LMFDB - Embedded newform 810.4.e.be.271.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,4,Mod(271,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("810.271");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	810.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:	$47.7915471046$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-1027})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 256x^{2} - 257x + 66049 $ x^4 - x^3 - 256x^2 - 257x + 66049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			271.2
Root			$14.1267 + 7.57870i$ of defining polynomial
Character	$\chi$	$=$	810.271
Dual form			810.4.e.be.541.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(15.1267 + 26.2002i) q^{7} -8.00000 q^{8} +10.0000 q^{10} +(26.6267 + 46.1188i) q^{11} +(9.12669 - 15.8079i) q^{13} +(-30.2534 + 52.4004i) q^{14} +(-8.00000 - 13.8564i) q^{16} -88.5068 q^{17} -71.5068 q^{19} +(10.0000 + 17.3205i) q^{20} +(-53.2534 + 92.2376i) q^{22} +(-16.1267 + 27.9322i) q^{23} +(-12.5000 - 21.6506i) q^{25} +36.5068 q^{26} -121.014 q^{28} +(133.133 + 230.594i) q^{29} +(39.1334 - 67.7811i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-88.5068 - 153.298i) q^{34} +151.267 q^{35} +413.041 q^{37} +(-71.5068 - 123.853i) q^{38} +(-20.0000 + 34.6410i) q^{40} +(38.2601 - 66.2685i) q^{41} +(2.74662 + 4.75729i) q^{43} -213.014 q^{44} -64.5068 q^{46} +(-129.394 - 224.116i) q^{47} +(-286.133 + 495.598i) q^{49} +(25.0000 - 43.3013i) q^{50} +(36.5068 + 63.2316i) q^{52} -579.774 q^{53} +266.267 q^{55} +(-121.014 - 209.602i) q^{56} +(-266.267 + 461.188i) q^{58} +(80.2736 - 139.038i) q^{59} +(251.760 + 436.061i) q^{61} +156.534 q^{62} +64.0000 q^{64} +(-45.6334 - 79.0394i) q^{65} +(-445.760 + 772.079i) q^{67} +(177.014 - 306.596i) q^{68} +(151.267 + 262.002i) q^{70} -993.760 q^{71} -116.561 q^{73} +(413.041 + 715.407i) q^{74} +(143.014 - 247.707i) q^{76} +(-805.547 + 1395.25i) q^{77} +(-501.321 - 868.313i) q^{79} -80.0000 q^{80} +153.041 q^{82} +(-257.986 - 446.846i) q^{83} +(-221.267 + 383.245i) q^{85} +(-5.49324 + 9.51458i) q^{86} +(-213.014 - 368.950i) q^{88} -957.760 q^{89} +552.226 q^{91} +(-64.5068 - 111.729i) q^{92} +(258.787 - 448.233i) q^{94} +(-178.767 + 309.633i) q^{95} +(866.855 + 1501.44i) q^{97} -1144.53 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{4} + 10 q^{5} + 5 q^{7} - 32 q^{8} + 40 q^{10} + 51 q^{11} - 19 q^{13} - 10 q^{14} - 32 q^{16} - 132 q^{17} - 64 q^{19} + 40 q^{20} - 102 q^{22} - 9 q^{23} - 50 q^{25} - 76 q^{26} - 40 q^{28}+ \cdots - 3468 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^4 + 10 * q^5 + 5 * q^7 - 32 * q^8 + 40 * q^10 + 51 * q^11 - 19 * q^13 - 10 * q^14 - 32 * q^16 - 132 * q^17 - 64 * q^19 + 40 * q^20 - 102 * q^22 - 9 * q^23 - 50 * q^25 - 76 * q^26 - 40 * q^28 + 255 * q^29 - 121 * q^31 + 64 * q^32 - 132 * q^34 + 50 * q^35 + 320 * q^37 - 64 * q^38 - 80 * q^40 - 180 * q^41 + 122 * q^43 - 408 * q^44 - 36 * q^46 + 93 * q^47 - 867 * q^49 + 100 * q^50 - 76 * q^52 - 1542 * q^53 + 510 * q^55 - 40 * q^56 - 510 * q^58 - 456 * q^59 + 674 * q^61 - 484 * q^62 + 256 * q^64 + 95 * q^65 - 1450 * q^67 + 264 * q^68 + 50 * q^70 - 3642 * q^71 + 1532 * q^73 + 320 * q^74 + 128 * q^76 - 1668 * q^77 + 326 * q^79 - 320 * q^80 - 720 * q^82 - 1476 * q^83 - 330 * q^85 - 244 * q^86 - 408 * q^88 - 3498 * q^89 + 2986 * q^91 - 36 * q^92 - 186 * q^94 - 160 * q^95 + 26 * q^97 - 3468 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$		0			0
$7$	15.1267	+	26.2002i	0.816764	+	1.41468i	0.908054	+	0.418853i	$0.137568\pi$
$7$	15.1267	+	26.2002i	0.816764	+	1.41468i	−0.0912896	+	0.995824i	$0.529099\pi$
$8$	−8.00000			−0.353553
$9$		0			0
$10$	10.0000			0.316228
$11$	26.6267	+	46.1188i	0.729841	+	1.26412i	0.956950	+	0.290252i	$0.0937392\pi$
$11$	26.6267	+	46.1188i	0.729841	+	1.26412i	−0.227109	+	0.973869i	$0.572928\pi$
$12$		0			0
$13$	9.12669	−	15.8079i	0.194714	−	0.337255i	−0.752092	−	0.659058i	$-0.770955\pi$
$13$	9.12669	−	15.8079i	0.194714	−	0.337255i	0.946807	+	0.321802i	$0.104289\pi$
$14$	−30.2534	+	52.4004i	−0.577540	+	1.00033i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−88.5068			−1.26271			−0.631354	−	0.775495i	$-0.717501\pi$
$17$	−88.5068			−1.26271			−0.631354	+	0.775495i	$0.717501\pi$
$18$		0			0
$19$	−71.5068			−0.863409			−0.431705	−	0.902015i	$-0.642088\pi$
$19$	−71.5068			−0.863409			−0.431705	+	0.902015i	$0.642088\pi$
$20$	10.0000	+	17.3205i	0.111803	+	0.193649i
$21$		0			0
$22$	−53.2534	+	92.2376i	−0.516075	+	0.893869i
$23$	−16.1267	+	27.9322i	−0.146202	+	0.253229i	−0.929821	−	0.368013i	$-0.880038\pi$
$23$	−16.1267	+	27.9322i	−0.146202	+	0.253229i	0.783619	+	0.621242i	$0.213372\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	36.5068			0.275368
$27$		0			0
$28$	−121.014			−0.816764
$29$	133.133	+	230.594i	0.852492	+	1.47656i	0.878953	+	0.476909i	$0.158243\pi$
$29$	133.133	+	230.594i	0.852492	+	1.47656i	−0.0264609	+	0.999650i	$0.508424\pi$
$30$		0			0
$31$	39.1334	−	67.7811i	0.226728	−	0.392705i	−0.730108	−	0.683331i	$-0.760530\pi$
$31$	39.1334	−	67.7811i	0.226728	−	0.392705i	0.956837	+	0.290627i	$0.0938638\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$		0			0
$34$	−88.5068	−	153.298i	−0.446435	−	0.773248i
$35$	151.267			0.730536
$36$		0			0
$37$	413.041			1.83523			0.917614	−	0.397472i	$-0.130113\pi$
$37$	413.041			1.83523			0.917614	+	0.397472i	$0.130113\pi$
$38$	−71.5068	−	123.853i	−0.305261	−	0.528728i
$39$		0			0
$40$	−20.0000	+	34.6410i	−0.0790569	+	0.136931i
$41$	38.2601	−	66.2685i	0.145737	−	0.252424i	−0.783910	−	0.620874i	$-0.786778\pi$
$41$	38.2601	−	66.2685i	0.145737	−	0.252424i	0.929648	+	0.368449i	$0.120111\pi$
