LMFDB - Embedded newform 882.2.f.o.295.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(295,882)]

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([4, 0]))

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

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

chi := DirichletCharacter("882.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.f (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:	$7.04280545828$
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			295.1
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	882.295
Dual form			882.2.f.o.589.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.349814 - 1.69636i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.794182 + 1.37556i) q^{5} +(-1.64400 - 0.545231i) q^{6} -1.00000 q^{8} +(-2.75526 + 1.18682i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.349814 - 1.69636i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.794182 + 1.37556i) q^{5} +(-1.64400 - 0.545231i) q^{6} -1.00000 q^{8} +(-2.75526 + 1.18682i) q^{9} +1.58836 q^{10} +(0.794182 - 1.37556i) q^{11} +(-1.29418 + 1.15113i) q^{12} +(-2.40545 - 4.16635i) q^{13} +(2.05563 - 1.82841i) q^{15} +(-0.500000 + 0.866025i) q^{16} -5.39926 q^{17} +(-0.349814 + 2.97954i) q^{18} -7.09888 q^{19} +(0.794182 - 1.37556i) q^{20} +(-0.794182 - 1.37556i) q^{22} +(-0.150186 - 0.260130i) q^{23} +(0.349814 + 1.69636i) q^{24} +(1.23855 - 2.14523i) q^{25} -4.81089 q^{26} +(2.97710 + 4.25874i) q^{27} +(4.13781 - 7.16689i) q^{29} +(-0.555632 - 2.69443i) q^{30} +(-1.35600 - 2.34867i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.61126 - 0.866025i) q^{33} +(-2.69963 + 4.67589i) q^{34} +(2.40545 + 1.79272i) q^{36} -1.00000 q^{37} +(-3.54944 + 6.14781i) q^{38} +(-6.22617 + 5.53795i) q^{39} +(-0.794182 - 1.37556i) q^{40} +(-2.93818 - 5.08907i) q^{41} +(-0.833104 + 1.44298i) q^{43} -1.58836 q^{44} +(-3.82072 - 2.84748i) q^{45} -0.300372 q^{46} +(1.33310 - 2.30900i) q^{47} +(1.64400 + 0.545231i) q^{48} +(-1.23855 - 2.14523i) q^{50} +(1.88874 + 9.15907i) q^{51} +(-2.40545 + 4.16635i) q^{52} -4.88874 q^{53} +(5.17673 - 0.448873i) q^{54} +2.52290 q^{55} +(2.48329 + 12.0422i) q^{57} +(-4.13781 - 7.16689i) q^{58} +(3.23855 + 5.60933i) q^{59} +(-2.61126 - 0.866025i) q^{60} +(-2.23855 + 3.87728i) q^{61} -2.71201 q^{62} +1.00000 q^{64} +(3.82072 - 6.61769i) q^{65} +(-2.05563 + 1.82841i) q^{66} +(5.02654 + 8.70623i) q^{67} +(2.69963 + 4.67589i) q^{68} +(-0.388736 + 0.345766i) q^{69} +12.7207 q^{71} +(2.75526 - 1.18682i) q^{72} +16.0531 q^{73} +(-0.500000 + 0.866025i) q^{74} +(-4.07234 - 1.35059i) q^{75} +(3.54944 + 6.14781i) q^{76} +(1.68292 + 8.16100i) q^{78} +(-4.19344 + 7.26325i) q^{79} -1.58836 q^{80} +(6.18292 - 6.53999i) q^{81} -5.87636 q^{82} +(-1.18292 + 2.04887i) q^{83} +(-4.28799 - 7.42702i) q^{85} +(0.833104 + 1.44298i) q^{86} +(-13.6051 - 4.51212i) q^{87} +(-0.794182 + 1.37556i) q^{88} +3.21015 q^{89} +(-4.37636 + 1.88510i) q^{90} +(-0.150186 + 0.260130i) q^{92} +(-3.50983 + 3.12186i) q^{93} +(-1.33310 - 2.30900i) q^{94} +(-5.63781 - 9.76497i) q^{95} +(1.29418 - 1.15113i) 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} + 4 q^{3} - 3 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 + 4 * q^3 - 3 * q^4 - q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9	$ 6 q + 3 q^{2} + 4 q^{3} - 3 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} - 2 q^{10} - q^{11} - 2 q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} - 8 q^{17} + 4 q^{18} - 6 q^{19} - q^{20} + q^{22} - 7 q^{23} - 4 q^{24} + 2 q^{25} - 16 q^{26} + 7 q^{27} - 5 q^{29} - 3 q^{30} - 20 q^{31} + 3 q^{32} - 15 q^{33} - 4 q^{34} + 8 q^{36} - 6 q^{37} - 3 q^{38} + 4 q^{39} + q^{40} - 6 q^{43} + 2 q^{44} + 12 q^{45} - 14 q^{46} + 9 q^{47} - 2 q^{48} - 2 q^{50} + 12 q^{51} - 8 q^{52} - 30 q^{53} + 8 q^{54} + 26 q^{55} + 22 q^{57} + 5 q^{58} + 14 q^{59} - 15 q^{60} - 8 q^{61} - 40 q^{62} + 6 q^{64} - 12 q^{65} - 12 q^{66} + q^{67} + 4 q^{68} - 3 q^{69} + 14 q^{71} + 4 q^{72} + 38 q^{73} - 3 q^{74} - 17 q^{75} + 3 q^{76} + 5 q^{78} + 5 q^{79} + 2 q^{80} + 32 q^{81} - 2 q^{83} - 2 q^{85} + 6 q^{86} - 63 q^{87} + q^{88} - 18 q^{89} + 9 q^{90} - 7 q^{92} + q^{93} - 9 q^{94} - 4 q^{95} + 2 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 + 4 * q^3 - 3 * q^4 - q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 - 2 * q^10 - q^11 - 2 * q^12 - 8 * q^13 + 12 * q^15 - 3 * q^16 - 8 * q^17 + 4 * q^18 - 6 * q^19 - q^20 + q^22 - 7 * q^23 - 4 * q^24 + 2 * q^25 - 16 * q^26 + 7 * q^27 - 5 * q^29 - 3 * q^30 - 20 * q^31 + 3 * q^32 - 15 * q^33 - 4 * q^34 + 8 * q^36 - 6 * q^37 - 3 * q^38 + 4 * q^39 + q^40 - 6 * q^43 + 2 * q^44 + 12 * q^45 - 14 * q^46 + 9 * q^47 - 2 * q^48 - 2 * q^50 + 12 * q^51 - 8 * q^52 - 30 * q^53 + 8 * q^54 + 26 * q^55 + 22 * q^57 + 5 * q^58 + 14 * q^59 - 15 * q^60 - 8 * q^61 - 40 * q^62 + 6 * q^64 - 12 * q^65 - 12 * q^66 + q^67 + 4 * q^68 - 3 * q^69 + 14 * q^71 + 4 * q^72 + 38 * q^73 - 3 * q^74 - 17 * q^75 + 3 * q^76 + 5 * q^78 + 5 * q^79 + 2 * q^80 + 32 * q^81 - 2 * q^83 - 2 * q^85 + 6 * q^86 - 63 * q^87 + q^88 - 18 * q^89 + 9 * q^90 - 7 * q^92 + q^93 - 9 * q^94 - 4 * q^95 + 2 * q^96 - 28 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.349814	−	1.69636i	−0.201965	−	0.979393i
$3$	−0.349814	−	1.69636i	−0.201965	−	0.979393i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.794182	+	1.37556i	0.355169	+	0.615171i	0.987147	−	0.159816i	$-0.0510900\pi$
$5$	0.794182	+	1.37556i	0.355169	+	0.615171i	−0.631978	+	0.774986i	$0.717757\pi$
$6$	−1.64400	−	0.545231i	−0.671159	−	0.222590i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−2.75526	+	1.18682i	−0.918420	+	0.395607i
$10$	1.58836			0.502285
$11$	0.794182	−	1.37556i	0.239455	−	0.414748i	−0.721103	−	0.692828i	$-0.756365\pi$
$11$	0.794182	−	1.37556i	0.239455	−	0.414748i	0.960558	+	0.278080i	$0.0896979\pi$
$12$	−1.29418	+	1.15113i	−0.373598	+	0.332302i
$13$	−2.40545	−	4.16635i	−0.667151	−	1.15554i	−0.978697	−	0.205308i	$-0.934180\pi$
$13$	−2.40545	−	4.16635i	−0.667151	−	1.15554i	0.311547	−	0.950231i	$-0.399153\pi$
$14$		0			0
$15$	2.05563	−	1.82841i	0.530762	−	0.472093i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−5.39926			−1.30951			−0.654756	−	0.755840i	$-0.727229\pi$
$17$	−5.39926			−1.30951			−0.654756	+	0.755840i	$0.727229\pi$
$18$	−0.349814	+	2.97954i	−0.0824520	+	0.702283i
$19$	−7.09888			−1.62860			−0.814298	−	0.580447i	$-0.802878\pi$
$19$	−7.09888			−1.62860			−0.814298	+	0.580447i	$0.802878\pi$
$20$	0.794182	−	1.37556i	0.177584	−	0.307585i
$21$		0			0
$22$	−0.794182	−	1.37556i	−0.169320	−	0.293271i
$23$	−0.150186	−	0.260130i	−0.0313159	−	0.0542408i	0.849943	−	0.526875i	$-0.176636\pi$
$23$	−0.150186	−	0.260130i	−0.0313159	−	0.0542408i	−0.881259	+	0.472634i	$0.843303\pi$
$24$	0.349814	+	1.69636i	0.0714055	+	0.346268i
$25$	1.23855	−	2.14523i	0.247710	−	0.429046i
$26$	−4.81089			−0.943494
$27$	2.97710	+	4.25874i	0.572943	+	0.819595i
$28$		0			0
$29$	4.13781	−	7.16689i	0.768371	−	1.33086i	−0.170074	−	0.985431i	$-0.554401\pi$
$29$	4.13781	−	7.16689i	0.768371	−	1.33086i	0.938446	−	0.345427i	$-0.112266\pi$
$30$	−0.555632	−	2.69443i	−0.101444	−	0.491934i
$31$	−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
$33$	−2.61126	−	0.866025i	−0.454563	−	0.150756i
$34$	−2.69963	+	4.67589i	−0.462982	+	0.801909i
$35$		0			0
