LMFDB - Embedded newform 403.2.r.a.218.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(218,403)]

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([5, 0]))

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

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

chi := DirichletCharacter("403.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.r (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			218.15
Character	$\chi$	$=$	403.218
Dual form			403.2.r.a.342.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453928 + 0.262075i) q^{2} +(0.409673 + 0.709575i) q^{3} +(-0.862633 + 1.49412i) q^{4} +4.38147i q^{5} +(-0.371924 - 0.214730i) q^{6} +(2.35938 + 1.36219i) q^{7} -1.95260i q^{8} +(1.16434 - 2.01669i) q^{9} +O(q^{10})$	\(q+(-0.453928 + 0.262075i) q^{2} +(0.409673 + 0.709575i) q^{3} +(-0.862633 + 1.49412i) q^{4} +4.38147i q^{5} +(-0.371924 - 0.214730i) q^{6} +(2.35938 + 1.36219i) q^{7} -1.95260i q^{8} +(1.16434 - 2.01669i) q^{9} +(-1.14828 - 1.98887i) q^{10} +(-0.756232 + 0.436611i) q^{11} -1.41359 q^{12} +(-0.333611 + 3.59008i) q^{13} -1.42798 q^{14} +(-3.10898 + 1.79497i) q^{15} +(-1.21354 - 2.10191i) q^{16} +(2.50485 - 4.33853i) q^{17} +1.22057i q^{18} +(2.34529 + 1.35405i) q^{19} +(-6.54647 - 3.77960i) q^{20} +2.23221i q^{21} +(0.228850 - 0.396379i) q^{22} +(-2.55386 - 4.42341i) q^{23} +(1.38552 - 0.799928i) q^{24} -14.1973 q^{25} +(-0.789437 - 1.71707i) q^{26} +4.36603 q^{27} +(-4.07055 + 2.35014i) q^{28} +(-0.0534285 - 0.0925408i) q^{29} +(0.940835 - 1.62957i) q^{30} -1.00000i q^{31} +(4.48372 + 2.58868i) q^{32} +(-0.619616 - 0.357735i) q^{33} +2.62584i q^{34} +(-5.96839 + 10.3375i) q^{35} +(2.00879 + 3.47933i) q^{36} +(-1.21695 + 0.702608i) q^{37} -1.41946 q^{38} +(-2.68410 + 1.23404i) q^{39} +8.55527 q^{40} +(9.69756 - 5.59889i) q^{41} +(-0.585006 - 1.01326i) q^{42} +(-2.90718 + 5.03539i) q^{43} -1.50654i q^{44} +(8.83607 + 5.10151i) q^{45} +(2.31853 + 1.33861i) q^{46} +4.74585i q^{47} +(0.994308 - 1.72219i) q^{48} +(0.211107 + 0.365647i) q^{49} +(6.44455 - 3.72076i) q^{50} +4.10468 q^{51} +(-5.07625 - 3.59538i) q^{52} +9.61754 q^{53} +(-1.98186 + 1.14423i) q^{54} +(-1.91300 - 3.31341i) q^{55} +(2.65981 - 4.60692i) q^{56} +2.21888i q^{57} +(0.0485053 + 0.0280045i) q^{58} +(-2.16761 - 1.25147i) q^{59} -6.19361i q^{60} +(-4.02071 + 6.96408i) q^{61} +(0.262075 + 0.453928i) q^{62} +(5.49422 - 3.17209i) q^{63} +2.14044 q^{64} +(-15.7299 - 1.46171i) q^{65} +0.375014 q^{66} +(-4.86116 + 2.80659i) q^{67} +(4.32154 + 7.48512i) q^{68} +(2.09249 - 3.62431i) q^{69} -6.25666i q^{70} +(-11.1889 - 6.45993i) q^{71} +(-3.93779 - 2.27348i) q^{72} -7.36642i q^{73} +(0.368272 - 0.637866i) q^{74} +(-5.81626 - 10.0741i) q^{75} +(-4.04625 + 2.33611i) q^{76} -2.37898 q^{77} +(0.894978 - 1.26360i) q^{78} +15.3485 q^{79} +(9.20946 - 5.31709i) q^{80} +(-1.70436 - 2.95205i) q^{81} +(-2.93466 + 5.08298i) q^{82} -2.54610i q^{83} +(-3.33519 - 1.92557i) q^{84} +(19.0092 + 10.9749i) q^{85} -3.04760i q^{86} +(0.0437764 - 0.0758229i) q^{87} +(0.852526 + 1.47662i) q^{88} +(7.05928 - 4.07568i) q^{89} -5.34792 q^{90} +(-5.67748 + 8.01592i) q^{91} +8.81218 q^{92} +(0.709575 - 0.409673i) q^{93} +(-1.24377 - 2.15427i) q^{94} +(-5.93276 + 10.2758i) q^{95} +4.24204i q^{96} +(2.44073 + 1.40916i) q^{97} +(-0.191654 - 0.110652i) q^{98} +2.03345i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) $ 68 * q + 32 * q^4 - 34 * q^9	$ 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) $ 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.453928	+	0.262075i	−0.320975	+	0.185315i	−0.651827	−	0.758368i	$-0.725997\pi$
$2$	−0.453928	+	0.262075i	−0.320975	+	0.185315i	0.330852	+	0.943683i	$0.392664\pi$
$3$	0.409673	+	0.709575i	0.236525	+	0.409673i	0.959715	−	0.280976i	$-0.0906582\pi$
$3$	0.409673	+	0.709575i	0.236525	+	0.409673i	−0.723190	+	0.690649i	$0.757325\pi$
$4$	−0.862633	+	1.49412i	−0.431317	+	0.747062i
$5$			4.38147i			1.95945i	0.200336	+	0.979727i	$0.435797\pi$
$5$			4.38147i			1.95945i	−0.200336	+	0.979727i	$0.564203\pi$
$6$	−0.371924	−	0.214730i	−0.151837	−	0.0876633i
$7$	2.35938	+	1.36219i	0.891761	+	0.514858i	0.874518	−	0.484993i	$-0.161178\pi$
$7$	2.35938	+	1.36219i	0.891761	+	0.514858i	0.0172427	+	0.999851i	$0.494511\pi$
$8$		−	1.95260i		−	0.690348i
$9$	1.16434	−	2.01669i	0.388112	−	0.672230i
$10$	−1.14828	−	1.98887i	−0.363117	−	0.628937i
$11$	−0.756232	+	0.436611i	−0.228012	+	0.131643i	−0.609655	−	0.792667i	$-0.708692\pi$
$11$	−0.756232	+	0.436611i	−0.228012	+	0.131643i	0.381642	+	0.924310i	$0.375359\pi$
$12$	−1.41359			−0.408068
$13$	−0.333611	+	3.59008i	−0.0925269	+	0.995710i
$13$	−0.333611	+	3.59008i	−0.0925269	+	0.995710i
$14$	−1.42798			−0.381644
$15$	−3.10898	+	1.79497i	−0.802736	+	0.463460i
$16$	−1.21354	−	2.10191i	−0.303385	−	0.525477i
$17$	2.50485	−	4.33853i	0.607516	−	1.05225i	−0.384132	−	0.923278i	$-0.625499\pi$
$17$	2.50485	−	4.33853i	0.607516	−	1.05225i	0.991648	−	0.128971i	$-0.0411673\pi$
$18$			1.22057i			0.287692i
$19$	2.34529	+	1.35405i	0.538047	+	0.310641i	0.744287	−	0.667860i	$-0.232789\pi$
$19$	2.34529	+	1.35405i	0.538047	+	0.310641i	−0.206240	+	0.978501i	$0.566123\pi$
$20$	−6.54647	−	3.77960i	−1.46383	−	0.845145i
$21$			2.23221i			0.487107i
$22$	0.228850	−	0.396379i	0.0487909	−	0.0845083i
$23$	−2.55386	−	4.42341i	−0.532517	−	0.922346i	−0.999279	−	0.0379630i	$-0.987913\pi$
$23$	−2.55386	−	4.42341i	−0.532517	−	0.922346i	0.466763	−	0.884383i	$-0.345420\pi$
$24$	1.38552	−	0.799928i	0.282817	−	0.163285i
$25$	−14.1973			−2.83946
$26$	−0.789437	−	1.71707i	−0.154821	−	0.336745i
$27$	4.36603			0.840242
$28$	−4.07055	+	2.35014i	−0.769262	+	0.444134i
$29$	−0.0534285	−	0.0925408i	−0.00992142	−	0.0171844i	0.861022	−	0.508568i	$-0.169825\pi$
$29$	−0.0534285	−	0.0925408i	−0.00992142	−	0.0171844i	−0.870943	+	0.491383i	$0.836491\pi$
$30$	0.940835	−	1.62957i	0.171772	−	0.297518i
$31$		−	1.00000i		−	0.179605i
$31$		−	1.00000i		−	0.179605i
$32$	4.48372	+	2.58868i	0.792617	+	0.457618i
$33$	−0.619616	−	0.357735i	−0.107861	−	0.0622737i
$34$			2.62584i			0.450328i
$35$	−5.96839	+	10.3375i	−1.00884	+	1.74736i
$36$	2.00879	+	3.47933i	0.334798	+	0.579888i
$37$	−1.21695	+	0.702608i	−0.200066	+	0.115508i	−0.596686	−	0.802475i	$-0.703516\pi$
$37$	−1.21695	+	0.702608i	−0.200066	+	0.115508i	0.396620	+	0.917983i	$0.370183\pi$
$38$	−1.41946			−0.230266
$39$	−2.68410	+	1.23404i	−0.429801	+	0.197604i
$40$	8.55527			1.35271
$41$	9.69756	−	5.59889i	1.51450	−	0.874399i	0.514649	−	0.857401i	$-0.327922\pi$
$41$	9.69756	−	5.59889i	1.51450	−	0.874399i	0.999856	−	0.0169981i	$-0.00541094\pi$
$42$	−0.585006	−	1.01326i	−0.0902683	−	0.156349i
$43$	−2.90718	+	5.03539i	−0.443341	+	0.767889i	−0.997935	−	0.0642318i	$-0.979540\pi$
$43$	−2.90718	+	5.03539i	−0.443341	+	0.767889i	0.554594	+	0.832121i	$0.312874\pi$
$44$		−	1.50654i		−	0.227119i
$45$	8.83607	+	5.10151i	1.31720	+	0.760488i
$46$	2.31853	+	1.33861i	0.341849	+	0.197367i
$47$			4.74585i			0.692254i	0.938188	+	0.346127i	$0.112503\pi$
$47$			4.74585i			0.692254i	−0.938188	+	0.346127i	$0.887497\pi$
$48$	0.994308	−	1.72219i	0.143516	−	0.248577i
$49$	0.211107	+	0.365647i	0.0301581	+	0.0522353i
$50$	6.44455	−	3.72076i	0.911397	−	0.526195i
$51$	4.10468			0.574771
$52$	−5.07625	−	3.59538i	−0.703949	−	0.498590i
$53$	9.61754			1.32107			0.660535	−	0.750795i	$-0.270329\pi$
$53$	9.61754			1.32107			0.660535	+	0.750795i	$0.270329\pi$
$54$	−1.98186	+	1.14423i	−0.269697	+	0.155710i
$55$	−1.91300	−	3.31341i	−0.257949	−	0.446780i
$56$	2.65981	−	4.60692i	0.355432	−	0.615626i
$57$			2.21888i			0.293898i
$58$	0.0485053	+	0.0280045i	0.00636906	+	0.00367718i
$59$	−2.16761	−	1.25147i	−0.282199	−	0.162928i	0.352219	−	0.935917i	$-0.385427\pi$
$59$	−2.16761	−	1.25147i	−0.282199	−	0.162928i	−0.634419	+	0.772990i	$0.718760\pi$
$60$		−	6.19361i		−	0.799591i
$61$	−4.02071	+	6.96408i	−0.514800	+	0.891659i	0.485053	+	0.874485i	$0.338800\pi$
$61$	−4.02071	+	6.96408i	−0.514800	+	0.891659i	−0.999853	+	0.0171744i	$0.994533\pi$
$62$	0.262075	+	0.453928i	0.0332836	+	0.0576489i
$63$	5.49422	−	3.17209i	0.692206	−	0.399645i
$64$	2.14044			0.267555
$65$	−15.7299	−	1.46171i	−1.95105	−	0.181302i
$66$	0.375014			0.0461610
$67$	−4.86116	+	2.80659i	−0.593885	+	0.342879i	−0.766632	−	0.642087i	$-0.778069\pi$
$67$	−4.86116	+	2.80659i	−0.593885	+	0.342879i	0.172747	+	0.984966i	$0.444736\pi$
$68$	4.32154	+	7.48512i	0.524064	+	0.907705i
$69$	2.09249	−	3.62431i	0.251907	−	0.436315i
$70$		−	6.25666i		−	0.747814i
$71$	−11.1889	−	6.45993i	−1.32788	−	0.766653i	−0.342910	−	0.939368i	$-0.611413\pi$
