LMFDB - Embedded newform 320.3.i.a.273.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(177,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("320.177");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.i (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:	$8.71936845953$
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			273.7
Character	$\chi$	$=$	320.273
Dual form			320.3.i.a.177.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77329i q^{3} +(4.55712 + 2.05735i) q^{5} +(5.39242 + 5.39242i) q^{7} +1.30888 q^{9} +O(q^{10})$	\(q-2.77329i q^{3} +(4.55712 + 2.05735i) q^{5} +(5.39242 + 5.39242i) q^{7} +1.30888 q^{9} +(-2.98007 + 2.98007i) q^{11} +21.2000i q^{13} +(5.70562 - 12.6382i) q^{15} +(6.66924 - 6.66924i) q^{17} +(-14.3102 + 14.3102i) q^{19} +(14.9547 - 14.9547i) q^{21} +(-2.07267 + 2.07267i) q^{23} +(16.5346 + 18.7512i) q^{25} -28.5895i q^{27} +(17.5413 - 17.5413i) q^{29} +23.6474 q^{31} +(8.26459 + 8.26459i) q^{33} +(13.4798 + 35.6680i) q^{35} -65.3234i q^{37} +58.7936 q^{39} -1.18249i q^{41} -9.57434 q^{43} +(5.96472 + 2.69282i) q^{45} +(47.2286 - 47.2286i) q^{47} +9.15649i q^{49} +(-18.4957 - 18.4957i) q^{51} -99.2178 q^{53} +(-19.7116 + 7.44949i) q^{55} +(39.6863 + 39.6863i) q^{57} +(54.7400 + 54.7400i) q^{59} +(-12.1054 - 12.1054i) q^{61} +(7.05803 + 7.05803i) q^{63} +(-43.6157 + 96.6108i) q^{65} -109.074 q^{67} +(5.74812 + 5.74812i) q^{69} +73.1674i q^{71} +(17.0166 - 17.0166i) q^{73} +(52.0023 - 45.8553i) q^{75} -32.1396 q^{77} +2.15129i q^{79} -67.5069 q^{81} -76.4850i q^{83} +(44.1134 - 16.6716i) q^{85} +(-48.6470 - 48.6470i) q^{87} -38.7296 q^{89} +(-114.319 + 114.319i) q^{91} -65.5810i q^{93} +(-94.6543 + 35.7722i) q^{95} +(8.53929 - 8.53929i) q^{97} +(-3.90055 + 3.90055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{5} - 108 q^{9}+O(q^{10}) $ 44 * q - 2 * q^5 - 108 * q^9	$ 44 q - 2 q^{5} - 108 q^{9} + 4 q^{11} + 4 q^{15} - 4 q^{17} - 32 q^{19} - 4 q^{21} + 8 q^{31} - 4 q^{33} - 96 q^{35} - 72 q^{39} - 124 q^{43} - 34 q^{45} + 4 q^{47} + 100 q^{51} - 4 q^{53} + 36 q^{57} - 64 q^{59} - 36 q^{61} + 200 q^{63} - 4 q^{65} + 292 q^{67} - 60 q^{69} + 48 q^{73} - 96 q^{75} + 192 q^{77} + 100 q^{81} + 48 q^{85} - 36 q^{87} - 188 q^{91} - 380 q^{95} - 4 q^{97} + 92 q^{99}+O(q^{100}) $ 44 * q - 2 * q^5 - 108 * q^9 + 4 * q^11 + 4 * q^15 - 4 * q^17 - 32 * q^19 - 4 * q^21 + 8 * q^31 - 4 * q^33 - 96 * q^35 - 72 * q^39 - 124 * q^43 - 34 * q^45 + 4 * q^47 + 100 * q^51 - 4 * q^53 + 36 * q^57 - 64 * q^59 - 36 * q^61 + 200 * q^63 - 4 * q^65 + 292 * q^67 - 60 * q^69 + 48 * q^73 - 96 * q^75 + 192 * q^77 + 100 * q^81 + 48 * q^85 - 36 * q^87 - 188 * q^91 - 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 $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0
$2$		0			0
$3$		−	2.77329i		−	0.924429i	−0.886768	−	0.462215i	$-0.847055\pi$
$3$		−	2.77329i		−	0.924429i	0.886768	−	0.462215i	$-0.152945\pi$
$4$		0			0
$5$	4.55712	+	2.05735i	0.911424	+	0.411470i
$5$	4.55712	+	2.05735i	0.911424	+	0.411470i
$6$		0			0
$7$	5.39242	+	5.39242i	0.770346	+	0.770346i	0.978167	−	0.207821i	$-0.0666370\pi$
$7$	5.39242	+	5.39242i	0.770346	+	0.770346i	−0.207821	+	0.978167i	$0.566637\pi$
$8$		0			0
$9$	1.30888			0.145431
$10$		0			0
$11$	−2.98007	+	2.98007i	−0.270915	+	0.270915i	−0.829469	−	0.558553i	$-0.811357\pi$
$11$	−2.98007	+	2.98007i	−0.270915	+	0.270915i	0.558553	+	0.829469i	$0.311357\pi$
$12$		0			0
$13$			21.2000i			1.63077i	0.578921	+	0.815383i	$0.303474\pi$
$13$			21.2000i			1.63077i	−0.578921	+	0.815383i	$0.696526\pi$
$14$		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	−0.975069	−	0.221901i	$-0.928774\pi$
$19$	−14.3102	+	14.3102i	−0.753169	+	0.753169i	0.221901	+	0.975069i	$0.428774\pi$
$20$		0			0
$21$	14.9547	−	14.9547i	0.712131	−	0.712131i
$22$		0			0
$23$	−2.07267	+	2.07267i	−0.0901163	+	0.0901163i	−0.750728	−	0.660612i	$-0.770297\pi$
$23$	−2.07267	+	2.07267i	−0.0901163	+	0.0901163i	0.660612	+	0.750728i	$0.270297\pi$
$24$		0			0
$25$	16.5346	+	18.7512i	0.661386	+	0.750046i
$26$		0			0
$27$		−	28.5895i		−	1.05887i
$28$		0			0
$29$	17.5413	−	17.5413i	0.604872	−	0.604872i	−0.336730	−	0.941601i	$-0.609321\pi$
$29$	17.5413	−	17.5413i	0.604872	−	0.604872i	0.941601	+	0.336730i	$0.109321\pi$
$30$		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
$35$	13.4798	+	35.6680i	0.385138	+	1.01909i
$36$		0			0
$37$		−	65.3234i		−	1.76550i	−0.469845	−	0.882749i	$-0.655690\pi$
$37$		−	65.3234i		−	1.76550i	0.469845	−	0.882749i	$-0.344310\pi$
$38$		0			0
$39$	58.7936			1.50753
$40$		0			0
$41$		−	1.18249i		−	0.0288413i	−0.999896	−	0.0144207i	$-0.995410\pi$
$41$		−	1.18249i		−	0.0288413i	0.999896	−	0.0144207i	$-0.00459040\pi$
$42$		0			0
$43$	−9.57434			−0.222659			−0.111330	−	0.993784i	$-0.535511\pi$
