LMFDB - Embedded newform 350.3.p.e.193.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,3,Mod(93,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 4]))

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

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

chi := DirichletCharacter("350.93");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	350.p (of order $12$, degree $4$, 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:	$9.53680925261$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} - 2 x^{15} + 2 x^{14} - 8 x^{13} - 722 x^{12} + 1354 x^{11} - 1232 x^{10} + 9306 x^{9} + \cdots + 52200625 $ x^16 - 2x^15 + 2x^14 - 8x^13 - 722x^12 + 1354x^11 - 1232x^10 + 9306x^9 + 505731x^8 - 1157418x^7 + 1256080x^6 - 9824090x^5 + 5294974x^4 + 30978760x^3 + 12152450x^2 + 35619250*x + 52200625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.4
Root			$1.35330 - 5.05060i$ of defining polynomial
Character	$\chi$	$=$	350.193
Dual form			350.3.p.e.107.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 + 0.366025i) q^{2} +(5.05060 - 1.35330i) q^{3} +(1.73205 + 1.00000i) q^{4} +7.39459 q^{6} +(-1.26709 + 6.88437i) q^{7} +(2.00000 + 2.00000i) q^{8} +(15.8829 - 9.16999i) q^{9} +O(q^{10})$	\(q+(1.36603 + 0.366025i) q^{2} +(5.05060 - 1.35330i) q^{3} +(1.73205 + 1.00000i) q^{4} +7.39459 q^{6} +(-1.26709 + 6.88437i) q^{7} +(2.00000 + 2.00000i) q^{8} +(15.8829 - 9.16999i) q^{9} +(5.56894 - 9.64568i) q^{11} +(10.1012 + 2.70661i) q^{12} +(-9.62415 - 9.62415i) q^{13} +(-4.25073 + 8.94043i) q^{14} +(2.00000 + 3.46410i) q^{16} +(2.29193 + 8.55361i) q^{17} +(25.0529 - 6.71290i) q^{18} +(-5.79257 + 3.34434i) q^{19} +(2.91708 + 36.4849i) q^{21} +(11.1379 - 11.1379i) q^{22} +(-7.37457 + 27.5223i) q^{23} +(12.8078 + 7.39459i) q^{24} +(-9.62415 - 16.6695i) q^{26} +(34.5327 - 34.5327i) q^{27} +(-9.07903 + 10.6570i) q^{28} -29.0733i q^{29} +(-11.9038 + 20.6179i) q^{31} +(1.46410 + 5.46410i) q^{32} +(15.0729 - 56.2529i) q^{33} +12.5233i q^{34} +36.6800 q^{36} +(14.9820 + 4.01442i) q^{37} +(-9.13690 + 2.44823i) q^{38} +(-61.6321 - 35.5833i) q^{39} -9.18256 q^{41} +(-9.36960 + 50.9071i) q^{42} +(-55.1244 - 55.1244i) q^{43} +(19.2914 - 11.1379i) q^{44} +(-20.1477 + 34.8968i) q^{46} +(-8.55361 - 2.29193i) q^{47} +(14.7892 + 14.7892i) q^{48} +(-45.7890 - 17.4462i) q^{49} +(23.1513 + 40.0992i) q^{51} +(-7.04537 - 26.2937i) q^{52} +(-13.8047 + 3.69897i) q^{53} +(59.8123 - 34.5327i) q^{54} +(-16.3029 + 11.2346i) q^{56} +(-24.7300 + 24.7300i) q^{57} +(10.6416 - 39.7149i) q^{58} +(67.7986 + 39.1435i) q^{59} +(-10.7196 - 18.5670i) q^{61} +(-23.8075 + 23.8075i) q^{62} +(43.0045 + 120.963i) q^{63} +8.00000i q^{64} +(41.1800 - 71.3259i) q^{66} +(-13.7678 - 51.3823i) q^{67} +(-4.58386 + 17.1072i) q^{68} +148.984i q^{69} -101.186 q^{71} +(50.1058 + 13.4258i) q^{72} +(101.181 - 27.1115i) q^{73} +(18.9964 + 10.9676i) q^{74} -13.3774 q^{76} +(59.3481 + 50.5605i) q^{77} +(-71.1666 - 71.1666i) q^{78} +(-11.7992 + 6.81228i) q^{79} +(45.1475 - 78.1978i) q^{81} +(-12.5436 - 3.36105i) q^{82} +(-28.4835 - 28.4835i) q^{83} +(-31.4324 + 66.1108i) q^{84} +(-55.1244 - 95.4783i) q^{86} +(-39.3451 - 146.838i) q^{87} +(30.4292 - 8.15349i) q^{88} +(-6.56157 + 3.78833i) q^{89} +(78.4508 - 54.0615i) q^{91} +(-40.2954 + 40.2954i) q^{92} +(-32.2188 + 120.242i) q^{93} +(-10.8455 - 6.26167i) q^{94} +(14.7892 + 25.6156i) q^{96} +(-74.4232 + 74.4232i) q^{97} +(-56.1632 - 40.5919i) q^{98} -204.268i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 2 q^{3} - 8 q^{6} - 12 q^{7} + 32 q^{8}+O(q^{10}) $ 16 * q + 8 * q^2 - 2 * q^3 - 8 * q^6 - 12 * q^7 + 32 * q^8	$ 16 q + 8 q^{2} - 2 q^{3} - 8 q^{6} - 12 q^{7} + 32 q^{8} + 40 q^{11} - 4 q^{12} - 16 q^{13} + 32 q^{16} - 46 q^{17} + 52 q^{18} - 20 q^{21} + 80 q^{22} - 54 q^{23} - 16 q^{26} + 52 q^{27} + 36 q^{28} - 208 q^{31} - 32 q^{32} + 22 q^{33} + 208 q^{36} + 38 q^{37} - 36 q^{38} - 72 q^{41} - 184 q^{42} - 144 q^{43} + 108 q^{46} - 46 q^{47} - 16 q^{48} - 136 q^{51} + 16 q^{52} - 30 q^{53} - 48 q^{56} + 492 q^{57} - 132 q^{58} - 120 q^{61} - 416 q^{62} + 292 q^{63} - 44 q^{66} + 74 q^{67} + 92 q^{68} + 16 q^{71} + 104 q^{72} + 54 q^{73} - 144 q^{76} - 570 q^{77} - 168 q^{78} + 244 q^{81} - 36 q^{82} - 64 q^{83} - 144 q^{86} + 236 q^{87} + 80 q^{88} + 336 q^{91} + 216 q^{92} - 142 q^{93} - 16 q^{96} - 136 q^{97} + 268 q^{98}+O(q^{100}) $ 16 * q + 8 * q^2 - 2 * q^3 - 8 * q^6 - 12 * q^7 + 32 * q^8 + 40 * q^11 - 4 * q^12 - 16 * q^13 + 32 * q^16 - 46 * q^17 + 52 * q^18 - 20 * q^21 + 80 * q^22 - 54 * q^23 - 16 * q^26 + 52 * q^27 + 36 * q^28 - 208 * q^31 - 32 * q^32 + 22 * q^33 + 208 * q^36 + 38 * q^37 - 36 * q^38 - 72 * q^41 - 184 * q^42 - 144 * q^43 + 108 * q^46 - 46 * q^47 - 16 * q^48 - 136 * q^51 + 16 * q^52 - 30 * q^53 - 48 * q^56 + 492 * q^57 - 132 * q^58 - 120 * q^61 - 416 * q^62 + 292 * q^63 - 44 * q^66 + 74 * q^67 + 92 * q^68 + 16 * q^71 + 104 * q^72 + 54 * q^73 - 144 * q^76 - 570 * q^77 - 168 * q^78 + 244 * q^81 - 36 * q^82 - 64 * q^83 - 144 * q^86 + 236 * q^87 + 80 * q^88 + 336 * q^91 + 216 * q^92 - 142 * q^93 - 16 * q^96 - 136 * q^97 + 268 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$3$	5.05060	−	1.35330i	1.68353	−	0.451101i	0.714825	−	0.699304i	$-0.246506\pi$
$3$	5.05060	−	1.35330i	1.68353	−	0.451101i	0.968708	+	0.248202i	$0.0798398\pi$
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	7.39459			1.23243
$7$	−1.26709	+	6.88437i	−0.181013	+	0.983481i
$7$	−1.26709	+	6.88437i	−0.181013	+	0.983481i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	15.8829	−	9.16999i	1.76477	−	1.01889i
$10$		0			0
$11$	5.56894	−	9.64568i	0.506267	−	0.876880i	−0.493707	−	0.869629i	$-0.664358\pi$
$11$	5.56894	−	9.64568i	0.506267	−	0.876880i	0.999974	−	0.00725183i	$-0.00230835\pi$
$12$	10.1012	+	2.70661i	0.841767	+	0.225551i
$13$	−9.62415	−	9.62415i	−0.740319	−	0.740319i	0.232320	−	0.972639i	$-0.425368\pi$
$13$	−9.62415	−	9.62415i	−0.740319	−	0.740319i	−0.972639	+	0.232320i	$0.925368\pi$
$14$	−4.25073	+	8.94043i	−0.303623	+	0.638602i
$15$		0			0
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	2.29193	+	8.55361i	0.134820	+	0.503153i	0.999999	+	0.00169021i	$0.000538011\pi$
$17$	2.29193	+	8.55361i	0.134820	+	0.503153i	−0.865179	+	0.501463i	$0.832795\pi$
$18$	25.0529	−	6.71290i	1.39183	−	0.372939i
$19$	−5.79257	+	3.34434i	−0.304872	+	0.176018i	−0.644629	−	0.764495i	$-0.722988\pi$
$19$	−5.79257	+	3.34434i	−0.304872	+	0.176018i	0.339758	+	0.940513i	$0.389655\pi$
$20$		0			0
$21$	2.91708	+	36.4849i	0.138909	+	1.73738i
$22$	11.1379	−	11.1379i	0.506267	−	0.506267i
$23$	−7.37457	+	27.5223i	−0.320633	+	1.19662i	0.597996	+	0.801499i	$0.295964\pi$
$23$	−7.37457	+	27.5223i	−0.320633	+	1.19662i	−0.918629	+	0.395121i	$0.870703\pi$
$24$	12.8078	+	7.39459i	0.533659	+	0.308108i
$25$		0			0
$26$	−9.62415	−	16.6695i	−0.370160	−	0.641135i
$27$	34.5327	−	34.5327i	1.27899	−	1.27899i
$28$	−9.07903	+	10.6570i	−0.324251	+	0.380607i
$29$		−	29.0733i		−	1.00253i	−0.865294	−	0.501265i	$-0.832868\pi$
$29$		−	29.0733i		−	1.00253i	0.865294	−	0.501265i	$-0.167132\pi$
$30$		0			0
$31$	−11.9038	+	20.6179i	−0.383992	+	0.665094i	−0.991629	−	0.129121i	$-0.958784\pi$
$31$	−11.9038	+	20.6179i	−0.383992	+	0.665094i	0.607637	+	0.794215i	$0.292118\pi$
$32$	1.46410	+	5.46410i	0.0457532	+	0.170753i
$33$	15.0729	−	56.2529i	0.456756	−	1.70463i
$34$			12.5233i			0.368334i
$35$		0			0
$36$	36.6800			1.01889
$37$	14.9820	+	4.01442i	0.404919	+	0.108498i	0.455529	−	0.890221i	$-0.349450\pi$
$37$	14.9820	+	4.01442i	0.404919	+	0.108498i	−0.0506104	+	0.998718i	$0.516117\pi$
$38$	−9.13690	+	2.44823i	−0.240445	+	0.0644270i
$39$	−61.6321	−	35.5833i	−1.58031	−	0.912393i
$40$		0			0
$41$	−9.18256			−0.223965			−0.111982	−	0.993710i	$-0.535720\pi$
$41$	−9.18256			−0.223965			−0.111982	+	0.993710i	$0.535720\pi$
$42$	−9.36960	+	50.9071i	−0.223086	+	1.21207i
$43$	−55.1244	−	55.1244i	−1.28196	−	1.28196i	−0.939549	−	0.342414i	$-0.888756\pi$
$43$	−55.1244	−	55.1244i	−1.28196	−	1.28196i	−0.342414	−	0.939549i	$-0.611244\pi$
$44$	19.2914	−	11.1379i	0.438440	−	0.253134i
$45$		0			0
$46$	−20.1477	+	34.8968i	−0.437993	+	0.758627i
$47$	−8.55361	−	2.29193i	−0.181992	−	0.0487645i	0.166672	−	0.986012i	$-0.446698\pi$
$47$	−8.55361	−	2.29193i	−0.181992	−	0.0487645i	−0.348664	+	0.937248i	$0.613364\pi$
$48$	14.7892	+	14.7892i	0.308108	+	0.308108i
$49$	−45.7890	−	17.4462i	−0.934469	−	0.356045i
$50$		0			0
$51$	23.1513	+	40.0992i	0.453946	+	0.786258i
$52$	−7.04537	−	26.2937i	−0.135488	−	0.505647i
$53$	−13.8047	+	3.69897i	−0.260467	+	0.0697918i	−0.386689	−	0.922210i	$-0.626381\pi$
