LMFDB - Embedded newform 882.2.h.p.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(67,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("882.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.h (of order $3$, degree $2$, not 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	882.67
Dual form			882.2.h.p.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.29418 - 1.15113i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.58836 q^{5} +(-1.64400 + 0.545231i) q^{6} -1.00000 q^{8} +(0.349814 + 2.97954i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.29418 - 1.15113i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.58836 q^{5} +(-1.64400 + 0.545231i) q^{6} -1.00000 q^{8} +(0.349814 + 2.97954i) q^{9} +(-0.794182 + 1.37556i) q^{10} -1.58836 q^{11} +(-0.349814 + 1.69636i) q^{12} +(-2.40545 + 4.16635i) q^{13} +(2.05563 + 1.82841i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.69963 - 4.67589i) q^{17} +(2.75526 + 1.18682i) q^{18} +(3.54944 + 6.14781i) q^{19} +(0.794182 + 1.37556i) q^{20} +(-0.794182 + 1.37556i) q^{22} +0.300372 q^{23} +(1.29418 + 1.15113i) q^{24} -2.47710 q^{25} +(2.40545 + 4.16635i) q^{26} +(2.97710 - 4.25874i) q^{27} +(4.13781 + 7.16689i) q^{29} +(2.61126 - 0.866025i) q^{30} +(-1.35600 - 2.34867i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.05563 + 1.82841i) q^{33} +(-2.69963 - 4.67589i) q^{34} +(2.40545 - 1.79272i) q^{36} +(0.500000 + 0.866025i) q^{37} +7.09888 q^{38} +(7.90909 - 2.62305i) q^{39} +1.58836 q^{40} +(-2.93818 + 5.08907i) q^{41} +(-0.833104 - 1.44298i) q^{43} +(0.794182 + 1.37556i) q^{44} +(-0.555632 - 4.73259i) q^{45} +(0.150186 - 0.260130i) q^{46} +(1.33310 - 2.30900i) q^{47} +(1.64400 - 0.545231i) q^{48} +(-1.23855 + 2.14523i) q^{50} +(-8.87636 + 2.94384i) q^{51} +4.81089 q^{52} +(2.44437 - 4.23377i) q^{53} +(-2.19963 - 4.70761i) q^{54} +2.52290 q^{55} +(2.48329 - 12.0422i) q^{57} +8.27561 q^{58} +(3.23855 + 5.60933i) q^{59} +(0.555632 - 2.69443i) q^{60} +(-2.23855 + 3.87728i) q^{61} -2.71201 q^{62} +1.00000 q^{64} +(3.82072 - 6.61769i) q^{65} +(2.61126 - 0.866025i) q^{66} +(5.02654 + 8.70623i) q^{67} -5.39926 q^{68} +(-0.388736 - 0.345766i) q^{69} +12.7207 q^{71} +(-0.349814 - 2.97954i) q^{72} +(-8.02654 + 13.9024i) q^{73} +1.00000 q^{74} +(3.20582 + 2.85146i) q^{75} +(3.54944 - 6.14781i) q^{76} +(1.68292 - 8.16100i) q^{78} +(-4.19344 + 7.26325i) q^{79} +(0.794182 - 1.37556i) q^{80} +(-8.75526 + 2.08457i) q^{81} +(2.93818 + 5.08907i) q^{82} +(-1.18292 - 2.04887i) q^{83} +(-4.28799 + 7.42702i) q^{85} -1.66621 q^{86} +(2.89493 - 14.0384i) q^{87} +1.58836 q^{88} +(-1.60507 - 2.78007i) q^{89} +(-4.37636 - 1.88510i) q^{90} +(-0.150186 - 0.260130i) q^{92} +(-0.948699 + 4.60054i) q^{93} +(-1.33310 - 2.30900i) q^{94} +(-5.63781 - 9.76497i) q^{95} +(0.349814 - 1.69636i) q^{96} +(-0.712008 - 1.23323i) q^{97} +(-0.555632 - 4.73259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9	$ 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} + q^{10} + 2 q^{11} + 4 q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} + 4 q^{17} + 4 q^{18} + 3 q^{19} - q^{20} + q^{22} + 14 q^{23} + 2 q^{24} - 4 q^{25} + 8 q^{26} + 7 q^{27} - 5 q^{29} + 15 q^{30} - 20 q^{31} + 3 q^{32} + 12 q^{33} - 4 q^{34} + 8 q^{36} + 3 q^{37} + 6 q^{38} + q^{39} - 2 q^{40} - 6 q^{43} - q^{44} - 3 q^{45} + 7 q^{46} + 9 q^{47} - 2 q^{48} - 2 q^{50} - 18 q^{51} + 16 q^{52} + 15 q^{53} - q^{54} + 26 q^{55} + 22 q^{57} - 10 q^{58} + 14 q^{59} + 3 q^{60} - 8 q^{61} - 40 q^{62} + 6 q^{64} - 12 q^{65} + 15 q^{66} + q^{67} - 8 q^{68} - 3 q^{69} + 14 q^{71} + 4 q^{72} - 19 q^{73} + 6 q^{74} + 25 q^{75} + 3 q^{76} + 5 q^{78} + 5 q^{79} - q^{80} - 40 q^{81} - 2 q^{83} - 2 q^{85} - 12 q^{86} + 36 q^{87} - 2 q^{88} + 9 q^{89} + 9 q^{90} - 7 q^{92} + 37 q^{93} - 9 q^{94} - 4 q^{95} - 4 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 + q^10 + 2 * q^11 + 4 * q^12 - 8 * q^13 + 12 * q^15 - 3 * q^16 + 4 * q^17 + 4 * q^18 + 3 * q^19 - q^20 + q^22 + 14 * q^23 + 2 * q^24 - 4 * q^25 + 8 * q^26 + 7 * q^27 - 5 * q^29 + 15 * q^30 - 20 * q^31 + 3 * q^32 + 12 * q^33 - 4 * q^34 + 8 * q^36 + 3 * q^37 + 6 * q^38 + q^39 - 2 * q^40 - 6 * q^43 - q^44 - 3 * q^45 + 7 * q^46 + 9 * q^47 - 2 * q^48 - 2 * q^50 - 18 * q^51 + 16 * q^52 + 15 * q^53 - q^54 + 26 * q^55 + 22 * q^57 - 10 * q^58 + 14 * q^59 + 3 * q^60 - 8 * q^61 - 40 * q^62 + 6 * q^64 - 12 * q^65 + 15 * q^66 + q^67 - 8 * q^68 - 3 * q^69 + 14 * q^71 + 4 * q^72 - 19 * q^73 + 6 * q^74 + 25 * q^75 + 3 * q^76 + 5 * q^78 + 5 * q^79 - q^80 - 40 * q^81 - 2 * q^83 - 2 * q^85 - 12 * q^86 + 36 * q^87 - 2 * q^88 + 9 * q^89 + 9 * q^90 - 7 * q^92 + 37 * q^93 - 9 * q^94 - 4 * q^95 - 4 * q^96 - 28 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.29418	−	1.15113i	−0.747196	−	0.664603i
$3$	−1.29418	−	1.15113i	−0.747196	−	0.664603i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.58836			−0.710338			−0.355169	−	0.934802i	$-0.615577\pi$
$5$	−1.58836			−0.710338			−0.355169	+	0.934802i	$0.615577\pi$
$6$	−1.64400	+	0.545231i	−0.671159	+	0.222590i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	0.349814	+	2.97954i	0.116605	+	0.993178i
$10$	−0.794182	+	1.37556i	−0.251142	+	0.434991i
$11$	−1.58836			−0.478910			−0.239455	−	0.970907i	$-0.576969\pi$
$11$	−1.58836			−0.478910			−0.239455	+	0.970907i	$0.576969\pi$
$12$	−0.349814	+	1.69636i	−0.100983	+	0.489696i
$13$	−2.40545	+	4.16635i	−0.667151	+	1.15554i	0.311547	+	0.950231i	$0.399153\pi$
$13$	−2.40545	+	4.16635i	−0.667151	+	1.15554i	−0.978697	+	0.205308i	$0.934180\pi$
$14$		0			0
$15$	2.05563	+	1.82841i	0.530762	+	0.472093i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.69963	−	4.67589i	0.654756	−	1.13407i	−0.327199	−	0.944955i	$-0.606105\pi$
$17$	2.69963	−	4.67589i	0.654756	−	1.13407i	0.981955	−	0.189115i	$-0.0605620\pi$
$18$	2.75526	+	1.18682i	0.649421	+	0.279736i
$19$	3.54944	+	6.14781i	0.814298	+	1.41041i	0.909831	+	0.414979i	$0.136211\pi$
$19$	3.54944	+	6.14781i	0.814298	+	1.41041i	−0.0955331	+	0.995426i	$0.530456\pi$
$20$	0.794182	+	1.37556i	0.177584	+	0.307585i
$21$		0			0
$22$	−0.794182	+	1.37556i	−0.169320	+	0.293271i
$23$	0.300372			0.0626319			0.0313159	−	0.999510i	$-0.490030\pi$
$23$	0.300372			0.0626319			0.0313159	+	0.999510i	$0.490030\pi$
$24$	1.29418	+	1.15113i	0.264174	+	0.234973i
$25$	−2.47710			−0.495420
$26$	2.40545	+	4.16635i	0.471747	+	0.817089i
$27$	2.97710	−	4.25874i	0.572943	−	0.819595i
$28$		0			0
$29$	4.13781	+	7.16689i	0.768371	+	1.33086i	0.938446	+	0.345427i	$0.112266\pi$
$29$	4.13781	+	7.16689i	0.768371	+	1.33086i	−0.170074	+	0.985431i	$0.554401\pi$
$30$	2.61126	−	0.866025i	0.476749	−	0.158114i
$31$	−1.35600	−	2.34867i	−0.243545	−	0.421833i	0.718176	−	0.695861i	$-0.244977\pi$
$31$	−1.35600	−	2.34867i	−0.243545	−	0.421833i	−0.961722	+	0.274028i	$0.911644\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.05563	+	1.82841i	0.357840	+	0.318285i
$34$	−2.69963	−	4.67589i	−0.462982	−	0.801909i
$35$		0			0
$36$	2.40545	−	1.79272i	0.400908	−	0.298786i
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	7.09888			1.15159
$39$	7.90909	−	2.62305i	1.26647	−	0.420024i
$40$	1.58836			0.251142
$41$	−2.93818	+	5.08907i	−0.458866	+	0.794780i	−0.998901	−	0.0468628i	$-0.985078\pi$
$41$	−2.93818	+	5.08907i	−0.458866	+	0.794780i	0.540035	+	0.841643i	$0.318411\pi$
$42$		0			0
$43$	−0.833104	−	1.44298i	−0.127047	−	0.220052i	0.795484	−	0.605974i	$-0.207217\pi$
$43$	−0.833104	−	1.44298i	−0.127047	−	0.220052i	−0.922531	+	0.385922i	$0.873883\pi$
$44$	0.794182	+	1.37556i	0.119727	+	0.207374i
$45$	−0.555632	−	4.73259i	−0.0828287	−	0.705492i
$46$	0.150186	−	0.260130i	0.0221437	−	0.0383540i
$47$	1.33310	−	2.30900i	0.194453	−	0.336803i	−0.752268	−	0.658857i	$-0.771040\pi$
$47$	1.33310	−	2.30900i	0.194453	−	0.336803i	0.946721	+	0.322055i	$0.104373\pi$
$48$	1.64400	−	0.545231i	0.237290	−	0.0786973i
$49$		0			0
$50$	−1.23855	+	2.14523i	−0.175157	+	0.303382i
$51$	−8.87636	+	2.94384i	−1.24294	+	0.412220i
$52$	4.81089			0.667151
$53$	2.44437	−	4.23377i	0.335760	−	0.581553i	−0.647871	−	0.761750i	$-0.724340\pi$
$53$	2.44437	−	4.23377i	0.335760	−	0.581553i	0.983630	+	0.180197i	$0.0576736\pi$
$54$	−2.19963	−	4.70761i	−0.299331	−	0.640625i
$55$	2.52290			0.340188
$56$		0			0
$57$	2.48329	−	12.0422i	0.328920	−	1.59503i
$58$	8.27561			1.08664
$59$	3.23855	+	5.60933i	0.421623	+	0.730273i	0.996098	−	0.0882491i	$-0.0281271\pi$
$59$	3.23855	+	5.60933i	0.421623	+	0.730273i	−0.574475	+	0.818522i	$0.694794\pi$
$60$	0.555632	−	2.69443i	0.0717318	−	0.347850i
$61$	−2.23855	+	3.87728i	−0.286617	+	0.496435i	−0.973000	−	0.230805i	$-0.925864\pi$
$61$	−2.23855	+	3.87728i	−0.286617	+	0.496435i	0.686383	+	0.727240i	$0.259197\pi$
$62$	−2.71201			−0.344425
$63$		0			0
