LMFDB - Embedded newform 168.2.ba.c.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(5,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

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

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

chi := DirichletCharacter("168.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.2
Character	$\chi$	$=$	168.101
Dual form			168.2.ba.c.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37674 + 0.323405i) q^{2} +(-0.609093 - 1.62142i) q^{3} +(1.79082 - 0.890488i) q^{4} +(2.24840 - 1.29811i) q^{5} +(1.36294 + 2.03529i) q^{6} +(-2.53678 - 0.751482i) q^{7} +(-2.17750 + 1.80513i) q^{8} +(-2.25801 + 1.97519i) q^{9} +O(q^{10})$	\(q+(-1.37674 + 0.323405i) q^{2} +(-0.609093 - 1.62142i) q^{3} +(1.79082 - 0.890488i) q^{4} +(2.24840 - 1.29811i) q^{5} +(1.36294 + 2.03529i) q^{6} +(-2.53678 - 0.751482i) q^{7} +(-2.17750 + 1.80513i) q^{8} +(-2.25801 + 1.97519i) q^{9} +(-2.67564 + 2.51430i) q^{10} +(1.63808 - 2.83724i) q^{11} +(-2.53463 - 2.36128i) q^{12} -0.912635 q^{13} +(3.73552 + 0.214186i) q^{14} +(-3.47427 - 2.85492i) q^{15} +(2.41406 - 3.18940i) q^{16} +(2.39448 - 4.14736i) q^{17} +(2.46990 - 3.44958i) q^{18} +(-2.66693 - 4.61926i) q^{19} +(2.87052 - 4.32685i) q^{20} +(0.326671 + 4.57092i) q^{21} +(-1.33763 + 4.43590i) q^{22} +(-4.45569 + 2.57249i) q^{23} +(4.25317 + 2.43115i) q^{24} +(0.870190 - 1.50721i) q^{25} +(1.25646 - 0.295151i) q^{26} +(4.57796 + 2.45811i) q^{27} +(-5.21211 + 0.913209i) q^{28} +1.35950 q^{29} +(5.70646 + 2.80689i) q^{30} +(8.18469 + 4.72543i) q^{31} +(-2.29206 + 5.17170i) q^{32} +(-5.59810 - 0.927874i) q^{33} +(-1.95529 + 6.48421i) q^{34} +(-6.67920 + 1.60340i) q^{35} +(-2.28480 + 5.54794i) q^{36} +(-1.59746 + 0.922292i) q^{37} +(5.16556 + 5.49701i) q^{38} +(0.555880 + 1.47977i) q^{39} +(-2.55263 + 6.88528i) q^{40} +5.91833 q^{41} +(-1.92800 - 6.18731i) q^{42} -8.00125i q^{43} +(0.406978 - 6.53967i) q^{44} +(-2.51288 + 7.37217i) q^{45} +(5.30236 - 4.98264i) q^{46} +(3.29243 + 5.70266i) q^{47} +(-6.64176 - 1.97156i) q^{48} +(5.87055 + 3.81269i) q^{49} +(-0.710584 + 2.35646i) q^{50} +(-8.18307 - 1.35633i) q^{51} +(-1.63436 + 0.812691i) q^{52} +(0.841712 - 1.45789i) q^{53} +(-7.09762 - 1.90364i) q^{54} -8.50565i q^{55} +(6.88037 - 2.94287i) q^{56} +(-5.86535 + 7.13777i) q^{57} +(-1.87168 + 0.439670i) q^{58} +(1.50266 + 0.867561i) q^{59} +(-8.76406 - 2.01886i) q^{60} +(4.72347 + 8.18130i) q^{61} +(-12.7964 - 3.85872i) q^{62} +(7.21241 - 3.31379i) q^{63} +(1.48302 - 7.86134i) q^{64} +(-2.05197 + 1.18470i) q^{65} +(8.00720 - 0.533013i) q^{66} +(10.8634 + 6.27198i) q^{67} +(0.594903 - 9.55942i) q^{68} +(6.88502 + 5.65766i) q^{69} +(8.67697 - 4.36755i) q^{70} +0.603989i q^{71} +(1.35134 - 8.37699i) q^{72} +(-1.29220 - 0.746053i) q^{73} +(1.90101 - 1.78638i) q^{74} +(-2.97385 - 0.492910i) q^{75} +(-8.88938 - 5.89738i) q^{76} +(-6.28759 + 5.96647i) q^{77} +(-1.24387 - 1.85748i) q^{78} +(-0.0625152 - 0.108280i) q^{79} +(1.28756 - 10.3048i) q^{80} +(1.19722 - 8.92001i) q^{81} +(-8.14799 + 1.91402i) q^{82} -0.246431i q^{83} +(4.65536 + 7.89479i) q^{84} -12.4332i q^{85} +(2.58764 + 11.0156i) q^{86} +(-0.828064 - 2.20433i) q^{87} +(1.55466 + 9.13504i) q^{88} +(1.80671 + 3.12931i) q^{89} +(1.07538 - 10.9622i) q^{90} +(2.31516 + 0.685829i) q^{91} +(-5.68856 + 8.57461i) q^{92} +(2.67667 - 16.1491i) q^{93} +(-6.37708 - 6.78628i) q^{94} +(-11.9926 - 6.92395i) q^{95} +(9.78158 + 0.566352i) q^{96} -5.10324i q^{97} +(-9.31526 - 3.35052i) q^{98} +(1.90529 + 9.64204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.37674	+	0.323405i	−0.973501	+	0.228682i
$2$	−1.37674	+	0.323405i	−0.973501	+	0.228682i
$3$	−0.609093	−	1.62142i	−0.351660	−	0.936128i
$3$	−0.609093	−	1.62142i	−0.351660	−	0.936128i
$4$	1.79082	−	0.890488i	0.895409	−	0.445244i
$5$	2.24840	−	1.29811i	1.00551	−	0.580533i	0.0956384	−	0.995416i	$-0.469511\pi$
$5$	2.24840	−	1.29811i	1.00551	−	0.580533i	0.909875	+	0.414883i	$0.136177\pi$
$6$	1.36294	+	2.03529i	0.556417	+	0.830903i
$7$	−2.53678	−	0.751482i	−0.958814	−	0.284033i
$7$	−2.53678	−	0.751482i	−0.958814	−	0.284033i
$8$	−2.17750	+	1.80513i	−0.769863	+	0.638209i
$9$	−2.25801	+	1.97519i	−0.752670	+	0.658398i
$10$	−2.67564	+	2.51430i	−0.846111	+	0.795093i
$11$	1.63808	−	2.83724i	0.493900	−	0.855460i	−0.506075	−	0.862489i	$-0.668904\pi$
$11$	1.63808	−	2.83724i	0.493900	−	0.855460i	0.999975	+	0.00702958i	$0.00223760\pi$
$12$	−2.53463	−	2.36128i	−0.731685	−	0.681643i
$13$	−0.912635			−0.253119			−0.126560	−	0.991959i	$-0.540394\pi$
$13$	−0.912635			−0.253119			−0.126560	+	0.991959i	$0.540394\pi$
$14$	3.73552	+	0.214186i	0.998360	+	0.0572435i
$15$	−3.47427	−	2.85492i	−0.897052	−	0.737138i
$16$	2.41406	−	3.18940i	0.603516	−	0.797351i
$17$	2.39448	−	4.14736i	0.580746	−	1.00588i	−0.414645	−	0.909983i	$-0.636094\pi$
$17$	2.39448	−	4.14736i	0.580746	−	1.00588i	0.995391	−	0.0958985i	$-0.0305724\pi$
$18$	2.46990	−	3.44958i	0.582162	−	0.813073i
$19$	−2.66693	−	4.61926i	−0.611836	−	1.05973i	−0.990931	−	0.134373i	$-0.957098\pi$
$19$	−2.66693	−	4.61926i	−0.611836	−	1.05973i	0.379095	−	0.925358i	$-0.376235\pi$
$20$	2.87052	−	4.32685i	0.641867	−	0.967514i
$21$	0.326671	+	4.57092i	0.0712854	+	0.997456i
$22$	−1.33763	+	4.43590i	−0.285184	+	0.945737i
$23$	−4.45569	+	2.57249i	−0.929075	+	0.536402i	−0.886519	−	0.462692i	$-0.846884\pi$
$23$	−4.45569	+	2.57249i	−0.929075	+	0.536402i	−0.0425563	+	0.999094i	$0.513550\pi$
$24$	4.25317	+	2.43115i	0.868176	+	0.496257i
$25$	0.870190	−	1.50721i	0.174038	−	0.301443i
$26$	1.25646	−	0.295151i	0.246412	−	0.0578838i
$27$	4.57796	+	2.45811i	0.881029	+	0.473063i
$28$	−5.21211	+	0.913209i	−0.984995	+	0.172580i
$29$	1.35950			0.252453			0.126227	−	0.992001i	$-0.459713\pi$
$29$	1.35950			0.252453			0.126227	+	0.992001i	$0.459713\pi$
$30$	5.70646	+	2.80689i	1.04185	+	0.512465i
$31$	8.18469	+	4.72543i	1.47001	+	0.848713i	0.999434	−	0.0336443i	$-0.0107113\pi$
$31$	8.18469	+	4.72543i	1.47001	+	0.848713i	0.470580	+	0.882357i	$0.344045\pi$
$32$	−2.29206	+	5.17170i	−0.405183	+	0.914235i
$33$	−5.59810	−	0.927874i	−0.974504	−	0.161522i
$34$	−1.95529	+	6.48421i	−0.335330	+	1.11203i
$35$	−6.67920	+	1.60340i	−1.12899	+	0.271024i
$36$	−2.28480	+	5.54794i	−0.380800	+	0.924657i
$37$	−1.59746	+	0.922292i	−0.262620	+	0.151624i	−0.625529	−	0.780201i	$-0.715117\pi$
$37$	−1.59746	+	0.922292i	−0.262620	+	0.151624i	0.362909	+	0.931825i	$0.381784\pi$
$38$	5.16556	+	5.49701i	0.837964	+	0.891733i
$39$	0.555880	+	1.47977i	0.0890121	+	0.236952i
$40$	−2.55263	+	6.88528i	−0.403605	+	1.08866i
$41$	5.91833			0.924288			0.462144	−	0.886805i	$-0.347080\pi$
$41$	5.91833			0.924288			0.462144	+	0.886805i	$0.347080\pi$
$42$	−1.92800	−	6.18731i	−0.297496	−	0.954723i
$43$		−	8.00125i		−	1.22018i	−0.792332	−	0.610090i	$-0.791133\pi$
$43$		−	8.00125i		−	1.22018i	0.792332	−	0.610090i	$-0.208867\pi$
$44$	0.406978	−	6.53967i	0.0613542	−	0.985892i
$45$	−2.51288	+	7.37217i	−0.374598	+	1.09898i
$46$	5.30236	−	4.98264i	0.781791	−	0.734650i
$47$	3.29243	+	5.70266i	0.480250	+	0.831818i	0.999743	−	0.0226567i	$-0.00721246\pi$
$47$	3.29243	+	5.70266i	0.480250	+	0.831818i	−0.519493	+	0.854475i	$0.673879\pi$
$48$	−6.64176	−	1.97156i	−0.958655	−	0.284571i
$49$	5.87055	+	3.81269i	0.838650	+	0.544671i
$50$	−0.710584	+	2.35646i	−0.100492	+	0.333254i
$51$	−8.18307	−	1.35633i	−1.14586	−	0.189924i
$52$	−1.63436	+	0.812691i	−0.226646	+	0.112700i
$53$	0.841712	−	1.45789i	0.115618	−	0.200256i	−0.802409	−	0.596775i	$-0.796448\pi$
$53$	0.841712	−	1.45789i	0.115618	−	0.200256i	0.918027	+	0.396519i	$0.129782\pi$
$54$	−7.09762	−	1.90364i	−0.965863	−	0.259052i
$55$		−	8.50565i		−	1.14690i
$56$	6.88037	−	2.94287i	0.919428	−	0.393258i
$57$	−5.86535	+	7.13777i	−0.776885	+	0.945421i
$58$	−1.87168	+	0.439670i	−0.245764	+	0.0577315i
$59$	1.50266	+	0.867561i	0.195630	+	0.112947i	0.594615	−	0.804010i	$-0.297304\pi$
$59$	1.50266	+	0.867561i	0.195630	+	0.112947i	−0.398986	+	0.916957i	$0.630638\pi$
$60$	−8.76406	−	2.01886i	−1.13144	−	0.260633i
$61$	4.72347	+	8.18130i	0.604779	+	1.04751i	0.992086	+	0.125557i	$0.0400718\pi$
$61$	4.72347	+	8.18130i	0.604779	+	1.04751i	−0.387308	+	0.921951i	$0.626595\pi$
$62$	−12.7964	−	3.85872i	−1.62515	−	0.490058i
$63$	7.21241	−	3.31379i	0.908678	−	0.417498i
$64$	1.48302	−	7.86134i	0.185378	−	0.982667i
$65$	−2.05197	+	1.18470i	−0.254515	+	0.146944i
$66$	8.00720	−	0.533013i	0.985618	−	0.0656094i
$67$	10.8634	+	6.27198i	1.32717	+	0.766245i	0.984862	−	0.173341i	$-0.0554564\pi$
$67$	10.8634	+	6.27198i	1.32717	+	0.766245i	0.342313	+	0.939586i	$0.388790\pi$
$68$	0.594903	−	9.55942i	0.0721426	−	1.15925i
$69$	6.88502	+	5.65766i	0.828860	+	0.681102i
$70$	8.67697	−	4.36755i	1.03710	−	0.522022i
$71$			0.603989i			0.0716803i	0.999358	+	0.0358401i	$0.0114107\pi$
$71$			0.603989i			0.0716803i	−0.999358	+	0.0358401i	$0.988589\pi$
$72$	1.35134	−	8.37699i	0.159257	−	0.987237i
$73$	−1.29220	−	0.746053i	−0.151241	−	0.0873189i	0.422470	−	0.906377i	$-0.361163\pi$
$73$	−1.29220	−	0.746053i	−0.151241	−	0.0873189i	−0.573711	+	0.819058i	$0.694497\pi$
$74$	1.90101	−	1.78638i	0.220988	−	0.207663i
$75$	−2.97385	−	0.492910i	−0.343391	−	0.0569164i
