LMFDB - Embedded newform 108.4.b.b.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(107,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("108.107");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.b (of order $2$, degree $1$, 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:	$6.37220628062$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3 x^{10} - 12 x^{9} + 73 x^{8} - 12 x^{7} + 589 x^{6} + 84 x^{5} + 2452 x^{4} + 852 x^{3} + \cdots + 9496 $ x^12 + 3x^10 - 12x^9 + 73x^8 - 12x^7 + 589x^6 + 84x^5 + 2452x^4 + 852x^3 + 6854x^2 - 888x + 9496
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			107.3
Root			$-1.29835 - 1.36719i$ of defining polynomial
Character	$\chi$	$=$	108.107
Dual form			108.4.b.b.107.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27435 - 1.68146i) q^{2} +(2.34537 + 7.64848i) q^{4} -5.83890i q^{5} +8.83113i q^{7} +(7.52641 - 21.3390i) q^{8} +O(q^{10})$	\(q+(-2.27435 - 1.68146i) q^{2} +(2.34537 + 7.64848i) q^{4} -5.83890i q^{5} +8.83113i q^{7} +(7.52641 - 21.3390i) q^{8} +(-9.81789 + 13.2797i) q^{10} +23.6146 q^{11} +54.6531 q^{13} +(14.8492 - 20.0851i) q^{14} +(-52.9984 + 35.8771i) q^{16} -117.211i q^{17} -109.576i q^{19} +(44.6587 - 13.6944i) q^{20} +(-53.7080 - 39.7070i) q^{22} -33.5763 q^{23} +90.9072 q^{25} +(-124.300 - 91.8970i) q^{26} +(-67.5447 + 20.7123i) q^{28} +40.0490i q^{29} -292.510i q^{31} +(180.863 + 7.51762i) q^{32} +(-197.086 + 266.580i) q^{34} +51.5641 q^{35} +283.265 q^{37} +(-184.248 + 249.215i) q^{38} +(-124.596 - 43.9460i) q^{40} +367.472i q^{41} +323.337i q^{43} +(55.3851 + 180.616i) q^{44} +(76.3644 + 56.4572i) q^{46} +66.2249 q^{47} +265.011 q^{49} +(-206.755 - 152.857i) q^{50} +(128.182 + 418.013i) q^{52} +158.506i q^{53} -137.883i q^{55} +(188.447 + 66.4667i) q^{56} +(67.3408 - 91.0856i) q^{58} -848.630 q^{59} -348.716 q^{61} +(-491.844 + 665.270i) q^{62} +(-398.706 - 321.212i) q^{64} -319.114i q^{65} -194.285i q^{67} +(896.489 - 274.905i) q^{68} +(-117.275 - 86.7031i) q^{70} +939.761 q^{71} -473.826 q^{73} +(-644.246 - 476.300i) q^{74} +(838.091 - 256.997i) q^{76} +208.544i q^{77} +273.221i q^{79} +(209.483 + 309.453i) q^{80} +(617.890 - 835.761i) q^{82} +338.366 q^{83} -684.386 q^{85} +(543.679 - 735.383i) q^{86} +(177.733 - 503.912i) q^{88} -739.884i q^{89} +482.648i q^{91} +(-78.7490 - 256.807i) q^{92} +(-150.619 - 111.355i) q^{94} -639.805 q^{95} -448.629 q^{97} +(-602.729 - 445.606i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4}+O(q^{10}) $ 12 * q + 6 * q^4	$ 12 q + 6 q^{4} + 42 q^{10} - 72 q^{13} + 114 q^{16} + 66 q^{22} - 384 q^{25} - 282 q^{28} - 324 q^{34} - 240 q^{37} + 774 q^{40} + 1752 q^{46} + 288 q^{49} + 924 q^{52} - 948 q^{58} + 144 q^{61} - 3066 q^{64} - 3558 q^{70} + 156 q^{73} + 576 q^{76} + 5832 q^{82} - 168 q^{85} + 5022 q^{88} - 3444 q^{94} + 516 q^{97}+O(q^{100}) $ 12 * q + 6 * q^4 + 42 * q^10 - 72 * q^13 + 114 * q^16 + 66 * q^22 - 384 * q^25 - 282 * q^28 - 324 * q^34 - 240 * q^37 + 774 * q^40 + 1752 * q^46 + 288 * q^49 + 924 * q^52 - 948 * q^58 + 144 * q^61 - 3066 * q^64 - 3558 * q^70 + 156 * q^73 + 576 * q^76 + 5832 * q^82 - 168 * q^85 + 5022 * q^88 - 3444 * q^94 + 516 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.27435	−	1.68146i	−0.804106	−	0.594486i
$2$	−2.27435	−	1.68146i	−0.804106	−	0.594486i
$3$		0			0
$3$		0			0
$4$	2.34537	+	7.64848i	0.293172	+	0.956060i
$5$		−	5.83890i		−	0.522247i	−0.965305	−	0.261124i	$-0.915907\pi$
$5$		−	5.83890i		−	0.522247i	0.965305	−	0.261124i	$-0.0840930\pi$
$6$		0			0
$7$			8.83113i			0.476836i	0.971163	+	0.238418i	$0.0766288\pi$
$7$			8.83113i			0.476836i	−0.971163	+	0.238418i	$0.923371\pi$
$8$	7.52641	−	21.3390i	0.332623	−	0.943060i
$9$		0			0
$10$	−9.81789	+	13.2797i	−0.310469	+	0.419942i
$11$	23.6146			0.647279			0.323639	−	0.946180i	$-0.395094\pi$
$11$	23.6146			0.647279			0.323639	+	0.946180i	$0.395094\pi$
$12$		0			0
$13$	54.6531			1.16600			0.583001	−	0.812471i	$-0.301878\pi$
$13$	54.6531			1.16600			0.583001	+	0.812471i	$0.301878\pi$
$14$	14.8492	−	20.0851i	0.283473	−	0.383427i
$15$		0			0
$16$	−52.9984	+	35.8771i	−0.828101	+	0.560580i
$17$		−	117.211i		−	1.67223i	−0.548553	−	0.836116i	$-0.684821\pi$
$17$		−	117.211i		−	1.67223i	0.548553	−	0.836116i	$-0.315179\pi$
$18$		0			0
$19$		−	109.576i		−	1.32308i	−0.749910	−	0.661539i	$-0.769903\pi$
$19$		−	109.576i		−	1.32308i	0.749910	−	0.661539i	$-0.230097\pi$
$20$	44.6587	−	13.6944i	0.499300	−	0.153108i
$21$		0			0
$22$	−53.7080	−	39.7070i	−0.520481	−	0.384799i
$23$	−33.5763			−0.304397			−0.152199	−	0.988350i	$-0.548635\pi$
$23$	−33.5763			−0.304397			−0.152199	+	0.988350i	$0.548635\pi$
$24$		0			0
$25$	90.9072			0.727258
$26$	−124.300	−	91.8970i	−0.937589	−	0.693173i
$27$		0			0
$28$	−67.5447	+	20.7123i	−0.455884	+	0.139795i
$29$			40.0490i			0.256445i	0.991745	+	0.128223i	$0.0409272\pi$
$29$			40.0490i			0.256445i	−0.991745	+	0.128223i	$0.959073\pi$
$30$		0			0
$31$		−	292.510i		−	1.69472i	−0.531020	−	0.847359i	$-0.678191\pi$
$31$		−	292.510i		−	1.69472i	0.531020	−	0.847359i	$-0.321809\pi$
$32$	180.863	+	7.51762i	0.999137	+	0.0415294i
$33$		0			0
$34$	−197.086	+	266.580i	−0.994119	+	1.34465i
$35$	51.5641			0.249026
$36$		0			0
$37$	283.265			1.25861			0.629304	−	0.777159i	$-0.283340\pi$
$37$	283.265			1.25861			0.629304	+	0.777159i	$0.283340\pi$
$38$	−184.248	+	249.215i	−0.786552	+	1.06390i
$39$		0			0
$40$	−124.596	−	43.9460i	−0.492510	−	0.173712i
$41$			367.472i			1.39974i	0.714269	+	0.699871i	$0.246759\pi$
$41$			367.472i			1.39974i	−0.714269	+	0.699871i	$0.753241\pi$
$42$		0			0
$43$			323.337i			1.14671i	0.819308	+	0.573354i	$0.194358\pi$
$43$			323.337i			1.14671i	−0.819308	+	0.573354i	$0.805642\pi$
$44$	55.3851	+	180.616i	0.189764	+	0.618837i
$45$		0			0
$46$	76.3644	+	56.4572i	0.244768	+	0.180960i
$47$	66.2249			0.205530			0.102765	−	0.994706i	$-0.467231\pi$
$47$	66.2249			0.205530			0.102765	+	0.994706i	$0.467231\pi$
$48$		0			0
$49$	265.011			0.772627
$50$	−206.755	−	152.857i	−0.584792	−	0.432345i
$51$		0			0
$52$	128.182	+	418.013i	0.341839	+	1.11477i
$53$			158.506i			0.410801i	0.978678	+	0.205401i	$0.0658498\pi$
$53$			158.506i			0.410801i	−0.978678	+	0.205401i	$0.934150\pi$
$54$		0			0
$55$		−	137.883i		−	0.338040i
$56$	188.447	+	66.4667i	0.449685	+	0.158607i
$57$		0			0
$58$	67.3408	−	91.0856i	0.152453	−	0.206209i
$59$	−848.630			−1.87258			−0.936290	−	0.351228i	$-0.885764\pi$
$59$	−848.630			−1.87258			−0.936290	+	0.351228i	$0.885764\pi$
$60$		0			0
$61$	−348.716			−0.731943			−0.365972	−	0.930626i	$-0.619263\pi$
$61$	−348.716			−0.731943			−0.365972	+	0.930626i	$0.619263\pi$
