LMFDB - Embedded newform 588.4.i.l.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,4,Mod(361,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("588.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	588.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$34.6931230834$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 27x^{6} + 10x^{5} + 446x^{4} + 62x^{3} + 3061x^{2} + 2142x + 14161 $ x^8 - 2x^7 + 27x^6 + 10x^5 + 446x^4 + 62x^3 + 3061x^2 + 2142*x + 14161
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.2
Root			$2.46576 + 4.27083i$ of defining polynomial
Character	$\chi$	$=$	588.373
Dual form			588.4.i.l.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{3} +(-5.32752 + 9.22754i) q^{5} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 + 2.59808i) q^{3} +(-5.32752 + 9.22754i) q^{5} +(-4.50000 + 7.79423i) q^{9} +(3.32699 + 5.76252i) q^{11} -75.9335 q^{13} -31.9651 q^{15} +(-52.1435 - 90.3152i) q^{17} +(42.7472 - 74.0402i) q^{19} +(34.3366 - 59.4728i) q^{23} +(5.73498 + 9.93327i) q^{25} -27.0000 q^{27} +87.7843 q^{29} +(31.3841 + 54.3589i) q^{31} +(-9.98098 + 17.2876i) q^{33} +(-21.1047 + 36.5544i) q^{37} +(-113.900 - 197.281i) q^{39} -313.904 q^{41} +306.591 q^{43} +(-47.9477 - 83.0479i) q^{45} +(107.541 - 186.266i) q^{47} +(156.430 - 270.946i) q^{51} +(-262.512 - 454.684i) q^{53} -70.8986 q^{55} +256.483 q^{57} +(180.246 + 312.195i) q^{59} +(400.363 - 693.449i) q^{61} +(404.537 - 700.679i) q^{65} +(20.1143 + 34.8390i) q^{67} +206.020 q^{69} -298.781 q^{71} +(258.563 + 447.844i) q^{73} +(-17.2049 + 29.7998i) q^{75} +(611.233 - 1058.69i) q^{79} +(-40.5000 - 70.1481i) q^{81} -1328.55 q^{83} +1111.18 q^{85} +(131.676 + 228.070i) q^{87} +(-319.969 + 554.203i) q^{89} +(-94.1524 + 163.077i) q^{93} +(455.473 + 788.902i) q^{95} -1425.65 q^{97} -59.8859 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{3} - 36 q^{9}+O(q^{10}) $ 8 * q + 12 * q^3 - 36 * q^9	$ 8 q + 12 q^{3} - 36 q^{9} + 48 q^{17} + 192 q^{19} - 192 q^{23} - 324 q^{25} - 216 q^{27} + 192 q^{29} + 48 q^{31} - 256 q^{37} - 2016 q^{41} - 224 q^{43} + 864 q^{47} - 144 q^{51} + 648 q^{53} - 4704 q^{55} + 1152 q^{57} + 336 q^{59} + 960 q^{61} + 360 q^{65} - 720 q^{67} - 1152 q^{69} - 2688 q^{71} + 672 q^{73} + 972 q^{75} + 1984 q^{79} - 324 q^{81} - 6240 q^{83} + 1360 q^{85} + 288 q^{87} + 2160 q^{89} - 144 q^{93} + 3744 q^{95} - 4032 q^{97}+O(q^{100}) $ 8 * q + 12 * q^3 - 36 * q^9 + 48 * q^17 + 192 * q^19 - 192 * q^23 - 324 * q^25 - 216 * q^27 + 192 * q^29 + 48 * q^31 - 256 * q^37 - 2016 * q^41 - 224 * q^43 + 864 * q^47 - 144 * q^51 + 648 * q^53 - 4704 * q^55 + 1152 * q^57 + 336 * q^59 + 960 * q^61 + 360 * q^65 - 720 * q^67 - 1152 * q^69 - 2688 * q^71 + 672 * q^73 + 972 * q^75 + 1984 * q^79 - 324 * q^81 - 6240 * q^83 + 1360 * q^85 + 288 * q^87 + 2160 * q^89 - 144 * q^93 + 3744 * q^95 - 4032 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$		0			0
$5$	−5.32752	+	9.22754i	−0.476508	+	0.825336i	−0.999638	−	0.0269168i	$-0.991431\pi$
$5$	−5.32752	+	9.22754i	−0.476508	+	0.825336i	0.523129	+	0.852253i	$0.324764\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	3.32699	+	5.76252i	0.0911933	+	0.157951i	0.908014	−	0.418941i	$-0.137599\pi$
$11$	3.32699	+	5.76252i	0.0911933	+	0.157951i	−0.816820	+	0.576892i	$0.804265\pi$
$12$		0			0
$13$	−75.9335			−1.62001			−0.810006	−	0.586422i	$-0.800536\pi$
$13$	−75.9335			−1.62001			−0.810006	+	0.586422i	$0.800536\pi$
$14$		0			0
$15$	−31.9651			−0.550224
$16$		0			0
$17$	−52.1435	−	90.3152i	−0.743921	−	1.28851i	−0.950697	−	0.310121i	$-0.899631\pi$
$17$	−52.1435	−	90.3152i	−0.743921	−	1.28851i	0.206776	−	0.978388i	$-0.433703\pi$
$18$		0			0
$19$	42.7472	−	74.0402i	0.516151	−	0.894000i	−0.483673	−	0.875249i	$-0.660698\pi$
$19$	42.7472	−	74.0402i	0.516151	−	0.894000i	0.999824	−	0.0187511i	$-0.00596900\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	34.3366	−	59.4728i	0.311291	−	0.539171i	−0.667351	−	0.744743i	$-0.732572\pi$
$23$	34.3366	−	59.4728i	0.311291	−	0.539171i	0.978642	+	0.205572i	$0.0659054\pi$
$24$		0			0
$25$	5.73498	+	9.93327i	0.0458798	+	0.0794662i
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	87.7843			0.562108			0.281054	−	0.959692i	$-0.409316\pi$
$29$	87.7843			0.562108			0.281054	+	0.959692i	$0.409316\pi$
$30$		0			0
$31$	31.3841	+	54.3589i	0.181831	+	0.314940i	0.942504	−	0.334195i	$-0.108464\pi$
$31$	31.3841	+	54.3589i	0.181831	+	0.314940i	−0.760673	+	0.649135i	$0.775131\pi$
$32$		0			0
$33$	−9.98098	+	17.2876i	−0.0526505	+	0.0911933i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−21.1047	+	36.5544i	−0.0937726	+	0.162419i	−0.909096	−	0.416587i	$-0.863226\pi$
$37$	−21.1047	+	36.5544i	−0.0937726	+	0.162419i	0.815323	+	0.579006i	$0.196559\pi$
$38$		0			0
$39$	−113.900	−	197.281i	−0.467657	−	0.810006i
$40$		0			0
$41$	−313.904			−1.19570			−0.597848	−	0.801609i	$-0.703977\pi$
$41$	−313.904			−1.19570			−0.597848	+	0.801609i	$0.703977\pi$
$42$		0			0
$43$	306.591			1.08732			0.543659	−	0.839306i	$-0.317038\pi$
$43$	306.591			1.08732			0.543659	+	0.839306i	$0.317038\pi$
$44$		0			0
$45$	−47.9477	−	83.0479i	−0.158836	−	0.275112i
$46$		0			0
$47$	107.541	−	186.266i	0.333754	−	0.578079i	−0.649491	−	0.760369i	$-0.725018\pi$
$47$	107.541	−	186.266i	0.333754	−	0.578079i	0.983245	+	0.182291i	$0.0583513\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	156.430	−	270.946i	0.429503	−	0.743921i
$52$		0			0
$53$	−262.512	−	454.684i	−0.680354	−	1.17841i	−0.974873	−	0.222762i	$-0.928493\pi$
$53$	−262.512	−	454.684i	−0.680354	−	1.17841i	0.294519	−	0.955646i	$-0.404841\pi$
$54$		0			0
$55$	−70.8986			−0.173818
$56$		0			0
$57$	256.483			0.596000
$58$		0			0
$59$	180.246	+	312.195i	0.397729	+	0.688886i	0.993445	−	0.114308i	$-0.0364652\pi$
$59$	180.246	+	312.195i	0.397729	+	0.688886i	−0.595717	+	0.803195i	$0.703132\pi$
$60$		0			0
$61$	400.363	−	693.449i	0.840348	−	1.45553i	−0.0492530	−	0.998786i	$-0.515684\pi$
$61$	400.363	−	693.449i	0.840348	−	1.45553i	0.889601	−	0.456739i	$-0.150983\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	404.537	−	700.679i	0.771949	−	1.33705i
$66$		0			0
$67$	20.1143	+	34.8390i	0.0366769	+	0.0635262i	0.883781	−	0.467900i	$-0.154989\pi$
$67$	20.1143	+	34.8390i	0.0366769	+	0.0635262i	−0.847104	+	0.531427i	$0.821656\pi$