$71$	−11.1889	−	6.45993i	−1.32788	−	0.766653i	−0.984972	+	0.172715i	$0.944746\pi$
$72$	−3.93779	−	2.27348i	−0.464073	−	0.267932i
$73$		−	7.36642i		−	0.862174i	−0.902310	−	0.431087i	$-0.858130\pi$
$73$		−	7.36642i		−	0.862174i	0.902310	−	0.431087i	$-0.141870\pi$
$74$	0.368272	−	0.637866i	0.0428108	−	0.0741505i
$75$	−5.81626	−	10.0741i	−0.671603	−	1.16325i
$76$	−4.04625	+	2.33611i	−0.464137	+	0.267970i
$77$	−2.37898			−0.271110
$78$	0.894978	−	1.26360i	0.101336	−	0.143075i
$79$	15.3485			1.72685			0.863423	−	0.504481i	$-0.168316\pi$
$79$	15.3485			1.72685			0.863423	+	0.504481i	$0.168316\pi$
$80$	9.20946	−	5.31709i	1.02965	−	0.594468i
$81$	−1.70436	−	2.95205i	−0.189374	−	0.328005i
$82$	−2.93466	+	5.08298i	−0.324079	+	0.561321i
$83$		−	2.54610i		−	0.279471i	−0.990189	−	0.139736i	$-0.955375\pi$
$83$		−	2.54610i		−	0.279471i	0.990189	−	0.139736i	$-0.0446253\pi$
$84$	−3.33519	−	1.92557i	−0.363899	−	0.210097i
$85$	19.0092	+	10.9749i	2.06183	+	1.19040i
$86$		−	3.04760i		−	0.328631i
$87$	0.0437764	−	0.0758229i	0.00469332	−	0.00812907i
$88$	0.852526	+	1.47662i	0.0908796	+	0.157408i
$89$	7.05928	−	4.07568i	0.748282	−	0.432021i	−0.0767906	−	0.997047i	$-0.524467\pi$
$89$	7.05928	−	4.07568i	0.748282	−	0.432021i	0.825073	+	0.565026i	$0.191134\pi$
$90$	−5.34792			−0.563720
$91$	−5.67748	+	8.01592i	−0.595162	+	0.840297i
$92$	8.81218			0.918733
$93$	0.709575	−	0.409673i	0.0735795	−	0.0424811i
$94$	−1.24377	−	2.15427i	−0.128285	−	0.222196i
$95$	−5.93276	+	10.2758i	−0.608688	+	1.05428i
$96$			4.24204i			0.432952i
$97$	2.44073	+	1.40916i	0.247819	+	0.143078i	0.618765	−	0.785576i	$-0.287633\pi$
$97$	2.44073	+	1.40916i	0.247819	+	0.143078i	−0.370946	+	0.928654i	$0.620967\pi$
$98$	−0.191654	−	0.110652i	−0.0193600	−	0.0111775i
$99$			2.03345i			0.204369i
$100$	12.2471	−	21.2126i	1.22471	−	2.12126i
$101$	0.419293	+	0.726237i	0.0417212	+	0.0722633i	0.886132	−	0.463433i	$-0.153383\pi$
$101$	0.419293	+	0.726237i	0.0417212	+	0.0722633i	−0.844411	+	0.535696i	$0.820049\pi$
$102$	−1.86323	+	1.07574i	−0.184487	+	0.106514i
$103$	3.54682			0.349479			0.174740	−	0.984615i	$-0.444092\pi$
$103$	3.54682			0.349479			0.174740	+	0.984615i	$0.444092\pi$
$104$	7.01000	+	0.651408i	0.687387	+	0.0638758i
$105$	−9.78035			−0.954464
$106$	−4.36567	+	2.52052i	−0.424031	+	0.244814i
$107$	−1.43623	−	2.48762i	−0.138846	−	0.240488i	0.788214	−	0.615401i	$-0.211006\pi$
$107$	−1.43623	−	2.48762i	−0.138846	−	0.240488i	−0.927060	+	0.374913i	$0.877673\pi$
$108$	−3.76628	+	6.52339i	−0.362410	+	0.627713i
$109$			5.46514i			0.523466i	0.965140	+	0.261733i	$0.0842940\pi$
$109$			5.46514i			0.523466i	−0.965140	+	0.261733i	$0.915706\pi$
$110$	1.73673	+	1.00270i	0.165590	+	0.0956036i
$111$	−0.997106	−	0.575679i	−0.0946411	−	0.0546411i
$112$		−	6.61226i		−	0.624800i
$113$	−1.47711	+	2.55842i	−0.138955	+	0.240676i	−0.927101	−	0.374811i	$-0.877708\pi$
$113$	−1.47711	+	2.55842i	−0.138955	+	0.240676i	0.788147	+	0.615488i	$0.211041\pi$
$114$	−0.581513	−	1.00721i	−0.0544637	−	0.0943339i
$115$	19.3811	−	11.1897i	1.80729	−	1.04344i
$116$	0.184357			0.0171171
$117$	6.85165	+	4.85285i	0.633435	+	0.448646i
$118$	1.31192			0.120772
$119$	11.8198	−	6.82416i	1.08352	−	0.625569i
$120$	3.50486	+	6.07060i	0.319949	+	0.554167i
$121$	−5.11874	+	8.86592i	−0.465340	+	0.805993i
$122$		−	4.21492i		−	0.381601i
$123$	7.94566	+	4.58743i	0.716436	+	0.413634i
$124$	1.49412	+	0.862633i	0.134176	+	0.0774667i
$125$		−	40.2978i		−	3.60434i
$126$	−1.66265	+	2.87980i	−0.148121	+	0.256553i
$127$	1.74003	+	3.01382i	0.154403	+	0.267433i	0.932841	−	0.360287i	$-0.117321\pi$
$127$	1.74003	+	3.01382i	0.154403	+	0.267433i	−0.778439	+	0.627721i	$0.783988\pi$
$128$	−9.93904	+	5.73831i	−0.878496	+	0.507200i
$129$	−4.76398			−0.419445
$130$	7.52329	−	3.45890i	0.659837	−	0.303365i
$131$	−15.9927			−1.39729			−0.698643	−	0.715471i	$-0.746212\pi$
$131$	−15.9927			−1.39729			−0.698643	+	0.715471i	$0.746212\pi$
$132$	1.06900	−	0.617188i	0.0930447	−	0.0537194i
$133$	3.68895	+	6.38945i	0.319873	+	0.554036i
$134$	1.47108	−	2.54798i	0.127082	−	0.220112i
$135$			19.1296i			1.64642i
$136$	−8.47142	−	4.89098i	−0.726418	−	0.419398i
$137$	6.25418	+	3.61085i	0.534331	+	0.308496i	0.742778	−	0.669538i	$-0.233508\pi$
$137$	6.25418	+	3.61085i	0.534331	+	0.308496i	−0.208448	+	0.978034i	$0.566841\pi$
$138$			2.19356i			0.186729i
$139$	−0.218961	+	0.379252i	−0.0185720	+	0.0321677i	−0.875162	−	0.483830i	$-0.839245\pi$
$139$	−0.218961	+	0.379252i	−0.0185720	+	0.0321677i	0.856590	+	0.515998i	$0.172579\pi$
$140$	−10.2971	−	17.8350i	−0.870260	−	1.50733i
$141$	−3.36754	+	1.94425i	−0.283598	+	0.163735i
$142$	6.77195			0.568290
$143$	−1.31518	−	2.86059i	−0.109981	−	0.239215i
$144$	−5.65186			−0.470989
$145$	0.405465	−	0.234095i	0.0336720	−	0.0194406i
$146$	1.93056	+	3.34382i	0.159774	+	0.276736i
$147$	−0.172969	+	0.299592i	−0.0142663	+	0.0247099i
$148$		−	2.42437i		−	0.199282i
$149$	15.4921	+	8.94437i	1.26916	+	0.732752i	0.974830	−	0.222951i	$-0.0715691\pi$
$149$	15.4921	+	8.94437i	1.26916	+	0.732752i	0.294333	+	0.955703i	$0.404902\pi$
$150$	5.28032	+	3.04859i	0.431136	+	0.248917i
$151$			22.5246i			1.83303i	0.400002	+	0.916514i	$0.369009\pi$
$151$			22.5246i			1.83303i	−0.400002	+	0.916514i	$0.630991\pi$
$152$	2.64393	−	4.57942i	0.214451	−	0.371440i
$153$	−5.83298	−	10.1030i	−0.471569	−	0.816781i
$154$	1.07989	−	0.623472i	0.0870196	−	0.0502408i
$155$	4.38147			0.351928
$156$	0.471589	−	5.07491i	0.0377573	−	0.406318i
$157$	−5.75182			−0.459045			−0.229522	−	0.973303i	$-0.573716\pi$
$157$	−5.75182			−0.459045			−0.229522	+	0.973303i	$0.573716\pi$
$158$	−6.96713	+	4.02247i	−0.554275	+	0.320011i
$159$	3.94005	+	6.82436i	0.312466	+	0.541207i
$160$	−11.3422	+	19.6453i	−0.896681	+	1.55310i
$161$		−	13.9153i		−	1.09668i
$162$	1.54732	+	0.893343i	0.121569	+	0.0701877i
$163$	7.12650	+	4.11449i	0.558191	+	0.322271i	0.752419	−	0.658685i	$-0.228887\pi$
$163$	7.12650	+	4.11449i	0.558191	+	0.322271i	−0.194228	+	0.980956i	$0.562220\pi$
$164$			19.3191i			1.50857i
$165$	1.56741	−	2.71483i	0.122023	−	0.211349i
$166$	0.667271	+	1.15575i	0.0517903	+	0.0897034i
$167$	10.4985	−	6.06130i	0.812396	−	0.469037i	−0.0353910	−	0.999374i	$-0.511268\pi$
$167$	10.4985	−	6.06130i	0.812396	−	0.469037i	0.847787	+	0.530336i	$0.177934\pi$
$168$	4.35860			0.336274
$169$	−12.7774	−	2.39538i	−0.982878	−	0.184260i
$170$	−11.5050			−0.882397
$171$	5.46142	−	3.15315i	0.417645	−	0.241127i
$172$	−5.01566	−	8.68738i	−0.382441	−	0.662407i
$173$	−7.57278	+	13.1164i	−0.575748	+	0.997225i	0.420212	+	0.907426i	$0.361956\pi$
$173$	−7.57278	+	13.1164i	−0.575748	+	0.997225i	−0.995960	+	0.0897986i	$0.971378\pi$
$174$			0.0458908i			0.00347898i
$175$	−33.4968	−	19.3394i	−2.53212	−	1.46192i
$176$	1.83543	+	1.05969i	0.138351	+	0.0798769i
$177$		−	2.05078i		−	0.154146i
$178$	−2.13627	+	3.70013i	−0.160120	+	0.277336i
$179$	−6.87802	−	11.9131i	−0.514088	−	0.890426i	−0.999866	−	0.0163440i	$-0.994797\pi$
$179$	−6.87802	−	11.9131i	−0.514088	−	0.890426i	0.485779	−	0.874082i	$-0.338536\pi$
$180$	−15.2446	+	8.80146i	−1.13626	+	0.656022i
$181$	−1.49398			−0.111046			−0.0555232	−	0.998457i	$-0.517683\pi$
$181$	−1.49398			−0.111046			−0.0555232	+	0.998457i	$0.517683\pi$
$182$	0.476390	−	5.12657i	0.0353124	−	0.380007i
$183$	−6.58871			−0.487052
$184$	−8.63716	+	4.98667i	−0.636740	+	0.367622i
$185$	−3.07846	−	5.33205i	−0.226333	−	0.392020i
$186$	−0.214730	+	0.371924i	−0.0157448	+	0.0272708i
$187$			4.37458i			0.319901i
$188$	−7.09089	−	4.09393i	−0.517157	−	0.298581i
$189$	10.3011	+	5.94734i	0.749295	+	0.432606i
$190$		−	6.21931i		−	0.451196i
$191$	−9.39581	+	16.2740i	−0.679857	+	1.17755i	0.295167	+	0.955446i	$0.404625\pi$
$191$	−9.39581	+	16.2740i	−0.679857	+	1.17755i	−0.975024	+	0.222101i	$0.928709\pi$
$192$	0.876881	+	1.51880i	0.0632834	+	0.109610i
$193$	7.40623	−	4.27599i	0.533112	−	0.307792i	−0.209171	−	0.977879i	$-0.567076\pi$
$193$	7.40623	−	4.27599i	0.533112	−	0.307792i	0.742283	+	0.670087i	$0.233743\pi$
$194$	−1.47722			−0.106058
$195$	−5.40691	−	11.7603i	−0.387197	−	0.842175i
$196$	−0.728430			−0.0520307
$197$	16.3447	−	9.43664i	1.16451	−	0.672333i	0.212133	−	0.977241i	$-0.431959\pi$
$197$	16.3447	−	9.43664i	1.16451	−	0.672333i	0.952382	+	0.304908i	$0.0986257\pi$
$198$	−0.532916	−	0.923037i	−0.0378727	−	0.0655974i
$199$	6.11894	−	10.5983i	0.433760	−	0.751295i	−0.563433	−	0.826161i	$-0.690520\pi$
$199$	6.11894	−	10.5983i	0.433760	−	0.751295i	0.997194	+	0.0748669i	$0.0238532\pi$
$200$			27.7217i			1.96022i
$201$	−3.98297	−	2.29957i	−0.280937	−	0.162199i
