LMFDB - Embedded newform 136.4.k.a.89.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,4,Mod(81,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("136.81");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	136.k (of order $4$, degree $2$, 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:	$8.02425976078$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 142x^{12} + 7785x^{10} + 208489x^{8} + 2822686x^{6} + 17977041x^{4} + 45020416x^{2} + 31719424 $ x^14 + 142x^12 + 7785x^10 + 208489x^8 + 2822686x^6 + 17977041x^4 + 45020416x^2 + 31719424
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{17} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			89.2
Root			$-5.35029i$ of defining polynomial
Character	$\chi$	$=$	136.89
Dual form			136.4.k.a.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.35029 + 5.35029i) q^{3} +(-11.0962 + 11.0962i) q^{5} +(19.2933 + 19.2933i) q^{7} -30.2512i q^{9} +O(q^{10})$	\(q+(-5.35029 + 5.35029i) q^{3} +(-11.0962 + 11.0962i) q^{5} +(19.2933 + 19.2933i) q^{7} -30.2512i q^{9} +(-19.4859 - 19.4859i) q^{11} -14.9336 q^{13} -118.736i q^{15} +(-69.0049 + 12.3012i) q^{17} -143.163i q^{19} -206.450 q^{21} +(136.829 + 136.829i) q^{23} -121.253i q^{25} +(17.3951 + 17.3951i) q^{27} +(-48.0943 + 48.0943i) q^{29} +(168.014 - 168.014i) q^{31} +208.510 q^{33} -428.166 q^{35} +(-146.236 + 146.236i) q^{37} +(79.8992 - 79.8992i) q^{39} +(-50.0956 - 50.0956i) q^{41} +335.263i q^{43} +(335.675 + 335.675i) q^{45} -380.039 q^{47} +401.462i q^{49} +(303.382 - 435.012i) q^{51} -163.666i q^{53} +432.440 q^{55} +(765.964 + 765.964i) q^{57} +436.943i q^{59} +(-391.332 - 391.332i) q^{61} +(583.646 - 583.646i) q^{63} +(165.707 - 165.707i) q^{65} +307.709 q^{67} -1464.15 q^{69} +(-279.640 + 279.640i) q^{71} +(-116.969 + 116.969i) q^{73} +(648.738 + 648.738i) q^{75} -751.894i q^{77} +(-18.2130 - 18.2130i) q^{79} +630.646 q^{81} -80.2810i q^{83} +(629.198 - 902.192i) q^{85} -514.637i q^{87} -1227.86 q^{89} +(-288.119 - 288.119i) q^{91} +1797.84i q^{93} +(1588.57 + 1588.57i) q^{95} +(-912.788 + 912.788i) q^{97} +(-589.472 + 589.472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 4 q^{3} + 8 q^{5} - 10 q^{7}+O(q^{10}) $ 14 * q - 4 * q^3 + 8 * q^5 - 10 * q^7	$ 14 q - 4 q^{3} + 8 q^{5} - 10 q^{7} + 16 q^{11} + 72 q^{13} - 40 q^{17} - 60 q^{21} + 246 q^{23} + 572 q^{27} + 260 q^{29} + 566 q^{31} - 904 q^{33} - 804 q^{35} - 28 q^{37} + 476 q^{39} - 786 q^{41} - 604 q^{45} + 448 q^{47} - 380 q^{51} + 1612 q^{55} + 1004 q^{57} + 660 q^{61} - 2250 q^{63} - 796 q^{65} - 284 q^{67} - 2532 q^{69} + 326 q^{71} + 730 q^{73} - 864 q^{75} + 342 q^{79} - 950 q^{81} + 4148 q^{85} - 4516 q^{89} - 3112 q^{91} + 3356 q^{95} - 1194 q^{97} + 2876 q^{99}+O(q^{100}) $ 14 * q - 4 * q^3 + 8 * q^5 - 10 * q^7 + 16 * q^11 + 72 * q^13 - 40 * q^17 - 60 * q^21 + 246 * q^23 + 572 * q^27 + 260 * q^29 + 566 * q^31 - 904 * q^33 - 804 * q^35 - 28 * q^37 + 476 * q^39 - 786 * q^41 - 604 * q^45 + 448 * q^47 - 380 * q^51 + 1612 * q^55 + 1004 * q^57 + 660 * q^61 - 2250 * q^63 - 796 * q^65 - 284 * q^67 - 2532 * q^69 + 326 * q^71 + 730 * q^73 - 864 * q^75 + 342 * q^79 - 950 * q^81 + 4148 * q^85 - 4516 * q^89 - 3112 * q^91 + 3356 * q^95 - 1194 * q^97 + 2876 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−5.35029	+	5.35029i	−1.02966	+	1.02966i	−0.0301178	+	0.999546i	$0.509588\pi$
$3$	−5.35029	+	5.35029i	−1.02966	+	1.02966i	−0.999546	+	0.0301178i	$0.990412\pi$
$4$		0			0
$5$	−11.0962	+	11.0962i	−0.992477	+	0.992477i	−0.999972	−	0.00749462i	$-0.997614\pi$
$5$	−11.0962	+	11.0962i	−0.992477	+	0.992477i	0.00749462	+	0.999972i	$0.497614\pi$
$6$		0			0
$7$	19.2933	+	19.2933i	1.04174	+	1.04174i	0.999090	+	0.0426499i	$0.0135800\pi$
$7$	19.2933	+	19.2933i	1.04174	+	1.04174i	0.0426499	+	0.999090i	$0.486420\pi$
$8$		0			0
$9$		−	30.2512i		−	1.12042i
$10$		0			0
$11$	−19.4859	−	19.4859i	−0.534111	−	0.534111i	0.387682	−	0.921793i	$-0.373276\pi$
$11$	−19.4859	−	19.4859i	−0.534111	−	0.534111i	−0.921793	+	0.387682i	$0.873276\pi$
$12$		0			0
$13$	−14.9336			−0.318603			−0.159301	−	0.987230i	$-0.550924\pi$
$13$	−14.9336			−0.318603			−0.159301	+	0.987230i	$0.550924\pi$
$14$		0			0
$15$		−	118.736i		−	2.04384i
$16$		0			0
$17$	−69.0049	+	12.3012i	−0.984480	+	0.175499i
$17$	−69.0049	+	12.3012i	−0.984480	+	0.175499i
$18$		0			0
$19$		−	143.163i		−	1.72862i	−0.502957	−	0.864312i	$-0.667754\pi$
$19$		−	143.163i		−	1.72862i	0.502957	−	0.864312i	$-0.332246\pi$
$20$		0			0
$21$	−206.450			−2.14528
$22$		0			0
$23$	136.829	+	136.829i	1.24047	+	1.24047i	0.959806	+	0.280664i	$0.0905548\pi$
$23$	136.829	+	136.829i	1.24047	+	1.24047i	0.280664	+	0.959806i	$0.409445\pi$
$24$		0			0
$25$		−	121.253i		−	0.970022i
$26$		0			0
$27$	17.3951	+	17.3951i	0.123989	+	0.123989i
$28$		0			0
$29$	−48.0943	+	48.0943i	−0.307962	+	0.307962i	−0.844119	−	0.536157i	$-0.819876\pi$
$29$	−48.0943	+	48.0943i	−0.307962	+	0.307962i	0.536157	+	0.844119i	$0.319876\pi$
$30$		0			0
$31$	168.014	−	168.014i	0.973423	−	0.973423i	−0.0262326	−	0.999656i	$-0.508351\pi$
$31$	168.014	−	168.014i	0.973423	−	0.973423i	0.999656	+	0.0262326i	$0.00835105\pi$
$32$		0			0
$33$	208.510			1.09991
$34$		0			0
$35$	−428.166			−2.06781
$36$		0			0
$37$	−146.236	+	146.236i	−0.649758	+	0.649758i	−0.952934	−	0.303177i	$-0.901953\pi$
$37$	−146.236	+	146.236i	−0.649758	+	0.649758i	0.303177	+	0.952934i	$0.401953\pi$
$38$		0			0
$39$	79.8992	−	79.8992i	0.328054	−	0.328054i
$40$		0			0
$41$	−50.0956	−	50.0956i	−0.190820	−	0.190820i	0.605230	−	0.796050i	$-0.293081\pi$
$41$	−50.0956	−	50.0956i	−0.190820	−	0.190820i	−0.796050	+	0.605230i	$0.793081\pi$
$42$		0			0
$43$			335.263i			1.18900i	0.804095	+	0.594501i	$0.202650\pi$
$43$			335.263i			1.18900i	−0.804095	+	0.594501i	$0.797350\pi$
$44$		0			0
$45$	335.675	+	335.675i	1.11199	+	1.11199i
$46$		0			0
$47$	−380.039			−1.17945			−0.589727	−	0.807602i	$-0.700765\pi$
$47$	−380.039			−1.17945			−0.589727	+	0.807602i	$0.700765\pi$
$48$		0			0
$49$			401.462i			1.17044i
$50$		0			0
$51$	303.382	−	435.012i	0.832979	−	1.19439i
$52$		0			0
$53$		−	163.666i		−	0.424173i	−0.977251	−	0.212087i	$-0.931974\pi$
$53$		−	163.666i		−	0.424173i	0.977251	−	0.212087i	$-0.0680259\pi$
$54$		0			0
$55$	432.440			1.06019
$56$		0			0
$57$	765.964	+	765.964i	1.77990	+	1.77990i
$58$		0			0
