LMFDB - Embedded newform 840.2.cq.b.11.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(11,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 3, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.cq (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [128,0,0,0,64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.20
Character	$\chi$	$=$	840.11
Dual form			840.2.cq.b.611.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.739970 - 1.20517i) q^{2} +(0.999729 - 1.41441i) q^{3} +(-0.904890 + 1.78358i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.44437 - 0.158230i) q^{6} +(1.31611 - 2.29518i) q^{7} +(2.81912 - 0.229249i) q^{8} +(-1.00109 - 2.82804i) q^{9} +(0.673727 - 1.24342i) q^{10} +(4.33482 + 2.50271i) q^{11} +(1.61807 + 3.06298i) q^{12} -1.33854i q^{13} +(-3.73997 + 0.112230i) q^{14} +(1.72478 + 0.158588i) q^{15} +(-2.36235 - 3.22789i) q^{16} +(5.90615 + 3.40992i) q^{17} +(-2.66751 + 3.29915i) q^{18} +(3.05769 + 5.29608i) q^{19} +(-1.99707 + 0.108135i) q^{20} +(-1.93057 - 4.15607i) q^{21} +(-0.191435 - 7.07615i) q^{22} +(0.707474 + 1.22538i) q^{23} +(2.49411 - 4.21657i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.61318 + 0.990480i) q^{26} +(-5.00081 - 1.41134i) q^{27} +(2.90272 + 4.42427i) q^{28} -6.41887 q^{29} +(-1.08516 - 2.19600i) q^{30} +(-3.36538 - 1.94300i) q^{31} +(-2.14211 + 5.23559i) q^{32} +(7.87349 - 3.62916i) q^{33} +(-0.260828 - 9.64117i) q^{34} +(2.64574 - 0.00781089i) q^{35} +(5.94993 + 0.773546i) q^{36} +(7.76468 - 4.48294i) q^{37} +(4.12010 - 7.60399i) q^{38} +(-1.89324 - 1.33818i) q^{39} +(1.60810 + 2.32681i) q^{40} -6.55003i q^{41} +(-3.58022 + 5.40204i) q^{42} -2.94890 q^{43} +(-8.38633 + 5.46685i) q^{44} +(1.94861 - 2.28099i) q^{45} +(0.953288 - 1.75937i) q^{46} +(-1.19963 - 2.07781i) q^{47} +(-6.92726 + 0.114301i) q^{48} +(-3.53573 - 6.04141i) q^{49} +(1.41370 - 0.0382455i) q^{50} +(10.7275 - 4.94470i) q^{51} +(2.38740 + 1.21123i) q^{52} +(-2.34909 + 4.06874i) q^{53} +(1.99955 + 7.07120i) q^{54} +5.00542i q^{55} +(3.18409 - 6.77212i) q^{56} +(10.5477 + 0.969824i) q^{57} +(4.74977 + 7.73585i) q^{58} +(-7.92470 - 4.57533i) q^{59} +(-1.84359 + 2.93278i) q^{60} +(9.49973 - 5.48467i) q^{61} +(0.148622 + 5.49363i) q^{62} +(-7.80841 - 1.42433i) q^{63} +(7.89489 - 1.29256i) q^{64} +(1.15921 - 0.669271i) q^{65} +(-10.1999 - 6.80346i) q^{66} +(6.48128 - 11.2259i) q^{67} +(-11.4263 + 7.44852i) q^{68} +(2.44047 + 0.224393i) q^{69} +(-1.96718 - 3.18280i) q^{70} -4.54230 q^{71} +(-3.47051 - 7.74310i) q^{72} +(-0.242334 + 0.419735i) q^{73} +(-11.1484 - 6.04055i) q^{74} +(0.725047 + 1.57299i) q^{75} +(-12.2129 + 0.661286i) q^{76} +(11.4493 - 6.65538i) q^{77} +(-0.211797 + 3.27190i) q^{78} +(-8.94551 + 5.16469i) q^{79} +(1.61426 - 3.65980i) q^{80} +(-6.99566 + 5.66223i) q^{81} +(-7.89392 + 4.84682i) q^{82} +11.7036i q^{83} +(9.15965 + 0.317444i) q^{84} +6.81983i q^{85} +(2.18210 + 3.55394i) q^{86} +(-6.41712 + 9.07888i) q^{87} +(12.7941 + 6.06169i) q^{88} +(-6.36443 + 3.67451i) q^{89} +(-4.19090 - 0.660559i) q^{90} +(-3.07220 - 1.76166i) q^{91} +(-2.82576 + 0.153005i) q^{92} +(-6.11266 + 2.81753i) q^{93} +(-1.61644 + 2.98328i) q^{94} +(-3.05769 + 5.29608i) q^{95} +(5.26372 + 8.26398i) q^{96} -10.1416 q^{97} +(-4.66461 + 8.73163i) q^{98} +(2.73825 - 14.7645i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 64 q^{5} + 2 q^{12} + 6 q^{14} + 8 q^{16} - 4 q^{18} - 8 q^{21} + 4 q^{22} + 20 q^{24} - 64 q^{25} + 16 q^{26} - 6 q^{28} + 10 q^{32} + 24 q^{34} + 20 q^{36} + 16 q^{38} + 18 q^{42} - 6 q^{44} + 8 q^{46}+ \cdots - 14 q^{98}+O(q^{100}) $ 128 * q + 64 * q^5 + 2 * q^12 + 6 * q^14 + 8 * q^16 - 4 * q^18 - 8 * q^21 + 4 * q^22 + 20 * q^24 - 64 * q^25 + 16 * q^26 - 6 * q^28 + 10 * q^32 + 24 * q^34 + 20 * q^36 + 16 * q^38 + 18 * q^42 - 6 * q^44 + 8 * q^46 - 44 * q^48 + 8 * q^49 + 20 * q^51 - 6 * q^52 - 16 * q^54 + 18 * q^56 - 8 * q^58 - 2 * q^60 + 20 * q^62 + 28 * q^63 + 22 * q^66 + 32 * q^67 + 2 * q^68 - 40 * q^69 - 6 * q^70 + 48 * q^71 - 54 * q^72 - 8 * q^73 + 26 * q^74 - 24 * q^76 - 84 * q^78 - 8 * q^80 + 4 * q^81 - 12 * q^82 + 6 * q^84 - 46 * q^86 + 36 * q^87 - 20 * q^88 - 8 * q^90 - 24 * q^91 + 40 * q^92 + 12 * q^94 + 22 * q^96 + 32 * q^97 - 14 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.739970	−	1.20517i	−0.523238	−	0.852187i
$2$	−0.739970	−	1.20517i	−0.523238	−	0.852187i
$3$	0.999729	−	1.41441i	0.577194	−	0.816607i
$3$	0.999729	−	1.41441i	0.577194	−	0.816607i
$4$	−0.904890	+	1.78358i	−0.452445	+	0.891792i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−2.44437	−	0.158230i	−0.997911	−	0.0645971i
$7$	1.31611	−	2.29518i	0.497441	−	0.867498i
$7$	1.31611	−	2.29518i	0.497441	−	0.867498i
$8$	2.81912	−	0.229249i	0.996710	−	0.0810518i
$9$	−1.00109	−	2.82804i	−0.333695	−	0.942681i
$10$	0.673727	−	1.24342i	0.213051	−	0.393204i
$11$	4.33482	+	2.50271i	1.30700	+	0.754596i	0.981594	−	0.190979i	$-0.0611664\pi$
$11$	4.33482	+	2.50271i	1.30700	+	0.754596i	0.325404	+	0.945575i	$0.394500\pi$
$12$	1.61807	+	3.06298i	0.467096	+	0.884207i
$13$		−	1.33854i		−	0.371245i	−0.982621	−	0.185622i	$-0.940570\pi$
$13$		−	1.33854i		−	0.371245i	0.982621	−	0.185622i	$-0.0594301\pi$
$14$	−3.73997	+	0.112230i	−0.999550	+	0.0299947i
$15$	1.72478	+	0.158588i	0.445335	+	0.0409472i
$16$	−2.36235	−	3.22789i	−0.590587	−	0.806974i
$17$	5.90615	+	3.40992i	1.43245	+	0.827026i	0.997307	−	0.0733352i	$-0.0233643\pi$
$17$	5.90615	+	3.40992i	1.43245	+	0.827026i	0.435144	+	0.900361i	$0.356698\pi$
$18$	−2.66751	+	3.29915i	−0.628739	+	0.777617i
$19$	3.05769	+	5.29608i	0.701482	+	1.21500i	0.967946	+	0.251158i	$0.0808114\pi$
$19$	3.05769	+	5.29608i	0.701482	+	1.21500i	−0.266464	+	0.963845i	$0.585855\pi$
$20$	−1.99707	+	0.108135i	−0.446559	+	0.0241797i
$21$	−1.93057	−	4.15607i	−0.421285	−	0.906928i
$22$	−0.191435	−	7.07615i	−0.0408140	−	1.50864i
$23$	0.707474	+	1.22538i	0.147518	+	0.255509i	0.930310	−	0.366775i	$-0.119538\pi$
$23$	0.707474	+	1.22538i	0.147518	+	0.255509i	−0.782791	+	0.622284i	$0.786205\pi$
$24$	2.49411	−	4.21657i	0.509107	−	0.860703i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.61318	+	0.990480i	−0.316370	+	0.194249i
$27$	−5.00081	−	1.41134i	−0.962407	−	0.271612i
$28$	2.90272	+	4.42427i	0.548563	+	0.836109i
$29$	−6.41887			−1.19195			−0.595977	−	0.803002i	$-0.703235\pi$
$29$	−6.41887			−1.19195			−0.595977	+	0.803002i	$0.703235\pi$
$30$	−1.08516	−	2.19600i	−0.198121	−	0.400934i
$31$	−3.36538	−	1.94300i	−0.604440	−	0.348974i	0.166346	−	0.986067i	$-0.446803\pi$
$31$	−3.36538	−	1.94300i	−0.604440	−	0.348974i	−0.770786	+	0.637094i	$0.780136\pi$
$32$	−2.14211	+	5.23559i	−0.378675	+	0.925530i
$33$	7.87349	−	3.62916i	1.37060	−	0.631756i
$34$	−0.260828	−	9.64117i	−0.0447316	−	1.65345i
$35$	2.64574	−	0.00781089i	0.447212	−	0.00132028i
$36$	5.94993	+	0.773546i	0.991654	+	0.128924i
$37$	7.76468	−	4.48294i	1.27651	−	0.736991i	0.300302	−	0.953844i	$-0.402913\pi$
$37$	7.76468	−	4.48294i	1.27651	−	0.736991i	0.976204	+	0.216853i	$0.0695793\pi$
$38$	4.12010	−	7.60399i	0.668368	−	1.23353i
$39$	−1.89324	−	1.33818i	−0.303161	−	0.214280i
$40$	1.60810	+	2.32681i	0.254262	+	0.367900i
$41$		−	6.55003i		−	1.02294i	−0.859301	−	0.511471i	$-0.829101\pi$
$41$		−	6.55003i		−	1.02294i	0.859301	−	0.511471i	$-0.170899\pi$
$42$	−3.58022	+	5.40204i	−0.552440	+	0.833553i
$43$	−2.94890			−0.449703			−0.224852	−	0.974393i	$-0.572190\pi$
$43$	−2.94890			−0.449703			−0.224852	+	0.974393i	$0.572190\pi$
$44$	−8.38633	+	5.46685i	−1.26429	+	0.824158i
$45$	1.94861	−	2.28099i	0.290482	−	0.340029i
$46$	0.953288	−	1.75937i	0.140555	−	0.259405i
$47$	−1.19963	−	2.07781i	−0.174983	−	0.303080i	0.765172	−	0.643826i	$-0.222654\pi$
$47$	−1.19963	−	2.07781i	−0.174983	−	0.303080i	−0.940156	+	0.340746i	$0.889321\pi$
$48$	−6.92726	+	0.114301i	−0.999864	+	0.0164979i
$49$	−3.53573	−	6.04141i	−0.505105	−	0.863058i
$50$	1.41370	−	0.0382455i	0.199927	−	0.00540873i
$51$	10.7275	−	4.94470i	1.50216	−	0.692396i
$52$	2.38740	+	1.21123i	0.331073	+	0.167968i
$53$	−2.34909	+	4.06874i	−0.322672	+	0.558885i	−0.981039	−	0.193813i	$-0.937915\pi$
$53$	−2.34909	+	4.06874i	−0.322672	+	0.558885i	0.658366	+	0.752698i	$0.271248\pi$
$54$	1.99955	+	7.07120i	0.272104	+	0.962268i
$55$			5.00542i			0.674931i
$56$	3.18409	−	6.77212i	0.425492	−	0.904962i
$57$	10.5477	+	0.969824i	1.39707	+	0.128456i
$58$	4.74977	+	7.73585i	0.623675	+	1.01577i
$59$	−7.92470	−	4.57533i	−1.03171	−	0.595657i	−0.114234	−	0.993454i	$-0.536441\pi$
$59$	−7.92470	−	4.57533i	−1.03171	−	0.595657i	−0.917473	+	0.397797i	$0.869775\pi$
$60$	−1.84359	+	2.93278i	−0.238006	+	0.378620i
$61$	9.49973	−	5.48467i	1.21632	−	0.702240i	0.252188	−	0.967678i	$-0.418850\pi$
$61$	9.49973	−	5.48467i	1.21632	−	0.702240i	0.964128	+	0.265438i	$0.0855165\pi$
$62$	0.148622	+	5.49363i	0.0188750	+	0.697692i
$63$	−7.80841	−	1.42433i	−0.983767	−	0.179449i
$64$	7.89489	−	1.29256i	0.986861	−	0.161570i
$65$	1.15921	−	0.669271i	0.143782	−	0.0830128i
$66$	−10.1999	−	6.80346i	−1.25552	−	0.837448i
$67$	6.48128	−	11.2259i	0.791815	−	1.37146i	−0.133028	−	0.991112i	$-0.542470\pi$
$67$	6.48128	−	11.2259i	0.791815	−	1.37146i	0.924842	−	0.380351i	$-0.124197\pi$
$68$	−11.4263	+	7.44852i	−1.38564	+	0.903265i
$69$	2.44047	+	0.224393i	0.293798	+	0.0270138i
