LMFDB - Embedded newform 420.2.l.h.239.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(239,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("420.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.l (of order $2$, degree $1$, 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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 9 x^{14} - 16 x^{13} + 18 x^{12} - 4 x^{11} - 36 x^{10} + 102 x^{9} - 170 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 9x^14 - 16x^13 + 18x^12 - 4x^11 - 36x^10 + 102x^9 - 170x^8 + 204x^7 - 144x^6 - 32x^5 + 288x^4 - 512x^3 + 576x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			239.9
Root			$-0.556656 - 1.30005i$ of defining polynomial
Character	$\chi$	$=$	420.239
Dual form			420.2.l.h.239.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.538162 - 1.30782i) q^{2} +(-0.520627 - 1.65195i) q^{3} +(-1.42076 - 1.40763i) q^{4} +(-1.50700 + 1.65195i) q^{5} +(-2.44063 - 0.208135i) q^{6} +1.00000 q^{7} +(-2.60553 + 1.10056i) q^{8} +(-2.45790 + 1.72010i) q^{9} +O(q^{10})$	\(q+(0.538162 - 1.30782i) q^{2} +(-0.520627 - 1.65195i) q^{3} +(-1.42076 - 1.40763i) q^{4} +(-1.50700 + 1.65195i) q^{5} +(-2.44063 - 0.208135i) q^{6} +1.00000 q^{7} +(-2.60553 + 1.10056i) q^{8} +(-2.45790 + 1.72010i) q^{9} +(1.34944 + 2.85990i) q^{10} -5.78918 q^{11} +(-1.58566 + 3.07988i) q^{12} -1.25147i q^{13} +(0.538162 - 1.30782i) q^{14} +(3.51353 + 1.62944i) q^{15} +(0.0371333 + 3.99983i) q^{16} -2.15265 q^{17} +(0.926828 + 4.14017i) q^{18} +1.25147i q^{19} +(4.46644 - 0.225727i) q^{20} +(-0.520627 - 1.65195i) q^{21} +(-3.11552 + 7.57118i) q^{22} -6.02744i q^{23} +(3.17458 + 3.73123i) q^{24} +(-0.457896 - 4.97899i) q^{25} +(-1.63669 - 0.673492i) q^{26} +(4.12117 + 3.16480i) q^{27} +(-1.42076 - 1.40763i) q^{28} +3.22440i q^{29} +(4.02186 - 3.71815i) q^{30} -6.00738i q^{31} +(5.25102 + 2.10399i) q^{32} +(3.01400 + 9.56346i) q^{33} +(-1.15847 + 2.81527i) q^{34} +(-1.50700 + 1.65195i) q^{35} +(5.91336 + 1.01596i) q^{36} +5.63054i q^{37} +(1.63669 + 0.673492i) q^{38} +(-2.06736 + 0.651547i) q^{39} +(2.10846 - 5.96275i) q^{40} -4.40224i q^{41} +(-2.44063 - 0.208135i) q^{42} -6.28530 q^{43} +(8.22505 + 8.14905i) q^{44} +(0.862526 - 6.65252i) q^{45} +(-7.88278 - 3.24374i) q^{46} -8.45566i q^{47} +(6.58819 - 2.14376i) q^{48} +1.00000 q^{49} +(-6.75802 - 2.08066i) q^{50} +(1.12073 + 3.55607i) q^{51} +(-1.76161 + 1.77804i) q^{52} -9.92391 q^{53} +(6.35683 - 3.68656i) q^{54} +(8.72430 - 9.56346i) q^{55} +(-2.60553 + 1.10056i) q^{56} +(2.06736 - 0.651547i) q^{57} +(4.21692 + 1.73525i) q^{58} +7.14873 q^{59} +(-2.69824 - 7.26082i) q^{60} +3.72601 q^{61} +(-7.85655 - 3.23295i) q^{62} +(-2.45790 + 1.72010i) q^{63} +(5.57754 - 5.73508i) q^{64} +(2.06736 + 1.88596i) q^{65} +(14.1293 + 1.20493i) q^{66} -6.51634 q^{67} +(3.05840 + 3.03014i) q^{68} +(-9.95705 + 3.13804i) q^{69} +(1.34944 + 2.85990i) q^{70} -16.2113 q^{71} +(4.51104 - 7.18683i) q^{72} -10.3348i q^{73} +(7.36370 + 3.03014i) q^{74} +(-7.98666 + 3.34862i) q^{75} +(1.76161 - 1.77804i) q^{76} -5.78918 q^{77} +(-0.260474 + 3.05437i) q^{78} +7.68732i q^{79} +(-6.66349 - 5.96640i) q^{80} +(3.08251 - 8.45566i) q^{81} +(-5.75732 - 2.36912i) q^{82} -2.78032i q^{83} +(-1.58566 + 3.07988i) q^{84} +(3.24404 - 3.55607i) q^{85} +(-3.38251 + 8.22001i) q^{86} +(5.32655 - 1.67871i) q^{87} +(15.0839 - 6.37134i) q^{88} +17.0943i q^{89} +(-8.23609 - 4.70816i) q^{90} -1.25147i q^{91} +(-8.48443 + 8.56356i) q^{92} +(-9.92391 + 3.12760i) q^{93} +(-11.0584 - 4.55052i) q^{94} +(-2.06736 - 1.88596i) q^{95} +(0.741876 - 9.76983i) q^{96} -5.43221i q^{97} +(0.538162 - 1.30782i) q^{98} +(14.2292 - 9.95798i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{4} - 10 q^{6} + 16 q^{7}+O(q^{10}) $ 16 * q + 6 * q^4 - 10 * q^6 + 16 * q^7	$ 16 q + 6 q^{4} - 10 q^{6} + 16 q^{7} + 14 q^{10} + 16 q^{12} + 24 q^{15} - 10 q^{16} + 8 q^{18} - 12 q^{22} + 6 q^{24} + 32 q^{25} - 24 q^{27} + 6 q^{28} - 26 q^{30} - 76 q^{34} + 6 q^{36} + 2 q^{40} - 10 q^{42} - 16 q^{43} + 12 q^{45} - 52 q^{46} + 28 q^{48} + 16 q^{49} - 44 q^{52} - 6 q^{54} + 8 q^{55} + 4 q^{58} + 36 q^{60} + 40 q^{61} + 6 q^{64} - 8 q^{66} + 56 q^{67} - 64 q^{69} + 14 q^{70} - 16 q^{72} - 12 q^{75} + 44 q^{76} + 20 q^{78} + 16 q^{81} + 44 q^{82} + 16 q^{84} - 16 q^{85} - 16 q^{87} + 4 q^{88} - 10 q^{90} - 56 q^{94} + 34 q^{96}+O(q^{100}) $ 16 * q + 6 * q^4 - 10 * q^6 + 16 * q^7 + 14 * q^10 + 16 * q^12 + 24 * q^15 - 10 * q^16 + 8 * q^18 - 12 * q^22 + 6 * q^24 + 32 * q^25 - 24 * q^27 + 6 * q^28 - 26 * q^30 - 76 * q^34 + 6 * q^36 + 2 * q^40 - 10 * q^42 - 16 * q^43 + 12 * q^45 - 52 * q^46 + 28 * q^48 + 16 * q^49 - 44 * q^52 - 6 * q^54 + 8 * q^55 + 4 * q^58 + 36 * q^60 + 40 * q^61 + 6 * q^64 - 8 * q^66 + 56 * q^67 - 64 * q^69 + 14 * q^70 - 16 * q^72 - 12 * q^75 + 44 * q^76 + 20 * q^78 + 16 * q^81 + 44 * q^82 + 16 * q^84 - 16 * q^85 - 16 * q^87 + 4 * q^88 - 10 * q^90 - 56 * q^94 + 34 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

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 $

$2$	0.538162	−	1.30782i	0.380538	−	0.924765i
$2$	0.538162	−	1.30782i	0.380538	−	0.924765i
$3$	−0.520627	−	1.65195i	−0.300584	−	0.953755i
$3$	−0.520627	−	1.65195i	−0.300584	−	0.953755i
$4$	−1.42076	−	1.40763i	−0.710381	−	0.703817i
$5$	−1.50700	+	1.65195i	−0.673951	+	0.738776i
$5$	−1.50700	+	1.65195i	−0.673951	+	0.738776i
$6$	−2.44063	−	0.208135i	−0.996383	−	0.0849709i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.60553	+	1.10056i	−0.921193	+	0.389107i
$9$	−2.45790	+	1.72010i	−0.819299	+	0.573367i
$10$	1.34944	+	2.85990i	0.426730	+	0.904379i
$11$	−5.78918			−1.74550			−0.872752	−	0.488164i	$-0.837667\pi$
$11$	−5.78918			−1.74550			−0.872752	+	0.488164i	$0.837667\pi$
$12$	−1.58566	+	3.07988i	−0.457740	+	0.889086i
$13$		−	1.25147i		−	0.347094i	−0.984826	−	0.173547i	$-0.944477\pi$
$13$		−	1.25147i		−	0.347094i	0.984826	−	0.173547i	$-0.0555229\pi$
$14$	0.538162	−	1.30782i	0.143830	−	0.349528i
$15$	3.51353	+	1.62944i	0.907190	+	0.420721i
$16$	0.0371333	+	3.99983i	0.00928334	+	0.999957i
$17$	−2.15265			−0.522094			−0.261047	−	0.965326i	$-0.584068\pi$
$17$	−2.15265			−0.522094			−0.261047	+	0.965326i	$0.584068\pi$
$18$	0.926828	+	4.14017i	0.218455	+	0.975847i
$19$			1.25147i			0.287106i	0.989643	+	0.143553i	$0.0458528\pi$
$19$			1.25147i			0.287106i	−0.989643	+	0.143553i	$0.954147\pi$
$20$	4.46644	−	0.225727i	0.998725	−	0.0504741i
$21$	−0.520627	−	1.65195i	−0.113610	−	0.360486i
$22$	−3.11552	+	7.57118i	−0.664231	+	1.61418i
$23$		−	6.02744i		−	1.25681i	−0.777887	−	0.628404i	$-0.783709\pi$
$23$		−	6.02744i		−	1.25681i	0.777887	−	0.628404i	$-0.216291\pi$
$24$	3.17458	+	3.73123i	0.648008	+	0.761633i
$25$	−0.457896	−	4.97899i	−0.0915792	−	0.995798i
$26$	−1.63669	−	0.673492i	−0.320981	−	0.132083i
$27$	4.12117	+	3.16480i	0.793120	+	0.609066i
$28$	−1.42076	−	1.40763i	−0.268499	−	0.266018i
$29$			3.22440i			0.598755i	0.954135	+	0.299378i	$0.0967790\pi$
$29$			3.22440i			0.598755i	−0.954135	+	0.299378i	$0.903221\pi$
$30$	4.02186	−	3.71815i	0.734288	−	0.678838i
$31$		−	6.00738i		−	1.07896i	−0.841999	−	0.539479i	$-0.818621\pi$
$31$		−	6.00738i		−	1.07896i	0.841999	−	0.539479i	$-0.181379\pi$
$32$	5.25102	+	2.10399i	0.928258	+	0.371937i
$33$	3.01400	+	9.56346i	0.524670	+	1.66478i
$34$	−1.15847	+	2.81527i	−0.198677	+	0.482814i
$35$	−1.50700	+	1.65195i	−0.254730	+	0.279231i
$36$	5.91336	+	1.01596i	0.985560	+	0.169327i
$37$			5.63054i			0.925654i	0.886449	+	0.462827i	$0.153165\pi$
$37$			5.63054i			0.925654i	−0.886449	+	0.462827i	$0.846835\pi$
$38$	1.63669	+	0.673492i	0.265506	+	0.109255i
$39$	−2.06736	+	0.651547i	−0.331043	+	0.104331i
$40$	2.10846	−	5.96275i	0.333376	−	0.942794i
$41$		−	4.40224i		−	0.687514i	−0.939059	−	0.343757i	$-0.888300\pi$
$41$		−	4.40224i		−	0.687514i	0.939059	−	0.343757i	$-0.111700\pi$
$42$	−2.44063	−	0.208135i	−0.376598	−	0.0321160i
$43$	−6.28530			−0.958499			−0.479249	−	0.877679i	$-0.659091\pi$
$43$	−6.28530			−0.958499			−0.479249	+	0.877679i	$0.659091\pi$
$44$	8.22505	+	8.14905i	1.23997	+	1.22852i
$45$	0.862526	−	6.65252i	0.128578	−	0.991699i
$46$	−7.88278	−	3.24374i	−1.16225	−	0.478263i
$47$		−	8.45566i		−	1.23338i	−0.787204	−	0.616692i	$-0.788472\pi$
$47$		−	8.45566i		−	1.23338i	0.787204	−	0.616692i	$-0.211528\pi$
$48$	6.58819	−	2.14376i	0.950924	−	0.309425i
$49$	1.00000			0.142857
$50$	−6.75802	−	2.08066i	−0.955729	−	0.294250i
$51$	1.12073	+	3.55607i	0.156933	+	0.497950i
$52$	−1.76161	+	1.77804i	−0.244291	+	0.246569i
$53$	−9.92391			−1.36315			−0.681577	−	0.731746i	$-0.738706\pi$
$53$	−9.92391			−1.36315			−0.681577	+	0.731746i	$0.738706\pi$
$54$	6.35683	−	3.68656i	0.865055	−	0.501677i
$55$	8.72430	−	9.56346i	1.17638	−	1.28954i
