LMFDB - Embedded newform 250.4.d.a.201.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,4,Mod(51,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("250.51");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	250.d (of order $5$, degree $4$, 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:	$14.7504775014$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 78 x^{10} - 335 x^{9} + 1991 x^{8} - 6020 x^{7} + 20827 x^{6} - 42752 x^{5} + \cdots + 11005 $ x^12 - 6x^11 + 78x^10 - 335x^9 + 1991x^8 - 6020x^7 + 20827x^6 - 42752x^5 + 86341x^4 - 107815x^3 + 97905x^2 - 50215*x + 11005
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{3} $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.3
Root			$0.500000 + 3.48876i$ of defining polynomial
Character	$\chi$	$=$	250.201
Dual form			250.4.d.a.51.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61803 - 1.17557i) q^{2} +(1.33712 + 4.11522i) q^{3} +(1.23607 + 3.80423i) q^{4} +(2.67423 - 8.23044i) q^{6} -17.3088 q^{7} +(2.47214 - 7.60845i) q^{8} +(6.69632 - 4.86516i) q^{9} +O(q^{10})$	\(q+(-1.61803 - 1.17557i) q^{2} +(1.33712 + 4.11522i) q^{3} +(1.23607 + 3.80423i) q^{4} +(2.67423 - 8.23044i) q^{6} -17.3088 q^{7} +(2.47214 - 7.60845i) q^{8} +(6.69632 - 4.86516i) q^{9} +(-21.0492 - 15.2931i) q^{11} +(-14.0025 + 10.1734i) q^{12} +(54.1436 - 39.3376i) q^{13} +(28.0063 + 20.3478i) q^{14} +(-12.9443 + 9.40456i) q^{16} +(20.1609 - 62.0488i) q^{17} -16.5542 q^{18} +(-2.96374 + 9.12145i) q^{19} +(-23.1439 - 71.2296i) q^{21} +(16.0801 + 49.4896i) q^{22} +(89.1539 + 64.7741i) q^{23} +34.6160 q^{24} -133.850 q^{26} +(123.492 + 89.7218i) q^{27} +(-21.3949 - 65.8467i) q^{28} +(73.5566 + 226.384i) q^{29} +(0.922132 - 2.83803i) q^{31} +32.0000 q^{32} +(34.7893 - 107.071i) q^{33} +(-105.564 + 76.6965i) q^{34} +(26.7853 + 19.4606i) q^{36} +(255.618 - 185.717i) q^{37} +(15.5183 - 11.2747i) q^{38} +(234.279 + 170.214i) q^{39} +(355.587 - 258.349i) q^{41} +(-46.2878 + 142.459i) q^{42} -132.682 q^{43} +(32.1603 - 98.9791i) q^{44} +(-68.1075 - 209.613i) q^{46} +(48.8583 + 150.370i) q^{47} +(-56.0098 - 40.6935i) q^{48} -43.4043 q^{49} +282.302 q^{51} +(216.575 + 157.351i) q^{52} +(-117.885 - 362.814i) q^{53} +(-94.3391 - 290.346i) q^{54} +(-42.7898 + 131.693i) q^{56} -41.4996 q^{57} +(147.113 - 452.768i) q^{58} +(433.655 - 315.069i) q^{59} +(-101.881 - 74.0212i) q^{61} +(-4.82835 + 3.50800i) q^{62} +(-115.905 + 84.2102i) q^{63} +(-51.7771 - 37.6183i) q^{64} +(-182.159 + 132.346i) q^{66} +(269.366 - 829.025i) q^{67} +260.968 q^{68} +(-147.350 + 453.498i) q^{69} +(-236.933 - 729.205i) q^{71} +(-20.4621 - 62.9759i) q^{72} +(704.932 + 512.163i) q^{73} -631.922 q^{74} -38.3634 q^{76} +(364.336 + 264.706i) q^{77} +(-178.973 - 550.824i) q^{78} +(-89.5152 - 275.500i) q^{79} +(-135.043 + 415.619i) q^{81} -879.060 q^{82} +(-360.724 + 1110.19i) q^{83} +(242.366 - 176.089i) q^{84} +(214.684 + 155.977i) q^{86} +(-833.266 + 605.403i) q^{87} +(-168.393 + 122.345i) q^{88} +(219.056 + 159.154i) q^{89} +(-937.163 + 680.889i) q^{91} +(-136.215 + 419.227i) q^{92} +12.9121 q^{93} +(97.7165 - 300.741i) q^{94} +(42.7877 + 131.687i) q^{96} +(-63.7550 - 196.218i) q^{97} +(70.2296 + 51.0248i) q^{98} -215.355 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - q^{3} - 12 q^{4} - 2 q^{6} - 58 q^{7} - 24 q^{8} - 26 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 - q^3 - 12 * q^4 - 2 * q^6 - 58 * q^7 - 24 * q^8 - 26 * q^9	\( 12 q - 6 q^{2} - q^{3} - 12 q^{4} - 2 q^{6} - 58 q^{7} - 24 q^{8} - 26 q^{9} - 46 q^{11} + 36 q^{12} + 19 q^{13} + 4 q^{14} - 48 q^{16} - 178 q^{17} - 72 q^{18} + 130 q^{19} - 221 q^{21} + 158 q^{22} + 259 q^{23} - 128 q^{24} + 128 q^{26} + 215 q^{27} + 108 q^{28} + 15 q^{29} + 309 q^{31} + 384 q^{32} + 608 q^{33} + 304 q^{34} - 104 q^{36} + 557 q^{37} - 110 q^{38} + 1158 q^{39} - 596 q^{41} - 442 q^{42} - 746 q^{43} + 316 q^{44} - 292 q^{46} + 1442 q^{47} + 144 q^{48} - 834 q^{49} + 2724 q^{51} + 76 q^{52} - 96 q^{53} - 510 q^{54} + 216 q^{56} - 1280 q^{57} + 30 q^{58} + 975 q^{59} - 2016 q^{61} - 592 q^{62} - 1206 q^{63} - 192 q^{64} - 1014 q^{66} - 68 q^{67} + 208 q^{68} + 783 q^{69} + 1384 q^{71} + 352 q^{72} + 3834 q^{73} - 2656 q^{74} - 600 q^{76} + 1059 q^{77} - 664 q^{78} - 4550 q^{79} + 1227 q^{81} - 1012 q^{82} - 1211 q^{83} + 1236 q^{84} - 382 q^{86} - 1625 q^{87} - 368 q^{88} + 1685 q^{89} - 3271 q^{91} - 584 q^{92} - 4552 q^{93} + 2884 q^{94} - 32 q^{96} + 4247 q^{97} + 1952 q^{98} - 1202 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - q^3 - 12 * q^4 - 2 * q^6 - 58 * q^7 - 24 * q^8 - 26 * q^9 - 46 * q^11 + 36 * q^12 + 19 * q^13 + 4 * q^14 - 48 * q^16 - 178 * q^17 - 72 * q^18 + 130 * q^19 - 221 * q^21 + 158 * q^22 + 259 * q^23 - 128 * q^24 + 128 * q^26 + 215 * q^27 + 108 * q^28 + 15 * q^29 + 309 * q^31 + 384 * q^32 + 608 * q^33 + 304 * q^34 - 104 * q^36 + 557 * q^37 - 110 * q^38 + 1158 * q^39 - 596 * q^41 - 442 * q^42 - 746 * q^43 + 316 * q^44 - 292 * q^46 + 1442 * q^47 + 144 * q^48 - 834 * q^49 + 2724 * q^51 + 76 * q^52 - 96 * q^53 - 510 * q^54 + 216 * q^56 - 1280 * q^57 + 30 * q^58 + 975 * q^59 - 2016 * q^61 - 592 * q^62 - 1206 * q^63 - 192 * q^64 - 1014 * q^66 - 68 * q^67 + 208 * q^68 + 783 * q^69 + 1384 * q^71 + 352 * q^72 + 3834 * q^73 - 2656 * q^74 - 600 * q^76 + 1059 * q^77 - 664 * q^78 - 4550 * q^79 + 1227 * q^81 - 1012 * q^82 - 1211 * q^83 + 1236 * q^84 - 382 * q^86 - 1625 * q^87 - 368 * q^88 + 1685 * q^89 - 3271 * q^91 - 584 * q^92 - 4552 * q^93 + 2884 * q^94 - 32 * q^96 + 4247 * q^97 + 1952 * q^98 - 1202 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−1.61803	−	1.17557i	−0.572061	−	0.415627i
$2$	−1.61803	−	1.17557i	−0.572061	−	0.415627i
$3$	1.33712	+	4.11522i	0.257328	+	0.791974i	0.993362	+	0.115030i	$0.0366963\pi$
$3$	1.33712	+	4.11522i	0.257328	+	0.791974i	−0.736034	+	0.676944i	$0.763304\pi$
$4$	1.23607	+	3.80423i	0.154508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	2.67423	−	8.23044i	0.181958	−	0.560010i
$7$	−17.3088			−0.934589			−0.467295	−	0.884102i	$-0.654771\pi$
$7$	−17.3088			−0.934589			−0.467295	+	0.884102i	$0.654771\pi$
$8$	2.47214	−	7.60845i	0.109254	−	0.336249i
$9$	6.69632	−	4.86516i	0.248012	−	0.180191i
$10$		0			0
$11$	−21.0492	−	15.2931i	−0.576960	−	0.419186i	0.260667	−	0.965429i	$-0.416058\pi$
$11$	−21.0492	−	15.2931i	−0.576960	−	0.419186i	−0.837627	+	0.546243i	$0.816058\pi$
$12$	−14.0025	+	10.1734i	−0.336847	+	0.244733i
$13$	54.1436	−	39.3376i	1.15513	−	0.839254i	0.165979	−	0.986129i	$-0.446922\pi$
$13$	54.1436	−	39.3376i	1.15513	−	0.839254i	0.989155	+	0.146875i	$0.0469216\pi$
$14$	28.0063	+	20.3478i	0.534642	+	0.388440i
$15$		0			0
$16$	−12.9443	+	9.40456i	−0.202254	+	0.146946i
$17$	20.1609	−	62.0488i	0.287631	−	0.885238i	−0.697966	−	0.716131i	$-0.745912\pi$
$17$	20.1609	−	62.0488i	0.287631	−	0.885238i	0.985598	−	0.169107i	$-0.0540885\pi$
$18$	−16.5542			−0.216770
$19$	−2.96374	+	9.12145i	−0.0357857	+	0.110137i	−0.967354	−	0.253430i	$-0.918441\pi$
$19$	−2.96374	+	9.12145i	−0.0357857	+	0.110137i	0.931568	+	0.363567i	$0.118441\pi$
$20$		0			0
$21$	−23.1439	−	71.2296i	−0.240496	−	0.740170i
$22$	16.0801	+	49.4896i	0.155832	+	0.479600i
$23$	89.1539	+	64.7741i	0.808255	+	0.587232i	0.913324	−	0.407233i	$-0.133506\pi$
$23$	89.1539	+	64.7741i	0.808255	+	0.587232i	−0.105069	+	0.994465i	$0.533506\pi$
$24$	34.6160			0.294415
$25$		0			0
$26$	−133.850			−1.00962
$27$	123.492	+	89.7218i	0.880220	+	0.639518i
$28$	−21.3949	−	65.8467i	−0.144402	−	0.444424i
$29$	73.5566	+	226.384i	0.471004	+	1.44960i	0.851272	+	0.524725i	$0.175832\pi$
$29$	73.5566	+	226.384i	0.471004	+	1.44960i	−0.380268	+	0.924876i	$0.624168\pi$
$30$		0			0
$31$	0.922132	−	2.83803i	0.00534257	−	0.0164428i	−0.948350	−	0.317227i	$-0.897248\pi$
$31$	0.922132	−	2.83803i	0.00534257	−	0.0164428i	0.953692	+	0.300784i	$0.0972483\pi$
$32$	32.0000			0.176777
$33$	34.7893	−	107.071i	0.183517	−	0.564806i
$34$	−105.564	+	76.6965i	−0.532471	+	0.386863i
$35$		0			0
$36$	26.7853	+	19.4606i	0.124006	+	0.0900955i
$37$	255.618	−	185.717i	1.13577	−	0.825182i	0.149242	−	0.988801i	$-0.452317\pi$
$37$	255.618	−	185.717i	1.13577	−	0.825182i	0.986524	+	0.163619i	$0.0523167\pi$
$38$	15.5183	−	11.2747i	0.0662475	−	0.0481316i
$39$	234.279	+	170.214i	0.961916	+	0.698873i
$40$		0			0
$41$	355.587	−	258.349i	1.35447	−	0.984083i	0.355698	−	0.934601i	$-0.384243\pi$
$41$	355.587	−	258.349i	1.35447	−	0.984083i	0.998775	−	0.0494818i	$-0.0157570\pi$
$42$	−46.2878	+	142.459i	−0.170056	+	0.523380i
$43$	−132.682			−0.470554			−0.235277	−	0.971928i	$-0.575600\pi$
