LMFDB - Embedded newform 1020.3.bc.a.701.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1020,3,Mod(701,1020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1020, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 0, 3]))

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

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

chi := DirichletCharacter("1020.701");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1020.bc (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:	$27.7929869648$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			701.9
Character	$\chi$	$=$	1020.701
Dual form			1020.3.bc.a.761.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.67349 + 1.36106i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(-6.29057 - 6.29057i) q^{7} +(5.29505 - 7.27753i) q^{9} +O(q^{10})$	\(q+(-2.67349 + 1.36106i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(-6.29057 - 6.29057i) q^{7} +(5.29505 - 7.27753i) q^{9} +(-12.3064 + 12.3064i) q^{11} -24.0578 q^{13} +(6.37917 + 2.07513i) q^{15} +(-1.72279 - 16.9125i) q^{17} +22.8963i q^{19} +(25.3796 + 8.25592i) q^{21} +(-3.75727 + 3.75727i) q^{23} +5.00000i q^{25} +(-4.25109 + 26.6632i) q^{27} +(-14.5288 - 14.5288i) q^{29} +(26.0569 - 26.0569i) q^{31} +(16.1513 - 49.6509i) q^{33} +19.8925i q^{35} +(34.5048 - 34.5048i) q^{37} +(64.3182 - 32.7440i) q^{39} +(-33.5211 + 33.5211i) q^{41} +57.1028i q^{43} +(-19.8790 + 3.13459i) q^{45} -91.0534i q^{47} +30.1425i q^{49} +(27.6247 + 42.8705i) q^{51} -28.9108 q^{53} +38.9164 q^{55} +(-31.1632 - 61.2130i) q^{57} +62.7773 q^{59} +(37.8695 + 37.8695i) q^{61} +(-79.0886 + 12.4710i) q^{63} +(38.0387 + 38.0387i) q^{65} +23.4261 q^{67} +(4.93115 - 15.1589i) q^{69} +(-72.3495 - 72.3495i) q^{71} +(-8.89859 + 8.89859i) q^{73} +(-6.80529 - 13.3674i) q^{75} +154.829 q^{77} +(89.3154 + 89.3154i) q^{79} +(-24.9250 - 77.0697i) q^{81} +62.1090 q^{83} +(-24.0170 + 29.4649i) q^{85} +(58.6170 + 19.0680i) q^{87} +7.26610i q^{89} +(151.337 + 151.337i) q^{91} +(-34.1978 + 105.128i) q^{93} +(36.2023 - 36.2023i) q^{95} +(-0.821540 + 0.821540i) q^{97} +(24.3974 + 154.724i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 8 q^{3}+O(q^{10}) $ 96 * q - 8 * q^3	$ 96 q - 8 q^{3} + 64 q^{21} + 100 q^{27} - 24 q^{31} + 40 q^{33} + 24 q^{37} - 52 q^{39} - 40 q^{45} - 4 q^{51} + 80 q^{55} + 192 q^{57} + 144 q^{61} + 28 q^{63} - 320 q^{67} + 208 q^{69} + 152 q^{73} - 40 q^{75} + 224 q^{79} + 488 q^{81} - 288 q^{91} + 80 q^{97} - 212 q^{99}+O(q^{100}) $ 96 * q - 8 * q^3 + 64 * q^21 + 100 * q^27 - 24 * q^31 + 40 * q^33 + 24 * q^37 - 52 * q^39 - 40 * q^45 - 4 * q^51 + 80 * q^55 + 192 * q^57 + 144 * q^61 + 28 * q^63 - 320 * q^67 + 208 * q^69 + 152 * q^73 - 40 * q^75 + 224 * q^79 + 488 * q^81 - 288 * q^91 + 80 * q^97 - 212 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1020\mathbb{Z}\right)^\times$.

$n$	$241$	$341$	$511$	$817$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$	$1$

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
$3$	−2.67349	+	1.36106i	−0.891162	+	0.453686i
$3$	−2.67349	+	1.36106i	−0.891162	+	0.453686i
$4$		0			0
$5$	−1.58114	−	1.58114i	−0.316228	−	0.316228i
$5$	−1.58114	−	1.58114i	−0.316228	−	0.316228i
$6$		0			0
$7$	−6.29057	−	6.29057i	−0.898652	−	0.898652i	0.0966646	−	0.995317i	$-0.469183\pi$
$7$	−6.29057	−	6.29057i	−0.898652	−	0.898652i	−0.995317	+	0.0966646i	$0.969183\pi$
$8$		0			0
$9$	5.29505	−	7.27753i	0.588338	−	0.808615i
$10$		0			0
$11$	−12.3064	+	12.3064i	−1.11877	+	1.11877i	−0.126845	+	0.991923i	$0.540485\pi$
$11$	−12.3064	+	12.3064i	−1.11877	+	1.11877i	−0.991923	+	0.126845i	$0.959515\pi$
$12$		0			0
$13$	−24.0578			−1.85060			−0.925300	−	0.379237i	$-0.876187\pi$
$13$	−24.0578			−1.85060			−0.925300	+	0.379237i	$0.876187\pi$
$14$		0			0
$15$	6.37917	+	2.07513i	0.425278	+	0.138342i
$16$		0			0
$17$	−1.72279	−	16.9125i	−0.101340	−	0.994852i
$17$	−1.72279	−	16.9125i	−0.101340	−	0.994852i
$18$		0			0
$19$			22.8963i			1.20507i	0.798092	+	0.602535i	$0.205843\pi$
$19$			22.8963i			1.20507i	−0.798092	+	0.602535i	$0.794157\pi$
$20$		0			0
$21$	25.3796	+	8.25592i	1.20855	+	0.393139i
$22$		0			0
$23$	−3.75727	+	3.75727i	−0.163360	+	0.163360i	−0.784053	−	0.620694i	$-0.786851\pi$
$23$	−3.75727	+	3.75727i	−0.163360	+	0.163360i	0.620694	+	0.784053i	$0.286851\pi$
$24$		0			0
$25$			5.00000i			0.200000i
$26$		0			0
$27$	−4.25109	+	26.6632i	−0.157448	+	0.987527i
$28$		0			0
$29$	−14.5288	−	14.5288i	−0.500993	−	0.500993i	0.410754	−	0.911746i	$-0.365266\pi$
$29$	−14.5288	−	14.5288i	−0.500993	−	0.500993i	−0.911746	+	0.410754i	$0.865266\pi$
$30$		0			0
$31$	26.0569	−	26.0569i	0.840546	−	0.840546i	−0.148384	−	0.988930i	$-0.547407\pi$
$31$	26.0569	−	26.0569i	0.840546	−	0.840546i	0.988930	+	0.148384i	$0.0474070\pi$
$32$		0			0
$33$	16.1513	−	49.6509i	0.489434	−	1.50457i
$34$		0			0
$35$			19.8925i			0.568358i
$36$		0			0
$37$	34.5048	−	34.5048i	0.932563	−	0.932563i	−0.0653029	−	0.997865i	$-0.520801\pi$
$37$	34.5048	−	34.5048i	0.932563	−	0.932563i	0.997865	+	0.0653029i	$0.0208014\pi$
$38$		0			0
$39$	64.3182	−	32.7440i	1.64918	−	0.839591i
$40$		0			0
$41$	−33.5211	+	33.5211i	−0.817588	+	0.817588i	−0.985758	−	0.168170i	$-0.946214\pi$
$41$	−33.5211	+	33.5211i	−0.817588	+	0.817588i	0.168170	+	0.985758i	$0.446214\pi$
$42$		0			0
$43$			57.1028i			1.32797i	0.747745	+	0.663986i	$0.231137\pi$
$43$			57.1028i			1.32797i	−0.747745	+	0.663986i	$0.768863\pi$
$44$		0			0
$45$	−19.8790	+	3.13459i	−0.441755	+	0.0696575i
$46$		0			0
$47$		−	91.0534i		−	1.93731i	−0.248415	−	0.968654i	$-0.579910\pi$
$47$		−	91.0534i		−	1.93731i	0.248415	−	0.968654i	$-0.420090\pi$
$48$		0			0
$49$			30.1425i			0.615152i
$50$		0			0
$51$	27.6247	+	42.8705i	0.541661	+	0.840597i
$52$		0			0
$53$	−28.9108			−0.545487			−0.272743	−	0.962087i	$-0.587931\pi$
$53$	−28.9108			−0.545487			−0.272743	+	0.962087i	$0.587931\pi$
$54$		0			0
$55$	38.9164			0.707571
$56$		0			0
$57$	−31.1632	−	61.2130i	−0.546723	−	1.07391i
$58$		0			0
$59$	62.7773			1.06402			0.532011	−	0.846737i	$-0.321436\pi$
$59$	62.7773			1.06402			0.532011	+	0.846737i	$0.321436\pi$
$60$		0			0
$61$	37.8695	+	37.8695i	0.620812	+	0.620812i	0.945739	−	0.324927i	$-0.105340\pi$
$61$	37.8695	+	37.8695i	0.620812	+	0.620812i	−0.324927	+	0.945739i	$0.605340\pi$
$62$		0			0
$63$	−79.0886	+	12.4710i	−1.25538	+	0.197952i
$64$		0			0
$65$	38.0387	+	38.0387i	0.585211	+	0.585211i
$66$		0			0
$67$	23.4261			0.349644			0.174822	−	0.984600i	$-0.444065\pi$
