LMFDB - Embedded newform 804.2.c.b.671.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(671,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("804.671");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.c (of order $2$, degree $1$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$128$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			671.8
Character	$\chi$	$=$	804.671
Dual form			804.2.c.b.671.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39093 + 0.255554i) q^{2} +(1.65649 + 0.506011i) q^{3} +(1.86938 - 0.710916i) q^{4} +2.60371i q^{5} +(-2.43338 - 0.280506i) q^{6} +2.89039i q^{7} +(-2.41851 + 1.46656i) q^{8} +(2.48790 + 1.67640i) q^{9} +O(q^{10})$	\(q+(-1.39093 + 0.255554i) q^{2} +(1.65649 + 0.506011i) q^{3} +(1.86938 - 0.710916i) q^{4} +2.60371i q^{5} +(-2.43338 - 0.280506i) q^{6} +2.89039i q^{7} +(-2.41851 + 1.46656i) q^{8} +(2.48790 + 1.67640i) q^{9} +(-0.665387 - 3.62158i) q^{10} +3.13662 q^{11} +(3.45634 - 0.231693i) q^{12} +5.12990 q^{13} +(-0.738650 - 4.02034i) q^{14} +(-1.31750 + 4.31301i) q^{15} +(2.98920 - 2.65795i) q^{16} -0.537965i q^{17} +(-3.88892 - 1.69597i) q^{18} -8.08261i q^{19} +(1.85102 + 4.86733i) q^{20} +(-1.46257 + 4.78790i) q^{21} +(-4.36282 + 0.801574i) q^{22} -5.12854 q^{23} +(-4.74833 + 1.20555i) q^{24} -1.77929 q^{25} +(-7.13534 + 1.31096i) q^{26} +(3.27291 + 4.03585i) q^{27} +(2.05482 + 5.40325i) q^{28} +4.94932i q^{29} +(0.730355 - 6.33579i) q^{30} +0.241206i q^{31} +(-3.47852 + 4.46093i) q^{32} +(5.19577 + 1.58716i) q^{33} +(0.137479 + 0.748273i) q^{34} -7.52573 q^{35} +(5.84263 + 1.36515i) q^{36} -9.79271 q^{37} +(2.06554 + 11.2424i) q^{38} +(8.49762 + 2.59579i) q^{39} +(-3.81850 - 6.29709i) q^{40} +4.04845i q^{41} +(0.810771 - 7.03340i) q^{42} -3.02636i q^{43} +(5.86354 - 2.22987i) q^{44} +(-4.36486 + 6.47777i) q^{45} +(7.13345 - 1.31062i) q^{46} -11.7709 q^{47} +(6.29652 - 2.89029i) q^{48} -1.35435 q^{49} +(2.47486 - 0.454703i) q^{50} +(0.272216 - 0.891132i) q^{51} +(9.58976 - 3.64693i) q^{52} -13.6619i q^{53} +(-5.58377 - 4.77719i) q^{54} +8.16683i q^{55} +(-4.23894 - 6.99044i) q^{56} +(4.08989 - 13.3888i) q^{57} +(-1.26482 - 6.88416i) q^{58} +9.66333 q^{59} +(0.603261 + 8.99931i) q^{60} +10.5873 q^{61} +(-0.0616412 - 0.335502i) q^{62} +(-4.84546 + 7.19101i) q^{63} +(3.69838 - 7.09380i) q^{64} +13.3568i q^{65} +(-7.63257 - 0.879840i) q^{66} +1.00000i q^{67} +(-0.382448 - 1.00566i) q^{68} +(-8.49536 - 2.59510i) q^{69} +(10.4678 - 1.92323i) q^{70} +4.47112 q^{71} +(-8.47558 - 0.405728i) q^{72} -2.88507 q^{73} +(13.6210 - 2.50256i) q^{74} +(-2.94736 - 0.900339i) q^{75} +(-5.74606 - 15.1095i) q^{76} +9.06605i q^{77} +(-12.4830 - 1.43897i) q^{78} +10.8286i q^{79} +(6.92052 + 7.78299i) q^{80} +(3.37934 + 8.34147i) q^{81} +(-1.03460 - 5.63112i) q^{82} -7.05254 q^{83} +(0.669684 + 9.99018i) q^{84} +1.40070 q^{85} +(0.773396 + 4.20945i) q^{86} +(-2.50441 + 8.19848i) q^{87} +(-7.58594 + 4.60005i) q^{88} -7.16263i q^{89} +(4.41581 - 10.1256i) q^{90} +14.8274i q^{91} +(-9.58721 + 3.64596i) q^{92} +(-0.122053 + 0.399556i) q^{93} +(16.3726 - 3.00810i) q^{94} +21.0447 q^{95} +(-8.01941 + 5.62930i) q^{96} -5.26621 q^{97} +(1.88381 - 0.346110i) q^{98} +(7.80360 + 5.25824i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.39093	+	0.255554i	−0.983538	+	0.180704i
$2$	−1.39093	+	0.255554i	−0.983538	+	0.180704i
$3$	1.65649	+	0.506011i	0.956374	+	0.292146i
$3$	1.65649	+	0.506011i	0.956374	+	0.292146i
$4$	1.86938	−	0.710916i	0.934692	−	0.355458i
$5$			2.60371i			1.16441i	0.813041	+	0.582206i	$0.197810\pi$
$5$			2.60371i			1.16441i	−0.813041	+	0.582206i	$0.802190\pi$
$6$	−2.43338	−	0.280506i	−0.993421	−	0.114516i
$7$			2.89039i			1.09246i	0.837634	+	0.546232i	$0.183938\pi$
$7$			2.89039i			1.09246i	−0.837634	+	0.546232i	$0.816062\pi$
$8$	−2.41851	+	1.46656i	−0.855072	+	0.518509i
$9$	2.48790	+	1.67640i	0.829302	+	0.558801i
$10$	−0.665387	−	3.62158i	−0.210414	−	1.14524i
$11$	3.13662			0.945726			0.472863	−	0.881136i	$-0.343221\pi$
$11$	3.13662			0.945726			0.472863	+	0.881136i	$0.343221\pi$
$12$	3.45634	−	0.231693i	0.997761	−	0.0668841i
$13$	5.12990			1.42278			0.711389	−	0.702798i	$-0.248066\pi$
$13$	5.12990			1.42278			0.711389	+	0.702798i	$0.248066\pi$
$14$	−0.738650	−	4.02034i	−0.197412	−	1.07448i
$15$	−1.31750	+	4.31301i	−0.340178	+	1.11361i
$16$	2.98920	−	2.65795i	0.747299	−	0.664487i
$17$		−	0.537965i		−	0.130476i	−0.997870	−	0.0652378i	$-0.979219\pi$
$17$		−	0.537965i		−	0.130476i	0.997870	−	0.0652378i	$-0.0207806\pi$
$18$	−3.88892	−	1.69597i	−0.916627	−	0.399744i
$19$		−	8.08261i		−	1.85428i	−0.374717	−	0.927139i	$-0.622260\pi$
$19$		−	8.08261i		−	1.85428i	0.374717	−	0.927139i	$-0.377740\pi$
$20$	1.85102	+	4.86733i	0.413900	+	1.08837i
$21$	−1.46257	+	4.78790i	−0.319159	+	1.04480i
$22$	−4.36282	+	0.801574i	−0.930157	+	0.170896i
$23$	−5.12854			−1.06937			−0.534687	−	0.845050i	$-0.679571\pi$
$23$	−5.12854			−1.06937			−0.534687	+	0.845050i	$0.679571\pi$
$24$	−4.74833	+	1.20555i	−0.969249	+	0.246082i
$25$	−1.77929			−0.355857
$26$	−7.13534	+	1.31096i	−1.39936	+	0.257101i
$27$	3.27291	+	4.03585i	0.629871	+	0.776700i
$28$	2.05482	+	5.40325i	0.388325	+	1.02112i
$29$			4.94932i			0.919065i	0.888161	+	0.459533i	$0.151983\pi$
$29$			4.94932i			0.919065i	−0.888161	+	0.459533i	$0.848017\pi$
$30$	0.730355	−	6.33579i	0.133344	−	1.15675i
$31$			0.241206i			0.0433220i	0.999765	+	0.0216610i	$0.00689544\pi$
$31$			0.241206i			0.0433220i	−0.999765	+	0.0216610i	$0.993105\pi$
$32$	−3.47852	+	4.46093i	−0.614922	+	0.788588i
$33$	5.19577	+	1.58716i	0.904467	+	0.276290i
$34$	0.137479	+	0.748273i	0.0235774	+	0.128328i
$35$	−7.52573			−1.27208
$36$	5.84263	+	1.36515i	0.973772	+	0.227525i
$37$	−9.79271			−1.60991			−0.804956	−	0.593335i	$-0.797811\pi$
$37$	−9.79271			−1.60991			−0.804956	+	0.593335i	$0.797811\pi$
$38$	2.06554	+	11.2424i	0.335075	+	1.82375i
$39$	8.49762	+	2.59579i	1.36071	+	0.415659i
$40$	−3.81850	−	6.29709i	−0.603758	−	0.995657i
$41$			4.04845i			0.632262i	0.948716	+	0.316131i	$0.102384\pi$
$41$			4.04845i			0.632262i	−0.948716	+	0.316131i	$0.897616\pi$
$42$	0.810771	−	7.03340i	0.125105	−	1.08528i
$43$		−	3.02636i		−	0.461515i	−0.973011	−	0.230757i	$-0.925880\pi$
$43$		−	3.02636i		−	0.461515i	0.973011	−	0.230757i	$-0.0741204\pi$
$44$	5.86354	−	2.22987i	0.883962	−	0.336166i
$45$	−4.36486	+	6.47777i	−0.650675	+	0.965649i
$46$	7.13345	−	1.31062i	1.05177	−	0.193240i
$47$	−11.7709			−1.71697			−0.858483	−	0.512842i	$-0.828593\pi$
$47$	−11.7709			−1.71697			−0.858483	+	0.512842i	$0.828593\pi$
$48$	6.29652	−	2.89029i	0.908825	−	0.417178i
$49$	−1.35435			−0.193479
$50$	2.47486	−	0.454703i	0.349999	−	0.0643047i
$51$	0.272216	−	0.891132i	0.0381179	−	0.124783i
$52$	9.58976	−	3.64693i	1.32986	−	0.505738i
$53$		−	13.6619i		−	1.87660i	−0.345819	−	0.938301i	$-0.612399\pi$
$53$		−	13.6619i		−	1.87660i	0.345819	−	0.938301i	$-0.387601\pi$
$54$	−5.58377	−	4.77719i	−0.759854	−	0.650093i
$55$			8.16683i			1.10121i
$56$	−4.23894	−	6.99044i	−0.566452	−	0.934136i
$57$	4.08989	−	13.3888i	0.541720	−	1.77338i
$58$	−1.26482	−	6.88416i	−0.166078	−	0.903935i
$59$	9.66333			1.25806			0.629029	−	0.777382i	$-0.283453\pi$
$59$	9.66333			1.25806			0.629029	+	0.777382i	$0.283453\pi$
$60$	0.603261	+	8.99931i	0.0778807	+	1.16181i
$61$	10.5873			1.35556			0.677780	−	0.735265i	$-0.262942\pi$
$61$	10.5873			1.35556			0.677780	+	0.735265i	$0.262942\pi$
$62$	−0.0616412	−	0.335502i	−0.00782844	−	0.0426088i
$63$	−4.84546	+	7.19101i	−0.610471	+	0.905983i
$64$	3.69838	−	7.09380i	0.462298	−	0.886725i
$65$			13.3568i			1.65670i
$66$	−7.63257	−	0.879840i	−0.939504	−	0.108301i
$67$			1.00000i			0.122169i
$67$			1.00000i			0.122169i
$68$	−0.382448	−	1.00566i	−0.0463786	−	0.121955i
$69$	−8.49536	−	2.59510i	−1.02272	−	0.312413i
$70$	10.4678	−	1.92323i	1.25114	−	0.229870i
$71$	4.47112			0.530624			0.265312	−	0.964163i	$-0.414525\pi$
$71$	4.47112			0.530624			0.265312	+	0.964163i	$0.414525\pi$
$72$	−8.47558	−	0.405728i	−0.998856	−	0.0478155i
$73$	−2.88507			−0.337671			−0.168836	−	0.985644i	$-0.554001\pi$
$73$	−2.88507			−0.337671			−0.168836	+	0.985644i	$0.554001\pi$
