LMFDB - Embedded newform 84.4.i.a.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,4,Mod(25,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("84.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	84.i (of order $3$, 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:	$4.95616044048$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{193})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 49x^{2} + 48x + 2304 $ x^4 - x^3 + 49x^2 + 48x + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.2
Root			$3.72311 - 6.44862i$ of defining polynomial
Character	$\chi$	$=$	84.37
Dual form			84.4.i.a.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 2.59808i) q^{3} +(0.723111 - 1.25246i) q^{5} +(-12.3924 - 13.7633i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 2.59808i) q^{3} +(0.723111 - 1.25246i) q^{5} +(-12.3924 - 13.7633i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-23.0618 - 39.9442i) q^{11} -32.2311 q^{13} -4.33867 q^{15} +(-38.8924 - 67.3637i) q^{17} +(-6.33067 + 10.9650i) q^{19} +(-17.1693 + 52.8414i) q^{21} +(50.4622 - 87.4031i) q^{23} +(61.4542 + 106.442i) q^{25} +27.0000 q^{27} +213.908 q^{29} +(-21.0378 - 36.4385i) q^{31} +(-69.1853 + 119.833i) q^{33} +(-26.1991 + 5.56874i) q^{35} +(-155.040 + 268.537i) q^{37} +(48.3467 + 83.7389i) q^{39} +44.0320 q^{41} +381.339 q^{43} +(6.50800 + 11.2722i) q^{45} +(179.032 - 310.093i) q^{47} +(-35.8547 + 341.121i) q^{49} +(-116.677 + 202.091i) q^{51} +(-92.4920 - 160.201i) q^{53} -66.7049 q^{55} +37.9840 q^{57} +(-227.325 - 393.738i) q^{59} +(-5.92444 + 10.2614i) q^{61} +(163.040 - 34.6549i) q^{63} +(-23.3067 + 40.3683i) q^{65} +(-295.180 - 511.266i) q^{67} -302.773 q^{69} +494.366 q^{71} +(-487.825 - 844.937i) q^{73} +(184.363 - 319.325i) q^{75} +(-263.970 + 812.411i) q^{77} +(-149.667 + 259.231i) q^{79} +(-40.5000 - 70.1481i) q^{81} -1406.07 q^{83} -112.494 q^{85} +(-320.863 - 555.750i) q^{87} +(347.629 - 602.112i) q^{89} +(399.422 + 443.605i) q^{91} +(-63.1133 + 109.316i) q^{93} +(9.15555 + 15.8579i) q^{95} +481.940 q^{97} +415.112 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} - 11 q^{5} + 6 q^{7} - 18 q^{9}+O(q^{10}) $ 4 * q - 6 * q^3 - 11 * q^5 + 6 * q^7 - 18 * q^9	$ 4 q - 6 q^{3} - 11 q^{5} + 6 q^{7} - 18 q^{9} + 5 q^{11} + 10 q^{13} + 66 q^{15} - 100 q^{17} - 67 q^{19} - 27 q^{21} - 76 q^{23} + 93 q^{25} + 108 q^{27} + 550 q^{29} - 362 q^{31} + 15 q^{33} - 466 q^{35} + 5 q^{37} - 15 q^{39} - 324 q^{41} + 1442 q^{43} - 99 q^{45} + 216 q^{47} + 190 q^{49} - 300 q^{51} - 495 q^{53} - 1406 q^{55} + 402 q^{57} - 173 q^{59} + 532 q^{61} + 27 q^{63} - 510 q^{65} - 111 q^{67} + 456 q^{69} + 3200 q^{71} - 1215 q^{73} + 279 q^{75} - 653 q^{77} - 1460 q^{79} - 162 q^{81} - 2818 q^{83} + 328 q^{85} - 825 q^{87} + 1974 q^{89} + 1945 q^{91} - 1086 q^{93} - 658 q^{95} + 1122 q^{97} - 90 q^{99}+O(q^{100}) $ 4 * q - 6 * q^3 - 11 * q^5 + 6 * q^7 - 18 * q^9 + 5 * q^11 + 10 * q^13 + 66 * q^15 - 100 * q^17 - 67 * q^19 - 27 * q^21 - 76 * q^23 + 93 * q^25 + 108 * q^27 + 550 * q^29 - 362 * q^31 + 15 * q^33 - 466 * q^35 + 5 * q^37 - 15 * q^39 - 324 * q^41 + 1442 * q^43 - 99 * q^45 + 216 * q^47 + 190 * q^49 - 300 * q^51 - 495 * q^53 - 1406 * q^55 + 402 * q^57 - 173 * q^59 + 532 * q^61 + 27 * q^63 - 510 * q^65 - 111 * q^67 + 456 * q^69 + 3200 * q^71 - 1215 * q^73 + 279 * q^75 - 653 * q^77 - 1460 * q^79 - 162 * q^81 - 2818 * q^83 + 328 * q^85 - 825 * q^87 + 1974 * q^89 + 1945 * q^91 - 1086 * q^93 - 658 * q^95 + 1122 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$		0			0
$5$	0.723111	−	1.25246i	0.0646770	−	0.112024i	−0.831874	−	0.554965i	$-0.812732\pi$
$5$	0.723111	−	1.25246i	0.0646770	−	0.112024i	0.896551	+	0.442941i	$0.146065\pi$
$6$		0			0
$7$	−12.3924	−	13.7633i	−0.669129	−	0.743146i
$7$	−12.3924	−	13.7633i	−0.669129	−	0.743146i
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	−23.0618	−	39.9442i	−0.632126	−	1.09487i	−0.987116	−	0.160005i	$-0.948849\pi$
$11$	−23.0618	−	39.9442i	−0.632126	−	1.09487i	0.354990	−	0.934870i	$-0.384484\pi$
$12$		0			0
$13$	−32.2311			−0.687639			−0.343819	−	0.939036i	$-0.611721\pi$
$13$	−32.2311			−0.687639			−0.343819	+	0.939036i	$0.611721\pi$
$14$		0			0
$15$	−4.33867			−0.0746826
$16$		0			0
$17$	−38.8924	−	67.3637i	−0.554871	−	0.961064i	−0.997914	−	0.0645639i	$-0.979434\pi$
$17$	−38.8924	−	67.3637i	−0.554871	−	0.961064i	0.443043	−	0.896500i	$-0.353899\pi$
$18$		0			0
$19$	−6.33067	+	10.9650i	−0.0764397	+	0.132397i	−0.901711	−	0.432338i	$-0.857689\pi$
$19$	−6.33067	+	10.9650i	−0.0764397	+	0.132397i	0.825272	+	0.564736i	$0.191022\pi$
$20$		0			0
$21$	−17.1693	+	52.8414i	−0.178412	+	0.549092i
$22$		0			0
$23$	50.4622	−	87.4031i	0.457483	−	0.792383i	−0.541345	−	0.840801i	$-0.682085\pi$
$23$	50.4622	−	87.4031i	0.457483	−	0.792383i	0.998827	+	0.0484177i	$0.0154179\pi$
$24$		0			0
$25$	61.4542	+	106.442i	0.491634	+	0.851535i
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	213.908			1.36972			0.684859	−	0.728676i	$-0.259864\pi$
$29$	213.908			1.36972			0.684859	+	0.728676i	$0.259864\pi$
$30$		0			0
$31$	−21.0378	−	36.4385i	−0.121887	−	0.211114i	0.798625	−	0.601829i	$-0.205561\pi$
$31$	−21.0378	−	36.4385i	−0.121887	−	0.211114i	−0.920512	+	0.390715i	$0.872228\pi$
$32$		0			0
$33$	−69.1853	+	119.833i	−0.364958	+	0.632126i
$34$		0			0
$35$	−26.1991	+	5.56874i	−0.126527	+	0.0268940i
$36$		0			0
$37$	−155.040	+	268.537i	−0.688876	+	1.19317i	0.283326	+	0.959024i	$0.408562\pi$
$37$	−155.040	+	268.537i	−0.688876	+	1.19317i	−0.972202	+	0.234145i	$0.924771\pi$
$38$		0			0
$39$	48.3467	+	83.7389i	0.198504	+	0.343819i
$40$		0			0
$41$	44.0320			0.167723			0.0838615	−	0.996477i	$-0.473275\pi$
$41$	44.0320			0.167723			0.0838615	+	0.996477i	$0.473275\pi$
$42$		0			0
$43$	381.339			1.35241			0.676205	−	0.736714i	$-0.263624\pi$
$43$	381.339			1.35241			0.676205	+	0.736714i	$0.263624\pi$
$44$		0			0
$45$	6.50800	+	11.2722i	0.0215590	+	0.0373413i
$46$		0			0
$47$	179.032	−	310.093i	0.555628	−	0.962375i	−0.442227	−	0.896903i	$-0.645811\pi$
$47$	179.032	−	310.093i	0.555628	−	0.962375i	0.997854	−	0.0654721i	$-0.0208553\pi$
$48$		0			0
$49$	−35.8547	+	341.121i	−0.104533	+	0.994521i
$50$		0			0
$51$	−116.677	+	202.091i	−0.320355	+	0.554871i
$52$		0			0
$53$	−92.4920	−	160.201i	−0.239712	−	0.415194i	0.720919	−	0.693019i	$-0.243720\pi$
$53$	−92.4920	−	160.201i	−0.239712	−	0.415194i	−0.960632	+	0.277825i	$0.910386\pi$
$54$		0			0
$55$	−66.7049			−0.163536
$56$		0			0
$57$	37.9840			0.0882650
$58$		0			0
$59$	−227.325	−	393.738i	−0.501613	−	0.868820i	−0.999998	−	0.00186377i	$-0.999407\pi$
$59$	−227.325	−	393.738i	−0.501613	−	0.868820i	0.498385	−	0.866956i	$-0.333927\pi$
$60$		0			0
$61$	−5.92444	+	10.2614i	−0.0124352	+	0.0215384i	−0.872176	−	0.489192i	$-0.837292\pi$
