LMFDB - Embedded newform 392.3.k.n.275.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(67,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("392.67");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.k (of order $6$, degree $2$, not 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:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - x^{15} + 3 x^{14} + 6 x^{13} - 22 x^{12} + 44 x^{11} - 20 x^{10} - 112 x^{9} + 368 x^{8} + \cdots + 65536 $ x^16 - x^15 + 3x^14 + 6x^13 - 22x^12 + 44x^11 - 20x^10 - 112x^9 + 368x^8 - 448x^7 - 320x^6 + 2816x^5 - 5632x^4 + 6144x^3 + 12288x^2 - 16384x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.2
Root			$0.288997 - 1.97901i$ of defining polynomial
Character	$\chi$	$=$	392.275
Dual form			392.3.k.n.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56937 + 1.23978i) q^{2} +(0.0487183 + 0.0843825i) q^{3} +(0.925871 - 3.89137i) q^{4} +(-3.00119 - 1.73274i) q^{5} +(-0.181073 - 0.0720276i) q^{6} +(3.37142 + 7.25490i) q^{8} +(4.49525 - 7.78601i) q^{9} +O(q^{10})$	\(q+(-1.56937 + 1.23978i) q^{2} +(0.0487183 + 0.0843825i) q^{3} +(0.925871 - 3.89137i) q^{4} +(-3.00119 - 1.73274i) q^{5} +(-0.181073 - 0.0720276i) q^{6} +(3.37142 + 7.25490i) q^{8} +(4.49525 - 7.78601i) q^{9} +(6.85820 - 1.00151i) q^{10} +(1.46433 + 2.53629i) q^{11} +(0.373471 - 0.111454i) q^{12} +19.1586i q^{13} -0.337664i q^{15} +(-14.2855 - 7.20582i) q^{16} +(-7.19487 - 12.4619i) q^{17} +(2.59823 + 17.7923i) q^{18} +(4.04872 - 7.01259i) q^{19} +(-9.52143 + 10.0744i) q^{20} +(-5.44254 - 2.16494i) q^{22} +(-14.5144 - 8.37990i) q^{23} +(-0.447937 + 0.637935i) q^{24} +(-6.49525 - 11.2501i) q^{25} +(-23.7525 - 30.0670i) q^{26} +1.75293 q^{27} -27.1649i q^{29} +(0.418630 + 0.529921i) q^{30} +(-38.8779 + 22.4461i) q^{31} +(31.3530 - 6.40234i) q^{32} +(-0.142679 + 0.247128i) q^{33} +(26.7415 + 10.6373i) q^{34} +(-26.1362 - 24.7015i) q^{36} +(-34.2675 - 19.7844i) q^{37} +(2.34014 + 16.0249i) q^{38} +(-1.61665 + 0.933373i) q^{39} +(2.45256 - 27.6151i) q^{40} -45.8766 q^{41} +61.0334 q^{43} +(11.2254 - 3.34997i) q^{44} +(-26.9822 + 15.5782i) q^{45} +(33.1678 - 4.84354i) q^{46} +(-40.0790 - 23.1396i) q^{47} +(-0.0879212 - 1.55650i) q^{48} +(24.1412 + 9.60292i) q^{50} +(0.701044 - 1.21424i) q^{51} +(74.5532 + 17.7384i) q^{52} +(8.39546 - 4.84712i) q^{53} +(-2.75101 + 2.17326i) q^{54} -10.1492i q^{55} +0.788986 q^{57} +(33.6786 + 42.6319i) q^{58} +(-57.2770 - 99.2066i) q^{59} +(-1.31397 - 0.312633i) q^{60} +(-6.47814 - 3.74016i) q^{61} +(33.1855 - 83.4265i) q^{62} +(-41.2671 + 48.9186i) q^{64} +(33.1968 - 57.4985i) q^{65} +(-0.0824679 - 0.564728i) q^{66} +(6.02950 + 10.4434i) q^{67} +(-55.1553 + 16.4598i) q^{68} -1.63302i q^{69} -129.187i q^{71} +(71.6421 + 6.36270i) q^{72} +(-9.14268 - 15.8356i) q^{73} +(78.3069 - 11.4353i) q^{74} +(0.632875 - 1.09617i) q^{75} +(-23.5400 - 22.2478i) q^{76} +(1.37995 - 3.46911i) q^{78} +(36.9073 + 21.3084i) q^{79} +(30.3877 + 46.3790i) q^{80} +(-40.3719 - 69.9261i) q^{81} +(71.9976 - 56.8771i) q^{82} +109.670 q^{83} +49.8673i q^{85} +(-95.7842 + 75.6682i) q^{86} +(2.29224 - 1.32343i) q^{87} +(-13.4637 + 19.1745i) q^{88} +(-40.4581 + 70.0755i) q^{89} +(23.0316 - 57.9001i) q^{90} +(-46.0478 + 48.7223i) q^{92} +(-3.78812 - 2.18707i) q^{93} +(91.5872 - 13.3746i) q^{94} +(-24.3019 + 14.0307i) q^{95} +(2.06771 + 2.33373i) q^{96} -162.086 q^{97} +26.3301 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9}+O(q^{10}) $ 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9	$ 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9} + 16 q^{10} + 32 q^{11} + 30 q^{12} + 71 q^{16} - 80 q^{17} + 29 q^{18} + 56 q^{19} + 216 q^{20} + 132 q^{22} + 22 q^{24} + 16 q^{25} + 24 q^{26} + 64 q^{27} - 96 q^{30} + 19 q^{32} + 32 q^{33} - 148 q^{34} - 66 q^{36} - 14 q^{38} + 84 q^{40} - 256 q^{41} - 50 q^{44} + 152 q^{46} - 268 q^{48} + 66 q^{50} + 368 q^{51} + 132 q^{52} - 228 q^{54} + 112 q^{57} - 24 q^{58} + 104 q^{59} - 192 q^{60} - 240 q^{62} - 110 q^{64} + 72 q^{65} - 276 q^{66} - 304 q^{67} - 190 q^{68} + 209 q^{72} - 112 q^{73} - 8 q^{74} + 72 q^{75} - 140 q^{76} - 608 q^{78} + 124 q^{80} - 48 q^{81} + 450 q^{82} - 144 q^{83} - 210 q^{86} + 486 q^{88} - 512 q^{89} + 368 q^{90} - 944 q^{92} + 472 q^{94} + 558 q^{96} - 128 q^{97} + 512 q^{99}+O(q^{100}) $ 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9 + 16 * q^10 + 32 * q^11 + 30 * q^12 + 71 * q^16 - 80 * q^17 + 29 * q^18 + 56 * q^19 + 216 * q^20 + 132 * q^22 + 22 * q^24 + 16 * q^25 + 24 * q^26 + 64 * q^27 - 96 * q^30 + 19 * q^32 + 32 * q^33 - 148 * q^34 - 66 * q^36 - 14 * q^38 + 84 * q^40 - 256 * q^41 - 50 * q^44 + 152 * q^46 - 268 * q^48 + 66 * q^50 + 368 * q^51 + 132 * q^52 - 228 * q^54 + 112 * q^57 - 24 * q^58 + 104 * q^59 - 192 * q^60 - 240 * q^62 - 110 * q^64 + 72 * q^65 - 276 * q^66 - 304 * q^67 - 190 * q^68 + 209 * q^72 - 112 * q^73 - 8 * q^74 + 72 * q^75 - 140 * q^76 - 608 * q^78 + 124 * q^80 - 48 * q^81 + 450 * q^82 - 144 * q^83 - 210 * q^86 + 486 * q^88 - 512 * q^89 + 368 * q^90 - 944 * q^92 + 472 * q^94 + 558 * q^96 - 128 * q^97 + 512 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.56937	+	1.23978i	−0.784687	+	0.619892i
$2$	−1.56937	+	1.23978i	−0.784687	+	0.619892i
$3$	0.0487183	+	0.0843825i	0.0162394	+	0.0281275i	0.874031	−	0.485870i	$-0.161497\pi$
$3$	0.0487183	+	0.0843825i	0.0162394	+	0.0281275i	−0.857791	+	0.513998i	$0.828164\pi$
$4$	0.925871	−	3.89137i	0.231468	−	0.972843i
$5$	−3.00119	−	1.73274i	−0.600237	−	0.346547i	0.168898	−	0.985634i	$-0.445979\pi$
$5$	−3.00119	−	1.73274i	−0.600237	−	0.346547i	−0.769135	+	0.639086i	$0.779313\pi$
$6$	−0.181073	−	0.0720276i	−0.0301789	−	0.0120046i
$7$		0			0
$7$		0			0
$8$	3.37142	+	7.25490i	0.421428	+	0.906862i
$9$	4.49525	−	7.78601i	0.499473	−	0.865112i
$10$	6.85820	−	1.00151i	0.685820	−	0.100151i
$11$	1.46433	+	2.53629i	0.133121	+	0.230572i	0.924878	−	0.380264i	$-0.124167\pi$
$11$	1.46433	+	2.53629i	0.133121	+	0.230572i	−0.791757	+	0.610836i	$0.790833\pi$
$12$	0.373471	−	0.111454i	0.0311225	−	0.00928779i
$13$			19.1586i			1.47374i	0.676036	+	0.736869i	$0.263696\pi$
$13$			19.1586i			1.47374i	−0.676036	+	0.736869i	$0.736304\pi$
$14$		0			0
$15$		−	0.337664i		−	0.0225109i
$16$	−14.2855	−	7.20582i	−0.892845	−	0.450363i
$17$	−7.19487	−	12.4619i	−0.423228	−	0.733052i	0.573025	−	0.819538i	$-0.305770\pi$
$17$	−7.19487	−	12.4619i	−0.423228	−	0.733052i	−0.996253	+	0.0864856i	$0.972436\pi$
$18$	2.59823	+	17.7923i	0.144346	+	0.988461i
$19$	4.04872	−	7.01259i	0.213090	−	0.369083i	−0.739590	−	0.673058i	$-0.764980\pi$
$19$	4.04872	−	7.01259i	0.213090	−	0.369083i	0.952680	+	0.303975i	$0.0983138\pi$
$20$	−9.52143	+	10.0744i	−0.476071	+	0.503722i
$21$		0			0
$22$	−5.44254	−	2.16494i	−0.247388	−	0.0984064i
$23$	−14.5144	−	8.37990i	−0.631062	−	0.364344i	0.150101	−	0.988671i	$-0.452040\pi$
$23$	−14.5144	−	8.37990i	−0.631062	−	0.364344i	−0.781163	+	0.624327i	$0.785373\pi$
$24$	−0.447937	+	0.637935i	−0.0186640	+	0.0265806i
$25$	−6.49525	−	11.2501i	−0.259810	−	0.450004i
$26$	−23.7525	−	30.0670i	−0.913558	−	1.15642i
$27$	1.75293			0.0649234
$28$		0			0
$29$		−	27.1649i		−	0.936720i	−0.883538	−	0.468360i	$-0.844845\pi$
$29$		−	27.1649i		−	0.936720i	0.883538	−	0.468360i	$-0.155155\pi$
$30$	0.418630	+	0.529921i	0.0139543	+	0.0176640i
$31$	−38.8779	+	22.4461i	−1.25412	+	0.724069i	−0.971926	−	0.235287i	$-0.924397\pi$
$31$	−38.8779	+	22.4461i	−1.25412	+	0.724069i	−0.282198	+	0.959356i	$0.591064\pi$
$32$	31.3530	−	6.40234i	0.979781	−	0.200073i
$33$	−0.142679	+	0.247128i	−0.00432362	+	0.00748872i
$34$	26.7415	+	10.6373i	0.786515	+	0.312861i
$35$		0			0
$36$	−26.1362	−	24.7015i	−0.726006	−	0.686154i
$37$	−34.2675	−	19.7844i	−0.926149	−	0.534713i	−0.0405576	−	0.999177i	$-0.512913\pi$
$37$	−34.2675	−	19.7844i	−0.926149	−	0.534713i	−0.885592	+	0.464465i	$0.846247\pi$
$38$	2.34014	+	16.0249i	0.0615826	+	0.421708i
$39$	−1.61665	+	0.933373i	−0.0414526	+	0.0239327i
$40$	2.45256	−	27.6151i	0.0613140	−	0.690377i
$41$	−45.8766			−1.11894			−0.559471	−	0.828850i	$-0.688996\pi$
$41$	−45.8766			−1.11894			−0.559471	+	0.828850i	$0.688996\pi$
$42$		0			0
$43$	61.0334			1.41938			0.709690	−	0.704514i	$-0.248835\pi$
$43$	61.0334			1.41938			0.709690	+	0.704514i	$0.248835\pi$
$44$	11.2254	−	3.34997i	0.255124	−	0.0761357i
$45$	−26.9822	+	15.5782i	−0.599604	+	0.346182i
$46$	33.1678	−	4.84354i	0.721040	−	0.105294i
$47$	−40.0790	−	23.1396i	−0.852746	−	0.492333i	0.00883070	−	0.999961i	$-0.497189\pi$
$47$	−40.0790	−	23.1396i	−0.852746	−	0.492333i	−0.861576	+	0.507628i	$0.830522\pi$
$48$	−0.0879212	−	1.55650i	−0.00183169	−	0.0324272i
$49$		0			0
$50$	24.1412	+	9.60292i	0.482824	+	0.192058i
$51$	0.701044	−	1.21424i	0.0137460	−	0.0238087i
$52$	74.5532	+	17.7384i	1.43371	+	0.341123i
$53$	8.39546	−	4.84712i	0.158405	−	0.0914551i	−0.418702	−	0.908124i	$-0.637515\pi$