$68$		0			0
$69$	206.020			0.359447
$70$		0			0
$71$	−298.781			−0.499419			−0.249709	−	0.968321i	$-0.580335\pi$
$71$	−298.781			−0.499419			−0.249709	+	0.968321i	$0.580335\pi$
$72$		0			0
$73$	258.563	+	447.844i	0.414555	+	0.718030i	0.995382	−	0.0959971i	$-0.0306040\pi$
$73$	258.563	+	447.844i	0.414555	+	0.718030i	−0.580827	+	0.814027i	$0.697271\pi$
$74$		0			0
$75$	−17.2049	+	29.7998i	−0.0264887	+	0.0458798i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	611.233	−	1058.69i	0.870494	−	1.50774i	0.00900832	−	0.999959i	$-0.497133\pi$
$79$	611.233	−	1058.69i	0.870494	−	1.50774i	0.861486	−	0.507781i	$-0.169534\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−1328.55			−1.75696			−0.878479	−	0.477782i	$-0.841441\pi$
$83$	−1328.55			−1.75696			−0.878479	+	0.477782i	$0.841441\pi$
$84$		0			0
$85$	1111.18			1.41794
$86$		0			0
$87$	131.676	+	228.070i	0.162267	+	0.281054i
$88$		0			0
$89$	−319.969	+	554.203i	−0.381086	+	0.660060i	−0.991218	−	0.132240i	$-0.957783\pi$
$89$	−319.969	+	554.203i	−0.381086	+	0.660060i	0.610132	+	0.792300i	$0.291116\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−94.1524	+	163.077i	−0.104980	+	0.181831i
$94$		0			0
$95$	455.473	+	788.902i	0.491900	+	0.851996i
$96$		0			0
$97$	−1425.65			−1.49230			−0.746149	−	0.665779i	$-0.768099\pi$
$97$	−1425.65			−1.49230			−0.746149	+	0.665779i	$0.768099\pi$
$98$		0			0
$99$	−59.8859			−0.0607956
$100$		0			0
$101$	−496.085	−	859.244i	−0.488736	−	0.846515i	0.511180	−	0.859473i	$-0.329208\pi$
$101$	−496.085	−	859.244i	−0.488736	−	0.846515i	−0.999916	+	0.0129585i	$0.995875\pi$
$102$		0			0
$103$	133.786	−	231.724i	0.127984	−	0.221674i	−0.794912	−	0.606725i	$-0.792483\pi$
$103$	133.786	−	231.724i	0.127984	−	0.221674i	0.922895	+	0.385051i	$0.125816\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	768.312	−	1330.76i	0.694164	−	1.20233i	−0.276298	−	0.961072i	$-0.589108\pi$
$107$	768.312	−	1330.76i	0.694164	−	1.20233i	0.970462	−	0.241255i	$-0.0775591\pi$
$108$		0			0
$109$	−499.410	−	865.004i	−0.438852	−	0.760113i	0.558750	−	0.829336i	$-0.311281\pi$
$109$	−499.410	−	865.004i	−0.438852	−	0.760113i	−0.997601	+	0.0692232i	$0.977948\pi$
$110$		0			0
$111$	−126.628			−0.108279
$112$		0			0
$113$	939.006			0.781719			0.390860	−	0.920450i	$-0.372178\pi$
$113$	939.006			0.781719			0.390860	+	0.920450i	$0.372178\pi$
$114$		0			0
$115$	365.858	+	633.685i	0.296665	+	0.513839i
$116$		0			0
$117$	341.701	−	591.843i	0.270002	−	0.467657i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	643.362	−	1114.34i	0.483368	−	0.837217i
$122$		0			0
$123$	−470.856	−	815.546i	−0.345168	−	0.597848i
$124$		0			0
$125$	−1454.09			−1.04046
$126$		0			0
$127$	−1621.27			−1.13279			−0.566397	−	0.824133i	$-0.691663\pi$
$127$	−1621.27			−1.13279			−0.566397	+	0.824133i	$0.691663\pi$
$128$		0			0
$129$	459.887	+	796.547i	0.313882	+	0.543659i
$130$		0			0
$131$	759.214	−	1315.00i	0.506357	−	0.877037i	−0.493616	−	0.869680i	$-0.664325\pi$
$131$	759.214	−	1315.00i	0.506357	−	0.877037i	0.999973	−	0.00735640i	$-0.00234164\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	143.843	−	249.144i	0.0917041	−	0.158836i
$136$		0			0
$137$	1242.50	+	2152.07i	0.774844	+	1.34207i	0.934882	+	0.354958i	$0.115505\pi$
$137$	1242.50	+	2152.07i	0.774844	+	1.34207i	−0.160038	+	0.987111i	$0.551162\pi$
$138$		0			0
$139$	1655.36			1.01011			0.505057	−	0.863086i	$-0.331471\pi$
$139$	1655.36			1.01011			0.505057	+	0.863086i	$0.331471\pi$
$140$		0			0
$141$	645.244			0.385386
$142$		0			0
$143$	−252.630	−	437.568i	−0.147734	−	0.255883i
$144$		0			0
$145$	−467.673	+	810.033i	−0.267849	+	0.463928i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−175.095	+	303.274i	−0.0962709	+	0.166746i	−0.910138	−	0.414305i	$-0.864025\pi$
$149$	−175.095	+	303.274i	−0.0962709	+	0.166746i	0.813867	+	0.581051i	$0.197358\pi$
$150$		0			0
$151$	−1669.07	−	2890.91i	−0.899516	−	1.55801i	−0.828114	−	0.560560i	$-0.810586\pi$
$151$	−1669.07	−	2890.91i	−0.899516	−	1.55801i	−0.0714022	−	0.997448i	$-0.522747\pi$
$152$		0			0
$153$	938.583			0.495947
$154$		0			0
$155$	−668.799			−0.346576
$156$		0			0
$157$	−871.836	−	1510.06i	−0.443185	−	0.767620i	0.554738	−	0.832025i	$-0.312818\pi$
$157$	−871.836	−	1510.06i	−0.443185	−	0.767620i	−0.997924	+	0.0644052i	$0.979485\pi$
$158$		0			0
$159$	787.535	−	1364.05i	0.392803	−	0.680354i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1715.78	+	2971.82i	−0.824480	+	1.42804i	0.0778354	+	0.996966i	$0.475199\pi$
$163$	−1715.78	+	2971.82i	−0.824480	+	1.42804i	−0.902316	+	0.431076i	$0.858134\pi$
$164$		0			0
$165$	−106.348	−	184.200i	−0.0501768	−	0.0869088i
$166$		0			0
$167$	−3381.05			−1.56667			−0.783335	−	0.621600i	$-0.786483\pi$
$167$	−3381.05			−1.56667			−0.783335	+	0.621600i	$0.786483\pi$
$168$		0			0
$169$	3568.89			1.62444
$170$		0			0
$171$	384.724	+	666.362i	0.172050	+	0.298000i
$172$		0			0
$173$	−670.501	+	1161.34i	−0.294666	+	0.510377i	−0.974907	−	0.222612i	$-0.928542\pi$
$173$	−670.501	+	1161.34i	−0.294666	+	0.510377i	0.680241	+	0.732988i	$0.261875\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−540.737	+	936.584i	−0.229629	+	0.397729i
$178$		0			0
$179$	−562.574	−	974.407i	−0.234909	−	0.406875i	0.724337	−	0.689446i	$-0.242146\pi$
$179$	−562.574	−	974.407i	−0.234909	−	0.406875i	−0.959246	+	0.282571i	$0.908813\pi$
$180$		0			0
$181$	3535.04			1.45170			0.725848	−	0.687855i	$-0.241447\pi$
$181$	3535.04			1.45170			0.725848	+	0.687855i	$0.241447\pi$
$182$		0			0
$183$	2402.18			0.970350
$184$		0			0
$185$	−224.871	−	389.488i	−0.0893668	−	0.154788i
$186$		0			0
$187$	346.962	−	600.956i	0.135681	−	0.235007i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1319.95	+	2286.21i	−0.500041	+	0.866097i	0.499959	+	0.866049i	$0.333349\pi$
$191$	−1319.95	+	2286.21i	−0.500041	+	0.866097i	−1.00000		4.78599e-5i	$0.999985\pi$
$192$		0			0
$193$	−523.526	−	906.774i	−0.195255	−	0.338192i	0.751729	−	0.659472i	$-0.229220\pi$
$193$	−523.526	−	906.774i	−0.195255	−	0.338192i	−0.946984	+	0.321280i	$0.895887\pi$
$194$		0			0
$195$	2427.22			0.891370
$196$		0			0
$197$	−4585.45			−1.65837			−0.829187	−	0.558972i	$-0.811196\pi$
$197$	−4585.45			−1.65837			−0.829187	+	0.558972i	$0.811196\pi$
$198$		0			0
$199$	415.371	+	719.444i	0.147964	+	0.256282i	0.930475	−	0.366356i	$-0.119395\pi$
