LMFDB - Embedded newform 441.4.e.p.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,4,Mod(226,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("441.226");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	441.e (of order $3$, degree $2$, not 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:	$26.0198423125$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$2.13746 - 0.656712i$ of defining polynomial
Character	$\chi$	$=$	441.226
Dual form			441.4.e.p.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.63746 + 4.56821i) q^{2} +(-9.91238 - 17.1687i) q^{4} +(-5.27492 + 9.13642i) q^{5} +62.3746 q^{8} +O(q^{10})$	\(q+(-2.63746 + 4.56821i) q^{2} +(-9.91238 - 17.1687i) q^{4} +(-5.27492 + 9.13642i) q^{5} +62.3746 q^{8} +(-27.8248 - 48.1939i) q^{10} +(17.3746 + 30.0937i) q^{11} +37.2990 q^{13} +(-85.2114 + 147.590i) q^{16} +(5.27492 + 9.13642i) q^{17} +(-29.2990 + 50.7474i) q^{19} +209.148 q^{20} -183.299 q^{22} +(-62.6736 + 108.554i) q^{23} +(6.85050 + 11.8654i) q^{25} +(-98.3746 + 170.390i) q^{26} +35.4020 q^{29} +(145.897 + 252.701i) q^{31} +(-199.985 - 346.384i) q^{32} -55.6495 q^{34} +(129.949 - 225.077i) q^{37} +(-154.550 - 267.688i) q^{38} +(-329.021 + 569.881i) q^{40} -338.248 q^{41} +6.80397 q^{43} +(344.447 - 596.599i) q^{44} +(-330.598 - 572.613i) q^{46} +(-125.347 + 217.108i) q^{47} -72.2716 q^{50} +(-369.722 - 640.377i) q^{52} +(-268.450 - 464.969i) q^{53} -366.598 q^{55} +(-93.3713 + 161.724i) q^{58} +(17.9452 + 31.0820i) q^{59} +(28.8970 - 50.0511i) q^{61} -1539.19 q^{62} +746.423 q^{64} +(-196.749 + 340.780i) q^{65} +(-240.846 - 417.157i) q^{67} +(104.574 - 181.127i) q^{68} -363.752 q^{71} +(290.650 + 503.420i) q^{73} +(685.468 + 1187.26i) q^{74} +1161.69 q^{76} +(346.846 - 600.754i) q^{79} +(-898.966 - 1557.05i) q^{80} +(892.114 - 1545.19i) q^{82} +1334.39 q^{83} -111.299 q^{85} +(-17.9452 + 31.0820i) q^{86} +(1083.73 + 1877.08i) q^{88} +(176.519 - 305.740i) q^{89} +2484.98 q^{92} +(-661.196 - 1145.23i) q^{94} +(-309.100 - 535.376i) q^{95} -1445.88 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - 17 q^{4} - 6 q^{5} + 174 q^{8}+O(q^{10}) $ 4 * q - 3 * q^2 - 17 * q^4 - 6 * q^5 + 174 * q^8	$ 4 q - 3 q^{2} - 17 q^{4} - 6 q^{5} + 174 q^{8} - 66 q^{10} - 6 q^{11} - 32 q^{13} - 137 q^{16} + 6 q^{17} + 64 q^{19} + 444 q^{20} - 552 q^{22} + 6 q^{23} + 118 q^{25} - 318 q^{26} + 504 q^{29} + 40 q^{31} - 279 q^{32} - 132 q^{34} + 248 q^{37} - 588 q^{38} - 546 q^{40} - 900 q^{41} + 752 q^{43} + 804 q^{44} - 960 q^{46} + 12 q^{47} + 330 q^{50} - 890 q^{52} - 1104 q^{53} - 1104 q^{55} + 306 q^{58} - 804 q^{59} - 428 q^{61} - 4224 q^{62} + 2578 q^{64} - 636 q^{65} - 148 q^{67} + 222 q^{68} - 1908 q^{71} + 1072 q^{73} + 1398 q^{74} + 3016 q^{76} + 572 q^{79} - 1950 q^{80} + 1530 q^{82} + 3888 q^{83} - 264 q^{85} + 804 q^{86} + 1164 q^{88} - 366 q^{89} + 5712 q^{92} - 1920 q^{94} - 1176 q^{95} - 1616 q^{97}+O(q^{100}) $ 4 * q - 3 * q^2 - 17 * q^4 - 6 * q^5 + 174 * q^8 - 66 * q^10 - 6 * q^11 - 32 * q^13 - 137 * q^16 + 6 * q^17 + 64 * q^19 + 444 * q^20 - 552 * q^22 + 6 * q^23 + 118 * q^25 - 318 * q^26 + 504 * q^29 + 40 * q^31 - 279 * q^32 - 132 * q^34 + 248 * q^37 - 588 * q^38 - 546 * q^40 - 900 * q^41 + 752 * q^43 + 804 * q^44 - 960 * q^46 + 12 * q^47 + 330 * q^50 - 890 * q^52 - 1104 * q^53 - 1104 * q^55 + 306 * q^58 - 804 * q^59 - 428 * q^61 - 4224 * q^62 + 2578 * q^64 - 636 * q^65 - 148 * q^67 + 222 * q^68 - 1908 * q^71 + 1072 * q^73 + 1398 * q^74 + 3016 * q^76 + 572 * q^79 - 1950 * q^80 + 1530 * q^82 + 3888 * q^83 - 264 * q^85 + 804 * q^86 + 1164 * q^88 - 366 * q^89 + 5712 * q^92 - 1920 * q^94 - 1176 * q^95 - 1616 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.63746	+	4.56821i	−0.932482	+	1.61511i	−0.153420	+	0.988161i	$0.549029\pi$
$2$	−2.63746	+	4.56821i	−0.932482	+	1.61511i	−0.779063	+	0.626946i	$0.784305\pi$
$3$		0			0
$3$		0			0
$4$	−9.91238	−	17.1687i	−1.23905	−	2.14609i
$5$	−5.27492	+	9.13642i	−0.471803	+	0.817187i	−0.999480	−	0.0322587i	$-0.989730\pi$
$5$	−5.27492	+	9.13642i	−0.471803	+	0.817187i	0.527677	+	0.849445i	$0.323063\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	62.3746			2.75659
$9$		0			0
$10$	−27.8248	−	48.1939i	−0.879896	−	1.52402i
$11$	17.3746	+	30.0937i	0.476240	+	0.824871i	0.999629	−	0.0272223i	$-0.00866619\pi$
$11$	17.3746	+	30.0937i	0.476240	+	0.824871i	−0.523390	+	0.852093i	$0.675333\pi$
$12$		0			0
$13$	37.2990			0.795760			0.397880	−	0.917437i	$-0.369746\pi$
$13$	37.2990			0.795760			0.397880	+	0.917437i	$0.369746\pi$
$14$		0			0
$15$		0			0
$16$	−85.2114	+	147.590i	−1.33143	+	2.30610i
$17$	5.27492	+	9.13642i	0.0752562	+	0.130348i	0.901198	−	0.433408i	$-0.142689\pi$
$17$	5.27492	+	9.13642i	0.0752562	+	0.130348i	−0.825941	+	0.563756i	$0.809356\pi$
$18$		0			0
$19$	−29.2990	+	50.7474i	−0.353771	+	0.612750i	−0.986907	−	0.161291i	$-0.948434\pi$
$19$	−29.2990	+	50.7474i	−0.353771	+	0.612750i	0.633136	+	0.774041i	$0.281768\pi$
$20$	209.148			2.33834
$21$		0			0
$22$	−183.299			−1.77634
$23$	−62.6736	+	108.554i	−0.568189	+	0.984132i	0.428556	+	0.903515i	$0.359022\pi$
$23$	−62.6736	+	108.554i	−0.568189	+	0.984132i	−0.996745	+	0.0806171i	$0.974311\pi$
$24$		0			0
$25$	6.85050	+	11.8654i	0.0548040	+	0.0949233i
$26$	−98.3746	+	170.390i	−0.742032	+	1.28524i
$27$		0			0
$28$		0			0
$29$	35.4020			0.226689			0.113345	−	0.993556i	$-0.463844\pi$
$29$	35.4020			0.226689			0.113345	+	0.993556i	$0.463844\pi$
$30$		0			0
$31$	145.897	+	252.701i	0.845286	+	1.46408i	0.885372	+	0.464883i	$0.153904\pi$
$31$	145.897	+	252.701i	0.845286	+	1.46408i	−0.0400859	+	0.999196i	$0.512763\pi$
$32$	−199.985	−	346.384i	−1.10477	−	1.91352i
$33$		0			0
$34$	−55.6495			−0.280700
$35$		0			0
$36$		0			0
$37$	129.949	−	225.077i	0.577389	−	1.00007i	−0.418388	−	0.908268i	$-0.637405\pi$
$37$	129.949	−	225.077i	0.577389	−	1.00007i	0.995778	−	0.0917993i	$-0.0292618\pi$
$38$	−154.550	−	267.688i	−0.659771	−	1.14276i
$39$		0			0
$40$	−329.021	+	569.881i	−1.30057	+	2.25265i
$41$	−338.248			−1.28842			−0.644212	−	0.764847i	$-0.722815\pi$
$41$	−338.248			−1.28842			−0.644212	+	0.764847i	$0.722815\pi$
$42$		0			0
$43$	6.80397			0.0241301			0.0120651	−	0.999927i	$-0.496159\pi$
$43$	6.80397			0.0241301			0.0120651	+	0.999927i	$0.496159\pi$
$44$	344.447	−	596.599i	1.18017	−	2.04411i
$45$		0			0
$46$	−330.598	−	572.613i	−1.05965	−	1.83537i
$47$	−125.347	+	217.108i	−0.389016	+	0.673796i	−0.992317	−	0.123717i	$-0.960518\pi$
$47$	−125.347	+	217.108i	−0.389016	+	0.673796i	0.603301	+	0.797513i	$0.293852\pi$
$48$		0			0
$49$		0			0
$50$	−72.2716			−0.204415
$51$		0			0
$52$	−369.722	−	640.377i	−0.985984	−	1.70777i
$53$	−268.450	−	464.969i	−0.695745	−	1.20507i	−0.969929	−	0.243388i	$-0.921741\pi$
$53$	−268.450	−	464.969i	−0.695745	−	1.20507i	0.274184	−	0.961677i	$-0.411592\pi$
$54$		0			0
$55$	−366.598			−0.898765
$56$		0			0
$57$		0			0
$58$	−93.3713	+	161.724i	−0.211384	+	0.366127i
$59$	17.9452	+	31.0820i	0.0395977	+	0.0685853i	0.885145	−	0.465315i	$-0.154059\pi$
