7889	+	27.6224i	−1.22726	+	1.71307i
$261$	−2.12696	+	3.68401i	−0.131656	+	0.228034i
$262$	3.94818	−	2.27948i	0.243919	−	0.140827i
$263$	−3.32582			−0.205079			−0.102539	−	0.994729i	$-0.532697\pi$
$263$	−3.32582			−0.205079			−0.102539	+	0.994729i	$0.532697\pi$
$264$	−59.7401			−3.67675
$265$	21.4583	−	12.3890i	1.31818	−	0.761049i
$266$	−50.1594	−	28.9595i	−3.07547	−	1.77562i
$267$	−12.2659	+	7.08169i	−0.750658	+	0.433393i
$268$	−28.1109	−	16.2298i	−1.71715	−	0.991395i
$269$	11.6874	−	20.2431i	0.712591	−	1.23424i	−0.251290	−	0.967912i	$-0.580855\pi$
$269$	11.6874	−	20.2431i	0.712591	−	1.23424i	0.963881	−	0.266332i	$-0.0858119\pi$
$270$	12.3973	−	21.4728i	0.754476	−	1.30679i
$271$			6.25054i			0.379693i	0.981814	+	0.189847i	$0.0607990\pi$
$271$			6.25054i			0.379693i	−0.981814	+	0.189847i	$0.939201\pi$
$272$	−4.21947	−	7.30833i	−0.255843	−	0.443133i
$273$	28.8363	−	40.2512i	1.74525	−	2.43611i
$274$	5.38225	−	9.32233i	0.325154	−	0.563183i
$275$			4.02051i			0.242446i
$276$	−2.18052	−	3.77678i	−0.131252	−	0.227335i
$277$	8.80477			0.529027			0.264514	−	0.964382i	$-0.414789\pi$
$277$	8.80477			0.529027			0.264514	+	0.964382i	$0.414789\pi$
$278$		−	0.965909i		−	0.0579314i
$279$	−17.6058	−	18.1198i	−1.05403	−	1.08480i
$280$			55.7073i			3.32915i
$281$			10.4028i			0.620582i	0.950642	+	0.310291i	$0.100426\pi$
$281$			10.4028i			0.620582i	−0.950642	+	0.310291i	$0.899574\pi$
$282$	−8.02529	−	13.9002i	−0.477899	−	0.827745i
$283$	−31.1494			−1.85164			−0.925820	−	0.377964i	$-0.876624\pi$
$283$	−31.1494			−1.85164			−0.925820	+	0.377964i	$0.876624\pi$
$284$	12.6417	+	7.29870i	0.750148	+	0.433098i
$285$	15.8338	+	27.4249i	0.937913	+	1.62451i
$286$	33.6348	+	24.0962i	1.98887	+	1.42484i
$287$	50.1405			2.95970
$288$	−3.86005	−	2.22860i	−0.227455	−	0.131321i
$289$	5.39755	−	9.34883i	0.317503	−	0.549931i
$290$	−2.75310	+	4.76851i	−0.161668	+	0.280016i
$291$	11.3422	−	6.54841i	0.664890	−	0.383875i
$292$	−20.9673	−	12.1055i	−1.22702	−	0.708419i
$293$	8.62827	−	4.98153i	0.504069	−	0.291024i	−0.226323	−	0.974052i	$-0.572671\pi$
$293$	8.62827	−	4.98153i	0.504069	−	0.291024i	0.730392	+	0.683028i	$0.239337\pi$
$294$		−	120.131i		−	7.00621i
$295$	−25.1618			−1.46498
$296$	5.32802	+	9.22841i	0.309685	+	0.536390i
$297$	−17.2776	−	9.97523i	−1.00255	−	0.578822i
$298$	−4.30995	−	7.46506i	−0.249669	−	0.432439i
$299$	−0.143906	+	1.46290i	−0.00832231	+	0.0846019i
$300$	4.55009	−	7.88099i	0.262700	−	0.455009i
$301$	−3.70847	−	2.14108i	−0.213752	−	0.123410i
$302$	−42.7419			−2.45952
$303$	−2.10248	−	3.64159i	−0.120784	−	0.209204i
$304$	−13.9908	+	8.07761i	−0.802429	+	0.463283i
$305$	9.11459	+	5.26231i	0.521900	+	0.301319i
$306$		−	27.4461i		−	1.56899i
$307$	−13.0385	+	7.52780i	−0.744148	+	0.429634i	−0.823576	−	0.567206i	$-0.808024\pi$
$307$	−13.0385	+	7.52780i	−0.744148	+	0.429634i	0.0794274	+	0.996841i	$0.474691\pi$
$308$	92.1017			5.24798
$309$	3.68054			0.209379
$310$	−22.7886	−	23.4539i	−1.29431	−	1.33209i
$311$	4.64555			0.263425			0.131712	−	0.991288i	$-0.457952\pi$
$311$	4.64555			0.263425			0.131712	+	0.991288i	$0.457952\pi$
$312$	−18.8152	−	41.5128i	−1.06520	−	2.35020i
$313$	5.78428	+	10.0187i	0.326947	+	0.566289i	0.981904	−	0.189377i	$-0.0606469\pi$
$313$	5.78428	+	10.0187i	0.326947	+	0.566289i	−0.654958	+	0.755666i	$0.727314\pi$
$314$			53.2378i			3.00439i
$315$	−27.4503	+	47.5453i	−1.54665	+	2.67888i
$316$	15.3763	+	26.6326i	0.864986	+	1.49820i
$317$	24.9713	−	14.4172i	1.40253	−	0.809750i	0.407876	−	0.913037i	$-0.366270\pi$
$317$	24.9713	−	14.4172i	1.40253	−	0.809750i	0.994652	+	0.103288i	$0.0329362\pi$
$318$			68.2908i			3.82956i
$319$	3.83688	+	2.21522i	0.214824	+	0.124029i
$320$	−19.1898	−	11.0792i	−1.07274	−	0.619347i
$321$	−24.4725	+	42.3877i	−1.36592	+	2.36585i
$322$	2.47590	+	4.28839i	0.137977	+	0.238983i
$323$	10.2870	+	5.93923i	0.572387	+	0.330468i
$324$	−3.94068	−	6.82546i	−0.218927	−	0.379192i
$325$	−2.79381	+	1.26626i	−0.154972	+	0.0702395i
$326$	23.8611			1.32154
$327$	−34.7876	+	20.0846i	−1.92376	+	1.11068i
$328$	23.0770	−	39.9705i	1.27421	−	2.20700i
$329$	6.02146	+	10.4295i	0.331974	+	0.574996i
$330$	−65.9970	−	38.1034i	−3.63302	−	2.09752i
$331$	−12.3911	−	7.15398i	−0.681074	−	0.393218i	0.119185	−	0.992872i	$-0.461972\pi$
$331$	−12.3911	−	7.15398i	−0.681074	−	0.393218i	−0.800260	+	0.599654i	$0.795305\pi$
$332$	−13.8581	−	8.00100i	−0.760564	−	0.439112i
$333$			10.5017i			0.575492i
$334$	13.9307	+	24.1286i	0.762251	+	1.32026i
$335$	−10.0758	−	17.4519i	−0.550502	−	0.953497i
$336$	−40.2913	−	23.2622i	−2.19807	−	1.26906i
$337$	7.97797			0.434588			0.217294	−	0.976106i	$-0.430277\pi$
$337$	7.97797			0.434588			0.217294	+	0.976106i	$0.430277\pi$
$338$	−6.15092	+	30.9616i	−0.334566	+	1.68409i
$339$	−5.00546			−0.271860
$340$		−	23.4753i		−	1.27313i
$341$	−18.8717	+	18.3364i	−1.02196	+	0.992971i
$342$	−52.5420			−2.84114
$343$			55.1219i			2.97630i
$344$	−3.41361	+	1.97085i	−0.184050	+	0.106261i
$345$		−	2.70743i		−	0.145763i
$346$	37.9172	+	21.8915i	2.03844	+	1.17689i
$347$	−8.88038	−	15.3813i	−0.476724	−	0.825710i	0.522921	−	0.852381i	$-0.324842\pi$
$347$	−8.88038	−	15.3813i	−0.476724	−	0.825710i	−0.999644	+	0.0266719i	$0.991509\pi$
$348$	−5.01403	−	8.68455i	−0.268780	−	0.465541i
$349$		−	16.1953i		−	0.866912i	−0.901175	−	0.433456i	$-0.857294\pi$
$349$		−	16.1953i		−	0.866912i	0.901175	−	0.433456i	$-0.142706\pi$
$350$	−5.16646	+	8.94858i	−0.276159	+	0.478322i
$351$	1.49009	−	15.1477i	0.0795349	−	0.808526i
$352$	−2.32108	+	4.02022i	−0.123714	+	0.214279i
$353$	−12.9006	+	7.44817i	−0.686631	+	0.396426i	−0.802349	−	0.596856i	$-0.796416\pi$
$353$	−12.9006	+	7.44817i	−0.686631	+	0.396426i	0.115718	+	0.993282i	$0.463083\pi$
$354$	34.6744	−	60.0579i	1.84293	−	3.19204i
$355$	4.53119	+	7.84825i	0.240491	+	0.416542i
$356$		−	20.0996i		−	1.06528i
$357$			34.2080i			1.81048i
$358$	16.4043	−	9.47103i	0.866994	−	0.500559i