$67$	23.4261			0.349644			0.174822	+	0.984600i	$0.444065\pi$
$68$		0			0
$69$	4.93115	−	15.1589i	0.0714659	−	0.219694i
$70$		0			0
$71$	−72.3495	−	72.3495i	−1.01901	−	1.01901i	−0.999816	−	0.0191908i	$-0.993891\pi$
$71$	−72.3495	−	72.3495i	−1.01901	−	1.01901i	−0.0191908	−	0.999816i	$-0.506109\pi$
$72$		0			0
$73$	−8.89859	+	8.89859i	−0.121898	+	0.121898i	−0.765424	−	0.643526i	$-0.777471\pi$
$73$	−8.89859	+	8.89859i	−0.121898	+	0.121898i	0.643526	+	0.765424i	$0.277471\pi$
$74$		0			0
$75$	−6.80529	−	13.3674i	−0.0907371	−	0.178232i
$76$		0			0
$77$	154.829			2.01077
$78$		0			0
$79$	89.3154	+	89.3154i	1.13058	+	1.13058i	0.990082	+	0.140494i	$0.0448690\pi$
$79$	89.3154	+	89.3154i	1.13058	+	1.13058i	0.140494	+	0.990082i	$0.455131\pi$
$80$		0			0
$81$	−24.9250	−	77.0697i	−0.307716	−	0.951478i
$82$		0			0
$83$	62.1090			0.748301			0.374150	−	0.927368i	$-0.377934\pi$
$83$	62.1090			0.748301			0.374150	+	0.927368i	$0.377934\pi$
$84$		0			0
$85$	−24.0170	+	29.4649i	−0.282553	+	0.346646i
$86$		0			0
$87$	58.6170	+	19.0680i	0.673759	+	0.219172i
$88$		0			0
$89$			7.26610i			0.0816415i	0.999166	+	0.0408208i	$0.0129973\pi$
$89$			7.26610i			0.0816415i	−0.999166	+	0.0408208i	$0.987003\pi$
$90$		0			0
$91$	151.337	+	151.337i	1.66305	+	1.66305i
$92$		0			0
$93$	−34.1978	+	105.128i	−0.367719	+	1.13041i
$94$		0			0
$95$	36.2023	−	36.2023i	0.381077	−	0.381077i
$96$		0			0
$97$	−0.821540	+	0.821540i	−0.00846948	+	0.00846948i	−0.711329	−	0.702859i	$-0.751906\pi$
$97$	−0.821540	+	0.821540i	−0.00846948	+	0.00846948i	0.702859	+	0.711329i	$0.251906\pi$
$98$		0			0
$99$	24.3974	+	154.724i	0.246438	+	1.56287i
$100$		0			0
$101$			174.692i			1.72962i	0.502098	+	0.864811i	$0.332562\pi$
$101$			174.692i			1.72962i	−0.502098	+	0.864811i	$0.667438\pi$
$102$		0			0
$103$	149.414			1.45062			0.725308	−	0.688424i	$-0.241697\pi$
$103$	149.414			1.45062			0.725308	+	0.688424i	$0.241697\pi$
$104$		0			0
$105$	−27.0749	−	53.1824i	−0.257856	−	0.506499i
$106$		0			0
$107$	94.8207	+	94.8207i	0.886175	+	0.886175i	0.994153	−	0.107979i	$-0.0344378\pi$
$107$	94.8207	+	94.8207i	0.886175	+	0.886175i	−0.107979	+	0.994153i	$0.534438\pi$
$108$		0			0
$109$	−44.4487	−	44.4487i	−0.407786	−	0.407786i	0.473180	−	0.880966i	$-0.343106\pi$
$109$	−44.4487	−	44.4487i	−0.407786	−	0.407786i	−0.880966	+	0.473180i	$0.843106\pi$
$110$		0			0
$111$	−45.2851	+	139.211i	−0.407974	+	1.25415i
$112$		0			0
$113$	−37.2627	+	37.2627i	−0.329759	+	0.329759i	−0.852495	−	0.522736i	$-0.824911\pi$
$113$	−37.2627	+	37.2627i	−0.329759	+	0.329759i	0.522736	+	0.852495i	$0.324911\pi$
$114$		0			0
$115$	11.8815			0.103318
$116$		0			0
$117$	−127.387	+	175.081i	−1.08878	+	1.49642i
$118$		0			0
$119$	−95.5518	+	117.226i	−0.802956	+	0.985096i
$120$		0			0
$121$		−	181.897i		−	1.50328i
$122$		0			0
$123$	43.9940	−	135.242i	0.357675	−	1.09953i
$124$		0			0
$125$	7.90569	−	7.90569i	0.0632456	−	0.0632456i
$126$		0			0
$127$			29.1690i			0.229677i	0.993384	+	0.114839i	$0.0366351\pi$
$127$			29.1690i			0.229677i	−0.993384	+	0.114839i	$0.963365\pi$
$128$		0			0
$129$	−77.7202	−	152.663i	−0.602482	−	1.18344i
$130$		0			0
$131$	−149.091	−	149.091i	−1.13810	−	1.13810i	−0.988790	−	0.149312i	$-0.952294\pi$
$131$	−149.091	−	149.091i	−1.13810	−	1.13810i	−0.149312	−	0.988790i	$-0.547706\pi$
$132$		0			0
$133$	144.031	−	144.031i	1.08294	−	1.08294i
$134$		0			0
$135$	48.8798	−	35.4367i	0.362073	−	0.262494i
$136$		0			0
$137$			106.362i			0.776365i	0.921582	+	0.388183i	$0.126897\pi$
$137$			106.362i			0.776365i	−0.921582	+	0.388183i	$0.873103\pi$
$138$		0			0
$139$	−114.652	+	114.652i	−0.824835	+	0.824835i	−0.986797	−	0.161962i	$-0.948218\pi$
$139$	−114.652	+	114.652i	−0.824835	+	0.824835i	0.161962	+	0.986797i	$0.448218\pi$
$140$		0			0
$141$	123.929	+	243.430i	0.878929	+	1.72645i
$142$		0			0
$143$	296.066	−	296.066i	2.07039	−	2.07039i
$144$		0			0
$145$			45.9440i			0.316856i
$146$		0			0
$147$	−41.0256	−	80.5854i	−0.279086	−	0.548200i
$148$		0			0
$149$		−	156.483i		−	1.05022i	−0.851033	−	0.525112i	$-0.824024\pi$
$149$		−	156.483i		−	1.05022i	0.851033	−	0.525112i	$-0.175976\pi$
$150$		0			0
$151$			285.404i			1.89009i	0.326933	+	0.945047i	$0.393985\pi$
$151$			285.404i			1.89009i	−0.326933	+	0.945047i	$0.606015\pi$
$152$		0			0
$153$	−132.203	−	77.0147i	−0.864074	−	0.503364i
$154$		0			0
$155$	−82.3993			−0.531608
$156$		0			0
$157$	159.247			1.01431			0.507155	−	0.861855i	$-0.330697\pi$
$157$	159.247			1.01431			0.507155	+	0.861855i	$0.330697\pi$
$158$		0			0
$159$	77.2926	−	39.3493i	0.486117	−	0.247480i
$160$		0			0
$161$	47.2707			0.293607
$162$		0			0
$163$	−136.212	−	136.212i	−0.835658	−	0.835658i	0.152626	−	0.988284i	$-0.451227\pi$
$163$	−136.212	−	136.212i	−0.835658	−	0.835658i	−0.988284	+	0.152626i	$0.951227\pi$
$164$		0			0
$165$	−104.042	+	52.9674i	−0.630560	+	0.321015i
$166$		0			0
$167$	−102.681	−	102.681i	−0.614858	−	0.614858i	0.329350	−	0.944208i	$-0.393170\pi$
$167$	−102.681	−	102.681i	−0.614858	−	0.614858i	−0.944208	+	0.329350i	$0.893170\pi$
$168$		0			0
$169$	409.777			2.42472
$170$		0			0
$171$	166.629	+	121.237i	0.974438	+	0.708989i
$172$		0			0
$173$	−173.344	−	173.344i	−1.00199	−	1.00199i	−0.999998	−	0.00199190i	$-0.999366\pi$
$173$	−173.344	−	173.344i	−1.00199	−	1.00199i	−0.00199190	−	0.999998i	$-0.500634\pi$
$174$		0			0
$175$	31.4528	−	31.4528i	0.179730	−	0.179730i
$176$		0			0
$177$	−167.834	+	85.4435i	−0.948216	+	0.482732i
$178$		0			0
$179$	108.141			0.604138			0.302069	−	0.953286i	$-0.402323\pi$
$179$	108.141			0.604138			0.302069	+	0.953286i	$0.402323\pi$
$180$		0			0
$181$	−3.97525	−	3.97525i	−0.0219627	−	0.0219627i	0.696040	−	0.718003i	$-0.254944\pi$
$181$	−3.97525	−	3.97525i	−0.0219627	−	0.0219627i	−0.718003	+	0.696040i	$0.754944\pi$
$182$		0			0
$183$	−152.786	−	49.7010i	−0.834898	−	0.271590i
$184$		0			0
$185$	−109.114			−0.589804
$186$		0			0
$187$	229.334	+	186.931i	1.22638	+	0.999632i
$188$		0			0
$189$	194.469	−	140.985i	1.02893	−	0.745953i
$190$		0			0
$191$			184.990i			0.968535i	0.874920	+	0.484267i	$0.160914\pi$
$191$			184.990i			0.968535i	−0.874920	+	0.484267i	$0.839086\pi$
$192$		0			0
$193$	−46.1304	−	46.1304i	−0.239018	−	0.239018i	0.577426	−	0.816443i	$-0.304057\pi$
$193$	−46.1304	−	46.1304i	−0.239018	−	0.239018i	−0.816443	+	0.577426i	$0.804057\pi$
$194$		0			0
$195$	−153.469	−	49.9231i	−0.787019	−	0.256016i
$196$		0			0
$197$	119.195	−	119.195i	0.605053	−	0.605053i	−0.336596	−	0.941649i	$-0.609276\pi$
