LMFDB - Embedded newform 201.4.m.b.4.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(4,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("201.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.m (of order $33$, degree $20$, 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:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$18$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			4.10
Character	$\chi$	$=$	201.4
Dual form			201.4.m.b.151.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.598865 + 0.0571847i) q^{2} +(-2.52376 - 1.62192i) q^{3} +(-7.50006 - 1.44552i) q^{4} +(-2.98516 - 20.7622i) q^{5} +(-1.41864 - 1.11563i) q^{6} +(11.0160 - 15.4698i) q^{7} +(-9.02663 - 2.65046i) q^{8} +(3.73874 + 8.18669i) q^{9} +O(q^{10})$	\(q+(0.598865 + 0.0571847i) q^{2} +(-2.52376 - 1.62192i) q^{3} +(-7.50006 - 1.44552i) q^{4} +(-2.98516 - 20.7622i) q^{5} +(-1.41864 - 1.11563i) q^{6} +(11.0160 - 15.4698i) q^{7} +(-9.02663 - 2.65046i) q^{8} +(3.73874 + 8.18669i) q^{9} +(-0.600425 - 12.6045i) q^{10} +(-44.3843 + 34.9042i) q^{11} +(16.5838 + 15.8127i) q^{12} +(-0.722811 + 2.97947i) q^{13} +(7.48172 - 8.63436i) q^{14} +(-26.1409 + 57.2406i) q^{15} +(51.4735 + 20.6069i) q^{16} +(104.112 - 20.0659i) q^{17} +(1.77084 + 5.11652i) q^{18} +(-28.3068 - 39.7513i) q^{19} +(-7.62332 + 160.033i) q^{20} +(-52.8925 + 21.1749i) q^{21} +(-28.5762 + 18.3648i) q^{22} +(-111.994 + 57.7367i) q^{23} +(18.4822 + 21.3296i) q^{24} +(-302.223 + 88.7405i) q^{25} +(-0.603247 + 1.74297i) q^{26} +(3.84250 - 26.7252i) q^{27} +(-104.982 + 100.100i) q^{28} +(14.3484 + 24.8521i) q^{29} +(-18.9282 + 32.7845i) q^{30} +(-16.6412 - 68.5961i) q^{31} +(96.5425 + 49.7711i) q^{32} +(168.627 - 16.1019i) q^{33} +(63.4963 - 6.06317i) q^{34} +(-354.071 - 182.537i) q^{35} +(-16.2067 - 66.8051i) q^{36} +(127.353 - 220.581i) q^{37} +(-14.6788 - 25.4244i) q^{38} +(6.65667 - 6.34712i) q^{39} +(-28.0835 + 195.325i) q^{40} +(-168.312 + 486.306i) q^{41} +(-32.8863 + 9.65630i) q^{42} +(-7.55303 - 8.71666i) q^{43} +(383.339 - 197.625i) q^{44} +(158.813 - 102.063i) q^{45} +(-70.3707 + 28.1722i) q^{46} +(8.24056 - 172.991i) q^{47} +(-96.4840 - 135.493i) q^{48} +(-5.77784 - 16.6940i) q^{49} +(-186.065 + 35.8611i) q^{50} +(-295.298 - 118.220i) q^{51} +(9.72801 - 21.3014i) q^{52} +(182.251 - 210.329i) q^{53} +(3.82941 - 15.7850i) q^{54} +(857.183 + 817.322i) q^{55} +(-140.439 + 110.443i) q^{56} +(6.96600 + 146.234i) q^{57} +(7.17157 + 15.7036i) q^{58} +(-706.335 - 207.399i) q^{59} +(278.801 - 391.521i) q^{60} +(571.911 + 449.756i) q^{61} +(-6.04321 - 42.0314i) q^{62} +(167.832 + 32.3470i) q^{63} +(-318.178 - 204.480i) q^{64} +(64.0181 + 6.11299i) q^{65} +101.906 q^{66} +(371.121 - 403.773i) q^{67} -809.850 q^{68} +(376.290 + 35.9313i) q^{69} +(-201.603 - 129.562i) q^{70} +(-793.170 - 152.871i) q^{71} +(-12.0497 - 83.8075i) q^{72} +(-97.4445 - 76.6312i) q^{73} +(88.8809 - 124.816i) q^{74} +(906.668 + 266.222i) q^{75} +(154.841 + 339.055i) q^{76} +(51.0237 + 1071.12i) q^{77} +(4.34941 - 3.42041i) q^{78} +(-251.060 - 239.385i) q^{79} +(274.188 - 1130.22i) q^{80} +(-53.0437 + 61.2157i) q^{81} +(-128.605 + 281.607i) q^{82} +(558.466 + 223.576i) q^{83} +(427.305 - 82.3564i) q^{84} +(-727.403 - 2101.69i) q^{85} +(-4.02479 - 5.65202i) q^{86} +(4.09634 - 85.9927i) q^{87} +(493.152 - 197.428i) q^{88} +(-1030.76 + 662.432i) q^{89} +(100.944 - 52.0403i) q^{90} +(38.1292 + 44.0035i) q^{91} +(923.419 - 271.140i) q^{92} +(-69.2591 + 200.111i) q^{93} +(14.8274 - 103.127i) q^{94} +(-740.826 + 706.376i) q^{95} +(-162.925 - 282.195i) q^{96} +(498.015 - 862.587i) q^{97} +(-2.50551 - 10.3278i) q^{98} +(-451.691 - 232.863i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 2 q^{2} + 108 q^{3} + 90 q^{4} + 4 q^{5} - 27 q^{6} - 22 q^{7} + 183 q^{8} - 324 q^{9}+O(q^{10}) $ 360 * q - 2 * q^2 + 108 * q^3 + 90 * q^4 + 4 * q^5 - 27 * q^6 - 22 * q^7 + 183 * q^8 - 324 * q^9	\( 360 q - 2 q^{2} + 108 q^{3} + 90 q^{4} + 4 q^{5} - 27 q^{6} - 22 q^{7} + 183 q^{8} - 324 q^{9} + 19 q^{10} + 192 q^{11} - 105 q^{12} + 46 q^{13} - 14 q^{14} + 54 q^{15} + 346 q^{16} + 228 q^{17} - 18 q^{18} + 88 q^{19} + 180 q^{20} + 66 q^{21} - 247 q^{22} + 676 q^{23} + 144 q^{24} - 1120 q^{25} + 333 q^{26} + 972 q^{27} - 3894 q^{28} - 2210 q^{29} + 702 q^{30} + 96 q^{31} - 1970 q^{32} - 708 q^{33} - 26 q^{34} + 1272 q^{35} + 315 q^{36} - 3616 q^{37} - 20 q^{38} - 138 q^{39} - 5357 q^{40} + 288 q^{41} - 618 q^{42} - 1680 q^{43} + 2951 q^{44} + 36 q^{45} - 1125 q^{46} - 40 q^{47} - 1038 q^{48} - 4954 q^{49} - 3590 q^{50} - 90 q^{51} + 9120 q^{52} + 3896 q^{53} + 54 q^{54} - 1076 q^{55} + 3557 q^{56} + 660 q^{57} + 3232 q^{58} + 116 q^{59} + 3618 q^{60} - 672 q^{61} + 3882 q^{62} - 1584 q^{63} - 11581 q^{64} - 15380 q^{65} - 5166 q^{66} - 288 q^{67} + 13898 q^{68} - 1632 q^{69} - 5058 q^{70} - 15102 q^{71} - 2016 q^{72} - 146 q^{73} - 3531 q^{74} + 3360 q^{75} + 10770 q^{76} + 3594 q^{77} + 1905 q^{78} + 2852 q^{79} + 27997 q^{80} - 2916 q^{81} + 8824 q^{82} + 5278 q^{83} + 6765 q^{84} - 5290 q^{85} + 5973 q^{86} + 228 q^{87} + 13872 q^{88} + 1462 q^{89} + 171 q^{90} + 74 q^{91} - 3144 q^{92} + 3144 q^{93} + 3262 q^{94} + 1600 q^{95} - 855 q^{96} + 6626 q^{97} + 15491 q^{98} + 144 q^{99}+O(q^{100}) \) 360 * q - 2 * q^2 + 108 * q^3 + 90 * q^4 + 4 * q^5 - 27 * q^6 - 22 * q^7 + 183 * q^8 - 324 * q^9 + 19 * q^10 + 192 * q^11 - 105 * q^12 + 46 * q^13 - 14 * q^14 + 54 * q^15 + 346 * q^16 + 228 * q^17 - 18 * q^18 + 88 * q^19 + 180 * q^20 + 66 * q^21 - 247 * q^22 + 676 * q^23 + 144 * q^24 - 1120 * q^25 + 333 * q^26 + 972 * q^27 - 3894 * q^28 - 2210 * q^29 + 702 * q^30 + 96 * q^31 - 1970 * q^32 - 708 * q^33 - 26 * q^34 + 1272 * q^35 + 315 * q^36 - 3616 * q^37 - 20 * q^38 - 138 * q^39 - 5357 * q^40 + 288 * q^41 - 618 * q^42 - 1680 * q^43 + 2951 * q^44 + 36 * q^45 - 1125 * q^46 - 40 * q^47 - 1038 * q^48 - 4954 * q^49 - 3590 * q^50 - 90 * q^51 + 9120 * q^52 + 3896 * q^53 + 54 * q^54 - 1076 * q^55 + 3557 * q^56 + 660 * q^57 + 3232 * q^58 + 116 * q^59 + 3618 * q^60 - 672 * q^61 + 3882 * q^62 - 1584 * q^63 - 11581 * q^64 - 15380 * q^65 - 5166 * q^66 - 288 * q^67 + 13898 * q^68 - 1632 * q^69 - 5058 * q^70 - 15102 * q^71 - 2016 * q^72 - 146 * q^73 - 3531 * q^74 + 3360 * q^75 + 10770 * q^76 + 3594 * q^77 + 1905 * q^78 + 2852 * q^79 + 27997 * q^80 - 2916 * q^81 + 8824 * q^82 + 5278 * q^83 + 6765 * q^84 - 5290 * q^85 + 5973 * q^86 + 228 * q^87 + 13872 * q^88 + 1462 * q^89 + 171 * q^90 + 74 * q^91 - 3144 * q^92 + 3144 * q^93 + 3262 * q^94 + 1600 * q^95 - 855 * q^96 + 6626 * q^97 + 15491 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{1}{33}\right)$

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 $

$2$	0.598865	+	0.0571847i	0.211731	+	0.0202178i	0.200382	−	0.979718i	$-0.435782\pi$
$2$	0.598865	+	0.0571847i	0.211731	+	0.0202178i	0.0113484	+	0.999936i	$0.496388\pi$
$3$	−2.52376	−	1.62192i	−0.485698	−	0.312139i
$3$	−2.52376	−	1.62192i	−0.485698	−	0.312139i
$4$	−7.50006	−	1.44552i	−0.937508	−	0.180690i
$5$	−2.98516	−	20.7622i	−0.267001	−	1.85703i	−0.476437	−	0.879208i	$-0.658072\pi$
$5$	−2.98516	−	20.7622i	−0.267001	−	1.85703i	0.209437	−	0.977822i	$-0.432837\pi$
$6$	−1.41864	−	1.11563i	−0.0965264	−	0.0759092i
$7$	11.0160	−	15.4698i	0.594807	−	0.835289i	−0.401958	−	0.915658i	$-0.631670\pi$
$7$	11.0160	−	15.4698i	0.594807	−	0.835289i	0.996765	+	0.0803687i	$0.0256098\pi$
$8$	−9.02663	−	2.65046i	−0.398924	−	0.117135i
$9$	3.73874	+	8.18669i	0.138472	+	0.303211i
$10$	−0.600425	−	12.6045i	−0.0189871	−	0.398589i
$11$	−44.3843	+	34.9042i	−1.21658	+	0.956728i	−0.999810	−	0.0194948i	$-0.993794\pi$
$11$	−44.3843	+	34.9042i	−1.21658	+	0.956728i	−0.216769	+	0.976223i	$0.569552\pi$
$12$	16.5838	+	15.8127i	0.398945	+	0.380393i
$13$	−0.722811	+	2.97947i	−0.0154209	+	0.0635659i	−0.979002	−	0.203850i	$-0.934655\pi$
$13$	−0.722811	+	2.97947i	−0.0154209	+	0.0635659i	0.963581	+	0.267416i	$0.0861697\pi$
$14$	7.48172	−	8.63436i	0.142827	−	0.164831i
$15$	−26.1409	+	57.2406i	−0.449970	+	0.985297i
$16$	51.4735	+	20.6069i	0.804273	+	0.321983i
$17$	104.112	−	20.0659i	1.48534	−	0.286276i	0.618866	−	0.785496i	$-0.287592\pi$
$17$	104.112	−	20.0659i	1.48534	−	0.286276i	0.866475	+	0.499220i	$0.166380\pi$
$18$	1.77084	+	5.11652i	0.0231885	+	0.0669986i
$19$	−28.3068	−	39.7513i	−0.341791	−	0.479978i	0.607526	−	0.794300i	$-0.292162\pi$
$19$	−28.3068	−	39.7513i	−0.341791	−	0.479978i	−0.949316	+	0.314322i	$0.898223\pi$
$20$	−7.62332	+	160.033i	−0.0852313	+	1.78922i
$21$	−52.8925	+	21.1749i	−0.549623	+	0.220036i
$22$	−28.5762	+	18.3648i	−0.276930	+	0.177972i
$23$	−111.994	+	57.7367i	−1.01532	+	0.523432i	−0.883792	−	0.467881i	$-0.845018\pi$
$23$	−111.994	+	57.7367i	−1.01532	+	0.523432i	−0.131525	+	0.991313i	$0.541987\pi$
$24$	18.4822	+	21.3296i	0.157194	+	0.181412i
$25$	−302.223	+	88.7405i	−2.41778	+	0.709924i
$26$	−0.603247	+	1.74297i	−0.00455025	+	0.0131471i
$27$	3.84250	−	26.7252i	0.0273885	−	0.190491i
$28$	−104.982	+	100.100i	−0.708564	+	0.675614i
$29$	14.3484	+	24.8521i	0.0918767	+	0.159135i	0.908301	−	0.418318i	$-0.137380\pi$
$29$	14.3484	+	24.8521i	0.0918767	+	0.159135i	−0.816424	+	0.577453i	$0.804047\pi$
$30$	−18.9282	+	32.7845i	−0.115193	+	0.199520i
$31$	−16.6412	−	68.5961i	−0.0964146	−	0.397427i	0.903071	−	0.429491i	$-0.141307\pi$
$31$	−16.6412	−	68.5961i	−0.0964146	−	0.397427i	−0.999486	+	0.0320644i	$0.989792\pi$
$32$	96.5425	+	49.7711i	0.533327	+	0.274949i
$33$	168.627	−	16.1019i	0.889522	−	0.0849391i
$34$	63.4963	−	6.06317i	0.320280	−	0.0305831i
$35$	−354.071	−	182.537i	−1.70997	−	0.881552i
$36$	−16.2067	−	66.8051i	−0.0750312	−	0.309283i
$37$	127.353	−	220.581i	0.565855	−	0.980090i	−0.431114	−	0.902297i	$-0.641879\pi$
$37$	127.353	−	220.581i	0.565855	−	0.980090i	0.996970	−	0.0777926i	$-0.0247872\pi$
$38$	−14.6788	−	25.4244i	−0.0626635	−	0.108536i
$39$	6.65667	−	6.34712i	0.0273313	−	0.0260603i
$40$	−28.0835	+	195.325i	−0.111010	+	0.772090i
$41$	−168.312	+	486.306i	−0.641120	+	1.85240i	−0.132985	+	0.991118i	$0.542456\pi$
$41$	−168.312	+	486.306i	−0.641120	+	1.85240i	−0.508135	+	0.861277i	$0.669665\pi$