$43$	−132.682			−0.470554			−0.235277	+	0.971928i	$0.575600\pi$
$44$	32.1603	−	98.9791i	0.110190	−	0.339129i
$45$		0			0
$46$	−68.1075	−	209.613i	−0.218302	−	0.671865i
$47$	48.8583	+	150.370i	0.151632	+	0.466676i	0.997804	−	0.0662342i	$-0.0210984\pi$
$47$	48.8583	+	150.370i	0.151632	+	0.466676i	−0.846172	+	0.532910i	$0.821098\pi$
$48$	−56.0098	−	40.6935i	−0.168423	−	0.122367i
$49$	−43.4043			−0.126543
$50$		0			0
$51$	282.302			0.775101
$52$	216.575	+	157.351i	0.577567	+	0.419627i
$53$	−117.885	−	362.814i	−0.305524	−	0.940307i	−0.979481	−	0.201536i	$-0.935407\pi$
$53$	−117.885	−	362.814i	−0.305524	−	0.940307i	0.673957	−	0.738771i	$-0.264593\pi$
$54$	−94.3391	−	290.346i	−0.237739	−	0.731687i
$55$		0			0
$56$	−42.7898	+	131.693i	−0.102108	+	0.314255i
$57$	−41.4996			−0.0964343
$58$	147.113	−	452.768i	0.333050	−	1.02502i
$59$	433.655	−	315.069i	0.956899	−	0.695228i	0.00447077	−	0.999990i	$-0.498577\pi$
$59$	433.655	−	315.069i	0.956899	−	0.695228i	0.952429	+	0.304762i	$0.0985769\pi$
$60$		0			0
$61$	−101.881	−	74.0212i	−0.213845	−	0.155368i	0.475706	−	0.879604i	$-0.342192\pi$
$61$	−101.881	−	74.0212i	−0.213845	−	0.155368i	−0.689552	+	0.724236i	$0.742192\pi$
$62$	−4.82835	+	3.50800i	−0.00989033	+	0.00718575i
$63$	−115.905	+	84.2102i	−0.231789	+	0.168405i
$64$	−51.7771	−	37.6183i	−0.101127	−	0.0734732i
$65$		0			0
$66$	−182.159	+	132.346i	−0.339731	+	0.246829i
$67$	269.366	−	829.025i	0.491169	−	1.51166i	−0.331673	−	0.943394i	$-0.607613\pi$
$67$	269.366	−	829.025i	0.491169	−	1.51166i	0.822842	−	0.568270i	$-0.192387\pi$
$68$	260.968			0.465397
$69$	−147.350	+	453.498i	−0.257086	+	0.791228i
$70$		0			0
$71$	−236.933	−	729.205i	−0.396039	−	1.21888i	−0.928149	−	0.372208i	$-0.878601\pi$
$71$	−236.933	−	729.205i	−0.396039	−	1.21888i	0.532110	−	0.846675i	$-0.321399\pi$
$72$	−20.4621	−	62.9759i	−0.0334928	−	0.103080i
$73$	704.932	+	512.163i	1.13022	+	0.821152i	0.985727	−	0.168353i	$-0.0538450\pi$
$73$	704.932	+	512.163i	1.13022	+	0.821152i	0.144493	+	0.989506i	$0.453845\pi$
$74$	−631.922			−0.992695
$75$		0			0
$76$	−38.3634			−0.0579025
$77$	364.336	+	264.706i	0.539221	+	0.391767i
$78$	−178.973	−	550.824i	−0.259805	−	0.799596i
$79$	−89.5152	−	275.500i	−0.127484	−	0.392356i	0.866861	−	0.498549i	$-0.166134\pi$
$79$	−89.5152	−	275.500i	−0.127484	−	0.392356i	−0.994345	+	0.106193i	$0.966134\pi$
$80$		0			0
$81$	−135.043	+	415.619i	−0.185244	+	0.570122i
$82$	−879.060			−1.18385
$83$	−360.724	+	1110.19i	−0.477043	+	1.46819i	0.366139	+	0.930560i	$0.380680\pi$
$83$	−360.724	+	1110.19i	−0.477043	+	1.46819i	−0.843182	+	0.537628i	$0.819320\pi$
$84$	242.366	−	176.089i	0.314813	−	0.228725i
$85$		0			0
$86$	214.684	+	155.977i	0.269186	+	0.195575i
$87$	−833.266	+	605.403i	−1.02684	+	0.746046i
$88$	−168.393	+	122.345i	−0.203986	+	0.148205i
$89$	219.056	+	159.154i	0.260898	+	0.189554i	0.710543	−	0.703654i	$-0.248449\pi$
$89$	219.056	+	159.154i	0.260898	+	0.189554i	−0.449645	+	0.893207i	$0.648449\pi$
$90$		0			0
$91$	−937.163	+	680.889i	−1.07958	+	0.784358i
$92$	−136.215	+	419.227i	−0.154363	+	0.475081i
$93$	12.9121			0.0143970
$94$	97.7165	−	300.741i	0.107220	−	0.329990i
$95$		0			0
$96$	42.7877	+	131.687i	0.0454896	+	0.140003i
$97$	−63.7550	−	196.218i	−0.0667354	−	0.205391i	0.912128	−	0.409905i	$-0.134438\pi$
$97$	−63.7550	−	196.218i	−0.0667354	−	0.205391i	−0.978863	+	0.204515i	$0.934438\pi$
$98$	70.2296	+	51.0248i	0.0723904	+	0.0525947i
$99$	−215.355			−0.218626
$100$		0			0
$101$	1436.09			1.41481			0.707406	−	0.706807i	$-0.249865\pi$
$101$	1436.09			1.41481			0.707406	+	0.706807i	$0.249865\pi$
$102$	−456.774	−	331.866i	−0.443405	−	0.322153i
$103$	−43.6322	−	134.286i	−0.0417399	−	0.128462i	0.928015	−	0.372542i	$-0.121514\pi$
$103$	−43.6322	−	134.286i	−0.0417399	−	0.128462i	−0.969755	+	0.244080i	$0.921514\pi$
$104$	−165.448	−	509.197i	−0.155995	−	0.480105i
$105$		0			0
$106$	−235.771	+	725.627i	−0.216038	+	0.664897i
$107$	−427.679			−0.386404			−0.193202	−	0.981159i	$-0.561887\pi$
$107$	−427.679			−0.386404			−0.193202	+	0.981159i	$0.561887\pi$
$108$	−188.678	+	580.692i	−0.168107	+	0.517381i
$109$	2.91048	−	2.11459i	0.00255755	−	0.00185817i	−0.586506	−	0.809945i	$-0.699497\pi$
$109$	2.91048	−	2.11459i	0.00255755	−	0.00185817i	0.589063	+	0.808087i	$0.299497\pi$
$110$		0			0
$111$	1106.06	+	803.598i	0.945787	+	0.687155i
$112$	224.050	−	162.782i	0.189025	−	0.137334i
$113$	−1536.72	+	1116.49i	−1.27932	+	0.929478i	−0.999532	−	0.0305853i	$-0.990263\pi$
$113$	−1536.72	+	1116.49i	−1.27932	+	0.929478i	−0.279784	+	0.960063i	$0.590263\pi$
$114$	67.1478	+	48.7857i	0.0551664	+	0.0400807i
$115$		0			0
$116$	−770.295	+	559.652i	−0.616552	+	0.447952i
$117$	171.179	−	526.835i	0.135261	−	0.416290i
$118$	−1072.05			−0.836361
$119$	−348.961	+	1073.99i	−0.268817	+	0.827334i
$120$		0			0
$121$	−202.114	−	622.042i	−0.151851	−	0.467349i
$122$	77.8304	+	239.537i	0.0577577	+	0.177760i
$123$	1538.63	+	1117.88i	1.12791	+	0.819476i
$124$	11.9363			0.00864447
$125$		0			0
$126$	286.534			0.202591
$127$	−1979.73	−	1438.36i	−1.38325	−	1.00499i	−0.996568	−	0.0827737i	$-0.973622\pi$
$127$	−1979.73	−	1438.36i	−1.38325	−	1.00499i	−0.386679	−	0.922214i	$-0.626378\pi$
$128$	39.5542	+	121.735i	0.0273135	+	0.0840623i
$129$	−177.411	−	546.015i	−0.121087	−	0.372666i
$130$		0			0
$131$	−707.355	+	2177.01i	−0.471770	+	1.45196i	0.378494	+	0.925604i	$0.376442\pi$
$131$	−707.355	+	2177.01i	−0.471770	+	1.45196i	−0.850264	+	0.526356i	$0.823558\pi$
$132$	450.323			0.296936
$133$	51.2988	−	157.882i	0.0334449	−	0.102933i
$134$	−1410.42	+	1024.73i	−0.909267	+	0.660621i
$135$		0			0
$136$	−422.255	−	306.786i	−0.266236	−	0.193432i
$137$	−41.9615	+	30.4868i	−0.0261680	+	0.0190121i	−0.600792	−	0.799405i	$-0.705148\pi$
$137$	−41.9615	+	30.4868i	−0.0261680	+	0.0190121i	0.574624	+	0.818417i	$0.305148\pi$
$138$	771.537	−	560.555i	0.475925	−	0.345779i
$139$	−1525.92	−	1108.64i	−0.931127	−	0.676504i	0.0151413	−	0.999885i	$-0.495180\pi$
$139$	−1525.92	−	1108.64i	−0.931127	−	0.676504i	−0.946269	+	0.323382i	$0.895180\pi$
$140$		0			0
$141$	−553.477	+	402.125i	−0.330576	+	0.240177i
$142$	−473.866	+	1458.41i	−0.280042	+	0.861881i
$143$	−1741.27			−1.01827
$144$	−40.9242	+	125.952i	−0.0236830	+	0.0728888i
$145$		0			0
$146$	−538.520	−	1657.39i	−0.305262	−	0.939499i
$147$	−58.0365	−	178.618i	−0.0325631	−	0.100219i
$148$	1022.47	+	742.869i	0.567883	+	0.412591i
$149$	−712.590			−0.391796			−0.195898	−	0.980624i	$-0.562762\pi$
$149$	−712.590			−0.391796			−0.195898	+	0.980624i	$0.562762\pi$
$150$		0			0
$151$	2245.13			1.20998			0.604988	−	0.796235i	$-0.293178\pi$
$151$	2245.13			1.20998			0.604988	+	0.796235i	$0.293178\pi$
$152$	62.0733	+	45.0989i	0.0331238	+	0.0240658i
$153$	−166.874	−	513.584i	−0.0881760	−	0.271378i
$154$	−278.328	−	856.606i	−0.145639	−	0.448229i
$155$		0			0
$156$	−357.947	+	1101.65i	−0.183710	+	0.565400i
$157$	1018.81			0.517895			0.258948	−	0.965891i	$-0.416624\pi$
$157$	1018.81			0.517895			0.258948	+	0.965891i	$0.416624\pi$
$158$	−179.030	+	550.999i	−0.0901449	+	0.277438i
$159$	1335.43	−	970.247i	0.666079	−	0.483935i
$160$		0			0
$161$	−1543.15	−	1121.16i	−0.755387	−	0.548820i
$162$	707.094	−	513.734i	0.342929	−	0.249153i
$163$	3223.93	−	2342.32i	1.54919	−	1.12555i	0.604963	−	0.796253i	$-0.293188\pi$
$163$	3223.93	−	2342.32i	1.54919	−	1.12555i	0.944226	−	0.329298i	$-0.106812\pi$
$164$	1422.35	+	1033.40i	0.677237	+	0.492041i
$165$		0			0
$166$	1888.77	−	1372.28i	0.883117	−	0.641622i
$167$	−141.591	+	435.774i	−0.0656088	+	0.201923i	−0.978487	−	0.206309i	$-0.933855\pi$
$167$	−141.591	+	435.774i	−0.0656088	+	0.201923i	0.912878	+	0.408232i	$0.133855\pi$
$168$	−599.162			−0.275157
$169$	705.172	−	2170.30i	0.320970	−	0.987845i
$170$		0			0
$171$	24.5312	+	75.4991i	0.0109704	+	0.0337635i
$172$	−164.004	−	504.752i	−0.0727046	−	0.223762i
$173$	−1049.54	−	762.537i	−0.461244	−	0.335113i	0.332775	−	0.943006i	$-0.392015\pi$
$173$	−1049.54	−	762.537i	−0.461244	−	0.335113i	−0.794019	+	0.607893i	$0.792015\pi$
$174$	2059.95			0.897495
$175$		0			0
$176$	416.291			0.178290
$177$	1876.42	+	1363.30i	0.796840	+	0.578938i
$178$	−167.344	−	515.033i	−0.0704662	−	0.216873i
$179$	584.916	+	1800.19i	0.244238	+	0.751688i	0.995761	+	0.0919806i	$0.0293198\pi$
$179$	584.916	+	1800.19i	0.244238	+	0.751688i	−0.751523	+	0.659707i	$0.770680\pi$
$180$		0			0
$181$	1235.09	−	3801.21i	0.507200	−	1.56100i	−0.289839	−	0.957075i	$-0.593602\pi$
$181$	1235.09	−	3801.21i	0.507200	−	1.56100i	0.797040	−	0.603927i	$-0.206398\pi$
$182$	2316.79			0.943584
$183$	168.386	−	518.239i	0.0680189	−	0.209341i
