LMFDB - Embedded newform 392.3.k.n.67.1

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			67.1
Root			$-0.575587 + 1.91538i$ of defining polynomial
Character	$\chi$	$=$	392.67
Dual form			392.3.k.n.275.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94657 - 0.459219i) q^{2} +(-2.61182 + 4.52380i) q^{3} +(3.57824 + 1.78780i) q^{4} +(5.42814 - 3.13394i) q^{5} +(7.16148 - 7.60647i) q^{6} +(-6.14428 - 5.12327i) q^{8} +(-9.14316 - 15.8364i) q^{9} +O(q^{10})$	\(q+(-1.94657 - 0.459219i) q^{2} +(-2.61182 + 4.52380i) q^{3} +(3.57824 + 1.78780i) q^{4} +(5.42814 - 3.13394i) q^{5} +(7.16148 - 7.60647i) q^{6} +(-6.14428 - 5.12327i) q^{8} +(-9.14316 - 15.8364i) q^{9} +(-12.0054 + 3.60771i) q^{10} +(-4.90344 + 8.49301i) q^{11} +(-17.4333 + 11.5178i) q^{12} +2.41653i q^{13} +32.7411i q^{15} +(9.60754 + 12.7943i) q^{16} +(3.44726 - 5.97083i) q^{17} +(10.5254 + 35.0253i) q^{18} +(1.38818 + 2.40441i) q^{19} +(25.0260 - 1.50954i) q^{20} +(13.4450 - 14.2804i) q^{22} +(-37.0947 + 21.4166i) q^{23} +(39.2243 - 14.4144i) q^{24} +(7.14316 - 12.3723i) q^{25} +(1.10972 - 4.70393i) q^{26} +48.5083 q^{27} +37.3505i q^{29} +(15.0353 - 63.7327i) q^{30} +(6.20797 + 3.58417i) q^{31} +(-12.8263 - 29.3170i) q^{32} +(-25.6138 - 44.3643i) q^{33} +(-9.45224 + 10.0396i) q^{34} +(-4.40402 - 73.0126i) q^{36} +(0.175502 - 0.101326i) q^{37} +(-1.59804 - 5.31782i) q^{38} +(-10.9319 - 6.31153i) q^{39} +(-49.4080 - 8.55402i) q^{40} -63.5494 q^{41} -35.3384 q^{43} +(-32.7295 + 21.6236i) q^{44} +(-99.2607 - 57.3082i) q^{45} +(82.0421 - 24.6543i) q^{46} +(-32.8335 + 18.9564i) q^{47} +(-82.9721 + 10.0461i) q^{48} +(-19.5862 + 20.8032i) q^{50} +(18.0072 + 31.1894i) q^{51} +(-4.32027 + 8.64691i) q^{52} +(-47.3414 - 27.3326i) q^{53} +(-94.4246 - 22.2759i) q^{54} +61.4684i q^{55} -14.5027 q^{57} +(17.1521 - 72.7051i) q^{58} +(52.3975 - 90.7551i) q^{59} +(-58.5345 + 117.155i) q^{60} +(37.9032 - 21.8834i) q^{61} +(-10.4383 - 9.82765i) q^{62} +(11.5043 + 62.9575i) q^{64} +(7.57325 + 13.1173i) q^{65} +(29.4859 + 98.1204i) q^{66} +(-15.5510 + 26.9352i) q^{67} +(23.0098 - 15.2020i) q^{68} -223.745i q^{69} -23.1294i q^{71} +(-24.9561 + 144.146i) q^{72} +(-34.6138 + 59.9528i) q^{73} +(-0.388158 + 0.116644i) q^{74} +(37.3132 + 64.6284i) q^{75} +(0.668652 + 11.0853i) q^{76} +(18.3813 + 17.3059i) q^{78} +(-17.2624 + 9.96642i) q^{79} +(92.2478 + 39.3401i) q^{80} +(-44.4063 + 76.9139i) q^{81} +(123.703 + 29.1831i) q^{82} +5.11617 q^{83} -43.2140i q^{85} +(68.7885 + 16.2281i) q^{86} +(-168.966 - 97.5525i) q^{87} +(73.6400 - 27.0618i) q^{88} +(-8.99444 - 15.5788i) q^{89} +(166.901 + 157.137i) q^{90} +(-171.022 + 10.3158i) q^{92} +(-32.4282 + 18.7224i) q^{93} +(72.6178 - 21.8222i) q^{94} +(15.0705 + 8.70097i) q^{95} +(166.124 + 18.5470i) q^{96} -12.4864 q^{97} +179.332 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 $

$2$	−1.94657	−	0.459219i	−0.973283	−	0.229610i
$2$	−1.94657	−	0.459219i	−0.973283	−	0.229610i
$3$	−2.61182	+	4.52380i	−0.870605	+	1.50793i	−0.00923321	+	0.999957i	$0.502939\pi$
$3$	−2.61182	+	4.52380i	−0.870605	+	1.50793i	−0.861372	+	0.507975i	$0.830394\pi$
$4$	3.57824	+	1.78780i	0.894559	+	0.446950i
$5$	5.42814	−	3.13394i	1.08563	−	0.626788i	0.153219	−	0.988192i	$-0.451036\pi$
$5$	5.42814	−	3.13394i	1.08563	−	0.626788i	0.932409	+	0.361404i	$0.117703\pi$
$6$	7.16148	−	7.60647i	1.19358	−	1.26775i
$7$		0			0
$7$		0			0
$8$	−6.14428	−	5.12327i	−0.768035	−	0.640408i
$9$	−9.14316	−	15.8364i	−1.01591	−	1.75960i
$10$	−12.0054	+	3.60771i	−1.20054	+	0.360771i
$11$	−4.90344	+	8.49301i	−0.445767	+	0.772092i	−0.998105	−	0.0615286i	$-0.980402\pi$
$11$	−4.90344	+	8.49301i	−0.445767	+	0.772092i	0.552338	+	0.833620i	$0.313736\pi$
$12$	−17.4333	+	11.5178i	−1.45278	+	0.959817i
$13$			2.41653i			0.185887i	0.995671	+	0.0929434i	$0.0296276\pi$
$13$			2.41653i			0.185887i	−0.995671	+	0.0929434i	$0.970372\pi$
$14$		0			0
$15$			32.7411i			2.18274i
$16$	9.60754	+	12.7943i	0.600471	+	0.799646i
$17$	3.44726	−	5.97083i	0.202780	−	0.351225i	−0.746643	−	0.665225i	$-0.768336\pi$
$17$	3.44726	−	5.97083i	0.202780	−	0.351225i	0.949423	+	0.313999i	$0.101669\pi$
$18$	10.5254	+	35.0253i	0.584743	+	1.94585i
$19$	1.38818	+	2.40441i	0.0730624	+	0.126548i	0.900242	−	0.435390i	$-0.143389\pi$
$19$	1.38818	+	2.40441i	0.0730624	+	0.126548i	−0.827180	+	0.561938i	$0.810056\pi$
$20$	25.0260	−	1.50954i	1.25130	−	0.0754769i
$21$		0			0
$22$	13.4450	−	14.2804i	0.611137	−	0.649111i
$23$	−37.0947	+	21.4166i	−1.61281	+	0.931157i	−0.624097	+	0.781347i	$0.714533\pi$
$23$	−37.0947	+	21.4166i	−1.61281	+	0.931157i	−0.988715	+	0.149811i	$0.952134\pi$
$24$	39.2243	−	14.4144i	1.63435	−	0.600602i
$25$	7.14316	−	12.3723i	0.285726	−	0.494893i
$26$	1.10972	−	4.70393i	0.0426814	−	0.180920i
$27$	48.5083			1.79660
$28$		0			0
$29$			37.3505i			1.28795i	0.765048	+	0.643974i	$0.222715\pi$
$29$			37.3505i			1.28795i	−0.765048	+	0.643974i	$0.777285\pi$
$30$	15.0353	−	63.7327i	0.501178	−	2.12442i
$31$	6.20797	+	3.58417i	0.200257	+	0.115619i	0.596775	−	0.802408i	$-0.296448\pi$
$31$	6.20797	+	3.58417i	0.200257	+	0.115619i	−0.396518	+	0.918027i	$0.629782\pi$
$32$	−12.8263	−	29.3170i	−0.400822	−	0.916156i
$33$	−25.6138	−	44.3643i	−0.776175	−	1.34437i
$34$	−9.45224	+	10.0396i	−0.278007	+	0.295281i
$35$		0			0
$36$	−4.40402	−	73.0126i	−0.122334	−	2.02813i
$37$	0.175502	−	0.101326i	0.00474330	−	0.00273855i	−0.497626	−	0.867391i	$-0.665795\pi$
$37$	0.175502	−	0.101326i	0.00474330	−	0.00273855i	0.502370	+	0.864653i	$0.332462\pi$
$38$	−1.59804	−	5.31782i	−0.0420538	−	0.139943i
$39$	−10.9319	−	6.31153i	−0.280305	−	0.161834i
$40$	−49.4080	−	8.55402i	−1.23520	−	0.213851i
$41$	−63.5494			−1.54999			−0.774993	−	0.631970i	$-0.782247\pi$
$41$	−63.5494			−1.54999			−0.774993	+	0.631970i	$0.782247\pi$
$42$		0			0
$43$	−35.3384			−0.821823			−0.410911	−	0.911675i	$-0.634789\pi$
$43$	−35.3384			−0.821823			−0.410911	+	0.911675i	$0.634789\pi$
$44$	−32.7295	+	21.6236i	−0.743852	+	0.491446i
$45$	−99.2607	−	57.3082i	−2.20579	−	1.27352i
$46$	82.0421	−	24.6543i	1.78352	−	0.535962i
$47$	−32.8335	+	18.9564i	−0.698586	+	0.403329i	−0.806820	−	0.590797i	$-0.798814\pi$
$47$	−32.8335	+	18.9564i	−0.698586	+	0.403329i	0.108235	+	0.994125i	$0.465480\pi$
$48$	−82.9721	+	10.0461i	−1.72859	+	0.209294i
$49$		0			0
$50$	−19.5862	+	20.8032i	−0.391725	+	0.416065i
$51$	18.0072	+	31.1894i	0.353083	+	0.611557i
$52$	−4.32027	+	8.64691i	−0.0830821	+	0.166287i
$53$	−47.3414	−	27.3326i	−0.893234	−	0.515709i	−0.0182349	−	0.999834i	$-0.505805\pi$
$53$	−47.3414	−	27.3326i	−0.893234	−	0.515709i	−0.874999	+	0.484125i	$0.839138\pi$
$54$	−94.4246	−	22.2759i	−1.74860	−	0.412517i
$55$			61.4684i			1.11761i
$56$		0			0
$57$	−14.5027			−0.254434
$58$	17.1521	−	72.7051i	0.295725	−	1.25354i
$59$	52.3975	−	90.7551i	0.888093	−	1.53822i	0.0459650	−	0.998943i	$-0.485364\pi$
$59$	52.3975	−	90.7551i	0.888093	−	1.53822i	0.842128	−	0.539278i	$-0.181303\pi$
$60$	−58.5345	+	117.155i	−0.975576	+	1.95259i
$61$	37.9032	−	21.8834i	0.621364	−	0.358745i	−0.156036	−	0.987751i	$-0.549872\pi$
$61$	37.9032	−	21.8834i	0.621364	−	0.358745i	0.777400	+	0.629007i	$0.216538\pi$
$62$	−10.4383	−	9.82765i	−0.168360	−	0.158511i
$63$		0			0
$64$	11.5043	+	62.9575i	0.179755	+	0.983711i
$65$	7.57325	+	13.1173i	0.116512	+	0.201804i
$66$	29.4859	+	98.1204i	0.446756	+	1.48667i
$67$	−15.5510	+	26.9352i	−0.232105	+	0.402018i	−0.958427	−	0.285336i	$-0.907895\pi$
$67$	−15.5510	+	26.9352i	−0.232105	+	0.402018i	0.726322	+	0.687354i	$0.241228\pi$
$68$	23.0098	−	15.2020i	0.338379	−	0.223559i
$69$		−	223.745i		−	3.24268i
$70$		0			0
$71$		−	23.1294i		−	0.325766i	−0.986645	−	0.162883i	$-0.947921\pi$
$71$		−	23.1294i		−	0.325766i	0.986645	−	0.162883i	$-0.0520794\pi$
$72$	−24.9561	+	144.146i	−0.346612	+	2.00203i
$73$	−34.6138	+	59.9528i	−0.474161	+	0.821271i	−0.999562	−	0.0295834i	$-0.990582\pi$
$73$	−34.6138	+	59.9528i	−0.474161	+	0.821271i	0.525401	+	0.850855i	$0.323915\pi$
$74$	−0.388158	+	0.116644i	−0.00524537	+	0.00157627i
$75$	37.3132	+	64.6284i	0.497510	+	0.861712i
$76$	0.668652	+	11.0853i	0.00879806	+	0.145860i
$77$		0			0
$78$	18.3813	+	17.3059i	0.235657	+	0.221871i
$79$	−17.2624	+	9.96642i	−0.218511	+	0.126157i	−0.605261	−	0.796027i	$-0.706931\pi$
$79$	−17.2624	+	9.96642i	−0.218511	+	0.126157i	0.386750	+	0.922185i	$0.373598\pi$
