LMFDB - Embedded newform 1960.2.q.s.961.1

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:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
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			961.1
Root			$1.28078 + 2.21837i$ of defining polynomial
Character	$\chi$	$=$	1960.961
Dual form			1960.2.q.s.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28078 - 2.21837i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-1.78078 + 3.08440i) q^{9} +O(q^{10})$	\(q+(-1.28078 - 2.21837i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-1.78078 + 3.08440i) q^{9} +(1.28078 + 2.21837i) q^{11} -5.68466 q^{13} +2.56155 q^{15} +(-1.71922 - 2.97778i) q^{17} +(-0.561553 + 0.972638i) q^{19} +(2.56155 - 4.43674i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.43845 q^{27} +4.56155 q^{29} +(5.12311 + 8.87348i) q^{31} +(3.28078 - 5.68247i) q^{33} +(-4.12311 + 7.14143i) q^{37} +(7.28078 + 12.6107i) q^{39} +7.12311 q^{41} +1.12311 q^{43} +(-1.78078 - 3.08440i) q^{45} +(-3.28078 + 5.68247i) q^{47} +(-4.40388 + 7.62775i) q^{51} +(2.43845 + 4.22351i) q^{53} -2.56155 q^{55} +2.87689 q^{57} +(2.00000 + 3.46410i) q^{59} +(7.56155 - 13.0970i) q^{61} +(2.84233 - 4.92306i) q^{65} +(7.12311 + 12.3376i) q^{67} -13.1231 q^{69} +(-6.12311 - 10.6055i) q^{73} +(-1.28078 + 2.21837i) q^{75} +(5.84233 - 10.1192i) q^{79} +(3.50000 + 6.06218i) q^{81} +12.0000 q^{83} +3.43845 q^{85} +(-5.84233 - 10.1192i) q^{87} +(1.56155 - 2.70469i) q^{89} +(13.1231 - 22.7299i) q^{93} +(-0.561553 - 0.972638i) q^{95} +13.6847 q^{97} -9.12311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} - 2 q^{5} - 3 q^{9}+O(q^{10}) $ 4 * q - q^3 - 2 * q^5 - 3 * q^9	$ 4 q - q^{3} - 2 q^{5} - 3 q^{9} + q^{11} + 2 q^{13} + 2 q^{15} - 11 q^{17} + 6 q^{19} + 2 q^{23} - 2 q^{25} + 14 q^{27} + 10 q^{29} + 4 q^{31} + 9 q^{33} + 25 q^{39} + 12 q^{41} - 12 q^{43} - 3 q^{45} - 9 q^{47} + 3 q^{51} + 18 q^{53} - 2 q^{55} + 28 q^{57} + 8 q^{59} + 22 q^{61} - q^{65} + 12 q^{67} - 36 q^{69} - 8 q^{73} - q^{75} + 11 q^{79} + 14 q^{81} + 48 q^{83} + 22 q^{85} - 11 q^{87} - 2 q^{89} + 36 q^{93} + 6 q^{95} + 30 q^{97} - 20 q^{99}+O(q^{100}) $ 4 * q - q^3 - 2 * q^5 - 3 * q^9 + q^11 + 2 * q^13 + 2 * q^15 - 11 * q^17 + 6 * q^19 + 2 * q^23 - 2 * q^25 + 14 * q^27 + 10 * q^29 + 4 * q^31 + 9 * q^33 + 25 * q^39 + 12 * q^41 - 12 * q^43 - 3 * q^45 - 9 * q^47 + 3 * q^51 + 18 * q^53 - 2 * q^55 + 28 * q^57 + 8 * q^59 + 22 * q^61 - q^65 + 12 * q^67 - 36 * q^69 - 8 * q^73 - q^75 + 11 * q^79 + 14 * q^81 + 48 * q^83 + 22 * q^85 - 11 * q^87 - 2 * q^89 + 36 * q^93 + 6 * q^95 + 30 * q^97 - 20 * 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
$3$	−1.28078	−	2.21837i	−0.739457	−	1.28078i	−0.952740	−	0.303786i	$-0.901749\pi$
$3$	−1.28078	−	2.21837i	−0.739457	−	1.28078i	0.213284	−	0.976990i	$-0.431584\pi$
$4$		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
$9$	−1.78078	+	3.08440i	−0.593592	+	1.02813i
$10$		0			0
$11$	1.28078	+	2.21837i	0.386169	+	0.668864i	0.991931	−	0.126782i	$-0.0404650\pi$
$11$	1.28078	+	2.21837i	0.386169	+	0.668864i	−0.605762	+	0.795646i	$0.707132\pi$
$12$		0			0
$13$	−5.68466			−1.57664			−0.788320	−	0.615265i	$-0.789049\pi$
$13$	−5.68466			−1.57664			−0.788320	+	0.615265i	$0.789049\pi$
$14$		0			0
$15$	2.56155			0.661390
$16$		0			0
$17$	−1.71922	−	2.97778i	−0.416973	−	0.722218i	0.578660	−	0.815569i	$-0.303576\pi$
$17$	−1.71922	−	2.97778i	−0.416973	−	0.722218i	−0.995633	+	0.0933503i	$0.970242\pi$
$18$		0			0
$19$	−0.561553	+	0.972638i	−0.128829	+	0.223138i	−0.923223	−	0.384264i	$-0.874455\pi$
$19$	−0.561553	+	0.972638i	−0.128829	+	0.223138i	0.794394	+	0.607403i	$0.207789\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.56155	−	4.43674i	0.534121	−	0.925124i	−0.465085	−	0.885266i	$-0.653976\pi$
$23$	2.56155	−	4.43674i	0.534121	−	0.925124i	0.999205	−	0.0398580i	$-0.0126905\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	1.43845			0.276829
$28$		0			0
$29$	4.56155			0.847059			0.423530	−	0.905882i	$-0.360791\pi$
$29$	4.56155			0.847059			0.423530	+	0.905882i	$0.360791\pi$
$30$		0			0
$31$	5.12311	+	8.87348i	0.920137	+	1.59372i	0.799201	+	0.601064i	$0.205256\pi$
$31$	5.12311	+	8.87348i	0.920137	+	1.59372i	0.120936	+	0.992660i	$0.461411\pi$
$32$		0			0
$33$	3.28078	−	5.68247i	0.571110	−	0.989191i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.12311	+	7.14143i	−0.677834	+	1.17404i	0.297797	+	0.954629i	$0.403748\pi$
$37$	−4.12311	+	7.14143i	−0.677834	+	1.17404i	−0.975632	+	0.219414i	$0.929585\pi$
$38$		0			0
$39$	7.28078	+	12.6107i	1.16586	+	2.01932i
$40$		0			0
$41$	7.12311			1.11244			0.556221	−	0.831034i	$-0.312251\pi$
$41$	7.12311			1.11244			0.556221	+	0.831034i	$0.312251\pi$
$42$		0			0
$43$	1.12311			0.171272			0.0856360	−	0.996326i	$-0.472708\pi$
$43$	1.12311			0.171272			0.0856360	+	0.996326i	$0.472708\pi$
$44$		0			0
$45$	−1.78078	−	3.08440i	−0.265462	−	0.459794i
$46$		0			0
$47$	−3.28078	+	5.68247i	−0.478550	+	0.828874i	−0.999698	−	0.0245932i	$-0.992171\pi$
$47$	−3.28078	+	5.68247i	−0.478550	+	0.828874i	0.521147	+	0.853467i	$0.325504\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−4.40388	+	7.62775i	−0.616667	+	1.06810i
$52$		0			0
$53$	2.43845	+	4.22351i	0.334946	+	0.580144i	0.983475	−	0.181046i	$-0.0579484\pi$
$53$	2.43845	+	4.22351i	0.334946	+	0.580144i	−0.648528	+	0.761191i	$0.724615\pi$
$54$		0			0
$55$	−2.56155			−0.345400
$56$		0			0
$57$	2.87689			0.381054
$58$		0			0
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$		0			0
$61$	7.56155	−	13.0970i	0.968158	−	1.67690i	0.267277	−	0.963620i	$-0.413876\pi$
$61$	7.56155	−	13.0970i	0.968158	−	1.67690i	0.700881	−	0.713278i	$-0.252790\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.84233	−	4.92306i	0.352548	−	0.610630i
$66$		0			0
$67$	7.12311	+	12.3376i	0.870226	+	1.50728i	0.861763	+	0.507311i	$0.169361\pi$
$67$	7.12311	+	12.3376i	0.870226	+	1.50728i	0.00846293	+	0.999964i	$0.497306\pi$
$68$		0			0
$69$	−13.1231			−1.57984
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−6.12311	−	10.6055i	−0.716655	−	1.24128i	−0.962318	−	0.271928i	$-0.912339\pi$
$73$	−6.12311	−	10.6055i	−0.716655	−	1.24128i	0.245662	−	0.969355i	$-0.420995\pi$
