LMFDB - Embedded newform 980.4.i.i.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,4,Mod(361,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("980.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	980.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$57.8218718056$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	980.961
Dual form			980.4.i.i.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +(2.50000 - 4.33013i) q^{5} +(13.0000 - 22.5167i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} +(2.50000 - 4.33013i) q^{5} +(13.0000 - 22.5167i) q^{9} +(3.50000 + 6.06218i) q^{11} -23.0000 q^{13} -5.00000 q^{15} +(12.5000 + 21.6506i) q^{17} +(31.0000 - 53.6936i) q^{19} +(43.0000 - 74.4782i) q^{23} +(-12.5000 - 21.6506i) q^{25} -53.0000 q^{27} -29.0000 q^{29} +(6.00000 + 10.3923i) q^{31} +(3.50000 - 6.06218i) q^{33} +(75.0000 - 129.904i) q^{37} +(11.5000 + 19.9186i) q^{39} +204.000 q^{41} -178.000 q^{43} +(-65.0000 - 112.583i) q^{45} +(-16.5000 + 28.5788i) q^{47} +(12.5000 - 21.6506i) q^{51} +(-226.000 - 391.443i) q^{53} +35.0000 q^{55} -62.0000 q^{57} +(-60.0000 - 103.923i) q^{59} +(-460.000 + 796.743i) q^{61} +(-57.5000 + 99.5929i) q^{65} +(150.000 + 259.808i) q^{67} -86.0000 q^{69} +520.000 q^{71} +(-185.000 - 320.429i) q^{73} +(-12.5000 + 21.6506i) q^{75} +(506.500 - 877.284i) q^{79} +(-324.500 - 562.050i) q^{81} -636.000 q^{83} +125.000 q^{85} +(14.5000 + 25.1147i) q^{87} +(-146.000 + 252.879i) q^{89} +(6.00000 - 10.3923i) q^{93} +(-155.000 - 268.468i) q^{95} -1381.00 q^{97} +182.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} + 5 q^{5} + 26 q^{9}+O(q^{10}) $ 2 * q - q^3 + 5 * q^5 + 26 * q^9	$ 2 q - q^{3} + 5 q^{5} + 26 q^{9} + 7 q^{11} - 46 q^{13} - 10 q^{15} + 25 q^{17} + 62 q^{19} + 86 q^{23} - 25 q^{25} - 106 q^{27} - 58 q^{29} + 12 q^{31} + 7 q^{33} + 150 q^{37} + 23 q^{39} + 408 q^{41} - 356 q^{43} - 130 q^{45} - 33 q^{47} + 25 q^{51} - 452 q^{53} + 70 q^{55} - 124 q^{57} - 120 q^{59} - 920 q^{61} - 115 q^{65} + 300 q^{67} - 172 q^{69} + 1040 q^{71} - 370 q^{73} - 25 q^{75} + 1013 q^{79} - 649 q^{81} - 1272 q^{83} + 250 q^{85} + 29 q^{87} - 292 q^{89} + 12 q^{93} - 310 q^{95} - 2762 q^{97} + 364 q^{99}+O(q^{100}) $ 2 * q - q^3 + 5 * q^5 + 26 * q^9 + 7 * q^11 - 46 * q^13 - 10 * q^15 + 25 * q^17 + 62 * q^19 + 86 * q^23 - 25 * q^25 - 106 * q^27 - 58 * q^29 + 12 * q^31 + 7 * q^33 + 150 * q^37 + 23 * q^39 + 408 * q^41 - 356 * q^43 - 130 * q^45 - 33 * q^47 + 25 * q^51 - 452 * q^53 + 70 * q^55 - 124 * q^57 - 120 * q^59 - 920 * q^61 - 115 * q^65 + 300 * q^67 - 172 * q^69 + 1040 * q^71 - 370 * q^73 - 25 * q^75 + 1013 * q^79 - 649 * q^81 - 1272 * q^83 + 250 * q^85 + 29 * q^87 - 292 * q^89 + 12 * q^93 - 310 * q^95 - 2762 * q^97 + 364 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i	0.813894	−	0.581013i	$-0.197344\pi$
$3$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i	−0.910119	+	0.414346i	$0.864010\pi$
$4$		0			0
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	13.0000	−	22.5167i	0.481481	−	0.833950i
$10$		0			0
$11$	3.50000	+	6.06218i	0.0959354	+	0.166165i	0.909999	−	0.414611i	$-0.136082\pi$
$11$	3.50000	+	6.06218i	0.0959354	+	0.166165i	−0.814063	+	0.580776i	$0.802749\pi$
$12$		0			0
$13$	−23.0000			−0.490696			−0.245348	−	0.969435i	$-0.578902\pi$
$13$	−23.0000			−0.490696			−0.245348	+	0.969435i	$0.578902\pi$
$14$		0			0
$15$	−5.00000			−0.0860663
$16$		0			0
$17$	12.5000	+	21.6506i	0.178335	+	0.308885i	0.941310	−	0.337542i	$-0.109596\pi$
$17$	12.5000	+	21.6506i	0.178335	+	0.308885i	−0.762975	+	0.646428i	$0.776262\pi$
$18$		0			0
$19$	31.0000	−	53.6936i	0.374310	−	0.648324i	−0.615914	−	0.787814i	$-0.711213\pi$
$19$	31.0000	−	53.6936i	0.374310	−	0.648324i	0.990223	+	0.139490i	$0.0445463\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	43.0000	−	74.4782i	0.389831	−	0.675208i	−0.602595	−	0.798047i	$-0.705867\pi$
$23$	43.0000	−	74.4782i	0.389831	−	0.675208i	0.992427	+	0.122839i	$0.0392000\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$		0			0
$27$	−53.0000			−0.377772
$28$		0			0
$29$	−29.0000			−0.185695			−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−29.0000			−0.185695			−0.0928477	+	0.995680i	$0.529597\pi$
$30$		0			0
$31$	6.00000	+	10.3923i	0.0347623	+	0.0602101i	0.882883	−	0.469593i	$-0.155599\pi$
$31$	6.00000	+	10.3923i	0.0347623	+	0.0602101i	−0.848121	+	0.529803i	$0.822266\pi$
$32$		0			0
$33$	3.50000	−	6.06218i	0.0184628	−	0.0319785i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	75.0000	−	129.904i	0.333241	−	0.577191i	−0.649904	−	0.760016i	$-0.725191\pi$
$37$	75.0000	−	129.904i	0.333241	−	0.577191i	0.983145	+	0.182825i	$0.0585243\pi$
$38$		0			0
$39$	11.5000	+	19.9186i	0.0472173	+	0.0817827i
$40$		0			0
$41$	204.000			0.777060			0.388530	−	0.921436i	$-0.372983\pi$
$41$	204.000			0.777060			0.388530	+	0.921436i	$0.372983\pi$
$42$		0			0
$43$	−178.000			−0.631273			−0.315637	−	0.948880i	$-0.602218\pi$
$43$	−178.000			−0.631273			−0.315637	+	0.948880i	$0.602218\pi$
$44$		0			0
$45$	−65.0000	−	112.583i	−0.215325	−	0.372954i
$46$		0			0
$47$	−16.5000	+	28.5788i	−0.0512079	+	0.0886947i	−0.890493	−	0.454997i	$-0.849640\pi$
$47$	−16.5000	+	28.5788i	−0.0512079	+	0.0886947i	0.839285	+	0.543691i	$0.182974\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	12.5000	−	21.6506i	0.0343206	−	0.0594450i
$52$		0			0
$53$	−226.000	−	391.443i	−0.585726	−	1.01451i	−0.994784	−	0.101999i	$-0.967476\pi$
$53$	−226.000	−	391.443i	−0.585726	−	1.01451i	0.409058	−	0.912508i	$-0.365857\pi$
$54$		0			0
$55$	35.0000			0.0858073
$56$		0			0
$57$	−62.0000			−0.144072
$58$		0			0
$59$	−60.0000	−	103.923i	−0.132396	−	0.229316i	0.792204	−	0.610256i	$-0.208934\pi$
$59$	−60.0000	−	103.923i	−0.132396	−	0.229316i	−0.924600	+	0.380941i	$0.875600\pi$
$60$		0			0
$61$	−460.000	+	796.743i	−0.965524	+	1.67234i	−0.257323	+	0.966325i	$0.582841\pi$
$61$	−460.000	+	796.743i	−0.965524	+	1.67234i	−0.708201	+	0.706011i	$0.750493\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−57.5000	+	99.5929i	−0.109723	+	0.190046i
$66$		0			0
$67$	150.000	+	259.808i	0.273514	+	0.473740i	0.969759	−	0.244064i	$-0.0784808\pi$
$67$	150.000	+	259.808i	0.273514	+	0.473740i	−0.696245	+	0.717804i	$0.745147\pi$
$68$		0			0
$69$	−86.0000			−0.150046
$70$		0			0
$71$	520.000			0.869192			0.434596	−	0.900625i	$-0.356891\pi$
