LMFDB - Embedded newform 48.3.l.a.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,3,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	48.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.30790526893$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 $ x^16 - 6x^14 - 4x^13 + 10x^12 + 56x^11 + 88x^10 - 128x^9 - 496x^8 - 512x^7 + 1408x^6 + 3584x^5 + 2560x^4 - 4096x^3 - 24576*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.6
Root			$-1.25564 + 1.55672i$ of defining polynomial
Character	$\chi$	$=$	48.19
Dual form			48.3.l.a.43.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25564 + 1.55672i) q^{2} +(1.22474 - 1.22474i) q^{3} +(-0.846753 + 3.90935i) q^{4} +(0.909023 - 0.909023i) q^{5} +(3.44442 + 0.368750i) q^{6} -0.654713 q^{7} +(-7.14897 + 3.59057i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.25564 + 1.55672i) q^{2} +(1.22474 - 1.22474i) q^{3} +(-0.846753 + 3.90935i) q^{4} +(0.909023 - 0.909023i) q^{5} +(3.44442 + 0.368750i) q^{6} -0.654713 q^{7} +(-7.14897 + 3.59057i) q^{8} -3.00000i q^{9} +(2.55650 + 0.273691i) q^{10} +(-13.3760 - 13.3760i) q^{11} +(3.75090 + 5.82501i) q^{12} +(8.32795 + 8.32795i) q^{13} +(-0.822082 - 1.01921i) q^{14} -2.22664i q^{15} +(-14.5660 - 6.62050i) q^{16} -3.93529 q^{17} +(4.67016 - 3.76691i) q^{18} +(16.8974 - 16.8974i) q^{19} +(2.78397 + 4.32340i) q^{20} +(-0.801857 + 0.801857i) q^{21} +(4.02729 - 37.6181i) q^{22} -23.1787 q^{23} +(-4.35814 + 13.1532i) q^{24} +23.3474i q^{25} +(-2.50740 + 23.4212i) q^{26} +(-3.67423 - 3.67423i) q^{27} +(0.554380 - 2.55950i) q^{28} +(35.6105 + 35.6105i) q^{29} +(3.46626 - 2.79585i) q^{30} +45.5687i q^{31} +(-7.98336 - 30.9882i) q^{32} -32.7644 q^{33} +(-4.94130 - 6.12615i) q^{34} +(-0.595149 + 0.595149i) q^{35} +(11.7280 + 2.54026i) q^{36} +(10.1527 - 10.1527i) q^{37} +(47.5215 + 5.08752i) q^{38} +20.3992 q^{39} +(-3.23467 + 9.76249i) q^{40} -28.4661i q^{41} +(-2.25511 - 0.241425i) q^{42} +(22.7354 + 22.7354i) q^{43} +(63.6176 - 40.9653i) q^{44} +(-2.72707 - 2.72707i) q^{45} +(-29.1040 - 36.0827i) q^{46} +10.7746i q^{47} +(-25.9481 + 9.73123i) q^{48} -48.5714 q^{49} +(-36.3453 + 29.3158i) q^{50} +(-4.81973 + 4.81973i) q^{51} +(-39.6086 + 25.5051i) q^{52} +(41.5142 - 41.5142i) q^{53} +(1.10625 - 10.3333i) q^{54} -24.3182 q^{55} +(4.68053 - 2.35079i) q^{56} -41.3900i q^{57} +(-10.7217 + 100.149i) q^{58} +(-21.0646 - 21.0646i) q^{59} +(8.70472 + 1.88541i) q^{60} +(-68.7531 - 68.7531i) q^{61} +(-70.9377 + 57.2178i) q^{62} +1.96414i q^{63} +(38.2157 - 51.3377i) q^{64} +15.1406 q^{65} +(-41.1402 - 51.0050i) q^{66} +(67.8242 - 67.8242i) q^{67} +(3.33222 - 15.3844i) q^{68} +(-28.3880 + 28.3880i) q^{69} +(-1.67377 - 0.179189i) q^{70} +33.3094 q^{71} +(10.7717 + 21.4469i) q^{72} -18.6331i q^{73} +(28.5531 + 3.05682i) q^{74} +(28.5946 + 28.5946i) q^{75} +(51.7499 + 80.3657i) q^{76} +(8.75745 + 8.75745i) q^{77} +(25.6140 + 31.7559i) q^{78} +6.29222i q^{79} +(-19.2590 + 7.22265i) q^{80} -9.00000 q^{81} +(44.3137 - 35.7431i) q^{82} +(-72.0774 + 72.0774i) q^{83} +(-2.45576 - 3.81371i) q^{84} +(-3.57727 + 3.57727i) q^{85} +(-6.84524 + 63.9400i) q^{86} +87.2275 q^{87} +(143.652 + 47.5973i) q^{88} +10.6131i q^{89} +(0.821074 - 7.66949i) q^{90} +(-5.45242 - 5.45242i) q^{91} +(19.6266 - 90.6135i) q^{92} +(55.8101 + 55.8101i) q^{93} +(-16.7730 + 13.5290i) q^{94} -30.7202i q^{95} +(-47.7302 - 28.1750i) q^{96} +143.631 q^{97} +(-60.9880 - 75.6120i) q^{98} +(-40.1280 + 40.1280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} - 12 q^{8}+O(q^{10}) $ 16 * q + 12 * q^4 - 12 * q^8	$ 16 q + 12 q^{4} - 12 q^{8} - 56 q^{10} + 32 q^{11} - 24 q^{12} - 44 q^{14} + 32 q^{16} + 12 q^{18} - 32 q^{19} + 80 q^{20} + 32 q^{22} - 128 q^{23} + 36 q^{24} - 100 q^{26} - 120 q^{28} + 32 q^{29} + 72 q^{30} + 160 q^{32} + 96 q^{34} + 96 q^{35} + 12 q^{36} - 96 q^{37} + 168 q^{38} + 48 q^{40} - 60 q^{42} + 160 q^{43} + 88 q^{44} + 136 q^{46} - 144 q^{48} + 112 q^{49} - 236 q^{50} - 96 q^{51} - 48 q^{52} - 160 q^{53} - 36 q^{54} - 256 q^{55} - 224 q^{56} + 144 q^{58} - 128 q^{59} - 72 q^{60} - 32 q^{61} - 276 q^{62} - 408 q^{64} - 32 q^{65} + 72 q^{66} + 320 q^{67} - 448 q^{68} + 96 q^{69} - 384 q^{70} + 512 q^{71} + 60 q^{72} + 348 q^{74} + 192 q^{75} + 72 q^{76} + 224 q^{77} + 396 q^{78} + 552 q^{80} - 144 q^{81} - 40 q^{82} - 160 q^{83} + 72 q^{84} + 160 q^{85} + 528 q^{86} + 480 q^{88} - 24 q^{90} - 480 q^{91} + 496 q^{92} + 312 q^{94} - 480 q^{96} - 440 q^{98} + 96 q^{99}+O(q^{100}) $ 16 * q + 12 * q^4 - 12 * q^8 - 56 * q^10 + 32 * q^11 - 24 * q^12 - 44 * q^14 + 32 * q^16 + 12 * q^18 - 32 * q^19 + 80 * q^20 + 32 * q^22 - 128 * q^23 + 36 * q^24 - 100 * q^26 - 120 * q^28 + 32 * q^29 + 72 * q^30 + 160 * q^32 + 96 * q^34 + 96 * q^35 + 12 * q^36 - 96 * q^37 + 168 * q^38 + 48 * q^40 - 60 * q^42 + 160 * q^43 + 88 * q^44 + 136 * q^46 - 144 * q^48 + 112 * q^49 - 236 * q^50 - 96 * q^51 - 48 * q^52 - 160 * q^53 - 36 * q^54 - 256 * q^55 - 224 * q^56 + 144 * q^58 - 128 * q^59 - 72 * q^60 - 32 * q^61 - 276 * q^62 - 408 * q^64 - 32 * q^65 + 72 * q^66 + 320 * q^67 - 448 * q^68 + 96 * q^69 - 384 * q^70 + 512 * q^71 + 60 * q^72 + 348 * q^74 + 192 * q^75 + 72 * q^76 + 224 * q^77 + 396 * q^78 + 552 * q^80 - 144 * q^81 - 40 * q^82 - 160 * q^83 + 72 * q^84 + 160 * q^85 + 528 * q^86 + 480 * q^88 - 24 * q^90 - 480 * q^91 + 496 * q^92 + 312 * q^94 - 480 * q^96 - 440 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.25564	+	1.55672i	0.627818	+	0.778360i
$2$	1.25564	+	1.55672i	0.627818	+	0.778360i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$4$	−0.846753	+	3.90935i	−0.211688	+	0.977337i
$5$	0.909023	−	0.909023i	0.181805	−	0.181805i	−0.610337	−	0.792142i	$-0.708966\pi$
$5$	0.909023	−	0.909023i	0.181805	−	0.181805i	0.792142	+	0.610337i	$0.208966\pi$
$6$	3.44442	+	0.368750i	0.574070	+	0.0614583i
$7$	−0.654713			−0.0935305			−0.0467652	−	0.998906i	$-0.514891\pi$
$7$	−0.654713			−0.0935305			−0.0467652	+	0.998906i	$0.514891\pi$
$8$	−7.14897	+	3.59057i	−0.893622	+	0.448821i
$9$		−	3.00000i		−	0.333333i
$10$	2.55650	+	0.273691i	0.255650	+	0.0273691i
$11$	−13.3760	−	13.3760i	−1.21600	−	1.21600i	−0.969021	−	0.246980i	$-0.920562\pi$
$11$	−13.3760	−	13.3760i	−1.21600	−	1.21600i	−0.246980	−	0.969021i	$-0.579438\pi$
$12$	3.75090	+	5.82501i	0.312575	+	0.485418i
$13$	8.32795	+	8.32795i	0.640612	+	0.640612i	0.950706	−	0.310094i	$-0.100361\pi$
$13$	8.32795	+	8.32795i	0.640612	+	0.640612i	−0.310094	+	0.950706i	$0.600361\pi$
$14$	−0.822082	−	1.01921i	−0.0587202	−	0.0728004i
$15$		−	2.22664i		−	0.148443i
$16$	−14.5660	−	6.62050i	−0.910376	−	0.413781i
$17$	−3.93529			−0.231488			−0.115744	−	0.993279i	$-0.536925\pi$
$17$	−3.93529			−0.231488			−0.115744	+	0.993279i	$0.536925\pi$
$18$	4.67016	−	3.76691i	0.259453	−	0.209273i
$19$	16.8974	−	16.8974i	0.889336	−	0.889336i	−0.105123	−	0.994459i	$-0.533524\pi$
$19$	16.8974	−	16.8974i	0.889336	−	0.889336i	0.994459	+	0.105123i	$0.0335236\pi$
$20$	2.78397	+	4.32340i	0.139198	+	0.216170i
$21$	−0.801857	+	0.801857i	−0.0381837	+	0.0381837i
$22$	4.02729	−	37.6181i	0.183059	−	1.70991i
$23$	−23.1787			−1.00777			−0.503884	−	0.863771i	$-0.668096\pi$
$23$	−23.1787			−1.00777			−0.503884	+	0.863771i	$0.668096\pi$
$24$	−4.35814	+	13.1532i	−0.181589	+	0.548050i
$25$			23.3474i			0.933894i
$26$	−2.50740	+	23.4212i	−0.0964386	+	0.900814i
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	0.554380	−	2.55950i	0.0197993	−	0.0914108i
$29$	35.6105	+	35.6105i	1.22795	+	1.22795i	0.964739	+	0.263209i	$0.0847809\pi$
$29$	35.6105	+	35.6105i	1.22795	+	1.22795i	0.263209	+	0.964739i	$0.415219\pi$
$30$	3.46626	−	2.79585i	0.115542	−	0.0931951i
$31$			45.5687i			1.46996i	0.678089	+	0.734980i	$0.262808\pi$
$31$			45.5687i			1.46996i	−0.678089	+	0.734980i	$0.737192\pi$
$32$	−7.98336	−	30.9882i	−0.249480	−	0.968380i
$33$	−32.7644			−0.992860
$34$	−4.94130	−	6.12615i	−0.145332	−	0.180181i
$35$	−0.595149	+	0.595149i	−0.0170043	+	0.0170043i
$36$	11.7280	+	2.54026i	0.325779	+	0.0705627i
$37$	10.1527	−	10.1527i	0.274398	−	0.274398i	−0.556470	−	0.830868i	$-0.687844\pi$
$37$	10.1527	−	10.1527i	0.274398	−	0.274398i	0.830868	+	0.556470i	$0.187844\pi$
$38$	47.5215	+	5.08752i	1.25057	+	0.133882i
$39$	20.3992			0.523057
$40$	−3.23467	+	9.76249i	−0.0808669	+	0.244062i
$41$		−	28.4661i		−	0.694295i	−0.937811	−	0.347148i	$-0.887150\pi$
$41$		−	28.4661i		−	0.694295i	0.937811	−	0.347148i	$-0.112850\pi$
$42$	−2.25511	−	0.241425i	−0.0536930	−	0.00574823i
$43$	22.7354	+	22.7354i	0.528730	+	0.528730i	0.920194	−	0.391464i	$-0.128031\pi$
$43$	22.7354	+	22.7354i	0.528730	+	0.528730i	−0.391464	+	0.920194i	$0.628031\pi$
$44$	63.6176	−	40.9653i	1.44586	−	0.931030i
$45$	−2.72707	−	2.72707i	−0.0606015	−	0.0606015i
$46$	−29.1040	−	36.0827i	−0.632696	−	0.784407i
$47$			10.7746i			0.229247i	0.993409	+	0.114623i	$0.0365661\pi$
$47$			10.7746i			0.229247i	−0.993409	+	0.114623i	$0.963434\pi$
$48$	−25.9481	+	9.73123i	−0.540585	+	0.202734i
$49$	−48.5714			−0.991252
$50$	−36.3453	+	29.3158i	−0.726906	+	0.586316i
$51$	−4.81973	+	4.81973i	−0.0945045	+	0.0945045i
$52$	−39.6086	+	25.5051i	−0.761703	+	0.490484i
$53$	41.5142	−	41.5142i	0.783287	−	0.783287i	−0.197097	−	0.980384i	$-0.563151\pi$