$74$		0			0
$75$	−1.28078	+	2.21837i	−0.147891	+	0.256155i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	5.84233	−	10.1192i	0.657313	−	1.13850i	−0.323995	−	0.946059i	$-0.605026\pi$
$79$	5.84233	−	10.1192i	0.657313	−	1.13850i	0.981308	−	0.192441i	$-0.0616405\pi$
$80$		0			0
$81$	3.50000	+	6.06218i	0.388889	+	0.673575i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	3.43845			0.372952
$86$		0			0
$87$	−5.84233	−	10.1192i	−0.626363	−	1.08489i
$88$		0			0
$89$	1.56155	−	2.70469i	0.165524	−	0.286696i	−0.771317	−	0.636451i	$-0.780402\pi$
$89$	1.56155	−	2.70469i	0.165524	−	0.286696i	0.936841	+	0.349755i	$0.113735\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	13.1231	−	22.7299i	1.36080	−	2.35698i
$94$		0			0
$95$	−0.561553	−	0.972638i	−0.0576141	−	0.0997906i
$96$		0			0
$97$	13.6847			1.38947			0.694733	−	0.719267i	$-0.255522\pi$
$97$	13.6847			1.38947			0.694733	+	0.719267i	$0.255522\pi$
$98$		0			0
$99$	−9.12311			−0.916907
$100$		0			0
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	−4.40388	+	7.62775i	−0.433927	+	0.751584i	−0.997207	−	0.0746818i	$-0.976206\pi$
$103$	−4.40388	+	7.62775i	−0.433927	+	0.751584i	0.563280	+	0.826266i	$0.309539\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.43845	+	5.95557i	−0.332407	+	0.575746i	−0.982983	−	0.183695i	$-0.941194\pi$
$107$	−3.43845	+	5.95557i	−0.332407	+	0.575746i	0.650576	+	0.759441i	$0.274528\pi$
$108$		0			0
$109$	4.28078	+	7.41452i	0.410024	+	0.710182i	0.994892	−	0.100946i	$-0.0321870\pi$
$109$	4.28078	+	7.41452i	0.410024	+	0.710182i	−0.584868	+	0.811129i	$0.698854\pi$
$110$		0			0
$111$	21.1231			2.00492
$112$		0			0
$113$	−8.24621			−0.775738			−0.387869	−	0.921714i	$-0.626789\pi$
$113$	−8.24621			−0.775738			−0.387869	+	0.921714i	$0.626789\pi$
$114$		0			0
$115$	2.56155	+	4.43674i	0.238866	+	0.413728i
$116$		0			0
$117$	10.1231	−	17.5337i	0.935881	−	1.62099i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	2.21922	−	3.84381i	0.201748	−	0.349437i
$122$		0			0
$123$	−9.12311	−	15.8017i	−0.822603	−	1.42479i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	10.2462			0.909204			0.454602	−	0.890695i	$-0.349781\pi$
$127$	10.2462			0.909204			0.454602	+	0.890695i	$0.349781\pi$
$128$		0			0
$129$	−1.43845	−	2.49146i	−0.126648	−	0.219361i
$130$		0			0
$131$	−3.43845	+	5.95557i	−0.300419	+	0.520340i	−0.976231	−	0.216734i	$-0.930460\pi$
$131$	−3.43845	+	5.95557i	−0.300419	+	0.520340i	0.675812	+	0.737074i	$0.263793\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.719224	+	1.24573i	−0.0619009	+	0.107216i
$136$		0			0
$137$	−8.68466	−	15.0423i	−0.741980	−	1.28515i	−0.951592	−	0.307363i	$-0.900553\pi$
$137$	−8.68466	−	15.0423i	−0.741980	−	1.28515i	0.209612	−	0.977785i	$-0.432780\pi$
$138$		0			0
$139$	3.36932			0.285782			0.142891	−	0.989738i	$-0.454360\pi$
$139$	3.36932			0.285782			0.142891	+	0.989738i	$0.454360\pi$
$140$		0			0
$141$	16.8078			1.41547
$142$		0			0
$143$	−7.28078	−	12.6107i	−0.608849	−	1.05456i
$144$		0			0
$145$	−2.28078	+	3.95042i	−0.189408	+	0.328065i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−8.12311	+	14.0696i	−0.665471	+	1.15263i	0.313687	+	0.949527i	$0.398436\pi$
$149$	−8.12311	+	14.0696i	−0.665471	+	1.15263i	−0.979157	+	0.203103i	$0.934898\pi$
$150$		0			0
$151$	−0.403882	−	0.699544i	−0.0328675	−	0.0569281i	0.849124	−	0.528194i	$-0.177131\pi$
$151$	−0.403882	−	0.699544i	−0.0328675	−	0.0569281i	−0.881991	+	0.471266i	$0.843797\pi$
$152$		0			0
$153$	12.2462			0.990048
$154$		0			0
$155$	−10.2462			−0.822995
$156$		0			0
$157$	6.12311	+	10.6055i	0.488677	+	0.846413i	0.999915	−	0.0130257i	$-0.00414631\pi$
$157$	6.12311	+	10.6055i	0.488677	+	0.846413i	−0.511238	+	0.859439i	$0.670813\pi$
$158$		0			0
$159$	6.24621	−	10.8188i	0.495357	−	0.857983i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	10.8078	−	18.7196i	0.846529	−	1.46623i	−0.0377569	−	0.999287i	$-0.512021\pi$
$163$	10.8078	−	18.7196i	0.846529	−	1.46623i	0.884286	−	0.466945i	$-0.154645\pi$
$164$		0			0
$165$	3.28078	+	5.68247i	0.255408	+	0.442380i
$166$		0			0
$167$	24.8078			1.91968			0.959841	−	0.280544i	$-0.0905148\pi$
$167$	24.8078			1.91968			0.959841	+	0.280544i	$0.0905148\pi$
$168$		0			0
$169$	19.3153			1.48580
$170$		0			0
$171$	−2.00000	−	3.46410i	−0.152944	−	0.264906i
$172$		0			0
$173$	−11.0885	+	19.2059i	−0.843046	+	1.46020i	0.0442611	+	0.999020i	$0.485907\pi$
$173$	−11.0885	+	19.2059i	−0.843046	+	1.46020i	−0.887307	+	0.461179i	$0.847427\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.12311	−	8.87348i	0.385076	−	0.666972i
$178$		0			0
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	0.931038	−	0.364922i	$-0.118904\pi$
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	−0.781551	+	0.623841i	$0.785571\pi$
$180$		0			0
$181$	3.12311			0.232139			0.116069	−	0.993241i	$-0.462971\pi$
$181$	3.12311			0.232139			0.116069	+	0.993241i	$0.462971\pi$
$182$		0			0
$183$	−38.7386			−2.86364
$184$		0			0
$185$	−4.12311	−	7.14143i	−0.303137	−	0.525048i
$186$		0			0
$187$	4.40388	−	7.62775i	0.322044	−	0.557796i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.84233	+	10.1192i	−0.422736	+	0.732200i	−0.996206	−	0.0870262i	$-0.972264\pi$
$191$	−5.84233	+	10.1192i	−0.422736	+	0.732200i	0.573470	+	0.819227i	$0.305597\pi$
$192$		0			0
$193$	−2.43845	−	4.22351i	−0.175523	−	0.304015i	0.764819	−	0.644245i	$-0.222828\pi$
$193$	−2.43845	−	4.22351i	−0.175523	−	0.304015i	−0.940342	+	0.340230i	$0.889495\pi$
$194$		0			0
$195$	−14.5616			−1.04277
$196$		0			0
$197$	−4.87689			−0.347464			−0.173732	−	0.984793i	$-0.555583\pi$
$197$	−4.87689			−0.347464			−0.173732	+	0.984793i	$0.555583\pi$
$198$		0			0
$199$	−1.12311	−	1.94528i	−0.0796148	−	0.137897i	0.823469	−	0.567361i	$-0.192036\pi$
$199$	−1.12311	−	1.94528i	−0.0796148	−	0.137897i	−0.903084	+	0.429464i	$0.858702\pi$
$200$		0			0
$201$	18.2462	−	31.6034i	1.28699	−	2.22913i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−3.56155	+	6.16879i	−0.248750	+	0.430847i
$206$		0			0
$207$	9.12311	+	15.8017i	0.634100	+	1.09829i
$208$		0			0
$209$	−2.87689			−0.198999
$210$		0			0
$211$	−13.4384			−0.925141			−0.462570	−	0.886583i	$-0.653073\pi$