$59$	17.9452	+	31.0820i	0.0395977	+	0.0685853i	−0.845547	+	0.533900i	$0.820726\pi$
$60$		0			0
$61$	28.8970	−	50.0511i	0.0606538	−	0.105056i	−0.834104	−	0.551607i	$-0.814015\pi$
$61$	28.8970	−	50.0511i	0.0606538	−	0.105056i	0.894758	+	0.446552i	$0.147348\pi$
$62$	−1539.19			−3.15286
$63$		0			0
$64$	746.423			1.45786
$65$	−196.749	+	340.780i	−0.375442	+	0.650285i
$66$		0			0
$67$	−240.846	−	417.157i	−0.439164	−	0.760654i	0.558462	−	0.829530i	$-0.311392\pi$
$67$	−240.846	−	417.157i	−0.439164	−	0.760654i	−0.997625	+	0.0688767i	$0.978059\pi$
$68$	104.574	−	181.127i	0.186492	−	0.323013i
$69$		0			0
$70$		0			0
$71$	−363.752			−0.608021			−0.304010	−	0.952669i	$-0.598326\pi$
$71$	−363.752			−0.608021			−0.304010	+	0.952669i	$0.598326\pi$
$72$		0			0
$73$	290.650	+	503.420i	0.465999	+	0.807135i	0.999246	−	0.0388253i	$-0.0123616\pi$
$73$	290.650	+	503.420i	0.465999	+	0.807135i	−0.533247	+	0.845960i	$0.679028\pi$
$74$	685.468	+	1187.26i	1.07681	+	1.86509i
$75$		0			0
$76$	1161.69			1.75336
$77$		0			0
$78$		0			0
$79$	346.846	−	600.754i	0.493964	−	0.855571i	−0.506012	−	0.862527i	$-0.668881\pi$
$79$	346.846	−	600.754i	0.493964	−	0.855571i	0.999976	+	0.00695559i	$0.00221405\pi$
$80$	−898.966	−	1557.05i	−1.25634	−	2.17605i
$81$		0			0
$82$	892.114	−	1545.19i	1.20143	−	2.08094i
$83$	1334.39			1.76468			0.882341	−	0.470611i	$-0.155967\pi$
$83$	1334.39			1.76468			0.882341	+	0.470611i	$0.155967\pi$
$84$		0			0
$85$	−111.299			−0.142024
$86$	−17.9452	+	31.0820i	−0.0225009	+	0.0389728i
$87$		0			0
$88$	1083.73	+	1877.08i	1.31280	+	2.27383i
$89$	176.519	−	305.740i	0.210236	−	0.364139i	−0.741552	−	0.670895i	$-0.765910\pi$
$89$	176.519	−	305.740i	0.210236	−	0.364139i	0.951788	+	0.306756i	$0.0992435\pi$
$90$		0			0
$91$		0			0
$92$	2484.98			2.81605
$93$		0			0
$94$	−661.196	−	1145.23i	−0.725502	−	1.25661i
$95$	−309.100	−	535.376i	−0.333821	−	0.578194i
$96$		0			0
$97$	−1445.88			−1.51347			−0.756735	−	0.653722i	$-0.773207\pi$
$97$	−1445.88			−1.51347			−0.756735	+	0.653722i	$0.773207\pi$
$98$		0			0
$99$		0			0
$100$	135.809	−	235.229i	0.135809	−	0.235229i
$101$	−237.426	−	411.234i	−0.233909	−	0.405142i	0.725046	−	0.688700i	$-0.241818\pi$
$101$	−237.426	−	411.234i	−0.233909	−	0.405142i	−0.958955	+	0.283558i	$0.908485\pi$
$102$		0			0
$103$	−999.794	+	1731.69i	−0.956433	+	1.65659i	−0.225380	+	0.974271i	$0.572362\pi$
$103$	−999.794	+	1731.69i	−0.956433	+	1.65659i	−0.731053	+	0.682320i	$0.760971\pi$
$104$	2326.51			2.19359
$105$		0			0
$106$	2832.10			2.59508
$107$	583.368	−	1010.42i	0.527068	−	0.912909i	−0.472434	−	0.881366i	$-0.656625\pi$
$107$	583.368	−	1010.42i	0.527068	−	0.912909i	0.999502	−	0.0315431i	$-0.0100421\pi$
$108$		0			0
$109$	668.588	+	1158.03i	0.587515	+	1.01761i	0.994557	+	0.104196i	$0.0332270\pi$
$109$	668.588	+	1158.03i	0.587515	+	1.01761i	−0.407042	+	0.913410i	$0.633440\pi$
$110$	966.887	−	1674.70i	0.838082	−	1.45160i
$111$		0			0
$112$		0			0
$113$	−906.578			−0.754723			−0.377361	−	0.926066i	$-0.623169\pi$
$113$	−906.578			−0.754723			−0.377361	+	0.926066i	$0.623169\pi$
$114$		0			0
$115$	−661.196	−	1145.23i	−0.536146	−	0.928633i
$116$	−350.918	−	607.807i	−0.280878	−	0.486496i
$117$		0			0
$118$	−189.319			−0.147697
$119$		0			0
$120$		0			0
$121$	61.7475	−	106.950i	0.0463918	−	0.0803530i
$122$	152.429	+	264.015i	0.113117	+	0.195925i
$123$		0			0
$124$	2892.37	−	5009.74i	2.09470	−	3.62813i
$125$	−1463.27			−1.04703
$126$		0			0
$127$	−1714.89			−1.19820			−0.599101	−	0.800674i	$-0.704475\pi$
$127$	−1714.89			−1.19820			−0.599101	+	0.800674i	$0.704475\pi$
$128$	−368.782	+	638.749i	−0.254656	+	0.441078i
$129$		0			0
$130$	−1037.84	−	1797.58i	−0.700186	−	1.21276i
$131$	−235.306	+	407.561i	−0.156937	+	0.271823i	−0.933763	−	0.357893i	$-0.883495\pi$
$131$	−235.306	+	407.561i	−0.156937	+	0.271823i	0.776826	+	0.629716i	$0.216829\pi$
$132$		0			0
$133$		0			0
$134$	2540.88			1.63805
$135$		0			0
$136$	329.021	+	569.881i	0.207451	+	0.359315i
$137$	−221.955	−	384.438i	−0.138415	−	0.239742i	0.788482	−	0.615058i	$-0.210868\pi$
$137$	−221.955	−	384.438i	−0.138415	−	0.239742i	−0.926897	+	0.375316i	$0.877534\pi$
$138$		0			0
$139$	−1669.98			−1.01904			−0.509518	−	0.860460i	$-0.670176\pi$
$139$	−1669.98			−1.01904			−0.509518	+	0.860460i	$0.670176\pi$
$140$		0			0
$141$		0			0
$142$	959.382	−	1661.70i	0.566969	−	0.982019i
$143$	648.055	+	1122.46i	0.378972	+	0.656400i
$144$		0			0
$145$	−186.743	+	323.448i	−0.106953	+	0.185247i
$146$	−3066.30			−1.73814
$147$		0			0
$148$	−5152.39			−2.86165
$149$	371.935	−	644.211i	0.204497	−	0.354200i	−0.745475	−	0.666534i	$-0.767777\pi$
$149$	371.935	−	644.211i	0.204497	−	0.354200i	0.949973	+	0.312334i	$0.101111\pi$
$150$		0			0
$151$	−303.382	−	525.473i	−0.163503	−	0.283195i	0.772620	−	0.634869i	$-0.218946\pi$
$151$	−303.382	−	525.473i	−0.163503	−	0.283195i	−0.936123	+	0.351674i	$0.885613\pi$
$152$	−1827.51	+	3165.35i	−0.975203	+	1.68910i
$153$		0			0
$154$		0			0
$155$	−3078.38			−1.59523
$156$		0			0
$157$	1557.39	+	2697.48i	0.791678	+	1.37123i	0.924927	+	0.380144i	$0.124125\pi$
$157$	1557.39	+	2697.48i	0.791678	+	1.37123i	−0.133250	+	0.991083i	$0.542541\pi$
$158$	1829.58	+	3168.93i	0.921226	+	1.59561i
$159$		0			0
$160$	4219.61			2.08493
$161$		0			0
$162$		0			0
$163$	−1206.54	+	2089.78i	−0.579774	+	1.00420i	0.415730	+	0.909488i	$0.363526\pi$
$163$	−1206.54	+	2089.78i	−0.579774	+	1.00420i	−0.995505	+	0.0947109i	$0.969807\pi$
$164$	3352.84	+	5807.28i	1.59642	+	2.76508i
$165$		0			0
$166$	−3519.40	+	6095.79i	−1.64553	+	2.85015i
$167$	−610.475			−0.282874			−0.141437	−	0.989947i	$-0.545172\pi$
$167$	−610.475			−0.282874			−0.141437	+	0.989947i	$0.545172\pi$
$168$		0			0
$169$	−805.784			−0.366766
$170$	293.547	−	508.437i	0.132435	−	0.229385i
$171$		0			0
$172$	−67.4435	−	116.816i	−0.0298984	−	0.0517855i
$173$	−1896.90	+	3285.54i	−0.833636	+	1.44390i	0.0615006	+	0.998107i	$0.480411\pi$
$173$	−1896.90	+	3285.54i	−0.833636	+	1.44390i	−0.895136	+	0.445792i	$0.852922\pi$
$174$		0			0
$175$		0			0
$176$	−5922.05			−2.53631
$177$		0			0
$178$	931.124	+	1612.75i	0.392082	+	0.679107i
$179$	−1402.34	−	2428.92i	−0.585562	−	1.01422i	−0.994805	−	0.101798i	$-0.967540\pi$
$179$	−1402.34	−	2428.92i	−0.585562	−	1.01422i	0.409243	−	0.912426i	$-0.365793\pi$
$180$		0			0
$181$	−3106.04			−1.27553			−0.637763	−	0.770232i	$-0.720140\pi$
$181$	−3106.04			−1.27553			−0.637763	+	0.770232i	$0.720140\pi$
$182$		0			0
$183$		0			0
$184$	−3909.24	+	6771.00i	−1.56627	+	2.71285i
$185$	1370.94	+	2374.53i	0.544828	+	0.943670i
$186$		0			0
$187$	−183.299	+	317.483i	−0.0716800	+	0.124153i
$188$	4969.95			1.92804
$189$		0			0
$190$	3260.95			1.24513
$191$	130.976	−	226.857i	0.0496182	−	0.0859413i	−0.840150	−	0.542355i	$-0.817533\pi$
$191$	130.976	−	226.857i	0.0496182	−	0.0859413i	0.889768	+	0.456413i	$0.150866\pi$
$192$		0			0
$193$	−2025.54	−	3508.33i	−0.755447	−	1.30847i	−0.945152	−	0.326632i	$-0.894086\pi$
$193$	−2025.54	−	3508.33i	−0.755447	−	1.30847i	0.189704	−	0.981841i	$-0.439247\pi$
