LMFDB - Embedded newform 464.3.l.e.273.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [464,3,Mod(17,464)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(464, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("464.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	464.l (of order $4$, 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:	$12.6430842663$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} + 8 x^{12} + 26 x^{11} + 743 x^{10} - 2298 x^{9} + 3586 x^{8} + 2776 x^{7} + \cdots + 1623602 $ x^14 - 4x^13 + 8x^12 + 26x^11 + 743x^10 - 2298x^9 + 3586x^8 + 2776x^7 + 108967x^6 - 332156x^5 + 505068x^4 - 40690x^3 + 294849x^2 - 978486*x + 1623602
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 232)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			273.7
Root			$-3.14226 - 3.14226i$ of defining polynomial
Character	$\chi$	$=$	464.273
Dual form			464.3.l.e.17.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.14226 + 3.14226i) q^{3} +2.76807i q^{5} +4.43633 q^{7} +10.7476i q^{9} +O(q^{10})$	\(q+(3.14226 + 3.14226i) q^{3} +2.76807i q^{5} +4.43633 q^{7} +10.7476i q^{9} +(0.207826 + 0.207826i) q^{11} +11.2631i q^{13} +(-8.69801 + 8.69801i) q^{15} +(8.91941 + 8.91941i) q^{17} +(-7.81315 - 7.81315i) q^{19} +(13.9401 + 13.9401i) q^{21} -9.38434 q^{23} +17.3378 q^{25} +(-5.49137 + 5.49137i) q^{27} +(0.343649 + 28.9980i) q^{29} +(-18.3310 - 18.3310i) q^{31} +1.30609i q^{33} +12.2801i q^{35} +(-25.0046 + 25.0046i) q^{37} +(-35.3915 + 35.3915i) q^{39} +(20.8657 - 20.8657i) q^{41} +(0.636461 + 0.636461i) q^{43} -29.7501 q^{45} +(41.9477 - 41.9477i) q^{47} -29.3190 q^{49} +56.0542i q^{51} -83.3052 q^{53} +(-0.575278 + 0.575278i) q^{55} -49.1019i q^{57} +64.5900 q^{59} +(2.97373 + 2.97373i) q^{61} +47.6798i q^{63} -31.1770 q^{65} +6.49066i q^{67} +(-29.4880 - 29.4880i) q^{69} -6.84394i q^{71} +(32.2459 - 32.2459i) q^{73} +(54.4798 + 54.4798i) q^{75} +(0.921984 + 0.921984i) q^{77} +(-63.7591 - 63.7591i) q^{79} +62.2177 q^{81} +0.509763 q^{83} +(-24.6896 + 24.6896i) q^{85} +(-90.0393 + 92.1990i) q^{87} +(89.8675 + 89.8675i) q^{89} +49.9666i q^{91} -115.201i q^{93} +(21.6274 - 21.6274i) q^{95} +(87.1890 - 87.1890i) q^{97} +(-2.23363 + 2.23363i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 4 q^{3} - 8 q^{7}+O(q^{10}) $ 14 * q - 4 * q^3 - 8 * q^7	$ 14 q - 4 q^{3} - 8 q^{7} + 6 q^{15} - 34 q^{17} - 50 q^{19} - 28 q^{21} + 12 q^{23} - 102 q^{25} + 38 q^{27} + 6 q^{29} - 60 q^{31} + 38 q^{37} - 82 q^{39} + 18 q^{41} + 48 q^{43} + 260 q^{45} + 136 q^{47} + 66 q^{49} - 60 q^{53} + 86 q^{55} - 60 q^{59} + 106 q^{61} - 272 q^{65} - 180 q^{69} + 182 q^{73} + 42 q^{75} + 260 q^{77} + 72 q^{79} - 6 q^{81} - 332 q^{83} - 144 q^{85} + 312 q^{87} + 30 q^{89} - 340 q^{95} + 58 q^{97} + 594 q^{99}+O(q^{100}) $ 14 * q - 4 * q^3 - 8 * q^7 + 6 * q^15 - 34 * q^17 - 50 * q^19 - 28 * q^21 + 12 * q^23 - 102 * q^25 + 38 * q^27 + 6 * q^29 - 60 * q^31 + 38 * q^37 - 82 * q^39 + 18 * q^41 + 48 * q^43 + 260 * q^45 + 136 * q^47 + 66 * q^49 - 60 * q^53 + 86 * q^55 - 60 * q^59 + 106 * q^61 - 272 * q^65 - 180 * q^69 + 182 * q^73 + 42 * q^75 + 260 * q^77 + 72 * q^79 - 6 * q^81 - 332 * q^83 - 144 * q^85 + 312 * q^87 + 30 * q^89 - 340 * q^95 + 58 * q^97 + 594 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	3.14226	+	3.14226i	1.04742	+	1.04742i	0.998818	+	0.0486015i	$0.0154764\pi$
$3$	3.14226	+	3.14226i	1.04742	+	1.04742i	0.0486015	+	0.998818i	$0.484524\pi$
$4$		0			0
$5$			2.76807i			0.553615i	0.960925	+	0.276807i	$0.0892764\pi$
$5$			2.76807i			0.553615i	−0.960925	+	0.276807i	$0.910724\pi$
$6$		0			0
$7$	4.43633			0.633761			0.316880	−	0.948465i	$-0.397365\pi$
$7$	4.43633			0.633761			0.316880	+	0.948465i	$0.397365\pi$
$8$		0			0
$9$			10.7476i			1.19418i
$10$		0			0
$11$	0.207826	+	0.207826i	0.0188933	+	0.0188933i	0.716490	−	0.697597i	$-0.245747\pi$
$11$	0.207826	+	0.207826i	0.0188933	+	0.0188933i	−0.697597	+	0.716490i	$0.745747\pi$
$12$		0			0
$13$			11.2631i			0.866389i	0.901300	+	0.433195i	$0.142614\pi$
$13$			11.2631i			0.866389i	−0.901300	+	0.433195i	$0.857386\pi$
$14$		0			0
$15$	−8.69801	+	8.69801i	−0.579867	+	0.579867i
$16$		0			0
$17$	8.91941	+	8.91941i	0.524671	+	0.524671i	0.918979	−	0.394307i	$-0.129015\pi$
$17$	8.91941	+	8.91941i	0.524671	+	0.524671i	−0.394307	+	0.918979i	$0.629015\pi$
$18$		0			0
$19$	−7.81315	−	7.81315i	−0.411219	−	0.411219i	0.470944	−	0.882163i	$-0.343913\pi$
$19$	−7.81315	−	7.81315i	−0.411219	−	0.411219i	−0.882163	+	0.470944i	$0.843913\pi$
$20$		0			0
$21$	13.9401	+	13.9401i	0.663814	+	0.663814i
$22$		0			0
$23$	−9.38434			−0.408015			−0.204007	−	0.978969i	$-0.565397\pi$
$23$	−9.38434			−0.408015			−0.204007	+	0.978969i	$0.565397\pi$
$24$		0			0
$25$	17.3378			0.693511
$26$		0			0
$27$	−5.49137	+	5.49137i	−0.203384	+	0.203384i
$28$		0			0
$29$	0.343649	+	28.9980i	0.0118500	+	0.999930i
$29$	0.343649	+	28.9980i	0.0118500	+	0.999930i
$30$		0			0
$31$	−18.3310	−	18.3310i	−0.591322	−	0.591322i	0.346666	−	0.937988i	$-0.387314\pi$
$31$	−18.3310	−	18.3310i	−0.591322	−	0.591322i	−0.937988	+	0.346666i	$0.887314\pi$
$32$		0			0
$33$			1.30609i			0.0395784i
$34$		0			0
$35$			12.2801i			0.350859i
$36$		0			0
$37$	−25.0046	+	25.0046i	−0.675799	+	0.675799i	−0.959047	−	0.283247i	$-0.908588\pi$
$37$	−25.0046	+	25.0046i	−0.675799	+	0.675799i	0.283247	+	0.959047i	$0.408588\pi$
$38$		0			0
$39$	−35.3915	+	35.3915i	−0.907473	+	0.907473i
$40$		0			0
$41$	20.8657	−	20.8657i	0.508919	−	0.508919i	−0.405275	−	0.914195i	$-0.632824\pi$
$41$	20.8657	−	20.8657i	0.508919	−	0.508919i	0.914195	+	0.405275i	$0.132824\pi$
$42$		0			0
$43$	0.636461	+	0.636461i	0.0148014	+	0.0148014i	0.714469	−	0.699667i	$-0.246668\pi$
$43$	0.636461	+	0.636461i	0.0148014	+	0.0148014i	−0.699667	+	0.714469i	$0.746668\pi$
$44$		0			0
$45$	−29.7501			−0.661114
$46$		0			0
$47$	41.9477	−	41.9477i	0.892504	−	0.892504i	−0.102254	−	0.994758i	$-0.532605\pi$
$47$	41.9477	−	41.9477i	0.892504	−	0.892504i	0.994758	+	0.102254i	$0.0326055\pi$
$48$		0			0
$49$	−29.3190			−0.598347
$50$		0			0
$51$			56.0542i			1.09910i
$52$		0			0
$53$	−83.3052			−1.57180			−0.785898	−	0.618356i	$-0.787799\pi$
$53$	−83.3052			−1.57180			−0.785898	+	0.618356i	$0.787799\pi$
$54$		0			0
$55$	−0.575278	+	0.575278i	−0.0104596	+	0.0104596i
$56$		0			0
$57$		−	49.1019i		−	0.861437i