$184$	713.231	−	518.193i	0.285761	−	0.207618i
$185$		0			0
$186$	−20.8922	−	15.1791i	−0.00823598	−	0.00598379i
$187$	−1373.29	+	997.753i	−0.537031	+	0.390176i
$188$	−511.650	+	371.736i	−0.198489	+	0.144211i
$189$	−2137.49	−	1552.98i	−0.822644	−	0.597686i
$190$		0			0
$191$	−3300.50	+	2397.95i	−1.25034	+	0.908428i	−0.998242	−	0.0592730i	$-0.981122\pi$
$191$	−3300.50	+	2397.95i	−1.25034	+	0.908428i	−0.252102	+	0.967701i	$0.581122\pi$
$192$	85.5754	−	263.374i	0.0321660	−	0.0989968i
$193$	−1635.27			−0.609891			−0.304946	−	0.952370i	$-0.598638\pi$
$193$	−1635.27			−0.609891			−0.304946	+	0.952370i	$0.598638\pi$
$194$	−127.510	+	392.435i	−0.0471891	+	0.145233i
$195$		0			0
$196$	−53.6506	−	165.120i	−0.0195520	−	0.0601748i
$197$	414.894	+	1276.91i	0.150050	+	0.461808i	0.997626	−	0.0688672i	$-0.0219385\pi$
$197$	414.894	+	1276.91i	0.150050	+	0.461808i	−0.847575	+	0.530675i	$0.821938\pi$
$198$	348.452	+	253.165i	0.125068	+	0.0908670i
$199$	2884.91			1.02767			0.513833	−	0.857890i	$-0.328225\pi$
$199$	2884.91			1.02767			0.513833	+	0.857890i	$0.328225\pi$
$200$		0			0
$201$	3771.79			1.32359
$202$	−2323.64	−	1688.22i	−0.809360	−	0.588034i
$203$	−1273.18	−	3918.44i	−0.440195	−	1.35478i
$204$	348.944	+	1073.94i	0.119760	+	0.368583i
$205$		0			0
$206$	−87.2643	+	268.572i	−0.0295145	+	0.0908364i
$207$	912.139			0.306271
$208$	−330.896	+	1018.39i	−0.110305	+	0.339485i
$209$	201.879	−	146.674i	0.0668148	−	0.0485438i
$210$		0			0
$211$	−4139.00	−	3007.16i	−1.35043	−	0.981144i	−0.998990	−	0.0449336i	$-0.985692\pi$
$211$	−4139.00	−	3007.16i	−1.35043	−	0.981144i	−0.351439	−	0.936211i	$-0.614308\pi$
$212$	1234.51	−	896.924i	0.399936	−	0.290571i
$213$	2684.03	−	1950.06i	0.863412	−	0.627306i
$214$	691.999	+	502.766i	0.221047	+	0.160600i
$215$		0			0
$216$	987.932	−	717.775i	0.311205	−	0.226104i
$217$	−15.9610	+	49.1230i	−0.00499311	+	0.0153672i
$218$	−7.19510			−0.00223538
$219$	−1165.09	+	3585.77i	−0.359494	+	1.10641i
$220$		0			0
$221$	−1349.27	−	4152.63i	−0.410687	−	1.26396i
$222$	−844.953	−	2600.50i	−0.255448	−	0.786189i
$223$	1531.08	+	1112.40i	0.459771	+	0.334043i	0.793442	−	0.608646i	$-0.208287\pi$
$223$	1531.08	+	1112.40i	0.459771	+	0.334043i	−0.333670	+	0.942690i	$0.608287\pi$
$224$	−553.883			−0.165214
$225$		0			0
$226$	3798.99			1.11816
$227$	4758.75	+	3457.43i	1.39141	+	1.01092i	0.995709	+	0.0925346i	$0.0294969\pi$
$227$	4758.75	+	3457.43i	1.39141	+	1.01092i	0.395697	+	0.918381i	$0.370503\pi$
$228$	−51.2963	−	157.874i	−0.0148999	−	0.0458572i
$229$	−111.725	−	343.853i	−0.0322401	−	0.0992247i	0.933642	−	0.358209i	$-0.116612\pi$
$229$	−111.725	−	343.853i	−0.0322401	−	0.0992247i	−0.965882	+	0.258984i	$0.916612\pi$
$230$		0			0
$231$	−602.163	+	1853.27i	−0.171513	+	0.527861i
$232$	1904.27			0.538887
$233$	−759.494	+	2337.48i	−0.213546	+	0.657226i	0.785708	+	0.618598i	$0.212299\pi$
$233$	−759.494	+	2337.48i	−0.213546	+	0.657226i	−0.999254	+	0.0386284i	$0.987701\pi$
$234$	−896.305	+	651.203i	−0.250399	+	0.181925i
$235$		0			0
$236$	1734.62	+	1260.27i	0.478450	+	0.347614i
$237$	1014.05	−	736.749i	0.277931	−	0.201928i
$238$	1827.19	−	1327.53i	0.497642	−	0.361558i
$239$	4815.05	+	3498.34i	1.30318	+	0.946815i	0.999981	−	0.00611331i	$-0.00194594\pi$
$239$	4815.05	+	3498.34i	1.30318	+	0.946815i	0.303197	+	0.952928i	$0.401946\pi$
$240$		0			0
$241$	−3914.90	+	2844.34i	−1.04639	+	0.760249i	−0.971523	−	0.236945i	$-0.923854\pi$
$241$	−3914.90	+	2844.34i	−1.04639	+	0.760249i	−0.0748694	+	0.997193i	$0.523854\pi$
$242$	−404.227	+	1244.08i	−0.107375	+	0.330466i
$243$	2230.45			0.588822
$244$	155.661	−	479.075i	0.0408408	−	0.125695i
$245$		0			0
$246$	−1175.41	−	3617.52i	−0.304639	−	0.937581i
$247$	198.349	+	610.455i	0.0510957	+	0.157256i
$248$	−19.3134	−	14.0320i	−0.00494517	−	0.00359287i
$249$	−5051.02			−1.28552
$250$		0			0
$251$	−101.973			−0.0256434			−0.0128217	−	0.999918i	$-0.504081\pi$
$251$	−101.973			−0.0256434			−0.0128217	+	0.999918i	$0.504081\pi$
$252$	−463.622	−	336.841i	−0.115895	−	0.0842023i
$253$	−886.017	−	2726.88i	−0.220172	−	0.677619i
$254$	1512.38	+	4654.62i	0.373602	+	1.14983i
$255$		0			0
$256$	79.1084	−	243.470i	0.0193136	−	0.0594410i
$257$	−697.647			−0.169331			−0.0846655	−	0.996409i	$-0.526982\pi$
$257$	−697.647			−0.169331			−0.0846655	+	0.996409i	$0.526982\pi$
$258$	−354.822	+	1092.03i	−0.0856212	+	0.263515i
$259$	−4424.45	+	3214.55i	−1.06147	+	0.771206i
$260$		0			0
$261$	1593.95	+	1158.07i	0.378020	+	0.274647i
$262$	3703.76	−	2690.94i	0.873355	−	0.634530i
$263$	2959.37	−	2150.11i	0.693850	−	0.504112i	−0.184073	−	0.982912i	$-0.558928\pi$
$263$	2959.37	−	2150.11i	0.693850	−	0.504112i	0.877924	+	0.478801i	$0.158928\pi$
$264$	−728.637	−	529.386i	−0.169866	−	0.123415i
$265$		0			0
$266$	−268.604	+	195.152i	−0.0619142	+	0.0449833i
$267$	−362.049	+	1114.27i	−0.0829852	+	0.255402i
$268$	3486.75			0.794729
$269$	1330.22	−	4094.00i	0.301506	−	0.927940i	−0.679452	−	0.733720i	$-0.737782\pi$
$269$	1330.22	−	4094.00i	0.301506	−	0.927940i	0.980958	−	0.194220i	$-0.0622176\pi$
$270$		0			0
$271$	132.874	+	408.945i	0.0297842	+	0.0916665i	0.964844	−	0.262825i	$-0.0846541\pi$
$271$	132.874	+	408.945i	0.0297842	+	0.0916665i	−0.935059	+	0.354491i	$0.884654\pi$
$272$	322.574	+	992.781i	0.0719078	+	0.221309i
$273$	−4055.10	−	2946.20i	−0.898996	−	0.653159i
$274$	103.735			0.0228716
$275$		0			0
$276$	−1907.34			−0.415973
$277$	−1390.64	−	1010.36i	−0.301643	−	0.219157i	0.426659	−	0.904413i	$-0.359690\pi$
$277$	−1390.64	−	1010.36i	−0.301643	−	0.219157i	−0.728303	+	0.685256i	$0.759690\pi$
$278$	1165.70	+	3587.65i	0.251489	+	0.774003i
$279$	−7.63258	−	23.4907i	−0.00163782	−	0.00504068i
$280$		0			0
$281$	−839.390	+	2583.38i	−0.178199	+	0.548439i	−0.999765	−	0.0216739i	$-0.993100\pi$
$281$	−839.390	+	2583.38i	−0.178199	+	0.548439i	0.821567	+	0.570113i	$0.193100\pi$
$282$	1368.27			0.288934
$283$	−998.541	+	3073.19i	−0.209742	+	0.645521i	0.789743	+	0.613438i	$0.210214\pi$
$283$	−998.541	+	3073.19i	−0.209742	+	0.645521i	−0.999485	+	0.0320827i	$0.989786\pi$
$284$	2481.20	−	1802.69i	0.518422	−	0.376656i
$285$		0			0
$286$	2817.44	+	2046.99i	0.582513	+	0.423220i
$287$	−6154.80	+	4471.73i	−1.26588	+	0.919713i
$288$	214.282	−	155.685i	0.0438427	−	0.0318536i
$289$	531.107	+	385.872i	0.108102	+	0.0785410i
$290$		0			0
$291$	722.231	−	524.731i	0.145491	−	0.105705i
$292$	−1077.04	+	3314.79i	−0.215853	+	0.664326i
$293$	−6070.89			−1.21046			−0.605231	−	0.796050i	$-0.706919\pi$
$293$	−6070.89			−1.21046			−0.605231	+	0.796050i	$0.706919\pi$
$294$	−116.073	+	357.236i	−0.0230256	+	0.0708654i
$295$		0			0
$296$	−781.099	−	2403.97i	−0.153380	−	0.472055i
$297$	−1227.27	−	3777.14i	−0.239775	−	0.737952i
$298$	1152.99	+	837.700i	0.224131	+	0.162841i
$299$	7375.18			1.42648
$300$		0			0
$301$	2296.57			0.439774
$302$	−3632.70	−	2639.31i	−0.692181	−	0.502899i
$303$	1920.22	+	5909.82i	0.364071	+	1.12050i
$304$	−47.4198	−	145.943i	−0.00894642	−	0.0275343i
$305$		0			0
$306$	−333.747	+	1027.17i	−0.0623499	+	0.191893i
$307$	−8228.56			−1.52973			−0.764867	−	0.644188i	$-0.777196\pi$
$307$	−8228.56			−1.52973			−0.764867	+	0.644188i	$0.777196\pi$
$308$	−556.657	+	1713.21i	−0.102982	+	0.316946i
$309$	494.275	−	359.112i	0.0909978	−	0.0661138i
$310$		0			0
$311$	−3664.69	−	2662.56i	−0.668186	−	0.485465i	0.201232	−	0.979544i	$-0.435506\pi$
$311$	−3664.69	−	2662.56i	−0.668186	−	0.485465i	−0.869417	+	0.494078i	$0.835506\pi$
$312$	1874.23	−	1361.71i	0.340089	−	0.247089i
$313$	−1153.86	+	838.330i	−0.208371	+	0.151390i	−0.687076	−	0.726585i	$-0.741106\pi$
$313$	−1153.86	+	838.330i	−0.208371	+	0.151390i	0.478705	+	0.877976i	$0.341106\pi$
$314$	−1648.46	−	1197.68i	−0.296268	−	0.215251i
$315$		0			0
$316$	937.416	−	681.072i	0.166879	−	0.121245i
$317$	2115.85	−	6511.91i	0.374883	−	1.15377i	−0.568674	−	0.822563i	$-0.692544\pi$
$317$	2115.85	−	6511.91i	0.374883	−	1.15377i	0.943557	−	0.331209i	$-0.107456\pi$
$318$	−3301.37			−0.582174
$319$	1913.81	−	5890.10i	0.335902	−	1.03380i
$320$		0			0
$321$	−571.856	−	1759.99i	−0.0994327	−	0.306022i
$322$	1178.86	+	3628.16i	0.204023	+	0.627918i
$323$	506.223	+	367.793i	0.0872044	+	0.0633577i
$324$	−1748.03			−0.299731
$325$		0			0
$326$	−7970.00			−1.35404
$327$	12.5936	+	9.14981i	0.00212975	+	0.00154736i
$328$	−1086.58	−	3344.14i	−0.182915	−	0.562956i
$329$	−845.680	−	2602.73i	−0.141714	−	0.436150i
$330$		0			0
$331$	−2434.24	+	7491.83i	−0.404224	+	1.24407i	0.517317	+	0.855794i	$0.326931\pi$
$331$	−2434.24	+	7491.83i	−0.404224	+	1.24407i	−0.921541	+	0.388280i	$0.873069\pi$
$332$	−4669.31			−0.771872