$194$	3813.44	−	6605.07i	1.41128	−	2.44442i
$195$		0			0
$196$		0			0
$197$	2874.83			1.03971			0.519855	−	0.854254i	$-0.325986\pi$
$197$	2874.83			1.03971			0.519855	+	0.854254i	$0.325986\pi$
$198$		0			0
$199$	−1533.49	−	2656.07i	−0.546261	−	0.946151i	−0.998526	−	0.0542680i	$-0.982717\pi$
$199$	−1533.49	−	2656.07i	−0.546261	−	0.946151i	0.452266	−	0.891883i	$-0.350616\pi$
$200$	427.297	+	740.100i	0.151072	+	0.261665i
$201$		0			0
$202$	2504.81			0.872463
$203$		0			0
$204$		0			0
$205$	1784.23	−	3090.37i	0.607882	−	1.05288i
$206$	−5273.83	−	9134.54i	−1.78371	−	3.08948i
$207$		0			0
$208$	−3178.30	+	5504.98i	−1.05950	+	1.83510i
$209$	−2036.23			−0.673919
$210$		0			0
$211$	595.422			0.194268			0.0971340	−	0.995271i	$-0.469032\pi$
$211$	595.422			0.194268			0.0971340	+	0.995271i	$0.469032\pi$
$212$	−5321.96	+	9217.90i	−1.72412	+	2.98626i
$213$		0			0
$214$	3077.22	+	5329.90i	0.982964	+	1.70254i
$215$	−35.8904	+	62.1640i	−0.0113847	+	0.0197188i
$216$		0			0
$217$		0			0
$218$	−7053.49			−2.19139
$219$		0			0
$220$	3633.86	+	6294.03i	1.11361	+	1.92883i
$221$	196.749	+	340.780i	0.0598859	+	0.103725i
$222$		0			0
$223$	3779.79			1.13504			0.567520	−	0.823360i	$-0.307903\pi$
$223$	3779.79			1.13504			0.567520	+	0.823360i	$0.307903\pi$
$224$		0			0
$225$		0			0
$226$	2391.06	−	4141.44i	0.703766	−	1.21896i
$227$	−913.809	−	1582.76i	−0.267188	−	0.462783i	0.700947	−	0.713214i	$-0.252761\pi$
$227$	−913.809	−	1582.76i	−0.267188	−	0.462783i	−0.968135	+	0.250431i	$0.919428\pi$
$228$		0			0
$229$	−425.125	+	736.338i	−0.122677	+	0.212483i	−0.920823	−	0.389982i	$-0.872481\pi$
$229$	−425.125	+	736.338i	−0.122677	+	0.212483i	0.798146	+	0.602465i	$0.205815\pi$
$230$	6975.51			1.99979
$231$		0			0
$232$	2208.18			0.624890
$233$	−3295.55	+	5708.06i	−0.926604	+	1.60492i	−0.137642	+	0.990482i	$0.543952\pi$
$233$	−3295.55	+	5708.06i	−0.926604	+	1.60492i	−0.788962	+	0.614443i	$0.789381\pi$
$234$		0			0
$235$	−1322.39	−	2290.45i	−0.367078	−	0.635798i
$236$	355.759	−	616.193i	0.0981269	−	0.169961i
$237$		0			0
$238$		0			0
$239$	182.556			0.0494083			0.0247042	−	0.999695i	$-0.492136\pi$
$239$	182.556			0.0494083			0.0247042	+	0.999695i	$0.492136\pi$
$240$		0			0
$241$	761.949	+	1319.73i	0.203657	+	0.352745i	0.949704	−	0.313149i	$-0.101384\pi$
$241$	761.949	+	1319.73i	0.203657	+	0.352745i	−0.746047	+	0.665894i	$0.768050\pi$
$242$	325.713	+	564.152i	0.0865191	+	0.149856i
$243$		0			0
$244$	−1145.75			−0.300612
$245$		0			0
$246$		0			0
$247$	−1092.82	+	1892.83i	−0.281517	+	0.487602i
$248$	9100.27	+	15762.1i	2.33011	+	4.03587i
$249$		0			0
$250$	3859.32	−	6684.54i	0.976339	−	1.69107i
$251$	2357.73			0.592903			0.296451	−	0.955048i	$-0.404197\pi$
$251$	2357.73			0.592903			0.296451	+	0.955048i	$0.404197\pi$
$252$		0			0
$253$	−4355.71			−1.08238
$254$	4522.94	−	7833.97i	1.11730	−	1.93522i
$255$		0			0
$256$	1040.40	+	1802.02i	0.254003	+	0.439946i
$257$	−1391.27	+	2409.76i	−0.337686	+	0.584890i	−0.983997	−	0.178185i	$-0.942978\pi$
$257$	−1391.27	+	2409.76i	−0.337686	+	0.584890i	0.646311	+	0.763074i	$0.276311\pi$
$258$		0			0
$259$		0			0
$260$	7801.01			1.86076
$261$		0			0
$262$	−1241.22	−	2149.85i	−0.292682	−	0.506940i
$263$	1021.89	+	1769.97i	0.239591	+	0.414984i	0.960597	−	0.277945i	$-0.0896532\pi$
$263$	1021.89	+	1769.97i	0.239591	+	0.414984i	−0.721006	+	0.692929i	$0.756320\pi$
$264$		0			0
$265$	5664.21			1.31302
$266$		0			0
$267$		0			0
$268$	−4774.70	+	8270.03i	−1.08829	+	1.88497i
$269$	−1726.42	−	2990.24i	−0.391307	−	0.677763i	0.601315	−	0.799012i	$-0.294644\pi$
$269$	−1726.42	−	2990.24i	−0.391307	−	0.677763i	−0.992622	+	0.121248i	$0.961310\pi$
$270$		0			0
$271$	1322.15	−	2290.02i	0.296364	−	0.513318i	−0.678937	−	0.734196i	$-0.737559\pi$
$271$	1322.15	−	2290.02i	0.296364	−	0.513318i	0.975301	+	0.220879i	$0.0708925\pi$
$272$	−1797.93			−0.400793
$273$		0			0
$274$	2341.59			0.516280
$275$	−238.049	+	412.313i	−0.0521996	+	0.0904124i
$276$		0			0
$277$	−1339.74	−	2320.50i	−0.290604	−	0.503341i	0.683349	−	0.730092i	$-0.260523\pi$
$277$	−1339.74	−	2320.50i	−0.290604	−	0.503341i	−0.973953	+	0.226751i	$0.927190\pi$
$278$	4404.50	−	7628.82i	0.950232	−	1.64585i
$279$		0			0
$280$		0			0
$281$	1019.69			0.216476			0.108238	−	0.994125i	$-0.465479\pi$
$281$	1019.69			0.216476			0.108238	+	0.994125i	$0.465479\pi$
$282$		0			0
$283$	216.103	+	374.301i	0.0453922	+	0.0786216i	0.887829	−	0.460174i	$-0.152213\pi$
$283$	216.103	+	374.301i	0.0453922	+	0.0786216i	−0.842437	+	0.538795i	$0.818880\pi$
$284$	3605.65	+	6245.17i	0.753366	+	1.30487i
$285$		0			0
$286$	−6836.87			−1.41354
$287$		0			0
$288$		0			0
$289$	2400.85	−	4158.40i	0.488673	−	0.846406i
$290$	−985.051	−	1706.16i	−0.199463	−	0.345480i
$291$		0			0
$292$	5762.05	−	9980.17i	1.15479	−	2.00016i
$293$	−2245.92			−0.447809			−0.223904	−	0.974611i	$-0.571880\pi$
$293$	−2245.92			−0.447809			−0.223904	+	0.974611i	$0.571880\pi$
$294$		0			0
$295$	−378.638			−0.0747293
$296$	8105.48	−	14039.1i	1.59163	−	2.75678i
$297$		0			0
$298$	1961.93	+	3398.16i	0.381381	+	0.660571i
$299$	−2337.66	+	4048.95i	−0.452142	+	0.783133i
$300$		0			0
$301$		0			0
$302$	3200.63			0.609853
$303$		0			0
$304$	−4993.22	−	8648.51i	−0.942042	−	1.63166i
$305$	304.859	+	528.031i	0.0572333	+	0.0991310i
$306$		0			0
$307$	3197.08			0.594354			0.297177	−	0.954822i	$-0.403955\pi$
$307$	3197.08			0.594354			0.297177	+	0.954822i	$0.403955\pi$
$308$		0			0
$309$		0			0
$310$	8119.10	−	14062.7i	1.48753	−	2.57647i
$311$	1677.80	+	2906.04i	0.305915	+	0.529860i	0.977465	−	0.211100i	$-0.0677045\pi$
$311$	1677.80	+	2906.04i	0.305915	+	0.529860i	−0.671550	+	0.740959i	$0.734371\pi$
$312$		0			0
$313$	−1128.20	+	1954.09i	−0.203736	+	0.352881i	−0.949729	−	0.313072i	$-0.898642\pi$
$313$	−1128.20	+	1954.09i	−0.203736	+	0.352881i	0.745993	+	0.665954i	$0.231975\pi$
$314$	−16430.2			−2.95290
$315$		0			0
$316$	−13752.3			−2.44818
$317$	−3069.59	+	5316.69i	−0.543866	+	0.942004i	0.454811	+	0.890588i	$0.349707\pi$
$317$	−3069.59	+	5316.69i	−0.543866	+	0.942004i	−0.998677	+	0.0514158i	$0.983627\pi$
$318$		0			0
$319$	615.095	+	1065.38i	0.107958	+	0.186989i
$320$	−3937.32	+	6819.64i	−0.687821	+	1.19134i
$321$		0			0
$322$		0			0
$323$	−618.199			−0.106494
$324$		0			0
$325$	255.517	+	442.568i	0.0436108	+	0.0755362i
$326$	−6364.38	−	11023.4i	−1.08126	−	1.87280i
$327$		0			0
$328$	−21098.0			−3.55166
$329$		0			0
$330$		0			0
$331$	−3514.91	+	6088.00i	−0.583676	+	1.01096i	0.411363	+	0.911472i	$0.365053\pi$
$331$	−3514.91	+	6088.00i	−0.583676	+	1.01096i	−0.995039	+	0.0994849i	$0.968280\pi$
$332$	−13227.0	−	22909.8i	−2.18652	−	3.78717i
$333$		0			0
$334$	1610.10	−	2788.78i	0.263775	−	0.456872i
$335$	5081.76			0.828795
$336$		0			0
$337$	10328.4			1.66951			0.834757	−	0.550619i	$-0.185608\pi$
$337$	10328.4			1.66951			0.834757	+	0.550619i	$0.185608\pi$
$338$	2125.22	−	3680.99i	0.342003	−	0.592366i
$339$		0			0
$340$	1103.24	+	1910.86i	0.175975	+	0.304797i
$341$	−5069.80	+	8781.15i	−0.805118	+	1.39450i
