LMFDB - Embedded newform 670.2.e.i.171.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(171,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("670.171");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 31x^{6} - 2x^{5} + 597x^{4} - 4x^{3} + 5860x^{2} + 5264x + 35344 $ x^8 - 2x^7 + 31x^6 - 2x^5 + 597x^4 - 4x^3 + 5860x^2 + 5264*x + 35344
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			171.4
Root			$2.31630 - 4.01195i$ of defining polynomial
Character	$\chi$	$=$	670.171
Dual form			670.2.e.i.431.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +2.41421 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.20711 - 2.09077i) q^{6} +(0.707107 - 1.22474i) q^{7} +1.00000 q^{8} +2.82843 q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +2.41421 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.20711 - 2.09077i) q^{6} +(0.707107 - 1.22474i) q^{7} +1.00000 q^{8} +2.82843 q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-1.20711 + 2.09077i) q^{12} +(3.27575 + 5.67376i) q^{13} -1.41421 q^{14} +2.41421 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.60920 + 2.78721i) q^{17} +(-1.41421 - 2.44949i) q^{18} +(-1.31630 - 2.27990i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(1.70711 - 2.95680i) q^{21} -2.00000 q^{22} +(-3.92550 - 6.79916i) q^{23} +2.41421 q^{24} +1.00000 q^{25} +(3.27575 - 5.67376i) q^{26} -0.414214 q^{27} +(0.707107 + 1.22474i) q^{28} +(-3.68996 + 6.39120i) q^{29} +(-1.20711 - 2.09077i) q^{30} +(1.66188 - 2.87845i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.41421 - 4.18154i) q^{33} +(1.60920 - 2.78721i) q^{34} +(0.707107 - 1.22474i) q^{35} +(-1.41421 + 2.44949i) q^{36} +(-0.402089 - 0.696439i) q^{37} +(-1.31630 + 2.27990i) q^{38} +(7.90835 + 13.6977i) q^{39} +1.00000 q^{40} +(3.64473 - 6.31286i) q^{41} -3.41421 q^{42} +1.09046 q^{43} +(1.00000 + 1.73205i) q^{44} +2.82843 q^{45} +(-3.92550 + 6.79916i) q^{46} +(1.15443 - 1.99953i) q^{47} +(-1.20711 - 2.09077i) q^{48} +(2.50000 + 4.33013i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(3.88494 + 6.72892i) q^{51} -6.55149 q^{52} +0.918888 q^{53} +(0.207107 + 0.358719i) q^{54} +(1.00000 - 1.73205i) q^{55} +(0.707107 - 1.22474i) q^{56} +(-3.17784 - 5.50417i) q^{57} +7.37992 q^{58} -4.63261 q^{59} +(-1.20711 + 2.09077i) q^{60} +(0.259787 + 0.449965i) q^{61} -3.32375 q^{62} +(2.00000 - 3.46410i) q^{63} +1.00000 q^{64} +(3.27575 + 5.67376i) q^{65} -4.82843 q^{66} +(-6.07609 + 5.48463i) q^{67} -3.21839 q^{68} +(-9.47699 - 16.4146i) q^{69} -1.41421 q^{70} +(-1.10920 + 1.92118i) q^{71} +2.82843 q^{72} +(-2.21923 - 3.84382i) q^{73} +(-0.402089 + 0.696439i) q^{74} +2.41421 q^{75} +2.63261 q^{76} +(-1.41421 - 2.44949i) q^{77} +(7.90835 - 13.6977i) q^{78} +(0.804178 - 1.39288i) q^{79} +(-0.500000 - 0.866025i) q^{80} -9.48528 q^{81} -7.28946 q^{82} +(-4.07609 - 7.05999i) q^{83} +(1.70711 + 2.95680i) q^{84} +(1.60920 + 2.78721i) q^{85} +(-0.545230 - 0.944367i) q^{86} +(-8.90835 + 15.4297i) q^{87} +(1.00000 - 1.73205i) q^{88} +2.26521 q^{89} +(-1.41421 - 2.44949i) q^{90} +9.26521 q^{91} +7.85100 q^{92} +(4.01212 - 6.94920i) q^{93} -2.30885 q^{94} +(-1.31630 - 2.27990i) q^{95} +(-1.20711 + 2.09077i) q^{96} +(-0.131017 - 0.226928i) q^{97} +(2.50000 - 4.33013i) q^{98} +(2.82843 - 4.89898i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 8 q^{5} - 4 q^{6} + 8 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 8 * q^5 - 4 * q^6 + 8 * q^8	$ 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 8 q^{5} - 4 q^{6} + 8 q^{8} - 4 q^{10} + 8 q^{11} - 4 q^{12} + 8 q^{15} - 4 q^{16} + 2 q^{17} + 6 q^{19} - 4 q^{20} + 8 q^{21} - 16 q^{22} - 4 q^{23} + 8 q^{24} + 8 q^{25} + 8 q^{27} + 8 q^{29} - 4 q^{30} + 6 q^{31} - 4 q^{32} + 8 q^{33} + 2 q^{34} + 2 q^{37} + 6 q^{38} + 4 q^{39} + 8 q^{40} - 10 q^{41} - 16 q^{42} + 12 q^{43} + 8 q^{44} - 4 q^{46} - 4 q^{48} + 20 q^{49} - 4 q^{50} - 6 q^{51} - 12 q^{53} - 4 q^{54} + 8 q^{55} + 6 q^{57} - 16 q^{58} - 4 q^{59} - 4 q^{60} - 12 q^{62} + 16 q^{63} + 8 q^{64} - 16 q^{66} - 30 q^{67} - 4 q^{68} + 4 q^{69} + 2 q^{71} - 6 q^{73} + 2 q^{74} + 8 q^{75} - 12 q^{76} + 4 q^{78} - 4 q^{79} - 4 q^{80} - 8 q^{81} + 20 q^{82} - 14 q^{83} + 8 q^{84} + 2 q^{85} - 6 q^{86} - 12 q^{87} + 8 q^{88} - 48 q^{89} + 8 q^{91} + 8 q^{92} + 26 q^{93} + 6 q^{95} - 4 q^{96} - 14 q^{97} + 20 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 8 * q^5 - 4 * q^6 + 8 * q^8 - 4 * q^10 + 8 * q^11 - 4 * q^12 + 8 * q^15 - 4 * q^16 + 2 * q^17 + 6 * q^19 - 4 * q^20 + 8 * q^21 - 16 * q^22 - 4 * q^23 + 8 * q^24 + 8 * q^25 + 8 * q^27 + 8 * q^29 - 4 * q^30 + 6 * q^31 - 4 * q^32 + 8 * q^33 + 2 * q^34 + 2 * q^37 + 6 * q^38 + 4 * q^39 + 8 * q^40 - 10 * q^41 - 16 * q^42 + 12 * q^43 + 8 * q^44 - 4 * q^46 - 4 * q^48 + 20 * q^49 - 4 * q^50 - 6 * q^51 - 12 * q^53 - 4 * q^54 + 8 * q^55 + 6 * q^57 - 16 * q^58 - 4 * q^59 - 4 * q^60 - 12 * q^62 + 16 * q^63 + 8 * q^64 - 16 * q^66 - 30 * q^67 - 4 * q^68 + 4 * q^69 + 2 * q^71 - 6 * q^73 + 2 * q^74 + 8 * q^75 - 12 * q^76 + 4 * q^78 - 4 * q^79 - 4 * q^80 - 8 * q^81 + 20 * q^82 - 14 * q^83 + 8 * q^84 + 2 * q^85 - 6 * q^86 - 12 * q^87 + 8 * q^88 - 48 * q^89 + 8 * q^91 + 8 * q^92 + 26 * q^93 + 6 * q^95 - 4 * q^96 - 14 * q^97 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	2.41421			1.39385			0.696923	−	0.717146i	$-0.254552\pi$
$3$	2.41421			1.39385			0.696923	+	0.717146i	$0.254552\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.20711	−	2.09077i	−0.492799	−	0.853553i
$7$	0.707107	−	1.22474i	0.267261	−	0.462910i	−0.700892	−	0.713267i	$-0.747215\pi$
$7$	0.707107	−	1.22474i	0.267261	−	0.462910i	0.968154	+	0.250357i	$0.0805480\pi$
$8$	1.00000			0.353553
$9$	2.82843			0.942809
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	−1.20711	+	2.09077i	−0.348462	+	0.603553i
$13$	3.27575	+	5.67376i	0.908529	+	1.57362i	0.816109	+	0.577898i	$0.196127\pi$
$13$	3.27575	+	5.67376i	0.908529	+	1.57362i	0.0924194	+	0.995720i	$0.470540\pi$
$14$	−1.41421			−0.377964
$15$	2.41421			0.623347
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.60920	+	2.78721i	0.390287	+	0.675997i	0.992487	−	0.122348i	$-0.0390423\pi$
$17$	1.60920	+	2.78721i	0.390287	+	0.675997i	−0.602200	+	0.798345i	$0.705709\pi$
$18$	−1.41421	−	2.44949i	−0.333333	−	0.577350i
$19$	−1.31630	−	2.27990i	−0.301981	−	0.523046i	0.674604	−	0.738180i	$-0.264314\pi$
$19$	−1.31630	−	2.27990i	−0.301981	−	0.523046i	−0.976584	+	0.215134i	$0.930981\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	1.70711	−	2.95680i	0.372521	−	0.645226i
$22$	−2.00000			−0.426401
$23$	−3.92550	−	6.79916i	−0.818523	−	1.41772i	−0.906770	−	0.421625i	$-0.861460\pi$
$23$	−3.92550	−	6.79916i	−0.818523	−	1.41772i	0.0882473	−	0.996099i	$-0.471873\pi$
$24$	2.41421			0.492799
$25$	1.00000			0.200000
$26$	3.27575	−	5.67376i	0.642427	−	1.11272i
$27$	−0.414214			−0.0797154
$28$	0.707107	+	1.22474i	0.133631	+	0.231455i
$29$	−3.68996	+	6.39120i	−0.685208	+	1.18682i	0.288163	+	0.957581i	$0.406956\pi$
$29$	−3.68996	+	6.39120i	−0.685208	+	1.18682i	−0.973371	+	0.229234i	$0.926378\pi$
$30$	−1.20711	−	2.09077i	−0.220387	−	0.381721i
$31$	1.66188	−	2.87845i	0.298482	−	0.516986i	−0.677307	−	0.735700i	$-0.736853\pi$
$31$	1.66188	−	2.87845i	0.298482	−	0.516986i	0.975789	+	0.218715i	$0.0701864\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.41421	−	4.18154i	0.420261	−	0.727913i
$34$	1.60920	−	2.78721i	0.275975	−	0.478002i
$35$	0.707107	−	1.22474i	0.119523	−	0.207020i
$36$	−1.41421	+	2.44949i	−0.235702	+	0.408248i
$37$	−0.402089	−	0.696439i	−0.0661030	−	0.114494i	0.831080	−	0.556153i	$-0.187723\pi$
$37$	−0.402089	−	0.696439i	−0.0661030	−	0.114494i	−0.897183	+	0.441659i	$0.854390\pi$
$38$	−1.31630	+	2.27990i	−0.213532	+	0.369849i
$39$	7.90835	+	13.6977i	1.26635	+	2.19338i
$40$	1.00000			0.158114
$41$	3.64473	−	6.31286i	0.569211	−	0.985903i	−0.427433	−	0.904047i	$-0.640582\pi$
$41$	3.64473	−	6.31286i	0.569211	−	0.985903i	0.996644	−	0.0818556i	$-0.0260846\pi$
$42$	−3.41421			−0.526825
$43$	1.09046			0.166294			0.0831469	−	0.996537i	$-0.473503\pi$
$43$	1.09046			0.166294			0.0831469	+	0.996537i	$0.473503\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$	2.82843			0.421637
$46$	−3.92550	+	6.79916i	−0.578783	+	1.00248i
$47$	1.15443	−	1.99953i	0.168390	−	0.291661i	−0.769464	−	0.638691i	$-0.779476\pi$
$47$	1.15443	−	1.99953i	0.168390	−	0.291661i	0.937854	+	0.347030i	$0.112810\pi$
$48$	−1.20711	−	2.09077i	−0.174231	−	0.301777i
$49$	2.50000	+	4.33013i	0.357143	+	0.618590i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	3.88494	+	6.72892i	0.544001	+	0.942237i
$52$	−6.55149			−0.908529
$53$	0.918888			0.126219			0.0631095	−	0.998007i	$-0.479898\pi$
$53$	0.918888			0.126219			0.0631095	+	0.998007i	$0.479898\pi$
$54$	0.207107	+	0.358719i	0.0281837	+	0.0488155i