$61$	−5.92444	+	10.2614i	−0.0124352	+	0.0215384i	0.859741	+	0.510731i	$0.170625\pi$
$62$		0			0
$63$	163.040	−	34.6549i	0.326049	−	0.0693032i
$64$		0			0
$65$	−23.3067	+	40.3683i	−0.0444744	+	0.0770319i
$66$		0			0
$67$	−295.180	−	511.266i	−0.538238	−	0.932255i	−0.998999	−	0.0447309i	$-0.985757\pi$
$67$	−295.180	−	511.266i	−0.538238	−	0.932255i	0.460761	−	0.887524i	$-0.347576\pi$
$68$		0			0
$69$	−302.773			−0.528255
$70$		0			0
$71$	494.366			0.826345			0.413172	−	0.910653i	$-0.364421\pi$
$71$	494.366			0.826345			0.413172	+	0.910653i	$0.364421\pi$
$72$		0			0
$73$	−487.825	−	844.937i	−0.782131	−	1.35469i	−0.930698	−	0.365789i	$-0.880799\pi$
$73$	−487.825	−	844.937i	−0.782131	−	1.35469i	0.148567	−	0.988902i	$-0.452534\pi$
$74$		0			0
$75$	184.363	−	319.325i	0.283845	−	0.491634i
$76$		0			0
$77$	−263.970	+	812.411i	−0.390678	+	1.20237i
$78$		0			0
$79$	−149.667	+	259.231i	−0.213150	+	0.369187i	−0.952699	−	0.303916i	$-0.901706\pi$
$79$	−149.667	+	259.231i	−0.213150	+	0.369187i	0.739549	+	0.673103i	$0.235039\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−1406.07			−1.85947			−0.929735	−	0.368229i	$-0.879964\pi$
$83$	−1406.07			−1.85947			−0.929735	+	0.368229i	$0.879964\pi$
$84$		0			0
$85$	−112.494			−0.143550
$86$		0			0
$87$	−320.863	−	555.750i	−0.395403	−	0.684859i
$88$		0			0
$89$	347.629	−	602.112i	0.414030	−	0.717120i	−0.581296	−	0.813692i	$-0.697454\pi$
$89$	347.629	−	602.112i	0.414030	−	0.717120i	0.995326	+	0.0965715i	$0.0307877\pi$
$90$		0			0
$91$	399.422	+	443.605i	0.460119	+	0.511016i
$92$		0			0
$93$	−63.1133	+	109.316i	−0.0703715	+	0.121887i
$94$		0			0
$95$	9.15555	+	15.8579i	0.00988779	+	0.0171261i
$96$		0			0
$97$	481.940			0.504470			0.252235	−	0.967666i	$-0.418834\pi$
$97$	481.940			0.504470			0.252235	+	0.967666i	$0.418834\pi$
$98$		0			0
$99$	415.112			0.421417
$100$		0			0
$101$	592.052	+	1025.46i	0.583281	+	1.01027i	0.995087	+	0.0990014i	$0.0315648\pi$
$101$	592.052	+	1025.46i	0.583281	+	1.01027i	−0.411806	+	0.911272i	$0.635102\pi$
$102$		0			0
$103$	641.765	−	1111.57i	0.613932	−	1.06336i	−0.376639	−	0.926360i	$-0.622920\pi$
$103$	641.765	−	1111.57i	0.613932	−	1.06336i	0.990571	−	0.137001i	$-0.0437465\pi$
$104$		0			0
$105$	53.7667	+	59.7142i	0.0499723	+	0.0555001i
$106$		0			0
$107$	−806.684	+	1397.22i	−0.728833	+	1.26238i	0.228544	+	0.973533i	$0.426603\pi$
$107$	−806.684	+	1397.22i	−0.728833	+	1.26238i	−0.957377	+	0.288842i	$0.906730\pi$
$108$		0			0
$109$	76.9164	+	133.223i	0.0675895	+	0.117069i	0.897840	−	0.440322i	$-0.145136\pi$
$109$	76.9164	+	133.223i	0.0675895	+	0.117069i	−0.830250	+	0.557391i	$0.811803\pi$
$110$		0			0
$111$	930.240			0.795446
$112$		0			0
$113$	1581.08			1.31625			0.658123	−	0.752910i	$-0.271350\pi$
$113$	1581.08			1.31625			0.658123	+	0.752910i	$0.271350\pi$
$114$		0			0
$115$	−72.9796	−	126.404i	−0.0591772	−	0.102498i
$116$		0			0
$117$	145.040	−	251.217i	0.114606	−	0.198504i
$118$		0			0
$119$	−445.172	+	1370.09i	−0.342931	+	1.05543i
$120$		0			0
$121$	−398.191	+	689.687i	−0.299167	+	0.518172i
$122$		0			0
$123$	−66.0480	−	114.398i	−0.0484175	−	0.0838615i
$124$		0			0
$125$	358.531			0.256544
$126$		0			0
$127$	1916.30			1.33893			0.669465	−	0.742844i	$-0.266523\pi$
$127$	1916.30			1.33893			0.669465	+	0.742844i	$0.266523\pi$
$128$		0			0
$129$	−572.008	−	990.747i	−0.390407	−	0.676205i
$130$		0			0
$131$	−1250.24	+	2165.48i	−0.833849	+	1.44427i	0.0611158	+	0.998131i	$0.480534\pi$
$131$	−1250.24	+	2165.48i	−0.833849	+	1.44427i	−0.894964	+	0.446137i	$0.852799\pi$
$132$		0			0
$133$	229.367	−	48.7530i	0.149539	−	0.0317851i
$134$		0			0
$135$	19.5240	−	33.8166i	0.0124471	−	0.0215590i
$136$		0			0
$137$	−145.446	−	251.920i	−0.0907030	−	0.157102i	0.817104	−	0.576490i	$-0.195578\pi$
$137$	−145.446	−	251.920i	−0.0907030	−	0.157102i	−0.907807	+	0.419388i	$0.862245\pi$
$138$		0			0
$139$	−1348.77			−0.823028			−0.411514	−	0.911403i	$-0.635000\pi$
$139$	−1348.77			−0.823028			−0.411514	+	0.911403i	$0.635000\pi$
$140$		0			0
$141$	−1074.19			−0.641584
$142$		0			0
$143$	743.307	+	1287.44i	0.434674	+	0.752878i
$144$		0			0
$145$	154.680	−	267.913i	0.0885892	−	0.153441i
$146$		0			0
$147$	940.040	−	418.528i	0.527437	−	0.234827i
$148$		0			0
$149$	1424.40	−	2467.14i	0.783165	−	1.35648i	−0.146924	−	0.989148i	$-0.546937\pi$
$149$	1424.40	−	2467.14i	0.783165	−	1.35648i	0.930089	−	0.367334i	$-0.119729\pi$
$150$		0			0
$151$	744.656	+	1289.78i	0.401320	+	0.695106i	0.993885	−	0.110416i	$-0.0352183\pi$
$151$	744.656	+	1289.78i	0.401320	+	0.695106i	−0.592566	+	0.805522i	$0.701885\pi$
$152$		0			0
$153$	700.064			0.369914
$154$		0			0
$155$	−60.8506			−0.0315331
$156$		0			0
$157$	−1821.69	−	3155.26i	−0.926030	−	1.60393i	−0.789896	−	0.613241i	$-0.789865\pi$
$157$	−1821.69	−	3155.26i	−0.926030	−	1.60393i	−0.136134	−	0.990690i	$-0.543468\pi$
$158$		0			0
$159$	−277.476	+	480.603i	−0.138398	+	0.239712i
$160$		0			0
$161$	−1828.30	+	388.614i	−0.894971	+	0.190230i
$162$		0			0
$163$	−384.581	+	666.114i	−0.184802	+	0.320087i	−0.943510	−	0.331345i	$-0.892498\pi$
$163$	−384.581	+	666.114i	−0.184802	+	0.320087i	0.758708	+	0.651431i	$0.225831\pi$
$164$		0			0
$165$	100.057	+	173.304i	0.0472088	+	0.0817681i
$166$		0			0
$167$	−2399.78			−1.11198			−0.555991	−	0.831188i	$-0.687661\pi$
$167$	−2399.78			−1.11198			−0.555991	+	0.831188i	$0.687661\pi$
$168$		0			0
$169$	−1158.16			−0.527153
$170$		0			0
$171$	−56.9760	−	98.6853i	−0.0254799	−	0.0441325i
$172$		0			0
$173$	1668.32	−	2889.62i	0.733181	−	1.26991i	−0.222335	−	0.974970i	$-0.571368\pi$
$173$	1668.32	−	2889.62i	0.733181	−	1.26991i	0.955517	−	0.294937i	$-0.0952986\pi$
$174$		0			0
$175$	703.419	−	2164.88i	0.303848	−	0.935142i
$176$		0			0
$177$	−681.975	+	1181.21i	−0.289607	+	0.501613i
$178$		0			0
$179$	−1230.89	−	2131.96i	−0.513970	−	0.890223i	−0.999869	−	0.0162074i	$-0.994841\pi$
$179$	−1230.89	−	2131.96i	−0.513970	−	0.890223i	0.485898	−	0.874015i	$-0.338493\pi$
$180$		0			0
$181$	1316.74			0.540732			0.270366	−	0.962758i	$-0.412855\pi$
$181$	1316.74			0.540732			0.270366	+	0.962758i	$0.412855\pi$
$182$		0			0
$183$	35.5466			0.0143589
$184$		0			0
$185$	224.222	+	388.364i	0.0891089	+	0.154341i
$186$		0			0
$187$	−1793.86	+	3107.05i	−0.701497	+	1.21503i
$188$		0			0
$189$	−334.596	−	371.608i	−0.128774	−	0.143019i
$190$		0			0
$191$	1633.98	−	2830.14i	0.619010	−	1.07216i	−0.370657	−	0.928770i	$-0.620867\pi$
$191$	1633.98	−	2830.14i	0.619010	−	1.07216i	0.989667	−	0.143387i	$-0.0457994\pi$
$192$		0			0
$193$	−116.836	−	202.366i	−0.0435753	−	0.0754747i	0.843415	−	0.537262i	$-0.180542\pi$
$193$	−116.836	−	202.366i	−0.0435753	−	0.0754747i	−0.886990	+	0.461788i	$0.847208\pi$
$194$		0			0
$195$	139.840			0.0513546
$196$		0			0
