LMFDB - Embedded newform 680.2.co.a.99.89

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			99.89
Character	$\chi$	$=$	680.99
Dual form			680.2.co.a.419.89

$q$-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} +(-2.03379 - 0.929359i) 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} +(-3.15543 + 0.208056i) 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} +(5.60114 + 4.04093i) 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} +(-3.78831 + 2.37670i) 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} +(3.27258 + 3.78024i) 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} +(9.68443 + 1.27113i) 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} +(-3.12069 + 5.50103i) 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} +(-9.96314 - 10.7061i) 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} +(6.61082 + 2.50938i) 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} +(-5.11945 - 1.21099i) 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} +(12.9085 - 4.91721i) 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} +(0.523948 + 1.40574i) q^{65} +(-9.04588 + 4.87700i) q^{66} +0.662256 q^{67} +(7.07382 - 4.23805i) q^{68} -20.8260i q^{69} +(12.6745 + 7.31104i) 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} +(-7.63606 - 13.4239i) 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} +(-0.192774 + 8.94219i) 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} +(-5.88993 - 7.09287i) 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} +(-19.5875 - 6.64053i) 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} +(15.8088 + 0.568217i) 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	−0.786189	−	0.617986i	$-0.787949\pi$
$3$	−3.02940	−	0.602586i	−1.74903	−	0.347903i	−0.962837	+	0.270083i	$0.912949\pi$
$4$	1.09916	−	1.67088i	0.549581	−	0.835441i
$5$	−2.03379	−	0.929359i	−0.909537	−	0.415622i
$5$	−2.03379	−	0.929359i	−0.909537	−	0.415622i
$6$	−4.17548	+	1.28302i	−1.70463	+	0.523791i
$7$	−3.84724	−	2.57064i	−1.45412	−	0.971612i	−0.996598	−	0.0824138i	$-0.973737\pi$
$7$	−3.84724	−	2.57064i	−1.45412	−	0.971612i	−0.457522	−	0.889198i	$-0.651263\pi$
$8$	0.246876	−	2.81763i	0.0872837	−	0.996183i
$9$	6.04253	+	2.50290i	2.01418	+	0.834300i
$10$	−3.15543	+	0.208056i	−0.997833	+	0.0657930i
$11$	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	0.638251	−	0.769828i	$-0.279658\pi$
$13$	−0.474407	−	0.474407i	−0.131577	−	0.131577i	−0.769828	+	0.638251i	$0.779658\pi$
$14$	−6.51437	−	0.617983i	−1.74104	−	0.165163i
$15$	5.60114	+	4.04093i	1.44621	+	1.04336i
$16$	−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	$0.676348\pi$
$20$	−3.78831	+	2.37670i	−0.847092	+	0.531447i
$21$	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	$0.185638\pi$
$23$	1.31540	+	6.61299i	0.274281	+	1.37890i	−0.560424	+	0.828206i	$0.689362\pi$
$24$	−2.44575	+	8.38698i	−0.499237	+	1.71199i
$25$	3.27258	+	3.78024i	0.654517	+	0.756048i
$26$	−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	$0.496623\pi$
$30$	9.68443	+	1.27113i	1.76813	+	0.232076i
$31$	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	$-0.793267\pi$
$37$	1.03900	−	5.22343i	0.170811	−	0.858727i	0.967215	−	0.253961i	$-0.0817334\pi$
$38$	−6.31917	+	7.75660i	−1.02511	+	1.25829i
$39$	1.15130	+	1.72304i	0.184355	+	0.275907i
$40$	−3.12069	+	5.50103i	−0.493424	+	0.869789i
$41$	−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	−0.849039	−	0.528330i	$-0.822818\pi$
$43$	0.819076	−	1.97742i	0.124908	−	0.301554i	0.973947	+	0.226776i	$0.0728184\pi$
$44$	1.76937	−	4.35999i	0.266742	−	0.657294i
$45$	−9.96314	−	10.7061i	−1.48522	−	1.59596i
$46$	6.07564	+	7.34918i	0.895804	+	1.08358i
$47$	−1.24163	−	1.24163i	−0.181110	−	0.181110i	0.610729	−	0.791840i	$-0.290876\pi$
$47$	−1.24163	−	1.24163i	−0.181110	−	0.181110i	−0.791840	+	0.610729i	$0.790876\pi$
$48$	2.58426	+	12.0817i	0.373005	+	1.74385i
$49$	5.51427	+	13.3126i	0.787752	+	1.90180i
$50$	6.61082	+	2.50938i	0.934912	+	0.354880i
$51$	−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	−0.529240	−	0.848472i	$-0.677523\pi$
$53$	−2.20958	+	0.915237i	−0.303509	+	0.125717i	0.225731	+	0.974190i	$0.427523\pi$
$54$	−15.3959	−	1.46052i	−2.09511	−	0.198752i
$55$	−5.11945	−	1.21099i	−0.690306	−	0.163290i
$56$	−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	$0.111034\pi$
$60$	12.9085	−	4.91721i	1.66648	−	0.634809i
$61$	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
$65$	0.523948	+	1.40574i	0.0649878	+	0.174360i
$66$	−9.04588	+	4.87700i	−1.11347	+	0.600317i
$67$	0.662256			0.0809074			0.0404537	−	0.999181i	$-0.487120\pi$
$67$	0.662256			0.0809074			0.0404537	+	0.999181i	$0.487120\pi$
$68$	7.07382	−	4.23805i	0.857827	−	0.513939i
$69$		−	20.8260i		−	2.50716i
$70$	12.6745	+	7.31104i	1.51489	+	0.873836i
$71$	−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	0.869294	−	0.494296i	$-0.164574\pi$
$73$	0.683178	+	1.02245i	0.0799600	+	0.119669i	−0.789334	+	0.613964i	$0.789574\pi$
$74$	−2.21224	−	7.19955i	−0.257168	−	0.836931i
$75$	−7.63606	−	13.4239i	−0.881736	−	1.55006i
$76$	−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	$-0.131152\pi$
$80$	−0.192774	+	8.94219i	−0.0215528	+	0.999768i
$81$	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	−0.643204	−	0.765695i	$-0.722395\pi$
