LMFDB - Embedded newform 350.3.p.e.107.4

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			107.4
Root			$1.35330 + 5.05060i$ of defining polynomial
Character	$\chi$	$=$	350.107
Dual form			350.3.p.e.193.4

$q$ -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} +(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})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + 8 q^{2} - 2 q^{3} - 8 q^{6} - 12 q^{7} + 32 q^{8} + 40 q^{11} - 4 q^{12} - 16 q^{13} + 32 q^{16} - 46 q^{17} + 52 q^{18} - 20 q^{21} + 80 q^{22} - 54 q^{23} - 16 q^{26} + 52 q^{27} + 36 q^{28} - 208 q^{31}+ \cdots + 268 q^{98}+O(q^{100})$ 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

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	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	0.968708	−	0.248202i	$-0.0798398\pi$
$3$	5.05060	+	1.35330i	1.68353	+	0.451101i	0.714825	+	0.699304i	$0.246506\pi$
$4$	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	0.999974	+	0.00725183i	$0.00230835\pi$
$11$	5.56894	+	9.64568i	0.506267	+	0.876880i	−0.493707	+	0.869629i	$0.664358\pi$
$12$	10.1012	−	2.70661i	0.841767	−	0.225551i
$13$	−9.62415	+	9.62415i	−0.740319	+	0.740319i	−0.972639	−	0.232320i	$-0.925368\pi$
$13$	−9.62415	+	9.62415i	−0.740319	+	0.740319i	0.232320	+	0.972639i	$0.425368\pi$
$14$	−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	−0.865179	−	0.501463i	$-0.832795\pi$
$17$	2.29193	−	8.55361i	0.134820	−	0.503153i	0.999999	−	0.00169021i	$-0.000538011\pi$
$18$	25.0529	+	6.71290i	1.39183	+	0.372939i
$19$	−5.79257	−	3.34434i	−0.304872	−	0.176018i	0.339758	−	0.940513i	$-0.389655\pi$
$19$	−5.79257	−	3.34434i	−0.304872	−	0.176018i	−0.644629	+	0.764495i	$0.722988\pi$
$20$		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	−0.918629	−	0.395121i	$-0.870703\pi$
$23$	−7.37457	−	27.5223i	−0.320633	−	1.19662i	0.597996	−	0.801499i	$-0.295964\pi$
$24$	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	$0.167132\pi$
$29$			29.0733i			1.00253i	−0.865294	+	0.501265i	$0.832868\pi$
$30$		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	$0.958784\pi$
$32$	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	−0.0506104	−	0.998718i	$-0.516117\pi$
$37$	14.9820	−	4.01442i	0.404919	−	0.108498i	0.455529	+	0.890221i	$0.349450\pi$
$38$	−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	−0.342414	+	0.939549i	$0.611244\pi$
$43$	−55.1244	+	55.1244i	−1.28196	+	1.28196i	−0.939549	+	0.342414i	$0.888756\pi$
$44$	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	−0.348664	−	0.937248i	$-0.613364\pi$
$47$	−8.55361	+	2.29193i	−0.181992	+	0.0487645i	0.166672	+	0.986012i	$0.446698\pi$
$48$	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	0.126223	−	0.992002i	$-0.459715\pi$
$53$	−13.8047	−	3.69897i	−0.260467	−	0.0697918i	−0.386689	+	0.922210i	$0.626381\pi$
$54$	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	0.200454	−	0.979703i	$-0.435758\pi$
$59$	67.7986	−	39.1435i	1.14913	−	0.663450i	0.948675	+	0.316253i	$0.102425\pi$
$60$		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
$63$	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	0.783809	+	0.621001i	$0.213274\pi$
$67$	−13.7678	+	51.3823i	−0.205490	+	0.766900i	−0.989300	+	0.145898i	$0.953393\pi$
$68$	−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	0.873314	−	0.487157i	$-0.161966\pi$
$73$	101.181	+	27.1115i	1.38605	+	0.371390i	0.512734	+	0.858548i	$0.328633\pi$
$74$	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	0.423459	−	0.905915i	$-0.360816\pi$