$42$	−32.8863	+	9.65630i	−0.120821	+	0.0354762i
$43$	−7.55303	−	8.71666i	−0.0267867	−	0.0309135i	0.742198	−	0.670180i	$-0.233783\pi$
$43$	−7.55303	−	8.71666i	−0.0267867	−	0.0309135i	−0.768985	+	0.639267i	$0.779238\pi$
$44$	383.339	−	197.625i	1.31342	−	0.677116i
$45$	158.813	−	102.063i	0.526099	−	0.338104i
$46$	−70.3707	+	28.1722i	−0.225557	+	0.0902992i
$47$	8.24056	−	172.991i	0.0255747	−	0.536879i	−0.949333	−	0.314271i	$-0.898240\pi$
$47$	8.24056	−	172.991i	0.0255747	−	0.536879i	0.974908	−	0.222608i	$-0.0714569\pi$
$48$	−96.4840	−	135.493i	−0.290131	−	0.407431i
$49$	−5.77784	−	16.6940i	−0.0168450	−	0.0486704i
$50$	−186.065	+	35.8611i	−0.526272	+	0.101431i
$51$	−295.298	−	118.220i	−0.810785	−	0.324589i
$52$	9.72801	−	21.3014i	0.0259429	−	0.0568071i
$53$	182.251	−	210.329i	0.472341	−	0.545111i	−0.468720	−	0.883347i	$-0.655285\pi$
$53$	182.251	−	210.329i	0.472341	−	0.545111i	0.941061	+	0.338236i	$0.109830\pi$
$54$	3.82941	−	15.7850i	0.00965031	−	0.0397791i
$55$	857.183	+	817.322i	2.10150	+	2.00378i
$56$	−140.439	+	110.443i	−0.335124	+	0.263545i
$57$	6.96600	+	146.234i	0.0161872	+	0.339811i
$58$	7.17157	+	15.7036i	0.0162358	+	0.0355513i
$59$	−706.335	−	207.399i	−1.55859	−	0.457644i	−0.614938	−	0.788576i	$-0.710819\pi$
$59$	−706.335	−	207.399i	−1.55859	−	0.457644i	−0.943655	+	0.330931i	$0.892637\pi$
$60$	278.801	−	391.521i	0.599884	−	0.842419i
$61$	571.911	+	449.756i	1.20042	+	0.944021i	0.999368	−	0.0355589i	$-0.0113211\pi$
$61$	571.911	+	449.756i	1.20042	+	0.944021i	0.201053	+	0.979580i	$0.435564\pi$
$62$	−6.04321	−	42.0314i	−0.0123788	−	0.0860967i
$63$	167.832	+	32.3470i	0.335632	+	0.0646879i
$64$	−318.178	−	204.480i	−0.621441	−	0.399376i
$65$	64.0181	+	6.11299i	0.122161	+	0.0116650i
$66$	101.906			0.190057
$67$	371.121	−	403.773i	0.676710	−	0.736249i
$67$	371.121	−	403.773i	0.676710	−	0.736249i
$68$	−809.850			−1.44425
$69$	376.290	+	35.9313i	0.656521	+	0.0626902i
$70$	−201.603	−	129.562i	−0.344231	−	0.221224i
$71$	−793.170	−	152.871i	−1.32580	−	0.255528i	−0.523286	−	0.852157i	$-0.675294\pi$
$71$	−793.170	−	152.871i	−1.32580	−	0.255528i	−0.802517	+	0.596630i	$0.796506\pi$
$72$	−12.0497	−	83.8075i	−0.0197232	−	0.137178i
$73$	−97.4445	−	76.6312i	−0.156233	−	0.122863i	0.536982	−	0.843593i	$-0.319564\pi$
$73$	−97.4445	−	76.6312i	−0.156233	−	0.122863i	−0.693216	+	0.720730i	$0.743807\pi$
$74$	88.8809	−	124.816i	0.139624	−	0.196075i
$75$	906.668	+	266.222i	1.39591	+	0.409875i
$76$	154.841	+	339.055i	0.233704	+	0.511741i
$77$	51.0237	+	1071.12i	0.0755154	+	1.58526i
$78$	4.34941	−	3.42041i	0.00631376	−	0.00496520i
$79$	−251.060	−	239.385i	−0.357550	−	0.340923i	0.489919	−	0.871768i	$-0.337026\pi$
$79$	−251.060	−	239.385i	−0.357550	−	0.340923i	−0.847469	+	0.530844i	$0.821875\pi$
$80$	274.188	−	1130.22i	0.383190	−	1.57953i
$81$	−53.0437	+	61.2157i	−0.0727623	+	0.0839722i
$82$	−128.605	+	281.607i	−0.173196	+	0.379247i
$83$	558.466	+	223.576i	0.738550	+	0.295671i	0.710270	−	0.703929i	$-0.248573\pi$
$83$	558.466	+	223.576i	0.738550	+	0.295671i	0.0282797	+	0.999600i	$0.490997\pi$
$84$	427.305	−	82.3564i	0.555034	−	0.106974i
$85$	−727.403	−	2101.69i	−0.928211	−	2.68189i
$86$	−4.02479	−	5.65202i	−0.00504656	−	0.00708690i
$87$	4.09634	−	85.9927i	0.00504797	−	0.105970i
$88$	493.152	−	197.428i	0.597389	−	0.239158i
$89$	−1030.76	+	662.432i	−1.22765	+	0.788963i	−0.983523	−	0.180781i	$-0.942138\pi$
$89$	−1030.76	+	662.432i	−1.22765	+	0.788963i	−0.244126	+	0.969743i	$0.578501\pi$
$90$	100.944	−	52.0403i	0.118227	−	0.0609503i
$91$	38.1292	+	44.0035i	0.0439234	+	0.0506903i
$92$	923.419	−	271.140i	1.04645	−	0.307264i
$93$	−69.2591	+	200.111i	−0.0772240	+	0.223124i
$94$	14.8274	−	103.127i	0.0162695	−	0.113157i
$95$	−740.826	+	706.376i	−0.800076	+	0.762870i
$96$	−162.925	−	282.195i	−0.173213	−	0.300014i
$97$	498.015	−	862.587i	0.521296	−	0.902912i	−0.478397	−	0.878144i	$-0.658782\pi$
$97$	498.015	−	862.587i	0.521296	−	0.902912i	0.999693	−	0.0247682i	$-0.00788476\pi$
$98$	−2.50551	−	10.3278i	−0.00258259	−	0.0106456i
$99$	−451.691	−	232.863i	−0.458552	−	0.236400i
$100$	2394.96	−	228.691i	2.39496	−	0.228691i
$101$	−1074.70	+	102.621i	−1.05878	+	0.101101i	−0.609888	−	0.792488i	$-0.708786\pi$
$101$	−1074.70	+	102.621i	−1.05878	+	0.101101i	−0.448887	+	0.893588i	$0.648180\pi$
$102$	−170.084	−	87.6842i	−0.165106	−	0.0851179i
$103$	−60.2106	−	248.192i	−0.0575993	−	0.237428i	0.935734	−	0.352707i	$-0.114739\pi$
$103$	−60.2106	−	248.192i	−0.0575993	−	0.237428i	−0.993333	+	0.115279i	$0.963224\pi$
$104$	14.4215	−	24.9788i	0.0135975	−	0.0235516i
$105$	597.531	+	1034.95i	0.555363	+	0.961917i
$106$	121.171	−	115.537i	0.111030	−	0.105867i
$107$	116.145	−	807.804i	0.104936	−	0.729845i	−0.867629	−	0.497212i	$-0.834357\pi$
$107$	116.145	−	807.804i	0.104936	−	0.729845i	0.972565	−	0.232632i	$-0.0747339\pi$
$108$	−67.4507	+	194.886i	−0.0600967	+	0.173638i
$109$	−1247.25	+	366.226i	−1.09601	+	0.321817i	−0.779266	−	0.626694i	$-0.784408\pi$
$109$	−1247.25	+	366.226i	−1.09601	+	0.321817i	−0.316744	+	0.948511i	$0.602590\pi$
$110$	466.599	+	538.484i	0.404440	+	0.466749i
$111$	−679.173	+	350.138i	−0.580759	+	0.299402i
$112$	885.815	−	569.278i	0.747336	−	0.480284i
$113$	262.465	−	105.075i	0.218501	−	0.0874746i	−0.259829	−	0.965655i	$-0.583666\pi$
$113$	262.465	−	105.075i	0.218501	−	0.0874746i	0.478330	+	0.878180i	$0.341242\pi$
$114$	−4.19067	+	87.9730i	−0.00344291	+	0.0722756i
$115$	1533.06	+	2152.88i	1.24312	+	1.74572i
$116$	−71.6894	−	207.133i	−0.0573810	−	0.165792i
$117$	−27.0944	+	5.22202i	−0.0214092	+	0.00412629i
$118$	−411.139	−	164.595i	−0.320749	−	0.128409i
$119$	836.477	−	1831.63i	0.644368	−	1.41097i
$120$	387.678	−	447.404i	0.294917	−	0.340352i
$121$	437.867	−	1804.91i	0.328976	−	1.35606i
$122$	316.778	+	302.047i	0.235080	+	0.224148i
$123$	1213.53	−	954.330i	0.889596	−	0.699586i
$124$	25.6534	+	538.530i	0.0185785	+	0.390012i
$125$	1655.43	+	3624.89i	1.18453	+	2.59376i
$126$	98.6590	+	28.9689i	0.0697559	+	0.0204822i
$127$	−709.438	+	996.267i	−0.495689	+	0.696097i	−0.984320	−	0.176393i	$-0.943557\pi$
$127$	−709.438	+	996.267i	−0.495689	+	0.696097i	0.488631	+	0.872490i	$0.337496\pi$
$128$	−861.881	−	677.791i	−0.595158	−	0.468038i
$129$	4.92429	+	34.2492i	0.00336093	+	0.0233758i
$130$	37.9887	+	7.32171i	0.0256294	+	0.00493967i
$131$	−1272.31	−	817.664i	−0.848567	−	0.545341i	0.0425604	−	0.999094i	$-0.486449\pi$
$131$	−1272.31	−	817.664i	−0.848567	−	0.545341i	−0.891128	+	0.453753i	$0.850085\pi$
$132$	−1287.99	−	122.988i	−0.849281	−	0.0810965i
$133$	−926.771			−0.604220
$134$	245.341	−	220.583i	0.158166	−	0.142205i
$135$	−566.345			−0.361061
$136$	−992.962	−	94.8163i	−0.626072	−	0.0597826i
$137$	−2334.20	−	1500.10i	−1.45565	−	0.935490i	−0.998947	−	0.0458718i	$-0.985393\pi$
$137$	−2334.20	−	1500.10i	−1.45565	−	0.935490i	−0.456704	−	0.889619i	$-0.650970\pi$
$138$	223.292	+	43.0360i	0.137738	+	0.0265469i
$139$	−220.900	−	1536.39i	−0.134795	−	0.937520i	−0.939183	−	0.343416i	$-0.888416\pi$
$139$	−220.900	−	1536.39i	−0.134795	−	0.937520i	0.804388	−	0.594104i	$-0.202493\pi$
$140$	2391.70	+	1880.85i	1.44382	+	1.13544i
$141$	−301.375	+	423.222i	−0.180002	+	0.252778i
$142$	−466.260	−	136.906i	−0.275547	−	0.0809079i
$143$	−71.9145	−	157.471i	−0.0420545	−	0.0920865i
$144$	23.7437	+	498.441i	0.0137406	+	0.288450i
$145$	473.153	−	372.091i	0.270988	−	0.213107i
$146$	−53.9740	−	51.4641i	−0.0305953	−	0.0291726i
$147$	−12.4944	+	51.5028i	−0.00701036	+	0.0288971i
$148$	−1274.01	+	1470.28i	−0.707586	+	0.816597i
$149$	28.0150	−	61.3442i	0.0154032	−	0.0337283i	−0.901774	−	0.432208i	$-0.857735\pi$
$149$	28.0150	−	61.3442i	0.0154032	−	0.0337283i	0.917177	+	0.398479i	$0.130462\pi$
$150$	527.748	+	211.278i	0.287270	+	0.115005i
$151$	358.296	−	69.0559i	0.193098	−	0.0372165i	−0.0917854	−	0.995779i	$-0.529257\pi$
$151$	358.296	−	69.0559i	0.193098	−	0.0372165i	0.284883	+	0.958562i	$0.408045\pi$
$152$	150.156	+	433.846i	0.0801266	+	0.231511i
$153$	553.519	+	777.309i	0.292480	+	0.410730i
$154$	−30.6953	+	644.373i	−0.0160617	+	0.337176i
$155$	−1374.53	+	550.279i	−0.712291	+	0.285158i
$156$	−59.1003	+	37.9815i	−0.0303321	+	0.0194933i
$157$	−594.311	+	306.388i	−0.302109	+	0.155748i	−0.602615	−	0.798032i	$-0.705875\pi$
$157$	−594.311	+	306.388i	−0.302109	+	0.155748i	0.300506	+	0.953780i	$0.402844\pi$
$158$	−136.662	−	157.716i	−0.0688117	−	0.0794129i
$159$	−801.095	+	235.223i	−0.399566	+	0.117323i
$160$	745.165	−	2153.01i	0.368190	−	1.06382i
$161$	−340.545	+	2368.54i	−0.166700	+	1.15942i
$162$	−35.2666	+	33.6267i	−0.0171038	+	0.0163084i
$163$	−384.981	−	666.807i	−0.184994	−	0.320419i	0.758580	−	0.651579i	$-0.225893\pi$
$163$	−384.981	−	666.807i	−0.184994	−	0.320419i	−0.943575	+	0.331160i	$0.892560\pi$
$164$	1965.31	−	3404.02i	0.935764	−	1.62079i
$165$	−837.691	−	3453.01i	−0.395237	−	1.62919i
$166$	321.661	+	165.828i	0.150396	+	0.0775345i
$167$	−3445.49	+	329.004i	−1.59653	+	0.152450i	−0.855055	−	0.518537i	$-0.826477\pi$
$167$	−3445.49	+	329.004i	−1.59653	+	0.152450i	−0.741470	+	0.670986i	$0.765871\pi$
$168$	533.564	−	50.9492i	0.245032	−	0.0233977i
$169$	1944.42	+	1002.42i	0.885033	+	0.456266i
$170$	−315.432	−	1300.23i	−0.142309	−	0.586605i
$171$	219.600	−	380.359i	0.0982061	−	0.170098i
$172$	44.0481	+	76.2935i	0.0195270	+	0.0338217i
$173$	2413.38	−	2301.15i	1.06061	−	1.01129i	0.0606984	−	0.998156i	$-0.480667\pi$
$173$	2413.38	−	2301.15i	1.06061	−	1.01129i	0.999914	−	0.0131355i	$-0.00418127\pi$
$174$	7.37062	−	51.2638i	0.00321129	−	0.0223350i
$175$	−1956.48	+	5652.88i	−0.845120	+	2.44181i
$176$	−3003.88	+	882.019i	−1.28651	+	0.377754i
$177$	1446.24	+	1669.04i	0.614157	+	0.708775i
$178$	−655.170	+	337.764i	−0.275882	+	0.142227i
$179$	−937.029	+	602.192i	−0.391267	+	0.251452i	−0.721452	−	0.692464i	$-0.756525\pi$
$179$	−937.029	+	602.192i	−0.391267	+	0.251452i	0.330185	+	0.943916i	$0.392889\pi$
$180$	−1338.64	+	535.912i	−0.554314	+	0.221914i
$181$	−55.9581	+	1174.70i	−0.0229797	+	0.482404i	0.957818	+	0.287376i	$0.0927829\pi$
$181$	−55.9581	+	1174.70i	−0.0229797	+	0.482404i	−0.980798	+	0.195028i	$0.937520\pi$
$182$	20.3179	+	28.5326i	0.00827509	+	0.0116207i