$59$			436.943i			0.964154i	0.876129	+	0.482077i	$0.160118\pi$
$59$			436.943i			0.964154i	−0.876129	+	0.482077i	$0.839882\pi$
$60$		0			0
$61$	−391.332	−	391.332i	−0.821392	−	0.821392i	0.164916	−	0.986308i	$-0.447265\pi$
$61$	−391.332	−	391.332i	−0.821392	−	0.821392i	−0.986308	+	0.164916i	$0.947265\pi$
$62$		0			0
$63$	583.646	−	583.646i	1.16718	−	1.16718i
$64$		0			0
$65$	165.707	−	165.707i	0.316206	−	0.316206i
$66$		0			0
$67$	307.709			0.561084			0.280542	−	0.959842i	$-0.409486\pi$
$67$	307.709			0.561084			0.280542	+	0.959842i	$0.409486\pi$
$68$		0			0
$69$	−1464.15			−2.55454
$70$		0			0
$71$	−279.640	+	279.640i	−0.467424	+	0.467424i	−0.901079	−	0.433655i	$-0.857224\pi$
$71$	−279.640	+	279.640i	−0.467424	+	0.467424i	0.433655	+	0.901079i	$0.357224\pi$
$72$		0			0
$73$	−116.969	+	116.969i	−0.187537	+	0.187537i	−0.794630	−	0.607093i	$-0.792335\pi$
$73$	−116.969	+	116.969i	−0.187537	+	0.187537i	0.607093	+	0.794630i	$0.292335\pi$
$74$		0			0
$75$	648.738	+	648.738i	0.998797	+	0.998797i
$76$		0			0
$77$		−	751.894i		−	1.11281i
$78$		0			0
$79$	−18.2130	−	18.2130i	−0.0259382	−	0.0259382i	0.694019	−	0.719957i	$-0.255838\pi$
$79$	−18.2130	−	18.2130i	−0.0259382	−	0.0259382i	−0.719957	+	0.694019i	$0.755838\pi$
$80$		0			0
$81$	630.646			0.865083
$82$		0			0
$83$		−	80.2810i		−	0.106169i	−0.998590	−	0.0530843i	$-0.983095\pi$
$83$		−	80.2810i		−	0.106169i	0.998590	−	0.0530843i	$-0.0169052\pi$
$84$		0			0
$85$	629.198	−	902.192i	0.802895	−	1.15125i
$86$		0			0
$87$		−	514.637i		−	0.634195i
$88$		0			0
$89$	−1227.86			−1.46239			−0.731196	−	0.682167i	$-0.761038\pi$
$89$	−1227.86			−1.46239			−0.731196	+	0.682167i	$0.761038\pi$
$90$		0			0
$91$	−288.119	−	288.119i	−0.331901	−	0.331901i
$92$		0			0
$93$			1797.84i			2.00460i
$94$		0			0
$95$	1588.57	+	1588.57i	1.71562	+	1.71562i
$96$		0			0
$97$	−912.788	+	912.788i	−0.955460	+	0.955460i	−0.999050	−	0.0435899i	$-0.986121\pi$
$97$	−912.788	+	912.788i	−0.955460	+	0.955460i	0.0435899	+	0.999050i	$0.486121\pi$
$98$		0			0
$99$	−589.472	+	589.472i	−0.598426	+	0.598426i
$100$		0			0
$101$	388.489			0.382734			0.191367	−	0.981519i	$-0.438708\pi$
$101$	388.489			0.382734			0.191367	+	0.981519i	$0.438708\pi$
$102$		0			0
$103$	−1638.75			−1.56768			−0.783838	−	0.620966i	$-0.786741\pi$
$103$	−1638.75			−1.56768			−0.783838	+	0.620966i	$0.786741\pi$
$104$		0			0
$105$	2290.81	−	2290.81i	2.12915	−	2.12915i
$106$		0			0
$107$	−684.188	+	684.188i	−0.618158	+	0.618158i	−0.945059	−	0.326900i	$-0.893996\pi$
$107$	−684.188	+	684.188i	−0.618158	+	0.618158i	0.326900	+	0.945059i	$0.393996\pi$
$108$		0			0
$109$	847.352	+	847.352i	0.744602	+	0.744602i	0.973460	−	0.228858i	$-0.0734992\pi$
$109$	847.352	+	847.352i	0.744602	+	0.744602i	−0.228858	+	0.973460i	$0.573499\pi$
$110$		0			0
$111$		−	1564.81i		−	1.33806i
$112$		0			0
$113$	−928.939	−	928.939i	−0.773338	−	0.773338i	0.205350	−	0.978689i	$-0.434167\pi$
$113$	−928.939	−	928.939i	−0.773338	−	0.773338i	−0.978689	+	0.205350i	$0.934167\pi$
$114$		0			0
$115$	−3036.57			−2.46228
$116$		0			0
$117$			451.760i			0.356968i
$118$		0			0
$119$	−1568.66	−	1094.00i	−1.20840	−	0.842748i
$120$		0			0
$121$		−	571.600i		−	0.429452i
$122$		0			0
$123$	536.052			0.392961
$124$		0			0
$125$	−41.5798	−	41.5798i	−0.0297521	−	0.0297521i
$126$		0			0
$127$		−	1130.34i		−	0.789772i	−0.918730	−	0.394886i	$-0.870784\pi$
$127$		−	1130.34i		−	0.789772i	0.918730	−	0.394886i	$-0.129216\pi$
$128$		0			0
$129$	−1793.75	−	1793.75i	−1.22427	−	1.22427i
$130$		0			0
$131$	−740.941	+	740.941i	−0.494171	+	0.494171i	−0.909617	−	0.415447i	$-0.863625\pi$
$131$	−740.941	+	740.941i	−0.494171	+	0.494171i	0.415447	+	0.909617i	$0.363625\pi$
$132$		0			0
$133$	2762.09	−	2762.09i	1.80078	−	1.80078i
$134$		0			0
$135$	−386.041			−0.246112
$136$		0			0
$137$	1558.45			0.971877			0.485938	−	0.873993i	$-0.338478\pi$
$137$	1558.45			0.971877			0.485938	+	0.873993i	$0.338478\pi$
$138$		0			0
$139$	1379.78	−	1379.78i	0.841952	−	0.841952i	−0.147161	−	0.989113i	$-0.547014\pi$
$139$	1379.78	−	1379.78i	0.841952	−	0.841952i	0.989113	+	0.147161i	$0.0470135\pi$
$140$		0			0
$141$	2033.32	−	2033.32i	1.21444	−	1.21444i
$142$		0			0
$143$	290.995	+	290.995i	0.170169	+	0.170169i
$144$		0			0
$145$		−	1067.33i		−	0.611290i
$146$		0			0
$147$	−2147.94	−	2147.94i	−1.20516	−	1.20516i
$148$		0			0
$149$	−3079.38			−1.69310			−0.846551	−	0.532307i	$-0.821325\pi$
$149$	−3079.38			−1.69310			−0.846551	+	0.532307i	$0.821325\pi$
$150$		0			0
$151$			1605.38i			0.865192i	0.901588	+	0.432596i	$0.142402\pi$
$151$			1605.38i			0.865192i	−0.901588	+	0.432596i	$0.857598\pi$
$152$		0			0
$153$	372.127	+	2087.49i	0.196632	+	1.10303i
$154$		0			0
$155$			3728.63i			1.93220i
$156$		0			0
$157$	1544.32			0.785033			0.392517	−	0.919745i	$-0.371605\pi$
$157$	1544.32			0.785033			0.392517	+	0.919745i	$0.371605\pi$
$158$		0			0
$159$	875.659	+	875.659i	0.436756	+	0.436756i
$160$		0			0
$161$			5279.76i			2.58449i
$162$		0			0
$163$	2305.16	+	2305.16i	1.10769	+	1.10769i	0.993453	+	0.114242i	$0.0364438\pi$
$163$	2305.16	+	2305.16i	1.10769	+	1.10769i	0.114242	+	0.993453i	$0.463556\pi$
$164$		0			0
$165$	−2313.68	+	2313.68i	−1.09163	+	1.09163i
$166$		0			0
$167$	844.106	−	844.106i	0.391131	−	0.391131i	−0.483960	−	0.875090i	$-0.660802\pi$
$167$	844.106	−	844.106i	0.391131	−	0.391131i	0.875090	+	0.483960i	$0.160802\pi$
$168$		0			0
$169$	−1973.99			−0.898492
$170$		0			0
$171$	−4330.86			−1.93678
$172$		0			0
$173$	−196.428	+	196.428i	−0.0863245	+	0.0863245i	−0.748950	−	0.662626i	$-0.769442\pi$
$173$	−196.428	+	196.428i	−0.0863245	+	0.0863245i	0.662626	+	0.748950i	$0.269442\pi$
$174$		0			0
$175$	2339.37	−	2339.37i	1.01051	−	1.01051i
$176$		0			0
$177$	−2337.77	−	2337.77i	−0.992755	−	0.992755i
$178$		0			0
$179$			2921.33i			1.21983i	0.792465	+	0.609917i	$0.208797\pi$
$179$			2921.33i			1.21983i	−0.792465	+	0.609917i	$0.791203\pi$
$180$		0			0
$181$	2721.02	+	2721.02i	1.11741	+	1.11741i	0.992120	+	0.125292i	$0.0399867\pi$
$181$	2721.02	+	2721.02i	1.11741	+	1.11741i	0.125292	+	0.992120i	$0.460013\pi$
$182$		0			0
$183$	4187.48			1.69151
$184$		0			0
$185$		−	3245.34i		−	1.28974i
$186$		0			0
$187$	1584.32	+	1104.92i	0.619557	+	0.432085i
$188$		0			0
$189$			671.218i			0.258328i
$190$		0			0
$191$	4703.27			1.78176			0.890881	−	0.454236i	$-0.150088\pi$