$197$	−31.8632			−0.0115236			−0.00576182	−	0.999983i	$-0.501834\pi$
$197$	−31.8632			−0.0115236			−0.00576182	+	0.999983i	$0.501834\pi$
$198$		0			0
$199$	739.451	+	1280.77i	0.263408	+	0.456237i	0.967145	−	0.254224i	$-0.0818200\pi$
$199$	739.451	+	1280.77i	0.263408	+	0.456237i	−0.703737	+	0.710461i	$0.748487\pi$
$200$		0			0
$201$	−885.539	+	1533.80i	−0.310752	+	0.538238i
$202$		0			0
$203$	−2650.85	−	2944.08i	−0.916518	−	1.01790i
$204$		0			0
$205$	31.8400	−	55.1485i	0.0108478	−	0.0187890i
$206$		0			0
$207$	454.160	+	786.628i	0.152494	+	0.264128i
$208$		0			0
$209$	583.986			0.193278
$210$		0			0
$211$	−4498.67			−1.46778			−0.733889	−	0.679269i	$-0.762297\pi$
$211$	−4498.67			−1.46778			−0.733889	+	0.679269i	$0.762297\pi$
$212$		0			0
$213$	−741.549	−	1284.40i	−0.238545	−	0.413172i
$214$		0			0
$215$	275.750	−	477.613i	0.0874698	−	0.151502i
$216$		0			0
$217$	−240.803	+	741.111i	−0.0753308	+	0.231843i
$218$		0			0
$219$	−1463.47	+	2534.81i	−0.451564	+	0.782131i
$220$		0			0
$221$	1253.55	+	2171.21i	0.381551	+	0.660865i
$222$		0			0
$223$	5382.75			1.61639			0.808196	−	0.588913i	$-0.200444\pi$
$223$	5382.75			1.61639			0.808196	+	0.588913i	$0.200444\pi$
$224$		0			0
$225$	−1106.18			−0.327756
$226$		0			0
$227$	2712.78	+	4698.68i	0.793188	+	1.37384i	0.923983	+	0.382433i	$0.124914\pi$
$227$	2712.78	+	4698.68i	0.793188	+	1.37384i	−0.130795	+	0.991409i	$0.541753\pi$
$228$		0			0
$229$	−994.873	+	1723.17i	−0.287088	+	0.497250i	−0.973113	−	0.230327i	$-0.926020\pi$
$229$	−994.873	+	1723.17i	−0.287088	+	0.497250i	0.686026	+	0.727577i	$0.259354\pi$
$230$		0			0
$231$	2506.66	−	532.802i	0.713966	−	0.151757i
$232$		0			0
$233$	3148.83	−	5453.93i	0.885351	−	1.53347i	0.0400396	−	0.999198i	$-0.487252\pi$
$233$	3148.83	−	5453.93i	0.885351	−	1.53347i	0.845311	−	0.534274i	$-0.179415\pi$
$234$		0			0
$235$	−258.920	−	448.463i	−0.0718727	−	0.124487i
$236$		0			0
$237$	898.003			0.246125
$238$		0			0
$239$	3395.77			0.919054			0.459527	−	0.888164i	$-0.348019\pi$
$239$	3395.77			0.919054			0.459527	+	0.888164i	$0.348019\pi$
$240$		0			0
$241$	3186.97	+	5519.99i	0.851829	+	1.47541i	0.879556	+	0.475795i	$0.157840\pi$
$241$	3186.97	+	5519.99i	0.851829	+	1.47541i	−0.0277273	+	0.999616i	$0.508827\pi$
$242$		0			0
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	401.315	+	291.575i	0.104649	+	0.0760328i
$246$		0			0
$247$	204.044	−	353.415i	0.0525629	−	0.0910416i
$248$		0			0
$249$	2109.10	+	3653.07i	0.536783	+	0.929735i
$250$		0			0
$251$	−2650.91			−0.666630			−0.333315	−	0.942815i	$-0.608167\pi$
$251$	−2650.91			−0.666630			−0.333315	+	0.942815i	$0.608167\pi$
$252$		0			0
$253$	−4654.99			−1.15675
$254$		0			0
$255$	168.741	+	292.269i	0.0414392	+	0.0717748i
$256$		0			0
$257$	936.035	−	1621.26i	0.227192	−	0.393507i	−0.729783	−	0.683679i	$-0.760379\pi$
$257$	936.035	−	1621.26i	0.227192	−	0.393507i	0.956975	+	0.290171i	$0.0937123\pi$
$258$		0			0
$259$	5617.27	−	1193.98i	1.34765	−	0.286448i
$260$		0			0
$261$	−962.588	+	1667.25i	−0.228286	+	0.395403i
$262$		0			0
$263$	−3063.05	−	5305.35i	−0.718158	−	1.24389i	−0.961729	−	0.274003i	$-0.911652\pi$
$263$	−3063.05	−	5305.35i	−0.718158	−	1.24389i	0.243570	−	0.969883i	$-0.421681\pi$
$264$		0			0
$265$	−267.528			−0.0620155
$266$		0			0
$267$	−2085.78			−0.478080
$268$		0			0
$269$	4252.06	+	7364.78i	0.963764	+	1.66929i	0.712899	+	0.701267i	$0.247382\pi$
$269$	4252.06	+	7364.78i	0.963764	+	1.66929i	0.250866	+	0.968022i	$0.419285\pi$
$270$		0			0
$271$	−1060.77	+	1837.31i	−0.237776	+	0.411840i	−0.960076	−	0.279740i	$-0.909752\pi$
$271$	−1060.77	+	1837.31i	−0.237776	+	0.411840i	0.722300	+	0.691580i	$0.243085\pi$
$272$		0			0
$273$	553.387	−	1703.14i	0.122683	−	0.377577i
$274$		0			0
$275$	2834.49	−	4909.48i	0.621549	−	1.07655i
$276$		0			0
$277$	4010.68	+	6946.71i	0.869959	+	1.50681i	0.862038	+	0.506844i	$0.169188\pi$
$277$	4010.68	+	6946.71i	0.869959	+	1.50681i	0.00792096	+	0.999969i	$0.497479\pi$
$278$		0			0
$279$	378.680			0.0812580
$280$		0			0
$281$	−8244.17			−1.75020			−0.875100	−	0.483943i	$-0.839204\pi$
$281$	−8244.17			−1.75020			−0.875100	+	0.483943i	$0.839204\pi$
$282$		0			0
$283$	−3050.64	−	5283.86i	−0.640784	−	1.10987i	−0.985258	−	0.171074i	$-0.945276\pi$
$283$	−3050.64	−	5283.86i	−0.640784	−	1.10987i	0.344475	−	0.938796i	$-0.388057\pi$
$284$		0			0
$285$	27.4666	−	47.5736i	0.00570872	−	0.00988779i
$286$		0			0
$287$	−545.664	−	606.024i	−0.112228	−	0.124643i
$288$		0			0
$289$	−568.744	+	985.094i	−0.115763	+	0.200508i
$290$		0			0
$291$	−722.911	−	1252.12i	−0.145628	−	0.252235i
$292$		0			0
$293$	−1965.98			−0.391993			−0.195996	−	0.980605i	$-0.562794\pi$
$293$	−1965.98			−0.391993			−0.195996	+	0.980605i	$0.562794\pi$
$294$		0			0
$295$	−657.524			−0.129771
$296$		0			0
$297$	−622.668	−	1078.49i	−0.121653	−	0.210709i
$298$		0			0
$299$	−1626.45	+	2817.10i	−0.314583	+	0.544873i
$300$		0			0
$301$	−4725.72	−	5248.46i	−0.904936	−	1.00504i
$302$		0			0
$303$	1776.16	−	3076.39i	0.336758	−	0.583281i
$304$		0			0
$305$	8.56806	+	14.8403i	0.00160854	+	0.00278608i
$306$		0			0
$307$	997.810			0.185498			0.0927492	−	0.995690i	$-0.470435\pi$
$307$	997.810			0.185498			0.0927492	+	0.995690i	$0.470435\pi$
$308$		0			0
$309$	−3850.59			−0.708908
$310$		0			0
$311$	3450.72	+	5976.82i	0.629171	+	1.08976i	0.987718	+	0.156245i	$0.0499388\pi$
$311$	3450.72	+	5976.82i	0.629171	+	1.08976i	−0.358547	+	0.933512i	$0.616728\pi$
$312$		0			0
$313$	3170.86	−	5492.08i	0.572612	−	0.991792i	−0.423685	−	0.905810i	$-0.639264\pi$
$313$	3170.86	−	5492.08i	0.572612	−	0.991792i	0.996297	−	0.0859827i	$-0.0274030\pi$
$314$		0			0
$315$	74.4920	−	229.261i	0.0133243	−	0.0410076i
$316$		0			0
$317$	−612.487	+	1060.86i	−0.108519	+	0.187961i	−0.915171	−	0.403067i	$-0.867944\pi$
$317$	−612.487	+	1060.86i	−0.108519	+	0.187961i	0.806651	+	0.591028i	$0.201278\pi$
$318$		0			0
$319$	−4933.11	−	8544.40i	−0.865834	−	1.49967i
$320$		0			0
$321$	4840.10			0.841583
$322$		0			0
$323$	984.860			0.169657
$324$		0			0
$325$	−1980.74	−	3430.74i	−0.338066	−	0.585548i
$326$		0			0
$327$	230.749	−	399.670i	0.0390228	−	0.0675895i
$328$		0			0
$329$	−6486.53	+	1378.74i	−1.08697	+	0.231041i
$330$		0			0
$331$	−1868.15	+	3235.73i	−0.310220	+	0.537317i	−0.978410	−	0.206674i	$-0.933736\pi$
$331$	−1868.15	+	3235.73i	−0.310220	+	0.537317i	0.668190	+	0.743991i	$0.267069\pi$
$332$		0			0
$333$	−1395.36	−	2416.83i	−0.229625	−	0.397723i
$334$		0			0
$335$	−853.790			−0.139246
$336$		0			0
$337$	−3928.18			−0.634960			−0.317480	−	0.948265i	$-0.602837\pi$
$337$	−3928.18			−0.634960			−0.317480	+	0.948265i	$0.602837\pi$
$338$		0			0
$339$	−2371.63	−	4107.78i	−0.379968	−	0.658123i
$340$		0			0
$341$	−970.337	+	1680.67i	−0.154096	+	0.266902i
$342$		0			0