$202$	−0.380657	−	0.219773i	−0.0267830	−	0.0154632i
$203$		−	0.291118i		−	0.0204325i
$204$	−3.54084	+	6.13291i	−0.247908	+	0.429389i
$205$	24.5314	+	42.4896i	1.71335	+	2.96760i
$206$	−1.61000	+	0.929535i	−0.112174	+	0.0647638i
$207$	−11.8942			−0.826704
$208$	7.95088	−	3.65548i	0.551295	−	0.253462i
$209$	−2.36478			−0.163575
$210$	4.43957	−	2.56319i	0.306359	−	0.176877i
$211$	−12.5848	−	21.7975i	−0.866375	−	1.50061i	−0.865676	−	0.500605i	$-0.833111\pi$
$211$	−12.5848	−	21.7975i	−0.866375	−	1.50061i	−0.000699245	−	1.00000i	$-0.500223\pi$
$212$	−8.29641	+	14.3698i	−0.569800	+	0.986922i
$213$		−	10.5858i		−	0.725330i
$214$	1.30389	+	0.752801i	0.0891320	+	0.0514604i
$215$	−22.0624	−	12.7377i	−1.50464	−	0.868707i
$216$		−	8.52510i		−	0.580060i
$217$	1.36219	−	2.35938i	0.0924713	−	0.160165i
$218$	−1.43228	−	2.48078i	−0.0970062	−	0.168020i
$219$	5.22702	−	3.01782i	0.353209	−	0.203926i
$220$	6.60086			0.445030
$221$	14.7401	+	10.4400i	0.991523	+	0.702271i
$222$	0.603485			0.0405033
$223$	9.75005	−	5.62919i	0.652912	−	0.376959i	−0.136659	−	0.990618i	$-0.543637\pi$
$223$	9.75005	−	5.62919i	0.652912	−	0.376959i	0.789571	+	0.613659i	$0.210303\pi$
$224$	7.05252	+	12.2153i	0.471217	+	0.816171i
$225$	−16.5304	+	28.6316i	−1.10203	+	1.90877i
$226$		−	1.54845i		−	0.103002i
$227$	−22.3914	−	12.9277i	−1.48617	−	0.858040i	−0.486294	−	0.873795i	$-0.661651\pi$
$227$	−22.3914	−	12.9277i	−1.48617	−	0.858040i	−0.999876	+	0.0157550i	$0.994985\pi$
$228$	−3.31528	−	1.91408i	−0.219560	−	0.126763i
$229$			19.7618i			1.30589i	0.757404	+	0.652947i	$0.226468\pi$
$229$			19.7618i			1.30589i	−0.757404	+	0.652947i	$0.773532\pi$
$230$	−5.86507	+	10.1586i	−0.386731	+	0.669838i
$231$	−0.974604	−	1.68806i	−0.0641243	−	0.111066i
$232$	−0.180695	+	0.104324i	−0.0118632	+	0.00684923i
$233$	1.28655			0.0842850			0.0421425	−	0.999112i	$-0.486582\pi$
$233$	1.28655			0.0842850			0.0421425	+	0.999112i	$0.486582\pi$
$234$	−4.38197	−	0.407197i	−0.286458	−	0.0266193i
$235$	−20.7938			−1.35644
$236$	3.73971	−	2.15912i	0.243434	−	0.140547i
$237$	6.28788	+	10.8909i	0.408442	+	0.707442i
$238$	−3.57688	+	6.19535i	−0.231855	+	0.401585i
$239$		−	20.2206i		−	1.30796i	−0.756511	−	0.653981i	$-0.773098\pi$
$239$		−	20.2206i		−	1.30796i	0.756511	−	0.653981i	$-0.226902\pi$
$240$	7.54574	+	4.35653i	0.487075	+	0.281213i
$241$	10.3893	+	5.99826i	0.669233	+	0.386382i	0.795786	−	0.605578i	$-0.207058\pi$
$241$	10.3893	+	5.99826i	0.669233	+	0.386382i	−0.126553	+	0.991960i	$0.540391\pi$
$242$		−	5.36598i		−	0.344938i
$243$	7.94550	−	13.7620i	0.509704	−	0.882834i
$244$	−6.93680	−	12.0149i	−0.444083	−	0.769175i
$245$	−1.60207	+	0.924958i	−0.102353	+	0.0590934i
$246$	−4.80900			−0.306611
$247$	−5.64359	+	7.96807i	−0.359093	+	0.506996i
$248$	−1.95260			−0.123990
$249$	1.80665	−	1.04307i	0.114492	−	0.0661019i
$250$	10.5611	+	18.2923i	0.667939	+	1.15691i
$251$	−5.31089	+	9.19874i	−0.335221	+	0.580619i	−0.983527	−	0.180760i	$-0.942144\pi$
$251$	−5.31089	+	9.19874i	−0.335221	+	0.580619i	0.648307	+	0.761379i	$0.275478\pi$
$252$			10.9454i			0.689495i
$253$	3.86262	+	2.23008i	0.242841	+	0.140204i
$254$	−1.57969	−	0.912037i	−0.0991188	−	0.0572263i
$255$			17.9846i			1.12624i
$256$	0.867297	−	1.50220i	0.0542061	−	0.0938876i
$257$	4.29932	+	7.44664i	0.268184	+	0.464509i	0.968393	−	0.249429i	$-0.0802430\pi$
$257$	4.29932	+	7.44664i	0.268184	+	0.464509i	−0.700209	+	0.713938i	$0.746910\pi$
$258$	2.16250	−	1.24852i	0.134631	−	0.0777295i
$259$	−3.82833			−0.237881
$260$	15.7531	−	22.2415i	0.976964	−	1.37936i
$261$	−0.248835			−0.0154025
$262$	7.25951	−	4.19128i	0.448494	−	0.258938i
$263$	−10.8040	−	18.7130i	−0.666200	−	1.15389i	−0.978958	−	0.204060i	$-0.934586\pi$
$263$	−10.8040	−	18.7130i	−0.666200	−	1.15389i	0.312758	−	0.949833i	$-0.398747\pi$
$264$	−0.698514	+	1.20986i	−0.0429906	+	0.0744618i
$265$			42.1390i			2.58858i
$266$	−3.34903	−	1.93357i	−0.205342	−	0.118555i
$267$	5.78399	+	3.33939i	0.353975	+	0.204367i
$268$		−	9.68423i		−	0.591558i
$269$	10.4803	−	18.1524i	0.638996	−	1.10677i	−0.346658	−	0.937992i	$-0.612683\pi$
$269$	10.4803	−	18.1524i	0.638996	−	1.10677i	0.985653	−	0.168782i	$-0.0539833\pi$
$270$	−5.01340	−	8.68347i	−0.305106	−	0.528459i
$271$	−15.4666	+	8.92965i	−0.939530	+	0.542438i	−0.889813	−	0.456326i	$-0.849165\pi$
$271$	−15.4666	+	8.92965i	−0.939530	+	0.542438i	−0.0497168	+	0.998763i	$0.515832\pi$
$272$	−12.1589			−0.737244
$273$	−8.01380	−	0.744687i	−0.485017	−	0.0450705i
$274$	−3.78526			−0.228676
$275$	10.7365	−	6.19870i	0.647433	−	0.373796i
$276$	3.61011	+	6.25290i	0.217303	+	0.376380i
$277$	12.2591	−	21.2333i	0.736577	−	1.27579i	−0.217452	−	0.976071i	$-0.569774\pi$
$277$	12.2591	−	21.2333i	0.736577	−	1.27579i	0.954028	−	0.299717i	$-0.0968922\pi$
$278$		−	0.229537i		−	0.0137667i
$279$	−2.01669	−	1.16434i	−0.120736	−	0.0697070i
$280$	20.1851	+	11.6539i	1.20629	+	0.696452i
$281$			10.8226i			0.645620i	0.946464	+	0.322810i	$0.104627\pi$
$281$			10.8226i			0.645620i	−0.946464	+	0.322810i	$0.895373\pi$
$282$	1.01908	−	1.76510i	0.0606852	−	0.105110i
$283$	0.0411289	+	0.0712373i	0.00244486	+	0.00423462i	0.867245	−	0.497881i	$-0.165888\pi$
$283$	0.0411289	+	0.0712373i	0.00244486	+	0.00423462i	−0.864800	+	0.502116i	$0.832555\pi$
$284$	19.3039	−	11.1451i	1.14548	−	0.661340i
$285$	−9.72196			−0.575879
$286$	1.34669	+	0.953826i	0.0796313	+	0.0564009i
$287$	30.5069			1.80077
$288$	10.4411	−	6.02818i	0.615248	−	0.355214i
$289$	−4.04858	−	7.01234i	−0.238152	−	0.412491i
$290$	−0.122701	+	0.212525i	−0.00720526	+	0.0124799i
$291$			2.30917i			0.135366i
$292$	11.0063	+	6.35451i	0.644097	+	0.371870i
$293$	−20.9068	−	12.0705i	−1.22139	−	0.705168i	−0.256173	−	0.966631i	$-0.582462\pi$
$293$	−20.9068	−	12.0705i	−1.22139	−	0.705168i	−0.965214	+	0.261463i	$0.915795\pi$
$294$		−	0.181324i		−	0.0105750i
$295$	5.48329	−	9.49734i	0.319249	−	0.552956i
$296$	1.37191	+	2.37622i	0.0797408	+	0.138115i
$297$	−3.30173	+	1.90625i	−0.191586	+	0.110612i
$298$	−9.37639			−0.543160
$299$	16.7324	−	7.69287i	0.967661	−	0.444890i
$300$	20.0692			1.15869
$301$	−13.7183	+	7.92025i	−0.790708	+	0.456516i
$302$	−5.90315	−	10.2246i	−0.339688	−	0.588357i
$303$	−0.343546	+	0.595039i	−0.0197362	+	0.0341841i
$304$		−	6.57279i		−	0.376975i
$305$	−30.5129	−	17.6167i	−1.74717	−	1.00873i
$306$	5.29550	+	3.05736i	0.302724	+	0.174778i
$307$		−	4.60376i		−	0.262750i	−0.991333	−	0.131375i	$-0.958061\pi$
$307$		−	4.60376i		−	0.262750i	0.991333	−	0.131375i	$-0.0419392\pi$
$308$	2.05219	−	3.55449i	0.116934	−	0.202536i
$309$	1.45304	+	2.51674i	0.0826605	+	0.143172i
$310$	−1.98887	+	1.14828i	−0.112960	+	0.0652177i
$311$	−27.1510			−1.53959			−0.769797	−	0.638289i	$-0.779642\pi$
$311$	−27.1510			−1.53959			−0.769797	+	0.638289i	$0.779642\pi$
$312$	2.40958	+	5.24098i	0.136416	+	0.296712i
$313$	34.6764			1.96002			0.980012	−	0.198936i	$-0.0637486\pi$
$313$	34.6764			1.96002			0.980012	+	0.198936i	$0.0637486\pi$
$314$	2.61091	−	1.50741i	0.147342	−	0.0850680i
$315$	13.8984	+	24.0728i	0.783087	+	1.35635i
$316$	−13.2402	+	22.9326i	−0.744817	+	1.29006i
$317$		−	2.78353i		−	0.156339i	−0.996940	−	0.0781693i	$-0.975093\pi$
$317$		−	2.78353i		−	0.156339i	0.996940	−	0.0781693i	$-0.0249075\pi$
$318$	−3.57699	−	2.06518i	−0.200588	−	0.115809i
$319$	0.0808086	+	0.0466549i	0.00452441	+	0.00261217i
$320$			9.37829i			0.524262i
$321$	1.17677	−	2.03822i	0.0656809	−	0.113763i
$322$	3.64686	+	6.31656i	0.203232	+	0.352008i
$323$	11.7492	−	6.78342i	0.653744	−	0.377439i
$324$	5.88097			0.326720
$325$	4.73637	−	50.9695i	0.262727	−	2.82728i
$326$	−4.31322			−0.238887
$327$	−3.87793	+	2.23892i	−0.214450	+	0.123813i
$328$	−10.9324	−	18.9355i	−0.603640	−	1.04554i
$329$	−6.46474	+	11.1973i	−0.356413	+	0.617325i
$330$			1.64311i			0.0904505i
$331$	−26.9376	−	15.5524i	−1.48062	−	0.854839i	−0.480866	−	0.876794i	$-0.659678\pi$
$331$	−26.9376	−	15.5524i	−1.48062	−	0.854839i	−0.999759	+	0.0219549i	$0.993011\pi$
$332$	3.80420	+	2.19635i	0.208782	+	0.120541i
$333$			3.27229i			0.179320i
$334$	−3.17703	+	5.50278i	−0.173839	+	0.301099i
$335$	−12.2970	−	21.2990i	−0.671857	−	1.16369i
$336$	4.69189	−	2.70887i	0.255964	−	0.147781i
$337$	1.72542			0.0939899			0.0469949	−	0.998895i	$-0.485036\pi$
$337$	1.72542			0.0939899			0.0469949	+	0.998895i	$0.485036\pi$
$338$	6.42779	−	2.26131i	0.349626	−	0.122999i
$339$	−2.42052			−0.131465
$340$	−32.7959	+	18.9347i	−1.77861	+	1.02688i
$341$	0.436611	+	0.756232i	0.0236438	+	0.0409522i
$342$	−1.65272	+	2.86260i	−0.0893691	+	0.154792i
$343$		−	17.9204i		−	0.967608i
$344$	9.83210	+	5.67656i	0.530111	+	0.306060i