$199$	415.371	+	719.444i	0.147964	+	0.256282i	−0.782511	+	0.622637i	$0.786061\pi$
$200$		0			0
$201$	−60.3429	+	104.517i	−0.0211754	+	0.0366769i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1672.33	−	2896.56i	0.569759	−	0.986852i
$206$		0			0
$207$	309.030	+	535.255i	0.103764	+	0.179724i
$208$		0			0
$209$	568.878			0.188278
$210$		0			0
$211$	−2630.08			−0.858114			−0.429057	−	0.903277i	$-0.641154\pi$
$211$	−2630.08			−0.858114			−0.429057	+	0.903277i	$0.641154\pi$
$212$		0			0
$213$	−448.171	−	776.255i	−0.144170	−	0.249709i
$214$		0			0
$215$	−1633.37	+	2829.08i	−0.518116	+	0.897404i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−775.689	+	1343.53i	−0.239343	+	0.414555i
$220$		0			0
$221$	3959.44	+	6857.94i	1.20516	+	2.08740i
$222$		0			0
$223$	863.988			0.259448			0.129724	−	0.991550i	$-0.458591\pi$
$223$	863.988			0.259448			0.129724	+	0.991550i	$0.458591\pi$
$224$		0			0
$225$	−103.230			−0.0305865
$226$		0			0
$227$	−2080.18	−	3602.97i	−0.608221	−	1.05347i	−0.991533	−	0.129851i	$-0.958550\pi$
$227$	−2080.18	−	3602.97i	−0.608221	−	1.05347i	0.383312	−	0.923619i	$-0.374783\pi$
$228$		0			0
$229$	−90.6052	+	156.933i	−0.0261457	+	0.0452856i	−0.878802	−	0.477186i	$-0.841657\pi$
$229$	−90.6052	+	156.933i	−0.0261457	+	0.0452856i	0.852657	+	0.522472i	$0.174990\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1075.22	+	1862.34i	−0.302319	+	0.523631i	−0.976661	−	0.214788i	$-0.931094\pi$
$233$	−1075.22	+	1862.34i	−0.302319	+	0.523631i	0.674342	+	0.738419i	$0.264427\pi$
$234$		0			0
$235$	1145.85	+	1984.67i	0.318073	+	0.550918i
$236$		0			0
$237$	3667.40			1.00516
$238$		0			0
$239$	−6939.47			−1.87815			−0.939073	−	0.343719i	$-0.888313\pi$
$239$	−6939.47			−1.87815			−0.939073	+	0.343719i	$0.888313\pi$
$240$		0			0
$241$	−103.085	−	178.548i	−0.0275530	−	0.0477232i	0.851920	−	0.523672i	$-0.175438\pi$
$241$	−103.085	−	178.548i	−0.0275530	−	0.0477232i	−0.879473	+	0.475949i	$0.842105\pi$
$242$		0			0
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3245.94	+	5622.13i	−0.836171	+	1.44829i
$248$		0			0
$249$	−1992.83	−	3451.68i	−0.507190	−	0.878479i
$250$		0			0
$251$	−5011.93			−1.26036			−0.630180	−	0.776449i	$-0.717019\pi$
$251$	−5011.93			−1.26036			−0.630180	+	0.776449i	$0.717019\pi$
$252$		0			0
$253$	456.951			0.113551
$254$		0			0
$255$	1666.77	+	2886.94i	0.409323	+	0.708969i
$256$		0			0
$257$	−2931.54	+	5077.58i	−0.711535	+	1.23241i	0.252746	+	0.967533i	$0.418666\pi$
$257$	−2931.54	+	5077.58i	−0.711535	+	1.23241i	−0.964281	+	0.264882i	$0.914667\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−395.029	+	684.211i	−0.0936847	+	0.162267i
$262$		0			0
$263$	2819.78	+	4884.00i	0.661122	+	1.14510i	0.980321	+	0.197409i	$0.0632526\pi$
$263$	2819.78	+	4884.00i	0.661122	+	1.14510i	−0.319200	+	0.947688i	$0.603414\pi$
$264$		0			0
$265$	5594.15			1.29678
$266$		0			0
$267$	−1919.81			−0.440040
$268$		0			0
$269$	−1488.32	−	2577.84i	−0.337339	−	0.584289i	0.646592	−	0.762836i	$-0.276194\pi$
$269$	−1488.32	−	2577.84i	−0.337339	−	0.584289i	−0.983931	+	0.178547i	$0.942860\pi$
$270$		0			0
$271$	−1403.67	+	2431.22i	−0.314637	+	0.544968i	−0.979360	−	0.202122i	$-0.935216\pi$
$271$	−1403.67	+	2431.22i	−0.314637	+	0.544968i	0.664723	+	0.747090i	$0.268550\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−38.1605	+	66.0959i	−0.00836787	+	0.0144936i
$276$		0			0
$277$	959.194	+	1661.37i	0.208059	+	0.360369i	0.951103	−	0.308874i	$-0.0999520\pi$
$277$	959.194	+	1661.37i	0.208059	+	0.360369i	−0.743044	+	0.669243i	$0.766619\pi$
$278$		0			0
$279$	−564.915			−0.121221
$280$		0			0
$281$	5209.50			1.10595			0.552977	−	0.833197i	$-0.313492\pi$
$281$	5209.50			1.10595			0.552977	+	0.833197i	$0.313492\pi$
$282$		0			0
$283$	3748.35	+	6492.33i	0.787337	+	1.36371i	0.927593	+	0.373592i	$0.121874\pi$
$283$	3748.35	+	6492.33i	0.787337	+	1.36371i	−0.140256	+	0.990115i	$0.544793\pi$
$284$		0			0
$285$	−1366.42	+	2366.71i	−0.283999	+	0.491900i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−2981.39	+	5163.92i	−0.606837	+	1.05107i
$290$		0			0
$291$	−2138.48	−	3703.95i	−0.430789	−	0.746149i
$292$		0			0
$293$	3358.94			0.669732			0.334866	−	0.942266i	$-0.391309\pi$
$293$	3358.94			0.669732			0.334866	+	0.942266i	$0.391309\pi$
$294$		0			0
$295$	−3841.05			−0.758084
$296$		0			0
$297$	−89.8289	−	155.588i	−0.0175502	−	0.0303978i
$298$		0			0
$299$	−2607.30	+	4515.98i	−0.504294	+	0.873463i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	1488.25	−	2577.73i	0.282172	−	0.488736i
$304$		0			0
$305$	4265.89	+	7388.73i	0.800865	+	1.38714i
$306$		0			0
$307$	7330.92			1.36286			0.681429	−	0.731884i	$-0.261359\pi$
$307$	7330.92			1.36286			0.681429	+	0.731884i	$0.261359\pi$
$308$		0			0
$309$	802.716			0.147783
$310$		0			0
$311$	−1019.27	−	1765.42i	−0.185843	−	0.321890i	0.758017	−	0.652235i	$-0.226168\pi$
$311$	−1019.27	−	1765.42i	−0.185843	−	0.321890i	−0.943860	+	0.330345i	$0.892835\pi$
$312$		0			0
$313$	2069.44	−	3584.37i	0.373711	−	0.647286i	−0.616423	−	0.787416i	$-0.711419\pi$
$313$	2069.44	−	3584.37i	0.373711	−	0.647286i	0.990133	+	0.140130i	$0.0447520\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3776.13	−	6540.44i	0.669049	−	1.15883i	−0.309122	−	0.951022i	$-0.600035\pi$
$317$	3776.13	−	6540.44i	0.669049	−	1.15883i	0.978171	−	0.207804i	$-0.0666316\pi$
$318$		0			0
$319$	292.058	+	505.859i	0.0512605	+	0.0887858i
$320$		0			0
$321$	4609.87			0.801552
$322$		0			0
$323$	−8915.94			−1.53590
$324$		0			0
$325$	−435.477	−	754.268i	−0.0743258	−	0.128736i
$326$		0			0
$327$	1498.23	−	2595.01i	0.253371	−	0.438852i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−2788.85	+	4830.43i	−0.463109	+	0.802128i	−0.999114	−	0.0420865i	$-0.986599\pi$
$331$	−2788.85	+	4830.43i	−0.463109	+	0.802128i	0.536005	+	0.844215i	$0.319933\pi$
$332$		0			0
$333$	−189.942	−	328.989i	−0.0312575	−	0.0541396i
$334$		0			0
$335$	−428.637			−0.0699073
$336$		0			0
$337$	4467.16			0.722083			0.361041	−	0.932550i	$-0.382421\pi$
$337$	4467.16			0.722083			0.361041	+	0.932550i	$0.382421\pi$
$338$		0			0
$339$	1408.51	+	2439.61i	0.225663	+	0.390860i
$340$		0			0
$341$	−208.830	+	361.704i	−0.0331635	+	0.0574409i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−1097.58	+	1901.06i	−0.171280	+	0.296665i
