LMFDB - Embedded newform 680.2.co.a.99.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(99,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 8, 8, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.99"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.co (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$832$
Relative dimension:	$104$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			99.16
Character	$\chi$	$=$	680.99
Dual form			680.2.co.a.419.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.24482 + 0.671133i) q^{2} +(3.02940 + 0.602586i) q^{3} +(1.09916 - 1.67088i) q^{4} +(-0.0803191 - 2.23462i) q^{5} +(-4.17548 + 1.28302i) q^{6} +(3.84724 + 2.57064i) q^{7} +(-0.246876 + 2.81763i) q^{8} +(6.04253 + 2.50290i) q^{9} +(1.59971 + 2.72780i) q^{10} +(2.30746 - 0.458983i) q^{11} +(4.33665 - 4.39943i) q^{12} +(0.474407 + 0.474407i) q^{13} +(-6.51437 - 0.617983i) q^{14} +(1.10323 - 6.81798i) q^{15} +(-1.58369 - 3.67314i) q^{16} +(-3.71414 - 1.79030i) q^{17} +(-9.20166 + 0.939681i) q^{18} +(-6.53598 + 2.70729i) q^{19} +(-3.82208 - 2.32201i) q^{20} +(10.1058 + 10.1058i) q^{21} +(-2.56434 + 2.11997i) q^{22} +(-1.31540 - 6.61299i) q^{23} +(-2.44575 + 8.38698i) q^{24} +(-4.98710 + 0.358966i) q^{25} +(-0.908942 - 0.272162i) q^{26} +(9.09245 + 6.07538i) q^{27} +(8.52398 - 3.60273i) q^{28} +(-4.89597 + 3.27138i) q^{29} +(3.20244 + 9.22758i) q^{30} +(0.996655 - 5.01052i) q^{31} +(4.43657 + 3.50953i) q^{32} +7.26681 q^{33} +(5.82497 - 0.264070i) q^{34} +(5.43542 - 8.80361i) q^{35} +(10.8238 - 7.34527i) q^{36} +(-1.03900 + 5.22343i) q^{37} +(6.31917 - 7.75660i) q^{38} +(1.15130 + 1.72304i) q^{39} +(6.31618 + 0.325365i) q^{40} +(-3.57941 - 2.39169i) q^{41} +(-19.3623 - 5.79759i) q^{42} +(-0.819076 + 1.97742i) q^{43} +(1.76937 - 4.35999i) q^{44} +(5.10771 - 13.7038i) q^{45} +(6.07564 + 7.34918i) q^{46} +(1.24163 + 1.24163i) q^{47} +(-2.58426 - 12.0817i) q^{48} +(5.51427 + 13.3126i) q^{49} +(5.96713 - 3.79385i) q^{50} +(-10.1728 - 7.66164i) q^{51} +(1.31413 - 0.271228i) q^{52} +(2.20958 - 0.915237i) q^{53} +(-15.3959 - 1.46052i) q^{54} +(-1.21099 - 5.11945i) q^{55} +(-8.19292 + 10.2055i) q^{56} +(-21.4315 + 4.26299i) q^{57} +(3.89907 - 7.35813i) q^{58} +(0.257860 - 0.622529i) q^{59} +(-10.1794 - 9.33743i) q^{60} +(3.33081 + 2.22558i) q^{61} +(2.12207 + 6.90609i) q^{62} +(16.8130 + 25.1625i) q^{63} +(-7.87810 - 1.39121i) q^{64} +(1.02202 - 1.09823i) q^{65} +(-9.04588 + 4.87700i) q^{66} -0.662256 q^{67} +(-7.07382 + 4.23805i) q^{68} -20.8260i q^{69} +(-0.857731 + 14.6068i) q^{70} +(-2.50239 - 0.497757i) q^{71} +(-8.54401 + 16.4077i) q^{72} +(-0.683178 - 1.02245i) q^{73} +(-2.21224 - 7.19955i) q^{74} +(-15.3242 - 1.91770i) q^{75} +(-2.66053 + 13.8966i) q^{76} +(10.0572 + 4.16585i) q^{77} +(-2.58955 - 1.37220i) q^{78} +(-0.742184 - 3.73121i) q^{79} +(-8.08088 + 3.83398i) q^{80} +(10.0095 + 10.0095i) q^{81} +(6.06087 + 0.574962i) q^{82} +(5.07078 - 2.10039i) q^{83} +(27.9935 - 5.77770i) q^{84} +(-3.70234 + 8.44350i) q^{85} +(-0.307511 - 3.01125i) q^{86} +(-16.8031 + 6.96009i) q^{87} +(0.723589 + 6.61489i) q^{88} +(5.59049 - 5.59049i) q^{89} +(2.83890 + 20.4868i) q^{90} +(0.605626 + 3.04469i) q^{91} +(-12.4954 - 5.07085i) q^{92} +(6.03854 - 14.5783i) q^{93} +(-2.37891 - 0.712309i) q^{94} +(6.57474 + 14.3880i) q^{95} +(11.3254 + 13.3052i) q^{96} +(11.5356 - 7.70783i) q^{97} +(-15.7988 - 12.8710i) q^{98} +(15.0917 + 3.00193i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 832 q - 16 q^{4} - 16 q^{6} - 32 q^{9} - 8 q^{10} - 32 q^{11} - 16 q^{14} - 32 q^{19} - 8 q^{20} - 32 q^{24} - 16 q^{25} - 48 q^{26} + 56 q^{30} + 48 q^{34} - 32 q^{35} + 48 q^{36} - 72 q^{40} - 32 q^{41}+ \cdots - 128 q^{99}+O(q^{100}) $ 832 * q - 16 * q^4 - 16 * q^6 - 32 * q^9 - 8 * q^10 - 32 * q^11 - 16 * q^14 - 32 * q^19 - 8 * q^20 - 32 * q^24 - 16 * q^25 - 48 * q^26 + 56 * q^30 + 48 * q^34 - 32 * q^35 + 48 * q^36 - 72 * q^40 - 32 * q^41 - 48 * q^44 - 32 * q^46 - 32 * q^49 - 32 * q^51 + 32 * q^54 - 16 * q^56 - 32 * q^59 - 112 * q^60 - 16 * q^64 - 96 * q^65 - 48 * q^66 - 80 * q^70 - 16 * q^74 - 16 * q^75 - 16 * q^76 - 104 * q^80 - 32 * q^81 - 192 * q^86 - 32 * q^89 + 72 * q^90 - 32 * q^91 - 16 * q^94 + 288 * q^96 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$e\left(\frac{9}{16}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.24482	+	0.671133i	−0.880222	+	0.474563i
$2$	−1.24482	+	0.671133i	−0.880222	+	0.474563i
$3$	3.02940	+	0.602586i	1.74903	+	0.347903i	0.962837	−	0.270083i	$-0.0870510\pi$
$3$	3.02940	+	0.602586i	1.74903	+	0.347903i	0.786189	+	0.617986i	$0.212051\pi$
$4$	1.09916	−	1.67088i	0.549581	−	0.835441i
$5$	−0.0803191	−	2.23462i	−0.0359198	−	0.999355i
$5$	−0.0803191	−	2.23462i	−0.0359198	−	0.999355i
$6$	−4.17548	+	1.28302i	−1.70463	+	0.523791i
$7$	3.84724	+	2.57064i	1.45412	+	0.971612i	0.996598	+	0.0824138i	$0.0262629\pi$
$7$	3.84724	+	2.57064i	1.45412	+	0.971612i	0.457522	+	0.889198i	$0.348737\pi$
$8$	−0.246876	+	2.81763i	−0.0872837	+	0.996183i
$9$	6.04253	+	2.50290i	2.01418	+	0.834300i
$10$	1.59971	+	2.72780i	0.505874	+	0.862607i
$11$	2.30746	−	0.458983i	0.695726	−	0.138389i	0.165456	−	0.986217i	$-0.447090\pi$
$11$	2.30746	−	0.458983i	0.695726	−	0.138389i	0.530270	+	0.847829i	$0.322090\pi$
$12$	4.33665	−	4.39943i	1.25188	−	1.27001i
$13$	0.474407	+	0.474407i	0.131577	+	0.131577i	0.769828	−	0.638251i	$-0.220342\pi$
$13$	0.474407	+	0.474407i	0.131577	+	0.131577i	−0.638251	+	0.769828i	$0.720342\pi$
$14$	−6.51437	−	0.617983i	−1.74104	−	0.165163i
$15$	1.10323	−	6.81798i	0.284854	−	1.76039i
$16$	−1.58369	−	3.67314i	−0.395922	−	0.918284i
$17$	−3.71414	−	1.79030i	−0.900810	−	0.434213i
$17$	−3.71414	−	1.79030i	−0.900810	−	0.434213i
$18$	−9.20166	+	0.939681i	−2.16885	+	0.221485i
$19$	−6.53598	+	2.70729i	−1.49946	+	0.621095i	−0.973350	−	0.229324i	$-0.926348\pi$
$19$	−6.53598	+	2.70729i	−1.49946	+	0.621095i	−0.526106	+	0.850419i	$0.676348\pi$
$20$	−3.82208	−	2.32201i	−0.854642	−	0.519217i
$21$	10.1058	+	10.1058i	2.20527	+	2.20527i
$22$	−2.56434	+	2.11997i	−0.546719	+	0.451978i
$23$	−1.31540	−	6.61299i	−0.274281	−	1.37890i	−0.834705	−	0.550697i	$-0.814362\pi$
$23$	−1.31540	−	6.61299i	−0.274281	−	1.37890i	0.560424	−	0.828206i	$-0.310638\pi$
$24$	−2.44575	+	8.38698i	−0.499237	+	1.71199i
$25$	−4.98710	+	0.358966i	−0.997420	+	0.0717933i
$26$	−0.908942	−	0.272162i	−0.178258	−	0.0533753i
$27$	9.09245	+	6.07538i	1.74984	+	1.16921i
$28$	8.52398	−	3.60273i	1.61088	−	0.680852i
$29$	−4.89597	+	3.27138i	−0.909158	+	0.607480i	−0.919768	−	0.392464i	$-0.871623\pi$
$29$	−4.89597	+	3.27138i	−0.909158	+	0.607480i	0.0106093	+	0.999944i	$0.496623\pi$
$30$	3.20244	+	9.22758i	0.584683	+	1.68472i
$31$	0.996655	−	5.01052i	0.179005	−	0.899917i	−0.781978	−	0.623306i	$-0.785789\pi$
$31$	0.996655	−	5.01052i	0.179005	−	0.899917i	0.960982	−	0.276610i	$-0.0892111\pi$
$32$	4.43657	+	3.50953i	0.784283	+	0.620403i
$33$	7.26681			1.26499
$34$	5.82497	−	0.264070i	0.998974	−	0.0452877i
$35$	5.43542	−	8.80361i	0.918753	−	1.48808i
$36$	10.8238	−	7.34527i	1.80396	−	1.22421i
$37$	−1.03900	+	5.22343i	−0.170811	+	0.858727i	0.796403	+	0.604766i	$0.206733\pi$
$37$	−1.03900	+	5.22343i	−0.170811	+	0.858727i	−0.967215	+	0.253961i	$0.918267\pi$
$38$	6.31917	−	7.75660i	1.02511	−	1.25829i
$39$	1.15130	+	1.72304i	0.184355	+	0.275907i
$40$	6.31618	+	0.325365i	0.998676	+	0.0514447i
$41$	−3.57941	−	2.39169i	−0.559010	−	0.373519i	0.243734	−	0.969842i	$-0.421628\pi$
$41$	−3.57941	−	2.39169i	−0.559010	−	0.373519i	−0.802744	+	0.596323i	$0.796628\pi$
$42$	−19.3623	−	5.79759i	−2.98766	−	0.894587i
$43$	−0.819076	+	1.97742i	−0.124908	+	0.301554i	−0.973947	−	0.226776i	$-0.927182\pi$
$43$	−0.819076	+	1.97742i	−0.124908	+	0.301554i	0.849039	+	0.528330i	$0.177182\pi$
$44$	1.76937	−	4.35999i	0.266742	−	0.657294i
$45$	5.10771	−	13.7038i	0.761413	−	2.04285i
$46$	6.07564	+	7.34918i	0.895804	+	1.08358i
$47$	1.24163	+	1.24163i	0.181110	+	0.181110i	0.791840	−	0.610729i	$-0.209124\pi$
$47$	1.24163	+	1.24163i	0.181110	+	0.181110i	−0.610729	+	0.791840i	$0.709124\pi$
$48$	−2.58426	−	12.0817i	−0.373005	−	1.74385i
$49$	5.51427	+	13.3126i	0.787752	+	1.90180i
$50$	5.96713	−	3.79385i	0.843880	−	0.536532i
$51$	−10.1728	−	7.66164i	−1.42448	−	1.07284i
$52$	1.31413	−	0.271228i	0.182237	−	0.0376126i
$53$	2.20958	−	0.915237i	0.303509	−	0.125717i	−0.225731	−	0.974190i	$-0.572477\pi$
$53$	2.20958	−	0.915237i	0.303509	−	0.125717i	0.529240	+	0.848472i	$0.322477\pi$
$54$	−15.3959	−	1.46052i	−2.09511	−	0.198752i
$55$	−1.21099	−	5.11945i	−0.163290	−	0.690306i
$56$	−8.19292	+	10.2055i	−1.09482	+	1.36376i
$57$	−21.4315	+	4.26299i	−2.83867	+	0.564646i
$58$	3.89907	−	7.35813i	0.511973	−	0.966170i
$59$	0.257860	−	0.622529i	0.0335705	−	0.0810463i	−0.906205	−	0.422838i	$-0.861034\pi$
$59$	0.257860	−	0.622529i	0.0335705	−	0.0810463i	0.939776	+	0.341792i	$0.111034\pi$
$60$	−10.1794	−	9.33743i	−1.31416	−	1.20546i
$61$	3.33081	+	2.22558i	0.426467	+	0.284956i	0.750224	−	0.661184i	$-0.229946\pi$
$61$	3.33081	+	2.22558i	0.426467	+	0.284956i	−0.323756	+	0.946140i	$0.604946\pi$
$62$	2.12207	+	6.90609i	0.269503	+	0.877075i
$63$	16.8130	+	25.1625i	2.11824	+	3.17017i
$64$	−7.87810	−	1.39121i	−0.984763	−	0.173901i
$65$	1.02202	−	1.09823i	0.126766	−	0.136218i
$66$	−9.04588	+	4.87700i	−1.11347	+	0.600317i
$67$	−0.662256			−0.0809074			−0.0404537	−	0.999181i	$-0.512880\pi$
$67$	−0.662256			−0.0809074			−0.0404537	+	0.999181i	$0.512880\pi$