$359$	2.93159	+	1.69255i	0.154723	+	0.0893295i	0.575363	−	0.817898i	$-0.304861\pi$
$359$	2.93159	+	1.69255i	0.154723	+	0.0893295i	−0.420639	+	0.907228i	$0.638194\pi$
$360$	25.2678	+	43.7650i	1.33173	+	2.30662i
$361$	1.86987	−	3.23870i	0.0984140	−	0.170458i
$362$	−26.9602	−	15.5655i	−1.41700	−	0.818103i
$363$	−15.5590	+	26.9490i	−0.816635	+	1.41445i
$364$	29.0075	+	64.0005i	1.52041	+	3.35454i
$365$	−7.51534	−	13.0170i	−0.393371	−	0.681338i
$366$	−25.1208	+	14.5035i	−1.31309	+	0.758111i
$367$	7.68287	−	13.3071i	0.401043	−	0.694627i	−0.592809	−	0.805343i	$-0.701981\pi$
$367$	7.68287	−	13.3071i	0.401043	−	0.694627i	0.993852	+	0.110716i	$0.0353145\pi$
$368$	1.38120			0.0719998
$369$	39.3917	−	22.7428i	2.05065	−	1.18394i
$370$			13.5933i			0.706680i
$371$		−	51.2394i		−	2.66021i
$372$	57.7439	−	14.5855i	2.99388	−	0.756222i
$373$	9.53437			0.493671			0.246835	−	0.969057i	$-0.420609\pi$
$373$	9.53437			0.493671			0.246835	+	0.969057i	$0.420609\pi$
$374$	−28.5850			−1.47810
$375$	−23.8630	+	13.7773i	−1.23228	+	0.711456i
$376$	11.0854			0.571686
$377$	−0.330907	+	3.36389i	−0.0170426	+	0.173249i
$378$	−25.6369	−	44.4044i	−1.31862	−	2.28392i
$379$	−3.39336	+	1.95916i	−0.174305	+	0.100635i	−0.584614	−	0.811311i	$-0.698754\pi$
$379$	−3.39336	+	1.95916i	−0.174305	+	0.100635i	0.410309	+	0.911947i	$0.365421\pi$
$380$	−44.9403			−2.30539
$381$	−19.8171	+	34.3242i	−1.01526	+	1.75848i
$382$	−25.8043	−	14.8981i	−1.32026	−	0.762253i
$383$	−8.84392	−	5.10604i	−0.451903	−	0.260906i	0.256730	−	0.966483i	$-0.417355\pi$
$383$	−8.84392	−	5.10604i	−0.451903	−	0.260906i	−0.708634	+	0.705577i	$0.750688\pi$
$384$	48.2181	−	27.8387i	2.46062	−	1.42064i
$385$	49.5183	+	28.5894i	2.52368	+	1.45705i
$386$	−7.73879	−	13.4040i	−0.393894	−	0.682245i
$387$	−3.88462			−0.197466
$388$			18.5860i			0.943563i
$389$	16.8293	+	29.1492i	0.853280	+	1.47792i	0.878231	+	0.478236i	$0.158724\pi$
$389$	16.8293	+	29.1492i	0.853280	+	1.47792i	−0.0249513	+	0.999689i	$0.507943\pi$
$390$	5.69183	−	57.8613i	0.288217	−	2.92992i
$391$	−0.507777	−	0.879495i	−0.0256794	−	0.0444780i
$392$	71.8535	+	41.4846i	3.62915	+	2.09529i
$393$	−2.57732	+	4.46405i	−0.130009	+	0.225181i
$394$	23.6597	−	40.9798i	1.19196	−	2.06453i
$395$			19.0919i			0.960619i
$396$	72.3575	−	41.7756i	3.63610	−	2.09930i
$397$	−19.4081	+	11.2052i	−0.974063	+	0.562375i	−0.900472	−	0.434913i	$-0.856779\pi$
$397$	−19.4081	+	11.2052i	−0.974063	+	0.562375i	−0.0735902	+	0.997289i	$0.523446\pi$
$398$	8.84724	+	5.10796i	0.443472	+	0.256039i
$399$	65.4867			3.27844
$400$	1.44107	+	2.49601i	0.0720535	+	0.124800i
$401$		−	31.0420i		−	1.55016i	−0.631862	−	0.775081i	$-0.717709\pi$
$401$		−	31.0420i		−	1.55016i	0.631862	−	0.775081i	$-0.282291\pi$
$402$	55.5403			2.77010
$403$	−18.6854	−	7.33866i	−0.930786	−	0.365565i
$404$	5.96736			0.296887
$405$		−	4.89292i		−	0.243131i
$406$	5.69325	+	9.86099i	0.282551	+	0.489393i
$407$	10.9375			0.542153
$408$	27.2696	+	15.7441i	1.35005	+	0.779449i
$409$	−0.861027	+	0.497114i	−0.0425751	+	0.0245807i	−0.521136	−	0.853473i	$-0.674492\pi$
$409$	−0.861027	+	0.497114i	−0.0425751	+	0.0245807i	0.478561	+	0.878054i	$0.341158\pi$
$410$	50.9878	−	29.4378i	2.51811	−	1.45383i
$411$			12.1710i			0.600351i
$412$	−2.61157	+	4.52338i	−0.128663	+	0.222851i
$413$	−26.0166	+	45.0621i	−1.28019	+	2.21736i
$414$	3.89027	+	2.24605i	0.191196	+	0.110387i
$415$	−4.96720	−	8.60344i	−0.243830	−	0.422326i
$416$	−3.52463	−	0.346719i	−0.172809	−	0.0169993i
$417$	0.546058	+	0.945799i	0.0267406	+	0.0463160i
$418$			54.7222i			2.67655i
$419$	−5.05509			−0.246957			−0.123479	−	0.992347i	$-0.539405\pi$
$419$	−5.05509			−0.246957			−0.123479	+	0.992347i	$0.539405\pi$
$420$	−64.7104	−	112.082i	−3.15754	−	5.46903i
$421$	−2.21929	−	1.28131i	−0.108162	−	0.0624472i	0.444943	−	0.895559i	$-0.353224\pi$
$421$	−2.21929	−	1.28131i	−0.108162	−	0.0624472i	−0.553105	+	0.833112i	$0.686557\pi$
$422$	57.9848	−	33.4776i	2.82266	−	1.62966i
$423$	9.46123	+	5.46244i	0.460021	+	0.265593i
$424$	−40.8464	−	23.5827i	−1.98368	−	1.14528i
$425$	1.05958	−	1.83524i	0.0513970	−	0.0890222i
$426$	−24.9769			−1.21014
$427$	18.8484	−	10.8821i	0.912139	−	0.526624i
$428$	−34.7296	−	60.1535i	−1.67872	−	2.90763i
$429$	−46.5569	−	4.57981i	−2.24779	−	0.221115i
$430$	−5.02818			−0.242480
$431$	13.3276	−	7.69468i	0.641967	−	0.370640i	−0.143405	−	0.989664i	$-0.545805\pi$
$431$	13.3276	−	7.69468i	0.641967	−	0.370640i	0.785372	+	0.619024i	$0.212472\pi$
$432$	−14.3017			−0.688090
$433$	−26.7208			−1.28412			−0.642059	−	0.766655i	$-0.721920\pi$
$433$	−26.7208			−1.28412			−0.642059	+	0.766655i	$0.721920\pi$
$434$	−65.5661	+	16.5613i	−3.14727	+	0.794967i
$435$		−	6.22564i		−	0.298496i
$436$		−	57.0053i		−	2.73006i
$437$	−1.68368	+	0.972071i	−0.0805412	+	0.0465005i
$438$	41.4263			1.97942
$439$	19.3670	−	33.5446i	0.924336	−	1.60100i	0.131711	−	0.991288i	$-0.457953\pi$
$439$	19.3670	−	33.5446i	0.924336	−	1.60100i	0.792625	−	0.609709i	$-0.208714\pi$
$440$	45.5811	−	26.3163i	2.17299	−	1.25458i
$441$	40.8839	+	70.8131i	1.94685	+	3.37205i
$442$	−9.00287	−	19.8634i	−0.428223	−	0.944807i
$443$	10.4061	−	18.0239i	0.494409	−	0.856341i	−0.505570	−	0.862785i	$-0.668718\pi$
$443$	10.4061	−	18.0239i	0.494409	−	0.856341i	0.999979	+	0.00644397i	$0.00205119\pi$
$444$	−21.4397	−	12.3782i	−1.01748	−	0.587445i
$445$	6.23915	−	10.8065i	0.295764	−	0.512278i
$446$	−12.1298	−	21.0094i	−0.574361	−	0.994823i
$447$	8.44044	+	4.87309i	0.399219	+	0.230489i
$448$	−39.6833	+	22.9112i	−1.87486	+	1.08245i
$449$			17.8411i			0.841976i	0.907066	+	0.420988i	$0.138317\pi$
$449$			17.8411i			0.841976i	−0.907066	+	0.420988i	$0.861683\pi$
$450$			9.37364i			0.441878i
$451$	−23.6865	−	41.0263i	−1.11536	−	1.93185i
$452$	3.55169	−	6.15171i	0.167058	−	0.289352i
$453$	41.8520	−	24.1633i	1.96638	−	1.13529i
$454$	14.5754	−	25.2454i	0.684058	−	1.18482i
$455$	−4.27064	+	43.4139i	−0.200211	+	2.03528i
