LMFDB - Embedded newform 128.4.k.a.5.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(5,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("128.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.k (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$752$
Relative dimension:	$47$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			5.13
Character	$\chi$	$=$	128.5
Dual form			128.4.k.a.77.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.88791 + 2.10613i) q^{2} +(-3.74897 - 1.13724i) q^{3} +(-0.871580 - 7.95238i) q^{4} +(4.16267 + 0.409988i) q^{5} +(9.47289 - 5.74882i) q^{6} +(10.4814 + 15.6865i) q^{7} +(18.3942 + 13.1777i) q^{8} +(-9.68822 - 6.47346i) q^{9} +O(q^{10})$	\(q+(-1.88791 + 2.10613i) q^{2} +(-3.74897 - 1.13724i) q^{3} +(-0.871580 - 7.95238i) q^{4} +(4.16267 + 0.409988i) q^{5} +(9.47289 - 5.74882i) q^{6} +(10.4814 + 15.6865i) q^{7} +(18.3942 + 13.1777i) q^{8} +(-9.68822 - 6.47346i) q^{9} +(-8.72225 + 7.99312i) q^{10} +(-7.59489 + 14.2090i) q^{11} +(-5.77622 + 30.8044i) q^{12} +(-2.44661 - 24.8409i) q^{13} +(-52.8257 - 7.53955i) q^{14} +(-15.1395 - 6.27098i) q^{15} +(-62.4807 + 13.8623i) q^{16} +(-104.589 + 43.3223i) q^{17} +(31.9245 - 8.18334i) q^{18} +(0.782054 - 0.952936i) q^{19} +(-0.367726 - 33.4605i) q^{20} +(-21.4551 - 70.7280i) q^{21} +(-15.5876 - 42.8213i) q^{22} +(-34.1537 - 171.702i) q^{23} +(-53.9732 - 70.3215i) q^{24} +(-105.438 - 20.9730i) q^{25} +(56.9371 + 41.7445i) q^{26} +(96.0631 + 117.053i) q^{27} +(115.610 - 97.0239i) q^{28} +(-200.470 + 107.154i) q^{29} +(41.7895 - 20.0467i) q^{30} +(18.0309 + 18.0309i) q^{31} +(88.7623 - 157.763i) q^{32} +(44.6321 - 44.6321i) q^{33} +(106.213 - 302.068i) q^{34} +(37.1993 + 69.5950i) q^{35} +(-43.0354 + 82.6866i) q^{36} +(-52.1555 + 42.8030i) q^{37} +(0.530559 + 3.44617i) q^{38} +(-19.0777 + 95.9100i) q^{39} +(71.1665 + 62.3960i) q^{40} +(-432.962 + 86.1215i) q^{41} +(189.468 + 88.3409i) q^{42} +(-262.977 + 79.7732i) q^{43} +(119.615 + 48.0132i) q^{44} +(-37.6749 - 30.9190i) q^{45} +(426.107 + 252.227i) q^{46} +(75.9743 + 183.418i) q^{47} +(250.003 + 19.0862i) q^{48} +(-4.94626 + 11.9413i) q^{49} +(243.230 - 182.472i) q^{50} +(441.370 - 43.4711i) q^{51} +(-195.412 + 41.1072i) q^{52} +(272.411 + 145.607i) q^{53} +(-427.888 - 18.6646i) q^{54} +(-37.4406 + 56.0338i) q^{55} +(-13.9155 + 426.662i) q^{56} +(-4.01561 + 2.68315i) q^{57} +(152.791 - 624.513i) q^{58} +(-47.7917 + 485.237i) q^{59} +(-36.6739 + 125.861i) q^{60} +(58.6666 - 193.398i) q^{61} +(-72.0161 + 3.93470i) q^{62} -219.825i q^{63} +(164.695 + 484.788i) q^{64} -104.407i q^{65} +(9.73961 + 178.262i) q^{66} +(134.527 - 443.475i) q^{67} +(435.674 + 793.975i) q^{68} +(-67.2251 + 682.547i) q^{69} +(-216.805 - 53.0426i) q^{70} +(-331.383 + 221.423i) q^{71} +(-92.9018 - 246.743i) q^{72} +(610.888 - 914.258i) q^{73} +(8.31641 - 190.655i) q^{74} +(371.434 + 198.536i) q^{75} +(-8.25973 - 5.38863i) q^{76} +(-302.495 + 29.7932i) q^{77} +(-165.982 - 221.250i) q^{78} +(102.639 - 247.793i) q^{79} +(-265.770 + 32.0878i) q^{80} +(-106.627 - 257.421i) q^{81} +(636.011 - 1074.46i) q^{82} +(681.532 + 559.319i) q^{83} +(-543.756 + 232.264i) q^{84} +(-453.133 + 137.456i) q^{85} +(328.465 - 704.469i) q^{86} +(873.415 - 173.733i) q^{87} +(-326.945 + 161.281i) q^{88} +(29.5576 - 148.596i) q^{89} +(136.246 - 20.9760i) q^{90} +(364.022 - 298.745i) q^{91} +(-1335.67 + 421.256i) q^{92} +(-47.0918 - 88.1025i) q^{93} +(-529.736 - 186.266i) q^{94} +(3.64613 - 3.64613i) q^{95} +(-512.181 + 490.506i) q^{96} +(-884.383 - 884.383i) q^{97} +(-15.8119 - 32.9616i) q^{98} +(165.563 - 88.4951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 5696 q^{50} - 16 q^{51} + 6608 q^{52} - 16 q^{53} + 3440 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 4768 q^{58} - 16 q^{59} - 9808 q^{60} - 16 q^{61} - 5872 q^{62} - 12112 q^{64} - 10960 q^{66} - 16 q^{67} - 4144 q^{68} - 16 q^{69} - 4048 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 5248 q^{74} - 16 q^{75} + 11888 q^{76} - 16 q^{77} + 14096 q^{78} - 16 q^{79} + 10016 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 5696 * q^50 - 16 * q^51 + 6608 * q^52 - 16 * q^53 + 3440 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 4768 * q^58 - 16 * q^59 - 9808 * q^60 - 16 * q^61 - 5872 * q^62 - 12112 * q^64 - 10960 * q^66 - 16 * q^67 - 4144 * q^68 - 16 * q^69 - 4048 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 5248 * q^74 - 16 * q^75 + 11888 * q^76 - 16 * q^77 + 14096 * q^78 - 16 * q^79 + 10016 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{1}{32}\right)$	$1$

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 $

$2$	−1.88791	+	2.10613i	−0.667478	+	0.744630i
$2$	−1.88791	+	2.10613i	−0.667478	+	0.744630i
$3$	−3.74897	−	1.13724i	−0.721489	−	0.218861i	−0.0918765	−	0.995770i	$-0.529286\pi$
$3$	−3.74897	−	1.13724i	−0.721489	−	0.218861i	−0.629613	+	0.776909i	$0.716786\pi$
$4$	−0.871580	−	7.95238i	−0.108948	−	0.994048i
$5$	4.16267	+	0.409988i	0.372321	+	0.0366704i	0.282447	−	0.959283i	$-0.408854\pi$
$5$	4.16267	+	0.409988i	0.372321	+	0.0366704i	0.0898735	+	0.995953i	$0.471354\pi$
$6$	9.47289	−	5.74882i	0.644549	−	0.391158i
$7$	10.4814	+	15.6865i	0.565941	+	0.846991i	0.998508	−	0.0546112i	$-0.0173919\pi$
$7$	10.4814	+	15.6865i	0.565941	+	0.846991i	−0.432567	+	0.901602i	$0.642392\pi$
$8$	18.3942	+	13.1777i	0.812918	+	0.582379i
$9$	−9.68822	−	6.47346i	−0.358823	−	0.239758i
$10$	−8.72225	+	7.99312i	−0.275822	+	0.252765i
$11$	−7.59489	+	14.2090i	−0.208177	+	0.389472i	−0.964241	−	0.265025i	$-0.914620\pi$
$11$	−7.59489	+	14.2090i	−0.208177	+	0.389472i	0.756064	+	0.654497i	$0.227120\pi$
$12$	−5.77622	+	30.8044i	−0.138954	+	0.741039i
$13$	−2.44661	−	24.8409i	−0.0521975	−	0.529970i	−0.985357	−	0.170507i	$-0.945460\pi$
$13$	−2.44661	−	24.8409i	−0.0521975	−	0.529970i	0.933159	−	0.359464i	$-0.117040\pi$
$14$	−52.8257	−	7.53955i	−1.00845	−	0.143931i
$15$	−15.1395	−	6.27098i	−0.260600	−	0.107944i
$16$	−62.4807	+	13.8623i	−0.976261	+	0.216598i
$17$	−104.589	+	43.3223i	−1.49216	+	0.618071i	−0.971785	−	0.235870i	$-0.924206\pi$
$17$	−104.589	+	43.3223i	−1.49216	+	0.618071i	−0.520371	+	0.853941i	$0.674206\pi$
$18$	31.9245	−	8.18334i	0.418037	−	0.107157i
$19$	0.782054	−	0.952936i	0.00944292	−	0.0115062i	−0.768268	−	0.640129i	$-0.778881\pi$
$19$	0.782054	−	0.952936i	0.00944292	−	0.0115062i	0.777711	+	0.628623i	$0.216381\pi$
$20$	−0.367726	−	33.4605i	−0.00411130	−	0.374100i
$21$	−21.4551	−	70.7280i	−0.222947	−	0.734958i
$22$	−15.5876	−	42.8213i	−0.151059	−	0.414978i
$23$	−34.1537	−	171.702i	−0.309632	−	1.55663i	−0.751615	−	0.659603i	$-0.770725\pi$
$23$	−34.1537	−	171.702i	−0.309632	−	1.55663i	0.441982	−	0.897024i	$-0.354275\pi$
$24$	−53.9732	−	70.3215i	−0.459051	−	0.598096i
$25$	−105.438	−	20.9730i	−0.843507	−	0.167784i
$26$	56.9371	+	41.7445i	0.429472	+	0.314875i
$27$	96.0631	+	117.053i	0.684717	+	0.834330i
$28$	115.610	−	97.0239i	0.780291	−	0.654850i
$29$	−200.470	+	107.154i	−1.28367	+	0.686135i	−0.965129	−	0.261775i	$-0.915692\pi$
$29$	−200.470	+	107.154i	−1.28367	+	0.686135i	−0.318539	+	0.947910i	$0.603192\pi$
$30$	41.7895	−	20.0467i	0.254323	−	0.122000i
$31$	18.0309	+	18.0309i	0.104466	+	0.104466i	0.757408	−	0.652942i	$-0.226465\pi$
$31$	18.0309	+	18.0309i	0.104466	+	0.104466i	−0.652942	+	0.757408i	$0.726465\pi$
$32$	88.7623	−	157.763i	0.490347	−	0.871527i
$33$	44.6321	−	44.6321i	0.235438	−	0.235438i
$34$	106.213	−	302.068i	0.535746	−	1.52365i
$35$	37.1993	+	69.5950i	0.179652	+	0.336106i
$36$	−43.0354	+	82.6866i	−0.199238	+	0.382808i
$37$	−52.1555	+	42.8030i	−0.231738	+	0.190183i	−0.743095	−	0.669186i	$-0.766643\pi$
$37$	−52.1555	+	42.8030i	−0.231738	+	0.190183i	0.511357	+	0.859368i	$0.329143\pi$
$38$	0.530559	+	3.44617i	0.00226495	+	0.0147116i
$39$	−19.0777	+	95.9100i	−0.0783301	+	0.393792i
$40$	71.1665	+	62.3960i	0.281310	+	0.246642i
$41$	−432.962	+	86.1215i	−1.64920	+	0.328047i	−0.930226	−	0.366988i	$-0.880389\pi$
$41$	−432.962	+	86.1215i	−1.64920	+	0.328047i	−0.718976	+	0.695034i	$0.755389\pi$
$42$	189.468	+	88.3409i	0.696083	+	0.324555i
$43$	−262.977	+	79.7732i	−0.932642	+	0.282914i	−0.719807	−	0.694174i	$-0.755770\pi$
$43$	−262.977	+	79.7732i	−0.932642	+	0.282914i	−0.212835	+	0.977088i	$0.568270\pi$
$44$	119.615	+	48.0132i	0.409834	+	0.164506i
$45$	−37.6749	−	30.9190i	−0.124805	−	0.102425i
$46$	426.107	+	252.227i	1.36578	+	0.808452i
$47$	75.9743	+	183.418i	0.235787	+	0.569240i	0.996839	−	0.0794508i	$-0.0253167\pi$
$47$	75.9743	+	183.418i	0.235787	+	0.569240i	−0.761052	+	0.648691i	$0.775317\pi$
$48$	250.003	+	19.0862i	0.751767	+	0.0573927i
$49$	−4.94626	+	11.9413i	−0.0144206	+	0.0348143i
$50$	243.230	−	182.472i	0.687959	−	0.516109i
$51$	441.370	−	43.4711i	1.21185	−	0.119356i
$52$	−195.412	+	41.1072i	−0.521129	+	0.109626i
$53$	272.411	+	145.607i	0.706010	+	0.377370i	0.784992	−	0.619506i	$-0.212667\pi$
$53$	272.411	+	145.607i	0.706010	+	0.377370i	−0.0789819	+	0.996876i	$0.525167\pi$
$54$	−427.888	−	18.6646i	−1.07830	−	0.0470358i
$55$	−37.4406	+	56.0338i	−0.0917907	+	0.137375i
$56$	−13.9155	+	426.662i	−0.0332060	+	1.01813i
$57$	−4.01561	+	2.68315i	−0.00933124	+	0.00623494i
$58$	152.791	−	624.513i	0.345903	−	1.41384i
$59$	−47.7917	+	485.237i	−0.105457	+	1.07072i	0.786189	+	0.617986i	$0.212051\pi$
$59$	−47.7917	+	485.237i	−0.105457	+	1.07072i	−0.891646	+	0.452734i	$0.850449\pi$
$60$	−36.6739	+	125.861i	−0.0789098	+	0.270809i
$61$	58.6666	−	193.398i	0.123139	−	0.405936i	−0.873598	−	0.486648i	$-0.838219\pi$
$61$	58.6666	−	193.398i	0.123139	−	0.405936i	0.996737	+	0.0807123i	$0.0257195\pi$
$62$	−72.0161	+	3.93470i	−0.147517	+	0.00805979i
