LMFDB - Embedded newform 136.4.k.b.89.4

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} + 119x^{12} + 5319x^{10} + 112122x^{8} + 1120191x^{6} + 4382607x^{4} + 1699337x^{2} + 2704 $ x^14 + 119x^12 + 5319x^10 + 112122x^8 + 1120191x^6 + 4382607x^4 + 1699337x^2 + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{15}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			89.4
Root			$0.0399724i$ of defining polynomial
Character	$\chi$	$=$	136.89
Dual form			136.4.k.b.81.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0399724 - 0.0399724i) q^{3} +(-1.97903 + 1.97903i) q^{5} +(-4.30175 - 4.30175i) q^{7} +26.9968i q^{9} +O(q^{10})$	\(q+(0.0399724 - 0.0399724i) q^{3} +(-1.97903 + 1.97903i) q^{5} +(-4.30175 - 4.30175i) q^{7} +26.9968i q^{9} +(36.5044 + 36.5044i) q^{11} +19.2351 q^{13} +0.158213i q^{15} +(-57.9167 + 39.4798i) q^{17} +25.0096i q^{19} -0.343902 q^{21} +(105.841 + 105.841i) q^{23} +117.167i q^{25} +(2.15838 + 2.15838i) q^{27} +(-14.6850 + 14.6850i) q^{29} +(161.487 - 161.487i) q^{31} +2.91833 q^{33} +17.0266 q^{35} +(-249.300 + 249.300i) q^{37} +(0.768872 - 0.768872i) q^{39} +(-155.469 - 155.469i) q^{41} -51.0771i q^{43} +(-53.4276 - 53.4276i) q^{45} +261.156 q^{47} -305.990i q^{49} +(-0.736967 + 3.89317i) q^{51} -102.139i q^{53} -144.487 q^{55} +(0.999693 + 0.999693i) q^{57} -694.356i q^{59} +(-154.454 - 154.454i) q^{61} +(116.133 - 116.133i) q^{63} +(-38.0669 + 38.0669i) q^{65} -442.817 q^{67} +8.46145 q^{69} +(382.069 - 382.069i) q^{71} +(-190.365 + 190.365i) q^{73} +(4.68344 + 4.68344i) q^{75} -314.065i q^{77} +(-22.3403 - 22.3403i) q^{79} -728.741 q^{81} +669.427i q^{83} +(36.4873 - 192.751i) q^{85} +1.17399i q^{87} +1184.49 q^{89} +(-82.7445 - 82.7445i) q^{91} -12.9100i q^{93} +(-49.4948 - 49.4948i) q^{95} +(218.714 - 218.714i) q^{97} +(-985.502 + 985.502i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 6 q^{3} + 6 q^{5} + 10 q^{7}+O(q^{10}) $ 14 * q + 6 * q^3 + 6 * q^5 + 10 * q^7	$ 14 q + 6 q^{3} + 6 q^{5} + 10 q^{7} - 66 q^{11} - 124 q^{13} + 130 q^{17} - 148 q^{21} - 162 q^{23} - 204 q^{27} + 158 q^{29} - 350 q^{31} + 116 q^{33} + 236 q^{35} + 582 q^{37} - 320 q^{39} + 878 q^{41} - 26 q^{45} - 448 q^{47} - 590 q^{51} + 1460 q^{55} + 292 q^{57} - 1130 q^{61} + 114 q^{63} + 20 q^{65} - 64 q^{67} + 2076 q^{69} - 3274 q^{71} - 1426 q^{73} + 946 q^{75} + 1718 q^{79} + 166 q^{81} - 2018 q^{85} + 476 q^{89} + 2128 q^{91} - 2444 q^{95} + 1926 q^{97} + 3870 q^{99}+O(q^{100}) $ 14 * q + 6 * q^3 + 6 * q^5 + 10 * q^7 - 66 * q^11 - 124 * q^13 + 130 * q^17 - 148 * q^21 - 162 * q^23 - 204 * q^27 + 158 * q^29 - 350 * q^31 + 116 * q^33 + 236 * q^35 + 582 * q^37 - 320 * q^39 + 878 * q^41 - 26 * q^45 - 448 * q^47 - 590 * q^51 + 1460 * q^55 + 292 * q^57 - 1130 * q^61 + 114 * q^63 + 20 * q^65 - 64 * q^67 + 2076 * q^69 - 3274 * q^71 - 1426 * q^73 + 946 * q^75 + 1718 * q^79 + 166 * q^81 - 2018 * q^85 + 476 * q^89 + 2128 * q^91 - 2444 * q^95 + 1926 * q^97 + 3870 * 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
$3$	0.0399724	−	0.0399724i	0.00769269	−	0.00769269i	−0.703250	−	0.710943i	$-0.748269\pi$
$3$	0.0399724	−	0.0399724i	0.00769269	−	0.00769269i	0.710943	+	0.703250i	$0.248269\pi$
$4$		0			0
$5$	−1.97903	+	1.97903i	−0.177010	+	0.177010i	−0.790051	−	0.613041i	$-0.789946\pi$
$5$	−1.97903	+	1.97903i	−0.177010	+	0.177010i	0.613041	+	0.790051i	$0.289946\pi$
$6$		0			0
$7$	−4.30175	−	4.30175i	−0.232273	−	0.232273i	0.581368	−	0.813641i	$-0.302518\pi$
$7$	−4.30175	−	4.30175i	−0.232273	−	0.232273i	−0.813641	+	0.581368i	$0.802518\pi$
$8$		0			0
$9$			26.9968i			0.999882i
$10$		0			0
$11$	36.5044	+	36.5044i	1.00059	+	1.00059i	1.00000		0.000590210i	$0.000187870\pi$
$11$	36.5044	+	36.5044i	1.00059	+	1.00059i	0.000590210		1.00000i	$0.499812\pi$
$12$		0			0
$13$	19.2351			0.410373			0.205187	−	0.978723i	$-0.434220\pi$
$13$	19.2351			0.410373			0.205187	+	0.978723i	$0.434220\pi$
$14$		0			0
$15$			0.158213i			0.00272337i
$16$		0			0
$17$	−57.9167	+	39.4798i	−0.826286	+	0.563250i
$17$	−57.9167	+	39.4798i	−0.826286	+	0.563250i
$18$		0			0
$19$			25.0096i			0.301979i	0.988535	+	0.150989i	$0.0482459\pi$
$19$			25.0096i			0.301979i	−0.988535	+	0.150989i	$0.951754\pi$
$20$		0			0
$21$	−0.343902			−0.00357360
$22$		0			0
$23$	105.841	+	105.841i	0.959540	+	0.959540i	0.999213	−	0.0396723i	$-0.0126314\pi$
$23$	105.841	+	105.841i	0.959540	+	0.959540i	−0.0396723	+	0.999213i	$0.512631\pi$
$24$		0			0
$25$			117.167i			0.937335i
$26$		0			0
$27$	2.15838	+	2.15838i	0.0153845	+	0.0153845i
$28$		0			0
$29$	−14.6850	+	14.6850i	−0.0940322	+	0.0940322i	−0.752558	−	0.658526i	$-0.771180\pi$
$29$	−14.6850	+	14.6850i	−0.0940322	+	0.0940322i	0.658526	+	0.752558i	$0.271180\pi$
$30$		0			0
$31$	161.487	−	161.487i	0.935608	−	0.935608i	−0.0624410	−	0.998049i	$-0.519889\pi$
$31$	161.487	−	161.487i	0.935608	−	0.935608i	0.998049	+	0.0624410i	$0.0198885\pi$
$32$		0			0
$33$	2.91833			0.0153944
$34$		0			0
$35$	17.0266			0.0822292
$36$		0			0
$37$	−249.300	+	249.300i	−1.10769	+	1.10769i	−0.114240	+	0.993453i	$0.536443\pi$
$37$	−249.300	+	249.300i	−1.10769	+	1.10769i	−0.993453	+	0.114240i	$0.963557\pi$
$38$		0			0
$39$	0.768872	−	0.768872i	0.00315687	−	0.00315687i
$40$		0			0
$41$	−155.469	−	155.469i	−0.592199	−	0.592199i	0.346026	−	0.938225i	$-0.387531\pi$
$41$	−155.469	−	155.469i	−0.592199	−	0.592199i	−0.938225	+	0.346026i	$0.887531\pi$
$42$		0			0
$43$		−	51.0771i		−	0.181144i	−0.995890	−	0.0905719i	$-0.971131\pi$
$43$		−	51.0771i		−	0.181144i	0.995890	−	0.0905719i	$-0.0288695\pi$
$44$		0			0
$45$	−53.4276	−	53.4276i	−0.176989	−	0.176989i
$46$		0			0
$47$	261.156			0.810501			0.405250	−	0.914206i	$-0.367184\pi$
$47$	261.156			0.810501			0.405250	+	0.914206i	$0.367184\pi$
$48$		0			0
$49$		−	305.990i		−	0.892099i
$50$		0			0
$51$	−0.736967	+	3.89317i	−0.00202345	+	0.0106893i
$52$		0			0
$53$		−	102.139i		−	0.264713i	−0.991202	−	0.132357i	$-0.957746\pi$
$53$		−	102.139i		−	0.264713i	0.991202	−	0.132357i	$-0.0422544\pi$
$54$		0			0
$55$	−144.487			−0.354229
$56$		0			0
$57$	0.999693	+	0.999693i	0.00232303	+	0.00232303i
$58$		0			0
$59$		−	694.356i		−	1.53216i	−0.642745	−	0.766080i	$-0.722204\pi$
$59$		−	694.356i		−	1.53216i	0.642745	−	0.766080i	$-0.277796\pi$
$60$		0			0
$61$	−154.454	−	154.454i	−0.324194	−	0.324194i	0.526179	−	0.850374i	$-0.323624\pi$
$61$	−154.454	−	154.454i	−0.324194	−	0.324194i	−0.850374	+	0.526179i	$0.823624\pi$