$53$	41.5142	−	41.5142i	0.783287	−	0.783287i	0.980384	+	0.197097i	$0.0631514\pi$
$54$	1.10625	−	10.3333i	0.0204861	−	0.191357i
$55$	−24.3182			−0.442149
$56$	4.68053	−	2.35079i	0.0835809	−	0.0419784i
$57$		−	41.3900i		−	0.726140i
$58$	−10.7217	+	100.149i	−0.184857	+	1.72671i
$59$	−21.0646	−	21.0646i	−0.357027	−	0.357027i	0.505689	−	0.862716i	$-0.331238\pi$
$59$	−21.0646	−	21.0646i	−0.357027	−	0.357027i	−0.862716	+	0.505689i	$0.831238\pi$
$60$	8.70472	+	1.88541i	0.145079	+	0.0314236i
$61$	−68.7531	−	68.7531i	−1.12710	−	1.12710i	−0.990647	−	0.136453i	$-0.956430\pi$
$61$	−68.7531	−	68.7531i	−1.12710	−	1.12710i	−0.136453	−	0.990647i	$-0.543570\pi$
$62$	−70.9377	+	57.2178i	−1.14416	+	0.922867i
$63$			1.96414i			0.0311768i
$64$	38.2157	−	51.3377i	0.597120	−	0.802152i
$65$	15.1406			0.232932
$66$	−41.1402	−	51.0050i	−0.623336	−	0.772803i
$67$	67.8242	−	67.8242i	1.01230	−	1.01230i	0.0123779	−	0.999923i	$-0.496060\pi$
$67$	67.8242	−	67.8242i	1.01230	−	1.01230i	0.999923	−	0.0123779i	$-0.00394012\pi$
$68$	3.33222	−	15.3844i	0.0490033	−	0.226242i
$69$	−28.3880	+	28.3880i	−0.411420	+	0.411420i
$70$	−1.67377	−	0.179189i	−0.0239110	−	0.00255985i
$71$	33.3094			0.469147			0.234573	−	0.972098i	$-0.424631\pi$
$71$	33.3094			0.469147			0.234573	+	0.972098i	$0.424631\pi$
$72$	10.7717	+	21.4469i	0.149607	+	0.297874i
$73$		−	18.6331i		−	0.255248i	−0.991823	−	0.127624i	$-0.959265\pi$
$73$		−	18.6331i		−	0.255248i	0.991823	−	0.127624i	$-0.0407351\pi$
$74$	28.5531	+	3.05682i	0.385853	+	0.0413083i
$75$	28.5946	+	28.5946i	0.381261	+	0.381261i
$76$	51.7499	+	80.3657i	0.680920	+	1.05744i
$77$	8.75745	+	8.75745i	0.113733	+	0.113733i
$78$	25.6140	+	31.7559i	0.328385	+	0.407127i
$79$			6.29222i			0.0796483i	0.999207	+	0.0398242i	$0.0126798\pi$
$79$			6.29222i			0.0796483i	−0.999207	+	0.0398242i	$0.987320\pi$
$80$	−19.2590	+	7.22265i	−0.240738	+	0.0902832i
$81$	−9.00000			−0.111111
$82$	44.3137	−	35.7431i	0.540411	−	0.435891i
$83$	−72.0774	+	72.0774i	−0.868402	+	0.868402i	−0.992296	−	0.123894i	$-0.960462\pi$
$83$	−72.0774	+	72.0774i	−0.868402	+	0.868402i	0.123894	+	0.992296i	$0.460462\pi$
$84$	−2.45576	−	3.81371i	−0.0292353	−	0.0454013i
$85$	−3.57727	+	3.57727i	−0.0420855	+	0.0420855i
$86$	−6.84524	+	63.9400i	−0.0795958	+	0.743489i
$87$	87.2275			1.00262
$88$	143.652	+	47.5973i	1.63241	+	0.540878i
$89$			10.6131i			0.119248i	0.998221	+	0.0596240i	$0.0189902\pi$
$89$			10.6131i			0.119248i	−0.998221	+	0.0596240i	$0.981010\pi$
$90$	0.821074	−	7.66949i	0.00912304	−	0.0852165i
$91$	−5.45242	−	5.45242i	−0.0599167	−	0.0599167i
$92$	19.6266	−	90.6135i	0.213333	−	0.984930i
$93$	55.8101	+	55.8101i	0.600108	+	0.600108i
$94$	−16.7730	+	13.5290i	−0.178436	+	0.143925i
$95$		−	30.7202i		−	0.323371i
$96$	−47.7302	−	28.1750i	−0.497189	−	0.293490i
$97$	143.631			1.48073			0.740366	−	0.672204i	$-0.234652\pi$
$97$	143.631			1.48073			0.740366	+	0.672204i	$0.234652\pi$
$98$	−60.9880	−	75.6120i	−0.622326	−	0.771551i
$99$	−40.1280	+	40.1280i	−0.405334	+	0.405334i
$100$	−91.2730	−	19.7694i	−0.912730	−	0.197694i
$101$	−90.3100	+	90.3100i	−0.894159	+	0.894159i	−0.994912	−	0.100753i	$-0.967875\pi$
$101$	−90.3100	+	90.3100i	−0.894159	+	0.894159i	0.100753	+	0.994912i	$0.467875\pi$
$102$	−13.5548	−	1.45114i	−0.132890	−	0.0142269i
$103$	−95.1656			−0.923938			−0.461969	−	0.886896i	$-0.652857\pi$
$103$	−95.1656			−0.923938			−0.461969	+	0.886896i	$0.652857\pi$
$104$	−89.4384	−	29.6343i	−0.859984	−	0.284945i
$105$			1.45781i			0.0138839i
$106$	116.753	+	12.4992i	1.10144	+	0.117917i
$107$	27.2524	+	27.2524i	0.254695	+	0.254695i	0.822892	−	0.568197i	$-0.192359\pi$
$107$	27.2524	+	27.2524i	0.254695	+	0.254695i	−0.568197	+	0.822892i	$0.692359\pi$
$108$	17.4750	−	11.2527i	0.161806	−	0.104192i
$109$	−132.413	−	132.413i	−1.21480	−	1.21480i	−0.969430	−	0.245366i	$-0.921092\pi$
$109$	−132.413	−	132.413i	−1.21480	−	1.21480i	−0.245366	−	0.969430i	$-0.578908\pi$
$110$	−30.5348	−	37.8566i	−0.277589	−	0.344151i
$111$		−	24.8690i		−	0.224045i
$112$	9.53657	+	4.33453i	0.0851479	+	0.0387012i
$113$	37.9551			0.335886			0.167943	−	0.985797i	$-0.446288\pi$
$113$	37.9551			0.335886			0.167943	+	0.985797i	$0.446288\pi$
$114$	64.4326	−	51.9708i	0.565198	−	0.455884i
$115$	−21.0699	+	21.0699i	−0.183217	+	0.183217i
$116$	−169.367	+	109.061i	−1.46006	+	0.940177i
$117$	24.9838	−	24.9838i	0.213537	−	0.213537i
$118$	6.34219	−	59.2411i	0.0537474	−	0.502044i
$119$	2.57649			0.0216512
$120$	7.99490	+	15.9182i	0.0666242	+	0.132652i
$121$			236.835i			1.95731i
$122$	20.7004	−	193.358i	0.169675	−	1.58490i
$123$	−34.8637	−	34.8637i	−0.283445	−	0.283445i
$124$	−178.144	−	38.5854i	−1.43665	−	0.311173i
$125$	43.9488	+	43.9488i	0.351591	+	0.351591i
$126$	−3.05762	+	2.46625i	−0.0242668	+	0.0195734i
$127$		−	96.5399i		−	0.760157i	−0.924954	−	0.380078i	$-0.875897\pi$
$127$		−	96.5399i		−	0.760157i	0.924954	−	0.380078i	$-0.124103\pi$
$128$	127.903	−	4.97043i	0.999246	−	0.0388315i
$129$	55.6901			0.431706
$130$	19.0111	+	23.5697i	0.146239	+	0.181305i
$131$	−54.5082	+	54.5082i	−0.416093	+	0.416093i	−0.883855	−	0.467762i	$-0.845061\pi$
$131$	−54.5082	+	54.5082i	−0.416093	+	0.416093i	0.467762	+	0.883855i	$0.345061\pi$
$132$	27.7433	−	128.087i	0.210177	−	0.970359i
$133$	−11.0629	+	11.0629i	−0.0831801	+	0.0831801i
$134$	190.746	+	20.4207i	1.42348	+	0.152393i
$135$	−6.67992			−0.0494809
$136$	28.1333	−	14.1299i	0.206863	−	0.103897i
$137$		−	25.9333i		−	0.189294i	−0.995511	−	0.0946471i	$-0.969828\pi$
$137$		−	25.9333i		−	0.189294i	0.995511	−	0.0946471i	$-0.0301723\pi$
$138$	−79.8371	−	8.54713i	−0.578530	−	0.0619358i
$139$	3.64066	+	3.64066i	0.0261918	+	0.0261918i	0.720081	−	0.693890i	$-0.244104\pi$
$139$	3.64066	+	3.64066i	0.0261918	+	0.0261918i	−0.693890	+	0.720081i	$0.744104\pi$
$140$	−1.82270	−	2.83059i	−0.0130193	−	0.0202185i
$141$	13.1961	+	13.1961i	0.0935896	+	0.0935896i
$142$	41.8245	+	51.8534i	0.294539	+	0.365165i
$143$		−	222.789i		−	1.55797i
$144$	−19.8615	+	43.6981i	−0.137927	+	0.303459i
$145$	64.7415			0.446493
$146$	29.0066	−	23.3964i	0.198675	−	0.160250i
$147$	−59.4875	+	59.4875i	−0.404677	+	0.404677i
$148$	31.0937	+	48.2874i	0.210093	+	0.326266i
$149$	−18.9718	+	18.9718i	−0.127328	+	0.127328i	−0.767899	−	0.640571i	$-0.778698\pi$
$149$	−18.9718	+	18.9718i	−0.127328	+	0.127328i	0.640571	+	0.767899i	$0.278698\pi$
$150$	−8.60933	+	80.4181i	−0.0573956	+	0.536121i
$151$	−103.209			−0.683503			−0.341751	−	0.939790i	$-0.611020\pi$
$151$	−103.209			−0.683503			−0.341751	+	0.939790i	$0.611020\pi$
$152$	−60.1278	+	181.470i	−0.395578	+	1.19388i
$153$			11.8059i			0.0771626i
$154$	−2.63672	+	24.6291i	−0.0171216	+	0.159929i
$155$	41.4230	+	41.4230i	0.267245	+	0.267245i
$156$	−17.2731	+	79.7477i	−0.110725	+	0.511203i
$157$	88.2067	+	88.2067i	0.561826	+	0.561826i	0.929826	−	0.368000i	$-0.119957\pi$
$157$	88.2067	+	88.2067i	0.561826	+	0.561826i	−0.368000	+	0.929826i	$0.619957\pi$
$158$	−9.79522	+	7.90074i	−0.0619951	+	0.0500047i
$159$		−	101.689i		−	0.639551i
$160$	−35.4260	−	20.9119i	−0.221412	−	0.130699i
$161$	15.1754			0.0942571
$162$	−11.3007	−	14.0105i	−0.0697576	−	0.0864844i
$163$	18.8038	−	18.8038i	0.115361	−	0.115361i	−0.647070	−	0.762431i	$-0.724006\pi$
$163$	18.8038	−	18.8038i	0.115361	−	0.115361i	0.762431	+	0.647070i	$0.224006\pi$
$164$	111.284	+	24.1037i	0.678561	+	0.146974i
$165$	−29.7836	+	29.7836i	−0.180507	+	0.180507i
$166$	−202.707	−	21.7013i	−1.22113	−	0.130731i
$167$	267.105			1.59943			0.799715	−	0.600380i	$-0.204984\pi$
$167$	267.105			1.59943			0.799715	+	0.600380i	$0.204984\pi$
$168$	2.85333	−	8.61157i	0.0169841	−	0.0512594i
$169$		−	30.2905i		−	0.179234i
$170$	−10.0606	−	1.07706i	−0.0591798	−	0.00633562i
$171$	−50.6922	−	50.6922i	−0.296445	−	0.296445i
$172$	−108.132	+	69.6293i	−0.628673	+	0.404822i
$173$	−153.520	−	153.520i	−0.887396	−	0.887396i	0.106876	−	0.994272i	$-0.465915\pi$
$173$	−153.520	−	153.520i	−0.887396	−	0.887396i	−0.994272	+	0.106876i	$0.965915\pi$
$174$	109.526	+	135.789i	0.629460	+	0.780396i
$175$		−	15.2858i		−	0.0873476i
$176$	106.279	+	283.391i	0.603859	+	1.61018i
$177$	−51.5975			−0.291511
$178$	−16.5216	+	13.3262i	−0.0928179	+	0.0748661i
$179$	123.581	−	123.581i	0.690399	−	0.690399i	−0.271921	−	0.962320i	$-0.587659\pi$
$179$	123.581	−	123.581i	0.690399	−	0.690399i	0.962320	+	0.271921i	$0.0876589\pi$
$180$	12.9702	−	8.35191i	0.0720567	−	0.0463995i
$181$	122.965	−	122.965i	0.679364	−	0.679364i	−0.280493	−	0.959856i	$-0.590498\pi$
$181$	122.965	−	122.965i	0.679364	−	0.679364i	0.959856	+	0.280493i	$0.0904978\pi$
$182$	1.64163	−	15.3341i	0.00901995	−	0.0842536i
$183$	−168.410			−0.920273
$184$	165.704	−	83.2246i	0.900564	−	0.452307i
$185$		−	18.4581i		−	0.0997737i
$186$	−16.8035	+	156.958i	−0.0903412	+	0.843859i
$187$	52.6385	+	52.6385i	0.281489	+	0.281489i
$188$	−42.1217	−	9.12342i	−0.224051	−	0.0485288i
$189$	2.40557	+	2.40557i	0.0127279	+	0.0127279i
$190$	47.8228	−	38.5734i	0.251699	−	0.203018i
$191$			193.992i			1.01566i	0.861456	+	0.507832i	$0.169553\pi$
$191$			193.992i			1.01566i	−0.861456	+	0.507832i	$0.830447\pi$
$192$	−16.0712	−	109.680i	−0.0837040	−	0.571250i
$193$	141.555			0.733444			0.366722	−	0.930331i	$-0.380480\pi$
