LMFDB - Embedded newform 48.3.l.a.43.5

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			43.5
Root			$-0.455024 - 1.94755i$ of defining polynomial
Character	$\chi$	$=$	48.43
Dual form			48.3.l.a.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.455024 - 1.94755i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(-3.58591 - 1.77236i) q^{4} +(-3.40572 - 3.40572i) q^{5} +(-2.94254 + 1.82796i) q^{6} +12.1303 q^{7} +(-5.08344 + 6.17727i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(0.455024 - 1.94755i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(-3.58591 - 1.77236i) q^{4} +(-3.40572 - 3.40572i) q^{5} +(-2.94254 + 1.82796i) q^{6} +12.1303 q^{7} +(-5.08344 + 6.17727i) q^{8} +3.00000i q^{9} +(-8.18251 + 5.08314i) q^{10} +(9.81086 - 9.81086i) q^{11} +(2.22113 + 6.56251i) q^{12} +(-7.76859 + 7.76859i) q^{13} +(5.51959 - 23.6244i) q^{14} +8.34229i q^{15} +(9.71745 + 12.7111i) q^{16} +9.73087 q^{17} +(5.84265 + 1.36507i) q^{18} +(11.2823 + 11.2823i) q^{19} +(6.17643 + 18.2488i) q^{20} +(-14.8566 - 14.8566i) q^{21} +(-14.6430 - 23.5713i) q^{22} -20.2635 q^{23} +(13.7915 - 1.33965i) q^{24} -1.80207i q^{25} +(11.5948 + 18.6646i) q^{26} +(3.67423 - 3.67423i) q^{27} +(-43.4982 - 21.4994i) q^{28} +(-16.4069 + 16.4069i) q^{29} +(16.2470 + 3.79594i) q^{30} +26.3542i q^{31} +(29.1771 - 13.1414i) q^{32} -24.0316 q^{33} +(4.42778 - 18.9514i) q^{34} +(-41.3125 - 41.3125i) q^{35} +(5.31709 - 10.7577i) q^{36} +(-23.7263 - 23.7263i) q^{37} +(27.1066 - 16.8392i) q^{38} +19.0291 q^{39} +(38.3509 - 3.72526i) q^{40} +24.7452i q^{41} +(-35.6940 + 22.1738i) q^{42} +(29.8844 - 29.8844i) q^{43} +(-52.5692 + 17.7924i) q^{44} +(10.2172 - 10.2172i) q^{45} +(-9.22036 + 39.4641i) q^{46} +31.3325i q^{47} +(3.66642 - 27.4692i) q^{48} +98.1448 q^{49} +(-3.50963 - 0.819987i) q^{50} +(-11.9178 - 11.9178i) q^{51} +(41.6262 - 14.0887i) q^{52} +(36.8742 + 36.8742i) q^{53} +(-5.48389 - 8.82762i) q^{54} -66.8262 q^{55} +(-61.6638 + 74.9322i) q^{56} -27.6359i q^{57} +(24.4877 + 39.4188i) q^{58} +(-14.1325 + 14.1325i) q^{59} +(14.7856 - 29.9147i) q^{60} +(-42.5199 + 42.5199i) q^{61} +(51.3260 + 11.9918i) q^{62} +36.3910i q^{63} +(-12.3172 - 62.8036i) q^{64} +52.9153 q^{65} +(-10.9350 + 46.8028i) q^{66} +(48.7789 + 48.7789i) q^{67} +(-34.8940 - 17.2467i) q^{68} +(24.8176 + 24.8176i) q^{69} +(-99.2565 + 61.6601i) q^{70} +7.73935 q^{71} +(-18.5318 - 15.2503i) q^{72} -85.4163i q^{73} +(-57.0041 + 35.4121i) q^{74} +(-2.20708 + 2.20708i) q^{75} +(-20.4610 - 60.4537i) q^{76} +(119.009 - 119.009i) q^{77} +(8.65869 - 37.0601i) q^{78} -105.294i q^{79} +(10.1954 - 76.3854i) q^{80} -9.00000 q^{81} +(48.1926 + 11.2597i) q^{82} +(-62.1229 - 62.1229i) q^{83} +(26.9430 + 79.6054i) q^{84} +(-33.1407 - 33.1407i) q^{85} +(-44.6033 - 71.7996i) q^{86} +40.1885 q^{87} +(10.7313 + 110.477i) q^{88} +127.172i q^{89} +(-15.2494 - 24.5475i) q^{90} +(-94.2355 + 94.2355i) q^{91} +(72.6629 + 35.9142i) q^{92} +(32.2771 - 32.2771i) q^{93} +(61.0215 + 14.2570i) q^{94} -76.8489i q^{95} +(-51.8294 - 19.6397i) q^{96} -147.348 q^{97} +(44.6582 - 191.142i) q^{98} +(29.4326 + 29.4326i) 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 $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.455024	−	1.94755i	0.227512	−	0.973775i
$2$	0.455024	−	1.94755i	0.227512	−	0.973775i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$4$	−3.58591	−	1.77236i	−0.896477	−	0.443091i
$5$	−3.40572	−	3.40572i	−0.681145	−	0.681145i	0.279113	−	0.960258i	$-0.409960\pi$
$5$	−3.40572	−	3.40572i	−0.681145	−	0.681145i	−0.960258	+	0.279113i	$0.909960\pi$
$6$	−2.94254	+	1.82796i	−0.490423	+	0.304661i
$7$	12.1303			1.73290			0.866452	−	0.499261i	$-0.166395\pi$
$7$	12.1303			1.73290			0.866452	+	0.499261i	$0.166395\pi$
$8$	−5.08344	+	6.17727i	−0.635430	+	0.772158i
$9$			3.00000i			0.333333i
$10$	−8.18251	+	5.08314i	−0.818251	+	0.508314i
$11$	9.81086	−	9.81086i	0.891896	−	0.891896i	−0.102805	−	0.994702i	$-0.532782\pi$
$11$	9.81086	−	9.81086i	0.891896	−	0.891896i	0.994702	+	0.102805i	$0.0327818\pi$
$12$	2.22113	+	6.56251i	0.185094	+	0.546876i
$13$	−7.76859	+	7.76859i	−0.597584	+	0.597584i	−0.939669	−	0.342085i	$-0.888867\pi$
$13$	−7.76859	+	7.76859i	−0.597584	+	0.597584i	0.342085	+	0.939669i	$0.388867\pi$
$14$	5.51959	−	23.6244i	0.394256	−	1.68746i
$15$			8.34229i			0.556153i
$16$	9.71745	+	12.7111i	0.607341	+	0.794442i
$17$	9.73087			0.572404			0.286202	−	0.958169i	$-0.407607\pi$
$17$	9.73087			0.572404			0.286202	+	0.958169i	$0.407607\pi$
$18$	5.84265	+	1.36507i	0.324592	+	0.0758373i
$19$	11.2823	+	11.2823i	0.593806	+	0.593806i	0.938657	−	0.344851i	$-0.112071\pi$
$19$	11.2823	+	11.2823i	0.593806	+	0.593806i	−0.344851	+	0.938657i	$0.612071\pi$
$20$	6.17643	+	18.2488i	0.308821	+	0.912440i
$21$	−14.8566	−	14.8566i	−0.707455	−	0.707455i
$22$	−14.6430	−	23.5713i	−0.665589	−	1.07142i
$23$	−20.2635			−0.881020			−0.440510	−	0.897748i	$-0.645202\pi$
$23$	−20.2635			−0.881020			−0.440510	+	0.897748i	$0.645202\pi$
$24$	13.7915	−	1.33965i	0.574646	−	0.0558189i
$25$		−	1.80207i		−	0.0720830i
$26$	11.5948	+	18.6646i	0.445955	+	0.717870i
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	−43.4982	−	21.4994i	−1.55351	−	0.767834i
$29$	−16.4069	+	16.4069i	−0.565754	+	0.565754i	−0.930936	−	0.365182i	$-0.881007\pi$
$29$	−16.4069	+	16.4069i	−0.565754	+	0.565754i	0.365182	+	0.930936i	$0.381007\pi$
$30$	16.2470	+	3.79594i	0.541568	+	0.126531i
$31$			26.3542i			0.850134i	0.905162	+	0.425067i	$0.139749\pi$
$31$			26.3542i			0.850134i	−0.905162	+	0.425067i	$0.860251\pi$
$32$	29.1771	−	13.1414i	0.911785	−	0.410668i
$33$	−24.0316			−0.728230
$34$	4.42778	−	18.9514i	0.130229	−	0.557393i
$35$	−41.3125	−	41.3125i	−1.18036	−	1.18036i
$36$	5.31709	−	10.7577i	0.147697	−	0.298826i
$37$	−23.7263	−	23.7263i	−0.641250	−	0.641250i	0.309613	−	0.950863i	$-0.399801\pi$
$37$	−23.7263	−	23.7263i	−0.641250	−	0.641250i	−0.950863	+	0.309613i	$0.899801\pi$
$38$	27.1066	−	16.8392i	0.713332	−	0.443136i
$39$	19.0291			0.487925
$40$	38.3509	−	3.72526i	0.958772	−	0.0931315i
$41$			24.7452i			0.603542i	0.953380	+	0.301771i	$0.0975779\pi$
$41$			24.7452i			0.603542i	−0.953380	+	0.301771i	$0.902422\pi$
$42$	−35.6940	+	22.1738i	−0.849856	+	0.527948i
$43$	29.8844	−	29.8844i	0.694987	−	0.694987i	−0.268338	−	0.963325i	$-0.586474\pi$
$43$	29.8844	−	29.8844i	0.694987	−	0.694987i	0.963325	+	0.268338i	$0.0864744\pi$
$44$	−52.5692	+	17.7924i	−1.19476	+	0.404373i
$45$	10.2172	−	10.2172i	0.227048	−	0.227048i
$46$	−9.22036	+	39.4641i	−0.200443	+	0.857915i
$47$			31.3325i			0.666648i	0.942812	+	0.333324i	$0.108170\pi$
$47$			31.3325i			0.666648i	−0.942812	+	0.333324i	$0.891830\pi$
$48$	3.66642	−	27.4692i	0.0763837	−	0.572275i
$49$	98.1448			2.00295
$50$	−3.50963	−	0.819987i	−0.0701926	−	0.0163997i
$51$	−11.9178	−	11.9178i	−0.233683	−	0.233683i
$52$	41.6262	−	14.0887i	0.800504	−	0.270936i
$53$	36.8742	+	36.8742i	0.695739	+	0.695739i	0.963489	−	0.267750i	$-0.0862800\pi$
$53$	36.8742	+	36.8742i	0.695739	+	0.695739i	−0.267750	+	0.963489i	$0.586280\pi$
$54$	−5.48389	−	8.82762i	−0.101554	−	0.163474i
$55$	−66.8262			−1.21502
$56$	−61.6638	+	74.9322i	−1.10114	+	1.33808i
$57$		−	27.6359i		−	0.484841i
$58$	24.4877	+	39.4188i	0.422202	+	0.679634i
$59$	−14.1325	+	14.1325i	−0.239534	+	0.239534i	−0.816657	−	0.577123i	$-0.804175\pi$
$59$	−14.1325	+	14.1325i	−0.239534	+	0.239534i	0.577123	+	0.816657i	$0.304175\pi$
$60$	14.7856	−	29.9147i	0.246426	−	0.498578i
$61$	−42.5199	+	42.5199i	−0.697048	+	0.697048i	−0.963773	−	0.266725i	$-0.914059\pi$
$61$	−42.5199	+	42.5199i	−0.697048	+	0.697048i	0.266725	+	0.963773i	$0.414059\pi$
$62$	51.3260	+	11.9918i	0.827839	+	0.193416i
$63$			36.3910i			0.577634i
$64$	−12.3172	−	62.8036i	−0.192457	−	0.981305i
$65$	52.9153			0.814082
$66$	−10.9350	+	46.8028i	−0.165681	+	0.709133i
$67$	48.7789	+	48.7789i	0.728044	+	0.728044i	0.970230	−	0.242186i	$-0.0778644\pi$
$67$	48.7789	+	48.7789i	0.728044	+	0.728044i	−0.242186	+	0.970230i	$0.577864\pi$
$68$	−34.8940	−	17.2467i	−0.513147	−	0.253627i
$69$	24.8176	+	24.8176i	0.359675	+	0.359675i
$70$	−99.2565	+	61.6601i	−1.41795	+	0.880858i
$71$	7.73935			0.109005			0.0545025	−	0.998514i	$-0.482643\pi$
$71$	7.73935			0.109005			0.0545025	+	0.998514i	$0.482643\pi$
$72$	−18.5318	−	15.2503i	−0.257386	−	0.211810i
$73$		−	85.4163i		−	1.17009i	−0.811002	−	0.585043i	$-0.801077\pi$
$73$		−	85.4163i		−	1.17009i	0.811002	−	0.585043i	$-0.198923\pi$
$74$	−57.0041	+	35.4121i	−0.770326	+	0.478541i
$75$	−2.20708	+	2.20708i	−0.0294278	+	0.0294278i
$76$	−20.4610	−	60.4537i	−0.269223	−	0.795443i
$77$	119.009	−	119.009i	1.54557	−	1.54557i