$74$	13.6210	−	2.50256i	1.58341	−	0.290917i
$75$	−2.94736	−	0.900339i	−0.340332	−	0.103962i
$76$	−5.74606	−	15.1095i	−0.659118	−	1.73318i
$77$			9.06605i			1.03317i
$78$	−12.4830	−	1.43897i	−1.41342	−	0.162931i
$79$			10.8286i			1.21831i	0.793050	+	0.609157i	$0.208492\pi$
$79$			10.8286i			1.21831i	−0.793050	+	0.609157i	$0.791508\pi$
$80$	6.92052	+	7.78299i	0.773738	+	0.870165i
$81$	3.37934	+	8.34147i	0.375482	+	0.926829i
$82$	−1.03460	−	5.63112i	−0.114252	−	0.621854i
$83$	−7.05254			−0.774117			−0.387059	−	0.922055i	$-0.626509\pi$
$83$	−7.05254			−0.774117			−0.387059	+	0.922055i	$0.626509\pi$
$84$	0.669684	+	9.99018i	0.0730685	+	1.09002i
$85$	1.40070			0.151928
$86$	0.773396	+	4.20945i	0.0833975	+	0.453917i
$87$	−2.50441	+	8.19848i	−0.268501	+	0.878970i
$88$	−7.58594	+	4.60005i	−0.808664	+	0.490367i
$89$		−	7.16263i		−	0.759238i	−0.925143	−	0.379619i	$-0.876055\pi$
$89$		−	7.16263i		−	0.759238i	0.925143	−	0.379619i	$-0.123945\pi$
$90$	4.41581	−	10.1256i	0.465467	−	1.06733i
$91$			14.8274i			1.55433i
$92$	−9.58721	+	3.64596i	−0.999536	+	0.380117i
$93$	−0.122053	+	0.399556i	−0.0126563	+	0.0414320i
$94$	16.3726	−	3.00810i	1.68870	−	0.310262i
$95$	21.0447			2.15915
$96$	−8.01941	+	5.62930i	−0.818478	+	0.574538i
$97$	−5.26621			−0.534702			−0.267351	−	0.963599i	$-0.586148\pi$
$97$	−5.26621			−0.534702			−0.267351	+	0.963599i	$0.586148\pi$
$98$	1.88381	−	0.346110i	0.190294	−	0.0349624i
$99$	7.80360	+	5.25824i	0.784292	+	0.528473i
$100$	−3.32617	+	1.26492i	−0.332617	+	0.126492i
$101$		−	10.4079i		−	1.03562i	−0.855495	−	0.517810i	$-0.826747\pi$
$101$		−	10.4079i		−	1.03562i	0.855495	−	0.517810i	$-0.173253\pi$
$102$	−0.150902	+	1.30907i	−0.0149416	+	0.129617i
$103$		−	0.00173282i		−	0.000170740i	−1.00000		8.53699e-5i	$-0.999973\pi$
$103$		−	0.00173282i		−	0.000170740i	1.00000		8.53699e-5i	$-2.71741e-5\pi$
$104$	−12.4067	+	7.52332i	−1.21658	+	0.737723i
$105$	−12.4663	−	3.80810i	−1.21658	−	0.371633i
$106$	3.49134	+	19.0027i	0.339109	+	1.84571i
$107$	2.95907			0.286064			0.143032	−	0.989718i	$-0.454315\pi$
$107$	2.95907			0.286064			0.143032	+	0.989718i	$0.454315\pi$
$108$	8.98747	+	5.21780i	0.864820	+	0.502083i
$109$	−16.3226			−1.56342			−0.781710	−	0.623643i	$-0.785652\pi$
$109$	−16.3226			−1.56342			−0.781710	+	0.623643i	$0.785652\pi$
$110$	−2.08706	−	11.3595i	−0.198994	−	1.08309i
$111$	−16.2215	−	4.95522i	−1.53968	−	0.470329i
$112$	7.68251	+	8.63995i	0.725929	+	0.816398i
$113$		−	15.5422i		−	1.46209i	−0.682328	−	0.731046i	$-0.739033\pi$
$113$		−	15.5422i		−	1.46209i	0.682328	−	0.731046i	$-0.260967\pi$
$114$	−2.26722	+	19.6680i	−0.212345	+	1.84208i
$115$		−	13.3532i		−	1.24519i
$116$	3.51855	+	9.25218i	0.326689	+	0.859043i
$117$	12.7627	+	8.59978i	1.17991	+	0.795050i
$118$	−13.4410	+	2.46950i	−1.23735	+	0.227336i
$119$	1.55493			0.142540
$120$	−3.13890	−	12.3633i	−0.286541	−	1.12861i
$121$	−1.16163			−0.105603
$122$	−14.7262	+	2.70561i	−1.33324	+	0.244955i
$123$	−2.04856	+	6.70622i	−0.184713	+	0.604679i
$124$	0.171477	+	0.450908i	0.0153991	+	0.0404927i
$125$			8.38579i			0.750048i
$126$	4.90202	−	11.2405i	0.436706	−	1.00138i
$127$			15.8546i			1.40687i	0.710760	+	0.703434i	$0.248351\pi$
$127$			15.8546i			1.40687i	−0.710760	+	0.703434i	$0.751649\pi$
$128$	−3.33135	+	10.8121i	−0.294453	+	0.955666i
$129$	1.53137	−	5.01312i	0.134830	−	0.441381i
$130$	−3.41337	−	18.5783i	−0.299372	−	1.62943i
$131$	0.830906			0.0725966			0.0362983	−	0.999341i	$-0.488443\pi$
$131$	0.830906			0.0725966			0.0362983	+	0.999341i	$0.488443\pi$
$132$	10.8412	−	0.726733i	0.943608	−	0.0632540i
$133$	23.3619			2.02573
$134$	−0.255554	−	1.39093i	−0.0220765	−	0.120158i
$135$	−10.5082	+	8.52168i	−0.904399	+	0.733430i
$136$	0.788960	+	1.30107i	0.0676527	+	0.111566i
$137$		−	7.67384i		−	0.655621i	−0.944744	−	0.327810i	$-0.893689\pi$
$137$		−	7.67384i		−	0.655621i	0.944744	−	0.327810i	$-0.106311\pi$
$138$	12.4797	+	1.43859i	1.06234	+	0.122461i
$139$		−	5.01542i		−	0.425402i	−0.977117	−	0.212701i	$-0.931774\pi$
$139$		−	5.01542i		−	0.425402i	0.977117	−	0.212701i	$-0.0682261\pi$
$140$	−14.0685	+	5.35016i	−1.18900	+	0.452171i
$141$	−19.4984	−	5.95622i	−1.64206	−	0.501605i
$142$	−6.21902	+	1.14261i	−0.521889	+	0.0958858i
$143$	16.0905			1.34556
$144$	11.8926	−	1.60162i	0.991053	−	0.133469i
$145$	−12.8866			−1.07017
$146$	4.01293	−	0.737289i	0.332112	−	0.0610185i
$147$	−2.24347	−	0.685318i	−0.185038	−	0.0565241i
$148$	−18.3063	+	6.96179i	−1.50477	+	0.572256i
$149$		−	13.6112i		−	1.11507i	−0.830154	−	0.557535i	$-0.811747\pi$
$149$		−	13.6112i		−	1.11507i	0.830154	−	0.557535i	$-0.188253\pi$
$150$	4.32967	+	0.499100i	0.353516	+	0.0407513i
$151$		−	7.06893i		−	0.575262i	−0.957741	−	0.287631i	$-0.907132\pi$
$151$		−	7.06893i		−	0.575262i	0.957741	−	0.287631i	$-0.0928676\pi$
$152$	11.8537	+	19.5479i	0.961459	+	1.58554i
$153$	0.901846	−	1.33841i	0.0729099	−	0.108204i
$154$	−2.31686	−	12.6103i	−0.186698	−	1.01616i
$155$	−0.628031			−0.0504446
$156$	17.7307	−	1.18856i	1.41959	−	0.0951613i
$157$	−2.96479			−0.236616			−0.118308	−	0.992977i	$-0.537747\pi$
$157$	−2.96479			−0.236616			−0.118308	+	0.992977i	$0.537747\pi$
$158$	−2.76729	−	15.0619i	−0.220154	−	1.19826i
$159$	6.91306	−	22.6307i	0.548241	−	1.79473i
$160$	−11.6149	−	9.05705i	−0.918242	−	0.716023i
$161$		−	14.8235i		−	1.16825i
$162$	−6.83213	−	10.7388i	−0.536783	−	0.843721i
$163$		−	1.41672i		−	0.110966i	−0.998460	−	0.0554830i	$-0.982330\pi$
$163$		−	1.41672i		−	0.110966i	0.998460	−	0.0554830i	$-0.0176699\pi$
$164$	2.87811	+	7.56812i	0.224743	+	0.590971i
$165$	−4.13251	+	13.5283i	−0.321715	+	1.05317i
$166$	9.80961	−	1.80230i	0.761373	−	0.139886i
$167$	22.3132			1.72665			0.863324	−	0.504651i	$-0.168379\pi$
$167$	22.3132			1.72665			0.863324	+	0.504651i	$0.168379\pi$
$168$	−3.48451	−	13.7245i	−0.268836	−	1.05887i
$169$	13.3159			1.02430
$170$	−1.94828	+	0.357955i	−0.149426	+	0.0274539i
$171$	13.5497	−	20.1088i	1.03617	−	1.53776i
$172$	−2.15148	−	5.65742i	−0.164049	−	0.431374i
$173$			2.80929i			0.213587i	0.994281	+	0.106793i	$0.0340583\pi$
$173$			2.80929i			0.213587i	−0.994281	+	0.106793i	$0.965942\pi$
$174$	1.38831	−	12.0435i	0.105248	−	0.913019i
$175$		−	5.14283i		−	0.388761i
$176$	9.37597	−	8.33697i	0.706740	−	0.628423i
$177$	16.0072	+	4.88975i	1.20317	+	0.367536i
$178$	1.83044	+	9.96274i	0.137197	+	0.746739i
$179$	−2.18653			−0.163429			−0.0817144	−	0.996656i	$-0.526040\pi$
$179$	−2.18653			−0.163429			−0.0817144	+	0.996656i	$0.526040\pi$
$180$	−3.55446	+	15.2125i	−0.264933	+	1.13387i
$181$	8.83532			0.656724			0.328362	−	0.944552i	$-0.393503\pi$
$181$	8.83532			0.656724			0.328362	+	0.944552i	$0.393503\pi$
$182$	−3.78920	−	20.6239i	−0.280874	−	1.52875i
$183$	17.5377	+	5.35727i	1.29642	+	0.396021i
$184$	12.4034	−	7.52133i	0.914393	−	0.554480i
$185$		−	25.4973i		−	1.87460i
$186$	0.0676598	−	0.586946i	0.00496106	−	0.0430370i
$187$		−	1.68739i		−	0.123394i
$188$	−22.0044	+	8.36814i	−1.60484	+	0.610309i
$189$	−11.6652	+	9.45997i	−0.848517	+	0.688112i
$190$	−29.2718	+	5.37806i	−2.12360	+	0.390166i
$191$	11.3374			0.820349			0.410174	−	0.912007i	$-0.365468\pi$
$191$	11.3374			0.820349			0.410174	+	0.912007i	$0.365468\pi$
$192$	9.71587	−	9.87937i	0.701182	−	0.712982i
$193$	−14.4765			−1.04204			−0.521019	−	0.853545i	$-0.674448\pi$
$193$	−14.4765			−1.04204			−0.521019	+	0.853545i	$0.674448\pi$
$194$	7.32493	−	1.34580i	0.525900	−	0.0966227i
$195$	−6.75867	+	22.1253i	−0.483998	+	1.58443i
$196$	−2.53181	+	0.962831i	−0.180843	+	0.0687736i
$197$			9.67681i			0.689444i	0.938705	+	0.344722i	$0.112027\pi$
$197$			9.67681i			0.689444i	−0.938705	+	0.344722i	$0.887973\pi$
$198$	−12.1980	−	5.31961i	−0.866877	−	0.378048i
$199$		−	18.5428i		−	1.31447i	−0.753687	−	0.657233i	$-0.771727\pi$
$199$		−	18.5428i		−	1.31447i	0.753687	−	0.657233i	$-0.228273\pi$
$200$	4.30322	−	2.60943i	0.304284	−	0.184515i
$201$	−0.506011	+	1.65649i	−0.0356913	+	0.116840i
$202$	2.65977	+	14.4766i	0.187141	+	1.01857i
$203$	−14.3055			−1.00405
$204$	−0.124643	−	1.85939i	−0.00872675	−	0.130183i
$205$	−10.5410			−0.736214
$206$	0.000442828		0.00241023i	3.08533e−5		0.000167929i
$207$	−12.7593	−	8.59750i	−0.886834	−	0.597568i