$346$		0			0
$347$	−4894.21	−	8477.01i	−0.757161	−	1.31144i	−0.944293	−	0.329106i	$-0.893253\pi$
$347$	−4894.21	−	8477.01i	−0.757161	−	1.31144i	0.187132	−	0.982335i	$-0.440081\pi$
$348$		0			0
$349$	4746.95			0.728075			0.364038	−	0.931384i	$-0.381398\pi$
$349$	4746.95			0.728075			0.364038	+	0.931384i	$0.381398\pi$
$350$		0			0
$351$	2050.20			0.311771
$352$		0			0
$353$	−4717.33	−	8170.65i	−0.711269	−	1.23195i	−0.964381	−	0.264517i	$-0.914787\pi$
$353$	−4717.33	−	8170.65i	−0.711269	−	1.23195i	0.253112	−	0.967437i	$-0.418546\pi$
$354$		0			0
$355$	1591.76	−	2757.01i	0.237977	−	0.412189i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5653.77	+	9792.62i	−0.831183	+	1.43965i	0.0659178	+	0.997825i	$0.479002\pi$
$359$	−5653.77	+	9792.62i	−0.831183	+	1.43965i	−0.897101	+	0.441826i	$0.854331\pi$
$360$		0			0
$361$	−225.138	−	389.950i	−0.0328237	−	0.0568523i
$362$		0			0
$363$	3860.17			0.558145
$364$		0			0
$365$	−5510.00			−0.790155
$366$		0			0
$367$	3044.80	+	5273.76i	0.433072	+	0.750103i	0.997136	−	0.0756282i	$-0.0240962\pi$
$367$	3044.80	+	5273.76i	0.433072	+	0.750103i	−0.564064	+	0.825731i	$0.690763\pi$
$368$		0			0
$369$	1412.57	−	2446.64i	0.199283	−	0.345168i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	1300.92	−	2253.26i	0.180588	−	0.312787i	−0.761493	−	0.648173i	$-0.775533\pi$
$373$	1300.92	−	2253.26i	0.180588	−	0.312787i	0.942081	+	0.335386i	$0.108867\pi$
$374$		0			0
$375$	−2181.14	−	3777.85i	−0.300356	−	0.520232i
$376$		0			0
$377$	−6665.77			−0.910622
$378$		0			0
$379$	10416.2			1.41173			0.705865	−	0.708347i	$-0.250559\pi$
$379$	10416.2			1.41173			0.705865	+	0.708347i	$0.250559\pi$
$380$		0			0
$381$	−2431.91	−	4212.19i	−0.327009	−	0.566397i
$382$		0			0
$383$	−832.230	+	1441.47i	−0.111031	+	0.192312i	−0.916186	−	0.400753i	$-0.868749\pi$
$383$	−832.230	+	1441.47i	−0.111031	+	0.192312i	0.805155	+	0.593064i	$0.202082\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1379.66	+	2389.64i	−0.181220	+	0.313882i
$388$		0			0
$389$	667.078	+	1155.41i	0.0869465	+	0.150596i	0.906219	−	0.422809i	$-0.138956\pi$
$389$	667.078	+	1155.41i	0.0869465	+	0.150596i	−0.819272	+	0.573404i	$0.805622\pi$
$390$		0			0
$391$	−7161.73			−0.926302
$392$		0			0
$393$	4555.28			0.584691
$394$		0			0
$395$	6512.71	+	11280.4i	0.829596	+	1.43690i
$396$		0			0
$397$	2222.44	−	3849.38i	0.280960	−	0.486637i	−0.690662	−	0.723178i	$-0.742681\pi$
$397$	2222.44	−	3849.38i	0.280960	−	0.486637i	0.971621	+	0.236541i	$0.0760139\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1324.91	−	2294.81i	0.164995	−	0.285779i	−0.771659	−	0.636037i	$-0.780573\pi$
$401$	1324.91	−	2294.81i	0.164995	−	0.285779i	0.936653	+	0.350258i	$0.113906\pi$
$402$		0			0
$403$	−2383.11	−	4127.66i	−0.294568	−	0.510207i
$404$		0			0
$405$	863.059			0.105891
$406$		0			0
$407$	−280.860			−0.0342057
$408$		0			0
$409$	−4796.33	−	8307.49i	−0.579862	−	1.00435i	−0.995495	−	0.0948173i	$-0.969773\pi$
$409$	−4796.33	−	8307.49i	−0.579862	−	1.00435i	0.415633	−	0.909532i	$-0.363560\pi$
$410$		0			0
$411$	−3727.49	+	6456.20i	−0.447356	+	0.774844i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	7077.89	−	12259.3i	0.837205	−	1.45008i
$416$		0			0
$417$	2483.04	+	4300.76i	0.291595	+	0.505057i
$418$		0			0
$419$	−16850.1			−1.96463			−0.982317	−	0.187224i	$-0.940051\pi$
$419$	−16850.1			−1.96463			−0.982317	+	0.187224i	$0.940051\pi$
$420$		0			0
$421$	1691.10			0.195770			0.0978849	−	0.995198i	$-0.468792\pi$
$421$	1691.10			0.195770			0.0978849	+	0.995198i	$0.468792\pi$
$422$		0			0
$423$	967.867	+	1676.39i	0.111251	+	0.192693i
$424$		0			0
$425$	598.084	−	1035.91i	0.0682619	−	0.118233i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	757.891	−	1312.71i	0.0852944	−	0.147734i
$430$		0			0
$431$	3394.67	+	5879.74i	0.379386	+	0.657117i	0.990973	−	0.134061i	$-0.0428018\pi$
$431$	3394.67	+	5879.74i	0.379386	+	0.657117i	−0.611587	+	0.791177i	$0.709468\pi$
$432$		0			0
$433$	−10386.6			−1.15276			−0.576382	−	0.817180i	$-0.695536\pi$
$433$	−10386.6			−1.15276			−0.576382	+	0.817180i	$0.695536\pi$
$434$		0			0
$435$	−2806.04			−0.309286
$436$		0			0
$437$	−2935.59	−	5084.58i	−0.321346	−	0.556587i
$438$		0			0
$439$	−2106.13	+	3647.92i	−0.228975	+	0.396596i	−0.957505	−	0.288418i	$-0.906871\pi$
$439$	−2106.13	+	3647.92i	−0.228975	+	0.396596i	0.728530	+	0.685014i	$0.240204\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	904.980	−	1567.47i	0.0970585	−	0.168110i	−0.813407	−	0.581694i	$-0.802390\pi$
$443$	904.980	−	1567.47i	0.0970585	−	0.168110i	0.910466	+	0.413584i	$0.135723\pi$
$444$		0			0
$445$	−3409.28	−	5905.05i	−0.363181	−	0.629048i
$446$		0			0
$447$	−1050.57			−0.111164
$448$		0			0
$449$	1768.29			0.185859			0.0929297	−	0.995673i	$-0.470377\pi$
$449$	1768.29			0.185859			0.0929297	+	0.995673i	$0.470377\pi$
$450$		0			0
$451$	−1044.36	−	1808.88i	−0.109040	−	0.188862i
$452$		0			0
$453$	5007.21	−	8672.74i	0.519336	−	0.899516i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−2186.30	+	3786.79i	−0.223788	+	0.387611i	−0.955955	−	0.293513i	$-0.905176\pi$
$457$	−2186.30	+	3786.79i	−0.223788	+	0.387611i	0.732167	+	0.681125i	$0.238509\pi$
$458$		0			0
$459$	1407.87	+	2438.51i	0.143168	+	0.247974i
$460$		0			0
$461$	1164.34			0.117633			0.0588165	−	0.998269i	$-0.481267\pi$
$461$	1164.34			0.117633			0.0588165	+	0.998269i	$0.481267\pi$
$462$		0			0
$463$	−14893.9			−1.49498			−0.747491	−	0.664272i	$-0.768742\pi$
$463$	−14893.9			−1.49498			−0.747491	+	0.664272i	$0.768742\pi$
$464$		0			0
$465$	−1003.20	−	1737.59i	−0.100048	−	0.173288i
$466$		0			0
$467$	9580.14	−	16593.3i	0.949285	−	1.64421i	0.202349	−	0.979314i	$-0.435143\pi$
$467$	9580.14	−	16593.3i	0.949285	−	1.64421i	0.746936	−	0.664896i	$-0.231524\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	2615.51	−	4530.19i	0.255873	−	0.443185i
$472$		0			0
$473$	1020.03	+	1766.74i	0.0991562	+	0.171744i
$474$		0			0
$475$	980.616			0.0947237
$476$		0			0
$477$	4725.21			0.453569
$478$		0			0
$479$	−4703.14	−	8146.08i	−0.448626	−	0.777043i	0.549671	−	0.835381i	$-0.314753\pi$
$479$	−4703.14	−	8146.08i	−0.448626	−	0.777043i	−0.998297	+	0.0583380i	$0.981420\pi$
$480$		0			0
$481$	1602.55	−	2775.70i	0.151913	−	0.263121i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7595.19	−	13155.3i	0.711092	−	1.23165i