$62$	−491.844	+	665.270i	−1.00749	+	1.36273i
$63$		0			0
$64$	−398.706	−	321.212i	−0.778723	−	0.627368i
$65$		−	319.114i		−	0.608942i
$66$		0			0
$67$		−	194.285i		−	0.354264i	−0.984187	−	0.177132i	$-0.943318\pi$
$67$		−	194.285i		−	0.354264i	0.984187	−	0.177132i	$-0.0566819\pi$
$68$	896.489	−	274.905i	1.59875	−	0.490251i
$69$		0			0
$70$	−117.275	−	86.7031i	−0.200244	−	0.148043i
$71$	939.761			1.57083			0.785417	−	0.618968i	$-0.212449\pi$
$71$	939.761			1.57083			0.785417	+	0.618968i	$0.212449\pi$
$72$		0			0
$73$	−473.826			−0.759686			−0.379843	−	0.925051i	$-0.624022\pi$
$73$	−473.826			−0.759686			−0.379843	+	0.925051i	$0.624022\pi$
$74$	−644.246	−	476.300i	−1.01205	−	0.748226i
$75$		0			0
$76$	838.091	−	256.997i	1.26494	−	0.387889i
$77$			208.544i			0.308646i
$78$		0			0
$79$			273.221i			0.389112i	0.980891	+	0.194556i	$0.0623265\pi$
$79$			273.221i			0.389112i	−0.980891	+	0.194556i	$0.937673\pi$
$80$	209.483	+	309.453i	0.292761	+	0.432473i
$81$		0			0
$82$	617.890	−	835.761i	0.832128	−	1.12554i
$83$	338.366			0.447476			0.223738	−	0.974649i	$-0.428174\pi$
$83$	338.366			0.447476			0.223738	+	0.974649i	$0.428174\pi$
$84$		0			0
$85$	−684.386			−0.873318
$86$	543.679	−	735.383i	0.681702	−	0.922074i
$87$		0			0
$88$	177.733	−	503.912i	0.215300	−	0.610423i
$89$		−	739.884i		−	0.881208i	−0.897702	−	0.440604i	$-0.854764\pi$
$89$		−	739.884i		−	0.881208i	0.897702	−	0.440604i	$-0.145236\pi$
$90$		0			0
$91$			482.648i			0.555992i
$92$	−78.7490	−	256.807i	−0.0892407	−	0.291022i
$93$		0			0
$94$	−150.619	−	111.355i	−0.165268	−	0.122185i
$95$	−639.805			−0.690974
$96$		0			0
$97$	−448.629			−0.469602			−0.234801	−	0.972044i	$-0.575444\pi$
$97$	−448.629			−0.469602			−0.234801	+	0.972044i	$0.575444\pi$
$98$	−602.729	−	445.606i	−0.621274	−	0.459316i
$99$		0			0
$100$	213.211	+	695.302i	0.213211	+	0.695302i
$101$		−	1152.87i		−	1.13580i	−0.823099	−	0.567898i	$-0.807757\pi$
$101$		−	1152.87i		−	1.13580i	0.823099	−	0.567898i	$-0.192243\pi$
$102$		0			0
$103$			1389.90i			1.32962i	0.747013	+	0.664809i	$0.231487\pi$
$103$			1389.90i			1.32962i	−0.747013	+	0.664809i	$0.768513\pi$
$104$	411.341	−	1166.24i	0.387840	−	1.09961i
$105$		0			0
$106$	266.522	−	360.499i	0.244216	−	0.330328i
$107$	245.479			0.221788			0.110894	−	0.993832i	$-0.464629\pi$
$107$	245.479			0.221788			0.110894	+	0.993832i	$0.464629\pi$
$108$		0			0
$109$	−644.998			−0.566785			−0.283393	−	0.959004i	$-0.591460\pi$
$109$	−644.998			−0.566785			−0.283393	+	0.959004i	$0.591460\pi$
$110$	−231.846	+	313.596i	−0.200960	+	0.271820i
$111$		0			0
$112$	−316.835	−	468.036i	−0.267305	−	0.394868i
$113$			825.442i			0.687177i	0.939120	+	0.343589i	$0.111643\pi$
$113$			825.442i			0.687177i	−0.939120	+	0.343589i	$0.888357\pi$
$114$		0			0
$115$			196.049i			0.158971i
$116$	−306.314	+	93.9299i	−0.245177	+	0.0751825i
$117$		0			0
$118$	1930.09	+	1426.94i	1.50575	+	1.11322i
$119$	1035.11			0.797380
$120$		0			0
$121$	−773.351			−0.581030
$122$	793.104	+	586.353i	0.588560	+	0.435130i
$123$		0			0
$124$	2237.25	−	686.044i	1.62025	−	0.496844i
$125$		−	1260.66i		−	0.902056i
$126$		0			0
$127$			754.649i			0.527278i	0.964621	+	0.263639i	$0.0849228\pi$
$127$			754.649i			0.527278i	−0.964621	+	0.263639i	$0.915077\pi$
$128$	366.694	+	1400.96i	0.253214	+	0.967410i
$129$		0			0
$130$	−536.578	+	725.778i	−0.362008	+	0.489654i
$131$	−2026.43			−1.35153			−0.675765	−	0.737117i	$-0.736186\pi$
$131$	−2026.43			−1.35153			−0.675765	+	0.737117i	$0.736186\pi$
$132$		0			0
$133$	967.681			0.630892
$134$	−326.682	+	441.873i	−0.210605	+	0.284865i
$135$		0			0
$136$	−2501.17	−	882.181i	−1.57701	−	0.556223i
$137$			1882.88i			1.17420i	0.809515	+	0.587099i	$0.199730\pi$
$137$			1882.88i			1.17420i	−0.809515	+	0.587099i	$0.800270\pi$
$138$		0			0
$139$			93.7277i			0.0571934i	0.999591	+	0.0285967i	$0.00910385\pi$
$139$			93.7277i			0.0571934i	−0.999591	+	0.0285967i	$0.990896\pi$
$140$	120.937	+	394.387i	0.0730075	+	0.238084i
$141$		0			0
$142$	−2137.35	−	1580.17i	−1.26312	−	0.933839i
$143$	1290.61			0.754729
$144$		0			0
$145$	233.842			0.133928
$146$	1077.65	+	796.719i	0.610868	+	0.451623i
$147$		0			0
$148$	664.363	+	2166.55i	0.368989	+	1.20331i
$149$			2764.69i			1.52008i	0.649874	+	0.760042i	$0.274822\pi$
$149$			2764.69i			1.52008i	−0.649874	+	0.760042i	$0.725178\pi$
$150$		0			0
$151$		−	3694.11i		−	1.99088i	−0.0954051	−	0.995439i	$-0.530415\pi$
$151$		−	3694.11i		−	1.99088i	0.0954051	−	0.995439i	$-0.469585\pi$
$152$	−2338.25	−	824.715i	−1.24774	−	0.440087i
$153$		0			0
$154$	350.658	−	474.302i	0.183486	−	0.248184i
$155$	−1707.94			−0.885062
$156$		0			0
$157$	812.401			0.412972			0.206486	−	0.978450i	$-0.433797\pi$
$157$	812.401			0.412972			0.206486	+	0.978450i	$0.433797\pi$
$158$	459.411	−	621.402i	0.231322	−	0.312887i
$159$		0			0
$160$	43.8947	−	1056.04i	0.0216886	−	0.521797i
$161$		−	296.516i		−	0.145148i
$162$		0			0
$163$		−	1034.18i		−	0.496953i	−0.968638	−	0.248477i	$-0.920070\pi$
$163$		−	1034.18i		−	0.496953i	0.968638	−	0.248477i	$-0.0799299\pi$
$164$	−2810.60	+	861.859i	−1.33824	+	0.410365i
$165$		0			0
$166$	−769.564	−	568.949i	−0.359818	−	0.266018i
$167$	1453.29			0.673409			0.336704	−	0.941610i	$-0.390688\pi$
$167$	1453.29			0.673409			0.336704	+	0.941610i	$0.390688\pi$
$168$		0			0
$169$	789.957			0.359562
$170$	1556.54	+	1150.77i	0.702240	+	0.519176i
$171$		0			0
$172$	−2473.04	+	758.346i	−1.09632	+	0.336182i
$173$			634.902i			0.279022i	0.990221	+	0.139511i	$0.0445530\pi$
$173$			634.902i			0.279022i	−0.990221	+	0.139511i	$0.955447\pi$
$174$		0			0
$175$			802.813i			0.346783i
$176$	−1251.54	+	847.223i	−0.536012	+	0.362851i
$177$		0			0
$178$	−1244.09	+	1682.76i	−0.523866	+	0.708584i
$179$	−2909.35			−1.21483			−0.607417	−	0.794383i	$-0.707794\pi$
$179$	−2909.35			−1.21483			−0.607417	+	0.794383i	$0.707794\pi$
$180$		0			0
$181$	1354.46			0.556222			0.278111	−	0.960549i	$-0.410292\pi$
$181$	1354.46			0.556222			0.278111	+	0.960549i	$0.410292\pi$
$182$	811.554	−	1097.71i	0.330530	−	0.447076i
$183$		0			0
$184$	−252.709	+	716.484i	−0.101250	+	0.287065i
$185$		−	1653.96i		−	0.657305i
$186$		0			0
$187$		−	2767.90i		−	1.08240i
$188$	155.322	+	506.520i	0.0602555	+	0.196499i
$189$		0			0
$190$	1455.14	+	1075.81i	0.555616	+	0.410775i
$191$	3488.40			1.32153			0.660765	−	0.750593i	$-0.270232\pi$
$191$	3488.40			1.32153			0.660765	+	0.750593i	$0.270232\pi$
$192$		0			0
$193$	2912.99			1.08643			0.543217	−	0.839592i	$-0.317206\pi$
$193$	2912.99			1.08643			0.543217	+	0.839592i	$0.317206\pi$
$194$	1020.34	+	754.352i	0.377609	+	0.279172i
$195$		0			0
$196$	621.550	+	2026.93i	0.226513	+	0.738678i