$83$	−5.07078	+	2.10039i	−0.556590	+	0.230547i	0.0866138	+	0.996242i	$0.472395\pi$
$84$	27.9935	−	5.77770i	3.05434	−	0.630398i
$85$	−5.88993	−	7.09287i	−0.638852	−	0.769329i
$86$	−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	$0.112372\pi$
$90$	−19.5875	−	6.64053i	−2.06471	−	0.699974i
$91$	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
$95$	15.8088	+	0.568217i	1.62195	+	0.0582978i
$96$	11.3254	+	13.3052i	1.15589	+	1.35796i
$97$	−11.5356	+	7.70783i	−1.17126	+	0.782612i	−0.980014	−	0.198930i	$-0.936253\pi$
$97$	−11.5356	+	7.70783i	−1.17126	+	0.782612i	−0.191247	+	0.981542i	$0.561253\pi$
$98$	15.7988	+	12.8710i	1.59592	+	1.30017i
$99$	15.0917	+	3.00193i	1.51677	+	0.301705i
$100$	9.91343	−	1.31301i	0.991343	−	0.131301i
$101$	−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	$-0.635647\pi$
$103$	−8.39042			−0.826733			−0.413367	+	0.910565i	$0.635647\pi$
$104$	−1.45382	+	1.21958i	−0.142559	+	0.119590i
$105$	−11.1611	−	29.9450i	−1.08922	−	2.92233i
$106$	−2.13628	+	2.62223i	−0.207494	+	0.254693i
$107$	−2.87140	−	4.29736i	−0.277589	−	0.415441i	0.666310	−	0.745675i	$-0.267873\pi$
$107$	−2.87140	−	4.29736i	−0.277589	−	0.415441i	−0.943899	+	0.330233i	$0.892873\pi$
$108$	−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	$0.939221\pi$
$110$	−7.18553	+	1.92837i	−0.685114	+	0.183863i
$111$	−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	$0.111692\pi$
$113$	2.15817	+	10.8499i	0.203024	+	1.02067i	−0.736043	+	0.676935i	$0.763308\pi$
$114$	23.8173	−	19.6900i	2.23070	−	1.84414i
$115$	3.47059	−	14.6719i	0.323634	−	1.36816i
$116$	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
$120$	12.7687	−	14.7844i	1.16561	−	1.34962i
$121$	−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
$125$	−3.14254	−	10.7296i	−0.281077	−	0.959685i
$126$	−37.8166	−	20.0390i	−3.36897	−	1.78522i
$127$	−1.16418	+	2.81058i	−0.103304	+	0.249399i	−0.967078	−	0.254482i	$-0.918095\pi$
$127$	−1.16418	+	2.81058i	−0.103304	+	0.249399i	0.863773	+	0.503881i	$0.168095\pi$
$128$	−10.7405	+	3.55545i	−0.949337	+	0.314260i
$129$	−3.67288	+	5.49685i	−0.323379	+	0.483971i
$130$	1.59566	+	1.39825i	0.139949	+	0.122635i
$131$	−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	$-0.718443\pi$
$137$		−	18.1100i		−	1.54724i	0.633647	−	0.773622i	$-0.281557\pi$
$138$	−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	$0.757414\pi$
$140$	20.6842	+	0.594648i	1.74813	+	0.0502569i
$141$	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
$145$	12.9976	−	2.10318i	1.07940	−	0.174660i
$146$	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	$0.00383975\pi$
$150$	−18.5147	−	11.5855i	−1.51172	−	0.945954i
$151$	−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
$155$	−6.68356	+	9.26409i	−0.536836	+	0.744110i
$156$	4.14446	−	0.0297849i	0.331822	−	0.00238470i
$157$	−3.51971	+	3.51971i	−0.280903	+	0.280903i	−0.833469	−	0.552566i	$-0.813649\pi$
$157$	−3.51971	+	3.51971i	−0.280903	+	0.280903i	0.552566	+	0.833469i	$0.313649\pi$
$158$	−3.42803	−	4.14659i	−0.272719	−	0.329885i
$159$	7.24521	−	1.44116i	0.574582	−	0.114292i
$160$	5.76143	+	11.2608i	0.455481	+	0.890245i
$161$	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	0.776503	−	0.630114i	$-0.216992\pi$
$163$	6.27516	+	4.19293i	0.491509	+	0.328416i	−0.284994	+	0.958529i	$0.591992\pi$
$164$	−7.93058	+	3.35193i	−0.619274	+	0.261741i
$165$	14.7791	+	6.75348i	1.15056	+	0.525757i
$166$	−4.90258	+	6.01777i	−0.380514	+	0.467070i
$167$	6.97603	+	1.38762i	0.539822	+	0.107377i	0.457468	−	0.889226i	$-0.348756\pi$
$167$	6.97603	+	1.38762i	0.539822	+	0.107377i	0.0823535	+	0.996603i	$0.473756\pi$
$168$	30.9693	−	25.9796i	2.38934	−	2.00437i
$169$		−	12.5499i		−	0.965375i
$170$	−12.0922	−	4.87643i	−0.927427	−	0.374005i
$171$	−46.2699			−3.53835
$172$	−2.40375	−	3.54209i	−0.183284	−	0.270082i
$173$	0.767815	−	3.86007i	0.0583759	−	0.293475i	−0.940558	−	0.339632i	$-0.889697\pi$
$173$	0.767815	−	3.86007i	0.0583759	−	0.293475i	0.998934	+	0.0461568i	$0.0146974\pi$
$174$	16.2458	−	19.9412i	1.23159	−	1.51174i
$175$	−2.87277	−	22.9561i	−0.217161	−	1.73532i
$176$	−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	$0.625961\pi$
$180$	−28.8396	+	4.87955i	−2.14958	+	0.363700i
$181$	−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
$185$	−6.96756	+	9.65774i	−0.512265	+	0.710051i
$186$	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
$190$	20.0605	−	9.90250i	1.45534	−	0.718403i
$191$	−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	−0.998218	−	0.0596648i	$-0.980997\pi$
$193$	−26.3626	+	5.24384i	−1.89762	+	0.377460i	−0.899401	+	0.437125i	$0.855997\pi$
$194$	−9.18676	+	17.3368i	−0.659571	+	1.24471i
$195$	−0.740174	−	4.57427i	−0.0530049	−	0.327570i
$196$	28.3049	+	5.41902i	2.02178	+	0.387073i
$197$	2.39931	−	3.59083i	0.170944	−	0.255836i	−0.736099	−	0.676874i	$-0.763334\pi$
$197$	2.39931	−	3.59083i	0.170944	−	0.255836i	0.907043	+	0.421038i	$0.138334\pi$
$198$	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	$0.500425\pi$
$200$	11.4592	−	8.28769i	0.810291	−	0.586028i
$201$	−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
$210$	−33.9907	−	29.7856i	−2.34558	−	2.05540i
$211$	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
$215$	−3.50356	+	3.26045i	−0.238941	+	0.222361i