$342$		0			0
$343$		0			0
$344$	424.395			0.0665170
$345$		0			0
$346$	−10006.0	−	17330.9i	−1.55470	−	2.69282i
$347$	983.768	+	1703.94i	0.152194	+	0.263608i	0.932034	−	0.362371i	$-0.118033\pi$
$347$	983.768	+	1703.94i	0.152194	+	0.263608i	−0.779840	+	0.625980i	$0.784699\pi$
$348$		0			0
$349$	4365.46			0.669564			0.334782	−	0.942296i	$-0.391337\pi$
$349$	4365.46			0.669564			0.334782	+	0.942296i	$0.391337\pi$
$350$		0			0
$351$		0			0
$352$	6949.30	−	12036.5i	1.05227	−	1.82258i
$353$	3035.79	+	5258.15i	0.457731	+	0.792813i	0.998841	−	0.0481389i	$-0.0153290\pi$
$353$	3035.79	+	5258.15i	0.457731	+	0.792813i	−0.541110	+	0.840952i	$0.681996\pi$
$354$		0			0
$355$	1918.76	−	3323.40i	0.286866	−	0.496866i
$356$	−6998.90			−1.04197
$357$		0			0
$358$	14794.4			2.18411
$359$	4819.02	−	8346.79i	0.708463	−	1.22709i	−0.256965	−	0.966421i	$-0.582722\pi$
$359$	4819.02	−	8346.79i	0.708463	−	1.22709i	0.965427	−	0.260673i	$-0.0839443\pi$
$360$		0			0
$361$	1712.64	+	2966.37i	0.249692	+	0.432479i
$362$	8192.06	−	14189.1i	1.18941	−	2.06011i
$363$		0			0
$364$		0			0
$365$	−6132.61			−0.879439
$366$		0			0
$367$	261.362	+	452.693i	0.0371744	+	0.0643879i	0.884014	−	0.467460i	$-0.154831\pi$
$367$	261.362	+	452.693i	0.0371744	+	0.0643879i	−0.846840	+	0.531848i	$0.821498\pi$
$368$	−10681.0	−	18500.0i	−1.51301	−	2.62060i
$369$		0			0
$370$	−14463.1			−2.03217
$371$		0			0
$372$		0			0
$373$	−1614.92	+	2797.12i	−0.224175	+	0.388283i	−0.956072	−	0.293133i	$-0.905302\pi$
$373$	−1614.92	+	2797.12i	−0.224175	+	0.388283i	0.731896	+	0.681416i	$0.238636\pi$
$374$	−966.887	−	1674.70i	−0.133681	−	0.231542i
$375$		0			0
$376$	−7818.48	+	13542.0i	−1.07236	+	1.85738i
$377$	1320.46			0.180390
$378$		0			0
$379$	6639.71			0.899892			0.449946	−	0.893056i	$-0.351443\pi$
$379$	6639.71			0.899892			0.449946	+	0.893056i	$0.351443\pi$
$380$	−6127.82	+	10613.7i	−0.827239	+	1.43282i
$381$		0			0
$382$	690.887	+	1196.65i	0.0925363	+	0.160278i
$383$	7112.22	−	12318.7i	0.948871	−	1.64349i	0.201063	−	0.979578i	$-0.435561\pi$
$383$	7112.22	−	12318.7i	0.948871	−	1.64349i	0.747809	−	0.663914i	$-0.231106\pi$
$384$		0			0
$385$		0			0
$386$	21369.1			2.81777
$387$		0			0
$388$	14332.1	+	24823.9i	1.87526	+	3.24805i
$389$	1460.91	+	2530.37i	0.190414	+	0.329807i	0.945388	−	0.325948i	$-0.105684\pi$
$389$	1460.91	+	2530.37i	0.190414	+	0.329807i	−0.754973	+	0.655755i	$0.772350\pi$
$390$		0			0
$391$	−1322.39			−0.171039
$392$		0			0
$393$		0			0
$394$	−7582.24	+	13132.8i	−0.969512	+	1.67924i
$395$	3659.16	+	6337.86i	0.466108	+	0.807322i
$396$		0			0
$397$	405.970	−	703.161i	0.0513226	−	0.0888933i	−0.839223	−	0.543788i	$-0.816990\pi$
$397$	405.970	−	703.161i	0.0513226	−	0.0888933i	0.890545	+	0.454894i	$0.150323\pi$
$398$	16178.0			2.03751
$399$		0			0
$400$	−2334.96			−0.291870
$401$	1169.32	−	2025.32i	0.145618	−	0.252218i	−0.783985	−	0.620780i	$-0.786816\pi$
$401$	1169.32	−	2025.32i	0.145618	−	0.252218i	0.929603	+	0.368561i	$0.120150\pi$
$402$		0			0
$403$	5441.81	+	9425.50i	0.672645	+	1.16506i
$404$	−4706.91	+	8152.61i	−0.579648	+	1.00398i
$405$		0			0
$406$		0			0
$407$	9031.21			1.09990
$408$		0			0
$409$	−1363.79	−	2362.15i	−0.164877	−	0.285576i	0.771734	−	0.635945i	$-0.219390\pi$
$409$	−1363.79	−	2362.15i	−0.164877	−	0.285576i	−0.936612	+	0.350369i	$0.886056\pi$
$410$	9411.65	+	16301.5i	1.13368	+	1.96359i
$411$		0			0
$412$	39641.3			4.74026
$413$		0			0
$414$		0			0
$415$	−7038.81	+	12191.6i	−0.832582	+	1.44207i
$416$	−7459.23	−	12919.8i	−0.879132	−	1.52270i
$417$		0			0
$418$	5370.48	−	9301.94i	0.628418	−	1.08845i
$419$	13306.3			1.55144			0.775721	−	0.631076i	$-0.217386\pi$
$419$	13306.3			1.55144			0.775721	+	0.631076i	$0.217386\pi$
$420$		0			0
$421$	−11007.5			−1.27428			−0.637138	−	0.770750i	$-0.719882\pi$
$421$	−11007.5			−1.27428			−0.637138	+	0.770750i	$0.719882\pi$
$422$	−1570.40	+	2720.01i	−0.181151	+	0.313763i
$423$		0			0
$424$	−16744.5	−	29002.3i	−1.91789	−	3.32187i
$425$	−72.2716	+	125.178i	−0.00824868	+	0.0142871i
$426$		0			0
$427$		0			0
$428$	−23130.2			−2.61225
$429$		0			0
$430$	−189.319	−	327.910i	−0.0212320	−	0.0367749i
$431$	−3262.81	−	5651.36i	−0.364650	−	0.631592i	0.624070	−	0.781368i	$-0.285478\pi$
$431$	−3262.81	−	5651.36i	−0.364650	−	0.631592i	−0.988720	+	0.149776i	$0.952145\pi$
$432$		0			0
$433$	11716.3			1.30034			0.650171	−	0.759788i	$-0.274697\pi$
$433$	11716.3			1.30034			0.650171	+	0.759788i	$0.274697\pi$
$434$		0			0
$435$		0			0
$436$	13254.6	−	22957.6i	1.45592	−	2.52172i
$437$	−3672.55	−	6361.04i	−0.402018	−	0.696315i
$438$		0			0
$439$	−7305.69	+	12653.8i	−0.794264	+	1.37571i	0.129042	+	0.991639i	$0.458810\pi$
$439$	−7305.69	+	12653.8i	−0.794264	+	1.37571i	−0.923306	+	0.384066i	$0.874524\pi$
$440$	−22866.4			−2.47753
$441$		0			0
$442$	−2075.67			−0.223370
$443$	−7619.89	+	13198.0i	−0.817228	+	1.41548i	0.0904888	+	0.995897i	$0.471157\pi$
$443$	−7619.89	+	13198.0i	−0.817228	+	1.41548i	−0.907717	+	0.419583i	$0.862176\pi$
$444$		0			0
$445$	1862.25	+	3225.51i	0.198380	+	0.343604i
$446$	−9969.05	+	17266.9i	−1.05840	+	1.83321i
$447$		0			0
$448$		0			0
$449$	−10678.8			−1.12241			−0.561206	−	0.827676i	$-0.689662\pi$
$449$	−10678.8			−1.12241			−0.561206	+	0.827676i	$0.689662\pi$
$450$		0			0
$451$	−5876.91	−	10179.1i	−0.613598	−	1.06278i
$452$	8986.34	+	15564.8i	0.935137	+	1.61971i
$453$		0			0
$454$	9640.53			0.996592
$455$		0			0
$456$		0			0
$457$	−2114.12	+	3661.76i	−0.216399	+	0.374814i	−0.953704	−	0.300746i	$-0.902764\pi$
$457$	−2114.12	+	3661.76i	−0.216399	+	0.374814i	0.737306	+	0.675559i	$0.236098\pi$
$458$	−2242.50	−	3884.12i	−0.228788	−	0.396273i
$459$		0			0
$460$	−13108.0	+	22703.8i	−1.32862	+	2.30124i
$461$	910.121			0.0919492			0.0459746	−	0.998943i	$-0.485361\pi$
$461$	910.121			0.0919492			0.0459746	+	0.998943i	$0.485361\pi$
$462$		0			0
$463$	4456.16			0.447290			0.223645	−	0.974671i	$-0.428204\pi$
$463$	4456.16			0.447290			0.223645	+	0.974671i	$0.428204\pi$
$464$	−3016.65	+	5224.99i	−0.301820	+	0.522768i
$465$		0			0
$466$	−17383.8	−	30109.5i	−1.72808	−	2.99313i
$467$	2214.71	−	3835.99i	0.219453	−	0.380104i	−0.735188	−	0.677864i	$-0.762906\pi$
$467$	2214.71	−	3835.99i	0.219453	−	0.380104i	0.954641	+	0.297759i	$0.0962393\pi$
$468$		0			0
$469$		0			0
$470$	13951.0			1.36918
$471$		0			0
$472$	1119.32	+	1938.73i	0.109155	+	0.189062i
$473$	118.216	+	204.757i	0.0114917	+	0.0199043i
$474$		0			0
$475$	−802.851			−0.0775523
$476$		0			0
$477$		0			0
$478$	−481.485	+	833.957i	−0.0460724	+	0.0797998i
$479$	−1376.43	−	2384.04i	−0.131296	−	0.227411i	0.792881	−	0.609377i	$-0.208580\pi$
$479$	−1376.43	−	2384.04i	−0.131296	−	0.227411i	−0.924176	+	0.381966i	$0.875247\pi$
$480$		0			0
$481$	4846.95	−	8395.16i	0.459463	−	0.795814i
$482$	−8038.43			−0.759628
$483$		0			0
$484$	−2448.26			−0.229927
$485$	7626.88	−	13210.1i	0.714060	−	1.23679i
$486$		0			0
$487$	335.299	+	580.755i	0.0311989	+	0.0540380i	0.881203	−	0.472738i	$-0.156734\pi$