$71$	520.000			0.869192			0.434596	+	0.900625i	$0.356891\pi$
$72$		0			0
$73$	−185.000	−	320.429i	−0.296611	−	0.513746i	0.678747	−	0.734372i	$-0.262523\pi$
$73$	−185.000	−	320.429i	−0.296611	−	0.513746i	−0.975358	+	0.220626i	$0.929190\pi$
$74$		0			0
$75$	−12.5000	+	21.6506i	−0.0192450	+	0.0333333i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	506.500	−	877.284i	0.721338	−	1.24939i	−0.239126	−	0.970989i	$-0.576861\pi$
$79$	506.500	−	877.284i	0.721338	−	1.24939i	0.960464	−	0.278405i	$-0.0898059\pi$
$80$		0			0
$81$	−324.500	−	562.050i	−0.445130	−	0.770988i
$82$		0			0
$83$	−636.000			−0.841085			−0.420543	−	0.907273i	$-0.638160\pi$
$83$	−636.000			−0.841085			−0.420543	+	0.907273i	$0.638160\pi$
$84$		0			0
$85$	125.000			0.159508
$86$		0			0
$87$	14.5000	+	25.1147i	0.0178685	+	0.0309492i
$88$		0			0
$89$	−146.000	+	252.879i	−0.173887	+	0.301182i	−0.939776	−	0.341792i	$-0.888966\pi$
$89$	−146.000	+	252.879i	−0.173887	+	0.301182i	0.765888	+	0.642974i	$0.222300\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	6.00000	−	10.3923i	0.00669001	−	0.0115874i
$94$		0			0
$95$	−155.000	−	268.468i	−0.167396	−	0.289939i
$96$		0			0
$97$	−1381.00			−1.44556			−0.722780	−	0.691078i	$-0.757136\pi$
$97$	−1381.00			−1.44556			−0.722780	+	0.691078i	$0.757136\pi$
$98$		0			0
$99$	182.000			0.184765
$100$		0			0
$101$	−639.000	−	1106.78i	−0.629533	−	1.09038i	−0.987645	−	0.156705i	$-0.949913\pi$
$101$	−639.000	−	1106.78i	−0.629533	−	1.09038i	0.358112	−	0.933679i	$-0.383421\pi$
$102$		0			0
$103$	437.500	−	757.772i	0.418526	−	0.724908i	−0.577266	−	0.816556i	$-0.695880\pi$
$103$	437.500	−	757.772i	0.418526	−	0.724908i	0.995791	+	0.0916485i	$0.0292136\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	993.000	−	1719.93i	0.897168	−	1.55394i	0.0660688	−	0.997815i	$-0.478954\pi$
$107$	993.000	−	1719.93i	0.897168	−	1.55394i	0.831099	−	0.556125i	$-0.187712\pi$
$108$		0			0
$109$	111.500	+	193.124i	0.0979795	+	0.169705i	0.910848	−	0.412742i	$-0.135429\pi$
$109$	111.500	+	193.124i	0.0979795	+	0.169705i	−0.812869	+	0.582447i	$0.802095\pi$
$110$		0			0
$111$	−150.000			−0.128265
$112$		0			0
$113$	−930.000			−0.774222			−0.387111	−	0.922033i	$-0.626527\pi$
$113$	−930.000			−0.774222			−0.387111	+	0.922033i	$0.626527\pi$
$114$		0			0
$115$	−215.000	−	372.391i	−0.174338	−	0.301962i
$116$		0			0
$117$	−299.000	+	517.883i	−0.236261	+	0.409216i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	641.000	−	1110.24i	0.481593	−	0.834143i
$122$		0			0
$123$	−102.000	−	176.669i	−0.0747726	−	0.129510i
$124$		0			0
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−2056.00			−1.43654			−0.718270	−	0.695765i	$-0.755066\pi$
$127$	−2056.00			−1.43654			−0.718270	+	0.695765i	$0.755066\pi$
$128$		0			0
$129$	89.0000	+	154.153i	0.0607443	+	0.105212i
$130$		0			0
$131$	−721.000	+	1248.81i	−0.480871	+	0.832892i	−0.999759	−	0.0219495i	$-0.993013\pi$
$131$	−721.000	+	1248.81i	−0.480871	+	0.832892i	0.518888	+	0.854842i	$0.326346\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−132.500	+	229.497i	−0.0844725	+	0.146311i
$136$		0			0
$137$	454.000	+	786.351i	0.283123	+	0.490383i	0.972152	−	0.234350i	$-0.0752962\pi$
$137$	454.000	+	786.351i	0.283123	+	0.490383i	−0.689029	+	0.724733i	$0.741963\pi$
$138$		0			0
$139$	−1690.00			−1.03125			−0.515626	−	0.856814i	$-0.672440\pi$
$139$	−1690.00			−1.03125			−0.515626	+	0.856814i	$0.672440\pi$
$140$		0			0
$141$	33.0000			0.0197099
$142$		0			0
$143$	−80.5000	−	139.430i	−0.0470752	−	0.0815366i
$144$		0			0
$145$	−72.5000	+	125.574i	−0.0415227	+	0.0719195i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1007.00	−	1744.18i	0.553669	−	0.958983i	−0.444337	−	0.895860i	$-0.646561\pi$
$149$	1007.00	−	1744.18i	0.553669	−	0.958983i	0.998006	−	0.0631228i	$-0.0201060\pi$
$150$		0			0
$151$	−309.500	−	536.070i	−0.166800	−	0.288906i	0.770493	−	0.637448i	$-0.220010\pi$
$151$	−309.500	−	536.070i	−0.166800	−	0.288906i	−0.937293	+	0.348543i	$0.886677\pi$
$152$		0			0
$153$	650.000			0.343460
$154$		0			0
$155$	60.0000			0.0310924
$156$		0			0
$157$	−723.000	−	1252.27i	−0.367527	−	0.636575i	0.621652	−	0.783294i	$-0.286462\pi$
$157$	−723.000	−	1252.27i	−0.367527	−	0.636575i	−0.989178	+	0.146719i	$0.953129\pi$
$158$		0			0
$159$	−226.000	+	391.443i	−0.112723	+	0.195242i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1319.00	−	2284.58i	0.633816	−	1.09780i	−0.352948	−	0.935643i	$-0.614821\pi$
$163$	1319.00	−	2284.58i	0.633816	−	1.09780i	0.986765	−	0.162159i	$-0.0518458\pi$
$164$		0			0
$165$	−17.5000	−	30.3109i	−0.00825681	−	0.0143012i
$166$		0			0
$167$	−11.0000			−0.00509704			−0.00254852	−	0.999997i	$-0.500811\pi$
$167$	−11.0000			−0.00509704			−0.00254852	+	0.999997i	$0.500811\pi$
$168$		0			0
$169$	−1668.00			−0.759217
$170$		0			0
$171$	−806.000	−	1396.03i	−0.360447	−	0.624312i
$172$		0			0
$173$	−1633.50	+	2829.30i	−0.717877	+	1.24340i	0.243962	+	0.969785i	$0.421553\pi$
$173$	−1633.50	+	2829.30i	−0.717877	+	1.24340i	−0.961839	+	0.273615i	$0.911781\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−60.0000	+	103.923i	−0.0254795	+	0.0441318i
$178$		0			0
$179$	−1838.00	−	3183.51i	−0.767478	−	1.32931i	−0.938926	−	0.344118i	$-0.888178\pi$
$179$	−1838.00	−	3183.51i	−0.767478	−	1.32931i	0.171448	−	0.985193i	$-0.445155\pi$
$180$		0			0
$181$	780.000			0.320315			0.160157	−	0.987092i	$-0.448800\pi$
$181$	780.000			0.320315			0.160157	+	0.987092i	$0.448800\pi$
$182$		0			0
$183$	920.000			0.371630
$184$		0			0
$185$	−375.000	−	649.519i	−0.149030	−	0.258128i
$186$		0			0
$187$	−87.5000	+	151.554i	−0.0342173	+	0.0592661i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	141.500	−	245.085i	0.0536051	−	0.0928468i	−0.837978	−	0.545705i	$-0.816262\pi$
$191$	141.500	−	245.085i	0.0536051	−	0.0928468i	0.891583	+	0.452858i	$0.149595\pi$
$192$		0			0
$193$	242.000	+	419.156i	0.0902567	+	0.156329i	0.907619	−	0.419795i	$-0.137898\pi$
$193$	242.000	+	419.156i	0.0902567	+	0.156329i	−0.817362	+	0.576124i	$0.804565\pi$
$194$		0			0
$195$	115.000			0.0422324
$196$		0			0
$197$	−360.000			−0.130198			−0.0650988	−	0.997879i	$-0.520736\pi$
$197$	−360.000			−0.130198			−0.0650988	+	0.997879i	$0.520736\pi$
$198$		0			0
$199$	−516.000	−	893.738i	−0.183810	−	0.318369i	0.759365	−	0.650665i	$-0.225510\pi$