$197$	119.195	−	119.195i	0.605053	−	0.605053i	0.941649	+	0.336596i	$0.109276\pi$
$198$		0			0
$199$	76.3435	−	76.3435i	0.383636	−	0.383636i	−0.488775	−	0.872410i	$-0.662556\pi$
$199$	76.3435	−	76.3435i	0.383636	−	0.383636i	0.872410	+	0.488775i	$0.162556\pi$
$200$		0			0
$201$	−62.6295	+	31.8843i	−0.311589	+	0.158628i
$202$		0			0
$203$			182.789i			0.900436i
$204$		0			0
$205$	106.003			0.517088
$206$		0			0
$207$	7.44874	+	47.2386i	0.0359843	+	0.228206i
$208$		0			0
$209$	−281.772	−	281.772i	−1.34819	−	1.34819i
$210$		0			0
$211$	−95.7385	−	95.7385i	−0.453737	−	0.453737i	0.442856	−	0.896593i	$-0.353965\pi$
$211$	−95.7385	−	95.7385i	−0.453737	−	0.453737i	−0.896593	+	0.442856i	$0.853965\pi$
$212$		0			0
$213$	291.897	+	94.9535i	1.37041	+	0.445791i
$214$		0			0
$215$	90.2874	−	90.2874i	0.419942	−	0.419942i
$216$		0			0
$217$	−327.826			−1.51072
$218$		0			0
$219$	11.6788	−	35.9017i	0.0533276	−	0.163935i
$220$		0			0
$221$	41.4465	+	406.877i	0.187541	+	1.84107i
$222$		0			0
$223$		−	21.1312i		−	0.0947589i	−0.998877	−	0.0473795i	$-0.984913\pi$
$223$		−	21.1312i		−	0.0947589i	0.998877	−	0.0473795i	$-0.0150870\pi$
$224$		0			0
$225$	36.3877	+	26.4752i	0.161723	+	0.117668i
$226$		0			0
$227$	−8.39210	+	8.39210i	−0.0369696	+	0.0369696i	−0.725350	−	0.688380i	$-0.758322\pi$
$227$	−8.39210	+	8.39210i	−0.0369696	+	0.0369696i	0.688380	+	0.725350i	$0.258322\pi$
$228$		0			0
$229$		−	142.633i		−	0.622852i	−0.950270	−	0.311426i	$-0.899193\pi$
$229$		−	142.633i		−	0.622852i	0.950270	−	0.311426i	$-0.100807\pi$
$230$		0			0
$231$	−413.933	+	210.731i	−1.79192	+	0.912256i
$232$		0			0
$233$	93.7967	+	93.7967i	0.402561	+	0.402561i	0.879135	−	0.476574i	$-0.158121\pi$
$233$	93.7967	+	93.7967i	0.402561	+	0.402561i	−0.476574	+	0.879135i	$0.658121\pi$
$234$		0			0
$235$	−143.968	+	143.968i	−0.612630	+	0.612630i
$236$		0			0
$237$	−360.347	−	117.220i	−1.52045	−	0.494600i
$238$		0			0
$239$			189.845i			0.794331i	0.917747	+	0.397166i	$0.130006\pi$
$239$			189.845i			0.794331i	−0.917747	+	0.397166i	$0.869994\pi$
$240$		0			0
$241$	269.048	−	269.048i	1.11638	−	1.11638i	0.124116	−	0.992268i	$-0.460391\pi$
$241$	269.048	−	269.048i	1.11638	−	1.11638i	0.992268	−	0.124116i	$-0.0396095\pi$
$242$		0			0
$243$	171.533	+	172.121i	0.705897	+	0.708315i
$244$		0			0
$245$	47.6594	−	47.6594i	0.194528	−	0.194528i
$246$		0			0
$247$		−	550.835i		−	2.23010i
$248$		0			0
$249$	−166.047	+	84.5338i	−0.666857	+	0.339493i
$250$		0			0
$251$			189.846i			0.756358i	0.925732	+	0.378179i	$0.123450\pi$
$251$			189.846i			0.756358i	−0.925732	+	0.378179i	$0.876550\pi$
$252$		0			0
$253$		−	92.4773i		−	0.365523i
$254$		0			0
$255$	24.1057	−	111.463i	0.0945320	−	0.437108i
$256$		0			0
$257$	24.6062			0.0957441			0.0478721	−	0.998853i	$-0.484756\pi$
$257$	24.6062			0.0957441			0.0478721	+	0.998853i	$0.484756\pi$
$258$		0			0
$259$	−434.110			−1.67610
$260$		0			0
$261$	−182.664	+	28.8031i	−0.699863	+	0.110357i
$262$		0			0
$263$	−352.840			−1.34160			−0.670798	−	0.741640i	$-0.734048\pi$
$263$	−352.840			−1.34160			−0.670798	+	0.741640i	$0.734048\pi$
$264$		0			0
$265$	45.7120	+	45.7120i	0.172498	+	0.172498i
$266$		0			0
$267$	−9.88957	−	19.4258i	−0.0370396	−	0.0727558i
$268$		0			0
$269$	−344.160	−	344.160i	−1.27941	−	1.27941i	−0.941000	−	0.338406i	$-0.890112\pi$
$269$	−344.160	−	344.160i	−1.27941	−	1.27941i	−0.338406	−	0.941000i	$-0.609888\pi$
$270$		0			0
$271$	302.423			1.11595			0.557977	−	0.829857i	$-0.311578\pi$
$271$	302.423			1.11595			0.557977	+	0.829857i	$0.311578\pi$
$272$		0			0
$273$	−610.576	−	198.619i	−2.23654	−	0.727543i
$274$		0			0
$275$	−61.5322	−	61.5322i	−0.223754	−	0.223754i
$276$		0			0
$277$	−20.9001	+	20.9001i	−0.0754517	+	0.0754517i	−0.743826	−	0.668374i	$-0.766991\pi$
$277$	−20.9001	+	20.9001i	−0.0754517	+	0.0754517i	0.668374	+	0.743826i	$0.266991\pi$
$278$		0			0
$279$	−51.6575	−	327.603i	−0.185152	−	1.17420i
$280$		0			0
$281$	162.959			0.579926			0.289963	−	0.957038i	$-0.406357\pi$
$281$	162.959			0.579926			0.289963	+	0.957038i	$0.406357\pi$
$282$		0			0
$283$	31.0296	+	31.0296i	0.109645	+	0.109645i	0.759801	−	0.650156i	$-0.225296\pi$
$283$	31.0296	+	31.0296i	0.109645	+	0.109645i	−0.650156	+	0.759801i	$0.725296\pi$
$284$		0			0
$285$	−47.5129	+	146.060i	−0.166712	+	0.512490i
$286$		0			0
$287$	421.734			1.46945
$288$		0			0
$289$	−283.064	+	58.2732i	−0.979460	+	0.201637i
$290$		0			0
$291$	1.07821	−	3.31454i	0.00370520	−	0.0113902i
$292$		0			0
$293$		−	314.503i		−	1.07339i	−0.843777	−	0.536694i	$-0.819673\pi$
$293$		−	314.503i		−	1.07339i	0.843777	−	0.536694i	$-0.180327\pi$
$294$		0			0
$295$	−99.2596	−	99.2596i	−0.336473	−	0.336473i
$296$		0			0
$297$	−275.814	−	380.445i	−0.928666	−	1.28096i
$298$		0			0
$299$	90.3917	−	90.3917i	0.302313	−	0.302313i
$300$		0			0
$301$	359.209	−	359.209i	1.19339	−	1.19339i
$302$		0			0
$303$	−237.766	−	467.036i	−0.784705	−	1.54137i
$304$		0			0
$305$		−	119.754i		−	0.392636i
$306$		0			0
$307$	−37.7267			−0.122888			−0.0614441	−	0.998111i	$-0.519571\pi$
$307$	−37.7267			−0.122888			−0.0614441	+	0.998111i	$0.519571\pi$
$308$		0			0
$309$	−399.455	+	203.360i	−1.29273	+	0.658124i
$310$		0			0
$311$	92.5674	+	92.5674i	0.297644	+	0.297644i	0.840090	−	0.542446i	$-0.182502\pi$
$311$	92.5674	+	92.5674i	0.297644	+	0.297644i	−0.542446	+	0.840090i	$0.682502\pi$
$312$		0			0
$313$	−33.2728	−	33.2728i	−0.106303	−	0.106303i	0.651955	−	0.758258i	$-0.273949\pi$
$313$	−33.2728	−	33.2728i	−0.106303	−	0.106303i	−0.758258	+	0.651955i	$0.773949\pi$
$314$		0			0
$315$	144.768	+	105.332i	0.459582	+	0.334387i
$316$		0			0
$317$	−308.110	+	308.110i	−0.971955	+	0.971955i	−0.999617	−	0.0276619i	$-0.991194\pi$
$317$	−308.110	+	308.110i	−0.971955	+	0.971955i	0.0276619	+	0.999617i	$0.491194\pi$
$318$		0			0
$319$	357.595			1.12099
$320$		0			0
$321$	−382.558	−	124.445i	−1.19177	−	0.387680i
$322$		0			0
$323$	387.234	−	39.4455i	1.19887	−	0.122122i
$324$		0			0
$325$		−	120.289i		−	0.370120i
$326$		0			0
$327$	179.330	+	58.3357i	0.548410	+	0.178397i
$328$		0			0
$329$	−572.778	+	572.778i	−1.74097	+	1.74097i
$330$		0			0
$331$			460.121i			1.39009i	0.718965	+	0.695047i	$0.244616\pi$
$331$			460.121i			1.39009i	−0.718965	+	0.695047i	$0.755384\pi$
$332$		0			0
$333$	−68.4053	−	433.815i	−0.205421	−	1.30275i
$334$		0			0
$335$	−37.0400	−	37.0400i	−0.110567	−	0.110567i
$336$		0			0
$337$	−137.534	+	137.534i	−0.408114	+	0.408114i	−0.881081	−	0.472966i	$-0.843183\pi$
