LMFDB - Embedded newform 144.4.l.a.107.8

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			107.8
Character	$\chi$	$=$	144.107
Dual form			144.4.l.a.35.8

$q$-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 $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

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

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	−0.548093	−	0.836418i	$-0.684646\pi$
$5$	3.22357	−	3.22357i	0.288325	−	0.288325i	0.836418	+	0.548093i	$0.184646\pi$
$6$		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	0.659084	−	0.752069i	$-0.270944\pi$
$11$	−3.39235	−	3.39235i	−0.0929847	−	0.0929847i	−0.752069	+	0.659084i	$0.770944\pi$
$12$		0			0
$13$	−54.1435	+	54.1435i	−1.15513	+	1.15513i	−0.169623	+	0.985509i	$0.554255\pi$
$13$	−54.1435	+	54.1435i	−1.15513	+	1.15513i	−0.985509	+	0.169623i	$0.945745\pi$
$14$	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	$0.168453\pi$
$17$			70.7730i			1.00970i	−0.863206	+	0.504852i	$0.831547\pi$
$18$		0			0
$19$	32.5595	+	32.5595i	0.393140	+	0.393140i	0.875805	−	0.482665i	$-0.160331\pi$
$19$	32.5595	+	32.5595i	0.393140	+	0.393140i	−0.482665	+	0.875805i	$0.660331\pi$
$20$	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	$-0.976287\pi$
$23$		−	16.4197i		−	0.148858i	0.997226	−	0.0744291i	$-0.0237135\pi$
$24$		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	0.791254	−	0.611487i	$-0.209428\pi$
$29$	28.0742	+	28.0742i	0.179767	+	0.179767i	−0.611487	+	0.791254i	$0.709428\pi$
$30$		0			0
$31$			174.864i			1.01311i	0.862207	+	0.506556i	$0.169082\pi$
$31$			174.864i			1.01311i	−0.862207	+	0.506556i	$0.830918\pi$
$32$	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	0.917304	−	0.398187i	$-0.130360\pi$
$37$	116.834	+	116.834i	0.519117	+	0.519117i	−0.398187	+	0.917304i	$0.630360\pi$
$38$	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	−0.519954	−	0.854194i	$-0.674051\pi$
$43$	94.2456	−	94.2456i	0.334240	−	0.334240i	0.854194	+	0.519954i	$0.174051\pi$
$44$	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	−0.886045	−	0.463600i	$-0.846558\pi$
$53$	−162.999	+	162.999i	−0.422445	+	0.422445i	0.463600	+	0.886045i	$0.346558\pi$
$54$		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	−0.889130	−	0.457655i	$-0.848690\pi$
$59$	−610.346	−	610.346i	−1.34678	−	1.34678i	−0.457655	−	0.889130i	$-0.651310\pi$
$60$		0			0
$61$	−531.488	+	531.488i	−1.11557	+	1.11557i	−0.123191	+	0.992383i	$0.539313\pi$
$61$	−531.488	+	531.488i	−1.11557	+	1.11557i	−0.992383	+	0.123191i	$0.960687\pi$
$62$	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	0.999681	+	0.0252516i	$0.00803869\pi$
$67$	562.092	+	562.092i	1.02493	+	1.02493i	0.0252516	+	0.999681i	$0.491961\pi$
$68$	−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	$-0.571132\pi$
$71$		−	1166.76i		−	1.95027i	0.221612	−	0.975135i	$-0.428868\pi$
$72$		0			0
$73$		−	308.564i		−	0.494721i	−0.968923	−	0.247361i	$-0.920437\pi$
$73$		−	308.564i		−	0.494721i	0.968923	−	0.247361i	$-0.0795633\pi$
$74$	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	$-0.686202\pi$
$79$		−	1170.83i		−	1.66746i	0.552176	−	0.833728i	$-0.313798\pi$
$80$	−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	−0.945715	−	0.324996i	$-0.894637\pi$
$83$	−469.366	+	469.366i	−0.620719	+	0.620719i	0.324996	+	0.945715i	$0.394637\pi$
$84$		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	−0.916969	−	0.398958i	$-0.869372\pi$
$101$	−525.800	+	525.800i	−0.518011	+	0.518011i	0.398958	+	0.916969i	$0.369372\pi$
$102$		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	0.973504	−	0.228670i	$-0.0734376\pi$
$107$	824.395	+	824.395i	0.744834	+	0.744834i	−0.228670	+	0.973504i	$0.573438\pi$
$108$		0			0
