LMFDB - Embedded newform 392.3.k.o.67.4

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			67.4
Root			$0.288997 + 1.97901i$ of defining polynomial
Character	$\chi$	$=$	392.67
Dual form			392.3.k.o.275.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.288997 - 1.97901i) q^{2} +(-0.0487183 + 0.0843825i) q^{3} +(-3.83296 + 1.14386i) q^{4} +(-3.00119 + 1.73274i) q^{5} +(0.181073 + 0.0720276i) q^{6} +(3.37142 + 7.25490i) q^{8} +(4.49525 + 7.78601i) q^{9} +O(q^{10})$	\(q+(-0.288997 - 1.97901i) q^{2} +(-0.0487183 + 0.0843825i) q^{3} +(-3.83296 + 1.14386i) 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} +(4.29644 + 5.43862i) q^{10} +(1.46433 - 2.53629i) q^{11} +(0.0902137 - 0.379162i) q^{12} -19.1586i q^{13} -0.337664i q^{15} +(13.3832 - 8.76872i) q^{16} +(7.19487 - 12.4619i) q^{17} +(14.1095 - 11.1463i) 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} +(-0.776436 - 0.0689571i) q^{24} +(-6.49525 + 11.2501i) q^{25} +(-37.9150 + 5.53678i) q^{26} -1.75293 q^{27} -27.1649i q^{29} +(-0.668240 + 0.0975839i) q^{30} +(-38.8779 - 22.4461i) q^{31} +(-21.2211 - 23.9513i) 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} +(-12.7079 + 10.0391i) q^{38} +(1.61665 + 0.933373i) q^{39} +(-22.6891 - 15.9315i) q^{40} +45.8766 q^{41} +61.0334 q^{43} +(-2.71156 + 11.3965i) q^{44} +(-26.9822 - 15.5782i) q^{45} +(-20.7785 - 26.3024i) 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} +(21.9147 + 73.4341i) q^{52} +(-8.39546 - 4.84712i) q^{53} +(0.506593 + 3.46907i) q^{54} +10.1492i q^{55} +0.788986 q^{57} +(-53.7596 + 7.85058i) q^{58} +(57.2770 - 99.2066i) q^{59} +(0.386239 + 1.29425i) 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} +(0.447834 - 0.353783i) q^{66} +(6.02950 - 10.4434i) q^{67} +(-13.3231 + 55.9958i) q^{68} +1.63302i q^{69} -129.187i q^{71} +(-41.3313 + 58.8625i) q^{72} +(9.14268 - 15.8356i) q^{73} +(-49.0567 - 62.0981i) 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} +(-24.9716 + 49.5061i) q^{80} +(-40.3719 + 69.9261i) q^{81} +(-13.2582 - 90.7903i) q^{82} -109.670 q^{83} +49.8673i q^{85} +(-17.6385 - 120.786i) q^{86} +(2.29224 + 1.32343i) q^{87} +(23.3374 + 2.07265i) 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} +(57.3763 + 72.6295i) q^{94} +(24.3019 + 14.0307i) q^{95} +(3.05493 - 0.623822i) 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 $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.288997	−	1.97901i	−0.144499	−	0.989505i
$2$	−0.288997	−	1.97901i	−0.144499	−	0.989505i
$3$	−0.0487183	+	0.0843825i	−0.0162394	+	0.0281275i	−0.874031	−	0.485870i	$-0.838503\pi$
$3$	−0.0487183	+	0.0843825i	−0.0162394	+	0.0281275i	0.857791	+	0.513998i	$0.171836\pi$
$4$	−3.83296	+	1.14386i	−0.958240	+	0.285964i
$5$	−3.00119	+	1.73274i	−0.600237	+	0.346547i	−0.769135	−	0.639086i	$-0.779313\pi$
$5$	−3.00119	+	1.73274i	−0.600237	+	0.346547i	0.168898	+	0.985634i	$0.445979\pi$
$6$	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
$10$	4.29644	+	5.43862i	0.429644	+	0.543862i
$11$	1.46433	−	2.53629i	0.133121	−	0.230572i	−0.791757	−	0.610836i	$-0.790833\pi$
$11$	1.46433	−	2.53629i	0.133121	−	0.230572i	0.924878	+	0.380264i	$0.124167\pi$
$12$	0.0902137	−	0.379162i	0.00751781	−	0.0315968i
$13$		−	19.1586i		−	1.47374i	−0.676036	−	0.736869i	$-0.736304\pi$
$13$		−	19.1586i		−	1.47374i	0.676036	−	0.736869i	$-0.263696\pi$
$14$		0			0
$15$		−	0.337664i		−	0.0225109i
$16$	13.3832	−	8.76872i	0.836449	−	0.548045i
$17$	7.19487	−	12.4619i	0.423228	−	0.733052i	−0.573025	−	0.819538i	$-0.694230\pi$
$17$	7.19487	−	12.4619i	0.423228	−	0.733052i	0.996253	+	0.0864856i	$0.0275637\pi$
$18$	14.1095	−	11.1463i	0.783859	−	0.619238i
$19$	−4.04872	−	7.01259i	−0.213090	−	0.369083i	0.739590	−	0.673058i	$-0.235020\pi$
$19$	−4.04872	−	7.01259i	−0.213090	−	0.369083i	−0.952680	+	0.303975i	$0.901686\pi$
$20$	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	$-0.547960\pi$
$23$	14.5144	−	8.37990i	0.631062	−	0.364344i	0.781163	+	0.624327i	$0.214627\pi$
$24$	−0.776436	−	0.0689571i	−0.0323515	−	0.00287321i
$25$	−6.49525	+	11.2501i	−0.259810	+	0.450004i
$26$	−37.9150	+	5.53678i	−1.45827	+	0.212953i
$27$	−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	$-0.155155\pi$
$30$	−0.668240	+	0.0975839i	−0.0222747	+	0.00325280i
$31$	−38.8779	−	22.4461i	−1.25412	−	0.724069i	−0.282198	−	0.959356i	$-0.591064\pi$
$31$	−38.8779	−	22.4461i	−1.25412	−	0.724069i	−0.971926	+	0.235287i	$0.924397\pi$
$32$	−21.2211	−	23.9513i	−0.663159	−	0.748479i
$33$	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	$-0.487087\pi$
$37$	34.2675	−	19.7844i	0.926149	−	0.534713i	0.885592	+	0.464465i	$0.153753\pi$
$38$	−12.7079	+	10.0391i	−0.334419	+	0.264186i
$39$	1.61665	+	0.933373i	0.0414526	+	0.0239327i
$40$	−22.6891	−	15.9315i	−0.567227	−	0.398288i
$41$	45.8766			1.11894			0.559471	−	0.828850i	$-0.311004\pi$
$41$	45.8766			1.11894			0.559471	+	0.828850i	$0.311004\pi$
$42$		0			0
$43$	61.0334			1.41938			0.709690	−	0.704514i	$-0.248835\pi$
$43$	61.0334			1.41938			0.709690	+	0.704514i	$0.248835\pi$
$44$	−2.71156	+	11.3965i	−0.0616264	+	0.259011i
$45$	−26.9822	−	15.5782i	−0.599604	−	0.346182i
$46$	−20.7785	−	26.3024i	−0.451707	−	0.571791i
$47$	−40.0790	+	23.1396i	−0.852746	+	0.492333i	−0.861576	−	0.507628i	$-0.830522\pi$
$47$	−40.0790	+	23.1396i	−0.852746	+	0.492333i	0.00883070	+	0.999961i	$0.497189\pi$
$48$	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
$52$	21.9147	+	73.4341i	0.421436	+	1.41219i
$53$	−8.39546	−	4.84712i	−0.158405	−	0.0914551i	0.418702	−	0.908124i	$-0.362485\pi$
$53$	−8.39546	−	4.84712i	−0.158405	−	0.0914551i	−0.577107	+	0.816669i	$0.695818\pi$
$54$	0.506593	+	3.46907i	0.00938135	+	0.0642421i
$55$			10.1492i			0.184531i
$56$		0			0
$57$	0.788986			0.0138419
$58$	−53.7596	+	7.85058i	−0.926889	+	0.135355i
$59$	57.2770	−	99.2066i	0.970796	−	1.68147i	0.277632	−	0.960687i	$-0.410450\pi$
$59$	57.2770	−	99.2066i	0.970796	−	1.68147i	0.693164	−	0.720780i	$-0.256216\pi$
$60$	0.386239	+	1.29425i	0.00643732	+	0.0215709i
$61$	−6.47814	+	3.74016i	−0.106199	+	0.0613141i	−0.552159	−	0.833739i	$-0.686196\pi$
$61$	−6.47814	+	3.74016i	−0.106199	+	0.0613141i	0.445960	+	0.895053i	$0.352862\pi$
$62$	−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
$66$	0.447834	−	0.353783i	0.00678537	−	0.00536035i
$67$	6.02950	−	10.4434i	0.0899925	−	0.155872i	−0.817515	−	0.575907i	$-0.804649\pi$
$67$	6.02950	−	10.4434i	0.0899925	−	0.155872i	0.907508	+	0.420035i	$0.137982\pi$
$68$	−13.3231	+	55.9958i	−0.195927	+	0.823468i
$69$			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	$-0.363738\pi$
$72$	−41.3313	+	58.8625i	−0.574046	+	0.817535i
$73$	9.14268	−	15.8356i	0.125242	−	0.216926i	−0.796585	−	0.604526i	$-0.793363\pi$
$73$	9.14268	−	15.8356i	0.125242	−	0.216926i	0.921828	+	0.387600i	$0.126696\pi$
