LMFDB - Embedded newform 350.3.p.e.93.1

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			93.1
Root			$-5.05060 + 1.35330i$ of defining polynomial
Character	$\chi$	$=$	350.93
Dual form			350.3.p.e.207.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 - 1.36603i) q^{2} +(-1.35330 + 5.05060i) q^{3} +(-1.73205 + 1.00000i) q^{4} +7.39459 q^{6} +(-6.88437 + 1.26709i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-15.8829 - 9.16999i) q^{9} +O(q^{10})$	\(q+(-0.366025 - 1.36603i) q^{2} +(-1.35330 + 5.05060i) q^{3} +(-1.73205 + 1.00000i) q^{4} +7.39459 q^{6} +(-6.88437 + 1.26709i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-15.8829 - 9.16999i) q^{9} +(5.56894 + 9.64568i) q^{11} +(-2.70661 - 10.1012i) q^{12} +(-9.62415 - 9.62415i) q^{13} +(4.25073 + 8.94043i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-8.55361 - 2.29193i) q^{17} +(-6.71290 + 25.0529i) q^{18} +(5.79257 + 3.34434i) q^{19} +(2.91708 - 36.4849i) q^{21} +(11.1379 - 11.1379i) q^{22} +(27.5223 - 7.37457i) q^{23} +(-12.8078 + 7.39459i) q^{24} +(-9.62415 + 16.6695i) q^{26} +(34.5327 - 34.5327i) q^{27} +(10.6570 - 9.07903i) q^{28} -29.0733i q^{29} +(-11.9038 - 20.6179i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-56.2529 + 15.0729i) q^{33} +12.5233i q^{34} +36.6800 q^{36} +(-4.01442 - 14.9820i) q^{37} +(2.44823 - 9.13690i) q^{38} +(61.6321 - 35.5833i) q^{39} -9.18256 q^{41} +(-50.9071 + 9.36960i) q^{42} +(-55.1244 - 55.1244i) q^{43} +(-19.2914 - 11.1379i) q^{44} +(-20.1477 - 34.8968i) q^{46} +(2.29193 + 8.55361i) q^{47} +(14.7892 + 14.7892i) q^{48} +(45.7890 - 17.4462i) q^{49} +(23.1513 - 40.0992i) q^{51} +(26.2937 + 7.04537i) q^{52} +(3.69897 - 13.8047i) q^{53} +(-59.8123 - 34.5327i) q^{54} +(-16.3029 - 11.2346i) q^{56} +(-24.7300 + 24.7300i) q^{57} +(-39.7149 + 10.6416i) q^{58} +(-67.7986 + 39.1435i) q^{59} +(-10.7196 + 18.5670i) q^{61} +(-23.8075 + 23.8075i) q^{62} +(120.963 + 43.0045i) q^{63} +8.00000i q^{64} +(41.1800 + 71.3259i) q^{66} +(51.3823 + 13.7678i) q^{67} +(17.1072 - 4.58386i) q^{68} +148.984i q^{69} -101.186 q^{71} +(-13.4258 - 50.1058i) q^{72} +(-27.1115 + 101.181i) q^{73} +(-18.9964 + 10.9676i) q^{74} -13.3774 q^{76} +(-50.5605 - 59.3481i) q^{77} +(-71.1666 - 71.1666i) q^{78} +(11.7992 + 6.81228i) q^{79} +(45.1475 + 78.1978i) q^{81} +(3.36105 + 12.5436i) q^{82} +(-28.4835 - 28.4835i) q^{83} +(31.4324 + 66.1108i) q^{84} +(-55.1244 + 95.4783i) q^{86} +(146.838 + 39.3451i) q^{87} +(-8.15349 + 30.4292i) q^{88} +(6.56157 + 3.78833i) q^{89} +(78.4508 + 54.0615i) q^{91} +(-40.2954 + 40.2954i) q^{92} +(120.242 - 32.2188i) q^{93} +(10.8455 - 6.26167i) q^{94} +(14.7892 - 25.6156i) q^{96} +(-74.4232 + 74.4232i) q^{97} +(-40.5919 - 56.1632i) 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 $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$2$	−0.366025	−	1.36603i	−0.183013	−	0.683013i
$3$	−1.35330	+	5.05060i	−0.451101	+	1.68353i	0.248202	+	0.968708i	$0.420160\pi$
$3$	−1.35330	+	5.05060i	−0.451101	+	1.68353i	−0.699304	+	0.714825i	$0.746506\pi$
$4$	−1.73205	+	1.00000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	7.39459			1.23243
$7$	−6.88437	+	1.26709i	−0.983481	+	0.181013i
$7$	−6.88437	+	1.26709i	−0.983481	+	0.181013i
$8$	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	0.999974	+	0.00725183i	$0.00230835\pi$
$11$	5.56894	+	9.64568i	0.506267	+	0.876880i	−0.493707	+	0.869629i	$0.664358\pi$
$12$	−2.70661	−	10.1012i	−0.225551	−	0.841767i
$13$	−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
$17$	−8.55361	−	2.29193i	−0.503153	−	0.134820i	−0.00169021	−	0.999999i	$-0.500538\pi$
$17$	−8.55361	−	2.29193i	−0.503153	−	0.134820i	−0.501463	+	0.865179i	$0.667205\pi$
$18$	−6.71290	+	25.0529i	−0.372939	+	1.39183i
$19$	5.79257	+	3.34434i	0.304872	+	0.176018i	0.644629	−	0.764495i	$-0.277012\pi$
$19$	5.79257	+	3.34434i	0.304872	+	0.176018i	−0.339758	+	0.940513i	$0.610345\pi$
$20$		0			0
$21$	2.91708	−	36.4849i	0.138909	−	1.73738i
$22$	11.1379	−	11.1379i	0.506267	−	0.506267i
$23$	27.5223	−	7.37457i	1.19662	−	0.320633i	0.395121	−	0.918629i	$-0.370703\pi$
$23$	27.5223	−	7.37457i	1.19662	−	0.320633i	0.801499	+	0.597996i	$0.204036\pi$
$24$	−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
$28$	10.6570	−	9.07903i	0.380607	−	0.324251i
$29$		−	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	0.607637	−	0.794215i	$-0.292118\pi$
$31$	−11.9038	−	20.6179i	−0.383992	−	0.665094i	−0.991629	+	0.129121i	$0.958784\pi$
$32$	−5.46410	−	1.46410i	−0.170753	−	0.0457532i
$33$	−56.2529	+	15.0729i	−1.70463	+	0.456756i
$34$			12.5233i			0.368334i
$35$		0			0
$36$	36.6800			1.01889
$37$	−4.01442	−	14.9820i	−0.108498	−	0.404919i	0.890221	−	0.455529i	$-0.150550\pi$
$37$	−4.01442	−	14.9820i	−0.108498	−	0.404919i	−0.998718	+	0.0506104i	$0.983883\pi$
$38$	2.44823	−	9.13690i	0.0644270	−	0.240445i
$39$	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	$0.535720\pi$
$42$	−50.9071	+	9.36960i	−1.21207	+	0.223086i
$43$	−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
$47$	2.29193	+	8.55361i	0.0487645	+	0.181992i	0.986012	−	0.166672i	$-0.0533022\pi$
$47$	2.29193	+	8.55361i	0.0487645	+	0.181992i	−0.937248	+	0.348664i	$0.886636\pi$
$48$	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
$52$	26.2937	+	7.04537i	0.505647	+	0.135488i
$53$	3.69897	−	13.8047i	0.0697918	−	0.260467i	−0.922210	−	0.386689i	$-0.873619\pi$
$53$	3.69897	−	13.8047i	0.0697918	−	0.260467i	0.992002	+	0.126223i	$0.0402853\pi$
$54$	−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
$58$	−39.7149	+	10.6416i	−0.684740	+	0.183476i
$59$	−67.7986	+	39.1435i	−1.14913	+	0.663450i	−0.948675	−	0.316253i	$-0.897575\pi$
$59$	−67.7986	+	39.1435i	−1.14913	+	0.663450i	−0.200454	+	0.979703i	$0.564242\pi$
$60$		0			0
$61$	−10.7196	+	18.5670i	−0.175732	+	0.304376i	−0.940414	−	0.340031i	$-0.889562\pi$
$61$	−10.7196	+	18.5670i	−0.175732	+	0.304376i	0.764682	+	0.644407i	$0.222896\pi$
$62$	−23.8075	+	23.8075i	−0.383992	+	0.383992i
