LMFDB - Embedded newform 144.4.l.a.35.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,4,Mod(35,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("144.35");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	144.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.49627504083$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			35.8
Character	$\chi$	$=$	144.35
Dual form			144.4.l.a.107.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73660 + 2.23254i) q^{2} +(-1.96847 - 7.75404i) q^{4} +(3.22357 + 3.22357i) q^{5} -13.1030 q^{7} +(20.7296 + 9.07094i) q^{8} +O(q^{10})$	\(q+(-1.73660 + 2.23254i) q^{2} +(-1.96847 - 7.75404i) q^{4} +(3.22357 + 3.22357i) q^{5} -13.1030 q^{7} +(20.7296 + 9.07094i) q^{8} +(-12.7948 + 1.59871i) q^{10} +(-3.39235 + 3.39235i) q^{11} +(-54.1435 - 54.1435i) q^{13} +(22.7547 - 29.2531i) q^{14} +(-56.2502 + 30.5272i) q^{16} -70.7730i q^{17} +(32.5595 - 32.5595i) q^{19} +(18.6502 - 31.3412i) q^{20} +(-1.68242 - 13.4647i) q^{22} +16.4197i q^{23} -104.217i q^{25} +(214.903 - 26.8522i) q^{26} +(25.7930 + 101.601i) q^{28} +(28.0742 - 28.0742i) q^{29} -174.864i q^{31} +(29.5307 - 178.594i) q^{32} +(158.004 + 122.904i) q^{34} +(-42.2385 - 42.2385i) q^{35} +(116.834 - 116.834i) q^{37} +(16.1477 + 129.233i) q^{38} +(37.5826 + 96.0642i) q^{40} -19.6290 q^{41} +(94.2456 + 94.2456i) q^{43} +(32.9822 + 19.6267i) q^{44} +(-36.6576 - 28.5143i) q^{46} -372.603 q^{47} -171.310 q^{49} +(232.669 + 180.983i) q^{50} +(-313.251 + 526.411i) q^{52} +(-162.999 - 162.999i) q^{53} -21.8710 q^{55} +(-271.621 - 118.857i) q^{56} +(13.9233 + 111.430i) q^{58} +(-610.346 + 610.346i) q^{59} +(-531.488 - 531.488i) q^{61} +(390.391 + 303.668i) q^{62} +(347.436 + 376.075i) q^{64} -349.071i q^{65} +(562.092 - 562.092i) q^{67} +(-548.777 + 139.315i) q^{68} +(167.650 - 20.9480i) q^{70} +1166.76i q^{71} +308.564i q^{73} +(57.9431 + 463.729i) q^{74} +(-316.560 - 188.375i) q^{76} +(44.4501 - 44.4501i) q^{77} +1170.83i q^{79} +(-279.733 - 82.9199i) q^{80} +(34.0877 - 43.8226i) q^{82} +(-469.366 - 469.366i) q^{83} +(228.142 - 228.142i) q^{85} +(-374.074 + 46.7406i) q^{86} +(-101.094 + 39.5504i) q^{88} +1534.65 q^{89} +(709.445 + 709.445i) q^{91} +(127.319 - 32.3217i) q^{92} +(647.061 - 831.851i) q^{94} +209.916 q^{95} -139.670 q^{97} +(297.497 - 382.458i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 120 q^{10} - 144 q^{16} - 48 q^{19} + 72 q^{22} + 72 q^{28} - 984 q^{34} - 1272 q^{40} + 864 q^{43} - 1416 q^{46} + 2352 q^{49} - 648 q^{52} - 576 q^{55} + 1128 q^{58} + 1824 q^{61} + 3024 q^{64} + 816 q^{67} + 2664 q^{70} + 1920 q^{76} + 1200 q^{82} - 480 q^{85} - 4560 q^{88} - 3600 q^{91} - 11304 q^{94}+O(q^{100}) $ 48 * q - 120 * q^10 - 144 * q^16 - 48 * q^19 + 72 * q^22 + 72 * q^28 - 984 * q^34 - 1272 * q^40 + 864 * q^43 - 1416 * q^46 + 2352 * q^49 - 648 * q^52 - 576 * q^55 + 1128 * q^58 + 1824 * q^61 + 3024 * q^64 + 816 * q^67 + 2664 * q^70 + 1920 * q^76 + 1200 * q^82 - 480 * q^85 - 4560 * q^88 - 3600 * q^91 - 11304 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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 $

$2$	−1.73660	+	2.23254i	−0.613979	+	0.789322i
$2$	−1.73660	+	2.23254i	−0.613979	+	0.789322i
$3$		0			0
$3$		0			0
$4$	−1.96847	−	7.75404i	−0.246059	−	0.969255i
$5$	3.22357	+	3.22357i	0.288325	+	0.288325i	0.836418	−	0.548093i	$-0.184646\pi$
$5$	3.22357	+	3.22357i	0.288325	+	0.288325i	−0.548093	+	0.836418i	$0.684646\pi$
$6$		0			0
$7$	−13.1030			−0.707497			−0.353749	−	0.935341i	$-0.615093\pi$
$7$	−13.1030			−0.707497			−0.353749	+	0.935341i	$0.615093\pi$
$8$	20.7296	+	9.07094i	0.916129	+	0.400883i
$9$		0			0
$10$	−12.7948	+	1.59871i	−0.404607	+	0.0505557i
$11$	−3.39235	+	3.39235i	−0.0929847	+	0.0929847i	−0.752069	−	0.659084i	$-0.770944\pi$
$11$	−3.39235	+	3.39235i	−0.0929847	+	0.0929847i	0.659084	+	0.752069i	$0.270944\pi$
$12$		0			0
$13$	−54.1435	−	54.1435i	−1.15513	−	1.15513i	−0.985509	−	0.169623i	$-0.945745\pi$
$13$	−54.1435	−	54.1435i	−1.15513	−	1.15513i	−0.169623	−	0.985509i	$-0.554255\pi$
$14$	22.7547	−	29.2531i	0.434389	−	0.558443i
$15$		0			0
$16$	−56.2502	+	30.5272i	−0.878910	+	0.476988i
$17$		−	70.7730i		−	1.00970i	−0.863206	−	0.504852i	$-0.831547\pi$
$17$		−	70.7730i		−	1.00970i	0.863206	−	0.504852i	$-0.168453\pi$
$18$		0			0
$19$	32.5595	−	32.5595i	0.393140	−	0.393140i	−0.482665	−	0.875805i	$-0.660331\pi$
$19$	32.5595	−	32.5595i	0.393140	−	0.393140i	0.875805	+	0.482665i	$0.160331\pi$
$20$	18.6502	−	31.3412i	0.208515	−	0.350405i
$21$		0			0
$22$	−1.68242	−	13.4647i	−0.0163042	−	0.130486i
$23$			16.4197i			0.148858i	0.997226	+	0.0744291i	$0.0237135\pi$
$23$			16.4197i			0.148858i	−0.997226	+	0.0744291i	$0.976287\pi$
$24$		0			0
$25$		−	104.217i		−	0.833738i
$26$	214.903	−	26.8522i	1.62100	−	0.202544i
$27$		0			0
$28$	25.7930	+	101.601i	0.174086	+	0.685745i
$29$	28.0742	−	28.0742i	0.179767	−	0.179767i	−0.611487	−	0.791254i	$-0.709428\pi$
$29$	28.0742	−	28.0742i	0.179767	−	0.179767i	0.791254	+	0.611487i	$0.209428\pi$
$30$		0			0
$31$		−	174.864i		−	1.01311i	−0.862207	−	0.506556i	$-0.830918\pi$
$31$		−	174.864i		−	1.01311i	0.862207	−	0.506556i	$-0.169082\pi$
$32$	29.5307	−	178.594i	0.163135	−	0.986604i
$33$		0			0
$34$	158.004	+	122.904i	0.796982	+	0.619938i
$35$	−42.2385	−	42.2385i	−0.203989	−	0.203989i
$36$		0			0
$37$	116.834	−	116.834i	0.519117	−	0.519117i	−0.398187	−	0.917304i	$-0.630360\pi$
$37$	116.834	−	116.834i	0.519117	−	0.519117i	0.917304	+	0.398187i	$0.130360\pi$
$38$	16.1477	+	129.233i	0.0689344	+	0.551694i
$39$		0			0
$40$	37.5826	+	96.0642i	0.148558	+	0.379727i
$41$	−19.6290			−0.0747692			−0.0373846	−	0.999301i	$-0.511903\pi$
$41$	−19.6290			−0.0747692			−0.0373846	+	0.999301i	$0.511903\pi$
$42$		0			0
$43$	94.2456	+	94.2456i	0.334240	+	0.334240i	0.854194	−	0.519954i	$-0.174051\pi$
$43$	94.2456	+	94.2456i	0.334240	+	0.334240i	−0.519954	+	0.854194i	$0.674051\pi$
$44$	32.9822	+	19.6267i	0.113006	+	0.0672462i
$45$		0			0
$46$	−36.6576	−	28.5143i	−0.117497	−	0.0913959i
$47$	−372.603			−1.15638			−0.578189	−	0.815903i	$-0.696240\pi$
$47$	−372.603			−1.15638			−0.578189	+	0.815903i	$0.696240\pi$
$48$		0			0
$49$	−171.310			−0.499447
$50$	232.669	+	180.983i	0.658088	+	0.511898i
$51$		0			0
$52$	−313.251	+	526.411i	−0.835387	+	1.40385i
$53$	−162.999	−	162.999i	−0.422445	−	0.422445i	0.463600	−	0.886045i	$-0.346558\pi$
$53$	−162.999	−	162.999i	−0.422445	−	0.422445i	−0.886045	+	0.463600i	$0.846558\pi$
$54$		0			0
$55$	−21.8710			−0.0536196
$56$	−271.621	−	118.857i	−0.648159	−	0.283623i
$57$		0			0
$58$	13.9233	+	111.430i	0.0315209	+	0.252268i
$59$	−610.346	+	610.346i	−1.34678	+	1.34678i	−0.457655	+	0.889130i	$0.651310\pi$
$59$	−610.346	+	610.346i	−1.34678	+	1.34678i	−0.889130	+	0.457655i	$0.848690\pi$
$60$		0			0
$61$	−531.488	−	531.488i	−1.11557	−	1.11557i	−0.992383	−	0.123191i	$-0.960687\pi$
$61$	−531.488	−	531.488i	−1.11557	−	1.11557i	−0.123191	−	0.992383i	$-0.539313\pi$
$62$	390.391	+	303.668i	0.799672	+	0.622030i
$63$		0			0
$64$	347.436	+	376.075i	0.678586	+	0.734521i
$65$		−	349.071i		−	0.666106i
$66$		0			0
$67$	562.092	−	562.092i	1.02493	−	1.02493i	0.0252516	−	0.999681i	$-0.491961\pi$
$67$	562.092	−	562.092i	1.02493	−	1.02493i	0.999681	−	0.0252516i	$-0.00803869\pi$
$68$	−548.777	+	139.315i	−0.978661	+	0.248447i
$69$		0			0
$70$	167.650	−	20.9480i	0.286258	−	0.0357680i