$76$	−8.88938	−	5.89738i	−1.01968	−	0.676476i
$77$	−6.28759	+	5.96647i	−0.716537	+	0.679943i
$78$	−1.24387	−	1.85748i	−0.140840	−	0.210318i
$79$	−0.0625152	−	0.108280i	−0.00703351	−	0.0121824i	0.862487	−	0.506079i	$-0.168906\pi$
$79$	−0.0625152	−	0.108280i	−0.00703351	−	0.0121824i	−0.869521	+	0.493896i	$0.835572\pi$
$80$	1.28756	−	10.3048i	0.143954	−	1.15211i
$81$	1.19722	−	8.92001i	0.133025	−	0.991113i
$82$	−8.14799	+	1.91402i	−0.899795	+	0.211368i
$83$		−	0.246431i		−	0.0270493i	−0.999909	−	0.0135247i	$-0.995695\pi$
$83$		−	0.246431i		−	0.0270493i	0.999909	−	0.0135247i	$-0.00430516\pi$
$84$	4.65536	+	7.89479i	0.507941	+	0.861392i
$85$		−	12.4332i		−	1.34857i
$86$	2.58764	+	11.0156i	0.279033	+	1.18785i
$87$	−0.828064	−	2.20433i	−0.0887778	−	0.236329i
$88$	1.55466	+	9.13504i	0.165727	+	0.973798i
$89$	1.80671	+	3.12931i	0.191511	+	0.331706i	0.945751	−	0.324892i	$-0.105328\pi$
$89$	1.80671	+	3.12931i	0.191511	+	0.331706i	−0.754241	+	0.656598i	$0.771995\pi$
$90$	1.07538	−	10.9622i	0.113355	−	1.15552i
$91$	2.31516	+	0.685829i	0.242695	+	0.0718944i
$92$	−5.68856	+	8.57461i	−0.593073	+	0.893964i
$93$	2.67667	−	16.1491i	0.277558	−	1.67458i
$94$	−6.37708	−	6.78628i	−0.657746	−	0.699951i
$95$	−11.9926	−	6.92395i	−1.23042	−	0.710382i
$96$	9.78158	+	0.566352i	0.998328	+	0.0578031i
$97$		−	5.10324i		−	0.518155i	−0.965857	−	0.259078i	$-0.916581\pi$
$97$		−	5.10324i		−	0.518155i	0.965857	−	0.259078i	$-0.0834185\pi$
$98$	−9.31526	−	3.35052i	−0.940983	−	0.338454i
$99$	1.90529	+	9.64204i	0.191489	+	0.969061i
$100$	0.216197	−	3.47404i	0.0216197	−	0.347404i
$101$	−6.33114	−	3.65529i	−0.629972	−	0.363715i	0.150769	−	0.988569i	$-0.451825\pi$
$101$	−6.33114	−	3.65529i	−0.629972	−	0.363715i	−0.780741	+	0.624854i	$0.785158\pi$
$102$	11.7046	−	0.779137i	1.15893	−	0.0771460i
$103$	0.670566	−	0.387151i	0.0660728	−	0.0381472i	−0.466600	−	0.884469i	$-0.654521\pi$
$103$	0.670566	−	0.387151i	0.0660728	−	0.0381472i	0.532672	+	0.846321i	$0.321188\pi$
$104$	1.98726	−	1.64742i	0.194867	−	0.161543i
$105$	6.66805	+	9.85318i	0.650735	+	0.961572i
$106$	−0.687329	+	2.27934i	−0.0667593	+	0.221389i
$107$	7.26435	+	12.5822i	0.702271	+	1.21637i	0.967667	+	0.252229i	$0.0811638\pi$
$107$	7.26435	+	12.5822i	0.702271	+	1.21637i	−0.265397	+	0.964139i	$0.585503\pi$
$108$	10.3872	+	0.325406i	0.999510	+	0.0313122i
$109$	−12.8015	−	7.39093i	−1.22616	−	0.707923i	−0.259934	−	0.965626i	$-0.583701\pi$
$109$	−12.8015	−	7.39093i	−1.22616	−	0.707923i	−0.966224	+	0.257703i	$0.917034\pi$
$110$	2.75077	+	11.7101i	0.262275	+	1.11651i
$111$	2.46842	+	2.02839i	0.234292	+	0.192526i
$112$	−8.52073	+	6.27671i	−0.805134	+	0.593093i
$113$		−	16.2708i		−	1.53063i	−0.643657	−	0.765314i	$-0.722584\pi$
$113$		−	16.2708i		−	1.53063i	0.643657	−	0.765314i	$-0.277416\pi$
$114$	5.76666	−	11.7237i	0.540097	−	1.09803i
$115$	−6.67877	+	11.5680i	−0.622798	+	1.07872i
$116$	2.43462	−	1.21062i	0.226049	−	0.112403i
$117$	2.06074	−	1.80263i	0.190515	−	0.166653i
$118$	−2.34934	−	0.708437i	−0.216275	−	0.0652170i
$119$	−9.19094	+	8.72154i	−0.842532	+	0.799503i
$120$	12.7187	−	0.0549029i	1.16106	−	0.00501193i
$121$	0.133385	+	0.231029i	0.0121259	+	0.0210026i
$122$	−9.14886	−	9.73591i	−0.828299	−	0.881448i
$123$	−3.60482	−	9.59610i	−0.325035	−	0.865251i
$124$	18.8652	+	1.17402i	1.69415	+	0.105431i
$125$			8.46270i			0.756927i
$126$	−8.85790	+	6.89475i	−0.789125	+	0.614233i
$127$	−1.59996			−0.141973			−0.0709867	−	0.997477i	$-0.522615\pi$
$127$	−1.59996			−0.141973			−0.0709867	+	0.997477i	$0.522615\pi$
$128$	0.500664	+	11.3026i	0.0442529	+	0.999020i
$129$	−12.9734	+	4.87351i	−1.14224	+	0.429089i
$130$	2.44188	−	2.29464i	0.214167	−	0.201253i
$131$	−7.96684	+	4.59965i	−0.696066	+	0.401874i	−0.805880	−	0.592078i	$-0.798308\pi$
$131$	−7.96684	+	4.59965i	−0.696066	+	0.401874i	0.109815	+	0.993952i	$0.464974\pi$
$132$	−10.8514	+	3.32339i	−0.944497	+	0.289264i
$133$	3.29414	+	13.7222i	0.285638	+	1.18987i
$134$	−16.9844	−	5.12161i	−1.46723	−	0.442439i
$135$	13.4840	−	0.415906i	1.16051	−	0.0357955i
$136$	2.27254	+	13.3532i	0.194868	+	1.14503i
$137$	2.43936	+	1.40836i	0.208408	+	0.120325i	0.600571	−	0.799571i	$-0.294940\pi$
$137$	2.43936	+	1.40836i	0.208408	+	0.120325i	−0.392163	+	0.919896i	$0.628273\pi$
$138$	−11.3086	−	5.56246i	−0.962651	−	0.473508i
$139$	2.80505			0.237921			0.118960	−	0.992899i	$-0.462044\pi$
$139$	2.80505			0.237921			0.118960	+	0.992899i	$0.462044\pi$
$140$	−10.5334	+	8.81915i	−0.890237	+	0.745354i
$141$	7.24101	−	8.81187i	0.609803	−	0.742093i
$142$	−0.195333	−	0.831534i	−0.0163920	−	0.0697808i
$143$	−1.49497	+	2.58936i	−0.125016	+	0.216533i
$144$	0.848715	+	11.9699i	0.0707263	+	0.997496i
$145$	3.05670	−	1.76479i	0.253845	−	0.146558i
$146$	2.02030	+	0.609216i	0.167201	+	0.0504190i
$147$	2.60627	−	11.8409i	0.214961	−	0.976623i
$148$	−2.03947	+	3.07417i	−0.167643	+	0.252696i
$149$	−8.67025	−	15.0173i	−0.710295	−	1.23027i	−0.964746	−	0.263181i	$-0.915228\pi$
$149$	−8.67025	−	15.0173i	−0.710295	−	1.23027i	0.254451	−	0.967086i	$-0.418105\pi$
$150$	4.25363	−	0.283150i	0.347307	−	0.0231191i
$151$	−6.41551	+	11.1120i	−0.522087	+	0.904281i	0.477583	+	0.878587i	$0.341513\pi$
$151$	−6.41551	+	11.1120i	−0.522087	+	0.904281i	−0.999670	+	0.0256942i	$0.991820\pi$
$152$	14.1456	+	5.24429i	1.14736	+	0.425368i
$153$	2.78508	+	14.0943i	0.225160	+	1.13946i
$154$	6.72678	−	10.2477i	0.542059	−	0.825784i
$155$	24.5366			1.97082
$156$	2.31319	+	2.15499i	0.185204	+	0.172537i
$157$	8.55356	−	14.8152i	0.682648	−	1.18238i	−0.291521	−	0.956564i	$-0.594161\pi$
$157$	8.55356	−	14.8152i	0.682648	−	1.18238i	0.974170	−	0.225817i	$-0.0725052\pi$
$158$	0.121085	+	0.128855i	0.00963302	+	0.0102511i
$159$	−2.87653	−	0.476779i	−0.228124	−	0.0378110i
$160$	1.55998	+	14.6034i	0.123327	+	1.15450i
$161$	13.2363	−	3.17749i	1.04317	−	0.250421i
$162$	1.23652	+	12.6677i	0.0971499	+	0.995270i
$163$	−21.6390	+	12.4933i	−1.69489	+	0.978547i	−0.744436	+	0.667694i	$0.767282\pi$
$163$	−21.6390	+	12.4933i	−1.69489	+	0.978547i	−0.950458	+	0.310853i	$0.899385\pi$
$164$	10.5987	−	5.27020i	0.827616	−	0.411534i
$165$	−13.7912	+	5.18073i	−1.07365	+	0.403320i
$166$	0.0796970	+	0.339271i	0.00618568	+	0.0263325i
$167$	9.89286			0.765532			0.382766	−	0.923845i	$-0.374972\pi$
$167$	9.89286			0.765532			0.382766	+	0.923845i	$0.374972\pi$
$168$	−8.96242	−	9.36349i	−0.691466	−	0.722409i
$169$	−12.1671			−0.935931
$170$	4.02096	+	17.1173i	0.308393	+	1.31283i
$171$	15.1459	+	5.16263i	1.15823	+	0.394796i
$172$	−7.12502	−	14.3288i	−0.543278	−	1.09256i
$173$	13.3755	−	7.72235i	1.01692	−	0.587120i	0.103710	−	0.994608i	$-0.466929\pi$
$173$	13.3755	−	7.72235i	1.01692	−	0.587120i	0.913211	+	0.407488i	$0.133595\pi$
$174$	1.85292	+	2.76698i	0.140469	+	0.209764i
$175$	−3.34013	+	3.16954i	−0.252490	+	0.239595i
$176$	−5.09467	−	12.0738i	−0.384026	−	0.910095i
$177$	0.491421	−	2.96487i	0.0369375	−	0.222853i
$178$	−3.49940	−	3.72394i	−0.262291	−	0.279121i
$179$	6.07462	−	10.5216i	0.454038	−	0.786418i	−0.544594	−	0.838700i	$-0.683316\pi$
$179$	6.07462	−	10.5216i	0.454038	−	0.786418i	0.998632	+	0.0522822i	$0.0166495\pi$
$180$	2.06472	+	15.4399i	0.153895	+	1.15082i
$181$	−1.41922			−0.105489			−0.0527447	−	0.998608i	$-0.516797\pi$
$181$	−1.41922			−0.105489			−0.0527447	+	0.998608i	$0.516797\pi$
$182$	−3.40917	−	0.195473i	−0.252704	−	0.0144894i
$183$	10.3883	−	12.6419i	0.767924	−	0.934517i
$184$	5.05858	−	13.6447i	0.372924	−	1.00590i
$185$	−2.39448	+	4.14736i	−0.176045	+	0.304920i
$186$	1.53760	+	23.0987i	0.112743	+	1.69368i
$187$	−7.84469	−	13.5874i	−0.573661	−	0.993610i
$188$	10.9743	+	7.28055i	0.800383	+	0.530989i
$189$	−9.76607	−	9.67594i	−0.710377	−	0.703821i
$190$	18.7500	+	5.65399i	1.36026	+	0.410184i
$191$	3.62414	−	2.09240i	0.262234	−	0.151401i	−0.363119	−	0.931743i	$-0.618288\pi$
$191$	3.62414	−	2.09240i	0.262234	−	0.151401i	0.625353	+	0.780342i	$0.284955\pi$
$192$	−13.6498	+	2.38369i	−0.985092	+	0.172028i
$193$	−13.1905	+	22.8467i	−0.949476	+	1.64454i	−0.202946	+	0.979190i	$0.565051\pi$
$193$	−13.1905	+	22.8467i	−0.949476	+	1.64454i	−0.746531	+	0.665351i	$0.768282\pi$
$194$	1.65041	+	7.02582i	0.118493	+	0.504425i
$195$	3.17074	+	2.60550i	0.227061	+	0.186584i
$196$	13.9082	+	1.60019i	0.993446	+	0.114299i
$197$	−12.6908			−0.904184			−0.452092	−	0.891971i	$-0.649322\pi$
$197$	−12.6908			−0.904184			−0.452092	+	0.891971i	$0.649322\pi$
$198$	−5.74137	−	12.6584i	−0.408022	−	0.899592i
$199$	0.939591	+	0.542473i	0.0666058	+	0.0384549i	0.532933	−	0.846157i	$-0.321090\pi$
$199$	0.939591	+	0.542473i	0.0666058	+	0.0384549i	−0.466327	+	0.884612i	$0.654423\pi$
$200$	0.825874	+	4.85276i	0.0583981	+	0.343142i
$201$	3.55270	−	21.4344i	0.250588	−	1.51186i
$202$	9.89847	+	2.98485i	0.696454	+	0.210014i
$203$	−3.44876	−	1.02164i	−0.242056	−	0.0717052i
$204$	−15.8622	+	4.85799i	−1.11058	+	0.340127i
$205$	13.3067	−	7.68265i	0.929384	−	0.536580i
$206$	−0.797987	+	0.749871i	−0.0555984	+	0.0522460i
$207$	4.97982	−	14.6096i	0.346121	−	1.01543i
$208$	−2.20316	+	2.91076i	−0.152762	+	0.201825i
$209$	−17.4746			−1.20874
$210$	−12.3667	−	11.4088i	−0.853385	−	0.787280i
$211$			7.89074i			0.543221i	0.962407	+	0.271610i	$0.0875562\pi$