$74$	−49.0567	−	62.0981i	−0.662928	−	0.839164i
$75$	−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	$-0.753600\pi$
$79$	−36.9073	+	21.3084i	−0.467180	+	0.269727i	0.247878	+	0.968791i	$0.420267\pi$
$80$	−24.9716	+	49.5061i	−0.312144	+	0.618826i
$81$	−40.3719	+	69.9261i	−0.498418	+	0.863286i
$82$	−13.2582	−	90.7903i	−0.161686	−	1.10720i
$83$	−109.670			−1.32133			−0.660663	−	0.750683i	$-0.729725\pi$
$83$	−109.670			−1.32133			−0.660663	+	0.750683i	$0.729725\pi$
$84$		0			0
$85$			49.8673i			0.586674i
$86$	−17.6385	−	120.786i	−0.205099	−	1.40448i
$87$	2.29224	+	1.32343i	0.0263476	+	0.0152118i
$88$	23.3374	+	2.07265i	0.265198	+	0.0235529i
$89$	40.4581	+	70.0755i	0.454585	+	0.787365i	0.998664	−	0.0516693i	$-0.0164542\pi$
$89$	40.4581	+	70.0755i	0.454585	+	0.787365i	−0.544079	+	0.839034i	$0.683121\pi$
$90$	−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
$94$	57.3763	+	72.6295i	0.610386	+	0.772655i
$95$	24.3019	+	14.0307i	0.255810	+	0.147692i
$96$	3.05493	−	0.623822i	0.0318222	−	0.00649815i
$97$	162.086			1.67099			0.835495	−	0.549498i	$-0.185181\pi$
$97$	162.086			1.67099			0.835495	+	0.549498i	$0.185181\pi$
$98$		0			0
$99$	26.3301			0.265961
$100$	12.0275	−	50.5509i	0.120275	−	0.505509i
$101$	−92.5150	−	53.4135i	−0.915990	−	0.528847i	−0.0336364	−	0.999434i	$-0.510709\pi$
$101$	−92.5150	−	53.4135i	−0.915990	−	0.528847i	−0.882354	+	0.470587i	$0.844042\pi$
$102$	2.20040	−	1.73829i	0.0215725	−	0.0170420i
$103$	109.662	−	63.3132i	1.06468	−	0.614691i	0.137954	−	0.990439i	$-0.455947\pi$
$103$	109.662	−	63.3132i	1.06468	−	0.614691i	0.926722	+	0.375748i	$0.122614\pi$
$104$	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	0.587878	−	0.808949i	$-0.299963\pi$
$107$	−43.5096	−	75.3608i	−0.406632	−	0.704306i	−0.994510	+	0.104643i	$0.966630\pi$
$108$	6.71892	−	2.00510i	0.0622123	−	0.0185658i
$109$	164.477	+	94.9607i	1.50896	+	0.871199i	0.999945	+	0.0104412i	$0.00332359\pi$
$109$	164.477	+	94.9607i	1.50896	+	0.871199i	0.509015	+	0.860758i	$0.330010\pi$
$110$	20.0853	−	2.93309i	0.182594	−	0.0266644i
$111$			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	$0.556901\pi$
$114$	−0.228015	−	1.56141i	−0.00200013	−	0.0136966i
$115$	−29.0403	+	50.2993i	−0.252524	+	0.437385i
$116$	31.0728	+	104.122i	0.267869	+	0.897603i
$117$	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
$122$	9.27398	+	11.7394i	0.0760162	+	0.0962247i
$123$	−2.23503	+	3.87119i	−0.0181710	+	0.0314731i
$124$	174.692	+	41.5645i	1.40881	+	0.335197i
$125$		−	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	$0.793194\pi$
$128$	108.736	+	67.5306i	0.849504	+	0.527583i
$129$	−2.97344	+	5.15015i	−0.0230499	+	0.0399236i
$130$	104.196	−	82.3137i	0.801510	−	0.633182i
$131$	−30.9325	−	53.5766i	−0.236126	−	0.408982i	0.723474	−	0.690352i	$-0.242544\pi$
$131$	−30.9325	−	53.5766i	−0.236126	−	0.408982i	−0.959599	+	0.281371i	$0.909211\pi$
$132$	−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
$136$	114.667	+	10.1838i	0.843137	+	0.0748810i
$137$	−52.9715	+	91.7494i	−0.386653	+	0.669703i	−0.991997	−	0.126261i	$-0.959702\pi$
$137$	−52.9715	+	91.7494i	−0.386653	+	0.669703i	0.605344	+	0.795964i	$0.293036\pi$
$138$	3.23176	−	0.471938i	0.0234185	−	0.00341984i
$139$	−185.384			−1.33370			−0.666848	−	0.745194i	$-0.732357\pi$
$139$	−185.384			−1.33370			−0.666848	+	0.745194i	$0.732357\pi$
$140$		0			0
$141$		−	4.50930i		−	0.0319808i
$142$	−255.662	+	37.3346i	−1.80043	+	0.262920i
$143$	−48.5918	−	28.0545i	−0.339803	−	0.196185i
$144$	128.434	+	64.7839i	0.891903	+	0.449888i
$145$	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	$-0.615810\pi$
$149$	41.0579	−	23.7048i	0.275556	−	0.159093i	0.631410	+	0.775449i	$0.282477\pi$
$150$	−1.98644	+	1.56926i	−0.0132429	+	0.0104617i
$151$	−99.2255	−	57.2879i	−0.657122	−	0.379390i	0.134057	−	0.990974i	$-0.457199\pi$
$151$	−99.2255	−	57.2879i	−0.657122	−	0.379390i	−0.791180	+	0.611584i	$0.790533\pi$
$152$	37.2257	−	53.0154i	0.244906	−	0.348786i
$153$	129.371			0.845563
$154$		0			0
$155$	155.573			1.00370
$156$	−7.26420	−	1.72837i	−0.0465654	−	0.0110793i
$157$	254.694	+	147.047i	1.62225	+	0.936608i	0.986316	+	0.164867i	$0.0527196\pi$
$157$	254.694	+	147.047i	1.62225	+	0.936608i	0.635937	+	0.771741i	$0.280614\pi$
$158$	52.8357	+	66.8818i	0.334403	+	0.423302i
$159$	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	−0.999590	−	0.0286465i	$-0.990880\pi$
$163$	−85.5104	−	148.108i	−0.524603	−	0.908640i	0.474986	−	0.879993i	$-0.342453\pi$
$164$	−175.843	+	52.4763i	−1.07222	+	0.319977i
$165$	−0.856414	−	0.494451i	−0.00519039	−	0.00299667i
$166$	31.6943	+	217.038i	0.190930	+	1.30746i
$167$			120.657i			0.722499i	0.932469	+	0.361249i	$0.117650\pi$
$167$			120.657i			0.722499i	−0.932469	+	0.361249i	$0.882350\pi$
$168$		0			0
$169$	−198.052			−1.17190
$170$	98.6878	−	14.4115i	0.580516	−	0.0847735i
$171$	36.4000	−	63.0467i	0.212866	−	0.368694i
$172$	−233.939	+	69.8134i	−1.36011	+	0.405892i
$173$	−93.8242	+	54.1694i	−0.542336	+	0.313118i	−0.746025	−	0.665918i	$-0.768040\pi$
$173$	−93.8242	+	54.1694i	−0.542336	+	0.313118i	0.203689	+	0.979036i	$0.434707\pi$
$174$	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
$178$	126.988	−	100.319i	0.713414	−	0.563587i
$179$	80.7188	−	139.809i	0.450943	−	0.781056i	−0.547502	−	0.836805i	$-0.684421\pi$
$179$	80.7188	−	139.809i	0.450943	−	0.781056i	0.998445	+	0.0557481i	$0.0177544\pi$
$180$	121.241	+	28.8468i	0.673560	+	0.160260i
$181$		−	7.14696i		−	0.0394860i	−0.999805	−	0.0197430i	$-0.993715\pi$
$181$		−	7.14696i		−	0.0394860i	0.999805	−	0.0197430i	$-0.00628479\pi$
$182$		0			0
$183$		−	0.728856i		−	0.00398282i
$184$	109.730	+	77.0484i	0.596356	+	0.418741i
$185$	−68.5621	+	118.753i	−0.370606	+	0.641909i
$186$	−5.42300	−	6.86468i	−0.0291559	−	0.0369069i
$187$	−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	$-0.728125\pi$
$191$	−63.4782	+	36.6491i	−0.332347	+	0.191880i	0.324536	+	0.945873i	$0.394792\pi$
$192$	−2.11742	−	5.86545i	−0.0110282	−	0.0305492i
$193$	42.5353	−	73.6732i	0.220390	−	0.381727i	−0.734536	−	0.678569i	$-0.762600\pi$
$193$	42.5353	−	73.6732i	0.220390	−	0.381727i	0.954926	+	0.296843i	$0.0959337\pi$
$194$	−46.8424	−	320.770i	−0.241456	−	1.65345i
$195$	−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	$0.883971\pi$
$198$	−7.60934	−	52.1076i	−0.0384310	−	0.263170i
$199$	123.913	+	71.5411i	0.622677	+	0.359503i	0.777911	−	0.628375i	$-0.216280\pi$
$199$	123.913	+	71.5411i	0.622677	+	0.359503i	−0.155233	+	0.987878i	$0.549613\pi$
$200$	−103.517	−	9.19355i	−0.517583	−	0.0459677i
$201$	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
$206$	−156.989	−	198.724i	−0.762084	−	0.964680i
$207$	130.492	+	75.3396i	0.630396	+	0.363959i
$208$	−167.996	−	256.403i	−0.807674	−	1.23271i
