LMFDB - Embedded newform 684.3.g.d.343.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(343,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("684.343");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			343.5
Character	$\chi$	$=$	684.343
Dual form			684.3.g.d.343.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58671 - 1.21751i) q^{2} +(1.03532 + 3.86369i) q^{4} +1.46825 q^{5} +6.38949i q^{7} +(3.06136 - 7.39108i) q^{8} +O(q^{10})$	\(q+(-1.58671 - 1.21751i) q^{2} +(1.03532 + 3.86369i) q^{4} +1.46825 q^{5} +6.38949i q^{7} +(3.06136 - 7.39108i) q^{8} +(-2.32969 - 1.78762i) q^{10} +9.33972i q^{11} -22.7114 q^{13} +(7.77929 - 10.1383i) q^{14} +(-13.8562 + 8.00028i) q^{16} -5.17560 q^{17} +4.35890i q^{19} +(1.52010 + 5.67287i) q^{20} +(11.3712 - 14.8194i) q^{22} -37.0351i q^{23} -22.8442 q^{25} +(36.0364 + 27.6514i) q^{26} +(-24.6870 + 6.61513i) q^{28} +23.0104 q^{29} -19.9233i q^{31} +(31.7263 + 4.17604i) q^{32} +(8.21218 + 6.30136i) q^{34} +9.38136i q^{35} +24.3546 q^{37} +(5.30702 - 6.91632i) q^{38} +(4.49483 - 10.8520i) q^{40} -57.3392 q^{41} -78.8346i q^{43} +(-36.0858 + 9.66955i) q^{44} +(-45.0908 + 58.7641i) q^{46} -50.2690i q^{47} +8.17447 q^{49} +(36.2473 + 27.8132i) q^{50} +(-23.5134 - 87.7497i) q^{52} +82.4964 q^{53} +13.7130i q^{55} +(47.2252 + 19.5605i) q^{56} +(-36.5109 - 28.0155i) q^{58} -86.4304i q^{59} -114.416 q^{61} +(-24.2570 + 31.6126i) q^{62} +(-45.2562 - 45.2535i) q^{64} -33.3459 q^{65} +64.7258i q^{67} +(-5.35837 - 19.9969i) q^{68} +(11.4219 - 14.8855i) q^{70} +25.1687i q^{71} -58.1281 q^{73} +(-38.6437 - 29.6520i) q^{74} +(-16.8414 + 4.51283i) q^{76} -59.6760 q^{77} +47.6673i q^{79} +(-20.3444 + 11.7464i) q^{80} +(90.9809 + 69.8114i) q^{82} -51.5116i q^{83} -7.59907 q^{85} +(-95.9823 + 125.088i) q^{86} +(69.0306 + 28.5922i) q^{88} +4.37527 q^{89} -145.114i q^{91} +(143.092 - 38.3430i) q^{92} +(-61.2032 + 79.7624i) q^{94} +6.39995i q^{95} +16.1637 q^{97} +(-12.9705 - 9.95254i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 12 q^{4}+O(q^{10}) $ 36 * q - 12 * q^4	$ 36 q - 12 q^{4} + 8 q^{10} + 24 q^{13} - 92 q^{16} - 60 q^{22} + 44 q^{25} - 48 q^{28} - 148 q^{34} + 200 q^{37} + 180 q^{40} + 140 q^{46} - 332 q^{49} + 60 q^{52} - 64 q^{58} + 40 q^{61} + 60 q^{64} + 36 q^{70} - 200 q^{73} + 312 q^{82} + 16 q^{85} + 104 q^{88} + 184 q^{94} + 280 q^{97}+O(q^{100}) $ 36 * q - 12 * q^4 + 8 * q^10 + 24 * q^13 - 92 * q^16 - 60 * q^22 + 44 * q^25 - 48 * q^28 - 148 * q^34 + 200 * q^37 + 180 * q^40 + 140 * q^46 - 332 * q^49 + 60 * q^52 - 64 * q^58 + 40 * q^61 + 60 * q^64 + 36 * q^70 - 200 * q^73 + 312 * q^82 + 16 * q^85 + 104 * q^88 + 184 * q^94 + 280 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.58671	−	1.21751i	−0.793356	−	0.608757i
$2$	−1.58671	−	1.21751i	−0.793356	−	0.608757i
$3$		0			0
$3$		0			0
$4$	1.03532	+	3.86369i	0.258829	+	0.965923i
$5$	1.46825			0.293650			0.146825	−	0.989162i	$-0.453095\pi$
$5$	1.46825			0.293650			0.146825	+	0.989162i	$0.453095\pi$
$6$		0			0
$7$			6.38949i			0.912784i	0.889779	+	0.456392i	$0.150858\pi$
$7$			6.38949i			0.912784i	−0.889779	+	0.456392i	$0.849142\pi$
$8$	3.06136	−	7.39108i	0.382669	−	0.923885i
$9$		0			0
$10$	−2.32969	−	1.78762i	−0.232969	−	0.178762i
$11$			9.33972i			0.849065i	0.905413	+	0.424533i	$0.139562\pi$
$11$			9.33972i			0.849065i	−0.905413	+	0.424533i	$0.860438\pi$
$12$		0			0
$13$	−22.7114			−1.74703			−0.873514	−	0.486800i	$-0.838164\pi$
$13$	−22.7114			−1.74703			−0.873514	+	0.486800i	$0.838164\pi$
$14$	7.77929	−	10.1383i	0.555664	−	0.724163i
$15$		0			0
$16$	−13.8562	+	8.00028i	−0.866015	+	0.500018i
$17$	−5.17560			−0.304447			−0.152223	−	0.988346i	$-0.548643\pi$
$17$	−5.17560			−0.304447			−0.152223	+	0.988346i	$0.548643\pi$
$18$		0			0
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	1.52010	+	5.67287i	0.0760051	+	0.283643i
$21$		0			0
$22$	11.3712	−	14.8194i	0.516875	−	0.673611i
$23$		−	37.0351i		−	1.61022i	−0.593123	−	0.805112i	$-0.702105\pi$
$23$		−	37.0351i		−	1.61022i	0.593123	−	0.805112i	$-0.297895\pi$
$24$		0			0
$25$	−22.8442			−0.913770
$26$	36.0364	+	27.6514i	1.38602	+	1.06352i
$27$		0			0
$28$	−24.6870	+	6.61513i	−0.881679	+	0.236255i
$29$	23.0104			0.793461			0.396731	−	0.917935i	$-0.370145\pi$
$29$	23.0104			0.793461			0.396731	+	0.917935i	$0.370145\pi$
$30$		0			0
$31$		−	19.9233i		−	0.642688i	−0.946962	−	0.321344i	$-0.895865\pi$
$31$		−	19.9233i		−	0.642688i	0.946962	−	0.321344i	$-0.104135\pi$
$32$	31.7263	+	4.17604i	0.991448	+	0.130501i
$33$		0			0
$34$	8.21218	+	6.30136i	0.241535	+	0.185334i
$35$			9.38136i			0.268039i
$36$		0			0
$37$	24.3546			0.658232			0.329116	−	0.944290i	$-0.393249\pi$
$37$	24.3546			0.658232			0.329116	+	0.944290i	$0.393249\pi$
$38$	5.30702	−	6.91632i	0.139659	−	0.182008i
$39$		0			0
$40$	4.49483	−	10.8520i	0.112371	−	0.271299i
$41$	−57.3392			−1.39852			−0.699259	−	0.714868i	$-0.746487\pi$
$41$	−57.3392			−1.39852			−0.699259	+	0.714868i	$0.746487\pi$
$42$		0			0
$43$		−	78.8346i		−	1.83336i	−0.399618	−	0.916682i	$-0.630857\pi$
$43$		−	78.8346i		−	1.83336i	0.399618	−	0.916682i	$-0.369143\pi$
$44$	−36.0858	+	9.66955i	−0.820132	+	0.219763i
$45$		0			0
$46$	−45.0908	+	58.7641i	−0.980236	+	1.27748i
$47$		−	50.2690i		−	1.06955i	−0.844994	−	0.534776i	$-0.820396\pi$
$47$		−	50.2690i		−	1.06955i	0.844994	−	0.534776i	$-0.179604\pi$
$48$		0			0
$49$	8.17447			0.166826
$50$	36.2473	+	27.8132i	0.724945	+	0.556264i
$51$		0			0
$52$	−23.5134	−	87.7497i	−0.452181	−	1.68749i
$53$	82.4964			1.55654			0.778268	−	0.627932i	$-0.216098\pi$
$53$	82.4964			1.55654			0.778268	+	0.627932i	$0.216098\pi$
$54$		0			0
$55$			13.7130i			0.249328i
$56$	47.2252	+	19.5605i	0.843307	+	0.349294i
$57$		0			0
$58$	−36.5109	−	28.0155i	−0.629498	−	0.483025i
$59$		−	86.4304i		−	1.46492i	−0.680809	−	0.732461i	$-0.738372\pi$
$59$		−	86.4304i		−	1.46492i	0.680809	−	0.732461i	$-0.261628\pi$
$60$		0			0
$61$	−114.416			−1.87567			−0.937836	−	0.347080i	$-0.887173\pi$
$61$	−114.416			−1.87567			−0.937836	+	0.347080i	$0.887173\pi$
$62$	−24.2570	+	31.6126i	−0.391241	+	0.509881i
$63$		0			0
$64$	−45.2562	−	45.2535i	−0.707128	−	0.707085i
$65$	−33.3459			−0.513015
$66$		0			0
$67$			64.7258i			0.966057i	0.875605	+	0.483029i	$0.160463\pi$
$67$			64.7258i			0.966057i	−0.875605	+	0.483029i	$0.839537\pi$
$68$	−5.35837	−	19.9969i	−0.0787996	−	0.294072i
$69$		0			0
$70$	11.4219	−	14.8855i	0.163171	−	0.212650i
$71$			25.1687i			0.354489i	0.984167	+	0.177245i	$0.0567184\pi$
$71$			25.1687i			0.354489i	−0.984167	+	0.177245i	$0.943282\pi$
