LMFDB - Embedded newform 340.2.o.a.21.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [340,2,Mod(21,340)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(340, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("340.21"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 340 = 2^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	340.o (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.71491366872$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 6 x^{10} - 16 x^{9} + 9 x^{8} - 72 x^{7} + 114 x^{6} - 144 x^{5} + 391 x^{4} - 484 x^{3} + \cdots + 121 $ x^12 + 6x^10 - 16x^9 + 9x^8 - 72x^7 + 114x^6 - 144x^5 + 391x^4 - 484x^3 + 504x^2 - 396x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.4
Root			$0.671074 - 0.0762761i$ of defining polynomial
Character	$\chi$	$=$	340.21
Dual form			340.2.o.a.81.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.849725 - 0.849725i) q^{3} +(0.707107 - 0.707107i) q^{5} +(2.54612 + 2.54612i) q^{7} +1.55594i q^{9} +(0.311840 + 0.311840i) q^{11} +0.858277 q^{13} -1.20169i q^{15} +(0.348747 - 4.10833i) q^{17} -3.08768i q^{19} +4.32700 q^{21} +(-3.09623 - 3.09623i) q^{23} -1.00000i q^{25} +(3.87129 + 3.87129i) q^{27} +(-4.66072 + 4.66072i) q^{29} +(6.31903 - 6.31903i) q^{31} +0.529956 q^{33} +3.60075 q^{35} +(-7.36986 + 7.36986i) q^{37} +(0.729299 - 0.729299i) q^{39} +(-6.99464 - 6.99464i) q^{41} +7.07494i q^{43} +(1.10021 + 1.10021i) q^{45} +0.845726 q^{47} +5.96543i q^{49} +(-3.19461 - 3.78729i) q^{51} +4.78713i q^{53} +0.441008 q^{55} +(-2.62368 - 2.62368i) q^{57} -0.569172i q^{59} +(-1.35102 - 1.35102i) q^{61} +(-3.96160 + 3.96160i) q^{63} +(0.606894 - 0.606894i) q^{65} -10.0217 q^{67} -5.26189 q^{69} +(9.67657 - 9.67657i) q^{71} +(-1.97194 + 1.97194i) q^{73} +(-0.849725 - 0.849725i) q^{75} +1.58796i q^{77} +(2.69799 + 2.69799i) q^{79} +1.91125 q^{81} +0.152320i q^{83} +(-2.65843 - 3.15163i) q^{85} +7.92066i q^{87} -15.3828 q^{89} +(2.18528 + 2.18528i) q^{91} -10.7389i q^{93} +(-2.18332 - 2.18332i) q^{95} +(-9.93903 + 9.93903i) q^{97} +(-0.485203 + 0.485203i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} - 12 q^{11} + 16 q^{13} - 4 q^{17} + 16 q^{21} + 12 q^{23} - 20 q^{27} + 4 q^{29} - 8 q^{31} - 48 q^{33} - 8 q^{35} - 20 q^{37} + 36 q^{39} + 8 q^{41} + 8 q^{45} - 8 q^{47} + 24 q^{51} + 16 q^{55}+ \cdots - 40 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 - 12 * q^11 + 16 * q^13 - 4 * q^17 + 16 * q^21 + 12 * q^23 - 20 * q^27 + 4 * q^29 - 8 * q^31 - 48 * q^33 - 8 * q^35 - 20 * q^37 + 36 * q^39 + 8 * q^41 + 8 * q^45 - 8 * q^47 + 24 * q^51 + 16 * q^55 - 8 * q^61 + 4 * q^63 + 4 * q^65 + 32 * q^67 - 32 * q^69 + 28 * q^71 - 4 * q^75 - 24 * q^79 - 4 * q^81 - 4 * q^85 - 56 * q^89 - 4 * q^91 + 8 * q^95 - 44 * q^97 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/340\mathbb{Z}\right)^\times$.

$n$	$137$	$171$	$241$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	0.849725	−	0.849725i	0.490589	−	0.490589i	−0.417903	−	0.908492i	$-0.637235\pi$
$3$	0.849725	−	0.849725i	0.490589	−	0.490589i	0.908492	+	0.417903i	$0.137235\pi$
$4$		0			0
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$		0			0
$7$	2.54612	+	2.54612i	0.962342	+	0.962342i	0.999316	−	0.0369741i	$-0.0117719\pi$
$7$	2.54612	+	2.54612i	0.962342	+	0.962342i	−0.0369741	+	0.999316i	$0.511772\pi$
$8$		0			0
$9$			1.55594i			0.518645i
$10$		0			0
$11$	0.311840	+	0.311840i	0.0940232	+	0.0940232i	0.752554	−	0.658531i	$-0.228822\pi$
$11$	0.311840	+	0.311840i	0.0940232	+	0.0940232i	−0.658531	+	0.752554i	$0.728822\pi$
$12$		0			0
$13$	0.858277			0.238043			0.119022	−	0.992892i	$-0.462024\pi$
$13$	0.858277			0.238043			0.119022	+	0.992892i	$0.462024\pi$
$14$		0			0
$15$		−	1.20169i		−	0.310276i
$16$		0			0
$17$	0.348747	−	4.10833i	0.0845837	−	0.996416i
$17$	0.348747	−	4.10833i	0.0845837	−	0.996416i
$18$		0			0
$19$		−	3.08768i		−	0.708363i	−0.935177	−	0.354181i	$-0.884760\pi$
$19$		−	3.08768i		−	0.708363i	0.935177	−	0.354181i	$-0.115240\pi$
$20$		0			0
$21$	4.32700			0.944228
$22$		0			0
$23$	−3.09623	−	3.09623i	−0.645610	−	0.645610i	0.306319	−	0.951929i	$-0.400902\pi$
$23$	−3.09623	−	3.09623i	−0.645610	−	0.645610i	−0.951929	+	0.306319i	$0.900902\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$		0			0
$27$	3.87129	+	3.87129i	0.745030	+	0.745030i
$28$		0			0
$29$	−4.66072	+	4.66072i	−0.865475	+	0.865475i	−0.991968	−	0.126493i	$-0.959628\pi$
$29$	−4.66072	+	4.66072i	−0.865475	+	0.865475i	0.126493	+	0.991968i	$0.459628\pi$
$30$		0			0
$31$	6.31903	−	6.31903i	1.13493	−	1.13493i	0.145586	−	0.989346i	$-0.453493\pi$
$31$	6.31903	−	6.31903i	1.13493	−	1.13493i	0.989346	−	0.145586i	$-0.0465069\pi$
$32$		0			0
$33$	0.529956			0.0922534
$34$		0			0
$35$	3.60075			0.608639
$36$		0			0
$37$	−7.36986	+	7.36986i	−1.21160	+	1.21160i	−0.241097	+	0.970501i	$0.577507\pi$
$37$	−7.36986	+	7.36986i	−1.21160	+	1.21160i	−0.970501	+	0.241097i	$0.922493\pi$
$38$		0			0
$39$	0.729299	−	0.729299i	0.116781	−	0.116781i
$40$		0			0
$41$	−6.99464	−	6.99464i	−1.09238	−	1.09238i	−0.995274	−	0.0971056i	$-0.969042\pi$
$41$	−6.99464	−	6.99464i	−1.09238	−	1.09238i	−0.0971056	−	0.995274i	$-0.530958\pi$
$42$		0			0
$43$			7.07494i			1.07892i	0.842012	+	0.539459i	$0.181371\pi$
$43$			7.07494i			1.07892i	−0.842012	+	0.539459i	$0.818629\pi$
$44$		0			0
$45$	1.10021	+	1.10021i	0.164010	+	0.164010i
$46$		0			0
$47$	0.845726			0.123362			0.0616809	−	0.998096i	$-0.480354\pi$
$47$	0.845726			0.123362			0.0616809	+	0.998096i	$0.480354\pi$
$48$		0			0
$49$			5.96543i			0.852205i
$50$		0			0
$51$	−3.19461	−	3.78729i	−0.447335	−	0.530326i
$52$		0			0
$53$			4.78713i			0.657563i	0.944406	+	0.328782i	$0.106638\pi$
$53$			4.78713i			0.657563i	−0.944406	+	0.328782i	$0.893362\pi$
$54$		0			0
$55$	0.441008			0.0594655
$56$		0			0
$57$	−2.62368	−	2.62368i	−0.347515	−	0.347515i
$58$		0			0
$59$		−	0.569172i		−	0.0740999i	−0.999313	−	0.0370500i	$-0.988204\pi$
$59$		−	0.569172i		−	0.0740999i	0.999313	−	0.0370500i	$-0.0117961\pi$
$60$		0			0
$61$	−1.35102	−	1.35102i	−0.172981	−	0.172981i	0.615307	−	0.788288i	$-0.289032\pi$
$61$	−1.35102	−	1.35102i	−0.172981	−	0.172981i	−0.788288	+	0.615307i	$0.789032\pi$
$62$		0			0
$63$	−3.96160	+	3.96160i	−0.499114	+	0.499114i
$64$		0			0
$65$	0.606894	−	0.606894i	0.0752759	−	0.0752759i
$66$		0			0
$67$	−10.0217			−1.22435			−0.612175	−	0.790722i	$-0.709705\pi$
