LMFDB - Embedded newform 1960.2.q.q.961.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1960,2,Mod(361,1960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1960, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1960.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1960 = 2^{3} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1960.q (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:	$15.6506787962$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1960.961
Dual form			1960.2.q.q.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207107 + 0.358719i) q^{3} +(0.500000 - 0.866025i) q^{5} +(1.41421 - 2.44949i) q^{9} +O(q^{10})$	\(q+(0.207107 + 0.358719i) q^{3} +(0.500000 - 0.866025i) q^{5} +(1.41421 - 2.44949i) q^{9} +(-0.414214 - 0.717439i) q^{11} -2.00000 q^{13} +0.414214 q^{15} +(-3.82843 - 6.63103i) q^{17} +(-2.82843 + 4.89898i) q^{19} +(2.79289 - 4.83743i) q^{23} +(-0.500000 - 0.866025i) q^{25} +2.41421 q^{27} -7.82843 q^{29} +(0.414214 + 0.717439i) q^{31} +(0.171573 - 0.297173i) q^{33} +(-2.82843 + 4.89898i) q^{37} +(-0.414214 - 0.717439i) q^{39} -5.82843 q^{41} -6.89949 q^{43} +(-1.41421 - 2.44949i) q^{45} +(5.82843 - 10.0951i) q^{47} +(1.58579 - 2.74666i) q^{51} +(2.82843 + 4.89898i) q^{53} -0.828427 q^{55} -2.34315 q^{57} +(-2.00000 - 3.46410i) q^{59} +(3.32843 - 5.76500i) q^{61} +(-1.00000 + 1.73205i) q^{65} +(6.44975 + 11.1713i) q^{67} +2.31371 q^{69} -12.0000 q^{71} +(1.82843 + 3.16693i) q^{73} +(0.207107 - 0.358719i) q^{75} +(2.00000 - 3.46410i) q^{79} +(-3.74264 - 6.48244i) q^{81} +4.75736 q^{83} -7.65685 q^{85} +(-1.62132 - 2.80821i) q^{87} +(-2.67157 + 4.62730i) q^{89} +(-0.171573 + 0.297173i) q^{93} +(2.82843 + 4.89898i) q^{95} -6.00000 q^{97} -2.34315 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{5}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^5	$ 4 q - 2 q^{3} + 2 q^{5} + 4 q^{11} - 8 q^{13} - 4 q^{15} - 4 q^{17} + 14 q^{23} - 2 q^{25} + 4 q^{27} - 20 q^{29} - 4 q^{31} + 12 q^{33} + 4 q^{39} - 12 q^{41} + 12 q^{43} + 12 q^{47} + 12 q^{51} + 8 q^{55} - 32 q^{57} - 8 q^{59} + 2 q^{61} - 4 q^{65} + 6 q^{67} - 36 q^{69} - 48 q^{71} - 4 q^{73} - 2 q^{75} + 8 q^{79} + 2 q^{81} + 36 q^{83} - 8 q^{85} + 2 q^{87} - 22 q^{89} - 12 q^{93} - 24 q^{97} - 32 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^5 + 4 * q^11 - 8 * q^13 - 4 * q^15 - 4 * q^17 + 14 * q^23 - 2 * q^25 + 4 * q^27 - 20 * q^29 - 4 * q^31 + 12 * q^33 + 4 * q^39 - 12 * q^41 + 12 * q^43 + 12 * q^47 + 12 * q^51 + 8 * q^55 - 32 * q^57 - 8 * q^59 + 2 * q^61 - 4 * q^65 + 6 * q^67 - 36 * q^69 - 48 * q^71 - 4 * q^73 - 2 * q^75 + 8 * q^79 + 2 * q^81 + 36 * q^83 - 8 * q^85 + 2 * q^87 - 22 * q^89 - 12 * q^93 - 24 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$.

$n$	$981$	$1081$	$1177$	$1471$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	0.207107	+	0.358719i	0.119573	+	0.207107i	0.919599	−	0.392859i	$-0.128514\pi$
$3$	0.207107	+	0.358719i	0.119573	+	0.207107i	−0.800025	+	0.599966i	$0.795181\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.41421	−	2.44949i	0.471405	−	0.816497i
$10$		0			0
$11$	−0.414214	−	0.717439i	−0.124890	−	0.216316i	0.796800	−	0.604243i	$-0.206524\pi$
$11$	−0.414214	−	0.717439i	−0.124890	−	0.216316i	−0.921690	+	0.387927i	$0.873191\pi$
$12$		0			0
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$	0.414214			0.106949
$16$		0			0
$17$	−3.82843	−	6.63103i	−0.928530	−	1.60826i	−0.785783	−	0.618502i	$-0.787740\pi$
$17$	−3.82843	−	6.63103i	−0.928530	−	1.60826i	−0.142747	−	0.989759i	$-0.545593\pi$
$18$		0			0
$19$	−2.82843	+	4.89898i	−0.648886	+	1.12390i	0.334504	+	0.942394i	$0.391431\pi$
$19$	−2.82843	+	4.89898i	−0.648886	+	1.12390i	−0.983389	+	0.181509i	$0.941902\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.79289	−	4.83743i	0.582358	−	1.00867i	−0.412841	−	0.910803i	$-0.635463\pi$
$23$	2.79289	−	4.83743i	0.582358	−	1.00867i	0.995199	−	0.0978712i	$-0.0312033\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	2.41421			0.464616
$28$		0			0
$29$	−7.82843			−1.45370			−0.726851	−	0.686795i	$-0.759017\pi$
$29$	−7.82843			−1.45370			−0.726851	+	0.686795i	$0.759017\pi$
$30$		0			0
$31$	0.414214	+	0.717439i	0.0743950	+	0.128856i	0.900823	−	0.434187i	$-0.142964\pi$
$31$	0.414214	+	0.717439i	0.0743950	+	0.128856i	−0.826428	+	0.563042i	$0.809631\pi$
$32$		0			0
$33$	0.171573	−	0.297173i	0.0298670	−	0.0517312i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.82843	+	4.89898i	−0.464991	+	0.805387i	−0.999201	−	0.0399642i	$-0.987276\pi$
$37$	−2.82843	+	4.89898i	−0.464991	+	0.805387i	0.534211	+	0.845351i	$0.320609\pi$
$38$		0			0
$39$	−0.414214	−	0.717439i	−0.0663273	−	0.114882i
$40$		0			0
$41$	−5.82843			−0.910247			−0.455124	−	0.890428i	$-0.650405\pi$
$41$	−5.82843			−0.910247			−0.455124	+	0.890428i	$0.650405\pi$
$42$		0			0
$43$	−6.89949			−1.05216			−0.526082	−	0.850434i	$-0.676339\pi$
$43$	−6.89949			−1.05216			−0.526082	+	0.850434i	$0.676339\pi$
$44$		0			0
$45$	−1.41421	−	2.44949i	−0.210819	−	0.365148i
$46$		0			0
$47$	5.82843	−	10.0951i	0.850163	−	1.47253i	−0.0308969	−	0.999523i	$-0.509836\pi$
$47$	5.82843	−	10.0951i	0.850163	−	1.47253i	0.881060	−	0.473004i	$-0.156830\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	1.58579	−	2.74666i	0.222055	−	0.384610i
$52$		0			0
$53$	2.82843	+	4.89898i	0.388514	+	0.672927i	0.992250	−	0.124258i	$-0.0396551\pi$
$53$	2.82843	+	4.89898i	0.388514	+	0.672927i	−0.603736	+	0.797185i	$0.706322\pi$
$54$		0			0
$55$	−0.828427			−0.111705
$56$		0			0
$57$	−2.34315			−0.310357
$58$		0			0
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	0.705965	−	0.708247i	$-0.250514\pi$
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	−0.966342	+	0.257260i	$0.917180\pi$
$60$		0			0
$61$	3.32843	−	5.76500i	0.426161	−	0.738133i	−0.570367	−	0.821390i	$-0.693199\pi$
$61$	3.32843	−	5.76500i	0.426161	−	0.738133i	0.996528	+	0.0832569i	$0.0265322\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.00000	+	1.73205i	−0.124035	+	0.214834i
$66$		0			0
$67$	6.44975	+	11.1713i	0.787962	+	1.36479i	0.927213	+	0.374533i	$0.122197\pi$
$67$	6.44975	+	11.1713i	0.787962	+	1.36479i	−0.139251	+	0.990257i	$0.544470\pi$
$68$		0			0
$69$	2.31371			0.278538
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$	1.82843	+	3.16693i	0.214001	+	0.370661i	0.952963	−	0.303086i	$-0.0980170\pi$