$183$	−713.897	−	2062.67i	−0.288376	−	0.833208i
$184$	1163.95	−	224.334i	0.466347	−	0.0898810i
$185$	−4959.93	−	1985.65i	−1.97114	−	0.789126i
$186$	−52.9201	+	115.879i	−0.0208618	+	0.0456809i
$187$	−3920.54	+	4524.55i	−1.53315	+	1.76935i
$188$	−311.866	+	1285.53i	−0.120985	+	0.498707i
$189$	−371.104	−	353.847i	−0.142824	−	0.136183i
$190$	−484.049	+	380.660i	−0.184824	+	0.145347i
$191$	164.449	+	3452.22i	0.0622991	+	1.30782i	0.786224	+	0.617941i	$0.212033\pi$
$191$	164.449	+	3452.22i	0.0622991	+	1.30782i	−0.723925	+	0.689878i	$0.757664\pi$
$192$	471.353	+	1032.12i	0.177172	+	0.387952i
$193$	1695.21	+	497.758i	0.632247	+	0.185645i	0.582126	−	0.813099i	$-0.302221\pi$
$193$	1695.21	+	497.758i	0.632247	+	0.185645i	0.0501214	+	0.998743i	$0.484039\pi$
$194$	347.571	−	488.095i	0.128629	−	0.180635i
$195$	−151.652	−	119.260i	−0.0556923	−	0.0437969i
$196$	19.2027	+	133.558i	0.00699807	+	0.0486726i
$197$	4547.07	+	876.377i	1.64450	+	0.316951i	0.925696	−	0.378267i	$-0.123480\pi$
$197$	4547.07	+	876.377i	1.64450	+	0.316951i	0.718799	+	0.695218i	$0.244692\pi$
$198$	−257.186	−	165.283i	−0.0923101	−	0.0593241i
$199$	−1956.84	−	186.856i	−0.697069	−	0.0665621i	−0.259495	−	0.965744i	$-0.583556\pi$
$199$	−1956.84	−	186.856i	−0.697069	−	0.0665621i	−0.437574	+	0.899182i	$0.644162\pi$
$200$	2963.25			1.04767
$201$	−1591.51	+	417.097i	−0.558489	+	0.146367i
$202$	−649.467			−0.226219
$203$	542.517	+	51.8041i	0.187573	+	0.0179110i
$204$	2043.87	+	1313.51i	0.701467	+	0.450806i
$205$	10599.2	+	2042.83i	3.61113	+	0.695989i
$206$	−21.8653	−	152.076i	−0.00739527	−	0.0514353i
$207$	−891.387	−	700.995i	−0.299303	−	0.235374i
$208$	−98.6032	+	138.469i	−0.0328697	+	0.0461591i
$209$	2643.87	+	776.309i	0.875024	+	0.256930i
$210$	298.657	+	653.968i	0.0981395	+	0.214896i
$211$	−19.1641	−	402.303i	−0.00625265	−	0.131259i	−0.999835	−	0.0181505i	$-0.994222\pi$
$211$	−19.1641	−	402.303i	−0.00625265	−	0.131259i	0.993583	−	0.113109i	$-0.0360808\pi$
$212$	−1670.93	+	1314.03i	−0.541319	+	0.425698i
$213$	1753.83	+	1672.27i	0.564180	+	0.537944i
$214$	115.749	−	477.124i	0.0369740	−	0.152409i
$215$	−158.430	+	182.838i	−0.0502552	+	0.0579976i
$216$	−105.519	+	231.054i	−0.0332391	+	0.0727834i
$217$	−1244.49	−	498.217i	−0.389314	−	0.155858i
$218$	−767.878	+	147.996i	−0.238565	+	0.0459797i
$219$	121.637	+	351.446i	0.0375317	+	0.108441i
$220$	−5247.47	−	7369.04i	−1.60811	−	2.25828i
$221$	−15.4674	+	324.702i	−0.00470793	+	0.0988316i
$222$	−426.756	+	170.847i	−0.129018	+	0.0516510i
$223$	−15.9204	+	10.2314i	−0.00478075	+	0.00307240i	−0.543029	−	0.839714i	$-0.682723\pi$
$223$	−15.9204	+	10.2314i	−0.00478075	+	0.00307240i	0.538248	+	0.842786i	$0.319086\pi$
$224$	1833.46	−	945.213i	0.546889	−	0.281941i
$225$	−1856.42	−	2142.42i	−0.550051	−	0.634792i
$226$	163.190	−	47.9168i	0.0480319	−	0.0141034i
$227$	61.3578	−	177.282i	0.0179403	−	0.0518352i	−0.935675	−	0.352863i	$-0.885208\pi$
$227$	61.3578	−	177.282i	0.0179403	−	0.0518352i	0.953616	+	0.301027i	$0.0973295\pi$
$228$	159.139	−	1106.84i	0.0462247	−	0.321500i
$229$	−1827.07	+	1742.11i	−0.527233	+	0.502716i	−0.906289	−	0.422658i	$-0.861097\pi$
$229$	−1827.07	+	1742.11i	−0.527233	+	0.502716i	0.379056	+	0.925374i	$0.376249\pi$
$230$	794.986	+	1376.96i	0.227912	+	0.394755i
$231$	1608.50	−	2786.00i	0.458145	−	0.793531i
$232$	−63.6479	−	262.360i	−0.0180116	−	0.0742448i
$233$	−4998.82	−	2577.07i	−1.40551	−	0.724590i	−0.422194	−	0.906505i	$-0.638740\pi$
$233$	−4998.82	−	2577.07i	−1.40551	−	0.724590i	−0.983314	+	0.181915i	$0.941770\pi$
$234$	−16.5245	+	1.57790i	−0.00461641	+	0.000440814i
$235$	−3616.27	+	345.312i	−1.00383	+	0.0958540i
$236$	4997.76	+	2576.52i	1.37850	+	0.710667i
$237$	245.351	+	1011.35i	0.0672459	+	0.277191i
$238$	605.678	−	1049.07i	0.164959	−	0.285718i
$239$	−2310.32	−	4001.59i	−0.625280	−	1.08302i	−0.988487	−	0.151308i	$-0.951651\pi$
$239$	−2310.32	−	4001.59i	−0.625280	−	1.08302i	0.363206	−	0.931709i	$-0.381682\pi$
$240$	−2525.11	+	2407.69i	−0.679148	+	0.647566i
$241$	45.1866	−	314.280i	0.0120777	−	0.0840023i	−0.982891	−	0.184188i	$-0.941035\pi$
$241$	45.1866	−	314.280i	0.0120777	−	0.0840023i	0.994969	+	0.100186i	$0.0319436\pi$
$242$	365.437	−	1055.86i	0.0970710	−	0.280468i
$243$	233.157	−	68.4610i	0.0615515	−	0.0180732i
$244$	−3639.24	−	4199.90i	−0.954829	−	1.10193i
$245$	−329.356	+	169.795i	−0.0858849	+	0.0442767i
$246$	781.314	−	502.120i	0.202499	−	0.130138i
$247$	138.898	−	55.6065i	0.0357809	−	0.0143245i
$248$	−31.5968	+	663.298i	−0.00809032	+	0.169837i
$249$	−1046.81	−	1470.04i	−0.266422	−	0.374137i
$250$	784.091	+	2265.48i	0.198361	+	0.573127i
$251$	54.7395	−	10.5502i	0.0137654	−	0.00265307i	−0.182364	−	0.983231i	$-0.558375\pi$
$251$	54.7395	−	10.5502i	0.0137654	−	0.00265307i	0.196129	+	0.980578i	$0.437163\pi$
$252$	−1211.99	−	485.208i	−0.302970	−	0.121291i
$253$	2955.50	−	6471.65i	0.734431	−	1.60818i
$254$	−481.829	+	556.060i	−0.119026	+	0.137363i
$255$	−1572.99	+	6483.96i	−0.386292	+	1.59232i
$256$	1712.45	+	1632.81i	0.418077	+	0.398636i
$257$	−2536.04	+	1994.36i	−0.615540	+	0.484066i	−0.876576	−	0.481263i	$-0.840178\pi$
$257$	−2536.04	+	1994.36i	−0.615540	+	0.484066i	0.261036	+	0.965329i	$0.415936\pi$
$258$	0.990457	+	20.7922i	0.000239004	+	0.00501732i
$259$	−2009.43	−	4400.03i	−0.482084	−	1.05562i
$260$	−471.304	−	138.387i	−0.112419	−	0.0330093i
$261$	−149.812	+	210.381i	−0.0355291	+	0.0498937i
$262$	−715.185	−	562.427i	−0.168642	−	0.132622i
$263$	728.936	+	5069.86i	0.170905	+	1.18867i	0.876977	+	0.480532i	$0.159557\pi$
$263$	728.936	+	5069.86i	0.170905	+	1.18867i	−0.706072	+	0.708140i	$0.749534\pi$
$264$	−1564.81	−	301.593i	−0.364801	−	0.0703097i
$265$	−4910.94	−	3156.07i	−1.13840	−	0.731607i
$266$	−555.011	−	52.9971i	−0.127932	−	0.0122160i
$267$	3675.82			0.842533
$268$	−3367.09	+	2491.86i	−0.767454	+	0.567965i
$269$	7352.33			1.66647			0.833233	−	0.552923i	$-0.186487\pi$
$269$	7352.33			1.66647			0.833233	+	0.552923i	$0.186487\pi$
$270$	−339.164	−	32.3863i	−0.0764477	−	0.00729987i
$271$	4006.32	+	2574.71i	0.898032	+	0.577130i	0.906206	−	0.422837i	$-0.138966\pi$
$271$	4006.32	+	2574.71i	0.898032	+	0.577130i	−0.00817413	+	0.999967i	$0.502602\pi$
$272$	5772.49	+	1112.56i	1.28680	+	0.248010i
$273$	−24.8588	−	172.897i	−0.00551108	−	0.0383304i
$274$	−1312.09	−	1031.84i	−0.289293	−	0.227502i
$275$	10316.5	−	14487.5i	2.26222	−	3.17684i
$276$	−2770.26	−	813.420i	−0.604166	−	0.177399i
$277$	−3133.90	−	6862.28i	−0.679775	−	1.48850i	−0.862881	−	0.505407i	$-0.831343\pi$
$277$	−3133.90	−	6862.28i	−0.679775	−	1.48850i	0.183106	−	0.983093i	$-0.441385\pi$
$278$	−44.4312	−	932.725i	−0.00958563	−	0.201227i
$279$	499.358	−	392.699i	0.107153	−	0.0842663i
$280$	2712.27	+	2586.14i	0.578889	+	0.551969i
$281$	431.465	−	1778.52i	0.0915979	−	0.377572i	−0.907499	−	0.420054i	$-0.862011\pi$
$281$	431.465	−	1778.52i	0.0915979	−	0.377572i	0.999097	+	0.0424817i	$0.0135264\pi$
$282$	−204.685	+	236.219i	−0.0432227	+	0.0498816i
$283$	2672.79	−	5852.59i	0.561416	−	1.22933i	−0.389827	−	0.920888i	$-0.627465\pi$
$283$	2672.79	−	5852.59i	0.561416	−	1.22933i	0.951243	−	0.308442i	$-0.0998075\pi$
$284$	5727.85	+	2293.08i	1.19678	+	0.479118i
$285$	3015.36	−	581.162i	0.626717	−	0.120790i
$286$	−34.0622	−	98.4162i	−0.00704244	−	0.0203478i
$287$	5668.92	+	7960.88i	1.16594	+	1.63734i
$288$	−46.5138	+	976.444i	−0.00951684	+	0.199783i
$289$	5875.54	−	2352.21i	1.19592	−	0.478773i
$290$	304.633	−	195.776i	0.0616850	−	0.0396425i
$291$	−2655.92	+	1369.22i	−0.535027	+	0.275825i
$292$	620.068	+	715.597i	0.124270	+	0.143415i
$293$	1982.46	−	582.102i	0.395278	−	0.116064i	−0.0780520	−	0.996949i	$-0.524870\pi$
$293$	1982.46	−	582.102i	0.395278	−	0.116064i	0.473330	+	0.880885i	$0.343052\pi$
$294$	−10.4276	+	30.1287i	−0.00206855	+	0.00597667i
$295$	−2197.54	+	15284.2i	−0.433714	+	3.01655i
$296$	−1734.21	+	1653.56i	−0.340536	+	0.324700i
$297$	762.274	+	1320.30i	0.148928	+	0.257951i
$298$	20.2851	−	35.1349i	0.00394324	−	0.00682990i
$299$	−91.0746	−	375.414i	−0.0176153	−	0.0726113i
$300$	−6415.23	−	3307.28i	−1.23461	−	0.636487i
$301$	−218.049	+	20.8211i	−0.0417546	+	0.00398708i
$302$	218.520	−	20.8661i	0.0416371	−	0.00397587i
$303$	2878.72	+	1484.08i	0.545803	+	0.281381i
$304$	−637.899	−	2629.46i	−0.120349	−	0.496084i
$305$	7630.69	−	13216.7i	1.43256	−	2.48127i
$306$	287.033	+	497.156i	0.0536229	+	0.0928775i
$307$	164.014	−	156.387i	0.0304911	−	0.0290732i	−0.674680	−	0.738110i	$-0.735719\pi$
$307$	164.014	−	156.387i	0.0304911	−	0.0290732i	0.705171	+	0.709037i	$0.250870\pi$
$308$	1165.64	−	8107.21i	0.215645	−	1.49984i
$309$	−250.590	+	724.033i	−0.0461346	+	0.133297i
$310$	−854.627	+	250.941i	−0.156579	+	0.0459758i
$311$	3128.98	+	3611.04i	0.570509	+	0.658403i	0.965537	−	0.260267i	$-0.0838105\pi$
$311$	3128.98	+	3611.04i	0.570509	+	0.658403i	−0.395028	+	0.918669i	$0.629265\pi$
$312$	−76.9101	+	39.6499i	−0.0139557	+	0.00719466i
$313$	4953.32	−	3183.31i	0.894499	−	0.574860i	−0.0106548	−	0.999943i	$-0.503392\pi$
$313$	4953.32	−	3183.31i	0.894499	−	0.574860i	0.905154	+	0.425083i	$0.139755\pi$
$314$	−373.433	+	149.500i	−0.0671147	+	0.0268687i
$315$	170.590	−	3581.13i	0.0305132	−	0.640551i
$316$	1536.93	+	2158.32i	0.273605	+	0.384224i
$317$	1261.69	+	3645.42i	0.223545	+	0.645891i	0.999879	+	0.0155689i	$0.00495592\pi$
$317$	1261.69	+	3645.42i	0.223545	+	0.645891i	−0.776334	+	0.630322i	$0.782923\pi$
$318$	−493.199	+	95.0563i	−0.0869724	+	0.0167625i
$319$	−1504.28	−	602.224i	−0.264024	−	0.105699i
$320$	−3295.66	+	7216.48i	−0.575728	+	1.26067i
$321$	−1603.32	+	1850.33i	−0.278780	+	0.321730i
$322$	−339.385	+	1398.96i	−0.0587366	+	0.242115i
$323$	−3744.72	−	3570.58i	−0.645082	−	0.615085i
$324$	486.320	−	382.446i	0.0833881	−	0.0655771i
$325$	−45.9498	−	964.605i	−0.00784258	−	0.164636i
$326$	−192.421	−	421.342i	−0.0326908	−	0.0715828i
$327$	3741.75	+	1098.68i	0.632781	+	0.185801i
$328$	2808.22	−	3943.60i	0.472738	−	0.663868i
$329$	−2585.35	−	2033.14i	−0.433237	−	0.340701i
$330$	−304.205	−	2115.79i	−0.0507452	−	0.352941i
$331$	200.044	+	38.5554i	0.0332188	+	0.00640240i	0.205834	−	0.978587i	$-0.434009\pi$