$68$	−7.07382	+	4.23805i	−0.857827	+	0.513939i
$69$		−	20.8260i		−	2.50716i
$70$	−0.857731	+	14.6068i	−0.102518	+	1.74585i
$71$	−2.50239	−	0.497757i	−0.296979	−	0.0590729i	0.0443517	−	0.999016i	$-0.485878\pi$
$71$	−2.50239	−	0.497757i	−0.296979	−	0.0590729i	−0.341331	+	0.939943i	$0.610878\pi$
$72$	−8.54401	+	16.4077i	−1.00692	+	1.93367i
$73$	−0.683178	−	1.02245i	−0.0799600	−	0.119669i	0.789334	−	0.613964i	$-0.210426\pi$
$73$	−0.683178	−	1.02245i	−0.0799600	−	0.119669i	−0.869294	+	0.494296i	$0.835426\pi$
$74$	−2.21224	−	7.19955i	−0.257168	−	0.836931i
$75$	−15.3242	−	1.91770i	−1.76949	−	0.221437i
$76$	−2.66053	+	13.8966i	−0.305184	+	1.59405i
$77$	10.0572	+	4.16585i	1.14613	+	0.474742i
$78$	−2.58955	−	1.37220i	−0.293209	−	0.155371i
$79$	−0.742184	−	3.73121i	−0.0835022	−	0.419794i	−0.999813	−	0.0193266i	$-0.993848\pi$
$79$	−0.742184	−	3.73121i	−0.0835022	−	0.419794i	0.916311	−	0.400467i	$-0.131152\pi$
$80$	−8.08088	+	3.83398i	−0.903470	+	0.428652i
$81$	10.0095	+	10.0095i	1.11217	+	1.11217i
$82$	6.06087	+	0.574962i	0.669311	+	0.0634939i
$83$	5.07078	−	2.10039i	0.556590	−	0.230547i	−0.0866138	−	0.996242i	$-0.527605\pi$
$83$	5.07078	−	2.10039i	0.556590	−	0.230547i	0.643204	+	0.765695i	$0.277605\pi$
$84$	27.9935	−	5.77770i	3.05434	−	0.630398i
$85$	−3.70234	+	8.44350i	−0.401575	+	0.915826i
$86$	−0.307511	−	3.01125i	−0.0331598	−	0.324711i
$87$	−16.8031	+	6.96009i	−1.80149	+	0.746200i
$88$	0.723589	+	6.61489i	0.0771348	+	0.705150i
$89$	5.59049	−	5.59049i	0.592591	−	0.592591i	−0.345740	−	0.938330i	$-0.612372\pi$
$89$	5.59049	−	5.59049i	0.592591	−	0.592591i	0.938330	+	0.345740i	$0.112372\pi$
$90$	2.83890	+	20.4868i	0.299247	+	2.15950i
$91$	0.605626	+	3.04469i	0.0634869	+	0.319170i
$92$	−12.4954	−	5.07085i	−1.30273	−	0.528673i
$93$	6.03854	−	14.5783i	0.626167	−	1.51170i
$94$	−2.37891	−	0.712309i	−0.245366	−	0.0734691i
$95$	6.57474	+	14.3880i	0.674554	+	1.47618i
$96$	11.3254	+	13.3052i	1.15589	+	1.35796i
$97$	11.5356	−	7.70783i	1.17126	−	0.782612i	0.191247	−	0.981542i	$-0.438747\pi$
$97$	11.5356	−	7.70783i	1.17126	−	0.782612i	0.980014	+	0.198930i	$0.0637467\pi$
$98$	−15.7988	−	12.8710i	−1.59592	−	1.30017i
$99$	15.0917	+	3.00193i	1.51677	+	0.301705i
$100$	−4.88183	+	8.72741i	−0.488183	+	0.872741i
$101$	−9.64388			−0.959602			−0.479801	−	0.877377i	$-0.659291\pi$
$101$	−9.64388			−0.959602			−0.479801	+	0.877377i	$0.659291\pi$
$102$	17.8053	+	2.71007i	1.76299	+	0.268337i
$103$	8.39042			0.826733			0.413367	−	0.910565i	$-0.364353\pi$
$103$	8.39042			0.826733			0.413367	+	0.910565i	$0.364353\pi$
$104$	−1.45382	+	1.21958i	−0.142559	+	0.119590i
$105$	21.7710	−	23.3944i	2.12463	−	2.28306i
$106$	−2.13628	+	2.62223i	−0.207494	+	0.254693i
$107$	2.87140	+	4.29736i	0.277589	+	0.415441i	0.943899	−	0.330233i	$-0.107127\pi$
$107$	2.87140	+	4.29736i	0.277589	+	0.415441i	−0.666310	+	0.745675i	$0.732127\pi$
$108$	20.1453	−	8.51458i	1.93848	−	0.819316i
$109$	−8.15843	+	12.2099i	−0.781436	+	1.16950i	0.200390	+	0.979716i	$0.435779\pi$
$109$	−8.15843	+	12.2099i	−0.781436	+	1.16950i	−0.981826	+	0.189785i	$0.939221\pi$
$110$	4.94329	+	5.56007i	0.471325	+	0.530131i
$111$	−6.29513	+	15.1978i	−0.597507	+	1.44251i
$112$	3.34949	−	18.2025i	0.316497	−	1.71998i
$113$	−2.15817	−	10.8499i	−0.203024	−	1.02067i	−0.939067	−	0.343735i	$-0.888308\pi$
$113$	−2.15817	−	10.8499i	−0.203024	−	1.02067i	0.736043	−	0.676935i	$-0.236692\pi$
$114$	23.8173	−	19.6900i	2.23070	−	1.84414i
$115$	−14.6719	+	3.47059i	−1.36816	+	0.323634i
$116$	0.0846329	+	11.7764i	0.00785797	+	1.09341i
$117$	1.67923	+	4.05401i	0.155245	+	0.374794i
$118$	0.0968101	+	0.947995i	0.00891209	+	0.0872701i
$119$	−9.68694	−	16.4355i	−0.888000	−	1.50664i
$120$	18.9382	+	4.79170i	1.72881	+	0.437420i
$121$	−5.04896	+	2.09135i	−0.458996	+	0.190122i
$122$	−5.63993	−	0.535029i	−0.510615	−	0.0484393i
$123$	−9.40229	−	9.40229i	−0.847776	−	0.847776i
$124$	−7.27651	−	7.17266i	−0.653450	−	0.644124i
$125$	1.20271	+	11.1155i	0.107574	+	0.994197i
$126$	−37.8166	−	20.0390i	−3.36897	−	1.78522i
$127$	1.16418	−	2.81058i	0.103304	−	0.249399i	−0.863773	−	0.503881i	$-0.831905\pi$
$127$	1.16418	−	2.81058i	0.103304	−	0.249399i	0.967078	+	0.254482i	$0.0819050\pi$
$128$	10.7405	−	3.55545i	0.949337	−	0.314260i
$129$	−3.67288	+	5.49685i	−0.323379	+	0.483971i
$130$	−0.535174	+	2.05300i	−0.0469379	+	0.180060i
$131$	−2.06466	−	3.08997i	−0.180390	−	0.269972i	0.730244	−	0.683186i	$-0.239406\pi$
$131$	−2.06466	−	3.08997i	−0.180390	−	0.269972i	−0.910634	+	0.413214i	$0.864406\pi$
$132$	7.98739	−	12.1420i	0.695213	−	1.05682i
$133$	−32.1050	−	6.38607i	−2.78385	−	0.553743i
$134$	0.824390	−	0.444462i	0.0712164	−	0.0383956i
$135$	12.8459	−	20.8062i	1.10560	−	1.79071i
$136$	5.96135	−	10.0231i	0.511181	−	0.859473i
$137$			18.1100i			1.54724i	0.633647	+	0.773622i	$0.281557\pi$
$137$			18.1100i			1.54724i	−0.633647	+	0.773622i	$0.718443\pi$
$138$	13.9770	+	25.9247i	1.18981	+	2.20686i
$139$	−3.76434	+	18.9246i	−0.319287	+	1.60516i	0.404096	+	0.914717i	$0.367586\pi$
$139$	−3.76434	+	18.9246i	−0.319287	+	1.60516i	−0.723383	+	0.690447i	$0.757414\pi$
$140$	−8.73539	−	18.7585i	−0.738275	−	1.58538i
$141$	3.01321	+	4.50959i	0.253758	+	0.379776i
$142$	3.44909	−	1.05982i	0.289442	−	0.0889381i
$143$	1.31242	+	0.876931i	0.109750	+	0.0733327i
$144$	−0.376010	−	26.1589i	−0.0313342	−	2.17991i
$145$	7.70355	+	10.6779i	0.639745	+	0.886751i
$146$	1.53663	+	0.814262i	0.127173	+	0.0673888i
$147$	8.68294	+	43.6521i	0.716157	+	3.60036i
$148$	7.58570	+	7.47745i	0.623541	+	0.614642i
$149$	12.0584	−	12.0584i	0.987865	−	0.987865i	−0.0120627	−	0.999927i	$-0.503840\pi$
$149$	12.0584	−	12.0584i	0.987865	−	0.987865i	0.999927	+	0.0120627i	$0.00383975\pi$
$150$	20.3630	−	7.89741i	1.66263	−	0.644821i
$151$	−12.5641	+	5.20422i	−1.02245	+	0.423514i	−0.829983	−	0.557789i	$-0.811650\pi$
$151$	−12.5641	+	5.20422i	−1.02245	+	0.423514i	−0.192470	+	0.981303i	$0.561650\pi$
$152$	−6.01458	−	19.0843i	−0.487846	−	1.54794i
$153$	−17.9618	−	20.1141i	−1.45213	−	1.62613i
$154$	−15.3153	+	1.56401i	−1.23414	+	0.126032i
$155$	−11.2767	−	1.82471i	−0.905766	−	0.146564i
$156$	4.14446	−	0.0297849i	0.331822	−	0.00238470i
$157$	3.51971	−	3.51971i	0.280903	−	0.280903i	−0.552566	−	0.833469i	$-0.686351\pi$
$157$	3.51971	−	3.51971i	0.280903	−	0.280903i	0.833469	+	0.552566i	$0.186351\pi$
$158$	3.42803	+	4.14659i	0.272719	+	0.329885i
$159$	7.24521	−	1.44116i	0.574582	−	0.114292i
$160$	7.48615	−	10.1960i	0.591832	−	0.806062i
$161$	11.9390	−	28.8232i	0.940921	−	2.27159i
$162$	−19.1777	−	5.74233i	−1.50674	−	0.451160i
$163$	−6.27516	−	4.19293i	−0.491509	−	0.328416i	0.284994	−	0.958529i	$-0.408008\pi$
$163$	−6.27516	−	4.19293i	−0.491509	−	0.328416i	−0.776503	+	0.630114i	$0.783008\pi$
$164$	−7.93058	+	3.35193i	−0.619274	+	0.261741i
$165$	−0.583664	−	16.2386i	−0.0454382	−	1.26417i
$166$	−4.90258	+	6.01777i	−0.380514	+	0.467070i
$167$	−6.97603	−	1.38762i	−0.539822	−	0.107377i	−0.0823535	−	0.996603i	$-0.526244\pi$
$167$	−6.97603	−	1.38762i	−0.539822	−	0.107377i	−0.457468	+	0.889226i	$0.651244\pi$
$168$	−30.9693	+	25.9796i	−2.38934	+	2.00437i
$169$		−	12.5499i		−	0.965375i
$170$	−1.05795	−	12.9954i	−0.0811414	−	0.996703i
$171$	−46.2699			−3.53835
$172$	2.40375	+	3.54209i	0.183284	+	0.270082i
$173$	−0.767815	+	3.86007i	−0.0583759	+	0.293475i	−0.998934	−	0.0461568i	$-0.985303\pi$
$173$	−0.767815	+	3.86007i	−0.0583759	+	0.293475i	0.940558	+	0.339632i	$0.110303\pi$
$174$	16.2458	−	19.9412i	1.23159	−	1.51174i
$175$	−20.1093	−	11.4390i	−1.52012	−	0.864709i
$176$	−5.34021	−	7.74874i	−0.402534	−	0.584083i
$177$	1.15629	−	1.73051i	0.0869120	−	0.130073i
$178$	−3.20720	+	10.7111i	−0.240390	+	0.802833i
$179$	−0.0746106	−	0.0309047i	−0.00557666	−	0.00230993i	0.379893	−	0.925030i	$-0.375961\pi$
$179$	−0.0746106	−	0.0309047i	−0.00557666	−	0.00230993i	−0.385470	+	0.922720i	$0.625961\pi$
$180$	−17.2833	−	23.5971i	−1.28822	−	1.75882i
$181$	−3.90988	−	19.6563i	−0.290619	−	1.46104i	−0.799741	−	0.600346i	$-0.795030\pi$
$181$	−3.90988	−	19.6563i	−0.290619	−	1.46104i	0.509121	−	0.860695i	$-0.329970\pi$
$182$	−2.79729	−	3.38364i	−0.207349	−	0.250812i
$183$	8.74928	+	8.74928i	0.646765	+	0.646765i
$184$	18.9577	−	2.07374i	1.39758	−	0.152878i
$185$	11.7559	+	1.90224i	0.864308	+	0.139856i
$186$	2.26709	+	22.2001i	0.166231	+	1.62779i
$187$	−9.39195	−	2.42634i	−0.686807	−	0.177431i
$188$	3.43937	−	0.709866i	0.250842	−	0.0517723i
$189$	19.3632	+	46.7469i	1.40847	+	3.40034i
$190$	−17.8406	−	13.4980i	−1.29430	−	0.979246i
$191$	−7.64238	−	7.64238i	−0.552983	−	0.552983i	0.374317	−	0.927301i	$-0.377877\pi$
$191$	−7.64238	−	7.64238i	−0.552983	−	0.552983i	−0.927301	+	0.374317i	$0.877877\pi$
$192$	−23.0276	−	8.96177i	−1.66188	−	0.646760i
$193$	26.3626	−	5.24384i	1.89762	−	0.377460i	0.899401	−	0.437125i	$-0.144003\pi$
$193$	26.3626	−	5.24384i	1.89762	−	0.377460i	0.998218	+	0.0596648i	$0.0190032\pi$
$194$	−9.18676	+	17.3368i	−0.659571	+	1.24471i
$195$	3.75788	−	2.71111i	0.269107	−	0.194147i
$196$	28.3049	+	5.41902i	2.02178	+	0.387073i
$197$	−2.39931	+	3.59083i	−0.170944	+	0.255836i	−0.907043	−	0.421038i	$-0.861666\pi$
$197$	−2.39931	+	3.59083i	−0.170944	+	0.255836i	0.736099	+	0.676874i	$0.236666\pi$
$198$	−20.8012	+	6.39168i	−1.47828	+	0.454237i
$199$	−13.0589	+	8.72570i	−0.925723	+	0.618548i	−0.924389	−	0.381451i	$-0.875425\pi$
$199$	−13.0589	+	8.72570i	−0.925723	+	0.618548i	−0.00133382	+	0.999999i	$0.500425\pi$
$200$	0.219758	−	14.1404i	0.0155392	−	0.999879i