$193$	141.555			0.733444			0.366722	+	0.930331i	$0.380480\pi$
$194$	180.348	+	223.593i	0.929631	+	1.15254i
$195$	18.5434	−	18.5434i	0.0950942	−	0.0950942i
$196$	41.1279	−	189.882i	0.209836	−	0.968788i
$197$	28.9507	−	28.9507i	0.146958	−	0.146958i	−0.629800	−	0.776758i	$-0.716863\pi$
$197$	28.9507	−	28.9507i	0.146958	−	0.146958i	0.776758	+	0.629800i	$0.216863\pi$
$198$	−112.854	−	12.0819i	−0.569971	−	0.0610195i
$199$	−27.6253			−0.138821			−0.0694104	−	0.997588i	$-0.522112\pi$
$199$	−27.6253			−0.138821			−0.0694104	+	0.997588i	$0.522112\pi$
$200$	−83.8302	−	166.910i	−0.419151	−	0.834548i
$201$		−	166.135i		−	0.826541i
$202$	−253.984	−	27.1908i	−1.25735	−	0.134608i
$203$	−23.3147	−	23.3147i	−0.114851	−	0.114851i
$204$	−14.7609	−	22.9231i	−0.0723573	−	0.112368i
$205$	−25.8763	−	25.8763i	−0.126226	−	0.126226i
$206$	−119.493	−	148.146i	−0.580065	−	0.719156i
$207$			69.5360i			0.335923i
$208$	−66.1699	−	176.440i	−0.318124	−	0.848271i
$209$	−452.039			−2.16287
$210$	−2.26940	+	1.83048i	−0.0108067	+	0.00871658i
$211$	7.35041	−	7.35041i	0.0348361	−	0.0348361i	−0.689474	−	0.724310i	$-0.742158\pi$
$211$	7.35041	−	7.35041i	0.0348361	−	0.0348361i	0.724310	+	0.689474i	$0.242158\pi$
$212$	127.141	+	197.446i	0.599723	+	0.931348i
$213$	40.7955	−	40.7955i	0.191528	−	0.191528i
$214$	−8.20523	+	76.6435i	−0.0383422	+	0.358147i
$215$	41.3340			0.192251
$216$	39.4596	+	13.0744i	0.182683	+	0.0605298i
$217$		−	29.8345i		−	0.137486i
$218$	39.8673	−	372.392i	0.182877	−	1.70822i
$219$	−22.8208	−	22.8208i	−0.104205	−	0.104205i
$220$	20.5915	−	95.0683i	0.0935977	−	0.432129i
$221$	−32.7729	−	32.7729i	−0.148294	−	0.148294i
$222$	38.7141	−	31.2265i	0.174388	−	0.140660i
$223$			386.106i			1.73142i	0.500549	+	0.865708i	$0.333131\pi$
$223$			386.106i			1.73142i	−0.500549	+	0.865708i	$0.666869\pi$
$224$	5.22681	+	20.2884i	0.0233340	+	0.0905730i
$225$	70.0421			0.311298
$226$	47.6579	+	59.0855i	0.210875	+	0.261440i
$227$	−49.7286	+	49.7286i	−0.219069	+	0.219069i	−0.808106	−	0.589037i	$-0.799507\pi$
$227$	−49.7286	+	49.7286i	−0.219069	+	0.219069i	0.589037	+	0.808106i	$0.299507\pi$
$228$	161.808	+	35.0471i	0.709684	+	0.153715i
$229$	−191.870	+	191.870i	−0.837861	+	0.837861i	−0.988577	−	0.150716i	$-0.951842\pi$
$229$	−191.870	+	191.870i	−0.837861	+	0.837861i	0.150716	+	0.988577i	$0.451842\pi$
$230$	−59.2562	−	6.34380i	−0.257636	−	0.0275817i
$231$	21.4513			0.0928627
$232$	−382.440	−	126.717i	−1.64845	−	0.546193i
$233$		−	298.610i		−	1.28159i	−0.767712	−	0.640795i	$-0.778605\pi$
$233$		−	298.610i		−	1.28159i	0.767712	−	0.640795i	$-0.221395\pi$
$234$	70.2635	+	7.52221i	0.300271	+	0.0321462i
$235$	9.79435	+	9.79435i	0.0416781	+	0.0416781i
$236$	100.185	−	64.5123i	0.424514	−	0.273357i
$237$	7.70636	+	7.70636i	0.0325163	+	0.0325163i
$238$	3.23514	+	4.01087i	0.0135930	+	0.0168524i
$239$			247.352i			1.03495i	0.855700	+	0.517473i	$0.173127\pi$
$239$			247.352i			1.03495i	−0.855700	+	0.517473i	$0.826873\pi$
$240$	−14.7415	+	32.4333i	−0.0614229	+	0.135139i
$241$	−220.337			−0.914260			−0.457130	−	0.889400i	$-0.651123\pi$
$241$	−220.337			−0.914260			−0.457130	+	0.889400i	$0.651123\pi$
$242$	−368.686	+	297.379i	−1.52350	+	1.22884i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$	326.997	−	210.563i	1.34015	−	0.862963i
$245$	−44.1525	+	44.1525i	−0.180214	+	0.180214i
$246$	10.4969	−	98.0492i	0.0426702	−	0.398574i
$247$	281.441			1.13944
$248$	−163.618	−	325.770i	−0.659748	−	1.31359i
$249$			176.553i			0.709047i
$250$	−13.2322	+	123.600i	−0.0529290	+	0.494399i
$251$	162.716	+	162.716i	0.648272	+	0.648272i	0.952575	−	0.304303i	$-0.0984235\pi$
$251$	162.716	+	162.716i	0.648272	+	0.648272i	−0.304303	+	0.952575i	$0.598424\pi$
$252$	−7.67851	−	1.66314i	−0.0304703	−	0.00659977i
$253$	310.038	+	310.038i	1.22545	+	1.22545i
$254$	150.286	−	121.219i	0.591675	−	0.477240i
$255$			8.76249i			0.0343627i
$256$	168.338	+	192.869i	0.657570	+	0.753394i
$257$	101.165			0.393637			0.196819	−	0.980440i	$-0.436939\pi$
$257$	101.165			0.393637			0.196819	+	0.980440i	$0.436939\pi$
$258$	69.9265	+	86.6939i	0.271033	+	0.336023i
$259$	−6.64713	+	6.64713i	−0.0256646	+	0.0256646i
$260$	−12.8203	+	59.1899i	−0.0493090	+	0.227653i
$261$	106.831	−	106.831i	0.409316	−	0.409316i
$262$	−153.296	−	16.4115i	−0.585101	−	0.0626393i
$263$	−323.635			−1.23055			−0.615276	−	0.788312i	$-0.710955\pi$
$263$	−323.635			−1.23055			−0.615276	+	0.788312i	$0.710955\pi$
$264$	234.232	−	117.643i	0.887242	−	0.445616i
$265$		−	75.4747i		−	0.284810i
$266$	−31.1130	−	3.33087i	−0.116966	−	0.0125220i
$267$	12.9983	+	12.9983i	0.0486828	+	0.0486828i
$268$	207.718	+	322.579i	0.775068	+	1.20365i
$269$	1.51275	+	1.51275i	0.00562361	+	0.00562361i	0.709913	−	0.704289i	$-0.248734\pi$
$269$	1.51275	+	1.51275i	0.00562361	+	0.00562361i	−0.704289	+	0.709913i	$0.748734\pi$
$270$	−8.38756	−	10.3988i	−0.0310650	−	0.0385140i
$271$			166.098i			0.612909i	0.951885	+	0.306454i	$0.0991427\pi$
$271$			166.098i			0.612909i	−0.951885	+	0.306454i	$0.900857\pi$
$272$	57.3216	+	26.0536i	0.210741	+	0.0957854i
$273$	−13.3556			−0.0489218
$274$	40.3709	−	32.5628i	0.147339	−	0.118842i
$275$	312.294	−	312.294i	1.13562	−	1.13562i
$276$	−86.9409	−	135.016i	−0.315003	−	0.489189i
$277$	317.830	−	317.830i	1.14740	−	1.14740i	0.160338	−	0.987062i	$-0.448741\pi$
$277$	317.830	−	317.830i	1.14740	−	1.14740i	0.987062	−	0.160338i	$-0.0512586\pi$
$278$	−1.09614	+	10.2388i	−0.00394296	+	0.0368304i
$279$	136.706			0.489986
$280$	2.11778	−	6.39163i	0.00756352	−	0.0228272i
$281$			402.790i			1.43342i	0.697374	+	0.716708i	$0.254352\pi$
$281$			402.790i			1.43342i	−0.697374	+	0.716708i	$0.745648\pi$
$282$	−3.97313	+	37.1122i	−0.0140891	+	0.131604i
$283$	−192.406	−	192.406i	−0.679881	−	0.679881i	0.280092	−	0.959973i	$-0.409635\pi$
$283$	−192.406	−	192.406i	−0.679881	−	0.679881i	−0.959973	+	0.280092i	$0.909635\pi$
$284$	−28.2048	+	130.218i	−0.0993128	+	0.458515i
$285$	−37.6244	−	37.6244i	−0.132016	−	0.132016i
$286$	346.821	−	279.743i	1.21266	−	0.978121i
$287$			18.6371i			0.0649378i
$288$	−92.9645	+	23.9501i	−0.322793	+	0.0831600i
$289$	−273.513			−0.946413
$290$	81.2918	+	100.784i	0.280317	+	0.347532i
$291$	175.911	−	175.911i	0.604506	−	0.604506i
$292$	72.8434	+	15.7777i	0.249464	+	0.0540331i
$293$	−75.3645	+	75.3645i	−0.257217	+	0.257217i	−0.823921	−	0.566704i	$-0.808218\pi$
$293$	−75.3645	+	75.3645i	−0.257217	+	0.257217i	0.566704	+	0.823921i	$0.308218\pi$
$294$	−167.300	−	17.9107i	−0.569048	−	0.0609207i
$295$	−38.2964			−0.129818
$296$	−36.1276	+	109.036i	−0.122053	+	0.368364i
$297$			98.2932i			0.330953i
$298$	−53.3556	−	5.71210i	−0.179046	−	0.0191681i
$299$	−193.031	−	193.031i	−0.645588	−	0.645588i
$300$	−135.999	+	87.5736i	−0.453329	+	0.291912i
$301$	−14.8852	−	14.8852i	−0.0494524	−	0.0494524i
$302$	−129.593	−	160.667i	−0.429116	−	0.532011i
$303$			221.214i			0.730078i
$304$	−357.997	+	134.258i	−1.17762	+	0.441640i
$305$	−124.996			−0.409824
$306$	−18.3785	+	14.8239i	−0.0600603	+	0.0484441i
$307$	−111.544	+	111.544i	−0.363337	+	0.363337i	−0.865040	−	0.501703i	$-0.832707\pi$
$307$	−111.544	+	111.544i	−0.363337	+	0.363337i	0.501703	+	0.865040i	$0.332707\pi$
$308$	−41.6513	+	26.8205i	−0.135232	+	0.0870797i
$309$	−116.554	+	116.554i	−0.377196	+	0.377196i
$310$	−12.4718	+	116.496i	−0.0402315	+	0.375794i
$311$	−224.484			−0.721813			−0.360906	−	0.932602i	$-0.617533\pi$
$311$	−224.484			−0.721813			−0.360906	+	0.932602i	$0.617533\pi$
$312$	−145.834	+	73.2448i	−0.467415	+	0.234759i
$313$		−	488.339i		−	1.56019i	−0.625661	−	0.780095i	$-0.715171\pi$
$313$		−	488.339i		−	1.56019i	0.625661	−	0.780095i	$-0.284829\pi$
$314$	−26.5575	+	248.069i	−0.0845781	+	0.790027i
$315$	1.78545	+	1.78545i	0.00566809	+	0.00566809i
$316$	−24.5985	−	5.32795i	−0.0778433	−	0.0168606i
$317$	257.361	+	257.361i	0.811863	+	0.811863i	0.984913	−	0.173050i	$-0.0553621\pi$
$317$	257.361	+	257.361i	0.811863	+	0.811863i	−0.173050	+	0.984913i	$0.555362\pi$
$318$	158.301	−	127.684i	0.497801	−	0.401522i
$319$		−	952.652i		−	2.98637i
$320$	−11.9282	−	81.4061i	−0.0372757	−	0.254394i
$321$	66.7545			0.207958
$322$	19.0548	+	23.6238i	0.0591763	+	0.0733659i
$323$	−66.4962	+	66.4962i	−0.205871	+	0.205871i
$324$	7.62077	−	35.1841i	0.0235209	−	0.108593i
$325$	−194.436	+	194.436i	−0.598263	+	0.598263i
$326$	52.8829	+	5.66150i	0.162218	+	0.0173666i
$327$	−324.344			−0.991877
$328$	102.209	+	203.503i	0.311614	+	0.620437i
$329$		−	7.05427i		−	0.0214416i
$330$	−83.7620	−	8.96733i	−0.253824	−	0.0271737i
$331$	−123.553	−	123.553i	−0.373271	−	0.373271i	0.495396	−	0.868667i	$-0.335023\pi$
$331$	−123.553	−	123.553i	−0.373271	−	0.373271i	−0.868667	+	0.495396i	$0.835023\pi$
$332$	−220.744	−	342.807i	−0.664891	−	1.03255i
$333$	−30.4582	−	30.4582i	−0.0914661	−	0.0914661i
$334$	335.387	+	415.807i	1.00415	+	1.24493i
$335$		−	123.307i		−	0.368082i
$336$	16.9886	−	6.37117i	0.0505612	−	0.0189618i
$337$	−246.234			−0.730665			−0.365333	−	0.930877i	$-0.619045\pi$
$337$	−246.234			−0.730665			−0.365333	+	0.930877i	$0.619045\pi$
$338$	47.1538	−	38.0339i	0.139508	−	0.112526i
$339$	46.4853	−	46.4853i	0.137125	−	0.137125i
$340$	−10.9557	−	17.0139i	−0.0322228	−	0.0500408i