$208$	15.3343	−	13.6350i	1.06324	−	0.945418i
$209$		−	25.3521i		−	1.75364i
$210$	18.3129	+	2.11101i	1.26371	+	0.145674i
$211$			26.6463i			1.83440i	0.398423	+	0.917202i	$0.369558\pi$
$211$			26.6463i			1.83440i	−0.398423	+	0.917202i	$0.630442\pi$
$212$	−9.71244	−	25.5393i	−0.667053	−	1.75405i
$213$	7.40635	+	2.26244i	0.507475	+	0.155020i
$214$	−4.11587	+	0.756202i	−0.281355	+	0.0516929i
$215$	7.87974			0.537394
$216$	−13.8344	−	4.96082i	−0.941311	−	0.337541i
$217$	−0.697181			−0.0473277
$218$	22.7036	−	4.17129i	1.53768	−	0.282516i
$219$	−4.77908	−	1.45988i	−0.322940	−	0.0986493i
$220$	5.80593	+	15.2669i	0.391435	+	1.02930i
$221$		−	2.75971i		−	0.185638i
$222$	23.8293	+	2.74691i	1.59932	+	0.184361i
$223$		−	22.1167i		−	1.48105i	−0.672031	−	0.740523i	$-0.734578\pi$
$223$		−	22.1167i		−	1.48105i	0.672031	−	0.740523i	$-0.265422\pi$
$224$	−12.8938	−	10.0543i	−0.861505	−	0.671780i
$225$	−4.42669	−	2.98280i	−0.295113	−	0.198853i
$226$	3.97188	+	21.6182i	0.264205	+	1.43802i
$227$	−14.7383			−0.978216			−0.489108	−	0.872223i	$-0.662678\pi$
$227$	−14.7383			−0.978216			−0.489108	+	0.872223i	$0.662678\pi$
$228$	−1.87269	−	27.9363i	−0.124022	−	1.85013i
$229$	17.1738			1.13488			0.567438	−	0.823416i	$-0.307935\pi$
$229$	17.1738			1.13488			0.567438	+	0.823416i	$0.307935\pi$
$230$	3.41246	+	18.5734i	0.225011	+	1.22469i
$231$	−4.58752	+	15.0178i	−0.301837	+	0.988098i
$232$	−7.25849	−	11.9700i	−0.476543	−	0.785867i
$233$			5.34290i			0.350025i	0.984566	+	0.175013i	$0.0559966\pi$
$233$			5.34290i			0.350025i	−0.984566	+	0.175013i	$0.944003\pi$
$234$	−19.9498	−	8.70016i	−1.30416	−	0.568747i
$235$		−	30.6480i		−	1.99926i
$236$	18.0645	−	6.86981i	1.17590	−	0.447187i
$237$	−5.47940	+	17.9375i	−0.355925	+	1.16516i
$238$	−2.16280	+	0.397368i	−0.140193	+	0.0257575i
$239$	−18.4034			−1.19042			−0.595209	−	0.803571i	$-0.702931\pi$
$239$	−18.4034			−1.19042			−0.595209	+	0.803571i	$0.702931\pi$
$240$	7.52547	+	16.3943i	0.485767	+	1.05825i
$241$	−1.10051			−0.0708901			−0.0354451	−	0.999372i	$-0.511285\pi$
$241$	−1.10051			−0.0708901			−0.0354451	+	0.999372i	$0.511285\pi$
$242$	1.61575	−	0.296860i	0.103865	−	0.0190829i
$243$	1.37696	+	15.5275i	0.0883322	+	0.996091i
$244$	19.7917	−	7.52665i	1.26703	−	0.481844i
$245$		−	3.52634i		−	0.225289i
$246$	1.13562	−	9.85141i	0.0724042	−	0.628103i
$247$		−	41.4630i		−	2.63823i
$248$	−0.353745	−	0.583360i	−0.0224628	−	0.0370434i
$249$	−11.6825	−	3.56867i	−0.740345	−	0.226155i
$250$	−2.14302	−	11.6641i	−0.135537	−	0.737701i
$251$	−2.45480			−0.154945			−0.0774727	−	0.996994i	$-0.524685\pi$
$251$	−2.45480			−0.154945			−0.0774727	+	0.996994i	$0.524685\pi$
$252$	−3.94582	+	16.8875i	−0.248563	+	1.06381i
$253$	−16.0863			−1.01133
$254$	−4.05170	−	22.0527i	−0.254226	−	1.38371i
$255$	2.32025	+	0.708771i	0.145299	+	0.0443850i
$256$	1.87061	−	15.8903i	0.116913	−	0.993142i
$257$		−	19.2402i		−	1.20017i	−0.799935	−	0.600087i	$-0.795133\pi$
$257$		−	19.2402i		−	1.20017i	0.799935	−	0.600087i	$-0.204867\pi$
$258$	−0.848910	+	7.36426i	−0.0528509	+	0.458479i
$259$		−	28.3048i		−	1.75877i
$260$	9.49552	+	24.9689i	0.588887	+	1.54851i
$261$	−8.29705	+	12.3134i	−0.513575	+	0.762182i
$262$	−1.15573	+	0.212341i	−0.0714015	+	0.0131185i
$263$	−1.53590			−0.0947078			−0.0473539	−	0.998878i	$-0.515079\pi$
$263$	−1.53590			−0.0947078			−0.0473539	+	0.998878i	$0.515079\pi$
$264$	−14.8937	+	3.78135i	−0.916644	+	0.232726i
$265$	35.5715			2.18514
$266$	−32.4948	+	5.97022i	−1.99239	+	0.366058i
$267$	3.62437	−	11.8648i	0.221808	−	0.726115i
$268$	0.710916	+	1.86938i	0.0434261	+	0.114191i
$269$			1.08351i			0.0660627i	0.999454	+	0.0330314i	$0.0105161\pi$
$269$			1.08351i			0.0660627i	−0.999454	+	0.0330314i	$0.989484\pi$
$270$	12.4384	−	14.5385i	0.756977	−	0.884784i
$271$			31.2660i			1.89927i	0.313352	+	0.949637i	$0.398548\pi$
$271$			31.2660i			1.89927i	−0.313352	+	0.949637i	$0.601452\pi$
$272$	−1.42988	−	1.60808i	−0.0866994	−	0.0975044i
$273$	−7.50284	+	24.5614i	−0.454092	+	1.48653i
$274$	1.96108	+	10.6738i	0.118473	+	0.644828i
$275$	−5.58094			−0.336543
$276$	−17.7260	+	1.18825i	−1.06698	+	0.0715242i
$277$	16.3666			0.983375			0.491687	−	0.870772i	$-0.336380\pi$
$277$	16.3666			0.983375			0.491687	+	0.870772i	$0.336380\pi$
$278$	1.28171	+	6.97611i	0.0768718	+	0.418399i
$279$	−0.404359	+	0.600099i	−0.0242084	+	0.0359270i
$280$	18.2010	−	11.0370i	1.08772	−	0.659584i
$281$			14.2167i			0.848100i	0.905639	+	0.424050i	$0.139392\pi$
$281$			14.2167i			0.848100i	−0.905639	+	0.424050i	$0.860608\pi$
$282$	28.6431	+	3.30182i	1.70567	+	0.196620i
$283$		−	0.188096i		−	0.0111811i	−0.999984	−	0.00559057i	$-0.998220\pi$
$283$		−	0.188096i		−	0.0111811i	0.999984	−	0.00559057i	$-0.00177954\pi$
$284$	8.35824	−	3.17859i	0.495970	−	0.188615i
$285$	34.8604	+	10.6489i	2.06495	+	0.630785i
$286$	−22.3808	+	4.11199i	−1.32341	+	0.243147i
$287$	−11.7016			−0.690724
$288$	−16.1325	+	5.26696i	−0.950620	+	0.310358i
$289$	16.7106			0.982976
$290$	17.9243	−	3.29321i	1.05255	−	0.193384i
$291$	−8.72341	−	2.66476i	−0.511375	−	0.156211i
$292$	−5.39330	+	2.05104i	−0.315619	+	0.120028i
$293$		−	1.17556i		−	0.0686772i	−0.999410	−	0.0343386i	$-0.989068\pi$
$293$		−	1.17556i		−	0.0686772i	0.999410	−	0.0343386i	$-0.0109325\pi$
$294$	3.29565	+	0.379904i	0.192206	+	0.0221564i
$295$			25.1605i			1.46490i
$296$	23.6838	−	14.3616i	1.37659	−	0.834753i
$297$	10.2659	+	12.6589i	0.595685	+	0.734545i
$298$	3.47838	+	18.9322i	0.201497	+	1.09671i
$299$	−26.3089			−1.52148
$300$	−6.14982	+	0.412249i	−0.355060	+	0.0238012i
$301$	8.74735			0.504189
$302$	1.80649	+	9.83241i	0.103952	+	0.565791i
$303$	5.26649	−	17.2405i	0.302552	−	0.990440i
$304$	−21.4832	−	24.1605i	−1.23214	−	1.38570i
$305$			27.5661i			1.57843i
$306$	−0.912372	+	2.09210i	−0.0521569	+	0.119597i
$307$		−	5.47903i		−	0.312705i	−0.987701	−	0.156352i	$-0.950026\pi$
$307$		−	5.47903i		−	0.312705i	0.987701	−	0.156352i	$-0.0499736\pi$
$308$	6.44519	+	16.9479i	0.367249	+	0.965698i
$309$	0.000876826	−	0.00287039i	4.98809e−5	−	0.000163291i
$310$	0.873548	−	0.160496i	0.0496142	−	0.00911554i
$311$	−9.27227			−0.525782			−0.262891	−	0.964826i	$-0.584676\pi$
$311$	−9.27227			−0.525782			−0.262891	+	0.964826i	$0.584676\pi$
$312$	−24.3585	+	6.18436i	−1.37903	+	0.350120i
$313$	22.7364			1.28514			0.642569	−	0.766228i	$-0.277869\pi$
$313$	22.7364			1.28514			0.642569	+	0.766228i	$0.277869\pi$
$314$	4.12381	−	0.757662i	0.232720	−	0.0427573i
$315$	−18.7233	−	12.6162i	−1.05494	−	0.710840i
$316$	7.69823	+	20.2428i	0.433059	+	1.13875i
$317$			5.56216i			0.312402i	0.987725	+	0.156201i	$0.0499247\pi$
$317$			5.56216i			0.312402i	−0.987725	+	0.156201i	$0.950075\pi$
$318$	−3.83224	+	33.2445i	−0.214901	+	1.86426i
$319$			15.5241i			0.869183i
$320$	18.4702	+	9.62950i	1.03251	+	0.538305i
$321$	4.90167	+	1.49732i	0.273584	+	0.0835725i
$322$	3.78819	+	20.6185i	0.211108	+	1.14902i
$323$	−4.34816			−0.241938
$324$	12.2474	+	13.1910i	0.680409	+	0.732832i
$325$	−9.12755			−0.506306
$326$	0.362048	+	1.97056i	0.0200520	+	0.109139i
$327$	−27.0381	−	8.25941i	−1.49521	−	0.456746i
$328$	−5.93732	−	9.79123i	−0.327833	−	0.540630i
$329$		−	34.0226i		−	1.87573i
$330$	2.29084	−	19.8730i	0.126107	−	1.09397i
$331$		−	8.35781i		−	0.459387i	−0.973263	−	0.229693i	$-0.926228\pi$
$331$		−	8.35781i		−	0.459387i	0.973263	−	0.229693i	$-0.0737723\pi$
$332$	−13.1839	+	5.01376i	−0.723561	+	0.275166i
$333$	−24.3633	−	16.4165i	−1.33510	−	0.899621i
$334$	−31.0361	+	5.70222i	−1.69822	+	0.312012i
$335$	−2.60371			−0.142256
$336$	8.35407	+	18.1994i	0.455752	+	0.992859i
$337$	8.67869			0.472759			0.236379	−	0.971661i	$-0.424039\pi$
$337$	8.67869			0.472759			0.236379	+	0.971661i	$0.424039\pi$
$338$	−18.5215	+	3.40292i	−1.00744	+	0.185094i
$339$	7.86455	−	25.7455i	0.427144	−	1.39831i
$340$	2.61845	−	0.995781i	0.142005	−	0.0540038i
$341$			0.756572i			0.0409707i
$342$	−13.7079	+	31.4326i	−0.741237	+	1.69968i
$343$			16.3181i			0.881096i
$344$	4.43834	+	7.31927i	0.239299	+	0.394629i
$345$	6.75688	−	22.1194i	0.363778	−	1.19087i
$346$	−0.717925	−	3.90754i	−0.0385959	−	0.210070i
$347$	19.5109			1.04740			0.523699	−	0.851904i	$-0.324552\pi$