$63$	120.963	+	43.0045i	1.92004	+	0.682612i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	41.1800	+	71.3259i	0.623940	+	1.08070i
$67$	51.3823	+	13.7678i	0.766900	+	0.205490i	0.621001	−	0.783809i	$-0.286726\pi$
$67$	51.3823	+	13.7678i	0.766900	+	0.205490i	0.145898	+	0.989300i	$0.453393\pi$
$68$	17.1072	−	4.58386i	0.251577	−	0.0674098i
$69$			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	$0.752473\pi$
$72$	−13.4258	−	50.1058i	−0.186469	−	0.695913i
$73$	−27.1115	+	101.181i	−0.371390	+	1.38605i	0.487157	+	0.873314i	$0.338034\pi$
$73$	−27.1115	+	101.181i	−0.371390	+	1.38605i	−0.858548	+	0.512734i	$0.828633\pi$
$74$	−18.9964	+	10.9676i	−0.256708	+	0.148211i
$75$		0			0
$76$	−13.3774			−0.176018
$77$	−50.5605	−	59.3481i	−0.656630	−	0.770754i
$78$	−71.1666	−	71.1666i	−0.912393	−	0.912393i
$79$	11.7992	+	6.81228i	0.149357	+	0.0862314i	0.572816	−	0.819684i	$-0.305851\pi$
$79$	11.7992	+	6.81228i	0.149357	+	0.0862314i	−0.423459	+	0.905915i	$0.639184\pi$
$80$		0			0
$81$	45.1475	+	78.1978i	0.557377	+	0.965406i
$82$	3.36105	+	12.5436i	0.0409884	+	0.152971i
$83$	−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
$87$	146.838	+	39.3451i	1.68779	+	0.452242i
$88$	−8.15349	+	30.4292i	−0.0926533	+	0.345787i
$89$	6.56157	+	3.78833i	0.0737256	+	0.0425655i	0.536410	−	0.843958i	$-0.319780\pi$
$89$	6.56157	+	3.78833i	0.0737256	+	0.0425655i	−0.462684	+	0.886523i	$0.653114\pi$
$90$		0			0
$91$	78.4508	+	54.0615i	0.862097	+	0.594083i
$92$	−40.2954	+	40.2954i	−0.437993	+	0.437993i
$93$	120.242	−	32.2188i	1.29293	−	0.346439i
$94$	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	$0.432532\pi$
$98$	−40.5919	−	56.1632i	−0.414203	−	0.573093i
$99$		−	204.268i		−	2.06332i
$100$		0			0
$101$	−62.1520	−	107.650i	−0.615366	−	1.06585i	−0.990320	−	0.138802i	$-0.955675\pi$
$101$	−62.1520	−	107.650i	−0.615366	−	1.06585i	0.374954	−	0.927044i	$-0.377659\pi$
$102$	−63.2504	−	16.9479i	−0.620102	−	0.166156i
$103$	100.098	−	26.8210i	0.971820	−	0.260398i	0.262224	−	0.965007i	$-0.415544\pi$
$103$	100.098	−	26.8210i	0.971820	−	0.260398i	0.709596	+	0.704609i	$0.248877\pi$
$104$		−	38.4966i		−	0.370160i
$105$		0			0
$106$	−20.2115			−0.190675
$107$	−23.2341	−	86.7110i	−0.217142	−	0.810383i	−0.985402	−	0.170245i	$-0.945544\pi$
$107$	−23.2341	−	86.7110i	−0.217142	−	0.810383i	0.768260	−	0.640138i	$-0.221123\pi$
$108$	−25.2797	+	94.3450i	−0.234071	+	0.873565i
$109$	−145.926	+	84.2503i	−1.33877	+	0.772938i	−0.986625	−	0.163008i	$-0.947880\pi$
$109$	−145.926	+	84.2503i	−1.33877	+	0.772938i	−0.352143	+	0.935946i	$0.614547\pi$
$110$		0			0
$111$	81.1008			0.730638
$112$	−9.37941	+	26.3823i	−0.0837447	+	0.235556i
$113$	−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
$117$	64.6059	+	241.113i	0.552188	+	2.06079i
$118$	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
$122$	29.2866	+	7.84732i	0.240054	+	0.0643223i
$123$	12.4268	−	46.3775i	0.101031	−	0.377052i
$124$	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	$0.101980\pi$
$128$	10.9282	−	2.92820i	0.0853766	−	0.0228766i
$129$	353.011	−	203.811i	2.73652	−	1.57993i
$130$		0			0
$131$	−38.6646	+	66.9690i	−0.295149	+	0.511214i	−0.975020	−	0.222119i	$-0.928703\pi$
$131$	−38.6646	+	66.9690i	−0.295149	+	0.511214i	0.679870	+	0.733332i	$0.262036\pi$
$132$	82.3600	−	82.3600i	0.623940	−	0.623940i
$133$	−44.1157	−	15.6840i	−0.331697	−	0.117925i
$134$		−	75.2289i		−	0.561409i
$135$		0			0
$136$	−12.5233	−	21.6911i	−0.0920834	−	0.159493i
$137$	62.2804	+	16.6880i	0.454602	+	0.121810i	0.478852	−	0.877896i	$-0.341053\pi$
$137$	62.2804	+	16.6880i	0.454602	+	0.121810i	−0.0242501	+	0.999706i	$0.507720\pi$
$138$	203.516	−	54.5319i	1.47475	−	0.395159i
$139$			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
$142$	37.0368	+	138.223i	0.260822	+	0.973402i
$143$	39.2352	−	146.428i	0.274372	−	1.02397i
$144$	−63.5316	+	36.6800i	−0.441191	+	0.254722i
$145$		0			0
$146$	148.140			1.01466
$147$	26.1473	+	254.872i	0.177873	+	1.73382i
$148$	21.9352	+	21.9352i	0.148211	+	0.148211i
$149$	−47.3177	−	27.3189i	−0.317568	−	0.183348i	0.332740	−	0.943019i	$-0.392027\pi$
$149$	−47.3177	−	27.3189i	−0.317568	−	0.183348i	−0.650308	+	0.759670i	$0.725360\pi$
$150$		0			0
$151$	62.2354	+	107.795i	0.412155	+	0.713874i	0.995125	−	0.0986200i	$-0.0314428\pi$
$151$	62.2354	+	107.795i	0.412155	+	0.713874i	−0.582970	+	0.812494i	$0.698109\pi$
$152$	4.89645	+	18.2738i	0.0322135	+	0.120222i
$153$	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
$157$	−77.2347	−	20.6950i	−0.491941	−	0.131815i	0.00431635	−	0.999991i	$-0.498626\pi$
$157$	−77.2347	−	20.6950i	−0.491941	−	0.131815i	−0.496257	+	0.868176i	$0.665293\pi$
$158$	4.98693	−	18.6115i	0.0315629	−	0.117794i
$159$	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
$163$	−182.269	+	48.8390i	−1.11822	+	0.299626i	−0.770162	−	0.637848i	$-0.779825\pi$
$163$	−182.269	+	48.8390i	−1.11822	+	0.299626i	−0.348056	+	0.937474i	$0.613158\pi$
$164$	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	$0.414277\pi$
$168$	78.8040	−	67.1357i	0.469072	−	0.399617i
$169$			16.2485i			0.0961450i
$170$		0			0
$171$	−61.3351	−	106.236i	−0.358685	−	0.621260i
$172$	150.603	+	40.3539i	0.875597	+	0.234615i
$173$	−307.467	+	82.3855i	−1.77727	+	0.476217i	−0.990081	−	0.140500i	$-0.955129\pi$
$173$	−307.467	+	82.3855i	−1.77727	+	0.476217i	−0.787185	+	0.616717i	$0.788462\pi$
$174$		−	214.985i		−	1.23555i
$175$		0			0
$176$	44.5515			0.253134
$177$	−105.946	−	395.397i	−0.598566	−	2.23388i
$178$	2.77325	−	10.3499i	0.0155800	−	0.0581455i
$179$	−57.5525	+	33.2280i	−0.321522	+	0.185631i	−0.652071	−	0.758158i	$-0.726100\pi$
$179$	−57.5525	+	33.2280i	−0.321522	+	0.185631i	0.330549	+	0.943789i	$0.392766\pi$
$180$		0			0
$181$	−71.5932			−0.395543			−0.197771	−	0.980248i	$-0.563370\pi$
$181$	−71.5932			−0.395543			−0.197771	+	0.980248i	$0.563370\pi$
$182$	45.1344	−	126.954i	0.247991	−	0.697548i
$183$	−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
$187$	−25.5273	−	95.2690i	−0.136509	−	0.509460i