$62$		0			0
$63$	116.133	−	116.133i	0.232245	−	0.232245i
$64$		0			0
$65$	−38.0669	+	38.0669i	−0.0726403	+	0.0726403i
$66$		0			0
$67$	−442.817			−0.807444			−0.403722	−	0.914882i	$-0.632284\pi$
$67$	−442.817			−0.807444			−0.403722	+	0.914882i	$0.632284\pi$
$68$		0			0
$69$	8.46145			0.0147629
$70$		0			0
$71$	382.069	−	382.069i	0.638638	−	0.638638i	−0.311582	−	0.950219i	$-0.600859\pi$
$71$	382.069	−	382.069i	0.638638	−	0.638638i	0.950219	+	0.311582i	$0.100859\pi$
$72$		0			0
$73$	−190.365	+	190.365i	−0.305212	+	0.305212i	−0.843049	−	0.537837i	$-0.819242\pi$
$73$	−190.365	+	190.365i	−0.305212	+	0.305212i	0.537837	+	0.843049i	$0.319242\pi$
$74$		0			0
$75$	4.68344	+	4.68344i	0.00721062	+	0.00721062i
$76$		0			0
$77$		−	314.065i		−	0.464819i
$78$		0			0
$79$	−22.3403	−	22.3403i	−0.0318162	−	0.0318162i	0.691020	−	0.722836i	$-0.257162\pi$
$79$	−22.3403	−	22.3403i	−0.0318162	−	0.0318162i	−0.722836	+	0.691020i	$0.757162\pi$
$80$		0			0
$81$	−728.741			−0.999645
$82$		0			0
$83$			669.427i			0.885291i	0.896697	+	0.442645i	$0.145960\pi$
$83$			669.427i			0.885291i	−0.896697	+	0.442645i	$0.854040\pi$
$84$		0			0
$85$	36.4873	−	192.751i	0.0465600	−	0.245962i
$86$		0			0
$87$			1.17399i			0.00144672i
$88$		0			0
$89$	1184.49			1.41074			0.705371	−	0.708839i	$-0.250781\pi$
$89$	1184.49			1.41074			0.705371	+	0.708839i	$0.250781\pi$
$90$		0			0
$91$	−82.7445	−	82.7445i	−0.0953185	−	0.0953185i
$92$		0			0
$93$		−	12.9100i		−	0.0143947i
$94$		0			0
$95$	−49.4948	−	49.4948i	−0.0534533	−	0.0534533i
$96$		0			0
$97$	218.714	−	218.714i	0.228939	−	0.228939i	−0.583310	−	0.812249i	$-0.698243\pi$
$97$	218.714	−	218.714i	0.228939	−	0.228939i	0.812249	+	0.583310i	$0.198243\pi$
$98$		0			0
$99$	−985.502	+	985.502i	−1.00047	+	1.00047i
$100$		0			0
$101$	805.995			0.794054			0.397027	−	0.917807i	$-0.370042\pi$
$101$	805.995			0.794054			0.397027	+	0.917807i	$0.370042\pi$
$102$		0			0
$103$	531.840			0.508774			0.254387	−	0.967102i	$-0.418126\pi$
$103$	531.840			0.508774			0.254387	+	0.967102i	$0.418126\pi$
$104$		0			0
$105$	0.680594	−	0.680594i	0.000632563	−	0.000632563i
$106$		0			0
$107$	−849.213	+	849.213i	−0.767257	+	0.767257i	−0.977623	−	0.210366i	$-0.932535\pi$
$107$	−849.213	+	849.213i	−0.767257	+	0.767257i	0.210366	+	0.977623i	$0.432535\pi$
$108$		0			0
$109$	952.659	+	952.659i	0.837139	+	0.837139i	0.988481	−	0.151342i	$-0.0483596\pi$
$109$	952.659	+	952.659i	0.837139	+	0.837139i	−0.151342	+	0.988481i	$0.548360\pi$
$110$		0			0
$111$			19.9302i			0.0170423i
$112$		0			0
$113$	161.682	+	161.682i	0.134600	+	0.134600i	0.771197	−	0.636597i	$-0.219658\pi$
$113$	161.682	+	161.682i	0.134600	+	0.134600i	−0.636597	+	0.771197i	$0.719658\pi$
$114$		0			0
$115$	−418.927			−0.339697
$116$		0			0
$117$			519.286i			0.410325i
$118$		0			0
$119$	418.975	+	79.3110i	0.322751	+	0.0610960i
$120$		0			0
$121$			1334.14i			1.00236i
$122$		0			0
$123$	−12.4289			−0.00911119
$124$		0			0
$125$	−479.256	−	479.256i	−0.342928	−	0.342928i
$126$		0			0
$127$		−	140.286i		−	0.0980189i	−0.998798	−	0.0490095i	$-0.984394\pi$
$127$		−	140.286i		−	0.0980189i	0.998798	−	0.0490095i	$-0.0156064\pi$
$128$		0			0
$129$	−2.04167	−	2.04167i	−0.00139348	−	0.00139348i
$130$		0			0
$131$	−288.058	+	288.058i	−0.192120	+	0.192120i	−0.796612	−	0.604491i	$-0.793376\pi$
$131$	−288.058	+	288.058i	−0.192120	+	0.192120i	0.604491	+	0.796612i	$0.293376\pi$
$132$		0			0
$133$	107.585	−	107.585i	0.0701414	−	0.0701414i
$134$		0			0
$135$	−8.54301			−0.00544641
$136$		0			0
$137$	2753.80			1.71732			0.858661	−	0.512545i	$-0.171297\pi$
$137$	2753.80			1.71732			0.858661	+	0.512545i	$0.171297\pi$
$138$		0			0
$139$	−1595.40	+	1595.40i	−0.973523	+	0.973523i	−0.999658	−	0.0261350i	$-0.991680\pi$
$139$	−1595.40	+	1595.40i	−0.973523	+	0.973523i	0.0261350	+	0.999658i	$0.491680\pi$
$140$		0			0
$141$	10.4390	−	10.4390i	0.00623493	−	0.00623493i
$142$		0			0
$143$	702.166	+	702.166i	0.410616	+	0.410616i
$144$		0			0
$145$		−	58.1241i		−	0.0332893i
$146$		0			0
$147$	−12.2311	−	12.2311i	−0.00686264	−	0.00686264i
$148$		0			0
$149$	1689.36			0.928843			0.464422	−	0.885614i	$-0.346262\pi$
$149$	1689.36			0.928843			0.464422	+	0.885614i	$0.346262\pi$
$150$		0			0
$151$			658.964i			0.355137i	0.984108	+	0.177569i	$0.0568232\pi$
$151$			658.964i			0.355137i	−0.984108	+	0.177569i	$0.943177\pi$
$152$		0			0
$153$	−1065.83	−	1563.57i	−0.563184	−	0.826188i
$154$		0			0
$155$			639.175i			0.331224i
$156$		0			0
$157$	−1725.60			−0.877186			−0.438593	−	0.898686i	$-0.644523\pi$
$157$	−1725.60			−0.877186			−0.438593	+	0.898686i	$0.644523\pi$
$158$		0			0
$159$	−4.08272	−	4.08272i	−0.00203636	−	0.00203636i
$160$		0			0
$161$		−	910.605i		−	0.445750i
$162$		0			0
$163$	−1603.92	−	1603.92i	−0.770728	−	0.770728i	0.207505	−	0.978234i	$-0.433466\pi$
$163$	−1603.92	−	1603.92i	−0.770728	−	0.770728i	−0.978234	+	0.207505i	$0.933466\pi$
$164$		0			0
$165$	−5.77548	+	5.77548i	−0.00272497	+	0.00272497i
$166$		0			0
$167$	1736.33	−	1736.33i	0.804559	−	0.804559i	−0.179246	−	0.983804i	$-0.557366\pi$
$167$	1736.33	−	1736.33i	0.804559	−	0.804559i	0.983804	+	0.179246i	$0.0573657\pi$
$168$		0			0
$169$	−1827.01			−0.831594
$170$		0			0
$171$	−675.179			−0.301943
$172$		0			0
$173$	216.659	−	216.659i	0.0952153	−	0.0952153i	−0.657895	−	0.753110i	$-0.728553\pi$
$173$	216.659	−	216.659i	0.0952153	−	0.0952153i	0.753110	+	0.657895i	$0.228553\pi$
$174$		0			0
$175$	504.022	−	504.022i	0.217717	−	0.217717i
$176$		0			0
$177$	−27.7551	−	27.7551i	−0.0117864	−	0.0117864i
$178$		0			0
$179$		−	2741.86i		−	1.14490i	−0.819941	−	0.572448i	$-0.805994\pi$
$179$		−	2741.86i		−	1.14490i	0.819941	−	0.572448i	$-0.194006\pi$
$180$		0			0
$181$	1097.33	+	1097.33i	0.450628	+	0.450628i	0.895563	−	0.444935i	$-0.146773\pi$
$181$	1097.33	+	1097.33i	0.450628	+	0.450628i	−0.444935	+	0.895563i	$0.646773\pi$
$182$		0			0
$183$	−12.3478			−0.00498785
$184$		0			0
$185$		−	986.746i		−	0.392146i
$186$		0			0
$187$	−3555.40	−	673.029i	−1.39036	−	0.263191i
$188$		0			0
$189$		−	18.5696i		−	0.00714678i
$190$		0			0
$191$	3861.44			1.46285			0.731424	−	0.681923i	$-0.238856\pi$
$191$	3861.44			1.46285			0.731424	+	0.681923i	$0.238856\pi$
$192$		0			0
$193$	1043.68	+	1043.68i	0.389251	+	0.389251i	0.874420	−	0.485169i	$-0.161242\pi$
$193$	1043.68	+	1043.68i	0.389251	+	0.389251i	−0.485169	+	0.874420i	$0.661242\pi$