$71$			1166.76i			1.95027i	0.221612	+	0.975135i	$0.428868\pi$
$71$			1166.76i			1.95027i	−0.221612	+	0.975135i	$0.571132\pi$
$72$		0			0
$73$			308.564i			0.494721i	0.968923	+	0.247361i	$0.0795633\pi$
$73$			308.564i			0.494721i	−0.968923	+	0.247361i	$0.920437\pi$
$74$	57.9431	+	463.729i	0.0910236	+	0.728478i
$75$		0			0
$76$	−316.560	−	188.375i	−0.477789	−	0.284317i
$77$	44.4501	−	44.4501i	0.0657865	−	0.0657865i
$78$		0			0
$79$			1170.83i			1.66746i	0.552176	+	0.833728i	$0.313798\pi$
$79$			1170.83i			1.66746i	−0.552176	+	0.833728i	$0.686202\pi$
$80$	−279.733	−	82.9199i	−0.390939	−	0.115884i
$81$		0			0
$82$	34.0877	−	43.8226i	0.0459067	−	0.0590170i
$83$	−469.366	−	469.366i	−0.620719	−	0.620719i	0.324996	−	0.945715i	$-0.394637\pi$
$83$	−469.366	−	469.366i	−0.620719	−	0.620719i	−0.945715	+	0.324996i	$0.894637\pi$
$84$		0			0
$85$	228.142	−	228.142i	0.291123	−	0.291123i
$86$	−374.074	+	46.7406i	−0.469040	+	0.0586066i
$87$		0			0
$88$	−101.094	+	39.5504i	−0.122462	+	0.0479101i
$89$	1534.65			1.82778			0.913892	−	0.405957i	$-0.133062\pi$
$89$	1534.65			1.82778			0.913892	+	0.405957i	$0.133062\pi$
$90$		0			0
$91$	709.445	+	709.445i	0.817253	+	0.817253i
$92$	127.319	−	32.3217i	0.144282	−	0.0366279i
$93$		0			0
$94$	647.061	−	831.851i	0.709992	−	0.912754i
$95$	209.916			0.226704
$96$		0			0
$97$	−139.670			−0.146200			−0.0730998	−	0.997325i	$-0.523289\pi$
$97$	−139.670			−0.146200			−0.0730998	+	0.997325i	$0.523289\pi$
$98$	297.497	−	382.458i	0.306650	−	0.394225i
$99$		0			0
$100$	−808.104	+	205.149i	−0.808104	+	0.205149i
$101$	−525.800	−	525.800i	−0.518011	−	0.518011i	0.398958	−	0.916969i	$-0.369372\pi$
$101$	−525.800	−	525.800i	−0.518011	−	0.518011i	−0.916969	+	0.398958i	$0.869372\pi$
$102$		0			0
$103$	−221.106			−0.211517			−0.105758	−	0.994392i	$-0.533727\pi$
$103$	−221.106			−0.211517			−0.105758	+	0.994392i	$0.533727\pi$
$104$	−631.244	−	1613.51i	−0.595178	−	1.52132i
$105$		0			0
$106$	646.964	−	80.8383i	0.592818	−	0.0740728i
$107$	824.395	−	824.395i	0.744834	−	0.744834i	−0.228670	−	0.973504i	$-0.573438\pi$
$107$	824.395	−	824.395i	0.744834	−	0.744834i	0.973504	+	0.228670i	$0.0734376\pi$
$108$		0			0
$109$	−675.079	−	675.079i	−0.593219	−	0.593219i	0.345281	−	0.938500i	$-0.387784\pi$
$109$	−675.079	−	675.079i	−0.593219	−	0.593219i	−0.938500	+	0.345281i	$0.887784\pi$
$110$	37.9810	−	48.8278i	0.0329213	−	0.0423231i
$111$		0			0
$112$	737.049	−	399.999i	0.621826	−	0.337468i
$113$		−	1052.43i		−	0.876141i	−0.898941	−	0.438070i	$-0.855662\pi$
$113$		−	1052.43i		−	0.876141i	0.898941	−	0.438070i	$-0.144338\pi$
$114$		0			0
$115$	−52.9300	+	52.9300i	−0.0429195	+	0.0429195i
$116$	−272.952	−	162.425i	−0.218474	−	0.130007i
$117$		0			0
$118$	−302.698	−	2422.55i	−0.236149	−	1.88994i
$119$			927.341i			0.714363i
$120$		0			0
$121$			1307.98i			0.982708i
$122$	2109.55	−	263.589i	1.56549	−	0.195608i
$123$		0			0
$124$	−1355.90	+	344.215i	−0.981964	+	0.249285i
$125$	738.897	−	738.897i	0.528712	−	0.528712i
$126$		0			0
$127$			103.084i			0.0720254i	0.999351	+	0.0360127i	$0.0114657\pi$
$127$			103.084i			0.0720254i	−0.999351	+	0.0360127i	$0.988534\pi$
$128$	−1442.96	+	122.576i	−0.996411	+	0.0846429i
$129$		0			0
$130$	779.315	+	606.195i	0.525773	+	0.408975i
$131$	535.858	+	535.858i	0.357390	+	0.357390i	0.862850	−	0.505460i	$-0.168677\pi$
$131$	535.858	+	535.858i	0.357390	+	0.357390i	−0.505460	+	0.862850i	$0.668677\pi$
$132$		0			0
$133$	−426.628	+	426.628i	−0.278146	+	0.278146i
$134$	278.767	+	2231.02i	0.179715	+	1.43829i
$135$		0			0
$136$	641.977	−	1467.10i	0.404773	−	0.925020i
$137$	2093.02			1.30525			0.652625	−	0.757681i	$-0.273668\pi$
$137$	2093.02			1.30525			0.652625	+	0.757681i	$0.273668\pi$
$138$		0			0
$139$	1367.29	+	1367.29i	0.834331	+	0.834331i	0.988106	−	0.153775i	$-0.0491429\pi$
$139$	1367.29	+	1367.29i	0.834331	+	0.834331i	−0.153775	+	0.988106i	$0.549143\pi$
$140$	−244.374	+	410.665i	−0.147524	+	0.247911i
$141$		0			0
$142$	−2604.84	−	2026.19i	−1.53939	−	1.19743i
$143$	367.348			0.214819
$144$		0			0
$145$	180.998			0.103663
$146$	−688.881	−	535.850i	−0.390495	−	0.303749i
$147$		0			0
$148$	−1135.92	−	675.949i	−0.630891	−	0.375424i
$149$	713.205	+	713.205i	0.392135	+	0.392135i	0.875448	−	0.483313i	$-0.160567\pi$
$149$	713.205	+	713.205i	0.392135	+	0.392135i	−0.483313	+	0.875448i	$0.660567\pi$
$150$		0			0
$151$	−3184.13			−1.71603			−0.858017	−	0.513622i	$-0.828304\pi$
$151$	−3184.13			−1.71603			−0.858017	+	0.513622i	$0.828304\pi$
$152$	970.292	−	379.602i	0.517770	−	0.202564i
$153$		0			0
$154$	22.0448	+	176.428i	0.0115352	+	0.0923182i
$155$	563.686	−	563.686i	0.292105	−	0.292105i
$156$		0			0
$157$	−1517.94	−	1517.94i	−0.771622	−	0.771622i	0.206768	−	0.978390i	$-0.433706\pi$
$157$	−1517.94	−	1517.94i	−0.771622	−	0.771622i	−0.978390	+	0.206768i	$0.933706\pi$
$158$	−2613.93	−	2033.26i	−1.31616	−	1.02378i
$159$		0			0
$160$	670.905	−	480.517i	0.331498	−	0.237426i
$161$		−	215.148i		−	0.105317i
$162$		0			0
$163$	1433.43	−	1433.43i	0.688802	−	0.688802i	−0.273165	−	0.961967i	$-0.588070\pi$
$163$	1433.43	−	1433.43i	0.688802	−	0.688802i	0.961967	+	0.273165i	$0.0880705\pi$
$164$	38.6392	+	152.204i	0.0183976	+	0.0724704i
$165$		0			0
$166$	1862.98	−	232.780i	0.871056	−	0.108839i
$167$			1574.93i			0.729771i	0.931052	+	0.364886i	$0.118892\pi$
$167$			1574.93i			0.729771i	−0.931052	+	0.364886i	$0.881108\pi$
$168$		0			0
$169$			3666.05i			1.66866i
$170$	113.146	+	905.525i	0.0510463	+	0.408533i
$171$		0			0
$172$	545.264	−	916.304i	0.241721	−	0.406207i
$173$	−2323.05	+	2323.05i	−1.02092	+	1.02092i	−0.0211385	+	0.999777i	$0.506729\pi$
$173$	−2323.05	+	2323.05i	−1.02092	+	1.02092i	−0.999777	+	0.0211385i	$0.993271\pi$
$174$		0			0
$175$			1365.56i			0.589867i
$176$	87.2615	−	294.380i	0.0373726	−	0.126078i
$177$		0			0
$178$	−2665.07	+	3426.17i	−1.12222	+	1.44271i
$179$	−2499.16	−	2499.16i	−1.04355	−	1.04355i	−0.999007	−	0.0445458i	$-0.985816\pi$
$179$	−2499.16	−	2499.16i	−1.04355	−	1.04355i	−0.0445458	−	0.999007i	$-0.514184\pi$
$180$		0			0
$181$	1207.94	−	1207.94i	0.496053	−	0.496053i	−0.414154	−	0.910207i	$-0.635922\pi$
$181$	1207.94	−	1207.94i	0.496053	−	0.496053i	0.910207	+	0.414154i	$0.135922\pi$
$182$	−2815.88	+	351.845i	−1.14685	+	0.143300i
$183$		0			0
$184$	−148.942	+	340.374i	−0.0596747	+	0.136373i
$185$	753.243			0.299349
$186$		0			0
$187$	240.087	+	240.087i	0.0938871	+	0.0938871i
$188$	733.459	+	2889.18i	0.284537	+	1.12082i
$189$		0			0
$190$	−364.539	+	468.645i	−0.139192	+	0.178943i
$191$	1303.81			0.493930			0.246965	−	0.969024i	$-0.420567\pi$
$191$	1303.81			0.493930			0.246965	+	0.969024i	$0.420567\pi$
$192$		0			0
$193$	3208.56			1.19667			0.598335	−	0.801246i	$-0.295829\pi$
$193$	3208.56			1.19667			0.598335	+	0.801246i	$0.295829\pi$
$194$	242.551	−	311.820i	0.0897636	−	0.115399i
$195$		0			0
$196$	337.220	+	1328.35i	0.122894	+	0.484092i
$197$	−1476.04	−	1476.04i	−0.533824	−	0.533824i	0.387884	−	0.921708i	$-0.373206\pi$
$197$	−1476.04	−	1476.04i	−0.533824	−	0.533824i	−0.921708	+	0.387884i	$0.873206\pi$
$198$		0			0
$199$	−1698.58			−0.605072			−0.302536	−	0.953138i	$-0.597833\pi$
$199$	−1698.58			−0.605072			−0.302536	+	0.953138i	$0.597833\pi$
$200$	945.348	−	2160.39i	0.334231	−	0.763812i
$201$		0			0
$202$	2086.97	−	260.768i	0.726925	−	0.0908296i