$53$	−13.8047	+	3.69897i	−0.260467	+	0.0697918i	0.126223	+	0.992002i	$0.459715\pi$
$54$	59.8123	−	34.5327i	1.10764	−	0.639494i
$55$		0			0
$56$	−16.3029	+	11.2346i	−0.291123	+	0.200617i
$57$	−24.7300	+	24.7300i	−0.433860	+	0.433860i
$58$	10.6416	−	39.7149i	0.183476	−	0.684740i
$59$	67.7986	+	39.1435i	1.14913	+	0.663450i	0.948675	−	0.316253i	$-0.102425\pi$
$59$	67.7986	+	39.1435i	1.14913	+	0.663450i	0.200454	+	0.979703i	$0.435758\pi$
$60$		0			0
$61$	−10.7196	−	18.5670i	−0.175732	−	0.304376i	0.764682	−	0.644407i	$-0.222896\pi$
$61$	−10.7196	−	18.5670i	−0.175732	−	0.304376i	−0.940414	+	0.340031i	$0.889562\pi$
$62$	−23.8075	+	23.8075i	−0.383992	+	0.383992i
$63$	43.0045	+	120.963i	0.682612	+	1.92004i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	41.1800	−	71.3259i	0.623940	−	1.08070i
$67$	−13.7678	−	51.3823i	−0.205490	−	0.766900i	−0.989300	−	0.145898i	$-0.953393\pi$
$67$	−13.7678	−	51.3823i	−0.205490	−	0.766900i	0.783809	−	0.621001i	$-0.213274\pi$
$68$	−4.58386	+	17.1072i	−0.0674098	+	0.251577i
$69$			148.984i			2.15919i
$70$		0			0
$71$	−101.186			−1.42516			−0.712579	−	0.701591i	$-0.752473\pi$
$71$	−101.186			−1.42516			−0.712579	+	0.701591i	$0.752473\pi$
$72$	50.1058	+	13.4258i	0.695913	+	0.186469i
$73$	101.181	−	27.1115i	1.38605	−	0.371390i	0.512734	−	0.858548i	$-0.328633\pi$
$73$	101.181	−	27.1115i	1.38605	−	0.371390i	0.873314	+	0.487157i	$0.161966\pi$
$74$	18.9964	+	10.9676i	0.256708	+	0.148211i
$75$		0			0
$76$	−13.3774			−0.176018
$77$	59.3481	+	50.5605i	0.770754	+	0.656630i
$78$	−71.1666	−	71.1666i	−0.912393	−	0.912393i
$79$	−11.7992	+	6.81228i	−0.149357	+	0.0862314i	−0.572816	−	0.819684i	$-0.694149\pi$
$79$	−11.7992	+	6.81228i	−0.149357	+	0.0862314i	0.423459	+	0.905915i	$0.360816\pi$
$80$		0			0
$81$	45.1475	−	78.1978i	0.557377	−	0.965406i
$82$	−12.5436	−	3.36105i	−0.152971	−	0.0409884i
$83$	−28.4835	−	28.4835i	−0.343175	−	0.343175i	0.514385	−	0.857560i	$-0.328020\pi$
$83$	−28.4835	−	28.4835i	−0.343175	−	0.343175i	−0.857560	+	0.514385i	$0.828020\pi$
$84$	−31.4324	+	66.1108i	−0.374195	+	0.787034i
$85$		0			0
$86$	−55.1244	−	95.4783i	−0.640981	−	1.11021i
$87$	−39.3451	−	146.838i	−0.452242	−	1.68779i
$88$	30.4292	−	8.15349i	0.345787	−	0.0926533i
$89$	−6.56157	+	3.78833i	−0.0737256	+	0.0425655i	−0.536410	−	0.843958i	$-0.680220\pi$
$89$	−6.56157	+	3.78833i	−0.0737256	+	0.0425655i	0.462684	+	0.886523i	$0.346886\pi$
$90$		0			0
$91$	78.4508	−	54.0615i	0.862097	−	0.594083i
$92$	−40.2954	+	40.2954i	−0.437993	+	0.437993i
$93$	−32.2188	+	120.242i	−0.346439	+	1.29293i
$94$	−10.8455	−	6.26167i	−0.115378	−	0.0666136i
$95$		0			0
$96$	14.7892	+	25.6156i	0.154054	+	0.266829i
$97$	−74.4232	+	74.4232i	−0.767249	+	0.767249i	−0.977621	−	0.210372i	$-0.932532\pi$
$97$	−74.4232	+	74.4232i	−0.767249	+	0.767249i	0.210372	+	0.977621i	$0.432532\pi$
$98$	−56.1632	−	40.5919i	−0.573093	−	0.414203i
$99$		−	204.268i		−	2.06332i
$100$		0			0
$101$	−62.1520	+	107.650i	−0.615366	+	1.06585i	0.374954	+	0.927044i	$0.377659\pi$
$101$	−62.1520	+	107.650i	−0.615366	+	1.06585i	−0.990320	+	0.138802i	$0.955675\pi$
$102$	16.9479	+	63.2504i	0.166156	+	0.620102i
$103$	−26.8210	+	100.098i	−0.260398	+	0.971820i	0.704609	+	0.709596i	$0.251123\pi$
$103$	−26.8210	+	100.098i	−0.260398	+	0.971820i	−0.965007	+	0.262224i	$0.915544\pi$
$104$		−	38.4966i		−	0.370160i
$105$		0			0
$106$	−20.2115			−0.190675
$107$	86.7110	+	23.2341i	0.810383	+	0.217142i	0.640138	−	0.768260i	$-0.278877\pi$
$107$	86.7110	+	23.2341i	0.810383	+	0.217142i	0.170245	+	0.985402i	$0.445544\pi$
$108$	94.3450	−	25.2797i	0.873565	−	0.234071i
$109$	145.926	+	84.2503i	1.33877	+	0.772938i	0.986625	−	0.163008i	$-0.0521196\pi$
$109$	145.926	+	84.2503i	1.33877	+	0.772938i	0.352143	+	0.935946i	$0.385453\pi$
$110$		0			0
$111$	81.1008			0.730638
$112$	−26.3823	+	9.37941i	−0.235556	+	0.0837447i
$113$	−22.2552	−	22.2552i	−0.196949	−	0.196949i	0.601742	−	0.798691i	$-0.294474\pi$
$113$	−22.2552	−	22.2552i	−0.196949	−	0.196949i	−0.798691	+	0.601742i	$0.794474\pi$
$114$	−42.8336	+	24.7300i	−0.375734	+	0.216930i
$115$		0			0
$116$	29.0733	−	50.3565i	0.250632	−	0.434108i
$117$	−241.113	−	64.6059i	−2.06079	−	0.552188i
$118$	78.2871	+	78.2871i	0.663450	+	0.663450i
$119$	−61.7902	+	4.94032i	−0.519246	+	0.0415153i
$120$		0			0
$121$	−1.52615	−	2.64336i	−0.0126128	−	0.0218460i
$122$	−7.84732	−	29.2866i	−0.0643223	−	0.240054i
$123$	−46.3775	+	12.4268i	−0.377052	+	0.101031i
$124$	−41.2358	+	23.8075i	−0.332547	+	0.191996i
$125$		0			0
$126$	14.4698	+	180.979i	0.114840	+	1.43634i
$127$	80.5418	−	80.5418i	0.634187	−	0.634187i	−0.314928	−	0.949115i	$-0.601980\pi$
$127$	80.5418	−	80.5418i	0.634187	−	0.634187i	0.949115	+	0.314928i	$0.101980\pi$
$128$	−2.92820	+	10.9282i	−0.0228766	+	0.0853766i
$129$	−353.011	−	203.811i	−2.73652	−	1.57993i
$130$		0			0
$131$	−38.6646	−	66.9690i	−0.295149	−	0.511214i	0.679870	−	0.733332i	$-0.262036\pi$
$131$	−38.6646	−	66.9690i	−0.295149	−	0.511214i	−0.975020	+	0.222119i	$0.928703\pi$
$132$	82.3600	−	82.3600i	0.623940	−	0.623940i
$133$	−15.6840	−	44.1157i	−0.117925	−	0.331697i
$134$		−	75.2289i		−	0.561409i
$135$		0			0
$136$	−12.5233	+	21.6911i	−0.0920834	+	0.159493i
$137$	−16.6880	−	62.2804i	−0.121810	−	0.454602i	0.877896	−	0.478852i	$-0.158947\pi$
$137$	−16.6880	−	62.2804i	−0.121810	−	0.454602i	−0.999706	+	0.0242501i	$0.992280\pi$
$138$	−54.5319	+	203.516i	−0.395159	+	1.47475i
$139$			51.4750i			0.370324i	0.982708	+	0.185162i	$0.0592810\pi$
$139$			51.4750i			0.370324i	−0.982708	+	0.185162i	$0.940719\pi$
$140$		0			0
$141$	−46.3025			−0.328387
$142$	−138.223	−	37.0368i	−0.973402	−	0.260822i
$143$	−146.428	+	39.2352i	−1.02397	+	0.274372i
$144$	63.5316	+	36.6800i	0.441191	+	0.254722i
$145$		0			0
$146$	148.140			1.01466
$147$	−254.872	−	26.1473i	−1.73382	−	0.177873i
$148$	21.9352	+	21.9352i	0.148211	+	0.148211i
$149$	47.3177	−	27.3189i	0.317568	−	0.183348i	−0.332740	−	0.943019i	$-0.607973\pi$
$149$	47.3177	−	27.3189i	0.317568	−	0.183348i	0.650308	+	0.759670i	$0.274640\pi$
$150$		0			0
$151$	62.2354	−	107.795i	0.412155	−	0.713874i	−0.582970	−	0.812494i	$-0.698109\pi$
$151$	62.2354	−	107.795i	0.412155	−	0.713874i	0.995125	+	0.0986200i	$0.0314428\pi$
$152$	−18.2738	−	4.89645i	−0.120222	−	0.0322135i
$153$	114.839	+	114.839i	0.750582	+	0.750582i
$154$	62.5645	+	90.7899i	0.406263	+	0.589545i
$155$		0			0
$156$	−71.1666	−	123.264i	−0.456196	−	0.790155i
$157$	20.6950	+	77.2347i	0.131815	+	0.491941i	0.999991	−	0.00431635i	$-0.00137394\pi$
$157$	20.6950	+	77.2347i	0.131815	+	0.491941i	−0.868176	+	0.496257i	$0.834707\pi$
$158$	−18.6115	+	4.98693i	−0.117794	+	0.0315629i
$159$	−64.7163	+	37.3640i	−0.407021	+	0.234994i
$160$		0			0
$161$	−180.129	−	85.6424i	−1.11881	−	0.531940i
$162$	90.2951	−	90.2951i	0.557377	−	0.557377i
$163$	48.8390	−	182.269i	0.299626	−	1.11822i	−0.637848	−	0.770162i	$-0.720175\pi$
$163$	48.8390	−	182.269i	0.299626	−	1.11822i	0.937474	−	0.348056i	$-0.113158\pi$
$164$	−15.9047	−	9.18256i	−0.0969797	−	0.0559912i
$165$		0			0
$166$	−28.4835	−	49.3349i	−0.171587	−	0.297198i
$167$	−116.548	+	116.548i	−0.697892	+	0.697892i	−0.963955	−	0.266064i	$-0.914277\pi$
$167$	−116.548	+	116.548i	−0.697892	+	0.697892i	0.266064	+	0.963955i	$0.414277\pi$
$168$	−67.1357	+	78.8040i	−0.399617	+	0.469072i
$169$			16.2485i			0.0961450i
$170$		0			0
$171$	−61.3351	+	106.236i	−0.358685	+	0.621260i
$172$	−40.3539	−	150.603i	−0.234615	−	0.875597i
$173$	82.3855	−	307.467i	0.476217	−	1.77727i	−0.140500	−	0.990081i	$-0.544871\pi$
$173$	82.3855	−	307.467i	0.476217	−	1.77727i	0.616717	−	0.787185i	$-0.288462\pi$
$174$		−	214.985i		−	1.23555i
$175$		0			0
$176$	44.5515			0.253134
$177$	395.397	+	105.946i	2.23388	+	0.598566i
$178$	−10.3499	+	2.77325i	−0.0581455	+	0.0155800i
$179$	57.5525	+	33.2280i	0.321522	+	0.185631i	0.652071	−	0.758158i	$-0.273900\pi$
$179$	57.5525	+	33.2280i	0.321522	+	0.185631i	−0.330549	+	0.943789i	$0.607234\pi$
$180$		0			0
$181$	−71.5932			−0.395543			−0.197771	−	0.980248i	$-0.563370\pi$
$181$	−71.5932			−0.395543			−0.197771	+	0.980248i	$0.563370\pi$
$182$	126.954	−	45.1344i	0.697548	−	0.247991i
$183$	−79.2673	−	79.2673i	−0.433155	−	0.433155i
$184$	−69.7937	+	40.2954i	−0.379313	+	0.218997i
$185$		0			0
$186$	−88.0234	+	152.461i	−0.473244	+	0.819683i
$187$	95.2690	+	25.5273i	0.509460	+	0.136509i
$188$	−12.5233	−	12.5233i	−0.0666136	−	0.0666136i
$189$	193.980	+	281.491i	1.02635	+	1.48937i
$190$		0			0
$191$	166.665	+	288.672i	0.872590	+	1.51137i	0.859308	+	0.511458i	$0.170894\pi$