$343$	5139.26	−	3733.84i	0.809021	−	0.587780i
$344$		0			0
$345$	−218.939	+	379.213i	−0.0341660	+	0.0591772i
$346$		0			0
$347$	−271.003	−	469.390i	−0.0419256	−	0.0726173i	0.844301	−	0.535869i	$-0.180016\pi$
$347$	−271.003	−	469.390i	−0.0419256	−	0.0726173i	−0.886227	+	0.463252i	$0.846683\pi$
$348$		0			0
$349$	2331.24			0.357561			0.178780	−	0.983889i	$-0.442785\pi$
$349$	2331.24			0.357561			0.178780	+	0.983889i	$0.442785\pi$
$350$		0			0
$351$	−870.240			−0.132336
$352$		0			0
$353$	1280.15	+	2217.28i	0.193018	+	0.334318i	0.946249	−	0.323439i	$-0.104839\pi$
$353$	1280.15	+	2217.28i	0.193018	+	0.334318i	−0.753231	+	0.657756i	$0.771506\pi$
$354$		0			0
$355$	357.482	−	619.176i	0.0534455	−	0.0925703i
$356$		0			0
$357$	4227.35	−	898.542i	0.626709	−	0.133210i
$358$		0			0
$359$	2284.27	−	3956.46i	0.335819	−	0.581655i	−0.647823	−	0.761791i	$-0.724320\pi$
$359$	2284.27	−	3956.46i	0.335819	−	0.581655i	0.983642	+	0.180136i	$0.0576537\pi$
$360$		0			0
$361$	3349.35	+	5801.24i	0.488314	+	0.845785i
$362$		0			0
$363$	2389.15			0.345448
$364$		0			0
$365$	−1411.01			−0.202344
$366$		0			0
$367$	3190.91	+	5526.82i	0.453854	+	0.786098i	0.998621	−	0.0524893i	$-0.0167155\pi$
$367$	3190.91	+	5526.82i	0.453854	+	0.786098i	−0.544768	+	0.838587i	$0.683382\pi$
$368$		0			0
$369$	−198.144	+	343.195i	−0.0279538	+	0.0484175i
$370$		0			0
$371$	−1058.68	+	3258.27i	−0.148151	+	0.455960i
$372$		0			0
$373$	3186.01	−	5518.33i	0.442266	−	0.766027i	−0.555591	−	0.831456i	$-0.687508\pi$
$373$	3186.01	−	5518.33i	0.442266	−	0.766027i	0.997857	+	0.0654285i	$0.0208414\pi$
$374$		0			0
$375$	−537.796	−	931.490i	−0.0740578	−	0.128272i
$376$		0			0
$377$	−6894.51			−0.941870
$378$		0			0
$379$	1494.59			0.202564			0.101282	−	0.994858i	$-0.467706\pi$
$379$	1494.59			0.202564			0.101282	+	0.994858i	$0.467706\pi$
$380$		0			0
$381$	−2874.45	−	4978.69i	−0.386516	−	0.669465i
$382$		0			0
$383$	−4410.13	+	7638.57i	−0.588374	+	1.01909i	0.406072	+	0.913841i	$0.366898\pi$
$383$	−4410.13	+	7638.57i	−0.588374	+	1.01909i	−0.994446	+	0.105252i	$0.966435\pi$
$384$		0			0
$385$	826.637	+	918.077i	0.109427	+	0.121531i
$386$		0			0
$387$	−1716.02	+	2972.24i	−0.225402	+	0.390407i
$388$		0			0
$389$	4939.24	+	8555.01i	0.643777	+	1.11505i	0.984583	+	0.174921i	$0.0559669\pi$
$389$	4939.24	+	8555.01i	0.643777	+	1.11505i	−0.340806	+	0.940134i	$0.610700\pi$
$390$		0			0
$391$	−7850.40			−1.01537
$392$		0			0
$393$	7501.45			0.962845
$394$		0			0
$395$	216.452	+	374.906i	0.0275718	+	0.0477558i
$396$		0			0
$397$	−970.898	+	1681.64i	−0.122740	+	0.212593i	−0.920847	−	0.389923i	$-0.872502\pi$
$397$	−970.898	+	1681.64i	−0.122740	+	0.212593i	0.798107	+	0.602516i	$0.205835\pi$
$398$		0			0
$399$	−470.715	−	522.784i	−0.0590607	−	0.0655938i
$400$		0			0
$401$	−3792.48	+	6568.77i	−0.472288	+	0.818026i	−0.999497	−	0.0317090i	$-0.989905\pi$
$401$	−3792.48	+	6568.77i	−0.472288	+	0.818026i	0.527209	+	0.849735i	$0.323238\pi$
$402$		0			0
$403$	678.071	+	1174.45i	0.0838142	+	0.145170i
$404$		0			0
$405$	−117.144			−0.0143727
$406$		0			0
$407$	14302.0			1.74183
$408$		0			0
$409$	−4353.90	−	7541.18i	−0.526373	−	0.911705i	−0.999528	−	0.0307253i	$-0.990218\pi$
$409$	−4353.90	−	7541.18i	−0.526373	−	0.911705i	0.473155	−	0.880979i	$-0.343115\pi$
$410$		0			0
$411$	−436.339	+	755.761i	−0.0523674	+	0.0907030i
$412$		0			0
$413$	−2602.01	+	8008.11i	−0.310016	+	0.954124i
$414$		0			0
$415$	−1016.74	+	1761.05i	−0.120265	+	0.208305i
$416$		0			0
$417$	2023.15	+	3504.20i	0.237588	+	0.411514i
$418$		0			0
$419$	6647.96			0.775117			0.387558	−	0.921845i	$-0.373319\pi$
$419$	6647.96			0.775117			0.387558	+	0.921845i	$0.373319\pi$
$420$		0			0
$421$	11670.6			1.35105			0.675524	−	0.737338i	$-0.263917\pi$
$421$	11670.6			1.35105			0.675524	+	0.737338i	$0.263917\pi$
$422$		0			0
$423$	1611.29	+	2790.83i	0.185209	+	0.320792i
$424$		0			0
$425$	4780.21	−	8279.57i	0.545586	−	0.944983i
$426$		0			0
$427$	214.649	−	45.6246i	0.0243269	−	0.00517079i
$428$		0			0
$429$	2229.92	−	3862.33i	0.250959	−	0.434674i
$430$		0			0
$431$	782.821	+	1355.89i	0.0874876	+	0.151533i	0.906449	−	0.422316i	$-0.138783\pi$
$431$	782.821	+	1355.89i	0.0874876	+	0.151533i	−0.818961	+	0.573849i	$0.805450\pi$
$432$		0			0
$433$	15446.4			1.71434			0.857168	−	0.515037i	$-0.172222\pi$
$433$	15446.4			1.71434			0.857168	+	0.515037i	$0.172222\pi$
$434$		0			0
$435$	−928.077			−0.102294
$436$		0			0
$437$	638.919	+	1106.64i	0.0699397	+	0.121139i
$438$		0			0
$439$	−5348.70	+	9264.21i	−0.581502	+	1.00719i	0.413800	+	0.910368i	$0.364201\pi$
$439$	−5348.70	+	9264.21i	−0.581502	+	1.00719i	−0.995302	+	0.0968229i	$0.969132\pi$
$440$		0			0
$441$	−2497.43	−	1814.50i	−0.269672	−	0.195930i
$442$		0			0
$443$	526.981	−	912.758i	0.0565183	−	0.0978926i	−0.836382	−	0.548147i	$-0.815333\pi$
$443$	526.981	−	912.758i	0.0565183	−	0.0978926i	0.892900	+	0.450254i	$0.148667\pi$
$444$		0			0
$445$	−502.749	−	870.787i	−0.0535564	−	0.0927624i
$446$		0			0
$447$	−8546.42			−0.904321
$448$		0			0
$449$	1139.33			0.119752			0.0598759	−	0.998206i	$-0.480930\pi$
$449$	1139.33			0.119752			0.0598759	+	0.998206i	$0.480930\pi$
$450$		0			0
$451$	−1015.46	−	1758.82i	−0.106022	−	0.183636i
$452$		0			0
$453$	2233.97	−	3869.35i	0.231702	−	0.401320i
$454$		0			0
$455$	844.427	−	179.487i	0.0870051	−	0.0184933i
$456$		0			0
$457$	−2852.08	+	4939.95i	−0.291936	+	0.505648i	−0.974267	−	0.225395i	$-0.927633\pi$
$457$	−2852.08	+	4939.95i	−0.291936	+	0.505648i	0.682332	+	0.731043i	$0.260966\pi$
$458$		0			0
$459$	−1050.10	−	1818.82i	−0.106785	−	0.184957i
$460$		0			0
$461$	−6476.39			−0.654307			−0.327154	−	0.944971i	$-0.606089\pi$
$461$	−6476.39			−0.654307			−0.327154	+	0.944971i	$0.606089\pi$
$462$		0			0
$463$	−232.366			−0.0233239			−0.0116619	−	0.999932i	$-0.503712\pi$
$463$	−232.366			−0.0233239			−0.0116619	+	0.999932i	$0.503712\pi$
$464$		0			0
$465$	91.2759	+	158.094i	0.00910284	+	0.0157666i
$466$		0			0
$467$	518.583	−	898.212i	0.0513858	−	0.0890028i	−0.839188	−	0.543841i	$-0.816970\pi$
$467$	518.583	−	898.212i	0.0513858	−	0.0890028i	0.890574	+	0.454838i	$0.150303\pi$
$468$		0			0
$469$	−3378.69	+	10398.5i	−0.332651	+	1.02379i
$470$		0			0
$471$	−5465.07	+	9465.78i	−0.534644	+	0.926030i
$472$		0			0
$473$	−8794.35	−	15232.3i	−0.854893	−	1.48072i
$474$		0			0
$475$	−1556.18			−0.150321
$476$		0			0
$477$	1664.86			0.159808
$478$		0			0
$479$	−5142.32	−	8906.77i	−0.490519	−	0.849605i	0.509421	−	0.860517i	$-0.329860\pi$
$479$	−5142.32	−	8906.77i	−0.490519	−	0.849605i	−0.999940	+	0.0109129i	$0.996526\pi$
$480$		0			0
$481$	4997.11	−	8655.25i	0.473698	−	0.820469i
$482$		0			0
$483$	3752.10	+	4167.15i	0.353471	+	0.392571i
$484$		0			0
$485$	348.496	−	603.614i	0.0326276	−	0.0565127i
$486$		0			0
