LMFDB - Embedded newform 640.3.t.a.353.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,3,Mod(353,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("640.353");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	640.t (of order $4$, degree $2$, not 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:	$17.4387369191$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			353.16
Character	$\chi$	$=$	640.353
Dual form			640.3.t.a.417.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.77329 q^{3} +(2.05735 - 4.55712i) q^{5} +(-5.39242 - 5.39242i) q^{7} -1.30888 q^{9} +O(q^{10})$	\(q+2.77329 q^{3} +(2.05735 - 4.55712i) q^{5} +(-5.39242 - 5.39242i) q^{7} -1.30888 q^{9} +(2.98007 + 2.98007i) q^{11} -21.2000 q^{13} +(5.70562 - 12.6382i) q^{15} +(6.66924 - 6.66924i) q^{17} +(-14.3102 - 14.3102i) q^{19} +(-14.9547 - 14.9547i) q^{21} +(2.07267 - 2.07267i) q^{23} +(-16.5346 - 18.7512i) q^{25} -28.5895 q^{27} +(17.5413 + 17.5413i) q^{29} +23.6474 q^{31} +(8.26459 + 8.26459i) q^{33} +(-35.6680 + 13.4798i) q^{35} -65.3234 q^{37} -58.7936 q^{39} +1.18249i q^{41} +9.57434i q^{43} +(-2.69282 + 5.96472i) q^{45} +(47.2286 - 47.2286i) q^{47} +9.15649i q^{49} +(18.4957 - 18.4957i) q^{51} +99.2178i q^{53} +(19.7116 - 7.44949i) q^{55} +(-39.6863 - 39.6863i) q^{57} +(54.7400 - 54.7400i) q^{59} +(12.1054 - 12.1054i) q^{61} +(7.05803 + 7.05803i) q^{63} +(-43.6157 + 96.6108i) q^{65} -109.074i q^{67} +(5.74812 - 5.74812i) q^{69} -73.1674i q^{71} +(-17.0166 + 17.0166i) q^{73} +(-45.8553 - 52.0023i) q^{75} -32.1396i q^{77} +2.15129i q^{79} -67.5069 q^{81} +76.4850 q^{83} +(-16.6716 - 44.1134i) q^{85} +(48.6470 + 48.6470i) q^{87} +38.7296 q^{89} +(114.319 + 114.319i) q^{91} +65.5810 q^{93} +(-94.6543 + 35.7722i) q^{95} +(8.53929 - 8.53929i) q^{97} +(-3.90055 - 3.90055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4 q^{3} + 2 q^{5} + 108 q^{9}+O(q^{10}) $ 44 * q - 4 * q^3 + 2 * q^5 + 108 * q^9	$ 44 q - 4 q^{3} + 2 q^{5} + 108 q^{9} - 4 q^{11} + 4 q^{13} + 4 q^{15} - 4 q^{17} - 32 q^{19} + 4 q^{21} - 40 q^{27} + 8 q^{31} - 4 q^{33} - 4 q^{35} + 4 q^{37} + 72 q^{39} + 70 q^{45} + 4 q^{47} - 100 q^{51} - 36 q^{57} - 64 q^{59} + 36 q^{61} + 200 q^{63} - 4 q^{65} - 60 q^{69} - 48 q^{73} - 324 q^{75} + 100 q^{81} + 156 q^{83} + 52 q^{85} + 36 q^{87} + 188 q^{91} + 40 q^{93} - 380 q^{95} - 4 q^{97} + 92 q^{99}+O(q^{100}) $ 44 * q - 4 * q^3 + 2 * q^5 + 108 * q^9 - 4 * q^11 + 4 * q^13 + 4 * q^15 - 4 * q^17 - 32 * q^19 + 4 * q^21 - 40 * q^27 + 8 * q^31 - 4 * q^33 - 4 * q^35 + 4 * q^37 + 72 * q^39 + 70 * q^45 + 4 * q^47 - 100 * q^51 - 36 * q^57 - 64 * q^59 + 36 * q^61 + 200 * q^63 - 4 * q^65 - 60 * q^69 - 48 * q^73 - 324 * q^75 + 100 * q^81 + 156 * q^83 + 52 * q^85 + 36 * q^87 + 188 * q^91 + 40 * q^93 - 380 * q^95 - 4 * q^97 + 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	2.77329			0.924429			0.462215	−	0.886768i	$-0.347055\pi$
$3$	2.77329			0.924429			0.462215	+	0.886768i	$0.347055\pi$
$4$		0			0
$5$	2.05735	−	4.55712i	0.411470	−	0.911424i
$5$	2.05735	−	4.55712i	0.411470	−	0.911424i
$6$		0			0
$7$	−5.39242	−	5.39242i	−0.770346	−	0.770346i	0.207821	−	0.978167i	$-0.433363\pi$
$7$	−5.39242	−	5.39242i	−0.770346	−	0.770346i	−0.978167	+	0.207821i	$0.933363\pi$
$8$		0			0
$9$	−1.30888			−0.145431
$10$		0			0
$11$	2.98007	+	2.98007i	0.270915	+	0.270915i	0.829469	−	0.558553i	$-0.188643\pi$
$11$	2.98007	+	2.98007i	0.270915	+	0.270915i	−0.558553	+	0.829469i	$0.688643\pi$
$12$		0			0
$13$	−21.2000			−1.63077			−0.815383	−	0.578921i	$-0.803474\pi$
$13$	−21.2000			−1.63077			−0.815383	+	0.578921i	$0.803474\pi$
$14$		0			0
$15$	5.70562	−	12.6382i	0.380374	−	0.842546i
$16$		0			0
$17$	6.66924	−	6.66924i	0.392308	−	0.392308i	−0.483201	−	0.875509i	$-0.660526\pi$
$17$	6.66924	−	6.66924i	0.392308	−	0.392308i	0.875509	+	0.483201i	$0.160526\pi$
$18$		0			0
$19$	−14.3102	−	14.3102i	−0.753169	−	0.753169i	0.221901	−	0.975069i	$-0.428774\pi$
$19$	−14.3102	−	14.3102i	−0.753169	−	0.753169i	−0.975069	+	0.221901i	$0.928774\pi$
$20$		0			0
$21$	−14.9547	−	14.9547i	−0.712131	−	0.712131i
$22$		0			0
$23$	2.07267	−	2.07267i	0.0901163	−	0.0901163i	−0.660612	−	0.750728i	$-0.729703\pi$
$23$	2.07267	−	2.07267i	0.0901163	−	0.0901163i	0.750728	+	0.660612i	$0.229703\pi$
$24$		0			0
$25$	−16.5346	−	18.7512i	−0.661386	−	0.750046i
$26$		0			0
$27$	−28.5895			−1.05887
$28$		0			0
$29$	17.5413	+	17.5413i	0.604872	+	0.604872i	0.941601	−	0.336730i	$-0.109321\pi$
$29$	17.5413	+	17.5413i	0.604872	+	0.604872i	−0.336730	+	0.941601i	$0.609321\pi$
$30$		0			0
$31$	23.6474			0.762819			0.381410	−	0.924406i	$-0.375439\pi$
$31$	23.6474			0.762819			0.381410	+	0.924406i	$0.375439\pi$
$32$		0			0
$33$	8.26459	+	8.26459i	0.250442	+	0.250442i
$34$		0			0
$35$	−35.6680	+	13.4798i	−1.01909	+	0.385138i
$36$		0			0
$37$	−65.3234			−1.76550			−0.882749	−	0.469845i	$-0.844310\pi$
$37$	−65.3234			−1.76550			−0.882749	+	0.469845i	$0.844310\pi$
$38$		0			0
$39$	−58.7936			−1.50753
$40$		0			0
$41$			1.18249i			0.0288413i	0.999896	+	0.0144207i	$0.00459040\pi$
$41$			1.18249i			0.0288413i	−0.999896	+	0.0144207i	$0.995410\pi$
$42$		0			0
$43$			9.57434i			0.222659i	0.993784	+	0.111330i	$0.0355109\pi$
$43$			9.57434i			0.222659i	−0.993784	+	0.111330i	$0.964489\pi$
$44$		0			0
$45$	−2.69282	+	5.96472i	−0.0598404	+	0.132549i
$46$		0			0
$47$	47.2286	−	47.2286i	1.00486	−	1.00486i	0.00487524	−	0.999988i	$-0.498448\pi$
$47$	47.2286	−	47.2286i	1.00486	−	1.00486i	0.999988	−	0.00487524i	$-0.00155184\pi$
$48$		0			0
$49$			9.15649i			0.186867i
$50$		0			0
$51$	18.4957	−	18.4957i	0.362661	−	0.362661i
$52$		0			0
$53$			99.2178i			1.87203i	0.351955	+	0.936017i	$0.385517\pi$
$53$			99.2178i			1.87203i	−0.351955	+	0.936017i	$0.614483\pi$
$54$		0			0
$55$	19.7116	−	7.44949i	0.358392	−	0.135445i
$56$		0			0
$57$	−39.6863	−	39.6863i	−0.696251	−	0.696251i
$58$		0			0
$59$	54.7400	−	54.7400i	0.927796	−	0.927796i	−0.0697673	−	0.997563i	$-0.522226\pi$
$59$	54.7400	−	54.7400i	0.927796	−	0.927796i	0.997563	+	0.0697673i	$0.0222257\pi$
$60$		0			0
$61$	12.1054	−	12.1054i	0.198449	−	0.198449i	−0.600886	−	0.799335i	$-0.705185\pi$
$61$	12.1054	−	12.1054i	0.198449	−	0.198449i	0.799335	+	0.600886i	$0.205185\pi$
$62$		0			0
$63$	7.05803	+	7.05803i	0.112032	+	0.112032i
$64$		0			0
$65$	−43.6157	+	96.6108i	−0.671011	+	1.48632i
$66$		0			0
$67$		−	109.074i		−	1.62798i	−0.580882	−	0.813988i	$-0.697292\pi$
$67$		−	109.074i		−	1.62798i	0.580882	−	0.813988i	$-0.302708\pi$
$68$		0			0