$36$	2.40545	+	1.79272i	0.400908	+	0.298786i
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−3.54944	+	6.14781i	−0.575796	+	0.997307i
$39$	−6.22617	+	5.53795i	−0.996985	+	0.886781i
$40$	−0.794182	−	1.37556i	−0.125571	−	0.217496i
$41$	−2.93818	−	5.08907i	−0.458866	−	0.794780i	0.540035	−	0.841643i	$-0.318411\pi$
$41$	−2.93818	−	5.08907i	−0.458866	−	0.794780i	−0.998901	+	0.0468628i	$0.985078\pi$
$42$		0			0
$43$	−0.833104	+	1.44298i	−0.127047	+	0.220052i	−0.922531	−	0.385922i	$-0.873883\pi$
$43$	−0.833104	+	1.44298i	−0.127047	+	0.220052i	0.795484	+	0.605974i	$0.207217\pi$
$44$	−1.58836			−0.239455
$45$	−3.82072	−	2.84748i	−0.569560	−	0.424478i
$46$	−0.300372			−0.0442874
$47$	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
$51$	1.88874	+	9.15907i	0.264476	+	1.28253i
$52$	−2.40545	+	4.16635i	−0.333575	+	0.577769i
$53$	−4.88874			−0.671520			−0.335760	−	0.941948i	$-0.608993\pi$
$53$	−4.88874			−0.671520			−0.335760	+	0.941948i	$0.608993\pi$
$54$	5.17673	−	0.448873i	0.704463	−	0.0610839i
$55$	2.52290			0.340188
$56$		0			0
$57$	2.48329	+	12.0422i	0.328920	+	1.59503i
$58$	−4.13781	−	7.16689i	−0.543321	−	0.941059i
$59$	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	$0.694794\pi$
$60$	−2.61126	−	0.866025i	−0.337113	−	0.111803i
$61$	−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
$66$	−2.05563	+	1.82841i	−0.253031	+	0.225062i
$67$	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	$0.622857\pi$
$68$	2.69963	+	4.67589i	0.327378	+	0.567035i
$69$	−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	$0.227718\pi$
$72$	2.75526	−	1.18682i	0.324711	−	0.139868i
$73$	16.0531			1.87887			0.939436	−	0.342725i	$-0.111350\pi$
$73$	16.0531			1.87887			0.939436	+	0.342725i	$0.111350\pi$
$74$	−0.500000	+	0.866025i	−0.0581238	+	0.100673i
$75$	−4.07234	−	1.35059i	−0.470234	−	0.155953i
$76$	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	$0.323062\pi$
$80$	−1.58836			−0.177584
$81$	6.18292	−	6.53999i	0.686991	−	0.726666i
$82$	−5.87636			−0.648935
$83$	−1.18292	+	2.04887i	−0.129842	+	0.224893i	−0.923615	−	0.383321i	$-0.874780\pi$
$83$	−1.18292	+	2.04887i	−0.129842	+	0.224893i	0.793773	+	0.608214i	$0.208114\pi$
$84$		0			0
$85$	−4.28799	−	7.42702i	−0.465098	−	0.805573i
$86$	0.833104	+	1.44298i	0.0898359	+	0.155600i
$87$	−13.6051	−	4.51212i	−1.45862	−	0.483750i
$88$	−0.794182	+	1.37556i	−0.0846601	+	0.146636i
$89$	3.21015			0.340275			0.170138	−	0.985420i	$-0.445579\pi$
$89$	3.21015			0.340275			0.170138	+	0.985420i	$0.445579\pi$
$90$	−4.37636	+	1.88510i	−0.461308	+	0.198707i
$91$		0			0
$92$	−0.150186	+	0.260130i	−0.0156580	+	0.0271204i
$93$	−3.50983	+	3.12186i	−0.363953	+	0.323722i
$94$	−1.33310	−	2.30900i	−0.137499	−	0.238156i
$95$	−5.63781	−	9.76497i	−0.578427	−	1.00186i
$96$	1.29418	−	1.15113i	0.132087	−	0.117486i
$97$	−0.712008	+	1.23323i	−0.0722934	+	0.125216i	−0.899906	−	0.436084i	$-0.856365\pi$
$97$	−0.712008	+	1.23323i	−0.0722934	+	0.125216i	0.827613	+	0.561300i	$0.189698\pi$
$98$		0			0
$99$	−0.555632	+	4.73259i	−0.0558431	+	0.475643i
$100$	−2.47710			−0.247710
$101$	6.01671	−	10.4212i	0.598685	−	1.03695i	−0.394330	−	0.918969i	$-0.629023\pi$
$101$	6.01671	−	10.4212i	0.598685	−	1.03695i	0.993015	−	0.117984i	$-0.0376432\pi$
$102$	8.87636	+	2.94384i	0.878890	+	0.291484i
$103$	−3.04944	−	5.28179i	−0.300470	−	0.520430i	0.675772	−	0.737111i	$-0.263810\pi$
$103$	−3.04944	−	5.28179i	−0.300470	−	0.520430i	−0.976243	+	0.216680i	$0.930477\pi$
$104$	2.40545	+	4.16635i	0.235873	+	0.408545i
$105$		0			0
$106$	−2.44437	+	4.23377i	−0.237418	+	0.411220i
$107$	3.08650			0.298384			0.149192	−	0.988808i	$-0.452333\pi$
$107$	3.08650			0.298384			0.149192	+	0.988808i	$0.452333\pi$
$108$	2.19963	−	4.70761i	0.211659	−	0.452990i
$109$	−2.28799			−0.219150			−0.109575	−	0.993979i	$-0.534949\pi$
$109$	−2.28799			−0.219150			−0.109575	+	0.993979i	$0.534949\pi$
$110$	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	−0.806104	−	0.591774i	$-0.798428\pi$
$113$	−9.73236	−	16.8569i	−0.915543	−	1.58577i	−0.109440	−	0.993993i	$-0.534906\pi$
$114$	11.6705	+	3.87053i	1.09305	+	0.362509i
$115$	0.238550	−	0.413181i	0.0222449	−	0.0385293i
$116$	−8.27561			−0.768371
$117$	11.5723	+	8.62456i	1.06986	+	0.797341i
$118$	6.47710			0.596265
$119$		0			0
$120$	−2.05563	+	1.82841i	−0.187653	+	0.166910i
$121$	4.23855	+	7.34138i	0.385323	+	0.667399i
$122$	2.23855	+	3.87728i	0.202669	+	0.351033i
$123$	−7.60507	+	6.76443i	−0.685726	+	0.609928i
$124$	−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
$129$	2.73924	+	0.908468i	0.241177	+	0.0799862i
$130$	−3.82072	−	6.61769i	−0.335100	−	0.580410i
$131$	−1.58836	−	2.75113i	−0.138776	−	0.240367i	0.788258	−	0.615345i	$-0.210983\pi$
$131$	−1.58836	−	2.75113i	−0.138776	−	0.240367i	−0.927034	+	0.374978i	$0.877650\pi$
$132$	0.555632	+	2.69443i	0.0483616	+	0.234520i
$133$		0			0
$134$	10.0531			0.868454
$135$	−3.49381	+	7.47741i	−0.300699	+	0.643553i
$136$	5.39926			0.462982
$137$	10.6316	−	18.4145i	0.908320	−	1.57326i	0.0919231	−	0.995766i	$-0.470699\pi$
$137$	10.6316	−	18.4145i	0.908320	−	1.57326i	0.816397	−	0.577491i	$-0.195968\pi$
$138$	0.105074	+	0.509538i	0.00894452	+	0.0433748i
$139$	−6.52654	−	11.3043i	−0.553574	−	0.958818i	−0.998013	−	0.0630092i	$-0.979930\pi$
$139$	−6.52654	−	11.3043i	−0.553574	−	0.958818i	0.444439	−	0.895809i	$-0.353403\pi$
$140$		0			0
$141$	−4.38323	−	1.45370i	−0.369135	−	0.122424i
$142$	6.36033	−	11.0164i	0.533747	−	0.924478i
$143$	−7.64145			−0.639010
$144$	0.349814	−	2.97954i	0.0291512	−	0.248295i
$145$	13.1447			1.09161
$146$	8.02654	−	13.9024i	0.664281	−	1.15057i
$147$		0			0
$148$	0.500000	+	0.866025i	0.0410997	+	0.0711868i
$149$	−2.60439	−	4.51093i	−0.213360	−	0.369550i	0.739404	−	0.673262i	$-0.235107\pi$
$149$	−2.60439	−	4.51093i	−0.213360	−	0.369550i	−0.952764	+	0.303712i	$0.901774\pi$
$150$	−3.20582	+	2.85146i	−0.261754	+	0.232820i
$151$	0.261450	−	0.452845i	0.0212765	−	0.0368520i	−0.855191	−	0.518313i	$-0.826560\pi$
$151$	0.261450	−	0.452845i	0.0212765	−	0.0368520i	0.876468	+	0.481461i	$0.159894\pi$
$152$	7.09888			0.575796
$153$	14.8764	−	6.40794i	1.20268	−	0.518052i
$154$		0			0
$155$	2.15383	−	3.73054i	0.173000	−	0.299644i
$156$	7.90909	+	2.62305i	0.633234	+	0.210012i
$157$	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
$159$	1.71015	+	8.29305i	0.135624	+	0.657681i
$160$	−0.794182	+	1.37556i	−0.0627856	+	0.108748i
$161$		0			0
$162$	−2.57234	−	8.62456i	−0.202102	−	0.677610i
$163$	−21.9629			−1.72026			−0.860132	−	0.510071i	$-0.829619\pi$
$163$	−21.9629			−1.72026			−0.860132	+	0.510071i	$0.829619\pi$
$164$	−2.93818	+	5.08907i	−0.229433	+	0.397390i
$165$	−0.882546	−	4.27974i	−0.0687061	−	0.333177i
$166$	1.18292	+	2.04887i	0.0918122	+	0.159023i
$167$	−1.65019	−	2.85821i	−0.127695	−	0.221175i	0.795088	−	0.606494i	$-0.207425\pi$
$167$	−1.65019	−	2.85821i	−0.127695	−	0.221175i	−0.922783	+	0.385319i	$0.874091\pi$
$168$		0			0
$169$	−5.07234	+	8.78555i	−0.390180	+	0.675812i
$170$	−8.57598			−0.657748
$171$	19.5593	−	8.42510i	1.49574	−	0.644283i
$172$	1.66621			0.127047
$173$	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
$177$	8.38255	−	7.45596i	0.630071	−	0.560425i
$178$	1.60507	−	2.78007i	0.120305	−	0.208375i
$179$	16.0741			1.20144			0.600718	−	0.799461i	$-0.294881\pi$
$179$	16.0741			1.20144			0.600718	+	0.799461i	$0.294881\pi$