$70$	−1.96718	−	3.18280i	−0.235123	−	0.380417i
$71$	−4.54230			−0.539072			−0.269536	−	0.962990i	$-0.586870\pi$
$71$	−4.54230			−0.539072			−0.269536	+	0.962990i	$0.586870\pi$
$72$	−3.47051	−	7.74310i	−0.409003	−	0.912533i
$73$	−0.242334	+	0.419735i	−0.0283630	+	0.0491262i	−0.879859	−	0.475236i	$-0.842363\pi$
$73$	−0.242334	+	0.419735i	−0.0283630	+	0.0491262i	0.851495	+	0.524362i	$0.175696\pi$
$74$	−11.1484	−	6.04055i	−1.29597	−	0.702200i
$75$	0.725047	+	1.57299i	0.0837212	+	0.181634i
$76$	−12.2129	+	0.661286i	−1.40091	+	0.0758548i
$77$	11.4493	−	6.65538i	1.30476	−	0.758451i
$78$	−0.211797	+	3.27190i	−0.0239813	+	0.370469i
$79$	−8.94551	+	5.16469i	−1.00645	+	0.581073i	−0.910150	−	0.414279i	$-0.864034\pi$
$79$	−8.94551	+	5.16469i	−1.00645	+	0.581073i	−0.0962985	+	0.995352i	$0.530700\pi$
$80$	1.61426	−	3.65980i	0.180480	−	0.409178i
$81$	−6.99566	+	5.66223i	−0.777295	+	0.629136i
$82$	−7.89392	+	4.84682i	−0.871738	+	0.535242i
$83$			11.7036i			1.28464i	0.766437	+	0.642320i	$0.222028\pi$
$83$			11.7036i			1.28464i	−0.766437	+	0.642320i	$0.777972\pi$
$84$	9.15965	+	0.317444i	0.999400	+	0.0346360i
$85$			6.81983i			0.739714i
$86$	2.18210	+	3.55394i	0.235302	+	0.383231i
$87$	−6.41712	+	9.07888i	−0.687988	+	0.973358i
$88$	12.7941	+	6.06169i	1.36386	+	0.646178i
$89$	−6.36443	+	3.67451i	−0.674629	+	0.389497i	−0.797828	−	0.602885i	$-0.794018\pi$
$89$	−6.36443	+	3.67451i	−0.674629	+	0.389497i	0.123200	+	0.992382i	$0.460684\pi$
$90$	−4.19090	−	0.660559i	−0.441760	−	0.0696290i
$91$	−3.07220	−	1.76166i	−0.322054	−	0.184672i
$92$	−2.82576	+	0.153005i	−0.294605	+	0.0159519i
$93$	−6.11266	+	2.81753i	−0.633853	+	0.292165i
$94$	−1.61644	+	2.98328i	−0.166723	+	0.307702i
$95$	−3.05769	+	5.29608i	−0.313712	+	0.543366i
$96$	5.26372	+	8.26398i	0.537226	+	0.843439i
$97$	−10.1416			−1.02973			−0.514864	−	0.857272i	$-0.672157\pi$
$97$	−10.1416			−1.02973			−0.514864	+	0.857272i	$0.672157\pi$
$98$	−4.66461	+	8.73163i	−0.471197	+	0.882028i
$99$	2.73825	−	14.7645i	0.275204	−	1.48389i
$100$	−1.09218	−	1.67545i	−0.109218	−	0.167545i
$101$	−0.868841	+	1.50488i	−0.0864529	+	0.149741i	−0.906009	−	0.423258i	$-0.860887\pi$
$101$	−0.868841	+	1.50488i	−0.0864529	+	0.149741i	0.819556	+	0.572998i	$0.194220\pi$
$102$	−13.8973	−	9.26964i	−1.37604	−	0.917831i
$103$	−5.09600	+	2.94218i	−0.502124	+	0.289901i	−0.729590	−	0.683885i	$-0.760289\pi$
$103$	−5.09600	+	2.94218i	−0.502124	+	0.289901i	0.227467	+	0.973786i	$0.426956\pi$
$104$	−0.306859	−	3.77351i	−0.0300900	−	0.370023i
$105$	2.63397	−	3.74996i	0.257050	−	0.365958i
$106$	6.64180	−	0.179684i	0.645109	−	0.0174525i
$107$	−4.19466	+	2.42179i	−0.405514	+	0.234123i	−0.688860	−	0.724894i	$-0.741889\pi$
$107$	−4.19466	+	2.42179i	−0.405514	+	0.234123i	0.283347	+	0.959018i	$0.408555\pi$
$108$	7.04242	−	7.64227i	0.677657	−	0.735378i
$109$	6.33338	+	3.65658i	0.606628	+	0.350237i	0.771645	−	0.636054i	$-0.219434\pi$
$109$	6.33338	+	3.65658i	0.606628	+	0.350237i	−0.165017	+	0.986291i	$0.552768\pi$
$110$	6.03240	−	3.70386i	0.575167	−	0.353149i
$111$	1.42188	−	15.4641i	0.134959	−	1.46779i
$112$	−10.5177	+	1.17377i	−0.993830	+	0.110911i
$113$		−	0.486213i		−	0.0457391i	−0.999738	−	0.0228695i	$-0.992720\pi$
$113$		−	0.486213i		−	0.0457391i	0.999738	−	0.0228695i	$-0.00728023\pi$
$114$	−6.63614	−	13.4294i	−0.621532	−	1.25778i
$115$	−0.707474	+	1.22538i	−0.0659723	+	0.114267i
$116$	5.80837	−	11.4486i	0.539293	−	1.06297i
$117$	−3.78545	+	1.33999i	−0.349965	+	0.123883i
$118$	0.349971	+	12.9362i	0.0322174	+	1.19088i
$119$	15.5995	−	9.06788i	1.43000	−	0.831251i
$120$	4.89871	+	0.0516749i	0.447189	+	0.00471725i
$121$	7.02712	+	12.1713i	0.638829	+	1.10648i
$122$	−13.6395	−	7.39034i	−1.23486	−	0.669090i
$123$	−9.26439	−	6.54825i	−0.835342	−	0.590436i
$124$	6.51081	−	4.24424i	0.584688	−	0.381144i
$125$	−1.00000			−0.0894427
$126$	4.06142	+	10.4645i	0.361820	+	0.932248i
$127$			8.03417i			0.712918i	0.934311	+	0.356459i	$0.116016\pi$
$127$			8.03417i			0.712918i	−0.934311	+	0.356459i	$0.883984\pi$
$128$	−7.39974	−	8.55826i	−0.654051	−	0.756451i
$129$	−2.94810	+	4.17094i	−0.259566	+	0.367231i
$130$	−1.66437	−	0.901811i	−0.145975	−	0.0790941i
$131$	12.7613	−	7.36771i	1.11496	−	0.643720i	0.174847	−	0.984596i	$-0.444057\pi$
$131$	12.7613	−	7.36771i	1.11496	−	0.643720i	0.940108	+	0.340875i	$0.110723\pi$
$132$	−0.651721	+	17.3270i	−0.0567250	+	1.50812i
$133$	16.1797	−	0.0477666i	1.40296	−	0.00414189i
$134$	−18.3251	+	0.495759i	−1.58305	+	0.0428271i
$135$	−1.27815	−	5.03650i	−0.110006	−	0.433473i
$136$	17.4319	+	8.25899i	1.49477	+	0.708202i
$137$	−4.54539	−	2.62428i	−0.388339	−	0.224207i	0.293101	−	0.956081i	$-0.405313\pi$
$137$	−4.54539	−	2.62428i	−0.388339	−	0.224207i	−0.681440	+	0.731874i	$0.738646\pi$
$138$	−1.53544	−	3.10723i	−0.130705	−	0.264505i
$139$	−8.53551			−0.723972			−0.361986	−	0.932183i	$-0.617901\pi$
$139$	−8.53551			−0.723972			−0.361986	+	0.932183i	$0.617901\pi$
$140$	−2.38017	+	4.72597i	−0.201161	+	0.399417i
$141$	−4.13817	−	0.380492i	−0.348497	−	0.0320432i
$142$	3.36117	+	5.47427i	0.282063	+	0.459390i
$143$	3.34998	−	5.80234i	0.280140	−	0.485216i
$144$	−6.76371	+	9.91222i	−0.563643	+	0.826019i
$145$	−3.20943	−	5.55890i	−0.266529	−	0.461642i
$146$	0.685173	−	0.0185363i	0.0567053	−	0.00153408i
$147$	−12.0798	−	1.03881i	−0.996323	−	0.0856794i
$148$	0.969525	+	17.9055i	0.0796945	+	1.47183i
$149$	6.09770	+	10.5615i	0.499543	+	0.865234i	1.00000		0.000527481i	$-0.000167903\pi$
$149$	6.09770	+	10.5615i	0.499543	+	0.865234i	−0.500457	+	0.865762i	$0.666835\pi$
$150$	1.35922	−	2.03777i	0.110980	−	0.166384i
$151$	−6.39021	−	3.68939i	−0.520028	−	0.300238i	0.216918	−	0.976190i	$-0.430399\pi$
$151$	−6.39021	−	3.68939i	−0.520028	−	0.300238i	−0.736946	+	0.675952i	$0.763733\pi$
$152$	9.83412	+	14.2293i	0.797653	+	1.15415i
$153$	3.73083	−	20.1165i	0.301620	−	1.62632i
$154$	−16.4930	−	8.87358i	−1.32904	−	0.715053i
$155$		−	3.88600i		−	0.312131i
$156$	4.09993	−	2.16585i	0.328257	−	0.173407i
$157$	19.2824	+	11.1327i	1.53890	+	0.888484i	0.998903	+	0.0468169i	$0.0149077\pi$
$157$	19.2824	+	11.1327i	1.53890	+	0.888484i	0.539996	+	0.841667i	$0.318426\pi$
$158$	12.8438	+	6.95918i	1.02179	+	0.553643i
$159$	3.40640	+	7.39020i	0.270145	+	0.586081i
$160$	−5.60521	+	0.762673i	−0.443130	+	0.0602946i
$161$	3.74358	−	0.0110520i	0.295036	−	0.000871020i
$162$	12.0005	+	4.24111i	0.942852	+	0.333213i
$163$	−1.69845	−	2.94180i	−0.133033	−	0.230420i	0.791811	−	0.610766i	$-0.209138\pi$
$163$	−1.69845	−	2.94180i	−0.133033	−	0.230420i	−0.924844	+	0.380346i	$0.875805\pi$
$164$	11.6825	+	5.92705i	0.912252	+	0.462825i
$165$	7.07970	+	5.00406i	0.551154	+	0.389566i
$166$	14.1049	−	8.66033i	1.09475	−	0.672172i
$167$	−3.48566			−0.269728			−0.134864	−	0.990864i	$-0.543060\pi$
$167$	−3.48566			−0.269728			−0.134864	+	0.990864i	$0.543060\pi$
$168$	−6.39529	−	11.2739i	−0.493407	−	0.869798i
$169$	11.2083			0.862177
$170$	8.21908	−	5.04647i	0.630375	−	0.387046i
$171$	11.9165	−	13.9491i	0.911279	−	1.06671i
$172$	2.66843	−	5.25962i	0.203466	−	0.401042i
$173$	−6.05041	−	10.4796i	−0.460004	−	0.796751i	0.538956	−	0.842334i	$-0.318819\pi$
$173$	−6.05041	−	10.4796i	−0.460004	−	0.796751i	−0.998961	+	0.0455831i	$0.985485\pi$
$174$	15.6901	+	1.01566i	1.18946	+	0.0769968i
$175$	1.32963	+	2.28737i	0.100511	+	0.172909i
$176$	−2.16188	−	19.9046i	−0.162958	−	1.50037i
$177$	−14.3939	+	6.63465i	−1.08191	+	0.498691i
$178$	9.13791	+	4.95123i	0.684915	+	0.371110i
$179$	12.1532	+	7.01667i	0.908376	+	0.524451i	0.879908	−	0.475144i	$-0.157604\pi$
$179$	12.1532	+	7.01667i	0.908376	+	0.524451i	0.0284674	+	0.999595i	$0.490937\pi$
$180$	2.30505	+	5.53956i	0.171808	+	0.412894i
$181$			12.5037i			0.929392i	0.885470	+	0.464696i	$0.153836\pi$
$181$			12.5037i			0.929392i	−0.885470	+	0.464696i	$0.846164\pi$
$182$	0.150224	+	5.00611i	0.0111354	+	0.371078i
$183$	1.73960	−	18.9197i	0.128595	−	1.39858i
$184$	2.27537	+	3.29231i	0.167743	+	0.242712i
$185$	7.76468	+	4.48294i	0.570871	+	0.329592i
$186$	7.91880	+	5.28193i	0.580635	+	0.387290i
$187$	17.0681	+	29.5628i	1.24814	+	2.16184i
$188$	4.79149	−	0.259443i	0.349455	−	0.0189218i
$189$	−9.82087	+	9.62032i	−0.714363	+	0.699775i
$190$	8.64529	−	0.233886i	0.627195	−	0.0169678i
$191$	10.5240	+	18.2280i	0.761487	+	1.31893i	0.942084	+	0.335377i	$0.108864\pi$
$191$	10.5240	+	18.2280i	0.761487	+	1.31893i	−0.180597	+	0.983557i	$0.557803\pi$
$192$	6.06454	−	12.4588i	0.437671	−	0.899135i
$193$	−2.36945	+	4.10401i	−0.170557	+	0.295413i	−0.938615	−	0.344967i	$-0.887890\pi$
$193$	−2.36945	+	4.10401i	−0.170557	+	0.295413i	0.768058	+	0.640381i	$0.221223\pi$
$194$	7.50450	+	12.2224i	0.538792	+	0.877520i
$195$	0.212276	−	2.30868i	0.0152014	−	0.165328i
$196$	13.9748	−	0.839473i	0.998201	−	0.0599623i
$197$	−13.9415			−0.993292			−0.496646	−	0.867953i	$-0.665435\pi$
$197$	−13.9415			−0.993292			−0.496646	+	0.867953i	$0.665435\pi$
$198$	−19.8200	+	7.62521i	−1.40855	+	0.541900i
$199$	−16.6988	−	9.64104i	−1.18374	−	0.683435i	−0.226867	−	0.973926i	$-0.572848\pi$
$199$	−16.6988	−	9.64104i	−1.18374	−	0.683435i	−0.956878	+	0.290491i	$0.906182\pi$
$200$	−1.21103	+	2.55606i	−0.0856324	+	0.180740i
$201$	−9.39846	−	20.3900i	−0.662916	−	1.43820i
$202$	2.45656	−	0.0664585i	0.172843	−	0.00467600i
$203$	−8.44790	+	14.7325i	−0.592927	+	1.03402i