$191$	4703.27			1.78176			0.890881	+	0.454236i	$0.150088\pi$
$192$		0			0
$193$	−0.729961	−	0.729961i	−0.000272247	−	0.000272247i	0.706971	−	0.707243i	$-0.250061\pi$
$193$	−0.729961	−	0.729961i	−0.000272247	−	0.000272247i	−0.707243	+	0.706971i	$0.750061\pi$
$194$		0			0
$195$			1773.16i			0.651172i
$196$		0			0
$197$	1894.63	+	1894.63i	0.685212	+	0.685212i	0.961170	−	0.275958i	$-0.0889951\pi$
$197$	1894.63	+	1894.63i	0.685212	+	0.685212i	−0.275958	+	0.961170i	$0.588995\pi$
$198$		0			0
$199$	−307.524	+	307.524i	−0.109547	+	0.109547i	−0.759756	−	0.650209i	$-0.774681\pi$
$199$	−307.524	+	307.524i	−0.109547	+	0.109547i	0.650209	+	0.759756i	$0.274681\pi$
$200$		0			0
$201$	−1646.33	+	1646.33i	−0.577729	+	0.577729i
$202$		0			0
$203$	−1855.80			−0.641632
$204$		0			0
$205$	1111.75			0.378769
$206$		0			0
$207$	4139.25	−	4139.25i	1.38984	−	1.38984i
$208$		0			0
$209$	−2789.66	+	2789.66i	−0.923276	+	0.923276i
$210$		0			0
$211$	−2462.22	−	2462.22i	−0.803346	−	0.803346i	0.180271	−	0.983617i	$-0.442303\pi$
$211$	−2462.22	−	2462.22i	−0.803346	−	0.803346i	−0.983617	+	0.180271i	$0.942303\pi$
$212$		0			0
$213$		−	2992.31i		−	0.962580i
$214$		0			0
$215$	−3720.15	−	3720.15i	−1.18006	−	1.18006i
$216$		0			0
$217$	6483.07			2.02811
$218$		0			0
$219$		−	1251.64i		−	0.386200i
$220$		0			0
$221$	1030.49	−	183.701i	0.313658	−	0.0559144i
$222$		0			0
$223$		−	1266.45i		−	0.380304i	−0.981755	−	0.190152i	$-0.939102\pi$
$223$		−	1266.45i		−	0.380304i	0.981755	−	0.190152i	$-0.0608981\pi$
$224$		0			0
$225$	−3668.05			−1.08683
$226$		0			0
$227$	−471.282	−	471.282i	−0.137798	−	0.137798i	0.634843	−	0.772641i	$-0.281065\pi$
$227$	−471.282	−	471.282i	−0.137798	−	0.137798i	−0.772641	+	0.634843i	$0.781065\pi$
$228$		0			0
$229$			2984.03i			0.861094i	0.902568	+	0.430547i	$0.141679\pi$
$229$			2984.03i			0.861094i	−0.902568	+	0.430547i	$0.858321\pi$
$230$		0			0
$231$	4022.85	+	4022.85i	1.14582	+	1.14582i
$232$		0			0
$233$	−1618.96	+	1618.96i	−0.455200	+	0.455200i	−0.897076	−	0.441876i	$-0.854313\pi$
$233$	−1618.96	+	1618.96i	−0.455200	+	0.455200i	0.441876	+	0.897076i	$0.354313\pi$
$234$		0			0
$235$	4217.00	−	4217.00i	1.17058	−	1.17058i
$236$		0			0
$237$	194.890			0.0534153
$238$		0			0
$239$	−4629.51			−1.25296			−0.626481	−	0.779437i	$-0.715505\pi$
$239$	−4629.51			−1.25296			−0.626481	+	0.779437i	$0.715505\pi$
$240$		0			0
$241$	−1247.49	+	1247.49i	−0.333435	+	0.333435i	−0.853889	−	0.520455i	$-0.825763\pi$
$241$	−1247.49	+	1247.49i	−0.333435	+	0.333435i	0.520455	+	0.853889i	$0.325763\pi$
$242$		0			0
$243$	−3843.81	+	3843.81i	−1.01473	+	1.01473i
$244$		0			0
$245$	−4454.72	−	4454.72i	−1.16164	−	1.16164i
$246$		0			0
$247$			2137.94i			0.550744i
$248$		0			0
$249$	429.527	+	429.527i	0.109318	+	0.109318i
$250$		0			0
$251$	3922.83			0.986482			0.493241	−	0.869893i	$-0.335812\pi$
$251$	3922.83			0.986482			0.493241	+	0.869893i	$0.335812\pi$
$252$		0			0
$253$		−	5332.47i		−	1.32510i
$254$		0			0
$255$	1460.60	+	8193.38i	0.358691	+	2.01212i
$256$		0			0
$257$		−	2527.59i		−	0.613488i	−0.951792	−	0.306744i	$-0.900760\pi$
$257$		−	2527.59i		−	0.613488i	0.951792	−	0.306744i	$-0.0992395\pi$
$258$		0			0
$259$	−5642.75			−1.35376
$260$		0			0
$261$	1454.91	+	1454.91i	0.345046	+	0.345046i
$262$		0			0
$263$		−	4435.11i		−	1.03985i	−0.854212	−	0.519925i	$-0.825960\pi$
$263$		−	4435.11i		−	1.03985i	0.854212	−	0.519925i	$-0.174040\pi$
$264$		0			0
$265$	1816.07	+	1816.07i	0.420983	+	0.420983i
$266$		0			0
$267$	6569.41	−	6569.41i	1.50577	−	1.50577i
$268$		0			0
$269$	−4571.25	+	4571.25i	−1.03611	+	1.03611i	−0.0367874	+	0.999323i	$0.511712\pi$
$269$	−4571.25	+	4571.25i	−1.03611	+	1.03611i	−0.999323	+	0.0367874i	$0.988288\pi$
$270$		0			0
$271$	1568.16			0.351508			0.175754	−	0.984434i	$-0.443764\pi$
$271$	1568.16			0.351508			0.175754	+	0.984434i	$0.443764\pi$
$272$		0			0
$273$	3083.04			0.683494
$274$		0			0
$275$	−2362.72	+	2362.72i	−0.518099	+	0.518099i
$276$		0			0
$277$	1591.03	−	1591.03i	0.345110	−	0.345110i	−0.513174	−	0.858284i	$-0.671531\pi$
$277$	1591.03	−	1591.03i	0.345110	−	0.345110i	0.858284	+	0.513174i	$0.171531\pi$
$278$		0			0
$279$	−5082.62	−	5082.62i	−1.09064	−	1.09064i
$280$		0			0
$281$			7143.64i			1.51656i	0.651928	+	0.758281i	$0.273960\pi$
$281$			7143.64i			1.51656i	−0.651928	+	0.758281i	$0.726040\pi$
$282$		0			0
$283$	2206.75	+	2206.75i	0.463525	+	0.463525i	0.899809	−	0.436284i	$-0.143706\pi$
$283$	2206.75	+	2206.75i	0.463525	+	0.463525i	−0.436284	+	0.899809i	$0.643706\pi$
$284$		0			0
$285$	−16998.6			−3.53302
$286$		0			0
$287$		−	1933.02i		−	0.397570i
$288$		0			0
$289$	4610.36	−	1697.69i	0.938400	−	0.345550i
$290$		0			0
$291$		−	9767.37i		−	1.96761i
$292$		0			0
$293$	1978.92			0.394573			0.197287	−	0.980346i	$-0.436787\pi$
$293$	1978.92			0.394573			0.197287	+	0.980346i	$0.436787\pi$
$294$		0			0
$295$	−4848.42	−	4848.42i	−0.956901	−	0.956901i
$296$		0			0
$297$		−	677.919i		−	0.132447i
$298$		0			0
$299$	−2043.35	−	2043.35i	−0.395217	−	0.395217i
$300$		0			0
$301$	−6468.32	+	6468.32i	−1.23863	+	1.23863i
$302$		0			0
$303$	−2078.53	+	2078.53i	−0.394087	+	0.394087i
$304$		0			0
$305$	8684.61			1.63042
$306$		0			0
$307$	−5460.22			−1.01509			−0.507543	−	0.861627i	$-0.669446\pi$
$307$	−5460.22			−1.01509			−0.507543	+	0.861627i	$0.669446\pi$
$308$		0			0
$309$	8767.77	−	8767.77i	1.61418	−	1.61418i
$310$		0			0
$311$	5556.59	−	5556.59i	1.01314	−	1.01314i	0.0132240	−	0.999913i	$-0.495791\pi$
$311$	5556.59	−	5556.59i	1.01314	−	1.01314i	0.999913	−	0.0132240i	$-0.00420946\pi$
$312$		0			0
$313$	−1546.15	−	1546.15i	−0.279213	−	0.279213i	0.553582	−	0.832795i	$-0.313261\pi$
$313$	−1546.15	−	1546.15i	−0.279213	−	0.279213i	−0.832795	+	0.553582i	$0.813261\pi$
$314$		0			0
$315$			12952.5i			2.31680i
$316$		0			0
$317$	−2792.81	−	2792.81i	−0.494825	−	0.494825i	0.414997	−	0.909823i	$-0.363782\pi$
$317$	−2792.81	−	2792.81i	−0.494825	−	0.494825i	−0.909823	+	0.414997i	$0.863782\pi$
$318$		0			0
$319$	1874.32			0.328971
$320$		0			0
$321$		−	7321.21i		−	1.27299i
$322$		0			0
$323$	1761.08	+	9878.95i	0.303371	+	1.70179i
$324$		0			0
$325$			1810.74i			0.309052i
$326$		0			0
$327$	−9067.16			−1.53338
$328$		0			0
$329$	−7332.20	−	7332.20i	−1.22869	−	1.22869i
$330$		0			0
$331$		−	8109.44i		−	1.34663i	−0.739355	−	0.673316i	$-0.764869\pi$
$331$		−	8109.44i		−	1.34663i	0.739355	−	0.673316i	$-0.235131\pi$