$180$	−0.555632	+	4.73259i	−0.0414144	+	0.352746i
$181$	−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
$184$	0.150186	+	0.260130i	0.0110719	+	0.0191770i
$185$	−0.794182	−	1.37556i	−0.0583894	−	0.101133i
$186$	0.948699	+	4.60054i	0.0695620	+	0.337328i
$187$	−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	$-0.167254\pi$
$192$	−0.349814	−	1.69636i	−0.0252457	−	0.122424i
$193$	−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	$0.947646\pi$
$194$	0.712008	+	1.23323i	0.0511192	+	0.0885410i
$195$	−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	$0.725189\pi$
$198$	3.82072	+	2.84748i	0.271527	+	0.202362i
$199$	18.0989			1.28300			0.641498	−	0.767125i	$-0.278313\pi$
$199$	18.0989			1.28300			0.641498	+	0.767125i	$0.278313\pi$
$200$	−1.23855	+	2.14523i	−0.0875787	+	0.151691i
$201$	13.0105	−	11.5724i	0.917691	−	0.816252i
$202$	−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
$206$	−6.09888			−0.424929
$207$	0.722528	+	0.538481i	0.0502192	+	0.0374270i
$208$	4.81089			0.333575
$209$	−5.63781	+	9.76497i	−0.389975	+	0.675457i
$210$		0			0
$211$	0.166208	+	0.287880i	0.0114422	+	0.0198185i	0.871690	−	0.490058i	$-0.163024\pi$
$211$	0.166208	+	0.287880i	0.0114422	+	0.0198185i	−0.860248	+	0.509877i	$0.829691\pi$
$212$	2.44437	+	4.23377i	0.167880	+	0.290776i
$213$	−4.44987	−	21.5788i	−0.304900	−	1.47856i
$214$	1.54325	−	2.67299i	0.105495	−	0.182722i
$215$	−2.64654			−0.180493
$216$	−2.97710	−	4.25874i	−0.202566	−	0.289771i
$217$		0			0
$218$	−1.14400	+	1.98146i	−0.0774812	+	0.134201i
$219$	−5.61559	−	27.2318i	−0.379467	−	1.84015i
$220$	−1.26145	−	2.18490i	−0.0850469	−	0.147306i
$221$	12.9876	+	22.4952i	0.873642	+	1.51319i
$222$	1.64400	+	0.545231i	0.110338	+	0.0365935i
$223$	−3.16621	+	5.48403i	−0.212025	+	0.367238i	−0.952348	−	0.305013i	$-0.901339\pi$
$223$	−3.16621	+	5.48403i	−0.212025	+	0.367238i	0.740323	+	0.672251i	$0.234672\pi$
$224$		0			0
$225$	−0.866524	+	7.38061i	−0.0577683	+	0.492040i
$226$	−19.4647			−1.29477
$227$	−11.6545	+	20.1862i	−0.773537	+	1.33981i	0.162075	+	0.986778i	$0.448181\pi$
$227$	−11.6545	+	20.1862i	−0.773537	+	1.33981i	−0.935613	+	0.353028i	$0.885152\pi$
$228$	9.18725	−	8.17172i	0.608440	−	0.541185i
$229$	−2.47710	−	4.29046i	−0.163691	−	0.283522i	0.772498	−	0.635017i	$-0.219007\pi$
$229$	−2.47710	−	4.29046i	−0.163691	−	0.283522i	−0.936190	+	0.351495i	$0.885673\pi$
$230$	−0.238550	−	0.413181i	−0.0157295	−	0.0272443i
$231$		0			0
$232$	−4.13781	+	7.16689i	−0.271660	+	0.470529i
$233$	14.2756			0.935226			0.467613	−	0.883933i	$-0.345114\pi$
$233$	14.2756			0.935226			0.467613	+	0.883933i	$0.345114\pi$
$234$	13.2553	−	5.70966i	0.866523	−	0.373252i
$235$	4.23491			0.276255
$236$	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	0.935196	−	0.354132i	$-0.115224\pi$
$239$	2.48762	+	4.30868i	0.160911	+	0.278706i	−0.774285	+	0.632837i	$0.781890\pi$
$240$	0.555632	+	2.69443i	0.0358659	+	0.173925i
$241$	−6.50000	+	11.2583i	−0.418702	+	0.725213i	−0.995809	−	0.0914555i	$-0.970848\pi$
$241$	−6.50000	+	11.2583i	−0.418702	+	0.725213i	0.577107	+	0.816668i	$0.304181\pi$
$242$	8.47710			0.544929
$243$	−13.2570	−	8.20066i	−0.850440	−	0.526073i
$244$	4.47710			0.286617
$245$		0			0
$246$	2.05563	+	9.96840i	0.131062	+	0.635562i
$247$	17.0760	+	29.5765i	1.08652	+	1.88191i
$248$	1.35600	+	2.34867i	0.0861063	+	0.149141i
$249$	3.88942	+	1.28993i	0.246482	+	0.0817458i
$250$	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
$255$	−11.0989	+	9.87205i	−0.695039	+	0.618211i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.493810	−	0.855304i	−0.0308030	−	0.0533524i	0.850213	−	0.526439i	$-0.176473\pi$
$257$	−0.493810	−	0.855304i	−0.0308030	−	0.0533524i	−0.881016	+	0.473087i	$0.843140\pi$
$258$	2.15638	−	1.91802i	0.134250	−	0.119410i
$259$		0			0
$260$	−7.64145			−0.473902
$261$	−2.89493	+	24.6575i	−0.179191	+	1.52626i
$262$	−3.17673			−0.196259
$263$	−8.59269	+	14.8830i	−0.529848	+	0.917724i	0.469545	+	0.882908i	$0.344418\pi$
$263$	−8.59269	+	14.8830i	−0.529848	+	0.917724i	−0.999394	+	0.0348158i	$0.988916\pi$
$264$	2.61126	+	0.866025i	0.160712	+	0.0533002i
$265$	−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
$269$	22.9047			1.39652			0.698262	−	0.715843i	$-0.253957\pi$
$269$	22.9047			1.39652			0.698262	+	0.715843i	$0.253957\pi$
$270$	4.72872	+	6.76443i	0.287781	+	0.411670i
$271$	14.0073			0.850882			0.425441	−	0.904986i	$-0.360119\pi$
$271$	14.0073			0.850882			0.425441	+	0.904986i	$0.360119\pi$
$272$	2.69963	−	4.67589i	0.163689	−	0.283518i
$273$		0			0
$274$	−10.6316	−	18.4145i	−0.642279	−	1.11246i
$275$	−1.96727	−	3.40741i	−0.118631	−	0.205474i
$276$	0.493810	+	0.163772i	0.0297239	+	0.00985792i
$277$	−14.1476	+	24.5044i	−0.850049	+	1.47233i	0.0311139	+	0.999516i	$0.490095\pi$
$277$	−14.1476	+	24.5044i	−0.850049	+	1.47233i	−0.881163	+	0.472813i	$0.843239\pi$
$278$	−13.0531			−0.782872
$279$	6.52359	+	4.86186i	0.390557	+	0.291072i
$280$		0			0
$281$	−8.79782	+	15.2383i	−0.524834	+	0.909039i	0.474748	+	0.880122i	$0.342539\pi$
$281$	−8.79782	+	15.2383i	−0.524834	+	0.909039i	−0.999582	+	0.0289175i	$0.990794\pi$
$282$	−3.45056	+	3.06914i	−0.205478	+	0.182765i
$283$	−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
$285$	−14.5927	+	12.9797i	−0.864397	+	0.768849i
$286$	−3.82072	+	6.61769i	−0.225924	+	0.391312i
$287$		0			0
$288$	−2.40545	−	1.79272i	−0.141742	−	0.105637i
$289$	12.1520			0.714822
$290$	6.57234	−	11.3836i	0.385941	−	0.668470i
$291$	2.34108	+	0.776418i	0.137236	+	0.0455144i
$292$	−8.02654	−	13.9024i	−0.469718	−	0.813575i
$293$	7.04256	+	12.1981i	0.411431	+	0.712619i	0.995046	−	0.0994108i	$-0.0316958\pi$
$293$	7.04256	+	12.1981i	0.411431	+	0.712619i	−0.583616	+	0.812030i	$0.698362\pi$
$294$		0			0
$295$	−5.14400	+	8.90966i	−0.299495	+	0.518741i
$296$	1.00000			0.0581238
$297$	8.22253	−	0.712974i	0.477119	−	0.0413710i
$298$	−5.20877			−0.301736
$299$	−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
$303$	−19.7829	−	6.56099i	−1.13650	−	0.376919i
$304$	3.54944	−	6.14781i	0.203574	−	0.352601i
$305$	−7.11126			−0.407190
$306$	1.88874	−	16.0873i	0.107972	−	0.919648i
$307$	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
$310$	−2.15383	−	3.73054i	−0.122329	−	0.211880i
$311$	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	$0.826015\pi$
$312$	6.22617	−	5.53795i	0.352487	−	0.313525i
$313$	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	$0.277943\pi$
$318$	8.03706	+	2.66549i	0.450696	+	0.149473i
$319$	−6.57234	−	11.3836i	−0.367981	−	0.637361i
$320$	0.794182	+	1.37556i	0.0443961	+	0.0768963i
$321$	−1.07970	−	5.23582i	−0.0602631	−	0.292235i
$322$		0			0
$323$	38.3287			2.13267
$324$	−8.75526	−	2.08457i	−0.486403	−	0.115809i
$325$	−11.9171			−0.661040
$326$	−10.9814	+	19.0204i	−0.608205	+	1.05344i
$327$	0.800372	+	3.88125i	0.0442607	+	0.214634i
$328$	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	$0.0249876\pi$
$332$	2.36584			0.129842
$333$	2.75526	−	1.18682i	0.150987	−	0.0650373i
$334$	−3.30037			−0.180588
$335$	−7.98398	+	13.8287i	−0.436211	+	0.755540i
$336$		0			0
$337$	−4.21201	−	7.29541i	−0.229443	−	0.397406i	0.728200	−	0.685364i	$-0.240357\pi$
$337$	−4.21201	−	7.29541i	−0.229443	−	0.397406i	−0.957643	+	0.287958i	$0.907024\pi$
$338$	5.07234	+	8.78555i	0.275899	+	0.477871i
$339$	−25.1909	+	22.4064i	−1.36818	+	1.21695i