$67$	−10.0217			−1.22435			−0.612175	+	0.790722i	$0.709705\pi$
$68$		0			0
$69$	−5.26189			−0.633458
$70$		0			0
$71$	9.67657	−	9.67657i	1.14840	−	1.14840i	0.161529	−	0.986868i	$-0.448357\pi$
$71$	9.67657	−	9.67657i	1.14840	−	1.14840i	0.986868	−	0.161529i	$-0.0516426\pi$
$72$		0			0
$73$	−1.97194	+	1.97194i	−0.230798	+	0.230798i	−0.813026	−	0.582228i	$-0.802181\pi$
$73$	−1.97194	+	1.97194i	−0.230798	+	0.230798i	0.582228	+	0.813026i	$0.302181\pi$
$74$		0			0
$75$	−0.849725	−	0.849725i	−0.0981177	−	0.0981177i
$76$		0			0
$77$			1.58796i			0.180965i
$78$		0			0
$79$	2.69799	+	2.69799i	0.303548	+	0.303548i	0.842400	−	0.538852i	$-0.181142\pi$
$79$	2.69799	+	2.69799i	0.303548	+	0.303548i	−0.538852	+	0.842400i	$0.681142\pi$
$80$		0			0
$81$	1.91125			0.212361
$82$		0			0
$83$			0.152320i			0.0167193i	0.999965	+	0.00835966i	$0.00266099\pi$
$83$			0.152320i			0.0167193i	−0.999965	+	0.00835966i	$0.997339\pi$
$84$		0			0
$85$	−2.65843	−	3.15163i	−0.288347	−	0.341842i
$86$		0			0
$87$			7.92066i			0.849184i
$88$		0			0
$89$	−15.3828			−1.63057			−0.815284	−	0.579061i	$-0.803419\pi$
$89$	−15.3828			−1.63057			−0.815284	+	0.579061i	$0.803419\pi$
$90$		0			0
$91$	2.18528	+	2.18528i	0.229079	+	0.229079i
$92$		0			0
$93$		−	10.7389i		−	1.11357i
$94$		0			0
$95$	−2.18332	−	2.18332i	−0.224004	−	0.224004i
$96$		0			0
$97$	−9.93903	+	9.93903i	−1.00916	+	1.00916i	−0.00919831	+	0.999958i	$0.502928\pi$
$97$	−9.93903	+	9.93903i	−1.00916	+	1.00916i	−0.999958	+	0.00919831i	$0.997072\pi$
$98$		0			0
$99$	−0.485203	+	0.485203i	−0.0487647	+	0.0487647i
$100$		0			0
$101$	−1.90033			−0.189090			−0.0945448	−	0.995521i	$-0.530140\pi$
$101$	−1.90033			−0.189090			−0.0945448	+	0.995521i	$0.530140\pi$
$102$		0			0
$103$	6.36254			0.626920			0.313460	−	0.949601i	$-0.398512\pi$
$103$	6.36254			0.626920			0.313460	+	0.949601i	$0.398512\pi$
$104$		0			0
$105$	3.05965	−	3.05965i	0.298591	−	0.298591i
$106$		0			0
$107$	−8.44271	+	8.44271i	−0.816187	+	0.816187i	−0.985553	−	0.169366i	$-0.945828\pi$
$107$	−8.44271	+	8.44271i	−0.816187	+	0.816187i	0.169366	+	0.985553i	$0.445828\pi$
$108$		0			0
$109$	2.17688	+	2.17688i	0.208507	+	0.208507i	0.803633	−	0.595125i	$-0.202898\pi$
$109$	2.17688	+	2.17688i	0.208507	+	0.208507i	−0.595125	+	0.803633i	$0.702898\pi$
$110$		0			0
$111$			12.5247i			1.18879i
$112$		0			0
$113$	−4.19151	−	4.19151i	−0.394304	−	0.394304i	0.481914	−	0.876218i	$-0.339942\pi$
$113$	−4.19151	−	4.19151i	−0.394304	−	0.394304i	−0.876218	+	0.481914i	$0.839942\pi$
$114$		0			0
$115$	−4.37874			−0.408319
$116$		0			0
$117$			1.33542i			0.123460i
$118$		0			0
$119$	11.3482	−	9.57234i	1.04029	−	0.877495i
$120$		0			0
$121$		−	10.8055i		−	0.982319i
$122$		0			0
$123$	−11.8870			−1.07182
$124$		0			0
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$		−	5.36196i		−	0.475797i	−0.971290	−	0.237899i	$-0.923541\pi$
$127$		−	5.36196i		−	0.475797i	0.971290	−	0.237899i	$-0.0764586\pi$
$128$		0			0
$129$	6.01175	+	6.01175i	0.529305	+	0.529305i
$130$		0			0
$131$	10.9340	−	10.9340i	0.955311	−	0.955311i	−0.0437326	−	0.999043i	$-0.513925\pi$
$131$	10.9340	−	10.9340i	0.955311	−	0.955311i	0.999043	+	0.0437326i	$0.0139249\pi$
$132$		0			0
$133$	7.86160	−	7.86160i	0.681687	−	0.681687i
$134$		0			0
$135$	5.47483			0.471199
$136$		0			0
$137$	−0.858277			−0.0733276			−0.0366638	−	0.999328i	$-0.511673\pi$
$137$	−0.858277			−0.0733276			−0.0366638	+	0.999328i	$0.511673\pi$
$138$		0			0
$139$	−0.207354	+	0.207354i	−0.0175876	+	0.0175876i	−0.715846	−	0.698258i	$-0.753959\pi$
$139$	−0.207354	+	0.207354i	−0.0175876	+	0.0175876i	0.698258	+	0.715846i	$0.253959\pi$
$140$		0			0
$141$	0.718634	−	0.718634i	0.0605199	−	0.0605199i
$142$		0			0
$143$	0.267645	+	0.267645i	0.0223816	+	0.0223816i
$144$		0			0
$145$			6.59126i			0.547374i
$146$		0			0
$147$	5.06897	+	5.06897i	0.418082	+	0.418082i
$148$		0			0
$149$	14.9584			1.22544			0.612720	−	0.790300i	$-0.290076\pi$
$149$	14.9584			1.22544			0.612720	+	0.790300i	$0.290076\pi$
$150$		0			0
$151$			14.9851i			1.21947i	0.792604	+	0.609736i	$0.208725\pi$
$151$			14.9851i			1.21947i	−0.792604	+	0.609736i	$0.791275\pi$
$152$		0			0
$153$	6.39230	+	0.542629i	0.516787	+	0.0438689i
$154$		0			0
$155$		−	8.93646i		−	0.717794i
$156$		0			0
$157$	−6.98286			−0.557293			−0.278646	−	0.960394i	$-0.589886\pi$
$157$	−6.98286			−0.557293			−0.278646	+	0.960394i	$0.589886\pi$
$158$		0			0
$159$	4.06774	+	4.06774i	0.322593	+	0.322593i
$160$		0			0
$161$		−	15.7668i		−	1.24259i
$162$		0			0
$163$	8.69117	+	8.69117i	0.680745	+	0.680745i	0.960168	−	0.279423i	$-0.0901433\pi$
$163$	8.69117	+	8.69117i	0.680745	+	0.680745i	−0.279423	+	0.960168i	$0.590143\pi$
$164$		0			0
$165$	0.374735	−	0.374735i	0.0291731	−	0.0291731i
$166$		0			0
$167$	9.57929	−	9.57929i	0.741268	−	0.741268i	−0.231554	−	0.972822i	$-0.574381\pi$
$167$	9.57929	−	9.57929i	0.741268	−	0.741268i	0.972822	+	0.231554i	$0.0743810\pi$
$168$		0			0
$169$	−12.2634			−0.943335
$170$		0			0
$171$	4.80424			0.367389
$172$		0			0
$173$	13.0860	−	13.0860i	0.994913	−	0.994913i	−0.00507425	−	0.999987i	$-0.501615\pi$
$173$	13.0860	−	13.0860i	0.994913	−	0.994913i	0.999987	+	0.00507425i	$0.00161519\pi$
$174$		0			0
$175$	2.54612	−	2.54612i	0.192468	−	0.192468i
$176$		0			0
$177$	−0.483640	−	0.483640i	−0.0363526	−	0.0363526i
$178$		0			0
$179$		−	6.50504i		−	0.486209i	−0.970000	−	0.243105i	$-0.921834\pi$
$179$		−	6.50504i		−	0.486209i	0.970000	−	0.243105i	$-0.0781659\pi$
$180$		0			0
$181$	15.5163	+	15.5163i	1.15332	+	1.15332i	0.985884	+	0.167433i	$0.0535477\pi$
$181$	15.5163	+	15.5163i	1.15332	+	1.15332i	0.167433	+	0.985884i	$0.446452\pi$
$182$		0			0
$183$	−2.29600			−0.169725
$184$		0			0
$185$			10.4226i			0.766282i
$186$		0			0
$187$	1.38989	−	1.17239i	0.101639	−	0.0857334i
$188$		0			0
$189$			19.7135i			1.43395i
$190$		0			0
$191$	−6.33757			−0.458570			−0.229285	−	0.973359i	$-0.573639\pi$
$191$	−6.33757			−0.458570			−0.229285	+	0.973359i	$0.573639\pi$
$192$		0			0
$193$	15.9020	+	15.9020i	1.14465	+	1.14465i	0.987588	+	0.157066i	$0.0502035\pi$
$193$	15.9020	+	15.9020i	1.14465	+	1.14465i	0.157066	+	0.987588i	$0.449797\pi$
$194$		0			0
$195$		−	1.03138i		−	0.0738590i
$196$		0			0
$197$	3.04218	+	3.04218i	0.216746	+	0.216746i	0.807126	−	0.590380i	$-0.201022\pi$
$197$	3.04218	+	3.04218i	0.216746	+	0.216746i	−0.590380	+	0.807126i	$0.701022\pi$