$64$	1.00000			0.125000
$65$	3.82072	−	6.61769i	0.473902	−	0.820823i
$66$	2.61126	−	0.866025i	0.321424	−	0.106600i
$67$	5.02654	+	8.70623i	0.614090	+	1.06363i	0.990543	+	0.137199i	$0.0438101\pi$
$67$	5.02654	+	8.70623i	0.614090	+	1.06363i	−0.376454	+	0.926435i	$0.622857\pi$
$68$	−5.39926			−0.654756
$69$	−0.388736	−	0.345766i	−0.0467983	−	0.0416253i
$70$		0			0
$71$	12.7207			1.50967			0.754833	−	0.655917i	$-0.227718\pi$
$71$	12.7207			1.50967			0.754833	+	0.655917i	$0.227718\pi$
$72$	−0.349814	−	2.97954i	−0.0412260	−	0.351142i
$73$	−8.02654	+	13.9024i	−0.939436	+	1.62715i	−0.172909	+	0.984938i	$0.555317\pi$
$73$	−8.02654	+	13.9024i	−0.939436	+	1.62715i	−0.766527	+	0.642213i	$0.778017\pi$
$74$	1.00000			0.116248
$75$	3.20582	+	2.85146i	0.370176	+	0.329258i
$76$	3.54944	−	6.14781i	0.407149	−	0.705203i
$77$		0			0
$78$	1.68292	−	8.16100i	0.190553	−	0.924051i
$79$	−4.19344	+	7.26325i	−0.471799	+	0.817179i	−0.999479	−	0.0322635i	$-0.989728\pi$
$79$	−4.19344	+	7.26325i	−0.471799	+	0.817179i	0.527681	+	0.849443i	$0.323062\pi$
$80$	0.794182	−	1.37556i	0.0887922	−	0.153793i
$81$	−8.75526	+	2.08457i	−0.972807	+	0.231619i
$82$	2.93818	+	5.08907i	0.324467	+	0.561994i
$83$	−1.18292	−	2.04887i	−0.129842	−	0.224893i	0.793773	−	0.608214i	$-0.208114\pi$
$83$	−1.18292	−	2.04887i	−0.129842	−	0.224893i	−0.923615	+	0.383321i	$0.874780\pi$
$84$		0			0
$85$	−4.28799	+	7.42702i	−0.465098	+	0.805573i
$86$	−1.66621			−0.179672
$87$	2.89493	−	14.0384i	0.310369	−	1.50507i
$88$	1.58836			0.169320
$89$	−1.60507	−	2.78007i	−0.170138	−	0.294687i	0.768330	−	0.640054i	$-0.221088\pi$
$89$	−1.60507	−	2.78007i	−0.170138	−	0.294687i	−0.938468	+	0.345367i	$0.887755\pi$
$90$	−4.37636	−	1.88510i	−0.461308	−	0.198707i
$91$		0			0
$92$	−0.150186	−	0.260130i	−0.0156580	−	0.0271204i
$93$	−0.948699	+	4.60054i	−0.0983755	+	0.477053i
$94$	−1.33310	−	2.30900i	−0.137499	−	0.238156i
$95$	−5.63781	−	9.76497i	−0.578427	−	1.00186i
$96$	0.349814	−	1.69636i	0.0357027	−	0.173134i
$97$	−0.712008	−	1.23323i	−0.0722934	−	0.125216i	0.827613	−	0.561300i	$-0.189698\pi$
$97$	−0.712008	−	1.23323i	−0.0722934	−	0.125216i	−0.899906	+	0.436084i	$0.856365\pi$
$98$		0			0
$99$	−0.555632	−	4.73259i	−0.0558431	−	0.475643i
$100$	1.23855	+	2.14523i	0.123855	+	0.214523i
$101$	−12.0334			−1.19737			−0.598685	−	0.800985i	$-0.704310\pi$
$101$	−12.0334			−1.19737			−0.598685	+	0.800985i	$0.704310\pi$
$102$	−1.88874	+	9.15907i	−0.187013	+	0.906883i
$103$	6.09888			0.600941			0.300470	−	0.953791i	$-0.402856\pi$
$103$	6.09888			0.600941			0.300470	+	0.953791i	$0.402856\pi$
$104$	2.40545	−	4.16635i	0.235873	−	0.408545i
$105$		0			0
$106$	−2.44437	−	4.23377i	−0.237418	−	0.411220i
$107$	−1.54325	−	2.67299i	−0.149192	−	0.258408i	0.781737	−	0.623608i	$-0.214334\pi$
$107$	−1.54325	−	2.67299i	−0.149192	−	0.258408i	−0.930929	+	0.365200i	$0.881001\pi$
$108$	−5.17673	−	0.448873i	−0.498131	−	0.0431929i
$109$	1.14400	−	1.98146i	0.109575	−	0.189789i	−0.806023	−	0.591884i	$-0.798384\pi$
$109$	1.14400	−	1.98146i	0.109575	−	0.189789i	0.915598	+	0.402095i	$0.131718\pi$
$110$	1.26145	−	2.18490i	0.120275	−	0.208322i
$111$	0.349814	−	1.69636i	0.0332029	−	0.161011i
$112$		0			0
$113$	−9.73236	+	16.8569i	−0.915543	+	1.58577i	−0.109440	+	0.993993i	$0.534906\pi$
$113$	−9.73236	+	16.8569i	−0.915543	+	1.58577i	−0.806104	+	0.591774i	$0.798428\pi$
$114$	−9.18725	−	8.17172i	−0.860465	−	0.765351i
$115$	−0.477100			−0.0444898
$116$	4.13781	−	7.16689i	0.384186	−	0.665429i
$117$	−13.2553	−	5.70966i	−1.22545	−	0.527858i
$118$	6.47710			0.596265
$119$		0			0
$120$	−2.05563	−	1.82841i	−0.187653	−	0.166910i
$121$	−8.47710			−0.770645
$122$	2.23855	+	3.87728i	0.202669	+	0.351033i
$123$	9.66071	−	3.20397i	0.871077	−	0.288892i
$124$	−1.35600	+	2.34867i	−0.121773	+	0.210917i
$125$	11.8764			1.06225
$126$		0			0
$127$	−13.4400			−1.19260			−0.596302	−	0.802760i	$-0.703364\pi$
$127$	−13.4400			−1.19260			−0.596302	+	0.802760i	$0.703364\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−0.582863	+	2.82648i	−0.0513182	+	0.248858i
$130$	−3.82072	−	6.61769i	−0.335100	−	0.580410i
$131$	3.17673			0.277552			0.138776	−	0.990324i	$-0.455683\pi$
$131$	3.17673			0.277552			0.138776	+	0.990324i	$0.455683\pi$
$132$	0.555632	−	2.69443i	0.0483616	−	0.234520i
$133$		0			0
$134$	10.0531			0.868454
$135$	−4.72872	+	6.76443i	−0.406983	+	0.582190i
$136$	−2.69963	+	4.67589i	−0.231491	+	0.400955i
$137$	−21.2632			−1.81664			−0.908320	−	0.418275i	$-0.862635\pi$
$137$	−21.2632			−1.81664			−0.908320	+	0.418275i	$0.862635\pi$
$138$	−0.493810	+	0.163772i	−0.0420359	+	0.0139412i
$139$	−6.52654	+	11.3043i	−0.553574	+	0.958818i	0.444439	+	0.895809i	$0.353403\pi$
$139$	−6.52654	+	11.3043i	−0.553574	+	0.958818i	−0.998013	+	0.0630092i	$0.979930\pi$
$140$		0			0
$141$	−4.38323	+	1.45370i	−0.369135	+	0.122424i
$142$	6.36033	−	11.0164i	0.533747	−	0.924478i
$143$	3.82072	−	6.61769i	0.319505	−	0.553399i
$144$	−2.75526	−	1.18682i	−0.229605	−	0.0989016i
$145$	−6.57234	−	11.3836i	−0.545803	−	0.945359i
$146$	8.02654	+	13.9024i	0.664281	+	1.15057i
$147$		0			0
$148$	0.500000	−	0.866025i	0.0410997	−	0.0711868i
$149$	5.20877			0.426719			0.213360	−	0.976974i	$-0.431559\pi$
$149$	5.20877			0.426719			0.213360	+	0.976974i	$0.431559\pi$
$150$	4.07234	−	1.35059i	0.332505	−	0.110275i
$151$	−0.522900			−0.0425530			−0.0212765	−	0.999774i	$-0.506773\pi$
$151$	−0.522900			−0.0425530			−0.0212765	+	0.999774i	$0.506773\pi$
$152$	−3.54944	−	6.14781i	−0.287898	−	0.498654i
$153$	14.8764	+	6.40794i	1.20268	+	0.518052i
$154$		0			0
$155$	2.15383	+	3.73054i	0.173000	+	0.299644i
$156$	−6.22617	−	5.53795i	−0.498493	−	0.443391i
$157$	4.43199	+	7.67643i	0.353711	+	0.612646i	0.986897	−	0.161354i	$-0.0515862\pi$
$157$	4.43199	+	7.67643i	0.353711	+	0.612646i	−0.633185	+	0.774000i	$0.718253\pi$
$158$	4.19344	+	7.26325i	0.333612	+	0.577833i
$159$	−8.03706	+	2.66549i	−0.637381	+	0.211387i
$160$	−0.794182	−	1.37556i	−0.0627856	−	0.108748i
$161$		0			0
$162$	−2.57234	+	8.62456i	−0.202102	+	0.677610i
$163$	10.9814	+	19.0204i	0.860132	+	1.48979i	0.871801	+	0.489860i	$0.162952\pi$
$163$	10.9814	+	19.0204i	0.860132	+	1.48979i	−0.0116689	+	0.999932i	$0.503714\pi$
$164$	5.87636			0.458866
$165$	−3.26509	−	2.90418i	−0.254187	−	0.226090i
$166$	−2.36584			−0.183624
$167$	−1.65019	+	2.85821i	−0.127695	+	0.221175i	−0.922783	−	0.385319i	$-0.874091\pi$
$167$	−1.65019	+	2.85821i	−0.127695	+	0.221175i	0.795088	+	0.606494i	$0.207425\pi$
$168$		0			0
$169$	−5.07234	−	8.78555i	−0.390180	−	0.675812i
$170$	4.28799	+	7.42702i	0.328874	+	0.569626i
$171$	−17.0760	+	12.7263i	−1.30583	+	0.973203i
$172$	−0.833104	+	1.44298i	−0.0635236	+	0.110026i
$173$	9.55377	−	16.5476i	0.726360	−	1.25809i	−0.232052	−	0.972703i	$-0.574544\pi$
$173$	9.55377	−	16.5476i	0.726360	−	1.25809i	0.958412	−	0.285389i	$-0.0921227\pi$
$174$	−10.7101	−	9.52628i	−0.811934	−	0.722185i
$175$		0			0
$176$	0.794182	−	1.37556i	0.0598637	−	0.103687i
$177$	2.26578	−	10.9875i	0.170307	−	0.825870i
$178$	−3.21015			−0.240611
$179$	−8.03706	+	13.9206i	−0.600718	+	1.04047i	0.391994	+	0.919968i	$0.371785\pi$
$179$	−8.03706	+	13.9206i	−0.600718	+	1.04047i	−0.992712	+	0.120507i	$0.961548\pi$
$180$	−3.82072	+	2.84748i	−0.284780	+	0.212239i
$181$	−8.05308			−0.598581			−0.299291	−	0.954162i	$-0.596750\pi$
$181$	−8.05308			−0.598581			−0.299291	+	0.954162i	$0.596750\pi$
$182$		0			0
$183$	7.36033	−	2.44105i	0.544092	−	0.180448i
$184$	−0.300372			−0.0221437
$185$	−0.794182	−	1.37556i	−0.0583894	−	0.101133i
$186$	3.50983	+	3.12186i	0.257353	+	0.228906i
$187$	−4.28799	+	7.42702i	−0.313569	+	0.543118i
$188$	−2.66621			−0.194453
$189$		0			0
$190$	−11.2756			−0.818019
$191$	11.9814	−	20.7524i	0.866946	−	1.50159i	0.00184390	−	0.999998i	$-0.499413\pi$
$191$	11.9814	−	20.7524i	0.866946	−	1.50159i	0.865102	−	0.501596i	$-0.167254\pi$
$192$	−1.29418	−	1.15113i	−0.0933995	−	0.0830754i
$193$	−4.88255	−	8.45682i	−0.351453	−	0.608735i	0.635051	−	0.772470i	$-0.280979\pi$
$193$	−4.88255	−	8.45682i	−0.351453	−	0.608735i	−0.986504	+	0.163735i	$0.947646\pi$
$194$	−1.42402			−0.102238
$195$	−12.5625	+	4.16635i	−0.899620	+	0.298359i
$196$		0			0
$197$	−18.2436			−1.29980			−0.649900	−	0.760020i	$-0.725189\pi$
$197$	−18.2436			−1.29980			−0.649900	+	0.760020i	$0.725189\pi$
$198$	−4.37636	−	1.88510i	−0.311014	−	0.133968i
$199$	−9.04944	+	15.6741i	−0.641498	+	1.11111i	0.343601	+	0.939116i	$0.388353\pi$
$199$	−9.04944	+	15.6741i	−0.641498	+	1.11111i	−0.985098	+	0.171991i	$0.944980\pi$
$200$	2.47710			0.175157
$201$	3.51671	−	17.0536i	0.248050	−	1.20287i
$202$	−6.01671	+	10.4212i	−0.423334	+	0.733236i
$203$		0			0
$204$	6.98762	+	6.21523i	0.489231	+	0.435153i
$205$	4.66690	−	8.08330i	0.325950	−	0.564562i