$487$	335.299	+	580.755i	0.0311989	+	0.0540380i	−0.850004	+	0.526776i	$0.823401\pi$
$488$	1802.44	−	3121.92i	0.167198	−	0.289595i
$489$		0			0
$490$		0			0
$491$	8244.70			0.757797			0.378898	−	0.925438i	$-0.376303\pi$
$491$	8244.70			0.757797			0.378898	+	0.925438i	$0.376303\pi$
$492$		0			0
$493$	186.743	+	323.448i	0.0170598	+	0.0295484i
$494$	−5764.56	−	9984.50i	−0.525019	−	0.909360i
$495$		0			0
$496$	−49728.3			−4.50175
$497$		0			0
$498$		0			0
$499$	−4082.46	+	7071.02i	−0.366244	+	0.634353i	−0.988975	−	0.148083i	$-0.952690\pi$
$499$	−4082.46	+	7071.02i	−0.366244	+	0.634353i	0.622731	+	0.782436i	$0.286023\pi$
$500$	14504.5	+	25122.5i	1.29732	+	2.24703i
$501$		0			0
$502$	−6218.42	+	10770.6i	−0.552872	+	0.957602i
$503$	8175.59			0.724715			0.362357	−	0.932039i	$-0.381972\pi$
$503$	8175.59			0.724715			0.362357	+	0.932039i	$0.381972\pi$
$504$		0			0
$505$	5009.61			0.441435
$506$	11488.0	−	19897.8i	1.00930	−	1.74815i
$507$		0			0
$508$	16998.6	+	29442.4i	1.48463	+	2.57145i
$509$	439.224	−	760.758i	0.0382480	−	0.0662475i	−0.846268	−	0.532758i	$-0.821156\pi$
$509$	439.224	−	760.758i	0.0382480	−	0.0662475i	0.884516	+	0.466510i	$0.154489\pi$
$510$		0			0
$511$		0			0
$512$	−16876.5			−1.45673
$513$		0			0
$514$	−7338.86	−	12711.3i	−0.629773	−	1.09080i
$515$	−10547.7	−	18269.1i	−0.902496	−	1.56317i
$516$		0			0
$517$	−8711.42			−0.741060
$518$		0			0
$519$		0			0
$520$	−12272.1	+	21256.0i	−1.03494	+	1.79257i
$521$	−5856.30	−	10143.4i	−0.492455	−	0.852957i	0.507507	−	0.861647i	$-0.330567\pi$
$521$	−5856.30	−	10143.4i	−0.492455	−	0.852957i	−0.999962	+	0.00869048i	$0.997234\pi$
$522$		0			0
$523$	−3670.91	+	6358.20i	−0.306917	+	0.531596i	−0.977686	−	0.210070i	$-0.932631\pi$
$523$	−3670.91	+	6358.20i	−0.306917	+	0.531596i	0.670769	+	0.741666i	$0.265964\pi$
$524$	9329.75			0.777809
$525$		0			0
$526$	−10780.8			−0.893659
$527$	−1539.19	+	2665.95i	−0.127226	+	0.220362i
$528$		0			0
$529$	−1772.46	−	3069.99i	−0.145678	−	0.252321i
$530$	−14939.1	+	25875.3i	−1.22437	+	2.12066i
$531$		0			0
$532$		0			0
$533$	−12616.3			−1.02528
$534$		0			0
$535$	6154.44	+	10659.8i	0.497345	+	0.861426i
$536$	−15022.6	−	26020.0i	−1.21060	−	2.09681i
$537$		0			0
$538$	18213.4			1.45955
$539$		0			0
$540$		0			0
$541$	7934.36	−	13742.7i	0.630545	−	1.09214i	−0.356895	−	0.934144i	$-0.616165\pi$
$541$	7934.36	−	13742.7i	0.630545	−	1.09214i	0.987440	−	0.157992i	$-0.0505020\pi$
$542$	6974.21	+	12079.7i	0.552709	+	0.957319i
$543$		0			0
$544$	2109.80	−	3654.29i	0.166282	−	0.288008i
$545$	−14107.0			−1.10877
$546$		0			0
$547$	2315.26			0.180975			0.0904875	−	0.995898i	$-0.471157\pi$
$547$	2315.26			0.180975			0.0904875	+	0.995898i	$0.471157\pi$
$548$	−4400.21	+	7621.38i	−0.343006	+	0.594104i
$549$		0			0
$550$	−1255.69	−	2174.92i	−0.0973505	−	0.168616i
$551$	−1037.24	+	1796.56i	−0.0801961	+	0.138904i
$552$		0			0
$553$		0			0
$554$	14134.1			1.08393
$555$		0			0
$556$	16553.5	+	28671.5i	1.26263	+	2.18694i
$557$	−2409.52	−	4173.42i	−0.183294	−	0.317475i	0.759706	−	0.650266i	$-0.225343\pi$
$557$	−2409.52	−	4173.42i	−0.183294	−	0.317475i	−0.943000	+	0.332792i	$0.892009\pi$
$558$		0			0
$559$	253.781			0.0192018
$560$		0			0
$561$		0			0
$562$	−2689.39	+	4658.17i	−0.201860	+	0.349631i
$563$	−1270.43	−	2200.45i	−0.0951017	−	0.164721i	0.814549	−	0.580094i	$-0.196984\pi$
$563$	−1270.43	−	2200.45i	−0.0951017	−	0.164721i	−0.909651	+	0.415373i	$0.863651\pi$
$564$		0			0
$565$	4782.12	−	8282.88i	0.356081	−	0.616750i
$566$	−2279.85			−0.169310
$567$		0			0
$568$	−22688.9			−1.67607
$569$	−12110.0	+	20975.1i	−0.892227	+	1.54538i	−0.0550275	+	0.998485i	$0.517525\pi$
$569$	−12110.0	+	20975.1i	−0.892227	+	1.54538i	−0.837200	+	0.546898i	$0.815809\pi$
$570$		0			0
$571$	5886.04	+	10194.9i	0.431389	+	0.747188i	0.996993	−	0.0774891i	$-0.0246903\pi$
$571$	5886.04	+	10194.9i	0.431389	+	0.747188i	−0.565604	+	0.824677i	$0.691357\pi$
$572$	12847.5	−	22252.6i	0.939129	−	1.62662i
$573$		0			0
$574$		0			0
$575$	−1717.38			−0.124556
$576$		0			0
$577$	5292.13	+	9166.24i	0.381827	+	0.661344i	0.991324	−	0.131445i	$-0.0419616\pi$
$577$	5292.13	+	9166.24i	0.381827	+	0.661344i	−0.609496	+	0.792789i	$0.708628\pi$
$578$	12664.3	+	21935.2i	0.911358	+	1.57852i
$579$		0			0
$580$	7404.25			0.530077
$581$		0			0
$582$		0			0
$583$	9328.42	−	16157.3i	0.662682	−	1.14780i
$584$	18129.1	+	31400.6i	1.28457	+	2.22494i
$585$		0			0
$586$	5923.52	−	10259.8i	0.417574	−	0.723259i
$587$	−8712.63			−0.612621			−0.306311	−	0.951932i	$-0.599095\pi$
$587$	−8712.63			−0.612621			−0.306311	+	0.951932i	$0.599095\pi$
$588$		0			0
$589$	−17098.6			−1.19615
$590$	998.641	−	1729.70i	0.0696838	−	0.120696i
$591$		0			0
$592$	22146.2	+	38358.3i	1.53750	+	2.66304i
$593$	7681.43	−	13304.6i	0.531937	−	0.921341i	−0.467368	−	0.884063i	$-0.654798\pi$
$593$	7681.43	−	13304.6i	0.531937	−	0.921341i	0.999305	−	0.0372786i	$-0.0118689\pi$
$594$		0			0
$595$		0			0
$596$	−14747.0			−1.01353
$597$		0			0
$598$	−12331.0	−	21357.9i	−0.843229	−	1.46052i
$599$	13001.9	+	22519.9i	0.886883	+	1.53613i	0.843540	+	0.537066i	$0.180467\pi$
$599$	13001.9	+	22519.9i	0.886883	+	1.53613i	0.0433430	+	0.999060i	$0.486199\pi$
$600$		0			0
$601$	−20567.7			−1.39596			−0.697982	−	0.716115i	$-0.745918\pi$
$601$	−20567.7			−1.39596			−0.697982	+	0.716115i	$0.745918\pi$
$602$		0			0
$603$		0			0
$604$	−6014.48	+	10417.4i	−0.405175	+	0.701783i
$605$	651.426	+	1128.30i	0.0437756	+	0.0758216i
$606$		0			0
$607$	9821.04	−	17010.5i	0.656711	−	1.13746i	−0.324751	−	0.945800i	$-0.605280\pi$
$607$	9821.04	−	17010.5i	0.656711	−	1.13746i	0.981462	−	0.191657i	$-0.0613862\pi$
$608$	23437.4			1.56334
$609$		0			0
$610$	−3216.21			−0.213476
$611$	−4675.33	+	8097.90i	−0.309564	+	0.536180i
$612$		0			0
$613$	−4227.29	−	7321.89i	−0.278530	−	0.482428i	0.692490	−	0.721428i	$-0.256514\pi$
$613$	−4227.29	−	7321.89i	−0.278530	−	0.482428i	−0.971020	+	0.239000i	$0.923180\pi$
$614$	−8432.16	+	14604.9i	−0.554225	+	0.959946i
$615$		0			0
$616$		0			0
$617$	24168.4			1.57696			0.788479	−	0.615061i	$-0.210869\pi$
$617$	24168.4			1.57696			0.788479	+	0.615061i	$0.210869\pi$
$618$		0			0
$619$	−1018.78	−	1764.58i	−0.0661523	−	0.114579i	0.831052	−	0.556194i	$-0.187739\pi$
$619$	−1018.78	−	1764.58i	−0.0661523	−	0.114579i	−0.897205	+	0.441615i	$0.854406\pi$
$620$	30514.0	+	52851.9i	1.97657	+	3.42352i
$621$		0			0
$622$	−17700.5			−1.14104
$623$		0			0
$624$		0			0
$625$	6862.33	−	11885.9i	0.439189	−	0.760698i
$626$	−5951.14	−	10307.7i	−0.379961	−	0.658111i
$627$		0			0
$628$	30874.9	−	53476.9i	1.96185	−	3.39803i
$629$	2741.87			0.173808
$630$		0			0
$631$	12339.5			0.778489			0.389244	−	0.921135i	$-0.372736\pi$
$631$	12339.5			0.778489			0.389244	+	0.921135i	$0.372736\pi$
$632$	21634.3	−	37471.8i	1.36166	−	2.35846i
$633$		0			0
$634$	−16191.9	−	28045.1i	−1.01429	−	1.75680i
$635$	9045.89	−	15667.9i	0.565315	−	0.979154i
$636$		0			0
$637$		0			0
$638$	−6489.15			−0.402677
$639$		0			0
$640$	−3890.59	−	6738.70i	−0.240295	−	0.416204i