$58$		0			0
$59$	64.5900			1.09475			0.547373	−	0.836889i	$-0.315628\pi$
$59$	64.5900			1.09475			0.547373	+	0.836889i	$0.315628\pi$
$60$		0			0
$61$	2.97373	+	2.97373i	0.0487496	+	0.0487496i	0.731061	−	0.682312i	$-0.239025\pi$
$61$	2.97373	+	2.97373i	0.0487496	+	0.0487496i	−0.682312	+	0.731061i	$0.739025\pi$
$62$		0			0
$63$			47.6798i			0.756822i
$64$		0			0
$65$	−31.1770			−0.479646
$66$		0			0
$67$			6.49066i			0.0968754i	0.998826	+	0.0484377i	$0.0154242\pi$
$67$			6.49066i			0.0968754i	−0.998826	+	0.0484377i	$0.984576\pi$
$68$		0			0
$69$	−29.4880	−	29.4880i	−0.427363	−	0.427363i
$70$		0			0
$71$		−	6.84394i		−	0.0963935i	−0.998838	−	0.0481968i	$-0.984653\pi$
$71$		−	6.84394i		−	0.0963935i	0.998838	−	0.0481968i	$-0.0153475\pi$
$72$		0			0
$73$	32.2459	−	32.2459i	0.441725	−	0.441725i	−0.450867	−	0.892591i	$-0.648885\pi$
$73$	32.2459	−	32.2459i	0.441725	−	0.441725i	0.892591	+	0.450867i	$0.148885\pi$
$74$		0			0
$75$	54.4798	+	54.4798i	0.726397	+	0.726397i
$76$		0			0
$77$	0.921984	+	0.921984i	0.0119738	+	0.0119738i
$78$		0			0
$79$	−63.7591	−	63.7591i	−0.807077	−	0.807077i	0.177113	−	0.984190i	$-0.443324\pi$
$79$	−63.7591	−	63.7591i	−0.807077	−	0.807077i	−0.984190	+	0.177113i	$0.943324\pi$
$80$		0			0
$81$	62.2177			0.768119
$82$		0			0
$83$	0.509763			0.00614173			0.00307086	−	0.999995i	$-0.499023\pi$
$83$	0.509763			0.00614173			0.00307086	+	0.999995i	$0.499023\pi$
$84$		0			0
$85$	−24.6896	+	24.6896i	−0.290466	+	0.290466i
$86$		0			0
$87$	−90.0393	+	92.1990i	−1.03493	+	1.05976i
$88$		0			0
$89$	89.8675	+	89.8675i	1.00975	+	1.00975i	0.999952	+	0.00979542i	$0.00311803\pi$
$89$	89.8675	+	89.8675i	1.00975	+	1.00975i	0.00979542	+	0.999952i	$0.496882\pi$
$90$		0			0
$91$			49.9666i			0.549084i
$92$		0			0
$93$		−	115.201i		−	1.23872i
$94$		0			0
$95$	21.6274	−	21.6274i	0.227657	−	0.227657i
$96$		0			0
$97$	87.1890	−	87.1890i	0.898856	−	0.898856i	−0.0964789	−	0.995335i	$-0.530758\pi$
$97$	87.1890	−	87.1890i	0.898856	−	0.898856i	0.995335	+	0.0964789i	$0.0307580\pi$
$98$		0			0
$99$	−2.23363	+	2.23363i	−0.0225619	+	0.0225619i
$100$		0			0
$101$	71.5193	+	71.5193i	0.708112	+	0.708112i	0.966138	−	0.258026i	$-0.0830719\pi$
$101$	71.5193	+	71.5193i	0.708112	+	0.708112i	−0.258026	+	0.966138i	$0.583072\pi$
$102$		0			0
$103$	109.524			1.06334			0.531669	−	0.846952i	$-0.321565\pi$
$103$	109.524			1.06334			0.531669	+	0.846952i	$0.321565\pi$
$104$		0			0
$105$	−38.5872	+	38.5872i	−0.367497	+	0.367497i
$106$		0			0
$107$	118.703			1.10938			0.554688	−	0.832058i	$-0.312837\pi$
$107$	118.703			1.10938			0.554688	+	0.832058i	$0.312837\pi$
$108$		0			0
$109$			20.9160i			0.191890i	0.995387	+	0.0959448i	$0.0305872\pi$
$109$			20.9160i			0.191890i	−0.995387	+	0.0959448i	$0.969413\pi$
$110$		0			0
$111$	−157.142			−1.41569
$112$		0			0
$113$	−64.5928	+	64.5928i	−0.571617	+	0.571617i	−0.932580	−	0.360963i	$-0.882448\pi$
$113$	−64.5928	+	64.5928i	−0.571617	+	0.571617i	0.360963	+	0.932580i	$0.382448\pi$
$114$		0			0
$115$		−	25.9765i		−	0.225883i
$116$		0			0
$117$	−121.051			−1.03462
$118$		0			0
$119$	39.5694	+	39.5694i	0.332516	+	0.332516i
$120$		0			0
$121$		−	120.914i		−	0.999286i
$122$		0			0
$123$	131.131			1.06610
$124$		0			0
$125$			117.194i			0.937552i
$126$		0			0
$127$	−87.3350	−	87.3350i	−0.687677	−	0.687677i	0.274041	−	0.961718i	$-0.411640\pi$
$127$	−87.3350	−	87.3350i	−0.687677	−	0.687677i	−0.961718	+	0.274041i	$0.911640\pi$
$128$		0			0
$129$			3.99985i			0.0310066i
$130$		0			0
$131$	159.264	−	159.264i	1.21576	−	1.21576i	0.246652	−	0.969104i	$-0.420670\pi$
$131$	159.264	−	159.264i	1.21576	−	1.21576i	0.969104	−	0.246652i	$-0.0793304\pi$
$132$		0			0
$133$	−34.6617	−	34.6617i	−0.260614	−	0.260614i
$134$		0			0
$135$	−15.2005	−	15.2005i	−0.112596	−	0.112596i
$136$		0			0
$137$	−57.8100	−	57.8100i	−0.421971	−	0.421971i	0.463911	−	0.885882i	$-0.346446\pi$
$137$	−57.8100	−	57.8100i	−0.421971	−	0.421971i	−0.885882	+	0.463911i	$0.846446\pi$
$138$		0			0
$139$	−153.501			−1.10432			−0.552161	−	0.833737i	$-0.686197\pi$
$139$	−153.501			−1.10432			−0.552161	+	0.833737i	$0.686197\pi$
$140$		0			0
$141$	263.621			1.86965
$142$		0			0
$143$	−2.34076	+	2.34076i	−0.0163689	+	0.0163689i
$144$		0			0
$145$	−80.2685	+	0.951245i	−0.553576	+	0.00656031i
$146$		0			0
$147$	−92.1279	−	92.1279i	−0.626721	−	0.626721i
$148$		0			0
$149$		−	106.536i		−	0.715005i	−0.933912	−	0.357502i	$-0.883628\pi$
$149$		−	106.536i		−	0.715005i	0.933912	−	0.357502i	$-0.116372\pi$
$150$		0			0
$151$			174.703i			1.15697i	0.815692	+	0.578487i	$0.196357\pi$
$151$			174.703i			1.15697i	−0.815692	+	0.578487i	$0.803643\pi$
$152$		0			0
$153$	−95.8622	+	95.8622i	−0.626550	+	0.626550i
$154$		0			0
$155$	50.7415	−	50.7415i	0.327365	−	0.327365i
$156$		0			0
$157$	130.877	−	130.877i	0.833610	−	0.833610i	−0.154398	−	0.988009i	$-0.549344\pi$
$157$	130.877	−	130.877i	0.833610	−	0.833610i	0.988009	+	0.154398i	$0.0493439\pi$
$158$		0			0
$159$	−261.766	−	261.766i	−1.64633	−	1.64633i
$160$		0			0
$161$	−41.6320			−0.258584
$162$		0			0
$163$	196.899	−	196.899i	1.20797	−	1.20797i	0.236284	−	0.971684i	$-0.424070\pi$
$163$	196.899	−	196.899i	1.20797	−	1.20797i	0.971684	−	0.236284i	$-0.0759296\pi$
$164$		0			0
$165$	−3.61534			−0.0219112
$166$		0			0
$167$		−	152.890i		−	0.915510i	−0.889078	−	0.457755i	$-0.848654\pi$
$167$		−	152.890i		−	0.915510i	0.889078	−	0.457755i	$-0.151346\pi$
$168$		0			0
$169$	42.1435			0.249370
$170$		0			0
$171$	83.9726	−	83.9726i	0.491068	−	0.491068i
$172$		0			0
$173$		−	219.463i		−	1.26857i	−0.773097	−	0.634287i	$-0.781294\pi$
$173$		−	219.463i		−	1.26857i	0.773097	−	0.634287i	$-0.218706\pi$
$174$		0			0
$175$	76.9160			0.439520
$176$		0			0
$177$	202.958	+	202.958i	1.14666	+	1.14666i
$178$		0			0
$179$		−	69.0498i		−	0.385753i	−0.981223	−	0.192876i	$-0.938218\pi$
$179$		−	69.0498i		−	0.385753i	0.981223	−	0.192876i	$-0.0617817\pi$
$180$		0			0
$181$	199.119			1.10010			0.550052	−	0.835130i	$-0.314608\pi$
$181$	199.119			1.10010			0.550052	+	0.835130i	$0.314608\pi$
$182$		0			0
$183$			18.6884i			0.102123i
$184$		0			0
$185$	−69.2145	−	69.2145i	−0.374133	−	0.374133i
$186$		0			0
$187$			3.70737i			0.0198255i
$188$		0			0
$189$	−24.3615	+	24.3615i	−0.128897	+	0.128897i
$190$		0			0
$191$	−116.870	−	116.870i	−0.611886	−	0.611886i	0.331551	−	0.943437i	$-0.392428\pi$