$347$	19.5109			1.04740			0.523699	+	0.851904i	$0.324552\pi$
$348$	1.14672	+	17.1065i	0.0614709	+	0.917007i
$349$	−4.07790			−0.218285			−0.109142	−	0.994026i	$-0.534810\pi$
$349$	−4.07790			−0.218285			−0.109142	+	0.994026i	$0.534810\pi$
$350$	1.31427	+	7.15332i	0.0702506	+	0.382361i
$351$	16.7897	+	20.7035i	0.896167	+	1.10507i
$352$	−10.9108	+	13.9922i	−0.581547	+	0.745788i
$353$			1.47353i			0.0784281i	0.999231	+	0.0392141i	$0.0124854\pi$
$353$			1.47353i			0.0784281i	−0.999231	+	0.0392141i	$0.987515\pi$
$354$	−23.5145	−	2.71062i	−1.24978	−	0.144068i
$355$			11.6415i			0.617866i
$356$	−5.09203	−	13.3897i	−0.269877	−	0.709654i
$357$	2.57572	+	0.786811i	0.136322	+	0.0416425i
$358$	3.04131	−	0.558775i	0.160738	−	0.0295322i
$359$	18.8230			0.993441			0.496720	−	0.867911i	$-0.334537\pi$
$359$	18.8230			0.993441			0.496720	+	0.867911i	$0.334537\pi$
$360$	1.05640	−	22.0679i	0.0556770	−	1.16308i
$361$	−46.3286			−2.43835
$362$	−12.2893	+	2.25790i	−0.645913	+	0.118672i
$363$	−1.92423	−	0.587800i	−0.100996	−	0.0308515i
$364$	10.5410	+	27.7181i	0.552501	+	1.45282i
$365$		−	7.51186i		−	0.393189i
$366$	−25.7628	−	2.96979i	−1.34664	−	0.155233i
$367$			4.83690i			0.252484i	0.991999	+	0.126242i	$0.0402916\pi$
$367$			4.83690i			0.252484i	−0.991999	+	0.126242i	$0.959708\pi$
$368$	−15.3302	+	13.6314i	−0.799143	+	0.710586i
$369$	−6.78684	+	10.0722i	−0.353309	+	0.524336i
$370$	6.51594	+	35.4651i	0.338748	+	1.84374i
$371$	39.4881			2.05012
$372$	0.0558859	+	0.833693i	0.00289755	+	0.0432250i
$373$	4.48557			0.232254			0.116127	−	0.993234i	$-0.462952\pi$
$373$	4.48557			0.232254			0.116127	+	0.993234i	$0.462952\pi$
$374$	0.431219	+	2.34704i	0.0222978	+	0.121363i
$375$	−4.24331	+	13.8910i	−0.219123	+	0.717327i
$376$	28.4681	−	17.2628i	1.46813	−	0.890262i
$377$			25.3895i			1.30763i
$378$	13.8079	−	16.1393i	0.710204	−	0.830114i
$379$		−	0.465906i		−	0.0239320i	−0.999928	−	0.0119660i	$-0.996191\pi$
$379$		−	0.465906i		−	0.0239320i	0.999928	−	0.0119660i	$-0.00380899\pi$
$380$	39.3407	−	14.9610i	2.01814	−	0.767485i
$381$	−8.02261	+	26.2630i	−0.411011	+	1.34549i
$382$	−15.7696	+	2.89733i	−0.806844	+	0.148240i
$383$	1.39234			0.0711454			0.0355727	−	0.999367i	$-0.488674\pi$
$383$	1.39234			0.0711454			0.0355727	+	0.999367i	$0.488674\pi$
$384$	−10.9894	+	16.2245i	−0.560801	+	0.827951i
$385$	−23.6053			−1.20304
$386$	20.1358	−	3.69951i	1.02488	−	0.188300i
$387$	5.07339	−	7.52928i	0.257895	−	0.382735i
$388$	−9.84456	+	3.74383i	−0.499782	+	0.190064i
$389$		−	24.3328i		−	1.23372i	−0.787072	−	0.616862i	$-0.788404\pi$
$389$		−	24.3328i		−	1.23372i	0.787072	−	0.616862i	$-0.211596\pi$
$390$	3.74665	−	32.5020i	0.189719	−	1.64580i
$391$			2.75897i			0.139527i
$392$	3.27552	−	1.98624i	0.165439	−	0.100320i
$393$	1.37639	+	0.420448i	0.0694295	+	0.0212088i
$394$	−2.47294	−	13.4598i	−0.124585	−	0.678094i
$395$	−28.1945			−1.41862
$396$	18.3261	+	4.28196i	0.920921	+	0.215177i
$397$	13.2159			0.663285			0.331643	−	0.943405i	$-0.392397\pi$
$397$	13.2159			0.663285			0.331643	+	0.943405i	$0.392397\pi$
$398$	4.73869	+	25.7918i	0.237529	+	1.29283i
$399$	38.6987	+	11.8214i	1.93736	+	0.591810i
$400$	−5.31864	+	4.72925i	−0.265932	+	0.236463i
$401$			1.22666i			0.0612565i	0.999531	+	0.0306283i	$0.00975080\pi$
$401$			1.22666i			0.0612565i	−0.999531	+	0.0306283i	$0.990249\pi$
$402$	0.280506	−	2.43338i	0.0139904	−	0.121366i
$403$			1.23737i			0.0616375i
$404$	−7.39911	−	19.4563i	−0.368119	−	0.967987i
$405$	−21.7187	+	8.79881i	−1.07921	+	0.437217i
$406$	19.8979	−	3.65581i	0.987517	−	0.181435i
$407$	−30.7160			−1.52253
$408$	0.648544	+	2.55444i	0.0321077	+	0.126463i
$409$	15.7033			0.776481			0.388240	−	0.921558i	$-0.373083\pi$
$409$	15.7033			0.776481			0.388240	+	0.921558i	$0.373083\pi$
$410$	14.6618	−	2.69379i	0.724094	−	0.133037i
$411$	3.88305	−	12.7116i	0.191537	−	0.627018i
$412$	−0.00123189	−	0.00323931i	−6.06908e−5	−	0.000159589i
$413$			27.9308i			1.37438i
$414$	19.9445	+	8.69785i	0.980217	+	0.427476i
$415$		−	18.3628i		−	0.901392i
$416$	−17.8445	+	22.8841i	−0.874897	+	1.12199i
$417$	2.53786	−	8.30798i	0.124279	−	0.406844i
$418$	6.47881	+	35.2630i	0.316889	+	1.72477i
$419$	−15.0320			−0.734361			−0.367180	−	0.930150i	$-0.619677\pi$
$419$	−15.0320			−0.734361			−0.367180	+	0.930150i	$0.619677\pi$
$420$	−26.0115	+	1.74366i	−1.26923	+	0.0850819i
$421$	−9.76119			−0.475731			−0.237866	−	0.971298i	$-0.576448\pi$
$421$	−9.76119			−0.475731			−0.237866	+	0.971298i	$0.576448\pi$
$422$	−6.80955	−	37.0631i	−0.331484	−	1.80421i
$423$	−29.2850	−	19.7328i	−1.42388	−	0.959443i
$424$	20.0360	+	33.0414i	0.973034	+	1.60463i
$425$			0.957193i			0.0464307i
$426$	−10.8799	−	1.25418i	−0.527133	−	0.0607650i
$427$			30.6013i			1.48090i
$428$	5.53164	−	2.10365i	0.267382	−	0.101684i
$429$	26.6538	+	8.14199i	1.28686	+	0.393099i
$430$	−10.9602	+	2.01370i	−0.528547	+	0.0971091i
$431$	20.9130			1.00734			0.503672	−	0.863895i	$-0.331982\pi$
$431$	20.9130			1.00734			0.503672	+	0.863895i	$0.331982\pi$
$432$	20.5104	+	3.36474i	0.986809	+	0.161886i
$433$	−21.7276			−1.04416			−0.522081	−	0.852896i	$-0.674844\pi$
$433$	−21.7276			−1.04416			−0.522081	+	0.852896i	$0.674844\pi$
$434$	0.969731	−	0.178167i	0.0465486	−	0.00855229i
$435$	−21.3464	−	6.52075i	−1.02348	−	0.312646i
$436$	−30.5132	+	11.6040i	−1.46132	+	0.555730i
$437$			41.4520i			1.98292i
$438$	7.02045	+	0.809278i	0.335450	+	0.0386688i
$439$		−	28.9489i		−	1.38166i	−0.723019	−	0.690828i	$-0.757246\pi$
$439$		−	28.9489i		−	1.38166i	0.723019	−	0.690828i	$-0.242754\pi$
$440$	−11.9772	−	19.7516i	−0.570989	−	0.941619i
$441$	−3.36950	−	2.27044i	−0.160452	−	0.108116i
$442$	0.705253	+	3.83856i	0.0335455	+	0.182582i
$443$	20.9377			0.994782			0.497391	−	0.867526i	$-0.334291\pi$
$443$	20.9377			0.994782			0.497391	+	0.867526i	$0.334291\pi$
$444$	−33.8470	+	2.26891i	−1.60631	+	0.107678i
$445$	18.6494			0.884066
$446$	5.65201	+	30.7629i	0.267631	+	1.45666i
$447$	6.88740	−	22.5467i	0.325763	−	1.06642i
$448$	20.5038	+	10.6898i	0.968715	+	0.505044i
$449$			19.0209i			0.897654i	0.893619	+	0.448827i	$0.148158\pi$
$449$			19.0209i			0.897654i	−0.893619	+	0.448827i	$0.851842\pi$
$450$	6.91949	+	3.01761i	0.326188	+	0.142252i
$451$			12.6984i			0.597947i
$452$	−11.0492	−	29.0544i	−0.519712	−	1.36661i
$453$	3.57696	−	11.7096i	0.168060	−	0.550165i
$454$	20.5000	−	3.76643i	0.962112	−	0.176767i
$455$	−38.6062			−1.80989
$456$	9.74401	+	38.3789i	0.456305	+	1.79726i
$457$	−8.99556			−0.420795			−0.210397	−	0.977616i	$-0.567476\pi$
$457$	−8.99556			−0.420795			−0.210397	+	0.977616i	$0.567476\pi$
$458$	−23.8876	+	4.38882i	−1.11619	+	0.205076i
$459$	2.17115	−	1.76071i	0.101340	−	0.0821828i
$460$	−9.49301	−	24.9623i	−0.442614	−	1.16387i
$461$		−	29.0327i		−	1.35219i	−0.736816	−	0.676094i	$-0.763671\pi$
$461$		−	29.0327i		−	1.35219i	0.736816	−	0.676094i	$-0.236329\pi$
$462$	2.54308	−	22.0611i	0.118315	−	1.02637i
$463$			3.45414i			0.160528i	0.996774	+	0.0802638i	$0.0255763\pi$
$463$			3.45414i			0.160528i	−0.996774	+	0.0802638i	$0.974424\pi$
$464$	13.1550	+	14.7945i	0.610707	+	0.686817i
$465$	−1.04033	−	0.317791i	−0.0482439	−	0.0147372i
$466$	−1.36540	−	7.43162i	−0.0632509	−	0.344263i
$467$	19.7530			0.914062			0.457031	−	0.889451i	$-0.348913\pi$
$467$	19.7530			0.914062			0.457031	+	0.889451i	$0.348913\pi$
$468$	29.9721	+	7.00310i	1.38546	+	0.323718i
$469$	−2.89039			−0.133466
$470$	7.83222	+	42.6293i	0.361273	+	1.96635i
$471$	−4.91113	−	1.50021i	−0.226293	−	0.0691263i
$472$	−23.3709	+	14.1719i	−1.07573	+	0.652314i
$473$		−	9.49252i		−	0.436466i
$474$	3.03749	−	26.3501i	0.139517	−	1.21030i
$475$			14.3813i			0.659858i
$476$	2.90676	−	1.10542i	0.133231	−	0.0506670i
$477$	22.9028	−	33.9894i	1.04865	−	1.55627i
$478$	25.5979	−	4.70306i	1.17082	−	0.215113i
$479$	21.6257			0.988102			0.494051	−	0.869433i	$-0.335516\pi$
$479$	21.6257			0.988102			0.494051	+	0.869433i	$0.335516\pi$
$480$	−14.6570	−	20.8802i	−0.669000	−	0.953046i
$481$	−50.2356			−2.29055
$482$	1.53074	−	0.281240i	0.0697231	−	0.0128101i
$483$	7.50085	−	24.5549i	0.341300	−	1.11729i
$484$	−2.17154	+	0.825824i	−0.0987064	+	0.0375375i