$487$	−5422.92	−	9392.77i	−0.504591	−	0.873977i	−0.999986	−	0.00530928i	$-0.998310\pi$
$487$	−5422.92	−	9392.77i	−0.504591	−	0.873977i	0.495395	−	0.868668i	$-0.335023\pi$
$488$		0			0
$489$	2307.49			0.213391
$490$		0			0
$491$	8442.11			0.775941			0.387971	−	0.921672i	$-0.373176\pi$
$491$	8442.11			0.775941			0.387971	+	0.921672i	$0.373176\pi$
$492$		0			0
$493$	−8319.42	−	14409.7i	−0.760016	−	1.31639i
$494$		0			0
$495$	300.172	−	519.913i	0.0272560	−	0.0472088i
$496$		0			0
$497$	−6126.41	−	6804.09i	−0.552931	−	0.614095i
$498$		0			0
$499$	−4905.42	+	8496.45i	−0.440074	+	0.762231i	−0.997694	−	0.0678654i	$-0.978381\pi$
$499$	−4905.42	+	8496.45i	−0.440074	+	0.762231i	0.557620	+	0.830096i	$0.311714\pi$
$500$		0			0
$501$	3599.68	+	6234.82i	0.321001	+	0.555991i
$502$		0			0
$503$	−6433.96			−0.570330			−0.285165	−	0.958478i	$-0.592048\pi$
$503$	−6433.96			−0.570330			−0.285165	+	0.958478i	$0.592048\pi$
$504$		0			0
$505$	1712.48			0.150900
$506$		0			0
$507$	1737.23	+	3008.98i	0.152176	+	0.263577i
$508$		0			0
$509$	10280.3	−	17806.0i	0.895220	−	1.55057i	0.0616885	−	0.998095i	$-0.480351\pi$
$509$	10280.3	−	17806.0i	0.895220	−	1.55057i	0.833532	−	0.552471i	$-0.186315\pi$
$510$		0			0
$511$	−5583.75	+	17184.9i	−0.483387	+	1.48770i
$512$		0			0
$513$	−170.928	+	296.056i	−0.0147108	+	0.0254799i
$514$		0			0
$515$	−928.135	−	1607.58i	−0.0794146	−	0.137550i
$516$		0			0
$517$	−16515.2			−1.40491
$518$		0			0
$519$	−10009.9			−0.846605
$520$		0			0
$521$	−9563.06	−	16563.7i	−0.804156	−	1.39284i	−0.916859	−	0.399211i	$-0.869284\pi$
$521$	−9563.06	−	16563.7i	−0.804156	−	1.39284i	0.112703	−	0.993629i	$-0.464049\pi$
$522$		0			0
$523$	1522.33	−	2636.75i	0.127279	−	0.220454i	−0.795343	−	0.606160i	$-0.792709\pi$
$523$	1522.33	−	2636.75i	0.127279	−	0.220454i	0.922621	+	0.385707i	$0.126042\pi$
$524$		0			0
$525$	−6679.66	+	1419.79i	−0.555285	+	0.118028i
$526$		0			0
$527$	−1636.42	+	2834.36i	−0.135263	+	0.234282i
$528$		0			0
$529$	990.629	+	1715.82i	0.0814193	+	0.141022i
$530$		0			0
$531$	4091.85			0.334409
$532$		0			0
$533$	−1419.20			−0.115333
$534$		0			0
$535$	1166.64	+	2020.69i	0.0942774	+	0.163293i
$536$		0			0
$537$	−3692.66	+	6395.87i	−0.296741	+	0.513970i
$538$		0			0
$539$	14452.7	−	6434.67i	1.15495	−	0.514213i
$540$		0			0
$541$	2947.55	−	5105.30i	0.234242	−	0.405719i	−0.724810	−	0.688949i	$-0.758072\pi$
$541$	2947.55	−	5105.30i	0.234242	−	0.405719i	0.959052	+	0.283230i	$0.0914058\pi$
$542$		0			0
$543$	−1975.11	−	3420.99i	−0.156096	−	0.270366i
$544$		0			0
$545$	222.476			0.0174860
$546$		0			0
$547$	11151.1			0.871641			0.435821	−	0.900034i	$-0.356458\pi$
$547$	11151.1			0.871641			0.435821	+	0.900034i	$0.356458\pi$
$548$		0			0
$549$	−53.3200	−	92.3529i	−0.00414506	−	0.00717946i
$550$		0			0
$551$	−1354.18	+	2345.51i	−0.104701	+	0.181347i
$552$		0			0
$553$	5422.61	−	1152.60i	0.416985	−	0.0886320i
$554$		0			0
$555$	672.667	−	1165.09i	0.0514471	−	0.0891089i
$556$		0			0
$557$	−872.173	−	1510.65i	−0.0663468	−	0.114916i	0.830944	−	0.556356i	$-0.187801\pi$
$557$	−872.173	−	1510.65i	−0.0663468	−	0.114916i	−0.897291	+	0.441440i	$0.854468\pi$
$558$		0			0
$559$	−12291.0			−0.929969
$560$		0			0
$561$	10763.1			0.810019
$562$		0			0
$563$	−5762.19	−	9980.41i	−0.431345	−	0.747112i	0.565644	−	0.824650i	$-0.308628\pi$
$563$	−5762.19	−	9980.41i	−0.431345	−	0.747112i	−0.996989	+	0.0775374i	$0.975294\pi$
$564$		0			0
$565$	1143.30	−	1980.25i	0.0851309	−	0.147451i
$566$		0			0
$567$	−463.572	+	1426.72i	−0.0343354	+	0.105673i
$568$		0			0
$569$	−1411.38	+	2444.58i	−0.103986	+	0.180110i	−0.913324	−	0.407235i	$-0.866493\pi$
$569$	−1411.38	+	2444.58i	−0.103986	+	0.180110i	0.809337	+	0.587344i	$0.199826\pi$
$570$		0			0
$571$	2583.82	+	4475.31i	0.189369	+	0.327996i	0.945040	−	0.326955i	$-0.106023\pi$
$571$	2583.82	+	4475.31i	0.189369	+	0.327996i	−0.755671	+	0.654951i	$0.772689\pi$
$572$		0			0
$573$	−9803.90			−0.714771
$574$		0			0
$575$	12404.5			0.899656
$576$		0			0
$577$	7357.61	+	12743.7i	0.530851	+	0.919461i	0.999352	+	0.0359981i	$0.0114610\pi$
$577$	7357.61	+	12743.7i	0.530851	+	0.919461i	−0.468501	+	0.883463i	$0.655206\pi$
$578$		0			0
$579$	−350.508	+	607.097i	−0.0251582	+	0.0435753i
$580$		0			0
$581$	17424.6	+	19352.1i	1.24423	+	1.38186i
$582$		0			0
$583$	−4266.06	+	7389.03i	−0.303057	+	0.524910i
$584$		0			0
$585$	−209.760	−	363.315i	−0.0148248	−	0.0256773i
$586$		0			0
$587$	9981.64			0.701851			0.350925	−	0.936403i	$-0.385867\pi$
$587$	9981.64			0.701851			0.350925	+	0.936403i	$0.385867\pi$
$588$		0			0
$589$	532.733			0.0372680
$590$		0			0
$591$	47.7947	+	82.7829i	0.00332659	+	0.00576182i
$592$		0			0
$593$	837.605	−	1450.78i	0.0580039	−	0.100466i	−0.835565	−	0.549391i	$-0.814860\pi$
$593$	837.605	−	1450.78i	0.0580039	−	0.100466i	0.893569	+	0.448925i	$0.148193\pi$
$594$		0			0
$595$	1394.08	+	1548.29i	0.0960532	+	0.106678i
$596$		0			0
$597$	2218.35	−	3842.30i	0.152079	−	0.263408i
$598$		0			0
$599$	−519.955	−	900.588i	−0.0354671	−	0.0614308i	0.847747	−	0.530401i	$-0.177959\pi$
$599$	−519.955	−	900.588i	−0.0354671	−	0.0614308i	−0.883214	+	0.468970i	$0.844625\pi$
$600$		0			0
$601$	4472.61			0.303563			0.151782	−	0.988414i	$-0.451499\pi$
$601$	4472.61			0.303563			0.151782	+	0.988414i	$0.451499\pi$
$602$		0			0
$603$	5313.23			0.358825
$604$		0			0
$605$	575.873	+	997.441i	0.0386984	+	0.0670277i
$606$		0			0
$607$	8895.38	−	15407.3i	0.594814	−	1.03025i	−0.398759	−	0.917056i	$-0.630559\pi$
$607$	8895.38	−	15407.3i	0.594814	−	1.03025i	0.993573	−	0.113193i	$-0.0361078\pi$
$608$		0			0
$609$	−3672.67	+	11303.2i	−0.244374	+	0.752101i
$610$		0			0
$611$	−5770.40	+	9994.63i	−0.382071	+	0.661766i
$612$		0			0
$613$	2163.37	+	3747.06i	0.142541	+	0.246888i	0.928453	−	0.371450i	$-0.121139\pi$
$613$	2163.37	+	3747.06i	0.142541	+	0.246888i	−0.785912	+	0.618339i	$0.787806\pi$
$614$		0			0
$615$	−191.040			−0.0125260
$616$		0			0
$617$	−18866.2			−1.23100			−0.615498	−	0.788139i	$-0.711045\pi$
$617$	−18866.2			−1.23100			−0.615498	+	0.788139i	$0.711045\pi$
$618$		0			0
$619$	5089.69	+	8815.60i	0.330488	+	0.572422i	0.982608	−	0.185694i	$-0.0594534\pi$
$619$	5089.69	+	8815.60i	0.330488	+	0.572422i	−0.652120	+	0.758116i	$0.726120\pi$
$620$		0			0
$621$	1362.48	−	2359.88i	0.0880426	−	0.152494i
$622$		0			0
$623$	−12595.0	+	2677.12i	−0.809965	+	0.172162i
$624$		0			0
$625$	−7422.52	+	12856.2i	−0.475041	+	0.822796i
$626$		0			0
$627$	−875.979	−	1517.24i	−0.0557946	−	0.0966391i
$628$		0			0
$629$	24119.5			1.52895
$630$		0			0
$631$	−1661.72			−0.104837			−0.0524184	−	0.998625i	$-0.516693\pi$
$631$	−1661.72			−0.104837			−0.0524184	+	0.998625i	$0.516693\pi$
$632$		0			0
$633$	6748.01	+	11687.9i	0.423711	+	0.733889i
$634$		0			0