$199$	−516.000	−	893.738i	−0.183810	−	0.318369i	−0.943175	+	0.332296i	$0.892177\pi$
$200$		0			0
$201$	150.000	−	259.808i	0.0526377	−	0.0911712i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	510.000	−	883.346i	0.173756	−	0.300954i
$206$		0			0
$207$	−1118.00	−	1936.43i	−0.375393	−	0.650200i
$208$		0			0
$209$	434.000			0.143638
$210$		0			0
$211$	−513.000			−0.167376			−0.0836881	−	0.996492i	$-0.526670\pi$
$211$	−513.000			−0.167376			−0.0836881	+	0.996492i	$0.526670\pi$
$212$		0			0
$213$	−260.000	−	450.333i	−0.0836381	−	0.144865i
$214$		0			0
$215$	−445.000	+	770.763i	−0.141157	+	0.244491i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−185.000	+	320.429i	−0.0570828	+	0.0988704i
$220$		0			0
$221$	−287.500	−	497.965i	−0.0875083	−	0.151569i
$222$		0			0
$223$	−907.000			−0.272364			−0.136182	−	0.990684i	$-0.543483\pi$
$223$	−907.000			−0.272364			−0.136182	+	0.990684i	$0.543483\pi$
$224$		0			0
$225$	−650.000			−0.192593
$226$		0			0
$227$	−2850.50	−	4937.21i	−0.833455	−	1.44359i	−0.895282	−	0.445500i	$-0.853026\pi$
$227$	−2850.50	−	4937.21i	−0.833455	−	1.44359i	0.0618268	−	0.998087i	$-0.480307\pi$
$228$		0			0
$229$	1022.00	−	1770.16i	0.294916	−	0.510809i	−0.680050	−	0.733166i	$-0.738042\pi$
$229$	1022.00	−	1770.16i	0.294916	−	0.510809i	0.974965	+	0.222357i	$0.0713751\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1364.00	−	2362.52i	0.383513	−	0.664265i	−0.608048	−	0.793900i	$-0.708047\pi$
$233$	1364.00	−	2362.52i	0.383513	−	0.664265i	0.991562	+	0.129635i	$0.0413807\pi$
$234$		0			0
$235$	82.5000	+	142.894i	0.0229009	+	0.0396655i
$236$		0			0
$237$	−1013.00			−0.277643
$238$		0			0
$239$	7095.00			1.92024			0.960120	−	0.279588i	$-0.0901979\pi$
$239$	7095.00			1.92024			0.960120	+	0.279588i	$0.0901979\pi$
$240$		0			0
$241$	1309.00	+	2267.25i	0.349876	+	0.606003i	0.986227	−	0.165397i	$-0.0528904\pi$
$241$	1309.00	+	2267.25i	0.349876	+	0.606003i	−0.636351	+	0.771399i	$0.719557\pi$
$242$		0			0
$243$	−1040.00	+	1801.33i	−0.274552	+	0.475537i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−713.000	+	1234.95i	−0.183672	+	0.318130i
$248$		0			0
$249$	318.000	+	550.792i	0.0809335	+	0.140181i
$250$		0			0
$251$	−3318.00			−0.834384			−0.417192	−	0.908818i	$-0.636986\pi$
$251$	−3318.00			−0.834384			−0.417192	+	0.908818i	$0.636986\pi$
$252$		0			0
$253$	602.000			0.149595
$254$		0			0
$255$	−62.5000	−	108.253i	−0.0153486	−	0.0265846i
$256$		0			0
$257$	−839.000	+	1453.19i	−0.203640	+	0.352714i	−0.949698	−	0.313166i	$-0.898610\pi$
$257$	−839.000	+	1453.19i	−0.203640	+	0.352714i	0.746059	+	0.665880i	$0.231944\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−377.000	+	652.983i	−0.0894089	+	0.154861i
$262$		0			0
$263$	449.000	+	777.691i	0.105272	+	0.182336i	0.913849	−	0.406054i	$-0.133095\pi$
$263$	449.000	+	777.691i	0.105272	+	0.182336i	−0.808577	+	0.588390i	$0.799762\pi$
$264$		0			0
$265$	−2260.00			−0.523889
$266$		0			0
$267$	292.000			0.0669293
$268$		0			0
$269$	2451.00	+	4245.26i	0.555539	+	0.962223i	0.997861	+	0.0653662i	$0.0208215\pi$
$269$	2451.00	+	4245.26i	0.555539	+	0.962223i	−0.442322	+	0.896856i	$0.645845\pi$
$270$		0			0
$271$	3520.00	−	6096.82i	0.789021	−	1.36662i	−0.137546	−	0.990495i	$-0.543921\pi$
$271$	3520.00	−	6096.82i	0.789021	−	1.36662i	0.926567	−	0.376130i	$-0.122745\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	87.5000	−	151.554i	0.0191871	−	0.0332330i
$276$		0			0
$277$	1201.00	+	2080.19i	0.260509	+	0.451215i	0.966377	−	0.257128i	$-0.0827762\pi$
$277$	1201.00	+	2080.19i	0.260509	+	0.451215i	−0.705868	+	0.708343i	$0.749443\pi$
$278$		0			0
$279$	312.000			0.0669496
$280$		0			0
$281$	−6525.00			−1.38523			−0.692614	−	0.721309i	$-0.743541\pi$
$281$	−6525.00			−1.38523			−0.692614	+	0.721309i	$0.743541\pi$
$282$		0			0
$283$	2054.50	+	3558.50i	0.431545	+	0.747459i	0.997007	−	0.0773163i	$-0.0246351\pi$
$283$	2054.50	+	3558.50i	0.431545	+	0.747459i	−0.565461	+	0.824775i	$0.691302\pi$
$284$		0			0
$285$	−155.000	+	268.468i	−0.0322155	+	0.0557988i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	2144.00	−	3713.52i	0.436393	−	0.755855i
$290$		0			0
$291$	690.500	+	1195.98i	0.139099	+	0.240927i
$292$		0			0
$293$	3495.00			0.696860			0.348430	−	0.937335i	$-0.386715\pi$
$293$	3495.00			0.696860			0.348430	+	0.937335i	$0.386715\pi$
$294$		0			0
$295$	−600.000			−0.118418
$296$		0			0
$297$	−185.500	−	321.295i	−0.0362418	−	0.0627726i
$298$		0			0
$299$	−989.000	+	1713.00i	−0.191289	+	0.331322i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−639.000	+	1106.78i	−0.121154	+	0.209844i
$304$		0			0
$305$	2300.00	+	3983.72i	0.431795	+	0.747892i
$306$		0			0
$307$	803.000			0.149282			0.0746411	−	0.997210i	$-0.476219\pi$
$307$	803.000			0.149282			0.0746411	+	0.997210i	$0.476219\pi$
$308$		0			0
$309$	−875.000			−0.161091
$310$		0			0
$311$	2719.00	+	4709.45i	0.495757	+	0.858676i	0.999988	−	0.00489279i	$-0.00155743\pi$
$311$	2719.00	+	4709.45i	0.495757	+	0.858676i	−0.504231	+	0.863569i	$0.668224\pi$
$312$		0			0
$313$	−340.500	+	589.763i	−0.0614895	+	0.106503i	−0.895131	−	0.445802i	$-0.852918\pi$
$313$	−340.500	+	589.763i	−0.0614895	+	0.106503i	0.833642	+	0.552305i	$0.186252\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4607.00	+	7979.56i	−0.816262	+	1.41381i	0.0921570	+	0.995744i	$0.470624\pi$
$317$	−4607.00	+	7979.56i	−0.816262	+	1.41381i	−0.908419	+	0.418062i	$0.862710\pi$
$318$		0			0
$319$	−101.500	−	175.803i	−0.0178148	−	0.0308561i
$320$		0			0
$321$	−1986.00			−0.345320
$322$		0			0
$323$	1550.00			0.267010
$324$		0			0
$325$	287.500	+	497.965i	0.0490696	+	0.0849911i
$326$		0			0
$327$	111.500	−	193.124i	0.0188562	−	0.0326598i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1350.00	−	2338.27i	0.224177	−	0.388287i	−0.731895	−	0.681417i	$-0.761364\pi$
$331$	1350.00	−	2338.27i	0.224177	−	0.388287i	0.956072	+	0.293131i	$0.0946972\pi$
$332$		0			0
$333$	−1950.00	−	3377.50i	−0.320899	−	0.555813i
$334$		0			0
$335$	1500.00			0.244638
$336$		0			0
$337$	−3834.00			−0.619737			−0.309868	−	0.950779i	$-0.600285\pi$
$337$	−3834.00			−0.619737			−0.309868	+	0.950779i	$0.600285\pi$
$338$		0			0
$339$	465.000	+	805.404i	0.0744995	+	0.129037i
$340$		0			0
$341$	−42.0000	+	72.7461i	−0.00666988	+	0.0115526i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−215.000	+	372.391i	−0.0335513	+	0.0581126i