$56$	−2.60553	+	1.10056i	−0.348178	+	0.147069i
$57$	2.06736	−	0.651547i	0.273829	−	0.0862995i
$58$	4.21692	+	1.73525i	0.553708	+	0.227849i
$59$	7.14873			0.930685			0.465343	−	0.885131i	$-0.345931\pi$
$59$	7.14873			0.930685			0.465343	+	0.885131i	$0.345931\pi$
$60$	−2.69824	−	7.26082i	−0.348341	−	0.937368i
$61$	3.72601			0.477066			0.238533	−	0.971134i	$-0.423333\pi$
$61$	3.72601			0.477066			0.238533	+	0.971134i	$0.423333\pi$
$62$	−7.85655	−	3.23295i	−0.997782	−	0.410585i
$63$	−2.45790	+	1.72010i	−0.309666	+	0.216712i
$64$	5.57754	−	5.73508i	0.697192	−	0.716885i
$65$	2.06736	+	1.88596i	0.256425	+	0.233925i
$66$	14.1293	+	1.20493i	1.73919	+	0.148317i
$67$	−6.51634			−0.796097			−0.398049	−	0.917364i	$-0.630312\pi$
$67$	−6.51634			−0.796097			−0.398049	+	0.917364i	$0.630312\pi$
$68$	3.05840	+	3.03014i	0.370886	+	0.367459i
$69$	−9.95705	+	3.13804i	−1.19869	+	0.377776i
$70$	1.34944	+	2.85990i	0.161289	+	0.341823i
$71$	−16.2113			−1.92393			−0.961963	−	0.273180i	$-0.911925\pi$
$71$	−16.2113			−1.92393			−0.961963	+	0.273180i	$0.911925\pi$
$72$	4.51104	−	7.18683i	0.531631	−	0.846976i
$73$		−	10.3348i		−	1.20960i	−0.796378	−	0.604800i	$-0.793253\pi$
$73$		−	10.3348i		−	1.20960i	0.796378	−	0.604800i	$-0.206747\pi$
$74$	7.36370	+	3.03014i	0.856013	+	0.352247i
$75$	−7.98666	+	3.34862i	−0.922220	+	0.386665i
$76$	1.76161	−	1.77804i	0.202070	−	0.203955i
$77$	−5.78918			−0.659739
$78$	−0.260474	+	3.05437i	−0.0294929	+	0.345839i
$79$			7.68732i			0.864891i	0.901660	+	0.432446i	$0.142349\pi$
$79$			7.68732i			0.864891i	−0.901660	+	0.432446i	$0.857651\pi$
$80$	−6.66349	−	5.96640i	−0.745000	−	0.667064i
$81$	3.08251	−	8.45566i	0.342501	−	0.939518i
$82$	−5.75732	−	2.36912i	−0.635789	−	0.261625i
$83$		−	2.78032i		−	0.305180i	−0.988290	−	0.152590i	$-0.951239\pi$
$83$		−	2.78032i		−	0.305180i	0.988290	−	0.152590i	$-0.0487614\pi$
$84$	−1.58566	+	3.07988i	−0.173009	+	0.336043i
$85$	3.24404	−	3.55607i	0.351866	−	0.385710i
$86$	−3.38251	+	8.22001i	−0.364745	+	0.886386i
$87$	5.32655	−	1.67871i	0.571066	−	0.179976i
$88$	15.0839	−	6.37134i	1.60795	−	0.679187i
$89$			17.0943i			1.81199i	0.423289	+	0.905995i	$0.360876\pi$
$89$			17.0943i			1.81199i	−0.423289	+	0.905995i	$0.639124\pi$
$90$	−8.23609	−	4.70816i	−0.868160	−	0.496284i
$91$		−	1.25147i		−	0.131189i
$92$	−8.48443	+	8.56356i	−0.884563	+	0.892813i
$93$	−9.92391	+	3.12760i	−1.02906	+	0.324317i
$94$	−11.0584	−	4.55052i	−1.14059	−	0.469350i
$95$	−2.06736	−	1.88596i	−0.212107	−	0.193496i
$96$	0.741876	−	9.76983i	0.0757174	−	0.997129i
$97$		−	5.43221i		−	0.551557i	−0.961221	−	0.275779i	$-0.911064\pi$
$97$		−	5.43221i		−	0.551557i	0.961221	−	0.275779i	$-0.0889357\pi$
$98$	0.538162	−	1.30782i	0.0543626	−	0.132109i
$99$	14.2292	−	9.95798i	1.43009	−	1.00081i
$100$	−6.35803	+	7.71851i	−0.635803	+	0.771851i
$101$		−	2.78032i		−	0.276652i	−0.990387	−	0.138326i	$-0.955828\pi$
$101$		−	2.78032i		−	0.276652i	0.990387	−	0.138326i	$-0.0441722\pi$
$102$	5.25382	+	0.448042i	0.520206	+	0.0443628i
$103$	−9.36951			−0.923205			−0.461602	−	0.887087i	$-0.652725\pi$
$103$	−9.36951			−0.923205			−0.461602	+	0.887087i	$0.652725\pi$
$104$	1.37731	+	3.26073i	0.135057	+	0.319741i
$105$	3.51353	+	1.62944i	0.342886	+	0.159017i
$106$	−5.34067	+	12.9786i	−0.518732	+	1.26060i
$107$		−	0.165861i		−	0.0160344i	−0.999968	−	0.00801719i	$-0.997448\pi$
$107$		−	0.165861i		−	0.0160344i	0.999968	−	0.00801719i	$-0.00255198\pi$
$108$	−1.40033	−	10.2975i	−0.134747	−	0.990880i
$109$	3.76556			0.360675			0.180337	−	0.983605i	$-0.442281\pi$
$109$	3.76556			0.360675			0.180337	+	0.983605i	$0.442281\pi$
$110$	−7.81215	−	16.5565i	−0.744859	−	1.57860i
$111$	9.30138	−	2.93141i	0.882848	−	0.278237i
$112$	0.0371333	+	3.99983i	0.00350877	+	0.377948i
$113$	7.68246			0.722705			0.361352	−	0.932429i	$-0.382315\pi$
$113$	7.68246			0.722705			0.361352	+	0.932429i	$0.382315\pi$
$114$	0.260474	−	3.05437i	0.0243957	−	0.286068i
$115$	9.95705	+	9.08336i	0.928499	+	0.847027i
$116$	4.53877	−	4.58110i	0.421414	−	0.425345i
$117$	2.15265	+	3.07598i	0.199012	+	0.284374i
$118$	3.84718	−	9.34922i	0.354161	−	0.860665i
$119$	−2.15265			−0.197333
$120$	−10.9479	−	0.378706i	−0.999402	−	0.0345710i
$121$	22.5146			2.04679
$122$	2.00520	−	4.87293i	0.181542	−	0.441174i
$123$	−7.27229	+	2.29192i	−0.655721	+	0.206656i
$124$	−8.45619	+	8.53506i	−0.759389	+	0.766471i
$125$	8.91510	+	6.74692i	0.797391	+	0.603463i
$126$	0.926828	+	4.14017i	0.0825684	+	0.368835i
$127$	−4.76726			−0.423026			−0.211513	−	0.977375i	$-0.567839\pi$
$127$	−4.76726			−0.423026			−0.211513	+	0.977375i	$0.567839\pi$
$128$	−4.49880	−	10.3808i	−0.397642	−	0.917541i
$129$	3.27229	+	10.3830i	0.288109	+	0.914173i
$130$	3.57907	−	1.68878i	0.313905	−	0.148116i
$131$	17.0044			1.48568			0.742840	−	0.669469i	$-0.233478\pi$
$131$	17.0044			1.48568			0.742840	+	0.669469i	$0.233478\pi$
$132$	9.17966	−	17.8300i	0.798987	−	1.55190i
$133$			1.25147i			0.108516i
$134$	−3.50685	+	8.52217i	−0.302945	+	0.736203i
$135$	−11.4387	+	2.03863i	−0.984487	+	0.175457i
$136$	5.60878	−	2.36912i	0.480949	−	0.203150i
$137$	11.3395			0.968803			0.484401	−	0.874846i	$-0.339037\pi$
$137$	11.3395			0.968803			0.484401	+	0.874846i	$0.339037\pi$
$138$	−1.25452	+	14.7108i	−0.106792	+	1.25226i
$139$		−	5.86068i		−	0.497097i	−0.968620	−	0.248548i	$-0.920047\pi$
$139$		−	5.86068i		−	0.497097i	0.968620	−	0.248548i	$-0.0799535\pi$
$140$	4.46644	−	0.225727i	0.377483	−	0.0190774i
$141$	−13.9683	+	4.40224i	−1.17635	+	0.370735i
$142$	−8.72430	+	21.2014i	−0.732127	+	1.77918i
$143$			7.24497i			0.605855i
$144$	−6.97138	−	9.76729i	−0.580948	−	0.813941i
$145$	−5.32655	−	4.85917i	−0.442346	−	0.403532i
$146$	−13.5160	−	5.56181i	−1.11860	−	0.460299i
$147$	−0.520627	−	1.65195i	−0.0429406	−	0.136251i
$148$	7.92573	−	7.99966i	0.651491	−	0.657568i
$149$		−	20.2947i		−	1.66261i	−0.555817	−	0.831305i	$-0.687595\pi$
$149$		−	20.2947i		−	1.66261i	0.555817	−	0.831305i	$-0.312405\pi$
$150$	0.0812521	+	12.2472i	0.00663421	+	0.999978i
$151$		−	3.98455i		−	0.324258i	−0.986770	−	0.162129i	$-0.948164\pi$
$151$		−	3.98455i		−	0.324258i	0.986770	−	0.162129i	$-0.0518360\pi$
$152$	−1.37731	−	3.26073i	−0.111715	−	0.264480i
$153$	5.29099	−	3.70277i	0.427751	−	0.299352i
$154$	−3.11552	+	7.57118i	−0.251056	+	0.610103i
$155$	9.92391	+	9.05313i	0.797108	+	0.727165i
$156$	3.85437	+	1.98440i	0.308597	+	0.158879i
$157$			1.25147i			0.0998779i	0.998752	+	0.0499390i	$0.0159027\pi$
$157$			1.25147i			0.0998779i	−0.998752	+	0.0499390i	$0.984097\pi$
$158$	10.0536	+	4.13703i	0.799821	+	0.329124i
$159$	5.16665	+	16.3938i	0.409742	+	1.30012i
$160$	−11.3890	+	5.50372i	−0.900379	+	0.435107i
$161$		−	6.02744i		−	0.475029i
$162$	−9.39955	−	8.58187i	−0.738499	−	0.674255i
$163$	−14.9124			−1.16803			−0.584014	−	0.811743i	$-0.698519\pi$
$163$	−14.9124			−1.16803			−0.584014	+	0.811743i	$0.698519\pi$
$164$	−6.19674	+	6.25454i	−0.483884	+	0.488397i
$165$	−20.3405	−	9.43315i	−1.58350	−	0.734370i
$166$	−3.63615	−	1.49626i	−0.282220	−	0.116133i
$167$			17.2930i			1.33817i	0.743185	+	0.669086i	$0.233314\pi$
$167$			17.2930i			1.33817i	−0.743185	+	0.669086i	$0.766686\pi$
$168$	3.17458	+	3.73123i	0.244924	+	0.287870i
$169$	11.4338			0.879525
$170$	−2.90487	−	6.15636i	−0.222793	−	0.472171i
$171$	−2.15265	−	3.07598i	−0.164617	−	0.235226i
$172$	8.92992	+	8.84740i	0.680900	+	0.674608i
$173$	24.9257			1.89506			0.947532	−	0.319662i	$-0.103569\pi$
$173$	24.9257			1.89506			0.947532	+	0.319662i	$0.103569\pi$
$174$	0.671111	−	7.86956i	0.0508768	−	0.596590i
$175$	−0.457896	−	4.97899i	−0.0346137	−	0.376376i
$176$	−0.214972	−	23.1557i	−0.0162041	−	1.74543i
$177$	−3.72182	−	11.8094i	−0.279749	−	0.887646i
$178$	22.3562	+	9.19950i	1.67567	+	0.689531i
$179$	8.50828			0.635939			0.317969	−	0.948101i	$-0.396999\pi$
$179$	8.50828			0.635939			0.317969	+	0.948101i	$0.396999\pi$
$180$	−10.5898	+	8.23753i	−0.789314	+	0.613990i
$181$	−21.0096			−1.56163			−0.780816	−	0.624761i	$-0.785196\pi$
$181$	−21.0096			−1.56163			−0.780816	+	0.624761i	$0.785196\pi$
$182$	−1.63669	−	0.673492i	−0.121319	−	0.0499226i
$183$	−1.93986	−	6.15519i	−0.143398	−	0.455004i
$184$	6.63356	+	15.7047i	0.489032	+	1.15776i
$185$	−9.30138	−	8.48522i	−0.683851	−	0.623846i
$186$	−1.25035	+	14.6618i	−0.0916800	+	1.07506i
$187$	12.4621			0.911317
$188$	−11.9025	+	12.0135i	−0.868077	+	0.876173i
$189$	4.12117	+	3.16480i	0.299771	+	0.230205i
$190$	−3.57907	+	1.68878i	−0.259653	+	0.122517i
$191$	3.63653			0.263130			0.131565	−	0.991308i	$-0.458000\pi$
$191$	3.63653			0.263130			0.131565	+	0.991308i	$0.458000\pi$
$192$	−12.3779	−	6.22799i	−0.893297	−	0.449467i
$193$		−	0.342895i		−	0.0246821i	−0.999924	−	0.0123411i	$-0.996072\pi$
$193$		−	0.342895i		−	0.0246821i	0.999924	−	0.0123411i	$-0.00392838\pi$