$63$		−	219.825i		−	0.439609i
$64$	164.695	+	484.788i	0.321670	+	0.946852i
$65$		−	104.407i		−	0.199233i
$66$	9.73961	+	178.262i	0.0181646	+	0.332463i
$67$	134.527	−	443.475i	0.245299	−	0.808643i	−0.744679	−	0.667423i	$-0.767397\pi$
$67$	134.527	−	443.475i	0.245299	−	0.808643i	0.989978	−	0.141220i	$-0.0451026\pi$
$68$	435.674	+	793.975i	0.776959	+	1.41594i
$69$	−67.2251	+	682.547i	−0.117289	+	1.19086i
$70$	−216.805	−	53.0426i	−0.370188	−	0.0905686i
$71$	−331.383	+	221.423i	−0.553915	+	0.370114i	−0.800801	−	0.598930i	$-0.795593\pi$
$71$	−331.383	+	221.423i	−0.553915	+	0.370114i	0.246886	+	0.969045i	$0.420593\pi$
$72$	−92.9018	−	246.743i	−0.152064	−	0.403874i
$73$	610.888	−	914.258i	0.979438	−	1.46583i	0.0970673	−	0.995278i	$-0.469054\pi$
$73$	610.888	−	914.258i	0.979438	−	1.46583i	0.882371	−	0.470555i	$-0.155946\pi$
$74$	8.31641	−	190.655i	0.0130644	−	0.299502i
$75$	371.434	+	198.536i	0.571860	+	0.305666i
$76$	−8.25973	−	5.38863i	−0.0124665	−	0.00813314i
$77$	−302.495	+	29.7932i	−0.447695	+	0.0440941i
$78$	−165.982	−	221.250i	−0.240946	−	0.321174i
$79$	102.639	−	247.793i	0.146175	−	0.352898i	−0.833786	−	0.552088i	$-0.813831\pi$
$79$	102.639	−	247.793i	0.146175	−	0.352898i	0.979961	+	0.199190i	$0.0638312\pi$
$80$	−265.770	+	32.0878i	−0.371425	+	0.0448441i
$81$	−106.627	−	257.421i	−0.146265	−	0.353115i
$82$	636.011	−	1074.46i	0.856532	−	1.44701i
$83$	681.532	+	559.319i	0.901299	+	0.739677i	0.966086	−	0.258222i	$-0.0831367\pi$
$83$	681.532	+	559.319i	0.901299	+	0.739677i	−0.0647866	+	0.997899i	$0.520637\pi$
$84$	−543.756	+	232.264i	−0.706293	+	0.301692i
$85$	−453.133	+	137.456i	−0.578226	+	0.175403i
$86$	328.465	−	704.469i	0.411852	−	0.883312i
$87$	873.415	−	173.733i	1.07632	−	0.214094i
$88$	−326.945	+	161.281i	−0.396051	+	0.195371i
$89$	29.5576	−	148.596i	0.0352034	−	0.176979i	−0.959184	−	0.282784i	$-0.908742\pi$
$89$	29.5576	−	148.596i	0.0352034	−	0.176979i	0.994387	+	0.105805i	$0.0337419\pi$
$90$	136.246	−	20.9760i	0.159574	−	0.0245673i
$91$	364.022	−	298.745i	0.419339	−	0.344143i
$92$	−1335.67	+	421.256i	−1.51363	+	0.477380i
$93$	−47.0918	−	88.1025i	−0.0525074	−	0.0982345i
$94$	−529.736	−	186.266i	−0.581256	−	0.204381i
$95$	3.64613	−	3.64613i	0.00393774	−	0.00393774i
$96$	−512.181	+	490.506i	−0.544524	+	0.521480i
$97$	−884.383	−	884.383i	−0.925727	−	0.925727i	0.0716996	−	0.997426i	$-0.477158\pi$
$97$	−884.383	−	884.383i	−0.925727	−	0.925727i	−0.997426	+	0.0716996i	$0.977158\pi$
$98$	−15.8119	−	32.9616i	−0.0162984	−	0.0339758i
$99$	165.563	−	88.4951i	0.168078	−	0.0898393i
$100$	−74.8873	+	856.766i	−0.0748873	+	0.856766i
$101$	3.12165	+	3.80374i	0.00307540	+	0.00374738i	0.774546	−	0.632518i	$-0.217978\pi$
$101$	3.12165	+	3.80374i	0.00307540	+	0.00374738i	−0.771470	+	0.636265i	$0.780478\pi$
$102$	−741.711	+	1011.65i	−0.720004	+	0.982045i
$103$	−526.960	−	104.819i	−0.504106	−	0.100273i	−0.0635152	−	0.997981i	$-0.520231\pi$
$103$	−526.960	−	104.819i	−0.504106	−	0.100273i	−0.440591	+	0.897708i	$0.645231\pi$
$104$	282.343	−	489.169i	0.266211	−	0.461221i
$105$	−60.3130	−	303.214i	−0.0560566	−	0.281816i
$106$	−820.955	+	298.841i	−0.752247	+	0.273830i
$107$	26.7747	+	88.2642i	0.0241907	+	0.0797460i	0.968205	−	0.250160i	$-0.0804831\pi$
$107$	26.7747	+	88.2642i	0.0241907	+	0.0797460i	−0.944014	+	0.329906i	$0.892983\pi$
$108$	847.125	−	865.952i	0.754765	−	0.771539i
$109$	−117.907	+	143.671i	−0.103610	+	0.126249i	−0.822234	−	0.569150i	$-0.807272\pi$
$109$	−117.907	+	143.671i	−0.103610	+	0.126249i	0.718624	+	0.695399i	$0.244772\pi$
$110$	−47.3301	−	184.642i	−0.0410249	−	0.160045i
$111$	244.207	−	101.154i	0.208820	−	0.0864963i
$112$	−872.334	−	834.807i	−0.735963	−	0.704302i
$113$	−107.701	−	44.6114i	−0.0896611	−	0.0371388i	0.337402	−	0.941361i	$-0.390452\pi$
$113$	−107.701	−	44.6114i	−0.0896611	−	0.0371388i	−0.427063	+	0.904222i	$0.640452\pi$
$114$	1.93006	−	13.5229i	0.00158567	−	0.0111100i
$115$	−71.7750	−	728.743i	−0.0582004	−	0.590919i
$116$	1026.85	+	1500.82i	0.821903	+	1.20127i
$117$	−137.103	+	256.502i	−0.108335	+	0.202680i
$118$	−931.747	−	1016.74i	−0.726901	−	0.793208i
$119$	−1775.82	−	1186.56i	−1.36797	−	0.914050i
$120$	−195.842	−	314.854i	−0.148982	−	0.239517i
$121$	595.249	+	890.854i	0.447220	+	0.669312i
$122$	296.564	+	488.678i	0.220079	+	0.362646i
$123$	1721.10	+	169.514i	1.26168	+	0.124264i
$124$	127.673	−	159.104i	0.0924627	−	0.115225i
$125$	−930.645	−	282.308i	−0.665915	−	0.202003i
$126$	462.980	+	415.010i	0.327346	+	0.293429i
$127$	−649.991			−0.454153			−0.227076	−	0.973877i	$-0.572917\pi$
$127$	−649.991			−0.454153			−0.227076	+	0.973877i	$0.572917\pi$
$128$	−1331.96	−	568.368i	−0.919762	−	0.392477i
$129$	1076.61			0.734811
$130$	219.896	+	197.112i	0.148355	+	0.132984i
$131$	1958.96	+	594.243i	1.30653	+	0.396330i	0.865385	−	0.501107i	$-0.167074\pi$
$131$	1958.96	+	594.243i	1.30653	+	0.396330i	0.441141	+	0.897438i	$0.354574\pi$
$132$	−393.832	−	316.031i	−0.259687	−	0.208386i
$133$	23.1452	+	2.27961i	0.0150898	+	0.00148622i
$134$	680.042	+	1120.57i	0.438408	+	0.722408i
$135$	351.889	+	526.639i	0.224339	+	0.335747i
$136$	−2494.73	−	581.369i	−1.57295	−	0.366559i
$137$	−1187.97	−	793.779i	−0.740843	−	0.495016i	0.126970	−	0.991907i	$-0.459475\pi$
$137$	−1187.97	−	793.779i	−0.740843	−	0.495016i	−0.867813	+	0.496891i	$0.834475\pi$
$138$	−1310.62	−	1430.17i	−0.808459	−	0.882206i
$139$	−415.327	+	777.021i	−0.253436	+	0.474145i	−0.976178	−	0.216973i	$-0.930382\pi$
$139$	−415.327	+	777.021i	−0.253436	+	0.474145i	0.722742	+	0.691118i	$0.242882\pi$
$140$	521.024	−	356.481i	0.314532	−	0.215201i
$141$	−76.2353	−	774.030i	−0.0455331	−	0.462306i
$142$	159.276	−	1115.96i	0.0941277	−	0.659505i
$143$	371.547	+	153.900i	0.217275	+	0.0899981i
$144$	695.064	+	270.166i	0.402236	+	0.156346i
$145$	−878.424	+	363.855i	−0.503097	+	0.208390i
$146$	772.246	+	3012.65i	0.437750	+	1.70773i
$147$	32.1235	−	39.1426i	0.0180238	−	0.0219621i
$148$	385.843	+	377.455i	0.214298	+	0.209639i
$149$	887.361	+	2925.24i	0.487889	+	1.60835i	0.762630	+	0.646835i	$0.223908\pi$
$149$	887.361	+	2925.24i	0.487889	+	1.60835i	−0.274741	+	0.961518i	$0.588592\pi$
$150$	−1119.38	+	407.471i	−0.609311	+	0.221799i
$151$	413.118	+	2076.89i	0.222643	+	1.11930i	0.916760	+	0.399439i	$0.130795\pi$
$151$	413.118	+	2076.89i	0.222643	+	1.11930i	−0.694117	+	0.719863i	$0.744205\pi$
$152$	26.9428	−	7.22282i	0.0143773	−	0.00385426i
$153$	1293.73	+	257.339i	0.683607	+	0.135978i
$154$	508.335	−	693.341i	0.265992	−	0.362799i
$155$	67.6642	+	82.4491i	0.0350640	+	0.0427256i
$156$	779.340	+	68.1197i	0.399982	+	0.0349612i
$157$	−246.628	+	131.825i	−0.125370	+	0.0670114i	−0.532889	−	0.846185i	$-0.678894\pi$
$157$	−246.628	+	131.825i	−0.125370	+	0.0670114i	0.407520	+	0.913196i	$0.366394\pi$
$158$	328.111	+	683.983i	0.165210	+	0.344397i
$159$	−855.671	−	855.671i	−0.426787	−	0.426787i
$160$	434.169	−	620.326i	0.214526	−	0.306507i
$161$	2335.43	−	2335.43i	1.14321	−	1.14321i
$162$	743.466	+	261.417i	0.360569	+	0.126783i
$163$	−787.583	−	1473.46i	−0.378456	−	0.708041i	0.618519	−	0.785770i	$-0.287733\pi$
$163$	−787.583	−	1473.46i	−0.378456	−	0.708041i	−0.996975	+	0.0777291i	$0.975233\pi$
$164$	1062.23	+	3368.02i	0.505770	+	1.60365i
$165$	204.087	−	167.490i	0.0962920	−	0.0790248i
$166$	−2464.67	+	379.451i	−1.15238	+	0.177416i
$167$	−400.270	+	2012.29i	−0.185472	+	0.932431i	0.770156	+	0.637856i	$0.220178\pi$
$167$	−400.270	+	2012.29i	−0.185472	+	0.932431i	−0.955628	+	0.294576i	$0.904822\pi$
$168$	537.384	−	1583.72i	0.246786	−	0.727299i
$169$	1543.70	−	307.062i	0.702641	−	0.139764i
$170$	565.974	−	1213.86i	0.255342	−	0.547642i
$171$	−13.7455	+	4.16966i	−0.00614705	+	0.00186469i
$172$	863.592	+	2021.76i	0.382839	+	0.896268i
$173$	−1908.16	−	1565.99i	−0.838582	−	0.688206i	0.113670	−	0.993519i	$-0.463739\pi$
$173$	−1908.16	−	1565.99i	−0.838582	−	0.688206i	−0.952252	+	0.305312i	$0.901239\pi$
$174$	−1283.03	+	2167.52i	−0.559000	+	0.944364i
$175$	−776.147	−	1873.78i	−0.335264	−	0.809399i
$176$	277.565	−	993.074i	0.118876	−	0.425317i
$177$	731.000	−	1764.79i	0.310425	−	0.749433i
$178$	257.161	+	342.789i	0.108287	+	0.144343i
$179$	3559.30	−	350.560i	1.48622	−	0.146380i	0.677916	−	0.735139i	$-0.262883\pi$
$179$	3559.30	−	350.560i	1.48622	−	0.146380i	0.808309	+	0.588759i	$0.200383\pi$
$180$	−213.043	+	326.553i	−0.0882182	+	0.135221i
$181$	2699.80	+	1443.07i	1.10870	+	0.592612i	0.920980	−	0.389610i	$-0.127390\pi$
$181$	2699.80	+	1443.07i	1.10870	+	0.592612i	0.187720	+	0.982223i	$0.439890\pi$
$182$	−58.0448	+	1330.68i	−0.0236405	+	0.541960i
$183$	−439.879	+	658.325i	−0.177687	+	0.265928i
$184$	1634.42	−	3608.40i	0.654841	−	1.44573i
$185$	−234.655	+	156.792i	−0.0932551	+	0.0623111i
$186$	274.461	+	67.1483i	0.108196	+	0.0264707i
$187$	178.776	−	1815.14i	0.0699112	−	0.709820i
$188$	1392.39	−	764.040i	0.540164	−	0.296401i
$189$	−829.281	+	2733.77i	−0.319160	+	1.05213i
$190$	0.795658	+	14.5628i	0.000303806	+	0.00556051i
$191$		−	4426.32i		−	1.67684i	−0.545021	−	0.838422i	$-0.683478\pi$
$191$		−	4426.32i		−	1.67684i	0.545021	−	0.838422i	$-0.316522\pi$
$192$	−66.1172	−	2004.75i	−0.0248521	−	0.753545i
$193$		−	2125.65i		−	0.792787i	−0.918081	−	0.396393i	$-0.870262\pi$
$193$		−	2125.65i		−	0.792787i	0.918081	−	0.396393i	$-0.129738\pi$
$194$	3532.26	−	192.990i	1.30723	−	0.0714221i
$195$	−118.736	+	391.420i	−0.0436044	+	0.143745i
$196$	99.2730	+	28.9267i	0.0361782	+	0.0105418i
$197$	−289.091	+	2935.19i	−0.104553	+	1.06154i	0.789552	+	0.613684i	$0.210313\pi$
$197$	−289.091	+	2935.19i	−0.104553	+	1.06154i	−0.894105	+	0.447858i	$0.852187\pi$