$216$	−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
$220$	−7.65052	+	7.22292i	−0.515798	+	0.486969i
$221$	−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	−0.639882	−	0.768473i	$-0.721017\pi$
$223$	−8.19765	+	3.39558i	−0.548955	+	0.227385i	0.0909273	+	0.995858i	$0.471017\pi$
$224$	8.04681	+	24.9069i	0.537650	+	1.66416i
$225$	10.3131	+	31.0332i	0.687543	+	2.06888i
$226$	9.96824	+	12.0577i	0.663078	+	0.802068i
$227$	15.6337	−	3.10973i	1.03764	−	0.206400i	0.353262	−	0.935525i	$-0.385073\pi$
$227$	15.6337	−	3.10973i	1.03764	−	0.206400i	0.684381	+	0.729125i	$0.260073\pi$
$228$	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	$0.489283\pi$
$230$	−5.52653	−	20.5931i	−0.364409	−	1.35787i
$231$	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	−0.796925	−	0.604078i	$-0.793541\pi$
$233$	−8.30073	+	5.54637i	−0.543799	+	0.363355i	0.253126	+	0.967433i	$0.418541\pi$
$234$	−4.81112	−	3.91954i	−0.314513	−	0.256228i
$235$	1.37129	+	3.67913i	0.0894533	+	0.240000i
$236$	−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	$-0.159678\pi$
$240$	5.97243	−	26.9733i	0.385519	−	1.74112i
$241$	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
$245$	1.15736	−	32.1998i	0.0739408	−	2.05717i
$246$	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
$250$	−11.1129	−	11.2474i	−0.702841	−	0.711347i
$251$	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
$255$	13.5689	+	25.0363i	0.849718	+	1.56784i
$256$	−10.9839	+	11.6342i	−0.686491	+	0.727139i
$257$	−11.5256	−	27.8252i	−0.718946	−	1.73569i	−0.676331	−	0.736598i	$-0.736431\pi$
$257$	−11.5256	−	27.8252i	−0.718946	−	1.73569i	−0.0426152	−	0.999092i	$-0.513569\pi$
$258$	−0.882960	+	9.30759i	−0.0549707	+	0.579465i
$259$	−17.4249	+	17.4249i	−1.08273	+	1.08273i
$260$	2.92472	+	0.669676i	0.181384	+	0.0415315i
$261$	−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	−0.968586	−	0.248678i	$-0.920004\pi$
$263$	−1.74904	+	4.22255i	−0.107850	+	0.260374i	0.860736	+	0.509052i	$0.170004\pi$
$264$	−1.79400	+	20.4752i	−0.110413	+	1.26016i
$265$	5.34439	+	0.192094i	0.328303	+	0.0118002i
$266$	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	$0.958150\pi$
$270$	29.9546	+	17.2787i	1.82298	+	1.05155i
$271$	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
$275$	9.28643	+	7.22070i	0.559993	+	0.435424i
$276$	−34.7979	−	22.8912i	−2.09458	−	1.37789i
$277$	8.62180	−	5.76090i	0.518034	−	0.346139i	−0.268908	−	0.963166i	$-0.586663\pi$
$277$	8.62180	−	5.76090i	0.518034	−	0.346139i	0.786942	+	0.617027i	$0.211663\pi$
$278$	8.01500	+	26.0841i	0.480708	+	1.56442i
$279$	18.5632	−	27.7817i	1.11135	−	1.66325i
$280$	26.1472	−	13.1416i	1.56259	−	0.785362i
$281$	−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	$-0.938092\pi$
$283$	−2.50060	−	12.5713i	−0.148645	−	0.747289i	0.832501	−	0.554023i	$-0.186908\pi$
$284$	−3.58223	+	3.63409i	−0.212566	+	0.215643i
$285$	−47.5489	−	11.2475i	−2.81656	−	0.666246i
$286$	−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
$290$	14.7682	−	11.3412i	0.867220	−	0.665980i
$291$	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	−0.993391	−	0.114778i	$-0.963384\pi$
$293$	−15.0394	+	15.0394i	−0.878613	+	0.878613i	0.114778	+	0.993391i	$0.463384\pi$
$294$	−40.1051	−	48.5117i	−2.33898	−	2.82926i
$295$	−1.10298	+	1.02645i	−0.0642183	+	0.0597620i
$296$	−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
$300$	−30.8230	−	1.99606i	−1.77956	−	0.115242i
$301$	−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	$0.279785\pi$
$307$			26.9859i			1.54017i	−0.637943	+	0.770083i	$0.720215\pi$
$308$	−18.0152	+	12.2255i	−1.02651	+	0.696614i
$309$	25.4180	+	5.05595i	1.44598	+	0.287623i
$310$	−2.10240	+	16.0177i	−0.119409	+	0.909744i
$311$	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	$-0.501223\pi$
$313$	16.3030	−	24.3992i	0.921501	−	1.37912i	0.925343	−	0.379131i	$-0.123777\pi$
$314$	−2.01922	+	6.74360i	−0.113951	+	0.380564i
$315$	10.8091	+	66.8004i	0.609026	+	3.76378i
$316$	−7.05019	−	2.86110i	−0.396604	−	0.160949i
$317$	12.7689	−	2.53989i	0.717171	−	0.142654i	0.177002	−	0.984211i	$-0.443360\pi$
$317$	12.7689	−	2.53989i	0.717171	−	0.142654i	0.540169	+	0.841556i	$0.318360\pi$
$318$	8.05178	−	6.65649i	0.451521	−	0.373277i
$319$	−9.79575	+	9.79575i	−0.548457	+	0.548457i
$320$	14.7295	+	10.1510i	0.823402	+	0.567459i
$321$	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
$325$	0.240835	−	3.34591i	0.0133591	−	0.185597i
$326$	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
$330$	22.9299	−	1.51190i	1.26225	−	0.0832274i
$331$	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
$335$	−1.34689	−	0.615473i	−0.0735883	−	0.0336269i
$336$	21.1155	−	53.1245i	1.15195	−	2.89818i
$337$	−1.51971	+	7.64009i	−0.0827838	+	0.416182i	0.917064	+	0.398740i	$0.130552\pi$
$337$	−1.51971	+	7.64009i	−0.0827838	+	0.416182i	−0.999848	+	0.0174423i	$0.994448\pi$
$338$	−8.42264	−	15.6224i	−0.458131	−	0.849744i
$339$		−	34.1691i		−	1.85581i
$340$	−18.3253	+	2.04517i	−0.993830	+	0.110915i
$341$		−	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
$345$	−19.3549	+	42.3557i	−1.04203	+	2.28036i
$346$	−1.63483	−	5.32040i	−0.0878887	−	0.286026i
$347$	7.66148	−	11.4662i	0.411290	−	0.615538i	−0.566767	−	0.823878i	$-0.691806\pi$
$347$	7.66148	−	11.4662i	0.411290	−	0.615538i	0.978057	+	0.208340i	$0.0668060\pi$