$73$	1.82843	+	3.16693i	0.214001	+	0.370661i	−0.738962	+	0.673747i	$0.764684\pi$
$74$		0			0
$75$	0.207107	−	0.358719i	0.0239146	−	0.0414214i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$		0			0
$81$	−3.74264	−	6.48244i	−0.415849	−	0.720272i
$82$		0			0
$83$	4.75736			0.522188			0.261094	−	0.965313i	$-0.415917\pi$
$83$	4.75736			0.522188			0.261094	+	0.965313i	$0.415917\pi$
$84$		0			0
$85$	−7.65685			−0.830502
$86$		0			0
$87$	−1.62132	−	2.80821i	−0.173824	−	0.301072i
$88$		0			0
$89$	−2.67157	+	4.62730i	−0.283186	+	0.490493i	−0.972168	−	0.234286i	$-0.924725\pi$
$89$	−2.67157	+	4.62730i	−0.283186	+	0.490493i	0.688982	+	0.724779i	$0.258058\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−0.171573	+	0.297173i	−0.0177913	+	0.0308154i
$94$		0			0
$95$	2.82843	+	4.89898i	0.290191	+	0.502625i
$96$		0			0
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$		0			0
$99$	−2.34315			−0.235495
$100$		0			0
$101$	−5.74264	−	9.94655i	−0.571414	−	0.989718i	−0.996421	−	0.0845282i	$-0.973062\pi$
$101$	−5.74264	−	9.94655i	−0.571414	−	0.989718i	0.425007	−	0.905190i	$-0.360272\pi$
$102$		0			0
$103$	3.79289	−	6.56948i	0.373725	−	0.647310i	−0.616410	−	0.787425i	$-0.711414\pi$
$103$	3.79289	−	6.56948i	0.373725	−	0.647310i	0.990135	+	0.140115i	$0.0447471\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.79289	−	4.83743i	0.269999	−	0.467652i	−0.698862	−	0.715256i	$-0.746310\pi$
$107$	2.79289	−	4.83743i	0.269999	−	0.467652i	0.968861	+	0.247604i	$0.0796432\pi$
$108$		0			0
$109$	−9.15685	−	15.8601i	−0.877068	−	1.51913i	−0.854544	−	0.519379i	$-0.826163\pi$
$109$	−9.15685	−	15.8601i	−0.877068	−	1.51913i	−0.0225237	−	0.999746i	$-0.507170\pi$
$110$		0			0
$111$	−2.34315			−0.222402
$112$		0			0
$113$	11.3137			1.06430			0.532152	−	0.846649i	$-0.321383\pi$
$113$	11.3137			1.06430			0.532152	+	0.846649i	$0.321383\pi$
$114$		0			0
$115$	−2.79289	−	4.83743i	−0.260439	−	0.451093i
$116$		0			0
$117$	−2.82843	+	4.89898i	−0.261488	+	0.452911i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.15685	−	8.93193i	0.468805	−	0.811994i
$122$		0			0
$123$	−1.20711	−	2.09077i	−0.108841	−	0.188518i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−4.34315			−0.385392			−0.192696	−	0.981259i	$-0.561723\pi$
$127$	−4.34315			−0.385392			−0.192696	+	0.981259i	$0.561723\pi$
$128$		0			0
$129$	−1.42893	−	2.47498i	−0.125810	−	0.217910i
$130$		0			0
$131$	6.82843	−	11.8272i	0.596602	−	1.03335i	−0.396716	−	0.917941i	$-0.629850\pi$
$131$	6.82843	−	11.8272i	0.596602	−	1.03335i	0.993319	−	0.115404i	$-0.0368164\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.20711	−	2.09077i	0.103891	−	0.179945i
$136$		0			0
$137$	2.00000	+	3.46410i	0.170872	+	0.295958i	0.938725	−	0.344668i	$-0.112008\pi$
$137$	2.00000	+	3.46410i	0.170872	+	0.295958i	−0.767853	+	0.640626i	$0.778675\pi$
$138$		0			0
$139$	−2.48528			−0.210799			−0.105399	−	0.994430i	$-0.533612\pi$
$139$	−2.48528			−0.210799			−0.105399	+	0.994430i	$0.533612\pi$
$140$		0			0
$141$	4.82843			0.406627
$142$		0			0
$143$	0.828427	+	1.43488i	0.0692766	+	0.119991i
$144$		0			0
$145$	−3.91421	+	6.77962i	−0.325058	+	0.563017i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.32843	+	4.03295i	−0.190752	+	0.330392i	−0.945500	−	0.325623i	$-0.894426\pi$
$149$	−2.32843	+	4.03295i	−0.190752	+	0.330392i	0.754748	+	0.656015i	$0.227759\pi$
$150$		0			0
$151$	5.58579	+	9.67487i	0.454565	+	0.787329i	0.998663	−	0.0516921i	$-0.0164614\pi$
$151$	5.58579	+	9.67487i	0.454565	+	0.787329i	−0.544098	+	0.839022i	$0.683128\pi$
$152$		0			0
$153$	−21.6569			−1.75085
$154$		0			0
$155$	0.828427			0.0665409
$156$		0			0
$157$	0.656854	+	1.13770i	0.0524227	+	0.0907987i	0.891046	−	0.453913i	$-0.149972\pi$
$157$	0.656854	+	1.13770i	0.0524227	+	0.0907987i	−0.838623	+	0.544712i	$0.816639\pi$
$158$		0			0
$159$	−1.17157	+	2.02922i	−0.0929118	+	0.160928i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	7.82843	−	13.5592i	0.613170	−	1.06204i	−0.377533	−	0.925996i	$-0.623227\pi$
$163$	7.82843	−	13.5592i	0.613170	−	1.06204i	0.990703	−	0.136045i	$-0.0434392\pi$
$164$		0			0
$165$	−0.171573	−	0.297173i	−0.0133569	−	0.0231349i
$166$		0			0
$167$	−2.07107			−0.160264			−0.0801320	−	0.996784i	$-0.525534\pi$
$167$	−2.07107			−0.160264			−0.0801320	+	0.996784i	$0.525534\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	8.00000	+	13.8564i	0.611775	+	1.05963i
$172$		0			0
$173$	5.17157	−	8.95743i	0.393187	−	0.681021i	−0.599681	−	0.800239i	$-0.704706\pi$
$173$	5.17157	−	8.95743i	0.393187	−	0.681021i	0.992868	+	0.119219i	$0.0380390\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.828427	−	1.43488i	0.0622684	−	0.107852i
$178$		0			0
$179$	3.24264	+	5.61642i	0.242366	+	0.419791i	0.961388	−	0.275197i	$-0.0887431\pi$
$179$	3.24264	+	5.61642i	0.242366	+	0.419791i	−0.719022	+	0.694988i	$0.755410\pi$
$180$		0			0
$181$	4.17157			0.310071			0.155035	−	0.987909i	$-0.450451\pi$
$181$	4.17157			0.310071			0.155035	+	0.987909i	$0.450451\pi$
$182$		0			0
$183$	2.75736			0.203830
$184$		0			0
$185$	2.82843	+	4.89898i	0.207950	+	0.360180i
$186$		0			0
$187$	−3.17157	+	5.49333i	−0.231928	+	0.401712i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.75736	−	4.77589i	0.199516	−	0.345571i	−0.748856	−	0.662733i	$-0.769397\pi$
$191$	2.75736	−	4.77589i	0.199516	−	0.345571i	0.948371	+	0.317162i	$0.102730\pi$
$192$		0			0
$193$	2.65685	+	4.60181i	0.191245	+	0.331245i	0.945663	−	0.325149i	$-0.105414\pi$
$193$	2.65685	+	4.60181i	0.191245	+	0.331245i	−0.754418	+	0.656394i	$0.772081\pi$
$194$		0			0
$195$	−0.828427			−0.0593249
$196$		0			0
$197$	0.343146			0.0244481			0.0122241	−	0.999925i	$-0.496109\pi$
$197$	0.343146			0.0244481			0.0122241	+	0.999925i	$0.496109\pi$
$198$		0			0
$199$	−11.6569	−	20.1903i	−0.826332	−	1.43125i	−0.900897	−	0.434034i	$-0.857090\pi$
$199$	−11.6569	−	20.1903i	−0.826332	−	1.43125i	0.0745642	−	0.997216i	$-0.476243\pi$
$200$		0			0
$201$	−2.67157	+	4.62730i	−0.188438	+	0.326385i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−2.91421	+	5.04757i	−0.203538	+	0.352537i
$206$		0			0
$207$	−7.89949	−	13.6823i	−0.549053	−	0.950987i
$208$		0			0
$209$	4.68629			0.324158
$210$		0			0
$211$	26.6274			1.83311			0.916553	−	0.399912i	$-0.130959\pi$