$345$	15.8798	+	9.16821i	0.854940	+	0.493600i
$346$		−	7.93855i		−	0.426779i
$347$	6.61488	−	11.4573i	0.355105	−	0.615060i	−0.632031	−	0.774943i	$-0.717778\pi$
$347$	6.61488	−	11.4573i	0.355105	−	0.615060i	0.987136	+	0.159883i	$0.0511117\pi$
$348$	0.0755259	+	0.130815i	0.00404862	+	0.00701241i
$349$	−4.57107	+	2.63911i	−0.244684	+	0.141268i	−0.617328	−	0.786706i	$-0.711785\pi$
$349$	−4.57107	+	2.63911i	−0.244684	+	0.141268i	0.372644	+	0.927974i	$0.378451\pi$
$350$	20.2735			1.08366
$351$	−1.45655	+	15.6744i	−0.0777450	+	0.836638i
$352$	−4.52097			−0.240969
$353$	12.3745	−	7.14440i	0.658626	−	0.380258i	−0.133127	−	0.991099i	$-0.542502\pi$
$353$	12.3745	−	7.14440i	0.658626	−	0.380258i	0.791753	+	0.610841i	$0.209169\pi$
$354$	0.537458	+	0.930904i	0.0285656	+	0.0494770i
$355$	28.3040	−	49.0240i	1.50222	−	2.60192i
$356$			14.0633i			0.745351i
$357$	9.68449	+	5.59135i	0.512558	+	0.295925i
$358$	6.24425	+	3.60512i	0.330019	+	0.190536i
$359$		−	6.12621i		−	0.323329i	−0.986846	−	0.161665i	$-0.948314\pi$
$359$		−	6.12621i		−	0.323329i	0.986846	−	0.161665i	$-0.0516863\pi$
$360$	9.96120	−	17.2533i	0.525002	−	0.909329i
$361$	−5.83307	−	10.1032i	−0.307004	−	0.531746i
$362$	0.678157	−	0.391534i	0.0356431	−	0.0205786i
$363$	−8.38804			−0.440258
$364$	−7.07920	−	15.3977i	−0.371051	−	0.807057i
$365$	32.2758			1.68939
$366$	2.99080	−	1.72674i	0.156332	−	0.0902581i
$367$	4.00876	+	6.94338i	0.209256	+	0.362442i	0.951480	−	0.307710i	$-0.0995626\pi$
$367$	4.00876	+	6.94338i	0.209256	+	0.362442i	−0.742225	+	0.670151i	$0.766229\pi$
$368$	−6.19841	+	10.7360i	−0.323115	+	0.559651i
$369$		−	26.0759i		−	1.35746i
$370$	2.79480	+	1.61358i	0.145294	+	0.0838858i
$371$	22.6914	+	13.1009i	1.17808	+	0.680164i
$372$			1.41359i			0.0732912i
$373$	−12.1129	+	20.9801i	−0.627180	+	1.08631i	0.360935	+	0.932591i	$0.382458\pi$
$373$	−12.1129	+	20.9801i	−0.627180	+	1.08631i	−0.988115	+	0.153716i	$0.950876\pi$
$374$	−1.14647	−	1.98574i	−0.0592825	−	0.102680i
$375$	28.5943	−	16.5089i	1.47660	−	0.852517i
$376$	9.26675			0.477896
$377$	0.350054	−	0.160940i	0.0180287	−	0.00828883i
$378$	−6.23461			−0.320674
$379$	−19.9310	+	11.5072i	−1.02379	+	0.591084i	−0.915199	−	0.403003i	$-0.867967\pi$
$379$	−19.9310	+	11.5072i	−1.02379	+	0.591084i	−0.108589	+	0.994087i	$0.534633\pi$
$380$	−10.2356	−	17.7286i	−0.525074	−	0.909456i
$381$	−1.42569	+	2.46936i	−0.0730401	+	0.126509i
$382$		−	9.84963i		−	0.503951i
$383$	29.1737	+	16.8435i	1.49071	+	0.860660i	0.999943	−	0.0106324i	$-0.00338445\pi$
$383$	29.1737	+	16.8435i	1.49071	+	0.860660i	0.490764	+	0.871293i	$0.336718\pi$
$384$	−8.14352	−	4.70166i	−0.415572	−	0.239931i
$385$		−	10.4234i		−	0.531228i
$386$	−2.24126	+	3.88198i	−0.114077	+	0.197588i
$387$	6.76987	+	11.7258i	0.344132	+	0.596054i
$388$	−4.21091	+	2.43117i	−0.213777	+	0.123424i
$389$	−8.90551			−0.451527			−0.225764	−	0.974182i	$-0.572488\pi$
$389$	−8.90551			−0.451527			−0.225764	+	0.974182i	$0.572488\pi$
$390$	5.53644	+	3.92132i	0.280348	+	0.198564i
$391$	−25.5882			−1.29405
$392$	0.713963	−	0.412207i	0.0360606	−	0.0208196i
$393$	−6.55176	−	11.3480i	−0.330493	−	0.572430i
$394$	−4.94622	+	8.56710i	−0.249187	+	0.431604i
$395$			67.2492i			3.38368i
$396$	−3.03822	−	1.75412i	−0.152676	−	0.0881477i
$397$	16.6469	+	9.61107i	0.835482	+	0.482366i	0.855726	−	0.517429i	$-0.173111\pi$
$397$	16.6469	+	9.61107i	0.835482	+	0.482366i	−0.0202440	+	0.999795i	$0.506444\pi$
$398$			6.41449i			0.321529i
$399$	−3.02253	+	5.23517i	−0.151316	+	0.262086i
$400$	17.2290	+	29.8415i	0.861449	+	1.49207i
$401$	−18.0075	+	10.3966i	−0.899250	+	0.519182i	−0.876957	−	0.480570i	$-0.840430\pi$
$401$	−18.0075	+	10.3966i	−0.899250	+	0.519182i	−0.0222929	+	0.999751i	$0.507097\pi$
$402$	2.41064			0.120232
$403$	3.59008	+	0.333611i	0.178835	+	0.0166183i
$404$	−1.44678			−0.0719802
$405$	12.9343	−	7.46763i	0.642711	−	0.371069i
$406$	0.0762949	+	0.132147i	0.00378645	+	0.00655832i
$407$	0.613532	−	1.06267i	0.0304117	−	0.0526746i
$408$		−	8.01480i		−	0.396792i
$409$	−2.27837	−	1.31542i	−0.112658	−	0.0650432i	0.442612	−	0.896713i	$-0.354052\pi$
$409$	−2.27837	−	1.31542i	−0.112658	−	0.0650432i	−0.555270	+	0.831670i	$0.687385\pi$
$410$	−22.2709	−	12.8581i	−1.09988	−	0.635018i
$411$			5.91707i			0.291868i
$412$	−3.05961	+	5.29940i	−0.150736	+	0.261083i
$413$	−3.40948	−	5.90539i	−0.167769	−	0.290585i
$414$	5.39911	−	3.11718i	0.265352	−	0.153201i
$415$	11.1557			0.547611
$416$	−10.7894	+	15.2333i	−0.528993	+	0.746875i
$417$	−0.358810			−0.0175710
$418$	1.07344	−	0.619750i	0.0525036	−	0.0303130i
$419$	−3.27724	−	5.67635i	−0.160104	−	0.277308i	0.774802	−	0.632204i	$-0.217850\pi$
$419$	−3.27724	−	5.67635i	−0.160104	−	0.277308i	−0.934906	+	0.354896i	$0.884516\pi$
$420$	8.43685	−	14.6131i	0.411676	−	0.713044i
$421$		−	30.3654i		−	1.47992i	−0.672652	−	0.739959i	$-0.734845\pi$
$421$		−	30.3654i		−	1.47992i	0.672652	−	0.739959i	$-0.265155\pi$
$422$	11.4252	+	6.59634i	0.556170	+	0.321105i
$423$	9.57091	+	5.52577i	0.465354	+	0.268672i
$424$		−	18.7792i		−	0.911999i
$425$	−35.5622	+	61.5955i	−1.72502	+	2.98782i
$426$	2.77429	+	4.80521i	0.134415	+	0.232813i
$427$	−18.9728	+	10.9539i	−0.918156	+	0.530098i
$428$	4.95576			0.239546
$429$	1.49101	−	2.10513i	0.0719866	−	0.101637i
$430$	13.3530			0.643938
$431$	14.2635	−	8.23505i	0.687050	−	0.396668i	−0.115456	−	0.993313i	$-0.536833\pi$
$431$	14.2635	−	8.23505i	0.687050	−	0.396668i	0.802506	+	0.596644i	$0.203500\pi$
$432$	−5.29834	−	9.17699i	−0.254917	−	0.441528i
$433$	13.5555	−	23.4788i	0.651435	−	1.12832i	−0.331340	−	0.943511i	$-0.607501\pi$
$433$	13.5555	−	23.4788i	0.651435	−	1.12832i	0.982775	−	0.184807i	$-0.0591659\pi$
$434$			1.42798i			0.0685453i
$435$	0.332216	+	0.191805i	0.0159285	+	0.00919635i
$436$	−8.16560	−	4.71441i	−0.391062	−	0.225779i
$437$		−	13.8323i		−	0.661687i
$438$	−1.58179	+	2.73975i	−0.0755810	+	0.130910i
$439$	−9.78239	−	16.9436i	−0.466888	−	0.808674i	0.532397	−	0.846495i	$-0.321292\pi$
$439$	−9.78239	−	16.9436i	−0.466888	−	0.808674i	−0.999285	+	0.0378214i	$0.987958\pi$
$440$	−6.46976	+	3.73532i	−0.308434	+	0.178074i
$441$	0.983196			0.0468188
$442$	−9.42699	−	0.876008i	−0.448396	−	0.0416675i
$443$	11.2441			0.534221			0.267111	−	0.963666i	$-0.413931\pi$
$443$	11.2441			0.534221			0.267111	+	0.963666i	$0.413931\pi$
$444$	1.72027	−	0.993200i	0.0816405	−	0.0471352i
$445$	17.8575	+	30.9301i	0.846525	+	1.46623i
$446$	−2.95055	+	5.11049i	−0.139712	+	0.241989i
$447$			14.6571i			0.693256i
$448$	5.05011	+	2.91568i	0.238595	+	0.137753i
$449$	21.0522	+	12.1545i	0.993514	+	0.573605i	0.906323	−	0.422586i	$-0.138878\pi$
$449$	21.0522	+	12.1545i	0.993514	+	0.573605i	0.0871909	+	0.996192i	$0.472211\pi$
$450$		−	17.3289i		−	0.816891i
$451$	−4.88907	+	8.46811i	−0.230217	+	0.398748i
$452$	−2.54840	−	4.41396i	−0.119867	−	0.207615i
$453$	−15.9829	+	9.22773i	−0.750942	+	0.433557i
$454$	13.5521			0.636032
$455$	−35.1216	−	24.8757i	−1.64652	−	1.16619i
$456$	4.33258			0.202892
$457$	27.1411	−	15.6699i	1.26961	−	0.733008i	0.294693	−	0.955592i	$-0.404783\pi$
$457$	27.1411	−	15.6699i	1.26961	−	0.733008i	0.974913	+	0.222584i	$0.0714492\pi$
$458$	−5.17907	−	8.97041i	−0.242002	−	0.419160i
$459$	10.9363	−	18.9421i	0.510461	−	0.884144i
$460$			38.6103i			1.80022i
$461$	−9.22687	−	5.32714i	−0.429738	−	0.248110i	0.269497	−	0.963001i	$-0.413143\pi$
$461$	−9.22687	−	5.32714i	−0.429738	−	0.248110i	−0.699235	+	0.714892i	$0.746476\pi$
$462$	0.884800	+	0.510839i	0.0411646	+	0.0237664i
$463$		−	32.0596i		−	1.48994i	−0.667100	−	0.744968i	$-0.732465\pi$
$463$		−	32.0596i		−	1.48994i	0.667100	−	0.744968i	$-0.267535\pi$
$464$	−0.129675	+	0.224604i	−0.00602001	+	0.0104270i
$465$	1.79497	+	3.10898i	0.0832398	+	0.144176i
$466$	−0.584003	+	0.337174i	−0.0270534	+	0.0156193i
$467$	37.7048			1.74477			0.872384	−	0.488821i	$-0.162573\pi$
$467$	37.7048			1.74477			0.872384	+	0.488821i	$0.162573\pi$
$468$	−13.1612	+	6.05098i	−0.608378	+	0.279707i
$469$	−15.2924			−0.706137
$470$	9.43889	−	5.44955i	0.435384	−	0.251369i
$471$	−2.35636	−	4.08134i	−0.108576	−	0.188058i
$472$	−2.44362	+	4.23248i	−0.112477	+	0.194816i
$473$		−	5.07723i		−	0.233451i
$474$	−5.70849	−	3.29580i	−0.262200	−	0.151381i
$475$	−33.2968	−	19.2239i	−1.52776	−	0.882055i
$476$			23.5470i			1.07927i
$477$	11.1980	−	19.3956i	0.512723	−	0.888063i
$478$	5.29932	+	9.17868i	0.242385	+	0.419823i
$479$	−2.97765	+	1.71915i	−0.136052	+	0.0785499i	−0.566481	−	0.824075i	$-0.691696\pi$
$479$	−2.97765	+	1.71915i	−0.136052	+	0.0785499i	0.430429	+	0.902625i	$0.358362\pi$
$480$	−18.5864			−0.848349
$481$	−2.11643	−	4.60336i	−0.0965011	−	0.209895i