$72$		0			0
$73$	−58.1281			−0.796275			−0.398137	−	0.917326i	$-0.630343\pi$
$73$	−58.1281			−0.796275			−0.398137	+	0.917326i	$0.630343\pi$
$74$	−38.6437	−	29.6520i	−0.522212	−	0.400703i
$75$		0			0
$76$	−16.8414	+	4.51283i	−0.221598	+	0.0593794i
$77$	−59.6760			−0.775013
$78$		0			0
$79$			47.6673i			0.603383i	0.953406	+	0.301692i	$0.0975513\pi$
$79$			47.6673i			0.603383i	−0.953406	+	0.301692i	$0.902449\pi$
$80$	−20.3444	+	11.7464i	−0.254305	+	0.146830i
$81$		0			0
$82$	90.9809	+	69.8114i	1.10952	+	0.851358i
$83$		−	51.5116i		−	0.620622i	−0.950635	−	0.310311i	$-0.899567\pi$
$83$		−	51.5116i		−	0.620622i	0.950635	−	0.310311i	$-0.100433\pi$
$84$		0			0
$85$	−7.59907			−0.0894008
$86$	−95.9823	+	125.088i	−1.11607	+	1.45451i
$87$		0			0
$88$	69.0306	+	28.5922i	0.784439	+	0.324911i
$89$	4.37527			0.0491603			0.0245801	−	0.999698i	$-0.492175\pi$
$89$	4.37527			0.0491603			0.0245801	+	0.999698i	$0.492175\pi$
$90$		0			0
$91$		−	145.114i		−	1.59466i
$92$	143.092	−	38.3430i	1.55535	−	0.416772i
$93$		0			0
$94$	−61.2032	+	79.7624i	−0.651098	+	0.848536i
$95$			6.39995i			0.0673679i
$96$		0			0
$97$	16.1637			0.166636			0.0833178	−	0.996523i	$-0.473448\pi$
$97$	16.1637			0.166636			0.0833178	+	0.996523i	$0.473448\pi$
$98$	−12.9705	−	9.95254i	−0.132352	−	0.101556i
$99$		0			0
$100$	−23.6510	−	88.2631i	−0.236510	−	0.882631i
$101$	−188.996			−1.87124			−0.935621	−	0.353005i	$-0.885160\pi$
$101$	−188.996			−1.87124			−0.935621	+	0.353005i	$0.885160\pi$
$102$		0			0
$103$			124.907i			1.21268i	0.795204	+	0.606342i	$0.207364\pi$
$103$			124.907i			1.21268i	−0.795204	+	0.606342i	$0.792636\pi$
$104$	−69.5275	+	167.862i	−0.668534	+	1.61405i
$105$		0			0
$106$	−130.898	−	100.441i	−1.23489	−	0.947553i
$107$		−	36.4119i		−	0.340298i	−0.985418	−	0.170149i	$-0.945575\pi$
$107$		−	36.4119i		−	0.340298i	0.985418	−	0.170149i	$-0.0544250\pi$
$108$		0			0
$109$	−6.16177			−0.0565300			−0.0282650	−	0.999600i	$-0.508998\pi$
$109$	−6.16177			−0.0565300			−0.0282650	+	0.999600i	$0.508998\pi$
$110$	16.6958	−	21.7587i	0.151780	−	0.197806i
$111$		0			0
$112$	−51.1177	−	88.5343i	−0.456408	−	0.790485i
$113$	−132.916			−1.17625			−0.588123	−	0.808772i	$-0.700133\pi$
$113$	−132.916			−1.17625			−0.588123	+	0.808772i	$0.700133\pi$
$114$		0			0
$115$		−	54.3768i		−	0.472842i
$116$	23.8230	+	88.9050i	0.205371	+	0.766423i
$117$		0			0
$118$	−105.230	+	137.140i	−0.891782	+	1.16221i
$119$		−	33.0694i		−	0.277894i
$120$		0			0
$121$	33.7697			0.279088
$122$	181.545	+	139.303i	1.48808	+	1.14183i
$123$		0			0
$124$	76.9777	−	20.6269i	0.620788	−	0.166346i
$125$	−70.2473			−0.561978
$126$		0			0
$127$			79.3189i			0.624558i	0.949990	+	0.312279i	$0.101092\pi$
$127$			79.3189i			0.624558i	−0.949990	+	0.312279i	$0.898908\pi$
$128$	16.7118	+	126.904i	0.130561	+	0.991440i
$129$		0			0
$130$	52.9104	+	40.5992i	0.407003	+	0.312301i
$131$			20.4646i			0.156218i	0.996945	+	0.0781091i	$0.0248882\pi$
$131$			20.4646i			0.156218i	−0.996945	+	0.0781091i	$0.975112\pi$
$132$		0			0
$133$	−27.8511			−0.209407
$134$	78.8046	−	102.701i	0.588094	−	0.766428i
$135$		0			0
$136$	−15.8443	+	38.2533i	−0.116502	+	0.281274i
$137$	−241.403			−1.76206			−0.881032	−	0.473057i	$-0.843151\pi$
$137$	−241.403			−1.76206			−0.881032	+	0.473057i	$0.843151\pi$
$138$		0			0
$139$		−	108.101i		−	0.777703i	−0.921300	−	0.388852i	$-0.872872\pi$
$139$		−	108.101i		−	0.777703i	0.921300	−	0.388852i	$-0.127128\pi$
$140$	−36.2467	+	9.71267i	−0.258905	+	0.0693762i
$141$		0			0
$142$	30.6433	−	39.9355i	0.215798	−	0.281236i
$143$		−	212.118i		−	1.48334i
$144$		0			0
$145$	33.7850			0.233000
$146$	92.2325	+	70.7718i	0.631730	+	0.484738i
$147$		0			0
$148$	25.2147	+	94.0986i	0.170369	+	0.635801i
$149$	−211.062			−1.41652			−0.708262	−	0.705950i	$-0.750520\pi$
$149$	−211.062			−1.41652			−0.708262	+	0.705950i	$0.750520\pi$
$150$		0			0
$151$			122.207i			0.809318i	0.914468	+	0.404659i	$0.132610\pi$
$151$			122.207i			0.809318i	−0.914468	+	0.404659i	$0.867390\pi$
$152$	32.2170	+	13.3441i	0.211954	+	0.0877904i
$153$		0			0
$154$	94.6887	+	72.6564i	0.614861	+	0.471795i
$155$		−	29.2524i		−	0.188725i
$156$		0			0
$157$	−163.540			−1.04165			−0.520827	−	0.853662i	$-0.674376\pi$
$157$	−163.540			−1.04165			−0.520827	+	0.853662i	$0.674376\pi$
$158$	58.0356	−	75.6343i	0.367314	−	0.478698i
$159$		0			0
$160$	46.5822	+	6.13146i	0.291139	+	0.0383216i
$161$	236.636			1.46979
$162$		0			0
$163$			79.0594i			0.485027i	0.970148	+	0.242514i	$0.0779719\pi$
$163$			79.0594i			0.485027i	−0.970148	+	0.242514i	$0.922028\pi$
$164$	−59.3642	−	221.541i	−0.361977	−	1.35086i
$165$		0			0
$166$	−62.7162	+	81.7342i	−0.377808	+	0.492374i
$167$		−	266.850i		−	1.59790i	−0.601395	−	0.798952i	$-0.705388\pi$
$167$		−	266.850i		−	1.59790i	0.601395	−	0.798952i	$-0.294612\pi$
$168$		0			0
$169$	346.806			2.05210
$170$	12.0575	+	9.25198i	0.0709267	+	0.0544234i
$171$		0			0
$172$	304.593	−	81.6187i	1.77089	−	0.474527i
$173$	231.160			1.33618			0.668092	−	0.744079i	$-0.267111\pi$
$173$	231.160			1.33618			0.668092	+	0.744079i	$0.267111\pi$
$174$		0			0
$175$		−	145.963i		−	0.834074i
$176$	−74.7203	−	129.413i	−0.424547	−	0.735303i
$177$		0			0
$178$	−6.94229	−	5.32695i	−0.0390016	−	0.0299267i
$179$			25.6269i			0.143167i	0.997435	+	0.0715834i	$0.0228052\pi$
$179$			25.6269i			0.143167i	−0.997435	+	0.0715834i	$0.977195\pi$
$180$		0			0
$181$	140.431			0.775859			0.387930	−	0.921689i	$-0.373190\pi$
$181$	140.431			0.775859			0.387930	+	0.921689i	$0.373190\pi$
$182$	−176.678	+	230.254i	−0.970760	+	1.26513i
$183$		0			0
$184$	−273.730	−	113.378i	−1.48766	−	0.616183i
$185$	35.7586			0.193290
$186$		0			0
$187$		−	48.3386i		−	0.258495i
$188$	194.224	−	52.0442i	1.03311	−	0.276831i
$189$		0			0
$190$	7.79204	−	10.1549i	0.0410107	−	0.0534468i
$191$			342.544i			1.79342i	0.442615	+	0.896712i	$0.354051\pi$
$191$			342.544i			1.79342i	−0.442615	+	0.896712i	$0.645949\pi$
$192$		0			0
$193$	148.829			0.771134			0.385567	−	0.922680i	$-0.374006\pi$
$193$	148.829			0.771134			0.385567	+	0.922680i	$0.374006\pi$
$194$	−25.6471	−	19.6795i	−0.132201	−	0.101441i
$195$		0			0
$196$	8.46315	+	31.5836i	0.0431793	+	0.161141i
$197$	−16.3370			−0.0829288			−0.0414644	−	0.999140i	$-0.513202\pi$
$197$	−16.3370			−0.0829288			−0.0414644	+	0.999140i	$0.513202\pi$
$198$		0			0
$199$		−	23.7453i		−	0.119323i	−0.998219	−	0.0596616i	$-0.980998\pi$
$199$		−	23.7453i		−	0.119323i	0.998219	−	0.0596616i	$-0.0190022\pi$
$200$	−69.9343	+	168.844i	−0.349672	+	0.844218i
$201$		0			0