$332$		0			0
$333$	4423.82	+	4423.82i	0.727999	+	0.727999i
$334$		0			0
$335$	−3414.41	+	3414.41i	−0.556864	+	0.556864i
$336$		0			0
$337$	−7342.66	+	7342.66i	−1.18689	+	1.18689i	−0.208961	+	0.977924i	$0.567008\pi$
$337$	−7342.66	+	7342.66i	−1.18689	+	1.18689i	−0.977924	+	0.208961i	$0.932992\pi$
$338$		0			0
$339$	9940.19			1.59256
$340$		0			0
$341$	−6547.79			−1.03983
$342$		0			0
$343$	−1127.93	+	1127.93i	−0.177559	+	0.177559i
$344$		0			0
$345$	16246.6	−	16246.6i	2.53532	−	2.53532i
$346$		0			0
$347$	3722.76	+	3722.76i	0.575932	+	0.575932i	0.933780	−	0.357848i	$-0.116489\pi$
$347$	3722.76	+	3722.76i	0.575932	+	0.575932i	−0.357848	+	0.933780i	$0.616489\pi$
$348$		0			0
$349$			6107.66i			0.936778i	0.883522	+	0.468389i	$0.155165\pi$
$349$			6107.66i			0.936778i	−0.883522	+	0.468389i	$0.844835\pi$
$350$		0			0
$351$	−259.772	−	259.772i	−0.0395031	−	0.0395031i
$352$		0			0
$353$	6086.21			0.917667			0.458834	−	0.888522i	$-0.348267\pi$
$353$	6086.21			0.917667			0.458834	+	0.888522i	$0.348267\pi$
$354$		0			0
$355$		−	6205.89i		−	0.927816i
$356$		0			0
$357$	14246.0	−	2539.58i	2.11199	−	0.376495i
$358$		0			0
$359$			9977.07i			1.46677i	0.679815	+	0.733384i	$0.262060\pi$
$359$			9977.07i			1.46677i	−0.679815	+	0.733384i	$0.737940\pi$
$360$		0			0
$361$	−13636.6			−1.98814
$362$		0			0
$363$	3058.23	+	3058.23i	0.442191	+	0.442191i
$364$		0			0
$365$		−	2595.83i		−	0.372252i
$366$		0			0
$367$	418.231	+	418.231i	0.0594864	+	0.0594864i	0.736224	−	0.676738i	$-0.236607\pi$
$367$	418.231	+	418.231i	0.0594864	+	0.0594864i	−0.676738	+	0.736224i	$0.736607\pi$
$368$		0			0
$369$	−1515.45	+	1515.45i	−0.213798	+	0.213798i
$370$		0			0
$371$	3157.65	−	3157.65i	0.441878	−	0.441878i
$372$		0			0
$373$	−8442.99			−1.17201			−0.586007	−	0.810306i	$-0.699301\pi$
$373$	−8442.99			−1.17201			−0.586007	+	0.810306i	$0.699301\pi$
$374$		0			0
$375$	444.929			0.0612694
$376$		0			0
$377$	718.222	−	718.222i	0.0981176	−	0.0981176i
$378$		0			0
$379$	778.897	−	778.897i	0.105565	−	0.105565i	−0.652351	−	0.757917i	$-0.726217\pi$
$379$	778.897	−	778.897i	0.105565	−	0.105565i	0.757917	+	0.652351i	$0.226217\pi$
$380$		0			0
$381$	6047.62	+	6047.62i	0.813200	+	0.813200i
$382$		0			0
$383$			862.185i			0.115028i	0.998345	+	0.0575139i	$0.0183173\pi$
$383$			862.185i			0.115028i	−0.998345	+	0.0575139i	$0.981683\pi$
$384$		0			0
$385$	8343.19	+	8343.19i	1.10444	+	1.10444i
$386$		0			0
$387$	10142.1			1.33218
$388$		0			0
$389$			1744.95i			0.227435i	0.993513	+	0.113718i	$0.0362760\pi$
$389$			1744.95i			0.227435i	−0.993513	+	0.113718i	$0.963724\pi$
$390$		0			0
$391$	−11125.0	−	7758.71i	−1.43892	−	1.00352i
$392$		0			0
$393$		−	7928.51i		−	1.01766i
$394$		0			0
$395$	404.191			0.0514862
$396$		0			0
$397$	−3833.72	−	3833.72i	−0.484657	−	0.484657i	0.421958	−	0.906615i	$-0.361343\pi$
$397$	−3833.72	−	3833.72i	−0.484657	−	0.484657i	−0.906615	+	0.421958i	$0.861343\pi$
$398$		0			0
$399$			29555.9i			3.70839i
$400$		0			0
$401$	−75.1740	−	75.1740i	−0.00936162	−	0.00936162i	0.702410	−	0.711772i	$-0.252107\pi$
$401$	−75.1740	−	75.1740i	−0.00936162	−	0.00936162i	−0.711772	+	0.702410i	$0.752107\pi$
$402$		0			0
$403$	−2509.05	+	2509.05i	−0.310135	+	0.310135i
$404$		0			0
$405$	−6997.79	+	6997.79i	−0.858576	+	0.858576i
$406$		0			0
$407$	5699.08			0.694085
$408$		0			0
$409$	10332.4			1.24916			0.624578	−	0.780962i	$-0.285271\pi$
$409$	10332.4			1.24916			0.624578	+	0.780962i	$0.285271\pi$
$410$		0			0
$411$	−8338.15	+	8338.15i	−1.00071	+	1.00071i
$412$		0			0
$413$	−8430.07	+	8430.07i	−1.00440	+	1.00440i
$414$		0			0
$415$	890.817	+	890.817i	0.105370	+	0.105370i
$416$		0			0
$417$			14764.4i			1.73385i
$418$		0			0
$419$	−2977.35	−	2977.35i	−0.347143	−	0.347143i	0.511901	−	0.859044i	$-0.328941\pi$
$419$	−2977.35	−	2977.35i	−0.347143	−	0.347143i	−0.859044	+	0.511901i	$0.828941\pi$
$420$		0			0
$421$	12912.6			1.49483			0.747413	−	0.664360i	$-0.231296\pi$
$421$	12912.6			1.49483			0.747413	+	0.664360i	$0.231296\pi$
$422$		0			0
$423$			11496.6i			1.32148i
$424$		0			0
$425$	1491.55	+	8367.04i	0.170238	+	0.954967i
$426$		0			0
$427$		−	15100.2i		−	1.71135i
$428$		0			0
$429$	−3113.81			−0.350434
$430$		0			0
$431$	−7268.01	−	7268.01i	−0.812269	−	0.812269i	0.172705	−	0.984974i	$-0.444749\pi$
$431$	−7268.01	−	7268.01i	−0.812269	−	0.812269i	−0.984974	+	0.172705i	$0.944749\pi$
$432$		0			0
$433$			11357.2i			1.26049i	0.776395	+	0.630246i	$0.217046\pi$
$433$			11357.2i			1.26049i	−0.776395	+	0.630246i	$0.782954\pi$
$434$		0			0
$435$	5710.54	+	5710.54i	0.629424	+	0.629424i
$436$		0			0
$437$	19588.8	−	19588.8i	2.14431	−	2.14431i
$438$		0			0
$439$	−5398.02	+	5398.02i	−0.586864	+	0.586864i	−0.936781	−	0.349917i	$-0.886210\pi$
$439$	−5398.02	+	5398.02i	−0.586864	+	0.586864i	0.349917	+	0.936781i	$0.386210\pi$
$440$		0			0
$441$	12144.7			1.31139
$442$		0			0
$443$	−10551.6			−1.13165			−0.565825	−	0.824526i	$-0.691442\pi$
$443$	−10551.6			−1.13165			−0.565825	+	0.824526i	$0.691442\pi$
$444$		0			0
$445$	13624.6	−	13624.6i	1.45139	−	1.45139i
$446$		0			0
$447$	16475.6	−	16475.6i	1.74333	−	1.74333i
$448$		0			0
$449$	3288.21	+	3288.21i	0.345613	+	0.345613i	0.858473	−	0.512859i	$-0.171414\pi$
$449$	3288.21	+	3288.21i	0.345613	+	0.345613i	−0.512859	+	0.858473i	$0.671414\pi$
$450$		0			0
$451$			1952.31i			0.203838i
$452$		0			0
$453$	−8589.26	−	8589.26i	−0.890858	−	0.890858i
$454$		0			0
$455$	6394.06			0.658809
$456$		0			0
$457$			3775.73i			0.386480i	0.981152	+	0.193240i	$0.0618996\pi$
$457$			3775.73i			0.386480i	−0.981152	+	0.193240i	$0.938100\pi$
$458$		0			0
$459$	−1414.33	−	986.368i	−0.143824	−	0.100304i
$460$		0			0
$461$		−	5585.95i		−	0.564347i	−0.959363	−	0.282173i	$-0.908945\pi$
$461$		−	5585.95i		−	0.564347i	0.959363	−	0.282173i	$-0.0910553\pi$
$462$		0			0
$463$	−10571.9			−1.06116			−0.530579	−	0.847636i	$-0.678025\pi$
$463$	−10571.9			−1.06116			−0.530579	+	0.847636i	$0.678025\pi$
$464$		0			0
$465$	−19949.3	−	19949.3i	−1.98952	−	1.98952i
$466$		0			0
$467$			7914.84i			0.784272i	0.919907	+	0.392136i	$0.128264\pi$
$467$			7914.84i			0.784272i	−0.919907	+	0.392136i	$0.871736\pi$
$468$		0			0
$469$	5936.72	+	5936.72i	0.584504	+	0.584504i
$470$		0			0
$471$	−8262.57	+	8262.57i	−0.808321	+	0.808321i
$472$		0			0
$473$	6532.89	−	6532.89i	0.635059	−	0.635059i