$79$	−11.7992	−	6.81228i	−0.149357	−	0.0862314i	−0.572816	+	0.819684i	$0.694149\pi$
$80$		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	−0.857560	−	0.514385i	$-0.828020\pi$
$83$	−28.4835	+	28.4835i	−0.343175	+	0.343175i	0.514385	+	0.857560i	$0.328020\pi$
$84$	−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	0.462684	−	0.886523i	$-0.346886\pi$
$89$	−6.56157	−	3.78833i	−0.0737256	−	0.0425655i	−0.536410	+	0.843958i	$0.680220\pi$
$90$		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	0.210372	−	0.977621i	$-0.432532\pi$
$97$	−74.4232	−	74.4232i	−0.767249	−	0.767249i	−0.977621	+	0.210372i	$0.932532\pi$
$98$	−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	−0.990320	−	0.138802i	$-0.955675\pi$
$101$	−62.1520	−	107.650i	−0.615366	−	1.06585i	0.374954	−	0.927044i	$-0.377659\pi$
$102$	16.9479	−	63.2504i	0.166156	−	0.620102i
$103$	−26.8210	−	100.098i	−0.260398	−	0.971820i	−0.965007	−	0.262224i	$-0.915544\pi$
$103$	−26.8210	−	100.098i	−0.260398	−	0.971820i	0.704609	−	0.709596i	$-0.251123\pi$
$104$			38.4966i			0.370160i
$105$		0			0
$106$	−20.2115			−0.190675
$107$	86.7110	−	23.2341i	0.810383	−	0.217142i	0.170245	−	0.985402i	$-0.445544\pi$
$107$	86.7110	−	23.2341i	0.810383	−	0.217142i	0.640138	+	0.768260i	$0.278877\pi$
$108$	94.3450	+	25.2797i	0.873565	+	0.234071i
$109$	145.926	−	84.2503i	1.33877	−	0.772938i	0.352143	−	0.935946i	$-0.385453\pi$
$109$	145.926	−	84.2503i	1.33877	−	0.772938i	0.986625	+	0.163008i	$0.0521196\pi$
$110$		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	−0.798691	−	0.601742i	$-0.794474\pi$
$113$	−22.2552	+	22.2552i	−0.196949	+	0.196949i	0.601742	+	0.798691i	$0.294474\pi$
$114$	−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	0.949115	−	0.314928i	$-0.101980\pi$
$127$	80.5418	+	80.5418i	0.634187	+	0.634187i	−0.314928	+	0.949115i	$0.601980\pi$
$128$	−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	−0.975020	−	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
$133$	−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	−0.999706	−	0.0242501i	$-0.992280\pi$
$137$	−16.6880	+	62.2804i	−0.121810	+	0.454602i	0.877896	+	0.478852i	$0.158947\pi$
$138$	−54.5319	−	203.516i	−0.395159	−	1.47475i
$139$		−	51.4750i		−	0.370324i	−0.982708	−	0.185162i	$-0.940719\pi$
$139$		−	51.4750i		−	0.370324i	0.982708	−	0.185162i	$-0.0592810\pi$
$140$		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	0.650308	−	0.759670i	$-0.274640\pi$
$149$	47.3177	+	27.3189i	0.317568	+	0.183348i	−0.332740	+	0.943019i	$0.607973\pi$
$150$		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	$0.698109\pi$
$152$	−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	−0.868176	−	0.496257i	$-0.834707\pi$
$157$	20.6950	−	77.2347i	0.131815	−	0.491941i	0.999991	+	0.00431635i	$0.00137394\pi$
$158$	−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	0.937474	+	0.348056i	$0.113158\pi$
$163$	48.8390	+	182.269i	0.299626	+	1.11822i	−0.637848	+	0.770162i	$0.720175\pi$
$164$	−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	0.266064	−	0.963955i	$-0.414277\pi$
$167$	−116.548	−	116.548i	−0.697892	−	0.697892i	−0.963955	+	0.266064i	$0.914277\pi$
$168$	−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	0.616717	+	0.787185i	$0.288462\pi$
$173$	82.3855	+	307.467i	0.476217	+	1.77727i	−0.140500	+	0.990081i	$0.544871\pi$
$174$			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	−0.330549	−	0.943789i	$-0.607234\pi$
$179$	57.5525	−	33.2280i	0.321522	−	0.185631i	0.652071	+	0.758158i	$0.273900\pi$