$485$		−	13.7117i		−	0.622614i
$486$	−5.88338	−	21.2458i	−0.266875	−	0.963731i
$487$		−	40.3439i		−	1.82816i	−0.405538	−	0.914078i	$-0.632916\pi$
$487$		−	40.3439i		−	1.82816i	0.405538	−	0.914078i	$-0.367084\pi$
$488$	−25.6054	+	15.5269i	−1.15910	+	0.702869i
$489$	0.716877	−	2.34678i	0.0324183	−	0.106125i
$490$	0.901168	+	4.90489i	0.0407106	+	0.221581i
$491$	−2.10393			−0.0949492			−0.0474746	−	0.998872i	$-0.515117\pi$
$491$	−2.10393			−0.0949492			−0.0474746	+	0.998872i	$0.515117\pi$
$492$	0.938000	+	13.9929i	0.0422883	+	0.630846i
$493$	2.66256			0.119916
$494$	10.5960	+	57.6722i	0.476738	+	2.59480i
$495$	−13.6909	+	20.3183i	−0.615360	+	0.913239i
$496$	0.641115	+	0.721014i	0.0287869	+	0.0323745i
$497$			12.9233i			0.579688i
$498$	17.1615	+	1.97828i	0.769025	+	0.0886489i
$499$		−	3.96304i		−	0.177410i	−0.996058	−	0.0887049i	$-0.971727\pi$
$499$		−	3.96304i		−	0.177410i	0.996058	−	0.0887049i	$-0.0282728\pi$
$500$	5.96159	+	15.6763i	0.266611	+	0.701064i
$501$	36.9615	+	11.2907i	1.65132	+	0.504433i
$502$	3.41446	−	0.627333i	0.152395	−	0.0279992i
$503$	−6.23728			−0.278106			−0.139053	−	0.990285i	$-0.544406\pi$
$503$	−6.23728			−0.278106			−0.139053	+	0.990285i	$0.544406\pi$
$504$	1.17271	−	24.4977i	0.0522368	−	1.09122i
$505$	27.0990			1.20589
$506$	22.3749	−	4.11090i	0.994686	−	0.182752i
$507$	22.0576	+	6.73798i	0.979612	+	0.299244i
$508$	11.2713	+	29.6384i	0.500082	+	1.31499i
$509$			36.3220i			1.60995i	0.593312	+	0.804973i	$0.297820\pi$
$509$			36.3220i			1.60995i	−0.593312	+	0.804973i	$0.702180\pi$
$510$	−3.40843	−	0.392905i	−0.150928	−	0.0173981i
$511$		−	8.33896i		−	0.368894i
$512$	1.45893	+	22.5803i	0.0644762	+	0.997919i
$513$	32.6202	−	26.4536i	1.44022	−	1.16796i
$514$	4.91692	+	26.7619i	0.216876	+	1.18042i
$515$	0.00451175			0.000198812
$516$	−0.701186	−	10.4601i	−0.0308680	−	0.460481i
$517$	−36.9209			−1.62378
$518$	7.23338	+	39.3700i	0.317817	+	1.72982i
$519$	−1.42153	+	4.65356i	−0.0623984	+	0.204269i
$520$	−19.5885	−	32.3034i	−0.859014	−	1.41660i
$521$		−	26.1623i		−	1.14619i	−0.819488	−	0.573096i	$-0.805742\pi$
$521$		−	26.1623i		−	1.14619i	0.819488	−	0.573096i	$-0.194258\pi$
$522$	8.39389	−	19.2475i	0.367391	−	0.842440i
$523$			16.4105i			0.717582i	0.933418	+	0.358791i	$0.116811\pi$
$523$			16.4105i			0.717582i	−0.933418	+	0.358791i	$0.883189\pi$
$524$	1.55328	−	0.590704i	0.0678555	−	0.0258050i
$525$	2.60233	−	8.51903i	0.113575	−	0.371801i
$526$	2.13634	−	0.392505i	0.0931487	−	0.0171141i
$527$	0.129761			0.00565246
$528$	19.7498	−	9.06574i	0.859499	−	0.394536i
$529$	3.30191			0.143561
$530$	−49.4775	+	9.09043i	−2.14917	+	0.394863i
$531$	24.0414	+	16.1996i	1.04331	+	0.703005i
$532$	43.6724	−	16.6083i	1.89344	−	0.720063i
$533$			20.7682i			0.899569i
$534$	−2.00916	+	17.4294i	−0.0869449	+	0.754243i
$535$			7.70455i			0.333097i
$536$	−1.46656	−	2.41851i	−0.0633459	−	0.104464i
$537$	−3.62196	−	1.10641i	−0.156299	−	0.0477450i
$538$	−0.276895	−	1.50709i	−0.0119378	−	0.0649751i
$539$	−4.24809			−0.182978
$540$	−13.5856	+	23.4007i	−0.584632	+	1.00701i
$541$	−30.0867			−1.29353			−0.646764	−	0.762690i	$-0.723878\pi$
$541$	−30.0867			−1.29353			−0.646764	+	0.762690i	$0.723878\pi$
$542$	−7.99014	−	43.4889i	−0.343206	−	1.86801i
$543$	14.6356	+	4.47077i	0.628073	+	0.191859i
$544$	2.39982	+	1.87132i	0.102892	+	0.0802323i
$545$		−	42.4992i		−	1.82047i
$546$	4.15918	−	36.0807i	0.177996	−	1.54411i
$547$			13.6119i			0.582001i	0.956723	+	0.291001i	$0.0939882\pi$
$547$			13.6119i			0.582001i	−0.956723	+	0.291001i	$0.906012\pi$
$548$	−5.45546	−	14.3454i	−0.233046	−	0.612804i
$549$	26.3401	+	17.7485i	1.12417	+	0.757488i
$550$	7.76270	−	1.42623i	0.331003	−	0.0608146i
$551$	40.0034			1.70420
$552$	24.3520	−	6.18272i	1.03649	−	0.263154i
$553$	−31.2989			−1.33097
$554$	−22.7649	+	4.18255i	−0.967186	+	0.177699i
$555$	12.9019	−	42.2360i	0.547657	−	1.79282i
$556$	−3.56554	−	9.37575i	−0.151213	−	0.397620i
$557$			15.9410i			0.675443i	0.941246	+	0.337722i	$0.109656\pi$
$557$			15.9410i			0.675443i	−0.941246	+	0.337722i	$0.890344\pi$
$558$	0.409079	−	0.938032i	0.0173177	−	0.0397101i
$559$		−	15.5249i		−	0.656633i
$560$	−22.4959	+	20.0030i	−0.950624	+	0.845281i
$561$	0.853838	−	2.79514i	0.0360491	−	0.118011i
$562$	−3.63314	−	19.7745i	−0.153255	−	0.834138i
$563$	19.7107			0.830706			0.415353	−	0.909660i	$-0.363658\pi$
$563$	19.7107			0.830706			0.415353	+	0.909660i	$0.363658\pi$
$564$	−40.6844	+	2.72725i	−1.71312	+	0.114838i
$565$	40.4674			1.70248
$566$	0.0480686	+	0.261629i	0.00202047	+	0.0109971i
$567$	−24.1101	+	9.76762i	−1.01253	+	0.410201i
$568$	−10.8134	+	6.55718i	−0.453722	+	0.275133i
$569$		−	32.0631i		−	1.34416i	−0.740480	−	0.672078i	$-0.765402\pi$
$569$		−	32.0631i		−	1.34416i	0.740480	−	0.672078i	$-0.234598\pi$
$570$	−51.2098	−	5.90318i	−2.14494	−	0.247257i
$571$			14.4930i			0.606515i	0.952909	+	0.303257i	$0.0980742\pi$
$571$			14.4930i			0.606515i	−0.952909	+	0.303257i	$0.901926\pi$
$572$	30.0794	−	11.4390i	1.25768	−	0.478289i
$573$	18.7803	+	5.73688i	0.784560	+	0.239661i
$574$	16.2761	−	2.99039i	0.679353	−	0.124816i
$575$	9.12513			0.380544
$576$	21.0933	−	11.4487i	0.878887	−	0.477030i
$577$	7.34117			0.305617			0.152808	−	0.988256i	$-0.451168\pi$
$577$	7.34117			0.305617			0.152808	+	0.988256i	$0.451168\pi$
$578$	−23.2433	+	4.27045i	−0.966794	+	0.177627i
$579$	−23.9801	−	7.32525i	−0.996578	−	0.304427i
$580$	−24.0899	+	9.16126i	−1.00028	+	0.380401i
$581$		−	20.3846i		−	0.845696i
$582$	12.8147	+	1.47720i	0.531185	+	0.0612320i
$583$		−	42.8521i		−	1.77475i
$584$	6.97756	−	4.23113i	0.288733	−	0.175085i
$585$	−22.3913	+	33.2303i	−0.925767	+	1.37390i
$586$	0.300420	+	1.63513i	0.0124102	+	0.0675466i
$587$	−21.6138			−0.892099			−0.446049	−	0.895008i	$-0.647169\pi$
$587$	−21.6138			−0.892099			−0.446049	+	0.895008i	$0.647169\pi$
$588$	−4.68111	+	0.313795i	−0.193046	+	0.0129407i
$589$	1.94958			0.0803310
$590$	−6.42985	−	34.9965i	−0.264713	−	1.44078i
$591$	−4.89658	+	16.0295i	−0.201418	+	0.659366i
$592$	−29.2724	+	26.0285i	−1.20309	+	1.06977i
$593$			28.7481i			1.18054i	0.807205	+	0.590271i	$0.200979\pi$
$593$			28.7481i			1.18054i	−0.807205	+	0.590271i	$0.799021\pi$
$594$	−17.5141	−	14.9842i	−0.718614	−	0.614810i
$595$			4.04858i			0.165975i
$596$	−9.67638	−	25.4445i	−0.396360	−	1.04225i
$597$	9.38289	−	30.7160i	0.384016	−	1.25712i
$598$	36.5939	−	6.72333i	1.49644	−	0.274938i
$599$	8.35373			0.341324			0.170662	−	0.985330i	$-0.445409\pi$
$599$	8.35373			0.341324			0.170662	+	0.985330i	$0.445409\pi$
$600$	8.44863	−	2.14502i	0.344914	−	0.0875701i
$601$	−45.3779			−1.85100			−0.925501	−	0.378744i	$-0.876356\pi$
$601$	−45.3779			−1.85100			−0.925501	+	0.378744i	$0.876356\pi$
$602$	−12.1670	+	2.23542i	−0.495888	+	0.0911088i
$603$	−1.67640	+	2.48790i	−0.0682684	+	0.101315i
$604$	−5.02542	−	13.2146i	−0.204481	−	0.537693i
$605$		−	3.02456i		−	0.122966i
$606$	−2.91947	+	25.3262i	−0.118595	+	1.02881i
$607$		−	28.3073i		−	1.14896i	−0.818520	−	0.574478i	$-0.805205\pi$
$607$		−	28.3073i		−	1.14896i	0.818520	−	0.574478i	$-0.194795\pi$
$608$	36.0560	+	28.1156i	1.46226	+	1.14024i
$609$	−23.6968	−	7.23872i	−0.960243	−	0.293328i
$610$	−7.04462	−	38.3426i	−0.285228	−	1.55245i
$611$	−60.3837			−2.44286
$612$	0.734404	−	3.14313i	0.0296865	−	0.127054i
$613$	−8.18630			−0.330642			−0.165321	−	0.986240i	$-0.552866\pi$
$613$	−8.18630			−0.330642			−0.165321	+	0.986240i	$0.552866\pi$
$614$	1.40019	+	7.62096i	0.0565069	+	0.307557i
$615$	−17.4610	−	5.33386i	−0.704096	−	0.215082i
$616$	−13.2959	−	21.9263i	−0.535708	−	0.883437i
$617$		−	2.70557i		−	0.108922i	−0.998516	−	0.0544611i	$-0.982656\pi$
$617$		−	2.70557i		−	0.108922i	0.998516	−	0.0544611i	$-0.0173441\pi$
$618$	−0.000486066		0.00421660i	−1.95524e−5		0.000169617i
$619$			18.3004i			0.735557i	0.929913	+	0.367779i	$0.119882\pi$
$619$			18.3004i			0.735557i	−0.929913	+	0.367779i	$0.880118\pi$
$620$	−1.17403	+	0.446477i	−0.0471502	+	0.0179309i
$621$	−16.7852	−	20.6980i	−0.673568	−	0.830583i
$622$	12.8971	−	2.36956i	0.517126	−	0.0950108i
$623$	20.7028			0.829440
$624$	32.3005	−	14.8269i	1.29306	−	0.593552i
$625$	−30.7306			−1.22922
$626$	−31.6248	+	5.81037i	−1.26398	+	0.232229i