$635$	1385.70	−	2400.10i	0.0865980	−	0.149992i
$636$		0			0
$637$	1155.64	−	10994.7i	0.0718806	−	0.683871i
$638$		0			0
$639$	−2224.65	+	3853.20i	−0.137724	+	0.238545i
$640$		0			0
$641$	1138.82	+	1972.50i	0.0701728	+	0.121543i	0.898977	−	0.437996i	$-0.144312\pi$
$641$	1138.82	+	1972.50i	0.0701728	+	0.121543i	−0.828804	+	0.559539i	$0.810978\pi$
$642$		0			0
$643$	1217.38			0.0746638			0.0373319	−	0.999303i	$-0.488114\pi$
$643$	1217.38			0.0746638			0.0373319	+	0.999303i	$0.488114\pi$
$644$		0			0
$645$	−1654.50			−0.101001
$646$		0			0
$647$	−5365.90	−	9294.01i	−0.326052	−	0.564738i	0.655673	−	0.755045i	$-0.272385\pi$
$647$	−5365.90	−	9294.01i	−0.326052	−	0.564738i	−0.981725	+	0.190307i	$0.939052\pi$
$648$		0			0
$649$	−10485.0	+	18160.6i	−0.634166	+	1.09841i
$650$		0			0
$651$	2286.67	−	486.041i	0.137667	−	0.0292618i
$652$		0			0
$653$	−7614.03	+	13187.9i	−0.456294	+	0.790324i	−0.998762	−	0.0497526i	$-0.984157\pi$
$653$	−7614.03	+	13187.9i	−0.456294	+	0.790324i	0.542468	+	0.840077i	$0.317490\pi$
$654$		0			0
$655$	1808.13	+	3131.77i	0.107862	+	0.186822i
$656$		0			0
$657$	8780.85			0.521421
$658$		0			0
$659$	10590.8			0.626038			0.313019	−	0.949747i	$-0.398660\pi$
$659$	10590.8			0.626038			0.313019	+	0.949747i	$0.398660\pi$
$660$		0			0
$661$	1934.15	+	3350.04i	0.113812	+	0.197128i	0.917304	−	0.398187i	$-0.130361\pi$
$661$	1934.15	+	3350.04i	0.113812	+	0.197128i	−0.803492	+	0.595315i	$0.797027\pi$
$662$		0			0
$663$	3760.64	−	6513.62i	0.220288	−	0.381551i
$664$		0			0
$665$	104.796	−	322.528i	0.00611103	−	0.0188077i
$666$		0			0
$667$	10794.3	−	18696.3i	0.626622	−	1.08534i
$668$		0			0
$669$	−8074.12	−	13984.8i	−0.466612	−	0.808196i
$670$		0			0
$671$	546.512			0.0314424
$672$		0			0
$673$	11028.7			0.631687			0.315843	−	0.948811i	$-0.397713\pi$
$673$	11028.7			0.631687			0.315843	+	0.948811i	$0.397713\pi$
$674$		0			0
$675$	1659.26	+	2873.93i	0.0946150	+	0.163878i
$676$		0			0
$677$	−9396.24	+	16274.8i	−0.533422	+	0.923914i	0.465816	+	0.884882i	$0.345761\pi$
$677$	−9396.24	+	16274.8i	−0.533422	+	0.923914i	−0.999238	+	0.0390325i	$0.987572\pi$
$678$		0			0
$679$	−5972.42	−	6633.07i	−0.337556	−	0.374895i
$680$		0			0
$681$	8138.35	−	14096.0i	0.457947	−	0.793188i
$682$		0			0
$683$	10121.9	+	17531.6i	0.567062	+	0.982181i	0.996855	+	0.0792531i	$0.0252535\pi$
$683$	10121.9	+	17531.6i	0.567062	+	0.982181i	−0.429792	+	0.902928i	$0.641413\pi$
$684$		0			0
$685$	−420.695			−0.0234656
$686$		0			0
$687$	5969.24			0.331500
$688$		0			0
$689$	2981.12	+	5163.45i	0.164835	+	0.285503i
$690$		0			0
$691$	9601.45	−	16630.2i	0.528591	−	0.915546i	−0.470854	−	0.882211i	$-0.656054\pi$
$691$	9601.45	−	16630.2i	0.528591	−	0.915546i	0.999444	−	0.0333346i	$-0.0106127\pi$
$692$		0			0
$693$	−5144.25	−	5713.29i	−0.281983	−	0.313175i
$694$		0			0
$695$	−975.308	+	1689.28i	−0.0532310	+	0.0921988i
$696$		0			0
$697$	−1712.51	−	2966.16i	−0.0930646	−	0.161193i
$698$		0			0
$699$	−18893.0			−1.02231
$700$		0			0
$701$	−22156.9			−1.19380			−0.596900	−	0.802316i	$-0.703601\pi$
$701$	−22156.9			−1.19380			−0.596900	+	0.802316i	$0.703601\pi$
$702$		0			0
$703$	−1963.01	−	3400.04i	−0.105315	−	0.182411i
$704$		0			0
$705$	−776.760	+	1345.39i	−0.0414957	+	0.0718727i
$706$		0			0
$707$	6776.76	−	20856.6i	0.360490	−	1.10947i
$708$		0			0
$709$	13604.5	−	23563.8i	0.720634	−	1.24817i	−0.240112	−	0.970745i	$-0.577184\pi$
$709$	13604.5	−	23563.8i	0.720634	−	1.24817i	0.960746	−	0.277429i	$-0.0894823\pi$
$710$		0			0
$711$	−1347.00	−	2333.08i	−0.0710501	−	0.123062i
$712$		0			0
$713$	−4246.45			−0.223045
$714$		0			0
$715$	2149.97			0.112454
$716$		0			0
$717$	−5093.65	−	8822.46i	−0.265308	−	0.459527i
$718$		0			0
$719$	−10776.2	+	18664.9i	−0.558947	+	0.968125i	0.438638	+	0.898664i	$0.355461\pi$
$719$	−10776.2	+	18664.9i	−0.558947	+	0.968125i	−0.997585	+	0.0694605i	$0.977872\pi$
$720$		0			0
$721$	−23251.9	+	4942.29i	−1.20103	+	0.255285i
$722$		0			0
$723$	9560.91	−	16560.0i	0.491804	−	0.851829i
$724$		0			0
$725$	13145.6	+	22768.8i	0.673399	+	1.16636i
$726$		0			0
$727$	−20599.1			−1.05086			−0.525431	−	0.850836i	$-0.676096\pi$
$727$	−20599.1			−1.05086			−0.525431	+	0.850836i	$0.676096\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−14831.2	−	25688.4i	−0.750412	−	1.29975i
$732$		0			0
$733$	−9880.58	+	17113.7i	−0.497882	+	0.862357i	−0.999997	−	0.00244415i	$-0.999222\pi$
$733$	−9880.58	+	17113.7i	−0.497882	+	0.862357i	0.502115	+	0.864801i	$0.332555\pi$
$734$		0			0
$735$	155.561	−	1480.01i	0.00780676	−	0.0742734i
$736$		0			0
$737$	−13614.7	+	23581.4i	−0.680468	+	1.17861i
$738$		0			0
$739$	−16704.4	−	28933.0i	−0.831506	−	1.44021i	−0.896844	−	0.442348i	$-0.854146\pi$
$739$	−16704.4	−	28933.0i	−0.831506	−	1.44021i	0.0653376	−	0.997863i	$-0.479188\pi$
$740$		0			0
$741$	−1224.27			−0.0606944
$742$		0			0
$743$	−36225.4			−1.78867			−0.894335	−	0.447398i	$-0.852351\pi$
$743$	−36225.4			−1.78867			−0.894335	+	0.447398i	$0.852351\pi$
$744$		0			0
$745$	−2060.00	−	3568.03i	−0.101306	−	0.175466i
$746$		0			0
$747$	6327.31	−	10959.2i	0.309912	−	0.536783i
$748$		0			0
$749$	29227.1	−	6212.34i	1.42581	−	0.303063i
$750$		0			0
$751$	13660.2	−	23660.2i	0.663740	−	1.14963i	−0.315885	−	0.948797i	$-0.602302\pi$
$751$	13660.2	−	23660.2i	0.663740	−	1.14963i	0.979625	−	0.200834i	$-0.0643651\pi$
$752$		0			0
$753$	3976.37	+	6887.28i	0.192440	+	0.333315i
$754$		0			0
$755$	2153.88			0.103825
$756$		0			0
$757$	−9918.43			−0.476211			−0.238105	−	0.971239i	$-0.576526\pi$
$757$	−9918.43			−0.476211			−0.238105	+	0.971239i	$0.576526\pi$
$758$		0			0
$759$	6982.49	+	12094.0i	0.333924	+	0.578373i
$760$		0			0
$761$	2817.52	−	4880.08i	0.134211	−	0.232461i	−0.791084	−	0.611707i	$-0.790483\pi$
$761$	2817.52	−	4880.08i	0.134211	−	0.232461i	0.925296	+	0.379246i	$0.123817\pi$
$762$		0			0
$763$	880.403	−	2709.58i	0.0417729	−	0.128563i
$764$		0			0
$765$	506.224	−	876.806i	0.0239249	−	0.0414392i
$766$		0			0
$767$	7326.93	+	12690.6i	0.344929	+	0.597434i
$768$		0			0
$769$	12089.3			0.566907			0.283453	−	0.958986i	$-0.408520\pi$
$769$	12089.3			0.566907			0.283453	+	0.958986i	$0.408520\pi$
$770$		0			0
$771$	−5616.21			−0.262338
$772$		0			0
$773$	7085.68	+	12272.8i	0.329695	+	0.571049i	0.982451	−	0.186519i	$-0.0597207\pi$
$773$	7085.68	+	12272.8i	0.329695	+	0.571049i	−0.652756	+	0.757568i	$0.726387\pi$
$774$		0			0
$775$	2585.72	−	4478.60i	0.119848	−	0.207582i
$776$		0			0
$777$	−11527.9	−	12803.1i	−0.532256	−	0.591132i
$778$		0			0
$779$	−278.752	+	482.812i	−0.0128207	+	0.0222061i
$780$		0			0
$781$	−11401.0	−	19747.0i	−0.522354	−	0.904744i
$782$		0			0
$783$	5775.53			0.263602
$784$		0			0
$785$	−5269.14			−0.239571
$786$		0			0
$787$	12853.8	+	22263.5i	0.582197	+	1.00840i	0.995218	+	0.0976740i	$0.0311403\pi$