$209$	−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	$0.585469\pi$
$212$	37.7239	+	8.97562i	0.177943	+	0.0423378i
$213$	10.9011	+	6.29375i	0.0511788	+	0.0295481i
$214$	−136.566	+	107.885i	−0.638157	+	0.504135i
$215$	−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
$220$	−11.6092	−	38.9014i	−0.0527692	−	0.176825i
$221$	−238.752	−	137.844i	−1.08033	−	0.623727i
$222$	7.62996	−	1.11421i	0.0343692	−	0.00501897i
$223$			311.438i			1.39658i	0.715814	+	0.698291i	$0.246056\pi$
$223$			311.438i			1.39658i	−0.715814	+	0.698291i	$0.753944\pi$
$224$		0			0
$225$	−116.791			−0.519072
$226$	11.6133	+	79.5261i	0.0513862	+	0.351885i
$227$	−37.1791	+	64.3960i	−0.163784	+	0.283683i	−0.936223	−	0.351407i	$-0.885703\pi$
$227$	−37.1791	+	64.3960i	−0.163784	+	0.283683i	0.772439	+	0.635090i	$0.219037\pi$
$228$	−3.02415	+	0.902488i	−0.0132638	+	0.00395828i
$229$	−67.7847	+	39.1355i	−0.296003	+	0.170897i	−0.640646	−	0.767836i	$-0.721333\pi$
$229$	−67.7847	+	39.1355i	−0.296003	+	0.170897i	0.344643	+	0.938734i	$0.388000\pi$
$230$	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	0.748735	−	0.662869i	$-0.230661\pi$
$233$	−46.5287	−	80.5900i	−0.199694	−	0.345880i	−0.948429	+	0.316989i	$0.897328\pi$
$234$	−213.547	−	270.318i	−0.912594	−	1.15520i
$235$	80.1898	−	138.893i	0.341233	−	0.591033i
$236$	−106.062	+	445.772i	−0.449416	+	1.88886i
$237$		−	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	$-0.208852\pi$
$240$	−2.96088	−	4.51901i	−0.0123370	−	0.0188292i
$241$	−111.874	+	193.771i	−0.464207	+	0.804029i	−0.999165	−	0.0408488i	$-0.986994\pi$
$241$	−111.874	+	193.771i	−0.464207	+	0.804029i	0.534959	+	0.844878i	$0.320327\pi$
$242$	176.434	−	139.380i	0.729065	−	0.575951i
$243$	−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
$248$	31.7708	−	357.730i	0.128108	−	1.44246i
$249$	5.34294	−	9.25424i	0.0214576	−	0.0371656i
$250$	−260.547	+	38.0479i	−1.04219	+	0.152192i
$251$	−310.605			−1.23747			−0.618734	−	0.785600i	$-0.712354\pi$
$251$	−310.605			−1.23747			−0.618734	+	0.785600i	$0.712354\pi$
$252$		0			0
$253$		−	49.0838i		−	0.194007i
$254$	304.088	−	44.4063i	1.19720	−	0.174828i
$255$	−4.20793	−	2.42945i	−0.0165017	−	0.00952724i
$256$	102.219	−	234.707i	0.399293	−	0.916823i
$257$	−87.7358	−	151.963i	−0.341385	−	0.591295i	0.643306	−	0.765610i	$-0.277562\pi$
$257$	−87.7358	−	151.963i	−0.341385	−	0.591295i	−0.984690	+	0.174314i	$0.944229\pi$
$258$	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
$262$	−97.0892	+	76.6991i	−0.370569	+	0.292745i
$263$	−270.310	−	156.064i	−1.02779	−	0.593398i	−0.111443	−	0.993771i	$-0.535547\pi$
$263$	−270.310	−	156.064i	−1.02779	−	0.593398i	−0.916352	+	0.400373i	$0.868880\pi$
$264$	−1.31185	+	1.86830i	−0.00496915	+	0.00707688i
$265$	33.5951			0.126774
$266$		0			0
$267$	−7.88419			−0.0295288
$268$	−11.1651	+	46.9260i	−0.0416607	+	0.175097i
$269$	−123.683	−	71.4084i	−0.459788	−	0.265459i	0.252167	−	0.967684i	$-0.418857\pi$
$269$	−123.683	−	71.4084i	−0.459788	−	0.265459i	−0.711955	+	0.702225i	$0.752190\pi$
$270$	−7.53137	−	9.53354i	−0.0278939	−	0.0353094i
$271$	−230.464	+	133.059i	−0.850421	+	0.490991i	−0.860793	−	0.508955i	$-0.830032\pi$
$271$	−230.464	+	133.059i	−0.850421	+	0.490991i	0.0103718	+	0.999946i	$0.496699\pi$
$272$	−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
$276$	−1.86794	−	6.25929i	−0.00676789	−	0.0226786i
$277$	−317.606	−	183.370i	−1.14659	−	0.661986i	−0.198539	−	0.980093i	$-0.563620\pi$
$277$	−317.606	−	183.370i	−1.14659	−	0.661986i	−0.948055	+	0.318107i	$0.896953\pi$
$278$	53.5754	+	366.876i	0.192717	+	1.31970i
$279$		−	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	$0.415188\pi$
$282$	−8.92394	+	1.30317i	−0.0316452	+	0.00462118i
$283$	−163.869	+	283.830i	−0.579043	+	1.00293i	0.416546	+	0.909115i	$0.363241\pi$
$283$	−163.869	+	283.830i	−0.579043	+	1.00293i	−0.995589	+	0.0938180i	$0.970093\pi$
$284$	147.771	+	495.167i	0.520320	+	1.74355i
$285$	−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
$290$	147.740	−	116.712i	0.509447	−	0.402456i
$291$	−7.89655	+	13.6772i	−0.0271359	+	0.0470008i
$292$	−16.9299	+	71.1551i	−0.0579791	+	0.243682i
$293$			259.881i			0.886966i	0.896283	+	0.443483i	$0.146257\pi$
$293$			259.881i			0.886966i	−0.896283	+	0.443483i	$0.853743\pi$
$294$		0			0
$295$			396.983i			1.34571i
$296$	259.064	+	181.906i	0.875215	+	0.614547i
$297$	−2.56687	+	4.44595i	−0.00864267	+	0.0149695i
$298$	−58.7776	−	74.4034i	−0.197240	−	0.249676i
$299$	−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
$304$	−115.676	−	58.3486i	−0.380514	−	0.191936i
$305$	12.9614	−	22.4498i	0.0424964	−	0.0736060i
$306$	−37.3879	−	256.027i	−0.122183	−	0.836689i
$307$	290.462			0.946131			0.473065	−	0.881027i	$-0.343147\pi$
$307$	290.462			0.946131			0.473065	+	0.881027i	$0.343147\pi$
$308$		0			0
$309$			12.3380i			0.0399289i
$310$	−44.9602	−	307.880i	−0.145033	−	0.993162i
$311$	64.8723	+	37.4540i	0.208593	+	0.120431i	0.600657	−	0.799507i	$-0.294906\pi$
$311$	64.8723	+	37.4540i	0.208593	+	0.120431i	−0.392065	+	0.919938i	$0.628239\pi$
$312$	−1.32112	+	14.8754i	−0.00423436	+	0.0476776i
$313$	−142.254	−	246.391i	−0.454485	−	0.787190i	0.544174	−	0.838972i	$-0.316843\pi$
$313$	−142.254	−	246.391i	−0.454485	−	0.787190i	−0.998658	+	0.0517821i	$0.983510\pi$
$314$	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	$-0.660509\pi$
$317$	10.6202	−	6.13157i	0.0335022	−	0.0193425i	0.516658	+	0.856192i	$0.327176\pi$
$318$	−1.17107	−	1.48239i	−0.00368260	−	0.00466160i
$319$	−68.8982	−	39.7784i	−0.215982	−	0.124697i
$320$	39.0871	−	218.319i	0.122147	−	0.682246i
$321$	8.47885			0.0264139
$322$		0			0
$323$	−116.520			−0.360743
$324$	74.7583	−	314.204i	0.230736	−	0.969765i
$325$	215.536	+	124.440i	0.663188	+	0.382892i
$326$	−268.395	+	212.029i	−0.823299	+	0.650395i
$327$	−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	0.680940	−	0.732340i	$-0.261572\pi$
$331$	−97.2329	−	168.412i	−0.293755	−	0.508798i	−0.974694	+	0.223541i	$0.928238\pi$
$332$	420.361	−	125.447i	1.26615	−	0.377852i
$333$	308.082	+	177.871i	0.925172	+	0.534148i
$334$	238.782	−	34.8696i	0.714916	−	0.104400i
$335$			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	$0.499718\pi$
$338$	57.2364	+	391.946i	0.169338	+	1.15960i
$339$	1.95773	−	3.39089i	0.00577502	−	0.0100026i
$340$	−57.0410	−	191.139i	−0.167768	−	0.562174i
$341$	−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
$346$	134.317	+	170.024i	0.388199	+	0.491399i
$347$	102.433	−	177.420i	0.295197	−	0.511296i	−0.679834	−	0.733366i	$-0.737948\pi$
$347$	102.433	−	177.420i	0.295197	−	0.511296i	0.975031	+	0.222070i	$0.0712814\pi$
$348$	−10.2999	−	2.45065i	−0.0295974	−	0.00704208i
$349$		−	128.396i		−	0.367898i	−0.982936	−	0.183949i	$-0.941112\pi$
$349$		−	128.396i		−	0.367898i	0.982936	−	0.183949i	$-0.0588882\pi$
$350$		0			0