$456$	30.1400	−	52.2040i	1.41143	−	2.44468i
$457$			22.1733i			1.03722i	0.855010	+	0.518612i	$0.173551\pi$
$457$			22.1733i			1.03722i	−0.855010	+	0.518612i	$0.826449\pi$
$458$	2.29682	+	3.97821i	0.107323	+	0.185890i
$459$	5.25781	+	9.10679i	0.245413	+	0.425068i
$460$	3.32743	+	1.92109i	0.155142	+	0.0895715i
$461$		−	22.4898i		−	1.04745i	−0.851886	−	0.523727i	$-0.824541\pi$
$461$		−	22.4898i		−	1.04745i	0.851886	−	0.523727i	$-0.175459\pi$
$462$	−136.478	+	78.7956i	−6.34953	+	3.66590i
$463$			6.96342i			0.323618i	0.986822	+	0.161809i	$0.0517328\pi$
$463$			6.96342i			0.323618i	−0.986822	+	0.161809i	$0.948267\pi$
$464$	3.17601			0.147442
$465$	35.5734	+	10.0825i	1.64967	+	0.467564i
$466$			10.0469i			0.465412i
$467$	19.6568			0.909609			0.454805	−	0.890591i	$-0.349709\pi$
$467$	19.6568			0.909609			0.454805	+	0.890591i	$0.349709\pi$
$468$	51.8184	+	37.1232i	2.39531	+	1.71602i
$469$	−41.6725			−1.92426
$470$	12.2464	+	7.07048i	0.564886	+	0.326137i
$471$	−30.0970	−	52.1295i	−1.38679	−	2.40200i
$472$	23.9481	+	41.4792i	1.10230	+	1.90924i
$473$			4.04582i			0.186027i
$474$	−45.5698	−	26.3097i	−2.09309	−	1.20845i
$475$	−3.51332	−	2.02842i	−0.161202	−	0.0930702i
$476$	−42.0417	−	24.2728i	−1.92698	−	1.11254i
$477$	−23.2412	−	40.2549i	−1.06414	−	1.84315i
$478$	−32.7038	+	56.6447i	−1.49584	+	2.59087i
$479$	−15.7799	+	9.11052i	−0.721002	+	0.416271i	−0.815121	−	0.579290i	$-0.803330\pi$
$479$	−15.7799	+	9.11052i	−0.721002	+	0.416271i	0.0941196	+	0.995561i	$0.469996\pi$
$480$	6.52313			0.297739
$481$	3.44478	+	7.60037i	0.157069	+	0.346547i
$482$	17.2651	+	29.9041i	0.786405	+	1.36209i
$483$	−4.84872	−	2.79941i	−0.220624	−	0.127377i
$484$	−22.0802	−	38.2440i	−1.00364	−	1.73836i
$485$	−5.76931	+	9.99274i	−0.261971	+	0.453747i
$486$	38.3108	+	22.1187i	1.73781	+	1.00333i
$487$	−31.2775	−	18.0580i	−1.41732	−	0.818288i	−0.421254	−	0.906943i	$-0.638410\pi$
$487$	−31.2775	−	18.0580i	−1.41732	−	0.818288i	−0.996062	+	0.0886542i	$0.971743\pi$
$488$		−	20.0338i		−	0.906889i
$489$	−23.3643	+	13.4894i	−1.05657	+	0.610011i
$490$	52.9194	+	91.6590i	2.39065	+	4.14073i
$491$	0.702004	−	1.21591i	0.0316810	−	0.0548731i	−0.849750	−	0.527186i	$-0.823247\pi$
$491$	0.702004	−	1.21591i	0.0316810	−	0.0548731i	0.881431	+	0.472312i	$0.156581\pi$
$492$			107.226i			4.83413i
$493$	−1.16761	−	2.02236i	−0.0525866	−	0.0910827i
$494$	−38.0259	+	17.2348i	−1.71087	+	0.775430i
$495$	51.8704			2.33140
$496$	−5.14358	+	18.1477i	−0.230954	+	0.814857i
$497$	18.7405			0.840625
$498$	27.3803			1.22694
$499$	14.4311	−	8.33182i	0.646027	−	0.372984i	−0.140906	−	0.990023i	$-0.545001\pi$
$499$	14.4311	−	8.33182i	0.646027	−	0.372984i	0.786932	+	0.617039i	$0.211668\pi$
$500$		−	39.1034i		−	1.74876i
$501$	−27.2812	−	15.7508i	−1.21884	−	0.703695i
$502$	−21.2309	+	12.2577i	−0.947581	+	0.547086i
$503$	17.1202	+	29.6530i	0.763352	+	1.32216i	0.941114	+	0.338090i	$0.109781\pi$
$503$	17.1202	+	29.6530i	0.763352	+	1.32216i	−0.177762	+	0.984073i	$0.556886\pi$
$504$	104.504			4.65500
$505$	3.20833	+	1.85233i	0.142769	+	0.0824277i
$506$	2.33925	−	4.05170i	0.103992	−	0.180120i
$507$	−11.4807	−	33.7943i	−0.509874	−	1.50086i
$508$	−28.1229	−	48.7104i	−1.24775	−	2.16117i
$509$	18.0616	+	10.4279i	0.800567	+	0.462208i	0.843670	−	0.536863i	$-0.180391\pi$
$509$	18.0616	+	10.4279i	0.800567	+	0.462208i	−0.0431021	+	0.999071i	$0.513724\pi$
$510$	20.0838	+	34.7861i	0.889324	+	1.54035i
$511$	−31.0826			−1.37501
$512$			34.5248i			1.52579i
$513$	17.4337	−	10.0654i	0.769718	−	0.444397i
$514$	−13.2739	−	7.66366i	−0.585484	−	0.338030i
$515$	−2.80821	+	1.62132i	−0.123745	+	0.0714440i
$516$	4.57874	−	7.93061i	0.201568	−	0.349125i
$517$	5.68911	−	9.85383i	0.250207	−	0.433371i
$518$	24.3440	+	14.0550i	1.06961	+	0.617542i
$519$	−49.5036			−2.17297
$520$	32.6427	+	23.3855i	1.43148	+	1.02552i
$521$	6.98837	+	12.1042i	0.306166	+	0.530296i	0.977520	−	0.210841i	$-0.0676203\pi$
$521$	6.98837	+	12.1042i	0.306166	+	0.530296i	−0.671354	+	0.741137i	$0.734287\pi$
$522$	8.94552	+	5.16470i	0.391535	+	0.226053i
$523$	12.5120			0.547112			0.273556	−	0.961856i	$-0.411800\pi$
$523$	12.5120			0.547112			0.273556	+	0.961856i	$0.411800\pi$
$524$	−3.65754	−	6.33505i	−0.159780	−	0.276748i
$525$		−	11.6830i		−	0.509889i
$526$			8.07577i			0.352120i
$527$	13.4468	−	3.39651i	0.585751	−	0.147954i
$528$			43.9565i			1.91296i
$529$	−22.8338			−0.992773
$530$	−30.0830	−	52.1052i	−1.30672	−	2.26331i
$531$			47.2026i			2.04842i
$532$	−46.4670	+	80.4832i	−2.01460	+	3.48939i
$533$	21.0486	−	29.3808i	0.911717	−	1.27262i
$534$	17.1958	+	29.7840i	0.744135	+	1.28888i
$535$		−	43.1218i		−	1.86432i
$536$	−19.1796	+	33.2200i	−0.828431	+	1.43488i
$537$	−10.7085	+	18.5477i	−0.462106	+	0.800392i
$538$	−49.1544	−	28.3793i	−2.11920	−	1.22352i
$539$	73.7515	−	42.5805i	3.17670	−	1.83407i
$540$	−34.4541	−	19.8921i	−1.48267	−	0.856019i
$541$	−3.15730	+	1.82287i	−0.135743	+	0.0783713i	−0.566334	−	0.824176i	$-0.691639\pi$
$541$	−3.15730	+	1.82287i	−0.135743	+	0.0783713i	0.430591	+	0.902547i	$0.358305\pi$
$542$	15.1776			0.651933
$543$	35.1985			1.51051
$544$	2.11900	−	1.22341i	0.0908515	−	0.0524531i
$545$	17.6951	−	30.6487i	0.757973	−	1.31285i
$546$	−97.7380	−	70.0203i	−4.18280	−	2.99659i
$547$	−9.42960	+	16.3325i	−0.403180	+	0.698329i	−0.994108	−	0.108396i	$-0.965429\pi$
$547$	−9.42960	+	16.3325i	−0.403180	+	0.698329i	0.590927	+	0.806725i	$0.298762\pi$
$548$	−14.9581	−	8.63609i	−0.638980	−	0.368916i
$549$	9.87187	−	17.0986i	0.421321	−	0.729750i
$550$	9.76261			0.416279
$551$	−3.87155	+	2.23524i	−0.164934	+	0.0952244i
$552$	−4.46320	+	2.57683i	−0.189966	+	0.109677i
$553$	34.1915	+	19.7405i	1.45397	+	0.839451i
$554$		−	21.3798i		−	0.908339i
$555$	−7.68468	−	13.3102i	−0.326196	−	0.564989i
$556$	−1.54985			−0.0657283
$557$			10.7520i			0.455578i	0.973711	+	0.227789i	$0.0731496\pi$
$557$			10.7520i			0.455578i	−0.973711	+	0.227789i	$0.926850\pi$