$191$	166.665	+	288.672i	0.872590	+	1.51137i	0.0132816	+	0.999912i	$0.495772\pi$
$192$	10.8264	+	40.4048i	0.0563877	+	0.210442i
$193$	95.9658	−	25.7140i	0.497232	−	0.133233i	−0.00148294	−	0.999999i	$-0.500472\pi$
$193$	95.9658	−	25.7140i	0.497232	−	0.133233i	0.498715	+	0.866766i	$0.333805\pi$
$194$	−128.905	+	74.4232i	−0.664457	+	0.383625i
$195$		0			0
$196$	−61.8626	−	76.0067i	−0.315626	−	0.387789i
$197$	131.527	−	131.527i	0.667651	−	0.667651i	−0.289521	−	0.957172i	$-0.593496\pi$
$197$	131.527	−	131.527i	0.667651	−	0.667651i	0.957172	+	0.289521i	$0.0934960\pi$
$198$	74.7674	−	279.036i	0.377613	−	1.40927i
$199$	211.873	+	122.325i	1.06469	+	0.614697i	0.926725	−	0.375741i	$-0.122612\pi$
$199$	211.873	+	122.325i	1.06469	+	0.614697i	0.137961	+	0.990438i	$0.455945\pi$
$200$		0			0
$201$	−139.072	−	240.879i	−0.691899	−	1.19840i
$202$	−124.304	+	124.304i	−0.615366	+	0.615366i
$203$	200.152	+	36.8385i	0.985968	+	0.181470i
$204$			92.6050i			0.453946i
$205$		0			0
$206$	−73.2765	+	126.919i	−0.355711	+	0.616109i
$207$	135.249	+	504.758i	0.653379	+	2.43844i
$208$	14.0907	−	52.5873i	0.0677439	−	0.252824i
$209$			74.4977i			0.356448i
$210$		0			0
$211$	203.685			0.965329			0.482665	−	0.875805i	$-0.339669\pi$
$211$	203.685			0.965329			0.482665	+	0.875805i	$0.339669\pi$
$212$	−27.6095	−	7.39793i	−0.130233	−	0.0348959i
$213$	−511.051	+	136.936i	−2.39930	+	0.642891i
$214$	109.945	+	63.4769i	0.513762	+	0.296621i
$215$		0			0
$216$	138.131			0.639494
$217$	−126.858	−	108.075i	−0.584600	−	0.498039i
$218$	168.501	+	168.501i	0.772938	+	0.772938i
$219$	474.337	−	273.859i	2.16592	−	1.25050i
$220$		0			0
$221$	60.2633	−	104.379i	0.272685	−	0.472303i
$222$	110.786	+	29.6850i	0.499035	+	0.133716i
$223$	194.661	+	194.661i	0.872921	+	0.872921i	0.992790	−	0.119869i	$-0.0382474\pi$
$223$	194.661	+	194.661i	0.872921	+	0.872921i	−0.119869	+	0.992790i	$0.538247\pi$
$224$	−39.4720	+	3.15591i	−0.176214	+	0.0140889i
$225$		0			0
$226$	−22.2552	−	38.5472i	−0.0984744	−	0.170563i
$227$	59.0356	+	220.324i	0.260069	+	0.970589i	0.965200	+	0.261513i	$0.0842213\pi$
$227$	59.0356	+	220.324i	0.260069	+	0.970589i	−0.705132	+	0.709077i	$0.749112\pi$
$228$	−67.5637	+	18.1036i	−0.296332	+	0.0794019i
$229$	161.759	−	93.3917i	0.706372	−	0.407824i	−0.103344	−	0.994646i	$-0.532954\pi$
$229$	161.759	−	93.3917i	0.706372	−	0.407824i	0.809716	+	0.586821i	$0.199621\pi$
$230$		0			0
$231$	368.167	+	175.045i	1.59380	+	0.757771i
$232$	58.1467	−	58.1467i	0.250632	−	0.250632i
$233$	87.0627	−	324.922i	0.373660	−	1.39452i	−0.481634	−	0.876373i	$-0.659956\pi$
$233$	87.0627	−	324.922i	0.373660	−	1.39452i	0.855293	−	0.518144i	$-0.173377\pi$
$234$	−305.719	−	176.507i	−1.30649	−	0.754302i
$235$		0			0
$236$	78.2871	+	135.597i	0.331725	+	0.574564i
$237$	−50.3740	+	50.3740i	−0.212549	+	0.212549i
$238$	−86.2153	−	15.8682i	−0.362249	−	0.0666731i
$239$			83.6738i			0.350099i	0.984560	+	0.175050i	$0.0560086\pi$
$239$			83.6738i			0.350099i	−0.984560	+	0.175050i	$0.943991\pi$
$240$		0			0
$241$	−57.1739	+	99.0280i	−0.237236	+	0.410905i	−0.959920	−	0.280274i	$-0.909575\pi$
$241$	−57.1739	+	99.0280i	−0.237236	+	0.410905i	0.722684	+	0.691178i	$0.242908\pi$
$242$	−1.11722	−	4.16951i	−0.00461660	−	0.0172294i
$243$	8.43820	−	31.4918i	0.0347251	−	0.129596i
$244$		−	42.8786i		−	0.175732i
$245$		0			0
$246$	−67.9013			−0.276022
$247$	87.9349	+	23.5621i	0.356012	+	0.0953931i
$248$	−65.0433	+	17.4283i	−0.262272	+	0.0702754i
$249$	−182.406	−	105.312i	−0.732553	−	0.422940i
$250$		0			0
$251$	−2.86375			−0.0114094			−0.00570468	−	0.999984i	$-0.501816\pi$
$251$	−2.86375			−0.0114094			−0.00570468	+	0.999984i	$0.501816\pi$
$252$	−46.4768	+	252.518i	−0.184432	+	1.00206i
$253$	224.403	+	224.403i	0.886967	+	0.886967i
$254$	139.502	−	80.5418i	0.549222	−	0.317094i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	82.9396	+	22.2236i	0.322722	+	0.0864731i	0.416543	−	0.909116i	$-0.363241\pi$
$257$	82.9396	+	22.2236i	0.322722	+	0.0864731i	−0.0938211	+	0.995589i	$0.529908\pi$
$258$	−407.622	−	407.622i	−1.57993	−	1.57993i
$259$	−46.6202	+	98.0550i	−0.180001	+	0.378591i
$260$		0			0
$261$	−266.602	−	461.769i	−1.02146	−	1.76923i
$262$	−28.3044	−	105.634i	−0.108032	−	0.403182i
$263$	−244.691	+	65.5647i	−0.930384	+	0.249296i	−0.692018	−	0.721880i	$-0.743278\pi$
$263$	−244.691	+	65.5647i	−0.930384	+	0.249296i	−0.238365	+	0.971176i	$0.576612\pi$
$264$	142.652	−	82.3600i	0.540348	−	0.311970i
$265$		0			0
$266$	−5.27722	−	66.0039i	−0.0198392	−	0.248135i
$267$	−28.0131	+	28.0131i	−0.104918	+	0.104918i
$268$	27.5357	−	102.765i	0.102745	−	0.383450i
$269$	−435.001	−	251.148i	−1.61710	−	0.933636i	−0.987664	−	0.156587i	$-0.949951\pi$
$269$	−435.001	−	251.148i	−1.61710	−	0.933636i	−0.629441	−	0.777049i	$-0.716716\pi$
$270$		0			0
$271$	99.2563	+	171.917i	0.366259	+	0.634380i	0.988977	−	0.148066i	$-0.0473049\pi$
$271$	99.2563	+	171.917i	0.366259	+	0.634380i	−0.622718	+	0.782446i	$0.713972\pi$
$272$	−25.0467	+	25.0467i	−0.0920834	+	0.0920834i
$273$	323.062	−	379.211i	1.18338	−	1.38905i
$274$		−	91.1849i		−	0.332792i
$275$		0			0
$276$	−148.984	+	258.048i	−0.539797	+	0.934956i
$277$	−98.4162	−	367.294i	−0.355293	−	1.32597i	−0.880115	−	0.474760i	$-0.842535\pi$
$277$	−98.4162	−	367.294i	−0.355293	−	1.32597i	0.524822	−	0.851212i	$-0.324132\pi$
$278$	−18.8412	+	70.3162i	−0.0677740	+	0.252936i
$279$			436.629i			1.56498i
$280$		0			0
$281$	135.599			0.482558			0.241279	−	0.970456i	$-0.422433\pi$
$281$	135.599			0.482558			0.241279	+	0.970456i	$0.422433\pi$
$282$	−63.2504	−	16.9479i	−0.224292	−	0.0600989i
$283$	340.827	−	91.3244i	1.20434	−	0.322701i	0.399799	−	0.916603i	$-0.369080\pi$
$283$	340.827	−	91.3244i	1.20434	−	0.322701i	0.804538	+	0.593902i	$0.202413\pi$
$284$	−175.260	−	101.186i	−0.617112	−	0.356290i
$285$		0			0
$286$	−214.385			−0.749599
$287$	11.6351	−	63.2161i	0.0405405	−	0.220265i
$288$	73.3599	+	73.3599i	0.254722	+	0.254722i
$289$	182.370	−	105.291i	0.631039	−	0.364330i
$290$		0			0
$291$	−275.164	+	476.599i	−0.945582	+	1.63780i
$292$	202.363	+	54.2230i	0.693024	+	0.185695i
$293$	−73.2341	−	73.2341i	−0.249946	−	0.249946i	0.571003	−	0.820948i	$-0.306555\pi$
$293$	−73.2341	−	73.2341i	−0.249946	−	0.249946i	−0.820948	+	0.571003i	$0.806555\pi$
$294$	−338.591	−	129.007i	−1.15167	−	0.438801i
$295$		0			0
$296$	21.9352	+	37.9928i	0.0741053	+	0.128354i
$297$	−140.781	−	525.402i	−0.474010	−	1.76903i
$298$	74.6366	−	19.9988i	0.250458	−	0.0671101i
$299$	335.852	−	193.904i	1.12325	−	0.648510i
$300$		0			0
$301$	449.344	−	309.649i	1.49284	−	1.02873i
$302$	124.471	−	124.471i	0.412155	−	0.412155i
$303$	−168.221	+	627.810i	−0.555185	+	2.07198i
$304$	−23.1703	−	13.3774i	−0.0762180	−	0.0440045i
$305$		0			0
$306$	114.839	+	198.907i	0.375291	+	0.650023i
$307$	394.192	−	394.192i	1.28401	−	1.28401i	0.345652	−	0.938363i	$-0.387658\pi$
$307$	394.192	−	394.192i	1.28401	−	1.28401i	0.938363	−	0.345652i	$-0.112342\pi$
$308$	52.2333	+	146.922i	0.169589	+	0.477018i
$309$			541.849i			1.75356i
$310$		0			0
$311$	−117.796	+	204.029i	−0.378766	+	0.656041i	−0.990883	−	0.134726i	$-0.956985\pi$
$311$	−117.796	+	204.029i	−0.378766	+	0.656041i	0.612117	+	0.790767i	$0.290318\pi$
$312$	−52.0976	−	194.431i	−0.166979	−	0.623176i
$313$	−94.8023	+	353.807i	−0.302883	+	1.13037i	0.631870	+	0.775075i	$0.282288\pi$
$313$	−94.8023	+	353.807i	−0.302883	+	1.13037i	−0.934752	+	0.355300i	$0.884379\pi$
$314$			113.079i			0.360126i
$315$		0			0
$316$	−27.2491			−0.0862314
$317$	−19.9576	−	5.34762i	−0.0629577	−	0.0168695i	0.227203	−	0.973847i	$-0.427042\pi$
$317$	−19.9576	−	5.34762i	−0.0629577	−	0.0168695i	−0.290160	+	0.956978i	$0.593709\pi$
$318$	−102.080	+	27.3523i	−0.321007	+	0.0860136i
$319$	−280.432	−	161.908i	−0.879098	−	0.507548i
$320$		0			0
$321$	469.385			1.46226
$322$	−214.714	−	182.922i	−0.666813	−	0.568079i
$323$	−41.8823	−	41.8823i	−0.129667	−	0.129667i
$324$	156.396	−	90.2951i	0.482703	−	0.278689i
$325$		0			0
$326$	133.431	−	231.108i	0.409296	−	0.708922i
$327$	851.029	+	228.032i	2.60253	+	0.697347i
$328$	−18.3651	−	18.3651i	−0.0559912	−	0.0559912i
$329$	26.6167	−	55.9821i	0.0809017	−	0.170158i
$330$		0			0
$331$	−70.6868	−	122.433i	−0.213555	−	0.369889i	0.739269	−	0.673410i	$-0.235171\pi$
$331$	−70.6868	−	122.433i	−0.213555	−	0.369889i	−0.952825	+	0.303521i	$0.901838\pi$
$332$	−20.8514	−	77.8184i	−0.0628054	−	0.234393i
$333$	274.770	−	73.6243i	0.825134	−	0.221094i
$334$	−201.867	+	116.548i	−0.604392	+	0.348946i
$335$		0			0
$336$	−120.553	+	83.0749i	−0.358790	+	0.247247i
$337$	−226.963	+	226.963i	−0.673482	+	0.673482i	−0.958517	−	0.285035i	$-0.907995\pi$