$180$		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	0.0132816	−	0.999912i	$-0.495772\pi$
$191$	166.665	−	288.672i	0.872590	−	1.51137i	0.859308	−	0.511458i	$-0.170894\pi$
$192$	10.8264	−	40.4048i	0.0563877	−	0.210442i
$193$	95.9658	+	25.7140i	0.497232	+	0.133233i	0.498715	−	0.866766i	$-0.333805\pi$
$193$	95.9658	+	25.7140i	0.497232	+	0.133233i	−0.00148294	+	0.999999i	$0.500472\pi$
$194$	−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	0.957172	−	0.289521i	$-0.0934960\pi$
$197$	131.527	+	131.527i	0.667651	+	0.667651i	−0.289521	+	0.957172i	$0.593496\pi$
$198$	74.7674	+	279.036i	0.377613	+	1.40927i
$199$	211.873	−	122.325i	1.06469	−	0.614697i	0.137961	−	0.990438i	$-0.455945\pi$
$199$	211.873	−	122.325i	1.06469	−	0.614697i	0.926725	+	0.375741i	$0.122612\pi$
$200$		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	−0.119869	−	0.992790i	$-0.538247\pi$
$223$	194.661	−	194.661i	0.872921	−	0.872921i	0.992790	+	0.119869i	$0.0382474\pi$
$224$	−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	−0.705132	−	0.709077i	$-0.749112\pi$
$227$	59.0356	−	220.324i	0.260069	−	0.970589i	0.965200	−	0.261513i	$-0.0842213\pi$
$228$	−67.5637	−	18.1036i	−0.296332	−	0.0794019i
$229$	161.759	+	93.3917i	0.706372	+	0.407824i	0.809716	−	0.586821i	$-0.199621\pi$
$229$	161.759	+	93.3917i	0.706372	+	0.407824i	−0.103344	+	0.994646i	$0.532954\pi$
$230$		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	0.855293	+	0.518144i	$0.173377\pi$
$233$	87.0627	+	324.922i	0.373660	+	1.39452i	−0.481634	+	0.876373i	$0.659956\pi$
$234$	−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	$-0.943991\pi$
$239$		−	83.6738i		−	0.350099i	0.984560	−	0.175050i	$-0.0560086\pi$
$240$		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	$0.909575\pi$
$242$	−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	−0.0938211	−	0.995589i	$-0.529908\pi$
$257$	82.9396	−	22.2236i	0.322722	−	0.0864731i	0.416543	+	0.909116i	$0.363241\pi$
$258$	−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	−0.238365	−	0.971176i	$-0.576612\pi$
$263$	−244.691	−	65.5647i	−0.930384	−	0.249296i	−0.692018	+	0.721880i	$0.743278\pi$
$264$	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	−0.629441	+	0.777049i	$0.716716\pi$
$269$	−435.001	+	251.148i	−1.61710	+	0.933636i	−0.987664	+	0.156587i	$0.949951\pi$
$270$		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
$273$	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	0.524822	+	0.851212i	$0.324132\pi$
$277$	−98.4162	+	367.294i	−0.355293	+	1.32597i	−0.880115	+	0.474760i	$0.842535\pi$
$278$	−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	0.804538	−	0.593902i	$-0.202413\pi$
$283$	340.827	+	91.3244i	1.20434	+	0.322701i	0.399799	+	0.916603i	$0.369080\pi$
$284$	−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	−0.820948	−	0.571003i	$-0.806555\pi$
$293$	−73.2341	+	73.2341i	−0.249946	+	0.249946i	0.571003	+	0.820948i	$0.306555\pi$
$294$	−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	0.938363	+	0.345652i	$0.112342\pi$
$307$	394.192	+	394.192i	1.28401	+	1.28401i	0.345652	+	0.938363i	$0.387658\pi$
$308$	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	0.612117	−	0.790767i	$-0.290318\pi$
$311$	−117.796	−	204.029i	−0.378766	−	0.656041i	−0.990883	+	0.134726i	$0.956985\pi$
$312$	−52.0976	+	194.431i	−0.166979	+	0.623176i
$313$	−94.8023	−	353.807i	−0.302883	−	1.13037i	−0.934752	−	0.355300i	$-0.884379\pi$
$313$	−94.8023	−	353.807i	−0.302883	−	1.13037i	0.631870	−	0.775075i	$-0.282288\pi$
$314$		−	113.079i		−	0.360126i
