LMFDB - Embedded newform 168.2.v.a.107.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(11,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 4]))

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

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

chi := DirichletCharacter("168.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.v (of order $6$, 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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.12
Character	$\chi$	$=$	168.107
Dual form			168.2.v.a.11.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.389211 + 1.35960i) q^{2} +(1.72608 - 0.143748i) q^{3} +(-1.69703 - 1.05834i) q^{4} +(1.77783 - 3.07929i) q^{5} +(-0.476367 + 2.40272i) q^{6} +(-0.793456 + 2.52397i) q^{7} +(2.09943 - 1.89537i) q^{8} +(2.95867 - 0.496241i) q^{9} +(3.49466 + 3.61563i) q^{10} +(0.396703 - 0.229036i) q^{11} +(-3.08134 - 1.58283i) q^{12} -0.799063i q^{13} +(-3.12277 - 2.06114i) q^{14} +(2.62603 - 5.57065i) q^{15} +(1.75982 + 3.59208i) q^{16} +(-5.48456 + 3.16651i) q^{17} +(-0.476858 + 4.21576i) q^{18} +(-2.61696 + 4.53272i) q^{19} +(-6.27598 + 3.34410i) q^{20} +(-1.00675 + 4.47062i) q^{21} +(0.156997 + 0.628501i) q^{22} +(1.55053 - 2.68559i) q^{23} +(3.35131 - 3.57333i) q^{24} +(-3.82137 - 6.61880i) q^{25} +(1.08641 + 0.311004i) q^{26} +(5.03556 - 1.28185i) q^{27} +(4.01774 - 3.44351i) q^{28} -2.60340 q^{29} +(6.55179 + 5.73851i) q^{30} +(-4.42520 + 2.55489i) q^{31} +(-5.56873 + 0.994581i) q^{32} +(0.651815 - 0.452359i) q^{33} +(-2.17055 - 8.68926i) q^{34} +(6.36142 + 6.93048i) q^{35} +(-5.54615 - 2.28915i) q^{36} +(2.89424 + 1.67099i) q^{37} +(-5.14413 - 5.32221i) q^{38} +(-0.114864 - 1.37924i) q^{39} +(-2.10396 - 9.83439i) q^{40} -10.1452i q^{41} +(-5.68643 - 3.10879i) q^{42} +3.56359 q^{43} +(-0.915615 - 0.0311657i) q^{44} +(3.73195 - 9.99285i) q^{45} +(3.04785 + 3.15336i) q^{46} +(-2.15923 + 3.73989i) q^{47} +(3.55394 + 5.94723i) q^{48} +(-5.74086 - 4.00532i) q^{49} +(10.4862 - 2.61943i) q^{50} +(-9.01159 + 6.25404i) q^{51} +(-0.845682 + 1.35603i) q^{52} +(1.16913 + 2.02499i) q^{53} +(-0.217084 + 7.34526i) q^{54} -1.62875i q^{55} +(3.11805 + 6.80278i) q^{56} +(-3.86551 + 8.19999i) q^{57} +(1.01327 - 3.53959i) q^{58} +(1.49741 - 0.864528i) q^{59} +(-10.3521 + 6.67433i) q^{60} +(-4.60841 - 2.66067i) q^{61} +(-1.75130 - 7.01090i) q^{62} +(-1.09508 + 7.86135i) q^{63} +(0.815178 - 7.95836i) q^{64} +(-2.46055 - 1.42060i) q^{65} +(0.361335 + 1.06227i) q^{66} +(0.00979145 + 0.0169593i) q^{67} +(12.6587 + 0.430877i) q^{68} +(2.29028 - 4.85842i) q^{69} +(-11.8986 + 5.95157i) q^{70} -9.04022 q^{71} +(5.27096 - 6.64959i) q^{72} +(4.15674 + 7.19969i) q^{73} +(-3.39835 + 3.28465i) q^{74} +(-7.54741 - 10.8752i) q^{75} +(9.23823 - 4.92251i) q^{76} +(0.263315 + 1.18300i) q^{77} +(1.91993 + 0.380647i) q^{78} +(10.8825 + 6.28304i) q^{79} +(14.1897 + 0.967099i) q^{80} +(8.50749 - 2.93643i) q^{81} +(13.7934 + 3.94861i) q^{82} -0.694004i q^{83} +(6.43993 - 6.52130i) q^{84} +22.5181i q^{85} +(-1.38699 + 4.84506i) q^{86} +(-4.49367 + 0.374235i) q^{87} +(0.398740 - 1.23274i) q^{88} +(-7.02189 - 4.05409i) q^{89} +(12.1338 + 8.96329i) q^{90} +(2.01681 + 0.634021i) q^{91} +(-5.47357 + 2.91654i) q^{92} +(-7.27097 + 5.04605i) q^{93} +(-4.24437 - 4.39129i) q^{94} +(9.30504 + 16.1168i) q^{95} +(-9.46909 + 2.51722i) q^{96} +7.05333 q^{97} +(7.68004 - 6.24636i) q^{98} +(1.06006 - 0.874504i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9} + 6 q^{10} + 10 q^{12} - 10 q^{16} - 10 q^{18} - 4 q^{19} - 20 q^{22} - 8 q^{24} - 16 q^{25} - 8 q^{27} - 22 q^{28} - 12 q^{30} - 14 q^{33} - 56 q^{34} + 4 q^{36}+ \cdots - 44 q^{99}+O(q^{100}) $ 56 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9 + 6 * q^10 + 10 * q^12 - 10 * q^16 - 10 * q^18 - 4 * q^19 - 20 * q^22 - 8 * q^24 - 16 * q^25 - 8 * q^27 - 22 * q^28 - 12 * q^30 - 14 * q^33 - 56 * q^34 + 4 * q^36 + 14 * q^40 - 8 * q^42 - 16 * q^43 - 12 * q^46 + 64 * q^48 - 16 * q^49 - 34 * q^51 - 8 * q^52 + 32 * q^54 + 4 * q^57 - 18 * q^58 + 40 * q^60 + 4 * q^64 - 20 * q^66 - 36 * q^67 - 42 * q^70 + 22 * q^72 + 4 * q^73 + 104 * q^76 + 28 * q^78 - 10 * q^81 + 52 * q^82 + 4 * q^84 + 46 * q^88 + 140 * q^90 + 72 * q^91 - 46 * q^96 - 32 * q^97 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$-1$

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 $

$2$	−0.389211	+	1.35960i	−0.275214	+	0.961383i
$2$	−0.389211	+	1.35960i	−0.275214	+	0.961383i
$3$	1.72608	−	0.143748i	0.996550	−	0.0829931i
$3$	1.72608	−	0.143748i	0.996550	−	0.0829931i
$4$	−1.69703	−	1.05834i	−0.848515	−	0.529171i
$5$	1.77783	−	3.07929i	0.795070	−	1.37710i	−0.127724	−	0.991810i	$-0.540767\pi$
$5$	1.77783	−	3.07929i	0.795070	−	1.37710i	0.922795	−	0.385292i	$-0.125899\pi$
$6$	−0.476367	+	2.40272i	−0.194476	+	0.980907i
$7$	−0.793456	+	2.52397i	−0.299898	+	0.953971i
$7$	−0.793456	+	2.52397i	−0.299898	+	0.953971i
$8$	2.09943	−	1.89537i	0.742259	−	0.670113i
$9$	2.95867	−	0.496241i	0.986224	−	0.165414i
$10$	3.49466	+	3.61563i	1.10511	+	1.14336i
$11$	0.396703	−	0.229036i	0.119610	−	0.0690571i	−0.439001	−	0.898486i	$-0.644668\pi$
$11$	0.396703	−	0.229036i	0.119610	−	0.0690571i	0.558612	+	0.829429i	$0.311334\pi$
$12$	−3.08134	−	1.58283i	−0.889505	−	0.456925i
$13$		−	0.799063i		−	0.221620i	−0.993842	−	0.110810i	$-0.964655\pi$
$13$		−	0.799063i		−	0.221620i	0.993842	−	0.110810i	$-0.0353445\pi$
$14$	−3.12277	−	2.06114i	−0.834596	−	0.550863i
$15$	2.62603	−	5.57065i	0.678037	−	1.43834i
$16$	1.75982	+	3.59208i	0.439956	+	0.898020i
$17$	−5.48456	+	3.16651i	−1.33020	+	0.767993i	−0.985330	−	0.170657i	$-0.945411\pi$
$17$	−5.48456	+	3.16651i	−1.33020	+	0.767993i	−0.344872	+	0.938650i	$0.612078\pi$
$18$	−0.476858	+	4.21576i	−0.112396	+	0.993663i
$19$	−2.61696	+	4.53272i	−0.600373	+	1.03988i	0.392392	+	0.919798i	$0.371648\pi$
$19$	−2.61696	+	4.53272i	−0.600373	+	1.03988i	−0.992764	+	0.120078i	$0.961686\pi$
$20$	−6.27598	+	3.34410i	−1.40335	+	0.747763i
$21$	−1.00675	+	4.47062i	−0.219690	+	0.975570i
$22$	0.156997	+	0.628501i	0.0334719	+	0.133997i
$23$	1.55053	−	2.68559i	0.323307	−	0.559985i	−0.657861	−	0.753139i	$-0.728539\pi$
$23$	1.55053	−	2.68559i	0.323307	−	0.559985i	0.981168	+	0.193155i	$0.0618719\pi$
$24$	3.35131	−	3.57333i	0.684084	−	0.729404i
$25$	−3.82137	−	6.61880i	−0.764273	−	1.32376i
$26$	1.08641	+	0.311004i	0.213062	+	0.0609928i
$27$	5.03556	−	1.28185i	0.969094	−	0.246693i
$28$	4.01774	−	3.44351i	0.759282	−	0.650762i
$29$	−2.60340			−0.483440			−0.241720	−	0.970346i	$-0.577712\pi$
$29$	−2.60340			−0.483440			−0.241720	+	0.970346i	$0.577712\pi$
$30$	6.55179	+	5.73851i	1.19619	+	1.04770i
$31$	−4.42520	+	2.55489i	−0.794790	+	0.458872i	−0.841646	−	0.540030i	$-0.818413\pi$
$31$	−4.42520	+	2.55489i	−0.794790	+	0.458872i	0.0468563	+	0.998902i	$0.485080\pi$
$32$	−5.56873	+	0.994581i	−0.984423	+	0.175819i
$33$	0.651815	−	0.452359i	0.113466	−	0.0787457i
$34$	−2.17055	−	8.68926i	−0.372245	−	1.49020i
$35$	6.36142	+	6.93048i	1.07528	+	1.17146i
$36$	−5.54615	−	2.28915i	−0.924358	−	0.381526i
$37$	2.89424	+	1.67099i	0.475810	+	0.274709i	0.718669	−	0.695352i	$-0.244752\pi$
$37$	2.89424	+	1.67099i	0.475810	+	0.274709i	−0.242859	+	0.970062i	$0.578085\pi$
$38$	−5.14413	−	5.32221i	−0.834489	−	0.863376i
$39$	−0.114864	−	1.37924i	−0.0183929	−	0.220856i
$40$	−2.10396	−	9.83439i	−0.332666	−	1.55495i
$41$		−	10.1452i		−	1.58441i	−0.610256	−	0.792205i	$-0.708933\pi$
$41$		−	10.1452i		−	1.58441i	0.610256	−	0.792205i	$-0.291067\pi$
$42$	−5.68643	−	3.10879i	−0.877434	−	0.479697i
$43$	3.56359			0.543442			0.271721	−	0.962376i	$-0.412407\pi$
$43$	3.56359			0.543442			0.271721	+	0.962376i	$0.412407\pi$
$44$	−0.915615	−	0.0311657i	−0.138034	−	0.00469840i
$45$	3.73195	−	9.99285i	0.556326	−	1.48965i
$46$	3.04785	+	3.15336i	0.449381	+	0.464937i
$47$	−2.15923	+	3.73989i	−0.314956	+	0.545519i	−0.979428	−	0.201794i	$-0.935323\pi$
$47$	−2.15923	+	3.73989i	−0.314956	+	0.545519i	0.664472	+	0.747313i	$0.268656\pi$
$48$	3.55394	+	5.94723i	0.512967	+	0.858408i
$49$	−5.74086	−	4.00532i	−0.820122	−	0.572188i
$50$	10.4862	−	2.61943i	1.48298	−	0.370443i
$51$	−9.01159	+	6.25404i	−1.26188	+	0.875741i
$52$	−0.845682	+	1.35603i	−0.117275	+	0.188048i
$53$	1.16913	+	2.02499i	0.160592	+	0.278154i	0.935081	−	0.354433i	$-0.115326\pi$
$53$	1.16913	+	2.02499i	0.160592	+	0.278154i	−0.774489	+	0.632587i	$0.781993\pi$
$54$	−0.217084	+	7.34526i	−0.0295414	+	0.999564i
$55$		−	1.62875i		−	0.219621i
$56$	3.11805	+	6.80278i	0.416666	+	0.909059i
$57$	−3.86551	+	8.19999i	−0.511999	+	1.08612i
$58$	1.01327	−	3.53959i	0.133049	−	0.464771i
$59$	1.49741	−	0.864528i	0.194946	−	0.112552i	−0.399350	−	0.916798i	$-0.630764\pi$
$59$	1.49741	−	0.864528i	0.194946	−	0.112552i	0.594296	+	0.804247i	$0.297431\pi$
$60$	−10.3521	+	6.67433i	−1.33645	+	0.861652i
$61$	−4.60841	−	2.66067i	−0.590047	−	0.340664i	0.175069	−	0.984556i	$-0.443985\pi$
$61$	−4.60841	−	2.66067i	−0.590047	−	0.340664i	−0.765116	+	0.643892i	$0.777318\pi$
$62$	−1.75130	−	7.01090i	−0.222415	−	0.890385i
$63$	−1.09508	+	7.86135i	−0.137967	+	0.990437i
$64$	0.815178	−	7.95836i	0.101897	−	0.994795i
$65$	−2.46055	−	1.42060i	−0.305193	−	0.176204i
$66$	0.361335	+	1.06227i	0.0444773	+	0.130757i
$67$	0.00979145	+	0.0169593i	0.00119622	+	0.00207191i	0.866623	−	0.498964i	$-0.166286\pi$