$211$	−13.4384			−0.925141			−0.462570	+	0.886583i	$0.653073\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.561553	+	0.972638i	−0.0382976	+	0.0663334i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−15.6847	+	27.1666i	−1.05987	+	1.83575i
$220$		0			0
$221$	9.77320	+	16.9277i	0.657417	+	1.13868i
$222$		0			0
$223$	12.3153			0.824696			0.412348	−	0.911026i	$-0.364709\pi$
$223$	12.3153			0.824696			0.412348	+	0.911026i	$0.364709\pi$
$224$		0			0
$225$	3.56155			0.237437
$226$		0			0
$227$	11.8423	+	20.5115i	0.786003	+	1.36140i	0.928398	+	0.371587i	$0.121186\pi$
$227$	11.8423	+	20.5115i	0.786003	+	1.36140i	−0.142395	+	0.989810i	$0.545480\pi$
$228$		0			0
$229$	−6.68466	+	11.5782i	−0.441735	+	0.765107i	−0.997818	−	0.0660194i	$-0.978970\pi$
$229$	−6.68466	+	11.5782i	−0.441735	+	0.765107i	0.556084	+	0.831126i	$0.312303\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.56155	−	16.5611i	0.626398	−	1.08495i	−0.361871	−	0.932228i	$-0.617862\pi$
$233$	9.56155	−	16.5611i	0.626398	−	1.08495i	0.988269	−	0.152725i	$-0.0488049\pi$
$234$		0			0
$235$	−3.28078	−	5.68247i	−0.214014	−	0.370684i
$236$		0			0
$237$	−29.9309			−1.94422
$238$		0			0
$239$	19.0540			1.23250			0.616250	−	0.787551i	$-0.288651\pi$
$239$	19.0540			1.23250			0.616250	+	0.787551i	$0.288651\pi$
$240$		0			0
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	0.832019	−	0.554747i	$-0.187185\pi$
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	−0.896435	+	0.443176i	$0.853852\pi$
$242$		0			0
$243$	11.1231	−	19.2658i	0.713548	−	1.23590i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.19224	−	5.52911i	0.203117	−	0.351809i
$248$		0			0
$249$	−15.3693	−	26.6204i	−0.973991	−	1.68700i
$250$		0			0
$251$	−11.3693			−0.717625			−0.358812	−	0.933410i	$-0.616818\pi$
$251$	−11.3693			−0.717625			−0.358812	+	0.933410i	$0.616818\pi$
$252$		0			0
$253$	13.1231			0.825043
$254$		0			0
$255$	−4.40388	−	7.62775i	−0.275782	−	0.477668i
$256$		0			0
$257$	−7.24621	+	12.5508i	−0.452006	+	0.782898i	−0.998511	−	0.0545585i	$-0.982625\pi$
$257$	−7.24621	+	12.5508i	−0.452006	+	0.782898i	0.546504	+	0.837456i	$0.315958\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−8.12311	+	14.0696i	−0.502808	+	0.870888i
$262$		0			0
$263$	7.68466	+	13.3102i	0.473856	+	0.820743i	0.999552	−	0.0299295i	$-0.00952826\pi$
$263$	7.68466	+	13.3102i	0.473856	+	0.820743i	−0.525696	+	0.850673i	$0.676195\pi$
$264$		0			0
$265$	−4.87689			−0.299585
$266$		0			0
$267$	−8.00000			−0.489592
$268$		0			0
$269$	6.12311	+	10.6055i	0.373332	+	0.646631i	0.990076	−	0.140534i	$-0.0448818\pi$
$269$	6.12311	+	10.6055i	0.373332	+	0.646631i	−0.616744	+	0.787164i	$0.711548\pi$
$270$		0			0
$271$	−5.12311	+	8.87348i	−0.311207	+	0.539025i	−0.978624	−	0.205658i	$-0.934066\pi$
$271$	−5.12311	+	8.87348i	−0.311207	+	0.539025i	0.667417	+	0.744684i	$0.267400\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.28078	−	2.21837i	0.0772337	−	0.133773i
$276$		0			0
$277$	−4.12311	−	7.14143i	−0.247733	−	0.429087i	0.715163	−	0.698958i	$-0.246352\pi$
$277$	−4.12311	−	7.14143i	−0.247733	−	0.429087i	−0.962897	+	0.269871i	$0.913019\pi$
$278$		0			0
$279$	−36.4924			−2.18474
$280$		0			0
$281$	−15.4384			−0.920981			−0.460490	−	0.887665i	$-0.652326\pi$
$281$	−15.4384			−0.920981			−0.460490	+	0.887665i	$0.652326\pi$
$282$		0			0
$283$	−3.84233	−	6.65511i	−0.228403	−	0.395605i	0.728932	−	0.684586i	$-0.240017\pi$
$283$	−3.84233	−	6.65511i	−0.228403	−	0.395605i	−0.957335	+	0.288981i	$0.906684\pi$
$284$		0			0
$285$	−1.43845	+	2.49146i	−0.0852063	+	0.147582i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	2.58854	−	4.48348i	0.152267	−	0.263734i
$290$		0			0
$291$	−17.5270	−	30.3576i	−1.02745	−	1.77960i
$292$		0			0
$293$	−5.05398			−0.295256			−0.147628	−	0.989043i	$-0.547164\pi$
$293$	−5.05398			−0.295256			−0.147628	+	0.989043i	$0.547164\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$		0			0
$297$	1.84233	+	3.19101i	0.106903	+	0.185161i
$298$		0			0
$299$	−14.5616	+	25.2213i	−0.842116	+	1.45859i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−7.68466	+	13.3102i	−0.441472	+	0.764652i
$304$		0			0
$305$	7.56155	+	13.0970i	0.432973	+	0.749932i
$306$		0			0
$307$	−16.3153			−0.931166			−0.465583	−	0.885004i	$-0.654155\pi$
$307$	−16.3153			−0.931166			−0.465583	+	0.885004i	$0.654155\pi$
$308$		0			0
$309$	22.5616			1.28348
$310$		0			0
$311$	10.5616	+	18.2931i	0.598891	+	1.03731i	0.992985	+	0.118239i	$0.0377250\pi$
$311$	10.5616	+	18.2931i	0.598891	+	1.03731i	−0.394094	+	0.919070i	$0.628942\pi$
$312$		0			0
$313$	−7.15767	+	12.3974i	−0.404575	+	0.700745i	−0.994272	−	0.106880i	$-0.965914\pi$
$313$	−7.15767	+	12.3974i	−0.404575	+	0.700745i	0.589696	+	0.807625i	$0.299247\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.00000	−	8.66025i	0.280828	−	0.486408i	−0.690761	−	0.723083i	$-0.742724\pi$
$317$	5.00000	−	8.66025i	0.280828	−	0.486408i	0.971589	+	0.236675i	$0.0760576\pi$
$318$		0			0
$319$	5.84233	+	10.1192i	0.327108	+	0.566567i
$320$		0			0
$321$	17.6155			0.983203
$322$		0			0
$323$	3.86174			0.214873
$324$		0			0
$325$	2.84233	+	4.92306i	0.157664	+	0.273082i
$326$		0			0
$327$	10.9654	−	18.9927i	0.606390	−	1.05030i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	6.00000	−	10.3923i	0.329790	−	0.571213i	−0.652680	−	0.757634i	$-0.726355\pi$
$331$	6.00000	−	10.3923i	0.329790	−	0.571213i	0.982470	+	0.186421i	$0.0596888\pi$
$332$		0			0
$333$	−14.6847	−	25.4346i	−0.804714	−	1.39381i
$334$		0			0
$335$	−14.2462			−0.778354
$336$		0			0
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$		0			0
$339$	10.5616	+	18.2931i	0.573625	+	0.993547i
$340$		0			0
$341$	−13.1231	+	22.7299i	−0.710656	+	1.23089i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	6.56155	−	11.3649i	0.353262	−	0.611868i
$346$		0			0
$347$	−3.43845	−	5.95557i	−0.184586	−	0.319711i	0.758851	−	0.651264i	$-0.225761\pi$
$347$	−3.43845	−	5.95557i	−0.184586	−	0.319711i	−0.943437	+	0.331552i	$0.892428\pi$
$348$		0			0
$349$	−28.2462			−1.51199			−0.755993	−	0.654580i	$-0.772845\pi$
$349$	−28.2462			−1.51199			−0.755993	+	0.654580i	$0.772845\pi$
$350$		0			0
$351$	−8.17708			−0.436460