$198$	−126.185	+	515.768i	−0.0452910	+	0.185121i
$199$	−1692.50	+	1130.89i	−0.602904	+	0.402847i	−0.819223	−	0.573475i	$-0.805595\pi$
$199$	−1692.50	+	1130.89i	−0.602904	+	0.402847i	0.216319	+	0.976323i	$0.430595\pi$
$200$	−1663.08	−	1775.22i	−0.587988	−	0.627635i
$201$	−1008.67	+	1509.58i	−0.353962	+	0.529741i
$202$	−13.9046	−	0.606521i	−0.00484317	−	0.000211261i
$203$	−3782.07	−	2021.56i	−1.30763	−	0.698943i
$204$	−730.388	−	3472.05i	−0.250674	−	1.19163i
$205$	−1837.59	+	180.987i	−0.626062	+	0.0616617i
$206$	1215.62	−	911.959i	0.411146	−	0.308443i
$207$	−780.620	+	1884.58i	−0.262110	+	0.632790i
$208$	497.217	+	1518.16i	0.165749	+	0.506083i
$209$	7.60069	+	18.3497i	0.00251555	+	0.00607308i
$210$	752.474	+	445.414i	0.247265	+	0.146364i
$211$	2245.75	+	1843.04i	0.732721	+	0.601329i	0.924980	−	0.380016i	$-0.124081\pi$
$211$	2245.75	+	1843.04i	0.732721	+	0.601329i	−0.192259	+	0.981344i	$0.561581\pi$
$212$	920.492	−	2293.22i	0.298206	−	0.742921i
$213$	1494.16	−	453.247i	0.480648	−	0.145803i
$214$	−236.444	−	110.244i	−0.0755280	−	0.0352156i
$215$	−1127.39	+	224.253i	−0.357617	+	0.0711344i
$216$	224.511	+	3419.00i	0.0707223	+	1.07701i
$217$	−93.8527	+	471.829i	−0.0293601	+	0.147603i
$218$	−79.9904	−	519.566i	−0.0248515	−	0.161419i
$219$	−3329.93	+	2732.80i	−1.02747	+	0.843221i
$220$	478.235	+	248.904i	0.146557	+	0.0762777i
$221$	1332.05	+	2492.10i	0.405446	+	0.758536i
$222$	−247.998	+	705.301i	−0.0749752	+	0.213228i
$223$	149.378	−	149.378i	0.0448568	−	0.0448568i	−0.684323	−	0.729179i	$-0.739902\pi$
$223$	149.378	−	149.378i	0.0448568	−	0.0448568i	0.729179	+	0.684323i	$0.239902\pi$
$224$	3405.10	−	261.208i	1.01568	−	0.0779139i
$225$	885.743	+	885.743i	0.262442	+	0.262442i
$226$	297.288	−	142.611i	0.0875015	−	0.0419750i
$227$	−3167.28	+	1692.95i	−0.926077	+	0.494999i	−0.864236	−	0.503087i	$-0.832197\pi$
$227$	−3167.28	+	1692.95i	−0.926077	+	0.494999i	−0.0618418	+	0.998086i	$0.519697\pi$
$228$	24.8373	+	29.5951i	0.00721444	+	0.00859642i
$229$	−3478.61	−	4238.70i	−1.00381	−	1.22315i	−0.974687	−	0.223573i	$-0.928228\pi$
$229$	−3478.61	−	4238.70i	−1.00381	−	1.22315i	−0.0291249	−	0.999576i	$-0.509272\pi$
$230$	1670.33	+	1224.64i	0.478863	+	0.351087i
$231$	1167.93	+	232.315i	0.332658	+	0.0661697i
$232$	−5099.53	−	670.735i	−1.44311	−	0.189810i
$233$	874.513	+	4396.48i	0.245885	+	1.23615i	0.884470	+	0.466597i	$0.154520\pi$
$233$	874.513	+	4396.48i	0.245885	+	1.23615i	−0.638585	+	0.769552i	$0.720480\pi$
$234$	−281.388	−	773.010i	−0.0786107	−	0.215954i
$235$	241.057	+	794.659i	0.0669142	+	0.220587i
$236$	3900.45	−	42.8654i	1.07584	−	0.0118233i
$237$	−666.591	+	812.244i	−0.182699	+	0.222620i
$238$	5851.64	−	1499.98i	1.59372	−	0.408525i
$239$	−6193.96	+	2565.62i	−1.67638	+	0.694377i	−0.999143	−	0.0413918i	$-0.986821\pi$
$239$	−6193.96	+	2565.62i	−1.67638	+	0.694377i	−0.677232	+	0.735769i	$0.736821\pi$
$240$	1032.86	+	181.948i	0.277794	+	0.0489361i
$241$	2444.69	+	1012.62i	0.653428	+	0.270659i	0.684670	−	0.728853i	$-0.259946\pi$
$241$	2444.69	+	1012.62i	0.653428	+	0.270659i	−0.0312421	+	0.999512i	$0.509946\pi$
$242$	−3000.03	−	428.179i	−0.796899	−	0.113737i
$243$	−293.747	−	2982.47i	−0.0775470	−	0.787347i
$244$	−1589.11	−	297.978i	−0.416935	−	0.0781806i
$245$	−25.4855	+	47.6799i	−0.00664574	+	0.0124333i
$246$	−3606.30	+	3304.84i	−0.934673	+	0.856540i
$247$	−25.5851	−	17.0954i	−0.00659086	−	0.00440387i
$248$	94.0580	+	569.270i	0.0240834	+	0.145761i
$249$	−1918.96	−	2871.93i	−0.488391	−	0.730929i
$250$	2351.55	−	1427.09i	0.594901	−	0.361028i
$251$	−5244.55	−	516.543i	−1.31886	−	0.129896i	−0.586017	−	0.810299i	$-0.699305\pi$
$251$	−5244.55	−	516.543i	−1.31886	−	0.129896i	−0.732838	+	0.680403i	$0.761805\pi$
$252$	−1748.13	+	191.595i	−0.436992	+	0.0478943i
$253$	2699.12	+	818.769i	0.670720	+	0.203461i
$254$	1227.13	−	1368.97i	0.303137	−	0.338176i
$255$	1855.10			0.455573
$256$	3711.67	−	1732.25i	0.906171	−	0.422912i
$257$	1916.75			0.465227			0.232614	−	0.972569i	$-0.425272\pi$
$257$	1916.75			0.465227			0.232614	+	0.972569i	$0.425272\pi$
$258$	−2032.55	+	2267.49i	−0.490470	+	0.547162i
$259$	−1218.09	−	369.504i	−0.292233	−	0.0886480i
$260$	−830.288	+	90.9995i	−0.198047	+	0.0217060i
$261$	2635.85	+	259.609i	0.625116	+	0.0615685i
$262$	−4949.89	+	3003.94i	−1.16720	+	0.708337i
$263$	−3109.89	−	4654.28i	−0.729141	−	1.09124i	−0.991980	−	0.126397i	$-0.959659\pi$
$263$	−3109.89	−	4654.28i	−0.729141	−	1.09124i	0.262839	−	0.964840i	$-0.415341\pi$
$264$	1409.12	−	232.823i	0.328505	−	0.0542775i
$265$	1074.26	+	717.799i	0.249024	+	0.166393i
$266$	−48.4973	+	44.4432i	−0.0111788	+	0.0102443i
$267$	−279.800	+	523.469i	−0.0641329	+	0.119984i
$268$	−3643.93	−	683.283i	−0.830554	−	0.155739i
$269$	123.152	+	1250.39i	0.0279135	+	0.283411i	0.999001	+	0.0446869i	$0.0142290\pi$
$269$	123.152	+	1250.39i	0.0279135	+	0.283411i	−0.971088	+	0.238724i	$0.923271\pi$
$270$	−1773.51	−	253.124i	−0.399749	−	0.0570541i
$271$	−1306.67	−	541.240i	−0.292895	−	0.121321i	0.231398	−	0.972859i	$-0.425670\pi$
$271$	−1306.67	−	541.240i	−0.292895	−	0.121321i	−0.524292	+	0.851538i	$0.675670\pi$
$272$	5934.27	−	4156.65i	1.32286	−	0.926596i
$273$	−1704.45	+	706.007i	−0.377868	+	0.156518i
$274$	3914.59	−	1003.45i	0.863100	−	0.221242i
$275$	1098.80	−	1338.89i	0.240946	−	0.293593i
$276$	5486.47	−	60.2955i	1.19655	−	0.0131499i
$277$	1285.22	+	4236.81i	0.278778	+	0.919009i	0.978788	+	0.204876i	$0.0656790\pi$
$277$	1285.22	+	4236.81i	0.278778	+	0.919009i	−0.700010	+	0.714133i	$0.746821\pi$
$278$	−852.409	−	2341.68i	−0.183900	−	0.505197i
$279$	−57.9649	−	291.409i	−0.0124382	−	0.0625312i
$280$	−232.852	+	1770.35i	−0.0496984	+	0.377852i
$281$	−6264.01	−	1245.99i	−1.32982	−	0.264518i	−0.521495	−	0.853254i	$-0.674625\pi$
$281$	−6264.01	−	1245.99i	−1.32982	−	0.264518i	−0.808325	+	0.588737i	$0.799625\pi$
$282$	1774.13	+	1300.74i	0.374639	+	0.274673i
$283$	1587.96	+	1934.94i	0.333549	+	0.406431i	0.912595	−	0.408864i	$-0.134075\pi$
$283$	1587.96	+	1934.94i	0.333549	+	0.406431i	−0.579046	+	0.815295i	$0.696575\pi$
$284$	2049.67	+	2442.30i	0.428259	+	0.510295i
$285$	−17.8157	+	9.52271i	−0.00370285	+	0.00197922i
$286$	−1025.58	+	491.977i	−0.212041	+	0.101718i
$287$	−5888.98	−	5888.98i	−1.21120	−	1.21120i
$288$	−1881.22	+	953.847i	−0.384903	+	0.195160i
$289$	5588.09	−	5588.09i	1.13741	−	1.13741i
$290$	892.060	−	2537.00i	0.180633	−	0.513717i
$291$	2309.77	+	4321.28i	0.465296	+	0.870508i
$292$	−7802.96	−	4061.16i	−1.56381	−	0.813909i
$293$	6308.22	−	5177.02i	1.25778	−	1.03224i	0.260005	−	0.965607i	$-0.416276\pi$
$293$	6308.22	−	5177.02i	1.25778	−	1.03224i	0.997778	−	0.0666280i	$-0.0212241\pi$
$294$	21.7931	+	141.554i	0.00432313	+	0.0280803i
$295$	−397.883	+	2000.29i	−0.0785275	+	0.394785i
$296$	−1523.41	+	100.035i	−0.299143	+	0.0196434i
$297$	−2392.80	+	475.958i	−0.467490	+	0.0929896i
$298$	−7836.19	−	3653.69i	−1.52328	−	0.710243i
$299$	−4181.67	+	1268.50i	−0.808804	+	0.245348i
$300$	1255.10	−	3126.82i	0.241543	−	0.601757i
$301$	−4007.72	−	3289.05i	−0.767446	−	0.629827i
$302$	−5154.13	−	3050.90i	−0.982075	−	0.581322i
$303$	−7.37720	−	17.8101i	−0.00139871	−	0.00337678i
$304$	−35.6534	+	70.3811i	−0.00672653	+	0.0132784i
$305$	323.501	−	781.000i	0.0607331	−	0.146623i
$306$	−2984.44	+	2238.93i	−0.557546	+	0.418272i
$307$	7113.16	−	700.586i	1.32238	−	0.130243i	0.587932	−	0.808911i	$-0.299942\pi$
$307$	7113.16	−	700.586i	1.32238	−	0.130243i	0.734445	+	0.678668i	$0.237442\pi$
$308$	500.575	+	2379.59i	0.0926069	+	0.440226i
$309$	1856.35	+	992.242i	0.341761	+	0.182675i
$310$	−301.393	−	13.1468i	−0.0552192	−	0.00240868i
$311$	−1983.90	+	2969.11i	−0.361725	+	0.541360i	−0.967039	−	0.254627i	$-0.918047\pi$
$311$	−1983.90	+	2969.11i	−0.361725	+	0.541360i	0.605314	+	0.795987i	$0.293047\pi$
$312$	−1614.79	+	1512.79i	−0.293012	+	0.274503i
$313$	−3309.90	+	2211.61i	−0.597722	+	0.399385i	−0.817302	−	0.576210i	$-0.804531\pi$
$313$	−3309.90	+	2211.61i	−0.597722	+	0.399385i	0.219580	+	0.975594i	$0.429531\pi$
$314$	187.970	−	768.304i	0.0337826	−	0.138083i
$315$	90.1255	−	915.060i	0.0161206	−	0.163676i
$316$	−2060.00	−	600.255i	−0.366722	−	0.106858i
$317$	1360.41	−	4484.66i	0.241035	−	0.794585i	−0.750053	−	0.661377i	$-0.769972\pi$
$317$	1360.41	−	4484.66i	0.241035	−	0.794585i	0.991088	−	0.133208i	$-0.0425278\pi$
$318$	3417.59	−	186.725i	0.602669	−	0.0329277i
$319$		−	3662.31i		−	0.642790i
$320$	486.814	+	2085.54i	0.0850430	+	0.364329i
$321$		−	361.349i		−	0.0628303i
$322$	509.637	+	9327.80i	0.0882018	+	1.61434i
$323$	−40.5111	+	133.547i	−0.00697864	+	0.0230055i
$324$	−1954.18	+	1072.30i	−0.335078	+	0.183866i
$325$	−263.021	+	2670.49i	−0.0448916	+	0.455792i
$326$	4590.20	+	1123.02i	0.779839	+	0.190792i
$327$	605.419	−	404.528i	0.102384	−	0.0684111i
$328$	−9098.88	−	4121.32i	−1.53171	−	0.693785i
$329$	−2080.87	+	3114.25i	−0.348700	+	0.521866i
$330$	−32.5426	+	746.042i	−0.00542851	+	0.124449i
$331$	1600.46	+	855.463i	0.265768	+	0.142056i	0.598899	−	0.800825i	$-0.295605\pi$
$331$	1600.46	+	855.463i	0.265768	+	0.142056i	−0.333131	+	0.942881i	$0.608105\pi$
$332$	3853.90	−	5907.29i	0.637080	−	0.976520i
$333$	782.378	−	77.0575i	0.128751	−	0.0126809i
$334$	−3482.48	−	4642.06i	−0.570518	−	0.760485i
$335$	741.810	−	1790.89i	0.120983	−	0.292080i
$336$	2320.98	+	4121.72i	0.376845	+	0.669220i
$337$	−1671.78	−	4036.04i	−0.270231	−	0.652394i	0.729262	−	0.684234i	$-0.239863\pi$
$337$	−1671.78	−	4036.04i	−0.270231	−	0.652394i	−0.999493	+	0.0318397i	$0.989863\pi$
$338$	−2267.66	+	3830.95i	−0.364925	+	0.616497i
$339$	353.036	+	289.729i	0.0565613	+	0.0464186i
$340$	1488.05	+	3483.68i	0.237355	+	0.555674i