$198$		0			0
$199$	16.3409	−	16.3409i	1.15838	−	1.15838i	0.173553	−	0.984825i	$-0.444475\pi$
$199$	16.3409	−	16.3409i	1.15838	−	1.15838i	0.984825	−	0.173553i	$-0.0555248\pi$
$200$		0			0
$201$	−8.51572	+	8.51572i	−0.600653	+	0.600653i
$202$		0			0
$203$	−23.7335			−1.66577
$204$		0			0
$205$	−9.89192			−0.690882
$206$		0			0
$207$	4.81754	−	4.81754i	0.334842	−	0.334842i
$208$		0			0
$209$	0.962862	−	0.962862i	0.0666025	−	0.0666025i
$210$		0			0
$211$	−9.01244	−	9.01244i	−0.620442	−	0.620442i	0.325202	−	0.945644i	$-0.394568\pi$
$211$	−9.01244	−	9.01244i	−0.620442	−	0.620442i	−0.945644	+	0.325202i	$0.894568\pi$
$212$		0			0
$213$		−	16.4448i		−	1.12678i
$214$		0			0
$215$	5.00274	+	5.00274i	0.341184	+	0.341184i
$216$		0			0
$217$	32.1780			2.18439
$218$		0			0
$219$			3.35121i			0.226454i
$220$		0			0
$221$	0.299322	−	3.52609i	0.0201346	−	0.237190i
$222$		0			0
$223$			19.0411i			1.27509i	0.770414	+	0.637544i	$0.220050\pi$
$223$			19.0411i			1.27509i	−0.770414	+	0.637544i	$0.779950\pi$
$224$		0			0
$225$	1.55594			0.103729
$226$		0			0
$227$	−15.3745	−	15.3745i	−1.02044	−	1.02044i	−0.999787	−	0.0206578i	$-0.993424\pi$
$227$	−15.3745	−	15.3745i	−1.02044	−	1.02044i	−0.0206578	−	0.999787i	$-0.506576\pi$
$228$		0			0
$229$		−	18.8958i		−	1.24867i	−0.781157	−	0.624335i	$-0.785370\pi$
$229$		−	18.8958i		−	1.24867i	0.781157	−	0.624335i	$-0.214630\pi$
$230$		0			0
$231$	1.34933	+	1.34933i	0.0887794	+	0.0887794i
$232$		0			0
$233$	−5.51283	+	5.51283i	−0.361158	+	0.361158i	−0.864239	−	0.503081i	$-0.832200\pi$
$233$	−5.51283	+	5.51283i	−0.361158	+	0.361158i	0.503081	+	0.864239i	$0.332200\pi$
$234$		0			0
$235$	0.598018	−	0.598018i	0.0390104	−	0.0390104i
$236$		0			0
$237$	4.58510			0.297834
$238$		0			0
$239$	0.792708			0.0512760			0.0256380	−	0.999671i	$-0.491838\pi$
$239$	0.792708			0.0512760			0.0256380	+	0.999671i	$0.491838\pi$
$240$		0			0
$241$	16.5867	−	16.5867i	1.06844	−	1.06844i	0.0709640	−	0.997479i	$-0.477392\pi$
$241$	16.5867	−	16.5867i	1.06844	−	1.06844i	0.997479	−	0.0709640i	$-0.0226076\pi$
$242$		0			0
$243$	−9.98983	+	9.98983i	−0.640848	+	0.640848i
$244$		0			0
$245$	4.21820	+	4.21820i	0.269491	+	0.269491i
$246$		0			0
$247$		−	2.65009i		−	0.168621i
$248$		0			0
$249$	0.129430	+	0.129430i	0.00820231	+	0.00820231i
$250$		0			0
$251$	−17.8958			−1.12957			−0.564787	−	0.825236i	$-0.691042\pi$
$251$	−17.8958			−1.12957			−0.564787	+	0.825236i	$0.691042\pi$
$252$		0			0
$253$		−	1.93106i		−	0.121405i
$254$		0			0
$255$	−4.93695	−	0.419087i	−0.309164	−	0.0262443i
$256$		0			0
$257$		−	6.06659i		−	0.378424i	−0.981936	−	0.189212i	$-0.939407\pi$
$257$		−	6.06659i		−	0.378424i	0.981936	−	0.189212i	$-0.0605933\pi$
$258$		0			0
$259$	−37.5291			−2.33194
$260$		0			0
$261$	−7.25179	−	7.25179i	−0.448874	−	0.448874i
$262$		0			0
$263$		−	11.2282i		−	0.692359i	−0.938168	−	0.346179i	$-0.887479\pi$
$263$		−	11.2282i		−	0.692359i	0.938168	−	0.346179i	$-0.112521\pi$
$264$		0			0
$265$	3.38501	+	3.38501i	0.207940	+	0.207940i
$266$		0			0
$267$	−13.0711	+	13.0711i	−0.799938	+	0.799938i
$268$		0			0
$269$	−1.47645	+	1.47645i	−0.0900205	+	0.0900205i	−0.750683	−	0.660663i	$-0.770275\pi$
$269$	−1.47645	+	1.47645i	−0.0900205	+	0.0900205i	0.660663	+	0.750683i	$0.270275\pi$
$270$		0			0
$271$	−16.8696			−1.02476			−0.512378	−	0.858760i	$-0.671235\pi$
$271$	−16.8696			−1.02476			−0.512378	+	0.858760i	$0.671235\pi$
$272$		0			0
$273$	3.71376			0.224767
$274$		0			0
$275$	0.311840	−	0.311840i	0.0188046	−	0.0188046i
$276$		0			0
$277$	6.22053	−	6.22053i	0.373755	−	0.373755i	−0.495088	−	0.868843i	$-0.664864\pi$
$277$	6.22053	−	6.22053i	0.373755	−	0.373755i	0.868843	+	0.495088i	$0.164864\pi$
$278$		0			0
$279$	9.83201	+	9.83201i	0.588627	+	0.588627i
$280$		0			0
$281$			16.4278i			0.980000i	0.871722	+	0.490000i	$0.163003\pi$
$281$			16.4278i			0.980000i	−0.871722	+	0.490000i	$0.836997\pi$
$282$		0			0
$283$	11.4555	+	11.4555i	0.680960	+	0.680960i	0.960217	−	0.279256i	$-0.0900879\pi$
$283$	11.4555	+	11.4555i	0.680960	+	0.680960i	−0.279256	+	0.960217i	$0.590088\pi$
$284$		0			0
$285$	−3.71044			−0.219788
$286$		0			0
$287$		−	35.6184i		−	2.10249i
$288$		0			0
$289$	−16.7568	−	2.86554i	−0.985691	−	0.168561i
$290$		0			0
$291$			16.8909i			0.990161i
$292$		0			0
$293$	4.18148			0.244284			0.122142	−	0.992513i	$-0.461024\pi$
$293$	4.18148			0.244284			0.122142	+	0.992513i	$0.461024\pi$
$294$		0			0
$295$	−0.402466	−	0.402466i	−0.0234325	−	0.0234325i
$296$		0			0
$297$			2.41444i			0.140100i
$298$		0			0
$299$	−2.65743	−	2.65743i	−0.153683	−	0.153683i
$300$		0			0
$301$	−18.0136	+	18.0136i	−1.03829	+	1.03829i
$302$		0			0
$303$	−1.61476	+	1.61476i	−0.0927653	+	0.0927653i
$304$		0			0
$305$	−1.91064			−0.109403
$306$		0			0
$307$	−3.68898			−0.210541			−0.105271	−	0.994444i	$-0.533571\pi$
$307$	−3.68898			−0.210541			−0.105271	+	0.994444i	$0.533571\pi$
$308$		0			0
$309$	5.40641	−	5.40641i	0.307560	−	0.307560i
$310$		0			0
$311$	−20.3769	+	20.3769i	−1.15547	+	1.15547i	−0.170027	+	0.985439i	$0.554385\pi$
$311$	−20.3769	+	20.3769i	−1.15547	+	1.15547i	−0.985439	+	0.170027i	$0.945615\pi$
$312$		0			0
$313$	−8.16252	−	8.16252i	−0.461373	−	0.461373i	0.437732	−	0.899105i	$-0.355782\pi$
$313$	−8.16252	−	8.16252i	−0.461373	−	0.461373i	−0.899105	+	0.437732i	$0.855782\pi$
$314$		0			0
$315$			5.60254i			0.315668i
$316$		0			0
$317$	10.5677	+	10.5677i	0.593539	+	0.593539i	0.938585	−	0.345047i	$-0.112137\pi$
$317$	10.5677	+	10.5677i	0.593539	+	0.593539i	−0.345047	+	0.938585i	$0.612137\pi$
$318$		0			0
$319$	−2.90680			−0.162749
$320$		0			0
$321$			14.3479i			0.800824i
$322$		0			0
$323$	−12.6852	−	1.07682i	−0.705824	−	0.0599159i
$324$		0			0
$325$		−	0.858277i		−	0.0476087i
$326$		0			0
$327$	3.69950			0.204583
$328$		0			0
$329$	2.15332	+	2.15332i	0.118716	+	0.118716i
$330$		0			0
$331$			16.5607i			0.910257i	0.890426	+	0.455128i	$0.150407\pi$
$331$			16.5607i			0.910257i	−0.890426	+	0.455128i	$0.849593\pi$
$332$		0			0
$333$	−11.4670	−	11.4670i	−0.628390	−	0.628390i
$334$		0			0
$335$	−7.08644	+	7.08644i	−0.387174	+	0.387174i
$336$		0			0
$337$	20.5030	−	20.5030i	1.11687	−	1.11687i	0.124672	−	0.992198i	$-0.460212\pi$
$337$	20.5030	−	20.5030i	1.11687	−	1.11687i	0.992198	−	0.124672i	$-0.0397880\pi$
$338$		0			0
$339$	−7.12326			−0.386882
$340$		0			0