$333$	808.154	−	2487.24i	0.132993	−	0.409310i
$334$	741.382	−	538.646i	0.121457	−	0.0882437i
$335$		0			0
$336$	969.465	+	704.357i	0.157407	+	0.114363i
$337$	2764.03	−	2008.18i	0.446784	−	0.324607i	−0.341541	−	0.939867i	$-0.610949\pi$
$337$	2764.03	−	2008.18i	0.446784	−	0.324607i	0.788325	+	0.615260i	$0.210949\pi$
$338$	−3692.33	+	2682.63i	−0.594190	+	0.431704i
$339$	−6649.39	−	4831.07i	−1.06533	−	0.774005i
$340$		0			0
$341$	−62.8124	+	45.6359i	−0.00997502	+	0.00724728i
$342$	49.0623	−	150.998i	0.00775727	−	0.0238744i
$343$	6688.21			1.05285
$344$	−328.008	+	1009.50i	−0.0514099	+	0.158223i
$345$		0			0
$346$	801.779	+	2467.62i	0.124578	+	0.383411i
$347$	1417.00	+	4361.07i	0.219217	+	0.674682i	0.998827	+	0.0484164i	$0.0154175\pi$
$347$	1417.00	+	4361.07i	0.219217	+	0.674682i	−0.779610	+	0.626266i	$0.784583\pi$
$348$	−3333.06	−	2421.61i	−0.513422	−	0.373023i
$349$	−7646.87			−1.17286			−0.586429	−	0.810001i	$-0.699467\pi$
$349$	−7646.87			−1.17286			−0.586429	+	0.810001i	$0.699467\pi$
$350$		0			0
$351$	10215.7			1.55349
$352$	−673.573	−	489.380i	−0.101993	−	0.0741023i
$353$	1181.84	+	3637.32i	0.178195	+	0.548428i	0.999765	−	0.0216800i	$-0.00690151\pi$
$353$	1181.84	+	3637.32i	0.178195	+	0.548428i	−0.821570	+	0.570108i	$0.806902\pi$
$354$	−1433.46	−	4411.74i	−0.215219	−	0.662376i
$355$		0			0
$356$	−334.689	+	1030.07i	−0.0498271	+	0.153352i
$357$	−4886.31			−0.724401
$358$	1169.83	−	3600.37i	0.172703	−	0.531524i
$359$	−2952.25	+	2144.94i	−0.434022	+	0.315335i	−0.783255	−	0.621701i	$-0.786442\pi$
$359$	−2952.25	+	2144.94i	−0.434022	+	0.315335i	0.349233	+	0.937036i	$0.386442\pi$
$360$		0			0
$361$	5474.63	+	3977.55i	0.798167	+	0.579903i
$362$	−6467.00	+	4698.55i	−0.938945	+	0.682183i
$363$	2289.59	−	1663.48i	0.331053	−	0.240524i
$364$	−3748.65	−	2723.56i	−0.539788	−	0.392179i
$365$		0			0
$366$	−881.681	+	640.579i	−0.125919	+	0.0914852i
$367$	2362.81	−	7271.98i	0.336070	−	1.03432i	−0.630122	−	0.776496i	$-0.716995\pi$
$367$	2362.81	−	7271.98i	0.336070	−	1.03432i	0.966193	−	0.257822i	$-0.0830047\pi$
$368$	−1763.20			−0.249765
$369$	1124.21	−	3459.98i	0.158602	−	0.488128i
$370$		0			0
$371$	2040.46	+	6279.88i	0.285540	+	0.878801i
$372$	15.9602	+	49.1206i	0.00222446	+	0.00684619i
$373$	783.098	+	568.954i	0.108706	+	0.0789794i	0.640810	−	0.767699i	$-0.278599\pi$
$373$	783.098	+	568.954i	0.108706	+	0.0789794i	−0.532104	+	0.846679i	$0.678599\pi$
$374$	3394.96			0.469383
$375$		0			0
$376$	1264.87			0.173486
$377$	12888.0	+	9363.71i	1.76066	+	1.27919i
$378$	1632.90	+	5025.55i	0.222189	+	0.683826i
$379$	682.104	+	2099.30i	0.0924468	+	0.284522i	0.986580	−	0.163279i	$-0.0522072\pi$
$379$	682.104	+	2099.30i	0.0924468	+	0.284522i	−0.894133	+	0.447801i	$0.852207\pi$
$380$		0			0
$381$	3272.03	−	10070.3i	0.439976	−	1.35411i
$382$	8159.28			1.09284
$383$	−2001.64	+	6160.40i	−0.267047	+	0.821885i	0.724168	+	0.689623i	$0.242224\pi$
$383$	−2001.64	+	6160.40i	−0.267047	+	0.821885i	−0.991215	+	0.132262i	$0.957776\pi$
$384$	−448.079	+	325.548i	−0.0595466	+	0.0432632i
$385$		0			0
$386$	2645.92	+	1922.37i	0.348895	+	0.253487i
$387$	−888.480	+	645.519i	−0.116703	+	0.0847896i
$388$	667.651	−	485.077i	0.0873578	−	0.0634692i
$389$	−3868.36	−	2810.53i	−0.504199	−	0.366322i	0.306419	−	0.951897i	$-0.400869\pi$
$389$	−3868.36	−	2810.53i	−0.504199	−	0.366322i	−0.810619	+	0.585574i	$0.800869\pi$
$390$		0			0
$391$	5816.58	−	4225.99i	0.752319	−	0.546592i
$392$	−107.301	+	330.239i	−0.0138253	+	0.0425500i
$393$	−9904.71			−1.27131
$394$	829.787	−	2553.82i	0.106102	−	0.326548i
$395$		0			0
$396$	−266.194	−	819.260i	−0.0337796	−	0.103963i
$397$	−2754.67	−	8478.00i	−0.348244	−	1.07179i	−0.959824	−	0.280603i	$-0.909466\pi$
$397$	−2754.67	−	8478.00i	−0.348244	−	1.07179i	0.611580	−	0.791183i	$-0.290534\pi$
$398$	−4667.88	−	3391.41i	−0.587888	−	0.427126i
$399$	718.310			0.0901265
$400$		0			0
$401$	−9368.71			−1.16671			−0.583356	−	0.812217i	$-0.698261\pi$
$401$	−9368.71			−1.16671			−0.583356	+	0.812217i	$0.698261\pi$
$402$	−6102.89	−	4434.01i	−0.757175	−	0.550120i
$403$	−61.7139	−	189.936i	−0.00762826	−	0.0234774i
$404$	1775.10	+	5463.20i	0.218601	+	0.672784i
$405$		0			0
$406$	−2546.36	+	7836.88i	−0.311265	+	0.957976i
$407$	−8220.74			−1.00120
$408$	697.888	−	2147.88i	0.0846829	−	0.260627i
$409$	−3551.64	+	2580.41i	−0.429382	+	0.311964i	−0.781402	−	0.624028i	$-0.785495\pi$
$409$	−3551.64	+	2580.41i	−0.429382	+	0.311964i	0.352020	+	0.935992i	$0.385495\pi$
$410$		0			0
$411$	−181.567	−	131.916i	−0.0217909	−	0.0158320i
$412$	456.922	−	331.973i	0.0546382	−	0.0396970i
$413$	−7506.06	+	5453.47i	−0.894308	+	0.649753i
$414$	−1475.87	−	1072.28i	−0.175206	−	0.127294i
$415$		0			0
$416$	1732.60	−	1258.80i	0.204201	−	0.148361i
$417$	2521.99	−	7761.87i	0.296168	−	0.911512i
$418$	−499.074			−0.0583983
$419$	−2015.43	+	6202.86i	−0.234989	+	0.723221i	0.762134	+	0.647419i	$0.224152\pi$
$419$	−2015.43	+	6202.86i	−0.234989	+	0.723221i	−0.997123	+	0.0758020i	$0.975848\pi$
$420$		0			0
$421$	4356.30	+	13407.3i	0.504306	+	1.55210i	0.801934	+	0.597413i	$0.203805\pi$
$421$	4356.30	+	13407.3i	0.504306	+	1.55210i	−0.297627	+	0.954682i	$0.596195\pi$
$422$	3161.92	+	9731.37i	0.364738	+	1.12255i
$423$	1058.75	+	769.224i	0.121697	+	0.0884183i
$424$	−3051.88			−0.349557
$425$		0			0
$426$	−6635.29			−0.754650
$427$	1763.45	+	1281.22i	0.199858	+	0.145205i
$428$	−528.640	−	1626.99i	−0.0597028	−	0.183746i
$429$	−2328.28	−	7165.72i	−0.262029	−	0.806443i
$430$		0			0
$431$	1259.25	−	3875.58i	0.140733	−	0.433133i	−0.855704	−	0.517465i	$-0.826876\pi$
$431$	1259.25	−	3875.58i	0.140733	−	0.433133i	0.996438	+	0.0843322i	$0.0268757\pi$
$432$	−2442.30			−0.272003
$433$	−576.796	+	1775.20i	−0.0640163	+	0.197022i	−0.977949	−	0.208844i	$-0.933030\pi$
$433$	−576.796	+	1775.20i	−0.0640163	+	0.197022i	0.913933	+	0.405866i	$0.133030\pi$
$434$	83.5730	−	60.7194i	0.00924340	−	0.00671572i
$435$		0			0
$436$	11.6419	+	8.45835i	0.00127878	+	0.000929086i
$437$	−855.062	+	621.239i	−0.0935999	+	0.0680043i
$438$	6100.47	−	4432.25i	0.665507	−	0.483519i
$439$	11021.4	+	8007.55i	1.19823	+	0.870568i	0.994110	−	0.108377i	$-0.0345652\pi$
$439$	11021.4	+	8007.55i	1.19823	+	0.870568i	0.204125	+	0.978945i	$0.434565\pi$
$440$		0			0
$441$	−290.649	+	211.169i	−0.0313842	+	0.0228019i
$442$	−2698.54	+	8305.26i	−0.290399	+	0.893758i
$443$	3798.21			0.407356			0.203678	−	0.979038i	$-0.434710\pi$
$443$	3798.21			0.407356			0.203678	+	0.979038i	$0.434710\pi$
$444$	−1689.91	+	5201.00i	−0.180629	+	0.555920i
$445$		0			0
$446$	−1169.64	−	3599.80i	−0.124180	−	0.382187i
$447$	−952.815	−	2932.46i	−0.100820	−	0.310292i
$448$	896.201	+	651.128i	0.0945123	+	0.0686672i
$449$	14616.5			1.53629			0.768145	−	0.640276i	$-0.221180\pi$
$449$	14616.5			1.53629			0.768145	+	0.640276i	$0.221180\pi$
$450$		0			0
$451$	−11435.8			−1.19399
$452$	−6146.89	−	4465.98i	−0.639658	−	0.464739i
$453$	3002.00	+	9239.21i	0.311361	+	0.958270i
$454$	−3635.36	−	11188.5i	−0.375806	−	1.15661i
$455$		0			0
$456$	−102.593	+	315.748i	−0.0105358	+	0.0324260i
$457$	2485.82			0.254446			0.127223	−	0.991874i	$-0.459394\pi$
$457$	2485.82			0.254446			0.127223	+	0.991874i	$0.459394\pi$
$458$	−223.449	+	687.706i	−0.0227972	+	0.0701625i
$459$	8056.83	−	5853.63i	0.819304	−	0.595259i
$460$		0			0
$461$	2332.84	+	1694.91i	0.235686	+	0.171236i	0.699359	−	0.714770i	$-0.253469\pi$
$461$	2332.84	+	1694.91i	0.235686	+	0.171236i	−0.463673	+	0.886006i	$0.653469\pi$
$462$	3152.97	−	2290.76i	0.317509	−	0.230684i
$463$	−6726.66	+	4887.21i	−0.675194	+	0.490557i	−0.871760	−	0.489934i	$-0.837021\pi$
$463$	−6726.66	+	4887.21i	−0.675194	+	0.490557i	0.196566	+	0.980491i	$0.437021\pi$
$464$	−3081.18	−	2238.61i	−0.308276	−	0.223976i
$465$		0			0
$466$	3976.76	−	2889.29i	0.395322	−	0.287218i
$467$	−1052.15	+	3238.18i	−0.104256	+	0.320868i	−0.989555	−	0.144155i	$-0.953954\pi$
$467$	−1052.15	+	3238.18i	−0.104256	+	0.320868i	0.885299	+	0.465022i	$0.153954\pi$
$468$	2215.79			0.218856
$469$	−4662.42	+	14349.5i	−0.459042	+	1.41278i
$470$		0			0
$471$	1362.26	+	4192.61i	0.133269	+	0.410160i
$472$	−1325.13	−	4078.34i	−0.129225	−	0.397713i
$473$	2792.84	+	2029.12i	0.271491	+	0.197250i
$474$	−2506.87			−0.242920
$475$		0			0
$476$	−4517.05			−0.434955
$477$	−2554.54	−	1855.98i	−0.245208	−	0.178154i
$478$	−3678.37	−	11320.9i	−0.351976	−	1.08327i
$479$	4207.14	+	12948.2i	0.401313	+	1.23511i	0.923935	+	0.382550i	$0.124954\pi$
$479$	4207.14	+	12948.2i	0.401313	+	1.23511i	−0.522622	+	0.852565i	$0.675046\pi$
$480$		0			0
$481$	6534.40	−	20110.8i	0.619424	−	1.90639i