$787$	12853.8	+	22263.5i	0.582197	+	1.00840i	−0.413021	+	0.910721i	$0.635526\pi$
$788$		0			0
$789$	−9189.14	+	15916.1i	−0.414629	+	0.718158i
$790$		0			0
$791$	−19593.5	−	21760.9i	−0.880739	−	0.978164i
$792$		0			0
$793$	190.951	−	330.737i	0.00855092	−	0.0148106i
$794$		0			0
$795$	401.292	+	695.058i	0.0179023	+	0.0310078i
$796$		0			0
$797$	−6194.68			−0.275316			−0.137658	−	0.990480i	$-0.543957\pi$
$797$	−6194.68			−0.275316			−0.137658	+	0.990480i	$0.543957\pi$
$798$		0			0
$799$	−27852.0			−1.23321
$800$		0			0
$801$	3128.66	+	5419.01i	0.138010	+	0.239040i
$802$		0			0
$803$	−22500.2	+	38971.5i	−0.988811	+	1.71267i
$804$		0			0
$805$	−835.340	+	2570.90i	−0.0365738	+	0.112562i
$806$		0			0
$807$	12756.2	−	22094.3i	0.556430	−	0.963764i
$808$		0			0
$809$	−15407.5	−	26686.7i	−0.669593	−	1.15977i	−0.978018	−	0.208520i	$-0.933135\pi$
$809$	−15407.5	−	26686.7i	−0.669593	−	1.15977i	0.308425	−	0.951249i	$-0.400198\pi$
$810$		0			0
$811$	43024.1			1.86286			0.931431	−	0.363917i	$-0.118561\pi$
$811$	43024.1			1.86286			0.931431	+	0.363917i	$0.118561\pi$
$812$		0			0
$813$	6364.63			0.274560
$814$		0			0
$815$	556.190	+	963.349i	0.0239049	+	0.0414045i
$816$		0			0
$817$	−2414.13	+	4181.39i	−0.103378	+	0.179056i
$818$		0			0
$819$	−5254.96	+	1116.96i	−0.224204	+	0.0476556i
$820$		0			0
$821$	5576.12	−	9658.12i	0.237038	−	0.410561i	−0.722825	−	0.691031i	$-0.757157\pi$
$821$	5576.12	−	9658.12i	0.237038	−	0.410561i	0.959863	+	0.280470i	$0.0904902\pi$
$822$		0			0
$823$	22456.4	+	38895.6i	0.951130	+	1.64741i	0.742985	+	0.669308i	$0.233409\pi$
$823$	22456.4	+	38895.6i	0.951130	+	1.64741i	0.208145	+	0.978098i	$0.433257\pi$
$824$		0			0
$825$	−17006.9			−0.717703
$826$		0			0
$827$	−3213.42			−0.135117			−0.0675584	−	0.997715i	$-0.521521\pi$
$827$	−3213.42			−0.135117			−0.0675584	+	0.997715i	$0.521521\pi$
$828$		0			0
$829$	4397.45	+	7616.61i	0.184234	+	0.319102i	0.943318	−	0.331890i	$-0.107686\pi$
$829$	4397.45	+	7616.61i	0.184234	+	0.319102i	−0.759084	+	0.650992i	$0.774353\pi$
$830$		0			0
$831$	12032.0	−	20840.1i	0.502271	−	0.869959i
$832$		0			0
$833$	24373.6	−	10851.7i	1.01380	−	0.451368i
$834$		0			0
$835$	−1735.31	+	3005.65i	−0.0719197	+	0.124568i
$836$		0			0
$837$	−568.020	−	983.840i	−0.0234572	−	0.0406290i
$838$		0			0
$839$	45817.0			1.88532			0.942658	−	0.333761i	$-0.108318\pi$
$839$	45817.0			1.88532			0.942658	+	0.333761i	$0.108318\pi$
$840$		0			0
$841$	21367.8			0.876125
$842$		0			0
$843$	12366.3	+	21419.0i	0.505239	+	0.875100i
$844$		0			0
$845$	−837.475	+	1450.55i	−0.0340947	+	0.0590537i
$846$		0			0
$847$	14426.9	−	3066.50i	0.585259	−	0.124399i
$848$		0			0
$849$	−9151.92	+	15851.6i	−0.369957	+	0.640784i
$850$		0			0
$851$	15647.3	+	27102.0i	0.630298	+	1.09171i
$852$		0			0
$853$	−16373.6			−0.657234			−0.328617	−	0.944463i	$-0.606583\pi$
$853$	−16373.6			−0.657234			−0.328617	+	0.944463i	$0.606583\pi$
$854$		0			0
$855$	−164.800			−0.00659186
$856$		0			0
$857$	2215.10	+	3836.67i	0.0882922	+	0.152927i	0.906789	−	0.421584i	$-0.138526\pi$
$857$	2215.10	+	3836.67i	0.0882922	+	0.152927i	−0.818497	+	0.574511i	$0.805192\pi$
$858$		0			0
$859$	−2472.19	+	4281.97i	−0.0981958	+	0.170080i	−0.910938	−	0.412544i	$-0.864640\pi$
$859$	−2472.19	+	4281.97i	−0.0981958	+	0.170080i	0.812742	+	0.582624i	$0.197974\pi$
$860$		0			0
$861$	−756.000	+	2326.71i	−0.0299238	+	0.0920954i
$862$		0			0
$863$	−6589.31	+	11413.0i	−0.259911	+	0.450178i	−0.966218	−	0.257727i	$-0.917026\pi$
$863$	−6589.31	+	11413.0i	−0.259911	+	0.450178i	0.706307	+	0.707905i	$0.250360\pi$
$864$		0			0
$865$	−2412.77	−	4179.04i	−0.0948399	−	0.164268i
$866$		0			0
$867$	3412.47			0.133672
$868$		0			0
$869$	13806.4			0.538951
$870$		0			0
$871$	9513.96	+	16478.7i	0.370113	+	0.641054i
$872$		0			0
$873$	−2168.73	+	3756.35i	−0.0840784	+	0.145628i
$874$		0			0
$875$	−4443.07	−	4934.55i	−0.171661	−	0.190649i
$876$		0			0
$877$	6492.95	−	11246.1i	0.250001	−	0.433015i	−0.713524	−	0.700630i	$-0.752902\pi$
$877$	6492.95	−	11246.1i	0.250001	−	0.433015i	0.963526	+	0.267615i	$0.0862356\pi$
$878$		0			0
$879$	2948.97	+	5107.77i	0.113159	+	0.195996i
$880$		0			0
$881$	36877.4			1.41025			0.705126	−	0.709082i	$-0.250890\pi$
$881$	36877.4			1.41025			0.705126	+	0.709082i	$0.250890\pi$
$882$		0			0
$883$	−24874.5			−0.948012			−0.474006	−	0.880522i	$-0.657192\pi$
$883$	−24874.5			−0.948012			−0.474006	+	0.880522i	$0.657192\pi$
$884$		0			0
$885$	986.287	+	1708.30i	0.0374618	+	0.0648857i
$886$		0			0
$887$	−2205.32	+	3819.72i	−0.0834806	+	0.144593i	−0.904743	−	0.425958i	$-0.859937\pi$
$887$	−2205.32	+	3819.72i	−0.0834806	+	0.144593i	0.821262	+	0.570551i	$0.193270\pi$
$888$		0			0
$889$	−23747.6	−	26374.5i	−0.895917	−	0.995021i
$890$		0			0
$891$	−1868.00	+	3235.48i	−0.0702362	+	0.121653i
$892$		0			0
$893$	2266.78	+	3926.18i	0.0849440	+	0.147127i
$894$		0			0
$895$	−3560.27			−0.132968
$896$		0			0
$897$	9758.72			0.363249
$898$		0			0
$899$	−4500.16	−	7794.50i	−0.166951	−	0.289167i
$900$		0			0
$901$	−7194.48	+	12461.2i	−0.266019	+	0.460758i
$902$		0			0
$903$	−6547.33	+	20150.5i	−0.241286	+	0.742598i
$904$		0			0
$905$	952.149	−	1649.17i	0.0349729	−	0.0605749i
$906$		0			0
$907$	3637.00	+	6299.46i	0.133147	+	0.230618i	0.924888	−	0.380239i	$-0.124158\pi$
$907$	3637.00	+	6299.46i	0.133147	+	0.230618i	−0.791741	+	0.610857i	$0.790825\pi$
$908$		0			0
$909$	−10656.9			−0.388854
$910$		0			0
$911$	−49491.9			−1.79993			−0.899967	−	0.435957i	$-0.856410\pi$
$911$	−49491.9			−1.79993			−0.899967	+	0.435957i	$0.856410\pi$
$912$		0			0
$913$	32426.4	+	56164.2i	1.17542	+	2.03589i
$914$		0			0
$915$	25.7042	−	44.5209i	0.000928692	−	0.00160854i
$916$		0			0
$917$	45297.7	−	9628.22i	1.63125	−	0.346730i
$918$		0			0
$919$	2507.95	−	4343.89i	0.0900213	−	0.155922i	−0.817499	−	0.575931i	$-0.804640\pi$
$919$	2507.95	−	4343.89i	0.0900213	−	0.155922i	0.907520	+	0.420009i	$0.137973\pi$
$920$		0			0
$921$	−1496.71	−	2592.39i	−0.0535488	−	0.0927492i
$922$		0			0
$923$	−15934.0			−0.568227
$924$		0			0
$925$	−38111.4			−1.35470
$926$		0			0
$927$	5775.89	+	10004.1i	0.204644	+	0.354454i
$928$		0			0
$929$	26079.1	−	45170.4i	0.921021	−	1.59525i	0.123181	−	0.992384i	$-0.460690\pi$
$929$	26079.1	−	45170.4i	0.921021	−	1.59525i	0.797839	−	0.602870i	$-0.205976\pi$
$930$		0			0
$931$	−3513.42	−	2552.67i	−0.123682	−	0.0898608i
$932$		0			0
$933$	10352.1	−	17930.4i	0.363252	−	0.629171i
$934$		0			0
$935$	2594.32	+	4493.49i	0.0907414	+	0.157169i
$936$		0			0
$937$	−14821.9			−0.516766			−0.258383	−	0.966042i	$-0.583190\pi$
$937$	−14821.9			−0.516766			−0.258383	+	0.966042i	$0.583190\pi$
$938$		0			0
$939$	−19025.1			−0.661195
$940$		0			0
$941$	−13246.1	−	22943.0i	−0.458886	−	0.794814i	0.540016	−	0.841655i	$-0.318418\pi$