$341$	3.94105			0.213420
$342$		0			0
$343$	2.63413	−	2.63413i	0.142230	−	0.142230i
$344$		0			0
$345$	−3.72072	+	3.72072i	−0.200317	+	0.200317i
$346$		0			0
$347$	14.6519	+	14.6519i	0.786558	+	0.786558i	0.980928	−	0.194370i	$-0.0622664\pi$
$347$	14.6519	+	14.6519i	0.786558	+	0.786558i	−0.194370	+	0.980928i	$0.562266\pi$
$348$		0			0
$349$			12.4314i			0.665436i	0.943026	+	0.332718i	$0.107966\pi$
$349$			12.4314i			0.665436i	−0.943026	+	0.332718i	$0.892034\pi$
$350$		0			0
$351$	3.32264	+	3.32264i	0.177349	+	0.177349i
$352$		0			0
$353$	16.1927			0.861852			0.430926	−	0.902387i	$-0.358187\pi$
$353$	16.1927			0.861852			0.430926	+	0.902387i	$0.358187\pi$
$354$		0			0
$355$		−	13.6847i		−	0.726310i
$356$		0			0
$357$	1.50903	−	17.7767i	0.0798663	−	0.940845i
$358$		0			0
$359$		−	24.3479i		−	1.28503i	−0.766272	−	0.642516i	$-0.777891\pi$
$359$		−	24.3479i		−	1.28503i	0.766272	−	0.642516i	$-0.222109\pi$
$360$		0			0
$361$	9.46622			0.498222
$362$		0			0
$363$	−9.18171	−	9.18171i	−0.481915	−	0.481915i
$364$		0			0
$365$			2.78874i			0.145970i
$366$		0			0
$367$	18.5690	+	18.5690i	0.969292	+	0.969292i	0.999542	−	0.0302501i	$-0.00963037\pi$
$367$	18.5690	+	18.5690i	0.969292	+	0.969292i	−0.0302501	+	0.999542i	$0.509630\pi$
$368$		0			0
$369$	10.8832	−	10.8832i	0.566558	−	0.566558i
$370$		0			0
$371$	−12.1886	+	12.1886i	−0.632801	+	0.632801i
$372$		0			0
$373$	−23.3722			−1.21017			−0.605083	−	0.796162i	$-0.706860\pi$
$373$	−23.3722			−1.21017			−0.605083	+	0.796162i	$0.706860\pi$
$374$		0			0
$375$	−1.20169			−0.0620551
$376$		0			0
$377$	−4.00019	+	4.00019i	−0.206020	+	0.206020i
$378$		0			0
$379$	13.6593	−	13.6593i	0.701633	−	0.701633i	−0.263128	−	0.964761i	$-0.584754\pi$
$379$	13.6593	−	13.6593i	0.701633	−	0.701633i	0.964761	+	0.263128i	$0.0847542\pi$
$380$		0			0
$381$	−4.55619	−	4.55619i	−0.233421	−	0.233421i
$382$		0			0
$383$			2.49777i			0.127630i	0.997962	+	0.0638150i	$0.0203267\pi$
$383$			2.49777i			0.127630i	−0.997962	+	0.0638150i	$0.979673\pi$
$384$		0			0
$385$	1.12286	+	1.12286i	0.0572261	+	0.0572261i
$386$		0			0
$387$	−11.0082			−0.559576
$388$		0			0
$389$			30.5541i			1.54915i	0.632480	+	0.774577i	$0.282037\pi$
$389$			30.5541i			1.54915i	−0.632480	+	0.774577i	$0.717963\pi$
$390$		0			0
$391$	−13.8002	+	11.6405i	−0.697904	+	0.588688i
$392$		0			0
$393$		−	18.5818i		−	0.937329i
$394$		0			0
$395$	3.81554			0.191981
$396$		0			0
$397$	−19.4586	−	19.4586i	−0.976601	−	0.976601i	0.0231310	−	0.999732i	$-0.492637\pi$
$397$	−19.4586	−	19.4586i	−0.976601	−	0.976601i	−0.999732	+	0.0231310i	$0.992637\pi$
$398$		0			0
$399$		−	13.3604i		−	0.668856i
$400$		0			0
$401$	−1.18566	−	1.18566i	−0.0592090	−	0.0592090i	0.676882	−	0.736091i	$-0.263331\pi$
$401$	−1.18566	−	1.18566i	−0.0592090	−	0.0592090i	−0.736091	+	0.676882i	$0.763331\pi$
$402$		0			0
$403$	5.42348	−	5.42348i	0.270163	−	0.270163i
$404$		0			0
$405$	1.35146	−	1.35146i	0.0671546	−	0.0671546i
$406$		0			0
$407$	−4.59643			−0.227837
$408$		0			0
$409$	−31.7380			−1.56934			−0.784671	−	0.619912i	$-0.787168\pi$
$409$	−31.7380			−1.56934			−0.784671	+	0.619912i	$0.787168\pi$
$410$		0			0
$411$	−0.729299	+	0.729299i	−0.0359737	+	0.0359737i
$412$		0			0
$413$	1.44918	−	1.44918i	0.0713095	−	0.0713095i
$414$		0			0
$415$	0.107707	+	0.107707i	0.00528711	+	0.00528711i
$416$		0			0
$417$			0.352388i			0.0172565i
$418$		0			0
$419$	17.6144	+	17.6144i	0.860520	+	0.860520i	0.991398	−	0.130878i	$-0.0417798\pi$
$419$	17.6144	+	17.6144i	0.860520	+	0.860520i	−0.130878	+	0.991398i	$0.541780\pi$
$420$		0			0
$421$	13.7355			0.669429			0.334714	−	0.942320i	$-0.391360\pi$
$421$	13.7355			0.669429			0.334714	+	0.942320i	$0.391360\pi$
$422$		0			0
$423$			1.31590i			0.0639810i
$424$		0			0
$425$	−4.10833	−	0.348747i	−0.199283	−	0.0169167i
$426$		0			0
$427$		−	6.87973i		−	0.332934i
$428$		0			0
$429$	0.454849			0.0219603
$430$		0			0
$431$	4.51255	+	4.51255i	0.217362	+	0.217362i	0.807386	−	0.590024i	$-0.200882\pi$
$431$	4.51255	+	4.51255i	0.217362	+	0.217362i	−0.590024	+	0.807386i	$0.700882\pi$
$432$		0			0
$433$		−	7.91233i		−	0.380242i	−0.981761	−	0.190121i	$-0.939112\pi$
$433$		−	7.91233i		−	0.380242i	0.981761	−	0.190121i	$-0.0608881\pi$
$434$		0			0
$435$	5.60075	+	5.60075i	0.268536	+	0.268536i
$436$		0			0
$437$	−9.56019	+	9.56019i	−0.457326	+	0.457326i
$438$		0			0
$439$	0.196069	−	0.196069i	0.00935784	−	0.00935784i	−0.702412	−	0.711770i	$-0.747894\pi$
$439$	0.196069	−	0.196069i	0.00935784	−	0.00935784i	0.711770	+	0.702412i	$0.247894\pi$
$440$		0			0
$441$	−9.28183			−0.441992
$442$		0			0
$443$	−5.95467			−0.282915			−0.141457	−	0.989944i	$-0.545179\pi$
$443$	−5.95467			−0.282915			−0.141457	+	0.989944i	$0.545179\pi$
$444$		0			0
$445$	−10.8772	+	10.8772i	−0.515631	+	0.515631i
$446$		0			0
$447$	12.7105	−	12.7105i	0.601187	−	0.601187i
$448$		0			0
$449$	27.3267	+	27.3267i	1.28963	+	1.28963i	0.935013	+	0.354612i	$0.115387\pi$
$449$	27.3267	+	27.3267i	1.28963	+	1.28963i	0.354612	+	0.935013i	$0.384613\pi$
$450$		0			0
$451$		−	4.36241i		−	0.205418i
$452$		0			0
$453$	12.7332	+	12.7332i	0.598259	+	0.598259i
$454$		0			0
$455$	3.09045			0.144882
$456$		0			0
$457$		−	34.8965i		−	1.63239i	−0.577777	−	0.816194i	$-0.696080\pi$
$457$		−	34.8965i		−	1.63239i	0.577777	−	0.816194i	$-0.303920\pi$
$458$		0			0
$459$	17.2546	−	14.5544i	0.805378	−	0.679343i
$460$		0			0
$461$			24.9983i			1.16429i	0.813087	+	0.582143i	$0.197786\pi$
$461$			24.9983i			1.16429i	−0.813087	+	0.582143i	$0.802214\pi$
$462$		0			0
$463$	12.0549			0.560240			0.280120	−	0.959965i	$-0.409626\pi$
$463$	12.0549			0.560240			0.280120	+	0.959965i	$0.409626\pi$
$464$		0			0
$465$	−7.59353	−	7.59353i	−0.352142	−	0.352142i
$466$		0			0
$467$		−	9.71659i		−	0.449630i	−0.974401	−	0.224815i	$-0.927822\pi$
$467$		−	9.71659i		−	0.449630i	0.974401	−	0.224815i	$-0.0721778\pi$
$468$		0			0
$469$	−25.5165	−	25.5165i	−1.17824	−	1.17824i
$470$		0			0
$471$	−5.93350	+	5.93350i	−0.273401	+	0.273401i
$472$		0			0
$473$	−2.20625	+	2.20625i	−0.101443	+	0.101443i
$474$		0			0
$475$	−3.08768			−0.141673
$476$		0			0
$477$	−7.44847			−0.341042
$478$		0			0
$479$	24.2119	−	24.2119i	1.10627	−	1.10627i	0.112635	−	0.993636i	$-0.464071\pi$
$479$	24.2119	−	24.2119i	1.10627	−	1.10627i	0.993636	−	0.112635i	$-0.0359290\pi$
$480$		0			0
$481$	−6.32538	+	6.32538i	−0.288413	+	0.288413i