$341$	−393.144	+	119.259i	−0.0624338	+	0.0189391i
$342$	17.1685	−	36.8218i	0.00271452	−	0.00582191i
$343$	6107.53	−	1214.86i	0.961445	−	0.191243i
$344$	−5888.49	−	1998.07i	−0.922925	−	0.313165i
$345$	−559.672	+	2813.66i	−0.0873383	+	0.439080i
$346$	6900.61	−	1062.39i	1.07219	−	0.165071i
$347$	6507.84	−	5340.84i	1.00680	−	0.826258i	0.0219646	−	0.999759i	$-0.493008\pi$
$347$	6507.84	−	5340.84i	1.00680	−	0.826258i	0.984834	+	0.173501i	$0.0555079\pi$
$348$	−2142.84	−	6794.31i	−0.330082	−	1.04659i
$349$	−1054.00	−	1971.90i	−0.161660	−	0.302445i	0.788029	−	0.615638i	$-0.211102\pi$
$349$	−1054.00	−	1971.90i	−0.161660	−	0.302445i	−0.949690	+	0.313192i	$0.898602\pi$
$350$	5411.73	+	1902.87i	0.826484	+	0.290608i
$351$	2672.67	−	2672.67i	0.406430	−	0.406430i
$352$	1567.53	+	2459.42i	0.237356	+	0.372408i
$353$	347.799	+	347.799i	0.0524404	+	0.0524404i	0.732841	−	0.680400i	$-0.238194\pi$
$353$	347.799	+	347.799i	0.0524404	+	0.0524404i	−0.680400	+	0.732841i	$0.738194\pi$
$354$	2336.82	+	4871.35i	0.350848	+	0.731382i
$355$	−1470.22	+	785.850i	−0.219806	+	0.117489i
$356$	−1207.46	−	105.540i	−0.179761	−	0.0157124i
$357$	5308.07	+	6467.91i	0.786927	+	0.958874i
$358$	−5981.31	+	8158.17i	−0.883023	+	1.20439i
$359$	12800.5	+	2546.17i	1.88185	+	0.374323i	0.995977	−	0.0896087i	$-0.0285616\pi$
$359$	12800.5	+	2546.17i	1.88185	+	0.374323i	0.885871	+	0.463932i	$0.153562\pi$
$360$	−285.558	−	1065.20i	−0.0418062	−	0.155947i
$361$	1337.83	+	6725.72i	0.195047	+	0.980568i
$362$	−8136.29	+	2961.74i	−1.18131	+	0.430016i
$363$	−1218.46	−	4016.72i	−0.176178	−	0.580780i
$364$	−2693.01	−	2634.46i	−0.387780	−	0.379350i
$365$	2917.76	−	3555.30i	0.418418	−	0.509844i
$366$	−556.067	−	2169.30i	−0.0794155	−	0.309812i
$367$	9383.56	−	3886.80i	1.33465	−	0.552832i	0.402675	−	0.915343i	$-0.368081\pi$
$367$	9383.56	−	3886.80i	1.33465	−	0.552832i	0.931979	+	0.362511i	$0.118081\pi$
$368$	4514.13	+	10254.6i	0.639444	+	1.45261i
$369$	4752.14	+	1968.40i	0.670424	+	0.277699i
$370$	112.785	−	790.224i	0.0158470	−	0.111032i
$371$	571.184	+	5799.33i	0.0799310	+	0.811553i
$372$	−659.581	+	451.280i	−0.0919292	+	0.0628973i
$373$	5190.16	−	9710.10i	0.720472	−	1.34791i	−0.208596	−	0.978002i	$-0.566889\pi$
$373$	5190.16	−	9710.10i	0.720472	−	1.34791i	0.929069	−	0.369907i	$-0.120611\pi$
$374$	3485.42	+	3803.36i	0.481889	+	0.525847i
$375$	3167.91	+	2116.73i	0.436240	+	0.291486i
$376$	−1019.55	+	4375.01i	−0.139838	+	0.600063i
$377$	3152.26	+	4717.69i	0.430635	+	0.644491i
$378$	−4192.08	−	6907.69i	−0.570416	−	0.939930i
$379$	−7221.95	−	711.300i	−0.978804	−	0.0964038i	−0.404056	−	0.914734i	$-0.632400\pi$
$379$	−7221.95	−	711.300i	−0.978804	−	0.0964038i	−0.574748	+	0.818330i	$0.694900\pi$
$380$	−32.1733	−	25.8175i	−0.00434330	−	0.00348529i
$381$	2436.80	+	739.194i	0.327666	+	0.0993965i
$382$	9322.41	+	8356.50i	1.24863	+	1.11926i
$383$	3655.95			0.487755			0.243877	−	0.969806i	$-0.421581\pi$
$383$	3655.95			0.487755			0.243877	+	0.969806i	$0.421581\pi$
$384$	4347.10	+	3645.54i	0.577700	+	0.484469i
$385$	−1271.40			−0.168303
$386$	4476.91	+	4013.05i	0.590333	+	0.529167i
$387$	3064.19	+	929.512i	0.402484	+	0.122092i
$388$	−6262.14	+	7803.76i	−0.819361	+	1.02107i
$389$	−9789.02	−	964.134i	−1.27589	−	0.125665i	−0.562718	−	0.826649i	$-0.690244\pi$
$389$	−9789.02	−	964.134i	−1.27589	−	0.125665i	−0.713176	+	0.700985i	$0.752744\pi$
$390$	−600.220	−	989.041i	−0.0779315	−	0.128415i
$391$	11010.7	+	16478.6i	1.42413	+	2.13135i
$392$	−248.342	+	154.471i	−0.0319979	+	0.0199030i
$393$	−6668.28	−	4455.60i	−0.855903	−	0.571896i
$394$	−5636.12	−	6150.25i	−0.720669	−	0.786408i
$395$	528.846	−	989.402i	0.0673649	−	0.126031i
$396$	−848.048	−	1239.49i	−0.107616	−	0.157289i
$397$	−1012.69	−	10282.0i	−0.128023	−	1.29984i	−0.817666	−	0.575692i	$-0.804733\pi$
$397$	−1012.69	−	10282.0i	−0.128023	−	1.29984i	0.689643	−	0.724149i	$-0.257767\pi$
$398$	813.480	−	5699.64i	0.102452	−	0.717832i
$399$	−84.1783	−	34.8678i	−0.0105619	−	0.00437487i
$400$	6878.60	−	151.208i	0.859825	−	0.0189010i
$401$	−1325.94	+	549.222i	−0.165123	+	0.0683961i	−0.463714	−	0.885985i	$-0.653483\pi$
$401$	−1325.94	+	549.222i	−0.165123	+	0.0683961i	0.298591	+	0.954381i	$0.403483\pi$
$402$	−1275.10	−	4974.36i	−0.158200	−	0.617160i
$403$	403.788	−	492.017i	0.0499109	−	0.0608166i
$404$	27.5280	−	28.1398i	0.00339002	−	0.00346536i
$405$	−338.315	−	1115.28i	−0.0415087	−	0.136836i
$406$	11397.9	−	4149.01i	1.39327	−	0.507172i
$407$	−212.073	−	1066.16i	−0.0258282	−	0.129847i
$408$	8691.51	+	5016.63i	1.05464	+	0.608727i
$409$	−7111.40	−	1414.55i	−0.859746	−	0.171014i	−0.254520	−	0.967068i	$-0.581917\pi$
$409$	−7111.40	−	1414.55i	−0.859746	−	0.171014i	−0.605226	+	0.796053i	$0.706917\pi$
$410$	3088.02	−	4211.89i	0.371967	−	0.507342i
$411$	3550.96	+	4326.86i	0.426171	+	0.519290i
$412$	−374.272	+	4281.95i	−0.0447550	+	0.512030i
$413$	−8112.59	+	4336.27i	−0.966573	+	0.516644i
$414$	−2495.44	−	5202.01i	−0.296242	−	0.617548i
$415$	2607.68	+	2607.68i	0.308448	+	0.308448i
$416$	−4136.14	−	1818.95i	−0.487479	−	0.214378i
$417$	2440.70	−	2440.70i	0.286623	−	0.286623i
$418$	−52.9963	−	18.6345i	−0.00620128	−	0.00218049i
$419$	−5701.15	−	10666.1i	−0.664725	−	1.24361i	−0.957776	−	0.287515i	$-0.907171\pi$
$419$	−5701.15	−	10666.1i	−0.664725	−	1.24361i	0.293051	−	0.956097i	$-0.405329\pi$
$420$	−2358.70	+	743.907i	−0.274031	+	0.0864260i
$421$	−9882.67	+	8110.49i	−1.14407	+	0.938911i	−0.998726	−	0.0504712i	$-0.983928\pi$
$421$	−9882.67	+	8110.49i	−1.14407	+	0.938911i	−0.145340	+	0.989382i	$0.546428\pi$
$422$	−8121.48	+	1250.35i	−0.936842	+	0.144233i
$423$	451.295	−	2268.81i	0.0518740	−	0.260788i
$424$	3092.02	+	6268.08i	0.354156	+	0.717936i
$425$	11936.3	−	2374.28i	1.36235	−	0.270987i
$426$	−1866.24	+	4002.58i	−0.212252	+	0.455225i
$427$	3648.64	−	1106.80i	0.413513	−	0.125438i
$428$	678.574	−	289.852i	0.0766358	−	0.0327348i
$429$	−1217.90	−	999.502i	−0.137064	−	0.112486i
$430$	1656.11	−	2797.81i	0.185732	−	0.313773i
$431$	1032.60	+	2492.91i	0.115403	+	0.278607i	0.971018	−	0.239005i	$-0.0768212\pi$
$431$	1032.60	+	2492.91i	0.115403	+	0.278607i	−0.855616	+	0.517612i	$0.826821\pi$
$432$	−7624.71	−	5981.92i	−0.849176	−	0.666215i
$433$	−3761.82	+	9081.84i	−0.417510	+	1.00796i	0.565557	+	0.824709i	$0.308661\pi$
$433$	−3761.82	+	9081.84i	−0.417510	+	1.00796i	−0.983067	+	0.183248i	$0.941339\pi$
$434$	−816.549	−	1088.44i	−0.0903125	−	0.120384i
$435$	3706.97	−	365.105i	0.408588	−	0.0402424i
$436$	1245.29	+	812.424i	0.136786	+	0.0892386i
$437$	−190.331	−	101.734i	−0.0208347	−	0.0111364i
$438$	530.970	−	12172.5i	0.0579241	−	1.32792i
$439$	−6577.44	+	9843.84i	−0.715089	+	1.07021i	0.278856	+	0.960333i	$0.410045\pi$
$439$	−6577.44	+	9843.84i	−0.715089	+	1.07021i	−0.993946	+	0.109874i	$0.964955\pi$
$440$	−1427.09	+	537.317i	−0.154622	+	0.0582172i
$441$	125.222	−	83.6708i	0.0135214	−	0.00903474i
$442$	−7763.48	−	1899.38i	−0.835455	−	0.204399i
$443$	−1698.99	+	17250.1i	−0.182215	+	1.85006i	0.275920	+	0.961181i	$0.411018\pi$
$443$	−1698.99	+	17250.1i	−0.182215	+	1.85006i	−0.458135	+	0.888883i	$0.651482\pi$
$444$	−1017.26	−	1853.86i	−0.108732	−	0.198154i
$445$	183.961	−	606.440i	0.0195969	−	0.0646022i
$446$	32.5972	+	596.621i	0.00346081	+	0.0633426i
$447$		−	11975.8i		−	1.26719i
$448$	−5878.39	+	7664.73i	−0.619929	+	0.808314i
$449$		−	4826.42i		−	0.507289i	−0.967297	−	0.253645i	$-0.918371\pi$
$449$		−	4826.42i		−	0.507289i	0.967297	−	0.253645i	$-0.0816294\pi$
$450$	−3537.69	+	193.287i	−0.370597	+	0.0202481i
$451$	2064.60	−	6806.06i	0.215561	−	0.710609i
$452$	−260.896	+	895.366i	−0.0271494	+	0.0931736i
$453$	813.145	−	8256.00i	0.0843374	−	0.856292i
$454$	2413.97	−	9866.83i	0.249545	−	1.01999i
$455$	1637.79	−	1094.33i	0.168749	−	0.112754i
$456$	−109.222	−	3.56225i	−0.0112166	−	0.000365828i
$457$	−7068.39	+	10578.6i	−0.723512	+	1.08281i	0.269291	+	0.963059i	$0.413211\pi$
$457$	−7068.39	+	10578.6i	−0.723512	+	1.08281i	−0.992804	+	0.119754i	$0.961789\pi$
$458$	15494.6	+	675.878i	1.58082	+	0.0689556i
$459$	−15118.2	−	8080.84i	−1.53738	−	0.821746i
$460$	−5732.69	+	1205.94i	−0.581061	+	0.122233i
$461$	−14144.8	+	1393.14i	−1.42904	+	0.140748i	−0.782746	−	0.622341i	$-0.786182\pi$
$461$	−14144.8	+	1393.14i	−1.42904	+	0.140748i	−0.646293	+	0.763089i	$0.723682\pi$
$462$	−2694.23	+	2021.22i	−0.271313	+	0.203540i
$463$	−6900.22	+	16658.6i	−0.692614	+	1.67212i	0.0468323	+	0.998903i	$0.485087\pi$
$463$	−6900.22	+	16658.6i	−0.692614	+	1.67212i	−0.739446	+	0.673215i	$0.764913\pi$
$464$	11040.1	−	9474.00i	1.10458	−	0.947887i
$465$	−159.907	−	386.049i	−0.0159473	−	0.0385002i
$466$	−10910.6	−	6458.32i	−1.08460	−	0.642008i
$467$	−5710.84	−	4686.76i	−0.565880	−	0.464406i	0.307430	−	0.951571i	$-0.400531\pi$
$467$	−5710.84	−	4686.76i	−0.565880	−	0.464406i	−0.873310	+	0.487165i	$0.838031\pi$
$468$	2159.30	+	866.734i	0.213277	+	0.0856085i
$469$	8366.59	−	2537.98i	0.823738	−	0.249878i
$470$	−2128.75	−	992.548i	−0.208919	−	0.0974103i
$471$	1074.52	−	213.734i	0.105119	−	0.0209095i
$472$	−7273.42	+	8295.78i	−0.709293	+	0.808992i
$473$	863.781	−	4342.52i	0.0839677	−	0.422134i
$474$	−452.227	−	2937.37i	−0.0438217	−	0.284637i
$475$	−102.444	+	84.0740i	−0.00989574	+	0.00812122i
$476$	−7888.23	+	15156.1i	−0.759572	+	1.45941i
$477$	−1696.60	−	3174.11i	−0.162855	−	0.304681i
$478$	6290.11	−	17889.0i	0.601889	−	1.71176i
$479$	−460.152	+	460.152i	−0.0438933	+	0.0438933i	−0.728713	−	0.684819i	$-0.759881\pi$
$479$	−460.152	+	460.152i	−0.0438933	+	0.0438933i	0.684819	+	0.728713i	$0.259881\pi$
$480$	−2333.15	+	1831.83i	−0.221860	+	0.174190i
$481$	1190.87	+	1190.87i	0.112887	+	0.112887i