$211$			7.89074i			0.543221i	−0.962407	+	0.271610i	$0.912444\pi$
$212$	0.209122	−	3.36035i	0.0143625	−	0.230790i
$213$	0.979320	−	0.367886i	0.0671019	−	0.0252071i
$214$	−14.0703	−	14.9731i	−0.961823	−	1.02354i
$215$	−10.3865	−	17.9900i	−0.708355	−	1.22691i
$216$	−14.4057	+	2.91128i	−0.980184	+	0.198087i
$217$	−17.2117	−	18.1381i	−1.16841	−	1.23129i
$218$	20.0145	+	6.03532i	1.35556	+	0.408764i
$219$	−0.422594	+	2.54962i	−0.0285563	+	0.172287i
$220$	−7.57418	−	15.2321i	−0.510651	−	1.02695i
$221$	−2.18528	+	3.78502i	−0.146998	+	0.254608i
$222$	−4.05437	−	1.99426i	−0.272111	−	0.133846i
$223$		−	11.5392i		−	0.772720i	−0.922348	−	0.386360i	$-0.873732\pi$
$223$		−	11.5392i		−	0.772720i	0.922348	−	0.386360i	$-0.126268\pi$
$224$	9.70091	−	11.3970i	0.648169	−	0.761496i
$225$	1.01214	+	5.12210i	0.0674760	+	0.341473i
$226$	5.26206	+	22.4006i	0.350027	+	1.49007i
$227$	−13.4825	−	7.78410i	−0.894862	−	0.516649i	−0.0193323	−	0.999813i	$-0.506154\pi$
$227$	−13.4825	−	7.78410i	−0.894862	−	0.516649i	−0.875530	+	0.483164i	$0.839487\pi$
$228$	−4.14768	+	18.0055i	−0.274687	+	1.19244i
$229$	1.78238	+	3.08717i	0.117783	+	0.204006i	0.918889	−	0.394517i	$-0.129088\pi$
$229$	1.78238	+	3.08717i	0.117783	+	0.204006i	−0.801106	+	0.598523i	$0.795755\pi$
$230$	5.45378	−	18.0860i	0.359612	−	1.19256i
$231$	13.5039	+	6.56069i	0.888491	+	0.431662i
$232$	−2.96032	+	2.45408i	−0.194354	+	0.161118i
$233$	−6.60666	+	3.81435i	−0.432816	+	0.249887i	−0.700546	−	0.713607i	$-0.747060\pi$
$233$	−6.60666	+	3.81435i	−0.432816	+	0.249887i	0.267729	+	0.963494i	$0.413727\pi$
$234$	−2.25412	+	3.14821i	−0.147356	+	0.205805i
$235$	14.8054	+	8.54789i	0.965796	+	0.557603i
$236$	3.46354	+	0.215544i	0.225458	+	0.0140307i
$237$	−0.137489	+	0.167316i	−0.00893087	+	0.0108683i
$238$	9.83293	−	14.9797i	0.637374	−	0.970988i
$239$			13.2745i			0.858658i	0.903148	+	0.429329i	$0.141250\pi$
$239$			13.2745i			0.858658i	−0.903148	+	0.429329i	$0.858750\pi$
$240$	−17.4926	+	4.18889i	−1.12914	+	0.270391i
$241$	9.92793	+	5.73189i	0.639514	+	0.369224i	0.784427	−	0.620221i	$-0.212957\pi$
$241$	9.92793	+	5.73189i	0.639514	+	0.369224i	−0.144913	+	0.989444i	$0.546290\pi$
$242$	−0.258352	−	0.274929i	−0.0166075	−	0.0176731i
$243$	−15.1923	+	3.49192i	−0.974588	+	0.224007i
$244$	15.7442	+	10.4450i	1.00792	+	0.668674i
$245$	18.1486	+	0.951816i	1.15947	+	0.0608093i
$246$	8.06631	+	12.0455i	0.514289	+	0.767994i
$247$	2.43393	+	4.21570i	0.154867	+	0.268238i
$248$	−26.3522	+	4.48479i	−1.67337	+	0.284784i
$249$	−0.399568	+	0.150099i	−0.0253216	+	0.00951217i
$250$	−2.73688	−	11.6509i	−0.173095	−	0.736870i
$251$			1.44903i			0.0914619i	0.998954	+	0.0457309i	$0.0145617\pi$
$251$			1.44903i			0.0914619i	−0.998954	+	0.0457309i	$0.985438\pi$
$252$	9.96523	−	12.3570i	0.627750	−	0.778415i
$253$			16.8558i			1.05972i
$254$	2.20272	−	0.517434i	0.138211	−	0.0324667i
$255$	−20.1594	+	7.57298i	−1.26243	+	0.474238i
$256$	−4.34461	−	15.3988i	−0.271538	−	0.962428i
$257$	6.03418	+	10.4515i	0.376402	+	0.651948i	0.990536	−	0.137254i	$-0.0438278\pi$
$257$	6.03418	+	10.4515i	0.376402	+	0.651948i	−0.614134	+	0.789202i	$0.710494\pi$
$258$	16.2849	−	10.9052i	1.01385	−	0.678929i
$259$	4.74549	−	1.13920i	0.294870	−	0.0707862i
$260$	−2.61973	+	3.94884i	−0.162469	+	0.244897i
$261$	−3.06977	+	2.68528i	−0.190014	+	0.166215i
$262$	9.48070	−	8.90904i	0.585720	−	0.550402i
$263$	21.7325	+	12.5473i	1.34008	+	0.773697i	0.986819	−	0.161827i	$-0.0517385\pi$
$263$	21.7325	+	12.5473i	1.34008	+	0.773697i	0.353264	+	0.935524i	$0.385072\pi$
$264$	13.8648	−	8.08485i	0.853320	−	0.497588i
$265$		−	4.37055i		−	0.268480i
$266$	−8.97300	−	17.8266i	−0.550170	−	1.09302i
$267$	3.97347	−	4.83547i	0.243172	−	0.295926i
$268$	25.0395	+	1.55826i	1.52953	+	0.0951860i
$269$	−6.61826	−	3.82105i	−0.403522	−	0.232974i	0.284480	−	0.958682i	$-0.408179\pi$
$269$	−6.61826	−	3.82105i	−0.403522	−	0.232974i	−0.688003	+	0.725708i	$0.741512\pi$
$270$	−18.4294	+	4.93337i	−1.12158	+	0.300236i
$271$	−9.27850	+	5.35694i	−0.563629	+	0.325411i	−0.754601	−	0.656184i	$-0.772169\pi$
$271$	−9.27850	+	5.35694i	−0.563629	+	0.325411i	0.190972	+	0.981595i	$0.438836\pi$
$272$	−7.44718	−	17.6489i	−0.451552	−	1.07012i
$273$	−0.298131	−	4.17158i	−0.0180437	−	0.252476i
$274$	−3.81383	−	1.15005i	−0.230402	−	0.0694769i
$275$	−2.85088	−	4.93787i	−0.171915	−	0.297765i
$276$	17.3679	+	4.00081i	1.04543	+	0.240820i
$277$	3.08910	+	1.78349i	0.185606	+	0.107160i	0.589924	−	0.807459i	$-0.299158\pi$
$277$	3.08910	+	1.78349i	0.185606	+	0.107160i	−0.404318	+	0.914618i	$0.632491\pi$
$278$	−3.86182	+	0.907166i	−0.231616	+	0.0544082i
$279$	−27.8148	+	5.49627i	−1.66523	+	0.329053i
$280$	11.6496	−	15.5482i	0.696198	−	0.929185i
$281$		−	4.26336i		−	0.254331i	−0.991882	−	0.127165i	$-0.959412\pi$
$281$		−	4.26336i		−	0.254331i	0.991882	−	0.127165i	$-0.0405879\pi$
$282$	−7.11918	+	14.4734i	−0.423941	+	0.861879i
$283$	11.3202	−	19.6072i	0.672918	−	1.16553i	−0.304154	−	0.952623i	$-0.598374\pi$
$283$	11.3202	−	19.6072i	0.672918	−	1.16553i	0.977073	−	0.212906i	$-0.0682928\pi$
$284$	0.537845	+	1.08163i	0.0319152	+	0.0641832i
$285$	−3.92200	+	23.6624i	−0.232319	+	1.40164i
$286$	1.22077	−	4.04836i	0.0721856	−	0.239384i
$287$	−15.0135	−	4.44752i	−0.886220	−	0.262529i
$288$	−5.03960	−	16.2050i	−0.296961	−	0.954890i
$289$	−2.96705	−	5.13907i	−0.174532	−	0.302298i
$290$	−3.63754	+	3.41820i	−0.213604	+	0.200724i
$291$	−8.27449	+	3.10835i	−0.485059	+	0.182215i
$292$	−2.97845	−	0.185355i	−0.174301	−	0.0108471i
$293$			5.96057i			0.348220i	0.984726	+	0.174110i	$0.0557049\pi$
$293$			5.96057i			0.348220i	−0.984726	+	0.174110i	$0.944295\pi$
$294$	0.241261	+	17.1447i	0.0140706	+	0.999901i
$295$	4.50477			0.262278
$296$	1.81361	−	4.89191i	0.105414	−	0.284336i
$297$	14.4733	−	8.96219i	0.839826	−	0.520039i
$298$	16.7933	+	17.8709i	0.972813	+	1.03523i
$299$	4.06642	−	2.34775i	0.235167	−	0.135774i
$300$	−5.76456	+	1.76547i	−0.332817	+	0.101929i
$301$	−6.01280	+	20.2975i	−0.346572	+	1.16993i
$302$	5.23881	−	17.3731i	0.301460	−	0.999710i
$303$	−2.07050	+	12.4919i	−0.118947	+	0.717639i
$304$	−21.1708	−	2.64526i	−1.21423	−	0.151716i
$305$	21.2405	+	12.2632i	1.21623	+	0.702189i
$306$	−8.39250	−	18.5035i	−0.479767	−	1.05777i
$307$	5.42113			0.309400			0.154700	−	0.987961i	$-0.450559\pi$
$307$	5.42113			0.309400			0.154700	+	0.987961i	$0.450559\pi$
$308$	−5.94686	+	16.2839i	−0.338854	+	0.927861i
$309$	−1.03617	−	0.851458i	−0.0589458	−	0.0484378i
$310$	−33.7804	+	7.93525i	−1.91860	+	0.450692i
$311$	12.1809	−	21.0979i	0.690714	−	1.19635i	−0.280890	−	0.959740i	$-0.590630\pi$
$311$	12.1809	−	21.0979i	0.690714	−	1.19635i	0.971604	−	0.236612i	$-0.0760370\pi$
$312$	−3.88160	−	2.21876i	−0.219752	−	0.125612i
$313$	14.1392	−	8.16327i	0.799195	−	0.461415i	−0.0439948	−	0.999032i	$-0.514009\pi$
$313$	14.1392	−	8.16327i	0.799195	−	0.461415i	0.843189	+	0.537617i	$0.180675\pi$
$314$	−6.98471	+	23.1629i	−0.394170	+	1.30716i
$315$	11.9147	−	16.8132i	0.671316	−	0.947317i
$316$	−0.208375	−	0.138240i	−0.0117220	−	0.00777660i
$317$	9.94185	+	17.2198i	0.558390	+	0.967160i	0.997631	+	0.0687904i	$0.0219140\pi$
$317$	9.94185	+	17.2198i	0.558390	+	0.967160i	−0.439241	+	0.898369i	$0.644753\pi$
$318$	4.11442	−	0.273884i	0.230725	−	0.0153586i
$319$	2.22697	−	3.85723i	0.124687	−	0.215964i
$320$	−6.87048	−	19.6005i	−0.384072	−	1.09570i
$321$	15.9764	−	19.4423i	0.891716	−	1.08516i
$322$	−17.1953	+	8.65526i	−0.958257	+	0.482339i
$323$	−25.5436			−1.42128
$324$	−5.79916	−	17.0402i	−0.322176	−	0.946680i
$325$	−0.794166	+	1.37554i	−0.0440524	+	0.0763010i
$326$	25.7508	−	24.1981i	1.42621	−	1.34021i
$327$	−4.18652	+	25.2583i	−0.231515	+	1.39679i
$328$	−12.8872	+	10.6833i	−0.711575	+	0.589889i
$329$	−4.06674	−	16.9406i	−0.224207	−	0.933966i
$330$	17.3114	−	11.5927i	0.952964	−	0.638156i
$331$	1.90300	−	1.09870i	0.104599	−	0.0603900i	−0.446788	−	0.894640i	$-0.647432\pi$
$331$	1.90300	−	1.09870i	0.104599	−	0.0603900i	0.551387	+	0.834250i	$0.314099\pi$
$332$	−0.219444	−	0.441313i	−0.0120435	−	0.0242202i
$333$	1.78537	−	5.23783i	0.0978376	−	0.287031i
$334$	−13.6199	+	3.19940i	−0.745247	+	0.175063i
$335$	32.5669			1.77932
$336$	15.3671	+	9.99259i	0.838345	+	0.545141i
$337$	29.4138			1.60227			0.801135	−	0.598484i	$-0.204230\pi$
$337$	29.4138			1.60227			0.801135	+	0.598484i	$0.204230\pi$
$338$	16.7509	−	3.93490i	0.911130	−	0.214030i
$339$	−26.3818	+	9.91044i	−1.43286	+	0.538261i
$340$	−11.0716	−	22.2656i	−0.600443	−	1.20752i
$341$	26.8144	−	15.4813i	1.45208	−	0.838358i
$342$	−22.5215	−	2.20934i	−1.21783	−	0.119467i
$343$	−12.0271	−	14.0836i	−0.649405	−	0.760443i
$344$	14.4433	+	17.4227i	0.778730	+	0.939371i
$345$	22.8245	+	3.78312i	1.22883	+	0.203676i
$346$	−15.9171	+	14.9574i	−0.855710	+	0.804113i
$347$	−6.43016	+	11.1374i	−0.345189	+	0.597885i	−0.985388	−	0.170324i	$-0.945518\pi$
$347$	−6.43016	+	11.1374i	−0.345189	+	0.597885i	0.640199	+	0.768209i	$0.278852\pi$
$348$	−3.44584	−	3.21017i	−0.184716	−	0.172083i
$349$	−30.0571			−1.60892			−0.804460	−	0.594006i	$-0.797545\pi$
$349$	−30.0571			−1.60892			−0.804460	+	0.594006i	$0.797545\pi$
$350$	3.57344	−	5.44385i	0.191008	−	0.290986i