$341$	609.528	−	609.528i	1.78747	−	1.78747i
$342$	15.2626	−	142.564i	0.0446273	−	0.416855i
$343$	63.8813			0.186243
$344$	−244.168	−	80.9018i	−0.709790	−	0.235180i
$345$			51.6106i			0.149596i
$346$	46.2221	−	431.752i	0.133590	−	1.24784i
$347$	−123.212	−	123.212i	−0.355076	−	0.355076i	0.506918	−	0.861994i	$-0.330785\pi$
$347$	−123.212	−	123.212i	−0.355076	−	0.355076i	−0.861994	+	0.506918i	$0.830785\pi$
$348$	−73.8601	+	341.003i	−0.212242	+	0.979893i
$349$	115.371	+	115.371i	0.330575	+	0.330575i	0.852805	−	0.522230i	$-0.174900\pi$
$349$	115.371	+	115.371i	0.330575	+	0.330575i	−0.522230	+	0.852805i	$0.674900\pi$
$350$	23.7957	−	19.1934i	0.0679878	−	0.0548384i
$351$		−	61.1977i		−	0.174352i
$352$	−307.712	+	521.283i	−0.874183	+	1.48092i
$353$	650.544			1.84290			0.921451	−	0.388495i	$-0.127005\pi$
$353$	650.544			1.84290			0.921451	+	0.388495i	$0.127005\pi$
$354$	−64.7877	−	80.3228i	−0.183016	−	0.226901i
$355$	30.2790	−	30.2790i	0.0852930	−	0.0852930i
$356$	−41.4902	−	8.98665i	−0.116546	−	0.0252434i
$357$	3.15554	−	3.15554i	0.00883906	−	0.00883906i
$358$	347.555	+	37.2083i	0.970824	+	0.103934i
$359$	94.4878			0.263197			0.131599	−	0.991303i	$-0.457989\pi$
$359$	94.4878			0.263197			0.131599	+	0.991303i	$0.457989\pi$
$360$	29.2875	+	9.70402i	0.0813540	+	0.0269556i
$361$		−	210.044i		−	0.581838i
$362$	345.821	+	37.0226i	0.955306	+	0.102272i
$363$	290.063	+	290.063i	0.799070	+	0.799070i
$364$	25.9323	−	16.6986i	0.0712425	−	0.0458752i
$365$	−16.9379	−	16.9379i	−0.0464053	−	0.0464053i
$366$	−211.462	−	262.167i	−0.577764	−	0.716304i
$367$			131.379i			0.357982i	0.983851	+	0.178991i	$0.0572832\pi$
$367$			131.379i			0.357982i	−0.983851	+	0.178991i	$0.942717\pi$
$368$	337.621	+	153.455i	0.917449	+	0.416996i
$369$	−85.3983			−0.231432
$370$	28.7341	−	23.1767i	0.0776598	−	0.0626398i
$371$	−27.1799	+	27.1799i	−0.0732612	+	0.0732612i
$372$	−265.438	+	170.924i	−0.713544	+	0.459472i
$373$	−275.796	+	275.796i	−0.739400	+	0.739400i	−0.972462	−	0.233062i	$-0.925126\pi$
$373$	−275.796	+	275.796i	−0.739400	+	0.739400i	0.233062	+	0.972462i	$0.425126\pi$
$374$	−15.8486	+	148.038i	−0.0423758	+	0.395824i
$375$	107.652			0.287073
$376$	−38.6869	−	77.0273i	−0.102891	−	0.204860i
$377$			593.125i			1.57328i
$378$	−0.724276	+	6.76532i	−0.00191608	+	0.0178977i
$379$	−13.0427	−	13.0427i	−0.0344135	−	0.0344135i	0.689691	−	0.724104i	$-0.257747\pi$
$379$	−13.0427	−	13.0427i	−0.0344135	−	0.0344135i	−0.724104	+	0.689691i	$0.757747\pi$
$380$	120.096	+	26.0124i	0.316042	+	0.0684538i
$381$	−118.237	−	118.237i	−0.310333	−	0.310333i
$382$	−301.991	+	243.583i	−0.790553	+	0.637653i
$383$			121.974i			0.318470i	0.987241	+	0.159235i	$0.0509027\pi$
$383$			121.974i			0.318470i	−0.987241	+	0.159235i	$0.949097\pi$
$384$	150.562	−	162.737i	0.392087	−	0.423793i
$385$	15.9214			0.0413544
$386$	177.741	+	220.361i	0.460470	+	0.570883i
$387$	68.2062	−	68.2062i	0.176243	−	0.176243i
$388$	−121.620	+	561.504i	−0.313454	+	1.44717i
$389$	−233.267	+	233.267i	−0.599659	+	0.599659i	−0.940222	−	0.340563i	$-0.889382\pi$
$389$	−233.267	+	233.267i	−0.599659	+	0.599659i	0.340563	+	0.940222i	$0.389382\pi$
$390$	52.1505	+	5.58309i	0.133719	+	0.0143156i
$391$	91.2149			0.233286
$392$	347.235	−	174.399i	0.885804	−	0.444894i
$393$			133.517i			0.339738i
$394$	81.4198	+	8.71657i	0.206649	+	0.0221233i
$395$	5.71977	+	5.71977i	0.0144804	+	0.0144804i
$396$	−122.896	−	190.853i	−0.310343	−	0.481952i
$397$	−83.7693	−	83.7693i	−0.211006	−	0.211006i	0.593689	−	0.804695i	$-0.297671\pi$
$397$	−83.7693	−	83.7693i	−0.211006	−	0.211006i	−0.804695	+	0.593689i	$0.797671\pi$
$398$	−34.6874	−	43.0049i	−0.0871542	−	0.108053i
$399$			27.0986i			0.0679162i
$400$	154.571	−	340.078i	0.386428	−	0.850195i
$401$	589.134			1.46916			0.734581	−	0.678521i	$-0.237379\pi$
$401$	589.134			1.46916			0.734581	+	0.678521i	$0.237379\pi$
$402$	258.625	−	208.605i	0.643346	−	0.518917i
$403$	−379.494	+	379.494i	−0.941673	+	0.941673i
$404$	−276.583	−	429.524i	−0.684612	−	1.06318i
$405$	−8.18120	+	8.18120i	−0.0202005	+	0.0202005i
$406$	7.01965	−	65.5691i	0.0172898	−	0.161500i
$407$	−271.606			−0.667337
$408$	17.1506	−	51.7617i	0.0420357	−	0.126867i
$409$			449.285i			1.09850i	0.835659	+	0.549248i	$0.185086\pi$
$409$			449.285i			1.09850i	−0.835659	+	0.549248i	$0.814914\pi$
$410$	7.79092	−	72.7735i	0.0190023	−	0.177496i
$411$	−31.7617	−	31.7617i	−0.0772790	−	0.0772790i
$412$	80.5818	−	372.036i	0.195587	−	0.902999i
$413$	13.7913	+	13.7913i	0.0333929	+	0.0333929i
$414$	−108.248	+	87.3120i	−0.261469	+	0.210899i
$415$			131.040i			0.315759i
$416$	191.583	−	324.553i	0.460536	−	0.780175i
$417$	8.91777			0.0213855
$418$	−567.597	−	703.698i	−1.35789	−	1.68349i
$419$	−218.639	+	218.639i	−0.521811	+	0.521811i	−0.918118	−	0.396307i	$-0.870292\pi$
$419$	−218.639	+	218.639i	−0.521811	+	0.521811i	0.396307	+	0.918118i	$0.370292\pi$
$420$	−5.69910	−	1.23441i	−0.0135693	−	0.00293906i
$421$	−61.2101	+	61.2101i	−0.145392	+	0.145392i	−0.776056	−	0.630664i	$-0.782783\pi$
$421$	−61.2101	+	61.2101i	−0.145392	+	0.145392i	0.630664	+	0.776056i	$0.282783\pi$
$422$	20.6720	+	2.21308i	0.0489857	+	0.00524427i
$423$	32.3238			0.0764156
$424$	−147.725	+	445.844i	−0.348407	+	1.05152i
$425$		−	91.8787i		−	0.216185i
$426$	114.732	+	12.2828i	0.269323	+	0.0288330i
$427$	45.0136	+	45.0136i	0.105418	+	0.105418i
$428$	−129.615	+	83.4631i	−0.302839	+	0.195007i
$429$	−272.860	−	272.860i	−0.636038	−	0.636038i
$430$	51.9004	+	64.3454i	0.120699	+	0.149640i
$431$		−	501.119i		−	1.16269i	−0.813657	−	0.581345i	$-0.802527\pi$
$431$		−	501.119i		−	1.16269i	0.813657	−	0.581345i	$-0.197473\pi$
$432$	29.1937	+	77.8443i	0.0675780	+	0.180195i
$433$	75.5505			0.174482			0.0872408	−	0.996187i	$-0.472195\pi$
$433$	75.5505			0.174482			0.0872408	+	0.996187i	$0.472195\pi$
$434$	46.4439	−	37.4612i	0.107014	−	0.0863162i
$435$	79.2918	−	79.2918i	0.182280	−	0.182280i
$436$	629.769	−	405.527i	1.44442	−	0.930108i
$437$	−391.659	+	391.659i	−0.896245	+	0.896245i
$438$	6.87096	−	64.1803i	0.0156871	−	0.146530i
$439$	717.251			1.63383			0.816915	−	0.576758i	$-0.195682\pi$
$439$	717.251			1.63383			0.816915	+	0.576758i	$0.195682\pi$
$440$	173.850	−	87.3160i	0.395114	−	0.198446i
$441$			145.714i			0.330417i
$442$	9.86737	−	92.1692i	0.0223244	−	0.208528i
$443$	299.093	+	299.093i	0.675153	+	0.675153i	0.958899	−	0.283746i	$-0.0915773\pi$
$443$	299.093	+	299.093i	0.675153	+	0.675153i	−0.283746	+	0.958899i	$0.591577\pi$
$444$	97.2217	+	21.0579i	0.218968	+	0.0474277i
$445$	9.64753	+	9.64753i	0.0216798	+	0.0216798i
$446$	−601.059	+	484.809i	−1.34767	+	1.08702i
$447$			46.4714i			0.103963i
$448$	−25.0203	+	33.6115i	−0.0558489	+	0.0750257i
$449$	−44.5560			−0.0992339			−0.0496170	−	0.998768i	$-0.515800\pi$
$449$	−44.5560			−0.0992339			−0.0496170	+	0.998768i	$0.515800\pi$
$450$	87.9474	+	109.036i	0.195439	+	0.242302i
$451$	−380.763	+	380.763i	−0.844263	+	0.844263i
$452$	−32.1386	+	148.380i	−0.0711031	+	0.328274i
$453$	−126.405	+	126.405i	−0.279039	+	0.279039i
$454$	−139.855	−	14.9725i	−0.308050	−	0.0329790i
$455$	−9.91275			−0.0217863
$456$	148.613	+	295.896i	0.325907	+	0.648895i
$457$		−	641.227i		−	1.40312i	−0.712609	−	0.701562i	$-0.752486\pi$
$457$		−	641.227i		−	1.40312i	0.712609	−	0.701562i	$-0.247514\pi$
$458$	−539.607	−	57.7689i	−1.17818	−	0.126133i
$459$	14.4592	+	14.4592i	0.0315015	+	0.0315015i
$460$	−64.5287	−	100.211i	−0.140280	−	0.217850i
$461$	−393.690	−	393.690i	−0.853991	−	0.853991i	0.136631	−	0.990622i	$-0.456373\pi$
$461$	−393.690	−	393.690i	−0.853991	−	0.853991i	−0.990622	+	0.136631i	$0.956373\pi$
$462$	26.9350	+	33.3936i	0.0583009	+	0.0722806i
$463$		−	395.861i		−	0.854991i	−0.904018	−	0.427495i	$-0.859396\pi$
$463$		−	395.861i		−	0.854991i	0.904018	−	0.427495i	$-0.140604\pi$
$464$	−282.944	−	754.462i	−0.609792	−	1.62600i
$465$	101.465			0.218205
$466$	464.853	−	374.946i	0.997538	−	0.804606i
$467$	−83.1457	+	83.1457i	−0.178042	+	0.178042i	−0.790502	−	0.612460i	$-0.790180\pi$
$467$	−83.1457	+	83.1457i	−0.178042	+	0.178042i	0.612460	+	0.790502i	$0.290180\pi$
$468$	76.5154	+	118.826i	0.163495	+	0.253901i
$469$	−44.4054	+	44.4054i	−0.0946810	+	0.0946810i
$470$	−2.94891	+	27.5452i	−0.00627428	+	0.0586068i
$471$	216.061			0.458729
$472$	226.224	+	74.9564i	0.479288	+	0.158806i
$473$		−	608.217i		−	1.28587i
$474$	−2.32025	+	21.6730i	−0.00489505	+	0.0457237i
$475$	394.509	+	394.509i	0.830546	+	0.830546i
$476$	−2.18165	+	10.0724i	−0.00458330	+	0.0211605i
$477$	−124.543	−	124.543i	−0.261096	−	0.261096i
$478$	−385.058	+	310.584i	−0.805560	+	0.649758i
$479$			430.043i			0.897793i	0.893584	+	0.448896i	$0.148183\pi$
$479$			430.043i			0.897793i	−0.893584	+	0.448896i	$0.851817\pi$
$480$	−68.9995	+	17.7761i	−0.143749	+	0.0370335i
$481$	169.103			0.351565
$482$	−276.663	−	343.003i	−0.573989	−	0.711624i
$483$	18.5860	−	18.5860i	0.0384803	−	0.0384803i
$484$	−925.871	−	200.541i	−1.91296	−	0.414340i
$485$	130.564	−	130.564i	0.269204	−	0.269204i
$486$	−30.9998	−	3.31875i	−0.0637855	−	0.00682870i
$487$	573.790			1.17821			0.589107	−	0.808055i	$-0.299480\pi$
$487$	573.790			1.17821			0.589107	+	0.808055i	$0.299480\pi$
$488$	738.376	+	244.652i	1.51307	+	0.501335i