$197$			2432.66i			0.879795i	0.898048	+	0.439897i	$0.144985\pi$
$197$			2432.66i			0.879795i	−0.898048	+	0.439897i	$0.855015\pi$
$198$		0			0
$199$			563.190i			0.200621i	0.994956	+	0.100310i	$0.0319836\pi$
$199$			563.190i			0.200621i	−0.994956	+	0.100310i	$0.968016\pi$
$200$	684.205	−	1939.87i	0.241903	−	0.685847i
$201$		0			0
$202$	−1938.51	+	2622.05i	−0.675215	+	0.913299i
$203$	−353.678			−0.122282
$204$		0			0
$205$	2145.63			0.731012
$206$	2337.06	−	3161.12i	0.790440	−	1.06915i
$207$		0			0
$208$	−2896.53	+	1960.79i	−0.965567	+	0.653637i
$209$		−	2587.60i		−	0.856401i
$210$		0			0
$211$		−	1447.62i		−	0.472314i	−0.971715	−	0.236157i	$-0.924112\pi$
$211$		−	1447.62i		−	0.472314i	0.971715	−	0.236157i	$-0.0758879\pi$
$212$	−1212.33	+	371.756i	−0.392751	+	0.120435i
$213$		0			0
$214$	−558.306	−	412.763i	−0.178341	−	0.131850i
$215$	1887.93			0.598865
$216$		0			0
$217$	2583.19			0.808103
$218$	1466.95	+	1084.54i	0.455755	+	0.336946i
$219$		0			0
$220$	1054.60	−	323.388i	0.323186	−	0.0991037i
$221$		−	6405.96i		−	1.94983i
$222$		0			0
$223$			5049.28i			1.51625i	0.652107	+	0.758127i	$0.273885\pi$
$223$			5049.28i			1.51625i	−0.652107	+	0.758127i	$0.726115\pi$
$224$	−66.3891	+	1597.23i	−0.0198027	+	0.476425i
$225$		0			0
$226$	1387.95	−	1877.35i	0.408517	−	0.552563i
$227$	−5716.54			−1.67145			−0.835727	−	0.549146i	$-0.814953\pi$
$227$	−5716.54			−1.67145			−0.835727	+	0.549146i	$0.814953\pi$
$228$		0			0
$229$	−2582.55			−0.745240			−0.372620	−	0.927984i	$-0.621540\pi$
$229$	−2582.55			−0.745240			−0.372620	+	0.927984i	$0.621540\pi$
$230$	329.648	−	445.884i	0.0945059	−	0.127829i
$231$		0			0
$232$	854.606	+	301.425i	0.241843	+	0.0852997i
$233$		−	587.204i		−	0.165103i	−0.996587	−	0.0825516i	$-0.973693\pi$
$233$		−	587.204i		−	0.165103i	0.996587	−	0.0825516i	$-0.0263069\pi$
$234$		0			0
$235$		−	386.681i		−	0.107337i
$236$	−1990.35	−	6490.73i	−0.548988	−	1.79030i
$237$		0			0
$238$	−2354.20	−	1740.50i	−0.641178	−	0.474032i
$239$	5583.00			1.51102			0.755512	−	0.655135i	$-0.227388\pi$
$239$	5583.00			1.51102			0.755512	+	0.655135i	$0.227388\pi$
$240$		0			0
$241$	−2056.95			−0.549791			−0.274895	−	0.961474i	$-0.588643\pi$
$241$	−2056.95			−0.549791			−0.274895	+	0.961474i	$0.588643\pi$
$242$	1758.87	+	1300.36i	0.467209	+	0.345414i
$243$		0			0
$244$	−817.870	−	2667.15i	−0.214585	−	0.699781i
$245$		−	1547.37i		−	0.403503i
$246$		0			0
$247$		−	5988.67i		−	1.54271i
$248$	−6241.86	−	2201.55i	−1.59822	−	0.563703i
$249$		0			0
$250$	−2119.75	+	2867.19i	−0.536260	+	0.725348i
$251$	−1256.79			−0.316047			−0.158023	−	0.987435i	$-0.550512\pi$
$251$	−1256.79			−0.316047			−0.158023	+	0.987435i	$0.550512\pi$
$252$		0			0
$253$	−792.890			−0.197030
$254$	1268.91	−	1716.34i	0.313460	−	0.423987i
$255$		0			0
$256$	1521.67	−	3802.86i	0.371501	−	0.928432i
$257$			643.773i			0.156255i	0.996943	+	0.0781273i	$0.0248941\pi$
$257$			643.773i			0.156255i	−0.996943	+	0.0781273i	$0.975106\pi$
$258$		0			0
$259$			2501.55i			0.600150i
$260$	2440.74	−	748.442i	0.582185	−	0.178525i
$261$		0			0
$262$	4608.83	+	3407.37i	1.08677	+	0.803466i
$263$	917.108			0.215024			0.107512	−	0.994204i	$-0.465712\pi$
$263$	917.108			0.215024			0.107512	+	0.994204i	$0.465712\pi$
$264$		0			0
$265$	925.501			0.214540
$266$	−2200.85	−	1627.12i	−0.507304	−	0.375057i
$267$		0			0
$268$	1485.98	−	455.671i	0.338697	−	0.103860i
$269$			6577.00i			1.49073i	0.666656	+	0.745366i	$0.267725\pi$
$269$			6577.00i			1.49073i	−0.666656	+	0.745366i	$0.732275\pi$
$270$		0			0
$271$		−	4656.21i		−	1.04371i	−0.853035	−	0.521854i	$-0.825241\pi$
$271$		−	4656.21i		−	1.04371i	0.853035	−	0.521854i	$-0.174759\pi$
$272$	4205.20	+	6212.02i	0.937419	+	1.38478i
$273$		0			0
$274$	3165.99	−	4282.33i	0.698045	−	0.944179i
$275$	2146.74			0.470739
$276$		0			0
$277$	−2881.42			−0.625010			−0.312505	−	0.949916i	$-0.601168\pi$
$277$	−2881.42			−0.625010			−0.312505	+	0.949916i	$0.601168\pi$
$278$	157.600	−	213.170i	0.0340007	−	0.0459895i
$279$		0			0
$280$	388.093	−	1100.33i	0.0828320	−	0.234847i
$281$			2604.93i			0.553015i	0.961012	+	0.276507i	$0.0891771\pi$
$281$			2604.93i			0.553015i	−0.961012	+	0.276507i	$0.910823\pi$
$282$		0			0
$283$			5786.02i			1.21535i	0.794187	+	0.607674i	$0.207897\pi$
$283$			5786.02i			1.21535i	−0.794187	+	0.607674i	$0.792103\pi$
$284$	2204.09	+	7187.74i	0.460524	+	1.50181i
$285$		0			0
$286$	−2935.30	−	2170.11i	−0.606882	−	0.448676i
$287$	−3245.19			−0.667448
$288$		0			0
$289$	−8825.50			−1.79636
$290$	−531.840	−	393.197i	−0.107692	−	0.0796183i
$291$		0			0
$292$	−1111.30	−	3624.04i	−0.222719	−	0.726305i
$293$		−	3279.55i		−	0.653902i	−0.945041	−	0.326951i	$-0.893979\pi$
$293$		−	3279.55i		−	0.653902i	0.945041	−	0.326951i	$-0.106021\pi$
$294$		0			0
$295$			4955.07i			0.977950i
$296$	2131.97	−	6044.60i	0.418643	−	1.18694i
$297$		0			0
$298$	4648.73	−	6287.89i	0.903669	−	1.22231i
$299$	−1835.05			−0.354928
$300$		0			0
$301$	−2855.43			−0.546792
$302$	−6211.50	+	8401.72i	−1.18355	+	1.60088i
$303$		0			0
$304$	3931.27	+	5807.37i	0.741691	+	1.09564i
$305$			2036.12i			0.382255i
$306$		0			0
$307$			3014.47i			0.560407i	0.959941	+	0.280203i	$0.0904019\pi$
$307$			3014.47i			0.560407i	−0.959941	+	0.280203i	$0.909598\pi$
$308$	−1595.04	+	489.113i	−0.295084	+	0.0904863i
$309$		0			0
$310$	3884.45	+	2871.83i	0.711684	+	0.526157i
$311$	6230.80			1.13606			0.568032	−	0.823006i	$-0.307705\pi$
$311$	6230.80			1.13606			0.568032	+	0.823006i	$0.307705\pi$
$312$		0			0
$313$	−3922.49			−0.708346			−0.354173	−	0.935180i	$-0.615238\pi$
$313$	−3922.49			−0.708346			−0.354173	+	0.935180i	$0.615238\pi$
$314$	−1847.69	−	1366.02i	−0.332073	−	0.245506i
$315$		0			0
$316$	−2089.73	+	640.807i	−0.372014	+	0.114077i
$317$			6882.19i			1.21938i	0.792641	+	0.609689i	$0.208705\pi$
$317$			6882.19i			1.21938i	−0.792641	+	0.609689i	$0.791295\pi$
$318$		0			0
$319$			945.741i			0.165992i
$320$	−1875.53	+	2328.01i	−0.327641	+	0.406686i
$321$		0			0
$322$	−498.581	+	674.383i	−0.0862883	+	0.116714i
$323$	−12843.6			−2.21249
$324$		0			0
$325$	4968.36			0.847984
$326$	−1738.94	+	2352.10i	−0.295432	+	0.399603i
$327$		0			0
$328$	7841.48	+	2765.74i	1.32004	+	0.465587i
$329$			584.841i			0.0980040i
$330$		0			0
$331$			9489.08i			1.57573i	0.615847	+	0.787866i	$0.288814\pi$
$331$			9489.08i			1.57573i	−0.615847	+	0.787866i	$0.711186\pi$
$332$	793.595	+	2587.98i	0.131187	+	0.427813i
$333$		0			0
$334$	−3305.31	−	2443.66i	−0.541492	−	0.400332i
$335$	−1134.41			−0.185013
$336$		0			0
$337$	4578.52			0.740083			0.370041	−	0.929015i	$-0.379344\pi$
$337$	4578.52			0.740083			0.370041	+	0.929015i	$0.379344\pi$