$337$	−137.534	+	137.534i	−0.408114	+	0.408114i	0.472966	+	0.881081i	$0.343183\pi$
$338$		0			0
$339$	48.9046	−	150.338i	0.144261	−	0.443475i
$340$		0			0
$341$			641.336i			1.88075i
$342$		0			0
$343$	−118.625	+	118.625i	−0.345844	+	0.345844i
$344$		0			0
$345$	−31.7651	+	16.1715i	−0.0920728	+	0.0468738i
$346$		0			0
$347$	145.446	−	145.446i	0.419152	−	0.419152i	−0.465759	−	0.884912i	$-0.654219\pi$
$347$	145.446	−	145.446i	0.419152	−	0.419152i	0.884912	+	0.465759i	$0.154219\pi$
$348$		0			0
$349$		−	84.8581i		−	0.243146i	−0.992582	−	0.121573i	$-0.961206\pi$
$349$		−	84.8581i		−	0.243146i	0.992582	−	0.121573i	$-0.0387939\pi$
$350$		0			0
$351$	102.272	−	641.459i	0.291373	−	1.82752i
$352$		0			0
$353$		−	66.9089i		−	0.189544i	−0.995499	−	0.0947719i	$-0.969788\pi$
$353$		−	66.9089i		−	0.189544i	0.995499	−	0.0947719i	$-0.0302122\pi$
$354$		0			0
$355$			228.789i			0.644476i
$356$		0			0
$357$	95.9044	−	443.454i	0.268640	−	1.24217i
$358$		0			0
$359$	−309.636			−0.862496			−0.431248	−	0.902233i	$-0.641927\pi$
$359$	−309.636			−0.862496			−0.431248	+	0.902233i	$0.641927\pi$
$360$		0			0
$361$	−163.242			−0.452194
$362$		0			0
$363$	247.572	+	486.299i	0.682018	+	1.33967i
$364$		0			0
$365$	28.1398			0.0770954
$366$		0			0
$367$	493.367	+	493.367i	1.34432	+	1.34432i	0.891704	+	0.452620i	$0.149510\pi$
$367$	493.367	+	493.367i	1.34432	+	1.34432i	0.452620	+	0.891704i	$0.350490\pi$
$368$		0			0
$369$	66.4552	+	421.447i	0.180095	+	1.14213i
$370$		0			0
$371$	181.865	+	181.865i	0.490203	+	0.490203i
$372$		0			0
$373$	−124.869			−0.334770			−0.167385	−	0.985892i	$-0.553532\pi$
$373$	−124.869			−0.334770			−0.167385	+	0.985892i	$0.553532\pi$
$374$		0			0
$375$	−10.3757	+	31.8959i	−0.0276684	+	0.0850556i
$376$		0			0
$377$	349.530	+	349.530i	0.927137	+	0.927137i
$378$		0			0
$379$	301.080	−	301.080i	0.794405	−	0.794405i	−0.187802	−	0.982207i	$-0.560136\pi$
$379$	301.080	−	301.080i	0.794405	−	0.794405i	0.982207	+	0.187802i	$0.0601363\pi$
$380$		0			0
$381$	−39.7007	−	77.9828i	−0.104201	−	0.204679i
$382$		0			0
$383$	−75.3731			−0.196797			−0.0983983	−	0.995147i	$-0.531372\pi$
$383$	−75.3731			−0.196797			−0.0983983	+	0.995147i	$0.531372\pi$
$384$		0			0
$385$	−244.806	−	244.806i	−0.635860	−	0.635860i
$386$		0			0
$387$	415.567	+	302.362i	1.07382	+	0.781297i
$388$		0			0
$389$	486.743			1.25127			0.625634	−	0.780117i	$-0.284840\pi$
$389$	486.743			1.25127			0.625634	+	0.780117i	$0.284840\pi$
$390$		0			0
$391$	70.0178	+	57.0718i	0.179074	+	0.145964i
$392$		0			0
$393$	601.515	+	195.672i	1.53057	+	0.497892i
$394$		0			0
$395$		−	282.440i		−	0.715039i
$396$		0			0
$397$	−318.769	−	318.769i	−0.802944	−	0.802944i	0.180611	−	0.983555i	$-0.442193\pi$
$397$	−318.769	−	318.769i	−0.802944	−	0.802944i	−0.983555	+	0.180611i	$0.942193\pi$
$398$		0			0
$399$	−189.030	+	581.099i	−0.473760	+	1.45639i
$400$		0			0
$401$	116.374	−	116.374i	0.290210	−	0.290210i	−0.546953	−	0.837163i	$-0.684212\pi$
$401$	116.374	−	116.374i	0.290210	−	0.290210i	0.837163	+	0.546953i	$0.184212\pi$
$402$		0			0
$403$	−626.872	+	626.872i	−1.55551	+	1.55551i
$404$		0			0
$405$	−82.4481	+	161.268i	−0.203576	+	0.398192i
$406$		0			0
$407$			849.263i			2.08664i
$408$		0			0
$409$	250.502			0.612474			0.306237	−	0.951955i	$-0.400930\pi$
$409$	250.502			0.612474			0.306237	+	0.951955i	$0.400930\pi$
$410$		0			0
$411$	−144.765	−	284.357i	−0.352226	−	0.691867i
$412$		0			0
$413$	−394.905	−	394.905i	−0.956186	−	0.956186i
$414$		0			0
$415$	−98.2029	−	98.2029i	−0.236633	−	0.236633i
$416$		0			0
$417$	150.473	−	462.569i	0.360846	−	1.10928i
$418$		0			0
$419$	299.357	−	299.357i	0.714457	−	0.714457i	−0.253008	−	0.967464i	$-0.581420\pi$
$419$	299.357	−	299.357i	0.714457	−	0.714457i	0.967464	+	0.253008i	$0.0814198\pi$
$420$		0			0
$421$	−80.4125			−0.191004			−0.0955018	−	0.995429i	$-0.530446\pi$
$421$	−80.4125			−0.191004			−0.0955018	+	0.995429i	$0.530446\pi$
$422$		0			0
$423$	−662.644	−	482.132i	−1.56654	−	1.13979i
$424$		0			0
$425$	84.5624	−	8.61393i	0.198970	−	0.0202681i
$426$		0			0
$427$		−	476.442i		−	1.11579i
$428$		0			0
$429$	−388.565	+	1194.49i	−0.905746	+	2.78436i
$430$		0			0
$431$	−325.077	+	325.077i	−0.754240	+	0.754240i	−0.975268	−	0.221028i	$-0.929059\pi$
$431$	−325.077	+	325.077i	−0.754240	+	0.754240i	0.221028	+	0.975268i	$0.429059\pi$
$432$		0			0
$433$			405.923i			0.937467i	0.883340	+	0.468734i	$0.155290\pi$
$433$			405.923i			0.937467i	−0.883340	+	0.468734i	$0.844710\pi$
$434$		0			0
$435$	−62.5325	−	122.831i	−0.143753	−	0.282370i
$436$		0			0
$437$	−86.0278	−	86.0278i	−0.196860	−	0.196860i
$438$		0			0
$439$	208.410	−	208.410i	0.474738	−	0.474738i	−0.428706	−	0.903444i	$-0.641030\pi$
$439$	208.410	−	208.410i	0.474738	−	0.474738i	0.903444	+	0.428706i	$0.141030\pi$
$440$		0			0
$441$	219.363	+	159.606i	0.497421	+	0.361918i
$442$		0			0
$443$		−	687.598i		−	1.55214i	−0.630647	−	0.776070i	$-0.717210\pi$
$443$		−	687.598i		−	1.55214i	0.630647	−	0.776070i	$-0.282790\pi$
$444$		0			0
$445$	11.4887	−	11.4887i	0.0258173	−	0.0258173i
$446$		0			0
$447$	212.983	+	418.356i	0.476471	+	0.935919i
$448$		0			0
$449$	−104.129	+	104.129i	−0.231913	+	0.231913i	−0.813491	−	0.581578i	$-0.802436\pi$
$449$	−104.129	+	104.129i	−0.231913	+	0.231913i	0.581578	+	0.813491i	$0.302436\pi$
$450$		0			0
$451$		−	825.051i		−	1.82938i
$452$		0			0
$453$	−388.452	−	763.024i	−0.857509	−	1.68438i
$454$		0			0
$455$		−	478.570i		−	1.05180i
$456$		0			0
$457$		−	40.8247i		−	0.0893320i	−0.999002	−	0.0446660i	$-0.985778\pi$
$457$		−	40.8247i		−	0.0893320i	0.999002	−	0.0446660i	$-0.0142224\pi$
$458$		0			0
$459$	458.265	+	25.9614i	0.998399	+	0.0565608i
$460$		0			0
$461$	298.234			0.646927			0.323464	−	0.946241i	$-0.395153\pi$
$461$	298.234			0.646927			0.323464	+	0.946241i	$0.395153\pi$
$462$		0			0
$463$	549.714			1.18729			0.593644	−	0.804728i	$-0.297689\pi$
$463$	549.714			1.18729			0.593644	+	0.804728i	$0.297689\pi$
$464$		0			0
$465$	220.293	−	112.150i	0.473749	−	0.241183i
$466$		0			0
$467$	−672.000			−1.43897			−0.719486	−	0.694507i	$-0.755623\pi$
$467$	−672.000			−1.43897			−0.719486	+	0.694507i	$0.755623\pi$
$468$		0			0
$469$	−147.364	−	147.364i	−0.314208	−	0.314208i
$470$		0			0
$471$	−425.744	+	216.744i	−0.903915	+	0.460178i
$472$		0			0
$473$	−702.732	−	702.732i	−1.48569	−	1.48569i
$474$		0			0
$475$	−114.482			−0.241014
$476$		0			0
$477$	−153.084	+	210.399i	−0.320931	+	0.441089i