$43$	−9.57434			−0.222659			−0.111330	+	0.993784i	$0.535511\pi$
$44$		0			0
$45$	5.96472	+	2.69282i	0.132549	+	0.0598404i
$46$		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
$53$	−99.2178			−1.87203			−0.936017	−	0.351955i	$-0.885517\pi$
$53$	−99.2178			−1.87203			−0.936017	+	0.351955i	$0.885517\pi$
$54$		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	0.997563	−	0.0697673i	$-0.0222257\pi$
$59$	54.7400	+	54.7400i	0.927796	+	0.927796i	−0.0697673	+	0.997563i	$0.522226\pi$
$60$		0			0
$61$	−12.1054	−	12.1054i	−0.198449	−	0.198449i	0.600886	−	0.799335i	$-0.294815\pi$
$61$	−12.1054	−	12.1054i	−0.198449	−	0.198449i	−0.799335	+	0.600886i	$0.794815\pi$
$62$		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
$67$	−109.074			−1.62798			−0.813988	−	0.580882i	$-0.802708\pi$
$67$	−109.074			−1.62798			−0.813988	+	0.580882i	$0.802708\pi$
$68$		0			0
$69$	5.74812	+	5.74812i	0.0833061	+	0.0833061i
$70$		0			0
$71$			73.1674i			1.03053i	0.857032	+	0.515263i	$0.172306\pi$
$71$			73.1674i			1.03053i	−0.857032	+	0.515263i	$0.827694\pi$
$72$		0			0
$73$	17.0166	−	17.0166i	0.233103	−	0.233103i	−0.580883	−	0.813987i	$-0.697293\pi$
$73$	17.0166	−	17.0166i	0.233103	−	0.233103i	0.813987	+	0.580883i	$0.197293\pi$
$74$		0			0
$75$	52.0023	−	45.8553i	0.693364	−	0.611404i
$76$		0			0
$77$	−32.1396			−0.417397
$78$		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
$83$		−	76.4850i		−	0.921506i	−0.887528	−	0.460753i	$-0.847579\pi$
$83$		−	76.4850i		−	0.921506i	0.887528	−	0.460753i	$-0.152421\pi$
$84$		0			0
$85$	44.1134	−	16.6716i	0.518982	−	0.196136i
$86$		0			0
$87$	−48.6470	−	48.6470i	−0.559161	−	0.559161i
$88$		0			0
$89$	−38.7296			−0.435164			−0.217582	−	0.976042i	$-0.569817\pi$
$89$	−38.7296			−0.435164			−0.217582	+	0.976042i	$0.569817\pi$
$90$		0			0
$91$	−114.319	+	114.319i	−1.25626	+	1.25626i
$92$		0			0
$93$		−	65.5810i		−	0.705172i
$94$		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	$-0.599585\pi$
$101$	65.0118	−	65.0118i	0.643681	−	0.643681i	0.951458	+	0.307777i	$0.0995852\pi$
$102$		0			0
$103$	−32.9039	+	32.9039i	−0.319456	+	0.319456i	−0.848558	−	0.529102i	$-0.822529\pi$
$103$	−32.9039	+	32.9039i	−0.319456	+	0.319456i	0.529102	+	0.848558i	$0.322529\pi$
$104$		0			0
$105$	98.9176	−	37.3834i	0.942073	−	0.356033i
$106$		0			0
$107$		−	19.9537i		−	0.186484i	−0.995643	−	0.0932418i	$-0.970277\pi$
$107$		−	19.9537i		−	0.186484i	0.995643	−	0.0932418i	$-0.0297230\pi$
$108$		0			0
$109$	−31.4162	+	31.4162i	−0.288222	+	0.288222i	−0.836377	−	0.548155i	$-0.815330\pi$
$109$	−31.4162	+	31.4162i	−0.288222	+	0.288222i	0.548155	+	0.836377i	$0.315330\pi$
$110$		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
$115$	−13.7096	+	5.18121i	−0.119214	+	0.0450540i
$116$		0			0
$117$			27.7482i			0.237164i
$118$		0			0
$119$	71.9267			0.604426
$120$		0			0
$121$			103.238i			0.853210i
$122$		0			0
$123$	−3.27939			−0.0266617
$124$		0			0
$125$	36.7727	+	119.469i	0.294181	+	0.955750i
$126$		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	$-0.268860\pi$
$131$	−10.9705	−	10.9705i	−0.0837444	−	0.0837444i	−0.747738	+	0.663994i	$0.768860\pi$
$132$		0			0
$133$	−154.333			−1.16040
$134$		0			0
$135$	58.8185	−	130.286i	0.435693	−	0.965079i
$136$		0			0
$137$	−122.401	−	122.401i	−0.893436	−	0.893436i	0.101408	−	0.994845i	$-0.467665\pi$
$137$	−122.401	−	122.401i	−0.893436	−	0.893436i	−0.994845	+	0.101408i	$0.967665\pi$
$138$		0			0
$139$	−163.514	−	163.514i	−1.17636	−	1.17636i	−0.980665	−	0.195693i	$-0.937305\pi$
$139$	−163.514	−	163.514i	−1.17636	−	1.17636i	−0.195693	−	0.980665i	$-0.562695\pi$
$140$		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
$147$	25.3936			0.172745
$148$		0			0
$149$	182.956	+	182.956i	1.22789	+	1.22789i	0.964759	+	0.263134i	$0.0847562\pi$
$149$	182.956	+	182.956i	1.22789	+	1.22789i	0.263134	+	0.964759i	$0.415244\pi$
$150$		0			0
$151$		−	100.104i		−	0.662938i	−0.943466	−	0.331469i	$-0.892456\pi$
$151$		−	100.104i		−	0.662938i	0.943466	−	0.331469i	$-0.107544\pi$
$152$		0			0
$153$	8.72923	−	8.72923i	0.0570538	−	0.0570538i
$154$		0			0
$155$	107.764	+	48.6509i	0.695251	+	0.313877i
$156$		0			0
$157$	27.8875			0.177627			0.0888136	−	0.996048i	$-0.471692\pi$
$157$	27.8875			0.177627			0.0888136	+	0.996048i	$0.471692\pi$
$158$		0			0
$159$			275.159i			1.73056i
$160$		0			0
$161$	−22.3535			−0.138841
$162$		0			0
$163$			122.177i			0.749552i	0.927115	+	0.374776i	$0.122280\pi$
$163$			122.177i			0.749552i	−0.927115	+	0.374776i	$0.877720\pi$
$164$		0			0
$165$	20.6596	+	54.6658i	0.125209	+	0.331308i
$166$		0			0
$167$	102.217	+	102.217i	0.612078	+	0.612078i	0.943487	−	0.331409i	$-0.107524\pi$
$167$	102.217	+	102.217i	0.612078	+	0.612078i	−0.331409	+	0.943487i	$0.607524\pi$