$188$	−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	0.0132816	−	0.999912i	$-0.495772\pi$
$191$	166.665	−	288.672i	0.872590	−	1.51137i	0.859308	−	0.511458i	$-0.170894\pi$
$192$	−40.4048	−	10.8264i	−0.210442	−	0.0563877i
$193$	−25.7140	+	95.9658i	−0.133233	+	0.497232i	−0.999999	−	0.00148294i	$-0.999528\pi$
$193$	−25.7140	+	95.9658i	−0.133233	+	0.497232i	0.866766	+	0.498715i	$0.166195\pi$
$194$	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	$0.0934960\pi$
$198$	−279.036	+	74.7674i	−1.40927	+	0.377613i
$199$	−211.873	+	122.325i	−1.06469	+	0.614697i	−0.926725	−	0.375741i	$-0.877388\pi$
$199$	−211.873	+	122.325i	−1.06469	+	0.614697i	−0.137961	+	0.990438i	$0.544055\pi$
$200$		0			0
$201$	−139.072	+	240.879i	−0.691899	+	1.19840i
$202$	−124.304	+	124.304i	−0.615366	+	0.615366i
$203$	36.8385	+	200.152i	0.181470	+	0.985968i
$204$			92.6050i			0.453946i
$205$		0			0
$206$	−73.2765	−	126.919i	−0.355711	−	0.616109i
$207$	−504.758	−	135.249i	−2.43844	−	0.653379i
$208$	−52.5873	+	14.0907i	−0.252824	+	0.0677439i
$209$			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	$0.339669\pi$
$212$	7.39793	+	27.6095i	0.0348959	+	0.130233i
$213$	136.936	−	511.051i	0.642891	−	2.39930i
$214$	−109.945	+	63.4769i	−0.513762	+	0.296621i
$215$		0			0
$216$	138.131			0.639494
$217$	108.075	+	126.858i	0.498039	+	0.584600i
$218$	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
$222$	−29.6850	−	110.786i	−0.133716	−	0.499035i
$223$	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
$227$	−220.324	−	59.0356i	−0.970589	−	0.260069i	−0.261513	−	0.965200i	$-0.584221\pi$
$227$	−220.324	−	59.0356i	−0.970589	−	0.260069i	−0.709077	+	0.705132i	$0.750888\pi$
$228$	18.1036	−	67.5637i	0.0794019	−	0.296332i
$229$	−161.759	−	93.3917i	−0.706372	−	0.407824i	0.103344	−	0.994646i	$-0.467046\pi$
$229$	−161.759	−	93.3917i	−0.706372	−	0.407824i	−0.809716	+	0.586821i	$0.800379\pi$
$230$		0			0
$231$	368.167	−	175.045i	1.59380	−	0.757771i
$232$	58.1467	−	58.1467i	0.250632	−	0.250632i
$233$	−324.922	+	87.0627i	−1.39452	+	0.373660i	−0.876373	−	0.481634i	$-0.840044\pi$
$233$	−324.922	+	87.0627i	−1.39452	+	0.373660i	−0.518144	+	0.855293i	$0.673377\pi$
$234$	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
$238$	−15.8682	−	86.2153i	−0.0666731	−	0.362249i
$239$			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	0.722684	−	0.691178i	$-0.242908\pi$
$241$	−57.1739	−	99.0280i	−0.237236	−	0.410905i	−0.959920	+	0.280274i	$0.909575\pi$
$242$	4.16951	+	1.11722i	0.0172294	+	0.00461660i
$243$	−31.4918	+	8.43820i	−0.129596	+	0.0347251i
$244$		−	42.8786i		−	0.175732i
$245$		0			0
$246$	−67.9013			−0.276022
$247$	−23.5621	−	87.9349i	−0.0953931	−	0.356012i
$248$	17.4283	−	65.0433i	0.0702754	−	0.262272i
$249$	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	$0.501816\pi$
$252$	−252.518	+	46.4768i	−1.00206	+	0.184432i
$253$	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
$257$	−22.2236	−	82.9396i	−0.0864731	−	0.322722i	0.909116	−	0.416543i	$-0.136759\pi$
$257$	−22.2236	−	82.9396i	−0.0864731	−	0.322722i	−0.995589	+	0.0938211i	$0.970092\pi$
$258$	−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
$262$	105.634	+	28.3044i	0.403182	+	0.108032i
$263$	65.5647	−	244.691i	0.249296	−	0.930384i	−0.721880	−	0.692018i	$-0.756722\pi$
$263$	65.5647	−	244.691i	0.249296	−	0.930384i	0.971176	−	0.238365i	$-0.0766116\pi$
$264$	−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
$268$	−102.765	+	27.5357i	−0.383450	+	0.102745i
$269$	435.001	−	251.148i	1.61710	−	0.933636i	0.629441	−	0.777049i	$-0.283284\pi$
$269$	435.001	−	251.148i	1.61710	−	0.933636i	0.987664	−	0.156587i	$-0.0500493\pi$
$270$		0			0
$271$	99.2563	−	171.917i	0.366259	−	0.634380i	−0.622718	−	0.782446i	$-0.713972\pi$
$271$	99.2563	−	171.917i	0.366259	−	0.634380i	0.988977	+	0.148066i	$0.0473049\pi$
$272$	−25.0467	+	25.0467i	−0.0920834	+	0.0920834i
$273$	−379.211	+	323.062i	−1.38905	+	1.18338i
$274$		−	91.1849i		−	0.332792i
$275$		0			0
$276$	−148.984	−	258.048i	−0.539797	−	0.934956i
$277$	367.294	+	98.4162i	1.32597	+	0.355293i	0.851212	−	0.524822i	$-0.175868\pi$
$277$	367.294	+	98.4162i	1.32597	+	0.355293i	0.474760	+	0.880115i	$0.342535\pi$
$278$	70.3162	−	18.8412i	0.252936	−	0.0677740i
$279$			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	$0.422433\pi$
$282$	16.9479	+	63.2504i	0.0600989	+	0.224292i
$283$	−91.3244	+	340.827i	−0.322701	+	1.20434i	0.593902	+	0.804538i	$0.297587\pi$
$283$	−91.3244	+	340.827i	−0.322701	+	1.20434i	−0.916603	+	0.399799i	$0.869080\pi$
$284$	175.260	−	101.186i	0.617112	−	0.356290i
$285$		0			0
$286$	−214.385			−0.749599
$287$	63.2161	−	11.6351i	0.220265	−	0.0405405i
$288$	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
$292$	−54.2230	−	202.363i	−0.185695	−	0.693024i
$293$	−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
$297$	525.402	+	140.781i	1.76903	+	0.474010i
$298$	−19.9988	+	74.6366i	−0.0671101	+	0.250458i
$299$	−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
$303$	627.810	−	168.221i	2.07198	−	0.555185i
$304$	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	$-0.112342\pi$
$308$	146.922	+	52.2333i	0.477018	+	0.169589i
$309$			541.849i			1.75356i
$310$		0			0
$311$	−117.796	−	204.029i	−0.378766	−	0.656041i	0.612117	−	0.790767i	$-0.290318\pi$
$311$	−117.796	−	204.029i	−0.378766	−	0.656041i	−0.990883	+	0.134726i	$0.956985\pi$
$312$	194.431	+	52.0976i	0.623176	+	0.166979i
$313$	353.807	−	94.8023i	1.13037	−	0.302883i	0.355300	−	0.934752i	$-0.384379\pi$
$313$	353.807	−	94.8023i	1.13037	−	0.302883i	0.775075	+	0.631870i	$0.217712\pi$
$314$			113.079i			0.360126i
$315$		0			0
$316$	−27.2491			−0.0862314
$317$	5.34762	+	19.9576i	0.0168695	+	0.0629577i	0.973847	−	0.227203i	$-0.0729580\pi$
$317$	5.34762	+	19.9576i	0.0168695	+	0.0629577i	−0.956978	+	0.290160i	$0.906291\pi$
$318$	27.3523	−	102.080i	0.0860136	−	0.321007i
$319$	280.432	−	161.908i	0.879098	−	0.507548i
$320$		0			0
$321$	469.385			1.46226