$204$	−0.887962	+	23.6079i	−0.0621698	+	1.65288i
$205$	5.67249	−	3.27501i	0.396184	−	0.228737i
$206$	7.31672	+	3.96444i	0.509780	+	0.276216i
$207$	2.75719	−	3.22748i	0.191638	−	0.224325i
$208$	−4.32067	+	3.16210i	−0.299585	+	0.219252i
$209$			30.6101i			2.11734i
$210$	−6.46841	−	0.399543i	−0.446363	−	0.0275711i
$211$	−7.88888			−0.543093			−0.271547	−	0.962425i	$-0.587535\pi$
$211$	−7.88888			−0.543093			−0.271547	+	0.962425i	$0.587535\pi$
$212$	−5.13128	−	7.87156i	−0.352418	−	0.540621i
$213$	−4.54107	+	6.42466i	−0.311149	+	0.440210i
$214$	6.02260	+	3.26325i	0.411697	+	0.223071i
$215$	−1.47445	−	2.55382i	−0.100557	−	0.174169i
$216$	−14.4214	−	2.83229i	−0.981255	−	0.192713i
$217$	−8.88874	+	5.16696i	−0.603407	+	0.350756i
$218$	−0.279695	−	10.3386i	−0.0189433	−	0.700217i
$219$	0.351407	+	0.762379i	0.0237459	+	0.0515168i
$220$	−8.92759	−	4.52935i	−0.601898	−	0.305369i
$221$	4.56431	−	7.90562i	0.307029	−	0.531790i
$222$	−19.6891	+	9.72938i	−1.32145	+	0.652993i
$223$		−	9.06519i		−	0.607050i	−0.952823	−	0.303525i	$-0.901836\pi$
$223$		−	9.06519i		−	0.607050i	0.952823	−	0.303525i	$-0.0981636\pi$
$224$	9.19739	+	11.8071i	0.614527	+	0.788896i
$225$	2.94970	+	0.547056i	0.196647	+	0.0364704i
$226$	−0.585971	+	0.359783i	−0.0389782	+	0.0239324i
$227$	6.64226	+	3.83491i	0.440862	+	0.254532i	0.703963	−	0.710236i	$-0.251412\pi$
$227$	6.64226	+	3.83491i	0.440862	+	0.254532i	−0.263101	+	0.964768i	$0.584745\pi$
$228$	−11.2742	+	17.9351i	−0.746654	+	1.18778i
$229$	−13.1244	+	7.57737i	−0.867285	+	0.500727i	−0.866445	−	0.499273i	$-0.833601\pi$
$229$	−13.1244	+	7.57737i	−0.867285	+	0.500727i	−0.000839635		1.00000i	$0.500267\pi$
$230$	2.00031	−	0.0541153i	0.131896	−	0.00356826i
$231$	2.03275	−	22.8475i	0.133745	−	1.50325i
$232$	−18.0956	+	1.47152i	−1.18803	+	0.0966099i
$233$	13.0180	−	7.51596i	0.852839	−	0.492387i	−0.00876859	−	0.999962i	$-0.502791\pi$
$233$	13.0180	−	7.51596i	0.852839	−	0.492387i	0.861608	+	0.507575i	$0.169458\pi$
$234$	4.41605	+	3.57058i	0.288686	+	0.233416i
$235$	1.19963	−	2.07781i	0.0782550	−	0.135542i
$236$	15.3315	−	9.99420i	0.997993	−	0.650567i
$237$	−1.63811	+	17.8159i	−0.106407	+	1.15726i
$238$	−22.4715	−	12.0901i	−1.45661	−	0.783688i
$239$	−27.1897			−1.75876			−0.879378	−	0.476124i	$-0.842041\pi$
$239$	−27.1897			−1.75876			−0.879378	+	0.476124i	$0.842041\pi$
$240$	−3.56262	−	5.94203i	−0.229966	−	0.383557i
$241$	13.1644	−	22.8013i	0.847991	−	1.46876i	−0.0350070	−	0.999387i	$-0.511145\pi$
$241$	13.1644	−	22.8013i	0.847991	−	1.46876i	0.882998	−	0.469377i	$-0.155521\pi$
$242$	9.46872	−	17.4753i	0.608672	−	1.12336i
$243$	1.01492	+	15.5554i	0.0651074	+	0.997878i
$244$	1.18617	+	21.9066i	0.0759367	+	1.40243i
$245$	3.46415	−	6.08274i	0.221316	−	0.388612i
$246$	−1.03641	+	16.0107i	−0.0660791	+	1.02081i
$247$	7.08902	−	4.09285i	0.451063	−	0.260422i
$248$	−9.93284	−	4.70605i	−0.630736	−	0.298834i
$249$	16.5537	+	11.7004i	1.04905	+	0.741486i
$250$	0.739970	+	1.20517i	0.0467998	+	0.0762219i
$251$		−	10.1741i		−	0.642187i	−0.947048	−	0.321093i	$-0.895950\pi$
$251$		−	10.1741i		−	0.642187i	0.947048	−	0.321093i	$-0.104050\pi$
$252$	9.60616	−	12.6381i	0.605131	−	0.796126i
$253$			7.08241i			0.445267i
$254$	9.68258	−	5.94505i	0.607539	−	0.373025i
$255$	9.64600	+	6.81798i	0.604056	+	0.426958i
$256$	−4.83861	+	15.2508i	−0.302413	+	0.953177i
$257$	−13.2179	+	7.63137i	−0.824511	+	0.476032i	−0.851970	−	0.523591i	$-0.824592\pi$
$257$	−13.2179	+	7.63137i	−0.824511	+	0.476032i	0.0274586	+	0.999623i	$0.491259\pi$
$258$	7.20822	+	0.466605i	0.448764	+	0.0290495i
$259$	−0.0700316	−	23.7214i	−0.00435155	−	1.47398i
$260$	0.144743	+	2.67317i	0.00897659	+	0.165783i
$261$	6.42583	+	18.1528i	0.397749	+	1.12363i
$262$	−18.3223	−	9.92765i	−1.13196	−	0.613332i
$263$	−8.95529	+	15.5110i	−0.552207	+	0.956450i	0.445908	+	0.895079i	$0.352881\pi$
$263$	−8.95529	+	15.5110i	−0.552207	+	0.956450i	−0.998115	+	0.0613715i	$0.980453\pi$
$264$	21.3644	−	12.0360i	1.31488	−	0.740767i
$265$	−4.69818			−0.288607
$266$	−12.0301	−	19.4640i	−0.737610	−	1.19342i
$267$	−1.16546	+	12.6754i	−0.0713252	+	0.775722i
$268$	14.1575	+	21.7181i	0.864808	+	1.32665i
$269$	7.89989	−	13.6830i	0.481665	−	0.834268i	−0.518114	−	0.855312i	$-0.673366\pi$
$269$	7.89989	−	13.6830i	0.481665	−	0.834268i	0.999779	+	0.0210437i	$0.00669890\pi$
$270$	−5.12406	+	5.26726i	−0.311841	+	0.320555i
$271$	−19.2408	+	11.1087i	−1.16879	+	0.674803i	−0.953396	−	0.301723i	$-0.902438\pi$
$271$	−19.2408	+	11.1087i	−1.16879	+	0.674803i	−0.215398	+	0.976526i	$0.569105\pi$
$272$	−2.94553	−	27.1198i	−0.178599	−	1.64438i
$273$	−5.56307	+	2.58415i	−0.336692	+	0.156400i
$274$	0.200734	+	7.41987i	0.0121268	+	0.448251i
$275$	−4.33482	+	2.50271i	−0.261400	+	0.150919i
$276$	−2.60858	+	4.14973i	−0.157018	+	0.249784i
$277$	15.9572	+	9.21289i	0.958775	+	0.553549i	0.895796	−	0.444466i	$-0.146607\pi$
$277$	15.9572	+	9.21289i	0.958775	+	0.553549i	0.0629791	+	0.998015i	$0.479940\pi$
$278$	6.31602	+	10.2868i	0.378810	+	0.616960i
$279$	−2.12586	+	11.4625i	−0.127272	+	0.686245i
$280$	7.45687	−	0.628553i	0.445633	−	0.0375632i
$281$		−	5.53176i		−	0.329997i	−0.986294	−	0.164999i	$-0.947238\pi$
$281$		−	5.53176i		−	0.329997i	0.986294	−	0.164999i	$-0.0527620\pi$
$282$	2.60356	+	5.26877i	0.155040	+	0.313751i
$283$	−0.765939	+	1.32665i	−0.0455303	+	0.0788609i	−0.887892	−	0.460051i	$-0.847831\pi$
$283$	−0.765939	+	1.32665i	−0.0455303	+	0.0788609i	0.842362	+	0.538912i	$0.181164\pi$
$284$	4.11028	−	8.10158i	0.243900	−	0.480741i
$285$	4.43394	+	9.61945i	0.262644	+	0.569807i
$286$	−9.47172	+	0.256243i	−0.560074	+	0.0151520i
$287$	−15.0335	−	8.62052i	−0.887400	−	0.508853i
$288$	16.9509	+	0.816707i	0.998841	+	0.0481249i
$289$	14.7550	+	25.5565i	0.867944	+	1.50332i
$290$	−4.32456	+	7.98134i	−0.253947	+	0.468681i
$291$	−10.1389	+	14.3444i	−0.594352	+	0.840883i
$292$	−0.529347	−	0.812037i	−0.0309777	−	0.0475209i
$293$	27.9448			1.63255			0.816276	−	0.577662i	$-0.196035\pi$
$293$	27.9448			1.63255			0.816276	+	0.577662i	$0.196035\pi$
$294$	7.68672	+	15.3269i	0.448299	+	0.893884i
$295$		−	9.15065i		−	0.532772i
$296$	20.8619	−	14.4180i	1.21257	−	0.838029i
$297$	−18.1455	−	18.6335i	−1.05291	−	1.08122i
$298$	8.21637	−	15.1640i	0.475961	−	0.878427i
$299$	1.64022	−	0.946983i	0.0948565	−	0.0547654i
$300$	−3.46165	−	0.130203i	−0.199859	−	0.00751727i
$301$	−3.88107	+	6.76827i	−0.223701	+	0.390117i
$302$	0.282205	+	10.4313i	0.0162391	+	0.600257i
$303$	1.25990	+	2.73336i	0.0723794	+	0.157028i
$304$	9.87184	−	22.3811i	0.566189	−	1.28364i
$305$	9.49973	+	5.48467i	0.543953	+	0.314051i
$306$	−27.0045	+	10.3893i	−1.54375	+	0.593915i
$307$	−4.72906			−0.269902			−0.134951	−	0.990852i	$-0.543088\pi$
$307$	−4.72906			−0.269902			−0.134951	+	0.990852i	$0.543088\pi$
$308$	1.51011	+	26.4431i	0.0860468	+	1.50674i
$309$	−0.933186	+	10.1492i	−0.0530871	+	0.577367i
$310$	−4.68331	+	2.87553i	−0.265994	+	0.163319i
$311$	−4.79664	+	8.30803i	−0.271993	+	0.471105i	−0.969372	−	0.245597i	$-0.921016\pi$
$311$	−4.79664	+	8.30803i	−0.271993	+	0.471105i	0.697379	+	0.716702i	$0.254349\pi$
$312$	−5.64405	−	3.33846i	−0.319531	−	0.189003i
$313$	−14.5341	−	25.1737i	−0.821514	−	1.42290i	−0.904555	−	0.426358i	$-0.859796\pi$
$313$	−14.5341	−	25.1737i	−0.821514	−	1.42290i	0.0830407	−	0.996546i	$-0.473537\pi$
$314$	−0.851549	−	31.4764i	−0.0480557	−	1.77632i
$315$	−2.67070	−	7.47445i	−0.150477	−	0.421137i
$316$	−1.11697	−	20.6285i	−0.0628343	−	1.16045i
$317$	10.4572	+	18.1124i	0.587334	+	1.01729i	0.994580	+	0.103974i	$0.0331557\pi$
$317$	10.4572	+	18.1124i	0.587334	+	1.01729i	−0.407246	+	0.913318i	$0.633511\pi$
$318$	6.38585	−	9.57383i	0.358101	−	0.536874i
$319$	−27.8246	−	16.0646i	−1.55788	−	0.899443i
$320$	5.06684	+	6.19089i	0.283245	+	0.346082i
$321$	−0.768132	+	8.35409i	−0.0428730	+	0.466280i
$322$	−2.78346	−	4.50349i	−0.155116	−	0.250970i
$323$			41.7059i			2.32058i
$324$	−3.76876	−	17.6010i	−0.209376	−	0.977835i
$325$	1.15921	+	0.669271i	0.0643015	+	0.0371245i
$326$	−2.28858	+	4.22377i	−0.126753	+	0.233933i
$327$	11.5035	−	5.30238i	0.636148	−	0.293222i
$328$	−1.50159	−	18.4653i	−0.0829113	−	1.01958i
$329$	−6.34780	+	0.0187403i	−0.349965	+	0.00103319i
$330$	0.792008	−	12.2351i	0.0435986	−	0.673521i
$331$	5.52466	+	9.56899i	0.303663	+	0.525959i	0.976963	−	0.213410i	$-0.0684571\pi$
$331$	5.52466	+	9.56899i	0.303663	+	0.525959i	−0.673300	+	0.739369i	$0.735124\pi$
$332$	−20.8744	−	10.5905i	−1.14563	−	0.581229i
$333$	−20.4511	−	17.4711i	−1.12071	−	0.957408i
$334$	2.57928	+	4.20083i	0.141132	+	0.229859i
$335$	12.9626			0.708220
$336$	−8.85466	+	16.0498i	−0.483062	+	0.875586i
$337$	9.86221			0.537229			0.268614	−	0.963248i	$-0.413434\pi$
$337$	9.86221			0.537229			0.268614	+	0.963248i	$0.413434\pi$
$338$	−8.29381	−	13.5080i	−0.451124	−	0.734736i
$339$	−0.687702	−	0.486081i	−0.0373509	−	0.0264003i
$340$	−12.1637	−	6.17119i	−0.659672	−	0.334680i
$341$	−9.72555	−	16.8451i	−0.526668	−	0.912215i
$342$	−25.6290	−	4.03957i	−1.38586	−	0.218435i
$343$	−18.5195	+	0.164027i	−0.999961	+	0.00885662i
$344$	−8.31331	+	0.676033i	−0.448224	+	0.0364493i
$345$	1.02590	+	2.22570i	0.0552328	+	0.119828i
$346$	−8.15264	+	15.0464i	−0.438289	+	0.808899i
$347$	−21.7241	−	12.5424i	−1.16621	−	0.673312i	−0.213426	−	0.976959i	$-0.568462\pi$