$558$	−43.9985	+	42.7505i	−1.86260	+	1.80977i
$559$	−2.81139	+	1.27423i	−0.118909	+	0.0538943i
$560$	40.9891			1.73211
$561$	27.9899	−	16.1600i	1.18173	−	0.682275i
$562$	25.2602			1.06554
$563$	−9.28886	+	16.0888i	−0.391479	+	0.678061i	−0.992645	−	0.121063i	$-0.961370\pi$
$563$	−9.28886	+	16.0888i	−0.391479	+	0.678061i	0.601166	+	0.799124i	$0.294703\pi$
$564$	−22.3036	+	12.8770i	−0.939150	+	0.542218i
$565$	3.81912	−	2.20497i	0.160671	−	0.0927637i
$566$			75.6371i			3.17927i
$567$	−8.76268	−	5.05914i	−0.367998	−	0.212464i
$568$	8.62522	−	14.9393i	0.361906	−	0.626840i
$569$	13.1217	−	22.7274i	0.550090	−	0.952783i	−0.448178	−	0.893944i	$-0.647927\pi$
$569$	13.1217	−	22.7274i	0.550090	−	0.952783i	0.998267	−	0.0588390i	$-0.0187398\pi$
$570$	66.5934	−	38.4477i	2.78929	−	1.61040i
$571$	−10.6760	+	18.4914i	−0.446777	+	0.773841i	−0.998174	−	0.0604023i	$-0.980762\pi$
$571$	−10.6760	+	18.4914i	−0.446777	+	0.773841i	0.551397	+	0.834243i	$0.314095\pi$
$572$	38.6636	−	53.9687i	1.61661	−	2.25654i
$573$	33.6894			1.40739
$574$		−	121.751i		−	5.08181i
$575$	0.173420	+	0.300373i	0.00723213	+	0.0125264i
$576$	−20.7841	+	35.9992i	−0.866006	+	1.49997i
$577$	−2.21121	+	1.27664i	−0.0920539	+	0.0531474i	−0.545320	−	0.838228i	$-0.683592\pi$
$577$	−2.21121	+	1.27664i	−0.0920539	+	0.0531474i	0.453266	+	0.891375i	$0.350259\pi$
$578$	−22.7009	−	13.1063i	−0.944231	−	0.545152i
$579$	15.1553	+	8.74994i	0.629835	+	0.363635i
$580$	7.65130	+	4.41748i	0.317703	+	0.183426i
$581$	−20.5437			−0.852298
$582$	−15.9009	−	27.5411i	−0.659112	−	1.14162i
$583$	−41.9254	+	24.2056i	−1.73637	+	1.00249i
$584$	−14.3056	+	24.7781i	−0.591971	+	1.02532i
$585$	16.3366	+	36.0442i	0.675436	+	1.49024i
$586$	−12.0962	−	20.9512i	−0.499688	−	0.865486i
$587$			1.67786i			0.0692529i	0.999400	+	0.0346264i	$0.0110241\pi$
$587$			1.67786i			0.0692529i	−0.999400	+	0.0346264i	$0.988976\pi$
$588$	−192.757			−7.94916
$589$	−6.50216	−	25.7421i	−0.267917	−	1.06068i
$590$			61.0981i			2.51537i
$591$			53.5022i			2.20079i
$592$	6.79022	−	3.92034i	0.279076	−	0.161125i
$593$			8.62049i			0.354001i	0.984211	+	0.177000i	$0.0566394\pi$
$593$			8.62049i			0.354001i	−0.984211	+	0.177000i	$0.943361\pi$
$594$	−24.2219	+	41.9536i	−0.993836	+	1.72138i
$595$	−15.0691	−	26.1004i	−0.617771	−	1.07001i
$596$	−11.9781	+	6.91553i	−0.490640	+	0.283271i
$597$	−11.5507			−0.472740
$598$	3.55223	+	0.349434i	0.145261	+	0.0142894i
$599$	−6.43015	+	11.1373i	−0.262729	+	0.455060i	−0.966966	−	0.254905i	$-0.917956\pi$
$599$	−6.43015	+	11.1373i	−0.262729	+	0.455060i	0.704237	+	0.709965i	$0.251289\pi$
$600$	−9.31335	−	5.37706i	−0.380216	−	0.219518i
$601$	−4.73732	−	8.20528i	−0.193239	−	0.334701i	0.753083	−	0.657926i	$-0.228566\pi$
$601$	−4.73732	−	8.20528i	−0.193239	−	0.334701i	−0.946322	+	0.323226i	$0.895233\pi$
$602$	−5.19899	+	9.00491i	−0.211895	+	0.367013i
$603$	−32.7389	+	18.9018i	−1.33323	+	0.769742i
$604$			68.5815i			2.79054i
$605$		−	27.4157i		−	1.11461i
$606$	−8.84253	+	5.10524i	−0.359203	+	0.207386i
$607$	−6.89431	+	11.9413i	−0.279831	+	0.484682i	−0.971343	−	0.237683i	$-0.923612\pi$
$607$	−6.89431	+	11.9413i	−0.279831	+	0.484682i	0.691511	+	0.722366i	$0.256945\pi$
$608$	−2.34205	−	4.05655i	−0.0949826	−	0.164515i
$609$	−11.1494	−	6.43713i	−0.451798	−	0.260846i
$610$	12.7780	−	22.1321i	0.517364	−	0.896101i
$611$	8.63911	+	0.849831i	0.349501	+	0.0343805i
$612$	−44.0387			−1.78016
$613$	−35.4721	+	20.4798i	−1.43271	+	0.827173i	−0.997327	−	0.0730736i	$-0.976719\pi$
$613$	−35.4721	+	20.4798i	−1.43271	+	0.827173i	−0.435380	+	0.900247i	$0.643386\pi$
$614$	18.2790	+	31.6602i	0.737682	+	1.27770i
$615$	−33.2842	+	57.6499i	−1.34215	+	2.32467i
$616$		−	108.841i		−	4.38533i
$617$	21.4639	−	12.3922i	0.864105	−	0.498891i	−0.00128001	−	0.999999i	$-0.500407\pi$
$617$	21.4639	−	12.3922i	0.864105	−	0.498891i	0.865385	+	0.501108i	$0.167074\pi$
$618$		−	8.93710i		−	0.359503i
$619$		−	16.6086i		−	0.667556i	−0.942652	−	0.333778i	$-0.891676\pi$
$619$		−	16.6086i		−	0.667556i	0.942652	−	0.333778i	$-0.108324\pi$
$620$	−37.6329	+	36.5655i	−1.51137	+	1.46850i
$621$	−1.72109			−0.0690648
$622$		−	11.2803i		−	0.452300i
$623$	−12.9022	−	22.3472i	−0.516915	−	0.895323i
$624$	−30.5449	+	13.8441i	−1.22278	+	0.554209i
$625$	14.2650	−	24.7076i	0.570599	−	0.988306i
$626$	24.3274	−	14.0454i	0.972317	−	0.561367i
$627$	−30.9361	−	53.5829i	−1.23547	−	2.13990i
$628$	85.4228			3.40874
$629$	−4.99265	−	2.88251i	−0.199070	−	0.114933i
$630$	115.450	+	66.6549i	4.59963	+	2.65560i
$631$	32.7695	+	18.9195i	1.30453	+	0.753172i	0.981178	−	0.193107i	$-0.0618563\pi$
$631$	32.7695	+	18.9195i	1.30453	+	0.753172i	0.323354	+	0.946278i	$0.395190\pi$
$632$	31.4730	−	18.1709i	1.25193	−	0.722801i
$633$	−37.8517	+	65.5611i	−1.50447	+	2.60582i
$634$	−35.0079	−	60.6354i	−1.39034	−	2.40814i
$635$		−	34.9187i		−	1.38571i
$636$	109.576			4.34497
$637$	52.8168	+	37.8384i	2.09268	+	1.49921i
$638$	5.37901	−	9.31672i	0.212957	−	0.368853i
$639$	14.7230	−	8.50032i	0.582433	−	0.336268i
$640$	−24.5266	+	42.4814i	−0.969500	+	1.67922i
$641$	−6.33241	+	10.9681i	−0.250115	+	0.433212i	−0.963557	−	0.267502i	$-0.913802\pi$
$641$	−6.33241	+	10.9681i	−0.250115	+	0.433212i	0.713442	+	0.700714i	$0.247135\pi$
$642$	102.926	+	59.4243i	4.06216	+	2.34529i
$643$		−	43.3982i		−	1.71146i	−0.517424	−	0.855729i	$-0.673109\pi$
$643$		−	43.3982i		−	1.71146i	0.517424	−	0.855729i	$-0.326891\pi$
$644$	6.88094	−	3.97271i	0.271147	−	0.156547i
$645$	4.92349	−	2.84258i	0.193862	−	0.111926i
$646$	14.4217	−	24.9790i	0.567413	−	0.982788i
$647$	−24.4558			−0.961456			−0.480728	−	0.876870i	$-0.659628\pi$
$647$	−24.4558			−0.961456			−0.480728	+	0.876870i	$0.659628\pi$
$648$	−8.06597	+	4.65689i	−0.316861	+	0.182940i
$649$	49.1613			1.92975
$650$	3.07474	+	6.78393i	0.120601	+	0.266088i
$651$	54.8384	−	53.2830i	2.14929	−	2.08832i
$652$		−	38.2863i		−	1.49941i
