LMFDB - Embedded newform 780.2.r.a.73.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [780,2,Mod(73,780)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(780, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("780.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	780.r (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.22833135766$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			73.6
Character	$\chi$	$=$	780.73
Dual form			780.2.r.a.577.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{3} +(1.62796 + 1.53289i) q^{5} -2.13466i q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{3} +(1.62796 + 1.53289i) q^{5} -2.13466i q^{7} +1.00000i q^{9} +(1.89894 - 1.89894i) q^{11} +(1.37361 + 3.33364i) q^{13} +(-0.0672190 - 2.23506i) q^{15} +(-1.22748 - 1.22748i) q^{17} +(0.581270 - 0.581270i) q^{19} +(-1.50943 + 1.50943i) q^{21} +(4.10913 - 4.10913i) q^{23} +(0.300476 + 4.99096i) q^{25} +(0.707107 - 0.707107i) q^{27} -1.81712i q^{29} +(4.74497 + 4.74497i) q^{31} -2.68551 q^{33} +(3.27221 - 3.47513i) q^{35} -6.00961i q^{37} +(1.38595 - 3.32853i) q^{39} +(3.85523 + 3.85523i) q^{41} +(3.78653 - 3.78653i) q^{43} +(-1.53289 + 1.62796i) q^{45} +2.75112i q^{47} +2.44322 q^{49} +1.73592i q^{51} +(-7.79380 - 7.79380i) q^{53} +(6.00227 - 0.180517i) q^{55} -0.822039 q^{57} +(0.434208 + 0.434208i) q^{59} +13.1423 q^{61} +2.13466 q^{63} +(-2.87394 + 7.53263i) q^{65} +1.27294 q^{67} -5.81118 q^{69} +(-1.66190 - 1.66190i) q^{71} -0.637019 q^{73} +(3.31667 - 3.74161i) q^{75} +(-4.05360 - 4.05360i) q^{77} -0.837401i q^{79} -1.00000 q^{81} -5.22354i q^{83} +(-0.116687 - 3.87988i) q^{85} +(-1.28490 + 1.28490i) q^{87} +(-3.92688 - 3.92688i) q^{89} +(7.11620 - 2.93220i) q^{91} -6.71041i q^{93} +(1.83731 - 0.0552566i) q^{95} +6.15970 q^{97} +(1.89894 + 1.89894i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q+O(q^{10}) $ 28 * q	$ 28 q + 8 q^{11} - 4 q^{13} - 4 q^{15} - 4 q^{17} - 16 q^{19} + 8 q^{21} - 8 q^{23} + 12 q^{25} - 8 q^{33} + 8 q^{39} + 12 q^{41} + 16 q^{43} + 4 q^{45} - 36 q^{49} + 36 q^{53} + 40 q^{55} + 16 q^{59} + 8 q^{61} - 40 q^{65} + 48 q^{67} - 8 q^{69} + 8 q^{71} + 48 q^{73} - 48 q^{77} - 28 q^{81} - 4 q^{85} - 24 q^{87} - 36 q^{89} - 24 q^{91} + 72 q^{95} - 72 q^{97} + 8 q^{99}+O(q^{100}) $ 28 * q + 8 * q^11 - 4 * q^13 - 4 * q^15 - 4 * q^17 - 16 * q^19 + 8 * q^21 - 8 * q^23 + 12 * q^25 - 8 * q^33 + 8 * q^39 + 12 * q^41 + 16 * q^43 + 4 * q^45 - 36 * q^49 + 36 * q^53 + 40 * q^55 + 16 * q^59 + 8 * q^61 - 40 * q^65 + 48 * q^67 - 8 * q^69 + 8 * q^71 + 48 * q^73 - 48 * q^77 - 28 * q^81 - 4 * q^85 - 24 * q^87 - 36 * q^89 - 24 * q^91 + 72 * q^95 - 72 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/780\mathbb{Z}\right)^\times$.

$n$	$157$	$301$	$391$	$521$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		0			0
$5$	1.62796	+	1.53289i	0.728044	+	0.685531i
$5$	1.62796	+	1.53289i	0.728044	+	0.685531i
$6$		0			0
$7$		−	2.13466i		−	0.806826i	−0.915018	−	0.403413i	$-0.867824\pi$
$7$		−	2.13466i		−	0.806826i	0.915018	−	0.403413i	$-0.132176\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	1.89894	−	1.89894i	0.572553	−	0.572553i	−0.360288	−	0.932841i	$-0.617322\pi$
$11$	1.89894	−	1.89894i	0.572553	−	0.572553i	0.932841	+	0.360288i	$0.117322\pi$
$12$		0			0
$13$	1.37361	+	3.33364i	0.380972	+	0.924587i
$13$	1.37361	+	3.33364i	0.380972	+	0.924587i
$14$		0			0
$15$	−0.0672190	−	2.23506i	−0.0173559	−	0.577089i
$16$		0			0
$17$	−1.22748	−	1.22748i	−0.297708	−	0.297708i	0.542408	−	0.840115i	$-0.317513\pi$
$17$	−1.22748	−	1.22748i	−0.297708	−	0.297708i	−0.840115	+	0.542408i	$0.817513\pi$
$18$		0			0
$19$	0.581270	−	0.581270i	0.133352	−	0.133352i	−0.637280	−	0.770632i	$-0.719941\pi$
$19$	0.581270	−	0.581270i	0.133352	−	0.133352i	0.770632	+	0.637280i	$0.219941\pi$
$20$		0			0
$21$	−1.50943	+	1.50943i	−0.329385	+	0.329385i
$22$		0			0
$23$	4.10913	−	4.10913i	0.856812	−	0.856812i	−0.134149	−	0.990961i	$-0.542830\pi$
$23$	4.10913	−	4.10913i	0.856812	−	0.856812i	0.990961	+	0.134149i	$0.0428300\pi$
$24$		0			0
$25$	0.300476	+	4.99096i	0.0600953	+	0.998193i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$		−	1.81712i		−	0.337431i	−0.985665	−	0.168715i	$-0.946038\pi$
$29$		−	1.81712i		−	0.337431i	0.985665	−	0.168715i	$-0.0539619\pi$
$30$		0			0
$31$	4.74497	+	4.74497i	0.852223	+	0.852223i	0.990407	−	0.138184i	$-0.0441265\pi$
$31$	4.74497	+	4.74497i	0.852223	+	0.852223i	−0.138184	+	0.990407i	$0.544127\pi$
$32$		0			0
$33$	−2.68551			−0.467487
$34$		0			0
$35$	3.27221	−	3.47513i	0.553104	−	0.587405i
$36$		0			0
$37$		−	6.00961i		−	0.987974i	−0.869469	−	0.493987i	$-0.835539\pi$
$37$		−	6.00961i		−	0.987974i	0.869469	−	0.493987i	$-0.164461\pi$
$38$		0			0
$39$	1.38595	−	3.32853i	0.221930	−	0.532992i
$40$		0			0
$41$	3.85523	+	3.85523i	0.602086	+	0.602086i	0.940866	−	0.338780i	$-0.110014\pi$
$41$	3.85523	+	3.85523i	0.602086	+	0.602086i	−0.338780	+	0.940866i	$0.610014\pi$
$42$		0			0
$43$	3.78653	−	3.78653i	0.577440	−	0.577440i	−0.356757	−	0.934197i	$-0.616118\pi$
$43$	3.78653	−	3.78653i	0.577440	−	0.577440i	0.934197	+	0.356757i	$0.116118\pi$
$44$		0			0
$45$	−1.53289	+	1.62796i	−0.228510	+	0.242681i
$46$		0			0
$47$			2.75112i			0.401292i	0.979664	+	0.200646i	$0.0643041\pi$
$47$			2.75112i			0.401292i	−0.979664	+	0.200646i	$0.935696\pi$
$48$		0			0
$49$	2.44322			0.349032
$50$		0			0
$51$			1.73592i			0.243077i
$52$		0			0
$53$	−7.79380	−	7.79380i	−1.07056	−	1.07056i	−0.997314	−	0.0732468i	$-0.976664\pi$
$53$	−7.79380	−	7.79380i	−1.07056	−	1.07056i	−0.0732468	−	0.997314i	$-0.523336\pi$
$54$		0			0
$55$	6.00227	−	0.180517i	0.809346	−	0.0243409i
$56$		0			0
$57$	−0.822039			−0.108882
$58$		0			0
$59$	0.434208	+	0.434208i	0.0565290	+	0.0565290i	0.734806	−	0.678277i	$-0.237273\pi$
$59$	0.434208	+	0.434208i	0.0565290	+	0.0565290i	−0.678277	+	0.734806i	$0.737273\pi$
$60$		0			0
$61$	13.1423			1.68270			0.841352	−	0.540488i	$-0.181760\pi$
$61$	13.1423			1.68270			0.841352	+	0.540488i	$0.181760\pi$
$62$		0			0
$63$	2.13466			0.268942
$64$		0			0
$65$	−2.87394	+	7.53263i	−0.356469	+	0.934307i
$66$		0			0
$67$	1.27294			0.155515			0.0777573	−	0.996972i	$-0.475224\pi$
$67$	1.27294			0.155515			0.0777573	+	0.996972i	$0.475224\pi$
$68$		0			0
$69$	−5.81118			−0.699584
$70$		0			0
$71$	−1.66190	−	1.66190i	−0.197231	−	0.197231i	0.601581	−	0.798812i	$-0.294538\pi$
$71$	−1.66190	−	1.66190i	−0.197231	−	0.197231i	−0.798812	+	0.601581i	$0.794538\pi$