$168$		0			0
$169$	−280.439			−1.65940
$170$		0			0
$171$	−18.7303	+	18.7303i	−0.109534	+	0.109534i
$172$		0			0
$173$			144.968i			0.837968i	0.907994	+	0.418984i	$0.137614\pi$
$173$			144.968i			0.837968i	−0.907994	+	0.418984i	$0.862386\pi$
$174$		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	−0.479882	−	0.877333i	$-0.659320\pi$
$179$	71.1438	−	71.1438i	0.397451	−	0.397451i	0.877333	+	0.479882i	$0.159320\pi$
$180$		0			0
$181$	−192.954	+	192.954i	−1.06604	+	1.06604i	−0.0683832	+	0.997659i	$0.521784\pi$
$181$	−192.954	+	192.954i	−1.06604	+	1.06604i	−0.997659	+	0.0683832i	$0.978216\pi$
$182$		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
$187$			39.7496i			0.212565i
$188$		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
$195$	267.929	+	120.959i	1.37400	+	0.620302i
$196$		0			0
$197$		−	67.8338i		−	0.344334i	−0.985068	−	0.172167i	$-0.944923\pi$
$197$		−	67.8338i		−	0.344334i	0.985068	−	0.172167i	$-0.0550768\pi$
$198$		0			0
$199$	−278.771			−1.40086			−0.700430	−	0.713721i	$-0.747009\pi$
$199$	−278.771			−1.40086			−0.700430	+	0.713721i	$0.747009\pi$
$200$		0			0
$201$			302.495i			1.50495i
$202$		0			0
$203$	189.180			0.931922
$204$		0			0
$205$	2.43280	−	5.38876i	0.0118673	−	0.0262866i
$206$		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	$-0.221642\pi$
$211$	26.5489	+	26.5489i	0.125824	+	0.125824i	−0.641391	+	0.767215i	$0.721642\pi$
$212$		0			0
$213$	202.914			0.952648
$214$		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
$227$	346.057			1.52448			0.762240	−	0.647294i	$-0.224100\pi$
$227$	346.057			1.52448			0.762240	+	0.647294i	$0.224100\pi$
$228$		0			0
$229$	73.4761	+	73.4761i	0.320856	+	0.320856i	0.849096	−	0.528239i	$-0.177148\pi$
$229$	73.4761	+	73.4761i	0.320856	+	0.320856i	−0.528239	+	0.849096i	$0.677148\pi$
$230$		0			0
$231$			89.1323i			0.385854i
$232$		0			0
$233$	86.7985	−	86.7985i	0.372526	−	0.372526i	−0.495871	−	0.868396i	$-0.665151\pi$
$233$	86.7985	−	86.7985i	0.372526	−	0.372526i	0.868396	+	0.495871i	$0.165151\pi$
$234$		0			0
$235$	312.392	−	118.061i	1.32933	−	0.502385i
$236$		0			0
$237$	5.96613			0.0251736
$238$		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
$243$		−	70.0893i		−	0.288433i
$244$		0			0
$245$	−18.8381	+	41.7272i	−0.0768902	+	0.170315i
$246$		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	$-0.715555\pi$
$251$	38.3371	−	38.3371i	0.152737	−	0.152737i	0.779339	+	0.626602i	$0.215555\pi$
$252$		0			0
$253$		−	12.3534i		−	0.0488277i
$254$		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	−0.840730	−	0.541454i	$-0.817874\pi$
$263$	−78.7097	+	78.7097i	−0.299276	+	0.299276i	0.541454	+	0.840730i	$0.317874\pi$
$264$		0			0
$265$	−452.147	−	204.126i	−1.70622	−	0.770285i
$266$		0			0
$267$			107.408i			0.402279i
$268$		0			0
$269$	98.2650	−	98.2650i	0.365297	−	0.365297i	−0.500461	−	0.865759i	$-0.666836\pi$
$269$	98.2650	−	98.2650i	0.365297	−	0.365297i	0.865759	+	0.500461i	$0.166836\pi$
$270$		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
$275$	−105.154	−	6.60535i	−0.382378	−	0.0240195i
$276$		0			0
$277$		−	340.610i		−	1.22964i	−0.788668	−	0.614819i	$-0.789229\pi$
$277$		−	340.610i		−	1.22964i	0.788668	−	0.614819i	$-0.210771\pi$
$278$		0			0
$279$	30.9516			0.110938
$280$		0			0
$281$		−	103.541i		−	0.368474i	−0.982882	−	0.184237i	$-0.941019\pi$
$281$		−	103.541i		−	0.368474i	0.982882	−	0.184237i	$-0.0589814\pi$
$282$		0			0
$283$	−561.986			−1.98582			−0.992908	−	0.118887i	$-0.962068\pi$
$283$	−561.986			−1.98582			−0.992908	+	0.118887i	$0.962068\pi$
$284$		0			0
$285$	99.2066	+	262.504i	0.348093	+	0.921065i
$286$		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
$293$	1.90920			0.00651604			0.00325802	−	0.999995i	$-0.498963\pi$
$293$	1.90920			0.00651604			0.00325802	+	0.999995i	$0.498963\pi$
$294$		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
$307$	−465.516			−1.51634			−0.758169	−	0.652058i	$-0.773906\pi$
$307$	−465.516			−1.51634			−0.758169	+	0.652058i	$0.773906\pi$
$308$		0			0
$309$	91.2520	+	91.2520i	0.295314	+	0.295314i
$310$		0			0
$311$		−	212.375i		−	0.682879i	−0.939904	−	0.341439i	$-0.889086\pi$
$311$		−	212.375i		−	0.682879i	0.939904	−	0.341439i	$-0.110914\pi$
$312$		0			0
$313$	46.0307	−	46.0307i	0.147063	−	0.147063i	−0.629742	−	0.776805i	$-0.716839\pi$
$313$	46.0307	−	46.0307i	0.147063	−	0.147063i	0.776805	+	0.629742i	$0.216839\pi$
$314$		0			0
$315$	17.6435	+	46.6851i	0.0560110	+	0.148207i
$316$		0			0
$317$	−430.649			−1.35851			−0.679257	−	0.733901i	$-0.737698\pi$
$317$	−430.649			−1.35851			−0.679257	+	0.733901i	$0.737698\pi$
$318$		0			0
$319$			104.548i			0.327738i
$320$		0			0
$321$	−55.3375			−0.172391
$322$		0			0