$53$	8.39546	−	4.84712i	0.158405	−	0.0914551i	0.577107	+	0.816669i	$0.304182\pi$
$54$	−2.75101	+	2.17326i	−0.0509446	+	0.0402455i
$55$		−	10.1492i		−	0.184531i
$56$		0			0
$57$	0.788986			0.0138419
$58$	33.6786	+	42.6319i	0.580665	+	0.735032i
$59$	−57.2770	−	99.2066i	−0.970796	−	1.68147i	−0.693164	−	0.720780i	$-0.743784\pi$
$59$	−57.2770	−	99.2066i	−0.970796	−	1.68147i	−0.277632	−	0.960687i	$-0.589550\pi$
$60$	−1.31397	−	0.312633i	−0.0218996	−	0.00521055i
$61$	−6.47814	−	3.74016i	−0.106199	−	0.0613141i	0.445960	−	0.895053i	$-0.352862\pi$
$61$	−6.47814	−	3.74016i	−0.106199	−	0.0613141i	−0.552159	+	0.833739i	$0.686196\pi$
$62$	33.1855	−	83.4265i	0.535251	−	1.34559i
$63$		0			0
$64$	−41.2671	+	48.9186i	−0.644798	+	0.764353i
$65$	33.1968	−	57.4985i	0.510720	−	0.884592i
$66$	−0.0824679	−	0.564728i	−0.00124951	−	0.00855648i
$67$	6.02950	+	10.4434i	0.0899925	+	0.155872i	0.907508	−	0.420035i	$-0.137982\pi$
$67$	6.02950	+	10.4434i	0.0899925	+	0.155872i	−0.817515	+	0.575907i	$0.804649\pi$
$68$	−55.1553	+	16.4598i	−0.811108	+	0.242056i
$69$		−	1.63302i		−	0.0236669i
$70$		0			0
$71$		−	129.187i		−	1.81953i	−0.415124	−	0.909765i	$-0.636262\pi$
$71$		−	129.187i		−	1.81953i	0.415124	−	0.909765i	$-0.363738\pi$
$72$	71.6421	+	6.36270i	0.995029	+	0.0883708i
$73$	−9.14268	−	15.8356i	−0.125242	−	0.216926i	0.796585	−	0.604526i	$-0.206637\pi$
$73$	−9.14268	−	15.8356i	−0.125242	−	0.216926i	−0.921828	+	0.387600i	$0.873304\pi$
$74$	78.3069	−	11.4353i	1.05820	−	0.154530i
$75$	0.632875	−	1.09617i	0.00843833	−	0.0146156i
$76$	−23.5400	−	22.2478i	−0.309737	−	0.292734i
$77$		0			0
$78$	1.37995	−	3.46911i	0.0176916	−	0.0444758i
$79$	36.9073	+	21.3084i	0.467180	+	0.269727i	0.715059	−	0.699064i	$-0.246400\pi$
$79$	36.9073	+	21.3084i	0.467180	+	0.269727i	−0.247878	+	0.968791i	$0.579733\pi$
$80$	30.3877	+	46.3790i	0.379847	+	0.579738i
$81$	−40.3719	−	69.9261i	−0.498418	−	0.863286i
$82$	71.9976	−	56.8771i	0.878019	−	0.693623i
$83$	109.670			1.32133			0.660663	−	0.750683i	$-0.270275\pi$
$83$	109.670			1.32133			0.660663	+	0.750683i	$0.270275\pi$
$84$		0			0
$85$			49.8673i			0.586674i
$86$	−95.7842	+	75.6682i	−1.11377	+	0.879863i
$87$	2.29224	−	1.32343i	0.0263476	−	0.0152118i
$88$	−13.4637	+	19.1745i	−0.152996	+	0.217892i
$89$	−40.4581	+	70.0755i	−0.454585	+	0.787365i	−0.998664	−	0.0516693i	$-0.983546\pi$
$89$	−40.4581	+	70.0755i	−0.454585	+	0.787365i	0.544079	+	0.839034i	$0.316879\pi$
$90$	23.0316	−	57.9001i	0.255906	−	0.643334i
$91$		0			0
$92$	−46.0478	+	48.7223i	−0.500519	+	0.529590i
$93$	−3.78812	−	2.18707i	−0.0407325	−	0.0235169i
$94$	91.5872	−	13.3746i	0.974332	−	0.142283i
$95$	−24.3019	+	14.0307i	−0.255810	+	0.147692i
$96$	2.06771	+	2.33373i	0.0215386	+	0.0243097i
$97$	−162.086			−1.67099			−0.835495	−	0.549498i	$-0.814819\pi$
$97$	−162.086			−1.67099			−0.835495	+	0.549498i	$0.814819\pi$
$98$		0			0
$99$	26.3301			0.265961
$100$	−49.7921	+	14.8593i	−0.497921	+	0.148593i
$101$	−92.5150	+	53.4135i	−0.915990	+	0.528847i	−0.882354	−	0.470587i	$-0.844042\pi$
$101$	−92.5150	+	53.4135i	−0.915990	+	0.528847i	−0.0336364	+	0.999434i	$0.510709\pi$
$102$	0.405199	+	2.77474i	0.00397254	+	0.0272034i
$103$	109.662	+	63.3132i	1.06468	+	0.614691i	0.926722	−	0.375748i	$-0.122614\pi$
$103$	109.662	+	63.3132i	1.06468	+	0.614691i	0.137954	+	0.990439i	$0.455947\pi$
$104$	−138.994	+	64.5916i	−1.33648	+	0.621074i
$105$		0			0
$106$	−7.16623	+	18.0155i	−0.0676060	+	0.169958i
$107$	−43.5096	+	75.3608i	−0.406632	+	0.704306i	−0.994510	−	0.104643i	$-0.966630\pi$
$107$	−43.5096	+	75.3608i	−0.406632	+	0.704306i	0.587878	+	0.808949i	$0.299963\pi$
$108$	1.62299	−	6.82131i	0.0150277	−	0.0631603i
$109$	−164.477	+	94.9607i	−1.50896	+	0.871199i	−0.509015	+	0.860758i	$0.669990\pi$
$109$	−164.477	+	94.9607i	−1.50896	+	0.871199i	−0.999945	+	0.0104412i	$0.996676\pi$
$110$	12.5828	+	15.9279i	0.114389	+	0.144799i
$111$		−	3.85544i		−	0.0347337i
$112$		0			0
$113$	−40.1848			−0.355617			−0.177809	−	0.984065i	$-0.556901\pi$
$113$	−40.1848			−0.355617			−0.177809	+	0.984065i	$0.556901\pi$
$114$	−1.23821	+	0.978173i	−0.0108615	+	0.00858046i
$115$	29.0403	+	50.2993i	0.252524	+	0.437385i
$116$	−105.709	−	25.1512i	−0.911281	−	0.216821i
$117$	149.169	+	86.1227i	1.27495	+	0.736091i
$118$	212.884	+	84.6812i	1.80410	+	0.717638i
$119$		0			0
$120$	2.44971	−	1.13841i	0.0204143	−	0.00948672i
$121$	56.2115	−	97.3611i	0.464558	−	0.804637i
$122$	14.8036	−	2.16179i	0.121341	−	0.0177196i
$123$	−2.23503	−	3.87119i	−0.0181710	−	0.0314731i
$124$	51.3503	+	172.070i	0.414116	+	1.38766i
$125$			131.655i			1.05324i
$126$		0			0
$127$			153.657i			1.20989i	0.796266	+	0.604947i	$0.206806\pi$
$127$			153.657i			1.20989i	−0.796266	+	0.604947i	$0.793194\pi$
$128$	4.11494	−	127.934i	0.0321480	−	0.999483i
$129$	2.97344	+	5.15015i	0.0230499	+	0.0399236i
$130$	19.1876	+	131.393i	0.147597	+	1.01072i
$131$	30.9325	−	53.5766i	0.236126	−	0.408982i	−0.723474	−	0.690352i	$-0.757456\pi$
$131$	30.9325	−	53.5766i	0.236126	−	0.408982i	0.959599	+	0.281371i	$0.0907890\pi$
$132$	0.829563	+	0.784026i	0.00628457	+	0.00593959i
$133$		0			0
$134$	−22.4101	−	8.91433i	−0.167240	−	0.0665248i
$135$	−5.26088	−	3.03737i	−0.0389695	−	0.0224990i
$136$	66.1528	−	94.2123i	0.486417	−	0.692738i
$137$	−52.9715	−	91.7494i	−0.386653	−	0.669703i	0.605344	−	0.795964i	$-0.293036\pi$
$137$	−52.9715	−	91.7494i	−0.386653	−	0.669703i	−0.991997	+	0.126261i	$0.959702\pi$
$138$	2.02459	+	2.56282i	0.0146709	+	0.0185711i
$139$	185.384			1.33370			0.666848	−	0.745194i	$-0.267643\pi$
$139$	185.384			1.33370			0.666848	+	0.745194i	$0.267643\pi$
$140$		0			0
$141$		−	4.50930i		−	0.0319808i
$142$	160.163	+	202.742i	1.12791	+	1.42776i
$143$	−48.5918	+	28.0545i	−0.339803	+	0.196185i
$144$	−120.322	+	78.8352i	−0.835567	+	0.547467i
$145$	−47.0696	+	81.5269i	−0.324618	+	0.562254i
$146$	33.9810	+	13.5170i	0.232747	+	0.0925823i
$147$		0			0
$148$	−108.716	+	115.030i	−0.734565	+	0.777229i
$149$	−41.0579	−	23.7048i	−0.275556	−	0.159093i	0.355854	−	0.934542i	$-0.384190\pi$
$149$	−41.0579	−	23.7048i	−0.275556	−	0.159093i	−0.631410	+	0.775449i	$0.717523\pi$
$150$	0.365798	+	2.50493i	0.00243866	+	0.0166995i
$151$	99.2255	−	57.2879i	0.657122	−	0.379390i	−0.134057	−	0.990974i	$-0.542801\pi$
$151$	99.2255	−	57.2879i	0.657122	−	0.379390i	0.791180	+	0.611584i	$0.209467\pi$
$152$	64.5255	+	5.73066i	0.424510	+	0.0377017i
$153$	−129.371			−0.845563
$154$		0			0
$155$	155.573			1.00370
$156$	2.13529	+	7.15517i	0.0136878	+	0.0458665i
$157$	254.694	−	147.047i	1.62225	−	0.936608i	0.635937	−	0.771741i	$-0.280614\pi$
$157$	254.694	−	147.047i	1.62225	−	0.936608i	0.986316	−	0.164867i	$-0.0527196\pi$
$158$	−84.3391	+	12.3161i	−0.533792	+	0.0779503i
$159$	0.818024	+	0.472287i	0.00514481	+	0.00297036i
$160$	−105.190	−	35.1118i	−0.657436	−	0.219449i
$161$		0			0
$162$	150.052	+	59.6879i	0.926246	+	0.368444i
$163$	−85.5104	+	148.108i	−0.524603	+	0.908640i	0.474986	+	0.879993i	$0.342453\pi$
$163$	−85.5104	+	148.108i	−0.524603	+	0.908640i	−0.999590	+	0.0286465i	$0.990880\pi$
$164$	−42.4758	+	178.523i	−0.258999	+	1.08855i
$165$	0.856414	−	0.494451i	0.00519039	−	0.00299667i
$166$	−172.113	+	135.967i	−1.03683	+	0.819079i
$167$		−	120.657i		−	0.722499i	−0.932469	−	0.361249i	$-0.882350\pi$
$167$		−	120.657i		−	0.722499i	0.932469	−	0.361249i	$-0.117650\pi$
$168$		0			0
$169$	−198.052			−1.17190
$170$	−61.8246	−	78.2604i	−0.363674	−	0.460355i
$171$	−36.4000	−	63.0467i	−0.212866	−	0.368694i
$172$	56.5090	−	237.503i	0.328541	−	1.38083i
$173$	−93.8242	−	54.1694i	−0.542336	−	0.313118i	0.203689	−	0.979036i	$-0.434707\pi$
$173$	−93.8242	−	54.1694i	−0.542336	−	0.313118i	−0.746025	+	0.665918i	$0.768040\pi$
$174$	−1.95662	+	4.91884i	−0.0112450	+	0.0282692i
$175$		0			0
$176$	−2.64266	−	46.7840i	−0.0150151	−	0.265818i
$177$	5.58087	−	9.66635i	0.0315303	−	0.0546121i
$178$	−23.3846	−	160.134i	−0.131374	−	0.899629i
$179$	80.7188	+	139.809i	0.450943	+	0.781056i	0.998445	−	0.0557481i	$-0.0177544\pi$
$179$	80.7188	+	139.809i	0.450943	+	0.781056i	−0.547502	+	0.836805i	$0.684421\pi$
$180$	35.6384	+	119.421i	0.197991	+	0.663450i
$181$			7.14696i			0.0394860i	0.999805	+	0.0197430i	$0.00628479\pi$
$181$			7.14696i			0.0394860i	−0.999805	+	0.0197430i	$0.993715\pi$
$182$		0			0
$183$		−	0.728856i		−	0.00398282i
$184$	11.8611	−	133.553i	0.0644627	−	0.725830i
$185$	68.5621	+	118.753i	0.370606	+	0.641909i
$186$	8.65648	−	1.26412i	0.0465402	−	0.00679633i
$187$	21.0713	−	36.4966i	0.112681	−	0.195169i
$188$	−127.153	+	134.538i	−0.676346	+	0.715628i
$189$		0			0
$190$	20.7437	−	52.1486i	0.109178	−	0.274466i
$191$	63.4782	+	36.6491i	0.332347	+	0.191880i	0.656882	−	0.753993i	$-0.271875\pi$
$191$	63.4782	+	36.6491i	0.332347	+	0.191880i	−0.324536	+	0.945873i	$0.605208\pi$
$192$	−6.13834	−	1.09899i	−0.0319705	−	0.00572390i
$193$	42.5353	+	73.6732i	0.220390	+	0.381727i	0.954926	−	0.296843i	$-0.0959337\pi$