$206$	3.04944	−	5.28179i	0.212465	−	0.368000i
$207$	0.105074	+	0.894969i	0.00730317	+	0.0622046i
$208$	−2.40545	−	4.16635i	−0.166788	−	0.288885i
$209$	−5.63781	−	9.76497i	−0.389975	−	0.675457i
$210$		0			0
$211$	0.166208	−	0.287880i	0.0114422	−	0.0198185i	−0.860248	−	0.509877i	$-0.829691\pi$
$211$	0.166208	−	0.287880i	0.0114422	−	0.0198185i	0.871690	+	0.490058i	$0.163024\pi$
$212$	−4.88874			−0.335760
$213$	−16.4629	−	14.6431i	−1.12802	−	1.00333i
$214$	−3.08650			−0.210989
$215$	1.32327	+	2.29197i	0.0902464	+	0.156311i
$216$	−2.97710	+	4.25874i	−0.202566	+	0.289771i
$217$		0			0
$218$	−1.14400	−	1.98146i	−0.0774812	−	0.134201i
$219$	26.3912	−	8.75264i	1.78335	−	0.591449i
$220$	−1.26145	−	2.18490i	−0.0850469	−	0.147306i
$221$	12.9876	+	22.4952i	0.873642	+	1.51319i
$222$	−1.29418	−	1.15113i	−0.0868598	−	0.0772586i
$223$	−3.16621	−	5.48403i	−0.212025	−	0.367238i	0.740323	−	0.672251i	$-0.234672\pi$
$223$	−3.16621	−	5.48403i	−0.212025	−	0.367238i	−0.952348	+	0.305013i	$0.901339\pi$
$224$		0			0
$225$	−0.866524	−	7.38061i	−0.0577683	−	0.492040i
$226$	9.73236	+	16.8569i	0.647387	+	1.12131i
$227$	23.3090			1.54707			0.773537	−	0.633751i	$-0.218485\pi$
$227$	23.3090			1.54707			0.773537	+	0.633751i	$0.218485\pi$
$228$	−11.6705	+	3.87053i	−0.772900	+	0.256332i
$229$	4.95420			0.327383			0.163691	−	0.986512i	$-0.447660\pi$
$229$	4.95420			0.327383			0.163691	+	0.986512i	$0.447660\pi$
$230$	−0.238550	+	0.413181i	−0.0157295	+	0.0272443i
$231$		0			0
$232$	−4.13781	−	7.16689i	−0.271660	−	0.470529i
$233$	−7.13781	−	12.3630i	−0.467613	−	0.809930i	0.531702	−	0.846932i	$-0.321553\pi$
$233$	−7.13781	−	12.3630i	−0.467613	−	0.809930i	−0.999315	+	0.0370017i	$0.988219\pi$
$234$	−11.5723	+	8.62456i	−0.756508	+	0.563805i
$235$	−2.11745	+	3.66754i	−0.138127	+	0.239244i
$236$	3.23855	−	5.60933i	0.210812	−	0.365136i
$237$	13.7880	−	4.57279i	0.895626	−	0.297034i
$238$		0			0
$239$	2.48762	−	4.30868i	0.160911	−	0.278706i	−0.774285	−	0.632837i	$-0.781890\pi$
$239$	2.48762	−	4.30868i	0.160911	−	0.278706i	0.935196	+	0.354132i	$0.115224\pi$
$240$	−2.61126	+	0.866025i	−0.168556	+	0.0559017i
$241$	13.0000			0.837404			0.418702	−	0.908124i	$-0.362485\pi$
$241$	13.0000			0.837404			0.418702	+	0.908124i	$0.362485\pi$
$242$	−4.23855	+	7.34138i	−0.272464	+	0.471922i
$243$	13.7305	+	7.38061i	0.880812	+	0.473466i
$244$	4.47710			0.286617
$245$		0			0
$246$	2.05563	−	9.96840i	0.131062	−	0.635562i
$247$	−34.1520			−2.17304
$248$	1.35600	+	2.34867i	0.0861063	+	0.149141i
$249$	−0.827603	+	4.01330i	−0.0524472	+	0.254333i
$250$	5.93818	−	10.2852i	0.375563	−	0.650495i
$251$	−2.43268			−0.153549			−0.0767746	−	0.997048i	$-0.524462\pi$
$251$	−2.43268			−0.153549			−0.0767746	+	0.997048i	$0.524462\pi$
$252$		0			0
$253$	−0.477100			−0.0299950
$254$	−6.71998	+	11.6393i	−0.421649	+	0.730318i
$255$	14.0989	−	4.67589i	0.882906	−	0.292816i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.987620			0.0616061			0.0308030	−	0.999525i	$-0.490194\pi$
$257$	0.987620			0.0616061			0.0308030	+	0.999525i	$0.490194\pi$
$258$	2.15638	+	1.91802i	0.134250	+	0.119410i
$259$		0			0
$260$	−7.64145			−0.473902
$261$	−19.9065	+	14.8358i	−1.23218	+	0.918314i
$262$	1.58836	−	2.75113i	0.0981295	−	0.169965i
$263$	17.1854			1.05970			0.529848	−	0.848092i	$-0.322249\pi$
$263$	17.1854			1.05970			0.529848	+	0.848092i	$0.322249\pi$
$264$	−2.05563	−	1.82841i	−0.126515	−	0.112531i
$265$	−3.88255	+	6.72477i	−0.238503	+	0.413099i
$266$		0			0
$267$	−1.12296	+	5.44556i	−0.0687237	+	0.333263i
$268$	5.02654	−	8.70623i	0.307045	−	0.531817i
$269$	−11.4523	+	19.8360i	−0.698262	+	1.20942i	0.270807	+	0.962634i	$0.412709\pi$
$269$	−11.4523	+	19.8360i	−0.698262	+	1.20942i	−0.969069	+	0.246791i	$0.920624\pi$
$270$	3.49381	+	7.47741i	0.212627	+	0.455060i
$271$	−7.00364	−	12.1307i	−0.425441	−	0.736885i	0.571021	−	0.820936i	$-0.306548\pi$
$271$	−7.00364	−	12.1307i	−0.425441	−	0.736885i	−0.996462	+	0.0840504i	$0.973214\pi$
$272$	2.69963	+	4.67589i	0.163689	+	0.283518i
$273$		0			0
$274$	−10.6316	+	18.4145i	−0.642279	+	1.11246i
$275$	3.93454			0.237261
$276$	−0.105074	+	0.509538i	−0.00632473	+	0.0306706i
$277$	28.2953			1.70010			0.850049	−	0.526703i	$-0.176572\pi$
$277$	28.2953			1.70010			0.850049	+	0.526703i	$0.176572\pi$
$278$	6.52654	+	11.3043i	0.391436	+	0.677987i
$279$	6.52359	−	4.86186i	0.390557	−	0.291072i
$280$		0			0
$281$	−8.79782	−	15.2383i	−0.524834	−	0.909039i	−0.999582	−	0.0289175i	$-0.990794\pi$
$281$	−8.79782	−	15.2383i	−0.524834	−	0.909039i	0.474748	−	0.880122i	$-0.342539\pi$
$282$	−0.932677	+	4.52284i	−0.0555401	+	0.269331i
$283$	−9.26145	−	16.0413i	−0.550536	−	0.953556i	−0.998236	−	0.0593725i	$-0.981090\pi$
$283$	−9.26145	−	16.0413i	−0.550536	−	0.953556i	0.447700	−	0.894184i	$-0.352243\pi$
$284$	−6.36033	−	11.0164i	−0.377416	−	0.653704i
$285$	−3.94437	+	19.1275i	−0.233644	+	1.13301i
$286$	−3.82072	−	6.61769i	−0.225924	−	0.391312i
$287$		0			0
$288$	−2.40545	+	1.79272i	−0.141742	+	0.105637i
$289$	−6.07598	−	10.5239i	−0.357411	−	0.619054i
$290$	−13.1447			−0.771882
$291$	−0.498141	+	2.41564i	−0.0292015	+	0.141607i
$292$	16.0531			0.939436
$293$	7.04256	−	12.1981i	0.411431	−	0.712619i	−0.583616	−	0.812030i	$-0.698362\pi$
$293$	7.04256	−	12.1981i	0.411431	−	0.712619i	0.995046	+	0.0994108i	$0.0316958\pi$
$294$		0			0
$295$	−5.14400	−	8.90966i	−0.299495	−	0.518741i
$296$	−0.500000	−	0.866025i	−0.0290619	−	0.0503367i
$297$	−4.72872	+	6.76443i	−0.274388	+	0.392512i
$298$	2.60439	−	4.51093i	0.150868	−	0.261311i
$299$	−0.722528	+	1.25146i	−0.0417849	+	0.0723736i
$300$	0.866524	−	4.20205i	0.0500288	−	0.242605i
$301$		0			0
$302$	−0.261450	+	0.452845i	−0.0150448	+	0.0260583i
$303$	15.5734	+	13.8520i	0.894671	+	0.795776i
$304$	−7.09888			−0.407149
$305$	3.55563	−	6.15854i	0.203595	−	0.352637i
$306$	12.9876	−	9.67933i	0.742453	−	0.553330i
$307$	5.85532			0.334180			0.167090	−	0.985942i	$-0.446563\pi$
$307$	5.85532			0.334180			0.167090	+	0.985942i	$0.446563\pi$
$308$		0			0
$309$	−7.89307	−	7.02059i	−0.449021	−	0.399387i
$310$	4.30766			0.244658
$311$	0.405446	+	0.702253i	0.0229907	+	0.0398211i	0.877292	−	0.479957i	$-0.159348\pi$
$311$	0.405446	+	0.702253i	0.0229907	+	0.0398211i	−0.854301	+	0.519778i	$0.826015\pi$
$312$	−7.90909	+	2.62305i	−0.447764	+	0.148501i
$313$	5.28799	−	9.15907i	0.298895	−	0.517701i	−0.676988	−	0.735994i	$-0.736715\pi$
$313$	5.28799	−	9.15907i	0.298895	−	0.517701i	0.975883	+	0.218292i	$0.0700486\pi$
$314$	8.86398			0.500223
$315$		0			0
$316$	8.38688			0.471799
$317$	−6.09820	+	10.5624i	−0.342509	+	0.593243i	−0.984898	−	0.173136i	$-0.944610\pi$
$317$	−6.09820	+	10.5624i	−0.342509	+	0.593243i	0.642389	+	0.766379i	$0.277943\pi$
$318$	−1.71015	+	8.29305i	−0.0959004	+	0.465051i
$319$	−6.57234	−	11.3836i	−0.367981	−	0.637361i
$320$	−1.58836			−0.0887922
$321$	−1.07970	+	5.23582i	−0.0602631	+	0.292235i
$322$		0			0
$323$	38.3287			2.13267
$324$	6.18292	+	6.53999i	0.343495	+	0.363333i
$325$	5.95853	−	10.3205i	0.330520	−	0.572477i
$326$	21.9629			1.21641
$327$	−3.76145	+	1.24748i	−0.208009	+	0.0689860i
$328$	2.93818	−	5.08907i	0.162234	−	0.280997i
$329$		0			0
$330$	−4.14764	+	1.37556i	−0.228320	+	0.0757223i
$331$	7.83310	−	13.5673i	0.430546	−	0.745728i	−0.566374	−	0.824148i	$-0.691654\pi$
$331$	7.83310	−	13.5673i	0.430546	−	0.745728i	0.996920	+	0.0784202i	$0.0249876\pi$
$332$	−1.18292	+	2.04887i	−0.0649211	+	0.112447i
$333$	−2.40545	+	1.79272i	−0.131818	+	0.0982402i
$334$	1.65019	+	2.85821i	0.0902942	+	0.156394i
$335$	−7.98398	−	13.8287i	−0.436211	−	0.755540i
$336$		0			0
$337$	−4.21201	+	7.29541i	−0.229443	+	0.397406i	−0.957643	−	0.287958i	$-0.907024\pi$
$337$	−4.21201	+	7.29541i	−0.229443	+	0.397406i	0.728200	+	0.685364i	$0.240357\pi$
$338$	−10.1447			−0.551798
$339$	31.9999	−	10.6128i	1.73800	−	0.576407i
$340$	8.57598			0.465098
$341$	2.15383	+	3.73054i	0.116636	+	0.202020i
$342$	2.48329	+	21.1514i	0.134281	+	1.14374i
$343$		0			0
$344$	0.833104	+	1.44298i	0.0449179	+	0.0778002i
$345$	0.617454	+	0.549202i	0.0332426	+	0.0295681i
$346$	−9.55377	−	16.5476i	−0.513614	−	0.889606i
$347$	−0.283662	−	0.491316i	−0.0152277	−	0.0263752i	0.858311	−	0.513130i	$-0.171514\pi$
$347$	−0.283662	−	0.491316i	−0.0152277	−	0.0263752i	−0.873539	+	0.486754i	$0.838181\pi$
$348$	−13.6051	+	4.51212i	−0.729309	+	0.241875i
$349$	0.00364189	+	0.00630794i	0.000194946	+	0.000337656i	0.866123	−	0.499831i	$-0.166605\pi$
$349$	0.00364189	+	0.00630794i	0.000194946	+	0.000337656i	−0.865928	+	0.500169i	$0.833271\pi$
$350$		0			0
$351$	10.5822	+	22.6478i	0.564835	+	1.20885i
$352$	−0.794182	−	1.37556i	−0.0423300	−	0.0733178i
$353$	−6.65383			−0.354148			−0.177074	−	0.984198i	$-0.556663\pi$
$353$	−6.65383			−0.354148			−0.177074	+	0.984198i	$0.556663\pi$