$482$	−6748.07	+	3237.09i	−0.637689	+	0.305903i
$483$	−11411.4	+	6099.51i	−1.07502	+	0.574612i
$484$	6565.60	−	5510.10i	0.616604	−	0.517477i
$485$	−3318.81	−	4043.98i	−0.310721	−	0.378614i
$486$	6836.04	+	5011.97i	0.638043	+	0.467793i
$487$	10532.2	+	2094.98i	0.979996	+	0.194933i	0.658997	−	0.752146i	$-0.270981\pi$
$487$	10532.2	+	2094.98i	0.979996	+	0.194933i	0.321000	+	0.947079i	$0.395981\pi$
$488$	3627.67	−	2784.31i	0.336510	−	0.258278i
$489$	1276.95	+	6419.64i	0.118089	+	0.593673i
$490$	−52.3059	−	143.691i	−0.00482233	−	0.0132476i
$491$	−3633.32	−	11977.4i	−0.333950	−	1.10088i	−0.949757	−	0.312988i	$-0.898670\pi$
$491$	−3633.32	−	11977.4i	−0.333950	−	1.10088i	0.615808	−	0.787896i	$-0.288830\pi$
$492$	−152.040	−	13834.6i	−0.0139319	−	1.26771i
$493$	16324.9	−	19892.0i	1.49135	−	1.81722i
$494$	84.3077	−	21.6110i	0.00767851	−	0.00196827i
$495$	725.466	−	300.498i	0.0658733	−	0.0272856i
$496$	−1376.53	−	876.632i	−0.124613	−	0.0793588i
$497$	−6946.71	−	2877.42i	−0.626967	−	0.259698i
$498$	9671.50	+	1380.36i	0.870261	+	0.124208i
$499$	−371.481	−	3771.71i	−0.0333262	−	0.338366i	−0.997362	−	0.0725927i	$-0.976873\pi$
$499$	−371.481	−	3771.71i	−0.0333262	−	0.338366i	0.964035	−	0.265774i	$-0.0856273\pi$
$500$	−1433.89	+	7646.90i	−0.128251	+	0.683959i
$501$	3789.06	−	7088.83i	0.337889	−	0.632147i
$502$	10989.1	−	10070.5i	0.977031	−	0.895357i
$503$	−14906.3	−	9960.08i	−1.32135	−	0.882899i	−0.323362	−	0.946275i	$-0.604813\pi$
$503$	−14906.3	−	9960.08i	−1.32135	−	0.882899i	−0.997990	+	0.0633765i	$0.979813\pi$
$504$	2896.79	−	4043.51i	0.256019	−	0.357366i
$505$	11.4349	+	17.1135i	0.00100762	+	0.00150801i
$506$	−6820.13	+	4138.94i	−0.599194	+	0.363633i
$507$	−6136.50	−	604.392i	−0.537537	−	0.0529428i
$508$	566.519	+	5168.98i	0.0494788	+	0.451449i
$509$	−12646.2	−	3836.17i	−1.10124	−	0.334057i	−0.313203	−	0.949686i	$-0.601402\pi$
$509$	−12646.2	−	3836.17i	−1.10124	−	0.334057i	−0.788036	+	0.615629i	$0.788902\pi$
$510$	−3502.27	+	3907.09i	−0.304084	+	0.339233i
$511$	20744.4			1.79585
$512$	−3358.97	+	11087.6i	−0.289935	+	0.957046i
$513$	186.671			0.0160657
$514$	−3618.65	+	4036.92i	−0.310529	+	0.346422i
$515$	−2150.59	−	652.374i	−0.184012	−	0.0558195i
$516$	−938.355	−	8561.64i	−0.0800558	−	0.730437i
$517$	−3183.22	−	313.519i	−0.270789	−	0.0266703i
$518$	3077.87	−	1867.87i	0.261069	−	0.158435i
$519$	5372.73	+	8040.86i	0.454406	+	0.680067i
$520$	1375.85	−	1920.49i	0.116029	−	0.161960i
$521$	13735.3	+	9177.65i	1.15500	+	0.771747i	0.977200	−	0.212320i	$-0.0681018\pi$
$521$	13735.3	+	9177.65i	1.15500	+	0.771747i	0.177800	+	0.984067i	$0.443102\pi$
$522$	−5523.03	+	5061.34i	−0.463097	+	0.424384i
$523$	1548.19	−	2896.46i	0.129441	−	0.242167i	−0.808849	−	0.588016i	$-0.799909\pi$
$523$	1548.19	−	2896.46i	0.129441	−	0.242167i	0.938290	+	0.345849i	$0.112409\pi$
$524$	3018.26	−	16096.3i	0.251629	−	1.34193i
$525$	778.813	+	7907.42i	0.0647432	+	0.657349i
$526$	15673.7	+	2237.03i	1.29925	+	0.185436i
$527$	−2666.98	−	1104.70i	−0.220446	−	0.0913119i
$528$	−2169.94	+	3407.34i	−0.178853	+	0.280844i
$529$	−17074.4	+	7072.43i	−1.40333	+	0.581280i
$530$	−3539.89	+	907.396i	−0.290119	+	0.0743675i
$531$	3604.18	−	4391.71i	0.294554	−	0.358915i
$532$	−2.04462	−	186.046i	−0.000166627	−	0.0151619i
$533$	3198.62	+	10544.4i	0.259939	+	0.856905i
$534$	−574.257	−	1577.56i	−0.0465365	−	0.127842i
$535$	75.2670	+	378.393i	0.00608238	+	0.0305782i
$536$	8318.51	−	6384.62i	0.670345	−	0.514503i
$537$	−13742.4	−	2733.53i	−1.10433	−	0.219665i
$538$	−2865.98	−	2101.25i	−0.229668	−	0.168385i
$539$	−132.108	−	160.975i	−0.0105572	−	0.0128640i
$540$	3881.34	−	3257.36i	0.309308	−	0.259583i
$541$	−314.669	+	168.194i	−0.0250068	+	0.0133664i	−0.483853	−	0.875149i	$-0.660763\pi$
$541$	−314.669	+	168.194i	−0.0250068	+	0.0133664i	0.458846	+	0.888516i	$0.348263\pi$
$542$	3606.80	−	1730.20i	0.285840	−	0.137119i
$543$	−8480.35	−	8480.35i	−0.670215	−	0.670215i
$544$	−2448.91	+	20345.7i	−0.193008	+	1.60352i
$545$	−549.713	+	549.713i	−0.0432057	+	0.0432057i
$546$	1730.91	−	4922.68i	0.135671	−	0.385844i
$547$	6499.35	+	12159.4i	0.508029	+	0.950456i	0.996944	+	0.0781241i	$0.0248930\pi$
$547$	6499.35	+	12159.4i	0.508029	+	0.950456i	−0.488914	+	0.872332i	$0.662607\pi$
$548$	−5277.02	+	10139.1i	−0.411356	+	0.790364i
$549$	−1820.33	+	1493.91i	−0.141511	+	0.116135i
$550$	745.445	+	4841.92i	0.0577925	+	0.375382i
$551$	−54.6681	+	274.835i	−0.00422675	+	0.0212493i
$552$	−10231.0	+	11669.1i	−0.788876	+	0.899761i
$553$	4962.81	−	987.164i	0.381627	−	0.0759104i
$554$	−11349.7	−	5291.88i	−0.870400	−	0.405831i
$555$	1058.02	−	320.948i	0.0809201	−	0.0245468i
$556$	6541.16	+	2625.60i	0.498933	+	0.200270i
$557$	−8419.87	−	6910.01i	−0.640505	−	0.525649i	0.257137	−	0.966375i	$-0.417221\pi$
$557$	−8419.87	−	6910.01i	−0.640505	−	0.525649i	−0.897642	+	0.440726i	$0.854721\pi$
$558$	723.179	+	428.073i	0.0548649	+	0.0324763i
$559$	2625.04	+	6337.40i	0.198618	+	0.479505i
$560$	−3288.98	−	3832.68i	−0.248187	−	0.289215i
$561$	−2734.47	+	6601.60i	−0.205792	+	0.496827i
$562$	14450.1	−	10840.5i	1.08459	−	0.813664i
$563$	13040.0	−	1284.33i	0.976146	−	0.0961420i	0.402653	−	0.915353i	$-0.368088\pi$
$563$	13040.0	−	1284.33i	0.976146	−	0.0961420i	0.573493	+	0.819211i	$0.305588\pi$
$564$	−6088.94	+	1280.88i	−0.454593	+	0.0956291i
$565$	−430.036	−	229.859i	−0.0320208	−	0.0171155i
$566$	−7073.16	−	308.533i	−0.525278	−	0.0229128i
$567$	2920.43	−	4370.74i	0.216308	−	0.323728i
$568$	−9013.40	−	293.970i	−0.665834	−	0.0217161i
$569$	−7475.48	+	4994.96i	−0.550771	+	0.368013i	−0.799599	−	0.600534i	$-0.794955\pi$
$569$	−7475.48	+	4994.96i	−0.550771	+	0.368013i	0.248828	+	0.968548i	$0.419955\pi$
$570$	13.5785	−	55.5003i	0.000997788	−	0.00407834i
$571$	−1808.25	+	18359.5i	−0.132527	+	1.34557i	0.667052	+	0.745012i	$0.267556\pi$
$571$	−1808.25	+	18359.5i	−0.132527	+	1.34557i	−0.799579	+	0.600561i	$0.794944\pi$
$572$	900.036	−	3088.82i	0.0657909	−	0.225787i
$573$	−5033.78	+	16594.1i	−0.366997	+	1.20983i
$574$	23520.8	−	1285.09i	1.71035	−	0.0934473i
$575$			18820.3i			1.36498i
$576$	1542.66	−	5762.88i	0.111593	−	0.416875i
$577$		−	17065.9i		−	1.23130i	−0.788018	−	0.615652i	$-0.788893\pi$
$577$		−	17065.9i		−	1.23130i	0.788018	−	0.615652i	$-0.211107\pi$
$578$	1219.43	+	22319.1i	0.0877539	+	1.60614i
$579$	−2417.37	+	7969.01i	−0.173510	+	0.571987i
$580$	3659.13	+	6668.43i	0.261961	+	0.477399i
$581$	−1630.35	+	16553.3i	−0.116417	+	1.18201i
$582$	−13461.8	−	3293.51i	−0.958781	−	0.234571i
$583$	−4137.87	+	2764.83i	−0.293950	+	0.196411i
$584$	23284.6	−	8766.95i	1.64987	−	0.621197i
$585$	−675.878	+	1011.52i	−0.0477677	+	0.0714894i
$586$	−1005.87	+	23059.7i	−0.0709081	+	1.62558i
$587$	−8128.02	−	4344.52i	−0.571515	−	0.305481i	0.160208	−	0.987083i	$-0.448783\pi$
$587$	−8128.02	−	4344.52i	−0.571515	−	0.305481i	−0.731723	+	0.681602i	$0.761283\pi$
$588$	−339.275	−	221.342i	−0.0237950	−	0.0155238i
$589$	31.2834	−	3.08114i	0.00218847	−	0.000215546i
$590$	−3461.71	−	4614.37i	−0.241553	−	0.321984i
$591$	4421.80	−	10675.2i	0.307764	−	0.743009i
$592$	2665.37	−	3397.35i	0.185044	−	0.235862i
$593$	3773.78	+	9110.71i	0.261333	+	0.630914i	0.999021	−	0.0442273i	$-0.0140826\pi$
$593$	3773.78	+	9110.71i	0.261333	+	0.630914i	−0.737688	+	0.675141i	$0.764083\pi$
$594$	3514.97	−	5938.13i	0.242796	−	0.410176i
$595$	−6905.67	−	5667.33i	−0.475806	−	0.390484i
$596$	22489.2	−	9606.21i	1.54563	−	0.660211i
$597$	7631.20	−	2314.90i	0.523156	−	0.158698i
$598$	5223.01	−	11202.0i	0.357165	−	0.766024i
$599$	−19637.3	+	3906.10i	−1.33950	+	0.266442i	−0.812270	−	0.583282i	$-0.801768\pi$
$599$	−19637.3	+	3906.10i	−1.33950	+	0.266442i	−0.527227	+	0.849725i	$0.676768\pi$
$600$	4215.99	+	8546.56i	0.286862	+	0.581520i
$601$	1024.59	−	5150.94i	0.0695403	−	0.349603i	−0.930312	−	0.366768i	$-0.880464\pi$
$601$	1024.59	−	5150.94i	0.0695403	−	0.349603i	0.999853	+	0.0171656i	$0.00546424\pi$
$602$	14493.4	−	2231.35i	0.981241	−	0.151068i
$603$	−4174.14	+	3425.63i	−0.281898	+	0.231347i
$604$	16156.1	−	5095.45i	1.08838	−	0.343263i
$605$	2112.59	+	3952.38i	0.141965	+	0.265598i
$606$	51.4380	+	18.0866i	0.00344806	+	0.00121241i
$607$	−1996.77	+	1996.77i	−0.133520	+	0.133520i	−0.770708	−	0.637188i	$-0.780097\pi$
$607$	−1996.77	+	1996.77i	−0.133520	+	0.133520i	0.637188	+	0.770708i	$0.280097\pi$
$608$	−80.9214	−	207.964i	−0.00539769	−	0.0138718i
$609$	11879.9	+	11879.9i	0.790470	+	0.790470i
$610$	1034.15	+	2155.79i	0.0686417	+	0.143091i
$611$	4370.39	−	2336.02i	0.289373	−	0.154673i
$612$	918.868	−	10512.5i	0.0606912	−	0.694352i
$613$	−6337.06	−	7721.73i	−0.417539	−	0.508773i	0.521184	−	0.853444i	$-0.325490\pi$
$613$	−6337.06	−	7721.73i	−0.417539	−	0.508773i	−0.938723	+	0.344671i	$0.887990\pi$
$614$	−11953.5	+	16303.9i	−0.785674	+	1.07162i
$615$	7094.89	+	1411.26i	0.465193	+	0.0925325i
$616$	−5956.77	−	3438.17i	−0.389618	−	0.224883i
$617$	255.371	+	1283.84i	0.0166626	+	0.0837688i	0.988222	−	0.153028i	$-0.0489025\pi$
$617$	255.371	+	1283.84i	0.0166626	+	0.0837688i	−0.971559	+	0.236797i	$0.923902\pi$
$618$	−5594.42	+	2036.46i	−0.364144	+	0.132554i
$619$	−708.171	−	2334.53i	−0.0459835	−	0.151587i	0.930942	−	0.365166i	$-0.118988\pi$
$619$	−708.171	−	2334.53i	−0.0459835	−	0.151587i	−0.976926	+	0.213579i	$0.931488\pi$
$620$	596.692	−	609.952i	0.0386511	−	0.0395101i
$621$	16817.4	−	20492.1i	1.08673	−	1.32418i
$622$	−2507.92	−	9783.77i	−0.161669	−	0.630697i
$623$	2640.76	−	1093.84i	0.169823	−	0.0703430i
$624$	−137.543	−	6256.98i	−0.00882394	−	0.401410i
$625$	8656.87	+	3585.79i	0.554040	+	0.229491i
$626$	1590.87	−	11146.4i	0.101572	−	0.711662i
$627$	−7.62680	−	77.4362i	−0.000485782	−	0.00493222i