$323$			190.876i			0.590948i
$324$		0			0
$325$	−397.524	+	350.534i	−1.22315	+	1.07857i
$326$		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	$-0.752519\pi$
$331$	−3.70469	+	3.70469i	−0.0111924	+	0.0111924i	0.701488	+	0.712681i	$0.252519\pi$
$332$		0			0
$333$		−	85.5005i		−	0.256758i
$334$		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
$347$			231.886i			0.668259i	0.942527	+	0.334130i	$0.108442\pi$
$347$			231.886i			0.668259i	−0.942527	+	0.334130i	$0.891558\pi$
$348$		0			0
$349$	205.898	−	205.898i	0.589965	−	0.589965i	−0.347657	−	0.937622i	$-0.613022\pi$
$349$	205.898	−	205.898i	0.589965	−	0.589965i	0.937622	+	0.347657i	$0.113022\pi$
$350$		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
$355$	−150.531	+	333.432i	−0.424030	+	0.939246i
$356$		0			0
$357$		−	199.473i		−	0.558749i
$358$		0			0
$359$	108.844			0.303187			0.151593	−	0.988443i	$-0.451560\pi$
$359$	108.844			0.303187			0.151593	+	0.988443i	$0.451560\pi$
$360$		0			0
$361$		−	48.5638i		−	0.134526i
$362$		0			0
$363$	286.310			0.788732
$364$		0			0
$365$	112.555	−	42.5375i	0.308371	−	0.116541i
$366$		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
$373$	205.735			0.551569			0.275784	−	0.961220i	$-0.411062\pi$
$373$	205.735			0.551569			0.275784	+	0.961220i	$0.411062\pi$
$374$		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	0.486953	−	0.873428i	$-0.338108\pi$
$379$	−146.474	−	146.474i	−0.386475	−	0.386475i	−0.873428	+	0.486953i	$0.838108\pi$
$380$		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
$387$	−12.5317			−0.0323815
$388$		0			0
$389$	91.3251	+	91.3251i	0.234769	+	0.234769i	0.814680	−	0.579911i	$-0.196913\pi$
$389$	91.3251	+	91.3251i	0.234769	+	0.234769i	−0.579911	+	0.814680i	$0.696913\pi$
$390$		0			0
$391$			27.6463i			0.0707067i
$392$		0			0
$393$	−30.4244	+	30.4244i	−0.0774158	+	0.0774158i
$394$		0			0
$395$	−4.42594	+	9.80366i	−0.0112049	+	0.0248194i
$396$		0			0
$397$	−181.720			−0.457732			−0.228866	−	0.973458i	$-0.573502\pi$
$397$	−181.720			−0.457732			−0.228866	+	0.973458i	$0.573502\pi$
$398$		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
$403$			501.324i			1.24398i
$404$		0			0
$405$	−307.637	−	138.885i	−0.759597	−	0.342926i
$406$		0			0
$407$	194.668	+	194.668i	0.478301	+	0.478301i
$408$		0			0
$409$	−724.291			−1.77088			−0.885441	−	0.464752i	$-0.846144\pi$
$409$	−724.291			−1.77088			−0.885441	+	0.464752i	$0.846144\pi$
$410$		0			0
$411$	−339.453	+	339.453i	−0.825919	+	0.825919i
$412$		0			0
$413$			590.362i			1.42945i
$414$		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	−0.792442	−	0.609947i	$-0.791191\pi$
$419$	−76.4657	+	76.4657i	−0.182496	+	0.182496i	0.609947	+	0.792442i	$0.291191\pi$
$420$		0			0
$421$	470.702	−	470.702i	1.11806	−	1.11806i	0.126030	−	0.992026i	$-0.459776\pi$
$421$	470.702	−	470.702i	1.11806	−	1.11806i	0.992026	−	0.126030i	$-0.0402236\pi$
$422$		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
$427$		−	130.555i		−	0.305749i
$428$		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
$435$	−121.606	−	321.774i	−0.279555	−	0.739710i
$436$		0			0
$437$		−	59.3208i		−	0.135745i
$438$		0			0
$439$	155.719			0.354714			0.177357	−	0.984147i	$-0.443245\pi$
$439$	155.719			0.354714			0.177357	+	0.984147i	$0.443245\pi$
$440$		0			0
$441$			11.9847i			0.0271763i
$442$		0			0
$443$	728.951			1.64549			0.822744	−	0.568412i	$-0.192442\pi$
$443$	728.951			1.64549			0.822744	+	0.568412i	$0.192442\pi$
$444$		0			0
$445$	−176.496	−	79.6803i	−0.396619	−	0.179057i
$446$		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
$453$	−277.616			−0.612839
$454$		0			0
$455$	−756.161	+	285.772i	−1.66189	+	0.628070i
$456$		0			0
$457$	227.434	+	227.434i	0.497667	+	0.497667i	0.910711	−	0.413044i	$-0.135534\pi$
$457$	227.434	+	227.434i	0.497667	+	0.497667i	−0.413044	+	0.910711i	$0.635534\pi$
$458$		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	$-0.116295\pi$
$461$	265.869	+	265.869i	0.576722	+	0.576722i	−0.357277	+	0.933999i	$0.616295\pi$
$462$		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
$467$	−632.343			−1.35405			−0.677027	−	0.735958i	$-0.736732\pi$
$467$	−632.343			−1.35405			−0.677027	+	0.735958i	$0.736732\pi$
$468$		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
$475$	−504.947	−	31.7187i	−1.06305	−	0.0667762i
$476$		0			0
$477$	−129.864			−0.272252
$478$		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
$483$			61.9926i			0.128349i
$484$		0			0
$485$	56.4828	−	21.3463i	0.116459	−	0.0440129i
$486$		0			0
$487$	285.326	+	285.326i	0.585886	+	0.585886i	0.936515	−	0.350629i	$-0.114032\pi$
$487$	285.326	+	285.326i	0.585886	+	0.585886i	−0.350629	+	0.936515i	$0.614032\pi$
$488$		0			0
$489$	338.832			0.692908
$490$		0			0