$338$	−1796.64	−	1328.28i	−0.289126	−	0.213755i
$339$		0			0
$340$	−1605.14	−	5234.51i	−0.256032	−	0.834945i
$341$		−	6907.50i		−	1.09696i
$342$		0			0
$343$			5369.42i			0.845253i
$344$	6899.69	+	2433.57i	1.08141	+	0.381422i
$345$		0			0
$346$	1067.56	−	1443.99i	0.165875	−	0.224363i
$347$	942.483			0.145807			0.0729037	−	0.997339i	$-0.476773\pi$
$347$	942.483			0.145807			0.0729037	+	0.997339i	$0.476773\pi$
$348$		0			0
$349$	−2124.84			−0.325903			−0.162951	−	0.986634i	$-0.552101\pi$
$349$	−2124.84			−0.325903			−0.162951	+	0.986634i	$0.552101\pi$
$350$	1349.90	−	1825.88i	0.206158	−	0.278850i
$351$		0			0
$352$	4271.01	+	177.526i	0.646721	+	0.0268811i
$353$			3881.60i			0.585260i	0.956226	+	0.292630i	$0.0945304\pi$
$353$			3881.60i			0.585260i	−0.956226	+	0.292630i	$0.905470\pi$
$354$		0			0
$355$		−	5487.18i		−	0.820363i
$356$	5658.98	−	1735.30i	0.842488	−	0.258345i
$357$		0			0
$358$	6616.90	+	4891.97i	0.976855	+	0.722202i
$359$	8050.44			1.18353			0.591763	−	0.806112i	$-0.298432\pi$
$359$	8050.44			1.18353			0.591763	+	0.806112i	$0.298432\pi$
$360$		0			0
$361$	−5147.94			−0.750537
$362$	−3080.52	−	2277.47i	−0.447261	−	0.330666i
$363$		0			0
$364$	−3691.52	+	1131.99i	−0.531562	+	0.163001i
$365$			2766.62i			0.396744i
$366$		0			0
$367$		−	6890.96i		−	0.980123i	−0.871688	−	0.490062i	$-0.836974\pi$
$367$		−	6890.96i		−	0.980123i	0.871688	−	0.490062i	$-0.163026\pi$
$368$	1779.49	−	1204.62i	0.252072	−	0.170639i
$369$		0			0
$370$	−2781.07	+	3761.69i	−0.390759	+	0.528543i
$371$	−1399.79			−0.195885
$372$		0			0
$373$	−10512.5			−1.45930			−0.729649	−	0.683822i	$-0.760316\pi$
$373$	−10512.5			−1.45930			−0.729649	+	0.683822i	$0.760316\pi$
$374$	−4654.12	+	6295.18i	−0.643472	+	0.870364i
$375$		0			0
$376$	498.436	−	1413.17i	0.0683640	−	0.193827i
$377$			2188.80i			0.299016i
$378$		0			0
$379$		−	3139.69i		−	0.425528i	−0.977104	−	0.212764i	$-0.931753\pi$
$379$		−	3139.69i		−	0.425528i	0.977104	−	0.212764i	$-0.0682466\pi$
$380$	−1500.58	−	4893.53i	−0.202574	−	0.660613i
$381$		0			0
$382$	−7933.87	−	5865.62i	−1.06265	−	0.785631i
$383$	5117.53			0.682751			0.341375	−	0.939927i	$-0.389107\pi$
$383$	5117.53			0.682751			0.341375	+	0.939927i	$0.389107\pi$
$384$		0			0
$385$	1217.67			0.161190
$386$	−6625.17	−	4898.08i	−0.873607	−	0.645870i
$387$		0			0
$388$	−1052.20	−	3431.33i	−0.137674	−	0.448967i
$389$		−	787.004i		−	0.102578i	−0.998684	−	0.0512888i	$-0.983667\pi$
$389$		−	787.004i		−	0.102578i	0.998684	−	0.0512888i	$-0.0163329\pi$
$390$		0			0
$391$			3935.52i			0.509023i
$392$	1994.58	−	5655.07i	0.256994	−	0.728634i
$393$		0			0
$394$	4090.42	−	5532.72i	0.523026	−	0.707448i
$395$	1595.31			0.203212
$396$		0			0
$397$	11160.6			1.41092			0.705458	−	0.708752i	$-0.250741\pi$
$397$	11160.6			1.41092			0.705458	+	0.708752i	$0.250741\pi$
$398$	946.983	−	1280.89i	0.119266	−	0.161320i
$399$		0			0
$400$	−4817.94	+	3261.49i	−0.602242	+	0.407686i
$401$		−	13224.6i		−	1.64689i	−0.567394	−	0.823447i	$-0.692048\pi$
$401$		−	13224.6i		−	1.64689i	0.567394	−	0.823447i	$-0.307952\pi$
$402$		0			0
$403$		−	15986.5i		−	1.97605i
$404$	8817.74	−	2703.92i	1.08589	−	0.332983i
$405$		0			0
$406$	804.388	+	594.695i	0.0983279	+	0.0726952i
$407$	6689.20			0.814671
$408$		0			0
$409$	8153.09			0.985683			0.492841	−	0.870119i	$-0.335958\pi$
$409$	8153.09			0.985683			0.492841	+	0.870119i	$0.335958\pi$
$410$	−4879.93	−	3607.80i	−0.587811	−	0.434577i
$411$		0			0
$412$	−10630.6	+	3259.83i	−1.27119	+	0.389806i
$413$		−	7494.36i		−	0.892914i
$414$		0			0
$415$		−	1975.69i		−	0.233693i
$416$	9884.73	+	410.861i	1.16500	+	0.0484233i
$417$		0			0
$418$	−4350.94	+	5885.11i	−0.509119	+	0.688637i
$419$	−11682.5			−1.36212			−0.681061	−	0.732226i	$-0.738481\pi$
$419$	−11682.5			−1.36212			−0.681061	+	0.732226i	$0.738481\pi$
$420$		0			0
$421$	9595.77			1.11085			0.555426	−	0.831566i	$-0.312555\pi$
$421$	9595.77			1.11085			0.555426	+	0.831566i	$0.312555\pi$
$422$	−2434.12	+	3292.40i	−0.280784	+	0.379790i
$423$		0			0
$424$	3382.36	+	1192.98i	0.387410	+	0.136642i
$425$		−	10655.4i		−	1.21614i
$426$		0			0
$427$		−	3079.56i		−	0.349017i
$428$	575.740	+	1877.54i	0.0650220	+	0.212043i
$429$		0			0
$430$	−4293.83	−	3174.49i	−0.481551	−	0.356017i
$431$	−4294.48			−0.479948			−0.239974	−	0.970779i	$-0.577139\pi$
$431$	−4294.48			−0.479948			−0.239974	+	0.970779i	$0.577139\pi$
$432$		0			0
$433$	168.392			0.0186892			0.00934460	−	0.999956i	$-0.497025\pi$
$433$	168.392			0.0186892			0.00934460	+	0.999956i	$0.497025\pi$
$434$	−5875.09	−	4343.53i	−0.649800	−	0.480406i
$435$		0			0
$436$	−1512.76	−	4933.25i	−0.166166	−	0.541881i
$437$			3679.16i			0.402742i
$438$		0			0
$439$		−	1459.53i		−	0.158677i	−0.996848	−	0.0793387i	$-0.974719\pi$
$439$		−	1459.53i		−	0.158677i	0.996848	−	0.0793387i	$-0.0252809\pi$
$440$	−2942.29	−	1037.77i	−0.318792	−	0.112440i
$441$		0			0
$442$	−10771.4	+	14569.4i	−1.15914	+	1.56787i
$443$	333.411			0.0357581			0.0178790	−	0.999840i	$-0.494309\pi$
$443$	333.411			0.0357581			0.0178790	+	0.999840i	$0.494309\pi$
$444$		0			0
$445$	−4320.11			−0.460209
$446$	8490.16	−	11483.8i	0.901392	−	1.21923i
$447$		0			0
$448$	2836.67	−	3521.03i	0.299152	−	0.371323i
$449$			11454.3i			1.20393i	0.798523	+	0.601964i	$0.205615\pi$
$449$			11454.3i			1.20393i	−0.798523	+	0.601964i	$0.794385\pi$
$450$		0			0
$451$			8677.70i			0.906024i
$452$	−6313.37	+	1935.97i	−0.656982	+	0.201461i
$453$		0			0
$454$	13001.4	+	9612.14i	1.34402	+	0.993656i
$455$	2818.14			0.290365
$456$		0			0
$457$	9680.26			0.990861			0.495431	−	0.868648i	$-0.335010\pi$
$457$	9680.26			0.990861			0.495431	+	0.868648i	$0.335010\pi$
$458$	5873.64	+	4342.46i	0.599252	+	0.443035i
$459$		0			0
$460$	−1499.47	+	459.808i	−0.151986	+	0.0466057i
$461$		−	14806.9i		−	1.49593i	−0.663737	−	0.747966i	$-0.731030\pi$
$461$		−	14806.9i		−	1.49593i	0.663737	−	0.747966i	$-0.268970\pi$
$462$		0			0
$463$			3658.08i			0.367183i	0.983003	+	0.183591i	$0.0587723\pi$
$463$			3658.08i			0.367183i	−0.983003	+	0.183591i	$0.941228\pi$
$464$	−1436.84	−	2122.53i	−0.143758	−	0.212362i
$465$		0			0
$466$	−987.361	+	1335.51i	−0.0981516	+	0.132760i
$467$	9852.37			0.976260			0.488130	−	0.872771i	$-0.337679\pi$
$467$	9852.37			0.976260			0.488130	+	0.872771i	$0.337679\pi$
$468$		0			0
$469$	1715.75			0.168926
$470$	−650.189	+	879.449i	−0.0638106	+	0.0863106i
$471$		0			0
$472$	−6387.14	+	18108.9i	−0.622864	+	1.76595i
$473$			7635.47i			0.742240i
$474$		0			0
$475$		−	9961.26i		−	0.962219i
$476$	2427.72	+	7917.01i	0.233769	+	0.762343i
$477$		0			0
$478$	−12697.7	−	9387.61i	−1.21502	−	0.898283i
$479$	−11107.9			−1.05957			−0.529784	−	0.848133i	$-0.677727\pi$