$628$	1263.28	+	1846.38i	0.0802712	+	0.117323i
$629$	3600.59	−	6736.23i	0.228243	−	0.427013i
$630$	1757.09	+	1917.37i	0.111118	+	0.121254i
$631$	−9455.60	−	6318.03i	−0.596548	−	0.398600i	0.220318	−	0.975428i	$-0.429290\pi$
$631$	−9455.60	−	6318.03i	−0.596548	−	0.398600i	−0.816866	+	0.576828i	$0.804290\pi$
$632$	5153.32	−	3205.41i	0.324348	−	0.201747i
$633$	−6323.29	−	9463.47i	−0.397043	−	0.594217i
$634$	6876.96	+	11331.8i	0.430787	+	0.709850i
$635$	−2705.70	−	266.488i	−0.169091	−	0.0166540i
$636$	−6058.84	+	7550.41i	−0.377749	+	0.470744i
$637$	308.734	+	93.6535i	0.0192033	+	0.00582525i
$638$	7713.31	+	6914.12i	0.478641	+	0.429048i
$639$	4643.89			0.287495
$640$	−5311.48	−	2912.02i	−0.328054	−	0.179856i
$641$	4554.01			0.280612			0.140306	−	0.990108i	$-0.455191\pi$
$641$	4554.01			0.280612			0.140306	+	0.990108i	$0.455191\pi$
$642$	761.048	+	682.195i	0.0467853	+	0.0419378i
$643$	8102.39	+	2457.83i	0.496932	+	0.150743i	0.528795	−	0.848750i	$-0.322644\pi$
$643$	8102.39	+	2457.83i	0.496932	+	0.150743i	−0.0318632	+	0.999492i	$0.510144\pi$
$644$	−20607.7	−	16536.7i	−1.26096	−	1.01186i
$645$	4481.59	+	441.398i	0.273585	+	0.0269458i
$646$	−204.787	−	337.447i	−0.0124725	−	0.0205522i
$647$	−9221.83	−	13801.4i	−0.560351	−	0.838625i	0.437821	−	0.899062i	$-0.355751\pi$
$647$	−9221.83	−	13801.4i	−0.560351	−	0.838625i	−0.998172	+	0.0604371i	$0.980751\pi$
$648$	1430.90	−	6140.17i	0.0867454	−	0.372235i
$649$	−6531.79	−	4364.40i	−0.395062	−	0.263972i
$650$	−5127.85	−	5595.61i	−0.309432	−	0.337658i
$651$	888.433	−	1662.14i	0.0534876	−	0.100068i
$652$	−11031.1	+	7547.41i	−0.662595	+	0.453342i
$653$	2136.93	+	21696.6i	0.128062	+	1.30024i	0.817516	+	0.575906i	$0.195351\pi$
$653$	2136.93	+	21696.6i	0.128062	+	1.30024i	−0.689453	+	0.724330i	$0.742149\pi$
$654$	−290.988	+	2038.80i	−0.0173984	+	0.121901i
$655$	7910.87	+	3276.79i	0.471914	+	0.195473i
$656$	25857.9	−	11382.8i	1.53900	−	0.677473i
$657$	−11836.8	+	4902.97i	−0.702890	+	0.291147i
$658$	−2630.51	−	10262.0i	−0.155848	−	0.607986i
$659$	4529.09	−	5518.71i	0.267721	−	0.326219i	−0.621745	−	0.783219i	$-0.713576\pi$
$659$	4529.09	−	5518.71i	0.267721	−	0.326219i	0.889467	+	0.457000i	$0.151076\pi$
$660$	−1509.82	−	1477.00i	−0.0890452	−	0.0871093i
$661$	−3688.33	−	12158.8i	−0.217034	−	0.715465i	−0.996077	−	0.0884942i	$-0.971795\pi$
$661$	−3688.33	−	12158.8i	−0.217034	−	0.715465i	0.779043	−	0.626971i	$-0.215705\pi$
$662$	−4823.24	+	1755.74i	−0.283173	+	0.103080i
$663$	−2159.72	−	10857.7i	−0.126511	−	0.636012i
$664$	5165.70	+	19269.3i	0.301910	+	1.12619i
$665$	95.4114	+	18.9785i	0.00556375	+	0.00110670i
$666$	−1314.77	+	1793.27i	−0.0764958	+	0.104336i
$667$	25245.3	+	30761.5i	1.46552	+	1.78574i
$668$	16351.4	+	1429.23i	0.947088	+	0.0827821i
$669$	−729.890	+	390.134i	−0.0421811	+	0.0225463i
$670$	2371.37	+	4943.39i	0.136738	+	0.285044i
$671$	2302.43	+	2302.43i	0.132466	+	0.132466i
$672$	−13062.7	−	2893.15i	−0.749857	−	0.166080i
$673$	−12329.8	+	12329.8i	−0.706208	+	0.706208i	−0.965736	−	0.259528i	$-0.916433\pi$
$673$	−12329.8	+	12329.8i	−0.706208	+	0.706208i	0.259528	+	0.965736i	$0.416433\pi$
$674$	11656.6	+	4098.69i	0.666165	+	0.234237i
$675$	−7673.78	−	14356.6i	−0.437576	−	0.818648i
$676$	−3787.33	−	12008.5i	−0.215483	−	0.683232i
$677$	2964.92	−	2433.25i	0.168318	−	0.138135i	−0.546463	−	0.837483i	$-0.684026\pi$
$677$	2964.92	−	2433.25i	0.168318	−	0.138135i	0.714781	+	0.699348i	$0.246526\pi$
$678$	−1276.71	+	196.557i	−0.0723181	+	0.0111338i
$679$	4603.31	−	23142.4i	0.260175	−	1.30799i
$680$	−10146.4	−	3442.86i	−0.572201	−	0.194158i
$681$	13799.3	−	2744.85i	0.776491	−	0.154454i
$682$	491.046	−	1053.16i	0.0275706	−	0.0591315i
$683$	−7038.53	+	2135.11i	−0.394322	+	0.119616i	−0.481218	−	0.876601i	$-0.659805\pi$
$683$	−7038.53	+	2135.11i	−0.394322	+	0.119616i	0.0868957	+	0.996217i	$0.472305\pi$
$684$	45.1390	+	105.675i	0.00252329	+	0.00590731i
$685$	−4619.71	−	3791.30i	−0.257679	−	0.211472i
$686$	−8971.82	+	15156.8i	−0.499338	+	0.843571i
$687$	8220.79	+	19846.7i	0.456540	+	1.10218i
$688$	15325.2	−	8629.75i	0.849224	−	0.478206i
$689$	2950.51	−	7123.17i	0.163143	−	0.393862i
$690$	−4869.33	−	6490.69i	−0.268655	−	0.358110i
$691$	−15537.1	+	1530.27i	−0.855368	+	0.0842464i	−0.516188	−	0.856475i	$-0.672649\pi$
$691$	−15537.1	+	1530.27i	−0.855368	+	0.0842464i	−0.339180	+	0.940722i	$0.610149\pi$
$692$	−10790.2	+	16539.3i	−0.592748	+	0.908569i
$693$	3123.50	+	1669.55i	0.171215	+	0.0915164i
$694$	−1037.70	+	23789.4i	−0.0567588	+	1.30120i
$695$	−2047.44	+	3064.21i	−0.111746	+	0.167240i
$696$	18355.2	+	8313.94i	0.999644	+	0.452786i
$697$	41552.2	−	27764.3i	2.25811	−	1.50882i
$698$	6142.95	+	1502.91i	0.333115	+	0.0814983i
$699$	1721.31	−	17476.8i	0.0931417	−	0.945683i
$700$	−14224.6	+	7805.37i	−0.768055	+	0.421450i
$701$	−2841.55	+	9367.33i	−0.153101	+	0.504706i	−0.999617	−	0.0276561i	$-0.991196\pi$
$701$	−2841.55	+	9367.33i	−0.153101	+	0.504706i	0.846516	+	0.532363i	$0.178696\pi$
$702$	583.231	+	10674.8i	0.0313570	+	0.573922i
$703$			83.1751i			0.00446232i
$704$	−8139.22	−	1341.76i	−0.435736	−	0.0718314i
$705$		−	3253.29i		−	0.173796i
$706$	−1389.12	+	75.8967i	−0.0740515	+	0.00404591i
$707$	−26.9481	+	88.8360i	−0.00143351	+	0.00472563i
$708$	−14671.4	−	4275.03i	−0.778792	−	0.226929i
$709$	−1390.05	+	14113.4i	−0.0736310	+	0.747588i	0.885503	+	0.464635i	$0.153814\pi$
$709$	−1390.05	+	14113.4i	−0.0736310	+	0.747588i	−0.959134	+	0.282954i	$0.908686\pi$
$710$	1120.55	−	4580.10i	0.0592300	−	0.242096i
$711$	−2598.47	+	1736.24i	−0.137061	+	0.0915812i
$712$	2501.85	−	2343.81i	0.131687	−	0.123368i
$713$	2480.12	−	3711.76i	0.130268	−	0.194960i
$714$	−23643.4	−	1031.33i	−1.23926	−	0.0540570i
$715$	1483.53	+	792.964i	0.0775957	+	0.0414757i
$716$	−5890.00	−	27999.3i	−0.307430	−	1.46143i
$717$	26138.7	−	2574.43i	1.36146	−	0.134092i
$718$	−29528.7	+	22152.5i	−1.53482	+	1.15143i
$719$	4967.63	−	11992.9i	0.257665	−	0.622058i	−0.741118	−	0.671375i	$-0.765704\pi$
$719$	4967.63	−	11992.9i	0.257665	−	0.622058i	0.998783	+	0.0493162i	$0.0157042\pi$
$720$	2782.56	+	1409.58i	0.144028	+	0.0729610i
$721$	−3879.03	−	9364.81i	−0.200364	−	0.483722i
$722$	−16690.9	−	9879.91i	−0.860350	−	0.509269i
$723$	−8013.46	−	6576.48i	−0.412205	−	0.338288i
$724$	9122.78	−	22727.6i	0.468295	−	1.16666i
$725$	23384.6	−	7093.64i	1.19791	−	0.363381i
$726$	10760.1	+	5016.98i	0.550061	+	0.256471i
$727$	4199.85	−	835.402i	0.214256	−	0.0426181i	−0.0867953	−	0.996226i	$-0.527663\pi$
$727$	4199.85	−	835.402i	0.214256	−	0.0426181i	0.301051	+	0.953608i	$0.402663\pi$
$728$	10632.7	−	698.202i	0.541310	−	0.0355455i
$729$	−3758.19	+	18893.7i	−0.190936	+	0.959900i
$730$	1979.46	+	12857.3i	0.100360	+	0.651876i
$731$	24048.6	−	19736.2i	1.21679	−	0.998591i
$732$	5618.64	+	2924.30i	0.283703	+	0.147657i
$733$	10771.1	+	20151.3i	0.542755	+	1.01542i	0.992497	+	0.122265i	$0.0390159\pi$
$733$	10771.1	+	20151.3i	0.542755	+	1.01542i	−0.449742	+	0.893158i	$0.648484\pi$
$734$	−9529.23	+	27101.0i	−0.479196	+	1.36283i
$735$	149.768	−	149.768i	0.00751600	−	0.00751600i
$736$	−30119.9	−	9852.48i	−1.50847	−	0.493434i
$737$	5279.64	+	5279.64i	0.263878	+	0.263878i
$738$	−13117.3	+	6292.46i	−0.654275	+	0.313860i
$739$	−32874.4	+	17571.7i	−1.63641	+	0.874677i	−0.642277	+	0.766472i	$0.722010\pi$
$739$	−32874.4	+	17571.7i	−1.63641	+	0.874677i	−0.994129	+	0.108205i	$0.965490\pi$
$740$	1451.39	+	1729.41i	0.0721001	+	0.0859114i
$741$	76.4763	+	93.1866i	0.00379140	+	0.00461983i
$742$	−13292.5	−	9745.64i	−0.657659	−	0.482175i
$743$	5786.31	+	1150.97i	0.285706	+	0.0568304i	0.335863	−	0.941911i	$-0.390972\pi$
$743$	5786.31	+	1150.97i	0.285706	+	0.0568304i	−0.0501571	+	0.998741i	$0.515972\pi$
$744$	294.774	−	2241.14i	0.0145255	−	0.110436i
$745$	2494.48	+	12540.6i	0.122672	+	0.616715i
$746$	10652.2	+	29263.0i	0.522794	+	1.43618i
$747$	−2982.10	−	9830.67i	−0.146063	−	0.481507i
$748$	−14590.5	+	160.348i	−0.713212	+	0.00783810i
$749$	−1103.92	+	1345.13i	−0.0538536	+	0.0656209i
$750$	−10438.8	+	2675.84i	−0.508230	+	0.130277i
$751$	−24306.7	+	10068.1i	−1.18104	+	0.489204i	−0.884828	−	0.465918i	$-0.845724\pi$
$751$	−24306.7	+	10068.1i	−1.18104	+	0.489204i	−0.296214	+	0.955122i	$0.595724\pi$
$752$	−7289.52	−	10406.9i	−0.353486	−	0.504656i
$753$	19074.2	+	7900.79i	0.923111	+	0.382365i
$754$	−15887.3	−	2267.51i	−0.767347	−	0.109520i
$755$	868.180	+	8814.78i	0.0418494	+	0.424904i
$756$	22462.8	+	4212.05i	1.08064	+	0.202634i
$757$	133.070	−	248.956i	0.00638904	−	0.0119530i	−0.878706	−	0.477362i	$-0.841593\pi$
$757$	133.070	−	248.956i	0.00638904	−	0.0119530i	0.885096	+	0.465409i	$0.154093\pi$
$758$	15132.5	−	13867.5i	0.725115	−	0.664500i
$759$	−9187.78	−	6139.08i	−0.439388	−	0.293590i
$760$	115.115	−	19.0200i	0.00549431	−	0.000907801i
$761$	−19630.8	−	29379.5i	−0.935104	−	1.39948i	−0.916667	−	0.399652i	$-0.869131\pi$
$761$	−19630.8	−	29379.5i	−0.935104	−	1.39948i	−0.0184372	−	0.999830i	$-0.505869\pi$
$762$	−6157.30	+	3736.68i	−0.292724	+	0.177645i
$763$	−3489.52	−	343.688i	−0.165569	−	0.0163071i
$764$	−35199.8	+	3857.89i	−1.66686	+	0.182688i
$765$	5279.87	+	1601.63i	0.249535	+	0.0756956i
$766$	−6902.10	+	7699.90i	−0.325565	+	0.363197i
$767$	12170.6			0.572955
$768$	−15884.9	+	2273.09i	−0.746352	+	0.106801i
$769$	−18022.9			−0.845152			−0.422576	−	0.906328i	$-0.638874\pi$
$769$	−18022.9			−0.845152			−0.422576	+	0.906328i	$0.638874\pi$
$770$	2400.30	−	2677.74i	0.112339	−	0.125324i
$771$	−7185.82	−	2179.80i	−0.335656	−	0.101820i
$772$	−16904.0	+	1852.68i	−0.788068	+	0.0863721i
$773$	−40511.8	−	3990.07i	−1.88501	−	0.185657i	−0.911035	−	0.412330i	$-0.864715\pi$