$42$		0			0
$43$	2.74662	+	4.75729i	0.00974083	+	0.0168716i	0.870855	−	0.491540i	$-0.163566\pi$
$43$	2.74662	+	4.75729i	0.00974083	+	0.0168716i	−0.861114	+	0.508412i	$0.830233\pi$
$44$	−213.014			−0.729841
$45$		0			0
$46$	−64.5068			−0.206761
$47$	−129.394	−	224.116i	−0.401574	−	0.695547i	0.592342	−	0.805687i	$-0.298204\pi$
$47$	−129.394	−	224.116i	−0.401574	−	0.695547i	−0.993916	+	0.110140i	$0.964870\pi$
$48$		0			0
$49$	−286.133	+	495.598i	−0.834208	+	1.44489i
$50$	25.0000	−	43.3013i	0.0707107	−	0.122474i
$51$		0			0
$52$	36.5068	+	63.2316i	0.0973572	+	0.168628i
$53$	−579.774			−1.50260			−0.751302	−	0.659958i	$-0.770574\pi$
$53$	−579.774			−1.50260			−0.751302	+	0.659958i	$0.770574\pi$
$54$		0			0
$55$	266.267			0.652789
$56$	−121.014	−	209.602i	−0.288770	−	0.500164i
$57$		0			0
$58$	−266.267	+	461.188i	−0.602803	+	1.04408i
$59$	80.2736	−	139.038i	0.177131	−	0.306800i	−0.763766	−	0.645494i	$-0.776652\pi$
$59$	80.2736	−	139.038i	0.177131	−	0.306800i	0.940897	+	0.338694i	$0.109985\pi$
$60$		0			0
$61$	251.760	+	436.061i	0.528436	+	0.915278i	0.999450	+	0.0331522i	$0.0105546\pi$
$61$	251.760	+	436.061i	0.528436	+	0.915278i	−0.471015	+	0.882125i	$0.656112\pi$
$62$	156.534			0.320642
$63$		0			0
$64$	64.0000			0.125000
$65$	−45.6334	−	79.0394i	−0.0870790	−	0.150825i
$66$		0			0
$67$	−445.760	+	772.079i	−0.812810	+	1.40783i	0.0980799	+	0.995179i	$0.468730\pi$
$67$	−445.760	+	772.079i	−0.812810	+	1.40783i	−0.910890	+	0.412650i	$0.864603\pi$
$68$	177.014	−	306.596i	0.315677	−	0.546769i
$69$		0			0
$70$	151.267	+	262.002i	0.258284	+	0.447360i
$71$	−993.760			−1.66109			−0.830547	−	0.556949i	$-0.811972\pi$
$71$	−993.760			−1.66109			−0.830547	+	0.556949i	$0.811972\pi$
$72$		0			0
$73$	−116.561			−0.186882			−0.0934412	−	0.995625i	$-0.529787\pi$
$73$	−116.561			−0.186882			−0.0934412	+	0.995625i	$0.529787\pi$
$74$	413.041	+	715.407i	0.648851	+	1.12384i
$75$		0			0
$76$	143.014	−	247.707i	0.215852	−	0.373867i
$77$	−805.547	+	1395.25i	−1.19222	+	2.06498i
$78$		0			0
$79$	−501.321	−	868.313i	−0.713962	−	1.23662i	−0.963358	−	0.268217i	$-0.913565\pi$
$79$	−501.321	−	868.313i	−0.713962	−	1.23662i	0.249396	−	0.968402i	$-0.419768\pi$
$80$	−80.0000			−0.111803
$81$		0			0
$82$	153.041			0.206104
$83$	−257.986	−	446.846i	−0.341177	−	0.590936i	0.643475	−	0.765468i	$-0.277492\pi$
$83$	−257.986	−	446.846i	−0.341177	−	0.590936i	−0.984652	+	0.174532i	$0.944159\pi$
$84$		0			0
$85$	−221.267	+	383.245i	−0.282350	+	0.489045i
$86$	−5.49324	+	9.51458i	−0.00688781	+	0.0119300i
$87$		0			0
$88$	−213.014	−	368.950i	−0.258038	−	0.446934i
$89$	−957.760			−1.14070			−0.570350	−	0.821401i	$-0.693193\pi$
$89$	−957.760			−1.14070			−0.570350	+	0.821401i	$0.693193\pi$
$90$		0			0
$91$	552.226			0.636143
$92$	−64.5068	−	111.729i	−0.0731010	−	0.126615i