$69$	5.74812	−	5.74812i	0.0833061	−	0.0833061i
$70$		0			0
$71$		−	73.1674i		−	1.03053i	−0.857032	−	0.515263i	$-0.827694\pi$
$71$		−	73.1674i		−	1.03053i	0.857032	−	0.515263i	$-0.172306\pi$
$72$		0			0
$73$	−17.0166	+	17.0166i	−0.233103	+	0.233103i	−0.813987	−	0.580883i	$-0.802707\pi$
$73$	−17.0166	+	17.0166i	−0.233103	+	0.233103i	0.580883	+	0.813987i	$0.302707\pi$
$74$		0			0
$75$	−45.8553	−	52.0023i	−0.611404	−	0.693364i
$76$		0			0
$77$		−	32.1396i		−	0.417397i
$78$		0			0
$79$			2.15129i			0.0272315i	0.999907	+	0.0136157i	$0.00433416\pi$
$79$			2.15129i			0.0272315i	−0.999907	+	0.0136157i	$0.995666\pi$
$80$		0			0
$81$	−67.5069			−0.833419
$82$		0			0
$83$	76.4850			0.921506			0.460753	−	0.887528i	$-0.347579\pi$
$83$	76.4850			0.921506			0.460753	+	0.887528i	$0.347579\pi$
$84$		0			0
$85$	−16.6716	−	44.1134i	−0.196136	−	0.518982i
$86$		0			0
$87$	48.6470	+	48.6470i	0.559161	+	0.559161i
$88$		0			0
$89$	38.7296			0.435164			0.217582	−	0.976042i	$-0.430183\pi$
$89$	38.7296			0.435164			0.217582	+	0.976042i	$0.430183\pi$
$90$		0			0
$91$	114.319	+	114.319i	1.25626	+	1.25626i
$92$		0			0
$93$	65.5810			0.705172
$94$		0			0
$95$	−94.6543	+	35.7722i	−0.996361	+	0.376550i
$96$		0			0
$97$	8.53929	−	8.53929i	0.0880339	−	0.0880339i	−0.661718	−	0.749752i	$-0.730173\pi$
$97$	8.53929	−	8.53929i	0.0880339	−	0.0880339i	0.749752	+	0.661718i	$0.230173\pi$
$98$		0			0
$99$	−3.90055	−	3.90055i	−0.0393995	−	0.0393995i
$100$		0			0
$101$	−65.0118	−	65.0118i	−0.643681	−	0.643681i	0.307777	−	0.951458i	$-0.400415\pi$
$101$	−65.0118	−	65.0118i	−0.643681	−	0.643681i	−0.951458	+	0.307777i	$0.900415\pi$
$102$		0			0
$103$	32.9039	−	32.9039i	0.319456	−	0.319456i	−0.529102	−	0.848558i	$-0.677471\pi$
$103$	32.9039	−	32.9039i	0.319456	−	0.319456i	0.848558	+	0.529102i	$0.177471\pi$
$104$		0			0
$105$	−98.9176	+	37.3834i	−0.942073	+	0.356033i
$106$		0			0
$107$	−19.9537			−0.186484			−0.0932418	−	0.995643i	$-0.529723\pi$
$107$	−19.9537			−0.186484			−0.0932418	+	0.995643i	$0.529723\pi$
$108$		0			0
$109$	−31.4162	−	31.4162i	−0.288222	−	0.288222i	0.548155	−	0.836377i	$-0.315330\pi$
$109$	−31.4162	−	31.4162i	−0.288222	−	0.288222i	−0.836377	+	0.548155i	$0.815330\pi$
$110$		0			0
$111$	−181.161			−1.63208
$112$		0			0
$113$	−48.1807	−	48.1807i	−0.426378	−	0.426378i	0.461014	−	0.887393i	$-0.347486\pi$
$113$	−48.1807	−	48.1807i	−0.426378	−	0.426378i	−0.887393	+	0.461014i	$0.847486\pi$
$114$		0			0
$115$	−5.18121	−	13.7096i	−0.0450540	−	0.119214i
$116$		0			0
$117$	27.7482			0.237164
$118$		0			0
$119$	−71.9267			−0.604426
$120$		0			0
$121$		−	103.238i		−	0.853210i
$122$		0			0
$123$			3.27939i			0.0266617i
$124$		0			0
$125$	−119.469	+	36.7727i	−0.955750	+	0.294181i
$126$		0			0
$127$	165.164	−	165.164i	1.30051	−	1.30051i	0.372456	−	0.928050i	$-0.378516\pi$
$127$	165.164	−	165.164i	1.30051	−	1.30051i	0.928050	−	0.372456i	$-0.121484\pi$
$128$		0			0
$129$			26.5524i			0.205832i
$130$		0			0
$131$	10.9705	−	10.9705i	0.0837444	−	0.0837444i	−0.663994	−	0.747738i	$-0.731140\pi$
$131$	10.9705	−	10.9705i	0.0837444	−	0.0837444i	0.747738	+	0.663994i	$0.231140\pi$
$132$		0			0
$133$			154.333i			1.16040i
$134$		0			0
$135$	−58.8185	+	130.286i	−0.435693	+	0.965079i
$136$		0			0
$137$	122.401	+	122.401i	0.893436	+	0.893436i	0.994845	−	0.101408i	$-0.0323349\pi$
$137$	122.401	+	122.401i	0.893436	+	0.893436i	−0.101408	+	0.994845i	$0.532335\pi$
$138$		0			0
$139$	−163.514	+	163.514i	−1.17636	+	1.17636i	−0.195693	+	0.980665i	$0.562695\pi$
$139$	−163.514	+	163.514i	−1.17636	+	1.17636i	−0.980665	+	0.195693i	$0.937305\pi$
$140$		0			0
$141$	130.978	−	130.978i	0.928925	−	0.928925i
$142$		0			0
$143$	−63.1774	−	63.1774i	−0.441800	−	0.441800i
$144$		0			0
$145$	116.026	−	43.8492i	0.800181	−	0.302408i
$146$		0			0
$147$			25.3936i			0.172745i
$148$		0			0
$149$	182.956	−	182.956i	1.22789	−	1.22789i	0.263134	−	0.964759i	$-0.415244\pi$
$149$	182.956	−	182.956i	1.22789	−	1.22789i	0.964759	−	0.263134i	$-0.0847562\pi$
$150$		0			0
$151$			100.104i			0.662938i	0.943466	+	0.331469i	$0.107544\pi$
$151$			100.104i			0.662938i	−0.943466	+	0.331469i	$0.892456\pi$
$152$		0			0
$153$	−8.72923	+	8.72923i	−0.0570538	+	0.0570538i
$154$		0			0
$155$	48.6509	−	107.764i	0.313877	−	0.695251i
$156$		0			0
$157$			27.8875i			0.177627i	0.996048	+	0.0888136i	$0.0283076\pi$
$157$			27.8875i			0.177627i	−0.996048	+	0.0888136i	$0.971692\pi$
$158$		0			0
$159$			275.159i			1.73056i
$160$		0			0
$161$	−22.3535			−0.138841
$162$		0			0
$163$	−122.177			−0.749552			−0.374776	−	0.927115i	$-0.622280\pi$
$163$	−122.177			−0.749552			−0.374776	+	0.927115i	$0.622280\pi$
$164$		0			0
$165$	54.6658	−	20.6596i	0.331308	−	0.125209i
$166$		0			0
$167$	−102.217	−	102.217i	−0.612078	−	0.612078i	0.331409	−	0.943487i	$-0.392476\pi$
$167$	−102.217	−	102.217i	−0.612078	−	0.612078i	−0.943487	+	0.331409i	$0.892476\pi$
$168$		0			0
$169$	280.439			1.65940
$170$		0			0
$171$	18.7303	+	18.7303i	0.109534	+	0.109534i
$172$		0			0
$173$	−144.968			−0.837968			−0.418984	−	0.907994i	$-0.637614\pi$
$173$	−144.968			−0.837968			−0.418984	+	0.907994i	$0.637614\pi$
$174$		0			0
$175$	−11.9524	+	190.276i	−0.0682992	+	1.08729i
$176$		0			0
$177$	151.810	−	151.810i	0.857682	−	0.857682i
$178$		0			0
$179$	71.1438	+	71.1438i	0.397451	+	0.397451i	0.877333	−	0.479882i	$-0.159320\pi$
$179$	71.1438	+	71.1438i	0.397451	+	0.397451i	−0.479882	+	0.877333i	$0.659320\pi$
$180$		0			0
$181$	192.954	+	192.954i	1.06604	+	1.06604i	0.997659	+	0.0683832i	$0.0217841\pi$
$181$	192.954	+	192.954i	1.06604	+	1.06604i	0.0683832	+	0.997659i	$0.478216\pi$
$182$		0			0
$183$	33.5717	−	33.5717i	0.183452	−	0.183452i
$184$		0			0
$185$	−134.393	+	297.687i	−0.726449	+	1.60912i
$186$		0			0
$187$	39.7496			0.212565
$188$		0			0
$189$	154.167	+	154.167i	0.815696	+	0.815696i
$190$		0			0
$191$	209.558			1.09716			0.548581	−	0.836097i	$-0.315168\pi$
$191$	209.558			1.09716			0.548581	+	0.836097i	$0.315168\pi$
$192$		0			0
$193$	−90.2693	−	90.2693i	−0.467717	−	0.467717i	0.433457	−	0.901174i	$-0.357293\pi$
$193$	−90.2693	−	90.2693i	−0.467717	−	0.467717i	−0.901174	+	0.433457i	$0.857293\pi$
$194$		0			0
$195$	−120.959	+	267.929i	−0.620302	+	1.37400i
$196$		0			0
$197$	−67.8338			−0.344334			−0.172167	−	0.985068i	$-0.555077\pi$
$197$	−67.8338			−0.344334			−0.172167	+	0.985068i	$0.555077\pi$
$198$		0			0
$199$	278.771			1.40086			0.700430	−	0.713721i	$-0.252991\pi$
$199$	278.771			1.40086			0.700430	+	0.713721i	$0.252991\pi$
$200$		0			0