$627$	12.8284	−	41.9954i	0.512318	−	1.67713i
$628$	−5.54232	+	2.10771i	−0.221163	+	0.0841069i
$629$			5.26813i			0.210054i
$630$	29.2669	+	12.7634i	1.16602	+	0.508506i
$631$			20.1278i			0.801275i	0.916237	+	0.400638i	$0.131211\pi$
$631$			20.1278i			0.801275i	−0.916237	+	0.400638i	$0.868789\pi$
$632$	−15.8808	−	26.1891i	−0.631706	−	1.04175i
$633$	−13.4833	+	44.1392i	−0.535913	+	1.75438i
$634$	−1.42143	−	7.73658i	−0.0564522	−	0.307259i
$635$	−41.2807			−1.63818
$636$	−3.16536	−	47.2201i	−0.125515	−	1.87240i
$637$	−6.94769			−0.275278
$638$	−3.96724	−	21.5930i	−0.157065	−	0.854874i
$639$	11.1237	+	7.49540i	0.440048	+	0.296513i
$640$	−28.1516	−	8.67386i	−1.11279	−	0.342865i
$641$		−	46.1614i		−	1.82326i	−0.411007	−	0.911632i	$-0.634823\pi$
$641$		−	46.1614i		−	1.82326i	0.411007	−	0.911632i	$-0.365177\pi$
$642$	−7.20053	−	0.830037i	−0.284182	−	0.0327589i
$643$			45.4882i			1.79388i	0.442151	+	0.896941i	$0.354216\pi$
$643$			45.4882i			1.79388i	−0.442151	+	0.896941i	$0.645784\pi$
$644$	−10.5382	−	27.7108i	−0.415265	−	1.09196i
$645$	13.0527	+	3.98724i	0.513949	+	0.156997i
$646$	6.04800	−	1.11119i	0.237955	−	0.0437191i
$647$	−33.6238			−1.32189			−0.660943	−	0.750436i	$-0.729844\pi$
$647$	−33.6238			−1.32189			−0.660943	+	0.750436i	$0.729844\pi$
$648$	−20.4063	−	15.2179i	−0.801634	−	0.597816i
$649$	30.3102			1.18978
$650$	12.6958	−	2.33258i	0.497971	−	0.0914913i
$651$	−1.15487	−	0.352781i	−0.0452630	−	0.0138266i
$652$	−1.00717	−	2.64839i	−0.0394438	−	0.103719i
$653$			9.90614i			0.387657i	0.981035	+	0.193829i	$0.0620906\pi$
$653$			9.90614i			0.387657i	−0.981035	+	0.193829i	$0.937909\pi$
$654$	39.7190	+	4.57858i	1.55313	+	0.179037i
$655$			2.16344i			0.0845324i
$656$	10.7606	+	12.1016i	0.420130	+	0.472489i
$657$	−7.17777	−	4.83653i	−0.280031	−	0.188691i
$658$	8.69459	+	47.3231i	0.338951	+	1.84485i
$659$	−27.0741			−1.05466			−0.527328	−	0.849662i	$-0.676806\pi$
$659$	−27.0741			−1.05466			−0.527328	+	0.849662i	$0.676806\pi$
$660$	1.89220	+	28.2274i	0.0736538	+	1.09875i
$661$	15.6830			0.609997			0.304999	−	0.952353i	$-0.401344\pi$
$661$	15.6830			0.609997			0.304999	+	0.952353i	$0.401344\pi$
$662$	2.13587	+	11.6251i	0.0830129	+	0.451824i
$663$	1.39644	−	4.57142i	0.0542333	−	0.177539i
$664$	17.0566	−	10.3430i	0.661926	−	0.401386i
$665$			60.8275i			2.35879i
$666$	38.0831	+	16.6081i	1.47569	+	0.643553i
$667$		−	25.3828i		−	0.982825i
$668$	41.7119	−	15.8628i	1.61388	−	0.613750i
$669$	11.1913	−	36.6361i	0.432681	−	1.41643i
$670$	3.62158	−	0.665387i	0.139914	−	0.0257061i
$671$	33.2082			1.28199
$672$	−16.2709	−	23.1792i	−0.627663	−	0.894158i
$673$	36.2637			1.39786			0.698931	−	0.715189i	$-0.253659\pi$
$673$	36.2637			1.39786			0.698931	+	0.715189i	$0.253659\pi$
$674$	−12.0715	+	2.21787i	−0.464976	+	0.0854292i
$675$	−5.82343	−	7.18093i	−0.224144	−	0.276394i
$676$	24.8925	−	9.46646i	0.957403	−	0.364095i
$677$			32.9930i			1.26802i	0.773323	+	0.634012i	$0.218593\pi$
$677$			32.9930i			1.26802i	−0.773323	+	0.634012i	$0.781407\pi$
$678$	−4.35969	+	37.8201i	−0.167433	+	1.45247i
$679$		−	15.2214i		−	0.584143i
$680$	−3.38761	+	2.05422i	−0.129909	+	0.0787757i
$681$	−24.4138	−	7.45775i	−0.935540	−	0.285782i
$682$	−0.193345	−	1.05234i	−0.00740356	−	0.0402962i
$683$	−4.62379			−0.176924			−0.0884622	−	0.996080i	$-0.528195\pi$
$683$	−4.62379			−0.176924			−0.0884622	+	0.996080i	$0.528195\pi$
$684$	11.0340	−	47.2237i	0.421896	−	1.80564i
$685$	19.9804			0.763413
$686$	−4.17016	−	22.6974i	−0.159217	−	0.866591i
$687$	28.4482	+	8.69013i	1.08537	+	0.331549i
$688$	−8.04390	−	9.04637i	−0.306671	−	0.344890i
$689$		−	70.0840i		−	2.66999i
$690$	−3.74565	+	32.4934i	−0.142595	+	1.23700i
$691$			36.7601i			1.39842i	0.714916	+	0.699211i	$0.246465\pi$
$691$			36.7601i			1.39842i	−0.714916	+	0.699211i	$0.753535\pi$
$692$	1.99717	+	5.25165i	0.0759210	+	0.199638i
$693$	−15.1984	+	22.5555i	−0.577338	+	0.856811i
$694$	−27.1383	+	4.98607i	−1.03015	+	0.189269i
$695$	13.0587			0.495344
$696$	−5.96666	−	23.5010i	−0.226165	−	0.890803i
$697$	2.17793			0.0824948
$698$	5.67208	−	1.04212i	0.214691	−	0.0394449i
$699$	−2.70357	+	8.85046i	−0.102258	+	0.334755i
$700$	−3.65612	−	9.61392i	−0.138188	−	0.363372i
$701$			38.7119i			1.46213i	0.682308	+	0.731065i	$0.260976\pi$
$701$			38.7119i			1.46213i	−0.682308	+	0.731065i	$0.739024\pi$
$702$	−28.6442	−	24.5065i	−1.08110	−	0.924939i
$703$			79.1507i			2.98523i
$704$	11.6004	−	22.2505i	0.437207	−	0.838598i
$705$	15.5083	−	50.7681i	0.584075	−	1.91204i
$706$	−0.376566	−	2.04958i	−0.0141723	−	0.0771370i
$707$	30.0828			1.13138
$708$	33.3998	−	2.23893i	1.25524	−	0.0841441i
$709$	18.4442			0.692687			0.346343	−	0.938108i	$-0.387423\pi$
$709$	18.4442			0.692687			0.346343	+	0.938108i	$0.387423\pi$
$710$	−2.97502	−	16.1925i	−0.111651	−	0.607694i
$711$	−18.1531	+	26.9406i	−0.680795	+	1.01035i
$712$	10.5045	+	17.3229i	0.393671	+	0.649203i
$713$		−	1.23704i		−	0.0463274i
$714$	−3.78372	−	0.436167i	−0.141602	−	0.0163231i
$715$			41.8950i			1.56678i
$716$	−4.08746	+	1.55444i	−0.152756	+	0.0580920i
$717$	−30.4850	−	9.31234i	−1.13848	−	0.347776i
$718$	−26.1815	+	4.81029i	−0.977086	+	0.179518i
$719$	−31.4138			−1.17154			−0.585768	−	0.810479i	$-0.699207\pi$
$719$	−31.4138			−1.17154			−0.585768	+	0.810479i	$0.699207\pi$
$720$	4.17016	+	30.9649i	0.155413	+	1.15399i
$721$	0.00500852			0.000186527
$722$	64.4400	−	11.8395i	2.39821	−	0.440619i
$723$	−1.82298	−	0.556871i	−0.0677974	−	0.0207102i
$724$	16.5166	−	6.28116i	0.613835	−	0.233438i
$725$		−	8.80625i		−	0.327056i
$726$	2.82669	+	0.325845i	0.104908	+	0.0120933i
$727$		−	14.1225i		−	0.523774i	−0.965099	−	0.261887i	$-0.915655\pi$
$727$		−	14.1225i		−	0.523774i	0.965099	−	0.261887i	$-0.0843448\pi$
$728$	−21.7453	−	35.8602i	−0.805936	−	1.32907i
$729$	−5.57618	+	26.4179i	−0.206525	+	0.978441i
$730$	1.91968	+	10.4485i	0.0710507	+	0.386716i
$731$	−1.62807			−0.0602164
$732$	36.5932	−	2.45300i	1.35252	−	0.0906654i
$733$	17.6493			0.651893			0.325947	−	0.945388i	$-0.394317\pi$
$733$	17.6493			0.651893			0.325947	+	0.945388i	$0.394317\pi$
$734$	−1.23609	−	6.72780i	−0.0456249	−	0.248328i
$735$	1.78437	−	5.84133i	0.0658173	−	0.215461i
$736$	17.8397	−	22.8780i	0.657582	−	0.843296i
$737$			3.13662i			0.115539i
$738$	6.86606	−	15.7441i	0.252743	−	0.579549i
$739$			0.103030i			0.00379003i	0.999998	+	0.00189502i	$0.000603202\pi$
$739$			0.103030i			0.00379003i	−0.999998	+	0.00189502i	$0.999397\pi$
$740$	−18.1265	−	47.6643i	−0.666342	−	1.75218i
$741$	20.9807	−	68.6830i	0.770747	−	2.52313i
$742$	−54.9253	+	10.0913i	−2.01637	+	0.370465i
$743$	−22.7858			−0.835929			−0.417965	−	0.908463i	$-0.637256\pi$
$743$	−22.7858			−0.835929			−0.417965	+	0.908463i	$0.637256\pi$
$744$	−0.290787	−	1.14533i	−0.0106608	−	0.0419898i
$745$	35.4395			1.29840
$746$	−6.23913	+	1.14630i	−0.228431	+	0.0419692i
$747$	−17.5461	−	11.8229i	−0.641977	−	0.432578i
$748$	−1.19959	−	3.15438i	−0.0438614	−	0.115336i
$749$			8.55287i			0.312515i
$750$	2.35227	−	20.4058i	0.0858926	−	0.745114i
$751$		−	3.39755i		−	0.123978i	−0.998077	−	0.0619892i	$-0.980256\pi$
$751$		−	3.39755i		−	0.123978i	0.998077	−	0.0619892i	$-0.0197444\pi$
$752$	−35.1856	+	31.2865i	−1.28309	+	1.14090i
$753$	−4.06634	−	1.24216i	−0.148186	−	0.0452667i
$754$	−6.48838	−	35.3151i	−0.236293	−	1.28610i
$755$	18.4054			0.669842
$756$	−15.0815	+	25.9773i	−0.548508	+	0.944785i
$757$	−18.0423			−0.655759			−0.327880	−	0.944719i	$-0.606334\pi$
$757$	−18.0423			−0.655759			−0.327880	+	0.944719i	$0.606334\pi$
$758$	0.119064	+	0.648044i	0.00432460	+	0.0235380i
$759$	−26.6467	−	8.13983i	−0.967214	−	0.295457i
$760$	−50.8969	+	30.8635i	−1.84623	+	1.11954i
$761$			47.3690i			1.71713i	0.512708	+	0.858563i	$0.328642\pi$
$761$			47.3690i			1.71713i	−0.512708	+	0.858563i	$0.671358\pi$
$762$	4.44731	−	38.5802i	0.161109	−	1.39761i
$763$		−	47.1786i		−	1.70798i
$764$	21.1940	−	8.05997i	0.766774	−	0.291599i
$765$	3.48481	+	2.34814i	0.125994	+	0.0848973i
$766$	−1.93665	+	0.355818i	−0.0699741	+	0.0128562i
$767$	49.5719			1.78994
$768$	11.1393	−	25.3755i	0.401955	−	0.915660i
$769$	−44.6839			−1.61134			−0.805672	−	0.592362i	$-0.798196\pi$