$474$		0			0
$475$	−17358.9			−1.67680
$476$		0			0
$477$	−4951.09			−0.475251
$478$		0			0
$479$	2407.11	−	2407.11i	0.229611	−	0.229611i	−0.582919	−	0.812530i	$-0.698090\pi$
$479$	2407.11	−	2407.11i	0.229611	−	0.229611i	0.812530	+	0.582919i	$0.198090\pi$
$480$		0			0
$481$	2183.83	−	2183.83i	0.207015	−	0.207015i
$482$		0			0
$483$	−28248.3	−	28248.3i	−2.66116	−	2.66116i
$484$		0			0
$485$		−	20257.0i		−	1.89654i
$486$		0			0
$487$	4355.19	+	4355.19i	0.405241	+	0.405241i	0.880075	−	0.474834i	$-0.157492\pi$
$487$	4355.19	+	4355.19i	0.405241	+	0.405241i	−0.474834	+	0.880075i	$0.657492\pi$
$488$		0			0
$489$	−24666.6			−2.28111
$490$		0			0
$491$		−	11421.3i		−	1.04977i	−0.851173	−	0.524886i	$-0.824108\pi$
$491$		−	11421.3i		−	1.04977i	0.851173	−	0.524886i	$-0.175892\pi$
$492$		0			0
$493$	2727.13	−	3910.36i	0.249135	−	0.357229i
$494$		0			0
$495$		−	13081.8i		−	1.18785i
$496$		0			0
$497$	−10790.3			−0.973869
$498$		0			0
$499$	15694.2	+	15694.2i	1.40795	+	1.40795i	0.770437	+	0.637516i	$0.220038\pi$
$499$	15694.2	+	15694.2i	1.40795	+	1.40795i	0.637516	+	0.770437i	$0.279962\pi$
$500$		0			0
$501$			9032.42i			0.805467i
$502$		0			0
$503$	11684.8	+	11684.8i	1.03579	+	1.03579i	0.999335	+	0.0364533i	$0.0116060\pi$
$503$	11684.8	+	11684.8i	1.03579	+	1.03579i	0.0364533	+	0.999335i	$0.488394\pi$
$504$		0			0
$505$	−4310.77	+	4310.77i	−0.379855	+	0.379855i
$506$		0			0
$507$	10561.4	−	10561.4i	0.925145	−	0.925145i
$508$		0			0
$509$	5728.79			0.498869			0.249434	−	0.968392i	$-0.419755\pi$
$509$	5728.79			0.498869			0.249434	+	0.968392i	$0.419755\pi$
$510$		0			0
$511$	−4513.44			−0.390730
$512$		0			0
$513$	2490.34	−	2490.34i	0.214330	−	0.214330i
$514$		0			0
$515$	18183.9	−	18183.9i	1.55588	−	1.55588i
$516$		0			0
$517$	7405.40	+	7405.40i	0.629959	+	0.629959i
$518$		0			0
$519$		−	2101.89i		−	0.177770i
$520$		0			0
$521$	−3554.38	−	3554.38i	−0.298887	−	0.298887i	0.541691	−	0.840578i	$-0.317784\pi$
$521$	−3554.38	−	3554.38i	−0.298887	−	0.298887i	−0.840578	+	0.541691i	$0.817784\pi$
$522$		0			0
$523$	−2159.94			−0.180588			−0.0902942	−	0.995915i	$-0.528781\pi$
$523$	−2159.94			−0.180588			−0.0902942	+	0.995915i	$0.528781\pi$
$524$		0			0
$525$			25032.6i			2.08097i
$526$		0			0
$527$	−9526.99	+	13660.5i	−0.787481	+	1.12915i
$528$		0			0
$529$			25277.3i			2.07753i
$530$		0			0
$531$	13218.1			1.08025
$532$		0			0
$533$	748.108	+	748.108i	0.0607958	+	0.0607958i
$534$		0			0
$535$		−	15183.8i		−	1.22702i
$536$		0			0
$537$	−15630.0	−	15630.0i	−1.25602	−	1.25602i
$538$		0			0
$539$	7822.85	−	7822.85i	0.625147	−	0.625147i
$540$		0			0
$541$	−6926.55	+	6926.55i	−0.550454	+	0.550454i	−0.926572	−	0.376118i	$-0.877259\pi$
$541$	−6926.55	+	6926.55i	−0.550454	+	0.550454i	0.376118	+	0.926572i	$0.377259\pi$
$542$		0			0
$543$	−29116.5			−2.30112
$544$		0			0
$545$	−18804.8			−1.47800
$546$		0			0
$547$	2282.02	−	2282.02i	0.178377	−	0.178377i	−0.612271	−	0.790648i	$-0.709744\pi$
$547$	2282.02	−	2282.02i	0.178377	−	0.178377i	0.790648	+	0.612271i	$0.209744\pi$
$548$		0			0
$549$	−11838.3	+	11838.3i	−0.920301	+	0.920301i
$550$		0			0
$551$	6885.33	+	6885.33i	0.532350	+	0.532350i
$552$		0			0
$553$		−	702.777i		−	0.0540418i
$554$		0			0
$555$	17363.5	+	17363.5i	1.32800	+	1.32800i
$556$		0			0
$557$	3227.09			0.245487			0.122744	−	0.992438i	$-0.460831\pi$
$557$	3227.09			0.245487			0.122744	+	0.992438i	$0.460831\pi$
$558$		0			0
$559$		−	5006.68i		−	0.378820i
$560$		0			0
$561$	−14388.2	+	2564.93i	−1.08284	+	0.193033i
$562$		0			0
$563$			691.814i			0.0517877i	0.999665	+	0.0258939i	$0.00824319\pi$
$563$			691.814i			0.0517877i	−0.999665	+	0.0258939i	$0.991757\pi$
$564$		0			0
$565$	20615.4			1.53504
$566$		0			0
$567$	12167.2	+	12167.2i	0.901192	+	0.901192i
$568$		0			0
$569$		−	16009.5i		−	1.17953i	−0.807574	−	0.589767i	$-0.799220\pi$
$569$		−	16009.5i		−	1.17953i	0.807574	−	0.589767i	$-0.200780\pi$
$570$		0			0
$571$	2759.50	+	2759.50i	0.202244	+	0.202244i	0.800961	−	0.598717i	$-0.204323\pi$
$571$	2759.50	+	2759.50i	0.202244	+	0.202244i	−0.598717	+	0.800961i	$0.704323\pi$
$572$		0			0
$573$	−25163.9	+	25163.9i	−1.83462	+	1.83462i
$574$		0			0
$575$	16590.9	−	16590.9i	1.20328	−	1.20328i
$576$		0			0
$577$	−9319.85			−0.672427			−0.336214	−	0.941786i	$-0.609146\pi$
$577$	−9319.85			−0.672427			−0.336214	+	0.941786i	$0.609146\pi$
$578$		0			0
$579$	7.81101			0.000560647
$580$		0			0
$581$	1548.89	−	1548.89i	0.110600	−	0.110600i
$582$		0			0
$583$	−3189.17	+	3189.17i	−0.226556	+	0.226556i
$584$		0			0
$585$	−5012.84	−	5012.84i	−0.354283	−	0.354283i
$586$		0			0
$587$		−	8107.85i		−	0.570097i	−0.958513	−	0.285048i	$-0.907990\pi$
$587$		−	8107.85i		−	0.570097i	0.958513	−	0.285048i	$-0.0920096\pi$
$588$		0			0
$589$	−24053.3	−	24053.3i	−1.68268	−	1.68268i
$590$		0			0
$591$	−20273.6			−1.41108
$592$		0			0
$593$		−	10498.1i		−	0.726988i	−0.931597	−	0.363494i	$-0.881584\pi$
$593$		−	10498.1i		−	0.726988i	0.931597	−	0.363494i	$-0.118416\pi$
$594$		0			0
$595$	29545.6	−	5266.95i	2.03571	−	0.362897i
$596$		0			0
$597$		−	3290.68i		−	0.225592i
$598$		0			0
$599$	7810.47			0.532767			0.266383	−	0.963867i	$-0.414171\pi$
$599$	7810.47			0.532767			0.266383	+	0.963867i	$0.414171\pi$
$600$		0			0
$601$	11591.4	+	11591.4i	0.786726	+	0.786726i	0.980956	−	0.194230i	$-0.0622207\pi$
$601$	11591.4	+	11591.4i	0.786726	+	0.786726i	−0.194230	+	0.980956i	$0.562221\pi$
$602$		0			0
$603$		−	9308.59i		−	0.628648i
$604$		0			0
$605$	6342.61	+	6342.61i	0.426221	+	0.426221i
$606$		0			0
$607$	−10294.4	+	10294.4i	−0.688366	+	0.688366i	−0.961871	−	0.273504i	$-0.911817\pi$
$607$	−10294.4	+	10294.4i	−0.688366	+	0.688366i	0.273504	+	0.961871i	$0.411817\pi$
$608$		0			0
$609$	9929.05	−	9929.05i	0.660666	−	0.660666i
$610$		0			0
$611$	5675.35			0.375778
$612$		0			0
$613$	−17951.0			−1.18276			−0.591381	−	0.806392i	$-0.701417\pi$
$613$	−17951.0			−1.18276			−0.591381	+	0.806392i	$0.701417\pi$
$614$		0			0
$615$	−5948.16	+	5948.16i	−0.390005	+	0.390005i
$616$		0			0
$617$	68.7998	−	68.7998i	0.00448910	−	0.00448910i	−0.704859	−	0.709348i	$-0.748990\pi$
$617$	68.7998	−	68.7998i	0.00448910	−	0.00448910i	0.709348	+	0.704859i	$0.248990\pi$
$618$		0			0
$619$	14370.3	+	14370.3i	0.933100	+	0.933100i	0.997898	−	0.0647980i	$-0.0206403\pi$
$619$	14370.3	+	14370.3i	0.933100	+	0.933100i	−0.0647980	+	0.997898i	$0.520640\pi$