$351$	−4.17801	−	2.24335i	−0.223005	−	0.119741i
$352$	10.9188	+	14.9748i	0.581971	+	0.798159i
$353$	−12.1069	+	20.9698i	−0.644387	+	1.11611i	0.340056	+	0.940405i	$0.389554\pi$
$353$	−12.1069	+	20.9698i	−0.644387	+	1.11611i	−0.984443	+	0.175705i	$0.943779\pi$
$354$	0.282295	+	4.24078i	0.0150038	+	0.225395i
$355$	0.784045	+	1.35801i	0.0416128	+	0.0720755i
$356$	6.02209	+	3.99517i	0.319170	+	0.211744i
$357$	19.7394	+	9.59014i	1.04472	+	0.507564i
$358$	−4.96044	+	16.4500i	−0.262168	+	0.869409i
$359$	−3.16884	+	1.82953i	−0.167245	+	0.0965590i	−0.581286	−	0.813699i	$-0.697450\pi$
$359$	−3.16884	+	1.82953i	−0.167245	+	0.0965590i	0.414041	+	0.910258i	$0.364117\pi$
$360$	−7.83592	−	20.5890i	−0.412989	−	1.08513i
$361$	−4.72503	+	8.18398i	−0.248686	+	0.430736i
$362$	1.95389	−	0.458981i	0.102694	−	0.0241235i
$363$	0.293351	−	0.356991i	0.0153970	−	0.0187372i
$364$	4.75675	−	0.833426i	0.249322	−	0.0436834i
$365$	−3.87384			−0.202766
$366$	−10.2135	+	20.7642i	−0.533868	+	1.08536i
$367$	−15.1950	−	8.77283i	−0.793172	−	0.457938i	0.0479063	−	0.998852i	$-0.484745\pi$
$367$	−15.1950	−	8.77283i	−0.793172	−	0.457938i	−0.841078	+	0.540914i	$0.818078\pi$
$368$	−2.55159	+	20.4212i	−0.133011	+	1.06453i
$369$	−13.3636	+	11.6898i	−0.695684	+	0.608549i
$370$	1.95529	−	6.48421i	0.101651	−	0.337098i
$371$	−3.23082	+	3.06582i	−0.167736	+	0.159169i
$372$	−9.58711	−	31.3036i	−0.497068	−	1.62302i
$373$	−3.25687	+	1.88036i	−0.168635	+	0.0973612i	−0.581942	−	0.813230i	$-0.697707\pi$
$373$	−3.25687	+	1.88036i	−0.168635	+	0.0973612i	0.413307	+	0.910592i	$0.364374\pi$
$374$	15.1943	+	16.1693i	0.785680	+	0.836094i
$375$	13.7216	−	5.15458i	0.708581	−	0.266181i
$376$	−17.4633	−	6.47428i	−0.900601	−	0.333886i
$377$	−1.24073			−0.0639008
$378$	16.5746	+	10.1628i	0.852504	+	0.522720i
$379$			12.2799i			0.630774i	0.948963	+	0.315387i	$0.102134\pi$
$379$			12.2799i			0.630774i	−0.948963	+	0.315387i	$0.897866\pi$
$380$	−27.6423	−	1.72024i	−1.41802	−	0.0882465i
$381$	0.974524	+	2.59421i	0.0499264	+	0.132905i
$382$	−4.31281	+	4.05275i	−0.220662	+	0.207357i
$383$	3.77515	+	6.53874i	0.192901	+	0.334114i	0.946210	−	0.323552i	$-0.104877\pi$
$383$	3.77515	+	6.53874i	0.192901	+	0.334114i	−0.753309	+	0.657666i	$0.771544\pi$
$384$	18.0214	−	7.69614i	0.919649	−	0.392742i
$385$	−6.39184	+	21.5770i	−0.325758	+	1.09967i
$386$	10.7712	−	35.7198i	0.548240	−	1.81809i
$387$	15.8040	+	18.0669i	0.803364	+	0.918393i
$388$	−4.54437	−	9.13897i	−0.230705	−	0.463961i
$389$	−18.2949	+	31.6877i	−0.927588	+	1.60663i	−0.140244	+	0.990117i	$0.544789\pi$
$389$	−18.2949	+	31.6877i	−0.927588	+	1.60663i	−0.787345	+	0.616513i	$0.788545\pi$
$390$	−5.20791	−	2.56167i	−0.263713	−	0.129715i
$391$			24.6391i			1.24605i
$392$	−19.6655	+	2.29495i	−0.993259	+	0.115913i
$393$	12.3105	+	10.1160i	0.620984	+	0.510283i
$394$	17.4720	−	4.10428i	0.880224	−	0.206770i
$395$	−0.281118	−	0.162304i	−0.0141446	−	0.00816638i
$396$	11.9982	+	15.5705i	0.602930	+	0.782447i
$397$	3.83449	+	6.64152i	0.192447	+	0.333329i	0.946061	−	0.323989i	$-0.105024\pi$
$397$	3.83449	+	6.64152i	0.192447	+	0.333329i	−0.753613	+	0.657318i	$0.771691\pi$
$398$	−1.46901	−	0.442975i	−0.0736348	−	0.0222043i
$399$	20.2430	−	13.6993i	1.01342	−	0.685822i
$400$	−2.70642	−	6.41389i	−0.135321	−	0.320695i
$401$	−20.5062	+	11.8393i	−1.02403	+	0.591224i	−0.915269	−	0.402844i	$-0.868022\pi$
$401$	−20.5062	+	11.8393i	−1.02403	+	0.591224i	−0.108761	+	0.994068i	$0.534688\pi$
$402$	2.04083	+	30.6585i	0.101788	+	1.52911i
$403$	−7.46964	−	4.31260i	−0.372089	−	0.214826i
$404$	−14.5929	−	0.908149i	−0.726025	−	0.0451821i
$405$	−8.88735	−	21.6099i	−0.441616	−	1.07380i
$406$	5.07845	+	0.291186i	0.252039	+	0.0144513i
$407$			6.04316i			0.299548i
$408$	20.2670	−	11.8181i	1.00337	−	0.585083i
$409$	13.5659	+	7.83230i	0.670793	+	0.387283i	0.796377	−	0.604800i	$-0.206747\pi$
$409$	13.5659	+	7.83230i	0.670793	+	0.387283i	−0.125584	+	0.992083i	$0.540080\pi$
$410$	−15.8353	+	14.8805i	−0.782050	+	0.734894i
$411$	0.797753	−	4.81305i	0.0393502	−	0.237410i
$412$	0.856108	−	1.29045i	0.0421774	−	0.0635759i
$413$	−3.15997	−	3.33004i	−0.155492	−	0.163860i
$414$	−2.13110	+	21.7240i	−0.104738	+	1.06768i
$415$	−0.319895	−	0.554074i	−0.0157030	−	0.0271984i
$416$	2.09182	−	4.71987i	0.102560	−	0.231411i
$417$	−1.70854	−	4.54816i	−0.0836674	−	0.222724i
$418$	24.0579	−	5.65136i	1.17671	−	0.276417i
$419$		−	35.4540i		−	1.73204i	−0.500009	−	0.866020i	$-0.666670\pi$
$419$		−	35.4540i		−	1.73204i	0.500009	−	0.866020i	$-0.333330\pi$
$420$	20.7154	+	11.7074i	1.01081	+	0.571264i
$421$			8.00460i			0.390120i	0.980791	+	0.195060i	$0.0624902\pi$
$421$			8.00460i			0.390120i	−0.980791	+	0.195060i	$0.937510\pi$
$422$	−2.55190	−	10.8635i	−0.124225	−	0.528826i
$423$	−18.6982	−	6.37347i	−0.909137	−	0.309889i
$424$	0.798847	+	4.69395i	0.0387954	+	0.227958i
$425$	−4.16730	−	7.21798i	−0.202144	−	0.350123i
$426$	−1.22929	+	0.823199i	−0.0595594	+	0.0398841i
$427$	−5.83434	−	24.3038i	−0.282343	−	1.17614i
$428$	24.2134	+	16.0637i	1.17040	+	0.776466i
$429$	5.10902	+	0.846811i	0.246666	+	0.0408844i
$430$	20.1176	+	21.4085i	0.970156	+	1.03241i
$431$	−25.8583	−	14.9293i	−1.24555	−	0.719118i	−0.275331	−	0.961350i	$-0.588787\pi$
$431$	−25.8583	−	14.9293i	−1.24555	−	0.719118i	−0.970219	+	0.242231i	$0.922121\pi$
$432$	18.8914	−	8.66694i	0.908912	−	0.416988i
$433$		−	1.70747i		−	0.0820557i	−0.999158	−	0.0410278i	$-0.986937\pi$
$433$		−	1.70747i		−	0.0820557i	0.999158	−	0.0410278i	$-0.0130632\pi$
$434$	29.5620	+	19.4050i	1.41902	+	0.931470i
$435$	−4.72328	−	3.88128i	−0.226464	−	0.186093i
$436$	−29.5066	−	1.83626i	−1.41311	−	0.0879410i
$437$	23.7660	+	13.7213i	1.13688	+	0.656379i
$438$	−0.242757	−	3.64683i	−0.0115994	−	0.174252i
$439$	14.3026	−	8.25762i	0.682627	−	0.394115i	−0.118217	−	0.992988i	$-0.537718\pi$
$439$	14.3026	−	8.25762i	0.682627	−	0.394115i	0.800844	+	0.598873i	$0.204385\pi$
$440$	15.3538	+	18.5211i	0.731963	+	0.882957i
$441$	−20.7866	+	2.98637i	−0.989837	+	0.142208i
$442$	1.78447	−	5.91772i	0.0848786	−	0.281477i
$443$	7.12265	+	12.3368i	0.338407	+	0.586138i	0.984133	−	0.177431i	$-0.0567785\pi$
$443$	7.12265	+	12.3368i	0.338407	+	0.586138i	−0.645726	+	0.763569i	$0.723445\pi$
$444$	6.22676	+	1.43437i	0.295509	+	0.0680723i
$445$	8.12438	+	4.69062i	0.385133	+	0.222356i
$446$	3.73182	+	15.8864i	0.176707	+	0.752244i
$447$	−19.0684	+	23.2051i	−0.901904	+	1.09756i
$448$	−9.66976	+	18.8281i	−0.456853	+	0.889542i
$449$			2.18010i			0.102885i	0.998676	+	0.0514426i	$0.0163819\pi$
$449$			2.18010i			0.102885i	−0.998676	+	0.0514426i	$0.983618\pi$
$450$	−3.04996	−	6.72446i	−0.143777	−	0.316994i
$451$	9.69470	−	16.7917i	0.456506	−	0.790691i
$452$	−14.4890	−	29.1381i	−0.681503	−	1.37054i
$453$	21.9249	+	3.63400i	1.03012	+	0.170740i
$454$	21.0792	+	6.35638i	0.989297	+	0.298320i
$455$	6.09568	−	1.46332i	0.285770	−	0.0686015i
$456$	−0.112796	−	26.1302i	−0.00528217	−	1.22366i
$457$	−16.0855	−	27.8609i	−0.752447	−	1.30328i	−0.946633	−	0.322312i	$-0.895540\pi$
$457$	−16.0855	−	27.8609i	−0.752447	−	1.30328i	0.194186	−	0.980965i	$-0.437793\pi$
$458$	−3.45227	−	3.67379i	−0.161314	−	0.171665i
$459$	21.1565	−	13.1005i	0.987499	−	0.611481i
$460$	−1.65933	+	26.6635i	−0.0773665	+	1.24319i
$461$		−	13.9258i		−	0.648588i	−0.945956	−	0.324294i	$-0.894873\pi$
$461$		−	13.9258i		−	0.648588i	0.945956	−	0.324294i	$-0.105127\pi$
$462$	−20.7131	−	4.66513i	−0.963660	−	0.217041i
$463$	15.5838			0.724239			0.362120	−	0.932132i	$-0.382053\pi$
$463$	15.5838			0.724239			0.362120	+	0.932132i	$0.382053\pi$
$464$	3.28192	−	4.33600i	0.152359	−	0.201294i
$465$	−14.9451	−	39.7841i	−0.693061	−	1.84494i
$466$	7.86206	−	7.38799i	0.364203	−	0.342242i
$467$	−16.6230	+	9.59729i	−0.769220	+	0.444110i	−0.832596	−	0.553880i	$-0.813147\pi$
$467$	−16.6230	+	9.59729i	−0.769220	+	0.444110i	0.0633760	+	0.997990i	$0.479813\pi$
$468$	2.08519	−	5.06325i	0.0963879	−	0.234049i
$469$	−22.8448	−	24.0743i	−1.05488	−	1.11165i
$470$	−23.1476	−	6.98008i	−1.06772	−	0.321967i
$471$	−29.2316	−	4.84508i	−1.34692	−	0.223249i
$472$	−4.83810	+	0.823380i	−0.222692	+	0.0378991i
$473$	−22.7015	−	13.1067i	−1.04381	−	0.602647i
$474$	0.135176	−	0.274815i	0.00620883	−	0.0126227i
$475$	−9.28294			−0.425931
$476$	−8.69287	+	23.8031i	−0.398437	+	1.09101i
$477$	0.979016	+	4.95447i	0.0448261	+	0.226850i
$478$	−4.29305	−	18.2755i	−0.196359	−	0.835904i
$479$	3.02090	−	5.23235i	0.138028	−	0.239072i	−0.788722	−	0.614750i	$-0.789257\pi$
$479$	3.02090	−	5.23235i	0.138028	−	0.239072i	0.926750	+	0.375678i	$0.122590\pi$
$480$	22.7280	−	11.4242i	1.03739	−	0.521441i
$481$	1.45790	−	0.841716i	0.0664743	−	0.0383790i
$482$	−15.5219	−	4.68058i	−0.707003	−	0.213195i
$483$	−13.2142	−	19.5262i	−0.601267	−	0.888474i
$484$	0.444596	+	0.294954i	0.0202089	+	0.0134070i
$485$	−6.62457	−	11.4741i	−0.300806	−	0.521012i
$486$	19.7865	−	9.72074i	0.897536	−	0.440942i
$487$	11.1385	−	19.2925i	0.504735	−	0.874227i	−0.495250	−	0.868751i	$-0.664923\pi$
$487$	11.1385	−	19.2925i	0.504735	−	0.874227i	0.999985	−	0.00547672i	$-0.00174330\pi$
$488$	−25.0537	−	9.28830i	−1.13413	−	0.420462i
$489$	33.4370	+	27.4763i	1.51207	+	1.24252i
$490$	−25.2937	+	4.55895i	−1.14265	+	0.205953i