$194$		0			0
$195$			3.04325i			0.00111760i
$196$		0			0
$197$	−3782.22	−	3782.22i	−1.36788	−	1.36788i	−0.863460	−	0.504416i	$-0.831708\pi$
$197$	−3782.22	−	3782.22i	−1.36788	−	1.36788i	−0.504416	−	0.863460i	$-0.668292\pi$
$198$		0			0
$199$	2619.61	−	2619.61i	0.933162	−	0.933162i	−0.0647402	−	0.997902i	$-0.520622\pi$
$199$	2619.61	−	2619.61i	0.933162	−	0.933162i	0.997902	+	0.0647402i	$0.0206219\pi$
$200$		0			0
$201$	−17.7005	+	17.7005i	−0.00621141	+	0.00621141i
$202$		0			0
$203$	126.342			0.0436822
$204$		0			0
$205$	615.356			0.209650
$206$		0			0
$207$	−2857.38	+	2857.38i	−0.959427	+	0.959427i
$208$		0			0
$209$	−912.960	+	912.960i	−0.302157	+	0.302157i
$210$		0			0
$211$	−708.196	−	708.196i	−0.231063	−	0.231063i	0.582074	−	0.813136i	$-0.302242\pi$
$211$	−708.196	−	708.196i	−0.231063	−	0.231063i	−0.813136	+	0.582074i	$0.802242\pi$
$212$		0			0
$213$		−	30.5444i		−	0.00982568i
$214$		0			0
$215$	101.083	+	101.083i	0.0320643	+	0.0320643i
$216$		0			0
$217$	−1389.35			−0.434632
$218$		0			0
$219$			15.2187i			0.00469581i
$220$		0			0
$221$	−1114.03	+	759.398i	−0.339086	+	0.231143i
$222$		0			0
$223$		−	4456.87i		−	1.33836i	−0.743101	−	0.669180i	$-0.766646\pi$
$223$		−	4456.87i		−	1.33836i	0.743101	−	0.669180i	$-0.233354\pi$
$224$		0			0
$225$	−3163.13			−0.937224
$226$		0			0
$227$	2485.09	+	2485.09i	0.726613	+	0.726613i	0.969943	−	0.243331i	$-0.0782401\pi$
$227$	2485.09	+	2485.09i	0.726613	+	0.726613i	−0.243331	+	0.969943i	$0.578240\pi$
$228$		0			0
$229$		−	4609.76i		−	1.33023i	−0.746743	−	0.665113i	$-0.768383\pi$
$229$		−	4609.76i		−	1.33023i	0.746743	−	0.665113i	$-0.231617\pi$
$230$		0			0
$231$	−12.5539	−	12.5539i	−0.00357571	−	0.00357571i
$232$		0			0
$233$	2019.71	−	2019.71i	0.567877	−	0.567877i	−0.363656	−	0.931533i	$-0.618472\pi$
$233$	2019.71	−	2019.71i	0.567877	−	0.567877i	0.931533	+	0.363656i	$0.118472\pi$
$234$		0			0
$235$	−516.837	+	516.837i	−0.143467	+	0.143467i
$236$		0			0
$237$	−1.78599			−0.000489504
$238$		0			0
$239$	6534.60			1.76857			0.884285	−	0.466947i	$-0.154646\pi$
$239$	6534.60			1.76857			0.884285	+	0.466947i	$0.154646\pi$
$240$		0			0
$241$	−2360.27	+	2360.27i	−0.630863	+	0.630863i	−0.948285	−	0.317421i	$-0.897183\pi$
$241$	−2360.27	+	2360.27i	−0.630863	+	0.630863i	0.317421	+	0.948285i	$0.397183\pi$
$242$		0			0
$243$	−87.4058	+	87.4058i	−0.0230744	+	0.0230744i
$244$		0			0
$245$	605.564	+	605.564i	0.157911	+	0.157911i
$246$		0			0
$247$			481.062i			0.123924i
$248$		0			0
$249$	26.7586	+	26.7586i	0.00681026	+	0.00681026i
$250$		0			0
$251$	2225.36			0.559616			0.279808	−	0.960056i	$-0.409729\pi$
$251$	2225.36			0.559616			0.279808	+	0.960056i	$0.409729\pi$
$252$		0			0
$253$			7727.34i			1.92021i
$254$		0			0
$255$	−6.24623	−	9.16320i	−0.00153394	−	0.00225028i
$256$		0			0
$257$			4927.60i			1.19601i	0.801491	+	0.598006i	$0.204040\pi$
$257$			4927.60i			1.19601i	−0.801491	+	0.598006i	$0.795960\pi$
$258$		0			0
$259$	2144.85			0.514574
$260$		0			0
$261$	−396.448	−	396.448i	−0.0940210	−	0.0940210i
$262$		0			0
$263$		−	5423.64i		−	1.27162i	−0.771846	−	0.635810i	$-0.780666\pi$
$263$		−	5423.64i		−	1.27162i	0.771846	−	0.635810i	$-0.219334\pi$
$264$		0			0
$265$	202.136	+	202.136i	0.0468570	+	0.0468570i
$266$		0			0
$267$	47.3470	−	47.3470i	0.0108524	−	0.0108524i
$268$		0			0
$269$	−1401.41	+	1401.41i	−0.317641	+	0.317641i	−0.847860	−	0.530220i	$-0.822109\pi$
$269$	−1401.41	+	1401.41i	−0.317641	+	0.317641i	0.530220	+	0.847860i	$0.322109\pi$
$270$		0			0
$271$	−3510.15			−0.786812			−0.393406	−	0.919365i	$-0.628703\pi$
$271$	−3510.15			−0.786812			−0.393406	+	0.919365i	$0.628703\pi$
$272$		0			0
$273$	−6.61499			−0.00146651
$274$		0			0
$275$	−4277.11	+	4277.11i	−0.937888	+	0.937888i
$276$		0			0
$277$	−5410.58	+	5410.58i	−1.17361	+	1.17361i	−0.192270	+	0.981342i	$0.561585\pi$
$277$	−5410.58	+	5410.58i	−1.17361	+	1.17361i	−0.981342	+	0.192270i	$0.938415\pi$
$278$		0			0
$279$	4359.62	+	4359.62i	0.935497	+	0.935497i
$280$		0			0
$281$		−	4519.42i		−	0.959451i	−0.877419	−	0.479726i	$-0.840736\pi$
$281$		−	4519.42i		−	0.959451i	0.877419	−	0.479726i	$-0.159264\pi$
$282$		0			0
$283$	3295.00	+	3295.00i	0.692111	+	0.692111i	0.962696	−	0.270585i	$-0.0872171\pi$
$283$	3295.00	+	3295.00i	0.692111	+	0.692111i	−0.270585	+	0.962696i	$0.587217\pi$
$284$		0			0
$285$	−3.95685			−0.000822399
$286$		0			0
$287$			1337.57i			0.275103i
$288$		0			0
$289$	1795.69	−	4573.08i	0.365498	−	0.930812i
$290$		0			0
$291$		−	17.4851i		−	0.00352231i
$292$		0			0
$293$	6222.10			1.24061			0.620305	−	0.784360i	$-0.287009\pi$
$293$	6222.10			1.24061			0.620305	+	0.784360i	$0.287009\pi$
$294$		0			0
$295$	1374.15	+	1374.15i	0.271208	+	0.271208i
$296$		0			0
$297$			157.581i			0.0307871i
$298$		0			0
$299$	2035.87	+	2035.87i	0.393770	+	0.393770i
$300$		0			0
$301$	−219.721	+	219.721i	−0.0420747	+	0.0420747i
$302$		0			0
$303$	32.2175	−	32.2175i	0.00610841	−	0.00610841i
$304$		0			0
$305$	611.341			0.114771
$306$		0			0
$307$	478.173			0.0888951			0.0444475	−	0.999012i	$-0.485847\pi$
$307$	478.173			0.0888951			0.0444475	+	0.999012i	$0.485847\pi$
$308$		0			0
$309$	21.2589	−	21.2589i	0.00391384	−	0.00391384i
$310$		0			0
$311$	−5088.61	+	5088.61i	−0.927809	+	0.927809i	−0.997564	−	0.0697553i	$-0.977778\pi$
$311$	−5088.61	+	5088.61i	−0.927809	+	0.927809i	0.0697553	+	0.997564i	$0.477778\pi$
$312$		0			0
$313$	6588.67	+	6588.67i	1.18982	+	1.18982i	0.977117	+	0.212703i	$0.0682268\pi$
$313$	6588.67	+	6588.67i	1.18982	+	1.18982i	0.212703	+	0.977117i	$0.431773\pi$
$314$		0			0
$315$			459.664i			0.0822195i
$316$		0			0
$317$	−939.884	−	939.884i	−0.166527	−	0.166527i	0.618924	−	0.785451i	$-0.287569\pi$
$317$	−939.884	−	939.884i	−0.166527	−	0.166527i	−0.785451	+	0.618924i	$0.787569\pi$
$318$		0			0
$319$	−1072.13			−0.188175
$320$		0			0
$321$			67.8901i			0.0118045i
$322$		0			0
$323$	−987.374	−	1448.47i	−0.170090	−	0.249521i
$324$		0			0
$325$			2253.72i			0.384657i
$326$		0			0
$327$	76.1600			0.0128797
$328$		0			0
$329$	−1123.43	−	1123.43i	−0.188257	−	0.188257i
$330$		0			0
$331$		−	10372.7i		−	1.72246i	−0.508218	−	0.861229i	$-0.669695\pi$
$331$		−	10372.7i		−	1.72246i	0.508218	−	0.861229i	$-0.330305\pi$
$332$		0			0
$333$	−6730.30	−	6730.30i	−1.10756	−	1.10756i
$334$		0			0
$335$	876.350	−	876.350i	0.142926	−	0.142926i
$336$		0			0