$354$	−8.38255	−	7.45596i	−0.445527	−	0.396280i
$355$	−20.2051			−1.07237
$356$	−1.60507	+	2.78007i	−0.0850688	+	0.147343i
$357$		0			0
$358$	8.03706	+	13.9206i	0.424772	+	0.735727i
$359$	−0.398568	−	0.690339i	−0.0210356	−	0.0364347i	0.855316	−	0.518107i	$-0.173363\pi$
$359$	−0.398568	−	0.690339i	−0.0210356	−	0.0364347i	−0.876352	+	0.481672i	$0.840030\pi$
$360$	0.555632	+	4.73259i	0.0292844	+	0.249429i
$361$	−15.6971	+	27.1881i	−0.826162	+	1.43095i
$362$	−4.02654	+	6.97418i	−0.211630	+	0.366555i
$363$	10.9709	+	9.75822i	0.575823	+	0.512174i
$364$		0			0
$365$	12.7491	−	22.0820i	0.667317	−	1.15583i
$366$	1.56615	−	7.59476i	0.0818641	−	0.396985i
$367$	15.4327			0.805579			0.402790	−	0.915293i	$-0.368041\pi$
$367$	15.4327			0.805579			0.402790	+	0.915293i	$0.368041\pi$
$368$	−0.150186	+	0.260130i	−0.00782898	+	0.0135602i
$369$	−16.1909	−	6.97418i	−0.842864	−	0.363061i
$370$	−1.58836			−0.0825751
$371$		0			0
$372$	4.45853	−	1.47867i	0.231164	−	0.0766655i
$373$	10.2422			0.530321			0.265160	−	0.964204i	$-0.414575\pi$
$373$	10.2422			0.530321			0.265160	+	0.964204i	$0.414575\pi$
$374$	4.28799	+	7.42702i	0.221727	+	0.384042i
$375$	−15.3702	−	13.6712i	−0.793712	−	0.705977i
$376$	−1.33310	+	2.30900i	−0.0687496	+	0.119078i
$377$	−39.8131			−2.05048
$378$		0			0
$379$	25.0087			1.28461			0.642304	−	0.766450i	$-0.277979\pi$
$379$	25.0087			1.28461			0.642304	+	0.766450i	$0.277979\pi$
$380$	−5.63781	+	9.76497i	−0.289213	+	0.500932i
$381$	17.3938	+	15.4711i	0.891109	+	0.792608i
$382$	−11.9814	−	20.7524i	−0.613023	−	1.06179i
$383$	6.26695			0.320226			0.160113	−	0.987099i	$-0.448814\pi$
$383$	6.26695			0.320226			0.160113	+	0.987099i	$0.448814\pi$
$384$	−1.64400	+	0.545231i	−0.0838948	+	0.0278237i
$385$		0			0
$386$	−9.76509			−0.497030
$387$	4.00797	−	2.98704i	0.203737	−	0.151840i
$388$	−0.712008	+	1.23323i	−0.0361467	+	0.0626080i
$389$	−21.6342			−1.09690			−0.548448	−	0.836185i	$-0.684781\pi$
$389$	−21.6342			−1.09690			−0.548448	+	0.836185i	$0.684781\pi$
$390$	−2.67309	+	12.9626i	−0.135357	+	0.656388i
$391$	0.810892	−	1.40451i	0.0410086	−	0.0710290i
$392$		0			0
$393$	−4.11126	−	3.65682i	−0.207386	−	0.184462i
$394$	−9.12178	+	15.7994i	−0.459549	+	0.795962i
$395$	6.66071	−	11.5367i	0.335137	−	0.580473i
$396$	−3.82072	+	2.84748i	−0.191999	+	0.143091i
$397$	−2.05308	−	3.55605i	−0.103041	−	0.178473i	0.809895	−	0.586575i	$-0.199524\pi$
$397$	−2.05308	−	3.55605i	−0.103041	−	0.178473i	−0.912936	+	0.408102i	$0.866191\pi$
$398$	9.04944	+	15.6741i	0.453608	+	0.785671i
$399$		0			0
$400$	1.23855	−	2.14523i	0.0619275	−	0.107262i
$401$	16.7417			0.836041			0.418021	−	0.908438i	$-0.362724\pi$
$401$	16.7417			0.836041			0.418021	+	0.908438i	$0.362724\pi$
$402$	−13.0105	−	11.5724i	−0.648906	−	0.577178i
$403$	13.0472			0.649926
$404$	6.01671	+	10.4212i	0.299343	+	0.518476i
$405$	13.9065	−	3.31105i	0.691022	−	0.164527i
$406$		0			0
$407$	−0.794182	−	1.37556i	−0.0393661	−	0.0681842i
$408$	8.87636	−	2.94384i	0.439445	−	0.145742i
$409$	−4.38255	−	7.59079i	−0.216703	−	0.375341i	0.737095	−	0.675789i	$-0.236197\pi$
$409$	−4.38255	−	7.59079i	−0.216703	−	0.375341i	−0.953798	+	0.300449i	$0.902864\pi$
$410$	−4.66690	−	8.08330i	−0.230482	−	0.399206i
$411$	27.5185	+	24.4767i	1.35739	+	1.20735i
$412$	−3.04944	−	5.28179i	−0.150235	−	0.260215i
$413$		0			0
$414$	0.827603	+	0.356487i	0.0406744	+	0.0175204i
$415$	1.87890	+	3.25436i	0.0922318	+	0.159750i
$416$	−4.81089			−0.235873
$417$	21.4592	−	7.11695i	1.05086	−	0.348518i
$418$	−11.2756			−0.551508
$419$	0.210149	−	0.363988i	0.0102664	−	0.0177820i	−0.860847	−	0.508865i	$-0.830065\pi$
$419$	0.210149	−	0.363988i	0.0102664	−	0.0177820i	0.871113	+	0.491083i	$0.163399\pi$
$420$		0			0
$421$	3.28799	+	5.69497i	0.160247	+	0.277556i	0.934957	−	0.354761i	$-0.115438\pi$
$421$	3.28799	+	5.69497i	0.160247	+	0.277556i	−0.774710	+	0.632316i	$0.782104\pi$
$422$	−0.166208	−	0.287880i	−0.00809086	−	0.0140138i
$423$	7.34610	+	3.16431i	0.357179	+	0.153854i
$424$	−2.44437	+	4.23377i	−0.118709	+	0.205610i
$425$	−6.68725	+	11.5827i	−0.324379	+	0.561841i
$426$	−20.9127	+	6.93570i	−1.01323	+	0.336036i
$427$		0			0
$428$	−1.54325	+	2.67299i	−0.0745959	+	0.129204i
$429$	−12.5625	+	4.16635i	−0.606524	+	0.201154i
$430$	2.64654			0.127628
$431$	11.0439	−	19.1287i	0.531968	−	0.921395i	−0.467336	−	0.884080i	$-0.654786\pi$
$431$	11.0439	−	19.1287i	0.531968	−	0.921395i	0.999304	−	0.0373155i	$-0.0118806\pi$
$432$	2.19963	+	4.70761i	0.105830	+	0.226495i
$433$	9.43268			0.453306			0.226653	−	0.973976i	$-0.427222\pi$
$433$	9.43268			0.453306			0.226653	+	0.973976i	$0.427222\pi$
$434$		0			0
$435$	−4.59820	+	22.2981i	−0.220467	+	1.06911i
$436$	−2.28799			−0.109575
$437$	1.06615	+	1.84663i	0.0510010	+	0.0883363i
$438$	5.61559	−	27.2318i	0.268323	−	1.30118i
$439$	−15.6032	+	27.0256i	−0.744701	+	1.28986i	0.205634	+	0.978629i	$0.434074\pi$
$439$	−15.6032	+	27.0256i	−0.744701	+	1.28986i	−0.950334	+	0.311231i	$0.899259\pi$
$440$	−2.52290			−0.120275
$441$		0			0
$442$	25.9752			1.23552
$443$	−6.52723	+	11.3055i	−0.310118	+	0.537140i	−0.978388	−	0.206779i	$-0.933702\pi$
$443$	−6.52723	+	11.3055i	−0.310118	+	0.537140i	0.668270	+	0.743919i	$0.267035\pi$
$444$	−1.64400	+	0.545231i	−0.0780206	+	0.0258755i
$445$	2.54944	+	4.41576i	0.120855	+	0.209327i
$446$	−6.33242			−0.299849
$447$	−6.74110	−	5.99596i	−0.318843	−	0.283599i
$448$		0			0
$449$	−9.91706			−0.468015			−0.234008	−	0.972235i	$-0.575184\pi$
$449$	−9.91706			−0.468015			−0.234008	+	0.972235i	$0.575184\pi$
$450$	−6.82505	−	2.93987i	−0.321736	−	0.138587i
$451$	4.66690	−	8.08330i	0.219756	−	0.380628i
$452$	19.4647			0.915543
$453$	0.676728	+	0.601924i	0.0317955	+	0.0282809i
$454$	11.6545	−	20.1862i	0.546974	−	0.947386i
$455$		0			0
$456$	−2.48329	+	12.0422i	−0.116291	+	0.563930i
$457$	12.2615	−	21.2375i	0.573566	−	0.993446i	−0.422629	−	0.906303i	$-0.638893\pi$
$457$	12.2615	−	21.2375i	0.573566	−	0.993446i	0.996196	−	0.0871436i	$-0.0277739\pi$
$458$	2.47710	−	4.29046i	0.115747	−	0.200480i
$459$	−11.8764	−	25.4176i	−0.554341	−	1.18639i
$460$	0.238550	+	0.413181i	0.0111224	+	0.0192646i
$461$	−1.75526	−	3.04020i	−0.0817506	−	0.141596i	0.822251	−	0.569125i	$-0.192718\pi$
$461$	−1.75526	−	3.04020i	−0.0817506	−	0.141596i	−0.904002	+	0.427528i	$0.859384\pi$
$462$		0			0
$463$	8.69413	−	15.0587i	0.404050	−	0.699836i	−0.590160	−	0.807286i	$-0.700935\pi$
$463$	8.69413	−	15.0587i	0.404050	−	0.699836i	0.994210	+	0.107451i	$0.0342687\pi$
$464$	−8.27561			−0.384186
$465$	1.50688	−	7.30733i	0.0698798	−	0.338869i
$466$	−14.2756			−0.661305
$467$	−6.69894	−	11.6029i	−0.309990	−	0.536918i	0.668370	−	0.743829i	$-0.266992\pi$
$467$	−6.69894	−	11.6029i	−0.309990	−	0.536918i	−0.978360	+	0.206911i	$0.933659\pi$
$468$	1.68292	+	14.3342i	0.0777929	+	0.662600i
$469$		0			0
$470$	2.11745	+	3.66754i	0.0976709	+	0.169171i
$471$	3.10074	−	15.0365i	0.142875	−	0.692844i
$472$	−3.23855	−	5.60933i	−0.149066	−	0.258190i
$473$	1.32327	+	2.29197i	0.0608441	+	0.105385i
$474$	2.93385	−	14.2271i	0.134756	−	0.653474i
$475$	−8.79232	−	15.2287i	−0.403419	−	0.698743i
$476$		0			0
$477$	13.4697	+	5.80205i	0.616737	+	0.265658i
$478$	−2.48762	−	4.30868i	−0.113781	−	0.197075i
$479$	−20.8058			−0.950641			−0.475321	−	0.879813i	$-0.657668\pi$
$479$	−20.8058			−0.950641			−0.475321	+	0.879813i	$0.657668\pi$
$480$	−0.555632	+	2.69443i	−0.0253610	+	0.122984i
$481$	−4.81089			−0.219358
$482$	6.50000	−	11.2583i	0.296067	−	0.512803i
$483$		0			0
$484$	4.23855	+	7.34138i	0.192661	+	0.333699i
$485$	1.13093	+	1.95882i	0.0513528	+	0.0889456i
$486$	13.2570	−	8.20066i	0.601352	−	0.371989i
$487$	16.2472	−	28.1410i	0.736231	−	1.27519i	−0.217950	−	0.975960i	$-0.569937\pi$
$487$	16.2472	−	28.1410i	0.736231	−	1.27519i	0.954181	−	0.299230i	$-0.0967298\pi$
$488$	2.23855	−	3.87728i	0.101334	−	0.175516i
$489$	7.68292	−	37.2569i	0.347434	−	1.68481i
$490$		0			0
$491$	−9.66071	+	16.7328i	−0.435982	+	0.755142i	−0.997375	−	0.0724067i	$-0.976932\pi$
$491$	−9.66071	+	16.7328i	−0.435982	+	0.755142i	0.561394	+	0.827549i	$0.310265\pi$
$492$	−7.60507	−	6.76443i	−0.342863	−	0.304964i
$493$	44.6822			2.01238
$494$	−17.0760	+	29.5765i	−0.768285	+	1.33071i
$495$	0.882546	+	7.51707i	0.0396675	+	0.337867i
$496$	2.71201			0.121773
$497$		0			0
$498$	3.06182	+	2.72338i	0.137204	+	0.122037i
$499$	−11.1506			−0.499169			−0.249585	−	0.968353i	$-0.580294\pi$
$499$	−11.1506			−0.499169			−0.249585	+	0.968353i	$0.580294\pi$
$500$	−5.93818	−	10.2852i	−0.265563	−	0.459969i
$501$	5.42580	−	1.79947i	0.242407	−	0.0803942i
$502$	−1.21634	+	2.10676i	−0.0542878	+	0.0940293i
$503$	40.7651			1.81763			0.908813	−	0.417204i	$-0.136990\pi$
$503$	40.7651			1.81763			0.908813	+	0.417204i	$0.136990\pi$
$504$		0			0
$505$	19.1135			0.850537