$67$	0.00979145	+	0.0169593i	0.00119622	+	0.00207191i	−0.865427	+	0.501036i	$0.832953\pi$
$68$	12.6587	+	0.430877i	1.53510	+	0.0522515i
$69$	2.29028	−	4.85842i	0.275717	−	0.584885i
$70$	−11.8986	+	5.95157i	−1.42216	+	0.711349i
$71$	−9.04022			−1.07288			−0.536439	−	0.843939i	$-0.680231\pi$
$71$	−9.04022			−1.07288			−0.536439	+	0.843939i	$0.680231\pi$
$72$	5.27096	−	6.64959i	0.621188	−	0.783661i
$73$	4.15674	+	7.19969i	0.486510	+	0.842660i	0.999880	−	0.0155078i	$-0.00493650\pi$
$73$	4.15674	+	7.19969i	0.486510	+	0.842660i	−0.513370	+	0.858167i	$0.671603\pi$
$74$	−3.39835	+	3.28465i	−0.395050	+	0.381832i
$75$	−7.54741	−	10.8752i	−0.871499	−	1.25576i
$76$	9.23823	−	4.92251i	1.05970	−	0.564651i
$77$	0.263315	+	1.18300i	0.0300076	+	0.134815i
$78$	1.91993	+	0.380647i	0.217389	+	0.0430998i
$79$	10.8825	+	6.28304i	1.22438	+	0.706897i	0.965849	−	0.259105i	$-0.0834277\pi$
$79$	10.8825	+	6.28304i	1.22438	+	0.706897i	0.258533	+	0.966003i	$0.416761\pi$
$80$	14.1897	+	0.967099i	1.58646	+	0.108125i
$81$	8.50749	−	2.93643i	0.945277	−	0.326270i
$82$	13.7934	+	3.94861i	1.52322	+	0.436051i
$83$		−	0.694004i		−	0.0761768i	−0.999274	−	0.0380884i	$-0.987873\pi$
$83$		−	0.694004i		−	0.0761768i	0.999274	−	0.0380884i	$-0.0121268\pi$
$84$	6.43993	−	6.52130i	0.702654	−	0.711532i
$85$			22.5181i			2.44243i
$86$	−1.38699	+	4.84506i	−0.149563	+	0.522456i
$87$	−4.49367	+	0.374235i	−0.481772	+	0.0401222i
$88$	0.398740	−	1.23274i	0.0425058	−	0.131411i
$89$	−7.02189	−	4.05409i	−0.744319	−	0.429733i	0.0793185	−	0.996849i	$-0.474726\pi$
$89$	−7.02189	−	4.05409i	−0.744319	−	0.429733i	−0.823638	+	0.567116i	$0.808059\pi$
$90$	12.1338	+	8.96329i	1.27901	+	0.944814i
$91$	2.01681	+	0.634021i	0.211419	+	0.0664634i
$92$	−5.47357	+	2.91654i	−0.570659	+	0.304070i
$93$	−7.27097	+	5.04605i	−0.753965	+	0.523251i
$94$	−4.24437	−	4.39129i	−0.437773	−	0.452927i
$95$	9.30504	+	16.1168i	0.954677	+	1.65355i
$96$	−9.46909	+	2.51722i	−0.966435	+	0.256912i
$97$	7.05333			0.716157			0.358078	−	0.933692i	$-0.383432\pi$
$97$	7.05333			0.716157			0.358078	+	0.933692i	$0.383432\pi$
$98$	7.68004	−	6.24636i	0.775801	−	0.630978i
$99$	1.06006	−	0.874504i	0.106540	−	0.0878909i
$100$	−0.519985	+	15.2766i	−0.0519985	+	1.52766i
$101$	3.34348	+	5.79108i	0.332689	+	0.576234i	0.983038	−	0.183402i	$-0.0587108\pi$
$101$	3.34348	+	5.79108i	0.332689	+	0.576234i	−0.650349	+	0.759635i	$0.725378\pi$
$102$	−4.99559	−	14.6863i	−0.494637	−	1.45416i
$103$	−5.48751	−	3.16822i	−0.540701	−	0.312174i	0.204662	−	0.978833i	$-0.434390\pi$
$103$	−5.48751	−	3.16822i	−0.540701	−	0.312174i	−0.745363	+	0.666659i	$0.767724\pi$
$104$	−1.51452	−	1.67757i	−0.148510	−	0.164500i
$105$	11.9765	+	11.0481i	1.16879	+	1.07818i
$106$	−3.20822	+	0.801402i	−0.311610	+	0.0778390i
$107$	3.09681	+	1.78795i	0.299380	+	0.172847i	0.642164	−	0.766567i	$-0.278037\pi$
$107$	3.09681	+	1.78795i	0.299380	+	0.172847i	−0.342784	+	0.939414i	$0.611370\pi$
$108$	−9.90213	−	3.15400i	−0.952833	−	0.303494i
$109$	−0.488061	+	0.281782i	−0.0467478	+	0.0269899i	−0.523192	−	0.852215i	$-0.675259\pi$
$109$	−0.488061	+	0.281782i	−0.0467478	+	0.0269899i	0.476444	+	0.879205i	$0.341926\pi$
$110$	2.21445	+	0.633928i	0.211140	+	0.0604426i
$111$	5.23588	+	2.46821i	0.496968	+	0.234273i
$112$	−10.4626	+	1.59159i	−0.988627	+	0.150391i
$113$			1.41462i			0.133076i	0.997784	+	0.0665381i	$0.0211954\pi$
$113$			1.41462i			0.133076i	−0.997784	+	0.0665381i	$0.978805\pi$
$114$	−9.64422	−	8.44707i	−0.903264	−	0.791141i
$115$	−5.51315	−	9.54906i	−0.514104	−	0.890454i
$116$	4.41805	+	2.75529i	0.410206	+	0.255822i
$117$	−0.396527	−	2.36416i	−0.0366590	−	0.218567i
$118$	0.592606	+	2.37236i	0.0545538	+	0.218393i
$119$	−3.64043	−	16.3554i	−0.333718	−	1.49929i
$120$	−5.04527	−	16.6725i	−0.460568	−	1.52198i
$121$	−5.39508	+	9.34456i	−0.490462	+	0.849506i
$122$	5.41109	−	5.23004i	0.489897	−	0.473506i
$123$	−1.45835	−	17.5113i	−0.131495	−	1.57894i
$124$	10.2137	+	0.347652i	0.917213	+	0.0312200i
$125$	−9.39666			−0.840463
$126$	−10.2621	−	4.54859i	−0.914219	−	0.405221i
$127$		−	15.7043i		−	1.39353i	−0.717299	−	0.696766i	$-0.754622\pi$
$127$		−	15.7043i		−	1.39353i	0.717299	−	0.696766i	$-0.245378\pi$
$128$	10.5029	+	4.20580i	0.928336	+	0.371743i
$129$	6.15102	−	0.512260i	0.541567	−	0.0451019i
$130$	2.88912	−	2.79245i	0.253392	−	0.244914i
$131$	−1.16617	−	0.673290i	−0.101889	−	0.0588256i	0.448190	−	0.893938i	$-0.352069\pi$
$131$	−1.16617	−	0.673290i	−0.101889	−	0.0588256i	−0.550079	+	0.835113i	$0.685402\pi$
$132$	−1.58490	+	0.0778238i	−0.137948	+	0.00677370i
$133$	−9.36400	−	10.2016i	−0.811961	−	0.884595i
$134$	−0.0268688	+	0.00671173i	−0.00232111	+	0.000579805i
$135$	5.00517	−	17.7849i	0.430776	−	1.53068i
$136$	−5.51273	+	17.0431i	−0.472713	+	1.46144i
$137$	7.79136	−	4.49834i	0.665661	−	0.384320i	−0.128770	−	0.991675i	$-0.541103\pi$
$137$	7.79136	−	4.49834i	0.665661	−	0.384320i	0.794431	+	0.607355i	$0.207769\pi$
$138$	5.71411	+	5.00481i	0.486417	+	0.426038i
$139$	−16.0176			−1.35859			−0.679296	−	0.733864i	$-0.737715\pi$
$139$	−16.0176			−1.35859			−0.679296	+	0.733864i	$0.737715\pi$
$140$	−3.46070	−	18.4938i	−0.292482	−	1.56301i
$141$	−3.18939	+	6.76572i	−0.268595	+	0.569777i
$142$	3.51855	−	12.2911i	0.295270	−	1.03145i
$143$	−0.183014	−	0.316990i	−0.0153044	−	0.0265081i
$144$	6.98927	+	9.75449i	0.582439	+	0.812874i
$145$	−4.62841	+	8.01664i	−0.384369	+	0.665746i
$146$	−11.4065	+	2.84931i	−0.944013	+	0.235811i
$147$	−10.4849	−	6.08824i	−0.864781	−	0.502150i
$148$	−3.14313	−	5.89882i	−0.258364	−	0.484880i
$149$	3.34348	−	5.79108i	0.273909	−	0.474424i	−0.695951	−	0.718090i	$-0.745017\pi$
$149$	3.34348	−	5.79108i	0.273909	−	0.474424i	0.969859	+	0.243666i	$0.0783501\pi$
$150$	17.7235	−	6.02871i	1.44712	−	0.492242i
$151$	−3.66278	+	2.11471i	−0.298073	+	0.172093i	−0.641577	−	0.767059i	$-0.721719\pi$
$151$	−3.66278	+	2.11471i	−0.298073	+	0.172093i	0.343504	+	0.939151i	$0.388386\pi$
$152$	3.09703	+	14.4762i	0.251202	+	1.17418i
$153$	−14.6557	+	12.0903i	−1.18484	+	0.977446i
$154$	−1.71089	−	0.102431i	−0.137867	−	0.00825413i
$155$			18.1687i			1.45934i
$156$	−1.26478	+	2.46218i	−0.101264	+	0.197132i
$157$	19.9382	−	11.5113i	1.59124	−	0.918702i	0.598144	−	0.801389i	$-0.295905\pi$
$157$	19.9382	−	11.5113i	1.59124	−	0.918702i	0.993095	−	0.117313i	$-0.0374281\pi$
$158$	−12.7780	+	12.3505i	−1.01657	+	0.982552i
$159$	2.30910	+	3.32723i	0.183123	+	0.263866i
$160$	−6.83766	+	18.9160i	−0.540565	+	1.49544i
$161$	5.54808	+	6.04438i	0.437250	+	0.476364i
$162$	0.681165	+	12.7097i	0.0535174	+	0.998567i
$163$	10.4009	−	18.0148i	0.814658	−	1.41103i	−0.0949145	−	0.995485i	$-0.530258\pi$
$163$	10.4009	−	18.0148i	0.814658	−	1.41103i	0.909573	−	0.415544i	$-0.136409\pi$
$164$	−10.7371	+	17.2167i	−0.838424	+	1.34440i
$165$	−0.234130	−	2.81135i	−0.0182270	−	0.218863i
$166$	0.943568	+	0.270114i	0.0732351	+	0.0209649i
$167$	7.53905			0.583390			0.291695	−	0.956511i	$-0.405781\pi$
$167$	7.53905			0.583390			0.291695	+	0.956511i	$0.405781\pi$
$168$	6.35987	+	11.2939i	0.490675	+	0.871343i
$169$	12.3615			0.950885
$170$	−30.6156	−	8.76429i	−2.34811	−	0.672190i
$171$	−5.49342	+	14.7095i	−0.420093	+	1.12486i
$172$	−6.04751	−	3.77150i	−0.461119	−	0.287574i
$173$	7.77603	−	13.4685i	0.591201	−	1.02399i	−0.402870	−	0.915257i	$-0.631987\pi$
$173$	7.77603	−	13.4685i	0.591201	−	1.02399i	0.994071	−	0.108733i	$-0.0346793\pi$
$174$	1.24017	−	6.25526i	0.0940174	−	0.474210i
$175$	19.7377	−	4.39329i	1.49203	−	0.332102i
$176$	1.52084	+	1.02192i	0.114638	+	0.0770304i
$177$	2.46036	−	1.70749i	0.184932	−	0.128343i
$178$	8.24494	−	7.96908i	0.617985	−	0.597308i
$179$	7.81218	−	4.51037i	0.583910	−	0.337121i	−0.178776	−	0.983890i	$-0.557214\pi$
$179$	7.81218	−	4.51037i	0.583910	−	0.337121i	0.762686	+	0.646769i	$0.223880\pi$
$180$	−16.9091	+	13.0085i	−1.26033	+	0.969596i
$181$		−	10.4041i		−	0.773330i	−0.922220	−	0.386665i	$-0.873627\pi$
$181$		−	10.4041i		−	0.773330i	0.922220	−	0.386665i	$-0.126373\pi$
$182$	−1.64698	+	2.49529i	−0.122082	+	0.184963i
$183$	−8.33693	−	3.93006i	−0.616284	−	0.290519i
$184$	−1.83496	−	8.57702i	−0.135275	−	0.632306i
$185$	10.2909	−	5.94148i	0.756605	−	0.436826i
$186$	−4.03068	−	11.8496i	−0.295543	−	0.868855i
$187$	−1.45049	+	2.51233i	−0.106071	+	0.183720i
$188$	7.62236	−	4.06151i	0.555918	−	0.296216i
$189$	−0.760132	+	13.7267i	−0.0552915	+	0.998470i
$190$	−25.5340	+	6.37831i	−1.85243	+	0.462731i
$191$	−7.33838	+	12.7104i	−0.530986	+	0.919695i	0.468360	+	0.883538i	$0.344845\pi$
$191$	−7.33838	+	12.7104i	−0.530986	+	0.919695i	−0.999346	+	0.0361574i	$0.988488\pi$
$192$	0.263059	−	13.8539i	0.0189846	−	0.999820i
$193$	8.06569	+	13.9702i	0.580581	+	1.00560i	0.995411	+	0.0956969i	$0.0305080\pi$
$193$	8.06569	+	13.9702i	0.580581	+	1.00560i	−0.414829	+	0.909899i	$0.636159\pi$
$194$	−2.74523	+	9.58971i	−0.197096	+	0.688501i
$195$	−4.45130	−	2.09836i	−0.318764	−	0.150267i
$196$	5.50341	+	12.8729i	0.393101	+	0.919495i
$197$	21.9480			1.56373			0.781863	−	0.623450i	$-0.214269\pi$
$197$	21.9480			1.56373			0.781863	+	0.623450i	$0.214269\pi$
$198$	0.776391	+	1.78162i	0.0551757	+	0.126614i
$199$	−13.8171	+	7.97732i	−0.979470	+	0.565497i	−0.902110	−	0.431506i	$-0.857982\pi$
$199$	−13.8171	+	7.97732i	−0.979470	+	0.565497i	−0.0773599	+	0.997003i	$0.524649\pi$
$200$	−20.5677	−	6.65279i	−1.45436	−	0.470424i
$201$	0.0193387	+	0.0278655i	0.00136404	+	0.00196548i