$201$		−	302.495i		−	1.50495i
$202$		0			0
$203$		−	189.180i		−	0.931922i
$204$		0			0
$205$	5.38876	+	2.43280i	0.0262866	+	0.0118673i
$206$		0			0
$207$	−2.71288	+	2.71288i	−0.0131057	+	0.0131057i
$208$		0			0
$209$		−	85.2908i		−	0.408090i
$210$		0			0
$211$	−26.5489	+	26.5489i	−0.125824	+	0.125824i	−0.767215	−	0.641391i	$-0.778358\pi$
$211$	−26.5489	+	26.5489i	−0.125824	+	0.125824i	0.641391	+	0.767215i	$0.278358\pi$
$212$		0			0
$213$		−	202.914i		−	0.952648i
$214$		0			0
$215$	43.6314	+	19.6977i	0.202937	+	0.0916174i
$216$		0			0
$217$	−127.517	−	127.517i	−0.587635	−	0.587635i
$218$		0			0
$219$	−47.1918	+	47.1918i	−0.215488	+	0.215488i
$220$		0			0
$221$	−141.388	+	141.388i	−0.639763	+	0.639763i
$222$		0			0
$223$	−90.1705	−	90.1705i	−0.404352	−	0.404352i	0.475412	−	0.879764i	$-0.342299\pi$
$223$	−90.1705	−	90.1705i	−0.404352	−	0.404352i	−0.879764	+	0.475412i	$0.842299\pi$
$224$		0			0
$225$	21.6418	+	24.5430i	0.0961860	+	0.109080i
$226$		0			0
$227$			346.057i			1.52448i	0.647294	+	0.762240i	$0.275900\pi$
$227$			346.057i			1.52448i	−0.647294	+	0.762240i	$0.724100\pi$
$228$		0			0
$229$	73.4761	−	73.4761i	0.320856	−	0.320856i	−0.528239	−	0.849096i	$-0.677148\pi$
$229$	73.4761	−	73.4761i	0.320856	−	0.320856i	0.849096	+	0.528239i	$0.177148\pi$
$230$		0			0
$231$		−	89.1323i		−	0.385854i
$232$		0			0
$233$	−86.7985	+	86.7985i	−0.372526	+	0.372526i	−0.868396	−	0.495871i	$-0.834849\pi$
$233$	−86.7985	+	86.7985i	−0.372526	+	0.372526i	0.495871	+	0.868396i	$0.334849\pi$
$234$		0			0
$235$	−118.061	−	312.392i	−0.502385	−	1.32933i
$236$		0			0
$237$			5.96613i			0.0251736i
$238$		0			0
$239$			204.791i			0.856868i	0.903573	+	0.428434i	$0.140935\pi$
$239$			204.791i			0.856868i	−0.903573	+	0.428434i	$0.859065\pi$
$240$		0			0
$241$	98.8804			0.410292			0.205146	−	0.978731i	$-0.434233\pi$
$241$	98.8804			0.410292			0.205146	+	0.978731i	$0.434233\pi$
$242$		0			0
$243$	70.0893			0.288433
$244$		0			0
$245$	41.7272	+	18.8381i	0.170315	+	0.0768902i
$246$		0			0
$247$	303.376	+	303.376i	1.22824	+	1.22824i
$248$		0			0
$249$	212.115			0.851867
$250$		0			0
$251$	−38.3371	−	38.3371i	−0.152737	−	0.152737i	0.626602	−	0.779339i	$-0.284445\pi$
$251$	−38.3371	−	38.3371i	−0.152737	−	0.152737i	−0.779339	+	0.626602i	$0.784445\pi$
$252$		0			0
$253$	12.3534			0.0488277
$254$		0			0
$255$	−46.2350	−	122.339i	−0.181314	−	0.479762i
$256$		0			0
$257$	166.481	−	166.481i	0.647785	−	0.647785i	−0.304672	−	0.952457i	$-0.598547\pi$
$257$	166.481	−	166.481i	0.647785	−	0.647785i	0.952457	+	0.304672i	$0.0985468\pi$
$258$		0			0
$259$	352.252	+	352.252i	1.36005	+	1.36005i
$260$		0			0
$261$	−22.9594	−	22.9594i	−0.0879671	−	0.0879671i
$262$		0			0
$263$	78.7097	−	78.7097i	0.299276	−	0.299276i	−0.541454	−	0.840730i	$-0.682126\pi$
$263$	78.7097	−	78.7097i	0.299276	−	0.299276i	0.840730	+	0.541454i	$0.182126\pi$
$264$		0			0
$265$	452.147	+	204.126i	1.70622	+	0.770285i
$266$		0			0
$267$	107.408			0.402279
$268$		0			0
$269$	98.2650	+	98.2650i	0.365297	+	0.365297i	0.865759	−	0.500461i	$-0.166836\pi$
$269$	98.2650	+	98.2650i	0.365297	+	0.365297i	−0.500461	+	0.865759i	$0.666836\pi$
$270$		0			0
$271$	115.967			0.427922			0.213961	−	0.976842i	$-0.431363\pi$
$271$	115.967			0.427922			0.213961	+	0.976842i	$0.431363\pi$
$272$		0			0
$273$	317.040	+	317.040i	1.16132	+	1.16132i
$274$		0			0
$275$	6.60535	−	105.154i	0.0240195	−	0.382378i
$276$		0			0
$277$	−340.610			−1.22964			−0.614819	−	0.788668i	$-0.710771\pi$
$277$	−340.610			−1.22964			−0.614819	+	0.788668i	$0.710771\pi$
$278$		0			0
$279$	−30.9516			−0.110938
$280$		0			0
$281$			103.541i			0.368474i	0.982882	+	0.184237i	$0.0589814\pi$
$281$			103.541i			0.368474i	−0.982882	+	0.184237i	$0.941019\pi$
$282$		0			0
$283$			561.986i			1.98582i	0.118887	+	0.992908i	$0.462068\pi$
$283$			561.986i			1.98582i	−0.118887	+	0.992908i	$0.537932\pi$
$284$		0			0
$285$	−262.504	+	99.2066i	−0.921065	+	0.348093i
$286$		0			0
$287$	6.37651	−	6.37651i	0.0222178	−	0.0222178i
$288$		0			0
$289$			200.043i			0.692189i
$290$		0			0
$291$	23.6819	−	23.6819i	0.0813811	−	0.0813811i
$292$		0			0
$293$		−	1.90920i		−	0.00651604i	−0.999995	−	0.00325802i	$-0.998963\pi$
$293$		−	1.90920i		−	0.00651604i	0.999995	−	0.00325802i	$-0.00103706\pi$
$294$		0			0
$295$	−136.837	−	362.076i	−0.463855	−	1.22737i
$296$		0			0
$297$	−85.1986	−	85.1986i	−0.286864	−	0.286864i
$298$		0			0
$299$	−43.9406	+	43.9406i	−0.146959	+	0.146959i
$300$		0			0
$301$	51.6289	−	51.6289i	0.171525	−	0.171525i
$302$		0			0
$303$	−180.296	−	180.296i	−0.595037	−	0.595037i
$304$		0			0
$305$	−30.2607	−	80.0707i	−0.0992154	−	0.262527i
$306$		0			0
$307$		−	465.516i		−	1.51634i	−0.652058	−	0.758169i	$-0.726094\pi$
$307$		−	465.516i		−	1.51634i	0.652058	−	0.758169i	$-0.273906\pi$
$308$		0			0
$309$	91.2520	−	91.2520i	0.295314	−	0.295314i
$310$		0			0
$311$			212.375i			0.682879i	0.939904	+	0.341439i	$0.110914\pi$
$311$			212.375i			0.682879i	−0.939904	+	0.341439i	$0.889086\pi$
$312$		0			0
$313$	−46.0307	+	46.0307i	−0.147063	+	0.147063i	−0.776805	−	0.629742i	$-0.783161\pi$
$313$	−46.0307	+	46.0307i	−0.147063	+	0.147063i	0.629742	+	0.776805i	$0.283161\pi$
$314$		0			0
$315$	46.6851	−	17.6435i	0.148207	−	0.0560110i
$316$		0			0
$317$		−	430.649i		−	1.35851i	−0.733901	−	0.679257i	$-0.762302\pi$
$317$		−	430.649i		−	1.35851i	0.733901	−	0.679257i	$-0.237698\pi$
$318$		0			0
$319$			104.548i			0.327738i
$320$		0			0
$321$	−55.3375			−0.172391
$322$		0			0
$323$	−190.876			−0.590948
$324$		0			0
$325$	350.534	+	397.524i	1.07857	+	1.22315i
$326$		0			0
$327$	−87.1261	−	87.1261i	−0.266441	−	0.266441i
$328$		0			0
$329$	−509.353			−1.54819
$330$		0			0
$331$	3.70469	+	3.70469i	0.0111924	+	0.0111924i	0.712681	−	0.701488i	$-0.247481\pi$
$331$	3.70469	+	3.70469i	0.0111924	+	0.0111924i	−0.701488	+	0.712681i	$0.747481\pi$
$332$		0			0
$333$	85.5005			0.256758
$334$		0			0
$335$	−497.065	−	224.404i	−1.48378	−	0.669862i
$336$		0			0
$337$	−226.237	+	226.237i	−0.671327	+	0.671327i	−0.958022	−	0.286695i	$-0.907443\pi$
$337$	−226.237	+	226.237i	−0.671327	+	0.671327i	0.286695	+	0.958022i	$0.407443\pi$
$338$		0			0
$339$	−133.619	−	133.619i	−0.394156	−	0.394156i
$340$		0			0
$341$	70.4709	+	70.4709i	0.206659	+	0.206659i
$342$		0			0
$343$	−214.853	+	214.853i	−0.626394	+	0.626394i
$344$		0			0
$345$	−14.3690	−	38.0207i	−0.0416492	−	0.110205i
$346$		0			0
$347$	231.886			0.668259			0.334130	−	0.942527i	$-0.391558\pi$
$347$	231.886			0.668259			0.334130	+	0.942527i	$0.391558\pi$