$55$	1.00000	−	1.73205i	0.134840	−	0.233550i
$56$	0.707107	−	1.22474i	0.0944911	−	0.163663i
$57$	−3.17784	−	5.50417i	−0.420915	−	0.729046i
$58$	7.37992			0.969031
$59$	−4.63261			−0.603114			−0.301557	−	0.953448i	$-0.597506\pi$
$59$	−4.63261			−0.603114			−0.301557	+	0.953448i	$0.597506\pi$
$60$	−1.20711	+	2.09077i	−0.155837	+	0.269917i
$61$	0.259787	+	0.449965i	0.0332623	+	0.0576121i	0.882177	−	0.470917i	$-0.156077\pi$
$61$	0.259787	+	0.449965i	0.0332623	+	0.0576121i	−0.848915	+	0.528529i	$0.822744\pi$
$62$	−3.32375			−0.422117
$63$	2.00000	−	3.46410i	0.251976	−	0.436436i
$64$	1.00000			0.125000
$65$	3.27575	+	5.67376i	0.406306	+	0.703743i
$66$	−4.82843			−0.594338
$67$	−6.07609	+	5.48463i	−0.742313	+	0.670054i
$67$	−6.07609	+	5.48463i	−0.742313	+	0.670054i
$68$	−3.21839			−0.390287
$69$	−9.47699	−	16.4146i	−1.14090	−	1.97609i
$70$	−1.41421			−0.169031
$71$	−1.10920	+	1.92118i	−0.131637	+	0.228003i	−0.924308	−	0.381648i	$-0.875357\pi$
$71$	−1.10920	+	1.92118i	−0.131637	+	0.228003i	0.792671	+	0.609650i	$0.208690\pi$
$72$	2.82843			0.333333
$73$	−2.21923	−	3.84382i	−0.259741	−	0.449885i	0.706431	−	0.707782i	$-0.250304\pi$
$73$	−2.21923	−	3.84382i	−0.259741	−	0.449885i	−0.966173	+	0.257896i	$0.916971\pi$
$74$	−0.402089	+	0.696439i	−0.0467419	+	0.0809594i
$75$	2.41421			0.278769
$76$	2.63261			0.301981
$77$	−1.41421	−	2.44949i	−0.161165	−	0.279145i
$78$	7.90835	−	13.6977i	0.895445	−	1.55096i
$79$	0.804178	−	1.39288i	0.0904771	−	0.156711i	−0.817235	−	0.576305i	$-0.804494\pi$
$79$	0.804178	−	1.39288i	0.0904771	−	0.156711i	0.907712	+	0.419594i	$0.137827\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−9.48528			−1.05392
$82$	−7.28946			−0.804986
$83$	−4.07609	−	7.05999i	−0.447409	−	0.774935i	0.550808	−	0.834632i	$-0.314320\pi$
$83$	−4.07609	−	7.05999i	−0.447409	−	0.774935i	−0.998217	+	0.0596972i	$0.980986\pi$
$84$	1.70711	+	2.95680i	0.186261	+	0.322613i
$85$	1.60920	+	2.78721i	0.174542	+	0.302315i
$86$	−0.545230	−	0.944367i	−0.0587937	−	0.101834i
$87$	−8.90835	+	15.4297i	−0.955076	+	1.65424i
$88$	1.00000	−	1.73205i	0.106600	−	0.184637i
$89$	2.26521			0.240112			0.120056	−	0.992767i	$-0.461693\pi$
$89$	2.26521			0.240112			0.120056	+	0.992767i	$0.461693\pi$
$90$	−1.41421	−	2.44949i	−0.149071	−	0.258199i
$91$	9.26521			0.971258
$92$	7.85100			0.818523
$93$	4.01212	−	6.94920i	0.416038	−	0.720599i
$94$	−2.30885			−0.238140
$95$	−1.31630	−	2.27990i	−0.135050	−	0.233913i
$96$	−1.20711	+	2.09077i	−0.123200	+	0.213388i
$97$	−0.131017	−	0.226928i	−0.0133027	−	0.0230410i	0.859297	−	0.511476i	$-0.170901\pi$
$97$	−0.131017	−	0.226928i	−0.0133027	−	0.0230410i	−0.872600	+	0.488435i	$0.837568\pi$
$98$	2.50000	−	4.33013i	0.252538	−	0.437409i
$99$	2.82843	−	4.89898i	0.284268	−	0.492366i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−6.16814	+	10.6835i	−0.613753	+	1.06305i	0.376849	+	0.926275i	$0.377008\pi$
$101$	−6.16814	+	10.6835i	−0.613753	+	1.06305i	−0.990602	+	0.136776i	$0.956326\pi$
$102$	3.88494	−	6.72892i	0.384667	−	0.666262i
$103$	−8.20125	+	14.2050i	−0.808093	+	1.39966i	0.106091	+	0.994356i	$0.466167\pi$
$103$	−8.20125	+	14.2050i	−0.808093	+	1.39966i	−0.914183	+	0.405301i	$0.867167\pi$
$104$	3.27575	+	5.67376i	0.321213	+	0.556358i
$105$	1.70711	−	2.95680i	0.166597	−	0.288554i
$106$	−0.459444	−	0.795780i	−0.0446251	−	0.0772930i
$107$	1.16153			0.112289			0.0561446	−	0.998423i	$-0.482119\pi$
$107$	1.16153			0.112289			0.0561446	+	0.998423i	$0.482119\pi$
$108$	0.207107	−	0.358719i	0.0199289	−	0.0345178i
$109$	−13.2520			−1.26931			−0.634655	−	0.772795i	$-0.718858\pi$
$109$	−13.2520			−1.26931			−0.634655	+	0.772795i	$0.718858\pi$
$110$	−2.00000			−0.190693
$111$	−0.970729	−	1.68135i	−0.0921375	−	0.159587i
$112$	−1.41421			−0.133631
$113$	9.00626	−	15.5993i	0.847238	−	1.46746i	−0.0364255	−	0.999336i	$-0.511597\pi$
$113$	9.00626	−	15.5993i	0.847238	−	1.46746i	0.883663	−	0.468123i	$-0.155070\pi$
$114$	−3.17784	+	5.50417i	−0.297632	+	0.515513i
$115$	−3.92550	−	6.79916i	−0.366055	−	0.634025i
$116$	−3.68996	−	6.39120i	−0.342604	−	0.593408i
$117$	9.26521	+	16.0478i	0.856569	+	1.48362i
$118$	2.31630	+	4.01195i	0.213233	+	0.369330i
$119$	4.55149			0.417235
$120$	2.41421			0.220387
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	0.259787	−	0.449965i	0.0235200	−	0.0407379i
$123$	8.79916	−	15.2406i	0.793393	−	1.37420i
$124$	1.66188	+	2.87845i	0.149241	+	0.258493i
$125$	1.00000			0.0894427
$126$	−4.00000			−0.356348
$127$	4.04682	−	7.00930i	0.359097	−	0.621974i	−0.628713	−	0.777637i	$-0.716418\pi$
$127$	4.04682	−	7.00930i	0.359097	−	0.621974i	0.987810	+	0.155663i	$0.0497514\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	2.63261			0.231788
$130$	3.27575	−	5.67376i	0.287302	−	0.497622i
$131$	−2.65200			−0.231706			−0.115853	−	0.993266i	$-0.536960\pi$
$131$	−2.65200			−0.231706			−0.115853	+	0.993266i	$0.536960\pi$
$132$	2.41421	+	4.18154i	0.210130	+	0.363956i
$133$	−3.72307			−0.322831
$134$	7.78787	+	2.51973i	0.672770	+	0.217672i
$135$	−0.414214			−0.0356498
$136$	1.60920	+	2.78721i	0.137987	+	0.239001i
$137$	−15.5414			−1.32780			−0.663898	−	0.747823i	$-0.731099\pi$
$137$	−15.5414			−1.32780			−0.663898	+	0.747823i	$0.731099\pi$
$138$	−9.47699	+	16.4146i	−0.806735	+	1.39731i
$139$	−22.2209			−1.88475			−0.942375	−	0.334559i	$-0.891413\pi$
$139$	−22.2209			−1.88475			−0.942375	+	0.334559i	$0.891413\pi$
$140$	0.707107	+	1.22474i	0.0597614	+	0.103510i
$141$	2.78703	−	4.82728i	0.234710	−	0.406530i
$142$	2.21839			0.186163
$143$	13.1030			1.09573
$144$	−1.41421	−	2.44949i	−0.117851	−	0.204124i
$145$	−3.68996	+	6.39120i	−0.306435	+	0.530760i
$146$	−2.21923	+	3.84382i	−0.183665	+	0.318117i
$147$	6.03553	+	10.4539i	0.497802	+	0.862219i
$148$	0.804178			0.0661030
$149$	7.91721			0.648603			0.324302	−	0.945954i	$-0.394871\pi$
$149$	7.91721			0.648603			0.324302	+	0.945954i	$0.394871\pi$
$150$	−1.20711	−	2.09077i	−0.0985599	−	0.170711i
$151$	2.38613	+	4.13290i	0.194180	+	0.336330i	0.946632	−	0.322318i	$-0.104462\pi$
$151$	2.38613	+	4.13290i	0.194180	+	0.336330i	−0.752451	+	0.658648i	$0.771129\pi$
$152$	−1.31630	−	2.27990i	−0.106766	−	0.184925i
$153$	4.55149	+	7.88342i	0.367966	+	0.637337i
$154$	−1.41421	+	2.44949i	−0.113961	+	0.197386i
$155$	1.66188	−	2.87845i	0.133485	−	0.231203i
$156$	−15.8167			−1.26635
$157$	8.59950	+	14.8948i	0.686315	+	1.18873i	0.973022	+	0.230714i	$0.0741061\pi$
$157$	8.59950	+	14.8948i	0.686315	+	1.18873i	−0.286707	+	0.958018i	$0.592561\pi$
$158$	−1.60836			−0.127954
$159$	2.21839			0.175930
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−11.1030			−0.875038
$162$	4.74264	+	8.21449i	0.372617	+	0.645392i
$163$	1.59707	−	2.76621i	0.125092	−	0.216666i	−0.796677	−	0.604406i	$-0.793411\pi$
$163$	1.59707	−	2.76621i	0.125092	−	0.216666i	0.921769	+	0.387739i	$0.126744\pi$
$164$	3.64473	+	6.31286i	0.284606	+	0.492951i
$165$	2.41421	−	4.18154i	0.187946	−	0.325532i
$166$	−4.07609	+	7.05999i	−0.316366	+	0.547962i
$167$	−7.61546	+	13.1904i	−0.589302	+	1.02070i	0.405022	+	0.914307i	$0.367264\pi$
$167$	−7.61546	+	13.1904i	−0.589302	+	1.02070i	−0.994324	+	0.106394i	$0.966070\pi$
$168$	1.70711	−	2.95680i	0.131706	−	0.228122i
$169$	−14.9610	+	25.9133i	−1.15085	+	1.99333i
$170$	1.60920	−	2.78721i	0.123420	−	0.213769i
$171$	−3.72307	−	6.44854i	−0.284710	−	0.493132i
$172$	−0.545230	+	0.944367i	−0.0415734	+	0.0720073i
$173$	−5.50626	−	9.53713i	−0.418633	−	0.725094i	0.577169	−	0.816625i	$-0.304157\pi$
$173$	−5.50626	−	9.53713i	−0.418633	−	0.725094i	−0.995802	+	0.0915305i	$0.970824\pi$
$174$	17.8167			1.35068
$175$	0.707107	−	1.22474i	0.0534522	−	0.0925820i
$176$	−2.00000			−0.150756
$177$	−11.1841			−0.840648
$178$	−1.13261	−	1.96173i	−0.0848924	−	0.147038i
$179$	−20.2216			−1.51143			−0.755716	−	0.654900i	$-0.772711\pi$
$179$	−20.2216			−1.51143			−0.755716	+	0.654900i	$0.772711\pi$
$180$	−1.41421	+	2.44949i	−0.105409	+	0.182574i
$181$	−10.4544	+	18.1076i	−0.777071	+	1.34593i	0.156552	+	0.987670i	$0.449962\pi$
$181$	−10.4544	+	18.1076i	−0.777071	+	1.34593i	−0.933623	+	0.358257i	$0.883371\pi$
$182$	−4.63261	−	8.02391i	−0.343392	−	0.594772i
$183$	0.627182	+	1.08631i	0.0463626	+	0.0803024i
$184$	−3.92550	−	6.79916i	−0.289392	−	0.501241i
$185$	−0.402089	−	0.696439i	−0.0295622	−	0.0512032i
$186$	−8.02425			−0.588366
$187$	6.43678			0.470704
$188$	1.15443	+	1.99953i	0.0841952	+	0.145830i
$189$	−0.292893	+	0.507306i	−0.0213048	+	0.0369011i
$190$	−1.31630	+	2.27990i	−0.0954946	+	0.165402i
$191$	7.83226	+	13.5659i	0.566723	+	0.981592i	0.996887	+	0.0788418i	$0.0251222\pi$
$191$	7.83226	+	13.5659i	0.566723	+	0.981592i	−0.430165	+	0.902751i	$0.641544\pi$
$192$	2.41421			0.174231
$193$	15.7162			1.13128			0.565638	−	0.824653i	$-0.308630\pi$