$203$	−367.857	+	367.857i	−0.127185	+	0.127185i
$204$		0			0
$205$	−63.2755	−	63.2755i	−0.0215578	−	0.0215578i
$206$	383.972	−	493.628i	0.129867	−	0.166955i
$207$		0			0
$208$	4698.44	+	1392.74i	1.56624	+	0.464273i
$209$			220.907i			0.0731121i
$210$		0			0
$211$	3141.93	−	3141.93i	1.02511	−	1.02511i	0.0254381	−	0.999676i	$-0.491902\pi$
$211$	3141.93	−	3141.93i	1.02511	−	1.02511i	0.999676	−	0.0254381i	$-0.00809808\pi$
$212$	−943.040	+	1584.76i	−0.305511	+	0.513403i
$213$		0			0
$214$	408.854	+	3272.14i	0.130601	+	1.04523i
$215$			607.614i			0.192739i
$216$		0			0
$217$			2291.25i			0.716774i
$218$	2679.48	−	334.802i	0.832465	−	0.104017i
$219$		0			0
$220$	43.0524	+	169.588i	0.0131936	+	0.0519711i
$221$	−3831.90	+	3831.90i	−1.16634	+	1.16634i
$222$		0			0
$223$		−	869.633i		−	0.261143i	−0.991439	−	0.130572i	$-0.958319\pi$
$223$		−	869.633i		−	0.261143i	0.991439	−	0.130572i	$-0.0416812\pi$
$224$	−386.941	+	2340.13i	−0.115418	+	0.698020i
$225$		0			0
$226$	2349.58	+	1827.64i	0.691557	+	0.537932i
$227$	−1203.65	−	1203.65i	−0.351935	−	0.351935i	0.508894	−	0.860829i	$-0.330055\pi$
$227$	−1203.65	−	1203.65i	−0.351935	−	0.351935i	−0.860829	+	0.508894i	$0.830055\pi$
$228$		0			0
$229$	3001.80	−	3001.80i	0.866220	−	0.866220i	−0.125832	−	0.992052i	$-0.540160\pi$
$229$	3001.80	−	3001.80i	0.866220	−	0.866220i	0.992052	+	0.125832i	$0.0401599\pi$
$230$	−26.2503	−	210.086i	−0.00752564	−	0.0602290i
$231$		0			0
$232$	836.628	−	327.309i	0.236756	−	0.0926245i
$233$	−5006.57			−1.40769			−0.703844	−	0.710355i	$-0.748534\pi$
$233$	−5006.57			−1.40769			−0.703844	+	0.710355i	$0.748534\pi$
$234$		0			0
$235$	−1201.11	−	1201.11i	−0.333412	−	0.333412i
$236$	5934.10	+	3531.20i	1.63677	+	0.973989i
$237$		0			0
$238$	−2070.33	−	1610.42i	−0.563863	−	0.438604i
$239$	659.973			0.178620			0.0893098	−	0.996004i	$-0.471534\pi$
$239$	659.973			0.178620			0.0893098	+	0.996004i	$0.471534\pi$
$240$		0			0
$241$	−1088.72			−0.290998			−0.145499	−	0.989358i	$-0.546479\pi$
$241$	−1088.72			−0.290998			−0.145499	+	0.989358i	$0.546479\pi$
$242$	−2920.13	−	2271.44i	−0.775673	−	0.603362i
$243$		0			0
$244$	−3074.96	+	5167.39i	−0.806779	+	1.35577i
$245$	−552.231	−	552.231i	−0.144003	−	0.144003i
$246$		0			0
$247$	−3525.77			−0.908258
$248$	1586.18	−	3624.86i	0.406139	−	0.928142i
$249$		0			0
$250$	366.452	+	2932.78i	0.0927059	+	0.741942i
$251$	3317.58	−	3317.58i	0.834277	−	0.834277i	−0.153821	−	0.988099i	$-0.549158\pi$
$251$	3317.58	−	3317.58i	0.834277	−	0.834277i	0.988099	+	0.153821i	$0.0491581\pi$
$252$		0			0
$253$	−55.7013	−	55.7013i	−0.0138415	−	0.0138415i
$254$	−230.139	−	179.015i	−0.0568512	−	0.0442221i
$255$		0			0
$256$	2232.18	−	3434.33i	0.544965	−	0.838459i
$257$			7233.11i			1.75560i	0.479028	+	0.877800i	$0.340989\pi$
$257$			7233.11i			1.75560i	−0.479028	+	0.877800i	$0.659011\pi$
$258$		0			0
$259$	−1530.88	+	1530.88i	−0.367274	+	0.367274i
$260$	−2706.71	+	687.136i	−0.645627	+	0.163901i
$261$		0			0
$262$	−2126.89	+	265.756i	−0.501526	+	0.0626659i
$263$		−	7081.78i		−	1.66039i	−0.557476	−	0.830193i	$-0.688230\pi$
$263$		−	7081.78i		−	1.66039i	0.557476	−	0.830193i	$-0.311770\pi$
$264$		0			0
$265$		−	1050.88i		−	0.243603i
$266$	−211.584	−	1693.35i	−0.0487709	−	0.390322i
$267$		0			0
$268$	−5464.95	−	3252.02i	−1.24561	−	0.741227i
$269$	−1277.73	+	1277.73i	−0.289607	+	0.289607i	−0.836925	−	0.547318i	$-0.815649\pi$
$269$	−1277.73	+	1277.73i	−0.289607	+	0.289607i	0.547318	+	0.836925i	$0.315649\pi$
$270$		0			0
$271$		−	5785.88i		−	1.29693i	−0.761246	−	0.648463i	$-0.775412\pi$
$271$		−	5785.88i		−	1.29693i	0.761246	−	0.648463i	$-0.224588\pi$
$272$	2160.50	+	3981.00i	0.481617	+	0.887439i
$273$		0			0
$274$	−3634.74	+	4672.76i	−0.801396	+	1.03026i
$275$	353.541	+	353.541i	0.0775249	+	0.0775249i
$276$		0			0
$277$	2243.55	−	2243.55i	0.486648	−	0.486648i	−0.420598	−	0.907247i	$-0.638180\pi$
$277$	2243.55	−	2243.55i	0.486648	−	0.486648i	0.907247	+	0.420598i	$0.138180\pi$
$278$	−5426.96	+	678.101i	−1.17082	+	0.146294i
$279$		0			0
$280$	−492.447	−	1258.73i	−0.105105	−	0.268656i
$281$	645.762			0.137092			0.0685461	−	0.997648i	$-0.478164\pi$
$281$	645.762			0.137092			0.0685461	+	0.997648i	$0.478164\pi$
$282$		0			0
$283$	−4732.85	−	4732.85i	−0.994130	−	0.994130i	0.00585324	−	0.999983i	$-0.498137\pi$
$283$	−4732.85	−	4732.85i	−0.994130	−	0.994130i	−0.999983	+	0.00585324i	$0.998137\pi$
$284$	9047.12	−	2296.74i	1.89031	−	0.479881i
$285$		0			0
$286$	−637.934	+	820.119i	−0.131895	+	0.169562i
$287$	257.200			0.0528990
$288$		0			0
$289$	−95.8192			−0.0195032
$290$	−314.321	+	404.086i	−0.0636468	+	0.0818233i
$291$		0			0
$292$	2392.62	−	607.399i	0.479511	−	0.121731i
$293$	−648.055	−	648.055i	−0.129214	−	0.129214i	0.639542	−	0.768756i	$-0.279124\pi$
$293$	−648.055	−	648.055i	−0.129214	−	0.129214i	−0.768756	+	0.639542i	$0.779124\pi$
$294$		0			0
$295$	−3934.99			−0.776623
$296$	3481.71	−	1362.13i	0.683684	−	0.267474i
$297$		0			0
$298$	−2830.81	+	353.710i	−0.550283	+	0.0687580i
$299$	889.020	−	889.020i	0.171951	−	0.171951i
$300$		0			0
$301$	−1234.90	−	1234.90i	−0.236474	−	0.236474i
$302$	5529.55	−	7108.71i	1.05361	−	1.35450i
$303$		0			0
$304$	−837.529	+	2825.43i	−0.158012	+	0.533058i
$305$		−	3426.57i		−	0.643295i
$306$		0			0
$307$	3406.50	−	3406.50i	0.633288	−	0.633288i	−0.315604	−	0.948891i	$-0.602207\pi$
$307$	3406.50	−	3406.50i	0.633288	−	0.633288i	0.948891	+	0.315604i	$0.102207\pi$
$308$	−432.166	−	257.169i	−0.0799512	−	0.0475765i
$309$		0			0
$310$	279.557	+	2237.34i	0.0512186	+	0.409912i
$311$			7811.27i			1.42423i	0.702061	+	0.712117i	$0.252263\pi$
$311$			7811.27i			1.42423i	−0.702061	+	0.712117i	$0.747737\pi$
$312$		0			0
$313$		−	3161.73i		−	0.570963i	−0.958384	−	0.285481i	$-0.907847\pi$
$313$		−	3161.73i		−	0.570963i	0.958384	−	0.285481i	$-0.0921535\pi$
$314$	6024.90	−	752.814i	1.08282	−	0.135299i
$315$		0			0
$316$	9078.68	−	2304.75i	1.61619	−	0.410292i
$317$	318.480	−	318.480i	0.0564278	−	0.0564278i	−0.678330	−	0.734758i	$-0.737296\pi$
$317$	318.480	−	318.480i	0.0564278	−	0.0564278i	0.734758	+	0.678330i	$0.237296\pi$
$318$		0			0
$319$			190.475i			0.0334312i
$320$	−92.3175	+	2332.29i	−0.0161272	+	0.407434i
$321$		0			0
$322$	480.326	+	373.624i	0.0831289	+	0.0646623i
$323$	−2304.33	−	2304.33i	−0.396955	−	0.396955i
$324$		0			0
$325$	−5642.69	+	5642.69i	−0.963077	+	0.963077i
$326$	710.901	+	5689.47i	0.120777	+	0.966597i
$327$		0			0
$328$	−406.903	−	178.054i	−0.0684983	−	0.0299737i
$329$	4882.23			0.818134
$330$		0			0
$331$	2065.35	+	2065.35i	0.342966	+	0.342966i	0.857481	−	0.514515i	$-0.172028\pi$
$331$	2065.35	+	2065.35i	0.342966	+	0.342966i	−0.514515	+	0.857481i	$0.672028\pi$
$332$	−2715.55	+	4563.42i	−0.448901	+	0.754368i
$333$		0			0
$334$	−3516.10	−	2735.02i	−0.576025	−	0.448064i
$335$	3623.89			0.591027
$336$		0			0
$337$	6794.49			1.09828			0.549138	−	0.835731i	$-0.314956\pi$
$337$	6794.49			1.09828			0.549138	+	0.835731i	$0.314956\pi$
$338$	−8184.60	−	6366.44i	−1.31711	−	1.02452i
$339$		0			0
$340$	−2218.11	−	1319.93i	−0.353806	−	0.210539i
$341$	593.199	+	593.199i	0.0942040	+	0.0942040i
$342$		0			0
$343$	6739.03			1.06086
$344$	1098.78	+	2808.57i	0.172216	+	0.440198i
$345$		0			0
$346$	−1152.11	−	9220.51i	−0.179010	−	1.43265i
$347$	3999.59	−	3999.59i	0.618759	−	0.618759i	−0.326454	−	0.945213i	$-0.605854\pi$