$506$	−0.238550	+	0.413181i	−0.0106048	+	0.0183681i
$507$	−3.54875	+	17.2090i	−0.157606	+	0.764279i
$508$	6.71998	+	11.6393i	0.298151	+	0.516413i
$509$	−1.44506			−0.0640510			−0.0320255	−	0.999487i	$-0.510196\pi$
$509$	−1.44506			−0.0640510			−0.0320255	+	0.999487i	$0.510196\pi$
$510$	3.00000	−	14.5479i	0.132842	−	0.644194i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	36.7490	+	3.18650i	1.62251	+	0.140687i
$514$	0.493810	−	0.855304i	0.0217810	−	0.0377259i
$515$	−9.68725			−0.426871
$516$	2.73924	−	0.908468i	0.120588	−	0.0399931i
$517$	−2.11745	+	3.66754i	−0.0931255	+	0.161298i
$518$		0			0
$519$	−31.4127	+	10.4180i	−1.37887	+	0.457301i
$520$	−3.82072	+	6.61769i	−0.167550	+	0.290205i
$521$	−9.64214	+	16.7007i	−0.422430	+	0.731670i	−0.996177	−	0.0873630i	$-0.972156\pi$
$521$	−9.64214	+	16.7007i	−0.422430	+	0.731670i	0.573747	+	0.819033i	$0.305489\pi$
$522$	2.89493	+	24.6575i	0.126707	+	1.07923i
$523$	18.3454	+	31.7752i	0.802189	+	1.38943i	0.918173	+	0.396180i	$0.129665\pi$
$523$	18.3454	+	31.7752i	0.802189	+	1.38943i	−0.115984	+	0.993251i	$0.537002\pi$
$524$	−1.58836	−	2.75113i	−0.0693880	−	0.120184i
$525$		0			0
$526$	8.59269	−	14.8830i	0.374659	−	0.648929i
$527$	−14.6428			−0.637851
$528$	−2.61126	+	0.866025i	−0.113641	+	0.0376889i
$529$	−22.9098			−0.996077
$530$	3.88255	+	6.72477i	0.168647	+	0.292105i
$531$	−15.5803	+	11.6116i	−0.676128	+	0.503900i
$532$		0			0
$533$	−14.1353	−	24.4830i	−0.612266	−	1.06048i
$534$	4.15452	+	3.69529i	0.179784	+	0.159911i
$535$	2.45125	+	4.24568i	0.105977	+	0.183557i
$536$	−5.02654	−	8.70623i	−0.217114	−	0.376052i
$537$	26.4258	−	8.76411i	1.14036	−	0.378199i
$538$	11.4523	+	19.8360i	0.493745	+	0.855192i
$539$		0			0
$540$	8.22253	+	0.712974i	0.353841	+	0.0306815i
$541$	−1.62543	−	2.81532i	−0.0698825	−	0.121040i	0.828967	−	0.559298i	$-0.188929\pi$
$541$	−1.62543	−	2.81532i	−0.0698825	−	0.121040i	−0.898849	+	0.438258i	$0.855596\pi$
$542$	−14.0073			−0.601664
$543$	10.4222	+	9.27012i	0.447258	+	0.397819i
$544$	5.39926			0.231491
$545$	−1.81708	+	3.14728i	−0.0778352	+	0.134815i
$546$		0			0
$547$	−2.95853	−	5.12432i	−0.126498	−	0.219100i	0.795820	−	0.605534i	$-0.207040\pi$
$547$	−2.95853	−	5.12432i	−0.126498	−	0.219100i	−0.922317	+	0.386433i	$0.873707\pi$
$548$	10.6316	+	18.4145i	0.454160	+	0.786628i
$549$	−12.3356	−	5.31351i	−0.526470	−	0.226775i
$550$	1.96727	−	3.40741i	0.0838846	−	0.145292i
$551$	−29.3738	+	50.8769i	−1.25137	+	2.16743i
$552$	0.388736	+	0.345766i	0.0165457	+	0.0147168i
$553$		0			0
$554$	14.1476	−	24.5044i	0.601076	−	1.04109i
$555$	−0.555632	+	2.69443i	−0.0235853	+	0.114372i
$556$	13.0531			0.553574
$557$	12.8040	−	22.1772i	0.542523	−	0.939678i	−0.456235	−	0.889859i	$-0.650802\pi$
$557$	12.8040	−	22.1772i	0.542523	−	0.939678i	0.998758	−	0.0498188i	$-0.0158644\pi$
$558$	−0.948699	−	8.08052i	−0.0401616	−	0.342076i
$559$	8.01594			0.339038
$560$		0			0
$561$	14.0989	−	4.67589i	0.595255	−	0.197416i
$562$	−17.5956			−0.742228
$563$	−23.3189	−	40.3895i	−0.982773	−	1.70221i	−0.651443	−	0.758698i	$-0.725836\pi$
$563$	−23.3189	−	40.3895i	−0.982773	−	1.70221i	−0.331330	−	0.943515i	$-0.607497\pi$
$564$	3.45056	+	3.06914i	0.145295	+	0.129234i
$565$	15.4585	−	26.7750i	0.650345	−	1.12643i
$566$	−18.5229			−0.778576
$567$		0			0
$568$	−12.7207			−0.533747
$569$	−15.5989	+	27.0181i	−0.653939	+	1.13266i	0.328219	+	0.944602i	$0.393551\pi$
$569$	−15.5989	+	27.0181i	−0.653939	+	1.13266i	−0.982159	+	0.188054i	$0.939782\pi$
$570$	14.5927	+	12.9797i	0.611221	+	0.543658i
$571$	7.83812	+	13.5760i	0.328015	+	0.568139i	0.982118	−	0.188267i	$-0.0602869\pi$
$571$	7.83812	+	13.5760i	0.328015	+	0.568139i	−0.654103	+	0.756406i	$0.726954\pi$
$572$	−7.64145			−0.319505
$573$	−39.3948	+	13.0653i	−1.64574	+	0.545811i
$574$		0			0
$575$	−0.744051			−0.0310291
$576$	0.349814	+	2.97954i	0.0145756	+	0.124147i
$577$	−6.99567	+	12.1169i	−0.291234	+	0.504431i	−0.974102	−	0.226110i	$-0.927399\pi$
$577$	−6.99567	+	12.1169i	−0.291234	+	0.504431i	0.682868	+	0.730542i	$0.260732\pi$
$578$	−12.1520			−0.505455
$579$	−3.41597	+	16.5651i	−0.141963	+	0.688422i
$580$	−6.57234	+	11.3836i	−0.272902	+	0.472680i
$581$		0			0
$582$	1.84294	+	1.63922i	0.0763921	+	0.0679480i
$583$	−3.88255	+	6.72477i	−0.160799	+	0.278511i
$584$	8.02654	−	13.9024i	0.332141	−	0.575285i
$585$	21.0542	+	9.06902i	0.870483	+	0.374958i
$586$	−7.04256	−	12.1981i	−0.290926	−	0.503898i
$587$	−1.44801	−	2.50803i	−0.0597658	−	0.103517i	0.834594	−	0.550865i	$-0.185702\pi$
$587$	−1.44801	−	2.50803i	−0.0597658	−	0.103517i	−0.894360	+	0.447348i	$0.852369\pi$
$588$		0			0
$589$	9.62612	−	16.6729i	0.396637	−	0.686996i
$590$	−10.2880			−0.423550
$591$	23.6105	+	21.0007i	0.971206	+	0.863852i
$592$	−1.00000			−0.0410997
$593$	2.04394	+	3.54021i	0.0839346	+	0.145379i	0.904937	−	0.425546i	$-0.139918\pi$
$593$	2.04394	+	3.54021i	0.0839346	+	0.145379i	−0.821002	+	0.570925i	$0.806585\pi$
$594$	3.49381	+	7.47741i	0.143353	+	0.306802i
$595$		0			0
$596$	−2.60439	−	4.51093i	−0.106680	−	0.184775i
$597$	29.7545	−	9.86807i	1.21777	−	0.403873i
$598$	0.722528	+	1.25146i	0.0295464	+	0.0511758i
$599$	9.88255	+	17.1171i	0.403790	+	0.699385i	0.994180	−	0.107734i	$-0.0343593\pi$
$599$	9.88255	+	17.1171i	0.403790	+	0.699385i	−0.590390	+	0.807118i	$0.701026\pi$
$600$	−3.20582	−	2.85146i	−0.130877	−	0.116410i
$601$	13.4320	+	23.2649i	0.547902	+	0.948994i	0.998418	+	0.0562261i	$0.0179068\pi$
$601$	13.4320	+	23.2649i	0.547902	+	0.948994i	−0.450516	+	0.892768i	$0.648760\pi$
$602$		0			0
$603$	−24.1822	+	18.0223i	−0.984773	+	0.733926i
$604$	0.261450	+	0.452845i	0.0106383	+	0.0184260i
$605$	13.4647			0.547419
$606$	19.7829	−	6.56099i	0.803625	−	0.266522i
$607$	15.2422			0.618661			0.309331	−	0.950955i	$-0.399895\pi$
$607$	15.2422			0.618661			0.309331	+	0.950955i	$0.399895\pi$
$608$	−3.54944	+	6.14781i	−0.143949	+	0.249327i
$609$		0			0
$610$	−3.55563	−	6.15854i	−0.143963	−	0.249352i
$611$	6.41342	+	11.1084i	0.259459	+	0.449396i
$612$	−1.88874	−	16.0873i	−0.0763476	−	0.650290i
$613$	−1.36033	+	2.35617i	−0.0549434	+	0.0951648i	−0.892189	−	0.451662i	$-0.850831\pi$
$613$	−1.36033	+	2.35617i	−0.0549434	+	0.0951648i	0.837246	+	0.546827i	$0.184165\pi$
$614$	2.92766	−	5.07085i	0.118151	−	0.204643i
$615$	−15.3447	+	5.08907i	−0.618759	+	0.205211i
$616$		0			0
$617$	−9.21812	+	15.9663i	−0.371108	+	0.642777i	−0.989736	−	0.142906i	$-0.954355\pi$
$617$	−9.21812	+	15.9663i	−0.371108	+	0.642777i	0.618629	+	0.785684i	$0.287689\pi$
$618$	−10.0265	+	3.32530i	−0.403327	+	0.133763i
$619$	−0.107546			−0.00432262			−0.00216131	−	0.999998i	$-0.500688\pi$
$619$	−0.107546			−0.00432262			−0.00216131	+	0.999998i	$0.500688\pi$
$620$	2.15383	−	3.73054i	0.0864998	−	0.149822i
$621$	0.894237	−	1.27921i	0.0358845	−	0.0513328i
$622$	0.810892			0.0325138
$623$		0			0
$624$	−1.68292	+	8.16100i	−0.0673706	+	0.326701i
$625$	−6.47848			−0.259139
$626$	−5.28799	−	9.15907i	−0.211351	−	0.366070i
$627$	−3.94437	+	19.1275i	−0.157523	+	0.763878i
$628$	4.43199	−	7.67643i	0.176856	−	0.306323i
$629$	5.39926			0.215282
$630$		0			0
$631$	35.7266			1.42225			0.711126	−	0.703064i	$-0.248185\pi$
$631$	35.7266			1.42225			0.711126	+	0.703064i	$0.248185\pi$
$632$	4.19344	−	7.26325i	0.166806	−	0.288916i
$633$	−0.546489	+	0.181243i	−0.0217210	+	0.00720376i
$634$	6.09820	+	10.5624i	0.242190	+	0.419486i
$635$	21.3475			0.847152
$636$	6.32691	+	5.62755i	0.250878	+	0.223147i
$637$		0			0
$638$	−13.1447			−0.520403
$639$	4.44987	+	37.9017i	0.176034	+	1.49937i
$640$	−0.794182	+	1.37556i	−0.0313928	+	0.0543739i
$641$	17.3128			0.683813			0.341906	−	0.939734i	$-0.388927\pi$
$641$	17.3128			0.683813			0.341906	+	0.939734i	$0.388927\pi$
$642$	3.99450	+	3.55296i	0.157650	+	0.140224i
$643$	−14.4821	+	25.0838i	−0.571119	+	0.989207i	0.425332	+	0.905037i	$0.360157\pi$
$643$	−14.4821	+	25.0838i	−0.571119	+	0.989207i	−0.996451	+	0.0841700i	$0.973176\pi$
$644$		0			0
$645$	0.925798	−	4.48949i	0.0364533	−	0.176773i
$646$	19.1643	−	33.1936i	0.754011	−	1.30599i
$647$	−1.27816	+	2.21384i	−0.0502497	+	0.0870350i	−0.890056	−	0.455851i	$-0.849335\pi$
$647$	−1.27816	+	2.21384i	−0.0502497	+	0.0870350i	0.839807	+	0.542886i	$0.182668\pi$
$648$	8.75526	−	2.08457i	0.343939	−	0.0818895i
$649$	−5.14400	−	8.90966i	−0.201920	−	0.349735i
$650$	−5.95853	−	10.3205i	−0.233713	−	0.404802i
$651$		0			0
$652$	10.9814	−	19.0204i	0.430066	−	0.744896i
$653$	29.9766			1.17308			0.586538	−	0.809922i	$-0.300491\pi$
$653$	29.9766			1.17308			0.586538	+	0.809922i	$0.300491\pi$
$654$	−0.800372	+	3.88125i	−0.0312970	+	0.151769i
$655$	−5.04580			−0.197156
$656$	−2.93818	−	5.08907i	−0.114717	−	0.198695i
$657$	−44.2304	−	19.0521i	−1.72559	−	0.743294i
$658$		0			0
$659$	−7.63162	−	13.2183i	−0.297286	−	0.514914i	0.678228	−	0.734851i	$-0.262748\pi$