$211$	26.6274			1.83311			0.916553	+	0.399912i	$0.130959\pi$
$212$		0			0
$213$	−2.48528	−	4.30463i	−0.170289	−	0.294949i
$214$		0			0
$215$	−3.44975	+	5.97514i	−0.235271	+	0.407501i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−0.757359	+	1.31178i	−0.0511776	+	0.0886422i
$220$		0			0
$221$	7.65685	+	13.2621i	0.515056	+	0.892103i
$222$		0			0
$223$	14.9706			1.00250			0.501252	−	0.865302i	$-0.332873\pi$
$223$	14.9706			1.00250			0.501252	+	0.865302i	$0.332873\pi$
$224$		0			0
$225$	−2.82843			−0.188562
$226$		0			0
$227$	7.00000	+	12.1244i	0.464606	+	0.804722i	0.999184	−	0.0403978i	$-0.0128625\pi$
$227$	7.00000	+	12.1244i	0.464606	+	0.804722i	−0.534577	+	0.845120i	$0.679529\pi$
$228$		0			0
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	−0.999088	−	0.0426906i	$-0.986407\pi$
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	0.536515	+	0.843891i	$0.319740\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.82843	+	10.0951i	−0.381833	+	0.661354i	−0.991324	−	0.131439i	$-0.958040\pi$
$233$	−5.82843	+	10.0951i	−0.381833	+	0.661354i	0.609491	+	0.792793i	$0.291374\pi$
$234$		0			0
$235$	−5.82843	−	10.0951i	−0.380205	−	0.658534i
$236$		0			0
$237$	1.65685			0.107624
$238$		0			0
$239$	−30.4853			−1.97193			−0.985964	−	0.166955i	$-0.946606\pi$
$239$	−30.4853			−1.97193			−0.985964	+	0.166955i	$0.946606\pi$
$240$		0			0
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$		0			0
$243$	5.17157	−	8.95743i	0.331757	−	0.574619i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	5.65685	−	9.79796i	0.359937	−	0.623429i
$248$		0			0
$249$	0.985281	+	1.70656i	0.0624397	+	0.108149i
$250$		0			0
$251$	27.4558			1.73300			0.866499	−	0.499179i	$-0.166365\pi$
$251$	27.4558			1.73300			0.866499	+	0.499179i	$0.166365\pi$
$252$		0			0
$253$	−4.62742			−0.290923
$254$		0			0
$255$	−1.58579	−	2.74666i	−0.0993058	−	0.172003i
$256$		0			0
$257$	7.65685	−	13.2621i	0.477621	−	0.827265i	−0.522050	−	0.852915i	$-0.674832\pi$
$257$	7.65685	−	13.2621i	0.477621	−	0.827265i	0.999671	+	0.0256506i	$0.00816572\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−11.0711	+	19.1757i	−0.685282	+	1.18694i
$262$		0			0
$263$	7.86396	+	13.6208i	0.484913	+	0.839893i	0.999850	−	0.0173347i	$-0.00551807\pi$
$263$	7.86396	+	13.6208i	0.484913	+	0.839893i	−0.514937	+	0.857228i	$0.672185\pi$
$264$		0			0
$265$	5.65685			0.347498
$266$		0			0
$267$	−2.21320			−0.135446
$268$		0			0
$269$	−3.32843	−	5.76500i	−0.202938	−	0.351499i	0.746536	−	0.665345i	$-0.231716\pi$
$269$	−3.32843	−	5.76500i	−0.202938	−	0.351499i	−0.949474	+	0.313847i	$0.898382\pi$
$270$		0			0
$271$	−1.65685	+	2.86976i	−0.100647	+	0.174325i	−0.911951	−	0.410298i	$-0.865425\pi$
$271$	−1.65685	+	2.86976i	−0.100647	+	0.174325i	0.811305	+	0.584624i	$0.198758\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.414214	+	0.717439i	−0.0249780	+	0.0432632i
$276$		0			0
$277$	−14.3137	−	24.7921i	−0.860027	−	1.48961i	−0.871901	−	0.489682i	$-0.837113\pi$
$277$	−14.3137	−	24.7921i	−0.860027	−	1.48961i	0.0118739	−	0.999930i	$-0.496220\pi$
$278$		0			0
$279$	2.34315			0.140280
$280$		0			0
$281$	2.68629			0.160251			0.0801254	−	0.996785i	$-0.474468\pi$
$281$	2.68629			0.160251			0.0801254	+	0.996785i	$0.474468\pi$
$282$		0			0
$283$	9.00000	+	15.5885i	0.534994	+	0.926638i	0.999164	+	0.0408910i	$0.0130196\pi$
$283$	9.00000	+	15.5885i	0.534994	+	0.926638i	−0.464169	+	0.885747i	$0.653647\pi$
$284$		0			0
$285$	−1.17157	+	2.02922i	−0.0693980	+	0.120201i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−20.8137	+	36.0504i	−1.22434	+	2.12061i
$290$		0			0
$291$	−1.24264	−	2.15232i	−0.0728449	−	0.126171i
$292$		0			0
$293$	−16.9706			−0.991431			−0.495715	−	0.868485i	$-0.665094\pi$
$293$	−16.9706			−0.991431			−0.495715	+	0.868485i	$0.665094\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$		0			0
$297$	−1.00000	−	1.73205i	−0.0580259	−	0.100504i
$298$		0			0
$299$	−5.58579	+	9.67487i	−0.323034	+	0.559512i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	2.37868	−	4.11999i	0.136652	−	0.236687i
$304$		0			0
$305$	−3.32843	−	5.76500i	−0.190585	−	0.330103i
$306$		0			0
$307$	−4.75736			−0.271517			−0.135758	−	0.990742i	$-0.543347\pi$
$307$	−4.75736			−0.271517			−0.135758	+	0.990742i	$0.543347\pi$
$308$		0			0
$309$	3.14214			0.178750
$310$		0			0
$311$	10.8284	+	18.7554i	0.614024	+	1.06352i	0.990555	+	0.137116i	$0.0437834\pi$
$311$	10.8284	+	18.7554i	0.614024	+	1.06352i	−0.376531	+	0.926404i	$0.622883\pi$
$312$		0			0
$313$	10.4853	−	18.1610i	0.592663	−	1.02652i	−0.401209	−	0.915987i	$-0.631410\pi$
$313$	10.4853	−	18.1610i	0.592663	−	1.02652i	0.993872	−	0.110536i	$-0.0352568\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.0000	−	19.0526i	0.617822	−	1.07010i	−0.372061	−	0.928208i	$-0.621349\pi$
$317$	11.0000	−	19.0526i	0.617822	−	1.07010i	0.989882	−	0.141890i	$-0.0453179\pi$
$318$		0			0
$319$	3.24264	+	5.61642i	0.181553	+	0.314459i
$320$		0			0
$321$	2.31371			0.129139
$322$		0			0
$323$	43.3137			2.41004
$324$		0			0
$325$	1.00000	+	1.73205i	0.0554700	+	0.0960769i
$326$		0			0
$327$	3.79289	−	6.56948i	0.209747	−	0.363293i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−13.2426	+	22.9369i	−0.727881	+	1.26073i	0.229896	+	0.973215i	$0.426162\pi$
$331$	−13.2426	+	22.9369i	−0.727881	+	1.26073i	−0.957777	+	0.287512i	$0.907172\pi$
$332$		0			0
$333$	8.00000	+	13.8564i	0.438397	+	0.759326i
$334$		0			0
$335$	12.8995			0.704775
$336$		0			0
$337$	24.9706			1.36023			0.680117	−	0.733104i	$-0.261929\pi$
$337$	24.9706			1.36023			0.680117	+	0.733104i	$0.261929\pi$
$338$		0			0
$339$	2.34315	+	4.05845i	0.127262	+	0.220425i
$340$		0			0
$341$	0.343146	−	0.594346i	0.0185824	−	0.0321856i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	1.15685	−	2.00373i	0.0622829	−	0.107877i
$346$		0			0
$347$	−5.69239	−	9.85951i	−0.305583	−	0.529286i	0.671808	−	0.740726i	$-0.265518\pi$
$347$	−5.69239	−	9.85951i	−0.305583	−	0.529286i	−0.977391	+	0.211440i	$0.932185\pi$
$348$		0			0
$349$	−9.82843			−0.526104			−0.263052	−	0.964782i	$-0.584729\pi$
$349$	−9.82843			−0.526104			−0.263052	+	0.964782i	$0.584729\pi$
$350$		0			0
$351$	−4.82843			−0.257722
$352$		0			0
$353$	16.8284	+	29.1477i	0.895687	+	1.55138i	0.832952	+	0.553345i	$0.186649\pi$
$353$	16.8284	+	29.1477i	0.895687	+	1.55138i	0.0627345	+	0.998030i	$0.480018\pi$