$478$		0			0
$479$	270.029	+	270.029i	0.563735	+	0.563735i	0.930366	−	0.366632i	$-0.119489\pi$
$479$	270.029	+	270.029i	0.563735	+	0.563735i	−0.366632	+	0.930366i	$0.619489\pi$
$480$		0			0
$481$	−830.110	+	830.110i	−1.72580	+	1.72580i
$482$		0			0
$483$	−126.378	+	64.3382i	−0.261651	+	0.133205i
$484$		0			0
$485$	2.59794			0.00535657
$486$		0			0
$487$	−137.843	−	137.843i	−0.283046	−	0.283046i	0.551277	−	0.834323i	$-0.314141\pi$
$487$	−137.843	−	137.843i	−0.283046	−	0.283046i	−0.834323	+	0.551277i	$0.814141\pi$
$488$		0			0
$489$	549.554	+	178.769i	1.12383	+	0.365580i
$490$		0			0
$491$	37.0629			0.0754844			0.0377422	−	0.999288i	$-0.487983\pi$
$491$	37.0629			0.0754844			0.0377422	+	0.999288i	$0.487983\pi$
$492$		0			0
$493$	−220.688	+	270.748i	−0.447643	+	0.549184i
$494$		0			0
$495$	206.064	−	283.215i	0.416291	−	0.572152i
$496$		0			0
$497$			910.238i			1.83147i
$498$		0			0
$499$	−300.616	−	300.616i	−0.602437	−	0.602437i	0.338522	−	0.940959i	$-0.390073\pi$
$499$	−300.616	−	300.616i	−0.602437	−	0.602437i	−0.940959	+	0.338522i	$0.890073\pi$
$500$		0			0
$501$	414.272	+	134.762i	0.826890	+	0.268986i
$502$		0			0
$503$	−114.698	+	114.698i	−0.228028	+	0.228028i	−0.811868	−	0.583841i	$-0.801549\pi$
$503$	−114.698	+	114.698i	−0.228028	+	0.228028i	0.583841	+	0.811868i	$0.301549\pi$
$504$		0			0
$505$	276.212	−	276.212i	0.546954	−	0.546954i
$506$		0			0
$507$	−1095.53	+	557.731i	−2.16082	+	1.10006i
$508$		0			0
$509$			515.736i			1.01323i	0.862171	+	0.506617i	$0.169104\pi$
$509$			515.736i			1.01323i	−0.862171	+	0.506617i	$0.830896\pi$
$510$		0			0
$511$	111.954			0.219089
$512$		0			0
$513$	−610.490	−	97.3344i	−1.19004	−	0.189736i
$514$		0			0
$515$	−236.244	−	236.244i	−0.458725	−	0.458725i
$516$		0			0
$517$	1120.54	+	1120.54i	2.16740	+	2.16740i
$518$		0			0
$519$	699.365	+	227.502i	1.34752	+	0.438347i
$520$		0			0
$521$	501.560	−	501.560i	0.962686	−	0.962686i	−0.0366423	−	0.999328i	$-0.511666\pi$
$521$	501.560	−	501.560i	0.962686	−	0.962686i	0.999328	+	0.0366423i	$0.0116662\pi$
$522$		0			0
$523$	314.174			0.600715			0.300357	−	0.953827i	$-0.402894\pi$
$523$	314.174			0.600715			0.300357	+	0.953827i	$0.402894\pi$
$524$		0			0
$525$	−41.2796	+	126.898i	−0.0786278	+	0.241710i
$526$		0			0
$527$	−485.578	−	395.797i	−0.921400	−	0.751038i
$528$		0			0
$529$			500.766i			0.946627i
$530$		0			0
$531$	332.409	−	456.864i	0.626005	−	0.860384i
$532$		0			0
$533$	806.444	−	806.444i	1.51303	−	1.51303i
$534$		0			0
$535$		−	299.849i		−	0.560466i
$536$		0			0
$537$	−289.113	+	147.186i	−0.538385	+	0.274089i
$538$		0			0
$539$	−370.946	−	370.946i	−0.688212	−	0.688212i
$540$		0			0
$541$	281.043	−	281.043i	0.519489	−	0.519489i	−0.397928	−	0.917417i	$-0.630271\pi$
$541$	281.043	−	281.043i	0.519489	−	0.519489i	0.917417	+	0.397928i	$0.130271\pi$
$542$		0			0
$543$	16.0383	+	5.21723i	0.0295365	+	0.00960816i
$544$		0			0
$545$			140.559i			0.257906i
$546$		0			0
$547$	−75.3296	+	75.3296i	−0.137714	+	0.137714i	−0.772603	−	0.634889i	$-0.781046\pi$
$547$	−75.3296	+	75.3296i	−0.137714	+	0.137714i	0.634889	+	0.772603i	$0.281046\pi$
$548$		0			0
$549$	476.118	−	75.0759i	0.867246	−	0.136750i
$550$		0			0
$551$	332.656	−	332.656i	0.603731	−	0.603731i
$552$		0			0
$553$		−	1123.69i		−	2.03199i
$554$		0			0
$555$	291.714	−	148.510i	0.525611	−	0.267586i
$556$		0			0
$557$			453.080i			0.813430i	0.913555	+	0.406715i	$0.133326\pi$
$557$			453.080i			0.813430i	−0.913555	+	0.406715i	$0.866674\pi$
$558$		0			0
$559$		−	1373.77i		−	2.45754i
$560$		0			0
$561$	−867.545	−	187.621i	−1.54643	−	0.334440i
$562$		0			0
$563$	174.265			0.309529			0.154764	−	0.987951i	$-0.450538\pi$
$563$	174.265			0.309529			0.154764	+	0.987951i	$0.450538\pi$
$564$		0			0
$565$	117.835			0.208558
$566$		0			0
$567$	−328.020	+	641.605i	−0.578519	+	1.13158i
$568$		0			0
$569$	462.238			0.812369			0.406184	−	0.913791i	$-0.366859\pi$
$569$	462.238			0.812369			0.406184	+	0.913791i	$0.366859\pi$
$570$		0			0
$571$	134.635	+	134.635i	0.235788	+	0.235788i	0.815103	−	0.579316i	$-0.196680\pi$
$571$	134.635	+	134.635i	0.235788	+	0.235788i	−0.579316	+	0.815103i	$0.696680\pi$
$572$		0			0
$573$	−251.782	−	494.568i	−0.439410	−	0.863121i
$574$		0			0
$575$	−18.7864	−	18.7864i	−0.0326719	−	0.0326719i
$576$		0			0
$577$	868.124			1.50455			0.752274	−	0.658851i	$-0.228957\pi$
$577$	868.124			1.50455			0.752274	+	0.658851i	$0.228957\pi$
$578$		0			0
$579$	186.115	+	60.5429i	0.321443	+	0.104565i
$580$		0			0
$581$	−390.701	−	390.701i	−0.672462	−	0.672462i
$582$		0			0
$583$	355.789	−	355.789i	0.610273	−	0.610273i
$584$		0			0
$585$	478.245	−	75.4112i	0.817512	−	0.128908i
$586$		0			0
$587$	−567.952			−0.967551			−0.483775	−	0.875192i	$-0.660735\pi$
$587$	−567.952			−0.967551			−0.483775	+	0.875192i	$0.660735\pi$
$588$		0			0
$589$	596.608	+	596.608i	1.01292	+	1.01292i
$590$		0			0
$591$	−156.435	+	480.899i	−0.264696	+	0.813704i
$592$		0			0
$593$	462.385			0.779739			0.389870	−	0.920870i	$-0.372520\pi$
$593$	462.385			0.779739			0.389870	+	0.920870i	$0.372520\pi$
$594$		0			0
$595$	336.432	−	34.2706i	0.565432	−	0.0575976i
$596$		0			0
$597$	−100.195	+	308.011i	−0.167831	+	0.515931i
$598$		0			0
$599$			161.307i			0.269293i	0.990894	+	0.134647i	$0.0429899\pi$
$599$			161.307i			0.269293i	−0.990894	+	0.134647i	$0.957010\pi$
$600$		0			0
$601$	−167.731	−	167.731i	−0.279087	−	0.279087i	0.553658	−	0.832744i	$-0.313232\pi$
$601$	−167.731	−	167.731i	−0.279087	−	0.279087i	−0.832744	+	0.553658i	$0.813232\pi$
$602$		0			0
$603$	124.043	−	170.485i	0.205709	−	0.282727i
$604$		0			0
$605$	−287.605	+	287.605i	−0.475379	+	0.475379i
$606$		0			0
$607$	−131.083	+	131.083i	−0.215953	+	0.215953i	−0.806791	−	0.590838i	$-0.798797\pi$
$607$	−131.083	+	131.083i	−0.215953	+	0.215953i	0.590838	+	0.806791i	$0.298797\pi$
$608$		0			0
$609$	−248.786	−	488.683i	−0.408515	−	0.802434i
$610$		0			0
$611$			2190.55i			3.58518i
$612$		0			0
$613$	−202.356			−0.330108			−0.165054	−	0.986285i	$-0.552780\pi$
$613$	−202.356			−0.330108			−0.165054	+	0.986285i	$0.552780\pi$
$614$		0			0
$615$	−283.398	+	144.276i	−0.460809	+	0.234596i
$616$		0			0
$617$	533.650	+	533.650i	0.864911	+	0.864911i	0.991904	−	0.126993i	$-0.0405326\pi$
$617$	533.650	+	533.650i	0.864911	+	0.864911i	−0.126993	+	0.991904i	$0.540533\pi$
$618$		0			0
$619$	577.426	+	577.426i	0.932837	+	0.932837i	0.997882	−	0.0650452i	$-0.0207192\pi$
$619$	577.426	+	577.426i	0.932837	+	0.932837i	−0.0650452	+	0.997882i	$0.520719\pi$