$202$	−9.17487	+	2.29185i	−0.645542	+	0.161254i
$203$	2.06568	−	6.57091i	0.144983	−	0.461188i
$204$	21.9119	−	1.07594i	1.53414	−	0.0753311i
$205$	−31.2400	−	18.0364i	−2.18189	−	1.25972i
$206$	6.44331	−	6.22773i	0.448927	−	0.433906i
$207$	3.25480	−	8.71522i	0.226224	−	0.605750i
$208$	2.87030	−	1.40621i	0.199019	−	0.0975030i
$209$			2.39752i			0.165840i
$210$	−19.6824	+	11.9833i	−1.35821	+	0.826924i
$211$	20.9923			1.44517			0.722586	−	0.691281i	$-0.242953\pi$
$211$	20.9923			1.44517			0.722586	+	0.691281i	$0.242953\pi$
$212$	0.159087	−	4.67381i	0.0109261	−	0.320999i
$213$	−15.6041	+	1.29952i	−1.06918	+	0.0890414i
$214$	−3.63621	+	3.51454i	−0.248566	+	0.240249i
$215$	6.33546	−	10.9733i	0.432074	−	0.748375i
$216$	8.14220	−	12.2354i	0.554007	−	0.832512i
$217$	−2.93727	−	13.1963i	−0.199395	−	0.895821i
$218$	−0.193153	−	0.773241i	−0.0130820	−	0.0523705i
$219$	8.20979	+	11.8297i	0.554766	+	0.799375i
$220$	−1.72378	+	2.76404i	−0.116217	+	0.186352i
$221$	2.53024	+	4.38251i	0.170203	+	0.294800i
$222$	−5.39365	+	6.15805i	−0.361998	+	0.413302i
$223$			7.05072i			0.472151i	0.971735	+	0.236075i	$0.0758613\pi$
$223$			7.05072i			0.472151i	−0.971735	+	0.236075i	$0.924139\pi$
$224$	1.90825	−	14.8445i	0.127500	−	0.991839i
$225$	−14.5907	−	17.6865i	−0.972713	−	1.17910i
$226$	−1.92332	−	0.550585i	−0.127937	−	0.0366244i
$227$	−17.9681	+	10.3739i	−1.19258	+	0.688539i	−0.958892	−	0.283771i	$-0.908414\pi$
$227$	−17.9681	+	10.3739i	−1.19258	+	0.688539i	−0.233693	+	0.972310i	$0.575081\pi$
$228$	15.2383	−	9.82460i	1.00918	−	0.650650i
$229$	19.0453	+	10.9958i	1.25855	+	0.726623i	0.972792	−	0.231680i	$-0.0744221\pi$
$229$	19.0453	+	10.9958i	1.25855	+	0.726623i	0.285756	+	0.958302i	$0.407755\pi$
$230$	15.1287	−	3.77909i	0.997556	−	0.249186i
$231$	0.624556	+	2.00409i	0.0410927	+	0.131859i
$232$	−5.46565	+	4.93440i	−0.358838	+	0.323959i
$233$	−15.1401	−	8.74112i	−0.991858	−	0.572650i	−0.0860289	−	0.996293i	$-0.527418\pi$
$233$	−15.1401	−	8.74112i	−0.991858	−	0.572650i	−0.905829	+	0.423643i	$0.860751\pi$
$234$	3.36865	+	0.381039i	0.220216	+	0.0249093i
$235$	7.67748	+	13.2978i	0.500824	+	0.867452i
$236$	−3.45611	−	0.117639i	−0.224974	−	0.00765764i
$237$	19.6873	+	9.28065i	1.27883	+	0.602843i
$238$	23.6537	+	1.41615i	1.53324	+	0.0917953i
$239$	−6.60546			−0.427271			−0.213636	−	0.976913i	$-0.568531\pi$
$239$	−6.60546			−0.427271			−0.213636	+	0.976913i	$0.568531\pi$
$240$	24.6316	−	0.370463i	1.58996	−	0.0239133i
$241$	−5.27959	−	9.14453i	−0.340089	−	0.589051i	0.644360	−	0.764722i	$-0.277124\pi$
$241$	−5.27959	−	9.14453i	−0.340089	−	0.589051i	−0.984449	+	0.175671i	$0.943790\pi$
$242$	−10.6051	−	10.9722i	−0.681718	−	0.705318i
$243$	14.2625	−	6.29143i	0.914937	−	0.403596i
$244$	5.00472	+	9.39251i	0.320394	+	0.601294i
$245$	−22.5398	+	10.5570i	−1.44002	+	0.674462i
$246$	24.3760	+	4.83282i	1.55416	+	0.308129i
$247$	3.62192	+	2.09112i	0.230457	+	0.133055i
$248$	−4.44793	+	13.7512i	−0.282444	+	0.873201i
$249$	−0.0997618	−	1.19790i	−0.00632215	−	0.0759140i
$250$	3.65728	−	12.7757i	0.231307	−	0.808007i
$251$		−	6.66647i		−	0.420784i	−0.977617	−	0.210392i	$-0.932526\pi$
$251$		−	6.66647i		−	0.420784i	0.977617	−	0.210392i	$-0.0674741\pi$
$252$	10.1784	−	12.1820i	0.641178	−	0.767392i
$253$		−	1.42051i		−	0.0893066i
$254$	21.3516	+	6.11228i	1.33972	+	0.383519i
$255$	3.23694	+	38.8680i	0.202705	+	2.43401i
$256$	−9.80605	+	12.6428i	−0.612878	+	0.790177i
$257$	0.887844	+	0.512597i	0.0553822	+	0.0319749i	0.527435	−	0.849595i	$-0.323154\pi$
$257$	0.887844	+	0.512597i	0.0553822	+	0.0319749i	−0.472053	+	0.881570i	$0.656487\pi$
$258$	−1.69757	+	8.56231i	−0.105686	+	0.533066i
$259$	−6.51398	+	5.97912i	−0.404759	+	0.371525i
$260$	2.67214	+	5.01490i	0.165719	+	0.311011i
$261$	−7.70262	+	1.29191i	−0.476780	+	0.0799675i
$262$	1.36929	−	1.32348i	0.0845952	−	0.0817647i
$263$	−8.60208	−	14.8992i	−0.530427	−	0.918726i	−0.999370	−	0.0354978i	$-0.988698\pi$
$263$	−8.60208	−	14.8992i	−0.530427	−	0.918726i	0.468943	−	0.883228i	$-0.344635\pi$
$264$	0.511051	−	2.18512i	0.0314530	−	0.134485i
$265$	8.31406			0.510729
$266$	17.5147	−	8.76071i	1.07390	−	0.537153i
$267$	−12.7031	−	5.98828i	−0.777416	−	0.366477i
$268$	0.00133235	−	0.0391431i	8.13864e−5	−	0.00239105i
$269$	−3.92637	−	6.80068i	−0.239395	−	0.414644i	0.721146	−	0.692783i	$-0.243616\pi$
$269$	−3.92637	−	6.80068i	−0.239395	−	0.414644i	−0.960541	+	0.278139i	$0.910282\pi$
$270$	22.2323	+	13.7271i	1.35301	+	0.835405i
$271$	−15.7096	−	9.06993i	−0.954289	−	0.550959i	−0.0598783	−	0.998206i	$-0.519071\pi$
$271$	−15.7096	−	9.06993i	−0.954289	−	0.550959i	−0.894411	+	0.447247i	$0.852405\pi$
$272$	−21.0262	−	14.1285i	−1.27490	−	0.856665i
$273$	3.57231	+	0.804454i	0.216206	+	0.0486878i
$274$	3.08347	+	12.3439i	0.186279	+	0.745725i
$275$	−3.03189	−	1.75046i	−0.182830	−	0.105557i
$276$	−9.02854	+	5.82099i	−0.543454	+	0.350382i
$277$	19.2898	−	11.1370i	1.15901	−	0.669157i	0.207946	−	0.978140i	$-0.433322\pi$
$277$	19.2898	−	11.1370i	1.15901	−	0.669157i	0.951067	+	0.308983i	$0.0999888\pi$
$278$	6.23421	−	21.7775i	0.373903	−	1.30613i
$279$	−11.8249	+	9.75505i	−0.707937	+	0.584020i
$280$	26.4911	+	2.49281i	1.58315	+	0.148974i
$281$			17.9109i			1.06847i	0.845335	+	0.534236i	$0.179401\pi$
$281$			17.9109i			1.06847i	−0.845335	+	0.534236i	$0.820599\pi$
$282$	−7.95734	−	6.96959i	−0.473853	−	0.415033i
$283$	−2.24283	−	3.88469i	−0.133322	−	0.230921i	0.791633	−	0.610997i	$-0.209231\pi$
$283$	−2.24283	−	3.88469i	−0.133322	−	0.230921i	−0.924955	+	0.380076i	$0.875898\pi$
$284$	15.3415	+	9.56765i	0.910352	+	0.567736i
$285$	18.3780	+	26.4812i	1.08862	+	1.56861i
$286$	0.502211	−	0.125451i	0.0296964	−	0.00741805i
$287$	25.6061	+	8.04974i	1.51148	+	0.475161i
$288$	−15.9825	+	5.70607i	−0.941779	+	0.336234i
$289$	11.5536	−	20.0115i	0.679625	−	1.17715i
$290$	−9.09801	−	9.41296i	−0.534254	−	0.552748i
$291$	12.1746	−	1.01390i	0.713686	−	0.0594361i
$292$	0.565620	−	16.6173i	0.0331004	−	0.972456i
$293$	−24.7711			−1.44714			−0.723570	−	0.690251i	$-0.757500\pi$
$293$	−24.7711			−1.44714			−0.723570	+	0.690251i	$0.757500\pi$
$294$	12.3584	−	11.8857i	0.720758	−	0.693187i
$295$		−	6.14794i		−	0.357947i
$296$	9.24338	−	1.97752i	0.537261	−	0.114941i
$297$	1.70403	−	1.66184i	0.0988778	−	0.0964298i
$298$	6.57224	+	6.79975i	0.380719	+	0.393899i
$299$	−2.14596	−	1.23897i	−0.124104	−	0.0716514i
$300$	1.29845	+	26.4433i	0.0749663	+	1.52671i
$301$	−2.82755	+	8.99439i	−0.162977	+	0.518428i
$302$	−1.44957	−	5.80299i	−0.0834131	−	0.333925i
$303$	6.60356	+	9.51522i	0.379364	+	0.546635i
$304$	−20.8873	−	1.42357i	−1.19797	−	0.0816473i
$305$	−16.3860	+	9.46044i	−0.938257	+	0.541703i
$306$	−10.7339	−	24.6316i	−0.613616	−	1.40809i
$307$	7.72188			0.440711			0.220355	−	0.975420i	$-0.429278\pi$
$307$	7.72188			0.440711			0.220355	+	0.975420i	$0.429278\pi$
$308$	0.805161	−	2.28626i	0.0458783	−	0.130272i
$309$	−9.92729	−	4.67976i	−0.564744	−	0.266222i
$310$	−24.7021	−	7.07144i	−1.40299	−	0.401631i
$311$	−10.0093	−	17.3367i	−0.567577	−	0.983072i	−0.996805	−	0.0798757i	$-0.974548\pi$
$311$	−10.0093	−	17.3367i	−0.567577	−	0.983072i	0.429228	−	0.903196i	$-0.358786\pi$
$312$	−2.85532	−	2.67791i	−0.161650	−	0.151607i
$313$	−8.54501	+	14.8004i	−0.482993	+	0.836568i	−0.999809	−	0.0195284i	$-0.993784\pi$
$313$	−8.54501	+	14.8004i	−0.482993	+	0.836568i	0.516817	+	0.856096i	$0.327117\pi$
$314$	7.89063	+	31.5883i	0.445294	+	1.78263i
$315$	22.2605	+	17.3482i	1.25424	+	0.977461i
$316$	−11.8184	−	22.1800i	−0.664837	−	1.24772i
$317$	−7.67062	+	13.2859i	−0.430825	+	0.746210i	−0.996945	−	0.0781127i	$-0.975111\pi$
$317$	−7.67062	+	13.2859i	−0.430825	+	0.746210i	0.566120	+	0.824323i	$0.308444\pi$
$318$	−5.42243	+	1.84446i	−0.304075	+	0.103432i
$319$	−1.03278	+	0.596274i	−0.0578244	+	0.0333849i
$320$	−23.0569	−	16.6588i	−1.28892	−	0.931255i
$321$	5.60235	+	2.64097i	0.312693	+	0.147405i
$322$	−10.3773	+	5.19064i	−0.578305	+	0.289263i
$323$		−	33.1466i		−	1.84433i
$324$	−17.5452	−	4.02063i	−0.974734	−	0.223368i
$325$	−5.28884	+	3.05351i	−0.293372	+	0.169378i
$326$	20.4448	+	21.1526i	1.13234	+	1.17153i
$327$	−0.801925	+	0.556536i	−0.0443465	+	0.0307765i
$328$	−19.2288	−	21.2990i	−1.06173	−	1.17604i
$329$	−7.72613	−	8.41727i	−0.425955	−	0.464059i
$330$	3.91344	+	0.775883i	0.215428	+	0.0427110i
$331$	−6.86143	+	11.8844i	−0.377138	+	0.653223i	−0.990645	−	0.136467i	$-0.956425\pi$
$331$	−6.86143	+	11.8844i	−0.377138	+	0.653223i	0.613506	+	0.789690i	$0.289759\pi$
$332$	−0.734493	+	1.17774i	−0.0403106	+	0.0646371i
$333$	9.39233	+	3.50768i	0.514696	+	0.192219i
$334$	−2.93428	+	10.2501i	−0.160557	+	0.560861i
$335$	0.0696302			0.00380430
$336$	−17.8305	+	4.25118i	−0.972735	+	0.231921i
$337$	−15.7338			−0.857074			−0.428537	−	0.903524i	$-0.640971\pi$
$337$	−15.7338			−0.857074			−0.428537	+	0.903524i	$0.640971\pi$
$338$	−4.81123	+	16.8067i	−0.261696	+	0.914164i
$339$	0.203349	+	2.44174i	0.0110444	+	0.132617i
$340$	23.8319	−	38.2139i	1.29246	−	2.07244i
$341$	−1.17033	+	2.02706i	−0.0633767	+	0.109772i
$342$	−17.8609	−	13.1939i	−0.965807	−	0.713447i
$343$	14.6644	−	11.3117i	0.791804	−	0.610775i
$344$	7.48149	−	6.75430i	0.403375	−	0.364167i
$345$	−10.8888	−	15.6899i	−0.586232	−	0.844715i
$346$	15.2853	+	15.8144i	0.821740	+	0.850187i
$347$	−18.5301	+	10.6984i	−0.994748	+	0.574318i	−0.906690	−	0.421798i	$-0.861399\pi$