$659$	−7.63162	−	13.2183i	−0.297286	−	0.514914i	−0.975514	+	0.219937i	$0.929415\pi$
$660$	−0.882546	+	4.27974i	−0.0343531	+	0.166589i
$661$	−13.6261	−	23.6011i	−0.529994	−	0.917977i	−0.999388	−	0.0349881i	$-0.988861\pi$
$661$	−13.6261	−	23.6011i	−0.529994	−	0.917977i	0.469393	−	0.882989i	$-0.344473\pi$
$662$	−7.83310	−	13.5673i	−0.304442	−	0.527309i
$663$	9.08650	−	44.0633i	0.352891	−	1.71128i
$664$	1.18292	+	2.04887i	0.0459061	+	0.0795117i
$665$		0			0
$666$	0.349814	+	2.97954i	0.0135550	+	0.115455i
$667$	1.24288	+	2.15273i	0.0481245	+	0.0833541i
$668$	3.30037			0.127695
$669$	−2.21517	+	10.7420i	−0.0856433	+	0.415311i
$670$	−15.9680			−0.616896
$671$	3.55563	−	6.15854i	0.137264	−	0.237748i
$672$		0			0
$673$	23.2280	+	40.2320i	0.895372	+	1.55083i	0.833344	+	0.552755i	$0.186423\pi$
$673$	23.2280	+	40.2320i	0.895372	+	1.55083i	0.0620280	+	0.998074i	$0.480243\pi$
$674$	4.21201	+	7.29541i	0.162240	+	0.281009i
$675$	−7.37457	+	10.5493i	−0.283847	+	0.406044i
$676$	−5.07234	+	8.78555i	−0.195090	+	0.337906i
$677$	2.54944	−	4.41576i	0.0979830	−	0.169712i	−0.812867	−	0.582450i	$-0.802094\pi$
$677$	2.54944	−	4.41576i	0.0979830	−	0.169712i	0.910850	+	0.412738i	$0.135428\pi$
$678$	6.80903	−	33.0191i	0.261499	−	1.26809i
$679$		0			0
$680$	4.28799	−	7.42702i	0.164437	−	0.284813i
$681$	−30.1661	−	26.8317i	−1.15597	−	1.02819i
$682$	4.30766			0.164949
$683$	−7.77197	+	13.4614i	−0.297386	+	0.515088i	−0.975537	−	0.219835i	$-0.929448\pi$
$683$	−7.77197	+	13.4614i	−0.297386	+	0.515088i	0.678151	+	0.734923i	$0.262782\pi$
$684$	19.5593	+	8.42510i	0.747868	+	0.322142i
$685$	33.7738			1.29043
$686$		0			0
$687$	−6.41164	−	5.70291i	−0.244619	−	0.217580i
$688$	1.66621			0.0635236
$689$	11.7596	+	20.3682i	0.448005	+	0.775967i
$690$	0.784350	−	0.260130i	0.0298597	−	0.00990297i
$691$	11.6483	−	20.1755i	0.443123	−	0.767512i	−0.554796	−	0.831986i	$-0.687204\pi$
$691$	11.6483	−	20.1755i	0.443123	−	0.767512i	0.997919	+	0.0644744i	$0.0205371\pi$
$692$	−19.1075			−0.726360
$693$		0			0
$694$	−0.567323			−0.0215353
$695$	10.3665	−	17.9553i	0.393225	−	0.681085i
$696$	−2.89493	+	14.0384i	−0.109732	+	0.532124i
$697$	15.8640	+	27.4772i	0.600891	+	1.04077i
$698$	0.00728378			0.000275695
$699$	−4.99381	+	24.2165i	−0.188883	+	0.915954i
$700$		0			0
$701$	−45.6464			−1.72404			−0.862020	−	0.506874i	$-0.830801\pi$
$701$	−45.6464			−1.72404			−0.862020	+	0.506874i	$0.830801\pi$
$702$	24.9047	+	2.15948i	0.939967	+	0.0815044i
$703$	−3.54944	+	6.14781i	−0.133870	+	0.231869i
$704$	−1.58836			−0.0598637
$705$	6.96217	−	2.30900i	0.262211	−	0.0869621i
$706$	−3.32691	+	5.76238i	−0.125210	+	0.216870i
$707$		0			0
$708$	−10.6483	+	3.53152i	−0.400189	+	0.132723i
$709$	−9.00069	+	15.5897i	−0.338028	+	0.585482i	−0.984062	−	0.177827i	$-0.943093\pi$
$709$	−9.00069	+	15.5897i	−0.338028	+	0.585482i	0.646034	+	0.763309i	$0.276427\pi$
$710$	−10.1025	+	17.4981i	−0.379141	+	0.656692i
$711$	−23.1080	−	9.95371i	−0.866619	−	0.373293i
$712$	1.60507	+	2.78007i	0.0601527	+	0.104188i
$713$	−0.407305	−	0.705474i	−0.0152537	−	0.0264202i
$714$		0			0
$715$	−6.06870	+	10.5113i	−0.226957	+	0.393100i
$716$	16.0741			0.600718
$717$	−8.17928	+	2.71266i	−0.305461	+	0.101306i
$718$	−0.797135			−0.0297488
$719$	−18.4389	−	31.9371i	−0.687654	−	1.19105i	−0.972595	−	0.232506i	$-0.925307\pi$
$719$	−18.4389	−	31.9371i	−0.687654	−	1.19105i	0.284941	−	0.958545i	$-0.408026\pi$
$720$	4.37636	+	1.88510i	0.163097	+	0.0702536i
$721$		0			0
$722$	15.6971	+	27.1881i	0.584185	+	1.01184i
$723$	−16.8244	−	14.9646i	−0.625705	−	0.556541i
$724$	4.02654	+	6.97418i	0.149645	+	0.259193i
$725$	−10.2498	−	17.7531i	−0.380666	−	0.659334i
$726$	13.9363	−	4.62198i	0.517225	−	0.171538i
$727$	−15.2429	−	26.4014i	−0.565327	−	0.979175i	−0.997019	−	0.0771543i	$-0.975417\pi$
$727$	−15.2429	−	26.4014i	−0.565327	−	0.979175i	0.431692	−	0.902021i	$-0.357917\pi$
$728$		0			0
$729$	−9.27375	−	25.3574i	−0.343472	−	0.939163i
$730$	−12.7491	−	22.0820i	−0.471864	−	0.817293i
$731$	−8.99628			−0.332739
$732$	−5.79418	−	5.15371i	−0.214159	−	0.190487i
$733$	−6.15059			−0.227177			−0.113589	−	0.993528i	$-0.536235\pi$
$733$	−6.15059			−0.227177			−0.113589	+	0.993528i	$0.536235\pi$
$734$	7.71634	−	13.3651i	0.284815	−	0.493314i
$735$		0			0
$736$	0.150186	+	0.260130i	0.00553593	+	0.00958851i
$737$	−7.98398	−	13.8287i	−0.294094	−	0.509385i
$738$	−14.1353	+	10.5346i	−0.520326	+	0.387785i
$739$	−20.3912	+	35.3186i	−0.750103	+	1.29922i	0.197670	+	0.980269i	$0.436663\pi$
$739$	−20.3912	+	35.3186i	−0.750103	+	1.29922i	−0.947772	+	0.318947i	$0.896671\pi$
$740$	−0.794182	+	1.37556i	−0.0291947	+	0.0505667i
$741$	44.1989	+	39.3132i	1.62369	+	1.44421i
$742$		0			0
$743$	7.25271	−	12.5621i	0.266076	−	0.460858i	−0.701769	−	0.712405i	$-0.747606\pi$
$743$	7.25271	−	12.5621i	0.266076	−	0.460858i	0.967845	+	0.251547i	$0.0809394\pi$
$744$	0.948699	−	4.60054i	0.0347810	−	0.168664i
$745$	−8.27342			−0.303115
$746$	5.12110	−	8.87000i	0.187497	−	0.324754i
$747$	5.69089	−	4.24127i	0.208219	−	0.155180i
$748$	8.57598			0.313569
$749$		0			0
$750$	−19.5247	+	6.47536i	−0.712941	+	0.236447i
$751$	4.18911			0.152863			0.0764314	−	0.997075i	$-0.475647\pi$
$751$	4.18911			0.152863			0.0764314	+	0.997075i	$0.475647\pi$
$752$	1.33310	+	2.30900i	0.0486133	+	0.0842007i
$753$	3.14833	+	2.80032i	0.114731	+	0.102049i
$754$	−19.9065	+	34.4791i	−0.724953	+	1.25566i
$755$	0.830556			0.0302270
$756$		0			0
$757$	2.38688			0.0867525			0.0433763	−	0.999059i	$-0.486189\pi$
$757$	2.38688			0.0867525			0.0433763	+	0.999059i	$0.486189\pi$
$758$	12.5043	−	21.6581i	0.454178	−	0.786659i
$759$	0.617454	+	0.549202i	0.0224122	+	0.0199348i
$760$	5.63781	+	9.76497i	0.204505	+	0.354213i
$761$	−3.63416			−0.131738			−0.0658692	−	0.997828i	$-0.520982\pi$
$761$	−3.63416			−0.131738			−0.0658692	+	0.997828i	$0.520982\pi$
$762$	22.0952	−	7.32788i	0.800426	−	0.265461i
$763$		0			0
$764$	−23.9629			−0.866946
$765$	−23.6291	−	10.1781i	−0.854311	−	0.367992i
$766$	3.13348	−	5.42734i	0.113217	−	0.196098i
$767$	−31.1606			−1.12515
$768$	−0.349814	+	1.69636i	−0.0126228	+	0.0612120i
$769$	19.9672	−	34.5842i	0.720035	−	1.24714i	−0.240950	−	0.970538i	$-0.577459\pi$
$769$	19.9672	−	34.5842i	0.720035	−	1.24714i	0.960985	−	0.276600i	$-0.0892078\pi$
$770$		0			0
$771$	−1.27816	−	1.13688i	−0.0460318	−	0.0409436i
$772$	−4.88255	+	8.45682i	−0.175727	+	0.304368i
$773$	−18.0698	+	31.2978i	−0.649925	+	1.12570i	0.333215	+	0.942851i	$0.391867\pi$
$773$	−18.0698	+	31.2978i	−0.649925	+	1.12570i	−0.983140	+	0.182853i	$0.941467\pi$
$774$	−0.582863	−	4.96452i	−0.0209506	−	0.178446i
$775$	3.35896	+	5.81788i	0.120657	+	0.208985i
$776$	0.712008	+	1.23323i	0.0255596	+	0.0442705i
$777$		0			0
$778$	−10.8171	+	18.7357i	−0.387811	+	0.671709i
$779$	−41.7156			−1.49462
$780$	9.88942	+	8.79628i	0.354098	+	0.314957i
$781$	−20.2051			−0.722994
$782$	−0.810892	−	1.40451i	−0.0289974	−	0.0502251i
$783$	42.8406	+	3.71470i	1.53100	+	0.132753i
$784$		0			0
$785$	−7.03961	−	12.1930i	−0.251254	−	0.435186i
$786$	−5.22253	+	1.73205i	−0.186281	+	0.0617802i
$787$	−22.3189	−	38.6574i	−0.795582	−	1.37799i	−0.922469	−	0.386071i	$-0.873832\pi$
$787$	−22.3189	−	38.6574i	−0.795582	−	1.37799i	0.126888	−	0.991917i	$-0.459501\pi$
$788$	9.12178	+	15.7994i	0.324950	+	0.562830i
$789$	−22.2410	−	19.7826i	−0.791801	−	0.704278i
$790$	−6.66071	−	11.5367i	−0.236977	−	0.410457i
$791$		0			0
$792$	0.555632	+	4.73259i	0.0197435	+	0.168165i
$793$	−10.7694	−	18.6532i	−0.382433	−	0.662394i
$794$	−4.10617			−0.145722
$795$	12.7658	−	4.23377i	0.452756	−	0.150156i
$796$	18.0989			0.641498
$797$	−26.2836	+	45.5245i	−0.931012	+	1.61256i	−0.149418	+	0.988774i	$0.547740\pi$
$797$	−26.2836	+	45.5245i	−0.931012	+	1.61256i	−0.781595	+	0.623786i	$0.785593\pi$
$798$		0			0
$799$	−7.19777	−	12.4669i	−0.254639	−	0.441047i
$800$	−1.23855	−	2.14523i	−0.0437894	−	0.0758454i
$801$	7.72184	−	5.75488i	0.272838	−	0.203339i
$802$	8.37085	−	14.4987i	0.295585	−	0.511969i
$803$	12.7491	−	22.0820i	0.449905	−	0.779258i
$804$	−16.5272	+	5.48125i	−0.582870	+	0.193309i
$805$		0			0
$806$	6.52359	−	11.2992i	0.229784	−	0.397997i
$807$	37.6552	−	12.4883i	1.32553	−	0.439611i
$808$	12.0334			0.423334
$809$	7.40290	−	12.8222i	0.260272	−	0.450804i	−0.706042	−	0.708170i	$-0.749521\pi$
$809$	7.40290	−	12.8222i	0.260272	−	0.450804i	0.966314	+	0.257365i	$0.0828544\pi$
$810$	4.08582	−	13.6989i	0.143561	−	0.481332i
$811$	−27.0704			−0.950571			−0.475285	−	0.879832i	$-0.657655\pi$
$811$	−27.0704			−0.950571			−0.475285	+	0.879832i	$0.657655\pi$
$812$		0			0
$813$	−4.89995	+	23.7614i	−0.171849	+	0.833348i
$814$	−1.58836			−0.0556721
$815$	−17.4425	−	30.2113i	−0.610984	−	1.05826i
$816$	1.88874	−	9.15907i	0.0661190	−	0.320632i