$489$		−	46.0597i		−	0.0941916i
$490$	−124.172	−	13.2936i	−0.253413	−	0.0271297i
$491$	−489.133	−	489.133i	−0.996197	−	0.996197i	0.00379588	−	0.999993i	$-0.498792\pi$
$491$	−489.133	−	489.133i	−0.996197	−	0.996197i	−0.999993	+	0.00379588i	$0.998792\pi$
$492$	165.815	−	106.773i	0.337023	−	0.217019i
$493$	−140.138	−	140.138i	−0.284255	−	0.284255i
$494$	353.388	+	438.125i	0.715360	+	0.886893i
$495$			72.9546i			0.147383i
$496$	301.688	−	663.755i	0.608242	−	1.33822i
$497$	−21.8081			−0.0438795
$498$	−274.843	+	221.686i	−0.551894	+	0.445153i
$499$	260.469	−	260.469i	0.521982	−	0.521982i	−0.396188	−	0.918170i	$-0.629667\pi$
$499$	260.469	−	260.469i	0.521982	−	0.521982i	0.918170	+	0.396188i	$0.129667\pi$
$500$	−209.025	+	134.598i	−0.418050	+	0.269195i
$501$	327.135	−	327.135i	0.652965	−	0.652965i
$502$	−48.9911	+	457.616i	−0.0975919	+	0.911586i
$503$	−975.416			−1.93920			−0.969598	−	0.244701i	$-0.921310\pi$
$503$	−975.416			−1.93920			−0.969598	+	0.244701i	$0.921310\pi$
$504$	−7.05237	−	14.0416i	−0.0139928	−	0.0278603i
$505$			164.188i			0.325124i
$506$	−93.3472	+	871.938i	−0.184481	+	1.72320i
$507$	−37.0981	−	37.0981i	−0.0731719	−	0.0731719i
$508$	377.408	+	81.7454i	0.742929	+	0.160916i
$509$	−420.191	−	420.191i	−0.825523	−	0.825523i	0.161371	−	0.986894i	$-0.448408\pi$
$509$	−420.191	−	420.191i	−0.825523	−	0.825523i	−0.986894	+	0.161371i	$0.948408\pi$
$510$	−13.6407	+	11.0025i	−0.0267466	+	0.0215735i
$511$			12.1994i			0.0238735i
$512$	−88.8714	+	504.228i	−0.173577	+	0.984820i
$513$	−124.170			−0.242047
$514$	127.026	+	157.485i	0.247133	+	0.306391i
$515$	−86.5077	+	86.5077i	−0.167976	+	0.167976i
$516$	−47.1557	+	217.712i	−0.0913871	+	0.421923i
$517$	144.121	−	144.121i	0.278764	−	0.278764i
$518$	−18.6941	−	2.00134i	−0.0360890	−	0.00386359i
$519$	−376.044			−0.724556
$520$	−108.240	+	54.3633i	−0.208153	+	0.104545i
$521$			396.333i			0.760716i	0.924839	+	0.380358i	$0.124199\pi$
$521$			396.333i			0.760716i	−0.924839	+	0.380358i	$0.875801\pi$
$522$	300.448	+	32.1651i	0.575571	+	0.0616190i
$523$	564.600	+	564.600i	1.07954	+	1.07954i	0.996550	+	0.0829913i	$0.0264474\pi$
$523$	564.600	+	564.600i	1.07954	+	1.07954i	0.0829913	+	0.996550i	$0.473553\pi$
$524$	−166.937	−	259.246i	−0.318581	−	0.494745i
$525$	−18.7212	−	18.7212i	−0.0356595	−	0.0356595i
$526$	−406.368	−	503.809i	−0.772563	−	0.957812i
$527$		−	179.326i		−	0.340278i
$528$	477.247	+	216.917i	0.903876	+	0.410827i
$529$	8.25115			0.0155976
$530$	117.493	−	94.7688i	0.221685	−	0.178809i
$531$	−63.1938	+	63.1938i	−0.119009	+	0.119009i
$532$	−33.8813	−	52.6165i	−0.0636867	−	0.0989032i
$533$	237.064	−	237.064i	0.444773	−	0.444773i
$534$	−3.91357	+	36.5559i	−0.00732878	+	0.0684567i
$535$	49.5461			0.0926095
$536$	−241.346	+	728.401i	−0.450273	+	1.35896i
$537$		−	302.711i		−	0.563708i
$538$	−0.455463	+	4.25439i	−0.000846586	+	0.00790779i
$539$	649.691	+	649.691i	1.20536	+	1.20536i
$540$	5.65624	−	26.1142i	0.0104745	−	0.0483596i
$541$	−29.5601	−	29.5601i	−0.0546398	−	0.0546398i	0.679259	−	0.733899i	$-0.262301\pi$
$541$	−29.5601	−	29.5601i	−0.0546398	−	0.0546398i	−0.733899	+	0.679259i	$0.762301\pi$
$542$	−258.568	+	208.559i	−0.477064	+	0.384795i
$543$		−	301.201i		−	0.554698i
$544$	31.4169	+	121.948i	0.0577516	+	0.224168i
$545$	−240.733			−0.441711
$546$	−16.7698	−	20.7910i	−0.0307140	−	0.0380788i
$547$	−138.608	+	138.608i	−0.253397	+	0.253397i	−0.822362	−	0.568965i	$-0.807344\pi$
$547$	−138.608	+	138.608i	−0.253397	+	0.253397i	0.568965	+	0.822362i	$0.307344\pi$
$548$	101.382	+	21.9591i	0.185004	+	0.0400713i
$549$	−206.259	+	206.259i	−0.375700	+	0.375700i
$550$	878.283	+	94.0265i	1.59688	+	0.170957i
$551$	1203.45			2.18412
$552$	101.016	−	304.874i	0.183000	−	0.552307i
$553$		−	4.11960i		−	0.00744955i
$554$	893.851	+	95.6932i	1.61345	+	0.172731i
$555$	−22.6065	−	22.6065i	−0.0407324	−	0.0407324i
$556$	−17.3154	+	11.1499i	−0.0311428	+	0.0200538i
$557$	60.4400	+	60.4400i	0.108510	+	0.108510i	0.759277	−	0.650767i	$-0.225553\pi$
$557$	60.4400	+	60.4400i	0.108510	+	0.108510i	−0.650767	+	0.759277i	$0.725553\pi$
$558$	171.653	+	212.813i	0.307622	+	0.381386i
$559$			378.678i			0.677421i
$560$	12.6091	−	4.72877i	0.0225163	−	0.00844423i
$561$	128.938			0.229835
$562$	−627.031	+	505.758i	−1.11571	+	0.899924i
$563$	267.325	−	267.325i	0.474822	−	0.474822i	−0.428649	−	0.903471i	$-0.641010\pi$
$563$	267.325	−	267.325i	0.474822	−	0.474822i	0.903471	+	0.428649i	$0.141010\pi$
$564$	−62.7621	+	40.4144i	−0.111280	+	0.0716568i
$565$	34.5021	−	34.5021i	0.0610656	−	0.0610656i
$566$	57.9303	−	541.115i	0.102350	−	0.956034i
$567$	5.89242			0.0103923
$568$	−238.128	+	119.600i	−0.419240	+	0.210563i
$569$		−	315.715i		−	0.554859i	−0.960746	−	0.277429i	$-0.910518\pi$
$569$		−	315.715i		−	0.554859i	0.960746	−	0.277429i	$-0.0894825\pi$
$570$	11.3281	−	105.813i	0.0198738	−	0.185637i
$571$	−670.572	−	670.572i	−1.17438	−	1.17438i	−0.981154	−	0.193228i	$-0.938104\pi$
$571$	−670.572	−	670.572i	−1.17438	−	1.17438i	−0.193228	−	0.981154i	$-0.561896\pi$
$572$	870.962	+	188.648i	1.52266	+	0.329803i
$573$	237.591	+	237.591i	0.414643	+	0.414643i
$574$	−29.0128	+	23.4015i	−0.0505449	+	0.0407691i
$575$		−	541.161i		−	0.941149i
$576$	−154.013	−	114.647i	−0.267384	−	0.199040i
$577$	413.628			0.716859			0.358430	−	0.933557i	$-0.383312\pi$
$577$	413.628			0.716859			0.358430	+	0.933557i	$0.383312\pi$
$578$	−343.434	−	425.784i	−0.594176	−	0.736650i
$579$	173.368	−	173.368i	0.299427	−	0.299427i
$580$	−54.8200	+	253.097i	−0.0945173	+	0.436374i
$581$	47.1900	−	47.1900i	0.0812220	−	0.0812220i
$582$	494.726	+	52.9639i	0.850044	+	0.0910033i
$583$	−1110.59			−1.90495
$584$	66.9035	+	133.208i	0.114561	+	0.228095i
$585$		−	45.4218i		−	0.0776441i
$586$	−211.952	−	22.6910i	−0.361693	−	0.0387218i
$587$	−420.085	−	420.085i	−0.715647	−	0.715647i	0.252064	−	0.967711i	$-0.418891\pi$
$587$	−420.085	−	420.085i	−0.715647	−	0.715647i	−0.967711	+	0.252064i	$0.918891\pi$
$588$	−182.186	−	282.929i	−0.309841	−	0.481171i
$589$	769.993	+	769.993i	1.30729	+	1.30729i
$590$	−48.0863	−	59.6167i	−0.0815023	−	0.101045i
$591$		−	70.9145i		−	0.119991i
$592$	−215.101	+	80.6687i	−0.363347	+	0.136265i
$593$	−740.798			−1.24924			−0.624619	−	0.780930i	$-0.714746\pi$
$593$	−740.798			−1.24924			−0.624619	+	0.780930i	$0.714746\pi$
$594$	−153.015	+	123.421i	−0.257601	+	0.207779i
$595$	2.34209	−	2.34209i	0.00393628	−	0.00393628i
$596$	−58.1031	−	90.2320i	−0.0974885	−	0.151396i
$597$	−33.8340	+	33.8340i	−0.0566733	+	0.0566733i
$598$	58.1183	−	542.872i	0.0971878	−	0.907812i
$599$	435.161			0.726479			0.363240	−	0.931696i	$-0.381671\pi$
$599$	435.161			0.726479			0.363240	+	0.931696i	$0.381671\pi$
$600$	−307.092	−	101.751i	−0.511821	−	0.169585i
$601$			380.001i			0.632280i	0.948712	+	0.316140i	$0.102387\pi$
$601$			380.001i			0.632280i	−0.948712	+	0.316140i	$0.897613\pi$
$602$	4.48167	−	41.8624i	0.00744463	−	0.0695388i
$603$	−203.473	−	203.473i	−0.337434	−	0.337434i
$604$	87.3924	−	403.480i	0.144689	−	0.668013i
$605$	215.288	+	215.288i	0.355849	+	0.355849i
$606$	−344.367	+	277.764i	−0.568263	+	0.458356i
$607$			181.813i			0.299527i	0.988722	+	0.149763i	$0.0478512\pi$
$607$			181.813i			0.299527i	−0.988722	+	0.149763i	$0.952149\pi$
$608$	−658.517	−	388.721i	−1.08309	−	0.639344i
$609$	−57.1090			−0.0937751
$610$	−156.950	−	194.584i	−0.257295	−	0.318990i
$611$	−89.7303	+	89.7303i	−0.146858	+	0.146858i
$612$	−46.1533	−	9.99666i	−0.0754139	−	0.0163344i
$613$	55.1479	−	55.1479i	0.0899640	−	0.0899640i	−0.660693	−	0.750657i	$-0.729737\pi$
$613$	55.1479	−	55.1479i	0.0899640	−	0.0899640i	0.750657	+	0.660693i	$0.229737\pi$
$614$	−313.703	−	33.5841i	−0.510917	−	0.0546973i
$615$	−63.3838			−0.103063
$616$	−94.0510	−	31.1626i	−0.152680	−	0.0505886i
$617$			579.674i			0.939504i	0.882798	+	0.469752i	$0.155657\pi$
$617$			579.674i			0.939504i	−0.882798	+	0.469752i	$0.844343\pi$
$618$	−327.790	−	35.0923i	−0.530405	−	0.0567837i
$619$	91.1070	+	91.1070i	0.147184	+	0.147184i	0.776859	−	0.629675i	$-0.216812\pi$
$619$	91.1070	+	91.1070i	0.147184	+	0.147184i	−0.629675	+	0.776859i	$0.716812\pi$
$620$	−197.012	+	126.862i	−0.317761	+	0.204616i
$621$	85.1639	+	85.1639i	0.137140	+	0.137140i
$622$	−281.870	−	349.458i	−0.453167	−	0.561830i
$623$		−	6.94852i		−	0.0111533i
$624$	−297.136	−	135.053i	−0.476179	−	0.216431i
$625$	−503.783			−0.806053
$626$	760.208	−	613.177i	1.21439	−	0.979516i
$627$	−553.633	+	553.633i	−0.882987	+	0.882987i
$628$	−419.520	+	270.141i	−0.668025	+	0.430162i
$629$	−39.9540	+	39.9540i	−0.0635199	+	0.0635199i
$630$	−0.537568	+	5.02132i	−0.000853283	+	0.00797034i
$631$	−693.474			−1.09901			−0.549504	−	0.835491i	$-0.685183\pi$
$631$	−693.474			−1.09901			−0.549504	+	0.835491i	$0.685183\pi$
$632$	−22.5926	−	44.9829i	−0.0357478	−	0.0711755i
$633$		−	18.0048i		−	0.0284435i
$634$	−77.4869	+	723.790i	−0.122219	+	1.14162i
$635$	−87.7570	−	87.7570i	−0.138200	−	0.138200i
$636$	397.536	+	86.1051i	0.625057	+	0.135385i
$637$	−404.500	−	404.500i	−0.635007	−	0.635007i
$638$	1483.01	−	1196.19i	2.32447	−	1.87490i
$639$		−	99.9283i		−	0.156382i
$640$	111.749	−	120.785i	0.174608	−	0.188727i