$191$	−116.870	−	116.870i	−0.611886	−	0.611886i	−0.943437	+	0.331551i	$0.892428\pi$
$192$		0			0
$193$	−207.218	−	207.218i	−1.07367	−	1.07367i	−0.997061	−	0.0766088i	$-0.975591\pi$
$193$	−207.218	−	207.218i	−1.07367	−	1.07367i	−0.0766088	−	0.997061i	$-0.524409\pi$
$194$		0			0
$195$	−97.9662	−	97.9662i	−0.502391	−	0.502391i
$196$		0			0
$197$	228.523			1.16002			0.580009	−	0.814610i	$-0.303049\pi$
$197$	228.523			1.16002			0.580009	+	0.814610i	$0.303049\pi$
$198$		0			0
$199$	−318.157			−1.59878			−0.799389	−	0.600814i	$-0.794843\pi$
$199$	−318.157			−1.59878			−0.799389	+	0.600814i	$0.794843\pi$
$200$		0			0
$201$	−20.3953	+	20.3953i	−0.101469	+	0.101469i
$202$		0			0
$203$	1.52454	+	128.644i	0.00751004	+	0.633716i
$204$		0			0
$205$	57.7578	+	57.7578i	0.281745	+	0.281745i
$206$		0			0
$207$		−	100.859i		−	0.487242i
$208$		0			0
$209$		−	3.24755i		−	0.0155385i
$210$		0			0
$211$	−144.679	+	144.679i	−0.685682	+	0.685682i	−0.961274	−	0.275593i	$-0.911126\pi$
$211$	−144.679	+	144.679i	−0.685682	+	0.685682i	0.275593	+	0.961274i	$0.411126\pi$
$212$		0			0
$213$	21.5054	−	21.5054i	0.100964	−	0.100964i
$214$		0			0
$215$	−1.76177	+	1.76177i	−0.00819428	+	0.00819428i
$216$		0			0
$217$	−81.3222	−	81.3222i	−0.374757	−	0.374757i
$218$		0			0
$219$	202.650			0.925342
$220$		0			0
$221$	−100.460	+	100.460i	−0.454570	+	0.454570i
$222$		0			0
$223$	−224.555			−1.00698			−0.503488	−	0.864002i	$-0.667950\pi$
$223$	−224.555			−1.00698			−0.503488	+	0.864002i	$0.667950\pi$
$224$		0			0
$225$			186.339i			0.828174i
$226$		0			0
$227$	−138.585			−0.610508			−0.305254	−	0.952271i	$-0.598741\pi$
$227$	−138.585			−0.610508			−0.305254	+	0.952271i	$0.598741\pi$
$228$		0			0
$229$	−58.6196	+	58.6196i	−0.255981	+	0.255981i	−0.823417	−	0.567436i	$-0.807935\pi$
$229$	−58.6196	+	58.6196i	−0.255981	+	0.255981i	0.567436	+	0.823417i	$0.307935\pi$
$230$		0			0
$231$			5.79422i			0.0250832i
$232$		0			0
$233$	−433.837			−1.86196			−0.930982	−	0.365066i	$-0.881046\pi$
$233$	−433.837			−1.86196			−0.930982	+	0.365066i	$0.881046\pi$
$234$		0			0
$235$	116.114	+	116.114i	0.494103	+	0.494103i
$236$		0			0
$237$		−	400.695i		−	1.69070i
$238$		0			0
$239$	284.721			1.19130			0.595651	−	0.803243i	$-0.296894\pi$
$239$	284.721			1.19130			0.595651	+	0.803243i	$0.296894\pi$
$240$		0			0
$241$			365.521i			1.51668i	0.651858	+	0.758341i	$0.273990\pi$
$241$			365.521i			1.51668i	−0.651858	+	0.758341i	$0.726010\pi$
$242$		0			0
$243$	244.926	+	244.926i	1.00793	+	1.00793i
$244$		0			0
$245$		−	81.1572i		−	0.331254i
$246$		0			0
$247$	88.0000	−	88.0000i	0.356275	−	0.356275i
$248$		0			0
$249$	1.60181	+	1.60181i	0.00643297	+	0.00643297i
$250$		0			0
$251$	256.397	+	256.397i	1.02150	+	1.02150i	0.999764	+	0.0217380i	$0.00691997\pi$
$251$	256.397	+	256.397i	1.02150	+	1.02150i	0.0217380	+	0.999764i	$0.493080\pi$
$252$		0			0
$253$	−1.95031	−	1.95031i	−0.00770873	−	0.00770873i
$254$		0			0
$255$	−155.162			−0.608479
$256$		0			0
$257$	282.700			1.10000			0.549999	−	0.835165i	$-0.314628\pi$
$257$	282.700			1.10000			0.549999	+	0.835165i	$0.314628\pi$
$258$		0			0
$259$	−110.928	+	110.928i	−0.428295	+	0.428295i
$260$		0			0
$261$	−311.658	+	3.69339i	−1.19409	+	0.0141509i
$262$		0			0
$263$	225.944	+	225.944i	0.859102	+	0.859102i	0.991232	−	0.132130i	$-0.0421817\pi$
$263$	225.944	+	225.944i	0.859102	+	0.859102i	−0.132130	+	0.991232i	$0.542182\pi$
$264$		0			0
$265$		−	230.595i		−	0.870169i
$266$		0			0
$267$			564.774i			2.11526i
$268$		0			0
$269$	−27.3892	+	27.3892i	−0.101819	+	0.101819i	−0.756181	−	0.654362i	$-0.772937\pi$
$269$	−27.3892	+	27.3892i	−0.101819	+	0.101819i	0.654362	+	0.756181i	$0.272937\pi$
$270$		0			0
$271$	−47.4725	+	47.4725i	−0.175175	+	0.175175i	−0.789249	−	0.614074i	$-0.789530\pi$
$271$	−47.4725	+	47.4725i	−0.175175	+	0.175175i	0.614074	+	0.789249i	$0.289530\pi$
$272$		0			0
$273$	−157.008	+	157.008i	−0.575121	+	0.575121i
$274$		0			0
$275$	3.60324	+	3.60324i	0.0131027	+	0.0131027i
$276$		0			0
$277$	−214.443			−0.774164			−0.387082	−	0.922045i	$-0.626517\pi$
$277$	−214.443			−0.774164			−0.387082	+	0.922045i	$0.626517\pi$
$278$		0			0
$279$	197.014	−	197.014i	0.706143	−	0.706143i
$280$		0			0
$281$	122.160			0.434734			0.217367	−	0.976090i	$-0.430253\pi$
$281$	122.160			0.434734			0.217367	+	0.976090i	$0.430253\pi$
$282$		0			0
$283$			334.537i			1.18211i	0.806631	+	0.591055i	$0.201289\pi$
$283$			334.537i			1.18211i	−0.806631	+	0.591055i	$0.798711\pi$
$284$		0			0
$285$	135.918			0.476904
$286$		0			0
$287$	92.5670	−	92.5670i	0.322533	−	0.322533i
$288$		0			0
$289$		−	129.888i		−	0.449440i
$290$		0			0
$291$	547.941			1.88296
$292$		0			0
$293$	225.444	+	225.444i	0.769433	+	0.769433i	0.978007	−	0.208574i	$-0.0668822\pi$
$293$	225.444	+	225.444i	0.769433	+	0.769433i	−0.208574	+	0.978007i	$0.566882\pi$
$294$		0			0
$295$			178.790i			0.606067i
$296$		0			0
$297$	−2.28250			−0.00768518
$298$		0			0
$299$		−	105.696i		−	0.353500i
$300$		0			0
$301$	2.82355	+	2.82355i	0.00938056	+	0.00938056i
$302$		0			0
$303$			449.465i			1.48338i
$304$		0			0
$305$	−8.23149	+	8.23149i	−0.0269885	+	0.0269885i
$306$		0			0
$307$	−237.285	−	237.285i	−0.772915	−	0.772915i	0.205700	−	0.978615i	$-0.434053\pi$
$307$	−237.285	−	237.285i	−0.772915	−	0.772915i	−0.978615	+	0.205700i	$0.934053\pi$
$308$		0			0
$309$	344.152	+	344.152i	1.11376	+	1.11376i
$310$		0			0
$311$	207.900	+	207.900i	0.668488	+	0.668488i	0.957366	−	0.288878i	$-0.0932822\pi$
$311$	207.900	+	207.900i	0.668488	+	0.668488i	−0.288878	+	0.957366i	$0.593282\pi$
$312$		0			0
$313$	−147.497			−0.471236			−0.235618	−	0.971846i	$-0.575711\pi$
$313$	−147.497			−0.471236			−0.235618	+	0.971846i	$0.575711\pi$
$314$		0			0
$315$	−131.981			−0.418988
$316$		0			0
$317$	−212.450	+	212.450i	−0.670190	+	0.670190i	−0.957760	−	0.287570i	$-0.907153\pi$
$317$	−212.450	+	212.450i	−0.670190	+	0.670190i	0.287570	+	0.957760i	$0.407153\pi$
$318$		0			0
$319$	−5.95511	+	6.09795i	−0.0186681	+	0.0191158i
$320$		0			0
$321$	372.997	+	372.997i	1.16198	+	1.16198i
$322$		0			0
$323$		−	139.377i		−	0.431509i
$324$		0			0
$325$			195.276i			0.600850i
$326$		0			0
$327$	−65.7234	+	65.7234i	−0.200989	+	0.200989i
$328$		0			0
$329$	186.094	−	186.094i	0.565634	−	0.565634i
$330$		0			0