$337$	−5162.49	+	5162.49i	−0.834476	+	0.834476i	−0.988125	−	0.153649i	$-0.950897\pi$
$337$	−5162.49	+	5162.49i	−0.834476	+	0.834476i	0.153649	+	0.988125i	$0.450897\pi$
$338$		0			0
$339$	12.9256			0.00207087
$340$		0			0
$341$	11789.9			1.87232
$342$		0			0
$343$	−2791.79	+	2791.79i	−0.439483	+	0.439483i
$344$		0			0
$345$	−16.7455	+	16.7455i	−0.00261318	+	0.00261318i
$346$		0			0
$347$	−3136.83	−	3136.83i	−0.485285	−	0.485285i	0.421529	−	0.906815i	$-0.361493\pi$
$347$	−3136.83	−	3136.83i	−0.485285	−	0.485285i	−0.906815	+	0.421529i	$0.861493\pi$
$348$		0			0
$349$		−	3795.57i		−	0.582155i	−0.956699	−	0.291078i	$-0.905986\pi$
$349$		−	3795.57i		−	0.582155i	0.956699	−	0.291078i	$-0.0940138\pi$
$350$		0			0
$351$	41.5166	+	41.5166i	0.00631337	+	0.00631337i
$352$		0			0
$353$	−6298.80			−0.949721			−0.474860	−	0.880061i	$-0.657501\pi$
$353$	−6298.80			−0.949721			−0.474860	+	0.880061i	$0.657501\pi$
$354$		0			0
$355$			1512.26i			0.226091i
$356$		0			0
$357$	19.9177	−	13.5772i	0.00295282	−	0.00201283i
$358$		0			0
$359$			4063.54i			0.597397i	0.954348	+	0.298699i	$0.0965525\pi$
$359$			4063.54i			0.597397i	−0.954348	+	0.298699i	$0.903447\pi$
$360$		0			0
$361$	6233.52			0.908809
$362$		0			0
$363$	53.3288	+	53.3288i	0.00771085	+	0.00771085i
$364$		0			0
$365$		−	753.476i		−	0.108051i
$366$		0			0
$367$	−6960.90	−	6960.90i	−0.990071	−	0.990071i	0.00987975	−	0.999951i	$-0.496855\pi$
$367$	−6960.90	−	6960.90i	−0.990071	−	0.990071i	−0.999951	+	0.00987975i	$0.996855\pi$
$368$		0			0
$369$	4197.16	−	4197.16i	0.592128	−	0.592128i
$370$		0			0
$371$	−439.374	+	439.374i	−0.0614856	+	0.0614856i
$372$		0			0
$373$	10995.7			1.52638			0.763188	−	0.646177i	$-0.223633\pi$
$373$	10995.7			1.52638			0.763188	+	0.646177i	$0.223633\pi$
$374$		0			0
$375$	−38.3140			−0.00527607
$376$		0			0
$377$	−282.467	+	282.467i	−0.0385883	+	0.0385883i
$378$		0			0
$379$	57.7292	−	57.7292i	0.00782415	−	0.00782415i	−0.703184	−	0.711008i	$-0.748239\pi$
$379$	57.7292	−	57.7292i	0.00782415	−	0.00782415i	0.711008	+	0.703184i	$0.248239\pi$
$380$		0			0
$381$	−5.60758	−	5.60758i	−0.000754029	−	0.000754029i
$382$		0			0
$383$		−	1528.32i		−	0.203899i	−0.994790	−	0.101949i	$-0.967492\pi$
$383$		−	1528.32i		−	0.203899i	0.994790	−	0.101949i	$-0.0325080\pi$
$384$		0			0
$385$	621.546	+	621.546i	0.0822777	+	0.0822777i
$386$		0			0
$387$	1378.92			0.181122
$388$		0			0
$389$		−	7868.90i		−	1.02563i	−0.858500	−	0.512813i	$-0.828603\pi$
$389$		−	7868.90i		−	1.02563i	0.858500	−	0.512813i	$-0.171397\pi$
$390$		0			0
$391$	−10308.6	−	1951.39i	−1.33332	−	0.252394i
$392$		0			0
$393$			23.0287i			0.00295584i
$394$		0			0
$395$	88.4244			0.0112636
$396$		0			0
$397$	−7541.37	−	7541.37i	−0.953376	−	0.953376i	0.0455841	−	0.998961i	$-0.485485\pi$
$397$	−7541.37	−	7541.37i	−0.953376	−	0.953376i	−0.998961	+	0.0455841i	$0.985485\pi$
$398$		0			0
$399$		−	8.60085i		−	0.00107915i
$400$		0			0
$401$	−9284.96	−	9284.96i	−1.15628	−	1.15628i	−0.985269	−	0.171013i	$-0.945296\pi$
$401$	−9284.96	−	9284.96i	−1.15628	−	1.15628i	−0.171013	−	0.985269i	$-0.554704\pi$
$402$		0			0
$403$	3106.21	−	3106.21i	0.383949	−	0.383949i
$404$		0			0
$405$	1442.20	−	1442.20i	0.176947	−	0.176947i
$406$		0			0
$407$	−18201.1			−2.21669
$408$		0			0
$409$	12487.9			1.50975			0.754877	−	0.655867i	$-0.227697\pi$
$409$	12487.9			1.50975			0.754877	+	0.655867i	$0.227697\pi$
$410$		0			0
$411$	110.076	−	110.076i	0.0132108	−	0.0132108i
$412$		0			0
$413$	−2986.95	+	2986.95i	−0.355879	+	0.355879i
$414$		0			0
$415$	−1324.82	−	1324.82i	−0.156705	−	0.156705i
$416$		0			0
$417$			127.544i			0.0149780i
$418$		0			0
$419$	1686.42	+	1686.42i	0.196628	+	0.196628i	0.798553	−	0.601925i	$-0.205599\pi$
$419$	1686.42	+	1686.42i	0.196628	+	0.196628i	−0.601925	+	0.798553i	$0.705599\pi$
$420$		0			0
$421$	4179.68			0.483860			0.241930	−	0.970294i	$-0.422220\pi$
$421$	4179.68			0.483860			0.241930	+	0.970294i	$0.422220\pi$
$422$		0			0
$423$			7050.38i			0.810405i
$424$		0			0
$425$	−4625.72	−	6785.92i	−0.527954	−	0.774507i
$426$		0			0
$427$			1328.85i			0.150603i
$428$		0			0
$429$	56.1344			0.00631747
$430$		0			0
$431$	5546.33	+	5546.33i	0.619854	+	0.619854i	0.945494	−	0.325640i	$-0.105580\pi$
$431$	5546.33	+	5546.33i	0.619854	+	0.619854i	−0.325640	+	0.945494i	$0.605580\pi$
$432$		0			0
$433$		−	1323.79i		−	0.146922i	−0.997298	−	0.0734610i	$-0.976596\pi$
$433$		−	1323.79i		−	0.146922i	0.997298	−	0.0734610i	$-0.0234044\pi$
$434$		0			0
$435$	−2.32336	−	2.32336i	−0.000256084	−	0.000256084i
$436$		0			0
$437$	−2647.05	+	2647.05i	−0.289761	+	0.289761i
$438$		0			0
$439$	10146.7	−	10146.7i	1.10313	−	1.10313i	0.109103	−	0.994030i	$-0.465202\pi$
$439$	10146.7	−	10146.7i	1.10313	−	1.10313i	0.994030	−	0.109103i	$-0.0347979\pi$
$440$		0			0
$441$	8260.75			0.891993
$442$		0			0
$443$	5281.03			0.566387			0.283193	−	0.959063i	$-0.408606\pi$
$443$	5281.03			0.566387			0.283193	+	0.959063i	$0.408606\pi$
$444$		0			0
$445$	−2344.15	+	2344.15i	−0.249716	+	0.249716i
$446$		0			0
$447$	67.5277	−	67.5277i	0.00714530	−	0.00714530i
$448$		0			0
$449$	2107.89	+	2107.89i	0.221553	+	0.221553i	0.809152	−	0.587599i	$-0.199927\pi$
$449$	2107.89	+	2107.89i	0.221553	+	0.221553i	−0.587599	+	0.809152i	$0.699927\pi$
$450$		0			0
$451$		−	11350.6i		−	1.18510i
$452$		0			0
$453$	26.3404	+	26.3404i	0.00273196	+	0.00273196i
$454$		0			0
$455$	327.508			0.0337447
$456$		0			0
$457$			1746.31i			0.178750i	0.995998	+	0.0893750i	$0.0284870\pi$
$457$			1746.31i			0.178750i	−0.995998	+	0.0893750i	$0.971513\pi$
$458$		0			0
$459$	−210.219	−	39.7939i	−0.0213773	−	0.00404666i
$460$		0			0
$461$			12493.9i			1.26226i	0.775679	+	0.631128i	$0.217408\pi$
$461$			12493.9i			1.26226i	−0.775679	+	0.631128i	$0.782592\pi$
$462$		0			0
$463$	−9171.67			−0.920612			−0.460306	−	0.887760i	$-0.652260\pi$
$463$	−9171.67			−0.920612			−0.460306	+	0.887760i	$0.652260\pi$
$464$		0			0
$465$	25.5493	+	25.5493i	0.00254800	+	0.00254800i
$466$		0			0
$467$		−	2173.91i		−	0.215410i	−0.994183	−	0.107705i	$-0.965650\pi$
$467$		−	2173.91i		−	0.215410i	0.994183	−	0.107705i	$-0.0343502\pi$
$468$		0			0
$469$	1904.89	+	1904.89i	0.187547	+	0.187547i
$470$		0			0
$471$	−68.9765	+	68.9765i	−0.00674792	+	0.00674792i
$472$		0			0
$473$	1864.54	−	1864.54i	0.181251	−	0.181251i
$474$		0			0
$475$	−2930.30			−0.283055
$476$		0			0
$477$	2757.41			0.264682