$352$		0			0
$353$	11.4039	+	19.7521i	0.606967	+	1.05130i	0.991737	+	0.128286i	$0.0409475\pi$
$353$	11.4039	+	19.7521i	0.606967	+	1.05130i	−0.384770	+	0.923013i	$0.625719\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−16.0000	+	27.7128i	−0.844448	+	1.46263i	0.0416523	+	0.999132i	$0.486738\pi$
$359$	−16.0000	+	27.7128i	−0.844448	+	1.46263i	−0.886100	+	0.463494i	$0.846596\pi$
$360$		0			0
$361$	8.86932	+	15.3621i	0.466806	+	0.808532i
$362$		0			0
$363$	−11.3693			−0.596734
$364$		0			0
$365$	12.2462			0.640996
$366$		0			0
$367$	6.96543	+	12.0645i	0.363593	+	0.629761i	0.988549	−	0.150898i	$-0.0482166\pi$
$367$	6.96543	+	12.0645i	0.363593	+	0.629761i	−0.624957	+	0.780660i	$0.714883\pi$
$368$		0			0
$369$	−12.6847	+	21.9705i	−0.660337	+	1.14374i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	4.68466	−	8.11407i	0.242562	−	0.420130i	−0.718881	−	0.695133i	$-0.755345\pi$
$373$	4.68466	−	8.11407i	0.242562	−	0.420130i	0.961443	+	0.275003i	$0.0886787\pi$
$374$		0			0
$375$	−1.28078	−	2.21837i	−0.0661390	−	0.114556i
$376$		0			0
$377$	−25.9309			−1.33551
$378$		0			0
$379$	−0.492423			−0.0252940			−0.0126470	−	0.999920i	$-0.504026\pi$
$379$	−0.492423			−0.0252940			−0.0126470	+	0.999920i	$0.504026\pi$
$380$		0			0
$381$	−13.1231	−	22.7299i	−0.672317	−	1.16449i
$382$		0			0
$383$	13.1231	−	22.7299i	0.670559	−	1.16144i	−0.307186	−	0.951649i	$-0.599387\pi$
$383$	13.1231	−	22.7299i	0.670559	−	1.16144i	0.977746	−	0.209794i	$-0.0672792\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.00000	+	3.46410i	−0.101666	+	0.176090i
$388$		0			0
$389$	15.6501	+	27.1068i	0.793491	+	1.37437i	0.923793	+	0.382893i	$0.125072\pi$
$389$	15.6501	+	27.1068i	0.793491	+	1.37437i	−0.130302	+	0.991474i	$0.541595\pi$
$390$		0			0
$391$	−17.6155			−0.890856
$392$		0			0
$393$	17.6155			0.888586
$394$		0			0
$395$	5.84233	+	10.1192i	0.293959	+	0.509153i
$396$		0			0
$397$	−11.0885	+	19.2059i	−0.556518	+	0.963917i	0.441266	+	0.897376i	$0.354530\pi$
$397$	−11.0885	+	19.2059i	−0.556518	+	0.963917i	−0.997784	+	0.0665408i	$0.978804\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−7.96543	+	13.7965i	−0.397775	+	0.688966i	−0.993451	−	0.114258i	$-0.963551\pi$
$401$	−7.96543	+	13.7965i	−0.397775	+	0.688966i	0.595676	+	0.803225i	$0.296884\pi$
$402$		0			0
$403$	−29.1231	−	50.4427i	−1.45073	−	2.51273i
$404$		0			0
$405$	−7.00000			−0.347833
$406$		0			0
$407$	−21.1231			−1.04703
$408$		0			0
$409$	−7.24621	−	12.5508i	−0.358302	−	0.620597i	0.629375	−	0.777102i	$-0.283311\pi$
$409$	−7.24621	−	12.5508i	−0.358302	−	0.620597i	−0.987677	+	0.156504i	$0.949978\pi$
$410$		0			0
$411$	−22.2462	+	38.5316i	−1.09732	+	1.90062i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$		0			0
$417$	−4.31534	−	7.47439i	−0.211323	−	0.366022i
$418$		0			0
$419$	−1.75379			−0.0856782			−0.0428391	−	0.999082i	$-0.513640\pi$
$419$	−1.75379			−0.0856782			−0.0428391	+	0.999082i	$0.513640\pi$
$420$		0			0
$421$	−0.561553			−0.0273684			−0.0136842	−	0.999906i	$-0.504356\pi$
$421$	−0.561553			−0.0273684			−0.0136842	+	0.999906i	$0.504356\pi$
$422$		0			0
$423$	−11.6847	−	20.2384i	−0.568128	−	0.984026i
$424$		0			0
$425$	−1.71922	+	2.97778i	−0.0833946	+	0.144444i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−18.6501	+	32.3029i	−0.900435	+	1.55960i
$430$		0			0
$431$	−2.96543	−	5.13628i	−0.142840	−	0.247406i	0.785725	−	0.618576i	$-0.212290\pi$
$431$	−2.96543	−	5.13628i	−0.142840	−	0.247406i	−0.928565	+	0.371170i	$0.878957\pi$
$432$		0			0
$433$	36.2462			1.74188			0.870941	−	0.491388i	$-0.163510\pi$
$433$	36.2462			1.74188			0.870941	+	0.491388i	$0.163510\pi$
$434$		0			0
$435$	11.6847			0.560236
$436$		0			0
$437$	2.87689	+	4.98293i	0.137621	+	0.238366i
$438$		0			0
$439$	−5.43845	+	9.41967i	−0.259563	+	0.449576i	−0.966125	−	0.258075i	$-0.916912\pi$
$439$	−5.43845	+	9.41967i	−0.259563	+	0.449576i	0.706562	+	0.707651i	$0.250245\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.8078	+	18.7196i	−0.513492	+	0.889395i	0.486385	+	0.873745i	$0.338315\pi$
$443$	−10.8078	+	18.7196i	−0.513492	+	0.889395i	−0.999878	+	0.0156504i	$0.995018\pi$
$444$		0			0
$445$	1.56155	+	2.70469i	0.0740247	+	0.128215i
$446$		0			0
$447$	41.6155			1.96835
$448$		0			0
$449$	−33.6847			−1.58968			−0.794839	−	0.606821i	$-0.792445\pi$
$449$	−33.6847			−1.58968			−0.794839	+	0.606821i	$0.792445\pi$
$450$		0			0
$451$	9.12311	+	15.8017i	0.429590	+	0.744072i
$452$		0			0
$453$	−1.03457	+	1.79192i	−0.0486081	+	0.0841917i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−16.6847	+	28.8987i	−0.780475	+	1.35182i	0.151190	+	0.988505i	$0.451690\pi$
$457$	−16.6847	+	28.8987i	−0.780475	+	1.35182i	−0.931665	+	0.363318i	$0.881644\pi$
$458$		0			0
$459$	−2.47301	−	4.28338i	−0.115430	−	0.199931i
$460$		0			0
$461$	27.1231			1.26325			0.631624	−	0.775274i	$-0.282388\pi$
$461$	27.1231			1.26325			0.631624	+	0.775274i	$0.282388\pi$
$462$		0			0
$463$	10.2462			0.476182			0.238091	−	0.971243i	$-0.423478\pi$
$463$	10.2462			0.476182			0.238091	+	0.971243i	$0.423478\pi$
$464$		0			0
$465$	13.1231	+	22.7299i	0.608569	+	1.05407i
$466$		0			0
$467$	−10.7192	+	18.5662i	−0.496027	+	0.859143i	−0.999990	−	0.00458213i	$-0.998541\pi$
$467$	−10.7192	+	18.5662i	−0.496027	+	0.859143i	0.503963	+	0.863725i	$0.331875\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	15.6847	−	27.1666i	0.722711	−	1.25177i
$472$		0			0
$473$	1.43845	+	2.49146i	0.0661399	+	0.114558i
$474$		0			0
$475$	1.12311			0.0515316
$476$		0			0
$477$	−17.3693			−0.795286
$478$		0			0
$479$	3.68466	+	6.38202i	0.168356	+	0.291602i	0.937842	−	0.347062i	$-0.112821\pi$
$479$	3.68466	+	6.38202i	0.168356	+	0.291602i	−0.769486	+	0.638664i	$0.779487\pi$
$480$		0			0
$481$	23.4384	−	40.5966i	1.06870	−	1.85104i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−6.84233	+	11.8513i	−0.310694	+	0.538138i
$486$		0			0
$487$	2.56155	+	4.43674i	0.116075	+	0.201048i	0.918209	−	0.396096i	$-0.129635\pi$
$487$	2.56155	+	4.43674i	0.116075	+	0.201048i	−0.802134	+	0.597144i	$0.796302\pi$
$488$		0			0
$489$	−55.3693			−2.50389
$490$		0			0
$491$	−15.6847			−0.707839			−0.353919	−	0.935276i	$-0.615151\pi$