$482$	9678.15			0.914581
$483$	2550.46	−	7849.52i	0.240270	−	0.739474i
$484$	2116.56	−	1537.77i	0.198775	−	0.144419i
$485$		0			0
$486$	−3608.95	−	2622.06i	−0.336842	−	0.244730i
$487$	2612.65	−	1898.20i	0.243102	−	0.176624i	−0.459562	−	0.888146i	$-0.651994\pi$
$487$	2612.65	−	1898.20i	0.243102	−	0.176624i	0.702664	+	0.711522i	$0.251994\pi$
$488$	−815.051	+	592.169i	−0.0756058	+	0.0549308i
$489$	13949.9	+	10135.2i	1.29006	+	0.937282i
$490$		0			0
$491$	509.592	−	370.241i	0.0468383	−	0.0340300i	−0.564120	−	0.825693i	$-0.690784\pi$
$491$	509.592	−	370.241i	0.0468383	−	0.0340300i	0.610958	+	0.791663i	$0.290784\pi$
$492$	−2350.81	+	7235.05i	−0.215412	+	0.662970i
$493$	15529.8			1.41872
$494$	396.697	−	1220.91i	0.0361301	−	0.111197i
$495$		0			0
$496$	14.7541	+	45.4085i	0.00133564	+	0.00411069i
$497$	4101.04	+	12621.7i	0.370134	+	1.13916i
$498$	8172.72	+	5937.83i	0.735399	+	0.534298i
$499$	−4951.62			−0.444218			−0.222109	−	0.975022i	$-0.571294\pi$
$499$	−4951.62			−0.444218			−0.222109	+	0.975022i	$0.571294\pi$
$500$		0			0
$501$	−1982.63			−0.176801
$502$	164.996	+	119.877i	0.0146696	+	0.0106581i
$503$	−3168.86	−	9752.74i	−0.280899	−	0.864519i	−0.987598	−	0.157004i	$-0.949816\pi$
$503$	−3168.86	−	9752.74i	−0.280899	−	0.864519i	0.706699	−	0.707515i	$-0.250184\pi$
$504$	354.175	+	1090.04i	0.0313020	+	0.0963378i
$505$		0			0
$506$	−1772.03	+	5453.76i	−0.155685	+	0.479149i
$507$	9874.13			0.864942
$508$	3024.75	−	9309.24i	0.264177	−	0.813052i
$509$	2483.65	−	1804.48i	0.216279	−	0.157136i	−0.474371	−	0.880325i	$-0.657325\pi$
$509$	2483.65	−	1804.48i	0.216279	−	0.157136i	0.690650	+	0.723189i	$0.257325\pi$
$510$		0			0
$511$	−12201.5	−	8864.94i	−1.05629	−	0.767440i
$512$	−414.217	+	300.946i	−0.0357538	+	0.0259767i
$513$	−1184.39	+	860.509i	−0.101934	+	0.0740593i
$514$	1128.82	+	820.134i	0.0968677	+	0.0703785i
$515$		0			0
$516$	1857.87	−	1349.82i	0.158504	−	0.115160i
$517$	1271.20	−	3912.36i	0.108138	−	0.332815i
$518$	10937.8			0.927762
$519$	1734.65	−	5338.69i	0.146710	−	0.451527i
$520$		0			0
$521$	−2563.20	−	7888.71i	−0.215539	−	0.663360i	−0.999115	−	0.0420642i	$-0.986607\pi$
$521$	−2563.20	−	7888.71i	−0.215539	−	0.663360i	0.783576	−	0.621296i	$-0.213393\pi$
$522$	−1217.67	−	3747.61i	−0.102100	−	0.314230i
$523$	345.930	+	251.333i	0.0289225	+	0.0210134i	0.602153	−	0.798381i	$-0.294310\pi$
$523$	345.930	+	251.333i	0.0289225	+	0.0210134i	−0.573230	+	0.819394i	$0.694310\pi$
$524$	−9156.20			−0.763340
$525$		0			0
$526$	−7315.96			−0.606447
$527$	−157.505	−	114.434i	−0.0130191	−	0.00945890i
$528$	556.629	+	1713.13i	0.0458791	+	0.141201i
$529$	−7.07696	−	21.7806i	−0.000581652	−	0.00179014i
$530$		0			0
$531$	1371.03	−	4219.60i	0.112048	−	0.344849i
$532$	664.026			0.0541150
$533$	9089.93	−	27975.9i	0.738703	−	2.27349i
$534$	1895.71	−	1377.32i	0.153625	−	0.111615i
$535$		0			0
$536$	−5641.68	−	4098.92i	−0.454634	−	0.330311i
$537$	−6626.06	+	4814.11i	−0.532468	+	0.386861i
$538$	−6965.14	+	5060.47i	−0.558157	+	0.405525i
$539$	913.624	+	663.786i	0.0730103	+	0.0530451i
$540$		0			0
$541$	6485.80	−	4712.21i	0.515428	−	0.374480i	−0.299451	−	0.954112i	$-0.596804\pi$
$541$	6485.80	−	4712.21i	0.515428	−	0.374480i	0.814879	+	0.579632i	$0.196804\pi$
$542$	265.748	−	817.889i	0.0210606	−	0.0648180i
$543$	17294.2			1.36679
$544$	645.148	−	1985.56i	0.0508465	−	0.156489i
$545$		0			0
$546$	3097.82	+	9534.12i	0.242811	+	0.747294i
$547$	−2887.94	−	8888.15i	−0.225739	−	0.694753i	−0.998216	−	0.0597102i	$-0.980982\pi$
$547$	−2887.94	−	8888.15i	−0.225739	−	0.694753i	0.772477	−	0.635043i	$-0.219018\pi$
$548$	−167.846	−	121.947i	−0.0130840	−	0.00950607i
$549$	−1042.35			−0.0810321
$550$		0			0
$551$	−2282.95			−0.176510
$552$	3086.15	+	2242.22i	0.237962	+	0.172890i
$553$	1549.40	+	4768.58i	0.119145	+	0.366692i
$554$	1062.35	+	3269.58i	0.0814711	+	0.250742i
$555$		0			0
$556$	2331.40	−	7175.30i	0.177829	−	0.547303i
$557$	8146.38			0.619700			0.309850	−	0.950785i	$-0.399721\pi$
$557$	8146.38			0.619700			0.309850	+	0.950785i	$0.399721\pi$
$558$	−15.2652	+	46.9813i	−0.00115811	+	0.00356430i
$559$	−7183.88	+	5219.40i	−0.543553	+	0.394914i
$560$		0			0
$561$	−5942.22	−	4317.27i	−0.447202	−	0.324912i
$562$	4395.10	−	3193.23i	0.329886	−	0.239677i
$563$	−12602.1	+	9155.99i	−0.943370	+	0.685398i	−0.949229	−	0.314585i	$-0.898135\pi$
$563$	−12602.1	+	9155.99i	−0.943370	+	0.685398i	0.00585987	+	0.999983i	$0.498135\pi$
$564$	−2213.91	−	1608.50i	−0.165288	−	0.120089i
$565$		0			0
$566$	5228.43	−	3798.68i	0.388281	−	0.282103i
$567$	2337.43	−	7193.88i	0.173127	−	0.532830i
$568$	−6133.85			−0.453118
$569$	−3590.15	+	11049.3i	−0.264511	+	0.814082i	0.727294	+	0.686326i	$0.240777\pi$
$569$	−3590.15	+	11049.3i	−0.264511	+	0.814082i	−0.991806	+	0.127756i	$0.959223\pi$
$570$		0			0
$571$	6684.41	+	20572.5i	0.489901	+	1.50776i	0.824754	+	0.565491i	$0.191313\pi$
$571$	6684.41	+	20572.5i	0.489901	+	1.50776i	−0.334853	+	0.942270i	$0.608687\pi$
$572$	−2152.33	−	6624.20i	−0.157331	−	0.484216i
$573$	−14281.2	−	10375.9i	−1.04120	−	0.756476i
$574$	15215.5			1.10642
$575$		0			0
$576$	−529.734			−0.0383199
$577$	8139.27	+	5913.53i	0.587248	+	0.426661i	0.841330	−	0.540522i	$-0.181773\pi$
$577$	8139.27	+	5913.53i	0.587248	+	0.426661i	−0.254082	+	0.967183i	$0.581773\pi$
$578$	−405.730	−	1248.71i	−0.0291975	−	0.0898606i
$579$	−2186.54	−	6729.48i	−0.156942	−	0.483018i
$580$		0			0
$581$	6243.71	−	19216.2i	0.445840	−	1.37215i
$582$	−1785.45			−0.127164
$583$	−3067.16	+	9439.75i	−0.217888	+	0.670591i
$584$	5639.45	−	4097.30i	0.399593	−	0.290321i
$585$		0			0
$586$	9822.91	+	7136.76i	0.692458	+	0.503101i
$587$	5606.57	−	4073.41i	0.394222	−	0.286419i	−0.372962	−	0.927847i	$-0.621658\pi$
$587$	5606.57	−	4073.41i	0.394222	−	0.286419i	0.767183	+	0.641428i	$0.221658\pi$
$588$	607.766	−	441.568i	0.0426256	−	0.0309693i
$589$	23.1540	+	16.8224i	0.00161977	+	0.00117683i
$590$		0			0
$591$	−4700.01	+	3414.76i	−0.327128	+	0.237672i
$592$	−1562.20	+	4807.95i	−0.108456	+	0.333793i
$593$	8835.99			0.611890			0.305945	−	0.952049i	$-0.401028\pi$
$593$	8835.99			0.611890			0.305945	+	0.952049i	$0.401028\pi$
$594$	−2454.53	+	7554.28i	−0.169547	+	0.521811i
$595$		0			0
$596$	−880.809	−	2710.85i	−0.0605358	−	0.186310i
$597$	3857.45	+	11872.0i	0.264447	+	0.813885i
$598$	−11933.3	−	8670.04i	−0.816034	−	0.592883i
$599$	−6416.69			−0.437694			−0.218847	−	0.975759i	$-0.570230\pi$
$599$	−6416.69			−0.437694			−0.218847	+	0.975759i	$0.570230\pi$
$600$		0			0
$601$	−104.752			−0.00710971			−0.00355486	−	0.999994i	$-0.501132\pi$
$601$	−104.752			−0.00710971			−0.00355486	+	0.999994i	$0.501132\pi$
$602$	−3715.93	−	2699.78i	−0.251578	−	0.182782i
$603$	−2229.57	−	6861.92i	−0.150573	−	0.463415i
$604$	2775.14	+	8541.00i	0.186952	+	0.575378i
$605$		0			0
$606$	3840.43	−	11819.6i	0.257437	−	0.792310i
$607$	5057.18			0.338163			0.169081	−	0.985602i	$-0.445920\pi$
$607$	5057.18			0.338163			0.169081	+	0.985602i	$0.445920\pi$
$608$	−94.8396	+	291.886i	−0.00632607	+	0.0194697i
$609$	14422.9	−	10478.8i	0.959678	−	0.697247i
$610$		0			0
$611$	8560.58	+	6219.62i	0.566815	+	0.411815i
$612$	1747.52	−	1269.65i	0.115424	−	0.0838604i
$613$	−13156.8	+	9558.95i	−0.866879	+	0.629824i	−0.929748	−	0.368198i	$-0.879975\pi$
$613$	−13156.8	+	9558.95i	−0.866879	+	0.629824i	0.0628688	+	0.998022i	$0.479975\pi$
$614$	13314.1	+	9673.25i	0.875102	+	0.635799i
$615$		0			0
$616$	2914.69	−	2117.65i	0.190643	−	0.138510i
$617$	−1445.63	+	4449.19i	−0.0943256	+	0.290304i	−0.987077	−	0.160245i	$-0.948772\pi$
$617$	−1445.63	+	4449.19i	−0.0943256	+	0.290304i	0.892752	+	0.450549i	$0.148772\pi$
$618$	−1221.92			−0.0795350
$619$	4502.12	−	13856.1i	0.292335	−	0.899714i	−0.691769	−	0.722119i	$-0.743168\pi$
$619$	4502.12	−	13856.1i	0.292335	−	0.899714i	0.984104	−	0.177595i	$-0.0568318\pi$
$620$		0			0
$621$	5198.10	+	15998.1i	0.335898	+	1.03379i
$622$	2799.58	+	8616.21i	0.180471	+	0.555432i
$623$	−3791.61	−	2754.77i	−0.243833	−	0.177155i
$624$	−4633.36			−0.297248
$625$		0			0
$626$	2852.50			0.182123
$627$	873.532	+	634.658i	0.0556388	+	0.0404239i
$628$	1259.31	+	3875.77i	0.0800192	+	0.246274i
$629$	−6370.05	−	19605.0i	−0.403801	−	1.24277i
$630$		0			0
$631$	2067.63	−	6363.51i	0.130445	−	0.401470i	−0.864408	−	0.502790i	$-0.832307\pi$
$631$	2067.63	−	6363.51i	0.130445	−	0.401470i	0.994854	+	0.101321i	$0.0323068\pi$
$632$	−2317.42			−0.145858
$633$	6840.80	−	21053.8i	0.429538	−	1.32198i
$634$	−11078.7	+	8049.17i	−0.693995	+	0.504217i
$635$		0			0
$636$	5341.72	+	3880.99i	0.333039	+	0.241967i
$637$	−2350.06	+	1707.42i	−0.146174	+	0.106202i