$194$	−7.10433	−	2.92341i	−0.510061	−	0.209889i
$195$	2.03920	−	4.39707i	0.146030	−	0.314881i
$196$	−1.42076	−	1.40763i	−0.101483	−	0.100545i
$197$	−8.92752			−0.636060			−0.318030	−	0.948081i	$-0.603021\pi$
$197$	−8.92752			−0.636060			−0.318030	+	0.948081i	$0.603021\pi$
$198$	−5.36557	−	23.9682i	−0.381315	−	1.70334i
$199$		−	8.51032i		−	0.603280i	−0.953422	−	0.301640i	$-0.902466\pi$
$199$		−	8.51032i		−	0.603280i	0.953422	−	0.301640i	$-0.0975341\pi$
$200$	6.67274	+	12.4689i	0.471834	+	0.881688i
$201$	3.39258	+	10.7647i	0.239294	+	0.759282i
$202$	−3.63615	−	1.49626i	−0.255838	−	0.105277i
$203$			3.22440i			0.226308i
$204$	3.41337	−	6.62991i	0.238983	−	0.464187i
$205$	7.27229	+	6.63418i	0.507919	+	0.463351i
$206$	−5.04231	+	12.2536i	−0.351315	+	0.853748i
$207$	10.3678	+	14.8148i	0.720612	+	1.02970i
$208$	5.00565	−	0.0464712i	0.347079	−	0.00322219i
$209$		−	7.24497i		−	0.501145i
$210$	4.02186	−	3.71815i	0.277535	−	0.256577i
$211$			24.6542i			1.69726i	0.528983	+	0.848632i	$0.322574\pi$
$211$			24.6542i			1.69726i	−0.528983	+	0.848632i	$0.677426\pi$
$212$	14.0995	+	13.9692i	0.968359	+	0.959411i
$213$	8.44003	+	26.7803i	0.578301	+	1.83495i
$214$	−0.216915	−	0.0892601i	−0.0148280	−	0.00610169i
$215$	9.47195	−	10.3830i	0.645982	−	0.708116i
$216$	−14.2209	−	3.71037i	−0.967608	−	0.252459i
$217$		−	6.00738i		−	0.407808i
$218$	2.02648	−	4.92465i	0.137251	−	0.333540i
$219$	−17.0726	+	5.38058i	−1.15366	+	0.363586i
$220$	−25.8570	+	1.30678i	−1.74328	+	0.0881028i
$221$			2.69397i			0.181216i
$222$	1.17191	−	13.7421i	0.0786537	−	0.922307i
$223$	11.9141			0.797826			0.398913	−	0.916989i	$-0.369387\pi$
$223$	11.9141			0.797826			0.398913	+	0.916989i	$0.369387\pi$
$224$	5.25102	+	2.10399i	0.350849	+	0.140579i
$225$	9.68982	+	11.4502i	0.645988	+	0.763347i
$226$	4.13441	−	10.0472i	0.275017	−	0.668332i
$227$			16.3277i			1.08371i	0.840474	+	0.541853i	$0.182277\pi$
$227$			16.3277i			1.08371i	−0.840474	+	0.541853i	$0.817723\pi$
$228$	−3.85437	−	1.98440i	−0.255262	−	0.131420i
$229$	−17.5576			−1.16024			−0.580119	−	0.814532i	$-0.696994\pi$
$229$	−17.5576			−1.16024			−0.580119	+	0.814532i	$0.696994\pi$
$230$	17.2379	−	8.13366i	1.13663	−	0.536318i
$231$	3.01400	+	9.56346i	0.198307	+	0.629229i
$232$	−3.54864	−	8.40125i	−0.232980	−	0.551569i
$233$	−25.3883			−1.66324			−0.831622	−	0.555341i	$-0.812588\pi$
$233$	−25.3883			−1.66324			−0.831622	+	0.555341i	$0.812588\pi$
$234$	5.18128	−	1.15989i	0.338711	−	0.0758246i
$235$	13.9683	+	12.7427i	0.911195	+	0.831241i
$236$	−10.1566	−	10.0628i	−0.661142	−	0.655032i
$237$	12.6991	−	4.00222i	0.824895	−	0.259972i
$238$	−1.15847	+	2.81527i	−0.0750928	+	0.182487i
$239$	0.0205520			0.00132940			0.000664701	−	1.00000i	$-0.499788\pi$
$239$	0.0205520			0.00132940			0.000664701		1.00000i	$0.499788\pi$
$240$	−6.38703	+	14.1140i	−0.412281	+	0.911057i
$241$	−4.63049			−0.298276			−0.149138	−	0.988816i	$-0.547650\pi$
$241$	−4.63049			−0.298276			−0.149138	+	0.988816i	$0.547650\pi$
$242$	12.1165	−	29.4450i	0.778880	−	1.89280i
$243$	−15.5732	−	0.689915i	−0.999020	−	0.0442580i
$244$	−5.29377	−	5.24485i	−0.338899	−	0.335767i
$245$	−1.50700	+	1.65195i	−0.0962788	+	0.105539i
$246$	−0.916261	+	10.7442i	−0.0584187	+	0.685028i
$247$	1.56617			0.0996530
$248$	6.61148	+	15.6524i	0.419830	+	0.993928i
$249$	−4.59296	+	1.44751i	−0.291067	+	0.0917321i
$250$	13.6215	−	8.02837i	0.861499	−	0.507759i
$251$	−3.36218			−0.212219			−0.106109	−	0.994354i	$-0.533839\pi$
$251$	−3.36218			−0.212219			−0.106109	+	0.994354i	$0.533839\pi$
$252$	5.91336	+	1.01596i	0.372507	+	0.0639996i
$253$			34.8939i			2.19376i
$254$	−2.56556	+	6.23469i	−0.160977	+	0.391200i
$255$	−7.56340	−	3.50762i	−0.473639	−	0.219656i
$256$	−15.9972	+	0.297054i	−0.999828	+	0.0185659i
$257$	22.0005			1.37235			0.686176	−	0.727436i	$-0.259288\pi$
$257$	22.0005			1.37235			0.686176	+	0.727436i	$0.259288\pi$
$258$	15.3401	+	1.30819i	0.955032	+	0.0814445i
$259$			5.63054i			0.349864i
$260$	−0.282490	−	5.58960i	−0.0175193	−	0.346652i
$261$	−5.54629	−	7.92523i	−0.343307	−	0.490559i
$262$	9.15112	−	22.2386i	0.565358	−	1.37391i
$263$		−	6.50108i		−	0.400874i	−0.979707	−	0.200437i	$-0.935764\pi$
$263$		−	6.50108i		−	0.400874i	0.979707	−	0.200437i	$-0.0642362\pi$
$264$	−18.3782	−	21.6007i	−1.13110	−	1.32943i
$265$	14.9553	−	16.3938i	0.918699	−	1.00707i
$266$	1.63669	+	0.673492i	0.100352	+	0.0412945i
$267$	28.2389	−	8.89973i	1.72819	−	0.544655i
$268$	9.25817	+	9.17262i	0.565533	+	0.560307i
$269$		−	26.4585i		−	1.61320i	−0.591097	−	0.806601i	$-0.701305\pi$
$269$		−	26.4585i		−	1.61320i	0.591097	−	0.806601i	$-0.298695\pi$
$270$	−3.48973	+	16.0568i	−0.212378	+	0.977188i
$271$		−	0.247823i		−	0.0150542i	−0.999972	−	0.00752708i	$-0.997604\pi$
$271$		−	0.247823i		−	0.0150542i	0.999972	−	0.00752708i	$-0.00239597\pi$
$272$	−0.0799351	−	8.61023i	−0.00484678	−	0.522072i
$273$	−2.06736	+	0.651547i	−0.125123	+	0.0394334i
$274$	6.10251	−	14.8300i	0.368666	−	0.895915i
$275$	2.65084	+	28.8243i	0.159852	+	1.73817i
$276$	18.5638	+	9.55746i	1.11741	+	0.575291i
$277$		−	2.23531i		−	0.134306i	−0.997743	−	0.0671532i	$-0.978608\pi$
$277$		−	2.23531i		−	0.134306i	0.997743	−	0.0671532i	$-0.0213916\pi$
$278$	−7.66469	−	3.15400i	−0.459698	−	0.189164i
$279$	10.3333	+	14.7655i	0.618639	+	0.883989i
$280$	2.10846	−	5.96275i	0.126004	−	0.356343i
$281$			6.88040i			0.410450i	0.978715	+	0.205225i	$0.0657927\pi$
$281$			6.88040i			0.410450i	−0.978715	+	0.205225i	$0.934207\pi$
$282$	−1.75992	+	20.6371i	−0.104802	+	1.22892i
$283$	−24.5394			−1.45872			−0.729358	−	0.684132i	$-0.760181\pi$
$283$	−24.5394			−1.45872			−0.729358	+	0.684132i	$0.760181\pi$
$284$	23.0324	+	22.8196i	1.36672	+	1.35409i
$285$	−2.03920	+	4.39707i	−0.120791	+	0.260460i
$286$	9.47508	+	3.89897i	0.560273	+	0.230551i
$287$		−	4.40224i		−	0.259856i
$288$	−16.5255	+	3.86089i	−0.973777	+	0.227505i
$289$	−12.3661			−0.727418
$290$	−9.22144	+	4.35112i	−0.541502	+	0.255507i
$291$	−8.97375	+	2.82815i	−0.526051	+	0.165789i
$292$	−14.5476	+	14.6833i	−0.851337	+	0.859277i
$293$	−15.8374			−0.925233			−0.462616	−	0.886559i	$-0.653089\pi$
$293$	−15.8374			−0.925233			−0.462616	+	0.886559i	$0.653089\pi$
$294$	−2.44063	−	0.208135i	−0.142340	−	0.0121387i
$295$	−10.7731	+	11.8094i	−0.627237	+	0.687568i
$296$	−6.19674	−	14.6705i	−0.360178	−	0.852706i
$297$	−23.8582	−	18.3216i	−1.38439	−	1.06313i
$298$	−26.5418	−	10.9219i	−1.53752	−	0.632686i
$299$	−7.54314			−0.436231
$300$	16.0608	+	6.48471i	0.927269	+	0.374395i
$301$	−6.28530			−0.362279
$302$	−5.21105	−	2.14433i	−0.299862	−	0.123393i
$303$	−4.59296	+	1.44751i	−0.263859	+	0.0831572i
$304$	−5.00565	+	0.0464712i	−0.287094	+	0.00266530i
$305$	−5.61509	+	6.15519i	−0.321519	+	0.352445i
$306$	−1.99513	−	8.91233i	−0.114054	−	0.509484i
$307$	−11.8368			−0.675560			−0.337780	−	0.941225i	$-0.609676\pi$
$307$	−11.8368			−0.675560			−0.337780	+	0.941225i	$0.609676\pi$
$308$	8.22505	+	8.14905i	0.468666	+	0.464335i
$309$	4.87801	+	15.4780i	0.277500	+	0.880512i
$310$	17.1805	−	8.10659i	0.975787	−	0.460423i
$311$	−2.71910			−0.154186			−0.0770929	−	0.997024i	$-0.524564\pi$
$311$	−2.71910			−0.154186			−0.0770929	+	0.997024i	$0.524564\pi$
$312$	4.66951	−	3.97288i	0.264359	−	0.224920i
$313$			2.43363i			0.137557i	0.997632	+	0.0687785i	$0.0219102\pi$
$313$			2.43363i			0.137557i	−0.997632	+	0.0687785i	$0.978090\pi$
$314$	1.63669	+	0.673492i	0.0923636	+	0.0380074i
$315$	0.862526	−	6.65252i	0.0485979	−	0.374827i
$316$	10.8209	−	10.9219i	0.608725	−	0.614403i
$317$	−0.658065			−0.0369606			−0.0184803	−	0.999829i	$-0.505883\pi$
$317$	−0.658065			−0.0369606			−0.0184803	+	0.999829i	$0.505883\pi$
$318$	24.2206	+	2.06552i	1.35822	+	0.115828i
$319$		−	18.6666i		−	1.04513i
$320$	1.06872	+	17.8566i	0.0597435	+	0.998214i
$321$	−0.273994	+	0.0863516i	−0.0152929	+	0.00481967i
$322$	−7.88278	−	3.24374i	−0.439290	−	0.180767i
$323$		−	2.69397i		−	0.149896i
$324$	−16.2820	+	7.67444i	−0.904555	+	0.426358i
$325$	−6.23104	+	0.573042i	−0.345636	+	0.0317866i
$326$	−8.02529	+	19.5027i	−0.444479	+	1.08015i
$327$	−1.96045	−	6.22052i	−0.108413	−	0.343996i
$328$	4.84493	+	11.4702i	0.267516	+	0.633333i
$329$		−	8.45566i		−	0.466176i
$330$	−23.2833	+	21.5250i	−1.28170	+	1.18491i
$331$		−	31.7663i		−	1.74604i	−0.487688	−	0.873018i	$-0.662160\pi$
$331$		−	31.7663i		−	1.74604i	0.487688	−	0.873018i	$-0.337840\pi$
$332$	−3.91367	+	3.95018i	−0.214791	+	0.216794i
$333$	−9.68509	−	13.8393i	−0.530740	−	0.758387i
$334$	22.6160	+	9.30643i	1.23749	+	0.509225i
$335$	9.82013	−	10.7647i	0.536531	−	0.588137i
$336$	6.58819	−	2.14376i	0.359415	−	0.116952i
$337$			5.91231i			0.322064i	0.986949	+	0.161032i	$0.0514822\pi$
$337$			5.91231i			0.322064i	−0.986949	+	0.161032i	$0.948518\pi$