$491$	617.833	−	617.833i	1.25831	−	1.25831i	0.306418	−	0.951897i	$-0.400870\pi$
$491$	617.833	−	617.833i	1.25831	−	1.25831i	0.951897	−	0.306418i	$-0.0991305\pi$
$492$		0			0
$493$		−	233.974i		−	0.474592i
$494$		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	−0.128778	−	0.991673i	$-0.541106\pi$
$499$	430.585	−	430.585i	0.862895	−	0.862895i	0.991673	+	0.128778i	$0.0411056\pi$
$500$		0			0
$501$	283.477	−	283.477i	0.565823	−	0.565823i
$502$		0			0
$503$	−102.108	+	102.108i	−0.202998	+	0.202998i	−0.801283	−	0.598285i	$-0.795849\pi$
$503$	−102.108	+	102.108i	−0.202998	+	0.202998i	0.598285	+	0.801283i	$0.295849\pi$
$504$		0			0
$505$	430.018	−	162.514i	0.851521	−	0.321811i
$506$		0			0
$507$			777.737i			1.53400i
$508$		0			0
$509$	350.381	−	350.381i	0.688372	−	0.688372i	−0.273500	−	0.961872i	$-0.588181\pi$
$509$	350.381	−	350.381i	0.688372	−	0.688372i	0.961872	+	0.273500i	$0.0881813\pi$
$510$		0			0
$511$	183.521			0.359141
$512$		0			0
$513$	409.121	+	409.121i	0.797507	+	0.797507i
$514$		0			0
$515$	−217.642	+	82.2523i	−0.422606	+	0.159713i
$516$		0			0
$517$			281.489i			0.544466i
$518$		0			0
$519$	402.039			0.774642
$520$		0			0
$521$			89.0292i			0.170881i	0.996343	+	0.0854407i	$0.0272298\pi$
$521$			89.0292i			0.170881i	−0.996343	+	0.0854407i	$0.972770\pi$
$522$		0			0
$523$	399.222			0.763331			0.381666	−	0.924300i	$-0.375351\pi$
$523$	399.222			0.763331			0.381666	+	0.924300i	$0.375351\pi$
$524$		0			0
$525$	527.690	+	33.1473i	1.00512	+	0.0631378i
$526$		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
$533$	25.0688			0.0470334
$534$		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	$-0.186528\pi$
$541$	151.552	+	151.552i	0.280133	+	0.280133i	−0.553029	+	0.833162i	$0.686528\pi$
$542$		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
$547$	327.523			0.598762			0.299381	−	0.954134i	$-0.403220\pi$
$547$	327.523			0.598762			0.299381	+	0.954134i	$0.403220\pi$
$548$		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
$555$	−825.570	−	372.710i	−1.48751	−	0.671550i
$556$		0			0
$557$	609.704			1.09462			0.547311	−	0.836930i	$-0.315652\pi$
$557$	609.704			1.09462			0.547311	+	0.836930i	$0.315652\pi$
$558$		0			0
$559$		−	202.976i		−	0.363105i
$560$		0			0
$561$	110.237			0.196501
$562$		0			0
$563$		−	104.576i		−	0.185748i	−0.995678	−	0.0928738i	$-0.970395\pi$
$563$		−	104.576i		−	0.185748i	0.995678	−	0.0928738i	$-0.0296053\pi$
$564$		0			0
$565$	−120.441	−	318.690i	−0.213169	−	0.564053i
$566$		0			0
$567$	−364.026	−	364.026i	−0.642021	−	0.642021i
$568$		0			0
$569$	−153.954			−0.270569			−0.135284	−	0.990807i	$-0.543195\pi$
$569$	−153.954			−0.270569			−0.135284	+	0.990807i	$0.543195\pi$
$570$		0			0
$571$	−475.501	+	475.501i	−0.832751	+	0.832751i	−0.987892	−	0.155141i	$-0.950417\pi$
$571$	−475.501	+	475.501i	−0.832751	+	0.832751i	0.155141	+	0.987892i	$0.450417\pi$
$572$		0			0
$573$		−	581.164i		−	1.01425i
$574$		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
$587$		−	24.8014i		−	0.0422512i	−0.999777	−	0.0211256i	$-0.993275\pi$
$587$		−	24.8014i		−	0.0422512i	0.999777	−	0.0211256i	$-0.00672498\pi$
$588$		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
$595$	327.779	+	147.978i	0.550888	+	0.248703i
$596$		0			0
$597$			773.113i			1.29500i
$598$		0			0
$599$	−898.559			−1.50010			−0.750049	−	0.661382i	$-0.769970\pi$
$599$	−898.559			−1.50010			−0.750049	+	0.661382i	$0.769970\pi$
$600$		0			0
$601$			498.405i			0.829293i	0.909983	+	0.414646i	$0.136095\pi$
$601$			498.405i			0.829293i	−0.909983	+	0.414646i	$0.863905\pi$
$602$		0			0
$603$	−142.765			−0.236758
$604$		0			0
$605$	−212.397	+	470.469i	−0.351070	+	0.777635i
$606$		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
$613$	294.722			0.480787			0.240393	−	0.970676i	$-0.422724\pi$
$613$	294.722			0.480787			0.240393	+	0.970676i	$0.422724\pi$
$614$		0			0
$615$	−14.9446	−	6.74685i	−0.0243001	−	0.0109705i
$616$		0			0
$617$	248.885	+	248.885i	0.403379	+	0.403379i	0.879422	−	0.476043i	$-0.157929\pi$
$617$	248.885	+	248.885i	0.403379	+	0.403379i	−0.476043	+	0.879422i	$0.657929\pi$
$618$		0			0
$619$	320.358	+	320.358i	0.517541	+	0.517541i	0.916826	−	0.399286i	$-0.130742\pi$
$619$	320.358	+	320.358i	0.517541	+	0.517541i	−0.399286	+	0.916826i	$0.630742\pi$
$620$		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
$627$	−236.536			−0.377250
$628$		0			0
$629$	−435.658	−	435.658i	−0.692619	−	0.692619i
$630$		0			0
$631$			110.857i			0.175685i	0.996134	+	0.0878423i	$0.0279972\pi$
$631$			110.857i			0.175685i	−0.996134	+	0.0878423i	$0.972003\pi$
$632$		0			0
$633$	73.6276	−	73.6276i	0.116315	−	0.116315i
$634$		0			0
$635$	1092.47	−	412.873i	1.72043	−	0.650193i
$636$		0			0
$637$	−194.117			−0.304737