$347$	−18.5301	+	10.6984i	−0.994748	+	0.574318i	−0.0880576	+	0.996115i	$0.528066\pi$
$348$	8.02196	+	4.12076i	0.430022	+	0.220896i
$349$			15.7266i			0.841826i	0.907101	+	0.420913i	$0.138290\pi$
$349$			15.7266i			0.841826i	−0.907101	+	0.420913i	$0.861710\pi$
$350$	−1.70901	+	28.5454i	−0.0913507	+	1.52581i
$351$	−1.02428	−	4.02373i	−0.0546721	−	0.214771i
$352$	−1.98134	+	1.67000i	−0.105606	+	0.0890111i
$353$	−10.1824	+	5.87883i	−0.541956	+	0.312898i	−0.745871	−	0.666090i	$-0.767967\pi$
$353$	−10.1824	+	5.87883i	−0.541956	+	0.312898i	0.203915	+	0.978989i	$0.434633\pi$
$354$	1.36391	+	4.00968i	0.0724908	+	0.213112i
$355$	−16.0720	+	27.8375i	−0.853013	+	1.47746i
$356$	7.62574	+	14.3115i	0.404164	+	0.758507i
$357$	−8.63472	−	27.7073i	−0.456998	−	1.46643i
$358$	3.09171	+	12.3769i	0.163402	+	0.654141i
$359$	−10.2639	+	17.7776i	−0.541709	+	0.938268i	0.457097	+	0.889417i	$0.348889\pi$
$359$	−10.2639	+	17.7776i	−0.541709	+	0.938268i	−0.998806	+	0.0488509i	$0.984444\pi$
$360$	−11.1052	−	28.0527i	−0.585293	−	1.47851i
$361$	−4.19701	−	7.26943i	−0.220895	−	0.382601i
$362$	14.1454	+	4.04938i	0.743466	+	0.212831i
$363$	−7.96906	+	16.9050i	−0.418267	+	0.887280i
$364$	−2.75158	−	3.21043i	−0.144222	−	0.168272i
$365$	29.5599			1.54724
$366$	8.58814	−	9.80528i	0.448909	−	0.512530i
$367$	19.9290	−	11.5060i	1.04029	−	0.600609i	0.120372	−	0.992729i	$-0.461591\pi$
$367$	19.9290	−	11.5060i	1.04029	−	0.600609i	0.919914	+	0.392120i	$0.128258\pi$
$368$	12.3755	+	0.843451i	0.645118	+	0.0439679i
$369$	−5.03445	−	30.0162i	−0.262083	−	1.56258i
$370$	4.07270	+	16.3041i	0.211729	+	0.847608i
$371$	−6.03867	+	1.34411i	−0.313512	+	0.0697826i
$372$	17.6795	−	0.868122i	0.916640	−	0.0450100i
$373$	21.6640	+	12.5077i	1.12172	+	0.647624i	0.941839	−	0.336065i	$-0.109096\pi$
$373$	21.6640	+	12.5077i	1.12172	+	0.647624i	0.179878	+	0.983689i	$0.442430\pi$
$374$	−2.85122	−	2.94992i	−0.147433	−	0.152537i
$375$	−16.2193	+	1.35075i	−0.837563	+	0.0697526i
$376$	2.55532	+	11.9442i	0.131781	+	0.615973i
$377$			2.08028i			0.107140i
$378$	−18.3670	−	6.37605i	−0.944696	−	0.327949i
$379$	−11.7405			−0.603071			−0.301535	−	0.953455i	$-0.597499\pi$
$379$	−11.7405			−0.603071			−0.301535	+	0.953455i	$0.597499\pi$
$380$	1.26616	−	37.1986i	0.0649529	−	1.90825i
$381$	−2.25747	−	27.1068i	−0.115653	−	1.38872i
$382$	−14.4250	−	14.9243i	−0.738045	−	0.763594i
$383$	−8.93250	+	15.4715i	−0.456430	+	0.790559i	−0.998769	−	0.0496002i	$-0.984205\pi$
$383$	−8.93250	+	15.4715i	−0.456430	+	0.790559i	0.542340	+	0.840159i	$0.317539\pi$
$384$	18.7334	+	5.74974i	0.955985	+	0.293415i
$385$	4.11092	+	1.29234i	0.209512	+	0.0658639i
$386$	−22.1331	+	5.52878i	−1.12655	+	0.281407i
$387$	10.5435	−	1.76840i	0.535956	−	0.0898927i
$388$	−11.9697	−	7.46484i	−0.607670	−	0.378970i
$389$	−12.9460	−	22.4231i	−0.656386	−	1.13689i	−0.981544	−	0.191235i	$-0.938751\pi$
$389$	−12.9460	−	22.4231i	−0.656386	−	1.13689i	0.325158	−	0.945660i	$-0.394582\pi$
$390$	4.58543	−	5.23529i	0.232192	−	0.265099i
$391$			19.6391i			0.993190i
$392$	−19.6440	+	2.47216i	−0.992174	+	0.124863i
$393$	−2.10969	−	0.994514i	−0.106420	−	0.0501666i
$394$	−8.54238	+	29.8405i	−0.430359	+	1.50334i
$395$	38.6946	−	22.3404i	1.94694	−	1.12407i
$396$	−2.72447	+	0.362157i	−0.136910	+	0.0181991i
$397$	−17.5040	−	10.1060i	−0.878502	−	0.507203i	−0.00833784	−	0.999965i	$-0.502654\pi$
$397$	−17.5040	−	10.1060i	−0.878502	−	0.507203i	−0.870164	+	0.492762i	$0.835987\pi$
$398$	−5.46820	−	21.8906i	−0.274096	−	1.09728i
$399$	−17.6294	−	16.2628i	−0.882576	−	0.814156i
$400$	17.0503	−	25.3746i	0.852516	−	1.26873i
$401$	32.0937	+	18.5293i	1.60268	+	0.925309i	0.990948	+	0.134247i	$0.0428615\pi$
$401$	32.0937	+	18.5293i	1.60268	+	0.925309i	0.611735	+	0.791063i	$0.290472\pi$
$402$	−0.0454128	+	0.0154473i	−0.00226498	+	0.000770441i
$403$	2.04152	+	3.53601i	0.101695	+	0.176141i
$404$	0.454957	−	13.3662i	0.0226350	−	0.664992i
$405$	6.08275	−	31.4175i	0.302255	−	1.56115i
$406$	8.12983	+	5.36598i	0.403477	+	0.266309i
$407$	1.53087			0.0758825
$408$	−7.06547	+	30.2102i	−0.349793	+	1.49563i
$409$	−14.5304	−	25.1675i	−0.718484	−	1.24445i	−0.961600	−	0.274453i	$-0.911503\pi$
$409$	−14.5304	−	25.1675i	−0.718484	−	1.24445i	0.243117	−	0.969997i	$-0.421830\pi$
$410$	36.6812	−	35.4539i	1.81156	−	1.75094i
$411$	12.8018	−	8.88448i	0.631469	−	0.438239i
$412$	5.95942	+	11.1842i	0.293599	+	0.551008i
$413$	0.993917	+	4.46537i	0.0489075	+	0.219727i
$414$	10.5824	+	7.81729i	0.520098	+	0.384199i
$415$	−2.13704	−	1.23382i	−0.104903	−	0.0605659i
$416$	0.794732	+	4.44977i	0.0389650	+	0.218168i
$417$	−27.6475	+	2.30250i	−1.35391	+	0.112754i
$418$	−3.25967	−	0.933141i	−0.159436	−	0.0456414i
$419$			1.27248i			0.0621647i	0.999517	+	0.0310823i	$0.00989541\pi$
$419$			1.27248i			0.0621647i	−0.999517	+	0.0310823i	$0.990105\pi$
$420$	−8.63188	−	31.4242i	−0.421192	−	1.53334i
$421$			12.1006i			0.589749i	0.955536	+	0.294875i	$0.0952779\pi$
$421$			12.1006i			0.589749i	−0.955536	+	0.294875i	$0.904722\pi$
$422$	−8.17044	+	28.5412i	−0.397731	+	1.38936i
$423$	−4.53256	+	12.1366i	−0.220381	+	0.590102i
$424$	6.29260	+	2.03539i	0.305596	+	0.0988474i
$425$	41.9171	+	24.2008i	2.03328	+	1.17391i
$426$	4.30646	−	21.7211i	0.208649	−	1.05239i
$427$	10.3720	−	9.52038i	0.501937	−	0.460723i
$428$	−3.36313	−	6.31169i	−0.162563	−	0.305087i
$429$	−0.361463	−	0.520841i	−0.0174516	−	0.0251464i
$430$	12.4535	+	12.8846i	0.600562	+	0.621352i
$431$	8.36354	+	14.4861i	0.402858	+	0.697770i	0.994070	−	0.108746i	$-0.0346837\pi$
$431$	8.36354	+	14.4861i	0.402858	+	0.697770i	−0.591212	+	0.806516i	$0.701350\pi$
$432$	13.4662	+	15.8323i	0.647893	+	0.761731i
$433$	−14.1708			−0.681007			−0.340503	−	0.940243i	$-0.610597\pi$
$433$	−14.1708			−0.681007			−0.340503	+	0.940243i	$0.610597\pi$
$434$	19.0849	+	1.14261i	0.916104	+	0.0548472i
$435$	−6.83661	+	14.5027i	−0.327790	+	0.695349i
$436$	1.12648	+	0.0383430i	0.0539485	+	0.00183630i
$437$	8.11535	+	14.0562i	0.388210	+	0.672399i
$438$	−19.2790	+	6.55780i	−0.921185	+	0.313344i
$439$	−22.3364	−	12.8959i	−1.06606	−	0.615489i	−0.138957	−	0.990298i	$-0.544375\pi$
$439$	−22.3364	−	12.8959i	−1.06606	−	0.615489i	−0.927102	+	0.374809i	$0.877708\pi$
$440$	−3.08708	−	3.41944i	−0.147171	−	0.163016i
$441$	−18.9729	−	9.00158i	−0.903472	−	0.428646i
$442$	−6.94326	+	1.73440i	−0.330257	+	0.0824971i
$443$	−30.3993	−	17.5510i	−1.44431	−	0.833875i	−0.446181	−	0.894943i	$-0.647216\pi$
$443$	−30.3993	−	17.5510i	−1.44431	−	0.833875i	−0.998134	+	0.0610673i	$0.980550\pi$
$444$	−6.27323	−	9.72999i	−0.297714	−	0.461765i
$445$	−24.9675	+	14.4150i	−1.18357	+	0.683336i
$446$	−9.58616	−	2.74421i	−0.453918	−	0.129942i
$447$	4.93864	−	10.4765i	0.233590	−	0.495519i
$448$	19.4399	+	8.37209i	0.918447	+	0.395544i
$449$		−	13.8891i		−	0.655467i	−0.944770	−	0.327733i	$-0.893715\pi$
$449$		−	13.8891i		−	0.655467i	0.944770	−	0.327733i	$-0.106285\pi$
$450$	29.7255	−	12.9537i	1.40127	−	0.610644i
$451$	−2.32361	−	4.02462i	−0.109415	−	0.189512i
$452$	1.49715	−	2.40065i	0.0704201	−	0.112917i
$453$	−6.01825	+	4.17667i	−0.282762	+	0.196237i
$454$	−7.11097	−	28.4671i	−0.333734	−	1.33603i
$455$	5.53788	−	5.08317i	0.259620	−	0.238303i
$456$	7.42664	+	24.5418i	0.347784	+	1.14928i
$457$	3.77280	−	6.53468i	0.176484	−	0.305679i	−0.764190	−	0.644991i	$-0.776861\pi$
$457$	3.77280	−	6.53468i	0.176484	−	0.305679i	0.940674	+	0.339312i	$0.110194\pi$
$458$	−22.3625	+	21.6143i	−1.04493	+	1.00997i
$459$	−23.5588	+	22.9756i	−1.09963	+	1.07241i
$460$	−0.750191	+	22.0398i	−0.0349778	+	1.02761i
$461$	17.6339			0.821292			0.410646	−	0.911795i	$-0.365303\pi$
$461$	17.6339			0.821292			0.410646	+	0.911795i	$0.365303\pi$
$462$	−2.96785	+	0.0691334i	−0.138077	+	0.00321638i
$463$			29.5192i			1.37187i	0.727661	+	0.685937i	$0.240607\pi$
$463$			29.5192i			1.37187i	−0.727661	+	0.685937i	$0.759393\pi$
$464$	−4.58153	−	9.35163i	−0.212692	−	0.434138i
$465$	2.61171	+	31.3605i	0.121115	+	1.45431i
$466$	17.7771	−	17.1823i	0.823508	−	0.795955i
$467$	26.4319	+	15.2605i	1.22312	+	0.706170i	0.965582	−	0.260098i	$-0.0837549\pi$
$467$	26.4319	+	15.2605i	1.22312	+	0.706170i	0.257539	+	0.966268i	$0.417088\pi$
$468$	−1.82918	+	4.43172i	−0.0845537	+	0.204856i
$469$	−0.0505738	+	0.0112569i	−0.00233528	+	0.000519795i
$470$	−21.0679	+	5.26267i	−0.971788	+	0.242749i
$471$	32.7600	−	22.7355i	1.50950	−	1.04759i
$472$	1.50510	−	4.65314i	0.0692777	−	0.214178i
$473$	1.41368	−	0.816191i	0.0650013	−	0.0375285i
$474$	−20.2805	+	23.1547i	−0.931513	+	1.06353i
$475$	40.0015			1.83540
$476$	−11.1317	+	31.6084i	−0.510219	+	1.44877i
$477$	4.46396	+	5.41112i	0.204391	+	0.247758i
$478$	2.57091	−	8.98079i	0.117591	−	0.410772i
$479$	0.0969618	+	0.167943i	0.00443030	+	0.00767350i	0.868232	−	0.496158i	$-0.165256\pi$
$479$	0.0969618	+	0.167943i	0.00443030	+	0.00767350i	−0.863802	+	0.503832i	$0.831923\pi$
$480$	−9.08319	+	33.6333i	−0.414589	+	1.53514i
$481$	1.33523	−	2.31268i	0.0608811	−	0.105449i
$482$	14.4878	−	3.61899i	0.659900	−	0.164841i
$483$	10.4453	+	9.63553i	0.475276	+	0.438432i
$484$	19.0454	−	10.1482i	0.865699	−	0.461280i
$485$	12.5396	−	21.7193i	0.569395	−	0.986221i
$486$	3.00274	+	21.8400i	0.136207	+	0.990680i
$487$	−17.4486	+	10.0740i	−0.790673	+	0.456496i	−0.840200	−	0.542277i	$-0.817562\pi$
$487$	−17.4486	+	10.0740i	−0.790673	+	0.456496i	0.0495261	+	0.998773i	$0.484229\pi$