$338$	6.15326	−	14.9533i	0.334693	−	0.813355i
$339$	−3.99969	−	12.6911i	−0.217233	−	0.689284i
$340$	−9.61467	+	0.485911i	−0.521429	+	0.0263522i
$341$			34.7778i			1.88333i
$342$	−5.18128	+	1.15989i	−0.280172	+	0.0627199i
$343$	1.00000			0.0539949
$344$	16.3765	−	6.91735i	0.882962	−	0.372958i
$345$	9.82138	−	21.1776i	0.528765	−	1.14016i
$346$	13.4141	−	32.5982i	0.721144	−	1.75249i
$347$			3.68885i			0.198028i	0.995086	+	0.0990140i	$0.0315689\pi$
$347$			3.68885i			0.198028i	−0.995086	+	0.0990140i	$0.968431\pi$
$348$	−9.93077	−	5.11279i	−0.532345	−	0.274074i
$349$	11.8910			0.636512			0.318256	−	0.948005i	$-0.396903\pi$
$349$	11.8910			0.636512			0.318256	+	0.948005i	$0.396903\pi$
$350$	−6.75802	−	2.08066i	−0.361231	−	0.111216i
$351$	3.96064	−	5.15751i	0.211403	−	0.275287i
$352$	−30.3991	−	12.1804i	−1.62028	−	0.649217i
$353$	−9.94446			−0.529290			−0.264645	−	0.964346i	$-0.585255\pi$
$353$	−9.94446			−0.529290			−0.264645	+	0.964346i	$0.585255\pi$
$354$	−17.4474	−	1.48790i	−0.927320	−	0.0790811i
$355$	24.4304	−	26.7803i	1.29663	−	1.42135i
$356$	24.0625	−	24.2869i	1.27531	−	1.28720i
$357$	1.12073	+	3.55607i	0.0593151	+	0.188207i
$358$	4.57883	−	11.1273i	0.241999	−	0.588094i
$359$	−8.11240			−0.428156			−0.214078	−	0.976817i	$-0.568675\pi$
$359$	−8.11240			−0.428156			−0.214078	+	0.976817i	$0.568675\pi$
$360$	5.07416	+	18.2826i	0.267432	+	0.963577i
$361$	17.4338			0.917570
$362$	−11.3066	+	27.4767i	−0.594260	+	1.44414i
$363$	−11.7217	−	37.1931i	−0.615231	−	1.95213i
$364$	−1.76161	+	1.77804i	−0.0923333	+	0.0931945i
$365$	17.0726	+	15.5746i	0.893623	+	0.815211i
$366$	−9.09381	−	0.775513i	−0.475341	−	0.0405367i
$367$	−9.44861			−0.493213			−0.246607	−	0.969116i	$-0.579316\pi$
$367$	−9.44861			−0.493213			−0.246607	+	0.969116i	$0.579316\pi$
$368$	24.1087	−	0.223819i	1.25675	−	0.0116674i
$369$	7.57230	+	10.8202i	0.394198	+	0.563280i
$370$	−16.1028	+	7.59806i	−0.837143	+	0.395004i
$371$	−9.92391			−0.515224
$372$	18.5020	+	9.52565i	0.959286	+	0.493882i
$373$		−	21.8621i		−	1.13198i	−0.824413	−	0.565989i	$-0.808494\pi$
$373$		−	21.8621i		−	1.13198i	0.824413	−	0.565989i	$-0.191506\pi$
$374$	6.70662	−	16.2981i	0.346791	−	0.842755i
$375$	6.50415	−	18.2400i	0.335873	−	0.941907i
$376$	9.30596	+	22.0314i	0.479918	+	1.13618i
$377$	4.03522			0.207825
$378$	6.35683	−	3.68656i	0.326960	−	0.189616i
$379$		−	10.5331i		−	0.541052i	−0.962713	−	0.270526i	$-0.912802\pi$
$379$		−	10.5331i		−	0.541052i	0.962713	−	0.270526i	$-0.0871975\pi$
$380$	0.282490	+	5.58960i	0.0144914	+	0.286740i
$381$	2.48196	+	7.87529i	0.127155	+	0.403463i
$382$	1.95705	−	4.75591i	0.100131	−	0.243334i
$383$			11.1168i			0.568041i	0.958818	+	0.284021i	$0.0916684\pi$
$383$			11.1168i			0.568041i	−0.958818	+	0.284021i	$0.908332\pi$
$384$	−14.8064	+	12.8363i	−0.755585	+	0.655051i
$385$	8.72430	−	9.56346i	0.444632	−	0.487399i
$386$	−0.448443	−	0.184533i	−0.0228252	−	0.00939248i
$387$	15.4486	−	10.8113i	0.785297	−	0.549572i
$388$	−7.64656	+	7.71788i	−0.388195	+	0.391816i
$389$		−	28.9265i		−	1.46663i	−0.679888	−	0.733316i	$-0.737972\pi$
$389$		−	28.9265i		−	1.46663i	0.679888	−	0.733316i	$-0.262028\pi$
$390$	−4.65314	−	5.03323i	−0.235621	−	0.254867i
$391$			12.9750i			0.656172i
$392$	−2.60553	+	1.10056i	−0.131599	+	0.0555867i
$393$	−8.85294	−	28.0904i	−0.446572	−	1.41698i
$394$	−4.80446	+	11.6756i	−0.242045	+	0.588206i
$395$	−12.6991	−	11.5848i	−0.638961	−	0.582895i
$396$	−34.2335	−	5.88159i	−1.72030	−	0.295561i
$397$			4.90048i			0.245948i	0.992410	+	0.122974i	$0.0392432\pi$
$397$			4.90048i			0.245948i	−0.992410	+	0.122974i	$0.960757\pi$
$398$	−11.1299	−	4.57993i	−0.557893	−	0.229571i
$399$	2.06736	−	0.651547i	0.103498	−	0.0326181i
$400$	19.8981	−	2.01639i	0.994905	−	0.100820i
$401$			12.7420i			0.636304i	0.948040	+	0.318152i	$0.103062\pi$
$401$			12.7420i			0.636304i	−0.948040	+	0.318152i	$0.896938\pi$
$402$	15.9040	+	1.35628i	0.793218	+	0.0676451i
$403$	−7.51804			−0.374500
$404$	−3.91367	+	3.95018i	−0.194713	+	0.196529i
$405$	9.32301	+	17.8348i	0.463264	+	0.886220i
$406$	4.21692	+	1.73525i	0.209282	+	0.0861189i
$407$		−	32.5962i		−	1.61573i
$408$	−6.83376	−	8.03202i	−0.338321	−	0.397644i
$409$	23.2836			1.15130			0.575650	−	0.817696i	$-0.304749\pi$
$409$	23.2836			1.15130			0.575650	+	0.817696i	$0.304749\pi$
$410$	12.5900	−	5.94055i	0.621774	−	0.293383i
$411$	−5.90367	−	18.7324i	−0.291206	−	0.924001i
$412$	13.3118	+	13.1888i	0.655827	+	0.649767i
$413$	7.14873			0.351766
$414$	24.9546	−	5.58640i	1.22645	−	0.274556i
$415$	4.59296	+	4.18995i	0.225459	+	0.205676i
$416$	2.63308	−	6.57148i	0.129097	−	0.322193i
$417$	−9.68157	+	3.05123i	−0.474109	+	0.149419i
$418$	−9.47508	−	3.89897i	−0.463441	−	0.190705i
$419$	−26.0926			−1.27471			−0.637354	−	0.770571i	$-0.719971\pi$
$419$	−26.0926			−1.27471			−0.637354	+	0.770571i	$0.719971\pi$
$420$	−2.69824	−	7.26082i	−0.131660	−	0.354292i
$421$	−25.2576			−1.23098			−0.615490	−	0.788145i	$-0.711042\pi$
$421$	−25.2576			−1.23098			−0.615490	+	0.788145i	$0.711042\pi$
$422$	32.2431	+	13.2680i	1.56957	+	0.645874i
$423$	14.5446	+	20.7831i	0.707182	+	1.01051i
$424$	25.8570	−	10.9219i	1.25573	−	0.530412i
$425$	0.985690	+	10.7180i	0.0478130	+	0.519900i
$426$	39.5658	+	3.37414i	1.91697	+	0.163478i
$427$	3.72601			0.180314
$428$	−0.233471	+	0.235649i	−0.0112853	+	0.0113905i
$429$	11.9683	−	3.77192i	0.577837	−	0.182110i
$430$	−8.48162	−	17.9753i	−0.409020	−	0.866846i
$431$	24.8289			1.19597			0.597984	−	0.801508i	$-0.295969\pi$
$431$	24.8289			1.19597			0.597984	+	0.801508i	$0.295969\pi$
$432$	−12.5056	+	16.6015i	−0.601677	+	0.798740i
$433$			14.0871i			0.676983i	0.940970	+	0.338491i	$0.109917\pi$
$433$			14.0871i			0.676983i	−0.940970	+	0.338491i	$0.890083\pi$
$434$	−7.85655	−	3.23295i	−0.377126	−	0.155186i
$435$	−5.25397	+	11.3290i	−0.251909	+	0.543185i
$436$	−5.34996	−	5.30053i	−0.256217	−	0.253849i
$437$	7.54314			0.360837
$438$	−2.15104	+	25.2235i	−0.102781	+	1.20523i
$439$			6.79642i			0.324376i	0.986760	+	0.162188i	$0.0518550\pi$
$439$			6.79642i			0.324376i	−0.986760	+	0.162188i	$0.948145\pi$
$440$	−12.2062	+	34.5195i	−0.581910	+	1.64565i
$441$	−2.45790	+	1.72010i	−0.117043	+	0.0819096i
$442$	3.52321	+	1.44979i	0.167582	+	0.0689596i
$443$		−	28.5165i		−	1.35486i	−0.735587	−	0.677430i	$-0.763094\pi$
$443$		−	28.5165i		−	1.35486i	0.735587	−	0.677430i	$-0.236906\pi$
$444$	−17.3414	−	8.92810i	−0.822986	−	0.423709i
$445$	−28.2389	−	25.7611i	−1.33865	−	1.22119i
$446$	6.41171	−	15.5814i	0.303603	−	0.737802i
$447$	−33.5259	+	10.5660i	−1.58572	+	0.499753i
$448$	5.57754	−	5.73508i	0.263514	−	0.270957i
$449$		−	2.96656i		−	0.140001i	−0.997547	−	0.0700003i	$-0.977700\pi$
$449$		−	2.96656i		−	0.140001i	0.997547	−	0.0700003i	$-0.0223000\pi$
$450$	20.1895	−	6.51043i	0.951740	−	0.306905i
$451$			25.4854i			1.20006i
$452$	−10.9150	−	10.8141i	−0.513396	−	0.508652i
$453$	−6.58228	+	2.07446i	−0.309263	+	0.0974667i
$454$	21.3536	+	8.78693i	1.00217	+	0.412391i
$455$	2.06736	+	1.88596i	0.0969195	+	0.0884152i
$456$	−4.66951	+	3.97288i	−0.218670	+	0.186047i
$457$			1.30309i			0.0609561i	0.999535	+	0.0304781i	$0.00970297\pi$
$457$			1.30309i			0.0609561i	−0.999535	+	0.0304781i	$0.990297\pi$
$458$	−9.44883	+	22.9621i	−0.441515	+	1.07295i
$459$	−8.87144	−	6.81270i	−0.414083	−	0.317990i
$460$	−1.36056	−	26.9212i	−0.0634363	−	1.25521i
$461$			14.7025i			0.684762i	0.939561	+	0.342381i	$0.111233\pi$
$461$			14.7025i			0.684762i	−0.939561	+	0.342381i	$0.888767\pi$
$462$	14.1293	+	1.20493i	0.657353	+	0.0560586i
$463$	−10.0165			−0.465505			−0.232753	−	0.972536i	$-0.574773\pi$
$463$	−10.0165			−0.465505			−0.232753	+	0.972536i	$0.574773\pi$
$464$	−12.8970	+	0.119733i	−0.598730	+	0.00555845i
$465$	9.78869	−	21.1071i	0.453940	−	0.978820i
$466$	−13.6630	+	33.2033i	−0.632928	+	1.53811i
$467$		−	13.9720i		−	0.646546i	−0.946306	−	0.323273i	$-0.895217\pi$
$467$		−	13.9720i		−	0.646546i	0.946306	−	0.323273i	$-0.104783\pi$
$468$	1.27144	−	7.40037i	0.0587725	−	0.342082i
$469$	−6.51634			−0.300896
$470$	24.1823	−	11.4104i	1.11545	−	0.526322i
$471$	2.06736	−	0.651547i	0.0952591	−	0.0300217i
$472$	−18.6262	+	7.86761i	−0.857341	+	0.362136i
$473$	36.3867			1.67306
$474$	1.60000	−	18.7619i	0.0734906	−	0.861763i
$475$	6.23104	−	0.573042i	0.285900	−	0.0262930i
$476$	3.05840	+	3.03014i	0.140182	+	0.138886i
$477$	24.3919	−	17.0701i	1.11683	−	0.781587i
$478$	0.0110603	−	0.0268783i	0.000505888	−	0.00122938i
$479$	−40.5144			−1.85115			−0.925576	−	0.378563i	$-0.876418\pi$
$479$	−40.5144			−1.85115			−0.925576	+	0.378563i	$0.876418\pi$
$480$	15.0213	+	15.9487i	0.685625	+	0.727955i
$481$	7.04643			0.321289
$482$	−2.49196	+	6.05583i	−0.113506	+	0.275836i
$483$	−9.95705	+	3.13804i	−0.453061	+	0.142786i
$484$	−31.9880	−	31.6924i	−1.45400	−	1.44056i