$331$	200.044	+	38.5554i	0.0332188	+	0.00640240i	−0.172615	+	0.984989i	$0.555222\pi$
$332$	−3865.35	−	2484.11i	−0.638971	−	0.410642i
$333$	2281.97	+	217.901i	0.375529	+	0.0358586i
$334$	−2082.20			−0.341116
$335$	−9491.08	−	6499.97i	−1.54792	−	1.06009i
$336$	−3158.91			−0.512895
$337$	−10176.4	−	971.731i	−1.64494	−	0.157073i	−0.768920	−	0.639345i	$-0.779206\pi$
$337$	−10176.4	−	971.731i	−1.64494	−	0.157073i	−0.876021	+	0.482272i	$0.839812\pi$
$338$	1107.12	+	711.503i	0.178164	+	0.114499i
$339$	−832.822	−	160.513i	−0.133430	−	0.0257165i
$340$	2417.53	+	16814.3i	0.385615	+	2.68201i
$341$	3132.90	+	2463.74i	0.497525	+	0.391258i
$342$	153.262	−	215.226i	0.0242323	−	0.0340295i
$343$	5928.22	+	1740.68i	0.933218	+	0.274017i
$344$	45.0753	+	98.7011i	0.00706481	+	0.0154698i
$345$	−377.270	−	7919.87i	−0.0588740	−	1.23592i
$346$	1576.88	−	1240.07i	0.245010	−	0.192678i
$347$	−5457.15	−	5203.38i	−0.844251	−	0.804992i	0.138415	−	0.990374i	$-0.455799\pi$
$347$	−5457.15	−	5203.38i	−0.844251	−	0.804992i	−0.982666	+	0.185382i	$0.940648\pi$
$348$	−155.027	+	639.029i	−0.0238802	+	0.0984355i
$349$	997.981	−	1151.73i	0.153068	−	0.176650i	−0.674037	−	0.738698i	$-0.735441\pi$
$349$	997.981	−	1151.73i	0.153068	−	0.176650i	0.827104	+	0.562048i	$0.189986\pi$
$350$	−1494.93	+	3273.43i	−0.228306	+	0.499921i
$351$	76.8495	+	30.7659i	0.0116864	+	0.00467852i
$352$	−6022.19	+	1160.68i	−0.911886	+	0.175752i
$353$	123.795	+	357.683i	0.0186656	+	0.0539307i	0.953949	−	0.299969i	$-0.0969765\pi$
$353$	123.795	+	357.683i	0.0186656	+	0.0539307i	−0.935283	+	0.353900i	$0.884855\pi$
$354$	770.656	+	1082.24i	0.115706	+	0.162486i
$355$	−806.205	+	16924.3i	−0.120532	+	2.53028i
$356$	8688.35	−	3478.29i	1.29349	−	0.517835i
$357$	−5081.83	+	3265.89i	−0.753387	+	0.484172i
$358$	−595.590	+	307.048i	−0.0879271	+	0.0453296i
$359$	−667.999	−	770.911i	−0.0982051	−	0.113335i	0.704520	−	0.709685i	$-0.251163\pi$
$359$	−667.999	−	770.911i	−0.0982051	−	0.113335i	−0.802725	+	0.596350i	$0.796617\pi$
$360$	−1704.06	+	500.358i	−0.249478	+	0.0732532i
$361$	1464.47	−	4231.29i	0.213510	−	0.616897i
$362$	−100.686	+	700.290i	−0.0146187	+	0.101675i
$363$	−4032.50	+	3844.98i	−0.583062	+	0.555949i
$364$	−222.364	−	385.145i	−0.0320193	−	0.0554591i
$365$	−1300.15	+	2251.92i	−0.186446	+	0.322934i
$366$	−309.575	−	1276.09i	−0.0442124	−	0.182246i
$367$	−859.114	−	442.904i	−0.122194	−	0.0629956i	0.396045	−	0.918231i	$-0.370382\pi$
$367$	−859.114	−	442.904i	−0.122194	−	0.0629956i	−0.518240	+	0.855235i	$0.673413\pi$
$368$	−6954.48	+	664.072i	−0.985128	+	0.0940684i
$369$	−4610.51	+	440.250i	−0.650443	+	0.0621098i
$370$	−2856.78	−	1472.77i	−0.401397	−	0.206934i
$371$	−1246.07	−	5136.36i	−0.174373	−	0.718777i
$372$	808.711	−	1400.73i	0.112714	−	0.195227i
$373$	440.481	+	762.936i	0.0611454	+	0.105907i	0.894978	−	0.446111i	$-0.147191\pi$
$373$	440.481	+	762.936i	0.0611454	+	0.105907i	−0.833832	+	0.552018i	$0.813858\pi$
$374$	−2606.61	+	2485.40i	−0.360387	+	0.343628i
$375$	1701.37	−	11833.3i	0.234290	−	1.62952i
$376$	−532.889	+	1539.68i	−0.0730895	+	0.211178i
$377$	−84.4172	+	24.7871i	−0.0115324	+	0.00338621i
$378$	−202.006	−	233.128i	−0.0274870	−	0.0317217i
$379$	−9408.65	+	4850.50i	−1.27517	+	0.657397i	−0.956849	−	0.290586i	$-0.906150\pi$
$379$	−9408.65	+	4850.50i	−1.27517	+	0.657397i	−0.318323	+	0.947982i	$0.603120\pi$
$380$	6577.32	−	4226.99i	0.887920	−	0.570631i
$381$	3406.32	−	1363.68i	0.458034	−	0.183369i
$382$	−98.9309	+	2076.82i	−0.0132506	+	0.278165i
$383$	1235.96	+	1735.66i	0.164894	+	0.231561i	0.888753	−	0.458387i	$-0.151573\pi$
$383$	1235.96	+	1735.66i	0.164894	+	0.231561i	−0.723859	+	0.689948i	$0.757633\pi$
$384$	1075.86	+	3108.49i	0.142974	+	0.413097i
$385$	22086.5	−	4256.82i	2.92372	−	0.563501i
$386$	986.737	+	395.030i	0.130113	+	0.0520894i
$387$	43.1218	−	94.4236i	0.00566410	−	0.0124026i
$388$	−4982.03	+	5749.57i	−0.651866	+	0.752294i
$389$	1603.55	−	6609.91i	0.209005	−	0.861531i	−0.766622	−	0.642098i	$-0.778064\pi$
$389$	1603.55	−	6609.91i	0.209005	−	0.861531i	0.975628	−	0.219433i	$-0.0704207\pi$
$390$	−83.9990	−	80.0929i	−0.0109063	−	0.0103991i
$391$	−10501.3	+	8258.32i	−1.35825	+	1.06814i
$392$	7.90775	+	166.004i	0.00101888	+	0.0213890i
$393$	1884.82	+	4127.18i	0.241925	+	0.529742i
$394$	2672.97	+	784.854i	0.341782	+	0.100356i
$395$	−4220.72	+	5927.17i	−0.537639	+	0.755009i
$396$	3051.10	+	2399.41i	0.387181	+	0.304482i
$397$	−1528.30	−	10629.6i	−0.193207	−	1.34379i	−0.823451	−	0.567388i	$-0.807954\pi$
$397$	−1528.30	−	10629.6i	−0.193207	−	1.34379i	0.630243	−	0.776398i	$-0.282955\pi$
$398$	−1161.20	−	223.803i	−0.146245	−	0.0281865i
$399$	2338.95	+	1503.15i	0.293468	+	0.188601i
$400$	−17385.1	−	1660.08i	−2.17314	−	0.207510i
$401$	9217.50			1.14788			0.573940	−	0.818897i	$-0.305414\pi$
$401$	9217.50			1.14788			0.573940	+	0.818897i	$0.305414\pi$
$402$	−976.950	+	158.775i	−0.121209	+	0.0196990i
$403$	216.408			0.0267496
$404$	8208.63	+	783.829i	1.01088	+	0.0965271i
$405$	1429.32	+	918.567i	0.175366	+	0.112701i
$406$	321.932	+	62.0474i	0.0393528	+	0.00758463i
$407$	2046.75	+	14235.5i	0.249272	+	1.73373i
$408$	2352.21	+	1849.80i	0.285421	+	0.224458i
$409$	3562.27	−	5002.50i	0.430667	−	0.604787i	−0.541034	−	0.841001i	$-0.681967\pi$
$409$	3562.27	−	5002.50i	0.430667	−	0.604787i	0.971701	+	0.236214i	$0.0759065\pi$
$410$	6230.69	+	1829.50i	0.750517	+	0.220372i
$411$	3457.92	+	7571.79i	0.415004	+	0.908732i
$412$	92.8179	+	1948.49i	0.0110991	+	0.232998i
$413$	−10989.4	+	8642.14i	−1.30933	+	1.02967i
$414$	−493.735	−	470.775i	−0.0586129	−	0.0558873i
$415$	2974.83	−	12262.4i	0.351876	−	1.45045i
$416$	−218.074	+	251.670i	−0.0257018	+	0.0296614i
$417$	−1934.41	+	4235.77i	−0.227167	+	0.497426i
$418$	1538.93	+	616.093i	0.180075	+	0.0720911i
$419$	−4905.76	+	945.507i	−0.571985	+	0.110241i	−0.467039	−	0.884237i	$-0.654679\pi$
$419$	−4905.76	+	945.507i	−0.571985	+	0.110241i	−0.104946	+	0.994478i	$0.533467\pi$
$420$	−2985.48	−	8625.97i	−0.346848	−	1.00215i
$421$	−7567.04	−	10626.4i	−0.875997	−	1.23017i	−0.972046	−	0.234789i	$-0.924560\pi$
$421$	−7567.04	−	10626.4i	−0.875997	−	1.23017i	0.0960493	−	0.995377i	$-0.469379\pi$
$422$	11.5289	−	242.021i	0.00132990	−	0.0279180i
$423$	1447.03	−	579.304i	0.166329	−	0.0665880i
$424$	−2202.58	+	1415.51i	−0.252280	+	0.162130i
$425$	−29684.3	+	15303.3i	−3.38799	+	1.74663i
$426$	954.678	+	1101.76i	0.108578	+	0.125306i
$427$	13257.8	−	3892.83i	1.50255	−	0.441188i
$428$	−2038.79	+	5890.69i	−0.230254	+	0.665274i
$429$	−73.9104	+	514.058i	−0.00831802	+	0.0578531i
$430$	−105.334	+	100.436i	−0.0118132	+	0.0112638i
$431$	1980.43	+	3430.21i	0.221332	+	0.383358i	0.955213	−	0.295920i	$-0.0956262\pi$
$431$	1980.43	+	3430.21i	0.221332	+	0.383358i	−0.733881	+	0.679278i	$0.762293\pi$
$432$	748.510	−	1296.46i	0.0833627	−	0.144388i
$433$	2354.90	+	9707.04i	0.261361	+	1.07735i	0.939537	+	0.342446i	$0.111255\pi$
$433$	2354.90	+	9707.04i	0.261361	+	1.07735i	−0.678176	+	0.734899i	$0.737229\pi$
$434$	−716.789	−	369.530i	−0.0792787	−	0.0408710i
$435$	−1797.63	+	171.653i	−0.198137	+	0.0189198i
$436$	9883.85	−	943.793i	1.08567	−	0.103669i
$437$	5465.29	+	2817.56i	0.598262	+	0.308425i
$438$	52.7467	+	217.425i	0.00575419	+	0.0237191i
$439$	1352.39	−	2342.42i	0.147030	−	0.254664i	−0.783098	−	0.621898i	$-0.786362\pi$
$439$	1352.39	−	2342.42i	0.147030	−	0.254664i	0.930129	+	0.367234i	$0.119695\pi$
$440$	−5571.19	−	9649.59i	−0.603628	−	1.04551i
$441$	115.066	−	109.716i	0.0124248	−	0.0118471i
$442$	−27.8309	+	193.568i	−0.00299498	+	0.0208305i
$443$	−4402.16	+	12719.2i	−0.472128	+	1.36412i	0.418014	+	0.908441i	$0.362726\pi$
$443$	−4402.16	+	12719.2i	−0.472128	+	1.36412i	−0.890142	+	0.455684i	$0.849395\pi$
$444$	5599.97	−	1644.30i	0.598565	−	0.175755i
$445$	16830.6	+	19423.5i	1.79291	+	2.06913i
$446$	−10.1192	+	5.21683i	−0.00107435	+	0.000553865i
$447$	−170.199	+	109.380i	−0.0180092	+	0.0115738i
$448$	−6668.30	+	2669.59i	−0.703231	+	0.281531i
$449$	381.675	−	8012.34i	0.0401166	−	0.842151i	−0.885718	−	0.464223i	$-0.846334\pi$
$449$	381.675	−	8012.34i	0.0401166	−	0.842151i	0.925835	−	0.377928i	$-0.123363\pi$
$450$	−989.232	−	1389.18i	−0.103629	−	0.145526i
$451$	−9503.70	−	27459.1i	−0.992265	−	2.86696i
$452$	−2120.39	+	408.672i	−0.220652	+	0.0425272i
$453$	−1016.26	−	406.848i	−0.105404	−	0.0421973i
$454$	46.8828	−	102.659i	0.00484652	−	0.0106124i
$455$	799.789	−	923.006i	0.0824059	−	0.0951015i
$456$	324.708	−	1338.47i	0.0333462	−	0.137455i
$457$	134.826	+	128.556i	0.0138006	+	0.0131589i	0.696948	−	0.717122i	$-0.254541\pi$
$457$	134.826	+	128.556i	0.0138006	+	0.0131589i	−0.683147	+	0.730281i	$0.739389\pi$
$458$	−1193.79	+	938.809i	−0.121795	+	0.0957809i
$459$	−136.215	−	2859.51i	−0.0138518	−	0.290785i
$460$	−8386.03	−	18362.8i	−0.850001	−	1.86124i
$461$	−3868.38	−	1135.86i	−0.390821	−	0.114755i	0.0804174	−	0.996761i	$-0.474375\pi$
$461$	−3868.38	−	1135.86i	−0.390821	−	0.114755i	−0.471238	+	0.882006i	$0.656193\pi$
$462$	1122.59	−	1576.46i	0.113047	−	0.158752i
$463$	705.090	+	554.489i	0.0707739	+	0.0556572i	0.652919	−	0.757428i	$-0.273544\pi$
$463$	705.090	+	554.489i	0.0707739	+	0.0556572i	−0.582145	+	0.813085i	$0.697787\pi$
$464$	226.436	+	1574.90i	0.0226553	+	0.157571i
$465$	4361.50	+	840.610i	0.434967	+	0.0838330i
$466$	−2846.25	−	1829.17i	−0.282940	−	0.181834i
$467$	5105.43	+	487.509i	0.505891	+	0.0483067i	0.344882	−	0.938646i	$-0.387919\pi$
$467$	5105.43	+	487.509i	0.505891	+	0.0483067i	0.161009	+	0.986953i	$0.448525\pi$
$468$	210.758			0.0208169
$469$	−2158.02	−	10189.1i	−0.212469	−	1.00317i
$470$	−2185.41			−0.214479
$471$	1996.84	+	190.675i	0.195349	+	0.0186536i
$472$	5826.12	+	3744.22i	0.568155	+	0.365131i
$473$	639.484	+	123.250i	0.0621639	+	0.0119811i
$474$	89.0984	+	619.693i	0.00863381	+	0.0600495i
$475$	12082.5	+	9501.79i	1.16712	+	0.917836i
$476$	−8921.29	+	12528.2i	−0.859047	+	1.20636i
$477$	2403.28	+	705.668i	0.230689	+	0.0677365i
$478$	−1154.74	−	2528.52i	−0.110495	−	0.241950i
$479$	114.534	+	2404.37i	0.0109252	+	0.229349i	0.997726	+	0.0674073i	$0.0214727\pi$
$479$	114.534	+	2404.37i	0.0109252	+	0.229349i	−0.986800	+	0.161942i	$0.948224\pi$
$480$	−5372.64	+	4225.09i	−0.510888	+	0.401767i