$340$	−4.28799	+	7.42702i	−0.232549	+	0.402787i
$341$	−4.30766			−0.233273
$342$	2.48329	−	21.1514i	0.134281	−	1.14374i
$343$		0			0
$344$	0.833104	−	1.44298i	0.0449179	−	0.0778002i
$345$	−0.784350	−	0.260130i	−0.0422280	−	0.0140049i
$346$	−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	$0.838181\pi$
$348$	2.89493	+	14.0384i	0.155184	+	0.752537i
$349$	0.00364189	−	0.00630794i	0.000194946	−	0.000337656i	−0.865928	−	0.500169i	$-0.833271\pi$
$349$	0.00364189	−	0.00630794i	0.000194946	−	0.000337656i	0.866123	+	0.499831i	$0.166605\pi$
$350$		0			0
$351$	10.5822	−	22.6478i	0.564835	−	1.20885i
$352$	1.58836			0.0846601
$353$	3.32691	−	5.76238i	0.177074	−	0.306701i	−0.763803	−	0.645449i	$-0.776670\pi$
$353$	3.32691	−	5.76238i	0.177074	−	0.306701i	0.940877	+	0.338748i	$0.110004\pi$
$354$	−2.26578	−	10.9875i	−0.120425	−	0.583978i
$355$	10.1025	+	17.4981i	0.536186	+	0.928702i
$356$	−1.60507	−	2.78007i	−0.0850688	−	0.147343i
$357$		0			0
$358$	8.03706	−	13.9206i	0.424772	−	0.735727i
$359$	0.797135			0.0420712			0.0210356	−	0.999779i	$-0.493304\pi$
$359$	0.797135			0.0420712			0.0210356	+	0.999779i	$0.493304\pi$
$360$	3.82072	+	2.84748i	0.201370	+	0.150076i
$361$	31.3942			1.65232
$362$	−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
$366$	5.79418	−	5.15371i	0.302867	−	0.269389i
$367$	−7.71634	+	13.3651i	−0.402790	+	0.697652i	−0.994061	−	0.108820i	$-0.965293\pi$
$367$	−7.71634	+	13.3651i	−0.402790	+	0.697652i	0.591272	+	0.806472i	$0.298626\pi$
$368$	0.300372			0.0156580
$369$	14.1353	+	10.5346i	0.735852	+	0.548411i
$370$	−1.58836			−0.0825751
$371$		0			0
$372$	4.45853	+	1.47867i	0.231164	+	0.0766655i
$373$	−5.12110	−	8.87000i	−0.265160	−	0.459271i	0.702445	−	0.711738i	$-0.252092\pi$
$373$	−5.12110	−	8.87000i	−0.265160	−	0.459271i	−0.967606	+	0.252467i	$0.918758\pi$
$374$	4.28799	+	7.42702i	0.221727	+	0.384042i
$375$	−4.15452	−	20.1466i	−0.214538	−	1.04036i
$376$	−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
$381$	4.70149	+	22.7990i	0.240864	+	1.16803i
$382$	−11.9814	−	20.7524i	−0.613023	−	1.06179i
$383$	−3.13348	−	5.42734i	−0.160113	−	0.277324i	0.774796	−	0.632211i	$-0.217853\pi$
$383$	−3.13348	−	5.42734i	−0.160113	−	0.277324i	−0.934909	+	0.354887i	$0.884519\pi$
$384$	−1.64400	−	0.545231i	−0.0838948	−	0.0278237i
$385$		0			0
$386$	−9.76509			−0.497030
$387$	0.582863	−	4.96452i	0.0296286	−	0.252361i
$388$	1.42402			0.0722934
$389$	10.8171	−	18.7357i	0.548448	−	0.949940i	−0.449933	−	0.893062i	$-0.648552\pi$
$389$	10.8171	−	18.7357i	0.548448	−	0.949940i	0.998381	−	0.0568774i	$-0.0181144\pi$
$390$	−9.88942	+	8.79628i	−0.500770	+	0.445417i
$391$	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
$395$	−13.3214			−0.670273
$396$	4.37636	−	1.88510i	0.219920	−	0.0947299i
$397$	4.10617			0.206083			0.103041	−	0.994677i	$-0.467143\pi$
$397$	4.10617			0.206083			0.103041	+	0.994677i	$0.467143\pi$
$398$	9.04944	−	15.6741i	0.453608	−	0.785671i
$399$		0			0
$400$	1.23855	+	2.14523i	0.0619275	+	0.107262i
$401$	−8.37085	−	14.4987i	−0.418021	−	0.724033i	0.577720	−	0.816235i	$-0.303943\pi$
$401$	−8.37085	−	14.4987i	−0.418021	−	0.724033i	−0.995740	+	0.0922024i	$0.970609\pi$
$402$	−3.51671	−	17.0536i	−0.175398	−	0.850558i
$403$	−6.52359	+	11.2992i	−0.324963	+	0.562853i
$404$	−12.0334			−0.598685
$405$	13.9065	+	3.31105i	0.691022	+	0.164527i
$406$		0			0
$407$	−0.794182	+	1.37556i	−0.0393661	+	0.0681842i
$408$	−1.88874	−	9.15907i	−0.0935064	−	0.453442i
$409$	−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
$411$	−34.9567	−	11.5934i	−1.72429	−	0.571859i
$412$	−3.04944	+	5.28179i	−0.150235	+	0.260215i
$413$		0			0
$414$	0.827603	−	0.356487i	0.0406744	−	0.0175204i
$415$	−3.75781			−0.184464
$416$	2.40545	−	4.16635i	0.117937	−	0.204272i
$417$	−16.8931	+	15.0258i	−0.827257	+	0.735814i
$418$	5.63781	+	9.76497i	0.275754	+	0.477620i
$419$	0.210149	+	0.363988i	0.0102664	+	0.0177820i	0.871113	−	0.491083i	$-0.163399\pi$
$419$	0.210149	+	0.363988i	0.0102664	+	0.0177820i	−0.860847	+	0.508865i	$0.830065\pi$
$420$		0			0
$421$	3.28799	−	5.69497i	0.160247	−	0.277556i	−0.774710	−	0.632316i	$-0.782104\pi$
$421$	3.28799	−	5.69497i	0.160247	−	0.277556i	0.934957	+	0.354761i	$0.115438\pi$
$422$	0.332415			0.0161817
$423$	−0.932677	+	7.94406i	−0.0453483	+	0.386253i
$424$	4.88874			0.237418
$425$	−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
$429$	2.67309	+	12.9626i	0.129058	+	0.625842i
$430$	−1.32327	+	2.29197i	−0.0638138	+	0.110529i
$431$	−22.0879			−1.06394			−0.531968	−	0.846765i	$-0.678547\pi$
$431$	−22.0879			−1.06394			−0.531968	+	0.846765i	$0.678547\pi$
$432$	−5.17673	+	0.448873i	−0.249065	+	0.0215964i
$433$	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
$436$	1.14400	+	1.98146i	0.0547875	+	0.0948947i
$437$	1.06615	+	1.84663i	0.0510010	+	0.0883363i
$438$	−26.3912	−	8.75264i	−1.26102	−	0.418217i
$439$	−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	$0.267035\pi$
$444$	1.29418	−	1.15113i	0.0614192	−	0.0546301i
$445$	2.54944	+	4.41576i	0.120855	+	0.209327i
$446$	3.16621	+	5.48403i	0.149924	+	0.259676i
$447$	−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	$0.575184\pi$
$450$	5.95853	+	4.44074i	0.280888	+	0.209338i
$451$	−9.33379			−0.439511
$452$	−9.73236	+	16.8569i	−0.457772	+	0.792884i
$453$	−0.859646	−	0.285101i	−0.0403897	−	0.0133952i
$454$	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	$-0.0277739\pi$
$458$	−4.95420			−0.231495
$459$	−16.0741	−	22.9940i	−0.750276	−	1.07327i
$460$	−0.477100			−0.0222449
$461$	−1.75526	+	3.04020i	−0.0817506	+	0.141596i	−0.904002	−	0.427528i	$-0.859384\pi$
$461$	−1.75526	+	3.04020i	−0.0817506	+	0.141596i	0.822251	+	0.569125i	$0.192718\pi$
$462$		0			0
$463$	8.69413	+	15.0587i	0.404050	+	0.699836i	0.994210	−	0.107451i	$-0.0342687\pi$
$463$	8.69413	+	15.0587i	0.404050	+	0.699836i	−0.590160	+	0.807286i	$0.700935\pi$
$464$	4.13781	+	7.16689i	0.192093	+	0.332715i
$465$	−7.08177	−	2.34867i	−0.328409	−	0.108917i
$466$	7.13781	−	12.3630i	0.330652	−	0.572707i
$467$	13.3979			0.619980			0.309990	−	0.950740i	$-0.399674\pi$
$467$	13.3979			0.619980			0.309990	+	0.950740i	$0.399674\pi$
$468$	1.68292	−	14.3342i	0.0777929	−	0.662600i
$469$		0			0
$470$	2.11745	−	3.66754i	0.0976709	−	0.169171i
$471$	11.4716	−	10.2036i	0.528583	−	0.470155i
$472$	−3.23855	−	5.60933i	−0.149066	−	0.258190i
$473$	1.32327	+	2.29197i	0.0608441	+	0.105385i
$474$	10.8541	−	9.65436i	0.498547	−	0.443439i
$475$	−8.79232	+	15.2287i	−0.403419	+	0.698743i
$476$		0			0
$477$	13.4697	−	5.80205i	0.616737	−	0.265658i
$478$	4.97524			0.227562
$479$	10.4029	−	18.0183i	0.475321	−	0.823279i	−0.524280	−	0.851546i	$-0.675665\pi$
$479$	10.4029	−	18.0183i	0.475321	−	0.823279i	0.999600	+	0.0282667i	$0.00899876\pi$
$480$	2.61126	+	0.866025i	0.119187	+	0.0395285i
$481$	2.40545	+	4.16635i	0.109679	+	0.189969i
$482$	6.50000	+	11.2583i	0.296067	+	0.512803i
$483$		0			0
$484$	4.23855	−	7.34138i	0.192661	−	0.333699i
$485$	−2.26186			−0.102706
$486$	−13.7305	+	7.38061i	−0.622828	+	0.334791i
$487$	−32.4944			−1.47246			−0.736231	−	0.676730i	$-0.763397\pi$
$487$	−32.4944			−1.47246			−0.736231	+	0.676730i	$0.763397\pi$
$488$	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	0.561394	−	0.827549i	$-0.310265\pi$
$491$	−9.66071	−	16.7328i	−0.435982	−	0.755142i	−0.997375	+	0.0724067i	$0.976932\pi$