$337$	−226.963	+	226.963i	−0.673482	+	0.673482i	0.285035	+	0.958517i	$0.407995\pi$
$338$	−5.94737	+	22.1959i	−0.0175958	+	0.0656683i
$339$	−142.520	−	82.2841i	−0.420414	−	0.242726i
$340$		0			0
$341$	132.583	+	229.640i	0.388805	+	0.673430i
$342$	−122.670	+	122.670i	−0.358685	+	0.358685i
$343$	178.125	−	293.122i	0.519314	−	0.854584i
$344$		−	220.498i		−	0.640981i
$345$		0			0
$346$	225.081	−	389.852i	0.650524	−	1.12674i
$347$	149.887	+	559.385i	0.431950	+	1.61206i	0.748261	+	0.663404i	$0.230889\pi$
$347$	149.887	+	559.385i	0.431950	+	1.61206i	−0.316311	+	0.948656i	$0.602444\pi$
$348$	78.6902	−	293.676i	0.226121	−	0.843896i
$349$		−	46.5465i		−	0.133371i	−0.997774	−	0.0666856i	$-0.978758\pi$
$349$		−	46.5465i		−	0.133371i	0.997774	−	0.0666856i	$-0.0212424\pi$
$350$		0			0
$351$	−664.695			−1.89372
$352$	60.8585	+	16.3070i	0.172893	+	0.0463267i
$353$	−513.383	+	137.561i	−1.45434	+	0.389690i	−0.897532	−	0.440949i	$-0.854642\pi$
$353$	−513.383	+	137.561i	−1.45434	+	0.389690i	−0.556811	+	0.830639i	$0.687975\pi$
$354$	501.343	+	289.450i	1.41622	+	0.817657i
$355$		0			0
$356$	−15.1533			−0.0425655
$357$	−305.392	+	108.573i	−0.855439	+	0.304125i
$358$	66.4559	+	66.4559i	0.185631	+	0.185631i
$359$	61.5713	−	35.5482i	0.171508	−	0.0990201i	−0.411789	−	0.911279i	$-0.635096\pi$
$359$	61.5713	−	35.5482i	0.171508	−	0.0990201i	0.583297	+	0.812259i	$0.301763\pi$
$360$		0			0
$361$	−158.131	+	273.891i	−0.438035	+	0.758700i
$362$	−97.7982	−	26.2049i	−0.270161	−	0.0723893i
$363$	−11.2852	−	11.2852i	−0.0310888	−	0.0310888i
$364$	189.942	−	15.1865i	0.521820	−	0.0417211i
$365$		0			0
$366$	−79.2673	−	137.295i	−0.216577	−	0.375123i
$367$	36.5132	+	136.269i	0.0994911	+	0.371306i	0.997662	−	0.0683405i	$-0.0217704\pi$
$367$	36.5132	+	136.269i	0.0994911	+	0.371306i	−0.898171	+	0.439646i	$0.855104\pi$
$368$	−110.089	+	29.4983i	−0.299155	+	0.0801584i
$369$	−145.846	+	84.2040i	−0.395246	+	0.228195i
$370$		0			0
$371$	−7.97322	−	99.7237i	−0.0214912	−	0.268797i
$372$	−176.047	+	176.047i	−0.473244	+	0.473244i
$373$	78.3283	−	292.325i	0.209995	−	0.783714i	−0.777873	−	0.628421i	$-0.783701\pi$
$373$	78.3283	−	292.325i	0.209995	−	0.783714i	0.987869	−	0.155292i	$-0.0496319\pi$
$374$	120.796	+	69.7417i	0.322985	+	0.186475i
$375$		0			0
$376$	−12.5233	−	21.6911i	−0.0333068	−	0.0576890i
$377$	−279.806	+	279.806i	−0.742192	+	0.742192i
$378$	161.948	+	455.526i	0.428434	+	1.20510i
$379$		−	329.976i		−	0.870649i	−0.900274	−	0.435325i	$-0.856634\pi$
$379$		−	329.976i		−	0.870649i	0.900274	−	0.435325i	$-0.143366\pi$
$380$		0			0
$381$	297.787	−	515.782i	0.781593	−	1.35376i
$382$	122.007	+	455.336i	0.319390	+	1.19198i
$383$	−46.0298	+	171.786i	−0.120182	+	0.448527i	−0.999622	−	0.0274833i	$-0.991251\pi$
$383$	−46.0298	+	171.786i	−0.120182	+	0.448527i	0.879440	+	0.476010i	$0.157917\pi$
$384$			59.1567i			0.154054i
$385$		0			0
$386$	140.504			0.363999
$387$	−1381.03	−	370.045i	−3.56854	−	0.956188i
$388$	−203.328	+	54.4815i	−0.524041	+	0.140416i
$389$	−207.304	−	119.687i	−0.532914	−	0.307678i	0.209288	−	0.977854i	$-0.432885\pi$
$389$	−207.304	−	119.687i	−0.532914	−	0.307678i	−0.742202	+	0.670176i	$0.766219\pi$
$390$		0			0
$391$	−252.317			−0.645311
$392$	−56.6856	−	126.470i	−0.144606	−	0.322628i
$393$	−285.909	−	285.909i	−0.727503	−	0.727503i
$394$	227.812	−	131.527i	0.578202	−	0.333825i
$395$		0			0
$396$	204.268	−	353.803i	0.515829	−	0.893443i
$397$	−594.046	−	159.174i	−1.49634	−	0.400942i	−0.584466	−	0.811419i	$-0.698696\pi$
$397$	−594.046	−	159.174i	−1.49634	−	0.400942i	−0.911871	+	0.410476i	$0.865362\pi$
$398$	244.649	+	244.649i	0.614697	+	0.614697i
$399$	−138.915	−	201.586i	−0.348159	−	0.505227i
$400$		0			0
$401$	−243.686	−	422.077i	−0.607697	−	1.05256i	−0.991619	−	0.129197i	$-0.958760\pi$
$401$	−243.686	−	422.077i	−0.607697	−	1.05256i	0.383922	−	0.923366i	$-0.374573\pi$
$402$	−101.808	−	379.951i	−0.253253	−	0.945151i
$403$	312.993	−	83.8663i	0.776659	−	0.208105i
$404$	−215.301	+	124.304i	−0.532923	+	0.307683i
$405$		0			0
$406$	259.928	+	123.583i	0.640217	+	0.304391i
$407$	122.156	−	122.156i	0.300137	−	0.300137i
$408$	−33.8958	+	126.501i	−0.0830779	+	0.310051i
$409$	197.730	+	114.159i	0.483447	+	0.279119i	0.721852	−	0.692047i	$-0.243291\pi$
$409$	197.730	+	114.159i	0.483447	+	0.279119i	−0.238405	+	0.971166i	$0.576624\pi$
$410$		0			0
$411$	−168.569	−	291.970i	−0.410143	−	0.710388i
$412$	−146.553	+	146.553i	−0.355711	+	0.355711i
$413$	−355.385	+	417.152i	−0.860497	+	1.01005i
$414$			739.017i			1.78506i
$415$		0			0
$416$	38.4966	−	66.6781i	0.0925399	−	0.160284i
$417$	69.6614	+	259.980i	0.167054	+	0.623453i
$418$	−27.2680	+	101.766i	−0.0652345	+	0.243459i
$419$			312.625i			0.746121i	0.927807	+	0.373061i	$0.121692\pi$
$419$			312.625i			0.746121i	−0.927807	+	0.373061i	$0.878308\pi$
$420$		0			0
$421$	479.690			1.13941			0.569703	−	0.821851i	$-0.307058\pi$
$421$	479.690			1.13941			0.569703	+	0.821851i	$0.307058\pi$
$422$	278.238	+	74.5537i	0.659332	+	0.176668i
$423$	−156.873	+	42.0340i	−0.370858	+	0.0993711i
$424$	−35.0074	−	20.2115i	−0.0825646	−	0.0476687i
$425$		0			0
$426$	−748.231			−1.75641
$427$	141.404	−	50.2719i	0.331158	−	0.117733i
$428$	126.954	+	126.954i	0.296621	+	0.296621i
$429$	−686.451	+	396.323i	−1.60012	+	0.923829i
$430$		0			0
$431$	268.836	−	465.638i	0.623750	−	1.08037i	−0.365031	−	0.930995i	$-0.618942\pi$
$431$	268.836	−	465.638i	0.623750	−	1.08037i	0.988781	−	0.149371i	$-0.0477250\pi$
$432$	188.690	+	50.5593i	0.436782	+	0.117036i
$433$	−13.8191	−	13.8191i	−0.0319148	−	0.0319148i	0.690969	−	0.722884i	$-0.257184\pi$
$433$	−13.8191	−	13.8191i	−0.0319148	−	0.0319148i	−0.722884	+	0.690969i	$0.757184\pi$
$434$	−133.733	−	194.066i	−0.308142	−	0.447156i
$435$		0			0
$436$	168.501	+	291.851i	0.386469	+	0.669384i
$437$	−49.3261	−	184.088i	−0.112874	−	0.421253i
$438$	748.196	−	200.478i	1.70821	−	0.457713i
$439$	160.490	−	92.6588i	0.365580	−	0.211068i	−0.305945	−	0.952049i	$-0.598973\pi$
$439$	160.490	−	92.6588i	0.365580	−	0.211068i	0.671526	+	0.740981i	$0.265639\pi$
$440$		0			0
$441$	−887.243	+	142.788i	−2.01189	+	0.323783i
$442$	120.527	−	120.527i	0.272685	−	0.272685i
$443$	−44.0219	+	164.292i	−0.0993722	+	0.370862i	−0.997646	−	0.0685740i	$-0.978155\pi$
$443$	−44.0219	+	164.292i	−0.0993722	+	0.370862i	0.898274	+	0.439436i	$0.144822\pi$
$444$	140.471	+	81.1008i	0.316375	+	0.182659i
$445$		0			0
$446$	194.661	+	337.163i	0.436460	+	0.755972i
$447$	202.012	−	202.012i	0.451928	−	0.451928i
$448$	−55.0749	−	10.1367i	−0.122935	−	0.0226266i
$449$			136.021i			0.302943i	0.988462	+	0.151472i	$0.0484012\pi$
$449$			136.021i			0.302943i	−0.988462	+	0.151472i	$0.951599\pi$
$450$		0			0
$451$	−51.1371	+	88.5721i	−0.113386	+	0.196391i
$452$	−16.2919	−	60.8024i	−0.0360441	−	0.134518i
$453$	168.447	−	628.652i	0.371847	−	1.38775i
$454$			322.576i			0.710520i
$455$		0			0
$456$	−98.9201			−0.216930
$457$	744.760	+	199.558i	1.62967	+	0.436669i	0.953823	−	0.300370i	$-0.0971102\pi$
$457$	744.760	+	199.558i	1.62967	+	0.436669i	0.675850	+	0.737040i	$0.263777\pi$
$458$	255.151	−	68.3675i	0.557098	−	0.149274i
$459$	374.525	+	216.232i	0.815959	+	0.471094i
$460$		0			0
$461$	−174.788			−0.379149			−0.189574	−	0.981866i	$-0.560711\pi$
$461$	−174.788			−0.379149			−0.189574	+	0.981866i	$0.560711\pi$
$462$	438.855	+	373.874i	0.949902	+	0.809252i
$463$	219.730	+	219.730i	0.474578	+	0.474578i	0.903393	−	0.428814i	$-0.141069\pi$
$463$	219.730	+	219.730i	0.474578	+	0.474578i	−0.428814	+	0.903393i	$0.641069\pi$
$464$	100.713	−	58.1467i	0.217054	−	0.125316i
$465$		0			0
$466$	237.860	−	411.985i	0.510429	−	0.884088i
$467$	−749.905	−	200.936i	−1.60579	−	0.430270i	−0.659006	−	0.752137i	$-0.729023\pi$
$467$	−749.905	−	200.936i	−1.60579	−	0.430270i	−0.946785	+	0.321867i	$0.895690\pi$
$468$	−353.013	−	353.013i	−0.754302	−	0.754302i
$469$	371.179	−	29.6770i	0.791427	−	0.0632771i
$470$		0			0
$471$	209.044	+	362.075i	0.443830	+	0.768737i
$472$	57.3101	+	213.884i	0.121420	+	0.453145i
$473$	−838.697	+	224.728i	−1.77314	+	0.475112i
$474$	−87.2503	+	50.3740i	−0.184072	+	0.106274i
$475$		0			0
$476$	−111.964	−	53.2333i	−0.235219	−	0.111835i
$477$	−185.339	+	185.339i	−0.388552	+	0.388552i
$478$	−30.6267	+	114.300i	−0.0640726	+	0.239122i
$479$	−78.4044	−	45.2668i	−0.163684	−	0.0945028i	0.415921	−	0.909401i	$-0.363459\pi$
$479$	−78.4044	−	45.2668i	−0.163684	−	0.0945028i	−0.579604	+	0.814898i	$0.696793\pi$
$480$		0			0
$481$	−105.554	−	182.824i	−0.219446	−	0.380092i
$482$	−114.348	+	114.348i	−0.237236	+	0.237236i