$347$	−21.7241	−	12.5424i	−1.16621	−	0.673312i	−0.952784	+	0.303648i	$0.901795\pi$
$348$	−10.3862	−	19.6609i	−0.556757	−	1.05393i
$349$		−	33.6398i		−	1.80070i	−0.435167	−	0.900350i	$-0.643311\pi$
$349$		−	33.6398i		−	1.80070i	0.435167	−	0.900350i	$-0.356689\pi$
$350$	1.77279	−	3.29503i	0.0947598	−	0.176127i
$351$	−1.88913	+	6.69380i	−0.100834	+	0.357288i
$352$	−22.3888	+	17.3343i	−1.19333	+	0.923919i
$353$	−2.02063	−	1.16661i	−0.107547	−	0.0620924i	0.445262	−	0.895401i	$-0.353111\pi$
$353$	−2.02063	−	1.16661i	−0.107547	−	0.0620924i	−0.552809	+	0.833308i	$0.686444\pi$
$354$	18.6470	+	12.4377i	0.991075	+	0.661058i
$355$	−2.27115	−	3.93375i	−0.120540	−	0.208782i
$356$	−0.794685	−	14.6765i	−0.0421182	−	0.777855i
$357$	2.76960	−	31.1294i	0.146583	−	1.64754i
$358$	−0.536712	−	19.8389i	−0.0283661	−	1.04852i
$359$	7.76968	+	13.4575i	0.410068	+	0.710258i	0.994897	−	0.100898i	$-0.0321717\pi$
$359$	7.76968	+	13.4575i	0.410068	+	0.710258i	−0.584829	+	0.811157i	$0.698838\pi$
$360$	4.97047	−	6.87710i	0.261967	−	0.362455i
$361$	−9.19894	+	15.9330i	−0.484155	+	0.838581i
$362$	15.0691	−	9.25235i	0.792015	−	0.486293i
$363$	24.2404	+	2.22883i	1.27229	+	0.116983i
$364$	5.92207	−	3.88542i	0.310401	−	0.203651i
$365$	−0.484668			−0.0253687
$366$	−24.0887	+	11.9034i	−1.25914	+	0.622203i
$367$	10.3180	+	5.95710i	0.538595	+	0.310958i	0.744509	−	0.667612i	$-0.232684\pi$
$367$	10.3180	+	5.95710i	0.538595	+	0.310958i	−0.205914	+	0.978570i	$0.566017\pi$
$368$	2.28410	−	5.17843i	0.119067	−	0.269944i
$369$	−18.5238	+	6.55713i	−0.964308	+	0.341351i
$370$	−0.342904	−	12.6750i	−0.0178267	−	0.658944i
$371$	6.24686	+	10.7465i	0.324321	+	0.557930i
$372$	0.505969	−	13.4520i	0.0262333	−	0.697454i
$373$	20.4356	−	11.7985i	1.05811	−	0.610902i	0.133203	−	0.991089i	$-0.457474\pi$
$373$	20.4356	−	11.7985i	1.05811	−	0.610902i	0.924910	+	0.380187i	$0.124140\pi$
$374$	22.9984	−	42.4455i	1.18922	−	2.19481i
$375$	−0.999729	+	1.41441i	−0.0516258	+	0.0730396i
$376$	−3.85823	−	5.58259i	−0.198973	−	0.287900i
$377$			8.59192i			0.442506i
$378$	18.8613	+	4.71712i	0.970121	+	0.242622i
$379$	−23.1613			−1.18972			−0.594858	−	0.803831i	$-0.702792\pi$
$379$	−23.1613			−1.18972			−0.594858	+	0.803831i	$0.702792\pi$
$380$	−6.67913	−	10.2460i	−0.342632	−	0.525609i
$381$	11.3636	+	8.03199i	0.582174	+	0.411492i
$382$	14.1805	−	26.1714i	0.725540	−	1.33905i
$383$	−12.1924	−	21.1179i	−0.623003	−	1.07907i	−0.988923	−	0.148426i	$-0.952579\pi$
$383$	−12.1924	−	21.1179i	−0.623003	−	1.07907i	0.365921	−	0.930646i	$-0.380754\pi$
$384$	−19.5026	+	1.91030i	−0.995237	+	0.0974844i
$385$	11.4884	+	6.58766i	0.585501	+	0.335738i
$386$	6.69938	−	0.181242i	0.340989	−	0.00922496i
$387$	2.95210	+	8.33962i	0.150064	+	0.423927i
$388$	9.17706	−	18.0885i	0.465895	−	0.918303i
$389$	−16.2648	+	28.1715i	−0.824659	+	1.42835i	0.0775198	+	0.996991i	$0.475300\pi$
$389$	−16.2648	+	28.1715i	−0.824659	+	1.42835i	−0.902179	+	0.431361i	$0.858033\pi$
$390$	−2.93944	+	1.45253i	−0.148845	+	0.0735515i
$391$			9.64970i			0.488006i
$392$	−11.3526	−	16.2209i	−0.573395	−	0.819279i
$393$	2.33686	−	25.4153i	0.117879	−	1.28203i
$394$	10.3163	+	16.8019i	0.519727	+	0.846470i
$395$	−8.94551	−	5.16469i	−0.450097	−	0.259864i
$396$	23.8559	+	18.2441i	1.19880	+	0.916802i
$397$	25.2842	−	14.5978i	1.26898	−	0.732645i	0.294184	−	0.955749i	$-0.404952\pi$
$397$	25.2842	−	14.5978i	1.26898	−	0.732645i	0.974795	+	0.223104i	$0.0716190\pi$
$398$	0.737452	+	27.2590i	0.0369651	+	1.36637i
$399$	16.1078	−	22.9324i	0.806396	−	1.14806i
$400$	3.97661	−	0.431907i	0.198831	−	0.0215954i
$401$	−5.45967	+	3.15214i	−0.272643	+	0.157410i	−0.630088	−	0.776524i	$-0.716981\pi$
$401$	−5.45967	+	3.15214i	−0.272643	+	0.157410i	0.357445	+	0.933934i	$0.383648\pi$
$402$	−17.6189	+	26.4148i	−0.878753	+	1.31745i
$403$	−2.60079	+	4.50470i	−0.129555	+	0.224395i
$404$	−1.89787	−	2.91140i	−0.0944226	−	0.144848i
$405$	−8.40146	−	3.22730i	−0.417472	−	0.160366i
$406$	24.0064	−	0.720388i	1.19142	−	0.0357522i
$407$	44.8780			2.22452
$408$	29.1087	−	16.3990i	1.44109	−	0.811870i
$409$	−1.33703	+	2.31580i	−0.0661117	+	0.114509i	−0.897187	−	0.441652i	$-0.854393\pi$
$409$	−1.33703	+	2.31580i	−0.0661117	+	0.114509i	0.831075	+	0.556161i	$0.187726\pi$
$410$	−8.14443	−	4.41293i	−0.402225	−	0.217939i
$411$	−8.25595	+	3.80545i	−0.407236	+	0.187709i
$412$	−0.636304	−	11.7515i	−0.0313484	−	0.578954i
$413$	−20.9309	+	12.1670i	−1.02994	+	0.598700i
$414$	−5.92991	−	0.934656i	−0.291439	−	0.0459358i
$415$	−10.1356	+	5.85181i	−0.497539	+	0.287254i
$416$	7.00805	+	2.86730i	0.343598	+	0.140581i
$417$	−8.53319	+	12.0727i	−0.417872	+	0.591201i
$418$	36.8905	−	22.6505i	1.80437	−	1.10787i
$419$		−	19.3995i		−	0.947729i	−0.880598	−	0.473865i	$-0.842859\pi$
$419$		−	19.3995i		−	0.947729i	0.880598	−	0.473865i	$-0.157141\pi$
$420$	4.30491	+	8.09121i	0.210058	+	0.394811i
$421$		−	22.9458i		−	1.11831i	−0.829064	−	0.559154i	$-0.811126\pi$
$421$		−	22.9458i		−	1.11831i	0.829064	−	0.559154i	$-0.188874\pi$
$422$	5.83753	+	9.50748i	0.284167	+	0.462817i
$423$	−4.67522	+	5.47266i	−0.227317	+	0.266090i
$424$	−5.68961	+	12.0088i	−0.276312	+	0.583199i
$425$	−5.90615	+	3.40992i	−0.286490	+	0.165405i
$426$	11.1031	+	0.718729i	0.537946	+	0.0348225i
$427$	−0.0856804	−	29.0220i	−0.00414637	−	1.40447i
$428$	−0.523760	−	9.67299i	−0.0253169	−	0.467562i
$429$	−4.85779	−	10.5390i	−0.234536	−	0.508828i
$430$	−1.98675	+	3.66672i	−0.0958098	+	0.176825i
$431$	−2.43900	+	4.22447i	−0.117482	+	0.203485i	−0.918769	−	0.394795i	$-0.870816\pi$
$431$	−2.43900	+	4.22447i	−0.117482	+	0.203485i	0.801287	+	0.598280i	$0.204149\pi$
$432$	7.25803	+	19.4762i	0.349202	+	0.937047i
$433$	12.4056			0.596175			0.298088	−	0.954538i	$-0.403651\pi$
$433$	12.4056			0.596175			0.298088	+	0.954538i	$0.403651\pi$
$434$	12.8045	+	6.88908i	0.614635	+	0.330687i
$435$	−11.0711	−	1.01795i	−0.530819	−	0.0488071i
$436$	−12.2528	+	7.98732i	−0.586804	+	0.382523i
$437$	−4.32647	+	7.49367i	−0.206963	+	0.358471i
$438$	0.658769	−	0.987644i	0.0314772	−	0.0471915i
$439$	9.26855	−	5.35120i	0.442364	−	0.255399i	−0.262236	−	0.965004i	$-0.584460\pi$
$439$	9.26855	−	5.35120i	0.442364	−	0.255399i	0.704600	+	0.709605i	$0.251127\pi$
$440$	1.14749	+	14.1109i	0.0547043	+	0.672710i
$441$	−13.5458	+	16.0472i	−0.645038	+	0.764151i
$442$	−12.9051	+	0.349129i	−0.613833	+	0.0166064i
$443$	−31.1237	+	17.9693i	−1.47873	+	0.853745i	−0.999711	−	0.0240592i	$-0.992341\pi$
$443$	−31.1237	+	17.9693i	−1.47873	+	0.853745i	−0.479019	+	0.877804i	$0.659008\pi$
$444$	26.2950	+	16.5294i	1.24790	+	0.784449i
$445$	−6.36443	−	3.67451i	−0.301703	−	0.174188i
$446$	−10.9251	+	6.70797i	−0.517320	+	0.317631i
$447$	21.0343	+	1.93404i	0.994890	+	0.0914770i
$448$	7.42384	−	19.8214i	0.350744	−	0.936472i
$449$			14.9112i			0.703702i	0.936056	+	0.351851i	$0.114448\pi$
$449$			14.9112i			0.703702i	−0.936056	+	0.351851i	$0.885552\pi$
$450$	−1.52339	−	3.95971i	−0.0718133	−	0.186662i
$451$	16.3928	−	28.3932i	0.771908	−	1.33698i
$452$	0.867202	+	0.439969i	0.0407898	+	0.0206944i
$453$	−11.6068	+	5.34996i	−0.545333	+	0.251363i
$454$	−0.293336	−	10.8428i	−0.0137669	−	0.508878i
$455$	−0.0104552	−	3.54143i	−0.000490148	−	0.166025i
$456$	29.9575	+	0.316012i	1.40289	+	0.0147986i
$457$	7.04029	+	12.1941i	0.329331	+	0.570418i	0.982379	−	0.186899i	$-0.0598436\pi$
$457$	7.04029	+	12.1941i	0.329331	+	0.570418i	−0.653048	+	0.757316i	$0.726510\pi$
$458$	18.8437	+	10.2102i	0.880509	+	0.477089i
$459$	−24.7230	−	25.3879i	−1.15397	−	1.18501i
$460$	−1.54538	−	2.37067i	−0.0720539	−	0.110533i
$461$	−14.6784			−0.683642			−0.341821	−	0.939765i	$-0.611044\pi$
$461$	−14.6784			−0.683642			−0.341821	+	0.939765i	$0.611044\pi$
$462$	−29.0394	+	14.4566i	−1.35103	+	0.672583i
$463$		−	1.79330i		−	0.0833418i	−0.999131	−	0.0416709i	$-0.986732\pi$
$463$		−	1.79330i		−	0.0833418i	0.999131	−	0.0416709i	$-0.0132681\pi$
$464$	15.1636	+	20.7194i	0.703953	+	0.961875i
$465$	−5.49639	−	3.88495i	−0.254889	−	0.180160i
$466$	−18.6910	−	10.1274i	−0.865843	−	0.469143i
$467$	−4.64317	+	2.68073i	−0.214860	+	0.124050i	−0.603568	−	0.797311i	$-0.706255\pi$
$467$	−4.64317	+	2.68073i	−0.214860	+	0.124050i	0.388708	+	0.921361i	$0.372921\pi$
$468$	1.03542	−	7.96422i	0.0478625	−	0.368146i
$469$	−17.2355	−	29.6502i	−0.795860	−	1.36912i
$470$	−3.39181	+	0.0917605i	−0.156453	+	0.00423260i
$471$	35.0232	−	16.1434i	1.61379	−	0.743850i
$472$	−23.3896	−	11.0817i	−1.07659	−	0.510075i
$473$	−12.7830	−	7.38025i	−0.587761	−	0.339344i
$474$	22.6834	−	11.2090i	1.04188	−	0.514846i
$475$	−6.11538			−0.280593
$476$	2.05751	+	36.0284i	0.0943060	+	1.65136i
$477$	13.8582	+	2.57017i	0.634524	+	0.117680i
$478$	20.1196	+	32.7683i	0.920247	+	1.49879i
$479$	9.60194	−	16.6310i	0.438724	−	0.759892i	−0.558867	−	0.829257i	$-0.688764\pi$
$479$	9.60194	−	16.6310i	0.438724	−	0.759892i	0.997591	+	0.0693650i	$0.0220973\pi$
$480$	−4.52496	+	8.69050i	−0.206535	+	0.396665i
$481$	−6.00060	−	10.3934i	−0.273604	−	0.473896i
$482$	−37.2208	+	1.00695i	−1.69536	+	0.0458655i
$483$	3.72693	−	5.30599i	0.169581	−	0.241431i
$484$	−28.0674	+	1.51975i	−1.27579	+	0.0690798i
$485$	−5.07082	−	8.78292i	−0.230254	−	0.398812i
$486$	17.9959	−	12.7337i	0.816312	−	0.577611i
$487$	35.8006	+	20.6695i	1.62228	+	0.936625i	0.986308	+	0.164914i	$0.0527346\pi$