$491$	−15.6847			−0.707839			−0.353919	+	0.935276i	$0.615151\pi$
$492$		0			0
$493$	−7.84233	−	13.5833i	−0.353201	−	0.611762i
$494$		0			0
$495$	4.56155	−	7.90084i	0.205027	−	0.355116i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	10.4039	−	18.0201i	0.465742	−	0.806688i	−0.533493	−	0.845805i	$-0.679121\pi$
$499$	10.4039	−	18.0201i	0.465742	−	0.806688i	0.999235	+	0.0391162i	$0.0124542\pi$
$500$		0			0
$501$	−31.7732	−	55.0328i	−1.41952	−	2.45868i
$502$		0			0
$503$	16.1771			0.721300			0.360650	−	0.932701i	$-0.382555\pi$
$503$	16.1771			0.721300			0.360650	+	0.932701i	$0.382555\pi$
$504$		0			0
$505$	6.00000			0.266996
$506$		0			0
$507$	−24.7386	−	42.8486i	−1.09868	−	1.90297i
$508$		0			0
$509$	8.36932	−	14.4961i	0.370963	−	0.642528i	−0.618751	−	0.785588i	$-0.712361\pi$
$509$	8.36932	−	14.4961i	0.370963	−	0.642528i	0.989714	+	0.143060i	$0.0456942\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−0.807764	+	1.39909i	−0.0356637	+	0.0617713i
$514$		0			0
$515$	−4.40388	−	7.62775i	−0.194058	−	0.336119i
$516$		0			0
$517$	−16.8078			−0.739205
$518$		0			0
$519$	56.8078			2.49358
$520$		0			0
$521$	−2.12311	−	3.67733i	−0.0930149	−	0.161107i	0.815763	−	0.578386i	$-0.196317\pi$
$521$	−2.12311	−	3.67733i	−0.0930149	−	0.161107i	−0.908778	+	0.417279i	$0.862984\pi$
$522$		0			0
$523$	6.00000	−	10.3923i	0.262362	−	0.454424i	−0.704507	−	0.709697i	$-0.748832\pi$
$523$	6.00000	−	10.3923i	0.262362	−	0.454424i	0.966869	+	0.255273i	$0.0821653\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	17.6155	−	30.5110i	0.767344	−	1.32908i
$528$		0			0
$529$	−1.62311	−	2.81130i	−0.0705698	−	0.122230i
$530$		0			0
$531$	−14.2462			−0.618233
$532$		0			0
$533$	−40.4924			−1.75392
$534$		0			0
$535$	−3.43845	−	5.95557i	−0.148657	−	0.257482i
$536$		0			0
$537$	5.12311	−	8.87348i	0.221078	−	0.382919i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	10.2116	−	17.6871i	0.439033	−	0.760427i	−0.558582	−	0.829449i	$-0.688654\pi$
$541$	10.2116	−	17.6871i	0.439033	−	0.760427i	0.997615	+	0.0690218i	$0.0219878\pi$
$542$		0			0
$543$	−4.00000	−	6.92820i	−0.171656	−	0.297318i
$544$		0			0
$545$	−8.56155			−0.366737
$546$		0			0
$547$	12.0000			0.513083			0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000			0.513083			0.256541	+	0.966533i	$0.417417\pi$
$548$		0			0
$549$	26.9309	+	46.6456i	1.14938	+	1.99079i
$550$		0			0
$551$	−2.56155	+	4.43674i	−0.109126	+	0.189011i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−10.5616	+	18.2931i	−0.448313	+	0.776501i
$556$		0			0
$557$	−11.8078	−	20.4516i	−0.500311	−	0.866564i	−1.00000		0.000359173i	$-0.999886\pi$
$557$	−11.8078	−	20.4516i	−0.500311	−	0.866564i	0.499689	−	0.866205i	$-0.333448\pi$
$558$		0			0
$559$	−6.38447			−0.270034
$560$		0			0
$561$	−22.5616			−0.952550
$562$		0			0
$563$	20.2462	+	35.0675i	0.853276	+	1.47792i	0.878235	+	0.478229i	$0.158721\pi$
$563$	20.2462	+	35.0675i	0.853276	+	1.47792i	−0.0249591	+	0.999688i	$0.507946\pi$
$564$		0			0
$565$	4.12311	−	7.14143i	0.173460	−	0.300442i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	23.4924	−	40.6901i	0.984854	−	1.70582i	0.342268	−	0.939602i	$-0.388805\pi$
$569$	23.4924	−	40.6901i	0.984854	−	1.70582i	0.642585	−	0.766214i	$-0.277862\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$		0			0
$573$	29.9309			1.25038
$574$		0			0
$575$	−5.12311			−0.213648
$576$		0			0
$577$	−0.280776	−	0.486319i	−0.0116889	−	0.0202457i	0.860122	−	0.510089i	$-0.170387\pi$
$577$	−0.280776	−	0.486319i	−0.0116889	−	0.0202457i	−0.871811	+	0.489843i	$0.837054\pi$
$578$		0			0
$579$	−6.24621	+	10.8188i	−0.259584	+	0.449612i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−6.24621	+	10.8188i	−0.258692	+	0.448067i
$584$		0			0
$585$	10.1231	+	17.5337i	0.418539	+	0.724931i
$586$		0			0
$587$	−6.24621			−0.257809			−0.128904	−	0.991657i	$-0.541146\pi$
$587$	−6.24621			−0.257809			−0.128904	+	0.991657i	$0.541146\pi$
$588$		0			0
$589$	−11.5076			−0.474161
$590$		0			0
$591$	6.24621	+	10.8188i	0.256935	+	0.445024i
$592$		0			0
$593$	12.2116	−	21.1512i	0.501472	−	0.868575i	−0.498526	−	0.866875i	$-0.666125\pi$
$593$	12.2116	−	21.1512i	0.501472	−	0.868575i	0.999999	−	0.00170079i	$-0.000541377\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−2.87689	+	4.98293i	−0.117743	+	0.203938i
$598$		0			0
$599$	9.03457	+	15.6483i	0.369142	+	0.639373i	0.989432	−	0.145000i	$-0.0463182\pi$
$599$	9.03457	+	15.6483i	0.369142	+	0.639373i	−0.620289	+	0.784373i	$0.712985\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$		0			0
$603$	−50.7386			−2.06624
$604$		0			0
$605$	2.21922	+	3.84381i	0.0902243	+	0.156273i
$606$		0			0
$607$	−1.84233	+	3.19101i	−0.0747778	+	0.129519i	−0.900990	−	0.433841i	$-0.857158\pi$
$607$	−1.84233	+	3.19101i	−0.0747778	+	0.129519i	0.826212	+	0.563360i	$0.190491\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	18.6501	−	32.3029i	0.754502	−	1.30684i
$612$		0			0
$613$	16.3693	+	28.3525i	0.661150	+	1.14515i	0.980314	+	0.197446i	$0.0632649\pi$
$613$	16.3693	+	28.3525i	0.661150	+	1.14515i	−0.319163	+	0.947700i	$0.603402\pi$
$614$		0			0
$615$	18.2462			0.735758
$616$		0			0
$617$	−32.2462			−1.29818			−0.649092	−	0.760710i	$-0.724851\pi$
$617$	−32.2462			−1.29818			−0.649092	+	0.760710i	$0.724851\pi$
$618$		0			0
$619$	−17.6847	−	30.6307i	−0.710806	−	1.23115i	−0.964555	−	0.263883i	$-0.914997\pi$
$619$	−17.6847	−	30.6307i	−0.710806	−	1.23115i	0.253748	−	0.967270i	$-0.418336\pi$
$620$		0			0
$621$	3.68466	−	6.38202i	0.147860	−	0.256101i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	3.68466	+	6.38202i	0.147151	+	0.254873i
$628$		0			0
$629$	28.3542			1.13055
$630$		0			0
$631$	34.4233			1.37037			0.685185	−	0.728369i	$-0.259721\pi$
$631$	34.4233			1.37037			0.685185	+	0.728369i	$0.259721\pi$
$632$		0			0
$633$	17.2116	+	29.8114i	0.684102	+	1.18490i
$634$		0			0
$635$	−5.12311	+	8.87348i	−0.203304	+	0.352133i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−21.4924	−	37.2260i	−0.848900	−	1.47034i	−0.882191	−	0.470892i	$-0.843932\pi$
$641$	−21.4924	−	37.2260i	−0.848900	−	1.47034i	0.0332914	−	0.999446i	$-0.489401\pi$
$642$		0			0
$643$	7.05398			0.278182			0.139091	−	0.990280i	$-0.455582\pi$