$817$	5.91411	−	10.2435i	0.206908	−	0.358376i
$818$	−8.76509			−0.306464
$819$		0			0
$820$	−9.33379			−0.325950
$821$	−21.9091	+	37.9477i	−0.764632	+	1.32438i	0.175808	+	0.984424i	$0.443746\pi$
$821$	−21.9091	+	37.9477i	−0.764632	+	1.32438i	−0.940441	+	0.339958i	$0.889587\pi$
$822$	34.9567	−	11.5934i	1.21925	−	0.404365i
$823$	−15.6712	−	27.1434i	−0.546265	−	0.946158i	−0.998526	−	0.0542727i	$-0.982716\pi$
$823$	−15.6712	−	27.1434i	−0.546265	−	0.946158i	0.452262	−	0.891885i	$-0.350617\pi$
$824$	−6.09888			−0.212465
$825$	−5.09201	−	4.52915i	−0.177281	−	0.157685i
$826$		0			0
$827$	−14.7665			−0.513480			−0.256740	−	0.966480i	$-0.582648\pi$
$827$	−14.7665			−0.513480			−0.256740	+	0.966480i	$0.582648\pi$
$828$	0.722528	−	0.538481i	0.0251096	−	0.0187135i
$829$	15.0036	−	25.9871i	0.521098	−	0.902568i	−0.478601	−	0.878033i	$-0.658856\pi$
$829$	15.0036	−	25.9871i	0.521098	−	0.902568i	0.999699	−	0.0245357i	$-0.00781074\pi$
$830$	3.75781			0.130435
$831$	−36.6192	−	32.5715i	−1.27031	−	1.12989i
$832$	−2.40545	+	4.16635i	−0.0833938	+	0.144442i
$833$		0			0
$834$	4.56615	−	22.1427i	0.158113	−	0.766739i
$835$	2.62110	−	4.53987i	0.0907068	−	0.157109i
$836$	−5.63781	+	9.76497i	−0.194988	+	0.337728i
$837$	−14.0393	−	1.21735i	−0.485270	−	0.0420777i
$838$	−0.210149	−	0.363988i	−0.00725946	−	0.0125738i
$839$	−18.0167	−	31.2059i	−0.622006	−	1.07735i	−0.989112	−	0.147167i	$-0.952985\pi$
$839$	−18.0167	−	31.2059i	−0.622006	−	1.07735i	0.367106	−	0.930179i	$-0.380349\pi$
$840$		0			0
$841$	−19.7429	+	34.1957i	−0.680789	+	1.17916i
$842$	6.57598			0.226623
$843$	−6.15521	+	29.8485i	−0.211997	+	1.02804i
$844$	−0.332415			−0.0114422
$845$	8.05673	+	13.9547i	0.277160	+	0.480055i
$846$	6.41342	−	4.77975i	0.220498	−	0.164331i
$847$		0			0
$848$	2.44437	+	4.23377i	0.0839399	+	0.145388i
$849$	−6.47957	+	31.4215i	−0.222378	+	1.07838i
$850$	6.68725	+	11.5827i	0.229371	+	0.397282i
$851$	0.150186	+	0.260130i	0.00514831	+	0.00891713i
$852$	−4.44987	+	21.5788i	−0.152450	+	0.739278i
$853$	12.2658	+	21.2450i	0.419972	+	0.727413i	0.995936	−	0.0900617i	$-0.0287064\pi$
$853$	12.2658	+	21.2450i	0.419972	+	0.727413i	−0.575964	+	0.817475i	$0.695373\pi$
$854$		0			0
$855$	27.1229	−	20.2140i	0.927583	−	0.691303i
$856$	1.54325	+	2.67299i	0.0527473	+	0.0913610i
$857$	−29.0480			−0.992260			−0.496130	−	0.868248i	$-0.665246\pi$
$857$	−29.0480			−0.992260			−0.496130	+	0.868248i	$0.665246\pi$
$858$	−2.67309	+	12.9626i	−0.0912577	+	0.442537i
$859$	−25.2953			−0.863064			−0.431532	−	0.902098i	$-0.642027\pi$
$859$	−25.2953			−0.863064			−0.431532	+	0.902098i	$0.642027\pi$
$860$	1.32327	−	2.29197i	0.0451232	−	0.0781557i
$861$		0			0
$862$	−11.0439	−	19.1287i	−0.376158	−	0.651525i
$863$	−1.34981	−	2.33795i	−0.0459482	−	0.0795846i	0.842137	−	0.539264i	$-0.181298\pi$
$863$	−1.34981	−	2.33795i	−0.0459482	−	0.0795846i	−0.888085	+	0.459680i	$0.847964\pi$
$864$	5.17673	+	0.448873i	0.176116	+	0.0152710i
$865$	−15.1749	+	26.2836i	−0.515961	+	0.893671i
$866$	4.71634	−	8.16894i	0.160268	−	0.277592i
$867$	−4.25093	+	20.6141i	−0.144369	+	0.700091i
$868$		0			0
$869$	6.66071	−	11.5367i	0.225949	−	0.391355i
$870$	17.0116	+	15.1312i	0.576748	+	0.512996i
$871$	−48.3643			−1.63876
$872$	−1.14400	+	1.98146i	−0.0387406	+	0.0671007i
$873$	3.42539	−	2.55286i	0.115932	−	0.0864011i
$874$	2.13231			0.0721263
$875$		0			0
$876$	−20.7756	−	18.4791i	−0.701943	−	0.624352i
$877$	−11.0916			−0.374537			−0.187268	−	0.982309i	$-0.559963\pi$
$877$	−11.0916			−0.374537			−0.187268	+	0.982309i	$0.559963\pi$
$878$	15.6032	+	27.0256i	0.526583	+	0.912069i
$879$	−23.1559	+	7.67965i	−0.781029	+	0.259028i
$880$	−1.26145	+	2.18490i	−0.0425235	+	0.0736528i
$881$	40.3942			1.36091			0.680457	−	0.732788i	$-0.261781\pi$
$881$	40.3942			1.36091			0.680457	+	0.732788i	$0.261781\pi$
$882$		0			0
$883$	−33.2581			−1.11923			−0.559613	−	0.828754i	$-0.689050\pi$
$883$	−33.2581			−1.11923			−0.559613	+	0.828754i	$0.689050\pi$
$884$	12.9876	−	22.4952i	0.436821	−	0.756596i
$885$	−3.59888	+	17.4521i	−0.120975	+	0.586646i
$886$	6.52723	+	11.3055i	0.219287	+	0.379816i
$887$	−40.5672			−1.36211			−0.681056	−	0.732231i	$-0.738479\pi$
$887$	−40.5672			−1.36211			−0.681056	+	0.732231i	$0.738479\pi$
$888$	−0.349814	+	1.69636i	−0.0117390	+	0.0569260i
$889$		0			0
$890$	5.09888			0.170915
$891$	13.9065	−	3.31105i	0.465887	−	0.110924i
$892$	−3.16621	+	5.48403i	−0.106012	+	0.183619i
$893$	18.9271			0.633371
$894$	−8.56320	+	2.83998i	−0.286396	+	0.0949833i
$895$	12.7658	−	22.1110i	0.426713	−	0.739089i
$896$		0			0
$897$	2.37567	−	0.787890i	0.0793212	−	0.0263069i
$898$	−4.95853	+	8.58843i	−0.165468	+	0.286599i
$899$	11.2218	−	19.4367i	0.374267	−	0.648249i
$900$	−5.95853	+	4.44074i	−0.198618	+	0.148025i
$901$	−13.1978	−	22.8592i	−0.439681	−	0.761551i
$902$	−4.66690	−	8.08330i	−0.155391	−	0.269144i
$903$		0			0
$904$	9.73236	−	16.8569i	0.323693	−	0.560654i
$905$	12.7912			0.425195
$906$	0.859646	−	0.285101i	0.0285598	−	0.00947186i
$907$	30.1135			0.999901			0.499950	−	0.866054i	$-0.333352\pi$
$907$	30.1135			0.999901			0.499950	+	0.866054i	$0.333352\pi$
$908$	−11.6545	−	20.1862i	−0.386769	−	0.669903i
$909$	−4.20946	−	35.8540i	−0.139619	−	1.18920i
$910$		0			0
$911$	14.6113	+	25.3075i	0.484093	+	0.838473i	0.999833	−	0.0182717i	$-0.00581638\pi$
$911$	14.6113	+	25.3075i	0.484093	+	0.838473i	−0.515740	+	0.856745i	$0.672483\pi$
$912$	9.18725	+	8.17172i	0.304220	+	0.270593i
$913$	1.87890	+	3.25436i	0.0621826	+	0.107704i
$914$	−12.2615	−	21.2375i	−0.405573	−	0.702473i
$915$	−11.6909	+	3.87728i	−0.386489	+	0.128179i
$916$	−2.47710	−	4.29046i	−0.0818457	−	0.141761i
$917$		0			0
$918$	−27.9505	−	2.42358i	−0.922503	−	0.0799902i
$919$	−5.52359	−	9.56714i	−0.182206	−	0.315591i	0.760425	−	0.649426i	$-0.224991\pi$
$919$	−5.52359	−	9.56714i	−0.182206	−	0.315591i	−0.942632	+	0.333835i	$0.891657\pi$
$920$	0.477100			0.0157295
$921$	−7.57784	−	6.74021i	−0.249698	−	0.222097i
$922$	−3.51052			−0.115613
$923$	−30.5989	+	52.9988i	−1.00717	+	1.74448i
$924$		0			0
$925$	−1.23855	−	2.14523i	−0.0407233	−	0.0705348i
$926$	−8.69413	−	15.0587i	−0.285707	−	0.494859i
$927$	2.13348	+	18.1718i	0.0700725	+	0.596842i
$928$	−4.13781	+	7.16689i	−0.135830	+	0.235265i
$929$	−21.1669	+	36.6621i	−0.694463	+	1.20285i	0.275898	+	0.961187i	$0.411025\pi$
$929$	−21.1669	+	36.6621i	−0.694463	+	1.20285i	−0.970361	+	0.241659i	$0.922309\pi$
$930$	−5.57489	−	4.95866i	−0.182808	−	0.162601i
$931$		0			0
$932$	−7.13781	+	12.3630i	−0.233807	+	0.404965i
$933$	0.283662	−	1.37556i	0.00928666	−	0.0450339i
$934$	−13.3979			−0.438392
$935$	6.81089	−	11.7968i	0.222740	−	0.385797i
$936$	13.2553	+	5.70966i	0.433262	+	0.186626i
$937$	11.7651			0.384349			0.192174	−	0.981361i	$-0.438446\pi$
$937$	11.7651			0.384349			0.192174	+	0.981361i	$0.438446\pi$
$938$		0			0
$939$	−17.3869	+	5.76636i	−0.567399	+	0.188178i
$940$	4.23491			0.138127
$941$	7.28799	+	12.6232i	0.237582	+	0.411504i	0.960020	−	0.279932i	$-0.0903119\pi$
$941$	7.28799	+	12.6232i	0.237582	+	0.411504i	−0.722438	+	0.691436i	$0.756979\pi$
$942$	−11.4716	−	10.2036i	−0.373765	−	0.332450i
$943$	−0.882546	+	1.52861i	−0.0287397	+	0.0497785i
$944$	−6.47710			−0.210812
$945$		0			0
$946$	2.64654			0.0860466
$947$	−3.12178	+	5.40709i	−0.101444	+	0.175707i	−0.912280	−	0.409567i	$-0.865680\pi$
$947$	−3.12178	+	5.40709i	−0.101444	+	0.175707i	0.810836	+	0.585274i	$0.199013\pi$
$948$	−10.8541	−	9.65436i	−0.352526	−	0.313559i
$949$	−38.6148	−	66.8828i	−1.25349	−	2.17111i
$950$	−17.5846			−0.570521
$951$	20.0508	−	6.64985i	0.650192	−	0.215636i
$952$		0			0
$953$	28.0173			0.907570			0.453785	−	0.891111i	$-0.350073\pi$
$953$	28.0173			0.907570			0.453785	+	0.891111i	$0.350073\pi$
$954$	11.7596	−	8.76411i	0.380731	−	0.283749i
$955$	−19.0309	+	32.9624i	−0.615825	+	1.06664i
$956$	−4.97524			−0.160911
$957$	−4.59820	+	22.2981i	−0.148639	+	0.720795i
$958$	−10.4029	+	18.0183i	−0.336102	+	0.582146i
$959$		0			0
$960$	2.05563	+	1.82841i	0.0663452	+	0.0590116i
$961$	11.8225	−	20.4772i	0.381371	−	0.660554i
$962$	−2.40545	+	4.16635i	−0.0775547	+	0.134329i
$963$	7.42442	−	5.53322i	0.239249	−	0.178306i
$964$	−6.50000	−	11.2583i	−0.209351	−	0.362606i
$965$	7.75526	+	13.4325i	0.249651	+	0.432408i
$966$		0			0
$967$	15.7837	−	27.3381i	0.507568	−	0.879134i	−0.492393	−	0.870373i	$-0.663878\pi$
$967$	15.7837	−	27.3381i	0.507568	−	0.879134i	0.999962	−	0.00876132i	$-0.00278885\pi$
$968$	8.47710			0.272464
$969$	−49.6043	−	44.1212i	−1.59352	−	1.41738i
$970$	2.26186			0.0726238
$971$	−2.82141	−	4.88683i	−0.0905434	−	0.156826i	0.817196	−	0.576359i	$-0.195527\pi$
$971$	−2.82141	−	4.88683i	−0.0905434	−	0.156826i	−0.907740	+	0.419533i	$0.862194\pi$
$972$	−0.473458	−	15.5813i	−0.0151862	−	0.499769i
$973$		0			0