$488$	−14.7180	+	3.14875i	−0.666251	+	0.142537i
$489$	15.3631	−	32.5900i	0.694742	−	1.47377i
$490$	−5.58058	−	34.7541i	−0.252105	−	1.57003i
$491$		−	4.30244i		−	0.194167i	−0.995276	−	0.0970833i	$-0.969049\pi$
$491$		−	4.30244i		−	0.194167i	0.995276	−	0.0970833i	$-0.0309513\pi$
$492$	−16.0581	+	31.2607i	−0.723956	+	1.40934i
$493$	14.2785	−	8.24371i	0.643073	−	0.371278i
$494$	−4.25278	+	4.11048i	−0.191342	+	0.184939i
$495$	−0.808253	−	4.81894i	−0.0363283	−	0.216595i
$496$	−16.9649	−	11.3995i	−0.761748	−	0.511853i
$497$	7.17302	−	22.8173i	0.321754	−	1.02349i
$498$	1.66750	+	0.330600i	0.0747224	+	0.0148145i
$499$	−13.0198	+	22.5510i	−0.582848	+	1.00952i	0.412292	+	0.911052i	$0.364728\pi$
$499$	−13.0198	+	22.5510i	−0.582848	+	1.00952i	−0.995140	+	0.0984710i	$0.968605\pi$
$500$	15.9464	+	9.94489i	0.713145	+	0.444749i
$501$	13.0130	−	1.08373i	0.581377	−	0.0484173i
$502$	9.06375	+	2.59466i	0.404535	+	0.115805i
$503$	22.7182			1.01295			0.506476	−	0.862254i	$-0.330948\pi$
$503$	22.7182			1.01295			0.506476	+	0.862254i	$0.330948\pi$
$504$	12.6011	+	18.5799i	0.561297	+	0.827614i
$505$	23.7766			1.05804
$506$	1.93132	+	0.552877i	0.0858578	+	0.0245784i
$507$	21.3369	−	1.77694i	0.947604	−	0.0789169i
$508$	−16.6205	+	26.6507i	−0.737417	+	1.18243i
$509$	−18.1915	+	31.5087i	−0.806326	+	1.39660i	0.109067	+	0.994034i	$0.465214\pi$
$509$	−18.1915	+	31.5087i	−0.806326	+	1.39660i	−0.915392	+	0.402563i	$0.868120\pi$
$510$	−54.1048	−	10.7269i	−2.39580	−	0.474994i
$511$	−21.4700	+	4.77886i	−0.949776	+	0.211404i
$512$	−13.3726	−	18.2530i	−0.590991	−	0.806678i
$513$	−7.36760	+	26.1793i	−0.325288	+	1.15585i
$514$	−1.04249	+	1.00761i	−0.0459821	+	0.0444436i
$515$	−19.5117	+	11.2651i	−0.859790	+	0.496400i
$516$	−10.9806	−	5.64057i	−0.483395	−	0.248312i
$517$			1.97817i			0.0869997i
$518$	−5.59391	−	11.1836i	−0.245782	−	0.491377i
$519$	11.4860	−	24.3654i	0.504177	−	1.06952i
$520$	−7.85829	+	1.68120i	−0.344609	+	0.0737254i
$521$	−4.25083	+	2.45422i	−0.186232	+	0.107521i	−0.590218	−	0.807244i	$-0.700958\pi$
$521$	−4.25083	+	2.45422i	−0.186232	+	0.107521i	0.403985	+	0.914765i	$0.367625\pi$
$522$	1.24145	−	10.9753i	0.0543369	−	0.480377i
$523$	20.4680	−	35.4516i	0.895002	−	1.55019i	0.0612000	−	0.998126i	$-0.480507\pi$
$523$	20.4680	−	35.4516i	0.895002	−	1.55019i	0.833802	−	0.552064i	$-0.186159\pi$
$524$	1.26646	+	2.37680i	0.0553255	+	0.103831i
$525$	33.4373	−	10.4204i	1.45932	−	0.454784i
$526$	23.6050	−	5.89645i	1.02923	−	0.257098i
$527$	16.1802	−	28.0249i	0.704821	−	1.22079i
$528$	2.77199	+	1.54530i	0.120635	+	0.0672505i
$529$	6.69173	+	11.5904i	0.290945	+	0.503931i
$530$	−3.23592	+	11.3038i	−0.140559	+	0.491006i
$531$	4.00132	−	3.30093i	0.173642	−	0.143248i
$532$	5.09414	+	27.2228i	0.220859	+	1.18026i
$533$	−8.10662			−0.351137
$534$	13.0859	−	14.9404i	0.566280	−	0.646535i
$535$	11.0112	−	6.35733i	0.476057	−	0.274852i
$536$	0.0527005	+	0.0170464i	0.00227631	+	0.000736292i
$537$	12.8361	−	8.90822i	0.553917	−	0.384418i
$538$	10.7744	−	2.69140i	0.464517	−	0.116035i
$539$	−3.19478	−	0.274055i	−0.137609	−	0.0118044i
$540$	−27.3164	+	24.8843i	−1.17551	+	1.07085i
$541$	−7.39731	−	4.27084i	−0.318035	−	0.183618i	0.332481	−	0.943110i	$-0.392114\pi$
$541$	−7.39731	−	4.27084i	−0.318035	−	0.183618i	−0.650517	+	0.759492i	$0.725448\pi$
$542$	18.4458	−	17.8286i	0.792316	−	0.765806i
$543$	−1.49557	−	17.9582i	−0.0641810	−	0.770662i
$544$	27.3927	−	23.0883i	1.17445	−	0.989904i
$545$			2.00385i			0.0858353i
$546$	−2.48412	+	4.54381i	−0.106310	+	0.194457i
$547$	−0.501652			−0.0214491			−0.0107245	−	0.999942i	$-0.503414\pi$
$547$	−0.501652			−0.0214491			−0.0107245	+	0.999942i	$0.503414\pi$
$548$	−17.9830	−	0.612103i	−0.768194	−	0.0261478i
$549$	−14.9551	−	5.58516i	−0.638269	−	0.238369i
$550$	3.55998	−	3.44086i	0.151798	−	0.146719i
$551$	6.81301	−	11.8005i	0.290244	−	0.502718i
$552$	−4.40021	−	14.5408i	−0.187285	−	0.618898i
$553$	−24.4930	+	22.4819i	−1.04155	+	0.956028i
$554$	7.63405	+	30.5611i	0.324340	+	1.29842i
$555$	16.9089	−	11.7347i	0.717741	−	0.498112i
$556$	27.1823	+	16.9521i	1.15279	+	0.718928i
$557$	−8.85048	−	15.3295i	−0.375007	−	0.649531i	0.615321	−	0.788277i	$-0.289026\pi$
$557$	−8.85048	−	15.3295i	−0.375007	−	0.649531i	−0.990328	+	0.138745i	$0.955693\pi$
$558$	−8.66061	−	19.8739i	−0.366633	−	0.841329i
$559$		−	2.84753i		−	0.120438i
$560$	−13.6998	+	35.0471i	−0.578924	+	1.48101i
$561$	−2.14252	+	4.54498i	−0.0904572	+	0.191889i
$562$	−24.3516	−	6.97110i	−1.02721	−	0.294058i
$563$	0.214083	−	0.123601i	0.00902251	−	0.00520915i	−0.495482	−	0.868618i	$-0.665009\pi$
$563$	0.214083	−	0.123601i	0.00902251	−	0.00520915i	0.504504	+	0.863409i	$0.331675\pi$
$564$	12.5729	−	8.10617i	0.529416	−	0.341331i
$565$	4.35603	+	2.51495i	0.183260	+	0.105805i
$566$	6.15456	−	1.53739i	0.258696	−	0.0646212i
$567$	0.661144	+	23.8026i	0.0277654	+	0.999614i
$568$	−18.9793	+	17.1345i	−0.796353	+	0.718949i
$569$	22.8950	+	13.2184i	0.959809	+	0.554146i	0.896114	−	0.443824i	$-0.146378\pi$
$569$	22.8950	+	13.2184i	0.959809	+	0.554146i	0.0636947	+	0.997969i	$0.479712\pi$
$570$	−43.1568	+	14.6799i	−1.80764	+	0.614874i
$571$	−16.4357	−	28.4675i	−0.687814	−	1.19133i	−0.972544	−	0.232721i	$-0.925237\pi$
$571$	−16.4357	−	28.4675i	−0.687814	−	1.19133i	0.284730	−	0.958608i	$-0.408096\pi$
$572$	−0.0249033	+	0.731634i	−0.00104126	+	0.0305912i
$573$	−10.8395	+	22.9941i	−0.452826	+	0.960591i
$574$	−20.9106	+	31.6810i	−0.872792	+	1.32234i
$575$	−23.7005			−0.988380
$576$	−1.53742	−	23.9507i	−0.0640590	−	0.997946i
$577$	13.3055	+	23.0459i	0.553917	+	0.959413i	0.997987	+	0.0634205i	$0.0202009\pi$
$577$	13.3055	+	23.0459i	0.553917	+	0.959413i	−0.444070	+	0.895992i	$0.646466\pi$
$578$	22.7108	+	23.4970i	0.944646	+	0.977347i
$579$	15.9302	+	22.9542i	0.662036	+	0.953943i
$580$	16.3389	−	8.70604i	0.678436	−	0.361499i
$581$	1.75164	+	0.550661i	0.0726705	+	0.0228453i
$582$	−3.35997	+	16.9472i	−0.139275	+	0.702484i
$583$	0.927594	+	0.535547i	0.0384170	+	0.0221801i
$584$	22.3728	+	7.23666i	0.925793	+	0.299455i
$585$	−7.98492	−	2.98206i	−0.330136	−	0.123293i
$586$	9.64116	−	33.6788i	0.398273	−	1.39126i
$587$			23.5447i			0.971792i	0.874017	+	0.485896i	$0.161507\pi$
$587$			23.5447i			0.971792i	−0.874017	+	0.485896i	$0.838493\pi$
$588$	11.3498	+	21.4286i	0.468056	+	0.883699i
$589$		−	26.7442i		−	1.10198i
$590$	8.35874	+	2.39284i	0.344124	+	0.0985118i
$591$	37.8838	−	3.15498i	1.55833	−	0.129779i
$592$	−0.908981	+	13.3370i	−0.0373589	+	0.548147i
$593$	−4.37266	−	2.52456i	−0.179564	−	0.103671i	0.407524	−	0.913195i	$-0.366392\pi$
$593$	−4.37266	−	2.52456i	−0.179564	−	0.103671i	−0.587088	+	0.809523i	$0.699726\pi$
$594$	1.59621	+	2.96361i	0.0654935	+	0.121598i
$595$	−56.8351	−	17.8671i	−2.33001	−	0.732480i
$596$	−11.8029	+	6.28908i	−0.483467	+	0.257611i
$597$	−22.7027	+	15.7556i	−0.929159	+	0.644836i
$598$	2.51973	−	2.43542i	0.103039	−	0.0995919i
$599$	−7.88687	−	13.6605i	−0.322249	−	0.558151i	0.658703	−	0.752403i	$-0.271105\pi$
$599$	−7.88687	−	13.6605i	−0.322249	−	0.558151i	−0.980952	+	0.194252i	$0.937772\pi$
$600$	−36.4578	−	8.52665i	−1.48838	−	0.348099i
$601$	−3.65359			−0.149033			−0.0745165	−	0.997220i	$-0.523741\pi$
$601$	−3.65359			−0.149033			−0.0745165	+	0.997220i	$0.523741\pi$
$602$	−11.1283	−	7.34505i	−0.453554	−	0.299362i
$603$	0.0373856	+	0.0453181i	0.00152246	+	0.00184550i
$604$	8.45394	+	0.287755i	0.343986	+	0.0117086i
$605$	19.1831	+	33.2261i	0.779904	+	1.35083i
$606$	−15.5071	+	5.27478i	−0.629932	+	0.214273i
$607$	40.3527	+	23.2976i	1.63786	+	0.945622i	0.981567	+	0.191120i	$0.0612118\pi$
$607$	40.3527	+	23.2976i	1.63786	+	0.945622i	0.656298	+	0.754502i	$0.272122\pi$
$608$	10.0650	−	27.8443i	0.408191	−	1.12923i
$609$	2.62097	−	11.6388i	0.106207	−	0.471629i
$610$	−6.48483	−	25.9605i	−0.262563	−	1.05111i
$611$	2.98841	+	1.72536i	0.120898	+	0.0698005i
$612$	37.6669	−	5.00695i	1.52259	−	0.202394i
$613$	−18.5964	+	10.7366i	−0.751102	+	0.433649i	−0.826092	−	0.563536i	$-0.809441\pi$
$613$	−18.5964	+	10.7366i	−0.751102	+	0.433649i	0.0749902	+	0.997184i	$0.476107\pi$
$614$	−3.00544	+	10.4987i	−0.121290	+	0.423692i
$615$	−56.5152	−	26.6415i	−2.27891	−	1.07429i
$616$	2.79502	+	1.98453i	0.112615	+	0.0799592i
$617$			23.7350i			0.955536i	0.878486	+	0.477768i	$0.158554\pi$
$617$			23.7350i			0.955536i	−0.878486	+	0.477768i	$0.841446\pi$
$618$	10.2264	−	11.6757i	0.411367	−	0.469667i
$619$	−10.3184	−	17.8719i	−0.414730	−	0.718334i	0.580670	−	0.814139i	$-0.302791\pi$
$619$	−10.3184	−	17.8719i	−0.414730	−	0.718334i	−0.995400	+	0.0958052i	$0.969457\pi$
$620$	19.2287	−	30.8328i	0.772242	−	1.23827i
$621$	4.36524	−	15.5110i	0.175171	−	0.622435i
$622$	27.4667	−	6.86108i	1.10131	−	0.275104i
$623$	15.8040	−	14.5063i	0.633173	−	0.581183i
$624$	4.75221	−	2.83982i	0.190241	−	0.113684i
$625$	2.40116	−	4.15892i	0.0960462	−	0.166357i
$626$	−16.7968	−	17.3783i	−0.671336	−	0.694576i
$627$	0.344639	+	4.13830i	0.0137636	+	0.165268i
$628$	−46.0186	−	1.56638i	−1.83634	−	0.0625053i
$629$	−21.1649			−0.843899
$630$	−32.2507	+	23.5133i	−1.28490	+	0.936794i
$631$		−	1.83946i		−	0.0732279i	−0.999329	−	0.0366139i	$-0.988343\pi$
$631$		−	1.83946i		−	0.0732279i	0.999329	−	0.0366139i	$-0.0116572\pi$
$632$	34.7557	−	7.43562i	1.38251	−	0.295773i
$633$	36.2343	−	3.01761i	1.44019	−	0.119939i
$634$	−15.0780	−	15.6000i	−0.598825	−	0.619555i