$109$	−675.079	+	675.079i	−0.593219	+	0.593219i	−0.938500	−	0.345281i	$-0.887784\pi$
$109$	−675.079	+	675.079i	−0.593219	+	0.593219i	0.345281	+	0.938500i	$0.387784\pi$
$110$	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	$0.144338\pi$
$113$			1052.43i			0.876141i	−0.898941	+	0.438070i	$0.855662\pi$
$114$		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	$-0.988534\pi$
$127$		−	103.084i		−	0.0720254i	0.999351	−	0.0360127i	$-0.0114657\pi$
$128$	−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	−0.505460	−	0.862850i	$-0.668677\pi$
$131$	535.858	−	535.858i	0.357390	−	0.357390i	0.862850	+	0.505460i	$0.168677\pi$
$132$		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	−0.153775	−	0.988106i	$-0.549143\pi$
$139$	1367.29	−	1367.29i	0.834331	−	0.834331i	0.988106	+	0.153775i	$0.0491429\pi$
$140$	−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	−0.483313	−	0.875448i	$-0.660567\pi$
$149$	713.205	−	713.205i	0.392135	−	0.392135i	0.875448	+	0.483313i	$0.160567\pi$
$150$		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	−0.978390	−	0.206768i	$-0.933706\pi$
$157$	−1517.94	+	1517.94i	−0.771622	+	0.771622i	0.206768	+	0.978390i	$0.433706\pi$
$158$	−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	0.961967	−	0.273165i	$-0.0880705\pi$
$163$	1433.43	+	1433.43i	0.688802	+	0.688802i	−0.273165	+	0.961967i	$0.588070\pi$
$164$	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	$-0.881108\pi$
$167$		−	1574.93i		−	0.729771i	0.931052	−	0.364886i	$-0.118892\pi$
$168$		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	−0.999777	−	0.0211385i	$-0.993271\pi$
$173$	−2323.05	−	2323.05i	−1.02092	−	1.02092i	−0.0211385	−	0.999777i	$-0.506729\pi$
$174$		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	−0.0445458	+	0.999007i	$0.514184\pi$
$179$	−2499.16	+	2499.16i	−1.04355	+	1.04355i	−0.999007	+	0.0445458i	$0.985816\pi$
$180$		0			0
$181$	1207.94	+	1207.94i	0.496053	+	0.496053i	0.910207	−	0.414154i	$-0.135922\pi$
$181$	1207.94	+	1207.94i	0.496053	+	0.496053i	−0.414154	+	0.910207i	$0.635922\pi$
$182$	−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	−0.921708	−	0.387884i	$-0.873206\pi$
$197$	−1476.04	+	1476.04i	−0.533824	+	0.533824i	0.387884	+	0.921708i	$0.373206\pi$
$198$		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	0.999676	+	0.0254381i	$0.00809808\pi$
$211$	3141.93	+	3141.93i	1.02511	+	1.02511i	0.0254381	+	0.999676i	$0.491902\pi$
$212$	−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	$0.0416812\pi$
$223$			869.633i			0.261143i	−0.991439	+	0.130572i	$0.958319\pi$
$224$	−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	−0.860829	−	0.508894i	$-0.830055\pi$
$227$	−1203.65	+	1203.65i	−0.351935	+	0.351935i	0.508894	+	0.860829i	$0.330055\pi$
$228$		0			0
$229$	3001.80	+	3001.80i	0.866220	+	0.866220i	0.992052	−	0.125832i	$-0.0401599\pi$
$229$	3001.80	+	3001.80i	0.866220	+	0.866220i	−0.125832	+	0.992052i	$0.540160\pi$
$230$	−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	0.988099	−	0.153821i	$-0.0491581\pi$
$251$	3317.58	+	3317.58i	0.834277	+	0.834277i	−0.153821	+	0.988099i	$0.549158\pi$
$252$		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	$-0.659011\pi$
$257$		−	7233.11i		−	1.75560i	0.479028	−	0.877800i	$-0.340989\pi$
$258$		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	$0.311770\pi$
$263$			7081.78i			1.66039i	−0.557476	+	0.830193i	$0.688230\pi$
$264$		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	0.547318	−	0.836925i	$-0.315649\pi$
$269$	−1277.73	−	1277.73i	−0.289607	−	0.289607i	−0.836925	+	0.547318i	$0.815649\pi$
$270$		0			0
$271$			5785.88i			1.29693i	0.761246	+	0.648463i	$0.224588\pi$
$271$			5785.88i			1.29693i	−0.761246	+	0.648463i	$0.775412\pi$
$272$	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	0.907247	−	0.420598i	$-0.138180\pi$