$974$	−16.2472	−	28.1410i	−0.520594	−	0.901696i
$975$	−19.5916	+	6.49755i	−0.627433	+	0.208088i
$976$	−2.23855	−	3.87728i	−0.0716542	−	0.124109i
$977$	−3.24652	−	5.62314i	−0.103865	−	0.179900i	0.809409	−	0.587246i	$-0.199788\pi$
$977$	−3.24652	−	5.62314i	−0.103865	−	0.179900i	−0.913274	+	0.407346i	$0.866454\pi$
$978$	−28.4239	−	25.2820i	−0.908897	−	0.808430i
$979$	2.54944	+	4.41576i	0.0814805	+	0.141128i
$980$		0			0
$981$	6.30401	+	2.71543i	0.201272	+	0.0866971i
$982$	9.66071	+	16.7328i	0.308286	+	0.533966i
$983$	30.3063			0.966620			0.483310	−	0.875449i	$-0.339434\pi$
$983$	30.3063			0.966620			0.483310	+	0.875449i	$0.339434\pi$
$984$	−9.66071	+	3.20397i	−0.307972	+	0.102139i
$985$	28.9774			0.923298
$986$	22.3411	−	38.6959i	0.711485	−	1.23233i
$987$		0			0
$988$	17.0760	+	29.5765i	0.543259	+	0.940953i
$989$	−0.250241	−	0.433430i	−0.00795720	−	0.0137823i
$990$	6.95125	+	2.99423i	0.220925	+	0.0951628i
$991$	11.1669	−	19.3416i	0.354728	−	0.614407i	−0.632343	−	0.774688i	$-0.717907\pi$
$991$	11.1669	−	19.3416i	0.354728	−	0.614407i	0.987071	+	0.160281i	$0.0512401\pi$
$992$	1.35600	−	2.34867i	0.0430532	−	0.0745703i
$993$	−25.7552	+	8.54170i	−0.817316	+	0.271063i
$994$		0			0
$995$	14.3738	−	24.8962i	0.455680	−	0.789262i
$996$	3.88942	−	1.28993i	0.123241	−	0.0408729i
$997$	8.76509			0.277593			0.138797	−	0.990321i	$-0.455677\pi$
$997$	8.76509			0.277593			0.138797	+	0.990321i	$0.455677\pi$
$998$	−5.57530	+	9.65670i	−0.176483	+	0.305677i
$999$	5.17673	+	0.448873i	0.163784	+	0.0142017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.h.p.67.1		6
3.2	odd	2		2646.2.h.o.361.3		6
7.2	even	3		882.2.e.o.373.3		6
7.3	odd	6		882.2.f.n.589.3		6
7.4	even	3		882.2.f.o.589.1		6
7.5	odd	6		126.2.e.c.121.1	yes	6
7.6	odd	2		126.2.h.d.67.3	yes	6
9.2	odd	6		2646.2.e.p.2125.1		6
9.7	even	3		882.2.e.o.655.3		6
21.2	odd	6		2646.2.e.p.1549.1		6
21.5	even	6		378.2.e.d.37.3		6
21.11	odd	6		2646.2.f.m.1765.1		6
21.17	even	6		2646.2.f.l.1765.3		6
21.20	even	2		378.2.h.c.361.1		6
28.19	even	6		1008.2.q.g.625.3		6
28.27	even	2		1008.2.t.h.193.1		6
63.2	odd	6		2646.2.h.o.667.3		6
63.4	even	3		7938.2.a.bw.1.1		3
63.5	even	6		1134.2.g.l.163.3		6
63.11	odd	6		2646.2.f.m.883.1		6
63.13	odd	6		1134.2.g.m.487.1		6
63.16	even	3	inner	882.2.h.p.79.1		6
63.20	even	6		378.2.e.d.235.3		6
63.25	even	3		882.2.f.o.295.1		6
63.31	odd	6		7938.2.a.bv.1.3		3
63.32	odd	6		7938.2.a.bz.1.3		3
63.34	odd	6		126.2.e.c.25.1	✓	6
63.38	even	6		2646.2.f.l.883.3		6
63.40	odd	6		1134.2.g.m.163.1		6
63.41	even	6		1134.2.g.l.487.3		6
63.47	even	6		378.2.h.c.289.1		6
63.52	odd	6		882.2.f.n.295.3		6
63.59	even	6		7938.2.a.ca.1.1		3
63.61	odd	6		126.2.h.d.79.3	yes	6
84.47	odd	6		3024.2.q.g.2305.3		6
84.83	odd	2		3024.2.t.h.1873.1		6
252.47	odd	6		3024.2.t.h.289.1		6
252.83	odd	6		3024.2.q.g.2881.3		6
252.187	even	6		1008.2.t.h.961.1		6
252.223	even	6		1008.2.q.g.529.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.1	✓	6	63.34	odd	6
126.2.e.c.121.1	yes	6	7.5	odd	6
126.2.h.d.67.3	yes	6	7.6	odd	2
126.2.h.d.79.3	yes	6	63.61	odd	6
378.2.e.d.37.3		6	21.5	even	6
378.2.e.d.235.3		6	63.20	even	6
378.2.h.c.289.1		6	63.47	even	6
378.2.h.c.361.1		6	21.20	even	2
882.2.e.o.373.3		6	7.2	even	3
882.2.e.o.655.3		6	9.7	even	3
882.2.f.n.295.3		6	63.52	odd	6
882.2.f.n.589.3		6	7.3	odd	6
882.2.f.o.295.1		6	63.25	even	3
882.2.f.o.589.1		6	7.4	even	3
882.2.h.p.67.1		6	1.1	even	1	trivial
882.2.h.p.79.1		6	63.16	even	3	inner
1008.2.q.g.529.3		6	252.223	even	6
1008.2.q.g.625.3		6	28.19	even	6
1008.2.t.h.193.1		6	28.27	even	2
1008.2.t.h.961.1		6	252.187	even	6
1134.2.g.l.163.3		6	63.5	even	6
1134.2.g.l.487.3		6	63.41	even	6
1134.2.g.m.163.1		6	63.40	odd	6
1134.2.g.m.487.1		6	63.13	odd	6
2646.2.e.p.1549.1		6	21.2	odd	6
2646.2.e.p.2125.1		6	9.2	odd	6
2646.2.f.l.883.3		6	63.38	even	6
2646.2.f.l.1765.3		6	21.17	even	6
2646.2.f.m.883.1		6	63.11	odd	6
2646.2.f.m.1765.1		6	21.11	odd	6
2646.2.h.o.361.3		6	3.2	odd	2
2646.2.h.o.667.3		6	63.2	odd	6
3024.2.q.g.2305.3		6	84.47	odd	6
3024.2.q.g.2881.3		6	252.83	odd	6
3024.2.t.h.289.1		6	252.47	odd	6
3024.2.t.h.1873.1		6	84.83	odd	2
7938.2.a.bv.1.3		3	63.31	odd	6
7938.2.a.bw.1.1		3	63.4	even	3
7938.2.a.bz.1.3		3	63.32	odd	6
7938.2.a.ca.1.1		3	63.59	even	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.29418 - 1.15113i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.58836 q^{5} +(-1.64400 + 0.545231i) q^{6} -1.00000 q^{8} +(0.349814 + 2.97954i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.29418 - 1.15113i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.58836 q^{5} +(-1.64400 + 0.545231i) q^{6} -1.00000 q^{8} +(0.349814 + 2.97954i) q^{9} +(-0.794182 + 1.37556i) q^{10} -1.58836 q^{11} +(-0.349814 + 1.69636i) q^{12} +(-2.40545 + 4.16635i) q^{13} +(2.05563 + 1.82841i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.69963 - 4.67589i) q^{17} +(2.75526 + 1.18682i) q^{18} +(3.54944 + 6.14781i) q^{19} +(0.794182 + 1.37556i) q^{20} +(-0.794182 + 1.37556i) q^{22} +0.300372 q^{23} +(1.29418 + 1.15113i) q^{24} -2.47710 q^{25} +(2.40545 + 4.16635i) q^{26} +(2.97710 - 4.25874i) q^{27} +(4.13781 + 7.16689i) q^{29} +(2.61126 - 0.866025i) q^{30} +(-1.35600 - 2.34867i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.05563 + 1.82841i) q^{33} +(-2.69963 - 4.67589i) q^{34} +(2.40545 - 1.79272i) q^{36} +(0.500000 + 0.866025i) q^{37} +7.09888 q^{38} +(7.90909 - 2.62305i) q^{39} +1.58836 q^{40} +(-2.93818 + 5.08907i) q^{41} +(-0.833104 - 1.44298i) q^{43} +(0.794182 + 1.37556i) q^{44} +(-0.555632 - 4.73259i) q^{45} +(0.150186 - 0.260130i) q^{46} +(1.33310 - 2.30900i) q^{47} +(1.64400 - 0.545231i) q^{48} +(-1.23855 + 2.14523i) q^{50} +(-8.87636 + 2.94384i) q^{51} +4.81089 q^{52} +(2.44437 - 4.23377i) q^{53} +(-2.19963 - 4.70761i) q^{54} +2.52290 q^{55} +(2.48329 - 12.0422i) q^{57} +8.27561 q^{58} +(3.23855 + 5.60933i) q^{59} +(0.555632 - 2.69443i) q^{60} +(-2.23855 + 3.87728i) q^{61} -2.71201 q^{62} +1.00000 q^{64} +(3.82072 - 6.61769i) q^{65} +(2.61126 - 0.866025i) q^{66} +(5.02654 + 8.70623i) q^{67} -5.39926 q^{68} +(-0.388736 - 0.345766i) q^{69} +12.7207 q^{71} +(-0.349814 - 2.97954i) q^{72} +(-8.02654 + 13.9024i) q^{73} +1.00000 q^{74} +(3.20582 + 2.85146i) q^{75} +(3.54944 - 6.14781i) q^{76} +(1.68292 - 8.16100i) q^{78} +(-4.19344 + 7.26325i) q^{79} +(0.794182 - 1.37556i) q^{80} +(-8.75526 + 2.08457i) q^{81} +(2.93818 + 5.08907i) q^{82} +(-1.18292 - 2.04887i) q^{83} +(-4.28799 + 7.42702i) q^{85} -1.66621 q^{86} +(2.89493 - 14.0384i) q^{87} +1.58836 q^{88} +(-1.60507 - 2.78007i) q^{89} +(-4.37636 - 1.88510i) q^{90} +(-0.150186 - 0.260130i) q^{92} +(-0.948699 + 4.60054i) q^{93} +(-1.33310 - 2.30900i) q^{94} +(-5.63781 - 9.76497i) q^{95} +(0.349814 - 1.69636i) q^{96} +(-0.712008 - 1.23323i) q^{97} +(-0.555632 - 4.73259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9	\( 6 q + 3 q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} + q^{10} + 2 q^{11} + 4 q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} + 4 q^{17} + 4 q^{18} + 3 q^{19} - q^{20} + q^{22} + 14 q^{23} + 2 q^{24} - 4 q^{25} + 8 q^{26} + 7 q^{27} - 5 q^{29} + 15 q^{30} - 20 q^{31} + 3 q^{32} + 12 q^{33} - 4 q^{34} + 8 q^{36} + 3 q^{37} + 6 q^{38} + q^{39} - 2 q^{40} - 6 q^{43} - q^{44} - 3 q^{45} + 7 q^{46} + 9 q^{47} - 2 q^{48} - 2 q^{50} - 18 q^{51} + 16 q^{52} + 15 q^{53} - q^{54} + 26 q^{55} + 22 q^{57} - 10 q^{58} + 14 q^{59} + 3 q^{60} - 8 q^{61} - 40 q^{62} + 6 q^{64} - 12 q^{65} + 15 q^{66} + q^{67} - 8 q^{68} - 3 q^{69} + 14 q^{71} + 4 q^{72} - 19 q^{73} + 6 q^{74} + 25 q^{75} + 3 q^{76} + 5 q^{78} + 5 q^{79} - q^{80} - 40 q^{81} - 2 q^{83} - 2 q^{85} - 12 q^{86} + 36 q^{87} - 2 q^{88} + 9 q^{89} + 9 q^{90} - 7 q^{92} + 37 q^{93} - 9 q^{94} - 4 q^{95} - 4 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 + q^10 + 2 * q^11 + 4 * q^12 - 8 * q^13 + 12 * q^15 - 3 * q^16 + 4 * q^17 + 4 * q^18 + 3 * q^19 - q^20 + q^22 + 14 * q^23 + 2 * q^24 - 4 * q^25 + 8 * q^26 + 7 * q^27 - 5 * q^29 + 15 * q^30 - 20 * q^31 + 3 * q^32 + 12 * q^33 - 4 * q^34 + 8 * q^36 + 3 * q^37 + 6 * q^38 + q^39 - 2 * q^40 - 6 * q^43 - q^44 - 3 * q^45 + 7 * q^46 + 9 * q^47 - 2 * q^48 - 2 * q^50 - 18 * q^51 + 16 * q^52 + 15 * q^53 - q^54 + 26 * q^55 + 22 * q^57 - 10 * q^58 + 14 * q^59 + 3 * q^60 - 8 * q^61 - 40 * q^62 + 6 * q^64 - 12 * q^65 + 15 * q^66 + q^67 - 8 * q^68 - 3 * q^69 + 14 * q^71 + 4 * q^72 - 19 * q^73 + 6 * q^74 + 25 * q^75 + 3 * q^76 + 5 * q^78 + 5 * q^79 - q^80 - 40 * q^81 - 2 * q^83 - 2 * q^85 - 12 * q^86 + 36 * q^87 - 2 * q^88 + 9 * q^89 + 9 * q^90 - 7 * q^92 + 37 * q^93 - 9 * q^94 - 4 * q^95 - 4 * q^96 - 28 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

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