$653$	16.8506			0.659416			0.329708	−	0.944083i	$-0.393050\pi$
$653$	16.8506			0.659416			0.329708	+	0.944083i	$0.393050\pi$
$654$	48.7696	+	84.4714i	1.90704	+	3.30309i
$655$		−	4.54136i		−	0.177446i
$656$	−29.4101	−	16.9799i	−1.14827	−	0.662954i
$657$	−24.4193	+	14.0985i	−0.952686	+	0.550034i
$658$	25.3249	−	14.6213i	0.987267	−	0.569999i
$659$	−26.1683			−1.01937			−0.509686	−	0.860360i	$-0.670239\pi$
$659$	−26.1683			−1.01937			−0.509686	+	0.860360i	$0.670239\pi$
$660$	−61.1388	+	105.895i	−2.37982	+	4.12198i
$661$	6.55204	+	3.78282i	0.254845	+	0.147135i	0.621981	−	0.783033i	$-0.286328\pi$
$661$	6.55204	+	3.78282i	0.254845	+	0.147135i	−0.367136	+	0.930167i	$0.619662\pi$
$662$	−17.3713	+	30.0880i	−0.675156	+	1.16940i
$663$	20.0448	+	14.3603i	0.778477	+	0.557707i
$664$	−9.45517	+	16.3768i	−0.366932	+	0.635544i
$665$	−49.9657	+	28.8477i	−1.93759	+	1.11867i
$666$	25.5004			0.988120
$667$	0.382205			0.0147990
$668$	38.7155	−	22.3524i	1.49795	−	0.864841i
$669$	23.7545	+	13.7146i	0.918401	+	0.530239i
$670$	−42.3767	+	24.4662i	−1.63715	+	0.945211i
$671$	−17.8081	−	10.2815i	−0.687474	−	0.396913i
$672$	6.74472	−	11.6822i	0.260183	−	0.450651i
$673$	−9.92517	+	17.1909i	−0.382587	+	0.662660i	−0.991431	−	0.130630i	$-0.958300\pi$
$673$	−9.92517	+	17.1909i	−0.382587	+	0.662660i	0.608844	+	0.793290i	$0.291633\pi$
$674$		−	19.3721i		−	0.746187i
$675$	−1.79569	−	3.11023i	−0.0691162	−	0.119713i
$676$	49.6794	+	9.86945i	1.91075	+	0.379594i
$677$	−12.2128	+	21.1532i	−0.469377	+	0.812984i	−0.999387	−	0.0350070i	$-0.988855\pi$
$677$	−12.2128	+	21.1532i	−0.469377	+	0.812984i	0.530010	+	0.847991i	$0.322188\pi$
$678$			12.1543i			0.466783i
$679$	11.9306	+	20.6644i	0.457854	+	0.793027i
$680$	−27.7419			−1.06385
$681$			32.9597i			1.26302i
$682$	44.5245	+	45.8243i	1.70493	+	1.75470i
$683$		−	8.21428i		−	0.314311i	−0.987574	−	0.157155i	$-0.949768\pi$
$683$		−	8.21428i		−	0.314311i	0.987574	−	0.157155i	$-0.0502323\pi$
$684$			84.3062i			3.22353i
$685$	−5.36147	−	9.28635i	−0.204851	−	0.354813i
$686$	133.847			5.11031
$687$	−4.49800	−	2.59692i	−0.171610	−	0.0990788i
$688$	1.45014	+	2.51172i	0.0552861	+	0.0957584i
$689$	−30.0246	−	21.5099i	−1.14385	−	0.819462i
$690$	−6.57420			−0.250276
$691$	−13.2405	−	7.64443i	−0.503694	−	0.290808i	0.226544	−	0.974001i	$-0.427257\pi$
$691$	−13.2405	−	7.64443i	−0.503694	−	0.290808i	−0.730238	+	0.683193i	$0.760591\pi$
$692$	35.1260	−	60.8400i	1.33529	−	2.31279i
$693$	53.6325	−	92.8942i	2.03733	−	3.52876i
$694$	−37.3488	+	21.5634i	−1.41774	+	0.818534i
$695$	−0.833273	−	0.481090i	−0.0316078	−	0.0182488i
$696$	−10.2630	+	5.92532i	−0.389016	+	0.224599i
$697$			24.9697i			0.945794i
$698$	−39.3254			−1.48849
$699$	−5.67980	−	9.83770i	−0.214830	−	0.372096i
$700$	14.3584	+	8.28985i	0.542698	+	0.313327i
$701$	−4.10601	−	7.11182i	−0.155082	−	0.268610i	0.778007	−	0.628256i	$-0.216231\pi$
$701$	−4.10601	−	7.11182i	−0.155082	−	0.268610i	−0.933089	+	0.359646i	$0.882898\pi$
$702$	−36.7818	−	3.61823i	−1.38824	−	0.136561i
$703$	−5.51818	+	9.55777i	−0.208122	+	0.360478i
$704$	37.4930	+	21.6466i	1.41307	+	0.815837i
$705$	−15.9886			−0.602166
$706$	18.0857	+	31.3253i	0.680664	+	1.17894i
$707$	6.63465	−	3.83052i	0.249522	−	0.144061i
$708$	−96.3658	−	55.6368i	−3.62165	−	2.09096i
$709$			45.6697i			1.71516i	0.514351	+	0.857580i	$0.328033\pi$
$709$			45.6697i			1.71516i	−0.514351	+	0.857580i	$0.671967\pi$
$710$	19.0572	−	11.0027i	0.715202	−	0.412922i
$711$	35.8156			1.34319
$712$	−23.7527			−0.890170
$713$	−0.618986	+	2.18392i	−0.0231812	+	0.0817886i
$714$	83.0641			3.10860
$715$	37.5399	−	17.0145i	1.40391	−	0.636307i
$716$	−15.1967	−	26.3215i	−0.567929	−	0.983681i
$717$		−	73.9538i		−	2.76186i
$718$	4.10986	−	7.11849i	0.153379	−	0.265660i
$719$	18.9930	+	32.8969i	0.708320	+	1.22685i	0.965480	+	0.260478i	$0.0838801\pi$
$719$	18.9930	+	32.8969i	0.708320	+	1.22685i	−0.257159	+	0.966369i	$0.582787\pi$
$720$	32.2021	−	18.5919i	1.20010	−	0.692879i
$721$			6.70560i			0.249730i
$722$	−7.86423	−	4.54042i	−0.292676	−	0.168977i
$723$	−33.8113	−	19.5210i	−1.25746	−	0.725993i
$724$	−24.9756	+	43.2589i	−0.928209	+	1.60771i
$725$	0.398773	+	0.690696i	0.0148101	+	0.0256518i
$726$	65.4375	+	37.7804i	2.42862	+	1.40216i
$727$	12.4340	+	21.5363i	0.461152	+	0.798739i	0.999019	−	0.0442912i	$-0.0141029\pi$
$727$	12.4340	+	21.5363i	0.461152	+	0.798739i	−0.537867	+	0.843030i	$0.680770\pi$
$728$	75.6324	−	34.2795i	2.80312	−	1.27048i
$729$	−43.9490			−1.62774
$730$	−31.6078	+	18.2488i	−1.16986	+	0.675418i
$731$	1.06625	−	1.84679i	0.0394366	−	0.0683061i
$732$	23.2716	+	40.3076i	0.860144	+	1.48981i
$733$	−19.8536	−	11.4625i	−0.733311	−	0.423377i	0.0863211	−	0.996267i	$-0.472489\pi$
$733$	−19.8536	−	11.4625i	−0.733311	−	0.423377i	−0.819632	+	0.572890i	$0.805822\pi$
$734$	−32.3124	−	18.6556i	−1.19267	−	0.688590i
$735$	−103.635	−	59.8338i	−3.82264	−	2.20700i
$736$			0.400469i			0.0147615i
$737$	19.6862	+	34.0975i	0.725150	+	1.25600i
$738$	−55.2241	−	95.6510i	−2.03283	−	3.52096i
$739$	−16.2121	−	9.36006i	−0.596372	−	0.344315i	0.171241	−	0.985229i	$-0.445222\pi$
$739$	−16.2121	−	9.36006i	−0.596372	−	0.344315i	−0.767613	+	0.640914i	$0.778556\pi$
$740$	21.8111			0.801790
$741$	27.4908	−	38.3732i	1.00990	−	1.40967i
$742$	−124.420			−4.56759
$743$			33.2268i			1.21897i	0.792796	+	0.609487i	$0.208625\pi$
$743$			33.2268i			1.21897i	−0.792796	+	0.609487i	$0.791375\pi$
$744$	−17.2364	−	68.2387i	−0.631915	−	2.50175i
$745$	−8.58663			−0.314590
$746$		−	23.1514i		−	0.847633i
$747$	−16.1397	+	9.31825i	−0.590520	+	0.340937i
$748$			45.8661i			1.67703i
$749$	−77.2265	−	44.5867i	−2.82179	−	1.62916i
$750$	33.4540	+	57.9441i	1.22157	+	2.11582i
$751$	−6.80244	−	11.7822i	−0.248225	−	0.429938i	0.714809	−	0.699320i	$-0.246514\pi$
$751$	−6.80244	−	11.7822i	−0.248225	−	0.429938i	−0.963033	+	0.269382i	$0.913180\pi$
$752$		−	8.15659i		−	0.297440i