$482$	−6.28798			−0.286410
$483$	9.87397	−	5.70074i	0.449281	−	0.259393i
$484$	−8.83119	−	15.2961i	−0.401418	−	0.695276i
$485$	−6.17418	+	10.6940i	−0.280355	+	0.485590i
$486$			8.32928i			0.377824i
$487$	−12.9087	−	7.45284i	−0.584949	−	0.337721i	0.178149	−	0.984004i	$-0.442989\pi$
$487$	−12.9087	−	7.45284i	−0.584949	−	0.337721i	−0.763098	+	0.646283i	$0.776323\pi$
$488$	13.5981	+	7.85085i	0.615555	+	0.355391i
$489$			6.74238i			0.304901i
$490$	0.484817	−	0.839728i	0.0219018	−	0.0379350i
$491$	−17.2217	−	29.8288i	−0.777203	−	1.34615i	−0.933548	−	0.358452i	$-0.883305\pi$
$491$	−17.2217	−	29.8288i	−0.777203	−	1.34615i	0.156345	−	0.987702i	$-0.450029\pi$
$492$	−13.7084	+	7.91453i	−0.618021	+	0.356815i
$493$	−0.535322			−0.0241097
$494$	0.473546	−	5.09597i	0.0213058	−	0.229279i
$495$	−8.90949			−0.400452
$496$	−2.10191	+	1.21354i	−0.0943785	+	0.0544895i
$497$	−17.5993	−	30.4828i	−0.789435	−	1.36734i
$498$	−0.546726	+	0.946957i	−0.0244994	+	0.0424341i
$499$			21.5521i			0.964803i	0.875950	+	0.482401i	$0.160235\pi$
$499$			21.5521i			0.964803i	−0.875950	+	0.482401i	$0.839765\pi$
$500$	60.2099	+	34.7622i	2.69267	+	1.55461i
$501$	8.60188	+	4.96630i	0.384304	+	0.221878i
$502$		−	5.56742i		−	0.248486i
$503$	−7.78114	+	13.4773i	−0.346944	+	0.600924i	−0.985705	−	0.168481i	$-0.946114\pi$
$503$	−7.78114	+	13.4773i	−0.346944	+	0.600924i	0.638761	+	0.769405i	$0.279447\pi$
$504$	−6.19382	−	10.7280i	−0.275895	−	0.477863i
$505$	−3.18199	+	1.83712i	−0.141597	+	0.0817508i
$506$	−2.33780			−0.103928
$507$	−3.53486	−	10.0478i	−0.156989	−	0.446241i
$508$	−6.00403			−0.266386
$509$	−7.37810	+	4.25975i	−0.327029	+	0.188810i	−0.654521	−	0.756044i	$-0.727130\pi$
$509$	−7.37810	+	4.25975i	−0.327029	+	0.188810i	0.327493	+	0.944854i	$0.393796\pi$
$510$	−4.71331	−	8.16369i	−0.208709	−	0.361494i
$511$	10.0344	−	17.3802i	0.443897	−	0.768853i
$512$		−	22.0441i		−	0.974219i
$513$	10.2396	+	5.91184i	0.452090	+	0.261014i
$514$	−3.90316	−	2.25349i	−0.172161	−	0.0993972i
$515$			15.5403i			0.684788i
$516$	4.10956	−	7.11797i	0.180913	−	0.313351i
$517$	−2.07209	−	3.58896i	−0.0911304	−	0.157842i
$518$	1.73779	−	1.00331i	0.0763540	−	0.0440830i
$519$	−12.4095			−0.544715
$520$	−2.85413	+	30.7141i	−0.125162	+	1.34690i
$521$	11.5471			0.505885			0.252943	−	0.967481i	$-0.418602\pi$
$521$	11.5471			0.505885			0.252943	+	0.967481i	$0.418602\pi$
$522$	0.112953	−	0.0652134i	0.00494382	−	0.00285431i
$523$	−8.34640	−	14.4564i	−0.364963	−	0.632134i	0.623808	−	0.781578i	$-0.285585\pi$
$523$	−8.34640	−	14.4564i	−0.364963	−	0.632134i	−0.988770	+	0.149444i	$0.952252\pi$
$524$	13.7958	−	23.8950i	0.602672	−	1.04386i
$525$		−	31.6913i		−	1.38312i
$526$	9.80842	+	5.66290i	0.427668	+	0.246914i
$527$	−4.33853	−	2.50485i	−0.188989	−	0.109113i
$528$			1.73650i			0.0755715i
$529$	−1.54440	+	2.67497i	−0.0671477	+	0.116303i
$530$	−11.0436	−	19.1281i	−0.479703	−	0.830870i
$531$	−5.04766	+	2.91427i	−0.219050	+	0.126468i
$532$	−12.7288			−0.551866
$533$	16.8653	+	36.6829i	0.730516	+	1.58891i
$534$	−3.50069			−0.151490
$535$	10.8995	−	6.29281i	0.471225	−	0.272062i
$536$	5.48015	+	9.49189i	0.236706	+	0.409987i
$537$	5.63548	−	9.76094i	0.243189	−	0.421216i
$538$			10.9865i			0.473663i
$539$	−0.319291	−	0.184343i	−0.0137528	−	0.00794020i
$540$	−28.5820	−	16.5019i	−1.22998	−	0.710127i
$541$		−	4.84393i		−	0.208257i	−0.994564	−	0.104128i	$-0.966795\pi$
$541$		−	4.84393i		−	0.208257i	0.994564	−	0.104128i	$-0.0332053\pi$
$542$	4.68048	−	8.10683i	0.201044	−	0.348218i
$543$	−0.612042	−	1.06009i	−0.0262652	−	0.0454927i
$544$	22.4621	−	12.9685i	0.963055	−	0.556020i
$545$	−23.9454			−1.02571
$546$	3.83285	−	1.76219i	0.164031	−	0.0754146i
$547$	2.63481			0.112657			0.0563283	−	0.998412i	$-0.482061\pi$
$547$	2.63481			0.112657			0.0563283	+	0.998412i	$0.482061\pi$
$548$	−10.7901	+	6.22968i	−0.460931	+	0.266119i
$549$	9.36292	+	16.2171i	0.399600	+	0.692127i
$550$	−3.24905	+	5.62752i	−0.138540	+	0.239958i
$551$		−	0.289380i		−	0.0123280i
$552$	−7.07682	−	4.08581i	−0.301210	−	0.173903i
$553$	36.2130	+	20.9076i	1.53993	+	0.889081i
$554$			12.8512i			0.545995i
$555$	2.52232	−	4.36879i	0.107067	−	0.185445i
$556$	−0.377766	−	0.654311i	−0.0160209	−	0.0277489i
$557$	−12.0624	+	6.96421i	−0.511099	+	0.295083i	−0.733285	−	0.679921i	$-0.762014\pi$
$557$	−12.0624	+	6.96421i	−0.511099	+	0.295083i	0.222187	+	0.975004i	$0.428681\pi$
$558$	1.22057			0.0516710
$559$	−17.1076	−	12.1169i	−0.723574	−	0.512490i
$560$	28.9715			1.22427
$561$	−3.10409	+	1.79215i	−0.131055	+	0.0756646i
$562$	−2.83632	−	4.91266i	−0.119643	−	0.207228i
$563$	−0.645674	+	1.11834i	−0.0272119	+	0.0471324i	−0.879311	−	0.476249i	$-0.841996\pi$
$563$	−0.645674	+	1.11834i	−0.0272119	+	0.0471324i	0.852099	+	0.523381i	$0.175330\pi$
$564$		−	6.70869i		−	0.282487i
$565$	−11.2097	−	6.47190i	−0.471594	−	0.272275i
$566$	−0.0373391	−	0.0215577i	−0.00156948	−	0.000906139i
$567$		−	9.28665i		−	0.390003i
$568$	−12.6137	+	21.8475i	−0.529258	+	0.916701i
$569$	−6.14783	−	10.6483i	−0.257730	−	0.446402i	0.707903	−	0.706309i	$-0.249641\pi$
$569$	−6.14783	−	10.6483i	−0.257730	−	0.446402i	−0.965634	+	0.259907i	$0.916308\pi$
$570$	4.41307	−	2.54789i	0.184843	−	0.106719i
$571$	−21.7955			−0.912114			−0.456057	−	0.889950i	$-0.650739\pi$
$571$	−21.7955			−0.912114			−0.456057	+	0.889950i	$0.650739\pi$
$572$	5.40860	+	0.502598i	0.226145	+	0.0210147i
$573$	−15.3968			−0.643212
$574$	−13.8479	+	7.99511i	−0.578002	+	0.333709i
$575$	36.2579	+	62.8006i	1.51206	+	2.61897i
$576$	2.49219	−	4.31660i	0.103841	−	0.179858i
$577$		−	0.448513i		−	0.0186718i	−0.999956	−	0.00933592i	$-0.997028\pi$
$577$		−	0.448513i		−	0.0186718i	0.999956	−	0.00933592i	$-0.00297176\pi$
$578$	3.67552	+	2.12206i	0.152882	+	0.0882662i
$579$	6.06827	+	3.50352i	0.252189	+	0.145601i
$580$			0.807754i			0.0335401i
$581$	3.46827	−	6.00722i	0.143888	−	0.249221i
$582$	−0.605177	−	1.04820i	−0.0250854	−	0.0434492i
$583$	−7.27309	+	4.19912i	−0.301221	+	0.173910i
$584$	−14.3837			−0.595200
$585$	−21.2626	+	30.0203i	−0.879102	+	1.24119i
$586$	12.6535			0.522713
$587$	−32.8088	+	18.9422i	−1.35417	+	0.781828i	−0.988830	−	0.149048i	$-0.952379\pi$
$587$	−32.8088	+	18.9422i	−1.35417	+	0.781828i	−0.365336	+	0.930876i	$0.619046\pi$
$588$	−0.298418	−	0.516875i	−0.0123066	−	0.0213156i
$589$	1.35405	−	2.34529i	0.0557929	−	0.0966361i
$590$			5.74814i			0.236647i
$591$	13.3920	+	7.73187i	0.550873	+	0.318047i
$592$	2.95364	+	1.70528i	0.121394	+	0.0700867i
$593$			10.9324i			0.448939i	0.974481	+	0.224469i	$0.0720649\pi$
$593$			10.9324i			0.448939i	−0.974481	+	0.224469i	$0.927935\pi$
$594$	0.999164	−	1.73060i	0.0409962	−	0.0710075i
$595$	29.8999	+	51.7881i	1.22577	+	2.12310i
$596$	−26.7280	+	15.4314i	−1.09482	+	0.632096i
$597$	10.0271			0.410380
$598$	−5.57920	+	7.87716i	−0.228150	+	0.322121i
$599$	−15.9842			−0.653095			−0.326547	−	0.945181i	$-0.605885\pi$
$599$	−15.9842			−0.653095			−0.326547	+	0.945181i	$0.605885\pi$
$600$	−19.6706	+	11.3568i	−0.803049	+	0.463640i
$601$	14.0727	+	24.3746i	0.574036	+	0.994260i	0.996146	+	0.0877151i	$0.0279565\pi$
$601$	14.0727	+	24.3746i	0.574036	+	0.994260i	−0.422109	+	0.906545i	$0.638710\pi$
$602$	4.15140	−	7.19044i	0.169199	−	0.293061i
$603$			13.0713i			0.532303i
$604$	−33.6546	−	19.4305i	−1.36939	−	0.790616i
$605$	−38.8458	−	22.4276i	−1.57931	−	0.911813i
$606$		−	0.360140i		−	0.0146297i
$607$	9.75566	−	16.8973i	0.395970	−	0.685840i	−0.597255	−	0.802052i	$-0.703742\pi$
$607$	9.75566	−	16.8973i	0.395970	−	0.685840i	0.993224	+	0.116212i	$0.0370751\pi$
$608$	7.01042	+	12.1424i	0.284310	+	0.492440i
$609$	0.206570	−	0.119263i	0.00837064	−	0.00483279i
$610$	18.4676			0.747729
$611$	−17.0380	−	1.58327i	−0.689284	−	0.0640521i
$612$	20.1269			0.813581
$613$	10.3712	−	5.98781i	0.418889	−	0.241845i	−0.275713	−	0.961240i	$-0.588914\pi$
$613$	10.3712	−	5.98781i	0.418889	−	0.241845i	0.694602	+	0.719395i	$0.255581\pi$
$614$	1.20653	+	2.08977i	0.0486916	+	0.0843363i
$615$	−20.0997	+	34.8137i	−0.810498	+	1.40382i
$616$			4.64520i			0.187160i
$617$	8.96789	+	5.17762i	0.361034	+	0.208443i	0.669534	−	0.742781i	$-0.266494\pi$
$617$	8.96789	+	5.17762i	0.361034	+	0.208443i	−0.308500	+	0.951224i	$0.599827\pi$
$618$	−1.31915	−	0.761611i	−0.0530639	−	0.0306365i
$619$			30.1467i			1.21170i	0.795580	+	0.605849i	$0.207166\pi$
$619$			30.1467i			1.21170i	−0.795580	+	0.605849i	$0.792834\pi$
$620$	−3.77960	+	6.54647i	−0.151793	+	0.262912i
$621$	−11.1502	−	19.3127i	−0.447443	−	0.774994i
$622$	12.3246	−	7.11561i	0.494171	−	0.285310i
$623$	22.2073			0.889718