$72$		0			0
$73$	−0.637019			−0.0745575			−0.0372787	−	0.999305i	$-0.511869\pi$
$73$	−0.637019			−0.0745575			−0.0372787	+	0.999305i	$0.511869\pi$
$74$		0			0
$75$	3.31667	−	3.74161i	0.382977	−	0.432044i
$76$		0			0
$77$	−4.05360	−	4.05360i	−0.461950	−	0.461950i
$78$		0			0
$79$		−	0.837401i		−	0.0942149i	−0.998890	−	0.0471075i	$-0.985000\pi$
$79$		−	0.837401i		−	0.0942149i	0.998890	−	0.0471075i	$-0.0150003\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$		−	5.22354i		−	0.573358i	−0.958027	−	0.286679i	$-0.907449\pi$
$83$		−	5.22354i		−	0.573358i	0.958027	−	0.286679i	$-0.0925513\pi$
$84$		0			0
$85$	−0.116687	−	3.87988i	−0.0126564	−	0.420832i
$86$		0			0
$87$	−1.28490	+	1.28490i	−0.137756	+	0.137756i
$88$		0			0
$89$	−3.92688	−	3.92688i	−0.416248	−	0.416248i	0.467660	−	0.883908i	$-0.345097\pi$
$89$	−3.92688	−	3.92688i	−0.416248	−	0.416248i	−0.883908	+	0.467660i	$0.845097\pi$
$90$		0			0
$91$	7.11620	−	2.93220i	0.745981	−	0.307378i
$92$		0			0
$93$		−	6.71041i		−	0.695837i
$94$		0			0
$95$	1.83731	−	0.0552566i	0.188504	−	0.00566921i
$96$		0			0
$97$	6.15970			0.625422			0.312711	−	0.949848i	$-0.398763\pi$
$97$	6.15970			0.625422			0.312711	+	0.949848i	$0.398763\pi$
$98$		0			0
$99$	1.89894	+	1.89894i	0.190851	+	0.190851i
$100$		0			0
$101$			3.93730i			0.391776i	0.980626	+	0.195888i	$0.0627589\pi$
$101$			3.93730i			0.391776i	−0.980626	+	0.195888i	$0.937241\pi$
$102$		0			0
$103$	3.97517	−	3.97517i	0.391685	−	0.391685i	−0.483603	−	0.875288i	$-0.660672\pi$
$103$	3.97517	−	3.97517i	0.391685	−	0.391685i	0.875288	+	0.483603i	$0.160672\pi$
$104$		0			0
$105$	−4.77109	+	0.143490i	−0.465611	+	0.0140032i
$106$		0			0
$107$	−11.2103	+	11.2103i	−1.08375	+	1.08375i	−0.0875884	+	0.996157i	$0.527916\pi$
$107$	−11.2103	+	11.2103i	−1.08375	+	1.08375i	−0.996157	+	0.0875884i	$0.972084\pi$
$108$		0			0
$109$	−8.33542	+	8.33542i	−0.798388	+	0.798388i	−0.982841	−	0.184453i	$-0.940949\pi$
$109$	−8.33542	+	8.33542i	−0.798388	+	0.798388i	0.184453	+	0.982841i	$0.440949\pi$
$110$		0			0
$111$	−4.24944	+	4.24944i	−0.403339	+	0.403339i
$112$		0			0
$113$	−4.73416	−	4.73416i	−0.445353	−	0.445353i	0.448453	−	0.893806i	$-0.351975\pi$
$113$	−4.73416	−	4.73416i	−0.445353	−	0.445353i	−0.893806	+	0.448453i	$0.851975\pi$
$114$		0			0
$115$	12.9883	−	0.390622i	1.21117	−	0.0364257i
$116$		0			0
$117$	−3.33364	+	1.37361i	−0.308196	+	0.126991i
$118$		0			0
$119$	−2.62025	+	2.62025i	−0.240198	+	0.240198i
$120$		0			0
$121$			3.78804i			0.344367i
$122$		0			0
$123$		−	5.45212i		−	0.491601i
$124$		0			0
$125$	−7.16145	+	8.58566i	−0.640540	+	0.767925i
$126$		0			0
$127$	−5.26184	−	5.26184i	−0.466913	−	0.466913i	0.434000	−	0.900913i	$-0.357102\pi$
$127$	−5.26184	−	5.26184i	−0.466913	−	0.466913i	−0.900913	+	0.434000i	$0.857102\pi$
$128$		0			0
$129$	−5.35496			−0.471478
$130$		0			0
$131$	−21.1234			−1.84556			−0.922779	−	0.385330i	$-0.874088\pi$
$131$	−21.1234			−1.84556			−0.922779	+	0.385330i	$0.874088\pi$
$132$		0			0
$133$	−1.24081	−	1.24081i	−0.107592	−	0.107592i
$134$		0			0
$135$	2.23506	−	0.0672190i	0.192363	−	0.00578529i
$136$		0			0
$137$			13.1203i			1.12094i	0.828175	+	0.560470i	$0.189379\pi$
$137$			13.1203i			1.12094i	−0.828175	+	0.560470i	$0.810621\pi$
$138$		0			0
$139$			19.3191i			1.63862i	0.573349	+	0.819311i	$0.305644\pi$
$139$			19.3191i			1.63862i	−0.573349	+	0.819311i	$0.694356\pi$
$140$		0			0
$141$	1.94533	−	1.94533i	0.163827	−	0.163827i
$142$		0			0
$143$	8.93881	+	3.72199i	0.747501	+	0.311248i
$144$		0			0
$145$	2.78545	−	2.95819i	0.231319	−	0.245665i
$146$		0			0
$147$	−1.72762	−	1.72762i	−0.142492	−	0.142492i
$148$		0			0
$149$	−3.41550	+	3.41550i	−0.279808	+	0.279808i	−0.833032	−	0.553224i	$-0.813397\pi$
$149$	−3.41550	+	3.41550i	−0.279808	+	0.279808i	0.553224	+	0.833032i	$0.313397\pi$
$150$		0			0
$151$	−9.07740	+	9.07740i	−0.738709	+	0.738709i	−0.972328	−	0.233619i	$-0.924943\pi$
$151$	−9.07740	+	9.07740i	−0.738709	+	0.738709i	0.233619	+	0.972328i	$0.424943\pi$
$152$		0			0
$153$	1.22748	−	1.22748i	0.0992358	−	0.0992358i
$154$		0			0
$155$	0.451067	+	14.9981i	0.0362305	+	1.20468i
$156$		0			0
$157$	−16.7071	+	16.7071i	−1.33337	+	1.33337i	−0.431035	+	0.902335i	$0.641851\pi$
$157$	−16.7071	+	16.7071i	−1.33337	+	1.33337i	−0.902335	+	0.431035i	$0.858149\pi$
$158$		0			0
$159$			11.0221i			0.874109i
$160$		0			0
$161$	−8.77160	−	8.77160i	−0.691299	−	0.691299i
$162$		0			0
$163$	−5.73933			−0.449539			−0.224769	−	0.974412i	$-0.572163\pi$
$163$	−5.73933			−0.449539			−0.224769	+	0.974412i	$0.572163\pi$
$164$		0			0
$165$	−4.37189	−	4.11660i	−0.340351	−	0.320477i
$166$		0			0
$167$		−	12.4964i		−	0.967002i	−0.875344	−	0.483501i	$-0.839365\pi$
$167$		−	12.4964i		−	0.967002i	0.875344	−	0.483501i	$-0.160635\pi$
$168$		0			0
$169$	−9.22638	+	9.15827i	−0.709721	+	0.704483i
$170$		0			0
$171$	0.581270	+	0.581270i	0.0444508	+	0.0444508i
$172$		0			0
$173$	12.1397	−	12.1397i	0.922966	−	0.922966i	−0.0742720	−	0.997238i	$-0.523663\pi$
$173$	12.1397	−	12.1397i	0.922966	−	0.922966i	0.997238	+	0.0742720i	$0.0236633\pi$
$174$		0			0
$175$	10.6540	−	0.641415i	0.805368	−	0.0484865i
$176$		0			0
$177$		−	0.614063i		−	0.0461558i
$178$		0			0
$179$	3.88220			0.290169			0.145085	−	0.989419i	$-0.453655\pi$
$179$	3.88220			0.290169			0.145085	+	0.989419i	$0.453655\pi$
$180$		0			0
$181$			15.9058i			1.18227i	0.806572	+	0.591136i	$0.201320\pi$
$181$			15.9058i			1.18227i	−0.806572	+	0.591136i	$0.798680\pi$
$182$		0			0
$183$	−9.29304	−	9.29304i	−0.686961	−	0.686961i
$184$		0			0
$185$	9.21209	−	9.78338i	0.677286	−	0.719288i
$186$		0			0
$187$	−4.66183			−0.340906
$188$		0			0
$189$	−1.50943	−	1.50943i	−0.109795	−	0.109795i
$190$		0			0
$191$	−3.96501			−0.286898			−0.143449	−	0.989658i	$-0.545819\pi$
$191$	−3.96501			−0.286898			−0.143449	+	0.989658i	$0.545819\pi$
$192$		0			0
$193$	16.9136			1.21747			0.608734	−	0.793374i	$-0.291678\pi$
$193$	16.9136			1.21747			0.608734	+	0.793374i	$0.291678\pi$
$194$		0			0
$195$	7.35855	−	3.29419i	0.526957	−	0.235902i
$196$		0			0
$197$	−23.1980			−1.65279			−0.826396	−	0.563089i	$-0.809613\pi$
$197$	−23.1980			−1.65279			−0.826396	+	0.563089i	$0.809613\pi$
$198$		0			0
$199$	−24.2812			−1.72125			−0.860625	−	0.509239i	$-0.829927\pi$
$199$	−24.2812			−1.72125			−0.860625	+	0.509239i	$0.829927\pi$
$200$		0			0
$201$	−0.900106	−	0.900106i	−0.0634886	−	0.0634886i
$202$		0			0
$203$	−3.87894			−0.272248