$202$	299.882	+	230.105i	1.48456	+	1.13913i
$203$			147.024i			0.724259i
$204$		0			0
$205$	−84.1883			−0.410675
$206$	152.076	−	198.191i	0.738231	−	0.962091i
$207$		0			0
$208$	314.694	−	181.697i	1.51295	−	0.873544i
$209$	−40.7109			−0.194789
$210$		0			0
$211$			210.424i			0.997270i	0.866812	+	0.498635i	$0.166165\pi$
$211$			210.424i			0.997270i	−0.866812	+	0.498635i	$0.833835\pi$
$212$	85.4098	+	318.741i	0.402876	+	1.50349i
$213$		0			0
$214$	−44.3321	+	57.7753i	−0.207159	+	0.269978i
$215$		−	115.749i		−	0.538367i
$216$		0			0
$217$	127.300			0.586636
$218$	9.77695	+	7.50204i	0.0448484	+	0.0344130i
$219$		0			0
$220$	−52.9830	+	14.1973i	−0.240832	+	0.0645333i
$221$	117.545			0.531877
$222$		0			0
$223$		−	217.878i		−	0.977031i	−0.872555	−	0.488515i	$-0.837539\pi$
$223$		−	217.878i		−	0.977031i	0.872555	−	0.488515i	$-0.162461\pi$
$224$	−26.6827	+	202.715i	−0.119119	+	0.904978i
$225$		0			0
$226$	210.899	+	161.827i	0.933182	+	0.716048i
$227$		−	219.138i		−	0.965364i	−0.875796	−	0.482682i	$-0.839663\pi$
$227$		−	219.138i		−	0.965364i	0.875796	−	0.482682i	$-0.160337\pi$
$228$		0			0
$229$	5.20028			0.0227087			0.0113543	−	0.999936i	$-0.496386\pi$
$229$	5.20028			0.0227087			0.0113543	+	0.999936i	$0.496386\pi$
$230$	−66.2046	+	86.2804i	−0.287846	+	0.375132i
$231$		0			0
$232$	70.4429	−	170.072i	0.303633	−	0.733067i
$233$	254.277			1.09132			0.545660	−	0.838007i	$-0.316279\pi$
$233$	254.277			1.09132			0.545660	+	0.838007i	$0.316279\pi$
$234$		0			0
$235$		−	73.8074i		−	0.314074i
$236$	333.941	−	89.4827i	1.41500	−	0.379164i
$237$		0			0
$238$	−40.2625	+	52.4716i	−0.169170	+	0.220469i
$239$		−	56.1364i		−	0.234880i	−0.993080	−	0.117440i	$-0.962531\pi$
$239$		−	56.1364i		−	0.234880i	0.993080	−	0.117440i	$-0.0374688\pi$
$240$		0			0
$241$	−162.609			−0.674726			−0.337363	−	0.941375i	$-0.609535\pi$
$241$	−162.609			−0.674726			−0.337363	+	0.941375i	$0.609535\pi$
$242$	−53.5828	−	41.1151i	−0.221417	−	0.169897i
$243$		0			0
$244$	−118.457	−	442.068i	−0.485478	−	1.81175i
$245$	12.0022			0.0489884
$246$		0			0
$247$		−	98.9965i		−	0.400796i
$248$	−147.255	−	60.9924i	−0.593770	−	0.245937i
$249$		0			0
$250$	111.462	+	85.5271i	0.445849	+	0.342109i
$251$		−	364.538i		−	1.45234i	−0.687515	−	0.726171i	$-0.741298\pi$
$251$		−	364.538i		−	1.45234i	0.687515	−	0.726171i	$-0.258702\pi$
$252$		0			0
$253$	345.898			1.36718
$254$	96.5719	−	125.856i	0.380204	−	0.495497i
$255$		0			0
$256$	127.991	−	221.708i	0.499965	−	0.866046i
$257$	−21.3907			−0.0832321			−0.0416161	−	0.999134i	$-0.513251\pi$
$257$	−21.3907			−0.0832321			−0.0416161	+	0.999134i	$0.513251\pi$
$258$		0			0
$259$			155.613i			0.600823i
$260$	−34.5236	−	128.838i	−0.132783	−	0.495533i
$261$		0			0
$262$	24.9159	−	32.4714i	0.0950989	−	0.123937i
$263$		−	80.6177i		−	0.306531i	−0.988185	−	0.153266i	$-0.951021\pi$
$263$		−	80.6177i		−	0.306531i	0.988185	−	0.153266i	$-0.0489790\pi$
$264$		0			0
$265$	121.125			0.457077
$266$	44.1917	+	33.9092i	0.166134	+	0.127478i
$267$		0			0
$268$	−250.081	+	67.0116i	−0.933137	+	0.250043i
$269$	156.970			0.583533			0.291766	−	0.956490i	$-0.405757\pi$
$269$	156.970			0.583533			0.291766	+	0.956490i	$0.405757\pi$
$270$		0			0
$271$			190.237i			0.701980i	0.936379	+	0.350990i	$0.114155\pi$
$271$			190.237i			0.701980i	−0.936379	+	0.350990i	$0.885845\pi$
$272$	71.7143	−	41.4062i	0.263656	−	0.152229i
$273$		0			0
$274$	383.037	+	293.911i	1.39794	+	1.07267i
$275$		−	213.359i		−	0.775850i
$276$		0			0
$277$	−128.837			−0.465116			−0.232558	−	0.972582i	$-0.574710\pi$
$277$	−128.837			−0.465116			−0.232558	+	0.972582i	$0.574710\pi$
$278$	−131.614	+	171.525i	−0.473432	+	0.616996i
$279$		0			0
$280$	69.3384	+	28.7197i	0.247637	+	0.102570i
$281$	67.8107			0.241319			0.120660	−	0.992694i	$-0.461499\pi$
$281$	67.8107			0.241319			0.120660	+	0.992694i	$0.461499\pi$
$282$		0			0
$283$			446.393i			1.57736i	0.614803	+	0.788680i	$0.289235\pi$
$283$			446.393i			1.57736i	−0.614803	+	0.788680i	$0.710765\pi$
$284$	−97.2442	+	26.0576i	−0.342409	+	0.0917520i
$285$		0			0
$286$	−258.256	+	336.570i	−0.902994	+	1.17682i
$287$		−	366.368i		−	1.27654i
$288$		0			0
$289$	−262.213			−0.907312
$290$	−53.6071	−	41.1337i	−0.184852	−	0.141840i
$291$		0			0
$292$	−60.1809	−	224.589i	−0.206099	−	0.769140i
$293$	−428.704			−1.46315			−0.731577	−	0.681759i	$-0.761215\pi$
$293$	−428.704			−1.46315			−0.731577	+	0.681759i	$0.761215\pi$
$294$		0			0
$295$		−	126.901i		−	0.430174i
$296$	74.5580	−	180.007i	0.251885	−	0.608131i
$297$		0			0
$298$	334.895	+	256.971i	1.12381	+	0.862319i
$299$			841.118i			2.81310i
$300$		0			0
$301$	503.713			1.67346
$302$	148.789	−	193.908i	0.492678	−	0.642078i
$303$		0			0
$304$	−34.8724	−	60.3980i	−0.114712	−	0.198678i
$305$	−167.991			−0.550791
$306$		0			0
$307$		−	150.905i		−	0.491548i	−0.969327	−	0.245774i	$-0.920958\pi$
$307$		−	150.905i		−	0.491548i	0.969327	−	0.245774i	$-0.0790422\pi$
$308$	−61.7835	−	230.570i	−0.200596	−	0.748603i
$309$		0			0
$310$	−35.6153	+	46.4152i	−0.114888	+	0.149727i
$311$			446.649i			1.43617i	0.695955	+	0.718086i	$0.254981\pi$
$311$			446.649i			1.43617i	−0.695955	+	0.718086i	$0.745019\pi$
$312$		0			0
$313$	−116.567			−0.372420			−0.186210	−	0.982510i	$-0.559620\pi$
$313$	−116.567			−0.372420			−0.186210	+	0.982510i	$0.559620\pi$
$314$	259.491	+	199.112i	0.826403	+	0.634115i
$315$		0			0
$316$	−184.172	+	49.3507i	−0.582822	+	0.156173i
$317$	216.378			0.682580			0.341290	−	0.939958i	$-0.389136\pi$
$317$	216.378			0.682580			0.341290	+	0.939958i	$0.389136\pi$
$318$		0			0
$319$			214.910i			0.673700i
$320$	−66.4474	−	66.4434i	−0.207648	−	0.207636i
$321$		0			0
$322$	−375.473	−	288.107i	−1.16606	−	0.894743i
$323$		−	22.5599i		−	0.0698449i
$324$		0			0
$325$	518.824			1.59638
$326$	96.2560	−	125.445i	0.295264	−	0.384799i
$327$		0			0
$328$	−175.536	+	423.799i	−0.535170	+	1.29207i
$329$	321.193			0.976270
$330$		0			0
$331$		−	267.016i		−	0.806696i	−0.915047	−	0.403348i	$-0.867846\pi$
$331$		−	267.016i		−	0.806696i	0.915047	−	0.403348i	$-0.132154\pi$
$332$	199.025	−	53.3308i	0.599473	−	0.160635i
$333$		0			0
$334$	−324.894	+	423.414i	−0.972735	+	1.26771i
$335$			95.0337i			0.283683i
$336$		0			0
$337$	−91.5477			−0.271655			−0.135827	−	0.990733i	$-0.543369\pi$
$337$	−91.5477			−0.271655			−0.135827	+	0.990733i	$0.543369\pi$
$338$	−550.281	−	422.241i	−1.62805	−	1.24923i
$339$		0			0
$340$	−7.86743	−	29.3605i	−0.0231395	−	0.0863543i
$341$	186.078			0.545684
$342$		0			0
$343$			365.315i			1.06506i
$344$	−582.673	−	241.341i	−1.69382	−	0.701572i