$753$	13.8592	−	24.0049i	0.505059	−	0.874788i
$754$	8.16821	+	0.803509i	0.297469	+	0.0292621i
$755$	−21.2884	+	36.8727i	−0.774765	+	1.34193i
$756$	−71.2491	+	41.1357i	−2.59130	+	1.49609i
$757$	27.0423	−	46.8387i	0.982870	−	1.70238i	0.331827	−	0.943340i	$-0.392335\pi$
$757$	27.0423	−	46.8387i	0.982870	−	1.70238i	0.651043	−	0.759040i	$-0.274332\pi$
$758$	4.75724	+	8.23978i	0.172791	+	0.299282i
$759$			5.28979i			0.192007i
$760$			53.1081i			1.92643i
$761$	12.7103	−	7.33828i	0.460747	−	0.266013i	−0.251611	−	0.967828i	$-0.580960\pi$
$761$	12.7103	−	7.33828i	0.460747	−	0.266013i	0.712358	+	0.701816i	$0.247627\pi$
$762$	83.3461	+	48.1199i	3.01931	+	1.74320i
$763$	−36.5923	−	63.3798i	−1.32473	−	2.29450i
$764$	−23.9047	+	41.4042i	−0.864843	+	1.49795i
$765$	−23.6773	−	13.6701i	−0.856054	−	0.494243i
$766$	−12.3985	+	21.4748i	−0.447976	+	0.775917i
$767$	15.4834	+	34.1616i	0.559072	+	1.23350i
$768$	−42.4474	−	73.5211i	−1.53169	−	2.65296i
$769$	34.5188	−	19.9295i	1.24478	−	0.718675i	0.274718	−	0.961525i	$-0.411416\pi$
$769$	34.5188	−	19.9295i	1.24478	−	0.718675i	0.970064	+	0.242850i	$0.0780823\pi$
$770$	69.4208	−	120.240i	2.50175	−	4.33316i
$771$	17.3300			0.624124
$772$	−21.5074	+	12.4173i	−0.774067	+	0.446908i
$773$			34.5454i			1.24251i	0.783607	+	0.621257i	$0.213378\pi$
$773$			34.5454i			1.24251i	−0.783607	+	0.621257i	$0.786622\pi$
$774$			9.43265i			0.339050i
$775$	−4.59246	+	1.16001i	−0.164966	+	0.0416686i
$776$	21.9640			0.788462
$777$	−31.7829			−1.14021
$778$	70.7803	−	40.8650i	2.53760	−	1.46508i
$779$	47.8011			1.71265
$780$	−92.8413	−	9.13282i	−3.32425	−	0.327007i
$781$	−8.85305	−	15.3339i	−0.316787	−	0.548691i
$782$	−2.13559	+	1.23299i	−0.0763687	+	0.0440915i
$783$	−3.95757			−0.141432
$784$	30.5242	−	52.8695i	1.09015	−	1.88820i
$785$	45.9273	+	26.5162i	1.63922	+	0.946402i
$786$	10.8396	+	6.25825i	0.386636	+	0.223225i
$787$	−3.09869	+	1.78903i	−0.110456	+	0.0637719i	−0.554210	−	0.832377i	$-0.686980\pi$
$787$	−3.09869	+	1.78903i	−0.110456	+	0.0637719i	0.443754	+	0.896149i	$0.353646\pi$
$788$	−65.7542	−	37.9632i	−2.34240	−	1.35238i
$789$	−4.56547	−	7.90763i	−0.162535	−	0.281519i
$790$	46.3591			1.64938
$791$		−	9.11949i		−	0.324252i
$792$	−49.3682	−	85.5083i	−1.75422	−	3.03840i
$793$	1.53584	−	15.6128i	0.0545392	−	0.554428i
$794$	27.2086	+	47.1267i	0.965598	+	1.67246i
$795$	58.9133	+	34.0136i	2.08944	+	1.20634i
$796$	8.19597	−	14.1958i	0.290498	−	0.503158i
$797$	8.11712	−	14.0593i	0.287523	−	0.498005i	−0.685695	−	0.727889i	$-0.740502\pi$
$797$	8.11712	−	14.0593i	0.287523	−	0.498005i	0.973218	+	0.229885i	$0.0738349\pi$
$798$		−	159.015i		−	5.62907i
$799$	−5.19382	+	2.99865i	−0.183744	+	0.106085i
$800$	−0.723700	+	0.417829i	−0.0255867	+	0.0147725i
$801$	−20.2726	−	11.7044i	−0.716296	−	0.413554i
$802$	−75.3762			−2.66163
$803$	14.6835	+	25.4326i	0.518169	+	0.897496i
$804$		−	89.1171i		−	3.14292i
$805$	4.93269			0.173855
$806$	−17.8198	+	45.3719i	−0.627675	+	1.59816i
$807$	64.1747			2.25906
$808$		−	7.05191i		−	0.248085i
$809$	−20.1786	−	34.9504i	−0.709442	−	1.22879i	−0.965064	−	0.262013i	$-0.915614\pi$
$809$	−20.1786	−	34.9504i	−0.709442	−	1.22879i	0.255622	−	0.966777i	$-0.417720\pi$
$810$	−11.8810			−0.417456
$811$	29.6876	+	17.1401i	1.04247	+	0.601872i	0.920533	−	0.390665i	$-0.127755\pi$
$811$	29.6876	+	17.1401i	1.04247	+	0.601872i	0.121940	+	0.992537i	$0.461088\pi$
$812$	15.8225	−	9.13510i	0.555259	−	0.320579i
$813$	−14.8616	+	8.58034i	−0.521219	+	0.300926i
$814$		−	26.5585i		−	0.930876i
$815$	11.8845	−	20.5845i	0.416295	−	0.721044i
$816$	11.5844	−	20.0648i	0.405536	−	0.702409i
$817$	−3.53544	−	2.04119i	−0.123689	−	0.0714121i
$818$	1.20710	+	2.09075i	0.0422051	+	0.0731014i
$819$	81.4427	+	8.01154i	2.84584	+	0.279946i
$820$	−47.2345	−	81.8125i	−1.64950	−	2.85702i
$821$		−	23.7058i		−	0.827337i	−0.910428	−	0.413669i	$-0.864247\pi$
$821$		−	23.7058i		−	0.827337i	0.910428	−	0.413669i	$-0.135753\pi$
$822$	29.5537			1.03080
$823$	3.75741	+	6.50803i	0.130975	+	0.226856i	0.924053	−	0.382265i	$-0.124856\pi$
$823$	3.75741	+	6.50803i	0.130975	+	0.226856i	−0.793078	+	0.609121i	$0.791523\pi$
$824$	5.34549	+	3.08622i	0.186219	+	0.107514i
$825$	−9.55936	+	5.51910i	−0.332814	+	0.192150i
$826$	109.420	+	63.1736i	3.80721	+	2.19809i
$827$	6.53253	+	3.77156i	0.227158	+	0.131150i	0.609260	−	0.792970i	$-0.291466\pi$
$827$	6.53253	+	3.77156i	0.227158	+	0.131150i	−0.382102	+	0.924120i	$0.624800\pi$
$828$	3.60389	−	6.24213i	0.125244	−	0.216929i
$829$	−12.5772			−0.436823			−0.218411	−	0.975857i	$-0.570087\pi$
$829$	−12.5772			−0.436823			−0.218411	+	0.975857i	$0.570087\pi$
$830$	−20.8909	+	12.0614i	−0.725134	+	0.418656i
$831$	12.0866	+	20.9347i	0.419280	+	0.726215i
$832$	−3.23354	+	32.8711i	−0.112103	+	1.13960i
$833$	−44.8871			−1.55525
$834$	2.29659	−	1.32594i	0.0795245	−	0.0459135i
$835$	27.7537			0.960458
$836$	87.8045			3.03678
$837$	6.40933	−	22.6136i	0.221539	−	0.781640i
$838$			12.2748i			0.424025i
$839$			49.5833i			1.71181i	0.517136	+	0.855903i	$0.326998\pi$
$839$			49.5833i			1.71181i	−0.517136	+	0.855903i	$0.673002\pi$
$840$	−132.452	+	76.4714i	−4.57004	+	2.63851i
$841$	−28.1211			−0.969694
$842$	−3.11128	+	5.38889i	−0.107222	+	0.185714i
$843$	−24.7343	+	14.2804i	−0.851895	+	0.491842i
$844$	−53.7164	−	93.0395i	−1.84899	−	3.20255i
$845$	23.6464	+	20.7273i	0.813461	+	0.713041i
$846$	13.2639	−	22.9738i	0.456023	−	0.789855i
$847$	−49.0985	−	28.3470i	−1.68704	−	0.974015i
$848$	−17.3520	+	30.0546i	−0.595871	+	1.03208i
$849$	−42.7600	−	74.0624i	−1.46752	−	2.54182i
$850$	−4.45634	−	2.57287i	−0.152851	−	0.0882486i
$851$	0.817145	−	0.471779i	0.0280114	−	0.0161724i
$852$			40.0767i			1.37301i
$853$		−	51.5553i		−	1.76522i	−0.470105	−	0.882611i	$-0.655784\pi$
$853$		−	51.5553i		−	1.76522i	0.470105	−	0.882611i	$-0.344216\pi$
$854$	−26.4241	−	45.7678i	−0.904213	−	1.56614i
$855$	−26.1696	+	45.3270i	−0.894980	+	1.55015i