$322$	182.922	+	214.714i	0.568079	+	0.666813i
$323$	−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
$327$	−228.032	−	851.029i	−0.697347	−	2.60253i
$328$	−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	−0.952825	−	0.303521i	$-0.901838\pi$
$331$	−70.6868	+	122.433i	−0.213555	+	0.369889i	0.739269	+	0.673410i	$0.235171\pi$
$332$	77.8184	+	20.8514i	0.234393	+	0.0628054i
$333$	−73.6243	+	274.770i	−0.221094	+	0.825134i
$334$	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	$0.407995\pi$
$338$	22.1959	−	5.94737i	0.0656683	−	0.0175958i
$339$	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
$343$	−293.122	+	178.125i	−0.854584	+	0.519314i
$344$		−	220.498i		−	0.640981i
$345$		0			0
$346$	225.081	+	389.852i	0.650524	+	1.12674i
$347$	−559.385	−	149.887i	−1.61206	−	0.431950i	−0.663404	−	0.748261i	$-0.730889\pi$
$347$	−559.385	−	149.887i	−1.61206	−	0.431950i	−0.948656	+	0.316311i	$0.897556\pi$
$348$	−293.676	+	78.6902i	−0.843896	+	0.226121i
$349$		−	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
$352$	−16.3070	−	60.8585i	−0.0463267	−	0.172893i
$353$	137.561	−	513.383i	0.389690	−	1.45434i	−0.440949	−	0.897532i	$-0.645358\pi$
$353$	137.561	−	513.383i	0.389690	−	1.45434i	0.830639	−	0.556811i	$-0.187975\pi$
$354$	−501.343	+	289.450i	−1.41622	+	0.817657i
$355$		0			0
$356$	−15.1533			−0.0425655
$357$	−108.573	+	305.392i	−0.304125	+	0.855439i
$358$	66.4559	+	66.4559i	0.185631	+	0.185631i
$359$	−61.5713	−	35.5482i	−0.171508	−	0.0990201i	0.411789	−	0.911279i	$-0.364904\pi$
$359$	−61.5713	−	35.5482i	−0.171508	−	0.0990201i	−0.583297	+	0.812259i	$0.698237\pi$
$360$		0			0
$361$	−158.131	−	273.891i	−0.438035	−	0.758700i
$362$	26.2049	+	97.7982i	0.0723893	+	0.270161i
$363$	−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
$367$	−136.269	−	36.5132i	−0.371306	−	0.0994911i	0.0683405	−	0.997662i	$-0.478230\pi$
$367$	−136.269	−	36.5132i	−0.371306	−	0.0994911i	−0.439646	+	0.898171i	$0.644896\pi$
$368$	29.4983	−	110.089i	0.0801584	−	0.299155i
$369$	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
$373$	−292.325	+	78.3283i	−0.783714	+	0.209995i	−0.628421	−	0.777873i	$-0.716299\pi$
$373$	−292.325	+	78.3283i	−0.783714	+	0.209995i	−0.155292	+	0.987869i	$0.549632\pi$
$374$	−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
$378$	455.526	+	161.948i	1.20510	+	0.428434i
$379$		−	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
$382$	−455.336	−	122.007i	−1.19198	−	0.319390i
$383$	171.786	−	46.0298i	0.448527	−	0.120182i	−0.0274833	−	0.999622i	$-0.508749\pi$
$383$	171.786	−	46.0298i	0.448527	−	0.120182i	0.476010	+	0.879440i	$0.342083\pi$
$384$			59.1567i			0.154054i
$385$		0			0
$386$	140.504			0.363999
$387$	370.045	+	1381.03i	0.956188	+	3.56854i
$388$	54.4815	−	203.328i	0.140416	−	0.524041i
$389$	207.304	−	119.687i	0.532914	−	0.307678i	−0.209288	−	0.977854i	$-0.567115\pi$
$389$	207.304	−	119.687i	0.532914	−	0.307678i	0.742202	+	0.670176i	$0.233781\pi$
$390$		0			0
$391$	−252.317			−0.645311
$392$	126.470	+	56.6856i	0.322628	+	0.144606i
$393$	−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
$397$	159.174	+	594.046i	0.400942	+	1.49634i	0.811419	+	0.584466i	$0.198696\pi$
$397$	159.174	+	594.046i	0.400942	+	1.49634i	−0.410476	+	0.911871i	$0.634638\pi$
$398$	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	0.383922	+	0.923366i	$0.374573\pi$
$401$	−243.686	+	422.077i	−0.607697	+	1.05256i	−0.991619	+	0.129197i	$0.958760\pi$
$402$	379.951	+	101.808i	0.945151	+	0.253253i
$403$	−83.8663	+	312.993i	−0.208105	+	0.776659i
$404$	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
$408$	126.501	−	33.8958i	0.310051	−	0.0830779i
$409$	−197.730	+	114.159i	−0.483447	+	0.279119i	−0.721852	−	0.692047i	$-0.756709\pi$
$409$	−197.730	+	114.159i	−0.483447	+	0.279119i	0.238405	+	0.971166i	$0.423376\pi$
$410$		0			0
$411$	−168.569	+	291.970i	−0.410143	+	0.710388i
$412$	−146.553	+	146.553i	−0.355711	+	0.355711i
$413$	417.152	−	355.385i	1.01005	−	0.860497i
$414$			739.017i			1.78506i
$415$		0			0
$416$	38.4966	+	66.6781i	0.0925399	+	0.160284i
$417$	−259.980	−	69.6614i	−0.623453	−	0.167054i
$418$	101.766	−	27.2680i	0.243459	−	0.0652345i
$419$			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	$0.307058\pi$
$422$	−74.5537	−	278.238i	−0.176668	−	0.659332i
$423$	42.0340	−	156.873i	0.0993711	−	0.370858i
$424$	35.0074	−	20.2115i	0.0825646	−	0.0476687i
$425$		0			0
$426$	−748.231			−1.75641
$427$	50.2719	−	141.404i	0.117733	−	0.331158i
$428$	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	0.988781	+	0.149371i	$0.0477250\pi$
$431$	268.836	+	465.638i	0.623750	+	1.08037i	−0.365031	+	0.930995i	$0.618942\pi$
$432$	−50.5593	−	188.690i	−0.117036	−	0.436782i
$433$	−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
$437$	184.088	+	49.3261i	0.421253	+	0.112874i
$438$	−200.478	+	748.196i	−0.457713	+	1.70821i
$439$	−160.490	−	92.6588i	−0.365580	−	0.211068i	0.305945	−	0.952049i	$-0.401027\pi$
$439$	−160.490	−	92.6588i	−0.365580	−	0.211068i	−0.671526	+	0.740981i	$0.734361\pi$
$440$		0			0
$441$	−887.243	−	142.788i	−2.01189	−	0.323783i
$442$	120.527	−	120.527i	0.272685	−	0.272685i
$443$	164.292	−	44.0219i	0.370862	−	0.0993722i	−0.0685740	−	0.997646i	$-0.521845\pi$
$443$	164.292	−	44.0219i	0.370862	−	0.0993722i	0.439436	+	0.898274i	$0.355178\pi$
$444$	−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
$448$	−10.1367	−	55.0749i	−0.0226266	−	0.122935i
$449$			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
$452$	60.8024	+	16.2919i	0.134518	+	0.0360441i
$453$	−628.652	+	168.447i	−1.38775	+	0.371847i
$454$			322.576i			0.710520i
$455$		0			0
$456$	−98.9201			−0.216930
$457$	−199.558	−	744.760i	−0.436669	−	1.62967i	−0.737040	−	0.675850i	$-0.763777\pi$
$457$	−199.558	−	744.760i	−0.436669	−	1.62967i	0.300370	−	0.953823i	$-0.402890\pi$
$458$	−68.3675	+	255.151i	−0.149274	+	0.557098i
$459$	−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	$0.560711\pi$
$462$	−373.874	−	438.855i	−0.809252	−	0.949902i