$204$		0			0
$205$	0.366486	+	12.1858i	0.0255965	+	0.851094i
$206$		0			0
$207$	4.10913	+	4.10913i	0.285604	+	0.285604i
$208$		0			0
$209$		−	2.20760i		−	0.152703i
$210$		0			0
$211$	9.03724			0.622149			0.311075	−	0.950386i	$-0.399311\pi$
$211$	9.03724			0.622149			0.311075	+	0.950386i	$0.399311\pi$
$212$		0			0
$213$			2.35028i			0.161039i
$214$		0			0
$215$	11.9686	−	0.359955i	0.816255	−	0.0245487i
$216$		0			0
$217$	10.1289	−	10.1289i	0.687595	−	0.687595i
$218$		0			0
$219$	0.450441	+	0.450441i	0.0304380	+	0.0304380i
$220$		0			0
$221$	2.40590	−	5.77806i	0.161838	−	0.388675i
$222$		0			0
$223$		−	25.1082i		−	1.68137i	−0.541527	−	0.840684i	$-0.682153\pi$
$223$		−	25.1082i		−	1.68137i	0.541527	−	0.840684i	$-0.317847\pi$
$224$		0			0
$225$	−4.99096	+	0.300476i	−0.332731	+	0.0200318i
$226$		0			0
$227$	−10.2921			−0.683110			−0.341555	−	0.939862i	$-0.610954\pi$
$227$	−10.2921			−0.683110			−0.341555	+	0.939862i	$0.610954\pi$
$228$		0			0
$229$	1.77751	+	1.77751i	0.117461	+	0.117461i	0.763394	−	0.645933i	$-0.223532\pi$
$229$	1.77751	+	1.77751i	0.117461	+	0.117461i	−0.645933	+	0.763394i	$0.723532\pi$
$230$		0			0
$231$			5.73265i			0.377181i
$232$		0			0
$233$	−14.0627	+	14.0627i	−0.921280	+	0.921280i	−0.997120	−	0.0758398i	$-0.975836\pi$
$233$	−14.0627	+	14.0627i	−0.921280	+	0.921280i	0.0758398	+	0.997120i	$0.475836\pi$
$234$		0			0
$235$	−4.21717	+	4.47870i	−0.275098	+	0.292158i
$236$		0			0
$237$	−0.592132	+	0.592132i	−0.0384631	+	0.0384631i
$238$		0			0
$239$	21.1880	−	21.1880i	1.37054	−	1.37054i	0.510901	−	0.859640i	$-0.329312\pi$
$239$	21.1880	−	21.1880i	1.37054	−	1.37054i	0.859640	−	0.510901i	$-0.170688\pi$
$240$		0			0
$241$	1.79901	−	1.79901i	0.115885	−	0.115885i	−0.646786	−	0.762671i	$-0.723888\pi$
$241$	1.79901	−	1.79901i	0.115885	−	0.115885i	0.762671	+	0.646786i	$0.223888\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$	3.97746	+	3.74520i	0.254110	+	0.239272i
$246$		0			0
$247$	2.73619	+	1.13931i	0.174099	+	0.0724924i
$248$		0			0
$249$	−3.69360	+	3.69360i	−0.234072	+	0.234072i
$250$		0			0
$251$		−	19.4291i		−	1.22635i	−0.789946	−	0.613177i	$-0.789891\pi$
$251$		−	19.4291i		−	1.22635i	0.789946	−	0.613177i	$-0.210109\pi$
$252$		0			0
$253$		−	15.6060i		−	0.981140i
$254$		0			0
$255$	−2.66098	+	2.82600i	−0.166637	+	0.176971i
$256$		0			0
$257$	−7.19958	−	7.19958i	−0.449097	−	0.449097i	0.445957	−	0.895054i	$-0.352863\pi$
$257$	−7.19958	−	7.19958i	−0.449097	−	0.449097i	−0.895054	+	0.445957i	$0.852863\pi$
$258$		0			0
$259$	−12.8285			−0.797123
$260$		0			0
$261$	1.81712			0.112477
$262$		0			0
$263$	9.21874	+	9.21874i	0.568452	+	0.568452i	0.931695	−	0.363243i	$-0.118330\pi$
$263$	9.21874	+	9.21874i	0.568452	+	0.568452i	−0.363243	+	0.931695i	$0.618330\pi$
$264$		0			0
$265$	−0.740894	−	24.6350i	−0.0455127	−	1.51332i
$266$		0			0
$267$			5.55344i			0.339865i
$268$		0			0
$269$			1.62017i			0.0987834i	0.998779	+	0.0493917i	$0.0157283\pi$
$269$			1.62017i			0.0987834i	−0.998779	+	0.0493917i	$0.984272\pi$
$270$		0			0
$271$	6.91766	−	6.91766i	0.420218	−	0.420218i	−0.465061	−	0.885279i	$-0.653968\pi$
$271$	6.91766	−	6.91766i	0.420218	−	0.420218i	0.885279	+	0.465061i	$0.153968\pi$
$272$		0			0
$273$	−7.10529	−	2.95854i	−0.430032	−	0.179059i
$274$		0			0
$275$	10.0481	+	8.90696i	0.605926	+	0.537110i
$276$		0			0
$277$	7.18506	+	7.18506i	0.431709	+	0.431709i	0.889209	−	0.457501i	$-0.151255\pi$
$277$	7.18506	+	7.18506i	0.431709	+	0.431709i	−0.457501	+	0.889209i	$0.651255\pi$
$278$		0			0
$279$	−4.74497	+	4.74497i	−0.284074	+	0.284074i
$280$		0			0
$281$	10.6309	−	10.6309i	0.634185	−	0.634185i	−0.314930	−	0.949115i	$-0.601981\pi$
$281$	10.6309	−	10.6309i	0.634185	−	0.634185i	0.949115	+	0.314930i	$0.101981\pi$
$282$		0			0
$283$	−12.7919	+	12.7919i	−0.760399	+	0.760399i	−0.976394	−	0.215995i	$-0.930700\pi$
$283$	−12.7919	+	12.7919i	−0.760399	+	0.760399i	0.215995	+	0.976394i	$0.430700\pi$
$284$		0			0
$285$	−1.33824	−	1.26010i	−0.0792707	−	0.0746418i
$286$		0			0
$287$	8.22962	−	8.22962i	0.485779	−	0.485779i
$288$		0			0
$289$		−	13.9866i		−	0.822740i
$290$		0			0
$291$	−4.35556	−	4.35556i	−0.255328	−	0.255328i
$292$		0			0
$293$	−16.8122			−0.982178			−0.491089	−	0.871109i	$-0.663401\pi$
$293$	−16.8122			−0.982178			−0.491089	+	0.871109i	$0.663401\pi$
$294$		0			0
$295$	0.0412767	+	1.37247i	0.00240322	+	0.0799080i
$296$		0			0
$297$		−	2.68551i		−	0.155829i
$298$		0			0
$299$	19.3427	+	8.05402i	1.11862	+	0.465776i
$300$		0			0
$301$	−8.08296	−	8.08296i	−0.465894	−	0.465894i
$302$		0			0
$303$	2.78409	−	2.78409i	0.159942	−	0.159942i
$304$		0			0
$305$	21.3951	+	20.1458i	1.22508	+	1.15355i
$306$		0			0
$307$		−	14.6050i		−	0.833551i	−0.909009	−	0.416775i	$-0.863160\pi$
$307$		−	14.6050i		−	0.833551i	0.909009	−	0.416775i	$-0.136840\pi$
$308$		0			0
$309$	−5.62174			−0.319809
$310$		0			0
$311$			27.4910i			1.55887i	0.626481	+	0.779436i	$0.284494\pi$
$311$			27.4910i			1.55887i	−0.626481	+	0.779436i	$0.715506\pi$
$312$		0			0
$313$	4.82784	+	4.82784i	0.272886	+	0.272886i	0.830261	−	0.557375i	$-0.188191\pi$
$313$	4.82784	+	4.82784i	0.272886	+	0.272886i	−0.557375	+	0.830261i	$0.688191\pi$
$314$		0			0
$315$	3.47513	+	3.27221i	0.195802	+	0.184368i
$316$		0			0
$317$	−27.3999			−1.53893			−0.769464	−	0.638690i	$-0.779477\pi$
$317$	−27.3999			−1.53893			−0.769464	+	0.638690i	$0.779477\pi$
$318$		0			0
$319$	−3.45061	−	3.45061i	−0.193197	−	0.193197i
$320$		0			0
$321$	15.8538			0.884874
$322$		0			0
$323$	−1.42699			−0.0794000
$324$		0			0
$325$	−16.2254	+	7.85733i	−0.900021	+	0.435846i
$326$		0			0
$327$	11.7881			0.651881
$328$		0			0
$329$	5.87271			0.323773
$330$		0			0
$331$	−5.68185	−	5.68185i	−0.312303	−	0.312303i	0.533498	−	0.845801i	$-0.320877\pi$
$331$	−5.68185	−	5.68185i	−0.312303	−	0.312303i	−0.845801	+	0.533498i	$0.820877\pi$
$332$		0			0
$333$	6.00961			0.329325
$334$		0			0
$335$	2.07229	+	1.95128i	0.113221	+	0.106610i
$336$		0			0
$337$	15.7975	+	15.7975i	0.860544	+	0.860544i	0.991401	−	0.130858i	$-0.0417731\pi$
$337$	15.7975	+	15.7975i	0.860544	+	0.860544i	−0.130858	+	0.991401i	$0.541773\pi$
$338$		0			0
$339$			6.69512i			0.363629i
$340$		0			0
$341$	18.0209			0.975885
$342$		0			0
$343$		−	20.1581i		−	1.08843i
$344$		0			0
$345$	−9.46035	−	8.90793i	−0.509328	−	0.479587i
$346$		0			0
$347$	17.2806	−	17.2806i	0.927670	−	0.927670i	−0.0698847	−	0.997555i	$-0.522263\pi$