$348$	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	$0.0900575\pi$
$350$	−18.9827	−	26.6483i	−1.01467	−	1.42441i
$351$	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	−0.557371	−	0.830263i	$-0.688190\pi$
$353$	5.12718	−	5.12718i	0.272892	−	0.272892i	0.830263	+	0.557371i	$0.188190\pi$
$354$	−0.277972	+	2.93020i	−0.0147740	+	0.155738i
$355$	4.62674	+	3.33795i	0.245562	+	0.177160i
$356$	−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	$0.863837\pi$
$360$	−32.6254	+	25.4294i	−1.71951	+	1.34025i
$361$	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
$365$	−0.439217	−	2.71436i	−0.0229897	−	0.142076i
$366$	−16.7632	−	5.01936i	−0.876227	−	0.262366i
$367$	4.29723	−	6.43125i	0.224313	−	0.335709i	−0.702194	−	0.711986i	$-0.747796\pi$
$367$	4.29723	−	6.43125i	0.224313	−	0.335709i	0.926507	+	0.376277i	$0.122796\pi$
$368$	22.2072	−	15.3046i	1.15763	−	0.797806i
$369$	−15.6426	−	23.4108i	−0.814320	−	1.21872i
$370$	−2.19174	+	16.6983i	−0.113943	+	0.868104i
$371$	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	$0.216760\pi$
$373$			24.3172i			1.25910i	−0.776960	+	0.629549i	$0.783240\pi$
$374$	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	$0.0764732\pi$
$380$	18.3259	−	25.7901i	0.940098	−	1.32301i
$381$	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	0.0316735	−	0.999498i	$-0.489916\pi$
$383$	−12.7732	−	5.29085i	−0.652682	−	0.270350i	−0.684355	+	0.729149i	$0.739916\pi$
$384$	34.6798	−	4.29880i	1.76975	−	0.219372i
$385$	16.5827	+	17.8192i	0.845134	+	0.908153i
$386$	−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	$0.655764\pi$
$390$	−3.99133	−	5.19739i	−0.202109	−	0.263180i
$391$	−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
$395$	−1.95819	+	8.27825i	−0.0985273	+	0.416524i
$396$	21.6041	−	21.9169i	1.08565	−	1.10136i
$397$	−5.81201	−	29.2189i	−0.291696	−	1.46646i	−0.797244	−	0.603658i	$-0.793709\pi$
$397$	−5.81201	−	29.2189i	−0.291696	−	1.46646i	0.505547	−	0.862799i	$-0.331291\pi$
$398$	−10.3999	+	19.6262i	−0.521302	+	0.983773i
$399$	−93.4107	−	38.6920i	−4.67638	−	1.93702i
$400$	8.70257	−	18.0074i	0.435129	−	0.900368i
$401$	−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
$405$	−11.0548	−	29.6596i	−0.549316	−	1.47380i
$406$	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	$0.330919\pi$
$410$	11.7922	+	6.80207i	0.582374	+	0.335931i
$411$	−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
$415$	12.2649	+	0.440837i	0.602060	+	0.0216399i
$416$	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	$0.613111\pi$
$420$	−62.3024	−	14.2654i	−3.04005	−	0.696082i
$421$	−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
$425$	5.38704	+	19.8992i	0.261310	+	0.965255i
$426$	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
$430$	−2.17312	+	6.41003i	−0.104797	+	0.309119i
$431$	−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	−0.0276718	−	0.999617i	$-0.508809\pi$
$433$	−15.6913	−	6.49954i	−0.754075	−	0.312348i	−0.726403	+	0.687269i	$0.758809\pi$
$434$	−9.58900	+	32.0245i	−0.460287	+	1.53722i
$435$	−40.6425	−	1.46081i	−1.94866	−	0.0700406i
$436$	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	$0.0393899\pi$
$440$	−4.67599	+	14.1258i	−0.222919	+	0.673419i
$441$			94.2436i			4.48779i
$442$	−2.88868	−	2.63813i	−0.137401	−	0.125483i
$443$		−	36.5984i		−	1.73884i	−0.494071	−	0.869422i	$-0.664492\pi$
$443$		−	36.5984i		−	1.73884i	0.494071	−	0.869422i	$-0.335508\pi$
$444$	18.4743	+	27.2232i	0.876753	+	1.29196i
$445$	−16.5654	+	6.17429i	−0.785277	+	0.292690i
$446$	−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	$0.952113\pi$
$450$	33.6654	+	31.7093i	1.58700	+	1.49479i
$451$	−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
$455$	1.59789	−	6.75509i	0.0749104	−	0.316684i
$456$	−6.72062	−	61.4385i	−0.314722	−	2.87712i
$457$	1.92714	−	0.798247i	0.0901477	−	0.0373404i	−0.337154	−	0.941450i	$-0.609464\pi$
$457$	1.92714	−	0.798247i	0.0901477	−	0.0373404i	0.427302	+	0.904109i	$0.359464\pi$
$458$	17.6098	−	1.79833i	0.822853	−	0.0840304i
$459$	−22.8938	−	38.8430i	−1.06859	−	1.81304i
$460$	−20.7003	−	21.9257i	−0.965155	−	1.02229i
$461$	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	−0.935553	−	0.353186i	$-0.885098\pi$
$463$	−12.5310	+	12.5310i	−0.582367	+	0.582367i	0.353186	+	0.935553i	$0.385098\pi$
$464$	19.7699	+	12.8027i	0.917795	+	0.594350i
$465$	25.8296	−	24.0372i	1.19782	−	1.11470i
$466$	−6.61058	+	12.4751i	−0.306229	+	0.577900i
$467$	10.0201	+	4.15047i	0.463676	+	0.192061i	0.602277	−	0.798287i	$-0.294260\pi$
$467$	10.0201	+	4.15047i	0.463676	+	0.192061i	−0.138601	+	0.990348i	$0.544260\pi$
$468$	−8.61951	−	1.65022i	−0.398437	−	0.0762816i
$469$	−2.54786	−	1.70242i	−0.117649	−	0.0786106i
$470$	4.17620	+	3.65955i	0.192634	+	0.168802i
$471$	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	$0.278308\pi$
$480$	−10.6681	−	37.5853i	−0.486930	−	1.71553i
$481$	−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
$485$	30.6243	−	4.95539i	1.39058	−	0.225013i
$486$	−13.6418	−	7.22878i	−0.618804	−	0.327904i
$487$	−1.81761	+	0.361545i	−0.0823638	+	0.0163832i	−0.236100	−	0.971729i	$-0.575869\pi$
$487$	−1.81761	+	0.361545i	−0.0823638	+	0.0163832i	0.153736	+	0.988112i	$0.450869\pi$
$488$	7.09316	−	8.83557i	0.321092	−	0.399967i
$489$	−16.4834	−	16.4834i	−0.745405	−	0.745405i