$78$	8.65869	−	37.0601i	0.111009	−	0.475129i
$79$		−	105.294i		−	1.33283i	−0.745581	−	0.666416i	$-0.767828\pi$
$79$		−	105.294i		−	1.33283i	0.745581	−	0.666416i	$-0.232172\pi$
$80$	10.1954	−	76.3854i	0.127443	−	0.954817i
$81$	−9.00000			−0.111111
$82$	48.1926	+	11.2597i	0.587715	+	0.137313i
$83$	−62.1229	−	62.1229i	−0.748469	−	0.748469i	0.225723	−	0.974192i	$-0.427526\pi$
$83$	−62.1229	−	62.1229i	−0.748469	−	0.748469i	−0.974192	+	0.225723i	$0.927526\pi$
$84$	26.9430	+	79.6054i	0.320750	+	0.947684i
$85$	−33.1407	−	33.1407i	−0.389890	−	0.389890i
$86$	−44.6033	−	71.7996i	−0.518643	−	0.834879i
$87$	40.1885			0.461937
$88$	10.7313	+	110.477i	0.121947	+	1.25542i
$89$			127.172i			1.42890i	0.699685	+	0.714451i	$0.253324\pi$
$89$			127.172i			1.42890i	−0.699685	+	0.714451i	$0.746676\pi$
$90$	−15.2494	−	24.5475i	−0.169438	−	0.272750i
$91$	−94.2355	+	94.2355i	−1.03555	+	1.03555i
$92$	72.6629	+	35.9142i	0.789814	+	0.390372i
$93$	32.2771	−	32.2771i	0.347066	−	0.347066i
$94$	61.0215	+	14.2570i	0.649165	+	0.151670i
$95$		−	76.8489i		−	0.808936i
$96$	−51.8294	−	19.6397i	−0.539889	−	0.204580i
$97$	−147.348			−1.51905			−0.759525	−	0.650478i	$-0.774569\pi$
$97$	−147.348			−1.51905			−0.759525	+	0.650478i	$0.774569\pi$
$98$	44.6582	−	191.142i	0.455696	−	1.95043i
$99$	29.4326	+	29.4326i	0.297299	+	0.297299i
$100$	−3.19393	+	6.46207i	−0.0319393	+	0.0646207i
$101$	12.7690	+	12.7690i	0.126426	+	0.126426i	0.767489	−	0.641063i	$-0.221506\pi$
$101$	12.7690	+	12.7690i	0.126426	+	0.126426i	−0.641063	+	0.767489i	$0.721506\pi$
$102$	−28.6335	+	17.7877i	−0.280721	+	0.174389i
$103$	−17.7621			−0.172448			−0.0862240	−	0.996276i	$-0.527480\pi$
$103$	−17.7621			−0.172448			−0.0862240	+	0.996276i	$0.527480\pi$
$104$	−8.49746	−	87.4798i	−0.0817063	−	0.841152i
$105$			101.195i			0.963759i
$106$	88.5929	−	55.0357i	0.835782	−	0.519204i
$107$	−15.8889	+	15.8889i	−0.148494	+	0.148494i	−0.777445	−	0.628951i	$-0.783485\pi$
$107$	−15.8889	+	15.8889i	−0.148494	+	0.148494i	0.628951	+	0.777445i	$0.283485\pi$
$108$	−19.6875	+	6.66338i	−0.182292	+	0.0616980i
$109$	−79.3257	+	79.3257i	−0.727758	+	0.727758i	−0.970173	−	0.242414i	$-0.922061\pi$
$109$	−79.3257	+	79.3257i	−0.727758	+	0.727758i	0.242414	+	0.970173i	$0.422061\pi$
$110$	−30.4075	+	130.147i	−0.276432	+	1.18316i
$111$			58.1172i			0.523579i
$112$	117.876	+	154.189i	1.05246	+	1.37669i
$113$	−167.538			−1.48263			−0.741317	−	0.671155i	$-0.765799\pi$
$113$	−167.538			−1.48263			−0.741317	+	0.671155i	$0.765799\pi$
$114$	−53.8223	−	12.5750i	−0.472126	−	0.110307i
$115$	69.0118	+	69.0118i	0.600102	+	0.600102i
$116$	87.9125	−	29.7546i	0.757866	−	0.256505i
$117$	−23.3058	−	23.3058i	−0.199195	−	0.199195i
$118$	21.0932	+	33.9545i	0.178756	+	0.287750i
$119$	118.039			0.991921
$120$	−51.5325	−	42.4075i	−0.429438	−	0.353396i
$121$		−	71.5059i		−	0.590958i
$122$	63.4621	+	102.157i	0.520181	+	0.837355i
$123$	30.3066	−	30.3066i	0.246395	−	0.246395i
$124$	46.7092	−	94.5035i	0.376687	−	0.762125i
$125$	−91.2805	+	91.2805i	−0.730244	+	0.730244i
$126$	70.8733	+	16.5588i	0.562486	+	0.131419i
$127$		−	198.247i		−	1.56100i	−0.625156	−	0.780500i	$-0.714965\pi$
$127$		−	198.247i		−	1.56100i	0.625156	−	0.780500i	$-0.285035\pi$
$128$	−127.918	−	4.58871i	−0.999357	−	0.0358493i
$129$	−73.2016			−0.567454
$130$	24.0778	−	103.055i	0.185213	−	0.792733i
$131$	134.339	+	134.339i	1.02549	+	1.02549i	0.999667	+	0.0258197i	$0.00821957\pi$
$131$	134.339	+	134.339i	1.02549	+	1.02549i	0.0258197	+	0.999667i	$0.491780\pi$
$132$	86.1751	+	42.5927i	0.652841	+	0.322672i
$133$	136.858	+	136.858i	1.02901	+	1.02901i
$134$	117.195	−	72.8039i	0.874590	−	0.543313i
$135$	−25.0269			−0.185384
$136$	−49.4663	+	60.1102i	−0.363723	+	0.441987i
$137$		−	255.937i		−	1.86816i	−0.357069	−	0.934078i	$-0.616224\pi$
$137$		−	255.937i		−	1.86816i	0.357069	−	0.934078i	$-0.383776\pi$
$138$	59.6261	−	37.0409i	0.432073	−	0.268412i
$139$	−21.7231	+	21.7231i	−0.156281	+	0.156281i	−0.780917	−	0.624635i	$-0.785248\pi$
$139$	−21.7231	+	21.7231i	−0.156281	+	0.156281i	0.624635	+	0.780917i	$0.285248\pi$
$140$	74.9220	+	221.364i	0.535157	+	1.58117i
$141$	38.3743	−	38.3743i	0.272158	−	0.272158i
$142$	3.52159	−	15.0728i	0.0247999	−	0.106146i
$143$			152.433i			1.06597i
$144$	−38.1332	+	29.1523i	−0.264814	+	0.202447i
$145$	111.755			0.770722
$146$	−166.353	−	38.8665i	−1.13940	−	0.266209i
$147$	−120.202	−	120.202i	−0.817703	−	0.817703i
$148$	43.0286	+	127.132i	0.290734	+	0.858998i
$149$	−34.2444	−	34.2444i	−0.229828	−	0.229828i	0.582793	−	0.812621i	$-0.301960\pi$
$149$	−34.2444	−	34.2444i	−0.229828	−	0.229828i	−0.812621	+	0.582793i	$0.801960\pi$
$150$	3.29413	+	5.30268i	0.0219609	+	0.0353512i
$151$	−14.4645			−0.0957913			−0.0478956	−	0.998852i	$-0.515251\pi$
$151$	−14.4645			−0.0957913			−0.0478956	+	0.998852i	$0.515251\pi$
$152$	−127.047	+	12.3409i	−0.835835	+	0.0811898i
$153$			29.1926i			0.190801i
$154$	−177.624	−	285.928i	−1.15340	−	1.85667i
$155$	89.7550	−	89.7550i	0.579064	−	0.579064i
$156$	−68.2365	−	33.7265i	−0.437413	−	0.216195i
$157$	31.4652	−	31.4652i	0.200415	−	0.200415i	−0.599763	−	0.800178i	$-0.704738\pi$
$157$	31.4652	−	31.4652i	0.200415	−	0.200415i	0.800178	+	0.599763i	$0.204738\pi$
$158$	−205.065	−	47.9111i	−1.29788	−	0.303235i
$159$		−	90.3229i		−	0.568068i
$160$	−144.125	−	54.6133i	−0.900782	−	0.341333i
$161$	−245.802			−1.52672
$162$	−4.09522	+	17.5280i	−0.0252791	+	0.108197i
$163$	31.4002	+	31.4002i	0.192640	+	0.192640i	0.796836	−	0.604196i	$-0.206506\pi$
$163$	31.4002	+	31.4002i	0.192640	+	0.192640i	−0.604196	+	0.796836i	$0.706506\pi$
$164$	43.8576	−	88.7341i	0.267424	−	0.541062i
$165$	81.8450	+	81.8450i	0.496030	+	0.496030i
$166$	−149.255	+	92.7201i	−0.899126	+	0.558555i
$167$	36.4796			0.218441			0.109220	−	0.994018i	$-0.465165\pi$
$167$	36.4796			0.218441			0.109220	+	0.994018i	$0.465165\pi$
$168$	167.295	−	16.2504i	0.995805	−	0.0967288i
$169$			48.2981i			0.285788i
$170$	−79.6229	+	49.4633i	−0.468370	+	0.290961i
$171$	−33.8469	+	33.8469i	−0.197935	+	0.197935i
$172$	−160.129	+	54.1967i	−0.930982	+	0.315097i
$173$	97.6419	−	97.6419i	0.564404	−	0.564404i	−0.366151	−	0.930555i	$-0.619325\pi$
$173$	97.6419	−	97.6419i	0.564404	−	0.564404i	0.930555	+	0.366151i	$0.119325\pi$
$174$	18.2867	−	78.2691i	0.105096	−	0.449822i
$175$		−	21.8598i		−	0.124913i
$176$	220.043	+	29.3700i	1.25024	+	0.166875i
$177$	34.6175			0.195579
$178$	247.674	+	57.8664i	1.39143	+	0.325092i
$179$	89.7427	+	89.7427i	0.501356	+	0.501356i	0.911859	−	0.410503i	$-0.134647\pi$
$179$	89.7427	+	89.7427i	0.501356	+	0.501356i	−0.410503	+	0.911859i	$0.634647\pi$
$180$	−54.7464	+	18.5293i	−0.304147	+	0.102940i
$181$	−115.497	−	115.497i	−0.638108	−	0.638108i	0.311981	−	0.950088i	$-0.399008\pi$
$181$	−115.497	−	115.497i	−0.638108	−	0.638108i	−0.950088	+	0.311981i	$0.899008\pi$
$182$	140.649	+	226.408i	0.772796	+	1.24400i
$183$	104.152			0.569137
$184$	103.008	−	125.173i	0.559827	−	0.680287i
$185$			161.610i			0.873569i
$186$	−48.1744	−	77.5482i	−0.259002	−	0.416926i
$187$	95.4682	−	95.4682i	0.510525	−	0.510525i
$188$	55.5325	−	112.355i	0.295386	−	0.597634i
$189$	44.5697	−	44.5697i	0.235818	−	0.235818i
$190$	−149.667	−	34.9681i	−0.787722	−	0.184043i
$191$		−	62.6278i		−	0.327894i	−0.986469	−	0.163947i	$-0.947577\pi$
$191$		−	62.6278i		−	0.327894i	0.986469	−	0.163947i	$-0.0524227\pi$
$192$	−61.8329	+	92.0038i	−0.322046	+	0.479186i
$193$	223.342			1.15721			0.578607	−	0.815607i	$-0.303597\pi$
$193$	223.342			1.15721			0.578607	+	0.815607i	$0.303597\pi$
$194$	−67.0468	+	286.967i	−0.345602	+	1.47921i
$195$	−64.8078	−	64.8078i	−0.332348	−	0.332348i
$196$	−351.938	−	173.948i	−1.79560	−	0.887491i
$197$	29.0959	+	29.0959i	0.147695	+	0.147695i	0.777087	−	0.629393i	$-0.216696\pi$
$197$	29.0959	+	29.0959i	0.147695	+	0.147695i	−0.629393	+	0.777087i	$0.716696\pi$
$198$	70.7140	−	43.9289i	0.357141	−	0.221863i
$199$	11.6967			0.0587776			0.0293888	−	0.999568i	$-0.490644\pi$
$199$	11.6967			0.0587776			0.0293888	+	0.999568i	$0.490644\pi$
$200$	11.1319	+	9.16074i	0.0556595	+	0.0458037i
$201$		−	119.484i		−	0.594445i
$202$	30.6786	−	19.0581i	0.151874	−	0.0943472i
$203$	−199.021	+	199.021i	−0.980398	+	0.980398i
$204$	21.6135	+	63.8590i	0.105949	+	0.313034i
$205$	84.2755	−	84.2755i	0.411100	−	0.411100i
$206$	−8.08220	+	34.5927i	−0.0392340	+	0.167926i
$207$		−	60.7904i		−	0.293673i
$208$	−174.238	−	23.2562i	−0.837682	−	0.111809i
$209$	221.378			1.05923
$210$	197.082	+	46.0460i	0.938484	+	0.219267i
$211$	−0.215765	−	0.215765i	−0.00102258	−	0.00102258i	0.706595	−	0.707618i	$-0.250230\pi$