$351$			33.5837i			0.0956801i
$352$	−91.8223	+	18.7503i	−0.260859	+	0.0532679i
$353$	95.4207	−	165.274i	0.270314	−	0.468197i	−0.698628	−	0.715485i	$-0.746206\pi$
$353$	95.4207	−	165.274i	0.270314	−	0.468197i	0.968942	+	0.247288i	$0.0795393\pi$
$354$	17.5169	−	13.8381i	0.0494829	−	0.0390908i
$355$	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	$-0.569539\pi$
$359$	186.805	−	107.852i	0.520349	−	0.300424i	0.737077	+	0.675808i	$0.236205\pi$
$360$	22.0497	−	248.274i	0.0612493	−	0.689649i
$361$	147.716	−	255.851i	0.409185	−	0.708729i
$362$	−14.1439	+	2.06545i	−0.0390715	+	0.00570567i
$363$	−10.9541			−0.0301766
$364$		0			0
$365$			63.3674i			0.173609i
$366$	−1.44241	+	0.210637i	−0.00394102	+	0.000575512i
$367$	393.859	+	227.395i	1.07319	+	0.619604i	0.929050	−	0.369954i	$-0.120627\pi$
$367$	393.859	+	227.395i	1.07319	+	0.619604i	0.144135	+	0.989558i	$0.453960\pi$
$368$	120.768	−	239.423i	0.328174	−	0.650605i
$369$	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	$-0.827329\pi$
$373$	−312.417	+	180.374i	−0.837579	+	0.483576i	0.0188617	+	0.999822i	$0.493996\pi$
$374$	−66.1376	+	52.2478i	−0.176839	+	0.139700i
$375$	11.1094	+	6.41401i	0.0296250	+	0.0171040i
$376$	−302.999	−	212.756i	−0.805848	−	0.565840i
$377$	−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	$0.615221\pi$
$380$	−109.197	−	25.9813i	−0.287362	−	0.0683718i
$381$	−12.9659	−	7.48589i	−0.0340313	−	0.0196480i
$382$	90.8741	+	115.032i	0.237890	+	0.301132i
$383$	503.621	−	290.766i	1.31494	−	0.759180i	0.332029	−	0.943269i	$-0.392267\pi$
$383$	503.621	−	290.766i	1.31494	−	0.759180i	0.982910	+	0.184089i	$0.0589335\pi$
$384$	−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
$388$	−621.269	+	185.403i	−1.60121	+	0.477843i
$389$	443.646	+	256.139i	1.14048	+	0.658455i	0.946549	−	0.322560i	$-0.104543\pi$
$389$	443.646	+	256.139i	1.14048	+	0.658455i	0.193929	+	0.981016i	$0.437877\pi$
$390$	1.86957	+	12.8025i	0.00479377	+	0.0328270i
$391$		−	241.169i		−	0.616801i
$392$		0			0
$393$	6.02790			0.0153382
$394$	277.972	−	40.5926i	0.705513	−	0.103027i
$395$	73.8437	−	127.901i	0.186946	−	0.323800i
$396$	−100.922	+	30.1179i	−0.254855	+	0.0760553i
$397$	−70.4295	+	40.6625i	−0.177404	+	0.102424i	−0.586073	−	0.810259i	$-0.699327\pi$
$397$	−70.4295	+	40.6625i	−0.177404	+	0.102424i	0.408668	+	0.912683i	$0.365993\pi$
$398$	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	−0.981221	−	0.192888i	$-0.938215\pi$
$401$	−263.720	−	456.777i	−0.657657	−	1.13909i	0.323564	−	0.946206i	$-0.395119\pi$
$402$	1.84399	−	1.45673i	0.00458705	−	0.00362371i
$403$	−430.036	+	744.845i	−1.06709	+	1.84825i
$404$	415.704	+	98.9081i	1.02897	+	0.244822i
$405$		−	279.815i		−	0.690902i
$406$		0			0
$407$		−	115.883i		−	0.284726i
$408$	−6.44570	+	9.17972i	−0.0157983	+	0.0224993i
$409$	29.3363	−	50.8120i	0.0717270	−	0.124235i	−0.827931	−	0.560830i	$-0.810482\pi$
$409$	29.3363	−	50.8120i	0.0717270	−	0.124235i	0.899658	+	0.436595i	$0.143816\pi$
$410$	197.106	+	249.506i	0.480746	+	0.608550i
$411$	−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
$416$	−458.873	+	406.566i	−1.10306	+	0.977322i
$417$	9.03158	−	15.6432i	0.0216585	−	0.0375136i
$418$	6.85347	+	46.9315i	0.0163959	+	0.112276i
$419$	760.704			1.81552			0.907761	−	0.419487i	$-0.137790\pi$
$419$	760.704			1.81552			0.907761	+	0.419487i	$0.137790\pi$
$420$		0			0
$421$		−	46.2918i		−	0.109957i	−0.998488	−	0.0549784i	$-0.982491\pi$
$421$		−	46.2918i		−	0.109957i	0.998488	−	0.0549784i	$-0.0175090\pi$
$422$	32.3546	+	221.559i	0.0766696	+	0.525022i
$423$	−360.331	−	208.037i	−0.851846	−	0.491814i
$424$	6.86074	−	77.2499i	0.0161810	−	0.182193i
$425$	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
$430$	262.226	+	331.937i	0.609828	+	0.771947i
$431$	291.137	+	168.088i	0.675492	+	0.389996i	0.798154	−	0.602453i	$-0.205810\pi$
$431$	291.137	+	168.088i	0.675492	+	0.389996i	−0.122662	+	0.992448i	$0.539143\pi$
$432$	−23.4598	+	15.3710i	−0.0543051	+	0.0355810i
$433$	−372.694			−0.860725			−0.430363	−	0.902656i	$-0.641614\pi$
$433$	−372.694			−0.860725			−0.430363	+	0.902656i	$0.641614\pi$
$434$		0			0
$435$	−9.17260			−0.0210864
$436$	−739.054	−	175.843i	−1.69508	−	0.403309i
$437$	−117.530	−	67.8557i	−0.268946	−	0.155276i
$438$	2.79610	−	2.20888i	0.00638378	−	0.00504310i
$439$	344.226	−	198.739i	0.784115	−	0.452709i	−0.0537719	−	0.998553i	$-0.517124\pi$
$439$	344.226	−	198.739i	0.784115	−	0.452709i	0.837887	+	0.545844i	$0.183791\pi$
$440$	−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	0.669359	−	0.742939i	$-0.266569\pi$
$443$	−136.765	−	236.884i	−0.308725	−	0.534727i	−0.978084	+	0.208212i	$0.933236\pi$
$444$	−4.41007	−	14.7778i	−0.00993260	−	0.0332832i
$445$	−242.844	−	140.206i	−0.545718	−	0.315070i
$446$	616.339	−	90.0047i	1.38193	−	0.201804i
$447$			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	$0.341581\pi$
$450$	33.7523	+	231.131i	0.0750052	+	0.513624i
$451$	67.1785	−	116.357i	0.148955	−	0.257997i
$452$	154.027	−	45.9656i	0.340767	−	0.101694i
$453$	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	0.860475	−	0.509492i	$-0.170167\pi$
$457$	−5.02501	−	8.70357i	−0.0109956	−	0.0190450i	−0.871471	+	0.490447i	$0.836833\pi$
$458$	97.0392	+	122.837i	0.211876	+	0.268202i
$459$	−12.6121	+	21.8449i	−0.0274774	+	0.0475923i
$460$	53.7752	−	226.013i	0.116903	−	0.491333i
$461$			825.802i			1.79133i	0.444732	+	0.895664i	$0.353299\pi$
$461$			825.802i			1.79133i	−0.444732	+	0.895664i	$0.646701\pi$
$462$		0			0
$463$			114.707i			0.247748i	0.992298	+	0.123874i	$0.0395318\pi$
$463$			114.707i			0.247748i	−0.992298	+	0.123874i	$0.960468\pi$
$464$	−238.201	−	363.553i	−0.513365	−	0.783519i
$465$	−7.57924	+	13.1276i	−0.0162995	+	0.0282315i
$466$	−146.042	+	115.371i	−0.313394	+	0.247577i
$467$	100.864	+	174.701i	0.215982	+	0.374092i	0.953576	−	0.301153i	$-0.0973714\pi$
$467$	100.864	+	174.701i	0.215982	+	0.374092i	−0.737594	+	0.675245i	$0.764038\pi$
$468$	−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
$472$	912.838	+	81.0713i	1.93398	+	0.171761i
$473$	89.3730	−	154.799i	0.188949	−	0.327270i
$474$	−8.21772	+	1.20004i	−0.0173370	+	0.00253174i
$475$	105.190			0.221452
$476$		0			0
$477$		−	87.1561i		−	0.182717i
$478$	−577.090	+	84.2732i	−1.20730	+	0.176304i
$479$	−517.483	−	298.769i	−1.08034	−	0.623735i	−0.149352	−	0.988784i	$-0.547719\pi$
$479$	−517.483	−	298.769i	−1.08034	−	0.623735i	−0.930988	+	0.365050i	$0.881052\pi$
$480$	−8.08749	+	7.16559i	−0.0168489	+	0.0149283i
$481$	−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
$486$	−37.1060	+	29.3132i	−0.0763497	+	0.0603152i
$487$	298.887	+	172.562i	0.613730	+	0.354337i	0.774424	−	0.632667i	$-0.218040\pi$
$487$	298.887	+	172.562i	0.613730	+	0.354337i	−0.160694	+	0.987004i	$0.551373\pi$
$488$	−48.9750	−	34.3886i	−0.100359	−	0.0704685i