$80$	92.2478	+	39.3401i	1.15310	+	0.491751i
$81$	−44.4063	+	76.9139i	−0.548225	+	0.949554i
$82$	123.703	+	29.1831i	1.50857	+	0.355892i
$83$	5.11617			0.0616406			0.0308203	−	0.999525i	$-0.490188\pi$
$83$	5.11617			0.0616406			0.0308203	+	0.999525i	$0.490188\pi$
$84$		0			0
$85$		−	43.2140i		−	0.508400i
$86$	68.7885	+	16.2281i	0.799866	+	0.188698i
$87$	−168.966	−	97.5525i	−1.94214	−	1.12129i
$88$	73.6400	−	27.0618i	0.836819	−	0.307520i
$89$	−8.99444	−	15.5788i	−0.101061	−	0.175043i	0.811061	−	0.584962i	$-0.198890\pi$
$89$	−8.99444	−	15.5788i	−0.101061	−	0.175043i	−0.912122	+	0.409919i	$0.865557\pi$
$90$	166.901	+	157.137i	1.85445	+	1.74596i
$91$		0			0
$92$	−171.022	+	10.3158i	−1.85894	+	0.112129i
$93$	−32.4282	+	18.7224i	−0.348690	+	0.201316i
$94$	72.6178	−	21.8222i	0.772530	−	0.232151i
$95$	15.0705	+	8.70097i	0.158637	+	0.0915892i
$96$	166.124	+	18.5470i	1.73046	+	0.193198i
$97$	−12.4864			−0.128726			−0.0643629	−	0.997927i	$-0.520502\pi$
$97$	−12.4864			−0.128726			−0.0643629	+	0.997927i	$0.520502\pi$
$98$		0			0
$99$	179.332			1.81143
$100$	47.6791	−	31.5005i	0.476791	−	0.315005i
$101$	58.9549	+	34.0376i	0.583712	+	0.337006i	0.762607	−	0.646862i	$-0.223919\pi$
$101$	58.9549	+	34.0376i	0.583712	+	0.337006i	−0.178895	+	0.983868i	$0.557252\pi$
$102$	−20.7295	−	68.9815i	−0.203230	−	0.676289i
$103$	−50.4833	+	29.1465i	−0.490129	+	0.282976i	−0.724628	−	0.689140i	$-0.757988\pi$
$103$	−50.4833	+	29.1465i	−0.490129	+	0.282976i	0.234499	+	0.972116i	$0.424655\pi$
$104$	12.3805	−	14.8478i	0.119043	−	0.142768i
$105$		0			0
$106$	79.6015	+	74.9447i	0.750957	+	0.707026i
$107$	−67.9340	−	117.665i	−0.634897	−	1.09967i	−0.986537	−	0.163538i	$-0.947709\pi$
$107$	−67.9340	−	117.665i	−0.634897	−	1.09967i	0.351640	−	0.936135i	$-0.385624\pi$
$108$	173.574	+	86.7231i	1.60717	+	0.802992i
$109$	38.5365	+	22.2490i	0.353546	+	0.204120i	0.666246	−	0.745732i	$-0.267900\pi$
$109$	38.5365	+	22.2490i	0.353546	+	0.204120i	−0.312700	+	0.949852i	$0.601234\pi$
$110$	28.2274	−	119.652i	0.256613	−	1.08775i
$111$			1.05858i			0.00953677i
$112$		0			0
$113$	−133.391			−1.18045			−0.590224	−	0.807240i	$-0.700961\pi$
$113$	−133.391			−1.18045			−0.590224	+	0.807240i	$0.700961\pi$
$114$	28.2305	+	6.65993i	0.247636	+	0.0584204i
$115$	−134.237	+	232.505i	−1.16728	+	2.02178i
$116$	−66.7752	+	133.649i	−0.575648	+	1.15214i
$117$	38.2691	−	22.0947i	0.327087	−	0.188844i
$118$	−143.672	+	152.599i	−1.21756	+	1.29321i
$119$		0			0
$120$	167.741	−	201.170i	1.39784	−	1.67642i
$121$	12.4125	+	21.4991i	0.102583	+	0.177679i
$122$	−83.8304	+	25.1916i	−0.687134	+	0.206489i
$123$	165.979	−	287.485i	1.34943	−	2.33727i
$124$	15.8058	+	23.9236i	0.127466	+	0.192933i
$125$			67.1521i			0.537217i
$126$		0			0
$127$			130.977i			1.03131i	0.856795	+	0.515657i	$0.172452\pi$
$127$			130.977i			1.03131i	−0.856795	+	0.515657i	$0.827548\pi$
$128$	6.51744	−	127.834i	0.0509175	−	0.998703i
$129$	92.2973	−	159.864i	0.715483	−	1.23925i
$130$	−8.71814	−	29.0114i	−0.0670626	−	0.223165i
$131$	−26.6655	−	46.1861i	−0.203554	−	0.352565i	0.746117	−	0.665815i	$-0.231916\pi$
$131$	−26.6655	−	46.1861i	−0.203554	−	0.352565i	−0.949671	+	0.313249i	$0.898583\pi$
$132$	−12.3375	−	204.538i	−0.0934658	−	1.54953i
$133$		0			0
$134$	42.6403	−	45.2898i	0.318211	−	0.337983i
$135$	263.310	−	152.022i	1.95044	−	1.12609i
$136$	−51.7711	+	19.0252i	−0.380670	+	0.139891i
$137$	28.8589	−	49.9852i	0.210649	−	0.364855i	−0.741269	−	0.671208i	$-0.765776\pi$
$137$	28.8589	−	49.9852i	0.210649	−	0.364855i	0.951918	+	0.306353i	$0.0991089\pi$
$138$	−102.748	+	435.534i	−0.744551	+	3.15605i
$139$	172.422			1.24045			0.620224	−	0.784425i	$-0.287042\pi$
$139$	172.422			1.24045			0.620224	+	0.784425i	$0.287042\pi$
$140$		0			0
$141$		−	198.043i		−	1.40456i
$142$	−10.6215	+	45.0229i	−0.0747991	+	0.317063i
$143$	−20.5236	−	11.8493i	−0.143522	−	0.0828623i
$144$	114.773	−	269.130i	0.797037	−	1.86896i
$145$	117.054	+	202.744i	0.807270	+	1.39823i
$146$	94.9094	−	100.807i	0.650065	−	0.690457i
$147$		0			0
$148$	0.809139	−	0.0488062i	0.00546716	−	0.000329772i
$149$	−190.117	+	109.764i	−1.27596	+	0.736673i	−0.976102	−	0.217312i	$-0.930271\pi$
$149$	−190.117	+	109.764i	−1.27596	+	0.736673i	−0.299853	+	0.953985i	$0.596938\pi$
$150$	−42.9540	−	142.938i	−0.286360	−	0.952922i
$151$	−160.793	−	92.8340i	−1.06486	−	0.614795i	−0.138084	−	0.990421i	$-0.544094\pi$
$151$	−160.793	−	92.8340i	−1.06486	−	0.614795i	−0.926771	+	0.375626i	$0.877428\pi$
$152$	3.78902	−	21.8854i	0.0249278	−	0.143983i
$153$	−126.075			−0.824022
$154$		0			0
$155$	44.9304			0.289873
$156$	−27.8331	−	42.1281i	−0.178417	−	0.270052i
$157$	162.970	+	94.0909i	1.03803	+	0.599305i	0.919274	−	0.393619i	$-0.128777\pi$
$157$	162.970	+	94.0909i	1.03803	+	0.599305i	0.118753	+	0.992924i	$0.462110\pi$
$158$	38.1791	−	11.4731i	0.241640	−	0.0726145i
$159$	247.294	−	142.775i	1.55531	−	0.897957i
$160$	−161.501	−	118.940i	−1.00938	−	0.743375i
$161$		0			0
$162$	121.760	−	129.326i	0.751605	−	0.798307i
$163$	−27.2577	−	47.2117i	−0.167225	−	0.289642i	0.770218	−	0.637781i	$-0.220147\pi$
$163$	−27.2577	−	47.2117i	−0.167225	−	0.289642i	−0.937443	+	0.348138i	$0.886814\pi$
$164$	−227.395	−	113.614i	−1.38655	−	0.692766i
$165$	−278.070	−	160.544i	−1.68527	−	0.972994i
$166$	−9.95897	−	2.34945i	−0.0599938	−	0.0141533i
$167$			266.435i			1.59542i	0.603042	+	0.797709i	$0.293955\pi$
$167$			266.435i			1.59542i	−0.603042	+	0.797709i	$0.706045\pi$
$168$		0			0
$169$	163.160			0.965446
$170$	−19.8447	+	84.1190i	−0.116734	+	0.494817i
$171$	25.3848	−	43.9677i	0.148449	−	0.257121i
$172$	−126.449	−	63.1780i	−0.735169	−	0.367314i
$173$	99.4501	−	57.4175i	0.574856	−	0.331893i	−0.184231	−	0.982883i	$-0.558979\pi$
$173$	99.4501	−	57.4175i	0.574856	−	0.331893i	0.759086	+	0.650990i	$0.225646\pi$
$174$	284.105	+	267.485i	1.63279	+	1.53727i
$175$		0			0
$176$	−155.772	+	18.8606i	−0.885071	+	0.107162i
$177$	273.705	+	474.071i	1.54636	+	2.67837i
$178$	10.3542	+	34.4556i	0.0581695	+	0.193571i
$179$	−56.4243	+	97.7298i	−0.315220	+	0.545977i	−0.979484	−	0.201521i	$-0.935412\pi$
$179$	−56.4243	+	97.7298i	−0.315220	+	0.545977i	0.664264	+	0.747498i	$0.268745\pi$
$180$	−252.723	−	382.521i	−1.40401	−	2.12512i
$181$			60.9470i			0.336724i	0.985725	+	0.168362i	$0.0538477\pi$
$181$			60.9470i			0.336724i	−0.985725	+	0.168362i	$0.946152\pi$
$182$		0			0
$183$			228.622i			1.24930i
$184$	337.643	+	58.4562i	1.83502	+	0.317697i
$185$	0.635101	−	1.10003i	0.00343298	−	0.00594609i
$186$	71.7212	−	21.5528i	0.385598	−	0.115875i
$187$	33.8069	+	58.5552i	0.180785	+	0.313130i
$188$	−151.376	+	9.13083i	−0.805194	+	0.0485682i
$189$		0			0
$190$	−25.3401	−	23.8577i	−0.133369	−	0.125567i
$191$	154.550	−	89.2296i	0.809164	−	0.467171i	−0.0375017	−	0.999297i	$-0.511940\pi$
$191$	154.550	−	89.2296i	0.809164	−	0.467171i	0.846665	+	0.532126i	$0.178607\pi$
$192$	−314.854	−	112.390i	−1.63987	−	0.585366i
$193$	−110.794	+	191.901i	−0.574062	+	0.994304i	0.422081	+	0.906558i	$0.361300\pi$
$193$	−110.794	+	191.901i	−0.574062	+	0.994304i	−0.996143	+	0.0877458i	$0.972034\pi$
$194$	24.3056	+	5.73400i	0.125287	+	0.0295567i
$195$	−79.1198			−0.405742
$196$		0			0
$197$			242.298i			1.22994i	0.788550	+	0.614970i	$0.210832\pi$
$197$			242.298i			1.22994i	−0.788550	+	0.614970i	$0.789168\pi$
$198$	−349.081	−	82.3526i	−1.76304	−	0.415922i
$199$	257.250	+	148.523i	1.29271	+	0.746349i	0.979135	−	0.203213i	$-0.0651384\pi$
$199$	257.250	+	148.523i	1.29271	+	0.746349i	0.313580	+	0.949562i	$0.398472\pi$
$200$	−107.276	+	39.4226i	−0.536381	+	0.197113i
$201$	−81.2329	−	140.699i	−0.404144	−	0.699997i
$202$	−99.1289	−	93.3297i	−0.490737	−	0.462028i
$203$		0			0
$204$	8.67361	+	143.796i	0.0425177	+	0.704884i
$205$	−344.955	+	199.160i	−1.68271	+	0.971512i
$206$	111.654	−	33.5528i	0.542008	−	0.162877i
$207$	678.325	+	391.631i	3.27693	+	1.89194i
$208$	−30.9179	+	23.2169i	−0.148644	+	0.111620i
$209$	−27.2275			−0.130275
$210$		0			0
$211$	−141.020			−0.668341			−0.334171	−	0.942513i	$-0.608456\pi$
$211$	−141.020			−0.668341			−0.334171	+	0.942513i	$0.608456\pi$
$212$	−120.533	−	182.439i	−0.568554	−	0.860563i
$213$	104.633	+	60.4098i	0.491234	+	0.283614i
$214$	78.2038	+	260.239i	0.365439	+	1.21607i
$215$	−191.822	+	110.748i	−0.892194	+	0.515109i
$216$	−298.048	−	248.521i	−1.37985	−	1.15056i