$482$		0			0
$483$	−13.3974	−	13.3974i	−0.609603	−	0.609603i
$484$		0			0
$485$			14.0559i			0.638246i
$486$		0			0
$487$	21.7292	+	21.7292i	0.984645	+	0.984645i	0.999884	−	0.0152388i	$-0.00485086\pi$
$487$	21.7292	+	21.7292i	0.984645	+	0.984645i	−0.0152388	+	0.999884i	$0.504851\pi$
$488$		0			0
$489$	14.7702			0.667931
$490$		0			0
$491$		−	35.4594i		−	1.60026i	−0.599828	−	0.800129i	$-0.704764\pi$
$491$		−	35.4594i		−	1.60026i	0.599828	−	0.800129i	$-0.295236\pi$
$492$		0			0
$493$	17.5224	+	20.7732i	0.789168	+	0.935578i
$494$		0			0
$495$			0.686180i			0.0308415i
$496$		0			0
$497$	49.2754			2.21030
$498$		0			0
$499$	8.77320	+	8.77320i	0.392742	+	0.392742i	0.875664	−	0.482921i	$-0.160424\pi$
$499$	8.77320	+	8.77320i	0.392742	+	0.392742i	−0.482921	+	0.875664i	$0.660424\pi$
$500$		0			0
$501$		−	16.2795i		−	0.727315i
$502$		0			0
$503$	24.6020	+	24.6020i	1.09695	+	1.09695i	0.994765	+	0.102185i	$0.0325832\pi$
$503$	24.6020	+	24.6020i	1.09695	+	1.09695i	0.102185	+	0.994765i	$0.467417\pi$
$504$		0			0
$505$	−1.34373	+	1.34373i	−0.0597954	+	0.0597954i
$506$		0			0
$507$	−10.4205	+	10.4205i	−0.462790	+	0.462790i
$508$		0			0
$509$	18.4302			0.816902			0.408451	−	0.912780i	$-0.366069\pi$
$509$	18.4302			0.816902			0.408451	+	0.912780i	$0.366069\pi$
$510$		0			0
$511$	−10.0416			−0.444213
$512$		0			0
$513$	11.9533	−	11.9533i	0.527752	−	0.527752i
$514$		0			0
$515$	4.49900	−	4.49900i	0.198249	−	0.198249i
$516$		0			0
$517$	0.263731	+	0.263731i	0.0115989	+	0.0115989i
$518$		0			0
$519$		−	22.2391i		−	0.976186i
$520$		0			0
$521$	1.12348	+	1.12348i	0.0492205	+	0.0492205i	0.731289	−	0.682068i	$-0.238919\pi$
$521$	1.12348	+	1.12348i	0.0492205	+	0.0492205i	−0.682068	+	0.731289i	$0.738919\pi$
$522$		0			0
$523$	24.0707			1.05254			0.526270	−	0.850318i	$-0.323590\pi$
$523$	24.0707			1.05254			0.526270	+	0.850318i	$0.323590\pi$
$524$		0			0
$525$		−	4.32700i		−	0.188846i
$526$		0			0
$527$	−23.7569	−	28.1644i	−1.03487	−	1.22686i
$528$		0			0
$529$		−	3.82666i		−	0.166377i
$530$		0			0
$531$	0.885596			0.0384316
$532$		0			0
$533$	−6.00334	−	6.00334i	−0.260034	−	0.260034i
$534$		0			0
$535$			11.9398i			0.516202i
$536$		0			0
$537$	−5.52749	−	5.52749i	−0.238529	−	0.238529i
$538$		0			0
$539$	−1.86026	+	1.86026i	−0.0801270	+	0.0801270i
$540$		0			0
$541$	29.7186	−	29.7186i	1.27770	−	1.27770i	0.335754	−	0.941950i	$-0.391009\pi$
$541$	29.7186	−	29.7186i	1.27770	−	1.27770i	0.941950	−	0.335754i	$-0.108991\pi$
$542$		0			0
$543$	26.3691			1.13161
$544$		0			0
$545$	3.07857			0.131872
$546$		0			0
$547$	−8.75314	+	8.75314i	−0.374257	+	0.374257i	−0.869025	−	0.494768i	$-0.835253\pi$
$547$	−8.75314	+	8.75314i	−0.374257	+	0.374257i	0.494768	+	0.869025i	$0.335253\pi$
$548$		0			0
$549$	2.10211	−	2.10211i	0.0897158	−	0.0897158i
$550$		0			0
$551$	14.3908	+	14.3908i	0.613070	+	0.613070i
$552$		0			0
$553$			13.7388i			0.584234i
$554$		0			0
$555$	8.85630	+	8.85630i	0.375929	+	0.375929i
$556$		0			0
$557$	−34.0322			−1.44199			−0.720996	−	0.692939i	$-0.756316\pi$
$557$	−34.0322			−1.44199			−0.720996	+	0.692939i	$0.756316\pi$
$558$		0			0
$559$			6.07226i			0.256829i
$560$		0			0
$561$	0.184821	−	2.17723i	0.00780313	−	0.0919228i
$562$		0			0
$563$			43.2500i			1.82277i	0.411554	+	0.911386i	$0.364986\pi$
$563$			43.2500i			1.82277i	−0.411554	+	0.911386i	$0.635014\pi$
$564$		0			0
$565$	−5.92769			−0.249380
$566$		0			0
$567$	4.86628	+	4.86628i	0.204364	+	0.204364i
$568$		0			0
$569$			9.56042i			0.400794i	0.979715	+	0.200397i	$0.0642231\pi$
$569$			9.56042i			0.400794i	−0.979715	+	0.200397i	$0.935777\pi$
$570$		0			0
$571$	1.42521	+	1.42521i	0.0596434	+	0.0596434i	0.736299	−	0.676656i	$-0.236572\pi$
$571$	1.42521	+	1.42521i	0.0596434	+	0.0596434i	−0.676656	+	0.736299i	$0.736572\pi$
$572$		0			0
$573$	−5.38519	+	5.38519i	−0.224969	+	0.224969i
$574$		0			0
$575$	−3.09623	+	3.09623i	−0.129122	+	0.129122i
$576$		0			0
$577$	17.6730			0.735736			0.367868	−	0.929878i	$-0.380088\pi$
$577$	17.6730			0.735736			0.367868	+	0.929878i	$0.380088\pi$
$578$		0			0
$579$	27.0247			1.12311
$580$		0			0
$581$	−0.387825	+	0.387825i	−0.0160897	+	0.0160897i
$582$		0			0
$583$	−1.49282	+	1.49282i	−0.0618262	+	0.0618262i
$584$		0			0
$585$	0.944288	+	0.944288i	0.0390415	+	0.0390415i
$586$		0			0
$587$			38.9386i			1.60717i	0.595192	+	0.803583i	$0.297076\pi$
$587$			38.9386i			1.60717i	−0.595192	+	0.803583i	$0.702924\pi$
$588$		0			0
$589$	−19.5112	−	19.5112i	−0.803944	−	0.803944i
$590$		0			0
$591$	5.17003			0.212666
$592$		0			0
$593$			2.70134i			0.110931i	0.998461	+	0.0554653i	$0.0176642\pi$
$593$			2.70134i			0.110931i	−0.998461	+	0.0554653i	$0.982336\pi$
$594$		0			0
$595$	1.25575	−	14.7931i	0.0514809	−	0.606457i
$596$		0			0
$597$		−	27.7706i		−	1.13657i
$598$		0			0
$599$	−25.5707			−1.04479			−0.522396	−	0.852703i	$-0.674962\pi$
$599$	−25.5707			−1.04479			−0.522396	+	0.852703i	$0.674962\pi$
$600$		0			0
$601$	19.1635	+	19.1635i	0.781694	+	0.781694i	0.980117	−	0.198422i	$-0.0635818\pi$
$601$	19.1635	+	19.1635i	0.781694	+	0.781694i	−0.198422	+	0.980117i	$0.563582\pi$
$602$		0			0
$603$		−	15.5932i		−	0.635004i
$604$		0			0
$605$	−7.64065	−	7.64065i	−0.310637	−	0.310637i
$606$		0			0
$607$	−1.85412	+	1.85412i	−0.0752566	+	0.0752566i	−0.743733	−	0.668477i	$-0.766947\pi$
$607$	−1.85412	+	1.85412i	−0.0752566	+	0.0752566i	0.668477	+	0.743733i	$0.266947\pi$
$608$		0			0
$609$	−20.1669	+	20.1669i	−0.817206	+	0.817206i
$610$		0			0
$611$	0.725867			0.0293654
$612$		0			0
$613$	22.2141			0.897218			0.448609	−	0.893728i	$-0.351920\pi$
$613$	22.2141			0.897218			0.448609	+	0.893728i	$0.351920\pi$
$614$		0			0
$615$	−8.40541	+	8.40541i	−0.338939	+	0.338939i
$616$		0			0
$617$	−26.2279	+	26.2279i	−1.05590	+	1.05590i	−0.0575537	+	0.998342i	$0.518330\pi$
$617$	−26.2279	+	26.2279i	−1.05590	+	1.05590i	−0.998342	+	0.0575537i	$0.981670\pi$
$618$		0			0
$619$	−27.6655	−	27.6655i	−1.11197	−	1.11197i	−0.992884	−	0.119088i	$-0.962003\pi$
$619$	−27.6655	−	27.6655i	−1.11197	−	1.11197i	−0.119088	−	0.992884i	$-0.537997\pi$
$620$		0			0
$621$		−	23.9729i		−	0.961997i
$622$		0			0
$623$	−39.1663	−	39.1663i	−1.56916	−	1.56916i
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$		−	1.63633i		−	0.0653489i
$628$		0			0
$629$	27.7076	+	32.8480i	1.10477	+	1.30974i
$630$		0			0