$331$	−298.930	+	298.930i	−0.903112	+	0.903112i	−0.995704	−	0.0925923i	$-0.970485\pi$
$331$	−298.930	+	298.930i	−0.903112	+	0.903112i	0.0925923	+	0.995704i	$0.470485\pi$
$332$		0			0
$333$	−268.739	−	268.739i	−0.807024	−	0.807024i
$334$		0			0
$335$	−17.9666			−0.0536317
$336$		0			0
$337$	−160.491	+	160.491i	−0.476235	+	0.476235i	−0.903925	−	0.427690i	$-0.859327\pi$
$337$	−160.491	+	160.491i	−0.476235	+	0.476235i	0.427690	+	0.903925i	$0.359327\pi$
$338$		0			0
$339$	−405.934			−1.19745
$340$		0			0
$341$		−	7.61931i		−	0.0223440i
$342$		0			0
$343$	−347.449			−1.01297
$344$		0			0
$345$	81.6250	−	81.6250i	0.236594	−	0.236594i
$346$		0			0
$347$		−	373.769i		−	1.07715i	−0.842579	−	0.538573i	$-0.818964\pi$
$347$		−	373.769i		−	1.07715i	0.842579	−	0.538573i	$-0.181036\pi$
$348$		0			0
$349$	−244.162			−0.699606			−0.349803	−	0.936823i	$-0.613751\pi$
$349$	−244.162			−0.699606			−0.349803	+	0.936823i	$0.613751\pi$
$350$		0			0
$351$	−61.8497	−	61.8497i	−0.176210	−	0.176210i
$352$		0			0
$353$		−	104.830i		−	0.296968i	−0.988915	−	0.148484i	$-0.952561\pi$
$353$		−	104.830i		−	0.296968i	0.988915	−	0.148484i	$-0.0474394\pi$
$354$		0			0
$355$	18.9445			0.0533649
$356$		0			0
$357$			248.675i			0.696568i
$358$		0			0
$359$	19.0016	+	19.0016i	0.0529292	+	0.0529292i	0.733076	−	0.680147i	$-0.238084\pi$
$359$	19.0016	+	19.0016i	0.0529292	+	0.0529292i	−0.680147	+	0.733076i	$0.738084\pi$
$360$		0			0
$361$		−	238.909i		−	0.661798i
$362$		0			0
$363$	379.942	−	379.942i	1.04667	−	1.04667i
$364$		0			0
$365$	89.2590	+	89.2590i	0.244545	+	0.244545i
$366$		0			0
$367$	−384.003	−	384.003i	−1.04633	−	1.04633i	−0.998873	−	0.0474558i	$-0.984889\pi$
$367$	−384.003	−	384.003i	−1.04633	−	1.04633i	−0.0474558	−	0.998873i	$-0.515111\pi$
$368$		0			0
$369$	224.256	+	224.256i	0.607740	+	0.607740i
$370$		0			0
$371$	−369.569			−0.996143
$372$		0			0
$373$	110.372			0.295903			0.147951	−	0.988995i	$-0.452732\pi$
$373$	110.372			0.295903			0.147951	+	0.988995i	$0.452732\pi$
$374$		0			0
$375$	−368.254	+	368.254i	−0.982011	+	0.982011i
$376$		0			0
$377$	−326.606	+	3.87054i	−0.866328	+	0.0102667i
$378$		0			0
$379$	−64.1157	−	64.1157i	−0.169171	−	0.169171i	0.617444	−	0.786615i	$-0.288168\pi$
$379$	−64.1157	−	64.1157i	−0.169171	−	0.169171i	−0.786615	+	0.617444i	$0.788168\pi$
$380$		0			0
$381$		−	548.859i		−	1.44057i
$382$		0			0
$383$			572.880i			1.49577i	0.663828	+	0.747886i	$0.268931\pi$
$383$			572.880i			1.49577i	−0.663828	+	0.747886i	$0.731069\pi$
$384$		0			0
$385$	−2.55212	+	2.55212i	−0.00662888	+	0.00662888i
$386$		0			0
$387$	−6.84042	+	6.84042i	−0.0176755	+	0.0176755i
$388$		0			0
$389$	−390.915	+	390.915i	−1.00492	+	1.00492i	−0.00493398	+	0.999988i	$0.501571\pi$
$389$	−390.915	+	390.915i	−1.00492	+	1.00492i	−0.999988	+	0.00493398i	$0.998429\pi$
$390$		0			0
$391$	−83.7028	−	83.7028i	−0.214074	−	0.214074i
$392$		0			0
$393$	1000.90			2.54681
$394$		0			0
$395$	176.490	−	176.490i	0.446810	−	0.446810i
$396$		0			0
$397$	−556.439			−1.40161			−0.700805	−	0.713353i	$-0.747176\pi$
$397$	−556.439			−1.40161			−0.700805	+	0.713353i	$0.747176\pi$
$398$		0			0
$399$		−	217.832i		−	0.545945i
$400$		0			0
$401$	−235.904			−0.588290			−0.294145	−	0.955761i	$-0.595035\pi$
$401$	−235.904			−0.588290			−0.294145	+	0.955761i	$0.595035\pi$
$402$		0			0
$403$	206.463	−	206.463i	0.512315	−	0.512315i
$404$		0			0
$405$			172.223i			0.425242i
$406$		0			0
$407$	−10.3932			−0.0255361
$408$		0			0
$409$	223.018	+	223.018i	0.545276	+	0.545276i	0.925071	−	0.379795i	$-0.124006\pi$
$409$	223.018	+	223.018i	0.545276	+	0.545276i	−0.379795	+	0.925071i	$0.624006\pi$
$410$		0			0
$411$		−	363.308i		−	0.883961i
$412$		0			0
$413$	286.542			0.693807
$414$		0			0
$415$			1.41106i			0.00340015i
$416$		0			0
$417$	−482.339	−	482.339i	−1.15669	−	1.15669i
$418$		0			0
$419$		−	351.350i		−	0.838545i	−0.907860	−	0.419272i	$-0.862285\pi$
$419$		−	351.350i		−	0.838545i	0.907860	−	0.419272i	$-0.137715\pi$
$420$		0			0
$421$	−15.3059	+	15.3059i	−0.0363561	+	0.0363561i	−0.725051	−	0.688695i	$-0.758184\pi$
$421$	−15.3059	+	15.3059i	−0.0363561	+	0.0363561i	0.688695	+	0.725051i	$0.258184\pi$
$422$		0			0
$423$	450.837	+	450.837i	1.06581	+	1.06581i
$424$		0			0
$425$	154.643	+	154.643i	0.363865	+	0.363865i
$426$		0			0
$427$	13.1924	+	13.1924i	0.0308956	+	0.0308956i
$428$		0			0
$429$	−14.7105			−0.0342903
$430$		0			0
$431$	414.968			0.962803			0.481402	−	0.876500i	$-0.340128\pi$
$431$	414.968			0.962803			0.481402	+	0.876500i	$0.340128\pi$
$432$		0			0
$433$	−233.064	+	233.064i	−0.538255	+	0.538255i	−0.923016	−	0.384761i	$-0.874284\pi$
$433$	−233.064	+	233.064i	−0.538255	+	0.538255i	0.384761	+	0.923016i	$0.374284\pi$
$434$		0			0
$435$	−255.214	−	249.235i	−0.586698	−	0.572955i
$436$		0			0
$437$	73.3213	+	73.3213i	0.167783	+	0.167783i
$438$		0			0
$439$		−	842.583i		−	1.91932i	−0.281157	−	0.959662i	$-0.590718\pi$
$439$		−	842.583i		−	1.91932i	0.281157	−	0.959662i	$-0.409282\pi$
$440$		0			0
$441$		−	315.109i		−	0.714532i
$442$		0			0
$443$	−287.282	+	287.282i	−0.648493	+	0.648493i	−0.952629	−	0.304136i	$-0.901632\pi$
$443$	−287.282	+	287.282i	−0.648493	+	0.648493i	0.304136	+	0.952629i	$0.401632\pi$
$444$		0			0
$445$	−248.760	+	248.760i	−0.559011	+	0.559011i
$446$		0			0
$447$	334.763	−	334.763i	0.748910	−	0.748910i
$448$		0			0
$449$	100.459	+	100.459i	0.223739	+	0.223739i	0.810071	−	0.586332i	$-0.199429\pi$
$449$	100.459	+	100.459i	0.223739	+	0.223739i	−0.586332	+	0.810071i	$0.699429\pi$
$450$		0			0
$451$	8.67287			0.0192303
$452$		0			0
$453$	−548.962	+	548.962i	−1.21184	+	1.21184i
$454$		0			0
$455$	−138.311			−0.303981
$456$		0			0
$457$		−	631.508i		−	1.38186i	−0.722924	−	0.690928i	$-0.757202\pi$
$457$		−	631.508i		−	1.38186i	0.722924	−	0.690928i	$-0.242798\pi$
$458$		0			0
$459$	−97.9596			−0.213420
$460$		0			0
$461$	111.098	−	111.098i	0.240994	−	0.240994i	−0.576267	−	0.817261i	$-0.695491\pi$
$461$	111.098	−	111.098i	0.240994	−	0.240994i	0.817261	+	0.576267i	$0.195491\pi$
$462$		0			0
$463$		−	189.793i		−	0.409920i	−0.978770	−	0.204960i	$-0.934294\pi$
$463$		−	189.793i		−	0.409920i	0.978770	−	0.204960i	$-0.0657064\pi$
$464$		0			0
$465$	318.886			0.685776
$466$		0			0
$467$	−311.256	−	311.256i	−0.666500	−	0.666500i	0.290404	−	0.956904i	$-0.406210\pi$
$467$	−311.256	−	311.256i	−0.666500	−	0.666500i	−0.956904	+	0.290404i	$0.906210\pi$