$346$		0			0
$347$	1313.00	+	2274.18i	0.203128	+	0.351829i	0.949535	−	0.313662i	$-0.101556\pi$
$347$	1313.00	+	2274.18i	0.203128	+	0.351829i	−0.746406	+	0.665490i	$0.768222\pi$
$348$		0			0
$349$	8354.00			1.28132			0.640658	−	0.767826i	$-0.278662\pi$
$349$	8354.00			1.28132			0.640658	+	0.767826i	$0.278662\pi$
$350$		0			0
$351$	1219.00			0.185372
$352$		0			0
$353$	4106.50	+	7112.67i	0.619170	+	1.07243i	0.989638	+	0.143588i	$0.0458641\pi$
$353$	4106.50	+	7112.67i	0.619170	+	1.07243i	−0.370468	+	0.928845i	$0.620803\pi$
$354$		0			0
$355$	1300.00	−	2251.67i	0.194357	−	0.336637i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3216.00	+	5570.28i	−0.472797	+	0.818908i	−0.999515	−	0.0311319i	$-0.990089\pi$
$359$	−3216.00	+	5570.28i	−0.472797	+	0.818908i	0.526719	+	0.850040i	$0.323422\pi$
$360$		0			0
$361$	1507.50	+	2611.07i	0.219784	+	0.380677i
$362$		0			0
$363$	−1282.00			−0.185365
$364$		0			0
$365$	−1850.00			−0.265297
$366$		0			0
$367$	−5808.50	−	10060.6i	−0.826161	−	1.43095i	−0.901028	−	0.433760i	$-0.857187\pi$
$367$	−5808.50	−	10060.6i	−0.826161	−	1.43095i	0.0748671	−	0.997194i	$-0.476147\pi$
$368$		0			0
$369$	2652.00	−	4593.40i	0.374140	−	0.648029i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−5542.00	+	9599.03i	−0.769313	+	1.33249i	0.168622	+	0.985681i	$0.446068\pi$
$373$	−5542.00	+	9599.03i	−0.769313	+	1.33249i	−0.937936	+	0.346809i	$0.887265\pi$
$374$		0			0
$375$	62.5000	+	108.253i	0.00860663	+	0.0149071i
$376$		0			0
$377$	667.000			0.0911200
$378$		0			0
$379$	12292.0			1.66596			0.832978	−	0.553306i	$-0.186634\pi$
$379$	12292.0			1.66596			0.832978	+	0.553306i	$0.186634\pi$
$380$		0			0
$381$	1028.00	+	1780.55i	0.138231	+	0.239423i
$382$		0			0
$383$	5410.00	−	9370.39i	0.721770	−	1.25014i	−0.238519	−	0.971138i	$-0.576662\pi$
$383$	5410.00	−	9370.39i	0.721770	−	1.25014i	0.960290	−	0.279005i	$-0.0900047\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2314.00	+	4007.97i	−0.303946	+	0.526450i
$388$		0			0
$389$	−3750.50	−	6496.06i	−0.488838	−	0.846692i	0.511080	−	0.859533i	$-0.329246\pi$
$389$	−3750.50	−	6496.06i	−0.488838	−	0.846692i	−0.999918	+	0.0128414i	$0.995912\pi$
$390$		0			0
$391$	2150.00			0.278082
$392$		0			0
$393$	1442.00			0.185087
$394$		0			0
$395$	−2532.50	−	4386.42i	−0.322592	−	0.558746i
$396$		0			0
$397$	−3949.50	+	6840.73i	−0.499294	+	0.864803i	−1.00000		0.000815012i	$-0.999741\pi$
$397$	−3949.50	+	6840.73i	−0.499294	+	0.864803i	0.500706	+	0.865618i	$0.333074\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−876.500	+	1518.14i	−0.109153	+	0.189058i	−0.915427	−	0.402483i	$-0.868147\pi$
$401$	−876.500	+	1518.14i	−0.109153	+	0.189058i	0.806274	+	0.591542i	$0.201480\pi$
$402$		0			0
$403$	−138.000	−	239.023i	−0.0170577	−	0.0295449i
$404$		0			0
$405$	−3245.00			−0.398137
$406$		0			0
$407$	1050.00			0.127879
$408$		0			0
$409$	5917.00	+	10248.5i	0.715347	+	1.23902i	0.962826	+	0.270124i	$0.0870646\pi$
$409$	5917.00	+	10248.5i	0.715347	+	1.23902i	−0.247479	+	0.968893i	$0.579602\pi$
$410$		0			0
$411$	454.000	−	786.351i	0.0544870	−	0.0943743i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1590.00	+	2753.96i	−0.188072	+	0.325751i
$416$		0			0
$417$	845.000	+	1463.58i	0.0992322	+	0.171875i
$418$		0			0
$419$	6908.00			0.805436			0.402718	−	0.915324i	$-0.368065\pi$
$419$	6908.00			0.805436			0.402718	+	0.915324i	$0.368065\pi$
$420$		0			0
$421$	8377.00			0.969762			0.484881	−	0.874580i	$-0.338863\pi$
$421$	8377.00			0.969762			0.484881	+	0.874580i	$0.338863\pi$
$422$		0			0
$423$	429.000	+	743.050i	0.0493113	+	0.0854097i
$424$		0			0
$425$	312.500	−	541.266i	0.0356670	−	0.0617771i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−80.5000	+	139.430i	−0.00905962	+	0.0156917i
$430$		0			0
$431$	2143.50	+	3712.65i	0.239556	+	0.414924i	0.960587	−	0.277979i	$-0.0896647\pi$
$431$	2143.50	+	3712.65i	0.239556	+	0.414924i	−0.721031	+	0.692903i	$0.756331\pi$
$432$		0			0
$433$	15874.0			1.76179			0.880896	−	0.473310i	$-0.156941\pi$
$433$	15874.0			1.76179			0.880896	+	0.473310i	$0.156941\pi$
$434$		0			0
$435$	145.000			0.0159821
$436$		0			0
$437$	−2666.00	−	4617.65i	−0.291835	−	0.505474i
$438$		0			0
$439$	3823.00	−	6621.63i	0.415631	−	0.719893i	−0.579864	−	0.814713i	$-0.696894\pi$
$439$	3823.00	−	6621.63i	0.415631	−	0.719893i	0.995494	+	0.0948201i	$0.0302276\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	813.000	−	1408.16i	0.0871937	−	0.151024i	−0.819130	−	0.573608i	$-0.805543\pi$
$443$	813.000	−	1408.16i	0.0871937	−	0.151024i	0.906324	+	0.422584i	$0.138877\pi$
$444$		0			0
$445$	730.000	+	1264.40i	0.0777648	+	0.134693i
$446$		0			0
$447$	−2014.00			−0.213107
$448$		0			0
$449$	−841.000			−0.0883948			−0.0441974	−	0.999023i	$-0.514073\pi$
$449$	−841.000			−0.0883948			−0.0441974	+	0.999023i	$0.514073\pi$
$450$		0			0
$451$	714.000	+	1236.68i	0.0745476	+	0.129120i
$452$		0			0
$453$	−309.500	+	536.070i	−0.0321006	+	0.0555999i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−7712.00	+	13357.6i	−0.789392	+	1.36727i	0.136948	+	0.990578i	$0.456271\pi$
$457$	−7712.00	+	13357.6i	−0.789392	+	1.36727i	−0.926340	+	0.376689i	$0.877063\pi$
$458$		0			0
$459$	−662.500	−	1147.48i	−0.0673700	−	0.116688i
$460$		0			0
$461$	10568.0			1.06768			0.533840	−	0.845585i	$-0.320748\pi$
$461$	10568.0			1.06768			0.533840	+	0.845585i	$0.320748\pi$
$462$		0			0
$463$	4368.00			0.438441			0.219220	−	0.975675i	$-0.429649\pi$
$463$	4368.00			0.438441			0.219220	+	0.975675i	$0.429649\pi$
$464$		0			0
$465$	−30.0000	−	51.9615i	−0.00299186	−	0.00518206i
$466$		0			0
$467$	2164.50	−	3749.02i	0.214478	−	0.371486i	−0.738633	−	0.674108i	$-0.764528\pi$
$467$	2164.50	−	3749.02i	0.214478	−	0.371486i	0.953111	+	0.302621i	$0.0978617\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−723.000	+	1252.27i	−0.0707305	+	0.122509i
$472$		0			0
$473$	−623.000	−	1079.07i	−0.0605615	−	0.104896i
$474$		0			0
$475$	−1550.00			−0.149724
$476$		0			0
$477$	−11752.0			−1.12807
$478$		0			0
$479$	5531.00	+	9579.97i	0.527595	+	0.913821i	0.999483	+	0.0321623i	$0.0102393\pi$
$479$	5531.00	+	9579.97i	0.527595	+	0.913821i	−0.471888	+	0.881659i	$0.656427\pi$
$480$		0			0
$481$	−1725.00	+	2987.79i	−0.163520	+	0.283225i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3452.50	+	5979.91i	−0.323237	+	0.559863i