$856$	−71.0863	+	41.0417i	−2.42968	+	1.40278i
$857$	−9.72696	+	16.8476i	−0.332267	+	0.575502i	−0.982956	−	0.183842i	$-0.941147\pi$
$857$	−9.72696	+	16.8476i	−0.332267	+	0.575502i	0.650689	+	0.759344i	$0.274480\pi$
$858$	−11.1207	+	113.050i	−0.379655	+	3.85945i
$859$	3.87735	−	6.71576i	0.132293	−	0.229139i	−0.792267	−	0.610175i	$-0.791099\pi$
$859$	3.87735	−	6.71576i	0.132293	−	0.229139i	0.924560	+	0.381036i	$0.124433\pi$
$860$			8.06796i			0.275115i
$861$	68.8297	+	119.217i	2.34571	+	4.06289i
$862$	−18.6843	−	32.3621i	−0.636388	−	1.10226i
$863$	4.49210	+	2.59352i	0.152913	+	0.0882843i	0.574504	−	0.818502i	$-0.305195\pi$
$863$	4.49210	+	2.59352i	0.152913	+	0.0882843i	−0.421591	+	0.906786i	$0.638528\pi$
$864$		−	4.14668i		−	0.141073i
$865$	37.7708	−	21.8070i	1.28424	−	0.741459i
$866$			64.8835i			2.20483i
$867$	29.6377			1.00655
$868$	26.5734	+	105.204i	0.901959	+	3.57086i
$869$		−	37.3018i		−	1.26538i
$870$	−15.1171			−0.512518
$871$	−17.4938	+	24.4187i	−0.592754	+	0.827398i
$872$	−67.3658			−2.28130
$873$	18.7460	+	10.8230i	0.634455	+	0.366303i
$874$	2.36039	+	4.08831i	0.0798413	+	0.138289i
$875$	−25.1009	−	43.4761i	−0.848566	−	1.46976i
$876$		−	66.4705i		−	2.24583i
$877$	16.6043	+	9.58651i	0.560688	+	0.323713i	0.753422	−	0.657538i	$-0.228402\pi$
$877$	16.6043	+	9.58651i	0.560688	+	0.323713i	−0.192734	+	0.981251i	$0.561735\pi$
$878$	−81.4532	−	47.0270i	−2.74891	−	1.58708i
$879$	23.6887	+	13.6767i	0.798999	+	0.461302i
$880$	−19.3634	−	33.5384i	−0.652740	−	1.13058i
$881$	15.4181	−	26.7049i	0.519448	−	0.899710i	−0.480297	−	0.877106i	$-0.659471\pi$
$881$	15.4181	−	26.7049i	0.519448	−	0.899710i	0.999745	−	0.0226037i	$-0.00719558\pi$
$882$	171.949	−	99.2745i	5.78981	−	3.34275i
$883$	29.3502			0.987712			0.493856	−	0.869544i	$-0.335587\pi$
$883$	29.3502			0.987712			0.493856	+	0.869544i	$0.335587\pi$
$884$	−31.8718	+	14.4456i	−1.07197	+	0.485857i
$885$	−34.5406	−	59.8260i	−1.16107	−	2.01103i
$886$	−43.7657	−	25.2681i	−1.47034	−	0.848900i
$887$	16.7355	+	28.9867i	0.561922	+	0.973277i	0.997329	+	0.0730435i	$0.0232712\pi$
$887$	16.7355	+	28.9867i	0.561922	+	0.973277i	−0.435407	+	0.900234i	$0.643395\pi$
$888$	−14.6279	+	25.3363i	−0.490882	+	0.850232i
$889$	−62.5355	−	36.1049i	−2.09737	−	1.21092i
$890$	−26.2404	−	15.1499i	−0.879581	−	0.507826i
$891$			9.55981i			0.320266i
$892$	−33.7106	+	19.4628i	−1.12871	+	0.651663i
$893$	5.74052	+	9.94287i	0.192099	+	0.332725i
$894$	11.8329	−	20.4951i	0.395750	−	0.685459i
$895$		−	18.8689i		−	0.630719i
$896$	50.7196	+	87.8489i	1.69442	+	2.93483i
$897$	−3.67582	+	1.66602i	−0.122732	+	0.0556269i
$898$	43.3219			1.44567
$899$	−1.42333	+	5.02185i	−0.0474708	+	0.167488i
$900$	15.0405			0.501349
$901$	25.5169			0.850091
$902$	−99.6201	+	57.5157i	−3.31699	+	1.91506i
$903$		−	11.7566i		−	0.391234i
$904$	−7.26977	−	4.19721i	−0.241789	−	0.139597i
$905$	−26.8561	+	15.5054i	−0.892727	+	0.515416i
$906$	−58.6733	−	101.625i	−1.94929	−	3.37627i
$907$	11.4446			0.380012			0.190006	−	0.981783i	$-0.439149\pi$
$907$	11.4446			0.380012			0.190006	+	0.981783i	$0.439149\pi$
$908$	−40.5074	−	23.3870i	−1.34429	−	0.776124i
$909$	3.47490	−	6.01870i	0.115255	−	0.199628i
$910$	105.418	+	10.3700i	3.49457	+	0.343762i
$911$	11.4183	+	19.7771i	0.378306	+	0.655246i	0.990816	−	0.135217i	$-0.0431732\pi$
$911$	11.4183	+	19.7771i	0.378306	+	0.655246i	−0.612510	+	0.790463i	$0.709840\pi$
$912$	−38.4114	−	22.1769i	−1.27193	−	0.734349i
$913$	9.70492	+	16.8094i	0.321186	+	0.556311i
$914$	53.8413			1.78091
$915$			28.8951i			0.955241i
$916$	6.38324	−	3.68536i	0.210908	−	0.121768i
$917$	−8.13308	−	4.69564i	−0.268578	−	0.155064i
$918$	22.1131	−	12.7670i	0.729842	−	0.421375i
$919$	21.8307	−	37.8118i	0.720128	−	1.24730i	−0.240821	−	0.970570i	$-0.577417\pi$
$919$	21.8307	−	37.8118i	0.720128	−	1.24730i	0.960948	−	0.276728i	$-0.0892501\pi$
$920$	2.27025	−	3.93219i	0.0748479	−	0.129640i
$921$	−35.7969	−	20.6674i	−1.17955	−	0.681013i
$922$	−54.6098			−1.79848
$923$	7.86711	−	10.9813i	0.258949	−	0.361455i
$924$	126.431	+	218.986i	4.15929	+	7.20410i
$925$	1.70513	+	0.984460i	0.0560645	+	0.0323688i
$926$	16.9086			0.555652
$927$	3.04153	+	5.26809i	0.0998971	+	0.173027i
$928$			0.920862i			0.0302288i
$929$			34.6096i			1.13550i	0.823199	+	0.567752i	$0.192187\pi$
$929$			34.6096i			1.13550i	−0.823199	+	0.567752i	$0.807813\pi$
$930$	24.4823	−	86.3793i	0.802808	−	2.83249i
$931$			85.9304i			2.81626i
$932$	16.1207			0.528051
$933$	6.37711	+	11.0455i	0.208777	+	0.361613i
$934$		−	47.7308i		−	1.56180i
$935$	−14.2373	+	24.6598i	−0.465611	+	0.806461i
$936$	43.8702	−	61.2363i	1.43394	−	2.00157i
$937$	14.6770	+	25.4213i	0.479476	+	0.830477i	0.999723	−	0.0235390i	$-0.00749340\pi$
$937$	14.6770	+	25.4213i	0.479476	+	0.830477i	−0.520247	+	0.854016i	$0.674160\pi$
$938$			101.189i			3.30395i
$939$	−15.8806	+	27.5060i	−0.518243	+	0.897624i
$940$	11.3449	−	19.6500i	0.370031	−	0.640912i
$941$	−15.5737	−	8.99149i	−0.507689	−	0.293114i	0.224194	−	0.974544i	$-0.428025\pi$
$941$	−15.5737	−	8.99149i	−0.507689	−	0.293114i	−0.731883	+	0.681430i	$0.761358\pi$
$942$	−126.581	+	73.0815i	−4.12423	+	2.38113i
$943$	−3.53925	−	2.04339i	−0.115254	−	0.0665419i
$944$	30.5202	−	17.6209i	0.993349	−	0.573510i
$945$	−51.0759			−1.66150
$946$	9.82407			0.319408
$947$	44.1999	−	25.5188i	1.43630	−	0.829250i	0.438713	−	0.898627i	$-0.355435\pi$
$947$	44.1999	−	25.5188i	1.43630	−	0.829250i	0.997590	+	0.0693774i	$0.0221013\pi$
$948$	−42.2153	+	73.1190i	−1.37109	+	2.37480i
$949$	−13.0482	+	18.2134i	−0.423564	+	0.591232i
$950$	−4.92541	+	8.53106i	−0.159801	+	0.276784i
$951$	68.5580	+	39.5820i	2.22315	+	1.28353i
$952$	−28.6843	+	49.6826i	−0.929663	+	1.61022i
$953$	−36.9692			−1.19755			−0.598775	−	0.800917i	$-0.704346\pi$
$953$	−36.9692			−1.19755			−0.598775	+	0.800917i	$0.704346\pi$
$954$	−97.7472	+	56.4344i	−3.16468	+	1.82713i
$955$	−25.7046	+	14.8406i	−0.831783	+	0.480230i