$211$	−0.215765	−	0.215765i	−0.00102258	−	0.00102258i	−0.707618	+	0.706595i	$0.750230\pi$
$212$	−66.8728	−	197.582i	−0.315438	−	0.931989i
$213$	−9.47873	−	9.47873i	−0.0445011	−	0.0445011i
$214$	23.7146	+	38.1742i	0.110816	+	0.178384i
$215$	−203.556			−0.946773
$216$	4.01896	+	41.3745i	0.0186063	+	0.191549i
$217$			319.684i			1.47320i
$218$	118.396	+	190.586i	0.543099	+	0.874247i
$219$	−104.613	+	104.613i	−0.477686	+	0.477686i
$220$	239.632	+	118.440i	1.08924	+	0.538365i
$221$	−75.5951	+	75.5951i	−0.342059	+	0.342059i
$222$	113.186	+	26.4447i	0.509848	+	0.119120i
$223$			371.347i			1.66523i	0.553850	+	0.832617i	$0.313158\pi$
$223$			371.347i			1.66523i	−0.553850	+	0.832617i	$0.686842\pi$
$224$	353.928	−	159.409i	1.58004	−	0.711648i
$225$	5.40622			0.0240277
$226$	−76.2337	+	326.288i	−0.337317	+	1.44375i
$227$	−209.823	−	209.823i	−0.924330	−	0.924330i	0.0730018	−	0.997332i	$-0.476742\pi$
$227$	−209.823	−	209.823i	−0.924330	−	0.924330i	−0.997332	+	0.0730018i	$0.976742\pi$
$228$	−48.9809	+	99.0998i	−0.214829	+	0.434648i
$229$	152.751	+	152.751i	0.667037	+	0.667037i	0.957029	−	0.289992i	$-0.0936527\pi$
$229$	152.751	+	152.751i	0.667037	+	0.667037i	−0.289992	+	0.957029i	$0.593653\pi$
$230$	165.806	−	103.002i	0.720895	−	0.447834i
$231$	−291.511			−1.26195
$232$	−17.9462	−	184.753i	−0.0773544	−	0.796350i
$233$		−	272.899i		−	1.17124i	−0.810586	−	0.585619i	$-0.800851\pi$
$233$		−	272.899i		−	1.17124i	0.810586	−	0.585619i	$-0.199149\pi$
$234$	−55.9938	+	34.7845i	−0.239290	+	0.148652i
$235$	106.710	−	106.710i	0.454084	−	0.454084i
$236$	75.7259	−	25.6299i	0.320873	−	0.108601i
$237$	−128.958	+	128.958i	−0.544126	+	0.544126i
$238$	53.7104	−	229.886i	0.225674	−	0.965908i
$239$			104.650i			0.437866i	0.975740	+	0.218933i	$0.0702576\pi$
$239$			104.650i			0.437866i	−0.975740	+	0.218933i	$0.929742\pi$
$240$	−106.039	+	81.0658i	−0.441831	+	0.337774i
$241$	148.875			0.617737			0.308869	−	0.951105i	$-0.400050\pi$
$241$	148.875			0.617737			0.308869	+	0.951105i	$0.400050\pi$
$242$	−139.261	−	32.5369i	−0.575460	−	0.134450i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$	227.833	−	77.1117i	0.933743	−	0.316031i
$245$	−334.254	−	334.254i	−1.36430	−	1.36430i
$246$	−45.2334	−	72.8139i	−0.183876	−	0.295991i
$247$	−175.295			−0.709698
$248$	−162.797	−	133.970i	−0.656438	−	0.540201i
$249$			152.169i			0.611122i
$250$	136.239	+	219.308i	0.544954	+	0.877233i
$251$	143.712	−	143.712i	0.572558	−	0.572558i	−0.360284	−	0.932843i	$-0.617320\pi$
$251$	143.712	−	143.712i	0.572558	−	0.572558i	0.932843	+	0.360284i	$0.117320\pi$
$252$	64.4981	−	130.495i	0.255945	−	0.517836i
$253$	−198.802	+	198.802i	−0.785778	+	0.785778i
$254$	−386.096	−	90.2071i	−1.52006	−	0.355146i
$255$			81.1777i			0.318344i
$256$	−67.1424	+	247.038i	−0.262275	+	0.964993i
$257$	134.023			0.521489			0.260745	−	0.965408i	$-0.416032\pi$
$257$	134.023			0.521489			0.260745	+	0.965408i	$0.416032\pi$
$258$	−33.3085	+	142.564i	−0.129103	+	0.552573i
$259$	−287.807	−	287.807i	−1.11122	−	1.11122i
$260$	−189.749	−	93.7853i	−0.729806	−	0.360713i
$261$	−49.2206	−	49.2206i	−0.188585	−	0.188585i
$262$	322.759	−	200.504i	1.23190	−	0.765283i
$263$	290.386			1.10413			0.552066	−	0.833801i	$-0.313840\pi$
$263$	290.386			1.10413			0.552066	+	0.833801i	$0.313840\pi$
$264$	122.163	−	148.450i	0.462740	−	0.562309i
$265$		−	251.166i		−	0.947798i
$266$	328.812	−	204.264i	1.23613	−	0.767911i
$267$	155.754	−	155.754i	0.583347	−	0.583347i
$268$	−88.4627	−	261.371i	−0.330085	−	0.975264i
$269$	−74.2628	+	74.2628i	−0.276070	+	0.276070i	−0.831538	−	0.555468i	$-0.812539\pi$
$269$	−74.2628	+	74.2628i	−0.276070	+	0.276070i	0.555468	+	0.831538i	$0.312539\pi$
$270$	−11.3878	+	48.7411i	−0.0421771	+	0.180523i
$271$		−	70.8329i		−	0.261376i	−0.991424	−	0.130688i	$-0.958281\pi$
$271$		−	70.8329i		−	0.261376i	0.991424	−	0.130688i	$-0.0417186\pi$
$272$	94.5593	+	123.690i	0.347644	+	0.454742i
$273$	230.829			0.845527
$274$	−498.451	−	116.458i	−1.81916	−	0.425028i
$275$	−17.6799	−	17.6799i	−0.0642906	−	0.0642906i
$276$	−45.0077	−	132.979i	−0.163071	−	0.481809i
$277$	−96.6953	−	96.6953i	−0.349081	−	0.349081i	0.510686	−	0.859767i	$-0.329391\pi$
$277$	−96.6953	−	96.6953i	−0.349081	−	0.349081i	−0.859767	+	0.510686i	$0.829391\pi$
$278$	32.4223	+	52.1914i	0.116627	+	0.187739i
$279$	−79.0625			−0.283378
$280$	465.209	−	45.1886i	1.66146	−	0.161388i
$281$			138.151i			0.491640i	0.969316	+	0.245820i	$0.0790572\pi$
$281$			138.151i			0.491640i	−0.969316	+	0.245820i	$0.920943\pi$
$282$	−57.2746	−	92.1970i	−0.203101	−	0.326940i
$283$	−295.011	+	295.011i	−1.04244	+	1.04244i	−0.0433821	+	0.999059i	$0.513813\pi$
$283$	−295.011	+	295.011i	−1.04244	+	1.04244i	−0.999059	+	0.0433821i	$0.986187\pi$
$284$	−27.7526	−	13.7170i	−0.0977204	−	0.0482991i
$285$	−94.1203	+	94.1203i	−0.330247	+	0.330247i
$286$	296.871	+	69.3607i	1.03801	+	0.242520i
$287$			300.168i			1.04588i
$288$	39.4241	+	87.5313i	0.136889	+	0.303928i
$289$	−194.310			−0.672353
$290$	50.8510	−	217.648i	0.175348	−	0.750510i
$291$	180.464	+	180.464i	0.620150	+	0.620150i
$292$	−151.389	+	306.295i	−0.518455	+	1.04896i
$293$	−33.4759	−	33.4759i	−0.114252	−	0.114252i	0.647669	−	0.761922i	$-0.275744\pi$
$293$	−33.4759	−	33.4759i	−0.114252	−	0.114252i	−0.761922	+	0.647669i	$0.775744\pi$
$294$	−288.795	+	179.405i	−0.982296	+	0.610221i
$295$	96.2630			0.326315
$296$	267.174	−	25.9523i	0.902616	−	0.0876768i
$297$		−	72.0948i		−	0.242743i
$298$	−82.2748	+	51.1107i	−0.276090	+	0.171513i
$299$	157.418	−	157.418i	0.526483	−	0.526483i
$300$	11.8261	−	4.00264i	0.0394205	−	0.0133421i
$301$	362.508	−	362.508i	1.20434	−	1.20434i
$302$	−6.58169	+	28.1703i	−0.0217937	+	0.0932792i
$303$		−	31.2776i		−	0.103226i
$304$	−33.7749	+	253.046i	−0.111102	+	0.832387i
$305$	289.622			0.949582
$306$	56.8541	+	13.2833i	0.185798	+	0.0434096i
$307$	−92.6638	−	92.6638i	−0.301836	−	0.301836i	0.539896	−	0.841732i	$-0.318464\pi$
$307$	−92.6638	−	92.6638i	−0.301836	−	0.301836i	−0.841732	+	0.539896i	$0.818464\pi$
$308$	−637.682	+	215.828i	−2.07040	+	0.700739i
$309$	21.7541	+	21.7541i	0.0704016	+	0.0704016i
$310$	−133.962	−	215.643i	−0.432135	−	0.695623i
$311$	−18.5610			−0.0596817			−0.0298408	−	0.999555i	$-0.509500\pi$
$311$	−18.5610			−0.0596817			−0.0298408	+	0.999555i	$0.509500\pi$
$312$	−96.7332	+	117.548i	−0.310042	+	0.376755i
$313$			55.1534i			0.176209i	0.996111	+	0.0881045i	$0.0280809\pi$
$313$			55.1534i			0.176209i	−0.996111	+	0.0881045i	$0.971919\pi$
$314$	−46.9626	−	75.5975i	−0.149563	−	0.240756i
$315$	123.938	−	123.938i	0.393453	−	0.393453i
$316$	−186.619	+	377.573i	−0.590566	+	1.19485i
$317$	62.2977	−	62.2977i	0.196523	−	0.196523i	−0.601985	−	0.798507i	$-0.705623\pi$
$317$	62.2977	−	62.2977i	0.196523	−	0.196523i	0.798507	+	0.601985i	$0.205623\pi$
$318$	−175.908	−	41.0991i	−0.553171	−	0.129242i
$319$			321.931i			1.00919i
$320$	−171.943	+	255.841i	−0.537320	+	0.799502i
$321$	38.9197			0.121245
$322$	−111.846	+	478.712i	−0.347348	+	1.48668i
$323$	109.787	+	109.787i	0.339897	+	0.339897i
$324$	32.2732	+	15.9513i	0.0996085	+	0.0492323i
$325$	13.9996	+	13.9996i	0.0430756	+	0.0430756i
$326$	75.4414	−	46.8657i	0.231415	−	0.143760i
$327$	194.307			0.594212
$328$	−152.858	−	125.791i	−0.466030	−	0.383509i
$329$			380.073i			1.15524i
$330$	196.639	−	122.156i	0.595875	−	0.370169i
$331$	373.767	−	373.767i	1.12921	−	1.12921i	0.138899	−	0.990307i	$-0.455644\pi$
$331$	373.767	−	373.767i	1.12921	−	1.12921i	0.990307	−	0.138899i	$-0.0443564\pi$
$332$	112.663	+	332.871i	0.339345	+	1.00262i
$333$	71.1788	−	71.1788i	0.213750	−	0.213750i
$334$	16.5991	−	71.0459i	0.0496979	−	0.212712i
$335$		−	332.255i		−	0.991807i
$336$	44.4748	−	333.210i	0.132366	−	0.991698i
$337$	−519.936			−1.54284			−0.771419	−	0.636328i	$-0.780453\pi$
$337$	−519.936			−1.54284			−0.771419	+	0.636328i	$0.780453\pi$
$338$	94.0630	+	21.9768i	0.278293	+	0.0650201i
$339$	205.191	+	205.191i	0.605283	+	0.605283i
$340$	60.1020	+	177.577i	0.176771	+	0.522284i
$341$	258.557	+	258.557i	0.758231	+	0.758231i
$342$	50.5175	+	81.3198i	0.147712	+	0.237777i
$343$	596.142			1.73802
$344$	32.6883	+	336.520i	0.0950240	+	0.978255i
$345$		−	169.044i		−	0.489981i
$346$	−145.733	−	234.592i	−0.421194	−	0.678011i
$347$	122.160	−	122.160i	0.352045	−	0.352045i	−0.508825	−	0.860870i	$-0.669920\pi$
$347$	122.160	−	122.160i	0.352045	−	0.352045i	0.860870	+	0.508825i	$0.169920\pi$
$348$	−144.112	−	71.2286i	−0.414115	−	0.204680i
$349$	−279.483	+	279.483i	−0.800810	+	0.800810i	−0.983222	−	0.182412i	$-0.941609\pi$
$349$	−279.483	+	279.483i	−0.800810	+	0.800810i	0.182412	+	0.983222i	$0.441609\pi$
$350$	−42.5730	−	9.94671i	−0.121637	−	0.0284192i