$463$	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
$467$	200.936	+	749.905i	0.430270	+	1.60579i	0.752137	+	0.659006i	$0.229023\pi$
$467$	200.936	+	749.905i	0.430270	+	1.60579i	−0.321867	+	0.946785i	$0.604310\pi$
$468$	−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
$472$	−213.884	−	57.3101i	−0.453145	−	0.121420i
$473$	224.728	−	838.697i	0.475112	−	1.77314i
$474$	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
$478$	114.300	−	30.6267i	0.239122	−	0.0640726i
$479$	78.4044	−	45.2668i	0.163684	−	0.0945028i	−0.415921	−	0.909401i	$-0.636541\pi$
$479$	78.4044	−	45.2668i	0.163684	−	0.0945028i	0.579604	+	0.814898i	$0.303207\pi$
$480$		0			0
$481$	−105.554	+	182.824i	−0.219446	+	0.380092i
$482$	−114.348	+	114.348i	−0.237236	+	0.237236i
$483$	−188.776	−	1025.66i	−0.390840	−	2.12352i
$484$		−	6.10459i		−	0.0126128i
$485$		0			0
$486$	23.0536	+	39.9300i	0.0474354	+	0.0821605i
$487$	882.327	+	236.419i	1.81176	+	0.485460i	0.995711	−	0.0925219i	$-0.0294928\pi$
$487$	882.327	+	236.419i	1.81176	+	0.485460i	0.816050	+	0.577982i	$0.196159\pi$
$488$	−58.5732	+	15.6946i	−0.120027	+	0.0321611i
$489$		−	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	$0.857657\pi$
$492$	24.8536	+	92.7549i	0.0505154	+	0.188526i
$493$	−66.6341	+	248.682i	−0.135161	+	0.504426i
$494$	−111.497	+	64.3728i	−0.225702	+	0.130309i
$495$		0			0
$496$	−95.2301			−0.191996
$497$	696.603	−	128.212i	1.40162	−	0.257972i
$498$	−210.624	−	210.624i	−0.422940	−	0.422940i
$499$	559.499	+	323.027i	1.12124	+	0.647348i	0.941717	−	0.336406i	$-0.109211\pi$
$499$	559.499	+	323.027i	1.12124	+	0.647348i	0.179522	+	0.983754i	$0.442545\pi$
$500$		0			0
$501$	−430.912	−	746.362i	−0.860104	−	1.48974i
$502$	1.04821	+	3.91195i	0.00208806	+	0.00779274i
$503$	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
$507$	−82.0647	−	21.9892i	−0.161863	−	0.0433711i
$508$	−58.9607	+	220.044i	−0.116064	+	0.433158i
$509$	256.295	+	147.972i	0.503526	+	0.290711i	0.730169	−	0.683267i	$-0.239442\pi$
$509$	256.295	+	147.972i	0.503526	+	0.290711i	−0.226642	+	0.973978i	$0.572775\pi$
$510$		0			0
$511$	58.4396	−	730.923i	0.114363	−	1.43038i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	315.522	−	84.5438i	0.615052	−	0.164803i
$514$	−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
$518$	116.881	−	99.5750i	0.225640	−	0.192230i
$519$		−	1664.38i		−	3.20691i
$520$		0			0
$521$	−343.065	−	594.206i	−0.658474	−	1.14051i	−0.981011	−	0.193953i	$-0.937869\pi$
$521$	−343.065	−	594.206i	−0.658474	−	1.14051i	0.322537	−	0.946557i	$-0.395464\pi$
$522$	728.371	+	195.166i	1.39535	+	0.373882i
$523$	−445.117	+	119.269i	−0.851085	+	0.228047i	−0.657891	−	0.753113i	$-0.728551\pi$
$523$	−445.117	+	119.269i	−0.851085	+	0.228047i	−0.193194	+	0.981161i	$0.561885\pi$
$524$		−	154.658i		−	0.295149i
$525$		0			0
$526$	−358.252			−0.681088
$527$	54.5652	+	203.640i	0.103539	+	0.386414i
$528$	−60.2917	+	225.012i	−0.114189	+	0.426159i
$529$	244.964	−	141.430i	0.463069	−	0.267353i
$530$		0			0
$531$	1435.78			2.70392
$532$	92.0946	−	16.9503i	0.173110	−	0.0318614i
$533$	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
$537$	−89.9350	−	335.642i	−0.167477	−	0.625032i
$538$	−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	−0.929495	−	0.368834i	$-0.879757\pi$
$541$	−78.6223	+	136.178i	−0.145328	+	0.251715i	0.784167	+	0.620549i	$0.213090\pi$
$542$	−271.173	−	72.6607i	−0.500320	−	0.134060i
$543$	96.8874	−	361.589i	0.178430	−	0.665909i
$544$	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	$0.244572\pi$
$548$	−124.561	+	33.3760i	−0.227301	+	0.0609051i
$549$	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
$553$	−89.8618	−	31.9476i	−0.162499	−	0.0577714i
$554$		−	537.756i		−	0.970679i
$555$		0			0
$556$	−51.4750	−	89.1574i	−0.0925810	−	0.160355i
$557$	−543.313	−	145.580i	−0.975427	−	0.261365i	−0.264309	−	0.964438i	$-0.585144\pi$
$557$	−543.313	−	145.580i	−0.975427	−	0.261365i	−0.711117	+	0.703073i	$0.751811\pi$
$558$	596.447	−	159.817i	1.06890	−	0.286411i
$559$			1061.05i			1.89812i
$560$		0			0
$561$	515.712			0.919272
$562$	−49.6326	−	185.231i	−0.0883143	−	0.329593i
$563$	−217.122	+	810.309i	−0.385651	+	1.43927i	0.451486	+	0.892278i	$0.350894\pi$
$563$	−217.122	+	810.309i	−0.385651	+	1.43927i	−0.837138	+	0.546992i	$0.815773\pi$
$564$	80.1983	−	46.3025i	0.142196	−	0.0820967i
$565$		0			0
$566$	499.006			0.881636
$567$	−409.896	−	481.137i	−0.722920	−	0.848566i
$568$	−202.373	−	202.373i	−0.356290	−	0.356290i
$569$	271.713	+	156.874i	0.477527	+	0.275701i	0.719385	−	0.694611i	$-0.244424\pi$
$569$	271.713	+	156.874i	0.477527	+	0.275701i	−0.241858	+	0.970312i	$0.577757\pi$
$570$		0			0
$571$	340.272	+	589.368i	0.595923	+	1.03217i	0.993416	+	0.114564i	$0.0365470\pi$
$571$	340.272	+	589.368i	0.595923	+	1.03217i	−0.397493	+	0.917605i	$0.630120\pi$
$572$	78.4704	+	292.856i	0.137186	+	0.511985i
$573$	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
$577$	798.104	+	213.851i	1.38320	+	0.370626i	0.872281	−	0.489005i	$-0.162640\pi$
$577$	798.104	+	213.851i	1.38320	+	0.370626i	0.510915	+	0.859631i	$0.329307\pi$
$578$	−77.0787	+	287.662i	−0.133354	+	0.497684i
$579$	−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
$583$	153.755	−	41.1986i	0.263731	−	0.0706666i
$584$	−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	$0.113406\pi$
$588$	−300.160	−	415.303i	−0.510477	−	0.706298i
$589$		−	159.241i		−	0.270358i
$590$		0			0
$591$	486.295	+	842.287i	0.822834	+	1.42519i
$592$	−59.9280	−	16.0577i	−0.101230	−	0.0271244i
$593$	−174.587	+	46.7804i	−0.294413	+	0.0788876i	−0.403002	−	0.915199i	$-0.632033\pi$
$593$	−174.587	+	46.7804i	−0.294413	+	0.0788876i	0.108589	+	0.994087i	$0.465367\pi$
$594$		−	769.241i		−	1.29502i
$595$		0			0
$596$	109.276			0.183348
$597$	−331.085	−	1235.63i	−0.554581	−	2.06972i
$598$	−141.948	+	529.757i	−0.237371	+	0.885881i
$599$	−267.890	+	154.666i	−0.447229	+	0.258208i	−0.706659	−	0.707554i	$-0.749799\pi$
$599$	−267.890	+	154.666i	−0.447229	+	0.258208i	0.259430	+	0.965762i	$0.416465\pi$