$638$	−10020.8	+	7280.57i	−0.621832	+	0.451787i
$639$	−5134.28	−	3730.27i	−0.317854	−	0.230935i
$640$		0			0
$641$	502.371	−	364.994i	0.0309555	−	0.0224905i	−0.572200	−	0.820114i	$-0.693910\pi$
$641$	502.371	−	364.994i	0.0309555	−	0.0224905i	0.603155	+	0.797624i	$0.293910\pi$
$642$	−1143.71	+	3519.98i	−0.0703095	+	0.216390i
$643$	−27013.5			−1.65678			−0.828388	−	0.560155i	$-0.810742\pi$
$643$	−27013.5			−1.65678			−0.828388	+	0.560155i	$0.810742\pi$
$644$	2357.72	−	7256.33i	0.144266	−	0.444005i
$645$		0			0
$646$	−386.720	−	1190.20i	−0.0235531	−	0.0724890i
$647$	−2011.36	−	6190.32i	−0.122217	−	0.376146i	0.871167	−	0.490988i	$-0.163364\pi$
$647$	−2011.36	−	6190.32i	−0.122217	−	0.376146i	−0.993384	+	0.114842i	$0.963364\pi$
$648$	2828.37	+	2054.93i	0.171465	+	0.124576i
$649$	−13946.5			−0.843523
$650$		0			0
$651$	−223.494			−0.0134553
$652$	12895.7	+	9369.29i	0.774595	+	0.562776i
$653$	5754.14	+	17709.4i	0.344834	+	1.06129i	0.961672	+	0.274201i	$0.0884133\pi$
$653$	5754.14	+	17709.4i	0.344834	+	1.06129i	−0.616838	+	0.787090i	$0.711587\pi$
$654$	−9.62068	−	29.6094i	−0.000575227	−	0.00177037i
$655$		0			0
$656$	−2173.16	+	6688.29i	−0.129341	+	0.398070i
$657$	7212.20			0.428272
$658$	−1691.36	+	5205.47i	−0.100207	+	0.308405i
$659$	−989.013	+	718.560i	−0.0584621	+	0.0424752i	−0.616632	−	0.787251i	$-0.711504\pi$
$659$	−989.013	+	718.560i	−0.0584621	+	0.0424752i	0.558170	+	0.829726i	$0.311504\pi$
$660$		0			0
$661$	3178.24	+	2309.13i	0.187019	+	0.135877i	0.677355	−	0.735656i	$-0.263126\pi$
$661$	3178.24	+	2309.13i	0.187019	+	0.135877i	−0.490336	+	0.871533i	$0.663126\pi$
$662$	12745.9	−	9260.42i	0.748312	−	0.543680i
$663$	15284.8	−	11105.1i	0.895346	−	0.650507i
$664$	7555.10	+	5489.10i	0.441558	+	0.320811i
$665$		0			0
$666$	−4231.55	+	3074.40i	−0.246200	+	0.178875i
$667$	−8105.96	+	24947.6i	−0.470561	+	1.44824i
$668$	−1832.80			−0.106157
$669$	−2530.52	+	7788.15i	−0.146242	+	0.450086i
$670$		0			0
$671$	1012.50	+	3116.17i	0.0582523	+	0.179282i
$672$	−740.605	−	2279.35i	−0.0425141	−	0.130845i
$673$	14336.9	+	10416.4i	0.821169	+	0.596614i	0.917047	−	0.398779i	$-0.130566\pi$
$673$	14336.9	+	10416.4i	0.821169	+	0.596614i	−0.0958781	+	0.995393i	$0.530566\pi$
$674$	−6833.05			−0.390503
$675$		0			0
$676$	9127.93			0.519341
$677$	−14778.2	−	10737.0i	−0.838955	−	0.609536i	0.0831236	−	0.996539i	$-0.473510\pi$
$677$	−14778.2	−	10737.0i	−0.838955	−	0.609536i	−0.922079	+	0.387003i	$0.873510\pi$
$678$	5079.69	+	15633.7i	0.287735	+	0.885556i
$679$	1103.52	+	3396.30i	0.0623702	+	0.191956i
$680$		0			0
$681$	−7865.10	+	24206.3i	−0.442571	+	1.36209i
$682$	155.281			0.00871849
$683$	−164.344	+	505.800i	−0.00920713	+	0.0283366i	−0.955555	−	0.294814i	$-0.904742\pi$
$683$	−164.344	+	505.800i	−0.00920713	+	0.0283366i	0.946347	+	0.323151i	$0.104742\pi$
$684$	−256.894	+	186.644i	−0.0143605	+	0.0104335i
$685$		0			0
$686$	−10821.7	−	7862.46i	−0.602298	−	0.437595i
$687$	1265.64	−	919.543i	0.0702871	−	0.0510666i
$688$	1717.47	−	1247.82i	0.0951715	−	0.0691461i
$689$	−20655.0	−	15006.7i	−1.14208	−	0.829768i
$690$		0			0
$691$	−5513.91	+	4006.09i	−0.303559	+	0.220548i	−0.729128	−	0.684378i	$-0.760074\pi$
$691$	−5513.91	+	4006.09i	−0.303559	+	0.220548i	0.425569	+	0.904926i	$0.360074\pi$
$692$	1603.56	−	4935.24i	0.0880898	−	0.271112i
$693$	3727.55			0.204326
$694$	2834.00	−	8722.15i	0.155010	−	0.477072i
$695$		0			0
$696$	2546.23	+	7836.50i	0.138671	+	0.426784i
$697$	−8861.31	−	27272.3i	−0.481558	−	1.48208i
$698$	12372.9	+	8989.43i	0.670947	+	0.487471i
$699$	−10634.8			−0.575457
$700$		0			0
$701$	−26578.4			−1.43203			−0.716015	−	0.698085i	$-0.754036\pi$
$701$	−26578.4			−1.43203			−0.716015	+	0.698085i	$0.754036\pi$
$702$	−16529.4	−	12009.3i	−0.888692	−	0.645672i
$703$	936.426	+	2882.02i	0.0502389	+	0.154620i
$704$	514.564	+	1583.67i	0.0275474	+	0.0847822i
$705$		0			0
$706$	2363.67	−	7274.64i	0.126003	−	0.387797i
$707$	−24857.0			−1.32227
$708$	−2866.92	+	8823.47i	−0.152183	+	0.468371i
$709$	−7727.88	+	5614.63i	−0.409346	+	0.297408i	−0.773337	−	0.633995i	$-0.781414\pi$
$709$	−7727.88	+	5614.63i	−0.409346	+	0.297408i	0.363991	+	0.931403i	$0.381414\pi$
$710$		0			0
$711$	−1939.77	−	1409.33i	−0.102317	−	0.0743374i
$712$	1752.45	−	1273.23i	0.0922414	−	0.0670173i
$713$	266.042	−	193.291i	0.0139739	−	0.0101526i
$714$	7906.22	+	5744.21i	0.414402	+	0.301081i
$715$		0			0
$716$	−6125.32	+	4450.30i	−0.319712	+	0.232284i
$717$	−7958.15	+	24492.7i	−0.414508	+	1.27573i
$718$	7298.36			0.379349
$719$	7856.04	−	24178.4i	0.407484	−	1.25411i	−0.511319	−	0.859391i	$-0.670843\pi$
$719$	7856.04	−	24178.4i	0.407484	−	1.25411i	0.918803	−	0.394716i	$-0.129157\pi$
$720$		0			0
$721$	755.222	+	2324.33i	0.0390096	+	0.120059i
$722$	−4182.25	−	12871.6i	−0.215578	−	0.663480i
$723$	−16939.7	−	12307.4i	−0.871363	−	0.633083i
$724$	15987.3			0.820668
$725$		0			0
$726$	−5660.17			−0.289351
$727$	−8368.42	−	6080.01i	−0.426915	−	0.310172i	0.353499	−	0.935435i	$-0.384992\pi$
$727$	−8368.42	−	6080.01i	−0.426915	−	0.310172i	−0.780414	+	0.625263i	$0.784992\pi$
$728$	2863.72	+	8813.61i	0.145792	+	0.448701i
$729$	6628.53	+	20400.5i	0.336764	+	1.03645i
$730$		0			0
$731$	−2674.99	+	8232.76i	−0.135346	+	0.416552i
$732$	2179.63			0.110057
$733$	−382.494	+	1177.20i	−0.0192739	+	0.0593188i	−0.960231	−	0.279207i	$-0.909928\pi$
$733$	−382.494	+	1177.20i	−0.0192739	+	0.0593188i	0.940957	+	0.338526i	$0.109928\pi$
$734$	−12371.8	+	8988.67i	−0.622143	+	0.452013i
$735$		0			0
$736$	2852.92	+	2072.77i	0.142881	+	0.103809i
$737$	−18348.3	+	13330.8i	−0.917054	+	0.666278i
$738$	−5886.46	+	4276.77i	−0.293609	+	0.213320i
$739$	−26622.4	−	19342.3i	−1.32520	−	0.962812i	−0.999852	−	0.0172173i	$-0.994519\pi$
$739$	−26622.4	−	19342.3i	−1.32520	−	0.962812i	−0.325346	−	0.945595i	$-0.605481\pi$
$740$		0			0
$741$	−2246.94	+	1632.50i	−0.111395	+	0.0809329i
$742$	4080.91	−	12559.8i	0.201907	−	0.621406i
$743$	2700.91			0.133360			0.0666802	−	0.997774i	$-0.478759\pi$
$743$	2700.91			0.133360			0.0666802	+	0.997774i	$0.478759\pi$
$744$	31.9205	−	98.2412i	0.00157293	−	0.00484099i
$745$		0			0
$746$	−598.233	−	1841.17i	−0.0293604	−	0.0903621i
$747$	2985.75	+	9189.19i	0.146242	+	0.450087i
$748$	−5493.16	−	3991.01i	−0.268516	−	0.195088i
$749$	7402.62			0.361129
$750$		0			0
$751$	−20058.0			−0.974603			−0.487302	−	0.873234i	$-0.662019\pi$
$751$	−20058.0			−0.974603			−0.487302	+	0.873234i	$0.662019\pi$
$752$	−2046.60	−	1486.94i	−0.0992445	−	0.0721054i
$753$	−136.350	−	419.642i	−0.00659877	−	0.0203089i
$754$	−9845.58	−	30301.6i	−0.475537	−	1.46355i
$755$		0			0
$756$	3265.80	−	10051.1i	0.157111	−	0.483538i
$757$	−23344.1			−1.12081			−0.560406	−	0.828218i	$-0.689355\pi$
$757$	−23344.1			−1.12081			−0.560406	+	0.828218i	$0.689355\pi$
$758$	1364.21	−	4198.60i	0.0653698	−	0.201188i
$759$	10037.0	−	7292.31i	0.480000	−	0.348741i
$760$		0			0
$761$	13159.3	+	9560.79i	0.626839	+	0.455425i	0.855304	−	0.518127i	$-0.173371\pi$
$761$	13159.3	+	9560.79i	0.626839	+	0.455425i	−0.228465	+	0.973552i	$0.573371\pi$
$762$	−17132.5	+	12447.5i	−0.814497	+	0.591767i
$763$	−50.3770	+	36.6010i	−0.00239026	+	0.00173663i
$764$	−13202.0	−	9591.81i	−0.625172	−	0.454214i
$765$		0			0
$766$	10480.7	−	7614.68i	0.494365	−	0.359177i
$767$	11085.6	−	34117.9i	0.521874	−	1.60616i
$768$	1107.71			0.0520457
$769$	−145.783	+	448.675i	−0.00683626	+	0.0210398i	−0.954416	−	0.298478i	$-0.903521\pi$
$769$	−145.783	+	448.675i	−0.00683626	+	0.0210398i	0.947580	+	0.319518i	$0.103521\pi$
$770$		0			0
$771$	−932.835	−	2870.97i	−0.0435736	−	0.134106i
$772$	−2021.30	−	6220.92i	−0.0942334	−	0.290021i
$773$	5304.98	+	3854.29i	0.246839	+	0.179339i	0.704325	−	0.709878i	$-0.251250\pi$
$773$	5304.98	+	3854.29i	0.246839	+	0.179339i	−0.457486	+	0.889217i	$0.651250\pi$
$774$	2196.44			0.102002
$775$		0			0
$776$	−1650.52			−0.0763535
$777$	−19144.6	−	13909.3i	−0.883922	−	0.642207i
$778$	2955.16	+	9095.06i	0.136180	+	0.419118i
$779$	1302.65	+	4009.15i	0.0599132	+	0.184394i
$780$		0			0
$781$	−6164.57	+	18972.6i	−0.282440	+	0.869262i
$782$	−14379.4			−0.657551
$783$	−11228.0	+	34556.1i	−0.512458	+	1.57718i
$784$	561.837	−	408.198i	0.0255939	−	0.0185950i
$785$		0			0
$786$	16026.2	+	11643.7i	0.727270	+	0.528392i
$787$	−19206.4	+	13954.2i	−0.869927	+	0.632039i	−0.930567	−	0.366120i	$-0.880686\pi$
$787$	−19206.4	+	13954.2i	−0.869927	+	0.632039i	0.0606401	+	0.998160i	$0.480686\pi$
$788$	−4344.82	+	3156.70i	−0.196419	+	0.142706i
$789$	12805.2	+	9303.51i	0.577790	+	0.419789i
$790$		0			0
$791$	26598.9	−	19325.2i	1.19564	−	0.868680i