$351$			57.0872i			0.162642i
$352$	157.324	−	415.181i	0.446944	−	1.17949i
$353$	−212.266			−0.601320			−0.300660	−	0.953731i	$-0.597207\pi$
$353$	−212.266			−0.601320			−0.300660	+	0.953731i	$0.597207\pi$
$354$	15.7518	−	67.4193i	0.0444966	−	0.190450i
$355$	−26.3581	−	26.3581i	−0.0742482	−	0.0742482i
$356$	225.396	−	456.028i	0.633134	−	1.28098i
$357$	−144.567	−	144.567i	−0.404950	−	0.404950i
$358$	215.614	−	133.943i	0.602272	−	0.374144i
$359$	−435.033			−1.21179			−0.605895	−	0.795545i	$-0.707185\pi$
$359$	−435.033			−1.21179			−0.605895	+	0.795545i	$0.707185\pi$
$360$	11.1758	+	115.053i	0.0310438	+	0.319591i
$361$		−	106.419i		−	0.294789i
$362$	−277.491	+	172.383i	−0.766551	+	0.476196i
$363$	−87.5765	+	87.5765i	−0.241258	+	0.241258i
$364$	504.939	−	170.900i	1.38720	−	0.469505i
$365$	−290.905	+	290.905i	−0.796999	+	0.796999i
$366$	47.3917	−	202.842i	0.129486	−	0.554212i
$367$		−	125.535i		−	0.342058i	−0.985266	−	0.171029i	$-0.945291\pi$
$367$		−	125.535i		−	0.342058i	0.985266	−	0.171029i	$-0.0547091\pi$
$368$	−196.909	−	257.570i	−0.535079	−	0.699919i
$369$	−74.2357			−0.201181
$370$	314.744	+	73.5365i	0.850660	+	0.198747i
$371$	447.295	+	447.295i	1.20565	+	1.20565i
$372$	−172.950	+	58.5359i	−0.464918	+	0.157355i
$373$	−302.389	−	302.389i	−0.810694	−	0.810694i	0.174044	−	0.984738i	$-0.444317\pi$
$373$	−302.389	−	302.389i	−0.810694	−	0.810694i	−0.984738	+	0.174044i	$0.944317\pi$
$374$	−142.489	−	229.370i	−0.380986	−	0.613287i
$375$	223.591			0.596242
$376$	−193.549	−	159.277i	−0.514758	−	0.423608i
$377$		−	254.917i		−	0.676171i
$378$	−66.5214	−	107.082i	−0.175983	−	0.283285i
$379$	189.784	−	189.784i	0.500751	−	0.500751i	−0.410921	−	0.911671i	$-0.634793\pi$
$379$	189.784	−	189.784i	0.500751	−	0.500751i	0.911671	+	0.410921i	$0.134793\pi$
$380$	−136.204	+	275.573i	−0.358432	+	0.725192i
$381$	−242.802	+	242.802i	−0.637275	+	0.637275i
$382$	−121.971	−	28.4972i	−0.319296	−	0.0745999i
$383$		−	639.916i		−	1.67080i	−0.549644	−	0.835399i	$-0.685237\pi$
$383$		−	639.916i		−	1.67080i	0.549644	−	0.835399i	$-0.314763\pi$
$384$	151.047	+	162.287i	0.393350	+	0.422621i
$385$	−810.623			−2.10551
$386$	101.626	−	434.970i	0.263280	−	1.12687i
$387$	89.6533	+	89.6533i	0.231662	+	0.231662i
$388$	528.376	+	261.154i	1.36179	+	0.673078i
$389$	499.333	+	499.333i	1.28363	+	1.28363i	0.938586	+	0.345046i	$0.112137\pi$
$389$	499.333	+	499.333i	1.28363	+	1.28363i	0.345046	+	0.938586i	$0.387863\pi$
$390$	−155.706	+	96.7274i	−0.399245	+	0.248019i
$391$	−197.181			−0.504300
$392$	−498.913	+	606.266i	−1.27274	+	1.54660i
$393$		−	329.061i		−	0.837306i
$394$	69.9050	−	43.4264i	0.177424	−	0.110219i
$395$	−358.601	+	358.601i	−0.907851	+	0.907851i
$396$	−53.3772	−	157.708i	−0.134791	−	0.398252i
$397$	492.518	−	492.518i	1.24060	−	1.24060i	0.280846	−	0.959753i	$-0.409385\pi$
$397$	492.518	−	492.518i	1.24060	−	1.24060i	0.959753	−	0.280846i	$-0.0906151\pi$
$398$	5.32230	−	22.7800i	0.0133726	−	0.0572361i
$399$		−	335.233i		−	0.840182i
$400$	22.9063	−	17.5116i	0.0572657	−	0.0437789i
$401$	705.045			1.75822			0.879109	−	0.476621i	$-0.158138\pi$
$401$	705.045			1.75822			0.879109	+	0.476621i	$0.158138\pi$
$402$	−232.700	−	54.3679i	−0.578856	−	0.135243i
$403$	−204.735	−	204.735i	−0.508026	−	0.508026i
$404$	−23.1572	−	68.4200i	−0.0573198	−	0.169356i
$405$	30.6515	+	30.6515i	0.0756828	+	0.0756828i
$406$	297.044	+	478.162i	0.731635	+	1.17774i
$407$	−465.550			−1.14386
$408$	134.203	−	13.0360i	0.328930	−	0.0319510i
$409$			279.815i			0.684144i	0.939674	+	0.342072i	$0.111129\pi$
$409$			279.815i			0.684144i	−0.939674	+	0.342072i	$0.888871\pi$
$410$	−125.783	−	202.478i	−0.306789	−	0.493849i
$411$	−313.458	+	313.458i	−0.762671	+	0.762671i
$412$	63.6934	+	31.4810i	0.154596	+	0.0764102i
$413$	−171.432	+	171.432i	−0.415090	+	0.415090i
$414$	−118.392	−	27.6611i	−0.285972	−	0.0668142i
$415$			423.147i			1.01963i
$416$	−124.575	+	328.755i	−0.299459	+	0.790276i
$417$	53.2106			0.127603
$418$	100.732	−	431.146i	0.240987	−	1.03145i
$419$	−573.583	−	573.583i	−1.36893	−	1.36893i	−0.861965	−	0.506968i	$-0.830766\pi$
$419$	−573.583	−	573.583i	−1.36893	−	1.36893i	−0.506968	−	0.861965i	$-0.669234\pi$
$420$	179.354	−	362.875i	0.427033	−	0.863987i
$421$	−213.341	−	213.341i	−0.506749	−	0.506749i	0.406778	−	0.913527i	$-0.366652\pi$
$421$	−213.341	−	213.341i	−0.506749	−	0.506749i	−0.913527	+	0.406778i	$0.866652\pi$
$422$	−0.518392	+	0.322035i	−0.00122842	+	0.000763117i
$423$	−93.9974			−0.222216
$424$	−415.229	+	40.3338i	−0.979314	+	0.0951269i
$425$		−	17.5358i		−	0.0412606i
$426$	−22.7734	+	14.1473i	−0.0534586	+	0.0332095i
$427$	−515.781	+	515.781i	−1.20792	+	1.20792i
$428$	85.1369	−	28.8152i	0.198918	−	0.0673251i
$429$	186.692	−	186.692i	0.435178	−	0.435178i
$430$	−92.6230	+	396.436i	−0.215402	+	0.921944i
$431$			166.900i			0.387239i	0.981077	+	0.193619i	$0.0620227\pi$
$431$			166.900i			0.387239i	−0.981077	+	0.193619i	$0.937977\pi$
$432$	82.4076	+	10.9993i	0.190758	+	0.0254612i
$433$	233.153			0.538459			0.269230	−	0.963076i	$-0.413231\pi$
$433$	233.153			0.538459			0.269230	+	0.963076i	$0.413231\pi$
$434$	622.602	+	145.464i	1.43457	+	0.335171i
$435$	−136.871	−	136.871i	−0.314646	−	0.314646i
$436$	425.048	−	143.860i	0.974882	−	0.329955i
$437$	−228.619	−	228.619i	−0.523155	−	0.523155i
$438$	156.138	+	251.341i	0.356479	+	0.573838i
$439$	440.480			1.00337			0.501686	−	0.865050i	$-0.332713\pi$
$439$	440.480			1.00337			0.501686	+	0.865050i	$0.332713\pi$
$440$	339.707	−	412.803i	0.772061	−	0.938189i
$441$			294.434i			0.667651i
$442$	112.828	+	181.623i	0.255266	+	0.410912i
$443$	−312.524	+	312.524i	−0.705473	+	0.705473i	−0.965580	−	0.260107i	$-0.916242\pi$
$443$	−312.524	+	312.524i	−0.705473	+	0.705473i	0.260107	+	0.965580i	$0.416242\pi$
$444$	103.005	−	208.403i	0.231993	−	0.469376i
$445$	433.114	−	433.114i	0.973290	−	0.973290i
$446$	723.217	+	168.972i	1.62156	+	0.378861i
$447$			83.8814i			0.187654i
$448$	−149.412	−	761.827i	−0.333509	−	1.70051i
$449$	−734.338			−1.63550			−0.817748	−	0.575576i	$-0.804778\pi$
$449$	−734.338			−1.63550			−0.817748	+	0.575576i	$0.804778\pi$
$450$	2.45996	−	10.5289i	0.00546658	−	0.0233975i
$451$	242.772	+	242.772i	0.538297	+	0.538297i
$452$	600.774	+	296.938i	1.32915	+	0.656942i
$453$	17.7153	+	17.7153i	0.0391066	+	0.0391066i
$454$	−504.115	+	313.166i	−1.11039	+	0.689794i
$455$	641.880			1.41073
$456$	170.714	+	140.486i	0.374374	+	0.308082i
$457$			692.749i			1.51586i	0.652335	+	0.757931i	$0.273789\pi$
$457$			692.749i			1.51586i	−0.652335	+	0.757931i	$0.726211\pi$
$458$	366.997	−	227.986i	0.801303	−	0.497785i
$459$	35.7535	−	35.7535i	0.0778944	−	0.0778944i
$460$	−125.156	−	369.784i	−0.272078	−	0.803878i
$461$	298.447	−	298.447i	0.647391	−	0.647391i	−0.304971	−	0.952362i	$-0.598647\pi$
$461$	298.447	−	298.447i	0.647391	−	0.647391i	0.952362	+	0.304971i	$0.0986467\pi$
$462$	−132.645	+	567.733i	−0.287109	+	1.22886i
$463$			281.830i			0.608705i	0.952560	+	0.304352i	$0.0984400\pi$
$463$			281.830i			0.608705i	−0.952560	+	0.304352i	$0.901560\pi$
$464$	−367.982	−	49.1159i	−0.793065	−	0.105853i
$465$	−219.854			−0.472804
$466$	−531.484	−	124.175i	−1.14052	−	0.266471i
$467$	198.116	+	198.116i	0.424232	+	0.424232i	0.886658	−	0.462426i	$-0.153021\pi$
$467$	198.116	+	198.116i	0.424232	+	0.424232i	−0.462426	+	0.886658i	$0.653021\pi$
$468$	42.2660	+	124.879i	0.0903119	+	0.266835i
$469$	591.704	+	591.704i	1.26163	+	1.26163i
$470$	−159.267	−	256.378i	−0.338866	−	0.545485i
$471$	−77.0737			−0.163638
$472$	−15.4585	−	159.142i	−0.0327510	−	0.337166i
$473$		−	586.384i		−	1.23971i
$474$	192.473	+	309.831i	0.406061	+	0.653652i
$475$	20.3316	−	20.3316i	0.0428033	−	0.0428033i
$476$	−423.276	−	209.207i	−0.889234	−	0.439512i
$477$	−110.622	+	110.622i	−0.231913	+	0.231913i
$478$	203.811	+	47.6182i	0.426383	+	0.0996197i
$479$		−	917.713i		−	1.91589i	−0.286945	−	0.957947i	$-0.592640\pi$
$479$		−	917.713i		−	1.91589i	0.286945	−	0.957947i	$-0.407360\pi$
$480$	109.629	+	243.404i	0.228394	+	0.507091i
$481$	368.639			0.766401
$482$	67.7416	−	289.941i	0.140543	−	0.601537i
$483$	301.045	+	301.045i	0.623282	+	0.623282i
$484$	−126.735	+	256.413i	−0.261848	+	0.529780i
$485$	501.826	+	501.826i	1.03469	+	1.03469i
$486$	26.4829	−	16.4517i	0.0544915	−	0.0338512i
$487$	−426.183			−0.875119			−0.437559	−	0.899190i	$-0.644157\pi$
$487$	−426.183			−0.875119			−0.437559	+	0.899190i	$0.644157\pi$
$488$	−46.5093	−	478.805i	−0.0953059	−	0.981157i
$489$		−	76.9146i		−	0.157290i
$490$	−803.070	+	498.883i	−1.63892	+	1.01813i
$491$	−266.299	+	266.299i	−0.542361	+	0.542361i	−0.924220	−	0.381859i	$-0.875284\pi$