$348$		0			0
$349$	205.898	+	205.898i	0.589965	+	0.589965i	0.937622	−	0.347657i	$-0.113022\pi$
$349$	205.898	+	205.898i	0.589965	+	0.589965i	−0.347657	+	0.937622i	$0.613022\pi$
$350$		0			0
$351$	606.096			1.72677
$352$		0			0
$353$	−299.539	−	299.539i	−0.848551	−	0.848551i	0.141401	−	0.989952i	$-0.454839\pi$
$353$	−299.539	−	299.539i	−0.848551	−	0.848551i	−0.989952	+	0.141401i	$0.954839\pi$
$354$		0			0
$355$	−333.432	−	150.531i	−0.939246	−	0.424030i
$356$		0			0
$357$	−199.473			−0.558749
$358$		0			0
$359$	−108.844			−0.303187			−0.151593	−	0.988443i	$-0.548440\pi$
$359$	−108.844			−0.303187			−0.151593	+	0.988443i	$0.548440\pi$
$360$		0			0
$361$			48.5638i			0.134526i
$362$		0			0
$363$		−	286.310i		−	0.788732i
$364$		0			0
$365$	42.5375	+	112.555i	0.116541	+	0.308371i
$366$		0			0
$367$	−271.565	+	271.565i	−0.739960	+	0.739960i	−0.972570	−	0.232610i	$-0.925274\pi$
$367$	−271.565	+	271.565i	−0.739960	+	0.739960i	0.232610	+	0.972570i	$0.425274\pi$
$368$		0			0
$369$		−	1.54774i		−	0.00419442i
$370$		0			0
$371$	535.025	−	535.025i	1.44211	−	1.44211i
$372$		0			0
$373$		−	205.735i		−	0.551569i	−0.961220	−	0.275784i	$-0.911062\pi$
$373$		−	205.735i		−	0.551569i	0.961220	−	0.275784i	$-0.0889376\pi$
$374$		0			0
$375$	−331.321	+	101.981i	−0.883523	+	0.271950i
$376$		0			0
$377$	−371.875	−	371.875i	−0.986405	−	0.986405i
$378$		0			0
$379$	−146.474	+	146.474i	−0.386475	+	0.386475i	−0.873428	−	0.486953i	$-0.838108\pi$
$379$	−146.474	+	146.474i	−0.386475	+	0.386475i	0.486953	+	0.873428i	$0.338108\pi$
$380$		0			0
$381$	458.048	−	458.048i	1.20223	−	1.20223i
$382$		0			0
$383$	−77.8502	−	77.8502i	−0.203264	−	0.203264i	0.598133	−	0.801397i	$-0.295910\pi$
$383$	−77.8502	−	77.8502i	−0.203264	−	0.203264i	−0.801397	+	0.598133i	$0.795910\pi$
$384$		0			0
$385$	−146.464	−	66.1223i	−0.380426	−	0.171746i
$386$		0			0
$387$		−	12.5317i		−	0.0323815i
$388$		0			0
$389$	91.3251	−	91.3251i	0.234769	−	0.234769i	−0.579911	−	0.814680i	$-0.696913\pi$
$389$	91.3251	−	91.3251i	0.234769	−	0.234769i	0.814680	+	0.579911i	$0.196913\pi$
$390$		0			0
$391$		−	27.6463i		−	0.0707067i
$392$		0			0
$393$	30.4244	−	30.4244i	0.0774158	−	0.0774158i
$394$		0			0
$395$	9.80366	+	4.42594i	0.0248194	+	0.0112049i
$396$		0			0
$397$		−	181.720i		−	0.457732i	−0.973458	−	0.228866i	$-0.926498\pi$
$397$		−	181.720i		−	0.457732i	0.973458	−	0.228866i	$-0.0735017\pi$
$398$		0			0
$399$			428.011i			1.07271i
$400$		0			0
$401$	−559.201			−1.39452			−0.697258	−	0.716821i	$-0.745597\pi$
$401$	−559.201			−1.39452			−0.697258	+	0.716821i	$0.745597\pi$
$402$		0			0
$403$	−501.324			−1.24398
$404$		0			0
$405$	−138.885	+	307.637i	−0.342926	+	0.759597i
$406$		0			0
$407$	−194.668	−	194.668i	−0.478301	−	0.478301i
$408$		0			0
$409$	724.291			1.77088			0.885441	−	0.464752i	$-0.153856\pi$
$409$	724.291			1.77088			0.885441	+	0.464752i	$0.153856\pi$
$410$		0			0
$411$	339.453	+	339.453i	0.825919	+	0.825919i
$412$		0			0
$413$	−590.362			−1.42945
$414$		0			0
$415$	157.356	−	348.551i	0.379172	−	0.839882i
$416$		0			0
$417$	−453.471	+	453.471i	−1.08746	+	1.08746i
$418$		0			0
$419$	−76.4657	−	76.4657i	−0.182496	−	0.182496i	0.609947	−	0.792442i	$-0.291191\pi$
$419$	−76.4657	−	76.4657i	−0.182496	−	0.182496i	−0.792442	+	0.609947i	$0.791191\pi$
$420$		0			0
$421$	−470.702	−	470.702i	−1.11806	−	1.11806i	−0.992026	−	0.126030i	$-0.959776\pi$
$421$	−470.702	−	470.702i	−1.11806	−	1.11806i	−0.126030	−	0.992026i	$-0.540224\pi$
$422$		0			0
$423$	−61.8165	+	61.8165i	−0.146138	+	0.146138i
$424$		0			0
$425$	−235.329	−	14.7824i	−0.553716	−	0.0347822i
$426$		0			0
$427$	−130.555			−0.305749
$428$		0			0
$429$	−175.209	−	175.209i	−0.408413	−	0.408413i
$430$		0			0
$431$	−185.108			−0.429485			−0.214742	−	0.976671i	$-0.568891\pi$
$431$	−185.108			−0.429485			−0.214742	+	0.976671i	$0.568891\pi$
$432$		0			0
$433$	−354.954	−	354.954i	−0.819756	−	0.819756i	0.166317	−	0.986072i	$-0.446813\pi$
$433$	−354.954	−	354.954i	−0.819756	−	0.819756i	−0.986072	+	0.166317i	$0.946813\pi$
$434$		0			0
$435$	321.774	−	121.606i	0.739710	−	0.279555i
$436$		0			0
$437$	−59.3208			−0.135745
$438$		0			0
$439$	−155.719			−0.354714			−0.177357	−	0.984147i	$-0.556755\pi$
$439$	−155.719			−0.354714			−0.177357	+	0.984147i	$0.556755\pi$
$440$		0			0
$441$		−	11.9847i		−	0.0271763i
$442$		0			0
$443$		−	728.951i		−	1.64549i	−0.568412	−	0.822744i	$-0.692442\pi$
$443$		−	728.951i		−	1.64549i	0.568412	−	0.822744i	$-0.307558\pi$
$444$		0			0
$445$	79.6803	−	176.496i	0.179057	−	0.396619i
$446$		0			0
$447$	507.390	−	507.390i	1.13510	−	1.13510i
$448$		0			0
$449$			46.9465i			0.104558i	0.998633	+	0.0522790i	$0.0166485\pi$
$449$			46.9465i			0.104558i	−0.998633	+	0.0522790i	$0.983351\pi$
$450$		0			0
$451$	−3.52391	+	3.52391i	−0.00781355	+	0.00781355i
$452$		0			0
$453$			277.616i			0.612839i
$454$		0			0
$455$	756.161	−	285.772i	1.66189	−	0.628070i
$456$		0			0
$457$	−227.434	−	227.434i	−0.497667	−	0.497667i	0.413044	−	0.910711i	$-0.364466\pi$
$457$	−227.434	−	227.434i	−0.497667	−	0.497667i	−0.910711	+	0.413044i	$0.864466\pi$
$458$		0			0
$459$	−190.670	+	190.670i	−0.415403	+	0.415403i
$460$		0			0
$461$	−265.869	+	265.869i	−0.576722	+	0.576722i	−0.933999	−	0.357277i	$-0.883705\pi$
$461$	−265.869	+	265.869i	−0.576722	+	0.576722i	0.357277	+	0.933999i	$0.383705\pi$
$462$		0			0
$463$	−1.16661	−	1.16661i	−0.00251968	−	0.00251968i	0.705846	−	0.708366i	$-0.250567\pi$
$463$	−1.16661	−	1.16661i	−0.00251968	−	0.00251968i	−0.708366	+	0.705846i	$0.750567\pi$
$464$		0			0
$465$	134.923	−	298.860i	0.290157	−	0.642711i
$466$		0			0
$467$		−	632.343i		−	1.35405i	−0.735958	−	0.677027i	$-0.763268\pi$
$467$		−	632.343i		−	1.35405i	0.735958	−	0.677027i	$-0.236732\pi$
$468$		0			0
$469$	−588.175	+	588.175i	−1.25411	+	1.25411i
$470$		0			0
$471$			77.3400i			0.164204i
$472$		0			0
$473$	−28.5322	+	28.5322i	−0.0603217	+	0.0603217i
$474$		0			0
$475$	−31.7187	+	504.947i	−0.0667762	+	1.06305i
$476$		0			0
$477$		−	129.864i		−	0.272252i
$478$		0			0
$479$		−	552.415i		−	1.15327i	−0.817003	−	0.576633i	$-0.804366\pi$
$479$		−	552.415i		−	1.15327i	0.817003	−	0.576633i	$-0.195634\pi$
$480$		0			0
$481$	1384.85			2.87912
$482$		0			0
$483$	−61.9926			−0.128349
$484$		0			0
$485$	−21.3463	−	56.4828i	−0.0440129	−	0.116459i
$486$		0			0
$487$	−285.326	−	285.326i	−0.585886	−	0.585886i	0.350629	−	0.936515i	$-0.385968\pi$
$487$	−285.326	−	285.326i	−0.585886	−	0.585886i	−0.936515	+	0.350629i	$0.885968\pi$