$193$	15.7162			1.13128			0.565638	+	0.824653i	$0.308630\pi$
$194$	−0.131017	+	0.226928i	−0.00940646	+	0.0162925i
$195$	7.90835	+	13.6977i	0.566329	+	0.980910i
$196$	−5.00000			−0.357143
$197$	8.48528	−	14.6969i	0.604551	−	1.04711i	−0.387571	−	0.921840i	$-0.626686\pi$
$197$	8.48528	−	14.6969i	0.604551	−	1.04711i	0.992122	−	0.125274i	$-0.0399809\pi$
$198$	−5.65685			−0.402015
$199$	9.59448	+	16.6181i	0.680134	+	1.17803i	0.974940	+	0.222470i	$0.0714120\pi$
$199$	9.59448	+	16.6181i	0.680134	+	1.17803i	−0.294805	+	0.955557i	$0.595255\pi$
$200$	1.00000			0.0707107
$201$	−14.6690	+	13.2411i	−1.03467	+	0.933952i
$202$	12.3363			0.867978
$203$	5.21839	+	9.03852i	0.366259	+	0.634380i
$204$	−7.76989			−0.544001
$205$	3.64473	−	6.31286i	0.254559	−	0.440909i
$206$	16.4025			1.14282
$207$	−11.1030	−	19.2309i	−0.771711	−	1.33664i
$208$	3.27575	−	5.67376i	0.227132	−	0.393404i
$209$	−5.26521			−0.364202
$210$	−3.41421			−0.235603
$211$	11.7602	+	20.3692i	0.809605	+	1.40228i	0.913138	+	0.407651i	$0.133652\pi$
$211$	11.7602	+	20.3692i	0.809605	+	1.40228i	−0.103533	+	0.994626i	$0.533015\pi$
$212$	−0.459444	+	0.795780i	−0.0315547	+	0.0546544i
$213$	−2.67784	+	4.63815i	−0.183482	+	0.317801i
$214$	−0.580764	−	1.00591i	−0.0397002	−	0.0687628i
$215$	1.09046			0.0743688
$216$	−0.414214			−0.0281837
$217$	−2.35025	−	4.07075i	−0.159545	−	0.276340i
$218$	6.62599	+	11.4766i	0.448769	+	0.777291i
$219$	−5.35770	−	9.27981i	−0.362040	−	0.627071i
$220$	1.00000	+	1.73205i	0.0674200	+	0.116775i
$221$	−10.5426	+	18.2604i	−0.709174	+	1.22833i
$222$	−0.970729	+	1.68135i	−0.0651511	+	0.112845i
$223$	−25.0819			−1.67961			−0.839805	−	0.542889i	$-0.817331\pi$
$223$	−25.0819			−1.67961			−0.839805	+	0.542889i	$0.817331\pi$
$224$	0.707107	+	1.22474i	0.0472456	+	0.0818317i
$225$	2.82843			0.188562
$226$	−18.0125			−1.19818
$227$	9.79289	−	16.9618i	0.649977	−	1.12579i	−0.333151	−	0.942874i	$-0.608112\pi$
$227$	9.79289	−	16.9618i	0.649977	−	1.12579i	0.983128	−	0.182920i	$-0.0585549\pi$
$228$	6.35567			0.420915
$229$	2.75511	+	4.77200i	0.182063	+	0.315342i	0.942583	−	0.333972i	$-0.108389\pi$
$229$	2.75511	+	4.77200i	0.182063	+	0.315342i	−0.760520	+	0.649315i	$0.775056\pi$
$230$	−3.92550	+	6.79916i	−0.258840	+	0.448324i
$231$	−3.41421	−	5.91359i	−0.224639	−	0.389086i
$232$	−3.68996	+	6.39120i	−0.242258	+	0.419603i
$233$	10.0234	−	17.3611i	0.656655	−	1.13736i	−0.324821	−	0.945776i	$-0.605304\pi$
$233$	10.0234	−	17.3611i	0.656655	−	1.13736i	0.981476	−	0.191585i	$-0.0613627\pi$
$234$	9.26521	−	16.0478i	0.605686	−	1.04908i
$235$	1.15443	−	1.99953i	0.0753065	−	0.130435i
$236$	2.31630	−	4.01195i	0.150778	−	0.261156i
$237$	1.94146	−	3.36270i	0.126111	−	0.218431i
$238$	−2.27575	−	3.94171i	−0.147515	−	0.255503i
$239$	11.7699	−	20.3860i	0.761331	−	1.31866i	−0.180834	−	0.983514i	$-0.557880\pi$
$239$	11.7699	−	20.3860i	0.761331	−	1.31866i	0.942165	−	0.335150i	$-0.108787\pi$
$240$	−1.20711	−	2.09077i	−0.0779184	−	0.134959i
$241$	−10.4125			−0.670730			−0.335365	−	0.942088i	$-0.608860\pi$
$241$	−10.4125			−0.670730			−0.335365	+	0.942088i	$0.608860\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$	−21.6569			−1.38929
$244$	−0.519574			−0.0332623
$245$	2.50000	+	4.33013i	0.159719	+	0.276642i
$246$	−17.5983			−1.12203
$247$	8.62375	−	14.9368i	0.548716	−	0.950404i
$248$	1.66188	−	2.87845i	0.105529	−	0.182782i
$249$	−9.84055	−	17.0443i	−0.623620	−	1.08014i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−11.4513	−	19.8343i	−0.722802	−	1.25193i	−0.959872	−	0.280437i	$-0.909521\pi$
$251$	−11.4513	−	19.8343i	−0.722802	−	1.25193i	0.237070	−	0.971492i	$-0.423813\pi$
$252$	2.00000	+	3.46410i	0.125988	+	0.218218i
$253$	−15.7020			−0.987176
$254$	−8.09364			−0.507840
$255$	3.88494	+	6.72892i	0.243285	+	0.421381i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.05617	−	15.6857i	0.564908	−	0.978450i	−0.432150	−	0.901802i	$-0.642245\pi$
$257$	9.05617	−	15.6857i	0.564908	−	0.978450i	0.997058	−	0.0766480i	$-0.0244218\pi$
$258$	−1.31630	−	2.27990i	−0.0819494	−	0.141941i
$259$	−1.13728			−0.0706671
$260$	−6.55149			−0.406306
$261$	−10.4368	+	18.0770i	−0.646021	+	1.11894i
$262$	1.32600	+	2.29670i	0.0819205	+	0.141890i
$263$	4.50300			0.277667			0.138833	−	0.990316i	$-0.455665\pi$
$263$	4.50300			0.277667			0.138833	+	0.990316i	$0.455665\pi$
$264$	2.41421	−	4.18154i	0.148585	−	0.257356i
$265$	0.918888			0.0564468
$266$	1.86153	+	3.22427i	0.114138	+	0.197693i
$267$	5.46870			0.334679
$268$	−1.71178	−	8.00436i	−0.104564	−	0.488944i
$269$	−8.71372			−0.531285			−0.265642	−	0.964072i	$-0.585584\pi$
$269$	−8.71372			−0.531285			−0.265642	+	0.964072i	$0.585584\pi$
$270$	0.207107	+	0.358719i	0.0126041	+	0.0218310i
$271$	18.8846			1.14716			0.573579	−	0.819150i	$-0.305555\pi$
$271$	18.8846			1.14716			0.573579	+	0.819150i	$0.305555\pi$
$272$	1.60920	−	2.78721i	0.0975718	−	0.168999i
$273$	22.3682			1.35378
$274$	7.77072	+	13.4593i	0.469447	+	0.813105i
$275$	1.00000	−	1.73205i	0.0603023	−	0.104447i
$276$	18.9540			1.14090
$277$	−12.5095			−0.751625			−0.375812	−	0.926696i	$-0.622636\pi$
$277$	−12.5095			−0.751625			−0.375812	+	0.926696i	$0.622636\pi$
$278$	11.1104	+	19.2438i	0.666360	+	1.15417i
$279$	4.70050	−	8.14150i	0.281411	−	0.487419i
$280$	0.707107	−	1.22474i	0.0422577	−	0.0731925i
$281$	8.15685	+	14.1281i	0.486597	+	0.842811i	0.999881	−	0.0154078i	$-0.00490464\pi$
$281$	8.15685	+	14.1281i	0.486597	+	0.842811i	−0.513284	+	0.858219i	$0.671571\pi$
$282$	−5.57406			−0.331931
$283$	0.424258			0.0252195			0.0126098	−	0.999920i	$-0.495986\pi$
$283$	0.424258			0.0252195			0.0126098	+	0.999920i	$0.495986\pi$
$284$	−1.10920	−	1.92118i	−0.0658187	−	0.114001i
$285$	−3.17784	−	5.50417i	−0.188239	−	0.326039i
$286$	−6.55149	−	11.3475i	−0.387398	−	0.670993i
$287$	−5.15443	−	8.92773i	−0.304256	−	0.526987i
$288$	−1.41421	+	2.44949i	−0.0833333	+	0.144338i
$289$	3.32098	−	5.75210i	0.195352	−	0.338359i
$290$	7.37992			0.433364
$291$	−0.316303	−	0.547852i	−0.0185420	−	0.0321157i
$292$	4.43846			0.259741
$293$	11.7958			0.689119			0.344559	−	0.938765i	$-0.388028\pi$
$293$	11.7958			0.689119			0.344559	+	0.938765i	$0.388028\pi$
$294$	6.03553	−	10.4539i	0.351999	−	0.609681i
$295$	−4.63261			−0.269721
$296$	−0.402089	−	0.696439i	−0.0233710	−	0.0404797i
$297$	−0.414214	+	0.717439i	−0.0240351	+	0.0416300i
$298$	−3.95860	−	6.85650i	−0.229316	−	0.397187i
$299$	25.7179	−	44.5447i	1.48730	−	2.57608i
$300$	−1.20711	+	2.09077i	−0.0696923	+	0.120711i
$301$	0.771072	−	1.33554i	0.0444439	−	0.0769790i
$302$	2.38613	−	4.13290i	0.137306	−	0.237822i
$303$	−14.8912	+	25.7923i	−0.855477	+	1.48173i
$304$	−1.31630	+	2.27990i	−0.0754951	+	0.130761i
$305$	0.259787	+	0.449965i	0.0148754	+	0.0257649i
$306$	4.55149	−	7.88342i	0.260192	−	0.450665i
$307$	−6.16346	−	10.6754i	−0.351768	−	0.609279i	0.634792	−	0.772683i	$-0.281086\pi$
$307$	−6.16346	−	10.6754i	−0.351768	−	0.609279i	−0.986559	+	0.163404i	$0.947753\pi$
$308$	2.82843			0.161165
$309$	−19.7996	+	34.2938i	−1.12636	+	1.95091i
$310$	−3.32375			−0.188776
$311$	9.69432			0.549715			0.274857	−	0.961485i	$-0.411369\pi$
$311$	9.69432			0.549715			0.274857	+	0.961485i	$0.411369\pi$
$312$	7.90835	+	13.6977i	0.447722	+	0.775478i
$313$	−9.62424			−0.543994			−0.271997	−	0.962298i	$-0.587684\pi$
$313$	−9.62424			−0.543994			−0.271997	+	0.962298i	$0.587684\pi$
$314$	8.59950	−	14.8948i	0.485298	−	0.840560i
$315$	2.00000	−	3.46410i	0.112687	−	0.195180i
$316$	0.804178	+	1.39288i	0.0452386	+	0.0783555i
$317$	11.1962	+	19.3924i	0.628843	+	1.08919i	0.987784	+	0.155827i	$0.0498043\pi$
$317$	11.1962	+	19.3924i	0.628843	+	1.08919i	−0.358942	+	0.933360i	$0.616862\pi$
$318$	−1.10920	−	1.92118i	−0.0622006	−	0.107735i
$319$	7.37992	+	12.7824i	0.413196	+	0.715677i
$320$	1.00000			0.0559017
$321$	2.80418			0.156514
$322$	5.55149	+	9.61547i	0.309373	+	0.535849i
$323$	4.23638	−	7.33762i	0.235718	−	0.408276i
$324$	4.74264	−	8.21449i	0.263480	−	0.456361i
$325$	3.27575	+	5.67376i	0.181706	+	0.314724i
$326$	−3.19414			−0.176907
$327$	−31.9931			−1.76922
$328$	3.64473	−	6.31286i	0.201247	−	0.348569i
$329$	−1.63261	−	2.82776i	−0.0900084	−	0.155899i
$330$	−4.82843			−0.265796
$331$	14.0636	−	24.3589i	0.773006	−	1.33889i	−0.162902	−	0.986642i	$-0.552085\pi$
$331$	14.0636	−	24.3589i	0.773006	−	1.33889i	0.935908	−	0.352244i	$-0.114581\pi$
$332$	8.15218			0.447409
$333$	−1.13728	−	1.96983i	−0.0623225	−	0.107946i
$334$	15.2309			0.833399
$335$	−6.07609	+	5.48463i	−0.331972	+	0.299657i
$336$	−3.41421			−0.186261
$337$	9.70592	+	16.8111i	0.528715	+	0.915761i	0.999439	+	0.0334811i	$0.0106593\pi$
$337$	9.70592	+	16.8111i	0.528715	+	0.915761i	−0.470724	+	0.882280i	$0.656007\pi$
$338$	29.9221			1.62755
$339$	21.7430	−	37.6601i	1.18092	−	2.04541i
$340$	−3.21839			−0.174542
$341$	−3.32375	−	5.75691i	−0.179991	−	0.311754i