$217$		0			0
$218$	−64.7966	−	61.0059i	−0.297232	−	0.279844i
$219$	−180.810	−	313.171i	−0.825614	−	1.43001i
$220$	−109.893	+	219.948i	−0.499514	+	0.999765i
$221$	14.4287	+	8.33040i	0.0652882	+	0.0376941i
$222$	0.486121	−	2.06060i	0.00218973	−	0.00928198i
$223$		−	40.8267i		−	0.183079i	−0.995801	−	0.0915396i	$-0.970821\pi$
$223$		−	40.8267i		−	0.183079i	0.995801	−	0.0915396i	$-0.0291788\pi$
$224$		0			0
$225$	−261.244			−1.16108
$226$	259.654	+	61.2555i	1.14891	+	0.271042i
$227$	4.09299	−	7.08926i	0.0180308	−	0.0312302i	−0.856869	−	0.515534i	$-0.827594\pi$
$227$	4.09299	−	7.08926i	0.0180308	−	0.0312302i	0.874900	+	0.484304i	$0.160927\pi$
$228$	−51.8942	−	25.9280i	−0.227606	−	0.113719i
$229$	−287.738	+	166.126i	−1.25650	+	0.725440i	−0.972392	−	0.233352i	$-0.925031\pi$
$229$	−287.738	+	166.126i	−1.25650	+	0.725440i	−0.284107	+	0.958792i	$0.591697\pi$
$230$	368.071	−	390.942i	1.60031	−	1.69975i
$231$		0			0
$232$	191.356	−	229.492i	0.824812	−	0.989188i
$233$	−164.630	−	285.148i	−0.706568	−	1.22381i	−0.966123	−	0.258083i	$-0.916909\pi$
$233$	−164.630	−	285.148i	−0.706568	−	1.22381i	0.259555	−	0.965728i	$-0.416424\pi$
$234$	−84.6397	+	25.4349i	−0.361708	+	0.108696i
$235$	−118.817	+	205.797i	−0.505603	+	0.875730i
$236$	349.742	−	231.067i	1.48196	−	0.979096i
$237$		−	104.122i		−	0.439333i
$238$		0			0
$239$		−	137.719i		−	0.576230i	−0.957596	−	0.288115i	$-0.906971\pi$
$239$		−	137.719i		−	0.576230i	0.957596	−	0.288115i	$-0.0930286\pi$
$240$	−418.901	+	314.561i	−1.74542	+	1.31067i
$241$	100.927	−	174.810i	0.418783	−	0.725354i	−0.577034	−	0.816720i	$-0.695790\pi$
$241$	100.927	−	174.810i	0.418783	−	0.725354i	0.995817	+	0.0913661i	$0.0291234\pi$
$242$	−14.2890	−	47.5496i	−0.0590454	−	0.196486i
$243$	−13.6746	−	23.6851i	−0.0562741	−	0.0974696i
$244$	174.750	−	10.5407i	0.716188	−	0.0431995i
$245$		0			0
$246$	−455.108	+	483.387i	−1.85003	+	1.96499i
$247$	−5.81032	+	3.35459i	−0.0235235	+	0.0135813i
$248$	−19.7808	−	53.8273i	−0.0797614	−	0.217045i
$249$	−13.3625	+	23.1445i	−0.0536647	+	0.0929499i
$250$	30.8375	−	130.716i	0.123350	−	0.522864i
$251$	269.203			1.07252			0.536261	−	0.844052i	$-0.319836\pi$
$251$	269.203			1.07252			0.536261	+	0.844052i	$0.319836\pi$
$252$		0			0
$253$		−	420.061i		−	1.66032i
$254$	60.1470	−	254.955i	0.236799	−	1.00376i
$255$	195.492	+	112.867i	0.766633	+	0.442616i
$256$	−71.3904	+	245.844i	−0.278869	+	0.960329i
$257$	−121.180	−	209.889i	−0.471516	−	0.816690i	0.527953	−	0.849274i	$-0.322960\pi$
$257$	−121.180	−	209.889i	−0.471516	−	0.816690i	−0.999469	+	0.0325840i	$0.989626\pi$
$258$	−253.075	+	268.800i	−0.980912	+	1.04186i
$259$		0			0
$260$	3.64784	+	60.4761i	0.0140302	+	0.232600i
$261$	591.498	−	341.501i	2.26627	−	1.30843i
$262$	30.6967	+	102.150i	0.117163	+	0.389884i
$263$	−29.3124	−	16.9235i	−0.111454	−	0.0643479i	0.443237	−	0.896405i	$-0.353830\pi$
$263$	−29.3124	−	16.9235i	−0.111454	−	0.0643479i	−0.554691	+	0.832057i	$0.687163\pi$
$264$	−69.9122	+	403.813i	−0.264819	+	1.52959i
$265$	−342.634			−1.29296
$266$		0			0
$267$	93.9673			0.351937
$268$	−103.800	+	68.5783i	−0.387314	+	0.255889i
$269$	143.412	+	82.7990i	0.533130	+	0.307803i	0.742290	−	0.670078i	$-0.233740\pi$
$269$	143.412	+	82.7990i	0.533130	+	0.307803i	−0.209160	+	0.977881i	$0.567073\pi$
$270$	−582.361	+	175.004i	−2.15689	+	0.648163i
$271$	−128.439	+	74.1542i	−0.473944	+	0.273632i	−0.717889	−	0.696157i	$-0.754892\pi$
$271$	−128.439	+	74.1542i	−0.473944	+	0.273632i	0.243945	+	0.969789i	$0.421558\pi$
$272$	109.513	−	13.2595i	0.402620	−	0.0487483i
$273$		0			0
$274$	−79.1300	+	84.0468i	−0.288796	+	0.306740i
$275$	70.0521	+	121.334i	0.254735	+	0.441214i
$276$	400.011	−	800.612i	1.44932	−	2.90077i
$277$	414.270	+	239.179i	1.49556	+	0.863463i	0.999987	−	0.00510300i	$-0.00162434\pi$
$277$	414.270	+	239.179i	1.49556	+	0.863463i	0.495574	+	0.868566i	$0.334958\pi$
$278$	−335.631	−	79.1796i	−1.20731	−	0.284819i
$279$		−	131.083i		−	0.469830i
$280$		0			0
$281$	−226.066			−0.804506			−0.402253	−	0.915528i	$-0.631773\pi$
$281$	−226.066			−0.804506			−0.402253	+	0.915528i	$0.631773\pi$
$282$	−90.9451	+	385.504i	−0.322500	+	1.36703i
$283$	−127.314	+	220.514i	−0.449873	+	0.779202i	−0.998377	−	0.0569453i	$-0.981864\pi$
$283$	−127.314	+	220.514i	−0.449873	+	0.779202i	0.548505	+	0.836147i	$0.315197\pi$
$284$	41.3508	−	82.7625i	0.145601	−	0.291417i
$285$	−78.7229	+	45.4507i	−0.276221	+	0.159476i
$286$	34.5091	+	32.4903i	0.120661	+	0.113602i
$287$		0			0
$288$	−347.003	+	471.172i	−1.20487	+	1.63602i
$289$	120.733	+	209.115i	0.417760	+	0.723582i
$290$	−134.750	−	448.407i	−0.464654	−	1.54623i
$291$	32.6122	−	56.4860i	0.112069	−	0.194110i
$292$	−231.040	+	152.643i	−0.791232	+	0.522749i
$293$			149.558i			0.510437i	0.966883	+	0.255218i	$0.0821474\pi$
$293$			149.558i			0.510437i	−0.966883	+	0.255218i	$0.917853\pi$
$294$		0			0
$295$		−	656.842i		−	2.22658i
$296$	−1.59746	−	0.276568i	−0.00539681	−	0.000934351i
$297$	−237.858	+	411.981i	−0.800867	+	1.38714i
$298$	420.482	−	126.358i	1.41101	−	0.424020i
$299$	−51.7539	−	89.6403i	−0.173090	−	0.299800i
$300$	17.9728	+	297.964i	0.0599094	+	0.993214i
$301$		0			0
$302$	270.363	+	254.547i	0.895243	+	0.842870i
$303$	−307.959	+	177.800i	−1.01637	+	0.586799i
$304$	−17.4258	+	40.8613i	−0.0573216	+	0.134412i
$305$	137.163	−	237.573i	0.449714	−	0.778927i
$306$	245.414	+	57.8963i	0.802007	+	0.189203i
$307$	−271.779			−0.885272			−0.442636	−	0.896701i	$-0.645957\pi$
$307$	−271.779			−0.885272			−0.442636	+	0.896701i	$0.645957\pi$
$308$		0			0
$309$		−	304.502i		−	0.985442i
$310$	−87.4599	−	20.6329i	−0.282129	−	0.0665577i
$311$	−462.614	−	267.090i	−1.48750	−	0.858811i	−0.487605	−	0.873064i	$-0.662130\pi$
$311$	−462.614	−	267.090i	−1.48750	−	0.858811i	−0.999898	+	0.0142534i	$0.995463\pi$
$312$	34.8329	+	94.7867i	0.111644	+	0.303804i
$313$	−278.116	−	481.711i	−0.888550	−	1.53901i	−0.841590	−	0.540117i	$-0.818380\pi$
$313$	−278.116	−	481.711i	−0.888550	−	1.53901i	−0.0469600	−	0.998897i	$-0.514953\pi$
$314$	−274.024	−	257.993i	−0.872688	−	0.821634i
$315$		0			0
$316$	−79.5867	+	4.80057i	−0.251857	+	0.0151917i
$317$	335.549	−	193.730i	1.05852	−	0.611134i	0.133494	−	0.991050i	$-0.457380\pi$
$317$	335.549	−	193.730i	1.05852	−	0.611134i	0.925021	+	0.379916i	$0.124047\pi$
$318$	−546.939	+	164.359i	−1.71993	+	0.516853i
$319$	−317.218	−	183.146i	−0.994413	−	0.574125i
$320$	259.752	+	305.689i	0.811725	+	0.955277i
$321$	709.724			2.21098
$322$		0			0
$323$	19.1417			0.0592624
$324$	−296.403	+	195.826i	−0.914823	+	0.604403i
$325$	29.8980	+	17.2616i	0.0919940	+	0.0531127i
$326$	31.3784	+	104.418i	0.0962526	+	0.320300i
$327$	−201.300	+	116.221i	−0.615597	+	0.355415i
$328$	390.465	+	325.581i	1.19044	+	0.992624i
$329$		0			0
$330$	467.557	+	440.205i	1.41684	+	1.33395i
$331$	191.603	+	331.865i	0.578860	+	1.00261i	0.995610	+	0.0935935i	$0.0298354\pi$
$331$	191.603	+	331.865i	0.578860	+	1.00261i	−0.416751	+	0.909021i	$0.636831\pi$
$332$	18.3069	+	9.14670i	0.0551412	+	0.0275503i
$333$	−3.20929	−	1.85288i	−0.00963750	−	0.00556422i
$334$	122.352	−	518.633i	0.366323	−	1.55279i
$335$			194.944i			0.581923i
$336$		0			0
$337$	563.726			1.67278			0.836388	−	0.548138i	$-0.184663\pi$
$337$	563.726			1.67278			0.836388	+	0.548138i	$0.184663\pi$
$338$	−317.602	−	74.9264i	−0.939652	−	0.221676i
$339$	348.392	−	603.432i	1.02770	−	1.78004i
$340$	77.2581	−	154.630i	0.227230	−	0.454794i
$341$	−60.8809	+	35.1496i	−0.178536	+	0.103078i
$342$	−69.6040	+	73.9289i	−0.203520	+	0.216166i
$343$		0			0
$344$	217.129	+	181.048i	0.631188	+	0.526302i
$345$	−701.203	−	1214.52i	−2.03247	−	3.52035i
$346$	−219.953	+	66.0976i	−0.635703	+	0.191034i
$347$	−25.7945	+	44.6774i	−0.0743357	+	0.128753i	−0.900797	−	0.434240i	$-0.857017\pi$
$347$	−25.7945	+	44.6774i	−0.0743357	+	0.128753i	0.826462	+	0.562993i	$0.190350\pi$
$348$	−430.195	−	651.143i	−1.23619	−	1.87110i
$349$		−	586.383i		−	1.68018i	−0.542447	−	0.840090i	$-0.682502\pi$
$349$		−	586.383i		−	1.68018i	0.542447	−	0.840090i	$-0.317498\pi$
$350$		0			0
$351$			117.222i			0.333965i
$352$	311.882	+	34.8203i	0.886030	+	0.0989213i
$353$	151.922	−	263.136i	0.430373	−	0.745428i	−0.566532	−	0.824040i	$-0.691715\pi$
$353$	151.922	−	263.136i	0.430373	−	0.745428i	0.996905	+	0.0786114i	$0.0250486\pi$