$486$		0			0
$487$	−6230.39	−	10791.4i	−0.579725	−	1.00411i	−0.995511	−	0.0946505i	$-0.969827\pi$
$487$	−6230.39	−	10791.4i	−0.579725	−	1.00411i	0.415786	−	0.909463i	$-0.363507\pi$
$488$		0			0
$489$	−10294.7			−0.952028
$490$		0			0
$491$	12868.0			1.18274			0.591369	−	0.806401i	$-0.298588\pi$
$491$	12868.0			1.18274			0.591369	+	0.806401i	$0.298588\pi$
$492$		0			0
$493$	−4577.38	−	7928.26i	−0.418164	−	0.724281i
$494$		0			0
$495$	319.044	−	552.600i	0.0289696	−	0.0501768i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	6852.50	−	11868.9i	0.614750	−	1.06478i	−0.375679	−	0.926750i	$-0.622590\pi$
$499$	6852.50	−	11868.9i	0.614750	−	1.06478i	0.990428	−	0.138028i	$-0.0440763\pi$
$500$		0			0
$501$	−5071.58	−	8784.23i	−0.452258	−	0.783335i
$502$		0			0
$503$	−10126.1			−0.897616			−0.448808	−	0.893628i	$-0.648151\pi$
$503$	−10126.1			−0.897616			−0.448808	+	0.893628i	$0.648151\pi$
$504$		0			0
$505$	10571.6			0.931546
$506$		0			0
$507$	5353.34	+	9272.25i	0.468935	+	0.812219i
$508$		0			0
$509$	−3118.03	+	5400.59i	−0.271521	+	0.470288i	−0.969252	−	0.246072i	$-0.920860\pi$
$509$	−3118.03	+	5400.59i	−0.271521	+	0.470288i	0.697730	+	0.716360i	$0.254193\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−1154.17	+	1999.09i	−0.0993333	+	0.172050i
$514$		0			0
$515$	1425.50	+	2469.03i	0.121971	+	0.211259i
$516$		0			0
$517$	1431.15			0.121744
$518$		0			0
$519$	−4023.00			−0.340251
$520$		0			0
$521$	8508.38	+	14737.0i	0.715468	+	1.23923i	0.962779	+	0.270291i	$0.0871200\pi$
$521$	8508.38	+	14737.0i	0.715468	+	1.23923i	−0.247310	+	0.968936i	$0.579547\pi$
$522$		0			0
$523$	−2907.31	+	5035.61i	−0.243074	+	0.421017i	−0.961588	−	0.274496i	$-0.911489\pi$
$523$	−2907.31	+	5035.61i	−0.243074	+	0.421017i	0.718514	+	0.695512i	$0.244822\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3272.96	−	5668.93i	0.270536	−	0.468582i
$528$		0			0
$529$	3725.49	+	6452.74i	0.306196	+	0.530348i
$530$		0			0
$531$	−3244.42			−0.265152
$532$		0			0
$533$	23835.8			1.93704
$534$		0			0
$535$	8186.41	+	14179.3i	0.661550	+	1.14584i
$536$		0			0
$537$	1687.72	−	2923.22i	0.135625	−	0.234909i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	5034.59	−	8720.17i	0.400100	−	0.692993i	−0.593638	−	0.804732i	$-0.702309\pi$
$541$	5034.59	−	8720.17i	0.400100	−	0.692993i	0.993738	+	0.111739i	$0.0356421\pi$
$542$		0			0
$543$	5302.55	+	9184.29i	0.419069	+	0.725848i
$544$		0			0
$545$	10642.5			0.836466
$546$		0			0
$547$	−7437.51			−0.581362			−0.290681	−	0.956820i	$-0.593882\pi$
$547$	−7437.51			−0.581362			−0.290681	+	0.956820i	$0.593882\pi$
$548$		0			0
$549$	3603.27	+	6241.04i	0.280116	+	0.485175i
$550$		0			0
$551$	3752.53	−	6499.57i	0.290133	−	0.502525i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	674.614	−	1168.47i	0.0515960	−	0.0893668i
$556$		0			0
$557$	−10893.6	−	18868.2i	−0.828680	−	1.43532i	−0.899074	−	0.437796i	$-0.855759\pi$
$557$	−10893.6	−	18868.2i	−0.828680	−	1.43532i	0.0703944	−	0.997519i	$-0.477574\pi$
$558$		0			0
$559$	−23280.5			−1.76147
$560$		0			0
$561$	2081.77			0.156671
$562$		0			0
$563$	1286.24	+	2227.83i	0.0962851	+	0.166771i	0.910144	−	0.414292i	$-0.135971\pi$
$563$	1286.24	+	2227.83i	0.0962851	+	0.166771i	−0.813859	+	0.581062i	$0.802637\pi$
$564$		0			0
$565$	−5002.58	+	8664.72i	−0.372496	+	0.645181i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8790.29	−	15225.2i	0.647642	−	1.12175i	−0.336043	−	0.941847i	$-0.609089\pi$
$569$	8790.29	−	15225.2i	0.647642	−	1.12175i	0.983685	−	0.179902i	$-0.0575780\pi$
$570$		0			0
$571$	−3610.37	−	6253.35i	−0.264605	−	0.458309i	0.702855	−	0.711333i	$-0.251908\pi$
$571$	−3610.37	−	6253.35i	−0.264605	−	0.458309i	−0.967460	+	0.253024i	$0.918575\pi$
$572$		0			0
$573$	−7919.67			−0.577398
$574$		0			0
$575$	787.679			0.0571278
$576$		0			0
$577$	5577.54	+	9660.58i	0.402419	+	0.697011i	0.994017	−	0.109222i	$-0.0348360\pi$
$577$	5577.54	+	9660.58i	0.402419	+	0.697011i	−0.591598	+	0.806233i	$0.701503\pi$
$578$		0			0
$579$	1570.58	−	2720.32i	0.112731	−	0.195255i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1746.75	−	3025.46i	0.124088	−	0.214926i
$584$		0			0
$585$	3640.84	+	6306.11i	0.257316	+	0.445685i
$586$		0			0
$587$	15216.2			1.06992			0.534958	−	0.844879i	$-0.320327\pi$
$587$	15216.2			1.06992			0.534958	+	0.844879i	$0.320327\pi$
$588$		0			0
$589$	5366.33			0.375409
$590$		0			0
$591$	−6878.17	−	11913.3i	−0.478731	−	0.829187i
$592$		0			0
$593$	1921.95	−	3328.91i	0.133094	−	0.230526i	−0.791774	−	0.610815i	$-0.790842\pi$
$593$	1921.95	−	3328.91i	0.133094	−	0.230526i	0.924868	+	0.380289i	$0.124175\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1246.11	+	2158.33i	−0.0854272	+	0.147964i
$598$		0			0
$599$	−9373.48	−	16235.3i	−0.639382	−	1.10744i	−0.985569	−	0.169277i	$-0.945857\pi$
$599$	−9373.48	−	16235.3i	−0.639382	−	1.10744i	0.346186	−	0.938166i	$-0.387476\pi$
$600$		0			0
$601$	9864.63			0.669529			0.334764	−	0.942302i	$-0.391343\pi$
$601$	9864.63			0.669529			0.334764	+	0.942302i	$0.391343\pi$
$602$		0			0
$603$	−362.057			−0.0244513
$604$		0			0
$605$	6855.06	+	11873.3i	0.460657	+	0.797882i
$606$		0			0
$607$	11146.4	−	19306.2i	0.745336	−	1.29096i	−0.204701	−	0.978824i	$-0.565622\pi$
$607$	11146.4	−	19306.2i	0.745336	−	1.29096i	0.950038	−	0.312136i	$-0.101044\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−8165.94	+	14143.8i	−0.540685	+	0.936494i
$612$		0			0
$613$	−3023.39	−	5236.67i	−0.199206	−	0.345036i	0.749065	−	0.662497i	$-0.230503\pi$
$613$	−3023.39	−	5236.67i	−0.199206	−	0.345036i	−0.948271	+	0.317461i	$0.897170\pi$
$614$		0			0
$615$	10034.0			0.657901
$616$		0			0
$617$	−9383.68			−0.612273			−0.306137	−	0.951988i	$-0.599036\pi$
$617$	−9383.68			−0.612273			−0.306137	+	0.951988i	$0.599036\pi$
$618$		0			0
$619$	−1994.75	−	3455.00i	−0.129525	−	0.224343i	0.793968	−	0.607960i	$-0.208012\pi$
$619$	−1994.75	−	3455.00i	−0.129525	−	0.224343i	−0.923492	+	0.383617i	$0.874678\pi$
$620$		0			0
$621$	−927.089	+	1605.77i	−0.0599079	+	0.103764i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	7029.85	−	12176.1i	0.449910	−	0.779267i
$626$		0			0
$627$	853.317	+	1477.99i	0.0543512	+	0.0941391i
$628$		0			0
$629$	4401.88			0.279038
$630$		0			0
$631$	11434.0			0.721363			0.360681	−	0.932689i	$-0.382544\pi$