$620$		0			0
$621$	−84.2085	−	116.154i	−0.135602	−	0.187043i
$622$		0			0
$623$	45.7079	−	45.7079i	0.0733674	−	0.0733674i
$624$		0			0
$625$	−25.0000			−0.0400000
$626$		0			0
$627$	1136.82	+	369.806i	1.81311	+	0.589802i
$628$		0			0
$629$	−643.006	−	524.118i	−1.02227	−	0.833255i
$630$		0			0
$631$			98.8501i			0.156656i	0.996928	+	0.0783281i	$0.0249582\pi$
$631$			98.8501i			0.156656i	−0.996928	+	0.0783281i	$0.975042\pi$
$632$		0			0
$633$	386.261	+	125.650i	0.610207	+	0.198499i
$634$		0			0
$635$	46.1202	−	46.1202i	0.0726302	−	0.0726302i
$636$		0			0
$637$		−	725.161i		−	1.13840i
$638$		0			0
$639$	−909.619	+	143.432i	−1.42350	+	0.224463i
$640$		0			0
$641$	352.845	+	352.845i	0.550461	+	0.550461i	0.926574	−	0.376113i	$-0.122740\pi$
$641$	352.845	+	352.845i	0.550461	+	0.550461i	−0.376113	+	0.926574i	$0.622740\pi$
$642$		0			0
$643$	−282.015	+	282.015i	−0.438593	+	0.438593i	−0.891538	−	0.452945i	$-0.850373\pi$
$643$	−282.015	+	282.015i	−0.438593	+	0.438593i	0.452945	+	0.891538i	$0.350373\pi$
$644$		0			0
$645$	−118.496	+	364.269i	−0.183714	+	0.564757i
$646$		0			0
$647$		−	1000.07i		−	1.54570i	−0.634590	−	0.772849i	$-0.718831\pi$
$647$		−	1000.07i		−	1.54570i	0.634590	−	0.772849i	$-0.281169\pi$
$648$		0			0
$649$	−772.565	+	772.565i	−1.19039	+	1.19039i
$650$		0			0
$651$	876.437	−	446.190i	1.34629	−	0.685391i
$652$		0			0
$653$	−500.147	+	500.147i	−0.765923	+	0.765923i	−0.977386	−	0.211463i	$-0.932177\pi$
$653$	−500.147	+	500.147i	−0.765923	+	0.765923i	0.211463	+	0.977386i	$0.432177\pi$
$654$		0			0
$655$			471.468i			0.719799i
$656$		0			0
$657$	17.6413	+	111.878i	0.0268513	+	0.170286i
$658$		0			0
$659$		−	153.605i		−	0.233087i	−0.993186	−	0.116544i	$-0.962819\pi$
$659$		−	153.605i		−	0.233087i	0.993186	−	0.116544i	$-0.0371815\pi$
$660$		0			0
$661$		−	37.2209i		−	0.0563100i	−0.999604	−	0.0281550i	$-0.991037\pi$
$661$		−	37.2209i		−	0.0563100i	0.999604	−	0.0281550i	$-0.00896320\pi$
$662$		0			0
$663$	−664.589	−	1031.37i	−1.00240	−	1.55561i
$664$		0			0
$665$	−455.466			−0.684911
$666$		0			0
$667$	109.177			0.163684
$668$		0			0
$669$	28.7608	+	56.4941i	0.0429908	+	0.0844455i
$670$		0			0
$671$	−932.079			−1.38909
$672$		0			0
$673$	−297.412	−	297.412i	−0.441920	−	0.441920i	0.450737	−	0.892657i	$-0.351161\pi$
$673$	−297.412	−	297.412i	−0.441920	−	0.441920i	−0.892657	+	0.450737i	$0.851161\pi$
$674$		0			0
$675$	−133.316	−	21.2554i	−0.197505	−	0.0314895i
$676$		0			0
$677$	−518.454	−	518.454i	−0.765811	−	0.765811i	0.211555	−	0.977366i	$-0.432147\pi$
$677$	−518.454	−	518.454i	−0.765811	−	0.765811i	−0.977366	+	0.211555i	$0.932147\pi$
$678$		0			0
$679$	10.3359			0.0152222
$680$		0			0
$681$	11.0140	−	33.8583i	0.0161733	−	0.0497185i
$682$		0			0
$683$	403.885	+	403.885i	0.591339	+	0.591339i	0.937993	−	0.346654i	$-0.112682\pi$
$683$	403.885	+	403.885i	0.591339	+	0.591339i	−0.346654	+	0.937993i	$0.612682\pi$
$684$		0			0
$685$	168.173	−	168.173i	0.245508	−	0.245508i
$686$		0			0
$687$	194.132	+	381.327i	0.282579	+	0.555062i
$688$		0			0
$689$	695.530			1.00948
$690$		0			0
$691$	818.051	+	818.051i	1.18387	+	1.18387i	0.978734	+	0.205132i	$0.0657622\pi$
$691$	818.051	+	818.051i	1.18387	+	1.18387i	0.205132	+	0.978734i	$0.434238\pi$
$692$		0			0
$693$	819.827	−	1126.77i	1.18301	−	1.62594i
$694$		0			0
$695$	362.562			0.521672
$696$		0			0
$697$	624.675	+	509.175i	0.896234	+	0.730524i
$698$		0			0
$699$	−378.427	−	123.101i	−0.541383	−	0.176111i
$700$		0			0
$701$		−	701.073i		−	1.00010i	−0.865995	−	0.500052i	$-0.833314\pi$
$701$		−	701.073i		−	1.00010i	0.865995	−	0.500052i	$-0.166686\pi$
$702$		0			0
$703$	790.034	+	790.034i	1.12380	+	1.12380i
$704$		0			0
$705$	188.948	−	580.846i	0.268011	−	0.823894i
$706$		0			0
$707$	1098.91	−	1098.91i	1.55433	−	1.55433i
$708$		0			0
$709$	338.901	−	338.901i	0.477999	−	0.477999i	−0.426492	−	0.904491i	$-0.640251\pi$
$709$	338.901	−	338.901i	0.477999	−	0.477999i	0.904491	+	0.426492i	$0.140251\pi$
$710$		0			0
$711$	1122.93	−	177.067i	1.57936	−	0.249039i
$712$		0			0
$713$			195.806i			0.274623i
$714$		0			0
$715$	−936.243			−1.30943
$716$		0			0
$717$	−258.390	−	507.548i	−0.360377	−	0.707877i
$718$		0			0
$719$	425.617	+	425.617i	0.591957	+	0.591957i	0.938160	−	0.346203i	$-0.112529\pi$
$719$	425.617	+	425.617i	0.591957	+	0.591957i	−0.346203	+	0.938160i	$0.612529\pi$
$720$		0			0
$721$	−939.896	−	939.896i	−1.30360	−	1.30360i
$722$		0			0
$723$	−353.107	+	1085.49i	−0.488391	+	1.50137i
$724$		0			0
$725$	72.6439	−	72.6439i	0.100199	−	0.100199i
$726$		0			0
$727$	−556.487			−0.765456			−0.382728	−	0.923861i	$-0.625015\pi$
$727$	−556.487			−0.765456			−0.382728	+	0.923861i	$0.625015\pi$
$728$		0			0
$729$	−692.856	−	226.696i	−0.950420	−	0.310968i
$730$		0			0
$731$	965.750	−	98.3759i	1.32114	−	0.134577i
$732$		0			0
$733$			1408.29i			1.92128i	0.277805	+	0.960638i	$0.410393\pi$
$733$			1408.29i			1.92128i	−0.277805	+	0.960638i	$0.589607\pi$
$734$		0			0
$735$	−62.5495	+	192.284i	−0.0851014	+	0.261611i
$736$		0			0
$737$	−288.293	+	288.293i	−0.391170	+	0.391170i
$738$		0			0
$739$			957.359i			1.29548i	0.761862	+	0.647740i	$0.224286\pi$
$739$			957.359i			1.29548i	−0.761862	+	0.647740i	$0.775714\pi$
$740$		0			0
$741$	749.718	+	1472.65i	1.01177	+	1.98738i
$742$		0			0
$743$	742.686	+	742.686i	0.999578	+	0.999578i	1.00000		0.000422402i	$-0.000134455\pi$
$743$	742.686	+	742.686i	0.999578	+	0.999578i	−0.000422402		1.00000i	$0.500134\pi$
$744$		0			0
$745$	−247.422	+	247.422i	−0.332110	+	0.332110i
$746$		0			0
$747$	328.870	−	452.000i	0.440254	−	0.605087i
$748$		0			0
$749$		−	1192.95i		−	1.59273i
$750$		0			0
$751$	−920.718	+	920.718i	−1.22599	+	1.22599i	−0.260522	+	0.965468i	$0.583895\pi$
$751$	−920.718	+	920.718i	−1.22599	+	1.22599i	−0.965468	+	0.260522i	$0.916105\pi$
$752$		0			0
$753$	−258.391	−	507.550i	−0.343149	−	0.674037i
$754$		0			0
$755$	451.264	−	451.264i	0.597700	−	0.597700i
$756$		0			0
$757$			126.592i			0.167228i	0.996498	+	0.0836140i	$0.0266463\pi$
$757$			126.592i			0.167228i	−0.996498	+	0.0836140i	$0.973354\pi$
$758$		0			0
$759$	125.867	+	247.237i	0.165833	+	0.325740i
$760$		0			0
$761$		−	263.944i		−	0.346838i	−0.984848	−	0.173419i	$-0.944518\pi$
$761$		−	263.944i		−	0.346838i	0.984848	−	0.173419i	$-0.0554815\pi$
$762$		0			0
$763$			559.215i			0.732916i
$764$		0			0
$765$	87.2609	+	330.803i	0.114067	+	0.432422i
$766$		0			0
$767$	−1510.28			−1.96908
$768$		0			0