$491$	−266.299	+	266.299i	−0.542361	+	0.542361i	0.381859	+	0.924220i	$0.375284\pi$
$492$	−162.391	+	54.9623i	−0.330063	+	0.111712i
$493$	−159.653	+	159.653i	−0.323840	+	0.323840i
$494$	−79.7636	+	341.396i	−0.161465	+	0.691086i
$495$		−	200.479i		−	0.405007i
$496$	−334.989	+	256.095i	−0.675382	+	0.516321i
$497$	93.8809			0.188895
$498$	296.358	+	69.2408i	0.595096	+	0.139038i
$499$	−264.104	−	264.104i	−0.529266	−	0.529266i	0.391088	−	0.920353i	$-0.372099\pi$
$499$	−264.104	−	264.104i	−0.529266	−	0.529266i	−0.920353	+	0.391088i	$0.872099\pi$
$500$	489.106	−	165.541i	0.978211	−	0.331082i
$501$	−44.6782	−	44.6782i	−0.0891781	−	0.0891781i
$502$	−214.494	−	345.279i	−0.427279	−	0.687807i
$503$	−574.766			−1.14268			−0.571338	−	0.820715i	$-0.693575\pi$
$503$	−574.766			−1.14268			−0.571338	+	0.820715i	$0.693575\pi$
$504$	−224.797	−	184.991i	−0.446025	−	0.367046i
$505$		−	86.9756i		−	0.172229i
$506$	296.717	+	477.636i	0.586398	+	0.943946i
$507$	59.1528	−	59.1528i	0.116672	−	0.116672i
$508$	−351.366	+	710.895i	−0.691665	+	1.39940i
$509$	170.592	−	170.592i	0.335152	−	0.335152i	−0.519387	−	0.854539i	$-0.673840\pi$
$509$	170.592	−	170.592i	0.335152	−	0.335152i	0.854539	+	0.519387i	$0.173840\pi$
$510$	158.098	+	36.9378i	0.309996	+	0.0724271i
$511$		−	1036.13i		−	2.02765i
$512$	450.568	+	243.172i	0.880016	+	0.474944i
$513$	82.9077			0.161614
$514$	60.9835	−	261.016i	0.118645	−	0.507813i
$515$	60.4930	+	60.4930i	0.117462	+	0.117462i
$516$	262.494	+	129.740i	0.508709	+	0.251434i
$517$	307.398	+	307.398i	0.594581	+	0.594581i
$518$	−691.478	+	429.560i	−1.33490	+	0.829266i
$519$	−239.173			−0.460834
$520$	−268.992	+	326.872i	−0.517293	+	0.628600i
$521$			37.1210i			0.0712496i	0.999365	+	0.0356248i	$0.0113421\pi$
$521$			37.1210i			0.0712496i	−0.999365	+	0.0356248i	$0.988658\pi$
$522$	−118.256	+	73.4631i	−0.226545	+	0.140734i
$523$	−199.555	+	199.555i	−0.381558	+	0.381558i	−0.871663	−	0.490105i	$-0.836958\pi$
$523$	−199.555	+	199.555i	−0.381558	+	0.381558i	0.490105	+	0.871663i	$0.336958\pi$
$524$	−243.629	−	719.823i	−0.464941	−	1.37371i
$525$	−26.7726	+	26.7726i	−0.0509955	+	0.0509955i
$526$	132.133	−	565.542i	0.251203	−	1.07518i
$527$			256.449i			0.486620i
$528$	−233.526	−	305.467i	−0.442284	−	0.578536i
$529$	−118.392			−0.223804
$530$	−489.159	−	114.287i	−0.922942	−	0.215635i
$531$	−42.3976	−	42.3976i	−0.0798448	−	0.0798448i
$532$	−248.198	−	733.323i	−0.466538	−	1.37843i
$533$	−192.236	−	192.236i	−0.360667	−	0.360667i
$534$	−232.466	−	374.210i	−0.435330	−	0.700767i
$535$	108.226			0.202292
$536$	−549.286	+	53.3555i	−1.02479	+	0.0995439i
$537$		−	219.824i		−	0.409355i
$538$	110.839	+	178.422i	0.206021	+	0.331639i
$539$	962.884	−	962.884i	1.78643	−	1.78643i
$540$	89.7440	+	44.3567i	0.166193	+	0.0821421i
$541$	278.121	−	278.121i	0.514086	−	0.514086i	−0.401690	−	0.915776i	$-0.631577\pi$
$541$	278.121	−	278.121i	0.514086	−	0.514086i	0.915776	+	0.401690i	$0.131577\pi$
$542$	−137.951	−	32.2307i	−0.254521	−	0.0594661i
$543$			282.910i			0.521013i
$544$	283.919	−	127.877i	0.521910	−	0.235068i
$545$	540.323			0.991418
$546$	105.033	−	449.551i	0.192368	−	0.823353i
$547$	724.938	+	724.938i	1.32530	+	1.32530i	0.909421	+	0.415876i	$0.136525\pi$
$547$	724.938	+	724.938i	1.32530	+	1.32530i	0.415876	+	0.909421i	$0.363475\pi$
$548$	−453.614	+	917.767i	−0.827763	+	1.67476i
$549$	−127.560	−	127.560i	−0.232349	−	0.232349i
$550$	−42.4773	+	26.3877i	−0.0772314	+	0.0479777i
$551$	−370.215			−0.671897
$552$	−279.463	+	27.1460i	−0.506274	+	0.0491776i
$553$		−	1277.25i		−	2.30967i
$554$	−232.318	+	144.320i	−0.419346	+	0.260506i
$555$	197.931	−	197.931i	0.356633	−	0.356633i
$556$	116.398	−	39.3958i	0.209350	−	0.0708558i
$557$	268.298	−	268.298i	0.481685	−	0.481685i	−0.423985	−	0.905669i	$-0.639369\pi$
$557$	268.298	−	268.298i	0.481685	−	0.481685i	0.905669	+	0.423985i	$0.139369\pi$
$558$	−35.9753	+	153.978i	−0.0644719	+	0.275946i
$559$			464.320i			0.830625i
$560$	123.674	−	926.579i	0.220846	−	1.65461i
$561$	−233.848			−0.416842
$562$	269.056	+	62.8619i	0.478747	+	0.111854i
$563$	−78.4662	−	78.4662i	−0.139372	−	0.139372i	0.633979	−	0.773350i	$-0.281421\pi$
$563$	−78.4662	−	78.4662i	−0.139372	−	0.139372i	−0.773350	+	0.633979i	$0.781421\pi$
$564$	−205.620	+	69.5933i	−0.364574	+	0.123392i
$565$	570.587	+	570.587i	1.00989	+	1.00989i
$566$	440.311	+	708.785i	0.777935	+	1.25227i
$567$	−109.173			−0.192545
$568$	−39.3426	+	47.8080i	−0.0692651	+	0.0841691i
$569$			801.999i			1.40949i	0.709461	+	0.704744i	$0.248938\pi$
$569$			801.999i			1.40949i	−0.709461	+	0.704744i	$0.751062\pi$
$570$	140.477	+	226.131i	0.246451	+	0.396721i
$571$	79.9964	−	79.9964i	0.140099	−	0.140099i	−0.633579	−	0.773678i	$-0.718415\pi$
$571$	79.9964	−	79.9964i	0.140099	−	0.140099i	0.773678	+	0.633579i	$0.218415\pi$
$572$	270.167	−	546.611i	0.472320	−	0.955613i
$573$	−76.7031	+	76.7031i	−0.133862	+	0.133862i
$574$	584.592	+	136.583i	1.01845	+	0.237950i
$575$			36.5163i			0.0635066i
$576$	188.411	−	36.9517i	0.327102	−	0.0641522i
$577$	−237.186			−0.411068			−0.205534	−	0.978650i	$-0.565893\pi$
$577$	−237.186			−0.411068			−0.205534	+	0.978650i	$0.565893\pi$
$578$	−88.4158	+	378.429i	−0.152968	+	0.654721i
$579$	−273.537	−	273.537i	−0.472430	−	0.472430i
$580$	−400.742	−	198.070i	−0.690934	−	0.341500i
$581$	−753.571	−	753.571i	−1.29702	−	1.29702i
$582$	433.577	−	269.347i	0.744978	−	0.462795i
$583$	723.534			1.24105
$584$	527.639	+	434.209i	0.903492	+	0.743509i
$585$			158.746i			0.271361i
$586$	−80.4283	+	49.9637i	−0.137250	+	0.0852622i
$587$	−267.958	+	267.958i	−0.456487	+	0.456487i	−0.897500	−	0.441014i	$-0.854619\pi$
$587$	−267.958	+	267.958i	−0.456487	+	0.456487i	0.441014	+	0.897500i	$0.354619\pi$
$588$	217.992	+	644.076i	0.370734	+	1.09537i
$589$	−297.336	+	297.336i	−0.504815	+	0.504815i
$590$	43.8020	−	187.477i	0.0742407	−	0.317758i
$591$		−	71.2701i		−	0.120592i
$592$	71.0273	−	532.145i	0.119979	−	0.898893i
$593$	−607.086			−1.02375			−0.511877	−	0.859059i	$-0.671050\pi$
$593$	−607.086			−1.02375			−0.511877	+	0.859059i	$0.671050\pi$
$594$	−140.408	−	32.8049i	−0.236378	−	0.0552270i
$595$	−402.007	−	402.007i	−0.675642	−	0.675642i
$596$	62.1037	+	183.491i	0.104201	+	0.307871i
$597$	−14.3255	−	14.3255i	−0.0239958	−	0.0239958i
$598$	−234.951	−	378.210i	−0.392895	−	0.632457i
$599$	575.392			0.960587			0.480294	−	0.877108i	$-0.340530\pi$
$599$	575.392			0.960587			0.480294	+	0.877108i	$0.340530\pi$
$600$	−2.41416	−	24.8533i	−0.00402359	−	0.0414222i
$601$			310.094i			0.515963i	0.966150	+	0.257981i	$0.0830573\pi$
$601$			310.094i			0.515963i	−0.966150	+	0.257981i	$0.916943\pi$
$602$	−541.052	−	870.952i	−0.898758	−	1.44676i
$603$	−146.337	+	146.337i	−0.242681	+	0.242681i
$604$	51.8683	+	25.6363i	0.0858746	+	0.0424443i
$605$	−243.529	+	243.529i	−0.402528	+	0.402528i
$606$	−60.9148	−	14.2321i	−0.100519	−	0.0234853i
$607$			556.510i			0.916820i	0.888741	+	0.458410i	$0.151581\pi$
$607$			556.510i			0.916820i	−0.888741	+	0.458410i	$0.848419\pi$
$608$	477.451	+	180.920i	0.785281	+	0.297566i
$609$	487.499			0.800492
$610$	131.785	−	564.054i	0.216041	−	0.924679i
$611$	−243.409	−	243.409i	−0.398378	−	0.398378i
$612$	51.7400	−	104.682i	0.0845424	−	0.171049i
$613$	−326.241	−	326.241i	−0.532204	−	0.532204i	0.389024	−	0.921228i	$-0.372812\pi$
$613$	−326.241	−	326.241i	−0.532204	−	0.532204i	−0.921228	+	0.389024i	$0.872812\pi$
$614$	−222.632	+	138.303i	−0.362592	+	0.225249i
$615$	−206.432			−0.335662
$616$	130.175	+	1340.12i	0.211323	+	2.17553i
$617$			502.068i			0.813725i	0.913490	+	0.406862i	$0.133377\pi$
$617$			502.068i			0.813725i	−0.913490	+	0.406862i	$0.866623\pi$
$618$	52.2659	−	32.4686i	0.0845726	−	0.0525381i
$619$	304.429	−	304.429i	0.491808	−	0.491808i	−0.417067	−	0.908876i	$-0.636942\pi$
$619$	304.429	−	304.429i	0.491808	−	0.491808i	0.908876	+	0.417067i	$0.136942\pi$
$620$	−480.932	+	162.774i	−0.775696	+	0.262539i
$621$	−74.4527	+	74.4527i	−0.119892	+	0.119892i
$622$	−8.44570	+	36.1485i	−0.0135783	+	0.0581166i
$623$			1542.64i			2.47615i
$624$	184.914	+	241.880i	0.296337	+	0.387628i
$625$	576.701			0.922721
$626$	107.414	+	25.0961i	0.171588	+	0.0400896i
$627$	−271.132	−	271.132i	−0.432428	−	0.432428i
$628$	−168.599	+	57.0635i	−0.268470	+	0.0908654i
$629$	−230.877	−	230.877i	−0.367054	−	0.367054i
$630$	−184.980	−	297.769i	−0.293619	−	0.472650i
$631$	8.60592			0.0136385			0.00681927	−	0.999977i	$-0.497829\pi$
$631$	8.60592			0.0136385			0.00681927	+	0.999977i	$0.497829\pi$
$632$	650.427	+	535.254i	1.02916	+	0.846921i
$633$			0.528515i			0.000834936i
$634$	−92.9809	−	149.675i	−0.146658	−	0.236080i
