LMFDB - Embedded newform 91.2.h.b.16.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(16,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("91.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.6
Root			$0.217953 + 0.377506i$ of defining polynomial
Character	$\chi$	$=$	91.16
Dual form			91.2.h.b.74.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.85816 q^{2} +(-1.14703 + 1.98672i) q^{3} +1.45276 q^{4} +(0.0986811 - 0.170921i) q^{5} +(-2.13137 + 3.69165i) q^{6} +(1.03826 - 2.43352i) q^{7} -1.01686 q^{8} +(-1.13137 - 1.95960i) q^{9} +(0.183365 - 0.317598i) q^{10} +(2.09137 - 3.62236i) q^{11} +(-1.66637 + 2.88623i) q^{12} +(-2.72221 + 2.36423i) q^{13} +(1.92926 - 4.52187i) q^{14} +(0.226381 + 0.392104i) q^{15} -4.79501 q^{16} +0.841305 q^{17} +(-2.10227 - 3.64125i) q^{18} +(-0.675876 - 1.17065i) q^{19} +(0.143360 - 0.248307i) q^{20} +(3.64380 + 4.85406i) q^{21} +(3.88610 - 6.73092i) q^{22} -4.11519 q^{23} +(1.16637 - 2.02021i) q^{24} +(2.48052 + 4.29639i) q^{25} +(-5.05830 + 4.39312i) q^{26} -1.69131 q^{27} +(1.50835 - 3.53532i) q^{28} +(4.11931 + 7.13485i) q^{29} +(0.420653 + 0.728592i) q^{30} +(0.640350 + 1.10912i) q^{31} -6.87618 q^{32} +(4.79774 + 8.30993i) q^{33} +1.56328 q^{34} +(-0.313482 - 0.417603i) q^{35} +(-1.64362 - 2.84683i) q^{36} +3.04485 q^{37} +(-1.25589 - 2.17526i) q^{38} +(-1.57459 - 8.12012i) q^{39} +(-0.100344 + 0.173802i) q^{40} +(-2.69848 - 4.67390i) q^{41} +(6.77077 + 9.01963i) q^{42} +(-2.66389 + 4.61399i) q^{43} +(3.03826 - 5.26242i) q^{44} -0.446581 q^{45} -7.64669 q^{46} +(5.83204 - 10.1014i) q^{47} +(5.50003 - 9.52634i) q^{48} +(-4.84403 - 5.05326i) q^{49} +(4.60921 + 7.98339i) q^{50} +(-0.965006 + 1.67144i) q^{51} +(-3.95472 + 3.43466i) q^{52} +(-2.32398 - 4.02525i) q^{53} -3.14272 q^{54} +(-0.412757 - 0.714916i) q^{55} +(-1.05576 + 2.47454i) q^{56} +3.10101 q^{57} +(7.65434 + 13.2577i) q^{58} +6.05811 q^{59} +(0.328878 + 0.569634i) q^{60} +(5.68285 + 9.84298i) q^{61} +(1.18987 + 2.06092i) q^{62} +(-5.94338 + 0.718645i) q^{63} -3.18704 q^{64} +(0.135465 + 0.698587i) q^{65} +(8.91498 + 15.4412i) q^{66} +(-6.69851 + 11.6022i) q^{67} +1.22222 q^{68} +(4.72026 - 8.17574i) q^{69} +(-0.582500 - 0.775973i) q^{70} +(2.98520 - 5.17051i) q^{71} +(1.15044 + 1.99263i) q^{72} +(-1.94273 - 3.36491i) q^{73} +5.65782 q^{74} -11.3810 q^{75} +(-0.981887 - 1.70068i) q^{76} +(-6.64368 - 8.85034i) q^{77} +(-2.92585 - 15.0885i) q^{78} +(5.36669 - 9.29537i) q^{79} +(-0.473177 + 0.819566i) q^{80} +(5.33411 - 9.23895i) q^{81} +(-5.01421 - 8.68486i) q^{82} +3.07390 q^{83} +(5.29358 + 7.05180i) q^{84} +(0.0830210 - 0.143797i) q^{85} +(-4.94994 + 8.57354i) q^{86} -18.8999 q^{87} +(-2.12662 + 3.68341i) q^{88} -11.9841 q^{89} -0.829819 q^{90} +(2.92702 + 9.07924i) q^{91} -5.97840 q^{92} -2.93801 q^{93} +(10.8369 - 18.7700i) q^{94} -0.266785 q^{95} +(7.88721 - 13.6611i) q^{96} +(-9.73637 + 16.8639i) q^{97} +(-9.00098 - 9.38977i) q^{98} -9.46448 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + q^{3} + 8 q^{4} + q^{5} - 9 q^{6} - 3 q^{7} - 6 q^{8} + 3 q^{9} + 4 q^{10} + 4 q^{11} + 5 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 16 q^{16} - 10 q^{17} + 3 q^{18} - q^{19} - q^{20}+ \cdots - 20 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 + q^3 + 8 * q^4 + q^5 - 9 * q^6 - 3 * q^7 - 6 * q^8 + 3 * q^9 + 4 * q^10 + 4 * q^11 + 5 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 16 * q^16 - 10 * q^17 + 3 * q^18 - q^19 - q^20 - 9 * q^21 - 5 * q^22 + 2 * q^23 - 11 * q^24 + 7 * q^25 - 16 * q^26 - 8 * q^27 - q^28 + 3 * q^29 - 5 * q^30 + 16 * q^31 - 16 * q^32 + 16 * q^33 + 32 * q^34 + 20 * q^35 - 21 * q^36 + 26 * q^37 - 17 * q^38 - 20 * q^39 - 5 * q^40 - 8 * q^41 + 50 * q^42 - 11 * q^43 + 21 * q^44 + 14 * q^45 - 32 * q^46 - q^47 + 21 * q^48 - 3 * q^49 + 6 * q^50 - 20 * q^51 + 41 * q^52 - 2 * q^53 + 36 * q^54 + 9 * q^55 + 9 * q^56 + 42 * q^57 - 8 * q^58 - 26 * q^59 + 20 * q^60 - 5 * q^61 + 5 * q^62 - 40 * q^63 - 30 * q^64 - 5 * q^65 + 18 * q^66 - 11 * q^67 - 58 * q^68 + 23 * q^69 - 39 * q^70 + 6 * q^71 + 25 * q^72 - 30 * q^73 + 6 * q^74 + 6 * q^75 - 9 * q^76 + 11 * q^77 + 16 * q^78 + 7 * q^79 - 7 * q^80 - 6 * q^81 + q^82 - 54 * q^83 - 46 * q^84 - q^85 - 7 * q^86 - 32 * q^87 - 8 * q^89 - 16 * q^90 - 23 * q^91 + 54 * q^92 + 14 * q^93 + 45 * q^94 + 12 * q^95 + 19 * q^96 - 35 * q^97 + 20 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.85816			1.31392			0.656959	−	0.753926i	$-0.271842\pi$
$2$	1.85816			1.31392			0.656959	+	0.753926i	$0.271842\pi$
$3$	−1.14703	+	1.98672i	−0.662240	+	1.14703i	0.317785	+	0.948163i	$0.397061\pi$
$3$	−1.14703	+	1.98672i	−0.662240	+	1.14703i	−0.980026	+	0.198871i	$0.936272\pi$
$4$	1.45276			0.726381
$5$	0.0986811	−	0.170921i	0.0441315	−	0.0764381i	−0.843116	−	0.537732i	$-0.819281\pi$
$5$	0.0986811	−	0.170921i	0.0441315	−	0.0764381i	0.887247	+	0.461294i	$0.152615\pi$
$6$	−2.13137	+	3.69165i	−0.870130	+	1.50711i
$7$	1.03826	−	2.43352i	0.392426	−	0.919784i
$7$	1.03826	−	2.43352i	0.392426	−	0.919784i
$8$	−1.01686			−0.359513
$9$	−1.13137	−	1.95960i	−0.377125	−	0.653199i
$10$	0.183365	−	0.317598i	0.0579852	−	0.100433i
$11$	2.09137	−	3.62236i	0.630571	−	1.09218i	−0.356864	−	0.934156i	$-0.616154\pi$
$11$	2.09137	−	3.62236i	0.630571	−	1.09218i	0.987435	−	0.158025i	$-0.0505127\pi$
$12$	−1.66637	+	2.88623i	−0.481039	+	0.833184i
$13$	−2.72221	+	2.36423i	−0.755005	+	0.655719i
$13$	−2.72221	+	2.36423i	−0.755005	+	0.655719i
$14$	1.92926	−	4.52187i	0.515616	−	1.20852i
$15$	0.226381	+	0.392104i	0.0584514	+	0.101241i
$16$	−4.79501			−1.19875
$17$	0.841305			0.204047			0.102023	−	0.994782i	$-0.467468\pi$
$17$	0.841305			0.204047			0.102023	+	0.994782i	$0.467468\pi$
$18$	−2.10227	−	3.64125i	−0.495511	−	0.858250i
$19$	−0.675876	−	1.17065i	−0.155057	−	0.268566i	0.778023	−	0.628236i	$-0.216223\pi$
$19$	−0.675876	−	1.17065i	−0.155057	−	0.268566i	−0.933080	+	0.359670i	$0.882889\pi$
$20$	0.143360	−	0.248307i	0.0320563	−	0.0555232i
$21$	3.64380	+	4.85406i	0.795143	+	1.05924i
$22$	3.88610	−	6.73092i	0.828519	−	1.43504i
$23$	−4.11519			−0.858077			−0.429038	−	0.903286i	$-0.641147\pi$
$23$	−4.11519			−0.858077			−0.429038	+	0.903286i	$0.641147\pi$
$24$	1.16637	−	2.02021i	0.238084	−	0.412373i
$25$	2.48052	+	4.29639i	0.496105	+	0.859279i
$26$	−5.05830	+	4.39312i	−0.992015	+	0.861561i
$27$	−1.69131			−0.325492
$28$	1.50835	−	3.53532i	0.285051	−	0.668113i
$29$	4.11931	+	7.13485i	0.764936	+	1.32491i	0.940280	+	0.340401i	$0.110563\pi$
$29$	4.11931	+	7.13485i	0.764936	+	1.32491i	−0.175344	+	0.984507i	$0.556104\pi$
$30$	0.420653	+	0.728592i	0.0768003	+	0.133022i
$31$	0.640350	+	1.10912i	0.115010	+	0.199203i	0.917784	−	0.397080i	$-0.129977\pi$
$31$	0.640350	+	1.10912i	0.115010	+	0.199203i	−0.802774	+	0.596284i	$0.796643\pi$
$32$	−6.87618			−1.21555
$33$	4.79774	+	8.30993i	0.835180	+	1.44657i
$34$	1.56328			0.268100
$35$	−0.313482	−	0.417603i	−0.0529881	−	0.0705878i
$36$	−1.64362	−	2.84683i	−0.273936	−	0.474471i
$37$	3.04485			0.500570			0.250285	−	0.968172i	$-0.419476\pi$
$37$	3.04485			0.500570			0.250285	+	0.968172i	$0.419476\pi$
$38$	−1.25589	−	2.17526i	−0.203732	−	0.352874i
$39$	−1.57459	−	8.12012i	−0.252137	−	1.30026i
$40$	−0.100344	+	0.173802i	−0.0158659	+	0.0274805i
$41$	−2.69848	−	4.67390i	−0.421431	−	0.729941i	0.574648	−	0.818400i	$-0.305139\pi$
$41$	−2.69848	−	4.67390i	−0.421431	−	0.729941i	−0.996080	+	0.0884599i	$0.971805\pi$
$42$	6.77077	+	9.01963i	1.04475	+	1.39176i
$43$	−2.66389	+	4.61399i	−0.406239	+	0.703627i	−0.994465	−	0.105070i	$-0.966493\pi$
$43$	−2.66389	+	4.61399i	−0.406239	+	0.703627i	0.588226	+	0.808697i	$0.299827\pi$
$44$	3.03826	−	5.26242i	0.458035	−	0.793340i
$45$	−0.446581			−0.0665724
$46$	−7.64669			−1.12744
$47$	5.83204	−	10.1014i	0.850690	−	1.47344i	−0.0298969	−	0.999553i	$-0.509518\pi$
$47$	5.83204	−	10.1014i	0.850690	−	1.47344i	0.880587	−	0.473885i	$-0.157149\pi$
$48$	5.50003	−	9.52634i	0.793862	−	1.37501i
$49$	−4.84403	−	5.05326i	−0.692004	−	0.721894i
$50$	4.60921	+	7.98339i	0.651841	+	1.12902i
$51$	−0.965006	+	1.67144i	−0.135128	+	0.234048i
$52$	−3.95472	+	3.43466i	−0.548422	+	0.476302i
$53$	−2.32398	−	4.02525i	−0.319223	−	0.552911i	0.661103	−	0.750295i	$-0.270089\pi$
$53$	−2.32398	−	4.02525i	−0.319223	−	0.552911i	−0.980326	+	0.197384i	$0.936755\pi$
$54$	−3.14272			−0.427670
$55$	−0.412757	−	0.714916i	−0.0556562	−	0.0963993i
$56$	−1.05576	+	2.47454i	−0.141082	+	0.330674i
$57$	3.10101			0.410739
$58$	7.65434	+	13.2577i	1.00506	+	1.74082i
$59$	6.05811			0.788698			0.394349	−	0.918961i	$-0.370970\pi$
$59$	6.05811			0.788698			0.394349	+	0.918961i	$0.370970\pi$
$60$	0.328878	+	0.569634i	0.0424580	+	0.0735394i
$61$	5.68285	+	9.84298i	0.727614	+	1.26026i	0.957889	+	0.287139i	$0.0927042\pi$
$61$	5.68285	+	9.84298i	0.727614	+	1.26026i	−0.230275	+	0.973126i	$0.573962\pi$
$62$	1.18987	+	2.06092i	0.151114	+	0.261737i
$63$	−5.94338	+	0.718645i	−0.748795	+	0.0905407i
$64$	−3.18704			−0.398380