$486$		0			0
$487$	9349.00	+	16192.9i	0.869905	+	1.50672i	0.862093	+	0.506750i	$0.169153\pi$
$487$	9349.00	+	16192.9i	0.869905	+	1.50672i	0.00781160	+	0.999969i	$0.497513\pi$
$488$		0			0
$489$	−2638.00			−0.243956
$490$		0			0
$491$	3003.00			0.276015			0.138008	−	0.990431i	$-0.455930\pi$
$491$	3003.00			0.276015			0.138008	+	0.990431i	$0.455930\pi$
$492$		0			0
$493$	−362.500	−	627.868i	−0.0331160	−	0.0573586i
$494$		0			0
$495$	455.000	−	788.083i	0.0413146	−	0.0715590i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1645.50	−	2850.09i	0.147621	−	0.255686i	−0.782727	−	0.622365i	$-0.786172\pi$
$499$	1645.50	−	2850.09i	0.147621	−	0.255686i	0.930348	+	0.366679i	$0.119505\pi$
$500$		0			0
$501$	5.50000	+	9.52628i	0.000490463	+	0.000849507i
$502$		0			0
$503$	−12533.0			−1.11097			−0.555486	−	0.831526i	$-0.687468\pi$
$503$	−12533.0			−1.11097			−0.555486	+	0.831526i	$0.687468\pi$
$504$		0			0
$505$	−6390.00			−0.563072
$506$		0			0
$507$	834.000	+	1444.53i	0.0730557	+	0.126536i
$508$		0			0
$509$	1203.00	−	2083.66i	0.104758	−	0.181447i	−0.808881	−	0.587972i	$-0.799926\pi$
$509$	1203.00	−	2083.66i	0.104758	−	0.181447i	0.913639	+	0.406525i	$0.133260\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−1643.00	+	2845.76i	−0.141404	+	0.244919i
$514$		0			0
$515$	−2187.50	−	3788.86i	−0.187170	−	0.324189i
$516$		0			0
$517$	−231.000			−0.0196506
$518$		0			0
$519$	3267.00			0.276311
$520$		0			0
$521$	5049.00	+	8745.12i	0.424569	+	0.735376i	0.996380	−	0.0850097i	$-0.0270921\pi$
$521$	5049.00	+	8745.12i	0.424569	+	0.735376i	−0.571811	+	0.820386i	$0.693759\pi$
$522$		0			0
$523$	8050.00	−	13943.0i	0.673044	−	1.16575i	−0.303993	−	0.952674i	$-0.598320\pi$
$523$	8050.00	−	13943.0i	0.673044	−	1.16575i	0.977037	−	0.213072i	$-0.0683468\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−150.000	+	259.808i	−0.0123987	+	0.0214751i
$528$		0			0
$529$	2385.50	+	4131.81i	0.196063	+	0.339591i
$530$		0			0
$531$	−3120.00			−0.254984
$532$		0			0
$533$	−4692.00			−0.381300
$534$		0			0
$535$	−4965.00	−	8599.63i	−0.401226	−	0.694943i
$536$		0			0
$537$	−1838.00	+	3183.51i	−0.147701	+	0.255826i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−8417.50	+	14579.5i	−0.668940	+	1.15864i	0.309261	+	0.950977i	$0.399918\pi$
$541$	−8417.50	+	14579.5i	−0.668940	+	1.15864i	−0.978201	+	0.207661i	$0.933415\pi$
$542$		0			0
$543$	−390.000	−	675.500i	−0.0308223	−	0.0533858i
$544$		0			0
$545$	1115.00			0.0876355
$546$		0			0
$547$	−4104.00			−0.320794			−0.160397	−	0.987053i	$-0.551277\pi$
$547$	−4104.00			−0.320794			−0.160397	+	0.987053i	$0.551277\pi$
$548$		0			0
$549$	11960.0	+	20715.3i	0.929764	+	1.61040i
$550$		0			0
$551$	−899.000	+	1557.11i	−0.0695076	+	0.120391i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−375.000	+	649.519i	−0.0286808	+	0.0496767i
$556$		0			0
$557$	10140.0	+	17563.0i	0.771357	+	1.33603i	0.936820	+	0.349813i	$0.113755\pi$
$557$	10140.0	+	17563.0i	0.771357	+	1.33603i	−0.165463	+	0.986216i	$0.552912\pi$
$558$		0			0
$559$	4094.00			0.309763
$560$		0			0
$561$	175.000			0.0131702
$562$		0			0
$563$	8546.00	+	14802.1i	0.639735	+	1.10805i	0.985491	+	0.169729i	$0.0542893\pi$
$563$	8546.00	+	14802.1i	0.639735	+	1.10805i	−0.345755	+	0.938325i	$0.612377\pi$
$564$		0			0
$565$	−2325.00	+	4027.02i	−0.173121	+	0.299855i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−121.000	+	209.578i	−0.00891491	+	0.0154411i	−0.870448	−	0.492260i	$-0.836171\pi$
$569$	−121.000	+	209.578i	−0.00891491	+	0.0154411i	0.861534	+	0.507701i	$0.169504\pi$
$570$		0			0
$571$	−590.000	−	1021.91i	−0.0432412	−	0.0748960i	0.843595	−	0.536980i	$-0.180435\pi$
$571$	−590.000	−	1021.91i	−0.0432412	−	0.0748960i	−0.886836	+	0.462084i	$0.847102\pi$
$572$		0			0
$573$	−283.000			−0.0206326
$574$		0			0
$575$	−2150.00			−0.155933
$576$		0			0
$577$	−9210.50	−	15953.1i	−0.664537	−	1.15101i	−0.979410	−	0.201879i	$-0.935295\pi$
$577$	−9210.50	−	15953.1i	−0.664537	−	1.15101i	0.314873	−	0.949134i	$-0.398038\pi$
$578$		0			0
$579$	242.000	−	419.156i	0.0173699	−	0.0300856i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1582.00	−	2740.10i	0.112384	−	0.194654i
$584$		0			0
$585$	1495.00	+	2589.42i	0.105659	+	0.183007i
$586$		0			0
$587$	−19776.0			−1.39053			−0.695267	−	0.718752i	$-0.744714\pi$
$587$	−19776.0			−1.39053			−0.695267	+	0.718752i	$0.744714\pi$
$588$		0			0
$589$	744.000			0.0520475
$590$		0			0
$591$	180.000	+	311.769i	0.0125283	+	0.0216996i
$592$		0			0
$593$	1225.50	−	2122.63i	0.0848655	−	0.146991i	−0.820468	−	0.571692i	$-0.806287\pi$
$593$	1225.50	−	2122.63i	0.0848655	−	0.146991i	0.905334	+	0.424701i	$0.139621\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−516.000	+	893.738i	−0.0353743	+	0.0612701i
$598$		0			0
$599$	−9040.50	−	15658.6i	−0.616669	−	1.06810i	−0.990089	−	0.140440i	$-0.955148\pi$
$599$	−9040.50	−	15658.6i	−0.616669	−	1.06810i	0.373420	−	0.927662i	$-0.378185\pi$
$600$		0			0
$601$	18238.0			1.23784			0.618921	−	0.785453i	$-0.287570\pi$
$601$	18238.0			1.23784			0.618921	+	0.785453i	$0.287570\pi$
$602$		0			0
$603$	7800.00			0.526767
$604$		0			0
$605$	−3205.00	−	5551.22i	−0.215375	−	0.373040i
$606$		0			0
$607$	5462.50	−	9461.33i	0.365265	−	0.632658i	−0.623553	−	0.781781i	$-0.714312\pi$
$607$	5462.50	−	9461.33i	0.365265	−	0.632658i	0.988819	+	0.149123i	$0.0476449\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	379.500	−	657.313i	0.0251275	−	0.0435222i
$612$		0			0
$613$	−753.000	−	1304.23i	−0.0496140	−	0.0859340i	0.840152	−	0.542351i	$-0.182466\pi$
$613$	−753.000	−	1304.23i	−0.0496140	−	0.0859340i	−0.889766	+	0.456417i	$0.849132\pi$
$614$		0			0
$615$	−1020.00			−0.0668787
$616$		0			0
$617$	−24142.0			−1.57524			−0.787618	−	0.616164i	$-0.788686\pi$
$617$	−24142.0			−1.57524			−0.787618	+	0.616164i	$0.788686\pi$
$618$		0			0
$619$	8279.00	+	14339.6i	0.537579	+	0.931113i	0.999034	+	0.0439498i	$0.0139942\pi$
$619$	8279.00	+	14339.6i	0.537579	+	0.931113i	−0.461455	+	0.887164i	$0.652672\pi$
$620$		0			0
$621$	−2279.00	+	3947.34i	−0.147268	+	0.255075i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−217.000	−	375.855i	−0.0138216	−	0.0239397i
$628$		0			0
$629$	3750.00			0.237714
$630$		0			0
$631$	25025.0			1.57881			0.789405	−	0.613872i	$-0.210389\pi$
$631$	25025.0			1.57881			0.789405	+	0.613872i	$0.210389\pi$