$277$	2243.55	+	2243.55i	0.486648	+	0.486648i	−0.420598	+	0.907247i	$0.638180\pi$
$278$	−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	−0.999983	−	0.00585324i	$-0.998137\pi$
$283$	−4732.85	+	4732.85i	−0.994130	+	0.994130i	0.00585324	+	0.999983i	$0.498137\pi$
$284$	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	−0.768756	−	0.639542i	$-0.779124\pi$
$293$	−648.055	+	648.055i	−0.129214	+	0.129214i	0.639542	+	0.768756i	$0.279124\pi$
$294$		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	0.948891	−	0.315604i	$-0.102207\pi$
$307$	3406.50	+	3406.50i	0.633288	+	0.633288i	−0.315604	+	0.948891i	$0.602207\pi$
$308$	−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	$-0.747737\pi$
$311$		−	7811.27i		−	1.42423i	0.702061	−	0.712117i	$-0.252263\pi$
$312$		0			0
$313$			3161.73i			0.570963i	0.958384	+	0.285481i	$0.0921535\pi$
$313$			3161.73i			0.570963i	−0.958384	+	0.285481i	$0.907847\pi$
$314$	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	0.734758	−	0.678330i	$-0.237296\pi$
$317$	318.480	+	318.480i	0.0564278	+	0.0564278i	−0.678330	+	0.734758i	$0.737296\pi$
$318$		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	−0.514515	−	0.857481i	$-0.672028\pi$
$331$	2065.35	−	2065.35i	0.342966	−	0.342966i	0.857481	+	0.514515i	$0.172028\pi$
$332$	−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	0.945213	−	0.326454i	$-0.105854\pi$
$347$	3999.59	+	3999.59i	0.618759	+	0.618759i	−0.326454	+	0.945213i	$0.605854\pi$
$348$		0			0
$349$	1482.98	−	1482.98i	0.227456	−	0.227456i	−0.584173	−	0.811629i	$-0.698581\pi$
$349$	1482.98	−	1482.98i	0.227456	−	0.227456i	0.811629	+	0.584173i	$0.198581\pi$
$350$	−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	$0.170041\pi$
$353$			6753.68i			1.01831i	−0.860676	+	0.509153i	$0.829959\pi$
$354$		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	$0.206950\pi$
$359$			8234.72i			1.21062i	−0.795991	+	0.605309i	$0.793050\pi$
$360$		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	$-0.869997\pi$
$367$		−	5584.58i		−	0.794312i	0.917751	−	0.397156i	$-0.130003\pi$
$368$	−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	0.448946	−	0.893559i	$-0.351800\pi$
$373$	−3202.91	−	3202.91i	−0.444613	−	0.444613i	−0.893559	+	0.448946i	$0.851800\pi$
$374$	−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	−0.708570	−	0.705641i	$-0.750659\pi$
$379$	−21.6142	+	21.6142i	−0.00292941	+	0.00292941i	0.705641	+	0.708570i	$0.250659\pi$
$380$	−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	−0.330196	−	0.943912i	$-0.607115\pi$
$389$	4708.60	−	4708.60i	0.613716	−	0.613716i	0.943912	+	0.330196i	$0.107115\pi$
$390$		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	−0.0603890	−	0.998175i	$-0.519234\pi$
$397$	7418.04	−	7418.04i	0.937786	−	0.937786i	0.998175	+	0.0603890i	$0.0192341\pi$
$398$	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	$-0.687129\pi$
$401$		−	13363.8i		−	1.66423i	0.554600	−	0.832117i	$-0.312871\pi$
$402$		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	$0.0344059\pi$
$409$			1784.64i			0.215758i	−0.994164	+	0.107879i	$0.965594\pi$
$410$	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	0.284650	−	0.958632i	$-0.408123\pi$
$419$	10663.3	−	10663.3i	1.24328	−	1.24328i	0.958632	−	0.284650i	$-0.0918774\pi$
$420$		0			0
$421$	1980.40	+	1980.40i	0.229261	+	0.229261i	0.812384	−	0.583123i	$-0.198169\pi$
$421$	1980.40	+	1980.40i	0.229261	+	0.229261i	−0.583123	+	0.812384i	$0.698169\pi$
$422$	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	0.0217894	−	0.999763i	$-0.493064\pi$
$443$	−9118.69	−	9118.69i	−0.977973	−	0.977973i	−0.999763	+	0.0217894i	$0.993064\pi$
$444$		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	$0.0530063\pi$