$620$		0			0
$621$			4760.31i			0.307608i
$622$		0			0
$623$	−23689.5	−	23689.5i	−1.52343	−	1.52343i
$624$		0			0
$625$	16079.4			1.02908
$626$		0			0
$627$		−	29851.0i		−	1.90133i
$628$		0			0
$629$	8292.12	−	11889.9i	0.525642	−	0.753705i
$630$		0			0
$631$		−	14479.6i		−	0.913506i	−0.889594	−	0.456753i	$-0.849012\pi$
$631$		−	14479.6i		−	0.913506i	0.889594	−	0.456753i	$-0.150988\pi$
$632$		0			0
$633$	26347.2			1.65435
$634$		0			0
$635$	12542.5	+	12542.5i	0.783831	+	0.783831i
$636$		0			0
$637$		−	5995.28i		−	0.372907i
$638$		0			0
$639$	8459.45	+	8459.45i	0.523710	+	0.523710i
$640$		0			0
$641$	3035.22	−	3035.22i	0.187026	−	0.187026i	−0.607383	−	0.794409i	$-0.707781\pi$
$641$	3035.22	−	3035.22i	0.187026	−	0.187026i	0.794409	+	0.607383i	$0.207781\pi$
$642$		0			0
$643$	−6394.08	+	6394.08i	−0.392158	+	0.392158i	−0.875456	−	0.483298i	$-0.839439\pi$
$643$	−6394.08	+	6394.08i	−0.392158	+	0.392158i	0.483298	+	0.875456i	$0.339439\pi$
$644$		0			0
$645$	39807.8			2.43013
$646$		0			0
$647$	26904.9			1.63484			0.817418	−	0.576044i	$-0.195404\pi$
$647$	26904.9			1.63484			0.817418	+	0.576044i	$0.195404\pi$
$648$		0			0
$649$	8514.22	−	8514.22i	0.514965	−	0.514965i
$650$		0			0
$651$	−34686.3	+	34686.3i	−2.08827	+	2.08827i
$652$		0			0
$653$	15201.3	+	15201.3i	0.910983	+	0.910983i	0.996350	−	0.0853670i	$-0.0272063\pi$
$653$	15201.3	+	15201.3i	0.910983	+	0.910983i	−0.0853670	+	0.996350i	$0.527206\pi$
$654$		0			0
$655$		−	16443.3i		−	0.980906i
$656$		0			0
$657$	3538.46	+	3538.46i	0.210120	+	0.210120i
$658$		0			0
$659$	−7503.33			−0.443533			−0.221767	−	0.975100i	$-0.571182\pi$
$659$	−7503.33			−0.443533			−0.221767	+	0.975100i	$0.571182\pi$
$660$		0			0
$661$		−	8775.17i		−	0.516361i	−0.966097	−	0.258180i	$-0.916877\pi$
$661$		−	8775.17i		−	0.516361i	0.966097	−	0.258180i	$-0.0831229\pi$
$662$		0			0
$663$	−4530.58	+	6496.29i	−0.265389	+	0.380536i
$664$		0			0
$665$			61297.5i			3.57446i
$666$		0			0
$667$	−13161.4			−0.764035
$668$		0			0
$669$	6775.88	+	6775.88i	0.391585	+	0.391585i
$670$		0			0
$671$			15250.9i			0.877428i
$672$		0			0
$673$	−5176.23	−	5176.23i	−0.296477	−	0.296477i	0.543155	−	0.839632i	$-0.317230\pi$
$673$	−5176.23	−	5176.23i	−0.296477	−	0.296477i	−0.839632	+	0.543155i	$0.817230\pi$
$674$		0			0
$675$	2109.21	−	2109.21i	0.120272	−	0.120272i
$676$		0			0
$677$	−2184.72	+	2184.72i	−0.124026	+	0.124026i	−0.766395	−	0.642369i	$-0.777952\pi$
$677$	−2184.72	+	2184.72i	−0.124026	+	0.124026i	0.642369	+	0.766395i	$0.277952\pi$
$678$		0			0
$679$	−35221.4			−1.99068
$680$		0			0
$681$	5042.99			0.283771
$682$		0			0
$683$	4318.59	−	4318.59i	0.241942	−	0.241942i	−0.575711	−	0.817653i	$-0.695275\pi$
$683$	4318.59	−	4318.59i	0.241942	−	0.241942i	0.817653	+	0.575711i	$0.195275\pi$
$684$		0			0
$685$	−17292.9	+	17292.9i	−0.964566	+	0.964566i
$686$		0			0
$687$	−15965.5	−	15965.5i	−0.886638	−	0.886638i
$688$		0			0
$689$			2444.12i			0.135143i
$690$		0			0
$691$	13312.4	+	13312.4i	0.732892	+	0.732892i	0.971192	−	0.238299i	$-0.0765899\pi$
$691$	13312.4	+	13312.4i	0.732892	+	0.732892i	−0.238299	+	0.971192i	$0.576590\pi$
$692$		0			0
$693$	−22745.7			−1.24681
$694$		0			0
$695$			30620.7i			1.67124i
$696$		0			0
$697$	4073.08	+	2840.61i	0.221347	+	0.154370i
$698$		0			0
$699$		−	17323.8i		−	0.937406i
$700$		0			0
$701$	5817.03			0.313418			0.156709	−	0.987645i	$-0.449912\pi$
$701$	5817.03			0.313418			0.156709	+	0.987645i	$0.449912\pi$
$702$		0			0
$703$	20935.6	+	20935.6i	1.12319	+	1.12319i
$704$		0			0
$705$			45124.4i			2.41061i
$706$		0			0
$707$	7495.24	+	7495.24i	0.398709	+	0.398709i
$708$		0			0
$709$	−8757.23	+	8757.23i	−0.463871	+	0.463871i	−0.899922	−	0.436051i	$-0.856377\pi$
$709$	−8757.23	+	8757.23i	−0.463871	+	0.463871i	0.436051	+	0.899922i	$0.356377\pi$
$710$		0			0
$711$	−550.965	+	550.965i	−0.0290616	+	0.0290616i
$712$		0			0
$713$	45978.2			2.41501
$714$		0			0
$715$	−6457.89			−0.337778
$716$		0			0
$717$	24769.2	−	24769.2i	1.29013	−	1.29013i
$718$		0			0
$719$	−20810.4	+	20810.4i	−1.07941	+	1.07941i	−0.0828475	+	0.996562i	$0.526401\pi$
$719$	−20810.4	+	20810.4i	−1.07941	+	1.07941i	−0.996562	+	0.0828475i	$0.973599\pi$
$720$		0			0
$721$	−31616.8	−	31616.8i	−1.63311	−	1.63311i
$722$		0			0
$723$		−	13348.9i		−	0.686652i
$724$		0			0
$725$	5831.57	+	5831.57i	0.298730	+	0.298730i
$726$		0			0
$727$	801.834			0.0409056			0.0204528	−	0.999791i	$-0.493489\pi$
$727$	801.834			0.0409056			0.0204528	+	0.999791i	$0.493489\pi$
$728$		0			0
$729$		−	24103.5i		−	1.22459i
$730$		0			0
$731$	−4124.13	−	23134.8i	−0.208668	−	1.17055i
$732$		0			0
$733$			8656.84i			0.436218i	0.975924	+	0.218109i	$0.0699888\pi$
$733$			8656.84i			0.436218i	−0.975924	+	0.218109i	$0.930011\pi$
$734$		0			0
$735$	47668.1			2.39220
$736$		0			0
$737$	−5995.99	−	5995.99i	−0.299681	−	0.299681i
$738$		0			0
$739$			8510.42i			0.423628i	0.977310	+	0.211814i	$0.0679371\pi$
$739$			8510.42i			0.423628i	−0.977310	+	0.211814i	$0.932063\pi$
$740$		0			0
$741$	−11438.6	−	11438.6i	−0.567082	−	0.567082i
$742$		0			0
$743$	13603.2	−	13603.2i	0.671671	−	0.671671i	−0.286430	−	0.958101i	$-0.592469\pi$
$743$	13603.2	−	13603.2i	0.671671	−	0.671671i	0.958101	+	0.286430i	$0.0924687\pi$
$744$		0			0
$745$	34169.5	−	34169.5i	1.68037	−	1.68037i
$746$		0			0
$747$	−2428.60			−0.118953
$748$		0			0
$749$	−26400.5			−1.28792
$750$		0			0
$751$	−6451.38	+	6451.38i	−0.313468	+	0.313468i	−0.846251	−	0.532784i	$-0.821146\pi$
$751$	−6451.38	+	6451.38i	−0.313468	+	0.313468i	0.532784	+	0.846251i	$0.321146\pi$
$752$		0			0
$753$	−20988.3	+	20988.3i	−1.01575	+	1.01575i
$754$		0			0
$755$	−17813.7	−	17813.7i	−0.858684	−	0.858684i
$756$		0			0
$757$		−	1603.67i		−	0.0769965i	−0.999259	−	0.0384983i	$-0.987743\pi$
$757$		−	1603.67i		−	0.0769965i	0.999259	−	0.0384983i	$-0.0122574\pi$
$758$		0			0
$759$	28530.3	+	28530.3i	1.36440	+	1.36440i
$760$		0			0
$761$	8469.34			0.403434			0.201717	−	0.979444i	$-0.435348\pi$
$761$	8469.34			0.403434			0.201717	+	0.979444i	$0.435348\pi$
$762$		0			0
$763$			32696.4i			1.55136i
$764$		0			0
$765$	−27292.4	−	19034.0i	−1.28988	−	0.899577i
$766$		0			0
$767$		−	6525.13i		−	0.307182i
$768$		0			0
$769$	−31763.7			−1.48950			−0.744751	−	0.667343i	$-0.767432\pi$
$769$	−31763.7			−1.48950			−0.744751	+	0.667343i	$0.767432\pi$
$770$		0			0