$345$		0			0
$346$	−366.784	−	281.441i	−1.06007	−	0.813412i
$347$			221.079i			0.637116i	0.947903	+	0.318558i	$0.103198\pi$
$347$			221.079i			0.637116i	−0.947903	+	0.318558i	$0.896802\pi$
$348$		0			0
$349$	−649.433			−1.86084			−0.930420	−	0.366496i	$-0.880557\pi$
$349$	−649.433			−1.86084			−0.930420	+	0.366496i	$0.880557\pi$
$350$	−177.712	+	231.601i	−0.507749	+	0.661718i
$351$		0			0
$352$	−39.0030	+	296.315i	−0.110804	+	0.841804i
$353$	473.760			1.34210			0.671048	−	0.741414i	$-0.265845\pi$
$353$	473.760			1.34210			0.671048	+	0.741414i	$0.265845\pi$
$354$		0			0
$355$			36.9540i			0.104096i
$356$	4.52978	+	16.9047i	0.0127241	+	0.0474851i
$357$		0			0
$358$	31.2011	−	40.6625i	0.0871539	−	0.113582i
$359$			617.624i			1.72040i	0.509957	+	0.860200i	$0.329661\pi$
$359$			617.624i			1.72040i	−0.509957	+	0.860200i	$0.670339\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	−222.823	−	170.976i	−0.615533	−	0.472310i
$363$		0			0
$364$	560.675	−	150.239i	1.54032	−	0.412743i
$365$	−85.3465			−0.233826
$366$		0			0
$367$		−	101.299i		−	0.276019i	−0.990431	−	0.138010i	$-0.955929\pi$
$367$		−	101.299i		−	0.276019i	0.990431	−	0.138010i	$-0.0440705\pi$
$368$	296.292	+	513.168i	0.805140	+	1.39448i
$369$		0			0
$370$	−56.7386	−	43.5366i	−0.153348	−	0.117667i
$371$			527.110i			1.42078i
$372$		0			0
$373$	−181.952			−0.487807			−0.243904	−	0.969799i	$-0.578428\pi$
$373$	−181.952			−0.487807			−0.243904	+	0.969799i	$0.578428\pi$
$374$	−58.8530	+	76.6995i	−0.157361	+	0.205079i
$375$		0			0
$376$	−371.542	−	153.891i	−0.988144	−	0.409285i
$377$	−522.597			−1.38620
$378$		0			0
$379$		−	631.319i		−	1.66575i	−0.553461	−	0.832875i	$-0.686693\pi$
$379$		−	631.319i		−	1.66575i	0.553461	−	0.832875i	$-0.313307\pi$
$380$	−24.7275	+	6.62597i	−0.0650722	+	0.0174368i
$381$		0			0
$382$	417.052	−	543.519i	1.09176	−	1.42282i
$383$			212.170i			0.553970i	0.960874	+	0.276985i	$0.0893352\pi$
$383$			212.170i			0.553970i	−0.960874	+	0.276985i	$0.910665\pi$
$384$		0			0
$385$	−87.6193			−0.227582
$386$	−236.149	−	181.201i	−0.611784	−	0.469433i
$387$		0			0
$388$	16.7345	+	62.4514i	0.0431301	+	0.160957i
$389$	−347.500			−0.893316			−0.446658	−	0.894705i	$-0.647386\pi$
$389$	−347.500			−0.893316			−0.446658	+	0.894705i	$0.647386\pi$
$390$		0			0
$391$			191.679i			0.490227i
$392$	25.0250	−	60.4182i	0.0638392	−	0.154128i
$393$		0			0
$394$	25.9221	+	19.8905i	0.0657921	+	0.0504835i
$395$			69.9875i			0.177183i
$396$		0			0
$397$	−313.220			−0.788967			−0.394484	−	0.918903i	$-0.629077\pi$
$397$	−313.220			−0.788967			−0.394484	+	0.918903i	$0.629077\pi$
$398$	−28.9103	+	37.6770i	−0.0726389	+	0.0946658i
$399$		0			0
$400$	316.535	−	182.760i	0.791339	−	0.456901i
$401$	−484.232			−1.20756			−0.603780	−	0.797151i	$-0.706340\pi$
$401$	−484.232			−1.20756			−0.603780	+	0.797151i	$0.706340\pi$
$402$		0			0
$403$			452.486i			1.12279i
$404$	−195.670	−	730.221i	−0.484332	−	1.80748i
$405$		0			0
$406$	179.005	−	233.286i	0.440898	−	0.574595i
$407$			227.465i			0.558881i
$408$		0			0
$409$	−216.439			−0.529191			−0.264596	−	0.964359i	$-0.585238\pi$
$409$	−216.439			−0.529191			−0.264596	+	0.964359i	$0.585238\pi$
$410$	133.583	+	102.501i	0.325811	+	0.250001i
$411$		0			0
$412$	−482.600	+	129.318i	−1.17136	+	0.313878i
$413$	552.246			1.33716
$414$		0			0
$415$		−	75.6319i		−	0.182246i
$416$	−720.548	−	94.8434i	−1.73209	−	0.227989i
$417$		0			0
$418$	64.5965	+	49.5661i	0.154537	+	0.118579i
$419$		−	63.6377i		−	0.151880i	−0.997112	−	0.0759400i	$-0.975804\pi$
$419$		−	63.6377i		−	0.151880i	0.997112	−	0.0759400i	$-0.0241958\pi$
$420$		0			0
$421$	−85.5706			−0.203256			−0.101628	−	0.994822i	$-0.532405\pi$
$421$	−85.5706			−0.203256			−0.101628	+	0.994822i	$0.532405\pi$
$422$	256.194	−	333.882i	0.607095	−	0.791190i
$423$		0			0
$424$	252.551	−	609.738i	0.595639	−	1.43806i
$425$	118.233			0.278194
$426$		0			0
$427$		−	731.059i		−	1.71208i
$428$	140.685	−	37.6978i	0.328702	−	0.0880790i
$429$		0			0
$430$	−140.926	+	183.660i	−0.327735	+	0.427117i
$431$		−	116.175i		−	0.269547i	−0.990876	−	0.134773i	$-0.956969\pi$
$431$		−	116.175i		−	0.269547i	0.990876	−	0.134773i	$-0.0430306\pi$
$432$		0			0
$433$	223.452			0.516055			0.258028	−	0.966138i	$-0.416927\pi$
$433$	223.452			0.516055			0.258028	+	0.966138i	$0.416927\pi$
$434$	−201.988	−	154.990i	−0.465411	−	0.357119i
$435$		0			0
$436$	−6.37937	−	23.8072i	−0.0146316	−	0.0546036i
$437$	161.432			0.369411
$438$		0			0
$439$			194.178i			0.442319i	0.975238	+	0.221159i	$0.0709841\pi$
$439$			194.178i			0.442319i	−0.975238	+	0.221159i	$0.929016\pi$
$440$	101.354	+	41.9805i	0.230350	+	0.0954102i
$441$		0			0
$442$	−186.510	−	143.113i	−0.421968	−	0.323784i
$443$		−	329.812i		−	0.744498i	−0.928133	−	0.372249i	$-0.878587\pi$
$443$		−	329.812i		−	0.744498i	0.928133	−	0.372249i	$-0.121413\pi$
$444$		0			0
$445$	6.42398			0.0144359
$446$	−265.269	+	345.710i	−0.594775	+	0.775133i
$447$		0			0
$448$	289.146	−	289.164i	0.645416	−	0.645455i
$449$	28.5707			0.0636318			0.0318159	−	0.999494i	$-0.489871\pi$
$449$	28.5707			0.0636318			0.0318159	+	0.999494i	$0.489871\pi$
$450$		0			0
$451$		−	535.532i		−	1.18743i
$452$	−137.610	−	513.546i	−0.304446	−	1.13616i
$453$		0			0
$454$	−266.803	+	347.709i	−0.587673	+	0.765878i
$455$		−	213.063i		−	0.468271i
$456$		0			0
$457$	242.317			0.530235			0.265117	−	0.964216i	$-0.414589\pi$
$457$	242.317			0.530235			0.265117	+	0.964216i	$0.414589\pi$
$458$	−8.25136	−	6.33142i	−0.0180161	−	0.0138241i
$459$		0			0
$460$	210.095	−	56.2972i	0.456729	−	0.122385i
$461$	−54.2147			−0.117602			−0.0588012	−	0.998270i	$-0.518728\pi$
$461$	−54.2147			−0.117602			−0.0588012	+	0.998270i	$0.518728\pi$
$462$		0			0
$463$		−	363.355i		−	0.784784i	−0.919798	−	0.392392i	$-0.871648\pi$
$463$		−	363.355i		−	0.784784i	0.919798	−	0.392392i	$-0.128352\pi$
$464$	−318.837	+	184.089i	−0.687150	+	0.396745i
$465$		0			0
$466$	−403.465	−	309.587i	−0.865805	−	0.664349i
$467$			683.263i			1.46309i	0.681793	+	0.731545i	$0.261200\pi$
$467$			683.263i			1.46309i	−0.681793	+	0.731545i	$0.738800\pi$
$468$		0			0
$469$	−413.565			−0.881801
$470$	−89.8616	+	117.111i	−0.191195	+	0.249173i
$471$		0			0
$472$	−638.814	−	264.594i	−1.35342	−	0.560581i
$473$	736.293			1.55664
$474$		0			0
$475$		−	99.5757i		−	0.209633i
$476$	127.770	−	34.2373i	0.268424	−	0.0719270i
$477$		0			0
$478$	−68.3469	+	89.0723i	−0.142985	+	0.186344i
$479$		−	432.689i		−	0.903317i	−0.892191	−	0.451659i	$-0.850833\pi$
$479$		−	432.689i		−	0.903317i	0.892191	−	0.451659i	$-0.149167\pi$