$635$	−675.174	+	675.174i	−1.06327	+	1.06327i
$636$	−160.085	+	323.889i	−0.251706	+	0.509260i
$637$	−762.446	+	762.446i	−1.19693	+	1.19693i
$638$	626.977	+	146.486i	0.982723	+	0.229603i
$639$			23.2181i			0.0363350i
$640$	420.025	+	451.280i	0.656289	+	0.705126i
$641$	−445.780			−0.695445			−0.347722	−	0.937598i	$-0.613045\pi$
$641$	−445.780			−0.695445			−0.347722	+	0.937598i	$0.613045\pi$
$642$	17.7094	−	75.7980i	0.0275847	−	0.118065i
$643$	−118.001	−	118.001i	−0.183517	−	0.183517i	0.609369	−	0.792886i	$-0.291423\pi$
$643$	−118.001	−	118.001i	−0.183517	−	0.183517i	−0.792886	+	0.609369i	$0.791423\pi$
$644$	881.424	+	435.651i	1.36867	+	0.676477i
$645$	249.304	+	249.304i	0.386519	+	0.386519i
$646$	263.771	−	163.860i	0.408314	−	0.253653i
$647$	1081.35			1.67132			0.835662	−	0.549243i	$-0.185084\pi$
$647$	1081.35			1.67132			0.835662	+	0.549243i	$0.185084\pi$
$648$	45.7510	−	55.5954i	0.0706034	−	0.0857954i
$649$			277.305i			0.427280i
$650$	33.6350	−	20.8947i	0.0517462	−	0.0321458i
$651$	391.532	−	391.532i	0.601431	−	0.601431i
$652$	−56.9457	−	168.251i	−0.0873400	−	0.258054i
$653$	−586.227	+	586.227i	−0.897744	+	0.897744i	−0.995236	−	0.0974927i	$-0.968918\pi$
$653$	−586.227	+	586.227i	−0.897744	+	0.897744i	0.0974927	+	0.995236i	$0.468918\pi$
$654$	88.4145	−	378.423i	0.135190	−	0.578629i
$655$		−	915.041i		−	1.39701i
$656$	−314.538	+	240.461i	−0.479479	+	0.366556i
$657$	256.249			0.390029
$658$	740.211	+	172.942i	1.12494	+	0.262830i
$659$	469.999	+	469.999i	0.713201	+	0.713201i	0.967204	−	0.254003i	$-0.0817472\pi$
$659$	469.999	+	469.999i	0.713201	+	0.713201i	−0.254003	+	0.967204i	$0.581747\pi$
$660$	−148.429	−	438.548i	−0.224893	−	0.664466i
$661$	−884.745	−	884.745i	−1.33849	−	1.33849i	−0.897519	−	0.440976i	$-0.854632\pi$
$661$	−884.745	−	884.745i	−1.33849	−	1.33849i	−0.440976	−	0.897519i	$-0.645368\pi$
$662$	−557.857	−	898.003i	−0.842685	−	1.35650i
$663$	185.170			0.279290
$664$	699.548	−	67.9515i	1.05354	−	0.102337i
$665$		−	932.202i		−	1.40181i
$666$	−106.236	−	171.012i	−0.159514	−	0.256775i
$667$	332.460	−	332.460i	0.498441	−	0.498441i
$668$	−130.813	−	64.6552i	−0.195827	−	0.0967892i
$669$	454.805	−	454.805i	0.679829	−	0.679829i
$670$	−647.084	−	151.184i	−0.965797	−	0.225648i
$671$			834.314i			1.24339i
$672$	−628.707	−	238.236i	−0.935576	−	0.354517i
$673$	684.329			1.01683			0.508417	−	0.861111i	$-0.330231\pi$
$673$	684.329			1.01683			0.508417	+	0.861111i	$0.330231\pi$
$674$	−236.584	+	1012.60i	−0.351014	+	1.50238i
$675$	−6.62125	−	6.62125i	−0.00980925	−	0.00980925i
$676$	85.6018	−	173.192i	0.126630	−	0.256202i
$677$	−383.762	−	383.762i	−0.566857	−	0.566857i	0.364390	−	0.931246i	$-0.381278\pi$
$677$	−383.762	−	383.762i	−0.566857	−	0.566857i	−0.931246	+	0.364390i	$0.881278\pi$
$678$	492.987	−	306.253i	0.727119	−	0.451700i
$679$	−1787.38			−2.63237
$680$	373.188	−	36.2500i	0.548805	−	0.0533089i
$681$			513.959i			0.754712i
$682$	621.202	−	385.903i	0.910854	−	0.565840i
$683$	903.626	−	903.626i	1.32302	−	1.32302i	0.411709	−	0.911315i	$-0.364932\pi$
$683$	903.626	−	903.626i	1.32302	−	1.32302i	0.911315	−	0.411709i	$-0.135068\pi$
$684$	181.361	−	61.3829i	0.265148	−	0.0897410i
$685$	−871.652	+	871.652i	−1.27248	+	1.27248i
$686$	271.259	−	1161.02i	0.395421	−	1.69244i
$687$		−	374.163i		−	0.544633i
$688$	670.263	+	89.4625i	0.974220	+	0.130033i
$689$	−572.920			−0.831524
$690$	−329.221	−	76.9189i	−0.477132	−	0.111477i
$691$	−63.6870	−	63.6870i	−0.0921665	−	0.0921665i	0.659520	−	0.751687i	$-0.270759\pi$
$691$	−63.6870	−	63.6870i	−0.0921665	−	0.0921665i	−0.751687	+	0.659520i	$0.770759\pi$
$692$	−523.192	+	177.078i	−0.756057	+	0.255893i
$693$	357.027	+	357.027i	0.515190	+	0.515190i
$694$	−182.326	−	293.497i	−0.262718	−	0.422907i
$695$	147.966			0.212901
$696$	−204.296	+	248.255i	−0.293529	+	0.356688i
$697$			240.793i			0.345470i
$698$	417.135	+	671.478i	0.597615	+	0.962003i
$699$	−334.231	+	334.231i	−0.478156	+	0.478156i
$700$	−38.7434	+	78.3870i	−0.0553478	+	0.111981i
$701$	218.312	−	218.312i	0.311430	−	0.311430i	−0.534033	−	0.845463i	$-0.679324\pi$
$701$	218.312	−	218.312i	0.311430	−	0.311430i	0.845463	+	0.534033i	$0.179324\pi$
$702$	111.180	+	25.9761i	0.158376	+	0.0370029i
$703$		−	535.374i		−	0.761557i
$704$	−736.999	−	495.314i	−1.04687	−	0.703571i
$705$	−261.384			−0.370758
$706$	−96.5861	+	413.399i	−0.136808	+	0.585551i
$707$	154.893	+	154.893i	0.219084	+	0.219084i
$708$	−124.135	−	61.3548i	−0.175332	−	0.0866593i
$709$	−822.199	−	822.199i	−1.15966	−	1.15966i	−0.984548	−	0.175112i	$-0.943971\pi$
$709$	−822.199	−	822.199i	−1.15966	−	1.15966i	−0.175112	−	0.984548i	$-0.556029\pi$
$710$	−63.3273	+	39.3402i	−0.0891934	+	0.0554087i
$711$	315.881			0.444277
$712$	−785.577	−	646.473i	−1.10334	−	0.907968i
$713$		−	534.026i		−	0.748985i
$714$	−347.334	+	215.770i	−0.486462	+	0.302199i
$715$	519.145	−	519.145i	0.726077	−	0.726077i
$716$	−162.752	−	480.866i	−0.227307	−	0.671600i
$717$	128.169	−	128.169i	0.178758	−	0.178758i
$718$	−197.950	+	847.248i	−0.275697	+	1.18001i
$719$		−	340.913i		−	0.474149i	−0.971491	−	0.237074i	$-0.923811\pi$
$719$		−	340.913i		−	0.474149i	0.971491	−	0.237074i	$-0.0761885\pi$
$720$	229.156	+	30.5863i	0.318272	+	0.0424810i
$721$	−215.461			−0.298836
$722$	−207.256	−	48.4231i	−0.287058	−	0.0670680i
$723$	−182.334	−	182.334i	−0.252190	−	0.252190i
$724$	209.460	+	618.867i	0.289309	+	0.854788i
$725$	29.5664	+	29.5664i	0.0407813	+	0.0407813i
$726$	130.710	+	210.409i	0.180042	+	0.289820i
$727$	−803.090			−1.10466			−0.552331	−	0.833625i	$-0.686262\pi$
$727$	−803.090			−1.10466			−0.552331	+	0.833625i	$0.686262\pi$
$728$	−103.077	−	1061.16i	−0.141589	−	1.45763i
$729$		−	27.0000i		−	0.0370370i
$730$	434.183	+	698.920i	0.594771	+	0.957424i
$731$	290.802	−	290.802i	0.397813	−	0.397813i
$732$	−373.480	−	184.596i	−0.510218	−	0.252180i
$733$	481.592	−	481.592i	0.657015	−	0.657015i	−0.297658	−	0.954673i	$-0.596205\pi$
$733$	481.592	−	481.592i	0.657015	−	0.657015i	0.954673	+	0.297658i	$0.0962054\pi$
$734$	−244.486	−	57.1215i	−0.333087	−	0.0778222i
$735$			818.752i			1.11395i
$736$	−591.229	+	266.290i	−0.803301	+	0.361807i
$737$	957.127			1.29868
$738$	−33.7790	+	144.578i	−0.0457710	+	0.195905i
$739$	173.622	+	173.622i	0.234941	+	0.234941i	0.814752	−	0.579810i	$-0.196873\pi$
$739$	173.622	+	173.622i	0.234941	+	0.234941i	−0.579810	+	0.814752i	$0.696873\pi$
$740$	286.432	−	579.519i	0.387071	−	0.783134i
$741$	214.692	+	214.692i	0.289733	+	0.289733i
$742$	1074.66	−	667.600i	1.44833	−	0.899731i
$743$	1316.22			1.77149			0.885744	−	0.464173i	$-0.153649\pi$
$743$	1316.22			1.77149			0.885744	+	0.464173i	$0.153649\pi$
$744$	35.3054	+	363.463i	0.0474536	+	0.488526i
$745$			233.254i			0.313093i
$746$	−726.512	+	451.323i	−0.973876	+	0.604991i
$747$	186.369	−	186.369i	0.249490	−	0.249490i
$748$	−511.545	+	173.136i	−0.683883	+	0.231465i
$749$	−192.737	+	192.737i	−0.257326	+	0.257326i
$750$	101.739	−	435.454i	0.135652	−	0.580605i
$751$			322.977i			0.430062i	0.976607	+	0.215031i	$0.0689853\pi$
$751$			322.977i			0.430062i	−0.976607	+	0.215031i	$0.931015\pi$
$752$	−398.269	+	304.472i	−0.529613	+	0.404882i
$753$	−352.021			−0.467492
$754$	−496.463	−	115.993i	−0.658439	−	0.153837i
$755$	49.2621	+	49.2621i	0.0652478	+	0.0652478i
$756$	−238.816	+	80.8289i	−0.315895	+	0.106917i
$757$	−80.2744	−	80.2744i	−0.106043	−	0.106043i	0.652095	−	0.758138i	$-0.273890\pi$
$757$	−80.2744	−	80.2744i	−0.106043	−	0.106043i	−0.758138	+	0.652095i	$0.773890\pi$
$758$	−283.258	−	455.971i	−0.373692	−	0.601545i
$759$	486.963			0.641585
$760$	474.716	+	390.657i	0.624627	+	0.514023i
$761$			596.664i			0.784053i	0.919954	+	0.392027i	$0.128226\pi$
$761$			596.664i			0.784053i	−0.919954	+	0.392027i	$0.871774\pi$
$762$	362.388	+	583.350i	0.475575	+	0.765551i
$763$	−962.246	+	962.246i	−1.26113	+	1.26113i
$764$	−110.999	+	224.578i	−0.145287	+	0.293950i
$765$	99.4220	−	99.4220i	0.129963	−	0.129963i
$766$	−1246.27	−	291.177i	−1.62698	−	0.380127i
$767$		−	219.580i		−	0.286284i
$768$	384.791	−	220.327i	0.501030	−	0.286884i
$769$	1515.31			1.97050			0.985249	−	0.171129i	$-0.0547416\pi$
$769$	1515.31			1.97050			0.985249	+	0.171129i	$0.0547416\pi$
$770$	−368.853	+	1578.73i	−0.479030	+	2.05030i
$771$	−164.144	−	164.144i	−0.212897	−	0.212897i
$772$	−800.884	−	395.844i	−1.03741	−	0.512751i
$773$	607.901	+	607.901i	0.786418	+	0.786418i	0.980905	−	0.194487i	$-0.0623042\pi$
$773$	607.901	+	607.901i	0.786418	+	0.786418i	−0.194487	+	0.980905i	$0.562304\pi$
$774$	215.399	−	133.810i	0.278293	−	0.172881i
$775$	47.4922			0.0612802
$776$	749.034	−	910.207i	0.965250	−	1.17295i