$631$	11434.0			0.721363			0.360681	+	0.932689i	$0.382544\pi$
$632$		0			0
$633$	−3945.12	−	6833.14i	−0.247716	−	0.429057i
$634$		0			0
$635$	8637.37	−	14960.4i	0.539785	−	0.934935i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	1344.51	−	2328.76i	0.0832365	−	0.144170i
$640$		0			0
$641$	7548.63	+	13074.6i	0.465137	+	0.805641i	0.999208	−	0.0397989i	$-0.0126717\pi$
$641$	7548.63	+	13074.6i	0.465137	+	0.805641i	−0.534071	+	0.845440i	$0.679338\pi$
$642$		0			0
$643$	−4170.19			−0.255764			−0.127882	−	0.991789i	$-0.540818\pi$
$643$	−4170.19			−0.255764			−0.127882	+	0.991789i	$0.540818\pi$
$644$		0			0
$645$	−9800.23			−0.598269
$646$		0			0
$647$	−2281.94	−	3952.44i	−0.138659	−	0.240164i	0.788330	−	0.615252i	$-0.210946\pi$
$647$	−2281.94	−	3952.44i	−0.138659	−	0.240164i	−0.926989	+	0.375088i	$0.877613\pi$
$648$		0			0
$649$	−1199.35	+	2077.34i	−0.0725404	+	0.125644i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1909.52	+	3307.39i	−0.114434	+	0.198205i	−0.917553	−	0.397613i	$-0.869839\pi$
$653$	−1909.52	+	3307.39i	−0.114434	+	0.198205i	0.803119	+	0.595818i	$0.203172\pi$
$654$		0			0
$655$	8089.46	+	14011.4i	0.482567	+	0.835830i
$656$		0			0
$657$	−4654.13			−0.276370
$658$		0			0
$659$	−4326.02			−0.255717			−0.127859	−	0.991792i	$-0.540810\pi$
$659$	−4326.02			−0.255717			−0.127859	+	0.991792i	$0.540810\pi$
$660$		0			0
$661$	−14658.9	−	25389.9i	−0.862579	−	1.49403i	−0.869431	−	0.494054i	$-0.835515\pi$
$661$	−14658.9	−	25389.9i	−0.862579	−	1.49403i	0.00685243	−	0.999977i	$-0.497819\pi$
$662$		0			0
$663$	−11878.3	+	20573.8i	−0.695800	+	1.20516i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3014.22	−	5220.78i	0.174979	−	0.303072i
$668$		0			0
$669$	1295.98	+	2244.71i	0.0748962	+	0.129724i
$670$		0			0
$671$	5328.02			0.306536
$672$		0			0
$673$	−5483.56			−0.314080			−0.157040	−	0.987592i	$-0.550195\pi$
$673$	−5483.56			−0.314080			−0.157040	+	0.987592i	$0.550195\pi$
$674$		0			0
$675$	−154.844	−	268.198i	−0.00882957	−	0.0152933i
$676$		0			0
$677$	−6034.67	+	10452.4i	−0.342587	+	0.593378i	−0.984912	−	0.173054i	$-0.944636\pi$
$677$	−6034.67	+	10452.4i	−0.342587	+	0.593378i	0.642325	+	0.766432i	$0.277970\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	6240.53	−	10808.9i	0.351157	−	0.608221i
$682$		0			0
$683$	−15398.4	−	26670.7i	−0.862667	−	1.49418i	−0.869345	−	0.494205i	$-0.835459\pi$
$683$	−15398.4	−	26670.7i	−0.862667	−	1.49418i	0.00667825	−	0.999978i	$-0.497874\pi$
$684$		0			0
$685$	−26477.7			−1.47688
$686$		0			0
$687$	−543.631			−0.0301904
$688$		0			0
$689$	19933.4	+	34525.7i	1.10218	+	1.90903i
$690$		0			0
$691$	−3250.98	+	5630.87i	−0.178977	+	0.309997i	−0.941530	−	0.336928i	$-0.890612\pi$
$691$	−3250.98	+	5630.87i	−0.178977	+	0.309997i	0.762553	+	0.646925i	$0.223945\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−8818.98	+	15274.9i	−0.481328	+	0.833685i
$696$		0			0
$697$	16368.0	+	28350.3i	0.889504	+	1.54067i
$698$		0			0
$699$	−6451.34			−0.349088
$700$		0			0
$701$	−2235.98			−0.120473			−0.0602367	−	0.998184i	$-0.519186\pi$
$701$	−2235.98			−0.120473			−0.0602367	+	0.998184i	$0.519186\pi$
$702$		0			0
$703$	1804.33	+	3125.19i	0.0968016	+	0.167665i
$704$		0			0
$705$	−3437.56	+	5954.02i	−0.183639	+	0.318073i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−17782.2	+	30799.7i	−0.941926	+	1.63146i	−0.180134	+	0.983642i	$0.557653\pi$
$709$	−17782.2	+	30799.7i	−0.941926	+	1.63146i	−0.761792	+	0.647822i	$0.775680\pi$
$710$		0			0
$711$	5501.09	+	9528.18i	0.290165	+	0.502580i
$712$		0			0
$713$	4310.50			0.226409
$714$		0			0
$715$	5383.57			0.281586
$716$		0			0
$717$	−10409.2	−	18029.3i	−0.542174	−	0.939073i
$718$		0			0
$719$	−4962.07	+	8594.56i	−0.257377	+	0.445790i	−0.965538	−	0.260260i	$-0.916192\pi$
$719$	−4962.07	+	8594.56i	−0.257377	+	0.445790i	0.708161	+	0.706051i	$0.249525\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	309.254	−	535.644i	0.0159077	−	0.0275530i
$724$		0			0
$725$	503.441	+	871.985i	0.0257894	+	0.0446686i
$726$		0			0
$727$	−880.081			−0.0448974			−0.0224487	−	0.999748i	$-0.507146\pi$
$727$	−880.081			−0.0448974			−0.0224487	+	0.999748i	$0.507146\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−15986.7	−	27689.8i	−0.808879	−	1.40102i
$732$		0			0
$733$	−8668.08	+	15013.5i	−0.436784	+	0.756532i	−0.997439	−	0.0715172i	$-0.977216\pi$
$733$	−8668.08	+	15013.5i	−0.436784	+	0.756532i	0.560655	+	0.828049i	$0.310549\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−133.840	+	231.818i	−0.00668937	+	0.0115863i
$738$		0			0
$739$	12293.2	+	21292.4i	0.611924	+	1.05988i	0.990916	+	0.134483i	$0.0429375\pi$
$739$	12293.2	+	21292.4i	0.611924	+	1.05988i	−0.378992	+	0.925400i	$0.623729\pi$
$740$		0			0
$741$	−19475.6			−0.965527
$742$		0			0
$743$	14579.3			0.719870			0.359935	−	0.932977i	$-0.382799\pi$
$743$	14579.3			0.719870			0.359935	+	0.932977i	$0.382799\pi$
$744$		0			0
$745$	−1865.65	−	3231.40i	−0.0917478	−	0.158912i
$746$		0			0
$747$	5978.48	−	10355.0i	0.292826	−	0.507190i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−8042.98	+	13930.8i	−0.390802	+	0.676889i	−0.992556	−	0.121793i	$-0.961136\pi$
$751$	−8042.98	+	13930.8i	−0.390802	+	0.676889i	0.601753	+	0.798682i	$0.294469\pi$
$752$		0			0
$753$	−7517.90	−	13021.4i	−0.363834	−	0.630180i
$754$		0			0
$755$	35568.0			1.71451
$756$		0			0
$757$	−37017.3			−1.77730			−0.888651	−	0.458584i	$-0.848357\pi$
$757$	−37017.3			−1.77730			−0.888651	+	0.458584i	$0.848357\pi$
$758$		0			0
$759$	685.427	+	1187.19i	0.0327792	+	0.0567753i
$760$		0			0
$761$	12303.2	−	21309.8i	0.586060	−	1.01509i	−0.408682	−	0.912677i	$-0.634011\pi$
$761$	12303.2	−	21309.8i	0.586060	−	1.01509i	0.994742	−	0.102410i	$-0.0326552\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−5000.32	+	8660.81i	−0.236323	+	0.409323i
$766$		0			0
$767$	−13686.7	−	23706.0i	−0.644325	−	1.11600i
$768$		0			0
$769$	12715.6			0.596275			0.298137	−	0.954523i	$-0.403635\pi$
$769$	12715.6			0.596275			0.298137	+	0.954523i	$0.403635\pi$
$770$		0			0
$771$	−17589.2			−0.821610
$772$		0			0
$773$	1587.11	+	2748.96i	0.0738480	+	0.127908i	0.900585	−	0.434681i	$-0.143139\pi$
$773$	1587.11	+	2748.96i	0.0738480	+	0.127908i	−0.826737	+	0.562589i	$0.809805\pi$
$774$		0			0