$600$		0			0
$601$	−583.911			−0.971566			−0.485783	−	0.874079i	$-0.661465\pi$
$601$	−583.911			−0.971566			−0.485783	+	0.874079i	$0.661465\pi$
$602$	258.517	−	727.155i	0.429430	−	1.20790i
$603$	−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
$607$	43.6636	+	162.955i	0.0719335	+	0.268459i	0.992520	−	0.122078i	$-0.0389559\pi$
$607$	43.6636	+	162.955i	0.0719335	+	0.268459i	−0.920587	+	0.390537i	$0.872289\pi$
$608$	−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
$612$	−313.746	−	84.0680i	−0.512657	−	0.137366i
$613$	98.0152	−	365.798i	0.159894	−	0.596734i	−0.838742	−	0.544529i	$-0.816709\pi$
$613$	98.0152	−	365.798i	0.159894	−	0.596734i	0.998636	−	0.0522047i	$-0.0166248\pi$
$614$	−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	$0.891225\pi$
$618$	740.180	−	198.331i	1.19770	−	0.320923i
$619$	−506.750	+	292.572i	−0.818660	+	0.472653i	−0.849954	−	0.526857i	$-0.823370\pi$
$619$	−506.750	+	292.572i	−0.818660	+	0.472653i	0.0312944	+	0.999510i	$0.490037\pi$
$620$		0			0
$621$	695.754	−	1205.08i	1.12038	−	1.94055i
$622$	−235.592	+	235.592i	−0.378766	+	0.378766i
$623$	−49.9724	−	17.7661i	−0.0802126	−	0.0285171i
$624$		−	284.667i		−	0.456196i
$625$		0			0
$626$	−259.005	−	448.609i	−0.413746	−	0.716629i
$627$	−376.258	−	100.818i	−0.600092	−	0.160794i
$628$	154.469	−	41.3900i	0.245970	−	0.0659076i
$629$			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	$0.344453\pi$
$632$	9.97387	+	37.2230i	0.0157814	+	0.0588971i
$633$	−275.647	+	1028.73i	−0.435461	+	1.62516i
$634$	25.3052	−	14.6100i	0.0399136	−	0.0230441i
$635$		0			0
$636$	−149.456			−0.234994
$637$	−608.585	−	272.775i	−0.955392	−	0.428218i
$638$	−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	0.677912	−	0.735143i	$-0.262885\pi$
$641$	−190.823	−	330.516i	−0.297696	−	0.515625i	−0.975609	+	0.219518i	$0.929552\pi$
$642$	−171.807	−	641.192i	−0.267612	−	0.998742i
$643$	−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
$647$	−674.219	−	180.656i	−1.04207	−	0.279222i	−0.303098	−	0.952959i	$-0.598021\pi$
$647$	−674.219	−	180.656i	−1.04207	−	0.279222i	−0.738971	+	0.673738i	$0.764688\pi$
$648$	−66.1006	+	246.691i	−0.102007	+	0.380696i
$649$	−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
$653$	−1076.27	+	288.387i	−1.64820	+	0.441634i	−0.959108	−	0.283041i	$-0.908657\pi$
$653$	−1076.27	+	288.387i	−1.64820	+	0.441634i	−0.689091	+	0.724675i	$0.741990\pi$
$654$	−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
$658$	−66.7305	+	56.8499i	−0.101414	+	0.0863980i
$659$			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	0.940233	+	0.340533i	$0.110607\pi$
$661$	505.683	+	875.868i	0.765026	+	1.32506i	−0.175206	+	0.984532i	$0.556059\pi$
$662$	193.120	+	51.7464i	0.291722	+	0.0781667i
$663$	−608.731	+	163.109i	−0.918147	+	0.246017i
$664$		−	113.934i		−	0.171587i
$665$		0			0
$666$	402.291			0.604040
$667$	−214.403	−	800.165i	−0.321444	−	1.19965i
$668$	85.3190	−	318.415i	0.127723	−	0.476669i
$669$	−1246.59	+	719.720i	−1.86337	+	1.07582i
$670$		0			0
$671$	−238.788			−0.355869
$672$	−69.3569	+	195.086i	−0.103210	+	0.290307i
$673$	−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
$677$	−73.0294	−	272.549i	−0.107872	−	0.402584i	0.890783	−	0.454429i	$-0.150157\pi$
$677$	−73.0294	−	272.549i	−0.107872	−	0.402584i	−0.998655	+	0.0518447i	$0.983490\pi$
$678$	−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
$682$	−362.222	−	97.0572i	−0.531118	−	0.142313i
$683$	110.892	−	413.854i	0.162360	−	0.605935i	−0.836002	−	0.548726i	$-0.815113\pi$
$683$	110.892	−	413.854i	0.162360	−	0.605935i	0.998362	−	0.0572092i	$-0.0182202\pi$
$684$	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
$688$	−301.205	+	80.7077i	−0.437798	+	0.117308i
$689$	−168.458	+	97.2594i	−0.244497	+	0.141160i
$690$		0			0
$691$	23.9800	−	41.5345i	0.0347033	−	0.0601079i	−0.848152	−	0.529753i	$-0.822285\pi$
$691$	23.9800	−	41.5345i	0.0347033	−	0.0601079i	0.882855	+	0.469645i	$0.155618\pi$
$692$	450.163	−	450.163i	0.650524	−	0.650524i
$693$	258.826	+	1406.26i	0.373487	+	2.02923i
$694$			818.996i			1.18011i
$695$		0			0
$696$	214.985	+	372.366i	0.308887	+	0.535008i
$697$	78.5440	+	21.0458i	0.112689	+	0.0301948i
$698$	−63.5837	+	17.0372i	−0.0910942	+	0.0244086i
$699$		−	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	$0.737685\pi$
$702$	243.295	+	907.990i	0.346575	+	1.29343i
$703$	26.8511	−	100.210i	0.0381951	−	0.142546i
$704$	−77.1655	+	44.5515i	−0.109610	+	0.0632834i
$705$		0			0
$706$	−751.645			−1.06465
$707$	564.280	+	662.353i	0.798133	+	0.936850i
$708$	578.901	+	578.901i	0.817657	+	0.817657i
$709$	−619.824	−	357.856i	−0.874224	−	0.504733i	−0.00547406	−	0.999985i	$-0.501742\pi$
$709$	−619.824	−	357.856i	−0.874224	−	0.504733i	−0.868749	+	0.495252i	$0.835076\pi$
$710$		0			0
$711$	−124.937	−	216.397i	−0.175720	−	0.304356i
$712$	5.54650	+	20.6998i	0.00779002	+	0.0290728i
$713$	−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
$717$	−422.603	−	113.236i	−0.589404	−	0.157930i
$718$	−26.0231	+	97.1195i	−0.0362439	+	0.135264i
$719$	−66.9619	−	38.6605i	−0.0931320	−	0.0537698i	0.452711	−	0.891657i	$-0.350457\pi$
$719$	−66.9619	−	38.6605i	−0.0931320	−	0.0537698i	−0.545843	+	0.837888i	$0.683790\pi$
$720$		0			0
$721$	−655.123	+	311.478i	−0.908631	+	0.432009i
$722$	−316.262	+	316.262i	−0.438035	+	0.438035i
$723$	577.524	−	154.747i	0.798789	−	0.214035i
$724$	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	$0.984810\pi$
$728$	48.7786	+	265.025i	0.0670036	+	0.364045i
$729$			642.184i			0.880911i
$730$		0			0
$731$	345.171	+	597.854i	0.472190	+	0.817857i
$732$	216.562	+	58.0277i	0.295850	+	0.0792728i
$733$	1046.86	−	280.505i	1.42818	−	0.382681i	0.539804	−	0.841791i	$-0.318498\pi$
$733$	1046.86	−	280.505i	1.42818	−	0.382681i	0.888379	+	0.459110i	$0.151832\pi$
$734$			199.512i			0.271815i
$735$		0			0
$736$	−161.182			−0.218997
$737$	153.344	+	572.289i	0.208066	+	0.776512i
$738$	61.6416	−	230.050i	0.0835252	−	0.311720i