$315$		0			0
$316$	−27.2491			−0.0862314
$317$	−19.9576	+	5.34762i	−0.0629577	+	0.0168695i	−0.290160	−	0.956978i	$-0.593709\pi$
$317$	−19.9576	+	5.34762i	−0.0629577	+	0.0168695i	0.227203	+	0.973847i	$0.427042\pi$
$318$	−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	−0.952825	−	0.303521i	$-0.901838\pi$
$331$	−70.6868	+	122.433i	−0.213555	+	0.369889i	0.739269	+	0.673410i	$0.235171\pi$
$332$	−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	0.285035	−	0.958517i	$-0.407995\pi$
$337$	−226.963	−	226.963i	−0.673482	−	0.673482i	−0.958517	+	0.285035i	$0.907995\pi$
$338$	−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	−0.316311	−	0.948656i	$-0.602444\pi$
$347$	149.887	−	559.385i	0.431950	−	1.61206i	0.748261	−	0.663404i	$-0.230889\pi$
$348$	78.6902	+	293.676i	0.226121	+	0.843896i
$349$			46.5465i			0.133371i	0.997774	+	0.0666856i	$0.0212424\pi$
$349$			46.5465i			0.133371i	−0.997774	+	0.0666856i	$0.978758\pi$
$350$		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	−0.556811	−	0.830639i	$-0.687975\pi$
$353$	−513.383	−	137.561i	−1.45434	−	0.389690i	−0.897532	+	0.440949i	$0.854642\pi$
$354$	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	0.583297	−	0.812259i	$-0.301763\pi$
$359$	61.5713	+	35.5482i	0.171508	+	0.0990201i	−0.411789	+	0.911279i	$0.635096\pi$
$360$		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	−0.898171	−	0.439646i	$-0.855104\pi$
$367$	36.5132	−	136.269i	0.0994911	−	0.371306i	0.997662	+	0.0683405i	$0.0217704\pi$
$368$	−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	0.987869	+	0.155292i	$0.0496319\pi$
$373$	78.3283	+	292.325i	0.209995	+	0.783714i	−0.777873	+	0.628421i	$0.783701\pi$
$374$	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	$0.143366\pi$
$379$			329.976i			0.870649i	−0.900274	+	0.435325i	$0.856634\pi$
$380$		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	0.879440	−	0.476010i	$-0.157917\pi$
$383$	−46.0298	−	171.786i	−0.120182	−	0.448527i	−0.999622	+	0.0274833i	$0.991251\pi$
$384$		−	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	−0.742202	−	0.670176i	$-0.766219\pi$
$389$	−207.304	+	119.687i	−0.532914	+	0.307678i	0.209288	+	0.977854i	$0.432885\pi$
$390$		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	−0.911871	−	0.410476i	$-0.865362\pi$
$397$	−594.046	+	159.174i	−1.49634	+	0.400942i	−0.584466	+	0.811419i	$0.698696\pi$
$398$	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	$0.958760\pi$
$402$	−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	−0.238405	−	0.971166i	$-0.576624\pi$
$409$	197.730	−	114.159i	0.483447	−	0.279119i	0.721852	+	0.692047i	$0.243291\pi$
$410$		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	$-0.878308\pi$
$419$		−	312.625i		−	0.746121i	0.927807	−	0.373061i	$-0.121692\pi$
$420$		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	0.988781	+	0.149371i	$0.0477250\pi$
$431$	268.836	+	465.638i	0.623750	+	1.08037i	−0.365031	+	0.930995i	$0.618942\pi$
$432$	188.690	−	50.5593i	0.436782	−	0.117036i
$433$	−13.8191	+	13.8191i	−0.0319148	+	0.0319148i	−0.722884	−	0.690969i	$-0.757184\pi$
$433$	−13.8191	+	13.8191i	−0.0319148	+	0.0319148i	0.690969	+	0.722884i	$0.257184\pi$
$434$	−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	0.671526	−	0.740981i	$-0.265639\pi$
$439$	160.490	+	92.6588i	0.365580	+	0.211068i	−0.305945	+	0.952049i	$0.598973\pi$
$440$		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	0.898274	−	0.439436i	$-0.144822\pi$
$443$	−44.0219	−	164.292i	−0.0993722	−	0.370862i	−0.997646	+	0.0685740i	$0.978155\pi$