$481$	565.163	+	538.882i	0.0535743	+	0.0510829i
$482$	45.0327	−	185.627i	0.00425557	−	0.0175417i
$483$	4701.05	−	5425.30i	0.442868	−	0.511096i
$484$	−5893.07	+	12904.0i	−0.553444	+	1.21187i
$485$	−19395.9	−	7764.94i	−1.81592	−	0.726985i
$486$	143.544	−	27.6659i	0.0133977	−	0.00258220i
$487$	1364.73	+	3943.14i	0.126986	+	0.366901i	0.990516	−	0.137396i	$-0.0438731\pi$
$487$	1364.73	+	3943.14i	0.126986	+	0.366901i	−0.863531	+	0.504296i	$0.831752\pi$
$488$	−3970.37	−	5575.60i	−0.368299	−	0.517204i
$489$	−109.909	+	2307.27i	−0.0101641	+	0.213371i
$490$	−206.950	+	82.8501i	−0.0190796	+	0.00763834i
$491$	−560.312	+	360.090i	−0.0515000	+	0.0330971i	−0.566138	−	0.824311i	$-0.691563\pi$
$491$	−560.312	+	360.090i	−0.0515000	+	0.0330971i	0.514637	+	0.857408i	$0.327927\pi$
$492$	−10481.0	+	5403.36i	−0.960411	+	0.495126i
$493$	1992.51	+	2299.48i	0.182025	+	0.210068i
$494$	86.3612	−	25.3579i	0.00786554	−	0.00230953i
$495$	−3486.38	+	10073.2i	−0.316568	+	0.914664i
$496$	556.969	−	3873.81i	0.0504207	−	0.350683i
$497$	−11102.4	+	10586.1i	−1.00204	+	0.955439i
$498$	−542.835	−	940.218i	−0.0488454	−	0.0846028i
$499$	9801.61	−	16976.9i	0.879319	−	1.52303i	0.0272303	−	0.999629i	$-0.491331\pi$
$499$	9801.61	−	16976.9i	0.879319	−	1.52303i	0.852089	−	0.523397i	$-0.175335\pi$
$500$	−7175.98	−	29579.8i	−0.641840	−	2.64570i
$501$	9229.20	+	4757.98i	0.823015	+	0.424294i
$502$	33.3849	−	3.18787i	0.00296821	−	0.000283430i
$503$	−1003.19	+	95.7934i	−0.0889269	+	0.00849149i	−0.139425	−	0.990233i	$-0.544525\pi$
$503$	−1003.19	+	95.7934i	−0.0889269	+	0.00849149i	0.0504977	+	0.998724i	$0.483919\pi$
$504$	−1429.22	−	736.816i	−0.126315	−	0.0651198i
$505$	5338.78	+	22006.8i	0.470441	+	1.93918i
$506$	2140.03	−	3706.64i	0.188015	−	0.325652i
$507$	−3281.40	−	5683.55i	−0.287440	−	0.497861i
$508$	6760.95	−	6446.55i	0.590490	−	0.563031i
$509$	1722.07	−	11977.3i	0.149960	−	1.04299i	−0.766322	−	0.642457i	$-0.777915\pi$
$509$	1722.07	−	11977.3i	0.149960	−	1.04299i	0.916282	−	0.400535i	$-0.131176\pi$
$510$	−1312.79	+	3793.07i	−0.113983	+	0.329333i
$511$	−2258.91	+	663.277i	−0.195555	+	0.0574201i
$512$	6676.42	+	7705.00i	0.576287	+	0.665070i
$513$	−1171.13	+	603.760i	−0.100793	+	0.0519623i
$514$	−1632.79	+	1049.33i	−0.140116	+	0.0900468i
$515$	−4973.27	+	1991.00i	−0.425531	+	0.170357i
$516$	12.5754	−	263.989i	0.00107287	−	0.0225222i
$517$	5672.35	+	7965.70i	0.482533	+	0.677623i
$518$	−951.762	−	2749.93i	−0.0807297	−	0.233253i
$519$	−9823.09	+	1893.24i	−0.830801	+	0.160124i
$520$	−561.666	−	224.857i	−0.0473667	−	0.0189628i
$521$	−3406.19	+	7458.51i	−0.286426	+	0.627185i	−0.997081	−	0.0763560i	$-0.975671\pi$
$521$	−3406.19	+	7458.51i	−0.286426	+	0.627185i	0.710655	+	0.703541i	$0.248399\pi$
$522$	−101.748	+	117.423i	−0.00853136	+	0.00984571i
$523$	5171.95	−	21319.1i	0.432416	−	1.78244i	−0.171272	−	0.985224i	$-0.554788\pi$
$523$	5171.95	−	21319.1i	0.432416	−	1.78244i	0.603688	−	0.797221i	$-0.293697\pi$
$524$	8360.46	+	7971.68i	0.697001	+	0.664589i
$525$	14106.2	−	11093.3i	1.17266	−	0.922189i
$526$	146.616	+	3077.85i	0.0121535	+	0.255134i
$527$	−3108.99	−	6807.74i	−0.256982	−	0.562713i
$528$	9011.64	+	2646.06i	0.742768	+	0.218096i
$529$	2151.49	−	3021.35i	0.176830	−	0.248323i
$530$	−2760.51	−	2170.89i	−0.226243	−	0.177920i
$531$	−942.891	−	6557.95i	−0.0770584	−	0.535953i
$532$	6950.84	+	1339.66i	0.566461	+	0.109176i
$533$	−1327.28	−	852.988i	−0.107862	−	0.0693190i
$534$	2201.32	+	210.200i	0.178390	+	0.0170342i
$535$	−17118.5			−1.38336
$536$	−4420.15	+	2661.07i	−0.356197	+	0.214442i
$537$	3341.54			0.268526
$538$	4403.05	+	420.440i	0.352842	+	0.0336923i
$539$	839.134	+	539.279i	0.0670576	+	0.0430953i
$540$	4247.62	+	818.662i	0.338497	+	0.0652400i
$541$	1309.76	+	9109.60i	0.104087	+	0.723941i	0.973306	+	0.229513i	$0.0737134\pi$
$541$	1309.76	+	9109.60i	0.104087	+	0.723941i	−0.869219	+	0.494428i	$0.835378\pi$
$542$	2252.01	+	1771.00i	0.178473	+	0.140352i
$543$	2046.51	−	2873.91i	0.161738	−	0.227130i
$544$	11049.9	+	3244.55i	0.870884	+	0.255715i
$545$	11326.9	+	24802.5i	0.890260	+	1.94940i
$546$	−5.00003	−	104.963i	−0.000391907	−	0.00822715i
$547$	−8541.12	+	6716.81i	−0.667627	+	0.525028i	−0.893463	−	0.449138i	$-0.851731\pi$
$547$	−8541.12	+	6716.81i	−0.667627	+	0.525028i	0.225836	+	0.974165i	$0.427489\pi$
$548$	15338.2	+	14625.0i	1.19565	+	1.14005i
$549$	−1543.79	+	6363.57i	−0.120013	+	0.494701i
$550$	7006.67	−	8086.12i	0.543209	−	0.626897i
$551$	581.748	−	1273.85i	0.0449787	−	0.0984897i
$552$	−3301.39	−	1321.68i	−0.254559	−	0.101910i
$553$	−6468.91	+	1246.78i	−0.497443	+	0.0958743i
$554$	−1484.36	−	4288.79i	−0.113835	−	0.328905i
$555$	9297.09	+	13055.9i	0.711062	+	0.998547i
$556$	−564.121	+	11842.4i	−0.0430289	+	0.903288i
$557$	6230.88	−	2494.47i	0.473987	−	0.189756i	−0.122355	−	0.992486i	$-0.539044\pi$
$557$	6230.88	−	2494.47i	0.473987	−	0.189756i	0.596342	+	0.802731i	$0.296620\pi$
$558$	321.504	−	206.618i	0.0243913	−	0.0156754i
$559$	31.4304	−	16.2035i	0.00237812	−	0.00122600i
$560$	−14463.8	−	16692.1i	−1.09144	−	1.25959i
$561$	17233.0	−	5060.06i	1.29693	−	0.380812i
$562$	360.093	−	1040.42i	0.0270278	−	0.0780917i
$563$	1022.57	−	7112.13i	0.0765474	−	0.532399i	−0.915081	−	0.403271i	$-0.867873\pi$
$563$	1022.57	−	7112.13i	0.0765474	−	0.532399i	0.991628	−	0.129128i	$-0.0412177\pi$
$564$	2872.10	−	2738.55i	0.214428	−	0.204457i
$565$	−2965.09	−	5135.69i	−0.220783	−	0.382407i
$566$	1935.32	−	3352.07i	0.143723	−	0.248936i
$567$	362.665	+	1494.93i	0.0268615	+	0.110725i
$568$	6754.47	+	3482.17i	0.498964	+	0.257234i
$569$	15790.9	−	1507.85i	1.16343	−	0.111094i	0.504576	−	0.863367i	$-0.331649\pi$
$569$	15790.9	−	1507.85i	1.16343	−	0.111094i	0.658851	+	0.752273i	$0.271043\pi$
$570$	1839.03	−	175.606i	0.135137	−	0.0129041i
$571$	−14636.7	−	7545.72i	−1.07272	−	0.553027i	−0.170969	−	0.985276i	$-0.554690\pi$
$571$	−14636.7	−	7545.72i	−1.07272	−	0.553027i	−0.901754	+	0.432249i	$0.857720\pi$
$572$	311.736	+	1284.99i	0.0227873	+	0.0939306i
$573$	5184.20	−	8979.29i	0.377963	−	0.654651i
$574$	2939.68	+	5091.67i	0.213763	+	0.370248i
$575$	28723.4	−	27387.7i	2.08322	−	1.98634i
$576$	484.435	−	3369.32i	0.0350430	−	0.243730i
$577$	−1932.81	+	5584.49i	−0.139452	+	0.402921i	−0.993003	−	0.118089i	$-0.962323\pi$
$577$	−1932.81	+	5584.49i	−0.139452	+	0.402921i	0.853551	+	0.521010i	$0.174444\pi$
$578$	3653.17	−	1072.67i	0.262892	−	0.0771921i
$579$	−3470.97	−	4005.72i	−0.249134	−	0.287516i
$580$	−4086.54	+	2106.76i	−0.292559	+	0.150825i
$581$	9610.72	−	6176.44i	0.686265	−	0.441036i
$582$	−1668.84	+	668.101i	−0.118858	+	0.0475837i
$583$	−747.722	+	15696.6i	−0.0531175	+	1.11507i
$584$	676.488	+	949.994i	0.0479337	+	0.0673134i
$585$	189.302	+	546.951i	0.0133789	+	0.0386558i
$586$	1220.51	−	235.234i	0.0860391	−	0.0165827i
$587$	−23239.0	−	9303.51i	−1.63403	−	0.654169i	−0.640527	−	0.767936i	$-0.721284\pi$
$587$	−23239.0	−	9303.51i	−1.63403	−	0.654169i	−0.993507	+	0.113767i	$0.963708\pi$
$588$	168.157	−	368.213i	0.0117937	−	0.0258246i
$589$	−2255.73	+	2603.25i	−0.157802	+	0.182114i
$590$	−2190.05	+	9027.51i	−0.152819	+	0.629927i
$591$	−10054.3	−	9586.77i	−0.699795	−	0.667254i
$592$	11100.8	−	8729.75i	0.770674	−	0.606065i
$593$	−414.602	−	8703.56i	−0.0287110	−	0.602719i	−0.966678	−	0.255995i	$-0.917597\pi$
$593$	−414.602	−	8703.56i	−0.0287110	−	0.602719i	0.937967	−	0.346724i	$-0.112706\pi$
$594$	380.999	+	834.270i	0.0263174	+	0.0576272i
$595$	−40525.8	−	11899.4i	−2.79226	−	0.819881i
$596$	−298.788	+	419.589i	−0.0205350	+	0.0288373i
$597$	4635.53	+	3645.42i	0.317789	+	0.249912i
$598$	−33.0734	−	230.031i	−0.00226166	−	0.0157302i
$599$	−2941.32	−	566.892i	−0.200633	−	0.0386688i	0.0879447	−	0.996125i	$-0.471970\pi$
$599$	−2941.32	−	566.892i	−0.200633	−	0.0386688i	−0.288577	+	0.957457i	$0.593182\pi$
$600$	−7478.54	−	4806.17i	−0.508850	−	0.327018i
$601$	1808.28	+	172.670i	0.122731	+	0.0117194i	0.156241	−	0.987719i	$-0.450062\pi$
$601$	1808.28	+	172.670i	0.122731	+	0.0117194i	−0.0335098	+	0.999438i	$0.510669\pi$
$602$	−131.772			−0.00892134
$603$	4693.08	+	1528.65i	0.316944	+	0.103236i
$604$	−2787.07			−0.187755
$605$	−38781.2	−	3703.15i	−2.60608	−	0.248850i
$606$	1639.10	+	1053.38i	0.109874	+	0.0706119i
$607$	4720.41	+	909.784i	0.315643	+	0.0608352i	0.344612	−	0.938745i	$-0.388010\pi$
$607$	4720.41	+	909.784i	0.315643	+	0.0608352i	−0.0289692	+	0.999580i	$0.509222\pi$
$608$	−754.341	−	5246.55i	−0.0503167	−	0.349960i
$609$	−1285.16	−	1010.66i	−0.0855129	−	0.0672481i
$610$	5325.55	−	7478.68i	0.353484	−	0.496398i
$611$	509.464	+	149.592i	0.0337328	+	0.00990483i
$612$	−3027.81	−	6629.99i	−0.199987	−	0.437911i
$613$	220.850	+	4636.20i	0.0145514	+	0.305472i	0.994397	+	0.105714i	$0.0337127\pi$
$613$	220.850	+	4636.20i	0.0145514	+	0.305472i	−0.979845	+	0.199759i	$0.935984\pi$
$614$	107.165	−	84.2756i	0.00704370	−	0.00553923i
$615$	−23436.6	−	22346.8i	−1.53668	−	1.46522i
$616$	2378.38	−	9803.82i	0.155565	−	0.641246i
$617$	5739.69	−	6623.96i	0.374508	−	0.432205i	−0.536940	−	0.843620i	$-0.680420\pi$
$617$	5739.69	−	6623.96i	0.374508	−	0.432205i	0.911448	+	0.411415i	$0.134965\pi$
$618$	−191.473	+	419.268i	−0.0124631	+	0.0272904i
$619$	26380.1	+	10561.0i	1.71293	+	0.685755i	0.999882	−	0.0153580i	$-0.00488881\pi$
$619$	26380.1	+	10561.0i	1.71293	+	0.685755i	0.713050	+	0.701113i	$0.247313\pi$
$620$	11104.5	−	2140.22i	0.719303	−	0.138634i
$621$	1112.69	+	3214.90i	0.0719012	+	0.207745i
$622$	1667.34	+	2341.45i	0.107483	+	0.150939i
$623$	−1107.20	+	23243.0i	−0.0712024	+	1.49472i
$624$	473.437	−	189.535i	0.0303728	−	0.0121594i
$625$	37196.6	−	23904.8i	2.38058	−	1.52991i
$626$	3148.41	−	1623.12i	0.201015	−	0.103631i
$627$	−5413.37	−	6247.36i	−0.344799	−	0.397920i
$628$	4900.25	−	1438.84i	0.311372	−	0.0914270i
$629$	8832.74	−	25520.5i	0.559912	−	1.61776i
$630$	306.946	−	2134.86i	0.0194112	−	0.135008i
$631$	155.976	−	148.723i	0.00984042	−	0.00938283i	−0.685143	−	0.728409i	$-0.740260\pi$
$631$	155.976	−	148.723i	0.00984042	−	0.00938283i	0.694983	+	0.719026i	$0.255412\pi$
$632$	1631.75	+	2826.27i	0.102702	+	0.177884i
$633$	−604.139	+	1046.40i	−0.0379342	+	0.0657040i