$347$	17.2806	−	17.2806i	0.927670	−	0.927670i	0.997555	+	0.0698847i	$0.0222632\pi$
$348$		0			0
$349$	19.0865	+	19.0865i	1.02168	+	1.02168i	0.999760	+	0.0219165i	$0.00697681\pi$
$349$	19.0865	+	19.0865i	1.02168	+	1.02168i	0.0219165	+	0.999760i	$0.493023\pi$
$350$		0			0
$351$	3.32853	+	1.38595i	0.177664	+	0.0739766i
$352$		0			0
$353$			33.0078i			1.75683i	0.477901	+	0.878414i	$0.341398\pi$
$353$			33.0078i			1.75683i	−0.477901	+	0.878414i	$0.658602\pi$
$354$		0			0
$355$	−0.157983	−	5.25301i	−0.00838489	−	0.278801i
$356$		0			0
$357$	3.70560			0.196121
$358$		0			0
$359$	15.0109	+	15.0109i	0.792247	+	0.792247i	0.981859	−	0.189612i	$-0.0607230\pi$
$359$	15.0109	+	15.0109i	0.792247	+	0.792247i	−0.189612	+	0.981859i	$0.560723\pi$
$360$		0			0
$361$			18.3243i			0.964434i
$362$		0			0
$363$	2.67855	−	2.67855i	0.140587	−	0.140587i
$364$		0			0
$365$	−1.03704	−	0.976483i	−0.0542811	−	0.0511114i
$366$		0			0
$367$	−2.95951	+	2.95951i	−0.154485	+	0.154485i	−0.780118	−	0.625633i	$-0.784841\pi$
$367$	−2.95951	+	2.95951i	−0.154485	+	0.154485i	0.625633	+	0.780118i	$0.284841\pi$
$368$		0			0
$369$	−3.85523	+	3.85523i	−0.200695	+	0.200695i
$370$		0			0
$371$	−16.6371	+	16.6371i	−0.863756	+	0.863756i
$372$		0			0
$373$	3.69960	+	3.69960i	0.191558	+	0.191558i	0.796369	−	0.604811i	$-0.206751\pi$
$373$	3.69960	+	3.69960i	0.191558	+	0.191558i	−0.604811	+	0.796369i	$0.706751\pi$
$374$		0			0
$375$	11.1349	−	1.00707i	0.575003	−	0.0520048i
$376$		0			0
$377$	6.05764	−	2.49602i	0.311984	−	0.128552i
$378$		0			0
$379$	6.73427	−	6.73427i	0.345916	−	0.345916i	−0.512670	−	0.858586i	$-0.671343\pi$
$379$	6.73427	−	6.73427i	0.345916	−	0.345916i	0.858586	+	0.512670i	$0.171343\pi$
$380$		0			0
$381$			7.44137i			0.381233i
$382$		0			0
$383$		−	16.7639i		−	0.856597i	−0.903637	−	0.428299i	$-0.859113\pi$
$383$		−	16.7639i		−	0.856597i	0.903637	−	0.428299i	$-0.140887\pi$
$384$		0			0
$385$	−0.385343	−	12.8128i	−0.0196389	−	0.653001i
$386$		0			0
$387$	3.78653	+	3.78653i	0.192480	+	0.192480i
$388$		0			0
$389$	−20.1793			−1.02313			−0.511566	−	0.859244i	$-0.670934\pi$
$389$	−20.1793			−1.02313			−0.511566	+	0.859244i	$0.670934\pi$
$390$		0			0
$391$	−10.0877			−0.510159
$392$		0			0
$393$	14.9365	+	14.9365i	0.753446	+	0.753446i
$394$		0			0
$395$	1.28365	−	1.36325i	0.0645872	−	0.0685926i
$396$		0			0
$397$			26.6617i			1.33811i	0.743213	+	0.669055i	$0.233301\pi$
$397$			26.6617i			1.33811i	−0.743213	+	0.669055i	$0.766699\pi$
$398$		0			0
$399$			1.75478i			0.0878487i
$400$		0			0
$401$	21.5935	−	21.5935i	1.07833	−	1.07833i	0.0816678	−	0.996660i	$-0.473975\pi$
$401$	21.5935	−	21.5935i	1.07833	−	1.07833i	0.996660	−	0.0816678i	$-0.0260246\pi$
$402$		0			0
$403$	−9.30030	+	22.3358i	−0.463281	+	1.11263i
$404$		0			0
$405$	−1.62796	−	1.53289i	−0.0808937	−	0.0761701i
$406$		0			0
$407$	−11.4119	−	11.4119i	−0.565667	−	0.565667i
$408$		0			0
$409$	2.53012	−	2.53012i	0.125107	−	0.125107i	−0.641781	−	0.766888i	$-0.721804\pi$
$409$	2.53012	−	2.53012i	0.125107	−	0.125107i	0.766888	+	0.641781i	$0.221804\pi$
$410$		0			0
$411$	9.27742	−	9.27742i	0.457622	−	0.457622i
$412$		0			0
$413$	0.926887	−	0.926887i	0.0456091	−	0.0456091i
$414$		0			0
$415$	8.00713	−	8.50369i	0.393054	−	0.417430i
$416$		0			0
$417$	13.6606	−	13.6606i	0.668965	−	0.668965i
$418$		0			0
$419$		−	20.4939i		−	1.00119i	−0.865681	−	0.500596i	$-0.833114\pi$
$419$		−	20.4939i		−	1.00119i	0.865681	−	0.500596i	$-0.166886\pi$
$420$		0			0
$421$	−22.7083	−	22.7083i	−1.10674	−	1.10674i	−0.993577	−	0.113160i	$-0.963903\pi$
$421$	−22.7083	−	22.7083i	−1.10674	−	1.10674i	−0.113160	−	0.993577i	$-0.536097\pi$
$422$		0			0
$423$	−2.75112			−0.133764
$424$		0			0
$425$	5.75748	−	6.49513i	0.279279	−	0.315060i
$426$		0			0
$427$		−	28.0544i		−	1.35765i
$428$		0			0
$429$	−3.68885	−	8.95254i	−0.178099	−	0.432233i
$430$		0			0
$431$	−7.07318	−	7.07318i	−0.340703	−	0.340703i	0.515929	−	0.856632i	$-0.327447\pi$
$431$	−7.07318	−	7.07318i	−0.340703	−	0.340703i	−0.856632	+	0.515929i	$0.827447\pi$
$432$		0			0
$433$	27.4138	−	27.4138i	1.31742	−	1.31742i	0.401614	−	0.915809i	$-0.368449\pi$
$433$	27.4138	−	27.4138i	1.31742	−	1.31742i	0.915809	−	0.401614i	$-0.131551\pi$
$434$		0			0
$435$	−4.06137	+	0.122145i	−0.194728	+	0.00585641i
$436$		0			0
$437$		−	4.77702i		−	0.228516i
$438$		0			0
$439$	−37.5366			−1.79152			−0.895762	−	0.444533i	$-0.853370\pi$
$439$	−37.5366			−1.79152			−0.895762	+	0.444533i	$0.853370\pi$
$440$		0			0
$441$			2.44322i			0.116344i
$442$		0			0
$443$	6.57913	+	6.57913i	0.312584	+	0.312584i	0.845910	−	0.533326i	$-0.179058\pi$
$443$	6.57913	+	6.57913i	0.312584	+	0.312584i	−0.533326	+	0.845910i	$0.679058\pi$
$444$		0			0
$445$	−0.373296	−	12.4123i	−0.0176959	−	0.588397i
$446$		0			0
$447$	4.83024			0.228463
$448$		0			0
$449$	−12.5481	−	12.5481i	−0.592183	−	0.592183i	0.346038	−	0.938221i	$-0.387527\pi$
$449$	−12.5481	−	12.5481i	−0.592183	−	0.592183i	−0.938221	+	0.346038i	$0.887527\pi$
$450$		0			0
$451$	14.6417			0.689452
$452$		0			0
$453$	12.8374			0.603153
$454$		0			0
$455$	16.0796	+	6.13489i	0.753824	+	0.287608i
$456$		0			0
$457$	21.0694			0.985583			0.492791	−	0.870147i	$-0.335977\pi$
$457$	21.0694			0.985583			0.492791	+	0.870147i	$0.335977\pi$
$458$		0			0
$459$	−1.73592			−0.0810257
$460$		0			0
$461$	−11.1853	−	11.1853i	−0.520949	−	0.520949i	0.396909	−	0.917858i	$-0.370083\pi$
$461$	−11.1853	−	11.1853i	−0.520949	−	0.520949i	−0.917858	+	0.396909i	$0.870083\pi$
$462$		0			0
$463$	−38.6791			−1.79757			−0.898786	−	0.438389i	$-0.855549\pi$
$463$	−38.6791			−1.79757			−0.898786	+	0.438389i	$0.855549\pi$
$464$		0			0
$465$	10.2863	−	10.9242i	0.477017	−	0.506600i
$466$		0			0
$467$	13.3530	+	13.3530i	0.617904	+	0.617904i	0.944993	−	0.327090i	$-0.106068\pi$
$467$	13.3530	+	13.3530i	0.617904	+	0.617904i	−0.327090	+	0.944993i	$0.606068\pi$
$468$		0			0
$469$		−	2.71730i		−	0.125473i
$470$		0			0
$471$	23.6274			1.08869
$472$		0			0
$473$		−	14.3808i		−	0.661230i
$474$		0			0
$475$	3.07575	+	2.72644i	0.141125	+	0.125098i
$476$		0			0
$477$	7.79380	−	7.79380i	0.356854	−	0.356854i
$478$		0			0
$479$	−1.95863	−	1.95863i	−0.0894919	−	0.0894919i	0.660944	−	0.750436i	$-0.270156\pi$
$479$	−1.95863	−	1.95863i	−0.0894919	−	0.0894919i	−0.750436	+	0.660944i	$0.770156\pi$
$480$		0			0
$481$	20.0339	−	8.25488i	0.913467	−	0.376390i
$482$		0			0
$483$			12.4049i			0.564443i
$484$		0			0
$485$	10.0277	+	9.44216i	0.455335	+	0.428746i
$486$		0			0