$468$		0			0
$469$			28.7947i			0.0613959i
$470$		0			0
$471$	822.498			1.74628
$472$		0			0
$473$			0.264546i			0.000559294i
$474$		0			0
$475$	−135.463	−	135.463i	−0.285185	−	0.285185i
$476$		0			0
$477$		−	895.330i		−	1.87700i
$478$		0			0
$479$	−137.632	+	137.632i	−0.287331	+	0.287331i	−0.836024	−	0.548693i	$-0.815126\pi$
$479$	−137.632	+	137.632i	−0.287331	+	0.287331i	0.548693	+	0.836024i	$0.315126\pi$
$480$		0			0
$481$	−281.628	−	281.628i	−0.585505	−	0.585505i
$482$		0			0
$483$	−130.819	−	130.819i	−0.270846	−	0.270846i
$484$		0			0
$485$	241.346	+	241.346i	0.497620	+	0.497620i
$486$		0			0
$487$	−74.7622			−0.153516			−0.0767579	−	0.997050i	$-0.524457\pi$
$487$	−74.7622			−0.153516			−0.0767579	+	0.997050i	$0.524457\pi$
$488$		0			0
$489$	1237.41			2.53050
$490$		0			0
$491$	−326.901	+	326.901i	−0.665787	+	0.665787i	−0.956738	−	0.290951i	$-0.906028\pi$
$491$	−326.901	+	326.901i	−0.665787	+	0.665787i	0.290951	+	0.956738i	$0.406028\pi$
$492$		0			0
$493$	−255.580	+	261.710i	−0.518417	+	0.530852i
$494$		0			0
$495$	−6.18285	−	6.18285i	−0.0124906	−	0.0124906i
$496$		0			0
$497$		−	30.3619i		−	0.0610904i
$498$		0			0
$499$			756.037i			1.51511i	0.652774	+	0.757553i	$0.273605\pi$
$499$			756.037i			1.51511i	−0.652774	+	0.757553i	$0.726395\pi$
$500$		0			0
$501$	480.421	−	480.421i	0.958924	−	0.958924i
$502$		0			0
$503$	−276.155	+	276.155i	−0.549017	+	0.549017i	−0.926156	−	0.377140i	$-0.876908\pi$
$503$	−276.155	+	276.155i	−0.549017	+	0.549017i	0.377140	+	0.926156i	$0.376908\pi$
$504$		0			0
$505$	−197.971	+	197.971i	−0.392021	+	0.392021i
$506$		0			0
$507$	132.426	+	132.426i	0.261195	+	0.261195i
$508$		0			0
$509$	270.752			0.531929			0.265964	−	0.963983i	$-0.414310\pi$
$509$	270.752			0.531929			0.265964	+	0.963983i	$0.414310\pi$
$510$		0			0
$511$	143.053	−	143.053i	0.279948	−	0.279948i
$512$		0			0
$513$	85.8099			0.167271
$514$		0			0
$515$			303.170i			0.588679i
$516$		0			0
$517$	17.4356			0.0337246
$518$		0			0
$519$	689.611	−	689.611i	1.32873	−	1.32873i
$520$		0			0
$521$			445.270i			0.854646i	0.904099	+	0.427323i	$0.140543\pi$
$521$			445.270i			0.854646i	−0.904099	+	0.427323i	$0.859457\pi$
$522$		0			0
$523$	−896.222			−1.71362			−0.856809	−	0.515634i	$-0.827556\pi$
$523$	−896.222			−1.71362			−0.856809	+	0.515634i	$0.827556\pi$
$524$		0			0
$525$	241.690	+	241.690i	0.460362	+	0.460362i
$526$		0			0
$527$		−	327.003i		−	0.620499i
$528$		0			0
$529$	−440.934			−0.833524
$530$		0			0
$531$			694.187i			1.30732i
$532$		0			0
$533$	235.012	+	235.012i	0.440922	+	0.440922i
$534$		0			0
$535$			328.580i			0.614167i
$536$		0			0
$537$	216.972	−	216.972i	0.404045	−	0.404045i
$538$		0			0
$539$	−6.09325	−	6.09325i	−0.0113047	−	0.0113047i
$540$		0			0
$541$	572.291	+	572.291i	1.05784	+	1.05784i	0.998221	+	0.0596170i	$0.0189879\pi$
$541$	572.291	+	572.291i	1.05784	+	1.05784i	0.0596170	+	0.998221i	$0.481012\pi$
$542$		0			0
$543$	625.683	+	625.683i	1.15227	+	1.15227i
$544$		0			0
$545$	−57.8969			−0.106233
$546$		0			0
$547$	511.823			0.935691			0.467845	−	0.883810i	$-0.345030\pi$
$547$	511.823			0.935691			0.467845	+	0.883810i	$0.345030\pi$
$548$		0			0
$549$	−31.9604	+	31.9604i	−0.0582156	+	0.0582156i
$550$		0			0
$551$	223.881	−	229.251i	0.406317	−	0.416063i
$552$		0			0
$553$	−282.856	−	282.856i	−0.511494	−	0.511494i
$554$		0			0
$555$		−	434.980i		−	0.783748i
$556$		0			0
$557$		−	464.527i		−	0.833980i	−0.908911	−	0.416990i	$-0.863085\pi$
$557$		−	464.527i		−	0.833980i	0.908911	−	0.416990i	$-0.136915\pi$
$558$		0			0
$559$	−7.16850	+	7.16850i	−0.0128238	+	0.0128238i
$560$		0			0
$561$	−11.6495	+	11.6495i	−0.0207656	+	0.0207656i
$562$		0			0
$563$	−51.7315	+	51.7315i	−0.0918854	+	0.0918854i	−0.751555	−	0.659670i	$-0.770696\pi$
$563$	−51.7315	+	51.7315i	−0.0918854	+	0.0918854i	0.659670	+	0.751555i	$0.270696\pi$
$564$		0			0
$565$	−178.798	−	178.798i	−0.316456	−	0.316456i
$566$		0			0
$567$	276.018			0.486804
$568$		0			0
$569$	622.276	−	622.276i	1.09363	−	1.09363i	0.0984940	−	0.995138i	$-0.468597\pi$
$569$	622.276	−	622.276i	1.09363	−	1.09363i	0.995138	−	0.0984940i	$-0.0314025\pi$
$570$		0			0
$571$	536.750			0.940017			0.470009	−	0.882662i	$-0.344251\pi$
$571$	536.750			0.940017			0.470009	+	0.882662i	$0.344251\pi$
$572$		0			0
$573$		−	734.473i		−	1.28180i
$574$		0			0
$575$	−162.704			−0.282963
$576$		0			0
$577$	−425.166	+	425.166i	−0.736856	+	0.736856i	−0.971968	−	0.235112i	$-0.924454\pi$
$577$	−425.166	+	425.166i	−0.736856	+	0.736856i	0.235112	+	0.971968i	$0.424454\pi$
$578$		0			0
$579$		−	1302.27i		−	2.24917i
$580$		0			0
$581$	2.26148			0.00389239
$582$		0			0
$583$	−17.3130	−	17.3130i	−0.0296964	−	0.0296964i
$584$		0			0
$585$		−	335.077i		−	0.572782i
$586$		0			0
$587$	−233.074			−0.397059			−0.198529	−	0.980095i	$-0.563617\pi$
$587$	−233.074			−0.397059			−0.198529	+	0.980095i	$0.563617\pi$
$588$		0			0
$589$			286.446i			0.486325i
$590$		0			0
$591$	718.080	+	718.080i	1.21503	+	1.21503i
$592$		0			0
$593$		−	345.666i		−	0.582911i	−0.956584	−	0.291455i	$-0.905861\pi$
$593$		−	345.666i		−	0.582911i	0.956584	−	0.291455i	$-0.0941395\pi$
$594$		0			0
$595$	−109.531	+	109.531i	−0.184086	+	0.184086i
$596$		0			0
$597$	−999.731	−	999.731i	−1.67459	−	1.67459i
$598$		0			0
$599$	−352.618	−	352.618i	−0.588677	−	0.588677i	0.348596	−	0.937273i	$-0.386659\pi$
$599$	−352.618	−	352.618i	−0.588677	−	0.588677i	−0.937273	+	0.348596i	$0.886659\pi$
$600$		0			0
$601$	−769.567	−	769.567i	−1.28048	−	1.28048i	−0.940396	−	0.340083i	$-0.889545\pi$
$601$	−769.567	−	769.567i	−1.28048	−	1.28048i	−0.340083	−	0.940396i	$-0.610455\pi$
$602$		0			0
$603$	−69.7589			−0.115686
$604$		0			0
$605$	334.698			0.553220
$606$		0			0
$607$	−23.6009	+	23.6009i	−0.0388813	+	0.0388813i	−0.726280	−	0.687399i	$-0.758752\pi$
$607$	−23.6009	+	23.6009i	−0.0388813	+	0.0388813i	0.687399	+	0.726280i	$0.258752\pi$
$608$		0			0
$609$	−399.444	+	409.025i	−0.655901	+	0.671633i
$610$		0			0
$611$	472.459	+	472.459i	0.773256	+	0.773256i
$612$		0			0
$613$		−	95.5530i		−	0.155878i	−0.996958	−	0.0779389i	$-0.975166\pi$
$613$		−	95.5530i		−	0.155878i	0.996958	−	0.0779389i	$-0.0248339\pi$
$614$		0			0
$615$			362.980i			0.590211i
$616$		0			0
$617$	4.11174	−	4.11174i	0.00666409	−	0.00666409i	−0.703767	−	0.710431i	$-0.748500\pi$