$632$		0			0
$633$	256.500	+	444.271i	0.0161058	+	0.0278960i
$634$		0			0
$635$	−5140.00	+	8902.74i	−0.321220	+	0.556369i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	6760.00	−	11708.7i	0.418500	−	0.724863i
$640$		0			0
$641$	−4577.00	−	7927.60i	−0.282029	−	0.488489i	0.689855	−	0.723947i	$-0.257674\pi$
$641$	−4577.00	−	7927.60i	−0.282029	−	0.488489i	−0.971884	+	0.235459i	$0.924341\pi$
$642$		0			0
$643$	8225.00			0.504452			0.252226	−	0.967668i	$-0.418837\pi$
$643$	8225.00			0.504452			0.252226	+	0.967668i	$0.418837\pi$
$644$		0			0
$645$	890.000			0.0543313
$646$		0			0
$647$	−11844.0	−	20514.4i	−0.719684	−	1.24653i	−0.961125	−	0.276114i	$-0.910953\pi$
$647$	−11844.0	−	20514.4i	−0.719684	−	1.24653i	0.241441	−	0.970416i	$-0.422380\pi$
$648$		0			0
$649$	420.000	−	727.461i	0.0254028	−	0.0439990i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	7259.00	−	12573.0i	0.435018	−	0.753473i	−0.562279	−	0.826947i	$-0.690075\pi$
$653$	7259.00	−	12573.0i	0.435018	−	0.753473i	0.997297	+	0.0734745i	$0.0234087\pi$
$654$		0			0
$655$	3605.00	+	6244.04i	0.215052	+	0.372481i
$656$		0			0
$657$	−9620.00			−0.571251
$658$		0			0
$659$	30381.0			1.79587			0.897933	−	0.440132i	$-0.145068\pi$
$659$	30381.0			1.79587			0.897933	+	0.440132i	$0.145068\pi$
$660$		0			0
$661$	−12784.0	−	22142.5i	−0.752254	−	1.30294i	−0.946728	−	0.322035i	$-0.895633\pi$
$661$	−12784.0	−	22142.5i	−0.752254	−	1.30294i	0.194474	−	0.980908i	$-0.437700\pi$
$662$		0			0
$663$	−287.500	+	497.965i	−0.0168410	+	0.0291694i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1247.00	+	2159.87i	−0.0723899	+	0.125383i
$668$		0			0
$669$	453.500	+	785.485i	0.0262083	+	0.0453940i
$670$		0			0
$671$	−6440.00			−0.370512
$672$		0			0
$673$	19428.0			1.11277			0.556385	−	0.830925i	$-0.312188\pi$
$673$	19428.0			1.11277			0.556385	+	0.830925i	$0.312188\pi$
$674$		0			0
$675$	662.500	+	1147.48i	0.0377772	+	0.0654321i
$676$		0			0
$677$	−468.500	+	811.466i	−0.0265966	+	0.0460667i	−0.879017	−	0.476790i	$-0.841800\pi$
$677$	−468.500	+	811.466i	−0.0265966	+	0.0460667i	0.852421	+	0.522856i	$0.175134\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−2850.50	+	4937.21i	−0.160399	+	0.277818i
$682$		0			0
$683$	−7980.00	−	13821.8i	−0.447066	−	0.774341i	0.551127	−	0.834421i	$-0.314198\pi$
$683$	−7980.00	−	13821.8i	−0.447066	−	0.774341i	−0.998194	+	0.0600798i	$0.980864\pi$
$684$		0			0
$685$	4540.00			0.253233
$686$		0			0
$687$	−2044.00			−0.113513
$688$		0			0
$689$	5198.00	+	9003.20i	0.287414	+	0.497815i
$690$		0			0
$691$	−5130.00	+	8885.42i	−0.282423	+	0.489171i	−0.971981	−	0.235059i	$-0.924472\pi$
$691$	−5130.00	+	8885.42i	−0.282423	+	0.489171i	0.689558	+	0.724231i	$0.257805\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4225.00	+	7317.91i	−0.230595	+	0.399402i
$696$		0			0
$697$	2550.00	+	4416.73i	0.138577	+	0.240022i
$698$		0			0
$699$	−2728.00			−0.147614
$700$		0			0
$701$	−15465.0			−0.833245			−0.416623	−	0.909080i	$-0.636786\pi$
$701$	−15465.0			−0.833245			−0.416623	+	0.909080i	$0.636786\pi$
$702$		0			0
$703$	−4650.00	−	8054.04i	−0.249471	−	0.432096i
$704$		0			0
$705$	82.5000	−	142.894i	0.00440728	−	0.00763363i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	10502.5	−	18190.9i	0.556318	−	0.963572i	−0.441481	−	0.897270i	$-0.645547\pi$
$709$	10502.5	−	18190.9i	0.556318	−	0.963572i	0.997800	−	0.0663011i	$-0.0211198\pi$
$710$		0			0
$711$	−13169.0	−	22809.4i	−0.694622	−	1.20312i
$712$		0			0
$713$	1032.00			0.0542058
$714$		0			0
$715$	−805.000			−0.0421053
$716$		0			0
$717$	−3547.50	−	6144.45i	−0.184775	−	0.320040i
$718$		0			0
$719$	11.0000	−	19.0526i	0.000570557	−	0.000988234i	−0.865740	−	0.500494i	$-0.833152\pi$
$719$	11.0000	−	19.0526i	0.000570557	−	0.000988234i	0.866311	+	0.499506i	$0.166485\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	1309.00	−	2267.25i	0.0673337	−	0.116625i
$724$		0			0
$725$	362.500	+	627.868i	0.0185695	+	0.0321634i
$726$		0			0
$727$	−1816.00			−0.0926433			−0.0463217	−	0.998927i	$-0.514750\pi$
$727$	−1816.00			−0.0926433			−0.0463217	+	0.998927i	$0.514750\pi$
$728$		0			0
$729$	−15443.0			−0.784586
$730$		0			0
$731$	−2225.00	−	3853.81i	−0.112578	−	0.194991i
$732$		0			0
$733$	−12198.5	+	21128.4i	−0.614682	+	1.06466i	0.375758	+	0.926718i	$0.377382\pi$
$733$	−12198.5	+	21128.4i	−0.614682	+	1.06466i	−0.990440	+	0.137943i	$0.955951\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1050.00	+	1818.65i	−0.0524793	+	0.0908968i
$738$		0			0
$739$	−3032.50	−	5252.44i	−0.150950	−	0.261454i	0.780627	−	0.624998i	$-0.214900\pi$
$739$	−3032.50	−	5252.44i	−0.150950	−	0.261454i	−0.931577	+	0.363544i	$0.881567\pi$
$740$		0			0
$741$	1426.00			0.0706956
$742$		0			0
$743$	3660.00			0.180717			0.0903583	−	0.995909i	$-0.471199\pi$
$743$	3660.00			0.180717			0.0903583	+	0.995909i	$0.471199\pi$
$744$		0			0
$745$	−5035.00	−	8720.88i	−0.247608	−	0.428870i
$746$		0			0
$747$	−8268.00	+	14320.6i	−0.404967	+	0.701423i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	13538.5	−	23449.4i	0.657825	−	1.13939i	−0.323352	−	0.946279i	$-0.604810\pi$
$751$	13538.5	−	23449.4i	0.657825	−	1.13939i	0.981177	−	0.193108i	$-0.0618569\pi$
$752$		0			0
$753$	1659.00	+	2873.47i	0.0802886	+	0.139064i
$754$		0			0
$755$	−3095.00			−0.149190
$756$		0			0
$757$	−31424.0			−1.50875			−0.754376	−	0.656443i	$-0.772060\pi$
$757$	−31424.0			−1.50875			−0.754376	+	0.656443i	$0.772060\pi$
$758$		0			0
$759$	−301.000	−	521.347i	−0.0143947	−	0.0249324i
$760$		0			0
$761$	8449.00	−	14634.1i	0.402465	−	0.697090i	−0.591558	−	0.806263i	$-0.701487\pi$
$761$	8449.00	−	14634.1i	0.402465	−	0.697090i	0.994023	+	0.109173i	$0.0348201\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1625.00	−	2814.58i	0.0768000	−	0.133021i
$766$		0			0
$767$	1380.00	+	2390.23i	0.0649660	+	0.112524i
$768$		0			0
$769$	16294.0			0.764079			0.382039	−	0.924146i	$-0.375222\pi$
$769$	16294.0			0.764079			0.382039	+	0.924146i	$0.375222\pi$
$770$		0			0
$771$	1678.00			0.0783809
$772$		0			0
$773$	17639.5	+	30552.5i	0.820762	+	1.42160i	0.905116	+	0.425165i	$0.139784\pi$
$773$	17639.5	+	30552.5i	0.820762	+	1.42160i	−0.0843543	+	0.996436i	$0.526883\pi$
$774$		0			0
$775$	150.000	−	259.808i	0.00695246	−	0.0120420i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6324.00	−	10953.5i	0.290861	−	0.503786i