$65$	0.135465	+	0.698587i	0.0168023	+	0.0866490i
$66$	8.91498	+	15.4412i	1.09736	+	1.90068i
$67$	−6.69851	+	11.6022i	−0.818354	+	1.41743i	0.0885411	+	0.996073i	$0.471780\pi$
$67$	−6.69851	+	11.6022i	−0.818354	+	1.41743i	−0.906895	+	0.421357i	$0.861554\pi$
$68$	1.22222			0.148216
$69$	4.72026	−	8.17574i	0.568253	−	0.984243i
$70$	−0.582500	−	0.775973i	−0.0696221	−	0.0927465i
$71$	2.98520	−	5.17051i	0.354278	−	0.613627i	−0.632716	−	0.774384i	$-0.718060\pi$
$71$	2.98520	−	5.17051i	0.354278	−	0.613627i	0.986994	+	0.160757i	$0.0513934\pi$
$72$	1.15044	+	1.99263i	0.135581	+	0.234833i
$73$	−1.94273	−	3.36491i	−0.227380	−	0.393833i	0.729651	−	0.683820i	$-0.239683\pi$
$73$	−1.94273	−	3.36491i	−0.227380	−	0.393833i	−0.957031	+	0.289986i	$0.906349\pi$
$74$	5.65782			0.657708
$75$	−11.3810			−1.31416
$76$	−0.981887	−	1.70068i	−0.112630	−	0.195081i
$77$	−6.64368	−	8.85034i	−0.757118	−	1.00859i
$78$	−2.92585	−	15.0885i	−0.331287	−	1.70844i
$79$	5.36669	−	9.29537i	0.603799	−	1.04581i	−0.388441	−	0.921474i	$-0.626986\pi$
$79$	5.36669	−	9.29537i	0.603799	−	1.04581i	0.992240	−	0.124337i	$-0.0396805\pi$
$80$	−0.473177	+	0.819566i	−0.0529028	+	0.0916303i
$81$	5.33411	−	9.23895i	0.592679	−	1.02655i
$82$	−5.01421	−	8.68486i	−0.553726	−	0.959082i
$83$	3.07390			0.337404			0.168702	−	0.985667i	$-0.446042\pi$
$83$	3.07390			0.337404			0.168702	+	0.985667i	$0.446042\pi$
$84$	5.29358	+	7.05180i	0.577577	+	0.769415i
$85$	0.0830210	−	0.143797i	0.00900489	−	0.0155969i
$86$	−4.94994	+	8.57354i	−0.533765	+	0.924509i
$87$	−18.8999			−2.02629
$88$	−2.12662	+	3.68341i	−0.226698	+	0.392653i
$89$	−11.9841			−1.27032			−0.635159	−	0.772382i	$-0.719065\pi$
$89$	−11.9841			−1.27032			−0.635159	+	0.772382i	$0.719065\pi$
$90$	−0.829819			−0.0874706
$91$	2.92702	+	9.07924i	0.306836	+	0.951763i
$92$	−5.97840			−0.623291
$93$	−2.93801			−0.304658
$94$	10.8369	−	18.7700i	1.11774	−	1.93598i
$95$	−0.266785			−0.0273715
$96$	7.88721	−	13.6611i	0.804986	−	1.39428i
$97$	−9.73637	+	16.8639i	−0.988578	+	1.71227i	−0.363771	+	0.931488i	$0.618511\pi$
$97$	−9.73637	+	16.8639i	−0.988578	+	1.71227i	−0.624807	+	0.780779i	$0.714822\pi$
$98$	−9.00098	−	9.38977i	−0.909236	−	0.948510i
$99$	−9.46448			−0.951216
$100$	3.60361	+	6.24164i	0.360361	+	0.624164i
$101$	8.46697	−	14.6652i	0.842495	−	1.45924i	−0.0452843	−	0.998974i	$-0.514419\pi$
$101$	8.46697	−	14.6652i	0.842495	−	1.45924i	0.887779	−	0.460270i	$-0.152247\pi$
$102$	−1.79314	+	3.10580i	−0.177547	+	0.307520i
$103$	3.61712	−	6.26504i	0.356406	−	0.617313i	−0.630952	−	0.775822i	$-0.717335\pi$
$103$	3.61712	−	6.26504i	0.356406	−	0.617313i	0.987357	+	0.158509i	$0.0506688\pi$
$104$	2.76809	−	2.40408i	0.271434	−	0.235739i
$105$	1.18923	−	0.143797i	0.116057	−	0.0140331i
$106$	−4.31833	−	7.47957i	−0.419434	−	0.726480i
$107$	−9.85249			−0.952477			−0.476238	−	0.879316i	$-0.658000\pi$
$107$	−9.85249			−0.952477			−0.476238	+	0.879316i	$0.658000\pi$
$108$	−2.45707			−0.236431
$109$	6.90796	+	11.9649i	0.661662	+	1.14603i	0.980179	+	0.198115i	$0.0634821\pi$
$109$	6.90796	+	11.9649i	0.661662	+	1.14603i	−0.318516	+	0.947917i	$0.603185\pi$
$110$	−0.766969	−	1.32843i	−0.0731277	−	0.126661i
$111$	−3.49255	+	6.04927i	−0.331498	+	0.574171i
$112$	−4.97847	+	11.6687i	−0.470421	+	1.10259i
$113$	2.13432	−	3.69675i	0.200780	−	0.347761i	−0.748000	−	0.663699i	$-0.768986\pi$
$113$	2.13432	−	3.69675i	0.200780	−	0.347761i	0.948780	+	0.315938i	$0.102319\pi$
$114$	5.76218			0.539677
$115$	−0.406092	+	0.703371i	−0.0378682	+	0.0655897i
$116$	5.98437	+	10.3652i	0.555635	+	0.962388i
$117$	7.71277	+	2.65961i	0.713046	+	0.245881i
$118$	11.2569			1.03629
$119$	0.873495	−	2.04733i	0.0800732	−	0.187679i
$120$	−0.230197	−	0.398713i	−0.0210140	−	0.0363973i
$121$	−3.24765	−	5.62509i	−0.295240	−	0.511372i
$122$	10.5596	+	18.2898i	0.956026	+	1.65589i
$123$	12.3810			1.11636
$124$	0.930276	+	1.61129i	0.0835412	+	0.144698i
$125$	1.96593			0.175839
$126$	−11.0438	+	1.33536i	−0.983856	+	0.118963i
$127$	1.09512	+	1.89680i	0.0971761	+	0.168314i	0.910515	−	0.413477i	$-0.135686\pi$
$127$	1.09512	+	1.89680i	0.0971761	+	0.168314i	−0.813339	+	0.581791i	$0.802352\pi$
$128$	7.83033			0.692110
$129$	−6.11114	−	10.5848i	−0.538056	−	0.931941i
$130$	0.251715	+	1.29809i	0.0220769	+	0.113850i
$131$	−1.13806	+	1.97117i	−0.0994326	+	0.172222i	−0.911450	−	0.411411i	$-0.865036\pi$
$131$	−1.13806	+	1.97117i	−0.0994326	+	0.172222i	0.812017	+	0.583633i	$0.198369\pi$
$132$	6.96998	+	12.0724i	0.606659	+	1.05076i
$133$	−3.55054	+	0.429314i	−0.307871	+	0.0372262i
$134$	−12.4469	+	21.5587i	−1.07525	+	1.86239i
$135$	−0.166900	+	0.289079i	−0.0143645	+	0.0248800i
$136$	−0.855486			−0.0733573
$137$	13.4480			1.14894			0.574469	−	0.818526i	$-0.305209\pi$
$137$	13.4480			1.14894			0.574469	+	0.818526i	$0.305209\pi$
$138$	8.77101	−	15.1918i	0.746638	−	1.29321i
$139$	−2.02270	+	3.50342i	−0.171563	+	0.297156i	−0.938966	−	0.344009i	$-0.888215\pi$
$139$	−2.02270	+	3.50342i	−0.171563	+	0.297156i	0.767403	+	0.641165i	$0.221548\pi$
$140$	−0.455415	−	0.606678i	−0.0384896	−	0.0512736i
$141$	13.3791	+	23.1733i	1.12672	+	1.95154i
$142$	5.54698	−	9.60765i	0.465492	−	0.806256i
$143$	2.87093	+	14.8053i	0.240079	+	1.23808i
$144$	5.42494	+	9.39628i	0.452079	+	0.783023i
$145$	1.62599			0.135031
$146$	−3.60991	−	6.25255i	−0.298758	−	0.517465i
$147$	15.5957	−	3.82747i	1.28631	−	0.315684i
$148$	4.42344			0.363605
$149$	−7.67596	−	13.2952i	−0.628840	−	1.08918i	−0.987785	−	0.155823i	$-0.950197\pi$
$149$	−7.67596	−	13.2952i	−0.628840	−	1.08918i	0.358945	−	0.933359i	$-0.383136\pi$
$150$	−21.1477			−1.72670
$151$	−3.06054	−	5.30101i	−0.249063	−	0.431390i	0.714203	−	0.699939i	$-0.246789\pi$
$151$	−3.06054	−	5.30101i	−0.249063	−	0.431390i	−0.963266	+	0.268548i	$0.913456\pi$
$152$	0.687268	+	1.19038i	0.0557448	+	0.0965528i
$153$	−0.951831	−	1.64862i	−0.0769510	−	0.133283i
$154$	−12.3450	−	16.4454i	−0.994791	−	1.32520i
$155$	0.252762			0.0203023
$156$	−2.28751	−	11.7966i	−0.183147	−	0.944484i
$157$	−2.26834	−	3.92888i	−0.181033	−	0.313559i	0.761199	−	0.648518i	$-0.224611\pi$
$157$	−2.26834	−	3.92888i	−0.181033	−	0.313559i	−0.942233	+	0.334959i	$0.891278\pi$
$158$	9.97217	−	17.2723i	0.793343	−	1.37411i
$159$	10.6627			0.845611
$160$	−0.678549	+	1.17528i	−0.0536440	+	0.0929142i
$161$	−4.27265	+	10.0144i	−0.336732	+	0.789245i
$162$	9.91163	−	17.1674i	0.778731	−	1.34880i
$163$	−0.911271	−	1.57837i	−0.0713762	−	0.123627i	0.828128	−	0.560538i	$-0.189406\pi$
$163$	−0.911271	−	1.57837i	−0.0713762	−	0.123627i	−0.899505	+	0.436911i	$0.856072\pi$
$164$	−3.92025	−	6.79007i	−0.306120	−	0.530215i
$165$	1.89379			0.147431
$166$	5.71180			0.443322
$167$	5.35397	+	9.27336i	0.414303	+	0.717594i	0.995355	−	0.0962726i	$-0.0306921\pi$
$167$	5.35397	+	9.27336i	0.414303	+	0.717594i	−0.581052	+	0.813866i	$0.697359\pi$
$168$	−3.70522	−	4.93588i	−0.285864	−	0.380812i
$169$	1.82086	−	12.8718i	0.140066	−	0.990142i
$170$	0.154266	−	0.267197i	0.0118317	−	0.0204931i
$171$	−1.52934	+	2.64889i	−0.116951	+	0.202566i
$172$	−3.87000	+	6.70303i	−0.295085	+	0.511102i
$173$	6.74634	+	11.6850i	0.512915	+	0.888395i	0.999888	+	0.0149778i	$0.00476775\pi$
$173$	6.74634	+	11.6850i	0.512915	+	0.888395i	−0.486973	+	0.873417i	$0.661899\pi$
$174$	−35.1191			−2.66237
$175$	13.0308	−	1.57562i	0.985035	−	0.119106i
$176$	−10.0281	+	17.3692i	−0.755898	+	1.30925i
$177$	−6.94886	+	12.0358i	−0.522308	+	0.904664i
$178$	−22.2685			−1.66909
$179$	−5.23458	+	9.06657i	−0.391251	+	0.677667i	−0.992615	−	0.121309i	$-0.961291\pi$
$179$	−5.23458	+	9.06657i	−0.391251	+	0.677667i	0.601364	+	0.798975i	$0.294624\pi$
$180$	−0.648776			−0.0483569
$181$	12.5209			0.930674			0.465337	−	0.885133i	$-0.345933\pi$
$181$	12.5209			0.930674			0.465337	+	0.885133i	$0.345933\pi$
$182$	5.43888	+	16.8707i	0.403157	+	1.25054i
$183$	−26.0737			−1.92742
$184$	4.18455			0.308489
$185$	0.300469	−	0.520428i	0.0220909	−	0.0382626i
$186$	−5.45930			−0.400295
$187$	1.75948	−	3.04751i	0.128666	−	0.222856i
$188$	8.47256	−	14.6749i	0.617925	−	1.07028i
$189$	−1.75602	+	4.11583i	−0.127732	+	0.299382i
$190$	−0.495729			−0.0359640
$191$	−6.55685	−	11.3568i	−0.474437	−	0.821749i	0.525135	−	0.851019i	$-0.324015\pi$
$191$	−6.55685	−	11.3568i	−0.474437	−	0.821749i	−0.999572	+	0.0292704i	$0.990682\pi$
$192$	3.65565	−	6.33176i	0.263823	−	0.456956i
$193$	−0.520786	+	0.902028i	−0.0374870	+	0.0649294i	−0.884160	−	0.467184i	$-0.845269\pi$
$193$	−0.520786	+	0.902028i	−0.0374870	+	0.0649294i	0.846673	+	0.532113i	$0.178602\pi$
$194$	−18.0917	+	31.3358i	−1.29891	+	2.24978i
$195$	−1.54328	−	0.532172i	−0.110517	−	0.0381096i
$196$	−7.03722	−	7.34118i	−0.502658	−	0.524370i
$197$	−0.739167	−	1.28027i	−0.0526635	−	0.0912158i	0.838492	−	0.544914i	$-0.183438\pi$
$197$	−0.739167	−	1.28027i	−0.0526635	−	0.0912158i	−0.891155	+	0.453698i	$0.850104\pi$
$198$	−17.5865			−1.24982
$199$	14.0999			0.999512			0.499756	−	0.866166i	$-0.333423\pi$
$199$	14.0999			0.999512			0.499756	+	0.866166i	$0.333423\pi$