$771$	13523.3	+	13523.3i	0.631687	+	0.631687i
$772$		0			0
$773$		−	33322.0i		−	1.55047i	−0.631675	−	0.775233i	$-0.717632\pi$
$773$		−	33322.0i		−	1.55047i	0.631675	−	0.775233i	$-0.282368\pi$
$774$		0			0
$775$	−20372.1	−	20372.1i	−0.944242	−	0.944242i
$776$		0			0
$777$	30190.3	−	30190.3i	1.39392	−	1.39392i
$778$		0			0
$779$	−7171.84	+	7171.84i	−0.329856	+	0.329856i
$780$		0			0
$781$	10898.1			0.499313
$782$		0			0
$783$	−1673.21			−0.0763675
$784$		0			0
$785$	−17136.1	+	17136.1i	−0.779128	+	0.779128i
$786$		0			0
$787$	−12502.7	+	12502.7i	−0.566292	+	0.566292i	−0.931088	−	0.364796i	$-0.881139\pi$
$787$	−12502.7	+	12502.7i	−0.566292	+	0.566292i	0.364796	+	0.931088i	$0.381139\pi$
$788$		0			0
$789$	23729.1	+	23729.1i	1.07070	+	1.07070i
$790$		0			0
$791$		−	35844.6i		−	1.61123i
$792$		0			0
$793$	5843.99	+	5843.99i	0.261698	+	0.261698i
$794$		0			0
$795$	−19433.0			−0.866941
$796$		0			0
$797$		−	20313.3i		−	0.902803i	−0.892321	−	0.451401i	$-0.850924\pi$
$797$		−	20313.3i		−	0.902803i	0.892321	−	0.451401i	$-0.149076\pi$
$798$		0			0
$799$	26224.6	−	4674.93i	1.16115	−	0.206993i
$800$		0			0
$801$			37144.3i			1.63849i
$802$		0			0
$803$	4558.49			0.200331
$804$		0			0
$805$	−58585.5	−	58585.5i	−2.56505	−	2.56505i
$806$		0			0
$807$		−	48915.0i		−	2.13369i
$808$		0			0
$809$	−17867.0	−	17867.0i	−0.776478	−	0.776478i	0.202752	−	0.979230i	$-0.435011\pi$
$809$	−17867.0	−	17867.0i	−0.776478	−	0.776478i	−0.979230	+	0.202752i	$0.935011\pi$
$810$		0			0
$811$	−18965.9	+	18965.9i	−0.821187	+	0.821187i	−0.986278	−	0.165091i	$-0.947208\pi$
$811$	−18965.9	+	18965.9i	−0.821187	+	0.821187i	0.165091	+	0.986278i	$0.447208\pi$
$812$		0			0
$813$	−8390.09	+	8390.09i	−0.361935	+	0.361935i
$814$		0			0
$815$	−51157.2			−2.19872
$816$		0			0
$817$	47997.2			2.05534
$818$		0			0
$819$	−8715.94	+	8715.94i	−0.371868	+	0.371868i
$820$		0			0
$821$	8212.04	−	8212.04i	0.349089	−	0.349089i	−0.510681	−	0.859770i	$-0.670607\pi$
$821$	8212.04	−	8212.04i	0.349089	−	0.349089i	0.859770	+	0.510681i	$0.170607\pi$
$822$		0			0
$823$	27277.5	+	27277.5i	1.15533	+	1.15533i	0.985469	+	0.169857i	$0.0543307\pi$
$823$	27277.5	+	27277.5i	1.15533	+	1.15533i	0.169857	+	0.985469i	$0.445669\pi$
$824$		0			0
$825$		−	25282.5i		−	1.06694i
$826$		0			0
$827$	−14042.3	−	14042.3i	−0.590446	−	0.590446i	0.347306	−	0.937752i	$-0.387097\pi$
$827$	−14042.3	−	14042.3i	−0.590446	−	0.590446i	−0.937752	+	0.347306i	$0.887097\pi$
$828$		0			0
$829$	−28267.2			−1.18427			−0.592135	−	0.805839i	$-0.701715\pi$
$829$	−28267.2			−1.18427			−0.592135	+	0.805839i	$0.701715\pi$
$830$		0			0
$831$			17024.9i			0.710695i
$832$		0			0
$833$	−4938.47	−	27702.9i	−0.205412	−	1.15228i
$834$		0			0
$835$			18732.8i			0.776377i
$836$		0			0
$837$	5845.23			0.241387
$838$		0			0
$839$	11492.5	+	11492.5i	0.472903	+	0.472903i	0.902853	−	0.429949i	$-0.141469\pi$
$839$	11492.5	+	11492.5i	0.472903	+	0.472903i	−0.429949	+	0.902853i	$0.641469\pi$
$840$		0			0
$841$			19762.9i			0.810319i
$842$		0			0
$843$	−38220.5	−	38220.5i	−1.56155	−	1.56155i
$844$		0			0
$845$	21903.8	−	21903.8i	0.891733	−	0.891733i
$846$		0			0
$847$	11028.1	−	11028.1i	0.447377	−	0.447377i
$848$		0			0
$849$	−23613.5			−0.954551
$850$		0			0
$851$	−40018.6			−1.61201
$852$		0			0
$853$	−17004.9	+	17004.9i	−0.682575	+	0.682575i	−0.960580	−	0.278004i	$-0.910327\pi$
$853$	−17004.9	+	17004.9i	−0.682575	+	0.682575i	0.278004	+	0.960580i	$0.410327\pi$
$854$		0			0
$855$	48056.2	−	48056.2i	1.92221	−	1.92221i
$856$		0			0
$857$	24849.8	+	24849.8i	0.990492	+	0.990492i	0.999955	−	0.00946326i	$-0.00301229\pi$
$857$	24849.8	+	24849.8i	0.990492	+	0.990492i	−0.00946326	+	0.999955i	$0.503012\pi$
$858$		0			0
$859$		−	26478.4i		−	1.05172i	−0.850570	−	0.525862i	$-0.823743\pi$
$859$		−	26478.4i		−	1.05172i	0.850570	−	0.525862i	$-0.176257\pi$
$860$		0			0
$861$	10342.2	+	10342.2i	0.409363	+	0.409363i
$862$		0			0
$863$	11169.4			0.440568			0.220284	−	0.975436i	$-0.429302\pi$
$863$	11169.4			0.440568			0.220284	+	0.975436i	$0.429302\pi$
$864$		0			0
$865$		−	4359.22i		−	0.171350i
$866$		0			0
$867$	−15583.7	+	33749.9i	−0.610437	+	1.32204i
$868$		0			0
$869$			709.792i			0.0277078i
$870$		0			0
$871$	−4595.21			−0.178763
$872$		0			0
$873$	27613.0	+	27613.0i	1.07051	+	1.07051i
$874$		0			0
$875$		−	1604.42i		−	0.0619879i
$876$		0			0
$877$	−11168.2	−	11168.2i	−0.430014	−	0.430014i	0.458619	−	0.888633i	$-0.348344\pi$
$877$	−11168.2	−	11168.2i	−0.430014	−	0.430014i	−0.888633	+	0.458619i	$0.848344\pi$
$878$		0			0
$879$	−10587.8	+	10587.8i	−0.406278	+	0.406278i
$880$		0			0
$881$	6129.75	−	6129.75i	0.234411	−	0.234411i	−0.580120	−	0.814531i	$-0.696994\pi$
$881$	6129.75	−	6129.75i	0.234411	−	0.234411i	0.814531	+	0.580120i	$0.196994\pi$
$882$		0			0
$883$	39013.0			1.48685			0.743427	−	0.668817i	$-0.233199\pi$
$883$	39013.0			1.48685			0.743427	+	0.668817i	$0.233199\pi$
$884$		0			0
$885$	51880.9			1.97057
$886$		0			0
$887$	−25600.6	+	25600.6i	−0.969092	+	0.969092i	−0.999536	−	0.0304440i	$-0.990308\pi$
$887$	−25600.6	+	25600.6i	−0.969092	+	0.969092i	0.0304440	+	0.999536i	$0.490308\pi$
$888$		0			0
$889$	21807.9	−	21807.9i	0.822737	−	0.822737i
$890$		0			0
$891$	−12288.7	−	12288.7i	−0.462050	−	0.462050i
$892$		0			0
$893$			54407.5i			2.03883i
$894$		0			0
$895$	−32415.7	−	32415.7i	−1.21066	−	1.21066i
$896$		0			0
$897$	21865.0			0.813882
$898$		0			0
$899$			16161.0i			0.599555i
$900$		0			0
$901$	2013.28	+	11293.7i	0.0744419	+	0.417590i
$902$		0			0
$903$		−	69214.9i		−	2.55075i
$904$		0			0
$905$	−60386.1			−2.21801
$906$		0			0
$907$	−3285.90	−	3285.90i	−0.120294	−	0.120294i	0.644397	−	0.764691i	$-0.277108\pi$
$907$	−3285.90	−	3285.90i	−0.120294	−	0.120294i	−0.764691	+	0.644397i	$0.777108\pi$
$908$		0			0
$909$		−	11752.3i		−	0.428821i
$910$		0			0
$911$	31577.3	+	31577.3i	1.14841	+	1.14841i	0.986865	+	0.161545i	$0.0516477\pi$
$911$	31577.3	+	31577.3i	1.14841	+	1.14841i	0.161545	+	0.986865i	$0.448352\pi$
$912$		0			0
$913$	−1564.35	+	1564.35i	−0.0567057	+	0.0567057i
$914$		0			0
$915$	−46465.2	+	46465.2i	−1.67879	+	1.67879i
$916$		0			0
$917$	−28590.4			−1.02959
$918$		0			0
$919$	−2165.37			−0.0777247			−0.0388623	−	0.999245i	$-0.512373\pi$
$919$	−2165.37			−0.0777247			−0.0388623	+	0.999245i	$0.512373\pi$
$920$		0			0
$921$	29213.8	−	29213.8i	1.04520	−	1.04520i