$354$		0			0
$355$	−6.00000	+	10.3923i	−0.318447	+	0.551566i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	3.24264	−	5.61642i	0.171140	−	0.296423i	−0.767679	−	0.640835i	$-0.778588\pi$
$359$	3.24264	−	5.61642i	0.171140	−	0.296423i	0.938819	+	0.344412i	$0.111922\pi$
$360$		0			0
$361$	−6.50000	−	11.2583i	−0.342105	−	0.592544i
$362$		0			0
$363$	4.27208			0.224226
$364$		0			0
$365$	3.65685			0.191408
$366$		0			0
$367$	10.7929	+	18.6938i	0.563384	+	0.975810i	0.997198	+	0.0748078i	$0.0238343\pi$
$367$	10.7929	+	18.6938i	0.563384	+	0.975810i	−0.433814	+	0.901003i	$0.642832\pi$
$368$		0			0
$369$	−8.24264	+	14.2767i	−0.429095	+	0.743214i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−6.00000	+	10.3923i	−0.310668	+	0.538093i	−0.978507	−	0.206213i	$-0.933886\pi$
$373$	−6.00000	+	10.3923i	−0.310668	+	0.538093i	0.667839	+	0.744306i	$0.267219\pi$
$374$		0			0
$375$	−0.207107	−	0.358719i	−0.0106949	−	0.0185242i
$376$		0			0
$377$	15.6569			0.806369
$378$		0			0
$379$	4.68629			0.240719			0.120359	−	0.992730i	$-0.461595\pi$
$379$	4.68629			0.240719			0.120359	+	0.992730i	$0.461595\pi$
$380$		0			0
$381$	−0.899495	−	1.55797i	−0.0460825	−	0.0798173i
$382$		0			0
$383$	−0.449747	+	0.778985i	−0.0229810	+	0.0398043i	−0.877287	−	0.479966i	$-0.840649\pi$
$383$	−0.449747	+	0.778985i	−0.0229810	+	0.0398043i	0.854306	+	0.519770i	$0.173982\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−9.75736	+	16.9002i	−0.495994	+	0.859088i
$388$		0			0
$389$	−2.65685	−	4.60181i	−0.134708	−	0.233321i	0.790778	−	0.612103i	$-0.209676\pi$
$389$	−2.65685	−	4.60181i	−0.134708	−	0.233321i	−0.925486	+	0.378782i	$0.876343\pi$
$390$		0			0
$391$	−42.7696			−2.16295
$392$		0			0
$393$	5.65685			0.285351
$394$		0			0
$395$	−2.00000	−	3.46410i	−0.100631	−	0.174298i
$396$		0			0
$397$	−12.3137	+	21.3280i	−0.618007	+	1.07042i	0.371842	+	0.928296i	$0.378726\pi$
$397$	−12.3137	+	21.3280i	−0.618007	+	1.07042i	−0.989849	+	0.142124i	$0.954607\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	16.1569	−	27.9845i	0.806835	−	1.39748i	−0.108211	−	0.994128i	$-0.534512\pi$
$401$	16.1569	−	27.9845i	0.806835	−	1.39748i	0.915045	−	0.403351i	$-0.132155\pi$
$402$		0			0
$403$	−0.828427	−	1.43488i	−0.0412669	−	0.0714764i
$404$		0			0
$405$	−7.48528			−0.371947
$406$		0			0
$407$	4.68629			0.232291
$408$		0			0
$409$	−12.5711	−	21.7737i	−0.621599	−	1.07664i	−0.989188	−	0.146653i	$-0.953150\pi$
$409$	−12.5711	−	21.7737i	−0.621599	−	1.07664i	0.367589	−	0.929988i	$-0.380183\pi$
$410$		0			0
$411$	−0.828427	+	1.43488i	−0.0408633	+	0.0707773i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	2.37868	−	4.11999i	0.116765	−	0.202243i
$416$		0			0
$417$	−0.514719	−	0.891519i	−0.0252059	−	0.0436579i
$418$		0			0
$419$	15.3137			0.748124			0.374062	−	0.927404i	$-0.377965\pi$
$419$	15.3137			0.748124			0.374062	+	0.927404i	$0.377965\pi$
$420$		0			0
$421$	27.3431			1.33262			0.666312	−	0.745673i	$-0.267872\pi$
$421$	27.3431			1.33262			0.666312	+	0.745673i	$0.267872\pi$
$422$		0			0
$423$	−16.4853	−	28.5533i	−0.801542	−	1.38831i
$424$		0			0
$425$	−3.82843	+	6.63103i	−0.185706	+	0.321652i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.343146	+	0.594346i	−0.0165672	+	0.0286953i
$430$		0			0
$431$	0.414214	+	0.717439i	0.0199520	+	0.0345578i	0.875829	−	0.482622i	$-0.160315\pi$
$431$	0.414214	+	0.717439i	0.0199520	+	0.0345578i	−0.855877	+	0.517179i	$0.826982\pi$
$432$		0			0
$433$	19.3137			0.928158			0.464079	−	0.885794i	$-0.346385\pi$
$433$	19.3137			0.928158			0.464079	+	0.885794i	$0.346385\pi$
$434$		0			0
$435$	−3.24264			−0.155473
$436$		0			0
$437$	15.7990	+	27.3647i	0.755768	+	1.30903i
$438$		0			0
$439$	−9.17157	+	15.8856i	−0.437735	+	0.758180i	−0.997514	−	0.0704621i	$-0.977553\pi$
$439$	−9.17157	+	15.8856i	−0.437735	+	0.758180i	0.559779	+	0.828642i	$0.310886\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.79289	−	13.4977i	0.370252	−	0.641294i	−0.619353	−	0.785113i	$-0.712605\pi$
$443$	7.79289	−	13.4977i	0.370252	−	0.641294i	0.989604	+	0.143819i	$0.0459382\pi$
$444$		0			0
$445$	2.67157	+	4.62730i	0.126645	+	0.219355i
$446$		0			0
$447$	−1.92893			−0.0912354
$448$		0			0
$449$	−7.48528			−0.353252			−0.176626	−	0.984278i	$-0.556518\pi$
$449$	−7.48528			−0.353252			−0.176626	+	0.984278i	$0.556518\pi$
$450$		0			0
$451$	2.41421	+	4.18154i	0.113681	+	0.196901i
$452$		0			0
$453$	−2.31371	+	4.00746i	−0.108708	+	0.188287i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−14.4853	+	25.0892i	−0.677593	+	1.17363i	0.298111	+	0.954531i	$0.403643\pi$
$457$	−14.4853	+	25.0892i	−0.677593	+	1.17363i	−0.975704	+	0.219094i	$0.929690\pi$
$458$		0			0
$459$	−9.24264	−	16.0087i	−0.431410	−	0.747223i
$460$		0			0
$461$	−1.31371			−0.0611855			−0.0305928	−	0.999532i	$-0.509739\pi$
$461$	−1.31371			−0.0611855			−0.0305928	+	0.999532i	$0.509739\pi$
$462$		0			0
$463$	14.8995			0.692438			0.346219	−	0.938154i	$-0.387465\pi$
$463$	14.8995			0.692438			0.346219	+	0.938154i	$0.387465\pi$
$464$		0			0
$465$	0.171573	+	0.297173i	0.00795650	+	0.0137811i
$466$		0			0
$467$	−18.9350	+	32.7964i	−0.876209	+	1.51764i	−0.0207390	+	0.999785i	$0.506602\pi$
$467$	−18.9350	+	32.7964i	−0.876209	+	1.51764i	−0.855470	+	0.517853i	$0.826731\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−0.272078	+	0.471253i	−0.0125367	+	0.0217142i
$472$		0			0
$473$	2.85786	+	4.94997i	0.131405	+	0.227600i
$474$		0			0
$475$	5.65685			0.259554
$476$		0			0
$477$	16.0000			0.732590
$478$		0			0
$479$	−0.757359	−	1.31178i	−0.0346046	−	0.0599370i	0.848204	−	0.529669i	$-0.177684\pi$
$479$	−0.757359	−	1.31178i	−0.0346046	−	0.0599370i	−0.882809	+	0.469732i	$0.844351\pi$
$480$		0			0
$481$	5.65685	−	9.79796i	0.257930	−	0.446748i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.00000	+	5.19615i	−0.136223	+	0.235945i
$486$		0			0
$487$	19.1421	+	33.1552i	0.867413	+	1.50240i	0.864631	+	0.502407i	$0.167552\pi$
$487$	19.1421	+	33.1552i	0.867413	+	1.50240i	0.00278182	+	0.999996i	$0.499115\pi$
$488$		0			0
$489$	6.48528			0.293275
$490$		0			0
$491$	1.51472			0.0683583			0.0341791	−	0.999416i	$-0.489118\pi$
$491$	1.51472			0.0683583			0.0341791	+	0.999416i	$0.489118\pi$
$492$		0			0
$493$	29.9706	+	51.9105i	1.34981	+	2.33793i
$494$		0			0