$483$	−1025.66	−	188.776i	−2.12352	−	0.390840i
$484$		−	6.10459i		−	0.0126128i
$485$		0			0
$486$	23.0536	−	39.9300i	0.0474354	−	0.0821605i
$487$	−236.419	−	882.327i	−0.485460	−	1.81176i	−0.577982	−	0.816050i	$-0.696159\pi$
$487$	−236.419	−	882.327i	−0.485460	−	1.81176i	0.0925219	−	0.995711i	$-0.470507\pi$
$488$	15.6946	−	58.5732i	0.0321611	−	0.120027i
$489$		−	986.664i		−	2.01772i
$490$		0			0
$491$	−885.439			−1.80334			−0.901669	−	0.432427i	$-0.857657\pi$
$491$	−885.439			−1.80334			−0.901669	+	0.432427i	$0.857657\pi$
$492$	−92.7549	−	24.8536i	−0.188526	−	0.0505154i
$493$	248.682	−	66.6341i	0.504426	−	0.135161i
$494$	111.497	+	64.3728i	0.225702	+	0.130309i
$495$		0			0
$496$	−95.2301			−0.191996
$497$	128.212	−	696.603i	0.257972	−	1.40162i
$498$	−210.624	−	210.624i	−0.422940	−	0.422940i
$499$	−559.499	+	323.027i	−1.12124	+	0.647348i	−0.941717	−	0.336406i	$-0.890789\pi$
$499$	−559.499	+	323.027i	−1.12124	+	0.647348i	−0.179522	+	0.983754i	$0.557455\pi$
$500$		0			0
$501$	−430.912	+	746.362i	−0.860104	+	1.48974i
$502$	−3.91195	−	1.04821i	−0.00779274	−	0.00208806i
$503$	498.400	+	498.400i	0.990855	+	0.990855i	0.999959	−	0.00910371i	$-0.00289784\pi$
$503$	498.400	+	498.400i	0.990855	+	0.990855i	−0.00910371	+	0.999959i	$0.502898\pi$
$504$	−155.917	+	327.935i	−0.309358	+	0.650664i
$505$		0			0
$506$	224.403	+	388.677i	0.443483	+	0.768136i
$507$	21.9892	+	82.0647i	0.0433711	+	0.161863i
$508$	220.044	−	58.9607i	0.433158	−	0.116064i
$509$	−256.295	+	147.972i	−0.503526	+	0.290711i	−0.730169	−	0.683267i	$-0.760558\pi$
$509$	−256.295	+	147.972i	−0.503526	+	0.290711i	0.226642	+	0.973978i	$0.427225\pi$
$510$		0			0
$511$	58.4396	+	730.923i	0.114363	+	1.43038i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−84.5438	+	315.522i	−0.164803	+	0.615052i
$514$	105.163	+	60.7160i	0.204598	+	0.118124i
$515$		0			0
$516$	−407.622	−	706.023i	−0.789966	−	1.36826i
$517$	−69.7417	+	69.7417i	−0.134897	+	0.134897i
$518$	−99.5750	+	116.881i	−0.192230	+	0.225640i
$519$		−	1664.38i		−	3.20691i
$520$		0			0
$521$	−343.065	+	594.206i	−0.658474	+	1.14051i	0.322537	+	0.946557i	$0.395464\pi$
$521$	−343.065	+	594.206i	−0.658474	+	1.14051i	−0.981011	+	0.193953i	$0.937869\pi$
$522$	−195.166	−	728.371i	−0.373882	−	1.39535i
$523$	119.269	−	445.117i	0.228047	−	0.851085i	−0.753113	−	0.657891i	$-0.771449\pi$
$523$	119.269	−	445.117i	0.228047	−	0.851085i	0.981161	−	0.193194i	$-0.0618846\pi$
$524$		−	154.658i		−	0.295149i
$525$		0			0
$526$	−358.252			−0.681088
$527$	−203.640	−	54.5652i	−0.386414	−	0.103539i
$528$	225.012	−	60.2917i	0.426159	−	0.114189i
$529$	−244.964	−	141.430i	−0.463069	−	0.267353i
$530$		0			0
$531$	1435.78			2.70392
$532$	16.9503	−	92.0946i	0.0318614	−	0.173110i
$533$	88.3744	+	88.3744i	0.165806	+	0.165806i
$534$	−48.5202	+	28.0131i	−0.0908617	+	0.0524590i
$535$		0			0
$536$	75.2289	−	130.300i	0.140352	−	0.243097i
$537$	335.642	+	89.9350i	0.625032	+	0.167477i
$538$	−502.296	−	502.296i	−0.933636	−	0.933636i
$539$	−423.276	+	344.509i	−0.785300	+	0.639164i
$540$		0			0
$541$	−78.6223	−	136.178i	−0.145328	−	0.251715i	0.784167	−	0.620549i	$-0.213090\pi$
$541$	−78.6223	−	136.178i	−0.145328	−	0.251715i	−0.929495	+	0.368834i	$0.879757\pi$
$542$	72.6607	+	271.173i	0.134060	+	0.500320i
$543$	−361.589	+	96.8874i	−0.665909	+	0.178430i
$544$	−43.3821	+	25.0467i	−0.0797466	+	0.0460417i
$545$		0			0
$546$	580.112	−	399.763i	1.06248	−	0.732166i
$547$	13.1899	−	13.1899i	0.0241132	−	0.0241132i	−0.694947	−	0.719061i	$-0.744572\pi$
$547$	13.1899	−	13.1899i	0.0241132	−	0.0241132i	0.719061	+	0.694947i	$0.244572\pi$
$548$	33.3760	−	124.561i	0.0609051	−	0.227301i
$549$	−340.518	−	196.598i	−0.620251	−	0.358102i
$550$		0			0
$551$	97.2311	+	168.409i	0.176463	+	0.305643i
$552$	−297.968	+	297.968i	−0.539797	+	0.539797i
$553$	−31.9476	−	89.8618i	−0.0577714	−	0.162499i
$554$		−	537.756i		−	0.970679i
$555$		0			0
$556$	−51.4750	+	89.1574i	−0.0925810	+	0.160355i
$557$	145.580	+	543.313i	0.261365	+	0.975427i	0.964438	+	0.264309i	$0.0851439\pi$
$557$	145.580	+	543.313i	0.261365	+	0.975427i	−0.703073	+	0.711117i	$0.748189\pi$
$558$	−159.817	+	596.447i	−0.286411	+	1.06890i
$559$			1061.05i			1.89812i
$560$		0			0
$561$	515.712			0.919272
$562$	185.231	+	49.6326i	0.329593	+	0.0883143i
$563$	810.309	−	217.122i	1.43927	−	0.385651i	0.546992	−	0.837138i	$-0.315773\pi$
$563$	810.309	−	217.122i	1.43927	−	0.385651i	0.892278	+	0.451486i	$0.149106\pi$
$564$	−80.1983	−	46.3025i	−0.142196	−	0.0820967i
$565$		0			0
$566$	499.006			0.881636
$567$	481.137	+	409.896i	0.848566	+	0.722920i
$568$	−202.373	−	202.373i	−0.356290	−	0.356290i
$569$	−271.713	+	156.874i	−0.477527	+	0.275701i	−0.719385	−	0.694611i	$-0.755576\pi$
$569$	−271.713	+	156.874i	−0.477527	+	0.275701i	0.241858	+	0.970312i	$0.422243\pi$
$570$		0			0
$571$	340.272	−	589.368i	0.595923	−	1.03217i	−0.397493	−	0.917605i	$-0.630120\pi$
$571$	340.272	−	589.368i	0.595923	−	1.03217i	0.993416	−	0.114564i	$-0.0365470\pi$
$572$	−292.856	−	78.4704i	−0.511985	−	0.137186i
$573$	1232.42	+	1232.42i	2.15081	+	2.15081i
$574$	39.0326	−	82.0961i	0.0680010	−	0.143025i
$575$		0			0
$576$	73.3599	+	127.063i	0.127361	+	0.220596i
$577$	−213.851	−	798.104i	−0.370626	−	1.38320i	−0.859631	−	0.510915i	$-0.829307\pi$
$577$	−213.851	−	798.104i	−0.370626	−	1.38320i	0.489005	−	0.872281i	$-0.337360\pi$
$578$	287.662	−	77.0787i	0.497684	−	0.133354i
$579$	449.886	−	259.742i	0.777005	−	0.448604i
$580$		0			0
$581$	232.182	−	160.000i	0.399625	−	0.275387i
$582$	−550.329	+	550.329i	−0.945582	+	0.945582i
$583$	−41.1986	+	153.755i	−0.0706666	+	0.263731i
$584$	256.586	+	148.140i	0.439360	+	0.253664i
$585$		0			0
$586$	−73.2341	−	126.845i	−0.124973	−	0.216459i
$587$	345.401	−	345.401i	0.588417	−	0.588417i	−0.348786	−	0.937202i	$-0.613406\pi$
$587$	345.401	−	345.401i	0.588417	−	0.588417i	0.937202	+	0.348786i	$0.113406\pi$
$588$	−415.303	−	300.160i	−0.706298	−	0.510477i
$589$		−	159.241i		−	0.270358i
$590$		0			0
$591$	486.295	−	842.287i	0.822834	−	1.42519i
$592$	16.0577	+	59.9280i	0.0271244	+	0.101230i
$593$	46.7804	−	174.587i	0.0788876	−	0.294413i	−0.915199	−	0.403002i	$-0.867967\pi$
$593$	46.7804	−	174.587i	0.0788876	−	0.294413i	0.994087	+	0.108589i	$0.0346334\pi$
$594$		−	769.241i		−	1.29502i
$595$		0			0
$596$	109.276			0.183348
$597$	1235.63	+	331.085i	2.06972	+	0.554581i
$598$	529.757	−	141.948i	0.885881	−	0.237371i
$599$	267.890	+	154.666i	0.447229	+	0.258208i	0.706659	−	0.707554i	$-0.250201\pi$
$599$	267.890	+	154.666i	0.447229	+	0.258208i	−0.259430	+	0.965762i	$0.583535\pi$
$600$		0			0
$601$	−583.911			−0.971566			−0.485783	−	0.874079i	$-0.661465\pi$
$601$	−583.911			−0.971566			−0.485783	+	0.874079i	$0.661465\pi$
$602$	727.155	−	258.517i	1.20790	−	0.429430i
$603$	−689.848	−	689.848i	−1.14403	−	1.14403i
$604$	215.590	−	124.471i	0.356937	−	0.206078i
$605$		0			0
$606$	−459.589	+	796.031i	−0.758397	+	1.31358i
$607$	−162.955	−	43.6636i	−0.268459	−	0.0719335i	0.122078	−	0.992520i	$-0.461044\pi$
$607$	−162.955	−	43.6636i	−0.268459	−	0.0719335i	−0.390537	+	0.920587i	$0.627711\pi$
$608$	−26.7547	−	26.7547i	−0.0440045	−	0.0440045i
$609$	1060.74	−	84.8094i	1.74177	−	0.139260i
$610$		0			0
$611$	60.2633	+	104.379i	0.0986306	+	0.170833i
$612$	84.0680	+	313.746i	0.137366	+	0.512657i
$613$	−365.798	+	98.0152i	−0.596734	+	0.159894i	−0.544529	−	0.838742i	$-0.683291\pi$
$613$	−365.798	+	98.0152i	−0.596734	+	0.159894i	−0.0522047	+	0.998636i	$0.516625\pi$
$614$	682.761	−	394.192i	1.11199	−	0.642007i
$615$		0			0
$616$	17.5751	+	219.817i	0.0285310	+	0.356846i
$617$	−788.089	+	788.089i	−1.27729	+	1.27729i	−0.335114	+	0.942178i	$0.608775\pi$
$617$	−788.089	+	788.089i	−1.27729	+	1.27729i	−0.942178	+	0.335114i	$0.891225\pi$
$618$	−198.331	+	740.180i	−0.320923	+	1.19770i
$619$	506.750	+	292.572i	0.818660	+	0.472653i	0.849954	−	0.526857i	$-0.176630\pi$
$619$	506.750	+	292.572i	0.818660	+	0.472653i	−0.0312944	+	0.999510i	$0.509963\pi$
$620$		0			0
$621$	695.754	+	1205.08i	1.12038	+	1.94055i
$622$	−235.592	+	235.592i	−0.378766	+	0.378766i
$623$	−17.7661	−	49.9724i	−0.0285171	−	0.0802126i
$624$		−	284.667i		−	0.456196i
$625$		0			0
$626$	−259.005	+	448.609i	−0.413746	+	0.716629i
$627$	100.818	+	376.258i	0.160794	+	0.600092i
$628$	−41.3900	+	154.469i	−0.0659076	+	0.245970i
$629$			137.351i			0.218364i
$630$		0			0
$631$	592.443			0.938895			0.469448	−	0.882960i	$-0.344453\pi$
$631$	592.443			0.938895			0.469448	+	0.882960i	$0.344453\pi$
$632$	−37.2230	−	9.97387i	−0.0588971	−	0.0157814i
$633$	1028.73	−	275.647i	1.62516	−	0.435461i