$200$	−2.52233	−	4.36881i	−0.178356	−	0.308922i
$201$	−15.3668	−	26.6162i	−1.08389	−	1.87736i
$202$	15.7330	−	27.2503i	1.10697	−	1.91733i
$203$	21.6397	−	2.61657i	1.51881	−	0.183647i
$204$	−1.40192	+	2.42820i	−0.0981543	+	0.170008i
$205$	−1.06516			−0.0743937
$206$	6.72120	−	11.6415i	0.468288	−	0.811099i
$207$	4.65582	+	8.06412i	0.323602	+	0.560495i
$208$	13.0530	−	11.3365i	0.905064	−	0.786044i
$209$	−5.65402			−0.391097
$210$	2.20979	−	0.267197i	0.152490	−	0.0184384i
$211$	−13.2346	−	22.9230i	−0.911108	−	1.57809i	−0.812501	−	0.582959i	$-0.801895\pi$
$211$	−13.2346	−	22.9230i	−0.911108	−	1.57809i	−0.0986067	−	0.995126i	$-0.531439\pi$
$212$	−3.37619	−	5.84774i	−0.231878	−	0.401624i
$213$	6.84825	+	11.8615i	0.469234	+	0.812737i
$214$	−18.3075			−1.25148
$215$	0.525751	+	0.910628i	0.0358559	+	0.0621043i
$216$	1.71981			0.117019
$217$	3.36391	−	0.406748i	0.228357	−	0.0276118i
$218$	12.8361	+	22.2328i	0.869370	+	1.50579i
$219$	8.91352			0.602320
$220$	−0.599638	−	1.03860i	−0.0404276	−	0.0700227i
$221$	−2.29021	+	1.98904i	−0.154056	+	0.133797i
$222$	−6.48971	+	11.2405i	−0.435561	+	0.754414i
$223$	0.364024	+	0.630508i	0.0243769	+	0.0422219i	0.877956	−	0.478740i	$-0.158907\pi$
$223$	0.364024	+	0.630508i	0.0243769	+	0.0422219i	−0.853580	+	0.520962i	$0.825573\pi$
$224$	−7.13928	+	16.7333i	−0.477013	+	1.11804i
$225$	5.61280	−	9.72165i	0.374187	−	0.648110i
$226$	3.96591	−	6.86916i	0.263808	−	0.456929i
$227$	−2.85195			−0.189291			−0.0946454	−	0.995511i	$-0.530172\pi$
$227$	−2.85195			−0.189291			−0.0946454	+	0.995511i	$0.530172\pi$
$228$	4.50503			0.298353
$229$	−1.58676	+	2.74835i	−0.104856	+	0.181616i	−0.913679	−	0.406436i	$-0.866772\pi$
$229$	−1.58676	+	2.74835i	−0.104856	+	0.181616i	0.808823	+	0.588052i	$0.200105\pi$
$230$	−0.754584	+	1.30698i	−0.0497558	+	0.0861795i
$231$	25.2037	−	3.04751i	1.65828	−	0.200511i
$232$	−4.18874	−	7.25511i	−0.275004	−	0.476321i
$233$	−6.70354	+	11.6109i	−0.439163	+	0.760653i	−0.997625	−	0.0688769i	$-0.978058\pi$
$233$	−6.70354	+	11.6109i	−0.439163	+	0.760653i	0.558462	+	0.829530i	$0.311392\pi$
$234$	14.3316	+	4.94198i	0.936884	+	0.323068i
$235$	−1.15102	−	1.99363i	−0.0750845	−	0.130050i
$236$	8.80099			0.572896
$237$	12.3115	+	21.3242i	0.799721	+	1.38516i
$238$	1.62309	−	3.80427i	0.105210	−	0.246594i
$239$	−15.5538			−1.00609			−0.503046	−	0.864259i	$-0.667788\pi$
$239$	−15.5538			−1.00609			−0.503046	+	0.864259i	$0.667788\pi$
$240$	−1.08550	−	1.88014i	−0.0700687	−	0.121363i
$241$	−7.57574			−0.487996			−0.243998	−	0.969776i	$-0.578459\pi$
$241$	−7.57574			−0.487996			−0.243998	+	0.969776i	$0.578459\pi$
$242$	−6.03465	−	10.4523i	−0.387922	−	0.671900i
$243$	9.69985	+	16.8006i	0.622245	+	1.07776i
$244$	8.25583	+	14.2995i	0.528525	+	0.915433i
$245$	−1.34172	+	0.329283i	−0.0857194	+	0.0210371i
$246$	23.0059			1.46680
$247$	4.60756	+	1.58883i	0.293172	+	0.101095i
$248$	−0.651143	−	1.12781i	−0.0413476	−	0.0716162i
$249$	−3.52587	+	6.10698i	−0.223443	+	0.387014i
$250$	3.65302			0.231038
$251$	−0.637382	+	1.10398i	−0.0402312	+	0.0696825i	−0.885440	−	0.464754i	$-0.846143\pi$
$251$	−0.637382	+	1.10398i	−0.0402312	+	0.0696825i	0.845209	+	0.534436i	$0.179476\pi$
$252$	−8.63432	+	1.04402i	−0.543911	+	0.0657671i
$253$	−8.60638	+	14.9067i	−0.541079	+	0.937176i
$254$	2.03491	+	3.52456i	0.127682	+	0.221151i
$255$	0.190456	+	0.329879i	0.0119268	+	0.0206578i
$256$	20.9241			1.30776
$257$	−8.48019			−0.528980			−0.264490	−	0.964388i	$-0.585204\pi$
$257$	−8.48019			−0.528980			−0.264490	+	0.964388i	$0.585204\pi$
$258$	−11.3555	−	19.6683i	−0.706962	−	1.22449i
$259$	3.16135	−	7.40970i	0.196437	−	0.460416i
$260$	0.196798	+	1.01488i	0.0122049	+	0.0629402i
$261$	9.32095	−	16.1444i	0.576952	−	0.999311i
$262$	−2.11470	+	3.66276i	−0.130646	+	0.226286i
$263$	−6.39415	+	11.0750i	−0.394280	+	0.682913i	−0.993009	−	0.118038i	$-0.962339\pi$
$263$	−6.39415	+	11.0750i	−0.394280	+	0.682913i	0.598729	+	0.800952i	$0.295673\pi$
$264$	−4.87861	−	8.45000i	−0.300258	−	0.520062i
$265$	−0.917333			−0.0563513
$266$	−6.59747	+	0.797735i	−0.404517	+	0.0489122i
$267$	13.7462	−	23.8092i	0.841255	−	1.45710i
$268$	−9.73135	+	16.8552i	−0.594437	+	1.02959i
$269$	−4.71172			−0.287278			−0.143639	−	0.989630i	$-0.545880\pi$
$269$	−4.71172			−0.287278			−0.143639	+	0.989630i	$0.545880\pi$
$270$	−0.310127	+	0.537156i	−0.0188737	+	0.0326903i
$271$	−18.0112			−1.09410			−0.547052	−	0.837098i	$-0.684250\pi$
$271$	−18.0112			−1.09410			−0.547052	+	0.837098i	$0.684250\pi$
$272$	−4.03407			−0.244601
$273$	−21.3953	−	4.59901i	−1.29490	−	0.278345i
$274$	24.9885			1.50961
$275$	20.7508			1.25132
$276$	6.85742	−	11.8774i	0.412768	−	0.714936i
$277$	−26.1209			−1.56945			−0.784725	−	0.619844i	$-0.787196\pi$
$277$	−26.1209			−1.56945			−0.784725	+	0.619844i	$0.787196\pi$
$278$	−3.75850	+	6.50991i	−0.225420	+	0.390439i
$279$	1.44895	−	2.50965i	0.0867463	−	0.150249i
$280$	0.318766	+	0.424642i	0.0190499	+	0.0253772i
$281$	−3.66197			−0.218455			−0.109227	−	0.994017i	$-0.534838\pi$
$281$	−3.66197			−0.218455			−0.109227	+	0.994017i	$0.534838\pi$
$282$	24.8605	+	43.0596i	1.48042	+	2.56416i
$283$	−3.82263	+	6.62099i	−0.227232	+	0.393577i	−0.956987	−	0.290132i	$-0.906301\pi$
$283$	−3.82263	+	6.62099i	−0.227232	+	0.393577i	0.729755	+	0.683709i	$0.239634\pi$
$284$	4.33678	−	7.51153i	0.257341	−	0.445727i
$285$	0.306011	−	0.530027i	0.0181265	−	0.0313961i
$286$	5.33465	+	27.5106i	0.315445	+	1.62674i
$287$	−14.1757	+	1.71406i	−0.836768	+	0.101178i
$288$	7.77953	+	13.4745i	0.458413	+	0.793995i
$289$	−16.2922			−0.958365
$290$	3.02135			0.177420
$291$	−22.3359	−	38.6869i	−1.30935	−	2.26787i
$292$	−2.82233	−	4.88842i	−0.165164	−	0.286073i
$293$	8.57670	−	14.8553i	0.501056	−	0.867855i	−0.498943	−	0.866635i	$-0.666278\pi$
$293$	8.57670	−	14.8553i	0.501056	−	0.867855i	0.999999	−	0.00122001i	$-0.000388343\pi$
$294$	28.9793	−	7.11205i	1.69011	−	0.414783i
$295$	0.597821	−	1.03546i	0.0348065	−	0.0602866i
$296$	−3.09617			−0.179961
$297$	−3.53715	+	6.12652i	−0.205246	+	0.355497i
$298$	−14.2632	−	24.7045i	−0.826244	−	1.43110i
$299$	11.2024	−	9.72925i	0.647852	−	0.562657i
$300$	−16.5339			−0.954583
$301$	8.46242	+	11.2732i	0.487766	+	0.649774i
$302$	−5.68698	−	9.85014i	−0.327249	−	0.566812i
$303$	19.4238	+	33.6430i	1.11587	+	1.93274i
$304$	3.24083	+	5.61328i	0.185874	+	0.321944i
$305$	2.24316			0.128443
$306$	−1.76866	−	3.06340i	−0.101107	−	0.175123i
$307$	−28.0696			−1.60201			−0.801007	−	0.598655i	$-0.795702\pi$
$307$	−28.0696			−1.60201			−0.801007	+	0.598655i	$0.795702\pi$
$308$	−9.65169	−	12.8574i	−0.549956	−	0.732621i
$309$	8.29793	+	14.3724i	0.472052	+	0.817619i
$310$	0.469672			0.0266756
$311$	11.7670	+	20.3811i	0.667248	+	1.15571i	0.978671	+	0.205436i	$0.0658611\pi$
$311$	11.7670	+	20.3811i	0.667248	+	1.15571i	−0.311423	+	0.950271i	$0.600806\pi$
$312$	1.60113	+	8.25699i	0.0906464	+	0.467460i
$313$	1.67430	−	2.89997i	0.0946370	−	0.163916i	−0.814820	−	0.579714i	$-0.803164\pi$
$313$	1.67430	−	2.89997i	0.0946370	−	0.163916i	0.909457	+	0.415798i	$0.136498\pi$
$314$	−4.21494	−	7.30050i	−0.237863	−	0.411991i
$315$	−0.463668	+	1.08676i	−0.0261247	+	0.0612322i
$316$	7.79652	−	13.5040i	0.438588	−	0.759658i
$317$	3.63917	−	6.30323i	0.204396	−	0.354025i	−0.745544	−	0.666456i	$-0.767810\pi$
$317$	3.63917	−	6.30323i	0.204396	−	0.354025i	0.949940	+	0.312432i	$0.101144\pi$
$318$	19.8131			1.11106
$319$	34.4600			1.92939
$320$	−0.314501	+	0.544732i	−0.0175811	+	0.0304514i
$321$	11.3011	−	19.5742i	0.630768	−	1.09252i
$322$	−7.93926	+	18.6084i	−0.442438	+	1.03700i
$323$	−0.568618	−	0.984875i	−0.0316388	−	0.0547999i
$324$	7.74919	−	13.4220i	0.430511	−	0.745666i
$325$	−16.9102	−	5.83116i	−0.938007	−	0.323455i
$326$	−1.69329	−	2.93286i	−0.0937826	−	0.162436i
$327$	−31.6946			−1.75272
$328$	2.74396	+	4.75268i	0.151510	+	0.262423i
$329$	−18.5267	−	24.6802i	−1.02141	−	1.36067i
$330$	3.51896			0.193712
$331$	7.16168	+	12.4044i	0.393642	+	0.681807i	0.992927	−	0.118728i	$-0.0378818\pi$
$331$	7.16168	+	12.4044i	0.393642	+	0.681807i	−0.599285	+	0.800536i	$0.704548\pi$
$332$	4.46564			0.245084
$333$	−3.44486	−	5.96668i	−0.188777	−	0.326972i
$334$	9.94855	+	17.2314i	0.544360	+	0.942860i
$335$	1.32203	+	2.28983i	0.0722304	+	0.125107i
$336$	−17.4720	−	23.2753i	−0.953178	−	1.26977i
$337$	17.1802			0.935868			0.467934	−	0.883764i	$-0.344999\pi$
$337$	17.1802			0.935868			0.467934	+	0.883764i	$0.344999\pi$
$338$	3.38344	−	23.9180i	0.184035	−	1.30097i
$339$	4.89627	+	8.48060i	0.265929	+	0.460603i
$340$	0.120610	−	0.208902i	0.00654098	−	0.0113293i
$341$	5.35683			0.290089
$342$	−2.84175	+	4.92206i	−0.153664	+	0.266155i
$343$	−17.3266	+	6.54142i	−0.935547	+	0.353203i
$344$	2.70879	−	4.69176i	0.146048	−	0.252963i
$345$	−0.931602	−	1.61358i	−0.0501558	−	0.0868723i
$346$	12.5358	+	21.7126i	0.673928	+	1.16728i
$347$	−7.70278			−0.413507			−0.206753	−	0.978393i	$-0.566290\pi$
$347$	−7.70278			−0.413507			−0.206753	+	0.978393i	$0.566290\pi$
$348$	−27.4571			−1.47186