$487$	−17.7479			−0.804234			−0.402117	−	0.915588i	$-0.631725\pi$
$487$	−17.7479			−0.804234			−0.402117	+	0.915588i	$0.631725\pi$
$488$		0			0
$489$	4.05832	+	4.05832i	0.183524	+	0.183524i
$490$		0			0
$491$			24.6538i			1.11261i	0.830978	+	0.556306i	$0.187782\pi$
$491$			24.6538i			1.11261i	−0.830978	+	0.556306i	$0.812218\pi$
$492$		0			0
$493$	−2.23048	+	2.23048i	−0.100456	+	0.100456i
$494$		0			0
$495$	0.180517	+	6.00227i	0.00811364	+	0.269782i
$496$		0			0
$497$	−3.54759	+	3.54759i	−0.159131	+	0.159131i
$498$		0			0
$499$	0.763548	−	0.763548i	0.0341811	−	0.0341811i	−0.689810	−	0.723991i	$-0.742306\pi$
$499$	0.763548	−	0.763548i	0.0341811	−	0.0341811i	0.723991	+	0.689810i	$0.242306\pi$
$500$		0			0
$501$	−8.83631	+	8.83631i	−0.394777	+	0.394777i
$502$		0			0
$503$	17.2923	+	17.2923i	0.771026	+	0.771026i	0.978286	−	0.207260i	$-0.0664545\pi$
$503$	17.2923	+	17.2923i	0.771026	+	0.771026i	−0.207260	+	0.978286i	$0.566454\pi$
$504$		0			0
$505$	−6.03546	+	6.40975i	−0.268574	+	0.285230i
$506$		0			0
$507$	12.9999	+	0.0481545i	0.577346	+	0.00213862i
$508$		0			0
$509$	22.2401	−	22.2401i	0.985776	−	0.985776i	−0.0141241	−	0.999900i	$-0.504496\pi$
$509$	22.2401	−	22.2401i	0.985776	−	0.985776i	0.999900	+	0.0141241i	$0.00449598\pi$
$510$		0			0
$511$			1.35982i			0.0601549i
$512$		0			0
$513$		−	0.822039i		−	0.0362939i
$514$		0			0
$515$	12.5649	−	0.377887i	0.553676	−	0.0166517i
$516$		0			0
$517$	5.22421	+	5.22421i	0.229761	+	0.229761i
$518$		0			0
$519$	−17.1682			−0.753599
$520$		0			0
$521$	3.21481			0.140843			0.0704217	−	0.997517i	$-0.477565\pi$
$521$	3.21481			0.140843			0.0704217	+	0.997517i	$0.477565\pi$
$522$		0			0
$523$	7.33192	+	7.33192i	0.320603	+	0.320603i	0.848998	−	0.528396i	$-0.177206\pi$
$523$	7.33192	+	7.33192i	0.320603	+	0.320603i	−0.528396	+	0.848998i	$0.677206\pi$
$524$		0			0
$525$	−7.98708	−	7.07998i	−0.348585	−	0.308996i
$526$		0			0
$527$		−	11.6487i		−	0.507426i
$528$		0			0
$529$		−	10.7699i		−	0.468255i
$530$		0			0
$531$	−0.434208	+	0.434208i	−0.0188430	+	0.0188430i
$532$		0			0
$533$	−7.55638	+	18.1476i	−0.327303	+	0.786059i
$534$		0			0
$535$	−35.4342	+	1.06568i	−1.53195	+	0.0460733i
$536$		0			0
$537$	−2.74513	−	2.74513i	−0.118461	−	0.118461i
$538$		0			0
$539$	4.63954	−	4.63954i	0.199839	−	0.199839i
$540$		0			0
$541$	−0.865604	+	0.865604i	−0.0372152	+	0.0372152i	−0.725470	−	0.688254i	$-0.758377\pi$
$541$	−0.865604	+	0.865604i	−0.0372152	+	0.0372152i	0.688254	+	0.725470i	$0.258377\pi$
$542$		0			0
$543$	11.2471	−	11.2471i	0.482661	−	0.482661i
$544$		0			0
$545$	−26.3470	+	0.792381i	−1.12858	+	0.0339419i
$546$		0			0
$547$	14.4611	−	14.4611i	0.618311	−	0.618311i	−0.326787	−	0.945098i	$-0.605966\pi$
$547$	14.4611	−	14.4611i	0.618311	−	0.618311i	0.945098	+	0.326787i	$0.105966\pi$
$548$		0			0
$549$			13.1423i			0.560901i
$550$		0			0
$551$	−1.05624	−	1.05624i	−0.0449972	−	0.0449972i
$552$		0			0
$553$	−1.78757			−0.0760151
$554$		0			0
$555$	−13.4318	+	0.403960i	−0.570149	+	0.0171471i
$556$		0			0
$557$			20.5392i			0.870272i	0.900365	+	0.435136i	$0.143300\pi$
$557$			20.5392i			0.870272i	−0.900365	+	0.435136i	$0.856700\pi$
$558$		0			0
$559$	17.8242	+	7.42172i	0.753882	+	0.313905i
$560$		0			0
$561$	3.29641	+	3.29641i	0.139174	+	0.139174i
$562$		0			0
$563$	−3.91042	+	3.91042i	−0.164804	+	0.164804i	−0.784691	−	0.619887i	$-0.787179\pi$
$563$	−3.91042	+	3.91042i	−0.164804	+	0.164804i	0.619887	+	0.784691i	$0.287179\pi$
$564$		0			0
$565$	−0.450039	−	14.9640i	−0.0189333	−	0.629539i
$566$		0			0
$567$			2.13466i			0.0896473i
$568$		0			0
$569$	29.0908			1.21955			0.609775	−	0.792574i	$-0.291260\pi$
$569$	29.0908			1.21955			0.609775	+	0.792574i	$0.291260\pi$
$570$		0			0
$571$			27.8608i			1.16594i	0.812494	+	0.582969i	$0.198109\pi$
$571$			27.8608i			1.16594i	−0.812494	+	0.582969i	$0.801891\pi$
$572$		0			0
$573$	2.80368	+	2.80368i	0.117126	+	0.117126i
$574$		0			0
$575$	21.7432	+	19.2738i	0.906754	+	0.803773i
$576$		0			0
$577$	11.1273			0.463235			0.231618	−	0.972807i	$-0.425598\pi$
$577$	11.1273			0.463235			0.231618	+	0.972807i	$0.425598\pi$
$578$		0			0
$579$	−11.9597	−	11.9597i	−0.497029	−	0.497029i
$580$		0			0
$581$	−11.1505			−0.462600
$582$		0			0
$583$	−29.5999			−1.22590
$584$		0			0
$585$	−7.53263	−	2.87394i	−0.311436	−	0.118823i
$586$		0			0
$587$	−27.0251			−1.11545			−0.557723	−	0.830027i	$-0.688325\pi$
$587$	−27.0251			−1.11545			−0.557723	+	0.830027i	$0.688325\pi$
$588$		0			0
$589$	5.51622			0.227292
$590$		0			0
$591$	16.4035	+	16.4035i	0.674750	+	0.674750i
$592$		0			0
$593$	23.2668			0.955454			0.477727	−	0.878508i	$-0.341461\pi$
$593$	23.2668			0.955454			0.477727	+	0.878508i	$0.341461\pi$
$594$		0			0
$595$	−8.28222	+	0.249086i	−0.339538	+	0.0102115i
$596$		0			0
$597$	17.1694	+	17.1694i	0.702698	+	0.702698i
$598$		0			0
$599$		−	35.1115i		−	1.43462i	−0.696756	−	0.717308i	$-0.745374\pi$
$599$		−	35.1115i		−	1.43462i	0.696756	−	0.717308i	$-0.254626\pi$
$600$		0			0
$601$	−11.3510			−0.463015			−0.231508	−	0.972833i	$-0.574366\pi$
$601$	−11.3510			−0.463015			−0.231508	+	0.972833i	$0.574366\pi$
$602$		0			0
$603$			1.27294i			0.0518382i
$604$		0			0
$605$	−5.80666	+	6.16675i	−0.236074	+	0.250714i
$606$		0			0
$607$	−25.0768	+	25.0768i	−1.01784	+	1.01784i	−0.0179998	+	0.999838i	$0.505730\pi$
$607$	−25.0768	+	25.0768i	−1.01784	+	1.01784i	−0.999838	+	0.0179998i	$0.994270\pi$
$608$		0			0
$609$	2.74282	+	2.74282i	0.111145	+	0.111145i
$610$		0			0
$611$	−9.17125	+	3.77897i	−0.371029	+	0.152881i
$612$		0			0
$613$		−	32.7471i		−	1.32264i	−0.750103	−	0.661322i	$-0.769996\pi$
$613$		−	32.7471i		−	1.32264i	0.750103	−	0.661322i	$-0.230004\pi$
$614$		0			0
$615$	8.35752	−	8.87581i	0.337008	−	0.357907i
$616$		0			0
$617$	3.04921			0.122757			0.0613784	−	0.998115i	$-0.480450\pi$
$617$	3.04921			0.122757			0.0613784	+	0.998115i	$0.480450\pi$
$618$		0			0
$619$	−2.15135	−	2.15135i	−0.0864701	−	0.0864701i	0.662549	−	0.749019i	$-0.269475\pi$
$619$	−2.15135	−	2.15135i	−0.0864701	−	0.0864701i	−0.749019	+	0.662549i	$0.769475\pi$
$620$		0			0
$621$		−	5.81118i		−	0.233195i
$622$		0			0
$623$	−8.38255	+	8.38255i	−0.335840	+	0.335840i
$624$		0			0
$625$	−24.8194	+	2.99933i	−0.992777	+	0.119973i
$626$		0			0
$627$	−1.56101	+	1.56101i	−0.0623406	+	0.0623406i
$628$		0			0
$629$	−7.37667	+	7.37667i	−0.294127	+	0.294127i
$630$		0			0
$631$	−26.1168	+	26.1168i	−1.03969	+	1.03969i	−0.0405145	+	0.999179i	$0.512900\pi$