$485$	8.97375	+	8.18635i	0.407477	+	0.371723i
$486$	−9.28318	+	19.9956i	−0.421094	+	0.907017i
$487$	−2.19326			−0.0993861			−0.0496931	−	0.998765i	$-0.515824\pi$
$487$	−2.19326			−0.0993861			−0.0496931	+	0.998765i	$0.515824\pi$
$488$	−9.70821	+	4.10069i	−0.439470	+	0.185630i
$489$	7.76378	+	24.6346i	0.351090	+	1.11401i
$490$	1.34944	+	2.85990i	0.0609614	+	0.129197i
$491$	39.7569			1.79420			0.897101	−	0.441826i	$-0.145669\pi$
$491$	39.7569			1.79420			0.897101	+	0.441826i	$0.145669\pi$
$492$	13.5584	+	6.98045i	0.611259	+	0.314703i
$493$		−	6.94099i		−	0.312607i
$494$	0.842853	−	2.04826i	0.0379218	−	0.0921556i
$495$	−4.99332	+	38.5127i	−0.224433	+	1.73102i
$496$	24.0285	−	0.223074i	1.07891	−	0.0100163i
$497$	−16.2113			−0.727176
$498$	−0.578683	+	6.78574i	−0.0259314	+	0.304076i
$499$			13.5317i			0.605763i	0.953028	+	0.302882i	$0.0979487\pi$
$499$			13.5317i			0.605763i	−0.953028	+	0.302882i	$0.902051\pi$
$500$	−3.16906	−	22.1350i	−0.141725	−	0.989906i
$501$	28.5672	−	9.00319i	1.27629	−	0.402233i
$502$	−1.80940	+	4.39711i	−0.0807574	+	0.196253i
$503$		−	19.7144i		−	0.879020i	−0.898238	−	0.439510i	$-0.855152\pi$
$503$		−	19.7144i		−	0.879020i	0.898238	−	0.439510i	$-0.144848\pi$
$504$	4.51104	−	7.18683i	0.200938	−	0.320127i
$505$	4.59296	+	4.18995i	0.204384	+	0.186450i
$506$	45.6348	+	18.7786i	2.02872	+	0.834811i
$507$	−5.95276	−	18.8881i	−0.264371	−	0.838852i
$508$	6.77314	+	6.71056i	0.300510	+	0.297733i
$509$		−	33.3980i		−	1.48034i	−0.672420	−	0.740170i	$-0.734745\pi$
$509$		−	33.3980i		−	1.48034i	0.672420	−	0.740170i	$-0.265255\pi$
$510$	−8.65766	+	8.00387i	−0.383368	+	0.354417i
$511$		−	10.3348i		−	0.457186i
$512$	−8.22062	+	21.0813i	−0.363304	+	0.931671i
$513$	−3.96064	+	5.15751i	−0.174867	+	0.227710i
$514$	11.8398	−	28.7726i	0.522232	−	1.26910i
$515$	14.1199	−	15.4780i	0.622195	−	0.682041i
$516$	9.96633	−	19.3580i	0.438743	−	0.852188i
$517$			48.9513i			2.15288i
$518$	7.36370	+	3.03014i	0.323542	+	0.133137i
$519$	−12.9770	−	41.1760i	−0.569626	−	1.80743i
$520$	−7.46219	−	2.63866i	−0.327238	−	0.115713i
$521$		−	16.1254i		−	0.706466i	−0.935535	−	0.353233i	$-0.885082\pi$
$521$		−	16.1254i		−	0.706466i	0.935535	−	0.353233i	$-0.114918\pi$
$522$	−13.3495	+	2.98846i	−0.584294	+	0.130801i
$523$	38.0965			1.66585			0.832923	−	0.553390i	$-0.186666\pi$
$523$	38.0965			1.66585			0.832923	+	0.553390i	$0.186666\pi$
$524$	−24.1592	−	23.9360i	−1.05540	−	1.04565i
$525$	−7.98666	+	3.34862i	−0.348567	+	0.146146i
$526$	−8.50221	−	3.49864i	−0.370714	−	0.152548i
$527$			12.9318i			0.563317i
$528$	−38.1403	+	12.4106i	−1.65984	+	0.540103i
$529$	−13.3300			−0.579566
$530$	−13.3917	−	28.3814i	−0.581699	−	1.23281i
$531$	−17.5708	+	12.2965i	−0.762509	+	0.533624i
$532$	1.76161	−	1.77804i	0.0763754	−	0.0770877i
$533$	−5.50926			−0.238632
$534$	3.55792	−	41.7208i	0.153966	−	1.80544i
$535$	0.273994	+	0.249952i	0.0118458	+	0.0108064i
$536$	16.9785	−	7.17162i	0.733359	−	0.309767i
$537$	−4.42964	−	14.0553i	−0.191153	−	0.606530i
$538$	−34.6028	−	14.2389i	−1.49183	−	0.613885i
$539$	−5.78918			−0.249358
$540$	19.1213	+	13.2051i	0.822851	+	0.568257i
$541$	−21.2011			−0.911506			−0.455753	−	0.890106i	$-0.650630\pi$
$541$	−21.2011			−0.911506			−0.455753	+	0.890106i	$0.650630\pi$
$542$	−0.324106	−	0.133369i	−0.0139216	−	0.00572868i
$543$	10.9382	+	34.7069i	0.469401	+	1.48941i
$544$	−11.3036	−	4.52916i	−0.484638	−	0.194186i
$545$	−5.67470	+	6.22052i	−0.243077	+	0.266458i
$546$	−0.260474	+	3.05437i	−0.0111473	+	0.130715i
$547$	−13.8033			−0.590188			−0.295094	−	0.955468i	$-0.595351\pi$
$547$	−13.8033			−0.590188			−0.295094	+	0.955468i	$0.595351\pi$
$548$	−16.1108	−	15.9619i	−0.688219	−	0.681860i
$549$	−9.15813	+	6.40911i	−0.390860	+	0.273534i
$550$	39.1234	+	12.0453i	1.66823	+	0.513614i
$551$	−4.03522			−0.171906
$552$	22.4897	−	19.1346i	0.957227	−	0.814422i
$553$			7.68732i			0.326898i
$554$	−2.92337	−	1.20296i	−0.124202	−	0.0511087i
$555$	−9.17464	+	19.7831i	−0.389442	+	0.839745i
$556$	−8.24970	+	8.32664i	−0.349865	+	0.353128i
$557$	−36.0698			−1.52833			−0.764163	−	0.645023i	$-0.776848\pi$
$557$	−36.0698			−1.52833			−0.764163	+	0.645023i	$0.776848\pi$
$558$	24.8716	−	5.56781i	1.05290	−	0.235704i
$559$			7.86584i			0.332690i
$560$	−6.66349	−	5.96640i	−0.281584	−	0.252126i
$561$	−6.48809	−	20.5868i	−0.273927	−	0.869174i
$562$	8.99830	+	3.70277i	0.379570	+	0.156192i
$563$			1.37983i			0.0581529i	0.999577	+	0.0290764i	$0.00925662\pi$
$563$			1.37983i			0.0581529i	−0.999577	+	0.0290764i	$0.990743\pi$
$564$	26.0425	+	13.4078i	1.09658	+	0.564570i
$565$	−11.5775	+	12.6911i	−0.487068	+	0.533917i
$566$	−13.2062	+	32.0930i	−0.555097	+	1.34897i
$567$	3.08251	−	8.45566i	0.129453	−	0.355104i
$568$	42.2389	−	17.8415i	1.77231	−	0.748612i
$569$		−	2.27946i		−	0.0955598i	−0.998858	−	0.0477799i	$-0.984785\pi$
$569$		−	2.27946i		−	0.0955598i	0.998858	−	0.0477799i	$-0.0152146\pi$
$570$	4.65314	+	5.03323i	0.194898	+	0.210819i
$571$		−	14.4566i		−	0.604989i	−0.953151	−	0.302494i	$-0.902181\pi$
$571$		−	14.4566i		−	0.604989i	0.953151	−	0.302494i	$-0.0978194\pi$
$572$	10.1983	−	10.2934i	0.426411	−	0.430388i
$573$	−1.89328	−	6.00738i	−0.0790927	−	0.250962i
$574$	−5.75732	−	2.36912i	−0.240306	−	0.0988851i
$575$	−30.0106	+	2.75994i	−1.25153	+	0.115097i
$576$	−3.84409	+	23.6901i	−0.160171	+	0.987089i
$577$			25.3482i			1.05526i	0.849475	+	0.527629i	$0.176919\pi$
$577$			25.3482i			1.05526i	−0.849475	+	0.527629i	$0.823081\pi$
$578$	−6.65497	+	16.1726i	−0.276810	+	0.672691i
$579$	−0.566446	+	0.178520i	−0.0235407	+	0.00741904i
$580$	0.727834	+	14.4016i	0.0302217	+	0.597992i
$581$		−	2.78032i		−	0.115347i
$582$	−1.13063	+	13.2580i	−0.0468663	+	0.549563i
$583$	57.4513			2.37939
$584$	11.3741	+	26.9277i	0.470663	+	1.11427i
$585$	−8.32541	−	1.07942i	−0.344213	−	0.0446287i
$586$	−8.52311	+	20.7124i	−0.352086	+	0.855623i
$587$			23.5726i			0.972947i	0.873695	+	0.486473i	$0.161717\pi$
$587$			23.5726i			0.972947i	−0.873695	+	0.486473i	$0.838283\pi$
$588$	−1.58566	+	3.07988i	−0.0653914	+	0.127012i
$589$	7.51804			0.309775
$590$	9.64677	+	20.4446i	0.397151	+	0.841692i
$591$	4.64790	+	14.7478i	0.191189	+	0.606645i
$592$	−22.5212	+	0.209081i	−0.925614	+	0.00859316i
$593$	18.5551			0.761965			0.380982	−	0.924582i	$-0.375586\pi$
$593$	18.5551			0.761965			0.380982	+	0.924582i	$0.375586\pi$
$594$	−36.8009	+	21.3421i	−1.50996	+	0.875679i
$595$	3.24404	−	3.55607i	0.132993	−	0.145785i
$596$	−28.5676	+	28.8340i	−1.17017	+	1.18109i
$597$	−14.0586	+	4.43070i	−0.575382	+	0.181336i
$598$	−4.05943	+	9.86504i	−0.166003	+	0.403411i
$599$	−18.2041			−0.743798			−0.371899	−	0.928273i	$-0.621293\pi$
$599$	−18.2041			−0.743798			−0.371899	+	0.928273i	$0.621293\pi$
$600$	17.1241	−	17.5147i	0.699089	−	0.715035i
$601$	−21.5208			−0.877850			−0.438925	−	0.898524i	$-0.644641\pi$
$601$	−21.5208			−0.877850			−0.438925	+	0.898524i	$0.644641\pi$
$602$	−3.38251	+	8.22001i	−0.137861	+	0.335023i
$603$	16.0165	−	11.2088i	0.652241	−	0.456456i
$604$	−5.60878	+	5.66110i	−0.228218	+	0.230347i
$605$	−33.9296	+	37.1931i	−1.37943	+	1.51212i
$606$	−0.578683	+	6.78574i	−0.0235074	+	0.275652i
$607$	10.6531			0.432396			0.216198	−	0.976350i	$-0.430634\pi$
$607$	10.6531			0.432396			0.216198	+	0.976350i	$0.430634\pi$
$608$	−2.63308	+	6.57148i	−0.106785	+	0.266509i
$609$	5.32655	−	1.67871i	0.215843	−	0.0680246i
$610$	5.02801	+	10.6560i	0.203578	+	0.431449i
$611$	−10.5820			−0.428101
$612$	−12.7294	−	2.18701i	−0.514555	−	0.0884047i
$613$			37.5613i			1.51708i	0.651624	+	0.758542i	$0.274088\pi$
$613$			37.5613i			1.51708i	−0.651624	+	0.758542i	$0.725912\pi$
$614$	−6.37010	+	15.4803i	−0.257076	+	0.624734i
$615$	7.17320	−	15.4674i	0.289251	−	0.623706i
$616$	15.0839	−	6.37134i	0.607746	−	0.256709i
$617$	−9.19759			−0.370281			−0.185141	−	0.982712i	$-0.559274\pi$
$617$	−9.19759			−0.370281			−0.185141	+	0.982712i	$0.559274\pi$
$618$	22.8675	+	1.95012i	0.919866	+	0.0784455i
$619$			17.7722i			0.714325i	0.934042	+	0.357162i	$0.116256\pi$
$619$			17.7722i			0.714325i	−0.934042	+	0.357162i	$0.883744\pi$
$620$	−1.35603	−	26.8316i	−0.0544594	−	1.07758i
$621$	19.0756	−	24.8401i	0.765479	−	0.996799i
$622$	−1.46331	+	3.55607i	−0.0586736	+	0.142586i
$623$			17.0943i			0.684868i
$624$	−2.68284	−	8.24491i	−0.107400	−	0.330060i
$625$	−24.5807	+	4.55972i	−0.983226	+	0.182389i
$626$	3.18274	+	1.30969i	0.127208	+	0.0523457i
$627$	−11.9683	+	3.77192i	−0.477970	+	0.150636i
$628$	1.76161	−	1.77804i	0.0702958	−	0.0709514i
$629$		−	12.1206i		−	0.483279i
$630$	−8.23609	−	4.70816i	−0.328134	−	0.187578i
$631$			43.0769i			1.71486i	0.514597	+	0.857432i	$0.327942\pi$
$631$			43.0769i			1.71486i	−0.514597	+	0.857432i	$0.672058\pi$
$632$	−8.46036	−	20.0295i	−0.336535	−	0.796731i