$739$	1026.64	−	592.730i	1.38923	−	0.802070i	0.395999	−	0.918251i	$-0.370398\pi$
$739$	1026.64	−	592.730i	1.38923	−	0.802070i	0.993228	+	0.116181i	$0.0370652\pi$
$740$		0			0
$741$	476.011			0.642390
$742$	139.144	−	25.6098i	0.187525	−	0.0345145i
$743$	−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
$747$	191.207	+	713.594i	0.255967	+	0.955280i
$748$	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	−0.946837	−	0.321712i	$-0.895742\pi$
$751$	−146.301	+	253.400i	−0.194808	+	0.337417i	0.752030	+	0.659129i	$0.229075\pi$
$752$	34.2144	+	9.16773i	0.0454979	+	0.0121911i
$753$	3.87552	−	14.4637i	0.00514678	−	0.0192080i
$754$	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	$0.493833\pi$
$758$	−450.756	+	120.780i	−0.594665	+	0.159340i
$759$	−1437.05	+	829.683i	−1.89335	+	1.09313i
$760$		0			0
$761$	−308.160	+	533.749i	−0.404941	+	0.701378i	−0.994315	−	0.106482i	$-0.966041\pi$
$761$	−308.160	+	533.749i	−0.404941	+	0.701378i	0.589374	+	0.807860i	$0.299375\pi$
$762$	595.574	−	595.574i	0.781593	−	0.781593i
$763$	897.854	−	764.910i	1.17674	−	1.00250i
$764$			666.659i			0.872590i
$765$		0			0
$766$	−125.756	−	217.816i	−0.164172	−	0.284354i
$767$	1029.23	+	275.781i	1.34189	+	0.359558i
$768$	80.8096	−	21.6529i	0.105221	−	0.0281938i
$769$		−	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
$772$	−51.4279	−	191.932i	−0.0666165	−	0.248616i
$773$	85.9354	−	320.715i	0.111171	−	0.414897i	−0.887801	−	0.460228i	$-0.847768\pi$
$773$	85.9354	−	320.715i	0.111171	−	0.414897i	0.998972	+	0.0453311i	$0.0144343\pi$
$774$	1751.07	−	1010.98i	2.26236	−	1.30618i
$775$		0			0
$776$	−297.693			−0.383625
$777$	−558.328	+	102.762i	−0.718568	+	0.132255i
$778$	−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
$782$	92.3543	+	344.671i	0.118100	+	0.440756i
$783$	−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
$787$	−680.286	−	182.282i	−0.864404	−	0.231616i	−0.200738	−	0.979645i	$-0.564334\pi$
$787$	−680.286	−	182.282i	−0.864404	−	0.231616i	−0.663667	+	0.748029i	$0.731001\pi$
$788$	−96.2846	+	359.339i	−0.122189	+	0.456014i
$789$	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
$793$	281.859	−	75.5238i	0.355433	−	0.0952381i
$794$	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	$0.415462\pi$
$798$	−326.218	−	115.976i	−0.408794	−	0.145334i
$799$		−	78.4171i		−	0.0981441i
$800$		0			0
$801$	−69.4778	−	120.339i	−0.0867389	−	0.150236i
$802$	665.764	+	178.391i	0.830130	+	0.222433i
$803$	−1126.95	+	301.965i	−1.40342	+	0.376046i
$804$		−	556.287i		−	0.691899i
$805$		0			0
$806$	458.254			0.568554
$807$	679.759	+	2536.90i	0.842329	+	3.14361i
$808$	90.9969	−	339.605i	0.112620	−	0.420303i
$809$	772.252	−	445.860i	0.954576	−	0.551125i	0.0600765	−	0.998194i	$-0.480866\pi$
$809$	772.252	−	445.860i	0.954576	−	0.551125i	0.894499	+	0.447069i	$0.147532\pi$
$810$		0			0
$811$	−725.006			−0.893965			−0.446982	−	0.894543i	$-0.647501\pi$
$811$	−725.006			−0.893965			−0.446982	+	0.894543i	$0.647501\pi$
$812$	−263.958	−	309.834i	−0.325071	−	0.381569i
$813$	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
$817$	−134.957	−	503.666i	−0.165186	−	0.616483i
$818$	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	−0.539639	−	0.841897i	$-0.681439\pi$
$821$	377.073	−	653.109i	0.459285	−	0.795504i	0.998923	+	0.0463923i	$0.0147724\pi$
$822$	460.538	+	123.401i	0.560266	+	0.150123i
$823$	271.224	−	1012.22i	0.329556	−	1.22992i	−0.580096	−	0.814548i	$-0.696985\pi$
$823$	271.224	−	1012.22i	0.329556	−	1.22992i	0.909652	−	0.415371i	$-0.136348\pi$
$824$	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	$0.241904\pi$
$828$	1009.52	−	270.499i	1.21922	−	0.326690i
$829$	−159.407	+	92.0338i	−0.192289	+	0.111018i	−0.593053	−	0.805163i	$-0.702078\pi$
$829$	−159.407	+	92.0338i	−0.192289	+	0.111018i	0.400765	+	0.916181i	$0.368744\pi$
$830$		0			0
$831$	−994.122	+	1721.87i	−1.19630	+	2.07205i
$832$	76.9932	−	76.9932i	0.0925399	−	0.0925399i
$833$	−431.646	+	44.2827i	−0.518183	+	0.0531605i
$834$			380.637i			0.456399i
$835$		0			0
$836$	−74.4977	−	129.034i	−0.0891120	−	0.154347i
$837$	−1123.06	−	300.923i	−1.34177	−	0.359526i
$838$	427.054	−	114.429i	0.509610	−	0.136550i
$839$			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
$842$	−175.579	−	655.269i	−0.208526	−	0.778229i
$843$	−183.506	+	684.855i	−0.217683	+	0.812403i
$844$	−352.792	+	203.685i	−0.418000	+	0.241332i
$845$		0			0
$846$	−229.678			−0.271487
$847$	7.15718	−	20.1317i	0.00845004	−	0.0237682i
$848$	−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
$852$	273.872	+	1022.10i	0.321446	+	1.19965i
$853$	−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
$857$	−344.439	−	92.2922i	−0.401913	−	0.107692i	0.0521995	−	0.998637i	$-0.483377\pi$
$857$	−344.439	−	92.2922i	−0.401913	−	0.107692i	−0.454112	+	0.890944i	$0.650043\pi$
$858$	290.128	−	1082.77i	0.338145	−	1.26197i
$859$	1316.32	+	759.978i	1.53239	+	0.884724i	0.999251	+	0.0386951i	$0.0123201\pi$
$859$	1316.32	+	759.978i	1.53239	+	0.884724i	0.533136	+	0.846029i	$0.321013\pi$
$860$		0			0
$861$	−26.7863	+	335.025i	−0.0311107	+	0.389112i
$862$	537.672	−	537.672i	0.623750	−	0.623750i
$863$	−219.076	+	58.7013i	−0.253854	+	0.0680200i	−0.383502	−	0.923540i	$-0.625282\pi$
$863$	−219.076	+	58.7013i	−0.253854	+	0.0680200i	0.129648	+	0.991560i	$0.458615\pi$
$864$	−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
$868$	−314.049	−	111.650i	−0.361807	−	0.128629i
$869$			151.749i			0.174624i
$870$		0			0
$871$	−362.007	−	627.014i	−0.415622	−	0.719879i
$872$	−460.352	−	123.351i	−0.527927	−	0.141458i
$873$	1864.51	−	499.595i	2.13576	−	0.572274i
$874$		−	269.523i		−	0.308379i
$875$		0			0
$876$	1095.43			1.25050
$877$	252.641	+	942.868i	0.288074	+	1.07511i	0.946564	+	0.322517i	$0.104529\pi$
$877$	252.641	+	942.868i	0.288074	+	1.07511i	−0.658490	+	0.752590i	$0.728804\pi$
$878$	−67.8310	+	253.149i	−0.0772562	+	0.288324i
$879$	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	$0.409240\pi$
$882$	129.701	+	1264.26i	0.147053	+	1.43340i