$193$	42.5353	+	73.6732i	0.220390	+	0.381727i	−0.734536	+	0.678569i	$0.762600\pi$
$194$	254.374	−	200.952i	1.31120	−	1.03583i
$195$	6.46916			0.0331752
$196$		0			0
$197$			140.460i			0.712996i	0.934296	+	0.356498i	$0.116029\pi$
$197$			140.460i			0.712996i	−0.934296	+	0.356498i	$0.883971\pi$
$198$	−41.3218	+	32.6437i	−0.208696	+	0.164867i
$199$	123.913	−	71.5411i	0.622677	−	0.359503i	−0.155233	−	0.987878i	$-0.549613\pi$
$199$	123.913	−	71.5411i	0.622677	−	0.359503i	0.777911	+	0.628375i	$0.216280\pi$
$200$	59.7201	−	85.0512i	0.298601	−	0.425256i
$201$	−0.587494	+	1.01757i	−0.00292285	+	0.00506253i
$202$	78.9694	−	198.524i	0.390937	−	0.982794i
$203$		0			0
$204$	−4.07599	−	3.85225i	−0.0199804	−	0.0188836i
$205$	137.684	+	79.4921i	0.671631	+	0.387766i
$206$	−250.595	+	36.5947i	−1.21648	+	0.177644i
$207$	−130.492	+	75.3396i	−0.630396	+	0.363959i
$208$	138.053	−	273.690i	0.663718	−	1.31582i
$209$	23.7146			0.113467
$210$		0			0
$211$	−111.955			−0.530591			−0.265295	−	0.964167i	$-0.585469\pi$
$211$	−111.955			−0.530591			−0.265295	+	0.964167i	$0.585469\pi$
$212$	−11.0888	−	37.1576i	−0.0523058	−	0.175272i
$213$	10.9011	−	6.29375i	0.0511788	−	0.0295481i
$214$	−25.1483	−	172.212i	−0.117515	−	0.804728i
$215$	−183.173	−	105.755i	−0.851965	−	0.491882i
$216$	5.90987	+	12.7173i	0.0273605	+	0.0588766i
$217$		0			0
$218$	140.395	−	352.944i	0.644013	−	1.61901i
$219$	0.890831	−	1.54296i	0.00406772	−	0.00704550i
$220$	−39.4943	−	9.39684i	−0.179519	−	0.0427129i
$221$	238.752	−	137.844i	1.08033	−	0.623727i
$222$	4.77991	+	6.05063i	0.0215311	+	0.0272551i
$223$		−	311.438i		−	1.39658i	−0.715814	−	0.698291i	$-0.753944\pi$
$223$		−	311.438i		−	1.39658i	0.715814	−	0.698291i	$-0.246056\pi$
$224$		0			0
$225$	−116.791			−0.519072
$226$	63.0649	−	49.8204i	0.279048	−	0.220444i
$227$	37.1791	+	64.3960i	0.163784	+	0.283683i	0.936223	−	0.351407i	$-0.114297\pi$
$227$	37.1791	+	64.3960i	0.163784	+	0.283683i	−0.772439	+	0.635090i	$0.780963\pi$
$228$	0.730500	−	3.07024i	0.00320395	−	0.0134660i
$229$	−67.7847	−	39.1355i	−0.296003	−	0.170897i	0.344643	−	0.938734i	$-0.388000\pi$
$229$	−67.7847	−	39.1355i	−0.296003	−	0.170897i	−0.640646	+	0.767836i	$0.721333\pi$
$230$	−107.935	−	42.9347i	−0.469284	−	0.186673i
$231$		0			0
$232$	197.078	−	91.5842i	0.849476	−	0.394760i
$233$	−46.5287	+	80.5900i	−0.199694	+	0.345880i	−0.948429	−	0.316989i	$-0.897328\pi$
$233$	−46.5287	+	80.5900i	−0.199694	+	0.345880i	0.748735	+	0.662869i	$0.230661\pi$
$234$	−340.875	+	49.7785i	−1.45673	+	0.212728i
$235$	80.1898	+	138.893i	0.341233	+	0.591033i
$236$	−439.081	+	131.033i	−1.86051	+	0.555226i
$237$			4.15244i			0.0175208i
$238$		0			0
$239$		−	291.605i		−	1.22011i	−0.792361	−	0.610053i	$-0.791148\pi$
$239$		−	291.605i		−	1.22011i	0.792361	−	0.610053i	$-0.208852\pi$
$240$	−2.43314	+	4.82370i	−0.0101381	+	0.0200988i
$241$	111.874	+	193.771i	0.464207	+	0.804029i	0.999165	−	0.0408488i	$-0.0130062\pi$
$241$	111.874	+	193.771i	0.464207	+	0.804029i	−0.534959	+	0.844878i	$0.679673\pi$
$242$	32.4899	+	222.486i	0.134256	+	0.919364i
$243$	11.8219	−	20.4761i	0.0486498	−	0.0842639i
$244$	−20.5523	+	21.7459i	−0.0842306	+	0.0891227i
$245$		0			0
$246$	8.30703	+	3.30438i	0.0337684	+	0.0134325i
$247$	134.351	+	77.5677i	0.543932	+	0.314039i
$248$	−293.918	−	206.379i	−1.18515	−	0.832175i
$249$	5.34294	+	9.25424i	0.0214576	+	0.0371656i
$250$	−163.224	−	206.616i	−0.652895	−	0.826464i
$251$	310.605			1.23747			0.618734	−	0.785600i	$-0.287646\pi$
$251$	310.605			1.23747			0.618734	+	0.785600i	$0.287646\pi$
$252$		0			0
$253$		−	49.0838i		−	0.194007i
$254$	−190.501	−	241.145i	−0.750004	−	0.949389i
$255$	−4.20793	+	2.42945i	−0.0165017	+	0.00952724i
$256$	152.152	+	205.878i	0.594345	+	0.804210i
$257$	87.7358	−	151.963i	0.341385	−	0.591295i	−0.643306	−	0.765610i	$-0.722438\pi$
$257$	87.7358	−	151.963i	0.341385	−	0.591295i	0.984690	+	0.174314i	$0.0557708\pi$
$258$	−11.0515	−	4.39609i	−0.0428353	−	0.0170391i
$259$		0			0
$260$	−193.012	−	182.417i	−0.742354	−	0.701604i
$261$	−211.506	−	122.113i	−0.810368	−	0.467866i
$262$	17.8788	+	122.431i	0.0682397	+	0.467295i
$263$	270.310	−	156.064i	1.02779	−	0.593398i	0.111443	−	0.993771i	$-0.464453\pi$
$263$	270.310	−	156.064i	1.02779	−	0.593398i	0.916352	+	0.400373i	$0.131120\pi$
$264$	−2.27392	−	0.201952i	−0.00861333	−	0.000764970i
$265$	−33.5951			−0.126774
$266$		0			0
$267$	−7.88419			−0.0295288
$268$	46.2217	−	13.7938i	0.172469	−	0.0514693i
$269$	−123.683	+	71.4084i	−0.459788	+	0.265459i	−0.711955	−	0.702225i	$-0.752190\pi$
$269$	−123.683	+	71.4084i	−0.459788	+	0.265459i	0.252167	+	0.967684i	$0.418857\pi$
$270$	12.0220	−	1.75558i	0.0445258	−	0.00650216i
$271$	−230.464	−	133.059i	−0.850421	−	0.490991i	0.0103718	−	0.999946i	$-0.496699\pi$
$271$	−230.464	−	133.059i	−0.850421	−	0.490991i	−0.860793	+	0.508955i	$0.830032\pi$
$272$	12.9845	+	229.870i	0.0477371	+	0.845108i
$273$		0			0
$274$	196.882	+	78.3158i	0.718546	+	0.285824i
$275$	19.0224	−	32.9477i	0.0691723	−	0.119810i
$276$	−6.35468	−	1.51196i	−0.0230242	−	0.00547813i
$277$	317.606	−	183.370i	1.14659	−	0.661986i	0.198539	−	0.980093i	$-0.436380\pi$
$277$	317.606	−	183.370i	1.14659	−	0.661986i	0.948055	+	0.318107i	$0.103047\pi$
$278$	−290.936	+	229.836i	−1.04653	+	0.826747i
$279$			403.604i			1.44661i
$280$		0			0
$281$	147.977			0.526607			0.263303	−	0.964713i	$-0.415188\pi$
$281$	147.977			0.526607			0.263303	+	0.964713i	$0.415188\pi$
$282$	5.59055	+	7.07677i	0.0198247	+	0.0250949i
$283$	163.869	+	283.830i	0.579043	+	1.00293i	0.995589	+	0.0938180i	$0.0299072\pi$
$283$	163.869	+	283.830i	0.579043	+	1.00293i	−0.416546	+	0.909115i	$0.636759\pi$
$284$	−502.713	−	119.610i	−1.77012	−	0.421163i
$285$	−2.36790	−	1.36710i	−0.00830840	−	0.00479686i
$286$	41.4772	−	104.271i	0.145025	−	0.364585i
$287$		0			0
$288$	91.0909	−	272.895i	0.316288	−	0.947551i
$289$	40.9676	−	70.9580i	0.141756	−	0.245529i
$290$	−27.2060	−	186.302i	−0.0938137	−	0.642422i
$291$	−7.89655	−	13.6772i	−0.0271359	−	0.0470008i
$292$	−70.0871	+	20.9158i	−0.240024	+	0.0716296i
$293$		−	259.881i		−	0.886966i	−0.896283	−	0.443483i	$-0.853743\pi$
$293$		−	259.881i		−	0.886966i	0.896283	−	0.443483i	$-0.146257\pi$
$294$		0			0
$295$			396.983i			1.34571i
$296$	28.0033	−	315.309i	0.0946057	−	1.06523i
$297$	2.56687	+	4.44595i	0.00864267	+	0.0149695i
$298$	93.8240	−	13.7012i	0.314846	−	0.0459773i
$299$	160.547	−	278.076i	0.536947	−	0.930019i
$300$	−3.67965	−	3.47767i	−0.0122655	−	0.0115922i
$301$		0			0
$302$	−84.6974	+	212.924i	−0.280455	+	0.705047i
$303$	−9.01434	−	5.20443i	−0.0297503	−	0.0171763i
$304$	−108.369	+	71.0042i	−0.356479	+	0.233566i
$305$	12.9614	+	22.4498i	0.0424964	+	0.0736060i
$306$	203.032	−	160.392i	0.663502	−	0.524158i
$307$	−290.462			−0.946131			−0.473065	−	0.881027i	$-0.656853\pi$
$307$	−290.462			−0.946131			−0.473065	+	0.881027i	$0.656853\pi$
$308$		0			0
$309$			12.3380i			0.0399289i
$310$	−244.152	+	192.877i	−0.787587	+	0.622183i
$311$	64.8723	−	37.4540i	0.208593	−	0.120431i	−0.392065	−	0.919938i	$-0.628239\pi$
$311$	64.8723	−	37.4540i	0.208593	−	0.120431i	0.600657	+	0.799507i	$0.294906\pi$
$312$	−12.2219	−	8.58184i	−0.0391729	−	0.0275059i
$313$	142.254	−	246.391i	0.454485	−	0.787190i	−0.544174	−	0.838972i	$-0.683157\pi$
$313$	142.254	−	246.391i	0.454485	−	0.787190i	0.998658	+	0.0517821i	$0.0164901\pi$
$314$	−217.403	+	546.538i	−0.692365	+	1.74057i
$315$		0			0
$316$	117.090	−	123.891i	0.370539	−	0.392060i
$317$	−10.6202	−	6.13157i	−0.0335022	−	0.0193425i	0.483155	−	0.875535i	$-0.339491\pi$
$317$	−10.6202	−	6.13157i	−0.0335022	−	0.0193425i	−0.516658	+	0.856192i	$0.672824\pi$
$318$	−1.86932	+	0.272979i	−0.00587836	+	0.000858425i
$319$	68.8982	−	39.7784i	0.215982	−	0.124697i
$320$	208.613	−	75.3090i	0.651916	−	0.235341i
$321$	−8.47885			−0.0264139
$322$		0			0
$323$	−116.520			−0.360743
$324$	−309.488	+	92.3593i	−0.955209	+	0.285060i
$325$	215.536	−	124.440i	0.663188	−	0.382892i
$326$	−49.4245	−	338.452i	−0.151609	−	1.03820i
$327$	−16.0260	−	9.25264i	−0.0490093	−	0.0282955i
$328$	−154.669	−	332.830i	−0.471553	−	1.01473i
$329$		0			0
$330$	−0.731022	+	1.83775i	−0.00221522	+	0.00556893i
$331$	−97.2329	+	168.412i	−0.293755	+	0.508798i	−0.974694	−	0.223541i	$-0.928238\pi$
$331$	−97.2329	+	168.412i	−0.293755	+	0.508798i	0.680940	+	0.732340i	$0.261572\pi$
$332$	101.540	−	426.767i	0.305844	−	1.28544i
$333$	−308.082	+	177.871i	−0.925172	+	0.534148i
$334$	149.589	+	189.356i	0.447871	+	0.566936i
$335$		−	41.7901i		−	0.124747i
$336$		0			0
$337$	0.596077			0.00176877			0.000884387	−	1.00000i	$-0.499718\pi$
$337$	0.596077			0.00176877			0.000884387		1.00000i	$0.499718\pi$
$338$	310.817	−	245.541i	0.919577	−	0.726453i
$339$	−1.95773	−	3.39089i	−0.00577502	−	0.0100026i
$340$	194.052	+	46.1707i	0.570741	+	0.135796i
$341$	−113.860	−	65.7371i	−0.333900	−	0.192777i
$342$	135.290	+	53.8157i	0.395583	+	0.157356i
$343$		0			0