$444$	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	$-0.951599\pi$
$449$		−	136.021i		−	0.302943i	0.988462	−	0.151472i	$-0.0484012\pi$
$450$		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	0.675850	−	0.737040i	$-0.263777\pi$
$457$	744.760	−	199.558i	1.62967	−	0.436669i	0.953823	+	0.300370i	$0.0971102\pi$
$458$	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	−0.428814	−	0.903393i	$-0.641069\pi$
$463$	219.730	−	219.730i	0.474578	−	0.474578i	0.903393	+	0.428814i	$0.141069\pi$
$464$	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	−0.946785	−	0.321867i	$-0.895690\pi$
$467$	−749.905	+	200.936i	−1.60579	+	0.430270i	−0.659006	+	0.752137i	$0.729023\pi$
$468$	−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	−0.579604	−	0.814898i	$-0.696793\pi$
$479$	−78.4044	+	45.2668i	−0.163684	+	0.0945028i	0.415921	+	0.909401i	$0.363459\pi$
$480$		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	0.0925219	+	0.995711i	$0.470507\pi$
$487$	−236.419	+	882.327i	−0.485460	+	1.81176i	−0.577982	+	0.816050i	$0.696159\pi$
$488$	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	−0.179522	−	0.983754i	$-0.557455\pi$
$499$	−559.499	−	323.027i	−1.12124	−	0.647348i	−0.941717	+	0.336406i	$0.890789\pi$
$500$		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	−0.00910371	−	0.999959i	$-0.502898\pi$
$503$	498.400	−	498.400i	0.990855	−	0.990855i	0.999959	+	0.00910371i	$0.00289784\pi$
$504$	−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	0.226642	−	0.973978i	$-0.427225\pi$
$509$	−256.295	−	147.972i	−0.503526	−	0.290711i	−0.730169	+	0.683267i	$0.760558\pi$
$510$		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	−0.981011	−	0.193953i	$-0.937869\pi$
$521$	−343.065	−	594.206i	−0.658474	−	1.14051i	0.322537	−	0.946557i	$-0.395464\pi$
$522$	−195.166	+	728.371i	−0.373882	+	1.39535i
$523$	119.269	+	445.117i	0.228047	+	0.851085i	0.981161	+	0.193194i	$0.0618846\pi$
$523$	119.269	+	445.117i	0.228047	+	0.851085i	−0.753113	+	0.657891i	$0.771449\pi$
$524$			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	−0.929495	−	0.368834i	$-0.879757\pi$
$541$	−78.6223	+	136.178i	−0.145328	+	0.251715i	0.784167	+	0.620549i	$0.213090\pi$
$542$	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	0.719061	−	0.694947i	$-0.244572\pi$
$547$	13.1899	+	13.1899i	0.0241132	+	0.0241132i	−0.694947	+	0.719061i	$0.744572\pi$
$548$	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	−0.703073	−	0.711117i	$-0.748189\pi$
$557$	145.580	−	543.313i	0.261365	−	0.975427i	0.964438	−	0.264309i	$-0.0851439\pi$
$558$	−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	0.892278	−	0.451486i	$-0.149106\pi$
$563$	810.309	+	217.122i	1.43927	+	0.385651i	0.546992	+	0.837138i	$0.315773\pi$
$564$	−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	0.241858	−	0.970312i	$-0.422243\pi$
$569$	−271.713	−	156.874i	−0.477527	−	0.275701i	−0.719385	+	0.694611i	$0.755576\pi$
$570$		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	$0.630120\pi$
$572$	−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	0.489005	+	0.872281i	$0.337360\pi$
$577$	−213.851	+	798.104i	−0.370626	+	1.38320i	−0.859631	+	0.510915i	$0.829307\pi$
$578$	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	0.937202	−	0.348786i	$-0.113406\pi$
$587$	345.401	+	345.401i	0.588417	+	0.588417i	−0.348786	+	0.937202i	$0.613406\pi$
$588$	−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	0.994087	−	0.108589i	$-0.0346334\pi$