$643$	7.05398			0.278182			0.139091	+	0.990280i	$0.455582\pi$
$644$		0			0
$645$	2.87689			0.113278
$646$		0			0
$647$	−4.00000	−	6.92820i	−0.157256	−	0.272376i	0.776622	−	0.629967i	$-0.216932\pi$
$647$	−4.00000	−	6.92820i	−0.157256	−	0.272376i	−0.933878	+	0.357591i	$0.883598\pi$
$648$		0			0
$649$	−5.12311	+	8.87348i	−0.201099	+	0.348315i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.75379	−	4.76970i	0.107764	−	0.186653i	−0.807100	−	0.590415i	$-0.798964\pi$
$653$	2.75379	−	4.76970i	0.107764	−	0.186653i	0.914864	+	0.403762i	$0.132298\pi$
$654$		0			0
$655$	−3.43845	−	5.95557i	−0.134351	−	0.232703i
$656$		0			0
$657$	43.6155			1.70160
$658$		0			0
$659$	−20.8078			−0.810555			−0.405278	−	0.914194i	$-0.632825\pi$
$659$	−20.8078			−0.810555			−0.405278	+	0.914194i	$0.632825\pi$
$660$		0			0
$661$	−11.8078	−	20.4516i	−0.459269	−	0.795477i	0.539654	−	0.841887i	$-0.318555\pi$
$661$	−11.8078	−	20.4516i	−0.459269	−	0.795477i	−0.998922	+	0.0464102i	$0.985222\pi$
$662$		0			0
$663$	25.0346	−	43.3611i	0.972262	−	1.68401i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	11.6847	−	20.2384i	0.452432	−	0.783635i
$668$		0			0
$669$	−15.7732	−	27.3200i	−0.609827	−	1.05625i
$670$		0			0
$671$	38.7386			1.49549
$672$		0			0
$673$	0.384472			0.0148203			0.00741015	−	0.999973i	$-0.497641\pi$
$673$	0.384472			0.0148203			0.00741015	+	0.999973i	$0.497641\pi$
$674$		0			0
$675$	−0.719224	−	1.24573i	−0.0276829	−	0.0479482i
$676$		0			0
$677$	6.84233	−	11.8513i	0.262972	−	0.455481i	−0.704058	−	0.710142i	$-0.748631\pi$
$677$	6.84233	−	11.8513i	0.262972	−	0.455481i	0.967030	+	0.254661i	$0.0819640\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	30.3348	−	52.5413i	1.16243	−	2.01339i
$682$		0			0
$683$	10.4924	+	18.1734i	0.401481	+	0.695386i	0.993905	−	0.110241i	$-0.0351621\pi$
$683$	10.4924	+	18.1734i	0.401481	+	0.695386i	−0.592424	+	0.805627i	$0.701829\pi$
$684$		0			0
$685$	17.3693			0.663647
$686$		0			0
$687$	34.2462			1.30657
$688$		0			0
$689$	−13.8617	−	24.0092i	−0.528090	−	0.914679i
$690$		0			0
$691$	8.24621	−	14.2829i	0.313701	−	0.543345i	−0.665460	−	0.746434i	$-0.731764\pi$
$691$	8.24621	−	14.2829i	0.313701	−	0.543345i	0.979160	+	0.203088i	$0.0650978\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.68466	+	2.91791i	−0.0639027	+	0.110683i
$696$		0			0
$697$	−12.2462	−	21.2111i	−0.463858	−	0.803426i
$698$		0			0
$699$	−48.9848			−1.85278
$700$		0			0
$701$	−21.6847			−0.819018			−0.409509	−	0.912306i	$-0.634300\pi$
$701$	−21.6847			−0.819018			−0.409509	+	0.912306i	$0.634300\pi$
$702$		0			0
$703$	−4.63068	−	8.02058i	−0.174650	−	0.302502i
$704$		0			0
$705$	−8.40388	+	14.5560i	−0.316509	+	0.548209i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−16.5270	+	28.6256i	−0.620684	+	1.07506i	0.368675	+	0.929559i	$0.379812\pi$
$709$	−16.5270	+	28.6256i	−0.620684	+	1.07506i	−0.989359	+	0.145498i	$0.953522\pi$
$710$		0			0
$711$	20.8078	+	36.0401i	0.780352	+	1.35161i
$712$		0			0
$713$	52.4924			1.96586
$714$		0			0
$715$	14.5616			0.544571
$716$		0			0
$717$	−24.4039	−	42.2688i	−0.911380	−	1.57856i
$718$		0			0
$719$	−8.80776	+	15.2555i	−0.328474	+	0.568934i	−0.982209	−	0.187789i	$-0.939868\pi$
$719$	−8.80776	+	15.2555i	−0.328474	+	0.568934i	0.653735	+	0.756723i	$0.273201\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−2.56155	+	4.43674i	−0.0952652	+	0.165004i
$724$		0			0
$725$	−2.28078	−	3.95042i	−0.0847059	−	0.146715i
$726$		0			0
$727$	−16.9848			−0.629933			−0.314967	−	0.949103i	$-0.601993\pi$
$727$	−16.9848			−0.629933			−0.314967	+	0.949103i	$0.601993\pi$
$728$		0			0
$729$	−35.9848			−1.33277
$730$		0			0
$731$	−1.93087	−	3.34436i	−0.0714158	−	0.123696i
$732$		0			0
$733$	−10.2808	+	17.8068i	−0.379729	+	0.657710i	−0.991023	−	0.133694i	$-0.957316\pi$
$733$	−10.2808	+	17.8068i	−0.379729	+	0.657710i	0.611294	+	0.791404i	$0.290649\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−18.2462	+	31.6034i	−0.672108	+	1.16412i
$738$		0			0
$739$	5.28078	+	9.14657i	0.194257	+	0.336462i	0.946657	−	0.322244i	$-0.104437\pi$
$739$	5.28078	+	9.14657i	0.194257	+	0.336462i	−0.752400	+	0.658706i	$0.771104\pi$
$740$		0			0
$741$	−16.3542			−0.600785
$742$		0			0
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$		0			0
$745$	−8.12311	−	14.0696i	−0.297608	−	0.515471i
$746$		0			0
$747$	−21.3693	+	37.0127i	−0.781862	+	1.35423i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	21.8423	−	37.8320i	0.797038	−	1.38051i	−0.124499	−	0.992220i	$-0.539732\pi$
$751$	21.8423	−	37.8320i	0.797038	−	1.38051i	0.921537	−	0.388290i	$-0.126934\pi$
$752$		0			0
$753$	14.5616	+	25.2213i	0.530652	+	0.919117i
$754$		0			0
$755$	0.807764			0.0293975
$756$		0			0
$757$	−9.36932			−0.340534			−0.170267	−	0.985398i	$-0.554463\pi$
$757$	−9.36932			−0.340534			−0.170267	+	0.985398i	$0.554463\pi$
$758$		0			0
$759$	−16.8078	−	29.1119i	−0.610083	−	1.05670i
$760$		0			0
$761$	−13.0000	+	22.5167i	−0.471250	+	0.816228i	−0.999459	−	0.0328858i	$-0.989530\pi$
$761$	−13.0000	+	22.5167i	−0.471250	+	0.816228i	0.528209	+	0.849114i	$0.322864\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−6.12311	+	10.6055i	−0.221381	+	0.383444i
$766$		0			0
$767$	−11.3693	−	19.6922i	−0.410522	−	0.711045i
$768$		0			0
$769$	−22.9848			−0.828855			−0.414427	−	0.910082i	$-0.636018\pi$
$769$	−22.9848			−0.828855			−0.414427	+	0.910082i	$0.636018\pi$
$770$		0			0
$771$	37.1231			1.33696
$772$		0			0
$773$	4.59612	+	7.96071i	0.165311	+	0.286327i	0.936766	−	0.349957i	$-0.113804\pi$
$773$	4.59612	+	7.96071i	0.165311	+	0.286327i	−0.771455	+	0.636284i	$0.780471\pi$
$774$		0			0
$775$	5.12311	−	8.87348i	0.184027	−	0.318745i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.00000	+	6.92820i	−0.143315	+	0.248229i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	6.56155			0.234491
$784$		0			0
$785$	−12.2462			−0.437086
$786$		0			0
$787$	6.08854	+	10.5457i	0.217033	+	0.375912i	0.953900	−	0.300126i	$-0.0970287\pi$
$787$	6.08854	+	10.5457i	0.217033	+	0.375912i	−0.736867	+	0.676038i	$0.763695\pi$
$788$		0			0
$789$	19.6847	−	34.0948i	0.700792	−	1.21381i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−42.9848	+	74.4519i	−1.52644	+	2.64387i