$488$		0			0
$489$	−338.832			−0.692908
$490$		0			0
$491$	−617.833	−	617.833i	−1.25831	−	1.25831i	−0.951897	−	0.306418i	$-0.900870\pi$
$491$	−617.833	−	617.833i	−1.25831	−	1.25831i	−0.306418	−	0.951897i	$-0.599130\pi$
$492$		0			0
$493$	233.974			0.474592
$494$		0			0
$495$	−25.8001	+	9.75048i	−0.0521213	+	0.0196979i
$496$		0			0
$497$	−394.550	+	394.550i	−0.793862	+	0.793862i
$498$		0			0
$499$	430.585	+	430.585i	0.862895	+	0.862895i	0.991673	−	0.128778i	$-0.0411056\pi$
$499$	430.585	+	430.585i	0.862895	+	0.862895i	−0.128778	+	0.991673i	$0.541106\pi$
$500$		0			0
$501$	−283.477	−	283.477i	−0.565823	−	0.565823i
$502$		0			0
$503$	102.108	−	102.108i	0.202998	−	0.202998i	−0.598285	−	0.801283i	$-0.704151\pi$
$503$	102.108	−	102.108i	0.202998	−	0.202998i	0.801283	+	0.598285i	$0.204151\pi$
$504$		0			0
$505$	−430.018	+	162.514i	−0.851521	+	0.321811i
$506$		0			0
$507$	777.737			1.53400
$508$		0			0
$509$	350.381	+	350.381i	0.688372	+	0.688372i	0.961872	−	0.273500i	$-0.0881813\pi$
$509$	350.381	+	350.381i	0.688372	+	0.688372i	−0.273500	+	0.961872i	$0.588181\pi$
$510$		0			0
$511$	183.521			0.359141
$512$		0			0
$513$	409.121	+	409.121i	0.797507	+	0.797507i
$514$		0			0
$515$	−82.2523	−	217.642i	−0.159713	−	0.422606i
$516$		0			0
$517$	281.489			0.544466
$518$		0			0
$519$	−402.039			−0.774642
$520$		0			0
$521$		−	89.0292i		−	0.170881i	−0.996343	−	0.0854407i	$-0.972770\pi$
$521$		−	89.0292i		−	0.170881i	0.996343	−	0.0854407i	$-0.0272298\pi$
$522$		0			0
$523$		−	399.222i		−	0.763331i	−0.924300	−	0.381666i	$-0.875351\pi$
$523$		−	399.222i		−	0.763331i	0.924300	−	0.381666i	$-0.124649\pi$
$524$		0			0
$525$	−33.1473	+	527.690i	−0.0631378	+	1.00512i
$526$		0			0
$527$	157.710	−	157.710i	0.299260	−	0.299260i
$528$		0			0
$529$			520.408i			0.983758i
$530$		0			0
$531$	−71.6480	+	71.6480i	−0.134930	+	0.134930i
$532$		0			0
$533$		−	25.0688i		−	0.0470334i
$534$		0			0
$535$	−41.0518	+	90.9316i	−0.0767323	+	0.169966i
$536$		0			0
$537$	197.302	+	197.302i	0.367415	+	0.367415i
$538$		0			0
$539$	−27.2870	+	27.2870i	−0.0506252	+	0.0506252i
$540$		0			0
$541$	−151.552	+	151.552i	−0.280133	+	0.280133i	−0.833162	−	0.553029i	$-0.813472\pi$
$541$	−151.552	+	151.552i	−0.280133	+	0.280133i	0.553029	+	0.833162i	$0.313472\pi$
$542$		0			0
$543$	535.116	+	535.116i	0.985480	+	0.985480i
$544$		0			0
$545$	−207.801	+	78.5333i	−0.381287	+	0.144098i
$546$		0			0
$547$			327.523i			0.598762i	0.954134	+	0.299381i	$0.0967802\pi$
$547$			327.523i			0.598762i	−0.954134	+	0.299381i	$0.903220\pi$
$548$		0			0
$549$	−15.8445	+	15.8445i	−0.0288607	+	0.0288607i
$550$		0			0
$551$		−	502.039i		−	0.911141i
$552$		0			0
$553$	11.6006	−	11.6006i	0.0209777	−	0.0209777i
$554$		0			0
$555$	−372.710	+	825.570i	−0.671550	+	1.48751i
$556$		0			0
$557$			609.704i			1.09462i	0.836930	+	0.547311i	$0.184348\pi$
$557$			609.704i			1.09462i	−0.836930	+	0.547311i	$0.815652\pi$
$558$		0			0
$559$		−	202.976i		−	0.363105i
$560$		0			0
$561$	110.237			0.196501
$562$		0			0
$563$	104.576			0.185748			0.0928738	−	0.995678i	$-0.470395\pi$
$563$	104.576			0.185748			0.0928738	+	0.995678i	$0.470395\pi$
$564$		0			0
$565$	−318.690	+	120.441i	−0.564053	+	0.213169i
$566$		0			0
$567$	364.026	+	364.026i	0.642021	+	0.642021i
$568$		0			0
$569$	153.954			0.270569			0.135284	−	0.990807i	$-0.456805\pi$
$569$	153.954			0.270569			0.135284	+	0.990807i	$0.456805\pi$
$570$		0			0
$571$	475.501	+	475.501i	0.832751	+	0.832751i	0.987892	−	0.155141i	$-0.0495832\pi$
$571$	475.501	+	475.501i	0.832751	+	0.832751i	−0.155141	+	0.987892i	$0.549583\pi$
$572$		0			0
$573$	581.164			1.01425
$574$		0			0
$575$	−73.1359	−	4.59410i	−0.127193	−	0.00798974i
$576$		0			0
$577$	430.563	−	430.563i	0.746210	−	0.746210i	−0.227555	−	0.973765i	$-0.573073\pi$
$577$	430.563	−	430.563i	0.746210	−	0.746210i	0.973765	+	0.227555i	$0.0730731\pi$
$578$		0			0
$579$	−250.343	−	250.343i	−0.432371	−	0.432371i
$580$		0			0
$581$	−412.440	−	412.440i	−0.709879	−	0.709879i
$582$		0			0
$583$	−295.676	+	295.676i	−0.507163	+	0.507163i
$584$		0			0
$585$	57.0877	−	126.452i	0.0975858	−	0.216157i
$586$		0			0
$587$	−24.8014			−0.0422512			−0.0211256	−	0.999777i	$-0.506725\pi$
$587$	−24.8014			−0.0422512			−0.0211256	+	0.999777i	$0.506725\pi$
$588$		0			0
$589$	−338.399	−	338.399i	−0.574531	−	0.574531i
$590$		0			0
$591$	−188.123			−0.318312
$592$		0			0
$593$	714.962	+	714.962i	1.20567	+	1.20567i	0.972416	+	0.233255i	$0.0749375\pi$
$593$	714.962	+	714.962i	1.20567	+	1.20567i	0.233255	+	0.972416i	$0.425062\pi$
$594$		0			0
$595$	−147.978	+	327.779i	−0.248703	+	0.550888i
$596$		0			0
$597$	773.113			1.29500
$598$		0			0
$599$	898.559			1.50010			0.750049	−	0.661382i	$-0.230030\pi$
$599$	898.559			1.50010			0.750049	+	0.661382i	$0.230030\pi$
$600$		0			0
$601$		−	498.405i		−	0.829293i	−0.909983	−	0.414646i	$-0.863905\pi$
$601$		−	498.405i		−	0.829293i	0.909983	−	0.414646i	$-0.136095\pi$
$602$		0			0
$603$			142.765i			0.236758i
$604$		0			0
$605$	−470.469	−	212.397i	−0.777635	−	0.351070i
$606$		0			0
$607$	−476.327	+	476.327i	−0.784723	+	0.784723i	−0.980624	−	0.195900i	$-0.937237\pi$
$607$	−476.327	+	476.327i	−0.784723	+	0.784723i	0.195900	+	0.980624i	$0.437237\pi$
$608$		0			0
$609$		−	524.651i		−	0.861495i
$610$		0			0
$611$	−1001.24	+	1001.24i	−1.63870	+	1.63870i
$612$		0			0
$613$		−	294.722i		−	0.480787i	−0.970676	−	0.240393i	$-0.922724\pi$
$613$		−	294.722i		−	0.480787i	0.970676	−	0.240393i	$-0.0772764\pi$
$614$		0			0
$615$	14.9446	+	6.74685i	0.0243001	+	0.0109705i
$616$		0			0
$617$	−248.885	−	248.885i	−0.403379	−	0.403379i	0.476043	−	0.879422i	$-0.342071\pi$
$617$	−248.885	−	248.885i	−0.403379	−	0.403379i	−0.879422	+	0.476043i	$0.842071\pi$
$618$		0			0
$619$	320.358	−	320.358i	0.517541	−	0.517541i	−0.399286	−	0.916826i	$-0.630742\pi$
$619$	320.358	−	320.358i	0.517541	−	0.517541i	0.916826	+	0.399286i	$0.130742\pi$
$620$		0			0
$621$	−59.2567	+	59.2567i	−0.0954214	+	0.0954214i
$622$		0			0
$623$	−208.847	−	208.847i	−0.335227	−	0.335227i
$624$		0			0
$625$	−78.2113	+	620.087i	−0.125138	+	0.992139i
$626$		0			0
$627$		−	236.536i		−	0.377250i
$628$		0			0
$629$	−435.658	+	435.658i	−0.692619	+	0.692619i
$630$		0			0
$631$		−	110.857i		−	0.175685i	−0.996134	−	0.0878423i	$-0.972003\pi$
$631$		−	110.857i		−	0.175685i	0.996134	−	0.0878423i	$-0.0279972\pi$
$632$		0			0
$633$	−73.6276	+	73.6276i	−0.116315	+	0.116315i
$634$		0			0
$635$	−412.873	−	1092.47i	−0.650193	−	1.72043i
$636$		0			0