$631$	−26.1168	+	26.1168i	−1.03969	+	1.03969i	−0.999179	+	0.0405145i	$0.987100\pi$
$632$		0			0
$633$	−6.39029	−	6.39029i	−0.253991	−	0.253991i
$634$		0			0
$635$	−0.500201	−	16.6319i	−0.0198499	−	0.660016i
$636$		0			0
$637$	3.35604	+	8.14483i	0.132971	+	0.322710i
$638$		0			0
$639$	1.66190	−	1.66190i	0.0657437	−	0.0657437i
$640$		0			0
$641$		−	14.0903i		−	0.556534i	−0.960504	−	0.278267i	$-0.910240\pi$
$641$		−	14.0903i		−	0.556534i	0.960504	−	0.278267i	$-0.0897599\pi$
$642$		0			0
$643$		−	9.89537i		−	0.390235i	−0.980780	−	0.195118i	$-0.937491\pi$
$643$		−	9.89537i		−	0.390235i	0.980780	−	0.195118i	$-0.0625089\pi$
$644$		0			0
$645$	−8.71764	−	8.20858i	−0.343257	−	0.323213i
$646$		0			0
$647$	−7.48001	−	7.48001i	−0.294069	−	0.294069i	0.544616	−	0.838685i	$-0.316675\pi$
$647$	−7.48001	−	7.48001i	−0.294069	−	0.294069i	−0.838685	+	0.544616i	$0.816675\pi$
$648$		0			0
$649$	1.64907			0.0647317
$650$		0			0
$651$	−14.3244			−0.561419
$652$		0			0
$653$	10.0579	+	10.0579i	0.393595	+	0.393595i	0.875967	−	0.482372i	$-0.160225\pi$
$653$	10.0579	+	10.0579i	0.393595	+	0.393595i	−0.482372	+	0.875967i	$0.660225\pi$
$654$		0			0
$655$	−34.3879	−	32.3799i	−1.34365	−	1.26519i
$656$		0			0
$657$		−	0.637019i		−	0.0248525i
$658$		0			0
$659$			36.4548i			1.42008i	0.704164	+	0.710038i	$0.251322\pi$
$659$			36.4548i			1.42008i	−0.704164	+	0.710038i	$0.748678\pi$
$660$		0			0
$661$	−6.58265	+	6.58265i	−0.256035	+	0.256035i	−0.823439	−	0.567404i	$-0.807948\pi$
$661$	−6.58265	+	6.58265i	−0.256035	+	0.256035i	0.567404	+	0.823439i	$0.307948\pi$
$662$		0			0
$663$	−5.78693	+	2.38448i	−0.224746	+	0.0926055i
$664$		0			0
$665$	−0.117954	−	3.92202i	−0.00457407	−	0.152090i
$666$		0			0
$667$	−7.46678	−	7.46678i	−0.289115	−	0.289115i
$668$		0			0
$669$	−17.7542	+	17.7542i	−0.686415	+	0.686415i
$670$		0			0
$671$	24.9565	−	24.9565i	0.963437	−	0.963437i
$672$		0			0
$673$	−10.3834	+	10.3834i	−0.400252	+	0.400252i	−0.878322	−	0.478070i	$-0.841337\pi$
$673$	−10.3834	+	10.3834i	−0.400252	+	0.400252i	0.478070	+	0.878322i	$0.341337\pi$
$674$		0			0
$675$	3.74161	+	3.31667i	0.144015	+	0.127659i
$676$		0			0
$677$	−22.0470	+	22.0470i	−0.847334	+	0.847334i	−0.989800	−	0.142466i	$-0.954497\pi$
$677$	−22.0470	+	22.0470i	−0.847334	+	0.847334i	0.142466	+	0.989800i	$0.454497\pi$
$678$		0			0
$679$		−	13.1489i		−	0.504607i
$680$		0			0
$681$	7.27761	+	7.27761i	0.278879	+	0.278879i
$682$		0			0
$683$	−44.6066			−1.70682			−0.853412	−	0.521237i	$-0.825471\pi$
$683$	−44.6066			−1.70682			−0.853412	+	0.521237i	$0.825471\pi$
$684$		0			0
$685$	−20.1120	+	21.3592i	−0.768438	+	0.816093i
$686$		0			0
$687$		−	2.51377i		−	0.0959064i
$688$		0			0
$689$	15.2761	−	36.6874i	0.581973	−	1.39768i
$690$		0			0
$691$	−33.1306	−	33.1306i	−1.26035	−	1.26035i	−0.950924	−	0.309424i	$-0.899864\pi$
$691$	−33.1306	−	33.1306i	−1.26035	−	1.26035i	−0.309424	−	0.950924i	$-0.600136\pi$
$692$		0			0
$693$	4.05360	−	4.05360i	0.153983	−	0.153983i
$694$		0			0
$695$	−29.6141	+	31.4506i	−1.12333	+	1.19299i
$696$		0			0
$697$		−	9.46444i		−	0.358491i
$698$		0			0
$699$	19.8877			0.752222
$700$		0			0
$701$			5.40260i			0.204053i	0.994782	+	0.102027i	$0.0325327\pi$
$701$			5.40260i			0.204053i	−0.994782	+	0.102027i	$0.967467\pi$
$702$		0			0
$703$	−3.49320	−	3.49320i	−0.131749	−	0.131749i
$704$		0			0
$705$	6.14891	−	0.184927i	0.231581	−	0.00696477i
$706$		0			0
$707$	8.40480			0.316095
$708$		0			0
$709$	34.9371	+	34.9371i	1.31209	+	1.31209i	0.919873	+	0.392216i	$0.128292\pi$
$709$	34.9371	+	34.9371i	1.31209	+	1.31209i	0.392216	+	0.919873i	$0.371708\pi$
$710$		0			0
$711$	0.837401			0.0314050
$712$		0			0
$713$	38.9954			1.46039
$714$		0			0
$715$	8.84657	+	19.7615i	0.330843	+	0.739037i
$716$		0			0
$717$	−29.9644			−1.11904
$718$		0			0
$719$	23.4590			0.874872			0.437436	−	0.899249i	$-0.355887\pi$
$719$	23.4590			0.874872			0.437436	+	0.899249i	$0.355887\pi$
$720$		0			0
$721$	−8.48564	−	8.48564i	−0.316022	−	0.316022i
$722$		0			0
$723$	−2.54419			−0.0946194
$724$		0			0
$725$	9.06919	−	0.546002i	0.336821	−	0.0202780i
$726$		0			0
$727$	8.12835	+	8.12835i	0.301464	+	0.301464i	0.841586	−	0.540123i	$-0.181622\pi$
$727$	8.12835	+	8.12835i	0.301464	+	0.301464i	−0.540123	+	0.841586i	$0.681622\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−9.29577			−0.343817
$732$		0			0
$733$		−	15.4133i		−	0.569303i	−0.958631	−	0.284652i	$-0.908122\pi$
$733$		−	15.4133i		−	0.569303i	0.958631	−	0.284652i	$-0.0918779\pi$
$734$		0			0
$735$	−0.164231	−	5.46074i	−0.00605774	−	0.201422i
$736$		0			0
$737$	2.41724	−	2.41724i	0.0890403	−	0.0890403i
$738$		0			0
$739$	−6.33555	−	6.33555i	−0.233057	−	0.233057i	0.580910	−	0.813967i	$-0.302697\pi$
$739$	−6.33555	−	6.33555i	−0.233057	−	0.233057i	−0.813967	+	0.580910i	$0.802697\pi$
$740$		0			0
$741$	−1.12916	−	2.74039i	−0.0414809	−	0.100671i
$742$		0			0
$743$			44.7202i			1.64063i	0.571915	+	0.820313i	$0.306201\pi$
$743$			44.7202i			1.64063i	−0.571915	+	0.820313i	$0.693799\pi$
$744$		0			0
$745$	−10.7959	+	0.324684i	−0.395530	+	0.0118955i
$746$		0			0
$747$	5.22354			0.191119
$748$		0			0
$749$	23.9303	+	23.9303i	0.874394	+	0.874394i
$750$		0			0
$751$		−	4.64023i		−	0.169324i	−0.996410	−	0.0846621i	$-0.973019\pi$
$751$		−	4.64023i		−	0.169324i	0.996410	−	0.0846621i	$-0.0269811\pi$
$752$		0			0
$753$	−13.7384	+	13.7384i	−0.500657	+	0.500657i
$754$		0			0
$755$	−28.6923	+	0.862916i	−1.04422	+	0.0314047i
$756$		0			0
$757$	−20.4954	+	20.4954i	−0.744918	+	0.744918i	−0.973520	−	0.228602i	$-0.926584\pi$
$757$	−20.4954	+	20.4954i	−0.744918	+	0.744918i	0.228602	+	0.973520i	$0.426584\pi$
$758$		0			0
$759$	−11.0351	+	11.0351i	−0.400549	+	0.400549i
$760$		0			0
$761$	17.6249	−	17.6249i	0.638902	−	0.638902i	−0.311383	−	0.950285i	$-0.600792\pi$
$761$	17.6249	−	17.6249i	0.638902	−	0.638902i	0.950285	+	0.311383i	$0.100792\pi$
$762$		0			0
$763$	17.7933	+	17.7933i	0.644160	+	0.644160i
$764$		0			0
$765$	3.87988	−	0.116687i	0.140277	−	0.00421881i
$766$		0			0
$767$	−0.851061	+	2.04393i	−0.0307300	+	0.0738020i
$768$		0			0
$769$	35.6848	−	35.6848i	1.28683	−	1.28683i	0.350123	−	0.936704i	$-0.386140\pi$
$769$	35.6848	−	35.6848i	1.28683	−	1.28683i	0.936704	−	0.350123i	$-0.113860\pi$
$770$		0			0
$771$			10.1817i			0.366687i
$772$		0			0
$773$			10.4900i			0.377301i	0.982044	+	0.188650i	$0.0604113\pi$
$773$			10.4900i			0.377301i	−0.982044	+	0.188650i	$0.939589\pi$