$479$	−11107.9			−1.05957			−0.529784	+	0.848133i	$0.677727\pi$
$480$		0			0
$481$	15481.3			1.46754
$482$	4678.22	+	3458.68i	0.442090	+	0.326843i
$483$		0			0
$484$	−1813.80	−	5914.96i	−0.170342	−	0.555499i
$485$			2619.50i			0.245248i
$486$		0			0
$487$		−	11703.7i		−	1.08900i	−0.838761	−	0.544500i	$-0.816719\pi$
$487$		−	11703.7i		−	1.08900i	0.838761	−	0.544500i	$-0.183281\pi$
$488$	−2624.58	+	7441.26i	−0.243461	+	0.690266i
$489$		0			0
$490$	−2601.85	+	3519.28i	−0.239877	+	0.324459i
$491$	2851.25			0.262067			0.131034	−	0.991378i	$-0.458170\pi$
$491$	2851.25			0.262067			0.131034	+	0.991378i	$0.458170\pi$
$492$		0			0
$493$	4694.20			0.428836
$494$	−10069.7	+	13620.4i	−0.917122	+	1.24050i
$495$		0			0
$496$	10494.4	+	15502.6i	0.950024	+	1.40340i
$497$			8299.15i			0.749030i
$498$		0			0
$499$			14936.0i			1.33994i	0.742389	+	0.669969i	$0.233693\pi$
$499$			14936.0i			1.33994i	−0.742389	+	0.669969i	$0.766307\pi$
$500$	9642.14	−	2956.72i	0.862419	−	0.264457i
$501$		0			0
$502$	2858.38	+	2113.24i	0.254135	+	0.187885i
$503$	9047.91			0.802041			0.401020	−	0.916069i	$-0.368656\pi$
$503$	9047.91			0.802041			0.401020	+	0.916069i	$0.368656\pi$
$504$		0			0
$505$	−6731.52			−0.593166
$506$	1803.31	+	1333.21i	0.158433	+	0.117132i
$507$		0			0
$508$	−5771.92	+	1769.94i	−0.504109	+	0.154583i
$509$			15173.5i			1.32132i	0.750683	+	0.660662i	$0.229724\pi$
$509$			15173.5i			1.32132i	−0.750683	+	0.660662i	$0.770276\pi$
$510$		0			0
$511$		−	4184.41i		−	0.362246i
$512$	−9855.18	+	6090.42i	−0.850667	+	0.525705i
$513$		0			0
$514$	1082.48	−	1464.17i	0.0928913	−	0.125645i
$515$	8115.47			0.694389
$516$		0			0
$517$	1563.87			0.133035
$518$	4206.26	−	5689.42i	0.356781	−	0.482584i
$519$		0			0
$520$	−6809.57	−	2401.78i	−0.574268	−	0.202548i
$521$		−	7375.96i		−	0.620243i	−0.950697	−	0.310121i	$-0.899630\pi$
$521$		−	7375.96i		−	0.620243i	0.950697	−	0.310121i	$-0.100370\pi$
$522$		0			0
$523$		−	8514.96i		−	0.711918i	−0.934502	−	0.355959i	$-0.884154\pi$
$523$		−	8514.96i		−	0.711918i	0.934502	−	0.355959i	$-0.115846\pi$
$524$	−4752.75	−	15499.1i	−0.396230	−	1.29214i
$525$		0			0
$526$	−2085.83	−	1542.08i	−0.172902	−	0.127829i
$527$	−34285.4			−2.83396
$528$		0			0
$529$	−11039.6			−0.907342
$530$	−2104.92	−	1556.19i	−0.172513	−	0.127541i
$531$		0			0
$532$	2269.57	+	7401.29i	0.184960	+	0.603170i
$533$			20083.5i			1.63210i
$534$		0			0
$535$		−	1433.33i		−	0.115828i
$536$	−4145.84	−	1462.27i	−0.334092	−	0.117836i
$537$		0			0
$538$	11059.0	−	14958.4i	0.886220	−	1.19871i
$539$	6258.13			0.500105
$540$		0			0
$541$	−2214.98			−0.176025			−0.0880125	−	0.996119i	$-0.528052\pi$
$541$	−2214.98			−0.176025			−0.0880125	+	0.996119i	$0.528052\pi$
$542$	−7829.25	+	10589.9i	−0.620470	+	0.839252i
$543$		0			0
$544$	881.150	−	21199.2i	0.0694467	−	1.67079i
$545$			3766.08i			0.296002i
$546$		0			0
$547$			3906.55i			0.305360i	0.988276	+	0.152680i	$0.0487904\pi$
$547$			3906.55i			0.305360i	−0.988276	+	0.152680i	$0.951210\pi$
$548$	−14401.1	+	4416.05i	−1.12260	+	0.344242i
$549$		0			0
$550$	−4882.44	−	3609.66i	−0.378524	−	0.279848i
$551$	4388.41			0.339297
$552$		0			0
$553$	−2412.85			−0.185542
$554$	6553.37	+	4844.99i	0.502574	+	0.371560i
$555$		0			0
$556$	−716.874	+	219.827i	−0.0546803	+	0.0167675i
$557$			2978.14i			0.226549i	0.993564	+	0.113275i	$0.0361340\pi$
$557$			2978.14i			0.226549i	−0.993564	+	0.113275i	$0.963866\pi$
$558$		0			0
$559$			17671.4i			1.33706i
$560$	−2732.82	+	1849.97i	−0.206219	+	0.139599i
$561$		0			0
$562$	4380.09	−	5924.54i	0.328760	−	0.444682i
$563$	−8786.44			−0.657734			−0.328867	−	0.944376i	$-0.606667\pi$
$563$	−8786.44			−0.657734			−0.328867	+	0.944376i	$0.606667\pi$
$564$		0			0
$565$	4819.67			0.358876
$566$	9728.97	−	13159.5i	0.722507	−	0.977268i
$567$		0			0
$568$	7073.03	−	20053.6i	0.522496	−	1.48139i
$569$		−	19271.0i		−	1.41983i	−0.704288	−	0.709914i	$-0.748734\pi$
$569$		−	19271.0i		−	1.41983i	0.704288	−	0.709914i	$-0.251266\pi$
$570$		0			0
$571$		−	15535.7i		−	1.13861i	−0.822125	−	0.569307i	$-0.807212\pi$
$571$		−	15535.7i		−	1.13861i	0.822125	−	0.569307i	$-0.192788\pi$
$572$	3026.96	+	9871.20i	0.221265	+	0.721566i
$573$		0			0
$574$	7380.71	+	5456.66i	0.536699	+	0.396789i
$575$	−3052.33			−0.221375
$576$		0			0
$577$	3783.58			0.272985			0.136493	−	0.990641i	$-0.456417\pi$
$577$	3783.58			0.272985			0.136493	+	0.990641i	$0.456417\pi$
$578$	20072.3	+	14839.7i	1.44446	+	1.06791i
$579$		0			0
$580$	548.447	+	1788.54i	0.0392639	+	0.128043i
$581$			2988.15i			0.213373i
$582$		0			0
$583$			3743.06i			0.265903i
$584$	−3566.21	+	10111.0i	−0.252689	+	0.716429i
$585$		0			0
$586$	−5514.43	+	7458.85i	−0.388736	+	0.525806i
$587$	15515.4			1.09095			0.545477	−	0.838126i	$-0.316349\pi$
$587$	15515.4			1.09095			0.545477	+	0.838126i	$0.316349\pi$
$588$		0			0
$589$	−32052.1			−2.24225
$590$	8331.76	−	11269.6i	0.581378	−	0.786375i
$591$		0			0
$592$	−15012.6	+	10162.7i	−1.04225	+	0.705550i
$593$		−	14098.1i		−	0.976292i	−0.872762	−	0.488146i	$-0.837673\pi$
$593$		−	14098.1i		−	0.976292i	0.872762	−	0.488146i	$-0.162327\pi$
$594$		0			0
$595$		−	6043.90i		−	0.416430i
$596$	−21145.7	+	6484.24i	−1.45329	+	0.445646i
$597$		0			0
$598$	4173.55	+	3085.56i	0.285400	+	0.211000i
$599$	572.539			0.0390539			0.0195270	−	0.999809i	$-0.493784\pi$
$599$	572.539			0.0390539			0.0195270	+	0.999809i	$0.493784\pi$
$600$		0			0
$601$	−23463.4			−1.59250			−0.796249	−	0.604969i	$-0.793185\pi$
$601$	−23463.4			−1.59250			−0.796249	+	0.604969i	$0.793185\pi$
$602$	6494.26	+	4801.30i	0.439678	+	0.325060i
$603$		0			0
$604$	28254.3	−	8664.07i	1.90340	−	0.583669i
$605$			4515.52i			0.303441i
$606$		0			0
$607$		−	1980.51i		−	0.132433i	−0.997805	−	0.0662163i	$-0.978907\pi$
$607$		−	1980.51i		−	0.132433i	0.997805	−	0.0662163i	$-0.0210927\pi$
$608$	823.752	−	19818.3i	0.0549466	−	1.32194i
$609$		0			0
$610$	3423.66	−	4630.86i	0.227246	−	0.307374i
$611$	3619.39			0.239648
$612$		0			0
$613$	2479.01			0.163338			0.0816691	−	0.996660i	$-0.473975\pi$
$613$	2479.01			0.163338			0.0816691	+	0.996660i	$0.473975\pi$
$614$	5068.71	−	6855.97i	0.333154	−	0.450626i
$615$		0			0
$616$	4450.11	+	1569.58i	0.291072	+	0.102663i
$617$			20002.8i			1.30516i	0.757722	+	0.652578i	$0.226312\pi$
$617$			20002.8i			1.30516i	−0.757722	+	0.652578i	$0.773688\pi$
$618$		0			0
$619$			22292.4i			1.44751i	0.690058	+	0.723754i	$0.257585\pi$
$619$			22292.4i			1.44751i	−0.690058	+	0.723754i	$0.742415\pi$
$620$	−4005.75	−	13063.1i	−0.259475	−	0.846172i
$621$		0			0
$622$	−14171.0	−	10476.8i	−0.913516	−	0.675375i
$623$	6534.01			0.420192
$624$		0			0
$625$	4002.52			0.256161