$489$	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	$0.375805\pi$
$492$	4.13870	−	17.3947i	0.00841199	−	0.0353550i
$493$	−338.526	−	195.448i	−0.686665	−	0.396446i
$494$	192.334	+	243.466i	0.389341	+	0.492845i
$495$	−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	0.879381	+	0.476118i	$0.157956\pi$
$499$	425.158	+	736.396i	0.852021	+	1.47574i	−0.0273604	+	0.999626i	$0.508710\pi$
$500$	150.595	+	504.629i	0.301189	+	1.00926i
$501$	−10.1814	−	5.87822i	−0.0203221	−	0.0117330i
$502$	89.7639	+	614.689i	0.178812	+	1.22448i
$503$			459.256i			0.913033i	0.889715	+	0.456517i	$0.150903\pi$
$503$			459.256i			0.913033i	−0.889715	+	0.456517i	$0.849097\pi$
$504$		0			0
$505$	370.206			0.733082
$506$	−97.1373	+	14.1851i	−0.191971	+	0.0280338i
$507$	9.64873	−	16.7121i	0.0190310	−	0.0329627i
$508$	−175.761	−	588.960i	−0.345987	−	1.15937i
$509$	583.623	−	336.955i	1.14661	−	0.661994i	0.198549	−	0.980091i	$-0.436377\pi$
$509$	583.623	−	336.955i	1.14661	−	0.661994i	0.948058	+	0.318097i	$0.103044\pi$
$510$	−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
$514$	−275.381	+	217.547i	−0.535760	+	0.423243i
$515$	−219.410	+	380.029i	−0.426039	+	0.737921i
$516$	5.50605	−	23.1415i	0.0106706	−	0.0448479i
$517$			135.536i			0.262159i
$518$		0			0
$519$		−	10.5562i		−	0.0203394i
$520$	−305.225	+	434.691i	−0.586972	+	0.835944i
$521$	243.236	−	421.298i	0.466864	−	0.808633i	−0.532419	−	0.846481i	$-0.678717\pi$
$521$	243.236	−	421.298i	0.466864	−	0.808633i	0.999284	+	0.0378482i	$0.0120503\pi$
$522$	−302.788	−	383.282i	−0.580053	−	0.734257i
$523$	340.043	+	588.973i	0.650179	+	1.12614i	0.983079	+	0.183181i	$0.0586393\pi$
$523$	340.043	+	588.973i	0.650179	+	1.12614i	−0.332900	+	0.942962i	$0.608027\pi$
$524$	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
$528$	4.07650	+	2.05624i	0.00772064	+	0.00389440i
$529$	−124.054	+	214.869i	−0.234507	+	0.406179i
$530$	−9.70890	−	66.4851i	−0.0183187	−	0.125444i
$531$	1029.90			1.93954
$532$		0			0
$533$		−	878.931i		−	1.64903i
$534$	2.27851	+	15.6029i	0.00426687	+	0.0292189i
$535$	261.161	+	150.781i	0.488151	+	0.281834i
$536$	96.0938	+	8.53431i	0.179279	+	0.0159222i
$537$	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	$-0.403966\pi$
$541$	688.489	−	397.499i	1.27262	−	0.734749i	0.975481	+	0.220084i	$0.0706331\pi$
$542$	329.928	+	417.637i	0.608723	+	0.770548i
$543$	0.603078	+	0.348187i	0.00111064	+	0.000641229i
$544$	−451.162	+	92.1281i	−0.829341	+	0.169353i
$545$	−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	$0.735187\pi$
$548$	98.0896	−	412.264i	0.178996	−	0.752306i
$549$	−58.2418	−	33.6259i	−0.106087	−	0.0612494i
$550$	59.7065	−	47.1673i	0.108557	−	0.0857587i
$551$	−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
$556$	710.569	−	212.053i	1.27800	−	0.381389i
$557$	−360.057	−	207.879i	−0.646421	−	0.373212i	0.140662	−	0.990058i	$-0.455077\pi$
$557$	−360.057	−	207.879i	−0.646421	−	0.373212i	−0.787084	+	0.616846i	$0.788410\pi$
$558$	−798.737	+	116.641i	−1.43143	+	0.209033i
$559$		−	1169.31i		−	2.09179i
$560$		0			0
$561$	4.10624			0.00731950
$562$	−42.7648	−	292.847i	−0.0760940	−	0.521080i
$563$	48.2498	−	83.5711i	0.0857012	−	0.148439i	−0.819989	−	0.572380i	$-0.806020\pi$
$563$	48.2498	−	83.5711i	0.0857012	−	0.148439i	0.905690	+	0.423941i	$0.139354\pi$
$564$	5.15799	+	17.2840i	0.00914537	+	0.0306453i
$565$	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	0.671671	−	0.740849i	$-0.265577\pi$
$569$	−173.977	−	301.336i	−0.305759	−	0.529589i	−0.977430	+	0.211260i	$0.932243\pi$
$570$	3.38983	+	4.29100i	0.00594707	+	0.00752807i
$571$	6.86255	−	11.8863i	0.0120185	−	0.0208166i	−0.859954	−	0.510372i	$-0.829508\pi$
$571$	6.86255	−	11.8863i	0.0120185	−	0.0208166i	0.871972	+	0.489556i	$0.162841\pi$
$572$	218.341	+	51.9497i	0.381715	+	0.0908212i
$573$		−	7.14193i		−	0.0124641i
$574$		0			0
$575$			217.718i			0.378641i
$576$	−566.386	−	101.404i	−0.983310	−	0.176049i
$577$	413.660	−	716.480i	0.716915	−	1.24173i	−0.245302	−	0.969447i	$-0.578887\pi$
$577$	413.660	−	716.480i	0.716915	−	1.24173i	0.962216	−	0.272286i	$-0.0877797\pi$
$578$	128.587	−	101.582i	0.222469	−	0.175747i
$579$	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
$584$	145.709	+	12.9408i	0.249502	+	0.0221589i
$585$	−298.456	+	516.941i	−0.510181	+	0.883659i
$586$	514.307	−	75.1049i	0.877657	−	0.128165i
$587$	−675.987			−1.15160			−0.575798	−	0.817592i	$-0.695308\pi$
$587$	−675.987			−1.15160			−0.575798	+	0.817592i	$0.695308\pi$
$588$		0			0
$589$			363.512i			0.617169i
$590$	785.634	−	114.727i	1.33158	−	0.194453i
$591$	−11.8524	−	6.84298i	−0.0200548	−	0.0115786i
$592$	285.125	−	565.260i	0.481630	−	0.954831i
$593$	207.058	+	358.635i	0.349171	+	0.604781i	0.986102	−	0.166139i	$-0.0531301\pi$
$593$	207.058	+	358.635i	0.349171	+	0.604781i	−0.636932	+	0.770920i	$0.719797\pi$
$594$	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
$598$	−503.917	+	398.087i	−0.842671	+	0.665698i
$599$	626.399	+	361.652i	1.04574	+	0.603759i	0.921454	−	0.388487i	$-0.127002\pi$
$599$	626.399	+	361.652i	1.04574	+	0.603759i	0.124287	+	0.992246i	$0.460336\pi$
$600$	5.81893	−	8.28710i	0.00969821	−	0.0138118i
$601$	68.7503			0.114393			0.0571966	−	0.998363i	$-0.481784\pi$
$601$	68.7503			0.114393			0.0571966	+	0.998363i	$0.481784\pi$
$602$		0			0
$603$	108.416			0.179795
$604$	445.857	+	106.082i	0.738173	+	0.175633i
$605$	−337.402	−	194.799i	−0.557690	−	0.321982i
$606$	−12.9047	−	16.3354i	−0.0212950	−	0.0269561i
$607$	−122.338	+	70.6317i	−0.201545	+	0.116362i	−0.597376	−	0.801961i	$-0.703790\pi$
$607$	−122.338	+	70.6317i	−0.201545	+	0.116362i	0.395831	+	0.918323i	$0.370457\pi$
$608$	−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
$612$	−495.874	+	147.982i	−0.810252	+	0.241801i
$613$	83.7767	+	48.3685i	0.136667	+	0.0789046i	0.566774	−	0.823873i	$-0.308191\pi$
$613$	83.7767	+	48.3685i	0.136667	+	0.0789046i	−0.430108	+	0.902778i	$0.641524\pi$
$614$	−83.9428	−	574.828i	−0.136715	−	0.936201i
$615$		−	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	$0.344126\pi$
$618$	24.4171	−	3.56566i	0.0395099	−	0.00576967i
$619$	−78.9725	+	136.784i	−0.127581	+	0.220976i	−0.922739	−	0.385426i	$-0.874055\pi$
$619$	−78.9725	+	136.784i	−0.127581	+	0.220976i	0.795158	+	0.606402i	$0.207388\pi$
$620$	−596.305	+	177.953i	−0.961782	+	0.287021i
$621$	−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
$626$	−446.498	+	352.728i	−0.713256	+	0.563463i
$627$	1.15534	−	2.00110i	0.00184264	−	0.00319155i
$628$	−1144.43	−	272.294i	−1.82234	−	0.433589i
$629$		−	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	$-0.209459\pi$
$632$	−279.020	−	195.919i	−0.441488	−	0.309998i
$633$	5.45424	−	9.44701i	0.00861649	−	0.0149242i
$634$	−15.2036	−	19.2455i	−0.0239805	−	0.0303556i