$637$		−	194.117i		−	0.304737i
$638$		0			0
$639$			95.7673i			0.149871i
$640$		0			0
$641$	−370.450			−0.577926			−0.288963	−	0.957340i	$-0.593310\pi$
$641$	−370.450			−0.577926			−0.288963	+	0.957340i	$0.593310\pi$
$642$		0			0
$643$	686.295			1.06733			0.533667	−	0.845695i	$-0.320814\pi$
$643$	686.295			1.06733			0.533667	+	0.845695i	$0.320814\pi$
$644$		0			0
$645$	121.002	+	54.6275i	0.187601	+	0.0846938i
$646$		0			0
$647$	−499.985	−	499.985i	−0.772774	−	0.772774i	0.205817	−	0.978591i	$-0.434015\pi$
$647$	−499.985	−	499.985i	−0.772774	−	0.772774i	−0.978591	+	0.205817i	$0.934015\pi$
$648$		0			0
$649$	326.258			0.502708
$650$		0			0
$651$	−353.641	−	353.641i	−0.543227	−	0.543227i
$652$		0			0
$653$	−599.129			−0.917502			−0.458751	−	0.888565i	$-0.651703\pi$
$653$	−599.129			−0.917502			−0.458751	+	0.888565i	$0.651703\pi$
$654$		0			0
$655$	−27.4238	−	72.5641i	−0.0418684	−	0.110785i
$656$		0			0
$657$	22.2726	−	22.2726i	0.0339005	−	0.0339005i
$658$		0			0
$659$	55.5691	+	55.5691i	0.0843233	+	0.0843233i	0.748010	−	0.663687i	$-0.231009\pi$
$659$	55.5691	+	55.5691i	0.0843233	+	0.0843233i	−0.663687	+	0.748010i	$0.731009\pi$
$660$		0			0
$661$	−24.3517	−	24.3517i	−0.0368407	−	0.0368407i	0.688446	−	0.725287i	$-0.258293\pi$
$661$	−24.3517	−	24.3517i	−0.0368407	−	0.0368407i	−0.725287	+	0.688446i	$0.758293\pi$
$662$		0			0
$663$	−392.109	+	392.109i	−0.591416	+	0.591416i
$664$		0			0
$665$	703.315	+	317.517i	1.05762	+	0.477470i
$666$		0			0
$667$	72.7147			0.109018
$668$		0			0
$669$	−250.069	−	250.069i	−0.373795	−	0.373795i
$670$		0			0
$671$	72.1498			0.107526
$672$		0			0
$673$	−348.271	−	348.271i	−0.517490	−	0.517490i	0.399321	−	0.916811i	$-0.369246\pi$
$673$	−348.271	−	348.271i	−0.517490	−	0.517490i	−0.916811	+	0.399321i	$0.869246\pi$
$674$		0			0
$675$	472.717	+	536.086i	0.700321	+	0.794201i
$676$		0			0
$677$	780.155			1.15237			0.576185	−	0.817319i	$-0.304541\pi$
$677$	780.155			1.15237			0.576185	+	0.817319i	$0.304541\pi$
$678$		0			0
$679$	−92.0950			−0.135633
$680$		0			0
$681$			959.715i			1.40927i
$682$		0			0
$683$			170.375i			0.249451i	0.992191	+	0.124725i	$0.0398050\pi$
$683$			170.375i			0.249451i	−0.992191	+	0.124725i	$0.960195\pi$
$684$		0			0
$685$	809.616	−	305.974i	1.18192	−	0.446677i
$686$		0			0
$687$	203.770	−	203.770i	0.296609	−	0.296609i
$688$		0			0
$689$		−	2103.41i		−	3.05285i
$690$		0			0
$691$	−51.2626	+	51.2626i	−0.0741861	+	0.0741861i	−0.743226	−	0.669040i	$-0.766705\pi$
$691$	−51.2626	+	51.2626i	−0.0741861	+	0.0741861i	0.669040	+	0.743226i	$0.266705\pi$
$692$		0			0
$693$			42.0668i			0.0607025i
$694$		0			0
$695$	408.747	+	1081.56i	0.588125	+	1.55620i
$696$		0			0
$697$	7.88633	+	7.88633i	0.0113147	+	0.0113147i
$698$		0			0
$699$	−240.717	+	240.717i	−0.344374	+	0.344374i
$700$		0			0
$701$	−68.3903	+	68.3903i	−0.0975610	+	0.0975610i	−0.754203	−	0.656642i	$-0.771976\pi$
$701$	−68.3903	+	68.3903i	−0.0975610	+	0.0975610i	0.656642	+	0.754203i	$0.271976\pi$
$702$		0			0
$703$	934.792	+	934.792i	1.32972	+	1.32972i
$704$		0			0
$705$	−327.416	−	866.352i	−0.464420	−	1.22887i
$706$		0			0
$707$			701.142i			0.991714i
$708$		0			0
$709$	815.622	−	815.622i	1.15038	−	1.15038i	0.163908	−	0.986476i	$-0.447590\pi$
$709$	815.622	−	815.622i	1.15038	−	1.15038i	0.986476	−	0.163908i	$-0.0524101\pi$
$710$		0			0
$711$		−	2.81577i		−	0.00396030i
$712$		0			0
$713$	49.0133	−	49.0133i	0.0687424	−	0.0687424i
$714$		0			0
$715$	−417.885	+	157.929i	−0.584454	+	0.220880i
$716$		0			0
$717$			567.946i			0.792114i
$718$		0			0
$719$			125.050i			0.173922i	0.996212	+	0.0869612i	$0.0277156\pi$
$719$			125.050i			0.173922i	−0.996212	+	0.0869612i	$0.972284\pi$
$720$		0			0
$721$	−354.864			−0.492183
$722$		0			0
$723$	274.224			0.379286
$724$		0			0
$725$	38.8804	−	618.958i	0.0536282	−	0.853735i
$726$		0			0
$727$	307.763	+	307.763i	0.423333	+	0.423333i	0.886350	−	0.463016i	$-0.153233\pi$
$727$	307.763	+	307.763i	0.423333	+	0.423333i	−0.463016	+	0.886350i	$0.653233\pi$
$728$		0			0
$729$	801.940			1.10005
$730$		0			0
$731$	63.8535	+	63.8535i	0.0873510	+	0.0873510i
$732$		0			0
$733$	94.8581			0.129411			0.0647054	−	0.997904i	$-0.479389\pi$
$733$	94.8581			0.129411			0.0647054	+	0.997904i	$0.479389\pi$
$734$		0			0
$735$	115.722	+	52.2434i	0.157444	+	0.0710795i
$736$		0			0
$737$	325.049	−	325.049i	0.441044	−	0.441044i
$738$		0			0
$739$	−761.284	−	761.284i	−1.03015	−	1.03015i	−0.999531	−	0.0306228i	$-0.990251\pi$
$739$	−761.284	−	761.284i	−1.03015	−	1.03015i	−0.0306228	−	0.999531i	$-0.509749\pi$
$740$		0			0
$741$	841.348	+	841.348i	1.13542	+	1.13542i
$742$		0			0
$743$	700.467	−	700.467i	0.942754	−	0.942754i	−0.0556935	−	0.998448i	$-0.517737\pi$
$743$	700.467	−	700.467i	0.942754	−	0.942754i	0.998448	+	0.0556935i	$0.0177370\pi$
$744$		0			0
$745$	−457.348	−	1210.16i	−0.613890	−	1.62437i
$746$		0			0
$747$	−100.110			−0.134016
$748$		0			0
$749$	107.599	+	107.599i	0.143657	+	0.143657i
$750$		0			0
$751$	−268.325			−0.357291			−0.178645	−	0.983914i	$-0.557171\pi$
$751$	−268.325			−0.357291			−0.178645	+	0.983914i	$0.557171\pi$
$752$		0			0
$753$	−106.320	−	106.320i	−0.141195	−	0.141195i
$754$		0			0
$755$	456.184	+	205.948i	0.604217	+	0.272779i
$756$		0			0
$757$	777.969			1.02770			0.513850	−	0.857880i	$-0.328219\pi$
$757$	777.969			1.02770			0.513850	+	0.857880i	$0.328219\pi$
$758$		0			0
$759$	34.2596			0.0451378
$760$		0			0
$761$			1058.98i			1.39156i	0.718254	+	0.695781i	$0.244942\pi$
$761$			1058.98i			1.39156i	−0.718254	+	0.695781i	$0.755058\pi$
$762$		0			0
$763$			338.819i			0.444062i
$764$		0			0
$765$	21.8211	+	57.7392i	0.0285243	+	0.0754760i
$766$		0			0
$767$	−1160.49	+	1160.49i	−1.51302	+	1.51302i
$768$		0			0
$769$			262.583i			0.341461i	0.985318	+	0.170730i	$0.0546127\pi$
$769$			262.583i			0.341461i	−0.985318	+	0.170730i	$0.945387\pi$
$770$		0			0
$771$	461.699	−	461.699i	0.598832	−	0.598832i
$772$		0			0
$773$			405.962i			0.525177i	0.964908	+	0.262588i	$0.0845761\pi$
$773$			405.962i			0.525177i	−0.964908	+	0.262588i	$0.915424\pi$
$774$		0			0
$775$	−391.001	−	443.416i	−0.504518	−	0.572150i
$776$		0			0
$777$	976.895	+	976.895i	1.25727	+	1.25727i
$778$		0			0
$779$	16.9217	−	16.9217i	0.0217224	−	0.0217224i
$780$		0			0
$781$	218.044	−	218.044i	0.279185	−	0.279185i
$782$		0			0
$783$	−501.496	−	501.496i	−0.640480	−	0.640480i
$784$		0			0
$785$	127.087	+	57.3742i	0.161894	+	0.0730882i
$786$		0			0
$787$		−	107.060i		−	0.136036i	−0.997684	−	0.0680181i	$-0.978332\pi$