$201$	−2.00624	−	0.399066i	−0.141509	−	0.0281479i
$202$	12.0049	−	6.47233i	0.844662	−	0.455391i
$203$	−27.2455			−1.91226
$204$	−23.9832	+	8.57618i	−1.67916	+	0.600452i
$205$	−5.05703	+	8.19074i	−0.353198	+	0.572066i
$206$	−10.4446	+	5.63109i	−0.727708	+	0.392337i
$207$	8.60326	−	43.2515i	0.597968	−	3.00619i
$208$	0.991247	−	2.49387i	0.0687306	−	0.172919i
$209$	−13.8389	+	9.24687i	−0.957258	+	0.639620i
$210$	−11.4003	+	43.7331i	−0.786693	+	3.01787i
$211$	10.8875	+	7.27478i	0.749525	+	0.500817i	0.870700	−	0.491815i	$-0.163666\pi$
$211$	10.8875	+	7.27478i	0.749525	+	0.500817i	−0.121175	+	0.992631i	$0.538666\pi$
$212$	0.899429	−	4.69793i	0.0617730	−	0.322655i
$213$	−7.28082	−	3.01581i	−0.498873	−	0.206640i
$214$	−6.45848	−	3.42235i	−0.441493	−	0.233947i
$215$	4.48459	+	1.67150i	0.305846	+	0.113996i
$216$	−19.3629	+	24.1193i	−1.31748	+	1.64111i
$217$	16.7146	−	16.7146i	1.13466	−	1.13466i
$218$	1.96129	−	20.6746i	0.132835	−	1.40026i
$219$	−1.45351	−	3.50908i	−0.0982191	−	0.237122i
$220$	−9.88506	−	3.60368i	−0.666451	−	0.242960i
$221$	−0.912679	−	2.61134i	−0.0613934	−	0.175658i
$222$	−2.36342	−	23.1434i	−0.158623	−	1.55328i
$223$	8.19765	−	3.39558i	0.548955	−	0.227385i	−0.0909273	−	0.995858i	$-0.528983\pi$
$223$	8.19765	−	3.39558i	0.548955	−	0.227385i	0.639882	+	0.768473i	$0.278983\pi$
$224$	8.04681	+	24.9069i	0.537650	+	1.66416i
$225$	−31.0332	−	10.3131i	−2.06888	−	0.687543i
$226$	9.96824	+	12.0577i	0.663078	+	0.802068i
$227$	−15.6337	+	3.10973i	−1.03764	+	0.206400i	−0.684381	−	0.729125i	$-0.739927\pi$
$227$	−15.6337	+	3.10973i	−1.03764	+	0.206400i	−0.353262	+	0.935525i	$0.614927\pi$
$228$	−16.4337	+	40.4952i	−1.08835	+	2.68186i
$229$	11.5640	+	4.78996i	0.764170	+	0.316530i	0.730509	−	0.682904i	$-0.239283\pi$
$229$	11.5640	+	4.78996i	0.764170	+	0.316530i	0.0336619	+	0.999433i	$0.489283\pi$
$230$	15.9347	−	14.1670i	1.05070	−	0.934148i
$231$	27.9572	+	18.6804i	1.83945	+	1.22908i
$232$	−8.00885	−	14.6027i	−0.525807	−	0.958712i
$233$	8.30073	−	5.54637i	0.543799	−	0.363355i	−0.253126	−	0.967433i	$-0.581459\pi$
$233$	8.30073	−	5.54637i	0.543799	−	0.363355i	0.796925	+	0.604078i	$0.206459\pi$
$234$	−4.81112	−	3.91954i	−0.314513	−	0.256228i
$235$	2.67485	−	2.87431i	0.174488	−	0.187499i
$236$	−0.756742	−	1.11511i	−0.0492597	−	0.0725877i
$237$		−	11.7506i		−	0.763282i
$238$	23.0889	+	13.9580i	1.49663	+	0.904761i
$239$		−	14.8681i		−	0.961737i	−0.876793	−	0.480868i	$-0.840322\pi$
$239$		−	14.8681i		−	0.961737i	0.876793	−	0.480868i	$-0.159678\pi$
$240$	−26.7905	+	6.74524i	−1.72932	+	0.435403i
$241$	0.111847	−	0.562292i	0.00720469	−	0.0362204i	−0.977016	−	0.213167i	$-0.931622\pi$
$241$	0.111847	−	0.562292i	0.00720469	−	0.0362204i	0.984220	+	0.176947i	$0.0566221\pi$
$242$	4.88148	−	5.99187i	0.313793	−	0.385172i
$243$	6.06506	+	9.07700i	0.389074	+	0.582290i
$244$	7.37978	−	3.11913i	0.472442	−	0.199682i
$245$	29.3058	−	13.3916i	1.87228	−	0.855556i
$246$	18.0144	+	5.39398i	1.14855	+	0.343908i
$247$	−4.38507	−	1.81635i	−0.279015	−	0.115572i
$248$	13.8718	+	4.04518i	0.880858	+	0.256869i
$249$	16.6271	−	3.30734i	1.05370	−	0.209594i
$250$	−8.95712	−	13.0296i	−0.566498	−	0.824063i
$251$	6.76542	+	6.76542i	0.427029	+	0.427029i	0.887615	−	0.460586i	$-0.152361\pi$
$251$	6.76542	+	6.76542i	0.427029	+	0.427029i	−0.460586	+	0.887615i	$0.652361\pi$
$252$	60.5237	−	0.434965i	3.81264	−	0.0274002i
$253$	−6.07049	−	14.6555i	−0.381649	−	0.921381i
$254$	0.437077	+	4.28000i	0.0274246	+	0.268551i
$255$	−16.3038	+	23.3478i	−1.02098	+	1.46209i
$256$	−10.9839	+	11.6342i	−0.686491	+	0.727139i
$257$	11.5256	+	27.8252i	0.718946	+	1.73569i	0.676331	+	0.736598i	$0.263569\pi$
$257$	11.5256	+	27.8252i	0.718946	+	1.73569i	0.0426152	+	0.999092i	$0.486431\pi$
$258$	0.882960	−	9.30759i	0.0549707	−	0.579465i
$259$	−17.4249	+	17.4249i	−1.08273	+	1.08273i
$260$	−0.711643	−	2.91480i	−0.0441342	−	0.180768i
$261$	−37.7720	+	7.51332i	−2.33803	+	0.465063i
$262$	4.64391	+	2.46081i	0.286902	+	0.152029i
$263$	1.74904	−	4.22255i	0.107850	−	0.260374i	−0.860736	−	0.509052i	$-0.829996\pi$
$263$	1.74904	−	4.22255i	0.107850	−	0.260374i	0.968586	+	0.248678i	$0.0799961\pi$
$264$	−1.79400	+	20.4752i	−0.110413	+	1.26016i
$265$	−2.22268	−	4.86406i	−0.136538	−	0.298797i
$266$	44.2508	−	13.5972i	2.71319	−	0.833696i
$267$	20.3046	−	13.5671i	1.24262	−	0.830293i
$268$	−0.727926	+	1.10655i	−0.0444651	+	0.0675933i
$269$	−2.06052	+	10.3590i	−0.125632	+	0.631596i	0.865737	+	0.500499i	$0.166850\pi$
$269$	−2.06052	+	10.3590i	−0.125632	+	0.631596i	−0.991369	+	0.131097i	$0.958150\pi$
$270$	−2.02714	+	34.5213i	−0.123368	+	2.10090i
$271$	21.4104			1.30059			0.650296	−	0.759681i	$-0.274645\pi$
$271$	21.4104			1.30059			0.650296	+	0.759681i	$0.274645\pi$
$272$	−0.693990	+	16.4778i	−0.0420793	+	0.999114i
$273$			9.58853i			0.580324i
$274$	−12.1542	−	22.5438i	−0.734264	−	1.36192i
$275$	−11.3428	+	3.11729i	−0.683995	+	0.187980i
$276$	−34.7979	−	22.8912i	−2.09458	−	1.37789i
$277$	−8.62180	+	5.76090i	−0.518034	+	0.346139i	−0.786942	−	0.617027i	$-0.788337\pi$
$277$	−8.62180	+	5.76090i	−0.518034	+	0.346139i	0.268908	+	0.963166i	$0.413337\pi$
$278$	−8.01500	−	26.0841i	−0.480708	−	1.56442i
$279$	18.5632	−	27.7817i	1.11135	−	1.66325i
$280$	23.4635	+	17.4884i	1.40221	+	1.04513i
$281$	−26.5442	−	10.9950i	−1.58349	−	0.655905i	−0.594531	−	0.804072i	$-0.702662\pi$
$281$	−26.5442	−	10.9950i	−1.58349	−	0.655905i	−0.988962	+	0.148168i	$0.952662\pi$
$282$	−6.77744	−	3.59137i	−0.403591	−	0.213863i
$283$	2.50060	+	12.5713i	0.148645	+	0.747289i	0.981146	+	0.193266i	$0.0619080\pi$
$283$	2.50060	+	12.5713i	0.148645	+	0.747289i	−0.832501	+	0.554023i	$0.813092\pi$
$284$	−3.58223	+	3.63409i	−0.212566	+	0.215643i
$285$	11.2475	+	47.5489i	0.666246	+	2.81656i
$286$	−2.22227	−	0.210814i	−0.131405	−	0.0124657i
$287$	−7.62269	−	18.4028i	−0.449953	−	1.08628i
$288$	18.0241	+	32.3108i	1.06208	+	1.90393i
$289$	10.5896	+	13.2989i	0.622919	+	0.782286i
$290$	−16.7558	−	8.12197i	−0.983936	−	0.476938i
$291$	39.5906	−	16.3989i	2.32084	−	0.961323i
$292$	−2.45931	+	0.0176743i	−0.143920	+	0.00103431i
$293$	15.0394	−	15.0394i	0.878613	−	0.878613i	−0.114778	−	0.993391i	$-0.536616\pi$
$293$	15.0394	−	15.0394i	0.878613	−	0.878613i	0.993391	+	0.114778i	$0.0366156\pi$
$294$	−40.1051	−	48.5117i	−2.33898	−	2.82926i
$295$	−1.41183	−	0.526219i	−0.0821999	−	0.0306377i
$296$	−14.4612	−	4.21707i	−0.840540	−	0.245112i
$297$	23.7690	+	9.84543i	1.37922	+	0.571290i
$298$	−6.91778	+	23.1034i	−0.400736	+	1.33834i
$299$	2.51321	−	3.76128i	0.145343	−	0.217521i
$300$	−20.0481	+	23.4971i	−1.15747	+	1.35661i
$301$	−8.23444	+	5.50207i	−0.474625	+	0.317134i
$302$	12.1473	−	14.9105i	0.699001	−	0.858004i
$303$	−29.2152	−	5.81126i	−1.67837	−	0.333848i
$304$	20.2952	+	19.7200i	1.16401	+	1.13102i
$305$	4.70581	−	7.62188i	0.269454	−	0.436427i
$306$	35.8585	+	12.9837i	2.04990	+	0.742226i
$307$		−	26.9859i		−	1.54017i	−0.637943	−	0.770083i	$-0.720215\pi$
$307$		−	26.9859i		−	1.54017i	0.637943	−	0.770083i	$-0.279785\pi$
$308$	18.0152	−	12.2255i	1.02651	−	0.696614i
$309$	25.4180	+	5.05595i	1.44598	+	0.287623i
$310$	15.2621	−	5.29672i	0.866828	−	0.300834i
$311$	8.78046	+	13.1409i	0.497894	+	0.745151i	0.992270	−	0.124097i	$-0.0396033\pi$
$311$	8.78046	+	13.1409i	0.497894	+	0.745151i	−0.494376	+	0.869248i	$0.664603\pi$
$312$	−5.13912	+	2.81856i	−0.290945	+	0.159570i
$313$	−16.3030	+	24.3992i	−0.921501	+	1.37912i	0.00384177	+	0.999993i	$0.498777\pi$
$313$	−16.3030	+	24.3992i	−0.921501	+	1.37912i	−0.925343	+	0.379131i	$0.876223\pi$
$314$	−2.01922	+	6.74360i	−0.113951	+	0.380564i
$315$	54.8783	−	39.5918i	3.09204	−	2.23075i
$316$	−7.05019	−	2.86110i	−0.396604	−	0.160949i
$317$	−12.7689	+	2.53989i	−0.717171	+	0.142654i	−0.540169	−	0.841556i	$-0.681640\pi$
$317$	−12.7689	+	2.53989i	−0.717171	+	0.142654i	−0.177002	+	0.984211i	$0.556640\pi$
$318$	−8.05178	+	6.65649i	−0.451521	+	0.373277i
$319$	−9.79575	+	9.79575i	−0.548457	+	0.548457i
$320$	−2.47607	+	17.7164i	−0.138416	+	0.990374i
$321$	6.10911	+	14.7487i	0.340977	+	0.823192i
$322$	4.48232	+	43.8923i	0.249790	+	2.44602i
$323$	29.1224	+	1.64614i	1.62041	+	0.0915938i
$324$	27.7267	−	5.72263i	1.54037	−	0.317924i
$325$	−2.53621	−	2.19562i	−0.140684	−	0.121791i
$326$	10.6255	+	1.00798i	0.588490	+	0.0558269i
$327$	−32.0727	+	32.0727i	−1.77362	+	1.77362i
$328$	7.62257	−	9.49502i	0.420886	−	0.524275i
$329$	1.58506	+	7.96864i	0.0873873	+	0.439326i
$330$	11.6248	+	19.8224i	0.639925	+	1.09119i
$331$	3.67576	−	8.87408i	0.202038	−	0.487763i	−0.790090	−	0.612991i	$-0.789966\pi$
$331$	3.67576	−	8.87408i	0.202038	−	0.487763i	0.992128	+	0.125228i	$0.0399661\pi$
$332$	2.06411	−	10.7813i	0.113283	−	0.591703i
$333$	−19.3519	+	28.9622i	−1.06048	+	1.58712i
$334$	9.61519	−	2.95451i	0.526120	−	0.161663i
$335$	0.0531918	+	1.47989i	0.00290618	+	0.0808552i
$336$	21.1155	−	53.1245i	1.15195	−	2.89818i
$337$	1.51971	−	7.64009i	0.0827838	−	0.416182i	−0.917064	−	0.398740i	$-0.869448\pi$
$337$	1.51971	−	7.64009i	0.0827838	−	0.416182i	0.999848	−	0.0174423i	$-0.00555234\pi$
$338$	8.42264	+	15.6224i	0.458131	+	0.849744i
$339$		−	34.1691i		−	1.85581i
$340$	10.0386	+	15.4669i	0.544420	+	0.838813i
$341$		−	12.0190i		−	0.650868i
$342$	57.5978	−	31.0533i	3.11453	−	1.67917i
$343$	−6.68845	+	33.6251i	−0.361143	+	1.81559i
$344$	−5.36945	−	2.79603i	−0.289501	−	0.150752i
$345$	−46.5384	+	1.67273i	−2.50554	+	0.0900568i
$346$	−1.63483	−	5.32040i	−0.0878887	−	0.286026i