$342$	−3.72307	+	6.44854i	−0.201320	+	0.348697i
$343$	16.9706			0.916324
$344$	1.09046			0.0587937
$345$	−9.47699	−	16.4146i	−0.510224	−	0.883734i
$346$	−5.50626	+	9.53713i	−0.296019	+	0.512719i
$347$	7.29255	−	12.6311i	0.391484	−	0.678071i	−0.601161	−	0.799128i	$-0.705295\pi$
$347$	7.29255	−	12.6311i	0.391484	−	0.678071i	0.992646	+	0.121057i	$0.0386284\pi$
$348$	−8.90835	−	15.4297i	−0.477538	−	0.827120i
$349$	3.93043			0.210391			0.105196	−	0.994452i	$-0.466453\pi$
$349$	3.93043			0.210391			0.105196	+	0.994452i	$0.466453\pi$
$350$	−1.41421			−0.0755929
$351$	−1.35686	−	2.35015i	−0.0724238	−	0.125442i
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	−11.9635	−	20.7213i	−0.636751	−	1.10288i	−0.986141	−	0.165907i	$-0.946945\pi$
$353$	−11.9635	−	20.7213i	−0.636751	−	1.10288i	0.349391	−	0.936977i	$-0.386389\pi$
$354$	5.59205	+	9.68571i	0.297214	+	0.514790i
$355$	−1.10920	+	1.92118i	−0.0588700	+	0.101966i
$356$	−1.13261	+	1.96173i	−0.0600280	+	0.103971i
$357$	10.9883			0.581561
$358$	10.1108	+	17.5124i	0.534372	+	0.925559i
$359$	25.4846			1.34503			0.672513	−	0.740086i	$-0.265215\pi$
$359$	25.4846			1.34503			0.672513	+	0.740086i	$0.265215\pi$
$360$	2.82843			0.149071
$361$	6.03469	−	10.4524i	0.317615	−	0.550126i
$362$	20.9088			1.09894
$363$	8.44975	+	14.6354i	0.443497	+	0.768159i
$364$	−4.63261	+	8.02391i	−0.242814	+	0.420567i
$365$	−2.21923	−	3.84382i	−0.116160	−	0.201195i
$366$	0.627182	−	1.08631i	0.0327833	−	0.0567824i
$367$	12.3640	−	21.4150i	0.645394	−	1.11785i	−0.338817	−	0.940852i	$-0.610027\pi$
$367$	12.3640	−	21.4150i	0.645394	−	1.11785i	0.984210	−	0.177002i	$-0.0566399\pi$
$368$	−3.92550	+	6.79916i	−0.204631	+	0.354431i
$369$	10.3089	−	17.8555i	0.536657	−	0.929518i
$370$	−0.402089	+	0.696439i	−0.0209036	+	0.0362061i
$371$	0.649752	−	1.12540i	0.0337334	−	0.0584280i
$372$	4.01212	+	6.94920i	0.208019	+	0.360299i
$373$	2.18370	−	3.78227i	0.113068	−	0.195839i	−0.803938	−	0.594713i	$-0.797266\pi$
$373$	2.18370	−	3.78227i	0.113068	−	0.195839i	0.917006	+	0.398874i	$0.130599\pi$
$374$	−3.21839	−	5.57442i	−0.166419	−	0.288246i
$375$	2.41421			0.124669
$376$	1.15443	−	1.99953i	0.0595350	−	0.103118i
$377$	−48.3495			−2.49013
$378$	0.585786			0.0301296
$379$	−2.93379	−	5.08147i	−0.150699	−	0.261018i	0.780786	−	0.624799i	$-0.214819\pi$
$379$	−2.93379	−	5.08147i	−0.150699	−	0.261018i	−0.931484	+	0.363781i	$0.881486\pi$
$380$	2.63261			0.135050
$381$	9.76989	−	16.9219i	0.500526	−	0.866937i
$382$	7.83226	−	13.5659i	0.400733	−	0.694091i
$383$	16.2309	+	28.1128i	0.829361	+	1.43650i	0.898540	+	0.438891i	$0.144629\pi$
$383$	16.2309	+	28.1128i	0.829361	+	1.43650i	−0.0691790	+	0.997604i	$0.522038\pi$
$384$	−1.20711	−	2.09077i	−0.0615999	−	0.106694i
$385$	−1.41421	−	2.44949i	−0.0720750	−	0.124838i
$386$	−7.85810	−	13.6106i	−0.399967	−	0.692763i
$387$	3.08429			0.156783
$388$	0.262034			0.0133027
$389$	−15.6155	−	27.0468i	−0.791735	−	1.37133i	−0.924892	−	0.380231i	$-0.875845\pi$
$389$	−15.6155	−	27.0468i	−0.791735	−	1.37133i	0.133157	−	0.991095i	$-0.457489\pi$
$390$	7.90835	−	13.6977i	0.400455	−	0.693608i
$391$	12.6338	−	21.8824i	0.638918	−	1.10664i
$392$	2.50000	+	4.33013i	0.126269	+	0.218704i
$393$	−6.40249			−0.322963
$394$	−16.9706			−0.854965
$395$	0.804178	−	1.39288i	0.0404626	−	0.0700833i
$396$	2.82843	+	4.89898i	0.142134	+	0.246183i
$397$	−17.4493			−0.875756			−0.437878	−	0.899034i	$-0.644270\pi$
$397$	−17.4493			−0.875756			−0.437878	+	0.899034i	$0.644270\pi$
$398$	9.59448	−	16.6181i	0.480928	−	0.832991i
$399$	−8.98828			−0.449977
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	8.55387			0.427160			0.213580	−	0.976926i	$-0.431488\pi$
$401$	8.55387			0.427160			0.213580	+	0.976926i	$0.431488\pi$
$402$	18.8016	+	6.08318i	0.937738	+	0.303401i
$403$	21.7755			1.08472
$404$	−6.16814	−	10.6835i	−0.306876	−	0.531526i
$405$	−9.48528			−0.471327
$406$	5.21839	−	9.03852i	0.258984	−	0.448574i
$407$	−1.60836			−0.0797233
$408$	3.88494	+	6.72892i	0.192333	+	0.333131i
$409$	−12.8631	+	22.2796i	−0.636040	+	1.10165i	0.350253	+	0.936655i	$0.386096\pi$
$409$	−12.8631	+	22.2796i	−0.636040	+	1.10165i	−0.986294	+	0.164999i	$0.947238\pi$
$410$	−7.28946			−0.360001
$411$	−37.5204			−1.85074
$412$	−8.20125	−	14.2050i	−0.404046	−	0.699829i
$413$	−3.27575	+	5.67376i	−0.161189	+	0.279187i
$414$	−11.1030	+	19.2309i	−0.545682	+	0.945149i
$415$	−4.07609	−	7.05999i	−0.200087	−	0.346562i
$416$	−6.55149			−0.321213
$417$	−53.6459			−2.62705
$418$	2.63261	+	4.55981i	0.128765	+	0.223027i
$419$	11.2009	+	19.4005i	0.547200	+	0.947778i	0.998465	+	0.0553877i	$0.0176395\pi$
$419$	11.2009	+	19.4005i	0.547200	+	0.947778i	−0.451265	+	0.892390i	$0.649027\pi$
$420$	1.70711	+	2.95680i	0.0832983	+	0.144277i
$421$	1.75736	+	3.04384i	0.0856485	+	0.148347i	0.905667	−	0.423989i	$-0.139370\pi$
$421$	1.75736	+	3.04384i	0.0856485	+	0.148347i	−0.820019	+	0.572336i	$0.806037\pi$
$422$	11.7602	−	20.3692i	0.572477	−	0.991559i
$423$	3.26521	−	5.65551i	0.158760	−	0.274980i
$424$	0.918888			0.0446251
$425$	1.60920	+	2.78721i	0.0780575	+	0.135199i
$426$	5.35567			0.259483
$427$	0.734789			0.0355589
$428$	−0.580764	+	1.00591i	−0.0280723	+	0.0486227i
$429$	31.6334			1.52728
$430$	−0.545230	−	0.944367i	−0.0262933	−	0.0455414i
$431$	2.89080	−	5.00702i	0.139245	−	0.241180i	−0.787966	−	0.615719i	$-0.788866\pi$
$431$	2.89080	−	5.00702i	0.139245	−	0.241180i	0.927211	+	0.374539i	$0.122199\pi$
$432$	0.207107	+	0.358719i	0.00996443	+	0.0172589i
$433$	9.24180	−	16.0073i	0.444133	−	0.769260i	−0.553859	−	0.832611i	$-0.686845\pi$
$433$	9.24180	−	16.0073i	0.444133	−	0.769260i	0.997991	+	0.0633504i	$0.0201786\pi$
$434$	−2.35025	+	4.07075i	−0.112816	+	0.195402i
$435$	−8.90835	+	15.4297i	−0.427123	+	0.739798i
$436$	6.62599	−	11.4766i	0.317328	−	0.549628i
$437$	−10.3343	+	17.8995i	−0.494356	+	0.856250i
$438$	−5.35770	+	9.27981i	−0.256001	+	0.443406i
$439$	−2.71923	−	4.70985i	−0.129782	−	0.224789i	0.793810	−	0.608166i	$-0.208094\pi$
$439$	−2.71923	−	4.70985i	−0.129782	−	0.224789i	−0.923592	+	0.383377i	$0.874761\pi$
$440$	1.00000	−	1.73205i	0.0476731	−	0.0825723i
$441$	7.07107	+	12.2474i	0.336718	+	0.583212i
$442$	21.0853			1.00292
$443$	−8.01129	+	13.8760i	−0.380628	+	0.659266i	−0.991152	−	0.132731i	$-0.957625\pi$
$443$	−8.01129	+	13.8760i	−0.380628	+	0.659266i	0.610524	+	0.791997i	$0.290959\pi$
$444$	1.94146			0.0921375
$445$	2.26521			0.107381
$446$	12.5410	+	21.7216i	0.593832	+	1.02855i
$447$	19.1138			0.904053
$448$	0.707107	−	1.22474i	0.0334077	−	0.0578638i
$449$	−19.2899	+	33.4110i	−0.910345	+	1.57676i	−0.0967673	+	0.995307i	$0.530850\pi$
$449$	−19.2899	+	33.4110i	−0.910345	+	1.57676i	−0.813578	+	0.581456i	$0.802483\pi$
$450$	−1.41421	−	2.44949i	−0.0666667	−	0.115470i
$451$	−7.28946	−	12.6257i	−0.343247	−	0.594522i
$452$	9.00626	+	15.5993i	0.423619	+	0.733730i
$453$	5.76063	+	9.97770i	0.270658	+	0.468793i
$454$	−19.5858			−0.919207
$455$	9.26521			0.434360
$456$	−3.17784	−	5.50417i	−0.148816	−	0.257757i
$457$	5.28544	−	9.15466i	0.247243	−	0.428237i	−0.715517	−	0.698595i	$-0.753809\pi$
$457$	5.28544	−	9.15466i	0.247243	−	0.428237i	0.962760	+	0.270358i	$0.0871422\pi$
$458$	2.75511	−	4.77200i	0.128738	−	0.222981i
$459$	−0.666551	−	1.15450i	−0.0311119	−	0.0538874i
$460$	7.85100			0.366055
$461$	19.0961			0.889395			0.444697	−	0.895681i	$-0.353311\pi$
$461$	19.0961			0.889395			0.444697	+	0.895681i	$0.353311\pi$
$462$	−3.41421	+	5.91359i	−0.158844	+	0.275125i
$463$	0.523008	+	0.905877i	0.0243062	+	0.0420997i	0.877923	−	0.478802i	$-0.158929\pi$
$463$	0.523008	+	0.905877i	0.0243062	+	0.0420997i	−0.853616	+	0.520902i	$0.825596\pi$
$464$	7.37992			0.342604
$465$	4.01212	−	6.94920i	0.186058	−	0.322262i
$466$	−20.0468			−0.928651
$467$	−9.43344	−	16.3392i	−0.436528	−	0.756088i	0.560891	−	0.827889i	$-0.310459\pi$
$467$	−9.43344	−	16.3392i	−0.436528	−	0.756088i	−0.997419	+	0.0718015i	$0.977125\pi$
$468$	−18.5304			−0.856569
$469$	2.42082	+	11.3199i	0.111783	+	0.522703i
$470$	−2.30885			−0.106499
$471$	20.7610	+	35.9592i	0.956618	+	1.65691i
$472$	−4.63261			−0.213233
$473$	1.09046	−	1.88873i	0.0501394	−	0.0868441i
$474$	−3.88292			−0.178348
$475$	−1.31630	−	2.27990i	−0.0603961	−	0.104609i
$476$	−2.27575	+	3.94171i	−0.104309	+	0.180668i
$477$	2.59901			0.119000
$478$	−23.5398			−1.07668
$479$	2.83896	+	4.91723i	0.129716	+	0.224674i	0.923566	−	0.383439i	$-0.125260\pi$
$479$	2.83896	+	4.91723i	0.129716	+	0.224674i	−0.793851	+	0.608113i	$0.791927\pi$
$480$	−1.20711	+	2.09077i	−0.0550966	+	0.0954302i
$481$	2.63428	−	4.56271i	0.120113	−	0.208042i
$482$	5.20627	+	9.01752i	0.237139	+	0.410737i
$483$	−26.8050			−1.21967
$484$	−7.00000			−0.318182
$485$	−0.131017	−	0.226928i	−0.00594917	−	0.0103043i
$486$	10.8284	+	18.7554i	0.491187	+	0.850762i