$490$	−20.1696	−	40.8597i	−0.911171	−	1.84585i
$491$	−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
$495$	−27.9035	−	20.1309i	−1.25417	−	0.904817i
$496$	−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	$-0.324602\pi$
$500$	−21.3821	−	6.54275i	−0.956235	−	0.292601i
$501$	−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	$-0.575860\pi$
$503$	16.8664	−	25.2424i	0.752036	−	1.12550i	0.988107	−	0.153766i	$-0.0491400\pi$
$504$	−75.0493	+	41.1609i	−3.34296	+	1.83345i
$505$	19.6136	+	8.96263i	0.872794	+	0.398832i
$506$	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	$0.540228\pi$
$510$	33.6936	+	22.0592i	1.49198	+	0.976799i
$511$		−	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
$515$	17.0643	+	7.79772i	0.751945	+	0.343608i
$516$	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
$520$	4.09020	−	1.12925i	0.179367	−	0.0495210i
$521$	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	−0.319884	−	0.947457i	$-0.603644\pi$
$523$	14.3521	−	14.3521i	0.627573	−	0.627573i	0.947457	+	0.319884i	$0.103644\pi$
$524$	−7.43237	+	0.0534141i	−0.324685	+	0.00233341i
$525$	−5.13026	+	71.2745i	−0.223903	+	3.11067i
$526$	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
$530$	6.78174	−	3.34768i	0.294580	−	0.145414i
$531$	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
$535$	1.84603	+	11.4085i	0.0798110	+	0.493232i
$536$	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
$540$	48.8844	+	1.40537i	2.10365	+	0.0604776i
$541$	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	0.184008	−	0.982925i	$-0.441093\pi$
$547$	−0.517804	−	0.102998i	−0.0221397	−	0.00440386i	−0.206148	+	0.978521i	$0.566093\pi$
$548$	−30.2597	−	19.9058i	−1.29263	−	0.850335i
$549$	14.5562	+	21.7848i	0.621242	+	0.929754i
$550$	16.4060	+	2.75605i	0.699554	+	0.117518i
$551$	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
$555$	26.9272	−	25.0586i	1.14299	−	1.06368i
$556$	27.4832	+	27.0910i	1.16555	+	1.14891i
$557$	−7.07083	−	7.07083i	−0.299601	−	0.299601i	0.541257	−	0.840857i	$-0.317949\pi$
$557$	−7.07083	−	7.07083i	−0.299601	−	0.299601i	−0.840857	+	0.541257i	$0.817949\pi$
$558$	4.46258	−	47.0416i	0.188916	−	1.99143i
$559$	−1.32668	+	0.549528i	−0.0561125	+	0.0232426i
$560$	23.7288	−	33.9072i	1.00273	−	1.43284i
$561$	−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	0.993639	−	0.112615i	$-0.0359228\pi$
$563$	5.01599	+	12.1097i	0.211399	+	0.510362i	−0.782240	+	0.622978i	$0.785923\pi$
$564$	10.8470	−	0.0779539i	0.456741	−	0.00328245i
$565$	5.69416	−	24.0720i	0.239555	−	1.01272i
$566$	−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	$0.0363069\pi$
$570$	−66.7385	+	17.9105i	−2.79537	+	0.750187i
$571$	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
$575$	−20.6939	+	26.6141i	−0.862995	+	1.10988i
$576$	−44.1217	−	28.1245i	−1.83840	−	1.17186i
$577$	−35.4243			−1.47473			−0.737366	−	0.675493i	$-0.763931\pi$
$577$	−35.4243			−1.47473			−0.737366	+	0.675493i	$0.763931\pi$
$578$	22.1075	+	9.44767i	0.919551	+	0.392971i
$579$	83.0227			3.45031
$580$	10.7723	−	24.0293i	0.447297	−	0.997761i
$581$	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
$585$	−0.352443	+	9.80560i	−0.0145717	+	0.405412i
$586$	−8.62795	+	28.8149i	−0.356417	+	1.19033i
$587$	−3.42440	+	8.26724i	−0.141340	+	0.341226i	−0.978659	−	0.205489i	$-0.934122\pi$
$587$	−3.42440	+	8.26724i	−0.141340	+	0.341226i	0.837319	+	0.546714i	$0.184122\pi$
$588$	−82.4814	−	33.4725i	−3.40148	−	1.38038i
$589$	7.05083	+	35.4469i	0.290524	+	1.46056i
$590$	−0.684137	+	2.01799i	−0.0281655	+	0.0830794i
$591$	−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	0.0796440	−	0.996823i	$-0.474622\pi$
$593$	20.4753	−	8.48116i	0.840821	−	0.348280i	0.761177	+	0.648544i	$0.224622\pi$
$594$	−36.1957	+	3.69634i	−1.48513	+	0.151663i
$595$	4.42674	+	42.4289i	0.181479	+	1.73941i
$596$	−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	$0.665779\pi$
$600$	−39.7087	+	18.2016i	−1.62110	+	0.743076i
$601$	−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
$605$	12.2121	+	0.438940i	0.496493	+	0.0178455i
$606$	40.2678	−	12.3733i	1.63577	−	0.502631i
$607$	20.8307	+	31.1753i	0.845492	+	1.26537i	0.962239	+	0.272207i	$0.0877534\pi$
$607$	20.8307	+	31.1753i	0.845492	+	1.26537i	−0.116747	+	0.993162i	$0.537247\pi$
$608$	38.4987	+	10.9271i	1.56133	+	0.443153i
$609$	−82.5377	−	16.4178i	−3.34459	−	0.665281i
$610$	−10.9732	−	6.32965i	−0.444291	−	0.256280i
$611$			1.17808i			0.0476599i
$612$	53.3512	−	7.90349i	2.15660	−	0.319480i
$613$	−18.2924			−0.738821			−0.369411	−	0.929266i	$-0.620440\pi$
$613$	−18.2924			−0.738821			−0.369411	+	0.929266i	$0.620440\pi$
$614$	18.1111	+	33.5926i	0.730906	+	1.35569i
$615$	−10.3842	−	27.8604i	−0.418729	−	1.12344i
$616$	−14.2207	+	27.3092i	−0.572969	+	1.10032i
$617$	−10.0381	−	15.0231i	−0.404119	−	0.604806i	0.572469	−	0.819926i	$-0.305986\pi$
$617$	−10.0381	−	15.0231i	−0.404119	−	0.604806i	−0.976588	+	0.215120i	$0.930986\pi$
$618$	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	$0.823696\pi$
$620$	8.13289	+	21.3502i	0.326625	+	0.857443i
$621$	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
$625$	−3.58040	+	24.7423i	−0.143216	+	0.989691i
$626$	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
$630$	58.2874	+	75.9002i	2.32223	+	3.02394i