$449$			3154.04i			0.331511i	−0.986167	+	0.165756i	$0.946994\pi$
$450$		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	$0.271217\pi$
$457$			14705.8i			1.50527i	−0.658440	+	0.752633i	$0.728783\pi$
$458$	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	0.999651	−	0.0264114i	$-0.00840799\pi$
$461$	9633.21	+	9633.21i	0.973240	+	0.973240i	−0.0264114	+	0.999651i	$0.508408\pi$
$462$		0			0
$463$		−	13731.1i		−	1.37827i	−0.724632	−	0.689136i	$-0.757990\pi$
$463$		−	13731.1i		−	1.37827i	0.724632	−	0.689136i	$-0.242010\pi$
$464$	−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	−0.639370	−	0.768899i	$-0.720805\pi$
$467$	1307.20	−	1307.20i	0.129529	−	0.129529i	0.768899	+	0.639370i	$0.220805\pi$
$468$		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	0.103137	−	0.994667i	$-0.467112\pi$
$491$	−9699.69	−	9699.69i	−0.891530	−	0.891530i	−0.994667	+	0.103137i	$0.967112\pi$
$492$		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	0.147801	−	0.989017i	$-0.452780\pi$
$499$	−9376.88	−	9376.88i	−0.841216	−	0.841216i	−0.989017	+	0.147801i	$0.952780\pi$
$500$	−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	$0.138277\pi$
$503$			9495.92i			0.841753i	−0.907118	+	0.420877i	$0.861723\pi$
$504$		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	0.909530	−	0.415638i	$-0.136442\pi$
$509$	5671.64	+	5671.64i	0.493892	+	0.493892i	−0.415638	+	0.909530i	$0.636442\pi$
$510$		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	−0.781565	−	0.623824i	$-0.785578\pi$
$523$	−1886.67	+	1886.67i	−0.157741	+	0.157741i	0.623824	+	0.781565i	$0.285578\pi$
$524$	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	−0.801791	−	0.597605i	$-0.796119\pi$
$541$	−2569.34	+	2569.34i	−0.204186	+	0.204186i	0.597605	+	0.801791i	$0.296119\pi$
$542$	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	0.981764	−	0.190102i	$-0.0608820\pi$
$547$	10127.9	+	10127.9i	0.791662	+	0.791662i	−0.190102	+	0.981764i	$0.560882\pi$
$548$	−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	0.988938	−	0.148327i	$-0.0473887\pi$
$557$	11050.4	+	11050.4i	0.840612	+	0.840612i	−0.148327	+	0.988938i	$0.547389\pi$
$558$		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	−0.813582	−	0.581450i	$-0.802485\pi$
$563$	−3100.96	+	3100.96i	−0.232131	+	0.232131i	0.581450	+	0.813582i	$0.302485\pi$
$564$		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	−0.886394	−	0.462932i	$-0.846797\pi$
$571$	−5777.87	+	5777.87i	−0.423461	+	0.423461i	0.462932	+	0.886394i	$0.346797\pi$
$572$	−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	0.424853	−	0.905262i	$-0.360326\pi$
$587$	−6832.33	−	6832.33i	−0.480410	−	0.480410i	−0.905262	+	0.424853i	$0.860326\pi$
$588$		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	$-0.957913\pi$
$593$		−	3807.51i		−	0.263669i	0.991272	−	0.131835i	$-0.0420868\pi$
$594$		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	$0.0188055\pi$
$599$			1731.22i			0.118090i	−0.998255	+	0.0590449i	$0.981194\pi$
$600$		0			0
$601$			21704.9i			1.47315i	0.676356	+	0.736575i	$0.263558\pi$
$601$			21704.9i			1.47315i	−0.676356	+	0.736575i	$0.736442\pi$
$602$	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	$0.222300\pi$
$607$			19231.2i			1.28595i	−0.765888	+	0.642974i	$0.777700\pi$
$608$	−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	0.303508	−	0.952829i	$-0.401842\pi$
$613$	−9854.85	−	9854.85i	−0.649321	−	0.649321i	−0.952829	+	0.303508i	$0.901842\pi$
$614$	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	−0.876501	−	0.481399i	$-0.840129\pi$
$619$	−6084.79	+	6084.79i	−0.395102	+	0.395102i	0.481399	+	0.876501i	$0.340129\pi$
$620$	−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	$-0.975260\pi$
$641$		−	2520.18i		−	0.155290i	0.996981	−	0.0776451i	$-0.0247401\pi$