$641$	−218.329			−0.340607			−0.170304	−	0.985392i	$-0.554475\pi$
$641$	−218.329			−0.340607			−0.170304	+	0.985392i	$0.554475\pi$
$642$	83.8194	+	103.918i	0.130560	+	0.161866i
$643$	887.430	−	887.430i	1.38014	−	1.38014i	0.535787	−	0.844353i	$-0.320015\pi$
$643$	887.430	−	887.430i	1.38014	−	1.38014i	0.844353	−	0.535787i	$-0.179985\pi$
$644$	−12.8498	+	59.3259i	−0.0199531	+	0.0921210i
$645$	50.6236	−	50.6236i	0.0784861	−	0.0784861i
$646$	−187.011	−	20.0209i	−0.289491	−	0.0309921i
$647$	−223.177			−0.344941			−0.172470	−	0.985015i	$-0.555175\pi$
$647$	−223.177			−0.344941			−0.172470	+	0.985015i	$0.555175\pi$
$648$	64.3408	−	32.3151i	0.0992913	−	0.0498690i
$649$			563.520i			0.868290i
$650$	−546.822	−	58.5413i	−0.841265	−	0.0900635i
$651$	−36.5396	−	36.5396i	−0.0561284	−	0.0561284i
$652$	57.5884	+	89.4327i	0.0883258	+	0.137167i
$653$	539.691	+	539.691i	0.826479	+	0.826479i	0.987028	−	0.160549i	$-0.0513264\pi$
$653$	539.691	+	539.691i	0.826479	+	0.826479i	−0.160549	+	0.987028i	$0.551326\pi$
$654$	−407.258	−	504.913i	−0.622719	−	0.772037i
$655$			99.0983i			0.151295i
$656$	−188.460	+	414.638i	−0.287286	+	0.632070i
$657$	−55.8994			−0.0850828
$658$	10.9815	−	8.85760i	0.0166892	−	0.0134614i
$659$	625.166	−	625.166i	0.948659	−	0.948659i	−0.0500862	−	0.998745i	$-0.515950\pi$
$659$	625.166	−	625.166i	0.948659	−	0.948659i	0.998745	+	0.0500862i	$0.0159496\pi$
$660$	−91.2151	−	141.654i	−0.138205	−	0.214627i
$661$	−326.893	+	326.893i	−0.494544	+	0.494544i	−0.909734	−	0.415191i	$-0.863715\pi$
$661$	−326.893	+	326.893i	−0.494544	+	0.494544i	0.415191	+	0.909734i	$0.363715\pi$
$662$	37.1996	−	347.474i	0.0561928	−	0.524886i
$663$	−80.2770			−0.121081
$664$	256.481	−	774.078i	0.386266	−	1.16578i
$665$			20.1129i			0.0302450i
$666$	9.17045	−	85.6593i	0.0137694	−	0.128618i
$667$	−825.404	−	825.404i	−1.23749	−	1.23749i
$668$	−226.172	+	1044.21i	−0.338581	+	1.56318i
$669$	472.881	+	472.881i	0.706848	+	0.706848i
$670$	191.955	−	154.829i	0.286500	−	0.231089i
$671$			1839.28i			2.74111i
$672$	31.2496	+	18.4466i	0.0465023	+	0.0274502i
$673$	422.147			0.627262			0.313631	−	0.949545i	$-0.398455\pi$
$673$	422.147			0.627262			0.313631	+	0.949545i	$0.398455\pi$
$674$	−309.181	−	383.318i	−0.458725	−	0.568720i
$675$	85.7837	−	85.7837i	0.127087	−	0.127087i
$676$	118.416	+	25.6486i	0.175172	+	0.0379417i
$677$	−126.017	+	126.017i	−0.186140	+	0.186140i	−0.794025	−	0.607885i	$-0.792018\pi$
$677$	−126.017	+	126.017i	−0.186140	+	0.186140i	0.607885	+	0.794025i	$0.292018\pi$
$678$	130.733	+	13.9959i	0.192822	+	0.0206430i
$679$	−94.0372			−0.138494
$680$	12.7294	−	38.4183i	0.0187197	−	0.0564974i
$681$			121.810i			0.178869i
$682$	1714.21	+	183.518i	2.51350	+	0.269089i
$683$	621.906	+	621.906i	0.910551	+	0.910551i	0.996315	−	0.0857647i	$-0.0273333\pi$
$683$	621.906	+	621.906i	0.910551	+	0.910551i	−0.0857647	+	0.996315i	$0.527333\pi$
$684$	241.097	−	155.250i	0.352481	−	0.226973i
$685$	−23.5740	−	23.5740i	−0.0344145	−	0.0344145i
$686$	80.2117	+	99.4452i	0.116927	+	0.144964i
$687$			469.984i			0.684111i
$688$	−180.644	−	481.684i	−0.262564	−	0.700122i
$689$	691.456			1.00357
$690$	−80.3433	+	64.8042i	−0.116440	+	0.0939191i
$691$	−403.376	+	403.376i	−0.583758	+	0.583758i	−0.935934	−	0.352176i	$-0.885442\pi$
$691$	−403.376	+	403.376i	−0.583758	+	0.583758i	0.352176	+	0.935934i	$0.385442\pi$
$692$	730.154	−	470.168i	1.05514	−	0.679434i
$693$	26.2724	−	26.2724i	0.0379110	−	0.0379110i
$694$	37.0969	−	346.515i	0.0534537	−	0.499301i
$695$	6.61889			0.00952359
$696$	−623.587	+	313.196i	−0.895959	+	0.449995i
$697$			112.022i			0.160721i
$698$	−34.7361	+	324.463i	−0.0497652	+	0.464847i
$699$	−365.722	−	365.722i	−0.523207	−	0.523207i
$700$	59.7576	+	12.9433i	0.0853680	+	0.0184904i
$701$	466.593	+	466.593i	0.665611	+	0.665611i	0.956697	−	0.291086i	$-0.0940166\pi$
$701$	466.593	+	466.593i	0.665611	+	0.665611i	−0.291086	+	0.956697i	$0.594017\pi$
$702$	95.2676	−	76.8421i	0.135709	−	0.109462i
$703$		−	343.109i		−	0.488065i
$704$	−1197.87	+	175.521i	−1.70152	+	0.249319i
$705$	23.9912			0.0340300
$706$	816.847	+	1012.72i	1.15701	+	1.43444i
$707$	59.1272	−	59.1272i	0.0836311	−	0.0836311i
$708$	43.6903	−	201.713i	0.0617095	−	0.284905i
$709$	822.764	−	822.764i	1.16046	−	1.16046i	0.176081	−	0.984376i	$-0.443658\pi$
$709$	822.764	−	822.764i	1.16046	−	1.16046i	0.984376	−	0.176081i	$-0.0563422\pi$
$710$	85.1554	+	9.11650i	0.119937	+	0.0128401i
$711$	18.8767			0.0265494
$712$	−38.1069	−	75.8726i	−0.0535210	−	0.106563i
$713$		−	1056.22i		−	1.48138i
$714$	8.87451	+	0.950080i	0.0124293	+	0.00133064i
$715$	−202.521	−	202.521i	−0.283246	−	0.283246i
$716$	378.480	+	587.766i	0.528603	+	0.820902i
$717$	302.943	+	302.943i	0.422515	+	0.422515i
$718$	118.642	+	147.091i	0.165240	+	0.204862i
$719$		−	710.142i		−	0.987681i	−0.869553	−	0.493840i	$-0.835593\pi$
$719$		−	710.142i		−	0.987681i	0.869553	−	0.493840i	$-0.164407\pi$
$720$	21.6680	+	57.7771i	0.0300944	+	0.0802460i
$721$	62.3062			0.0864164
$722$	326.979	−	263.738i	0.452879	−	0.365289i
$723$	−269.856	+	269.856i	−0.373245	+	0.373245i
$724$	376.592	+	584.833i	0.520154	+	0.807781i
$725$	−831.411	+	831.411i	−1.14677	+	1.14677i
$726$	−87.3329	+	815.759i	−0.120293	+	1.12364i
$727$	−214.095			−0.294490			−0.147245	−	0.989100i	$-0.547041\pi$
$727$	−214.095			−0.294490			−0.147245	+	0.989100i	$0.547041\pi$
$728$	58.5565	+	19.4019i	0.0804347	+	0.0266510i
$729$			27.0000i			0.0370370i
$730$	5.09972	−	47.6355i	0.00698592	−	0.0652541i
$731$	−89.4704	−	89.4704i	−0.122395	−	0.122395i
$732$	142.602	−	658.373i	0.194811	−	0.899417i
$733$	−96.1768	−	96.1768i	−0.131210	−	0.131210i	0.638452	−	0.769662i	$-0.279575\pi$
$733$	−96.1768	−	96.1768i	−0.131210	−	0.131210i	−0.769662	+	0.638452i	$0.779575\pi$
$734$	−204.521	+	164.965i	−0.278638	+	0.224747i
$735$			108.151i			0.147144i
$736$	185.044	+	718.265i	0.251418	+	0.975903i
$737$	−1814.43			−2.46192
$738$	−107.229	−	132.941i	−0.145297	−	0.180137i
$739$	885.341	−	885.341i	1.19803	−	1.19803i	0.223268	−	0.974757i	$-0.428327\pi$
$739$	885.341	−	885.341i	1.19803	−	1.19803i	0.974757	−	0.223268i	$-0.0716726\pi$
$740$	72.1593	+	15.6295i	0.0975125	+	0.0211209i
$741$	344.694	−	344.694i	0.465174	−	0.465174i
$742$	−76.4396	−	8.18341i	−0.103018	−	0.0110289i
$743$	906.258			1.21973			0.609864	−	0.792506i	$-0.291224\pi$
$743$	906.258			1.21973			0.609864	+	0.792506i	$0.291224\pi$
$744$	−599.374	−	198.595i	−0.805611	−	0.266929i
$745$			34.4917i			0.0462976i
$746$	−775.637	−	83.0376i	−1.03973	−	0.111310i
$747$	216.232	+	216.232i	0.289467	+	0.289467i
$748$	−250.354	+	161.211i	−0.334698	+	0.215522i
$749$	−17.8425	−	17.8425i	−0.0238218	−	0.0238218i
$750$	135.172	+	167.584i	0.180229	+	0.223446i
$751$			1147.02i			1.52732i	0.645618	+	0.763661i	$0.276600\pi$
$751$			1147.02i			1.52732i	−0.645618	+	0.763661i	$0.723400\pi$
$752$	71.3333	−	156.943i	0.0948581	−	0.208701i
$753$	398.572			0.529312
$754$	−923.329	+	744.749i	−1.22457	+	0.987731i
$755$	−93.8192	+	93.8192i	−0.124264	+	0.124264i
$756$	−11.4411	+	7.36729i	−0.0151338	+	0.00974509i
$757$	525.591	−	525.591i	0.694308	−	0.694308i	−0.268869	−	0.963177i	$-0.586650\pi$
$757$	525.591	−	525.591i	0.694308	−	0.694308i	0.963177	+	0.268869i	$0.0866497\pi$
$758$	3.92694	−	36.6808i	0.00518066	−	0.0483915i
$759$	759.435			1.00057
$760$	110.303	+	219.618i	0.145135	+	0.288971i
$761$		−	788.107i		−	1.03562i	−0.855495	−	0.517810i	$-0.826747\pi$
$761$		−	788.107i		−	1.03562i	0.855495	−	0.517810i	$-0.173253\pi$
$762$	35.5991	−	332.524i	0.0467179	−	0.436383i
$763$	86.6925	+	86.6925i	0.113621	+	0.113621i
$764$	−758.382	−	164.263i	−0.992647	−	0.215004i
$765$	10.7318	+	10.7318i	0.0140285	+	0.0140285i
$766$	−189.879	+	153.155i	−0.247884	+	0.199941i
$767$		−	350.850i		−	0.457431i
$768$	442.386	+	30.0441i	0.576023	+	0.0391199i
$769$	−768.187			−0.998943			−0.499471	−	0.866330i	$-0.666472\pi$
$769$	−768.187			−0.998943			−0.499471	+	0.866330i	$0.666472\pi$
$770$	19.9915	+	24.7852i	0.0259630	+	0.0321886i
$771$	123.901	−	123.901i	0.160702	−	0.160702i
$772$	−119.862	+	553.387i	−0.155261	+	0.716822i
$773$	275.915	−	275.915i	0.356941	−	0.356941i	−0.505743	−	0.862684i	$-0.668782\pi$
$773$	275.915	−	275.915i	0.356941	−	0.356941i	0.862684	+	0.505743i	$0.168782\pi$
$774$	191.820	+	20.5357i	0.247830	+	0.0265319i
$775$	−1063.91			−1.37279
$776$	−1026.81	+	515.717i	−1.32321	+	0.664583i
$777$			16.2821i			0.0209551i
$778$	−656.031	−	70.2328i	−0.843227	−	0.0902735i
$779$	−481.003	−	481.003i	−0.617462	−	0.617462i
$780$	56.7908	+	88.1941i	0.0728088	+	0.113069i
$781$	−445.547	−	445.547i	−0.570483	−	0.570483i
$782$	114.533	+	141.996i	0.146461	+	0.181581i
$783$		−	261.683i		−	0.334205i
$784$	707.491	+	321.567i	0.902412	+	0.410162i
$785$	160.364			0.204285
$786$	−207.849	+	167.649i	−0.264439	+	0.213294i
$787$	240.824	−	240.824i	0.306002	−	0.306002i	−0.537354	−	0.843356i	$-0.680576\pi$
$787$	240.824	−	240.824i	0.306002	−	0.306002i	0.843356	+	0.537354i	$0.180576\pi$
$788$	88.6644	+	137.693i	0.112518	+	0.174737i
$789$	−396.371	+	396.371i	−0.502371	+	0.502371i
$790$	−1.72213	+	16.0860i	−0.00217991	+	0.0203621i
$791$	−24.8497			−0.0314156
$792$	142.792	−	430.956i	0.180293	−	0.544137i
$793$		−	1145.14i		−	1.44407i