$635$	−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
$640$	−443.351	−	14.2602i	−0.692736	−	0.0222816i
$641$	293.451	−	508.273i	0.457802	−	0.792937i	−0.541042	−	0.840996i	$-0.681970\pi$
$641$	293.451	−	508.273i	0.457802	−	0.792937i	0.998845	+	0.0480584i	$0.0153034\pi$
$642$	−2.45036	−	16.7797i	−0.00381677	−	0.0261366i
$643$	865.328			1.34577			0.672883	−	0.739749i	$-0.265056\pi$
$643$	865.328			1.34577			0.672883	+	0.739749i	$0.265056\pi$
$644$		0			0
$645$		−	20.6087i		−	0.0319515i
$646$	33.6740	+	230.594i	0.0521269	+	0.356957i
$647$	−115.080	−	66.4414i	−0.177867	−	0.102691i	0.408423	−	0.912793i	$-0.366079\pi$
$647$	−115.080	−	66.4414i	−0.177867	−	0.102691i	−0.586290	+	0.810101i	$0.699412\pi$
$648$	−643.418	−	57.1434i	−0.992928	−	0.0881843i
$649$	−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	$-0.756653\pi$
$653$	−315.501	+	182.155i	−0.483156	+	0.278950i	0.238575	+	0.971124i	$0.423320\pi$
$654$	22.9426	+	29.0417i	0.0350804	+	0.0444063i
$655$	185.668	+	107.196i	0.283463	+	0.163657i
$656$	613.975	−	402.279i	0.935938	−	0.613231i
$657$	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	$0.504564\pi$
$660$	3.84818	+	0.915596i	0.00583058	+	0.00138727i
$661$	−293.674	−	169.553i	−0.444288	−	0.256510i	0.261127	−	0.965304i	$-0.415906\pi$
$661$	−293.674	−	169.553i	−0.444288	−	0.256510i	−0.705415	+	0.708795i	$0.749239\pi$
$662$	−305.190	+	241.096i	−0.461011	+	0.364193i
$663$	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
$668$	−138.015	−	462.475i	−0.206609	−	0.692328i
$669$	−26.2799	−	15.1727i	−0.0392824	−	0.0226797i
$670$	82.7031	−	12.0772i	0.123437	−	0.0180257i
$671$			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	$0.332823\pi$
$674$	−0.172265	−	1.17964i	−0.000255585	−	0.00175021i
$675$	11.3857	−	19.7207i	0.0168678	−	0.0292158i
$676$	759.124	−	226.543i	1.12296	−	0.335122i
$677$	−856.280	+	494.374i	−1.26482	+	0.730242i	−0.974002	−	0.226538i	$-0.927259\pi$
$677$	−856.280	+	494.374i	−1.26482	+	0.730242i	−0.290813	+	0.956780i	$0.593926\pi$
$678$	−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
$682$	163.000	+	206.332i	0.239002	+	0.302540i
$683$	259.062	−	448.709i	0.379301	−	0.656968i	−0.611660	−	0.791121i	$-0.709498\pi$
$683$	259.062	−	448.709i	0.379301	−	0.656968i	0.990961	+	0.134153i	$0.0428312\pi$
$684$	−67.4035	+	283.292i	−0.0985431	+	0.414170i
$685$		−	367.143i		−	0.535975i
$686$		0			0
$687$		−	7.62646i		−	0.0111011i
$688$	816.821	−	535.184i	1.18724	−	0.777884i
$689$	−92.8640	+	160.845i	−0.134781	+	0.233447i
$690$	−8.88137	+	7.01616i	−0.0128715	+	0.0101683i
$691$	308.511	+	534.356i	0.446470	+	0.773309i	0.998153	−	0.0607450i	$-0.0193476\pi$
$691$	308.511	+	534.356i	0.446470	+	0.773309i	−0.551683	+	0.834054i	$0.686014\pi$
$692$	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
$696$	−1.87321	+	21.0918i	−0.00269140	+	0.0303043i
$697$	330.076	−	571.709i	0.473567	−	0.820243i
$698$	−254.098	+	37.1062i	−0.364037	+	0.0531608i
$699$	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	$-0.0221987\pi$
$702$	66.4625	−	9.70561i	0.0946760	−	0.0138256i
$703$	−277.479	−	160.203i	−0.394707	−	0.227884i
$704$	63.6434	+	176.298i	0.0904025	+	0.250424i
$705$	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	0.527028	−	0.849848i	$-0.323306\pi$
$709$	1082.31	−	624.872i	1.52653	−	0.881343i	0.999504	−	0.0314953i	$-0.0100269\pi$
$710$	702.597	−	555.042i	0.989573	−	0.781749i
$711$	−331.815	−	191.573i	−0.466688	−	0.269442i
$712$	−371.989	+	529.773i	−0.522456	+	0.744063i
$713$	−752.386			−1.05524
$714$		0			0
$715$	194.444			0.271950
$716$	−149.470	+	628.214i	−0.208758	+	0.877393i
$717$	24.6064	+	14.2065i	0.0343186	+	0.0198138i
$718$	−267.427	−	338.521i	−0.372460	−	0.471477i
$719$	−367.839	+	212.372i	−0.511599	+	0.295372i	−0.733491	−	0.679700i	$-0.762110\pi$
$719$	−367.839	+	212.372i	−0.511599	+	0.295372i	0.221892	+	0.975071i	$0.428777\pi$
$720$	−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
$724$	8.17510	+	27.3940i	0.0112916	+	0.0378370i
$725$	305.608	+	176.443i	0.421528	+	0.243369i
$726$	3.16571	+	21.6783i	0.00436048	+	0.0298599i
$727$		−	79.1445i		−	0.108865i	−0.998517	−	0.0544323i	$-0.982665\pi$
$727$		−	79.1445i		−	0.108865i	0.998517	−	0.0544323i	$-0.0173349\pi$
$728$		0			0
$729$	−724.390			−0.993676
$730$	125.405	−	18.3130i	0.171787	−	0.0250863i
$731$	439.127	−	760.591i	0.600721	−	1.04048i
$732$	0.833707	+	2.79368i	0.00113894	+	0.00381650i
$733$	−574.839	+	331.883i	−0.784227	+	0.452774i	−0.837926	−	0.545783i	$-0.816232\pi$
$733$	−574.839	+	331.883i	−0.784227	+	0.452774i	0.0536990	+	0.998557i	$0.482899\pi$
$734$	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
$738$	647.295	−	511.354i	0.877093	−	0.692892i
$739$	−416.056	+	720.630i	−0.562998	+	0.975142i	0.434235	+	0.900800i	$0.357019\pi$
$739$	−416.056	+	720.630i	−0.562998	+	0.975142i	−0.997233	+	0.0743418i	$0.976314\pi$
$740$	126.959	−	533.601i	0.171567	−	0.721083i
$741$		−	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	$0.938960\pi$
$744$	28.6384	+	20.1089i	0.0384924	+	0.0270281i
$745$	−82.1483	+	142.285i	−0.110266	+	0.190987i
$746$	447.250	+	566.149i	0.599530	+	0.758912i
$747$	−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	$-0.746984\pi$
$751$	−324.743	+	187.490i	−0.432414	+	0.249654i	0.267960	+	0.963430i	$0.413650\pi$
$752$	−333.480	+	661.124i	−0.443458	+	0.879154i
$753$	15.1321	−	26.2096i	0.0200958	−	0.0348069i
$754$	150.406	+	1029.96i	0.199477	+	1.36599i
$755$	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	$-0.0132692\pi$
$758$	77.5746	+	531.220i	0.102341	+	0.700817i
$759$	4.14181	+	2.39128i	0.00545694	+	0.00315056i
$760$	−19.8594	+	223.611i	−0.0261308	+	0.294225i
$761$	−233.753	−	404.871i	−0.307165	−	0.532025i	0.670576	−	0.741841i	$-0.266047\pi$
$761$	−233.753	−	404.871i	−0.307165	−	0.532025i	−0.977741	+	0.209815i	$0.932714\pi$
$762$	−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
$766$	−720.974	−	912.641i	−0.941219	−	1.19144i
$767$	−1900.66	−	1097.35i	−2.47804	−	1.43070i
$768$	14.8252	+	20.0600i	0.0193037	+	0.0261198i
$769$	900.573			1.17110			0.585548	−	0.810638i	$-0.300879\pi$
$769$	900.573			1.17110			0.585548	+	0.810638i	$0.300879\pi$
$770$		0			0
$771$	17.0974			0.0221756
$772$	−78.7643	+	331.041i	−0.102026	+	0.428809i
$773$	1058.94	+	611.381i	1.36991	+	0.790919i	0.990916	−	0.134479i	$-0.0429360\pi$
$773$	1058.94	+	611.381i	1.36991	+	0.790919i	0.378996	+	0.925398i	$0.376269\pi$
$774$	861.148	−	680.295i	1.11259	−	0.878935i
$775$	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
$780$	24.7960	−	7.39979i	0.0317898	−	0.00948691i
$781$	−327.655	−	189.172i	−0.419533	−	0.242217i
$782$	−477.277	+	69.6973i	−0.610328	+	0.0891270i
$783$			47.6182i			0.0608151i
$784$		0			0
$785$	−1019.18			−1.29832
$786$	−1.74205	−	11.9293i	−0.00221635	−	0.0151772i