$354$	−315.082	−	1048.50i	−0.890063	−	2.96187i
$355$	−72.4862	−	125.550i	−0.204187	−	0.353661i
$356$	−4.33239	−	71.8250i	−0.0121696	−	0.201756i
$357$		0			0
$358$	154.713	−	164.326i	0.432159	−	0.459012i
$359$	−100.571	+	58.0649i	−0.280143	+	0.161741i	−0.633488	−	0.773752i	$-0.718377\pi$
$359$	−100.571	+	58.0649i	−0.280143	+	0.161741i	0.353345	+	0.935493i	$0.385044\pi$
$360$	316.280	+	860.657i	0.878557	+	2.39071i
$361$	176.646	−	305.960i	0.489324	−	0.847534i
$362$	27.9880	−	118.637i	0.0773150	−	0.327727i
$363$	−129.677			−0.357237
$364$		0			0
$365$			433.910i			1.18879i
$366$	104.988	−	445.027i	0.286851	−	1.21592i
$367$	412.478	+	238.144i	1.12392	+	0.648894i	0.942398	−	0.334493i	$-0.108565\pi$
$367$	412.478	+	238.144i	1.12392	+	0.648894i	0.181520	+	0.983387i	$0.441898\pi$
$368$	−630.400	−	268.841i	−1.71304	−	0.730546i
$369$	581.042	+	1006.39i	1.57464	+	2.72736i
$370$	−1.74142	+	1.84962i	−0.00470654	+	0.00499898i
$371$		0			0
$372$	−149.507	+	9.01809i	−0.401902	+	0.0242422i
$373$	−42.6827	+	24.6428i	−0.114431	+	0.0660666i	−0.556123	−	0.831100i	$-0.687712\pi$
$373$	−42.6827	+	24.6428i	−0.114431	+	0.0660666i	0.441692	+	0.897167i	$0.354378\pi$
$374$	−38.9176	−	129.506i	−0.104058	−	0.346274i
$375$	−303.782	−	175.389i	−0.810086	−	0.467704i
$376$	298.857	+	51.7412i	0.794833	+	0.137610i
$377$	−90.2585			−0.239412
$378$		0			0
$379$	167.511			0.441983			0.220991	−	0.975276i	$-0.429071\pi$
$379$	167.511			0.441983			0.220991	+	0.975276i	$0.429071\pi$
$380$	38.3703	+	58.0772i	0.100974	+	0.152835i
$381$	−592.512	−	342.087i	−1.55515	−	0.897866i
$382$	−341.818	+	102.719i	−0.894812	+	0.268898i
$383$	−444.450	+	256.604i	−1.16044	+	0.669983i	−0.951411	−	0.307925i	$-0.900365\pi$
$383$	−444.450	+	256.604i	−1.16044	+	0.669983i	−0.209034	+	0.977908i	$0.567032\pi$
$384$	561.273	+	363.362i	1.46165	+	0.946256i
$385$		0			0
$386$	303.792	−	322.668i	0.787026	−	0.835929i
$387$	323.104	+	559.633i	0.834895	+	1.44608i
$388$	−44.6793	−	22.3232i	−0.115153	−	0.0575341i
$389$	614.357	+	354.699i	1.57932	+	0.911823i	0.994954	+	0.100336i	$0.0319916\pi$
$389$	614.357	+	354.699i	1.57932	+	0.911823i	0.584370	+	0.811487i	$0.301342\pi$
$390$	154.012	+	36.3333i	0.394902	+	0.0931623i
$391$			295.315i			0.755281i
$392$		0			0
$393$	278.582			0.708860
$394$	111.268	−	471.649i	0.282406	−	1.19708i
$395$	−62.4683	+	108.198i	−0.158148	+	0.273920i
$396$	641.691	+	320.609i	1.62043	+	0.809620i
$397$	267.952	−	154.702i	0.674941	−	0.389677i	−0.123005	−	0.992406i	$-0.539253\pi$
$397$	267.952	−	154.702i	0.674941	−	0.389677i	0.797946	+	0.602729i	$0.205920\pi$
$398$	−432.549	−	407.245i	−1.08681	−	1.02323i
$399$		0			0
$400$	226.924	−	27.4754i	0.567309	−	0.0686886i
$401$	264.036	+	457.324i	0.658445	+	1.14046i	0.981018	+	0.193915i	$0.0621186\pi$
$401$	264.036	+	457.324i	0.658445	+	1.14046i	−0.322574	+	0.946544i	$0.604548\pi$
$402$	93.5132	+	311.184i	0.232620	+	0.774091i
$403$	−8.66126	+	15.0017i	−0.0214920	+	0.0372252i
$404$	150.102	+	227.194i	0.371540	+	0.562362i
$405$			556.666i			1.37448i
$406$		0			0
$407$			1.98739i			0.00488302i
$408$	49.1503	−	283.892i	0.120466	−	0.695814i
$409$	−306.415	+	530.726i	−0.749181	+	1.29762i	0.199035	+	0.979992i	$0.436219\pi$
$409$	−306.415	+	530.726i	−0.749181	+	1.29762i	−0.948216	+	0.317627i	$0.897114\pi$
$410$	762.936	−	229.268i	1.86082	−	0.559190i
$411$	150.748	+	261.104i	0.366785	+	0.635290i
$412$	−232.749	+	14.0391i	−0.564926	+	0.0340756i
$413$		0			0
$414$	−1140.56	−	1073.84i	−2.75497	−	2.59381i
$415$	27.7713	−	16.0338i	0.0669188	−	0.0386356i
$416$	70.8453	−	30.9951i	0.170301	−	0.0745075i
$417$	−450.335	+	780.003i	−1.07994	+	1.87051i
$418$	53.0002	+	12.5034i	0.126795	+	0.0299124i
$419$	237.642			0.567165			0.283583	−	0.958948i	$-0.408477\pi$
$419$	237.642			0.567165			0.283583	+	0.958948i	$0.408477\pi$
$420$		0			0
$421$			394.516i			0.937092i	0.883439	+	0.468546i	$0.155222\pi$
$421$			394.516i			0.937092i	−0.883439	+	0.468546i	$0.844778\pi$
$422$	274.505	+	64.7591i	0.650485	+	0.153458i
$423$	600.404	+	346.644i	1.41940	+	0.819488i
$424$	150.847	+	410.481i	0.355770	+	0.968116i
$425$	−49.2487	−	85.3012i	−0.115879	−	0.200709i
$426$	−175.933	−	165.641i	−0.412989	−	0.388829i
$427$		0			0
$428$	−32.7220	−	542.486i	−0.0764533	−	1.26749i
$429$	107.208	−	61.8964i	0.249901	−	0.144281i
$430$	424.252	−	127.491i	0.986631	−	0.296490i
$431$	−314.678	−	181.679i	−0.730111	−	0.421530i	0.0883519	−	0.996089i	$-0.471840\pi$
$431$	−314.678	−	181.679i	−0.730111	−	0.421530i	−0.818463	+	0.574560i	$0.805173\pi$
$432$	466.045	+	620.632i	1.07881	+	1.43665i
$433$	−119.733			−0.276520			−0.138260	−	0.990396i	$-0.544151\pi$
$433$	−119.733			−0.276520			−0.138260	+	0.990396i	$0.544151\pi$
$434$		0			0
$435$	−1222.89			−2.81125
$436$	98.1157	+	148.508i	0.225036	+	0.340614i
$437$	−102.989	−	59.4605i	−0.235672	−	0.136065i
$438$	208.143	+	692.640i	0.475213	+	1.58137i
$439$	754.721	−	435.738i	1.71918	−	0.992570i	0.798755	−	0.601657i	$-0.205492\pi$
$439$	754.721	−	435.738i	1.71918	−	0.992570i	0.920427	−	0.390914i	$-0.127841\pi$
$440$	314.919	−	377.679i	0.715724	−	0.858361i
$441$		0			0
$442$	−24.2609	−	22.8416i	−0.0548889	−	0.0516778i
$443$	171.978	+	297.875i	0.388212	+	0.672403i	0.992209	−	0.124584i	$-0.0397595\pi$
$443$	171.978	+	297.875i	0.388212	+	0.672403i	−0.603997	+	0.796987i	$0.706426\pi$
$444$	−1.89253	+	3.78785i	−0.00426246	+	0.00853120i
$445$	−97.6462	−	56.3761i	−0.219430	−	0.126688i
$446$	−18.7484	+	79.4718i	−0.0420367	+	0.178188i
$447$		−	1146.74i		−	2.56541i
$448$		0			0
$449$	−242.849			−0.540866			−0.270433	−	0.962739i	$-0.587167\pi$
$449$	−242.849			−0.540866			−0.270433	+	0.962739i	$0.587167\pi$
$450$	508.529	+	119.968i	1.13006	+	0.266596i
$451$	311.611	−	539.726i	0.690933	−	1.19673i
$452$	−477.303	−	238.476i	−1.05598	−	0.527601i
$453$	839.924	−	484.930i	1.85414	−	1.07049i
$454$	−11.2228	+	11.9201i	−0.0247198	+	0.0262558i
$455$		0			0
$456$	89.1088	+	74.3013i	0.195414	+	0.162942i
$457$	21.1285	+	36.5957i	0.0462331	+	0.0800781i	0.888216	−	0.459426i	$-0.151945\pi$
$457$	21.1285	+	36.5957i	0.0462331	+	0.0800781i	−0.841983	+	0.539504i	$0.818612\pi$
$458$	636.390	−	191.240i	1.38950	−	0.417554i
$459$	167.221	−	289.635i	0.364315	−	0.631013i
$460$	−896.003	+	591.969i	−1.94783	+	1.28689i
$461$			816.370i			1.77087i	0.464766	+	0.885434i	$0.346139\pi$
$461$			816.370i			1.77087i	−0.464766	+	0.885434i	$0.653861\pi$
$462$		0			0
$463$		−	115.161i		−	0.248727i	−0.992237	−	0.124363i	$-0.960311\pi$
$463$		−	115.161i		−	0.248727i	0.992237	−	0.124363i	$-0.0396889\pi$
$464$	−477.875	+	358.846i	−1.02990	+	0.773375i
$465$	−117.350	+	203.256i	−0.252365	+	0.437109i
$466$	189.518	+	630.661i	0.406691	+	1.35335i
$467$	301.712	+	522.580i	0.646064	+	1.11902i	0.984055	+	0.177866i	$0.0569194\pi$
$467$	301.712	+	522.580i	0.646064	+	1.11902i	−0.337991	+	0.941149i	$0.609747\pi$
$468$	176.437	−	10.6424i	0.377002	−	0.0227403i
$469$		0			0
$470$	325.790	−	346.034i	0.693171	−	0.736242i
$471$	−851.296	+	491.496i	−1.80742	+	1.04352i
$472$	−786.907	+	289.178i	−1.66718	+	0.612666i
$473$	173.280	−	300.129i	0.366342	−	0.634523i
$474$	−47.8147	+	202.680i	−0.100875	+	0.427595i
$475$	39.6641			0.0835034
$476$		0			0
$477$			999.624i			2.09565i
$478$	−63.2432	+	268.079i	−0.132308	+	0.560835i
$479$	−137.348	−	79.2977i	−0.286738	−	0.165548i	0.349732	−	0.936850i	$-0.386273\pi$
$479$	−137.348	−	79.2977i	−0.286738	−	0.165548i	−0.636470	+	0.771302i	$0.719606\pi$
$480$	959.870	−	419.947i	1.99973	−	0.874889i
$481$	0.244858	+	0.424106i	0.000509060	+	0.000881717i
$482$	−276.737	+	293.932i	−0.574143	+	0.609818i
$483$		0			0
$484$	5.97880	+	99.1201i	0.0123529	+	0.204794i
$485$	−67.7780	+	39.1317i	−0.139749	+	0.0806838i
$486$	15.7419	+	52.3843i	0.0323906	+	0.107787i
$487$	−92.6539	−	53.4937i	−0.190254	−	0.109843i	0.401847	−	0.915707i	$-0.368368\pi$
$487$	−92.6539	−	53.4937i	−0.190254	−	0.109843i	−0.592102	+	0.805863i	$0.701702\pi$
$488$	−345.002	−	59.7303i	−0.706972	−	0.122398i
$489$	284.768			0.582348
$490$		0			0
$491$	616.591			1.25579			0.627893	−	0.778299i	$-0.283917\pi$
$491$	616.591			1.25579			0.627893	+	0.778299i	$0.283917\pi$
$492$	1107.88	−	731.950i	2.25179	−	1.48770i
$493$	223.013	+	128.757i	0.452360	+	0.261170i
$494$	12.8507	−	3.86172i	0.0260135	−	0.00781724i
$495$	973.438	−	562.015i	1.96654	−	1.13538i