$769$	116.182			0.151082			0.0755409	−	0.997143i	$-0.475932\pi$
$769$	116.182			0.151082			0.0755409	+	0.997143i	$0.475932\pi$
$770$		0			0
$771$	−65.7844	+	33.4905i	−0.0853235	+	0.0434377i
$772$		0			0
$773$	1333.03			1.72448			0.862242	−	0.506496i	$-0.169060\pi$
$773$	1333.03			1.72448			0.862242	+	0.506496i	$0.169060\pi$
$774$		0			0
$775$	130.285	+	130.285i	0.168109	+	0.168109i
$776$		0			0
$777$	1160.59	−	590.848i	1.49368	−	0.760422i
$778$		0			0
$779$	−767.511	−	767.511i	−0.985251	−	0.985251i
$780$		0			0
$781$	1780.73			2.28006
$782$		0			0
$783$	449.148	−	325.621i	0.573624	−	0.415864i
$784$		0			0
$785$	−251.791	−	251.791i	−0.320753	−	0.320753i
$786$		0			0
$787$	−188.004	+	188.004i	−0.238886	+	0.238886i	−0.816389	−	0.577502i	$-0.804027\pi$
$787$	−188.004	+	188.004i	−0.238886	+	0.238886i	0.577502	+	0.816389i	$0.304027\pi$
$788$		0			0
$789$	943.312	−	480.235i	1.19558	−	0.608663i
$790$		0			0
$791$	468.807			0.592677
$792$		0			0
$793$	−911.058	−	911.058i	−1.14887	−	1.14887i
$794$		0			0
$795$	−184.427	−	59.9937i	−0.231984	−	0.0754638i
$796$		0			0
$797$	313.441			0.393276			0.196638	−	0.980476i	$-0.436998\pi$
$797$	313.441			0.393276			0.196638	+	0.980476i	$0.436998\pi$
$798$		0			0
$799$	−1539.94	+	156.866i	−1.92733	+	0.196328i
$800$		0			0
$801$	52.8793	+	38.4743i	0.0660166	+	0.0480329i
$802$		0			0
$803$		−	219.020i		−	0.272752i
$804$		0			0
$805$	−74.7416	−	74.7416i	−0.0928467	−	0.0928467i
$806$		0			0
$807$	1388.53	+	451.685i	1.72061	+	0.559709i
$808$		0			0
$809$	−196.828	+	196.828i	−0.243298	+	0.243298i	−0.818213	−	0.574915i	$-0.805035\pi$
$809$	−196.828	+	196.828i	−0.243298	+	0.243298i	0.574915	+	0.818213i	$0.305035\pi$
$810$		0			0
$811$	655.686	−	655.686i	0.808490	−	0.808490i	−0.175915	−	0.984405i	$-0.556288\pi$
$811$	655.686	−	655.686i	0.808490	−	0.808490i	0.984405	+	0.175915i	$0.0562884\pi$
$812$		0			0
$813$	−808.524	+	411.615i	−0.994495	+	0.506292i
$814$		0			0
$815$			430.741i			0.528517i
$816$		0			0
$817$	−1307.44			−1.60030
$818$		0			0
$819$	1902.70	−	300.024i	2.32320	−	0.366330i
$820$		0			0
$821$	523.330	+	523.330i	0.637430	+	0.637430i	0.949921	−	0.312491i	$-0.101163\pi$
$821$	523.330	+	523.330i	0.637430	+	0.637430i	−0.312491	+	0.949921i	$0.601163\pi$
$822$		0			0
$823$	−1018.42	−	1018.42i	−1.23744	−	1.23744i	−0.961042	−	0.276403i	$-0.910858\pi$
$823$	−1018.42	−	1018.42i	−1.23744	−	1.23744i	−0.276403	−	0.961042i	$-0.589142\pi$
$824$		0			0
$825$	248.254	+	80.7566i	0.300914	+	0.0978868i
$826$		0			0
$827$	−746.034	+	746.034i	−0.902097	+	0.902097i	−0.995617	−	0.0935204i	$-0.970188\pi$
$827$	−746.034	+	746.034i	−0.902097	+	0.902097i	0.0935204	+	0.995617i	$0.470188\pi$
$828$		0			0
$829$	−550.517			−0.664074			−0.332037	−	0.943266i	$-0.607736\pi$
$829$	−550.517			−0.664074			−0.332037	+	0.943266i	$0.607736\pi$
$830$		0			0
$831$	27.4299	−	84.3225i	0.0330083	−	0.101471i
$832$		0			0
$833$	509.784	−	51.9290i	0.611985	−	0.0623398i
$834$		0			0
$835$			324.707i			0.388870i
$836$		0			0
$837$	583.992	+	805.533i	0.697720	+	0.962405i
$838$		0			0
$839$	591.156	−	591.156i	0.704596	−	0.704596i	−0.260798	−	0.965394i	$-0.583986\pi$
$839$	591.156	−	591.156i	0.704596	−	0.704596i	0.965394	+	0.260798i	$0.0839855\pi$
$840$		0			0
$841$		−	418.829i		−	0.498013i
$842$		0			0
$843$	−435.669	+	221.797i	−0.516808	+	0.263104i
$844$		0			0
$845$	−647.915	−	647.915i	−0.766763	−	0.766763i
$846$		0			0
$847$	−1144.24	+	1144.24i	−1.35093	+	1.35093i
$848$		0			0
$849$	−125.190	−	40.7241i	−0.147456	−	0.0479672i
$850$		0			0
$851$			259.288i			0.304686i
$852$		0			0
$853$	177.160	−	177.160i	0.207690	−	0.207690i	−0.595595	−	0.803285i	$-0.703084\pi$
$853$	177.160	−	177.160i	0.207690	−	0.207690i	0.803285	+	0.595595i	$0.203084\pi$
$854$		0			0
$855$	−71.7705	−	455.156i	−0.0839421	−	0.532346i
$856$		0			0
$857$	−149.352	+	149.352i	−0.174272	+	0.174272i	−0.788854	−	0.614581i	$-0.789325\pi$
$857$	−149.352	+	149.352i	−0.174272	+	0.174272i	0.614581	+	0.788854i	$0.289325\pi$
$858$		0			0
$859$			665.664i			0.774929i	0.921885	+	0.387464i	$0.126649\pi$
$859$			665.664i			0.774929i	−0.921885	+	0.387464i	$0.873351\pi$
$860$		0			0
$861$	−1127.50	+	574.004i	−1.30952	+	0.666671i
$862$		0			0
$863$			57.4716i			0.0665952i	0.999445	+	0.0332976i	$0.0106009\pi$
$863$			57.4716i			0.0665952i	−0.999445	+	0.0332976i	$0.989399\pi$
$864$		0			0
$865$			548.163i			0.633714i
$866$		0			0
$867$	677.454	−	541.059i	0.781377	−	0.624059i
$868$		0			0
$869$	−2198.31			−2.52970
$870$		0			0
$871$	−563.581			−0.647051
$872$		0			0
$873$	1.62869	+	10.3289i	0.00186563	+	0.0118315i
$874$		0			0
$875$	−99.4626			−0.113672
$876$		0			0
$877$	626.865	+	626.865i	0.714784	+	0.714784i	0.967532	−	0.252748i	$-0.0813345\pi$
$877$	626.865	+	626.865i	0.714784	+	0.714784i	−0.252748	+	0.967532i	$0.581334\pi$
$878$		0			0
$879$	428.056	+	840.818i	0.486981	+	0.956562i
$880$		0			0
$881$	296.732	+	296.732i	0.336813	+	0.336813i	0.855167	−	0.518353i	$-0.173455\pi$
$881$	296.732	+	296.732i	0.336813	+	0.336813i	−0.518353	+	0.855167i	$0.673455\pi$
$882$		0			0
$883$	−773.255			−0.875713			−0.437857	−	0.899045i	$-0.644262\pi$
$883$	−773.255			−0.875713			−0.437857	+	0.899045i	$0.644262\pi$
$884$		0			0
$885$	400.467	+	130.271i	0.452505	+	0.147199i
$886$		0			0
$887$	−617.167	−	617.167i	−0.695792	−	0.695792i	0.267708	−	0.963500i	$-0.413734\pi$
$887$	−617.167	−	617.167i	−0.695792	−	0.695792i	−0.963500	+	0.267708i	$0.913734\pi$
$888$		0			0
$889$	183.489	−	183.489i	0.206400	−	0.206400i
$890$		0			0
$891$	1255.19	+	641.717i	1.40875	+	0.720221i
$892$		0			0
$893$	2084.79			2.33459
$894$		0			0
$895$	−170.986	−	170.986i	−0.191045	−	0.191045i
$896$		0			0
$897$	−118.633	+	364.689i	−0.132255	+	0.406565i
$898$		0			0
$899$	−757.151			−0.842215
$900$		0			0
$901$	49.8072	+	488.953i	0.0552799	+	0.542679i
$902$		0			0
$903$	−471.436	+	1449.24i	−0.522077	+	1.60492i
$904$		0			0
$905$			12.5708i			0.0138904i
$906$		0			0
$907$	876.313	+	876.313i	0.966167	+	0.966167i	0.999446	−	0.0332795i	$-0.0105951\pi$
$907$	876.313	+	876.313i	0.966167	+	0.966167i	−0.0332795	+	0.999446i	$0.510595\pi$
$908$		0			0
$909$	1271.33	+	925.001i	1.39860	+	1.01760i
$910$		0			0
$911$	−183.047	+	183.047i	−0.200930	+	0.200930i	−0.800398	−	0.599469i	$-0.795379\pi$
$911$	−183.047	+	183.047i	−0.200930	+	0.200930i	0.599469	+	0.800398i	$0.295379\pi$
$912$		0			0
$913$	−764.340	+	764.340i	−0.837175	+	0.837175i
$914$		0			0
$915$	162.992	+	320.161i	0.178133	+	0.349902i