$922$		0			0
$923$	4176.03	−	4176.03i	0.148923	−	0.148923i
$924$		0			0
$925$	17731.5	+	17731.5i	0.630280	+	0.630280i
$926$		0			0
$927$			49574.1i			1.75645i
$928$		0			0
$929$	−34181.1	−	34181.1i	−1.20716	−	1.20716i	−0.971944	−	0.235211i	$-0.924422\pi$
$929$	−34181.1	−	34181.1i	−1.20716	−	1.20716i	−0.235211	−	0.971944i	$-0.575578\pi$
$930$		0			0
$931$	57474.6			2.02326
$932$		0			0
$933$			59458.8i			2.08638i
$934$		0			0
$935$	−29840.5	+	5319.53i	−1.04373	+	0.186061i
$936$		0			0
$937$			17983.4i			0.626993i	0.949589	+	0.313497i	$0.101500\pi$
$937$			17983.4i			0.626993i	−0.949589	+	0.313497i	$0.898500\pi$
$938$		0			0
$939$	16544.7			0.574991
$940$		0			0
$941$	8283.12	+	8283.12i	0.286952	+	0.286952i	0.835874	−	0.548922i	$-0.184961\pi$
$941$	8283.12	+	8283.12i	0.286952	+	0.286952i	−0.548922	+	0.835874i	$0.684961\pi$
$942$		0			0
$943$		−	13709.1i		−	0.473413i
$944$		0			0
$945$	−7447.99	−	7447.99i	−0.256384	−	0.256384i
$946$		0			0
$947$	−17284.0	+	17284.0i	−0.593087	+	0.593087i	−0.938464	−	0.345377i	$-0.887751\pi$
$947$	−17284.0	+	17284.0i	−0.593087	+	0.593087i	0.345377	+	0.938464i	$0.387751\pi$
$948$		0			0
$949$	1746.77	−	1746.77i	0.0597498	−	0.0597498i
$950$		0			0
$951$	29884.7			1.01901
$952$		0			0
$953$	9119.16			0.309967			0.154984	−	0.987917i	$-0.450468\pi$
$953$	9119.16			0.309967			0.154984	+	0.987917i	$0.450468\pi$
$954$		0			0
$955$	−52188.6	+	52188.6i	−1.76836	+	1.76836i
$956$		0			0
$957$	−10028.2	+	10028.2i	−0.338730	+	0.338730i
$958$		0			0
$959$	30067.6	+	30067.6i	1.01244	+	1.01244i
$960$		0			0
$961$		−	26666.1i		−	0.895106i
$962$		0			0
$963$	20697.5	+	20697.5i	0.692595	+	0.692595i
$964$		0			0
$965$	16.1996			0.000540399
$966$		0			0
$967$		−	14799.4i		−	0.492157i	−0.969250	−	0.246078i	$-0.920858\pi$
$967$		−	14799.4i		−	0.492157i	0.969250	−	0.246078i	$-0.0791421\pi$
$968$		0			0
$969$	−62277.6	−	43433.0i	−2.06465	−	1.43991i
$970$		0			0
$971$		−	24089.4i		−	0.796155i	−0.917352	−	0.398078i	$-0.869677\pi$
$971$		−	24089.4i		−	0.796155i	0.917352	−	0.398078i	$-0.130323\pi$
$972$		0			0
$973$	53240.9			1.75419
$974$		0			0
$975$	−9688.00	−	9688.00i	−0.318220	−	0.318220i
$976$		0			0
$977$			12428.9i			0.406995i	0.979075	+	0.203498i	$0.0652309\pi$
$977$			12428.9i			0.406995i	−0.979075	+	0.203498i	$0.934769\pi$
$978$		0			0
$979$	23926.0	+	23926.0i	0.781079	+	0.781079i
$980$		0			0
$981$	25633.4	−	25633.4i	0.834264	−	0.834264i
$982$		0			0
$983$	4207.41	−	4207.41i	0.136516	−	0.136516i	−0.635546	−	0.772063i	$-0.719225\pi$
$983$	4207.41	−	4207.41i	0.136516	−	0.136516i	0.772063	+	0.635546i	$0.219225\pi$
$984$		0			0
$985$	−42046.5			−1.36011
$986$		0			0
$987$	78458.8			2.53027
$988$		0			0
$989$	−45873.7	+	45873.7i	−1.47492	+	1.47492i
$990$		0			0
$991$	30577.3	−	30577.3i	0.980141	−	0.980141i	−0.0196652	−	0.999807i	$-0.506260\pi$
$991$	30577.3	−	30577.3i	0.980141	−	0.980141i	0.999807	+	0.0196652i	$0.00626004\pi$
$992$		0			0
$993$	43387.9	+	43387.9i	1.38658	+	1.38658i
$994$		0			0
$995$		−	6824.71i		−	0.217445i
$996$		0			0
$997$	18880.7	+	18880.7i	0.599757	+	0.599757i	0.940248	−	0.340491i	$-0.110593\pi$
$997$	18880.7	+	18880.7i	0.599757	+	0.599757i	−0.340491	+	0.940248i	$0.610593\pi$
$998$		0			0
$999$	−5087.58			−0.161125

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.k.a.89.2	yes	14
4.3	odd	2		272.4.o.g.225.6		14
17.8	even	8		2312.4.a.m.1.12		14
17.9	even	8		2312.4.a.m.1.3		14
17.13	even	4	inner	136.4.k.a.81.2	✓	14
68.47	odd	4		272.4.o.g.81.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.k.a.81.2	✓	14	17.13	even	4	inner
136.4.k.a.89.2	yes	14	1.1	even	1	trivial
272.4.o.g.81.6		14	68.47	odd	4
272.4.o.g.225.6		14	4.3	odd	2
2312.4.a.m.1.3		14	17.9	even	8
2312.4.a.m.1.12		14	17.8	even	8

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	136.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.35029 + 5.35029i) q^{3} +(-11.0962 + 11.0962i) q^{5} +(19.2933 + 19.2933i) q^{7} -30.2512i q^{9} +O(q^{10})\)	\(q+(-5.35029 + 5.35029i) q^{3} +(-11.0962 + 11.0962i) q^{5} +(19.2933 + 19.2933i) q^{7} -30.2512i q^{9} +(-19.4859 - 19.4859i) q^{11} -14.9336 q^{13} -118.736i q^{15} +(-69.0049 + 12.3012i) q^{17} -143.163i q^{19} -206.450 q^{21} +(136.829 + 136.829i) q^{23} -121.253i q^{25} +(17.3951 + 17.3951i) q^{27} +(-48.0943 + 48.0943i) q^{29} +(168.014 - 168.014i) q^{31} +208.510 q^{33} -428.166 q^{35} +(-146.236 + 146.236i) q^{37} +(79.8992 - 79.8992i) q^{39} +(-50.0956 - 50.0956i) q^{41} +335.263i q^{43} +(335.675 + 335.675i) q^{45} -380.039 q^{47} +401.462i q^{49} +(303.382 - 435.012i) q^{51} -163.666i q^{53} +432.440 q^{55} +(765.964 + 765.964i) q^{57} +436.943i q^{59} +(-391.332 - 391.332i) q^{61} +(583.646 - 583.646i) q^{63} +(165.707 - 165.707i) q^{65} +307.709 q^{67} -1464.15 q^{69} +(-279.640 + 279.640i) q^{71} +(-116.969 + 116.969i) q^{73} +(648.738 + 648.738i) q^{75} -751.894i q^{77} +(-18.2130 - 18.2130i) q^{79} +630.646 q^{81} -80.2810i q^{83} +(629.198 - 902.192i) q^{85} -514.637i q^{87} -1227.86 q^{89} +(-288.119 - 288.119i) q^{91} +1797.84i q^{93} +(1588.57 + 1588.57i) q^{95} +(-912.788 + 912.788i) q^{97} +(-589.472 + 589.472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 4 q^{3} + 8 q^{5} - 10 q^{7}+O(q^{10}) \) 14 * q - 4 * q^3 + 8 * q^5 - 10 * q^7	\( 14 q - 4 q^{3} + 8 q^{5} - 10 q^{7} + 16 q^{11} + 72 q^{13} - 40 q^{17} - 60 q^{21} + 246 q^{23} + 572 q^{27} + 260 q^{29} + 566 q^{31} - 904 q^{33} - 804 q^{35} - 28 q^{37} + 476 q^{39} - 786 q^{41} - 604 q^{45} + 448 q^{47} - 380 q^{51} + 1612 q^{55} + 1004 q^{57} + 660 q^{61} - 2250 q^{63} - 796 q^{65} - 284 q^{67} - 2532 q^{69} + 326 q^{71} + 730 q^{73} - 864 q^{75} + 342 q^{79} - 950 q^{81} + 4148 q^{85} - 4516 q^{89} - 3112 q^{91} + 3356 q^{95} - 1194 q^{97} + 2876 q^{99}+O(q^{100}) \) 14 * q - 4 * q^3 + 8 * q^5 - 10 * q^7 + 16 * q^11 + 72 * q^13 - 40 * q^17 - 60 * q^21 + 246 * q^23 + 572 * q^27 + 260 * q^29 + 566 * q^31 - 904 * q^33 - 804 * q^35 - 28 * q^37 + 476 * q^39 - 786 * q^41 - 604 * q^45 + 448 * q^47 - 380 * q^51 + 1612 * q^55 + 1004 * q^57 + 660 * q^61 - 2250 * q^63 - 796 * q^65 - 284 * q^67 - 2532 * q^69 + 326 * q^71 + 730 * q^73 - 864 * q^75 + 342 * q^79 - 950 * q^81 + 4148 * q^85 - 4516 * q^89 - 3112 * q^91 + 3356 * q^95 - 1194 * q^97 + 2876 * q^99

Introduction

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