$787$	−431.471	+	747.330i	−0.548248	+	0.949593i	0.450147	+	0.892954i	$0.351372\pi$
$787$	−431.471	+	747.330i	−0.548248	+	0.949593i	−0.998395	+	0.0566385i	$0.981962\pi$
$788$	−160.666	−	538.378i	−0.203891	−	0.683221i
$789$	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
$794$	100.825	+	127.629i	0.126984	+	0.160742i
$795$	−1.63670	+	2.83484i	−0.00205874	+	0.00356584i
$796$	−556.786	−	132.476i	−0.699479	−	0.166427i
$797$			1078.34i			1.35300i	0.736442	+	0.676500i	$0.236504\pi$
$797$			1078.34i			1.35300i	−0.736442	+	0.676500i	$0.763496\pi$
$798$		0			0
$799$			665.947i			0.833476i
$800$	407.291	−	83.1697i	0.509114	−	0.103962i
$801$	−363.739	+	630.014i	−0.454106	+	0.786534i
$802$	−827.752	+	653.912i	−1.03211	+	0.815352i
$803$	−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
$808$	75.6029	−	851.266i	0.0935680	−	1.05355i
$809$	−166.694	+	288.723i	−0.206050	+	0.356888i	−0.950467	−	0.310827i	$-0.899394\pi$
$809$	−166.694	+	288.723i	−0.206050	+	0.356888i	0.744417	+	0.667715i	$0.232727\pi$
$810$	−553.757	+	80.8658i	−0.683651	+	0.0998344i
$811$	−1246.04			−1.53642			−0.768211	−	0.640197i	$-0.778853\pi$
$811$	−1246.04			−1.53642			−0.768211	+	0.640197i	$0.778853\pi$
$812$		0			0
$813$		−	25.9295i		−	0.0318936i
$814$	−229.334	+	33.4900i	−0.281737	+	0.0411425i
$815$	513.265	+	296.334i	0.629773	+	0.363600i
$816$	20.0296	+	10.1032i	0.0245460	+	0.0123814i
$817$	−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	−0.539755	+	0.841822i	$0.681483\pi$
$821$	−1263.25	+	729.338i	−1.53867	+	0.888353i	−0.998917	+	0.0465306i	$0.985184\pi$
$822$	−16.2002	+	12.7979i	−0.0197083	+	0.0155693i
$823$	401.876	+	232.023i	0.488306	+	0.281924i	0.723872	−	0.689935i	$-0.242361\pi$
$823$	401.876	+	232.023i	0.488306	+	0.281924i	−0.235565	+	0.971859i	$0.575694\pi$
$824$	829.046	+	582.129i	1.00612	+	0.706467i
$825$	−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	$0.274184\pi$
$828$	−586.348	−	139.509i	−0.708150	−	0.168490i
$829$	−31.1210	−	17.9677i	−0.0375404	−	0.0216740i	0.481112	−	0.876659i	$-0.340233\pi$
$829$	−31.1210	−	17.9677i	−0.0375404	−	0.0216740i	−0.518653	+	0.854985i	$0.673566\pi$
$830$	−471.190	−	596.454i	−0.567699	−	0.718619i
$831$	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
$836$	90.8973	−	27.1262i	0.108729	−	0.0324476i
$837$	68.1503	+	39.3466i	0.0814221	+	0.0470091i
$838$	−219.841	−	1505.44i	−0.262341	−	1.79647i
$839$			734.676i			0.875656i	0.899059	+	0.437828i	$0.144252\pi$
$839$			734.676i			0.875656i	−0.899059	+	0.437828i	$0.855748\pi$
$840$		0			0
$841$	103.069			0.122555
$842$	−91.6119	+	13.3782i	−0.108803	+	0.0158886i
$843$	−7.20916	+	12.4866i	−0.00855179	+	0.0148121i
$844$	429.118	−	128.060i	0.508433	−	0.151730i
$845$	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
$850$	293.363	−	231.753i	0.345133	−	0.272651i
$851$	331.582	−	574.317i	0.389638	−	0.674873i
$852$	−48.9826	−	11.6544i	−0.0574913	−	0.0136789i
$853$			402.566i			0.471942i	0.971760	+	0.235971i	$0.0758270\pi$
$853$			402.566i			0.471942i	−0.971760	+	0.235971i	$0.924173\pi$
$854$		0			0
$855$			252.287i			0.295072i
$856$	400.046	−	569.730i	0.467343	−	0.665573i
$857$	−276.001	+	478.048i	−0.322055	+	0.557816i	−0.980912	−	0.194453i	$-0.937707\pi$
$857$	−276.001	+	478.048i	−0.322055	+	0.557816i	0.658857	+	0.752268i	$0.271040\pi$
$858$	−6.77798	−	8.57988i	−0.00789975	−	0.00999986i
$859$	165.058	+	285.889i	0.192152	+	0.332817i	0.945963	−	0.324274i	$-0.105120\pi$
$859$	165.058	+	285.889i	0.192152	+	0.332817i	−0.753811	+	0.657091i	$0.771787\pi$
$860$	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	$-0.890630\pi$
$863$	−967.063	+	558.334i	−1.12058	+	0.646969i	−0.179033	+	0.983843i	$0.557297\pi$
$864$	37.1991	+	41.9851i	0.0430546	+	0.0485938i
$865$	187.723	−	325.145i	0.217020	−	0.375890i
$866$	107.708	+	737.565i	0.124374	+	0.851692i
$867$	−7.98348			−0.00920817
$868$		0			0
$869$			124.810i			0.143625i
$870$	2.65086	+	18.1527i	0.00304696	+	0.0208651i
$871$	−200.081	−	115.517i	−0.229714	−	0.132625i
$872$	−134.410	+	1513.41i	−0.154140	+	1.73557i
$873$	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	$-0.666531\pi$
$877$	0.647303	−	0.373720i	0.000738087	−	0.000426135i	0.500369	+	0.865812i	$0.333198\pi$
$878$	−492.787	−	623.792i	−0.561261	−	0.710469i
$879$	−21.9294	−	12.6610i	−0.0249481	−	0.0144038i
$880$	88.9954	+	135.828i	0.101131	+	0.154351i
$881$	−247.826			−0.281301			−0.140650	−	0.990059i	$-0.544919\pi$
$881$	−247.826			−0.281301			−0.140650	+	0.990059i	$0.544919\pi$
$882$		0			0
$883$	−1613.74			−1.82757			−0.913784	−	0.406200i	$-0.866854\pi$
$883$	−1613.74			−1.82757			−0.913784	+	0.406200i	$0.866854\pi$
$884$	1072.80	+	255.251i	1.21358	+	0.288745i
$885$	−33.4985	−	19.3403i	−0.0378514	−	0.0218535i
$886$	−429.271	+	339.118i	−0.484505	+	0.382752i
$887$	−961.795	+	555.293i	−1.08432	+	0.626034i	−0.932059	−	0.362305i	$-0.881990\pi$
$887$	−961.795	+	555.293i	−1.08432	+	0.626034i	−0.152264	+	0.988340i	$0.548656\pi$
$888$	−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
$892$	−356.240	−	1193.73i	−0.399373	−	1.33826i
$893$	324.538	+	187.372i	0.363424	+	0.209823i
$894$	9.14189	−	1.33500i	0.0102258	−	0.00149329i
$895$			559.458i			0.625092i
$896$		0			0
$897$	31.2863			0.0348788
$898$	−123.894	−	848.405i	−0.137966	−	0.944771i
$899$	−609.747	+	1056.11i	−0.678250	+	1.17476i
$900$	447.656	−	133.592i	0.497396	−	0.148436i
$901$	−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
$906$	−13.8408	−	17.5203i	−0.0152768	−	0.0193381i
$907$	259.004	−	448.609i	0.285562	−	0.494607i	−0.687184	−	0.726484i	$-0.741153\pi$
$907$	259.004	−	448.609i	0.285562	−	0.494607i	0.972745	+	0.231876i	$0.0744865\pi$
$908$	68.8460	−	289.355i	0.0758216	−	0.318673i
$909$		−	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	$-0.198850\pi$
$912$	10.5591	−	6.91840i	0.0115780	−	0.00758597i
$913$	−160.593	+	278.155i	−0.175896	+	0.304661i
$914$	−15.7722	+	12.4598i	−0.0172563	+	0.0136322i
$915$	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	$-0.889391\pi$
$919$	−1025.08	+	591.831i	−1.11543	+	0.643994i	−0.175200	+	0.984533i	$0.556057\pi$
$920$	−462.823	−	41.1044i	−0.503069	−	0.0446787i
$921$	−14.1508	+	24.5099i	−0.0153646	+	0.0266123i
$922$	1634.27	−	238.654i	1.77253	−	0.258844i
$923$	−2475.03			−2.68151
$924$		0			0
$925$			514.018i			0.555695i
$926$	227.007	−	33.1501i	0.245148	−	0.0357992i
$927$	985.914	+	569.217i	1.06355	+	0.614043i
$928$	−650.635	+	576.468i	−0.701115	+	0.621194i
$929$	189.509	+	328.240i	0.203993	+	0.353326i	0.949811	−	0.312823i	$-0.101275\pi$
$929$	189.509	+	328.240i	0.203993	+	0.353326i	−0.745818	+	0.666149i	$0.767941\pi$
$930$	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
$934$	316.585	−	250.098i	0.338957	−	0.267771i
$935$	126.478	+	73.0221i	0.135271	+	0.0780985i