$347$	−7.66148	+	11.4662i	−0.411290	+	0.615538i	−0.978057	−	0.208340i	$-0.933194\pi$
$347$	−7.66148	+	11.4662i	−0.411290	+	0.615538i	0.566767	+	0.823878i	$0.308194\pi$
$348$	−6.83988	+	35.7263i	−0.366656	+	1.91513i
$349$	1.56644	−	3.78172i	0.0838496	−	0.202431i	−0.876394	−	0.481595i	$-0.840057\pi$
$349$	1.56644	−	3.78172i	0.0838496	−	0.202431i	0.960243	+	0.279165i	$0.0900575\pi$
$350$	32.7096	+	0.743501i	1.74840	+	0.0397418i
$351$	1.43132	+	7.19572i	0.0763981	+	0.384079i
$352$	11.8480	+	6.06180i	0.631503	+	0.323095i
$353$	−5.12718	+	5.12718i	−0.272892	+	0.272892i	−0.830263	−	0.557371i	$-0.811810\pi$
$353$	−5.12718	+	5.12718i	−0.272892	+	0.272892i	0.557371	+	0.830263i	$0.311810\pi$
$354$	−0.277972	+	2.93020i	−0.0147740	+	0.155738i
$355$	−0.911310	+	5.63189i	−0.0483673	+	0.298910i
$356$	−3.19620	−	15.4859i	−0.169398	−	0.820751i
$357$	−19.4419	−	55.6268i	−1.02897	−	2.94408i
$358$	0.113618	−	0.0116028i	0.00600490	−	0.000613226i
$359$	0.508478	+	1.22757i	0.0268364	+	0.0647889i	0.936730	−	0.350054i	$-0.113837\pi$
$359$	0.508478	+	1.22757i	0.0268364	+	0.0647889i	−0.909893	+	0.414843i	$0.863837\pi$
$360$	37.3514	+	17.7748i	1.96859	+	0.936814i
$361$	21.9545	−	21.9545i	1.15550	−	1.15550i
$362$	18.0591	+	21.8445i	0.949164	+	1.14812i
$363$	−16.5555	+	3.29310i	−0.868941	+	0.172843i
$364$	5.75299	+	2.33467i	0.301539	+	0.122370i
$365$	−2.22992	+	1.60877i	−0.116719	+	0.0842068i
$366$	−16.7632	−	5.01936i	−0.876227	−	0.262366i
$367$	−4.29723	+	6.43125i	−0.224313	+	0.335709i	−0.926507	−	0.376277i	$-0.877204\pi$
$367$	−4.29723	+	6.43125i	−0.224313	+	0.335709i	0.702194	+	0.711986i	$0.252204\pi$
$368$	−22.2072	+	15.3046i	−1.15763	+	0.797806i
$369$	−15.6426	−	23.4108i	−0.814320	−	1.21872i
$370$	−15.9106	+	5.52179i	−0.827153	+	0.287064i
$371$	10.8535	+	2.15890i	0.563487	+	0.112084i
$372$	−17.7213	−	26.1136i	−0.918808	−	1.35393i
$373$		−	24.3172i		−	1.25910i	−0.776960	−	0.629549i	$-0.783240\pi$
$373$		−	24.3172i		−	1.25910i	0.776960	−	0.629549i	$-0.216760\pi$
$374$	13.3197	−	3.28289i	0.688745	−	0.169754i
$375$	−3.05451	+	34.3980i	−0.157734	+	1.77630i
$376$	−3.80499	+	3.19193i	−0.196227	+	0.164611i
$377$	−3.87465	−	0.770715i	−0.199554	−	0.0396938i
$378$	−55.4771	−	45.1963i	−2.85343	−	2.32464i
$379$	21.8652	−	14.6099i	1.12314	−	0.750459i	0.151862	−	0.988402i	$-0.451473\pi$
$379$	21.8652	−	14.6099i	1.12314	−	0.750459i	0.971279	+	0.237943i	$0.0764732\pi$
$380$	31.2674	+	4.82912i	1.60398	+	0.247729i
$381$	5.22040	−	7.81287i	0.267449	−	0.400266i
$382$	14.6425	+	4.38435i	0.749173	+	0.224323i
$383$	12.7732	+	5.29085i	0.652682	+	0.270350i	0.684355	−	0.729149i	$-0.260084\pi$
$383$	12.7732	+	5.29085i	0.652682	+	0.270350i	−0.0316735	+	0.999498i	$0.510084\pi$
$384$	34.6798	−	4.29880i	1.76975	−	0.219372i
$385$	8.50132	−	22.8088i	0.433267	−	1.16244i
$386$	−29.2974	+	24.2204i	−1.49120	+	1.23279i
$387$	−9.89859	+	9.89859i	−0.503174	+	0.503174i
$388$	−0.199407	−	27.7467i	−0.0101234	−	1.40863i
$389$	−28.1359	+	11.6543i	−1.42655	+	0.590895i	−0.956496	−	0.291745i	$-0.905764\pi$
$389$	−28.1359	+	11.6543i	−1.42655	+	0.590895i	−0.470050	+	0.882640i	$0.655764\pi$
$390$	−2.85837	+	5.89689i	−0.144739	+	0.298601i
$391$	−6.95366	+	26.9165i	−0.351662	+	1.36123i
$392$	−38.8714	+	12.2506i	−1.96330	+	0.618749i
$393$	−4.39270	−	10.6049i	−0.221582	−	0.534947i
$394$	0.576795	−	6.08020i	0.0290585	−	0.306316i
$395$	−8.27825	+	1.95819i	−0.416524	+	0.0985273i
$396$	21.6041	−	21.9169i	1.08565	−	1.10136i
$397$	5.81201	+	29.2189i	0.291696	+	1.46646i	0.797244	+	0.603658i	$0.206291\pi$
$397$	5.81201	+	29.2189i	0.291696	+	1.46646i	−0.505547	+	0.862799i	$0.668709\pi$
$398$	10.3999	−	19.6262i	0.521302	−	0.983773i
$399$	−93.4107	−	38.6920i	−4.67638	−	1.93702i
$400$	9.21655	+	17.7498i	0.460827	+	0.887490i
$401$	−0.979570	+	1.46603i	−0.0489174	+	0.0732100i	−0.855122	−	0.518427i	$-0.826518\pi$
$401$	−0.979570	+	1.46603i	−0.0489174	+	0.0732100i	0.806205	+	0.591637i	$0.201518\pi$
$402$	2.76524	−	0.849687i	0.137917	−	0.0423786i
$403$	2.84985	−	1.90421i	0.141961	−	0.0948553i
$404$	−10.6002	+	16.1138i	−0.527379	+	0.801691i
$405$	21.5635	−	23.1714i	1.07150	−	1.15140i
$406$	33.9158	−	18.2854i	1.68321	−	0.907487i
$407$			12.5298i			0.621077i
$408$	24.0991	−	26.7718i	1.19308	−	1.32540i
$409$	20.4889			1.01311			0.506554	−	0.862208i	$-0.330919\pi$
$409$	20.4889			1.01311			0.506554	+	0.862208i	$0.330919\pi$
$410$	0.798020	−	13.5900i	0.0394114	−	0.671160i
$411$	−10.9128	+	54.8626i	−0.538291	+	2.70617i
$412$	9.22243	−	14.0194i	0.454356	−	0.690686i
$413$	2.59235	−	1.73215i	0.127561	−	0.0852336i
$414$	18.3180	+	59.6144i	0.900280	+	2.92989i
$415$	−5.10086	−	11.1626i	−0.250391	−	0.547950i
$416$	0.439795	+	3.76969i	0.0215627	+	0.184824i
$417$	−22.8074	+	55.0619i	−1.11688	+	2.69639i
$418$	11.0211	−	20.7985i	0.539060	−	1.01729i
$419$	−21.0452	+	4.18615i	−1.02812	+	0.204507i	−0.680208	−	0.733019i	$-0.738111\pi$
$419$	−21.0452	+	4.18615i	−1.02812	+	0.204507i	−0.347916	+	0.937526i	$0.613111\pi$
$420$	−15.1594	−	62.0910i	−0.739703	−	3.02973i
$421$	−6.24485	+	6.24485i	−0.304355	+	0.304355i	−0.842715	−	0.538360i	$-0.819044\pi$
$421$	−6.24485	+	6.24485i	−0.304355	+	0.304355i	0.538360	+	0.842715i	$0.319044\pi$
$422$	−18.4353	−	1.74886i	−0.897417	−	0.0851330i
$423$	4.39492	+	10.6103i	0.213688	+	0.515889i
$424$	2.03331	+	6.45172i	0.0987462	+	0.313323i
$425$	19.1654	+	7.59517i	0.929659	+	0.368420i
$426$	11.0873	−	1.13225i	0.537183	−	0.0548576i
$427$	7.09327	+	17.1247i	0.343267	+	0.828721i
$428$	10.3365	−	0.0742852i	0.499634	−	0.00359071i
$429$	3.44742	+	3.44742i	0.166443	+	0.166443i
$430$	−6.70431	+	0.929033i	−0.323311	+	0.0448020i
$431$	−7.66662	+	1.52499i	−0.369288	+	0.0734560i	−0.376246	−	0.926520i	$-0.622785\pi$
$431$	−7.66662	+	1.52499i	−0.369288	+	0.0734560i	0.00695775	+	0.999976i	$0.497785\pi$
$432$	7.91608	−	43.0193i	0.380862	−	2.06977i
$433$	15.6913	+	6.49954i	0.754075	+	0.312348i	0.726403	−	0.687269i	$-0.241191\pi$
$433$	15.6913	+	6.49954i	0.754075	+	0.312348i	0.0276718	+	0.999617i	$0.491191\pi$
$434$	−9.58900	+	32.0245i	−0.460287	+	1.53722i
$435$	16.9028	+	36.9897i	0.810428	+	1.77352i
$436$	11.4340	+	27.0525i	0.547587	+	1.29558i
$437$	26.5007	+	39.6611i	1.26770	+	1.89725i
$438$	4.16442	+	3.39268i	0.198984	+	0.162109i
$439$	0.593019	−	2.98131i	0.0283033	−	0.142290i	−0.964050	−	0.265721i	$-0.914390\pi$
$439$	0.593019	−	2.98131i	0.0283033	−	0.142290i	0.992353	+	0.123431i	$0.0393899\pi$
$440$	14.7237	−	2.14825i	0.701924	−	0.102414i
$441$			94.2436i			4.48779i
$442$	2.88868	+	2.63813i	0.137401	+	0.125483i
$443$			36.5984i			1.73884i	0.494071	+	0.869422i	$0.335508\pi$
$443$			36.5984i			1.73884i	−0.494071	+	0.869422i	$0.664492\pi$
$444$	18.4743	+	27.2232i	0.876753	+	1.29196i
$445$	−12.9417	−	12.0436i	−0.613494	−	0.570923i
$446$	−7.92572	+	9.72860i	−0.375294	+	0.460662i
$447$	43.7961	−	29.2636i	2.07148	−	1.38412i
$448$	−26.7327	−	25.6041i	−1.26300	−	1.20968i
$449$	−26.0335	−	17.3951i	−1.22860	−	0.820923i	−0.239894	−	0.970799i	$-0.577113\pi$
$449$	−26.0335	−	17.3951i	−1.22860	−	0.820923i	−0.988705	+	0.149876i	$0.952113\pi$
$450$	45.5522	−	7.98936i	2.14735	−	0.376622i
$451$	−9.35710	−	3.87584i	−0.440609	−	0.182506i
$452$	−20.5010	−	8.31970i	−0.964287	−	0.391326i
$453$	−41.1977	+	8.19474i	−1.93564	+	0.385022i
$454$	17.3741	−	14.3633i	0.815406	−	0.674104i
$455$	6.75509	−	1.59789i	0.316684	−	0.0749104i
$456$	−6.72062	−	61.4385i	−0.314722	−	2.87712i
$457$	−1.92714	+	0.798247i	−0.0901477	+	0.0373404i	−0.427302	−	0.904109i	$-0.640536\pi$
$457$	−1.92714	+	0.798247i	−0.0901477	+	0.0373404i	0.337154	+	0.941450i	$0.390536\pi$
$458$	−17.6098	+	1.79833i	−0.822853	+	0.0840304i
$459$	−22.8938	−	38.8430i	−1.06859	−	1.81304i
$460$	−10.3278	+	28.3297i	−0.481538	+	1.32088i
$461$	2.11083	+	5.09600i	0.0983113	+	0.237344i	0.965382	−	0.260841i	$-0.0839999\pi$
$461$	2.11083	+	5.09600i	0.0983113	+	0.237344i	−0.867070	+	0.498185i	$0.834000\pi$
$462$	−47.3387	−	4.49076i	−2.20240	−	0.208929i
$463$	12.5310	−	12.5310i	0.582367	−	0.582367i	−0.353186	−	0.935553i	$-0.614902\pi$
$463$	12.5310	−	12.5310i	0.582367	−	0.582367i	0.935553	+	0.353186i	$0.114902\pi$
$464$	19.7699	+	12.8027i	0.917795	+	0.594350i
$465$	−33.0621	−	12.3230i	−1.53322	−	0.571463i
$466$	−6.61058	+	12.4751i	−0.306229	+	0.577900i
$467$	−10.0201	−	4.15047i	−0.463676	−	0.192061i	0.138601	−	0.990348i	$-0.455740\pi$
$467$	−10.0201	−	4.15047i	−0.463676	−	0.192061i	−0.602277	+	0.798287i	$0.705740\pi$
$468$	8.61951	+	1.65022i	0.398437	+	0.0762816i
$469$	−2.54786	−	1.70242i	−0.117649	−	0.0786106i
$470$	−1.40067	+	5.37318i	−0.0646082	+	0.247846i
$471$	12.7835	−	8.54169i	0.589035	−	0.393580i
$472$	1.69040	+	0.880241i	0.0778069	+	0.0405164i
$473$	−0.982383	+	4.93877i	−0.0451700	+	0.227085i
$474$	7.88620	+	14.6274i	0.362225	+	0.671857i
$475$	31.6237	−	15.8477i	1.45100	−	0.727143i
$476$	−38.1092	−	1.87948i	−1.74673	−	0.0861458i
$477$	15.6422			0.716207
$478$	9.97846	+	18.5081i	0.456404	+	0.846541i
$479$	33.4364	+	6.65092i	1.52775	+	0.303888i	0.886240	−	0.463227i	$-0.153308\pi$
$479$	33.4364	+	6.65092i	1.52775	+	0.303888i	0.641509	+	0.767115i	$0.278308\pi$
$480$	28.8225	−	26.3766i	1.31556	−	1.20392i
$481$	−2.97094	+	1.98512i	−0.135463	+	0.0905137i
$482$	0.238143	+	0.775017i	0.0108471	+	0.0353011i
$483$	53.5363	−	80.1228i	2.43599	−	3.64571i
$484$	−2.05522	+	10.7349i	−0.0934193	+	0.487952i
$485$	−18.1506	−	25.1586i	−0.824178	−	1.14239i
$486$	−13.6418	−	7.22878i	−0.618804	−	0.327904i