$93$		0			0
$94$	258.787	−	448.233i	0.283956	−	0.491826i
$95$	−178.767	+	309.633i	−0.193064	+	0.334397i
$96$		0			0
$97$	866.855	+	1501.44i	0.907379	+	1.57163i	0.817692	+	0.575657i	$0.195253\pi$
$97$	866.855	+	1501.44i	0.907379	+	1.57163i	0.0896874	+	0.995970i	$0.471413\pi$
$98$	−1144.53			−1.17975
$99$		0			0
$100$	100.000			0.100000
$101$	495.427	+	858.105i	0.488088	+	0.845393i	0.999906	−	0.0137009i	$-0.00436126\pi$
$101$	495.427	+	858.105i	0.488088	+	0.845393i	−0.511818	+	0.859094i	$0.671028\pi$
$102$		0			0
$103$	637.701	−	1104.53i	0.610044	−	1.05663i	−0.381188	−	0.924497i	$-0.624485\pi$
$103$	637.701	−	1104.53i	0.610044	−	1.05663i	0.991232	−	0.132130i	$-0.0421816\pi$
$104$	−73.0135	+	126.463i	−0.0688420	+	0.119238i
$105$		0			0
$106$	−579.774	−	1004.20i	−0.531251	−	0.920154i
$107$	453.095			0.409367			0.204684	−	0.978828i	$-0.434383\pi$
$107$	453.095			0.409367			0.204684	+	0.978828i	$0.434383\pi$
$108$		0			0
$109$	−538.855			−0.473513			−0.236757	−	0.971569i	$-0.576084\pi$
$109$	−538.855			−0.473513			−0.236757	+	0.971569i	$0.576084\pi$
$110$	266.267	+	461.188i	0.230796	+	0.399750i
$111$		0			0
$112$	242.027	−	419.203i	0.204191	−	0.353669i
$113$	−677.267	+	1173.06i	−0.563822	+	0.976569i	0.433336	+	0.901232i	$0.357336\pi$
$113$	−677.267	+	1173.06i	−0.563822	+	0.976569i	−0.997158	+	0.0753363i	$0.975997\pi$
$114$		0			0
$115$	80.6334	+	139.661i	0.0653835	+	0.113248i
$116$	−1065.07			−0.852492
$117$		0			0
$118$	321.095			0.250501
$119$	−1338.81	−	2318.89i	−1.03134	−	1.78633i
$120$		0			0
$121$	−752.461	+	1303.30i	−0.565335	+	0.979189i
$122$	−503.520	+	872.123i	−0.373661	+	0.647199i
$123$		0			0
$124$	156.534	+	271.124i	0.113364	+	0.196352i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	721.240			0.503935			0.251967	−	0.967736i	$-0.418922\pi$
$127$	721.240			0.503935			0.251967	+	0.967736i	$0.418922\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$		0			0
$130$	91.2669	−	158.079i	0.0615741	−	0.106650i
$131$	−1072.57	+	1857.74i	−0.715349	+	1.23902i	0.247476	+	0.968894i	$0.420399\pi$
$131$	−1072.57	+	1857.74i	−0.715349	+	1.23902i	−0.962825	+	0.270126i	$0.912935\pi$
$132$		0			0
$133$	−1081.66	−	1873.49i	−0.705202	−	1.22145i
$134$	−1783.04			−1.14949
$135$		0			0
$136$	708.054			0.446435
$137$	11.2399	+	19.4680i	0.00700939	+	0.0121406i	0.869509	−	0.493917i	$-0.164435\pi$
$137$	11.2399	+	19.4680i	0.00700939	+	0.0121406i	−0.862499	+	0.506058i	$0.831102\pi$
$138$		0			0
$139$	−745.780	+	1291.73i	−0.455081	+	0.788224i	−0.998693	−	0.0511132i	$-0.983723\pi$
$139$	−745.780	+	1291.73i	−0.455081	+	0.788224i	0.543612	+	0.839337i	$0.317056\pi$
$140$	−302.534	+	524.004i	−0.182634	+	0.316332i
$141$		0			0
$142$	−993.760	−	1721.24i	−0.587285	−	1.01721i
$143$	972.054			0.568442
$144$		0			0
$145$	1331.33			0.762492