$626$	8921.13	+	6595.52i	0.569585	+	0.421102i
$627$		0			0
$628$	1905.38	+	6213.63i	0.121072	+	0.394826i
$629$		−	33201.9i		−	2.10469i
$630$		0			0
$631$			24203.8i			1.52700i	0.645807	+	0.763501i	$0.276521\pi$
$631$			24203.8i			1.52700i	−0.645807	+	0.763501i	$0.723479\pi$
$632$	5830.27	+	2056.38i	0.366955	+	0.129428i
$633$		0			0
$634$	11572.1	−	15652.5i	0.724903	−	0.980508i
$635$	4406.32			0.275370
$636$		0			0
$637$	14483.7			0.900885
$638$	1590.23	−	2150.95i	0.0986797	−	0.133475i
$639$		0			0
$640$	8180.07	−	2141.09i	0.505227	−	0.132241i
$641$			4423.87i			0.272593i	0.990668	+	0.136297i	$0.0435200\pi$
$641$			4423.87i			0.272593i	−0.990668	+	0.136297i	$0.956480\pi$
$642$		0			0
$643$			11961.5i			0.733619i	0.930296	+	0.366810i	$0.119550\pi$
$643$			11961.5i			0.733619i	−0.930296	+	0.366810i	$0.880450\pi$
$644$	2267.90	−	695.442i	0.138770	−	0.0425532i
$645$		0			0
$646$	29210.8	+	21596.0i	1.77908	+	1.31530i
$647$	−6287.16			−0.382030			−0.191015	−	0.981587i	$-0.561178\pi$
$647$	−6287.16			−0.382030			−0.191015	+	0.981587i	$0.561178\pi$
$648$		0			0
$649$	−20040.1			−1.21208
$650$	−11299.8	−	8354.10i	−0.681869	−	0.504115i
$651$		0			0
$652$	7909.92	−	2425.54i	0.475117	−	0.145693i
$653$		−	18793.2i		−	1.12624i	−0.826376	−	0.563119i	$-0.809601\pi$
$653$		−	18793.2i		−	1.12624i	0.826376	−	0.563119i	$-0.190399\pi$
$654$		0			0
$655$			11832.2i			0.705833i
$656$	−13183.8	−	19475.4i	−0.784667	−	1.15913i
$657$		0			0
$658$	983.387	−	1330.14i	0.0582620	−	0.0788056i
$659$	−20827.2			−1.23113			−0.615563	−	0.788088i	$-0.711071\pi$
$659$	−20827.2			−1.23113			−0.615563	+	0.788088i	$0.711071\pi$
$660$		0			0
$661$	−6038.16			−0.355306			−0.177653	−	0.984093i	$-0.556850\pi$
$661$	−6038.16			−0.355306			−0.177653	+	0.984093i	$0.556850\pi$
$662$	15955.5	−	21581.5i	0.936751	−	1.26705i
$663$		0			0
$664$	2546.68	−	7220.39i	0.148841	−	0.421996i
$665$		−	5650.20i		−	0.329482i
$666$		0			0
$667$		−	1344.70i		−	0.0780612i
$668$	3408.52	+	11115.5i	0.197425	+	0.643819i
$669$		0			0
$670$	2580.05	+	1907.47i	0.148770	+	0.109988i
$671$	−8234.79			−0.473771
$672$		0			0
$673$	−19811.5			−1.13474			−0.567368	−	0.823464i	$-0.692038\pi$
$673$	−19811.5			−1.13474			−0.567368	+	0.823464i	$0.692038\pi$
$674$	−10413.2	−	7698.60i	−0.595105	−	0.439969i
$675$		0			0
$676$	1852.75	+	6041.97i	0.105413	+	0.343763i
$677$		−	22962.5i		−	1.30357i	−0.758402	−	0.651787i	$-0.774020\pi$
$677$		−	22962.5i		−	1.30357i	0.758402	−	0.651787i	$-0.225980\pi$
$678$		0			0
$679$		−	3961.90i		−	0.223923i
$680$	−5150.97	+	14604.1i	−0.290486	+	0.823591i
$681$		0			0
$682$	−11614.7	+	15710.1i	−0.652125	+	0.882068i
$683$	33097.3			1.85422			0.927109	−	0.374791i	$-0.122286\pi$
$683$	33097.3			1.85422			0.927109	+	0.374791i	$0.122286\pi$
$684$		0			0
$685$	10993.9			0.613222
$686$	9028.48	−	12212.0i	0.502491	−	0.679672i
$687$		0			0
$688$	−11600.4	−	17136.4i	−0.642821	−	0.949589i
$689$			8662.84i			0.478995i
$690$		0			0
$691$			21151.0i			1.16443i	0.813034	+	0.582216i	$0.197814\pi$
$691$			21151.0i			1.16443i	−0.813034	+	0.582216i	$0.802186\pi$
$692$	−4856.04	+	1489.08i	−0.266761	+	0.0818012i
$693$		0			0
$694$	−2143.54	−	1584.75i	−0.117244	−	0.0866805i
$695$	547.267			0.0298691
$696$		0			0
$697$	43071.9			2.34069
$698$	4832.63	+	3572.83i	0.262060	+	0.193745i
$699$		0			0
$700$	−6140.30	+	1882.90i	−0.331545	+	0.101667i
$701$			18752.3i			1.01036i	0.863013	+	0.505182i	$0.168575\pi$
$701$			18752.3i			1.01036i	−0.863013	+	0.505182i	$0.831425\pi$
$702$		0			0
$703$		−	31039.1i		−	1.66524i
$704$	−9415.29	−	7585.30i	−0.504051	−	0.406082i
$705$		0			0
$706$	6526.76	−	8828.13i	0.347929	−	0.470611i
$707$	10181.2			0.541588
$708$		0			0
$709$	−25964.1			−1.37532			−0.687660	−	0.726033i	$-0.741362\pi$
$709$	−25964.1			−1.37532			−0.687660	+	0.726033i	$0.741362\pi$
$710$	−9226.47	+	12479.8i	−0.487695	+	0.659659i
$711$		0			0
$712$	−15788.4	−	5568.67i	−0.831032	−	0.293110i
$713$			9821.38i			0.515868i
$714$		0			0
$715$		−	7535.75i		−	0.394155i
$716$	−6823.52	−	22252.1i	−0.356155	−	1.16145i
$717$		0			0
$718$	−18309.6	−	13536.5i	−0.951681	−	0.703591i
$719$	−11741.1			−0.608998			−0.304499	−	0.952513i	$-0.598489\pi$
$719$	−11741.1			−0.608998			−0.304499	+	0.952513i	$0.598489\pi$
$720$		0			0
$721$	−12274.4			−0.634010
$722$	11708.2	+	8656.06i	0.603511	+	0.446184i
$723$		0			0
$724$	3176.72	+	10359.6i	0.163069	+	0.531782i
$725$			3640.74i			0.186502i
$726$		0			0
$727$		−	5637.87i		−	0.287616i	−0.989606	−	0.143808i	$-0.954065\pi$
$727$		−	5637.87i		−	0.287616i	0.989606	−	0.143808i	$-0.0459348\pi$
$728$	10299.2	+	3632.61i	0.524334	+	0.184936i
$729$		0			0
$730$	4651.97	−	6292.28i	0.235859	−	0.319024i
$731$	37898.8			1.91756
$732$		0			0
$733$	−23807.3			−1.19965			−0.599825	−	0.800131i	$-0.704763\pi$
$733$	−23807.3			−1.19965			−0.599825	+	0.800131i	$0.704763\pi$
$734$	−11586.9	+	15672.5i	−0.582670	+	0.788123i
$735$		0			0
$736$	−6072.71	−	252.414i	−0.304135	−	0.0126414i
$737$		−	4587.96i		−	0.229307i
$738$		0			0
$739$			3556.31i			0.177024i	0.996075	+	0.0885122i	$0.0282112\pi$
$739$			3556.31i			0.177024i	−0.996075	+	0.0885122i	$0.971789\pi$
$740$	12650.3	−	3879.15i	0.628423	−	0.192703i
$741$		0			0
$742$	3183.61	+	2353.69i	0.157512	+	0.116451i
$743$	−24054.6			−1.18772			−0.593860	−	0.804568i	$-0.702397\pi$
$743$	−24054.6			−1.18772			−0.593860	+	0.804568i	$0.702397\pi$
$744$		0			0
$745$	16142.8			0.793860
$746$	23909.2	+	17676.4i	1.17343	+	0.867533i
$747$		0			0
$748$	21170.2	−	6491.76i	1.03484	−	0.317329i
$749$			2167.86i			0.105757i
$750$		0			0
$751$		−	15373.0i		−	0.746960i	−0.927638	−	0.373480i	$-0.878164\pi$
$751$		−	15373.0i		−	0.746960i	0.927638	−	0.373480i	$-0.121836\pi$
$752$	−3509.82	+	2375.96i	−0.170199	+	0.115216i
$753$		0			0
$754$	3680.38	−	4978.11i	0.177761	−	0.240440i
$755$	−21569.6			−1.03973
$756$		0			0
$757$	26000.8			1.24837			0.624184	−	0.781277i	$-0.285431\pi$
$757$	26000.8			1.24837			0.624184	+	0.781277i	$0.285431\pi$
$758$	−5279.27	+	7140.77i	−0.252971	+	0.342170i
$759$		0			0
$760$	−4815.43	+	13652.8i	−0.229834	+	0.651630i
$761$		−	9461.72i		−	0.450706i	−0.974277	−	0.225353i	$-0.927646\pi$
$761$		−	9461.72i		−	0.450706i	0.974277	−	0.225353i	$-0.0723535\pi$
$762$		0			0
$763$		−	5696.06i		−	0.270264i
$764$	8181.61	+	26681.0i	0.387435	+	1.26346i
$765$		0			0
$766$	−11639.1	−	8604.93i	−0.549004	−	0.405886i
$767$	−46380.2			−2.18343
$768$		0			0
$769$	11196.2			0.525028			0.262514	−	0.964928i	$-0.415448\pi$
$769$	11196.2			0.525028			0.262514	+	0.964928i	$0.415448\pi$
$770$	−2769.40	−	2047.46i	−0.129613	−	0.0958250i
$771$		0			0
$772$	6832.05	+	22279.9i	0.318512	+	1.03870i