$487$	1.81761	−	0.361545i	0.0823638	−	0.0163832i	−0.153736	−	0.988112i	$-0.549131\pi$
$487$	1.81761	−	0.361545i	0.0823638	−	0.0163832i	0.236100	+	0.971729i	$0.424131\pi$
$488$	−7.09316	+	8.83557i	−0.321092	+	0.399967i
$489$	−16.4834	−	16.4834i	−0.745405	−	0.745405i
$490$	−27.4930	+	36.3382i	−1.24201	+	1.64159i
$491$	−4.80286	−	11.5951i	−0.216750	−	0.523281i	0.777682	−	0.628658i	$-0.216395\pi$
$491$	−4.80286	−	11.5951i	−0.216750	−	0.523281i	−0.994432	+	0.105376i	$0.966395\pi$
$492$	−26.0447	+	5.37548i	−1.17419	+	0.242345i
$493$	24.0411	−	3.38508i	1.08275	−	0.152456i
$494$	6.67764	−	0.681927i	0.300441	−	0.0306813i
$495$	5.49603	−	33.9654i	0.247028	−	1.52663i
$496$	−19.9827	+	4.27427i	−0.897251	+	0.191920i
$497$	−8.34775	−	8.34775i	−0.374448	−	0.374448i
$498$	−18.4781	+	15.2760i	−0.828024	+	0.684536i
$499$	−6.39294	−	32.1395i	−0.286187	−	1.43876i	−0.809751	−	0.586774i	$-0.800398\pi$
$499$	−6.39294	−	32.1395i	−0.286187	−	1.43876i	0.523564	−	0.851987i	$-0.324602\pi$
$500$	19.8946	+	10.2081i	0.889713	+	0.456520i
$501$	−20.2971	−	8.40732i	−0.906806	−	0.375611i
$502$	−12.9622	−	3.88124i	−0.578533	−	0.173228i
$503$	−16.8664	+	25.2424i	−0.752036	+	1.12550i	0.236072	+	0.971736i	$0.424140\pi$
$503$	−16.8664	+	25.2424i	−0.752036	+	1.12550i	−0.988107	+	0.153766i	$0.950860\pi$
$504$	−75.0493	+	41.1609i	−3.34296	+	1.83345i
$505$	0.774588	+	21.5505i	0.0344687	+	0.958983i
$506$	17.3924	+	14.1693i	0.773189	+	0.629904i
$507$	7.56238	−	38.0186i	0.335857	−	1.68847i
$508$	−3.41653	−	5.03450i	−0.151584	−	0.223370i
$509$	−5.68733			−0.252087			−0.126043	−	0.992025i	$-0.540228\pi$
$509$	−5.68733			−0.252087			−0.126043	+	0.992025i	$0.540228\pi$
$510$	4.62588	−	40.0058i	0.204837	−	1.77149i
$511$		−	5.68981i		−	0.251703i
$512$	5.86483	−	21.8541i	0.259191	−	0.965826i
$513$	−75.8759	−	15.0926i	−3.35000	−	0.666357i
$514$	−33.0217	−	26.9022i	−1.45653	−	1.18661i
$515$	−0.673912	−	18.7495i	−0.0296961	−	0.826199i
$516$	5.14750	+	12.1789i	0.226606	+	0.536145i
$517$	3.43490	+	2.29513i	0.151067	+	0.100940i
$518$	9.99645	−	33.3853i	0.439219	−	1.46686i
$519$	−4.65204	+	11.2310i	−0.204202	+	0.492987i
$520$	2.84208	+	3.15079i	0.124634	+	0.138171i
$521$	5.48013	−	1.09007i	0.240089	−	0.0477567i	−0.0735790	−	0.997289i	$-0.523442\pi$
$521$	5.48013	−	1.09007i	0.240089	−	0.0477567i	0.313668	+	0.949533i	$0.398442\pi$
$522$	41.9769	−	34.7028i	1.83728	−	1.51890i
$523$	−14.3521	+	14.3521i	−0.627573	+	0.627573i	−0.947457	−	0.319884i	$-0.896356\pi$
$523$	−14.3521	+	14.3521i	−0.627573	+	0.627573i	0.319884	+	0.947457i	$0.396356\pi$
$524$	−7.43237	+	0.0534141i	−0.324685	+	0.00233341i
$525$	−54.0263	−	46.7710i	−2.35790	−	2.04125i
$526$	0.656654	+	6.43016i	0.0286315	+	0.280368i
$527$	−12.6721	+	16.8255i	−0.552004	+	0.732928i
$528$	−11.5084	−	26.6920i	−0.500838	−	1.16162i
$529$	−20.7521	+	8.59579i	−0.902264	+	0.373730i
$530$	6.03128	+	4.56318i	0.261982	+	0.198212i
$531$	3.11625	−	3.11625i	0.135234	−	0.135234i
$532$	−45.9589	+	46.6243i	−1.99257	+	2.02142i
$533$	−0.563465	−	2.83273i	−0.0244064	−	0.122699i
$534$	−16.1703	+	30.5157i	−0.699756	+	1.32054i
$535$	9.37236	−	6.76167i	0.405202	−	0.292332i
$536$	0.163495	−	1.86599i	0.00706190	−	0.0805986i
$537$	−0.207403	−	0.138582i	−0.00895010	−	0.00598026i
$538$	−4.38725	−	14.2779i	−0.189148	−	0.615565i
$539$	18.8342	+	28.1874i	0.811247	+	1.21412i
$540$	−20.6450	−	44.3333i	−0.888417	−	1.90780i
$541$	1.32194	−	6.64586i	0.0568348	−	0.285728i	−0.941907	−	0.335873i	$-0.890969\pi$
$541$	1.32194	−	6.64586i	0.0568348	−	0.285728i	0.998742	+	0.0501457i	$0.0159686\pi$
$542$	−26.6522	+	14.3693i	−1.14481	+	0.617212i
$543$		−	61.9029i		−	2.65651i
$544$	−10.1949	−	20.9777i	−0.437103	−	0.899411i
$545$	27.9399	+	17.2503i	1.19682	+	0.738923i
$546$	−6.43518	−	11.9360i	−0.275400	−	0.510814i
$547$	0.517804	+	0.102998i	0.0221397	+	0.00440386i	0.206148	−	0.978521i	$-0.433907\pi$
$547$	0.517804	+	0.102998i	0.0221397	+	0.00440386i	−0.184008	+	0.982925i	$0.558907\pi$
$548$	30.2597	+	19.9058i	1.29263	+	0.850335i
$549$	14.5562	+	21.7848i	0.621242	+	0.929754i
$550$	12.0276	−	11.4930i	0.512859	−	0.490063i
$551$	23.1434	−	34.6365i	0.985940	−	1.47556i
$552$	58.6801	+	5.14144i	2.49759	+	0.218834i
$553$	6.73626	−	16.2628i	0.286455	−	0.691563i
$554$	6.86627	−	12.9577i	0.291720	−	0.550519i
$555$	34.4670	+	12.8466i	1.46304	+	0.545307i
$556$	27.4832	+	27.0910i	1.16555	+	1.14891i
$557$	7.07083	+	7.07083i	0.299601	+	0.299601i	0.840857	−	0.541257i	$-0.182051\pi$
$557$	7.07083	+	7.07083i	0.299601	+	0.299601i	−0.541257	+	0.840857i	$0.682051\pi$
$558$	−4.46258	+	47.0416i	−0.188916	+	1.99143i
$559$	−1.32668	+	0.549528i	−0.0561125	+	0.0232426i
$560$	−40.9449	−	6.02284i	−1.73024	−	0.254511i
$561$	−26.9899	−	13.0098i	−1.13952	−	0.549274i
$562$	40.4219	−	4.12791i	1.70509	−	0.174126i
$563$	−5.01599	−	12.1097i	−0.211399	−	0.510362i	0.782240	−	0.622978i	$-0.214077\pi$
$563$	−5.01599	−	12.1097i	−0.211399	−	0.510362i	−0.993639	+	0.112615i	$0.964077\pi$
$564$	10.8470	−	0.0779539i	0.456741	−	0.00328245i
$565$	−24.0720	+	5.69416i	−1.01272	+	0.239555i
$566$	−11.5498	−	13.9708i	−0.485476	−	0.587239i
$567$	12.7781	+	64.2397i	0.536629	+	2.69782i
$568$	2.02028	−	6.92794i	0.0847689	−	0.290690i
$569$	5.02147	−	12.1229i	0.210511	−	0.508219i	−0.782991	−	0.622033i	$-0.786307\pi$
$569$	5.02147	−	12.1229i	0.210511	−	0.508219i	0.993502	+	0.113814i	$0.0363069\pi$
$570$	−45.9128	−	51.6413i	−1.92308	−	2.16302i
$571$	6.28432	−	9.40515i	0.262991	−	0.393593i	−0.676349	−	0.736581i	$-0.736439\pi$
$571$	6.28432	−	9.40515i	0.262991	−	0.393593i	0.939340	+	0.342988i	$0.111439\pi$
$572$	2.90781	−	1.22901i	0.121582	−	0.0513875i
$573$	−18.5467	−	27.7570i	−0.774798	−	1.15957i
$574$	21.8396	+	17.7924i	0.911567	+	0.742639i
$575$	8.93389	+	32.5074i	0.372569	+	1.35565i
$576$	−44.1217	−	28.1245i	−1.83840	−	1.17186i
$577$	35.4243			1.47473			0.737366	−	0.675493i	$-0.236069\pi$
$577$	35.4243			1.47473			0.737366	+	0.675493i	$0.236069\pi$
$578$	−22.1075	−	9.44767i	−0.919551	−	0.392971i
$579$	83.0227			3.45031
$580$	26.3089	−	1.13499i	1.09242	−	0.0471279i
$581$	24.9079	+	4.95448i	1.03335	+	0.205546i
$582$	−38.2773	+	46.9843i	−1.58665	+	1.94756i
$583$	4.67844	−	3.12603i	0.193761	−	0.129467i
$584$	3.04954	−	1.67253i	0.126191	−	0.0692097i
$585$	8.92432	−	4.07806i	0.368975	−	0.168607i
$586$	−8.62795	+	28.8149i	−0.356417	+	1.19033i
$587$	3.42440	−	8.26724i	0.141340	−	0.341226i	−0.837319	−	0.546714i	$-0.815878\pi$
$587$	3.42440	−	8.26724i	0.141340	−	0.341226i	0.978659	+	0.205489i	$0.0658784\pi$
$588$	82.4814	+	33.4725i	3.40148	+	1.38038i
$589$	7.05083	+	35.4469i	0.290524	+	1.46056i
$590$	2.11064	−	0.292476i	0.0868936	−	0.0120411i
$591$	−9.43227	+	9.43227i	−0.387992	+	0.387992i
$592$	20.8318	−	4.45589i	0.856183	−	0.183136i
$593$	−20.4753	+	8.48116i	−0.840821	+	0.348280i	−0.761177	−	0.648544i	$-0.775378\pi$
$593$	−20.4753	+	8.48116i	−0.840821	+	0.348280i	−0.0796440	+	0.996823i	$0.525378\pi$
$594$	−36.1957	+	3.69634i	−1.48513	+	0.151663i
$595$	−35.9490	+	22.9668i	−1.47377	+	0.941546i
$596$	−6.89405	−	33.4023i	−0.282391	−	1.36821i
$597$	−44.8187	+	18.5645i	−1.83431	+	0.759796i
$598$	−0.604175	+	6.36882i	−0.0247066	+	0.260441i
$599$	9.05146	+	9.05146i	0.369832	+	0.369832i	0.867416	−	0.497584i	$-0.165779\pi$
$599$	9.05146	+	9.05146i	0.369832	+	0.369832i	−0.497584	+	0.867416i	$0.665779\pi$
$600$	9.18656	−	42.7046i	0.375040	−	1.74341i
$601$	−4.90373	−	24.6527i	−0.200027	−	1.00561i	−0.942112	−	0.335299i	$-0.891163\pi$
$601$	−4.90373	−	24.6527i	−0.200027	−	1.00561i	0.742084	−	0.670306i	$-0.233837\pi$
$602$	6.55778	−	12.3755i	0.267275	−	0.504388i
$603$	−4.00170	−	1.65756i	−0.162962	−	0.0675010i
$604$	−5.11434	+	26.7134i	−0.208099	+	1.08695i
$605$	5.07890	+	11.1146i	0.206487	+	0.451871i
$606$	40.2678	−	12.3733i	1.63577	−	0.502631i
$607$	−20.8307	−	31.1753i	−0.845492	−	1.26537i	−0.962239	−	0.272207i	$-0.912247\pi$
$607$	−20.8307	−	31.1753i	−0.845492	−	1.26537i	0.116747	−	0.993162i	$-0.462753\pi$
$608$	−38.4987	−	10.9271i	−1.56133	−	0.443153i
$609$	−82.5377	−	16.4178i	−3.34459	−	0.665281i
$610$	−0.742595	+	12.6461i	−0.0300668	+	0.512026i
$611$			1.17808i			0.0476599i
$612$	−53.3512	+	7.90349i	−2.15660	+	0.319480i
$613$	18.2924			0.738821			0.369411	−	0.929266i	$-0.379560\pi$
$613$	18.2924			0.738821			0.369411	+	0.929266i	$0.379560\pi$
$614$	18.1111	+	33.5926i	0.730906	+	1.35569i
$615$	−20.2554	+	21.7658i	−0.816777	+	0.877681i
$616$	−14.2207	+	27.3092i	−0.572969	+	1.10032i
$617$	10.0381	+	15.0231i	0.404119	+	0.604806i	0.976588	−	0.215120i	$-0.0690143\pi$
$617$	10.0381	+	15.0231i	0.404119	+	0.604806i	−0.572469	+	0.819926i	$0.694014\pi$
$618$	−35.0341	+	10.7651i	−1.40928	+	0.433035i
$619$	−17.1673	−	11.4709i	−0.690014	−	0.461053i	0.160479	−	0.987039i	$-0.448696\pi$
$619$	−17.1673	−	11.4709i	−0.690014	−	0.461053i	−0.850493	+	0.525987i	$0.823696\pi$
$620$	−15.4438	+	16.8364i	−0.620237	+	0.676165i
$621$	28.2162	−	68.1198i	1.13228	−	2.73355i
$622$	−19.7494	−	10.4652i	−0.791878	−	0.419616i
$623$	35.8791	−	7.13680i	1.43747	−	0.285930i
$624$	4.50566	−	6.95764i	0.180371	−	0.278528i
$625$	24.7423	−	3.58040i	0.989691	−	0.143216i
$626$	3.91925	−	41.3141i	0.156645	−	1.65124i
$627$	−47.4957	+	19.6734i	−1.89680	+	0.785679i
$628$	−2.01229	−	9.74975i	−0.0802991	−	0.389057i
$629$	13.2105	−	17.5404i	0.526739	−	0.699381i
$630$	−41.7423	+	86.1154i	−1.66305	+	3.43092i
$631$	3.60818	+	8.71092i	0.143639	+	0.346776i	0.979283	−	0.202496i	$-0.0649052\pi$