$593$	46.7804	+	174.587i	0.0788876	+	0.294413i	−0.915199	+	0.403002i	$0.867967\pi$
$594$			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	−0.259430	−	0.965762i	$-0.583535\pi$
$599$	267.890	−	154.666i	0.447229	−	0.258208i	0.706659	+	0.707554i	$0.250201\pi$
$600$		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	−0.390537	−	0.920587i	$-0.627711\pi$
$607$	−162.955	+	43.6636i	−0.268459	+	0.0719335i	0.122078	+	0.992520i	$0.461044\pi$
$608$	−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	−0.0522047	−	0.998636i	$-0.516625\pi$
$613$	−365.798	−	98.0152i	−0.596734	−	0.159894i	−0.544529	+	0.838742i	$0.683291\pi$
$614$	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	−0.942178	−	0.335114i	$-0.891225\pi$
$617$	−788.089	−	788.089i	−1.27729	−	1.27729i	−0.335114	−	0.942178i	$-0.608775\pi$
$618$	−198.331	−	740.180i	−0.320923	−	1.19770i
$619$	506.750	−	292.572i	0.818660	−	0.472653i	−0.0312944	−	0.999510i	$-0.509963\pi$
$619$	506.750	−	292.572i	0.818660	−	0.472653i	0.849954	+	0.526857i	$0.176630\pi$
$620$		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	0.677912	−	0.735143i	$-0.262885\pi$
$641$	−190.823	−	330.516i	−0.297696	−	0.515625i	−0.975609	+	0.219518i	$0.929552\pi$
$642$	641.192	−	171.807i	0.998742	−	0.267612i
$643$	−34.6664	+	34.6664i	−0.0539135	+	0.0539135i	−0.733550	−	0.679636i	$-0.762138\pi$
$643$	−34.6664	+	34.6664i	−0.0539135	+	0.0539135i	0.679636	+	0.733550i	$0.262138\pi$
$644$	−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	−0.673738	−	0.738971i	$-0.735312\pi$
$647$	180.656	−	674.219i	0.279222	−	1.04207i	0.952959	−	0.303098i	$-0.0980211\pi$
$648$	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	0.724675	+	0.689091i	$0.241990\pi$
$653$	288.387	+	1076.27i	0.441634	+	1.64820i	−0.283041	+	0.959108i	$0.591343\pi$
$654$	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	$-0.762419\pi$
$659$		−	894.905i		−	1.35797i	0.734150	−	0.678987i	$-0.237581\pi$
$660$		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	$0.556059\pi$
$662$	−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	−0.909305	−	0.416131i	$-0.863386\pi$
$673$	−331.906	+	331.906i	−0.493174	+	0.493174i	0.416131	+	0.909305i	$0.363386\pi$
$674$	−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	−0.0518447	−	0.998655i	$-0.516510\pi$
$677$	272.549	−	73.0294i	0.402584	−	0.107872i	0.454429	+	0.890783i	$0.349843\pi$
$678$	−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	−0.0572092	−	0.998362i	$-0.518220\pi$
$683$	−413.854	−	110.892i	−0.605935	−	0.162360i	−0.548726	+	0.836002i	$0.684887\pi$
$684$	−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	−0.848152	−	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
$693$	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	0.868749	−	0.495252i	$-0.164924\pi$
$709$	619.824	+	357.856i	0.874224	+	0.504733i	0.00547406	+	0.999985i	$0.498258\pi$
$710$		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	0.545843	−	0.837888i	$-0.316210\pi$
$719$	66.9619	+	38.6605i	0.0931320	+	0.0537698i	−0.452711	+	0.891657i	$0.649543\pi$
$720$		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	−0.998862	−	0.0477025i	$-0.984810\pi$
$727$	−760.852	−	760.852i	−1.04656	−	1.04656i	−0.0477025	−	0.998862i	$-0.515190\pi$
$728$	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	−0.841791	−	0.539804i	$-0.818498\pi$
$733$	−280.505	−	1046.86i	−0.382681	−	1.42818i	0.459110	−	0.888379i	$-0.348168\pi$
$734$		−	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	−0.993228	−	0.116181i	$-0.962935\pi$