$492$	9.66071	+	3.20397i	0.435538	+	0.144446i
$493$	−22.3411	+	38.6959i	−1.00619	+	1.74277i
$494$	34.1520			1.53657
$495$	−6.95125	+	2.99423i	−0.312435	+	0.134581i
$496$	2.71201			0.121773
$497$		0			0
$498$	3.06182	−	2.72338i	0.137204	−	0.122037i
$499$	5.57530	+	9.65670i	0.249585	+	0.432293i	0.963411	−	0.268030i	$-0.0863726\pi$
$499$	5.57530	+	9.65670i	0.249585	+	0.432293i	−0.713826	+	0.700323i	$0.753039\pi$
$500$	−5.93818	−	10.2852i	−0.265563	−	0.459969i
$501$	−4.27128	+	3.79915i	−0.190827	+	0.169733i
$502$	−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
$507$	16.6778	+	5.53120i	0.740688	+	0.245649i
$508$	6.71998	+	11.6393i	0.298151	+	0.516413i
$509$	0.722528	+	1.25146i	0.0320255	+	0.0554698i	0.881594	−	0.472009i	$-0.156471\pi$
$509$	0.722528	+	1.25146i	0.0320255	+	0.0554698i	−0.849568	+	0.527478i	$0.823138\pi$
$510$	3.00000	+	14.5479i	0.132842	+	0.644194i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−21.1341	−	30.2323i	−0.933093	−	1.33479i
$514$	−0.987620			−0.0435621
$515$	4.84362	−	8.38940i	0.213436	−	0.369681i
$516$	−0.582863	−	2.82648i	−0.0256591	−	0.124429i
$517$	−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
$521$	19.2843			0.844859			0.422430	−	0.906396i	$-0.361177\pi$
$521$	19.2843			0.844859			0.422430	+	0.906396i	$0.361177\pi$
$522$	19.9065	+	14.8358i	0.871286	+	0.649346i
$523$	−36.6908			−1.60438			−0.802189	−	0.597071i	$-0.796331\pi$
$523$	−36.6908			−1.60438			−0.802189	+	0.597071i	$0.796331\pi$
$524$	−1.58836	+	2.75113i	−0.0693880	+	0.120184i
$525$		0			0
$526$	8.59269	+	14.8830i	0.374659	+	0.648929i
$527$	7.32141	+	12.6811i	0.318926	+	0.552396i
$528$	2.05563	−	1.82841i	0.0894599	−	0.0795713i
$529$	11.4549	−	19.8404i	0.498039	−	0.862628i
$530$	−7.76509			−0.337294
$531$	−15.5803	−	11.6116i	−0.676128	−	0.503900i
$532$		0			0
$533$	−14.1353	+	24.4830i	−0.612266	+	1.06048i
$534$	−5.27747	−	1.75027i	−0.228379	−	0.0757417i
$535$	2.45125	+	4.24568i	0.105977	+	0.183557i
$536$	−5.02654	−	8.70623i	−0.217114	−	0.376052i
$537$	−5.62296	−	27.2675i	−0.242648	−	1.17668i
$538$	11.4523	−	19.8360i	0.493745	−	0.855192i
$539$		0			0
$540$	8.22253	−	0.712974i	0.353841	−	0.0306815i
$541$	3.25085			0.139765			0.0698825	−	0.997555i	$-0.477738\pi$
$541$	3.25085			0.139765			0.0698825	+	0.997555i	$0.477738\pi$
$542$	7.00364	−	12.1307i	0.300832	−	0.521057i
$543$	2.81708	+	13.6609i	0.120893	+	0.586246i
$544$	−2.69963	−	4.67589i	−0.115746	−	0.200477i
$545$	−1.81708	−	3.14728i	−0.0778352	−	0.134815i
$546$		0			0
$547$	−2.95853	+	5.12432i	−0.126498	+	0.219100i	−0.922317	−	0.386433i	$-0.873707\pi$
$547$	−2.95853	+	5.12432i	−0.126498	+	0.219100i	0.795820	+	0.605534i	$0.207040\pi$
$548$	−21.2632			−0.908320
$549$	1.56615	−	13.3397i	0.0668418	−	0.569324i
$550$	−3.93454			−0.167769
$551$	−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
$555$	−2.05563	+	1.82841i	−0.0872567	+	0.0776116i
$556$	−6.52654	+	11.3043i	−0.276787	+	0.479409i
$557$	−25.6080			−1.08505			−0.542523	−	0.840041i	$-0.682531\pi$
$557$	−25.6080			−1.08505			−0.542523	+	0.840041i	$0.682531\pi$
$558$	7.47229	−	3.21866i	0.316327	−	0.136257i
$559$	8.01594			0.339038
$560$		0			0
$561$	14.0989	+	4.67589i	0.595255	+	0.197416i
$562$	8.79782	+	15.2383i	0.371114	+	0.642788i
$563$	−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	$-0.607497\pi$
$564$	0.932677	+	4.52284i	0.0392728	+	0.190446i
$565$	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	$0.939782\pi$
$570$	3.94437	+	19.1275i	0.165211	+	0.801162i
$571$	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	$0.726954\pi$
$572$	3.82072	+	6.61769i	0.159752	+	0.276699i
$573$	−39.3948	−	13.0653i	−1.64574	−	0.545811i
$574$		0			0
$575$	−0.744051			−0.0310291
$576$	−2.75526	+	1.18682i	−0.114803	+	0.0494508i
$577$	13.9913			0.582467			0.291234	−	0.956652i	$-0.405934\pi$
$577$	13.9913			0.582467			0.291234	+	0.956652i	$0.405934\pi$
$578$	6.07598	−	10.5239i	0.252728	−	0.437737i
$579$	−12.6378	+	11.2409i	−0.525209	+	0.467154i
$580$	−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
$584$	−16.0531			−0.664281
$585$	−2.67309	+	22.7680i	−0.110519	+	0.941339i
$586$	14.0851			0.581851
$587$	−1.44801	+	2.50803i	−0.0597658	+	0.103517i	−0.894360	−	0.447348i	$-0.852369\pi$
$587$	−1.44801	+	2.50803i	−0.0597658	+	0.103517i	0.834594	+	0.550865i	$0.185702\pi$
$588$		0			0
$589$	9.62612	+	16.6729i	0.396637	+	0.686996i
$590$	5.14400	+	8.90966i	0.211775	+	0.366805i
$591$	6.38186	+	30.9476i	0.262515	+	1.27302i
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	−4.08788			−0.167869			−0.0839346	−	0.996471i	$-0.526749\pi$
$593$	−4.08788			−0.167869			−0.0839346	+	0.996471i	$0.526749\pi$
$594$	3.49381	−	7.47741i	0.143353	−	0.306802i
$595$		0			0
$596$	−2.60439	+	4.51093i	−0.106680	+	0.184775i
$597$	−6.33124	−	30.7022i	−0.259121	−	1.25656i
$598$	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	$0.701026\pi$
$600$	4.07234	+	1.35059i	0.166253	+	0.0551377i
$601$	13.4320	−	23.2649i	0.547902	−	0.948994i	−0.450516	−	0.892768i	$-0.648760\pi$
$601$	13.4320	−	23.2649i	0.547902	−	0.948994i	0.998418	−	0.0562261i	$-0.0179068\pi$
$602$		0			0
$603$	−24.1822	−	18.0223i	−0.984773	−	0.733926i
$604$	−0.522900			−0.0212765
$605$	−6.73236	+	11.6608i	−0.273709	+	0.474079i
$606$	−15.5734	+	13.8520i	−0.632628	+	0.562699i
$607$	−7.62110	−	13.2001i	−0.309331	−	0.535777i	0.668885	−	0.743366i	$-0.266772\pi$
$607$	−7.62110	−	13.2001i	−0.309331	−	0.535777i	−0.978216	+	0.207589i	$0.933438\pi$
$608$	−3.54944	−	6.14781i	−0.143949	−	0.249327i
$609$		0			0
$610$	−3.55563	+	6.15854i	−0.143963	+	0.249352i
$611$	−12.8268			−0.518918
$612$	−12.9876	−	9.67933i	−0.524993	−	0.391264i
$613$	2.72067			0.109887			0.0549434	−	0.998489i	$-0.482502\pi$
$613$	2.72067			0.109887			0.0549434	+	0.998489i	$0.482502\pi$
$614$	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	0.618629	−	0.785684i	$-0.287689\pi$
$617$	−9.21812	−	15.9663i	−0.371108	−	0.642777i	−0.989736	+	0.142906i	$0.954355\pi$
$618$	2.13348	+	10.3459i	0.0858210	+	0.416173i
$619$	0.0537728	−	0.0931373i	0.00216131	−	0.00374350i	−0.864943	−	0.501871i	$-0.832645\pi$
$619$	0.0537728	−	0.0931373i	0.00216131	−	0.00374350i	0.867104	+	0.498127i	$0.165979\pi$
$620$	−4.30766			−0.173000
$621$	0.660706	−	1.41403i	0.0265132	−	0.0567433i
$622$	0.810892			0.0325138
$623$		0			0
$624$	−1.68292	−	8.16100i	−0.0673706	−	0.326701i
$625$	3.23924	+	5.61053i	0.129570	+	0.224421i
$626$	−5.28799	−	9.15907i	−0.211351	−	0.366070i
$627$	18.5371	+	6.14781i	0.740299	+	0.245520i
$628$	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
$633$	0.430206	−	0.382652i	0.0170991	−	0.0152090i
$634$	6.09820	+	10.5624i	0.242190	+	0.419486i
$635$	−10.6738	−	18.4875i	−0.423576	−	0.733655i
$636$	6.32691	−	5.62755i	0.250878	−	0.223147i
$637$		0			0
$638$	−13.1447			−0.520403
$639$	−35.0488	+	15.0971i	−1.38651	+	0.597234i
$640$	1.58836			0.0627856
$641$	−8.65638	+	14.9933i	−0.341906	+	0.592199i	−0.984787	−	0.173767i	$-0.944406\pi$
$641$	−8.65638	+	14.9933i	−0.341906	+	0.592199i	0.642880	+	0.765967i	$0.277739\pi$
$642$	−5.07420	−	1.68286i	−0.200263	−	0.0664171i
$643$	−14.4821	−	25.0838i	−0.571119	−	0.989207i	−0.996451	−	0.0841700i	$-0.973176\pi$
$643$	−14.4821	−	25.0838i	−0.571119	−	0.989207i	0.425332	−	0.905037i	$-0.360157\pi$
$644$		0			0
$645$	0.925798	+	4.48949i	0.0364533	+	0.176773i