$496$	13.7862	+	113.862i	0.0277947	+	0.229561i
$497$		0			0
$498$	36.6394	−	38.9160i	0.0735731	−	0.0781446i
$499$	−277.045	−	479.856i	−0.555200	−	0.961635i	−0.997888	−	0.0649593i	$-0.979308\pi$
$499$	−277.045	−	479.856i	−0.555200	−	0.961635i	0.442688	−	0.896676i	$-0.354025\pi$
$500$	−120.055	+	240.286i	−0.240109	+	0.480572i
$501$	−1205.30	−	695.879i	−2.40578	−	1.38898i
$502$	−524.022	−	123.623i	−1.04387	−	0.246261i
$503$			148.158i			0.294548i	0.989096	+	0.147274i	$0.0470499\pi$
$503$			148.158i			0.294548i	−0.989096	+	0.147274i	$0.952950\pi$
$504$		0			0
$505$	426.688			0.844926
$506$	−192.900	+	817.675i	−0.381225	+	1.61596i
$507$	−426.145	+	738.104i	−0.840522	+	1.45583i
$508$	−234.160	+	468.666i	−0.460946	+	0.922570i
$509$	−158.386	+	91.4444i	−0.311172	+	0.179655i	−0.647451	−	0.762107i	$-0.724165\pi$
$509$	−158.386	+	91.4444i	−0.311172	+	0.179655i	0.336279	+	0.941762i	$0.390831\pi$
$510$	−328.706	−	309.477i	−0.644522	−	0.606817i
$511$		0			0
$512$	251.863	−	445.768i	0.491919	−	0.870641i
$513$	67.3385	+	116.634i	0.131264	+	0.227356i
$514$	139.499	+	464.211i	0.271399	+	0.903134i
$515$	−182.687	+	316.423i	−0.354732	+	0.614414i
$516$	616.066	−	407.021i	1.19393	−	0.788800i
$517$		−	371.807i		−	0.719163i
$518$		0			0
$519$			599.856i			1.15579i
$520$	20.6710	−	119.396i	0.0397520	−	0.229607i
$521$	49.1230	−	85.0836i	0.0942861	−	0.163308i	−0.815024	−	0.579427i	$-0.803277\pi$
$521$	49.1230	−	85.0836i	0.0942861	−	0.163308i	0.909310	+	0.416118i	$0.136610\pi$
$522$	−1308.21	+	393.128i	−2.50615	+	0.753118i
$523$	−287.382	−	497.760i	−0.549488	−	0.951740i	−0.998310	−	0.0581192i	$-0.981490\pi$
$523$	−287.382	−	497.760i	−0.549488	−	0.951740i	0.448822	−	0.893621i	$-0.351844\pi$
$524$	−12.8441	−	212.937i	−0.0245116	−	0.406369i
$525$		0			0
$526$	49.2868	+	46.4035i	0.0937012	+	0.0882196i
$527$	42.8010	−	24.7112i	0.0812163	−	0.0468903i
$528$	321.527	−	753.943i	0.608953	−	1.42792i
$529$	652.843	−	1130.76i	1.23411	−	2.13754i
$530$	666.960	+	157.344i	1.25842	+	0.296876i
$531$	−1916.31			−3.60888
$532$		0			0
$533$		−	153.569i		−	0.288122i
$534$	−182.914	−	43.1516i	−0.342535	−	0.0808082i
$535$	−737.510	−	425.802i	−1.37852	−	0.795891i
$536$	233.546	−	85.8252i	0.435720	−	0.160122i
$537$	−294.740	−	510.504i	−0.548864	−	0.950660i
$538$	−241.138	−	227.031i	−0.448212	−	0.421991i
$539$		0			0
$540$	1213.97	−	73.2251i	2.24809	−	0.135602i
$541$	320.996	−	185.327i	0.593338	−	0.342564i	−0.173078	−	0.984908i	$-0.555371\pi$
$541$	320.996	−	185.327i	0.593338	−	0.342564i	0.766416	+	0.642344i	$0.222038\pi$
$542$	284.068	−	85.3644i	0.524110	−	0.157499i
$543$	−275.712	−	159.182i	−0.507756	−	0.293153i
$544$	−219.262	−	24.4797i	−0.403056	−	0.0449994i
$545$	278.909			0.511759
$546$		0			0
$547$	−56.5966			−0.103467			−0.0517336	−	0.998661i	$-0.516475\pi$
$547$	−56.5966			−0.103467			−0.0517336	+	0.998661i	$0.516475\pi$
$548$	192.628	−	127.265i	0.351510	−	0.232235i
$549$	−693.110	−	400.167i	−1.26250	−	0.728902i
$550$	−80.6422	−	268.353i	−0.146622	−	0.487915i
$551$	−89.8057	+	51.8494i	−0.162987	+	0.0941005i
$552$	−1146.31	+	1374.75i	−2.07664	+	2.49049i
$553$		0			0
$554$	−696.569	−	655.819i	−1.25734	−	1.18379i
$555$	3.31753	+	5.74613i	0.00597753	+	0.0103534i
$556$	616.968	+	308.257i	1.10965	+	0.554418i
$557$	−131.224	−	75.7624i	−0.235591	−	0.136019i	0.377558	−	0.925986i	$-0.376764\pi$
$557$	−131.224	−	75.7624i	−0.235591	−	0.136019i	−0.613149	+	0.789968i	$0.710097\pi$
$558$	−60.1957	+	255.161i	−0.107878	+	0.457278i
$559$		−	85.3962i		−	0.152766i
$560$		0			0
$561$	−353.189			−0.629571
$562$	440.053	+	103.814i	0.783012	+	0.184722i
$563$	−159.024	+	275.438i	−0.282458	+	0.489232i	−0.971990	−	0.235024i	$-0.924483\pi$
$563$	−159.024	+	275.438i	−0.282458	+	0.489232i	0.689531	+	0.724256i	$0.257817\pi$
$564$	354.061	−	708.644i	0.627768	−	1.25646i
$565$	−724.063	+	418.038i	−1.28153	+	0.739891i
$566$	349.089	−	370.780i	0.616766	−	0.655089i
$567$		0			0
$568$	−118.498	+	142.114i	−0.208624	+	0.250200i
$569$	−178.327	−	308.871i	−0.313404	−	0.542831i	0.665693	−	0.746226i	$-0.268136\pi$
$569$	−178.327	−	308.871i	−0.313404	−	0.542831i	−0.979097	+	0.203394i	$0.934803\pi$
$570$	174.111	−	52.3217i	0.305458	−	0.0917924i
$571$	−415.507	+	719.679i	−0.727683	+	1.26038i	0.230177	+	0.973149i	$0.426069\pi$
$571$	−415.507	+	719.679i	−0.727683	+	1.26038i	−0.957860	+	0.287235i	$0.907264\pi$
$572$	−52.2541	−	79.0917i	−0.0913533	−	0.138272i
$573$			932.205i			1.62689i
$574$		0			0
$575$			611.929i			1.06422i
$576$	891.836	−	757.818i	1.54833	−	1.31566i
$577$	385.742	−	668.124i	0.668530	−	1.15793i	−0.309786	−	0.950806i	$-0.600257\pi$
$577$	385.742	−	668.124i	0.668530	−	1.15793i	0.978315	−	0.207121i	$-0.0664094\pi$
$578$	−138.985	−	462.499i	−0.240458	−	0.800172i
$579$	−578.746	−	1002.42i	−0.999562	−	1.73129i
$580$	56.3819	+	934.734i	0.0972102	+	1.61161i
$581$		0			0
$582$	−89.4212	+	94.9775i	−0.153645	+	0.163192i
$583$	464.271	−	268.047i	0.796349	−	0.459772i
$584$	519.831	−	191.031i	0.890121	−	0.327108i
$585$	138.487	−	239.866i	0.236730	−	0.410028i
$586$	68.6799	−	291.124i	0.117201	−	0.496799i
$587$	−144.376			−0.245956			−0.122978	−	0.992409i	$-0.539244\pi$
$587$	−144.376			−0.245956			−0.122978	+	0.992409i	$0.539244\pi$
$588$		0			0
$589$			19.9020i			0.0337894i
$590$	−301.634	+	1278.59i	−0.511245	+	2.16709i
$591$	−1096.11	−	632.838i	−1.85467	−	1.07079i
$592$	2.98255	+	1.27194i	0.00503809	+	0.00214855i
$593$	419.463	+	726.531i	0.707357	+	1.22518i	0.965834	+	0.259162i	$0.0834462\pi$
$593$	419.463	+	726.531i	0.707357	+	1.22518i	−0.258477	+	0.966018i	$0.583220\pi$
$594$	652.195	−	692.720i	1.09797	−	1.16620i
$595$		0			0
$596$	−876.521	+	52.8706i	−1.47067	+	0.0887090i
$597$	−1343.78	+	775.831i	−2.25089	+	1.29955i
$598$	59.5777	+	198.257i	0.0996283	+	0.331534i
$599$	616.039	+	355.670i	1.02845	+	0.593774i	0.916539	−	0.399945i	$-0.130971\pi$
$599$	616.039	+	355.670i	1.02845	+	0.593774i	0.111907	+	0.993719i	$0.464304\pi$
$600$	101.846	−	588.260i	0.169743	−	0.980434i
$601$	356.394			0.593002			0.296501	−	0.955033i	$-0.404180\pi$
$601$	356.394			0.593002			0.296501	+	0.955033i	$0.404180\pi$
$602$		0			0
$603$	568.742			0.943188
$604$	−409.387	−	619.648i	−0.677793	−	1.02591i
$605$	134.754	+	77.8003i	0.222734	+	0.128596i
$606$	681.111	−	204.679i	1.12395	−	0.337754i
$607$	52.2836	−	30.1860i	0.0861345	−	0.0497298i	−0.456314	−	0.889819i	$-0.650831\pi$
$607$	52.2836	−	30.1860i	0.0861345	−	0.0497298i	0.542449	+	0.840089i	$0.317497\pi$
$608$	52.6847	−	71.5370i	0.0866525	−	0.117660i
$609$		0			0
$610$	−376.094	+	399.463i	−0.616548	+	0.654858i
$611$	−45.8088	−	79.3431i	−0.0749735	−	0.129858i
$612$	−451.128	−	225.398i	−0.737136	−	0.368297i
$613$	418.281	+	241.495i	0.682351	+	0.393955i	0.800740	−	0.599012i	$-0.204440\pi$
$613$	418.281	+	241.495i	0.682351	+	0.393955i	−0.118389	+	0.992967i	$0.537773\pi$
$614$	529.035	+	124.806i	0.861621	+	0.203267i
$615$		−	2080.68i		−	3.38321i
$616$		0			0
$617$	712.490			1.15476			0.577382	−	0.816474i	$-0.304074\pi$
$617$	712.490			1.15476			0.577382	+	0.816474i	$0.304074\pi$
$618$	−139.833	+	592.732i	−0.226267	+	0.959114i
$619$	−46.5409	+	80.6112i	−0.0751872	+	0.130228i	−0.901168	−	0.433471i	$-0.857289\pi$
$619$	−46.5409	+	80.6112i	−0.0751872	+	0.130228i	0.825980	+	0.563699i	$0.190622\pi$
$620$	160.771	+	80.3265i	0.259309	+	0.129559i
$621$	−1799.40	+	1038.88i	−2.89758	+	1.67292i
$622$	777.855	+	732.350i	1.25057	+	1.17741i
$623$		0			0
$624$	−24.2767	−	200.504i	−0.0389049	−	0.321321i
$625$	389.030	+	673.819i	0.622447	+	1.07811i
$626$	320.160	+	1065.40i	0.511438	+	1.70192i
$627$	71.1133	−	123.172i	0.113418	−	0.196446i
$628$	414.930	+	628.038i	0.660717	+	1.00006i
$629$		−	1.39719i		−	0.00222129i
$630$		0			0
$631$		−	610.573i		−	0.967628i	−0.875171	−	0.483814i	$-0.839251\pi$
$631$		−	610.573i		−	0.967628i	0.875171	−	0.483814i	$-0.160749\pi$
$632$	157.125	+	27.2031i	0.248616	+	0.0430429i
$633$	368.318	−	637.946i	0.581861	−	1.00781i
$634$	−742.133	+	223.016i	−1.17056	+	0.351761i
$635$	410.473	+	710.961i	0.646415	+	1.11962i
$636$	1140.13	−	68.7711i	1.79266	−	0.108131i
$637$		0			0
$638$	533.381	+	502.178i	0.836021	+	0.787113i
$639$	−366.287	+	211.476i	−0.573219	+	0.330948i
$640$	−365.246	−	714.326i	−0.570697	−	1.11613i
$641$	−295.077	+	511.088i	−0.460338	+	0.797328i	−0.998978	−	0.0452077i	$-0.985605\pi$