$631$			11.5566i			0.460060i	0.973184	+	0.230030i	$0.0738825\pi$
$631$			11.5566i			0.460060i	−0.973184	+	0.230030i	$0.926118\pi$
$632$		0			0
$633$	−15.3162			−0.608764
$634$		0			0
$635$	−3.79148	−	3.79148i	−0.150460	−	0.150460i
$636$		0			0
$637$			5.11999i			0.202862i
$638$		0			0
$639$	15.0561	+	15.0561i	0.595611	+	0.595611i
$640$		0			0
$641$	−10.8245	+	10.8245i	−0.427541	+	0.427541i	−0.887790	−	0.460249i	$-0.847760\pi$
$641$	−10.8245	+	10.8245i	−0.427541	+	0.427541i	0.460249	+	0.887790i	$0.347760\pi$
$642$		0			0
$643$	−5.75529	+	5.75529i	−0.226966	+	0.226966i	−0.811424	−	0.584458i	$-0.801307\pi$
$643$	−5.75529	+	5.75529i	−0.226966	+	0.226966i	0.584458	+	0.811424i	$0.301307\pi$
$644$		0			0
$645$	8.50190			0.334762
$646$		0			0
$647$	13.3123			0.523359			0.261680	−	0.965155i	$-0.415724\pi$
$647$	13.3123			0.523359			0.261680	+	0.965155i	$0.415724\pi$
$648$		0			0
$649$	0.177490	−	0.177490i	0.00696711	−	0.00696711i
$650$		0			0
$651$	27.3424	−	27.3424i	1.07163	−	1.07163i
$652$		0			0
$653$	−4.90397	−	4.90397i	−0.191907	−	0.191907i	0.604612	−	0.796520i	$-0.293328\pi$
$653$	−4.90397	−	4.90397i	−0.191907	−	0.191907i	−0.796520	+	0.604612i	$0.793328\pi$
$654$		0			0
$655$		−	15.4631i		−	0.604192i
$656$		0			0
$657$	−3.06821	−	3.06821i	−0.119702	−	0.119702i
$658$		0			0
$659$	9.44123			0.367778			0.183889	−	0.982947i	$-0.441131\pi$
$659$	9.44123			0.367778			0.183889	+	0.982947i	$0.441131\pi$
$660$		0			0
$661$			1.09412i			0.0425562i	0.999774	+	0.0212781i	$0.00677354\pi$
$661$			1.09412i			0.0425562i	−0.999774	+	0.0212781i	$0.993226\pi$
$662$		0			0
$663$	−2.74186	−	3.25054i	−0.106485	−	0.126241i
$664$		0			0
$665$		−	11.1180i		−	0.431137i
$666$		0			0
$667$	28.8614			1.11752
$668$		0			0
$669$	16.1797	+	16.1797i	0.625544	+	0.625544i
$670$		0			0
$671$		−	0.842606i		−	0.0325284i
$672$		0			0
$673$	−35.2057	−	35.2057i	−1.35708	−	1.35708i	−0.877497	−	0.479582i	$-0.840788\pi$
$673$	−35.2057	−	35.2057i	−1.35708	−	1.35708i	−0.479582	−	0.877497i	$-0.659212\pi$
$674$		0			0
$675$	3.87129	−	3.87129i	0.149006	−	0.149006i
$676$		0			0
$677$	−4.78528	+	4.78528i	−0.183913	+	0.183913i	−0.793059	−	0.609145i	$-0.791513\pi$
$677$	−4.78528	+	4.78528i	−0.183913	+	0.183913i	0.609145	+	0.793059i	$0.291513\pi$
$678$		0			0
$679$	−50.6119			−1.94231
$680$		0			0
$681$	−26.1283			−1.00124
$682$		0			0
$683$	−0.594557	+	0.594557i	−0.0227501	+	0.0227501i	−0.718390	−	0.695640i	$-0.755121\pi$
$683$	−0.594557	+	0.594557i	−0.0227501	+	0.0227501i	0.695640	+	0.718390i	$0.255121\pi$
$684$		0			0
$685$	−0.606894	+	0.606894i	−0.0231882	+	0.0231882i
$686$		0			0
$687$	−16.0562	−	16.0562i	−0.612583	−	0.612583i
$688$		0			0
$689$			4.10869i			0.156528i
$690$		0			0
$691$	−20.8786	−	20.8786i	−0.794260	−	0.794260i	0.187923	−	0.982184i	$-0.439824\pi$
$691$	−20.8786	−	20.8786i	−0.794260	−	0.794260i	−0.982184	+	0.187923i	$0.939824\pi$
$692$		0			0
$693$	−2.47077			−0.0938566
$694$		0			0
$695$			0.293243i			0.0111234i
$696$		0			0
$697$	−31.1757	+	26.2969i	−1.18086	+	0.996067i
$698$		0			0
$699$			9.36877i			0.354360i
$700$		0			0
$701$	−41.7794			−1.57799			−0.788993	−	0.614402i	$-0.789397\pi$
$701$	−41.7794			−1.57799			−0.788993	+	0.614402i	$0.789397\pi$
$702$		0			0
$703$	22.7558	+	22.7558i	0.858251	+	0.858251i
$704$		0			0
$705$		−	1.01630i		−	0.0382761i
$706$		0			0
$707$	−4.83846	−	4.83846i	−0.181969	−	0.181969i
$708$		0			0
$709$	32.6543	−	32.6543i	1.22636	−	1.22636i	0.261028	−	0.965331i	$-0.415938\pi$
$709$	32.6543	−	32.6543i	1.22636	−	1.22636i	0.965331	−	0.261028i	$-0.0840616\pi$
$710$		0			0
$711$	−4.19791	+	4.19791i	−0.157434	+	0.157434i
$712$		0			0
$713$	−39.1304			−1.46545
$714$		0			0
$715$	0.378507			0.0141554
$716$		0			0
$717$	0.673583	−	0.673583i	0.0251554	−	0.0251554i
$718$		0			0
$719$	5.03927	−	5.03927i	0.187933	−	0.187933i	−0.606869	−	0.794802i	$-0.707575\pi$
$719$	5.03927	−	5.03927i	0.187933	−	0.187933i	0.794802	+	0.606869i	$0.207575\pi$
$720$		0			0
$721$	16.1998	+	16.1998i	0.603311	+	0.603311i
$722$		0			0
$723$		−	28.1882i		−	1.04833i
$724$		0			0
$725$	4.66072	+	4.66072i	0.173095	+	0.173095i
$726$		0			0
$727$	−23.6649			−0.877681			−0.438840	−	0.898565i	$-0.644611\pi$
$727$	−23.6649			−0.877681			−0.438840	+	0.898565i	$0.644611\pi$
$728$		0			0
$729$			22.7110i			0.841147i
$730$		0			0
$731$	29.0662	+	2.46737i	1.07505	+	0.0912588i
$732$		0			0
$733$			10.4809i			0.387122i	0.981088	+	0.193561i	$0.0620037\pi$
$733$			10.4809i			0.387122i	−0.981088	+	0.193561i	$0.937996\pi$
$734$		0			0
$735$	7.16861			0.264418
$736$		0			0
$737$	−3.12518	−	3.12518i	−0.115117	−	0.115117i
$738$		0			0
$739$			19.4369i			0.714996i	0.933914	+	0.357498i	$0.116370\pi$
$739$			19.4369i			0.714996i	−0.933914	+	0.357498i	$0.883630\pi$
$740$		0			0
$741$	−2.25184	−	2.25184i	−0.0827236	−	0.0827236i
$742$		0			0
$743$	36.7392	−	36.7392i	1.34783	−	1.34783i	0.459817	−	0.888014i	$-0.347915\pi$
$743$	36.7392	−	36.7392i	1.34783	−	1.34783i	0.888014	−	0.459817i	$-0.152085\pi$
$744$		0			0
$745$	10.5772	−	10.5772i	0.387518	−	0.387518i
$746$		0			0
$747$	−0.237001			−0.00867140
$748$		0			0
$749$	−42.9922			−1.57090
$750$		0			0
$751$	−26.7281	+	26.7281i	−0.975322	+	0.975322i	−0.999703	−	0.0243807i	$-0.992239\pi$
$751$	−26.7281	+	26.7281i	−0.975322	+	0.975322i	0.0243807	+	0.999703i	$0.492239\pi$
$752$		0			0
$753$	−15.2065	+	15.2065i	−0.554157	+	0.554157i
$754$		0			0
$755$	10.5961	+	10.5961i	0.385631	+	0.385631i
$756$		0			0
$757$			32.6953i			1.18833i	0.804344	+	0.594165i	$0.202517\pi$
$757$			32.6953i			1.18833i	−0.804344	+	0.594165i	$0.797483\pi$
$758$		0			0
$759$	−1.64087	−	1.64087i	−0.0595597	−	0.0595597i
$760$		0			0
$761$	20.9742			0.760314			0.380157	−	0.924922i	$-0.375870\pi$
$761$	20.9742			0.760314			0.380157	+	0.924922i	$0.375870\pi$
$762$		0			0
$763$			11.0852i			0.401311i
$764$		0			0
$765$	4.90374	−	4.13634i	0.177295	−	0.149550i
$766$		0			0
$767$		−	0.488508i		−	0.0176390i
$768$		0			0
$769$	−48.1965			−1.73801			−0.869005	−	0.494803i	$-0.835240\pi$
$769$	−48.1965			−1.73801			−0.869005	+	0.494803i	$0.835240\pi$
$770$		0			0
$771$	−5.15493	−	5.15493i	−0.185650	−	0.185650i
$772$		0			0
$773$			30.5076i			1.09728i	0.836059	+	0.548640i	$0.184854\pi$
$773$			30.5076i			1.09728i	−0.836059	+	0.548640i	$0.815146\pi$
$774$		0			0
$775$	−6.31903	−	6.31903i	−0.226986	−	0.226986i
$776$		0			0