$495$	−1.17157	+	2.02922i	−0.0526583	+	0.0912068i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−22.0711	+	38.2282i	−0.988037	+	1.71133i	−0.360461	+	0.932774i	$0.617381\pi$
$499$	−22.0711	+	38.2282i	−0.988037	+	1.71133i	−0.627576	+	0.778555i	$0.715953\pi$
$500$		0			0
$501$	−0.428932	−	0.742932i	−0.0191633	−	0.0331918i
$502$		0			0
$503$	3.92893			0.175182			0.0875912	−	0.996157i	$-0.472083\pi$
$503$	3.92893			0.175182			0.0875912	+	0.996157i	$0.472083\pi$
$504$		0			0
$505$	−11.4853			−0.511088
$506$		0			0
$507$	−1.86396	−	3.22848i	−0.0827814	−	0.143382i
$508$		0			0
$509$	−16.7426	+	28.9991i	−0.742105	+	1.28536i	0.209431	+	0.977823i	$0.432839\pi$
$509$	−16.7426	+	28.9991i	−0.742105	+	1.28536i	−0.951535	+	0.307539i	$0.900494\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−6.82843	+	11.8272i	−0.301482	+	0.522183i
$514$		0			0
$515$	−3.79289	−	6.56948i	−0.167135	−	0.289486i
$516$		0			0
$517$	−9.65685			−0.424708
$518$		0			0
$519$	4.28427			0.188059
$520$		0			0
$521$	18.3137	+	31.7203i	0.802338	+	1.38969i	0.918073	+	0.396410i	$0.129744\pi$
$521$	18.3137	+	31.7203i	0.802338	+	1.38969i	−0.115735	+	0.993280i	$0.536922\pi$
$522$		0			0
$523$	13.9706	−	24.1977i	0.610890	−	1.05809i	−0.380201	−	0.924904i	$-0.624145\pi$
$523$	13.9706	−	24.1977i	0.610890	−	1.05809i	0.991091	−	0.133189i	$-0.0425216\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.17157	−	5.49333i	0.138156	−	0.239293i
$528$		0			0
$529$	−4.10051	−	7.10228i	−0.178283	−	0.308795i
$530$		0			0
$531$	−11.3137			−0.490973
$532$		0			0
$533$	11.6569			0.504914
$534$		0			0
$535$	−2.79289	−	4.83743i	−0.120747	−	0.209140i
$536$		0			0
$537$	−1.34315	+	2.32640i	−0.0579610	+	0.100391i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	11.7426	−	20.3389i	0.504856	−	0.874435i	−0.495129	−	0.868820i	$-0.664879\pi$
$541$	11.7426	−	20.3389i	0.504856	−	0.874435i	0.999984	−	0.00561582i	$-0.00178758\pi$
$542$		0			0
$543$	0.863961	+	1.49642i	0.0370761	+	0.0642177i
$544$		0			0
$545$	−18.3137			−0.784473
$546$		0			0
$547$	−2.27208			−0.0971470			−0.0485735	−	0.998820i	$-0.515468\pi$
$547$	−2.27208			−0.0971470			−0.0485735	+	0.998820i	$0.515468\pi$
$548$		0			0
$549$	−9.41421	−	16.3059i	−0.401789	−	0.695919i
$550$		0			0
$551$	22.1421	−	38.3513i	0.943287	−	1.63382i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−1.17157	+	2.02922i	−0.0497305	+	0.0861358i
$556$		0			0
$557$	8.65685	+	14.9941i	0.366803	+	0.635321i	0.989064	−	0.147489i	$-0.0471191\pi$
$557$	8.65685	+	14.9941i	0.366803	+	0.635321i	−0.622261	+	0.782810i	$0.713786\pi$
$558$		0			0
$559$	13.7990			0.583635
$560$		0			0
$561$	−2.62742			−0.110930
$562$		0			0
$563$	−2.03553	−	3.52565i	−0.0857875	−	0.148588i	0.819939	−	0.572451i	$-0.194007\pi$
$563$	−2.03553	−	3.52565i	−0.0857875	−	0.148588i	−0.905727	+	0.423863i	$0.860674\pi$
$564$		0			0
$565$	5.65685	−	9.79796i	0.237986	−	0.412203i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	18.3137	−	31.7203i	0.767751	−	1.32978i	−0.171029	−	0.985266i	$-0.554709\pi$
$569$	18.3137	−	31.7203i	0.767751	−	1.32978i	0.938780	−	0.344517i	$-0.111957\pi$
$570$		0			0
$571$	10.4853	+	18.1610i	0.438795	+	0.760016i	0.997597	−	0.0692856i	$-0.0220720\pi$
$571$	10.4853	+	18.1610i	0.438795	+	0.760016i	−0.558801	+	0.829301i	$0.688739\pi$
$572$		0			0
$573$	2.28427			0.0954268
$574$		0			0
$575$	−5.58579			−0.232943
$576$		0			0
$577$	−11.1421	−	19.2987i	−0.463853	−	0.803417i	0.535296	−	0.844665i	$-0.320200\pi$
$577$	−11.1421	−	19.2987i	−0.463853	−	0.803417i	−0.999149	+	0.0412474i	$0.986867\pi$
$578$		0			0
$579$	−1.10051	+	1.90613i	−0.0457354	+	0.0792161i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	2.34315	−	4.05845i	0.0970432	−	0.168084i
$584$		0			0
$585$	2.82843	+	4.89898i	0.116941	+	0.202548i
$586$		0			0
$587$	22.6863			0.936363			0.468182	−	0.883632i	$-0.344909\pi$
$587$	22.6863			0.936363			0.468182	+	0.883632i	$0.344909\pi$
$588$		0			0
$589$	−4.68629			−0.193095
$590$		0			0
$591$	0.0710678	+	0.123093i	0.00292334	+	0.00506337i
$592$		0			0
$593$	14.9706	−	25.9298i	0.614767	−	1.06481i	−0.375658	−	0.926758i	$-0.622583\pi$
$593$	14.9706	−	25.9298i	0.614767	−	1.06481i	0.990425	−	0.138050i	$-0.0440834\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	4.82843	−	8.36308i	0.197614	−	0.342278i
$598$		0			0
$599$	−21.3137	−	36.9164i	−0.870855	−	1.50836i	−0.861114	−	0.508412i	$-0.830233\pi$
$599$	−21.3137	−	36.9164i	−0.870855	−	1.50836i	−0.00974040	−	0.999953i	$-0.503101\pi$
$600$		0			0
$601$	34.0000			1.38689			0.693444	−	0.720510i	$-0.256092\pi$
$601$	34.0000			1.38689			0.693444	+	0.720510i	$0.256092\pi$
$602$		0			0
$603$	36.4853			1.48580
$604$		0			0
$605$	−5.15685	−	8.93193i	−0.209656	−	0.363135i
$606$		0			0
$607$	13.6213	−	23.5928i	0.552872	−	0.957603i	−0.445193	−	0.895434i	$-0.646865\pi$
$607$	13.6213	−	23.5928i	0.552872	−	0.957603i	0.998066	−	0.0621685i	$-0.0198016\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−11.6569	+	20.1903i	−0.471586	+	0.816811i
$612$		0			0
$613$	−19.4853	−	33.7495i	−0.787003	−	1.36313i	−0.927795	−	0.373090i	$-0.878298\pi$
$613$	−19.4853	−	33.7495i	−0.787003	−	1.36313i	0.140792	−	0.990039i	$-0.455035\pi$
$614$		0			0
$615$	−2.41421			−0.0973505
$616$		0			0
$617$	−12.6863			−0.510731			−0.255365	−	0.966845i	$-0.582196\pi$
$617$	−12.6863			−0.510731			−0.255365	+	0.966845i	$0.582196\pi$
$618$		0			0
$619$	19.7279	+	34.1698i	0.792932	+	1.37340i	0.924144	+	0.382044i	$0.124780\pi$
$619$	19.7279	+	34.1698i	0.792932	+	1.37340i	−0.131212	+	0.991354i	$0.541887\pi$
$620$		0			0
$621$	6.74264	−	11.6786i	0.270573	−	0.468646i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	0.970563	+	1.68106i	0.0387605	+	0.0671352i
$628$		0			0
$629$	43.3137			1.72703
$630$		0			0
$631$	−1.51472			−0.0603000			−0.0301500	−	0.999545i	$-0.509598\pi$
$631$	−1.51472			−0.0603000			−0.0301500	+	0.999545i	$0.509598\pi$
$632$		0			0
$633$	5.51472	+	9.55177i	0.219190	+	0.379649i
$634$		0			0
$635$	−2.17157	+	3.76127i	−0.0861762	+	0.149262i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−16.9706	+	29.3939i	−0.671345	+	1.16280i
$640$		0			0
$641$	−7.05635	−	12.2220i	−0.278709	−	0.482738i	0.692355	−	0.721557i	$-0.256573\pi$
$641$	−7.05635	−	12.2220i	−0.278709	−	0.482738i	−0.971064	+	0.238819i	$0.923240\pi$
$642$		0			0