$491$	−4.63965			−0.209384			−0.104692	−	0.994505i	$-0.533386\pi$
$491$	−4.63965			−0.209384			−0.104692	+	0.994505i	$0.533386\pi$
$492$	−15.0008	−	13.9748i	−0.676288	−	0.630034i
$493$	3.25530	−	5.63834i	0.146611	−	0.253938i
$494$	−4.71427	−	5.01677i	−0.212105	−	0.225715i
$495$	16.8003	+	19.2058i	0.755117	+	0.863238i
$496$	34.8297	−	14.6968i	1.56390	−	0.659906i
$497$	0.453886	−	1.53219i	0.0203596	−	0.0687281i
$498$	0.501558	−	0.335870i	0.0224754	−	0.0150507i
$499$	16.8940	−	9.75377i	0.756280	−	0.436639i	−0.0716782	−	0.997428i	$-0.522835\pi$
$499$	16.8940	−	9.75377i	0.756280	−	0.436639i	0.827959	+	0.560789i	$0.189502\pi$
$500$	7.53594	+	15.1552i	0.337017	+	0.677760i
$501$	−6.02567	−	16.0405i	−0.269207	−	0.716636i
$502$	−0.468623	−	1.99493i	−0.0209157	−	0.0890383i
$503$	−33.9146			−1.51218			−0.756090	−	0.654468i	$-0.772893\pi$
$503$	−33.9146			−1.51218			−0.756090	+	0.654468i	$0.772893\pi$
$504$	−9.72321	+	20.2351i	−0.433106	+	0.901343i
$505$	−18.9799			−0.844594
$506$	−5.45125	−	23.2060i	−0.242338	−	1.03163i
$507$	7.41090	+	19.7280i	0.329130	+	0.876150i
$508$	−2.86524	+	1.42474i	−0.127124	+	0.0632128i
$509$	−20.9128	+	12.0740i	−0.926946	+	0.535172i	−0.885844	−	0.463983i	$-0.846420\pi$
$509$	−20.9128	+	12.0740i	−0.926946	+	0.535172i	−0.0411013	+	0.999155i	$0.513087\pi$
$510$	25.3052	−	16.9457i	1.12053	−	0.750367i
$511$	2.71739	+	2.86364i	0.120210	+	0.126680i
$512$	10.9615	+	19.7951i	0.484432	+	0.874829i
$513$	−0.854465	−	27.7024i	−0.0377256	−	1.22309i
$514$	−11.6876	−	12.4375i	−0.515516	−	0.548595i
$515$	1.00513	−	1.74094i	0.0442914	−	0.0767150i
$516$	−18.8932	+	20.2802i	−0.831727	+	0.892787i
$517$	21.5731			0.948782
$518$	−6.16488	+	3.10309i	−0.270869	+	0.136342i
$519$	−20.6681	−	16.9837i	−0.907230	−	0.745501i
$520$	2.32962	−	6.28375i	0.102160	−	0.275561i
$521$	2.98225	−	5.16541i	0.130655	−	0.226301i	−0.793274	−	0.608864i	$-0.791625\pi$
$521$	2.98225	−	5.16541i	0.130655	−	0.226301i	0.923929	+	0.382564i	$0.124959\pi$
$522$	3.35784	−	4.68971i	0.146969	−	0.205263i
$523$	−6.49701	−	11.2532i	−0.284095	−	0.492066i	0.688295	−	0.725431i	$-0.258360\pi$
$523$	−6.49701	−	11.2532i	−0.284095	−	0.492066i	−0.972389	+	0.233365i	$0.925026\pi$
$524$	−10.1712	+	15.3315i	−0.444332	+	0.669761i
$525$	7.17361	+	3.48520i	0.313082	+	0.152107i
$526$	−33.9778	−	10.2459i	−1.48150	−	0.446743i
$527$	39.1961	−	22.6299i	1.70741	−	0.985774i
$528$	−16.4735	+	15.6147i	−0.716918	+	0.679541i
$529$	1.73544	−	3.00587i	0.0754539	−	0.130690i
$530$	1.41346	+	6.01710i	0.0613966	+	0.261366i
$531$	−5.10662	+	1.00908i	−0.221609	+	0.0437905i
$532$	18.1187	+	21.6406i	0.785544	+	0.938239i
$533$	−5.40127			−0.233955
$534$	−3.90662	+	7.94222i	−0.169056	+	0.343694i
$535$	32.6663	+	18.8599i	1.41229	+	0.815383i
$536$	−34.9768	+	5.95258i	−1.51077	+	0.257112i
$537$	−20.7599	−	3.44091i	−0.895855	−	0.148486i
$538$	10.3474	+	3.12022i	0.446106	+	0.134522i
$539$	20.4340	−	10.4107i	0.880153	−	0.448418i
$540$	23.7770	−	12.7521i	1.02320	−	0.548764i
$541$	18.7480	−	10.8242i	0.806039	−	0.465367i	−0.0395397	−	0.999218i	$-0.512589\pi$
$541$	18.7480	−	10.8242i	0.806039	−	0.465367i	0.845578	+	0.533851i	$0.179256\pi$
$542$	11.0416	−	10.3758i	0.474278	−	0.445680i
$543$	0.864435	+	2.30115i	0.0370965	+	0.0987516i
$544$	15.9606	+	21.8895i	0.684304	+	0.938505i
$545$	−38.3770			−1.64389
$546$	1.75956	+	5.64676i	0.0753021	+	0.241659i
$547$			15.8930i			0.679536i	0.940509	+	0.339768i	$0.110349\pi$
$547$			15.8930i			0.679536i	−0.940509	+	0.339768i	$0.889651\pi$
$548$	5.62257	+	0.349905i	0.240184	+	0.0149472i
$549$	−26.8253	−	9.14368i	−1.14488	−	0.390243i
$550$	5.52185	+	5.87617i	0.235453	+	0.250561i
$551$	−3.62570	−	6.27989i	−0.154460	−	0.267532i
$552$	−25.2049	+	0.108802i	−1.07279	+	0.00463093i
$553$	0.0772175	+	0.321661i	0.00328362	+	0.0136784i
$554$	−4.82967	−	1.45637i	−0.205193	−	0.0618753i
$555$	8.18307	+	1.35633i	0.347352	+	0.0575729i
$556$	5.02333	−	2.49786i	0.213037	−	0.105933i
$557$	20.3420	−	35.2334i	0.861919	−	1.49289i	−0.00815471	−	0.999967i	$-0.502596\pi$
$557$	20.3420	−	35.2334i	0.861919	−	1.49289i	0.870074	−	0.492921i	$-0.164071\pi$
$558$	36.5161	−	16.5624i	1.54585	−	0.701141i
$559$			7.30223i			0.308851i
$560$	−11.0101	+	25.1734i	−0.465262	+	1.06377i
$561$	−17.2528	+	20.9956i	−0.728412	+	0.886433i
$562$	1.37879	+	5.86953i	0.0581608	+	0.247591i
$563$	38.8739	+	22.4439i	1.63834	+	0.945896i	0.981405	+	0.191950i	$0.0614810\pi$
$563$	38.8739	+	22.4439i	1.63834	+	0.945896i	0.656936	+	0.753947i	$0.271852\pi$
$564$	5.12047	−	22.2285i	0.215611	−	0.935988i
$565$	−21.1213	−	36.5832i	−0.888581	−	1.53907i
$566$	−9.24394	+	30.6550i	−0.388552	+	1.28853i
$567$	−9.74032	+	21.7285i	−0.409055	+	0.912510i
$568$	−1.09028	−	1.31519i	−0.0457470	−	0.0551840i
$569$	12.8893	−	7.44164i	0.540347	−	0.311970i	−0.204872	−	0.978789i	$-0.565678\pi$
$569$	12.8893	−	7.44164i	0.540347	−	0.311970i	0.745220	+	0.666819i	$0.232345\pi$
$570$	−2.25298	−	33.8454i	−0.0943668	−	1.41763i
$571$	−6.27344	−	3.62197i	−0.262535	−	0.151575i	0.362955	−	0.931807i	$-0.381768\pi$
$571$	−6.27344	−	3.62197i	−0.262535	−	0.151575i	−0.625490	+	0.780232i	$0.715101\pi$
$572$	−0.371422	+	5.96833i	−0.0155299	+	0.249549i
$573$	−5.60010	−	4.60179i	−0.233948	−	0.192243i
$574$	22.1080	+	1.26762i	0.922772	+	0.0529095i
$575$			8.95423i			0.373417i
$576$	12.1790	+	20.6802i	0.507458	+	0.861677i
$577$	20.2309	+	11.6803i	0.842223	+	0.486258i	0.858019	−	0.513617i	$-0.171695\pi$
$577$	20.2309	+	11.6803i	0.842223	+	0.486258i	−0.0157961	+	0.999875i	$0.505028\pi$
$578$	5.74685	+	6.11560i	0.239037	+	0.254376i
$579$	45.0784	+	7.47165i	1.87339	+	0.310511i
$580$	3.90247	−	5.88237i	0.162041	−	0.244252i
$581$	−0.185188	+	0.625142i	−0.00768291	+	0.0259353i
$582$	10.3866	−	6.95539i	0.430537	−	0.288310i
$583$	−2.75758	−	4.77627i	−0.114207	−	0.197813i
$584$	4.16049	−	0.708059i	0.172162	−	0.0292997i
$585$	2.29334	−	6.72810i	0.0948180	−	0.278173i
$586$	−1.92768	−	8.20615i	−0.0796316	−	0.338993i
$587$		−	8.33175i		−	0.343888i	−0.985107	−	0.171944i	$-0.944995\pi$
$587$		−	8.33175i		−	0.343888i	0.985107	−	0.171944i	$-0.0550048\pi$
$588$	−5.87684	−	23.5258i	−0.242357	−	0.970187i
$589$		−	50.4096i		−	2.07709i
$590$	−6.20189	+	1.45686i	−0.255328	+	0.0599781i
$591$	7.72990	+	20.5772i	0.317966	+	0.846432i
$592$	−0.914797	+	7.32141i	−0.0375979	+	0.300908i
$593$	19.8845	+	34.4410i	0.816560	+	1.41432i	0.908202	+	0.418531i	$0.137455\pi$
$593$	19.8845	+	34.4410i	0.816560	+	1.41432i	−0.0916424	+	0.995792i	$0.529212\pi$
$594$	−17.0275	+	17.0193i	−0.698648	+	0.698311i
$595$	−9.34332	+	31.5403i	−0.383039	+	1.29303i
$596$	−28.8996	−	19.1725i	−1.18377	−	0.785338i
$597$	0.307278	−	1.85389i	0.0125761	−	0.0758746i
$598$	−4.83912	+	4.54733i	−0.197886	+	0.185954i
$599$	12.0202	+	6.93989i	0.491134	+	0.283556i	0.725045	−	0.688702i	$-0.241819\pi$
$599$	12.0202	+	6.93989i	0.491134	+	0.283556i	−0.233911	+	0.972258i	$0.575152\pi$
$600$	7.36534	−	4.29488i	0.300689	−	0.175338i
$601$		−	17.2223i		−	0.702512i	−0.936279	−	0.351256i	$-0.885755\pi$
$601$		−	17.2223i		−	0.702512i	0.936279	−	0.351256i	$-0.114245\pi$
$602$	1.71375	−	29.8889i	0.0698474	−	1.21818i
$603$	−36.9180	+	7.29510i	−1.50342	+	0.297080i
$604$	−1.59392	+	25.6125i	−0.0648557	+	1.04216i
$605$	0.599803	+	0.346296i	0.0243855	+	0.0140790i
$606$	−1.18939	−	17.8676i	−0.0483157	−	0.725823i
$607$	7.37230	−	4.25640i	0.299233	−	0.172762i	−0.342865	−	0.939385i	$-0.611398\pi$
$607$	7.37230	−	4.25640i	0.299233	−	0.172762i	0.642098	+	0.766622i	$0.278064\pi$
$608$	30.0022	−	3.20492i	1.21675	−	0.129977i
$609$	0.444110	+	6.21417i	0.0179962	+	0.251811i
$610$	−33.2086	−	10.0139i	−1.34458	−	0.405453i
$611$	−3.00479	−	5.20445i	−0.121561	−	0.210549i
$612$	17.5384	+	22.7603i	0.708948	+	0.920031i
$613$	36.3973	+	21.0140i	1.47007	+	0.848747i	0.999436	−	0.0335801i	$-0.0106909\pi$
$613$	36.3973	+	21.0140i	1.47007	+	0.848747i	0.470637	+	0.882327i	$0.344024\pi$
$614$	−7.46348	+	1.75322i	−0.301202	+	0.0707542i
$615$	−20.5619	−	16.8964i	−0.829134	−	0.681328i
$616$	2.92098	−	24.3419i	0.117690	−	0.980764i
$617$			16.0083i			0.644471i	0.946660	+	0.322236i	$0.104434\pi$
$617$			16.0083i			0.644471i	−0.946660	+	0.322236i	$0.895566\pi$
$618$	1.70190	+	0.837132i	0.0684607	+	0.0336744i
$619$	−10.1543	+	17.5878i	−0.408136	+	0.706913i	−0.994681	−	0.103004i	$-0.967155\pi$
$619$	−10.1543	+	17.5878i	−0.408136	+	0.706913i	0.586545	+	0.809917i	$0.300488\pi$
$620$	43.9405	−	21.8495i	1.76469	−	0.877498i
$621$	−26.7214	+	0.824208i	−1.07229	+	0.0330743i
$622$	−9.94672	+	32.9856i	−0.398827	+	1.32260i
$623$	−2.23161	−	9.29609i	−0.0894075	−	0.372440i
$624$	6.06150	+	1.79932i	0.242654	+	0.0720304i
$625$	15.3365	+	26.5636i	0.613460	+	1.06254i
$626$	−16.8259	+	15.8114i	−0.672500	+	0.631950i
$627$	10.6437	+	28.3336i	0.425067	+	1.13154i
$628$	2.12511	−	34.1482i	0.0848013	−	1.36266i
$629$			8.83363i			0.352220i
$630$	−10.9659	+	27.0007i	−0.436893	+	1.07573i
$631$	−28.0435			−1.11639			−0.558197	−	0.829708i	$-0.688507\pi$
$631$	−28.0435			−1.11639			−0.558197	+	0.829708i	$0.688507\pi$
$632$	0.331585	+	0.122931i	0.0131898	+	0.00488992i
$633$	12.7942	−	4.80620i	0.508524	−	0.191029i
$634$	−19.2563	−	20.4919i	−0.764765	−	0.813837i