$780$		0			0
$781$	1820.00	+	3152.33i	0.0833863	+	0.144429i
$782$		0			0
$783$	1537.00			0.0701506
$784$		0			0
$785$	−7230.00			−0.328726
$786$		0			0
$787$	−18914.5	−	32760.9i	−0.856708	−	1.48386i	−0.875051	−	0.484030i	$-0.839173\pi$
$787$	−18914.5	−	32760.9i	−0.856708	−	1.48386i	0.0183436	−	0.999832i	$-0.494161\pi$
$788$		0			0
$789$	449.000	−	777.691i	0.0202596	−	0.0350907i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	10580.0	−	18325.1i	0.473779	−	0.820609i
$794$		0			0
$795$	1130.00	+	1957.22i	0.0504113	+	0.0873149i
$796$		0			0
$797$	−27741.0			−1.23292			−0.616460	−	0.787387i	$-0.711434\pi$
$797$	−27741.0			−1.23292			−0.616460	+	0.787387i	$0.711434\pi$
$798$		0			0
$799$	−825.000			−0.0365287
$800$		0			0
$801$	3796.00	+	6574.86i	0.167447	+	0.290027i
$802$		0			0
$803$	1295.00	−	2243.01i	0.0569110	−	0.0985728i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2451.00	−	4245.26i	0.106914	−	0.185180i
$808$		0			0
$809$	−13760.5	−	23833.9i	−0.598014	−	1.03579i	−0.993114	−	0.117153i	$-0.962623\pi$
$809$	−13760.5	−	23833.9i	−0.598014	−	1.03579i	0.395100	−	0.918638i	$-0.370710\pi$
$810$		0			0
$811$	−10694.0			−0.463030			−0.231515	−	0.972831i	$-0.574368\pi$
$811$	−10694.0			−0.463030			−0.231515	+	0.972831i	$0.574368\pi$
$812$		0			0
$813$	−7040.00			−0.303694
$814$		0			0
$815$	−6595.00	−	11422.9i	−0.283451	−	0.490952i
$816$		0			0
$817$	−5518.00	+	9557.46i	−0.236292	+	0.409269i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	6917.50	−	11981.5i	0.294059	−	0.509325i	−0.680707	−	0.732556i	$-0.738327\pi$
$821$	6917.50	−	11981.5i	0.294059	−	0.509325i	0.974766	+	0.223231i	$0.0716605\pi$
$822$		0			0
$823$	2598.00	+	4499.87i	0.110037	+	0.190590i	0.915785	−	0.401669i	$-0.131570\pi$
$823$	2598.00	+	4499.87i	0.110037	+	0.190590i	−0.805748	+	0.592259i	$0.798236\pi$
$824$		0			0
$825$	−175.000			−0.00738511
$826$		0			0
$827$	−22346.0			−0.939597			−0.469798	−	0.882774i	$-0.655673\pi$
$827$	−22346.0			−0.939597			−0.469798	+	0.882774i	$0.655673\pi$
$828$		0			0
$829$	11022.0	+	19090.7i	0.461773	+	0.799814i	0.999049	−	0.0435918i	$-0.0138801\pi$
$829$	11022.0	+	19090.7i	0.461773	+	0.799814i	−0.537276	+	0.843406i	$0.680547\pi$
$830$		0			0
$831$	1201.00	−	2080.19i	0.0501351	−	0.0868365i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−27.5000	+	47.6314i	−0.00113973	+	0.00197407i
$836$		0			0
$837$	−318.000	−	550.792i	−0.0131322	−	0.0227457i
$838$		0			0
$839$	21566.0			0.887415			0.443707	−	0.896172i	$-0.353663\pi$
$839$	21566.0			0.887415			0.443707	+	0.896172i	$0.353663\pi$
$840$		0			0
$841$	−23548.0			−0.965517
$842$		0			0
$843$	3262.50	+	5650.82i	0.133294	+	0.230871i
$844$		0			0
$845$	−4170.00	+	7222.65i	−0.169766	+	0.294044i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	2054.50	−	3558.50i	0.0830510	−	0.143848i
$850$		0			0
$851$	−6450.00	−	11171.7i	−0.259816	−	0.450014i
$852$		0			0
$853$	−6098.00			−0.244773			−0.122387	−	0.992483i	$-0.539055\pi$
$853$	−6098.00			−0.244773			−0.122387	+	0.992483i	$0.539055\pi$
$854$		0			0
$855$	−8060.00			−0.322393
$856$		0			0
$857$	−20257.0	−	35086.2i	−0.807428	−	1.39851i	−0.914640	−	0.404270i	$-0.867525\pi$
$857$	−20257.0	−	35086.2i	−0.807428	−	1.39851i	0.107211	−	0.994236i	$-0.465808\pi$
$858$		0			0
$859$	12442.0	−	21550.2i	0.494197	−	0.855975i	−0.505780	−	0.862662i	$-0.668795\pi$
$859$	12442.0	−	21550.2i	0.494197	−	0.855975i	0.999978	+	0.00668736i	$0.00212867\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	17984.0	−	31149.2i	0.709366	−	1.22866i	−0.255727	−	0.966749i	$-0.582315\pi$
$863$	17984.0	−	31149.2i	0.709366	−	1.22866i	0.965093	−	0.261908i	$-0.0843518\pi$
$864$		0			0
$865$	8167.50	+	14146.5i	0.321044	+	0.556065i
$866$		0			0
$867$	−4288.00			−0.167968
$868$		0			0
$869$	7091.00			0.276807
$870$		0			0
$871$	−3450.00	−	5975.58i	−0.134212	−	0.232462i
$872$		0			0
$873$	−17953.0	+	31095.5i	−0.696010	+	1.20553i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	4895.00	−	8478.39i	0.188475	−	0.326448i	−0.756267	−	0.654263i	$-0.772979\pi$
$877$	4895.00	−	8478.39i	0.188475	−	0.326448i	0.944742	+	0.327815i	$0.106312\pi$
$878$		0			0
$879$	−1747.50	−	3026.76i	−0.0670554	−	0.116143i
$880$		0			0
$881$	−47008.0			−1.79766			−0.898831	−	0.438296i	$-0.855582\pi$
$881$	−47008.0			−1.79766			−0.898831	+	0.438296i	$0.855582\pi$
$882$		0			0
$883$	23828.0			0.908127			0.454063	−	0.890969i	$-0.349974\pi$
$883$	23828.0			0.908127			0.454063	+	0.890969i	$0.349974\pi$
$884$		0			0
$885$	300.000	+	519.615i	0.0113948	+	0.0197364i
$886$		0			0
$887$	−11308.0	+	19586.0i	−0.428056	+	0.741414i	−0.996700	−	0.0811690i	$-0.974135\pi$
$887$	−11308.0	+	19586.0i	−0.428056	+	0.741414i	0.568645	+	0.822583i	$0.307468\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	2271.50	−	3934.35i	0.0854075	−	0.147930i
$892$		0			0
$893$	1023.00	+	1771.89i	0.0383353	+	0.0663986i
$894$		0			0
$895$	−18380.0			−0.686453
$896$		0			0
$897$	1978.00			0.0736271
$898$		0			0
$899$	−174.000	−	301.377i	−0.00645520	−	0.0111807i
$900$		0			0
$901$	5650.00	−	9786.09i	0.208911	−	0.361844i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1950.00	−	3377.50i	0.0716245	−	0.124057i
$906$		0			0
$907$	20203.0	+	34992.6i	0.739614	+	1.28105i	0.952669	+	0.304008i	$0.0983251\pi$
$907$	20203.0	+	34992.6i	0.739614	+	1.28105i	−0.213056	+	0.977040i	$0.568342\pi$
$908$		0			0
$909$	−33228.0			−1.21243
$910$		0			0
$911$	6368.00			0.231593			0.115797	−	0.993273i	$-0.463058\pi$
$911$	6368.00			0.231593			0.115797	+	0.993273i	$0.463058\pi$
$912$		0			0
$913$	−2226.00	−	3855.55i	−0.0806899	−	0.139759i
$914$		0			0
$915$	2300.00	−	3983.72i	0.0830991	−	0.143932i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	21152.5	−	36637.2i	0.759256	−	1.31507i	−0.183974	−	0.982931i	$-0.558896\pi$
$919$	21152.5	−	36637.2i	0.759256	−	1.31507i	0.943230	−	0.332139i	$-0.107770\pi$
$920$		0			0
$921$	−401.500	−	695.418i	−0.0143647	−	0.0248804i
$922$		0			0
$923$	−11960.0			−0.426509
$924$		0			0
$925$	−3750.00			−0.133296
$926$		0			0
$927$	−11375.0	−	19702.1i	−0.403025	−	0.698059i
$928$		0			0
$929$	−19334.0	+	33487.5i	−0.682807	+	1.18266i	0.291313	+	0.956628i	$0.405908\pi$
$929$	−19334.0	+	33487.5i	−0.682807	+	1.18266i	−0.974121	+	0.226029i	$0.927426\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	2719.00	−	4709.45i	0.0954084	−	0.165252i