$617$	4.11174	−	4.11174i	0.00666409	−	0.00666409i	0.710431	+	0.703767i	$0.248500\pi$
$618$		0			0
$619$	−306.293	+	306.293i	−0.494819	+	0.494819i	−0.909821	−	0.415002i	$-0.863781\pi$
$619$	−306.293	+	306.293i	−0.494819	+	0.494819i	0.415002	+	0.909821i	$0.363781\pi$
$620$		0			0
$621$	51.5329	−	51.5329i	0.0829838	−	0.0829838i
$622$		0			0
$623$	398.682	+	398.682i	0.639938	+	0.639938i
$624$		0			0
$625$	109.042			0.174468
$626$		0			0
$627$	10.2047	−	10.2047i	0.0162754	−	0.0162754i
$628$		0			0
$629$	−446.052			−0.709145
$630$		0			0
$631$		−	576.055i		−	0.912923i	−0.889743	−	0.456462i	$-0.849117\pi$
$631$		−	576.055i		−	0.912923i	0.889743	−	0.456462i	$-0.150883\pi$
$632$		0			0
$633$	−909.237			−1.43639
$634$		0			0
$635$	241.750	−	241.750i	0.380708	−	0.380708i
$636$		0			0
$637$		−	330.222i		−	0.518402i
$638$		0			0
$639$	73.5558			0.115111
$640$		0			0
$641$	−34.4488	−	34.4488i	−0.0537422	−	0.0537422i	0.679725	−	0.733467i	$-0.262099\pi$
$641$	−34.4488	−	34.4488i	−0.0537422	−	0.0537422i	−0.733467	+	0.679725i	$0.762099\pi$
$642$		0			0
$643$		−	642.429i		−	0.999111i	−0.866282	−	0.499556i	$-0.833497\pi$
$643$		−	642.429i		−	0.999111i	0.866282	−	0.499556i	$-0.166503\pi$
$644$		0			0
$645$	−11.0719			−0.0171657
$646$		0			0
$647$			251.396i			0.388557i	0.980946	+	0.194278i	$0.0622365\pi$
$647$			251.396i			0.388557i	−0.980946	+	0.194278i	$0.937764\pi$
$648$		0			0
$649$	13.4235	+	13.4235i	0.0206833	+	0.0206833i
$650$		0			0
$651$		−	511.071i		−	0.785055i
$652$		0			0
$653$	430.038	−	430.038i	0.658557	−	0.658557i	−0.296481	−	0.955039i	$-0.595813\pi$
$653$	430.038	−	430.038i	0.658557	−	0.658557i	0.955039	+	0.296481i	$0.0958132\pi$
$654$		0			0
$655$	440.855	+	440.855i	0.673060	+	0.673060i
$656$		0			0
$657$	346.566	+	346.566i	0.527497	+	0.527497i
$658$		0			0
$659$	267.913	+	267.913i	0.406545	+	0.406545i	0.880532	−	0.473987i	$-0.157186\pi$
$659$	267.913	+	267.913i	0.406545	+	0.406545i	−0.473987	+	0.880532i	$0.657186\pi$
$660$		0			0
$661$	−648.167			−0.980585			−0.490292	−	0.871558i	$-0.663110\pi$
$661$	−648.167			−0.980585			−0.490292	+	0.871558i	$0.663110\pi$
$662$		0			0
$663$	−631.342			−0.952250
$664$		0			0
$665$	95.9461	−	95.9461i	0.144280	−	0.144280i
$666$		0			0
$667$	−3.22492	−	272.127i	−0.00483496	−	0.407986i
$668$		0			0
$669$	−705.612	−	705.612i	−1.05473	−	1.05473i
$670$		0			0
$671$			1.23603i			0.00184208i
$672$		0			0
$673$			1086.30i			1.61412i	0.590468	+	0.807061i	$0.298943\pi$
$673$			1086.30i			1.61412i	−0.590468	+	0.807061i	$0.701057\pi$
$674$		0			0
$675$	−95.2082	+	95.2082i	−0.141049	+	0.141049i
$676$		0			0
$677$	−242.392	+	242.392i	−0.358039	+	0.358039i	−0.863090	−	0.505051i	$-0.831474\pi$
$677$	−242.392	+	242.392i	−0.358039	+	0.358039i	0.505051	+	0.863090i	$0.331474\pi$
$678$		0			0
$679$	386.799	−	386.799i	0.569660	−	0.569660i
$680$		0			0
$681$	−435.471	−	435.471i	−0.639458	−	0.639458i
$682$		0			0
$683$	−934.310			−1.36795			−0.683975	−	0.729505i	$-0.739750\pi$
$683$	−934.310			−1.36795			−0.683975	+	0.729505i	$0.739750\pi$
$684$		0			0
$685$	160.022	−	160.022i	0.233609	−	0.233609i
$686$		0			0
$687$	−368.396			−0.536239
$688$		0			0
$689$		−	938.271i		−	1.36179i
$690$		0			0
$691$	−784.538			−1.13537			−0.567683	−	0.823247i	$-0.692160\pi$
$691$	−784.538			−1.13537			−0.567683	+	0.823247i	$0.692160\pi$
$692$		0			0
$693$	−9.90910	+	9.90910i	−0.0142988	+	0.0142988i
$694$		0			0
$695$		−	424.901i		−	0.611369i
$696$		0			0
$697$	372.219			0.534031
$698$		0			0
$699$	−1363.23	−	1363.23i	−1.95026	−	1.95026i
$700$		0			0
$701$		−	638.589i		−	0.910969i	−0.890244	−	0.455484i	$-0.849466\pi$
$701$		−	638.589i		−	0.910969i	0.890244	−	0.455484i	$-0.150534\pi$
$702$		0			0
$703$	390.729			0.555803
$704$		0			0
$705$			729.723i			1.03507i
$706$		0			0
$707$	317.283	+	317.283i	0.448774	+	0.448774i
$708$		0			0
$709$		−	104.632i		−	0.147577i	−0.997274	−	0.0737885i	$-0.976491\pi$
$709$		−	104.632i		−	0.147577i	0.997274	−	0.0737885i	$-0.0235090\pi$
$710$		0			0
$711$	685.256	−	685.256i	0.963793	−	0.963793i
$712$		0			0
$713$	172.024	+	172.024i	0.241268	+	0.241268i
$714$		0			0
$715$	−6.47939	−	6.47939i	−0.00906208	−	0.00906208i
$716$		0			0
$717$	894.668	+	894.668i	1.24779	+	1.24779i
$718$		0			0
$719$	−664.811			−0.924633			−0.462317	−	0.886715i	$-0.652982\pi$
$719$	−664.811			−0.924633			−0.462317	+	0.886715i	$0.652982\pi$
$720$		0			0
$721$	485.883			0.673902
$722$		0			0
$723$	−1148.56	+	1148.56i	−1.58860	+	1.58860i
$724$		0			0
$725$	5.95810	+	502.760i	0.00821807	+	0.693462i
$726$		0			0
$727$	223.557	+	223.557i	0.307506	+	0.307506i	0.843942	−	0.536435i	$-0.180229\pi$
$727$	223.557	+	223.557i	0.307506	+	0.307506i	−0.536435	+	0.843942i	$0.680229\pi$
$728$		0			0
$729$			979.285i			1.34333i
$730$		0			0
$731$			11.3537i			0.0155318i
$732$		0			0
$733$	912.207	−	912.207i	1.24448	−	1.24448i	0.286362	−	0.958121i	$-0.407554\pi$
$733$	912.207	−	912.207i	1.24448	−	1.24448i	0.958121	−	0.286362i	$-0.0924461\pi$
$734$		0			0
$735$	255.017	−	255.017i	0.346962	−	0.346962i
$736$		0			0
$737$	−1.34893	+	1.34893i	−0.00183029	+	0.00183029i
$738$		0			0
$739$	−54.2609	−	54.2609i	−0.0734248	−	0.0734248i	0.669441	−	0.742866i	$-0.266534\pi$
$739$	−54.2609	−	54.2609i	−0.0734248	−	0.0734248i	−0.742866	+	0.669441i	$0.766534\pi$
$740$		0			0
$741$	553.038			0.746340
$742$		0			0
$743$	−589.082	+	589.082i	−0.792842	+	0.792842i	−0.981955	−	0.189113i	$-0.939439\pi$
$743$	−589.082	+	589.082i	−0.792842	+	0.792842i	0.189113	+	0.981955i	$0.439439\pi$
$744$		0			0
$745$	294.899			0.395837
$746$		0			0
$747$			5.47873i			0.00733430i
$748$		0			0
$749$	526.607			0.703080
$750$		0			0
$751$	549.273	−	549.273i	0.731389	−	0.731389i	−0.239506	−	0.970895i	$-0.576985\pi$
$751$	549.273	−	549.273i	0.731389	−	0.731389i	0.970895	+	0.239506i	$0.0769855\pi$
$752$		0			0
$753$			1611.33i			2.13988i
$754$		0			0
$755$	−483.591			−0.640518
$756$		0			0
$757$	1025.07	+	1025.07i	1.35412	+	1.35412i	0.881001	+	0.473114i	$0.156870\pi$
$757$	1025.07	+	1025.07i	1.35412	+	1.35412i	0.473114	+	0.881001i	$0.343130\pi$
$758$		0			0
$759$		−	12.2568i		−	0.0161486i
$760$		0			0
$761$	−950.582			−1.24912			−0.624561	−	0.780976i	$-0.714722\pi$
$761$	−950.582			−1.24912			−0.624561	+	0.780976i	$0.714722\pi$
$762$		0			0
$763$			92.7901i			0.121612i
$764$		0			0