$794$	25.2215	−	235.589i	0.0317651	−	0.296712i
$795$	−92.4373	−	92.4373i	−0.116273	−	0.116273i
$796$	23.3918	−	107.997i	0.0293867	−	0.135675i
$797$	−681.033	−	681.033i	−0.854496	−	0.854496i	0.136187	−	0.990683i	$-0.456515\pi$
$797$	−681.033	−	681.033i	−0.854496	−	0.854496i	−0.990683	+	0.136187i	$0.956515\pi$
$798$	−42.1849	+	34.0260i	−0.0528633	+	0.0426391i
$799$		−	42.4012i		−	0.0530678i
$800$	723.492	−	186.390i	0.904364	−	0.232988i
$801$	31.8392			0.0397493
$802$	739.739	+	917.117i	0.922367	+	1.14354i
$803$	−249.237	+	249.237i	−0.310382	+	0.310382i
$804$	649.478	+	140.675i	0.807809	+	0.174969i
$805$	13.7948	−	13.7948i	0.0171364	−	0.0171364i
$806$	−1067.27	−	114.259i	−1.32416	−	0.141761i
$807$	3.70547			0.00459166
$808$	321.360	−	969.888i	0.397723	−	1.20036i
$809$			445.322i			0.550459i	0.961379	+	0.275230i	$0.0887539\pi$
$809$			445.322i			0.550459i	−0.961379	+	0.275230i	$0.911246\pi$
$810$	−23.0085	−	2.46322i	−0.0284055	−	0.00304101i
$811$	223.787	+	223.787i	0.275939	+	0.275939i	0.831485	−	0.555546i	$-0.187491\pi$
$811$	223.787	+	223.787i	0.275939	+	0.275939i	−0.555546	+	0.831485i	$0.687491\pi$
$812$	110.887	−	71.4034i	0.136560	−	0.0879352i
$813$	203.428	+	203.428i	0.250219	+	0.250219i
$814$	−341.039	−	422.815i	−0.418966	−	0.519428i
$815$		−	34.1861i		−	0.0419462i
$816$	102.113	−	38.2953i	0.125139	−	0.0469305i
$817$	768.337			0.940437
$818$	−699.411	+	564.139i	−0.855026	+	0.689656i
$819$	−16.3573	+	16.3573i	−0.0199722	+	0.0199722i
$820$	123.070	−	79.2488i	0.150086	−	0.0966448i
$821$	382.528	−	382.528i	0.465929	−	0.465929i	−0.434664	−	0.900593i	$-0.643133\pi$
$821$	382.528	−	382.528i	0.465929	−	0.465929i	0.900593	+	0.434664i	$0.143133\pi$
$822$	9.56290	−	89.3251i	0.0116337	−	0.108668i
$823$	−730.046			−0.887055			−0.443527	−	0.896261i	$-0.646273\pi$
$823$	−730.046			−0.887055			−0.443527	+	0.896261i	$0.646273\pi$
$824$	680.337	−	341.698i	0.825651	−	0.414683i
$825$		−	764.962i		−	0.927227i
$826$	−4.15232	+	38.7860i	−0.00502702	+	0.0469564i
$827$	252.094	+	252.094i	0.304829	+	0.304829i	0.842900	−	0.538071i	$-0.180847\pi$
$827$	252.094	+	252.094i	0.304829	+	0.304829i	−0.538071	+	0.842900i	$0.680847\pi$
$828$	−271.841	−	58.8798i	−0.328310	−	0.0711109i
$829$	−870.285	−	870.285i	−1.04980	−	1.04980i	−0.998693	−	0.0511072i	$-0.983725\pi$
$829$	−870.285	−	870.285i	−1.04980	−	1.04980i	−0.0511072	−	0.998693i	$-0.516275\pi$
$830$	−203.992	+	164.539i	−0.245774	+	0.198239i
$831$		−	778.521i		−	0.936849i
$832$	745.796	−	109.280i	0.896390	−	0.131346i
$833$	191.143			0.229463
$834$	11.1975	+	13.8825i	0.0134262	+	0.0166456i
$835$	242.804	−	242.804i	0.290784	−	0.290784i
$836$	382.765	−	1767.18i	0.457853	−	2.11385i
$837$	167.430	−	167.430i	0.200036	−	0.200036i
$838$	−614.890	−	65.8284i	−0.733759	−	0.0785542i
$839$	550.145			0.655715			0.327858	−	0.944727i	$-0.393673\pi$
$839$	550.145			0.655715			0.327858	+	0.944727i	$0.393673\pi$
$840$	−5.23437	−	10.4219i	−0.00623139	−	0.0124070i
$841$			1695.21i			2.01571i
$842$	−172.145	−	18.4293i	−0.204447	−	0.0218876i
$843$	493.315	+	493.315i	0.585189	+	0.585189i
$844$	22.5113	+	34.9593i	0.0266722	+	0.0414210i
$845$	−27.5348	−	27.5348i	−0.0325855	−	0.0325855i
$846$	40.5869	+	50.3191i	0.0479751	+	0.0594788i
$847$		−	155.059i		−	0.183069i
$848$	−879.542	+	329.852i	−1.03720	+	0.388976i
$849$	−471.298			−0.555121
$850$	143.029	−	115.366i	0.168270	−	0.135725i
$851$	−235.327	+	235.327i	−0.276530	+	0.276530i
$852$	124.940	+	194.028i	0.146644	+	0.227732i
$853$	−676.266	+	676.266i	−0.792809	+	0.792809i	−0.981950	−	0.189141i	$-0.939430\pi$
$853$	−676.266	+	676.266i	−0.792809	+	0.792809i	0.189141	+	0.981950i	$0.439430\pi$
$854$	−13.5528	+	126.594i	−0.0158698	+	0.148237i
$855$	−92.1607			−0.107790
$856$	−292.678	−	96.9752i	−0.341914	−	0.113289i
$857$			291.272i			0.339874i	0.985455	+	0.169937i	$0.0543563\pi$
$857$			291.272i			0.339874i	−0.985455	+	0.169937i	$0.945644\pi$
$858$	82.1536	−	767.380i	0.0957501	−	0.894382i
$859$	988.357	+	988.357i	1.15059	+	1.15059i	0.986434	+	0.164156i	$0.0524899\pi$
$859$	988.357	+	988.357i	1.15059	+	1.15059i	0.164156	+	0.986434i	$0.447510\pi$
$860$	−34.9996	+	161.589i	−0.0406973	+	0.187894i
$861$	22.8257	+	22.8257i	0.0265107	+	0.0265107i
$862$	780.102	−	629.224i	0.904991	−	0.729958i
$863$			922.512i			1.06896i	0.845181	+	0.534480i	$0.179492\pi$
$863$			922.512i			1.06896i	−0.845181	+	0.534480i	$0.820508\pi$
$864$	−84.5250	+	143.191i	−0.0978299	+	0.165730i
$865$	−279.105			−0.322665
$866$	94.8640	+	117.611i	0.109543	+	0.135809i
$867$	−334.984	+	334.984i	−0.386372	+	0.386372i
$868$	116.633	+	25.2624i	0.134370	+	0.0291042i
$869$	84.1648	−	84.1648i	0.0968524	−	0.0968524i
$870$	222.997	+	23.8734i	0.256318	+	0.0274407i
$871$	1129.67			1.29698
$872$	1422.05	+	471.179i	1.63079	+	0.540343i
$873$		−	430.893i		−	0.493577i
$874$	−1101.49	−	117.922i	−1.26028	−	0.134922i
$875$	−28.7739	−	28.7739i	−0.0328845	−	0.0328845i
$876$	108.538	−	69.8910i	0.123902	−	0.0797842i
$877$	−406.278	−	406.278i	−0.463259	−	0.463259i	0.436463	−	0.899722i	$-0.356231\pi$
$877$	−406.278	−	406.278i	−0.463259	−	0.463259i	−0.899722	+	0.436463i	$0.856231\pi$
$878$	900.607	+	1116.56i	1.02575	+	1.27171i
$879$			184.605i			0.210017i
$880$	354.219	+	160.999i	0.402522	+	0.182953i
$881$	−1009.42			−1.14577			−0.572884	−	0.819637i	$-0.694175\pi$
$881$	−1009.42			−1.14577			−0.572884	+	0.819637i	$0.694175\pi$
$882$	−226.836	+	182.964i	−0.257184	+	0.207442i
$883$	56.3792	−	56.3792i	0.0638496	−	0.0638496i	−0.674461	−	0.738311i	$-0.735624\pi$
$883$	56.3792	−	56.3792i	0.0638496	−	0.0638496i	0.738311	+	0.674461i	$0.235624\pi$
$884$	155.871	−	100.370i	0.176325	−	0.113541i
$885$	−46.9033	+	46.9033i	−0.0529981	+	0.0529981i
$886$	−90.0518	+	841.156i	−0.101639	+	0.949386i
$887$	21.0431			0.0237239			0.0118620	−	0.999930i	$-0.496224\pi$
$887$	21.0431			0.0237239			0.0118620	+	0.999930i	$0.496224\pi$
$888$	89.2938	+	177.788i	0.100556	+	0.200212i
$889$			63.2060i			0.0710978i
$890$	−2.90471	+	27.1323i	−0.00326371	+	0.0304857i
$891$	120.384	+	120.384i	0.135111	+	0.135111i
$892$	−1509.42	−	326.936i	−1.69218	−	0.366520i
$893$	182.063	+	182.063i	0.203877	+	0.203877i
$894$	−72.3429	+	58.3511i	−0.0809204	+	0.0652697i
$895$		−	224.677i		−	0.251035i
$896$	−83.7401	+	3.25421i	−0.0934599	+	0.00363193i
$897$	−472.827			−0.527121
$898$	−55.9462	−	69.3613i	−0.0623009	−	0.0772397i
$899$	−1622.72	+	1622.72i	−1.80503	+	1.80503i
$900$	−59.3083	+	273.819i	−0.0658981	+	0.304243i
$901$	−163.371	+	163.371i	−0.181321	+	0.181321i
$902$	−1070.84	−	114.641i	−1.18718	−	0.127097i
$903$	−36.4610			−0.0403777
$904$	−271.340	+	136.280i	−0.300155	+	0.150753i
$905$		−	223.556i		−	0.247023i
$906$	−355.495	−	38.0583i	−0.392378	−	0.0420069i
$907$	496.202	+	496.202i	0.547080	+	0.547080i	0.925595	−	0.378515i	$-0.123565\pi$
$907$	496.202	+	496.202i	0.547080	+	0.547080i	−0.378515	+	0.925595i	$0.623565\pi$
$908$	−152.299	−	236.515i	−0.167730	−	0.260479i
$909$	270.930	+	270.930i	0.298053	+	0.298053i
$910$	−12.4468	−	15.4314i	−0.0136778	−	0.0169575i
$911$		−	1532.15i		−	1.68183i	−0.541163	−	0.840917i	$-0.682016\pi$
$911$		−	1532.15i		−	1.68183i	0.541163	−	0.840917i	$-0.317984\pi$
$912$	−274.023	+	602.887i	−0.300463	+	0.661061i
$913$	1928.21			2.11195
$914$	998.211	−	805.149i	1.09213	−	0.880907i
$915$	−153.088	+	153.088i	−0.167310	+	0.167310i
$916$	−587.621	−	912.554i	−0.641508	−	0.996238i
$917$	35.6872	−	35.6872i	0.0389174	−	0.0389174i
$918$	−4.35342	+	40.6644i	−0.00474229	+	0.0442967i
$919$	727.639			0.791773			0.395886	−	0.918299i	$-0.370437\pi$
$919$	727.639			0.791773			0.395886	+	0.918299i	$0.370437\pi$
$920$	74.9755	−	226.282i	0.0814951	−	0.245958i
$921$			273.227i			0.296663i
$922$	118.533	−	1107.20i	0.128561	−	1.20086i
$923$	277.399	+	277.399i	0.300541	+	0.300541i
$924$	−18.1639	+	83.8606i	−0.0196579	+	0.0907582i
$925$	237.040	+	237.040i	0.256259	+	0.256259i
$926$	616.244	−	497.057i	0.665490	−	0.536779i
$927$			285.497i			0.307979i
$928$	819.212	−	1387.79i	0.882772	−	1.49547i
$929$	1544.59			1.66264			0.831318	−	0.555797i	$-0.187587\pi$
$929$	1544.59			1.66264			0.831318	+	0.555797i	$0.187587\pi$
$930$	127.403	+	157.953i	0.136993	+	0.169842i
$931$	−820.729	+	820.729i	−0.881556	+	0.881556i
$932$	1167.37	+	252.849i	1.25255	+	0.271297i
$933$	−274.935	+	274.935i	−0.294679	+	0.294679i
$934$	−233.835	−	25.0338i	−0.250359	−	0.0268027i
$935$	95.6992			0.102352
$936$	−88.9028	+	268.315i	−0.0949816	+	0.286661i
$937$			716.111i			0.764259i	0.924109	+	0.382130i	$0.124809\pi$
$937$			716.111i			0.764259i	−0.924109	+	0.382130i	$0.875191\pi$
$938$	−124.884	−	13.3697i	−0.133138	−	0.0142534i
$939$	−598.091	−	598.091i	−0.636945	−	0.636945i
$940$	−46.5829	+	29.9961i	−0.0495563	+	0.0319108i
$941$	537.759	+	537.759i	0.571476	+	0.571476i	0.932541	−	0.361065i	$-0.117587\pi$
$941$	537.759	+	537.759i	0.571476	+	0.571476i	−0.361065	+	0.932541i	$0.617587\pi$
$942$	271.295	+	336.347i	0.287998	+	0.357056i
$943$			659.807i			0.699689i
$944$	167.369	+	446.285i	0.177298	+	0.472760i
$945$	4.37344			0.00462797
$946$	946.824	−	763.700i	1.00087	−	0.807294i
$947$	734.420	−	734.420i	0.775523	−	0.775523i	−0.203543	−	0.979066i	$-0.565246\pi$