$349$	−11.1850	−	19.3730i	−0.598721	−	1.03702i	−0.993010	−	0.118029i	$-0.962343\pi$
$349$	−11.1850	−	19.3730i	−0.598721	−	1.03702i	0.394289	−	0.918986i	$-0.370991\pi$
$350$	24.2133	−	2.92776i	1.29426	−	0.156495i
$351$	4.60409	−	3.99863i	0.245748	−	0.213431i
$352$	−14.3806	+	24.9080i	−0.766490	+	1.32760i
$353$	11.1311	−	19.2797i	0.592451	−	1.02616i	−0.401450	−	0.915881i	$-0.631494\pi$
$353$	11.1311	−	19.2797i	0.592451	−	1.02616i	0.993901	−	0.110275i	$-0.0351731\pi$
$354$	−12.9121	+	22.3644i	−0.686270	+	1.18865i
$355$	−0.589165	−	1.02046i	−0.0312697	−	0.0541606i
$356$	−17.4101			−0.922735
$357$	3.06555	+	4.08375i	0.162246	+	0.216135i
$358$	−9.72670	+	16.8471i	−0.514072	+	0.890399i
$359$	1.37921	−	2.38887i	0.0727920	−	0.126079i	−0.827332	−	0.561713i	$-0.810142\pi$
$359$	1.37921	−	2.38887i	0.0727920	−	0.126079i	0.900124	+	0.435634i	$0.143476\pi$
$360$	0.454108			0.0239336
$361$	8.58638	−	14.8721i	0.451915	−	0.782740i
$362$	23.2659			1.22283
$363$	14.9006			0.782081
$364$	4.25227	+	13.1900i	0.222880	+	0.691342i
$365$	−0.766844			−0.0401385
$366$	−48.4491			−2.53248
$367$	7.07485	−	12.2540i	0.369304	−	0.639654i	−0.620153	−	0.784481i	$-0.712929\pi$
$367$	7.07485	−	12.2540i	0.369304	−	0.639654i	0.989457	+	0.144827i	$0.0462626\pi$
$368$	19.7324			1.02862
$369$	−6.10597	+	10.5759i	−0.317864	+	0.550557i
$370$	0.558320	−	0.967039i	0.0290257	−	0.0502740i
$371$	−12.2084	+	1.47619i	−0.633830	+	0.0766397i
$372$	−4.26823			−0.221298
$373$	2.52142	+	4.36723i	0.130554	+	0.226127i	0.923890	−	0.382657i	$-0.124991\pi$
$373$	2.52142	+	4.36723i	0.130554	+	0.226127i	−0.793336	+	0.608784i	$0.791658\pi$
$374$	3.26940	−	5.66276i	0.169056	−	0.292814i
$375$	−2.25499	+	3.90576i	−0.116447	+	0.201693i
$376$	−5.93034	+	10.2716i	−0.305834	+	0.529720i
$377$	−28.0820	−	9.68358i	−1.44630	−	0.498730i
$378$	−3.26297	+	7.64787i	−0.167829	+	0.393364i
$379$	3.02982	+	5.24780i	0.155631	+	0.269561i	0.933289	−	0.359127i	$-0.116925\pi$
$379$	3.02982	+	5.24780i	0.155631	+	0.269561i	−0.777657	+	0.628688i	$0.783592\pi$
$380$	−0.387575			−0.0198822
$381$	−5.02456			−0.257416
$382$	−12.1837	−	21.1028i	−0.623371	−	1.07971i
$383$	2.27052	+	3.93266i	0.116018	+	0.200950i	0.918186	−	0.396149i	$-0.129654\pi$
$383$	2.27052	+	3.93266i	0.116018	+	0.200950i	−0.802168	+	0.597098i	$0.796320\pi$
$384$	−8.98165	+	15.5567i	−0.458343	+	0.793873i
$385$	−2.16831	+	0.262182i	−0.110507	+	0.0133620i
$386$	−0.967705	+	1.67611i	−0.0492549	+	0.0853120i
$387$	12.0554			0.612811
$388$	−14.1446	+	24.4992i	−0.718085	+	1.24376i
$389$	−2.25383	−	3.90374i	−0.114273	−	0.197927i	0.803216	−	0.595688i	$-0.203121\pi$
$389$	−2.25383	−	3.90374i	−0.114273	−	0.197927i	−0.917489	+	0.397761i	$0.869787\pi$
$390$	−2.86766	−	0.988862i	−0.145210	−	0.0500730i
$391$	−3.46213			−0.175088
$392$	4.92567	+	5.13843i	0.248784	+	0.259530i
$393$	−2.61078	−	4.52201i	−0.131697	−	0.228105i
$394$	−1.37349	−	2.37896i	−0.0691955	−	0.119850i
$395$	−1.05918	−	1.83456i	−0.0532932	−	0.0923065i
$396$	−13.7496			−0.690945
$397$	−2.00174	−	3.46712i	−0.100465	−	0.174010i	0.811412	−	0.584475i	$-0.198700\pi$
$397$	−2.00174	−	3.46712i	−0.100465	−	0.174010i	−0.911876	+	0.410465i	$0.865366\pi$
$398$	26.1998			1.31328
$399$	3.21966	−	7.54637i	0.161185	−	0.377791i
$400$	−11.8941	−	20.6012i	−0.594706	−	1.03006i
$401$	12.6135			0.629887			0.314944	−	0.949110i	$-0.398014\pi$
$401$	12.6135			0.629887			0.314944	+	0.949110i	$0.398014\pi$
$402$	−28.5541	−	49.4571i	−1.42415	−	2.46670i
$403$	−4.36537	−	1.50532i	−0.217455	−	0.0749853i
$404$	12.3005	−	21.3051i	0.611972	−	1.05997i
$405$	−1.05275	−	1.82342i	−0.0523116	−	0.0906064i
$406$	40.2101	−	4.86201i	1.99559	−	0.241297i
$407$	6.36790	−	11.0295i	0.315645	−	0.546713i
$408$	0.981272	−	1.69961i	0.0485802	−	0.0841434i
$409$	20.6952			1.02331			0.511657	−	0.859190i	$-0.329032\pi$
$409$	20.6952			1.02331			0.511657	+	0.859190i	$0.329032\pi$
$410$	−1.97923			−0.0977472
$411$	−15.4253	+	26.7174i	−0.760873	+	1.31787i
$412$	5.25482	−	9.10162i	0.258886	−	0.448404i
$413$	6.28990	−	14.7425i	0.309506	−	0.725432i
$414$	8.65126	+	14.9844i	0.425186	+	0.736444i
$415$	0.303336	−	0.525393i	0.0148902	−	0.0257905i
$416$	18.7184	−	16.2569i	0.917746	−	0.797058i
$417$	−4.64021	−	8.03708i	−0.227232	−	0.393577i
$418$	−10.5061			−0.513869
$419$	10.9088	+	18.8945i	0.532928	+	0.923058i	0.999261	+	0.0384484i	$0.0122415\pi$
$419$	10.9088	+	18.8945i	0.532928	+	0.923058i	−0.466333	+	0.884609i	$0.654425\pi$
$420$	1.72768	−	0.208902i	0.0843019	−	0.0101934i
$421$	9.42727			0.459457			0.229728	−	0.973255i	$-0.426216\pi$
$421$	9.42727			0.459457			0.229728	+	0.973255i	$0.426216\pi$
$422$	−24.5920	−	42.5947i	−1.19712	−	2.07348i
$423$	−26.3928			−1.28326
$424$	2.36315	+	4.09310i	0.114765	+	0.198779i
$425$	2.08688	+	3.61458i	0.101228	+	0.175333i
$426$	12.7251	+	22.0406i	0.616535	+	1.06787i
$427$	29.8534	−	3.60973i	1.44471	−	0.174687i
$428$	−14.3133			−0.691861
$429$	−32.7070	−	11.2784i	−1.57911	−	0.544528i
$430$	0.976930	+	1.69209i	0.0471118	+	0.0816000i
$431$	−10.2138	+	17.6908i	−0.491980	+	0.852134i	−0.999957	−	0.00923613i	$-0.997060\pi$
$431$	−10.2138	+	17.6908i	−0.491980	+	0.852134i	0.507977	+	0.861370i	$0.330393\pi$
$432$	8.10983			0.390184
$433$	−13.1743	+	22.8186i	−0.633117	+	1.09659i	0.353794	+	0.935323i	$0.384891\pi$
$433$	−13.1743	+	22.8186i	−0.633117	+	1.09659i	−0.986911	+	0.161267i	$0.948442\pi$
$434$	6.25069	−	0.755803i	0.300043	−	0.0362797i
$435$	−1.86507	+	3.23039i	−0.0894231	+	0.154885i
$436$	10.0356	+	17.3822i	0.480619	+	0.832457i
$437$	2.78136	+	4.81745i	0.133050	+	0.230450i
$438$	16.5628			0.791399
$439$	25.1310			1.19944			0.599720	−	0.800210i	$-0.295279\pi$
$439$	25.1310			1.19944			0.599720	+	0.800210i	$0.295279\pi$
$440$	0.419714	+	0.726967i	0.0200091	+	0.0346568i
$441$	−4.42195	+	15.2095i	−0.210569	+	0.724260i
$442$	−4.25558	+	3.69595i	−0.202417	+	0.175799i
$443$	−9.25995	+	16.0387i	−0.439953	+	0.762022i	−0.997685	−	0.0679994i	$-0.978338\pi$
$443$	−9.25995	+	16.0387i	−0.439953	+	0.762022i	0.557732	+	0.830021i	$0.311672\pi$
$444$	−5.07384	+	8.78815i	−0.240794	+	0.417067i
$445$	−1.18261	+	2.04834i	−0.0560611	+	0.0971006i
$446$	0.676415	+	1.17159i	0.0320292	+	0.0554762i
$447$	35.2184			1.66577
$448$	−3.30898	+	7.75573i	−0.156335	+	0.366424i
$449$	−5.82155	+	10.0832i	−0.274736	+	0.475856i	−0.970068	−	0.242832i	$-0.921924\pi$
$449$	−5.82155	+	10.0832i	−0.274736	+	0.475856i	0.695333	+	0.718688i	$0.255257\pi$
$450$	10.4295	−	18.0644i	0.491651	−	0.851564i
$451$	−22.5740			−1.06297
$452$	3.10066	−	5.37050i	0.145843	−	0.252607i
$453$	14.0422			0.659759
$454$	−5.29939			−0.248713
$455$	1.84067	+	0.395660i	0.0862920	+	0.0185488i
$456$	−3.15328			−0.147666
$457$	20.5184			0.959812			0.479906	−	0.877320i	$-0.340671\pi$
$457$	20.5184			0.959812			0.479906	+	0.877320i	$0.340671\pi$
$458$	−2.94845	+	5.10687i	−0.137772	+	0.238629i
$459$	−1.42291			−0.0664156
$460$	−0.589955	+	1.02183i	−0.0275068	+	0.0476431i
$461$	−1.02038	+	1.76734i	−0.0475236	+	0.0823134i	−0.888809	−	0.458278i	$-0.848466\pi$
$461$	−1.02038	+	1.76734i	−0.0475236	+	0.0823134i	0.841285	+	0.540592i	$0.181800\pi$
$462$	46.8325	−	5.66276i	2.17885	−	0.263456i
$463$	3.03155			0.140888			0.0704441	−	0.997516i	$-0.477558\pi$
$463$	3.03155			0.140888			0.0704441	+	0.997516i	$0.477558\pi$
$464$	−19.7521	−	34.2116i	−0.916968	−	1.58824i
$465$	−0.289926	+	0.502167i	−0.0134450	+	0.0232874i
$466$	−12.4563	+	21.5749i	−0.577025	+	0.999436i
$467$	6.46371	−	11.1955i	0.299105	−	0.518065i	−0.676827	−	0.736142i	$-0.736645\pi$
$467$	6.46371	−	11.1955i	0.299105	−	0.518065i	0.975931	+	0.218078i	$0.0699787\pi$
$468$	11.2048	+	3.86378i	0.517943	+	0.178603i
$469$	21.2793	+	28.3470i	0.982585	+	1.30894i
$470$	−2.13879	−	3.70449i	−0.0986549	−	0.170875i
$471$	10.4075			0.479550
$472$	−6.16022			−0.283547
$473$	11.1423	+	19.2991i	0.512326	+	0.887374i
$474$	22.8768	+	39.6238i	1.05077	+	1.81998i
$475$	3.35305	−	5.80766i	0.153849	−	0.266474i
$476$	1.26898	−	2.97429i	0.0581637	−	0.136326i
$477$	−5.25858	+	9.10814i	−0.240774	+	0.417033i
$478$	−28.9015			−1.32192
$479$	−18.2911	+	31.6810i	−0.835740	+	1.44754i	0.0576873	+	0.998335i	$0.481627\pi$
$479$	−18.2911	+	31.6810i	−0.835740	+	1.44754i	−0.893427	+	0.449209i	$0.851706\pi$
$480$	−1.55664	−	2.69618i	−0.0710505	−	0.123063i
$481$	−8.28872	+	7.19872i	−0.377933	+	0.328233i
$482$	−14.0769			−0.641187
$483$	−14.9949	−	19.9754i	−0.682293	−	0.908912i
$484$	−4.71806	−	8.17191i	−0.214457	−	0.371451i
$485$	1.92159	+	3.32829i	0.0872550	+	0.151130i
$486$	18.0239	+	31.2183i	0.817580	+	1.41609i
$487$	36.7496			1.66528			0.832642	−	0.553812i	$-0.186827\pi$
$487$	36.7496			1.66528			0.832642	+	0.553812i	$0.186827\pi$
$488$	−5.77864	−	10.0089i	−0.261587	−	0.453081i
$489$	4.18103			0.189073
$490$	−2.49313	+	0.611861i	−0.112628	+	0.0276411i
$491$	4.09899	+	7.09965i	0.184985	+	0.320403i	0.943571	−	0.331169i	$-0.107443\pi$
$491$	4.09899	+	7.09965i	0.184985	+	0.320403i	−0.758587	+	0.651572i	$0.774110\pi$
$492$	17.9866			0.810900