$646$	19.1643	−	33.1936i	0.754011	−	1.30599i
$647$	2.55632			0.100499			0.0502497	−	0.998737i	$-0.483998\pi$
$647$	2.55632			0.100499			0.0502497	+	0.998737i	$0.483998\pi$
$648$	−6.18292	+	6.53999i	−0.242888	+	0.256915i
$649$	10.2880			0.403839
$650$	−5.95853	+	10.3205i	−0.233713	+	0.404802i
$651$		0			0
$652$	10.9814	+	19.0204i	0.430066	+	0.744896i
$653$	−14.9883	−	25.9605i	−0.586538	−	1.01591i	−0.994682	−	0.102996i	$-0.967157\pi$
$653$	−14.9883	−	25.9605i	−0.586538	−	1.01591i	0.408144	−	0.912918i	$-0.366176\pi$
$654$	3.76145	+	1.24748i	0.147084	+	0.0487805i
$655$	2.52290	−	4.36979i	0.0985779	−	0.170742i
$656$	5.87636			0.229433
$657$	−44.2304	+	19.0521i	−1.72559	+	0.743294i
$658$		0			0
$659$	−7.63162	+	13.2183i	−0.297286	+	0.514914i	−0.975514	−	0.219937i	$-0.929415\pi$
$659$	−7.63162	+	13.2183i	−0.297286	+	0.514914i	0.678228	+	0.734851i	$0.262748\pi$
$660$	−3.26509	+	2.90418i	−0.127094	+	0.113045i
$661$	−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
$663$	33.6167	−	29.9008i	1.30556	−	1.16125i
$664$	1.18292	−	2.04887i	0.0459061	−	0.0795117i
$665$		0			0
$666$	0.349814	−	2.97954i	0.0135550	−	0.115455i
$667$	−2.48576			−0.0962491
$668$	−1.65019	+	2.85821i	−0.0638476	+	0.110587i
$669$	10.4105	+	3.45263i	0.402492	+	0.133486i
$670$	7.98398	+	13.8287i	0.308448	+	0.534248i
$671$	3.55563	+	6.15854i	0.137264	+	0.237748i
$672$		0			0
$673$	23.2280	−	40.2320i	0.895372	−	1.55083i	0.0620280	−	0.998074i	$-0.480243\pi$
$673$	23.2280	−	40.2320i	0.895372	−	1.55083i	0.833344	−	0.552755i	$-0.186423\pi$
$674$	−8.42402			−0.324481
$675$	12.8233	−	1.11190i	0.493568	−	0.0427972i
$676$	10.1447			0.390180
$677$	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
$681$	38.3200	+	12.7088i	1.46842	+	0.487003i
$682$	−2.15383	+	3.73054i	−0.0824743	+	0.142850i
$683$	15.5439			0.594772			0.297386	−	0.954757i	$-0.403885\pi$
$683$	15.5439			0.594772			0.297386	+	0.954757i	$0.403885\pi$
$684$	−17.0760	−	12.7263i	−0.652917	−	0.486601i
$685$	33.7738			1.29043
$686$		0			0
$687$	−6.41164	+	5.70291i	−0.244619	+	0.217580i
$688$	−0.833104	−	1.44298i	−0.0317618	−	0.0550130i
$689$	11.7596	+	20.3682i	0.448005	+	0.775967i
$690$	−0.617454	+	0.549202i	−0.0235061	+	0.0209078i
$691$	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
$696$	13.6051	+	4.51212i	0.515699	+	0.171032i
$697$	15.8640	+	27.4772i	0.600891	+	1.04077i
$698$	−0.00364189	−	0.00630794i	−0.000137848	−	0.000238759i
$699$	−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	$0.830801\pi$
$702$	−14.3225	−	20.4883i	−0.540568	−	0.773283i
$703$	7.09888			0.267739
$704$	0.794182	−	1.37556i	0.0299319	−	0.0518435i
$705$	−1.48143	−	7.18392i	−0.0557939	−	0.270562i
$706$	−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	$0.276427\pi$
$710$	20.2051			0.758282
$711$	2.93385	−	24.9890i	0.110028	−	0.937160i
$712$	−3.21015			−0.120305
$713$	−0.407305	+	0.705474i	−0.0152537	+	0.0264202i
$714$		0			0
$715$	−6.06870	−	10.5113i	−0.226957	−	0.393100i
$716$	−8.03706	−	13.9206i	−0.300359	−	0.520237i
$717$	6.43887	−	5.72713i	0.240464	−	0.213884i
$718$	0.398568	−	0.690339i	0.0148744	−	0.0257632i
$719$	36.8777			1.37531			0.687654	−	0.726039i	$-0.258641\pi$
$719$	36.8777			1.37531			0.687654	+	0.726039i	$0.258641\pi$
$720$	4.37636	−	1.88510i	0.163097	−	0.0702536i
$721$		0			0
$722$	15.6971	−	27.1881i	0.584185	−	1.01184i
$723$	21.3719	+	7.08800i	0.794831	+	0.263606i
$724$	4.02654	+	6.97418i	0.149645	+	0.259193i
$725$	−10.2498	−	17.7531i	−0.380666	−	0.659334i
$726$	−2.96541	−	14.3802i	−0.110057	−	0.533699i
$727$	−15.2429	+	26.4014i	−0.565327	+	0.979175i	0.431692	+	0.902021i	$0.357917\pi$
$727$	−15.2429	+	26.4014i	−0.565327	+	0.979175i	−0.997019	+	0.0771543i	$0.975417\pi$
$728$		0			0
$729$	−9.27375	+	25.3574i	−0.343472	+	0.939163i
$730$	25.4981			0.943729
$731$	4.49814	−	7.79101i	0.166370	−	0.288161i
$732$	−1.56615	−	7.59476i	−0.0578867	−	0.280711i
$733$	3.07530	+	5.32657i	0.113589	+	0.196741i	0.917215	−	0.398393i	$-0.130432\pi$
$733$	3.07530	+	5.32657i	0.113589	+	0.196741i	−0.803626	+	0.595135i	$0.797099\pi$
$734$	7.71634	+	13.3651i	0.284815	+	0.493314i
$735$		0			0
$736$	0.150186	−	0.260130i	0.00553593	−	0.00958851i
$737$	15.9680			0.588187
$738$	16.1909	−	6.97418i	0.595995	−	0.256723i
$739$	40.7824			1.50021			0.750103	−	0.661321i	$-0.230004\pi$
$739$	40.7824			1.50021			0.750103	+	0.661321i	$0.230004\pi$
$740$	−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	0.967845	−	0.251547i	$-0.0809394\pi$
$743$	7.25271	+	12.5621i	0.266076	+	0.460858i	−0.701769	+	0.712405i	$0.747606\pi$
$744$	3.50983	−	3.12186i	0.128677	−	0.114453i
$745$	4.13671	−	7.16500i	0.151557	−	0.262505i
$746$	−10.2422			−0.374993
$747$	0.827603	−	7.04909i	0.0302804	−	0.257913i
$748$	8.57598			0.313569
$749$		0			0
$750$	−19.5247	−	6.47536i	−0.712941	−	0.236447i
$751$	−2.09455	−	3.62787i	−0.0764314	−	0.132383i	0.825276	−	0.564729i	$-0.191019\pi$
$751$	−2.09455	−	3.62787i	−0.0764314	−	0.132383i	−0.901708	+	0.432346i	$0.857686\pi$
$752$	1.33310	+	2.30900i	0.0486133	+	0.0842007i
$753$	0.850985	+	4.12669i	0.0310116	+	0.150385i
$754$	−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
$759$	0.166896	+	0.809332i	0.00605795	+	0.0293769i
$760$	5.63781	+	9.76497i	0.204505	+	0.354213i
$761$	1.81708	+	3.14728i	0.0658692	+	0.114089i	0.897079	−	0.441870i	$-0.145685\pi$
$761$	1.81708	+	3.14728i	0.0658692	+	0.114089i	−0.831210	+	0.555959i	$0.812351\pi$
$762$	22.0952	+	7.32788i	0.800426	+	0.265461i
$763$		0			0
$764$	−23.9629			−0.866946
$765$	20.6291	+	15.3743i	0.745846	+	0.555859i
$766$	−6.26695			−0.226434
$767$	15.5803	−	26.9859i	0.562573	−	0.974404i
$768$	−1.29418	+	1.15113i	−0.0466998	+	0.0415377i
$769$	19.9672	+	34.5842i	0.720035	+	1.24714i	0.960985	+	0.276600i	$0.0892078\pi$
$769$	19.9672	+	34.5842i	0.720035	+	1.24714i	−0.240950	+	0.970538i	$0.577459\pi$
$770$		0			0
$771$	−1.27816	+	1.13688i	−0.0460318	+	0.0409436i
$772$	−4.88255	+	8.45682i	−0.175727	+	0.304368i
$773$	36.1396			1.29985			0.649925	−	0.759998i	$-0.274800\pi$
$773$	36.1396			1.29985			0.649925	+	0.759998i	$0.274800\pi$
$774$	−4.00797	−	2.98704i	−0.144064	−	0.107367i
$775$	−6.71791			−0.241315
$776$	0.712008	−	1.23323i	0.0255596	−	0.0442705i
$777$		0			0
$778$	−10.8171	−	18.7357i	−0.387811	−	0.671709i
$779$	20.8578	+	36.1267i	0.747308	+	1.29438i
$780$	2.67309	+	12.9626i	0.0957118	+	0.464137i
$781$	10.1025	−	17.4981i	0.361497	−	0.626131i
$782$	1.62178			0.0579949
$783$	42.8406	−	3.71470i	1.53100	−	0.132753i
$784$		0			0
$785$	−7.03961	+	12.1930i	−0.251254	+	0.435186i
$786$	1.11126	+	5.38887i	0.0396375	+	0.192215i
$787$	−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
$789$	28.2527	+	9.37001i	1.00582	+	0.333581i
$790$	−6.66071	+	11.5367i	−0.236977	+	0.410457i
$791$		0			0
$792$	0.555632	−	4.73259i	0.0197435	−	0.168165i
$793$	21.5388			0.764867
$794$	2.05308	−	3.55605i	0.0728612	−	0.126199i
$795$	−10.0494	+	8.93861i	−0.356417	+	0.317020i
$796$	−9.04944	−	15.6741i	−0.320749	−	0.555554i
$797$	−26.2836	−	45.5245i	−0.931012	−	1.61256i	−0.781595	−	0.623786i	$-0.785593\pi$
$797$	−26.2836	−	45.5245i	−0.931012	−	1.61256i	−0.149418	−	0.988774i	$-0.547740\pi$
$798$		0			0
$799$	−7.19777	+	12.4669i	−0.254639	+	0.441047i
$800$	2.47710			0.0875787
$801$	−8.84479	+	3.80987i	−0.312515	+	0.134615i
$802$	−16.7417			−0.591170
$803$	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