$643$	−26.0000			−1.02534			−0.512670	−	0.858586i	$-0.671344\pi$
$643$	−26.0000			−1.02534			−0.512670	+	0.858586i	$0.671344\pi$
$644$		0			0
$645$	−2.85786			−0.112528
$646$		0			0
$647$	−10.3787	−	17.9764i	−0.408028	−	0.706725i	0.586641	−	0.809847i	$-0.300450\pi$
$647$	−10.3787	−	17.9764i	−0.408028	−	0.706725i	−0.994669	+	0.103122i	$0.967117\pi$
$648$		0			0
$649$	−1.65685	+	2.86976i	−0.0650372	+	0.112648i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	7.82843	−	13.5592i	0.306350	−	0.530614i	−0.671211	−	0.741266i	$-0.734226\pi$
$653$	7.82843	−	13.5592i	0.306350	−	0.530614i	0.977561	+	0.210653i	$0.0675589\pi$
$654$		0			0
$655$	−6.82843	−	11.8272i	−0.266809	−	0.462126i
$656$		0			0
$657$	10.3431			0.403525
$658$		0			0
$659$	12.6863			0.494188			0.247094	−	0.968992i	$-0.420524\pi$
$659$	12.6863			0.494188			0.247094	+	0.968992i	$0.420524\pi$
$660$		0			0
$661$	−25.1569	−	43.5729i	−0.978488	−	1.69479i	−0.667907	−	0.744244i	$-0.732810\pi$
$661$	−25.1569	−	43.5729i	−0.978488	−	1.69479i	−0.310581	−	0.950547i	$-0.600524\pi$
$662$		0			0
$663$	−3.17157	+	5.49333i	−0.123174	+	0.213343i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−21.8640	+	37.8695i	−0.846576	+	1.46631i
$668$		0			0
$669$	3.10051	+	5.37023i	0.119872	+	0.207625i
$670$		0			0
$671$	−5.51472			−0.212893
$672$		0			0
$673$	−5.65685			−0.218056			−0.109028	−	0.994039i	$-0.534774\pi$
$673$	−5.65685			−0.218056			−0.109028	+	0.994039i	$0.534774\pi$
$674$		0			0
$675$	−1.20711	−	2.09077i	−0.0464616	−	0.0804738i
$676$		0			0
$677$	11.4853	−	19.8931i	0.441415	−	0.764554i	−0.556380	−	0.830928i	$-0.687810\pi$
$677$	11.4853	−	19.8931i	0.441415	−	0.764554i	0.997795	+	0.0663747i	$0.0211433\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−2.89949	+	5.02207i	−0.111109	+	0.192446i
$682$		0			0
$683$	0.964466	+	1.67050i	0.0369043	+	0.0639201i	0.883888	−	0.467699i	$-0.154917\pi$
$683$	0.964466	+	1.67050i	0.0369043	+	0.0639201i	−0.846983	+	0.531619i	$0.821584\pi$
$684$		0			0
$685$	4.00000			0.152832
$686$		0			0
$687$	−5.79899			−0.221245
$688$		0			0
$689$	−5.65685	−	9.79796i	−0.215509	−	0.373273i
$690$		0			0
$691$	−21.3848	+	37.0395i	−0.813515	+	1.40905i	0.0968739	+	0.995297i	$0.469116\pi$
$691$	−21.3848	+	37.0395i	−0.813515	+	1.40905i	−0.910389	+	0.413753i	$0.864218\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.24264	+	2.15232i	−0.0471360	+	0.0816420i
$696$		0			0
$697$	22.3137	+	38.6485i	0.845192	+	1.46392i
$698$		0			0
$699$	−4.82843			−0.182628
$700$		0			0
$701$	−11.0000			−0.415464			−0.207732	−	0.978186i	$-0.566608\pi$
$701$	−11.0000			−0.415464			−0.207732	+	0.978186i	$0.566608\pi$
$702$		0			0
$703$	−16.0000	−	27.7128i	−0.603451	−	1.04521i
$704$		0			0
$705$	2.41421	−	4.18154i	0.0909245	−	0.157486i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	17.7132	−	30.6802i	0.665233	−	1.15222i	−0.313989	−	0.949427i	$-0.601665\pi$
$709$	17.7132	−	30.6802i	0.665233	−	1.15222i	0.979222	−	0.202791i	$-0.0650013\pi$
$710$		0			0
$711$	−5.65685	−	9.79796i	−0.212149	−	0.367452i
$712$		0			0
$713$	4.62742			0.173298
$714$		0			0
$715$	1.65685			0.0619628
$716$		0			0
$717$	−6.31371	−	10.9357i	−0.235790	−	0.408400i
$718$		0			0
$719$	−12.8995	+	22.3426i	−0.481070	+	0.833238i	−0.999764	−	0.0217223i	$-0.993085\pi$
$719$	−12.8995	+	22.3426i	−0.481070	+	0.833238i	0.518694	+	0.854960i	$0.326418\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	2.07107	−	3.58719i	0.0770238	−	0.133409i
$724$		0			0
$725$	3.91421	+	6.77962i	0.145370	+	0.251789i
$726$		0			0
$727$	−38.0711			−1.41198			−0.705989	−	0.708223i	$-0.749497\pi$
$727$	−38.0711			−1.41198			−0.705989	+	0.708223i	$0.749497\pi$
$728$		0			0
$729$	−18.1716			−0.673021
$730$		0			0
$731$	26.4142	+	45.7508i	0.976965	+	1.69215i
$732$		0			0
$733$	3.82843	−	6.63103i	0.141406	−	0.244923i	−0.786620	−	0.617437i	$-0.788171\pi$
$733$	3.82843	−	6.63103i	0.141406	−	0.244923i	0.928026	+	0.372514i	$0.121504\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.34315	−	9.25460i	0.196817	−	0.340898i
$738$		0			0
$739$	−8.41421	−	14.5738i	−0.309522	−	0.536108i	0.668736	−	0.743500i	$-0.266836\pi$
$739$	−8.41421	−	14.5738i	−0.309522	−	0.536108i	−0.978258	+	0.207392i	$0.933502\pi$
$740$		0			0
$741$	4.68629			0.172155
$742$		0			0
$743$	−10.7574			−0.394649			−0.197325	−	0.980338i	$-0.563225\pi$
$743$	−10.7574			−0.394649			−0.197325	+	0.980338i	$0.563225\pi$
$744$		0			0
$745$	2.32843	+	4.03295i	0.0853070	+	0.147756i
$746$		0			0
$747$	6.72792	−	11.6531i	0.246162	−	0.426365i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	6.00000	−	10.3923i	0.218943	−	0.379221i	−0.735542	−	0.677479i	$-0.763072\pi$
$751$	6.00000	−	10.3923i	0.218943	−	0.379221i	0.954485	+	0.298259i	$0.0964058\pi$
$752$		0			0
$753$	5.68629	+	9.84895i	0.207220	+	0.358916i
$754$		0			0
$755$	11.1716			0.406575
$756$		0			0
$757$	6.00000			0.218074			0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000			0.218074			0.109037	+	0.994038i	$0.465223\pi$
$758$		0			0
$759$	−0.958369	−	1.65994i	−0.0347866	−	0.0602522i
$760$		0			0
$761$	−21.9706	+	38.0541i	−0.796432	+	1.37946i	0.125493	+	0.992094i	$0.459949\pi$
$761$	−21.9706	+	38.0541i	−0.796432	+	1.37946i	−0.921926	+	0.387367i	$0.873385\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−10.8284	+	18.7554i	−0.391503	+	0.678102i
$766$		0			0
$767$	4.00000	+	6.92820i	0.144432	+	0.250163i
$768$		0			0
$769$	−43.2548			−1.55981			−0.779905	−	0.625898i	$-0.784732\pi$
$769$	−43.2548			−1.55981			−0.779905	+	0.625898i	$0.784732\pi$
$770$		0			0
$771$	6.34315			0.228443
$772$		0			0
$773$	12.1716	+	21.0818i	0.437781	+	0.758259i	0.997518	−	0.0704113i	$-0.0224312\pi$
$773$	12.1716	+	21.0818i	0.437781	+	0.758259i	−0.559737	+	0.828670i	$0.689098\pi$
$774$		0			0
$775$	0.414214	−	0.717439i	0.0148790	−	0.0257712i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	16.4853	−	28.5533i	0.590647	−	1.02303i
$780$		0			0
$781$	4.97056	+	8.60927i	0.177861	+	0.308064i
$782$		0			0
$783$	−18.8995			−0.675413
$784$		0			0
$785$	1.31371			0.0468883
$786$		0			0
$787$	−0.792893	−	1.37333i	−0.0282636	−	0.0489540i	0.851548	−	0.524277i	$-0.175664\pi$
$787$	−0.792893	−	1.37333i	−0.0282636	−	0.0489540i	−0.879811	+	0.475323i	$0.842331\pi$
$788$		0			0