$344$	205.769	+	442.791i	0.598166	+	1.28718i
$345$	−2.82959	+	4.90099i	−0.00820171	+	0.0142058i
$346$	214.404	−	31.3096i	0.619664	−	0.0904903i
$347$	102.433	+	177.420i	0.295197	+	0.511296i	0.975031	−	0.222070i	$-0.0712814\pi$
$347$	102.433	+	177.420i	0.295197	+	0.511296i	−0.679834	+	0.733366i	$0.737948\pi$
$348$	−3.02762	−	10.1453i	−0.00870006	−	0.0291531i
$349$			128.396i			0.367898i	0.982936	+	0.183949i	$0.0588882\pi$
$349$			128.396i			0.367898i	−0.982936	+	0.183949i	$0.941112\pi$
$350$		0			0
$351$			33.5837i			0.0956801i
$352$	62.1494	+	70.1453i	0.176561	+	0.199276i
$353$	−95.4207	−	165.274i	−0.270314	−	0.468197i	0.698628	−	0.715485i	$-0.253794\pi$
$353$	−95.4207	−	165.274i	−0.270314	−	0.468197i	−0.968942	+	0.247288i	$0.920461\pi$
$354$	3.22571	+	22.0892i	0.00911218	+	0.0623989i
$355$	−223.846	+	387.713i	−0.630553	+	1.09215i
$356$	235.231	+	222.318i	0.660760	+	0.624489i
$357$		0			0
$358$	−300.011	−	119.339i	−0.838020	−	0.333349i
$359$	−186.805	−	107.852i	−0.520349	−	0.300424i	0.216728	−	0.976232i	$-0.430461\pi$
$359$	−186.805	−	107.852i	−0.520349	−	0.300424i	−0.737077	+	0.675808i	$0.763795\pi$
$360$	−203.986	−	143.232i	−0.566629	−	0.397868i
$361$	147.716	+	255.851i	0.409185	+	0.708729i
$362$	−8.86068	−	11.2163i	−0.0244770	−	0.0309841i
$363$	10.9541			0.0301766
$364$		0			0
$365$			63.3674i			0.173609i
$366$	0.903624	+	1.14385i	0.00246892	+	0.00312527i
$367$	393.859	−	227.395i	1.07319	−	0.619604i	0.144135	−	0.989558i	$-0.453960\pi$
$367$	393.859	−	227.395i	1.07319	−	0.619604i	0.929050	+	0.369954i	$0.120627\pi$
$368$	146.962	+	224.300i	0.399353	+	0.609510i
$369$	−206.227	+	357.196i	−0.558881	+	0.968010i
$370$	−254.828	−	101.366i	−0.688724	−	0.273962i
$371$		0			0
$372$	−12.0180	+	12.7160i	−0.0323065	+	0.0341829i
$373$	312.417	+	180.374i	0.837579	+	0.483576i	0.856441	−	0.516246i	$-0.172671\pi$
$373$	312.417	+	180.374i	0.837579	+	0.483576i	−0.0188617	+	0.999822i	$0.506004\pi$
$374$	12.1791	+	83.4008i	0.0325645	+	0.222997i
$375$	−11.1094	+	6.41401i	−0.0296250	+	0.0171040i
$376$	32.7525	−	368.783i	0.0871076	−	0.980805i
$377$	520.441			1.38048
$378$		0			0
$379$	−268.427			−0.708250			−0.354125	−	0.935198i	$-0.615221\pi$
$379$	−268.427			−0.708250			−0.354125	+	0.935198i	$0.615221\pi$
$380$	32.0983	+	107.558i	0.0844691	+	0.283048i
$381$	−12.9659	+	7.48589i	−0.0340313	+	0.0196480i
$382$	−145.058	+	21.1830i	−0.379733	+	0.0554529i
$383$	503.621	+	290.766i	1.31494	+	0.759180i	0.982910	−	0.184089i	$-0.0589335\pi$
$383$	503.621	+	290.766i	1.31494	+	0.759180i	0.332029	+	0.943269i	$0.392267\pi$
$384$	10.9959	−	5.88549i	0.0286350	−	0.0153268i
$385$		0			0
$386$	−158.093	−	62.8863i	−0.409566	−	0.162918i
$387$	274.360	−	475.206i	0.708942	−	1.22792i
$388$	−150.071	+	630.737i	−0.386780	+	1.62561i
$389$	−443.646	+	256.139i	−1.14048	+	0.658455i	−0.946549	−	0.322560i	$-0.895457\pi$
$389$	−443.646	+	256.139i	−1.14048	+	0.658455i	−0.193929	+	0.981016i	$0.562123\pi$
$390$	−10.1525	+	8.02036i	−0.0260321	+	0.0205650i
$391$			241.169i			0.616801i
$392$		0			0
$393$	6.02790			0.0153382
$394$	−174.140	−	220.435i	−0.441980	−	0.559479i
$395$	−73.8437	−	127.901i	−0.186946	−	0.323800i
$396$	24.3783	−	102.460i	0.0615614	−	0.258738i
$397$	−70.4295	−	40.6625i	−0.177404	−	0.102424i	0.408668	−	0.912683i	$-0.365993\pi$
$397$	−70.4295	−	40.6625i	−0.177404	−	0.102424i	−0.586073	+	0.810259i	$0.699327\pi$
$398$	−105.770	+	265.900i	−0.265754	+	0.668090i
$399$		0			0
$400$	11.7219	+	207.517i	0.0293047	+	0.518793i
$401$	−263.720	+	456.777i	−0.657657	+	1.13909i	0.323564	+	0.946206i	$0.395119\pi$
$401$	−263.720	+	456.777i	−0.657657	+	1.13909i	−0.981221	+	0.192888i	$0.938215\pi$
$402$	−0.339568	−	2.32531i	−0.000844697	−	0.00578436i
$403$	−430.036	−	744.845i	−1.06709	−	1.84825i
$404$	122.195	+	409.464i	0.302463	+	1.01353i
$405$			279.815i			0.690902i
$406$		0			0
$407$		−	115.883i		−	0.284726i
$408$	11.1727	+	0.992275i	0.0273841	+	0.00243205i
$409$	−29.3363	−	50.8120i	−0.0717270	−	0.124235i	0.827931	−	0.560830i	$-0.189518\pi$
$409$	−29.3363	−	50.8120i	−0.0717270	−	0.124235i	−0.899658	+	0.436595i	$0.856184\pi$
$410$	−314.631	+	45.9460i	−0.767393	+	0.112063i
$411$	5.16136	−	8.93974i	0.0125581	−	0.0217512i
$412$	347.908	−	368.114i	0.844436	−	0.893481i
$413$		0			0
$414$	111.386	−	280.018i	0.269048	−	0.676372i
$415$	−329.140	−	190.029i	−0.793109	−	0.457902i
$416$	122.660	+	600.679i	0.294855	+	1.44394i
$417$	9.03158	+	15.6432i	0.0216585	+	0.0375136i
$418$	−37.2171	+	29.4010i	−0.0890362	+	0.0703374i
$419$	−760.704			−1.81552			−0.907761	−	0.419487i	$-0.862210\pi$
$419$	−760.704			−1.81552			−0.907761	+	0.419487i	$0.862210\pi$
$420$		0			0
$421$		−	46.2918i		−	0.109957i	−0.998488	−	0.0549784i	$-0.982491\pi$
$421$		−	46.2918i		−	0.109957i	0.998488	−	0.0549784i	$-0.0175090\pi$
$422$	175.699	−	138.800i	0.416348	−	0.328909i
$423$	−360.331	+	208.037i	−0.851846	+	0.491814i
$424$	63.4700	+	44.5665i	0.149693	+	0.105110i
$425$	−93.4650	+	161.886i	−0.219918	+	0.380909i
$426$	−9.30501	+	23.3922i	−0.0218427	+	0.0549114i
$427$		0			0
$428$	252.972	+	239.086i	0.591057	+	0.558613i
$429$	−4.73462	−	2.73353i	−0.0110364	−	0.00637187i
$430$	418.579	−	61.1256i	0.973440	−	0.142153i
$431$	−291.137	+	168.088i	−0.675492	+	0.389996i	−0.798154	−	0.602453i	$-0.794190\pi$
$431$	−291.137	+	168.088i	−0.675492	+	0.389996i	0.122662	+	0.992448i	$0.460857\pi$
$432$	−25.0416	−	12.6313i	−0.0579666	−	0.0292391i
$433$	372.694			0.860725			0.430363	−	0.902656i	$-0.358386\pi$
$433$	372.694			0.860725			0.430363	+	0.902656i	$0.358386\pi$
$434$		0			0
$435$	−9.17260			−0.0210864
$436$	217.243	+	727.961i	0.498263	+	1.66964i
$437$	−117.530	+	67.8557i	−0.268946	+	0.155276i
$438$	0.514896	+	3.52593i	0.00117556	+	0.00805006i
$439$	344.226	+	198.739i	0.784115	+	0.452709i	0.837887	−	0.545844i	$-0.183791\pi$
$439$	344.226	+	198.739i	0.784115	+	0.452709i	−0.0537719	+	0.998553i	$0.517124\pi$
$440$	73.6313	−	34.2172i	0.167344	−	0.0777663i
$441$		0			0
$442$	−203.795	+	512.329i	−0.461075	+	1.15912i
$443$	−136.765	+	236.884i	−0.308725	+	0.534727i	−0.978084	−	0.208212i	$-0.933236\pi$
$443$	−136.765	+	236.884i	−0.308725	+	0.534727i	0.669359	+	0.742939i	$0.266569\pi$
$444$	−15.0029	−	3.56964i	−0.0337904	−	0.00803973i
$445$	242.844	−	140.206i	0.545718	−	0.315070i
$446$	386.116	+	488.763i	0.865730	+	1.09588i
$447$		−	4.61943i		−	0.0103343i
$448$		0			0
$449$	428.702			0.954792			0.477396	−	0.878688i	$-0.341581\pi$
$449$	428.702			0.954792			0.477396	+	0.878688i	$0.341581\pi$
$450$	183.289	−	144.796i	0.407309	−	0.321769i
$451$	−67.1785	−	116.357i	−0.148955	−	0.257997i
$452$	−37.2059	+	156.374i	−0.0823140	+	0.345960i
$453$	9.66819	+	5.58193i	0.0213426	+	0.0123221i
$454$	−138.185	−	54.9674i	−0.304372	−	0.121074i
$455$		0			0
$456$	2.66000	+	5.72401i	0.00583334	+	0.0125527i
$457$	−5.02501	+	8.70357i	−0.0109956	+	0.0190450i	−0.871471	−	0.490447i	$-0.836833\pi$
$457$	−5.02501	+	8.70357i	−0.0109956	+	0.0190450i	0.860475	+	0.509492i	$0.170167\pi$
$458$	154.899	−	22.6201i	0.338208	−	0.0493889i
$459$	−12.6121	−	21.8449i	−0.0274774	−	0.0475923i
$460$	222.621	−	66.4359i	0.483958	−	0.144426i
$461$		−	825.802i		−	1.79133i	−0.444732	−	0.895664i	$-0.646701\pi$
$461$		−	825.802i		−	1.79133i	0.444732	−	0.895664i	$-0.353299\pi$
$462$		0			0
$463$			114.707i			0.247748i	0.992298	+	0.123874i	$0.0395318\pi$
$463$			114.707i			0.247748i	−0.992298	+	0.123874i	$0.960468\pi$
$464$	−195.745	+	388.065i	−0.421865	+	0.836346i
$465$	7.57924	+	13.1276i	0.0162995	+	0.0282315i
$466$	−26.8933	−	184.161i	−0.0577110	−	0.395196i
$467$	−100.864	+	174.701i	−0.215982	+	0.374092i	−0.953576	−	0.301153i	$-0.902629\pi$
$467$	−100.864	+	174.701i	−0.215982	+	0.374092i	0.737594	+	0.675245i	$0.235962\pi$
$468$	473.247	−	500.733i	1.01121	−	1.06994i
$469$		0			0
$470$	−298.045	−	118.557i	−0.634138	−	0.252248i
$471$	24.8165	+	14.3278i	0.0526889	+	0.0304200i
$472$	526.629	−	750.006i	1.11574	−	1.58899i
$473$	89.3730	+	154.799i	0.188949	+	0.327270i
$474$	−5.14813	−	6.51673i	−0.0108610	−	0.0137484i
$475$	−105.190			−0.221452
$476$		0			0
$477$		−	87.1561i		−	0.182717i
$478$	361.528	+	457.638i	0.756334	+	0.957402i
$479$	−517.483	+	298.769i	−1.08034	+	0.623735i	−0.930988	−	0.365050i	$-0.881052\pi$
$479$	−517.483	+	298.769i	−1.08034	+	0.623735i	−0.149352	+	0.988784i	$0.547719\pi$
$480$	−2.16184	−	10.5868i	−0.00450383	−	0.0220558i
$481$	379.040	−	656.517i	0.788026	−	1.36490i
$482$	−415.806	−	165.400i	−0.862668	−	0.343154i
$483$		0			0
$484$	−326.824	−	308.884i	−0.675255	−	0.638189i
$485$	486.450	+	280.852i	1.00299	+	0.579077i
$486$	6.83299	+	46.7913i	0.0140597	+	0.0962784i
$487$	−298.887	+	172.562i	−0.613730	+	0.354337i	−0.774424	−	0.632667i	$-0.781960\pi$
$487$	−298.887	+	172.562i	−0.613730	+	0.354337i	0.160694	+	0.987004i	$0.448627\pi$
$488$	5.29392	−	59.6079i	0.0108482	−	0.122147i
$489$	−16.6637			−0.0340770
$490$		0			0