$807$	−8.01238	−	38.8545i	−0.282049	−	1.36774i
$808$	−6.01671	+	10.4212i	−0.211667	+	0.366618i
$809$	−14.8058			−0.520544			−0.260272	−	0.965535i	$-0.583812\pi$
$809$	−14.8058			−0.520544			−0.260272	+	0.965535i	$0.583812\pi$
$810$	9.82072	−	10.3879i	0.345065	−	0.364993i
$811$	−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
$814$	0.794182	+	1.37556i	0.0278361	+	0.0482135i
$815$	−17.4425	−	30.2113i	−0.610984	−	1.05826i
$816$	−8.87636	−	2.94384i	−0.310735	−	0.103055i
$817$	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	$0.889587\pi$
$822$	−27.5185	+	24.4767i	−0.959818	+	0.853722i
$823$	−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	$-0.350617\pi$
$824$	3.04944	+	5.28179i	0.106232	+	0.184000i
$825$	−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	$0.582648\pi$
$828$	0.105074	−	0.894969i	0.00365158	−	0.0311023i
$829$	−30.0073			−1.04220			−0.521098	−	0.853497i	$-0.674477\pi$
$829$	−30.0073			−1.04220			−0.521098	+	0.853497i	$0.674477\pi$
$830$	−1.87890	+	3.25436i	−0.0652177	+	0.112960i
$831$	46.5173	+	15.4275i	1.61367	+	0.535173i
$832$	−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
$836$	11.2756			0.389975
$837$	5.96541	−	12.7671i	0.206195	−	0.441295i
$838$	0.420297			0.0145189
$839$	−18.0167	+	31.2059i	−0.622006	+	1.07735i	0.367106	+	0.930179i	$0.380349\pi$
$839$	−18.0167	+	31.2059i	−0.622006	+	1.07735i	−0.989112	+	0.147167i	$0.952985\pi$
$840$		0			0
$841$	−19.7429	−	34.1957i	−0.680789	−	1.17916i
$842$	−3.28799	−	5.69497i	−0.113312	−	0.196262i
$843$	28.9272	+	9.59369i	0.996305	+	0.330424i
$844$	0.166208	−	0.287880i	0.00572110	−	0.00990923i
$845$	−16.1135			−0.554320
$846$	6.41342	+	4.77975i	0.220498	+	0.164331i
$847$		0			0
$848$	2.44437	−	4.23377i	0.0839399	−	0.145388i
$849$	−23.9720	+	21.3222i	−0.822717	+	0.731776i
$850$	6.68725	+	11.5827i	0.229371	+	0.397282i
$851$	0.150186	+	0.260130i	0.00514831	+	0.00891713i
$852$	−16.4629	+	14.6431i	−0.564008	+	0.501664i
$853$	12.2658	−	21.2450i	0.419972	−	0.727413i	−0.575964	−	0.817475i	$-0.695373\pi$
$853$	12.2658	−	21.2450i	0.419972	−	0.727413i	0.995936	+	0.0900617i	$0.0287064\pi$
$854$		0			0
$855$	27.1229	+	20.2140i	0.927583	+	0.691303i
$856$	−3.08650			−0.105495
$857$	14.5240	−	25.1563i	0.496130	−	0.859323i	−0.503860	−	0.863785i	$-0.668087\pi$
$857$	14.5240	−	25.1563i	0.496130	−	0.859323i	0.999990	+	0.00446273i	$0.00142053\pi$
$858$	12.5625	+	4.16635i	0.428877	+	0.142237i
$859$	12.6476	+	21.9064i	0.431532	+	0.747435i	0.997005	−	0.0773313i	$-0.0246399\pi$
$859$	12.6476	+	21.9064i	0.431532	+	0.747435i	−0.565474	+	0.824766i	$0.691307\pi$
$860$	1.32327	+	2.29197i	0.0451232	+	0.0781557i
$861$		0			0
$862$	−11.0439	+	19.1287i	−0.376158	+	0.651525i
$863$	2.69963			0.0918964			0.0459482	−	0.998944i	$-0.485369\pi$
$863$	2.69963			0.0918964			0.0459482	+	0.998944i	$0.485369\pi$
$864$	−2.19963	+	4.70761i	−0.0748329	+	0.160156i
$865$	30.3497			1.03192
$866$	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
$870$	−21.6098	−	7.16689i	−0.732641	−	0.242980i
$871$	24.1822	−	41.8847i	0.819381	−	1.41921i
$872$	2.28799			0.0774812
$873$	0.498141	−	4.24290i	0.0168595	−	0.143601i
$874$	2.13231			0.0721263
$875$		0			0
$876$	−20.7756	+	18.4791i	−0.701943	+	0.624352i
$877$	5.54580	+	9.60561i	0.187268	+	0.324358i	0.944339	−	0.328975i	$-0.106703\pi$
$877$	5.54580	+	9.60561i	0.187268	+	0.324358i	−0.757070	+	0.653334i	$0.773370\pi$
$878$	15.6032	+	27.0256i	0.526583	+	0.912069i
$879$	18.2287	−	16.2138i	0.614839	−	0.546877i
$880$	−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
$885$	16.9134	+	5.60933i	0.568538	+	0.188556i
$886$	6.52723	+	11.3055i	0.219287	+	0.379816i
$887$	20.2836	+	35.1322i	0.681056	+	1.17962i	0.974659	+	0.223696i	$0.0718124\pi$
$887$	20.2836	+	35.1322i	0.681056	+	1.17962i	−0.293603	+	0.955928i	$0.594854\pi$
$888$	−0.349814	−	1.69636i	−0.0117390	−	0.0569260i
$889$		0			0
$890$	5.09888			0.170915
$891$	−4.08582	−	13.6989i	−0.136880	−	0.458932i
$892$	6.33242			0.212025
$893$	−9.46355	+	16.3913i	−0.316686	+	0.548516i
$894$	1.82210	+	8.83594i	0.0609402	+	0.295518i
$895$	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
$899$	−22.4435			−0.748533
$900$	6.82505	−	2.93987i	0.227502	−	0.0979957i
$901$	26.3955			0.879363
$902$	−4.66690	+	8.08330i	−0.155391	+	0.269144i
$903$		0			0
$904$	9.73236	+	16.8569i	0.323693	+	0.560654i
$905$	−6.39561	−	11.0775i	−0.212597	−	0.368230i
$906$	−0.676728	+	0.601924i	−0.0224828	+	0.0199976i
$907$	−15.0567	+	26.0790i	−0.499950	+	0.865939i	−1.00000		5.72941e-5i	$-0.999982\pi$
$907$	−15.0567	+	26.0790i	−0.499950	+	0.865939i	0.500050	+	0.865997i	$0.333315\pi$
$908$	23.3090			0.773537
$909$	−4.20946	+	35.8540i	−0.139619	+	1.18920i
$910$		0			0
$911$	14.6113	−	25.3075i	0.484093	−	0.838473i	−0.515740	−	0.856745i	$-0.672483\pi$
$911$	14.6113	−	25.3075i	0.484093	−	0.838473i	0.999833	+	0.0182717i	$0.00581638\pi$
$912$	−11.6705	−	3.87053i	−0.386450	−	0.128166i
$913$	1.87890	+	3.25436i	0.0621826	+	0.107704i
$914$	−12.2615	−	21.2375i	−0.405573	−	0.702473i
$915$	2.48762	+	12.0632i	0.0822382	+	0.398799i
$916$	−2.47710	+	4.29046i	−0.0818457	+	0.141761i
$917$		0			0
$918$	−27.9505	+	2.42358i	−0.922503	+	0.0799902i
$919$	11.0472			0.364413			0.182206	−	0.983260i	$-0.441676\pi$
$919$	11.0472			0.364413			0.182206	+	0.983260i	$0.441676\pi$
$920$	−0.238550	+	0.413181i	−0.00786476	+	0.0136222i
$921$	−2.04827	−	9.93271i	−0.0674928	−	0.327294i
$922$	1.75526	+	3.04020i	0.0578064	+	0.100124i
$923$	−30.5989	−	52.9988i	−1.00717	−	1.74448i
$924$		0			0
$925$	−1.23855	+	2.14523i	−0.0407233	+	0.0705348i
$926$	17.3883			0.571413
$927$	14.6705	+	10.9336i	0.481844	+	0.359105i
$928$	8.27561			0.271660
$929$	−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
$933$	1.04944	−	0.933440i	0.0343572	−	0.0305594i
$934$	6.69894	−	11.6029i	0.219196	−	0.379659i
$935$	−13.6218			−0.445480
$936$	−11.5723	−	8.62456i	−0.378254	−	0.281903i
$937$	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
$940$	−2.11745	−	3.66754i	−0.0690637	−	0.119622i
$941$	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	$0.756979\pi$
$942$	−3.10074	−	15.0365i	−0.101028	−	0.489915i
$943$	−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	$0.199013\pi$
$948$	−2.93385	−	14.2271i	−0.0952869	−	0.462076i
$949$	−38.6148	−	66.8828i	−1.25349	−	2.17111i
$950$	8.79232	+	15.2287i	0.285261	+	0.494086i
$951$	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	$0.350073\pi$
$954$	1.71015	−	14.5662i	0.0553681	−	0.471597i
$955$	38.0617			1.23165
$956$	2.48762	−	4.30868i	0.0804554	−	0.139353i
$957$	−17.0116	+	15.1312i	−0.549907	+	0.489122i
$958$	−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
$962$	4.81089			0.155109
$963$	−8.50412	+	3.66312i	−0.274042	+	0.118043i
$964$	13.0000			0.418702
$965$	7.75526	−	13.4325i	0.249651	−	0.432408i
$966$		0			0
$967$	15.7837	+	27.3381i	0.507568	+	0.879134i	0.999962	+	0.00876132i	$0.00278885\pi$
$967$	15.7837	+	27.3381i	0.507568	+	0.879134i	−0.492393	+	0.870373i	$0.663878\pi$
$968$	−4.23855	−	7.34138i	−0.136232	−	0.235961i
$969$	−13.4079	−	65.0192i	−0.430724	−	2.08872i
$970$	−1.13093	+	1.95882i	−0.0363119	+	0.0628941i
$971$	5.64283			0.181087			0.0905434	−	0.995893i	$-0.471140\pi$
$971$	5.64283			0.181087			0.0905434	+	0.995893i	$0.471140\pi$
$972$	−0.473458	+	15.5813i	−0.0151862	+	0.499769i
$973$		0			0