$789$	−3.25736	+	5.64191i	−0.115965	+	0.200857i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−6.65685	+	11.5300i	−0.236392	+	0.409443i
$794$		0			0
$795$	1.17157	+	2.02922i	0.0415514	+	0.0719691i
$796$		0			0
$797$	35.3137			1.25088			0.625438	−	0.780274i	$-0.284920\pi$
$797$	35.3137			1.25088			0.625438	+	0.780274i	$0.284920\pi$
$798$		0			0
$799$	−89.2548			−3.15761
$800$		0			0
$801$	7.55635	+	13.0880i	0.266990	+	0.462441i
$802$		0			0
$803$	1.51472	−	2.62357i	0.0534533	−	0.0925838i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.37868	−	2.38794i	0.0485318	−	0.0840596i
$808$		0			0
$809$	17.9853	+	31.1514i	0.632329	+	1.09523i	0.987074	+	0.160263i	$0.0512342\pi$
$809$	17.9853	+	31.1514i	0.632329	+	1.09523i	−0.354746	+	0.934963i	$0.615433\pi$
$810$		0			0
$811$	−52.1421			−1.83096			−0.915479	−	0.402366i	$-0.868188\pi$
$811$	−52.1421			−1.83096			−0.915479	+	0.402366i	$0.868188\pi$
$812$		0			0
$813$	−1.37258			−0.0481386
$814$		0			0
$815$	−7.82843	−	13.5592i	−0.274218	−	0.474959i
$816$		0			0
$817$	19.5147	−	33.8005i	0.682734	−	1.18253i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	16.3137	−	28.2562i	0.569352	−	0.986147i	−0.427278	−	0.904120i	$-0.640527\pi$
$821$	16.3137	−	28.2562i	0.569352	−	0.986147i	0.996630	−	0.0820268i	$-0.0261393\pi$
$822$		0			0
$823$	−15.0061	−	25.9913i	−0.523080	−	0.906001i	−0.999639	−	0.0268584i	$-0.991450\pi$
$823$	−15.0061	−	25.9913i	−0.523080	−	0.906001i	0.476560	−	0.879142i	$-0.341884\pi$
$824$		0			0
$825$	−0.343146			−0.0119468
$826$		0			0
$827$	13.5269			0.470377			0.235188	−	0.971950i	$-0.424429\pi$
$827$	13.5269			0.470377			0.235188	+	0.971950i	$0.424429\pi$
$828$		0			0
$829$	2.65685	+	4.60181i	0.0922764	+	0.159827i	0.908469	−	0.417953i	$-0.137252\pi$
$829$	2.65685	+	4.60181i	0.0922764	+	0.159827i	−0.816192	+	0.577780i	$0.803919\pi$
$830$		0			0
$831$	5.92893	−	10.2692i	0.205672	−	0.356235i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.03553	+	1.79360i	−0.0358361	+	0.0620700i
$836$		0			0
$837$	1.00000	+	1.73205i	0.0345651	+	0.0598684i
$838$		0			0
$839$	−20.1421			−0.695384			−0.347692	−	0.937609i	$-0.613034\pi$
$839$	−20.1421			−0.695384			−0.347692	+	0.937609i	$0.613034\pi$
$840$		0			0
$841$	32.2843			1.11325
$842$		0			0
$843$	0.556349	+	0.963625i	0.0191617	+	0.0331890i
$844$		0			0
$845$	−4.50000	+	7.79423i	−0.154805	+	0.268130i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−3.72792	+	6.45695i	−0.127942	+	0.221602i
$850$		0			0
$851$	15.7990	+	27.3647i	0.541582	+	0.938048i
$852$		0			0
$853$	−12.6863			−0.434370			−0.217185	−	0.976130i	$-0.569688\pi$
$853$	−12.6863			−0.434370			−0.217185	+	0.976130i	$0.569688\pi$
$854$		0			0
$855$	16.0000			0.547188
$856$		0			0
$857$	−9.48528	−	16.4290i	−0.324011	−	0.561204i	0.657301	−	0.753628i	$-0.271698\pi$
$857$	−9.48528	−	16.4290i	−0.324011	−	0.561204i	−0.981312	+	0.192425i	$0.938365\pi$
$858$		0			0
$859$	−15.3137	+	26.5241i	−0.522497	+	0.904991i	0.477160	+	0.878816i	$0.341666\pi$
$859$	−15.3137	+	26.5241i	−0.522497	+	0.904991i	−0.999657	+	0.0261751i	$0.991667\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	28.0061	−	48.5080i	0.953339	−	1.65123i	0.215214	−	0.976567i	$-0.430955\pi$
$863$	28.0061	−	48.5080i	0.953339	−	1.65123i	0.738125	−	0.674664i	$-0.235711\pi$
$864$		0			0
$865$	−5.17157	−	8.95743i	−0.175839	−	0.304562i
$866$		0			0
$867$	−17.2426			−0.585591
$868$		0			0
$869$	−3.31371			−0.112410
$870$		0			0
$871$	−12.8995	−	22.3426i	−0.437083	−	0.757049i
$872$		0			0
$873$	−8.48528	+	14.6969i	−0.287183	+	0.497416i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	14.1421	−	24.4949i	0.477546	−	0.827134i	−0.522123	−	0.852870i	$-0.674860\pi$
$877$	14.1421	−	24.4949i	0.477546	−	0.827134i	0.999669	+	0.0257364i	$0.00819306\pi$
$878$		0			0
$879$	−3.51472	−	6.08767i	−0.118549	−	0.205332i
$880$		0			0
$881$	26.4558			0.891320			0.445660	−	0.895202i	$-0.352969\pi$
$881$	26.4558			0.891320			0.445660	+	0.895202i	$0.352969\pi$
$882$		0			0
$883$	6.68629			0.225012			0.112506	−	0.993651i	$-0.464112\pi$
$883$	6.68629			0.225012			0.112506	+	0.993651i	$0.464112\pi$
$884$		0			0
$885$	−0.828427	−	1.43488i	−0.0278473	−	0.0482329i
$886$		0			0
$887$	8.79289	−	15.2297i	0.295236	−	0.511365i	−0.679803	−	0.733394i	$-0.737935\pi$
$887$	8.79289	−	15.2297i	0.295236	−	0.511365i	0.975040	+	0.222030i	$0.0712682\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−3.10051	+	5.37023i	−0.103871	+	0.179910i
$892$		0			0
$893$	32.9706	+	57.1067i	1.10332	+	1.91100i
$894$		0			0
$895$	6.48528			0.216779
$896$		0			0
$897$	−4.62742			−0.154505
$898$		0			0
$899$	−3.24264	−	5.61642i	−0.108148	−	0.187318i
$900$		0			0
$901$	21.6569	−	37.5108i	0.721494	−	1.24966i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.08579	−	3.61269i	0.0693339	−	0.120090i
$906$		0			0
$907$	−23.1066	−	40.0218i	−0.767242	−	1.32890i	−0.939053	−	0.343772i	$-0.888295\pi$
$907$	−23.1066	−	40.0218i	−0.767242	−	1.32890i	0.171811	−	0.985130i	$-0.445038\pi$
$908$		0			0
$909$	−32.4853			−1.07747
$910$		0			0
$911$	−18.4853			−0.612445			−0.306222	−	0.951960i	$-0.599065\pi$
$911$	−18.4853			−0.612445			−0.306222	+	0.951960i	$0.599065\pi$
$912$		0			0
$913$	−1.97056	−	3.41311i	−0.0652161	−	0.112958i
$914$		0			0
$915$	1.37868	−	2.38794i	0.0455777	−	0.0789430i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	16.6274	−	28.7995i	0.548488	−	0.950009i	−0.449891	−	0.893084i	$-0.648537\pi$
$919$	16.6274	−	28.7995i	0.548488	−	0.950009i	0.998378	−	0.0569252i	$-0.0181296\pi$
$920$		0			0
$921$	−0.985281	−	1.70656i	−0.0324661	−	0.0562330i
$922$		0			0
$923$	24.0000			0.789970
$924$		0			0
$925$	5.65685			0.185996
$926$		0			0
$927$	−10.7279	−	18.5813i	−0.352351	−	0.610290i
$928$		0			0
$929$	4.60051	−	7.96831i	0.150938	−	0.261432i	−0.780635	−	0.624988i	$-0.785104\pi$
$929$	4.60051	−	7.96831i	0.150938	−	0.261432i	0.931572	+	0.363556i	$0.118437\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−4.48528	+	7.76874i	−0.146842	+	0.254337i
$934$		0			0
$935$	3.17157	+	5.49333i	0.103722	+	0.179651i
$936$		0			0
$937$	−18.6274			−0.608531			−0.304266	−	0.952587i	$-0.598411\pi$
$937$	−18.6274			−0.608531			−0.304266	+	0.952587i	$0.598411\pi$
$938$		0			0
$939$	8.68629			0.283466
$940$		0			0
$941$	−5.00000	−	8.66025i	−0.162995	−	0.282316i	0.772946	−	0.634472i	$-0.218782\pi$