$487$	−0.878680	−	1.52192i	−0.0398168	−	0.0689647i	0.845430	−	0.534086i	$-0.179344\pi$
$487$	−0.878680	−	1.52192i	−0.0398168	−	0.0689647i	−0.885247	+	0.465121i	$0.846011\pi$
$488$	0.259787	+	0.449965i	0.0117600	+	0.0203689i
$489$	3.85567	−	6.67822i	0.174359	−	0.302000i
$490$	2.50000	−	4.33013i	0.112938	−	0.195615i
$491$	33.4719			1.51056			0.755282	−	0.655400i	$-0.227500\pi$
$491$	33.4719			1.51056			0.755282	+	0.655400i	$0.227500\pi$
$492$	8.79916	+	15.2406i	0.396697	+	0.687099i
$493$	−23.7515			−1.06971
$494$	−17.2475			−0.776002
$495$	2.82843	−	4.89898i	0.127128	−	0.220193i
$496$	−3.32375			−0.149241
$497$	1.56864	+	2.71696i	0.0703631	+	0.121872i
$498$	−9.84055	+	17.0443i	−0.440966	+	0.763775i
$499$	−15.7999	−	27.3662i	−0.707301	−	1.22508i	−0.965855	−	0.259084i	$-0.916579\pi$
$499$	−15.7999	−	27.3662i	−0.707301	−	1.22508i	0.258554	−	0.965997i	$-0.416754\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−18.3853	+	31.8443i	−0.821397	+	1.42270i
$502$	−11.4513	+	19.8343i	−0.511098	+	0.885248i
$503$	−8.37106	+	14.4991i	−0.373247	+	0.646483i	−0.990063	−	0.140624i	$-0.955089\pi$
$503$	−8.37106	+	14.4991i	−0.373247	+	0.646483i	0.616816	+	0.787108i	$0.288422\pi$
$504$	2.00000	−	3.46410i	0.0890871	−	0.154303i
$505$	−6.16814	+	10.6835i	−0.274479	+	0.475411i
$506$	7.85100	+	13.5983i	0.349019	+	0.604519i
$507$	−36.1191	+	62.5602i	−1.60411	+	2.77839i
$508$	4.04682	+	7.00930i	0.179549	+	0.310987i
$509$	−11.0898			−0.491545			−0.245773	−	0.969328i	$-0.579042\pi$
$509$	−11.0898			−0.491545			−0.245773	+	0.969328i	$0.579042\pi$
$510$	3.88494	−	6.72892i	0.172028	−	0.297961i
$511$	−6.27693			−0.277675
$512$	1.00000			0.0441942
$513$	0.545230	+	0.944367i	0.0240725	+	0.0416948i
$514$	−18.1123			−0.798901
$515$	−8.20125	+	14.2050i	−0.361390	+	0.625946i
$516$	−1.31630	+	2.27990i	−0.0579470	+	0.100367i
$517$	−2.30885	−	3.99905i	−0.101543	−	0.175878i
$518$	0.568640	+	0.984913i	0.0249846	+	0.0432746i
$519$	−13.2933	−	23.0247i	−0.583511	−	1.01067i
$520$	3.27575	+	5.67376i	0.143651	+	0.248811i
$521$	18.5640			0.813304			0.406652	−	0.913583i	$-0.366696\pi$
$521$	18.5640			0.813304			0.406652	+	0.913583i	$0.366696\pi$
$522$	20.8736			0.913611
$523$	−16.0917	−	27.8716i	−0.703641	−	1.21874i	−0.967180	−	0.254093i	$-0.918223\pi$
$523$	−16.0917	−	27.8716i	−0.703641	−	1.21874i	0.263539	−	0.964649i	$-0.415110\pi$
$524$	1.32600	−	2.29670i	0.0579265	−	0.100332i
$525$	1.70711	−	2.95680i	0.0745042	−	0.129045i
$526$	−2.25150	−	3.89971i	−0.0981700	−	0.170035i
$527$	10.6971			0.465975
$528$	−4.82843			−0.210130
$529$	−19.3191	+	33.4616i	−0.839960	+	1.45485i
$530$	−0.459444	−	0.795780i	−0.0199570	−	0.0345665i
$531$	−13.1030			−0.568621
$532$	1.86153	−	3.22427i	0.0807077	−	0.139790i
$533$	47.7568			2.06858
$534$	−2.73435	−	4.73604i	−0.118327	−	0.204948i
$535$	1.16153			0.0502173
$536$	−6.07609	+	5.48463i	−0.262447	+	0.236900i
$537$	−48.8192			−2.10670
$538$	4.35686	+	7.54630i	0.187838	+	0.325344i
$539$	10.0000			0.430730
$540$	0.207107	−	0.358719i	0.00891246	−	0.0154368i
$541$	31.0853			1.33646			0.668230	−	0.743955i	$-0.267052\pi$
$541$	31.0853			1.33646			0.668230	+	0.743955i	$0.267052\pi$
$542$	−9.44230	−	16.3545i	−0.405581	−	0.702488i
$543$	−25.2392	+	43.7156i	−1.08312	+	1.87602i
$544$	−3.21839			−0.137987
$545$	−13.2520			−0.567653
$546$	−11.1841	−	19.3714i	−0.478635	−	0.829021i
$547$	6.83345	−	11.8359i	0.292177	−	0.506066i	−0.682147	−	0.731215i	$-0.738954\pi$
$547$	6.83345	−	11.8359i	0.292177	−	0.506066i	0.974324	+	0.225149i	$0.0722870\pi$
$548$	7.77072	−	13.4593i	0.331949	−	0.574952i
$549$	0.734789	+	1.27269i	0.0313600	+	0.0543172i
$550$	−2.00000			−0.0852803
$551$	19.4284			0.827678
$552$	−9.47699	−	16.4146i	−0.403368	−	0.698653i
$553$	−1.13728	−	1.96983i	−0.0483621	−	0.0837655i
$554$	6.25477	+	10.8336i	0.265740	+	0.460274i
$555$	−0.970729	−	1.68135i	−0.0412052	−	0.0713694i
$556$	11.1104	−	19.2438i	0.471187	−	0.816121i
$557$	−11.3678	+	19.6896i	−0.481669	+	0.834275i	−0.999779	−	0.0210390i	$-0.993303\pi$
$557$	−11.3678	+	19.6896i	−0.481669	+	0.834275i	0.518110	+	0.855314i	$0.326636\pi$
$558$	−9.40099			−0.397976
$559$	3.57207	+	6.18701i	0.151083	+	0.261683i
$560$	−1.41421			−0.0597614
$561$	15.5398			0.656090
$562$	8.15685	−	14.1281i	0.344076	−	0.595957i
$563$	−42.5717			−1.79418			−0.897091	−	0.441845i	$-0.854324\pi$
$563$	−42.5717			−1.79418			−0.897091	+	0.441845i	$0.854324\pi$
$564$	2.78703	+	4.82728i	0.117355	+	0.203265i
$565$	9.00626	−	15.5993i	0.378896	−	0.656268i
$566$	−0.212129	−	0.367418i	−0.00891644	−	0.0154437i
$567$	−6.70711	+	11.6170i	−0.281672	+	0.487870i
$568$	−1.10920	+	1.92118i	−0.0465408	+	0.0806111i
$569$	10.1888	−	17.6475i	0.427136	−	0.739821i	−0.569482	−	0.822004i	$-0.692856\pi$
$569$	10.1888	−	17.6475i	0.427136	−	0.739821i	0.996617	+	0.0821835i	$0.0261894\pi$
$570$	−3.17784	+	5.50417i	−0.133105	+	0.230544i
$571$	−4.60259	+	7.97191i	−0.192612	+	0.333614i	−0.946115	−	0.323830i	$-0.895029\pi$
$571$	−4.60259	+	7.97191i	−0.192612	+	0.333614i	0.753503	+	0.657445i	$0.228363\pi$
$572$	−6.55149	+	11.3475i	−0.273932	+	0.474464i
$573$	18.9088	+	32.7509i	0.789925	+	1.36819i
$574$	−5.15443	+	8.92773i	−0.215142	+	0.372636i
$575$	−3.92550	−	6.79916i	−0.163705	−	0.283545i
$576$	2.82843			0.117851
$577$	19.3354	−	33.4900i	0.804945	−	1.39421i	−0.111383	−	0.993778i	$-0.535528\pi$
$577$	19.3354	−	33.4900i	0.804945	−	1.39421i	0.916328	−	0.400428i	$-0.131139\pi$
$578$	−6.64195			−0.276269
$579$	37.9423			1.57683
$580$	−3.68996	−	6.39120i	−0.153217	−	0.265380i
$581$	−11.5289			−0.478300
$582$	−0.316303	+	0.547852i	−0.0131112	+	0.0227092i
$583$	0.918888	−	1.59156i	0.0380565	−	0.0659157i
$584$	−2.21923	−	3.84382i	−0.0918324	−	0.159058i
$585$	9.26521	+	16.0478i	0.383069	+	0.663496i
$586$	−5.89791	−	10.2155i	−0.243640	−	0.421997i
$587$	−12.7905	−	22.1538i	−0.527921	−	0.914386i	−0.999470	−	0.0325465i	$-0.989638\pi$
$587$	−12.7905	−	22.1538i	−0.527921	−	0.914386i	0.471549	−	0.881840i	$-0.343695\pi$
$588$	−12.0711			−0.497802
$589$	−8.75013			−0.360543
$590$	2.31630	+	4.01195i	0.0953607	+	0.165170i
$591$	20.4853	−	35.4815i	0.842652	−	1.45952i
$592$	−0.402089	+	0.696439i	−0.0165258	+	0.0286235i
$593$	−10.5920	−	18.3460i	−0.434963	−	0.753379i	0.562329	−	0.826913i	$-0.309905\pi$
$593$	−10.5920	−	18.3460i	−0.434963	−	0.753379i	−0.997293	+	0.0735348i	$0.976572\pi$
$594$	0.828427			0.0339908
$595$	4.55149			0.186593
$596$	−3.95860	+	6.85650i	−0.162151	+	0.280853i
$597$	23.1631	+	40.1197i	0.948003	+	1.64199i
$598$	−51.4358			−2.10336
$599$	−15.1498	+	26.2402i	−0.619004	+	1.07215i	0.370663	+	0.928767i	$0.379130\pi$
$599$	−15.1498	+	26.2402i	−0.619004	+	1.07215i	−0.989668	+	0.143380i	$0.954203\pi$
$600$	2.41421			0.0985599
$601$	−15.1011	−	26.1559i	−0.615986	−	1.06692i	−0.990211	−	0.139581i	$-0.955424\pi$
$601$	−15.1011	−	26.1559i	−0.615986	−	1.06692i	0.374224	−	0.927338i	$-0.377909\pi$
$602$	−1.54214			−0.0628531
$603$	−17.1858	+	15.5129i	−0.699859	+	0.631733i
$604$	−4.77226			−0.194180
$605$	3.50000	+	6.06218i	0.142295	+	0.246463i
$606$	29.7824			1.20983
$607$	5.63379	−	9.75801i	0.228669	−	0.396066i	−0.728745	−	0.684785i	$-0.759896\pi$
$607$	5.63379	−	9.75801i	0.228669	−	0.396066i	0.957414	+	0.288719i	$0.0932295\pi$
$608$	2.63261			0.106766
$609$	12.5983	+	21.8209i	0.510509	+	0.884228i
$610$	0.259787	−	0.449965i	0.0105185	−	0.0182185i
$611$	15.1264			0.611950
$612$	−9.10299			−0.367966
$613$	−6.03469	−	10.4524i	−0.243739	−	0.422168i	0.718037	−	0.696005i	$-0.245041\pi$
$613$	−6.03469	−	10.4524i	−0.243739	−	0.422168i	−0.961776	+	0.273836i	$0.911707\pi$
$614$	−6.16346	+	10.6754i	−0.248737	+	0.430825i
$615$	8.79916	−	15.2406i	0.354816	−	0.614560i
$616$	−1.41421	−	2.44949i	−0.0569803	−	0.0986928i
$617$	−3.94701			−0.158901			−0.0794503	−	0.996839i	$-0.525316\pi$
$617$	−3.94701			−0.158901			−0.0794503	+	0.996839i	$0.525316\pi$
$618$	39.5991			1.59291
$619$	21.6011	+	37.4143i	0.868223	+	1.50381i	0.863811	+	0.503816i	$0.168071\pi$
$619$	21.6011	+	37.4143i	0.868223	+	1.50381i	0.00441242	+	0.999990i	$0.498595\pi$
$620$	1.66188	+	2.87845i	0.0667426	+	0.115602i
$621$	1.62599	+	2.81631i	0.0652489	+	0.113014i
$622$	−4.84716	−	8.39553i	−0.194353	−	0.336630i
$623$	1.60175	−	2.77431i	0.0641726	−	0.111150i
$624$	7.90835	−	13.6977i	0.316587	−	0.548346i
$625$	1.00000			0.0400000
$626$	4.81212	+	8.33484i	0.192331	+	0.333127i
$627$	−12.7113			−0.507642
$628$	−17.1990			−0.686315
$629$	1.29408	−	2.24141i	0.0515984	−	0.0893710i
$630$	−4.00000			−0.159364
$631$	0.941458	+	1.63065i	0.0374789	+	0.0649153i	0.884156	−	0.467191i	$-0.154734\pi$
$631$	0.941458	+	1.63065i	0.0374789	+	0.0649153i	−0.846678	+	0.532106i	$0.821401\pi$
$632$	0.804178	−	1.39288i	0.0319885	−	0.0554057i
$633$	28.3916	+	49.1757i	1.12847	+	1.95456i