$787$		−	107.060i		−	0.136036i	0.997684	−	0.0680181i	$-0.0216676\pi$
$788$		0			0
$789$	218.285	−	218.285i	0.276660	−	0.276660i
$790$		0			0
$791$			519.622i			0.656918i
$792$		0			0
$793$	−256.634	+	256.634i	−0.323624	+	0.323624i
$794$		0			0
$795$	1253.93	+	566.099i	1.57728	+	0.712074i
$796$		0			0
$797$		−	615.958i		−	0.772846i	−0.922322	−	0.386423i	$-0.873711\pi$
$797$		−	615.958i		−	0.772846i	0.922322	−	0.386423i	$-0.126289\pi$
$798$		0			0
$799$		−	629.957i		−	0.788432i
$800$		0			0
$801$	−50.6924			−0.0632864
$802$		0			0
$803$	−101.421			−0.126303
$804$		0			0
$805$	−45.9889	+	101.867i	−0.0571290	+	0.126543i
$806$		0			0
$807$	272.517	+	272.517i	0.337692	+	0.337692i
$808$		0			0
$809$	−304.293			−0.376135			−0.188067	−	0.982156i	$-0.560222\pi$
$809$	−304.293			−0.376135			−0.188067	+	0.982156i	$0.560222\pi$
$810$		0			0
$811$	−20.2059	−	20.2059i	−0.0249148	−	0.0249148i	0.694540	−	0.719454i	$-0.255608\pi$
$811$	−20.2059	−	20.2059i	−0.0249148	−	0.0249148i	−0.719454	+	0.694540i	$0.755608\pi$
$812$		0			0
$813$	321.610			0.395584
$814$		0			0
$815$	−251.360	+	556.775i	−0.308418	+	0.683159i
$816$		0			0
$817$	137.011	−	137.011i	0.167700	−	0.167700i
$818$		0			0
$819$	−149.630	−	149.630i	−0.182699	−	0.182699i
$820$		0			0
$821$	381.316	+	381.316i	0.464453	+	0.464453i	0.900112	−	0.435659i	$-0.143485\pi$
$821$	381.316	+	381.316i	0.464453	+	0.464453i	−0.435659	+	0.900112i	$0.643485\pi$
$822$		0			0
$823$	420.324	−	420.324i	0.510721	−	0.510721i	−0.404026	−	0.914747i	$-0.632390\pi$
$823$	420.324	−	420.324i	0.510721	−	0.510721i	0.914747	+	0.404026i	$0.132390\pi$
$824$		0			0
$825$	18.3185	−	291.622i	0.0222043	−	0.353482i
$826$		0			0
$827$	−844.006			−1.02056			−0.510281	−	0.860007i	$-0.670459\pi$
$827$	−844.006			−1.02056			−0.510281	+	0.860007i	$0.670459\pi$
$828$		0			0
$829$	−222.833	−	222.833i	−0.268798	−	0.268798i	0.559818	−	0.828616i	$-0.310871\pi$
$829$	−222.833	−	222.833i	−0.268798	−	0.268798i	−0.828616	+	0.559818i	$0.810871\pi$
$830$		0			0
$831$	−944.609			−1.13671
$832$		0			0
$833$	61.0668	+	61.0668i	0.0733095	+	0.0733095i
$834$		0			0
$835$	−676.111	+	255.519i	−0.809714	+	0.306011i
$836$		0			0
$837$	−676.067			−0.807726
$838$		0			0
$839$	−554.445			−0.660841			−0.330420	−	0.943834i	$-0.607191\pi$
$839$	−554.445			−0.660841			−0.330420	+	0.943834i	$0.607191\pi$
$840$		0			0
$841$		−	225.607i		−	0.268260i
$842$		0			0
$843$			287.150i			0.340628i
$844$		0			0
$845$	576.960	−	1277.99i	0.682793	−	1.51242i
$846$		0			0
$847$	−556.705	+	556.705i	−0.657267	+	0.657267i
$848$		0			0
$849$			1558.55i			1.83575i
$850$		0			0
$851$	−135.394	+	135.394i	−0.159100	+	0.159100i
$852$		0			0
$853$		−	431.993i		−	0.506440i	−0.967409	−	0.253220i	$-0.918510\pi$
$853$		−	431.993i		−	0.506440i	0.967409	−	0.253220i	$-0.0814896\pi$
$854$		0			0
$855$	123.891	−	46.8215i	0.144902	−	0.0547620i
$856$		0			0
$857$	457.844	+	457.844i	0.534241	+	0.534241i	0.921831	−	0.387591i	$-0.126693\pi$
$857$	457.844	+	457.844i	0.534241	+	0.534241i	−0.387591	+	0.921831i	$0.626693\pi$
$858$		0			0
$859$	822.277	−	822.277i	0.957249	−	0.957249i	−0.0418737	−	0.999123i	$-0.513333\pi$
$859$	822.277	−	822.277i	0.957249	−	0.957249i	0.999123	+	0.0418737i	$0.0133327\pi$
$860$		0			0
$861$	17.6839	−	17.6839i	0.0205388	−	0.0205388i
$862$		0			0
$863$	−132.089	−	132.089i	−0.153058	−	0.153058i	0.626424	−	0.779482i	$-0.284518\pi$
$863$	−132.089	−	132.089i	−0.153058	−	0.153058i	−0.779482	+	0.626424i	$0.784518\pi$
$864$		0			0
$865$	−298.251	+	660.638i	−0.344798	+	0.763744i
$866$		0			0
$867$			554.775i			0.639879i
$868$		0			0
$869$	−6.41098	+	6.41098i	−0.00737742	+	0.00737742i
$870$		0			0
$871$			2312.37i			2.65485i
$872$		0			0
$873$	−11.1769	+	11.1769i	−0.0128029	+	0.0128029i
$874$		0			0
$875$	842.520	+	445.932i	0.962880	+	0.509637i
$876$		0			0
$877$			363.488i			0.414468i	0.978291	+	0.207234i	$0.0664461\pi$
$877$			363.488i			0.414468i	−0.978291	+	0.207234i	$0.933554\pi$
$878$		0			0
$879$		−	5.29476i		−	0.00602362i
$880$		0			0
$881$	−242.827			−0.275627			−0.137813	−	0.990458i	$-0.544007\pi$
$881$	−242.827			−0.275627			−0.137813	+	0.990458i	$0.544007\pi$
$882$		0			0
$883$	1629.94			1.84592			0.922959	−	0.384899i	$-0.125764\pi$
$883$	1629.94			1.84592			0.922959	+	0.384899i	$0.125764\pi$
$884$		0			0
$885$	−379.489	−	1004.14i	−0.428801	−	1.13462i
$886$		0			0
$887$	−196.533	−	196.533i	−0.221570	−	0.221570i	0.587589	−	0.809160i	$-0.300077\pi$
$887$	−196.533	−	196.533i	−0.221570	−	0.221570i	−0.809160	+	0.587589i	$0.800077\pi$
$888$		0			0
$889$	−1781.27			−2.00368
$890$		0			0
$891$	−201.175	−	201.175i	−0.225786	−	0.225786i
$892$		0			0
$893$	−1351.70			−1.51366
$894$		0			0
$895$	470.578	−	177.843i	0.525786	−	0.198707i
$896$		0			0
$897$	−121.860	+	121.860i	−0.135853	+	0.135853i
$898$		0			0
$899$	414.806	+	414.806i	0.461408	+	0.461408i
$900$		0			0
$901$	661.707	+	661.707i	0.734414	+	0.734414i
$902$		0			0
$903$	143.182	−	143.182i	0.158562	−	0.158562i
$904$		0			0
$905$	1276.29	−	482.340i	1.41026	−	0.532972i
$906$		0			0
$907$	−188.488			−0.207814			−0.103907	−	0.994587i	$-0.533134\pi$
$907$	−188.488			−0.207814			−0.103907	+	0.994587i	$0.533134\pi$
$908$		0			0
$909$	85.0925	+	85.0925i	0.0936112	+	0.0936112i
$910$		0			0
$911$	−1051.06			−1.15374			−0.576870	−	0.816836i	$-0.695726\pi$
$911$	−1051.06			−1.15374			−0.576870	+	0.816836i	$0.695726\pi$
$912$		0			0
$913$	227.930	+	227.930i	0.249650	+	0.249650i
$914$		0			0
$915$	−83.9216	−	222.059i	−0.0917176	−	0.242687i
$916$		0			0
$917$	−118.315			−0.129024
$918$		0			0
$919$	−158.471			−0.172439			−0.0862195	−	0.996276i	$-0.527479\pi$
$919$	−158.471			−0.172439			−0.0862195	+	0.996276i	$0.527479\pi$
$920$		0			0
$921$		−	1291.01i		−	1.40175i
$922$		0			0
$923$			1551.15i			1.68055i
$924$		0			0
$925$	1080.10	+	1224.89i	1.16768	+	1.32420i
$926$		0			0
$927$	−43.0673	+	43.0673i	−0.0464588	+	0.0464588i
$928$		0			0
$929$			1081.59i			1.16425i	0.813100	+	0.582124i	$0.197778\pi$
$929$			1081.59i			1.16425i	−0.813100	+	0.582124i	$0.802222\pi$
$930$		0			0
$931$	131.031	−	131.031i	0.140743	−	0.140743i
$932$		0			0
$933$			588.978i			0.631273i
$934$		0			0
$935$	81.7787	−	181.144i	0.0874639	−	0.193736i
$936$		0			0
$937$	484.345	+	484.345i	0.516910	+	0.516910i	0.916635	−	0.399725i	$-0.130894\pi$
$937$	484.345	+	484.345i	0.516910	+	0.516910i	−0.399725	+	0.916635i	$0.630894\pi$
$938$		0			0
$939$	−127.656	+	127.656i	−0.135949	+	0.135949i
$940$		0			0