$635$	−48.3581	−	27.9196i	−1.91903	−	1.10796i
$636$	−0.397256	−	8.09022i	−0.0157522	−	0.320798i
$637$	−3.20050	+	4.58730i	−0.126808	+	0.181756i
$638$	−0.408727	−	1.63624i	−0.0161817	−	0.0647794i
$639$	−26.7471	+	4.48613i	−1.05810	+	0.177468i
$640$	31.6233	−	24.8644i	1.25002	−	0.982851i
$641$	21.1148	−	12.1906i	0.833983	−	0.481500i	−0.0212316	−	0.999775i	$-0.506759\pi$
$641$	21.1148	−	12.1906i	0.833983	−	0.481500i	0.855214	+	0.518274i	$0.173425\pi$
$642$	−5.77116	+	6.58907i	−0.227769	+	0.260050i
$643$	−7.88201			−0.310836			−0.155418	−	0.987849i	$-0.549672\pi$
$643$	−7.88201			−0.310836			−0.155418	+	0.987849i	$0.549672\pi$
$644$	−3.01823	−	16.1293i	−0.118935	−	0.635582i
$645$	9.35808	−	19.8515i	0.368474	−	0.781652i
$646$	45.0662	+	12.9010i	1.77311	+	0.507584i
$647$	−2.44506	−	4.23496i	−0.0961251	−	0.166494i	0.813953	−	0.580931i	$-0.197312\pi$
$647$	−2.44506	−	4.23496i	−0.0961251	−	0.166494i	−0.910078	+	0.414438i	$0.863978\pi$
$648$	12.2952	−	22.2896i	0.483003	−	0.875619i
$649$	0.396017	−	0.685921i	0.0155450	−	0.0269247i
$650$	−2.09308	−	8.37916i	−0.0820975	−	0.328658i
$651$	−6.96689	−	22.3555i	−0.273054	−	0.876182i
$652$	−36.7164	+	19.5640i	−1.43793	+	0.766186i
$653$	21.3381	−	36.9587i	0.835024	−	1.44630i	−0.0589868	−	0.998259i	$-0.518787\pi$
$653$	21.3381	−	36.9587i	0.835024	−	1.44630i	0.894011	−	0.448045i	$-0.147880\pi$
$654$	−0.444549	−	1.30691i	−0.0173832	−	0.0511041i
$655$	−4.14651	+	2.39399i	−0.162018	+	0.0935410i
$656$	36.4422	−	17.8537i	1.42283	−	0.697070i
$657$	15.8712	+	19.2388i	0.619195	+	0.750576i
$658$	14.4512	−	7.22836i	0.563367	−	0.281791i
$659$		−	33.4550i		−	1.30322i	−0.758553	−	0.651611i	$-0.774093\pi$
$659$		−	33.4550i		−	1.30322i	0.758553	−	0.651611i	$-0.225907\pi$
$660$	−2.57804	+	5.01873i	−0.100350	+	0.195354i
$661$	−11.2595	+	6.50067i	−0.437944	+	0.252847i	−0.702725	−	0.711462i	$-0.748034\pi$
$661$	−11.2595	+	6.50067i	−0.437944	+	0.252847i	0.264781	+	0.964308i	$0.414700\pi$
$662$	−13.4874	−	13.9543i	−0.524204	−	0.542350i
$663$	4.99737	+	7.20082i	0.194082	+	0.279657i
$664$	−1.31539	−	1.45701i	−0.0510470	−	0.0565429i
$665$	−48.0615	+	10.6977i	−1.86374	+	0.414838i
$666$	−8.42463	+	11.4046i	−0.326448	+	0.441919i
$667$	−4.03665	+	6.99168i	−0.156300	+	0.270719i
$668$	−12.7940	−	7.97890i	−0.495015	−	0.308713i
$669$	1.01353	+	12.1701i	0.0391853	+	0.470522i
$670$	−0.0271008	+	0.0946693i	−0.00104700	+	0.00365739i
$671$	−2.43756			−0.0941009
$672$	1.15992	−	25.8970i	0.0447448	−	0.998998i
$673$	−12.3531			−0.476179			−0.238089	−	0.971243i	$-0.576521\pi$
$673$	−12.3531			−0.476179			−0.238089	+	0.971243i	$0.576521\pi$
$674$	6.12376	−	21.3917i	0.235878	−	0.823977i
$675$	−27.7270	−	28.4309i	−1.06721	−	1.09431i
$676$	−20.9778	−	13.0827i	−0.806840	−	0.503181i
$677$	2.07866	−	3.60034i	0.0798894	−	0.138372i	−0.823313	−	0.567588i	$-0.807877\pi$
$677$	2.07866	−	3.60034i	0.0798894	−	0.138372i	0.903202	+	0.429216i	$0.141210\pi$
$678$	−3.39894	−	0.673878i	−0.130535	−	0.0258801i
$679$	−5.59650	+	17.8024i	−0.214774	+	0.683193i
$680$	42.6801	+	47.2751i	1.63671	+	1.81292i
$681$	−29.5231	+	20.4890i	−1.13133	+	0.785140i
$682$	−2.30050	−	2.38013i	−0.0880905	−	0.0911400i
$683$	11.5310	−	6.65741i	0.441221	−	0.254739i	−0.262895	−	0.964825i	$-0.584677\pi$
$683$	11.5310	−	6.65741i	0.441221	−	0.254739i	0.704115	+	0.710086i	$0.251344\pi$
$684$	24.8902	−	19.1485i	0.951699	−	0.732161i
$685$		−	31.9892i		−	1.22224i
$686$	9.67187	+	24.3404i	0.369274	+	0.929321i
$687$	34.4542	+	16.2419i	1.31451	+	0.619665i
$688$	6.27128	+	12.8007i	0.239090	+	0.488022i
$689$	1.61810	−	0.934208i	0.0616445	−	0.0355905i
$690$	25.5700	−	8.69772i	0.973434	−	0.331116i
$691$	7.57239	−	13.1158i	0.288067	−	0.498947i	−0.685281	−	0.728279i	$-0.740321\pi$
$691$	7.57239	−	13.1158i	0.288067	−	0.498947i	0.973348	+	0.229332i	$0.0736540\pi$
$692$	−27.4504	+	14.6267i	−1.04351	+	0.556024i
$693$	1.36611	+	3.36943i	0.0518944	+	0.127994i
$694$	−7.33338	−	29.3575i	−0.278371	−	1.11439i
$695$	−28.4765	+	49.3228i	−1.08018	+	1.87092i
$696$	−8.72482	+	9.30283i	−0.330713	+	0.352623i
$697$	32.1248	+	55.6418i	1.21681	+	2.10758i
$698$	−21.3819	−	6.12096i	−0.809317	−	0.231682i
$699$	−27.3894	−	12.9115i	−1.03596	−	0.488357i
$700$	−38.1451	−	13.4337i	−1.44175	−	0.507748i
$701$	−51.6538			−1.95094			−0.975468	−	0.220142i	$-0.929348\pi$
$701$	−51.6538			−1.95094			−0.975468	+	0.220142i	$0.929348\pi$
$702$	5.86932	+	0.173464i	0.221523	+	0.00654698i
$703$	−15.1483	+	8.74585i	−0.571327	+	0.329856i
$704$	−1.49937	−	3.34381i	−0.0565096	−	0.126024i
$705$	15.1635	+	21.8494i	0.571089	+	0.822895i
$706$	−4.02975	−	16.1321i	−0.151662	−	0.607141i
$707$	−17.2694	+	3.84388i	−0.649483	+	0.144564i
$708$	−5.98241	+	0.293756i	−0.224833	+	0.0110400i
$709$	44.7941	+	25.8619i	1.68228	+	0.971263i	0.960143	+	0.279510i	$0.0901719\pi$
$709$	44.7941	+	25.8619i	1.68228	+	0.971263i	0.722134	+	0.691753i	$0.243161\pi$
$710$	−31.5925	−	32.6861i	−1.18565	−	1.22669i
$711$	35.3158	+	13.1891i	1.32445	+	0.494630i
$712$	−22.4259	+	4.79779i	−0.840447	+	0.179805i
$713$			15.8457i			0.593427i
$714$	41.0316	−	0.955796i	1.53557	−	0.0357698i
$715$	−1.30147			−0.0486724
$716$	−18.0310	−	0.613739i	−0.673851	−	0.0229365i
$717$	−11.4015	+	0.949523i	−0.425797	+	0.0354606i
$718$	−20.1757	−	20.8741i	−0.752949	−	0.779014i
$719$	−18.9896	+	32.8909i	−0.708191	+	1.22662i	0.257336	+	0.966322i	$0.417155\pi$
$719$	−18.9896	+	32.8909i	−0.708191	+	1.22662i	−0.965527	+	0.260302i	$0.916178\pi$
$720$	42.4627	−	4.18019i	1.58249	−	0.155787i
$721$	12.3506	−	11.3365i	0.459960	−	0.422193i
$722$	11.5170	−	2.87691i	0.428620	−	0.107068i
$723$	−10.4275	−	15.0252i	−0.387802	−	0.558794i
$724$	−11.0111	+	17.6560i	−0.409224	+	0.656182i
$725$	9.94856	+	17.2314i	0.369480	+	0.639958i
$726$	−19.8823	−	17.4143i	−0.737903	−	0.646306i
$727$		−	15.9886i		−	0.592984i	−0.955035	−	0.296492i	$-0.904183\pi$
$727$		−	15.9886i		−	0.592984i	0.955035	−	0.296492i	$-0.0958167\pi$
$728$	5.43585	−	2.49151i	0.201466	−	0.0923417i
$729$	23.7137	−	12.9097i	0.878285	−	0.478137i
$730$	−11.5050	+	40.1897i	−0.425821	+	1.48749i
$731$	−19.5447	+	11.2842i	−0.722888	+	0.417359i
$732$	9.98868	+	15.4928i	0.369192	+	0.572629i
$733$	−10.1169	−	5.84098i	−0.373675	−	0.215741i	0.301388	−	0.953502i	$-0.402550\pi$
$733$	−10.1169	−	5.84098i	−0.373675	−	0.215741i	−0.675063	+	0.737760i	$0.735883\pi$
$734$	7.88701	+	31.5738i	0.291115	+	1.16541i
$735$	−37.3879	+	21.4623i	−1.37907	+	0.791647i
$736$	−5.96344	+	16.4975i	−0.219815	+	0.608105i
$737$	0.00776859	+	0.00448520i	0.000286160	+	0.000165214i
$738$	42.7696	+	4.83780i	1.57437	+	0.178082i
$739$	8.47946	+	14.6869i	0.311922	+	0.540265i	0.978778	−	0.204922i	$-0.0656939\pi$
$739$	8.47946	+	14.6869i	0.311922	+	0.540265i	−0.666857	+	0.745186i	$0.732361\pi$
$740$	−23.7522	−	0.808475i	−0.873147	−	0.0297201i
$741$	6.55231	+	3.08878i	0.240705	+	0.113469i
$742$	0.522866	−	8.73333i	0.0191950	−	0.320611i
$743$	14.5437			0.533558			0.266779	−	0.963758i	$-0.414041\pi$
$743$	14.5437			0.533558			0.266779	+	0.963758i	$0.414041\pi$
$744$	−5.70075	+	24.3750i	−0.209000	+	0.893629i
$745$	−11.8883	−	20.5911i	−0.435553	−	0.754400i
$746$	−25.4373	+	24.5862i	−0.931326	+	0.900165i
$747$	−0.344393	−	2.05333i	−0.0126007	−	0.0751274i
$748$	5.12044	−	2.72838i	0.187222	−	0.0997594i
$749$	−6.96991	+	6.39761i	−0.254675	+	0.233764i
$750$	4.47626	−	22.5776i	0.163450	−	0.824416i
$751$	−9.37421	−	5.41220i	−0.342070	−	0.197494i	0.319117	−	0.947715i	$-0.396614\pi$
$751$	−9.37421	−	5.41220i	−0.342070	−	0.197494i	−0.661187	+	0.750221i	$0.729947\pi$
$752$	−17.2338	−	1.17457i	−0.628454	−	0.0428322i
$753$	−0.958294	−	11.5068i	−0.0349222	−	0.419333i
$754$	−2.82835	−	0.809668i	−0.103003	−	0.0294864i
$755$			15.0384i			0.547303i
$756$	15.8175	−	22.4901i	0.575277	−	0.817958i
$757$			13.5121i			0.491105i	0.969383	+	0.245552i	$0.0789694\pi$
$757$			13.5121i			0.491105i	−0.969383	+	0.245552i	$0.921031\pi$
$758$	4.56954	−	15.9624i	0.165973	−	0.579782i
$759$	−0.204196	−	2.45190i	−0.00741183	−	0.0889985i
$760$	50.0825	+	16.1996i	1.81668	+	0.587621i
$761$	−22.5165	−	12.9999i	−0.816221	−	0.471245i	0.0328907	−	0.999459i	$-0.489529\pi$
$761$	−22.5165	−	12.9999i	−0.816221	−	0.471245i	−0.849111	+	0.528214i	$0.822862\pi$
$762$	37.7331	+	7.48100i	1.36692	+	0.271008i
$763$	−0.323955	−	1.45543i	−0.0117280	−	0.0526903i
$764$	25.9054	−	13.8035i	0.937226	−	0.499393i
$765$	11.1744	+	66.6237i	0.404011	+	2.40879i
$766$	−17.5585	−	18.1663i	−0.634415	−	0.656376i
$767$	−0.690812	−	1.19652i	−0.0249438	−	0.0432039i
$768$	−15.1086	+	23.2321i	−0.545185	+	0.838316i
$769$	3.84206			0.138548			0.0692741	−	0.997598i	$-0.477932\pi$
$769$	3.84206			0.138548			0.0692741	+	0.997598i	$0.477932\pi$
$770$	−3.35708	+	5.08622i	−0.120981	+	0.183295i
$771$	1.60617	+	0.757155i	0.0578449	+	0.0272683i
$772$	1.09752	−	32.2441i	0.0395007	−	1.16049i
$773$	18.3710	+	31.8195i	0.660760	+	1.14447i	0.980416	+	0.196936i	$0.0630991\pi$
$773$	18.3710	+	31.8195i	0.660760	+	1.14447i	−0.319657	+	0.947533i	$0.603568\pi$
$774$	−1.69932	+	15.0232i	−0.0610809	+	0.539998i
$775$	33.8206	+	19.5263i	1.21487	+	0.701407i
$776$	14.8079	−	13.3686i	0.531574	−	0.479906i
$777$	−10.3841	+	11.2568i	−0.372529	+	0.403835i
$778$	35.5251	−	8.87405i	1.27364	−	0.318150i
$779$	45.9852	+	26.5495i	1.64759	+	0.951236i
$780$	5.33321	+	8.27198i	0.190959	+	0.296184i
$781$	−3.58628	+	2.07054i	−0.128327	+	0.0740897i