$491$	373.498			0.760689			0.380344	−	0.924845i	$-0.375805\pi$
$491$	373.498			0.760689			0.380344	+	0.924845i	$0.375805\pi$
$492$	−17.1336	+	5.11311i	−0.0348243	+	0.0103925i
$493$	−338.526	+	195.448i	−0.686665	+	0.396446i
$494$	−307.015	+	44.8337i	−0.621487	+	0.0907565i
$495$	−79.0217	−	45.6232i	−0.159640	−	0.0921680i
$496$	717.133	−	40.5082i	1.44583	−	0.0816698i
$497$		0			0
$498$	−19.8583	−	7.89927i	−0.0398761	−	0.0158620i
$499$	425.158	−	736.396i	0.852021	−	1.47574i	−0.0273604	−	0.999626i	$-0.508710\pi$
$499$	425.158	−	736.396i	0.852021	−	1.47574i	0.879381	−	0.476118i	$-0.157956\pi$
$500$	512.318	+	121.896i	1.02464	+	0.243791i
$501$	10.1814	−	5.87822i	0.0203221	−	0.0117330i
$502$	−487.455	+	385.083i	−0.971025	+	0.767097i
$503$		−	459.256i		−	0.913033i	−0.889715	−	0.456517i	$-0.849097\pi$
$503$		−	459.256i		−	0.913033i	0.889715	−	0.456517i	$-0.150903\pi$
$504$		0			0
$505$	370.206			0.733082
$506$	60.8533	+	77.0308i	0.120263	+	0.152235i
$507$	−9.64873	−	16.7121i	−0.0190310	−	0.0329627i
$508$	597.935	+	142.266i	1.17704	+	0.280052i
$509$	583.623	+	336.955i	1.14661	+	0.661994i	0.948058	−	0.318097i	$-0.103044\pi$
$509$	583.623	+	336.955i	1.14661	+	0.661994i	0.198549	+	0.980091i	$0.436377\pi$
$510$	3.59182	−	9.02963i	0.00704279	−	0.0177052i
$511$		0			0
$512$	−494.028	−	134.463i	−0.964898	−	0.262623i
$513$	7.09713	−	12.2926i	0.0138346	−	0.0239622i
$514$	50.7108	+	347.260i	0.0986592	+	0.675603i
$515$	−219.410	−	380.029i	−0.426039	−	0.737921i
$516$	22.7942	−	6.80238i	0.0441747	−	0.0131829i
$517$		−	135.536i		−	0.262159i
$518$		0			0
$519$		−	10.5562i		−	0.0203394i
$520$	529.066	+	46.9876i	1.01743	+	0.0903607i
$521$	−243.236	−	421.298i	−0.466864	−	0.808633i	0.532419	−	0.846481i	$-0.321283\pi$
$521$	−243.236	−	421.298i	−0.466864	−	0.808633i	−0.999284	+	0.0378482i	$0.987950\pi$
$522$	483.326	−	70.5807i	0.925912	−	0.135212i
$523$	−340.043	+	588.973i	−0.650179	+	1.12614i	0.332900	+	0.942962i	$0.391973\pi$
$523$	−340.043	+	588.973i	−0.650179	+	1.12614i	−0.983079	+	0.183181i	$0.941361\pi$
$524$	−179.847	−	169.975i	−0.343219	−	0.324379i
$525$		0			0
$526$	−230.732	+	580.048i	−0.438655	+	1.10275i
$527$	559.442	+	322.994i	1.06156	+	0.612892i
$528$	3.81901	−	2.50223i	0.00723297	−	0.00473907i
$529$	−124.054	−	214.869i	−0.234507	−	0.406179i
$530$	52.7233	−	41.6507i	0.0994779	−	0.0785862i
$531$	−1029.90			−1.93954
$532$		0			0
$533$		−	878.931i		−	1.64903i
$534$	12.3732	−	9.77470i	0.0231709	−	0.0183047i
$535$	261.161	−	150.781i	0.488151	−	0.281834i
$536$	−55.4378	+	78.9525i	−0.103429	+	0.147299i
$537$	−7.86496	+	13.6225i	−0.0146461	+	0.0253678i
$538$	105.574	−	265.407i	0.196234	−	0.493321i
$539$		0			0
$540$	−16.6904	+	17.6598i	−0.0309082	+	0.0327034i
$541$	−688.489	−	397.499i	−1.27262	−	0.734749i	−0.297142	−	0.954833i	$-0.596034\pi$
$541$	−688.489	−	397.499i	−1.27262	−	0.734749i	−0.975481	+	0.220084i	$0.929367\pi$
$542$	526.648	−	76.9071i	0.971676	−	0.141895i
$543$	−0.603078	+	0.348187i	−0.00111064	+	0.000641229i
$544$	−305.366	−	344.653i	−0.561335	−	0.633554i
$545$	658.167			1.20765
$546$		0			0
$547$	−736.752			−1.34690			−0.673448	−	0.739235i	$-0.735187\pi$
$547$	−736.752			−1.34690			−0.673448	+	0.739235i	$0.735187\pi$
$548$	−406.076	+	121.184i	−0.741014	+	0.221138i
$549$	−58.2418	+	33.6259i	−0.106087	+	0.0612494i
$550$	10.9948	+	75.2910i	0.0199906	+	0.136893i
$551$	−190.496	−	109.983i	−0.345728	−	0.199606i
$552$	11.8474	−	5.50559i	0.0214626	−	0.00997389i
$553$		0			0
$554$	−271.104	+	681.540i	−0.489357	+	1.23022i
$555$	−6.68046	+	11.5709i	−0.0120369	+	0.0208485i
$556$	171.641	−	721.397i	0.308708	−	1.29748i
$557$	360.057	−	207.879i	0.646421	−	0.373212i	−0.140662	−	0.990058i	$-0.544923\pi$
$557$	360.057	−	207.879i	0.646421	−	0.373212i	0.787084	+	0.616846i	$0.211590\pi$
$558$	−500.382	−	633.406i	−0.896742	−	1.13514i
$559$			1169.31i			2.09179i
$560$		0			0
$561$	4.10624			0.00731950
$562$	−232.231	+	183.459i	−0.413222	+	0.326439i
$563$	−48.2498	−	83.5711i	−0.0857012	−	0.148439i	0.819989	−	0.572380i	$-0.193980\pi$
$563$	−48.2498	−	83.5711i	−0.0857012	−	0.148439i	−0.905690	+	0.423941i	$0.860646\pi$
$564$	−17.5473	−	4.17503i	−0.0311123	−	0.00740253i
$565$	120.602	+	69.6296i	0.213455	+	0.123238i
$566$	−609.060	−	242.273i	−1.07608	−	0.428044i
$567$		0			0
$568$	937.235	−	435.542i	1.65006	−	0.766800i
$569$	−173.977	+	301.336i	−0.305759	+	0.529589i	−0.977430	−	0.211260i	$-0.932243\pi$
$569$	−173.977	+	301.336i	−0.305759	+	0.529589i	0.671671	+	0.740849i	$0.265577\pi$
$570$	5.41103	−	0.790179i	0.00949303	−	0.00138628i
$571$	6.86255	+	11.8863i	0.0120185	+	0.0208166i	0.871972	−	0.489556i	$-0.162841\pi$
$571$	6.86255	+	11.8863i	0.0120185	+	0.0208166i	−0.859954	+	0.510372i	$0.829508\pi$
$572$	64.1807	+	215.064i	0.112204	+	0.375985i
$573$			7.14193i			0.0124641i
$574$		0			0
$575$			217.718i			0.378641i
$576$	195.375	+	541.207i	0.339192	+	0.939596i
$577$	−413.660	−	716.480i	−0.716915	−	1.24173i	−0.962216	−	0.272286i	$-0.912220\pi$
$577$	−413.660	−	716.480i	−0.716915	−	1.24173i	0.245302	−	0.969447i	$-0.421113\pi$
$578$	23.6791	+	162.151i	0.0409672	+	0.280537i
$579$	−4.14449	+	7.17846i	−0.00715801	+	0.0123980i
$580$	273.671	+	258.649i	0.471847	+	0.445946i
$581$		0			0
$582$	29.3495	+	11.6747i	0.0504286	+	0.0200596i
$583$	24.5874	+	14.1956i	0.0421740	+	0.0243492i
$584$	84.0617	−	119.718i	0.143941	−	0.204996i
$585$	−298.456	−	516.941i	−0.510181	−	0.883659i
$586$	322.196	+	407.851i	0.549823	+	0.695991i
$587$	675.987			1.15160			0.575798	−	0.817592i	$-0.304692\pi$
$587$	675.987			1.15160			0.575798	+	0.817592i	$0.304692\pi$
$588$		0			0
$589$			363.512i			0.617169i
$590$	−492.174	−	623.015i	−0.834193	−	1.05596i
$591$	−11.8524	+	6.84298i	−0.0200548	+	0.0115786i
$592$	346.967	+	529.555i	0.586093	+	0.894519i
$593$	−207.058	+	358.635i	−0.349171	+	0.604781i	−0.986102	−	0.166139i	$-0.946870\pi$
$593$	−207.058	+	358.635i	−0.349171	+	0.604781i	0.636932	+	0.770920i	$0.280203\pi$
$594$	−9.54041	−	3.79500i	−0.0160613	−	0.00638889i
$595$		0			0
$596$	−130.258	+	137.824i	−0.218554	+	0.231248i
$597$	12.0736	+	6.97072i	0.0202238	+	0.0116762i
$598$	92.7954	+	635.449i	0.155176	+	1.06262i
$599$	−626.399	+	361.652i	−1.04574	+	0.603759i	−0.921454	−	0.388487i	$-0.872998\pi$
$599$	−626.399	+	361.652i	−1.04574	+	0.603759i	−0.124287	+	0.992246i	$0.539664\pi$
$600$	10.0863	+	0.895788i	0.0168105	+	0.00149298i
$601$	−68.7503			−0.114393			−0.0571966	−	0.998363i	$-0.518216\pi$
$601$	−68.7503			−0.114393			−0.0571966	+	0.998363i	$0.518216\pi$
$602$		0			0
$603$	108.416			0.179795
$604$	−131.058	−	439.164i	−0.216984	−	0.727093i
$605$	−337.402	+	194.799i	−0.557690	+	0.321982i
$606$	20.5992	−	3.00813i	0.0339922	−	0.00496392i
$607$	−122.338	−	70.6317i	−0.201545	−	0.116362i	0.395831	−	0.918323i	$-0.370457\pi$
$607$	−122.338	−	70.6317i	−0.201545	−	0.116362i	−0.597376	+	0.801961i	$0.703790\pi$
$608$	82.0424	−	245.787i	0.134938	−	0.404255i
$609$		0			0
$610$	−48.1742	−	19.1628i	−0.0789742	−	0.0314145i
$611$	443.323	−	767.858i	0.725569	−	1.25672i
$612$	−119.781	+	503.431i	−0.195721	+	0.822599i
$613$	−83.7767	+	48.3685i	−0.136667	+	0.0789046i	−0.566774	−	0.823873i	$-0.691809\pi$
$613$	−83.7767	+	48.3685i	−0.136667	+	0.0789046i	0.430108	+	0.902778i	$0.358476\pi$
$614$	455.844	−	360.110i	0.742417	−	0.586499i
$615$			15.4909i			0.0251884i
$616$		0			0
$617$	580.418			0.940709			0.470355	−	0.882478i	$-0.344126\pi$
$617$	580.418			0.940709			0.470355	+	0.882478i	$0.344126\pi$
$618$	−15.2965	−	19.3630i	−0.0247516	−	0.0313317i
$619$	78.9725	+	136.784i	0.127581	+	0.220976i	0.922739	−	0.385426i	$-0.125945\pi$
$619$	78.9725	+	136.784i	0.127581	+	0.220976i	−0.795158	+	0.606402i	$0.792612\pi$
$620$	144.040	−	605.392i	0.232323	−	0.976438i
$621$	−25.4428	−	14.6894i	−0.0409707	−	0.0236544i
$622$	−55.3740	+	139.207i	−0.0890257	+	0.223806i
$623$		0			0
$624$	29.8204	−	1.68445i	0.0477891	−	0.00269943i
$625$	65.7420	−	113.869i	0.105187	−	0.182190i
$626$	82.2219	+	563.043i	0.131345	+	0.899429i
$627$	1.15534	+	2.00110i	0.00184264	+	0.00319155i
$628$	−336.403	−	1127.25i	−0.535673	−	1.79499i
$629$			569.384i			0.905221i
$630$		0			0
$631$		−	771.793i		−	1.22313i	−0.791195	−	0.611564i	$-0.790541\pi$
$631$		−	771.793i		−	1.22313i	0.791195	−	0.611564i	$-0.209459\pi$
$632$	−30.1605	+	339.598i	−0.0477223	+	0.537339i
$633$	−5.45424	−	9.44701i	−0.00861649	−	0.0149242i
$634$	24.2689	−	3.54401i	0.0382790	−	0.00558993i
$635$	266.246	−	461.152i	0.419286	−	0.726224i
$636$	2.59523	−	2.74596i	0.00408055	−	0.00431755i
$637$		0			0
$638$	−58.8104	+	147.846i	−0.0921793	+	0.231733i
$639$	−1005.85	−	580.726i	−1.57410	−	0.908805i
$640$	−234.025	+	376.823i	−0.365664	+	0.588786i
$641$	293.451	+	508.273i	0.457802	+	0.792937i	0.998845	−	0.0480584i	$-0.0153034\pi$
$641$	293.451	+	508.273i	0.457802	+	0.792937i	−0.541042	+	0.840996i	$0.681970\pi$
$642$	13.3065	−	10.5119i	0.0207266	−	0.0163737i