$624$	5.85110	+	4.14419i	0.234232	+	0.165900i
$625$	105.577			4.22308
$626$	−15.7406	+	9.08782i	−0.629120	+	0.363222i
$627$	−0.968786	−	1.67799i	−0.0386896	−	0.0670123i
$628$	4.96171	−	8.59393i	0.197994	−	0.342935i
$629$			7.03972i			0.280692i
$630$	−12.6177	−	7.28486i	−0.502703	−	0.290236i
$631$	7.97754	+	4.60584i	0.317581	+	0.183355i	0.650314	−	0.759666i	$-0.274637\pi$
$631$	7.97754	+	4.60584i	0.317581	+	0.183355i	−0.332733	+	0.943021i	$0.607971\pi$
$632$		−	29.9696i		−	1.19213i
$633$	10.3113	−	17.8597i	0.409838	−	0.709861i
$634$	0.729494	+	1.26352i	0.0289719	+	0.0501808i
$635$	−13.2050	+	7.62389i	−0.524023	+	0.302545i
$636$	−13.5953			−0.539087
$637$	−1.38313	+	0.635906i	−0.0548017	+	0.0251955i
$638$	−0.0489083			−0.00193630
$639$	−26.0554	+	15.0431i	−1.03073	+	0.595095i
$640$	−25.1423	−	43.5477i	−0.993835	−	1.72137i
$641$	−15.9209	+	27.5758i	−0.628837	+	1.08918i	0.358948	+	0.933358i	$0.383136\pi$
$641$	−15.9209	+	27.5758i	−0.628837	+	1.08918i	−0.987785	+	0.155821i	$0.950198\pi$
$642$			1.23361i			0.0486867i
$643$	−4.48321	−	2.58838i	−0.176801	−	0.102076i	0.408988	−	0.912540i	$-0.365882\pi$
$643$	−4.48321	−	2.58838i	−0.176801	−	0.102076i	−0.585789	+	0.810464i	$0.699215\pi$
$644$	20.7912	+	12.0038i	0.819290	+	0.473017i
$645$		−	20.8732i		−	0.821883i
$646$	−3.55553	+	6.15836i	−0.139891	+	0.242297i
$647$	0.618111	+	1.07060i	0.0243005	+	0.0420896i	0.877920	−	0.478808i	$-0.158931\pi$
$647$	0.618111	+	1.07060i	0.0243005	+	0.0420896i	−0.853619	+	0.520897i	$0.825597\pi$
$648$	−5.76417	+	3.32794i	−0.226438	+	0.130734i
$649$	2.18562			0.0857932
$650$	11.2079	+	24.3778i	0.439609	+	0.956175i
$651$	2.23221			0.0874870
$652$	−12.2951	+	7.09858i	−0.481514	+	0.278002i
$653$	−6.82689	−	11.8245i	−0.267157	−	0.462729i	0.700970	−	0.713191i	$-0.252751\pi$
$653$	−6.82689	−	11.8245i	−0.267157	−	0.462729i	−0.968126	+	0.250462i	$0.919417\pi$
$654$	1.17353	−	2.03262i	0.0458887	−	0.0794816i
$655$		−	70.0714i		−	2.73792i
$656$	−23.5367	−	13.5889i	−0.918954	−	0.530559i
$657$	−14.8558	−	8.57698i	−0.579579	−	0.334620i
$658$		−	6.77699i		−	0.264195i
$659$	−14.6297	+	25.3394i	−0.569892	+	0.987082i	0.426684	+	0.904401i	$0.359682\pi$
$659$	−14.6297	+	25.3394i	−0.569892	+	0.987082i	−0.996576	+	0.0826815i	$0.973652\pi$
$660$	2.70420	+	4.68380i	0.105261	+	0.182317i
$661$	−9.40174	+	5.42809i	−0.365685	+	0.211128i	−0.671572	−	0.740940i	$-0.734380\pi$
$661$	−9.40174	+	5.42809i	−0.365685	+	0.211128i	0.305887	+	0.952068i	$0.401047\pi$
$662$	16.3036			0.633659
$663$	−1.36937	+	14.7362i	−0.0531818	+	0.572305i
$664$	−4.97152			−0.192933
$665$	−27.9952	+	16.1630i	−1.08561	+	0.626776i
$666$	−0.857586	−	1.48538i	−0.0332308	−	0.0575574i
$667$	−0.272898	+	0.472672i	−0.0105666	+	0.0183019i
$668$			20.9147i			0.809214i
$669$	7.98867	+	4.61226i	0.308860	+	0.178320i
$670$	11.1639	+	6.44548i	0.431299	+	0.249011i
$671$		−	7.02195i		−	0.271079i
$672$	−5.77846	+	10.0086i	−0.222909	+	0.386089i
$673$	−15.1083	−	26.1684i	−0.582384	−	1.00872i	−0.995196	−	0.0979019i	$-0.968787\pi$
$673$	−15.1083	−	26.1684i	−0.582384	−	1.00872i	0.412813	−	0.910816i	$-0.364546\pi$
$674$	−0.783218	+	0.452191i	−0.0301684	+	0.0174178i
$675$	−61.9858			−2.38584
$676$	14.6012	−	17.0247i	0.561585	−	0.654796i
$677$	−22.5373			−0.866180			−0.433090	−	0.901351i	$-0.642577\pi$
$677$	−22.5373			−0.866180			−0.433090	+	0.901351i	$0.642577\pi$
$678$	1.09874	−	0.634359i	0.0421969	−	0.0243624i
$679$	3.83907	+	6.64946i	0.147330	+	0.255183i
$680$	21.4297	−	37.1173i	0.821791	−	1.42338i
$681$		−	21.1845i		−	0.811791i
$682$	−0.396379	−	0.228850i	−0.0151781	−	0.00876311i
$683$	26.7862	+	15.4650i	1.02494	+	0.591752i	0.915532	−	0.402245i	$-0.131770\pi$
$683$	26.7862	+	15.4650i	1.02494	+	0.591752i	0.109412	+	0.993996i	$0.465103\pi$
$684$			10.8800i			0.416009i
$685$	−15.8209	+	27.4025i	−0.604484	+	1.04700i
$686$	4.69648	+	8.13454i	0.179312	+	0.310578i
$687$	−14.0224	+	8.09586i	−0.534989	+	0.308876i
$688$	14.1119			0.538011
$689$	−3.20851	+	34.5278i	−0.122235	+	1.31540i
$690$	−9.61104			−0.365886
$691$	−24.5736	+	14.1876i	−0.934822	+	0.539720i	−0.888334	−	0.459199i	$-0.848137\pi$
$691$	−24.5736	+	14.1876i	−0.934822	+	0.539720i	−0.0464889	+	0.998919i	$0.514803\pi$
$692$	−13.0651	−	22.6294i	−0.496659	−	0.860239i
$693$	−2.76993	+	4.79767i	−0.105221	+	0.182248i
$694$			6.93438i			0.263225i
$695$	−1.66168	−	0.959373i	−0.0630312	−	0.0363911i
$696$	−0.148052	−	0.0854778i	−0.00561189	−	0.00324003i
$697$		−	56.0976i		−	2.12485i
$698$	1.38329	−	2.39593i	0.0523583	−	0.0906873i
$699$	0.527067	+	0.912906i	0.0199355	+	0.0345293i
$700$	57.7909	−	33.3656i	2.18429	−	1.26110i
$701$	29.0993			1.09907			0.549533	−	0.835472i	$-0.314805\pi$
$701$	29.0993			1.09907			0.549533	+	0.835472i	$0.314805\pi$
$702$	−3.44670	−	7.49677i	−0.130087	−	0.282947i
$703$	−3.80548			−0.143526
$704$	−1.61867	+	0.934539i	−0.0610059	+	0.0352218i
$705$	−8.51867	−	14.7548i	−0.320832	−	0.555697i
$706$	−3.74474	+	6.48608i	−0.140935	+	0.244107i
$707$			2.28462i			0.0859221i
$708$	3.06412	+	1.76907i	0.115157	+	0.0664856i
$709$	−16.6034	−	9.58598i	−0.623554	−	0.360009i	0.154698	−	0.987962i	$-0.450560\pi$
$709$	−16.6034	−	9.58598i	−0.623554	−	0.360009i	−0.778251	+	0.627953i	$0.783893\pi$
$710$			29.6711i			1.11354i
$711$	17.8709	−	30.9532i	0.670210	−	1.16084i
$712$	−7.95817	−	13.7840i	−0.298245	−	0.516575i
$713$	−4.42341	+	2.55386i	−0.165658	+	0.0956428i
$714$	−5.86141			−0.219358
$715$	12.5336	−	5.76243i	0.468731	−	0.215503i
$716$	23.7328			0.886938
$717$	14.3480	−	8.28383i	0.535836	−	0.309365i
$718$	1.60553	+	2.78086i	0.0599178	+	0.103781i
$719$	19.7493	−	34.2067i	0.736523	−	1.27570i	−0.217529	−	0.976054i	$-0.569800\pi$
$719$	19.7493	−	34.2067i	0.736523	−	1.27570i	0.954052	−	0.299642i	$-0.0968671\pi$
$720$		−	24.7635i		−	0.922881i
$721$	8.36830	+	4.83144i	0.311652	+	0.179932i
$722$	5.29558	+	3.05741i	0.197081	+	0.113785i
$723$			9.82931i			0.365556i
$724$	1.28875	−	2.23219i	0.0478962	−	0.0829586i
$725$	0.758540	+	1.31383i	0.0281715	+	0.0487944i
$726$	3.80756	−	2.19830i	0.141312	−	0.0815865i
$727$	46.6832			1.73139			0.865693	−	0.500576i	$-0.166878\pi$
$727$	46.6832			1.73139			0.865693	+	0.500576i	$0.166878\pi$
$728$	15.6519	+	11.0858i	0.580098	+	0.410869i
$729$	2.79405			0.103483
$730$	−14.6509	+	8.45868i	−0.542253	+	0.313070i
$731$	14.5641	+	25.2258i	0.538674	+	0.933010i
$732$	5.68364	−	9.84436i	0.210073	−	0.363858i
$733$		−	41.6910i		−	1.53989i	−0.638108	−	0.769947i	$-0.720283\pi$
$733$		−	41.6910i		−	1.53989i	0.638108	−	0.769947i	$-0.279717\pi$
$734$	−3.63938	−	2.10119i	−0.134332	−	0.0775565i
$735$	−1.31265	−	0.757861i	−0.0484179	−	0.0279541i
$736$		−	26.4445i		−	0.974756i
$737$	2.45077	−	4.24486i	0.0902754	−	0.156362i
$738$	6.83386	+	11.8366i	0.251558	+	0.435711i
$739$	21.3938	−	12.3517i	0.786983	−	0.454365i	−0.0519167	−	0.998651i	$-0.516533\pi$
$739$	21.3938	−	12.3517i	0.786983	−	0.454365i	0.838899	+	0.544287i	$0.183200\pi$
$740$	10.6223			0.390484
$741$	−7.96596	−	0.740242i	−0.292637	−	0.0271935i
$742$	−13.7337			−0.504179
$743$	−17.1685	+	9.91222i	−0.629850	+	0.363644i	−0.780694	−	0.624914i	$-0.785134\pi$
$743$	−17.1685	+	9.91222i	−0.629850	+	0.363644i	0.150844	+	0.988558i	$0.451801\pi$
$744$	−0.799928	−	1.38552i	−0.0293268	−	0.0507955i
$745$	−39.1895	+	67.8783i	−1.43579	+	2.48687i
$746$		−	12.6979i		−	0.464904i
$747$	−5.13470	−	2.96452i	−0.187869	−	0.108466i
$748$	−6.53617	−	3.77366i	−0.238986	−	0.137979i
$749$		−	7.82566i		−	0.285943i
$750$	−8.65316	+	14.9877i	−0.315969	+	0.547274i
$751$	26.8462	+	46.4990i	0.979632	+	1.69677i	0.663713	+	0.747987i	$0.268979\pi$
$751$	26.8462	+	46.4990i	0.979632	+	1.69677i	0.315919	+	0.948786i	$0.397687\pi$
$752$	9.97536	−	5.75927i	0.363764	−	0.210019i
$753$	−8.70292			−0.317152
$754$	−0.116721	+	0.164795i	−0.00425071	+	0.00600150i
$755$	−98.6911			−3.59174
$756$	−17.7721	+	10.2608i	−0.646367	+	0.373180i
$757$	−7.91272	−	13.7052i	−0.287593	−	0.498125i	0.685642	−	0.727939i	$-0.259522\pi$
$757$	−7.91272	−	13.7052i	−0.287593	−	0.498125i	−0.973235	+	0.229814i	$0.926188\pi$
$758$	6.03149	−	10.4469i	0.219074	−	0.379447i
$759$			3.65442i			0.132647i
$760$	20.0646	+	11.5843i	0.727819	+	0.420207i
$761$	−3.01220	−	1.73909i	−0.109192	−	0.0630421i	0.444409	−	0.895824i	$-0.353414\pi$
$761$	−3.01220	−	1.73909i	−0.109192	−	0.0630421i	−0.553601	+	0.832782i	$0.686747\pi$
$762$		−	1.49455i		−	0.0541417i
$763$	−7.44455	+	12.8943i	−0.269511	+	0.466806i
$764$	−16.2103	−	28.0770i	−0.586467	−	1.01579i
$765$	44.2661	−	25.5571i	1.60044	−	0.924017i
$766$	−17.6570			−0.637974
$767$	5.21603	−	7.36441i	0.188340	−	0.265913i