$493$	3.46560	+	6.00259i	0.156083	+	0.270343i
$494$	8.56159	+	2.95231i	0.385204	+	0.132831i
$495$	−0.933965	+	1.61768i	−0.0419786	+	0.0727091i
$496$	−3.07048	−	5.31823i	−0.137869	−	0.238795i
$497$	−9.48313	−	12.6329i	−0.425376	−	0.566662i
$498$	−6.55163	+	11.3478i	−0.293585	+	0.508505i
$499$	21.6266	−	37.4584i	0.968141	−	1.67687i	0.267211	−	0.963638i	$-0.413898\pi$
$499$	21.6266	−	37.4584i	0.968141	−	1.67687i	0.700929	−	0.713231i	$-0.252769\pi$
$500$	2.85604			0.127726
$501$	−24.5648			−1.09747
$502$	−1.18436	+	2.05137i	−0.0528605	+	0.0915571i
$503$	−0.00909609	+	0.0157549i	−0.000405575	+	0.000702476i	−0.866228	−	0.499649i	$-0.833462\pi$
$503$	−0.00909609	+	0.0157549i	−0.000405575	+	0.000702476i	0.865823	+	0.500351i	$0.166796\pi$
$504$	6.04356	−	0.730758i	0.269201	−	0.0325505i
$505$	−1.67106	−	2.89436i	−0.0743612	−	0.128797i
$506$	−15.9920	+	27.6990i	−0.710933	+	1.23137i
$507$	23.4842	+	18.3820i	1.04297	+	0.816372i
$508$	1.59095	+	2.75560i	0.0705869	+	0.122260i
$509$	43.1006			1.91040			0.955200	−	0.295960i	$-0.0956394\pi$
$509$	43.1006			1.91040			0.955200	+	0.295960i	$0.0956394\pi$
$510$	0.353897	+	0.612968i	0.0156708	+	0.0271427i
$511$	−10.2056	+	1.23402i	−0.451471	+	0.0545897i
$512$	23.2197			1.02617
$513$	1.14311	+	1.97993i	0.0504697	+	0.0874161i
$514$	−15.7576			−0.695036
$515$	−0.713884	−	1.23648i	−0.0314575	−	0.0544859i
$516$	−8.87804	−	15.3772i	−0.390834	−	0.676944i
$517$	−24.3939	−	42.2514i	−1.07284	−	1.85822i
$518$	5.87430	−	13.7684i	0.258102	−	0.604949i
$519$	−30.9531			−1.35869
$520$	−0.137748	−	0.710362i	−0.00604065	−	0.0311514i
$521$	−10.4770	−	18.1467i	−0.459006	−	0.795022i	0.539903	−	0.841727i	$-0.318461\pi$
$521$	−10.4770	−	18.1467i	−0.459006	−	0.795022i	−0.998909	+	0.0467056i	$0.985128\pi$
$522$	17.3198	−	29.9988i	0.758068	−	1.31301i
$523$	−34.7403			−1.51909			−0.759543	−	0.650457i	$-0.774577\pi$
$523$	−34.7403			−1.51909			−0.759543	+	0.650457i	$0.774577\pi$
$524$	−1.65333	+	2.86365i	−0.0722260	+	0.125099i
$525$	−11.8164	+	27.6958i	−0.515712	+	1.20875i
$526$	−11.8814	+	20.5791i	−0.518052	+	0.897292i
$527$	0.538730	+	0.933107i	0.0234674	+	0.0406468i
$528$	−23.0052	−	39.8462i	−1.00117	−	1.73408i
$529$	−6.06520			−0.263704
$530$	−1.70455			−0.0740410
$531$	−6.85398	−	11.8714i	−0.297438	−	0.515177i
$532$	−5.15809	+	0.623691i	−0.223631	+	0.0270404i
$533$	18.3960	+	6.34352i	0.796819	+	0.274769i
$534$	25.5427	−	44.2413i	1.10534	−	1.91451i
$535$	−0.972255	+	1.68400i	−0.0420343	+	0.0728055i
$536$	6.81142	−	11.7977i	0.294209	−	0.509584i
$537$	−12.0085	−	20.7993i	−0.518205	−	0.897557i
$538$	−8.75513			−0.377460
$539$	−28.4353	+	6.97856i	−1.22480	+	0.300588i
$540$	−0.242466	+	0.419964i	−0.0104341	+	0.0180724i
$541$	1.64923	−	2.85655i	0.0709059	−	0.122813i	−0.828393	−	0.560148i	$-0.810744\pi$
$541$	1.64923	−	2.85655i	0.0709059	−	0.122813i	0.899299	+	0.437335i	$0.144078\pi$
$542$	−33.4678			−1.43756
$543$	−14.3619	+	24.8756i	−0.616330	+	1.06752i
$544$	−5.78497			−0.248029
$545$	2.72674			0.116801
$546$	−39.7559	−	8.54570i	−1.70140	−	0.365722i
$547$	21.9417			0.938161			0.469080	−	0.883155i	$-0.344585\pi$
$547$	21.9417			0.938161			0.469080	+	0.883155i	$0.344585\pi$
$548$	19.5367			0.834567
$549$	12.8589	−	22.2722i	0.548803	−	0.950554i
$550$	38.5583			1.64413
$551$	5.56828	−	9.64455i	0.237217	−	0.410871i
$552$	−4.79983	+	8.31354i	−0.204294	+	0.353848i
$553$	−17.0484	−	22.7110i	−0.724973	−	0.965768i
$554$	−48.5368			−2.06213
$555$	0.689297	+	1.19390i	0.0292590	+	0.0506781i
$556$	−2.93850	+	5.08963i	−0.124620	+	0.215848i
$557$	7.14329	−	12.3725i	0.302671	−	0.524241i	−0.674069	−	0.738668i	$-0.735455\pi$
$557$	7.14329	−	12.3725i	0.302671	−	0.524241i	0.976740	+	0.214427i	$0.0687884\pi$
$558$	2.69238	−	4.66334i	0.113978	−	0.197415i
$559$	−3.65686	−	18.8583i	−0.154669	−	0.797621i
$560$	1.50315	+	2.00241i	0.0635196	+	0.0846172i
$561$	4.03637	+	6.99119i	0.170416	+	0.295168i
$562$	−6.80453			−0.287032
$563$	6.78784			0.286073			0.143037	−	0.989717i	$-0.454313\pi$
$563$	6.78784			0.286073			0.143037	+	0.989717i	$0.454313\pi$
$564$	19.4366	+	33.6652i	0.818430	+	1.41756i
$565$	−0.421234	−	0.729599i	−0.0177215	−	0.0306945i
$566$	−7.10307	+	12.3029i	−0.298564	+	0.517128i
$567$	−16.9449	−	22.5731i	−0.711621	−	0.947981i
$568$	−3.03552	+	5.25767i	−0.127367	+	0.220607i
$569$	−17.3212			−0.726143			−0.363072	−	0.931761i	$-0.618272\pi$
$569$	−17.3212			−0.726143			−0.363072	+	0.931761i	$0.618272\pi$
$570$	0.568618	−	0.984875i	0.0238168	−	0.0412519i
$571$	6.50581	+	11.2684i	0.272260	+	0.471568i	0.969440	−	0.245328i	$-0.0788957\pi$
$571$	6.50581	+	11.2684i	0.272260	+	0.471568i	−0.697180	+	0.716896i	$0.745562\pi$
$572$	4.17078	+	21.5086i	0.174389	+	0.899318i
$573$	30.0837			1.25676
$574$	−26.3408	+	3.18501i	−1.09944	+	0.132940i
$575$	−10.2078	−	17.6805i	−0.425696	−	0.737327i
$576$	3.60574	+	6.24532i	0.150239	+	0.260222i
$577$	0.365767	+	0.633528i	0.0152271	+	0.0263741i	0.873539	−	0.486755i	$-0.161820\pi$
$577$	0.365767	+	0.633528i	0.0152271	+	0.0263741i	−0.858311	+	0.513129i	$0.828486\pi$
$578$	−30.2735			−1.25921
$579$	−1.19472	−	2.06931i	−0.0496508	−	0.0859978i
$580$	2.36218			0.0980842
$581$	3.19151	−	7.48039i	0.132406	−	0.310339i
$582$	−41.5037	−	71.8865i	−1.72038	−	2.97979i
$583$	−19.4412			−0.805173
$584$	1.97548	+	3.42163i	0.0817459	+	0.141588i
$585$	1.21569	−	1.05582i	0.0502625	−	0.0436527i
$586$	15.9369	−	27.6035i	0.658347	−	1.14029i
$587$	4.26142	+	7.38099i	0.175888	+	0.304646i	0.940468	−	0.339882i	$-0.110387\pi$
$587$	4.26142	+	7.38099i	0.175888	+	0.304646i	−0.764581	+	0.644528i	$0.777054\pi$
$588$	22.6568	−	5.56040i	0.934351	−	0.229307i
$589$	0.865594	−	1.49925i	0.0356662	−	0.0617756i
$590$	1.11085	−	1.92404i	0.0457329	−	0.0792117i
$591$	3.39140			0.139503
$592$	−14.6001			−0.600059
$593$	15.6547	−	27.1147i	0.642860	−	1.11347i	−0.341932	−	0.939725i	$-0.611081\pi$
$593$	15.6547	−	27.1147i	0.642860	−	1.11347i	0.984791	−	0.173741i	$-0.0555854\pi$
$594$	−6.57259	+	11.3841i	−0.269677	+	0.467093i
$595$	−0.263734	−	0.351332i	−0.0108120	−	0.0144032i
$596$	−11.1514	−	19.3147i	−0.456777	−	0.791161i
$597$	−16.1730	+	28.0125i	−0.661917	+	1.14647i
$598$	20.8159	−	18.0785i	0.851225	−	0.739285i
$599$	0.375116	+	0.649720i	0.0153268	+	0.0265468i	0.873587	−	0.486668i	$-0.161788\pi$
$599$	0.375116	+	0.649720i	0.0153268	+	0.0265468i	−0.858260	+	0.513215i	$0.828454\pi$
$600$	11.5728			0.472458
$601$	4.77652	+	8.27318i	0.194838	+	0.337470i	0.946848	−	0.321683i	$-0.104248\pi$
$601$	4.77652	+	8.27318i	0.194838	+	0.337470i	−0.752009	+	0.659153i	$0.770915\pi$
$602$	15.7245	+	20.9473i	0.640884	+	0.853750i
$603$	30.3141			1.23449
$604$	−4.44624	−	7.70111i	−0.180915	−	0.313354i
$605$	−1.28193			−0.0521177
$606$	36.0925	+	62.5141i	1.46616	+	2.53946i
$607$	−11.1197	−	19.2599i	−0.451336	−	0.781737i	0.547133	−	0.837045i	$-0.315719\pi$
$607$	−11.1197	−	19.2599i	−0.451336	−	0.781737i	−0.998469	+	0.0553087i	$0.982386\pi$
$608$	4.64745	+	8.04961i	0.188479	+	0.326455i
$609$	−19.6231	+	45.9934i	−0.795168	+	1.86374i
$610$	4.16815			0.168764
$611$	8.00594	+	41.2863i	0.323886	+	1.67027i
$612$	−1.38278	−	2.39505i	−0.0558957	−	0.0968143i
$613$	4.13993	−	7.17057i	0.167210	−	0.289617i	−0.770228	−	0.637769i	$-0.779857\pi$
$613$	4.13993	−	7.17057i	0.167210	−	0.289617i	0.937438	+	0.348152i	$0.113191\pi$
$614$	−52.1578			−2.10492
$615$	1.22177	−	2.11617i	0.0492665	−	0.0853321i
$616$	6.75567	+	8.99952i	0.272194	+	0.362601i
$617$	−10.1656	+	17.6073i	−0.409252	+	0.708845i	−0.994806	−	0.101789i	$-0.967543\pi$
$617$	−10.1656	+	17.6073i	−0.409252	+	0.708845i	0.585554	+	0.810633i	$0.300877\pi$
$618$	15.4189	+	26.7063i	0.620238	+	1.07428i
$619$	−2.67049	−	4.62542i	−0.107336	−	0.185911i	0.807354	−	0.590067i	$-0.200899\pi$
$619$	−2.67049	−	4.62542i	−0.107336	−	0.185911i	−0.914690	+	0.404156i	$0.867565\pi$
$620$	0.367203			0.0147472
$621$	6.96005			0.279297
$622$	21.8651	+	37.8714i	0.876709	+	1.51850i
$623$	−12.4427	+	29.1636i	−0.498506	+	1.16842i
$624$	7.55018	+	38.9360i	0.302249	+	1.55869i
$625$	−12.2086	+	21.1459i	−0.488345	+	0.845838i
$626$	3.11112	−	5.38862i	0.124345	−	0.215372i
$627$	6.48536	−	11.2330i	0.259000	−	0.448601i
$628$	−3.29536	−	5.70773i	−0.131499	−	0.227763i
$629$	2.56165			0.102140
$630$	−0.861570	+	2.01938i	−0.0343258	+	0.0804541i
$631$	−3.23331	+	5.60026i	−0.128716	+	0.222943i	−0.923179	−	0.384369i	$-0.874419\pi$
$631$	−3.23331	+	5.60026i	−0.128716	+	0.222943i	0.794463	+	0.607312i	$0.207752\pi$
$632$	−5.45714	+	9.45205i	−0.217074	+	0.375982i
$633$	60.7222			2.41349
$634$	6.76217	−	11.7124i	0.268560	−	0.465160i
$635$	0.432271			0.0171541
$636$	15.4904			0.614236
$637$	25.1335	+	2.30365i	0.995826	+	0.0912741i
$638$	64.0322			2.53506
$639$	−13.5095			−0.534428
$640$	0.772706	−	1.33837i	0.0305439	−	0.0529035i
$641$	23.3289			0.921434			0.460717	−	0.887547i	$-0.347592\pi$
$641$	23.3289			0.921434			0.460717	+	0.887547i	$0.347592\pi$
$642$	20.9993	−	36.3719i	0.828778	−	1.43549i