$634$	547.122	+	2255.27i	0.0342728	+	0.141275i
$635$	22802.5	+	11755.5i	1.42502	+	0.734651i
$636$	6348.28	−	606.187i	0.395795	−	0.0377938i
$637$	53.9154	−	5.14830i	0.00335354	−	0.000320225i
$638$	−866.425	−	446.673i	−0.0537651	−	0.0277178i
$639$	−1713.95	−	7064.98i	−0.106107	−	0.437381i
$640$	−11499.6	+	19917.9i	−0.710253	+	1.23019i
$641$	−4473.32	−	7748.01i	−0.275640	−	0.477423i	0.694656	−	0.719342i	$-0.255557\pi$
$641$	−4473.32	−	7748.01i	−0.275640	−	0.477423i	−0.970296	+	0.241919i	$0.922223\pi$
$642$	−1065.98	+	1016.41i	−0.0655310	+	0.0624837i
$643$	2794.38	−	19435.3i	0.171384	−	1.19200i	−0.704581	−	0.709623i	$-0.748865\pi$
$643$	2794.38	−	19435.3i	0.171384	−	1.19200i	0.875965	−	0.482375i	$-0.160226\pi$
$644$	5977.88	−	17271.9i	0.365779	−	1.05685i
$645$	696.390	−	204.479i	0.0425121	−	0.0124827i
$646$	−2038.40	−	2352.44i	−0.124148	−	0.143275i
$647$	−15862.0	+	8177.45i	−0.963835	+	0.496891i	−0.866945	−	0.498404i	$-0.833920\pi$
$647$	−15862.0	+	8177.45i	−0.963835	+	0.496891i	−0.0968897	+	0.995295i	$0.530889\pi$
$648$	641.056	−	411.981i	0.0388627	−	0.0249755i
$649$	38589.3	−	15448.8i	2.33399	−	0.934389i
$650$	27.6429	−	580.296i	0.00166807	−	0.0350171i
$651$	2332.71	+	3275.84i	0.140440	+	0.197220i
$652$	1923.50	+	5557.59i	0.115537	+	0.333822i
$653$	6208.81	−	1196.65i	0.372082	−	0.0717129i	0.000217465	−	1.00000i	$-0.499931\pi$
$653$	6208.81	−	1196.65i	0.372082	−	0.0717129i	0.371864	+	0.928287i	$0.378719\pi$
$654$	2177.98	+	871.931i	0.130223	+	0.0521333i
$655$	−13178.5	+	28856.9i	−0.786147	+	1.72142i
$656$	−18684.9	+	21563.5i	−1.11207	+	1.28340i
$657$	263.037	−	1084.25i	0.0156195	−	0.0643846i
$658$	−1432.01	−	1365.42i	−0.0848413	−	0.0808960i
$659$	15824.6	−	12444.6i	0.935415	−	0.735619i	−0.0291192	−	0.999576i	$-0.509270\pi$
$659$	15824.6	−	12444.6i	0.935415	−	0.735619i	0.964534	+	0.263957i	$0.0850278\pi$
$660$	1291.35	+	27108.7i	0.0761600	+	1.59879i
$661$	662.167	+	1449.94i	0.0389642	+	0.0853196i	0.928113	−	0.372298i	$-0.121430\pi$
$661$	662.167	+	1449.94i	0.0389642	+	0.0853196i	−0.889149	+	0.457618i	$0.848703\pi$
$662$	117.595	+	34.5289i	0.00690400	+	0.00202720i
$663$	565.677	−	794.382i	0.0331359	−	0.0465328i
$664$	−4448.49	−	3498.33i	−0.259992	−	0.204460i
$665$	2766.56	+	19241.8i	0.161327	+	1.12205i
$666$	1354.13	+	260.987i	0.0787860	+	0.0151848i
$667$	−3041.80	−	1954.85i	−0.176580	−	0.113481i
$668$	26316.9	+	2512.96i	1.52430	+	0.145553i
$669$	56.7737			0.00328102
$670$	−5312.18	−	4435.35i	−0.306309	−	0.255750i
$671$	−41082.2			−2.36358
$672$	−6160.27	−	588.235i	−0.353627	−	0.0337673i
$673$	−27813.3	−	17874.5i	−1.59305	−	1.02379i	−0.970465	−	0.241243i	$-0.922445\pi$
$673$	−27813.3	−	17874.5i	−1.59305	−	1.02379i	−0.622588	−	0.782550i	$-0.713919\pi$
$674$	−6038.74	−	1163.87i	−0.345109	−	0.0665143i
$675$	1210.32	+	8417.94i	0.0690150	+	0.480010i
$676$	−13134.2	−	10328.9i	−0.747282	−	0.587669i
$677$	8343.94	−	11717.4i	0.473683	−	0.665195i	−0.506739	−	0.862099i	$-0.669149\pi$
$677$	8343.94	−	11717.4i	0.473683	−	0.665195i	0.980423	+	0.196904i	$0.0630887\pi$
$678$	−489.569	−	143.750i	−0.0277313	−	0.00814263i
$679$	−7857.91	−	17206.4i	−0.444122	−	0.972491i
$680$	995.549	+	20899.1i	0.0561435	+	1.17860i
$681$	−442.389	+	347.899i	−0.0248934	+	0.0195764i
$682$	1735.30	+	1654.60i	0.0974310	+	0.0929003i
$683$	−1360.23	+	5606.96i	−0.0762048	+	0.314120i	−0.997138	−	0.0755994i	$-0.975913\pi$
$683$	−1360.23	+	5606.96i	−0.0762048	+	0.314120i	0.920933	+	0.389720i	$0.127428\pi$
$684$	−2196.83	+	2535.28i	−0.122804	+	0.141723i
$685$	−24177.5	+	52941.3i	−1.34857	+	2.95297i
$686$	3450.66	+	1381.44i	0.192051	+	0.0768856i
$687$	7436.67	−	1433.30i	0.412993	−	0.0795980i
$688$	−209.158	−	604.322i	−0.0115902	−	0.0334877i
$689$	494.935	+	695.039i	0.0273665	+	0.0384309i
$690$	226.962	−	4764.51i	0.0125221	−	0.262872i
$691$	26234.0	−	10502.5i	1.44427	−	0.578197i	0.488564	−	0.872528i	$-0.337521\pi$
$691$	26234.0	−	10502.5i	1.44427	−	0.578197i	0.955704	+	0.294331i	$0.0950968\pi$
$692$	−21426.9	+	13770.2i	−1.17706	+	0.756452i
$693$	−8578.15	+	4422.34i	−0.470212	+	0.242411i
$694$	−2970.54	−	3428.19i	−0.162479	−	0.187511i
$695$	−31239.6	+	9172.76i	−1.70501	+	0.500637i
$696$	−264.896	+	765.367i	−0.0144265	+	0.0416827i
$697$	−7765.10	+	54007.5i	−0.421986	+	2.93498i
$698$	663.517	−	632.662i	0.0359807	−	0.0343075i
$699$	8436.01	+	14611.6i	0.456480	+	0.790646i
$700$	22845.1	−	39568.8i	1.23352	−	2.13651i
$701$	−2398.95	−	9888.59i	−0.129254	−	0.532792i	−0.999213	−	0.0396677i	$-0.987370\pi$
$701$	−2398.95	−	9888.59i	−0.129254	−	0.532792i	0.869959	−	0.493124i	$-0.164145\pi$
$702$	44.2631	+	22.8192i	0.00237978	+	0.00122686i
$703$	−12373.3	+	1181.51i	−0.663826	+	0.0633877i
$704$	21259.3	−	2030.02i	1.13813	−	0.108678i
$705$	9686.68	+	4993.83i	0.517477	+	0.266778i
$706$	53.6827	+	221.283i	0.00286172	+	0.0117962i
$707$	−10251.3	+	17755.8i	−0.545318	+	0.944519i
$708$	−8434.22	−	14608.5i	−0.447708	−	0.775453i
$709$	−15120.4	+	14417.2i	−0.800926	+	0.763682i	−0.975273	−	0.221003i	$-0.929067\pi$
$709$	−15120.4	+	14417.2i	−0.800926	+	0.763682i	0.174347	+	0.984684i	$0.444219\pi$
$710$	−1450.62	+	10089.3i	−0.0766772	+	0.533302i
$711$	1021.13	−	2950.35i	0.0538611	−	0.155621i
$712$	11060.1	−	3247.53i	0.582154	−	0.170936i
$713$	5824.23	+	6721.52i	0.305917	+	0.353047i
$714$	−3230.09	+	1665.23i	−0.169304	+	0.0872823i
$715$	−3054.77	+	1963.18i	−0.159779	+	0.102684i
$716$	7898.25	−	3161.98i	0.412251	−	0.165040i
$717$	−659.576	+	13846.2i	−0.0343547	+	0.721194i
$718$	−355.957	−	499.871i	−0.0185017	−	0.0259819i
$719$	7719.64	+	22304.4i	0.400409	+	1.15690i	0.947479	+	0.319818i	$0.103622\pi$
$719$	7719.64	+	22304.4i	0.400409	+	1.15690i	−0.547070	+	0.837087i	$0.684257\pi$
$720$	10277.9	−	1980.90i	0.531991	−	0.102533i
$721$	−4502.75	−	1802.63i	−0.232581	−	0.0931115i
$722$	1118.98	−	2450.23i	0.0576790	−	0.126299i
$723$	−623.778	+	719.878i	−0.0320865	+	0.0370298i
$724$	2117.75	−	8729.47i	0.108709	−	0.448105i
$725$	−6541.79	−	6237.58i	−0.335112	−	0.319528i
$726$	−2634.80	+	2072.03i	−0.134692	+	0.105923i
$727$	−19.2114	−	403.296i	−0.000980070	−	0.0205742i	0.998324	−	0.0578665i	$-0.0184298\pi$
$727$	−19.2114	−	403.296i	−0.000980070	−	0.0205742i	−0.999304	+	0.0372923i	$0.988127\pi$
$728$	−227.549	−	498.263i	−0.0115845	−	0.0253666i
$729$	−699.470	−	205.383i	−0.0355368	−	0.0104345i
$730$	−907.389	+	1274.25i	−0.0460054	+	0.0646056i
$731$	−961.267	−	755.949i	−0.0486371	−	0.0382487i
$732$	2372.64	+	16502.1i	0.119803	+	0.833245i
$733$	−17184.3	−	3311.99i	−0.865914	−	0.166891i	−0.263096	−	0.964770i	$-0.584743\pi$
$733$	−17184.3	−	3311.99i	−0.865914	−	0.166891i	−0.602818	+	0.797879i	$0.705956\pi$
$734$	−489.166	−	314.368i	−0.0245987	−	0.0158086i
$735$	1106.61	+	105.668i	0.0555346	+	0.00530291i
$736$	−13685.8			−0.685413
$737$	−2378.56	+	30874.8i	−0.118881	+	1.54313i
$738$	−2786.25			−0.138975
$739$	−12743.2	−	1216.83i	−0.634326	−	0.0605707i	−0.227060	−	0.973881i	$-0.572911\pi$
$739$	−12743.2	−	1216.83i	−0.634326	−	0.0605707i	−0.407265	+	0.913310i	$0.633518\pi$
$740$	34329.4	+	22062.2i	1.70537	+	1.09598i
$741$	−440.736	−	84.9449i	−0.0218500	−	0.00421124i
$742$	−452.505	−	3147.24i	−0.0223881	−	0.155713i
$743$	−9064.58	−	7128.46i	−0.447574	−	0.351976i	0.368791	−	0.929512i	$-0.379772\pi$
$743$	−9064.58	−	7128.46i	−0.447574	−	0.351976i	−0.816365	+	0.577536i	$0.804014\pi$
$744$	1155.56	−	1622.76i	0.0569421	−	0.0799640i
$745$	−1357.27	−	398.531i	−0.0667471	−	0.0195987i
$746$	220.161	+	482.084i	0.0108052	+	0.0236600i
$747$	257.609	+	5407.88i	0.0126177	+	0.264878i
$748$	35944.6	−	28267.2i	1.75704	−	1.38175i
$749$	−11217.1	−	10695.5i	−0.547215	−	0.521768i
$750$	1695.58	−	6989.27i	0.0825517	−	0.340283i
$751$	−7867.66	+	9079.76i	−0.382283	+	0.441179i	−0.913982	−	0.405755i	$-0.867009\pi$
$751$	−7867.66	+	9079.76i	−0.382283	+	0.441179i	0.531698	+	0.846934i	$0.321554\pi$
$752$	3988.97	−	8734.63i	0.193435	−	0.423563i
$753$	−155.261	−	62.1571i	−0.00751398	−	0.00300814i
$754$	−51.9720	+	10.0168i	−0.00251022	+	0.000483806i
$755$	−2503.33	−	7232.89i	−0.120669	−	0.348651i
$756$	2271.81	+	3190.31i	0.109292	+	0.153479i
$757$	183.801	−	3858.45i	0.00882478	−	0.185255i	−0.990151	−	0.140004i	$-0.955288\pi$
$757$	183.801	−	3858.45i	0.00882478	−	0.185255i	0.998976	−	0.0452505i	$-0.0144086\pi$
$758$	−5911.89	+	2366.76i	−0.283284	+	0.113410i
$759$	−17955.5	+	11539.3i	−0.858687	+	0.551845i
$760$	8559.38	−	4412.67i	0.408528	−	0.210611i
$761$	−7344.83	−	8476.39i	−0.349869	−	0.403770i	0.553351	−	0.832948i	$-0.313349\pi$
$761$	−7344.83	−	8476.39i	−0.349869	−	0.403770i	−0.903220	+	0.429178i	$0.858803\pi$
$762$	2117.91	−	621.874i	0.100687	−	0.0295644i
$763$	−8074.26	+	23329.0i	−0.383103	+	1.10690i
$764$	3756.86	−	26129.5i	0.177904	−	1.23735i
$765$	14486.3	−	13812.7i	0.684646	−	0.652809i
$766$	640.918	+	1110.10i	0.0302315	+	0.0523624i
$767$	1128.48	−	1954.59i	0.0531255	−	0.0920160i
$768$	−1673.51	−	6898.28i	−0.0786295	−	0.324115i
$769$	−21070.9	−	10862.8i	−0.988081	−	0.509391i	−0.113119	−	0.993581i	$-0.536084\pi$
$769$	−21070.9	−	10862.8i	−0.988081	−	0.509391i	−0.874963	+	0.484190i	$0.839114\pi$
$770$	13470.3	−	1286.25i	0.630434	−	0.0601992i
$771$	9635.06	−	920.037i	0.450062	−	0.0429758i
$772$	−11994.6	−	6183.67i	−0.559193	−	0.288284i
$773$	−2755.86	−	11359.8i	−0.128230	−	0.528570i	−0.999300	−	0.0374115i	$-0.988089\pi$
$773$	−2755.86	−	11359.8i	−0.128230	−	0.528570i	0.871070	−	0.491158i	$-0.163426\pi$
$774$	31.2237	−	54.0811i	0.00145002	−	0.00251150i
$775$	11116.6	+	19254.5i	0.515252	+	0.892443i
$776$	−6781.65	+	6466.29i	−0.313720	+	0.299132i
$777$	−2065.20	+	14363.8i	−0.0953521	+	0.663188i
$778$	1338.29	−	3866.74i	0.0616711	−	0.178187i
$779$	24095.7	−	7075.13i	1.10824	−	0.325408i
$780$	965.004	+	1113.67i	0.0442983	+	0.0511230i
$781$	40540.1	−	20899.9i	1.85741	−	0.957563i
$782$	−6761.12	+	4345.11i	−0.309178	+	0.198697i
$783$	719.310	−	287.968i	0.0328302	−	0.0131432i
$784$	46.6050	−	978.360i	0.00212304	−	0.0445681i
$785$	8135.42	+	11424.6i	0.369892	+	0.519441i
$786$	892.741	+	2579.41i	0.0405127	+	0.117054i
$787$	−40982.7	+	7898.78i	−1.85626	+	0.357765i	−0.989913	−	0.141677i	$-0.954751\pi$