$631$	3.60818	+	8.71092i	0.143639	+	0.346776i	−0.835644	+	0.549272i	$0.814905\pi$
$632$	10.6964	−	1.17006i	0.425480	−	0.0465424i
$633$	28.5989	+	28.5989i	1.13670	+	1.13670i
$634$	14.1904	−	11.7313i	0.563571	−	0.465910i
$635$	−6.37411	−	2.37577i	−0.252949	−	0.0942794i
$636$	5.55564	−	13.6899i	0.220295	−	0.542842i
$637$	−3.69959	+	8.93160i	−0.146583	+	0.353883i
$638$	5.61971	−	18.7682i	0.222486	−	0.743041i
$639$	−13.8750	−	9.27095i	−0.548885	−	0.366753i
$640$	−8.80776	−	23.7155i	−0.348157	−	0.937436i
$641$	−13.4708	−	20.1605i	−0.532064	−	0.796290i	0.463915	−	0.885880i	$-0.346444\pi$
$641$	−13.4708	−	20.1605i	−0.532064	−	0.796290i	−0.995979	+	0.0895896i	$0.971444\pi$
$642$	−17.5031	−	14.2595i	−0.690792	−	0.562776i
$643$	3.81347	−	19.1716i	0.150388	−	0.756054i	−0.829812	−	0.558044i	$-0.811552\pi$
$643$	3.81347	−	19.1716i	0.150388	−	0.756054i	0.980200	−	0.198010i	$-0.0634479\pi$
$644$	−35.0373	−	51.6299i	−1.38066	−	2.03450i
$645$	12.5784	+	7.76600i	0.495274	+	0.305786i
$646$	−37.3569	+	17.4958i	−1.46979	+	0.688365i
$647$	31.9601			1.25648			0.628241	−	0.778018i	$-0.283775\pi$
$647$	31.9601			1.25648			0.628241	+	0.778018i	$0.283775\pi$
$648$	−30.6742	+	25.7320i	−1.20499	+	1.01085i
$649$	0.309272	−	1.55482i	0.0121400	−	0.0610318i
$650$	4.63068	+	1.03102i	0.181630	+	0.0404398i
$651$	60.7074	−	40.5634i	2.37931	−	1.58980i
$652$	−13.9033	+	5.87635i	−0.544495	+	0.230136i
$653$	32.2102	+	21.5222i	1.26048	+	0.842228i	0.992624	−	0.121230i	$-0.0386838\pi$
$653$	32.2102	+	21.5222i	1.26048	+	0.842228i	0.267859	+	0.963458i	$0.413684\pi$
$654$	18.3997	−	61.4498i	0.719487	−	2.40288i
$655$	−6.73910	+	4.86191i	−0.263319	+	0.189971i
$656$	−3.11631	+	16.9354i	−0.121672	+	0.661215i
$657$	−1.56904	−	7.88811i	−0.0612142	−	0.307744i
$658$	−7.32114	−	8.85575i	−0.285408	−	0.345233i
$659$	−13.6422	−	13.6422i	−0.531424	−	0.531424i	0.389572	−	0.920996i	$-0.372623\pi$
$659$	−13.6422	−	13.6422i	−0.531424	−	0.531424i	−0.920996	+	0.389572i	$0.872623\pi$
$660$	−27.7743	−	16.8736i	−1.08111	−	0.656804i
$661$	19.3537	−	8.01657i	0.752772	−	0.311808i	0.0269000	−	0.999638i	$-0.491436\pi$
$661$	19.3537	−	8.01657i	0.752772	−	0.311808i	0.725872	+	0.687830i	$0.241436\pi$
$662$	1.38002	+	13.5136i	0.0536359	+	0.525220i
$663$	−1.19131	−	8.46078i	−0.0462668	−	0.328590i
$664$	4.66626	+	14.8061i	0.181086	+	0.574589i
$665$	−11.6918	+	72.2555i	−0.453390	+	2.80195i
$666$	4.65221	−	49.0405i	0.180269	−	1.90028i
$667$	28.0738	+	28.0738i	1.08702	+	1.08702i
$668$	−9.98633	+	10.1309i	−0.386383	+	0.391977i
$669$	26.8801	−	5.34679i	1.03924	−	0.206719i
$670$	−1.05942	−	1.80650i	−0.0409289	−	0.0697913i
$671$	8.70723	+	3.60665i	0.336139	+	0.139233i
$672$	9.36851	+	80.3018i	0.361398	+	3.09771i
$673$	33.9787	+	22.7038i	1.30978	+	0.875169i	0.997204	−	0.0747236i	$-0.0238074\pi$
$673$	33.9787	+	22.7038i	1.30978	+	0.875169i	0.312578	+	0.949892i	$0.398807\pi$
$674$	3.23575	+	10.5305i	0.124636	+	0.405619i
$675$	−47.5258	−	27.0346i	−1.82927	−	1.04056i
$676$	−20.9694	−	13.7943i	−0.806514	−	0.530551i
$677$	−32.5951	−	6.48358i	−1.25273	−	0.249184i	−0.476243	−	0.879314i	$-0.658002\pi$
$677$	−32.5951	−	6.48358i	−1.25273	−	0.249184i	−0.776490	+	0.630130i	$0.783002\pi$
$678$	22.9320	+	42.5344i	0.880699	+	1.63353i
$679$	64.1942			2.46355
$680$	−22.8767	−	12.5163i	−0.877280	−	0.479980i
$681$	−49.2345			−1.88667
$682$	8.06638	+	14.9616i	0.308877	+	0.572908i
$683$	40.1356	+	7.98347i	1.53575	+	0.305479i	0.889244	−	0.457433i	$-0.151231\pi$
$683$	40.1356	+	7.98347i	1.53575	+	0.305479i	0.646503	+	0.762912i	$0.276231\pi$
$684$	−50.8581	+	77.3116i	−1.94461	+	2.95608i
$685$	40.4691	−	1.45458i	1.54625	−	0.0555767i
$686$	−14.2410	−	46.3461i	−0.543724	−	1.76950i
$687$	32.1456	+	21.4790i	1.22643	+	0.819476i
$688$	8.56051	−	0.123050i	0.326366	−	0.00469123i
$689$	1.48243	+	0.614044i	0.0564762	+	0.0233932i
$690$	56.8094	−	33.3157i	2.16270	−	1.26831i
$691$	−43.5640	+	8.66542i	−1.65725	+	0.329648i	−0.932997	−	0.359884i	$-0.882816\pi$
$691$	−43.5640	+	8.66542i	−1.65725	+	0.329648i	−0.724255	+	0.689532i	$0.757816\pi$
$692$	5.60576	+	5.52576i	0.213099	+	0.210058i
$693$	50.3445	+	50.3445i	1.91243	+	1.91243i
$694$	1.84182	−	19.4153i	0.0699145	−	0.736993i
$695$	42.5917	+	6.89188i	1.61560	+	0.261424i
$696$	−15.4627	−	49.0634i	−0.586112	−	1.85974i
$697$	9.01258	+	15.2913i	0.341376	+	0.579199i
$698$	0.588099	+	5.75886i	0.0222599	+	0.217976i
$699$	28.4884	−	11.8003i	1.07753	−	0.446328i
$700$	−41.2167	+	21.0270i	−1.55784	+	0.794746i
$701$	24.9507	+	24.9507i	0.942374	+	0.942374i	0.998428	−	0.0560536i	$-0.0178518\pi$
$701$	24.9507	+	24.9507i	0.942374	+	0.942374i	−0.0560536	+	0.998428i	$0.517852\pi$
$702$	−6.61102	−	7.99678i	−0.249517	−	0.301819i
$703$	−7.35043	−	36.9531i	−0.277227	−	1.39371i
$704$	−18.8170	+	0.405751i	−0.709191	+	0.0152923i
$705$	9.83522	−	7.09560i	0.370416	−	0.267236i
$706$	2.94140	−	9.82344i	0.110701	−	0.369710i
$707$	−37.1023	−	24.7910i	−1.39538	−	0.932361i
$708$	−1.62053	−	3.83413i	−0.0609031	−	0.144095i
$709$	40.1803	−	26.8476i	1.50900	−	1.00828i	0.521051	−	0.853525i	$-0.325540\pi$
$709$	40.1803	−	26.8476i	1.50900	−	1.00828i	0.987952	−	0.154758i	$-0.0494599\pi$
$710$	−2.64533	−	7.62231i	−0.0992774	−	0.286060i
$711$	4.85418	−	24.4036i	0.182046	−	0.915206i
$712$	14.3718	+	17.1321i	0.538606	+	0.642053i
$713$	−34.4455			−1.29000
$714$	61.5347	+	56.1974i	2.30288	+	2.10313i
$715$	1.85420	−	3.00320i	0.0693432	−	0.112313i
$716$	−0.133647	+	0.0906962i	−0.00499463	+	0.00338948i
$717$	8.95930	−	45.0414i	0.334591	−	1.68210i
$718$	−1.45683	−	1.18685i	−0.0543684	−	0.0442930i
$719$	−11.4596	−	17.1506i	−0.427373	−	0.639609i	0.553821	−	0.832636i	$-0.313169\pi$
$719$	−11.4596	−	17.1506i	−0.427373	−	0.639609i	−0.981193	+	0.193027i	$0.938169\pi$
$720$	−58.4251	+	2.94130i	−2.17737	+	0.109616i
$721$	32.2800	+	21.5688i	1.20217	+	0.803264i
$722$	−12.5951	+	42.0639i	−0.468740	+	1.56546i
$723$	0.677658	−	1.63601i	0.0252024	−	0.0608439i
$724$	−37.1409	−	15.0725i	−1.38033	−	0.560164i
$725$	23.2424	−	18.0722i	0.863199	−	0.671184i
$726$	18.3986	−	15.2103i	0.682835	−	0.564507i
$727$	−11.6539	−	11.6539i	−0.432220	−	0.432220i	0.457163	−	0.889383i	$-0.348866\pi$
$727$	−11.6539	−	11.6539i	−0.432220	−	0.432220i	−0.889383	+	0.457163i	$0.848866\pi$
$728$	−8.72833	+	0.954772i	−0.323493	+	0.0353862i
$729$	−3.34745	−	8.08147i	−0.123980	−	0.299314i
$730$	1.69615	−	3.49920i	0.0627773	−	0.129511i
$731$	6.58235	−	5.87803i	0.243457	−	0.217407i
$732$	24.2359	−	5.00214i	0.895783	−	0.184884i
$733$	18.1974	−	7.53760i	0.672136	−	0.278408i	−0.0203994	−	0.999792i	$-0.506494\pi$
$733$	18.1974	−	7.53760i	0.672136	−	0.278408i	0.692535	+	0.721384i	$0.256494\pi$
$734$	1.03305	−	10.8898i	0.0381307	−	0.401949i
$735$	96.8486	−	22.9092i	3.57232	−	0.845019i
$736$	17.3726	−	33.9555i	0.640362	−	1.25161i
$737$	−1.52813	+	0.303964i	−0.0562894	+	0.0111967i
$738$	35.1839	+	18.6440i	1.29514	+	0.686294i
$739$	−14.7461	+	35.6002i	−0.542443	+	1.30957i	0.380551	+	0.924760i	$0.375734\pi$
$739$	−14.7461	+	35.6002i	−0.542443	+	1.30957i	−0.922994	+	0.384814i	$0.874266\pi$
$740$	16.1000	−	17.5518i	0.591848	−	0.645216i
$741$	−12.1896	−	8.14485i	−0.447797	−	0.299209i
$742$	−14.9596	+	4.59671i	−0.549184	+	0.168751i
$743$	9.70475	+	14.5242i	0.356033	+	0.532841i	0.965647	−	0.259858i	$-0.0836756\pi$
$743$	9.70475	+	14.5242i	0.356033	+	0.532841i	−0.609614	+	0.792698i	$0.708676\pi$
$744$	39.5856	+	20.6134i	1.45128	+	0.755725i
$745$	−27.9146	−	25.9775i	−1.02271	−	0.951743i
$746$	16.3201	+	30.2706i	0.597521	+	1.10829i
$747$	35.8974			1.31342
$748$	−14.3774	+	13.0259i	−0.525689	+	0.476274i
$749$			23.9143i			0.873811i
$750$	−19.2833	−	44.8693i	−0.704126	−	1.63839i
$751$	−39.1835	−	7.79408i	−1.42983	−	0.284410i	−0.581354	−	0.813650i	$-0.697477\pi$
$751$	−39.1835	−	7.79408i	−1.42983	−	0.284410i	−0.848472	+	0.529240i	$0.822477\pi$
$752$	2.59432	−	6.52704i	0.0946051	−	0.238017i
$753$	16.4184	+	24.5719i	0.598321	+	0.895451i
$754$	5.34049	−	1.64100i	0.194489	−	0.0597617i
$755$	12.6386	+	27.6581i	0.459967	+	1.00658i
$756$	99.3918	+	19.0288i	3.61484	+	0.692069i
$757$	11.2462	+	4.65834i	0.408751	+	0.169310i	0.577578	−	0.816335i	$-0.303998\pi$
$757$	11.2462	+	4.65834i	0.408751	+	0.169310i	−0.168827	+	0.985646i	$0.553998\pi$
$758$	−17.4131	+	32.8612i	−0.632473	+	1.19357i
$759$	−9.55880	−	48.0553i	−0.346962	−	1.74430i
$760$	−42.1633	+	14.9732i	−1.52942	+	0.543134i
$761$	24.8892	+	24.8892i	0.902231	+	0.902231i	0.995629	−	0.0933975i	$-0.0297727\pi$
$761$	24.8892	+	24.8892i	0.902231	+	0.902231i	−0.0933975	+	0.995629i	$0.529773\pi$
$762$	−1.25498	+	13.2292i	−0.0454632	+	0.479244i
$763$	−62.7749	+	26.0022i	−2.27260	+	0.941343i
$764$	−21.1697	+	4.36930i	−0.765893	+	0.158076i
$765$	−43.5048	+	41.7535i	−1.57292	+	1.50960i
$766$	−19.4513	+	1.98638i	−0.702803	+	0.0717708i
$767$	0.417662	−	0.173001i	0.0150809	−	0.00624672i
$768$	−40.2851	+	28.6260i	−1.45366	+	1.03295i
$769$	5.65391	−	5.65391i	0.203885	−	0.203885i	−0.597777	−	0.801662i	$-0.703949\pi$
$769$	5.65391	−	5.65391i	0.203885	−	0.203885i	0.801662	+	0.597777i	$0.203949\pi$
$770$	4.72509	+	34.0984i	0.170281	+	1.22882i
$771$	18.1486	+	91.2390i	0.653604	+	3.28589i
$772$	20.2149	−	49.8126i	0.727549	−	1.79279i
$773$	−15.4563	+	37.3149i	−0.555925	+	1.34212i	0.357042	+	0.934089i	$0.383785\pi$
$773$	−15.4563	+	37.3149i	−0.555925	+	1.34212i	−0.912967	+	0.408034i	$0.866215\pi$
$774$	5.67871	−	18.9652i	0.204117	−	0.681692i
$775$	−3.17181	+	25.3457i	−0.113935	+	0.910446i
$776$	18.8700	+	34.4059i	0.677393	+	1.23510i