$480$		0			0
$481$	−553.125			−1.14995
$482$	258.014	+	197.979i	0.535298	+	0.410744i
$483$		0			0
$484$	34.9623	+	130.476i	0.0722361	+	0.269578i
$485$	23.7323			0.0489325
$486$		0			0
$487$			809.853i			1.66294i	0.555568	+	0.831471i	$0.312501\pi$
$487$			809.853i			1.66294i	−0.555568	+	0.831471i	$0.687499\pi$
$488$	−350.268	+	845.658i	−0.717762	+	1.73291i
$489$		0			0
$490$	−19.0440	−	14.6128i	−0.0388653	−	0.0298221i
$491$		−	296.648i		−	0.604171i	−0.953281	−	0.302085i	$-0.902317\pi$
$491$		−	296.648i		−	0.604171i	0.953281	−	0.302085i	$-0.0976827\pi$
$492$		0			0
$493$	−119.092			−0.241567
$494$	−120.530	+	157.079i	−0.243987	+	0.317974i
$495$		0			0
$496$	159.392	+	276.063i	0.321355	+	0.556578i
$497$	−160.815			−0.323572
$498$		0			0
$499$			30.5867i			0.0612960i	0.999530	+	0.0306480i	$0.00975708\pi$
$499$			30.5867i			0.0612960i	−0.999530	+	0.0306480i	$0.990243\pi$
$500$	−72.7281	−	271.414i	−0.145456	−	0.542828i
$501$		0			0
$502$	−443.830	+	578.417i	−0.884123	+	1.15222i
$503$			544.773i			1.08305i	0.840685	+	0.541524i	$0.182153\pi$
$503$			544.773i			1.08305i	−0.840685	+	0.541524i	$0.817847\pi$
$504$		0			0
$505$	−277.493			−0.549490
$506$	−548.840	−	421.136i	−1.08466	−	0.832284i
$507$		0			0
$508$	−306.464	+	82.1200i	−0.603275	+	0.161654i
$509$	−750.280			−1.47403			−0.737014	−	0.675877i	$-0.763765\pi$
$509$	−750.280			−1.47403			−0.737014	+	0.675877i	$0.763765\pi$
$510$		0			0
$511$		−	371.408i		−	0.726827i
$512$	−473.017	+	195.955i	−0.923862	+	0.382725i
$513$		0			0
$514$	33.9408	+	26.0434i	0.0660327	+	0.0506682i
$515$			183.394i			0.356105i
$516$		0			0
$517$	469.498			0.908120
$518$	189.461	−	246.913i	0.365756	−	0.476667i
$519$		0			0
$520$	−102.084	+	246.463i	−0.196315	+	0.473967i
$521$	449.862			0.863460			0.431730	−	0.902003i	$-0.357903\pi$
$521$	449.862			0.863460			0.431730	+	0.902003i	$0.357903\pi$
$522$		0			0
$523$		−	147.673i		−	0.282358i	−0.989984	−	0.141179i	$-0.954911\pi$
$523$		−	147.673i		−	0.282358i	0.989984	−	0.141179i	$-0.0450894\pi$
$524$	−79.0688	+	21.1873i	−0.150895	+	0.0404338i
$525$		0			0
$526$	−98.1532	+	127.917i	−0.186603	+	0.243188i
$527$			103.115i			0.195664i
$528$		0			0
$529$	−842.602			−1.59282
$530$	−192.191	−	147.472i	−0.362625	−	0.278249i
$531$		0			0
$532$	−28.8347	−	107.608i	−0.0542006	−	0.202271i
$533$	1302.25			2.44325
$534$		0			0
$535$		−	53.4618i		−	0.0999286i
$536$	478.394	+	198.149i	0.892526	+	0.369680i
$537$		0			0
$538$	−249.067	−	191.114i	−0.462949	−	0.355230i
$539$			76.3472i			0.141646i
$540$		0			0
$541$	267.803			0.495014			0.247507	−	0.968886i	$-0.420389\pi$
$541$	267.803			0.495014			0.247507	+	0.968886i	$0.420389\pi$
$542$	231.616	−	301.851i	0.427336	−	0.556920i
$543$		0			0
$544$	−164.203	−	21.6135i	−0.301843	−	0.0397306i
$545$	−9.04701			−0.0166000
$546$		0			0
$547$		−	931.607i		−	1.70312i	−0.524257	−	0.851560i	$-0.675657\pi$
$547$		−	931.607i		−	1.70312i	0.524257	−	0.851560i	$-0.324343\pi$
$548$	−249.928	−	932.706i	−0.456073	−	1.70202i
$549$		0			0
$550$	−259.767	+	338.539i	−0.472304	+	0.615526i
$551$			100.300i			0.182033i
$552$		0			0
$553$	−304.569			−0.550758
$554$	204.428	+	156.861i	0.369003	+	0.283143i
$555$		0			0
$556$	417.668	−	111.918i	0.751201	−	0.201292i
$557$	−96.1417			−0.172606			−0.0863031	−	0.996269i	$-0.527505\pi$
$557$	−96.1417			−0.172606			−0.0863031	+	0.996269i	$0.527505\pi$
$558$		0			0
$559$			1790.44i			3.20294i
$560$	−75.0535	−	129.990i	−0.134024	−	0.232126i
$561$		0			0
$562$	−107.596	−	82.5606i	−0.191452	−	0.146905i
$563$		−	205.785i		−	0.365515i	−0.983158	−	0.182758i	$-0.941498\pi$
$563$		−	205.785i		−	0.365515i	0.983158	−	0.182758i	$-0.0585024\pi$
$564$		0			0
$565$	−195.154			−0.345404
$566$	543.490	−	708.298i	0.960230	−	1.25141i
$567$		0			0
$568$	186.024	+	77.0504i	0.327507	+	0.135652i
$569$	497.783			0.874838			0.437419	−	0.899258i	$-0.355893\pi$
$569$	497.783			0.874838			0.437419	+	0.899258i	$0.355893\pi$
$570$		0			0
$571$		−	902.458i		−	1.58049i	−0.612792	−	0.790244i	$-0.709954\pi$
$571$		−	902.458i		−	1.58049i	0.612792	−	0.790244i	$-0.290046\pi$
$572$	819.557	−	219.609i	1.43279	−	0.383931i
$573$		0			0
$574$	−446.059	+	581.321i	−0.777106	+	1.01275i
$575$			846.040i			1.47137i
$576$		0			0
$577$	9.74046			0.0168812			0.00844061	−	0.999964i	$-0.497313\pi$
$577$	9.74046			0.0168812			0.00844061	+	0.999964i	$0.497313\pi$
$578$	416.057	+	319.248i	0.719822	+	0.552333i
$579$		0			0
$580$	34.9781	+	130.535i	0.0603071	+	0.225060i
$581$	329.133			0.566494
$582$		0			0
$583$			770.493i			1.32160i
$584$	−177.951	+	429.629i	−0.304710	+	0.735667i
$585$		0			0
$586$	680.230	+	521.954i	1.16080	+	0.890706i
$587$		−	674.185i		−	1.14853i	−0.818671	−	0.574263i	$-0.805289\pi$
$587$		−	674.185i		−	1.14853i	0.818671	−	0.574263i	$-0.194711\pi$
$588$		0			0
$589$	86.8438			0.147443
$590$	−154.504	+	201.356i	−0.261872	+	0.341282i
$591$		0			0
$592$	−337.463	+	194.843i	−0.570039	+	0.329127i
$593$	496.880			0.837908			0.418954	−	0.908007i	$-0.362397\pi$
$593$	496.880			0.837908			0.418954	+	0.908007i	$0.362397\pi$
$594$		0			0
$595$		−	48.5541i		−	0.0816036i
$596$	−218.516	−	815.479i	−0.366637	−	1.36825i
$597$		0			0
$598$	1024.07	−	1334.61i	1.71250	−	2.23179i
$599$			77.0314i			0.128600i	0.997931	+	0.0643000i	$0.0204814\pi$
$599$			77.0314i			0.128600i	−0.997931	+	0.0643000i	$0.979519\pi$
$600$		0			0
$601$	−686.862			−1.14287			−0.571433	−	0.820649i	$-0.693612\pi$
$601$	−686.862			−1.14287			−0.571433	+	0.820649i	$0.693612\pi$
$602$	−799.248	−	613.278i	−1.32765	−	1.01873i
$603$		0			0
$604$	−472.171	+	126.523i	−0.781739	+	0.209475i
$605$	49.5824			0.0819543
$606$		0			0
$607$			301.232i			0.496263i	0.968726	+	0.248132i	$0.0798166\pi$
$607$			301.232i			0.496263i	−0.968726	+	0.248132i	$0.920183\pi$
$608$	−18.2029	+	138.292i	−0.0299390	+	0.227454i
$609$		0			0
$610$	266.554	+	204.532i	0.436973	+	0.335298i
$611$			1141.68i			1.86854i
$612$		0			0
$613$	823.267			1.34301			0.671507	−	0.740999i	$-0.265647\pi$
$613$	823.267			1.34301			0.671507	+	0.740999i	$0.265647\pi$
$614$	−183.730	+	239.444i	−0.299234	+	0.389973i
$615$		0			0
$616$	−182.689	+	441.070i	−0.296574	+	0.716023i
$617$	366.129			0.593402			0.296701	−	0.954970i	$-0.404114\pi$
$617$	366.129			0.593402			0.296701	+	0.954970i	$0.404114\pi$
$618$		0			0
$619$			419.279i			0.677349i	0.940904	+	0.338674i	$0.109979\pi$
$619$			419.279i			0.677349i	−0.940904	+	0.338674i	$0.890021\pi$
$620$	113.022	−	30.2855i	0.182294	−	0.0488476i
$621$		0			0
$622$	543.802	−	708.704i	0.874280	−	1.13940i