$638$		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
$643$		−	686.295i		−	1.06733i	−0.845695	−	0.533667i	$-0.820814\pi$
$643$		−	686.295i		−	1.06733i	0.845695	−	0.533667i	$-0.179186\pi$
$644$		0			0
$645$	−54.6275	+	121.002i	−0.0846938	+	0.187601i
$646$		0			0
$647$	499.985	+	499.985i	0.772774	+	0.772774i	0.978591	−	0.205817i	$-0.0659851\pi$
$647$	499.985	+	499.985i	0.772774	+	0.772774i	−0.205817	+	0.978591i	$0.565985\pi$
$648$		0			0
$649$	−326.258			−0.502708
$650$		0			0
$651$	353.641	−	353.641i	0.543227	−	0.543227i
$652$		0			0
$653$			599.129i			0.917502i	0.888565	+	0.458751i	$0.151703\pi$
$653$			599.129i			0.917502i	−0.888565	+	0.458751i	$0.848297\pi$
$654$		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	−0.663687	−	0.748010i	$-0.731009\pi$
$659$	55.5691	−	55.5691i	0.0843233	−	0.0843233i	0.748010	+	0.663687i	$0.231009\pi$
$660$		0			0
$661$	24.3517	−	24.3517i	0.0368407	−	0.0368407i	−0.688446	−	0.725287i	$-0.741707\pi$
$661$	24.3517	−	24.3517i	0.0368407	−	0.0368407i	0.725287	+	0.688446i	$0.241707\pi$
$662$		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
$667$			72.7147i			0.109018i
$668$		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
$675$	536.086	−	472.717i	0.794201	−	0.700321i
$676$		0			0
$677$			780.155i			1.15237i	0.817319	+	0.576185i	$0.195459\pi$
$677$			780.155i			1.15237i	−0.817319	+	0.576185i	$0.804541\pi$
$678$		0			0
$679$	92.0950			0.135633
$680$		0			0
$681$		−	959.715i		−	1.40927i
$682$		0			0
$683$	−170.375			−0.249451			−0.124725	−	0.992191i	$-0.539805\pi$
$683$	−170.375			−0.249451			−0.124725	+	0.992191i	$0.539805\pi$
$684$		0			0
$685$	−305.974	−	809.616i	−0.446677	−	1.18192i
$686$		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	$-0.233295\pi$
$691$	51.2626	+	51.2626i	0.0741861	+	0.0741861i	−0.669040	+	0.743226i	$0.733295\pi$
$692$		0			0
$693$	−42.0668			−0.0607025
$694$		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	$-0.228024\pi$
$701$	68.3903	+	68.3903i	0.0975610	+	0.0975610i	−0.656642	+	0.754203i	$0.728024\pi$
$702$		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
$707$	701.142			0.991714
$708$		0			0
$709$	815.622	+	815.622i	1.15038	+	1.15038i	0.986476	+	0.163908i	$0.0524101\pi$
$709$	815.622	+	815.622i	1.15038	+	1.15038i	0.163908	+	0.986476i	$0.447590\pi$
$710$		0			0
$711$			2.81577i			0.00396030i
$712$		0			0
$713$	−49.0133	+	49.0133i	−0.0687424	+	0.0687424i
$714$		0			0
$715$	−157.929	−	417.885i	−0.220880	−	0.584454i
$716$		0			0
$717$	567.946			0.792114
$718$		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
$723$		−	274.224i		−	0.379286i
$724$		0			0
$725$	618.958	+	38.8804i	0.853735	+	0.0536282i
$726$		0			0
$727$	−307.763	−	307.763i	−0.423333	−	0.423333i	0.463016	−	0.886350i	$-0.346767\pi$
$727$	−307.763	−	307.763i	−0.423333	−	0.423333i	−0.886350	+	0.463016i	$0.846767\pi$
$728$		0			0
$729$	−801.940			−1.10005
$730$		0			0
$731$	−63.8535	+	63.8535i	−0.0873510	+	0.0873510i
$732$		0			0
$733$		−	94.8581i		−	0.129411i	−0.997904	−	0.0647054i	$-0.979389\pi$
$733$		−	94.8581i		−	0.129411i	0.997904	−	0.0647054i	$-0.0206108\pi$
$734$		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	−0.0306228	+	0.999531i	$0.509749\pi$
$739$	−761.284	+	761.284i	−1.03015	+	1.03015i	−0.999531	+	0.0306228i	$0.990251\pi$
$740$		0			0
$741$	−841.348	+	841.348i	−1.13542	+	1.13542i
$742$		0			0
$743$	−700.467	+	700.467i	−0.942754	+	0.942754i	−0.998448	−	0.0556935i	$-0.982263\pi$
$743$	−700.467	+	700.467i	−0.942754	+	0.942754i	0.0556935	+	0.998448i	$0.482263\pi$
$744$		0			0
$745$	457.348	+	1210.16i	0.613890	+	1.62437i
$746$		0			0
$747$		−	100.110i		−	0.134016i
$748$		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
$755$	205.948	−	456.184i	0.272779	−	0.604217i
$756$		0			0
$757$			777.969i			1.02770i	0.857880	+	0.513850i	$0.171781\pi$
$757$			777.969i			1.02770i	−0.857880	+	0.513850i	$0.828219\pi$
$758$		0			0
$759$	−34.2596			−0.0451378
$760$		0			0
$761$		−	1058.98i		−	1.39156i	−0.718254	−	0.695781i	$-0.755058\pi$
$761$		−	1058.98i		−	1.39156i	0.718254	−	0.695781i	$-0.244942\pi$
$762$		0			0
$763$	−338.819			−0.444062
$764$		0			0
$765$	57.7392	−	21.8211i	0.0754760	−	0.0285243i
$766$		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
$773$	−405.962			−0.525177			−0.262588	−	0.964908i	$-0.584576\pi$
$773$	−405.962			−0.525177			−0.262588	+	0.964908i	$0.584576\pi$
$774$		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
$787$	−107.060			−0.136036			−0.0680181	−	0.997684i	$-0.521668\pi$
$787$	−107.060			−0.136036			−0.0680181	+	0.997684i	$0.521668\pi$
$788$		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
$795$	−566.099	+	1253.93i	−0.712074	+	1.57728i
$796$		0			0