$642$		0			0
$643$	−9626.14	−	9626.14i	−0.590386	−	0.590386i	0.347350	−	0.937736i	$-0.387082\pi$
$643$	−9626.14	−	9626.14i	−0.590386	−	0.590386i	−0.937736	+	0.347350i	$0.887082\pi$
$644$	−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	$0.0173765\pi$
$647$			1795.90i			0.109126i	−0.998510	+	0.0545628i	$0.982623\pi$
$648$		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	0.769271	−	0.638922i	$-0.220620\pi$
$653$	2175.09	+	2175.09i	0.130349	+	0.130349i	−0.638922	+	0.769271i	$0.720620\pi$
$654$		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	−0.999193	−	0.0401752i	$-0.987208\pi$
$659$	−16223.9	+	16223.9i	−0.959017	+	0.959017i	0.0401752	+	0.999193i	$0.487208\pi$
$660$		0			0
$661$	−2953.68	−	2953.68i	−0.173805	−	0.173805i	0.614844	−	0.788649i	$-0.289219\pi$
$661$	−2953.68	−	2953.68i	−0.173805	−	0.173805i	−0.788649	+	0.614844i	$0.789219\pi$
$662$	−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	−0.618238	−	0.785991i	$-0.712153\pi$
$677$	2954.97	−	2954.97i	0.167753	−	0.167753i	0.785991	+	0.618238i	$0.212153\pi$
$678$		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	0.868224	−	0.496172i	$-0.165261\pi$
$683$	6641.03	+	6641.03i	0.372053	+	0.372053i	−0.496172	+	0.868224i	$0.665261\pi$
$684$		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	0.0187097	−	0.999825i	$-0.494044\pi$
$691$	−17821.2	−	17821.2i	−0.981115	−	0.981115i	−0.999825	+	0.0187097i	$0.994044\pi$
$692$	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	−0.999681	−	0.0252614i	$-0.991958\pi$
$701$	−19022.9	−	19022.9i	−1.02494	−	1.02494i	−0.0252614	−	0.999681i	$-0.508042\pi$
$702$		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	0.985006	−	0.172521i	$-0.0551912\pi$
$709$	15338.6	+	15338.6i	0.812485	+	0.812485i	−0.172521	+	0.985006i	$0.555191\pi$
$710$	−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	−0.493025	−	0.870015i	$-0.664109\pi$
$733$	7481.44	−	7481.44i	0.376989	−	0.376989i	0.870015	+	0.493025i	$0.164109\pi$
$734$	−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	0.961684	+	0.274160i	$0.0883998\pi$
$739$	24827.3	+	24827.3i	1.23584	+	1.23584i	0.274160	+	0.961684i	$0.411600\pi$
$740$	−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	$0.135120\pi$
$743$			16682.5i			0.823716i	−0.911248	+	0.411858i	$0.864880\pi$
$744$		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	$-0.820760\pi$
$751$		−	21972.3i		−	1.06762i	0.845605	−	0.533809i	$-0.179240\pi$
$752$	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	0.296502	−	0.955032i	$-0.404180\pi$
$757$	−13715.8	−	13715.8i	−0.658530	−	0.658530i	−0.955032	+	0.296502i	$0.904180\pi$
$758$	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	−0.879510	−	0.475880i	$-0.842130\pi$
$773$	−8674.66	+	8674.66i	−0.403630	+	0.403630i	0.475880	+	0.879510i	$0.342130\pi$
$774$		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	0.839050	−	0.544054i	$-0.183111\pi$
$787$	6512.95	+	6512.95i	0.294996	+	0.294996i	−0.544054	+	0.839050i	$0.683111\pi$
$788$	−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	0.905583	−	0.424169i	$-0.139434\pi$
$797$	10831.9	+	10831.9i	0.481413	+	0.481413i	−0.424169	+	0.905583i	$0.639434\pi$
$798$		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	−0.953514	−	0.301347i	$-0.902564\pi$
$811$	−15062.3	+	15062.3i	−0.652167	+	0.652167i	0.301347	+	0.953514i	$0.402564\pi$
$812$	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	0.0469030	−	0.998899i	$-0.485065\pi$
$821$	24601.7	−	24601.7i	1.04580	−	1.04580i	0.998899	−	0.0469030i	$-0.0149352\pi$
$822$		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	0.990632	+	0.136560i	$0.0436045\pi$
$827$	26807.5	+	26807.5i	1.12719	+	1.12719i	0.136560	+	0.990632i	$0.456396\pi$