$765$	−265.354	−	265.354i	−0.346867	−	0.346867i
$766$		0			0
$767$			727.481i			0.948476i
$768$		0			0
$769$	37.8431	−	37.8431i	0.0492107	−	0.0492107i	−0.682073	−	0.731284i	$-0.738921\pi$
$769$	37.8431	−	37.8431i	0.0492107	−	0.0492107i	0.731284	+	0.682073i	$0.238921\pi$
$770$		0			0
$771$	888.316	+	888.316i	1.15216	+	1.15216i
$772$		0			0
$773$	713.986	+	713.986i	0.923655	+	0.923655i	0.997286	−	0.0736302i	$-0.0234585\pi$
$773$	713.986	+	713.986i	0.923655	+	0.923655i	−0.0736302	+	0.997286i	$0.523458\pi$
$774$		0			0
$775$	−317.818	−	317.818i	−0.410088	−	0.410088i
$776$		0			0
$777$	−697.132			−0.897210
$778$		0			0
$779$	−326.054			−0.418554
$780$		0			0
$781$	1.42235	−	1.42235i	0.00182119	−	0.00182119i
$782$		0			0
$783$	−161.126	−	157.352i	−0.205780	−	0.200960i
$784$		0			0
$785$	362.277	+	362.277i	0.461499	+	0.461499i
$786$		0			0
$787$			1041.21i			1.32301i	0.749941	+	0.661504i	$0.230082\pi$
$787$			1041.21i			1.32301i	−0.749941	+	0.661504i	$0.769918\pi$
$788$		0			0
$789$			1419.95i			1.79968i
$790$		0			0
$791$	−286.555	+	286.555i	−0.362269	+	0.362269i
$792$		0			0
$793$	−33.4933	+	33.4933i	−0.0422361	+	0.0422361i
$794$		0			0
$795$	724.589	−	724.589i	0.911433	−	0.911433i
$796$		0			0
$797$	−257.713	−	257.713i	−0.323353	−	0.323353i	0.526699	−	0.850052i	$-0.323430\pi$
$797$	−257.713	−	257.713i	−0.323353	−	0.323353i	−0.850052	+	0.526699i	$0.823430\pi$
$798$		0			0
$799$	748.298			0.936543
$800$		0			0
$801$	−965.859	+	965.859i	−1.20582	+	1.20582i
$802$		0			0
$803$	13.4031			0.0166912
$804$		0			0
$805$		−	115.240i		−	0.143156i
$806$		0			0
$807$	−172.128			−0.213294
$808$		0			0
$809$	710.446	−	710.446i	0.878177	−	0.878177i	−0.115169	−	0.993346i	$-0.536741\pi$
$809$	710.446	−	710.446i	0.878177	−	0.878177i	0.993346	+	0.115169i	$0.0367408\pi$
$810$		0			0
$811$		−	887.475i		−	1.09430i	−0.837036	−	0.547148i	$-0.815713\pi$
$811$		−	887.475i		−	1.09430i	0.837036	−	0.547148i	$-0.184287\pi$
$812$		0			0
$813$	−298.342			−0.366964
$814$		0			0
$815$	545.030	+	545.030i	0.668749	+	0.668749i
$816$		0			0
$817$		−	9.94554i		−	0.0121732i
$818$		0			0
$819$	−537.020			−0.655703
$820$		0			0
$821$			634.321i			0.772620i	0.922369	+	0.386310i	$0.126250\pi$
$821$			634.321i			0.772620i	−0.922369	+	0.386310i	$0.873750\pi$
$822$		0			0
$823$	230.662	+	230.662i	0.280269	+	0.280269i	0.833216	−	0.552947i	$-0.186497\pi$
$823$	230.662	+	230.662i	0.280269	+	0.280269i	−0.552947	+	0.833216i	$0.686497\pi$
$824$		0			0
$825$			22.6446i			0.0274480i
$826$		0			0
$827$	520.099	−	520.099i	0.628898	−	0.628898i	−0.318892	−	0.947791i	$-0.603311\pi$
$827$	520.099	−	520.099i	0.628898	−	0.628898i	0.947791	+	0.318892i	$0.103311\pi$
$828$		0			0
$829$	392.874	+	392.874i	0.473913	+	0.473913i	0.903178	−	0.429266i	$-0.141228\pi$
$829$	392.874	+	392.874i	0.473913	+	0.473913i	−0.429266	+	0.903178i	$0.641228\pi$
$830$		0			0
$831$	−673.837	−	673.837i	−0.810874	−	0.810874i
$832$		0			0
$833$	−261.508	−	261.508i	−0.313936	−	0.313936i
$834$		0			0
$835$	423.211			0.506840
$836$		0			0
$837$	201.325			0.240531
$838$		0			0
$839$	−928.080	+	928.080i	−1.10617	+	1.10617i	−0.112526	+	0.993649i	$0.535894\pi$
$839$	−928.080	+	928.080i	−1.10617	+	1.10617i	−0.993649	+	0.112526i	$0.964106\pi$
$840$		0			0
$841$	−840.764	+	19.9302i	−0.999719	+	0.0236982i
$842$		0			0
$843$	383.859	+	383.859i	0.455349	+	0.455349i
$844$		0			0
$845$			116.656i			0.138055i
$846$		0			0
$847$		−	536.412i		−	0.633308i
$848$		0			0
$849$	−1051.20	+	1051.20i	−1.23817	+	1.23817i
$850$		0			0
$851$	234.651	−	234.651i	0.275736	−	0.275736i
$852$		0			0
$853$	480.100	−	480.100i	0.562837	−	0.562837i	−0.367275	−	0.930112i	$-0.619709\pi$
$853$	480.100	−	480.100i	0.562837	−	0.562837i	0.930112	+	0.367275i	$0.119709\pi$
$854$		0			0
$855$	232.442	+	232.442i	0.271862	+	0.271862i
$856$		0			0
$857$	440.715			0.514253			0.257127	−	0.966378i	$-0.417224\pi$
$857$	440.715			0.514253			0.257127	+	0.966378i	$0.417224\pi$
$858$		0			0
$859$	−850.091	+	850.091i	−0.989629	+	0.989629i	−0.999947	−	0.0103182i	$-0.996716\pi$
$859$	−850.091	+	850.091i	−0.989629	+	0.989629i	0.0103182	+	0.999947i	$0.496716\pi$
$860$		0			0
$861$	581.739			0.675655
$862$		0			0
$863$			416.930i			0.483117i	0.970386	+	0.241559i	$0.0776586\pi$
$863$			416.930i			0.483117i	−0.970386	+	0.241559i	$0.922341\pi$
$864$		0			0
$865$	607.491			0.702302
$866$		0			0
$867$	408.142	−	408.142i	0.470752	−	0.470752i
$868$		0			0
$869$		−	26.5016i		−	0.0304967i
$870$		0			0
$871$	−73.1046			−0.0839319
$872$		0			0
$873$	937.072	+	937.072i	1.07339	+	1.07339i
$874$		0			0
$875$			519.911i			0.594184i
$876$		0			0
$877$	−607.597			−0.692813			−0.346406	−	0.938085i	$-0.612598\pi$
$877$	−607.597			−0.692813			−0.346406	+	0.938085i	$0.612598\pi$
$878$		0			0
$879$			1416.81i			1.61184i
$880$		0			0
$881$	−116.619	−	116.619i	−0.132371	−	0.132371i	0.637817	−	0.770188i	$-0.279838\pi$
$881$	−116.619	−	116.619i	−0.132371	−	0.132371i	−0.770188	+	0.637817i	$0.779838\pi$
$882$		0			0
$883$			1435.34i			1.62553i	0.582593	+	0.812764i	$0.302038\pi$
$883$			1435.34i			1.62553i	−0.582593	+	0.812764i	$0.697962\pi$
$884$		0			0
$885$	−561.804	+	561.804i	−0.634807	+	0.634807i
$886$		0			0
$887$	−582.938	−	582.938i	−0.657202	−	0.657202i	0.297515	−	0.954717i	$-0.403842\pi$
$887$	−582.938	−	582.938i	−0.657202	−	0.657202i	−0.954717	+	0.297515i	$0.903842\pi$
$888$		0			0
$889$	−387.447	−	387.447i	−0.435823	−	0.435823i
$890$		0			0
$891$	12.9304	+	12.9304i	0.0145123	+	0.0145123i
$892$		0			0
$893$	−655.488			−0.734029
$894$		0			0
$895$	191.135			0.213558
$896$		0			0
$897$	332.125	−	332.125i	0.370263	−	0.370263i
$898$		0			0
$899$	525.262	−	537.861i	0.584273	−	0.598288i
$900$		0			0
$901$	−743.033	−	743.033i	−0.824676	−	0.824676i
$902$		0			0
$903$			17.7446i			0.0196508i
$904$		0			0
$905$			551.176i			0.609034i
$906$		0			0
$907$	−323.163	+	323.163i	−0.356299	+	0.356299i	−0.862447	−	0.506148i	$-0.831069\pi$
$907$	−323.163	+	323.163i	−0.356299	+	0.356299i	0.506148	+	0.862447i	$0.331069\pi$
$908$		0			0
$909$	−768.660	+	768.660i	−0.845611	+	0.845611i
$910$		0			0
$911$	949.914	−	949.914i	1.04272	−	1.04272i	0.0436700	−	0.999046i	$-0.486095\pi$
$911$	949.914	−	949.914i	1.04272	−	1.04272i	0.999046	−	0.0436700i	$-0.0139050\pi$
$912$		0			0
$913$	0.105942	+	0.105942i	0.000116037	+	0.000116037i