$773$			39575.0i			1.84141i	0.390255	+	0.920707i	$0.372387\pi$
$773$			39575.0i			1.84141i	−0.390255	+	0.920707i	$0.627613\pi$
$774$		0			0
$775$		−	26591.2i		−	1.23250i
$776$	−3376.56	+	9573.29i	−0.156201	+	0.442862i
$777$		0			0
$778$	−1323.32	+	1789.92i	−0.0609810	+	0.0824832i
$779$	40266.2			1.85197
$780$		0			0
$781$	22192.1			1.01677
$782$	6617.43	−	8950.77i	0.302607	−	0.409308i
$783$		0			0
$784$	−14045.2	+	9507.83i	−0.639813	+	0.433119i
$785$		−	4743.53i		−	0.215674i
$786$		0			0
$787$		−	25069.2i		−	1.13548i	−0.823209	−	0.567739i	$-0.807818\pi$
$787$		−	25069.2i		−	1.13548i	0.823209	−	0.567739i	$-0.192182\pi$
$788$	−18606.1	+	5705.49i	−0.841136	+	0.257931i
$789$		0			0
$790$	−3628.31	−	2682.46i	−0.163404	−	0.120807i
$791$	−7289.58			−0.327671
$792$		0			0
$793$	−19058.4			−0.853448
$794$	−25383.1	−	18766.1i	−1.13453	−	0.838770i
$795$		0			0
$796$	−4307.55	+	1320.89i	−0.191805	+	0.0588163i
$797$		−	5639.39i		−	0.250637i	−0.992117	−	0.125318i	$-0.960005\pi$
$797$		−	5639.39i		−	0.250637i	0.992117	−	0.125318i	$-0.0399952\pi$
$798$		0			0
$799$		−	7762.31i		−	0.343693i
$800$	16441.8	+	683.406i	0.726630	+	0.0302026i
$801$		0			0
$802$	−22236.6	+	30077.4i	−0.979056	+	1.32428i
$803$	−11189.2			−0.491729
$804$		0			0
$805$	−1731.33			−0.0758030
$806$	−26880.8	+	36359.1i	−1.17473	+	1.58895i
$807$		0			0
$808$	−24601.2	−	8677.01i	−1.07112	−	0.377792i
$809$			34032.0i			1.47899i	0.673163	+	0.739494i	$0.264935\pi$
$809$			34032.0i			1.47899i	−0.673163	+	0.739494i	$0.735065\pi$
$810$		0			0
$811$			20119.5i			0.871137i	0.900156	+	0.435569i	$0.143453\pi$
$811$			20119.5i			0.871137i	−0.900156	+	0.435569i	$0.856547\pi$
$812$	−829.507	−	2705.10i	−0.0358497	−	0.116909i
$813$		0			0
$814$	−15213.6	−	11247.6i	−0.655082	−	0.484311i
$815$	−6038.49			−0.259532
$816$		0			0
$817$	35430.0			1.51718
$818$	−18543.0	−	13709.1i	−0.792593	−	0.585975i
$819$		0			0
$820$	5032.31	+	16410.8i	0.214312	+	0.698891i
$821$			9057.81i			0.385042i	0.981293	+	0.192521i	$0.0616664\pi$
$821$			9057.81i			0.385042i	−0.981293	+	0.192521i	$0.938334\pi$
$822$		0			0
$823$			26277.7i			1.11298i	0.830853	+	0.556491i	$0.187853\pi$
$823$			26277.7i			1.11298i	−0.830853	+	0.556491i	$0.812147\pi$
$824$	29659.0	+	10460.9i	1.25391	+	0.442262i
$825$		0			0
$826$	−12601.5	+	17044.8i	−0.530825	+	0.717997i
$827$	21737.7			0.914018			0.457009	−	0.889462i	$-0.348921\pi$
$827$	21737.7			0.914018			0.457009	+	0.889462i	$0.348921\pi$
$828$		0			0
$829$	27552.6			1.15433			0.577167	−	0.816626i	$-0.304158\pi$
$829$	27552.6			1.15433			0.577167	+	0.816626i	$0.304158\pi$
$830$	−3322.04	+	4493.41i	−0.138927	+	0.187914i
$831$		0			0
$832$	−21790.5	−	17555.2i	−0.907993	−	0.731512i
$833$		−	31062.3i		−	1.29201i
$834$		0			0
$835$		−	8485.65i		−	0.351686i
$836$	19791.2	−	6068.88i	0.818771	−	0.251073i
$837$		0			0
$838$	26570.2	+	19643.7i	1.09529	+	0.809763i
$839$	12231.7			0.503320			0.251660	−	0.967816i	$-0.419023\pi$
$839$	12231.7			0.503320			0.251660	+	0.967816i	$0.419023\pi$
$840$		0			0
$841$	22785.1			0.934236
$842$	−21824.2	−	16134.9i	−0.893243	−	0.660387i
$843$		0			0
$844$	11072.1	−	3395.21i	0.451560	−	0.138469i
$845$		−	4612.48i		−	0.187780i
$846$		0			0
$847$		−	6829.56i		−	0.277056i
$848$	−5686.73	−	8400.57i	−0.230287	−	0.340185i
$849$		0			0
$850$	−17916.6	+	24234.1i	−0.722981	+	0.977907i
$851$	−9511.00			−0.383117
$852$		0			0
$853$	−2257.34			−0.0906093			−0.0453046	−	0.998973i	$-0.514426\pi$
$853$	−2257.34			−0.0906093			−0.0453046	+	0.998973i	$0.514426\pi$
$854$	−5178.16	+	7004.01i	−0.207486	+	0.280647i
$855$		0			0
$856$	1847.57	−	5238.27i	0.0737719	−	0.209159i
$857$			24908.2i			0.992820i	0.868088	+	0.496410i	$0.165349\pi$
$857$			24908.2i			0.992820i	−0.868088	+	0.496410i	$0.834651\pi$
$858$		0			0
$859$			11850.7i			0.470710i	0.971909	+	0.235355i	$0.0756253\pi$
$859$			11850.7i			0.470710i	−0.971909	+	0.235355i	$0.924375\pi$
$860$	4427.91	+	14439.8i	0.175570	+	0.572551i
$861$		0			0
$862$	9767.16	+	7221.00i	0.385929	+	0.285323i
$863$	−43145.0			−1.70182			−0.850910	−	0.525311i	$-0.823949\pi$
$863$	−43145.0			−1.70182			−0.850910	+	0.525311i	$0.823949\pi$
$864$		0			0
$865$	3707.13			0.145718
$866$	−382.984	−	283.145i	−0.0150281	−	0.0111105i
$867$		0			0
$868$	6058.55	+	19757.5i	0.236913	+	0.772595i
$869$			6452.01i			0.251864i
$870$		0			0
$871$		−	10618.3i		−	0.413072i
$872$	−4854.52	+	13763.6i	−0.188526	+	0.534513i
$873$		0			0
$874$	6186.37	−	8367.71i	0.239424	−	0.323847i
$875$	11133.1			0.430133
$876$		0			0
$877$	−14333.4			−0.551886			−0.275943	−	0.961174i	$-0.588990\pi$
$877$	−14333.4			−0.551886			−0.275943	+	0.961174i	$0.588990\pi$
$878$	−2454.14	+	3319.48i	−0.0943316	+	0.127593i
$879$		0			0
$880$	4946.85	+	7307.60i	0.189498	+	0.279931i
$881$			5066.51i			0.193752i	0.995296	+	0.0968758i	$0.0308850\pi$
$881$			5066.51i			0.193752i	−0.995296	+	0.0968758i	$0.969115\pi$
$882$		0			0
$883$		−	7046.42i		−	0.268551i	−0.990944	−	0.134276i	$-0.957129\pi$
$883$		−	7046.42i		−	0.268551i	0.990944	−	0.134276i	$-0.0428708\pi$
$884$	48995.8	−	15024.4i	1.86415	−	0.571634i
$885$		0			0
$886$	−758.295	−	560.618i	−0.0287533	−	0.0212577i
$887$	52122.7			1.97307			0.986534	−	0.163559i	$-0.0522974\pi$
$887$	52122.7			1.97307			0.986534	+	0.163559i	$0.0522974\pi$
$888$		0			0
$889$	−6664.41			−0.251425
$890$	9825.46	+	7264.10i	0.370056	+	0.273588i
$891$		0			0
$892$	−38619.3	+	11842.4i	−1.44963	+	0.444523i
$893$		−	7256.67i		−	0.271932i
$894$		0			0
$895$			16987.4i			0.634444i
$896$	−12372.1	+	3238.32i	−0.461296	+	0.120742i
$897$		0			0
$898$	19260.0	−	26051.2i	0.715719	−	0.968086i
$899$	11714.7			0.434602
$900$		0			0
$901$	18578.7			0.686955
$902$	14591.2	−	19736.2i	0.538619	−	0.728539i
$903$		0			0
$904$	17614.1	+	6212.61i	0.648049	+	0.228571i
$905$		−	7908.56i		−	0.290486i
$906$		0			0
$907$		−	41205.1i		−	1.50848i	−0.656599	−	0.754240i	$-0.728006\pi$
$907$		−	41205.1i		−	1.50848i	0.656599	−	0.754240i	$-0.271994\pi$
$908$	−13407.4	−	43722.8i	−0.490023	−	1.59801i
$909$		0			0
$910$	−6409.44	−	4738.59i	−0.233484	−	0.172618i
$911$	−34305.8			−1.24764			−0.623821	−	0.781567i	$-0.714420\pi$
$911$	−34305.8			−1.24764			−0.623821	+	0.781567i	$0.714420\pi$
$912$		0			0
$913$	7990.37			0.289642
$914$	−22016.3	−	16277.0i	−0.796757	−	0.589054i
$915$		0			0
$916$	−6057.05	−	19752.6i	−0.218483	−	0.712494i
$917$		−	17895.7i		−	0.644458i
$918$		0			0
$919$			43537.1i			1.56274i	0.624068	+	0.781370i	$0.285479\pi$
$919$			43537.1i			1.56274i	−0.624068	+	0.781370i	$0.714521\pi$
$920$	4183.48	+	1475.54i	0.149919	+	0.0528774i
$921$		0			0
$922$	−24897.2	+	33676.1i	−0.889312	+	1.20289i