$947$	734.420	−	734.420i	0.775523	−	0.775523i	0.979066	+	0.203543i	$0.0652457\pi$
$948$	−36.6522	+	23.6015i	−0.0386627	+	0.0248961i
$949$	155.176	−	155.176i	0.163515	−	0.163515i
$950$	−118.780	+	1109.50i	−0.125032	+	1.16790i
$951$	630.402			0.662884
$952$	−18.4193	+	9.25106i	−0.0193480	+	0.00971750i
$953$			138.512i			0.145343i	0.997356	+	0.0726714i	$0.0231524\pi$
$953$			138.512i			0.145343i	−0.997356	+	0.0726714i	$0.976848\pi$
$954$	37.4977	−	350.258i	0.0393057	−	0.367147i
$955$	176.343	+	176.343i	0.184652	+	0.184652i
$956$	−966.986	−	209.446i	−1.01149	−	0.219086i
$957$	−1166.76	−	1166.76i	−1.21918	−	1.21918i
$958$	−669.456	+	539.977i	−0.698806	+	0.563651i
$959$			16.9789i			0.0177048i
$960$	−114.311	−	85.0926i	−0.119074	−	0.0886381i
$961$	−1115.51			−1.16078
$962$	212.332	+	263.246i	0.220719	+	0.273644i
$963$	81.7572	−	81.7572i	0.0848984	−	0.0848984i
$964$	186.571	−	861.373i	0.193538	−	0.893541i
$965$	128.676	−	128.676i	0.133343	−	0.133343i
$966$	52.2704	+	5.59592i	0.0541102	+	0.00579288i
$967$	−701.820			−0.725770			−0.362885	−	0.931834i	$-0.618208\pi$
$967$	−701.820			−0.725770			−0.362885	+	0.931834i	$0.618208\pi$
$968$	−850.372	−	1693.13i	−0.878483	−	1.74910i
$969$			162.882i			0.168093i
$970$	367.192	+	39.3106i	0.378549	+	0.0405264i
$971$	−62.5684	−	62.5684i	−0.0644371	−	0.0644371i	0.674154	−	0.738591i	$-0.264508\pi$
$971$	−62.5684	−	62.5684i	−0.0644371	−	0.0644371i	−0.738591	+	0.674154i	$0.764508\pi$
$972$	−33.7581	−	52.4251i	−0.0347305	−	0.0539353i
$973$	−2.38359	−	2.38359i	−0.00244973	−	0.00244973i
$974$	720.472	+	893.230i	0.739704	+	0.917074i
$975$			476.268i			0.488480i
$976$	546.279	+	1456.64i	0.559712	+	1.49246i
$977$	1740.21			1.78117			0.890587	−	0.454814i	$-0.150294\pi$
$977$	1740.21			1.78117			0.890587	+	0.454814i	$0.150294\pi$
$978$	71.7020	−	57.8342i	0.0733149	−	0.0591352i
$979$	141.961	−	141.961i	0.145006	−	0.145006i
$980$	−135.221	−	209.994i	−0.137981	−	0.214279i
$981$	−397.239	+	397.239i	−0.404932	+	0.404932i
$982$	147.270	−	1375.62i	0.149969	−	1.40083i
$983$	−1451.81			−1.47692			−0.738460	−	0.674298i	$-0.764446\pi$
$983$	−1451.81			−1.47692			−0.738460	+	0.674298i	$0.764446\pi$
$984$	374.420	+	124.059i	0.380508	+	0.126077i
$985$		−	52.6337i		−	0.0534353i
$986$	42.1931	−	394.117i	0.0427922	−	0.399713i
$987$	−8.63968	−	8.63968i	−0.00875348	−	0.00875348i
$988$	−238.311	+	1100.25i	−0.241206	+	1.11362i
$989$	−526.976	−	526.976i	−0.532837	−	0.532837i
$990$	−113.570	+	91.6044i	−0.114717	+	0.0925297i
$991$		−	22.1684i		−	0.0223698i	−0.999937	−	0.0111849i	$-0.996440\pi$
$991$		−	22.1684i		−	0.0223698i	0.999937	−	0.0111849i	$-0.00356033\pi$
$992$	1412.09	−	363.792i	1.42348	−	0.366725i
$993$	−302.641			−0.304775
$994$	−27.3831	−	33.9491i	−0.0275484	−	0.0341541i
$995$	−25.1121	+	25.1121i	−0.0252382	+	0.0252382i
$996$	−690.206	−	149.497i	−0.692978	−	0.150097i
$997$	13.5020	−	13.5020i	0.0135426	−	0.0135426i	−0.700303	−	0.713846i	$-0.746952\pi$
$997$	13.5020	−	13.5020i	0.0135426	−	0.0135426i	0.713846	+	0.700303i	$0.246952\pi$
$998$	732.532	+	78.4228i	0.734000	+	0.0785799i
$999$	−74.6071			−0.0746817

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.3.l.a.19.6	✓	16
3.2	odd	2		144.3.m.c.19.3		16
4.3	odd	2		192.3.l.a.175.2		16
8.3	odd	2		384.3.l.b.223.7		16
8.5	even	2		384.3.l.a.223.3		16
12.11	even	2		576.3.m.c.559.5		16
16.3	odd	4		384.3.l.a.31.3		16
16.5	even	4		192.3.l.a.79.2		16
16.11	odd	4	inner	48.3.l.a.43.6	yes	16
16.13	even	4		384.3.l.b.31.7		16
24.5	odd	2		1152.3.m.f.991.4		16
24.11	even	2		1152.3.m.c.991.4		16
48.5	odd	4		576.3.m.c.271.5		16
48.11	even	4		144.3.m.c.91.3		16
48.29	odd	4		1152.3.m.c.415.4		16
48.35	even	4		1152.3.m.f.415.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.l.a.19.6	✓	16	1.1	even	1	trivial
48.3.l.a.43.6	yes	16	16.11	odd	4	inner
144.3.m.c.19.3		16	3.2	odd	2
144.3.m.c.91.3		16	48.11	even	4
192.3.l.a.79.2		16	16.5	even	4
192.3.l.a.175.2		16	4.3	odd	2
384.3.l.a.31.3		16	16.3	odd	4
384.3.l.a.223.3		16	8.5	even	2
384.3.l.b.31.7		16	16.13	even	4
384.3.l.b.223.7		16	8.3	odd	2
576.3.m.c.271.5		16	48.5	odd	4
576.3.m.c.559.5		16	12.11	even	2
1152.3.m.c.415.4		16	48.29	odd	4
1152.3.m.c.991.4		16	24.11	even	2
1152.3.m.f.415.4		16	48.35	even	4
1152.3.m.f.991.4		16	24.5	odd	2

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25564 + 1.55672i) q^{2} +(1.22474 - 1.22474i) q^{3} +(-0.846753 + 3.90935i) q^{4} +(0.909023 - 0.909023i) q^{5} +(3.44442 + 0.368750i) q^{6} -0.654713 q^{7} +(-7.14897 + 3.59057i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.25564 + 1.55672i) q^{2} +(1.22474 - 1.22474i) q^{3} +(-0.846753 + 3.90935i) q^{4} +(0.909023 - 0.909023i) q^{5} +(3.44442 + 0.368750i) q^{6} -0.654713 q^{7} +(-7.14897 + 3.59057i) q^{8} -3.00000i q^{9} +(2.55650 + 0.273691i) q^{10} +(-13.3760 - 13.3760i) q^{11} +(3.75090 + 5.82501i) q^{12} +(8.32795 + 8.32795i) q^{13} +(-0.822082 - 1.01921i) q^{14} -2.22664i q^{15} +(-14.5660 - 6.62050i) q^{16} -3.93529 q^{17} +(4.67016 - 3.76691i) q^{18} +(16.8974 - 16.8974i) q^{19} +(2.78397 + 4.32340i) q^{20} +(-0.801857 + 0.801857i) q^{21} +(4.02729 - 37.6181i) q^{22} -23.1787 q^{23} +(-4.35814 + 13.1532i) q^{24} +23.3474i q^{25} +(-2.50740 + 23.4212i) q^{26} +(-3.67423 - 3.67423i) q^{27} +(0.554380 - 2.55950i) q^{28} +(35.6105 + 35.6105i) q^{29} +(3.46626 - 2.79585i) q^{30} +45.5687i q^{31} +(-7.98336 - 30.9882i) q^{32} -32.7644 q^{33} +(-4.94130 - 6.12615i) q^{34} +(-0.595149 + 0.595149i) q^{35} +(11.7280 + 2.54026i) q^{36} +(10.1527 - 10.1527i) q^{37} +(47.5215 + 5.08752i) q^{38} +20.3992 q^{39} +(-3.23467 + 9.76249i) q^{40} -28.4661i q^{41} +(-2.25511 - 0.241425i) q^{42} +(22.7354 + 22.7354i) q^{43} +(63.6176 - 40.9653i) q^{44} +(-2.72707 - 2.72707i) q^{45} +(-29.1040 - 36.0827i) q^{46} +10.7746i q^{47} +(-25.9481 + 9.73123i) q^{48} -48.5714 q^{49} +(-36.3453 + 29.3158i) q^{50} +(-4.81973 + 4.81973i) q^{51} +(-39.6086 + 25.5051i) q^{52} +(41.5142 - 41.5142i) q^{53} +(1.10625 - 10.3333i) q^{54} -24.3182 q^{55} +(4.68053 - 2.35079i) q^{56} -41.3900i q^{57} +(-10.7217 + 100.149i) q^{58} +(-21.0646 - 21.0646i) q^{59} +(8.70472 + 1.88541i) q^{60} +(-68.7531 - 68.7531i) q^{61} +(-70.9377 + 57.2178i) q^{62} +1.96414i q^{63} +(38.2157 - 51.3377i) q^{64} +15.1406 q^{65} +(-41.1402 - 51.0050i) q^{66} +(67.8242 - 67.8242i) q^{67} +(3.33222 - 15.3844i) q^{68} +(-28.3880 + 28.3880i) q^{69} +(-1.67377 - 0.179189i) q^{70} +33.3094 q^{71} +(10.7717 + 21.4469i) q^{72} -18.6331i q^{73} +(28.5531 + 3.05682i) q^{74} +(28.5946 + 28.5946i) q^{75} +(51.7499 + 80.3657i) q^{76} +(8.75745 + 8.75745i) q^{77} +(25.6140 + 31.7559i) q^{78} +6.29222i q^{79} +(-19.2590 + 7.22265i) q^{80} -9.00000 q^{81} +(44.3137 - 35.7431i) q^{82} +(-72.0774 + 72.0774i) q^{83} +(-2.45576 - 3.81371i) q^{84} +(-3.57727 + 3.57727i) q^{85} +(-6.84524 + 63.9400i) q^{86} +87.2275 q^{87} +(143.652 + 47.5973i) q^{88} +10.6131i q^{89} +(0.821074 - 7.66949i) q^{90} +(-5.45242 - 5.45242i) q^{91} +(19.6266 - 90.6135i) q^{92} +(55.8101 + 55.8101i) q^{93} +(-16.7730 + 13.5290i) q^{94} -30.7202i q^{95} +(-47.7302 - 28.1750i) q^{96} +143.631 q^{97} +(-60.9880 - 75.6120i) q^{98} +(-40.1280 + 40.1280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} - 12 q^{8}+O(q^{10}) \) 16 * q + 12 * q^4 - 12 * q^8	\( 16 q + 12 q^{4} - 12 q^{8} - 56 q^{10} + 32 q^{11} - 24 q^{12} - 44 q^{14} + 32 q^{16} + 12 q^{18} - 32 q^{19} + 80 q^{20} + 32 q^{22} - 128 q^{23} + 36 q^{24} - 100 q^{26} - 120 q^{28} + 32 q^{29} + 72 q^{30} + 160 q^{32} + 96 q^{34} + 96 q^{35} + 12 q^{36} - 96 q^{37} + 168 q^{38} + 48 q^{40} - 60 q^{42} + 160 q^{43} + 88 q^{44} + 136 q^{46} - 144 q^{48} + 112 q^{49} - 236 q^{50} - 96 q^{51} - 48 q^{52} - 160 q^{53} - 36 q^{54} - 256 q^{55} - 224 q^{56} + 144 q^{58} - 128 q^{59} - 72 q^{60} - 32 q^{61} - 276 q^{62} - 408 q^{64} - 32 q^{65} + 72 q^{66} + 320 q^{67} - 448 q^{68} + 96 q^{69} - 384 q^{70} + 512 q^{71} + 60 q^{72} + 348 q^{74} + 192 q^{75} + 72 q^{76} + 224 q^{77} + 396 q^{78} + 552 q^{80} - 144 q^{81} - 40 q^{82} - 160 q^{83} + 72 q^{84} + 160 q^{85} + 528 q^{86} + 480 q^{88} - 24 q^{90} - 480 q^{91} + 496 q^{92} + 312 q^{94} - 480 q^{96} - 440 q^{98} + 96 q^{99}+O(q^{100}) \) 16 * q + 12 * q^4 - 12 * q^8 - 56 * q^10 + 32 * q^11 - 24 * q^12 - 44 * q^14 + 32 * q^16 + 12 * q^18 - 32 * q^19 + 80 * q^20 + 32 * q^22 - 128 * q^23 + 36 * q^24 - 100 * q^26 - 120 * q^28 + 32 * q^29 + 72 * q^30 + 160 * q^32 + 96 * q^34 + 96 * q^35 + 12 * q^36 - 96 * q^37 + 168 * q^38 + 48 * q^40 - 60 * q^42 + 160 * q^43 + 88 * q^44 + 136 * q^46 - 144 * q^48 + 112 * q^49 - 236 * q^50 - 96 * q^51 - 48 * q^52 - 160 * q^53 - 36 * q^54 - 256 * q^55 - 224 * q^56 + 144 * q^58 - 128 * q^59 - 72 * q^60 - 32 * q^61 - 276 * q^62 - 408 * q^64 - 32 * q^65 + 72 * q^66 + 320 * q^67 - 448 * q^68 + 96 * q^69 - 384 * q^70 + 512 * q^71 + 60 * q^72 + 348 * q^74 + 192 * q^75 + 72 * q^76 + 224 * q^77 + 396 * q^78 + 552 * q^80 - 144 * q^81 - 40 * q^82 - 160 * q^83 + 72 * q^84 + 160 * q^85 + 528 * q^86 + 480 * q^88 - 24 * q^90 - 480 * q^91 + 496 * q^92 + 312 * q^94 - 480 * q^96 - 440 * q^98 + 96 * q^99

Introduction

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