$974$	−16.2472	+	28.1410i	−0.520594	+	0.901696i
$975$	4.16876	+	20.2156i	0.133507	+	0.647417i
$976$	−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	$0.866454\pi$
$978$	36.1069	+	11.9748i	1.15457	+	0.382913i
$979$	2.54944	−	4.41576i	0.0814805	−	0.141128i
$980$		0			0
$981$	6.30401	−	2.71543i	0.201272	−	0.0866971i
$982$	−19.3214			−0.616571
$983$	−15.1531	+	26.2460i	−0.483310	+	0.837118i	−0.999816	−	0.0191658i	$-0.993899\pi$
$983$	−15.1531	+	26.2460i	−0.483310	+	0.837118i	0.516506	+	0.856283i	$0.327232\pi$
$984$	7.60507	−	6.76443i	0.242441	−	0.215642i
$985$	−14.4887	−	25.0952i	−0.461649	−	0.799599i
$986$	22.3411	+	38.6959i	0.711485	+	1.23233i
$987$		0			0
$988$	17.0760	−	29.5765i	0.543259	−	0.940953i
$989$	0.500482			0.0159144
$990$	−0.882546	+	7.51707i	−0.0280492	+	0.238908i
$991$	−22.3338			−0.709456			−0.354728	−	0.934969i	$-0.615427\pi$
$991$	−22.3338			−0.709456			−0.354728	+	0.934969i	$0.615427\pi$
$992$	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
$996$	−0.827603	−	4.01330i	−0.0262236	−	0.127166i
$997$	−4.38255	+	7.59079i	−0.138797	+	0.240403i	−0.927041	−	0.374959i	$-0.877657\pi$
$997$	−4.38255	+	7.59079i	−0.138797	+	0.240403i	0.788245	+	0.615362i	$0.210990\pi$
$998$	11.1506			0.352966
$999$	−2.97710	−	4.25874i	−0.0941913	−	0.134741i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.1	✓	6	7.5	odd	6
126.2.e.c.121.1	yes	6	63.31	odd	6
126.2.h.d.67.3	yes	6	63.40	odd	6
126.2.h.d.79.3	yes	6	7.3	odd	6
378.2.e.d.37.3		6	63.59	even	6
378.2.e.d.235.3		6	21.5	even	6
378.2.h.c.289.1		6	21.17	even	6
378.2.h.c.361.1		6	63.5	even	6
882.2.e.o.373.3		6	63.4	even	3
882.2.e.o.655.3		6	7.2	even	3
882.2.f.n.295.3		6	7.6	odd	2
882.2.f.n.589.3		6	63.13	odd	6
882.2.f.o.295.1		6	1.1	even	1	trivial
882.2.f.o.589.1		6	9.4	even	3	inner
882.2.h.p.67.1		6	63.58	even	3
882.2.h.p.79.1		6	7.4	even	3
1008.2.q.g.529.3		6	28.19	even	6
1008.2.q.g.625.3		6	252.31	even	6
1008.2.t.h.193.1		6	252.103	even	6
1008.2.t.h.961.1		6	28.3	even	6
1134.2.g.l.163.3		6	63.38	even	6
1134.2.g.l.487.3		6	63.47	even	6
1134.2.g.m.163.1		6	63.52	odd	6
1134.2.g.m.487.1		6	63.61	odd	6
2646.2.e.p.1549.1		6	63.32	odd	6
2646.2.e.p.2125.1		6	21.2	odd	6
2646.2.f.l.883.3		6	21.20	even	2
2646.2.f.l.1765.3		6	63.41	even	6
2646.2.f.m.883.1		6	3.2	odd	2
2646.2.f.m.1765.1		6	9.5	odd	6
2646.2.h.o.361.3		6	63.23	odd	6
2646.2.h.o.667.3		6	21.11	odd	6
3024.2.q.g.2305.3		6	252.59	odd	6
3024.2.q.g.2881.3		6	84.47	odd	6
3024.2.t.h.289.1		6	84.59	odd	6
3024.2.t.h.1873.1		6	252.131	odd	6
7938.2.a.bv.1.3		3	63.34	odd	6
7938.2.a.bw.1.1		3	9.7	even	3
7938.2.a.bz.1.3		3	9.2	odd	6
7938.2.a.ca.1.1		3	63.20	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.349814 - 1.69636i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.794182 + 1.37556i) q^{5} +(-1.64400 - 0.545231i) q^{6} -1.00000 q^{8} +(-2.75526 + 1.18682i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.349814 - 1.69636i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.794182 + 1.37556i) q^{5} +(-1.64400 - 0.545231i) q^{6} -1.00000 q^{8} +(-2.75526 + 1.18682i) q^{9} +1.58836 q^{10} +(0.794182 - 1.37556i) q^{11} +(-1.29418 + 1.15113i) q^{12} +(-2.40545 - 4.16635i) q^{13} +(2.05563 - 1.82841i) q^{15} +(-0.500000 + 0.866025i) q^{16} -5.39926 q^{17} +(-0.349814 + 2.97954i) q^{18} -7.09888 q^{19} +(0.794182 - 1.37556i) q^{20} +(-0.794182 - 1.37556i) q^{22} +(-0.150186 - 0.260130i) q^{23} +(0.349814 + 1.69636i) q^{24} +(1.23855 - 2.14523i) q^{25} -4.81089 q^{26} +(2.97710 + 4.25874i) q^{27} +(4.13781 - 7.16689i) q^{29} +(-0.555632 - 2.69443i) q^{30} +(-1.35600 - 2.34867i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.61126 - 0.866025i) q^{33} +(-2.69963 + 4.67589i) q^{34} +(2.40545 + 1.79272i) q^{36} -1.00000 q^{37} +(-3.54944 + 6.14781i) q^{38} +(-6.22617 + 5.53795i) q^{39} +(-0.794182 - 1.37556i) q^{40} +(-2.93818 - 5.08907i) q^{41} +(-0.833104 + 1.44298i) q^{43} -1.58836 q^{44} +(-3.82072 - 2.84748i) q^{45} -0.300372 q^{46} +(1.33310 - 2.30900i) q^{47} +(1.64400 + 0.545231i) q^{48} +(-1.23855 - 2.14523i) q^{50} +(1.88874 + 9.15907i) q^{51} +(-2.40545 + 4.16635i) q^{52} -4.88874 q^{53} +(5.17673 - 0.448873i) q^{54} +2.52290 q^{55} +(2.48329 + 12.0422i) q^{57} +(-4.13781 - 7.16689i) q^{58} +(3.23855 + 5.60933i) q^{59} +(-2.61126 - 0.866025i) q^{60} +(-2.23855 + 3.87728i) q^{61} -2.71201 q^{62} +1.00000 q^{64} +(3.82072 - 6.61769i) q^{65} +(-2.05563 + 1.82841i) q^{66} +(5.02654 + 8.70623i) q^{67} +(2.69963 + 4.67589i) q^{68} +(-0.388736 + 0.345766i) q^{69} +12.7207 q^{71} +(2.75526 - 1.18682i) q^{72} +16.0531 q^{73} +(-0.500000 + 0.866025i) q^{74} +(-4.07234 - 1.35059i) q^{75} +(3.54944 + 6.14781i) q^{76} +(1.68292 + 8.16100i) q^{78} +(-4.19344 + 7.26325i) q^{79} -1.58836 q^{80} +(6.18292 - 6.53999i) q^{81} -5.87636 q^{82} +(-1.18292 + 2.04887i) q^{83} +(-4.28799 - 7.42702i) q^{85} +(0.833104 + 1.44298i) q^{86} +(-13.6051 - 4.51212i) q^{87} +(-0.794182 + 1.37556i) q^{88} +3.21015 q^{89} +(-4.37636 + 1.88510i) q^{90} +(-0.150186 + 0.260130i) q^{92} +(-3.50983 + 3.12186i) q^{93} +(-1.33310 - 2.30900i) q^{94} +(-5.63781 - 9.76497i) q^{95} +(1.29418 - 1.15113i) q^{96} +(-0.712008 + 1.23323i) q^{97} +(-0.555632 + 4.73259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 4 q^{3} - 3 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 + 4 * q^3 - 3 * q^4 - q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9	\( 6 q + 3 q^{2} + 4 q^{3} - 3 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} - 2 q^{10} - q^{11} - 2 q^{12} - 8 q^{13} + 12 q^{15} - 3 q^{16} - 8 q^{17} + 4 q^{18} - 6 q^{19} - q^{20} + q^{22} - 7 q^{23} - 4 q^{24} + 2 q^{25} - 16 q^{26} + 7 q^{27} - 5 q^{29} - 3 q^{30} - 20 q^{31} + 3 q^{32} - 15 q^{33} - 4 q^{34} + 8 q^{36} - 6 q^{37} - 3 q^{38} + 4 q^{39} + q^{40} - 6 q^{43} + 2 q^{44} + 12 q^{45} - 14 q^{46} + 9 q^{47} - 2 q^{48} - 2 q^{50} + 12 q^{51} - 8 q^{52} - 30 q^{53} + 8 q^{54} + 26 q^{55} + 22 q^{57} + 5 q^{58} + 14 q^{59} - 15 q^{60} - 8 q^{61} - 40 q^{62} + 6 q^{64} - 12 q^{65} - 12 q^{66} + q^{67} + 4 q^{68} - 3 q^{69} + 14 q^{71} + 4 q^{72} + 38 q^{73} - 3 q^{74} - 17 q^{75} + 3 q^{76} + 5 q^{78} + 5 q^{79} + 2 q^{80} + 32 q^{81} - 2 q^{83} - 2 q^{85} + 6 q^{86} - 63 q^{87} + q^{88} - 18 q^{89} + 9 q^{90} - 7 q^{92} + q^{93} - 9 q^{94} - 4 q^{95} + 2 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 4 * q^3 - 3 * q^4 - q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 - 2 * q^10 - q^11 - 2 * q^12 - 8 * q^13 + 12 * q^15 - 3 * q^16 - 8 * q^17 + 4 * q^18 - 6 * q^19 - q^20 + q^22 - 7 * q^23 - 4 * q^24 + 2 * q^25 - 16 * q^26 + 7 * q^27 - 5 * q^29 - 3 * q^30 - 20 * q^31 + 3 * q^32 - 15 * q^33 - 4 * q^34 + 8 * q^36 - 6 * q^37 - 3 * q^38 + 4 * q^39 + q^40 - 6 * q^43 + 2 * q^44 + 12 * q^45 - 14 * q^46 + 9 * q^47 - 2 * q^48 - 2 * q^50 + 12 * q^51 - 8 * q^52 - 30 * q^53 + 8 * q^54 + 26 * q^55 + 22 * q^57 + 5 * q^58 + 14 * q^59 - 15 * q^60 - 8 * q^61 - 40 * q^62 + 6 * q^64 - 12 * q^65 - 12 * q^66 + q^67 + 4 * q^68 - 3 * q^69 + 14 * q^71 + 4 * q^72 + 38 * q^73 - 3 * q^74 - 17 * q^75 + 3 * q^76 + 5 * q^78 + 5 * q^79 + 2 * q^80 + 32 * q^81 - 2 * q^83 - 2 * q^85 + 6 * q^86 - 63 * q^87 + q^88 - 18 * q^89 + 9 * q^90 - 7 * q^92 + q^93 - 9 * q^94 - 4 * q^95 + 2 * q^96 - 28 * q^97 - 3 * q^99

Introduction

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