$635$	−3.59734	+	2.07693i	−0.142756	+	0.0824203i
$636$	−5.57591	+	1.70769i	−0.221099	+	0.0677144i
$637$	−5.35767	−	3.47960i	−0.212279	−	0.137867i
$638$	−1.81851	+	6.03062i	−0.0719957	+	0.238754i
$639$	−1.19299	−	1.36381i	−0.0471941	−	0.0539516i
$640$	15.7978	+	24.7629i	0.624462	+	0.978838i
$641$	−9.80778	−	5.66252i	−0.387384	−	0.223656i	0.293642	−	0.955915i	$-0.405133\pi$
$641$	−9.80778	−	5.66252i	−0.387384	−	0.223656i	−0.681026	+	0.732259i	$0.738466\pi$
$642$	−15.7076	+	31.9338i	−0.619929	+	1.26033i
$643$	−32.8892			−1.29702			−0.648512	−	0.761204i	$-0.724608\pi$
$643$	−32.8892			−1.29702			−0.648512	+	0.761204i	$0.724608\pi$
$644$	20.8743	−	17.4771i	0.822563	−	0.688693i
$645$	−22.8430	+	27.7985i	−0.899441	+	1.09457i
$646$	35.1669	−	8.26093i	1.38362	−	0.325022i
$647$	13.6188	−	23.5884i	0.535409	−	0.927356i	−0.463734	−	0.885974i	$-0.653491\pi$
$647$	13.6188	−	23.5884i	0.535409	−	0.927356i	0.999143	−	0.0413818i	$-0.0131760\pi$
$648$	13.4948	+	21.5845i	0.530127	+	0.847918i
$649$	4.92296	−	2.84227i	0.193243	−	0.111569i
$650$	0.648504	−	2.15059i	0.0254364	−	0.0843531i
$651$	−18.9259	+	38.9552i	−0.741763	+	1.52678i
$652$	−27.6263	+	41.6424i	−1.08193	+	1.63084i
$653$	12.2895	+	21.2860i	0.480926	+	0.832987i	0.999760	−	0.0218870i	$-0.00696741\pi$
$653$	12.2895	+	21.2860i	0.480926	+	0.832987i	−0.518835	+	0.854874i	$0.673634\pi$
$654$	−2.40493	−	36.1281i	−0.0940401	−	1.41272i
$655$	−11.9417	+	20.6837i	−0.466602	+	0.808179i
$656$	14.2872	−	18.8759i	0.557822	−	0.736982i
$657$	4.39140	−	0.867753i	0.171325	−	0.0338543i
$658$	11.0775	+	22.0076i	0.431847	+	0.857945i
$659$	12.1725			0.474172			0.237086	−	0.971489i	$-0.423808\pi$
$659$	12.1725			0.474172			0.237086	+	0.971489i	$0.423808\pi$
$660$	−20.0842	+	21.5587i	−0.781777	+	0.839171i
$661$	−4.00322	+	6.93378i	−0.155707	+	0.269693i	−0.933316	−	0.359055i	$-0.883099\pi$
$661$	−4.00322	+	6.93378i	−0.155707	+	0.269693i	0.777609	+	0.628748i	$0.216432\pi$
$662$	−2.26461	+	2.12806i	−0.0880167	+	0.0827095i
$663$	7.46816	+	1.23783i	0.290039	+	0.0480734i
$664$	0.444840	+	0.536604i	0.0172631	+	0.0208243i
$665$	25.2195	+	26.5768i	0.977970	+	1.03060i
$666$	−0.764045	+	7.78852i	−0.0296062	+	0.301799i
$667$	−6.05752	+	3.49731i	−0.234548	+	0.135416i
$668$	17.7163	−	8.80947i	0.685465	−	0.340849i
$669$	−18.7098	+	7.02843i	−0.723364	+	0.271735i
$670$	−44.8362	+	10.5323i	−1.73217	+	0.406899i
$671$	30.9497			1.19480
$672$	−24.3881	−	8.78739i	−0.940793	−	0.338981i
$673$	18.1260			0.698706			0.349353	−	0.936991i	$-0.386401\pi$
$673$	18.1260			0.698706			0.349353	+	0.936991i	$0.386401\pi$
$674$	−40.4951	+	9.51255i	−1.55981	+	0.366410i
$675$	7.68858	−	4.76094i	0.295934	−	0.183249i
$676$	−21.7891	+	10.8347i	−0.838041	+	0.416717i
$677$	−39.1458	+	22.6008i	−1.50449	+	0.868620i	−0.504508	+	0.863407i	$0.668326\pi$
$677$	−39.1458	+	22.6008i	−1.50449	+	0.868620i	−0.999986	+	0.00521277i	$0.998341\pi$
$678$	33.1158	−	22.1761i	1.27180	−	0.851668i
$679$	−3.83499	+	12.9458i	−0.147173	+	0.496815i
$680$	22.4435	+	27.0733i	0.860670	+	1.03821i
$681$	−4.40922	+	26.6020i	−0.168962	+	1.01939i
$682$	−31.9097	+	29.9856i	−1.22188	+	1.14821i
$683$	−6.38047	+	11.0513i	−0.244142	+	0.422866i	−0.961890	−	0.273437i	$-0.911840\pi$
$683$	−6.38047	+	11.0513i	−0.244142	+	0.422866i	0.717748	+	0.696303i	$0.245173\pi$
$684$	31.7208	−	4.24190i	1.21287	−	0.162193i
$685$	7.31285			0.279410
$686$	21.1129	+	15.4998i	0.806096	+	0.591785i
$687$	3.91996	−	4.77036i	0.149556	−	0.182000i
$688$	−25.5192	−	19.3155i	−0.972912	−	0.736397i
$689$	−0.768176	+	1.33052i	−0.0292652	+	0.0506888i
$690$	−32.6469	+	2.17320i	−1.24285	+	0.0827322i
$691$	7.47003	+	12.9385i	0.284173	+	0.492203i	0.972408	−	0.233285i	$-0.0749475\pi$
$691$	7.47003	+	12.9385i	0.284173	+	0.492203i	−0.688235	+	0.725488i	$0.741614\pi$
$692$	17.0764	−	25.7401i	0.649149	−	0.978490i
$693$	2.41250	−	25.8916i	0.0916433	−	0.983539i
$694$	5.25077	−	17.4128i	0.199316	−	0.660980i
$695$	6.30686	−	3.64127i	0.239233	−	0.138121i
$696$	5.78220	+	3.30516i	0.219174	+	0.125282i
$697$	14.1713	−	24.5454i	0.536776	−	0.929724i
$698$	41.3808	−	9.72062i	1.56629	−	0.367931i
$699$	10.2087	+	8.38887i	0.386130	+	0.317296i
$700$	−3.15912	+	8.65042i	−0.119404	+	0.326955i
$701$	−14.3141			−0.540636			−0.270318	−	0.962771i	$-0.587129\pi$
$701$	−14.3141			−0.540636			−0.270318	+	0.962771i	$0.587129\pi$
$702$	6.47754	+	1.73733i	0.244479	+	0.0655711i
$703$	8.52061	+	4.91938i	0.321361	+	0.185538i
$704$	−19.8752	−	17.0852i	−0.749074	−	0.643922i
$705$	4.84186	−	29.2122i	0.182355	−	1.10020i
$706$	9.88634	−	32.7854i	0.372077	−	1.23389i
$707$	13.3139	+	14.0304i	0.500719	+	0.527668i
$708$	−1.76014	−	5.74715i	−0.0661499	−	0.215991i
$709$	−5.67964	+	3.27914i	−0.213303	+	0.123151i	−0.602846	−	0.797858i	$-0.705967\pi$
$709$	−5.67964	+	3.27914i	−0.213303	+	0.123151i	0.389542	+	0.921009i	$0.372633\pi$
$710$	−1.51861	−	1.61605i	−0.0569924	−	0.0606495i
$711$	0.355033	+	0.121017i	0.0133148	+	0.00453848i
$712$	−9.58291	−	3.55273i	−0.359135	−	0.133144i
$713$	−48.6246			−1.82100
$714$	−30.2775	−	6.81929i	−1.13311	−	0.255205i
$715$			7.76255i			0.290303i
$716$	1.50923	−	24.2516i	0.0564025	−	0.906324i
$717$	21.5236	−	8.08543i	0.803813	−	0.301956i
$718$	3.77099	−	3.54361i	0.140732	−	0.132246i
$719$	−19.5665	−	33.8902i	−0.729708	−	1.26389i	−0.957007	−	0.290066i	$-0.906323\pi$
$719$	−19.5665	−	33.8902i	−0.729708	−	1.26389i	0.227299	−	0.973825i	$-0.427010\pi$
$720$	17.4466	+	25.8115i	0.650196	+	0.961936i
$721$	−1.99202	+	0.478202i	−0.0741866	+	0.0178092i
$722$	3.85838	−	12.7953i	0.143594	−	0.476192i
$723$	3.24677	−	19.5886i	0.120749	−	0.728508i
$724$	−2.54156	+	1.26379i	−0.0944563	+	0.0469686i
$725$	1.18303	−	2.04906i	0.0439365	−	0.0761002i
$726$	−0.288416	+	0.586354i	−0.0107041	+	0.0217617i
$727$		−	34.4829i		−	1.27890i	−0.768833	−	0.639450i	$-0.779162\pi$
$727$		−	34.4829i		−	1.27890i	0.768833	−	0.639450i	$-0.220838\pi$
$728$	−6.27927	+	2.68577i	−0.232725	+	0.0995411i
$729$	14.9154	+	22.5062i	0.552423	+	0.833564i
$730$	5.33327	−	1.25282i	0.197393	−	0.0463689i
$731$	−33.1841	−	19.1588i	−1.22736	−	0.708615i
$732$	7.34606	−	31.8900i	0.271518	−	1.17869i
$733$	9.89201	+	17.1335i	0.365370	+	0.632839i	0.988835	−	0.149012i	$-0.0476093\pi$
$733$	9.89201	+	17.1335i	0.365370	+	0.632839i	−0.623466	+	0.781851i	$0.714276\pi$
$734$	23.7567	+	7.16376i	0.876876	+	0.264419i
$735$	−9.51092	−	30.0063i	−0.350815	−	1.10680i
$736$	−3.09143	−	28.9398i	−0.113952	−	1.06673i
$737$	35.5902	−	20.5480i	1.31098	−	0.756896i
$738$	14.6177	−	20.4157i	0.538085	−	0.751513i
$739$	−6.03595	−	3.48486i	−0.222036	−	0.128193i	0.384857	−	0.922976i	$-0.374251\pi$
$739$	−6.03595	−	3.48486i	−0.222036	−	0.128193i	−0.606893	+	0.794784i	$0.707584\pi$
$740$	−0.594903	+	9.55942i	−0.0218691	+	0.351411i
$741$	5.35292	−	6.51418i	0.196645	−	0.239305i
$742$	3.45649	−	5.26569i	0.126892	−	0.193310i
$743$			45.3956i			1.66540i	0.553723	+	0.832701i	$0.313207\pi$
$743$			45.3956i			1.66540i	−0.553723	+	0.832701i	$0.686793\pi$
$744$	23.3227	+	39.9963i	0.855051	+	1.46634i
$745$	−38.9883	−	22.5099i	−1.42842	−	0.824700i
$746$	3.87575	−	3.64205i	0.141901	−	0.133345i
$747$	0.486749	+	0.556443i	0.0178092	+	0.0203592i
$748$	−26.1478	−	17.3470i	−0.956060	−	0.634268i
$749$	−8.97277	−	37.3774i	−0.327858	−	1.36574i
$750$	−17.2240	+	11.5341i	−0.628933	+	0.421167i
$751$	−10.3669	−	17.9560i	−0.378293	−	0.655223i	0.612521	−	0.790455i	$-0.290156\pi$
$751$	−10.3669	−	17.9560i	−0.378293	−	0.655223i	−0.990814	+	0.135231i	$0.956822\pi$
$752$	26.1362	+	3.26567i	0.953090	+	0.119087i
$753$	2.34949	−	0.882594i	0.0856200	−	0.0321635i
$754$	1.70816	−	0.401258i	0.0622075	−	0.0146130i
$755$			33.3122i			1.21236i
$756$	−26.1056	−	8.63128i	−0.949451	−	0.313917i
$757$			30.3555i			1.10329i	0.834079	+	0.551645i	$0.186000\pi$
$757$			30.3555i			1.10329i	−0.834079	+	0.551645i	$0.814000\pi$
$758$	−3.97137	−	16.9062i	−0.144247	−	0.614059i
$759$	27.3303	−	10.2668i	0.992029	−	0.372660i
$760$	38.6126	−	6.57134i	1.40063	−	0.238367i
$761$	6.12394	+	10.6070i	0.221993	+	0.384503i	0.955413	−	0.295273i	$-0.0954106\pi$
$761$	6.12394	+	10.6070i	0.221993	+	0.384503i	−0.733420	+	0.679775i	$0.762077\pi$
$762$	−2.18064	−	3.25638i	−0.0789964	−	0.117966i
$763$	26.9204	+	28.3693i	0.974585	+	1.02704i
$764$	4.62693	−	6.97436i	0.167396	−	0.252324i
$765$	24.5580	+	28.0743i	0.887896	+	1.01503i
$766$	−7.31205	−	7.78124i	−0.264195	−	0.281148i
$767$	−1.37138	−	0.791767i	−0.0495177	−	0.0285890i
$768$	−22.3217	+	16.4238i	−0.805466	+	0.592642i
$769$			19.0816i			0.688100i	0.938951	+	0.344050i	$0.111799\pi$
$769$			19.0816i			0.688100i	−0.938951	+	0.344050i	$0.888201\pi$
$770$	1.82179	−	31.7730i	0.0656526	−	1.14502i
$771$	13.2709	−	16.1499i	0.477940	−	0.581624i
$772$	−3.27717	+	52.6603i	−0.117948	+	1.89529i
$773$	9.07434	+	5.23907i	0.326381	+	0.188436i	0.654233	−	0.756293i	$-0.272991\pi$
$773$	9.07434	+	5.23907i	0.326381	+	0.188436i	−0.327852	+	0.944729i	$0.606325\pi$
$774$	−27.6009	−	19.7623i	−0.992095	−	0.710342i
$775$	14.2445	−	8.22405i	0.511677	−	0.295417i
$776$	9.21200	+	11.1123i	0.330691	+	0.398908i
$777$	−4.73756	−	7.00056i	−0.169959	−	0.251144i
$778$	14.9393	−	49.5423i	0.535601	−	1.77618i