$631$	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
$635$	4.97974	−	4.63419i	0.197615	−	0.183902i
$636$	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
$640$	25.1482	+	2.75078i	0.994071	+	0.108734i
$641$	−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	$0.188448\pi$
$643$	−3.81347	+	19.1716i	−0.150388	+	0.756054i	−0.980200	+	0.198010i	$0.936552\pi$
$644$	−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	$-0.716225\pi$
$647$	−31.9601			−1.25648			−0.628241	+	0.778018i	$0.716225\pi$
$648$	30.6742	−	25.7320i	1.20499	−	1.01085i
$649$	0.309272	−	1.55482i	0.0121400	−	0.0610318i
$650$	−1.94575	−	4.32669i	−0.0763187	−	0.169707i
$651$	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	−0.267859	−	0.963458i	$-0.586316\pi$
$653$	−32.2102	−	21.5222i	−1.26048	−	0.842228i	−0.992624	+	0.121230i	$0.961316\pi$
$654$	18.3997	−	61.4498i	0.719487	−	2.40288i
$655$	1.32737	+	8.20316i	0.0518648	+	0.320524i
$656$	−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	$0.872623\pi$
$660$	27.5289	−	17.2710i	1.07156	−	0.672275i
$661$	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
$665$	−59.3597	−	42.8249i	−2.30187	−	1.66068i
$666$	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
$670$	−2.08970	+	0.137786i	−0.0807321	+	0.00532314i
$671$	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	−0.312578	−	0.949892i	$-0.601193\pi$
$673$	−33.9787	−	22.7038i	−1.30978	−	0.875169i	−0.997204	+	0.0747236i	$0.976193\pi$
$674$	3.23575	+	10.5305i	0.124636	+	0.405619i
$675$	−6.78941	−	54.2538i	−0.261325	−	2.08823i
$676$	−20.9694	−	13.7943i	−0.806514	−	0.530551i
$677$	32.5951	+	6.48358i	1.25273	+	0.249184i	0.776490	−	0.630130i	$-0.216998\pi$
$677$	32.5951	+	6.48358i	1.25273	+	0.249184i	0.476243	+	0.879314i	$0.341998\pi$
$678$	−22.9320	−	42.5344i	−0.880699	−	1.63353i
$679$	64.1942			2.46355
$680$	−21.4392	+	14.8446i	−0.822155	+	0.569264i
$681$	−49.2345			−1.88667
$682$	−8.06638	−	14.9616i	−0.308877	−	0.572908i
$683$	−40.1356	−	7.98347i	−1.53575	−	0.305479i	−0.646503	−	0.762912i	$-0.723769\pi$
$683$	−40.1356	−	7.98347i	−1.53575	−	0.305479i	−0.889244	+	0.457433i	$0.848769\pi$
$684$	−50.8581	+	77.3116i	−1.94461	+	2.95608i
$685$	−16.8307	+	36.8320i	−0.643069	+	1.40728i
$686$	−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
$690$	4.33297	+	65.7150i	0.164954	+	2.50173i
$691$	−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
$695$	25.2436	−	34.9902i	0.957545	−	1.32725i
$696$	−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
$700$	−41.5146	−	20.4324i	−1.56910	−	0.772273i
$701$	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
$705$	−1.93720	−	11.9719i	−0.0729593	−	0.450888i
$706$	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	$-0.0494599\pi$
$710$	7.99968	+	1.05000i	0.300223	+	0.0394057i
$711$	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	$0.938169\pi$
$720$	−23.5463	+	53.5510i	−0.877517	+	1.99573i
$721$	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
$725$	−28.3891	−	7.80206i	−1.05434	−	0.289761i
$726$	18.3986	−	15.2103i	0.682835	−	0.564507i
$727$	11.6539	+	11.6539i	0.432220	+	0.432220i	0.889383	−	0.457163i	$-0.151134\pi$
$727$	11.6539	+	11.6539i	0.432220	+	0.432220i	−0.457163	+	0.889383i	$0.651134\pi$
$728$	8.72833	−	0.954772i	0.323493	−	0.0353862i
$729$	−3.34745	−	8.08147i	−0.123980	−	0.299314i
$730$	−2.36844	−	3.08412i	−0.0876601	−	0.114148i
$731$	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	−0.692535	−	0.721384i	$-0.743506\pi$
$733$	−18.1974	+	7.53760i	−0.672136	+	0.278408i	0.0203994	+	0.999792i	$0.493506\pi$
$734$	1.03305	−	10.8898i	0.0381307	−	0.401949i
$735$	−22.9092	+	96.8486i	−0.845019	+	3.57232i
$736$	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	$0.874266\pi$
$740$	8.47847	+	22.2574i	0.311675	+	0.818197i
$741$	−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	0.609614	−	0.792698i	$-0.291324\pi$
$743$	−9.70475	−	14.5242i	−0.356033	−	0.532841i	−0.965647	+	0.259858i	$0.916324\pi$
$744$	39.5856	+	20.6134i	1.45128	+	0.755725i
$745$	−35.7309	+	13.3177i	−1.30908	+	0.487921i
$746$	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
$750$	26.8879	+	40.7693i	0.981808	+	1.48869i
$751$	−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
$755$	30.3893	+	1.09228i	1.10598	+	0.0397523i
$756$	99.3918	+	19.0288i	3.61484	+	0.692069i
$757$	−11.2462	−	4.65834i	−0.408751	−	0.169310i	0.168827	−	0.985646i	$-0.446002\pi$
$757$	−11.2462	−	4.65834i	−0.408751	−	0.169310i	−0.577578	+	0.816335i	$0.696002\pi$
$758$	17.4131	−	32.8612i	0.632473	−	1.19357i
$759$	−9.55880	−	48.0553i	−0.346962	−	1.74430i
$760$	5.50384	−	44.4032i	0.199645	−	1.61067i
$761$	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
$765$	−17.8374	−	57.6008i	−0.644911	−	2.08256i
$766$	−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	$0.203949\pi$
$770$	32.6016	+	11.0526i	1.17488	+	0.398306i
$771$	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	$-0.616215\pi$
$773$	15.4563	−	37.3149i	0.555925	−	1.34212i	0.912967	−	0.408034i	$-0.133785\pi$
$774$	5.67871	−	18.9652i	0.204117	−	0.681692i
$775$	22.2026	−	12.6298i	0.797541	−	0.453674i
$776$	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
$780$	−8.45663	−	3.79111i	−0.302796	−	0.135744i
$781$	−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