$634$	11.1962	−	19.3924i	0.444659	−	0.770172i
$635$	4.04682	−	7.00930i	0.160593	−	0.278155i
$636$	−1.10920	+	1.92118i	−0.0439825	+	0.0761799i
$637$	−16.3787	+	28.3688i	−0.648949	+	1.12401i
$638$	7.37992	−	12.7824i	0.292174	−	0.506060i
$639$	−3.13728	+	5.43393i	−0.124109	+	0.214963i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−3.38251	+	5.85869i	−0.133601	+	0.231404i	−0.925062	−	0.379815i	$-0.875987\pi$
$641$	−3.38251	+	5.85869i	−0.133601	+	0.231404i	0.791461	+	0.611220i	$0.209321\pi$
$642$	−1.40209	−	2.42849i	−0.0553360	−	0.0958448i
$643$	24.1613			0.952831			0.476415	−	0.879220i	$-0.341936\pi$
$643$	24.1613			0.952831			0.476415	+	0.879220i	$0.341936\pi$
$644$	5.55149	−	9.61547i	0.218759	−	0.378903i
$645$	2.63261			0.103659
$646$	−8.47276			−0.333356
$647$	−2.61938	−	4.53691i	−0.102979	−	0.178364i	0.809932	−	0.586524i	$-0.199504\pi$
$647$	−2.61938	−	4.53691i	−0.102979	−	0.178364i	−0.912911	+	0.408160i	$0.866171\pi$
$648$	−9.48528			−0.372617
$649$	−4.63261	+	8.02391i	−0.181846	+	0.314966i
$650$	3.27575	−	5.67376i	0.128485	−	0.222543i
$651$	−5.67400	−	9.82766i	−0.222382	−	0.385176i
$652$	1.59707	+	2.76621i	0.0625461	+	0.108333i
$653$	−14.8200	−	25.6689i	−0.579950	−	1.00450i	−0.995484	−	0.0949258i	$-0.969739\pi$
$653$	−14.8200	−	25.6689i	−0.579950	−	1.00450i	0.415534	−	0.909578i	$-0.363595\pi$
$654$	15.9966	+	27.7069i	0.625515	+	1.08342i
$655$	−2.65200			−0.103622
$656$	−7.28946			−0.284606
$657$	−6.27693	−	10.8720i	−0.244887	−	0.424156i
$658$	−1.63261	+	2.82776i	−0.0636456	+	0.110237i
$659$	4.78738	−	8.29198i	0.186490	−	0.323010i	−0.757588	−	0.652733i	$-0.773622\pi$
$659$	4.78738	−	8.29198i	0.186490	−	0.323010i	0.944078	+	0.329724i	$0.106956\pi$
$660$	2.41421	+	4.18154i	0.0939731	+	0.162766i
$661$	37.4142			1.45524			0.727622	−	0.685978i	$-0.240625\pi$
$661$	37.4142			1.45524			0.727622	+	0.685978i	$0.240625\pi$
$662$	−28.1272			−1.09320
$663$	−25.4522	+	44.0845i	−0.988481	+	1.71210i
$664$	−4.07609	−	7.05999i	−0.158183	−	0.273981i
$665$	−3.72307			−0.144374
$666$	−1.13728	+	1.96983i	−0.0440687	+	0.0763292i
$667$	57.9397			2.24344
$668$	−7.61546	−	13.1904i	−0.294651	−	0.510350i
$669$	−60.5531			−2.34112
$670$	7.78787	+	2.51973i	0.300872	+	0.0973458i
$671$	1.03915			0.0401159
$672$	1.70711	+	2.95680i	0.0658531	+	0.114061i
$673$	40.8209			1.57353			0.786764	−	0.617253i	$-0.211755\pi$
$673$	40.8209			1.57353			0.786764	+	0.617253i	$0.211755\pi$
$674$	9.70592	−	16.8111i	0.373858	−	0.647541i
$675$	−0.414214			−0.0159431
$676$	−14.9610	−	25.9133i	−0.575424	−	0.996664i
$677$	19.5083	−	33.7893i	0.749763	−	1.29863i	−0.198173	−	0.980167i	$-0.563501\pi$
$677$	19.5083	−	33.7893i	0.749763	−	1.29863i	0.947936	−	0.318461i	$-0.103166\pi$
$678$	−43.4861			−1.67007
$679$	−0.370572			−0.0142212
$680$	1.60920	+	2.78721i	0.0617098	+	0.106885i
$681$	23.6421	−	40.9494i	0.905969	−	1.56918i
$682$	−3.32375	+	5.75691i	−0.127273	+	0.220443i
$683$	−9.28752	−	16.0865i	−0.355377	−	0.615531i	0.631805	−	0.775127i	$-0.282314\pi$
$683$	−9.28752	−	16.0865i	−0.355377	−	0.615531i	−0.987182	+	0.159596i	$0.948981\pi$
$684$	7.44613			0.284710
$685$	−15.5414			−0.593808
$686$	−8.48528	−	14.6969i	−0.323970	−	0.561132i
$687$	6.65143	+	11.5206i	0.253768	+	0.439539i
$688$	−0.545230	−	0.944367i	−0.0207867	−	0.0360036i
$689$	3.01004	+	5.21355i	0.114674	+	0.198620i
$690$	−9.47699	+	16.4146i	−0.360783	+	0.624894i
$691$	3.12475	−	5.41223i	0.118871	−	0.205891i	−0.800449	−	0.599400i	$-0.795406\pi$
$691$	3.12475	−	5.41223i	0.118871	−	0.205891i	0.919321	+	0.393509i	$0.128739\pi$
$692$	11.0125			0.418633
$693$	−4.00000	−	6.92820i	−0.151947	−	0.263181i
$694$	−14.5851			−0.553642
$695$	−22.2209			−0.842886
$696$	−8.90835	+	15.4297i	−0.337670	+	0.584862i
$697$	23.4603			0.888624
$698$	−1.96522	−	3.40385i	−0.0743845	−	0.128838i
$699$	24.1987	−	41.9133i	0.915277	−	1.58531i
$700$	0.707107	+	1.22474i	0.0267261	+	0.0462910i
$701$	17.8603	−	30.9350i	0.674576	−	1.16840i	−0.302017	−	0.953303i	$-0.597660\pi$
$701$	17.8603	−	30.9350i	0.674576	−	1.16840i	0.976593	−	0.215097i	$-0.0690068\pi$
$702$	−1.35686	+	2.35015i	−0.0512113	+	0.0887006i
$703$	−1.05854	+	1.83345i	−0.0399237	+	0.0691498i
$704$	1.00000	−	1.73205i	0.0376889	−	0.0652791i
$705$	2.78703	−	4.82728i	0.104966	−	0.181806i
$706$	−11.9635	+	20.7213i	−0.450251	+	0.779857i
$707$	8.72307	+	15.1088i	0.328065	+	0.568225i
$708$	5.59205	−	9.68571i	0.210162	−	0.364011i
$709$	16.6375	+	28.8169i	0.624833	+	1.08224i	0.988573	+	0.150742i	$0.0481663\pi$
$709$	16.6375	+	28.8169i	0.624833	+	1.08224i	−0.363740	+	0.931500i	$0.618500\pi$
$710$	2.21839			0.0832548
$711$	2.27456	−	3.93965i	0.0853026	−	0.147749i
$712$	2.26521			0.0848924
$713$	−26.0948			−0.977257
$714$	−5.49414	−	9.51613i	−0.205613	−	0.356132i
$715$	13.1030			0.490024
$716$	10.1108	−	17.5124i	0.377858	−	0.654469i
$717$	28.4150	−	49.2163i	1.06118	−	1.83801i
$718$	−12.7423	−	22.0703i	−0.475538	−	0.823656i
$719$	11.4075	+	19.7584i	0.425428	+	0.736864i	0.996460	−	0.0840642i	$-0.0267901\pi$
$719$	11.4075	+	19.7584i	0.425428	+	0.736864i	−0.571032	+	0.820928i	$0.693457\pi$
$720$	−1.41421	−	2.44949i	−0.0527046	−	0.0912871i
$721$	11.5983	+	20.0889i	0.431944	+	0.748148i
$722$	−12.0694			−0.449176
$723$	−25.1381			−0.934895
$724$	−10.4544	−	18.1076i	−0.388536	−	0.672963i
$725$	−3.68996	+	6.39120i	−0.137042	+	0.237363i
$726$	8.44975	−	14.6354i	0.313600	−	0.543170i
$727$	12.6645	+	21.9356i	0.469701	+	0.813546i	0.999400	−	0.0346396i	$-0.0110283\pi$
$727$	12.6645	+	21.9356i	0.469701	+	0.813546i	−0.529699	+	0.848186i	$0.677695\pi$
$728$	9.26521			0.343392
$729$	−23.8284			−0.882534
$730$	−2.21923	+	3.84382i	−0.0821374	+	0.142266i
$731$	1.75477	+	3.03934i	0.0649023	+	0.112414i
$732$	−1.25436			−0.0463626
$733$	−1.23987	+	2.14751i	−0.0457955	+	0.0793201i	−0.888015	−	0.459815i	$-0.847916\pi$
$733$	−1.23987	+	2.14751i	−0.0457955	+	0.0793201i	0.842219	+	0.539135i	$0.181249\pi$
$734$	−24.7279			−0.912724
$735$	6.03553	+	10.4539i	0.222624	+	0.385596i
$736$	7.85100			0.289392
$737$	3.42356	+	16.0087i	0.126109	+	0.589689i
$738$	−20.6177			−0.758948
$739$	12.5815	+	21.7918i	0.462818	+	0.801625i	0.999100	−	0.0424140i	$-0.0135048\pi$
$739$	12.5815	+	21.7918i	0.462818	+	0.801625i	−0.536282	+	0.844039i	$0.680172\pi$
$740$	0.804178			0.0295622
$741$	20.8196	−	36.0606i	0.764826	−	1.32472i
$742$	−1.29950			−0.0477063
$743$	−2.71421	−	4.70115i	−0.0995747	−	0.172468i	0.811934	−	0.583749i	$-0.198415\pi$
$743$	−2.71421	−	4.70115i	−0.0995747	−	0.172468i	−0.911509	+	0.411281i	$0.865082\pi$
$744$	4.01212	−	6.94920i	0.147092	−	0.254770i
$745$	7.91721			0.290064
$746$	−4.36739			−0.159902
$747$	−11.5289	−	19.9687i	−0.421821	−	0.730616i
$748$	−3.21839	+	5.57442i	−0.117676	+	0.203821i
$749$	0.821325	−	1.42258i	0.0300106	−	0.0519798i
$750$	−1.20711	−	2.09077i	−0.0440773	−	0.0763441i
$751$	8.95081			0.326620			0.163310	−	0.986575i	$-0.447783\pi$
$751$	8.95081			0.326620			0.163310	+	0.986575i	$0.447783\pi$
$752$	−2.30885			−0.0841952
$753$	−27.6460	−	47.8842i	−1.00748	−	1.74500i
$754$	24.1747	+	41.8719i	0.880392	+	1.52488i
$755$	2.38613	+	4.13290i	0.0868402	+	0.150412i
$756$	−0.292893	−	0.507306i	−0.0106524	−	0.0184505i
$757$	2.46063	−	4.26194i	0.0894332	−	0.154903i	−0.817839	−	0.575448i	$-0.804828\pi$
$757$	2.46063	−	4.26194i	0.0894332	−	0.154903i	0.907272	+	0.420545i	$0.138161\pi$
$758$	−2.93379	+	5.08147i	−0.106560	+	0.184567i
$759$	−37.9080			−1.37597
$760$	−1.31630	−	2.27990i	−0.0477473	−	0.0827008i
$761$	−27.7062			−1.00435			−0.502174	−	0.864767i	$-0.667466\pi$
$761$	−27.7062			−1.00435			−0.502174	+	0.864767i	$0.667466\pi$
$762$	−19.5398			−0.707851
$763$	−9.37057	+	16.2303i	−0.339237	+	0.587577i
$764$	−15.6645			−0.566723
$765$	4.55149	+	7.88342i	0.164560	+	0.285026i
$766$	16.2309	−	28.1128i	0.586447	−	1.01576i
$767$	−15.1752	−	26.2843i	−0.547946	−	0.949071i
$768$	−1.20711	+	2.09077i	−0.0435577	+	0.0754442i
$769$	26.5129	−	45.9217i	0.956081	−	1.65598i	0.224205	−	0.974542i	$-0.428022\pi$
$769$	26.5129	−	45.9217i	0.956081	−	1.65598i	0.731876	−	0.681438i	$-0.238645\pi$
$770$	−1.41421	+	2.44949i	−0.0509647	+	0.0882735i
$771$	21.8635	−	37.8687i	0.787396	−	1.36381i
$772$	−7.85810	+	13.6106i	−0.282819	+	0.489857i
$773$	−0.335877	+	0.581756i	−0.0120807	+	0.0209243i	−0.872003	−	0.489501i	$-0.837179\pi$
$773$	−0.335877	+	0.581756i	−0.0120807	+	0.0209243i	0.859922	+	0.510426i	$0.170512\pi$
$774$	−1.54214	−	2.67107i	−0.0554312	−	0.0960097i
$775$	1.66188	−	2.87845i	0.0596964	−	0.103397i
$776$	−0.131017	−	0.226928i	−0.00470323	−	0.00814624i
$777$	−2.74564			−0.0984992
$778$	−15.6155	+	27.0468i	−0.559841	+	0.969674i
$779$	−19.1903			−0.687563
$780$	−15.8167			−0.566329
$781$	2.21839	+	3.84237i	0.0793803	+	0.137491i
$782$	−25.2676			−0.903567
$783$	1.52843	−	2.64732i	0.0546217	−	0.0946075i