$769$	−44.6839			−1.61134			−0.805672	+	0.592362i	$0.798196\pi$
$770$	32.8334	−	6.03243i	1.18323	−	0.217394i
$771$	9.73578	−	31.8712i	0.350626	−	1.14781i
$772$	−27.0621	+	10.2915i	−0.973985	+	0.370401i
$773$			6.02927i			0.216858i	0.994104	+	0.108429i	$0.0345820\pi$
$773$			6.02927i			0.216858i	−0.994104	+	0.108429i	$0.965418\pi$
$774$	−5.13261	+	11.7692i	−0.184488	+	0.423037i
$775$		−	0.429175i		−	0.0154164i
$776$	12.7364	−	7.72323i	0.457209	−	0.277248i
$777$	14.3225	−	46.8865i	0.513818	−	1.68204i
$778$	6.21834	+	33.8453i	0.222938	+	1.21341i
$779$	32.7221			1.17239
$780$	3.09467	+	46.1655i	0.110807	+	1.65299i
$781$	14.0242			0.501825
$782$	−0.705066	−	3.83755i	−0.0252131	−	0.137230i
$783$	−19.9747	+	16.1986i	−0.713838	+	0.578892i
$784$	−4.04843	+	3.59980i	−0.144587	+	0.128564i
$785$		−	7.71943i		−	0.275518i
$786$	−2.02191	−	0.233074i	−0.0721190	−	0.00831348i
$787$			9.03092i			0.321918i	0.986961	+	0.160959i	$0.0514586\pi$
$787$			9.03092i			0.321918i	−0.986961	+	0.160959i	$0.948541\pi$
$788$	6.87939	+	18.0897i	0.245068	+	0.644418i
$789$	−2.54420	−	0.777184i	−0.0905760	−	0.0276685i
$790$	39.2167	−	7.20521i	1.39527	−	0.256350i
$791$	44.9231			1.59728
$792$	−26.5846	−	1.27261i	−0.944644	−	0.0452204i
$793$	54.3116			1.92866
$794$	−18.3824	+	3.37736i	−0.652366	+	0.119858i
$795$	58.9238	+	17.9996i	2.08981	+	0.638379i
$796$	−13.1824	−	34.6637i	−0.467238	−	1.22862i
$797$			3.50578i			0.124181i	0.998071	+	0.0620906i	$0.0197768\pi$
$797$			3.50578i			0.124181i	−0.998071	+	0.0620906i	$0.980223\pi$
$798$	−56.8483	−	6.55315i	−2.01241	−	0.231979i
$799$			6.33235i			0.224022i
$800$	6.18928	−	7.93726i	0.218824	−	0.280625i
$801$	12.0075	−	17.8200i	0.424263	−	0.629637i
$802$	−0.313478	−	1.70620i	−0.0110693	−	0.0602481i
$803$	−9.04934			−0.319344
$804$	0.231693	+	3.45634i	0.00817120	+	0.121896i
$805$	38.5960			1.36033
$806$	−0.316213	−	1.72109i	−0.0111381	−	0.0606228i
$807$	−0.548268	+	1.79482i	−0.0192999	+	0.0631806i
$808$	15.2638	+	25.1715i	0.536978	+	0.885531i
$809$		−	40.1395i		−	1.41123i	−0.708595	−	0.705615i	$-0.750671\pi$
$809$		−	40.1395i		−	1.41123i	0.708595	−	0.705615i	$-0.249329\pi$
$810$	27.9607	−	17.7889i	0.982439	−	0.625037i
$811$		−	9.92324i		−	0.348452i	−0.984706	−	0.174226i	$-0.944258\pi$
$811$		−	9.92324i		−	0.348452i	0.984706	−	0.174226i	$-0.0557423\pi$
$812$	−26.7424	+	10.1700i	−0.938474	+	0.356896i
$813$	−15.8210	+	51.7917i	−0.554865	+	1.81642i
$814$	42.7239	−	7.84958i	1.49747	−	0.275128i
$815$	3.68872			0.129210
$816$	−1.55488	−	3.38731i	−0.0544316	−	0.118580i
$817$	−24.4609			−0.855777
$818$	−21.8423	+	4.01305i	−0.763698	+	0.140313i
$819$	−24.8567	+	36.8892i	−0.868564	+	1.28901i
$820$	−19.7052	+	7.49375i	−0.688134	+	0.261693i
$821$		−	27.1722i		−	0.948317i	−0.880440	−	0.474158i	$-0.842752\pi$
$821$		−	27.1722i		−	0.948317i	0.880440	−	0.474158i	$-0.157248\pi$
$822$	−2.15256	+	18.6733i	−0.0750791	+	0.651308i
$823$			50.4905i			1.75999i	0.474983	+	0.879995i	$0.342454\pi$
$823$			50.4905i			1.75999i	−0.474983	+	0.879995i	$0.657546\pi$
$824$	0.00254129	+	0.00419084i	8.85300e−5	+	0.000145995i
$825$	−9.24475	−	2.82402i	−0.321861	−	0.0983197i
$826$	−7.13782	−	38.8498i	−0.248356	−	1.35176i
$827$	6.34851			0.220759			0.110380	−	0.993889i	$-0.464793\pi$
$827$	6.34851			0.220759			0.110380	+	0.993889i	$0.464793\pi$
$828$	−29.9642	−	7.00124i	−1.04133	−	0.243310i
$829$	−43.5389			−1.51217			−0.756084	−	0.654474i	$-0.772890\pi$
$829$	−43.5389			−1.51217			−0.756084	+	0.654474i	$0.772890\pi$
$830$	4.69267	+	25.5413i	0.162885	+	0.886553i
$831$	27.1111	+	8.28169i	0.940474	+	0.287289i
$832$	18.9723	−	36.3905i	0.657747	−	1.26161i
$833$			0.728594i			0.0252443i
$834$	−1.40685	+	12.2044i	−0.0487154	+	0.422604i
$835$			58.0970i			2.01053i
$836$	−18.0232	−	47.3928i	−0.623345	−	1.63911i
$837$	−0.973473	+	0.789446i	−0.0336482	+	0.0272872i
$838$	20.9085	−	3.84148i	0.722271	−	0.132702i
$839$	−35.7712			−1.23496			−0.617479	−	0.786587i	$-0.711846\pi$
$839$	−35.7712			−1.23496			−0.617479	+	0.786587i	$0.711846\pi$
$840$	35.7346	−	9.07265i	1.23296	−	0.313036i
$841$	4.50426			0.155319
$842$	13.5772	−	2.49451i	0.467900	−	0.0859664i
$843$	−7.19384	+	23.5499i	−0.247769	+	0.811101i
$844$	18.9432	+	49.8121i	0.652053	+	1.71460i
$845$			34.6706i			1.19271i
$846$	45.7762	+	19.9631i	1.57382	+	0.686347i
$847$		−	3.35758i		−	0.115368i
$848$	−36.3126	−	40.8380i	−1.24698	−	1.40238i
$849$	0.0951787	−	0.311579i	0.00326652	−	0.0106933i
$850$	−0.244614	−	1.33139i	−0.00839020	−	0.0456663i
$851$	50.2223			1.72160
$852$	15.4537	−	1.03593i	0.529436	−	0.0354903i
$853$	−50.8747			−1.74192			−0.870958	−	0.491358i	$-0.836501\pi$
$853$	−50.8747			−1.74192			−0.870958	+	0.491358i	$0.836501\pi$
$854$	−7.82027	−	42.5643i	−0.267604	−	1.45652i
$855$	52.3573	+	35.2795i	1.79058	+	1.20653i
$856$	−7.15654	+	4.33967i	−0.244606	+	0.148327i
$857$		−	6.95918i		−	0.237721i	−0.992911	−	0.118860i	$-0.962076\pi$
$857$		−	6.95918i		−	0.237721i	0.992911	−	0.118860i	$-0.0379241\pi$
$858$	−39.1543	−	4.51349i	−1.33671	−	0.154088i
$859$		−	35.7819i		−	1.22086i	−0.792069	−	0.610432i	$-0.790996\pi$
$859$		−	35.7819i		−	1.22086i	0.792069	−	0.610432i	$-0.209004\pi$
$860$	14.7303	−	5.60183i	0.502298	−	0.191021i
$861$	−19.3836	−	5.92115i	−0.660590	−	0.201792i
$862$	−29.0886	+	5.34440i	−0.990761	+	0.182031i
$863$	−22.3550			−0.760974			−0.380487	−	0.924786i	$-0.624244\pi$
$863$	−22.3550			−0.760974			−0.380487	+	0.924786i	$0.624244\pi$
$864$	−29.3885	+	0.561398i	−0.999818	+	0.0190992i
$865$	−7.31457			−0.248703
$866$	30.2216	−	5.55256i	1.02697	−	0.188684i
$867$	27.6809	+	8.45575i	0.940093	+	0.287172i
$868$	−1.30330	+	0.495637i	−0.0442368	+	0.0168230i
$869$			33.9652i			1.15219i
$870$	31.3579	+	3.61476i	1.06313	+	0.122552i
$871$			5.12990i			0.173820i
$872$	39.4763	−	23.9381i	1.33684	−	0.810646i
$873$	−13.1018	−	8.82829i	−0.443429	−	0.298792i
$874$	−10.5932	−	57.6569i	−0.358321	−	1.95027i
$875$	−24.2382			−0.819401
$876$	−9.97178	+	0.668451i	−0.336915	+	0.0225849i
$877$	51.8580			1.75112			0.875560	−	0.483110i	$-0.160493\pi$
$877$	51.8580			1.75112			0.875560	+	0.483110i	$0.160493\pi$
$878$	7.39800	+	40.2660i	0.249670	+	1.35891i
$879$	0.594849	−	1.94731i	0.0200637	−	0.0656810i
$880$	21.7070	+	24.4123i	0.731743	+	0.822937i
$881$			15.4678i			0.521125i	0.965457	+	0.260563i	$0.0839080\pi$
$881$			15.4678i			0.521125i	−0.965457	+	0.260563i	$0.916092\pi$
$882$	5.26697	+	2.29694i	0.177348	+	0.0773421i
$883$			17.8182i			0.599629i	0.953998	+	0.299815i	$0.0969248\pi$
$883$			17.8182i			0.599629i	−0.953998	+	0.299815i	$0.903075\pi$
$884$	−1.96192	−	5.15895i	−0.0659865	−	0.173514i
$885$	−12.7315	+	41.6780i	−0.427964	+	1.40099i
$886$	−29.1230	+	5.35072i	−0.978405	+	0.179761i
$887$	−7.35912			−0.247095			−0.123547	−	0.992339i	$-0.539427\pi$
$887$	−7.35912			−0.247095			−0.123547	+	0.992339i	$0.539427\pi$
$888$	46.4990	−	11.8056i	1.56041	−	0.396171i
$889$	−45.8260			−1.53695
$890$	−25.9400	+	4.76592i	−0.869512	+	0.159754i
$891$	10.5997	+	26.1640i	0.355103	+	0.876526i
$892$	−15.7231	−	41.3447i	−0.526449	−	1.38432i
$893$			95.1399i			3.18373i
$894$	−3.81801	+	33.1211i	−0.127693	+	1.10773i
$895$		−	5.69308i		−	0.190299i
$896$	−31.2513	−	9.62891i	−1.04403	−	0.321679i
$897$	−43.5804	−	13.3126i	−1.45511	−	0.444495i
$898$	−4.86087	−	26.4568i	−0.162209	−	0.882876i
$899$	−1.19381			−0.0398157
$900$	−10.3957	−	2.42900i	−0.346524	−	0.0809665i
$901$	−7.34961			−0.244851
$902$	−3.24514	−	17.6627i	−0.108051	−	0.588103i
$903$	14.4899	+	4.42626i	0.482193	+	0.147297i
$904$	22.7937	+	37.5891i	0.758107	+	1.25019i
$905$			23.0046i			0.764698i
$906$	−1.98288	+	17.2014i	−0.0658767	+	0.571477i
$907$			15.7764i			0.523846i	0.965089	+	0.261923i	$0.0843567\pi$
$907$			15.7764i			0.523846i	−0.965089	+	0.261923i	$0.915643\pi$
$908$	−27.5516	+	10.4777i	−0.914331	+	0.347715i
$909$	17.4478	−	25.8938i	0.578706	−	0.858842i
$910$	53.6986	−	9.86596i	1.78009	−	0.327053i
$911$	−23.9962			−0.795029			−0.397514	−	0.917596i	$-0.630127\pi$
$911$	−23.9962			−0.795029			−0.397514	+	0.917596i	$0.630127\pi$
$912$	−23.3611	−	50.8924i	−0.773564	−	1.68521i
$913$	−22.1211			−0.732103