$487$	35.8006	+	20.6695i	1.62228	+	0.936625i	0.635973	+	0.771711i	$0.280599\pi$
$488$	25.5235	−	17.6398i	1.15540	−	0.798514i
$489$	−5.85889	−	0.538706i	−0.264948	−	0.0243611i
$490$	−9.89412	+	0.326143i	−0.446971	+	0.0147337i
$491$		−	1.99983i		−	0.0902511i	−0.998981	−	0.0451256i	$-0.985631\pi$
$491$		−	1.99983i		−	0.0902511i	0.998981	−	0.0451256i	$-0.0143688\pi$
$492$	20.0626	−	10.5984i	0.904492	−	0.477812i
$493$	−37.9108	−	21.8878i	−1.70741	−	0.985776i
$494$	−10.1783	−	5.51492i	−0.457941	−	0.248128i
$495$	14.1555	−	5.01085i	0.636245	−	0.225221i
$496$	1.67839	+	15.4531i	0.0753621	+	0.693866i
$497$	−5.97815	+	10.4254i	−0.268157	+	0.467644i
$498$	1.85186	−	28.6080i	0.0829840	−	1.28196i
$499$	15.0041	+	25.9879i	0.671676	+	1.16338i	0.977428	+	0.211267i	$0.0677588\pi$
$499$	15.0041	+	25.9879i	0.671676	+	1.16338i	−0.305752	+	0.952111i	$0.598908\pi$
$500$	0.904890	−	1.78358i	0.0404679	−	0.0797643i
$501$	−3.48471	+	4.93013i	−0.155685	+	0.220262i
$502$	−12.2616	+	7.52856i	−0.547263	+	0.336016i
$503$	3.58141			0.159687			0.0798437	−	0.996807i	$-0.474558\pi$
$503$	3.58141			0.159687			0.0798437	+	0.996807i	$0.474558\pi$
$504$	−22.3394	−	2.22528i	−0.995075	−	0.0991221i
$505$	−1.73768			−0.0773259
$506$	8.53554	−	5.24077i	0.379451	−	0.232981i
$507$	11.2053	−	15.8531i	0.497643	−	0.704060i
$508$	−14.3296	−	7.27004i	−0.635775	−	0.322556i
$509$	−16.6320	−	28.8075i	−0.737201	−	1.27687i	−0.953751	−	0.300598i	$-0.902814\pi$
$509$	−16.6320	−	28.8075i	−0.737201	−	1.27687i	0.216550	−	0.976272i	$-0.430520\pi$
$510$	1.07910	−	16.6702i	0.0477834	−	0.738170i
$511$	0.644431	+	1.10862i	0.0285080	+	0.0490423i
$512$	21.9603	−	5.45378i	0.970519	−	0.241025i
$513$	−7.81640	−	30.8001i	−0.345103	−	1.35986i
$514$	18.9780	+	10.2829i	0.837083	+	0.453560i
$515$	−5.09600	−	2.94218i	−0.224556	−	0.129648i
$516$	−4.77152	−	9.03243i	−0.210055	−	0.397631i
$517$		−	12.0093i		−	0.528167i
$518$	−28.5366	+	17.6375i	−1.25383	+	0.774948i
$519$	−20.8712	−	1.91904i	−0.916144	−	0.0842365i
$520$	3.11453	−	2.15250i	0.136581	−	0.0943935i
$521$	−20.7768	−	11.9955i	−0.910246	−	0.525531i	−0.0297360	−	0.999558i	$-0.509467\pi$
$521$	−20.7768	−	11.9955i	−0.910246	−	0.525531i	−0.880510	+	0.474027i	$0.842800\pi$
$522$	17.1224	−	21.1768i	0.749427	−	0.926883i
$523$	7.81814	+	13.5414i	0.341863	+	0.592125i	0.984779	−	0.173813i	$-0.0556087\pi$
$523$	7.81814	+	13.5414i	0.341863	+	0.592125i	−0.642915	+	0.765937i	$0.722275\pi$
$524$	1.59341	+	29.4277i	0.0696086	+	1.28556i
$525$	4.56455	+	0.406110i	0.199213	+	0.0177241i
$526$	25.3201	−	0.684998i	1.10401	−	0.0298673i
$527$	−13.2509	−	22.9513i	−0.577220	−	0.999775i
$528$	−30.3145	−	16.8415i	−1.31927	−	0.732930i
$529$	10.4990	−	18.1847i	0.456477	−	0.790641i
$530$	3.47651	+	5.66213i	0.151010	+	0.245947i
$531$	−5.00592	+	26.9917i	−0.217238	+	1.17134i
$532$	−14.5557	+	28.9011i	−0.631068	+	1.25302i
$533$	−8.76748			−0.379762
$534$	16.1385	−	7.97483i	0.698380	−	0.345104i
$535$	−4.19466	−	2.42179i	−0.181351	−	0.104703i
$536$	15.6980	−	33.1330i	0.678050	−	1.43113i
$537$	22.0744	−	10.1748i	0.952579	−	0.439076i
$538$	−22.3361	+	0.604270i	−0.962978	+	0.0260519i
$539$	−0.206880	−	35.0373i	−0.00891095	−	1.50917i
$540$	10.1396	+	2.27778i	0.436339	+	0.0980200i
$541$	−28.7858	+	16.6195i	−1.23760	+	0.714527i	−0.968602	−	0.248615i	$-0.920025\pi$
$541$	−28.7858	+	16.6195i	−1.23760	+	0.714527i	−0.268994	+	0.963142i	$0.586691\pi$
$542$	27.6255	+	14.9684i	1.18662	+	0.642948i
$543$	17.6853	+	12.5003i	0.758948	+	0.536439i
$544$	−30.5045	+	23.6177i	−1.30787	+	1.01260i
$545$			7.31316i			0.313261i
$546$	7.23085	+	4.79227i	0.309452	+	0.205090i
$547$	−28.4785			−1.21765			−0.608826	−	0.793304i	$-0.708359\pi$
$547$	−28.4785			−1.21765			−0.608826	+	0.793304i	$0.708359\pi$
$548$	8.79370	−	5.73240i	0.375648	−	0.244876i
$549$	−25.0209	−	21.3750i	−1.06787	−	0.912264i
$550$	6.22384	+	3.37229i	0.265385	+	0.143795i
$551$	−19.6269	−	33.9948i	−0.836134	−	1.44823i
$552$	6.93141	+	0.0731172i	0.295021	+	0.00311208i
$553$	0.0806817	+	27.3289i	0.00343094	+	1.16214i
$554$	−0.704703	−	26.0485i	−0.0299399	−	1.10669i
$555$	14.1033	−	6.50068i	0.598651	−	0.275939i
$556$	7.72369	−	15.2238i	0.327558	−	0.645633i
$557$	−17.9703	+	31.1254i	−0.761424	+	1.31882i	0.180693	+	0.983540i	$0.442166\pi$
$557$	−17.9703	+	31.1254i	−0.761424	+	1.31882i	−0.942117	+	0.335285i	$0.891167\pi$
$558$	15.3874	−	5.91990i	0.651402	−	0.250609i
$559$			3.94723i			0.166950i
$560$	−6.27537	−	8.52172i	−0.265183	−	0.360108i
$561$	58.8771	+	5.41357i	2.48580	+	0.228561i
$562$	−6.66674	+	4.09334i	−0.281219	+	0.172667i
$563$	26.1627	+	15.1050i	1.10263	+	0.636601i	0.936909	−	0.349573i	$-0.113673\pi$
$563$	26.1627	+	15.1050i	1.10263	+	0.636601i	0.165716	+	0.986174i	$0.447007\pi$
$564$	4.42323	−	7.03647i	0.186251	−	0.296289i
$565$	0.421073	−	0.243107i	0.0177147	−	0.0102276i
$566$	2.16561	−	0.0585874i	0.0910274	−	0.00246261i
$567$	3.78882	+	23.5084i	0.159116	+	0.987260i
$568$	−12.8053	+	1.04132i	−0.537299	+	0.0436928i
$569$	−23.3749	+	13.4955i	−0.979929	+	0.565762i	−0.902249	−	0.431216i	$-0.858085\pi$
$569$	−23.3749	+	13.4955i	−0.979929	+	0.565762i	−0.0776801	+	0.996978i	$0.524751\pi$
$570$	8.31214	−	12.4618i	0.348157	−	0.521966i
$571$	−8.61580	+	14.9230i	−0.360560	+	0.624508i	−0.988053	−	0.154114i	$-0.950748\pi$
$571$	−8.61580	+	14.9230i	−0.360560	+	0.624508i	0.627493	+	0.778622i	$0.284081\pi$
$572$	7.31760	+	11.2255i	0.305964	+	0.469360i
$573$	36.3029	+	3.33794i	1.51658	+	0.139445i
$574$	0.735108	+	24.4969i	0.0306828	+	1.02248i
$575$	−1.41495			−0.0590074
$576$	−11.5589	−	21.0331i	−0.481620	−	0.876380i
$577$	−8.15001	+	14.1162i	−0.339289	+	0.587666i	−0.984299	−	0.176508i	$-0.943520\pi$
$577$	−8.15001	+	14.1162i	−0.339289	+	0.587666i	0.645010	+	0.764174i	$0.276853\pi$
$578$	19.8817	−	36.6934i	0.826971	−	1.52625i
$579$	3.43593	+	7.45427i	0.142792	+	0.309789i
$580$	12.8190	−	0.694104i	0.532278	−	0.0288211i
$581$	26.8620	+	15.4032i	1.11442	+	0.639033i
$582$	24.7900	+	1.60471i	1.02758	+	0.0665174i
$583$	−20.3658	+	11.7582i	−0.843464	+	0.486974i
$584$	−0.586945	+	1.23884i	−0.0242880	+	0.0512635i
$585$	−3.05320	−	2.60830i	−0.126234	−	0.107840i
$586$	−20.6783	−	33.6783i	−0.854212	−	1.39124i
$587$			3.86140i			0.159377i	0.996820	+	0.0796886i	$0.0253926\pi$
$587$			3.86140i			0.159377i	−0.996820	+	0.0796886i	$0.974607\pi$
$588$	12.7837	−	20.6053i	0.527189	−	0.849748i
$589$		−	23.7644i		−	0.979195i
$590$	−11.0281	+	6.77120i	−0.454021	+	0.278766i
$591$	−13.9377	+	19.7189i	−0.573322	+	0.811129i
$592$	−32.8134	−	14.4733i	−1.34862	−	0.594849i
$593$	14.2441	−	8.22381i	0.584933	−	0.337711i	−0.178158	−	0.984002i	$-0.557014\pi$
$593$	14.2441	−	8.22381i	0.584933	−	0.337711i	0.763091	+	0.646291i	$0.223681\pi$
$594$	−9.02948	+	35.6567i	−0.370484	+	1.46301i
$595$	15.6528	+	8.97562i	0.641701	+	0.367964i
$596$	−24.3551	+	1.31875i	−0.997625	+	0.0540181i
$597$	−30.3306	+	13.9804i	−1.24135	+	0.572180i
$598$	−2.35499	−	1.27602i	−0.0963029	−	0.0521802i
$599$	−13.3604	+	23.1409i	−0.545891	+	0.945512i	0.452659	+	0.891684i	$0.350476\pi$
$599$	−13.3604	+	23.1409i	−0.545891	+	0.945512i	−0.998550	+	0.0538279i	$0.982858\pi$
$600$	2.40460	+	4.26824i	0.0981675	+	0.174250i
$601$	−40.3828			−1.64725			−0.823624	−	0.567136i	$-0.808052\pi$
$601$	−40.3828			−1.64725			−0.823624	+	0.567136i	$0.808052\pi$
$602$	11.0288	−	0.330955i	0.449501	−	0.0134887i
$603$	−38.2357	−	7.09125i	−1.55708	−	0.288778i
$604$	12.3628	−	8.05899i	0.503034	−	0.327916i
$605$	−7.02712	+	12.1713i	−0.285693	+	0.494835i
$606$	2.36189	−	3.54101i	0.0959452	−	0.143844i
$607$	−12.9956	+	7.50302i	−0.527476	+	0.304538i	−0.739988	−	0.672620i	$-0.765169\pi$
$607$	−12.9956	+	7.50302i	−0.527476	+	0.304538i	0.212512	+	0.977158i	$0.431835\pi$
$608$	−34.2780	+	4.66404i	−1.39016	+	0.189152i
$609$	12.3921	+	26.6772i	0.502152	+	1.08102i
$610$	−0.419528	−	15.5073i	−0.0169862	−	0.627873i
$611$	−2.78124	+	1.60575i	−0.112517	+	0.0649617i
$612$	32.5034	+	24.8574i	1.31387	+	1.00480i
$613$	0.555571	+	0.320759i	0.0224393	+	0.0129553i	0.511178	−	0.859475i	$-0.329209\pi$
$613$	0.555571	+	0.320759i	0.0224393	+	0.0129553i	−0.488738	+	0.872430i	$0.662543\pi$
$614$	3.49936	+	5.69934i	0.141223	+	0.230007i
$615$	1.03875	−	11.2973i	0.0418866	−	0.455552i
$616$	30.7511	−	21.3871i	1.23900	−	0.861709i
$617$		−	13.6017i		−	0.547585i	−0.961789	−	0.273793i	$-0.911722\pi$
$617$		−	13.6017i		−	0.547585i	0.961789	−	0.273793i	$-0.0882782\pi$
$618$	12.9221	−	6.38544i	0.519802	−	0.256860i
$619$	1.09729	−	1.90056i	0.0441037	−	0.0763898i	−0.843131	−	0.537708i	$-0.819290\pi$
$619$	1.09729	−	1.90056i	0.0441037	−	0.0763898i	0.887235	+	0.461319i	$0.152623\pi$
$620$	6.93102	+	3.51641i	0.278356	+	0.141222i
$621$	−1.80852	−	7.12638i	−0.0725735	−	0.285972i
$622$	13.5620	−	0.366900i	0.543786	−	0.0147113i
$623$	0.0574024	+	19.4436i	0.00229978	+	0.778991i
$624$	0.152996	+	9.27243i	0.00612476	+	0.371194i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−19.5840	+	36.1439i	−0.782733	+	1.44460i
$627$	43.2950	+	30.6018i	1.72904	+	1.22212i
$628$	−37.3045	+	24.3179i	−1.48861	+	0.970389i
$629$	61.1458			2.43804
$630$	−7.03177	+	8.74952i	−0.280153	+	0.348589i
$631$			49.1497i			1.95662i	0.207145	+	0.978310i	$0.433583\pi$
$631$			49.1497i			1.95662i	−0.207145	+	0.978310i	$0.566417\pi$