$146$	−116.561	−	201.889i	−0.0660729	−	0.114442i
$147$		0			0
$148$	−826.081	+	1430.81i	−0.458807	+	0.794677i
$149$	733.642	−	1270.71i	0.403371	−	0.698659i	−0.590759	−	0.806848i	$-0.701172\pi$
$149$	733.642	−	1270.71i	0.403371	−	0.698659i	0.994130	+	0.108189i	$0.0345051\pi$
$150$		0			0
$151$	−668.160	−	1157.29i	−0.360094	−	0.623700i	0.627882	−	0.778308i	$-0.283922\pi$
$151$	−668.160	−	1157.29i	−0.360094	−	0.623700i	−0.987976	+	0.154608i	$0.950589\pi$
$152$	572.054			0.305261
$153$		0			0
$154$	−3222.19			−1.68605
$155$	−195.667	−	338.906i	−0.101396	−	0.175623i
$156$		0			0
$157$	−749.113	+	1297.50i	−0.380801	+	0.659566i	−0.991177	−	0.132545i	$-0.957685\pi$
$157$	−749.113	+	1297.50i	−0.380801	+	0.659566i	0.610376	+	0.792112i	$0.291018\pi$
$158$	1002.64	−	1736.63i	0.504848	−	0.874422i
$159$		0			0
$160$	−80.0000	−	138.564i	−0.0395285	−	0.0684653i
$161$	−975.774			−0.477651
$162$		0			0
$163$	1604.05			0.770793			0.385396	−	0.922751i	$-0.374065\pi$
$163$	1604.05			0.770793			0.385396	+	0.922751i	$0.374065\pi$
$164$	153.041	+	265.074i	0.0728686	+	0.126212i
$165$		0			0
$166$	515.973	−	893.691i	0.241249	−	0.417855i
$167$	−7.38514	+	12.7914i	−0.00342203	+	0.00592713i	−0.867731	−	0.497034i	$-0.834423\pi$
$167$	−7.38514	+	12.7914i	−0.00342203	+	0.00592713i	0.864309	+	0.502961i	$0.167756\pi$
$168$		0			0
$169$	931.907	+	1614.11i	0.424173	+	0.734688i
$170$	−885.068			−0.399303
$171$		0			0
$172$	−21.9730			−0.00974083
$173$	227.728	+	394.437i	0.100080	+	0.173344i	0.911717	−	0.410818i	$-0.134757\pi$
$173$	227.728	+	394.437i	0.100080	+	0.173344i	−0.811637	+	0.584162i	$0.801423\pi$
$174$		0			0
$175$	378.167	−	655.005i	0.163353	−	0.282936i
$176$	426.027	−	737.900i	0.182460	−	0.316030i
$177$		0			0
$178$	−957.760	−	1658.89i	−0.403299	−	0.698534i
$179$	−2766.07			−1.15500			−0.577502	−	0.816390i	$-0.695972\pi$
$179$	−2766.07			−1.15500			−0.577502	+	0.816390i	$0.695972\pi$
$180$		0			0
$181$	4154.77			1.70620			0.853099	−	0.521749i	$-0.174720\pi$
$181$	4154.77			1.70620			0.853099	+	0.521749i	$0.174720\pi$
$182$	552.226	+	956.484i	0.224911	+	0.389557i
$183$		0			0
$184$	129.014	−	223.458i	0.0516902	−	0.0895301i
$185$	1032.60	−	1788.52i	0.410370	−	0.710781i
$186$		0			0
$187$	−2356.64	−	4081.82i	−0.921576	−	1.59622i
$188$	1035.15			0.401574
$189$		0			0
$190$	−715.068			−0.273034
$191$	−1389.43	−	2406.56i	−0.526364	−	0.911688i	−0.999528	−	0.0307144i	$-0.990222\pi$
$191$	−1389.43	−	2406.56i	−0.526364	−	0.911688i	0.473165	−	0.880974i	$-0.343112\pi$
$192$		0			0
$193$	691.199	−	1197.19i	0.257791	−	0.446507i	−0.707859	−	0.706354i	$-0.750339\pi$
$193$	691.199	−	1197.19i	0.257791	−	0.446507i	0.965650	+	0.259847i	$0.0836721\pi$
$194$	−1733.71	+	3002.87i	−0.641614	+	1.11131i
$195$		0			0
$196$	−1144.53	−	1982.39i	−0.417104	−	0.722446i