$633$	40.7276	−	12.8356i	1.61878	−	0.510170i
$634$	−0.354146	+	0.860627i	−0.0140649	+	0.0341799i
$635$	7.18426	−	7.87529i	0.285099	−	0.312521i
$636$	15.7359	−	30.5645i	0.623970	−	1.21196i
$637$		−	1.25147i		−	0.0495849i
$638$	−24.4125	−	10.0457i	−0.966500	−	0.397712i
$639$	39.8457	−	27.8851i	1.57627	−	1.10312i
$640$	23.9283	+	8.21205i	0.945848	+	0.324610i
$641$			32.0090i			1.26428i	0.774855	+	0.632139i	$0.217823\pi$
$641$			32.0090i			1.26428i	−0.774855	+	0.632139i	$0.782177\pi$
$642$	−0.0345215	+	0.404805i	−0.00136245	+	0.0159764i
$643$	16.8762			0.665534			0.332767	−	0.943009i	$-0.392018\pi$
$643$	16.8762			0.665534			0.332767	+	0.943009i	$0.392018\pi$
$644$	−8.48443	+	8.56356i	−0.334333	+	0.337452i
$645$	−22.0836	−	10.2415i	−0.869541	−	0.403260i
$646$	−3.52321	−	1.44979i	−0.138619	−	0.0570413i
$647$		−	8.92011i		−	0.350686i	−0.984507	−	0.175343i	$-0.943897\pi$
$647$		−	8.92011i		−	0.350686i	0.984507	−	0.175343i	$-0.0561034\pi$
$648$	1.27441	+	25.4239i	0.0500635	+	0.998746i
$649$	−41.3853			−1.62452
$650$	−2.60388	+	8.45744i	−0.102132	+	0.331728i
$651$	−9.92391	+	3.12760i	−0.388949	+	0.122580i
$652$	21.1870	+	20.9912i	0.829746	+	0.822078i
$653$	−13.9805			−0.547101			−0.273550	−	0.961858i	$-0.588198\pi$
$653$	−13.9805			−0.547101			−0.273550	+	0.961858i	$0.588198\pi$
$654$	−9.19033	−	0.783745i	−0.359371	−	0.0306469i
$655$	−25.6256	+	28.0904i	−1.00128	+	1.09758i
$656$	17.6082	−	0.163470i	0.687485	−	0.00638243i
$657$	17.7769	+	25.4019i	0.693544	+	0.991023i
$658$	−11.0584	−	4.55052i	−0.431103	−	0.177398i
$659$	1.96153			0.0764102			0.0382051	−	0.999270i	$-0.487836\pi$
$659$	1.96153			0.0764102			0.0382051	+	0.999270i	$0.487836\pi$
$660$	15.6206	+	42.0342i	0.608030	+	1.63618i
$661$	−21.4255			−0.833357			−0.416678	−	0.909054i	$-0.636806\pi$
$661$	−21.4255			−0.833357			−0.416678	+	0.909054i	$0.636806\pi$
$662$	−41.5445	−	17.0954i	−1.61467	−	0.664433i
$663$	4.45031	−	1.40255i	0.172836	−	0.0544706i
$664$	3.05991	+	7.24420i	0.118748	+	0.281129i
$665$	−2.06736	−	1.88596i	−0.0801689	−	0.0731345i
$666$	−23.3114	+	5.21854i	−0.903297	+	0.202214i
$667$	19.4349			0.752521
$668$	24.3422	−	24.5692i	0.941828	−	0.950612i
$669$	−6.20279	−	19.6815i	−0.239814	−	0.760931i
$670$	−8.79339	−	18.6361i	−0.339718	−	0.719974i
$671$	−21.5705			−0.832721
$672$	0.741876	−	9.76983i	0.0286185	−	0.376879i
$673$		−	49.5149i		−	1.90866i	−0.298756	−	0.954330i	$-0.596572\pi$
$673$		−	49.5149i		−	1.90866i	0.298756	−	0.954330i	$-0.403428\pi$
$674$	7.73221	+	3.18178i	0.297834	+	0.122558i
$675$	13.8704	−	21.9684i	0.533873	−	0.845565i
$676$	−16.2448	−	16.0946i	−0.624798	−	0.619025i
$677$	−32.7175			−1.25744			−0.628718	−	0.777634i	$-0.716420\pi$
$677$	−32.7175			−1.25744			−0.628718	+	0.777634i	$0.716420\pi$
$678$	−18.7500	−	1.59899i	−0.720091	−	0.0614089i
$679$		−	5.43221i		−	0.208469i
$680$	−4.53877	+	12.8357i	−0.174054	+	0.492227i
$681$	26.9725	−	8.50062i	1.03359	−	0.325744i
$682$	45.4830	+	18.7161i	1.74163	+	0.716677i
$683$			6.93269i			0.265272i	0.991165	+	0.132636i	$0.0423441\pi$
$683$			6.93269i			0.265272i	−0.991165	+	0.132636i	$0.957656\pi$
$684$	−1.27144	+	7.40037i	−0.0486149	+	0.282960i
$685$	−17.0887	+	18.7324i	−0.652926	+	0.715728i
$686$	0.538162	−	1.30782i	0.0205471	−	0.0499326i
$687$	9.14095	+	29.0043i	0.348749	+	1.10658i
$688$	−0.233394	−	25.1401i	−0.00889807	−	0.958458i
$689$			12.4194i			0.473143i
$690$	−22.4109	−	24.2415i	−0.853169	−	0.922859i
$691$		−	22.4168i		−	0.852774i	−0.904541	−	0.426387i	$-0.859786\pi$
$691$		−	22.4168i		−	0.852774i	0.904541	−	0.426387i	$-0.140214\pi$
$692$	−35.4135	−	35.0862i	−1.34622	−	1.33378i
$693$	14.2292	−	9.95798i	0.540523	−	0.378272i
$694$	4.82434	+	1.98520i	0.183129	+	0.0753572i
$695$	9.68157	+	8.83205i	0.367243	+	0.335019i
$696$	−12.0310	+	10.2361i	−0.456032	+	0.387998i
$697$			9.47648i			0.358947i
$698$	6.39930	−	15.5513i	0.242217	−	0.588624i
$699$	13.2178	+	41.9403i	0.499945	+	1.58633i
$700$	−6.35803	+	7.71851i	−0.240311	+	0.291732i
$701$		−	28.2111i		−	1.06552i	−0.846267	−	0.532759i	$-0.821155\pi$
$701$		−	28.2111i		−	1.06552i	0.846267	−	0.532759i	$-0.178845\pi$
$702$	−4.61360	−	7.95536i	−0.174129	−	0.300256i
$703$	−7.04643			−0.265761
$704$	−32.2894	+	33.2014i	−1.21695	+	1.25132i
$705$	13.7780	−	29.7092i	0.518910	−	1.11891i
$706$	−5.35173	+	13.0055i	−0.201415	+	0.489469i
$707$		−	2.78032i		−	0.104565i
$708$	−11.3354	+	22.0173i	−0.426012	+	0.827459i
$709$	−8.32308			−0.312580			−0.156290	−	0.987711i	$-0.549953\pi$
$709$	−8.32308			−0.312580			−0.156290	+	0.987711i	$0.549953\pi$
$710$	−21.8761	−	46.3626i	−0.820997	−	1.73996i
$711$	−13.2230	−	18.8946i	−0.495900	−	0.708604i
$712$	−18.8133	−	44.5396i	−0.705057	−	1.66919i
$713$	−36.2091			−1.35604
$714$	5.25382	+	0.448042i	0.196619	+	0.0167676i
$715$	−11.9683	−	10.9182i	−0.447591	−	0.408317i
$716$	−12.0882	−	11.9765i	−0.451759	−	0.447584i
$717$	−0.0106999	−	0.0339510i	−0.000399597	−	0.00126792i
$718$	−4.36579	+	10.6095i	−0.162930	+	0.395944i
$719$	10.2622			0.382717			0.191358	−	0.981520i	$-0.438711\pi$
$719$	10.2622			0.382717			0.191358	+	0.981520i	$0.438711\pi$
$720$	26.6410	+	3.20293i	0.992850	+	0.119366i
$721$	−9.36951			−0.348939
$722$	9.38223	−	22.8002i	0.349170	−	0.848537i
$723$	2.41076	+	7.64936i	0.0896571	+	0.284483i
$724$	29.8497	+	29.5738i	1.10935	+	1.09910i
$725$	16.0542	−	1.47644i	0.596239	−	0.0548335i
$726$	−54.9499	−	4.68609i	−2.03938	−	0.173917i
$727$	−20.2338			−0.750429			−0.375214	−	0.926938i	$-0.622431\pi$
$727$	−20.2338			−0.750429			−0.375214	+	0.926938i	$0.622431\pi$
$728$	1.37731	+	3.26073i	0.0510467	+	0.120851i
$729$	6.96811	+	26.0854i	0.258078	+	0.966124i
$730$	29.5565	−	13.9462i	1.09394	−	0.516172i
$731$	13.5300			0.500427
$732$	−5.90817	+	11.4757i	−0.218372	+	0.424153i
$733$		−	26.9906i		−	0.996921i	−0.866912	−	0.498461i	$-0.833899\pi$
$733$		−	26.9906i		−	0.996921i	0.866912	−	0.498461i	$-0.166101\pi$
$734$	−5.08488	+	12.3570i	−0.187687	+	0.456107i
$735$	3.51353	+	1.62944i	0.129599	+	0.0601029i
$736$	12.6817	−	31.6502i	0.467453	−	1.16664i
$737$	37.7243			1.38959
$738$	18.2260	−	4.08012i	0.670909	−	0.150191i
$739$			47.1410i			1.73411i	0.498213	+	0.867055i	$0.333990\pi$
$739$			47.1410i			1.73411i	−0.498213	+	0.867055i	$0.666010\pi$
$740$	1.27096	+	25.1484i	0.0467216	+	0.924475i
$741$	−0.815389	−	2.58724i	−0.0299541	−	0.0950445i
$742$	−5.34067	+	12.9786i	−0.196062	+	0.476461i
$743$			26.1235i			0.958377i	0.877712	+	0.479188i	$0.159069\pi$
$743$			26.1235i			0.958377i	−0.877712	+	0.479188i	$0.840931\pi$
$744$	22.4149	−	19.0709i	0.821770	−	0.699173i
$745$	33.5259	+	30.5842i	1.22830	+	1.12052i
$746$	−28.5916	−	11.7654i	−1.04681	−	0.430761i
$747$	4.78243	+	6.83374i	0.174980	+	0.250033i
$748$	−17.7057	−	17.5420i	−0.647383	−	0.641401i
$749$		−	0.165861i		−	0.00606042i
$750$	−20.3542	−	18.3223i	−0.743231	−	0.669035i
$751$		−	16.8916i		−	0.616384i	−0.951324	−	0.308192i	$-0.900276\pi$
$751$		−	16.8916i		−	0.616384i	0.951324	−	0.308192i	$-0.0997238\pi$
$752$	33.8212	−	0.313987i	1.23333	−	0.0114499i
$753$	1.75044	+	5.55416i	0.0637896	+	0.202405i
$754$	2.17161	−	5.27733i	0.0790852	−	0.192189i
$755$	6.58228	+	6.00472i	0.239554	+	0.218534i
$756$	−1.40033	−	10.2975i	−0.0509295	−	0.374517i
$757$			5.23388i			0.190229i	0.995466	+	0.0951144i	$0.0303217\pi$
$757$			5.23388i			0.190229i	−0.995466	+	0.0951144i	$0.969678\pi$
$758$	−13.7754	−	5.66854i	−0.500346	−	0.205891i
$759$	57.6432	−	18.1667i	2.09231	−	0.659410i
$760$	7.46219	+	2.63866i	0.270682	+	0.0957144i
$761$			11.0771i			0.401544i	0.979638	+	0.200772i	$0.0643451\pi$
$761$			11.0771i			0.401544i	−0.979638	+	0.200772i	$0.935655\pi$
$762$	11.6351	+	0.992235i	0.421496	+	0.0359449i
$763$	3.76556			0.136322
$764$	−5.16665	−	5.11891i	−0.186923	−	0.185196i
$765$	−1.85672	+	14.3205i	−0.0671297	+	0.517760i
$766$	14.5387	+	5.98263i	0.525305	+	0.216161i
$767$		−	8.94640i		−	0.323036i
$768$	8.81931	+	26.2720i	0.318239	+	0.948010i
$769$	32.2304			1.16226			0.581128	−	0.813812i	$-0.302611\pi$
$769$	32.2304			1.16226			0.581128	+	0.813812i	$0.302611\pi$
$770$	−7.81215	−	16.5565i	−0.281530	−	0.596654i
$771$	−11.4540	−	36.3437i	−0.412507	−	1.30889i
$772$	−0.482670	+	0.487172i	−0.0173717	+	0.0175337i
$773$	8.49330			0.305483			0.152741	−	0.988266i	$-0.451190\pi$
$773$	8.49330			0.305483			0.152741	+	0.988266i	$0.451190\pi$
$774$	−5.82539	−	26.0222i	−0.209389	−	0.935348i
$775$	−29.9107	+	2.75076i	−1.07442	+	0.0988101i
$776$	5.97847	+	14.1538i	0.214615	+	0.508091i
$777$	9.30138	−	2.93141i	0.333685	−	0.105164i
$778$	−37.8305	−	15.5672i	−1.35629	−	0.558110i
$779$	5.50926			0.197390
$780$	−9.08668	+	3.37675i	−0.325355	+	0.120907i
$781$	93.8501			3.35822
$782$	16.9689	+	6.98264i	0.606805	+	0.249699i