$623$			27.9557i			0.0448727i
$624$		0			0
$625$	467.965			0.748745
$626$	184.959	+	141.922i	0.295462	+	0.226713i
$627$		0			0
$628$	−169.315	−	631.867i	−0.269610	−	1.00616i
$629$	−126.049			−0.200396
$630$		0			0
$631$			535.084i			0.847993i	0.905664	+	0.423996i	$0.139373\pi$
$631$			535.084i			0.847993i	−0.905664	+	0.423996i	$0.860627\pi$
$632$	352.313	+	145.926i	0.557457	+	0.230896i
$633$		0			0
$634$	−343.329	−	263.443i	−0.541529	−	0.415525i
$635$			116.460i			0.183401i
$636$		0			0
$637$	−185.653			−0.291449
$638$	261.657	−	341.001i	0.410120	−	0.534484i
$639$		0			0
$640$	24.5372	+	186.327i	0.0383393	+	0.291136i
$641$	647.399			1.00998			0.504992	−	0.863124i	$-0.331496\pi$
$641$	647.399			1.00998			0.504992	+	0.863124i	$0.331496\pi$
$642$		0			0
$643$		−	724.071i		−	1.12608i	−0.826429	−	0.563041i	$-0.809631\pi$
$643$		−	724.071i		−	1.12608i	0.826429	−	0.563041i	$-0.190369\pi$
$644$	244.992	+	914.287i	0.380423	+	1.41970i
$645$		0			0
$646$	−27.4670	+	35.7961i	−0.0425186	+	0.0554119i
$647$			281.255i			0.434707i	0.976093	+	0.217353i	$0.0697424\pi$
$647$			281.255i			0.434707i	−0.976093	+	0.217353i	$0.930258\pi$
$648$		0			0
$649$	807.236			1.24381
$650$	−823.224	−	631.676i	−1.26650	−	0.971809i
$651$		0			0
$652$	−305.461	+	81.8514i	−0.468499	+	0.125539i
$653$	−927.635			−1.42057			−0.710287	−	0.703912i	$-0.751435\pi$
$653$	−927.635			−1.42057			−0.710287	+	0.703912i	$0.751435\pi$
$654$		0			0
$655$			30.0471i			0.0458734i
$656$	794.506	−	458.730i	1.21114	−	0.699283i
$657$		0			0
$658$	−509.641	−	391.057i	−0.774530	−	0.594312i
$659$			333.439i			0.505977i	0.967469	+	0.252989i	$0.0814136\pi$
$659$			333.439i			0.505977i	−0.967469	+	0.252989i	$0.918586\pi$
$660$		0			0
$661$	264.400			0.400000			0.200000	−	0.979796i	$-0.435906\pi$
$661$	264.400			0.400000			0.200000	+	0.979796i	$0.435906\pi$
$662$	−325.096	+	423.678i	−0.491082	+	0.639997i
$663$		0			0
$664$	−380.727	−	157.695i	−0.573384	−	0.237493i
$665$	−40.8924			−0.0614923
$666$		0			0
$667$		−	852.193i		−	1.27765i
$668$	1031.03	−	276.274i	1.54345	−	0.413583i
$669$		0			0
$670$	115.705	−	150.791i	0.172694	−	0.225061i
$671$		−	1068.61i		−	1.59257i
$672$		0			0
$673$	−190.774			−0.283467			−0.141734	−	0.989905i	$-0.545268\pi$
$673$	−190.774			−0.283467			−0.141734	+	0.989905i	$0.545268\pi$
$674$	145.260	+	111.461i	0.215519	+	0.165372i
$675$		0			0
$676$	359.053	+	1339.95i	0.531144	+	1.98218i
$677$	518.388			0.765713			0.382856	−	0.923808i	$-0.374940\pi$
$677$	518.388			0.765713			0.382856	+	0.923808i	$0.374940\pi$
$678$		0			0
$679$			103.277i			0.152102i
$680$	−23.2634	+	56.1653i	−0.0342109	+	0.0825961i
$681$		0			0
$682$	−295.253	−	226.553i	−0.432922	−	0.332189i
$683$		−	1024.21i		−	1.49957i	−0.661679	−	0.749787i	$-0.730156\pi$
$683$		−	1024.21i		−	1.49957i	0.661679	−	0.749787i	$-0.269844\pi$
$684$		0			0
$685$	−354.440			−0.517430
$686$	444.777	−	579.651i	0.648363	−	0.844972i
$687$		0			0
$688$	630.699	+	1092.35i	0.916714	+	1.58772i
$689$	−1873.61			−2.71931
$690$		0			0
$691$			405.284i			0.586518i	0.956033	+	0.293259i	$0.0947399\pi$
$691$			405.284i			0.586518i	−0.956033	+	0.293259i	$0.905260\pi$
$692$	239.323	+	893.131i	0.345843	+	1.29065i
$693$		0			0
$694$	269.167	−	350.789i	0.387849	−	0.505460i
$695$		−	158.719i		−	0.228372i
$696$		0			0
$697$	296.765			0.425774
$698$	1030.46	+	790.694i	1.47631	+	1.13280i
$699$		0			0
$700$	563.956	−	151.118i	0.805652	−	0.215882i
$701$	93.5411			0.133440			0.0667198	−	0.997772i	$-0.478747\pi$
$701$	93.5411			0.133440			0.0667198	+	0.997772i	$0.478747\pi$
$702$		0			0
$703$			106.159i			0.151009i
$704$	422.654	−	422.680i	0.600361	−	0.600398i
$705$		0			0
$706$	−751.721	−	576.810i	−1.06476	−	0.817011i
$707$		−	1207.58i		−	1.70804i
$708$		0			0
$709$	597.864			0.843249			0.421625	−	0.906771i	$-0.361460\pi$
$709$	597.864			0.843249			0.421625	+	0.906771i	$0.361460\pi$
$710$	44.9920	−	58.6354i	0.0633690	−	0.0825850i
$711$		0			0
$712$	13.3942	−	32.3380i	0.0188121	−	0.0454185i
$713$	−737.864			−1.03487
$714$		0			0
$715$		−	311.442i		−	0.435583i
$716$	−99.0144	+	26.5319i	−0.138288	+	0.0370557i
$717$		0			0
$718$	751.966	−	979.991i	1.04731	−	1.36489i
$719$		−	1190.68i		−	1.65602i	−0.560714	−	0.828010i	$-0.689473\pi$
$719$		−	1190.68i		−	1.65602i	0.560714	−	0.828010i	$-0.310527\pi$
$720$		0			0
$721$	−798.088			−1.10692
$722$	30.1475	+	23.1328i	0.0417556	+	0.0320399i
$723$		0			0
$724$	145.390	+	542.580i	0.200815	+	0.749420i
$725$	−525.655			−0.725041
$726$		0			0
$727$		−	198.257i		−	0.272705i	−0.990660	−	0.136353i	$-0.956462\pi$
$727$		−	198.257i		−	0.272705i	0.990660	−	0.136353i	$-0.0435381\pi$
$728$	−1072.55	−	444.245i	−1.47328	−	0.610227i
$729$		0			0
$730$	135.420	+	103.911i	0.185507	+	0.142343i
$731$			408.016i			0.558162i
$732$		0			0
$733$	125.026			0.170568			0.0852841	−	0.996357i	$-0.472820\pi$
$733$	125.026			0.170568			0.0852841	+	0.996357i	$0.472820\pi$
$734$	−123.333	+	160.733i	−0.168029	+	0.218982i
$735$		0			0
$736$	154.660	−	1174.99i	0.210136	−	1.59645i
$737$	−604.521			−0.820245
$738$		0			0
$739$		−	1209.59i		−	1.63679i	−0.574657	−	0.818395i	$-0.694864\pi$
$739$		−	1209.59i		−	1.63679i	0.574657	−	0.818395i	$-0.305136\pi$
$740$	37.0214	+	138.160i	0.0500289	+	0.186703i
$741$		0			0
$742$	641.764	−	836.372i	0.864911	−	1.12719i
$743$		−	253.947i		−	0.341786i	−0.985290	−	0.170893i	$-0.945335\pi$
$743$		−	253.947i		−	0.341786i	0.985290	−	0.170893i	$-0.0546652\pi$
$744$		0			0
$745$	−309.892			−0.415962
$746$	288.706	+	221.529i	0.387005	+	0.296956i
$747$		0			0
$748$	186.765	−	50.0457i	0.249686	−	0.0669060i
$749$	232.654			0.310619
$750$		0			0
$751$			996.217i			1.32652i	0.748388	+	0.663261i	$0.230828\pi$
$751$			996.217i			1.32652i	−0.748388	+	0.663261i	$0.769172\pi$
$752$	402.166	+	696.539i	0.534795	+	0.926249i
$753$		0			0
$754$	829.211	+	636.269i	1.09975	+	0.843859i
$755$			179.430i			0.237656i
$756$		0			0
$757$	512.909			0.677555			0.338778	−	0.940866i	$-0.389987\pi$
$757$	512.909			0.677555			0.338778	+	0.940866i	$0.389987\pi$
$758$	−768.640	+	1001.72i	−1.01404	+	1.32153i
$759$		0			0
$760$	47.3026	+	19.5925i	0.0622402	+	0.0257796i
$761$	140.112			0.184115			0.0920576	−	0.995754i	$-0.470656\pi$
$761$	140.112			0.184115			0.0920576	+	0.995754i	$0.470656\pi$
$762$		0			0
$763$		−	39.3705i		−	0.0515996i
$764$	−1323.48	+	354.641i	−1.73231	+	0.464190i
$765$		0			0
$766$	258.321	−	336.653i	0.337233	−	0.439495i
$767$			1962.95i			2.55926i
$768$		0			0
$769$	914.743			1.18952			0.594761	−	0.803902i	$-0.297247\pi$