$641$	−295.077	+	511.088i	−0.460338	+	0.797328i	0.538640	+	0.842536i	$0.318938\pi$
$642$	−1381.52	−	325.919i	−2.15191	−	0.507662i
$643$	257.971			0.401199			0.200600	−	0.979673i	$-0.435711\pi$
$643$	257.971			0.401199			0.200600	+	0.979673i	$0.435711\pi$
$644$		0			0
$645$		−	1157.02i		−	1.79383i
$646$	−37.2607	−	8.79025i	−0.0576790	−	0.0136072i
$647$	−329.059	−	189.982i	−0.508591	−	0.293635i	0.223663	−	0.974667i	$-0.428198\pi$
$647$	−329.059	−	189.982i	−0.508591	−	0.293635i	−0.732254	+	0.681031i	$0.761532\pi$
$648$	666.895	−	245.075i	1.02916	−	0.378203i
$649$	513.856	+	890.024i	0.791765	+	1.37138i
$650$	−50.2716	−	47.3307i	−0.0773410	−	0.0728164i
$651$		0			0
$652$	−13.1293	−	217.666i	−0.0201370	−	0.333843i
$653$	825.126	−	476.386i	1.26359	−	0.729535i	0.289824	−	0.957080i	$-0.406403\pi$
$653$	825.126	−	476.386i	1.26359	−	0.729535i	0.973768	+	0.227545i	$0.0730698\pi$
$654$	445.215	−	133.790i	0.680757	−	0.204572i
$655$	−289.489	−	167.136i	−0.441968	−	0.255170i
$656$	−610.553	−	813.073i	−0.930722	−	1.23944i
$657$	1265.92			1.92681
$658$		0			0
$659$	−963.119			−1.46149			−0.730743	−	0.682653i	$-0.760826\pi$
$659$	−963.119			−1.46149			−0.730743	+	0.682653i	$0.760826\pi$
$660$	−707.981	−	1071.60i	−1.07270	−	1.62363i
$661$	−62.0782	−	35.8409i	−0.0939156	−	0.0542222i	0.452307	−	0.891862i	$-0.350601\pi$
$661$	−62.0782	−	35.8409i	−0.0939156	−	0.0542222i	−0.546222	+	0.837640i	$0.683935\pi$
$662$	−220.568	−	733.985i	−0.333184	−	1.10874i
$663$	−75.3701	+	43.5150i	−0.113680	+	0.0656334i
$664$	−31.4352	−	26.2115i	−0.0473422	−	0.0394752i
$665$		0			0
$666$	5.39621	+	5.08053i	0.00810242	+	0.00762842i
$667$	−799.921	−	1385.50i	−1.19928	−	2.07722i
$668$	−476.332	+	953.367i	−0.713072	+	1.42720i
$669$	184.692	+	106.632i	0.276071	+	0.159390i
$670$	89.5221	−	379.471i	0.133615	−	0.566375i
$671$			429.216i			0.639667i
$672$		0			0
$673$	−712.783			−1.05911			−0.529556	−	0.848275i	$-0.677642\pi$
$673$	−712.783			−1.05911			−0.529556	+	0.848275i	$0.677642\pi$
$674$	−1097.33	−	258.874i	−1.62808	−	0.384085i
$675$	346.502	−	600.160i	0.513337	−	0.889125i
$676$	583.826	+	291.698i	0.863648	+	0.431506i
$677$	664.698	−	383.763i	0.981828	−	0.566859i	0.0790065	−	0.996874i	$-0.474825\pi$
$677$	664.698	−	383.763i	0.981828	−	0.566859i	0.902822	+	0.430015i	$0.141492\pi$
$678$	−955.275	+	1014.63i	−1.40896	+	1.49651i
$679$		0			0
$680$	−221.397	+	265.519i	−0.325584	+	0.390469i
$681$	21.3803	+	37.0317i	0.0313954	+	0.0543784i
$682$	134.650	−	40.4633i	0.197434	−	0.0593304i
$683$	242.177	−	419.462i	0.354578	−	0.614147i	−0.632468	−	0.774587i	$-0.717958\pi$
$683$	242.177	−	419.462i	0.354578	−	0.614147i	0.987046	+	0.160440i	$0.0512912\pi$
$684$	169.438	−	111.944i	0.247717	−	0.163661i
$685$		−	361.769i		−	0.528130i
$686$		0			0
$687$		−	1735.56i		−	2.52629i
$688$	−339.515	−	452.131i	−0.493481	−	0.657168i
$689$	66.0499	−	114.402i	0.0958634	−	0.166040i
$690$	807.208	+	2686.15i	1.16987	+	3.89297i
$691$	−287.425	−	497.835i	−0.415956	−	0.720457i	0.579572	−	0.814921i	$-0.303220\pi$
$691$	−287.425	−	497.835i	−0.415956	−	0.720457i	−0.995528	+	0.0944642i	$0.969886\pi$
$692$	458.507	−	27.6565i	0.662582	−	0.0399661i
$693$		0			0
$694$	70.7274	−	75.1221i	0.101913	−	0.108245i
$695$	935.933	−	540.361i	1.34667	−	0.777498i
$696$	538.386	+	1465.05i	0.773543	+	2.10495i
$697$	−219.071	+	379.443i	−0.314306	+	0.544394i
$698$	−269.278	+	1141.43i	−0.385786	+	1.63529i
$699$	1719.94			2.46057
$700$		0			0
$701$			143.138i			0.204191i	0.994775	+	0.102096i	$0.0325548\pi$
$701$			143.138i			0.204191i	−0.994775	+	0.102096i	$0.967445\pi$
$702$	53.8304	−	228.180i	0.0766815	−	0.325042i
$703$	0.487259	+	0.281319i	0.000693114	+	0.000400169i
$704$	−591.110	−	211.002i	−0.839644	−	0.299719i
$705$	−620.655	−	1075.01i	−0.880361	−	1.52483i
$706$	−416.563	+	442.446i	−0.590032	+	0.626695i
$707$		0			0
$708$	131.837	+	2185.67i	0.186210	+	3.08710i
$709$	−221.106	+	127.656i	−0.311856	+	0.180050i	−0.647757	−	0.761847i	$-0.724293\pi$
$709$	−221.106	+	127.656i	−0.311856	+	0.180050i	0.335901	+	0.941897i	$0.390959\pi$
$710$	83.4443	+	277.678i	0.117527	+	0.391096i
$711$	315.665	+	182.249i	0.443973	+	0.256328i
$712$	−24.5501	+	141.802i	−0.0344805	+	0.199160i
$713$	−307.044			−0.430636
$714$		0			0
$715$	−148.540			−0.207748
$716$	−376.621	+	248.825i	−0.526007	+	0.347521i
$717$	623.013	+	359.697i	0.868916	+	0.501669i
$718$	222.433	−	66.8429i	0.309796	−	0.0930959i
$719$	−359.947	+	207.815i	−0.500621	+	0.289034i	−0.728970	−	0.684546i	$-0.760001\pi$
$719$	−359.947	+	207.815i	−0.500621	+	0.289034i	0.228349	+	0.973579i	$0.426667\pi$
$720$	−220.430	−	1820.57i	−0.306153	−	2.52857i
$721$		0			0
$722$	−484.355	+	514.451i	−0.670852	+	0.712537i
$723$	527.204	+	913.144i	0.729190	+	1.26299i
$724$	−108.961	+	218.083i	−0.150499	+	0.301219i
$725$	462.112	+	266.800i	0.637395	+	0.368000i
$726$	252.425	+	59.5502i	0.347693	+	0.0820250i
$727$		−	896.838i		−	1.23361i	−0.787114	−	0.616807i	$-0.788426\pi$
$727$		−	896.838i		−	1.23361i	0.787114	−	0.616807i	$-0.211574\pi$
$728$		0			0
$729$	−656.451			−0.900481
$730$	199.260	−	844.634i	0.272959	−	1.15703i
$731$	−121.821	+	211.000i	−0.166649	+	0.288645i
$732$	−408.730	+	818.063i	−0.558375	+	1.11757i
$733$	440.858	−	254.530i	0.601444	−	0.347244i	−0.168166	−	0.985759i	$-0.553784\pi$
$733$	440.858	−	254.530i	0.601444	−	0.347244i	0.769609	+	0.638515i	$0.220451\pi$
$734$	−693.555	−	652.981i	−0.944898	−	0.889620i
$735$		0			0
$736$	1103.66	+	812.808i	1.49954	+	1.10436i
$737$	−152.507	−	264.150i	−0.206930	−	0.358413i
$738$	−668.881	−	2225.84i	−0.906343	−	3.01604i
$739$	−370.714	+	642.095i	−0.501642	+	0.868870i	0.498356	+	0.866973i	$0.333937\pi$
$739$	−370.714	+	642.095i	−0.501642	+	0.868870i	−0.999998	+	0.00189750i	$0.999396\pi$
$740$	4.23917	−	2.80072i	0.00572861	−	0.00378476i
$741$		−	35.0463i		−	0.0472959i
$742$		0			0
$743$			1344.98i			1.81021i	0.425191	+	0.905104i	$0.360207\pi$
$743$			1344.98i			1.81021i	−0.425191	+	0.905104i	$0.639793\pi$
$744$	295.167	+	51.1024i	0.396730	+	0.0686860i
$745$	−687.989	+	1191.63i	−0.923476	+	1.59951i
$746$	94.4011	−	28.3682i	0.126543	−	0.0380271i
$747$	−46.7780	−	81.0218i	−0.0626211	−	0.108463i
$748$	16.2839	+	269.964i	0.0217699	+	0.360915i
$749$		0			0
$750$	510.790	+	480.909i	0.681054	+	0.641211i
$751$	23.9829	−	13.8465i	0.0319346	−	0.0184375i	−0.483948	−	0.875097i	$-0.660798\pi$
$751$	23.9829	−	13.8465i	0.0319346	−	0.0184375i	0.515882	+	0.856659i	$0.327464\pi$
$752$	−557.985	−	237.959i	−0.742001	−	0.316434i
$753$	−703.109	+	1217.82i	−0.933743	+	1.61729i
$754$	175.694	+	41.4484i	0.233016	+	0.0549714i
$755$	−1163.74			−1.54138
$756$		0			0
$757$			1341.69i			1.77238i	0.463318	+	0.886192i	$0.346659\pi$
$757$			1341.69i			1.77238i	−0.463318	+	0.886192i	$0.653341\pi$
$758$	−326.072	−	76.9244i	−0.430174	−	0.101483i
$759$	1900.27	+	1097.12i	2.50365	+	1.44548i
$760$	−48.0201	−	130.672i	−0.0631844	−	0.171936i
$761$	−56.0005	−	96.9958i	−0.0735881	−	0.127458i	0.826883	−	0.562374i	$-0.190112\pi$
$761$	−56.0005	−	96.9958i	−0.0735881	−	0.127458i	−0.900471	+	0.434915i	$0.856778\pi$
$762$	996.271	+	937.988i	1.30744	+	1.23096i
$763$		0			0
$764$	712.542	−	42.9796i	0.932647	−	0.0562560i
$765$	−684.355	+	395.113i	−0.894582	+	0.516487i
$766$	982.989	−	295.395i	1.28328	−	0.385634i
$767$	219.312	+	126.620i	0.285935	+	0.165085i
$768$	−925.691	−	965.056i	−1.20533	−	1.25658i
$769$	−140.749			−0.183028			−0.0915142	−	0.995804i	$-0.529171\pi$
$769$	−140.749			−0.183028			−0.0915142	+	0.995804i	$0.529171\pi$
$770$		0			0
$771$	1265.99			1.64202
$772$	−739.527	+	488.588i	−0.957936	+	0.632886i
$773$	−1147.60	−	662.568i	−1.48461	−	0.857138i	−0.484760	−	0.874647i	$-0.661093\pi$
$773$	−1147.60	−	662.568i	−1.48461	−	0.857138i	−0.999847	+	0.0175096i	$0.994426\pi$
$774$	−371.950	−	1237.74i	−0.480555	−	1.59915i
$775$	88.6891	−	51.2047i	0.114437	−	0.0660705i
$776$	76.7200	+	63.9712i	0.0988660	+	0.0824371i
$777$		0			0
$778$	−1033.00	−	972.570i	−1.32777	−	1.25009i
$779$	−88.2183	−	152.799i	−0.113246	−	0.196147i
$780$	−283.109	−	141.450i	−0.362960	−	0.181347i
$781$	196.438	+	113.414i	0.251522	+	0.145216i
$782$	135.614	−	574.850i	0.173420	−	0.735102i
$783$			1811.81i			2.31393i
$784$		0			0
$785$	1179.50			1.50255
$786$	−542.278	−	127.930i	−0.689921	−	0.162761i