$641$	−5111.32	−	8853.06i	−0.314953	−	0.545515i	0.664474	−	0.747311i	$-0.268655\pi$
$641$	−5111.32	−	8853.06i	−0.314953	−	0.545515i	−0.979428	+	0.201796i	$0.935322\pi$
$642$		0			0
$643$	1211.75			0.0743187			0.0371594	−	0.999309i	$-0.488169\pi$
$643$	1211.75			0.0743187			0.0371594	+	0.999309i	$0.488169\pi$
$644$		0			0
$645$		0			0
$646$	1630.48	−	2824.07i	0.0993037	−	0.171999i
$647$	1408.61	+	2439.78i	0.0855922	+	0.148250i	0.905643	−	0.424040i	$-0.139388\pi$
$647$	1408.61	+	2439.78i	0.0855922	+	0.148250i	−0.820051	+	0.572290i	$0.806055\pi$
$648$		0			0
$649$	−623.581	+	1080.07i	−0.0377160	+	0.0653260i
$650$	−2695.66			−0.162665
$651$		0			0
$652$	47838.6			2.87347
$653$	10493.1	−	18174.6i	0.628831	−	1.08917i	−0.358956	−	0.933355i	$-0.616867\pi$
$653$	10493.1	−	18174.6i	0.628831	−	1.08917i	0.987787	−	0.155812i	$-0.0497995\pi$
$654$		0			0
$655$	−2482.44	−	4299.70i	−0.148087	−	0.256494i
$656$	28822.5	−	49922.1i	1.71544	−	2.97124i
$657$		0			0
$658$		0			0
$659$	2384.09			0.140927			0.0704635	−	0.997514i	$-0.477552\pi$
$659$	2384.09			0.140927			0.0704635	+	0.997514i	$0.477552\pi$
$660$		0			0
$661$	−3788.55	−	6561.96i	−0.222931	−	0.386128i	0.732766	−	0.680481i	$-0.238229\pi$
$661$	−3788.55	−	6561.96i	−0.222931	−	0.386128i	−0.955697	+	0.294353i	$0.904896\pi$
$662$	−18540.8	−	32113.7i	−1.08854	−	1.88540i
$663$		0			0
$664$	83232.2			4.86451
$665$		0			0
$666$		0			0
$667$	−2218.77	+	3843.02i	−0.128802	+	0.223092i
$668$	6051.26	+	10481.1i	0.350494	+	0.607074i
$669$		0			0
$670$	−13402.9	+	23214.6i	−0.772837	+	1.33859i
$671$	2008.30			0.115543
$672$		0			0
$673$	11724.6			0.671547			0.335774	−	0.941943i	$-0.391002\pi$
$673$	11724.6			0.671547			0.335774	+	0.941943i	$0.391002\pi$
$674$	−27240.8	+	47182.5i	−1.55679	+	2.69644i
$675$		0			0
$676$	7987.23	+	13834.3i	0.454440	+	0.787113i
$677$	−16152.1	+	27976.3i	−0.916952	+	1.58821i	−0.112935	+	0.993602i	$0.536025\pi$
$677$	−16152.1	+	27976.3i	−0.916952	+	1.58821i	−0.804018	+	0.594606i	$0.797308\pi$
$678$		0			0
$679$		0			0
$680$	−6942.23			−0.391503
$681$		0			0
$682$	−26742.8	−	46319.9i	−1.50152	−	2.60070i
$683$	16683.6	+	28896.8i	0.934669	+	1.61889i	0.775223	+	0.631687i	$0.217637\pi$
$683$	16683.6	+	28896.8i	0.934669	+	1.61889i	0.159446	+	0.987207i	$0.449029\pi$
$684$		0			0
$685$	4683.18			0.261219
$686$		0			0
$687$		0			0
$688$	−579.776	+	1004.20i	−0.0321275	+	0.0556465i
$689$	−10012.9	−	17342.9i	−0.553646	−	0.958943i
$690$		0			0
$691$	−521.837	+	903.849i	−0.0287288	+	0.0497598i	−0.880032	−	0.474914i	$-0.842479\pi$
$691$	−521.837	+	903.849i	−0.0287288	+	0.0497598i	0.851304	+	0.524674i	$0.175813\pi$
$692$	75211.3			4.13166
$693$		0			0
$694$	−10378.6			−0.567674
$695$	8809.01	−	15257.6i	0.480784	−	0.832742i
$696$		0			0
$697$	−1784.23	−	3090.37i	−0.0969619	−	0.167943i
$698$	−11513.7	+	19942.4i	−0.624357	+	1.08142i
$699$		0			0
$700$		0			0
$701$	11305.7			0.609143			0.304572	−	0.952489i	$-0.401487\pi$
$701$	11305.7			0.609143			0.304572	+	0.952489i	$0.401487\pi$
$702$		0			0
$703$	7614.72	+	13189.1i	0.408527	+	0.707590i
$704$	12968.8	+	22462.6i	0.694289	+	1.20254i
$705$		0			0
$706$	−32027.1			−1.70730
$707$		0			0
$708$		0			0
$709$	6653.38	−	11524.0i	0.352430	−	0.610427i	−0.634245	−	0.773132i	$-0.718689\pi$
$709$	6653.38	−	11524.0i	0.352430	−	0.610427i	0.986675	+	0.162706i	$0.0520221\pi$
$710$	10121.3	+	17530.6i	0.534995	+	0.926639i
$711$		0			0
$712$	11010.3	−	19070.4i	0.579535	−	1.00378i
$713$	−36575.6			−1.92113
$714$		0			0
$715$	−13673.7			−0.715201
$716$	−27801.0	+	48152.8i	−1.45108	+	2.51334i
$717$		0			0
$718$	25419.9	+	44028.6i	1.32126	+	2.28849i
$719$	−5350.62	+	9267.55i	−0.277531	+	0.480697i	−0.970770	−	0.240010i	$-0.922849\pi$
$719$	−5350.62	+	9267.55i	−0.277531	+	0.480697i	0.693240	+	0.720707i	$0.256183\pi$
$720$		0			0
$721$		0			0
$722$	−18068.0			−0.931333
$723$		0			0
$724$	30788.3	+	53326.8i	1.58044	+	2.73740i
$725$	242.521	+	420.059i	0.0124235	+	0.0215181i
$726$		0			0
$727$	2121.14			0.108210			0.0541051	−	0.998535i	$-0.482769\pi$
$727$	2121.14			0.108210			0.0541051	+	0.998535i	$0.482769\pi$
$728$		0			0
$729$		0			0
$730$	16174.5	−	28015.1i	0.820062	−	1.42039i
$731$	35.8904	+	62.1640i	0.00181594	+	0.00314531i
$732$		0			0
$733$	−10792.0	+	18692.3i	−0.543809	+	0.941906i	0.454871	+	0.890557i	$0.349685\pi$
$733$	−10792.0	+	18692.3i	−0.543809	+	0.941906i	−0.998681	+	0.0513484i	$0.983648\pi$
$734$	−2757.33			−0.138658
$735$		0			0
$736$	50135.0			2.51087
$737$	8369.18	−	14495.8i	0.418294	−	0.724507i
$738$		0			0
$739$	4972.61	+	8612.81i	0.247524	+	0.428724i	0.962838	−	0.270079i	$-0.0870497\pi$
$739$	4972.61	+	8612.81i	0.247524	+	0.428724i	−0.715314	+	0.698803i	$0.753716\pi$
$740$	27178.5	−	47074.5i	1.35013	−	2.33850i
$741$		0			0
$742$		0			0
$743$	−2867.01			−0.141562			−0.0707808	−	0.997492i	$-0.522549\pi$
$743$	−2867.01			−0.141562			−0.0707808	+	0.997492i	$0.522549\pi$
$744$		0			0
$745$	3923.86	+	6796.32i	0.192965	+	0.334225i
$746$	−8518.57	−	14754.6i	−0.418079	−	0.724134i
$747$		0			0
$748$	7267.71			0.355259
$749$		0			0
$750$		0			0
$751$	5412.05	−	9373.94i	0.262967	−	0.455473i	−0.704062	−	0.710139i	$-0.748632\pi$
$751$	5412.05	−	9373.94i	0.262967	−	0.455473i	0.967029	+	0.254666i	$0.0819655\pi$
$752$	−21362.0	−	37000.1i	−1.03589	−	1.79422i
$753$		0			0
$754$	−3482.66	+	6032.14i	−0.168211	+	0.291349i
$755$	6401.26			0.308564
$756$		0			0
$757$	−14512.0			−0.696761			−0.348381	−	0.937353i	$-0.613268\pi$
$757$	−14512.0			−0.696761			−0.348381	+	0.937353i	$0.613268\pi$
$758$	−17512.0	+	30331.6i	−0.839134	+	1.45342i
$759$		0			0
$760$	−19280.0	−	33393.9i	−0.920208	−	1.59385i
$761$	16537.9	−	28644.5i	0.787778	−	1.36447i	−0.139547	−	0.990215i	$-0.544565\pi$
$761$	16537.9	−	28644.5i	0.787778	−	1.36447i	0.927325	−	0.374256i	$-0.122102\pi$
$762$		0			0
$763$		0			0
$764$	−5193.13			−0.245917
$765$		0			0
$766$	37516.4	+	64980.3i	1.76961	+	3.06506i
$767$	669.338	+	1159.33i	0.0315103	+	0.0545774i
$768$		0			0
$769$	−6728.44			−0.315518			−0.157759	−	0.987478i	$-0.550427\pi$
$769$	−6728.44			−0.315518			−0.157759	+	0.987478i	$0.550427\pi$
$770$		0			0
$771$		0			0
$772$	−40155.8	+	69551.8i	−1.87207	+	3.24252i
$773$	12116.6	+	20986.6i	0.563784	+	0.976503i	0.997162	+	0.0752907i	$0.0239885\pi$
$773$	12116.6	+	20986.6i	0.563784	+	0.976503i	−0.433377	+	0.901213i	$0.642678\pi$
$774$		0			0
$775$	−1998.93	+	3462.26i	−0.0926501	+	0.160475i
$776$	−90186.0			−4.17202
$777$		0			0
$778$	−15412.4			−0.710231
$779$	9910.32	−	17165.2i	0.455807	−	0.789481i
$780$		0			0
$781$	−6320.05	−	10946.6i	−0.289564	−	0.501539i
$782$	3487.75	−	6040.97i	0.159491	−	0.276246i
$783$		0			0
$784$		0			0
$785$	−32860.5			−1.49406
$786$		0			0
$787$	−8600.19	−	14896.0i	−0.389535	−	0.674694i	0.602852	−	0.797853i	$-0.294031\pi$
$787$	−8600.19	−	14896.0i	−0.389535	−	0.674694i	−0.992387	+	0.123159i	$0.960697\pi$
$788$	−28496.4	−	49357.2i	−1.28825	−	2.23131i
$789$		0			0
$790$	−38603.6			−1.73855
$791$		0			0
$792$		0			0
$793$	1077.83	−	1866.86i	0.0482659	−	0.0835990i