$634$	−25.3052	−	14.6100i	−0.0399136	−	0.0230441i
$635$		0			0
$636$	−149.456			−0.234994
$637$	272.775	+	608.585i	0.428218	+	0.955392i
$638$	−323.815	−	323.815i	−0.507548	−	0.507548i
$639$	−1607.13	+	927.877i	−2.51507	+	1.45208i
$640$		0			0
$641$	−190.823	+	330.516i	−0.297696	+	0.515625i	−0.975609	−	0.219518i	$-0.929552\pi$
$641$	−190.823	+	330.516i	−0.297696	+	0.515625i	0.677912	+	0.735143i	$0.262885\pi$
$642$	641.192	+	171.807i	0.998742	+	0.267612i
$643$	−34.6664	−	34.6664i	−0.0539135	−	0.0539135i	0.679636	−	0.733550i	$-0.262138\pi$
$643$	−34.6664	−	34.6664i	−0.0539135	−	0.0539135i	−0.733550	+	0.679636i	$0.762138\pi$
$644$	−226.350	−	328.466i	−0.351476	−	0.510040i
$645$		0			0
$646$	−41.8823	−	72.5423i	−0.0648333	−	0.112295i
$647$	180.656	+	674.219i	0.279222	+	1.04207i	0.952959	+	0.303098i	$0.0980211\pi$
$647$	180.656	+	674.219i	0.279222	+	1.04207i	−0.673738	+	0.738971i	$0.735312\pi$
$648$	246.691	−	66.1006i	0.380696	−	0.102007i
$649$	755.133	−	435.976i	1.16353	−	0.671766i
$650$		0			0
$651$	−786.967	−	374.164i	−1.20886	−	0.574752i
$652$	266.861	−	266.861i	0.409296	−	0.409296i
$653$	288.387	−	1076.27i	0.441634	−	1.64820i	−0.283041	−	0.959108i	$-0.591343\pi$
$653$	288.387	−	1076.27i	0.441634	−	1.64820i	0.724675	−	0.689091i	$-0.241990\pi$
$654$	1079.06	+	622.996i	1.64994	+	0.952594i
$655$		0			0
$656$	−18.3651	−	31.8093i	−0.0279956	−	0.0484898i
$657$	1358.44	−	1358.44i	2.06764	−	2.06764i
$658$	56.8499	−	66.7305i	0.0863980	−	0.101414i
$659$			894.905i			1.35797i	0.734150	+	0.678987i	$0.237581\pi$
$659$			894.905i			1.35797i	−0.734150	+	0.678987i	$0.762419\pi$
$660$		0			0
$661$	505.683	−	875.868i	0.765026	−	1.32506i	−0.175206	−	0.984532i	$-0.556059\pi$
$661$	505.683	−	875.868i	0.765026	−	1.32506i	0.940233	−	0.340533i	$-0.110607\pi$
$662$	−51.7464	−	193.120i	−0.0781667	−	0.291722i
$663$	163.109	−	608.731i	0.246017	−	0.918147i
$664$		−	113.934i		−	0.171587i
$665$		0			0
$666$	402.291			0.604040
$667$	800.165	+	214.403i	1.19965	+	0.321444i
$668$	−318.415	+	85.3190i	−0.476669	+	0.127723i
$669$	1246.59	+	719.720i	1.86337	+	1.07582i
$670$		0			0
$671$	−238.788			−0.355869
$672$	−195.086	+	69.3569i	−0.290307	+	0.103210i
$673$	−331.906	−	331.906i	−0.493174	−	0.493174i	0.416131	−	0.909305i	$-0.363386\pi$
$673$	−331.906	−	331.906i	−0.493174	−	0.493174i	−0.909305	+	0.416131i	$0.863386\pi$
$674$	−393.112	+	226.963i	−0.583253	+	0.336741i
$675$		0			0
$676$	−16.2485	+	28.1432i	−0.0240363	+	0.0416320i
$677$	272.549	+	73.0294i	0.402584	+	0.107872i	0.454429	−	0.890783i	$-0.349843\pi$
$677$	272.549	+	73.0294i	0.402584	+	0.107872i	−0.0518447	+	0.998655i	$0.516510\pi$
$678$	−164.568	−	164.568i	−0.242726	−	0.242726i
$679$	−418.055	−	606.657i	−0.615693	−	0.893456i
$680$		0			0
$681$	596.330	+	1032.87i	0.875668	+	1.51670i
$682$	97.0572	+	362.222i	0.142313	+	0.531118i
$683$	−413.854	+	110.892i	−0.605935	+	0.162360i	−0.548726	−	0.836002i	$-0.684887\pi$
$683$	−413.854	+	110.892i	−0.605935	+	0.162360i	−0.0572092	+	0.998362i	$0.518220\pi$
$684$	−212.471	+	122.670i	−0.310630	+	0.179342i
$685$		0			0
$686$	350.613	−	335.214i	0.511098	−	0.488650i
$687$	690.594	−	690.594i	1.00523	−	1.00523i
$688$	80.7077	−	301.205i	0.117308	−	0.437798i
$689$	168.458	+	97.2594i	0.244497	+	0.141160i
$690$		0			0
$691$	23.9800	+	41.5345i	0.0347033	+	0.0601079i	0.882855	−	0.469645i	$-0.155618\pi$
$691$	23.9800	+	41.5345i	0.0347033	+	0.0601079i	−0.848152	+	0.529753i	$0.822285\pi$
$692$	450.163	−	450.163i	0.650524	−	0.650524i
$693$	1406.26	+	258.826i	2.02923	+	0.373487i
$694$			818.996i			1.18011i
$695$		0			0
$696$	214.985	−	372.366i	0.308887	−	0.535008i
$697$	−21.0458	−	78.5440i	−0.0301948	−	0.112689i
$698$	17.0372	−	63.5837i	0.0244086	−	0.0910942i
$699$		−	1758.87i		−	2.51627i
$700$		0			0
$701$	−952.278			−1.35846			−0.679228	−	0.733927i	$-0.737685\pi$
$701$	−952.278			−1.35846			−0.679228	+	0.733927i	$0.737685\pi$
$702$	−907.990	−	243.295i	−1.29343	−	0.346575i
$703$	−100.210	+	26.8511i	−0.142546	+	0.0381951i
$704$	77.1655	+	44.5515i	0.109610	+	0.0632834i
$705$		0			0
$706$	−751.645			−1.06465
$707$	−662.353	−	564.280i	−0.936850	−	0.798133i
$708$	578.901	+	578.901i	0.817657	+	0.817657i
$709$	619.824	−	357.856i	0.874224	−	0.504733i	0.00547406	−	0.999985i	$-0.498258\pi$
$709$	619.824	−	357.856i	0.874224	−	0.504733i	0.868749	+	0.495252i	$0.164924\pi$
$710$		0			0
$711$	−124.937	+	216.397i	−0.175720	+	0.304356i
$712$	−20.6998	−	5.54650i	−0.0290728	−	0.00779002i
$713$	−479.667	−	479.667i	−0.672744	−	0.672744i
$714$	−456.913	+	36.5317i	−0.639935	+	0.0511648i
$715$		0			0
$716$	66.4559	+	115.105i	0.0928155	+	0.160761i
$717$	113.236	+	422.603i	0.157930	+	0.589404i
$718$	97.1195	−	26.0231i	0.135264	−	0.0362439i
$719$	66.9619	−	38.6605i	0.0931320	−	0.0537698i	−0.452711	−	0.891657i	$-0.649543\pi$
$719$	66.9619	−	38.6605i	0.0931320	−	0.0537698i	0.545843	+	0.837888i	$0.316210\pi$
$720$		0			0
$721$	−655.123	−	311.478i	−0.908631	−	0.432009i
$722$	−316.262	+	316.262i	−0.438035	+	0.438035i
$723$	−154.747	+	577.524i	−0.214035	+	0.798789i
$724$	−124.003	−	71.5932i	−0.171275	−	0.0988857i
$725$		0			0
$726$	−11.2852	−	19.5466i	−0.0155444	−	0.0269237i
$727$	−760.852	+	760.852i	−1.04656	+	1.04656i	−0.0477025	+	0.998862i	$0.515190\pi$
$727$	−760.852	+	760.852i	−1.04656	+	1.04656i	−0.998862	+	0.0477025i	$0.984810\pi$
$728$	265.025	+	48.7786i	0.364045	+	0.0670036i
$729$			642.184i			0.880911i
$730$		0			0
$731$	345.171	−	597.854i	0.472190	−	0.817857i
$732$	−58.0277	−	216.562i	−0.0792728	−	0.295850i
$733$	−280.505	+	1046.86i	−0.382681	+	1.42818i	0.459110	+	0.888379i	$0.348168\pi$
$733$	−280.505	+	1046.86i	−0.382681	+	1.42818i	−0.841791	+	0.539804i	$0.818498\pi$
$734$			199.512i			0.271815i
$735$		0			0
$736$	−161.182			−0.218997
$737$	−572.289	−	153.344i	−0.776512	−	0.208066i
$738$	−230.050	+	61.6416i	−0.311720	+	0.0835252i
$739$	−1026.64	−	592.730i	−1.38923	−	0.802070i	−0.395999	−	0.918251i	$-0.629602\pi$
$739$	−1026.64	−	592.730i	−1.38923	−	0.802070i	−0.993228	+	0.116181i	$0.962935\pi$
$740$		0			0
$741$	476.011			0.642390
$742$	25.6098	−	139.144i	0.0345145	−	0.187525i
$743$	−65.8954	−	65.8954i	−0.0886883	−	0.0886883i	0.661371	−	0.750059i	$-0.269975\pi$
$743$	−65.8954	−	65.8954i	−0.0886883	−	0.0886883i	−0.750059	+	0.661371i	$0.769975\pi$
$744$	−304.922	+	176.047i	−0.409841	+	0.236622i
$745$		0			0
$746$	213.997	−	370.653i	0.286859	−	0.496855i
$747$	−713.594	−	191.207i	−0.955280	−	0.255967i
$748$	139.483	+	139.483i	0.186475	+	0.186475i
$749$	−269.823	+	567.510i	−0.360244	+	0.757691i
$750$		0			0
$751$	−146.301	−	253.400i	−0.194808	−	0.337417i	0.752030	−	0.659129i	$-0.229075\pi$
$751$	−146.301	−	253.400i	−0.194808	−	0.337417i	−0.946837	+	0.321712i	$0.895742\pi$
$752$	−9.16773	−	34.2144i	−0.0121911	−	0.0454979i
$753$	−14.4637	+	3.87552i	−0.0192080	+	0.00514678i
$754$	−484.639	+	279.806i	−0.642757	+	0.371096i
$755$		0			0
$756$	54.4910	+	681.537i	0.0720781	+	0.901504i
$757$	−742.193	+	742.193i	−0.980440	+	0.980440i	−0.999812	−	0.0193719i	$-0.993833\pi$
$757$	−742.193	+	742.193i	−0.980440	+	0.980440i	0.0193719	+	0.999812i	$0.493833\pi$
$758$	120.780	−	450.756i	0.159340	−	0.594665i
$759$	1437.05	+	829.683i	1.89335	+	1.09313i
$760$		0			0
$761$	−308.160	−	533.749i	−0.404941	−	0.701378i	0.589374	−	0.807860i	$-0.299375\pi$
$761$	−308.160	−	533.749i	−0.404941	−	0.701378i	−0.994315	+	0.106482i	$0.966041\pi$
$762$	595.574	−	595.574i	0.781593	−	0.781593i
$763$	−764.910	+	897.854i	−1.00250	+	1.17674i
$764$			666.659i			0.872590i
$765$		0			0
$766$	−125.756	+	217.816i	−0.164172	+	0.284354i
$767$	−275.781	−	1029.23i	−0.359558	−	1.34189i
$768$	−21.6529	+	80.8096i	−0.0281938	+	0.105221i
$769$		−	743.180i		−	0.966424i	−0.875503	−	0.483212i	$-0.839470\pi$
$769$		−	743.180i		−	0.966424i	0.875503	−	0.483212i	$-0.160530\pi$
$770$		0			0
$771$	448.970			0.582321
$772$	191.932	+	51.4279i	0.248616	+	0.0666165i
$773$	−320.715	+	85.9354i	−0.414897	+	0.111171i	−0.460228	−	0.887801i	$-0.652232\pi$
$773$	−320.715	+	85.9354i	−0.414897	+	0.111171i	0.0453311	+	0.998972i	$0.485566\pi$
$774$	−1751.07	−	1010.98i	−2.26236	−	1.30618i
$775$		0			0
$776$	−297.693			−0.383625
$777$	−102.762	+	558.328i	−0.132255	+	0.718568i
$778$	−239.373	−	239.373i	−0.307678	−	0.307678i
$779$	53.1906	−	30.7096i	0.0682806	−	0.0394218i
$780$		0			0
$781$	−563.500	+	976.011i	−0.721511	+	1.24969i
$782$	−344.671	−	92.3543i	−0.440756	−	0.118100i
$783$	−1003.98	−	1003.98i	−1.28222	−	1.28222i
$784$	−31.1425	−	193.510i	−0.0397226	−	0.246824i
$785$		0			0
$786$	−285.909	−	495.208i	−0.363752	−	0.630036i