$643$	−865.328			−1.34577			−0.672883	−	0.739749i	$-0.734944\pi$
$643$	−865.328			−1.34577			−0.672883	+	0.739749i	$0.734944\pi$
$644$		0			0
$645$		−	20.6087i		−	0.0319515i
$646$	182.864	−	144.460i	0.283071	−	0.223622i
$647$	−115.080	+	66.4414i	−0.177867	+	0.102691i	−0.586290	−	0.810101i	$-0.699412\pi$
$647$	−115.080	+	66.4414i	−0.177867	+	0.102691i	0.408423	+	0.912793i	$0.366079\pi$
$648$	371.196	−	528.644i	0.572834	−	0.815809i
$649$	167.745	−	290.542i	0.258466	−	0.447677i
$650$	−183.978	+	462.511i	−0.283044	+	0.711555i
$651$		0			0
$652$	497.173	+	469.882i	0.762535	+	0.720677i
$653$	315.501	+	182.155i	0.483156	+	0.278950i	0.721731	−	0.692174i	$-0.243347\pi$
$653$	315.501	+	182.155i	0.483156	+	0.278950i	−0.238575	+	0.971124i	$0.576680\pi$
$654$	36.6221	−	5.34798i	0.0559972	−	0.00817733i
$655$	−185.668	+	107.196i	−0.283463	+	0.163657i
$656$	655.372	+	330.579i	0.999042	+	0.503931i
$657$	−164.395			−0.250220
$658$		0			0
$659$	−18.8972			−0.0286756			−0.0143378	−	0.999897i	$-0.504564\pi$
$659$	−18.8972			−0.0286756			−0.0143378	+	0.999897i	$0.504564\pi$
$660$	−1.13116	−	3.79042i	−0.00171388	−	0.00574307i
$661$	−293.674	+	169.553i	−0.444288	+	0.256510i	−0.705415	−	0.708795i	$-0.749239\pi$
$661$	−293.674	+	169.553i	−0.444288	+	0.256510i	0.261127	+	0.965304i	$0.415906\pi$
$662$	−56.2001	−	384.850i	−0.0848944	−	0.581344i
$663$	23.2632	+	13.4310i	0.0350878	+	0.0202579i
$664$	369.744	+	795.645i	0.556843	+	1.19826i
$665$		0			0
$666$	262.974	−	661.102i	0.394856	−	0.992646i
$667$	−227.639	+	394.283i	−0.341288	+	0.591128i
$668$	−469.522	−	111.713i	−0.702878	−	0.167235i
$669$	26.2799	−	15.1727i	0.0392824	−	0.0226797i
$670$	51.8107	+	65.5843i	0.0773294	+	0.0978871i
$671$		−	21.9073i		−	0.0326487i
$672$		0			0
$673$	674.869			1.00278			0.501389	−	0.865222i	$-0.332823\pi$
$673$	674.869			1.00278			0.501389	+	0.865222i	$0.332823\pi$
$674$	−0.935468	+	0.739006i	−0.00138793	+	0.00109645i
$675$	−11.3857	−	19.7207i	−0.0168678	−	0.0292158i
$676$	−183.370	+	770.692i	−0.271258	+	1.14008i
$677$	−856.280	−	494.374i	−1.26482	−	0.730242i	−0.290813	−	0.956780i	$-0.593926\pi$
$677$	−856.280	−	494.374i	−1.26482	−	0.730242i	−0.974002	+	0.226538i	$0.927259\pi$
$678$	7.27639	+	2.89441i	0.0107321	+	0.00426905i
$679$		0			0
$680$	−361.782	+	168.123i	−0.532032	+	0.247240i
$681$	−3.62260	+	6.27453i	−0.00531953	+	0.00921369i
$682$	260.189	−	37.9957i	0.381509	−	0.0557122i
$683$	259.062	+	448.709i	0.379301	+	0.656968i	0.990961	−	0.134153i	$-0.0428312\pi$
$683$	259.062	+	448.709i	0.379301	+	0.656968i	−0.611660	+	0.791121i	$0.709498\pi$
$684$	−279.040	+	83.2729i	−0.407953	+	0.121744i
$685$			367.143i			0.535975i
$686$		0			0
$687$		−	7.62646i		−	0.0111011i
$688$	−871.894	−	439.795i	−1.26729	−	0.639237i
$689$	92.8640	+	160.845i	0.134781	+	0.233447i
$690$	−1.63549	−	11.1996i	−0.00237027	−	0.0162313i
$691$	−308.511	+	534.356i	−0.446470	+	0.773309i	−0.998153	−	0.0607450i	$-0.980652\pi$
$691$	−308.511	+	534.356i	−0.446470	+	0.773309i	0.551683	+	0.834054i	$0.313986\pi$
$692$	−297.662	+	314.951i	−0.430148	+	0.455131i
$693$		0			0
$694$	−380.718	−	151.443i	−0.548585	−	0.218217i
$695$	−556.371	−	321.221i	−0.800534	−	0.462189i
$696$	17.3294	+	12.1682i	0.0248986	+	0.0174830i
$697$	330.076	+	571.709i	0.473567	+	0.820243i
$698$	−159.184	−	201.502i	−0.228057	−	0.288685i
$699$	−9.06718			−0.0129717
$700$		0			0
$701$		−	97.6954i		−	0.139366i	−0.997569	−	0.0696829i	$-0.977801\pi$
$701$		−	97.6954i		−	0.139366i	0.997569	−	0.0696829i	$-0.0221987\pi$
$702$	−41.6366	−	52.7054i	−0.0593113	−	0.0750790i
$703$	−277.479	+	160.203i	−0.394707	+	0.227884i
$704$	−184.501	−	33.0324i	−0.262075	−	0.0469210i
$705$	−7.81342	+	13.5332i	−0.0110829	+	0.0191961i
$706$	354.654	+	141.075i	0.502343	+	0.199823i
$707$		0			0
$708$	−32.4482	−	30.6670i	−0.0458308	−	0.0433150i
$709$	−1082.31	−	624.872i	−1.52653	−	0.881343i	−0.999504	−	0.0314953i	$-0.989973\pi$
$709$	−1082.31	−	624.872i	−1.52653	−	0.881343i	−0.527028	−	0.849848i	$-0.676694\pi$
$710$	−129.382	−	885.988i	−0.182228	−	1.24787i
$711$	331.815	−	191.573i	0.466688	−	0.269442i
$712$	−644.791	−	57.2654i	−0.905606	−	0.0804290i
$713$	752.386			1.05524
$714$		0			0
$715$	194.444			0.271950
$716$	618.784	−	184.662i	0.864224	−	0.257907i
$717$	24.6064	−	14.2065i	0.0343186	−	0.0198138i
$718$	426.881	−	62.3379i	0.594541	−	0.0868216i
$719$	−367.839	−	212.372i	−0.511599	−	0.295372i	0.221892	−	0.975071i	$-0.428777\pi$
$719$	−367.839	−	212.372i	−0.511599	−	0.295372i	−0.733491	+	0.679700i	$0.762110\pi$
$720$	497.708	−	28.1137i	0.691261	−	0.0390468i
$721$		0			0
$722$	−549.022	−	218.391i	−0.760418	−	0.302480i
$723$	−10.9006	+	18.8804i	−0.0150769	+	0.0261140i
$724$	27.8115	+	6.61716i	0.0384136	+	0.00913973i
$725$	−305.608	+	176.443i	−0.421528	+	0.243369i
$726$	−17.1911	+	13.5807i	−0.0236792	+	0.0187062i
$727$			79.1445i			0.108865i	0.998517	+	0.0544323i	$0.0173349\pi$
$727$			79.1445i			0.108865i	−0.998517	+	0.0544323i	$0.982665\pi$
$728$		0			0
$729$	−724.390			−0.993676
$730$	−78.5619	−	99.4472i	−0.107619	−	0.136229i
$731$	−439.127	−	760.591i	−0.600721	−	1.04048i
$732$	−2.83625	−	0.674827i	−0.00387466	−	0.000921895i
$733$	−574.839	−	331.883i	−0.784227	−	0.452774i	0.0536990	−	0.998557i	$-0.482899\pi$
$733$	−574.839	−	331.883i	−0.784227	−	0.452774i	−0.837926	+	0.545783i	$0.816232\pi$
$734$	−336.192	+	845.167i	−0.458027	+	1.15145i
$735$		0			0
$736$	−508.721	−	169.809i	−0.691198	−	0.230718i
$737$	−17.6584	+	30.5852i	−0.0239598	+	0.0414996i
$738$	−119.198	−	816.251i	−0.161515	−	1.10603i
$739$	−416.056	−	720.630i	−0.562998	−	0.975142i	−0.997233	−	0.0743418i	$-0.976314\pi$
$739$	−416.056	−	720.630i	−0.562998	−	0.975142i	0.434235	−	0.900800i	$-0.357019\pi$
$740$	525.592	−	156.851i	0.710260	−	0.211960i
$741$			15.1159i			0.0203993i
$742$		0			0
$743$			283.217i			0.381180i	0.981670	+	0.190590i	$0.0610401\pi$
$743$			283.217i			0.381180i	−0.981670	+	0.190590i	$0.938960\pi$
$744$	3.09564	−	34.8560i	0.00416081	−	0.0468495i
$745$	82.1483	+	142.285i	0.110266	+	0.190987i
$746$	−713.924	+	104.255i	−0.957002	+	0.139752i
$747$	492.995	−	853.892i	0.659966	−	1.14309i
$748$	−122.513	−	115.788i	−0.163787	−	0.154796i
$749$		0			0
$750$	9.48280	−	23.8392i	0.0126437	−	0.0317856i
$751$	324.743	+	187.490i	0.432414	+	0.249654i	0.700375	−	0.713776i	$-0.253016\pi$
$751$	324.743	+	187.490i	0.432414	+	0.249654i	−0.267960	+	0.963430i	$0.586350\pi$
$752$	405.810	+	619.364i	0.539641	+	0.823623i
$753$	15.1321	+	26.2096i	0.0200958	+	0.0348069i
$754$	−816.767	+	645.234i	−1.08324	+	0.855748i
$755$	−397.059			−0.525906
$756$		0			0
$757$		−	63.0951i		−	0.0833488i	−0.999131	−	0.0416744i	$-0.986731\pi$
$757$		−	63.0951i		−	0.0833488i	0.999131	−	0.0416744i	$-0.0132692\pi$
$758$	421.262	−	332.791i	0.555755	−	0.439039i
$759$	4.14181	−	2.39128i	0.00545694	−	0.00315056i
$760$	−183.723	−	129.004i	−0.241741	−	0.169743i
$761$	233.753	−	404.871i	0.307165	−	0.532025i	−0.670576	−	0.741841i	$-0.733953\pi$
$761$	233.753	−	404.871i	0.307165	−	0.532025i	0.977741	+	0.209815i	$0.0672863\pi$
$762$	11.0675	−	27.8231i	0.0145243	−	0.0365133i
$763$		0			0
$764$	201.388	−	213.085i	0.263597	−	0.278907i
$765$	388.267	+	224.166i	0.507538	+	0.293027i
$766$	−1150.86	+	168.061i	−1.50243	+	0.219401i
$767$	1900.66	−	1097.35i	2.47804	−	1.43070i
$768$	−9.95988	+	22.8690i	−0.0129686	+	0.0297774i
$769$	−900.573			−1.17110			−0.585548	−	0.810638i	$-0.699121\pi$
$769$	−900.573			−1.17110			−0.585548	+	0.810638i	$0.699121\pi$
$770$		0			0
$771$	17.0974			0.0221756
$772$	326.072	−	97.3085i	0.422373	−	0.126047i
$773$	1058.94	−	611.381i	1.36991	−	0.790919i	0.378996	−	0.925398i	$-0.376269\pi$
$773$	1058.94	−	611.381i	1.36991	−	0.790919i	0.990916	+	0.134479i	$0.0429360\pi$
$774$	158.579	+	1085.92i	0.204882	+	1.40300i
$775$	505.043	+	291.587i	0.651668	+	0.376241i
$776$	−546.460	−	1175.92i	−0.704201	−	1.51536i
$777$		0			0
$778$	378.689	−	952.003i	0.486747	−	1.22365i
$779$	−185.742	+	321.714i	−0.238436	+	0.412983i
$780$	5.98961	−	25.1739i	0.00767898	−	0.0322742i
$781$	327.655	−	189.172i	0.419533	−	0.242217i
$782$	−298.998	−	378.485i	−0.382350	−	0.483996i
$783$		−	47.6182i		−	0.0608151i
$784$		0			0
$785$	−1019.18			−1.29832
$786$	−9.46004	+	7.47330i	−0.0120357	+	0.00950801i
$787$	431.471	+	747.330i	0.548248	+	0.949593i	0.998395	+	0.0566385i	$0.0180383\pi$
$787$	431.471	+	747.330i	0.548248	+	0.949593i	−0.450147	+	0.892954i	$0.648628\pi$
$788$	546.582	+	130.048i	0.693633	+	0.165036i
$789$	26.3381	+	15.2063i	0.0333816	+	0.0192729i
$790$	274.458	+	109.174i	0.347415	+	0.138195i
$791$		0			0
$792$	88.7700	+	191.022i	0.112083	+	0.241190i
$793$	71.6561	−	124.112i	0.0903608	−	0.156510i
$794$	160.943	−	23.5027i	0.202699	−	0.0296004i
$795$	−1.63670	−	2.83484i	−0.00205874	−	0.00356584i
$796$	−163.666	−	548.428i	−0.205610	−	0.688980i
$797$		−	1078.34i		−	1.35300i	−0.736442	−	0.676500i	$-0.763496\pi$