$773$	−40511.8	−	3990.07i	−1.88501	−	0.185657i	−0.973971	+	0.226673i	$0.927215\pi$
$774$	−7742.59	+	4698.75i	−0.359563	+	0.218208i
$775$	−1522.98	−	2279.31i	−0.0705900	−	0.105645i
$776$	−4613.38	−	27921.7i	−0.213416	−	1.29166i
$777$	4146.37	+	2770.51i	0.191442	+	0.127917i
$778$	20511.4	−	18796.8i	0.945204	−	0.866191i
$779$	−256.531	+	479.937i	−0.0117987	+	0.0220738i
$780$	3216.21	+	603.080i	0.147640	+	0.0276843i
$781$	−629.392	−	6390.33i	−0.0288367	−	0.292783i
$782$	−55493.3	−	7920.27i	−2.53764	−	0.362185i
$783$	−31800.5	−	13172.2i	−1.45141	−	0.601195i
$784$	143.512	−	814.668i	0.00653753	−	0.0371114i
$785$	−1080.68	+	447.631i	−0.0491350	+	0.0203524i
$786$	21973.2	−	5632.49i	0.997147	−	0.255603i
$787$	17786.2	−	21672.5i	0.805602	−	0.981629i	−0.194397	−	0.980923i	$-0.562275\pi$
$787$	17786.2	−	21672.5i	0.805602	−	0.981629i	1.00000		0.000706501i	$-0.000224886\pi$
$788$	23593.7	−	259.292i	1.06661	−	0.0117219i
$789$	6365.86	+	20985.4i	0.287238	+	0.946896i
$790$	1085.40	+	2981.72i	0.0488818	+	0.134285i
$791$	−429.063	−	2157.05i	−0.0192866	−	0.0969605i
$792$	4211.56	+	553.942i	0.188954	+	0.0248528i
$793$	−4947.71	−	984.160i	−0.221561	−	0.0440713i
$794$	23567.0	+	17278.6i	1.05335	+	0.772285i
$795$	−3211.07	−	3912.70i	−0.143251	−	0.174552i
$796$	10468.4	+	12473.7i	0.466134	+	0.555426i
$797$	26317.5	−	14067.0i	1.16965	−	0.625193i	0.231984	−	0.972720i	$-0.425478\pi$
$797$	26317.5	−	14067.0i	1.16965	−	0.625193i	0.937670	+	0.347526i	$0.112978\pi$
$798$	232.357	−	111.463i	0.0103075	−	0.00494456i
$799$	−15892.2	−	15892.2i	−0.703662	−	0.703662i
$800$	−12667.7	+	14772.7i	−0.559839	+	0.652867i
$801$	−1248.29	+	1248.29i	−0.0550640	+	0.0550640i
$802$	1346.52	−	3829.48i	0.0592859	−	0.168608i
$803$	8351.11	+	15623.8i	0.367004	+	0.686616i
$804$	12883.9	+	6705.62i	0.565151	+	0.294141i
$805$	10679.1	−	8764.13i	0.467565	−	0.383721i
$806$	273.937	+	1779.31i	0.0119715	+	0.0777589i
$807$	960.293	−	4827.72i	0.0418883	−	0.210587i
$808$	7.29565	+	111.103i	0.000317649	+	0.00483736i
$809$	43343.2	−	8621.51i	1.88364	−	0.374680i	0.887379	−	0.461040i	$-0.152524\pi$
$809$	43343.2	−	8621.51i	1.88364	−	0.374680i	0.996264	+	0.0863605i	$0.0275237\pi$
$810$	2987.63	+	1393.01i	0.129598	+	0.0604262i
$811$	28074.0	−	8516.15i	1.21555	−	0.368733i	0.383556	−	0.923518i	$-0.374699\pi$
$811$	28074.0	−	8516.15i	1.21555	−	0.368733i	0.831994	+	0.554785i	$0.187199\pi$
$812$	−12779.8	+	31838.4i	−0.552320	+	1.37600i
$813$	4283.14	+	3515.08i	0.184768	+	0.151635i
$814$	2645.86	+	1566.17i	0.113928	+	0.0674376i
$815$	−2674.35	−	6456.45i	−0.114943	−	0.277497i
$816$	−26974.5	+	8834.50i	−1.15723	+	0.379006i
$817$	−129.644	+	312.987i	−0.00555160	+	0.0134027i
$818$	16404.9	−	12307.0i	0.701203	−	0.526045i
$819$	−5460.64	+	537.826i	−0.232980	+	0.0229465i
$820$	3040.88	+	14455.5i	0.129503	+	0.615618i
$821$	−1204.95	−	644.062i	−0.0512219	−	0.0273787i	0.445587	−	0.895239i	$-0.352995\pi$
$821$	−1204.95	−	644.062i	−0.0512219	−	0.0273787i	−0.496809	+	0.867860i	$0.665495\pi$
$822$	−15816.8	−	689.936i	−0.671139	−	0.0292753i
$823$	6222.70	−	9312.93i	0.263560	−	0.394445i	−0.675961	−	0.736938i	$-0.736271\pi$
$823$	6222.70	−	9312.93i	0.263560	−	0.394445i	0.939521	+	0.342493i	$0.111271\pi$
$824$	−8311.75	−	8872.20i	−0.351400	−	0.375095i
$825$	−5642.00	+	3769.87i	−0.238096	+	0.159091i
$826$	6183.10	−	25272.7i	0.260457	−	1.06459i
$827$	−2817.21	+	28603.6i	−0.118457	+	1.20272i	0.733716	+	0.679456i	$0.237784\pi$
$827$	−2817.21	+	28603.6i	−0.118457	+	1.20272i	−0.852173	+	0.523260i	$0.824716\pi$
$828$	15667.3	+	4565.22i	0.657580	+	0.191609i
$829$	−3407.26	+	11232.2i	−0.142749	+	0.470581i	−0.998938	−	0.0460827i	$-0.985326\pi$
$829$	−3407.26	+	11232.2i	−0.142749	+	0.470581i	0.856188	+	0.516664i	$0.172826\pi$
$830$	−10415.2	+	569.048i	−0.435562	+	0.0237975i
$831$		−	17345.3i		−	0.724069i
$832$	11639.6	−	5277.25i	0.485013	−	0.219899i
$833$		−	1463.22i		−	0.0608614i
$834$	532.610	+	9748.28i	0.0221137	+	0.404742i
$835$	−2491.21	+	8212.42i	−0.103248	+	0.340362i
$836$	139.299	−	76.4368i	0.00576287	−	0.00316223i
$837$	−378.470	+	3842.67i	−0.0156294	+	0.158688i
$838$	33227.5	+	8129.29i	1.36972	+	0.335109i
$839$	−4597.10	+	3071.69i	−0.189165	+	0.126396i	−0.646547	−	0.762874i	$-0.723787\pi$
$839$	−4597.10	+	3071.69i	−0.189165	+	0.126396i	0.457381	+	0.889271i	$0.348787\pi$
$840$	2886.26	−	6372.17i	0.118554	−	0.261739i
$841$	15156.6	−	22683.5i	0.621453	−	0.930069i
$842$	1575.83	−	36126.1i	0.0644973	−	1.47861i
$843$	22066.6	+	11794.8i	0.901558	+	0.481893i
$844$	12699.2	−	19465.5i	0.517921	−	0.793873i
$845$	6551.82	−	645.298i	0.266733	−	0.0262709i
$846$	3926.41	+	5233.81i	0.159566	+	0.212697i
$847$	−7735.33	+	18674.7i	−0.313801	+	0.757582i
$848$	−19038.9	−	5321.38i	−0.770988	−	0.215491i
$849$	−3752.74	−	9059.90i	−0.151700	−	0.366237i
$850$	−17534.2	+	29621.9i	−0.707550	+	1.19532i
$851$	9130.67	+	7493.35i	0.367797	+	0.301843i
$852$	−4906.67	−	11487.1i	−0.197300	−	0.461902i
$853$	−29356.9	+	8905.31i	−1.17838	+	0.357459i	−0.817929	−	0.575319i	$-0.804878\pi$
$853$	−29356.9	+	8905.31i	−1.17838	+	0.357459i	−0.360453	+	0.932777i	$0.617378\pi$
$854$	−4557.24	+	9774.07i	−0.182606	+	0.391641i
$855$	−58.9276	+	11.7214i	−0.00235705	+	0.000468847i
$856$	−670.623	+	1976.38i	−0.0267774	+	0.0789151i
$857$	4642.39	−	23338.9i	0.185042	−	0.930269i	−0.770954	−	0.636891i	$-0.780220\pi$
$857$	4642.39	−	23338.9i	0.185042	−	0.930269i	0.955996	−	0.293379i	$-0.0947797\pi$
$858$	4404.36	−	678.079i	0.175248	−	0.0269805i
$859$	−2345.97	+	1925.29i	−0.0931821	+	0.0764726i	−0.679831	−	0.733369i	$-0.737947\pi$
$859$	−2345.97	+	1925.29i	−0.0931821	+	0.0764726i	0.586649	+	0.809841i	$0.300447\pi$
$860$	2765.96	+	8770.01i	0.109672	+	0.347738i
$861$	15380.4	+	28774.8i	0.608785	+	1.13896i
$862$	−7199.86	−	2531.61i	−0.284487	−	0.100031i
$863$	−6410.45	+	6410.45i	−0.252855	+	0.252855i	−0.822140	−	0.569285i	$-0.807220\pi$
$863$	−6410.45	+	6410.45i	−0.252855	+	0.252855i	0.569285	+	0.822140i	$0.307220\pi$
$864$	26993.5	−	4765.32i	1.06289	−	0.187638i
$865$	−7301.01	−	7301.01i	−0.286985	−	0.286985i
$866$	−12025.6	−	25068.6i	−0.471877	−	0.983679i
$867$	−27304.6	+	14594.6i	−1.06956	+	0.571694i
$868$	3833.97	+	335.115i	0.149923	+	0.0131043i
$869$	2741.37	+	3340.37i	0.107013	+	0.130396i
$870$	−6229.48	+	8496.66i	−0.242758	+	0.331108i
$871$	−11345.4	−	2256.75i	−0.441361	−	0.0877921i
$872$	−4062.07	+	1088.96i	−0.157751	+	0.0422898i
$873$	2843.08	+	14293.1i	0.110222	+	0.554122i
$874$	573.594	−	208.798i	0.0221992	−	0.00808088i
$875$	−5326.02	−	17557.5i	−0.205774	−	0.678346i
$876$	24634.6	+	24099.0i	0.950142	+	0.929485i
$877$	−4250.87	+	5179.70i	−0.163674	+	0.199437i	−0.848388	−	0.529374i	$-0.822427\pi$
$877$	−4250.87	+	5179.70i	−0.163674	+	0.199437i	0.684715	+	0.728811i	$0.259927\pi$
$878$	−8314.79	−	32437.2i	−0.319602	−	1.24682i
$879$	−29536.8	+	12234.6i	−1.13339	+	0.469467i
$880$	1562.56	−	4020.04i	0.0598566	−	0.153995i
$881$	13866.2	+	5743.58i	0.530267	+	0.219644i	0.631720	−	0.775197i	$-0.282349\pi$
$881$	13866.2	+	5743.58i	0.530267	+	0.219644i	−0.101453	+	0.994840i	$0.532349\pi$
$882$	−60.1867	+	421.697i	−0.00229772	+	0.0160990i
$883$	−379.433	−	3852.45i	−0.0144609	−	0.146824i	0.985243	−	0.171162i	$-0.0547521\pi$
$883$	−379.433	−	3852.45i	−0.0144609	−	0.146824i	−0.999704	+	0.0243383i	$0.992252\pi$
$884$	18657.1	−	12765.1i	0.709849	−	0.485673i
$885$	3766.45	−	7046.54i	0.143060	−	0.267646i
$886$	−33123.5	−	36145.0i	−1.25599	−	1.37056i
$887$	−42947.5	−	28696.6i	−1.62575	−	1.08629i	−0.929718	−	0.368273i	$-0.879949\pi$
$887$	−42947.5	−	28696.6i	−1.62575	−	1.08629i	−0.696028	−	0.718015i	$-0.745051\pi$
$888$	5824.97	+	1357.44i	0.220127	+	0.0512983i
$889$	−6812.80	−	10196.1i	−0.257024	−	0.384663i
$890$	929.939	+	1532.35i	0.0350243	+	0.0577130i
$891$	4467.53	+	440.014i	0.167978	+	0.0165443i
$892$	−1318.10	−	1057.71i	−0.0494768	−	0.0397027i
$893$	234.202	+	71.0444i	0.00877634	+	0.00266227i
$894$	25222.5	+	22609.2i	0.943588	+	0.845821i
$895$	14959.9			0.558720
$896$	−5045.05	−	26851.0i	−0.188106	−	1.00115i
$897$	17119.5			0.637240
$898$	10165.1	+	9111.86i	0.377743	+	0.338604i
$899$	−5546.72	−	1682.58i	−0.205777	−	0.0624218i
$900$	6271.77	−	7815.76i	0.232288	−	0.289472i
$901$	−34799.3	−	3427.43i	−1.28672	−	0.126731i
$902$	10436.7	+	17197.5i	0.385259	+	0.634829i
$903$	11284.4	+	16888.3i	0.415860	+	0.622378i
$904$	−1393.21	−	2239.85i	−0.0512582	−	0.0824075i
$905$	10646.8	+	7113.93i	0.391061	+	0.261298i
$906$	15853.1	+	17299.2i	0.581328	+	0.634356i
$907$	−798.346	+	1493.60i	−0.0292267	+	0.0546794i	−0.896111	−	0.443830i	$-0.853619\pi$
$907$	−798.346	+	1493.60i	−0.0292267	+	0.0546794i	0.866884	+	0.498510i	$0.166119\pi$
$908$	16223.5	+	23711.9i	0.592946	+	0.866636i
$909$	−5.61985	−	57.0593i	−0.000205059	−	0.00208200i
$910$	−787.185	+	5515.40i	−0.0286757	+	0.200916i
$911$	−26227.4	−	10863.7i	−0.953844	−	0.395095i	−0.149170	−	0.988812i	$-0.547660\pi$
$911$	−26227.4	−	10863.7i	−0.953844	−	0.395095i	−0.804674	+	0.593717i	$0.797660\pi$
$912$	213.704	−	223.310i	0.00775925	−	0.00810805i
$913$	−13123.5	+	5435.95i	−0.475713	+	0.197047i
$914$	−8935.41	−	34858.4i	−0.323367	−	1.26150i
$915$	−2100.98	+	2560.05i	−0.0759084	+	0.0924946i
$916$	−30675.8	+	31357.6i	−1.10650	+	1.13110i
$917$	11211.0	+	36957.7i	0.403729	+	1.33092i
$918$	45561.1	−	16585.0i	1.63806	−	0.596281i
$919$	3649.63	+	18347.9i	0.131001	+	0.658588i	0.989354	+	0.145528i	$0.0464881\pi$
$919$	3649.63	+	18347.9i	0.131001	+	0.658588i	−0.858353	+	0.513060i	$0.828512\pi$
$920$	8282.94	−	14350.5i	0.296826	−	0.514263i
$921$	−27463.8	−	5462.88i	−0.982586	−	0.195449i