$883$	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
$887$	−36.9292	−	137.822i	−0.0416338	−	0.155379i	0.941980	−	0.335670i	$-0.108963\pi$
$887$	−36.9292	−	137.822i	−0.0416338	−	0.155379i	−0.983613	+	0.180291i	$0.942296\pi$
$888$	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
$892$	−531.825	−	142.502i	−0.596216	−	0.159756i
$893$	−15.3300	+	57.2123i	−0.0171668	+	0.0640675i
$894$	−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
$898$	185.809	−	49.7873i	0.206914	−	0.0554424i
$899$	−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
$903$	−2172.01	+	1850.41i	−2.40533	+	2.04918i
$904$		−	89.0208i		−	0.0984744i
$905$		0			0
$906$	460.205	+	797.099i	0.507953	+	0.879801i
$907$	−85.4170	−	22.8874i	−0.0941753	−	0.0252342i	0.211424	−	0.977395i	$-0.432190\pi$
$907$	−85.4170	−	22.8874i	−0.0941753	−	0.0252342i	−0.305599	+	0.952160i	$0.598857\pi$
$908$	440.647	−	118.071i	0.485295	−	0.130034i
$909$			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	$0.503432\pi$
$912$	36.2073	+	135.127i	0.0397009	+	0.148166i
$913$	116.120	−	433.366i	0.127185	−	0.474662i
$914$	−944.318	+	545.202i	−1.03317	+	0.596501i
$915$		0			0
$916$	373.567			0.407824
$917$	181.325	−	510.031i	0.197738	−	0.556195i
$918$	432.465	+	432.465i	0.471094	+	0.471094i
$919$	730.678	+	421.857i	0.795080	+	0.459039i	0.841748	−	0.539871i	$-0.181527\pi$
$919$	730.678	+	421.857i	0.795080	+	0.459039i	−0.0466681	+	0.998910i	$0.514860\pi$
$920$		0			0
$921$	1457.45	+	2524.37i	1.58246	+	2.74090i
$922$	63.9767	+	238.764i	0.0693890	+	0.258963i
$923$	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
$927$	−1835.79	−	491.897i	−1.98035	−	0.530634i
$928$	−42.5663	+	158.860i	−0.0458689	+	0.171185i
$929$	325.901	+	188.159i	0.350808	+	0.202539i	0.665041	−	0.746807i	$-0.268414\pi$
$929$	325.901	+	188.159i	0.350808	+	0.202539i	−0.314233	+	0.949346i	$0.601747\pi$
$930$		0			0
$931$	323.582	+	52.0756i	0.347564	+	0.0559351i
$932$	475.719	−	475.719i	0.510429	−	0.510429i
$933$	1189.88	−	318.828i	1.27533	−	0.341723i
$934$	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	$0.330867\pi$
$938$	95.3216	+	517.903i	0.101622	+	0.552135i
$939$			1915.23i			2.03965i
$940$		0			0
$941$	−462.718	−	801.452i	−0.491730	−	0.851702i	0.508224	−	0.861225i	$-0.330302\pi$
$941$	−462.718	−	801.452i	−0.491730	−	0.851702i	−0.999955	+	0.00952274i	$0.996969\pi$
$942$	−571.119	−	153.031i	−0.606284	−	0.162453i
$943$	−252.725	+	67.7175i	−0.268001	+	0.0718107i
$944$			313.148i			0.331725i
$945$		0			0
$946$	−1227.94			−1.29803
$947$	−233.763	−	872.417i	−0.246846	−	0.921243i	−0.972446	−	0.233126i	$-0.925104\pi$
$947$	−233.763	−	872.417i	−0.246846	−	0.921243i	0.725600	−	0.688116i	$-0.241562\pi$
$948$	36.8763	−	137.624i	0.0388991	−	0.145173i
$949$	1234.71	−	712.861i	1.30107	−	0.751170i
$950$		0			0
$951$	−108.035			−0.113601
$952$	113.700	+	133.461i	0.119433	+	0.140190i
$953$	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
$957$	438.221	+	1635.46i	0.457911	+	1.70895i
$958$	−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
$962$	288.378	+	77.2707i	0.299769	+	0.0803229i
$963$	−426.114	+	1590.28i	−0.442486	+	1.65138i
$964$	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	$0.272163\pi$
$968$	−8.33902	+	2.23443i	−0.00861469	+	0.00230830i
$969$	268.210	−	154.851i	0.276791	−	0.159805i
$970$		0			0
$971$	−541.576	+	938.036i	−0.557750	+	0.966052i	0.439934	+	0.898030i	$0.355002\pi$
$971$	−541.576	+	938.036i	−0.557750	+	0.966052i	−0.997684	+	0.0680216i	$0.978331\pi$
$972$	46.1072	−	46.1072i	0.0474354	−	0.0474354i
$973$	−65.2234	−	354.373i	−0.0670333	−	0.364207i
$974$		−	1291.82i		−	1.32630i
$975$		0			0
$976$	42.8786	+	74.2678i	0.0439329	+	0.0760941i
$977$	1837.47	+	492.348i	1.88072	+	0.503939i	0.999513	+	0.0312166i	$0.00993815\pi$
$977$	1837.47	+	492.348i	1.88072	+	0.503939i	0.881212	+	0.472722i	$0.156729\pi$
$978$	−1347.81	+	361.144i	−1.37813	+	0.369268i
$979$			84.3878i			0.0861980i
$980$		0			0
$981$	3090.30			3.15015
$982$	324.093	+	1209.53i	0.330034	+	1.23170i
$983$	245.579	−	916.515i	0.249826	−	0.932365i	−0.721069	−	0.692863i	$-0.756349\pi$
$983$	245.579	−	916.515i	0.249826	−	0.932365i	0.970896	−	0.239502i	$-0.0769842\pi$
$984$	117.609	−	67.9013i	0.119521	−	0.0690054i
$985$		0			0
$986$	364.096			0.369265
$987$	318.763	−	58.6694i	0.322962	−	0.0594421i
$988$	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	0.818769	+	0.574123i	$0.194657\pi$
$991$	898.430	+	1556.13i	0.906590	+	1.57026i	0.0878205	+	0.996136i	$0.472010\pi$
$992$	34.8566	+	130.087i	0.0351377	+	0.131136i
$993$	−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
$997$	−472.003	−	126.473i	−0.473423	−	0.126853i	0.0142155	−	0.999899i	$-0.495475\pi$
$997$	−472.003	−	126.473i	−0.473423	−	0.126853i	−0.487639	+	0.873046i	$0.662142\pi$
$998$	236.472	−	882.525i	0.236946	−	0.884294i
$999$	−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.93.1		16
5.2	odd	4	inner	350.3.p.e.107.4		16
5.3	odd	4		70.3.l.c.37.1	yes	16
5.4	even	2		70.3.l.c.23.4	✓	16
7.4	even	3	inner	350.3.p.e.193.4		16
35.4	even	6		70.3.l.c.53.1	yes	16
35.9	even	6		490.3.f.o.393.4		8
35.18	odd	12		70.3.l.c.67.4	yes	16
35.19	odd	6		490.3.f.p.393.1		8
35.23	odd	12		490.3.f.o.197.4		8
35.32	odd	12	inner	350.3.p.e.207.1		16
35.33	even	12		490.3.f.p.197.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.c.23.4	✓	16	5.4	even	2
70.3.l.c.37.1	yes	16	5.3	odd	4
70.3.l.c.53.1	yes	16	35.4	even	6
70.3.l.c.67.4	yes	16	35.18	odd	12
350.3.p.e.93.1		16	1.1	even	1	trivial
350.3.p.e.107.4		16	5.2	odd	4	inner
350.3.p.e.193.4		16	7.4	even	3	inner
350.3.p.e.207.1		16	35.32	odd	12	inner
490.3.f.o.197.4		8	35.23	odd	12
490.3.f.o.393.4		8	35.9	even	6
490.3.f.p.197.1		8	35.33	even	12
490.3.f.p.393.1		8	35.19	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)

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

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Database

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