$794$		0			0
$795$	6.24621	+	10.8188i	0.221530	+	0.383702i
$796$		0			0
$797$	−2.80776			−0.0994561			−0.0497281	−	0.998763i	$-0.515835\pi$
$797$	−2.80776			−0.0994561			−0.0497281	+	0.998763i	$0.515835\pi$
$798$		0			0
$799$	22.5616			0.798170
$800$		0			0
$801$	5.56155	+	9.63289i	0.196508	+	0.340362i
$802$		0			0
$803$	15.6847	−	27.1666i	0.553500	−	0.958689i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	15.6847	−	27.1666i	0.552126	−	0.956311i
$808$		0			0
$809$	16.5270	+	28.6256i	0.581058	+	1.00642i	0.995354	+	0.0962798i	$0.0306944\pi$
$809$	16.5270	+	28.6256i	0.581058	+	1.00642i	−0.414296	+	0.910142i	$0.635972\pi$
$810$		0			0
$811$	13.6155			0.478106			0.239053	−	0.971007i	$-0.423163\pi$
$811$	13.6155			0.478106			0.239053	+	0.971007i	$0.423163\pi$
$812$		0			0
$813$	26.2462			0.920495
$814$		0			0
$815$	10.8078	+	18.7196i	0.378579	+	0.655719i
$816$		0			0
$817$	−0.630683	+	1.09238i	−0.0220648	+	0.0382174i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.349907	+	0.606056i	−0.0122118	+	0.0211515i	−0.872067	−	0.489387i	$-0.837221\pi$
$821$	−0.349907	+	0.606056i	−0.0122118	+	0.0211515i	0.859855	+	0.510538i	$0.170554\pi$
$822$		0			0
$823$	17.1231	+	29.6581i	0.596874	+	1.03382i	0.993279	+	0.115740i	$0.0369241\pi$
$823$	17.1231	+	29.6581i	0.596874	+	1.03382i	−0.396406	+	0.918076i	$0.629743\pi$
$824$		0			0
$825$	−6.56155			−0.228444
$826$		0			0
$827$	33.1231			1.15180			0.575902	−	0.817519i	$-0.304651\pi$
$827$	33.1231			1.15180			0.575902	+	0.817519i	$0.304651\pi$
$828$		0			0
$829$	17.8078	+	30.8440i	0.618489	+	1.07125i	0.989762	+	0.142731i	$0.0455883\pi$
$829$	17.8078	+	30.8440i	0.618489	+	1.07125i	−0.371272	+	0.928524i	$0.621078\pi$
$830$		0			0
$831$	−10.5616	+	18.2931i	−0.366376	+	0.634582i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−12.4039	+	21.4842i	−0.429254	+	0.743490i
$836$		0			0
$837$	7.36932	+	12.7640i	0.254721	+	0.441189i
$838$		0			0
$839$	10.8769			0.375512			0.187756	−	0.982216i	$-0.439879\pi$
$839$	10.8769			0.375512			0.187756	+	0.982216i	$0.439879\pi$
$840$		0			0
$841$	−8.19224			−0.282491
$842$		0			0
$843$	19.7732	+	34.2482i	0.681025	+	1.17957i
$844$		0			0
$845$	−9.65767	+	16.7276i	−0.332234	+	0.575446i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−9.84233	+	17.0474i	−0.337788	+	0.585066i
$850$		0			0
$851$	21.1231	+	36.5863i	0.724091	+	1.25416i
$852$		0			0
$853$	32.2462			1.10409			0.552045	−	0.833815i	$-0.313848\pi$
$853$	32.2462			1.10409			0.552045	+	0.833815i	$0.313848\pi$
$854$		0			0
$855$	4.00000			0.136797
$856$		0			0
$857$	−1.63068	−	2.82443i	−0.0557031	−	0.0964806i	0.836829	−	0.547464i	$-0.184407\pi$
$857$	−1.63068	−	2.82443i	−0.0557031	−	0.0964806i	−0.892532	+	0.450983i	$0.851073\pi$
$858$		0			0
$859$	14.4924	−	25.1016i	0.494475	−	0.856456i	−0.505505	−	0.862824i	$-0.668694\pi$
$859$	14.4924	−	25.1016i	0.494475	−	0.856456i	0.999980	+	0.00636793i	$0.00202699\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.24621	−	3.89055i	0.0764619	−	0.132436i	−0.825259	−	0.564754i	$-0.808971\pi$
$863$	2.24621	−	3.89055i	0.0764619	−	0.132436i	0.901721	+	0.432318i	$0.142304\pi$
$864$		0			0
$865$	−11.0885	−	19.2059i	−0.377022	−	0.653021i
$866$		0			0
$867$	−13.2614			−0.450380
$868$		0			0
$869$	29.9309			1.01534
$870$		0			0
$871$	−40.4924	−	70.1349i	−1.37203	−	2.37643i
$872$		0			0
$873$	−24.3693	+	42.2089i	−0.824776	+	1.42855i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	23.2462	−	40.2636i	0.784969	−	1.35961i	−0.144049	−	0.989571i	$-0.546012\pi$
$877$	23.2462	−	40.2636i	0.784969	−	1.35961i	0.929018	−	0.370035i	$-0.120654\pi$
$878$		0			0
$879$	6.47301	+	11.2116i	0.218329	+	0.378157i
$880$		0			0
$881$	−20.1080			−0.677454			−0.338727	−	0.940885i	$-0.609996\pi$
$881$	−20.1080			−0.677454			−0.338727	+	0.940885i	$0.609996\pi$
$882$		0			0
$883$	38.2462			1.28709			0.643544	−	0.765409i	$-0.277463\pi$
$883$	38.2462			1.28709			0.643544	+	0.765409i	$0.277463\pi$
$884$		0			0
$885$	5.12311	+	8.87348i	0.172211	+	0.298279i
$886$		0			0
$887$	1.75379	−	3.03765i	0.0588865	−	0.101994i	−0.835079	−	0.550130i	$-0.814578\pi$
$887$	1.75379	−	3.03765i	0.0588865	−	0.101994i	0.893966	+	0.448135i	$0.147912\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−8.96543	+	15.5286i	−0.300353	+	0.520227i
$892$		0			0
$893$	−3.68466	−	6.38202i	−0.123302	−	0.213566i
$894$		0			0
$895$	−4.00000			−0.133705
$896$		0			0
$897$	74.6004			2.49083
$898$		0			0
$899$	23.3693	+	40.4768i	0.779410	+	1.34998i
$900$		0			0
$901$	8.38447	−	14.5223i	0.279327	−	0.483809i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.56155	+	2.70469i	−0.0519078	+	0.0899069i
$906$		0			0
$907$	−13.0540	−	22.6101i	−0.433450	−	0.750758i	0.563718	−	0.825968i	$-0.309371\pi$
$907$	−13.0540	−	22.6101i	−0.433450	−	0.750758i	−0.997168	+	0.0752099i	$0.976037\pi$
$908$		0			0
$909$	21.3693			0.708776
$910$		0			0
$911$	8.00000			0.265052			0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000			0.265052			0.132526	+	0.991180i	$0.457691\pi$
$912$		0			0
$913$	15.3693	+	26.6204i	0.508650	+	0.881008i
$914$		0			0
$915$	19.3693	−	33.5486i	0.640330	−	1.10908i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−3.28078	+	5.68247i	−0.108223	+	0.187447i	−0.915050	−	0.403340i	$-0.867849\pi$
$919$	−3.28078	+	5.68247i	−0.108223	+	0.187447i	0.806828	+	0.590787i	$0.201183\pi$
$920$		0			0
$921$	20.8963	+	36.1935i	0.688557	+	1.19262i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	8.24621			0.271134
$926$		0			0
$927$	−15.6847	−	27.1666i	−0.515152	−	0.892269i
$928$		0			0
$929$	5.56155	−	9.63289i	0.182469	−	0.316045i	−0.760252	−	0.649628i	$-0.774925\pi$
$929$	5.56155	−	9.63289i	0.182469	−	0.316045i	0.942721	+	0.333583i	$0.108258\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	27.0540	−	46.8589i	0.885707	−	1.53409i
$934$		0			0
$935$	4.40388	+	7.62775i	0.144022	+	0.249454i
$936$		0			0
$937$	17.1922			0.561646			0.280823	−	0.959760i	$-0.409393\pi$
$937$	17.1922			0.561646			0.280823	+	0.959760i	$0.409393\pi$
$938$		0			0
$939$	36.6695			1.19666
$940$		0			0
$941$	−26.6847	−	46.2192i	−0.869895	−	1.50670i	−0.862103	−	0.506733i	$-0.830853\pi$