$934$		0			0
$935$	437.500	+	757.772i	0.0153024	+	0.0265046i
$936$		0			0
$937$	16171.0			0.563803			0.281902	−	0.959443i	$-0.409035\pi$
$937$	16171.0			0.563803			0.281902	+	0.959443i	$0.409035\pi$
$938$		0			0
$939$	681.000			0.0236673
$940$		0			0
$941$	9120.00	+	15796.3i	0.315944	+	0.547231i	0.979638	−	0.200773i	$-0.0643454\pi$
$941$	9120.00	+	15796.3i	0.315944	+	0.547231i	−0.663694	+	0.748005i	$0.731012\pi$
$942$		0			0
$943$	8772.00	−	15193.5i	0.302922	−	0.524677i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−22964.0	+	39774.8i	−0.787993	+	1.36484i	0.139201	+	0.990264i	$0.455547\pi$
$947$	−22964.0	+	39774.8i	−0.787993	+	1.36484i	−0.927194	+	0.374580i	$0.877787\pi$
$948$		0			0
$949$	4255.00	+	7369.88i	0.145546	+	0.252093i
$950$		0			0
$951$	9214.00			0.314179
$952$		0			0
$953$	−14104.0			−0.479405			−0.239703	−	0.970846i	$-0.577050\pi$
$953$	−14104.0			−0.479405			−0.239703	+	0.970846i	$0.577050\pi$
$954$		0			0
$955$	−707.500	−	1225.43i	−0.0239729	−	0.0415224i
$956$		0			0
$957$	−101.500	+	175.803i	−0.00342845	+	0.00593825i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	14823.5	−	25675.1i	0.497583	−	0.861839i
$962$		0			0
$963$	−25818.0	−	44718.1i	−0.863939	−	1.49639i
$964$		0			0
$965$	2420.00			0.0807280
$966$		0			0
$967$	26914.0			0.895032			0.447516	−	0.894276i	$-0.352309\pi$
$967$	26914.0			0.895032			0.447516	+	0.894276i	$0.352309\pi$
$968$		0			0
$969$	−775.000	−	1342.34i	−0.0256931	−	0.0445017i
$970$		0			0
$971$	−5204.00	+	9013.59i	−0.171992	+	0.297899i	−0.939116	−	0.343600i	$-0.888354\pi$
$971$	−5204.00	+	9013.59i	−0.171992	+	0.297899i	0.767124	+	0.641499i	$0.221687\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	287.500	−	497.965i	0.00944346	−	0.0163565i
$976$		0			0
$977$	−19755.0	−	34216.7i	−0.646897	−	1.12046i	−0.983860	−	0.178941i	$-0.942733\pi$
$977$	−19755.0	−	34216.7i	−0.646897	−	1.12046i	0.336963	−	0.941518i	$-0.390600\pi$
$978$		0			0
$979$	−2044.00			−0.0667278
$980$		0			0
$981$	5798.00			0.188701
$982$		0			0
$983$	−26065.5	−	45146.8i	−0.845738	−	1.46486i	−0.884979	−	0.465631i	$-0.845827\pi$
$983$	−26065.5	−	45146.8i	−0.845738	−	1.46486i	0.0392410	−	0.999230i	$-0.487506\pi$
$984$		0			0
$985$	−900.000	+	1558.85i	−0.0291131	+	0.0504253i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−7654.00	+	13257.1i	−0.246090	+	0.426240i
$990$		0			0
$991$	24256.0	+	42012.6i	0.777515	+	1.34670i	0.933370	+	0.358915i	$0.116853\pi$
$991$	24256.0	+	42012.6i	0.777515	+	1.34670i	−0.155855	+	0.987780i	$0.549813\pi$
$992$		0			0
$993$	−2700.00			−0.0862859
$994$		0			0
$995$	−5160.00			−0.164405
$996$		0			0
$997$	−20475.5	−	35464.6i	−0.650417	−	1.12656i	−0.983022	−	0.183489i	$-0.941261\pi$
$997$	−20475.5	−	35464.6i	−0.650417	−	1.12656i	0.332605	−	0.943066i	$-0.392072\pi$
$998$		0			0
$999$	−3975.00	+	6884.90i	−0.125889	+	0.218047i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.4.i.i.961.1		2
7.2	even	3		140.4.a.d.1.1	✓	1
7.3	odd	6		980.4.i.k.361.1		2
7.4	even	3	inner	980.4.i.i.361.1		2
7.5	odd	6		980.4.a.g.1.1		1
7.6	odd	2		980.4.i.k.961.1		2
21.2	odd	6		1260.4.a.i.1.1		1
28.23	odd	6		560.4.a.h.1.1		1
35.2	odd	12		700.4.e.i.449.1		2
35.9	even	6		700.4.a.g.1.1		1
35.23	odd	12		700.4.e.i.449.2		2
56.37	even	6		2240.4.a.s.1.1		1
56.51	odd	6		2240.4.a.u.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.4.a.d.1.1	✓	1	7.2	even	3
560.4.a.h.1.1		1	28.23	odd	6
700.4.a.g.1.1		1	35.9	even	6
700.4.e.i.449.1		2	35.2	odd	12
700.4.e.i.449.2		2	35.23	odd	12
980.4.a.g.1.1		1	7.5	odd	6
980.4.i.i.361.1		2	7.4	even	3	inner
980.4.i.i.961.1		2	1.1	even	1	trivial
980.4.i.k.361.1		2	7.3	odd	6
980.4.i.k.961.1		2	7.6	odd	2
1260.4.a.i.1.1		1	21.2	odd	6
2240.4.a.s.1.1		1	56.37	even	6
2240.4.a.u.1.1		1	56.51	odd	6

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	980.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(2.50000 - 4.33013i) q^{5} +(13.0000 - 22.5167i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} +(2.50000 - 4.33013i) q^{5} +(13.0000 - 22.5167i) q^{9} +(3.50000 + 6.06218i) q^{11} -23.0000 q^{13} -5.00000 q^{15} +(12.5000 + 21.6506i) q^{17} +(31.0000 - 53.6936i) q^{19} +(43.0000 - 74.4782i) q^{23} +(-12.5000 - 21.6506i) q^{25} -53.0000 q^{27} -29.0000 q^{29} +(6.00000 + 10.3923i) q^{31} +(3.50000 - 6.06218i) q^{33} +(75.0000 - 129.904i) q^{37} +(11.5000 + 19.9186i) q^{39} +204.000 q^{41} -178.000 q^{43} +(-65.0000 - 112.583i) q^{45} +(-16.5000 + 28.5788i) q^{47} +(12.5000 - 21.6506i) q^{51} +(-226.000 - 391.443i) q^{53} +35.0000 q^{55} -62.0000 q^{57} +(-60.0000 - 103.923i) q^{59} +(-460.000 + 796.743i) q^{61} +(-57.5000 + 99.5929i) q^{65} +(150.000 + 259.808i) q^{67} -86.0000 q^{69} +520.000 q^{71} +(-185.000 - 320.429i) q^{73} +(-12.5000 + 21.6506i) q^{75} +(506.500 - 877.284i) q^{79} +(-324.500 - 562.050i) q^{81} -636.000 q^{83} +125.000 q^{85} +(14.5000 + 25.1147i) q^{87} +(-146.000 + 252.879i) q^{89} +(6.00000 - 10.3923i) q^{93} +(-155.000 - 268.468i) q^{95} -1381.00 q^{97} +182.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} + 5 q^{5} + 26 q^{9}+O(q^{10}) \) 2 * q - q^3 + 5 * q^5 + 26 * q^9	\( 2 q - q^{3} + 5 q^{5} + 26 q^{9} + 7 q^{11} - 46 q^{13} - 10 q^{15} + 25 q^{17} + 62 q^{19} + 86 q^{23} - 25 q^{25} - 106 q^{27} - 58 q^{29} + 12 q^{31} + 7 q^{33} + 150 q^{37} + 23 q^{39} + 408 q^{41} - 356 q^{43} - 130 q^{45} - 33 q^{47} + 25 q^{51} - 452 q^{53} + 70 q^{55} - 124 q^{57} - 120 q^{59} - 920 q^{61} - 115 q^{65} + 300 q^{67} - 172 q^{69} + 1040 q^{71} - 370 q^{73} - 25 q^{75} + 1013 q^{79} - 649 q^{81} - 1272 q^{83} + 250 q^{85} + 29 q^{87} - 292 q^{89} + 12 q^{93} - 310 q^{95} - 2762 q^{97} + 364 q^{99}+O(q^{100}) \) 2 * q - q^3 + 5 * q^5 + 26 * q^9 + 7 * q^11 - 46 * q^13 - 10 * q^15 + 25 * q^17 + 62 * q^19 + 86 * q^23 - 25 * q^25 - 106 * q^27 - 58 * q^29 + 12 * q^31 + 7 * q^33 + 150 * q^37 + 23 * q^39 + 408 * q^41 - 356 * q^43 - 130 * q^45 - 33 * q^47 + 25 * q^51 - 452 * q^53 + 70 * q^55 - 124 * q^57 - 120 * q^59 - 920 * q^61 - 115 * q^65 + 300 * q^67 - 172 * q^69 + 1040 * q^71 - 370 * q^73 - 25 * q^75 + 1013 * q^79 - 649 * q^81 - 1272 * q^83 + 250 * q^85 + 29 * q^87 - 292 * q^89 + 12 * q^93 - 310 * q^95 - 2762 * q^97 + 364 * q^99

Introduction

L-functions

Modular forms

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