$768$	1.42123			0.0512843
$769$	−0.387734	+	0.223858i	−0.0139820	+	0.00807253i	−0.506975	−	0.861961i	$-0.669236\pi$
$769$	−0.387734	+	0.223858i	−0.0139820	+	0.00807253i	0.492993	+	0.870033i	$0.335903\pi$
$770$	2.73173	+	4.73149i	0.0984446	+	0.170511i
$771$	−3.52263	+	6.10138i	−0.126865	+	0.219736i
$772$			14.7544i			0.531024i
$773$	4.28625	+	2.47467i	0.154166	+	0.0890075i	0.575098	−	0.818084i	$-0.304964\pi$
$773$	4.28625	+	2.47467i	0.154166	+	0.0890075i	−0.420933	+	0.907092i	$0.638297\pi$
$774$	−6.14607	−	3.54843i	−0.220916	−	0.127546i
$775$			14.1973i			0.509983i
$776$	2.75152	−	4.76577i	0.0987738	−	0.171081i
$777$	−1.56837	−	2.71649i	−0.0562648	−	0.0974535i
$778$	4.04246	−	2.33391i	0.144929	−	0.0836748i
$779$	30.3248			1.08650
$780$	22.2356	+	2.06625i	0.796161	+	0.0739838i
$781$	11.2819			0.403698
$782$	11.6152	−	6.70603i	0.415358	−	0.239807i
$783$	−0.233270	−	0.404036i	−0.00833639	−	0.0144391i
$784$	0.512372	−	0.887454i	0.0182990	−	0.0316948i
$785$		−	25.2014i		−	0.899478i
$786$	5.94805	+	3.43411i	0.212160	+	0.122491i
$787$	21.4808	+	12.4020i	0.765708	+	0.442082i	0.831341	−	0.555762i	$-0.187573\pi$
$787$	21.4808	+	12.4020i	0.765708	+	0.442082i	−0.0656333	+	0.997844i	$0.520907\pi$
$788$			32.5614i			1.15995i
$789$	8.85218	−	15.3324i	0.315146	−	0.545849i
$790$	−17.6244	−	30.5263i	−0.627047	−	1.08608i
$791$	−6.97010	+	4.02419i	−0.247828	+	0.143084i
$792$	3.97051			0.141086
$793$	−23.6603	−	16.7580i	−0.840201	−	0.595094i
$794$	−10.0753			−0.357559
$795$	−29.9008	+	17.2632i	−1.06047	+	0.612263i
$796$	10.5568	+	18.2849i	0.374176	+	0.648092i
$797$	6.22897	−	10.7889i	0.220641	−	0.382162i	−0.734361	−	0.678759i	$-0.762518\pi$
$797$	6.22897	−	10.7889i	0.220641	−	0.382162i	0.955003	+	0.296596i	$0.0958516\pi$
$798$		−	3.16852i		−	0.112164i
$799$	20.5900	+	11.8877i	0.728423	+	0.420555i
$800$	−63.6568	−	36.7522i	−2.25061	−	1.29939i
$801$		−	18.9818i		−	0.670690i
$802$	5.44939	−	9.43862i	0.192425	−	0.333289i
$803$	3.21626	+	5.57072i	0.113499	+	0.196586i
$804$	6.87168	−	3.96737i	0.242346	−	0.139918i
$805$	60.9697			2.14890
$806$	−1.71707	+	0.789437i	−0.0604812	+	0.0278067i
$807$	17.1740			0.604554
$808$	1.41805	−	0.818712i	0.0498868	−	0.0288022i
$809$	12.4705	+	21.5996i	0.438440	+	0.759401i	0.997569	−	0.0696797i	$-0.0221977\pi$
$809$	12.4705	+	21.5996i	0.438440	+	0.759401i	−0.559129	+	0.829081i	$0.688864\pi$
$810$	−3.91416	+	6.77953i	−0.137530	+	0.238208i
$811$			3.36510i			0.118165i	0.998253	+	0.0590823i	$0.0188174\pi$
$811$			3.36510i			0.118165i	−0.998253	+	0.0590823i	$0.981183\pi$
$812$	0.434967	+	0.251128i	0.0152643	+	0.00881287i
$813$	−12.6725	−	7.31648i	−0.444444	−	0.256600i
$814$			0.643167i			0.0225430i
$815$	−18.0275	+	31.2246i	−0.631476	+	1.09375i
$816$	−4.98119	−	8.62767i	−0.174377	−	0.302029i
$817$	−13.6364	+	7.87297i	−0.477077	+	0.275440i
$818$	1.37895			0.0482140
$819$	9.55513	+	20.7829i	0.333883	+	0.726215i
$820$	−84.6463			−2.95598
$821$	37.1777	−	21.4645i	1.29751	−	0.749117i	0.317536	−	0.948246i	$-0.397145\pi$
$821$	37.1777	−	21.4645i	1.29751	−	0.749117i	0.979973	+	0.199129i	$0.0638113\pi$
$822$	−1.55072	−	2.68592i	−0.0540875	−	0.0936823i
$823$	−13.2747	+	22.9924i	−0.462726	+	0.801466i	−0.999096	−	0.0425176i	$-0.986462\pi$
$823$	−13.2747	+	22.9924i	−0.462726	+	0.801466i	0.536369	+	0.843983i	$0.319795\pi$
$824$		−	6.92553i		−	0.241262i
$825$	8.79688	+	5.07888i	0.306268	+	0.176824i
$826$	3.09531	+	1.78708i	0.107700	+	0.0621804i
$827$			14.4511i			0.502515i	0.967920	+	0.251257i	$0.0808440\pi$
$827$			14.4511i			0.502515i	−0.967920	+	0.251257i	$0.919156\pi$
$828$	10.2603	−	17.7714i	0.356571	−	0.617599i
$829$	16.9858	+	29.4202i	0.589940	+	1.02181i	0.994240	+	0.107179i	$0.0341818\pi$
$829$	16.9858	+	29.4202i	0.589940	+	1.02181i	−0.404300	+	0.914626i	$0.632485\pi$
$830$	−5.06387	+	2.92363i	−0.175770	+	0.101481i
$831$	20.0889			0.696875
$832$	−0.714074	+	7.68436i	−0.0247561	+	0.266407i
$833$	2.11516			0.0732861
$834$	0.162874	−	0.0940352i	0.00563986	−	0.00325617i
$835$	26.5574	+	45.9988i	0.919057	+	1.59185i
$836$	2.03994	−	3.53327i	0.0705527	−	0.122201i
$837$		−	4.36603i		−	0.150912i
$838$	2.97526	+	1.71777i	0.102779	+	0.0593393i
$839$	17.3349	+	10.0083i	0.598466	+	0.345525i	0.768438	−	0.639924i	$-0.221034\pi$
$839$	17.3349	+	10.0083i	0.598466	+	0.345525i	−0.169972	+	0.985449i	$0.554368\pi$
$840$			19.0971i			0.658913i
$841$	14.4943	−	25.1048i	0.499803	−	0.865684i
$842$	7.95802	+	13.7837i	0.274251	+	0.475017i
$843$	−7.67941	+	4.43371i	−0.264493	+	0.152705i
$844$	43.4243			1.49473
$845$	10.4953	−	55.9839i	0.361049	−	1.92590i
$846$	−5.79267			−0.199156
$847$	−24.1541	+	13.9454i	−0.829944	+	0.479169i
$848$	−11.6713	−	20.2152i	−0.400793	−	0.694193i
$849$	−0.0336988	+	0.0583680i	−0.00115654	+	0.00200319i
$850$		−	37.2799i		−	1.27869i
$851$	6.21585	+	3.58873i	0.213077	+	0.123020i
$852$	15.8166	+	9.13170i	0.541867	+	0.312847i
$853$			41.2765i			1.41328i	0.707574	+	0.706640i	$0.249790\pi$
$853$			41.2765i			1.41328i	−0.707574	+	0.706640i	$0.750210\pi$
$854$	5.74151	−	9.94458i	0.196470	−	0.340297i
$855$	13.8154	+	23.9290i	0.472478	+	0.818356i
$856$	−4.85733	+	2.80438i	−0.166020	+	0.0958518i
$857$	−0.787514			−0.0269010			−0.0134505	−	0.999910i	$-0.504282\pi$
$857$	−0.787514			−0.0269010			−0.0134505	+	0.999910i	$0.504282\pi$
$858$	−0.125109	+	1.34633i	−0.00427114	+	0.0459630i
$859$	11.5452			0.393916			0.196958	−	0.980412i	$-0.436894\pi$
$859$	11.5452			0.393916			0.196958	+	0.980412i	$0.436894\pi$
$860$	38.0635	−	21.9760i	1.29796	−	0.749375i
$861$	12.4979	+	21.6469i	0.425926	+	0.737726i
$862$	−4.31641	+	7.47623i	−0.147017	+	0.254642i
$863$			12.9872i			0.442090i	0.975264	+	0.221045i	$0.0709468\pi$
$863$			12.9872i			0.442090i	−0.975264	+	0.221045i	$0.929053\pi$
$864$	19.5760	+	11.3022i	0.665990	+	0.384510i
$865$	−57.4693	−	33.1799i	−1.95402	−	1.12815i
$866$			14.2102i			0.482883i
$867$	3.31719	−	5.74553i	0.112658	−	0.195129i
$868$	2.35014	+	4.07055i	0.0797688	+	0.138164i
$869$	−11.6071	+	6.70134i	−0.393742	+	0.227327i
$870$	−0.201069			−0.00681689
$871$	−8.45416	−	18.3883i	−0.286458	−	0.623063i
$872$	10.6712			0.361374
$873$	5.68366	−	3.28146i	0.192363	−	0.111061i
$874$	3.62509	+	6.27885i	0.122621	+	0.212385i
$875$	54.8931	−	95.0777i	1.85573	−	3.21421i
$876$			10.4131i			0.351826i
$877$	18.8329	+	10.8732i	0.635942	+	0.367161i	0.783049	−	0.621959i	$-0.213663\pi$
$877$	18.8329	+	10.8732i	0.635942	+	0.367161i	−0.147108	+	0.989120i	$0.546996\pi$
$878$	8.88099	+	5.12744i	0.299719	+	0.173043i
$879$		−	19.7799i		−	0.667159i
$880$	−4.64299	+	8.04190i	−0.156515	+	0.271092i
$881$	24.0417	+	41.6415i	0.809987	+	1.40294i	0.912872	+	0.408245i	$0.133859\pi$
$881$	24.0417	+	41.6415i	0.809987	+	1.40294i	−0.102886	+	0.994693i	$0.532808\pi$
$882$	−0.446300	+	0.257671i	−0.0150277	+	0.00867624i
$883$	−17.0281			−0.573042			−0.286521	−	0.958074i	$-0.592499\pi$
$883$	−17.0281			−0.573042			−0.286521	+	0.958074i	$0.592499\pi$
$884$	−28.3139	+	13.0176i	−0.952301	+	0.437828i
$885$	8.98542			0.302042
$886$	−5.10399	+	2.94679i	−0.171472	+	0.0989993i
$887$	0.710442	+	1.23052i	0.0238543	+	0.0413169i	0.877706	−	0.479199i	$-0.159073\pi$
$887$	0.710442	+	1.23052i	0.0238543	+	0.0413169i	−0.853852	+	0.520516i	$0.825740\pi$
$888$	−1.12407	+	1.94695i	−0.0377214	+	0.0653353i
$889$			9.48098i			0.317982i
$890$	−16.2120	−	9.36000i	−0.543428	−	0.313748i
$891$	2.57779	+	1.48829i	0.0863592	+	0.0498595i
$892$			19.4237i			0.650354i
$893$	−6.42615	+	11.1304i	−0.215043	+	0.372465i
$894$	−3.84126	−	6.65325i	−0.128471	−	0.222518i
$895$	52.1969	−	30.1359i	1.74475	−	1.00733i
$896$	−31.2666			−1.04454
$897$	12.3135	+	8.72134i	0.411135	+	0.291197i
$898$	−12.7416			−0.425191
$899$	−0.0925408	+	0.0534285i	−0.00308641	+	0.00178194i
$900$	−28.5194	−	49.3971i	−0.950647	−	1.64657i
$901$	24.0905	−	41.7260i	0.802572	−	1.39010i
$902$		−	5.12521i		−	0.170651i
$903$	−11.2400	−	6.48943i	−0.374044	−	0.215955i
$904$	4.99558	+	2.88420i	0.166150	+	0.0959270i
$905$		−	6.54582i		−	0.217590i
$906$	4.83672	−	8.37745i	0.160689	−	0.278322i
$907$	−14.8424	−	25.7078i	−0.492834	−	0.853614i	0.507132	−	0.861868i	$-0.330706\pi$
$907$	−14.8424	−	25.7078i	−0.492834	−	0.853614i	−0.999966	+	0.00825486i	$0.997372\pi$
$908$	38.6311	−	22.3037i	1.28202	−	0.740174i
$909$	1.95279			0.0647700
$910$	22.4620	+	2.08729i	0.744606	+	0.0691930i
$911$	−40.1327			−1.32966			−0.664828	−	0.746996i	$-0.731495\pi$
$911$	−40.1327			−1.32966			−0.664828	+	0.746996i	$0.731495\pi$
$912$	4.66388	−	2.69269i	0.154437	−	0.0891640i
$913$	1.11166	+	1.92544i	0.0367904	+	0.0637229i