$797$		−	1078.34i		−	1.35300i	0.736442	−	0.676500i	$-0.236504\pi$
$798$		0			0
$799$			665.947i			0.833476i
$800$	−275.673	−	311.140i	−0.344591	−	0.388925i
$801$	363.739	+	630.014i	0.454106	+	0.786534i
$802$	−152.429	−	1043.81i	−0.190061	−	1.30151i
$803$	26.7758	−	46.3771i	0.0333447	−	0.0577547i
$804$	3.41579	+	3.22829i	0.00424850	+	0.00401529i
$805$		0			0
$806$	1598.33	+	635.788i	1.98305	+	0.788819i
$807$	−12.0512	−	6.95779i	−0.0149334	−	0.00862180i
$808$	−699.417	−	491.107i	−0.865615	−	0.607806i
$809$	−166.694	−	288.723i	−0.206050	−	0.356888i	0.744417	−	0.667715i	$-0.232727\pi$
$809$	−166.694	−	288.723i	−0.206050	−	0.356888i	−0.950467	+	0.310827i	$0.899394\pi$
$810$	−346.910	−	439.135i	−0.428284	−	0.542142i
$811$	1246.04			1.53642			0.768211	−	0.640197i	$-0.221147\pi$
$811$	1246.04			1.53642			0.768211	+	0.640197i	$0.221147\pi$
$812$		0			0
$813$		−	25.9295i		−	0.0318936i
$814$	143.670	+	181.864i	0.176499	+	0.223421i
$815$	513.265	−	296.334i	0.629773	−	0.363600i
$816$	−18.7644	+	12.2945i	−0.0229956	+	0.0150668i
$817$	247.107	−	428.002i	0.302456	−	0.523870i
$818$	109.036	+	43.3724i	0.133295	+	0.0530224i
$819$		0			0
$820$	436.811	−	462.181i	0.532696	−	0.563636i
$821$	1263.25	+	729.338i	1.53867	+	0.888353i	0.998917	+	0.0465306i	$0.0148165\pi$
$821$	1263.25	+	729.338i	1.53867	+	0.888353i	0.539755	+	0.841822i	$0.318517\pi$
$822$	2.98324	+	20.4288i	0.00362925	+	0.0248525i
$823$	−401.876	+	232.023i	−0.488306	+	0.281924i	−0.723872	−	0.689935i	$-0.757639\pi$
$823$	−401.876	+	232.023i	−0.488306	+	0.281924i	0.235565	+	0.971859i	$0.424306\pi$
$824$	−89.6151	+	1009.04i	−0.108756	+	1.22456i
$825$	3.70695			0.00449328
$826$		0			0
$827$	1077.41			1.30279			0.651394	−	0.758739i	$-0.274184\pi$
$827$	1077.41			1.30279			0.651394	+	0.758739i	$0.274184\pi$
$828$	172.355	+	577.547i	0.208159	+	0.697521i
$829$	−31.1210	+	17.9677i	−0.0375404	+	0.0216740i	−0.518653	−	0.854985i	$-0.673566\pi$
$829$	−31.1210	+	17.9677i	−0.0375404	+	0.0216740i	0.481112	+	0.876659i	$0.340233\pi$
$830$	752.139	−	109.836i	0.906192	−	0.132332i
$831$	30.9465	+	17.8670i	0.0372400	+	0.0215006i
$832$	−937.211	−	790.619i	−1.12646	−	0.950263i
$833$		0			0
$834$	−33.5681	−	13.3528i	−0.0402495	−	0.0160105i
$835$	−209.067	+	362.115i	−0.250380	+	0.433671i
$836$	21.9567	−	92.2825i	0.0262640	−	0.110386i
$837$	−68.1503	+	39.3466i	−0.0814221	+	0.0470091i
$838$	1193.83	−	943.109i	1.42462	−	1.12543i
$839$		−	734.676i		−	0.875656i	−0.899059	−	0.437828i	$-0.855748\pi$
$839$		−	734.676i		−	0.875656i	0.899059	−	0.437828i	$-0.144252\pi$
$840$		0			0
$841$	103.069			0.122555
$842$	57.3918	+	72.6492i	0.0681613	+	0.0862817i
$843$	7.20916	+	12.4866i	0.00855179	+	0.0148121i
$844$	−103.656	+	435.657i	−0.122815	+	0.516181i
$845$	594.390	+	343.171i	0.703420	+	0.406119i
$846$	307.573	−	773.221i	0.363561	−	0.913972i
$847$		0			0
$848$	−154.861	+	8.74753i	−0.182619	+	0.0103155i
$849$	−15.9669	+	27.6554i	−0.0188067	+	0.0325741i
$850$	−54.0223	−	369.937i	−0.0635556	−	0.435219i
$851$	331.582	+	574.317i	0.389638	+	0.674873i
$852$	−14.3983	−	48.2474i	−0.0168994	−	0.0566284i
$853$		−	402.566i		−	0.471942i	−0.971760	−	0.235971i	$-0.924173\pi$
$853$		−	402.566i		−	0.471942i	0.971760	−	0.235971i	$-0.0758270\pi$
$854$		0			0
$855$			252.287i			0.295072i
$856$	−693.424	−	61.5846i	−0.810075	−	0.0719446i
$857$	276.001	+	478.048i	0.322055	+	0.557816i	0.980912	−	0.194453i	$-0.0622930\pi$
$857$	276.001	+	478.048i	0.322055	+	0.557816i	−0.658857	+	0.752268i	$0.728960\pi$
$858$	10.8194	−	1.57997i	0.0126100	−	0.00184145i
$859$	−165.058	+	285.889i	−0.192152	+	0.332817i	−0.945963	−	0.324274i	$-0.894880\pi$
$859$	−165.058	+	285.889i	−0.192152	+	0.332817i	0.753811	+	0.657091i	$0.228213\pi$
$860$	−581.125	+	614.877i	−0.675727	+	0.714973i
$861$		0			0
$862$	248.510	−	624.740i	0.288295	−	0.724757i
$863$	967.063	+	558.334i	1.12058	+	0.646969i	0.941550	−	0.336874i	$-0.109370\pi$
$863$	967.063	+	558.334i	1.12058	+	0.646969i	0.179033	+	0.983843i	$0.442703\pi$
$864$	54.9597	−	11.2229i	0.0636108	−	0.0129894i
$865$	187.723	+	325.145i	0.217020	+	0.375890i
$866$	−584.896	+	462.060i	−0.675400	+	0.533557i
$867$	7.98348			0.00920817
$868$		0			0
$869$			124.810i			0.143625i
$870$	14.3952	−	11.3720i	0.0165462	−	0.0130713i
$871$	−200.081	+	115.517i	−0.229714	+	0.132625i
$872$	−1243.45	−	873.109i	−1.42597	−	1.00127i
$873$	−728.618	+	1262.00i	−0.834614	+	1.44559i
$874$	100.321	−	252.202i	0.114784	−	0.288561i
$875$		0			0
$876$	−5.17945	−	4.89514i	−0.00591262	−	0.00558806i
$877$	−0.647303	−	0.373720i	−0.000738087	−	0.000426135i	0.499631	−	0.866238i	$-0.333469\pi$
$877$	−0.647303	−	0.373720i	−0.000738087	−	0.000426135i	−0.500369	+	0.865812i	$0.666802\pi$
$878$	−786.614	+	114.870i	−0.895915	+	0.130832i
$879$	21.9294	−	12.6610i	0.0249481	−	0.0144038i
$880$	−73.1332	+	144.986i	−0.0831059	+	0.164757i
$881$	247.826			0.281301			0.140650	−	0.990059i	$-0.455081\pi$
$881$	247.826			0.281301			0.140650	+	0.990059i	$0.455081\pi$
$882$		0			0
$883$	−1613.74			−1.82757			−0.913784	−	0.406200i	$-0.866854\pi$
$883$	−1613.74			−1.82757			−0.913784	+	0.406200i	$0.866854\pi$
$884$	−315.347	−	1056.70i	−0.356727	−	1.19536i
$885$	−33.4985	+	19.3403i	−0.0378514	+	0.0218535i
$886$	−79.0495	−	541.319i	−0.0892207	−	0.610970i
$887$	−961.795	−	555.293i	−1.08432	−	0.626034i	−0.152264	−	0.988340i	$-0.548656\pi$
$887$	−961.795	−	555.293i	−1.08432	−	0.626034i	−0.932059	+	0.362305i	$0.881990\pi$
$888$	27.9708	−	12.9983i	0.0314987	−	0.0146377i
$889$		0			0
$890$	−207.288	+	521.111i	−0.232908	+	0.585518i
$891$	118.236	−	204.790i	0.132700	−	0.229843i
$892$	−1211.92	−	288.351i	−1.35865	−	0.323264i
$893$	−324.538	+	187.372i	−0.363424	+	0.209823i
$894$	5.72709	+	7.24961i	0.00640614	+	0.00810918i
$895$		−	559.458i		−	0.625092i
$896$		0			0
$897$	31.2863			0.0348788
$898$	−672.793	+	531.497i	−0.749213	+	0.591868i
$899$	609.747	+	1056.11i	0.678250	+	1.17476i
$900$	−108.134	+	454.478i	−0.120148	+	0.504975i
$901$	−120.808	−	69.7488i	−0.134083	−	0.0774127i
$902$	249.685	+	99.3202i	0.276813	+	0.110111i
$903$		0			0
$904$	−135.480	−	291.536i	−0.149867	−	0.322496i
$905$	12.3838	−	21.4494i	0.0136837	−	0.0237009i
$906$	−22.0934	+	3.22633i	−0.0243857	+	0.00356107i
$907$	259.004	+	448.609i	0.285562	+	0.494607i	0.972745	−	0.231876i	$-0.0744865\pi$
$907$	259.004	+	448.609i	0.285562	+	0.494607i	−0.687184	+	0.726484i	$0.741153\pi$
$908$	285.012	−	85.0551i	0.313890	−	0.0936730i
$909$			960.430i			1.05658i
$910$		0			0
$911$		−	1065.61i		−	1.16972i	−0.811135	−	0.584860i	$-0.801150\pi$
$911$		−	1065.61i		−	1.16972i	0.811135	−	0.584860i	$-0.198850\pi$
$912$	−11.2711	−	5.68529i	−0.0123586	−	0.00623387i
$913$	160.593	+	278.155i	0.175896	+	0.304661i
$914$	−2.90443	−	19.8891i	−0.00317771	−	0.0217605i
$915$	−1.26292	+	2.18743i	−0.00138024	+	0.00239064i
$916$	−215.051	+	227.541i	−0.234772	+	0.248407i
$917$		0			0
$918$	46.8761	+	18.6464i	0.0510632	+	0.0203120i
$919$	1025.08	+	591.831i	1.11543	+	0.643994i	0.940231	−	0.340538i	$-0.110609\pi$
$919$	1025.08	+	591.831i	1.11543	+	0.643994i	0.175200	+	0.984533i	$0.443943\pi$
$920$	−267.009	+	380.265i	−0.290227	+	0.413331i
$921$	−14.1508	−	24.5099i	−0.0153646	−	0.0266123i
$922$	1023.82	+	1295.99i	1.11043	+	1.40563i
$923$	2475.03			2.68151
$924$		0			0
$925$			514.018i			0.555695i
$926$	−142.212	−	180.019i	−0.153577	−	0.194404i
$927$	985.914	−	569.217i	1.06355	−	0.614043i
$928$	−173.919	−	851.700i	−0.187413	−	0.917781i
$929$	−189.509	+	328.240i	−0.203993	+	0.353326i	−0.949811	−	0.312823i	$-0.898725\pi$
$929$	−189.509	+	328.240i	−0.203993	+	0.353326i	0.745818	+	0.666149i	$0.232059\pi$
$930$	−28.1701	−	11.2055i	−0.0302904	−	0.0120490i
$931$		0			0
$932$	270.526	+	255.676i	0.290264	+	0.274331i
$933$	6.32093	+	3.64939i	0.00677485	+	0.00391146i
$934$	−58.2986	−	399.220i	−0.0624182	−	0.427431i
$935$	−126.478	+	73.0221i	−0.135271	+	0.0780985i
$936$	−121.900	+	1372.56i	−0.130235	+	1.46641i
$937$	−1316.09			−1.40458			−0.702289	−	0.711892i	$-0.747839\pi$
$937$	−1316.09			−1.40458			−0.702289	+	0.711892i	$0.747839\pi$
$938$		0			0
$939$	27.7214			0.0295223
$940$	614.729	−	183.451i	0.653967	−	0.195161i
$941$	430.441	−	248.515i	0.457430	−	0.264097i	−0.253533	−	0.967327i	$-0.581593\pi$
$941$	430.441	−	248.515i	0.457430	−	0.264097i	0.710963	+	0.703230i	$0.248259\pi$
$942$	−56.7097	+	8.28139i	−0.0602014	+	0.00879129i
$943$	665.872	+	384.442i	0.706121	+	0.407679i
$944$	103.367	+	1829.95i	0.109499	+	1.93850i
$945$		0			0
$946$	−332.176	−	132.134i	−0.351138	−	0.139676i
$947$	−404.243	+	700.170i	−0.426867	+	0.739356i	−0.996593	−	0.0824792i	$-0.973716\pi$
$947$	−404.243	+	700.170i	−0.426867	+	0.739356i	0.569726	+	0.821835i	$0.307050\pi$
$948$	16.1587	+	3.84462i	0.0170450	+	0.00405551i
$949$	303.387	−	175.161i	0.319692	−	0.184574i
$950$	165.082	−	130.413i	0.173771	−	0.137276i
$951$		−	1.19488i		−	0.00125644i
$952$		0			0