$922$	23769.9	−	32420.9i	0.849047	−	1.15805i
$923$	6311.11	+	7690.11i	0.225063	+	0.274239i
$924$	829.516	−	9490.27i	0.0295336	−	0.337886i
$925$	6396.90	−	3419.22i	0.227383	−	0.121539i
$926$	−22058.2	−	45982.7i	−0.782805	−	1.63184i
$927$	4426.77	+	4426.77i	0.156844	+	0.156844i
$928$	−889.289	+	41138.0i	−0.0314573	+	1.45520i
$929$	3479.70	−	3479.70i	0.122891	−	0.122891i	−0.642987	−	0.765877i	$-0.722305\pi$
$929$	3479.70	−	3479.70i	0.122891	−	0.122891i	0.765877	+	0.642987i	$0.222305\pi$
$930$	1114.96	+	392.042i	0.0393129	+	0.0138232i
$931$	7.51107	+	14.0522i	0.000264410	+	0.000494676i
$932$	34200.2	−	10786.3i	1.20200	−	0.379097i
$933$	10814.2	−	8874.95i	0.379464	−	0.311418i
$934$	20652.5	−	3179.58i	0.723523	−	0.111391i
$935$	1488.37	−	7482.55i	0.0520588	−	0.261717i
$936$	−5902.01	+	2911.44i	−0.206104	+	0.101670i
$937$	−25269.8	+	5026.47i	−0.881032	+	0.175248i	−0.614821	−	0.788667i	$-0.710772\pi$
$937$	−25269.8	+	5026.47i	−0.881032	+	0.175248i	−0.266211	+	0.963915i	$0.585772\pi$
$938$	−10450.1	+	22412.6i	−0.363760	+	0.780168i
$939$	14923.9	−	4527.10i	0.518660	−	0.157334i
$940$	6109.33	−	2609.59i	0.211983	−	0.0905482i
$941$	−14192.0	−	11647.1i	−0.491653	−	0.403489i	0.355633	−	0.934626i	$-0.384265\pi$
$941$	−14192.0	−	11647.1i	−0.491653	−	0.403489i	−0.847286	+	0.531136i	$0.821765\pi$
$942$	−1578.44	+	2666.58i	−0.0545948	+	0.0922314i
$943$	29574.5	+	71399.2i	1.02129	+	2.46562i
$944$	−3740.43	−	30980.5i	−0.128963	−	1.06814i
$945$	−4572.84	+	11039.8i	−0.157412	+	0.380026i
$946$	7515.18	+	10017.5i	0.258287	+	0.344290i
$947$	40414.0	−	3980.43i	1.38678	−	0.136586i	0.623079	−	0.782159i	$-0.285881\pi$
$947$	40414.0	−	3980.43i	1.38678	−	0.136586i	0.763698	+	0.645573i	$0.223381\pi$
$948$	7040.26	+	4593.05i	0.241199	+	0.157358i
$949$	−24205.6	−	12938.1i	−0.827972	−	0.442560i
$950$	16.3352	−	374.486i	0.000557877	−	0.0127894i
$951$	−10200.2	+	15265.7i	−0.347808	+	0.520532i
$952$	−17028.6	−	45227.1i	−0.579726	−	1.53973i
$953$	731.753	−	488.942i	0.0248728	−	0.0166195i	−0.543072	−	0.839686i	$-0.682739\pi$
$953$	731.753	−	488.942i	0.0248728	−	0.0166195i	0.567944	+	0.823067i	$0.307739\pi$
$954$	9888.13	+	2419.18i	0.335577	+	0.0821006i
$955$	1814.74	−	18425.3i	0.0614906	−	0.624324i
$956$	25801.3	+	47020.5i	0.872881	+	1.59075i
$957$	−4164.91	+	13729.9i	−0.140682	+	0.463766i
$958$	−100.414	−	1837.87i	−0.00338647	−	0.0619821i
$959$		−	26955.0i		−	0.907637i
$960$	546.700	−	8372.24i	0.0183799	−	0.281472i
$961$		−	29140.8i		−	0.978174i
$962$	−4756.37	+	259.871i	−0.159409	+	0.00870953i
$963$	311.976	−	1028.45i	0.0104396	−	0.0344146i
$964$	5922.02	−	20323.7i	0.197858	−	0.679026i
$965$	871.492	−	8848.40i	0.0290718	−	0.295171i
$966$	8697.31	−	35549.2i	0.289680	−	1.18403i
$967$	20380.2	−	13617.6i	0.677748	−	0.452857i	−0.168461	−	0.985708i	$-0.553880\pi$
$967$	20380.2	−	13617.6i	0.677748	−	0.452857i	0.846209	+	0.532852i	$0.178880\pi$
$968$	−790.276	+	24230.6i	−0.0262401	+	0.804546i
$969$	303.750	−	454.594i	0.0100700	−	0.0150709i
$970$	14782.8	+	644.830i	0.489327	+	0.0213446i
$971$	50139.5	+	26800.1i	1.65711	+	0.885743i	0.990047	+	0.140740i	$0.0449483\pi$
$971$	50139.5	+	26800.1i	1.65711	+	0.885743i	0.667062	+	0.745002i	$0.267552\pi$
$972$	−23461.7	+	4935.45i	−0.774212	+	0.162865i
$973$	−16541.9	+	1629.24i	−0.545026	+	0.0536803i
$974$	−24296.1	+	18227.0i	−0.799279	+	0.599621i
$975$	4023.04	−	9712.48i	0.132144	−	0.319024i
$976$	−984.597	+	12896.9i	−0.0322912	+	0.422971i
$977$	2321.27	+	5604.05i	0.0760124	+	0.183510i	0.957318	−	0.289036i	$-0.0933348\pi$
$977$	2321.27	+	5604.05i	0.0760124	+	0.183510i	−0.881306	+	0.472547i	$0.843335\pi$
$978$	−15931.4	−	9430.30i	−0.520889	−	0.308331i
$979$	1886.92	+	1548.56i	0.0616000	+	0.0505538i
$980$	401.382	+	161.113i	0.0130833	+	0.00525160i
$981$	2072.36	−	628.643i	0.0674468	−	0.0204598i
$982$	32085.4	+	14960.1i	1.04266	+	0.486147i
$983$	29587.5	−	5885.32i	0.960016	−	0.190959i	0.309879	−	0.950776i	$-0.399712\pi$
$983$	29587.5	−	5885.32i	0.960016	−	0.190959i	0.650137	+	0.759817i	$0.274712\pi$
$984$	29424.5	+	25798.3i	0.953272	+	0.835792i
$985$	−2406.78	+	12099.7i	−0.0778544	+	0.391400i
$986$	11075.1	+	71936.6i	0.357711	+	2.32346i
$987$	11342.8	−	9308.77i	0.365800	−	0.300204i
$988$	−113.650	+	218.363i	−0.00365960	+	0.00703142i
$989$	22678.9	+	42429.2i	0.729168	+	1.36418i
$990$	−736.727	+	2095.24i	−0.0236512	+	0.0672637i
$991$	−34815.8	+	34815.8i	−1.11600	+	1.11600i	−0.123682	+	0.992322i	$0.539470\pi$
$991$	−34815.8	+	34815.8i	−1.11600	+	1.11600i	−0.992322	+	0.123682i	$0.960530\pi$
$992$	4445.07	−	1244.15i	0.142269	−	0.0398203i
$993$	−5027.21	−	5027.21i	−0.160658	−	0.160658i
$994$	19175.0	−	9198.36i	0.611865	−	0.293515i
$995$	−7508.96	+	4013.62i	−0.239246	+	0.127880i
$996$	−21166.2	+	17763.4i	−0.673369	+	0.565117i
$997$	−23117.7	−	28168.9i	−0.734346	−	0.894804i	0.263205	−	0.964740i	$-0.415220\pi$
$997$	−23117.7	−	28168.9i	−0.734346	−	0.894804i	−0.997551	+	0.0699362i	$0.977720\pi$
$998$	8645.03	+	6338.26i	0.274202	+	0.201036i
$999$	−10020.4	−	1993.19i	−0.317350	−	0.0631249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.k.a.5.13	✓	752
128.77	even	32	inner	128.4.k.a.77.13	yes	752

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.4.k.a.5.13	✓	752	1.1	even	1	trivial
128.4.k.a.77.13	yes	752	128.77	even	32	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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.k (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.88791 + 2.10613i) q^{2} +(-3.74897 - 1.13724i) q^{3} +(-0.871580 - 7.95238i) q^{4} +(4.16267 + 0.409988i) q^{5} +(9.47289 - 5.74882i) q^{6} +(10.4814 + 15.6865i) q^{7} +(18.3942 + 13.1777i) q^{8} +(-9.68822 - 6.47346i) q^{9} +O(q^{10})\)	\(q+(-1.88791 + 2.10613i) q^{2} +(-3.74897 - 1.13724i) q^{3} +(-0.871580 - 7.95238i) q^{4} +(4.16267 + 0.409988i) q^{5} +(9.47289 - 5.74882i) q^{6} +(10.4814 + 15.6865i) q^{7} +(18.3942 + 13.1777i) q^{8} +(-9.68822 - 6.47346i) q^{9} +(-8.72225 + 7.99312i) q^{10} +(-7.59489 + 14.2090i) q^{11} +(-5.77622 + 30.8044i) q^{12} +(-2.44661 - 24.8409i) q^{13} +(-52.8257 - 7.53955i) q^{14} +(-15.1395 - 6.27098i) q^{15} +(-62.4807 + 13.8623i) q^{16} +(-104.589 + 43.3223i) q^{17} +(31.9245 - 8.18334i) q^{18} +(0.782054 - 0.952936i) q^{19} +(-0.367726 - 33.4605i) q^{20} +(-21.4551 - 70.7280i) q^{21} +(-15.5876 - 42.8213i) q^{22} +(-34.1537 - 171.702i) q^{23} +(-53.9732 - 70.3215i) q^{24} +(-105.438 - 20.9730i) q^{25} +(56.9371 + 41.7445i) q^{26} +(96.0631 + 117.053i) q^{27} +(115.610 - 97.0239i) q^{28} +(-200.470 + 107.154i) q^{29} +(41.7895 - 20.0467i) q^{30} +(18.0309 + 18.0309i) q^{31} +(88.7623 - 157.763i) q^{32} +(44.6321 - 44.6321i) q^{33} +(106.213 - 302.068i) q^{34} +(37.1993 + 69.5950i) q^{35} +(-43.0354 + 82.6866i) q^{36} +(-52.1555 + 42.8030i) q^{37} +(0.530559 + 3.44617i) q^{38} +(-19.0777 + 95.9100i) q^{39} +(71.1665 + 62.3960i) q^{40} +(-432.962 + 86.1215i) q^{41} +(189.468 + 88.3409i) q^{42} +(-262.977 + 79.7732i) q^{43} +(119.615 + 48.0132i) q^{44} +(-37.6749 - 30.9190i) q^{45} +(426.107 + 252.227i) q^{46} +(75.9743 + 183.418i) q^{47} +(250.003 + 19.0862i) q^{48} +(-4.94626 + 11.9413i) q^{49} +(243.230 - 182.472i) q^{50} +(441.370 - 43.4711i) q^{51} +(-195.412 + 41.1072i) q^{52} +(272.411 + 145.607i) q^{53} +(-427.888 - 18.6646i) q^{54} +(-37.4406 + 56.0338i) q^{55} +(-13.9155 + 426.662i) q^{56} +(-4.01561 + 2.68315i) q^{57} +(152.791 - 624.513i) q^{58} +(-47.7917 + 485.237i) q^{59} +(-36.6739 + 125.861i) q^{60} +(58.6666 - 193.398i) q^{61} +(-72.0161 + 3.93470i) q^{62} -219.825i q^{63} +(164.695 + 484.788i) q^{64} -104.407i q^{65} +(9.73961 + 178.262i) q^{66} +(134.527 - 443.475i) q^{67} +(435.674 + 793.975i) q^{68} +(-67.2251 + 682.547i) q^{69} +(-216.805 - 53.0426i) q^{70} +(-331.383 + 221.423i) q^{71} +(-92.9018 - 246.743i) q^{72} +(610.888 - 914.258i) q^{73} +(8.31641 - 190.655i) q^{74} +(371.434 + 198.536i) q^{75} +(-8.25973 - 5.38863i) q^{76} +(-302.495 + 29.7932i) q^{77} +(-165.982 - 221.250i) q^{78} +(102.639 - 247.793i) q^{79} +(-265.770 + 32.0878i) q^{80} +(-106.627 - 257.421i) q^{81} +(636.011 - 1074.46i) q^{82} +(681.532 + 559.319i) q^{83} +(-543.756 + 232.264i) q^{84} +(-453.133 + 137.456i) q^{85} +(328.465 - 704.469i) q^{86} +(873.415 - 173.733i) q^{87} +(-326.945 + 161.281i) q^{88} +(29.5576 - 148.596i) q^{89} +(136.246 - 20.9760i) q^{90} +(364.022 - 298.745i) q^{91} +(-1335.67 + 421.256i) q^{92} +(-47.0918 - 88.1025i) q^{93} +(-529.736 - 186.266i) q^{94} +(3.64613 - 3.64613i) q^{95} +(-512.181 + 490.506i) q^{96} +(-884.383 - 884.383i) q^{97} +(-15.8119 - 32.9616i) q^{98} +(165.563 - 88.4951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 5696 q^{50} - 16 q^{51} + 6608 q^{52} - 16 q^{53} + 3440 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 4768 q^{58} - 16 q^{59} - 9808 q^{60} - 16 q^{61} - 5872 q^{62} - 12112 q^{64} - 10960 q^{66} - 16 q^{67} - 4144 q^{68} - 16 q^{69} - 4048 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 5248 q^{74} - 16 q^{75} + 11888 q^{76} - 16 q^{77} + 14096 q^{78} - 16 q^{79} + 10016 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 5696 * q^50 - 16 * q^51 + 6608 * q^52 - 16 * q^53 + 3440 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 4768 * q^58 - 16 * q^59 - 9808 * q^60 - 16 * q^61 - 5872 * q^62 - 12112 * q^64 - 10960 * q^66 - 16 * q^67 - 4144 * q^68 - 16 * q^69 - 4048 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 5248 * q^74 - 16 * q^75 + 11888 * q^76 - 16 * q^77 + 14096 * q^78 - 16 * q^79 + 10016 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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