$478$		0			0
$479$	−11222.9	+	11222.9i	−1.07054	+	1.07054i	−0.0732221	+	0.997316i	$0.523328\pi$
$479$	−11222.9	+	11222.9i	−1.07054	+	1.07054i	−0.997316	+	0.0732221i	$0.976672\pi$
$480$		0			0
$481$	−4795.31	+	4795.31i	−0.454568	+	0.454568i
$482$		0			0
$483$	−36.3990	−	36.3990i	−0.00342901	−	0.00342901i
$484$		0			0
$485$			865.686i			0.0810491i
$486$		0			0
$487$	210.075	+	210.075i	0.0195470	+	0.0195470i	0.716813	−	0.697266i	$-0.245600\pi$
$487$	210.075	+	210.075i	0.0195470	+	0.0195470i	−0.697266	+	0.716813i	$0.745600\pi$
$488$		0			0
$489$	−128.225			−0.0118579
$490$		0			0
$491$			8812.02i			0.809941i	0.914330	+	0.404970i	$0.132718\pi$
$491$			8812.02i			0.809941i	−0.914330	+	0.404970i	$0.867282\pi$
$492$		0			0
$493$	270.746	−	1430.27i	0.0247338	−	0.130661i
$494$		0			0
$495$		−	3900.68i		−	0.354187i
$496$		0			0
$497$	−3287.13			−0.296676
$498$		0			0
$499$	13173.4	+	13173.4i	1.18180	+	1.18180i	0.979276	+	0.202529i	$0.0649159\pi$
$499$	13173.4	+	13173.4i	1.18180	+	1.18180i	0.202529	+	0.979276i	$0.435084\pi$
$500$		0			0
$501$		−	138.810i		−	0.0123784i
$502$		0			0
$503$	239.890	+	239.890i	0.0212647	+	0.0212647i	0.717659	−	0.696394i	$-0.245214\pi$
$503$	239.890	+	239.890i	0.0212647	+	0.0212647i	−0.696394	+	0.717659i	$0.745214\pi$
$504$		0			0
$505$	−1595.09	+	1595.09i	−0.140556	+	0.140556i
$506$		0			0
$507$	−73.0300	+	73.0300i	−0.00639719	+	0.00639719i
$508$		0			0
$509$	−9045.53			−0.787693			−0.393847	−	0.919176i	$-0.628856\pi$
$509$	−9045.53			−0.787693			−0.393847	+	0.919176i	$0.628856\pi$
$510$		0			0
$511$	1637.80			0.141785
$512$		0			0
$513$	−53.9802	+	53.9802i	−0.00464578	+	0.00464578i
$514$		0			0
$515$	−1052.53	+	1052.53i	−0.0900583	+	0.0900583i
$516$		0			0
$517$	9533.35	+	9533.35i	0.810979	+	0.810979i
$518$		0			0
$519$		−	17.3207i		−	0.00146492i
$520$		0			0
$521$	2882.23	+	2882.23i	0.242366	+	0.242366i	0.817828	−	0.575462i	$-0.195178\pi$
$521$	2882.23	+	2882.23i	0.242366	+	0.242366i	−0.575462	+	0.817828i	$0.695178\pi$
$522$		0			0
$523$	22649.5			1.89368			0.946839	−	0.321707i	$-0.104257\pi$
$523$	22649.5			1.89368			0.946839	+	0.321707i	$0.104257\pi$
$524$		0			0
$525$		−	40.2939i		−	0.00334966i
$526$		0			0
$527$	−2977.31	+	15728.2i	−0.246098	+	1.30006i
$528$		0			0
$529$			10237.7i			0.841436i
$530$		0			0
$531$	18745.4			1.53198
$532$		0			0
$533$	−2990.46	−	2990.46i	−0.243023	−	0.243023i
$534$		0			0
$535$		−	3361.24i		−	0.271625i
$536$		0			0
$537$	−109.599	−	109.599i	−0.00880733	−	0.00880733i
$538$		0			0
$539$	11170.0	−	11170.0i	0.892625	−	0.892625i
$540$		0			0
$541$	−8794.59	+	8794.59i	−0.698908	+	0.698908i	−0.964175	−	0.265267i	$-0.914540\pi$
$541$	−8794.59	+	8794.59i	−0.698908	+	0.698908i	0.265267	+	0.964175i	$0.414540\pi$
$542$		0			0
$543$	87.7256			0.00693308
$544$		0			0
$545$	−3770.69			−0.296364
$546$		0			0
$547$	−9867.73	+	9867.73i	−0.771323	+	0.771323i	−0.978338	−	0.207015i	$-0.933625\pi$
$547$	−9867.73	+	9867.73i	−0.771323	+	0.771323i	0.207015	+	0.978338i	$0.433625\pi$
$548$		0			0
$549$	4169.78	−	4169.78i	0.324156	−	0.324156i
$550$		0			0
$551$	−367.265	−	367.265i	−0.0283957	−	0.0283957i
$552$		0			0
$553$			192.205i			0.0147801i
$554$		0			0
$555$	−39.4426	−	39.4426i	−0.00301666	−	0.00301666i
$556$		0			0
$557$	−17027.0			−1.29526			−0.647629	−	0.761956i	$-0.724239\pi$
$557$	−17027.0			−1.29526			−0.647629	+	0.761956i	$0.724239\pi$
$558$		0			0
$559$		−	982.473i		−	0.0743366i
$560$		0			0
$561$	−169.020	+	115.215i	−0.0127202	+	0.00867093i
$562$		0			0
$563$		−	23996.7i		−	1.79634i	−0.439649	−	0.898170i	$-0.644897\pi$
$563$		−	23996.7i		−	1.79634i	0.439649	−	0.898170i	$-0.355103\pi$
$564$		0			0
$565$	−639.949			−0.0476510
$566$		0			0
$567$	3134.86	+	3134.86i	0.232190	+	0.232190i
$568$		0			0
$569$		−	442.338i		−	0.0325901i	−0.999867	−	0.0162951i	$-0.994813\pi$
$569$		−	442.338i		−	0.0325901i	0.999867	−	0.0162951i	$-0.00518711\pi$
$570$		0			0
$571$	4060.36	+	4060.36i	0.297584	+	0.297584i	0.840067	−	0.542483i	$-0.182516\pi$
$571$	4060.36	+	4060.36i	0.297584	+	0.297584i	−0.542483	+	0.840067i	$0.682516\pi$
$572$		0			0
$573$	154.351	−	154.351i	0.0112532	−	0.0112532i
$574$		0			0
$575$	−12401.1	+	12401.1i	−0.899411	+	0.899411i
$576$		0			0
$577$	−6432.83			−0.464129			−0.232064	−	0.972700i	$-0.574548\pi$
$577$	−6432.83			−0.464129			−0.232064	+	0.972700i	$0.574548\pi$
$578$		0			0
$579$	83.4363			0.00598877
$580$		0			0
$581$	2879.71	−	2879.71i	0.205629	−	0.205629i
$582$		0			0
$583$	3728.51	−	3728.51i	0.264870	−	0.264870i
$584$		0			0
$585$	−1027.68	−	1027.68i	−0.0726317	−	0.0726317i
$586$		0			0
$587$			5080.96i			0.357264i	0.983916	+	0.178632i	$0.0571671\pi$
$587$			5080.96i			0.357264i	−0.983916	+	0.178632i	$0.942833\pi$
$588$		0			0
$589$	4038.71	+	4038.71i	0.282534	+	0.282534i
$590$		0			0
$591$	−302.368			−0.0210453
$592$		0			0
$593$			15267.6i			1.05727i	0.848848	+	0.528637i	$0.177297\pi$
$593$			15267.6i			1.05727i	−0.848848	+	0.528637i	$0.822703\pi$
$594$		0			0
$595$	−986.125	+	672.207i	−0.0679449	+	0.0463156i
$596$		0			0
$597$		−	209.424i		−	0.0143570i
$598$		0			0
$599$	14852.3			1.01310			0.506551	−	0.862210i	$-0.330920\pi$
$599$	14852.3			1.01310			0.506551	+	0.862210i	$0.330920\pi$
$600$		0			0
$601$	−6958.91	−	6958.91i	−0.472313	−	0.472313i	0.430349	−	0.902662i	$-0.358390\pi$
$601$	−6958.91	−	6958.91i	−0.472313	−	0.472313i	−0.902662	+	0.430349i	$0.858390\pi$
$602$		0			0
$603$		−	11954.7i		−	0.807348i
$604$		0			0
$605$	−2640.31	−	2640.31i	−0.177428	−	0.177428i
$606$		0			0
$607$	2781.06	−	2781.06i	0.185964	−	0.185964i	−0.607985	−	0.793949i	$-0.708022\pi$
$607$	2781.06	−	2781.06i	0.185964	−	0.185964i	0.793949	+	0.607985i	$0.208022\pi$
$608$		0			0
$609$	5.05020	−	5.05020i	0.000336033	−	0.000336033i
$610$		0			0
$611$	5023.36			0.332608
$612$		0			0
$613$	3388.18			0.223242			0.111621	−	0.993751i	$-0.464396\pi$
$613$	3388.18			0.223242			0.111621	+	0.993751i	$0.464396\pi$
$614$		0			0
$615$	24.5972	−	24.5972i	0.00161277	−	0.00161277i
$616$		0			0
$617$	−8426.48	+	8426.48i	−0.549818	+	0.549818i	−0.926388	−	0.376570i	$-0.877103\pi$
$617$	−8426.48	+	8426.48i	−0.549818	+	0.549818i	0.376570	+	0.926388i	$0.377103\pi$
$618$		0			0
$619$	−5634.61	−	5634.61i	−0.365871	−	0.365871i	0.500098	−	0.865969i	$-0.333297\pi$
$619$	−5634.61	−	5634.61i	−0.365871	−	0.365871i	−0.865969	+	0.500098i	$0.833297\pi$
$620$		0			0