$914$		0			0
$915$	−51.7310			−0.0565366
$916$		0			0
$917$	706.547	−	706.547i	0.770498	−	0.770498i
$918$		0			0
$919$	810.818			0.882283			0.441141	−	0.897438i	$-0.354574\pi$
$919$	810.818			0.882283			0.441141	+	0.897438i	$0.354574\pi$
$920$		0			0
$921$		−	1491.22i		−	1.61913i
$922$		0			0
$923$	77.0837			0.0835143
$924$		0			0
$925$	−433.524	+	433.524i	−0.468674	+	0.468674i
$926$		0			0
$927$			1177.12i			1.26981i
$928$		0			0
$929$	−232.810			−0.250603			−0.125302	−	0.992119i	$-0.539990\pi$
$929$	−232.810			−0.250603			−0.125302	+	0.992119i	$0.539990\pi$
$930$		0			0
$931$	229.074	+	229.074i	0.246052	+	0.246052i
$932$		0			0
$933$			1306.55i			1.40037i
$934$		0			0
$935$	−10.2623			−0.0109757
$936$		0			0
$937$			70.4701i			0.0752082i	0.999293	+	0.0376041i	$0.0119726\pi$
$937$			70.4701i			0.0752082i	−0.999293	+	0.0376041i	$0.988027\pi$
$938$		0			0
$939$	−463.473	−	463.473i	−0.493581	−	0.493581i
$940$		0			0
$941$		−	1101.46i		−	1.17052i	−0.810846	−	0.585260i	$-0.800992\pi$
$941$		−	1101.46i		−	1.17052i	0.810846	−	0.585260i	$-0.199008\pi$
$942$		0			0
$943$	−195.811	+	195.811i	−0.207647	+	0.207647i
$944$		0			0
$945$	−67.4345	−	67.4345i	−0.0713592	−	0.0713592i
$946$		0			0
$947$	205.477	+	205.477i	0.216977	+	0.216977i	0.807223	−	0.590246i	$-0.200969\pi$
$947$	205.477	+	205.477i	0.216977	+	0.216977i	−0.590246	+	0.807223i	$0.700969\pi$
$948$		0			0
$949$	363.187	+	363.187i	0.382705	+	0.382705i
$950$		0			0
$951$	−1335.15			−1.40394
$952$		0			0
$953$	−517.717			−0.543249			−0.271625	−	0.962403i	$-0.587561\pi$
$953$	−517.717			−0.543249			−0.271625	+	0.962403i	$0.587561\pi$
$954$		0			0
$955$	323.505	−	323.505i	0.338749	−	0.338749i
$956$		0			0
$957$	−37.8738	+	0.448835i	−0.0395756	+	0.000469002i
$958$		0			0
$959$	−256.464	−	256.464i	−0.267428	−	0.267428i
$960$		0			0
$961$		−	288.950i		−	0.300677i
$962$		0			0
$963$			1275.77i			1.32479i
$964$		0			0
$965$	573.596	−	573.596i	0.594400	−	0.594400i
$966$		0			0
$967$	529.870	−	529.870i	0.547952	−	0.547952i	−0.377896	−	0.925848i	$-0.623352\pi$
$967$	529.870	−	529.870i	0.547952	−	0.547952i	0.925848	+	0.377896i	$0.123352\pi$
$968$		0			0
$969$	437.960	−	437.960i	0.451971	−	0.451971i
$970$		0			0
$971$	−551.288	−	551.288i	−0.567753	−	0.567753i	0.363745	−	0.931498i	$-0.381498\pi$
$971$	−551.288	−	551.288i	−0.567753	−	0.567753i	−0.931498	+	0.363745i	$0.881498\pi$
$972$		0			0
$973$	−680.979			−0.699876
$974$		0			0
$975$	−613.609	+	613.609i	−0.629342	+	0.629342i
$976$		0			0
$977$	1188.63			1.21661			0.608304	−	0.793704i	$-0.291850\pi$
$977$	1188.63			1.21661			0.608304	+	0.793704i	$0.291850\pi$
$978$		0			0
$979$			37.3536i			0.0381549i
$980$		0			0
$981$	−224.796			−0.229150
$982$		0			0
$983$	34.8545	−	34.8545i	0.0354573	−	0.0354573i	−0.689156	−	0.724613i	$-0.742018\pi$
$983$	34.8545	−	34.8545i	0.0354573	−	0.0354573i	0.724613	+	0.689156i	$0.242018\pi$
$984$		0			0
$985$			632.570i			0.642203i
$986$		0			0
$987$	1169.51			1.18491
$988$		0			0
$989$	−5.97277	−	5.97277i	−0.00603920	−	0.00603920i
$990$		0			0
$991$		−	336.096i		−	0.339149i	−0.985517	−	0.169574i	$-0.945761\pi$
$991$		−	336.096i		−	0.339149i	0.985517	−	0.169574i	$-0.0542393\pi$
$992$		0			0
$993$	−1878.63			−1.89187
$994$		0			0
$995$		−	880.681i		−	0.885107i
$996$		0			0
$997$	368.652	+	368.652i	0.369762	+	0.369762i	0.867390	−	0.497629i	$-0.165796\pi$
$997$	368.652	+	368.652i	0.369762	+	0.369762i	−0.497629	+	0.867390i	$0.665796\pi$
$998$		0			0
$999$		−	274.619i		−	0.274894i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.3.l.e.273.7		14
4.3	odd	2		232.3.j.a.41.1	yes	14
29.17	odd	4	inner	464.3.l.e.17.7		14
116.75	even	4		232.3.j.a.17.1	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
232.3.j.a.17.1	✓	14	116.75	even	4
232.3.j.a.41.1	yes	14	4.3	odd	2
464.3.l.e.17.7		14	29.17	odd	4	inner
464.3.l.e.273.7		14	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	464.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.14226 + 3.14226i) q^{3} +2.76807i q^{5} +4.43633 q^{7} +10.7476i q^{9} +O(q^{10})\)	\(q+(3.14226 + 3.14226i) q^{3} +2.76807i q^{5} +4.43633 q^{7} +10.7476i q^{9} +(0.207826 + 0.207826i) q^{11} +11.2631i q^{13} +(-8.69801 + 8.69801i) q^{15} +(8.91941 + 8.91941i) q^{17} +(-7.81315 - 7.81315i) q^{19} +(13.9401 + 13.9401i) q^{21} -9.38434 q^{23} +17.3378 q^{25} +(-5.49137 + 5.49137i) q^{27} +(0.343649 + 28.9980i) q^{29} +(-18.3310 - 18.3310i) q^{31} +1.30609i q^{33} +12.2801i q^{35} +(-25.0046 + 25.0046i) q^{37} +(-35.3915 + 35.3915i) q^{39} +(20.8657 - 20.8657i) q^{41} +(0.636461 + 0.636461i) q^{43} -29.7501 q^{45} +(41.9477 - 41.9477i) q^{47} -29.3190 q^{49} +56.0542i q^{51} -83.3052 q^{53} +(-0.575278 + 0.575278i) q^{55} -49.1019i q^{57} +64.5900 q^{59} +(2.97373 + 2.97373i) q^{61} +47.6798i q^{63} -31.1770 q^{65} +6.49066i q^{67} +(-29.4880 - 29.4880i) q^{69} -6.84394i q^{71} +(32.2459 - 32.2459i) q^{73} +(54.4798 + 54.4798i) q^{75} +(0.921984 + 0.921984i) q^{77} +(-63.7591 - 63.7591i) q^{79} +62.2177 q^{81} +0.509763 q^{83} +(-24.6896 + 24.6896i) q^{85} +(-90.0393 + 92.1990i) q^{87} +(89.8675 + 89.8675i) q^{89} +49.9666i q^{91} -115.201i q^{93} +(21.6274 - 21.6274i) q^{95} +(87.1890 - 87.1890i) q^{97} +(-2.23363 + 2.23363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 4 q^{3} - 8 q^{7}+O(q^{10}) \) 14 * q - 4 * q^3 - 8 * q^7	\( 14 q - 4 q^{3} - 8 q^{7} + 6 q^{15} - 34 q^{17} - 50 q^{19} - 28 q^{21} + 12 q^{23} - 102 q^{25} + 38 q^{27} + 6 q^{29} - 60 q^{31} + 38 q^{37} - 82 q^{39} + 18 q^{41} + 48 q^{43} + 260 q^{45} + 136 q^{47} + 66 q^{49} - 60 q^{53} + 86 q^{55} - 60 q^{59} + 106 q^{61} - 272 q^{65} - 180 q^{69} + 182 q^{73} + 42 q^{75} + 260 q^{77} + 72 q^{79} - 6 q^{81} - 332 q^{83} - 144 q^{85} + 312 q^{87} + 30 q^{89} - 340 q^{95} + 58 q^{97} + 594 q^{99}+O(q^{100}) \) 14 * q - 4 * q^3 - 8 * q^7 + 6 * q^15 - 34 * q^17 - 50 * q^19 - 28 * q^21 + 12 * q^23 - 102 * q^25 + 38 * q^27 + 6 * q^29 - 60 * q^31 + 38 * q^37 - 82 * q^39 + 18 * q^41 + 48 * q^43 + 260 * q^45 + 136 * q^47 + 66 * q^49 - 60 * q^53 + 86 * q^55 - 60 * q^59 + 106 * q^61 - 272 * q^65 - 180 * q^69 + 182 * q^73 + 42 * q^75 + 260 * q^77 + 72 * q^79 - 6 * q^81 - 332 * q^83 - 144 * q^85 + 312 * q^87 + 30 * q^89 - 340 * q^95 + 58 * q^97 + 594 * q^99

Introduction

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