$787$	182.282	+	680.286i	0.231616	+	0.864404i	0.979645	+	0.200738i	$0.0643339\pi$
$787$	182.282	+	680.286i	0.231616	+	0.864404i	−0.748029	+	0.663667i	$0.768999\pi$
$788$	359.339	−	96.2846i	0.456014	−	0.122189i
$789$	−1147.11	+	662.282i	−1.45387	+	0.839395i
$790$		0			0
$791$	181.412	−	125.014i	0.229346	−	0.158045i
$792$	408.537	−	408.537i	0.515829	−	0.515829i
$793$	−75.5238	+	281.859i	−0.0952381	+	0.355433i
$794$	−753.220	−	434.872i	−0.948640	−	0.547697i
$795$		0			0
$796$	244.649	+	423.745i	0.307348	+	0.532343i
$797$	−559.866	+	559.866i	−0.702467	+	0.702467i	−0.964940	−	0.262472i	$-0.915462\pi$
$797$	−559.866	+	559.866i	−0.702467	+	0.702467i	0.262472	+	0.964940i	$0.415462\pi$
$798$	−115.976	−	326.218i	−0.145334	−	0.408794i
$799$		−	78.4171i		−	0.0981441i
$800$		0			0
$801$	−69.4778	+	120.339i	−0.0867389	+	0.150236i
$802$	−178.391	−	665.764i	−0.222433	−	0.830130i
$803$	301.965	−	1126.95i	0.376046	−	1.40342i
$804$		−	556.287i		−	0.691899i
$805$		0			0
$806$	458.254			0.568554
$807$	−2536.90	−	679.759i	−3.14361	−	0.842329i
$808$	−339.605	+	90.9969i	−0.420303	+	0.112620i
$809$	−772.252	−	445.860i	−0.954576	−	0.551125i	−0.0600765	−	0.998194i	$-0.519134\pi$
$809$	−772.252	−	445.860i	−0.954576	−	0.551125i	−0.894499	+	0.447069i	$0.852468\pi$
$810$		0			0
$811$	−725.006			−0.893965			−0.446982	−	0.894543i	$-0.647501\pi$
$811$	−725.006			−0.893965			−0.446982	+	0.894543i	$0.647501\pi$
$812$	309.834	+	263.958i	0.381569	+	0.325071i
$813$	733.960	+	733.960i	0.902780	+	0.902780i
$814$	211.580	−	122.156i	0.259926	−	0.150068i
$815$		0			0
$816$	−92.6050	+	160.397i	−0.113487	+	0.196564i
$817$	503.666	+	134.957i	0.616483	+	0.165186i
$818$	228.319	+	228.319i	0.279119	+	0.279119i
$819$	750.282	−	1578.05i	0.916095	−	1.92680i
$820$		0			0
$821$	377.073	+	653.109i	0.459285	+	0.795504i	0.998923	−	0.0463923i	$-0.0147724\pi$
$821$	377.073	+	653.109i	0.459285	+	0.795504i	−0.539639	+	0.841897i	$0.681439\pi$
$822$	−123.401	−	460.538i	−0.150123	−	0.560266i
$823$	−1012.22	+	271.224i	−1.22992	+	0.329556i	−0.814548	−	0.580096i	$-0.803015\pi$
$823$	−1012.22	+	271.224i	−1.22992	+	0.329556i	−0.415371	+	0.909652i	$0.636348\pi$
$824$	−253.837	+	146.553i	−0.308055	+	0.177855i
$825$		0			0
$826$	−638.154	+	439.760i	−0.772583	+	0.532397i
$827$	29.7436	−	29.7436i	0.0359656	−	0.0359656i	−0.688895	−	0.724861i	$-0.741904\pi$
$827$	29.7436	−	29.7436i	0.0359656	−	0.0359656i	0.724861	+	0.688895i	$0.241904\pi$
$828$	−270.499	+	1009.52i	−0.326690	+	1.21922i
$829$	159.407	+	92.0338i	0.192289	+	0.111018i	0.593053	−	0.805163i	$-0.297922\pi$
$829$	159.407	+	92.0338i	0.192289	+	0.111018i	−0.400765	+	0.916181i	$0.631256\pi$
$830$		0			0
$831$	−994.122	−	1721.87i	−1.19630	−	2.07205i
$832$	76.9932	−	76.9932i	0.0925399	−	0.0925399i
$833$	44.2827	−	431.646i	0.0531605	−	0.518183i
$834$			380.637i			0.456399i
$835$		0			0
$836$	−74.4977	+	129.034i	−0.0891120	+	0.154347i
$837$	300.923	+	1123.06i	0.359526	+	1.34177i
$838$	−114.429	+	427.054i	−0.136550	+	0.509610i
$839$			230.146i			0.274310i	0.990550	+	0.137155i	$0.0437958\pi$
$839$			230.146i			0.274310i	−0.990550	+	0.137155i	$0.956204\pi$
$840$		0			0
$841$	−4.25956			−0.00506488
$842$	655.269	+	175.579i	0.778229	+	0.208526i
$843$	684.855	−	183.506i	0.812403	−	0.217683i
$844$	352.792	+	203.685i	0.418000	+	0.241332i
$845$		0			0
$846$	−229.678			−0.271487
$847$	20.1317	−	7.15718i	0.0237682	−	0.00845004i
$848$	−40.4230	−	40.4230i	−0.0476687	−	0.0476687i
$849$	1597.79	−	922.486i	1.88197	−	1.08656i
$850$		0			0
$851$	−220.972	+	382.734i	−0.259661	+	0.449746i
$852$	−1022.10	−	273.872i	−1.19965	−	0.321446i
$853$	−1144.00	−	1144.00i	−1.34115	−	1.34115i	−0.894912	−	0.446242i	$-0.852762\pi$
$853$	−1144.00	−	1144.00i	−1.34115	−	1.34115i	−0.446242	−	0.894912i	$-0.647238\pi$
$854$	211.563	−	16.9151i	0.247732	−	0.0198069i
$855$		0			0
$856$	126.954	+	219.890i	0.148310	+	0.256881i
$857$	92.2922	+	344.439i	0.107692	+	0.401913i	0.998637	−	0.0521995i	$-0.0166232\pi$
$857$	92.2922	+	344.439i	0.107692	+	0.401913i	−0.890944	+	0.454112i	$0.849957\pi$
$858$	−1082.77	+	290.128i	−1.26197	+	0.338145i
$859$	−1316.32	+	759.978i	−1.53239	+	0.884724i	−0.533136	+	0.846029i	$0.678987\pi$
$859$	−1316.32	+	759.978i	−1.53239	+	0.884724i	−0.999251	+	0.0386951i	$0.987680\pi$
$860$		0			0
$861$	−26.7863	−	335.025i	−0.0311107	−	0.389112i
$862$	537.672	−	537.672i	0.623750	−	0.623750i
$863$	58.7013	−	219.076i	0.0680200	−	0.253854i	−0.923540	−	0.383502i	$-0.874718\pi$
$863$	58.7013	−	219.076i	0.0680200	−	0.253854i	0.991560	+	0.129648i	$0.0413846\pi$
$864$	239.249	+	138.131i	0.276909	+	0.159873i
$865$		0			0
$866$	−13.8191	−	23.9354i	−0.0159574	−	0.0276391i
$867$	778.587	−	778.587i	0.898024	−	0.898024i
$868$	−111.650	−	314.049i	−0.128629	−	0.361807i
$869$			151.749i			0.174624i
$870$		0			0
$871$	−362.007	+	627.014i	−0.415622	+	0.719879i
$872$	123.351	+	460.352i	0.141458	+	0.527927i
$873$	−499.595	+	1864.51i	−0.572274	+	2.13576i
$874$		−	269.523i		−	0.308379i
$875$		0			0
$876$	1095.43			1.25050
$877$	−942.868	−	252.641i	−1.07511	−	0.288074i	−0.322517	−	0.946564i	$-0.604529\pi$
$877$	−942.868	−	252.641i	−1.07511	−	0.288074i	−0.752590	+	0.658490i	$0.771196\pi$
$878$	253.149	−	67.8310i	0.288324	−	0.0772562i
$879$	−468.984	−	270.768i	−0.533543	−	0.308041i
$880$		0			0
$881$	495.620			0.562566			0.281283	−	0.959625i	$-0.409240\pi$
$881$	495.620			0.562566			0.281283	+	0.959625i	$0.409240\pi$
$882$	−1264.26	−	129.701i	−1.43340	−	0.147053i
$883$	918.390	+	918.390i	1.04008	+	1.04008i	0.999163	+	0.0409167i	$0.0130278\pi$
$883$	918.390	+	918.390i	1.04008	+	1.04008i	0.0409167	+	0.999163i	$0.486972\pi$
$884$	208.758	−	120.527i	0.236152	−	0.136342i
$885$		0			0
$886$	−120.270	+	208.314i	−0.135745	+	0.235117i
$887$	137.822	+	36.9292i	0.155379	+	0.0416338i	0.335670	−	0.941980i	$-0.391037\pi$
$887$	137.822	+	36.9292i	0.155379	+	0.0416338i	−0.180291	+	0.983613i	$0.557704\pi$
$888$	162.202	+	162.202i	0.182659	+	0.182659i
$889$	452.426	+	656.533i	0.508915	+	0.738507i
$890$		0			0
$891$	−502.848	−	870.958i	−0.564363	−	0.977506i
$892$	142.502	+	531.825i	0.159756	+	0.596216i
$893$	57.2123	−	15.3300i	0.0640675	−	0.0171668i
$894$	349.895	−	202.012i	0.391381	−	0.225964i
$895$		0			0
$896$	−71.5235	−	34.0058i	−0.0798253	−	0.0379529i
$897$	1433.84	−	1433.84i	1.59849	−	1.59849i
$898$	−49.7873	+	185.809i	−0.0554424	+	0.206914i
$899$	599.432	+	346.082i	0.666776	+	0.384963i
$900$		0			0
$901$	−63.2790	−	109.602i	−0.0702319	−	0.121645i
$902$	−102.274	+	102.274i	−0.113386	+	0.113386i
$903$	1850.41	−	2172.01i	2.04918	−	2.40533i
$904$		−	89.0208i		−	0.0984744i
$905$		0			0
$906$	460.205	−	797.099i	0.507953	−	0.879801i
$907$	22.8874	+	85.4170i	0.0252342	+	0.0941753i	0.977395	−	0.211424i	$-0.0678100\pi$
$907$	22.8874	+	85.4170i	0.0252342	+	0.0941753i	−0.952160	+	0.305599i	$0.901143\pi$
$908$	−118.071	+	440.647i	−0.130034	+	0.485295i
$909$			2279.73i			2.50796i
$910$		0			0
$911$	−19.6420			−0.0215609			−0.0107805	−	0.999942i	$-0.503432\pi$
$911$	−19.6420			−0.0215609			−0.0107805	+	0.999942i	$0.503432\pi$
$912$	−135.127	−	36.2073i	−0.148166	−	0.0397009i
$913$	−433.366	+	116.120i	−0.474662	+	0.127185i
$914$	944.318	+	545.202i	1.03317	+	0.596501i
$915$		0			0
$916$	373.567			0.407824
$917$	510.031	−	181.325i	0.556195	−	0.197738i
$918$	432.465	+	432.465i	0.471094	+	0.471094i
$919$	−730.678	+	421.857i	−0.795080	+	0.459039i	−0.841748	−	0.539871i	$-0.818473\pi$
$919$	−730.678	+	421.857i	−0.795080	+	0.459039i	0.0466681	+	0.998910i	$0.485140\pi$
$920$		0			0
$921$	1457.45	−	2524.37i	1.58246	−	2.74090i
$922$	−238.764	−	63.9767i	−0.258963	−	0.0693890i
$923$	973.832	+	973.832i	1.05507	+	1.05507i
$924$	462.639	+	671.354i	0.500692	+	0.726574i
$925$		0			0
$926$	219.730	+	380.583i	0.237289	+	0.410997i
$927$	491.897	+	1835.79i	0.530634	+	1.98035i
$928$	158.860	−	42.5663i	0.171185	−	0.0458689i
$929$	−325.901	+	188.159i	−0.350808	+	0.202539i	−0.665041	−	0.746807i	$-0.731586\pi$
$929$	−325.901	+	188.159i	−0.350808	+	0.202539i	0.314233	+	0.949346i	$0.398253\pi$
$930$		0			0
$931$	323.582	−	52.0756i	0.347564	−	0.0559351i
$932$	475.719	−	475.719i	0.510429	−	0.510429i
$933$	−318.828	+	1189.88i	−0.341723	+	1.27533i
$934$	−950.841	−	548.968i	−1.01803	−	0.587760i
$935$		0			0
$936$	−353.013	−	611.437i	−0.377151	−	0.653245i
$937$	−333.039	+	333.039i	−0.355431	+	0.355431i	−0.862126	−	0.506694i	$-0.830867\pi$
$937$	−333.039	+	333.039i	−0.355431	+	0.355431i	0.506694	+	0.862126i	$0.330867\pi$
$938$	517.903	+	95.3216i	0.552135	+	0.101622i
$939$			1915.23i			2.03965i
$940$		0			0