$777$			704.981i			0.907311i
$778$	1199.68	−	745.267i	1.54201	−	0.957927i
$779$	−279.184	+	279.184i	−0.358387	+	0.358387i
$780$	117.532	+	347.258i	0.150682	+	0.445202i
$781$	75.9297	−	75.9297i	0.0972211	−	0.0972211i
$782$	−89.7221	+	384.020i	−0.114734	+	0.491074i
$783$			120.565i			0.153979i
$784$	953.717	+	1247.52i	1.21648	+	1.59123i
$785$	−214.324			−0.273024
$786$	−640.863	−	149.731i	−0.815348	−	0.190497i
$787$	356.009	+	356.009i	0.452362	+	0.452362i	0.896138	−	0.443776i	$-0.146361\pi$
$787$	356.009	+	356.009i	0.452362	+	0.452362i	−0.443776	+	0.896138i	$0.646361\pi$
$788$	−52.7666	−	155.904i	−0.0669627	−	0.197847i
$789$	−355.649	−	355.649i	−0.450760	−	0.450760i
$790$	535.222	+	861.566i	0.677496	+	1.09059i
$791$	−2032.29			−2.56926
$792$	−331.432	+	32.1940i	−0.418474	+	0.0406490i
$793$		−	660.640i		−	0.833089i
$794$	−735.096	−	1183.31i	−0.925814	−	1.49032i
$795$	−307.615	+	307.615i	−0.386937	+	0.386937i
$796$	−41.9434	−	20.7309i	−0.0526927	−	0.0260438i
$797$	971.380	−	971.380i	1.21880	−	1.21880i	0.250742	−	0.968054i	$-0.419326\pi$
$797$	971.380	−	971.380i	1.21880	−	1.21880i	0.968054	−	0.250742i	$-0.0806745\pi$
$798$	−652.882	−	152.539i	−0.818148	−	0.191151i
$799$			304.892i			0.381592i
$800$	−23.6818	−	52.5793i	−0.0296022	−	0.0657242i
$801$	−381.517			−0.476301
$802$	320.813	−	1373.11i	0.400016	−	1.71211i
$803$	−838.008	−	838.008i	−1.04360	−	1.04360i
$804$	−211.768	+	428.457i	−0.263393	+	0.532906i
$805$	837.135	+	837.135i	1.03992	+	1.03992i
$806$	−491.890	+	305.572i	−0.610285	+	0.379121i
$807$	181.906			0.225410
$808$	−143.788	+	13.9671i	−0.177956	+	0.0172860i
$809$		−	678.276i		−	0.838412i	−0.907891	−	0.419206i	$-0.862308\pi$
$809$		−	678.276i		−	0.838412i	0.907891	−	0.419206i	$-0.137692\pi$
$810$	73.6426	−	45.7482i	0.0909168	−	0.0564793i
$811$	204.625	−	204.625i	0.252312	−	0.252312i	−0.569606	−	0.821918i	$-0.692904\pi$
$811$	204.625	−	204.625i	0.252312	−	0.252312i	0.821918	+	0.569606i	$0.192904\pi$
$812$	1066.41	−	360.933i	1.31331	−	0.444498i
$813$	−86.7522	+	86.7522i	−0.106706	+	0.106706i
$814$	−211.836	+	906.682i	−0.260241	+	1.11386i
$815$		−	213.881i		−	0.262431i
$816$	35.6774	−	267.299i	0.0437223	−	0.327573i
$817$	674.331			0.825375
$818$	544.954	+	127.323i	0.666203	+	0.155651i
$819$	−282.706	−	282.706i	−0.345185	−	0.345185i
$820$	−451.571	+	152.837i	−0.550696	+	0.186387i
$821$	326.524	+	326.524i	0.397715	+	0.397715i	0.877426	−	0.479711i	$-0.159259\pi$
$821$	326.524	+	326.524i	0.397715	+	0.397715i	−0.479711	+	0.877426i	$0.659259\pi$
$822$	467.844	+	753.106i	0.569154	+	0.916187i
$823$	804.270			0.977241			0.488621	−	0.872496i	$-0.337500\pi$
$823$	804.270			0.977241			0.488621	+	0.872496i	$0.337500\pi$
$824$	90.2929	−	109.722i	0.109579	−	0.133157i
$825$			43.3067i			0.0524930i
$826$	255.867	+	411.879i	0.309767	+	0.498642i
$827$	848.530	−	848.530i	1.02603	−	1.02603i	0.0263821	−	0.999652i	$-0.491601\pi$
$827$	848.530	−	848.530i	1.02603	−	1.02603i	0.999652	−	0.0263821i	$-0.00839864\pi$
$828$	−107.743	+	217.989i	−0.130124	+	0.263271i
$829$	49.5139	−	49.5139i	0.0597273	−	0.0597273i	−0.676612	−	0.736340i	$-0.736553\pi$
$829$	49.5139	−	49.5139i	0.0597273	−	0.0597273i	0.736340	+	0.676612i	$0.236553\pi$
$830$	824.101	+	192.542i	0.992892	+	0.231978i
$831$			236.854i			0.285023i
$832$	583.582	+	392.207i	0.701421	+	0.471403i
$833$	955.034			1.14650
$834$	24.2121	−	103.630i	0.0290313	−	0.124257i
$835$	−124.240	−	124.240i	−0.148790	−	0.148790i
$836$	−793.842	−	392.363i	−0.949572	−	0.469334i
$837$	96.8313	+	96.8313i	0.115689	+	0.115689i
$838$	−1378.08	+	856.088i	−1.64448	+	1.02158i
$839$	866.213			1.03244			0.516218	−	0.856457i	$-0.327340\pi$
$839$	866.213			1.03244			0.516218	+	0.856457i	$0.327340\pi$
$840$	−625.106	−	514.417i	−0.744174	−	0.612401i
$841$			302.629i			0.359844i
$842$	−512.568	+	318.417i	−0.608751	+	0.378168i
$843$	169.199	−	169.199i	0.200711	−	0.200711i
$844$	0.391299	+	1.15613i	0.000463625	+	0.00136982i
$845$	164.490	−	164.490i	0.194663	−	0.194663i
$846$	−42.7711	+	183.065i	−0.0505568	+	0.216388i
$847$		−	867.390i		−	1.02407i
$848$	−110.387	+	827.033i	−0.130173	+	0.975274i
$849$	722.626			0.851149
$850$	−34.1518	−	7.97919i	−0.0401786	−	0.00938728i
$851$	480.776	+	480.776i	0.564954	+	0.564954i
$852$	17.1901	+	50.7896i	0.0201761	+	0.0596122i
$853$	313.947	+	313.947i	0.368050	+	0.368050i	0.866766	−	0.498715i	$-0.166195\pi$
$853$	313.947	+	313.947i	0.368050	+	0.368050i	−0.498715	+	0.866766i	$0.666195\pi$
$854$	769.816	+	1239.20i	0.901424	+	1.45106i
$855$	230.547			0.269645
$856$	−17.3796	−	178.920i	−0.0203033	−	0.209019i
$857$			473.297i			0.552272i	0.961119	+	0.276136i	$0.0890540\pi$
$857$			473.297i			0.552272i	−0.961119	+	0.276136i	$0.910946\pi$
$858$	−278.642	−	448.540i	−0.324758	−	0.522774i
$859$	−595.383	+	595.383i	−0.693112	+	0.693112i	−0.962915	−	0.269803i	$-0.913041\pi$
$859$	−595.383	+	595.383i	−0.693112	+	0.693112i	0.269803	+	0.962915i	$0.413041\pi$
$860$	729.934	+	360.776i	0.848760	+	0.419507i
$861$	367.629	−	367.629i	0.426979	−	0.426979i
$862$	325.046	+	75.9435i	0.377084	+	0.0881015i
$863$			742.134i			0.859947i	0.902842	+	0.429973i	$0.141477\pi$
$863$			742.134i			0.859947i	−0.902842	+	0.429973i	$0.858523\pi$
$864$	58.9190	−	155.488i	0.0681933	−	0.179963i
$865$	−665.083			−0.768882
$866$	106.090	−	454.077i	0.122506	−	0.524338i
$867$	237.980	+	237.980i	0.274487	+	0.274487i
$868$	566.597	−	1146.36i	0.652762	−	1.32069i
$869$	−1033.02	−	1033.02i	−1.18875	−	1.18875i
$870$	−328.843	+	204.283i	−0.377980	+	0.234809i
$871$	−757.887			−0.870134
$872$	−86.7682	−	893.263i	−0.0995048	−	1.02438i
$873$		−	442.044i		−	0.506350i
$874$	−549.274	+	341.220i	−0.628459	+	0.390411i
$875$	−1107.26	+	1107.26i	−1.26544	+	1.26544i
$876$	560.546	−	189.720i	0.639893	−	0.216576i
$877$	−791.224	+	791.224i	−0.902194	+	0.902194i	−0.995626	−	0.0934320i	$-0.970216\pi$
$877$	−791.224	+	791.224i	−0.902194	+	0.902194i	0.0934320	+	0.995626i	$0.470216\pi$
$878$	200.429	−	857.858i	0.228279	−	0.977059i
$879$			81.9989i			0.0932865i
$880$	−649.380	−	849.432i	−0.737932	−	0.965264i
$881$	−1524.92			−1.73090			−0.865450	−	0.500995i	$-0.832967\pi$
$881$	−1524.92			−1.73090			−0.865450	+	0.500995i	$0.832967\pi$
$882$	573.426	+	133.975i	0.650142	+	0.151899i
$883$	−314.328	−	314.328i	−0.355978	−	0.355978i	0.506350	−	0.862328i	$-0.330994\pi$
$883$	−314.328	−	314.328i	−0.355978	−	0.355978i	−0.862328	+	0.506350i	$0.830994\pi$
$884$	405.059	−	137.095i	0.458212	−	0.155085i
$885$	−117.898	−	117.898i	−0.133218	−	0.133218i
$886$	466.451	+	750.863i	0.526468	+	0.847475i
$887$	−1520.80			−1.71454			−0.857271	−	0.514866i	$-0.827842\pi$
$887$	−1520.80			−1.71454			−0.857271	+	0.514866i	$0.827842\pi$
$888$	−359.006	−	295.436i	−0.404286	−	0.332698i
$889$		−	2404.80i		−	2.70506i
$890$	−646.434	−	1040.59i	−0.726330	−	1.16920i
$891$	−88.2977	+	88.2977i	−0.0990996	+	0.0990996i
$892$	658.162	−	1331.62i	0.737850	−	1.49284i
$893$	−353.503	+	353.503i	−0.395860	+	0.395860i
$894$	163.363	+	38.1681i	0.182733	+	0.0426936i
$895$		−	611.278i		−	0.682992i
$896$	−1551.68	−	55.6625i	−1.73179	−	0.0621234i
$897$	−385.595			−0.429872
$898$	−334.141	+	1430.16i	−0.372095	+	1.59261i
$899$	−432.389	−	432.389i	−0.480967	−	0.480967i
$900$	−19.3862	−	9.58180i	−0.0215402	−	0.0106464i
$901$	358.818	+	358.818i	0.398244	+	0.398244i
$902$	583.278	−	362.344i	0.646649	−	0.401711i
$903$	−887.959			−0.983343
$904$	851.668	−	1034.92i	0.942111	−	1.14483i
$905$			786.705i			0.869288i
$906$	42.5623	−	26.4406i	0.0469783	−	0.0291838i
$907$	−216.886	+	216.886i	−0.239125	+	0.239125i	−0.816488	−	0.577363i	$-0.804082\pi$
$907$	−216.886	+	216.886i	−0.239125	+	0.239125i	0.577363	+	0.816488i	$0.304082\pi$
$908$	380.523	+	1124.29i	0.419078	+	1.23820i
$909$	−38.3071	+	38.3071i	−0.0421420	+	0.0421420i
$910$	292.071	−	1250.09i	0.320957	−	1.37373i
$911$			799.632i			0.877752i	0.898548	+	0.438876i	$0.144623\pi$
$911$			799.632i			0.877752i	−0.898548	+	0.438876i	$0.855377\pi$
$912$	351.282	−	268.551i	0.385178	−	0.294463i
$913$	−1218.96			−1.33511
$914$	1349.16	+	315.217i	1.47611	+	0.344877i
$915$	−354.714	−	354.714i	−0.387665	−	0.387665i
$916$	−277.021	−	818.483i	−0.302425	−	0.893541i
$917$	1629.57	+	1629.57i	1.77707	+	1.77707i
$918$	−53.3631	−	85.9005i	−0.0581297	−	0.0935735i
$919$	−640.590			−0.697051			−0.348525	−	0.937299i	$-0.613317\pi$
$919$	−640.590			−0.697051			−0.348525	+	0.937299i	$0.613317\pi$
$920$	−777.121	+	75.4867i	−0.844697	+	0.0820507i
$921$			226.979i			0.246448i
$922$	−445.440	−	717.042i	−0.483124	−	0.777702i
$923$	−60.1238	+	60.1238i	−0.0651396	+	0.0651396i
$924$	1045.33	+	516.664i	1.13131	+	0.559160i