$643$	1.79439	−	3.10797i	0.0707637	−	0.122566i	−0.828472	−	0.560030i	$-0.810790\pi$
$643$	1.79439	−	3.10797i	0.0707637	−	0.122566i	0.899236	+	0.437463i	$0.144123\pi$
$644$	−6.20714	+	14.5485i	−0.244596	+	0.573293i
$645$	−2.41222			−0.0949810
$646$	−1.05658	−	1.83006i	−0.0415707	−	0.0720026i
$647$	19.8262	−	34.3400i	0.779448	−	1.35004i	−0.152812	−	0.988255i	$-0.548833\pi$
$647$	19.8262	−	34.3400i	0.779448	−	1.35004i	0.932260	−	0.361788i	$-0.117834\pi$
$648$	−5.42402	+	9.39467i	−0.213076	+	0.369058i
$649$	12.6697	−	21.9446i	0.497331	−	0.861402i
$650$	−31.4218	−	10.8352i	−1.23246	−	0.424993i
$651$	−3.05042	+	7.14970i	−0.119556	+	0.280219i
$652$	−1.32386	−	2.29299i	−0.0518464	−	0.0898005i
$653$	18.1355			0.709699			0.354849	−	0.934923i	$-0.384532\pi$
$653$	18.1355			0.709699			0.354849	+	0.934923i	$0.384532\pi$
$654$	−58.8938			−2.30293
$655$	0.224610	+	0.389035i	0.00877623	+	0.0152009i
$656$	12.9392	+	22.4114i	0.505192	+	0.875017i
$657$	−4.39592	+	7.61395i	−0.171501	+	0.297048i
$658$	−34.4256	−	45.8599i	−1.34205	−	1.78780i
$659$	−6.74052	+	11.6749i	−0.262573	+	0.454791i	−0.966925	−	0.255061i	$-0.917905\pi$
$659$	−6.74052	+	11.6749i	−0.262573	+	0.454791i	0.704352	+	0.709851i	$0.251238\pi$
$660$	2.75122			0.107091
$661$	−5.15611	+	8.93064i	−0.200549	+	0.347362i	−0.948706	−	0.316161i	$-0.897606\pi$
$661$	−5.15611	+	8.93064i	−0.200549	+	0.347362i	0.748156	+	0.663523i	$0.230939\pi$
$662$	13.3076	+	23.0494i	0.517213	+	0.895839i
$663$	−1.32471	−	6.83150i	−0.0514476	−	0.265314i
$664$	−3.12571			−0.121301
$665$	−0.276992	+	0.649226i	−0.0107413	+	0.0251759i
$666$	−6.40111	−	11.0870i	−0.248038	−	0.429614i
$667$	−16.9517	−	29.3613i	−0.656374	−	1.13687i
$668$	7.77805	+	13.4720i	0.300942	+	0.521247i
$669$	−1.67019			−0.0645733
$670$	2.45655	+	4.25487i	0.0949049	+	0.164380i
$671$	47.5397			1.83525
$672$	−25.0554	−	33.3774i	−0.966535	−	1.28756i
$673$	4.61528	+	7.99390i	0.177906	+	0.308142i	0.941163	−	0.337953i	$-0.109734\pi$
$673$	4.61528	+	7.99390i	0.177906	+	0.308142i	−0.763257	+	0.646095i	$0.776401\pi$
$674$	31.9237			1.22965
$675$	−4.19533	−	7.26652i	−0.161478	−	0.279689i
$676$	2.64527	−	18.6997i	0.101741	−	0.719221i
$677$	10.5467	−	18.2674i	0.405343	−	0.702075i	−0.589018	−	0.808120i	$-0.700485\pi$
$677$	10.5467	−	18.2674i	0.405343	−	0.702075i	0.994361	+	0.106045i	$0.0338187\pi$
$678$	9.09807	+	15.7583i	0.349409	+	0.605194i
$679$	30.9297	+	41.2027i	1.18697	+	1.58122i
$680$	−0.0844203	+	0.146220i	−0.00323737	+	0.00560729i
$681$	3.27129	−	5.66604i	0.125356	−	0.217123i
$682$	9.95385			0.381153
$683$	−38.2212			−1.46249			−0.731246	−	0.682113i	$-0.761061\pi$
$683$	−38.2212			−1.46249			−0.731246	+	0.682113i	$0.761061\pi$
$684$	−2.22176	+	3.84821i	−0.0849512	+	0.147140i
$685$	1.32706	−	2.29854i	0.0507044	−	0.0878226i
$686$	−32.1955	+	12.1550i	−1.22923	+	0.464081i
$687$	−3.64013	−	6.30490i	−0.138880	−	0.240547i
$688$	12.7734	−	22.1241i	0.486980	−	0.843474i
$689$	15.8430	+	5.46317i	0.603570	+	0.208130i
$690$	−1.73107	−	2.99830i	−0.0659006	−	0.114143i
$691$	−26.2322			−0.997920			−0.498960	−	0.866625i	$-0.666285\pi$
$691$	−26.2322			−0.997920			−0.498960	+	0.866625i	$0.666285\pi$
$692$	9.80084	+	16.9755i	0.372572	+	0.645313i
$693$	−9.82661	+	23.0320i	−0.373282	+	0.874913i
$694$	−14.3130			−0.543314
$695$	0.399204	+	0.691442i	0.0151427	+	0.0262279i
$696$	19.2185			0.728476
$697$	−2.27024	−	3.93218i	−0.0859916	−	0.148942i
$698$	−20.7836	−	35.9982i	−0.786670	−	1.36255i
$699$	−15.3784	−	26.6361i	−0.581664	−	1.00747i
$700$	18.9306	−	2.28900i	0.715511	−	0.0865161i
$701$	−46.7346			−1.76514			−0.882570	−	0.470180i	$-0.844189\pi$
$701$	−46.7346			−1.76514			−0.882570	+	0.470180i	$0.844189\pi$
$702$	8.55515	−	7.43011i	0.322893	−	0.280431i
$703$	−2.05794	−	3.56446i	−0.0776167	−	0.134436i
$704$	−6.66528	+	11.5446i	−0.251207	+	0.435104i
$705$	5.28105			0.198896
$706$	20.6835	−	35.8248i	0.778433	−	1.34828i
$707$	−26.8972	−	35.8309i	−1.01157	−	1.34756i
$708$	−10.0950	+	17.4851i	−0.379395	+	0.657131i
$709$	23.7232	+	41.0898i	0.890944	+	1.54316i	0.838745	+	0.544524i	$0.183290\pi$
$709$	23.7232	+	41.0898i	0.890944	+	1.54316i	0.0521988	+	0.998637i	$0.483377\pi$
$710$	−1.09476	−	1.89619i	−0.0410858	−	0.0711626i
$711$	−24.2869			−0.910830
$712$	12.1861			0.456695
$713$	−2.63516	−	4.56423i	−0.0986876	−	0.170932i
$714$	5.69629	+	7.58827i	0.213178	+	0.283984i
$715$	2.81384	+	0.970301i	0.105232	+	0.0362872i
$716$	−7.60461	+	13.1716i	−0.284197	+	0.492244i
$717$	17.8408	−	30.9011i	0.666275	−	1.15402i
$718$	2.56280	−	4.43890i	0.0956428	−	0.165658i
$719$	24.6190	+	42.6413i	0.918133	+	1.59025i	0.802249	+	0.596990i	$0.203637\pi$
$719$	24.6190	+	42.6413i	0.918133	+	1.59025i	0.115884	+	0.993263i	$0.463030\pi$
$720$	2.14136			0.0798037
$721$	−11.4906	−	15.3071i	−0.427931	−	0.570066i
$722$	15.9549	−	27.6347i	0.593779	−	1.02846i
$723$	8.68963	−	15.0509i	0.323171	−	0.559748i
$724$	18.1900			0.676024
$725$	−20.4361	+	35.3963i	−0.758977	+	1.31459i
$726$	27.6878			1.02759
$727$	−32.0495			−1.18865			−0.594325	−	0.804225i	$-0.702581\pi$
$727$	−32.0495			−1.18865			−0.594325	+	0.804225i	$0.702581\pi$
$728$	−2.97636	−	9.23227i	−0.110311	−	0.342171i
$729$	−12.4996			−0.462947
$730$	−1.42492			−0.0527387
$731$	−2.24114	+	3.88178i	−0.0828917	+	0.143573i
$732$	−37.8789			−1.40004
$733$	−14.1005	+	24.4228i	−0.520813	+	0.902075i	0.478894	+	0.877873i	$0.341038\pi$
$733$	−14.1005	+	24.4228i	−0.520813	+	0.902075i	−0.999707	+	0.0242025i	$0.992295\pi$
$734$	13.1462	−	22.7699i	0.485236	−	0.840453i
$735$	0.884805	−	3.04332i	0.0326365	−	0.112255i
$736$	28.2968			1.04303
$737$	28.0181	+	48.5288i	1.03206	+	1.78758i
$738$	−11.3459	+	19.6516i	−0.417648	+	0.723387i
$739$	21.2685	−	36.8381i	0.782375	−	1.35511i	−0.148180	−	0.988960i	$-0.547342\pi$
$739$	21.2685	−	36.8381i	0.782375	−	1.35511i	0.930555	−	0.366153i	$-0.119325\pi$
$740$	0.436510	−	0.756058i	0.0160464	−	0.0277932i
$741$	−8.44160	+	7.33149i	−0.310110	+	0.269329i
$742$	−22.6852	+	2.74299i	−0.832801	+	0.100698i
$743$	−7.95711	−	13.7821i	−0.291918	−	0.505617i	0.682345	−	0.731030i	$-0.260960\pi$
$743$	−7.95711	−	13.7821i	−0.291918	−	0.505617i	−0.974263	+	0.225413i	$0.927627\pi$
$744$	2.98753			0.109528
$745$	−3.02989			−0.111007
$746$	4.68521	+	8.11502i	0.171538	+	0.297112i
$747$	−3.47773	−	6.02360i	−0.127243	−	0.220392i
$748$	2.55611	−	4.42731i	0.0934605	−	0.161878i
$749$	−10.2295	+	23.9762i	−0.373777	+	0.876072i
$750$	−4.19014	+	7.25754i	−0.153002	+	0.265008i
$751$	18.1996			0.664114			0.332057	−	0.943259i	$-0.392257\pi$
$751$	18.1996			0.664114			0.332057	+	0.943259i	$0.392257\pi$
$752$	−27.9646	+	48.4362i	−1.01977	+	1.76629i
$753$	−1.46220	−	2.53260i	−0.0532855	−	0.0922931i
$754$	−52.1809	−	17.9937i	−1.90032	−	0.655290i
$755$	−1.20807			−0.0439662
$756$	−2.55108	+	5.97932i	−0.0927818	+	0.217466i
$757$	22.4502	+	38.8849i	0.815967	+	1.41330i	0.908632	+	0.417598i	$0.137128\pi$
$757$	22.4502	+	38.8849i	0.815967	+	1.41330i	−0.0926649	+	0.995697i	$0.529539\pi$
$758$	5.62989	+	9.75126i	0.204487	+	0.354182i
$759$	−19.7436	−	34.1970i	−0.716648	−	1.24127i
$760$	0.271282			0.00984042
$761$	13.2444	+	22.9399i	0.480108	+	0.831572i	0.999740	−	0.0228184i	$-0.00726396\pi$
$761$	13.2444	+	22.9399i	0.480108	+	0.831572i	−0.519631	+	0.854391i	$0.673931\pi$
$762$	−9.33644			−0.338223
$763$	36.2892	−	4.38791i	1.31376	−	0.158853i
$764$	−9.52554	−	16.4987i	−0.344622	−	0.596903i
$765$	−0.375711			−0.0135839
$766$	4.21900	+	7.30752i	0.152439	+	0.264031i
$767$	−16.4914	+	14.3227i	−0.595471	+	0.517164i
$768$	−24.0006	+	41.5703i	−0.866049	+	1.50004i
$769$	−6.98127	−	12.0919i	−0.251751	−	0.436045i	0.712257	−	0.701919i	$-0.247673\pi$
$769$	−6.98127	−	12.0919i	−0.251751	−	0.436045i	−0.964008	+	0.265873i	$0.914340\pi$
$770$	−4.02907	+	0.487176i	−0.145198	+	0.0175566i
$771$	9.72707	−	16.8478i	0.350312	−	0.606758i
$772$	−0.756579	+	1.31043i	−0.0272299	+	0.0471635i
$773$	12.8113			0.460790			0.230395	−	0.973097i	$-0.425998\pi$
$773$	12.8113			0.460790			0.230395	+	0.973097i	$0.425998\pi$
$774$	22.4009			0.805184
$775$	−3.17681	+	5.50239i	−0.114114	+	0.197652i
$776$	9.90048	−	17.1481i	0.355406	−	0.615582i
$777$	11.0948	+	14.7799i	0.398025	+	0.530226i
$778$	−4.18797	−	7.25378i	−0.150146	−	0.260061i
$779$	−3.64767	+	6.31795i	−0.130691	+	0.226364i
$780$	−2.24202	−	0.773120i	−0.0802772	−	0.0276821i
$781$	−12.4863	−	21.6269i	−0.446795	−	0.773871i
$782$	−6.43320			−0.230051
$783$	−6.96701	−	12.0672i	−0.248981	−	0.431247i
$784$	23.2271	+	24.2304i	0.829540	+	0.865372i
$785$	−0.895370			−0.0319571
$786$	−4.85125	−	8.40262i	−0.173039	−	0.299712i
$787$	−27.3199			−0.973848			−0.486924	−	0.873444i	$-0.661881\pi$
$787$	−27.3199			−0.973848			−0.486924	+	0.873444i	$0.661881\pi$
$788$	−1.07383	−	1.85993i	−0.0382537	−	0.0662574i
$789$	−14.6686	−	25.4068i	−0.522217	−	0.904506i
$790$	−1.96813	−	3.40890i	−0.0700229	−	0.121283i
$791$	−6.78013	−	9.03210i	−0.241074	−	0.321145i
$792$	9.62401			0.341974
$793$	−38.7410	−	13.3591i	−1.37573	−	0.474396i