$774$		0			0
$775$	−22.2562	+	25.1077i	−0.799468	+	0.901897i
$776$		0			0
$777$	9.07111	+	9.07111i	0.325424	+	0.325424i
$778$		0			0
$779$	4.48186			0.160579
$780$		0			0
$781$	−6.31170			−0.225850
$782$		0			0
$783$	−1.28490	−	1.28490i	−0.0459185	−	0.0459185i
$784$		0			0
$785$	−52.8085	+	1.58821i	−1.88482	+	0.0566856i
$786$		0			0
$787$		−	16.0980i		−	0.573832i	−0.957956	−	0.286916i	$-0.907370\pi$
$787$		−	16.0980i		−	0.573832i	0.957956	−	0.286916i	$-0.0926301\pi$
$788$		0			0
$789$		−	13.0373i		−	0.464139i
$790$		0			0
$791$	−10.1058	+	10.1058i	−0.359322	+	0.359322i
$792$		0			0
$793$	18.0525	+	43.8119i	0.641062	+	1.55581i
$794$		0			0
$795$	−16.8957	+	17.9435i	−0.599229	+	0.636390i
$796$		0			0
$797$	17.8833	+	17.8833i	0.633460	+	0.633460i	0.948934	−	0.315474i	$-0.102164\pi$
$797$	17.8833	+	17.8833i	0.633460	+	0.633460i	−0.315474	+	0.948934i	$0.602164\pi$
$798$		0			0
$799$	3.37694	−	3.37694i	0.119468	−	0.119468i
$800$		0			0
$801$	3.92688	−	3.92688i	0.138749	−	0.138749i
$802$		0			0
$803$	−1.20966	+	1.20966i	−0.0426881	+	0.0426881i
$804$		0			0
$805$	−0.833845	−	27.7257i	−0.0293892	−	0.977202i
$806$		0			0
$807$	1.14563	−	1.14563i	0.0403282	−	0.0403282i
$808$		0			0
$809$		−	20.4265i		−	0.718157i	−0.933307	−	0.359079i	$-0.883091\pi$
$809$		−	20.4265i		−	0.718157i	0.933307	−	0.359079i	$-0.116909\pi$
$810$		0			0
$811$	4.25247	+	4.25247i	0.149325	+	0.149325i	0.777816	−	0.628492i	$-0.216327\pi$
$811$	4.25247	+	4.25247i	0.149325	+	0.149325i	−0.628492	+	0.777816i	$0.716327\pi$
$812$		0			0
$813$	−9.78305			−0.343106
$814$		0			0
$815$	−9.34337	−	8.79778i	−0.327284	−	0.308173i
$816$		0			0
$817$		−	4.40199i		−	0.154006i
$818$		0			0
$819$	2.93220	+	7.11620i	0.102459	+	0.248660i
$820$		0			0
$821$	−26.9521	−	26.9521i	−0.940636	−	0.940636i	0.0576979	−	0.998334i	$-0.481624\pi$
$821$	−26.9521	−	26.9521i	−0.940636	−	0.940636i	−0.998334	+	0.0576979i	$0.981624\pi$
$822$		0			0
$823$	−25.9491	+	25.9491i	−0.904528	+	0.904528i	−0.995824	−	0.0912955i	$-0.970899\pi$
$823$	−25.9491	+	25.9491i	−0.904528	+	0.904528i	0.0912955	+	0.995824i	$0.470899\pi$
$824$		0			0
$825$	−0.806933	−	13.4033i	−0.0280938	−	0.466642i
$826$		0			0
$827$		−	45.6260i		−	1.58657i	−0.608848	−	0.793287i	$-0.708368\pi$
$827$		−	45.6260i		−	1.58657i	0.608848	−	0.793287i	$-0.291632\pi$
$828$		0			0
$829$	−42.7307			−1.48410			−0.742049	−	0.670346i	$-0.766146\pi$
$829$	−42.7307			−1.48410			−0.742049	+	0.670346i	$0.766146\pi$
$830$		0			0
$831$		−	10.1612i		−	0.352489i
$832$		0			0
$833$	−2.99900	−	2.99900i	−0.103909	−	0.103909i
$834$		0			0
$835$	19.1557	−	20.3436i	0.662910	−	0.704020i
$836$		0			0
$837$	6.71041			0.231946
$838$		0			0
$839$	3.57427	+	3.57427i	0.123398	+	0.123398i	0.766109	−	0.642711i	$-0.222190\pi$
$839$	3.57427	+	3.57427i	0.123398	+	0.123398i	−0.642711	+	0.766109i	$0.722190\pi$
$840$		0			0
$841$	25.6981			0.886140
$842$		0			0
$843$	−15.0343			−0.517810
$844$		0			0
$845$	−29.0588	+	0.766212i	−0.999653	+	0.0263585i
$846$		0			0
$847$	8.08617			0.277844
$848$		0			0
$849$	18.0905			0.620863
$850$		0			0
$851$	−24.6943	−	24.6943i	−0.846508	−	0.846508i
$852$		0			0
$853$	−10.6644			−0.365141			−0.182571	−	0.983193i	$-0.558442\pi$
$853$	−10.6644			−0.365141			−0.182571	+	0.983193i	$0.558442\pi$
$854$		0			0
$855$	0.0552566	+	1.83731i	0.00188974	+	0.0628345i
$856$		0			0
$857$	17.7615	+	17.7615i	0.606720	+	0.606720i	0.942087	−	0.335367i	$-0.108860\pi$
$857$	17.7615	+	17.7615i	0.606720	+	0.606720i	−0.335367	+	0.942087i	$0.608860\pi$
$858$		0			0
$859$		−	0.529028i		−	0.0180502i	−0.999959	−	0.00902510i	$-0.997127\pi$
$859$		−	0.529028i		−	0.0180502i	0.999959	−	0.00902510i	$-0.00287282\pi$
$860$		0			0
$861$	−11.6384			−0.396637
$862$		0			0
$863$			16.5919i			0.564795i	0.959298	+	0.282397i	$0.0911296\pi$
$863$			16.5919i			0.564795i	−0.959298	+	0.282397i	$0.908870\pi$
$864$		0			0
$865$	38.3718	−	1.15403i	1.30468	−	0.0392381i
$866$		0			0
$867$	−9.89001	+	9.89001i	−0.335882	+	0.335882i
$868$		0			0
$869$	−1.59018	−	1.59018i	−0.0539430	−	0.0539430i
$870$		0			0
$871$	1.74853	+	4.24353i	0.0592466	+	0.143787i
$872$		0			0
$873$			6.15970i			0.208474i
$874$		0			0
$875$	18.3275	+	15.2873i	0.619582	+	0.516804i
$876$		0			0
$877$	−31.7095			−1.07075			−0.535377	−	0.844613i	$-0.679830\pi$
$877$	−31.7095			−1.07075			−0.535377	+	0.844613i	$0.679830\pi$
$878$		0			0
$879$	11.8880	+	11.8880i	0.400973	+	0.400973i
$880$		0			0
$881$		−	45.8764i		−	1.54561i	−0.634641	−	0.772807i	$-0.718852\pi$
$881$		−	45.8764i		−	1.54561i	0.634641	−	0.772807i	$-0.281148\pi$
$882$		0			0
$883$	−7.59797	+	7.59797i	−0.255692	+	0.255692i	−0.823299	−	0.567607i	$-0.807869\pi$
$883$	−7.59797	+	7.59797i	−0.255692	+	0.255692i	0.567607	+	0.823299i	$0.307869\pi$
$884$		0			0
$885$	0.941292	−	0.999666i	0.0316412	−	0.0336034i
$886$		0			0
$887$	−2.01004	+	2.01004i	−0.0674905	+	0.0674905i	−0.740046	−	0.672556i	$-0.765196\pi$
$887$	−2.01004	+	2.01004i	−0.0674905	+	0.0674905i	0.672556	+	0.740046i	$0.265196\pi$
$888$		0			0
$889$	−11.2323	+	11.2323i	−0.376718	+	0.376718i
$890$		0			0
$891$	−1.89894	+	1.89894i	−0.0636170	+	0.0636170i
$892$		0			0
$893$	1.59914	+	1.59914i	0.0535132	+	0.0535132i
$894$		0			0
$895$	6.32004	+	5.95099i	0.211256	+	0.198920i
$896$		0			0
$897$	−7.98232	−	19.3724i	−0.266522	−	0.646826i
$898$		0			0
$899$	8.62219	−	8.62219i	0.287566	−	0.287566i
$900$		0			0
$901$			19.1335i			0.637428i
$902$		0			0
$903$			11.4310i			0.380401i
$904$		0			0
$905$	−24.3820	+	25.8940i	−0.810484	+	0.860746i
$906$		0			0
$907$	24.3483	+	24.3483i	0.808472	+	0.808472i	0.984403	−	0.175931i	$-0.0562934\pi$
$907$	24.3483	+	24.3483i	0.808472	+	0.808472i	−0.175931	+	0.984403i	$0.556293\pi$
$908$		0			0
$909$	−3.93730			−0.130592
$910$		0			0
$911$	−41.9116			−1.38859			−0.694297	−	0.719689i	$-0.744284\pi$
$911$	−41.9116			−1.38859			−0.694297	+	0.719689i	$0.744284\pi$
$912$		0			0
$913$	−9.91920	−	9.91920i	−0.328278	−	0.328278i
$914$		0			0
$915$	−0.883414	−	29.3739i	−0.0292048	−	0.971070i
$916$		0			0
$917$			45.0912i			1.48904i
$918$		0			0
$919$			31.6303i			1.04339i	0.853133	+	0.521693i	$0.174699\pi$
$919$			31.6303i			1.04339i	−0.853133	+	0.521693i	$0.825301\pi$
$920$		0			0
$921$	−10.3273	+	10.3273i	−0.340296	+	0.340296i
$922$		0			0
$923$	3.25737	−	7.82299i	0.107218	−	0.257497i
$924$		0			0
$925$	29.9937	−	1.80575i	0.986188	−	0.0593726i
$926$		0			0
$927$	3.97517	+	3.97517i	0.130562	+	0.130562i