$923$	51360.8			1.83160
$924$		0			0
$925$	25750.9			0.915333
$926$	6150.93	−	8319.78i	0.218285	−	0.295254i
$927$		0			0
$928$	−301.073	+	7243.39i	−0.0106500	+	0.256224i
$929$		−	8764.21i		−	0.309520i	−0.987952	−	0.154760i	$-0.950539\pi$
$929$		−	8764.21i		−	0.309520i	0.987952	−	0.154760i	$-0.0494605\pi$
$930$		0			0
$931$		−	29038.9i		−	1.02225i
$932$	4491.22	−	1377.21i	0.157848	−	0.0484036i
$933$		0			0
$934$	−22407.8	−	16566.4i	−0.785016	−	0.580373i
$935$	−16161.5			−0.565281
$936$		0			0
$937$	−22745.0			−0.793006			−0.396503	−	0.918033i	$-0.629776\pi$
$937$	−22745.0			−0.793006			−0.396503	+	0.918033i	$0.629776\pi$
$938$	−3902.23	−	2884.97i	−0.135834	−	0.100424i
$939$		0			0
$940$	2957.52	−	906.912i	0.102621	−	0.0314683i
$941$		−	24740.5i		−	0.857084i	−0.903522	−	0.428542i	$-0.859027\pi$
$941$		−	24740.5i		−	0.857084i	0.903522	−	0.428542i	$-0.140973\pi$
$942$		0			0
$943$		−	12338.3i		−	0.426078i
$944$	44976.1	−	30446.4i	1.55068	−	1.04973i
$945$		0			0
$946$	12838.8	−	17365.8i	0.441252	−	0.596839i
$947$	−1886.69			−0.0647405			−0.0323703	−	0.999476i	$-0.510306\pi$
$947$	−1886.69			−0.0647405			−0.0323703	+	0.999476i	$0.510306\pi$
$948$		0			0
$949$	−25896.0			−0.885796
$950$	−16749.5	+	22655.4i	−0.572026	+	0.773726i
$951$		0			0
$952$	7790.65	−	22088.2i	0.265227	−	0.751977i
$953$		−	36292.1i		−	1.23360i	−0.787122	−	0.616798i	$-0.788430\pi$
$953$		−	36292.1i		−	1.23360i	0.787122	−	0.616798i	$-0.211570\pi$
$954$		0			0
$955$		−	20368.5i		−	0.690165i
$956$	13094.2	+	42701.5i	0.442989	+	1.44463i
$957$		0			0
$958$	25263.3	+	18677.5i	0.852004	+	0.629899i
$959$	−16627.9			−0.559900
$960$		0			0
$961$	−55770.8			−1.87207
$962$	−35210.0	−	26031.2i	−1.18006	−	0.872433i
$963$		0			0
$964$	−4824.31	−	15732.5i	−0.161183	−	0.525633i
$965$		−	17008.7i		−	0.567387i
$966$		0			0
$967$		−	12599.4i		−	0.418996i	−0.977809	−	0.209498i	$-0.932817\pi$
$967$		−	12599.4i		−	0.418996i	0.977809	−	0.209498i	$-0.0671830\pi$
$968$	−5820.55	+	16502.5i	−0.193264	+	0.547946i
$969$		0			0
$970$	4404.59	−	5957.67i	0.145797	−	0.197205i
$971$	−41974.3			−1.38725			−0.693625	−	0.720336i	$-0.743988\pi$
$971$	−41974.3			−1.38725			−0.693625	+	0.720336i	$0.743988\pi$
$972$		0			0
$973$	−827.721			−0.0272719
$974$	−19679.2	+	26618.3i	−0.647396	+	0.875671i
$975$		0			0
$976$	18481.4	−	12510.9i	0.606123	−	0.410312i
$977$		−	33488.8i		−	1.09662i	−0.836274	−	0.548312i	$-0.815271\pi$
$977$		−	33488.8i		−	1.09662i	0.836274	−	0.548312i	$-0.184729\pi$
$978$		0			0
$979$		−	17472.1i		−	0.570387i
$980$	11835.1	−	3629.17i	0.385773	−	0.118296i
$981$		0			0
$982$	−6484.74	−	4794.26i	−0.210730	−	0.155795i
$983$	3461.54			0.112315			0.0561576	−	0.998422i	$-0.482115\pi$
$983$	3461.54			0.112315			0.0561576	+	0.998422i	$0.482115\pi$
$984$		0			0
$985$	14204.0			0.459470
$986$	−10676.3	−	7893.11i	−0.344829	−	0.254937i
$987$		0			0
$988$	45804.2	−	14045.7i	1.47493	−	0.452280i
$989$		−	10856.5i		−	0.349055i
$990$		0			0
$991$			20067.6i			0.643256i	0.946866	+	0.321628i	$0.104230\pi$
$991$			20067.6i			0.643256i	−0.946866	+	0.321628i	$0.895770\pi$
$992$	2198.98	−	52904.2i	0.0703806	−	1.69326i
$993$		0			0
$994$	13954.7	−	18875.2i	0.445288	−	0.602299i
$995$	3288.41			0.104774
$996$		0			0
$997$	821.726			0.0261026			0.0130513	−	0.999915i	$-0.495846\pi$
$997$	821.726			0.0261026			0.0130513	+	0.999915i	$0.495846\pi$
$998$	25114.4	−	33969.9i	0.796575	−	1.07745i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.b.b.107.3	✓	12
3.2	odd	2	inner	108.4.b.b.107.10	yes	12
4.3	odd	2	inner	108.4.b.b.107.9	yes	12
8.3	odd	2		1728.4.c.j.1727.9		12
8.5	even	2		1728.4.c.j.1727.10		12
12.11	even	2	inner	108.4.b.b.107.4	yes	12
24.5	odd	2		1728.4.c.j.1727.4		12
24.11	even	2		1728.4.c.j.1727.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.b.b.107.3	✓	12	1.1	even	1	trivial
108.4.b.b.107.4	yes	12	12.11	even	2	inner
108.4.b.b.107.9	yes	12	4.3	odd	2	inner
108.4.b.b.107.10	yes	12	3.2	odd	2	inner
1728.4.c.j.1727.3		12	24.11	even	2
1728.4.c.j.1727.4		12	24.5	odd	2
1728.4.c.j.1727.9		12	8.3	odd	2
1728.4.c.j.1727.10		12	8.5	even	2

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.27435 - 1.68146i) q^{2} +(2.34537 + 7.64848i) q^{4} -5.83890i q^{5} +8.83113i q^{7} +(7.52641 - 21.3390i) q^{8} +O(q^{10})\)	\(q+(-2.27435 - 1.68146i) q^{2} +(2.34537 + 7.64848i) q^{4} -5.83890i q^{5} +8.83113i q^{7} +(7.52641 - 21.3390i) q^{8} +(-9.81789 + 13.2797i) q^{10} +23.6146 q^{11} +54.6531 q^{13} +(14.8492 - 20.0851i) q^{14} +(-52.9984 + 35.8771i) q^{16} -117.211i q^{17} -109.576i q^{19} +(44.6587 - 13.6944i) q^{20} +(-53.7080 - 39.7070i) q^{22} -33.5763 q^{23} +90.9072 q^{25} +(-124.300 - 91.8970i) q^{26} +(-67.5447 + 20.7123i) q^{28} +40.0490i q^{29} -292.510i q^{31} +(180.863 + 7.51762i) q^{32} +(-197.086 + 266.580i) q^{34} +51.5641 q^{35} +283.265 q^{37} +(-184.248 + 249.215i) q^{38} +(-124.596 - 43.9460i) q^{40} +367.472i q^{41} +323.337i q^{43} +(55.3851 + 180.616i) q^{44} +(76.3644 + 56.4572i) q^{46} +66.2249 q^{47} +265.011 q^{49} +(-206.755 - 152.857i) q^{50} +(128.182 + 418.013i) q^{52} +158.506i q^{53} -137.883i q^{55} +(188.447 + 66.4667i) q^{56} +(67.3408 - 91.0856i) q^{58} -848.630 q^{59} -348.716 q^{61} +(-491.844 + 665.270i) q^{62} +(-398.706 - 321.212i) q^{64} -319.114i q^{65} -194.285i q^{67} +(896.489 - 274.905i) q^{68} +(-117.275 - 86.7031i) q^{70} +939.761 q^{71} -473.826 q^{73} +(-644.246 - 476.300i) q^{74} +(838.091 - 256.997i) q^{76} +208.544i q^{77} +273.221i q^{79} +(209.483 + 309.453i) q^{80} +(617.890 - 835.761i) q^{82} +338.366 q^{83} -684.386 q^{85} +(543.679 - 735.383i) q^{86} +(177.733 - 503.912i) q^{88} -739.884i q^{89} +482.648i q^{91} +(-78.7490 - 256.807i) q^{92} +(-150.619 - 111.355i) q^{94} -639.805 q^{95} -448.629 q^{97} +(-602.729 - 445.606i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4}+O(q^{10}) \) 12 * q + 6 * q^4	\( 12 q + 6 q^{4} + 42 q^{10} - 72 q^{13} + 114 q^{16} + 66 q^{22} - 384 q^{25} - 282 q^{28} - 324 q^{34} - 240 q^{37} + 774 q^{40} + 1752 q^{46} + 288 q^{49} + 924 q^{52} - 948 q^{58} + 144 q^{61} - 3066 q^{64} - 3558 q^{70} + 156 q^{73} + 576 q^{76} + 5832 q^{82} - 168 q^{85} + 5022 q^{88} - 3444 q^{94} + 516 q^{97}+O(q^{100}) \) 12 * q + 6 * q^4 + 42 * q^10 - 72 * q^13 + 114 * q^16 + 66 * q^22 - 384 * q^25 - 282 * q^28 - 324 * q^34 - 240 * q^37 + 774 * q^40 + 1752 * q^46 + 288 * q^49 + 924 * q^52 - 948 * q^58 + 144 * q^61 - 3066 * q^64 - 3558 * q^70 + 156 * q^73 + 576 * q^76 + 5832 * q^82 - 168 * q^85 + 5022 * q^88 - 3444 * q^94 + 516 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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