$941$	−26.6847	−	46.2192i	−0.869895	−	1.50670i	−0.00779178	−	0.999970i	$-0.502480\pi$
$942$		0			0
$943$	18.2462	−	31.6034i	0.594178	−	1.02915i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−23.6155	+	40.9033i	−0.767402	+	1.32918i	0.171566	+	0.985173i	$0.445117\pi$
$947$	−23.6155	+	40.9033i	−0.767402	+	1.32918i	−0.938968	+	0.344006i	$0.888216\pi$
$948$		0			0
$949$	34.8078	+	60.2888i	1.12991	+	1.95706i
$950$		0			0
$951$	−25.6155			−0.830640
$952$		0			0
$953$	5.86174			0.189880			0.0949402	−	0.995483i	$-0.469734\pi$
$953$	5.86174			0.189880			0.0949402	+	0.995483i	$0.469734\pi$
$954$		0			0
$955$	−5.84233	−	10.1192i	−0.189053	−	0.327450i
$956$		0			0
$957$	14.9654	−	25.9209i	0.483764	−	0.837903i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−36.9924	+	64.0728i	−1.19330	+	2.06686i
$962$		0			0
$963$	−12.2462	−	21.2111i	−0.394629	−	0.683517i
$964$		0			0
$965$	4.87689			0.156993
$966$		0			0
$967$	−30.1080			−0.968206			−0.484103	−	0.875011i	$-0.660854\pi$
$967$	−30.1080			−0.968206			−0.484103	+	0.875011i	$0.660854\pi$
$968$		0			0
$969$	−4.94602	−	8.56677i	−0.158889	−	0.275204i
$970$		0			0
$971$	−13.3693	+	23.1563i	−0.429042	+	0.743122i	−0.996788	−	0.0800812i	$-0.974482\pi$
$971$	−13.3693	+	23.1563i	−0.429042	+	0.743122i	0.567747	+	0.823203i	$0.307815\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	7.28078	−	12.6107i	0.233171	−	0.403865i
$976$		0			0
$977$	27.4924	+	47.6183i	0.879561	+	1.52344i	0.851824	+	0.523828i	$0.175497\pi$
$977$	27.4924	+	47.6183i	0.879561	+	1.52344i	0.0277366	+	0.999615i	$0.491170\pi$
$978$		0			0
$979$	8.00000			0.255681
$980$		0			0
$981$	−30.4924			−0.973548
$982$		0			0
$983$	−8.08854	−	14.0098i	−0.257984	−	0.446842i	0.707717	−	0.706496i	$-0.249725\pi$
$983$	−8.08854	−	14.0098i	−0.257984	−	0.446842i	−0.965702	+	0.259654i	$0.916392\pi$
$984$		0			0
$985$	2.43845	−	4.22351i	0.0776954	−	0.134572i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.87689	−	4.98293i	0.0914799	−	0.158448i
$990$		0			0
$991$	−6.24621	−	10.8188i	−0.198417	−	0.343669i	0.749598	−	0.661893i	$-0.230247\pi$
$991$	−6.24621	−	10.8188i	−0.198417	−	0.343669i	−0.948015	+	0.318224i	$0.896914\pi$
$992$		0			0
$993$	−30.7386			−0.975461
$994$		0			0
$995$	2.24621			0.0712097
$996$		0			0
$997$	14.0346	+	24.3086i	0.444479	+	0.769860i	0.998016	−	0.0629644i	$-0.0200555\pi$
$997$	14.0346	+	24.3086i	0.444479	+	0.769860i	−0.553537	+	0.832825i	$0.686722\pi$
$998$		0			0
$999$	−5.93087	+	10.2726i	−0.187644	+	0.325010i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.2.q.s.961.1		4
7.2	even	3		280.2.a.d.1.2	✓	2
7.3	odd	6		1960.2.q.u.361.2		4
7.4	even	3	inner	1960.2.q.s.361.1		4
7.5	odd	6		1960.2.a.r.1.1		2
7.6	odd	2		1960.2.q.u.961.2		4
21.2	odd	6		2520.2.a.w.1.2		2
28.19	even	6		3920.2.a.bu.1.2		2
28.23	odd	6		560.2.a.g.1.1		2
35.2	odd	12		1400.2.g.k.449.1		4
35.9	even	6		1400.2.a.p.1.1		2
35.19	odd	6		9800.2.a.by.1.2		2
35.23	odd	12		1400.2.g.k.449.4		4
56.37	even	6		2240.2.a.be.1.1		2
56.51	odd	6		2240.2.a.bi.1.2		2
84.23	even	6		5040.2.a.bq.1.1		2
140.23	even	12		2800.2.g.u.449.1		4
140.79	odd	6		2800.2.a.bn.1.2		2
140.107	even	12		2800.2.g.u.449.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.a.d.1.2	✓	2	7.2	even	3
560.2.a.g.1.1		2	28.23	odd	6
1400.2.a.p.1.1		2	35.9	even	6
1400.2.g.k.449.1		4	35.2	odd	12
1400.2.g.k.449.4		4	35.23	odd	12
1960.2.a.r.1.1		2	7.5	odd	6
1960.2.q.s.361.1		4	7.4	even	3	inner
1960.2.q.s.961.1		4	1.1	even	1	trivial
1960.2.q.u.361.2		4	7.3	odd	6
1960.2.q.u.961.2		4	7.6	odd	2
2240.2.a.be.1.1		2	56.37	even	6
2240.2.a.bi.1.2		2	56.51	odd	6
2520.2.a.w.1.2		2	21.2	odd	6
2800.2.a.bn.1.2		2	140.79	odd	6
2800.2.g.u.449.1		4	140.23	even	12
2800.2.g.u.449.4		4	140.107	even	12
3920.2.a.bu.1.2		2	28.19	even	6
5040.2.a.bq.1.1		2	84.23	even	6
9800.2.a.by.1.2		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)

\(f(q)\)	\(=\)	\(q+(-1.28078 - 2.21837i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-1.78078 + 3.08440i) q^{9} +O(q^{10})\)	\(q+(-1.28078 - 2.21837i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-1.78078 + 3.08440i) q^{9} +(1.28078 + 2.21837i) q^{11} -5.68466 q^{13} +2.56155 q^{15} +(-1.71922 - 2.97778i) q^{17} +(-0.561553 + 0.972638i) q^{19} +(2.56155 - 4.43674i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.43845 q^{27} +4.56155 q^{29} +(5.12311 + 8.87348i) q^{31} +(3.28078 - 5.68247i) q^{33} +(-4.12311 + 7.14143i) q^{37} +(7.28078 + 12.6107i) q^{39} +7.12311 q^{41} +1.12311 q^{43} +(-1.78078 - 3.08440i) q^{45} +(-3.28078 + 5.68247i) q^{47} +(-4.40388 + 7.62775i) q^{51} +(2.43845 + 4.22351i) q^{53} -2.56155 q^{55} +2.87689 q^{57} +(2.00000 + 3.46410i) q^{59} +(7.56155 - 13.0970i) q^{61} +(2.84233 - 4.92306i) q^{65} +(7.12311 + 12.3376i) q^{67} -13.1231 q^{69} +(-6.12311 - 10.6055i) q^{73} +(-1.28078 + 2.21837i) q^{75} +(5.84233 - 10.1192i) q^{79} +(3.50000 + 6.06218i) q^{81} +12.0000 q^{83} +3.43845 q^{85} +(-5.84233 - 10.1192i) q^{87} +(1.56155 - 2.70469i) q^{89} +(13.1231 - 22.7299i) q^{93} +(-0.561553 - 0.972638i) q^{95} +13.6847 q^{97} -9.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} - 2 q^{5} - 3 q^{9}+O(q^{10}) \) 4 * q - q^3 - 2 * q^5 - 3 * q^9	\( 4 q - q^{3} - 2 q^{5} - 3 q^{9} + q^{11} + 2 q^{13} + 2 q^{15} - 11 q^{17} + 6 q^{19} + 2 q^{23} - 2 q^{25} + 14 q^{27} + 10 q^{29} + 4 q^{31} + 9 q^{33} + 25 q^{39} + 12 q^{41} - 12 q^{43} - 3 q^{45} - 9 q^{47} + 3 q^{51} + 18 q^{53} - 2 q^{55} + 28 q^{57} + 8 q^{59} + 22 q^{61} - q^{65} + 12 q^{67} - 36 q^{69} - 8 q^{73} - q^{75} + 11 q^{79} + 14 q^{81} + 48 q^{83} + 22 q^{85} - 11 q^{87} - 2 q^{89} + 36 q^{93} + 6 q^{95} + 30 q^{97} - 20 q^{99}+O(q^{100}) \) 4 * q - q^3 - 2 * q^5 - 3 * q^9 + q^11 + 2 * q^13 + 2 * q^15 - 11 * q^17 + 6 * q^19 + 2 * q^23 - 2 * q^25 + 14 * q^27 + 10 * q^29 + 4 * q^31 + 9 * q^33 + 25 * q^39 + 12 * q^41 - 12 * q^43 - 3 * q^45 - 9 * q^47 + 3 * q^51 + 18 * q^53 - 2 * q^55 + 28 * q^57 + 8 * q^59 + 22 * q^61 - q^65 + 12 * q^67 - 36 * q^69 - 8 * q^73 - q^75 + 11 * q^79 + 14 * q^81 + 48 * q^83 + 22 * q^85 - 11 * q^87 - 2 * q^89 + 36 * q^93 + 6 * q^95 + 30 * q^97 - 20 * q^99

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