$953$	−1345.58			−1.41194			−0.705969	−	0.708243i	$-0.749488\pi$
$953$	−1345.58			−1.41194			−0.705969	+	0.708243i	$0.749488\pi$
$954$	108.055	+	136.781i	0.113265	+	0.143376i
$955$	−127.007	−	219.982i	−0.132991	−	0.230347i
$956$	−1134.74	−	269.989i	−1.18697	−	0.282415i
$957$	6.71320	+	3.87587i	0.00701484	+	0.00405002i
$958$	441.715	−	1110.45i	0.461081	−	1.15913i
$959$		0			0
$960$	16.5180	+	13.9344i	0.0172063	+	0.0145150i
$961$	527.158	−	913.065i	0.548552	−	0.950119i
$962$	219.083	+	1500.25i	0.227737	+	1.55951i
$963$	391.173	+	677.532i	0.406203	+	0.703564i
$964$	857.616	−	255.935i	0.889643	−	0.265493i
$965$		−	294.809i		−	0.305502i
$966$		0			0
$967$		−	140.279i		−	0.145066i	−0.997366	−	0.0725330i	$-0.976892\pi$
$967$		−	140.279i		−	0.145066i	0.997366	−	0.0725330i	$-0.0231083\pi$
$968$	895.857	+	79.5632i	0.925473	+	0.0821934i
$969$	−5.67666	−	9.83226i	−0.00585826	−	0.0101468i
$970$	−1111.62	+	162.331i	−1.14600	+	0.167352i
$971$	719.336	−	1245.93i	0.740820	−	1.28314i	−0.211303	−	0.977421i	$-0.567771\pi$
$971$	719.336	−	1245.93i	0.740820	−	1.28314i	0.952122	−	0.305717i	$-0.0988961\pi$
$972$	−68.7346	−	64.9616i	−0.0707146	−	0.0668330i
$973$		0			0
$974$	255.125	−	641.370i	0.261935	−	0.658491i
$975$	21.0011	+	12.1250i	0.0215396	+	0.0124359i
$976$	65.5928	+	100.110i	0.0672057	+	0.102572i
$977$	−451.095	−	781.319i	−0.461714	−	0.799712i	0.537332	−	0.843371i	$-0.319432\pi$
$977$	−451.095	−	781.319i	−0.461714	−	0.799712i	−0.999047	+	0.0436581i	$0.986099\pi$
$978$	26.1515	−	20.6594i	0.0267398	−	0.0211241i
$979$	−236.976			−0.242059
$980$		0			0
$981$			1707.49i			1.74056i
$982$	−586.158	+	463.057i	−0.596903	+	0.471545i
$983$	435.778	−	251.597i	0.443315	−	0.255948i	−0.261688	−	0.965153i	$-0.584279\pi$
$983$	435.778	−	251.597i	0.443315	−	0.255948i	0.705003	+	0.709205i	$0.250946\pi$
$984$	20.5498	−	29.2663i	0.0208840	−	0.0297422i
$985$	243.380	−	421.547i	0.247087	−	0.427967i
$986$	288.960	−	726.430i	0.293063	−	0.736744i
$987$		0			0
$988$	426.237	−	450.993i	0.431414	−	0.456470i
$989$	−885.864	−	511.454i	−0.895717	−	0.517142i
$990$	180.577	−	26.3699i	0.182401	−	0.0266363i
$991$	−784.898	+	453.161i	−0.792026	+	0.457277i	−0.840675	−	0.541539i	$-0.817842\pi$
$991$	−784.898	+	453.161i	−0.792026	+	0.457277i	0.0486491	+	0.998816i	$0.484508\pi$
$992$	−1075.23	+	952.663i	−1.08390	+	0.960346i
$993$	−18.9481			−0.0190816
$994$		0			0
$995$	−495.847			−0.498339
$996$	40.9585	−	12.2231i	0.0411230	−	0.0122722i
$997$	−527.085	+	304.313i	−0.528671	+	0.305228i	−0.740475	−	0.672084i	$-0.765399\pi$
$997$	−527.085	+	304.313i	−0.528671	+	0.305228i	0.211804	+	0.977312i	$0.432066\pi$
$998$	245.739	+	1682.79i	0.246232	+	1.68616i
$999$	−60.0687	−	34.6807i	−0.0601288	−	0.0347154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.k.n.275.2		16
7.2	even	3		392.3.g.m.99.8		8
7.3	odd	6		392.3.k.o.67.4		16
7.4	even	3	inner	392.3.k.n.67.4		16
7.5	odd	6		56.3.g.b.43.8	yes	8
7.6	odd	2		392.3.k.o.275.2		16
8.3	odd	2	inner	392.3.k.n.275.4		16
21.5	even	6		504.3.g.b.379.1		8
28.19	even	6		224.3.g.b.15.3		8
28.23	odd	6		1568.3.g.m.687.6		8
56.3	even	6		392.3.k.o.67.2		16
56.5	odd	6		224.3.g.b.15.4		8
56.11	odd	6	inner	392.3.k.n.67.2		16
56.19	even	6		56.3.g.b.43.7	✓	8
56.27	even	2		392.3.k.o.275.4		16
56.37	even	6		1568.3.g.m.687.5		8
56.51	odd	6		392.3.g.m.99.7		8
84.47	odd	6		2016.3.g.b.1135.5		8
112.5	odd	12		1792.3.d.j.1023.8		16
112.19	even	12		1792.3.d.j.1023.7		16
112.61	odd	12		1792.3.d.j.1023.9		16
112.75	even	12		1792.3.d.j.1023.10		16
168.5	even	6		2016.3.g.b.1135.4		8
168.131	odd	6		504.3.g.b.379.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.7	✓	8	56.19	even	6
56.3.g.b.43.8	yes	8	7.5	odd	6
224.3.g.b.15.3		8	28.19	even	6
224.3.g.b.15.4		8	56.5	odd	6
392.3.g.m.99.7		8	56.51	odd	6
392.3.g.m.99.8		8	7.2	even	3
392.3.k.n.67.2		16	56.11	odd	6	inner
392.3.k.n.67.4		16	7.4	even	3	inner
392.3.k.n.275.2		16	1.1	even	1	trivial
392.3.k.n.275.4		16	8.3	odd	2	inner
392.3.k.o.67.2		16	56.3	even	6
392.3.k.o.67.4		16	7.3	odd	6
392.3.k.o.275.2		16	7.6	odd	2
392.3.k.o.275.4		16	56.27	even	2
504.3.g.b.379.1		8	21.5	even	6
504.3.g.b.379.2		8	168.131	odd	6
1568.3.g.m.687.5		8	56.37	even	6
1568.3.g.m.687.6		8	28.23	odd	6
1792.3.d.j.1023.7		16	112.19	even	12
1792.3.d.j.1023.8		16	112.5	odd	12
1792.3.d.j.1023.9		16	112.61	odd	12
1792.3.d.j.1023.10		16	112.75	even	12
2016.3.g.b.1135.4		8	168.5	even	6
2016.3.g.b.1135.5		8	84.47	odd	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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.56937 + 1.23978i) q^{2} +(0.0487183 + 0.0843825i) q^{3} +(0.925871 - 3.89137i) q^{4} +(-3.00119 - 1.73274i) q^{5} +(-0.181073 - 0.0720276i) q^{6} +(3.37142 + 7.25490i) q^{8} +(4.49525 - 7.78601i) q^{9} +O(q^{10})\)	\(q+(-1.56937 + 1.23978i) q^{2} +(0.0487183 + 0.0843825i) q^{3} +(0.925871 - 3.89137i) q^{4} +(-3.00119 - 1.73274i) q^{5} +(-0.181073 - 0.0720276i) q^{6} +(3.37142 + 7.25490i) q^{8} +(4.49525 - 7.78601i) q^{9} +(6.85820 - 1.00151i) q^{10} +(1.46433 + 2.53629i) q^{11} +(0.373471 - 0.111454i) q^{12} +19.1586i q^{13} -0.337664i q^{15} +(-14.2855 - 7.20582i) q^{16} +(-7.19487 - 12.4619i) q^{17} +(2.59823 + 17.7923i) q^{18} +(4.04872 - 7.01259i) q^{19} +(-9.52143 + 10.0744i) q^{20} +(-5.44254 - 2.16494i) q^{22} +(-14.5144 - 8.37990i) q^{23} +(-0.447937 + 0.637935i) q^{24} +(-6.49525 - 11.2501i) q^{25} +(-23.7525 - 30.0670i) q^{26} +1.75293 q^{27} -27.1649i q^{29} +(0.418630 + 0.529921i) q^{30} +(-38.8779 + 22.4461i) q^{31} +(31.3530 - 6.40234i) q^{32} +(-0.142679 + 0.247128i) q^{33} +(26.7415 + 10.6373i) q^{34} +(-26.1362 - 24.7015i) q^{36} +(-34.2675 - 19.7844i) q^{37} +(2.34014 + 16.0249i) q^{38} +(-1.61665 + 0.933373i) q^{39} +(2.45256 - 27.6151i) q^{40} -45.8766 q^{41} +61.0334 q^{43} +(11.2254 - 3.34997i) q^{44} +(-26.9822 + 15.5782i) q^{45} +(33.1678 - 4.84354i) q^{46} +(-40.0790 - 23.1396i) q^{47} +(-0.0879212 - 1.55650i) q^{48} +(24.1412 + 9.60292i) q^{50} +(0.701044 - 1.21424i) q^{51} +(74.5532 + 17.7384i) q^{52} +(8.39546 - 4.84712i) q^{53} +(-2.75101 + 2.17326i) q^{54} -10.1492i q^{55} +0.788986 q^{57} +(33.6786 + 42.6319i) q^{58} +(-57.2770 - 99.2066i) q^{59} +(-1.31397 - 0.312633i) q^{60} +(-6.47814 - 3.74016i) q^{61} +(33.1855 - 83.4265i) q^{62} +(-41.2671 + 48.9186i) q^{64} +(33.1968 - 57.4985i) q^{65} +(-0.0824679 - 0.564728i) q^{66} +(6.02950 + 10.4434i) q^{67} +(-55.1553 + 16.4598i) q^{68} -1.63302i q^{69} -129.187i q^{71} +(71.6421 + 6.36270i) q^{72} +(-9.14268 - 15.8356i) q^{73} +(78.3069 - 11.4353i) q^{74} +(0.632875 - 1.09617i) q^{75} +(-23.5400 - 22.2478i) q^{76} +(1.37995 - 3.46911i) q^{78} +(36.9073 + 21.3084i) q^{79} +(30.3877 + 46.3790i) q^{80} +(-40.3719 - 69.9261i) q^{81} +(71.9976 - 56.8771i) q^{82} +109.670 q^{83} +49.8673i q^{85} +(-95.7842 + 75.6682i) q^{86} +(2.29224 - 1.32343i) q^{87} +(-13.4637 + 19.1745i) q^{88} +(-40.4581 + 70.0755i) q^{89} +(23.0316 - 57.9001i) q^{90} +(-46.0478 + 48.7223i) q^{92} +(-3.78812 - 2.18707i) q^{93} +(91.5872 - 13.3746i) q^{94} +(-24.3019 + 14.0307i) q^{95} +(2.06771 + 2.33373i) q^{96} -162.086 q^{97} +26.3301 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9}+O(q^{10}) \) 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9	\( 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9} + 16 q^{10} + 32 q^{11} + 30 q^{12} + 71 q^{16} - 80 q^{17} + 29 q^{18} + 56 q^{19} + 216 q^{20} + 132 q^{22} + 22 q^{24} + 16 q^{25} + 24 q^{26} + 64 q^{27} - 96 q^{30} + 19 q^{32} + 32 q^{33} - 148 q^{34} - 66 q^{36} - 14 q^{38} + 84 q^{40} - 256 q^{41} - 50 q^{44} + 152 q^{46} - 268 q^{48} + 66 q^{50} + 368 q^{51} + 132 q^{52} - 228 q^{54} + 112 q^{57} - 24 q^{58} + 104 q^{59} - 192 q^{60} - 240 q^{62} - 110 q^{64} + 72 q^{65} - 276 q^{66} - 304 q^{67} - 190 q^{68} + 209 q^{72} - 112 q^{73} - 8 q^{74} + 72 q^{75} - 140 q^{76} - 608 q^{78} + 124 q^{80} - 48 q^{81} + 450 q^{82} - 144 q^{83} - 210 q^{86} + 486 q^{88} - 512 q^{89} + 368 q^{90} - 944 q^{92} + 472 q^{94} + 558 q^{96} - 128 q^{97} + 512 q^{99}+O(q^{100}) \) 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9 + 16 * q^10 + 32 * q^11 + 30 * q^12 + 71 * q^16 - 80 * q^17 + 29 * q^18 + 56 * q^19 + 216 * q^20 + 132 * q^22 + 22 * q^24 + 16 * q^25 + 24 * q^26 + 64 * q^27 - 96 * q^30 + 19 * q^32 + 32 * q^33 - 148 * q^34 - 66 * q^36 - 14 * q^38 + 84 * q^40 - 256 * q^41 - 50 * q^44 + 152 * q^46 - 268 * q^48 + 66 * q^50 + 368 * q^51 + 132 * q^52 - 228 * q^54 + 112 * q^57 - 24 * q^58 + 104 * q^59 - 192 * q^60 - 240 * q^62 - 110 * q^64 + 72 * q^65 - 276 * q^66 - 304 * q^67 - 190 * q^68 + 209 * q^72 - 112 * q^73 - 8 * q^74 + 72 * q^75 - 140 * q^76 - 608 * q^78 + 124 * q^80 - 48 * q^81 + 450 * q^82 - 144 * q^83 - 210 * q^86 + 486 * q^88 - 512 * q^89 + 368 * q^90 - 944 * q^92 + 472 * q^94 + 558 * q^96 - 128 * q^97 + 512 * q^99

Introduction

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