$621$			456.891i			0.0295240i
$622$		0			0
$623$	−5095.39	−	5095.39i	−0.327677	−	0.327677i
$624$		0			0
$625$	−12748.9			−0.815931
$626$		0			0
$627$			72.9864i			0.00464879i
$628$		0			0
$629$	4596.32	−	24280.9i	0.291363	−	1.53918i
$630$		0			0
$631$		−	15781.0i		−	0.995612i	−0.867288	−	0.497806i	$-0.834139\pi$
$631$		−	15781.0i		−	0.995612i	0.867288	−	0.497806i	$-0.165861\pi$
$632$		0			0
$633$	−56.6165			−0.00355498
$634$		0			0
$635$	277.631	+	277.631i	0.0173503	+	0.0173503i
$636$		0			0
$637$		−	5885.75i		−	0.366094i
$638$		0			0
$639$	10314.6	+	10314.6i	0.638562	+	0.638562i
$640$		0			0
$641$	−13468.8	+	13468.8i	−0.829930	+	0.829930i	−0.987507	−	0.157577i	$-0.949632\pi$
$641$	−13468.8	+	13468.8i	−0.829930	+	0.829930i	0.157577	+	0.987507i	$0.449632\pi$
$642$		0			0
$643$	18993.3	−	18993.3i	1.16489	−	1.16489i	0.181499	−	0.983391i	$-0.441905\pi$
$643$	18993.3	−	18993.3i	1.16489	−	1.16489i	0.983391	−	0.181499i	$-0.0580949\pi$
$644$		0			0
$645$	8.08108			0.000493321
$646$		0			0
$647$	−22573.9			−1.37167			−0.685835	−	0.727757i	$-0.740563\pi$
$647$	−22573.9			−1.37167			−0.685835	+	0.727757i	$0.740563\pi$
$648$		0			0
$649$	25347.1	−	25347.1i	1.53306	−	1.53306i
$650$		0			0
$651$	−55.5356	+	55.5356i	−0.00334349	+	0.00334349i
$652$		0			0
$653$	3162.80	+	3162.80i	0.189540	+	0.189540i	0.795497	−	0.605957i	$-0.207210\pi$
$653$	3162.80	+	3162.80i	0.189540	+	0.189540i	−0.605957	+	0.795497i	$0.707210\pi$
$654$		0			0
$655$		−	1140.15i		−	0.0680145i
$656$		0			0
$657$	−5139.24	−	5139.24i	−0.305176	−	0.305176i
$658$		0			0
$659$	−11439.0			−0.676174			−0.338087	−	0.941115i	$-0.609780\pi$
$659$	−11439.0			−0.676174			−0.338087	+	0.941115i	$0.609780\pi$
$660$		0			0
$661$		−	11381.6i		−	0.669730i	−0.942266	−	0.334865i	$-0.891309\pi$
$661$		−	11381.6i		−	0.669730i	0.942266	−	0.334865i	$-0.108691\pi$
$662$		0			0
$663$	−14.1756	+	74.8855i	−0.000830371	+	0.00438659i
$664$		0			0
$665$			425.829i			0.0248315i
$666$		0			0
$667$	−3108.55			−0.180455
$668$		0			0
$669$	−178.152	−	178.152i	−0.0102956	−	0.0102956i
$670$		0			0
$671$		−	11276.5i		−	0.648771i
$672$		0			0
$673$	−8821.52	−	8821.52i	−0.505267	−	0.505267i	0.407803	−	0.913070i	$-0.366295\pi$
$673$	−8821.52	−	8821.52i	−0.505267	−	0.505267i	−0.913070	+	0.407803i	$0.866295\pi$
$674$		0			0
$675$	−252.891	+	252.891i	−0.0144204	+	0.0144204i
$676$		0			0
$677$	−8725.07	+	8725.07i	−0.495320	+	0.495320i	−0.909978	−	0.414657i	$-0.863901\pi$
$677$	−8725.07	+	8725.07i	−0.495320	+	0.495320i	0.414657	+	0.909978i	$0.363901\pi$
$678$		0			0
$679$	−1881.71			−0.106352
$680$		0			0
$681$	198.670			0.0111792
$682$		0			0
$683$	−12158.3	+	12158.3i	−0.681146	+	0.681146i	−0.960258	−	0.279113i	$-0.909960\pi$
$683$	−12158.3	+	12158.3i	−0.681146	+	0.681146i	0.279113	+	0.960258i	$0.409960\pi$
$684$		0			0
$685$	−5449.86	+	5449.86i	−0.303983	+	0.303983i
$686$		0			0
$687$	−184.263	−	184.263i	−0.0102330	−	0.0102330i
$688$		0			0
$689$		−	1964.64i		−	0.108631i
$690$		0			0
$691$	2132.44	+	2132.44i	0.117398	+	0.117398i	0.763365	−	0.645967i	$-0.223546\pi$
$691$	2132.44	+	2132.44i	0.117398	+	0.117398i	−0.645967	+	0.763365i	$0.723546\pi$
$692$		0			0
$693$	8478.76			0.464764
$694$		0			0
$695$		−	6314.69i		−	0.344647i
$696$		0			0
$697$	15142.1	+	2866.36i	0.822882	+	0.155769i
$698$		0			0
$699$		−	161.465i		−	0.00873700i
$700$		0			0
$701$	−31729.0			−1.70954			−0.854770	−	0.519007i	$-0.826302\pi$
$701$	−31729.0			−1.70954			−0.854770	+	0.519007i	$0.826302\pi$
$702$		0			0
$703$	−6234.89	−	6234.89i	−0.334500	−	0.334500i
$704$		0			0
$705$			41.3184i			0.00220729i
$706$		0			0
$707$	−3467.19	−	3467.19i	−0.184437	−	0.184437i
$708$		0			0
$709$	18575.2	−	18575.2i	0.983930	−	0.983930i	−0.0159433	−	0.999873i	$-0.505075\pi$
$709$	18575.2	−	18575.2i	0.983930	−	0.983930i	0.999873	+	0.0159433i	$0.00507512\pi$
$710$		0			0
$711$	603.117	−	603.117i	0.0318124	−	0.0318124i
$712$		0			0
$713$	34183.9			1.79551
$714$		0			0
$715$	−2779.22			−0.145366
$716$		0			0
$717$	261.204	−	261.204i	0.0136051	−	0.0136051i
$718$		0			0
$719$	17278.6	−	17278.6i	0.896222	−	0.896222i	−0.0988778	−	0.995100i	$-0.531525\pi$
$719$	17278.6	−	17278.6i	0.896222	−	0.896222i	0.995100	+	0.0988778i	$0.0315253\pi$
$720$		0			0
$721$	−2287.84	−	2287.84i	−0.118174	−	0.118174i
$722$		0			0
$723$			188.691i			0.00970607i
$724$		0			0
$725$	−1720.59	−	1720.59i	−0.0881396	−	0.0881396i
$726$		0			0
$727$	−7209.98			−0.367818			−0.183909	−	0.982943i	$-0.558875\pi$
$727$	−7209.98			−0.367818			−0.183909	+	0.982943i	$0.558875\pi$
$728$		0			0
$729$		−	19669.0i		−	0.999290i
$730$		0			0
$731$	2016.51	+	2958.22i	0.102029	+	0.149677i
$732$		0			0
$733$			21640.2i			1.09045i	0.838290	+	0.545225i	$0.183556\pi$
$733$			21640.2i			1.09045i	−0.838290	+	0.545225i	$0.816444\pi$
$734$		0			0
$735$	48.4117			0.00242951
$736$		0			0
$737$	−16164.8	−	16164.8i	−0.807920	−	0.807920i
$738$		0			0
$739$			34704.0i			1.72748i	0.503940	+	0.863738i	$0.331883\pi$
$739$			34704.0i			1.72748i	−0.503940	+	0.863738i	$0.668117\pi$
$740$		0			0
$741$	19.2292	+	19.2292i	0.000953309	+	0.000953309i
$742$		0			0
$743$	−23978.2	+	23978.2i	−1.18395	+	1.18395i	−0.205241	+	0.978712i	$0.565798\pi$
$743$	−23978.2	+	23978.2i	−1.18395	+	1.18395i	−0.978712	+	0.205241i	$0.934202\pi$
$744$		0			0
$745$	−3343.30	+	3343.30i	−0.164415	+	0.164415i
$746$		0			0
$747$	−18072.4			−0.885186
$748$		0			0
$749$	7306.20			0.356426
$750$		0			0
$751$	431.344	−	431.344i	0.0209587	−	0.0209587i	−0.696550	−	0.717508i	$-0.745282\pi$
$751$	431.344	−	431.344i	0.0209587	−	0.0209587i	0.717508	+	0.696550i	$0.245282\pi$
$752$		0			0
$753$	88.9530	−	88.9530i	0.00430495	−	0.00430495i
$754$		0			0
$755$	−1304.11	−	1304.11i	−0.0628629	−	0.0628629i
$756$		0			0
$757$			11527.3i			0.553457i	0.960948	+	0.276729i	$0.0892503\pi$
$757$			11527.3i			0.553457i	−0.960948	+	0.276729i	$0.910750\pi$
$758$		0			0
$759$	308.880	+	308.880i	0.0147716	+	0.0147716i
$760$		0			0
$761$	35908.5			1.71049			0.855246	−	0.518223i	$-0.173406\pi$
$761$	35908.5			1.71049			0.855246	+	0.518223i	$0.173406\pi$
$762$		0			0
$763$		−	8196.19i		−	0.388889i
$764$		0			0
$765$	5203.66	+	985.040i	0.245933	+	0.0465545i
$766$		0			0
$767$		−	13356.0i		−	0.628758i
$768$		0			0
$769$	−4159.74			−0.195064			−0.0975320	−	0.995232i	$-0.531095\pi$
$769$	−4159.74			−0.195064			−0.0975320	+	0.995232i	$0.531095\pi$
$770$		0			0