$794$	−3.71956	−	6.44247i	−0.132002	−	0.228635i
$795$	1.05221	−	1.82248i	0.0373181	−	0.0646369i
$796$	20.4837			0.726027
$797$	14.7002	−	25.4614i	0.520707	−	0.901891i	−0.479003	−	0.877813i	$-0.659002\pi$
$797$	14.7002	−	25.4614i	0.520707	−	0.901891i	0.999710	−	0.0240775i	$-0.00766483\pi$
$798$	5.98265	−	14.0224i	0.211783	−	0.496386i
$799$	4.90652	−	8.49835i	0.173580	−	0.300650i
$800$	−17.0565	−	29.5428i	−0.603040	−	1.04450i
$801$	13.5586	+	23.4841i	0.479068	+	0.829770i
$802$	23.4379			0.827621
$803$	−16.2519			−0.573517
$804$	−22.3244	−	38.6669i	−0.787320	−	1.36368i
$805$	1.29004	+	1.71852i	0.0454679	+	0.0605697i
$806$	−8.11157	−	2.79713i	−0.285718	−	0.0985246i
$807$	5.40450	−	9.36087i	0.190247	−	0.329518i
$808$	−8.60968	+	14.9124i	−0.302888	+	0.524617i
$809$	3.00617	−	5.20683i	0.105691	−	0.183063i	−0.808329	−	0.588731i	$-0.799628\pi$
$809$	3.00617	−	5.20683i	0.105691	−	0.183063i	0.914020	+	0.405668i	$0.132961\pi$
$810$	−1.95618	−	3.38821i	−0.0687332	−	0.119049i
$811$	8.44807			0.296652			0.148326	−	0.988939i	$-0.452612\pi$
$811$	8.44807			0.296652			0.148326	+	0.988939i	$0.452612\pi$
$812$	31.4374	−	3.80125i	1.10323	−	0.133398i
$813$	20.6595	−	35.7833i	0.724560	−	1.25497i
$814$	11.8326	−	20.4946i	0.414732	−	0.718337i
$815$	−0.359701			−0.0125998
$816$	4.62721	−	8.01456i	0.161985	−	0.280566i
$817$	7.20184			0.251960
$818$	38.4551			1.34455
$819$	14.4801	−	16.0078i	0.505975	−	0.559358i
$820$	−1.54742			−0.0540382
$821$	−34.2635			−1.19581			−0.597903	−	0.801569i	$-0.703999\pi$
$821$	−34.2635			−1.19581			−0.597903	+	0.801569i	$0.703999\pi$
$822$	−28.6627	+	49.6452i	−0.999725	+	1.73157i
$823$	−6.23732			−0.217419			−0.108710	−	0.994074i	$-0.534672\pi$
$823$	−6.23732			−0.217419			−0.108710	+	0.994074i	$0.534672\pi$
$824$	−3.67809	+	6.37064i	−0.128132	+	0.221932i
$825$	−23.8018	+	41.2260i	−0.828673	+	1.43530i
$826$	11.6876	−	27.3940i	0.406665	−	0.953158i
$827$	19.5232			0.678889			0.339445	−	0.940626i	$-0.389761\pi$
$827$	19.5232			0.678889			0.339445	+	0.940626i	$0.389761\pi$
$828$	6.76380	+	11.7152i	0.235058	+	0.407133i
$829$	−16.3383	+	28.2988i	−0.567453	+	0.982857i	0.429364	+	0.903131i	$0.358738\pi$
$829$	−16.3383	+	28.2988i	−0.567453	+	0.982857i	−0.996817	+	0.0797254i	$0.974596\pi$
$830$	0.563647	−	0.976265i	0.0195645	−	0.0338866i
$831$	29.9615	−	51.8949i	1.03935	−	1.80021i
$832$	8.67580	−	7.53489i	0.300779	−	0.261225i
$833$	−4.07530	−	4.25133i	−0.141201	−	0.147300i
$834$	−8.62225	−	14.9342i	−0.298564	−	0.517128i
$835$	2.11334			0.0731353
$836$	−8.21395			−0.284085
$837$	−1.08303	−	1.87586i	−0.0374349	−	0.0648392i
$838$	20.2702	+	35.1091i	0.700223	+	1.21282i
$839$	−12.3713	+	21.4278i	−0.427106	+	0.739769i	−0.996615	−	0.0822161i	$-0.973800\pi$
$839$	−12.3713	+	21.4278i	−0.427106	+	0.739769i	0.569508	+	0.821985i	$0.307134\pi$
$840$	−1.20928	+	0.146220i	−0.0417241	+	0.00504508i
$841$	−19.4374	+	33.6665i	−0.670255	+	1.16092i
$842$	17.5174			0.603689
$843$	4.20040	−	7.27531i	0.144669	−	0.250575i
$844$	−19.2267	−	33.3017i	−0.661812	−	1.14629i
$845$	−2.02038	−	1.58143i	−0.0695032	−	0.0544029i
$846$	−49.0422			−1.68610
$847$	−17.0607	+	2.06289i	−0.586211	+	0.0708818i
$848$	11.1435	+	19.3011i	0.382670	+	0.662803i
$849$	−8.76938	−	15.1890i	−0.300964	−	0.521285i
$850$	3.87776	+	6.71647i	0.133006	+	0.230373i
$851$	−12.5301			−0.429528
$852$	9.94888	+	17.2320i	0.340843	+	0.590357i
$853$	18.2245			0.623994			0.311997	−	0.950083i	$-0.399002\pi$
$853$	18.2245			0.623994			0.311997	+	0.950083i	$0.399002\pi$
$854$	55.4724	−	6.70745i	1.89823	−	0.229524i
$855$	0.301833	+	0.522791i	0.0103225	+	0.0178791i
$856$	10.0186			0.342427
$857$	−1.27340	−	2.20559i	−0.0434984	−	0.0753414i	0.843457	−	0.537197i	$-0.180517\pi$
$857$	−1.27340	−	2.20559i	−0.0434984	−	0.0753414i	−0.886955	+	0.461856i	$0.847184\pi$
$858$	−60.7749	−	20.9571i	−2.07482	−	0.715465i
$859$	−27.0045	+	46.7732i	−0.921382	+	1.59588i	−0.124104	+	0.992269i	$0.539606\pi$
$859$	−27.0045	+	46.7732i	−0.921382	+	1.59588i	−0.797278	+	0.603612i	$0.793728\pi$
$860$	0.763792	+	1.32293i	0.0260451	+	0.0451114i
$861$	12.8547	−	30.1293i	0.438087	−	1.02681i
$862$	−18.9788	+	32.8723i	−0.646421	+	1.11963i
$863$	−0.621545	+	1.07655i	−0.0211576	+	0.0366461i	−0.876410	−	0.481565i	$-0.840069\pi$
$863$	−0.621545	+	1.07655i	−0.0211576	+	0.0366461i	0.855253	+	0.518211i	$0.173402\pi$
$864$	11.6297			0.395652
$865$	2.66295			0.0905429
$866$	−24.4800	+	42.4006i	−0.831864	+	1.44083i
$867$	18.6877	−	32.3681i	0.634668	−	1.09928i
$868$	4.88696	−	0.590908i	0.165874	−	0.0200567i
$869$	−22.4474	−	38.8801i	−0.761477	−	1.31892i
$870$	−3.46560	+	6.00259i	−0.117495	+	0.203507i
$871$	−9.19540	−	47.4203i	−0.311574	−	1.60678i
$872$	−7.02440	−	12.1666i	−0.237876	−	0.412013i
$873$	44.0619			1.49127
$874$	5.16821	+	8.95161i	0.174817	+	0.302793i
$875$	2.04116	−	4.78414i	0.0690036	−	0.161733i
$876$	12.9492			0.437514
$877$	−0.401330	−	0.695125i	−0.0135520	−	0.0234727i	0.859170	−	0.511690i	$-0.170981\pi$
$877$	−0.401330	−	0.695125i	−0.0135520	−	0.0234727i	−0.872722	+	0.488218i	$0.837647\pi$
$878$	46.6975			1.57597
$879$	19.6755	+	34.0790i	0.663639	+	1.14946i
$880$	1.97917	+	3.42803i	0.0667179	+	0.115559i
$881$	18.5318	+	32.0980i	0.624352	+	1.08141i	0.988666	+	0.150133i	$0.0479703\pi$
$881$	18.5318	+	32.0980i	0.624352	+	1.08141i	−0.364314	+	0.931276i	$0.618696\pi$
$882$	−8.21669	+	28.2616i	−0.276670	+	0.951619i
$883$	−22.8671			−0.769539			−0.384770	−	0.923013i	$-0.625719\pi$
$883$	−22.8671			−0.769539			−0.384770	+	0.923013i	$0.625719\pi$
$884$	−3.32713	+	2.88960i	−0.111904	+	0.0971877i
$885$	1.37144	+	2.37541i	0.0461005	+	0.0798484i
$886$	−17.2065	+	29.8025i	−0.578063	+	1.00123i
$887$	−49.2573			−1.65390			−0.826950	−	0.562276i	$-0.809926\pi$
$887$	−49.2573			−1.65390			−0.826950	+	0.562276i	$0.809926\pi$
$888$	3.55141	−	6.15123i	0.119178	−	0.206422i
$889$	5.75292	−	0.695616i	0.192947	−	0.0233302i
$890$	−2.19748	+	3.80614i	−0.0736597	+	0.127582i
$891$	−22.3112	−	38.6441i	−0.747452	−	1.29463i
$892$	0.528840	+	0.915978i	0.0177069	+	0.0306692i
$893$	−15.7669			−0.527620
$894$	65.4414			2.18869
$895$	1.03311	+	1.78940i	0.0345330	+	0.0598130i
$896$	8.12993	−	19.0552i	0.271602	−	0.636591i
$897$	6.47975	+	33.4159i	0.216353	+	1.11572i
$898$	−10.8174	+	18.7362i	−0.360980	+	0.625236i
$899$	−5.27559	+	9.13760i	−0.175951	+	0.304756i
$900$	8.15406	−	14.1233i	0.271802	−	0.470775i
$901$	−1.95518	−	3.38647i	−0.0651365	−	0.112820i
$902$	−41.9462			−1.39666
$903$	−32.1033	+	3.88178i	−1.06833	+	0.129177i
$904$	−2.17029	+	3.75906i	−0.0721829	+	0.125024i
$905$	1.23558	−	2.14009i	0.0410721	−	0.0711390i
$906$	26.0926			0.866870
$907$	2.50228	−	4.33407i	0.0830867	−	0.143910i	−0.821488	−	0.570226i	$-0.806855\pi$
$907$	2.50228	−	4.33407i	0.0830867	−	0.143910i	0.904574	+	0.426316i	$0.140189\pi$
$908$	−4.14321			−0.137497
$909$	−38.3172			−1.27090
$910$	3.42026	+	0.735200i	0.113381	+	0.0243716i
$911$	49.0582			1.62537			0.812685	−	0.582703i	$-0.198005\pi$
$911$	49.0582			1.62537			0.812685	+	0.582703i	$0.198005\pi$
$912$	−14.8694			−0.492374
$913$	6.42866	−	11.1348i	0.212757	−	0.368507i
$914$	38.1266			1.26111
$915$	−2.57298	+	4.45653i	−0.0850601	+	0.147328i
$916$	−2.30518	+	3.99270i	−0.0761654	+	0.131922i
$917$	3.61529	+	4.81608i	0.119387	+	0.159041i
$918$	−2.64399			−0.0872646
$919$	−14.8028	−	25.6392i	−0.488299	−	0.845758i	0.511611	−	0.859217i	$-0.329049\pi$
$919$	−14.8028	−	25.6392i	−0.488299	−	0.845758i	−0.999909	+	0.0134590i	$0.995716\pi$
$920$	0.412937	−	0.715227i	0.0136141	−	0.0235803i
$921$	32.1967	−	55.7664i	1.06092	−	1.83756i
$922$	−1.89602	+	3.28401i	−0.0624422	+	0.108153i
$923$	4.09794	+	21.1329i	0.134885	+	0.695598i
$924$	36.6150	−	4.42731i	1.20454	−	0.145648i
$925$	7.55282	+	13.0819i	0.248335	+	0.430129i
$926$	5.63311			0.185116
$927$	−16.3693			−0.537637
$928$	−28.3251	−	49.0605i	−0.929817	−	1.61049i
$929$	−8.41525	−	14.5756i	−0.276095	−	0.478211i	0.694316	−	0.719671i	$-0.255707\pi$
$929$	−8.41525	−	14.5756i	−0.276095	−	0.478211i	−0.970411	+	0.241460i	$0.922374\pi$
$930$	−0.538730	+	0.933107i	−0.0176656	+	0.0305978i
$931$	−2.64164	+	9.08604i	−0.0865764	+	0.297783i
$932$	−9.73865	+	16.8678i	−0.319000	+	0.552524i
$933$	−53.9888			−1.76751
$934$	12.0106	−	20.8030i	0.392999	−	0.680695i
$935$	−0.347255	−	0.601463i	−0.0113565	−	0.0196699i
$936$	−7.84277	−	2.70444i	−0.256349	−	0.0883973i
$937$	44.0131			1.43784			0.718922	−	0.695091i	$-0.244636\pi$
$937$	44.0131			1.43784			0.718922	+	0.695091i	$0.244636\pi$
$938$	39.5403	+	52.6734i	1.29104	+	1.71985i
$939$	3.84096	+	6.65273i	0.125345	+	0.217104i
$940$	−1.67216	−	2.89627i	−0.0545400	−	0.0944660i
$941$	−26.5338	−	45.9578i	−0.864976	−	1.49818i	−0.867071	−	0.498184i	$-0.834000\pi$
$941$	−26.5338	−	45.9578i	−0.864976	−	1.49818i	0.00209573	−	0.999998i	$-0.499333\pi$
$942$	19.3387			0.630090
$943$	11.1048	+	19.2340i	0.361620	+	0.626345i
$944$	−29.0487			−0.945453
$945$	0.530194	+	0.706295i	0.0172472	+	0.0229758i
$946$	20.7043	+	35.8609i	0.673154	+	1.16594i