$797$	−615.958			−0.772846			−0.386423	−	0.922322i	$-0.626289\pi$
$797$	−615.958			−0.772846			−0.386423	+	0.922322i	$0.626289\pi$
$798$		0			0
$799$		−	629.957i		−	0.788432i
$800$		0			0
$801$	−50.6924			−0.0632864
$802$		0			0
$803$			101.421i			0.126303i
$804$		0			0
$805$	−101.867	−	45.9889i	−0.126543	−	0.0571290i
$806$		0			0
$807$	−272.517	−	272.517i	−0.337692	−	0.337692i
$808$		0			0
$809$	304.293			0.376135			0.188067	−	0.982156i	$-0.439778\pi$
$809$	304.293			0.376135			0.188067	+	0.982156i	$0.439778\pi$
$810$		0			0
$811$	20.2059	−	20.2059i	0.0249148	−	0.0249148i	−0.694540	−	0.719454i	$-0.744392\pi$
$811$	20.2059	−	20.2059i	0.0249148	−	0.0249148i	0.719454	+	0.694540i	$0.244392\pi$
$812$		0			0
$813$		−	321.610i		−	0.395584i
$814$		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	$-0.856515\pi$
$821$	−381.316	+	381.316i	−0.464453	+	0.464453i	0.435659	+	0.900112i	$0.356515\pi$
$822$		0			0
$823$	−420.324	+	420.324i	−0.510721	+	0.510721i	−0.914747	−	0.404026i	$-0.867610\pi$
$823$	−420.324	+	420.324i	−0.510721	+	0.510721i	0.404026	+	0.914747i	$0.367610\pi$
$824$		0			0
$825$	−18.3185	+	291.622i	−0.0222043	+	0.353482i
$826$		0			0
$827$		−	844.006i		−	1.02056i	−0.860007	−	0.510281i	$-0.829541\pi$
$827$		−	844.006i		−	1.02056i	0.860007	−	0.510281i	$-0.170459\pi$
$828$		0			0
$829$	−222.833	+	222.833i	−0.268798	+	0.268798i	−0.828616	−	0.559818i	$-0.810871\pi$
$829$	−222.833	+	222.833i	−0.268798	+	0.268798i	0.559818	+	0.828616i	$0.310871\pi$
$830$		0			0
$831$	−944.609			−1.13671
$832$		0			0
$833$	61.0668	+	61.0668i	0.0733095	+	0.0733095i
$834$		0			0
$835$	255.519	+	676.111i	0.306011	+	0.809714i
$836$		0			0
$837$		−	676.067i		−	0.807726i
$838$		0			0
$839$	554.445			0.660841			0.330420	−	0.943834i	$-0.392809\pi$
$839$	554.445			0.660841			0.330420	+	0.943834i	$0.392809\pi$
$840$		0			0
$841$			225.607i			0.268260i
$842$		0			0
$843$	−287.150			−0.340628
$844$		0			0
$845$	−1277.99	−	576.960i	−1.51242	−	0.682793i
$846$		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
$853$	431.993			0.506440			0.253220	−	0.967409i	$-0.418510\pi$
$853$	431.993			0.506440			0.253220	+	0.967409i	$0.418510\pi$
$854$		0			0
$855$	−123.891	+	46.8215i	−0.144902	+	0.0547620i
$856$		0			0
$857$	−457.844	−	457.844i	−0.534241	−	0.534241i	0.387591	−	0.921831i	$-0.373307\pi$
$857$	−457.844	−	457.844i	−0.534241	−	0.534241i	−0.921831	+	0.387591i	$0.873307\pi$
$858$		0			0
$859$	822.277	+	822.277i	0.957249	+	0.957249i	0.999123	−	0.0418737i	$-0.0133327\pi$
$859$	822.277	+	822.277i	0.957249	+	0.957249i	−0.0418737	+	0.999123i	$0.513333\pi$
$860$		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
$867$	554.775			0.639879
$868$		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
$875$	−445.932	+	842.520i	−0.509637	+	0.962880i
$876$		0			0
$877$	363.488			0.414468			0.207234	−	0.978291i	$-0.433554\pi$
$877$	363.488			0.414468			0.207234	+	0.978291i	$0.433554\pi$
$878$		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
$883$		−	1629.94i		−	1.84592i	−0.384899	−	0.922959i	$-0.625764\pi$
$883$		−	1629.94i		−	1.84592i	0.384899	−	0.922959i	$-0.374236\pi$
$884$		0			0
$885$	1004.14	−	379.489i	1.13462	−	0.428801i
$886$		0			0
$887$	196.533	+	196.533i	0.221570	+	0.221570i	0.809160	−	0.587589i	$-0.199923\pi$
$887$	196.533	+	196.533i	0.221570	+	0.221570i	−0.587589	+	0.809160i	$0.699923\pi$
$888$		0			0
$889$	1781.27			2.00368
$890$		0			0
$891$	201.175	−	201.175i	0.225786	−	0.225786i
$892$		0			0
$893$			1351.70i			1.51366i
$894$		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
$907$		−	188.488i		−	0.207814i	−0.994587	−	0.103907i	$-0.966866\pi$
$907$		−	188.488i		−	0.207814i	0.994587	−	0.103907i	$-0.0331345\pi$
$908$		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
$915$	−222.059	+	83.9216i	−0.242687	+	0.0917176i
$916$		0			0
$917$		−	118.315i		−	0.129024i
$918$		0			0
$919$	158.471			0.172439			0.0862195	−	0.996276i	$-0.472521\pi$
$919$	158.471			0.172439			0.0862195	+	0.996276i	$0.472521\pi$
$920$		0			0
$921$			1291.01i			1.40175i
$922$		0			0
$923$	−1551.15			−1.68055
$924$		0			0
$925$	1224.89	−	1080.10i	1.32420	−	1.16768i
$926$		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
$933$	−588.978			−0.631273
$934$		0			0
$935$	−81.7787	+	181.144i	−0.0874639	+	0.193736i
$936$		0			0
$937$	−484.345	−	484.345i	−0.516910	−	0.516910i	0.399725	−	0.916635i	$-0.369106\pi$
$937$	−484.345	−	484.345i	−0.516910	−	0.516910i	−0.916635	+	0.399725i	$0.869106\pi$
$938$		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	$-0.112912\pi$
$941$	555.577	+	555.577i	0.590411	+	0.590411i	−0.347331	+	0.937742i	$0.612912\pi$
$942$		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
$947$	476.289			0.502945			0.251473	−	0.967864i	$-0.419085\pi$