$787$	−163.900	+	283.884i	−0.208260	+	0.360716i	−0.951166	−	0.308679i	$-0.900113\pi$
$787$	−163.900	+	283.884i	−0.208260	+	0.360716i	0.742907	+	0.669395i	$0.233447\pi$
$788$	−433.181	+	867.000i	−0.549722	+	1.10025i
$789$	153.117	−	88.4021i	0.194065	−	0.112043i
$790$	171.285	−	181.929i	0.216817	−	0.230289i
$791$		0			0
$792$	−1101.86	−	918.764i	−1.39124	−	1.16006i
$793$	52.8819	+	91.5941i	0.0666859	+	0.115503i
$794$	−592.627	+	178.089i	−0.746382	+	0.224293i
$795$	894.898	−	1550.01i	1.12566	−	1.94970i
$796$	654.971	+	991.364i	0.822828	+	1.24543i
$797$		−	393.650i		−	0.493915i	−0.969026	−	0.246958i	$-0.920569\pi$
$797$		−	393.650i		−	0.493915i	0.969026	−	0.246958i	$-0.0794308\pi$
$798$		0			0
$799$			261.391i			0.327148i
$800$	−454.339	−	50.7250i	−0.567924	−	0.0634062i
$801$	−164.475	+	284.879i	−0.205337	+	0.355655i
$802$	−303.952	−	1011.46i	−0.378992	−	1.26117i
$803$	−339.453	−	587.950i	−0.422731	−	0.732192i
$804$	−39.1278	−	648.684i	−0.0486664	−	0.806821i
$805$		0			0
$806$	23.7488	−	25.2245i	0.0294650	−	0.0312959i
$807$	−749.132	+	432.511i	−0.928292	+	0.535950i
$808$	−187.852	−	511.178i	−0.232490	−	0.632646i
$809$	−208.321	+	360.822i	−0.257504	+	0.446010i	−0.965573	−	0.260134i	$-0.916233\pi$
$809$	−208.321	+	360.822i	−0.257504	+	0.446010i	0.708069	+	0.706144i	$0.249567\pi$
$810$	255.632	−	1083.59i	0.315595	−	1.33776i
$811$	748.707			0.923190			0.461595	−	0.887091i	$-0.347277\pi$
$811$	748.707			0.923190			0.461595	+	0.887091i	$0.347277\pi$
$812$		0			0
$813$		−	774.708i		−	0.952901i
$814$	0.912647	−	3.86858i	0.00112119	−	0.00475256i
$815$	−295.917	−	170.848i	−0.363089	−	0.209629i
$816$	−226.043	+	530.044i	−0.277014	+	0.649564i
$817$	−49.0562	−	84.9678i	−0.0600443	−	0.104000i
$818$	840.176	−	892.382i	1.02711	−	1.09093i
$819$		0			0
$820$	−1590.39	+	95.9302i	−1.93950	+	0.116988i
$821$	479.925	−	277.085i	0.584561	−	0.337496i	−0.178383	−	0.983961i	$-0.557087\pi$
$821$	479.925	−	277.085i	0.584561	−	0.337496i	0.762944	+	0.646465i	$0.223753\pi$
$822$	−173.538	−	577.483i	−0.211117	−	0.702534i
$823$	−105.180	−	60.7260i	−0.127801	−	0.0737861i	0.434736	−	0.900558i	$-0.356842\pi$
$823$	−105.180	−	60.7260i	−0.127801	−	0.0737861i	−0.562538	+	0.826772i	$0.690175\pi$
$824$	459.509	+	79.5549i	0.557656	+	0.0965472i
$825$	−731.853			−0.887094
$826$		0			0
$827$	−1516.61			−1.83386			−0.916932	−	0.399043i	$-0.869343\pi$
$827$	−1516.61			−1.83386			−0.916932	+	0.399043i	$0.869343\pi$
$828$	1727.05	+	2614.06i	2.08581	+	3.15707i
$829$	−281.494	−	162.521i	−0.339559	−	0.196044i	0.320518	−	0.947242i	$-0.396143\pi$
$829$	−281.494	−	162.521i	−0.339559	−	0.196044i	−0.660077	+	0.751198i	$0.729476\pi$
$830$	−61.4217	+	18.4577i	−0.0740021	+	0.0222382i
$831$	−2164.00	+	1249.38i	−2.60409	+	1.50347i
$832$	−152.139	+	27.8005i	−0.182859	+	0.0334140i
$833$		0			0
$834$	1234.80	−	1311.53i	1.48057	−	1.57257i
$835$	834.991	+	1446.25i	0.999989	+	1.73203i
$836$	−97.4265	−	48.6774i	−0.116539	−	0.0582265i
$837$	301.138	+	173.862i	0.359783	+	0.207721i
$838$	−462.586	−	109.130i	−0.552012	−	0.130227i
$839$			1165.70i			1.38939i	0.719303	+	0.694696i	$0.244461\pi$
$839$			1165.70i			1.38939i	−0.719303	+	0.694696i	$0.755539\pi$
$840$		0			0
$841$	−554.058			−0.658808
$842$	181.169	−	767.950i	0.215165	−	0.912055i
$843$	590.443	−	1022.68i	0.700407	−	1.21314i
$844$	−504.603	−	252.116i	−0.597870	−	0.298715i
$845$	885.658	−	511.335i	1.04812	−	0.605130i
$846$	−1009.54	−	950.482i	−1.19331	−	1.12350i
$847$		0			0
$848$	−105.132	−	868.301i	−0.123976	−	1.02394i
$849$	−665.041	−	1151.88i	−0.783323	−	1.35675i
$850$	56.6938	+	188.660i	0.0666986	+	0.221953i
$851$	−4.34013	+	7.51733i	−0.00510004	+	0.00883352i
$852$	266.400	+	403.223i	0.312676	+	0.473266i
$853$			151.949i			0.178134i	0.996026	+	0.0890672i	$0.0283886\pi$
$853$			151.949i			0.178134i	−0.996026	+	0.0890672i	$0.971611\pi$
$854$		0			0
$855$		−	318.218i		−	0.372184i
$856$	−185.424	+	1071.01i	−0.216617	+	1.25118i
$857$	206.009	−	356.818i	0.240384	−	0.416357i	−0.720440	−	0.693517i	$-0.756060\pi$
$857$	206.009	−	356.818i	0.240384	−	0.416357i	0.960824	+	0.277160i	$0.0893934\pi$
$858$	−237.111	+	71.2535i	−0.276353	+	0.0830461i
$859$	79.9965	+	138.558i	0.0931274	+	0.161301i	0.908826	−	0.417176i	$-0.136980\pi$
$859$	79.9965	+	138.558i	0.0931274	+	0.161301i	−0.815698	+	0.578478i	$0.803647\pi$
$860$	−884.380	+	53.3446i	−1.02835	+	0.0620286i
$861$		0			0
$862$	529.110	+	498.157i	0.613817	+	0.577908i
$863$	859.885	−	496.455i	0.996391	−	0.575266i	0.0892122	−	0.996013i	$-0.471565\pi$
$863$	859.885	−	496.455i	0.996391	−	0.575266i	0.907178	+	0.420746i	$0.138232\pi$
$864$	−622.182	−	1422.12i	−0.720118	−	1.64597i
$865$	359.886	−	623.341i	0.416053	−	0.720625i
$866$	233.069	+	54.9839i	0.269133	+	0.0634918i
$867$	−1261.33			−1.45482
$868$		0			0
$869$		−	195.479i		−	0.224947i
$870$	2380.45	+	561.577i	2.73614	+	0.645491i
$871$	−65.0896	−	37.5795i	−0.0747298	−	0.0431453i
$872$	−122.791	−	334.137i	−0.140815	−	0.383184i
$873$	114.165	+	197.740i	0.130773	+	0.226506i
$874$	173.169	+	163.038i	0.198133	+	0.186542i
$875$		0			0
$876$	−87.0912	−	1443.85i	−0.0994192	−	1.64823i
$877$	−714.554	+	412.548i	−0.814771	+	0.470408i	−0.848610	−	0.529019i	$-0.822560\pi$
$877$	−714.554	+	412.548i	−0.814771	+	0.470408i	0.0338388	+	0.999427i	$0.489227\pi$
$878$	−1669.21	+	501.611i	−1.90115	+	0.571311i
$879$	−676.570	−	390.618i	−0.769704	−	0.444389i
$880$	−786.447	+	590.560i	−0.893690	+	0.671090i
$881$	−1352.83			−1.53556			−0.767780	−	0.640714i	$-0.778639\pi$
$881$	−1352.83			−1.53556			−0.767780	+	0.640714i	$0.778639\pi$
$882$		0			0
$883$	−1013.40			−1.14768			−0.573838	−	0.818969i	$-0.694546\pi$
$883$	−1013.40			−1.14768			−0.573838	+	0.818969i	$0.694546\pi$
$884$	36.7361	+	55.6038i	0.0415567	+	0.0629002i
$885$	2971.42	+	1715.55i	3.35754	+	1.93847i
$886$	−197.977	−	658.808i	−0.223450	−	0.743575i
$887$	202.442	−	116.880i	0.228233	−	0.131770i	−0.381524	−	0.924359i	$-0.624601\pi$
$887$	202.442	−	116.880i	0.228233	−	0.131770i	0.609756	+	0.792589i	$0.291267\pi$
$888$	5.42340	−	6.50422i	0.00610743	−	0.00732457i
$889$		0			0
$890$	164.186	+	154.581i	0.184478	+	0.173686i
$891$	−435.487	−	754.285i	−0.488762	−	0.846561i
$892$	72.9899	−	146.087i	0.0818273	−	0.163775i
$893$	−91.1580	−	52.6301i	−0.102081	−	0.0589363i
$894$	−526.603	+	2232.20i	−0.589042	+	2.49686i
$895$			707.322i			0.790304i
$896$		0			0
$897$	540.686			0.602772
$898$	472.721	+	111.521i	0.526416	+	0.124188i
$899$	−133.871	+	231.871i	−0.148911	+	0.257921i
$900$	−934.793	−	467.052i	−1.03866	−	0.518947i
$901$	−326.396	+	188.445i	−0.362260	+	0.209151i
$902$	−854.423	+	907.514i	−0.947254	+	1.00611i
$903$		0			0
$904$	819.589	+	683.396i	0.906625	+	0.755968i
$905$	191.004	+	330.829i	0.211054	+	0.365557i
$906$	−1857.66	+	558.240i	−2.05039	+	0.616159i
$907$	101.795	−	176.314i	0.112233	−	0.194393i	−0.804438	−	0.594037i	$-0.797533\pi$
$907$	101.795	−	176.314i	0.112233	−	0.194393i	0.916670	+	0.399645i	$0.130866\pi$
$908$	27.3199	−	18.0496i	0.0300880	−	0.0198784i
$909$		−	1244.85i		−	1.36947i
$910$		0			0
$911$			712.022i			0.781583i	0.920479	+	0.390792i	$0.127799\pi$
$911$			712.022i			0.781583i	−0.920479	+	0.390792i	$0.872201\pi$
$912$	−139.336	−	185.553i	−0.152780	−	0.203457i
$913$	−25.0869	+	43.4517i	−0.0274774	+	0.0475922i
$914$	−24.3226	−	80.9385i	−0.0266112	−	0.0885542i
$915$	716.487	+	1240.99i	0.783046	+	1.35628i
$916$	−1326.60	+	80.0185i	−1.44825	+	0.0873564i
$917$		0			0
$918$	−458.512	+	487.002i	−0.499468	+	0.530503i
$919$	−681.374	+	393.391i	−0.741430	+	0.428065i	−0.822589	−	0.568636i	$-0.807471\pi$
$919$	−681.374	+	393.391i	−0.741430	+	0.428065i	0.0811591	+	0.996701i	$0.474138\pi$
$920$	2015.97	−	740.844i	2.19127	−	0.805266i
$921$	709.836	−	1229.47i	0.770723	−	1.33493i
$922$	374.893	−	1589.12i	0.406608	−	1.72355i
$923$	55.8929			0.0605557
$924$		0			0
$925$		−	2.89516i		−	0.00312990i
$926$	−52.8839	+	224.168i	−0.0571101	+	0.242082i
$927$	923.154	+	532.983i	0.995851	+	0.574955i
$928$	1095.00	−	479.068i	1.17996	−	0.516237i
$929$	−828.996	−	1435.86i	−0.892353	−	1.54560i	−0.837047	−	0.547131i	$-0.815720\pi$
$929$	−828.996	−	1435.86i	−0.892353	−	1.54560i	−0.0553061	−	0.998469i	$-0.517613\pi$
$930$	321.768	−	341.761i	0.345987	−	0.367485i
$931$		0			0
$932$	−79.2981	−	1314.65i	−0.0850838	−	1.41057i