$771$	196.968	+	196.968i	0.00920055	+	0.00920055i
$772$		0			0
$773$			38339.5i			1.78393i	0.452106	+	0.891964i	$0.350673\pi$
$773$			38339.5i			1.78393i	−0.452106	+	0.891964i	$0.649327\pi$
$774$		0			0
$775$	18920.9	+	18920.9i	0.876978	+	0.876978i
$776$		0			0
$777$	85.7348	−	85.7348i	0.00395845	−	0.00395845i
$778$		0			0
$779$	3888.21	−	3888.21i	0.178831	−	0.178831i
$780$		0			0
$781$	27894.4			1.27803
$782$		0			0
$783$	−63.3915			−0.00289327
$784$		0			0
$785$	3415.03	−	3415.03i	0.155271	−	0.155271i
$786$		0			0
$787$	−10975.5	+	10975.5i	−0.497123	+	0.497123i	−0.910541	−	0.413418i	$-0.864335\pi$
$787$	−10975.5	+	10975.5i	−0.497123	+	0.497123i	0.413418	+	0.910541i	$0.364335\pi$
$788$		0			0
$789$	−216.796	−	216.796i	−0.00978217	−	0.00978217i
$790$		0			0
$791$		−	1391.03i		−	0.0625276i
$792$		0			0
$793$	−2970.95	−	2970.95i	−0.133041	−	0.133041i
$794$		0			0
$795$	16.1597			0.000720912
$796$		0			0
$797$		−	483.686i		−	0.0214969i	−0.999942	−	0.0107484i	$-0.996579\pi$
$797$		−	483.686i		−	0.0214969i	0.999942	−	0.0107484i	$-0.00342140\pi$
$798$		0			0
$799$	−15125.3	+	10310.4i	−0.669706	+	0.456515i
$800$		0			0
$801$			31977.5i			1.41057i
$802$		0			0
$803$	−13898.3			−0.610785
$804$		0			0
$805$	1802.12	+	1802.12i	0.0789023	+	0.0789023i
$806$		0			0
$807$			112.035i			0.00488702i
$808$		0			0
$809$	−11349.9	−	11349.9i	−0.493252	−	0.493252i	0.416077	−	0.909329i	$-0.363405\pi$
$809$	−11349.9	−	11349.9i	−0.493252	−	0.493252i	−0.909329	+	0.416077i	$0.863405\pi$
$810$		0			0
$811$	−7111.36	+	7111.36i	−0.307908	+	0.307908i	−0.844098	−	0.536189i	$-0.819863\pi$
$811$	−7111.36	+	7111.36i	−0.307908	+	0.307908i	0.536189	+	0.844098i	$0.319863\pi$
$812$		0			0
$813$	−140.309	+	140.309i	−0.00605270	+	0.00605270i
$814$		0			0
$815$	6348.42			0.272854
$816$		0			0
$817$	1277.42			0.0547016
$818$		0			0
$819$	2233.84	−	2233.84i	0.0953072	−	0.0953072i
$820$		0			0
$821$	29059.7	−	29059.7i	1.23531	−	1.23531i	0.273415	−	0.961896i	$-0.411847\pi$
$821$	29059.7	−	29059.7i	1.23531	−	1.23531i	0.961896	−	0.273415i	$-0.0881532\pi$
$822$		0			0
$823$	−3018.11	−	3018.11i	−0.127831	−	0.127831i	0.640297	−	0.768128i	$-0.278811\pi$
$823$	−3018.11	−	3018.11i	−0.127831	−	0.127831i	−0.768128	+	0.640297i	$0.778811\pi$
$824$		0			0
$825$			341.932i			0.0144298i
$826$		0			0
$827$	9959.68	+	9959.68i	0.418781	+	0.418781i	0.884783	−	0.466002i	$-0.154306\pi$
$827$	9959.68	+	9959.68i	0.418781	+	0.418781i	−0.466002	+	0.884783i	$0.654306\pi$
$828$		0			0
$829$	−42024.2			−1.76063			−0.880314	−	0.474391i	$-0.842668\pi$
$829$	−42024.2			−1.76063			−0.880314	+	0.474391i	$0.842668\pi$
$830$		0			0
$831$			432.548i			0.0180565i
$832$		0			0
$833$	12080.4	+	17721.9i	0.502475	+	0.737129i
$834$		0			0
$835$			6872.51i			0.284830i
$836$		0			0
$837$	697.099			0.0287876
$838$		0			0
$839$	32650.7	+	32650.7i	1.34354	+	1.34354i	0.892512	+	0.451024i	$0.148941\pi$
$839$	32650.7	+	32650.7i	1.34354	+	1.34354i	0.451024	+	0.892512i	$0.351059\pi$
$840$		0			0
$841$			23957.7i			0.982316i
$842$		0			0
$843$	−180.652	−	180.652i	−0.00738076	−	0.00738076i
$844$		0			0
$845$	3615.72	−	3615.72i	0.147201	−	0.147201i
$846$		0			0
$847$	5739.14	−	5739.14i	0.232821	−	0.232821i
$848$		0			0
$849$	263.418			0.0106484
$850$		0			0
$851$	−52772.4			−2.12575
$852$		0			0
$853$	33363.7	−	33363.7i	1.33922	−	1.33922i	0.442397	−	0.896819i	$-0.354128\pi$
$853$	33363.7	−	33363.7i	1.33922	−	1.33922i	0.896819	−	0.442397i	$-0.145872\pi$
$854$		0			0
$855$	1336.20	−	1336.20i	0.0534470	−	0.0534470i
$856$		0			0
$857$	11067.4	+	11067.4i	0.441139	+	0.441139i	0.892395	−	0.451255i	$-0.149024\pi$
$857$	11067.4	+	11067.4i	0.441139	+	0.441139i	−0.451255	+	0.892395i	$0.649024\pi$
$858$		0			0
$859$			34645.2i			1.37611i	0.725658	+	0.688056i	$0.241536\pi$
$859$			34645.2i			1.37611i	−0.725658	+	0.688056i	$0.758464\pi$
$860$		0			0
$861$	53.4660	+	53.4660i	0.00211628	+	0.00211628i
$862$		0			0
$863$	28318.9			1.11702			0.558508	−	0.829499i	$-0.311374\pi$
$863$	28318.9			1.11702			0.558508	+	0.829499i	$0.311374\pi$
$864$		0			0
$865$			857.550i			0.0337082i
$866$		0			0
$867$	−111.019	−	254.575i	−0.00434878	−	0.00997211i
$868$		0			0
$869$		−	1631.04i		−	0.0636700i
$870$		0			0
$871$	−8517.63			−0.331354
$872$		0			0
$873$	5904.59	+	5904.59i	0.228912	+	0.228912i
$874$		0			0
$875$			4123.28i			0.159306i
$876$		0			0
$877$	9654.78	+	9654.78i	0.371743	+	0.371743i	0.868112	−	0.496369i	$-0.165334\pi$
$877$	9654.78	+	9654.78i	0.371743	+	0.371743i	−0.496369	+	0.868112i	$0.665334\pi$
$878$		0			0
$879$	248.712	−	248.712i	0.00954363	−	0.00954363i
$880$		0			0
$881$	4554.04	−	4554.04i	0.174154	−	0.174154i	−0.614648	−	0.788802i	$-0.710702\pi$
$881$	4554.04	−	4554.04i	0.174154	−	0.174154i	0.788802	+	0.614648i	$0.210702\pi$
$882$		0			0
$883$	−35594.1			−1.35655			−0.678277	−	0.734807i	$-0.737273\pi$
$883$	−35594.1			−1.35655			−0.678277	+	0.734807i	$0.737273\pi$
$884$		0			0
$885$	109.856			0.00417264
$886$		0			0
$887$	22055.1	−	22055.1i	0.834881	−	0.834881i	−0.153299	−	0.988180i	$-0.548990\pi$
$887$	22055.1	−	22055.1i	0.834881	−	0.834881i	0.988180	+	0.153299i	$0.0489898\pi$
$888$		0			0
$889$	−603.477	+	603.477i	−0.0227671	+	0.0227671i
$890$		0			0
$891$	−26602.3	−	26602.3i	−1.00023	−	1.00023i
$892$		0			0
$893$			6531.41i			0.244754i
$894$		0			0
$895$	5426.24	+	5426.24i	0.202658	+	0.202658i
$896$		0			0
$897$	162.757			0.00605830
$898$		0			0
$899$			4742.85i			0.175954i
$900$		0			0
$901$	4032.41	+	5915.53i	0.149100	+	0.218729i
$902$		0			0
$903$			17.5655i			0.000647335i
$904$		0			0
$905$	−4343.30			−0.159532
$906$		0			0
$907$	−13912.2	−	13912.2i	−0.509313	−	0.509313i	0.405003	−	0.914315i	$-0.367271\pi$
$907$	−13912.2	−	13912.2i	−0.509313	−	0.509313i	−0.914315	+	0.405003i	$0.867271\pi$
$908$		0			0
$909$			21759.3i			0.793960i
$910$		0			0
$911$	25127.5	+	25127.5i	0.913843	+	0.913843i	0.996572	−	0.0827295i	$-0.0263638\pi$
$911$	25127.5	+	25127.5i	0.913843	+	0.913843i	−0.0827295	+	0.996572i	$0.526364\pi$
$912$		0			0
$913$	−24437.0	+	24437.0i	−0.885813	+	0.885813i
$914$		0			0
$915$	24.4367	−	24.4367i	0.000882901	−	0.000882901i
$916$		0			0
$917$	2478.31			0.0892485
$918$		0			0
$919$	378.693			0.0135930			0.00679648	−	0.999977i	$-0.497837\pi$
$919$	378.693			0.0135930			0.00679648	+	0.999977i	$0.497837\pi$
$920$		0			0
$921$	19.1137	−	19.1137i	0.000683842	−	0.000683842i