$783$	−10.2046	+	13.2883i	−0.364681	+	0.474885i
$784$	0.0371333	+	3.99983i	0.00132619	+	0.142851i
$785$	−2.06736	−	1.88596i	−0.0737874	−	0.0673129i
$786$	−41.5014	−	3.53921i	−1.48031	−	0.126240i
$787$	−20.2423			−0.721562			−0.360781	−	0.932651i	$-0.617490\pi$
$787$	−20.2423			−0.721562			−0.360781	+	0.932651i	$0.617490\pi$
$788$	12.6839	+	12.5667i	0.451845	+	0.447670i
$789$	−10.7395	+	3.38463i	−0.382336	+	0.120496i
$790$	−21.9850	+	10.3736i	−0.782190	+	0.369075i
$791$	7.68246			0.273157
$792$	−26.1152	+	41.6059i	−0.927964	+	1.47840i
$793$		−	4.66297i		−	0.165587i
$794$	6.40893	+	2.63726i	0.227444	+	0.0935927i
$795$	−34.8680	−	16.1705i	−1.23664	−	0.573507i
$796$	−11.9794	+	12.0911i	−0.424599	+	0.428559i
$797$	18.8977			0.669390			0.334695	−	0.942327i	$-0.391367\pi$
$797$	18.8977			0.669390			0.334695	+	0.942327i	$0.391367\pi$
$798$	0.260474	−	3.05437i	0.00922069	−	0.108123i
$799$			18.2021i			0.643943i
$800$	8.07134	−	27.1082i	0.285365	−	0.958419i
$801$	−29.4039	−	42.0160i	−1.03894	−	1.48456i
$802$	16.6642	+	6.85725i	0.588432	+	0.242138i
$803$			59.8302i			2.11136i
$804$	10.3327	−	20.0696i	0.364406	−	0.707799i
$805$	9.95705	+	9.08336i	0.350940	+	0.320146i
$806$	−4.04592	+	9.83221i	−0.142512	+	0.346325i
$807$	−43.7081	+	13.7750i	−1.53860	+	0.484902i
$808$	3.05991	+	7.24420i	0.107647	+	0.254850i
$809$			35.0938i			1.23383i	0.787029	+	0.616916i	$0.211618\pi$
$809$			35.0938i			1.23383i	−0.787029	+	0.616916i	$0.788382\pi$
$810$	28.3420	−	2.59474i	0.995835	−	0.0911698i
$811$		−	1.54486i		−	0.0542475i	−0.999632	−	0.0271238i	$-0.991365\pi$
$811$		−	1.54486i		−	0.0542475i	0.999632	−	0.0271238i	$-0.00863482\pi$
$812$	4.53877	−	4.58110i	0.159280	−	0.160765i
$813$	−0.409391	+	0.129023i	−0.0143580	+	0.00452504i
$814$	−42.6298	−	17.5420i	−1.49417	−	0.614848i
$815$	22.4730	−	24.6346i	0.787194	−	0.862911i
$816$	−14.1821	+	4.61476i	−0.496472	+	0.161549i
$817$		−	7.86584i		−	0.275191i
$818$	12.5304	−	30.4506i	0.438114	−	1.06468i
$819$	2.15265	+	3.07598i	0.0752196	+	0.107483i
$820$	−0.993705	−	19.6623i	−0.0347017	−	0.686638i
$821$		−	10.7091i		−	0.373751i	−0.982384	−	0.186875i	$-0.940164\pi$
$821$		−	10.7091i		−	0.373751i	0.982384	−	0.186875i	$-0.0598360\pi$
$822$	−27.6756	−	2.36016i	−0.965299	−	0.0823200i
$823$	24.1451			0.841646			0.420823	−	0.907143i	$-0.361741\pi$
$823$	24.1451			0.841646			0.420823	+	0.907143i	$0.361741\pi$
$824$	24.4125	−	10.3117i	0.850450	−	0.359225i
$825$	46.2362	−	19.3858i	1.60974	−	0.674925i
$826$	3.84718	−	9.34922i	0.133860	−	0.325301i
$827$			28.3687i			0.986477i	0.869894	+	0.493239i	$0.164187\pi$
$827$			28.3687i			0.986477i	−0.869894	+	0.493239i	$0.835813\pi$
$828$	6.12365	−	35.6424i	0.212812	−	1.23866i
$829$	6.84119			0.237604			0.118802	−	0.992918i	$-0.462095\pi$
$829$	6.84119			0.237604			0.118802	+	0.992918i	$0.462095\pi$
$830$	7.95143	−	3.75187i	0.275998	−	0.130229i
$831$	−3.69262	+	1.16376i	−0.128096	+	0.0403704i
$832$	−7.17726	−	6.98010i	−0.248827	−	0.241991i
$833$	−2.15265			−0.0745849
$834$	−1.21981	+	14.3038i	−0.0422387	+	0.495299i
$835$	−28.5672	−	26.0605i	−0.988608	−	0.901862i
$836$	−10.1983	+	10.2934i	−0.352714	+	0.356004i
$837$	19.0122	−	24.7574i	0.657156	−	0.855743i
$838$	−14.0421	+	34.1243i	−0.485075	+	1.17881i
$839$	13.3011			0.459204			0.229602	−	0.973285i	$-0.426258\pi$
$839$	13.3011			0.459204			0.229602	+	0.973285i	$0.426258\pi$
$840$	−10.9479	−	0.378706i	−0.377739	−	0.0130666i
$841$	18.6033			0.641492
$842$	−13.5927	+	33.0323i	−0.468435	+	1.13837i
$843$	11.3661	−	3.58212i	0.391469	−	0.123375i
$844$	34.7041	−	35.0278i	1.19456	−	1.20571i
$845$	−17.2308	+	18.8881i	−0.592757	+	0.649772i
$846$	35.0078	−	7.83694i	1.20359	−	0.269439i
$847$	22.5146			0.773612
$848$	−0.368508	−	39.6939i	−0.0126546	−	1.36310i
$849$	12.7759	+	40.5379i	0.438467	+	1.39126i
$850$	14.5476	+	4.47893i	0.498980	+	0.153626i
$851$	33.9377			1.16337
$852$	25.7056	−	49.9289i	0.880658	−	1.71054i
$853$		−	42.1115i		−	1.44187i	−0.693003	−	0.720935i	$-0.743713\pi$
$853$		−	42.1115i		−	1.44187i	0.693003	−	0.720935i	$-0.256287\pi$
$854$	2.00520	−	4.87293i	0.0686164	−	0.166748i
$855$	8.32541	+	1.07942i	0.284723	+	0.0369155i
$856$	0.182540	+	0.432155i	0.00623908	+	0.0147707i
$857$	39.6068			1.35294			0.676472	−	0.736468i	$-0.263508\pi$
$857$	39.6068			1.35294			0.676472	+	0.736468i	$0.263508\pi$
$858$	1.50793	−	17.6823i	0.0514800	−	0.603664i
$859$		−	15.2014i		−	0.518664i	−0.965788	−	0.259332i	$-0.916498\pi$
$859$		−	15.2014i		−	0.518664i	0.965788	−	0.259332i	$-0.0835023\pi$
$860$	−28.0729	+	1.41876i	−0.957277	+	0.0483794i
$861$	−7.27229	+	2.29192i	−0.247839	+	0.0781085i
$862$	13.3620	−	32.4716i	0.455111	−	1.10599i
$863$		−	34.3202i		−	1.16827i	−0.811655	−	0.584137i	$-0.801433\pi$
$863$		−	34.3202i		−	1.16827i	0.811655	−	0.584137i	$-0.198567\pi$
$864$	14.9816	+	25.2893i	0.509686	+	0.860361i
$865$	−37.5630	+	41.1760i	−1.27718	+	1.40003i
$866$	18.4233	+	7.58114i	0.626050	+	0.257618i
$867$	6.43812	+	20.4282i	0.218650	+	0.693779i
$868$	−8.45619	+	8.53506i	−0.287022	+	0.289699i
$869$		−	44.5033i		−	1.50967i
$870$	11.9888	+	12.9681i	0.406458	+	0.439659i
$871$			8.15498i			0.276321i
$872$	−9.81126	+	4.14422i	−0.332251	+	0.140341i
$873$	9.34395	+	13.3518i	0.316245	+	0.451890i
$874$	4.05943	−	9.86504i	0.137312	−	0.333690i
$875$	8.91510	+	6.74692i	0.301386	+	0.228087i
$876$	31.8301	+	16.3875i	1.07544	+	0.553682i
$877$		−	35.8474i		−	1.21048i	−0.796043	−	0.605240i	$-0.793077\pi$
$877$		−	35.8474i		−	1.21048i	0.796043	−	0.605240i	$-0.206923\pi$
$878$	8.88847	+	3.65758i	0.299971	+	0.123437i
$879$	8.24539	+	26.1627i	0.278110	+	0.882446i
$880$	38.5761	+	34.5406i	1.30040	+	1.16436i
$881$		−	50.3468i		−	1.69623i	−0.529815	−	0.848113i	$-0.677739\pi$
$881$		−	50.3468i		−	1.69623i	0.529815	−	0.848113i	$-0.322261\pi$
$882$	0.926828	+	4.14017i	0.0312079	+	0.139407i
$883$	10.0543			0.338353			0.169176	−	0.985586i	$-0.445889\pi$
$883$	10.0543			0.338353			0.169176	+	0.985586i	$0.445889\pi$
$884$	3.79212	−	3.82749i	0.127543	−	0.128732i
$885$	25.1173	+	11.6485i	0.844309	+	0.391559i
$886$	−37.2943	−	15.3465i	−1.25293	−	0.515576i
$887$		−	34.0330i		−	1.14271i	−0.820701	−	0.571357i	$-0.806417\pi$
$887$		−	34.0330i		−	1.14271i	0.820701	−	0.571357i	$-0.193583\pi$
$888$	−21.0088	+	17.8746i	−0.705009	+	0.599832i
$889$	−4.76726			−0.159889
$890$	−48.8879	+	23.0677i	−1.63873	+	0.773230i
$891$	−17.8452	+	48.9513i	−0.597836	+	1.63993i
$892$	−16.9271	−	16.7707i	−0.566761	−	0.561524i
$893$	10.5820			0.354112
$894$	−4.22405	+	49.5320i	−0.141273	+	1.65660i
$895$	−12.8220	+	14.0553i	−0.428592	+	0.469816i
$896$	−4.49880	−	10.3808i	−0.150294	−	0.346798i
$897$	3.92716	+	12.4609i	0.131124	+	0.416058i
$898$	−3.87971	−	1.59649i	−0.129468	−	0.0532756i
$899$	19.3702			0.646032
$900$	2.35076	−	29.9078i	0.0783588	−	0.996925i
$901$	21.3627			0.711695
$902$	33.3302	+	13.7153i	1.10977	+	0.456668i
$903$	3.27229	+	10.3830i	0.108895	+	0.345525i
$904$	−20.0168	+	8.45501i	−0.665750	+	0.281209i
$905$	31.6615	−	34.7069i	1.05246	−	1.15370i
$906$	−0.829325	+	9.72481i	−0.0275525	+	0.323085i
$907$	−44.0509			−1.46268			−0.731342	−	0.682011i	$-0.761106\pi$
$907$	−44.0509			−1.46268			−0.731342	+	0.682011i	$0.761106\pi$
$908$	22.9834	−	23.1977i	0.762730	−	0.769844i
$909$	4.78243	+	6.83374i	0.158623	+	0.226661i
$910$	3.57907	−	1.68878i	0.118645	−	0.0559824i
$911$	−7.25251			−0.240287			−0.120143	−	0.992757i	$-0.538335\pi$
$911$	−7.25251			−0.240287			−0.120143	+	0.992757i	$0.538335\pi$
$912$	2.68284	+	8.24491i	0.0888378	+	0.273016i
$913$			16.0958i			0.532693i
$914$	1.70421	+	0.701276i	0.0563701	+	0.0231961i
$915$	13.0914	+	6.07132i	0.432790	+	0.200712i
$916$	24.9452	+	24.7147i	0.824212	+	0.816595i
$917$	17.0044			0.561534
$918$	−13.6840	+	7.93586i	−0.451640	+	0.261923i
$919$		−	17.0959i		−	0.563942i	−0.959423	−	0.281971i	$-0.909012\pi$
$919$		−	17.0959i		−	0.563942i	0.959423	−	0.281971i	$-0.0909881\pi$
$920$	−35.9401	−	12.7086i	−1.18491	−	0.418990i
$921$	6.16253	+	19.5538i	0.203062	+	0.644319i
$922$	19.2281	+	7.91231i	0.633244	+	0.260578i
$923$			20.2879i			0.667784i
$924$	9.17966	−	17.8300i	0.301989	−	0.586564i
$925$	28.0344	−	2.57820i	0.921765	−	0.0847707i
$926$	−5.39049	+	13.0997i	−0.177143	+	0.430483i
$927$	23.0293	−	16.1165i	0.756380	−	0.529335i
$928$	−6.78411	+	16.9314i	−0.222699	+	0.555799i
$929$		−	26.6686i		−	0.874970i	−0.899226	−	0.437485i	$-0.855869\pi$
$929$		−	26.6686i		−	0.874970i	0.899226	−	0.437485i	$-0.144131\pi$
$930$	−22.3363	−	24.1609i	−0.732437	−	0.792266i
$931$			1.25147i			0.0410152i
$932$	36.0708	+	35.7375i	1.18154	+	1.17062i
$933$	1.41563	+	4.49182i	0.0463457	+	0.147055i
$934$	−18.2728	−	7.51919i	−0.597903	−	0.246035i
$935$	−18.7804	+	20.5868i	−0.614184	+	0.673259i
$936$	−8.99408	−	5.64542i	−0.293981	−	0.184526i