$347$	3999.59	−	3999.59i	0.618759	−	0.618759i	0.945213	+	0.326454i	$0.105854\pi$
$348$		0			0
$349$	1482.98	+	1482.98i	0.227456	+	0.227456i	0.811629	−	0.584173i	$-0.198581\pi$
$349$	1482.98	+	1482.98i	0.227456	+	0.227456i	−0.584173	+	0.811629i	$0.698581\pi$
$350$	−3048.67	−	2371.43i	−0.465595	−	0.362166i
$351$		0			0
$352$	505.676	+	706.033i	0.0765700	+	0.106908i
$353$		−	6753.68i		−	1.01831i	−0.860676	−	0.509153i	$-0.829959\pi$
$353$		−	6753.68i		−	1.01831i	0.860676	−	0.509153i	$-0.170041\pi$
$354$		0			0
$355$	−3761.14	+	3761.14i	−0.562311	+	0.562311i
$356$	−3020.92	−	11899.8i	−0.449743	−	1.77159i
$357$		0			0
$358$	9919.51	−	1239.45i	1.46442	−	0.182980i
$359$		−	8234.72i		−	1.21062i	−0.795991	−	0.605309i	$-0.793050\pi$
$359$		−	8234.72i		−	1.21062i	0.795991	−	0.605309i	$-0.206950\pi$
$360$		0			0
$361$			4738.76i			0.690882i
$362$	599.072	+	4794.49i	0.0869794	+	0.696112i
$363$		0			0
$364$	4104.54	−	6897.58i	0.591034	−	0.993219i
$365$	−994.677	+	994.677i	−0.142640	+	0.142640i
$366$		0			0
$367$			5584.58i			0.794312i	0.917751	+	0.397156i	$0.130003\pi$
$367$			5584.58i			0.794312i	−0.917751	+	0.397156i	$0.869997\pi$
$368$	−501.247	−	923.611i	−0.0710036	−	0.130833i
$369$		0			0
$370$	−1308.08	+	1681.65i	−0.183794	+	0.236283i
$371$	2135.78	+	2135.78i	0.298879	+	0.298879i
$372$		0			0
$373$	−3202.91	+	3202.91i	−0.444613	+	0.444613i	−0.893559	−	0.448946i	$-0.851800\pi$
$373$	−3202.91	+	3202.91i	−0.444613	+	0.444613i	0.448946	+	0.893559i	$0.351800\pi$
$374$	−952.937	+	119.070i	−0.131752	+	0.0164624i
$375$		0			0
$376$	−7723.93	−	3379.86i	−1.05939	−	0.463572i
$377$	−3040.08			−0.415310
$378$		0			0
$379$	−21.6142	−	21.6142i	−0.00292941	−	0.00292941i	0.705641	−	0.708570i	$-0.250659\pi$
$379$	−21.6142	−	21.6142i	−0.00292941	−	0.00292941i	−0.708570	+	0.705641i	$0.750659\pi$
$380$	−413.213	−	1627.69i	−0.0557826	−	0.219734i
$381$		0			0
$382$	−2264.20	+	2910.82i	−0.303263	+	0.389870i
$383$	−4947.98			−0.660131			−0.330065	−	0.943958i	$-0.607071\pi$
$383$	−4947.98			−0.660131			−0.330065	+	0.943958i	$0.607071\pi$
$384$		0			0
$385$	286.576			0.0379357
$386$	−5571.97	+	7163.24i	−0.734731	+	0.944558i
$387$		0			0
$388$	274.937	+	1083.01i	0.0359737	+	0.141705i
$389$	4708.60	+	4708.60i	0.613716	+	0.613716i	0.943912	−	0.330196i	$-0.107115\pi$
$389$	4708.60	+	4708.60i	0.613716	+	0.613716i	−0.330196	+	0.943912i	$0.607115\pi$
$390$		0			0
$391$	1162.07			0.150303
$392$	−3551.21	−	1553.95i	−0.457559	−	0.200220i
$393$		0			0
$394$	5858.59	−	732.033i	0.749116	−	0.0936022i
$395$	−3774.26	+	3774.26i	−0.480769	+	0.480769i
$396$		0			0
$397$	7418.04	+	7418.04i	0.937786	+	0.937786i	0.998175	−	0.0603890i	$-0.0192341\pi$
$397$	7418.04	+	7418.04i	0.937786	+	0.937786i	−0.0603890	+	0.998175i	$0.519234\pi$
$398$	2949.75	−	3792.15i	0.371501	−	0.477597i
$399$		0			0
$400$	3181.46	+	5862.24i	0.397683	+	0.732780i
$401$			13363.8i			1.66423i	0.554600	+	0.832117i	$0.312871\pi$
$401$			13363.8i			1.66423i	−0.554600	+	0.832117i	$0.687129\pi$
$402$		0			0
$403$	−9467.75	+	9467.75i	−1.17028	+	1.17028i
$404$	−3042.05	+	5112.10i	−0.374623	+	0.629546i
$405$		0			0
$406$	−182.437	−	1460.08i	−0.0223010	−	0.178479i
$407$			792.682i			0.0965400i
$408$		0			0
$409$		−	1784.64i		−	0.215758i	−0.994164	−	0.107879i	$-0.965594\pi$
$409$		−	1784.64i		−	0.215758i	0.994164	−	0.107879i	$-0.0344059\pi$
$410$	251.149	−	31.3811i	0.0302521	−	0.00378001i
$411$		0			0
$412$	435.241	+	1714.46i	0.0520456	+	0.205014i
$413$	7997.39	−	7997.39i	0.952847	−	0.952847i
$414$		0			0
$415$		−	3026.07i		−	0.357937i
$416$	−11268.6	+	8070.84i	−1.32810	+	0.951215i
$417$		0			0
$418$	−493.183	−	383.625i	−0.0577090	−	0.0448893i
$419$	10663.3	+	10663.3i	1.24328	+	1.24328i	0.958632	+	0.284650i	$0.0918774\pi$
$419$	10663.3	+	10663.3i	1.24328	+	1.24328i	0.284650	+	0.958632i	$0.408123\pi$
$420$		0			0
$421$	1980.40	−	1980.40i	0.229261	−	0.229261i	−0.583123	−	0.812384i	$-0.698169\pi$
$421$	1980.40	−	1980.40i	0.229261	−	0.229261i	0.812384	+	0.583123i	$0.198169\pi$
$422$	1558.22	+	12470.7i	0.179747	+	1.43854i
$423$		0			0
$424$	−1900.35	−	4857.46i	−0.217664	−	0.556365i
$425$	−7375.77			−0.841829
$426$		0			0
$427$	6964.10	+	6964.10i	0.789266	+	0.789266i
$428$	−8015.19	−	4769.59i	−0.905208	−	0.538661i
$429$		0			0
$430$	−1356.52	−	1055.18i	−0.152133	−	0.118338i
$431$	−3750.79			−0.419186			−0.209593	−	0.977789i	$-0.567214\pi$
$431$	−3750.79			−0.419186			−0.209593	+	0.977789i	$0.567214\pi$
$432$		0			0
$433$	−14507.9			−1.61017			−0.805086	−	0.593159i	$-0.797881\pi$
$433$	−14507.9			−1.61017			−0.805086	+	0.593159i	$0.797881\pi$
$434$	−5115.30	−	3978.97i	−0.565766	−	0.440084i
$435$		0			0
$436$	−3905.72	+	6563.47i	−0.429014	+	0.720947i
$437$	534.617	+	534.617i	0.0585222	+	0.0585222i
$438$		0			0
$439$	13109.7			1.42526			0.712632	−	0.701538i	$-0.247503\pi$
$439$	13109.7			1.42526			0.712632	+	0.701538i	$0.247503\pi$
$440$	−453.377	−	198.390i	−0.0491225	−	0.0214952i
$441$		0			0
$442$	−1900.41	−	15209.3i	−0.204510	−	1.63673i
$443$	−9118.69	+	9118.69i	−0.977973	+	0.977973i	−0.999763	−	0.0217894i	$-0.993064\pi$
$443$	−9118.69	+	9118.69i	−0.977973	+	0.977973i	0.0217894	+	0.999763i	$0.493064\pi$
$444$		0			0
$445$	4947.06	+	4947.06i	0.526995	+	0.526995i
$446$	1941.49	+	1510.20i	0.206126	+	0.160336i
$447$		0			0
$448$	−4552.47	−	4927.72i	−0.480098	−	0.519671i
$449$		−	3154.04i		−	0.331511i	−0.986167	−	0.165756i	$-0.946994\pi$
$449$		−	3154.04i		−	0.331511i	0.986167	−	0.165756i	$-0.0530063\pi$
$450$		0			0
$451$	66.5885	−	66.5885i	0.00695240	−	0.00695240i
$452$	−8160.55	+	2071.67i	−0.849204	+	0.215582i
$453$		0			0
$454$	4777.47	−	596.946i	0.493871	−	0.0617094i
$455$			4573.89i			0.471268i
$456$		0			0
$457$		−	14705.8i		−	1.50527i	−0.658440	−	0.752633i	$-0.728783\pi$
$457$		−	14705.8i		−	1.50527i	0.658440	−	0.752633i	$-0.271217\pi$
$458$	1488.73	+	11914.5i	0.151886	+	1.21557i
$459$		0			0
$460$	514.612	+	306.230i	0.0521607	+	0.0310392i
$461$	9633.21	−	9633.21i	0.973240	−	0.973240i	−0.0264114	−	0.999651i	$-0.508408\pi$
$461$	9633.21	−	9633.21i	0.973240	−	0.973240i	0.999651	+	0.0264114i	$0.00840799\pi$
$462$		0			0
$463$			13731.1i			1.37827i	0.724632	+	0.689136i	$0.242010\pi$
$463$			13731.1i			1.37827i	−0.724632	+	0.689136i	$0.757990\pi$
$464$	−722.154	+	2436.21i	−0.0722525	+	0.243746i
$465$		0			0
$466$	8694.38	−	11177.4i	0.864291	−	1.11112i
$467$	1307.20	+	1307.20i	0.129529	+	0.129529i	0.768899	−	0.639370i	$-0.220805\pi$
$467$	1307.20	+	1307.20i	0.129529	+	0.129529i	−0.639370	+	0.768899i	$0.720805\pi$
$468$		0			0
$469$	−7365.11	+	7365.11i	−0.725137	+	0.725137i
$470$	4767.38	−	595.685i	0.467878	−	0.0584615i
$471$		0			0
$472$	−18188.7	+	7115.85i	−1.77373	+	0.693927i
$473$	−639.428			−0.0621584
$474$		0			0
$475$	−3393.26	−	3393.26i	−0.327776	−	0.327776i
$476$	7190.64	−	1825.45i	0.692400	−	0.175776i
$477$		0			0
$478$	−1146.11	+	1473.42i	−0.109669	+	0.140988i
$479$	5950.85			0.567644			0.283822	−	0.958877i	$-0.408398\pi$
$479$	5950.85			0.567644			0.283822	+	0.958877i	$0.408398\pi$
$480$		0			0
$481$	−12651.6			−1.19930
$482$	1890.67	−	2430.61i	0.178667	−	0.229691i
$483$		0			0
$484$	10142.2	−	2574.73i	0.952494	−	0.241804i
$485$	−450.237	−	450.237i	−0.0421530	−	0.0421530i
$486$		0			0
$487$	13651.9			1.27028			0.635141	−	0.772396i	$-0.280942\pi$
$487$	13651.9			1.27028			0.635141	+	0.772396i	$0.280942\pi$