$777$	−31.8894	+	31.8894i	−1.14402	+	1.14402i
$778$		0			0
$779$	−21.5972	+	21.5972i	−0.773801	+	0.773801i
$780$		0			0
$781$	6.03507			0.215952
$782$		0			0
$783$	−36.0860			−1.28961
$784$		0			0
$785$	−4.93762	+	4.93762i	−0.176231	+	0.176231i
$786$		0			0
$787$	−10.1400	+	10.1400i	−0.361452	+	0.361452i	−0.864347	−	0.502895i	$-0.832268\pi$
$787$	−10.1400	+	10.1400i	−0.361452	+	0.361452i	0.502895	+	0.864347i	$0.332268\pi$
$788$		0			0
$789$	−9.54086	−	9.54086i	−0.339663	−	0.339663i
$790$		0			0
$791$		−	21.3442i		−	0.758911i
$792$		0			0
$793$	−1.15955	−	1.15955i	−0.0411770	−	0.0411770i
$794$		0			0
$795$	5.75266			0.204026
$796$		0			0
$797$			43.8868i			1.55455i	0.629161	+	0.777275i	$0.283399\pi$
$797$			43.8868i			1.55455i	−0.629161	+	0.777275i	$0.716601\pi$
$798$		0			0
$799$	0.294945	−	3.47452i	0.0104344	−	0.122920i
$800$		0			0
$801$		−	23.9346i		−	0.845687i
$802$		0			0
$803$	−1.22986			−0.0434007
$804$		0			0
$805$	−11.1488	−	11.1488i	−0.392943	−	0.392943i
$806$		0			0
$807$			2.50914i			0.0883260i
$808$		0			0
$809$	−11.5776	−	11.5776i	−0.407048	−	0.407048i	0.473660	−	0.880708i	$-0.342933\pi$
$809$	−11.5776	−	11.5776i	−0.407048	−	0.407048i	−0.880708	+	0.473660i	$0.842933\pi$
$810$		0			0
$811$	37.9966	−	37.9966i	1.33424	−	1.33424i	0.432705	−	0.901535i	$-0.357559\pi$
$811$	37.9966	−	37.9966i	1.33424	−	1.33424i	0.901535	−	0.432705i	$-0.142441\pi$
$812$		0			0
$813$	−14.3345	+	14.3345i	−0.502734	+	0.502734i
$814$		0			0
$815$	12.2912			0.430541
$816$		0			0
$817$	21.8452			0.764265
$818$		0			0
$819$	−3.40015	+	3.40015i	−0.118811	+	0.118811i
$820$		0			0
$821$	14.6216	−	14.6216i	0.510298	−	0.510298i	−0.404320	−	0.914618i	$-0.632492\pi$
$821$	14.6216	−	14.6216i	0.510298	−	0.510298i	0.914618	+	0.404320i	$0.132492\pi$
$822$		0			0
$823$	−11.3195	−	11.3195i	−0.394573	−	0.394573i	0.481740	−	0.876314i	$-0.340005\pi$
$823$	−11.3195	−	11.3195i	−0.394573	−	0.394573i	−0.876314	+	0.481740i	$0.840005\pi$
$824$		0			0
$825$		−	0.529956i		−	0.0184507i
$826$		0			0
$827$	12.3448	+	12.3448i	0.429269	+	0.429269i	0.888379	−	0.459110i	$-0.151832\pi$
$827$	12.3448	+	12.3448i	0.429269	+	0.429269i	−0.459110	+	0.888379i	$0.651832\pi$
$828$		0			0
$829$	−35.5735			−1.23552			−0.617759	−	0.786368i	$-0.711959\pi$
$829$	−35.5735			−1.23552			−0.617759	+	0.786368i	$0.711959\pi$
$830$		0			0
$831$		−	10.5715i		−	0.366720i
$832$		0			0
$833$	24.5080	+	2.08043i	0.849151	+	0.0720826i
$834$		0			0
$835$		−	13.5472i		−	0.468819i
$836$		0			0
$837$	48.9256			1.69112
$838$		0			0
$839$	34.1295	+	34.1295i	1.17828	+	1.17828i	0.980182	+	0.198100i	$0.0634771\pi$
$839$	34.1295	+	34.1295i	1.17828	+	1.17828i	0.198100	+	0.980182i	$0.436523\pi$
$840$		0			0
$841$		−	14.4447i		−	0.498093i
$842$		0			0
$843$	13.9591	+	13.9591i	0.480777	+	0.480777i
$844$		0			0
$845$	−8.67151	+	8.67151i	−0.298309	+	0.298309i
$846$		0			0
$847$	27.5121	−	27.5121i	0.945327	−	0.945327i
$848$		0			0
$849$	19.4681			0.668143
$850$		0			0
$851$	45.6376			1.56444
$852$		0			0
$853$	17.5597	−	17.5597i	0.601233	−	0.601233i	−0.339406	−	0.940640i	$-0.610226\pi$
$853$	17.5597	−	17.5597i	0.601233	−	0.601233i	0.940640	+	0.339406i	$0.110226\pi$
$854$		0			0
$855$	3.39711	−	3.39711i	0.116179	−	0.116179i
$856$		0			0
$857$	−8.24219	−	8.24219i	−0.281548	−	0.281548i	0.552178	−	0.833726i	$-0.313797\pi$
$857$	−8.24219	−	8.24219i	−0.281548	−	0.281548i	−0.833726	+	0.552178i	$0.813797\pi$
$858$		0			0
$859$		−	1.76702i		−	0.0602900i	−0.999546	−	0.0301450i	$-0.990403\pi$
$859$		−	1.76702i		−	0.0602900i	0.999546	−	0.0301450i	$-0.00959690\pi$
$860$		0			0
$861$	−30.2658	−	30.2658i	−1.03146	−	1.03146i
$862$		0			0
$863$	−46.0934			−1.56904			−0.784518	−	0.620106i	$-0.787090\pi$
$863$	−46.0934			−1.56904			−0.784518	+	0.620106i	$0.787090\pi$
$864$		0			0
$865$		−	18.5064i		−	0.629238i
$866$		0			0
$867$	−16.6735	+	11.8037i	−0.566263	+	0.400875i
$868$		0			0
$869$			1.68268i			0.0570811i
$870$		0			0
$871$	−8.60144			−0.291449
$872$		0			0
$873$	−15.4645	−	15.4645i	−0.523394	−	0.523394i
$874$		0			0
$875$		−	3.60075i		−	0.121728i
$876$		0			0
$877$	−20.4117	−	20.4117i	−0.689255	−	0.689255i	0.272813	−	0.962067i	$-0.412046\pi$
$877$	−20.4117	−	20.4117i	−0.689255	−	0.689255i	−0.962067	+	0.272813i	$0.912046\pi$
$878$		0			0
$879$	3.55310	−	3.55310i	0.119843	−	0.119843i
$880$		0			0
$881$	−8.10219	+	8.10219i	−0.272970	+	0.272970i	−0.830295	−	0.557325i	$-0.811828\pi$
$881$	−8.10219	+	8.10219i	−0.272970	+	0.272970i	0.557325	+	0.830295i	$0.311828\pi$
$882$		0			0
$883$	45.5357			1.53240			0.766199	−	0.642604i	$-0.222146\pi$
$883$	45.5357			1.53240			0.766199	+	0.642604i	$0.222146\pi$
$884$		0			0
$885$	−0.683970			−0.0229914
$886$		0			0
$887$	−21.2088	+	21.2088i	−0.712121	+	0.712121i	−0.966979	−	0.254858i	$-0.917971\pi$
$887$	−21.2088	+	21.2088i	−0.712121	+	0.712121i	0.254858	+	0.966979i	$0.417971\pi$
$888$		0			0
$889$	13.6522	−	13.6522i	0.457880	−	0.457880i
$890$		0			0
$891$	0.596004	+	0.596004i	0.0199669	+	0.0199669i
$892$		0			0
$893$		−	2.61133i		−	0.0873849i
$894$		0			0
$895$	−4.59976	−	4.59976i	−0.153753	−	0.153753i
$896$		0			0
$897$	−4.51616			−0.150790
$898$		0			0
$899$			58.9025i			1.96451i
$900$		0			0
$901$	19.6671	+	1.66950i	0.655207	+	0.0556191i
$902$		0			0
$903$			30.6132i			1.01874i
$904$		0			0
$905$	21.9433			0.729421
$906$		0			0
$907$	−21.1053	−	21.1053i	−0.700789	−	0.700789i	0.263791	−	0.964580i	$-0.415027\pi$
$907$	−21.1053	−	21.1053i	−0.700789	−	0.700789i	−0.964580	+	0.263791i	$0.915027\pi$
$908$		0			0
$909$		−	2.95679i		−	0.0980705i
$910$		0			0
$911$	28.9605	+	28.9605i	0.959504	+	0.959504i	0.999211	−	0.0397077i	$-0.0126427\pi$
$911$	28.9605	+	28.9605i	0.959504	+	0.959504i	−0.0397077	+	0.999211i	$0.512643\pi$
$912$		0			0
$913$	−0.0474995	+	0.0474995i	−0.00157200	+	0.00157200i
$914$		0			0
$915$	−1.62352	+	1.62352i	−0.0536718	+	0.0536718i
$916$		0			0
$917$	55.6787			1.83867
$918$		0			0
$919$	41.5906			1.37195			0.685973	−	0.727627i	$-0.259377\pi$
$919$	41.5906			1.37195			0.685973	+	0.727627i	$0.259377\pi$
$920$		0			0
$921$	−3.13461	+	3.13461i	−0.103289	+	0.103289i
$922$		0			0
$923$	8.30518	−	8.30518i	0.273368	−	0.273368i
$924$		0			0
$925$	7.36986	+	7.36986i	0.242320	+	0.242320i
$926$		0			0
$927$			9.89971i			0.325149i
$928$		0			0
$929$	−34.8304	−	34.8304i	−1.14275	−	1.14275i	−0.987945	−	0.154805i	$-0.950525\pi$