$784$	2.50000	−	4.33013i	0.0892857	−	0.154647i
$785$	8.59950	+	14.8948i	0.306929	+	0.531617i
$786$	3.20125	+	5.54472i	0.114185	+	0.197774i
$787$	18.8896	+	32.7178i	0.673342	+	1.16626i	0.976951	+	0.213466i	$0.0684752\pi$
$787$	18.8896	+	32.7178i	0.673342	+	1.16626i	−0.303608	+	0.952797i	$0.598191\pi$
$788$	8.48528	+	14.6969i	0.302276	+	0.523557i
$789$	10.8712			0.387025
$790$	−1.60836			−0.0572228
$791$	−12.7368	−	22.0607i	−0.452868	−	0.784390i
$792$	2.82843	−	4.89898i	0.100504	−	0.174078i
$793$	−1.70199	+	2.94794i	−0.0604396	+	0.104684i
$794$	8.72465	+	15.1115i	0.309626	+	0.536289i
$795$	2.21839			0.0786782
$796$	−19.1890			−0.680134
$797$	−25.5430	+	44.2418i	−0.904781	+	1.56713i	−0.0835696	+	0.996502i	$0.526632\pi$
$797$	−25.5430	+	44.2418i	−0.904781	+	1.56713i	−0.821211	+	0.570624i	$0.806701\pi$
$798$	4.49414	+	7.78408i	0.159091	+	0.275553i
$799$	7.43079			0.262883
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	6.40698			0.226380
$802$	−4.27693	−	7.40787i	−0.151024	−	0.261581i
$803$	−8.87692			−0.313260
$804$	−4.13261	−	19.3242i	−0.145746	−	0.681513i
$805$	−11.1030			−0.391329
$806$	−10.8878	−	18.8582i	−0.383505	−	0.664251i
$807$	−21.0368			−0.740530
$808$	−6.16814	+	10.6835i	−0.216994	+	0.375845i
$809$	36.7364			1.29158			0.645791	−	0.763514i	$-0.276528\pi$
$809$	36.7364			1.29158			0.645791	+	0.763514i	$0.276528\pi$
$810$	4.74264	+	8.21449i	0.166639	+	0.288628i
$811$	−23.3611	+	40.4626i	−0.820319	+	1.42083i	0.0851258	+	0.996370i	$0.472871\pi$
$811$	−23.3611	+	40.4626i	−0.820319	+	1.42083i	−0.905445	+	0.424464i	$0.860463\pi$
$812$	−10.4368			−0.366259
$813$	45.5914			1.59896
$814$	0.804178	+	1.39288i	0.0281864	+	0.0488203i
$815$	1.59707	−	2.76621i	0.0559430	−	0.0968961i
$816$	3.88494	−	6.72892i	0.136000	−	0.235559i
$817$	−1.43538	−	2.48615i	−0.0502175	−	0.0869792i
$818$	25.7262			0.899497
$819$	26.2060			0.915711
$820$	3.64473	+	6.31286i	0.127279	+	0.220455i
$821$	9.29171	+	16.0937i	0.324283	+	0.561674i	0.981367	−	0.192143i	$-0.0615437\pi$
$821$	9.29171	+	16.0937i	0.324283	+	0.561674i	−0.657084	+	0.753817i	$0.728210\pi$
$822$	18.7602	+	32.4936i	0.654337	+	1.13334i
$823$	0.495326	+	0.857929i	0.0172660	+	0.0299055i	0.874529	−	0.484973i	$-0.161170\pi$
$823$	0.495326	+	0.857929i	0.0172660	+	0.0299055i	−0.857263	+	0.514878i	$0.827837\pi$
$824$	−8.20125	+	14.2050i	−0.285704	+	0.494854i
$825$	2.41421	−	4.18154i	0.0840521	−	0.145583i
$826$	6.55149			0.227956
$827$	23.0025	+	39.8415i	0.799875	+	1.38542i	0.919697	+	0.392628i	$0.128434\pi$
$827$	23.0025	+	39.8415i	0.799875	+	1.38542i	−0.119823	+	0.992795i	$0.538233\pi$
$828$	22.2060			0.771711
$829$	−47.5540			−1.65162			−0.825809	−	0.563950i	$-0.809281\pi$
$829$	−47.5540			−1.65162			−0.825809	+	0.563950i	$0.809281\pi$
$830$	−4.07609	+	7.05999i	−0.141483	+	0.245056i
$831$	−30.2007			−1.04765
$832$	3.27575	+	5.67376i	0.113566	+	0.196702i
$833$	−8.04598	+	13.9360i	−0.278777	+	0.482855i
$834$	26.8230	+	46.4587i	0.928803	+	1.60873i
$835$	−7.61546	+	13.1904i	−0.263544	+	0.456471i
$836$	2.63261	−	4.55981i	0.0910506	−	0.157704i
$837$	−0.688372	+	1.19229i	−0.0237936	+	0.0412117i
$838$	11.2009	−	19.4005i	0.386929	−	0.670180i
$839$	−10.4677	+	18.1306i	−0.361386	+	0.625939i	−0.988189	−	0.153238i	$-0.951030\pi$
$839$	−10.4677	+	18.1306i	−0.361386	+	0.625939i	0.626803	+	0.779178i	$0.284363\pi$
$840$	1.70711	−	2.95680i	0.0589008	−	0.102019i
$841$	−12.7316	−	22.0518i	−0.439021	−	0.760407i
$842$	1.75736	−	3.04384i	0.0605626	−	0.104898i
$843$	19.6924	+	34.1082i	0.678242	+	1.17475i
$844$	−23.5204			−0.809605
$845$	−14.9610	+	25.9133i	−0.514675	+	0.891444i
$846$	−6.53042			−0.224521
$847$	9.89949			0.340151
$848$	−0.459444	−	0.795780i	−0.0157774	−	0.0273272i
$849$	1.02425			0.0351521
$850$	1.60920	−	2.78721i	0.0551950	−	0.0956005i
$851$	−3.15680	+	5.46774i	−0.108214	+	0.187432i
$852$	−2.67784	−	4.63815i	−0.0917411	−	0.158900i
$853$	23.1543	+	40.1044i	0.792787	+	1.37315i	0.924235	+	0.381824i	$0.124704\pi$
$853$	23.1543	+	40.1044i	0.792787	+	1.37315i	−0.131448	+	0.991323i	$0.541963\pi$
$854$	−0.367395	−	0.636346i	−0.0125720	−	0.0217753i
$855$	−3.72307	−	6.44854i	−0.127326	−	0.220535i
$856$	1.16153			0.0397002
$857$	1.22456			0.0418303			0.0209151	−	0.999781i	$-0.493342\pi$
$857$	1.22456			0.0418303			0.0209151	+	0.999781i	$0.493342\pi$
$858$	−15.8167	−	27.3953i	−0.539973	−	0.935261i
$859$	−0.168979	+	0.292680i	−0.00576548	+	0.00998610i	−0.868894	−	0.494999i	$-0.835169\pi$
$859$	−0.168979	+	0.292680i	−0.00576548	+	0.00998610i	0.863128	+	0.504985i	$0.168502\pi$
$860$	−0.545230	+	0.944367i	−0.0185922	+	0.0322026i
$861$	−12.4439	−	21.5534i	−0.424086	−	0.734539i
$862$	−5.78161			−0.196922
$863$	−37.7065			−1.28354			−0.641772	−	0.766896i	$-0.721800\pi$
$863$	−37.7065			−1.28354			−0.641772	+	0.766896i	$0.721800\pi$
$864$	0.207107	−	0.358719i	0.00704592	−	0.0122039i
$865$	−5.50626	−	9.53713i	−0.187219	−	0.324272i
$866$	−18.4836			−0.628098
$867$	8.01755	−	13.8868i	0.272290	−	0.471620i
$868$	4.70050			0.159545
$869$	−1.60836	−	2.78576i	−0.0545598	−	0.0945003i
$870$	17.8167			0.604043
$871$	−51.0222	−	16.5080i	−1.72882	−	0.559353i
$872$	−13.2520			−0.448769
$873$	−0.370572	−	0.641849i	−0.0125419	−	0.0217233i
$874$	20.6686			0.699125
$875$	0.707107	−	1.22474i	0.0239046	−	0.0414039i
$876$	10.7154			0.362040
$877$	−3.72743	−	6.45610i	−0.125866	−	0.218007i	0.796205	−	0.605027i	$-0.206838\pi$
$877$	−3.72743	−	6.45610i	−0.125866	−	0.218007i	−0.922071	+	0.387020i	$0.873504\pi$
$878$	−2.71923	+	4.70985i	−0.0917696	+	0.158950i
$879$	28.4776			0.960526
$880$	−2.00000			−0.0674200
$881$	5.64473	+	9.77696i	0.190176	+	0.329394i	0.945308	−	0.326178i	$-0.105761\pi$
$881$	5.64473	+	9.77696i	0.190176	+	0.329394i	−0.755133	+	0.655572i	$0.772428\pi$
$882$	7.07107	−	12.2474i	0.238095	−	0.412393i
$883$	0.404865	−	0.701246i	0.0136248	−	0.0235988i	−0.859133	−	0.511753i	$-0.828996\pi$
$883$	0.404865	−	0.701246i	0.0136248	−	0.0235988i	0.872757	+	0.488154i	$0.162330\pi$
$884$	−10.5426	−	18.2604i	−0.354587	−	0.614163i
$885$	−11.1841			−0.375949
$886$	16.0226			0.538289
$887$	−7.74907	−	13.4218i	−0.260188	−	0.450659i	0.706104	−	0.708109i	$-0.250451\pi$
$887$	−7.74907	−	13.4218i	−0.260188	−	0.450659i	−0.966292	+	0.257449i	$0.917118\pi$
$888$	−0.970729	−	1.68135i	−0.0325755	−	0.0564225i
$889$	−5.72307	−	9.91264i	−0.191945	−	0.332459i
$890$	−1.13261	−	1.96173i	−0.0379650	−	0.0657573i
$891$	−9.48528	+	16.4290i	−0.317769	+	0.550392i
$892$	12.5410	−	21.7216i	0.419902	−	0.727292i
$893$	−6.07830			−0.203402
$894$	−9.55692	−	16.5531i	−0.319631	−	0.553617i
$895$	−20.2216			−0.675932
$896$	−1.41421			−0.0472456
$897$	62.0884	−	107.540i	2.07307	−	3.59067i
$898$	38.5797			1.28742
$899$	12.2645	+	21.2428i	0.409044	+	0.708486i
$900$	−1.41421	+	2.44949i	−0.0471405	+	0.0816497i
$901$	1.47867	+	2.56113i	0.0492617	+	0.0853237i
$902$	−7.28946	+	12.6257i	−0.242712	+	0.420390i
$903$	1.86153	−	3.22427i	0.0619479	−	0.107297i
$904$	9.00626	−	15.5993i	0.299544	−	0.518825i
$905$	−10.4544	+	18.1076i	−0.347517	+	0.601917i
$906$	5.76063	−	9.97770i	0.191384	−	0.331487i
$907$	1.38494	−	2.39879i	0.0459863	−	0.0796505i	−0.842116	−	0.539296i	$-0.818690\pi$
$907$	1.38494	−	2.39879i	0.0459863	−	0.0796505i	0.888102	+	0.459646i	$0.152024\pi$
$908$	9.79289	+	16.9618i	0.324989	+	0.562897i
$909$	−17.4461	+	30.2176i	−0.578652	+	1.00225i
$910$	−4.63261	−	8.02391i	−0.153569	−	0.265990i
$911$	−15.8478			−0.525062			−0.262531	−	0.964924i	$-0.584557\pi$
$911$	−15.8478			−0.525062			−0.262531	+	0.964924i	$0.584557\pi$
$912$	−3.17784	+	5.50417i	−0.105229	+	0.182261i
$913$	−16.3044			−0.539596
$914$	−10.5709			−0.349654
$915$	0.627182	+	1.08631i	0.0207340	+	0.0359123i
$916$	−5.51023			−0.182063
$917$	−1.87525	+	3.24802i	−0.0619261	+	0.107259i
$918$	−0.666551	+	1.15450i	−0.0219995	+	0.0381042i
$919$	−13.1952	−	22.8547i	−0.435268	−	0.753907i	0.562049	−	0.827104i	$-0.310013\pi$
$919$	−13.1952	−	22.8547i	−0.435268	−	0.753907i	−0.997318	+	0.0731970i	$0.976680\pi$
$920$	−3.92550	−	6.79916i	−0.129420	−	0.224162i
$921$	−14.8799	−	25.7728i	−0.490310	−	0.849242i
$922$	−9.54806	−	16.5377i	−0.314449	−	0.544641i
$923$	−14.5338			−0.478385
$924$	6.82843			0.224639
$925$	−0.402089	−	0.696439i	−0.0132206	−	0.0228988i
$926$	0.523008	−	0.905877i	0.0171871	−	0.0297690i
$927$	−23.1966	+	40.1777i	−0.761877	+	1.31961i
$928$	−3.68996	−	6.39120i	−0.121129	−	0.209801i
$929$	29.7590			0.976362			0.488181	−	0.872742i	$-0.337661\pi$
$929$	29.7590			0.976362			0.488181	+	0.872742i	$0.337661\pi$
$930$	−8.02425			−0.263125
$931$	6.58151	−	11.3995i	0.215700	−	0.373604i
$932$	10.0234	+	17.3611i	0.328328	+	0.568680i
$933$	23.4042			0.766218
$934$	−9.43344	+	16.3392i	−0.308672	+	0.534635i
$935$	6.43678			0.210505
$936$	9.26521	+	16.0478i	0.302843	+	0.524539i