$782$	−26.7013	−	7.64373i	−0.954836	−	0.273339i
$783$	−13.1096	+	3.33718i	−0.468499	+	0.119261i
$784$	4.28453	−	27.6703i	0.153019	−	0.988223i
$785$		−	81.8606i		−	2.92173i
$786$	2.17325	−	2.48126i	0.0775174	−	0.0885035i
$787$	19.1854	+	33.2301i	0.683886	+	1.18453i	0.973785	+	0.227469i	$0.0730450\pi$
$787$	19.1854	+	33.2301i	0.683886	+	1.18453i	−0.289899	+	0.957057i	$0.593622\pi$
$788$	−37.2463	−	23.2285i	−1.32685	−	0.827479i
$789$	−16.9896	−	24.4807i	−0.604845	−	0.871535i
$790$	15.3136	+	61.3044i	0.544834	+	2.18111i
$791$	−3.57046	−	1.12244i	−0.126951	−	0.0399093i
$792$	0.568005	−	3.84515i	0.0201832	−	0.136631i
$793$	−2.12604	+	3.68241i	−0.0754979	+	0.130766i
$794$	20.5528	−	19.8652i	0.729392	−	0.704988i
$795$	14.3507	−	1.19513i	0.508967	−	0.0423870i
$796$	31.8908	+	1.08550i	1.13034	+	0.0384745i
$797$	−25.0108			−0.885927			−0.442964	−	0.896540i	$-0.646073\pi$
$797$	−25.0108			−0.885927			−0.442964	+	0.896540i	$0.646073\pi$
$798$	28.9724	−	17.6394i	1.02561	−	0.624426i
$799$		−	27.3489i		−	0.967535i
$800$	27.8631	+	33.0577i	0.985109	+	1.16877i
$801$	−22.7873	−	8.51018i	−0.805149	−	0.300692i
$802$	−37.6837	+	36.4228i	−1.33066	+	1.28613i
$803$	3.29798	+	1.90409i	0.116383	+	0.0671939i
$804$	−0.00332702	−	0.0677555i	−0.000117335	−	0.00238955i
$805$	28.4760	−	6.33828i	1.00365	−	0.223395i
$806$	−5.60215	+	1.39940i	−0.197327	+	0.0492916i
$807$	−7.75480	−	11.1741i	−0.272982	−	0.393346i
$808$	17.9956	+	5.82082i	0.633083	+	0.204776i
$809$	−32.0756	+	18.5188i	−1.12772	+	0.651087i	−0.943360	−	0.331772i	$-0.892354\pi$
$809$	−32.0756	+	18.5188i	−1.12772	+	0.651087i	−0.184357	+	0.982859i	$0.559020\pi$
$810$	40.3478	+	20.4982i	1.41768	+	0.720232i
$811$	1.97747			0.0694383			0.0347192	−	0.999397i	$-0.488946\pi$
$811$	1.97747			0.0694383			0.0347192	+	0.999397i	$0.488946\pi$
$812$	−10.4598	+	8.96484i	−0.367067	+	0.314604i
$813$	−28.4197	−	13.3972i	−0.996722	−	0.469859i
$814$	−0.595831	+	2.08137i	−0.0208839	+	0.0729521i
$815$	−36.9820	−	64.0546i	−1.29542	−	2.24374i
$816$	−38.3238	−	21.3643i	−1.34160	−	0.747902i
$817$	−9.32578	+	16.1527i	−0.326268	+	0.565112i
$818$	39.8731	−	9.96015i	1.39413	−	0.348249i
$819$	6.28171	+	0.875036i	0.219501	+	0.0305762i
$820$	33.9265	+	63.6709i	1.18476	+	2.22348i
$821$	6.85902	−	11.8802i	0.239382	−	0.414621i	−0.721155	−	0.692773i	$-0.756389\pi$
$821$	6.85902	−	11.8802i	0.239382	−	0.414621i	0.960537	+	0.278152i	$0.0897220\pi$
$822$	7.09673	+	20.8633i	0.247527	+	0.727693i
$823$	34.0169	−	19.6397i	1.18575	−	0.684596i	0.228416	−	0.973564i	$-0.426646\pi$
$823$	34.0169	−	19.6397i	1.18575	−	0.684596i	0.957339	+	0.288968i	$0.0933122\pi$
$824$	−17.5256	+	3.74941i	−0.610532	+	0.130617i
$825$	−5.48490	−	2.58560i	−0.190960	−	0.0900191i
$826$	−6.45797	−	0.386639i	−0.224701	−	0.0134529i
$827$			26.9376i			0.936713i	0.883540	+	0.468356i	$0.155154\pi$
$827$			26.9376i			0.936713i	−0.883540	+	0.468356i	$0.844846\pi$
$828$	−14.7472	+	11.3453i	−0.512500	+	0.394276i
$829$	−17.5320	+	10.1221i	−0.608910	+	0.351554i	−0.772539	−	0.634968i	$-0.781013\pi$
$829$	−17.5320	+	10.1221i	−0.608910	+	0.351554i	0.163629	+	0.986522i	$0.447680\pi$
$830$	2.50926	−	2.42531i	0.0870978	−	0.0841836i
$831$	31.6948	−	21.9962i	1.09948	−	0.763038i
$832$	−6.35923	−	0.651378i	−0.220467	−	0.0225825i
$833$	44.1690	+	3.78891i	1.53036	+	0.131278i
$834$	7.63024	−	38.4858i	0.264213	−	1.33265i
$835$	13.4032	−	23.2150i	0.463836	−	0.803387i
$836$	2.53740	−	4.06866i	0.0877577	−	0.140718i
$837$	−19.0084	+	18.5378i	−0.657025	+	0.640759i
$838$	−1.73006	−	0.495263i	−0.0597641	−	0.0171086i
$839$	45.3448			1.56548			0.782738	−	0.622352i	$-0.213823\pi$
$839$	45.3448			1.56548			0.782738	+	0.622352i	$0.213823\pi$
$840$	46.0840	+	0.494725i	1.59005	+	0.0170696i
$841$	−22.2223			−0.766286
$842$	−16.4521	−	4.70970i	−0.566975	−	0.162307i
$843$	2.57466	+	30.9155i	0.0886758	+	1.06479i
$844$	−35.6246	−	22.2171i	−1.22625	−	0.764743i
$845$	21.9767	−	38.0647i	0.756020	−	1.30946i
$846$	−14.7368	−	10.8862i	−0.506663	−	0.374274i
$847$	−19.3046	−	21.0315i	−0.663315	−	0.722652i
$848$	−5.21647	+	7.76323i	−0.179134	+	0.266591i
$849$	−4.42971	−	6.38287i	−0.152027	−	0.219059i
$850$	−49.2180	+	47.5712i	−1.68816	+	1.63168i
$851$	8.97520	−	5.18183i	0.307666	−	0.177631i
$852$	27.8560	+	14.3092i	0.954330	+	0.490224i
$853$			37.8961i			1.29754i	0.760986	+	0.648769i	$0.224716\pi$
$853$			37.8961i			1.29754i	−0.760986	+	0.648769i	$0.775284\pi$
$854$	8.90701	+	17.8072i	0.304792	+	0.609351i
$855$	35.5284	+	43.0668i	1.21505	+	1.47285i
$856$	9.89035	−	2.11593i	0.338045	−	0.0723211i
$857$	30.1090	−	17.3834i	1.02850	−	0.593806i	0.111947	−	0.993714i	$-0.464291\pi$
$857$	30.1090	−	17.3834i	1.02850	−	0.593806i	0.916555	+	0.399908i	$0.130958\pi$
$858$	0.848822	−	0.288729i	0.0289783	−	0.00985705i
$859$	−17.5062	+	30.3217i	−0.597305	+	1.03456i	0.395912	+	0.918288i	$0.370428\pi$
$859$	−17.5062	+	30.3217i	−0.597305	+	1.03456i	−0.993217	+	0.116274i	$0.962905\pi$
$860$	−22.3650	+	11.9170i	−0.762640	+	0.406366i
$861$	45.3552	+	10.2136i	1.54570	+	0.348079i
$862$	−22.9505	+	5.73294i	−0.781696	+	0.195265i
$863$	11.8510	−	20.5265i	0.403413	−	0.698732i	−0.590722	−	0.806875i	$-0.701157\pi$
$863$	11.8510	−	20.5265i	0.403413	−	0.698732i	0.994135	+	0.108143i	$0.0344905\pi$
$864$	−26.7668	+	12.1466i	−0.910625	+	0.413235i
$865$	−27.6490	−	47.8894i	−0.940093	−	1.62829i
$866$	5.51544	−	19.2667i	0.187422	−	0.654708i
$867$	17.0658	−	36.2021i	0.579586	−	1.22949i
$868$	−8.98154	+	25.5031i	−0.304853	+	0.865632i
$869$	5.75618			0.195265
$870$	−17.0569	−	14.9396i	−0.578285	−	0.506502i
$871$	0.0135515	−	0.00782398i	0.000459176	−	0.000265106i
$872$	−0.490568	+	1.51664i	−0.0166127	+	0.0513598i
$873$	20.8685	−	3.50015i	0.706291	−	0.118462i
$874$	−22.2694	+	5.56281i	−0.753274	+	0.188165i
$875$	7.45583	−	23.7169i	0.252053	−	0.801777i
$876$	−1.41241	−	28.7641i	−0.0477209	−	0.971848i
$877$	−6.02275	−	3.47724i	−0.203374	−	0.117418i	0.394854	−	0.918744i	$-0.370795\pi$
$877$	−6.02275	−	3.47724i	−0.203374	−	0.117418i	−0.598228	+	0.801326i	$0.704128\pi$
$878$	26.2269	−	25.3494i	0.885115	−	0.855500i
$879$	−42.7567	+	3.56080i	−1.44215	+	0.120103i
$880$	5.85060	−	2.86631i	0.197224	−	0.0966234i
$881$			23.8500i			0.803528i	0.915743	+	0.401764i	$0.131603\pi$
$881$			23.8500i			0.803528i	−0.915743	+	0.401764i	$0.868397\pi$
$882$	19.6230	−	22.2921i	0.660741	−	0.750614i
$883$	32.0357			1.07809			0.539044	−	0.842278i	$-0.318786\pi$
$883$	32.0357			1.07809			0.539044	+	0.842278i	$0.318786\pi$
$884$	0.344298	−	10.1151i	0.0115800	−	0.340208i
$885$	−0.883755	−	10.6118i	−0.0297071	−	0.356712i
$886$	35.6942	−	34.4999i	1.19917	−	1.15905i
$887$	−25.4399	+	44.0633i	−0.854190	+	1.47950i	0.0232053	+	0.999731i	$0.492613\pi$
$887$	−25.4399	+	44.0633i	−0.854190	+	1.47950i	−0.877395	+	0.479769i	$0.840720\pi$
$888$	15.6705	−	4.74208i	0.525868	−	0.159134i
$889$	39.6372	+	12.4607i	1.32939	+	0.417917i
$890$	−9.88101	−	39.5563i	−0.331212	−	1.32593i
$891$	2.70239	−	3.11341i	0.0905336	−	0.104303i
$892$	7.46207	−	11.9653i	0.249849	−	0.400627i
$893$	−11.3012	−	19.5743i	−0.378182	−	0.655030i
$894$	12.3216	+	10.7921i	0.412097	+	0.360943i
$895$		−	32.0747i		−	1.07214i
$896$	−18.9489	+	23.1719i	−0.633038	+	0.774120i
$897$	−3.88218	−	1.83007i	−0.129622	−	0.0611044i
$898$	18.8836	+	5.40578i	0.630155	+	0.180393i
$899$	11.5206	−	6.65141i	0.384233	−	0.221837i
$900$	6.04242	+	45.4565i	0.201414	+	1.51522i
$901$	−12.8243	−	7.40413i	−0.427241	−	0.246667i
$902$	6.37625	−	1.59276i	0.212306	−	0.0530332i
$903$	−3.58763	+	15.9315i	−0.119389	+	0.530165i
$904$	2.68122	+	2.96989i	0.0891761	+	0.0987770i
$905$	−32.0372	−	18.4967i	−1.06495	−	0.614851i
$906$	−3.33623	−	9.80803i	−0.110839	−	0.325850i
$907$	5.21438	+	9.03157i	0.173141	+	0.299888i	0.939516	−	0.342504i	$-0.111275\pi$
$907$	5.21438	+	9.03157i	0.173141	+	0.299888i	−0.766376	+	0.642393i	$0.777942\pi$
$908$	41.4715	+	1.41161i	1.37628	+	0.0468458i
$909$	12.7660	+	15.4747i	0.423423	+	0.513264i
$910$	4.75568	+	9.50774i	0.157649	+	0.315178i
$911$	9.95365			0.329779			0.164889	−	0.986312i	$-0.447273\pi$
$911$	9.95365			0.329779			0.164889	+	0.986312i	$0.447273\pi$
$912$	−36.2576	+	0.545321i	−1.20061	+	0.0180574i
$913$	−0.158952	−	0.275313i	−0.00526055	−	0.00911153i
$914$	7.41614	+	7.67287i	0.245304	+	0.253796i
$915$	−26.9235	+	18.6849i	−0.890063	+	0.617703i
$916$	−20.6831	−	38.8166i	−0.683389	−	1.28254i
$917$	2.62467	−	2.40916i	0.0866742	−	0.0795574i
$918$	−22.0683	−	40.9730i	−0.728361	−	1.35231i
$919$	−7.23519	−	4.17724i	−0.238667	−	0.137794i	0.375897	−	0.926661i	$-0.377335\pi$
$919$	−7.23519	−	4.17724i	−0.238667	−	0.137794i	−0.614564	+	0.788867i	$0.710668\pi$
$920$	−29.6734	−	9.59810i	−0.978303	−	0.316440i
$921$	13.3285	−	1.11001i	0.439190	−	0.0365760i
$922$	−6.86329	+	23.9750i	−0.226031	+	0.789576i
$923$			7.22370i			0.237771i
$924$	1.06112	−	4.06199i	0.0349084	−	0.133630i
$925$		−	25.5419i		−	0.839812i
$926$	−40.1343	−	11.4892i	−1.31890	−	0.377558i
$927$	−17.8080	−	6.65059i	−0.584890	−	0.218434i
$928$	14.4977	−	2.58929i	0.475909	−	0.0849978i
$929$	−45.0777	−	26.0256i	−1.47895	−	0.853872i	−0.479234	−	0.877687i	$-0.659085\pi$
$929$	−45.0777	−	26.0256i	−1.47895	−	0.853872i	−0.999716	+	0.0238151i	$0.992419\pi$
$930$	−43.6542	−	8.65494i	−1.43148	−	0.283807i
$931$	33.1786	−	15.5399i	1.08738	−	0.509300i
$932$	16.4420	+	30.8573i	0.538577	+	1.01076i