$928$		0			0
$929$	19.6715	−	19.6715i	0.645400	−	0.645400i	−0.306477	−	0.951878i	$-0.599150\pi$
$929$	19.6715	−	19.6715i	0.645400	−	0.645400i	0.951878	+	0.306477i	$0.0991504\pi$
$930$		0			0
$931$	1.42017	−	1.42017i	0.0465442	−	0.0465442i
$932$		0			0
$933$	19.4391	−	19.4391i	0.636407	−	0.636407i
$934$		0			0
$935$	−7.58924	−	7.14608i	−0.248195	−	0.233702i
$936$		0			0
$937$	9.54342	−	9.54342i	0.311770	−	0.311770i	−0.533825	−	0.845595i	$-0.679246\pi$
$937$	9.54342	−	9.54342i	0.311770	−	0.311770i	0.845595	+	0.533825i	$0.179246\pi$
$938$		0			0
$939$		−	6.82759i		−	0.222810i
$940$		0			0
$941$	10.4194	+	10.4194i	0.339662	+	0.339662i	0.856240	−	0.516578i	$-0.172794\pi$
$941$	10.4194	+	10.4194i	0.339662	+	0.339662i	−0.516578	+	0.856240i	$0.672794\pi$
$942$		0			0
$943$	31.6833			1.03175
$944$		0			0
$945$	−0.143490	−	4.77109i	−0.00466772	−	0.155204i
$946$		0			0
$947$			3.83373i			0.124580i	0.998058	+	0.0622898i	$0.0198403\pi$
$947$			3.83373i			0.124580i	−0.998058	+	0.0622898i	$0.980160\pi$
$948$		0			0
$949$	−0.875018	−	2.12360i	−0.0284043	−	0.0689349i
$950$		0			0
$951$	19.3746	+	19.3746i	0.628265	+	0.628265i
$952$		0			0
$953$	−27.0921	+	27.0921i	−0.877598	+	0.877598i	−0.993286	−	0.115687i	$-0.963093\pi$
$953$	−27.0921	+	27.0921i	−0.877598	+	0.877598i	0.115687	+	0.993286i	$0.463093\pi$
$954$		0			0
$955$	−6.45486	−	6.07794i	−0.208874	−	0.196677i
$956$		0			0
$957$			4.87990i			0.157745i
$958$		0			0
$959$	28.0073			0.904403
$960$		0			0
$961$			14.0296i			0.452566i
$962$		0			0
$963$	−11.2103	−	11.2103i	−0.361248	−	0.361248i
$964$		0			0
$965$	27.5346	+	25.9268i	0.886370	+	0.834612i
$966$		0			0
$967$	60.6472			1.95028			0.975141	−	0.221586i	$-0.0711234\pi$
$967$	60.6472			1.95028			0.975141	+	0.221586i	$0.0711234\pi$
$968$		0			0
$969$	1.00904	+	1.00904i	0.0324149	+	0.0324149i
$970$		0			0
$971$	−21.1997			−0.680331			−0.340165	−	0.940366i	$-0.610483\pi$
$971$	−21.1997			−0.680331			−0.340165	+	0.940366i	$0.610483\pi$
$972$		0			0
$973$	41.2397			1.32208
$974$		0			0
$975$	17.0290	+	5.91709i	0.545366	+	0.189499i
$976$		0			0
$977$	24.6849			0.789739			0.394869	−	0.918737i	$-0.370790\pi$
$977$	24.6849			0.789739			0.394869	+	0.918737i	$0.370790\pi$
$978$		0			0
$979$	−14.9138			−0.476648
$980$		0			0
$981$	−8.33542	−	8.33542i	−0.266129	−	0.266129i
$982$		0			0
$983$	−35.5810			−1.13486			−0.567428	−	0.823423i	$-0.692062\pi$
$983$	−35.5810			−1.13486			−0.567428	+	0.823423i	$0.692062\pi$
$984$		0			0
$985$	−37.7654	−	35.5601i	−1.20330	−	1.13304i
$986$		0			0
$987$	−4.15263	−	4.15263i	−0.132180	−	0.132180i
$988$		0			0
$989$		−	31.1187i		−	0.989516i
$990$		0			0
$991$	−5.07037			−0.161065			−0.0805327	−	0.996752i	$-0.525662\pi$
$991$	−5.07037			−0.161065			−0.0805327	+	0.996752i	$0.525662\pi$
$992$		0			0
$993$			8.03535i			0.254994i
$994$		0			0
$995$	−39.5287	−	37.2205i	−1.25315	−	1.17997i
$996$		0			0
$997$	21.7495	−	21.7495i	0.688814	−	0.688814i	−0.273156	−	0.961970i	$-0.588067\pi$
$997$	21.7495	−	21.7495i	0.688814	−	0.688814i	0.961970	+	0.273156i	$0.0880674\pi$
$998$		0			0
$999$	−4.24944	−	4.24944i	−0.134446	−	0.134446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	780.2.r.a.73.6	✓	28
3.2	odd	2		2340.2.u.i.73.5		28
5.2	odd	4		780.2.bm.a.697.6	yes	28
5.3	odd	4		3900.2.bm.b.2257.12		28
5.4	even	2		3900.2.r.b.3193.12		28
13.5	odd	4		780.2.bm.a.733.6	yes	28
15.2	even	4		2340.2.bp.i.1477.3		28
39.5	even	4		2340.2.bp.i.1513.3		28
65.18	even	4		3900.2.r.b.1357.12		28
65.44	odd	4		3900.2.bm.b.2293.12		28
65.57	even	4	inner	780.2.r.a.577.6	yes	28
195.122	odd	4		2340.2.u.i.577.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.r.a.73.6	✓	28	1.1	even	1	trivial
780.2.r.a.577.6	yes	28	65.57	even	4	inner
780.2.bm.a.697.6	yes	28	5.2	odd	4
780.2.bm.a.733.6	yes	28	13.5	odd	4
2340.2.u.i.73.5		28	3.2	odd	2
2340.2.u.i.577.5		28	195.122	odd	4
2340.2.bp.i.1477.3		28	15.2	even	4
2340.2.bp.i.1513.3		28	39.5	even	4
3900.2.r.b.1357.12		28	65.18	even	4
3900.2.r.b.3193.12		28	5.4	even	2
3900.2.bm.b.2257.12		28	5.3	odd	4
3900.2.bm.b.2293.12		28	65.44	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	780.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(1.62796 + 1.53289i) q^{5} -2.13466i q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{3} +(1.62796 + 1.53289i) q^{5} -2.13466i q^{7} +1.00000i q^{9} +(1.89894 - 1.89894i) q^{11} +(1.37361 + 3.33364i) q^{13} +(-0.0672190 - 2.23506i) q^{15} +(-1.22748 - 1.22748i) q^{17} +(0.581270 - 0.581270i) q^{19} +(-1.50943 + 1.50943i) q^{21} +(4.10913 - 4.10913i) q^{23} +(0.300476 + 4.99096i) q^{25} +(0.707107 - 0.707107i) q^{27} -1.81712i q^{29} +(4.74497 + 4.74497i) q^{31} -2.68551 q^{33} +(3.27221 - 3.47513i) q^{35} -6.00961i q^{37} +(1.38595 - 3.32853i) q^{39} +(3.85523 + 3.85523i) q^{41} +(3.78653 - 3.78653i) q^{43} +(-1.53289 + 1.62796i) q^{45} +2.75112i q^{47} +2.44322 q^{49} +1.73592i q^{51} +(-7.79380 - 7.79380i) q^{53} +(6.00227 - 0.180517i) q^{55} -0.822039 q^{57} +(0.434208 + 0.434208i) q^{59} +13.1423 q^{61} +2.13466 q^{63} +(-2.87394 + 7.53263i) q^{65} +1.27294 q^{67} -5.81118 q^{69} +(-1.66190 - 1.66190i) q^{71} -0.637019 q^{73} +(3.31667 - 3.74161i) q^{75} +(-4.05360 - 4.05360i) q^{77} -0.837401i q^{79} -1.00000 q^{81} -5.22354i q^{83} +(-0.116687 - 3.87988i) q^{85} +(-1.28490 + 1.28490i) q^{87} +(-3.92688 - 3.92688i) q^{89} +(7.11620 - 2.93220i) q^{91} -6.71041i q^{93} +(1.83731 - 0.0552566i) q^{95} +6.15970 q^{97} +(1.89894 + 1.89894i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q+O(q^{10}) \) 28 * q	\( 28 q + 8 q^{11} - 4 q^{13} - 4 q^{15} - 4 q^{17} - 16 q^{19} + 8 q^{21} - 8 q^{23} + 12 q^{25} - 8 q^{33} + 8 q^{39} + 12 q^{41} + 16 q^{43} + 4 q^{45} - 36 q^{49} + 36 q^{53} + 40 q^{55} + 16 q^{59} + 8 q^{61} - 40 q^{65} + 48 q^{67} - 8 q^{69} + 8 q^{71} + 48 q^{73} - 48 q^{77} - 28 q^{81} - 4 q^{85} - 24 q^{87} - 36 q^{89} - 24 q^{91} + 72 q^{95} - 72 q^{97} + 8 q^{99}+O(q^{100}) \) 28 * q + 8 * q^11 - 4 * q^13 - 4 * q^15 - 4 * q^17 - 16 * q^19 + 8 * q^21 - 8 * q^23 + 12 * q^25 - 8 * q^33 + 8 * q^39 + 12 * q^41 + 16 * q^43 + 4 * q^45 - 36 * q^49 + 36 * q^53 + 40 * q^55 + 16 * q^59 + 8 * q^61 - 40 * q^65 + 48 * q^67 - 8 * q^69 + 8 * q^71 + 48 * q^73 - 48 * q^77 - 28 * q^81 - 4 * q^85 - 24 * q^87 - 36 * q^89 - 24 * q^91 + 72 * q^95 - 72 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

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