$937$	34.6472			1.13188			0.565938	−	0.824448i	$-0.308514\pi$
$937$	34.6472			1.13188			0.565938	+	0.824448i	$0.308514\pi$
$938$	8.59289	−	7.75643i	0.280568	−	0.253257i
$939$	−23.2350			−0.758245
$940$	1.15443	+	1.99953i	0.0376532	+	0.0652173i
$941$	−9.03342			−0.294481			−0.147240	−	0.989101i	$-0.547039\pi$
$941$	−9.03342			−0.294481			−0.147240	+	0.989101i	$0.547039\pi$
$942$	20.7610	−	35.9592i	0.676431	−	1.17161i
$943$	−57.2295			−1.86365
$944$	2.31630	+	4.01195i	0.0753892	+	0.130578i
$945$	−0.292893	+	0.507306i	−0.00952782	+	0.0165027i
$946$	−2.18092			−0.0709079
$947$	−22.7038			−0.737774			−0.368887	−	0.929474i	$-0.620261\pi$
$947$	−22.7038			−0.737774			−0.368887	+	0.929474i	$0.620261\pi$
$948$	1.94146	+	3.36270i	0.0630556	+	0.109216i
$949$	14.5393	−	25.1828i	0.471965	−	0.817467i
$950$	−1.31630	+	2.27990i	−0.0427065	+	0.0739698i
$951$	27.0301	+	46.8175i	0.876510	+	1.51816i
$952$	4.55149			0.147515
$953$	15.3165			0.496151			0.248075	−	0.968741i	$-0.420202\pi$
$953$	15.3165			0.496151			0.248075	+	0.968741i	$0.420202\pi$
$954$	−1.29950	−	2.25081i	−0.0420730	−	0.0728726i
$955$	7.83226	+	13.5659i	0.253446	+	0.438981i
$956$	11.7699	+	20.3860i	0.380665	+	0.659332i
$957$	17.8167	+	30.8594i	0.575932	+	0.997544i
$958$	2.83896	−	4.91723i	0.0917227	−	0.158868i
$959$	−10.9895	+	19.0343i	−0.354868	+	0.614650i
$960$	2.41421			0.0779184
$961$	9.97633	+	17.2795i	0.321817	+	0.557404i
$962$	−5.26857			−0.169865
$963$	3.28530			0.105867
$964$	5.20627	−	9.01752i	0.167683	−	0.290435i
$965$	15.7162			0.505922
$966$	13.4025	+	23.2138i	0.431218	+	0.746892i
$967$	30.3870	−	52.6319i	0.977181	−	1.69253i	0.304638	−	0.952468i	$-0.401464\pi$
$967$	30.3870	−	52.6319i	0.977181	−	1.69253i	0.672542	−	0.740059i	$-0.265202\pi$
$968$	3.50000	+	6.06218i	0.112494	+	0.194846i
$969$	10.2275	−	17.7146i	0.328555	−	0.569074i
$970$	−0.131017	+	0.226928i	−0.00420670	+	0.00728621i
$971$	−9.66430	+	16.7391i	−0.310142	+	0.537182i	−0.978393	−	0.206754i	$-0.933710\pi$
$971$	−9.66430	+	16.7391i	−0.310142	+	0.537182i	0.668251	+	0.743936i	$0.267043\pi$
$972$	10.8284	−	18.7554i	0.347322	−	0.601579i
$973$	−15.7125	+	27.2149i	−0.503721	+	0.872470i
$974$	−0.878680	+	1.52192i	−0.0281547	+	0.0487654i
$975$	7.90835	+	13.6977i	0.253270	+	0.438676i
$976$	0.259787	−	0.449965i	0.00831559	−	0.0144030i
$977$	−2.69507	−	4.66800i	−0.0862230	−	0.149343i	0.819689	−	0.572809i	$-0.194146\pi$
$977$	−2.69507	−	4.66800i	−0.0862230	−	0.149343i	−0.905912	+	0.423467i	$0.860813\pi$
$978$	−7.71134			−0.246582
$979$	2.26521	−	3.92346i	0.0723964	−	0.125394i
$980$	−5.00000			−0.159719
$981$	−37.4823			−1.19672
$982$	−16.7359	−	28.9875i	−0.534065	−	0.925028i
$983$	−36.6319			−1.16838			−0.584188	−	0.811618i	$-0.698587\pi$
$983$	−36.6319			−1.16838			−0.584188	+	0.811618i	$0.698587\pi$
$984$	8.79916	−	15.2406i	0.280507	−	0.485852i
$985$	8.48528	−	14.6969i	0.270364	−	0.468283i
$986$	11.8757	+	20.5694i	0.378201	+	0.655063i
$987$	−3.94146	−	6.82681i	−0.125458	−	0.217300i
$988$	8.62375	+	14.9368i	0.274358	+	0.475202i
$989$	−4.28060	−	7.41422i	−0.136115	−	0.235759i
$990$	−5.65685			−0.179787
$991$	28.0562			0.891234			0.445617	−	0.895224i	$-0.352984\pi$
$991$	28.0562			0.891234			0.445617	+	0.895224i	$0.352984\pi$
$992$	1.66188	+	2.87845i	0.0527646	+	0.0913910i
$993$	33.9526	−	58.8076i	1.07745	−	1.86620i
$994$	1.56864	−	2.71696i	0.0497542	−	0.0861769i
$995$	9.59448	+	16.6181i	0.304165	+	0.526830i
$996$	19.6811			0.623620
$997$	11.6447			0.368791			0.184396	−	0.982852i	$-0.440967\pi$
$997$	11.6447			0.368791			0.184396	+	0.982852i	$0.440967\pi$
$998$	−15.7999	+	27.3662i	−0.500137	+	0.866263i
$999$	0.166551	+	0.288474i	0.00526943	+	0.00912693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.e.i.171.4	✓	8
67.29	even	3	inner	670.2.e.i.431.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.e.i.171.4	✓	8	1.1	even	1	trivial
670.2.e.i.431.4	yes	8	67.29	even	3	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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +2.41421 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.20711 - 2.09077i) q^{6} +(0.707107 - 1.22474i) q^{7} +1.00000 q^{8} +2.82843 q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +2.41421 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.20711 - 2.09077i) q^{6} +(0.707107 - 1.22474i) q^{7} +1.00000 q^{8} +2.82843 q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-1.20711 + 2.09077i) q^{12} +(3.27575 + 5.67376i) q^{13} -1.41421 q^{14} +2.41421 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.60920 + 2.78721i) q^{17} +(-1.41421 - 2.44949i) q^{18} +(-1.31630 - 2.27990i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(1.70711 - 2.95680i) q^{21} -2.00000 q^{22} +(-3.92550 - 6.79916i) q^{23} +2.41421 q^{24} +1.00000 q^{25} +(3.27575 - 5.67376i) q^{26} -0.414214 q^{27} +(0.707107 + 1.22474i) q^{28} +(-3.68996 + 6.39120i) q^{29} +(-1.20711 - 2.09077i) q^{30} +(1.66188 - 2.87845i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.41421 - 4.18154i) q^{33} +(1.60920 - 2.78721i) q^{34} +(0.707107 - 1.22474i) q^{35} +(-1.41421 + 2.44949i) q^{36} +(-0.402089 - 0.696439i) q^{37} +(-1.31630 + 2.27990i) q^{38} +(7.90835 + 13.6977i) q^{39} +1.00000 q^{40} +(3.64473 - 6.31286i) q^{41} -3.41421 q^{42} +1.09046 q^{43} +(1.00000 + 1.73205i) q^{44} +2.82843 q^{45} +(-3.92550 + 6.79916i) q^{46} +(1.15443 - 1.99953i) q^{47} +(-1.20711 - 2.09077i) q^{48} +(2.50000 + 4.33013i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(3.88494 + 6.72892i) q^{51} -6.55149 q^{52} +0.918888 q^{53} +(0.207107 + 0.358719i) q^{54} +(1.00000 - 1.73205i) q^{55} +(0.707107 - 1.22474i) q^{56} +(-3.17784 - 5.50417i) q^{57} +7.37992 q^{58} -4.63261 q^{59} +(-1.20711 + 2.09077i) q^{60} +(0.259787 + 0.449965i) q^{61} -3.32375 q^{62} +(2.00000 - 3.46410i) q^{63} +1.00000 q^{64} +(3.27575 + 5.67376i) q^{65} -4.82843 q^{66} +(-6.07609 + 5.48463i) q^{67} -3.21839 q^{68} +(-9.47699 - 16.4146i) q^{69} -1.41421 q^{70} +(-1.10920 + 1.92118i) q^{71} +2.82843 q^{72} +(-2.21923 - 3.84382i) q^{73} +(-0.402089 + 0.696439i) q^{74} +2.41421 q^{75} +2.63261 q^{76} +(-1.41421 - 2.44949i) q^{77} +(7.90835 - 13.6977i) q^{78} +(0.804178 - 1.39288i) q^{79} +(-0.500000 - 0.866025i) q^{80} -9.48528 q^{81} -7.28946 q^{82} +(-4.07609 - 7.05999i) q^{83} +(1.70711 + 2.95680i) q^{84} +(1.60920 + 2.78721i) q^{85} +(-0.545230 - 0.944367i) q^{86} +(-8.90835 + 15.4297i) q^{87} +(1.00000 - 1.73205i) q^{88} +2.26521 q^{89} +(-1.41421 - 2.44949i) q^{90} +9.26521 q^{91} +7.85100 q^{92} +(4.01212 - 6.94920i) q^{93} -2.30885 q^{94} +(-1.31630 - 2.27990i) q^{95} +(-1.20711 + 2.09077i) q^{96} +(-0.131017 - 0.226928i) q^{97} +(2.50000 - 4.33013i) q^{98} +(2.82843 - 4.89898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 8 q^{5} - 4 q^{6} + 8 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 8 * q^5 - 4 * q^6 + 8 * q^8	\( 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 8 q^{5} - 4 q^{6} + 8 q^{8} - 4 q^{10} + 8 q^{11} - 4 q^{12} + 8 q^{15} - 4 q^{16} + 2 q^{17} + 6 q^{19} - 4 q^{20} + 8 q^{21} - 16 q^{22} - 4 q^{23} + 8 q^{24} + 8 q^{25} + 8 q^{27} + 8 q^{29} - 4 q^{30} + 6 q^{31} - 4 q^{32} + 8 q^{33} + 2 q^{34} + 2 q^{37} + 6 q^{38} + 4 q^{39} + 8 q^{40} - 10 q^{41} - 16 q^{42} + 12 q^{43} + 8 q^{44} - 4 q^{46} - 4 q^{48} + 20 q^{49} - 4 q^{50} - 6 q^{51} - 12 q^{53} - 4 q^{54} + 8 q^{55} + 6 q^{57} - 16 q^{58} - 4 q^{59} - 4 q^{60} - 12 q^{62} + 16 q^{63} + 8 q^{64} - 16 q^{66} - 30 q^{67} - 4 q^{68} + 4 q^{69} + 2 q^{71} - 6 q^{73} + 2 q^{74} + 8 q^{75} - 12 q^{76} + 4 q^{78} - 4 q^{79} - 4 q^{80} - 8 q^{81} + 20 q^{82} - 14 q^{83} + 8 q^{84} + 2 q^{85} - 6 q^{86} - 12 q^{87} + 8 q^{88} - 48 q^{89} + 8 q^{91} + 8 q^{92} + 26 q^{93} + 6 q^{95} - 4 q^{96} - 14 q^{97} + 20 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 8 * q^5 - 4 * q^6 + 8 * q^8 - 4 * q^10 + 8 * q^11 - 4 * q^12 + 8 * q^15 - 4 * q^16 + 2 * q^17 + 6 * q^19 - 4 * q^20 + 8 * q^21 - 16 * q^22 - 4 * q^23 + 8 * q^24 + 8 * q^25 + 8 * q^27 + 8 * q^29 - 4 * q^30 + 6 * q^31 - 4 * q^32 + 8 * q^33 + 2 * q^34 + 2 * q^37 + 6 * q^38 + 4 * q^39 + 8 * q^40 - 10 * q^41 - 16 * q^42 + 12 * q^43 + 8 * q^44 - 4 * q^46 - 4 * q^48 + 20 * q^49 - 4 * q^50 - 6 * q^51 - 12 * q^53 - 4 * q^54 + 8 * q^55 + 6 * q^57 - 16 * q^58 - 4 * q^59 - 4 * q^60 - 12 * q^62 + 16 * q^63 + 8 * q^64 - 16 * q^66 - 30 * q^67 - 4 * q^68 + 4 * q^69 + 2 * q^71 - 6 * q^73 + 2 * q^74 + 8 * q^75 - 12 * q^76 + 4 * q^78 - 4 * q^79 - 4 * q^80 - 8 * q^81 + 20 * q^82 - 14 * q^83 + 8 * q^84 + 2 * q^85 - 6 * q^86 - 12 * q^87 + 8 * q^88 - 48 * q^89 + 8 * q^91 + 8 * q^92 + 26 * q^93 + 6 * q^95 - 4 * q^96 - 14 * q^97 + 20 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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