$794$	2141.46	+	3709.12i	0.0957148	+	0.165783i
$795$		0			0
$796$	−30401.0	+	52656.0i	−1.35369	+	2.34465i
$797$	−4208.87			−0.187059			−0.0935295	−	0.995617i	$-0.529815\pi$
$797$	−4208.87			−0.187059			−0.0935295	+	0.995617i	$0.529815\pi$
$798$		0			0
$799$	−2644.78			−0.117104
$800$	2739.99	−	4745.80i	0.121092	−	0.209737i
$801$		0			0
$802$	6168.05	+	10683.4i	0.271573	+	0.470378i
$803$	−10099.8	+	17493.4i	−0.443855	+	0.768779i
$804$		0			0
$805$		0			0
$806$	−57410.2			−2.50892
$807$		0			0
$808$	−14809.4	−	25650.6i	−0.644791	−	1.11681i
$809$	−11816.1	−	20466.0i	−0.513511	−	0.889428i	−0.999877	−	0.0156725i	$-0.995011\pi$
$809$	−11816.1	−	20466.0i	−0.513511	−	0.889428i	0.486366	−	0.873755i	$-0.338322\pi$
$810$		0			0
$811$	−28425.1			−1.23075			−0.615377	−	0.788233i	$-0.710996\pi$
$811$	−28425.1			−1.23075			−0.615377	+	0.788233i	$0.710996\pi$
$812$		0			0
$813$		0			0
$814$	−23819.4	+	41256.5i	−1.02564	+	1.77646i
$815$	−12728.8	−	22046.9i	−0.547079	−	0.947568i
$816$		0			0
$817$	−199.350	+	345.284i	−0.00853655	+	0.0147857i
$818$	14387.7			0.614981
$819$		0			0
$820$	−70743.7			−3.01278
$821$	19704.8	−	34129.7i	0.837640	−	1.45083i	−0.0542229	−	0.998529i	$-0.517268\pi$
$821$	19704.8	−	34129.7i	0.837640	−	1.45083i	0.891863	−	0.452306i	$-0.149399\pi$
$822$		0			0
$823$	−8173.28	−	14156.5i	−0.346176	−	0.599594i	0.639391	−	0.768882i	$-0.279187\pi$
$823$	−8173.28	−	14156.5i	−0.346176	−	0.599594i	−0.985567	+	0.169288i	$0.945853\pi$
$824$	−62361.7	+	108014.i	−2.63650	+	4.56655i
$825$		0			0
$826$		0			0
$827$	3738.87			0.157211			0.0786054	−	0.996906i	$-0.474953\pi$
$827$	3738.87			0.157211			0.0786054	+	0.996906i	$0.474953\pi$
$828$		0			0
$829$	−22598.1	−	39141.1i	−0.946761	−	1.63984i	−0.752186	−	0.658951i	$-0.771001\pi$
$829$	−22598.1	−	39141.1i	−0.946761	−	1.63984i	−0.194575	−	0.980888i	$-0.562333\pi$
$830$	−37129.1	−	64309.5i	−1.55274	−	2.68942i
$831$		0			0
$832$	27840.8			1.16010
$833$		0			0
$834$		0			0
$835$	3220.21	−	5577.56i	0.133461	−	0.231161i
$836$	20183.9	+	34959.5i	0.835018	+	1.44629i
$837$		0			0
$838$	−35094.8	+	60785.9i	−1.44669	+	2.50574i
$839$	15899.7			0.654254			0.327127	−	0.944980i	$-0.393920\pi$
$839$	15899.7			0.654254			0.327127	+	0.944980i	$0.393920\pi$
$840$		0			0
$841$	−23135.7			−0.948612
$842$	29031.7	−	50284.4i	1.18824	−	2.05809i
$843$		0			0
$844$	−5902.05	−	10222.6i	−0.240707	−	0.416917i
$845$	4250.44	−	7361.99i	0.173041	−	0.299716i
$846$		0			0
$847$		0			0
$848$	91500.0			3.70534
$849$		0			0
$850$	−381.227	−	660.304i	−0.0153835	−	0.0266450i
$851$	16288.7	+	28212.8i	0.656133	+	1.13645i
$852$		0			0
$853$	−33926.7			−1.36182			−0.680908	−	0.732369i	$-0.738415\pi$
$853$	−33926.7			−1.36182			−0.680908	+	0.732369i	$0.738415\pi$
$854$		0			0
$855$		0			0
$856$	36387.3	−	63024.7i	1.45291	−	2.51652i
$857$	17716.2	+	30685.4i	0.706154	+	1.22310i	0.966273	+	0.257519i	$0.0829049\pi$
$857$	17716.2	+	30685.4i	0.706154	+	1.22310i	−0.260119	+	0.965577i	$0.583762\pi$
$858$		0			0
$859$	−3390.09	+	5871.80i	−0.134655	+	0.233229i	−0.925465	−	0.378832i	$-0.876326\pi$
$859$	−3390.09	+	5871.80i	−0.134655	+	0.233229i	0.790811	+	0.612061i	$0.209659\pi$
$860$	1423.04			0.0564246
$861$		0			0
$862$	34422.1			1.36012
$863$	−15337.5	+	26565.4i	−0.604977	+	1.04785i	0.387078	+	0.922047i	$0.373485\pi$
$863$	−15337.5	+	26565.4i	−0.604977	+	1.04785i	−0.992055	+	0.125805i	$0.959849\pi$
$864$		0			0
$865$	−20012.0	−	34661.9i	−0.786624	−	1.36247i
$866$	−30901.2	+	53522.5i	−1.21255	+	2.10019i
$867$		0			0
$868$		0			0
$869$	24105.2			0.940981
$870$		0			0
$871$	−8983.30	−	15559.5i	−0.349469	−	0.605298i
$872$	41702.9	+	72231.5i	1.61954	+	2.80512i
$873$		0			0
$874$	38744.8			1.49950
$875$		0			0
$876$		0			0
$877$	−20430.6	+	35386.9i	−0.786652	+	1.36252i	0.141355	+	0.989959i	$0.454854\pi$
$877$	−20430.6	+	35386.9i	−0.786652	+	1.36252i	−0.928007	+	0.372562i	$0.878479\pi$
$878$	−38536.9	−	66747.9i	−1.48127	−	2.56564i
$879$		0			0
$880$	31238.3	−	54106.4i	1.19664	−	2.07264i
$881$	−43839.0			−1.67647			−0.838236	−	0.545308i	$-0.816413\pi$
$881$	−43839.0			−1.67647			−0.838236	+	0.545308i	$0.816413\pi$
$882$		0			0
$883$	44625.1			1.70074			0.850371	−	0.526183i	$-0.176377\pi$
$883$	44625.1			1.70074			0.850371	+	0.526183i	$0.176377\pi$
$884$	3900.50	−	6755.87i	0.148403	−	0.257041i
$885$		0			0
$886$	−40194.3	−	69618.6i	−1.52410	−	2.63982i
$887$	21983.7	−	38076.9i	0.832178	−	1.44137i	−0.0641300	−	0.997942i	$-0.520427\pi$
$887$	21983.7	−	38076.9i	0.832178	−	1.44137i	0.896308	−	0.443433i	$-0.146239\pi$
$888$		0			0
$889$		0			0
$890$	−19646.4			−0.739943
$891$		0			0
$892$	−37466.7	−	64894.3i	−1.40637	−	2.43590i
$893$	−7345.10	−	12722.1i	−0.275246	−	0.476739i
$894$		0			0
$895$	29588.9			1.10508
$896$		0			0
$897$		0			0
$898$	28164.9	−	48783.0i	1.04663	−	1.81282i
$899$	5165.04	+	8946.12i	0.191617	+	0.331891i
$900$		0			0
$901$	2832.10	−	4905.35i	0.104718	−	0.181377i
$902$	62000.4			2.28868
$903$		0			0
$904$	−56547.4			−2.08046
$905$	16384.1	−	28378.1i	0.601797	−	1.04234i
$906$		0			0
$907$	6792.15	+	11764.3i	0.248654	+	0.430682i	0.963153	−	0.268955i	$-0.0866783\pi$
$907$	6792.15	+	11764.3i	0.248654	+	0.430682i	−0.714498	+	0.699637i	$0.753345\pi$
$908$	−18116.0	+	31377.9i	−0.662117	+	1.14682i
$909$		0			0
$910$		0			0
$911$	16421.6			0.597226			0.298613	−	0.954374i	$-0.403476\pi$
$911$	16421.6			0.597226			0.298613	+	0.954374i	$0.403476\pi$
$912$		0			0
$913$	23184.5	+	40156.7i	0.840411	+	1.45563i
$914$	−11151.8	−	19315.5i	−0.403576	−	0.699014i
$915$		0			0
$916$	16856.0			0.608010
$917$		0			0
$918$		0			0
$919$	14743.6	−	25536.7i	0.529214	−	0.916625i	−0.470206	−	0.882557i	$-0.655820\pi$
$919$	14743.6	−	25536.7i	0.529214	−	0.916625i	0.999420	−	0.0340684i	$-0.0108464\pi$
$920$	−41241.8	−	71432.9i	−1.47794	−	2.55986i
$921$		0			0
$922$	−2400.41	+	4157.63i	−0.0857410	+	0.148508i
$923$	−13567.6			−0.483839
$924$		0			0
$925$	3560.85			0.126573
$926$	−11752.9	+	20356.7i	−0.417090	+	0.722422i
$927$		0			0
$928$	−7079.85	−	12262.7i	−0.250439	−	0.433773i
$929$	−1720.93	+	2980.73i	−0.0607769	+	0.105269i	−0.894813	−	0.446441i	$-0.852691\pi$
$929$	−1720.93	+	2980.73i	−0.0607769	+	0.105269i	0.834036	+	0.551710i	$0.186024\pi$
$930$		0			0
$931$		0			0
$932$	130667.			4.59242
$933$		0			0
$934$	11682.4	+	20234.6i	0.409273	+	0.708881i
$935$	−1933.77	−	3349.40i	−0.0676376	−	0.117152i
$936$		0			0
$937$	−5646.60			−0.196869			−0.0984346	−	0.995144i	$-0.531384\pi$
$937$	−5646.60			−0.196869			−0.0984346	+	0.995144i	$0.531384\pi$
$938$		0			0
$939$		0			0
$940$	−26216.1	+	45407.6i	−0.909654	+	1.57557i
$941$	22340.1	+	38694.1i	0.773927	+	1.34048i	0.935396	+	0.353603i	$0.115044\pi$
$941$	22340.1	+	38694.1i	0.773927	+	1.34048i	−0.161469	+	0.986878i	$0.551623\pi$
$942$		0			0
$943$	21199.2	−	36718.1i	0.732068	−	1.26798i
$944$	−6116.54			−0.210886
$945$		0			0
$946$	−1247.16			−0.0428633
$947$	−24462.3	+	42369.9i	−0.839406	+	1.45389i	0.0509860	+	0.998699i	$0.483764\pi$