$941$	−13246.1	−	22943.0i	−0.458886	−	0.794814i	−0.998902	+	0.0468405i	$0.985085\pi$
$942$		0			0
$943$	2221.95	−	3848.53i	0.0767304	−	0.132901i
$944$		0			0
$945$	−707.376	+	150.356i	−0.0243502	+	0.00517574i
$946$		0			0
$947$	−3205.12	+	5551.44i	−0.109982	+	0.190494i	−0.915763	−	0.401720i	$-0.868413\pi$
$947$	−3205.12	+	5551.44i	−0.109982	+	0.190494i	0.805781	+	0.592214i	$0.201746\pi$
$948$		0			0
$949$	15723.1	+	27233.3i	0.537824	+	0.931538i
$950$		0			0
$951$	3674.92			0.125307
$952$		0			0
$953$	−25108.5			−0.853458			−0.426729	−	0.904380i	$-0.640334\pi$
$953$	−25108.5			−0.853458			−0.426729	+	0.904380i	$0.640334\pi$
$954$		0			0
$955$	−2363.10	−	4093.02i	−0.0800715	−	0.138688i
$956$		0			0
$957$	−14799.3	+	25633.2i	−0.499890	+	0.865834i
$958$		0			0
$959$	−1664.81	+	5123.72i	−0.0560579	+	0.172527i
$960$		0			0
$961$	14010.3	−	24266.6i	0.470287	−	0.814561i
$962$		0			0
$963$	−7260.16	−	12575.0i	−0.242944	−	0.420792i
$964$		0			0
$965$	−337.941			−0.0112733
$966$		0			0
$967$	32928.1			1.09503			0.547516	−	0.836795i	$-0.315574\pi$
$967$	32928.1			1.09503			0.547516	+	0.836795i	$0.315574\pi$
$968$		0			0
$969$	−1477.29	−	2558.74i	−0.0489757	−	0.0848283i
$970$		0			0
$971$	15771.6	−	27317.2i	0.521251	−	0.902834i	−0.478443	−	0.878119i	$-0.658799\pi$
$971$	15771.6	−	27317.2i	0.521251	−	0.902834i	0.999695	−	0.0247155i	$-0.00786798\pi$
$972$		0			0
$973$	16714.5	+	18563.4i	0.550712	+	0.611630i
$974$		0			0
$975$	−5942.21	+	10292.2i	−0.195183	+	0.338066i
$976$		0			0
$977$	−26940.9	−	46663.0i	−0.882206	−	1.52803i	−0.848883	−	0.528581i	$-0.822724\pi$
$977$	−26940.9	−	46663.0i	−0.882206	−	1.52803i	−0.0333230	−	0.999445i	$-0.510609\pi$
$978$		0			0
$979$	−32067.8			−1.04688
$980$		0			0
$981$	−1384.50			−0.0450597
$982$		0			0
$983$	−17844.3	−	30907.3i	−0.578988	−	1.00284i	−0.995596	−	0.0937503i	$-0.970114\pi$
$983$	−17844.3	−	30907.3i	−0.578988	−	1.00284i	0.416608	−	0.909086i	$-0.363219\pi$
$984$		0			0
$985$	−23.0406	+	39.9075i	−0.000745314	+	0.00129092i
$986$		0			0
$987$	13311.9	+	14784.4i	0.429302	+	0.476790i
$988$		0			0
$989$	19243.2	−	33330.2i	0.618704	−	1.07163i
$990$		0			0
$991$	−7419.86	−	12851.6i	−0.237840	−	0.411951i	0.722254	−	0.691628i	$-0.243106\pi$
$991$	−7419.86	−	12851.6i	−0.237840	−	0.411951i	−0.960094	+	0.279676i	$0.909773\pi$
$992$		0			0
$993$	11208.9			0.358211
$994$		0			0
$995$	2138.82			0.0681459
$996$		0			0
$997$	−8686.03	−	15044.7i	−0.275917	−	0.477903i	0.694449	−	0.719542i	$-0.255648\pi$
$997$	−8686.03	−	15044.7i	−0.275917	−	0.477903i	−0.970366	+	0.241639i	$0.922315\pi$
$998$		0			0
$999$	−4186.08	+	7250.50i	−0.132574	+	0.229625i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.4.i.a.37.2	yes	4
3.2	odd	2		252.4.k.f.37.1		4
4.3	odd	2		336.4.q.i.289.2		4
7.2	even	3		588.4.a.i.1.1		2
7.3	odd	6		588.4.i.j.361.1		4
7.4	even	3	inner	84.4.i.a.25.2	✓	4
7.5	odd	6		588.4.a.f.1.2		2
7.6	odd	2		588.4.i.j.373.1		4
21.2	odd	6		1764.4.a.o.1.2		2
21.5	even	6		1764.4.a.y.1.1		2
21.11	odd	6		252.4.k.f.109.1		4
21.17	even	6		1764.4.k.q.361.2		4
21.20	even	2		1764.4.k.q.1549.2		4
28.11	odd	6		336.4.q.i.193.2		4
28.19	even	6		2352.4.a.bx.1.2		2
28.23	odd	6		2352.4.a.bt.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.i.a.25.2	✓	4	7.4	even	3	inner
84.4.i.a.37.2	yes	4	1.1	even	1	trivial
252.4.k.f.37.1		4	3.2	odd	2
252.4.k.f.109.1		4	21.11	odd	6
336.4.q.i.193.2		4	28.11	odd	6
336.4.q.i.289.2		4	4.3	odd	2
588.4.a.f.1.2		2	7.5	odd	6
588.4.a.i.1.1		2	7.2	even	3
588.4.i.j.361.1		4	7.3	odd	6
588.4.i.j.373.1		4	7.6	odd	2
1764.4.a.o.1.2		2	21.2	odd	6
1764.4.a.y.1.1		2	21.5	even	6
1764.4.k.q.361.2		4	21.17	even	6
1764.4.k.q.1549.2		4	21.20	even	2
2352.4.a.bt.1.1		2	28.23	odd	6
2352.4.a.bx.1.2		2	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	84.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 2.59808i) q^{3} +(0.723111 - 1.25246i) q^{5} +(-12.3924 - 13.7633i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 2.59808i) q^{3} +(0.723111 - 1.25246i) q^{5} +(-12.3924 - 13.7633i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-23.0618 - 39.9442i) q^{11} -32.2311 q^{13} -4.33867 q^{15} +(-38.8924 - 67.3637i) q^{17} +(-6.33067 + 10.9650i) q^{19} +(-17.1693 + 52.8414i) q^{21} +(50.4622 - 87.4031i) q^{23} +(61.4542 + 106.442i) q^{25} +27.0000 q^{27} +213.908 q^{29} +(-21.0378 - 36.4385i) q^{31} +(-69.1853 + 119.833i) q^{33} +(-26.1991 + 5.56874i) q^{35} +(-155.040 + 268.537i) q^{37} +(48.3467 + 83.7389i) q^{39} +44.0320 q^{41} +381.339 q^{43} +(6.50800 + 11.2722i) q^{45} +(179.032 - 310.093i) q^{47} +(-35.8547 + 341.121i) q^{49} +(-116.677 + 202.091i) q^{51} +(-92.4920 - 160.201i) q^{53} -66.7049 q^{55} +37.9840 q^{57} +(-227.325 - 393.738i) q^{59} +(-5.92444 + 10.2614i) q^{61} +(163.040 - 34.6549i) q^{63} +(-23.3067 + 40.3683i) q^{65} +(-295.180 - 511.266i) q^{67} -302.773 q^{69} +494.366 q^{71} +(-487.825 - 844.937i) q^{73} +(184.363 - 319.325i) q^{75} +(-263.970 + 812.411i) q^{77} +(-149.667 + 259.231i) q^{79} +(-40.5000 - 70.1481i) q^{81} -1406.07 q^{83} -112.494 q^{85} +(-320.863 - 555.750i) q^{87} +(347.629 - 602.112i) q^{89} +(399.422 + 443.605i) q^{91} +(-63.1133 + 109.316i) q^{93} +(9.15555 + 15.8579i) q^{95} +481.940 q^{97} +415.112 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} - 11 q^{5} + 6 q^{7} - 18 q^{9}+O(q^{10}) \) 4 * q - 6 * q^3 - 11 * q^5 + 6 * q^7 - 18 * q^9	\( 4 q - 6 q^{3} - 11 q^{5} + 6 q^{7} - 18 q^{9} + 5 q^{11} + 10 q^{13} + 66 q^{15} - 100 q^{17} - 67 q^{19} - 27 q^{21} - 76 q^{23} + 93 q^{25} + 108 q^{27} + 550 q^{29} - 362 q^{31} + 15 q^{33} - 466 q^{35} + 5 q^{37} - 15 q^{39} - 324 q^{41} + 1442 q^{43} - 99 q^{45} + 216 q^{47} + 190 q^{49} - 300 q^{51} - 495 q^{53} - 1406 q^{55} + 402 q^{57} - 173 q^{59} + 532 q^{61} + 27 q^{63} - 510 q^{65} - 111 q^{67} + 456 q^{69} + 3200 q^{71} - 1215 q^{73} + 279 q^{75} - 653 q^{77} - 1460 q^{79} - 162 q^{81} - 2818 q^{83} + 328 q^{85} - 825 q^{87} + 1974 q^{89} + 1945 q^{91} - 1086 q^{93} - 658 q^{95} + 1122 q^{97} - 90 q^{99}+O(q^{100}) \) 4 * q - 6 * q^3 - 11 * q^5 + 6 * q^7 - 18 * q^9 + 5 * q^11 + 10 * q^13 + 66 * q^15 - 100 * q^17 - 67 * q^19 - 27 * q^21 - 76 * q^23 + 93 * q^25 + 108 * q^27 + 550 * q^29 - 362 * q^31 + 15 * q^33 - 466 * q^35 + 5 * q^37 - 15 * q^39 - 324 * q^41 + 1442 * q^43 - 99 * q^45 + 216 * q^47 + 190 * q^49 - 300 * q^51 - 495 * q^53 - 1406 * q^55 + 402 * q^57 - 173 * q^59 + 532 * q^61 + 27 * q^63 - 510 * q^65 - 111 * q^67 + 456 * q^69 + 3200 * q^71 - 1215 * q^73 + 279 * q^75 - 653 * q^77 - 1460 * q^79 - 162 * q^81 - 2818 * q^83 + 328 * q^85 - 825 * q^87 + 1974 * q^89 + 1945 * q^91 - 1086 * q^93 - 658 * q^95 + 1122 * q^97 - 90 * q^99

Introduction

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