$792$	−532.387	+	1638.52i	−0.0238858	+	0.0735130i
$793$	−8428.05			−0.377413
$794$	−5509.34	+	16956.0i	−0.246246	+	0.757867i
$795$		0			0
$796$	3565.94	+	10974.8i	0.158783	+	0.488684i
$797$	7827.00	+	24089.0i	0.347863	+	1.07061i	0.960033	+	0.279886i	$0.0902966\pi$
$797$	7827.00	+	24089.0i	0.347863	+	1.07061i	−0.612171	+	0.790726i	$0.709703\pi$
$798$	−1162.25	−	844.424i	−0.0515579	−	0.0374590i
$799$	10315.3			0.456733
$800$		0			0
$801$	2241.18			0.0988617
$802$	15158.9	+	11013.6i	0.667430	+	0.484917i
$803$	−7005.66	−	21561.2i	−0.307876	−	0.947544i
$804$	4662.19	+	14348.7i	0.204506	+	0.629405i
$805$		0			0
$806$	−123.428	+	379.872i	−0.00539399	+	0.0166010i
$807$	18626.4			0.812490
$808$	3550.21	−	10926.4i	0.154574	−	0.475730i
$809$	16175.5	−	11752.2i	0.702965	−	0.510734i	−0.177931	−	0.984043i	$-0.556940\pi$
$809$	16175.5	−	11752.2i	0.702965	−	0.510734i	0.880897	+	0.473309i	$0.156940\pi$
$810$		0			0
$811$	−18960.5	−	13775.6i	−0.820953	−	0.596457i	0.0960321	−	0.995378i	$-0.469385\pi$
$811$	−18960.5	−	13775.6i	−0.820953	−	0.596457i	−0.916985	+	0.398921i	$0.869385\pi$
$812$	13332.9	−	9686.92i	0.576223	−	0.418651i
$813$	−1505.23	+	1093.61i	−0.0649331	+	0.0471767i
$814$	13301.4	+	9664.06i	0.572746	+	0.416124i
$815$		0			0
$816$	−3654.19	+	2654.93i	−0.156768	+	0.113898i
$817$	393.235	−	1210.25i	0.0168391	−	0.0518254i
$818$	8780.13			0.375293
$819$	−2962.91	+	9118.89i	−0.126413	+	0.389060i
$820$		0			0
$821$	12163.0	+	37433.9i	0.517042	+	1.59129i	0.779535	+	0.626358i	$0.215455\pi$
$821$	12163.0	+	37433.9i	0.517042	+	1.59129i	−0.262493	+	0.964934i	$0.584545\pi$
$822$	138.705	+	426.890i	0.00588551	+	0.0181138i
$823$	2822.27	+	2050.50i	0.119536	+	0.0868480i	0.645947	−	0.763382i	$-0.276463\pi$
$823$	2822.27	+	2050.50i	0.119536	+	0.0868480i	−0.526411	+	0.850230i	$0.676463\pi$
$824$	−1129.57			−0.0477555
$825$		0			0
$826$	18556.0			0.781654
$827$	25113.0	+	18245.6i	1.05594	+	0.767186i	0.973333	−	0.229396i	$-0.0736750\pi$
$827$	25113.0	+	18245.6i	1.05594	+	0.767186i	0.0826081	+	0.996582i	$0.473675\pi$
$828$	1127.47	+	3469.98i	0.0473214	+	0.145640i
$829$	4331.59	+	13331.3i	0.181474	+	0.558521i	0.999870	−	0.0161347i	$-0.00513605\pi$
$829$	4331.59	+	13331.3i	0.181474	+	0.558521i	−0.818395	+	0.574656i	$0.805136\pi$
$830$		0			0
$831$	2298.40	−	7073.74i	0.0959452	−	0.295289i
$832$	−4283.21			−0.178478
$833$	−875.068	+	2693.18i	−0.0363977	+	0.112021i
$834$	−13205.3	+	9594.20i	−0.548275	+	0.398345i
$835$		0			0
$836$	807.518	+	586.696i	0.0334074	+	0.0242719i
$837$	368.509	−	267.737i	0.0152181	−	0.0110566i
$838$	10552.9	−	7667.16i	0.435018	−	0.316059i
$839$	−18994.8	−	13800.5i	−0.781612	−	0.567874i	0.123851	−	0.992301i	$-0.460476\pi$
$839$	−18994.8	−	13800.5i	−0.781612	−	0.567874i	−0.905462	+	0.424427i	$0.860476\pi$
$840$		0			0
$841$	−26108.0	+	18968.6i	−1.07048	+	0.777751i
$842$	8712.60	−	26814.6i	0.356598	−	1.09750i
$843$	−11753.5			−0.480205
$844$	6323.83	−	19462.7i	0.257909	−	0.793762i
$845$		0			0
$846$	−808.810	−	2489.26i	−0.0328693	−	0.101161i
$847$	3498.35	+	10766.8i	0.141918	+	0.436779i
$848$	4938.04	+	3587.70i	0.199968	+	0.145285i
$849$	−13982.0			−0.565208
$850$		0			0
$851$	34819.0			1.40256
$852$	10736.1	+	7800.25i	0.431706	+	0.313653i
$853$	1556.41	+	4790.13i	0.0624741	+	0.192276i	0.977422	−	0.211296i	$-0.0677685\pi$
$853$	1556.41	+	4790.13i	0.0624741	+	0.192276i	−0.914948	+	0.403572i	$0.867769\pi$
$854$	−1347.15	−	4146.11i	−0.0539797	−	0.166132i
$855$		0			0
$856$	−1057.28	+	3253.97i	−0.0422162	+	0.129928i
$857$	−8927.91			−0.355860			−0.177930	−	0.984043i	$-0.556940\pi$
$857$	−8927.91			−0.355860			−0.177930	+	0.984043i	$0.556940\pi$
$858$	−4656.57	+	14331.4i	−0.185283	+	0.570242i
$859$	−31733.0	+	23055.4i	−1.26044	+	0.915761i	−0.998779	−	0.0493993i	$-0.984269\pi$
$859$	−31733.0	+	23055.4i	−1.26044	+	0.915761i	−0.261658	+	0.965161i	$0.584269\pi$
$860$		0			0
$861$	−26631.8	−	19349.1i	−1.05413	−	0.765873i
$862$	−6593.54	+	4790.49i	−0.260530	+	0.189286i
$863$	11626.1	−	8446.84i	0.458582	−	0.333179i	−0.334393	−	0.942434i	$-0.608531\pi$
$863$	11626.1	−	8446.84i	0.458582	−	0.333179i	0.792975	+	0.609254i	$0.208531\pi$
$864$	3951.73	+	2871.10i	0.155602	+	0.113052i
$865$		0			0
$866$	3020.14	−	2194.26i	0.118509	−	0.0861017i
$867$	−877.796	+	2701.58i	−0.0343847	+	0.105825i
$868$	−206.604			−0.00807902
$869$	−2329.02	+	7168.00i	−0.0909169	+	0.279813i
$870$		0			0
$871$	−18027.4	−	55482.6i	−0.701303	−	2.15839i
$872$	−8.89364	−	27.3718i	−0.000345386	−	0.00106299i
$873$	−1381.55	−	1003.76i	−0.0535607	−	0.0389141i
$874$	2113.83			0.0818093
$875$		0			0
$876$	−15081.2			−0.581674
$877$	9213.70	+	6694.14i	0.354760	+	0.257748i	0.750863	−	0.660458i	$-0.229638\pi$
$877$	9213.70	+	6694.14i	0.354760	+	0.257748i	−0.396103	+	0.918206i	$0.629638\pi$
$878$	−8419.64	−	25913.0i	−0.323632	−	0.996037i
$879$	−8117.48	−	24983.0i	−0.311486	−	0.958654i
$880$		0			0
$881$	−7799.98	+	24005.9i	−0.298284	+	0.918024i	0.683815	+	0.729656i	$0.260320\pi$
$881$	−7799.98	+	24005.9i	−0.298284	+	0.918024i	−0.982099	+	0.188368i	$0.939680\pi$
$882$	718.523			0.0274308
$883$	−3720.05	+	11449.1i	−0.141777	+	0.436346i	−0.996583	−	0.0826030i	$-0.973677\pi$
$883$	−3720.05	+	11449.1i	−0.141777	+	0.436346i	0.854805	+	0.518949i	$0.173677\pi$
$884$	14129.7	−	10265.9i	0.537596	−	0.390586i
$885$		0			0
$886$	−6145.64	−	4465.07i	−0.233033	−	0.169308i
$887$	38252.1	−	27791.8i	1.44801	−	1.05204i	0.461713	−	0.887029i	$-0.347235\pi$
$887$	38252.1	−	27791.8i	1.44801	−	1.05204i	0.986292	−	0.165009i	$-0.0527652\pi$
$888$	8848.46	−	6428.78i	0.334386	−	0.242946i
$889$	34266.8	+	24896.3i	1.29277	+	0.939251i
$890$		0			0
$891$	9198.65	−	6683.21i	0.345866	−	0.251286i
$892$	−2339.29	+	7199.59i	−0.0878085	+	0.270247i
$893$	−1516.40			−0.0568245
$894$	−1905.63	+	5864.92i	−0.0712906	+	0.219410i
$895$		0			0
$896$	−684.637	−	2107.09i	−0.0255269	−	0.0785637i
$897$	9861.46	+	30350.5i	0.367073	+	1.12973i
$898$	−23650.0	−	17182.7i	−0.878852	−	0.638523i
$899$	710.313			0.0263518
$900$		0			0
$901$	−24888.8			−0.920274
$902$	18503.5	+	13443.6i	0.683036	+	0.496255i
$903$	3070.78	+	9450.89i	0.113166	+	0.348290i
$904$	4695.81	+	14452.2i	0.172766	+	0.531718i
$905$		0			0
$906$	6004.01	−	18478.4i	0.220165	−	0.677599i
$907$	27755.0			1.01608			0.508042	−	0.861332i	$-0.330369\pi$
$907$	27755.0			1.01608			0.508042	+	0.861332i	$0.330369\pi$
$908$	−7270.72	+	22377.0i	−0.265735	+	0.817848i
$909$	9616.50	−	6986.80i	0.350890	−	0.254937i
$910$		0			0
$911$	32411.0	+	23548.0i	1.17873	+	0.856399i	0.992028	−	0.126017i	$-0.0402194\pi$
$911$	32411.0	+	23548.0i	1.17873	+	0.856399i	0.186704	+	0.982416i	$0.440219\pi$
$912$	537.182	−	390.286i	0.0195043	−	0.0141707i
$913$	24571.3	−	17852.1i	0.890679	−	0.647116i
$914$	−4022.14	−	2922.25i	−0.145559	−	0.105754i
$915$		0			0
$916$	1170.00	−	850.052i	0.0422028	−	0.0306621i
$917$	12243.5	−	37681.6i	0.440911	−	1.35699i
$918$	−19917.6			−0.716098
$919$	−4817.79	+	14827.6i	−0.172932	+	0.532229i	−0.999533	−	0.0305591i	$-0.990271\pi$
$919$	−4817.79	+	14827.6i	−0.172932	+	0.532229i	0.826601	+	0.562788i	$0.190271\pi$
$920$		0			0
$921$	−11002.5	−	33862.3i	−0.393644	−	1.21151i
$922$	−1782.13	−	5484.84i	−0.0636566	−	0.195915i
$923$	−41513.6	−	30161.4i	−1.48043	−	1.07560i
$924$	−7794.56			−0.277513
$925$		0			0
$926$	16629.2			0.590141
$927$	−945.497	−	686.944i	−0.0334997	−	0.0243389i
$928$	2353.81	+	7244.29i	0.0832625	+	0.256256i
$929$	193.077	+	594.230i	0.00681879	+	0.0209861i	0.954408	−	0.298505i	$-0.0964880\pi$
$929$	193.077	+	594.230i	0.00681879	+	0.0209861i	−0.947589	+	0.319491i	$0.896488\pi$
$930$		0			0
$931$	128.639	−	395.910i	0.00452843	−	0.0139371i
$932$	−9831.10			−0.345524
$933$	6056.88	−	18641.2i	0.212533	−	0.654109i
$934$	5509.13	−	4002.62i	0.193002	−	0.140224i
$935$		0			0
$936$	−3585.22	−	2604.81i	−0.125199	−	0.0909626i
$937$	19780.2	−	14371.1i	0.689637	−	0.501051i	−0.186904	−	0.982378i	$-0.559845\pi$
$937$	19780.2	−	14371.1i	0.689637	−	0.501051i	0.876541	+	0.481328i	$0.159845\pi$
$938$	24412.7	−	17736.9i	0.849791	−	0.617410i
$939$	−4992.76	−	3627.45i	−0.173517	−	0.126067i
$940$		0			0
$941$	17716.8	−	12872.0i	0.613765	−	0.445926i	−0.236973	−	0.971516i	$-0.576155\pi$
$941$	17716.8	−	12872.0i	0.613765	−	0.445926i	0.850738	+	0.525590i	$0.176155\pi$
$942$	2724.52	−	8385.22i	0.0942354	−	0.290027i
$943$	48436.3			1.67264
$944$	−2650.26	+	8156.67i	−0.0913758	+	0.281226i
$945$		0			0
$946$	−2133.54	−	6566.37i	−0.0733271	−	0.225678i
$947$	4019.13	+	12369.6i	0.137914	+	0.424454i	0.996032	−	0.0889978i	$-0.0283664\pi$