$632$	−24.0345	+	16.6106i	−0.956040	+	0.660736i
$633$	−7.88674	+	11.1581i	−0.313470	+	0.443494i
$634$	14.0906	−	26.0053i	0.559608	−	1.03280i
$635$	−6.95780	+	4.01709i	−0.276112	+	0.159413i
$636$	−16.2635	−	0.611717i	−0.644889	−	0.0242562i
$637$	−8.08667	+	4.73273i	−0.320406	+	0.187517i
$638$	1.22879	+	45.4208i	0.0486484	+	1.79823i
$639$	4.54723	+	12.8458i	0.179886	+	0.508173i
$640$	3.71180	−	10.6875i	0.146722	−	0.422460i
$641$	−6.97151	−	4.02500i	−0.275358	−	0.158978i	0.355962	−	0.934500i	$-0.384153\pi$
$641$	−6.97151	−	4.02500i	−0.275358	−	0.158978i	−0.631320	+	0.775522i	$0.717487\pi$
$642$	10.6365	−	5.25604i	0.419790	−	0.207439i
$643$	13.2852			0.523917			0.261958	−	0.965079i	$-0.415632\pi$
$643$	13.2852			0.523917			0.261958	+	0.965079i	$0.415632\pi$
$644$	−3.36782	+	6.68700i	−0.132711	+	0.263505i
$645$	−5.08619	−	0.467660i	−0.200269	−	0.0184141i
$646$	50.2628	−	30.8611i	1.97756	−	1.21421i
$647$	−1.65992	+	2.87507i	−0.0652583	+	0.113031i	−0.896809	−	0.442419i	$-0.854120\pi$
$647$	−1.65992	+	2.87507i	−0.0652583	+	0.113031i	0.831550	+	0.555450i	$0.187454\pi$
$648$	−18.4235	+	17.5662i	−0.723745	+	0.690067i
$649$	−22.9014	−	39.6664i	−0.898960	−	1.55704i
$650$	−0.0511932	−	1.89229i	−0.00200796	−	0.0742218i
$651$	−1.57814	+	17.7378i	−0.0618523	+	0.695201i
$652$	6.78386	−	0.367323i	0.265676	−	0.0143855i
$653$	3.03834	+	5.26256i	0.118899	+	0.205940i	0.919332	−	0.393483i	$-0.128730\pi$
$653$	3.03834	+	5.26256i	0.118899	+	0.205940i	−0.800432	+	0.599423i	$0.795397\pi$
$654$	−14.9026	−	9.94018i	−0.582737	−	0.388692i
$655$	12.7613	+	7.36771i	0.498623	+	0.287880i
$656$	−21.1428	+	15.4734i	−0.825487	+	0.604137i
$657$	1.42962	+	0.265141i	0.0557750	+	0.0103441i
$658$	4.71976	+	7.63633i	0.183995	+	0.297695i
$659$		−	24.0993i		−	0.938777i	−0.882992	−	0.469389i	$-0.844474\pi$
$659$		−	24.0993i		−	0.938777i	0.882992	−	0.469389i	$-0.155526\pi$
$660$	−15.3315	+	8.09911i	−0.596778	+	0.315257i
$661$	7.93475	+	4.58113i	0.308626	+	0.178185i	0.646311	−	0.763074i	$-0.276311\pi$
$661$	7.93475	+	4.58113i	0.308626	+	0.178185i	−0.337686	+	0.941259i	$0.609644\pi$
$662$	7.44422	−	13.7389i	0.289328	−	0.533979i
$663$	−6.61868	−	14.3593i	−0.257048	−	0.557668i
$664$	2.68304	+	32.9939i	0.104122	+	1.28041i
$665$	8.13122	+	13.9882i	0.315315	+	0.542437i
$666$	−5.92249	+	37.5751i	−0.229492	+	1.45601i
$667$	−4.54118	−	7.86555i	−0.175835	−	0.304555i
$668$	3.15414	−	6.21697i	0.122037	−	0.240542i
$669$	−12.8219	−	9.06273i	−0.495722	−	0.350385i
$670$	−9.59190	−	15.6221i	−0.370568	−	0.603536i
$671$	54.9062			2.11963
$672$	25.8949	−	1.20493i	0.998919	−	0.0464811i
$673$	27.8598			1.07392			0.536959	−	0.843609i	$-0.319573\pi$
$673$	27.8598			1.07392			0.536959	+	0.843609i	$0.319573\pi$
$674$	−7.29774	−	11.8857i	−0.281098	−	0.457819i
$675$	3.72266	−	3.62516i	0.143285	−	0.139533i
$676$	−10.1423	+	19.9910i	−0.390088	+	0.768883i
$677$	−16.9533	−	29.3640i	−0.651569	−	1.12855i	−0.982742	−	0.184981i	$-0.940778\pi$
$677$	−16.9533	−	29.3640i	−0.651569	−	1.12855i	0.331173	−	0.943570i	$-0.392556\pi$
$678$	−0.0769335	+	1.18849i	−0.00295461	+	0.0456435i
$679$	−13.3475	+	23.2769i	−0.512229	+	0.893286i
$680$	1.56344	+	19.2259i	0.0599552	+	0.737281i
$681$	12.0646	−	5.56098i	0.462315	−	0.213097i
$682$	−13.1047	+	24.1859i	−0.501806	+	0.926125i
$683$	31.3915	+	18.1239i	1.20116	+	0.693491i	0.960814	−	0.277196i	$-0.0894050\pi$
$683$	31.3915	+	18.1239i	1.20116	+	0.693491i	0.240348	+	0.970687i	$0.422738\pi$
$684$	14.0963	+	33.8765i	0.538985	+	1.29530i
$685$		−	5.24856i		−	0.200537i
$686$	13.9016	+	22.1979i	0.530765	+	0.847519i
$687$	−2.40336	+	26.1385i	−0.0916938	+	0.997247i
$688$	6.96634	+	9.51875i	0.265589	+	0.362899i
$689$	5.44618	+	3.14435i	0.207483	+	0.119790i
$690$	1.92322	−	2.88334i	0.0732158	−	0.109767i
$691$	13.2995	+	23.0354i	0.505937	+	0.876309i	0.999976	+	0.00686955i	$0.00218666\pi$
$691$	13.2995	+	23.0354i	0.505937	+	0.876309i	−0.494039	+	0.869440i	$0.664480\pi$
$692$	24.1662	−	1.30852i	0.918663	−	0.0497425i
$693$	−30.2834	−	25.7164i	−1.15037	−	0.976885i
$694$	0.959380	+	35.4623i	0.0364176	+	1.34613i
$695$	−4.26775	−	7.39197i	−0.161885	−	0.280393i
$696$	−16.0093	+	27.0656i	−0.606832	+	1.02592i
$697$	22.3350	−	38.6854i	0.846000	−	1.46531i
$698$	−40.5419	+	24.8925i	−1.53453	+	0.942194i
$699$	2.38388	−	25.9267i	0.0901665	−	0.980637i
$700$	−5.28290	+	0.301696i	−0.199675	+	0.0114030i
$701$	37.1096			1.40161			0.700805	−	0.713353i	$-0.252824\pi$
$701$	37.1096			1.40161			0.700805	+	0.713353i	$0.252824\pi$
$702$	9.46509	−	2.67648i	0.357237	−	0.101017i
$703$	47.4840	+	27.4149i	1.79089	+	1.03397i
$704$	37.4579	+	14.1556i	1.41175	+	0.533509i
$705$	−1.73957	−	3.77401i	−0.0655160	−	0.142137i
$706$	0.0892351	+	3.29846i	0.00335841	+	0.124139i
$707$	2.31048	+	3.97473i	0.0868946	+	0.149485i
$708$	1.19144	−	31.6764i	0.0447771	−	1.19047i
$709$	−13.4907	+	7.78887i	−0.506655	+	0.292517i	−0.731457	−	0.681887i	$-0.761160\pi$
$709$	−13.4907	+	7.78887i	−0.506655	+	0.292517i	0.224803	+	0.974404i	$0.427826\pi$
$710$	−3.06027	+	5.64799i	−0.114850	+	0.211965i
$711$	23.5612	+	20.1280i	0.883614	+	0.754859i
$712$	−17.0997	+	11.8179i	−0.640840	+	0.442895i
$713$		−	5.49849i		−	0.205920i
$714$	−39.5658	+	19.6970i	−1.48071	+	0.737141i
$715$	6.69997			0.250565
$716$	−23.5122	+	15.3270i	−0.878691	+	0.572797i
$717$	−27.1823	+	38.4573i	−1.01514	+	1.43621i
$718$	10.4693	−	19.3219i	0.390710	−	0.721088i
$719$	−3.63109	−	6.28922i	−0.135417	−	0.234548i	0.790340	−	0.612669i	$-0.209904\pi$
$719$	−3.63109	−	6.28922i	−0.135417	−	0.234548i	−0.925757	+	0.378120i	$0.876571\pi$
$720$	−11.9661	−	0.901435i	−0.445950	−	0.0335945i
$721$	0.0459620	+	15.5685i	0.00171172	+	0.579800i
$722$	26.0090	−	0.703636i	0.967956	−	0.0261866i
$723$	−19.0896	−	41.4149i	−0.709948	−	1.54024i
$724$	−22.3014	−	11.3145i	−0.828824	−	0.420498i
$725$	3.20943	−	5.55890i	0.119195	−	0.206452i
$726$	−15.2510	−	30.8632i	−0.566019	−	1.14544i
$727$		−	2.10062i		−	0.0779077i	−0.999241	−	0.0389539i	$-0.987597\pi$
$727$		−	2.10062i		−	0.0779077i	0.999241	−	0.0389539i	$-0.0124025\pi$
$728$	−9.06476	−	4.26204i	−0.335962	−	0.157962i
$729$	23.0163	+	14.1156i	0.852454	+	0.522802i
$730$	0.358640	+	0.584109i	0.0132738	+	0.0216189i
$731$	−17.4166	−	10.0555i	−0.644178	−	0.371916i
$732$	32.1707	+	20.2229i	1.18906	+	0.747461i
$733$	−1.55796	+	0.899490i	−0.0575447	+	0.0332234i	−0.528496	−	0.848936i	$-0.677244\pi$
$733$	−1.55796	+	0.899490i	−0.0575447	+	0.0332234i	0.470952	+	0.882159i	$0.343911\pi$
$734$	−0.455664	−	16.8430i	−0.0168189	−	0.621688i
$735$	−5.14025	−	10.9808i	−0.189601	−	0.405033i
$736$	−7.93107	+	1.07914i	−0.292343	+	0.0397777i
$737$	56.1904	−	32.4415i	2.06980	−	1.19500i
$738$	21.6095	+	17.4723i	0.795457	+	0.643163i
$739$	9.45723	−	16.3804i	0.347890	−	0.602563i	−0.637985	−	0.770049i	$-0.720232\pi$
$739$	9.45723	−	16.3804i	0.347890	−	0.602563i	0.985874	+	0.167486i	$0.0535650\pi$
$740$	−15.0219	+	9.79240i	−0.552216	+	0.359976i
$741$	1.29815	−	14.1185i	0.0476887	−	0.518655i
$742$	8.32890	−	15.4806i	0.305764	−	0.568312i
$743$	13.5490			0.497065			0.248533	−	0.968624i	$-0.420052\pi$
$743$	13.5490			0.497065			0.248533	+	0.968624i	$0.420052\pi$
$744$	−16.5864	+	9.34429i	−0.608087	+	0.342578i
$745$	−6.09770	+	10.5615i	−0.223402	+	0.386944i
$746$	−29.3409	−	15.8979i	−1.07425	−	0.582063i
$747$	33.0984	−	11.7163i	1.21101	−	0.428678i
$748$	−68.1724	+	3.69131i	−2.49263	+	0.134968i
$749$	0.0378327	+	12.8149i	0.00138238	+	0.468245i
$750$	2.44437	+	0.158230i	0.0892559	+	0.00577774i
$751$	−18.4224	+	10.6362i	−0.672243	+	0.388120i	−0.796926	−	0.604077i	$-0.793542\pi$
$751$	−18.4224	+	10.6362i	−0.672243	+	0.388120i	0.124683	+	0.992197i	$0.460209\pi$
$752$	−3.87303	+	8.78079i	−0.141235	+	0.320202i
$753$	−14.3904	−	10.1714i	−0.524414	−	0.370666i
$754$	10.3548	−	6.35776i	0.377098	−	0.231536i
$755$		−	7.37878i		−	0.268541i
$756$	−8.27185	−	26.2217i	−0.300844	−	0.953673i
$757$		−	5.99712i		−	0.217969i	−0.994043	−	0.108984i	$-0.965240\pi$
$757$		−	5.99712i		−	0.217969i	0.994043	−	0.108984i	$-0.0347599\pi$
$758$	17.1387	+	27.9134i	0.622504	+	1.01386i
$759$	10.0174	+	7.08049i	0.363608	+	0.257005i
$760$	−7.40588	+	15.6313i	−0.268640	+	0.567005i
$761$	6.73648	−	3.88931i	0.244197	−	0.140987i	−0.372907	−	0.927869i	$-0.621639\pi$
$761$	6.73648	−	3.88931i	0.244197	−	0.140987i	0.617104	+	0.786881i	$0.288306\pi$
$762$	1.27125	−	19.6385i	0.0460524	−	0.711429i
$763$	16.7279	−	9.72383i	0.605591	−	0.352026i
$764$	−42.0343	+	2.27602i	−1.52075	+	0.0823434i
$765$	19.2868	−	6.82723i	0.697315	−	0.246839i
$766$	−16.4287	+	30.3205i	−0.593593	+	1.09553i
$767$	−6.12426	+	10.6075i	−0.221134	+	0.383016i
$768$	16.7336	+	22.0904i	0.603820	+	0.797120i
$769$	−23.0230			−0.830232			−0.415116	−	0.909769i	$-0.636259\pi$
$769$	−23.0230			−0.830232			−0.415116	+	0.909769i	$0.636259\pi$
$770$	−0.561757	−	18.7201i	−0.0202443	−	0.674627i
$771$	−2.42048	+	26.3248i	−0.0871715	+	0.948064i
$772$	−5.17576	−	7.93980i	−0.186280	−	0.285760i
$773$	3.29928	−	5.71452i	0.118667	−	0.205537i	−0.800573	−	0.599236i	$-0.795471\pi$
$773$	3.29928	−	5.71452i	0.118667	−	0.205537i	0.919240	+	0.393699i	$0.128805\pi$
$774$	7.86623	−	9.72887i	0.282746	−	0.349697i
$775$	3.36538	−	1.94300i	0.120888	−	0.0697947i
$776$	−28.5905	+	2.32496i	−1.02634	+	0.0834612i