$777$	−63.2870	+	42.2870i	−2.27041	+	1.51704i
$778$	27.2026	−	33.3904i	0.975260	−	1.19710i
$779$	29.8700	+	5.94150i	1.07020	+	0.212876i
$780$	−0.399437	−	9.25892i	−0.0143022	−	0.331522i
$781$	−6.00264			−0.214791
$782$	−9.40848	−	38.1731i	−0.336447	−	1.36507i
$783$	−64.3912			−2.30115
$784$	40.1662	−	41.3377i	1.43451	−	1.47635i
$785$	−8.14793	−	7.58253i	−0.290812	−	0.270632i
$786$	12.5854	+	10.2531i	0.448907	+	0.365717i
$787$	9.12912	+	13.6627i	0.325418	+	0.487022i	0.957721	−	0.287699i	$-0.0928902\pi$
$787$	9.12912	+	13.6627i	0.325418	+	0.487022i	−0.632303	+	0.774721i	$0.717890\pi$
$788$	3.36261	+	7.95587i	0.119788	+	0.283416i
$789$	7.84300	−	11.7379i	0.279218	−	0.417879i
$790$	8.99073	−	7.99340i	0.319876	−	0.284392i
$791$	19.5881	−	47.2899i	0.696474	−	1.68144i
$792$	−12.1841	+	41.7818i	−0.432943	+	1.48465i
$793$	0.524331	+	2.63599i	0.0186195	+	0.0936068i
$794$	−26.8447	−	32.4717i	−0.952683	−	1.15238i
$795$	−3.80238	−	16.0746i	−0.134857	−	0.570106i
$796$	0.225740	+	31.4109i	0.00800114	+	1.11333i
$797$	16.2731	+	39.2868i	0.576424	+	1.39161i	0.896002	+	0.444050i	$0.146459\pi$
$797$	16.2731	+	39.2868i	0.576424	+	1.39161i	−0.319578	+	0.947560i	$0.603541\pi$
$798$	142.247	−	14.5264i	5.03549	−	0.514229i
$799$	−2.38869	−	6.83448i	−0.0845058	−	0.241787i
$800$	−23.3854	−	15.9098i	−0.826800	−	0.562496i
$801$	47.7732	−	19.7883i	1.68798	−	0.699185i
$802$	0.235489	−	2.48237i	0.00831539	−	0.0876554i
$803$	−2.04569	−	2.04569i	−0.0721910	−	0.0721910i
$804$	−2.87197	+	2.91355i	−0.101287	+	0.102753i
$805$	−65.3679	−	24.3640i	−2.30392	−	0.858719i
$806$	−2.26957	+	4.28302i	−0.0799423	+	0.150863i
$807$	−12.4843	+	30.1398i	−0.439469	+	1.06097i
$808$	2.38084	−	27.1729i	0.0837576	−	0.955940i
$809$	−7.20992	+	10.7904i	−0.253487	+	0.379371i	−0.936287	−	0.351235i	$-0.885762\pi$
$809$	−7.20992	+	10.7904i	−0.253487	+	0.379371i	0.682800	+	0.730605i	$0.260762\pi$
$810$	−11.2916	+	43.3162i	−0.396747	+	1.52198i
$811$	0.282462	+	0.422734i	0.00991857	+	0.0148442i	0.836396	−	0.548126i	$-0.184659\pi$
$811$	0.282462	+	0.422734i	0.00991857	+	0.0148442i	−0.826477	+	0.562970i	$0.809659\pi$
$812$	−29.9472	+	45.5240i	−1.05094	+	1.59758i
$813$	64.8608	+	12.9016i	2.27477	+	0.452480i
$814$	−8.40913	−	15.5973i	−0.294740	−	0.546685i
$815$	−8.86561	+	14.3594i	−0.310549	+	0.502988i
$816$	−12.0317	+	49.4998i	−0.421193	+	1.73284i
$817$		−	15.1419i		−	0.529747i
$818$	−25.5050	+	13.7507i	−0.891760	+	0.480784i
$819$	−3.96103	+	19.9135i	−0.138410	+	0.695832i
$820$	8.12727	+	17.4526i	0.283817	+	0.609473i
$821$	11.8178	+	17.6866i	0.412444	+	0.617267i	0.978289	−	0.207245i	$-0.0664498\pi$
$821$	11.8178	+	17.6866i	0.412444	+	0.617267i	−0.565845	+	0.824512i	$0.691450\pi$
$822$	−23.2355	−	75.6181i	−0.810433	−	2.63748i
$823$	−30.9347	−	20.6699i	−1.07832	−	0.720507i	−0.116221	−	0.993223i	$-0.537078\pi$
$823$	−30.9347	−	20.6699i	−1.07832	−	0.720507i	−0.962095	+	0.272716i	$0.912078\pi$
$824$	−2.07139	+	23.6411i	−0.0721603	+	0.823578i
$825$	−36.2403	+	2.60854i	−1.26173	+	0.0908177i
$826$	−2.06451	+	3.89603i	−0.0718334	+	0.135560i
$827$	−8.42546	−	42.3576i	−0.292982	−	1.47292i	−0.794231	−	0.607616i	$-0.792126\pi$
$827$	−8.42546	−	42.3576i	−0.292982	−	1.47292i	0.501249	−	0.865303i	$-0.332874\pi$
$828$	−62.8118	−	61.9154i	−2.18286	−	2.15171i
$829$	−25.1539	+	25.1539i	−0.873632	+	0.873632i	−0.992866	−	0.119234i	$-0.961956\pi$
$829$	−25.1539	+	25.1539i	−0.873632	+	0.873632i	0.119234	+	0.992866i	$0.461956\pi$
$830$	13.8412	+	10.4721i	0.480436	+	0.363491i
$831$	−29.5904	+	12.2567i	−1.02648	+	0.425181i
$832$	−3.07743	−	4.39743i	−0.106691	−	0.152453i
$833$	3.35290	−	59.3171i	0.116171	−	2.05521i
$834$	−8.56274	−	83.8491i	−0.296503	−	2.90346i
$835$	−2.54050	+	15.7003i	−0.0879176	+	0.543330i
$836$	0.239223	+	33.2870i	0.00827371	+	1.15125i
$837$	39.5029	−	39.5029i	1.36542	−	1.36542i
$838$	23.3880	−	19.3351i	0.807926	−	0.667921i
$839$	−32.7696	+	6.51827i	−1.13133	+	0.225036i	−0.725039	−	0.688707i	$-0.758178\pi$
$839$	−32.7696	+	6.51827i	−1.13133	+	0.225036i	−0.406292	+	0.913743i	$0.633178\pi$
$840$	60.5420	+	67.1182i	2.08890	+	2.31580i
$841$	2.17074	−	5.24064i	0.0748532	−	0.180712i
$842$	3.58260	−	11.9648i	0.123465	−	0.412336i
$843$	−73.7876	−	49.3033i	−2.54138	−	1.69810i
$844$	24.1224	−	10.1955i	0.830327	−	0.350945i
$845$	−28.0443	+	1.00800i	−0.964752	+	0.0346761i
$846$	−12.5918	−	10.2583i	−0.432915	−	0.352688i
$847$	−24.8007	−	4.93316i	−0.852161	−	0.169505i
$848$	−6.86107	−	6.66662i	−0.235610	−	0.228933i
$849$			39.5905i			1.35874i
$850$	−28.9549	+	3.40791i	−0.993145	+	0.116890i
$851$	35.9092			1.23095
$852$	−13.0419	+	8.85052i	−0.446807	+	0.303214i
$853$	4.54863	−	22.8675i	0.155742	−	0.782969i	−0.821395	−	0.570360i	$-0.806804\pi$
$853$	4.54863	−	22.8675i	0.155742	−	0.782969i	0.977137	−	0.212609i	$-0.0681962\pi$
$854$	−20.3228	−	16.5566i	−0.695432	−	0.566556i
$855$	3.71636	+	103.396i	0.127097	+	3.53607i
$856$	−12.8173	+	7.02965i	−0.438085	+	0.240268i
$857$	14.7329	−	22.0493i	0.503265	−	0.753189i	−0.489663	−	0.871912i	$-0.662880\pi$
$857$	14.7329	−	22.0493i	0.503265	−	0.753189i	0.992927	+	0.118723i	$0.0378800\pi$
$858$	−6.60511	−	1.97775i	−0.225495	−	0.0675192i
$859$	−25.9168	−	10.7351i	−0.884270	−	0.366277i	−0.106119	−	0.994353i	$-0.533842\pi$
$859$	−25.9168	−	10.7351i	−0.884270	−	0.366277i	−0.778151	+	0.628077i	$0.783842\pi$
$860$	7.72217	−	5.65597i	0.263324	−	0.192867i
$861$	−12.0029	−	60.3428i	−0.409059	−	2.05648i
$862$	8.52011	−	7.04366i	0.290196	−	0.239908i
$863$	18.4466	+	18.4466i	0.627928	+	0.627928i	0.947546	−	0.319618i	$-0.103555\pi$
$863$	18.4466	+	18.4466i	0.627928	+	0.627928i	−0.319618	+	0.947546i	$0.603555\pi$
$864$	19.0176	+	58.8641i	0.646991	+	2.00260i
$865$	8.68747	+	1.40574i	0.295383	+	0.0477966i
$866$	−23.8949	+	2.44017i	−0.811982	+	0.0829202i
$867$	24.0665	+	46.6688i	0.817342	+	1.58496i
$868$	−9.55610	−	46.3003i	−0.324355	−	1.57153i
$869$	−3.42512	−	8.26898i	−0.116189	−	0.280506i
$870$	−45.8660	−	34.7015i	−1.55500	−	1.17649i
$871$	−0.314179	−	0.314179i	−0.0106455	−	0.0106455i
$872$	−32.3890	−	26.0018i	−1.09683	−	0.880532i
$873$	88.9961	−	17.7024i	3.01206	−	0.599136i
$874$	−59.6066	−	31.5855i	−2.01622	−	1.06840i
$875$	−23.9468	+	45.8556i	−0.809548	+	1.55020i
$876$	−7.46090	−	1.42840i	−0.252080	−	0.0482613i
$877$	13.3258	−	19.9435i	0.449980	−	0.673443i	−0.535247	−	0.844696i	$-0.679781\pi$
$877$	13.3258	−	19.9435i	0.449980	−	0.673443i	0.985227	+	0.171253i	$0.0547814\pi$
$878$	1.26265	+	4.10919i	0.0426124	+	0.138679i
$879$	54.6231	−	36.4980i	1.84239	−	1.23105i
$880$	−16.8866	+	12.5557i	−0.569247	+	0.423254i
$881$	−44.7081	−	8.89300i	−1.50625	−	0.299613i	−0.628154	−	0.778089i	$-0.716189\pi$
$881$	−44.7081	−	8.89300i	−1.50625	−	0.299613i	−0.878101	+	0.478476i	$0.841189\pi$
$882$	−63.2500	−	117.316i	−2.12974	−	3.95025i
$883$	−27.6490			−0.930462			−0.465231	−	0.885189i	$-0.654029\pi$
$883$	−27.6490			−0.930462			−0.465231	+	0.885189i	$0.654029\pi$
$884$	−5.36643	−	1.34531i	−0.180493	−	0.0452476i
$885$	−3.95991	−	2.44488i	−0.133111	−	0.0821837i
$886$	−24.5624	−	45.5585i	−0.825190	−	1.53057i
$887$	5.71744	−	28.7435i	0.191973	−	0.965113i	−0.757875	−	0.652400i	$-0.773762\pi$
$887$	5.71744	−	28.7435i	0.191973	−	0.965113i	0.949848	−	0.312713i	$-0.101238\pi$
$888$	−41.2677	−	21.4893i	−1.38485	−	0.721134i
$889$	11.7039	−	7.82030i	0.392536	−	0.262284i
$890$	24.1929	+	6.30658i	0.810949	+	0.211397i
$891$	27.6907	+	18.5023i	0.927673	+	0.619852i
$892$	3.33693	−	17.4296i	0.111729	−	0.583586i
$893$	−11.4767	−	4.75382i	−0.384054	−	0.159080i
$894$	−34.8785	+	65.8209i	−1.16651	+	2.20138i
$895$	−0.0630678	+	0.169209i	−0.00210813	+	0.00565603i
$896$	50.4612	+	13.9314i	1.68579	+	0.465415i
$897$	9.88002	−	9.88002i	0.329884	−	0.329884i
$898$	44.0815	+	4.18177i	1.47102	+	0.139548i
$899$	11.5117	+	27.7918i	0.383938	+	0.926908i
$900$	−51.3425	+	40.5169i	−1.71142	+	1.35056i
$901$	−9.84522	−	0.556501i	−0.327992	−	0.0185397i
$902$	14.2491	−	1.45513i	0.474444	−	0.0484506i
$903$	−28.2609	+	11.7060i	−0.940464	+	0.389553i
$904$	31.1037	−	3.40237i	1.03449	−	0.113161i
$905$	−43.6104	+	10.3159i	−1.44966	+	0.342912i
$906$	45.7841	−	37.8501i	1.52107	−	1.25749i
$907$	−17.4275	+	3.46654i	−0.578669	+	0.115104i	−0.475743	−	0.879584i	$-0.657821\pi$
$907$	−17.4275	+	3.46654i	−0.578669	+	0.115104i	−0.102927	+	0.994689i	$0.532821\pi$
$908$	−11.9879	+	29.5401i	−0.397833	+	0.980322i
$909$	−58.2735	−	24.1377i	−1.93281	−	0.800596i
$910$	−7.33649	+	6.52266i	−0.243202	+	0.216224i
$911$	−18.7799	−	12.5483i	−0.622205	−	0.415744i	0.204114	−	0.978947i	$-0.434569\pi$
$911$	−18.7799	−	12.5483i	−0.622205	−	0.415744i	−0.826318	+	0.563203i	$0.809569\pi$
$912$	49.5994	+	71.9695i	1.64240	+	2.38315i
$913$	10.7366	−	7.17396i	0.355329	−	0.237424i
$914$	1.86321	−	2.28704i	0.0616296	−	0.0756486i
$915$	18.8486	−	20.2541i	0.623116	−	0.669579i
$916$	20.7142	−	14.0571i	0.684415	−	0.464461i
$917$		−	17.1954i		−	0.567841i
$918$	54.5676	+	32.9879i	1.80100	+	1.08876i
$919$		−	7.45779i		−	0.246010i	−0.992406	−	0.123005i	$-0.960747\pi$
$919$		−	7.45779i		−	0.246010i	0.992406	−	0.123005i	$-0.0392531\pi$
$920$	−6.15670	−	42.1968i	−0.202980	−	1.39119i
$921$	16.2613	−	81.7512i	0.535829	−	2.69379i
$922$	−6.04770	−	4.92696i	−0.199171	−	0.162261i
$923$	−0.951013	−	1.42329i	−0.0313030	−	0.0468482i
$924$	61.9421	−	26.1804i	2.03775	−	0.861271i
$925$	3.30658	−	26.4227i	0.108720	−	0.868774i
$926$	−7.18892	+	24.0089i	−0.236242	+	0.788982i