$488$	−6196.46	−	15838.6i	−0.574796	−	1.46922i
$489$		0			0
$490$	2191.88	−	273.876i	0.202080	−	0.0252499i
$491$	−9699.69	+	9699.69i	−0.891530	+	0.891530i	−0.994667	−	0.103137i	$-0.967112\pi$
$491$	−9699.69	+	9699.69i	−0.891530	+	0.891530i	0.103137	+	0.994667i	$0.467112\pi$
$492$		0			0
$493$	−1986.90	−	1986.90i	−0.181512	−	0.181512i
$494$	6122.84	−	7871.43i	0.557651	−	0.716908i
$495$		0			0
$496$	5338.11	+	9836.13i	0.483242	+	0.890434i
$497$		−	15288.1i		−	1.37981i
$498$		0			0
$499$	−9376.88	+	9376.88i	−0.841216	+	0.841216i	−0.989017	−	0.147801i	$-0.952780\pi$
$499$	−9376.88	+	9376.88i	−0.841216	+	0.841216i	0.147801	+	0.989017i	$0.452780\pi$
$500$	−7183.94	−	4274.94i	−0.642551	−	0.382362i
$501$		0			0
$502$	1645.33	+	13167.9i	0.146285	+	1.17074i
$503$		−	9495.92i		−	0.841753i	−0.907118	−	0.420877i	$-0.861723\pi$
$503$		−	9495.92i		−	0.841753i	0.907118	−	0.420877i	$-0.138277\pi$
$504$		0			0
$505$		−	3389.91i		−	0.298711i
$506$	221.086	−	27.6248i	0.0194239	−	0.00242702i
$507$		0			0
$508$	799.317	−	202.918i	0.0698110	−	0.0177225i
$509$	5671.64	−	5671.64i	0.493892	−	0.493892i	−0.415638	−	0.909530i	$-0.636442\pi$
$509$	5671.64	−	5671.64i	0.493892	−	0.493892i	0.909530	+	0.415638i	$0.136442\pi$
$510$		0			0
$511$		−	4043.12i		−	0.350014i
$512$	3790.88	+	10947.5i	0.327217	+	0.944949i
$513$		0			0
$514$	−16148.2	−	12561.0i	−1.38573	−	1.07790i
$515$	−712.750	−	712.750i	−0.0609855	−	0.0609855i
$516$		0			0
$517$	1264.00	−	1264.00i	0.107525	−	0.107525i
$518$	−759.230	−	6076.26i	−0.0643990	−	0.515397i
$519$		0			0
$520$	3166.40	−	7236.11i	0.267030	−	0.610240i
$521$	11983.5			1.00769			0.503846	−	0.863794i	$-0.331918\pi$
$521$	11983.5			1.00769			0.503846	+	0.863794i	$0.331918\pi$
$522$		0			0
$523$	−1886.67	−	1886.67i	−0.157741	−	0.157741i	0.623824	−	0.781565i	$-0.285578\pi$
$523$	−1886.67	−	1886.67i	−0.157741	−	0.157741i	−0.781565	+	0.623824i	$0.785578\pi$
$524$	3100.24	−	5209.89i	0.258463	−	0.434341i
$525$		0			0
$526$	15810.4	+	12298.2i	1.31058	+	1.01944i
$527$	−12375.6			−1.02294
$528$		0			0
$529$	11897.4			0.977841
$530$	2346.12	+	1824.94i	0.192281	+	0.149567i
$531$		0			0
$532$	4147.90	+	2468.29i	0.338034	+	0.201154i
$533$	1062.78	+	1062.78i	0.0863683	+	0.0863683i
$534$		0			0
$535$	5314.99			0.429508
$536$	16750.7	−	6553.27i	1.34985	−	0.528093i
$537$		0			0
$538$	−633.682	−	5071.47i	−0.0507806	−	0.406406i
$539$	581.145	−	581.145i	0.0464410	−	0.0464410i
$540$		0			0
$541$	−2569.34	−	2569.34i	−0.204186	−	0.204186i	0.597605	−	0.801791i	$-0.296119\pi$
$541$	−2569.34	−	2569.34i	−0.204186	−	0.204186i	−0.801791	+	0.597605i	$0.796119\pi$
$542$	12917.2	+	10047.7i	1.02369	+	0.796286i
$543$		0			0
$544$	−12639.7	−	2089.97i	−0.996178	−	0.164719i
$545$		−	4352.33i		−	0.342079i
$546$		0			0
$547$	10127.9	−	10127.9i	0.791662	−	0.791662i	−0.190102	−	0.981764i	$-0.560882\pi$
$547$	10127.9	−	10127.9i	0.791662	−	0.791662i	0.981764	+	0.190102i	$0.0608820\pi$
$548$	−4120.06	−	16229.4i	−0.321168	−	1.26512i
$549$		0			0
$550$	−1403.25	+	175.337i	−0.108791	+	0.0135934i
$551$		−	1828.17i		−	0.141348i
$552$		0			0
$553$		−	15341.5i		−	1.17972i
$554$	1112.67	+	8904.94i	0.0853304	+	0.682914i
$555$		0			0
$556$	7910.55	−	13293.5i	0.603385	−	1.01397i
$557$	11050.4	−	11050.4i	0.840612	−	0.840612i	−0.148327	−	0.988938i	$-0.547389\pi$
$557$	11050.4	−	11050.4i	0.840612	−	0.840612i	0.988938	+	0.148327i	$0.0473887\pi$
$558$		0			0
$559$		−	10205.6i		−	0.772183i
$560$	3665.35	+	1086.50i	0.276588	+	0.0819877i
$561$		0			0
$562$	−1121.43	+	1441.69i	−0.0841718	+	0.108210i
$563$	−3100.96	−	3100.96i	−0.232131	−	0.232131i	0.581450	−	0.813582i	$-0.302485\pi$
$563$	−3100.96	−	3100.96i	−0.232131	−	0.232131i	−0.813582	+	0.581450i	$0.802485\pi$
$564$		0			0
$565$	3392.57	−	3392.57i	0.252613	−	0.252613i
$566$	18785.3	−	2347.23i	1.39506	−	0.174314i
$567$		0			0
$568$	−10583.6	+	24186.6i	−0.781829	+	1.78670i
$569$	−12626.6			−0.930288			−0.465144	−	0.885235i	$-0.653997\pi$
$569$	−12626.6			−0.930288			−0.465144	+	0.885235i	$0.653997\pi$
$570$		0			0
$571$	−5777.87	−	5777.87i	−0.423461	−	0.423461i	0.462932	−	0.886394i	$-0.346797\pi$
$571$	−5777.87	−	5777.87i	−0.423461	−	0.423461i	−0.886394	+	0.462932i	$0.846797\pi$
$572$	−723.114	−	2848.43i	−0.0528582	−	0.208215i
$573$		0			0
$574$	−446.652	+	574.209i	−0.0324789	+	0.0417544i
$575$	1711.21			0.124109
$576$		0			0
$577$	−9644.17			−0.695827			−0.347913	−	0.937527i	$-0.613110\pi$
$577$	−9644.17			−0.695827			−0.347913	+	0.937527i	$0.613110\pi$
$578$	166.399	−	213.920i	0.0119746	−	0.0153943i
$579$		0			0
$580$	−356.290	−	1403.47i	−0.0255071	−	0.100476i
$581$	6150.13	+	6150.13i	0.439157	+	0.439157i
$582$		0			0
$583$	1105.90			0.0785619
$584$	−2798.96	+	6396.42i	−0.198325	+	0.453229i
$585$		0			0
$586$	2572.22	−	321.400i	0.181327	−	0.0226568i
$587$	−6832.33	+	6832.33i	−0.480410	+	0.480410i	−0.905262	−	0.424853i	$-0.860326\pi$
$587$	−6832.33	+	6832.33i	−0.480410	+	0.480410i	0.424853	+	0.905262i	$0.360326\pi$
$588$		0			0
$589$	−5693.48	−	5693.48i	−0.398295	−	0.398295i
$590$	6833.48	−	8785.01i	0.476830	−	0.613006i
$591$		0			0
$592$	−3005.32	+	10138.5i	−0.208645	+	0.703870i
$593$			3807.51i			0.263669i	0.991272	+	0.131835i	$0.0420868\pi$
$593$			3807.51i			0.263669i	−0.991272	+	0.131835i	$0.957913\pi$
$594$		0			0
$595$	−2989.35	+	2989.35i	−0.205969	+	0.205969i
$596$	4126.30	−	6934.15i	0.283590	−	0.476567i
$597$		0			0
$598$	440.905	+	3528.64i	0.0301504	+	0.241299i
$599$		−	1731.22i		−	0.118090i	−0.998255	−	0.0590449i	$-0.981194\pi$
$599$		−	1731.22i		−	0.118090i	0.998255	−	0.0590449i	$-0.0188055\pi$
$600$		0			0
$601$		−	21704.9i		−	1.47315i	−0.676356	−	0.736575i	$-0.736442\pi$
$601$		−	21704.9i		−	1.47315i	0.676356	−	0.736575i	$-0.263558\pi$
$602$	4901.50	−	612.444i	0.331844	−	0.0414640i
$603$		0			0
$604$	6267.88	+	24689.9i	0.422246	+	1.66327i
$605$	−4216.38	+	4216.38i	−0.283339	+	0.283339i
$606$		0			0
$607$		−	19231.2i		−	1.28595i	−0.765888	−	0.642974i	$-0.777700\pi$
$607$		−	19231.2i		−	1.28595i	0.765888	−	0.642974i	$-0.222300\pi$
$608$	−4853.44	−	6776.45i	−0.323739	−	0.452009i
$609$		0			0
$610$	7649.96	+	5950.57i	0.507767	+	0.394970i
$611$	20174.1	+	20174.1i	1.33577	+	1.33577i
$612$		0			0
$613$	−9854.85	+	9854.85i	−0.649321	+	0.649321i	−0.952829	−	0.303508i	$-0.901842\pi$
$613$	−9854.85	+	9854.85i	−0.649321	+	0.649321i	0.303508	+	0.952829i	$0.401842\pi$
$614$	1689.44	+	13520.9i	0.111043	+	0.888693i
$615$		0			0
$616$	1324.64	−	518.231i	0.0866416	−	0.0338963i
$617$	−17948.8			−1.17114			−0.585569	−	0.810622i	$-0.699129\pi$
$617$	−17948.8			−1.17114			−0.585569	+	0.810622i	$0.699129\pi$
$618$		0			0
$619$	−6084.79	−	6084.79i	−0.395102	−	0.395102i	0.481399	−	0.876501i	$-0.340129\pi$
$619$	−6084.79	−	6084.79i	−0.395102	−	0.395102i	−0.876501	+	0.481399i	$0.840129\pi$
$620$	−5480.44	−	3261.24i	−0.355000	−	0.211249i
$621$		0			0
$622$	−17439.0	−	13565.0i	−1.12418	−	0.874450i
$623$	−20108.6			−1.29315
$624$		0			0
$625$	−8263.38			−0.528856
$626$	7058.68	+	5490.64i	0.450674	+	0.350559i
$627$		0			0
$628$	−8782.14	+	14758.2i	−0.558034	+	0.937763i
$629$	−8268.68	−	8268.68i	−0.524155	−	0.524155i
$630$		0			0
$631$	10974.2			0.692352			0.346176	−	0.938170i	$-0.387480\pi$
$631$	10974.2			0.692352			0.346176	+	0.938170i	$0.387480\pi$
$632$	−10620.6	+	24271.0i	−0.668454	+	1.52761i
$633$		0			0