$787$	−40982.7	+	7898.78i	−1.85626	+	0.357765i	−0.866347	+	0.499442i	$0.833538\pi$
$788$	−32836.5	−	13145.8i	−1.48446	−	0.594287i
$789$	6383.26	−	13977.4i	0.288023	−	0.630682i
$790$	−2866.59	+	3308.22i	−0.129099	+	0.148989i
$791$	1265.82	−	5217.78i	0.0568993	−	0.234542i
$792$	3460.05	+	3299.15i	0.155237	+	0.148018i
$793$	−1753.42	+	1378.90i	−0.0785191	+	0.0617481i
$794$	−307.398	−	6453.07i	−0.0137395	−	0.288427i
$795$	7275.14	+	15930.3i	0.324557	+	0.710680i
$796$	14406.3	+	4230.08i	0.641481	+	0.188356i
$797$	8327.34	−	11694.1i	0.370100	−	0.519732i	−0.586963	−	0.809614i	$-0.699677\pi$
$797$	8327.34	−	11694.1i	0.370100	−	0.519732i	0.957063	+	0.289882i	$0.0936159\pi$
$798$	1314.76	+	1033.94i	0.0583232	+	0.0458659i
$799$	−2613.27	−	18175.7i	−0.115708	−	0.804769i
$800$	−33594.0	−	6474.72i	−1.48466	−	0.286145i
$801$	−9276.88	−	5961.89i	−0.409217	−	0.262988i
$802$	5520.04	+	527.100i	0.243042	+	0.0232077i
$803$	6999.76			0.307617
$804$	12539.3	−	827.702i	0.550035	−	0.0363070i
$805$	50192.8			2.19760
$806$	129.599	+	12.3752i	0.00566371	+	0.000540818i
$807$	−18555.5	−	11924.9i	−0.809399	−	0.520169i
$808$	9972.88	+	1922.12i	0.434214	+	0.0836878i
$809$	4877.09	+	33920.9i	0.211952	+	1.47416i	0.766627	+	0.642092i	$0.221933\pi$
$809$	4877.09	+	33920.9i	0.211952	+	1.47416i	−0.554675	+	0.832067i	$0.687157\pi$
$810$	803.441	+	631.833i	0.0348519	+	0.0274078i
$811$	10077.1	−	14151.3i	0.436319	−	0.612724i	−0.536609	−	0.843831i	$-0.680295\pi$
$811$	10077.1	−	14151.3i	0.436319	−	0.612724i	0.972929	+	0.231106i	$0.0742345\pi$
$812$	−3994.03	−	1172.75i	−0.172614	−	0.0506842i
$813$	−5935.02	−	12995.9i	−0.256027	−	0.560622i
$814$	411.678	+	8642.18i	0.0177264	+	0.372123i
$815$	−12695.2	+	9983.59i	−0.545635	+	0.429092i
$816$	−12763.9	−	12170.4i	−0.547581	−	0.522117i
$817$	−132.697	+	546.984i	−0.00568234	+	0.0234229i
$818$	2419.38	−	2792.12i	0.103413	−	0.119345i
$819$	−217.688	+	476.670i	−0.00928770	+	0.0203372i
$820$	−76541.9	−	30642.8i	−3.25971	−	1.30499i
$821$	9649.56	−	1859.80i	0.410197	−	0.0790590i	0.0200217	−	0.999800i	$-0.493626\pi$
$821$	9649.56	−	1859.80i	0.410197	−	0.0790590i	0.390175	+	0.920741i	$0.372414\pi$
$822$	1637.84	+	4732.22i	0.0694965	+	0.200797i
$823$	−2843.90	−	3993.69i	−0.120452	−	0.169151i	0.749947	−	0.661497i	$-0.230079\pi$
$823$	−2843.90	−	3993.69i	−0.120452	−	0.169151i	−0.870399	+	0.492346i	$0.836139\pi$
$824$	−114.322	+	2399.92i	−0.00483326	+	0.101463i
$825$	−49534.0	+	19830.4i	−2.09037	+	0.836857i
$826$	−7075.35	+	4547.05i	−0.298042	+	0.191540i
$827$	20598.0	−	10619.0i	0.866098	−	0.446504i	0.0328863	−	0.999459i	$-0.489530\pi$
$827$	20598.0	−	10619.0i	0.866098	−	0.446504i	0.833211	+	0.552955i	$0.186500\pi$
$828$	5672.16	+	6546.02i	0.238069	+	0.274746i
$829$	−40404.8	+	11863.9i	−1.69278	+	0.497046i	−0.979092	−	0.203416i	$-0.934796\pi$
$829$	−40404.8	+	11863.9i	−1.69278	+	0.497046i	−0.713690	+	0.700462i	$0.752977\pi$
$830$	2482.74	−	7173.42i	0.103828	−	0.299992i
$831$	−3220.88	+	22401.7i	−0.134454	+	0.935146i
$832$	839.225	−	800.200i	0.0349698	−	0.0333437i
$833$	−936.520	−	1622.10i	−0.0389538	−	0.0674699i
$834$	−1400.67	+	2426.04i	−0.0581551	+	0.100728i
$835$	17116.2	+	70553.9i	0.709377	+	2.92409i
$836$	−18707.0	−	9644.12i	−0.773917	−	0.398982i
$837$	−1897.19	+	181.159i	−0.0783469	+	0.00748122i
$838$	−2991.95	+	285.697i	−0.123336	+	0.0117771i
$839$	9453.38	+	4873.56i	0.388995	+	0.200541i	0.641619	−	0.767024i	$-0.278263\pi$
$839$	9453.38	+	4873.56i	0.388995	+	0.200541i	−0.252624	+	0.967565i	$0.581293\pi$
$840$	−2650.59	−	10925.9i	−0.108874	−	0.448784i
$841$	11782.7	−	20408.3i	0.483117	−	0.836784i
$842$	−3923.97	−	6796.51i	−0.160604	−	0.278175i
$843$	−3973.54	+	3788.76i	−0.162344	+	0.154795i
$844$	−437.805	+	3045.00i	−0.0178553	+	0.124186i
$845$	15008.0	−	43362.8i	0.610996	−	1.76536i
$846$	899.703	−	264.177i	0.0365632	−	0.0107359i
$847$	−23098.1	−	26656.6i	−0.937024	−	1.08138i
$848$	13715.3	−	7070.73i	0.555408	−	0.286333i
$849$	−16237.9	+	10435.5i	−0.656401	+	0.421843i
$850$	−18652.0	+	7467.13i	−0.752656	+	0.301318i
$851$	−1527.04	+	32056.6i	−0.0615117	+	1.29129i
$852$	−10736.5	−	15077.3i	−0.431722	−	0.606268i
$853$	7693.52	+	22229.0i	0.308817	+	0.892269i	0.987470	+	0.157809i	$0.0504432\pi$
$853$	7693.52	+	22229.0i	0.308817	+	0.892269i	−0.678652	+	0.734460i	$0.737436\pi$
$854$	8162.23	−	1573.14i	0.327056	−	0.0630348i
$855$	−8552.64	−	3423.96i	−0.342098	−	0.136955i
$856$	−3189.45	+	6983.91i	−0.127352	+	0.278861i
$857$	5301.84	−	6118.65i	0.211327	−	0.243885i	−0.640183	−	0.768222i	$-0.721142\pi$
$857$	5301.84	−	6118.65i	0.211327	−	0.243885i	0.851510	+	0.524338i	$0.175687\pi$
$858$	−73.6586	+	303.625i	−0.00293084	+	0.0120811i
$859$	3115.96	+	2971.06i	0.123766	+	0.118011i	0.749435	−	0.662078i	$-0.230325\pi$
$859$	3115.96	+	2971.06i	0.123766	+	0.118011i	−0.625669	+	0.780089i	$0.715174\pi$
$860$	1452.53	−	1142.29i	0.0575942	−	0.0452926i
$861$	−1395.06	−	29285.9i	−0.0552189	−	1.15919i
$862$	989.857	+	2167.48i	0.0391121	+	0.0856436i
$863$	10662.8	+	3130.88i	0.420587	+	0.123495i	0.485176	−	0.874416i	$-0.338756\pi$
$863$	10662.8	+	3130.88i	0.420587	+	0.123495i	−0.0645892	+	0.997912i	$0.520574\pi$
$864$	1701.11	−	2388.87i	0.0669824	−	0.0940637i
$865$	−54981.4	−	43237.9i	−2.16118	−	1.69957i
$866$	855.175	+	5947.87i	0.0335566	+	0.233391i
$867$	−18643.6	−	3593.25i	−0.730298	−	0.140753i
$868$	8613.53	+	5535.58i	0.336823	+	0.216463i
$869$	19498.7	+	1861.90i	0.761159	+	0.0726819i
$870$	−1086.35			−0.0423343
$871$	934.779	+	1397.59i	0.0363648	+	0.0543693i
$872$	12229.1			0.474921
$873$	8923.68	+	852.108i	0.345957	+	0.0330349i
$874$	3111.85	+	1999.87i	0.120435	+	0.0773987i
$875$	74312.3	+	14322.5i	2.87110	+	0.553360i
$876$	−404.261	−	2811.70i	−0.0155921	−	0.108446i
$877$	17335.6	+	13632.9i	0.667483	+	0.524914i	0.893417	−	0.449228i	$-0.148301\pi$
$877$	17335.6	+	13632.9i	0.667483	+	0.524914i	−0.225934	+	0.974143i	$0.572543\pi$
$878$	943.852	−	1325.46i	0.0362796	−	0.0509476i
$879$	−5947.37	−	1746.31i	−0.228214	−	0.0670096i
$880$	27279.7	+	59734.3i	1.04500	+	2.28823i
$881$	1575.16	+	33066.7i	0.0602367	+	1.26452i	0.803411	+	0.595425i	$0.203016\pi$
$881$	1575.16	+	33066.7i	0.0602367	+	1.26452i	−0.743174	+	0.669098i	$0.766680\pi$
$882$	75.1833	−	59.1248i	0.00287024	−	0.00225718i
$883$	−7234.47	−	6898.05i	−0.275718	−	0.262897i	0.539585	−	0.841931i	$-0.318581\pi$
$883$	−7234.47	−	6898.05i	−0.275718	−	0.262897i	−0.815303	+	0.579034i	$0.803430\pi$
$884$	585.369	−	2412.92i	0.0222716	−	0.0918047i
$885$	30335.9	−	35009.4i	1.15224	−	1.32975i
$886$	−3363.64	+	7365.35i	−0.127544	+	0.279282i
$887$	5348.13	+	2141.07i	0.202449	+	0.0810485i	0.470671	−	0.882309i	$-0.344012\pi$
$887$	5348.13	+	2141.07i	0.202449	+	0.0810485i	−0.268222	+	0.963357i	$0.586436\pi$
$888$	7058.67	−	1360.45i	0.266749	−	0.0514117i
$889$	7596.86	+	21949.7i	0.286604	+	0.828087i
$890$	8968.51	+	12594.5i	0.337781	+	0.474347i
$891$	217.623	−	4568.46i	0.00818253	−	0.171773i
$892$	134.193	−	53.7229i	0.00503714	−	0.00201657i
$893$	−7109.88	+	4569.24i	−0.266431	+	0.171225i
$894$	−108.181	+	55.7711i	−0.00404710	+	0.00208643i
$895$	15300.0	+	17657.2i	0.571423	+	0.659457i
$896$	−19979.7	+	5866.58i	−0.744951	+	0.218737i
$897$	−379.043	+	1095.17i	−0.0141091	+	0.0407656i
$898$	686.755	−	4776.49i	0.0255204	−	0.177498i
$899$	1465.98	−	1397.81i	0.0543863	−	0.0518572i
$900$	10826.4	+	18751.8i	0.400976	+	0.694511i
$901$	14754.0	−	25554.7i	0.545536	−	0.944896i
$902$	−4121.19	−	16987.8i	−0.152129	−	0.627086i
$903$	584.073	+	301.111i	0.0215246	+	0.0110967i
$904$	−2647.67	+	252.822i	−0.0974117	+	0.00930169i
$905$	24556.5	−	2344.87i	0.901975	−	0.0861281i
$906$	−585.336	−	301.761i	−0.0214641	−	0.0110655i
$907$	9415.74	+	38812.2i	0.344702	+	1.42088i	0.835444	+	0.549575i	$0.185210\pi$
$907$	9415.74	+	38812.2i	0.344702	+	1.42088i	−0.490743	+	0.871305i	$0.663274\pi$
$908$	−716.451	+	1240.93i	−0.0261853	+	0.0453543i
$909$	−4858.13	−	8414.53i	−0.177265	−	0.307032i
$910$	531.747	−	507.020i	0.0193706	−	0.0184698i
$911$	4117.25	−	28636.1i	0.149737	−	1.04144i	−0.766912	−	0.641752i	$-0.778208\pi$
$911$	4117.25	−	28636.1i	0.149737	−	1.04144i	0.916649	−	0.399692i	$-0.130883\pi$
$912$	−2654.87	+	7670.74i	−0.0963942	+	0.278513i
$913$	−32590.9	+	9569.54i	−1.18138	+	0.346885i
$914$	73.3909	+	84.6976i	0.00265597	+	0.00306515i
$915$	−40694.5	+	20979.5i	−1.47030	+	0.757990i
$916$	16221.4	−	10424.9i	0.585121	−	0.376034i
$917$	−26664.8	+	10675.0i	−0.960251	+	0.384426i
$918$	81.9456	−	1720.25i	0.00294619	−	0.0618482i
$919$	22914.0	+	32178.2i	0.822483	+	1.15502i	0.985714	+	0.168428i	$0.0538690\pi$
$919$	22914.0	+	32178.2i	0.822483	+	1.15502i	−0.163231	+	0.986588i	$0.552192\pi$
$920$	−8132.25	−	23496.6i	−0.291427	−	0.842022i
$921$	−667.579	+	128.665i	−0.0238843	+	0.00460333i
$922$	−2251.68	−	901.439i	−0.0804287	−	0.0321988i
$923$	1028.79	−	2252.73i	0.0366879	−	0.0803353i
$924$	−16091.1	+	18570.1i	−0.572897	+	0.661159i
$925$	−18914.3	+	77966.0i	−0.672324	+	2.77136i
$926$	390.546	+	372.384i	0.0138597	+	0.0132152i
$927$	1806.76	−	1420.85i	0.0640147	−	0.0503417i
$928$	148.310	+	3113.42i	0.00524626	+	0.110132i
$929$	−12892.6	−	28230.8i	−0.455319	−	0.997009i	−0.988530	−	0.151027i	$-0.951742\pi$
$929$	−12892.6	−	28230.8i	−0.455319	−	0.997009i	0.533211	−	0.845982i	$-0.320985\pi$
$930$	2563.88	+	752.823i	0.0904010	+	0.0265441i
$931$	−500.055	+	702.229i	−0.0176033	+	0.0247203i
$932$	33766.2	+	26554.1i	1.18675	+	0.933270i
$933$	−2039.98	−	14188.4i	−0.0715819	−	0.497863i
$934$	3029.59	+	583.905i	0.106136	+	0.0204560i
$935$	105643.	+	67892.7i	3.69508	+	2.37468i
$936$	258.412	+	24.6753i	0.00902398	+	0.000861686i
$937$	−21005.8			−0.732368			−0.366184	−	0.930542i	$-0.619336\pi$
$937$	−21005.8			−0.732368			−0.366184	+	0.930542i	$0.619336\pi$
$938$	−709.702	−	6225.30i	−0.0247043	−	0.216699i
$939$	−17664.1			−0.613893
$940$	27621.4	+	2637.53i	0.958416	+	0.0915177i
$941$	−46427.4	−	29837.1i	−1.60838	−	1.03365i	−0.962895	−	0.269877i	$-0.913017\pi$
$941$	−46427.4	−	29837.1i	−1.60838	−	1.03365i	−0.645490	−	0.763769i	$-0.723347\pi$
$942$	1184.93	+	228.377i	0.0409842	+	0.00789906i
$943$	−9227.83	−	64181.0i	−0.318663	−	2.21635i