$947$	476.289			0.502945			0.251473	+	0.967864i	$0.419085\pi$
$948$		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	−0.663343	−	0.748315i	$-0.730863\pi$
$953$	80.9782	−	80.9782i	0.0849719	−	0.0849719i	0.748315	+	0.663343i	$0.230863\pi$
$954$		0			0
$955$	954.980	+	431.134i	0.999979	+	0.451449i
$956$		0			0
$957$	289.943			0.302971
$958$		0			0
$959$		−	1320.07i		−	1.37651i
$960$		0			0
$961$	−401.801			−0.418107
$962$		0			0
$963$		−	26.1170i		−	0.0271205i
$964$		0			0
$965$	−225.652	−	597.083i	−0.233837	−	0.618739i
$966$		0			0
$967$	226.347	+	226.347i	0.234072	+	0.234072i	0.814390	−	0.580318i	$-0.197072\pi$
$967$	226.347	+	226.347i	0.234072	+	0.234072i	−0.580318	+	0.814390i	$0.697072\pi$
$968$		0			0
$969$	529.355			0.546290
$970$		0			0
$971$	375.576	−	375.576i	0.386793	−	0.386793i	−0.486749	−	0.873542i	$-0.661817\pi$
$971$	375.576	−	375.576i	0.386793	−	0.386793i	0.873542	+	0.486749i	$0.161817\pi$
$972$		0			0
$973$		−	1763.47i		−	1.81241i
$974$		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	−0.925345	−	0.379126i	$-0.876225\pi$
$983$	−536.933	+	536.933i	−0.546218	+	0.546218i	0.379126	+	0.925345i	$0.376225\pi$
$984$		0			0
$985$	139.558	−	309.126i	0.141683	−	0.313834i
$986$		0			0
$987$		−	1412.58i		−	1.43119i
$988$		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
$995$	−1270.39	−	573.530i	−1.27678	−	0.576412i
$996$		0			0
$997$		−	1493.41i		−	1.49790i	−0.662627	−	0.748950i	$-0.730558\pi$
$997$		−	1493.41i		−	1.49790i	0.662627	−	0.748950i	$-0.269442\pi$
$998$		0			0
$999$	−1867.56			−1.86943

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.14	✓	44	4.3	odd	2
80.3.i.a.37.14	yes	44	80.27	even	4
80.3.t.a.53.4	yes	44	16.11	odd	4
80.3.t.a.77.4	yes	44	20.7	even	4
320.3.i.a.177.16		44	80.37	odd	4	inner
320.3.i.a.273.7		44	1.1	even	1	trivial
320.3.t.a.17.7		44	5.2	odd	4
320.3.t.a.113.7		44	16.5	even	4
400.3.i.b.93.9		44	20.19	odd	2
400.3.i.b.357.9		44	80.43	even	4
400.3.t.b.157.19		44	20.3	even	4
400.3.t.b.293.19		44	80.59	odd	4
640.3.i.a.33.16		44	8.5	even	2
640.3.i.a.97.7		44	80.77	odd	4
640.3.i.b.33.7		44	8.3	odd	2
640.3.i.b.97.16		44	80.67	even	4
640.3.t.a.353.16		44	16.13	even	4
640.3.t.a.417.16		44	40.37	odd	4
640.3.t.b.353.7		44	16.3	odd	4
640.3.t.b.417.7		44	40.27	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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	320.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.77329i q^{3} +(4.55712 + 2.05735i) q^{5} +(5.39242 + 5.39242i) q^{7} +1.30888 q^{9} +O(q^{10})\)	\(q-2.77329i q^{3} +(4.55712 + 2.05735i) q^{5} +(5.39242 + 5.39242i) q^{7} +1.30888 q^{9} +(-2.98007 + 2.98007i) q^{11} +21.2000i q^{13} +(5.70562 - 12.6382i) q^{15} +(6.66924 - 6.66924i) q^{17} +(-14.3102 + 14.3102i) q^{19} +(14.9547 - 14.9547i) q^{21} +(-2.07267 + 2.07267i) q^{23} +(16.5346 + 18.7512i) q^{25} -28.5895i q^{27} +(17.5413 - 17.5413i) q^{29} +23.6474 q^{31} +(8.26459 + 8.26459i) q^{33} +(13.4798 + 35.6680i) q^{35} -65.3234i q^{37} +58.7936 q^{39} -1.18249i q^{41} -9.57434 q^{43} +(5.96472 + 2.69282i) q^{45} +(47.2286 - 47.2286i) q^{47} +9.15649i q^{49} +(-18.4957 - 18.4957i) q^{51} -99.2178 q^{53} +(-19.7116 + 7.44949i) q^{55} +(39.6863 + 39.6863i) q^{57} +(54.7400 + 54.7400i) q^{59} +(-12.1054 - 12.1054i) q^{61} +(7.05803 + 7.05803i) q^{63} +(-43.6157 + 96.6108i) q^{65} -109.074 q^{67} +(5.74812 + 5.74812i) q^{69} +73.1674i q^{71} +(17.0166 - 17.0166i) q^{73} +(52.0023 - 45.8553i) q^{75} -32.1396 q^{77} +2.15129i q^{79} -67.5069 q^{81} -76.4850i q^{83} +(44.1134 - 16.6716i) q^{85} +(-48.6470 - 48.6470i) q^{87} -38.7296 q^{89} +(-114.319 + 114.319i) q^{91} -65.5810i q^{93} +(-94.6543 + 35.7722i) q^{95} +(8.53929 - 8.53929i) q^{97} +(-3.90055 + 3.90055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{5} - 108 q^{9}+O(q^{10}) \) 44 * q - 2 * q^5 - 108 * q^9	\( 44 q - 2 q^{5} - 108 q^{9} + 4 q^{11} + 4 q^{15} - 4 q^{17} - 32 q^{19} - 4 q^{21} + 8 q^{31} - 4 q^{33} - 96 q^{35} - 72 q^{39} - 124 q^{43} - 34 q^{45} + 4 q^{47} + 100 q^{51} - 4 q^{53} + 36 q^{57} - 64 q^{59} - 36 q^{61} + 200 q^{63} - 4 q^{65} + 292 q^{67} - 60 q^{69} + 48 q^{73} - 96 q^{75} + 192 q^{77} + 100 q^{81} + 48 q^{85} - 36 q^{87} - 188 q^{91} - 380 q^{95} - 4 q^{97} + 92 q^{99}+O(q^{100}) \) 44 * q - 2 * q^5 - 108 * q^9 + 4 * q^11 + 4 * q^15 - 4 * q^17 - 32 * q^19 - 4 * q^21 + 8 * q^31 - 4 * q^33 - 96 * q^35 - 72 * q^39 - 124 * q^43 - 34 * q^45 + 4 * q^47 + 100 * q^51 - 4 * q^53 + 36 * q^57 - 64 * q^59 - 36 * q^61 + 200 * q^63 - 4 * q^65 + 292 * q^67 - 60 * q^69 + 48 * q^73 - 96 * q^75 + 192 * q^77 + 100 * q^81 + 48 * q^85 - 36 * q^87 - 188 * q^91 - 380 * q^95 - 4 * q^97 + 92 * q^99

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