$785$	10.4294	−	3.88727i	0.372242	−	0.138743i
$786$	12.5854	+	10.2531i	0.448907	+	0.365717i
$787$	−9.12912	−	13.6627i	−0.325418	−	0.487022i	0.632303	−	0.774721i	$-0.282110\pi$
$787$	−9.12912	−	13.6627i	−0.325418	−	0.487022i	−0.957721	+	0.287699i	$0.907110\pi$
$788$	−3.36261	−	7.95587i	−0.119788	−	0.283416i
$789$	7.84300	−	11.7379i	0.279218	−	0.417879i
$790$	3.11821	+	11.6191i	0.110941	+	0.413391i
$791$	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
$795$	−16.0746	−	3.80238i	−0.570106	−	0.134857i
$796$	0.225740	+	31.4109i	0.00800114	+	1.11333i
$797$	−16.2731	−	39.2868i	−0.576424	−	1.39161i	−0.896002	−	0.444050i	$-0.853541\pi$
$797$	−16.2731	−	39.2868i	−0.576424	−	1.39161i	0.319578	−	0.947560i	$-0.396459\pi$
$798$	−142.247	+	14.5264i	−5.03549	+	0.514229i
$799$	−2.38869	−	6.83448i	−0.0845058	−	0.241787i
$800$	−1.25219	−	28.2565i	−0.0442716	−	0.999020i
$801$	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
$805$	−51.0684	+	47.5247i	−1.79992	+	1.67502i
$806$	−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	$0.260762\pi$
$810$	−33.6667	−	29.5017i	−1.18293	−	1.03658i
$811$	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
$820$	19.2443	+	0.553251i	0.672038	+	0.0193204i
$821$	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	0.962095	−	0.272716i	$-0.0879220\pi$
$823$	30.9347	+	20.6699i	1.07832	+	0.720507i	0.116221	+	0.993223i	$0.462922\pi$
$824$	−2.07139	+	23.6411i	−0.0721603	+	0.823578i
$825$	−23.7812	−	27.4703i	−0.827957	−	0.956392i
$826$	−2.06451	+	3.89603i	−0.0718334	+	0.135560i
$827$	8.42546	+	42.3576i	0.292982	+	1.47292i	0.794231	+	0.607616i	$0.207874\pi$
$827$	8.42546	+	42.3576i	0.292982	+	1.47292i	−0.501249	+	0.865303i	$0.667126\pi$
$828$	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	$0.461956\pi$
$830$	15.5635	−	7.68262i	0.540216	−	0.266668i
$831$	−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
$835$	−12.8982	−	9.30536i	−0.446360	−	0.322025i
$836$	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	$0.633178\pi$
$840$	−87.1294	+	24.0553i	−3.00625	+	0.829987i
$841$	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
$845$	−11.6633	+	25.5238i	−0.401231	+	0.878045i
$846$	−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
$850$	20.0609	+	21.1556i	0.688085	+	0.725630i
$851$	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	$0.193196\pi$
$853$	−4.54863	+	22.8675i	−0.155742	+	0.782969i	−0.977137	+	0.212609i	$0.931804\pi$
$854$	−20.3228	−	16.5566i	−0.695432	−	0.566556i
$855$	94.1032	+	43.0014i	3.21826	+	1.47062i
$856$	−12.8173	+	7.02965i	−0.438085	+	0.240268i
$857$	−14.7329	+	22.0493i	−0.503265	+	0.753189i	−0.992927	−	0.118723i	$-0.962120\pi$
$857$	−14.7329	+	22.0493i	−0.503265	+	0.753189i	0.489663	+	0.871912i	$0.337120\pi$
$858$	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	$0.783842\pi$
$860$	1.59684	+	9.43779i	0.0544517	+	0.321826i
$861$	−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	0.319618	−	0.947546i	$-0.396445\pi$
$863$	−18.4466	−	18.4466i	−0.627928	−	0.627928i	−0.947546	+	0.319618i	$0.896445\pi$
$864$	19.0176	+	58.8641i	0.646991	+	2.00260i
$865$	−5.14896	+	7.13698i	−0.175070	+	0.242665i
$866$	−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
$870$	−51.5730	+	25.4580i	−1.74849	+	0.863108i
$871$	−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
$875$	−15.4919	+	49.3577i	−0.523722	+	1.66860i
$876$	−7.46090	−	1.42840i	−0.252080	−	0.0482613i
$877$	−13.3258	+	19.9435i	−0.449980	+	0.673443i	−0.985227	−	0.171253i	$-0.945219\pi$
$877$	−13.3258	+	19.9435i	−0.449980	+	0.673443i	0.535247	+	0.844696i	$0.320219\pi$
$878$	−1.26265	−	4.10919i	−0.0426124	−	0.138679i
$879$	54.6231	−	36.4980i	1.84239	−	1.23105i
$880$	3.65950	+	20.7223i	0.123362	+	0.698547i
$881$	−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	$-0.345971\pi$
$883$	27.6490			0.930462			0.465231	+	0.885189i	$0.345971\pi$
$884$	−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	$0.226238\pi$
$887$	−5.71744	+	28.7435i	−0.191973	+	0.965113i	−0.949848	+	0.312713i	$0.898762\pi$
$888$	41.2677	+	21.4893i	1.38485	+	0.721134i
$889$	11.7039	−	7.82030i	0.392536	−	0.262284i
$890$	−16.4772	+	18.8035i	−0.552318	+	0.630295i
$891$	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
$895$	0.123021	+	0.132194i	0.00411212	+	0.00441875i
$896$	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
$900$	63.1885	+	16.8784i	2.10628	+	0.562614i
$901$	−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
$905$	−10.3159	+	43.6104i	−0.342912	+	1.44966i
$906$	45.7841	−	37.8501i	1.52107	−	1.25749i
$907$	17.4275	−	3.46654i	0.578669	−	0.115104i	0.102927	−	0.994689i	$-0.467179\pi$
$907$	17.4275	−	3.46654i	0.578669	−	0.115104i	0.475743	+	0.879584i	$0.342179\pi$
$908$	11.9879	−	29.5401i	0.397833	−	0.980322i
$909$	−58.2735	−	24.1377i	−1.93281	−	0.800596i
$910$	−2.54447	−	9.48128i	−0.0843484	−	0.314301i
$911$	−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
$915$	9.66295	+	25.9254i	0.319447	+	0.857067i
$916$	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	$-0.0392531\pi$
$920$	−40.4832	−	13.4010i	−1.33469	−	0.441817i
$921$	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
$925$	23.1460	−	13.1664i	0.761037	−	0.432909i
$926$	−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	$0.175612\pi$