$739$	−1026.64	+	592.730i	−1.38923	+	0.802070i	−0.395999	+	0.918251i	$0.629602\pi$
$740$		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	−0.750059	−	0.661371i	$-0.769975\pi$
$743$	−65.8954	+	65.8954i	−0.0886883	+	0.0886883i	0.661371	+	0.750059i	$0.269975\pi$
$744$	−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	−0.946837	−	0.321712i	$-0.895742\pi$
$751$	−146.301	+	253.400i	−0.194808	+	0.337417i	0.752030	+	0.659129i	$0.229075\pi$
$752$	−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	0.0193719	−	0.999812i	$-0.493833\pi$
$757$	−742.193	−	742.193i	−0.980440	−	0.980440i	−0.999812	+	0.0193719i	$0.993833\pi$
$758$	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	−0.994315	−	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
$763$	−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	$0.160530\pi$
$769$			743.180i			0.966424i	−0.875503	+	0.483212i	$0.839470\pi$
$770$		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	0.0453311	−	0.998972i	$-0.485566\pi$
$773$	−320.715	−	85.9354i	−0.414897	−	0.111171i	−0.460228	+	0.887801i	$0.652232\pi$
$774$	−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	−0.748029	−	0.663667i	$-0.768999\pi$
$787$	182.282	−	680.286i	0.231616	−	0.864404i	0.979645	−	0.200738i	$-0.0643339\pi$
$788$	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	0.262472	−	0.964940i	$-0.415462\pi$
$797$	−559.866	−	559.866i	−0.702467	−	0.702467i	−0.964940	+	0.262472i	$0.915462\pi$
$798$	−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	−0.894499	−	0.447069i	$-0.852468\pi$
$809$	−772.252	+	445.860i	−0.954576	+	0.551125i	−0.0600765	+	0.998194i	$0.519134\pi$
$810$		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	−0.539639	−	0.841897i	$-0.681439\pi$
$821$	377.073	−	653.109i	0.459285	−	0.795504i	0.998923	+	0.0463923i	$0.0147724\pi$
$822$	−123.401	+	460.538i	−0.150123	+	0.560266i
$823$	−1012.22	−	271.224i	−1.22992	−	0.329556i	−0.415371	−	0.909652i	$-0.636348\pi$
$823$	−1012.22	−	271.224i	−1.22992	−	0.329556i	−0.814548	+	0.580096i	$0.803015\pi$
$824$	−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	0.724861	−	0.688895i	$-0.241904\pi$
$827$	29.7436	+	29.7436i	0.0359656	+	0.0359656i	−0.688895	+	0.724861i	$0.741904\pi$
$828$	−270.499	−	1009.52i	−0.326690	−	1.21922i
$829$	159.407	−	92.0338i	0.192289	−	0.111018i	−0.400765	−	0.916181i	$-0.631256\pi$
$829$	159.407	−	92.0338i	0.192289	−	0.111018i	0.593053	+	0.805163i	$0.297922\pi$
$830$		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	$-0.956204\pi$
$839$		−	230.146i		−	0.274310i	0.990550	−	0.137155i	$-0.0437958\pi$
$840$		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	−0.446242	+	0.894912i	$0.647238\pi$
$853$	−1144.00	+	1144.00i	−1.34115	+	1.34115i	−0.894912	+	0.446242i	$0.852762\pi$
$854$	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	−0.890944	−	0.454112i	$-0.849957\pi$
$857$	92.2922	−	344.439i	0.107692	−	0.401913i	0.998637	+	0.0521995i	$0.0166232\pi$
$858$	−1082.77	−	290.128i	−1.26197	−	0.338145i
$859$	−1316.32	−	759.978i	−1.53239	−	0.884724i	−0.999251	−	0.0386951i	$-0.987680\pi$
$859$	−1316.32	−	759.978i	−1.53239	−	0.884724i	−0.533136	−	0.846029i	$-0.678987\pi$
$860$		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	0.991560	−	0.129648i	$-0.0413846\pi$
$863$	58.7013	+	219.076i	0.0680200	+	0.253854i	−0.923540	+	0.383502i	$0.874718\pi$
$864$	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	−0.752590	−	0.658490i	$-0.771196\pi$
$877$	−942.868	+	252.641i	−1.07511	+	0.288074i	−0.322517	+	0.946564i	$0.604529\pi$