$941$	−462.718	+	801.452i	−0.491730	+	0.851702i	−0.999955	−	0.00952274i	$-0.996969\pi$
$941$	−462.718	+	801.452i	−0.491730	+	0.851702i	0.508224	+	0.861225i	$0.330302\pi$
$942$	153.031	+	571.119i	0.162453	+	0.606284i
$943$	67.7175	−	252.725i	0.0718107	−	0.268001i
$944$			313.148i			0.331725i
$945$		0			0
$946$	−1227.94			−1.29803
$947$	872.417	+	233.763i	0.921243	+	0.246846i	0.688116	−	0.725600i	$-0.258438\pi$
$947$	872.417	+	233.763i	0.921243	+	0.246846i	0.233126	+	0.972446i	$0.425104\pi$
$948$	−137.624	+	36.8763i	−0.145173	+	0.0388991i
$949$	−1234.71	−	712.861i	−1.30107	−	0.751170i
$950$		0			0
$951$	−108.035			−0.113601
$952$	−133.461	−	113.700i	−0.140190	−	0.119433i
$953$	336.361	+	336.361i	0.352950	+	0.352950i	0.861206	−	0.508256i	$-0.169710\pi$
$953$	336.361	+	336.361i	0.352950	+	0.352950i	−0.508256	+	0.861206i	$0.669710\pi$
$954$	−321.017	+	185.339i	−0.336496	+	0.194276i
$955$		0			0
$956$	−83.6738	+	144.927i	−0.0875249	+	0.151598i
$957$	−1635.46	−	438.221i	−1.70895	−	0.457911i
$958$	−90.5336	−	90.5336i	−0.0945028	−	0.0945028i
$959$	449.906	−	35.9714i	0.469141	−	0.0375093i
$960$		0			0
$961$	197.101	+	341.389i	0.205100	+	0.355244i
$962$	−77.2707	−	288.378i	−0.0803229	−	0.299769i
$963$	1590.28	−	426.114i	1.65138	−	0.442486i
$964$	−198.056	+	114.348i	−0.205452	+	0.118618i
$965$		0			0
$966$	−1331.98	−	633.290i	−1.37886	−	0.655580i
$967$	−95.1413	+	95.1413i	−0.0983881	+	0.0983881i	−0.754588	−	0.656199i	$-0.772163\pi$
$967$	−95.1413	+	95.1413i	−0.0983881	+	0.0983881i	0.656199	+	0.754588i	$0.272163\pi$
$968$	2.23443	−	8.33902i	0.00230830	−	0.00861469i
$969$	−268.210	−	154.851i	−0.276791	−	0.159805i
$970$		0			0
$971$	−541.576	−	938.036i	−0.557750	−	0.966052i	−0.997684	−	0.0680216i	$-0.978331\pi$
$971$	−541.576	−	938.036i	−0.557750	−	0.966052i	0.439934	−	0.898030i	$-0.355002\pi$
$972$	46.1072	−	46.1072i	0.0474354	−	0.0474354i
$973$	−354.373	−	65.2234i	−0.364207	−	0.0670333i
$974$		−	1291.82i		−	1.32630i
$975$		0			0
$976$	42.8786	−	74.2678i	0.0439329	−	0.0760941i
$977$	−492.348	−	1837.47i	−0.503939	−	1.88072i	−0.472722	−	0.881212i	$-0.656729\pi$
$977$	−492.348	−	1837.47i	−0.503939	−	1.88072i	−0.0312166	−	0.999513i	$-0.509938\pi$
$978$	361.144	−	1347.81i	0.369268	−	1.37813i
$979$			84.3878i			0.0861980i
$980$		0			0
$981$	3090.30			3.15015
$982$	−1209.53	−	324.093i	−1.23170	−	0.330034i
$983$	−916.515	+	245.579i	−0.932365	+	0.249826i	−0.692863	−	0.721069i	$-0.743651\pi$
$983$	−916.515	+	245.579i	−0.932365	+	0.249826i	−0.239502	+	0.970896i	$0.576984\pi$
$984$	−117.609	−	67.9013i	−0.119521	−	0.0690054i
$985$		0			0
$986$	364.096			0.369265
$987$	58.6694	−	318.763i	0.0594421	−	0.322962i
$988$	128.746	+	128.746i	0.130309	+	0.130309i
$989$	1923.67	−	1110.63i	1.94506	−	1.12298i
$990$		0			0
$991$	898.430	−	1556.13i	0.906590	−	1.57026i	0.0878205	−	0.996136i	$-0.472010\pi$
$991$	898.430	−	1556.13i	0.906590	−	1.57026i	0.818769	−	0.574123i	$-0.194657\pi$
$992$	−130.087	−	34.8566i	−0.131136	−	0.0351377i
$993$	−522.700	−	522.700i	−0.526385	−	0.526385i
$994$	430.115	−	904.649i	0.432712	−	0.910110i
$995$		0			0
$996$	−210.624	−	364.811i	−0.211470	−	0.366277i
$997$	126.473	+	472.003i	0.126853	+	0.473423i	0.999899	−	0.0142155i	$-0.00452508\pi$
$997$	126.473	+	472.003i	0.126853	+	0.473423i	−0.873046	+	0.487639i	$0.837858\pi$
$998$	−882.525	+	236.472i	−0.884294	+	0.236946i
$999$	655.997	−	378.740i	0.656654	−	0.379119i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.3.p.e.193.4		16
5.2	odd	4	inner	350.3.p.e.207.1		16
5.3	odd	4		70.3.l.c.67.4	yes	16
5.4	even	2		70.3.l.c.53.1	yes	16
7.2	even	3	inner	350.3.p.e.93.1		16
35.2	odd	12	inner	350.3.p.e.107.4		16
35.3	even	12		490.3.f.p.197.1		8
35.4	even	6		490.3.f.o.393.4		8
35.9	even	6		70.3.l.c.23.4	✓	16
35.18	odd	12		490.3.f.o.197.4		8
35.23	odd	12		70.3.l.c.37.1	yes	16
35.24	odd	6		490.3.f.p.393.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.c.23.4	✓	16	35.9	even	6
70.3.l.c.37.1	yes	16	35.23	odd	12
70.3.l.c.53.1	yes	16	5.4	even	2
70.3.l.c.67.4	yes	16	5.3	odd	4
350.3.p.e.93.1		16	7.2	even	3	inner
350.3.p.e.107.4		16	35.2	odd	12	inner
350.3.p.e.193.4		16	1.1	even	1	trivial
350.3.p.e.207.1		16	5.2	odd	4	inner
490.3.f.o.197.4		8	35.18	odd	12
490.3.f.o.393.4		8	35.4	even	6
490.3.f.p.197.1		8	35.3	even	12
490.3.f.p.393.1		8	35.24	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	350.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} +(5.05060 - 1.35330i) q^{3} +(1.73205 + 1.00000i) q^{4} +7.39459 q^{6} +(-1.26709 + 6.88437i) q^{7} +(2.00000 + 2.00000i) q^{8} +(15.8829 - 9.16999i) q^{9} +O(q^{10})\)	\(q+(1.36603 + 0.366025i) q^{2} +(5.05060 - 1.35330i) q^{3} +(1.73205 + 1.00000i) q^{4} +7.39459 q^{6} +(-1.26709 + 6.88437i) q^{7} +(2.00000 + 2.00000i) q^{8} +(15.8829 - 9.16999i) q^{9} +(5.56894 - 9.64568i) q^{11} +(10.1012 + 2.70661i) q^{12} +(-9.62415 - 9.62415i) q^{13} +(-4.25073 + 8.94043i) q^{14} +(2.00000 + 3.46410i) q^{16} +(2.29193 + 8.55361i) q^{17} +(25.0529 - 6.71290i) q^{18} +(-5.79257 + 3.34434i) q^{19} +(2.91708 + 36.4849i) q^{21} +(11.1379 - 11.1379i) q^{22} +(-7.37457 + 27.5223i) q^{23} +(12.8078 + 7.39459i) q^{24} +(-9.62415 - 16.6695i) q^{26} +(34.5327 - 34.5327i) q^{27} +(-9.07903 + 10.6570i) q^{28} -29.0733i q^{29} +(-11.9038 + 20.6179i) q^{31} +(1.46410 + 5.46410i) q^{32} +(15.0729 - 56.2529i) q^{33} +12.5233i q^{34} +36.6800 q^{36} +(14.9820 + 4.01442i) q^{37} +(-9.13690 + 2.44823i) q^{38} +(-61.6321 - 35.5833i) q^{39} -9.18256 q^{41} +(-9.36960 + 50.9071i) q^{42} +(-55.1244 - 55.1244i) q^{43} +(19.2914 - 11.1379i) q^{44} +(-20.1477 + 34.8968i) q^{46} +(-8.55361 - 2.29193i) q^{47} +(14.7892 + 14.7892i) q^{48} +(-45.7890 - 17.4462i) q^{49} +(23.1513 + 40.0992i) q^{51} +(-7.04537 - 26.2937i) q^{52} +(-13.8047 + 3.69897i) q^{53} +(59.8123 - 34.5327i) q^{54} +(-16.3029 + 11.2346i) q^{56} +(-24.7300 + 24.7300i) q^{57} +(10.6416 - 39.7149i) q^{58} +(67.7986 + 39.1435i) q^{59} +(-10.7196 - 18.5670i) q^{61} +(-23.8075 + 23.8075i) q^{62} +(43.0045 + 120.963i) q^{63} +8.00000i q^{64} +(41.1800 - 71.3259i) q^{66} +(-13.7678 - 51.3823i) q^{67} +(-4.58386 + 17.1072i) q^{68} +148.984i q^{69} -101.186 q^{71} +(50.1058 + 13.4258i) q^{72} +(101.181 - 27.1115i) q^{73} +(18.9964 + 10.9676i) q^{74} -13.3774 q^{76} +(59.3481 + 50.5605i) q^{77} +(-71.1666 - 71.1666i) q^{78} +(-11.7992 + 6.81228i) q^{79} +(45.1475 - 78.1978i) q^{81} +(-12.5436 - 3.36105i) q^{82} +(-28.4835 - 28.4835i) q^{83} +(-31.4324 + 66.1108i) q^{84} +(-55.1244 - 95.4783i) q^{86} +(-39.3451 - 146.838i) q^{87} +(30.4292 - 8.15349i) q^{88} +(-6.56157 + 3.78833i) q^{89} +(78.4508 - 54.0615i) q^{91} +(-40.2954 + 40.2954i) q^{92} +(-32.2188 + 120.242i) q^{93} +(-10.8455 - 6.26167i) q^{94} +(14.7892 + 25.6156i) q^{96} +(-74.4232 + 74.4232i) q^{97} +(-56.1632 - 40.5919i) q^{98} -204.268i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 2 q^{3} - 8 q^{6} - 12 q^{7} + 32 q^{8}+O(q^{10}) \) 16 * q + 8 * q^2 - 2 * q^3 - 8 * q^6 - 12 * q^7 + 32 * q^8	\( 16 q + 8 q^{2} - 2 q^{3} - 8 q^{6} - 12 q^{7} + 32 q^{8} + 40 q^{11} - 4 q^{12} - 16 q^{13} + 32 q^{16} - 46 q^{17} + 52 q^{18} - 20 q^{21} + 80 q^{22} - 54 q^{23} - 16 q^{26} + 52 q^{27} + 36 q^{28} - 208 q^{31} - 32 q^{32} + 22 q^{33} + 208 q^{36} + 38 q^{37} - 36 q^{38} - 72 q^{41} - 184 q^{42} - 144 q^{43} + 108 q^{46} - 46 q^{47} - 16 q^{48} - 136 q^{51} + 16 q^{52} - 30 q^{53} - 48 q^{56} + 492 q^{57} - 132 q^{58} - 120 q^{61} - 416 q^{62} + 292 q^{63} - 44 q^{66} + 74 q^{67} + 92 q^{68} + 16 q^{71} + 104 q^{72} + 54 q^{73} - 144 q^{76} - 570 q^{77} - 168 q^{78} + 244 q^{81} - 36 q^{82} - 64 q^{83} - 144 q^{86} + 236 q^{87} + 80 q^{88} + 336 q^{91} + 216 q^{92} - 142 q^{93} - 16 q^{96} - 136 q^{97} + 268 q^{98}+O(q^{100}) \) 16 * q + 8 * q^2 - 2 * q^3 - 8 * q^6 - 12 * q^7 + 32 * q^8 + 40 * q^11 - 4 * q^12 - 16 * q^13 + 32 * q^16 - 46 * q^17 + 52 * q^18 - 20 * q^21 + 80 * q^22 - 54 * q^23 - 16 * q^26 + 52 * q^27 + 36 * q^28 - 208 * q^31 - 32 * q^32 + 22 * q^33 + 208 * q^36 + 38 * q^37 - 36 * q^38 - 72 * q^41 - 184 * q^42 - 144 * q^43 + 108 * q^46 - 46 * q^47 - 16 * q^48 - 136 * q^51 + 16 * q^52 - 30 * q^53 - 48 * q^56 + 492 * q^57 - 132 * q^58 - 120 * q^61 - 416 * q^62 + 292 * q^63 - 44 * q^66 + 74 * q^67 + 92 * q^68 + 16 * q^71 + 104 * q^72 + 54 * q^73 - 144 * q^76 - 570 * q^77 - 168 * q^78 + 244 * q^81 - 36 * q^82 - 64 * q^83 - 144 * q^86 + 236 * q^87 + 80 * q^88 + 336 * q^91 + 216 * q^92 - 142 * q^93 - 16 * q^96 - 136 * q^97 + 268 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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