$930$	16.0211	−	47.2572i	0.525351	−	1.54962i
$931$	−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
$935$	−16.8463	−	13.6631i	−0.550933	−	0.446833i
$936$	−11.8373	+	3.73061i	−0.386913	+	0.121939i
$937$	12.2093	+	29.4759i	0.398862	+	0.962937i	0.987937	+	0.154859i	$0.0494922\pi$
$937$	12.2093	+	29.4759i	0.398862	+	0.962937i	−0.589075	+	0.808078i	$0.700508\pi$
$938$	−4.31418	−	0.409263i	−0.140863	−	0.0133629i
$939$	−64.0910	+	64.0910i	−2.09153	+	2.09153i
$940$	7.65467	+	1.75269i	0.249668	+	0.0571666i
$941$	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
$945$	4.06403	−	113.069i	0.132203	−	3.67812i
$946$	−2.09168	−	6.80720i	−0.0680065	−	0.221321i
$947$	−3.39667	+	2.26958i	−0.110377	+	0.0737515i	−0.609534	−	0.792760i	$-0.708643\pi$
$947$	−3.39667	+	2.26958i	−0.110377	+	0.0737515i	0.499157	+	0.866512i	$0.333643\pi$
$948$	19.6338	+	12.9158i	0.637677	+	0.419485i
$949$	0.160952	−	0.809161i	0.00522473	−	0.0262665i
$950$	−50.0018	+	1.49615i	−1.62227	+	0.0485415i
$951$	−40.2126			−1.30398
$952$	−48.7005	+	23.2367i	−1.57839	+	0.753107i
$953$			12.3069i			0.398660i	0.979932	+	0.199330i	$0.0638766\pi$
$953$			12.3069i			0.398660i	−0.979932	+	0.199330i	$0.936123\pi$
$954$	−19.4717	+	10.4980i	−0.630421	+	0.339885i
$955$	8.44046	+	22.6455i	0.273127	+	0.732791i
$956$	−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
$960$	−38.5046	−	39.6273i	−1.24273	−	1.27896i
$961$	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
$965$	58.4893	+	13.8354i	1.88284	+	0.445378i
$966$	−12.8701	+	135.669i	−0.414090	+	4.36507i
$967$	22.2182	+	53.6396i	0.714491	+	1.72493i	0.688463	+	0.725272i	$0.258286\pi$
$967$	22.2182	+	53.6396i	0.714491	+	1.72493i	0.0260278	+	0.999661i	$0.491714\pi$
$968$	4.64618	+	14.7424i	0.149334	+	0.473839i
$969$	87.2315	+	22.5356i	2.80228	+	0.723947i
$970$	34.7960	−	26.7215i	1.11723	−	0.857977i
$971$	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
$975$	−2.74578	+	9.99098i	−0.0879354	+	0.319967i
$976$	2.89988	−	15.7592i	0.0928228	−	0.504438i
$977$	18.1960	+	7.53703i	0.582141	+	0.241131i	0.654266	−	0.756265i	$-0.272978\pi$
$977$	18.1960	+	7.53703i	0.582141	+	0.241131i	−0.0721243	+	0.997396i	$0.522978\pi$
$978$	−31.5814	−	9.45633i	−1.00986	−	0.302380i
$979$	10.3339	−	15.4658i	0.330273	−	0.494289i
$980$	−52.5299	−	37.3265i	−1.67800	−	1.19235i
$981$	−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	−0.180498	−	0.983575i	$-0.557771\pi$
$983$	−22.6886	−	4.51305i	−0.723655	−	0.143944i	−0.543157	+	0.839631i	$0.682771\pi$
$984$	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
$990$	−48.2453	−	6.33245i	−1.53334	−	0.201258i
$991$	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
$995$	34.6684	−	5.60978i	1.09906	−	0.177842i
$996$	12.7497	−	31.4172i	0.403990	−	0.995492i
$997$	−28.0244	+	5.57440i	−0.887542	+	0.176543i	−0.617749	−	0.786375i	$-0.711955\pi$
$997$	−28.0244	+	5.57440i	−0.887542	+	0.176543i	−0.269793	+	0.962918i	$0.586955\pi$
$998$	−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.99.89	yes	832
5.4	even	2	inner	680.2.co.a.99.16	yes	832
8.3	odd	2	inner	680.2.co.a.99.11	✓	832
17.11	odd	16	inner	680.2.co.a.419.94	yes	832
40.19	odd	2	inner	680.2.co.a.99.94	yes	832
85.79	odd	16	inner	680.2.co.a.419.11	yes	832
136.11	even	16	inner	680.2.co.a.419.16	yes	832
680.419	even	16	inner	680.2.co.a.419.89	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.co.a.99.11	✓	832	8.3	odd	2	inner
680.2.co.a.99.16	yes	832	5.4	even	2	inner
680.2.co.a.99.89	yes	832	1.1	even	1	trivial
680.2.co.a.99.94	yes	832	40.19	odd	2	inner
680.2.co.a.419.11	yes	832	85.79	odd	16	inner
680.2.co.a.419.16	yes	832	136.11	even	16	inner
680.2.co.a.419.89	yes	832	680.419	even	16	inner
680.2.co.a.419.94	yes	832	17.11	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} +(-2.03379 - 0.929359i) 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} +(-3.15543 + 0.208056i) 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} +(5.60114 + 4.04093i) 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} +(-3.78831 + 2.37670i) 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} +(3.27258 + 3.78024i) 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} +(9.68443 + 1.27113i) 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} +(-3.12069 + 5.50103i) 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} +(-9.96314 - 10.7061i) 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} +(6.61082 + 2.50938i) 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} +(-5.11945 - 1.21099i) 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} +(12.9085 - 4.91721i) 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} +(0.523948 + 1.40574i) q^{65} +(-9.04588 + 4.87700i) q^{66} +0.662256 q^{67} +(7.07382 - 4.23805i) q^{68} -20.8260i q^{69} +(12.6745 + 7.31104i) 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} +(-7.63606 - 13.4239i) 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} +(-0.192774 + 8.94219i) 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} +(-5.88993 - 7.09287i) 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} +(-19.5875 - 6.64053i) 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} +(15.8088 + 0.568217i) 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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