$777$	−33.6217	−	23.6159i	−1.20617	−	0.847216i
$778$	45.9871	−	1.24411i	1.64872	−	0.0446036i
$779$	34.6894	−	20.0280i	1.24288	−	0.717576i
$780$	3.92565	+	2.46772i	0.140561	+	0.0883584i
$781$	−19.6901	−	11.3681i	−0.704566	−	0.406782i
$782$	11.6296	−	7.14049i	0.415873	−	0.255343i
$783$	32.0995	+	9.05917i	1.14714	+	0.323748i
$784$	−11.1484	+	25.6849i	−0.398157	+	0.917317i
$785$			22.2654i			0.794684i
$786$	−32.3591	+	15.9902i	−1.15421	+	0.570353i
$787$	−1.26822	+	2.19662i	−0.0452072	+	0.0783011i	−0.887744	−	0.460338i	$-0.847728\pi$
$787$	−1.26822	+	2.19662i	−0.0452072	+	0.0783011i	0.842536	+	0.538639i	$0.181061\pi$
$788$	12.6155	−	24.8659i	0.449410	−	0.885810i
$789$	12.9860	+	28.1732i	0.462314	+	1.00299i
$790$	0.395052	+	14.6026i	0.0140553	+	0.519538i
$791$	−1.11595	−	0.639908i	−0.0396785	−	0.0227525i
$792$	4.33471	−	42.2506i	0.154027	−	1.50131i
$793$	−7.34146	−	12.7158i	−0.260703	−	0.451551i
$794$	−36.3025	−	19.6699i	−1.28833	−	0.698059i
$795$	−4.69691	+	6.64513i	−0.166582	+	0.235679i
$796$	32.3062	−	21.0596i	1.14506	−	0.746438i
$797$	3.19170			0.113056			0.0565279	−	0.998401i	$-0.481997\pi$
$797$	3.19170			0.113056			0.0565279	+	0.998401i	$0.481997\pi$
$798$	−39.5568	−	2.44336i	−1.40030	−	0.0864939i
$799$		−	16.3625i		−	0.578863i
$800$	−3.46310	−	4.47291i	−0.122439	−	0.158141i
$801$	16.7630	+	14.3204i	0.592292	+	0.505986i
$802$	7.83887	+	4.24736i	0.276800	+	0.149980i
$803$	−2.10095	+	1.21298i	−0.0741409	+	0.0428053i
$804$	44.8719	+	1.68776i	1.58251	+	0.0595228i
$805$	1.88136	+	3.23651i	0.0663093	+	0.114072i
$806$	7.35345	−	0.198937i	0.259014	−	0.00700725i
$807$	−11.4556	−	24.8530i	−0.403256	−	0.874865i
$808$	−2.10438	+	4.44161i	−0.0740317	+	0.156255i
$809$	−3.31573	−	1.91434i	−0.116575	−	0.0673046i	0.440579	−	0.897714i	$-0.354773\pi$
$809$	−3.31573	−	1.91434i	−0.116575	−	0.0673046i	−0.557154	+	0.830409i	$0.688107\pi$
$810$	2.32736	+	12.5133i	0.0817752	+	0.439674i
$811$	−35.5849			−1.24955			−0.624777	−	0.780803i	$-0.714810\pi$
$811$	−35.5849			−1.24955			−0.624777	+	0.780803i	$0.714810\pi$
$812$	−18.6322	−	28.3988i	−0.653862	−	0.996603i
$813$	−3.52339	+	38.3199i	−0.123571	+	1.34394i
$814$	−33.2084	−	54.0858i	−1.16395	−	1.89571i
$815$	1.69845	−	2.94180i	0.0594941	−	0.103047i
$816$	−41.3032	−	22.9463i	−1.44590	−	0.803281i
$817$	−9.01683	−	15.6176i	−0.315459	−	0.546391i
$818$	3.78030	−	0.102270i	0.132175	−	0.00357580i
$819$	−1.90652	+	10.4519i	−0.0666193	+	0.365218i
$820$	0.708287	+	13.0809i	0.0247344	+	0.456804i
$821$	−25.1039	−	43.4812i	−0.876131	−	1.51750i	−0.855553	−	0.517715i	$-0.826783\pi$
$821$	−25.1039	−	43.4812i	−0.876131	−	1.51750i	−0.0205782	−	0.999788i	$-0.506551\pi$
$822$	10.6954	+	7.13394i	0.373044	+	0.248825i
$823$	−12.6322	−	7.29321i	−0.440331	−	0.254225i	0.263407	−	0.964685i	$-0.415154\pi$
$823$	−12.6322	−	7.29321i	−0.440331	−	0.254225i	−0.703738	+	0.710459i	$0.748487\pi$
$824$	−13.6917	+	9.46260i	−0.476975	+	0.329645i
$825$	−0.793798	+	8.63323i	−0.0276365	+	0.300570i
$826$	30.1516	+	16.2222i	1.04911	+	0.564443i
$827$		−	36.0428i		−	1.25333i	−0.779288	−	0.626666i	$-0.784419\pi$
$827$		−	36.0428i		−	1.25333i	0.779288	−	0.626666i	$-0.215581\pi$
$828$	3.26153	+	7.83819i	0.113346	+	0.272396i
$829$	13.7649	+	7.94718i	0.478076	+	0.276017i	0.719614	−	0.694374i	$-0.244319\pi$
$829$	13.7649	+	7.94718i	0.478076	+	0.276017i	−0.241539	+	0.970391i	$0.577652\pi$
$830$	14.5525	+	7.88504i	0.505125	+	0.273694i
$831$	28.9836	−	13.3596i	1.00543	−	0.463438i
$832$	−1.73015	−	10.5676i	−0.0599821	−	0.366367i
$833$	−0.281872	−	47.7380i	−0.00976628	−	1.65402i
$834$	20.8640	+	1.35057i	0.722460	+	0.0467665i
$835$	−1.74283	−	3.01867i	−0.0603131	−	0.104465i
$836$	−54.5956	−	27.6987i	−1.88823	−	0.957981i
$837$	14.0874	+	14.4663i	0.486932	+	0.500027i
$838$	−23.3798	+	14.3551i	−0.807642	+	0.495888i
$839$	−2.25063			−0.0777005			−0.0388502	−	0.999245i	$-0.512370\pi$
$839$	−2.25063			−0.0777005			−0.0388502	+	0.999245i	$0.512370\pi$
$840$	6.56582	−	11.1754i	0.226542	−	0.385589i
$841$	12.2018			0.420753
$842$	−27.6537	+	16.9792i	−0.953008	+	0.585141i
$843$	−7.82416	−	5.53026i	−0.269478	−	0.190472i
$844$	7.13857	−	14.0705i	0.245720	−	0.484326i
$845$	5.60415	+	9.70668i	0.192789	+	0.333920i
$846$	10.0550	+	1.58485i	0.345699	+	0.0544882i
$847$	37.1839	−	0.109776i	1.27765	−	0.00377196i
$848$	18.6828	−	2.02918i	0.641572	−	0.0696822i
$849$	1.11068	+	2.40963i	0.0381185	+	0.0826984i
$850$	8.47991	+	4.59470i	0.290859	+	0.157597i
$851$	10.9866	+	6.34313i	0.376616	+	0.217440i
$852$	−7.34976	−	13.9130i	−0.251799	−	0.476651i
$853$		−	2.24917i		−	0.0770101i	−0.999258	−	0.0385050i	$-0.987740\pi$
$853$		−	2.24917i		−	0.0770101i	0.999258	−	0.0385050i	$-0.0122596\pi$
$854$	−34.9132	+	21.5787i	−1.19471	+	0.738407i
$855$	18.0385	+	3.34546i	0.616905	+	0.114412i
$856$	−11.2701	+	7.78894i	−0.385203	+	0.266221i
$857$	12.9859	+	7.49740i	0.443589	+	0.256106i	0.705119	−	0.709089i	$-0.250894\pi$
$857$	12.9859	+	7.49740i	0.443589	+	0.256106i	−0.261530	+	0.965195i	$0.584227\pi$
$858$	−9.10671	+	13.6530i	−0.310898	+	0.466106i
$859$	17.9881	+	31.1563i	0.613746	+	1.06304i	0.990603	+	0.136768i	$0.0436715\pi$
$859$	17.9881	+	31.1563i	0.613746	+	1.06304i	−0.376857	+	0.926271i	$0.622995\pi$
$860$	5.88918	−	0.318879i	0.200819	−	0.0108737i
$861$	−27.2223	+	12.6453i	−0.927735	+	0.430950i
$862$	6.89600	−	0.186561i	0.234879	−	0.00635430i
$863$	8.08170	+	13.9979i	0.275104	+	0.476495i	0.970161	−	0.242460i	$-0.0779543\pi$
$863$	8.08170	+	13.9979i	0.275104	+	0.476495i	−0.695057	+	0.718955i	$0.744621\pi$
$864$	18.1015	−	23.1590i	0.615824	−	0.787884i
$865$	6.05041	−	10.4796i	0.205720	−	0.356318i
$866$	−9.17977	−	14.9509i	−0.311941	−	0.508053i
$867$	50.8983	+	4.67994i	1.72860	+	0.158939i
$868$	−1.17239	−	20.5294i	−0.0397936	−	0.696812i
$869$	−51.7029			−1.75390
$870$	6.96547	+	14.0959i	0.236152	+	0.477894i
$871$	−15.0263	−	8.67547i	−0.509148	−	0.293957i
$872$	18.6928	+	8.85642i	0.633019	+	0.299916i
$873$	10.1526	+	28.6810i	0.343615	+	0.970704i
$874$	12.2326	−	0.330936i	0.413775	−	0.0111941i
$875$	−1.31611	+	2.29518i	−0.0444925	+	0.0775914i
$876$	−1.67775	−	0.0631052i	−0.0566860	−	0.00213213i
$877$	30.7382	−	17.7467i	1.03796	−	0.599264i	0.118703	−	0.992930i	$-0.462126\pi$
$877$	30.7382	−	17.7467i	1.03796	−	0.599264i	0.919254	+	0.393665i	$0.128793\pi$
$878$	−13.3076	−	7.21049i	−0.449109	−	0.243342i
$879$	27.9372	−	39.5253i	0.942298	−	1.33315i
$880$	16.1570	−	11.8246i	0.544651	−	0.398606i
$881$		−	35.9974i		−	1.21278i	−0.795166	−	0.606392i	$-0.792616\pi$
$881$		−	35.9974i		−	1.21278i	0.795166	−	0.606392i	$-0.207384\pi$
$882$	29.3631	+	4.45062i	0.988707	+	0.149860i
$883$	12.2848			0.413416			0.206708	−	0.978403i	$-0.433725\pi$
$883$	12.2848			0.413416			0.206708	+	0.978403i	$0.433725\pi$
$884$	9.97015	+	15.2946i	0.335332	+	0.514412i
$885$	−12.9427	−	9.14817i	−0.435065	−	0.307512i
$886$	44.6867	+	24.2127i	1.50128	+	0.813443i
$887$	15.2277	+	26.3752i	0.511296	+	0.885591i	0.999914	+	0.0130931i	$0.00416779\pi$
$887$	15.2277	+	26.3752i	0.511296	+	0.885591i	−0.488618	+	0.872498i	$0.662499\pi$
$888$	0.463311	−	43.9212i	0.0155477	−	1.47390i
$889$	18.4399	+	10.5738i	0.618455	+	0.354635i
$890$	0.281066	+	10.3893i	0.00942137	+	0.348249i
$891$	−44.4958	+	7.03663i	−1.49067	+	0.235736i
$892$	16.1685	+	8.20300i	0.541363	+	0.274657i
$893$	7.33617	−	12.7066i	0.245496	−	0.425211i
$894$	−13.2339	−	26.7812i	−0.442608	−	0.895696i
$895$			14.0333i			0.469083i
$896$	−29.3816	+	5.72019i	−0.981571	+	0.191098i
$897$	0.300360	−	3.26667i	0.0100287	−	0.109071i
$898$	17.9706	−	11.0338i	0.599686	−	0.368203i
$899$	21.6019	+	12.4719i	0.720464	+	0.415960i
$900$	−3.64487	+	4.76601i	−0.121496	+	0.158867i
$901$	−27.7481	+	16.0204i	−0.924425	+	0.533717i
$902$	−46.3489	+	1.25390i	−1.54325	+	0.0417504i
$903$	5.69307	+	12.2558i	0.189453	+	0.407849i
$904$	−0.111464	−	1.37069i	−0.00370723	−	0.0455886i
$905$	−10.8285	+	6.25184i	−0.359952	+	0.207818i
$906$	15.0363	+	10.0294i	0.499547	+	0.333203i
$907$	−14.7188	+	25.4937i	−0.488730	+	0.846505i	−0.999916	−	0.0129648i	$-0.995873\pi$
$907$	−14.7188	+	25.4937i	−0.488730	+	0.846505i	0.511186	+	0.859470i	$0.329206\pi$
$908$	−12.8504	+	8.37686i	−0.426455	+	0.277996i
$909$	5.12564	+	0.950610i	0.170007	+	0.0315297i
$910$	−4.26031	+	2.63315i	−0.141228	+	0.0872882i
$911$	−47.2827			−1.56654			−0.783272	−	0.621679i	$-0.786451\pi$
$911$	−47.2827			−1.56654			−0.783272	+	0.621679i	$0.786451\pi$
$912$	−21.7868	−	36.3378i	−0.721432	−	1.20326i
$913$	−29.2908	+	50.7331i	−0.969383	+	1.67902i
$914$	9.48646	−	17.5081i	0.313784	−	0.579115i
$915$	17.2547	−	7.95329i	0.570423	−	0.262928i
$916$	−1.63876	−	30.2652i	−0.0541461	−	0.999989i
$917$	−0.115097	−	38.9861i	−0.00380083	−	1.28743i
$918$	−12.3026	+	48.5818i	−0.406045	+	1.60344i
$919$	40.4205	−	23.3368i	1.33335	−	0.769809i	0.347537	−	0.937666i	$-0.387018\pi$
$919$	40.4205	−	23.3368i	1.33335	−	0.769809i	0.985811	+	0.167857i	$0.0536848\pi$
$920$	−1.71354	+	3.61668i	−0.0564936	+	0.119239i
$921$	−4.72777	+	6.68881i	−0.155785	+	0.220404i
$922$	10.8616	+	17.6901i	0.357707	+	0.582591i
$923$			6.08006i			0.200128i
$924$	38.9110	+	24.3000i	1.28008	+	0.799412i
$925$			8.96588i			0.294796i
$926$	−2.16124	+	1.32699i	−0.0710228	+	0.0436076i
$927$	13.4221	+	11.4663i	0.440841	+	0.376604i