$634$	157.948	+	1264.09i	0.00989421	+	0.0791852i
$635$	−332.298	+	332.298i	−0.0207667	+	0.0207667i
$636$		0			0
$637$	9275.36	+	9275.36i	0.576928	+	0.576928i
$638$	−425.243	−	330.778i	−0.0263880	−	0.0205261i
$639$		0			0
$640$	−5046.61	−	4256.34i	−0.311695	−	0.262885i
$641$			2520.18i			0.155290i	0.996981	+	0.0776451i	$0.0247401\pi$
$641$			2520.18i			0.155290i	−0.996981	+	0.0776451i	$0.975260\pi$
$642$		0			0
$643$	−9626.14	+	9626.14i	−0.590386	+	0.590386i	−0.937736	−	0.347350i	$-0.887082\pi$
$643$	−9626.14	+	9626.14i	−0.590386	+	0.590386i	0.347350	+	0.937736i	$0.387082\pi$
$644$	−1668.26	+	423.512i	−0.102079	+	0.0259142i
$645$		0			0
$646$	9146.22	−	1142.82i	0.557048	−	0.0696033i
$647$		−	1795.90i		−	0.109126i	−0.998510	−	0.0545628i	$-0.982623\pi$
$647$		−	1795.90i		−	0.109126i	0.998510	−	0.0545628i	$-0.0173765\pi$
$648$		0			0
$649$		−	4141.02i		−	0.250461i
$650$	−2798.46	−	22396.6i	−0.168869	−	1.35149i
$651$		0			0
$652$	−13936.5	−	8293.19i	−0.837111	−	0.498139i
$653$	2175.09	−	2175.09i	0.130349	−	0.130349i	−0.638922	−	0.769271i	$-0.720620\pi$
$653$	2175.09	−	2175.09i	0.130349	−	0.130349i	0.769271	+	0.638922i	$0.220620\pi$
$654$		0			0
$655$			3454.75i			0.206089i
$656$	1104.14	−	599.219i	0.0657154	−	0.0356640i
$657$		0			0
$658$	−8478.46	+	10899.8i	−0.502317	+	0.645771i
$659$	−16223.9	−	16223.9i	−0.959017	−	0.959017i	0.0401752	−	0.999193i	$-0.487208\pi$
$659$	−16223.9	−	16223.9i	−0.959017	−	0.959017i	−0.999193	+	0.0401752i	$0.987208\pi$
$660$		0			0
$661$	−2953.68	+	2953.68i	−0.173805	+	0.173805i	−0.788649	−	0.614844i	$-0.789219\pi$
$661$	−2953.68	+	2953.68i	−0.173805	+	0.173805i	0.614844	+	0.788649i	$0.289219\pi$
$662$	−8197.65	+	1024.30i	−0.481285	+	0.0601367i
$663$		0			0
$664$	−5472.21	−	13987.4i	−0.319823	−	0.817494i
$665$	−2750.53			−0.160393
$666$		0			0
$667$	460.970	+	460.970i	0.0267598	+	0.0267598i
$668$	12212.1	−	3100.21i	0.707334	−	0.179567i
$669$		0			0
$670$	−6293.22	+	8090.47i	−0.362878	+	0.466511i
$671$	3605.99			0.207463
$672$		0			0
$673$	13136.0			0.752385			0.376193	−	0.926542i	$-0.377233\pi$
$673$	13136.0			0.752385			0.376193	+	0.926542i	$0.377233\pi$
$674$	−11799.3	+	15169.0i	−0.674319	+	0.866894i
$675$		0			0
$676$	28426.7	−	7216.51i	1.61736	−	0.410589i
$677$	2954.97	+	2954.97i	0.167753	+	0.167753i	0.785991	−	0.618238i	$-0.212153\pi$
$677$	2954.97	+	2954.97i	0.167753	+	0.167753i	−0.618238	+	0.785991i	$0.712153\pi$
$678$		0			0
$679$	1830.10			0.103436
$680$	6798.75	−	2659.84i	0.383412	−	0.150000i
$681$		0			0
$682$	−2354.49	+	294.194i	−0.132197	+	0.0165180i
$683$	6641.03	−	6641.03i	0.372053	−	0.372053i	−0.496172	−	0.868224i	$-0.665261\pi$
$683$	6641.03	−	6641.03i	0.372053	−	0.372053i	0.868224	+	0.496172i	$0.165261\pi$
$684$		0			0
$685$	6747.01	+	6747.01i	0.376336	+	0.376336i
$686$	−11703.0	+	15045.2i	−0.651343	+	0.837357i
$687$		0			0
$688$	−8178.39	−	2424.28i	−0.453195	−	0.134338i
$689$			17650.7i			0.975960i
$690$		0			0
$691$	−17821.2	+	17821.2i	−0.981115	+	0.981115i	−0.999825	−	0.0187097i	$-0.994044\pi$
$691$	−17821.2	+	17821.2i	−0.981115	+	0.981115i	0.0187097	+	0.999825i	$0.494044\pi$
$692$	22585.9	+	13440.2i	1.24073	+	0.738322i
$693$		0			0
$694$	1983.58	+	15874.9i	0.108495	+	0.868305i
$695$			8815.11i			0.481117i
$696$		0			0
$697$			1389.20i			0.0754948i
$698$	−5886.16	+	735.477i	−0.319190	+	0.0398828i
$699$		0			0
$700$	10588.6	−	2688.07i	0.571732	−	0.145142i
$701$	−19022.9	+	19022.9i	−1.02494	+	1.02494i	−0.0252614	+	0.999681i	$0.508042\pi$
$701$	−19022.9	+	19022.9i	−1.02494	+	1.02494i	−0.999681	+	0.0252614i	$0.991958\pi$
$702$		0			0
$703$		−	7608.10i		−	0.408172i
$704$	−2454.40	−	97.1512i	−0.131397	−	0.00520103i
$705$		0			0
$706$	15077.9	+	11728.4i	0.803772	+	0.625219i
$707$	6889.58	+	6889.58i	0.366491	+	0.366491i
$708$		0			0
$709$	15338.6	−	15338.6i	0.812485	−	0.812485i	−0.172521	−	0.985006i	$-0.555191\pi$
$709$	15338.6	−	15338.6i	0.812485	−	0.812485i	0.985006	+	0.172521i	$0.0551912\pi$
$710$	−1865.32	−	14928.5i	−0.0985973	−	0.789092i
$711$		0			0
$712$	31812.8	+	13920.7i	1.67449	+	0.732727i
$713$	2871.21			0.150810
$714$		0			0
$715$	1184.17	+	1184.17i	0.0619377	+	0.0619377i
$716$	−14459.1	+	24298.1i	−0.754693	+	1.26824i
$717$		0			0
$718$	18384.3	+	14300.4i	0.955567	+	0.743294i
$719$	−24937.9			−1.29350			−0.646751	−	0.762701i	$-0.723873\pi$
$719$	−24937.9			−1.29350			−0.646751	+	0.762701i	$0.723873\pi$
$720$		0			0
$721$	2897.16			0.149647
$722$	−10579.5	−	8229.30i	−0.545328	−	0.424187i
$723$		0			0
$724$	−11744.2	−	6988.63i	−0.602860	−	0.358744i
$725$	−2925.82	−	2925.82i	−0.149879	−	0.149879i
$726$		0			0
$727$	4479.75			0.228535			0.114267	−	0.993450i	$-0.463548\pi$
$727$	4479.75			0.228535			0.114267	+	0.993450i	$0.463548\pi$
$728$	8271.21	+	21141.9i	0.421087	+	1.07633i
$729$		0			0
$730$	−493.305	−	3948.01i	−0.0250110	−	0.200167i
$731$	6670.05	−	6670.05i	0.337484	−	0.337484i
$732$		0			0
$733$	7481.44	+	7481.44i	0.376989	+	0.376989i	0.870015	−	0.493025i	$-0.164109\pi$
$733$	7481.44	+	7481.44i	0.376989	+	0.376989i	−0.493025	+	0.870015i	$0.664109\pi$
$734$	−12467.8	−	9698.15i	−0.626968	−	0.487691i
$735$		0			0
$736$	2932.46	+	484.884i	0.146864	+	0.0242841i
$737$			3813.63i			0.190606i
$738$		0			0
$739$	24827.3	−	24827.3i	1.23584	−	1.23584i	0.274160	−	0.961684i	$-0.411600\pi$
$739$	24827.3	−	24827.3i	1.23584	−	1.23584i	0.961684	−	0.274160i	$-0.0883998\pi$
$740$	−1482.74	−	5840.68i	−0.0736575	−	0.290145i
$741$		0			0
$742$	−8477.19	+	1059.23i	−0.419417	+	0.0524063i
$743$		−	16682.5i		−	0.823716i	−0.911248	−	0.411858i	$-0.864880\pi$
$743$		−	16682.5i		−	0.823716i	0.911248	−	0.411858i	$-0.135120\pi$
$744$		0			0
$745$			4598.13i			0.226124i
$746$	−1588.47	−	12712.8i	−0.0779597	−	0.623926i
$747$		0			0
$748$	1389.04	−	2334.25i	0.0678988	−	0.114102i
$749$	−10802.1	+	10802.1i	−0.526968	+	0.526968i
$750$		0			0
$751$			21972.3i			1.06762i	0.845605	+	0.533809i	$0.179240\pi$
$751$			21972.3i			1.06762i	−0.845605	+	0.533809i	$0.820760\pi$
$752$	20959.0	−	11374.5i	1.01635	−	0.551578i
$753$		0			0
$754$	5279.38	−	6787.09i	0.254992	−	0.327813i
$755$	−10264.3	−	10264.3i	−0.494775	−	0.494775i
$756$		0			0
$757$	−13715.8	+	13715.8i	−0.658530	+	0.658530i	−0.955032	−	0.296502i	$-0.904180\pi$
$757$	−13715.8	+	13715.8i	−0.658530	+	0.658530i	0.296502	+	0.955032i	$0.404180\pi$
$758$	85.7898	−	10.7195i	0.00411085	−	0.000513652i
$759$		0			0
$760$	4351.48	+	1904.13i	0.207690	+	0.0908817i
$761$	−3346.07			−0.159389			−0.0796944	−	0.996819i	$-0.525394\pi$
$761$	−3346.07			−0.159389			−0.0796944	+	0.996819i	$0.525394\pi$
$762$		0			0
$763$	8845.59	+	8845.59i	0.419701	+	0.419701i
$764$	−2566.52	−	10109.8i	−0.121536	−	0.478744i
$765$		0			0
$766$	8592.64	−	11046.6i	0.405307	−	0.521056i
$767$	66092.6			3.11143
$768$		0			0
$769$	18053.3			0.846578			0.423289	−	0.905995i	$-0.360876\pi$
$769$	18053.3			0.846578			0.423289	+	0.905995i	$0.360876\pi$
$770$	−497.666	+	639.792i	−0.0232918	+	0.0299435i
$771$		0			0
$772$	−6315.96	−	24879.3i	−0.294451	−	1.15988i
$773$	−8674.66	−	8674.66i	−0.403630	−	0.403630i	0.475880	−	0.879510i	$-0.342130\pi$
$773$	−8674.66	−	8674.66i	−0.403630	−	0.403630i	−0.879510	+	0.475880i	$0.842130\pi$
$774$		0			0
$775$	−18223.8			−0.844670
$776$	−2895.32	−	1266.94i	−0.133938	−	0.0586089i
$777$		0			0
$778$	−18689.1	+	2335.21i	−0.861229	+	0.107611i