$929$	−34.8304	−	34.8304i	−1.14275	−	1.14275i	−0.154805	−	0.987945i	$-0.549475\pi$
$930$		0			0
$931$	18.4194			0.603670
$932$		0			0
$933$			34.6294i			1.13372i
$934$		0			0
$935$	0.153800	−	1.81181i	0.00502981	−	0.0592524i
$936$		0			0
$937$		−	6.06542i		−	0.198149i	−0.995080	−	0.0990743i	$-0.968412\pi$
$937$		−	6.06542i		−	0.198149i	0.995080	−	0.0990743i	$-0.0315881\pi$
$938$		0			0
$939$	−13.8718			−0.452689
$940$		0			0
$941$	−15.0698	−	15.0698i	−0.491261	−	0.491261i	0.417442	−	0.908704i	$-0.362927\pi$
$941$	−15.0698	−	15.0698i	−0.491261	−	0.491261i	−0.908704	+	0.417442i	$0.862927\pi$
$942$		0			0
$943$			43.3141i			1.41050i
$944$		0			0
$945$	13.9396	+	13.9396i	0.453454	+	0.453454i
$946$		0			0
$947$	−5.18941	+	5.18941i	−0.168633	+	0.168633i	−0.786378	−	0.617745i	$-0.788046\pi$
$947$	−5.18941	+	5.18941i	−0.168633	+	0.168633i	0.617745	+	0.786378i	$0.288046\pi$
$948$		0			0
$949$	−1.69247	+	1.69247i	−0.0549399	+	0.0549399i
$950$		0			0
$951$	17.9592			0.582367
$952$		0			0
$953$	20.8537			0.675517			0.337759	−	0.941233i	$-0.390331\pi$
$953$	20.8537			0.675517			0.337759	+	0.941233i	$0.390331\pi$
$954$		0			0
$955$	−4.48134	+	4.48134i	−0.145013	+	0.145013i
$956$		0			0
$957$	−2.46998	+	2.46998i	−0.0798430	+	0.0798430i
$958$		0			0
$959$	−2.18528	−	2.18528i	−0.0705662	−	0.0705662i
$960$		0			0
$961$		−	48.8604i		−	1.57614i
$962$		0			0
$963$	−13.1363	−	13.1363i	−0.423312	−	0.423312i
$964$		0			0
$965$	22.4889			0.723943
$966$		0			0
$967$		−	28.0955i		−	0.903492i	−0.892147	−	0.451746i	$-0.850801\pi$
$967$		−	28.0955i		−	0.903492i	0.892147	−	0.451746i	$-0.149199\pi$
$968$		0			0
$969$	−11.6939	+	9.86394i	−0.375664	+	0.316875i
$970$		0			0
$971$		−	39.4478i		−	1.26594i	−0.774176	−	0.632970i	$-0.781836\pi$
$971$		−	39.4478i		−	1.26594i	0.774176	−	0.632970i	$-0.218164\pi$
$972$		0			0
$973$	−1.05590			−0.0338505
$974$		0			0
$975$	−0.729299	−	0.729299i	−0.0233563	−	0.0233563i
$976$		0			0
$977$			35.4283i			1.13345i	0.823906	+	0.566726i	$0.191790\pi$
$977$			35.4283i			1.13345i	−0.823906	+	0.566726i	$0.808210\pi$
$978$		0			0
$979$	−4.79695	−	4.79695i	−0.153311	−	0.153311i
$980$		0			0
$981$	−3.38709	+	3.38709i	−0.108141	+	0.108141i
$982$		0			0
$983$	−10.6102	+	10.6102i	−0.338412	+	0.338412i	−0.855770	−	0.517357i	$-0.826916\pi$
$983$	−10.6102	+	10.6102i	−0.338412	+	0.338412i	0.517357	+	0.855770i	$0.326916\pi$
$984$		0			0
$985$	4.30229			0.137082
$986$		0			0
$987$	3.65945			0.116482
$988$		0			0
$989$	21.9057	−	21.9057i	0.696560	−	0.696560i
$990$		0			0
$991$	1.09187	−	1.09187i	0.0346844	−	0.0346844i	−0.689552	−	0.724236i	$-0.742192\pi$
$991$	1.09187	−	1.09187i	0.0346844	−	0.0346844i	0.724236	+	0.689552i	$0.242192\pi$
$992$		0			0
$993$	14.0720	+	14.0720i	0.446562	+	0.446562i
$994$		0			0
$995$		−	23.1096i		−	0.732622i
$996$		0			0
$997$	−6.30718	−	6.30718i	−0.199750	−	0.199750i	0.600143	−	0.799893i	$-0.295110\pi$
$997$	−6.30718	−	6.30718i	−0.199750	−	0.199750i	−0.799893	+	0.600143i	$0.795110\pi$
$998$		0			0
$999$	−57.0618			−1.80535

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	340.2.o.a.21.4	✓	12
3.2	odd	2		3060.2.be.b.361.3		12
4.3	odd	2		1360.2.bt.c.1041.3		12
5.2	odd	4		1700.2.m.c.1449.3		12
5.3	odd	4		1700.2.m.f.1449.4		12
5.4	even	2		1700.2.o.d.701.3		12
17.2	even	8		5780.2.c.h.5201.5		12
17.8	even	8		5780.2.a.n.1.3		6
17.9	even	8		5780.2.a.m.1.4		6
17.13	even	4	inner	340.2.o.a.81.4	yes	12
17.15	even	8		5780.2.c.h.5201.8		12
51.47	odd	4		3060.2.be.b.1441.3		12
68.47	odd	4		1360.2.bt.c.81.3		12
85.13	odd	4		1700.2.m.c.149.3		12
85.47	odd	4		1700.2.m.f.149.4		12
85.64	even	4		1700.2.o.d.1101.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
340.2.o.a.21.4	✓	12	1.1	even	1	trivial
340.2.o.a.81.4	yes	12	17.13	even	4	inner
1360.2.bt.c.81.3		12	68.47	odd	4
1360.2.bt.c.1041.3		12	4.3	odd	2
1700.2.m.c.149.3		12	85.13	odd	4
1700.2.m.c.1449.3		12	5.2	odd	4
1700.2.m.f.149.4		12	85.47	odd	4
1700.2.m.f.1449.4		12	5.3	odd	4
1700.2.o.d.701.3		12	5.4	even	2
1700.2.o.d.1101.3		12	85.64	even	4
3060.2.be.b.361.3		12	3.2	odd	2
3060.2.be.b.1441.3		12	51.47	odd	4
5780.2.a.m.1.4		6	17.9	even	8
5780.2.a.n.1.3		6	17.8	even	8
5780.2.c.h.5201.5		12	17.2	even	8
5780.2.c.h.5201.8		12	17.15	even	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 340 = 2^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	340.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.849725 - 0.849725i) q^{3} +(0.707107 - 0.707107i) q^{5} +(2.54612 + 2.54612i) q^{7} +1.55594i q^{9} +(0.311840 + 0.311840i) q^{11} +0.858277 q^{13} -1.20169i q^{15} +(0.348747 - 4.10833i) q^{17} -3.08768i q^{19} +4.32700 q^{21} +(-3.09623 - 3.09623i) q^{23} -1.00000i q^{25} +(3.87129 + 3.87129i) q^{27} +(-4.66072 + 4.66072i) q^{29} +(6.31903 - 6.31903i) q^{31} +0.529956 q^{33} +3.60075 q^{35} +(-7.36986 + 7.36986i) q^{37} +(0.729299 - 0.729299i) q^{39} +(-6.99464 - 6.99464i) q^{41} +7.07494i q^{43} +(1.10021 + 1.10021i) q^{45} +0.845726 q^{47} +5.96543i q^{49} +(-3.19461 - 3.78729i) q^{51} +4.78713i q^{53} +0.441008 q^{55} +(-2.62368 - 2.62368i) q^{57} -0.569172i q^{59} +(-1.35102 - 1.35102i) q^{61} +(-3.96160 + 3.96160i) q^{63} +(0.606894 - 0.606894i) q^{65} -10.0217 q^{67} -5.26189 q^{69} +(9.67657 - 9.67657i) q^{71} +(-1.97194 + 1.97194i) q^{73} +(-0.849725 - 0.849725i) q^{75} +1.58796i q^{77} +(2.69799 + 2.69799i) q^{79} +1.91125 q^{81} +0.152320i q^{83} +(-2.65843 - 3.15163i) q^{85} +7.92066i q^{87} -15.3828 q^{89} +(2.18528 + 2.18528i) q^{91} -10.7389i q^{93} +(-2.18332 - 2.18332i) q^{95} +(-9.93903 + 9.93903i) q^{97} +(-0.485203 + 0.485203i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 12 q^{11} + 16 q^{13} - 4 q^{17} + 16 q^{21} + 12 q^{23} - 20 q^{27} + 4 q^{29} - 8 q^{31} - 48 q^{33} - 8 q^{35} - 20 q^{37} + 36 q^{39} + 8 q^{41} + 8 q^{45} - 8 q^{47} + 24 q^{51} + 16 q^{55}+ \cdots - 40 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 - 12 * q^11 + 16 * q^13 - 4 * q^17 + 16 * q^21 + 12 * q^23 - 20 * q^27 + 4 * q^29 - 8 * q^31 - 48 * q^33 - 8 * q^35 - 20 * q^37 + 36 * q^39 + 8 * q^41 + 8 * q^45 - 8 * q^47 + 24 * q^51 + 16 * q^55 - 8 * q^61 + 4 * q^63 + 4 * q^65 + 32 * q^67 - 32 * q^69 + 28 * q^71 - 4 * q^75 - 24 * q^79 - 4 * q^81 - 4 * q^85 - 56 * q^89 - 4 * q^91 + 8 * q^95 - 44 * q^97 - 40 * q^99

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