$769$	914.743			1.18952			0.594761	+	0.803902i	$0.297247\pi$
$770$	139.027	+	106.678i	0.180554	+	0.138543i
$771$		0			0
$772$	154.085	+	575.029i	0.199592	+	0.744856i
$773$	352.461			0.455965			0.227982	−	0.973665i	$-0.426787\pi$
$773$	352.461			0.455965			0.227982	+	0.973665i	$0.426787\pi$
$774$		0			0
$775$			455.134i			0.587269i
$776$	49.4827	−	119.467i	0.0637664	−	0.153952i
$777$		0			0
$778$	551.382	+	423.086i	0.708718	+	0.543812i
$779$		−	249.936i		−	0.320842i
$780$		0			0
$781$	−235.069			−0.300984
$782$	233.372	−	304.139i	0.298430	−	0.388925i
$783$		0			0
$784$	−113.267	+	65.3980i	−0.144474	+	0.0834159i
$785$	−240.117			−0.305882
$786$		0			0
$787$			971.341i			1.23423i	0.786872	+	0.617116i	$0.211699\pi$
$787$			971.341i			1.23423i	−0.786872	+	0.617116i	$0.788301\pi$
$788$	−16.9139	−	63.1210i	−0.0214644	−	0.0801028i
$789$		0			0
$790$	85.2108	−	111.050i	0.107862	−	0.140570i
$791$		−	849.263i		−	1.07366i
$792$		0			0
$793$	2598.54			3.27685
$794$	496.990	+	381.350i	0.625932	+	0.480290i
$795$		0			0
$796$	91.7446	−	24.5839i	0.115257	−	0.0308843i
$797$	774.703			0.972024			0.486012	−	0.873952i	$-0.338451\pi$
$797$	774.703			0.972024			0.486012	+	0.873952i	$0.338451\pi$
$798$		0			0
$799$			260.172i			0.325622i
$800$	−724.764	−	95.3984i	−0.905955	−	0.119248i
$801$		0			0
$802$	768.337	+	589.560i	0.958026	+	0.735112i
$803$		−	542.900i		−	0.676089i
$804$		0			0
$805$	347.440			0.431603
$806$	550.909	−	717.966i	0.683509	−	0.890776i
$807$		0			0
$808$	−578.582	+	1396.88i	−0.716067	+	1.72881i
$809$	−1067.09			−1.31902			−0.659511	−	0.751695i	$-0.729236\pi$
$809$	−1067.09			−1.31902			−0.659511	+	0.751695i	$0.729236\pi$
$810$		0			0
$811$			1348.15i			1.66233i	0.556024	+	0.831166i	$0.312326\pi$
$811$			1348.15i			1.66233i	−0.556024	+	0.831166i	$0.687674\pi$
$812$	−568.057	+	152.217i	−0.699578	+	0.187459i
$813$		0			0
$814$	276.942	−	360.921i	0.340223	−	0.443392i
$815$			116.079i			0.142428i
$816$		0			0
$817$	343.632			0.420602
$818$	343.427	+	263.518i	0.419837	+	0.322149i
$819$		0			0
$820$	−87.1615	−	325.278i	−0.106294	−	0.396680i
$821$	−464.614			−0.565913			−0.282956	−	0.959133i	$-0.591315\pi$
$821$	−464.614			−0.565913			−0.282956	+	0.959133i	$0.591315\pi$
$822$		0			0
$823$		−	1030.57i		−	1.25221i	−0.779738	−	0.626106i	$-0.784648\pi$
$823$		−	1030.57i		−	1.25221i	0.779738	−	0.626106i	$-0.215352\pi$
$824$	923.194	+	382.383i	1.12038	+	0.464057i
$825$		0			0
$826$	−876.256	−	672.368i	−1.06084	−	0.814004i
$827$			805.473i			0.973969i	0.873411	+	0.486985i	$0.161903\pi$
$827$			805.473i			0.973969i	−0.873411	+	0.486985i	$0.838097\pi$
$828$		0			0
$829$	755.129			0.910892			0.455446	−	0.890263i	$-0.349480\pi$
$829$	755.129			0.910892			0.455446	+	0.890263i	$0.349480\pi$
$830$	−92.0830	+	120.006i	−0.110943	+	0.144586i
$831$		0			0
$832$	1027.83	+	1027.77i	1.23537	+	1.23530i
$833$	−42.3077			−0.0507896
$834$		0			0
$835$		−	391.802i		−	0.469224i
$836$	−42.1486	−	157.294i	−0.0504170	−	0.188151i
$837$		0			0
$838$	−77.4799	+	100.975i	−0.0924581	+	0.120495i
$839$			386.315i			0.460447i	0.973138	+	0.230223i	$0.0739457\pi$
$839$			386.315i			0.460447i	−0.973138	+	0.230223i	$0.926054\pi$
$840$		0			0
$841$	−311.522			−0.370419
$842$	135.776	+	104.184i	0.161254	+	0.123733i
$843$		0			0
$844$	−813.013	+	217.855i	−0.963286	+	0.258122i
$845$	509.197			0.602600
$846$		0			0
$847$			215.771i			0.254747i
$848$	−1143.09	+	659.995i	−1.34798	+	0.778295i
$849$		0			0
$850$	−187.601	−	143.950i	−0.220707	−	0.169353i
$851$		−	901.975i		−	1.05990i
$852$		0			0
$853$	−621.728			−0.728872			−0.364436	−	0.931228i	$-0.618738\pi$
$853$	−621.728			−0.728872			−0.364436	+	0.931228i	$0.618738\pi$
$854$	−890.075	+	1159.98i	−1.04224	+	1.35829i
$855$		0			0
$856$	−269.124	−	111.470i	−0.314397	−	0.130222i
$857$	−341.259			−0.398202			−0.199101	−	0.979979i	$-0.563802\pi$
$857$	−341.259			−0.398202			−0.199101	+	0.979979i	$0.563802\pi$
$858$		0			0
$859$			86.1874i			0.100335i	0.998741	+	0.0501673i	$0.0159754\pi$
$859$			86.1874i			0.100335i	−0.998741	+	0.0501673i	$0.984025\pi$
$860$	447.218	−	119.837i	0.520021	−	0.139345i
$861$		0			0
$862$	−141.444	+	184.336i	−0.164089	+	0.213847i
$863$			720.200i			0.834531i	0.908785	+	0.417266i	$0.137012\pi$
$863$			720.200i			0.834531i	−0.908785	+	0.417266i	$0.862988\pi$
$864$		0			0
$865$	339.400			0.392370
$866$	−354.554	−	272.056i	−0.409416	−	0.314152i
$867$		0			0
$868$	131.796	+	491.848i	0.151838	+	0.566645i
$869$	−445.199			−0.512312
$870$		0			0
$871$		−	1470.01i		−	1.68773i
$872$	−18.8634	+	45.5421i	−0.0216323	+	0.0522272i
$873$		0			0
$874$	−256.147	−	196.546i	−0.293074	−	0.224881i
$875$		−	448.844i		−	0.512965i
$876$		0			0
$877$	−1224.25			−1.39596			−0.697978	−	0.716119i	$-0.745917\pi$
$877$	−1224.25			−1.39596			−0.697978	+	0.716119i	$0.745917\pi$
$878$	236.415	−	308.105i	0.269265	−	0.350917i
$879$		0			0
$880$	−109.708	−	190.011i	−0.124668	−	0.215922i
$881$	−301.507			−0.342233			−0.171116	−	0.985251i	$-0.554737\pi$
$881$	−301.507			−0.342233			−0.171116	+	0.985251i	$0.554737\pi$
$882$		0			0
$883$		−	885.527i		−	1.00286i	−0.865198	−	0.501431i	$-0.832807\pi$
$883$		−	885.527i		−	1.00286i	0.865198	−	0.501431i	$-0.167193\pi$
$884$	121.696	+	454.157i	0.137665	+	0.513752i
$885$		0			0
$886$	−401.552	+	523.318i	−0.453219	+	0.590652i
$887$		−	1647.19i		−	1.85703i	−0.371291	−	0.928516i	$-0.621085\pi$
$887$		−	1647.19i		−	1.85703i	0.371291	−	0.928516i	$-0.378915\pi$
$888$		0			0
$889$	−506.807			−0.570086
$890$	−10.1930	−	7.82130i	−0.0114528	−	0.00878797i
$891$		0			0
$892$	841.813	−	225.572i	0.943737	−	0.252884i
$893$	219.117			0.245372
$894$		0			0
$895$			37.6267i			0.0420410i
$896$	−810.854	+	106.780i	−0.904971	+	0.119174i
$897$		0			0
$898$	−45.3335	−	34.7852i	−0.0504827	−	0.0387363i
$899$		−	458.444i		−	0.509948i
$900$		0			0
$901$	−426.968			−0.473883
$902$	−652.018	+	849.736i	−0.722858	+	0.942057i
$903$		0			0
$904$	−406.902	+	982.391i	−0.450113	+	1.08672i
$905$	206.187			0.227831
$906$		0			0
$907$		−	720.605i		−	0.794493i	−0.917712	−	0.397246i	$-0.869966\pi$
$907$		−	720.605i		−	0.794493i	0.917712	−	0.397246i	$-0.130034\pi$
$908$	846.681	−	226.877i	0.932468	−	0.249864i
$909$		0			0
$910$	−259.408	+	338.070i	−0.285064	+	0.371506i
$911$			616.939i			0.677211i	0.940928	+	0.338605i	$0.109955\pi$
$911$			616.939i			0.677211i	−0.940928	+	0.338605i	$0.890045\pi$
$912$		0			0
$913$	481.104			0.526948
$914$	−384.488	−	295.025i	−0.420665	−	0.322784i
$915$		0			0
$916$	5.38393	+	20.0923i	0.00587766	+	0.0219348i