$779$	−639.111	+	639.111i	−0.0293948	+	0.0293948i
$780$		0			0
$781$	−3958.07	−	3958.07i	−0.181345	−	0.181345i
$782$	−2018.05	+	2594.37i	−0.0922828	+	0.118637i
$783$		0			0
$784$	9636.25	−	5229.63i	0.438969	−	0.238230i
$785$		−	9786.36i		−	0.444956i
$786$		0			0
$787$	6512.95	−	6512.95i	0.294996	−	0.294996i	−0.544054	−	0.839050i	$-0.683111\pi$
$787$	6512.95	−	6512.95i	0.294996	−	0.294996i	0.839050	+	0.544054i	$0.183111\pi$
$788$	−8539.71	+	14350.8i	−0.386059	+	0.648763i
$789$		0			0
$790$	−1871.82	−	14980.6i	−0.0842994	−	0.674663i
$791$			13790.0i			0.619867i
$792$		0			0
$793$			57553.3i			2.57727i
$794$	−29443.2	+	3678.94i	−1.31600	+	0.164434i
$795$		0			0
$796$	3343.61	+	13170.9i	0.148883	+	0.586469i
$797$	10831.9	−	10831.9i	0.481413	−	0.481413i	−0.424169	−	0.905583i	$-0.639434\pi$
$797$	10831.9	−	10831.9i	0.481413	−	0.481413i	0.905583	+	0.424169i	$0.139434\pi$
$798$		0			0
$799$			26370.2i			1.16760i
$800$	−18612.6	−	3077.60i	−0.822569	−	0.136012i
$801$		0			0
$802$	−29835.3	−	23207.6i	−1.31362	−	1.02181i
$803$	−1046.76	−	1046.76i	−0.0460015	−	0.0460015i
$804$		0			0
$805$	693.543	−	693.543i	0.0303654	−	0.0303654i
$806$	−4695.48	−	37578.8i	−0.205200	−	1.64225i
$807$		0			0
$808$	−6130.15	−	15669.2i	−0.266904	−	0.682227i
$809$	18515.3			0.804651			0.402326	−	0.915497i	$-0.368202\pi$
$809$	18515.3			0.804651			0.402326	+	0.915497i	$0.368202\pi$
$810$		0			0
$811$	−15062.3	−	15062.3i	−0.652167	−	0.652167i	0.301347	−	0.953514i	$-0.402564\pi$
$811$	−15062.3	−	15062.3i	−0.652167	−	0.652167i	−0.953514	+	0.301347i	$0.902564\pi$
$812$	3576.50	+	2128.26i	0.154570	+	0.0919796i
$813$		0			0
$814$	−1769.69	−	1376.57i	−0.0762012	−	0.0592736i
$815$	9241.51			0.397197
$816$		0			0
$817$	6137.18			0.262806
$818$	3984.29	+	3099.20i	0.170302	+	0.132471i
$819$		0			0
$820$	−366.085	+	615.197i	−0.0155905	+	0.0261995i
$821$	24601.7	+	24601.7i	1.04580	+	1.04580i	0.998899	+	0.0469030i	$0.0149352\pi$
$821$	24601.7	+	24601.7i	1.04580	+	1.04580i	0.0469030	+	0.998899i	$0.485065\pi$
$822$		0			0
$823$	−24417.7			−1.03420			−0.517101	−	0.855924i	$-0.672989\pi$
$823$	−24417.7			−1.03420			−0.517101	+	0.855924i	$0.672989\pi$
$824$	−4583.45	−	2005.64i	−0.193777	−	0.0847933i
$825$		0			0
$826$	3966.26	+	31742.7i	0.167075	+	1.33713i
$827$	26807.5	−	26807.5i	1.12719	−	1.12719i	0.136560	−	0.990632i	$-0.456396\pi$
$827$	26807.5	−	26807.5i	1.12719	−	1.12719i	0.990632	−	0.136560i	$-0.0436045\pi$
$828$		0			0
$829$	−3214.77	−	3214.77i	−0.134685	−	0.134685i	0.636550	−	0.771235i	$-0.280361\pi$
$829$	−3214.77	−	3214.77i	−0.134685	−	0.134685i	−0.771235	+	0.636550i	$0.780361\pi$
$830$	6755.82	+	5255.06i	0.282528	+	0.219766i
$831$		0			0
$832$	1550.58	−	39173.4i	0.0646114	−	1.63233i
$833$			12124.2i			0.504294i
$834$		0			0
$835$	−5076.90	+	5076.90i	−0.210411	+	0.210411i
$836$	1712.92	−	434.848i	0.0708642	−	0.0179899i
$837$		0			0
$838$	−42324.0	+	5288.39i	−1.74470	+	0.218001i
$839$		−	40899.9i		−	1.68298i	−0.540271	−	0.841491i	$-0.681678\pi$
$839$		−	40899.9i		−	1.68298i	0.540271	−	0.841491i	$-0.318322\pi$
$840$		0			0
$841$			22812.7i			0.935367i
$842$	982.170	+	7860.49i	0.0401993	+	0.321722i
$843$		0			0
$844$	−30547.4	−	18177.8i	−1.24584	−	0.741359i
$845$	−11817.8	+	11817.8i	−0.481116	+	0.481116i
$846$		0			0
$847$		−	17138.6i		−	0.695263i
$848$	14144.6	+	4192.82i	0.572792	+	0.169790i
$849$		0			0
$850$	12808.7	−	16466.7i	0.516865	−	0.664474i
$851$	1918.37	+	1918.37i	0.0772749	+	0.0772749i
$852$		0			0
$853$	21139.7	−	21139.7i	0.848545	−	0.848545i	−0.141407	−	0.989952i	$-0.545163\pi$
$853$	21139.7	−	21139.7i	0.848545	−	0.848545i	0.989952	+	0.141407i	$0.0451626\pi$
$854$	−27641.5	+	3453.81i	−1.10758	+	0.138392i
$855$		0			0
$856$	24567.4	−	9611.38i	0.980956	−	0.383774i
$857$	2133.86			0.0850540			0.0425270	−	0.999095i	$-0.486459\pi$
$857$	2133.86			0.0850540			0.0425270	+	0.999095i	$0.486459\pi$
$858$		0			0
$859$	−14755.9	−	14755.9i	−0.586107	−	0.586107i	0.350468	−	0.936575i	$-0.386023\pi$
$859$	−14755.9	−	14755.9i	−0.586107	−	0.586107i	−0.936575	+	0.350468i	$0.886023\pi$
$860$	4711.47	−	1196.07i	0.186814	−	0.0474253i
$861$		0			0
$862$	6513.60	−	8373.79i	0.257371	−	0.330873i
$863$	13261.8			0.523101			0.261550	−	0.965190i	$-0.415766\pi$
$863$	13261.8			0.523101			0.261550	+	0.965190i	$0.415766\pi$
$864$		0			0
$865$	−14977.0			−0.588710
$866$	25194.3	−	32389.4i	0.988612	−	1.27094i
$867$		0			0
$868$	17766.4	−	4510.26i	0.694737	−	0.176369i
$869$	−3971.88	−	3971.88i	−0.155048	−	0.155048i
$870$		0			0
$871$	−60867.3			−2.36787
$872$	−7870.55	−	20117.8i	−0.305654	−	0.781277i
$873$		0			0
$874$	−2121.97	+	265.140i	−0.0821242	+	0.0102614i
$875$	−9681.80	+	9681.80i	−0.374062	+	0.374062i
$876$		0			0
$877$	17125.7	+	17125.7i	0.659399	+	0.659399i	0.955238	−	0.295839i	$-0.0955991\pi$
$877$	17125.7	+	17125.7i	0.659399	+	0.659399i	−0.295839	+	0.955238i	$0.595599\pi$
$878$	−22766.2	+	29267.9i	−0.875082	+	1.12499i
$879$		0			0
$880$	1230.25	−	667.659i	0.0471268	−	0.0255759i
$881$			34029.0i			1.30132i	0.759368	+	0.650662i	$0.225508\pi$
$881$			34029.0i			1.30132i	−0.759368	+	0.650662i	$0.774492\pi$
$882$		0			0
$883$	7536.29	−	7536.29i	0.287221	−	0.287221i	−0.548759	−	0.835981i	$-0.684900\pi$
$883$	7536.29	−	7536.29i	0.287221	−	0.287221i	0.835981	+	0.548759i	$0.184900\pi$
$884$	37255.7	+	22169.7i	1.41747	+	0.843494i
$885$		0			0
$886$	−4522.37	−	36193.3i	−0.171481	−	1.37239i
$887$			11775.4i			0.445749i	0.974847	+	0.222875i	$0.0715441\pi$
$887$			11775.4i			0.445749i	−0.974847	+	0.222875i	$0.928456\pi$
$888$		0			0
$889$		−	1350.71i		−	0.0509578i
$890$	−19635.5	+	2453.47i	−0.739533	+	0.0924049i
$891$		0			0
$892$	−6743.17	+	1711.85i	−0.253114	+	0.0642566i
$893$	−12131.8	+	12131.8i	−0.454619	+	0.454619i
$894$		0			0
$895$		−	16112.4i		−	0.601764i
$896$	18907.1	−	1606.12i	0.704958	−	0.0598846i
$897$		0			0
$898$	7041.53	+	5477.30i	0.261669	+	0.203541i
$899$	−4909.17	−	4909.17i	−0.182124	−	0.182124i
$900$		0			0
$901$	−11535.9	+	11535.9i	−0.426545	+	0.426545i
$902$	33.0242	+	264.299i	0.00121905	+	0.00975631i
$903$		0			0
$904$	9546.49	−	21816.4i	0.351230	−	0.802659i
$905$	7787.77			0.286049
$906$		0			0
$907$	24197.1	+	24197.1i	0.885833	+	0.885833i	0.994120	−	0.108287i	$-0.0345365\pi$
$907$	24197.1	+	24197.1i	0.885833	+	0.885833i	−0.108287	+	0.994120i	$0.534537\pi$
$908$	−6963.82	+	11702.5i	−0.254518	+	0.427712i
$909$		0			0
$910$	−10211.4	−	7942.99i	−0.371983	−	0.289349i
$911$	15777.4			0.573798			0.286899	−	0.957961i	$-0.407376\pi$
$911$	15777.4			0.573798			0.286899	+	0.957961i	$0.407376\pi$
$912$		0			0
$913$	3184.51			0.115435
$914$	32831.2	+	25538.0i	1.18814	+	0.924203i
$915$		0			0
$916$	−29185.0	−	17367.1i	−1.05273	−	0.626447i
$917$	−7021.37	−	7021.37i	−0.252853	−	0.252853i
$918$		0			0
$919$	24261.8			0.870863			0.435432	−	0.900222i	$-0.356596\pi$
$919$	24261.8			0.870863			0.435432	+	0.900222i	$0.356596\pi$
$920$	−1577.34	+	617.095i	−0.0565255	+	0.0221142i
$921$		0			0
$922$	4777.54	+	38235.5i	0.170651	+	1.36575i
$923$	63172.6	−	63172.6i	2.25282	−	2.25282i
$924$		0			0
$925$	−12176.1	−	12176.1i	−0.432808	−	0.432808i
$926$	−30655.3	−	23845.4i	−1.08790	−	0.846231i
$927$		0			0
$928$	−4184.85	−	5842.95i	−0.148033	−	0.206685i
$929$		−	19578.0i		−	0.691423i	−0.938341	−	0.345712i	$-0.887638\pi$
$929$		−	19578.0i		−	0.691423i	0.938341	−	0.345712i	$-0.112362\pi$