$947$	−27.8817			−0.906034			−0.453017	−	0.891502i	$-0.649652\pi$
$947$	−27.8817			−0.906034			−0.453017	+	0.891502i	$0.649652\pi$
$948$	17.8857	+	30.9790i	0.580902	+	1.00615i
$949$	13.2439	+	4.56694i	0.429917	+	0.148249i
$950$	6.23051	−	10.7916i	0.202145	−	0.350125i
$951$	8.34851	+	14.4600i	0.270719	+	0.468899i
$952$	−0.888219	+	2.08184i	−0.0287873	+	0.0674729i
$953$	18.1784	−	31.4859i	0.588856	−	1.01993i	−0.405527	−	0.914083i	$-0.632912\pi$
$953$	18.1784	−	31.4859i	0.588856	−	1.01993i	0.994383	−	0.105845i	$-0.0337548\pi$
$954$	−9.77130	+	16.9244i	−0.316357	+	0.547947i
$955$	−2.58815			−0.0837505
$956$	−22.5960			−0.730807
$957$	−39.5267	+	68.4623i	−1.27772	+	2.21307i
$958$	−33.9877	+	58.8685i	−1.09809	+	1.90195i
$959$	13.9625	−	32.7259i	0.450873	−	1.05677i
$960$	−0.721486	−	1.24965i	−0.0232859	−	0.0403323i
$961$	14.6799	−	25.4263i	0.473545	−	0.820205i
$962$	−15.4018	+	13.3764i	−0.496573	+	0.431272i
$963$	11.1469	+	19.3069i	0.359202	+	0.622157i
$964$	−11.0057			−0.354471
$965$	0.102784	+	0.178026i	0.00330872	+	0.00573087i
$966$	−27.8630	−	37.1175i	−0.896478	−	1.19424i
$967$	−15.2681			−0.490988			−0.245494	−	0.969398i	$-0.578950\pi$
$967$	−15.2681			−0.490988			−0.245494	+	0.969398i	$0.578950\pi$
$968$	3.30239	+	5.71990i	0.106143	+	0.183845i
$969$	2.60890			0.0838099
$970$	3.57063	+	6.18450i	0.114646	+	0.198572i
$971$	18.4460	+	31.9494i	0.591961	+	1.02531i	0.993968	+	0.109669i	$0.0349792\pi$
$971$	18.4460	+	31.9494i	0.591961	+	1.02531i	−0.402008	+	0.915636i	$0.631687\pi$
$972$	14.0916	+	24.4073i	0.451987	+	0.782865i
$973$	6.42554	+	8.55974i	0.205993	+	0.274413i
$974$	68.2867			2.18805
$975$	30.9814	−	26.9072i	0.992200	−	0.861721i
$976$	−27.2493	−	47.1972i	−0.872229	−	1.51074i
$977$	0.221957	−	0.384441i	0.00710104	−	0.0122994i	−0.862453	−	0.506137i	$-0.831073\pi$
$977$	0.221957	−	0.384441i	0.00710104	−	0.0122994i	0.869554	+	0.493838i	$0.164406\pi$
$978$	7.76904			0.248426
$979$	−25.0633	+	43.4109i	−0.801026	+	1.38742i
$980$	−1.94920	+	0.478370i	−0.0622649	+	0.0152810i
$981$	15.6310	−	27.0736i	0.499058	−	0.864394i
$982$	7.61658	+	13.1923i	0.243055	+	0.420983i
$983$	−22.7802	−	39.4564i	−0.726575	−	1.25846i	−0.958323	−	0.285688i	$-0.907778\pi$
$983$	−22.7802	−	39.4564i	−0.726575	−	1.25846i	0.231748	−	0.972776i	$-0.425556\pi$
$984$	−12.5897			−0.401344
$985$	−0.291767			−0.00929648
$986$	6.43964	+	11.1538i	0.205080	+	0.355209i
$987$	70.2835	−	8.49835i	2.23715	−	0.270505i
$988$	6.69369	+	2.30820i	0.212955	+	0.0734336i
$989$	10.9624	−	18.9875i	0.348585	−	0.603766i
$990$	−1.73546	+	3.00590i	−0.0551565	+	0.0955338i
$991$	−26.8148	+	46.4445i	−0.851799	+	1.47536i	0.0277842	+	0.999614i	$0.491155\pi$
$991$	−26.8148	+	46.4445i	−0.851799	+	1.47536i	−0.879583	+	0.475745i	$0.842178\pi$
$992$	−4.40316	−	7.62650i	−0.139801	−	0.242142i
$993$	−32.8588			−1.04274
$994$	−17.6212	−	23.4739i	−0.558910	−	0.744548i
$995$	1.39139	−	2.40996i	0.0441100	−	0.0764008i
$996$	−5.12225	+	8.87199i	−0.162305	+	0.281120i
$997$	29.0852			0.921139			0.460569	−	0.887624i	$-0.347645\pi$
$997$	29.0852			0.921139			0.460569	+	0.887624i	$0.347645\pi$
$998$	40.1857	−	69.6038i	1.27206	−	2.20327i
$999$	−5.14977			−0.162932

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.h.b.16.6	yes	12
3.2	odd	2		819.2.s.d.289.1		12
7.2	even	3		637.2.f.k.393.1		12
7.3	odd	6		637.2.g.l.263.1		12
7.4	even	3		91.2.g.b.81.1	yes	12
7.5	odd	6		637.2.f.j.393.1		12
7.6	odd	2		637.2.h.l.471.6		12
13.3	even	3		1183.2.e.h.170.1		12
13.9	even	3		91.2.g.b.9.1	✓	12
13.10	even	6		1183.2.e.g.170.6		12
21.11	odd	6		819.2.n.d.172.6		12
39.35	odd	6		819.2.n.d.100.6		12
91.9	even	3		637.2.f.k.295.1		12
91.16	even	3		8281.2.a.bz.1.6		6
91.23	even	6		8281.2.a.ce.1.1		6
91.48	odd	6		637.2.g.l.373.1		12
91.61	odd	6		637.2.f.j.295.1		12
91.68	odd	6		8281.2.a.ca.1.6		6
91.74	even	3	inner	91.2.h.b.74.6	yes	12
91.75	odd	6		8281.2.a.cf.1.1		6
91.81	even	3		1183.2.e.h.508.1		12
91.87	odd	6		637.2.h.l.165.6		12
91.88	even	6		1183.2.e.g.508.6		12
273.74	odd	6		819.2.s.d.802.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.1	✓	12	13.9	even	3
91.2.g.b.81.1	yes	12	7.4	even	3
91.2.h.b.16.6	yes	12	1.1	even	1	trivial
91.2.h.b.74.6	yes	12	91.74	even	3	inner
637.2.f.j.295.1		12	91.61	odd	6
637.2.f.j.393.1		12	7.5	odd	6
637.2.f.k.295.1		12	91.9	even	3
637.2.f.k.393.1		12	7.2	even	3
637.2.g.l.263.1		12	7.3	odd	6
637.2.g.l.373.1		12	91.48	odd	6
637.2.h.l.165.6		12	91.87	odd	6
637.2.h.l.471.6		12	7.6	odd	2
819.2.n.d.100.6		12	39.35	odd	6
819.2.n.d.172.6		12	21.11	odd	6
819.2.s.d.289.1		12	3.2	odd	2
819.2.s.d.802.1		12	273.74	odd	6
1183.2.e.g.170.6		12	13.10	even	6
1183.2.e.g.508.6		12	91.88	even	6
1183.2.e.h.170.1		12	13.3	even	3
1183.2.e.h.508.1		12	91.81	even	3
8281.2.a.bz.1.6		6	91.16	even	3
8281.2.a.ca.1.6		6	91.68	odd	6
8281.2.a.ce.1.1		6	91.23	even	6
8281.2.a.cf.1.1		6	91.75	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.85816 q^{2} +(-1.14703 + 1.98672i) q^{3} +1.45276 q^{4} +(0.0986811 - 0.170921i) q^{5} +(-2.13137 + 3.69165i) q^{6} +(1.03826 - 2.43352i) q^{7} -1.01686 q^{8} +(-1.13137 - 1.95960i) q^{9} +(0.183365 - 0.317598i) q^{10} +(2.09137 - 3.62236i) q^{11} +(-1.66637 + 2.88623i) q^{12} +(-2.72221 + 2.36423i) q^{13} +(1.92926 - 4.52187i) q^{14} +(0.226381 + 0.392104i) q^{15} -4.79501 q^{16} +0.841305 q^{17} +(-2.10227 - 3.64125i) q^{18} +(-0.675876 - 1.17065i) q^{19} +(0.143360 - 0.248307i) q^{20} +(3.64380 + 4.85406i) q^{21} +(3.88610 - 6.73092i) q^{22} -4.11519 q^{23} +(1.16637 - 2.02021i) q^{24} +(2.48052 + 4.29639i) q^{25} +(-5.05830 + 4.39312i) q^{26} -1.69131 q^{27} +(1.50835 - 3.53532i) q^{28} +(4.11931 + 7.13485i) q^{29} +(0.420653 + 0.728592i) q^{30} +(0.640350 + 1.10912i) q^{31} -6.87618 q^{32} +(4.79774 + 8.30993i) q^{33} +1.56328 q^{34} +(-0.313482 - 0.417603i) q^{35} +(-1.64362 - 2.84683i) q^{36} +3.04485 q^{37} +(-1.25589 - 2.17526i) q^{38} +(-1.57459 - 8.12012i) q^{39} +(-0.100344 + 0.173802i) q^{40} +(-2.69848 - 4.67390i) q^{41} +(6.77077 + 9.01963i) q^{42} +(-2.66389 + 4.61399i) q^{43} +(3.03826 - 5.26242i) q^{44} -0.446581 q^{45} -7.64669 q^{46} +(5.83204 - 10.1014i) q^{47} +(5.50003 - 9.52634i) q^{48} +(-4.84403 - 5.05326i) q^{49} +(4.60921 + 7.98339i) q^{50} +(-0.965006 + 1.67144i) q^{51} +(-3.95472 + 3.43466i) q^{52} +(-2.32398 - 4.02525i) q^{53} -3.14272 q^{54} +(-0.412757 - 0.714916i) q^{55} +(-1.05576 + 2.47454i) q^{56} +3.10101 q^{57} +(7.65434 + 13.2577i) q^{58} +6.05811 q^{59} +(0.328878 + 0.569634i) q^{60} +(5.68285 + 9.84298i) q^{61} +(1.18987 + 2.06092i) q^{62} +(-5.94338 + 0.718645i) q^{63} -3.18704 q^{64} +(0.135465 + 0.698587i) q^{65} +(8.91498 + 15.4412i) q^{66} +(-6.69851 + 11.6022i) q^{67} +1.22222 q^{68} +(4.72026 - 8.17574i) q^{69} +(-0.582500 - 0.775973i) q^{70} +(2.98520 - 5.17051i) q^{71} +(1.15044 + 1.99263i) q^{72} +(-1.94273 - 3.36491i) q^{73} +5.65782 q^{74} -11.3810 q^{75} +(-0.981887 - 1.70068i) q^{76} +(-6.64368 - 8.85034i) q^{77} +(-2.92585 - 15.0885i) q^{78} +(5.36669 - 9.29537i) q^{79} +(-0.473177 + 0.819566i) q^{80} +(5.33411 - 9.23895i) q^{81} +(-5.01421 - 8.68486i) q^{82} +3.07390 q^{83} +(5.29358 + 7.05180i) q^{84} +(0.0830210 - 0.143797i) q^{85} +(-4.94994 + 8.57354i) q^{86} -18.8999 q^{87} +(-2.12662 + 3.68341i) q^{88} -11.9841 q^{89} -0.829819 q^{90} +(2.92702 + 9.07924i) q^{91} -5.97840 q^{92} -2.93801 q^{93} +(10.8369 - 18.7700i) q^{94} -0.266785 q^{95} +(7.88721 - 13.6611i) q^{96} +(-9.73637 + 16.8639i) q^{97} +(-9.00098 - 9.38977i) q^{98} -9.46448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + q^{3} + 8 q^{4} + q^{5} - 9 q^{6} - 3 q^{7} - 6 q^{8} + 3 q^{9} + 4 q^{10} + 4 q^{11} + 5 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 16 q^{16} - 10 q^{17} + 3 q^{18} - q^{19} - q^{20}+ \cdots - 20 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 + q^3 + 8 * q^4 + q^5 - 9 * q^6 - 3 * q^7 - 6 * q^8 + 3 * q^9 + 4 * q^10 + 4 * q^11 + 5 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 16 * q^16 - 10 * q^17 + 3 * q^18 - q^19 - q^20 - 9 * q^21 - 5 * q^22 + 2 * q^23 - 11 * q^24 + 7 * q^25 - 16 * q^26 - 8 * q^27 - q^28 + 3 * q^29 - 5 * q^30 + 16 * q^31 - 16 * q^32 + 16 * q^33 + 32 * q^34 + 20 * q^35 - 21 * q^36 + 26 * q^37 - 17 * q^38 - 20 * q^39 - 5 * q^40 - 8 * q^41 + 50 * q^42 - 11 * q^43 + 21 * q^44 + 14 * q^45 - 32 * q^46 - q^47 + 21 * q^48 - 3 * q^49 + 6 * q^50 - 20 * q^51 + 41 * q^52 - 2 * q^53 + 36 * q^54 + 9 * q^55 + 9 * q^56 + 42 * q^57 - 8 * q^58 - 26 * q^59 + 20 * q^60 - 5 * q^61 + 5 * q^62 - 40 * q^63 - 30 * q^64 - 5 * q^65 + 18 * q^66 - 11 * q^67 - 58 * q^68 + 23 * q^69 - 39 * q^70 + 6 * q^71 + 25 * q^72 - 30 * q^73 + 6 * q^74 + 6 * q^75 - 9 * q^76 + 11 * q^77 + 16 * q^78 + 7 * q^79 - 7 * q^80 - 6 * q^81 + q^82 - 54 * q^83 - 46 * q^84 - q^85 - 7 * q^86 - 32 * q^87 - 8 * q^89 - 16 * q^90 - 23 * q^91 + 54 * q^92 + 14 * q^93 + 45 * q^94 + 12 * q^95 + 19 * q^96 - 35 * q^97 + 20 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more