$927$	50.6994	+	21.0004i	1.66519	+	0.689743i
$928$	−33.2023	−	2.66883i	−1.08992	−	0.0876087i
$929$	43.8254	−	8.71741i	1.43786	−	0.286009i	0.586230	−	0.810145i	$-0.300612\pi$
$929$	43.8254	−	8.71741i	1.43786	−	0.286009i	0.851635	+	0.524136i	$0.175612\pi$
$930$	49.4267	−	6.84919i	1.62077	−	0.224594i
$931$	−72.0822	−	72.0822i	−2.36240	−	2.36240i
$932$	−0.143489	−	19.9659i	−0.00470013	−	0.654005i
$933$	18.6810	+	45.1000i	0.611590	+	1.47651i
$934$	15.2588	−	1.55824i	0.499283	−	0.0509872i
$935$	−4.66760	+	21.1824i	−0.152647	+	0.692737i
$936$	−11.8373	+	3.73061i	−0.386913	+	0.121939i
$937$	−12.2093	−	29.4759i	−0.398862	−	0.962937i	−0.987937	−	0.154859i	$-0.950508\pi$
$937$	−12.2093	−	29.4759i	−0.398862	−	0.962937i	0.589075	−	0.808078i	$-0.299492\pi$
$938$	4.31418	+	0.409263i	0.140863	+	0.0133629i
$939$	−64.0910	+	64.0910i	−2.09153	+	2.09153i
$940$	−1.86253	−	7.62869i	−0.0607491	−	0.248820i
$941$	53.0362	−	10.5495i	1.72893	−	0.343905i	0.772310	−	0.635246i	$-0.219101\pi$
$941$	53.0362	−	10.5495i	1.72893	−	0.343905i	0.956619	+	0.291341i	$0.0941013\pi$
$942$	−10.1806	+	19.2123i	−0.331703	+	0.625972i
$943$	−11.1078	+	26.8166i	−0.361720	+	0.873270i
$944$	−2.69500	+	0.0387383i	−0.0877149	+	0.00126082i
$945$	102.907	−	47.0242i	3.34755	−	1.52970i
$946$	−2.09168	−	6.80720i	−0.0680065	−	0.221321i
$947$	3.39667	−	2.26958i	0.110377	−	0.0737515i	−0.499157	−	0.866512i	$-0.666357\pi$
$947$	3.39667	−	2.26958i	0.110377	−	0.0737515i	0.609534	+	0.792760i	$0.291357\pi$
$948$	−19.6338	−	12.9158i	−0.637677	−	0.419485i
$949$	0.160952	−	0.809161i	0.00522473	−	0.0262665i
$950$	−28.7300	+	40.9513i	−0.932123	+	1.32864i
$951$	−40.2126			−1.30398
$952$	48.7005	−	23.2367i	1.57839	−	0.753107i
$953$		−	12.3069i		−	0.398660i	−0.979932	−	0.199330i	$-0.936123\pi$
$953$		−	12.3069i		−	0.398660i	0.979932	−	0.199330i	$-0.0638766\pi$
$954$	−19.4717	+	10.4980i	−0.630421	+	0.339885i
$955$	−16.4640	+	17.6917i	−0.532763	+	0.572489i
$956$	−24.8428	−	16.3424i	−0.803474	−	0.528552i
$957$	−35.5781	+	23.7725i	−1.15008	+	0.768456i
$958$	−46.0860	+	14.1611i	−1.48897	+	0.457524i
$959$	−46.5544	+	69.6736i	−1.50332	+	2.24988i
$960$	−18.1766	+	52.1779i	−0.586648	+	1.68404i
$961$	4.52824	+	1.87566i	0.146072	+	0.0605052i
$962$	2.36601	−	4.46502i	0.0762833	−	0.143958i
$963$	6.59470	+	33.1538i	0.212511	+	1.06837i
$964$	−0.816585	−	0.804932i	−0.0263004	−	0.0259251i
$965$	−13.8354	−	58.4893i	−0.445378	−	1.88284i
$966$	−12.8701	+	135.669i	−0.414090	+	4.36507i
$967$	−22.2182	−	53.6396i	−0.714491	−	1.72493i	−0.688463	−	0.725272i	$-0.741714\pi$
$967$	−22.2182	−	53.6396i	−0.714491	−	1.72493i	−0.0260278	−	0.999661i	$-0.508286\pi$
$968$	−4.64618	−	14.7424i	−0.149334	−	0.473839i
$969$	87.2315	+	22.5356i	2.80228	+	0.723947i
$970$	39.4791	+	19.1365i	1.26760	+	0.614436i
$971$	18.4211	−	7.63026i	0.591160	−	0.244867i	−0.0669895	−	0.997754i	$-0.521339\pi$
$971$	18.4211	−	7.63026i	0.591160	−	0.244867i	0.658150	+	0.752887i	$0.271339\pi$
$972$	21.8331	−	0.156907i	0.700296	−	0.00503281i
$973$	−63.1307	+	63.1307i	−2.02388	+	2.02388i
$974$	−2.01996	+	1.66992i	−0.0647236	+	0.0535076i
$975$	−6.36015	−	8.17969i	−0.203688	−	0.261960i
$976$	2.89988	−	15.7592i	0.0928228	−	0.504438i
$977$	−18.1960	−	7.53703i	−0.582141	−	0.241131i	0.0721243	−	0.997396i	$-0.477022\pi$
$977$	−18.1960	−	7.53703i	−0.582141	−	0.241131i	−0.654266	+	0.756265i	$0.727022\pi$
$978$	31.5814	+	9.45633i	1.00986	+	0.302380i
$979$	10.3339	−	15.4658i	0.330273	−	0.494289i
$980$	9.83606	−	63.6860i	0.314201	−	2.03438i
$981$	−79.8579	+	53.3593i	−2.54967	+	1.70363i
$982$	13.7606	+	11.2105i	0.439118	+	0.357742i
$983$	22.6886	+	4.51305i	0.723655	+	0.143944i	0.543157	−	0.839631i	$-0.317229\pi$
$983$	22.6886	+	4.51305i	0.723655	+	0.143944i	0.180498	+	0.983575i	$0.442229\pi$
$984$	28.8134	−	24.1710i	0.918537	−	0.770543i
$985$	8.21686	+	5.07316i	0.261811	+	0.161644i
$986$	−27.6550	+	20.3486i	−0.880714	+	0.648031i
$987$			25.0954i			0.798794i
$988$	−7.85481	+	5.33046i	−0.249895	+	0.169585i
$989$	14.1541	+	2.81542i	0.450074	+	0.0895253i
$990$	15.9537	+	45.9695i	0.507043	+	1.46101i
$991$	20.1923	+	30.2199i	0.641429	+	0.959967i	0.999653	+	0.0263313i	$0.00838247\pi$
$991$	20.1923	+	30.2199i	0.641429	+	0.959967i	−0.358224	+	0.933636i	$0.616618\pi$
$992$	22.0063	−	18.7318i	0.698701	−	0.594734i
$993$	16.4828	−	24.6682i	0.523065	−	0.782821i
$994$	15.9939	+	4.78901i	0.507296	+	0.151898i
$995$	20.5475	+	28.4810i	0.651401	+	0.902907i
$996$	12.7497	−	31.4172i	0.403990	−	0.995492i
$997$	28.0244	−	5.57440i	0.887542	−	0.176543i	0.269793	−	0.962918i	$-0.413045\pi$
$997$	28.0244	−	5.57440i	0.887542	−	0.176543i	0.617749	+	0.786375i	$0.288045\pi$
$998$	29.5279	+	35.7174i	0.934690	+	1.13061i
$999$	−41.1814	+	41.1814i	−1.30292	+	1.30292i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.co.a.99.16	yes	832
5.4	even	2	inner	680.2.co.a.99.89	yes	832
8.3	odd	2	inner	680.2.co.a.99.94	yes	832
17.11	odd	16	inner	680.2.co.a.419.11	yes	832
40.19	odd	2	inner	680.2.co.a.99.11	✓	832
85.79	odd	16	inner	680.2.co.a.419.94	yes	832
136.11	even	16	inner	680.2.co.a.419.89	yes	832
680.419	even	16	inner	680.2.co.a.419.16	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.co.a.99.11	✓	832	40.19	odd	2	inner
680.2.co.a.99.16	yes	832	1.1	even	1	trivial
680.2.co.a.99.89	yes	832	5.4	even	2	inner
680.2.co.a.99.94	yes	832	8.3	odd	2	inner
680.2.co.a.419.11	yes	832	17.11	odd	16	inner
680.2.co.a.419.16	yes	832	680.419	even	16	inner
680.2.co.a.419.89	yes	832	136.11	even	16	inner
680.2.co.a.419.94	yes	832	85.79	odd	16	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.co (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24482 + 0.671133i) q^{2} +(3.02940 + 0.602586i) q^{3} +(1.09916 - 1.67088i) q^{4} +(-0.0803191 - 2.23462i) q^{5} +(-4.17548 + 1.28302i) q^{6} +(3.84724 + 2.57064i) q^{7} +(-0.246876 + 2.81763i) q^{8} +(6.04253 + 2.50290i) q^{9} +(1.59971 + 2.72780i) q^{10} +(2.30746 - 0.458983i) q^{11} +(4.33665 - 4.39943i) q^{12} +(0.474407 + 0.474407i) q^{13} +(-6.51437 - 0.617983i) q^{14} +(1.10323 - 6.81798i) q^{15} +(-1.58369 - 3.67314i) q^{16} +(-3.71414 - 1.79030i) q^{17} +(-9.20166 + 0.939681i) q^{18} +(-6.53598 + 2.70729i) q^{19} +(-3.82208 - 2.32201i) q^{20} +(10.1058 + 10.1058i) q^{21} +(-2.56434 + 2.11997i) q^{22} +(-1.31540 - 6.61299i) q^{23} +(-2.44575 + 8.38698i) q^{24} +(-4.98710 + 0.358966i) q^{25} +(-0.908942 - 0.272162i) q^{26} +(9.09245 + 6.07538i) q^{27} +(8.52398 - 3.60273i) q^{28} +(-4.89597 + 3.27138i) q^{29} +(3.20244 + 9.22758i) q^{30} +(0.996655 - 5.01052i) q^{31} +(4.43657 + 3.50953i) q^{32} +7.26681 q^{33} +(5.82497 - 0.264070i) q^{34} +(5.43542 - 8.80361i) q^{35} +(10.8238 - 7.34527i) q^{36} +(-1.03900 + 5.22343i) q^{37} +(6.31917 - 7.75660i) q^{38} +(1.15130 + 1.72304i) q^{39} +(6.31618 + 0.325365i) q^{40} +(-3.57941 - 2.39169i) q^{41} +(-19.3623 - 5.79759i) q^{42} +(-0.819076 + 1.97742i) q^{43} +(1.76937 - 4.35999i) q^{44} +(5.10771 - 13.7038i) q^{45} +(6.07564 + 7.34918i) q^{46} +(1.24163 + 1.24163i) q^{47} +(-2.58426 - 12.0817i) q^{48} +(5.51427 + 13.3126i) q^{49} +(5.96713 - 3.79385i) q^{50} +(-10.1728 - 7.66164i) q^{51} +(1.31413 - 0.271228i) q^{52} +(2.20958 - 0.915237i) q^{53} +(-15.3959 - 1.46052i) q^{54} +(-1.21099 - 5.11945i) q^{55} +(-8.19292 + 10.2055i) q^{56} +(-21.4315 + 4.26299i) q^{57} +(3.89907 - 7.35813i) q^{58} +(0.257860 - 0.622529i) q^{59} +(-10.1794 - 9.33743i) q^{60} +(3.33081 + 2.22558i) q^{61} +(2.12207 + 6.90609i) q^{62} +(16.8130 + 25.1625i) q^{63} +(-7.87810 - 1.39121i) q^{64} +(1.02202 - 1.09823i) q^{65} +(-9.04588 + 4.87700i) q^{66} -0.662256 q^{67} +(-7.07382 + 4.23805i) q^{68} -20.8260i q^{69} +(-0.857731 + 14.6068i) q^{70} +(-2.50239 - 0.497757i) q^{71} +(-8.54401 + 16.4077i) q^{72} +(-0.683178 - 1.02245i) q^{73} +(-2.21224 - 7.19955i) q^{74} +(-15.3242 - 1.91770i) q^{75} +(-2.66053 + 13.8966i) q^{76} +(10.0572 + 4.16585i) q^{77} +(-2.58955 - 1.37220i) q^{78} +(-0.742184 - 3.73121i) q^{79} +(-8.08088 + 3.83398i) q^{80} +(10.0095 + 10.0095i) q^{81} +(6.06087 + 0.574962i) q^{82} +(5.07078 - 2.10039i) q^{83} +(27.9935 - 5.77770i) q^{84} +(-3.70234 + 8.44350i) q^{85} +(-0.307511 - 3.01125i) q^{86} +(-16.8031 + 6.96009i) q^{87} +(0.723589 + 6.61489i) q^{88} +(5.59049 - 5.59049i) q^{89} +(2.83890 + 20.4868i) q^{90} +(0.605626 + 3.04469i) q^{91} +(-12.4954 - 5.07085i) q^{92} +(6.03854 - 14.5783i) q^{93} +(-2.37891 - 0.712309i) q^{94} +(6.57474 + 14.3880i) q^{95} +(11.3254 + 13.3052i) q^{96} +(11.5356 - 7.70783i) q^{97} +(-15.7988 - 12.8710i) q^{98} +(15.0917 + 3.00193i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 832 q - 16 q^{4} - 16 q^{6} - 32 q^{9} - 8 q^{10} - 32 q^{11} - 16 q^{14} - 32 q^{19} - 8 q^{20} - 32 q^{24} - 16 q^{25} - 48 q^{26} + 56 q^{30} + 48 q^{34} - 32 q^{35} + 48 q^{36} - 72 q^{40} - 32 q^{41}+ \cdots - 128 q^{99}+O(q^{100}) \) 832 * q - 16 * q^4 - 16 * q^6 - 32 * q^9 - 8 * q^10 - 32 * q^11 - 16 * q^14 - 32 * q^19 - 8 * q^20 - 32 * q^24 - 16 * q^25 - 48 * q^26 + 56 * q^30 + 48 * q^34 - 32 * q^35 + 48 * q^36 - 72 * q^40 - 32 * q^41 - 48 * q^44 - 32 * q^46 - 32 * q^49 - 32 * q^51 + 32 * q^54 - 16 * q^56 - 32 * q^59 - 112 * q^60 - 16 * q^64 - 96 * q^65 - 48 * q^66 - 80 * q^70 - 16 * q^74 - 16 * q^75 - 16 * q^76 - 104 * q^80 - 32 * q^81 - 192 * q^86 - 32 * q^89 + 72 * q^90 - 32 * q^91 - 16 * q^94 + 288 * q^96 - 128 * q^99

Introduction

L-functions

Modular forms

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