$930$		0			0
$931$	−5577.79	+	5577.79i	−0.196353	+	0.196353i
$932$	9855.29	+	38821.1i	0.346374	+	1.36441i
$933$		0			0
$934$	−5188.45	+	648.299i	−0.181768	+	0.0227120i
$935$			1547.87i			0.0541400i
$936$		0			0
$937$			23706.5i			0.826530i	0.910611	+	0.413265i	$0.135612\pi$
$937$			23706.5i			0.826530i	−0.910611	+	0.413265i	$0.864388\pi$
$938$	−3652.69	−	29233.1i	−0.127148	−	1.01759i
$939$		0			0
$940$	−6949.11	+	11677.8i	−0.241122	+	0.405201i
$941$	−516.925	+	516.925i	−0.0179078	+	0.0179078i	−0.716004	−	0.698096i	$-0.754031\pi$
$941$	−516.925	+	516.925i	−0.0179078	+	0.0179078i	0.698096	+	0.716004i	$0.254031\pi$
$942$		0			0
$943$		−	322.302i		−	0.0111300i
$944$	15699.9	−	52964.3i	0.541303	−	1.82610i
$945$		0			0
$946$	1110.43	−	1427.55i	0.0381640	−	0.0490630i
$947$	−9551.64	−	9551.64i	−0.327758	−	0.327758i	0.523976	−	0.851733i	$-0.324448\pi$
$947$	−9551.64	−	9551.64i	−0.327758	−	0.327758i	−0.851733	+	0.523976i	$0.824448\pi$
$948$		0			0
$949$	16706.7	−	16706.7i	0.571469	−	0.571469i
$950$	13468.3	−	1682.87i	0.459968	−	0.0574732i
$951$		0			0
$952$	−8411.85	+	19223.5i	−0.286376	+	0.654449i
$953$	12241.2			0.416089			0.208044	−	0.978119i	$-0.433290\pi$
$953$	12241.2			0.416089			0.208044	+	0.978119i	$0.433290\pi$
$954$		0			0
$955$	4202.94	+	4202.94i	0.142412	+	0.142412i
$956$	−1299.14	−	5117.46i	−0.0439510	−	0.173128i
$957$		0			0
$958$	−10334.2	+	13285.5i	−0.348522	+	0.448054i
$959$	−27425.0			−0.923461
$960$		0			0
$961$	−786.360			−0.0263959
$962$	21970.7	−	28245.2i	0.736344	−	0.946633i
$963$		0			0
$964$	2143.11	+	8441.97i	0.0716028	+	0.282052i
$965$	10343.0	+	10343.0i	0.345030	+	0.345030i
$966$		0			0
$967$	−12983.6			−0.431773			−0.215886	−	0.976418i	$-0.569264\pi$
$967$	−12983.6			−0.431773			−0.215886	+	0.976418i	$0.569264\pi$
$968$	−11864.6	+	27114.0i	−0.393950	+	0.900287i
$969$		0			0
$970$	1787.05	−	223.293i	0.0591533	−	0.00739123i
$971$	−35022.4	+	35022.4i	−1.15749	+	1.15749i	−0.172477	+	0.985014i	$0.555177\pi$
$971$	−35022.4	+	35022.4i	−1.15749	+	1.15749i	−0.985014	+	0.172477i	$0.944823\pi$
$972$		0			0
$973$	−17915.7	−	17915.7i	−0.590287	−	0.590287i
$974$	−23707.9	+	30478.5i	−0.779927	+	1.00266i
$975$		0			0
$976$	46121.1	+	13671.5i	1.51260	+	0.448374i
$977$		−	43174.5i		−	1.41379i	−0.707317	−	0.706897i	$-0.750095\pi$
$977$		−	43174.5i		−	1.41379i	0.707317	−	0.706897i	$-0.249905\pi$
$978$		0			0
$979$	−5206.08	+	5206.08i	−0.169956	+	0.169956i
$980$	−3194.97	+	5369.07i	−0.104142	+	0.175009i
$981$		0			0
$982$	−4810.51	−	38499.4i	−0.156323	−	1.25108i
$983$			43699.4i			1.41790i	0.705260	+	0.708949i	$0.250830\pi$
$983$			43699.4i			1.41790i	−0.705260	+	0.708949i	$0.749170\pi$
$984$		0			0
$985$		−	9516.21i		−	0.307829i
$986$	7886.26	−	985.391i	0.254716	−	0.0318268i
$987$		0			0
$988$	6940.39	+	27339.0i	0.223485	+	0.880333i
$989$	−1547.48	+	1547.48i	−0.0497544	+	0.0497544i
$990$		0			0
$991$		−	8324.37i		−	0.266834i	−0.991060	−	0.133417i	$-0.957405\pi$
$991$		−	8324.37i		−	0.266834i	0.991060	−	0.133417i	$-0.0425949\pi$
$992$	−31229.7	−	5163.85i	−0.999540	−	0.165274i
$993$		0			0
$994$	34131.3	+	26549.3i	1.08912	+	0.847175i
$995$	−5475.50	−	5475.50i	−0.174457	−	0.174457i
$996$		0			0
$997$	−563.783	+	563.783i	−0.0179089	+	0.0179089i	−0.716005	−	0.698096i	$-0.754031\pi$
$997$	−563.783	+	563.783i	−0.0179089	+	0.0179089i	0.698096	+	0.716005i	$0.254031\pi$
$998$	−4650.41	−	37218.1i	−0.147501	−	1.18048i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.4.l.a.35.8	✓	48
3.2	odd	2	inner	144.4.l.a.35.17	yes	48
4.3	odd	2		576.4.l.a.431.14		48
8.3	odd	2		1152.4.l.a.863.11		48
8.5	even	2		1152.4.l.b.863.11		48
12.11	even	2		576.4.l.a.431.11		48
16.3	odd	4		1152.4.l.b.287.14		48
16.5	even	4		576.4.l.a.143.11		48
16.11	odd	4	inner	144.4.l.a.107.17	yes	48
16.13	even	4		1152.4.l.a.287.14		48
24.5	odd	2		1152.4.l.b.863.14		48
24.11	even	2		1152.4.l.a.863.14		48
48.5	odd	4		576.4.l.a.143.14		48
48.11	even	4	inner	144.4.l.a.107.8	yes	48
48.29	odd	4		1152.4.l.a.287.11		48
48.35	even	4		1152.4.l.b.287.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.4.l.a.35.8	✓	48	1.1	even	1	trivial
144.4.l.a.35.17	yes	48	3.2	odd	2	inner
144.4.l.a.107.8	yes	48	48.11	even	4	inner
144.4.l.a.107.17	yes	48	16.11	odd	4	inner
576.4.l.a.143.11		48	16.5	even	4
576.4.l.a.143.14		48	48.5	odd	4
576.4.l.a.431.11		48	12.11	even	2
576.4.l.a.431.14		48	4.3	odd	2
1152.4.l.a.287.11		48	48.29	odd	4
1152.4.l.a.287.14		48	16.13	even	4
1152.4.l.a.863.11		48	8.3	odd	2
1152.4.l.a.863.14		48	24.11	even	2
1152.4.l.b.287.11		48	48.35	even	4
1152.4.l.b.287.14		48	16.3	odd	4
1152.4.l.b.863.11		48	8.5	even	2
1152.4.l.b.863.14		48	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73660 + 2.23254i) q^{2} +(-1.96847 - 7.75404i) q^{4} +(3.22357 + 3.22357i) q^{5} -13.1030 q^{7} +(20.7296 + 9.07094i) q^{8} +O(q^{10})\)	\(q+(-1.73660 + 2.23254i) q^{2} +(-1.96847 - 7.75404i) q^{4} +(3.22357 + 3.22357i) q^{5} -13.1030 q^{7} +(20.7296 + 9.07094i) q^{8} +(-12.7948 + 1.59871i) q^{10} +(-3.39235 + 3.39235i) q^{11} +(-54.1435 - 54.1435i) q^{13} +(22.7547 - 29.2531i) q^{14} +(-56.2502 + 30.5272i) q^{16} -70.7730i q^{17} +(32.5595 - 32.5595i) q^{19} +(18.6502 - 31.3412i) q^{20} +(-1.68242 - 13.4647i) q^{22} +16.4197i q^{23} -104.217i q^{25} +(214.903 - 26.8522i) q^{26} +(25.7930 + 101.601i) q^{28} +(28.0742 - 28.0742i) q^{29} -174.864i q^{31} +(29.5307 - 178.594i) q^{32} +(158.004 + 122.904i) q^{34} +(-42.2385 - 42.2385i) q^{35} +(116.834 - 116.834i) q^{37} +(16.1477 + 129.233i) q^{38} +(37.5826 + 96.0642i) q^{40} -19.6290 q^{41} +(94.2456 + 94.2456i) q^{43} +(32.9822 + 19.6267i) q^{44} +(-36.6576 - 28.5143i) q^{46} -372.603 q^{47} -171.310 q^{49} +(232.669 + 180.983i) q^{50} +(-313.251 + 526.411i) q^{52} +(-162.999 - 162.999i) q^{53} -21.8710 q^{55} +(-271.621 - 118.857i) q^{56} +(13.9233 + 111.430i) q^{58} +(-610.346 + 610.346i) q^{59} +(-531.488 - 531.488i) q^{61} +(390.391 + 303.668i) q^{62} +(347.436 + 376.075i) q^{64} -349.071i q^{65} +(562.092 - 562.092i) q^{67} +(-548.777 + 139.315i) q^{68} +(167.650 - 20.9480i) q^{70} +1166.76i q^{71} +308.564i q^{73} +(57.9431 + 463.729i) q^{74} +(-316.560 - 188.375i) q^{76} +(44.4501 - 44.4501i) q^{77} +1170.83i q^{79} +(-279.733 - 82.9199i) q^{80} +(34.0877 - 43.8226i) q^{82} +(-469.366 - 469.366i) q^{83} +(228.142 - 228.142i) q^{85} +(-374.074 + 46.7406i) q^{86} +(-101.094 + 39.5504i) q^{88} +1534.65 q^{89} +(709.445 + 709.445i) q^{91} +(127.319 - 32.3217i) q^{92} +(647.061 - 831.851i) q^{94} +209.916 q^{95} -139.670 q^{97} +(297.497 - 382.458i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 120 q^{10} - 144 q^{16} - 48 q^{19} + 72 q^{22} + 72 q^{28} - 984 q^{34} - 1272 q^{40} + 864 q^{43} - 1416 q^{46} + 2352 q^{49} - 648 q^{52} - 576 q^{55} + 1128 q^{58} + 1824 q^{61} + 3024 q^{64} + 816 q^{67} + 2664 q^{70} + 1920 q^{76} + 1200 q^{82} - 480 q^{85} - 4560 q^{88} - 3600 q^{91} - 11304 q^{94}+O(q^{100}) \) 48 * q - 120 * q^10 - 144 * q^16 - 48 * q^19 + 72 * q^22 + 72 * q^28 - 984 * q^34 - 1272 * q^40 + 864 * q^43 - 1416 * q^46 + 2352 * q^49 - 648 * q^52 - 576 * q^55 + 1128 * q^58 + 1824 * q^61 + 3024 * q^64 + 816 * q^67 + 2664 * q^70 + 1920 * q^76 + 1200 * q^82 - 480 * q^85 - 4560 * q^88 - 3600 * q^91 - 11304 * q^94

Introduction

L-functions

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