$941$	−5.00000	−	8.66025i	−0.162995	−	0.282316i	−0.935942	+	0.352155i	$0.885449\pi$
$942$		0			0
$943$	−16.2782	+	28.1946i	−0.530090	+	0.918143i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−5.55025	+	9.61332i	−0.180359	+	0.312391i	−0.942003	−	0.335605i	$-0.891059\pi$
$947$	−5.55025	+	9.61332i	−0.180359	+	0.312391i	0.761644	+	0.647996i	$0.224393\pi$
$948$		0			0
$949$	−3.65685	−	6.33386i	−0.118707	−	0.205606i
$950$		0			0
$951$	9.11270			0.295499
$952$		0			0
$953$	−54.6274			−1.76956			−0.884778	−	0.466013i	$-0.845690\pi$
$953$	−54.6274			−1.76956			−0.884778	+	0.466013i	$0.845690\pi$
$954$		0			0
$955$	−2.75736	−	4.77589i	−0.0892261	−	0.154544i
$956$		0			0
$957$	−1.34315	+	2.32640i	−0.0434177	+	0.0752017i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	15.1569	−	26.2524i	0.488931	−	0.846853i
$962$		0			0
$963$	−7.89949	−	13.6823i	−0.254558	−	0.440907i
$964$		0			0
$965$	5.31371			0.171054
$966$		0			0
$967$	−24.7574			−0.796143			−0.398072	−	0.917354i	$-0.630320\pi$
$967$	−24.7574			−0.796143			−0.398072	+	0.917354i	$0.630320\pi$
$968$		0			0
$969$	8.97056	+	15.5375i	0.288176	+	0.499135i
$970$		0			0
$971$	4.00000	−	6.92820i	0.128366	−	0.222337i	−0.794678	−	0.607032i	$-0.792360\pi$
$971$	4.00000	−	6.92820i	0.128366	−	0.222337i	0.923044	+	0.384695i	$0.125693\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−0.414214	+	0.717439i	−0.0132655	+	0.0229764i
$976$		0			0
$977$	−15.1421	−	26.2269i	−0.484440	−	0.839074i	0.515400	−	0.856949i	$-0.327643\pi$
$977$	−15.1421	−	26.2269i	−0.484440	−	0.839074i	−0.999840	+	0.0178751i	$0.994310\pi$
$978$		0			0
$979$	4.42641			0.141469
$980$		0			0
$981$	−51.7990			−1.65381
$982$		0			0
$983$	−20.6924	−	35.8403i	−0.659985	−	1.14313i	−0.980619	−	0.195924i	$-0.937229\pi$
$983$	−20.6924	−	35.8403i	−0.659985	−	1.14313i	0.320634	−	0.947203i	$-0.396104\pi$
$984$		0			0
$985$	0.171573	−	0.297173i	0.00546677	−	0.00946872i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−19.2696	+	33.3758i	−0.612736	+	1.06129i
$990$		0			0
$991$	−2.41421	−	4.18154i	−0.0766900	−	0.132831i	0.825130	−	0.564943i	$-0.191102\pi$
$991$	−2.41421	−	4.18154i	−0.0766900	−	0.132831i	−0.901820	+	0.432112i	$0.857769\pi$
$992$		0			0
$993$	−10.9706			−0.348140
$994$		0			0
$995$	−23.3137			−0.739094
$996$		0			0
$997$	−7.17157	−	12.4215i	−0.227126	−	0.393394i	0.729829	−	0.683630i	$-0.239600\pi$
$997$	−7.17157	−	12.4215i	−0.227126	−	0.393394i	−0.956955	+	0.290236i	$0.906266\pi$
$998$		0			0
$999$	−6.82843	+	11.8272i	−0.216042	+	0.374196i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.2.q.q.961.2		4
7.2	even	3		1960.2.a.t.1.1		2
7.3	odd	6		280.2.q.d.81.1	✓	4
7.4	even	3	inner	1960.2.q.q.361.2		4
7.5	odd	6		1960.2.a.p.1.2		2
7.6	odd	2		280.2.q.d.121.1	yes	4
21.17	even	6		2520.2.bi.k.361.2		4
21.20	even	2		2520.2.bi.k.1801.2		4
28.3	even	6		560.2.q.j.81.2		4
28.19	even	6		3920.2.a.bz.1.1		2
28.23	odd	6		3920.2.a.bp.1.2		2
28.27	even	2		560.2.q.j.401.2		4
35.3	even	12		1400.2.bh.g.249.2		8
35.9	even	6		9800.2.a.br.1.2		2
35.13	even	4		1400.2.bh.g.849.3		8
35.17	even	12		1400.2.bh.g.249.3		8
35.19	odd	6		9800.2.a.bz.1.1		2
35.24	odd	6		1400.2.q.h.1201.2		4
35.27	even	4		1400.2.bh.g.849.2		8
35.34	odd	2		1400.2.q.h.401.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.d.81.1	✓	4	7.3	odd	6
280.2.q.d.121.1	yes	4	7.6	odd	2
560.2.q.j.81.2		4	28.3	even	6
560.2.q.j.401.2		4	28.27	even	2
1400.2.q.h.401.2		4	35.34	odd	2
1400.2.q.h.1201.2		4	35.24	odd	6
1400.2.bh.g.249.2		8	35.3	even	12
1400.2.bh.g.249.3		8	35.17	even	12
1400.2.bh.g.849.2		8	35.27	even	4
1400.2.bh.g.849.3		8	35.13	even	4
1960.2.a.p.1.2		2	7.5	odd	6
1960.2.a.t.1.1		2	7.2	even	3
1960.2.q.q.361.2		4	7.4	even	3	inner
1960.2.q.q.961.2		4	1.1	even	1	trivial
2520.2.bi.k.361.2		4	21.17	even	6
2520.2.bi.k.1801.2		4	21.20	even	2
3920.2.a.bp.1.2		2	28.23	odd	6
3920.2.a.bz.1.1		2	28.19	even	6
9800.2.a.br.1.2		2	35.9	even	6
9800.2.a.bz.1.1		2	35.19	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:	\( N \)	\(=\)	\( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1960.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.207107 + 0.358719i) q^{3} +(0.500000 - 0.866025i) q^{5} +(1.41421 - 2.44949i) q^{9} +O(q^{10})\)	\(q+(0.207107 + 0.358719i) q^{3} +(0.500000 - 0.866025i) q^{5} +(1.41421 - 2.44949i) q^{9} +(-0.414214 - 0.717439i) q^{11} -2.00000 q^{13} +0.414214 q^{15} +(-3.82843 - 6.63103i) q^{17} +(-2.82843 + 4.89898i) q^{19} +(2.79289 - 4.83743i) q^{23} +(-0.500000 - 0.866025i) q^{25} +2.41421 q^{27} -7.82843 q^{29} +(0.414214 + 0.717439i) q^{31} +(0.171573 - 0.297173i) q^{33} +(-2.82843 + 4.89898i) q^{37} +(-0.414214 - 0.717439i) q^{39} -5.82843 q^{41} -6.89949 q^{43} +(-1.41421 - 2.44949i) q^{45} +(5.82843 - 10.0951i) q^{47} +(1.58579 - 2.74666i) q^{51} +(2.82843 + 4.89898i) q^{53} -0.828427 q^{55} -2.34315 q^{57} +(-2.00000 - 3.46410i) q^{59} +(3.32843 - 5.76500i) q^{61} +(-1.00000 + 1.73205i) q^{65} +(6.44975 + 11.1713i) q^{67} +2.31371 q^{69} -12.0000 q^{71} +(1.82843 + 3.16693i) q^{73} +(0.207107 - 0.358719i) q^{75} +(2.00000 - 3.46410i) q^{79} +(-3.74264 - 6.48244i) q^{81} +4.75736 q^{83} -7.65685 q^{85} +(-1.62132 - 2.80821i) q^{87} +(-2.67157 + 4.62730i) q^{89} +(-0.171573 + 0.297173i) q^{93} +(2.82843 + 4.89898i) q^{95} -6.00000 q^{97} -2.34315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{5}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^5	\( 4 q - 2 q^{3} + 2 q^{5} + 4 q^{11} - 8 q^{13} - 4 q^{15} - 4 q^{17} + 14 q^{23} - 2 q^{25} + 4 q^{27} - 20 q^{29} - 4 q^{31} + 12 q^{33} + 4 q^{39} - 12 q^{41} + 12 q^{43} + 12 q^{47} + 12 q^{51} + 8 q^{55} - 32 q^{57} - 8 q^{59} + 2 q^{61} - 4 q^{65} + 6 q^{67} - 36 q^{69} - 48 q^{71} - 4 q^{73} - 2 q^{75} + 8 q^{79} + 2 q^{81} + 36 q^{83} - 8 q^{85} + 2 q^{87} - 22 q^{89} - 12 q^{93} - 24 q^{97} - 32 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^5 + 4 * q^11 - 8 * q^13 - 4 * q^15 - 4 * q^17 + 14 * q^23 - 2 * q^25 + 4 * q^27 - 20 * q^29 - 4 * q^31 + 12 * q^33 + 4 * q^39 - 12 * q^41 + 12 * q^43 + 12 * q^47 + 12 * q^51 + 8 * q^55 - 32 * q^57 - 8 * q^59 + 2 * q^61 - 4 * q^65 + 6 * q^67 - 36 * q^69 - 48 * q^71 - 4 * q^73 - 2 * q^75 + 8 * q^79 + 2 * q^81 + 36 * q^83 - 8 * q^85 + 2 * q^87 - 22 * q^89 - 12 * q^93 - 24 * q^97 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more