$933$	2416.52	−	1395.18i	2.59006	−	1.49537i
$934$	−347.323	−	1155.79i	−0.371866	−	1.23746i
$935$	367.017	+	211.897i	0.392532	+	0.226628i
$936$	−348.333	−	60.3070i	−0.372151	−	0.0644306i
$937$	−333.736			−0.356175			−0.178088	−	0.984015i	$-0.556991\pi$
$937$	−333.736			−0.356175			−0.178088	+	0.984015i	$0.556991\pi$
$938$		0			0
$939$	2905.55			3.09430
$940$	−793.078	+	523.968i	−0.843700	+	0.557413i
$941$	470.533	+	271.662i	0.500035	+	0.288695i	0.728728	−	0.684803i	$-0.240112\pi$
$941$	470.533	+	271.662i	0.500035	+	0.288695i	−0.228693	+	0.973499i	$0.573445\pi$
$942$	1882.81	−	565.798i	1.99874	−	0.600635i
$943$	2357.34	−	1361.01i	2.49984	−	1.44328i
$944$	1664.56	−	201.542i	1.76331	−	0.213497i
$945$		0			0
$946$	−475.125	+	504.648i	−0.502247	+	0.533454i
$947$	179.864	+	311.534i	0.189930	+	0.328969i	0.945227	−	0.326414i	$-0.105840\pi$
$947$	179.864	+	311.534i	0.189930	+	0.328969i	−0.755296	+	0.655383i	$0.772507\pi$
$948$	186.149	−	372.572i	0.196360	−	0.393009i
$949$	−144.878	−	83.6451i	−0.152663	−	0.0881403i
$950$	−77.2088	−	18.2145i	−0.0812724	−	0.0191732i
$951$			2023.94i			2.12823i
$952$		0			0
$953$	−904.225			−0.948820			−0.474410	−	0.880304i	$-0.657339\pi$
$953$	−904.225			−0.948820			−0.474410	+	0.880304i	$0.657339\pi$
$954$	459.046	−	1945.83i	0.481181	−	2.03966i
$955$	559.281	−	968.702i	0.585634	−	1.01435i
$956$	246.214	−	492.791i	0.257546	−	0.515472i
$957$	1657.03	−	956.686i	1.73148	−	0.999672i
$958$	230.941	+	217.431i	0.241066	+	0.226963i
$959$		0			0
$960$	−2061.30	+	376.663i	−2.14719	+	0.392358i
$961$	−454.807	−	787.749i	−0.473265	−	0.819719i
$962$	−0.281874	−	0.937994i	−0.000293008	−	0.000975045i
$963$	−1242.26	+	2151.66i	−1.28999	+	2.23433i
$964$	673.666	−	445.075i	0.698823	−	0.461697i
$965$			1388.89i			1.43926i
$966$		0			0
$967$		−	920.961i		−	0.952390i	−0.879340	−	0.476195i	$-0.842016\pi$
$967$		−	920.961i		−	0.952390i	0.879340	−	0.476195i	$-0.157984\pi$
$968$	33.8798	−	195.689i	0.0349997	−	0.202159i
$969$	−49.9947	+	86.5933i	−0.0515941	+	0.0893636i
$970$	149.904	−	45.0474i	0.154541	−	0.0464406i
$971$	663.655	+	1149.48i	0.683476	+	1.18381i	0.973913	+	0.226921i	$0.0728658\pi$
$971$	663.655	+	1149.48i	0.683476	+	1.18381i	−0.290438	+	0.956894i	$0.593801\pi$
$972$	−6.58670	−	109.198i	−0.00677644	−	0.112344i
$973$		0			0
$974$	155.791	+	146.677i	0.159950	+	0.150593i
$975$	−156.176	+	90.1684i	−0.160181	+	0.0924805i
$976$	644.140	+	274.701i	0.659980	+	0.281456i
$977$	344.245	−	596.250i	0.352349	−	0.610286i	−0.634312	−	0.773077i	$-0.718716\pi$
$977$	344.245	−	596.250i	0.352349	−	0.610286i	0.986661	+	0.162791i	$0.0520497\pi$
$978$	−554.320	−	130.771i	−0.566789	−	0.133713i
$979$	176.415			0.180199
$980$		0			0
$981$		−	813.706i		−	0.829466i
$982$	−1200.24	−	283.151i	−1.22224	−	0.288341i
$983$	1461.05	+	843.539i	1.48632	+	0.858127i	0.999879	−	0.0155866i	$-0.00496158\pi$
$983$	1461.05	+	843.539i	1.48632	+	0.858127i	0.486441	+	0.873714i	$0.338295\pi$
$984$	−2492.68	+	916.029i	−2.53321	+	0.930924i
$985$	759.348	+	1315.23i	0.770912	+	1.33526i
$986$	−374.983	−	353.046i	−0.380307	−	0.358058i
$987$		0			0
$988$	−26.7880	+	1.61582i	−0.0271134	+	0.00163544i
$989$	1310.87	−	756.829i	1.32545	−	0.765246i
$990$	−2152.95	+	646.977i	−2.17470	+	0.653512i
$991$	−986.597	−	569.612i	−0.995557	−	0.574785i	−0.0886266	−	0.996065i	$-0.528248\pi$
$991$	−986.597	−	569.612i	−0.995557	−	0.574785i	−0.906931	+	0.421280i	$0.861581\pi$
$992$	25.4519	−	227.971i	0.0256572	−	0.229809i
$993$	−2001.72			−2.01583
$994$		0			0
$995$	1861.85			1.87121
$996$	−89.1920	+	58.9271i	−0.0895502	+	0.0591637i
$997$	−178.475	−	103.043i	−0.179012	−	0.103353i	0.407816	−	0.913064i	$-0.366290\pi$
$997$	−178.475	−	103.043i	−0.179012	−	0.103353i	−0.586828	+	0.809711i	$0.699624\pi$
$998$	318.927	+	1061.30i	0.319566	+	1.06342i
$999$	8.51331	−	4.91516i	0.00852183	−	0.00492008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.k.n.67.1		16
7.2	even	3	inner	392.3.k.n.275.6		16
7.3	odd	6		56.3.g.b.43.5	✓	8
7.4	even	3		392.3.g.m.99.5		8
7.5	odd	6		392.3.k.o.275.6		16
7.6	odd	2		392.3.k.o.67.1		16
8.3	odd	2	inner	392.3.k.n.67.6		16
21.17	even	6		504.3.g.b.379.4		8
28.3	even	6		224.3.g.b.15.7		8
28.11	odd	6		1568.3.g.m.687.2		8
56.3	even	6		56.3.g.b.43.6	yes	8
56.11	odd	6		392.3.g.m.99.6		8
56.19	even	6		392.3.k.o.275.1		16
56.27	even	2		392.3.k.o.67.6		16
56.45	odd	6		224.3.g.b.15.8		8
56.51	odd	6	inner	392.3.k.n.275.1		16
56.53	even	6		1568.3.g.m.687.1		8
84.59	odd	6		2016.3.g.b.1135.8		8
112.3	even	12		1792.3.d.j.1023.15		16
112.45	odd	12		1792.3.d.j.1023.1		16
112.59	even	12		1792.3.d.j.1023.2		16
112.101	odd	12		1792.3.d.j.1023.16		16
168.59	odd	6		504.3.g.b.379.3		8
168.101	even	6		2016.3.g.b.1135.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.5	✓	8	7.3	odd	6
56.3.g.b.43.6	yes	8	56.3	even	6
224.3.g.b.15.7		8	28.3	even	6
224.3.g.b.15.8		8	56.45	odd	6
392.3.g.m.99.5		8	7.4	even	3
392.3.g.m.99.6		8	56.11	odd	6
392.3.k.n.67.1		16	1.1	even	1	trivial
392.3.k.n.67.6		16	8.3	odd	2	inner
392.3.k.n.275.1		16	56.51	odd	6	inner
392.3.k.n.275.6		16	7.2	even	3	inner
392.3.k.o.67.1		16	7.6	odd	2
392.3.k.o.67.6		16	56.27	even	2
392.3.k.o.275.1		16	56.19	even	6
392.3.k.o.275.6		16	7.5	odd	6
504.3.g.b.379.3		8	168.59	odd	6
504.3.g.b.379.4		8	21.17	even	6
1568.3.g.m.687.1		8	56.53	even	6
1568.3.g.m.687.2		8	28.11	odd	6
1792.3.d.j.1023.1		16	112.45	odd	12
1792.3.d.j.1023.2		16	112.59	even	12
1792.3.d.j.1023.15		16	112.3	even	12
1792.3.d.j.1023.16		16	112.101	odd	12
2016.3.g.b.1135.1		8	168.101	even	6
2016.3.g.b.1135.8		8	84.59	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)

\(f(q)\)	\(=\)	\(q+(-1.94657 - 0.459219i) q^{2} +(-2.61182 + 4.52380i) q^{3} +(3.57824 + 1.78780i) q^{4} +(5.42814 - 3.13394i) q^{5} +(7.16148 - 7.60647i) q^{6} +(-6.14428 - 5.12327i) q^{8} +(-9.14316 - 15.8364i) q^{9} +O(q^{10})\)	\(q+(-1.94657 - 0.459219i) q^{2} +(-2.61182 + 4.52380i) q^{3} +(3.57824 + 1.78780i) q^{4} +(5.42814 - 3.13394i) q^{5} +(7.16148 - 7.60647i) q^{6} +(-6.14428 - 5.12327i) q^{8} +(-9.14316 - 15.8364i) q^{9} +(-12.0054 + 3.60771i) q^{10} +(-4.90344 + 8.49301i) q^{11} +(-17.4333 + 11.5178i) q^{12} +2.41653i q^{13} +32.7411i q^{15} +(9.60754 + 12.7943i) q^{16} +(3.44726 - 5.97083i) q^{17} +(10.5254 + 35.0253i) q^{18} +(1.38818 + 2.40441i) q^{19} +(25.0260 - 1.50954i) q^{20} +(13.4450 - 14.2804i) q^{22} +(-37.0947 + 21.4166i) q^{23} +(39.2243 - 14.4144i) q^{24} +(7.14316 - 12.3723i) q^{25} +(1.10972 - 4.70393i) q^{26} +48.5083 q^{27} +37.3505i q^{29} +(15.0353 - 63.7327i) q^{30} +(6.20797 + 3.58417i) q^{31} +(-12.8263 - 29.3170i) q^{32} +(-25.6138 - 44.3643i) q^{33} +(-9.45224 + 10.0396i) q^{34} +(-4.40402 - 73.0126i) q^{36} +(0.175502 - 0.101326i) q^{37} +(-1.59804 - 5.31782i) q^{38} +(-10.9319 - 6.31153i) q^{39} +(-49.4080 - 8.55402i) q^{40} -63.5494 q^{41} -35.3384 q^{43} +(-32.7295 + 21.6236i) q^{44} +(-99.2607 - 57.3082i) q^{45} +(82.0421 - 24.6543i) q^{46} +(-32.8335 + 18.9564i) q^{47} +(-82.9721 + 10.0461i) q^{48} +(-19.5862 + 20.8032i) q^{50} +(18.0072 + 31.1894i) q^{51} +(-4.32027 + 8.64691i) q^{52} +(-47.3414 - 27.3326i) q^{53} +(-94.4246 - 22.2759i) q^{54} +61.4684i q^{55} -14.5027 q^{57} +(17.1521 - 72.7051i) q^{58} +(52.3975 - 90.7551i) q^{59} +(-58.5345 + 117.155i) q^{60} +(37.9032 - 21.8834i) q^{61} +(-10.4383 - 9.82765i) q^{62} +(11.5043 + 62.9575i) q^{64} +(7.57325 + 13.1173i) q^{65} +(29.4859 + 98.1204i) q^{66} +(-15.5510 + 26.9352i) q^{67} +(23.0098 - 15.2020i) q^{68} -223.745i q^{69} -23.1294i q^{71} +(-24.9561 + 144.146i) q^{72} +(-34.6138 + 59.9528i) q^{73} +(-0.388158 + 0.116644i) q^{74} +(37.3132 + 64.6284i) q^{75} +(0.668652 + 11.0853i) q^{76} +(18.3813 + 17.3059i) q^{78} +(-17.2624 + 9.96642i) q^{79} +(92.2478 + 39.3401i) q^{80} +(-44.4063 + 76.9139i) q^{81} +(123.703 + 29.1831i) q^{82} +5.11617 q^{83} -43.2140i q^{85} +(68.7885 + 16.2281i) q^{86} +(-168.966 - 97.5525i) q^{87} +(73.6400 - 27.0618i) q^{88} +(-8.99444 - 15.5788i) q^{89} +(166.901 + 157.137i) q^{90} +(-171.022 + 10.3158i) q^{92} +(-32.4282 + 18.7224i) q^{93} +(72.6178 - 21.8222i) q^{94} +(15.0705 + 8.70097i) q^{95} +(166.124 + 18.5470i) q^{96} -12.4864 q^{97} +179.332 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

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