$914$	12.5122	−	2.29885i	0.413867	−	0.0760391i
$915$	−13.9488	+	45.6629i	−0.461132	+	1.50957i
$916$	32.1044	−	12.2091i	1.06076	−	0.403400i
$917$			2.40164i			0.0793092i
$918$	−2.56996	+	3.00387i	−0.0848214	+	0.0991425i
$919$			33.7583i			1.11358i	0.830652	+	0.556791i	$0.187968\pi$
$919$			33.7583i			1.11358i	−0.830652	+	0.556791i	$0.812032\pi$
$920$	19.5833	+	32.2949i	0.645643	+	1.06473i
$921$	2.77245	−	9.07595i	0.0913554	−	0.299063i
$922$	7.41941	+	40.3825i	0.244345	+	1.32993i
$923$	22.9364			0.754961
$924$	2.10054	+	31.3354i	0.0691028	+	1.03086i
$925$	17.4240			0.572898
$926$	−0.882719	−	4.80448i	−0.0290080	−	0.157885i
$927$	0.00290490	−	0.00431109i	9.54096e−5	−	0.000141595i
$928$	−22.0785	−	17.2163i	−0.724764	−	0.565153i
$929$			24.6520i			0.808807i	0.914581	+	0.404404i	$0.132521\pi$
$929$			24.6520i			0.808807i	−0.914581	+	0.404404i	$0.867479\pi$
$930$	1.52823	+	0.176166i	0.0501128	+	0.00577672i
$931$			10.9467i			0.358764i
$932$	3.79835	+	9.98794i	0.124419	+	0.327166i
$933$	−15.3594	−	4.69187i	−0.502844	−	0.153605i
$934$	−27.4751	+	5.04796i	−0.899014	+	0.165174i
$935$	4.39347			0.143682
$936$	−43.4789	−	2.08134i	−1.42115	−	0.0680309i
$937$	5.20521			0.170047			0.0850234	−	0.996379i	$-0.472903\pi$
$937$	5.20521			0.170047			0.0850234	+	0.996379i	$0.472903\pi$
$938$	4.02034	−	0.738650i	0.131269	−	0.0241178i
$939$	37.6626	+	11.5049i	1.22907	+	0.375447i
$940$	−21.7882	−	57.2930i	−0.710652	−	1.86869i
$941$		−	10.1658i		−	0.331395i	−0.986177	−	0.165698i	$-0.947012\pi$
$941$		−	10.1658i		−	0.331395i	0.986177	−	0.165698i	$-0.0529876\pi$
$942$	7.21444	+	0.831640i	0.235059	+	0.0270963i
$943$		−	20.7627i		−	0.676125i
$944$	28.8856	−	25.6846i	0.940146	−	0.835964i
$945$	−24.6310	−	30.3727i	−0.801246	−	0.988024i
$946$	2.42585	+	13.2034i	0.0788711	+	0.429281i
$947$	22.7646			0.739751			0.369876	−	0.929081i	$-0.379400\pi$
$947$	22.7646			0.739751			0.369876	+	0.929081i	$0.379400\pi$
$948$	2.50892	+	37.4274i	0.0814859	+	1.21559i
$949$	−14.8001			−0.480431
$950$	−3.67519	−	20.0034i	−0.119239	−	0.648995i
$951$	−2.81451	+	9.21365i	−0.0912669	+	0.298773i
$952$	−3.76061	+	2.28040i	−0.121882	+	0.0739082i
$953$		−	0.794923i		−	0.0257501i	−0.999917	−	0.0128750i	$-0.995902\pi$
$953$		−	0.794923i		−	0.0257501i	0.999917	−	0.0128750i	$-0.00409837\pi$
$954$	−23.1701	+	53.1299i	−0.750161	+	1.72014i
$955$			29.5194i			0.955224i
$956$	−34.4031	+	13.0833i	−1.11267	+	0.423143i
$957$	−7.85538	+	25.7155i	−0.253928	+	0.831264i
$958$	−30.0798	+	5.52652i	−0.971836	+	0.178554i
$959$	22.1804			0.716242
$960$	25.7230	+	25.2973i	0.830205	+	0.816466i
$961$	30.9418			0.998123
$962$	69.8744	−	12.8379i	2.25284	−	0.413911i
$963$	7.36189	+	4.96060i	0.237234	+	0.159853i
$964$	−2.05728	+	0.782370i	−0.0662604	+	0.0251984i
$965$		−	37.6924i		−	1.21336i
$966$	−4.15807	+	36.0711i	−0.133784	+	1.16057i
$967$		−	60.1849i		−	1.93542i	−0.252072	−	0.967708i	$-0.581112\pi$
$967$		−	60.1849i		−	1.93542i	0.252072	−	0.967708i	$-0.418888\pi$
$968$	2.80943	−	1.70361i	0.0902983	−	0.0547561i
$969$	−7.20268	−	2.20022i	−0.231383	−	0.0706812i
$970$	3.50406	+	19.0720i	0.112509	+	0.612364i
$971$	−26.2288			−0.841723			−0.420862	−	0.907125i	$-0.638272\pi$
$971$	−26.2288			−0.841723			−0.420862	+	0.907125i	$0.638272\pi$
$972$	13.6128	+	28.0480i	0.436632	+	0.899640i
$973$	14.4965			0.464737
$974$	10.3100	+	56.1156i	0.330355	+	1.79806i
$975$	−15.1197	−	4.61865i	−0.484217	−	0.147915i
$976$	31.6474	−	28.1404i	1.01301	−	0.900752i
$977$		−	24.9194i		−	0.797242i	−0.917116	−	0.398621i	$-0.869489\pi$
$977$		−	24.9194i		−	0.797242i	0.917116	−	0.398621i	$-0.130511\pi$
$978$	−0.397398	+	3.44741i	−0.0127074	+	0.110236i
$979$		−	22.4664i		−	0.718031i
$980$	−2.50693	−	6.59208i	−0.0800809	−	0.210576i
$981$	−40.6090	−	27.3632i	−1.29655	−	0.873640i
$982$	2.92643	−	0.537668i	0.0933861	−	0.0171577i
$983$	18.2842			0.583177			0.291588	−	0.956544i	$-0.405816\pi$
$983$	18.2842			0.583177			0.291588	+	0.956544i	$0.405816\pi$
$984$	−4.88062	−	19.2234i	−0.155588	−	0.612820i
$985$	−25.1956			−0.802797
$986$	−3.70344	+	0.680427i	−0.117942	+	0.0216692i
$987$	17.2158	−	56.3580i	0.547985	−	1.79389i
$988$	−29.4767	−	77.5103i	−0.937779	−	2.46593i
$989$			15.5208i			0.493532i
$990$	13.8507	−	31.7601i	0.440204	−	1.00940i
$991$		−	19.9367i		−	0.633309i	−0.948541	−	0.316654i	$-0.897440\pi$
$991$		−	19.9367i		−	0.633309i	0.948541	−	0.316654i	$-0.102560\pi$
$992$	−1.07600	−	0.839042i	−0.0341632	−	0.0266396i
$993$	4.22915	−	13.8446i	0.134208	−	0.439345i
$994$	−3.30259	−	17.9754i	−0.104752	−	0.570145i
$995$	48.2801			1.53058
$996$	−24.3760	+	1.63403i	−0.772384	+	0.0517761i
$997$	25.2498			0.799670			0.399835	−	0.916587i	$-0.369067\pi$
$997$	25.2498			0.799670			0.399835	+	0.916587i	$0.369067\pi$
$998$	1.01277	+	5.51231i	0.0320586	+	0.174489i
$999$	−32.0506	−	39.5219i	−1.01404	−	1.25042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.c.b.671.8	yes	128
3.2	odd	2	inner	804.2.c.b.671.121	yes	128
4.3	odd	2	inner	804.2.c.b.671.122	yes	128
12.11	even	2	inner	804.2.c.b.671.7	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.c.b.671.7	✓	128	12.11	even	2	inner
804.2.c.b.671.8	yes	128	1.1	even	1	trivial
804.2.c.b.671.121	yes	128	3.2	odd	2	inner
804.2.c.b.671.122	yes	128	4.3	odd	2	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39093 + 0.255554i) q^{2} +(1.65649 + 0.506011i) q^{3} +(1.86938 - 0.710916i) q^{4} +2.60371i q^{5} +(-2.43338 - 0.280506i) q^{6} +2.89039i q^{7} +(-2.41851 + 1.46656i) q^{8} +(2.48790 + 1.67640i) q^{9} +O(q^{10})\)	\(q+(-1.39093 + 0.255554i) q^{2} +(1.65649 + 0.506011i) q^{3} +(1.86938 - 0.710916i) q^{4} +2.60371i q^{5} +(-2.43338 - 0.280506i) q^{6} +2.89039i q^{7} +(-2.41851 + 1.46656i) q^{8} +(2.48790 + 1.67640i) q^{9} +(-0.665387 - 3.62158i) q^{10} +3.13662 q^{11} +(3.45634 - 0.231693i) q^{12} +5.12990 q^{13} +(-0.738650 - 4.02034i) q^{14} +(-1.31750 + 4.31301i) q^{15} +(2.98920 - 2.65795i) q^{16} -0.537965i q^{17} +(-3.88892 - 1.69597i) q^{18} -8.08261i q^{19} +(1.85102 + 4.86733i) q^{20} +(-1.46257 + 4.78790i) q^{21} +(-4.36282 + 0.801574i) q^{22} -5.12854 q^{23} +(-4.74833 + 1.20555i) q^{24} -1.77929 q^{25} +(-7.13534 + 1.31096i) q^{26} +(3.27291 + 4.03585i) q^{27} +(2.05482 + 5.40325i) q^{28} +4.94932i q^{29} +(0.730355 - 6.33579i) q^{30} +0.241206i q^{31} +(-3.47852 + 4.46093i) q^{32} +(5.19577 + 1.58716i) q^{33} +(0.137479 + 0.748273i) q^{34} -7.52573 q^{35} +(5.84263 + 1.36515i) q^{36} -9.79271 q^{37} +(2.06554 + 11.2424i) q^{38} +(8.49762 + 2.59579i) q^{39} +(-3.81850 - 6.29709i) q^{40} +4.04845i q^{41} +(0.810771 - 7.03340i) q^{42} -3.02636i q^{43} +(5.86354 - 2.22987i) q^{44} +(-4.36486 + 6.47777i) q^{45} +(7.13345 - 1.31062i) q^{46} -11.7709 q^{47} +(6.29652 - 2.89029i) q^{48} -1.35435 q^{49} +(2.47486 - 0.454703i) q^{50} +(0.272216 - 0.891132i) q^{51} +(9.58976 - 3.64693i) q^{52} -13.6619i q^{53} +(-5.58377 - 4.77719i) q^{54} +8.16683i q^{55} +(-4.23894 - 6.99044i) q^{56} +(4.08989 - 13.3888i) q^{57} +(-1.26482 - 6.88416i) q^{58} +9.66333 q^{59} +(0.603261 + 8.99931i) q^{60} +10.5873 q^{61} +(-0.0616412 - 0.335502i) q^{62} +(-4.84546 + 7.19101i) q^{63} +(3.69838 - 7.09380i) q^{64} +13.3568i q^{65} +(-7.63257 - 0.879840i) q^{66} +1.00000i q^{67} +(-0.382448 - 1.00566i) q^{68} +(-8.49536 - 2.59510i) q^{69} +(10.4678 - 1.92323i) q^{70} +4.47112 q^{71} +(-8.47558 - 0.405728i) q^{72} -2.88507 q^{73} +(13.6210 - 2.50256i) q^{74} +(-2.94736 - 0.900339i) q^{75} +(-5.74606 - 15.1095i) q^{76} +9.06605i q^{77} +(-12.4830 - 1.43897i) q^{78} +10.8286i q^{79} +(6.92052 + 7.78299i) q^{80} +(3.37934 + 8.34147i) q^{81} +(-1.03460 - 5.63112i) q^{82} -7.05254 q^{83} +(0.669684 + 9.99018i) q^{84} +1.40070 q^{85} +(0.773396 + 4.20945i) q^{86} +(-2.50441 + 8.19848i) q^{87} +(-7.58594 + 4.60005i) q^{88} -7.16263i q^{89} +(4.41581 - 10.1256i) q^{90} +14.8274i q^{91} +(-9.58721 + 3.64596i) q^{92} +(-0.122053 + 0.399556i) q^{93} +(16.3726 - 3.00810i) q^{94} +21.0447 q^{95} +(-8.01941 + 5.62930i) q^{96} -5.26621 q^{97} +(1.88381 - 0.346110i) q^{98} +(7.80360 + 5.25824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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