$944$	−32083.7	−	25230.9i	−1.10618	−	0.869911i
$945$	−6238.84	+	8761.23i	−0.214761	+	0.301590i
$946$	375.917	+	110.379i	0.0129198	+	0.00379359i
$947$	−21531.8	−	47148.1i	−0.738849	−	1.61785i	−0.785439	−	0.618939i	$-0.787563\pi$
$947$	−21531.8	−	47148.1i	−0.738849	−	1.61785i	0.0465902	−	0.998914i	$-0.485165\pi$
$948$	−378.222	−	7939.86i	−0.0129579	−	0.272020i
$949$	298.754	−	234.943i	0.0102192	−	0.00803643i
$950$	6692.44	+	6381.22i	0.228559	+	0.217931i
$951$	2728.38	−	11246.5i	0.0930325	−	0.383485i
$952$	−12405.2	+	14316.4i	−0.422327	+	0.487392i
$953$	22627.3	−	49546.8i	0.769118	−	1.68413i	0.0405337	−	0.999178i	$-0.487094\pi$
$953$	22627.3	−	49546.8i	0.769118	−	1.68413i	0.728585	−	0.684956i	$-0.240179\pi$
$954$	1398.89	+	560.031i	0.0474745	+	0.0190059i
$955$	71184.8	−	13719.7i	2.41203	−	0.464880i
$956$	11543.1	+	33351.7i	0.390515	+	1.12832i
$957$	2819.69	+	3959.70i	0.0952431	+	0.133750i
$958$	−68.9024	+	1446.44i	−0.00232373	+	0.0487812i
$959$	−48919.7	+	19584.5i	−1.64724	+	0.659454i
$960$	20022.0	−	12867.4i	0.673134	−	0.432597i
$961$	22050.8	−	11368.0i	0.740183	−	0.381591i
$962$	307.641	+	355.036i	0.0103105	+	0.0118990i
$963$	7047.48	−	2069.33i	0.235827	−	0.0692452i
$964$	−793.200	+	2291.80i	−0.0265013	+	0.0765705i
$965$	5274.10	−	36682.2i	0.175937	−	1.22367i
$966$	3125.54	−	2980.19i	0.104102	−	0.0992610i
$967$	−25504.5	−	44175.2i	−0.848160	−	1.46906i	−0.882848	−	0.469658i	$-0.844377\pi$
$967$	−25504.5	−	44175.2i	−0.848160	−	1.46906i	0.0346883	−	0.999398i	$-0.488956\pi$
$968$	−8736.31	+	15131.7i	−0.290078	+	0.502430i
$969$	3659.56	+	15084.9i	0.121323	+	0.500101i
$970$	−11171.5	−	5759.30i	−0.369788	−	0.190639i
$971$	43080.9	−	4113.72i	1.42382	−	0.135958i	0.645469	−	0.763786i	$-0.276662\pi$
$971$	43080.9	−	4113.72i	1.42382	−	0.135958i	0.778352	+	0.627828i	$0.216056\pi$
$972$	−1847.65	+	176.429i	−0.0609706	+	0.00582199i
$973$	−26201.1	−	13507.6i	−0.863277	−	0.445050i
$974$	591.804	+	2439.45i	0.0194688	+	0.0802516i
$975$	−1448.55	+	2508.96i	−0.0475802	+	0.0824113i
$976$	20170.2	+	34935.8i	0.661508	+	1.14577i
$977$	−11509.3	+	10974.1i	−0.376884	+	0.359358i	−0.854718	−	0.519092i	$-0.826270\pi$
$977$	−11509.3	+	10974.1i	−0.376884	+	0.359358i	0.477835	+	0.878450i	$0.341422\pi$
$978$	−197.761	+	1375.46i	−0.00646595	+	0.0449717i
$979$	22628.1	−	65379.6i	0.738710	−	2.13436i
$980$	2715.63	−	797.382i	0.0885181	−	0.0259912i
$981$	−7661.32	−	8841.64i	−0.249345	−	0.287759i
$982$	−356.143	+	183.604i	−0.0115733	+	0.00596645i
$983$	31249.5	−	20082.9i	1.01394	−	0.651621i	0.0755318	−	0.997143i	$-0.475935\pi$
$983$	31249.5	−	20082.9i	1.01394	−	0.651621i	0.938411	+	0.345522i	$0.112298\pi$
$984$	−13483.5	+	5397.98i	−0.436827	+	0.174879i
$985$	4621.80	−	97023.5i	0.149505	−	3.13850i
$986$	1061.75	+	1491.02i	0.0342931	+	0.0481580i
$987$	3227.21	+	9324.40i	0.104076	+	0.300708i
$988$	−1122.13	+	216.272i	−0.0361332	+	0.00696410i
$989$	1349.16	+	540.123i	0.0433781	+	0.0173660i
$990$	−2663.91	+	5833.15i	−0.0855198	+	0.187262i
$991$	20764.3	−	23963.2i	0.665589	−	0.768131i	−0.318091	−	0.948060i	$-0.603042\pi$
$991$	20764.3	−	23963.2i	0.665589	−	0.768131i	0.983679	+	0.179930i	$0.0575871\pi$
$992$	1807.52	−	7450.69i	0.0578516	−	0.238467i
$993$	−442.330	−	421.761i	−0.0141359	−	0.0134785i
$994$	−7254.22	+	5704.78i	−0.231479	+	0.182037i
$995$	1961.94	+	41186.2i	0.0625102	+	1.31225i
$996$	5726.18	+	12538.6i	0.182170	+	0.398896i
$997$	−16567.8	−	4864.76i	−0.526288	−	0.154532i	0.00778637	−	0.999970i	$-0.497521\pi$
$997$	−16567.8	−	4864.76i	−0.526288	−	0.154532i	−0.534074	+	0.845438i	$0.679340\pi$
$998$	6840.66	−	9606.36i	0.216971	−	0.304694i
$999$	−5405.72	−	4251.11i	−0.171201	−	0.134634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.m.b.4.10	✓	360
67.17	even	33	inner	201.4.m.b.151.10	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.m.b.4.10	✓	360	1.1	even	1	trivial
201.4.m.b.151.10	yes	360	67.17	even	33	inner

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.598865 + 0.0571847i) q^{2} +(-2.52376 - 1.62192i) q^{3} +(-7.50006 - 1.44552i) q^{4} +(-2.98516 - 20.7622i) q^{5} +(-1.41864 - 1.11563i) q^{6} +(11.0160 - 15.4698i) q^{7} +(-9.02663 - 2.65046i) q^{8} +(3.73874 + 8.18669i) q^{9} +O(q^{10})\)	\(q+(0.598865 + 0.0571847i) q^{2} +(-2.52376 - 1.62192i) q^{3} +(-7.50006 - 1.44552i) q^{4} +(-2.98516 - 20.7622i) q^{5} +(-1.41864 - 1.11563i) q^{6} +(11.0160 - 15.4698i) q^{7} +(-9.02663 - 2.65046i) q^{8} +(3.73874 + 8.18669i) q^{9} +(-0.600425 - 12.6045i) q^{10} +(-44.3843 + 34.9042i) q^{11} +(16.5838 + 15.8127i) q^{12} +(-0.722811 + 2.97947i) q^{13} +(7.48172 - 8.63436i) q^{14} +(-26.1409 + 57.2406i) q^{15} +(51.4735 + 20.6069i) q^{16} +(104.112 - 20.0659i) q^{17} +(1.77084 + 5.11652i) q^{18} +(-28.3068 - 39.7513i) q^{19} +(-7.62332 + 160.033i) q^{20} +(-52.8925 + 21.1749i) q^{21} +(-28.5762 + 18.3648i) q^{22} +(-111.994 + 57.7367i) q^{23} +(18.4822 + 21.3296i) q^{24} +(-302.223 + 88.7405i) q^{25} +(-0.603247 + 1.74297i) q^{26} +(3.84250 - 26.7252i) q^{27} +(-104.982 + 100.100i) q^{28} +(14.3484 + 24.8521i) q^{29} +(-18.9282 + 32.7845i) q^{30} +(-16.6412 - 68.5961i) q^{31} +(96.5425 + 49.7711i) q^{32} +(168.627 - 16.1019i) q^{33} +(63.4963 - 6.06317i) q^{34} +(-354.071 - 182.537i) q^{35} +(-16.2067 - 66.8051i) q^{36} +(127.353 - 220.581i) q^{37} +(-14.6788 - 25.4244i) q^{38} +(6.65667 - 6.34712i) q^{39} +(-28.0835 + 195.325i) q^{40} +(-168.312 + 486.306i) q^{41} +(-32.8863 + 9.65630i) q^{42} +(-7.55303 - 8.71666i) q^{43} +(383.339 - 197.625i) q^{44} +(158.813 - 102.063i) q^{45} +(-70.3707 + 28.1722i) q^{46} +(8.24056 - 172.991i) q^{47} +(-96.4840 - 135.493i) q^{48} +(-5.77784 - 16.6940i) q^{49} +(-186.065 + 35.8611i) q^{50} +(-295.298 - 118.220i) q^{51} +(9.72801 - 21.3014i) q^{52} +(182.251 - 210.329i) q^{53} +(3.82941 - 15.7850i) q^{54} +(857.183 + 817.322i) q^{55} +(-140.439 + 110.443i) q^{56} +(6.96600 + 146.234i) q^{57} +(7.17157 + 15.7036i) q^{58} +(-706.335 - 207.399i) q^{59} +(278.801 - 391.521i) q^{60} +(571.911 + 449.756i) q^{61} +(-6.04321 - 42.0314i) q^{62} +(167.832 + 32.3470i) q^{63} +(-318.178 - 204.480i) q^{64} +(64.0181 + 6.11299i) q^{65} +101.906 q^{66} +(371.121 - 403.773i) q^{67} -809.850 q^{68} +(376.290 + 35.9313i) q^{69} +(-201.603 - 129.562i) q^{70} +(-793.170 - 152.871i) q^{71} +(-12.0497 - 83.8075i) q^{72} +(-97.4445 - 76.6312i) q^{73} +(88.8809 - 124.816i) q^{74} +(906.668 + 266.222i) q^{75} +(154.841 + 339.055i) q^{76} +(51.0237 + 1071.12i) q^{77} +(4.34941 - 3.42041i) q^{78} +(-251.060 - 239.385i) q^{79} +(274.188 - 1130.22i) q^{80} +(-53.0437 + 61.2157i) q^{81} +(-128.605 + 281.607i) q^{82} +(558.466 + 223.576i) q^{83} +(427.305 - 82.3564i) q^{84} +(-727.403 - 2101.69i) q^{85} +(-4.02479 - 5.65202i) q^{86} +(4.09634 - 85.9927i) q^{87} +(493.152 - 197.428i) q^{88} +(-1030.76 + 662.432i) q^{89} +(100.944 - 52.0403i) q^{90} +(38.1292 + 44.0035i) q^{91} +(923.419 - 271.140i) q^{92} +(-69.2591 + 200.111i) q^{93} +(14.8274 - 103.127i) q^{94} +(-740.826 + 706.376i) q^{95} +(-162.925 - 282.195i) q^{96} +(498.015 - 862.587i) q^{97} +(-2.50551 - 10.3278i) q^{98} +(-451.691 - 232.863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 2 q^{2} + 108 q^{3} + 90 q^{4} + 4 q^{5} - 27 q^{6} - 22 q^{7} + 183 q^{8} - 324 q^{9}+O(q^{10}) \) 360 * q - 2 * q^2 + 108 * q^3 + 90 * q^4 + 4 * q^5 - 27 * q^6 - 22 * q^7 + 183 * q^8 - 324 * q^9	\( 360 q - 2 q^{2} + 108 q^{3} + 90 q^{4} + 4 q^{5} - 27 q^{6} - 22 q^{7} + 183 q^{8} - 324 q^{9} + 19 q^{10} + 192 q^{11} - 105 q^{12} + 46 q^{13} - 14 q^{14} + 54 q^{15} + 346 q^{16} + 228 q^{17} - 18 q^{18} + 88 q^{19} + 180 q^{20} + 66 q^{21} - 247 q^{22} + 676 q^{23} + 144 q^{24} - 1120 q^{25} + 333 q^{26} + 972 q^{27} - 3894 q^{28} - 2210 q^{29} + 702 q^{30} + 96 q^{31} - 1970 q^{32} - 708 q^{33} - 26 q^{34} + 1272 q^{35} + 315 q^{36} - 3616 q^{37} - 20 q^{38} - 138 q^{39} - 5357 q^{40} + 288 q^{41} - 618 q^{42} - 1680 q^{43} + 2951 q^{44} + 36 q^{45} - 1125 q^{46} - 40 q^{47} - 1038 q^{48} - 4954 q^{49} - 3590 q^{50} - 90 q^{51} + 9120 q^{52} + 3896 q^{53} + 54 q^{54} - 1076 q^{55} + 3557 q^{56} + 660 q^{57} + 3232 q^{58} + 116 q^{59} + 3618 q^{60} - 672 q^{61} + 3882 q^{62} - 1584 q^{63} - 11581 q^{64} - 15380 q^{65} - 5166 q^{66} - 288 q^{67} + 13898 q^{68} - 1632 q^{69} - 5058 q^{70} - 15102 q^{71} - 2016 q^{72} - 146 q^{73} - 3531 q^{74} + 3360 q^{75} + 10770 q^{76} + 3594 q^{77} + 1905 q^{78} + 2852 q^{79} + 27997 q^{80} - 2916 q^{81} + 8824 q^{82} + 5278 q^{83} + 6765 q^{84} - 5290 q^{85} + 5973 q^{86} + 228 q^{87} + 13872 q^{88} + 1462 q^{89} + 171 q^{90} + 74 q^{91} - 3144 q^{92} + 3144 q^{93} + 3262 q^{94} + 1600 q^{95} - 855 q^{96} + 6626 q^{97} + 15491 q^{98} + 144 q^{99}+O(q^{100}) \) 360 * q - 2 * q^2 + 108 * q^3 + 90 * q^4 + 4 * q^5 - 27 * q^6 - 22 * q^7 + 183 * q^8 - 324 * q^9 + 19 * q^10 + 192 * q^11 - 105 * q^12 + 46 * q^13 - 14 * q^14 + 54 * q^15 + 346 * q^16 + 228 * q^17 - 18 * q^18 + 88 * q^19 + 180 * q^20 + 66 * q^21 - 247 * q^22 + 676 * q^23 + 144 * q^24 - 1120 * q^25 + 333 * q^26 + 972 * q^27 - 3894 * q^28 - 2210 * q^29 + 702 * q^30 + 96 * q^31 - 1970 * q^32 - 708 * q^33 - 26 * q^34 + 1272 * q^35 + 315 * q^36 - 3616 * q^37 - 20 * q^38 - 138 * q^39 - 5357 * q^40 + 288 * q^41 - 618 * q^42 - 1680 * q^43 + 2951 * q^44 + 36 * q^45 - 1125 * q^46 - 40 * q^47 - 1038 * q^48 - 4954 * q^49 - 3590 * q^50 - 90 * q^51 + 9120 * q^52 + 3896 * q^53 + 54 * q^54 - 1076 * q^55 + 3557 * q^56 + 660 * q^57 + 3232 * q^58 + 116 * q^59 + 3618 * q^60 - 672 * q^61 + 3882 * q^62 - 1584 * q^63 - 11581 * q^64 - 15380 * q^65 - 5166 * q^66 - 288 * q^67 + 13898 * q^68 - 1632 * q^69 - 5058 * q^70 - 15102 * q^71 - 2016 * q^72 - 146 * q^73 - 3531 * q^74 + 3360 * q^75 + 10770 * q^76 + 3594 * q^77 + 1905 * q^78 + 2852 * q^79 + 27997 * q^80 - 2916 * q^81 + 8824 * q^82 + 5278 * q^83 + 6765 * q^84 - 5290 * q^85 + 5973 * q^86 + 228 * q^87 + 13872 * q^88 + 1462 * q^89 + 171 * q^90 + 74 * q^91 - 3144 * q^92 + 3144 * q^93 + 3262 * q^94 + 1600 * q^95 - 855 * q^96 + 6626 * q^97 + 15491 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more