$775$	−359.975	+	623.495i	−0.0166847	+	0.0288988i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−13418.5	+	23241.5i	−0.617160	+	1.06895i
$780$		0			0
$781$	−994.042	−	1721.73i	−0.0455437	−	0.0788840i
$782$		0			0
$783$	−2370.18			−0.108178
$784$		0			0
$785$	18578.9			0.844726
$786$		0			0
$787$	−7784.94	−	13483.9i	−0.352609	−	0.610736i	0.634097	−	0.773254i	$-0.281372\pi$
$787$	−7784.94	−	13483.9i	−0.352609	−	0.610736i	−0.986706	+	0.162517i	$0.948039\pi$
$788$		0			0
$789$	−8459.34	+	14652.0i	−0.381699	+	0.661122i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−30400.9	+	52656.0i	−1.36137	+	2.35797i
$794$		0			0
$795$	8391.23	+	14534.0i	0.374347	+	0.648389i
$796$		0			0
$797$	31514.5			1.40063			0.700314	−	0.713835i	$-0.253043\pi$
$797$	31514.5			1.40063			0.700314	+	0.713835i	$0.253043\pi$
$798$		0			0
$799$	−22430.2			−0.993146
$800$		0			0
$801$	−2879.72	−	4987.82i	−0.127029	−	0.220020i
$802$		0			0
$803$	−1720.48	+	2979.95i	−0.0756093	+	0.130959i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	4464.95	−	7733.52i	0.194763	−	0.337339i
$808$		0			0
$809$	−5514.54	−	9551.47i	−0.239655	−	0.415095i	0.720960	−	0.692976i	$-0.243701\pi$
$809$	−5514.54	−	9551.47i	−0.239655	−	0.415095i	−0.960615	+	0.277882i	$0.910368\pi$
$810$		0			0
$811$	20830.5			0.901920			0.450960	−	0.892544i	$-0.351082\pi$
$811$	20830.5			0.901920			0.450960	+	0.892544i	$0.351082\pi$
$812$		0			0
$813$	−8422.00			−0.363312
$814$		0			0
$815$	−18281.7	−	31664.9i	−0.785743	−	1.36095i
$816$		0			0
$817$	13105.9	−	22700.1i	0.561221	−	0.972063i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	4674.53	−	8096.53i	0.198712	−	0.344179i	−0.749399	−	0.662118i	$-0.769658\pi$
$821$	4674.53	−	8096.53i	0.198712	−	0.344179i	0.948111	+	0.317940i	$0.102991\pi$
$822$		0			0
$823$	16445.3	+	28484.1i	0.696533	+	1.20643i	0.969661	+	0.244452i	$0.0786082\pi$
$823$	16445.3	+	28484.1i	0.696533	+	1.20643i	−0.273129	+	0.961978i	$0.588058\pi$
$824$		0			0
$825$	−228.963			−0.00966238
$826$		0			0
$827$	−13081.2			−0.550033			−0.275016	−	0.961440i	$-0.588683\pi$
$827$	−13081.2			−0.550033			−0.275016	+	0.961440i	$0.588683\pi$
$828$		0			0
$829$	14395.6	+	24933.9i	0.603112	+	1.04462i	0.992347	+	0.123482i	$0.0394060\pi$
$829$	14395.6	+	24933.9i	0.603112	+	1.04462i	−0.389235	+	0.921138i	$0.627261\pi$
$830$		0			0
$831$	−2877.58	+	4984.12i	−0.120123	+	0.208059i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	18012.6	−	31198.8i	0.746531	−	1.29303i
$836$		0			0
$837$	−847.372	−	1467.69i	−0.0349934	−	0.0606103i
$838$		0			0
$839$	36766.8			1.51291			0.756455	−	0.654046i	$-0.226930\pi$
$839$	36766.8			1.51291			0.756455	+	0.654046i	$0.226930\pi$
$840$		0			0
$841$	−16682.9			−0.684034
$842$		0			0
$843$	7814.25	+	13534.7i	0.319261	+	0.552977i
$844$		0			0
$845$	−19013.4	+	32932.1i	−0.774058	+	1.34071i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−11245.1	+	19477.0i	−0.454569	+	0.787337i
$850$		0			0
$851$	1449.33	+	2510.31i	0.0583810	+	0.101119i
$852$		0			0
$853$	−5899.55			−0.236808			−0.118404	−	0.992966i	$-0.537778\pi$
$853$	−5899.55			−0.236808			−0.118404	+	0.992966i	$0.537778\pi$
$854$		0			0
$855$	−8198.51			−0.327934
$856$		0			0
$857$	21138.5	+	36613.0i	0.842564	+	1.45936i	0.887720	+	0.460384i	$0.152288\pi$
$857$	21138.5	+	36613.0i	0.842564	+	1.45936i	−0.0451553	+	0.998980i	$0.514378\pi$
$858$		0			0
$859$	−3171.73	+	5493.59i	−0.125981	+	0.218206i	−0.922116	−	0.386913i	$-0.873541\pi$
$859$	−3171.73	+	5493.59i	−0.125981	+	0.218206i	0.796135	+	0.605119i	$0.206875\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−3464.89	+	6001.36i	−0.136670	+	0.236719i	−0.926234	−	0.376949i	$-0.876973\pi$
$863$	−3464.89	+	6001.36i	−0.136670	+	0.236719i	0.789564	+	0.613668i	$0.210307\pi$
$864$		0			0
$865$	−7144.22	−	12374.1i	−0.280822	−	0.486397i
$866$		0			0
$867$	−17888.3			−0.700715
$868$		0			0
$869$	8134.27			0.317533
$870$		0			0
$871$	−1527.35	−	2645.44i	−0.0594170	−	0.102913i
$872$		0			0
$873$	6415.43	−	11111.8i	0.248716	−	0.430789i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1643.94	+	2847.39i	−0.0632976	+	0.109635i	−0.895938	−	0.444180i	$-0.853495\pi$
$877$	−1643.94	+	2847.39i	−0.0632976	+	0.109635i	0.832640	+	0.553815i	$0.186828\pi$
$878$		0			0
$879$	5038.41	+	8726.79i	0.193335	+	0.334866i
$880$		0			0
$881$	46875.9			1.79261			0.896304	−	0.443439i	$-0.146242\pi$
$881$	46875.9			1.79261			0.896304	+	0.443439i	$0.146242\pi$
$882$		0			0
$883$	42479.4			1.61897			0.809483	−	0.587144i	$-0.199748\pi$
$883$	42479.4			1.61897			0.809483	+	0.587144i	$0.199748\pi$
$884$		0			0
$885$	−5761.58	−	9979.35i	−0.218840	−	0.379042i
$886$		0			0
$887$	1840.08	−	3187.11i	0.0696547	−	0.120645i	−0.829095	−	0.559108i	$-0.811144\pi$
$887$	1840.08	−	3187.11i	0.0696547	−	0.120645i	0.898749	+	0.438463i	$0.144477\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	269.487	−	466.764i	0.0101326	−	0.0175502i
$892$		0			0
$893$	−9194.12	−	15924.7i	−0.344535	−	0.596752i
$894$		0			0
$895$	11988.5			0.447745
$896$		0			0
$897$	−15643.8			−0.582309
$898$		0			0
$899$	2755.04	+	4771.86i	0.102209	+	0.177031i
$900$		0			0
$901$	−27376.6	+	47417.6i	−1.01226	+	1.75328i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−18833.0	+	32619.7i	−0.691745	+	1.19814i
$906$		0			0
$907$	3551.09	+	6150.67i	0.130002	+	0.225171i	0.923677	−	0.383172i	$-0.125168\pi$
$907$	3551.09	+	6150.67i	0.130002	+	0.225171i	−0.793675	+	0.608342i	$0.791835\pi$
$908$		0			0
$909$	8929.53			0.325824
$910$		0			0
$911$	38119.0			1.38632			0.693161	−	0.720783i	$-0.256218\pi$
$911$	38119.0			1.38632			0.693161	+	0.720783i	$0.256218\pi$
$912$		0			0
$913$	−4420.08	−	7655.81i	−0.160223	−	0.277514i
$914$		0			0
$915$	−12797.7	+	22166.2i	−0.462380	+	0.800865i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−8595.28	+	14887.5i	−0.308522	+	0.534377i	−0.978039	−	0.208420i	$-0.933168\pi$
$919$	−8595.28	+	14887.5i	−0.308522	+	0.534377i	0.669517	+	0.742797i	$0.266501\pi$
$920$		0			0
$921$	10996.4	+	19046.3i	0.393423	+	0.681429i
$922$		0			0
$923$	22687.5			0.809065
$924$		0			0
$925$	−484.139			−0.0172091
$926$		0			0
$927$	1204.07	+	2085.52i	0.0426612	+	0.0738914i
$928$		0			0
$929$	16128.2	−	27934.9i	0.569591	−	0.986561i	−0.427015	−	0.904245i	$-0.640435\pi$