$925$	−42.7565	+	42.7565i	−0.0462232	+	0.0462232i
$926$	548.879	+	128.240i	0.592742	+	0.138488i
$927$		−	53.2864i		−	0.0574827i
$928$	−263.096	+	694.315i	−0.283509	+	0.748184i
$929$	118.633			0.127699			0.0638496	−	0.997960i	$-0.479662\pi$
$929$	118.633			0.127699			0.0638496	+	0.997960i	$0.479662\pi$
$930$	−100.039	+	428.177i	−0.107569	+	0.460405i
$931$	1107.30	+	1107.30i	1.18937	+	1.18937i
$932$	−483.676	+	978.589i	−0.518966	+	1.04999i
$933$	22.7325	+	22.7325i	0.0243649	+	0.0243649i
$934$	475.989	−	295.694i	0.509624	−	0.316589i
$935$	−650.277			−0.695483
$936$	262.439	−	25.4924i	0.280384	−	0.0272354i
$937$			731.334i			0.780506i	0.920708	+	0.390253i	$0.127612\pi$
$937$			731.334i			0.780506i	−0.920708	+	0.390253i	$0.872388\pi$
$938$	1421.61	−	883.135i	1.51558	−	0.941508i
$939$	67.5488	−	67.5488i	0.0719370	−	0.0719370i
$940$	−571.780	+	193.523i	−0.608276	+	0.205875i
$941$	980.281	−	980.281i	1.04174	−	1.04174i	0.0426536	−	0.999090i	$-0.486419\pi$
$941$	980.281	−	980.281i	1.04174	−	1.04174i	0.999090	−	0.0426536i	$-0.0135812\pi$
$942$	−35.0704	+	150.105i	−0.0372297	+	0.159347i
$943$		−	501.424i		−	0.531733i
$944$	−316.972	−	42.3074i	−0.335775	−	0.0448172i
$945$	−303.584			−0.321253
$946$	−1142.01	−	266.819i	−1.20720	−	0.282049i
$947$	−240.008	−	240.008i	−0.253441	−	0.253441i	0.568939	−	0.822380i	$-0.307354\pi$
$947$	−240.008	−	240.008i	−0.253441	−	0.253441i	−0.822380	+	0.568939i	$0.807354\pi$
$948$	690.991	−	233.871i	0.728894	−	0.246699i
$949$	663.564	+	663.564i	0.699225	+	0.699225i
$950$	−30.3454	−	48.8481i	−0.0319425	−	0.0514191i
$951$	−152.597			−0.160460
$952$	−600.043	+	729.156i	−0.630297	+	0.765920i
$953$		−	780.049i		−	0.818519i	−0.912418	−	0.409259i	$-0.865787\pi$
$953$		−	780.049i		−	0.818519i	0.912418	−	0.409259i	$-0.134213\pi$
$954$	165.107	+	265.779i	0.173068	+	0.278594i
$955$	−213.293	+	213.293i	−0.223344	+	0.223344i
$956$	185.478	−	375.265i	0.194014	−	0.392536i
$957$	394.284	−	394.284i	0.412000	−	0.412000i
$958$	−1787.29	−	417.582i	−1.86565	−	0.435889i
$959$		−	3104.60i		−	3.23733i
$960$	523.925	−	102.754i	0.545756	−	0.107035i
$961$	266.459			0.277272
$962$	167.740	−	717.943i	0.174365	−	0.746303i
$963$	−47.6666	−	47.6666i	−0.0494981	−	0.0494981i
$964$	−533.851	−	263.860i	−0.553787	−	0.273714i
$965$	−760.642	−	760.642i	−0.788230	−	0.788230i
$966$	723.283	−	449.318i	0.748741	−	0.465132i
$967$	1783.10			1.84395			0.921975	−	0.387249i	$-0.126575\pi$
$967$	1783.10			1.84395			0.921975	+	0.387249i	$0.126575\pi$
$968$	441.711	+	363.496i	0.456313	+	0.375513i
$969$		−	268.922i		−	0.277525i
$970$	1205.67	−	748.989i	1.24296	−	0.772154i
$971$	−159.340	+	159.340i	−0.164099	+	0.164099i	−0.784380	−	0.620281i	$-0.787019\pi$
$971$	−159.340	+	159.340i	−0.164099	+	0.164099i	0.620281	+	0.784380i	$0.287019\pi$
$972$	−19.9901	−	59.0626i	−0.0205660	−	0.0607640i
$973$	−263.509	+	263.509i	−0.270821	+	0.270821i
$974$	−193.923	+	830.013i	−0.199100	+	0.852169i
$975$		−	34.2918i		−	0.0351711i
$976$	−953.659	−	127.288i	−0.977110	−	0.130418i
$977$	−970.922			−0.993779			−0.496889	−	0.867814i	$-0.665525\pi$
$977$	−970.922			−0.993779			−0.496889	+	0.867814i	$0.665525\pi$
$978$	−149.795	−	34.9980i	−0.153165	−	0.0357853i
$979$	1247.67	+	1247.67i	1.27443	+	1.27443i
$980$	606.184	+	1791.02i	0.618555	+	1.82758i
$981$	−237.977	−	237.977i	−0.242586	−	0.242586i
$982$	397.459	+	639.804i	0.404744	+	0.651531i
$983$	1266.90			1.28881			0.644406	−	0.764684i	$-0.277105\pi$
$983$	1266.90			1.28881			0.644406	+	0.764684i	$0.277105\pi$
$984$	33.1501	+	341.274i	0.0336891	+	0.346823i
$985$		−	198.185i		−	0.201203i
$986$	238.287	+	383.579i	0.241670	+	0.389025i
$987$	465.492	−	465.492i	0.471623	−	0.471623i
$988$	628.593	+	310.687i	0.636227	+	0.314461i
$989$	−605.562	+	605.562i	−0.612297	+	0.612297i
$990$	−390.442	−	91.2225i	−0.394386	−	0.0921440i
$991$		−	222.422i		−	0.224442i	−0.993683	−	0.112221i	$-0.964204\pi$
$991$		−	222.422i		−	0.224442i	0.993683	−	0.112221i	$-0.0357964\pi$
$992$	346.330	+	768.938i	0.349123	+	0.775139i
$993$	−915.539			−0.921993
$994$	42.7180	−	182.838i	0.0429759	−	0.183941i
$995$	−39.8359	−	39.8359i	−0.0400360	−	0.0400360i
$996$	269.700	−	545.665i	0.270783	−	0.547857i
$997$	−441.746	−	441.746i	−0.443075	−	0.443075i	0.449969	−	0.893044i	$-0.351435\pi$
$997$	−441.746	−	441.746i	−0.443075	−	0.443075i	−0.893044	+	0.449969i	$0.851435\pi$
$998$	−634.528	+	394.181i	−0.635800	+	0.394971i
$999$	−174.352			−0.174526

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.3.l.a.43.5	yes	16
3.2	odd	2		144.3.m.c.91.4		16
4.3	odd	2		192.3.l.a.79.6		16
8.3	odd	2		384.3.l.b.31.3		16
8.5	even	2		384.3.l.a.31.7		16
12.11	even	2		576.3.m.c.271.6		16
16.3	odd	4	inner	48.3.l.a.19.5	✓	16
16.5	even	4		384.3.l.b.223.3		16
16.11	odd	4		384.3.l.a.223.7		16
16.13	even	4		192.3.l.a.175.6		16
24.5	odd	2		1152.3.m.f.415.3		16
24.11	even	2		1152.3.m.c.415.3		16
48.5	odd	4		1152.3.m.c.991.3		16
48.11	even	4		1152.3.m.f.991.3		16
48.29	odd	4		576.3.m.c.559.6		16
48.35	even	4		144.3.m.c.19.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.l.a.19.5	✓	16	16.3	odd	4	inner
48.3.l.a.43.5	yes	16	1.1	even	1	trivial
144.3.m.c.19.4		16	48.35	even	4
144.3.m.c.91.4		16	3.2	odd	2
192.3.l.a.79.6		16	4.3	odd	2
192.3.l.a.175.6		16	16.13	even	4
384.3.l.a.31.7		16	8.5	even	2
384.3.l.a.223.7		16	16.11	odd	4
384.3.l.b.31.3		16	8.3	odd	2
384.3.l.b.223.3		16	16.5	even	4
576.3.m.c.271.6		16	12.11	even	2
576.3.m.c.559.6		16	48.29	odd	4
1152.3.m.c.415.3		16	24.11	even	2
1152.3.m.c.991.3		16	48.5	odd	4
1152.3.m.f.415.3		16	24.5	odd	2
1152.3.m.f.991.3		16	48.11	even	4

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)

\(f(q)\)	\(=\)	\(q+(0.455024 - 1.94755i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(-3.58591 - 1.77236i) q^{4} +(-3.40572 - 3.40572i) q^{5} +(-2.94254 + 1.82796i) q^{6} +12.1303 q^{7} +(-5.08344 + 6.17727i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(0.455024 - 1.94755i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(-3.58591 - 1.77236i) q^{4} +(-3.40572 - 3.40572i) q^{5} +(-2.94254 + 1.82796i) q^{6} +12.1303 q^{7} +(-5.08344 + 6.17727i) q^{8} +3.00000i q^{9} +(-8.18251 + 5.08314i) q^{10} +(9.81086 - 9.81086i) q^{11} +(2.22113 + 6.56251i) q^{12} +(-7.76859 + 7.76859i) q^{13} +(5.51959 - 23.6244i) q^{14} +8.34229i q^{15} +(9.71745 + 12.7111i) q^{16} +9.73087 q^{17} +(5.84265 + 1.36507i) q^{18} +(11.2823 + 11.2823i) q^{19} +(6.17643 + 18.2488i) q^{20} +(-14.8566 - 14.8566i) q^{21} +(-14.6430 - 23.5713i) q^{22} -20.2635 q^{23} +(13.7915 - 1.33965i) q^{24} -1.80207i q^{25} +(11.5948 + 18.6646i) q^{26} +(3.67423 - 3.67423i) q^{27} +(-43.4982 - 21.4994i) q^{28} +(-16.4069 + 16.4069i) q^{29} +(16.2470 + 3.79594i) q^{30} +26.3542i q^{31} +(29.1771 - 13.1414i) q^{32} -24.0316 q^{33} +(4.42778 - 18.9514i) q^{34} +(-41.3125 - 41.3125i) q^{35} +(5.31709 - 10.7577i) q^{36} +(-23.7263 - 23.7263i) q^{37} +(27.1066 - 16.8392i) q^{38} +19.0291 q^{39} +(38.3509 - 3.72526i) q^{40} +24.7452i q^{41} +(-35.6940 + 22.1738i) q^{42} +(29.8844 - 29.8844i) q^{43} +(-52.5692 + 17.7924i) q^{44} +(10.2172 - 10.2172i) q^{45} +(-9.22036 + 39.4641i) q^{46} +31.3325i q^{47} +(3.66642 - 27.4692i) q^{48} +98.1448 q^{49} +(-3.50963 - 0.819987i) q^{50} +(-11.9178 - 11.9178i) q^{51} +(41.6262 - 14.0887i) q^{52} +(36.8742 + 36.8742i) q^{53} +(-5.48389 - 8.82762i) q^{54} -66.8262 q^{55} +(-61.6638 + 74.9322i) q^{56} -27.6359i q^{57} +(24.4877 + 39.4188i) q^{58} +(-14.1325 + 14.1325i) q^{59} +(14.7856 - 29.9147i) q^{60} +(-42.5199 + 42.5199i) q^{61} +(51.3260 + 11.9918i) q^{62} +36.3910i q^{63} +(-12.3172 - 62.8036i) q^{64} +52.9153 q^{65} +(-10.9350 + 46.8028i) q^{66} +(48.7789 + 48.7789i) q^{67} +(-34.8940 - 17.2467i) q^{68} +(24.8176 + 24.8176i) q^{69} +(-99.2565 + 61.6601i) q^{70} +7.73935 q^{71} +(-18.5318 - 15.2503i) q^{72} -85.4163i q^{73} +(-57.0041 + 35.4121i) q^{74} +(-2.20708 + 2.20708i) q^{75} +(-20.4610 - 60.4537i) q^{76} +(119.009 - 119.009i) q^{77} +(8.65869 - 37.0601i) q^{78} -105.294i q^{79} +(10.1954 - 76.3854i) q^{80} -9.00000 q^{81} +(48.1926 + 11.2597i) q^{82} +(-62.1229 - 62.1229i) q^{83} +(26.9430 + 79.6054i) q^{84} +(-33.1407 - 33.1407i) q^{85} +(-44.6033 - 71.7996i) q^{86} +40.1885 q^{87} +(10.7313 + 110.477i) q^{88} +127.172i q^{89} +(-15.2494 - 24.5475i) q^{90} +(-94.2355 + 94.2355i) q^{91} +(72.6629 + 35.9142i) q^{92} +(32.2771 - 32.2771i) q^{93} +(61.0215 + 14.2570i) q^{94} -76.8489i q^{95} +(-51.8294 - 19.6397i) q^{96} -147.348 q^{97} +(44.6582 - 191.142i) q^{98} +(29.4326 + 29.4326i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more