$917$	−130.758			−0.142593
$918$		0			0
$919$		−	13.0960i		−	0.0142503i	−0.999975	−	0.00712513i	$-0.997732\pi$
$919$		−	13.0960i		−	0.0142503i	0.999975	−	0.00712513i	$-0.00226802\pi$
$920$	−401.904	−	166.467i	−0.436852	−	0.180942i
$921$		0			0
$922$	86.0232	+	66.0072i	0.0933007	+	0.0715914i
$923$		−	571.616i		−	0.619302i
$924$		0			0
$925$	−556.362			−0.601472
$926$	−442.390	+	576.540i	−0.477743	+	0.622613i
$927$		0			0
$928$	730.035	+	96.0922i	0.786676	+	0.103548i
$929$	−429.548			−0.462377			−0.231188	−	0.972909i	$-0.574261\pi$
$929$	−429.548			−0.462377			−0.231188	+	0.972909i	$0.574261\pi$
$930$		0			0
$931$			35.6317i			0.0382725i
$932$	263.257	+	982.450i	0.282465	+	1.05413i
$933$		0			0
$934$	831.883	−	1084.14i	0.890667	−	1.16075i
$935$		−	70.9731i		−	0.0759071i
$936$		0			0
$937$	−13.9330			−0.0148698			−0.00743489	−	0.999972i	$-0.502367\pi$
$937$	−13.9330			−0.0148698			−0.00743489	+	0.999972i	$0.502367\pi$
$938$	656.208	+	503.521i	0.699583	+	0.536803i
$939$		0			0
$940$	285.169	−	76.4139i	0.303371	−	0.0812914i
$941$	−560.573			−0.595721			−0.297860	−	0.954609i	$-0.596273\pi$
$941$	−560.573			−0.595721			−0.297860	+	0.954609i	$0.596273\pi$
$942$		0			0
$943$			2123.57i			2.25193i
$944$	691.468	+	1197.60i	0.732487	+	1.26865i
$945$		0			0
$946$	−1168.29	−	896.448i	−1.23497	−	0.947619i
$947$			1022.02i			1.07922i	0.841916	+	0.539608i	$0.181428\pi$
$947$			1022.02i			1.07922i	−0.841916	+	0.539608i	$0.818572\pi$
$948$		0			0
$949$	1320.17			1.39111
$950$	−121.235	+	157.998i	−0.127616	+	0.166314i
$951$		0			0
$952$	−244.419	−	101.237i	−0.256742	−	0.106342i
$953$	−1648.92			−1.73024			−0.865120	−	0.501565i	$-0.832758\pi$
$953$	−1648.92			−1.73024			−0.865120	+	0.501565i	$0.832758\pi$
$954$		0			0
$955$			502.940i			0.526639i
$956$	216.894	−	58.1189i	0.226876	−	0.0607938i
$957$		0			0
$958$	−526.805	+	686.553i	−0.549901	+	0.716652i
$959$		−	1542.44i		−	1.60838i
$960$		0			0
$961$	564.060			0.586952
$962$	877.651	+	673.438i	0.912319	+	0.700040i
$963$		0			0
$964$	−168.351	−	628.271i	−0.174638	−	0.651733i
$965$	218.518			0.226443
$966$		0			0
$967$			1235.61i			1.27778i	0.769299	+	0.638889i	$0.220606\pi$
$967$			1235.61i			1.27778i	−0.769299	+	0.638889i	$0.779394\pi$
$968$	103.381	−	249.595i	0.106799	−	0.257846i
$969$		0			0
$970$	−37.6563	−	28.8944i	−0.0388209	−	0.0297880i
$971$		−	1012.04i		−	1.04226i	−0.853476	−	0.521131i	$-0.825510\pi$
$971$		−	1012.04i		−	1.04226i	0.853476	−	0.521131i	$-0.174490\pi$
$972$		0			0
$973$	690.708			0.709875
$974$	986.008	−	1285.00i	1.01233	−	1.31931i
$975$		0			0
$976$	1585.38	−	915.360i	1.62436	−	0.937869i
$977$	−303.876			−0.311030			−0.155515	−	0.987834i	$-0.549704\pi$
$977$	−303.876			−0.311030			−0.155515	+	0.987834i	$0.549704\pi$
$978$		0			0
$979$			40.8637i			0.0417403i
$980$	12.4260	+	46.3727i	0.0126796	+	0.0473190i
$981$		0			0
$982$	−361.173	+	470.695i	−0.367793	+	0.479323i
$983$		−	1429.58i		−	1.45431i	−0.686474	−	0.727154i	$-0.740843\pi$
$983$		−	1429.58i		−	1.45431i	0.686474	−	0.727154i	$-0.259157\pi$
$984$		0			0
$985$	−23.9867			−0.0243520
$986$	188.965	+	144.997i	0.191649	+	0.147056i
$987$		0			0
$988$	382.492	−	102.493i	0.387138	−	0.103737i
$989$	−2919.65			−2.95213
$990$		0			0
$991$		−	190.067i		−	0.191793i	−0.995391	−	0.0958966i	$-0.969428\pi$
$991$		−	190.067i		−	0.191793i	0.995391	−	0.0958966i	$-0.0305718\pi$
$992$	83.2006	−	632.095i	0.0838716	−	0.637192i
$993$		0			0
$994$	255.168	+	195.795i	0.256708	+	0.196977i
$995$		−	34.8640i		−	0.0350392i
$996$		0			0
$997$	−841.121			−0.843652			−0.421826	−	0.906677i	$-0.638611\pi$
$997$	−841.121			−0.843652			−0.421826	+	0.906677i	$0.638611\pi$
$998$	37.2397	−	48.5323i	0.0373144	−	0.0486295i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.d.343.5	✓	36
3.2	odd	2	inner	684.3.g.d.343.32	yes	36
4.3	odd	2	inner	684.3.g.d.343.6	yes	36
12.11	even	2	inner	684.3.g.d.343.31	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.g.d.343.5	✓	36	1.1	even	1	trivial
684.3.g.d.343.6	yes	36	4.3	odd	2	inner
684.3.g.d.343.31	yes	36	12.11	even	2	inner
684.3.g.d.343.32	yes	36	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.58671 - 1.21751i) q^{2} +(1.03532 + 3.86369i) q^{4} +1.46825 q^{5} +6.38949i q^{7} +(3.06136 - 7.39108i) q^{8} +O(q^{10})\)	\(q+(-1.58671 - 1.21751i) q^{2} +(1.03532 + 3.86369i) q^{4} +1.46825 q^{5} +6.38949i q^{7} +(3.06136 - 7.39108i) q^{8} +(-2.32969 - 1.78762i) q^{10} +9.33972i q^{11} -22.7114 q^{13} +(7.77929 - 10.1383i) q^{14} +(-13.8562 + 8.00028i) q^{16} -5.17560 q^{17} +4.35890i q^{19} +(1.52010 + 5.67287i) q^{20} +(11.3712 - 14.8194i) q^{22} -37.0351i q^{23} -22.8442 q^{25} +(36.0364 + 27.6514i) q^{26} +(-24.6870 + 6.61513i) q^{28} +23.0104 q^{29} -19.9233i q^{31} +(31.7263 + 4.17604i) q^{32} +(8.21218 + 6.30136i) q^{34} +9.38136i q^{35} +24.3546 q^{37} +(5.30702 - 6.91632i) q^{38} +(4.49483 - 10.8520i) q^{40} -57.3392 q^{41} -78.8346i q^{43} +(-36.0858 + 9.66955i) q^{44} +(-45.0908 + 58.7641i) q^{46} -50.2690i q^{47} +8.17447 q^{49} +(36.2473 + 27.8132i) q^{50} +(-23.5134 - 87.7497i) q^{52} +82.4964 q^{53} +13.7130i q^{55} +(47.2252 + 19.5605i) q^{56} +(-36.5109 - 28.0155i) q^{58} -86.4304i q^{59} -114.416 q^{61} +(-24.2570 + 31.6126i) q^{62} +(-45.2562 - 45.2535i) q^{64} -33.3459 q^{65} +64.7258i q^{67} +(-5.35837 - 19.9969i) q^{68} +(11.4219 - 14.8855i) q^{70} +25.1687i q^{71} -58.1281 q^{73} +(-38.6437 - 29.6520i) q^{74} +(-16.8414 + 4.51283i) q^{76} -59.6760 q^{77} +47.6673i q^{79} +(-20.3444 + 11.7464i) q^{80} +(90.9809 + 69.8114i) q^{82} -51.5116i q^{83} -7.59907 q^{85} +(-95.9823 + 125.088i) q^{86} +(69.0306 + 28.5922i) q^{88} +4.37527 q^{89} -145.114i q^{91} +(143.092 - 38.3430i) q^{92} +(-61.2032 + 79.7624i) q^{94} +6.39995i q^{95} +16.1637 q^{97} +(-12.9705 - 9.95254i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 12 q^{4}+O(q^{10}) \) 36 * q - 12 * q^4	\( 36 q - 12 q^{4} + 8 q^{10} + 24 q^{13} - 92 q^{16} - 60 q^{22} + 44 q^{25} - 48 q^{28} - 148 q^{34} + 200 q^{37} + 180 q^{40} + 140 q^{46} - 332 q^{49} + 60 q^{52} - 64 q^{58} + 40 q^{61} + 60 q^{64} + 36 q^{70} - 200 q^{73} + 312 q^{82} + 16 q^{85} + 104 q^{88} + 184 q^{94} + 280 q^{97}+O(q^{100}) \) 36 * q - 12 * q^4 + 8 * q^10 + 24 * q^13 - 92 * q^16 - 60 * q^22 + 44 * q^25 - 48 * q^28 - 148 * q^34 + 200 * q^37 + 180 * q^40 + 140 * q^46 - 332 * q^49 + 60 * q^52 - 64 * q^58 + 40 * q^61 + 60 * q^64 + 36 * q^70 - 200 * q^73 + 312 * q^82 + 16 * q^85 + 104 * q^88 + 184 * q^94 + 280 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more