$947$	4019.13	+	12369.6i	0.137914	+	0.424454i	−0.858118	+	0.513452i	$0.828366\pi$
$948$	4056.19	+	2947.00i	0.138965	+	0.100964i
$949$	58314.8			1.99471
$950$		0			0
$951$	29627.1			1.01023
$952$	7308.74	+	5310.11i	0.248821	+	0.180779i
$953$	−3103.03	−	9550.13i	−0.105474	−	0.324616i	0.884367	−	0.466792i	$-0.154590\pi$
$953$	−3103.03	−	9550.13i	−0.105474	−	0.324616i	−0.989841	+	0.142176i	$0.954590\pi$
$954$	1951.50	+	6006.09i	0.0662285	+	0.203830i
$955$		0			0
$956$	−7356.74	+	22641.7i	−0.248885	+	0.765989i
$957$	26798.0			0.905180
$958$	8414.27	−	25896.5i	0.283771	−	0.873358i
$959$	726.304	−	527.691i	0.0244563	−	0.0177685i
$960$		0			0
$961$	24094.2	+	17505.5i	0.808775	+	0.587610i
$962$	−34214.6	+	24858.3i	−1.14670	+	0.833124i
$963$	−2863.87	+	2080.72i	−0.0958328	+	0.0696266i
$964$	−15659.6	−	11377.4i	−0.523196	−	0.380124i
$965$		0			0
$966$	−13354.4	+	9702.55i	−0.444794	+	0.323162i
$967$	−6874.87	+	21158.7i	−0.228626	+	0.703637i	0.769278	+	0.638915i	$0.220616\pi$
$967$	−6874.87	+	21158.7i	−0.228626	+	0.703637i	−0.997903	+	0.0647226i	$0.979384\pi$
$968$	−5232.43			−0.173736
$969$	−836.668	+	2575.00i	−0.0277375	+	0.0853673i
$970$		0			0
$971$	−18681.4	−	57495.5i	−0.617420	−	1.90022i	−0.351092	−	0.936341i	$-0.614190\pi$
$971$	−18681.4	−	57495.5i	−0.617420	−	1.90022i	−0.266328	−	0.963882i	$-0.585810\pi$
$972$	2756.99	+	8485.15i	0.0909779	+	0.280001i
$973$	26411.9	+	19189.3i	0.870222	+	0.632253i
$974$	−6458.83			−0.212479
$975$		0			0
$976$	2014.92			0.0660819
$977$	−26109.3	−	18969.5i	−0.854974	−	0.621175i	0.0715386	−	0.997438i	$-0.477209\pi$
$977$	−26109.3	−	18969.5i	−0.854974	−	0.621175i	−0.926513	+	0.376263i	$0.877209\pi$
$978$	−10656.8	−	32798.3i	−0.348433	−	1.07237i
$979$	−2177.00	−	6700.11i	−0.0710696	−	0.218730i
$980$		0			0
$981$	9.20169	−	28.3199i	0.000299477	−	0.000921697i
$982$	−1259.78			−0.0409381
$983$	−1240.91	+	3819.12i	−0.0402633	+	0.123918i	−0.969168	−	0.246402i	$-0.920752\pi$
$983$	−1240.91	+	3819.12i	−0.0402633	+	0.123918i	0.928904	+	0.370319i	$0.120752\pi$
$984$	12309.0	−	8943.01i	0.398777	−	0.289728i
$985$		0			0
$986$	−25127.8	−	18256.4i	−0.811594	−	0.589657i
$987$	9580.05	−	6960.31i	0.308953	−	0.224467i
$988$	−2077.13	+	1509.13i	−0.0668851	+	0.0485949i
$989$	−11829.1	−	8594.35i	−0.380328	−	0.276324i
$990$		0			0
$991$	24821.0	−	18033.5i	0.795624	−	0.578055i	−0.114003	−	0.993480i	$-0.536367\pi$
$991$	24821.0	−	18033.5i	0.795624	−	0.578055i	0.909627	+	0.415425i	$0.136367\pi$
$992$	29.5082	−	90.8170i	0.000944443	−	0.00290670i
$993$	−34085.4			−1.08929
$994$	8202.07	−	25243.4i	0.261724	−	0.805505i
$995$		0			0
$996$	−6243.40	−	19215.2i	−0.198624	−	0.611303i
$997$	−7314.40	−	22511.4i	−0.232346	−	0.715089i	−0.997462	−	0.0711962i	$-0.977318\pi$
$997$	−7314.40	−	22511.4i	−0.232346	−	0.715089i	0.765116	−	0.643893i	$-0.222682\pi$
$998$	8011.89	+	5820.98i	0.254120	+	0.184629i
$999$	48229.5			1.52744

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.4.d.a.201.3		12
5.2	odd	4		250.4.e.a.49.6		24
5.3	odd	4		250.4.e.a.49.1		24
5.4	even	2		50.4.d.a.41.1	yes	12
25.2	odd	20		250.4.e.a.199.1		24
25.6	even	5		1250.4.a.e.1.5		6
25.11	even	5	inner	250.4.d.a.51.3		12
25.14	even	10		50.4.d.a.11.1	✓	12
25.19	even	10		1250.4.a.d.1.2		6
25.23	odd	20		250.4.e.a.199.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.d.a.11.1	✓	12	25.14	even	10
50.4.d.a.41.1	yes	12	5.4	even	2
250.4.d.a.51.3		12	25.11	even	5	inner
250.4.d.a.201.3		12	1.1	even	1	trivial
250.4.e.a.49.1		24	5.3	odd	4
250.4.e.a.49.6		24	5.2	odd	4
250.4.e.a.199.1		24	25.2	odd	20
250.4.e.a.199.6		24	25.23	odd	20
1250.4.a.d.1.2		6	25.19	even	10
1250.4.a.e.1.5		6	25.6	even	5

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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	250.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.61803 - 1.17557i) q^{2} +(1.33712 + 4.11522i) q^{3} +(1.23607 + 3.80423i) q^{4} +(2.67423 - 8.23044i) q^{6} -17.3088 q^{7} +(2.47214 - 7.60845i) q^{8} +(6.69632 - 4.86516i) q^{9} +O(q^{10})\)	\(q+(-1.61803 - 1.17557i) q^{2} +(1.33712 + 4.11522i) q^{3} +(1.23607 + 3.80423i) q^{4} +(2.67423 - 8.23044i) q^{6} -17.3088 q^{7} +(2.47214 - 7.60845i) q^{8} +(6.69632 - 4.86516i) q^{9} +(-21.0492 - 15.2931i) q^{11} +(-14.0025 + 10.1734i) q^{12} +(54.1436 - 39.3376i) q^{13} +(28.0063 + 20.3478i) q^{14} +(-12.9443 + 9.40456i) q^{16} +(20.1609 - 62.0488i) q^{17} -16.5542 q^{18} +(-2.96374 + 9.12145i) q^{19} +(-23.1439 - 71.2296i) q^{21} +(16.0801 + 49.4896i) q^{22} +(89.1539 + 64.7741i) q^{23} +34.6160 q^{24} -133.850 q^{26} +(123.492 + 89.7218i) q^{27} +(-21.3949 - 65.8467i) q^{28} +(73.5566 + 226.384i) q^{29} +(0.922132 - 2.83803i) q^{31} +32.0000 q^{32} +(34.7893 - 107.071i) q^{33} +(-105.564 + 76.6965i) q^{34} +(26.7853 + 19.4606i) q^{36} +(255.618 - 185.717i) q^{37} +(15.5183 - 11.2747i) q^{38} +(234.279 + 170.214i) q^{39} +(355.587 - 258.349i) q^{41} +(-46.2878 + 142.459i) q^{42} -132.682 q^{43} +(32.1603 - 98.9791i) q^{44} +(-68.1075 - 209.613i) q^{46} +(48.8583 + 150.370i) q^{47} +(-56.0098 - 40.6935i) q^{48} -43.4043 q^{49} +282.302 q^{51} +(216.575 + 157.351i) q^{52} +(-117.885 - 362.814i) q^{53} +(-94.3391 - 290.346i) q^{54} +(-42.7898 + 131.693i) q^{56} -41.4996 q^{57} +(147.113 - 452.768i) q^{58} +(433.655 - 315.069i) q^{59} +(-101.881 - 74.0212i) q^{61} +(-4.82835 + 3.50800i) q^{62} +(-115.905 + 84.2102i) q^{63} +(-51.7771 - 37.6183i) q^{64} +(-182.159 + 132.346i) q^{66} +(269.366 - 829.025i) q^{67} +260.968 q^{68} +(-147.350 + 453.498i) q^{69} +(-236.933 - 729.205i) q^{71} +(-20.4621 - 62.9759i) q^{72} +(704.932 + 512.163i) q^{73} -631.922 q^{74} -38.3634 q^{76} +(364.336 + 264.706i) q^{77} +(-178.973 - 550.824i) q^{78} +(-89.5152 - 275.500i) q^{79} +(-135.043 + 415.619i) q^{81} -879.060 q^{82} +(-360.724 + 1110.19i) q^{83} +(242.366 - 176.089i) q^{84} +(214.684 + 155.977i) q^{86} +(-833.266 + 605.403i) q^{87} +(-168.393 + 122.345i) q^{88} +(219.056 + 159.154i) q^{89} +(-937.163 + 680.889i) q^{91} +(-136.215 + 419.227i) q^{92} +12.9121 q^{93} +(97.7165 - 300.741i) q^{94} +(42.7877 + 131.687i) q^{96} +(-63.7550 - 196.218i) q^{97} +(70.2296 + 51.0248i) q^{98} -215.355 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - q^{3} - 12 q^{4} - 2 q^{6} - 58 q^{7} - 24 q^{8} - 26 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 - q^3 - 12 * q^4 - 2 * q^6 - 58 * q^7 - 24 * q^8 - 26 * q^9	\( 12 q - 6 q^{2} - q^{3} - 12 q^{4} - 2 q^{6} - 58 q^{7} - 24 q^{8} - 26 q^{9} - 46 q^{11} + 36 q^{12} + 19 q^{13} + 4 q^{14} - 48 q^{16} - 178 q^{17} - 72 q^{18} + 130 q^{19} - 221 q^{21} + 158 q^{22} + 259 q^{23} - 128 q^{24} + 128 q^{26} + 215 q^{27} + 108 q^{28} + 15 q^{29} + 309 q^{31} + 384 q^{32} + 608 q^{33} + 304 q^{34} - 104 q^{36} + 557 q^{37} - 110 q^{38} + 1158 q^{39} - 596 q^{41} - 442 q^{42} - 746 q^{43} + 316 q^{44} - 292 q^{46} + 1442 q^{47} + 144 q^{48} - 834 q^{49} + 2724 q^{51} + 76 q^{52} - 96 q^{53} - 510 q^{54} + 216 q^{56} - 1280 q^{57} + 30 q^{58} + 975 q^{59} - 2016 q^{61} - 592 q^{62} - 1206 q^{63} - 192 q^{64} - 1014 q^{66} - 68 q^{67} + 208 q^{68} + 783 q^{69} + 1384 q^{71} + 352 q^{72} + 3834 q^{73} - 2656 q^{74} - 600 q^{76} + 1059 q^{77} - 664 q^{78} - 4550 q^{79} + 1227 q^{81} - 1012 q^{82} - 1211 q^{83} + 1236 q^{84} - 382 q^{86} - 1625 q^{87} - 368 q^{88} + 1685 q^{89} - 3271 q^{91} - 584 q^{92} - 4552 q^{93} + 2884 q^{94} - 32 q^{96} + 4247 q^{97} + 1952 q^{98} - 1202 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - q^3 - 12 * q^4 - 2 * q^6 - 58 * q^7 - 24 * q^8 - 26 * q^9 - 46 * q^11 + 36 * q^12 + 19 * q^13 + 4 * q^14 - 48 * q^16 - 178 * q^17 - 72 * q^18 + 130 * q^19 - 221 * q^21 + 158 * q^22 + 259 * q^23 - 128 * q^24 + 128 * q^26 + 215 * q^27 + 108 * q^28 + 15 * q^29 + 309 * q^31 + 384 * q^32 + 608 * q^33 + 304 * q^34 - 104 * q^36 + 557 * q^37 - 110 * q^38 + 1158 * q^39 - 596 * q^41 - 442 * q^42 - 746 * q^43 + 316 * q^44 - 292 * q^46 + 1442 * q^47 + 144 * q^48 - 834 * q^49 + 2724 * q^51 + 76 * q^52 - 96 * q^53 - 510 * q^54 + 216 * q^56 - 1280 * q^57 + 30 * q^58 + 975 * q^59 - 2016 * q^61 - 592 * q^62 - 1206 * q^63 - 192 * q^64 - 1014 * q^66 - 68 * q^67 + 208 * q^68 + 783 * q^69 + 1384 * q^71 + 352 * q^72 + 3834 * q^73 - 2656 * q^74 - 600 * q^76 + 1059 * q^77 - 664 * q^78 - 4550 * q^79 + 1227 * q^81 - 1012 * q^82 - 1211 * q^83 + 1236 * q^84 - 382 * q^86 - 1625 * q^87 - 368 * q^88 + 1685 * q^89 - 3271 * q^91 - 584 * q^92 - 4552 * q^93 + 2884 * q^94 - 32 * q^96 + 4247 * q^97 + 1952 * q^98 - 1202 * q^99

Introduction

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