$878$	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	0.0409167	−	0.999163i	$-0.486972\pi$
$883$	918.390	−	918.390i	1.04008	−	1.04008i	0.999163	−	0.0409167i	$-0.0130278\pi$
$884$	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	−0.180291	−	0.983613i	$-0.557704\pi$
$887$	137.822	−	36.9292i	0.155379	−	0.0416338i	0.335670	+	0.941980i	$0.391037\pi$
$888$	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	−0.952160	−	0.305599i	$-0.901143\pi$
$907$	22.8874	−	85.4170i	0.0252342	−	0.0941753i	0.977395	+	0.211424i	$0.0678100\pi$
$908$	−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	0.0466681	−	0.998910i	$-0.485140\pi$
$919$	−730.678	−	421.857i	−0.795080	−	0.459039i	−0.841748	+	0.539871i	$0.818473\pi$
$920$		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	0.314233	−	0.949346i	$-0.398253\pi$
$929$	−325.901	−	188.159i	−0.350808	−	0.202539i	−0.665041	+	0.746807i	$0.731586\pi$
$930$		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	0.506694	−	0.862126i	$-0.330867\pi$
$937$	−333.039	−	333.039i	−0.355431	−	0.355431i	−0.862126	+	0.506694i	$0.830867\pi$
$938$	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	0.508224	−	0.861225i	$-0.330302\pi$
$941$	−462.718	−	801.452i	−0.491730	−	0.851702i	−0.999955	+	0.00952274i	$0.996969\pi$
$942$	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	0.233126	−	0.972446i	$-0.425104\pi$
$947$	872.417	−	233.763i	0.921243	−	0.246846i	0.688116	+	0.725600i	$0.258438\pi$
$948$	−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	−0.508256	−	0.861206i	$-0.669710\pi$
$953$	336.361	−	336.361i	0.352950	−	0.352950i	0.861206	+	0.508256i	$0.169710\pi$
$954$	−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	0.656199	−	0.754588i	$-0.272163\pi$
$967$	−95.1413	−	95.1413i	−0.0983881	−	0.0983881i	−0.754588	+	0.656199i	$0.772163\pi$
$968$	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	0.439934	+	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
$973$	−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	−0.0312166	+	0.999513i	$0.509938\pi$
$977$	−492.348	+	1837.47i	−0.503939	+	1.88072i	−0.472722	+	0.881212i	$0.656729\pi$
$978$	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	−0.239502	−	0.970896i	$-0.576984\pi$
$983$	−916.515	−	245.579i	−0.932365	−	0.249826i	−0.692863	+	0.721069i	$0.743651\pi$
$984$	−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	0.818769	+	0.574123i	$0.194657\pi$
$991$	898.430	+	1556.13i	0.906590	+	1.57026i	0.0878205	+	0.996136i	$0.472010\pi$
$992$	−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	−0.873046	−	0.487639i	$-0.837858\pi$
$997$	126.473	−	472.003i	0.126853	−	0.473423i	0.999899	+	0.0142155i	$0.00452508\pi$
$998$	−882.525	−	236.472i	−0.884294	−	0.236946i
$999$	655.997	+	378.740i	0.656654	+	0.379119i

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

)

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.c.23.4	✓	16	5.2	odd	4
70.3.l.c.37.1	yes	16	5.4	even	2
70.3.l.c.53.1	yes	16	35.32	odd	12
70.3.l.c.67.4	yes	16	35.4	even	6
350.3.p.e.93.1		16	5.3	odd	4	inner
350.3.p.e.107.4		16	1.1	even	1	trivial
350.3.p.e.193.4		16	35.18	odd	12	inner
350.3.p.e.207.1		16	7.4	even	3	inner
490.3.f.o.197.4		8	35.9	even	6
490.3.f.o.393.4		8	35.2	odd	12
490.3.f.p.197.1		8	35.19	odd	6
490.3.f.p.393.1		8	35.12	even	12

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	350.3.p.e.107.4

Level	$350$
Weight	$3$
Character	350.107
Analytic conductor	$9.537$
Analytic rank	$0$
Dimension	$16$
Inner twists	$4$