$779$	−15.7838	−	27.3383i	−0.565512	−	0.979496i
$780$	7.99839	+	1.84248i	0.286388	+	0.0659713i
$781$	1.71366	+	0.989382i	0.0613196	+	0.0354029i
$782$	−7.96841	−	33.9216i	−0.284950	−	1.21303i
$783$	6.22375	+	3.34180i	0.222419	+	0.119426i
$784$	26.3321	−	9.51948i	0.940432	−	0.339981i
$785$		−	44.4139i		−	1.58520i
$786$	−20.2199	−	9.94577i	−0.721221	−	0.354754i
$787$	6.93206	−	12.0067i	0.247101	−	0.427992i	−0.715619	−	0.698491i	$-0.753855\pi$
$787$	6.93206	−	12.0067i	0.247101	−	0.427992i	0.962720	+	0.270499i	$0.0871887\pi$
$788$	−22.7270	+	11.3010i	−0.809615	+	0.402583i
$789$	7.10727	−	42.8800i	0.253025	−	1.52657i
$790$	0.439516	+	0.132535i	0.0156373	+	0.00471537i
$791$	−12.2272	+	41.2755i	−0.434750	+	1.46759i
$792$	−21.5539	−	17.5563i	−0.765885	−	0.623834i
$793$	−4.31081	−	7.46654i	−0.153081	−	0.265145i
$794$	−7.42699	−	7.90355i	−0.263574	−	0.280487i
$795$	−7.08649	+	2.66207i	−0.251332	+	0.0944139i
$796$	2.16570	+	0.134776i	0.0767613	+	0.00477702i
$797$		−	29.4639i		−	1.04366i	−0.853048	−	0.521832i	$-0.825249\pi$
$797$		−	29.4639i		−	1.04366i	0.853048	−	0.521832i	$-0.174751\pi$
$798$	−23.4390	+	25.4070i	−0.829730	+	0.899399i
$799$	31.5346			1.11561
$800$	5.80032	+	7.95499i	0.205072	+	0.281251i
$801$	−10.2606	−	3.49741i	−0.362539	−	0.123575i
$802$	24.4028	−	22.9314i	0.861692	−	0.809734i
$803$	−4.23346	+	2.44419i	−0.149396	+	0.0862536i
$804$	−12.7248	−	41.5487i	−0.448769	−	1.46531i
$805$	25.6357	−	24.3265i	0.903540	−	0.857395i
$806$	11.6785	+	3.52160i	0.411356	+	0.124043i
$807$	−2.16440	+	13.0584i	−0.0761904	+	0.459676i
$808$	20.3843	−	3.46914i	0.717118	−	0.122044i
$809$	42.7554	+	24.6848i	1.50320	+	0.867873i	0.999993	+	0.00370713i	$0.00118002\pi$
$809$	42.7554	+	24.6848i	1.50320	+	0.867873i	0.503207	+	0.864166i	$0.332153\pi$
$810$	19.2243	+	26.8769i	0.675473	+	0.944358i
$811$	−0.180195			−0.00632751			−0.00316376	−	0.999995i	$-0.501007\pi$
$811$	−0.180195			−0.00632751			−0.00316376	+	0.999995i	$0.501007\pi$
$812$	−7.08587	+	1.24151i	−0.248665	+	0.0435684i
$813$	14.3373	+	11.7815i	0.502832	+	0.413194i
$814$	−1.95439	−	8.31985i	−0.0685012	−	0.291610i
$815$	−32.4353	+	56.1796i	−1.13616	+	1.96788i
$816$	−24.0803	+	22.8249i	−0.842980	+	0.799030i
$817$	−36.9598	+	21.3388i	−1.29306	+	0.746549i
$818$	−21.2098	−	6.39574i	−0.741582	−	0.223622i
$819$	−6.58230	+	3.02428i	−0.230004	+	0.105677i
$820$	16.9887	−	25.6077i	0.593270	−	0.894261i
$821$	−11.4858	−	19.8940i	−0.400857	−	0.694304i	0.592973	−	0.805223i	$-0.297954\pi$
$821$	−11.4858	−	19.8940i	−0.400857	−	0.694304i	−0.993830	+	0.110918i	$0.964621\pi$
$822$	0.458266	+	6.88430i	0.0159839	+	0.240118i
$823$	−22.0638	+	38.2157i	−0.769097	+	1.33212i	0.168956	+	0.985624i	$0.445960\pi$
$823$	−22.0638	+	38.2157i	−0.769097	+	1.33212i	−0.938053	+	0.346492i	$0.887373\pi$
$824$	−0.761300	+	2.05348i	−0.0265211	+	0.0715364i
$825$	−6.26992	+	7.63011i	−0.218290	+	0.265646i
$826$	5.42740	+	3.56264i	0.188843	+	0.123960i
$827$	19.7749			0.687641			0.343821	−	0.939035i	$-0.388279\pi$
$827$	19.7749			0.687641			0.343821	+	0.939035i	$0.388279\pi$
$828$	−4.09169	−	30.5975i	−0.142196	−	1.06334i
$829$	−13.8197	+	23.9365i	−0.479979	+	0.831349i	−0.999736	−	0.0229656i	$-0.992689\pi$
$829$	−13.8197	+	23.9365i	−0.479979	+	0.831349i	0.519757	+	0.854314i	$0.326023\pi$
$830$	0.619602	+	0.659360i	0.0215067	+	0.0228867i
$831$	1.01024	−	6.09504i	0.0350449	−	0.211435i
$832$	−1.35346	+	7.17453i	−0.0469227	+	0.248732i
$833$	29.8695	−	15.2179i	1.03492	−	0.527267i
$834$	3.82310	+	5.70908i	0.132383	+	0.197689i
$835$	22.2431	−	12.8420i	0.769753	−	0.444417i
$836$	−31.2938	+	15.5609i	−1.08232	+	0.538185i
$837$	25.8536	+	41.7517i	0.893630	+	1.44315i
$838$	11.4660	+	48.8109i	0.396086	+	1.68614i
$839$	28.3920			0.980200			0.490100	−	0.871666i	$-0.336960\pi$
$839$	28.3920			0.980200			0.490100	+	0.871666i	$0.336960\pi$
$840$	−32.3059	−	9.41862i	−1.11466	−	0.324973i
$841$	−27.1518			−0.936267
$842$	−2.58873	−	11.0202i	−0.0892134	−	0.379783i
$843$	−6.91270	+	2.59678i	−0.238086	+	0.0894380i
$844$	7.02661	+	14.1309i	0.241866	+	0.486405i
$845$	−27.3565	+	15.7943i	−0.941091	+	0.543339i
$846$	27.8037	+	2.72752i	0.955912	+	0.0937739i
$847$	−0.164754	−	0.686307i	−0.00566101	−	0.0235818i
$848$	−2.61785	−	6.20399i	−0.0898973	−	0.213046i
$849$	−38.6866	−	6.41223i	−1.32772	−	0.220067i
$850$	8.07161	+	8.58954i	0.276854	+	0.294619i
$851$	4.74518	−	8.21889i	0.162663	−	0.281740i
$852$	1.42619	−	1.53089i	0.0488603	−	0.0524474i
$853$	−30.7041			−1.05129			−0.525645	−	0.850704i	$-0.676176\pi$
$853$	−30.7041			−1.05129			−0.525645	+	0.850704i	$0.676176\pi$
$854$	15.8923	+	31.5731i	0.543824	+	1.08041i
$855$	40.7556	−	8.05342i	1.39381	−	0.275421i
$856$	−38.5306	−	14.2847i	−1.31695	−	0.488241i
$857$	−11.5192	+	19.9518i	−0.393487	+	0.681539i	−0.992907	−	0.118895i	$-0.962065\pi$
$857$	−11.5192	+	19.9518i	−0.393487	+	0.681539i	0.599420	+	0.800435i	$0.295398\pi$
$858$	−7.30765	+	0.486447i	−0.249479	+	0.0166070i
$859$	26.3268	+	45.5994i	0.898260	+	1.55583i	0.829717	+	0.558184i	$0.188502\pi$
$859$	26.3268	+	45.5994i	0.898260	+	1.55583i	0.0685424	+	0.997648i	$0.478165\pi$
$860$	−34.6202	−	22.9677i	−1.18054	−	0.783193i
$861$	1.93334	+	27.0522i	0.0658882	+	0.921936i
$862$	40.4283	+	12.1910i	1.37699	+	0.415228i
$863$	−22.4451	+	12.9587i	−0.764040	+	0.441119i	−0.830744	−	0.556654i	$-0.812085\pi$
$863$	−22.4451	+	12.9587i	−0.764040	+	0.441119i	0.0667045	+	0.997773i	$0.478752\pi$
$864$	−23.2056	+	18.0417i	−0.789469	+	0.613790i
$865$	20.0490	−	34.7258i	0.681685	−	1.18071i
$866$	0.552203	+	2.35074i	0.0187646	+	0.0798813i
$867$	−6.52539	+	7.94100i	−0.221614	+	0.269691i
$868$	−46.9748	−	17.1551i	−1.59443	−	0.582283i
$869$	−0.409620			−0.0138954
$870$	7.75794	+	3.81597i	0.263019	+	0.129374i
$871$	−9.91432	−	5.72403i	−0.335934	−	0.193951i
$872$	41.2168	−	7.01454i	1.39578	−	0.237542i
$873$	10.0799	+	11.5232i	0.341152	+	0.390000i
$874$	−37.1571	−	11.2046i	−1.25686	−	0.379002i
$875$	6.35957	−	21.4681i	0.214993	−	0.725753i
$876$	1.51362	+	4.94222i	0.0511403	+	0.166982i
$877$	−39.8660	+	23.0166i	−1.34618	+	0.777216i	−0.987706	−	0.156324i	$-0.950036\pi$
$877$	−39.8660	+	23.0166i	−1.34618	+	0.777216i	−0.358472	+	0.933540i	$0.616702\pi$
$878$	−17.0204	+	15.9941i	−0.574411	+	0.539775i
$879$	9.66459	−	3.63054i	0.325979	−	0.122455i
$880$	−27.1280	−	20.5332i	−0.914483	−	0.692173i
$881$	25.6170			0.863060			0.431530	−	0.902099i	$-0.357974\pi$
$881$	25.6170			0.863060			0.431530	+	0.902099i	$0.357974\pi$
$882$	27.6519	−	10.8339i	0.931087	−	0.364797i
$883$		−	54.2412i		−	1.82536i	−0.408674	−	0.912680i	$-0.634009\pi$
$883$		−	54.2412i		−	1.82536i	0.408674	−	0.912680i	$-0.365991\pi$
$884$	−0.542930	+	8.72426i	−0.0182607	+	0.293429i
$885$	−2.74382	−	7.30412i	−0.0922326	−	0.245525i
$886$	−13.7958	−	14.6810i	−0.463479	−	0.493219i
$887$	−17.2509	−	29.8794i	−0.579228	−	1.00325i	−0.995568	−	0.0940438i	$-0.970021\pi$
$887$	−17.2509	−	29.8794i	−0.579228	−	1.00325i	0.416340	−	0.909209i	$-0.363313\pi$
$888$	−9.03650	+	0.0390078i	−0.303245	+	0.00130902i
$889$	4.05875	+	1.20234i	0.136126	+	0.0403252i
$890$	−12.7021	−	3.83029i	−0.425776	−	0.128391i
$891$	−23.3471	−	18.0085i	−0.782156	−	0.603308i
$892$	−10.2755	−	20.6646i	−0.344049	−	0.691900i
$893$	17.5614	−	30.4172i	0.587669	−	1.01787i
$894$	18.7476	−	38.1141i	0.627012	−	1.27473i
$895$		−	31.5422i		−	1.05434i
$896$	7.22364	−	29.0486i	0.241325	−	0.970444i
$897$	−6.28352	−	5.16338i	−0.209800	−	0.172400i
$898$	−0.705055	−	3.00143i	−0.0235280	−	0.100159i
$899$	11.1271	+	6.42424i	0.371110	+	0.214260i
$900$	6.37372	+	8.27145i	0.212457	+	0.275715i
$901$	−4.03092	−	6.98176i	−0.134289	−	0.232596i
$902$	−7.91654	+	26.2531i	−0.263592	+	0.874133i
$903$	36.5731	−	2.61377i	1.21708	−	0.0869810i
$904$	29.3709	+	35.4297i	0.976862	+	1.17837i
$905$	−3.19096	+	1.84230i	−0.106071	+	0.0612402i
$906$	−31.3600	+	2.08754i	−1.04187	+	0.0693537i
$907$	−11.9718	−	6.91190i	−0.397516	−	0.229506i	0.287896	−	0.957662i	$-0.407044\pi$
$907$	−11.9718	−	6.91190i	−0.397516	−	0.229506i	−0.685412	+	0.728156i	$0.740378\pi$
$908$	−31.0763	−	1.93394i	−1.03130	−	0.0641802i
$909$	21.5157	−	4.25156i	0.713630	−	0.141015i
$910$	−7.91891	+	3.98598i	−0.262509	+	0.132134i
$911$			22.6663i			0.750969i	0.926829	+	0.375484i	$0.122524\pi$
$911$			22.6663i			0.750969i	−0.926829	+	0.375484i	$0.877476\pi$
$912$	8.60593	+	35.9380i	0.284971	+	1.19003i
$913$	−0.699183	−	0.403674i	−0.0231396	−	0.0133596i
$914$	31.1559	+	33.1550i	1.03054	+	1.09667i
$915$	6.94636	−	41.9092i	0.229640	−	1.38548i
$916$	5.94100	+	3.94137i	0.196296	+	0.130227i
$917$	23.6667	−	5.68140i	0.781543	−	0.187616i
$918$	−24.8901	+	24.8781i	−0.821497	+	0.821101i
$919$	−6.58509	−	11.4057i	−0.217222	−	0.376240i	0.736736	−	0.676181i	$-0.236366\pi$
$919$	−6.58509	−	11.4057i	−0.217222	−	0.376240i	−0.953958	+	0.299941i	$0.903033\pi$
$920$	−6.33864	−	37.2453i	−0.208979	−	1.22794i
$921$	−3.30198	−	8.78993i	−0.108804	−	0.289638i
$922$	4.50366	+	19.1722i	0.148320	+	0.631401i
$923$		−	0.551221i		−	0.0181437i
$924$	30.0252	−	0.276056i	0.987758	−	0.00908159i
$925$			3.21028i			0.105553i
$926$	−21.4548	+	5.03987i	−0.705048	+	0.165620i
$927$	−0.749446	+	2.19869i	−0.0246150	+	0.0722144i