$928$	13.7499	−	33.6065i	0.451363	−	1.10319i
$929$	28.4565	−	16.4294i	0.933628	−	0.539030i	0.0456708	−	0.998957i	$-0.485457\pi$
$929$	28.4565	−	16.4294i	0.933628	−	0.539030i	0.887957	+	0.459926i	$0.152124\pi$
$930$	−0.614882	+	9.49885i	−0.0201628	+	0.311479i
$931$	21.1846	−	37.1983i	0.694296	−	1.21912i
$932$	1.62548	+	30.0199i	0.0532442	+	0.983333i
$933$	6.95558	+	15.0902i	0.227715	+	0.494030i
$934$	6.66655	+	3.61216i	0.218136	+	0.118194i
$935$	−17.0681	+	29.5628i	−0.558185	+	0.966805i
$936$	−10.3645	+	4.64542i	−0.338773	+	0.151840i
$937$	43.3347			1.41568			0.707841	−	0.706372i	$-0.249669\pi$
$937$	43.3347			1.41568			0.707841	+	0.706372i	$0.249669\pi$
$938$	−22.9799	+	42.7120i	−0.750322	+	1.39460i
$939$	−50.1360	−	4.60985i	−1.63613	−	0.150437i
$940$	2.62043	+	4.01983i	0.0854689	+	0.131112i
$941$	−0.774811	+	1.34201i	−0.0252581	+	0.0437483i	−0.878378	−	0.477966i	$-0.841374\pi$
$941$	−0.774811	+	1.34201i	−0.0252581	+	0.0437483i	0.853120	+	0.521715i	$0.174707\pi$
$942$	−45.3718	−	30.2635i	−1.47829	−	0.986037i
$943$	8.02627	−	4.63397i	0.261371	−	0.150903i
$944$	3.95223	+	36.3886i	0.128634	+	1.18435i
$945$	−13.2419	−	3.69496i	−0.430758	−	0.120197i
$946$	0.564522	+	20.8669i	0.0183542	+	0.678440i
$947$	27.2806	−	15.7505i	0.886501	−	0.511821i	0.0137043	−	0.999906i	$-0.495638\pi$
$947$	27.2806	−	15.7505i	0.886501	−	0.511821i	0.872796	+	0.488085i	$0.162304\pi$
$948$	−30.2938	−	19.0431i	−0.983897	−	0.618491i
$949$	0.561832	+	0.324374i	0.0182379	+	0.0105296i
$950$	4.52520	+	7.37010i	0.146817	+	0.239118i
$951$	36.0726	+	3.31676i	1.16973	+	0.107553i
$952$	41.8981	−	29.1396i	1.35792	−	0.944421i
$953$		−	25.7024i		−	0.832584i	−0.909231	−	0.416292i	$-0.863329\pi$
$953$		−	25.7024i		−	0.832584i	0.909231	−	0.416292i	$-0.136671\pi$
$954$	−7.15716	−	18.6034i	−0.231722	−	0.602308i
$955$	−10.5240	+	18.2280i	−0.340547	+	0.589845i
$956$	24.6037	−	48.4952i	0.795740	−	1.56845i
$957$	−50.5389	+	23.2951i	−1.63369	+	0.753024i
$958$	−27.1485	+	0.734461i	−0.877127	+	0.0237294i
$959$	−12.0054	+	6.97867i	−0.387675	+	0.225353i
$960$	13.8219	−	0.977346i	0.446100	−	0.0315437i
$961$	−7.94948	−	13.7689i	−0.256435	−	0.444158i
$962$	−8.08553	+	14.9225i	−0.260688	+	0.481122i
$963$	11.0481	+	9.43827i	0.356022	+	0.304144i
$964$	28.7558	+	44.1125i	0.926163	+	1.42077i
$965$	−4.73891			−0.152551
$966$	−9.15246	−	0.565332i	−0.294476	−	0.0181893i
$967$		−	52.0041i		−	1.67234i	−0.548471	−	0.836169i	$-0.684790\pi$
$967$		−	52.0041i		−	1.67234i	0.548471	−	0.836169i	$-0.315210\pi$
$968$	22.6006	+	32.7015i	0.726410	+	1.05107i
$969$	58.9890	+	41.6945i	1.89500	+	1.33942i
$970$	−6.83269	+	12.6103i	−0.219384	+	0.404893i
$971$	−23.3282	+	13.4685i	−0.748638	+	0.432226i	−0.825202	−	0.564838i	$-0.808938\pi$
$971$	−23.3282	+	13.4685i	−0.748638	+	0.432226i	0.0765636	+	0.997065i	$0.475605\pi$
$972$	−28.6627	−	12.2657i	−0.919358	−	0.393423i
$973$	−11.2336	+	19.5906i	−0.360134	+	0.628044i
$974$	−1.58103	−	58.4408i	−0.0506595	−	1.87256i
$975$	2.10552	−	0.970505i	0.0674305	−	0.0310810i
$976$	−40.1456	−	17.7074i	−1.28503	−	0.566801i
$977$	33.9099	+	19.5779i	1.08487	+	0.626352i	0.932207	−	0.361926i	$-0.117881\pi$
$977$	33.9099	+	19.5779i	1.08487	+	0.626352i	0.152667	+	0.988278i	$0.451214\pi$
$978$	3.68616	+	7.45961i	0.117871	+	0.238532i
$979$	−36.7849			−1.17565
$980$	7.71441	+	11.6828i	0.246428	+	0.373193i
$981$	4.00071	−	21.5716i	0.127733	−	0.688729i
$982$	−2.41015	+	1.47981i	−0.0769108	+	0.0472228i
$983$	9.18593	−	15.9105i	0.292986	−	0.507466i	−0.681529	−	0.731791i	$-0.738685\pi$
$983$	9.18593	−	15.9105i	0.292986	−	0.507466i	0.974514	+	0.224326i	$0.0720179\pi$
$984$	−27.6186	−	16.3365i	−0.880450	−	0.520787i
$985$	−6.97076	−	12.0737i	−0.222107	−	0.384700i
$986$	1.67422	+	61.8854i	0.0533179	+	1.97083i
$987$	−6.31957	+	8.99709i	−0.201154	+	0.286381i
$988$	0.885159	+	16.3474i	0.0281607	+	0.520081i
$989$	−2.08627	−	3.61353i	−0.0663395	−	0.114903i
$990$	−16.5136	−	13.3520i	−0.524838	−	0.424355i
$991$	−15.7855	−	9.11377i	−0.501444	−	0.289509i	0.227866	−	0.973693i	$-0.426825\pi$
$991$	−15.7855	−	9.11377i	−0.501444	−	0.289509i	−0.729309	+	0.684184i	$0.760159\pi$
$992$	17.3818	−	13.4576i	0.551872	−	0.427280i
$993$	19.0576	+	1.75229i	0.604774	+	0.0556071i
$994$	16.9881	−	0.509782i	0.538830	−	0.0161693i
$995$		−	19.2821i		−	0.611283i
$996$	−35.8480	+	18.9373i	−1.13589	+	0.600050i
$997$	−2.50539	−	1.44649i	−0.0793464	−	0.0458107i	0.459802	−	0.888022i	$-0.347920\pi$
$997$	−2.50539	−	1.44649i	−0.0793464	−	0.0458107i	−0.539148	+	0.842211i	$0.681254\pi$
$998$	20.2173	−	37.3128i	0.639969	−	1.18112i
$999$	−45.1567	+	11.4598i	−1.42869	+	0.362572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.cq.b.11.20	yes	128
3.2	odd	2		840.2.cq.a.11.45	yes	128
7.2	even	3	inner	840.2.cq.b.611.23	yes	128
8.3	odd	2		840.2.cq.a.11.42	✓	128
21.2	odd	6		840.2.cq.a.611.42	yes	128
24.11	even	2	inner	840.2.cq.b.11.23	yes	128
56.51	odd	6		840.2.cq.a.611.45	yes	128
168.107	even	6	inner	840.2.cq.b.611.20	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cq.a.11.42	✓	128	8.3	odd	2
840.2.cq.a.11.45	yes	128	3.2	odd	2
840.2.cq.a.611.42	yes	128	21.2	odd	6
840.2.cq.a.611.45	yes	128	56.51	odd	6
840.2.cq.b.11.20	yes	128	1.1	even	1	trivial
840.2.cq.b.11.23	yes	128	24.11	even	2	inner
840.2.cq.b.611.20	yes	128	168.107	even	6	inner
840.2.cq.b.611.23	yes	128	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.cq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.739970 - 1.20517i) q^{2} +(0.999729 - 1.41441i) q^{3} +(-0.904890 + 1.78358i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.44437 - 0.158230i) q^{6} +(1.31611 - 2.29518i) q^{7} +(2.81912 - 0.229249i) q^{8} +(-1.00109 - 2.82804i) q^{9} +(0.673727 - 1.24342i) q^{10} +(4.33482 + 2.50271i) q^{11} +(1.61807 + 3.06298i) q^{12} -1.33854i q^{13} +(-3.73997 + 0.112230i) q^{14} +(1.72478 + 0.158588i) q^{15} +(-2.36235 - 3.22789i) q^{16} +(5.90615 + 3.40992i) q^{17} +(-2.66751 + 3.29915i) q^{18} +(3.05769 + 5.29608i) q^{19} +(-1.99707 + 0.108135i) q^{20} +(-1.93057 - 4.15607i) q^{21} +(-0.191435 - 7.07615i) q^{22} +(0.707474 + 1.22538i) q^{23} +(2.49411 - 4.21657i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.61318 + 0.990480i) q^{26} +(-5.00081 - 1.41134i) q^{27} +(2.90272 + 4.42427i) q^{28} -6.41887 q^{29} +(-1.08516 - 2.19600i) q^{30} +(-3.36538 - 1.94300i) q^{31} +(-2.14211 + 5.23559i) q^{32} +(7.87349 - 3.62916i) q^{33} +(-0.260828 - 9.64117i) q^{34} +(2.64574 - 0.00781089i) q^{35} +(5.94993 + 0.773546i) q^{36} +(7.76468 - 4.48294i) q^{37} +(4.12010 - 7.60399i) q^{38} +(-1.89324 - 1.33818i) q^{39} +(1.60810 + 2.32681i) q^{40} -6.55003i q^{41} +(-3.58022 + 5.40204i) q^{42} -2.94890 q^{43} +(-8.38633 + 5.46685i) q^{44} +(1.94861 - 2.28099i) q^{45} +(0.953288 - 1.75937i) q^{46} +(-1.19963 - 2.07781i) q^{47} +(-6.92726 + 0.114301i) q^{48} +(-3.53573 - 6.04141i) q^{49} +(1.41370 - 0.0382455i) q^{50} +(10.7275 - 4.94470i) q^{51} +(2.38740 + 1.21123i) q^{52} +(-2.34909 + 4.06874i) q^{53} +(1.99955 + 7.07120i) q^{54} +5.00542i q^{55} +(3.18409 - 6.77212i) q^{56} +(10.5477 + 0.969824i) q^{57} +(4.74977 + 7.73585i) q^{58} +(-7.92470 - 4.57533i) q^{59} +(-1.84359 + 2.93278i) q^{60} +(9.49973 - 5.48467i) q^{61} +(0.148622 + 5.49363i) q^{62} +(-7.80841 - 1.42433i) q^{63} +(7.89489 - 1.29256i) q^{64} +(1.15921 - 0.669271i) q^{65} +(-10.1999 - 6.80346i) q^{66} +(6.48128 - 11.2259i) q^{67} +(-11.4263 + 7.44852i) q^{68} +(2.44047 + 0.224393i) q^{69} +(-1.96718 - 3.18280i) q^{70} -4.54230 q^{71} +(-3.47051 - 7.74310i) q^{72} +(-0.242334 + 0.419735i) q^{73} +(-11.1484 - 6.04055i) q^{74} +(0.725047 + 1.57299i) q^{75} +(-12.2129 + 0.661286i) q^{76} +(11.4493 - 6.65538i) q^{77} +(-0.211797 + 3.27190i) q^{78} +(-8.94551 + 5.16469i) q^{79} +(1.61426 - 3.65980i) q^{80} +(-6.99566 + 5.66223i) q^{81} +(-7.89392 + 4.84682i) q^{82} +11.7036i q^{83} +(9.15965 + 0.317444i) q^{84} +6.81983i q^{85} +(2.18210 + 3.55394i) q^{86} +(-6.41712 + 9.07888i) q^{87} +(12.7941 + 6.06169i) q^{88} +(-6.36443 + 3.67451i) q^{89} +(-4.19090 - 0.660559i) q^{90} +(-3.07220 - 1.76166i) q^{91} +(-2.82576 + 0.153005i) q^{92} +(-6.11266 + 2.81753i) q^{93} +(-1.61644 + 2.98328i) q^{94} +(-3.05769 + 5.29608i) q^{95} +(5.26372 + 8.26398i) q^{96} -10.1416 q^{97} +(-4.66461 + 8.73163i) q^{98} +(2.73825 - 14.7645i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 64 q^{5} + 2 q^{12} + 6 q^{14} + 8 q^{16} - 4 q^{18} - 8 q^{21} + 4 q^{22} + 20 q^{24} - 64 q^{25} + 16 q^{26} - 6 q^{28} + 10 q^{32} + 24 q^{34} + 20 q^{36} + 16 q^{38} + 18 q^{42} - 6 q^{44} + 8 q^{46}+ \cdots - 14 q^{98}+O(q^{100}) \) 128 * q + 64 * q^5 + 2 * q^12 + 6 * q^14 + 8 * q^16 - 4 * q^18 - 8 * q^21 + 4 * q^22 + 20 * q^24 - 64 * q^25 + 16 * q^26 - 6 * q^28 + 10 * q^32 + 24 * q^34 + 20 * q^36 + 16 * q^38 + 18 * q^42 - 6 * q^44 + 8 * q^46 - 44 * q^48 + 8 * q^49 + 20 * q^51 - 6 * q^52 - 16 * q^54 + 18 * q^56 - 8 * q^58 - 2 * q^60 + 20 * q^62 + 28 * q^63 + 22 * q^66 + 32 * q^67 + 2 * q^68 - 40 * q^69 - 6 * q^70 + 48 * q^71 - 54 * q^72 - 8 * q^73 + 26 * q^74 - 24 * q^76 - 84 * q^78 - 8 * q^80 + 4 * q^81 - 12 * q^82 + 6 * q^84 - 46 * q^86 + 36 * q^87 - 20 * q^88 - 8 * q^90 - 24 * q^91 + 40 * q^92 + 12 * q^94 + 22 * q^96 + 32 * q^97 - 14 * q^98

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