$937$		−	59.8497i		−	1.95521i	−0.210460	−	0.977603i	$-0.567496\pi$
$937$		−	59.8497i		−	1.95521i	0.210460	−	0.977603i	$-0.432504\pi$
$938$	−3.50685	+	8.52217i	−0.114503	+	0.278259i
$939$	4.02024	−	1.26701i	0.131196	−	0.0413474i
$940$	−1.90867	−	37.7667i	−0.0622540	−	1.23181i
$941$			28.8016i			0.938904i	0.882958	+	0.469452i	$0.155548\pi$
$941$			28.8016i			0.938904i	−0.882958	+	0.469452i	$0.844452\pi$
$942$	0.260474	−	3.05437i	0.00848671	−	0.0995167i
$943$	−26.5342			−0.864074
$944$	0.265456	+	28.5937i	0.00863987	+	0.930645i
$945$	−11.4387	+	2.03863i	−0.372101	+	0.0663165i
$946$	19.5820	−	47.5871i	0.636665	−	1.54719i
$947$		−	16.9524i		−	0.550878i	−0.961319	−	0.275439i	$-0.911177\pi$
$947$		−	16.9524i		−	0.550878i	0.961319	−	0.275439i	$-0.0888231\pi$
$948$	−23.6761	−	12.1895i	−0.768963	−	0.395895i
$949$	−12.9337			−0.419845
$950$	2.60388	−	8.45744i	0.0844809	−	0.274396i
$951$	0.342606	+	1.08709i	0.0111098	+	0.0352514i
$952$	5.60878	−	2.36912i	0.181782	−	0.0767836i
$953$	0.716464			0.0232085			0.0116043	−	0.999933i	$-0.496306\pi$
$953$	0.716464			0.0232085			0.0116043	+	0.999933i	$0.496306\pi$
$954$	−9.19775	−	41.0867i	−0.297788	−	1.33023i
$955$	−5.48026	+	6.00738i	−0.177337	+	0.194394i
$956$	−0.0291996	−	0.0289298i	−0.000944382	−	0.000935655i
$957$	−30.8364	+	9.71834i	−0.996798	+	0.314149i
$958$	−21.8033	+	52.9854i	−0.704434	+	1.71188i
$959$	11.3395			0.366173
$960$	28.9418	−	11.0621i	0.934094	−	0.357028i
$961$	−5.08863			−0.164149
$962$	3.79212	−	9.21543i	0.122263	−	0.297117i
$963$	0.285297	+	0.407669i	0.00919358	+	0.0131369i
$964$	6.57883	+	6.51804i	0.211890	+	0.209932i
$965$	0.566446	+	0.516743i	0.0182345	+	0.0166345i
$966$	−1.25452	+	14.7108i	−0.0403636	+	0.473311i
$967$	−22.4139			−0.720784			−0.360392	−	0.932801i	$-0.617357\pi$
$967$	−22.4139			−0.720784			−0.360392	+	0.932801i	$0.617357\pi$
$968$	−58.6625	+	24.7787i	−1.88548	+	0.796418i
$969$	−4.45031	+	1.40255i	−0.142965	+	0.0450565i
$970$	15.5356	−	7.33043i	0.498817	−	0.235366i
$971$	−17.0969			−0.548664			−0.274332	−	0.961635i	$-0.588457\pi$
$971$	−17.0969			−0.548664			−0.274332	+	0.961635i	$0.588457\pi$
$972$	21.1546	+	22.9015i	0.678536	+	0.734567i
$973$		−	5.86068i		−	0.187885i
$974$	−1.18033	+	2.86838i	−0.0378202	+	0.0919088i
$975$	4.19068	+	9.99504i	0.134209	+	0.320098i
$976$	0.138359	+	14.9034i	0.00442877	+	0.477046i
$977$	−18.2715			−0.584556			−0.292278	−	0.956333i	$-0.594413\pi$
$977$	−18.2715			−0.584556			−0.292278	+	0.956333i	$0.594413\pi$
$978$	36.3956	+	3.10379i	1.16380	+	0.0992484i
$979$		−	98.9619i		−	3.16284i
$980$	4.46644	−	0.225727i	0.142675	−	0.00721059i
$981$	−9.25535	+	6.47714i	−0.295501	+	0.206799i
$982$	21.3956	−	51.9946i	0.682762	−	1.65922i
$983$			16.0403i			0.511605i	0.966729	+	0.255802i	$0.0823397\pi$
$983$			16.0403i			0.511605i	−0.966729	+	0.255802i	$0.917660\pi$
$984$	16.4258	−	13.9753i	0.523634	−	0.445515i
$985$	13.4538	−	14.7478i	0.428673	−	0.469905i
$986$	−9.07754	−	3.73538i	−0.289088	−	0.118959i
$987$	−13.9683	+	4.40224i	−0.444617	+	0.140125i
$988$	−2.22515	−	2.20459i	−0.0707916	−	0.0701374i
$989$			37.8842i			1.20465i
$990$	47.6802	+	27.2564i	1.51538	+	0.866266i
$991$		−	36.4251i		−	1.15708i	−0.815654	−	0.578540i	$-0.803623\pi$
$991$		−	36.4251i		−	1.15708i	0.815654	−	0.578540i	$-0.196377\pi$
$992$	12.6395	−	31.5449i	0.401304	−	1.00155i
$993$	−52.4765	+	16.5384i	−1.66529	+	0.524830i
$994$	−8.72430	+	21.2014i	−0.276718	+	0.672467i
$995$	14.0586	+	12.8251i	0.445689	+	0.406582i
$996$	8.56307	+	4.40864i	0.271331	+	0.139693i
$997$		−	4.54344i		−	0.143892i	−0.997409	−	0.0719462i	$-0.977079\pi$
$997$		−	4.54344i		−	0.143892i	0.997409	−	0.0719462i	$-0.0229210\pi$
$998$	17.6970	+	7.28227i	0.560189	+	0.230516i
$999$	−17.8195	+	23.2044i	−0.563784	+	0.734155i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.l.h.239.9	yes	16
3.2	odd	2	inner	420.2.l.h.239.8	yes	16
4.3	odd	2		420.2.l.g.239.10	yes	16
5.4	even	2		420.2.l.g.239.8	yes	16
12.11	even	2		420.2.l.g.239.7	✓	16
15.14	odd	2		420.2.l.g.239.9	yes	16
20.19	odd	2	inner	420.2.l.h.239.7	yes	16
60.59	even	2	inner	420.2.l.h.239.10	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.l.g.239.7	✓	16	12.11	even	2
420.2.l.g.239.8	yes	16	5.4	even	2
420.2.l.g.239.9	yes	16	15.14	odd	2
420.2.l.g.239.10	yes	16	4.3	odd	2
420.2.l.h.239.7	yes	16	20.19	odd	2	inner
420.2.l.h.239.8	yes	16	3.2	odd	2	inner
420.2.l.h.239.9	yes	16	1.1	even	1	trivial
420.2.l.h.239.10	yes	16	60.59	even	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.538162 - 1.30782i) q^{2} +(-0.520627 - 1.65195i) q^{3} +(-1.42076 - 1.40763i) q^{4} +(-1.50700 + 1.65195i) q^{5} +(-2.44063 - 0.208135i) q^{6} +1.00000 q^{7} +(-2.60553 + 1.10056i) q^{8} +(-2.45790 + 1.72010i) q^{9} +O(q^{10})\)	\(q+(0.538162 - 1.30782i) q^{2} +(-0.520627 - 1.65195i) q^{3} +(-1.42076 - 1.40763i) q^{4} +(-1.50700 + 1.65195i) q^{5} +(-2.44063 - 0.208135i) q^{6} +1.00000 q^{7} +(-2.60553 + 1.10056i) q^{8} +(-2.45790 + 1.72010i) q^{9} +(1.34944 + 2.85990i) q^{10} -5.78918 q^{11} +(-1.58566 + 3.07988i) q^{12} -1.25147i q^{13} +(0.538162 - 1.30782i) q^{14} +(3.51353 + 1.62944i) q^{15} +(0.0371333 + 3.99983i) q^{16} -2.15265 q^{17} +(0.926828 + 4.14017i) q^{18} +1.25147i q^{19} +(4.46644 - 0.225727i) q^{20} +(-0.520627 - 1.65195i) q^{21} +(-3.11552 + 7.57118i) q^{22} -6.02744i q^{23} +(3.17458 + 3.73123i) q^{24} +(-0.457896 - 4.97899i) q^{25} +(-1.63669 - 0.673492i) q^{26} +(4.12117 + 3.16480i) q^{27} +(-1.42076 - 1.40763i) q^{28} +3.22440i q^{29} +(4.02186 - 3.71815i) q^{30} -6.00738i q^{31} +(5.25102 + 2.10399i) q^{32} +(3.01400 + 9.56346i) q^{33} +(-1.15847 + 2.81527i) q^{34} +(-1.50700 + 1.65195i) q^{35} +(5.91336 + 1.01596i) q^{36} +5.63054i q^{37} +(1.63669 + 0.673492i) q^{38} +(-2.06736 + 0.651547i) q^{39} +(2.10846 - 5.96275i) q^{40} -4.40224i q^{41} +(-2.44063 - 0.208135i) q^{42} -6.28530 q^{43} +(8.22505 + 8.14905i) q^{44} +(0.862526 - 6.65252i) q^{45} +(-7.88278 - 3.24374i) q^{46} -8.45566i q^{47} +(6.58819 - 2.14376i) q^{48} +1.00000 q^{49} +(-6.75802 - 2.08066i) q^{50} +(1.12073 + 3.55607i) q^{51} +(-1.76161 + 1.77804i) q^{52} -9.92391 q^{53} +(6.35683 - 3.68656i) q^{54} +(8.72430 - 9.56346i) q^{55} +(-2.60553 + 1.10056i) q^{56} +(2.06736 - 0.651547i) q^{57} +(4.21692 + 1.73525i) q^{58} +7.14873 q^{59} +(-2.69824 - 7.26082i) q^{60} +3.72601 q^{61} +(-7.85655 - 3.23295i) q^{62} +(-2.45790 + 1.72010i) q^{63} +(5.57754 - 5.73508i) q^{64} +(2.06736 + 1.88596i) q^{65} +(14.1293 + 1.20493i) q^{66} -6.51634 q^{67} +(3.05840 + 3.03014i) q^{68} +(-9.95705 + 3.13804i) q^{69} +(1.34944 + 2.85990i) q^{70} -16.2113 q^{71} +(4.51104 - 7.18683i) q^{72} -10.3348i q^{73} +(7.36370 + 3.03014i) q^{74} +(-7.98666 + 3.34862i) q^{75} +(1.76161 - 1.77804i) q^{76} -5.78918 q^{77} +(-0.260474 + 3.05437i) q^{78} +7.68732i q^{79} +(-6.66349 - 5.96640i) q^{80} +(3.08251 - 8.45566i) q^{81} +(-5.75732 - 2.36912i) q^{82} -2.78032i q^{83} +(-1.58566 + 3.07988i) q^{84} +(3.24404 - 3.55607i) q^{85} +(-3.38251 + 8.22001i) q^{86} +(5.32655 - 1.67871i) q^{87} +(15.0839 - 6.37134i) q^{88} +17.0943i q^{89} +(-8.23609 - 4.70816i) q^{90} -1.25147i q^{91} +(-8.48443 + 8.56356i) q^{92} +(-9.92391 + 3.12760i) q^{93} +(-11.0584 - 4.55052i) q^{94} +(-2.06736 - 1.88596i) q^{95} +(0.741876 - 9.76983i) q^{96} -5.43221i q^{97} +(0.538162 - 1.30782i) q^{98} +(14.2292 - 9.95798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4} - 10 q^{6} + 16 q^{7}+O(q^{10}) \) 16 * q + 6 * q^4 - 10 * q^6 + 16 * q^7	\( 16 q + 6 q^{4} - 10 q^{6} + 16 q^{7} + 14 q^{10} + 16 q^{12} + 24 q^{15} - 10 q^{16} + 8 q^{18} - 12 q^{22} + 6 q^{24} + 32 q^{25} - 24 q^{27} + 6 q^{28} - 26 q^{30} - 76 q^{34} + 6 q^{36} + 2 q^{40} - 10 q^{42} - 16 q^{43} + 12 q^{45} - 52 q^{46} + 28 q^{48} + 16 q^{49} - 44 q^{52} - 6 q^{54} + 8 q^{55} + 4 q^{58} + 36 q^{60} + 40 q^{61} + 6 q^{64} - 8 q^{66} + 56 q^{67} - 64 q^{69} + 14 q^{70} - 16 q^{72} - 12 q^{75} + 44 q^{76} + 20 q^{78} + 16 q^{81} + 44 q^{82} + 16 q^{84} - 16 q^{85} - 16 q^{87} + 4 q^{88} - 10 q^{90} - 56 q^{94} + 34 q^{96}+O(q^{100}) \) 16 * q + 6 * q^4 - 10 * q^6 + 16 * q^7 + 14 * q^10 + 16 * q^12 + 24 * q^15 - 10 * q^16 + 8 * q^18 - 12 * q^22 + 6 * q^24 + 32 * q^25 - 24 * q^27 + 6 * q^28 - 26 * q^30 - 76 * q^34 + 6 * q^36 + 2 * q^40 - 10 * q^42 - 16 * q^43 + 12 * q^45 - 52 * q^46 + 28 * q^48 + 16 * q^49 - 44 * q^52 - 6 * q^54 + 8 * q^55 + 4 * q^58 + 36 * q^60 + 40 * q^61 + 6 * q^64 - 8 * q^66 + 56 * q^67 - 64 * q^69 + 14 * q^70 - 16 * q^72 - 12 * q^75 + 44 * q^76 + 20 * q^78 + 16 * q^81 + 44 * q^82 + 16 * q^84 - 16 * q^85 - 16 * q^87 + 4 * q^88 - 10 * q^90 - 56 * q^94 + 34 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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