$928$	−3.11607	+	7.03093i	−0.102290	+	0.230802i
$929$	−27.9226	−	48.3634i	−0.916111	−	1.58675i	−0.805267	−	0.592912i	$-0.797978\pi$
$929$	−27.9226	−	48.3634i	−0.916111	−	1.58675i	−0.110844	−	0.993838i	$-0.535355\pi$
$930$	33.4418	+	49.9390i	1.09660	+	1.63756i
$931$	1.95547	−	37.2858i	0.0640881	−	1.22199i
$932$	−8.43468	+	12.7140i	−0.276287	+	0.416460i
$933$	−41.6279	−	6.89973i	−1.36283	−	0.225887i
$934$	19.7817	−	18.5889i	0.647277	−	0.608248i
$935$	−35.2760	−	20.3666i	−1.15365	−	0.666058i
$936$	−1.23328	+	7.64513i	−0.0403110	+	0.249889i
$937$			32.0973i			1.04857i	0.851541	+	0.524287i	$0.175668\pi$
$937$			32.0973i			1.04857i	−0.851541	+	0.524287i	$0.824332\pi$
$938$	39.2371	+	25.7559i	1.28114	+	0.840960i
$939$	−21.8482	−	17.9534i	−0.712989	−	0.585887i
$940$	34.1255	+	2.12371i	1.11305	+	0.0692677i
$941$	24.3540	+	14.0608i	0.793919	+	0.458370i	0.841341	−	0.540505i	$-0.181767\pi$
$941$	24.3540	+	14.0608i	0.793919	+	0.458370i	−0.0474212	+	0.998875i	$0.515100\pi$
$942$	41.8112	−	2.78323i	1.36228	−	0.0906827i
$943$	−26.3702	+	15.2249i	−0.858733	+	0.495790i
$944$	6.39452	−	2.69825i	0.208124	−	0.0878204i
$945$	−34.5185	−	9.07789i	−1.12289	−	0.295304i
$946$	35.4928	+	10.7027i	1.15397	+	0.347976i
$947$	−10.9973	−	19.0479i	−0.357365	−	0.618974i	0.630155	−	0.776469i	$-0.282991\pi$
$947$	−10.9973	−	19.0479i	−0.357365	−	0.618974i	−0.987520	+	0.157495i	$0.949658\pi$
$948$	−0.0972252	+	0.422065i	−0.00315773	+	0.0137080i
$949$	1.17931	+	0.680874i	0.0382820	+	0.0221021i
$950$	12.7802	−	3.00215i	0.414644	−	0.0974026i
$951$	21.8650	−	26.6084i	0.709021	−	0.862836i
$952$	4.26976	−	35.5820i	0.138384	−	1.15322i
$953$		−	48.0977i		−	1.55804i	−0.627001	−	0.779018i	$-0.715718\pi$
$953$		−	48.0977i		−	1.55804i	0.627001	−	0.779018i	$-0.284282\pi$
$954$	−2.95015	−	6.50439i	−0.0955146	−	0.210587i
$955$	5.43234	−	9.40909i	0.175786	−	0.304471i
$956$	11.8208	+	23.7723i	0.382312	+	0.768850i
$957$	−7.61063	−	1.26145i	−0.246017	−	0.0407768i
$958$	−2.46682	+	8.18055i	−0.0796993	+	0.264301i
$959$	−5.12976	−	5.40584i	−0.165649	−	0.174564i
$960$	−27.5959	+	23.0785i	−0.890655	+	0.744855i
$961$	29.1595	+	50.5057i	0.940628	+	1.62921i
$962$	−1.73493	+	1.63031i	−0.0559363	+	0.0525634i
$963$	−41.2553	−	14.0623i	−1.32943	−	0.453151i
$964$	22.8833	+	1.42408i	0.737022	+	0.0458665i
$965$			68.4912i			2.20481i
$966$	24.5074	+	22.6090i	0.788512	+	0.727432i
$967$	11.0279			0.354635			0.177317	−	0.984154i	$-0.443258\pi$
$967$	11.0279			0.354635			0.177317	+	0.984154i	$0.443258\pi$
$968$	−0.707482	−	0.262289i	−0.0227393	−	0.00843030i
$969$	15.5584	+	41.4169i	0.499809	+	1.33050i
$970$	12.8311	+	13.6544i	0.411981	+	0.438417i
$971$	−2.36459	+	1.36519i	−0.0758832	+	0.0438112i	−0.537461	−	0.843288i	$-0.680617\pi$
$971$	−2.36459	+	1.36519i	−0.0758832	+	0.0438112i	0.461578	+	0.887099i	$0.347283\pi$
$972$	−24.0972	+	19.7820i	−0.772917	+	0.634507i
$973$	−7.11580	−	2.10794i	−0.228122	−	0.0675775i
$974$	−9.09556	+	30.1630i	−0.291441	+	0.966485i
$975$	2.71404	+	0.449847i	0.0869189	+	0.0144066i
$976$	37.4962	+	4.68509i	1.20023	+	0.149966i
$977$	−21.7078	−	12.5330i	−0.694494	−	0.400967i	0.110799	−	0.993843i	$-0.464659\pi$
$977$	−21.7078	−	12.5330i	−0.694494	−	0.400967i	−0.805294	+	0.592876i	$0.797992\pi$
$978$	−54.9199	−	27.0140i	−1.75615	−	0.863812i
$979$	11.8381			0.378348
$980$	33.3485	−	14.4566i	1.06528	−	0.461799i
$981$	43.5044	−	8.59658i	1.38899	−	0.274468i
$982$	6.38758	−	1.50048i	0.203836	−	0.0478824i
$983$	12.9850	−	22.4907i	0.414157	−	0.717342i	−0.581182	−	0.813773i	$-0.697410\pi$
$983$	12.9850	−	22.4907i	0.414157	−	0.717342i	0.995340	+	0.0964318i	$0.0307430\pi$
$984$	25.1717	+	14.3884i	0.802444	+	0.458684i
$985$	−28.5340	+	16.4741i	−0.909169	+	0.524909i
$986$	−2.65823	+	8.81530i	−0.0846552	+	0.280736i
$987$	−24.9908	+	16.9123i	−0.795467	+	0.538325i
$988$	8.11276	+	5.38216i	0.258101	+	0.171229i
$989$	20.5832	+	35.6511i	0.654507	+	1.13364i
$990$	−29.3409	−	21.0081i	−0.932515	−	0.667682i
$991$	−9.31944	+	16.1417i	−0.296042	+	0.512759i	−0.975227	−	0.221208i	$-0.929000\pi$
$991$	−9.31944	+	16.1417i	−0.296042	+	0.512759i	0.679185	+	0.733967i	$0.262333\pi$
$992$	−43.1983	+	31.4977i	−1.37155	+	1.00005i
$993$	−2.94056	−	2.41636i	−0.0933159	−	0.0766808i
$994$	−0.129366	+	2.25621i	−0.00410323	+	0.0715627i
$995$	2.81676			0.0892974
$996$	−0.581892	+	0.624612i	−0.0184380	+	0.0197916i
$997$	−12.6672	+	21.9402i	−0.401173	+	0.694853i	−0.993868	−	0.110575i	$-0.964731\pi$
$997$	−12.6672	+	21.9402i	−0.401173	+	0.694853i	0.592694	+	0.805427i	$0.298064\pi$
$998$	−20.1042	+	18.8920i	−0.636389	+	0.598016i
$999$	−9.58019	+	0.295496i	−0.303104	+	0.00934908i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.ba.c.101.2	yes	48
3.2	odd	2	inner	168.2.ba.c.101.23	yes	48
4.3	odd	2		672.2.bi.c.17.16		48
7.5	odd	6	inner	168.2.ba.c.5.17	yes	48
8.3	odd	2		672.2.bi.c.17.9		48
8.5	even	2	inner	168.2.ba.c.101.8	yes	48
12.11	even	2		672.2.bi.c.17.1		48
21.5	even	6	inner	168.2.ba.c.5.8	yes	48
24.5	odd	2	inner	168.2.ba.c.101.17	yes	48
24.11	even	2		672.2.bi.c.17.24		48
28.19	even	6		672.2.bi.c.593.24		48
56.5	odd	6	inner	168.2.ba.c.5.23	yes	48
56.19	even	6		672.2.bi.c.593.1		48
84.47	odd	6		672.2.bi.c.593.9		48
168.5	even	6	inner	168.2.ba.c.5.2	✓	48
168.131	odd	6		672.2.bi.c.593.16		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.2	✓	48	168.5	even	6	inner
168.2.ba.c.5.8	yes	48	21.5	even	6	inner
168.2.ba.c.5.17	yes	48	7.5	odd	6	inner
168.2.ba.c.5.23	yes	48	56.5	odd	6	inner
168.2.ba.c.101.2	yes	48	1.1	even	1	trivial
168.2.ba.c.101.8	yes	48	8.5	even	2	inner
168.2.ba.c.101.17	yes	48	24.5	odd	2	inner
168.2.ba.c.101.23	yes	48	3.2	odd	2	inner
672.2.bi.c.17.1		48	12.11	even	2
672.2.bi.c.17.9		48	8.3	odd	2
672.2.bi.c.17.16		48	4.3	odd	2
672.2.bi.c.17.24		48	24.11	even	2
672.2.bi.c.593.1		48	56.19	even	6
672.2.bi.c.593.9		48	84.47	odd	6
672.2.bi.c.593.16		48	168.131	odd	6
672.2.bi.c.593.24		48	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.37674 + 0.323405i) q^{2} +(-0.609093 - 1.62142i) q^{3} +(1.79082 - 0.890488i) q^{4} +(2.24840 - 1.29811i) q^{5} +(1.36294 + 2.03529i) q^{6} +(-2.53678 - 0.751482i) q^{7} +(-2.17750 + 1.80513i) q^{8} +(-2.25801 + 1.97519i) q^{9} +O(q^{10})\)	\(q+(-1.37674 + 0.323405i) q^{2} +(-0.609093 - 1.62142i) q^{3} +(1.79082 - 0.890488i) q^{4} +(2.24840 - 1.29811i) q^{5} +(1.36294 + 2.03529i) q^{6} +(-2.53678 - 0.751482i) q^{7} +(-2.17750 + 1.80513i) q^{8} +(-2.25801 + 1.97519i) q^{9} +(-2.67564 + 2.51430i) q^{10} +(1.63808 - 2.83724i) q^{11} +(-2.53463 - 2.36128i) q^{12} -0.912635 q^{13} +(3.73552 + 0.214186i) q^{14} +(-3.47427 - 2.85492i) q^{15} +(2.41406 - 3.18940i) q^{16} +(2.39448 - 4.14736i) q^{17} +(2.46990 - 3.44958i) q^{18} +(-2.66693 - 4.61926i) q^{19} +(2.87052 - 4.32685i) q^{20} +(0.326671 + 4.57092i) q^{21} +(-1.33763 + 4.43590i) q^{22} +(-4.45569 + 2.57249i) q^{23} +(4.25317 + 2.43115i) q^{24} +(0.870190 - 1.50721i) q^{25} +(1.25646 - 0.295151i) q^{26} +(4.57796 + 2.45811i) q^{27} +(-5.21211 + 0.913209i) q^{28} +1.35950 q^{29} +(5.70646 + 2.80689i) q^{30} +(8.18469 + 4.72543i) q^{31} +(-2.29206 + 5.17170i) q^{32} +(-5.59810 - 0.927874i) q^{33} +(-1.95529 + 6.48421i) q^{34} +(-6.67920 + 1.60340i) q^{35} +(-2.28480 + 5.54794i) q^{36} +(-1.59746 + 0.922292i) q^{37} +(5.16556 + 5.49701i) q^{38} +(0.555880 + 1.47977i) q^{39} +(-2.55263 + 6.88528i) q^{40} +5.91833 q^{41} +(-1.92800 - 6.18731i) q^{42} -8.00125i q^{43} +(0.406978 - 6.53967i) q^{44} +(-2.51288 + 7.37217i) q^{45} +(5.30236 - 4.98264i) q^{46} +(3.29243 + 5.70266i) q^{47} +(-6.64176 - 1.97156i) q^{48} +(5.87055 + 3.81269i) q^{49} +(-0.710584 + 2.35646i) q^{50} +(-8.18307 - 1.35633i) q^{51} +(-1.63436 + 0.812691i) q^{52} +(0.841712 - 1.45789i) q^{53} +(-7.09762 - 1.90364i) q^{54} -8.50565i q^{55} +(6.88037 - 2.94287i) q^{56} +(-5.86535 + 7.13777i) q^{57} +(-1.87168 + 0.439670i) q^{58} +(1.50266 + 0.867561i) q^{59} +(-8.76406 - 2.01886i) q^{60} +(4.72347 + 8.18130i) q^{61} +(-12.7964 - 3.85872i) q^{62} +(7.21241 - 3.31379i) q^{63} +(1.48302 - 7.86134i) q^{64} +(-2.05197 + 1.18470i) q^{65} +(8.00720 - 0.533013i) q^{66} +(10.8634 + 6.27198i) q^{67} +(0.594903 - 9.55942i) q^{68} +(6.88502 + 5.65766i) q^{69} +(8.67697 - 4.36755i) q^{70} +0.603989i q^{71} +(1.35134 - 8.37699i) q^{72} +(-1.29220 - 0.746053i) q^{73} +(1.90101 - 1.78638i) q^{74} +(-2.97385 - 0.492910i) q^{75} +(-8.88938 - 5.89738i) q^{76} +(-6.28759 + 5.96647i) q^{77} +(-1.24387 - 1.85748i) q^{78} +(-0.0625152 - 0.108280i) q^{79} +(1.28756 - 10.3048i) q^{80} +(1.19722 - 8.92001i) q^{81} +(-8.14799 + 1.91402i) q^{82} -0.246431i q^{83} +(4.65536 + 7.89479i) q^{84} -12.4332i q^{85} +(2.58764 + 11.0156i) q^{86} +(-0.828064 - 2.20433i) q^{87} +(1.55466 + 9.13504i) q^{88} +(1.80671 + 3.12931i) q^{89} +(1.07538 - 10.9622i) q^{90} +(2.31516 + 0.685829i) q^{91} +(-5.68856 + 8.57461i) q^{92} +(2.67667 - 16.1491i) q^{93} +(-6.37708 - 6.78628i) q^{94} +(-11.9926 - 6.92395i) q^{95} +(9.78158 + 0.566352i) q^{96} -5.10324i q^{97} +(-9.31526 - 3.35052i) q^{98} +(1.90529 + 9.64204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

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