$828$		0			0
$829$	−3214.77	+	3214.77i	−0.134685	+	0.134685i	−0.771235	−	0.636550i	$-0.780361\pi$
$829$	−3214.77	+	3214.77i	−0.134685	+	0.134685i	0.636550	+	0.771235i	$0.280361\pi$
$830$	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	$0.318322\pi$
$839$			40899.9i			1.68298i	−0.540271	+	0.841491i	$0.681678\pi$
$840$		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	0.989952	−	0.141407i	$-0.0451626\pi$
$853$	21139.7	+	21139.7i	0.848545	+	0.848545i	−0.141407	+	0.989952i	$0.545163\pi$
$854$	−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	−0.936575	−	0.350468i	$-0.886023\pi$
$859$	−14755.9	+	14755.9i	−0.586107	+	0.586107i	0.350468	+	0.936575i	$0.386023\pi$
$860$	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	−0.295839	−	0.955238i	$-0.595599\pi$
$877$	17125.7	−	17125.7i	0.659399	−	0.659399i	0.955238	+	0.295839i	$0.0955991\pi$
$878$	−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	$-0.774492\pi$
$881$		−	34029.0i		−	1.30132i	0.759368	−	0.650662i	$-0.225508\pi$
$882$		0			0
$883$	7536.29	+	7536.29i	0.287221	+	0.287221i	0.835981	−	0.548759i	$-0.184900\pi$
$883$	7536.29	+	7536.29i	0.287221	+	0.287221i	−0.548759	+	0.835981i	$0.684900\pi$
$884$	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	$-0.928456\pi$
$887$		−	11775.4i		−	0.445749i	0.974847	−	0.222875i	$-0.0715441\pi$
$888$		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	−0.108287	−	0.994120i	$-0.534537\pi$
$907$	24197.1	−	24197.1i	0.885833	−	0.885833i	0.994120	+	0.108287i	$0.0345365\pi$
$908$	−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	$0.112362\pi$
$929$			19578.0i			0.691423i	−0.938341	+	0.345712i	$0.887638\pi$
$930$		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	$-0.864388\pi$
$937$		−	23706.5i		−	0.826530i	0.910611	−	0.413265i	$-0.135612\pi$
$938$	−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	0.698096	−	0.716004i	$-0.254031\pi$
$941$	−516.925	−	516.925i	−0.0179078	−	0.0179078i	−0.716004	+	0.698096i	$0.754031\pi$
$942$		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	−0.851733	−	0.523976i	$-0.824448\pi$
$947$	−9551.64	+	9551.64i	−0.327758	+	0.327758i	0.523976	+	0.851733i	$0.324448\pi$
$948$		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	−0.985014	−	0.172477i	$-0.944823\pi$
$971$	−35022.4	−	35022.4i	−1.15749	−	1.15749i	−0.172477	−	0.985014i	$-0.555177\pi$
$972$		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	$0.249905\pi$
$977$			43174.5i			1.41379i	−0.707317	+	0.706897i	$0.750095\pi$
$978$		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	$-0.749170\pi$
$983$		−	43699.4i		−	1.41790i	0.705260	−	0.708949i	$-0.250830\pi$
$984$		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	$0.0425949\pi$
$991$			8324.37i			0.266834i	−0.991060	+	0.133417i	$0.957405\pi$
$992$	−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	0.698096	−	0.716005i	$-0.254031\pi$
$997$	−563.783	−	563.783i	−0.0179089	−	0.0179089i	−0.716005	+	0.698096i	$0.754031\pi$
$998$	−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.107.8	yes	48
3.2	odd	2	inner	144.4.l.a.107.17	yes	48
4.3	odd	2		576.4.l.a.143.14		48
8.3	odd	2		1152.4.l.a.287.11		48
8.5	even	2		1152.4.l.b.287.11		48
12.11	even	2		576.4.l.a.143.11		48
16.3	odd	4	inner	144.4.l.a.35.17	yes	48
16.5	even	4		1152.4.l.a.863.14		48
16.11	odd	4		1152.4.l.b.863.14		48
16.13	even	4		576.4.l.a.431.11		48
24.5	odd	2		1152.4.l.b.287.14		48
24.11	even	2		1152.4.l.a.287.14		48
48.5	odd	4		1152.4.l.a.863.11		48
48.11	even	4		1152.4.l.b.863.11		48
48.29	odd	4		576.4.l.a.431.14		48
48.35	even	4	inner	144.4.l.a.35.8	✓	48

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
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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