$956$	90.8892	+	52.4749i	2.93957	+	1.69716i
$957$			12.1637i			0.393196i
$958$	22.1222	+	38.3168i	0.714736	+	1.23796i
$959$	−22.1744			−0.716050
$960$		−	60.8353i		−	1.96345i
$961$	−26.3898	−	16.2659i	−0.851284	−	0.524706i
$962$	18.4552	−	8.36463i	0.595021	−	0.269687i
$963$	−80.8948			−2.60680
$964$	47.9826	−	27.7027i	1.54541	−	0.892245i
$965$	−15.4178			−0.496318
$966$	−6.79753	+	11.7737i	−0.218707	+	0.378812i
$967$	39.3134	−	22.6976i	1.26423	−	0.729906i	0.290343	−	0.956923i	$-0.406231\pi$
$967$	39.3134	−	22.6976i	1.26423	−	0.729906i	0.973891	+	0.227017i	$0.0728973\pi$
$968$	−45.1947	+	26.0932i	−1.45261	+	0.838667i
$969$			32.6120i			1.04765i
$970$	24.2644	+	14.0091i	0.779083	+	0.449804i
$971$	10.7787	−	18.6693i	0.345906	−	0.599127i	−0.639612	−	0.768698i	$-0.720905\pi$
$971$	10.7787	−	18.6693i	0.345906	−	0.599127i	0.985518	+	0.169571i	$0.0542383\pi$
$972$	35.4906	−	61.4715i	1.13836	−	1.97170i
$973$	−1.72316	+	0.994866i	−0.0552419	+	0.0318940i
$974$	−43.8486	+	75.9480i	−1.40500	+	2.43353i
$975$	−6.84589	−	4.90445i	−0.219244	−	0.157068i
$976$	−14.7408			−0.471842
$977$			43.8239i			1.40205i	0.713136	+	0.701026i	$0.247274\pi$
$977$			43.8239i			1.40205i	−0.713136	+	0.701026i	$0.752726\pi$
$978$	32.7550	+	56.7333i	1.04739	+	1.81413i
$979$	−12.1901	+	21.1138i	−0.389596	+	0.674800i
$980$	147.071	−	84.9118i	4.69803	−	2.71241i
$981$	−57.4957	−	33.1952i	−1.83570	−	1.05984i
$982$	−2.95247	−	1.70461i	−0.0942171	−	0.0543963i
$983$	21.4811	+	12.4021i	0.685139	+	0.395565i	0.801789	−	0.597608i	$-0.203882\pi$
$983$	21.4811	+	12.4021i	0.685139	+	0.395565i	−0.116649	+	0.993173i	$0.537215\pi$
$984$	126.714			4.03950
$985$	−23.5684	−	40.8216i	−0.750951	−	1.30069i
$986$	−4.91071	+	2.83520i	−0.156389	+	0.0902912i
$987$	−16.5318	+	28.6338i	−0.526212	+	0.911425i
$988$	27.6541	+	61.0144i	0.879794	+	1.94113i
$989$	0.174512	+	0.302264i	0.00554916	+	0.00961143i
$990$		−	125.952i		−	4.00301i
$991$	30.9556			0.983337			0.491669	−	0.870782i	$-0.336387\pi$
$991$	30.9556			0.983337			0.491669	+	0.870782i	$0.336387\pi$
$992$	−5.26182	−	1.49135i	−0.167063	−	0.0473503i
$993$		−	39.2821i		−	1.24658i
$994$		−	45.5057i		−	1.44335i
$995$	8.81308	−	5.08824i	0.279394	−	0.161308i
$996$		−	43.9331i		−	1.39207i
$997$	2.23183	−	3.86564i	0.0706826	−	0.122426i	−0.828518	−	0.559962i	$-0.810816\pi$
$997$	2.23183	−	3.86564i	0.0706826	−	0.122426i	0.899201	+	0.437536i	$0.144149\pi$
$998$	−20.2314	−	35.0417i	−0.640413	−	1.10923i
$999$	−8.46118	+	4.88506i	−0.267700	+	0.154557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.l.c.25.4	✓	68
13.12	even	2	inner	403.2.l.c.25.31	yes	68
31.5	even	3	inner	403.2.l.c.129.4	yes	68
403.129	even	6	inner	403.2.l.c.129.31	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.4	✓	68	1.1	even	1	trivial
403.2.l.c.25.31	yes	68	13.12	even	2	inner
403.2.l.c.129.4	yes	68	31.5	even	3	inner
403.2.l.c.129.31	yes	68	403.129	even	6	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.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.42820i q^{2} +(1.37274 + 2.37765i) q^{3} -3.89617 q^{4} +(-2.09477 - 1.20941i) q^{5} +(5.77342 - 3.33328i) q^{6} +(-4.33186 + 2.50100i) q^{7} +4.60429i q^{8} +(-2.26881 + 3.92970i) q^{9} +O(q^{10})\)	\(q-2.42820i q^{2} +(1.37274 + 2.37765i) q^{3} -3.89617 q^{4} +(-2.09477 - 1.20941i) q^{5} +(5.77342 - 3.33328i) q^{6} +(-4.33186 + 2.50100i) q^{7} +4.60429i q^{8} +(-2.26881 + 3.92970i) q^{9} +(-2.93671 + 5.08652i) q^{10} +(4.09276 + 2.36296i) q^{11} +(-5.34842 - 9.26373i) q^{12} +(-0.352975 + 3.58823i) q^{13} +(6.07293 + 10.5186i) q^{14} -6.64083i q^{15} +3.38782 q^{16} +(-1.24548 - 2.15724i) q^{17} +(9.54210 + 5.50914i) q^{18} +(-4.12975 + 2.38431i) q^{19} +(8.16158 + 4.71209i) q^{20} +(-11.8930 - 6.86643i) q^{21} +(5.73774 - 9.93806i) q^{22} +0.407695 q^{23} +(-10.9474 + 6.32048i) q^{24} +(0.425368 + 0.736759i) q^{25} +(8.71296 + 0.857096i) q^{26} -4.22150 q^{27} +(16.8777 - 9.74432i) q^{28} +0.937479 q^{29} -16.1253 q^{30} +(-1.51826 + 5.35676i) q^{31} +0.982276i q^{32} +12.9749i q^{33} +(-5.23821 + 3.02428i) q^{34} +12.0990 q^{35} +(8.83968 - 15.3108i) q^{36} +(2.00430 - 1.15719i) q^{37} +(5.78959 + 10.0279i) q^{38} +(-9.01610 + 4.08645i) q^{39} +(5.56850 - 9.64493i) q^{40} +(-8.68112 - 5.01205i) q^{41} +(-16.6731 + 28.8786i) q^{42} +(0.428046 + 0.741397i) q^{43} +(-15.9461 - 9.20649i) q^{44} +(9.50527 - 5.48787i) q^{45} -0.989966i q^{46} -2.40762i q^{47} +(4.65058 + 8.05504i) q^{48} +(9.00999 - 15.6058i) q^{49} +(1.78900 - 1.03288i) q^{50} +(3.41944 - 5.92264i) q^{51} +(1.37525 - 13.9804i) q^{52} +(-5.12189 + 8.87137i) q^{53} +10.2507i q^{54} +(-5.71559 - 9.89970i) q^{55} +(-11.5153 - 19.9451i) q^{56} +(-11.3381 - 6.54606i) q^{57} -2.27639i q^{58} +(9.00882 - 5.20124i) q^{59} +25.8738i q^{60} -4.35112 q^{61} +(13.0073 + 3.68664i) q^{62} -22.6972i q^{63} +9.16080 q^{64} +(5.07906 - 7.08962i) q^{65} +31.5056 q^{66} +(7.21500 + 4.16558i) q^{67} +(4.85261 + 8.40497i) q^{68} +(0.559658 + 0.969356i) q^{69} -29.3788i q^{70} +(-3.24465 - 1.87330i) q^{71} +(-18.0935 - 10.4463i) q^{72} +(5.38151 + 3.10702i) q^{73} +(-2.80988 - 4.86686i) q^{74} +(-1.16784 + 2.02275i) q^{75} +(16.0902 - 9.28968i) q^{76} -23.6390 q^{77} +(9.92272 + 21.8929i) q^{78} +(-3.94652 - 6.83557i) q^{79} +(-7.09669 - 4.09728i) q^{80} +(1.01142 + 1.75184i) q^{81} +(-12.1703 + 21.0795i) q^{82} +(3.55686 + 2.05355i) q^{83} +(46.3372 + 26.7528i) q^{84} +6.02522i q^{85} +(1.80026 - 1.03938i) q^{86} +(1.28691 + 2.22900i) q^{87} +(-10.8798 + 18.8443i) q^{88} +5.15881i q^{89} +(-13.3257 - 23.0807i) q^{90} +(-7.44513 - 16.4265i) q^{91} -1.58845 q^{92} +(-14.8207 + 3.74354i) q^{93} -5.84620 q^{94} +11.5345 q^{95} +(-2.33551 + 1.34841i) q^{96} -4.77033i q^{97} +(-37.8940 - 21.8781i) q^{98} +(-18.5714 + 10.7222i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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