$933$	−19.7690	−	28.4856i	−0.647207	−	0.932575i
$934$	−31.0357	+	29.9973i	−1.01552	+	0.981541i
$935$	5.15747	+	8.93299i	0.168667	+	0.292140i
$936$	−5.31344	−	4.21182i	−0.173675	−	0.137668i
$937$	−35.8998			−1.17280			−0.586398	−	0.810023i	$-0.699455\pi$
$937$	−35.8998			−1.17280			−0.586398	+	0.810023i	$0.699455\pi$
$938$	0.00437899	−	0.0731416i	0.000142979	−	0.00238816i
$939$	−12.6218	+	26.7749i	−0.411897	+	0.873767i
$940$	1.04470	−	30.6922i	0.0340743	−	1.00107i
$941$	−2.74621	−	4.75657i	−0.0895238	−	0.155060i	0.817786	−	0.575522i	$-0.195201\pi$
$941$	−2.74621	−	4.75657i	−0.0895238	−	0.155060i	−0.907310	+	0.420462i	$0.861868\pi$
$942$	18.1606	+	53.3895i	0.591704	+	1.73952i
$943$	−27.2458	−	15.7304i	−0.887245	−	0.512251i
$944$	5.74062	+	3.85738i	0.186841	+	0.125547i
$945$	40.9171	+	26.7444i	1.33103	+	0.869996i
$946$	0.559473	+	2.23972i	0.0181900	+	0.0728195i
$947$	−1.99491	−	1.15176i	−0.0648257	−	0.0374272i	0.467237	−	0.884132i	$-0.345250\pi$
$947$	−1.99491	−	1.15176i	−0.0648257	−	0.0374272i	−0.532063	+	0.846705i	$0.678583\pi$
$948$	−23.5878	−	36.5854i	−0.766095	−	1.18824i
$949$	5.75300	−	3.32150i	0.186750	−	0.107820i
$950$	−15.5690	+	54.3861i	−0.505126	+	1.76452i
$951$	−11.3302	+	24.0351i	−0.367408	+	0.779391i
$952$	−38.6422	−	27.4369i	−1.25240	−	0.889236i
$953$			27.0751i			0.877047i	0.898720	+	0.438524i	$0.144498\pi$
$953$			27.0751i			0.877047i	−0.898720	+	0.438524i	$0.855502\pi$
$954$	−9.09439	+	3.96313i	−0.294442	+	0.128311i
$955$	26.0928	+	45.1940i	0.844343	+	1.46244i
$956$	11.2097	+	6.99084i	0.362546	+	0.226100i
$957$	−1.69694	+	1.17767i	−0.0548542	+	0.0380688i
$958$	−0.266074	+	0.0664643i	−0.00859646	+	0.00214736i
$959$	5.17159	+	23.2344i	0.166999	+	0.750278i
$960$	−42.1926	−	25.4399i	−1.36176	−	0.821071i
$961$	−2.44506	+	4.23497i	−0.0788729	+	0.136612i
$962$	2.62464	+	2.71549i	0.0846217	+	0.0875511i
$963$	10.0497	+	3.75318i	0.323847	+	0.120945i
$964$	−0.718410	+	21.1062i	−0.0231384	+	0.679783i
$965$	57.3577			1.84641
$966$	−17.1659	+	10.4512i	−0.552304	+	0.336260i
$967$			33.0009i			1.06124i	0.847611	+	0.530618i	$0.178040\pi$
$967$			33.0009i			1.06124i	−0.847611	+	0.530618i	$0.821960\pi$
$968$	6.38478	+	29.8439i	0.205215	+	0.959218i
$969$	−4.76477	−	57.2136i	−0.153066	−	1.83796i
$970$	24.6490	+	25.5023i	0.791431	+	0.818828i
$971$	31.6718	+	18.2857i	1.01640	+	0.586817i	0.913058	−	0.407829i	$-0.133714\pi$
$971$	31.6718	+	18.2857i	1.01640	+	0.586817i	0.103339	+	0.994646i	$0.467047\pi$
$972$	−30.8623	−	4.41782i	−0.989909	−	0.141702i
$973$	12.7092	−	40.4279i	0.407439	−	1.29606i
$974$	−6.90539	−	27.6441i	−0.221263	−	0.885774i
$975$	−8.68999	+	6.03085i	−0.278302	+	0.193142i
$976$	1.44734	−	21.2361i	0.0463283	−	0.679750i
$977$	2.71660	−	1.56843i	0.0869117	−	0.0501785i	−0.455914	−	0.890024i	$-0.650688\pi$
$977$	2.71660	−	1.56843i	0.0869117	−	0.0501785i	0.542826	+	0.839845i	$0.317354\pi$
$978$	38.3300	+	33.5720i	1.22566	+	1.07352i
$979$	−3.71414			−0.118704
$980$	49.4237	+	5.93929i	1.57878	+	0.189724i
$981$	−1.30418	+	1.07590i	−0.0416393	+	0.0343508i
$982$	5.84961	+	1.67456i	0.186668	+	0.0534373i
$983$	5.06871	+	8.77927i	0.161667	+	0.280015i	0.935467	−	0.353415i	$-0.114980\pi$
$983$	5.06871	+	8.77927i	0.161667	+	0.280015i	−0.773800	+	0.633430i	$0.781646\pi$
$984$	−36.2521	−	33.9996i	−1.15567	−	1.08387i
$985$	39.0197	−	67.5842i	1.24327	−	2.15341i
$986$	5.65081	+	22.6216i	0.179958	+	0.720420i
$987$	−14.5458	−	13.4182i	−0.462999	−	0.427107i
$988$	−3.93339	−	7.38193i	−0.125138	−	0.234850i
$989$	5.52544	−	9.57034i	0.175699	−	0.304319i
$990$	6.86642	+	0.776683i	0.218229	+	0.0246846i
$991$	22.8644	−	13.2008i	0.726313	−	0.419337i	−0.0907589	−	0.995873i	$-0.528929\pi$
$991$	22.8644	−	13.2008i	0.726313	−	0.419337i	0.817072	+	0.576536i	$0.195596\pi$
$992$	22.1017	−	18.6287i	0.701731	−	0.591463i
$993$	−10.1350	+	21.4996i	−0.321624	+	0.682269i
$994$	28.2306	+	18.6332i	0.895419	+	0.591008i
$995$			56.7293i			1.79844i
$996$	−1.09849	+	2.13846i	−0.0348071	+	0.0677597i
$997$	−0.842124	+	0.486200i	−0.0266703	+	0.0153981i	−0.513276	−	0.858224i	$-0.671568\pi$
$997$	−0.842124	+	0.486200i	−0.0266703	+	0.0153981i	0.486606	+	0.873622i	$0.338235\pi$
$998$	−25.5929	−	26.4789i	−0.810131	−	0.838175i
$999$	16.7161	+	4.70438i	0.528874	+	0.148840i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.v.a.107.12	yes	56
3.2	odd	2	inner	168.2.v.a.107.17	yes	56
4.3	odd	2		672.2.bd.a.527.2		56
7.4	even	3	inner	168.2.v.a.11.7	✓	56
8.3	odd	2	inner	168.2.v.a.107.22	yes	56
8.5	even	2		672.2.bd.a.527.1		56
12.11	even	2		672.2.bd.a.527.19		56
21.11	odd	6	inner	168.2.v.a.11.22	yes	56
24.5	odd	2		672.2.bd.a.527.20		56
24.11	even	2	inner	168.2.v.a.107.7	yes	56
28.11	odd	6		672.2.bd.a.431.20		56
56.11	odd	6	inner	168.2.v.a.11.17	yes	56
56.53	even	6		672.2.bd.a.431.19		56
84.11	even	6		672.2.bd.a.431.1		56
168.11	even	6	inner	168.2.v.a.11.12	yes	56
168.53	odd	6		672.2.bd.a.431.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.v.a.11.7	✓	56	7.4	even	3	inner
168.2.v.a.11.12	yes	56	168.11	even	6	inner
168.2.v.a.11.17	yes	56	56.11	odd	6	inner
168.2.v.a.11.22	yes	56	21.11	odd	6	inner
168.2.v.a.107.7	yes	56	24.11	even	2	inner
168.2.v.a.107.12	yes	56	1.1	even	1	trivial
168.2.v.a.107.17	yes	56	3.2	odd	2	inner
168.2.v.a.107.22	yes	56	8.3	odd	2	inner
672.2.bd.a.431.1		56	84.11	even	6
672.2.bd.a.431.2		56	168.53	odd	6
672.2.bd.a.431.19		56	56.53	even	6
672.2.bd.a.431.20		56	28.11	odd	6
672.2.bd.a.527.1		56	8.5	even	2
672.2.bd.a.527.2		56	4.3	odd	2
672.2.bd.a.527.19		56	12.11	even	2
672.2.bd.a.527.20		56	24.5	odd	2

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.389211 + 1.35960i) q^{2} +(1.72608 - 0.143748i) q^{3} +(-1.69703 - 1.05834i) q^{4} +(1.77783 - 3.07929i) q^{5} +(-0.476367 + 2.40272i) q^{6} +(-0.793456 + 2.52397i) q^{7} +(2.09943 - 1.89537i) q^{8} +(2.95867 - 0.496241i) q^{9} +(3.49466 + 3.61563i) q^{10} +(0.396703 - 0.229036i) q^{11} +(-3.08134 - 1.58283i) q^{12} -0.799063i q^{13} +(-3.12277 - 2.06114i) q^{14} +(2.62603 - 5.57065i) q^{15} +(1.75982 + 3.59208i) q^{16} +(-5.48456 + 3.16651i) q^{17} +(-0.476858 + 4.21576i) q^{18} +(-2.61696 + 4.53272i) q^{19} +(-6.27598 + 3.34410i) q^{20} +(-1.00675 + 4.47062i) q^{21} +(0.156997 + 0.628501i) q^{22} +(1.55053 - 2.68559i) q^{23} +(3.35131 - 3.57333i) q^{24} +(-3.82137 - 6.61880i) q^{25} +(1.08641 + 0.311004i) q^{26} +(5.03556 - 1.28185i) q^{27} +(4.01774 - 3.44351i) q^{28} -2.60340 q^{29} +(6.55179 + 5.73851i) q^{30} +(-4.42520 + 2.55489i) q^{31} +(-5.56873 + 0.994581i) q^{32} +(0.651815 - 0.452359i) q^{33} +(-2.17055 - 8.68926i) q^{34} +(6.36142 + 6.93048i) q^{35} +(-5.54615 - 2.28915i) q^{36} +(2.89424 + 1.67099i) q^{37} +(-5.14413 - 5.32221i) q^{38} +(-0.114864 - 1.37924i) q^{39} +(-2.10396 - 9.83439i) q^{40} -10.1452i q^{41} +(-5.68643 - 3.10879i) q^{42} +3.56359 q^{43} +(-0.915615 - 0.0311657i) q^{44} +(3.73195 - 9.99285i) q^{45} +(3.04785 + 3.15336i) q^{46} +(-2.15923 + 3.73989i) q^{47} +(3.55394 + 5.94723i) q^{48} +(-5.74086 - 4.00532i) q^{49} +(10.4862 - 2.61943i) q^{50} +(-9.01159 + 6.25404i) q^{51} +(-0.845682 + 1.35603i) q^{52} +(1.16913 + 2.02499i) q^{53} +(-0.217084 + 7.34526i) q^{54} -1.62875i q^{55} +(3.11805 + 6.80278i) q^{56} +(-3.86551 + 8.19999i) q^{57} +(1.01327 - 3.53959i) q^{58} +(1.49741 - 0.864528i) q^{59} +(-10.3521 + 6.67433i) q^{60} +(-4.60841 - 2.66067i) q^{61} +(-1.75130 - 7.01090i) q^{62} +(-1.09508 + 7.86135i) q^{63} +(0.815178 - 7.95836i) q^{64} +(-2.46055 - 1.42060i) q^{65} +(0.361335 + 1.06227i) q^{66} +(0.00979145 + 0.0169593i) q^{67} +(12.6587 + 0.430877i) q^{68} +(2.29028 - 4.85842i) q^{69} +(-11.8986 + 5.95157i) q^{70} -9.04022 q^{71} +(5.27096 - 6.64959i) q^{72} +(4.15674 + 7.19969i) q^{73} +(-3.39835 + 3.28465i) q^{74} +(-7.54741 - 10.8752i) q^{75} +(9.23823 - 4.92251i) q^{76} +(0.263315 + 1.18300i) q^{77} +(1.91993 + 0.380647i) q^{78} +(10.8825 + 6.28304i) q^{79} +(14.1897 + 0.967099i) q^{80} +(8.50749 - 2.93643i) q^{81} +(13.7934 + 3.94861i) q^{82} -0.694004i q^{83} +(6.43993 - 6.52130i) q^{84} +22.5181i q^{85} +(-1.38699 + 4.84506i) q^{86} +(-4.49367 + 0.374235i) q^{87} +(0.398740 - 1.23274i) q^{88} +(-7.02189 - 4.05409i) q^{89} +(12.1338 + 8.96329i) q^{90} +(2.01681 + 0.634021i) q^{91} +(-5.47357 + 2.91654i) q^{92} +(-7.27097 + 5.04605i) q^{93} +(-4.24437 - 4.39129i) q^{94} +(9.30504 + 16.1168i) q^{95} +(-9.46909 + 2.51722i) q^{96} +7.05333 q^{97} +(7.68004 - 6.24636i) q^{98} +(1.06006 - 0.874504i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9} + 6 q^{10} + 10 q^{12} - 10 q^{16} - 10 q^{18} - 4 q^{19} - 20 q^{22} - 8 q^{24} - 16 q^{25} - 8 q^{27} - 22 q^{28} - 12 q^{30} - 14 q^{33} - 56 q^{34} + 4 q^{36}+ \cdots - 44 q^{99}+O(q^{100}) \) 56 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9 + 6 * q^10 + 10 * q^12 - 10 * q^16 - 10 * q^18 - 4 * q^19 - 20 * q^22 - 8 * q^24 - 16 * q^25 - 8 * q^27 - 22 * q^28 - 12 * q^30 - 14 * q^33 - 56 * q^34 + 4 * q^36 + 14 * q^40 - 8 * q^42 - 16 * q^43 - 12 * q^46 + 64 * q^48 - 16 * q^49 - 34 * q^51 - 8 * q^52 + 32 * q^54 + 4 * q^57 - 18 * q^58 + 40 * q^60 + 4 * q^64 - 20 * q^66 - 36 * q^67 - 42 * q^70 + 22 * q^72 + 4 * q^73 + 104 * q^76 + 28 * q^78 - 10 * q^81 + 52 * q^82 + 4 * q^84 + 46 * q^88 + 140 * q^90 + 72 * q^91 - 46 * q^96 - 32 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more