$936$	1127.72	+	791.849i	1.20483	+	0.845993i
$937$	1316.09			1.40458			0.702289	−	0.711892i	$-0.252161\pi$
$937$	1316.09			1.40458			0.702289	+	0.711892i	$0.252161\pi$
$938$		0			0
$939$	27.7214			0.0295223
$940$	−148.491	+	624.096i	−0.157969	+	0.663932i
$941$	430.441	+	248.515i	0.457430	+	0.264097i	0.710963	−	0.703230i	$-0.248259\pi$
$941$	430.441	+	248.515i	0.457430	+	0.264097i	−0.253533	+	0.967327i	$0.581593\pi$
$942$	35.5268	+	44.9714i	0.0377142	+	0.0477403i
$943$	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	0.569726	−	0.821835i	$-0.307050\pi$
$947$	−404.243	−	700.170i	−0.426867	−	0.739356i	−0.996593	+	0.0824792i	$0.973716\pi$
$948$	4.74980	+	15.9161i	0.00501033	+	0.0167892i
$949$	−303.387	−	175.161i	−0.319692	−	0.184574i
$950$	−30.3996	−	208.172i	−0.0319995	−	0.219128i
$951$			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	$0.749488\pi$
$954$	−172.483	+	25.1879i	−0.180800	+	0.0264024i
$955$	127.007	−	219.982i	0.132991	−	0.230347i
$956$	333.555	+	1117.71i	0.348907	+	1.16915i
$957$	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
$962$	−1189.71	+	939.857i	−1.23671	+	0.976982i
$963$	391.173	−	677.532i	0.406203	−	0.703564i
$964$	207.161	−	870.685i	0.214898	−	0.903200i
$965$			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	$-0.0231083\pi$
$968$	−516.832	+	736.054i	−0.533918	+	0.760386i
$969$	5.67666	−	9.83226i	0.00585826	−	0.0101468i
$970$	696.392	+	881.525i	0.717930	+	0.908788i
$971$	−719.336	−	1245.93i	−0.740820	−	1.28314i	−0.952122	−	0.305717i	$-0.901104\pi$
$971$	−719.336	−	1245.93i	−0.740820	−	1.28314i	0.211303	−	0.977421i	$-0.432229\pi$
$972$	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
$976$	−53.9018	+	106.860i	−0.0552272	+	0.109488i
$977$	−451.095	+	781.319i	−0.461714	+	0.799712i	−0.999047	−	0.0436581i	$-0.986099\pi$
$977$	−451.095	+	781.319i	−0.461714	+	0.799712i	0.537332	+	0.843371i	$0.319432\pi$
$978$	−4.81576	−	32.9776i	−0.00492409	−	0.0337194i
$979$	236.976			0.242059
$980$		0			0
$981$			1707.49i			1.74056i
$982$	−107.940	−	739.157i	−0.109918	−	0.752705i
$983$	435.778	+	251.597i	0.443315	+	0.255948i	0.705003	−	0.709205i	$-0.250946\pi$
$983$	435.778	+	251.597i	0.443315	+	0.255948i	−0.261688	+	0.965153i	$0.584279\pi$
$984$	−35.6203	−	3.16352i	−0.0361995	−	0.00321496i
$985$	−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
$990$	113.126	+	143.200i	0.114268	+	0.144646i
$991$	784.898	+	453.161i	0.792026	+	0.457277i	0.840675	−	0.541539i	$-0.182158\pi$
$991$	784.898	+	453.161i	0.792026	+	0.457277i	−0.0486491	+	0.998816i	$0.515492\pi$
$992$	287.416	+	1407.51i	0.289734	+	1.41886i
$993$	18.9481			0.0190816
$994$		0			0
$995$	−495.847			−0.498339
$996$	−9.89374	+	41.5827i	−0.00993347	+	0.0417497i
$997$	−527.085	−	304.313i	−0.528671	−	0.305228i	0.211804	−	0.977312i	$-0.432066\pi$
$997$	−527.085	−	304.313i	−0.528671	−	0.305228i	−0.740475	+	0.672084i	$0.765399\pi$
$998$	1334.47	−	1054.21i	1.33714	−	1.05632i
$999$	−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.o.67.4		16
7.2	even	3	inner	392.3.k.o.275.2		16
7.3	odd	6		392.3.g.m.99.8		8
7.4	even	3		56.3.g.b.43.8	yes	8
7.5	odd	6		392.3.k.n.275.2		16
7.6	odd	2		392.3.k.n.67.4		16
8.3	odd	2	inner	392.3.k.o.67.2		16
21.11	odd	6		504.3.g.b.379.1		8
28.3	even	6		1568.3.g.m.687.6		8
28.11	odd	6		224.3.g.b.15.3		8
56.3	even	6		392.3.g.m.99.7		8
56.11	odd	6		56.3.g.b.43.7	✓	8
56.19	even	6		392.3.k.n.275.4		16
56.27	even	2		392.3.k.n.67.2		16
56.45	odd	6		1568.3.g.m.687.5		8
56.51	odd	6	inner	392.3.k.o.275.4		16
56.53	even	6		224.3.g.b.15.4		8
84.11	even	6		2016.3.g.b.1135.5		8
112.11	odd	12		1792.3.d.j.1023.10		16
112.53	even	12		1792.3.d.j.1023.8		16
112.67	odd	12		1792.3.d.j.1023.7		16
112.109	even	12		1792.3.d.j.1023.9		16
168.11	even	6		504.3.g.b.379.2		8
168.53	odd	6		2016.3.g.b.1135.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.7	✓	8	56.11	odd	6
56.3.g.b.43.8	yes	8	7.4	even	3
224.3.g.b.15.3		8	28.11	odd	6
224.3.g.b.15.4		8	56.53	even	6
392.3.g.m.99.7		8	56.3	even	6
392.3.g.m.99.8		8	7.3	odd	6
392.3.k.n.67.2		16	56.27	even	2
392.3.k.n.67.4		16	7.6	odd	2
392.3.k.n.275.2		16	7.5	odd	6
392.3.k.n.275.4		16	56.19	even	6
392.3.k.o.67.2		16	8.3	odd	2	inner
392.3.k.o.67.4		16	1.1	even	1	trivial
392.3.k.o.275.2		16	7.2	even	3	inner
392.3.k.o.275.4		16	56.51	odd	6	inner
504.3.g.b.379.1		8	21.11	odd	6
504.3.g.b.379.2		8	168.11	even	6
1568.3.g.m.687.5		8	56.45	odd	6
1568.3.g.m.687.6		8	28.3	even	6
1792.3.d.j.1023.7		16	112.67	odd	12
1792.3.d.j.1023.8		16	112.53	even	12
1792.3.d.j.1023.9		16	112.109	even	12
1792.3.d.j.1023.10		16	112.11	odd	12
2016.3.g.b.1135.4		8	168.53	odd	6
2016.3.g.b.1135.5		8	84.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.288997 - 1.97901i) q^{2} +(-0.0487183 + 0.0843825i) q^{3} +(-3.83296 + 1.14386i) q^{4} +(-3.00119 + 1.73274i) q^{5} +(0.181073 + 0.0720276i) q^{6} +(3.37142 + 7.25490i) q^{8} +(4.49525 + 7.78601i) q^{9} +O(q^{10})\)	\(q+(-0.288997 - 1.97901i) q^{2} +(-0.0487183 + 0.0843825i) q^{3} +(-3.83296 + 1.14386i) 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} +(4.29644 + 5.43862i) q^{10} +(1.46433 - 2.53629i) q^{11} +(0.0902137 - 0.379162i) q^{12} -19.1586i q^{13} -0.337664i q^{15} +(13.3832 - 8.76872i) q^{16} +(7.19487 - 12.4619i) q^{17} +(14.1095 - 11.1463i) 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} +(-0.776436 - 0.0689571i) q^{24} +(-6.49525 + 11.2501i) q^{25} +(-37.9150 + 5.53678i) q^{26} -1.75293 q^{27} -27.1649i q^{29} +(-0.668240 + 0.0975839i) q^{30} +(-38.8779 - 22.4461i) q^{31} +(-21.2211 - 23.9513i) 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} +(-12.7079 + 10.0391i) q^{38} +(1.61665 + 0.933373i) q^{39} +(-22.6891 - 15.9315i) q^{40} +45.8766 q^{41} +61.0334 q^{43} +(-2.71156 + 11.3965i) q^{44} +(-26.9822 - 15.5782i) q^{45} +(-20.7785 - 26.3024i) 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} +(21.9147 + 73.4341i) q^{52} +(-8.39546 - 4.84712i) q^{53} +(0.506593 + 3.46907i) q^{54} +10.1492i q^{55} +0.788986 q^{57} +(-53.7596 + 7.85058i) q^{58} +(57.2770 - 99.2066i) q^{59} +(0.386239 + 1.29425i) 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} +(0.447834 - 0.353783i) q^{66} +(6.02950 - 10.4434i) q^{67} +(-13.3231 + 55.9958i) q^{68} +1.63302i q^{69} -129.187i q^{71} +(-41.3313 + 58.8625i) q^{72} +(9.14268 - 15.8356i) q^{73} +(-49.0567 - 62.0981i) 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} +(-24.9716 + 49.5061i) q^{80} +(-40.3719 + 69.9261i) q^{81} +(-13.2582 - 90.7903i) q^{82} -109.670 q^{83} +49.8673i q^{85} +(-17.6385 - 120.786i) q^{86} +(2.29224 + 1.32343i) q^{87} +(23.3374 + 2.07265i) 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} +(57.3763 + 72.6295i) q^{94} +(24.3019 + 14.0307i) q^{95} +(3.05493 - 0.623822i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more