$914$	−8.21339	+	14.2260i	−0.271675	+	0.470555i
$915$		−	28.8683i		−	0.954356i
$916$	−29.5265	−	17.0471i	−0.975584	−	0.563254i
$917$	−37.7327	−	21.7850i	−1.24604	−	0.719404i
$918$			11.4645i			0.378384i
$919$	26.6375	−	46.1376i	0.878691	−	1.52194i	0.0259129	−	0.999664i	$-0.491751\pi$
$919$	26.6375	−	46.1376i	0.878691	−	1.52194i	0.852778	−	0.522273i	$-0.174916\pi$
$920$	−21.8489	−	37.8435i	−0.720338	−	1.24766i
$921$	3.26671	−	1.88603i	0.107642	−	0.0621470i
$922$	5.58444			0.183914
$923$	26.9245	−	38.0141i	0.886229	−	1.25125i
$924$	3.36290			0.110631
$925$	17.2775	−	9.97515i	0.568079	−	0.327981i
$926$	8.40203	+	14.5527i	0.276108	+	0.478233i
$927$	4.12970	−	7.15284i	0.135637	−	0.234930i
$928$		−	0.553236i		−	0.0181609i
$929$	−45.2909	−	26.1487i	−1.48595	−	0.857912i	−0.486076	−	0.873917i	$-0.661572\pi$
$929$	−45.2909	−	26.1487i	−1.48595	−	0.857912i	−0.999872	+	0.0160042i	$0.994905\pi$
$930$	−1.62957	−	0.940835i	−0.0534358	−	0.0308512i
$931$			1.14340i			0.0374734i
$932$	−1.10982	+	1.92227i	−0.0363535	+	0.0629661i
$933$	−11.1230	−	19.2657i	−0.364152	−	0.630730i
$934$	−17.1152	+	9.88149i	−0.560028	+	0.323332i
$935$	−19.1671			−0.626832
$936$	9.47568	−	13.3785i	0.309722	−	0.437291i
$937$	−32.3523			−1.05690			−0.528452	−	0.848963i	$-0.677227\pi$
$937$	−32.3523			−1.05690			−0.528452	+	0.848963i	$0.677227\pi$
$938$	6.94164	−	4.00776i	0.226653	−	0.130858i
$939$	14.2060	+	24.6055i	0.463595	+	0.802969i
$940$	17.9374	−	31.0686i	0.585055	−	1.01335i
$941$		−	8.84261i		−	0.288261i	−0.989559	−	0.144130i	$-0.953962\pi$
$941$		−	8.84261i		−	0.288261i	0.989559	−	0.144130i	$-0.0460385\pi$
$942$	2.13924	+	1.23509i	0.0697001	+	0.0402414i
$943$	−49.5324	−	28.5975i	−1.61300	−	0.931264i
$944$			6.07483i			0.197719i
$945$	−26.0581	+	45.1340i	−0.847671	+	1.46821i
$946$	1.33062	+	2.30469i	0.0432620	+	0.0749320i
$947$	29.7877	−	17.1979i	0.967971	−	0.558858i	0.0693537	−	0.997592i	$-0.477906\pi$
$947$	29.7877	−	17.1979i	0.967971	−	0.558858i	0.898617	+	0.438734i	$0.144573\pi$
$948$	−21.6965			−0.704671
$949$	26.4461	+	2.45751i	0.858475	+	0.0797743i
$950$	20.1525			0.653833
$951$	1.97512	−	1.14034i	0.0640477	−	0.0369780i
$952$	−13.3248	−	23.0793i	−0.431861	−	0.748005i
$953$	−29.9450	+	51.8662i	−0.970013	+	1.68011i	−0.274518	+	0.961582i	$0.588518\pi$
$953$	−29.9450	+	51.8662i	−0.970013	+	1.68011i	−0.695495	+	0.718531i	$0.744815\pi$
$954$			11.7389i			0.380062i
$955$	−71.3042	−	41.1675i	−2.30735	−	1.33215i
$956$	30.2121	+	17.4430i	0.977128	+	0.564145i
$957$			0.0764530i			0.00247137i
$958$	0.901093	−	1.56074i	0.0291130	−	0.0504252i
$959$	9.83731	+	17.0387i	0.317663	+	0.550209i
$960$	−6.65459	+	3.84203i	−0.214776	+	0.124001i
$961$	−1.00000			−0.0322581
$962$	2.16713	+	1.53493i	0.0698712	+	0.0494881i
$963$	−6.68902			−0.215551
$964$	−17.9243	+	10.3486i	−0.577303	+	0.333306i
$965$	18.7351	+	32.4502i	0.603105	+	1.04461i
$966$	−2.98804	+	5.17544i	−0.0961388	+	0.166517i
$967$			45.9160i			1.47656i	0.674495	+	0.738279i	$0.264361\pi$
$967$			45.9160i			1.47656i	−0.674495	+	0.738279i	$0.735639\pi$
$968$	17.3116	+	9.99486i	0.556416	+	0.321247i
$969$	9.62668	+	5.55797i	0.309254	+	0.178548i
$970$		−	6.47240i		−	0.207816i
$971$	17.7895	−	30.8123i	0.570892	−	0.988814i	−0.425583	−	0.904920i	$-0.639931\pi$
$971$	17.7895	−	30.8123i	0.570892	−	0.988814i	0.996475	−	0.0838943i	$-0.0267358\pi$
$972$	13.7081	+	23.7431i	0.439688	+	0.761562i
$973$	−1.03322	+	0.596532i	−0.0331236	+	0.0191239i
$974$	7.81282			0.250339
$975$	38.1071	−	17.5200i	1.22040	−	0.561090i
$976$	19.5172			0.624729
$977$	41.3498	−	23.8733i	1.32290	−	0.763776i	0.338708	−	0.940891i	$-0.390010\pi$
$977$	41.3498	−	23.8733i	1.32290	−	0.763776i	0.984190	+	0.177116i	$0.0566767\pi$
$978$	−1.76701	−	3.06055i	−0.0565027	−	0.0978656i
$979$	−3.55897	+	6.16431i	−0.113745	+	0.197012i
$980$		−	3.19160i		−	0.101952i
$981$	11.0215	+	6.36326i	0.351889	+	0.203163i
$982$	15.6348	+	9.02674i	0.498926	+	0.288055i
$983$			11.0654i			0.352932i	0.984307	+	0.176466i	$0.0564666\pi$
$983$			11.0654i			0.352932i	−0.984307	+	0.176466i	$0.943533\pi$
$984$	8.95741	−	15.5147i	0.285552	−	0.494590i
$985$	41.3464	+	71.6141i	1.31741	+	2.28181i
$986$	0.242997	−	0.140295i	0.00773861	−	0.00446789i
$987$	−10.5937			−0.337202
$988$	−7.03694	−	15.3057i	−0.223875	−	0.486940i
$989$	29.6981			0.944346
$990$	4.04426	−	2.33496i	0.128535	−	0.0742098i
$991$	5.49333	+	9.51472i	0.174501	+	0.302245i	0.939989	−	0.341206i	$-0.110835\pi$
$991$	5.49333	+	9.51472i	0.174501	+	0.302245i	−0.765487	+	0.643451i	$0.777502\pi$
$992$	2.58868	−	4.48372i	0.0821906	−	0.142358i
$993$		−	25.4857i		−	0.808763i
$994$	15.9776	+	9.22467i	0.506779	+	0.292589i
$995$	46.4362	+	26.8100i	1.47213	+	0.849933i
$996$			3.59915i			0.114043i
$997$	−0.760150	+	1.31662i	−0.0240742	+	0.0416977i	−0.877812	−	0.479006i	$-0.840997\pi$
$997$	−0.760150	+	1.31662i	−0.0240742	+	0.0416977i	0.853737	+	0.520704i	$0.174330\pi$
$998$	−5.64826	−	9.78308i	−0.178793	−	0.309678i
$999$	−5.31325	+	3.06761i	−0.168104	+	0.0970548i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.r.a.218.15	✓	68
13.2	odd	12		5239.2.a.r.1.13		34
13.4	even	6	inner	403.2.r.a.342.15	yes	68
13.11	odd	12		5239.2.a.q.1.22		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.r.a.218.15	✓	68	1.1	even	1	trivial
403.2.r.a.342.15	yes	68	13.4	even	6	inner
5239.2.a.q.1.22		34	13.11	odd	12
5239.2.a.r.1.13		34	13.2	odd	12

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.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453928 + 0.262075i) q^{2} +(0.409673 + 0.709575i) q^{3} +(-0.862633 + 1.49412i) q^{4} +4.38147i q^{5} +(-0.371924 - 0.214730i) q^{6} +(2.35938 + 1.36219i) q^{7} -1.95260i q^{8} +(1.16434 - 2.01669i) q^{9} +O(q^{10})\)	\(q+(-0.453928 + 0.262075i) q^{2} +(0.409673 + 0.709575i) q^{3} +(-0.862633 + 1.49412i) q^{4} +4.38147i q^{5} +(-0.371924 - 0.214730i) q^{6} +(2.35938 + 1.36219i) q^{7} -1.95260i q^{8} +(1.16434 - 2.01669i) q^{9} +(-1.14828 - 1.98887i) q^{10} +(-0.756232 + 0.436611i) q^{11} -1.41359 q^{12} +(-0.333611 + 3.59008i) q^{13} -1.42798 q^{14} +(-3.10898 + 1.79497i) q^{15} +(-1.21354 - 2.10191i) q^{16} +(2.50485 - 4.33853i) q^{17} +1.22057i q^{18} +(2.34529 + 1.35405i) q^{19} +(-6.54647 - 3.77960i) q^{20} +2.23221i q^{21} +(0.228850 - 0.396379i) q^{22} +(-2.55386 - 4.42341i) q^{23} +(1.38552 - 0.799928i) q^{24} -14.1973 q^{25} +(-0.789437 - 1.71707i) q^{26} +4.36603 q^{27} +(-4.07055 + 2.35014i) q^{28} +(-0.0534285 - 0.0925408i) q^{29} +(0.940835 - 1.62957i) q^{30} -1.00000i q^{31} +(4.48372 + 2.58868i) q^{32} +(-0.619616 - 0.357735i) q^{33} +2.62584i q^{34} +(-5.96839 + 10.3375i) q^{35} +(2.00879 + 3.47933i) q^{36} +(-1.21695 + 0.702608i) q^{37} -1.41946 q^{38} +(-2.68410 + 1.23404i) q^{39} +8.55527 q^{40} +(9.69756 - 5.59889i) q^{41} +(-0.585006 - 1.01326i) q^{42} +(-2.90718 + 5.03539i) q^{43} -1.50654i q^{44} +(8.83607 + 5.10151i) q^{45} +(2.31853 + 1.33861i) q^{46} +4.74585i q^{47} +(0.994308 - 1.72219i) q^{48} +(0.211107 + 0.365647i) q^{49} +(6.44455 - 3.72076i) q^{50} +4.10468 q^{51} +(-5.07625 - 3.59538i) q^{52} +9.61754 q^{53} +(-1.98186 + 1.14423i) q^{54} +(-1.91300 - 3.31341i) q^{55} +(2.65981 - 4.60692i) q^{56} +2.21888i q^{57} +(0.0485053 + 0.0280045i) q^{58} +(-2.16761 - 1.25147i) q^{59} -6.19361i q^{60} +(-4.02071 + 6.96408i) q^{61} +(0.262075 + 0.453928i) q^{62} +(5.49422 - 3.17209i) q^{63} +2.14044 q^{64} +(-15.7299 - 1.46171i) q^{65} +0.375014 q^{66} +(-4.86116 + 2.80659i) q^{67} +(4.32154 + 7.48512i) q^{68} +(2.09249 - 3.62431i) q^{69} -6.25666i q^{70} +(-11.1889 - 6.45993i) q^{71} +(-3.93779 - 2.27348i) q^{72} -7.36642i q^{73} +(0.368272 - 0.637866i) q^{74} +(-5.81626 - 10.0741i) q^{75} +(-4.04625 + 2.33611i) q^{76} -2.37898 q^{77} +(0.894978 - 1.26360i) q^{78} +15.3485 q^{79} +(9.20946 - 5.31709i) q^{80} +(-1.70436 - 2.95205i) q^{81} +(-2.93466 + 5.08298i) q^{82} -2.54610i q^{83} +(-3.33519 - 1.92557i) q^{84} +(19.0092 + 10.9749i) q^{85} -3.04760i q^{86} +(0.0437764 - 0.0758229i) q^{87} +(0.852526 + 1.47662i) q^{88} +(7.05928 - 4.07568i) q^{89} -5.34792 q^{90} +(-5.67748 + 8.01592i) q^{91} +8.81218 q^{92} +(0.709575 - 0.409673i) q^{93} +(-1.24377 - 2.15427i) q^{94} +(-5.93276 + 10.2758i) q^{95} +4.24204i q^{96} +(2.44073 + 1.40916i) q^{97} +(-0.191654 - 0.110652i) q^{98} +2.03345i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) \) 68 * q + 32 * q^4 - 34 * q^9	\( 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) \) 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Introduction

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