$941$	−555.577	+	555.577i	−0.590411	+	0.590411i	−0.937742	−	0.347331i	$-0.887088\pi$
$941$	−555.577	+	555.577i	−0.590411	+	0.590411i	0.347331	+	0.937742i	$0.387088\pi$
$942$		0			0
$943$	2.45092	+	2.45092i	0.00259907	+	0.00259907i
$944$		0			0
$945$	1019.73	−	385.381i	1.07908	−	0.407811i
$946$		0			0
$947$			476.289i			0.502945i	0.967864	+	0.251473i	$0.0809149\pi$
$947$			476.289i			0.502945i	−0.967864	+	0.251473i	$0.919085\pi$
$948$		0			0
$949$	360.750	−	360.750i	0.380137	−	0.380137i
$950$		0			0
$951$		−	1194.31i		−	1.25585i
$952$		0			0
$953$	−80.9782	+	80.9782i	−0.0849719	+	0.0849719i	−0.748315	−	0.663343i	$-0.769137\pi$
$953$	−80.9782	+	80.9782i	−0.0849719	+	0.0849719i	0.663343	+	0.748315i	$0.269137\pi$
$954$		0			0
$955$	431.134	−	954.980i	0.451449	−	0.999979i
$956$		0			0
$957$			289.943i			0.302971i
$958$		0			0
$959$		−	1320.07i		−	1.37651i
$960$		0			0
$961$	−401.801			−0.418107
$962$		0			0
$963$	26.1170			0.0271205
$964$		0			0
$965$	−597.083	+	225.652i	−0.618739	+	0.233837i
$966$		0			0
$967$	−226.347	−	226.347i	−0.234072	−	0.234072i	0.580318	−	0.814390i	$-0.302928\pi$
$967$	−226.347	−	226.347i	−0.234072	−	0.234072i	−0.814390	+	0.580318i	$0.802928\pi$
$968$		0			0
$969$	−529.355			−0.546290
$970$		0			0
$971$	−375.576	−	375.576i	−0.386793	−	0.386793i	0.486749	−	0.873542i	$-0.338183\pi$
$971$	−375.576	−	375.576i	−0.386793	−	0.386793i	−0.873542	+	0.486749i	$0.838183\pi$
$972$		0			0
$973$	1763.47			1.81241
$974$		0			0
$975$	972.131	+	1102.45i	0.997058	+	1.13072i
$976$		0			0
$977$	201.023	−	201.023i	0.205756	−	0.205756i	−0.596705	−	0.802461i	$-0.703524\pi$
$977$	201.023	−	201.023i	0.205756	−	0.205756i	0.802461	+	0.596705i	$0.203524\pi$
$978$		0			0
$979$	115.417	+	115.417i	0.117893	+	0.117893i
$980$		0			0
$981$	41.1200	+	41.1200i	0.0419164	+	0.0419164i
$982$		0			0
$983$	536.933	−	536.933i	0.546218	−	0.546218i	−0.379126	−	0.925345i	$-0.623775\pi$
$983$	536.933	−	536.933i	0.546218	−	0.546218i	0.925345	+	0.379126i	$0.123775\pi$
$984$		0			0
$985$	−139.558	+	309.126i	−0.141683	+	0.313834i
$986$		0			0
$987$	−1412.58			−1.43119
$988$		0			0
$989$	19.8445	+	19.8445i	0.0200652	+	0.0200652i
$990$		0			0
$991$	1164.95			1.17553			0.587764	−	0.809032i	$-0.300008\pi$
$991$	1164.95			1.17553			0.587764	+	0.809032i	$0.300008\pi$
$992$		0			0
$993$	10.2742	+	10.2742i	0.0103466	+	0.0103466i
$994$		0			0
$995$	573.530	−	1270.39i	0.576412	−	1.27678i
$996$		0			0
$997$	−1493.41			−1.49790			−0.748950	−	0.662627i	$-0.769442\pi$
$997$	−1493.41			−1.49790			−0.748950	+	0.662627i	$0.769442\pi$
$998$		0			0
$999$	1867.56			1.86943

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.3.t.a.353.16		44
4.3	odd	2		640.3.t.b.353.7		44
5.2	odd	4		640.3.i.a.97.7		44
8.3	odd	2		80.3.t.a.53.4	yes	44
8.5	even	2		320.3.t.a.113.7		44
16.3	odd	4		640.3.i.b.33.7		44
16.5	even	4		320.3.i.a.273.7		44
16.11	odd	4		80.3.i.a.13.14	✓	44
16.13	even	4		640.3.i.a.33.16		44
20.7	even	4		640.3.i.b.97.16		44
40.3	even	4		400.3.i.b.357.9		44
40.19	odd	2		400.3.t.b.293.19		44
40.27	even	4		80.3.i.a.37.14	yes	44
40.37	odd	4		320.3.i.a.177.16		44
80.27	even	4		80.3.t.a.77.4	yes	44
80.37	odd	4		320.3.t.a.17.7		44
80.43	even	4		400.3.t.b.157.19		44
80.59	odd	4		400.3.i.b.93.9		44
80.67	even	4		640.3.t.b.417.7		44
80.77	odd	4	inner	640.3.t.a.417.16		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.14	✓	44	16.11	odd	4
80.3.i.a.37.14	yes	44	40.27	even	4
80.3.t.a.53.4	yes	44	8.3	odd	2
80.3.t.a.77.4	yes	44	80.27	even	4
320.3.i.a.177.16		44	40.37	odd	4
320.3.i.a.273.7		44	16.5	even	4
320.3.t.a.17.7		44	80.37	odd	4
320.3.t.a.113.7		44	8.5	even	2
400.3.i.b.93.9		44	80.59	odd	4
400.3.i.b.357.9		44	40.3	even	4
400.3.t.b.157.19		44	80.43	even	4
400.3.t.b.293.19		44	40.19	odd	2
640.3.i.a.33.16		44	16.13	even	4
640.3.i.a.97.7		44	5.2	odd	4
640.3.i.b.33.7		44	16.3	odd	4
640.3.i.b.97.16		44	20.7	even	4
640.3.t.a.353.16		44	1.1	even	1	trivial
640.3.t.a.417.16		44	80.77	odd	4	inner
640.3.t.b.353.7		44	4.3	odd	2
640.3.t.b.417.7		44	80.67	even	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	640.t (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.77329 q^{3} +(2.05735 - 4.55712i) q^{5} +(-5.39242 - 5.39242i) q^{7} -1.30888 q^{9} +O(q^{10})\)	\(q+2.77329 q^{3} +(2.05735 - 4.55712i) q^{5} +(-5.39242 - 5.39242i) q^{7} -1.30888 q^{9} +(2.98007 + 2.98007i) q^{11} -21.2000 q^{13} +(5.70562 - 12.6382i) q^{15} +(6.66924 - 6.66924i) q^{17} +(-14.3102 - 14.3102i) q^{19} +(-14.9547 - 14.9547i) q^{21} +(2.07267 - 2.07267i) q^{23} +(-16.5346 - 18.7512i) q^{25} -28.5895 q^{27} +(17.5413 + 17.5413i) q^{29} +23.6474 q^{31} +(8.26459 + 8.26459i) q^{33} +(-35.6680 + 13.4798i) q^{35} -65.3234 q^{37} -58.7936 q^{39} +1.18249i q^{41} +9.57434i q^{43} +(-2.69282 + 5.96472i) q^{45} +(47.2286 - 47.2286i) q^{47} +9.15649i q^{49} +(18.4957 - 18.4957i) q^{51} +99.2178i q^{53} +(19.7116 - 7.44949i) q^{55} +(-39.6863 - 39.6863i) q^{57} +(54.7400 - 54.7400i) q^{59} +(12.1054 - 12.1054i) q^{61} +(7.05803 + 7.05803i) q^{63} +(-43.6157 + 96.6108i) q^{65} -109.074i q^{67} +(5.74812 - 5.74812i) q^{69} -73.1674i q^{71} +(-17.0166 + 17.0166i) q^{73} +(-45.8553 - 52.0023i) q^{75} -32.1396i q^{77} +2.15129i q^{79} -67.5069 q^{81} +76.4850 q^{83} +(-16.6716 - 44.1134i) q^{85} +(48.6470 + 48.6470i) q^{87} +38.7296 q^{89} +(114.319 + 114.319i) q^{91} +65.5810 q^{93} +(-94.6543 + 35.7722i) q^{95} +(8.53929 - 8.53929i) q^{97} +(-3.90055 - 3.90055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{3} + 2 q^{5} + 108 q^{9}+O(q^{10}) \) 44 * q - 4 * q^3 + 2 * q^5 + 108 * q^9	\( 44 q - 4 q^{3} + 2 q^{5} + 108 q^{9} - 4 q^{11} + 4 q^{13} + 4 q^{15} - 4 q^{17} - 32 q^{19} + 4 q^{21} - 40 q^{27} + 8 q^{31} - 4 q^{33} - 4 q^{35} + 4 q^{37} + 72 q^{39} + 70 q^{45} + 4 q^{47} - 100 q^{51} - 36 q^{57} - 64 q^{59} + 36 q^{61} + 200 q^{63} - 4 q^{65} - 60 q^{69} - 48 q^{73} - 324 q^{75} + 100 q^{81} + 156 q^{83} + 52 q^{85} + 36 q^{87} + 188 q^{91} + 40 q^{93} - 380 q^{95} - 4 q^{97} + 92 q^{99}+O(q^{100}) \) 44 * q - 4 * q^3 + 2 * q^5 + 108 * q^9 - 4 * q^11 + 4 * q^13 + 4 * q^15 - 4 * q^17 - 32 * q^19 + 4 * q^21 - 40 * q^27 + 8 * q^31 - 4 * q^33 - 4 * q^35 + 4 * q^37 + 72 * q^39 + 70 * q^45 + 4 * q^47 - 100 * q^51 - 36 * q^57 - 64 * q^59 + 36 * q^61 + 200 * q^63 - 4 * q^65 - 60 * q^69 - 48 * q^73 - 324 * q^75 + 100 * q^81 + 156 * q^83 + 52 * q^85 + 36 * q^87 + 188 * q^91 + 40 * q^93 - 380 * q^95 - 4 * q^97 + 92 * q^99

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