$947$	−24462.3	+	42369.9i	−0.839406	+	1.45389i	−0.890392	+	0.455195i	$0.849570\pi$
$948$		0			0
$949$	10840.9	+	18777.1i	0.370824	+	0.642286i
$950$	2117.49	−	3667.59i	0.0723161	−	0.125255i
$951$		0			0
$952$		0			0
$953$	−52014.3			−1.76801			−0.884003	−	0.467482i	$-0.845161\pi$
$953$	−52014.3			−1.76801			−0.884003	+	0.467482i	$0.845161\pi$
$954$		0			0
$955$	1381.77	+	2393.30i	0.0468201	+	0.0810947i
$956$	−1809.57	−	3134.26i	−0.0612193	−	0.106035i
$957$		0			0
$958$	14521.1			0.489723
$959$		0			0
$960$		0			0
$961$	−27676.4	+	47936.9i	−0.929018	+	1.60911i
$962$	25567.3	+	44283.8i	0.856883	+	1.48417i
$963$		0			0
$964$	15105.4	−	26163.4i	0.504682	−	0.874135i
$965$	42738.2			1.42569
$966$		0			0
$967$	−47117.7			−1.56691			−0.783456	−	0.621448i	$-0.786545\pi$
$967$	−47117.7			−1.56691			−0.783456	+	0.621448i	$0.786545\pi$
$968$	3851.48	−	6670.95i	0.127883	−	0.221501i
$969$		0			0
$970$	40231.2	+	69682.4i	1.33170	+	2.30657i
$971$	4097.52	−	7097.12i	0.135423	−	0.234560i	−0.790336	−	0.612674i	$-0.790094\pi$
$971$	4097.52	−	7097.12i	0.135423	−	0.234560i	0.925759	+	0.378114i	$0.123427\pi$
$972$		0			0
$973$		0			0
$974$	−3537.35			−0.116370
$975$		0			0
$976$	4924.71	+	8529.85i	0.161512	+	0.279748i
$977$	2321.76	+	4021.40i	0.0760282	+	0.131685i	0.901533	−	0.432710i	$-0.142443\pi$
$977$	2321.76	+	4021.40i	0.0760282	+	0.131685i	−0.825505	+	0.564395i	$0.809109\pi$
$978$		0			0
$979$	12267.8			0.400490
$980$		0			0
$981$		0			0
$982$	−21745.1	+	37663.6i	−0.706632	+	1.22392i
$983$	−21993.3	−	38093.4i	−0.713607	−	1.23600i	−0.963494	−	0.267729i	$-0.913727\pi$
$983$	−21993.3	−	38093.4i	−0.713607	−	1.23600i	0.249887	−	0.968275i	$-0.419607\pi$
$984$		0			0
$985$	−15164.5	+	26265.6i	−0.490538	+	0.849638i
$986$	−1970.10			−0.0636317
$987$		0			0
$988$	43329.9			1.39525
$989$	−426.429	+	738.598i	−0.0137105	+	0.0237473i
$990$		0			0
$991$	−797.604	−	1381.49i	−0.0255668	−	0.0442831i	0.852959	−	0.521978i	$-0.174806\pi$
$991$	−797.604	−	1381.49i	−0.0255668	−	0.0442831i	−0.878526	+	0.477695i	$0.841472\pi$
$992$	58354.3	−	101073.i	1.86769	−	3.23494i
$993$		0			0
$994$		0			0
$995$	32356.0			1.03091
$996$		0			0
$997$	10750.6	+	18620.6i	0.341499	+	0.591494i	0.984711	−	0.174194i	$-0.0557321\pi$
$997$	10750.6	+	18620.6i	0.341499	+	0.591494i	−0.643212	+	0.765688i	$0.722399\pi$
$998$	−21534.6	−	37299.0i	−0.683032	−	1.18305i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.e.p.226.1		4
3.2	odd	2		147.4.e.m.79.2		4
7.2	even	3		441.4.a.r.1.2		2
7.3	odd	6		441.4.e.q.361.1		4
7.4	even	3	inner	441.4.e.p.361.1		4
7.5	odd	6		63.4.a.e.1.2		2
7.6	odd	2		441.4.e.q.226.1		4
21.2	odd	6		147.4.a.i.1.1		2
21.5	even	6		21.4.a.c.1.1	✓	2
21.11	odd	6		147.4.e.m.67.2		4
21.17	even	6		147.4.e.l.67.2		4
21.20	even	2		147.4.e.l.79.2		4
28.19	even	6		1008.4.a.ba.1.1		2
35.19	odd	6		1575.4.a.p.1.1		2
84.23	even	6		2352.4.a.bz.1.1		2
84.47	odd	6		336.4.a.m.1.2		2
105.47	odd	12		525.4.d.g.274.1		4
105.68	odd	12		525.4.d.g.274.4		4
105.89	even	6		525.4.a.n.1.2		2
168.5	even	6		1344.4.a.bg.1.1		2
168.131	odd	6		1344.4.a.bo.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.a.c.1.1	✓	2	21.5	even	6
63.4.a.e.1.2		2	7.5	odd	6
147.4.a.i.1.1		2	21.2	odd	6
147.4.e.l.67.2		4	21.17	even	6
147.4.e.l.79.2		4	21.20	even	2
147.4.e.m.67.2		4	21.11	odd	6
147.4.e.m.79.2		4	3.2	odd	2
336.4.a.m.1.2		2	84.47	odd	6
441.4.a.r.1.2		2	7.2	even	3
441.4.e.p.226.1		4	1.1	even	1	trivial
441.4.e.p.361.1		4	7.4	even	3	inner
441.4.e.q.226.1		4	7.6	odd	2
441.4.e.q.361.1		4	7.3	odd	6
525.4.a.n.1.2		2	105.89	even	6
525.4.d.g.274.1		4	105.47	odd	12
525.4.d.g.274.4		4	105.68	odd	12
1008.4.a.ba.1.1		2	28.19	even	6
1344.4.a.bg.1.1		2	168.5	even	6
1344.4.a.bo.1.1		2	168.131	odd	6
1575.4.a.p.1.1		2	35.19	odd	6
2352.4.a.bz.1.1		2	84.23	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.63746 + 4.56821i) q^{2} +(-9.91238 - 17.1687i) q^{4} +(-5.27492 + 9.13642i) q^{5} +62.3746 q^{8} +O(q^{10})\)	\(q+(-2.63746 + 4.56821i) q^{2} +(-9.91238 - 17.1687i) q^{4} +(-5.27492 + 9.13642i) q^{5} +62.3746 q^{8} +(-27.8248 - 48.1939i) q^{10} +(17.3746 + 30.0937i) q^{11} +37.2990 q^{13} +(-85.2114 + 147.590i) q^{16} +(5.27492 + 9.13642i) q^{17} +(-29.2990 + 50.7474i) q^{19} +209.148 q^{20} -183.299 q^{22} +(-62.6736 + 108.554i) q^{23} +(6.85050 + 11.8654i) q^{25} +(-98.3746 + 170.390i) q^{26} +35.4020 q^{29} +(145.897 + 252.701i) q^{31} +(-199.985 - 346.384i) q^{32} -55.6495 q^{34} +(129.949 - 225.077i) q^{37} +(-154.550 - 267.688i) q^{38} +(-329.021 + 569.881i) q^{40} -338.248 q^{41} +6.80397 q^{43} +(344.447 - 596.599i) q^{44} +(-330.598 - 572.613i) q^{46} +(-125.347 + 217.108i) q^{47} -72.2716 q^{50} +(-369.722 - 640.377i) q^{52} +(-268.450 - 464.969i) q^{53} -366.598 q^{55} +(-93.3713 + 161.724i) q^{58} +(17.9452 + 31.0820i) q^{59} +(28.8970 - 50.0511i) q^{61} -1539.19 q^{62} +746.423 q^{64} +(-196.749 + 340.780i) q^{65} +(-240.846 - 417.157i) q^{67} +(104.574 - 181.127i) q^{68} -363.752 q^{71} +(290.650 + 503.420i) q^{73} +(685.468 + 1187.26i) q^{74} +1161.69 q^{76} +(346.846 - 600.754i) q^{79} +(-898.966 - 1557.05i) q^{80} +(892.114 - 1545.19i) q^{82} +1334.39 q^{83} -111.299 q^{85} +(-17.9452 + 31.0820i) q^{86} +(1083.73 + 1877.08i) q^{88} +(176.519 - 305.740i) q^{89} +2484.98 q^{92} +(-661.196 - 1145.23i) q^{94} +(-309.100 - 535.376i) q^{95} -1445.88 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 17 q^{4} - 6 q^{5} + 174 q^{8}+O(q^{10}) \) 4 * q - 3 * q^2 - 17 * q^4 - 6 * q^5 + 174 * q^8	\( 4 q - 3 q^{2} - 17 q^{4} - 6 q^{5} + 174 q^{8} - 66 q^{10} - 6 q^{11} - 32 q^{13} - 137 q^{16} + 6 q^{17} + 64 q^{19} + 444 q^{20} - 552 q^{22} + 6 q^{23} + 118 q^{25} - 318 q^{26} + 504 q^{29} + 40 q^{31} - 279 q^{32} - 132 q^{34} + 248 q^{37} - 588 q^{38} - 546 q^{40} - 900 q^{41} + 752 q^{43} + 804 q^{44} - 960 q^{46} + 12 q^{47} + 330 q^{50} - 890 q^{52} - 1104 q^{53} - 1104 q^{55} + 306 q^{58} - 804 q^{59} - 428 q^{61} - 4224 q^{62} + 2578 q^{64} - 636 q^{65} - 148 q^{67} + 222 q^{68} - 1908 q^{71} + 1072 q^{73} + 1398 q^{74} + 3016 q^{76} + 572 q^{79} - 1950 q^{80} + 1530 q^{82} + 3888 q^{83} - 264 q^{85} + 804 q^{86} + 1164 q^{88} - 366 q^{89} + 5712 q^{92} - 1920 q^{94} - 1176 q^{95} - 1616 q^{97}+O(q^{100}) \) 4 * q - 3 * q^2 - 17 * q^4 - 6 * q^5 + 174 * q^8 - 66 * q^10 - 6 * q^11 - 32 * q^13 - 137 * q^16 + 6 * q^17 + 64 * q^19 + 444 * q^20 - 552 * q^22 + 6 * q^23 + 118 * q^25 - 318 * q^26 + 504 * q^29 + 40 * q^31 - 279 * q^32 - 132 * q^34 + 248 * q^37 - 588 * q^38 - 546 * q^40 - 900 * q^41 + 752 * q^43 + 804 * q^44 - 960 * q^46 + 12 * q^47 + 330 * q^50 - 890 * q^52 - 1104 * q^53 - 1104 * q^55 + 306 * q^58 - 804 * q^59 - 428 * q^61 - 4224 * q^62 + 2578 * q^64 - 636 * q^65 - 148 * q^67 + 222 * q^68 - 1908 * q^71 + 1072 * q^73 + 1398 * q^74 + 3016 * q^76 + 572 * q^79 - 1950 * q^80 + 1530 * q^82 + 3888 * q^83 - 264 * q^85 + 804 * q^86 + 1164 * q^88 - 366 * q^89 + 5712 * q^92 - 1920 * q^94 - 1176 * q^95 - 1616 * q^97

Introduction

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