$929$	16128.2	−	27934.9i	0.569591	−	0.986561i	0.996606	−	0.0823167i	$-0.0262319\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	3057.80	−	5296.26i	0.107297	−	0.185843i
$934$		0			0
$935$	3696.90	+	6403.22i	0.129306	+	0.223965i
$936$		0			0
$937$	−26213.6			−0.913940			−0.456970	−	0.889482i	$-0.651065\pi$
$937$	−26213.6			−0.913940			−0.456970	+	0.889482i	$0.651065\pi$
$938$		0			0
$939$	12416.6			0.431524
$940$		0			0
$941$	17120.0	+	29652.8i	0.593089	+	1.02726i	0.993813	+	0.111062i	$0.0354252\pi$
$941$	17120.0	+	29652.8i	0.593089	+	1.02726i	−0.400724	+	0.916199i	$0.631241\pi$
$942$		0			0
$943$	−10778.4	+	18668.7i	−0.372209	+	0.644685i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−18002.3	+	31180.8i	−0.617735	+	1.06995i	0.372163	+	0.928167i	$0.378616\pi$
$947$	−18002.3	+	31180.8i	−0.617735	+	1.06995i	−0.989898	+	0.141781i	$0.954717\pi$
$948$		0			0
$949$	−19633.6	−	34006.4i	−0.671584	−	1.16322i
$950$		0			0
$951$	22656.8			0.772551
$952$		0			0
$953$	−29488.1			−1.00232			−0.501161	−	0.865354i	$-0.667093\pi$
$953$	−29488.1			−1.00232			−0.501161	+	0.865354i	$0.667093\pi$
$954$		0			0
$955$	−14064.1	−	24359.7i	−0.476548	−	0.825405i
$956$		0			0
$957$	−876.174	+	1517.58i	−0.0295953	+	0.0512605i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	12925.6	−	22387.7i	0.433875	−	0.751494i
$962$		0			0
$963$	6914.81	+	11976.8i	0.231388	+	0.400776i
$964$		0			0
$965$	11156.4			0.372163
$966$		0			0
$967$	−56009.0			−1.86260			−0.931298	−	0.364259i	$-0.881322\pi$
$967$	−56009.0			−1.86260			−0.931298	+	0.364259i	$0.881322\pi$
$968$		0			0
$969$	−13373.9	−	23164.3i	−0.443377	−	0.767951i
$970$		0			0
$971$	6788.44	−	11757.9i	0.224358	−	0.388599i	−0.731769	−	0.681553i	$-0.761305\pi$
$971$	6788.44	−	11757.9i	0.224358	−	0.388599i	0.956127	+	0.292954i	$0.0946383\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	1306.43	−	2262.80i	0.0429120	−	0.0743258i
$976$		0			0
$977$	15887.6	+	27518.1i	0.520254	+	0.901107i	0.999723	+	0.0235477i	$0.00749615\pi$
$977$	15887.6	+	27518.1i	0.520254	+	0.901107i	−0.479468	+	0.877559i	$0.659171\pi$
$978$		0			0
$979$	−4258.14			−0.139010
$980$		0			0
$981$	8989.38			0.292568
$982$		0			0
$983$	16377.7	+	28367.0i	0.531401	+	0.920414i	0.999328	+	0.0366471i	$0.0116677\pi$
$983$	16377.7	+	28367.0i	0.531401	+	0.920414i	−0.467927	+	0.883767i	$0.654999\pi$
$984$		0			0
$985$	24429.1	−	42312.4i	0.790228	−	1.36872i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	10527.3	−	18233.8i	0.338472	−	0.586251i
$990$		0			0
$991$	20398.5	+	35331.3i	0.653865	+	1.13253i	0.982177	+	0.187958i	$0.0601869\pi$
$991$	20398.5	+	35331.3i	0.653865	+	1.13253i	−0.328312	+	0.944569i	$0.606480\pi$
$992$		0			0
$993$	−16733.1			−0.534752
$994$		0			0
$995$	−8851.60			−0.282025
$996$		0			0
$997$	−8685.25	−	15043.3i	−0.275892	−	0.477859i	0.694468	−	0.719524i	$-0.255640\pi$
$997$	−8685.25	−	15043.3i	−0.275892	−	0.477859i	−0.970360	+	0.241665i	$0.922307\pi$
$998$		0			0
$999$	569.826	−	986.968i	0.0180465	−	0.0312575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.4.i.l.373.2		8
3.2	odd	2		1764.4.k.bb.1549.3		8
7.2	even	3		588.4.a.j.1.3	✓	4
7.3	odd	6		588.4.i.k.361.3		8
7.4	even	3	inner	588.4.i.l.361.2		8
7.5	odd	6		588.4.a.k.1.2	yes	4
7.6	odd	2		588.4.i.k.373.3		8
21.2	odd	6		1764.4.a.bc.1.2		4
21.5	even	6		1764.4.a.ba.1.3		4
21.11	odd	6		1764.4.k.bb.361.3		8
21.17	even	6		1764.4.k.bd.361.2		8
21.20	even	2		1764.4.k.bd.1549.2		8
28.19	even	6		2352.4.a.cl.1.2		4
28.23	odd	6		2352.4.a.cq.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.4.a.j.1.3	✓	4	7.2	even	3
588.4.a.k.1.2	yes	4	7.5	odd	6
588.4.i.k.361.3		8	7.3	odd	6
588.4.i.k.373.3		8	7.6	odd	2
588.4.i.l.361.2		8	7.4	even	3	inner
588.4.i.l.373.2		8	1.1	even	1	trivial
1764.4.a.ba.1.3		4	21.5	even	6
1764.4.a.bc.1.2		4	21.2	odd	6
1764.4.k.bb.361.3		8	21.11	odd	6
1764.4.k.bb.1549.3		8	3.2	odd	2
1764.4.k.bd.361.2		8	21.17	even	6
1764.4.k.bd.1549.2		8	21.20	even	2
2352.4.a.cl.1.2		4	28.19	even	6
2352.4.a.cq.1.3		4	28.23	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	588.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} +(-5.32752 + 9.22754i) q^{5} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{3} +(-5.32752 + 9.22754i) q^{5} +(-4.50000 + 7.79423i) q^{9} +(3.32699 + 5.76252i) q^{11} -75.9335 q^{13} -31.9651 q^{15} +(-52.1435 - 90.3152i) q^{17} +(42.7472 - 74.0402i) q^{19} +(34.3366 - 59.4728i) q^{23} +(5.73498 + 9.93327i) q^{25} -27.0000 q^{27} +87.7843 q^{29} +(31.3841 + 54.3589i) q^{31} +(-9.98098 + 17.2876i) q^{33} +(-21.1047 + 36.5544i) q^{37} +(-113.900 - 197.281i) q^{39} -313.904 q^{41} +306.591 q^{43} +(-47.9477 - 83.0479i) q^{45} +(107.541 - 186.266i) q^{47} +(156.430 - 270.946i) q^{51} +(-262.512 - 454.684i) q^{53} -70.8986 q^{55} +256.483 q^{57} +(180.246 + 312.195i) q^{59} +(400.363 - 693.449i) q^{61} +(404.537 - 700.679i) q^{65} +(20.1143 + 34.8390i) q^{67} +206.020 q^{69} -298.781 q^{71} +(258.563 + 447.844i) q^{73} +(-17.2049 + 29.7998i) q^{75} +(611.233 - 1058.69i) q^{79} +(-40.5000 - 70.1481i) q^{81} -1328.55 q^{83} +1111.18 q^{85} +(131.676 + 228.070i) q^{87} +(-319.969 + 554.203i) q^{89} +(-94.1524 + 163.077i) q^{93} +(455.473 + 788.902i) q^{95} -1425.65 q^{97} -59.8859 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{3} - 36 q^{9}+O(q^{10}) \) 8 * q + 12 * q^3 - 36 * q^9	\( 8 q + 12 q^{3} - 36 q^{9} + 48 q^{17} + 192 q^{19} - 192 q^{23} - 324 q^{25} - 216 q^{27} + 192 q^{29} + 48 q^{31} - 256 q^{37} - 2016 q^{41} - 224 q^{43} + 864 q^{47} - 144 q^{51} + 648 q^{53} - 4704 q^{55} + 1152 q^{57} + 336 q^{59} + 960 q^{61} + 360 q^{65} - 720 q^{67} - 1152 q^{69} - 2688 q^{71} + 672 q^{73} + 972 q^{75} + 1984 q^{79} - 324 q^{81} - 6240 q^{83} + 1360 q^{85} + 288 q^{87} + 2160 q^{89} - 144 q^{93} + 3744 q^{95} - 4032 q^{97}+O(q^{100}) \) 8 * q + 12 * q^3 - 36 * q^9 + 48 * q^17 + 192 * q^19 - 192 * q^23 - 324 * q^25 - 216 * q^27 + 192 * q^29 + 48 * q^31 - 256 * q^37 - 2016 * q^41 - 224 * q^43 + 864 * q^47 - 144 * q^51 + 648 * q^53 - 4704 * q^55 + 1152 * q^57 + 336 * q^59 + 960 * q^61 + 360 * q^65 - 720 * q^67 - 1152 * q^69 - 2688 * q^71 + 672 * q^73 + 972 * q^75 + 1984 * q^79 - 324 * q^81 - 6240 * q^83 + 1360 * q^85 + 288 * q^87 + 2160 * q^89 - 144 * q^93 + 3744 * q^95 - 4032 * q^97

Introduction

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