$922$		0			0
$923$	7349.14	−	7349.14i	0.262080	−	0.262080i
$924$		0			0
$925$	−29209.7	−	29209.7i	−1.03828	−	1.03828i
$926$		0			0
$927$			14358.0i			0.508714i
$928$		0			0
$929$	−9344.29	−	9344.29i	−0.330007	−	0.330007i	0.522582	−	0.852589i	$-0.324969\pi$
$929$	−9344.29	−	9344.29i	−0.330007	−	0.330007i	−0.852589	+	0.522582i	$0.824969\pi$
$930$		0			0
$931$	7652.68			0.269395
$932$		0			0
$933$			406.808i			0.0142747i
$934$		0			0
$935$	8368.21	−	5704.31i	0.292695	−	0.199520i
$936$		0			0
$937$		−	34950.5i		−	1.21855i	−0.792959	−	0.609275i	$-0.791460\pi$
$937$		−	34950.5i		−	1.21855i	0.792959	−	0.609275i	$-0.208540\pi$
$938$		0			0
$939$	526.730			0.0183058
$940$		0			0
$941$	−9450.53	−	9450.53i	−0.327395	−	0.327395i	0.524200	−	0.851595i	$-0.324364\pi$
$941$	−9450.53	−	9450.53i	−0.327395	−	0.327395i	−0.851595	+	0.524200i	$0.824364\pi$
$942$		0			0
$943$		−	32910.0i		−	1.13648i
$944$		0			0
$945$	36.7499	+	36.7499i	0.00126505	+	0.00126505i
$946$		0			0
$947$	18549.3	−	18549.3i	0.636506	−	0.636506i	−0.313186	−	0.949692i	$-0.601396\pi$
$947$	18549.3	−	18549.3i	0.636506	−	0.636506i	0.949692	+	0.313186i	$0.101396\pi$
$948$		0			0
$949$	−3661.68	+	3661.68i	−0.125251	+	0.125251i
$950$		0			0
$951$	−75.1388			−0.00256208
$952$		0			0
$953$	−19074.4			−0.648352			−0.324176	−	0.945997i	$-0.605087\pi$
$953$	−19074.4			−0.648352			−0.324176	+	0.945997i	$0.605087\pi$
$954$		0			0
$955$	−7641.92	+	7641.92i	−0.258939	+	0.258939i
$956$		0			0
$957$	−42.8557	+	42.8557i	−0.00144757	+	0.00144757i
$958$		0			0
$959$	−11846.2	−	11846.2i	−0.398887	−	0.398887i
$960$		0			0
$961$		−	22364.8i		−	0.750724i
$962$		0			0
$963$	−22926.0	−	22926.0i	−0.767166	−	0.767166i
$964$		0			0
$965$	−4130.94			−0.137803
$966$		0			0
$967$		−	6142.31i		−	0.204264i	−0.994771	−	0.102132i	$-0.967434\pi$
$967$		−	6142.31i		−	0.204264i	0.994771	−	0.102132i	$-0.0325664\pi$
$968$		0			0
$969$	−97.3666	−	18.4312i	−0.00322793	−	0.000611039i
$970$		0			0
$971$		−	56958.3i		−	1.88247i	−0.337750	−	0.941236i	$-0.609666\pi$
$971$		−	56958.3i		−	1.88247i	0.337750	−	0.941236i	$-0.390334\pi$
$972$		0			0
$973$	13726.0			0.452246
$974$		0			0
$975$	90.0863	+	90.0863i	0.00295905	+	0.00295905i
$976$		0			0
$977$			11185.4i			0.366277i	0.983087	+	0.183138i	$0.0586257\pi$
$977$			11185.4i			0.366277i	−0.983087	+	0.183138i	$0.941374\pi$
$978$		0			0
$979$	43239.2	+	43239.2i	1.41157	+	1.41157i
$980$		0			0
$981$	−25718.7	+	25718.7i	−0.837040	+	0.837040i
$982$		0			0
$983$	20875.7	−	20875.7i	0.677348	−	0.677348i	−0.282052	−	0.959399i	$-0.591015\pi$
$983$	20875.7	−	20875.7i	0.677348	−	0.677348i	0.959399	+	0.282052i	$0.0910150\pi$
$984$		0			0
$985$	14970.3			0.484256
$986$		0			0
$987$	−89.8121			−0.00289641
$988$		0			0
$989$	5406.06	−	5406.06i	0.173815	−	0.173815i
$990$		0			0
$991$	30805.3	−	30805.3i	0.987450	−	0.987450i	−0.0124723	−	0.999922i	$-0.503970\pi$
$991$	30805.3	−	30805.3i	0.987450	−	0.987450i	0.999922	+	0.0124723i	$0.00397017\pi$
$992$		0			0
$993$	−414.620	−	414.620i	−0.0132503	−	0.0132503i
$994$		0			0
$995$			10368.6i			0.330358i
$996$		0			0
$997$	−28690.5	−	28690.5i	−0.911370	−	0.911370i	0.0850098	−	0.996380i	$-0.472908\pi$
$997$	−28690.5	−	28690.5i	−0.911370	−	0.911370i	−0.996380	+	0.0850098i	$0.972908\pi$
$998$		0			0
$999$	−1076.17			−0.0340825

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.k.b.89.4	yes	14
4.3	odd	2		272.4.o.f.225.4		14
17.8	even	8		2312.4.a.l.1.7		14
17.9	even	8		2312.4.a.l.1.8		14
17.13	even	4	inner	136.4.k.b.81.4	✓	14
68.47	odd	4		272.4.o.f.81.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.k.b.81.4	✓	14	17.13	even	4	inner
136.4.k.b.89.4	yes	14	1.1	even	1	trivial
272.4.o.f.81.4		14	68.47	odd	4
272.4.o.f.225.4		14	4.3	odd	2
2312.4.a.l.1.7		14	17.8	even	8
2312.4.a.l.1.8		14	17.9	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)

\(f(q)\)	\(=\)	\(q+(0.0399724 - 0.0399724i) q^{3} +(-1.97903 + 1.97903i) q^{5} +(-4.30175 - 4.30175i) q^{7} +26.9968i q^{9} +O(q^{10})\)	\(q+(0.0399724 - 0.0399724i) q^{3} +(-1.97903 + 1.97903i) q^{5} +(-4.30175 - 4.30175i) q^{7} +26.9968i q^{9} +(36.5044 + 36.5044i) q^{11} +19.2351 q^{13} +0.158213i q^{15} +(-57.9167 + 39.4798i) q^{17} +25.0096i q^{19} -0.343902 q^{21} +(105.841 + 105.841i) q^{23} +117.167i q^{25} +(2.15838 + 2.15838i) q^{27} +(-14.6850 + 14.6850i) q^{29} +(161.487 - 161.487i) q^{31} +2.91833 q^{33} +17.0266 q^{35} +(-249.300 + 249.300i) q^{37} +(0.768872 - 0.768872i) q^{39} +(-155.469 - 155.469i) q^{41} -51.0771i q^{43} +(-53.4276 - 53.4276i) q^{45} +261.156 q^{47} -305.990i q^{49} +(-0.736967 + 3.89317i) q^{51} -102.139i q^{53} -144.487 q^{55} +(0.999693 + 0.999693i) q^{57} -694.356i q^{59} +(-154.454 - 154.454i) q^{61} +(116.133 - 116.133i) q^{63} +(-38.0669 + 38.0669i) q^{65} -442.817 q^{67} +8.46145 q^{69} +(382.069 - 382.069i) q^{71} +(-190.365 + 190.365i) q^{73} +(4.68344 + 4.68344i) q^{75} -314.065i q^{77} +(-22.3403 - 22.3403i) q^{79} -728.741 q^{81} +669.427i q^{83} +(36.4873 - 192.751i) q^{85} +1.17399i q^{87} +1184.49 q^{89} +(-82.7445 - 82.7445i) q^{91} -12.9100i q^{93} +(-49.4948 - 49.4948i) q^{95} +(218.714 - 218.714i) q^{97} +(-985.502 + 985.502i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 6 q^{3} + 6 q^{5} + 10 q^{7}+O(q^{10}) \) 14 * q + 6 * q^3 + 6 * q^5 + 10 * q^7	\( 14 q + 6 q^{3} + 6 q^{5} + 10 q^{7} - 66 q^{11} - 124 q^{13} + 130 q^{17} - 148 q^{21} - 162 q^{23} - 204 q^{27} + 158 q^{29} - 350 q^{31} + 116 q^{33} + 236 q^{35} + 582 q^{37} - 320 q^{39} + 878 q^{41} - 26 q^{45} - 448 q^{47} - 590 q^{51} + 1460 q^{55} + 292 q^{57} - 1130 q^{61} + 114 q^{63} + 20 q^{65} - 64 q^{67} + 2076 q^{69} - 3274 q^{71} - 1426 q^{73} + 946 q^{75} + 1718 q^{79} + 166 q^{81} - 2018 q^{85} + 476 q^{89} + 2128 q^{91} - 2444 q^{95} + 1926 q^{97} + 3870 q^{99}+O(q^{100}) \) 14 * q + 6 * q^3 + 6 * q^5 + 10 * q^7 - 66 * q^11 - 124 * q^13 + 130 * q^17 - 148 * q^21 - 162 * q^23 - 204 * q^27 + 158 * q^29 - 350 * q^31 + 116 * q^33 + 236 * q^35 + 582 * q^37 - 320 * q^39 + 878 * q^41 - 26 * q^45 - 448 * q^47 - 590 * q^51 + 1460 * q^55 + 292 * q^57 - 1130 * q^61 + 114 * q^63 + 20 * q^65 - 64 * q^67 + 2076 * q^69 - 3274 * q^71 - 1426 * q^73 + 946 * q^75 + 1718 * q^79 + 166 * q^81 - 2018 * q^85 + 476 * q^89 + 2128 * q^91 - 2444 * q^95 + 1926 * q^97 + 3870 * q^99

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