$916$		0			0
$917$			1875.74i			2.04552i
$918$		0			0
$919$	237.681			0.258630			0.129315	−	0.991604i	$-0.458722\pi$
$919$	237.681			0.258630			0.129315	+	0.991604i	$0.458722\pi$
$920$		0			0
$921$	100.862	−	51.3482i	0.109513	−	0.0557526i
$922$		0			0
$923$	1740.57	+	1740.57i	1.88577	+	1.88577i
$924$		0			0
$925$	172.524	+	172.524i	0.186513	+	0.186513i
$926$		0			0
$927$	791.152	−	1087.36i	0.853454	−	1.17299i
$928$		0			0
$929$	608.555	−	608.555i	0.655065	−	0.655065i	−0.299143	−	0.954208i	$-0.596701\pi$
$929$	608.555	−	608.555i	0.655065	−	0.655065i	0.954208	+	0.299143i	$0.0967009\pi$
$930$		0			0
$931$	−690.152			−0.741302
$932$		0			0
$933$	−373.467	−	121.488i	−0.400286	−	0.130212i
$934$		0			0
$935$	−67.0447	−	658.173i	−0.0717055	−	0.703928i
$936$		0			0
$937$		−	1505.78i		−	1.60703i	−0.595286	−	0.803514i	$-0.702961\pi$
$937$		−	1505.78i		−	1.60703i	0.595286	−	0.803514i	$-0.297039\pi$
$938$		0			0
$939$	134.240	+	43.6681i	0.142961	+	0.0465049i
$940$		0			0
$941$	811.174	−	811.174i	0.862034	−	0.862034i	−0.129540	−	0.991574i	$-0.541350\pi$
$941$	811.174	−	811.174i	0.862034	−	0.862034i	0.991574	+	0.129540i	$0.0413502\pi$
$942$		0			0
$943$		−	251.896i		−	0.267122i
$944$		0			0
$945$	−530.399	−	84.5649i	−0.561269	−	0.0894866i
$946$		0			0
$947$	641.494	+	641.494i	0.677396	+	0.677396i	0.959410	−	0.282014i	$-0.0910025\pi$
$947$	641.494	+	641.494i	0.677396	+	0.677396i	−0.282014	+	0.959410i	$0.591002\pi$
$948$		0			0
$949$	214.080	−	214.080i	0.225585	−	0.225585i
$950$		0			0
$951$	404.372	−	1243.08i	0.425207	−	1.30713i
$952$		0			0
$953$			170.900i			0.179329i	0.995972	+	0.0896643i	$0.0285794\pi$
$953$			170.900i			0.179329i	−0.995972	+	0.0896643i	$0.971421\pi$
$954$		0			0
$955$	292.495	−	292.495i	0.306278	−	0.306278i
$956$		0			0
$957$	−956.026	+	486.708i	−0.998982	+	0.508577i
$958$		0			0
$959$	669.077	−	669.077i	0.697682	−	0.697682i
$960$		0			0
$961$		−	396.928i		−	0.413036i
$962$		0			0
$963$	1192.14	−	187.981i	1.23794	−	0.195203i
$964$		0			0
$965$			145.877i			0.151168i
$966$		0			0
$967$		−	680.971i		−	0.704210i	−0.935960	−	0.352105i	$-0.885466\pi$
$967$		−	680.971i		−	0.704210i	0.935960	−	0.352105i	$-0.114534\pi$
$968$		0			0
$969$	−981.576	+	632.504i	−1.01298	+	0.652739i
$970$		0			0
$971$	−800.611			−0.824522			−0.412261	−	0.911066i	$-0.635261\pi$
$971$	−800.611			−0.824522			−0.412261	+	0.911066i	$0.635261\pi$
$972$		0			0
$973$	1442.45			1.48248
$974$		0			0
$975$	163.720	+	321.591i	0.167918	+	0.329837i
$976$		0			0
$977$	498.800			0.510542			0.255271	−	0.966870i	$-0.417835\pi$
$977$	498.800			0.510542			0.255271	+	0.966870i	$0.417835\pi$
$978$		0			0
$979$	−89.4198	−	89.4198i	−0.0913379	−	0.0913379i
$980$		0			0
$981$	−558.834	+	88.1189i	−0.569658	+	0.0898256i
$982$		0			0
$983$	123.849	+	123.849i	0.125991	+	0.125991i	0.767290	−	0.641300i	$-0.221605\pi$
$983$	123.849	+	123.849i	0.125991	+	0.125991i	−0.641300	+	0.767290i	$0.721605\pi$
$984$		0			0
$985$	−376.929			−0.382669
$986$		0			0
$987$	751.730	−	2310.90i	0.761631	−	2.34133i
$988$		0			0
$989$	−214.551	−	214.551i	−0.216937	−	0.216937i
$990$		0			0
$991$	97.5355	−	97.5355i	0.0984213	−	0.0984213i	−0.656182	−	0.754603i	$-0.727829\pi$
$991$	97.5355	−	97.5355i	0.0984213	−	0.0984213i	0.754603	+	0.656182i	$0.227829\pi$
$992$		0			0
$993$	−626.251	−	1230.13i	−0.630665	−	1.23880i
$994$		0			0
$995$	−241.419			−0.242632
$996$		0			0
$997$	580.961	+	580.961i	0.582709	+	0.582709i	0.935647	−	0.352937i	$-0.114817\pi$
$997$	580.961	+	580.961i	0.582709	+	0.582709i	−0.352937	+	0.935647i	$0.614817\pi$
$998$		0			0
$999$	773.327	+	1066.69i	0.774101	+	1.06776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1020.3.bc.a.701.9	✓	96
3.2	odd	2	inner	1020.3.bc.a.701.16	yes	96
17.13	even	4	inner	1020.3.bc.a.761.16	yes	96
51.47	odd	4	inner	1020.3.bc.a.761.9	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1020.3.bc.a.701.9	✓	96	1.1	even	1	trivial
1020.3.bc.a.701.16	yes	96	3.2	odd	2	inner
1020.3.bc.a.761.9	yes	96	51.47	odd	4	inner
1020.3.bc.a.761.16	yes	96	17.13	even	4	inner

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:	\( N \)	\(=\)	\( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1020.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.67349 + 1.36106i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(-6.29057 - 6.29057i) q^{7} +(5.29505 - 7.27753i) q^{9} +O(q^{10})\)	\(q+(-2.67349 + 1.36106i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(-6.29057 - 6.29057i) q^{7} +(5.29505 - 7.27753i) q^{9} +(-12.3064 + 12.3064i) q^{11} -24.0578 q^{13} +(6.37917 + 2.07513i) q^{15} +(-1.72279 - 16.9125i) q^{17} +22.8963i q^{19} +(25.3796 + 8.25592i) q^{21} +(-3.75727 + 3.75727i) q^{23} +5.00000i q^{25} +(-4.25109 + 26.6632i) q^{27} +(-14.5288 - 14.5288i) q^{29} +(26.0569 - 26.0569i) q^{31} +(16.1513 - 49.6509i) q^{33} +19.8925i q^{35} +(34.5048 - 34.5048i) q^{37} +(64.3182 - 32.7440i) q^{39} +(-33.5211 + 33.5211i) q^{41} +57.1028i q^{43} +(-19.8790 + 3.13459i) q^{45} -91.0534i q^{47} +30.1425i q^{49} +(27.6247 + 42.8705i) q^{51} -28.9108 q^{53} +38.9164 q^{55} +(-31.1632 - 61.2130i) q^{57} +62.7773 q^{59} +(37.8695 + 37.8695i) q^{61} +(-79.0886 + 12.4710i) q^{63} +(38.0387 + 38.0387i) q^{65} +23.4261 q^{67} +(4.93115 - 15.1589i) q^{69} +(-72.3495 - 72.3495i) q^{71} +(-8.89859 + 8.89859i) q^{73} +(-6.80529 - 13.3674i) q^{75} +154.829 q^{77} +(89.3154 + 89.3154i) q^{79} +(-24.9250 - 77.0697i) q^{81} +62.1090 q^{83} +(-24.0170 + 29.4649i) q^{85} +(58.6170 + 19.0680i) q^{87} +7.26610i q^{89} +(151.337 + 151.337i) q^{91} +(-34.1978 + 105.128i) q^{93} +(36.2023 - 36.2023i) q^{95} +(-0.821540 + 0.821540i) q^{97} +(24.3974 + 154.724i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 8 q^{3}+O(q^{10}) \) 96 * q - 8 * q^3	\( 96 q - 8 q^{3} + 64 q^{21} + 100 q^{27} - 24 q^{31} + 40 q^{33} + 24 q^{37} - 52 q^{39} - 40 q^{45} - 4 q^{51} + 80 q^{55} + 192 q^{57} + 144 q^{61} + 28 q^{63} - 320 q^{67} + 208 q^{69} + 152 q^{73} - 40 q^{75} + 224 q^{79} + 488 q^{81} - 288 q^{91} + 80 q^{97} - 212 q^{99}+O(q^{100}) \) 96 * q - 8 * q^3 + 64 * q^21 + 100 * q^27 - 24 * q^31 + 40 * q^33 + 24 * q^37 - 52 * q^39 - 40 * q^45 - 4 * q^51 + 80 * q^55 + 192 * q^57 + 144 * q^61 + 28 * q^63 - 320 * q^67 + 208 * q^69 + 152 * q^73 - 40 * q^75 + 224 * q^79 + 488 * q^81 - 288 * q^91 + 80 * q^97 - 212 * q^99

Introduction

L-functions

Modular forms

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