$197$	2733.58			0.988629			0.494314	−	0.869283i	$-0.335419\pi$
$197$	2733.58			0.988629			0.494314	+	0.869283i	$0.335419\pi$
$198$		0			0
$199$	3371.47			1.20099			0.600496	−	0.799628i	$-0.294970\pi$
$199$	3371.47			1.20099			0.600496	+	0.799628i	$0.294970\pi$
$200$	100.000	+	173.205i	0.0353553	+	0.0612372i
$201$		0			0
$202$	−990.855	+	1716.21i	−0.345130	+	0.597783i
$203$	−4027.74	+	6976.24i	−1.39257	+	2.41200i
$204$		0			0
$205$	−191.301	−	331.342i	−0.0651757	−	0.112888i
$206$	2550.80			0.862733
$207$		0			0
$208$	−292.054			−0.0973572
$209$	−1903.99	−	3297.80i	−0.630151	−	1.09145i
$210$		0			0
$211$	2843.97	−	4925.90i	0.927900	−	1.60717i	0.141071	−	0.989999i	$-0.454945\pi$
$211$	2843.97	−	4925.90i	0.927900	−	1.60717i	0.786829	−	0.617171i	$-0.211721\pi$
$212$	1159.55	−	2008.39i	0.375651	−	0.650647i
$213$		0			0
$214$	453.095	+	784.783i	0.144733	+	0.250685i
$215$	27.4662			0.00871247
$216$		0			0
$217$	2367.84			0.740734
$218$	−538.855	−	933.324i	−0.167412	−	0.289966i
$219$		0			0
$220$	−532.534	+	922.376i	−0.163197	+	0.282666i
$221$	−807.774	+	1399.10i	−0.245868	+	0.425855i
$222$		0			0
$223$	2712.70	+	4698.53i	0.814599	+	1.41093i	0.909616	+	0.415451i	$0.136376\pi$
$223$	2712.70	+	4698.53i	0.814599	+	1.41093i	−0.0950167	+	0.995476i	$0.530290\pi$
$224$	968.108			0.288770
$225$		0			0
$226$	−2709.07			−0.797365
$227$	1983.20	+	3435.01i	0.579867	+	1.00436i	0.995494	+	0.0948239i	$0.0302288\pi$
$227$	1983.20	+	3435.01i	0.579867	+	1.00436i	−0.415627	+	0.909535i	$0.636438\pi$
$228$		0			0
$229$	298.294	−	516.660i	0.0860778	−	0.149091i	−0.819772	−	0.572690i	$-0.805900\pi$
$229$	298.294	−	516.660i	0.0860778	−	0.149091i	0.905850	+	0.423599i	$0.139233\pi$
$230$	−161.267	+	279.322i	−0.0462331	+	0.0800782i
$231$		0			0
$232$	−1065.07	−	1844.75i	−0.301401	−	0.522042i
$233$	1330.40			0.374066			0.187033	−	0.982354i	$-0.440113\pi$
$233$	1330.40			0.374066			0.187033	+	0.982354i	$0.440113\pi$
$234$		0			0
$235$	−1293.94			−0.359179
$236$	321.095	+	556.152i	0.0885656	+	0.153400i
$237$		0			0
$238$	2677.63	−	4637.79i	0.729264	−	1.26312i
$239$	−167.375	+	289.902i	−0.0452995	+	0.0784611i	−0.887786	−	0.460256i	$-0.847758\pi$
$239$	−167.375	+	289.902i	−0.0452995	+	0.0784611i	0.842487	+	0.538717i	$0.181091\pi$
$240$		0			0
$241$	1894.06	+	3280.60i	0.506253	+	0.876855i	0.999974	+	0.00723489i	$0.00230296\pi$
$241$	1894.06	+	3280.60i	0.506253	+	0.876855i	−0.493721	+	0.869620i	$0.664364\pi$
$242$	−3009.84			−0.799505
$243$		0			0
$244$	−2014.08			−0.528436
$245$	1430.67	+	2477.99i	0.373069	+	0.646175i
$246$		0			0
$247$	−652.620	+	1130.37i	−0.168118	+	0.291189i
$248$	−313.068	+	542.249i	−0.0801605	+	0.138842i
$249$		0			0
$250$	−125.000	−	216.506i	−0.0316228	−	0.0547723i
$251$	3636.79			0.914550			0.457275	−	0.889325i	$-0.348826\pi$
$251$	3636.79			0.914550			0.457275	+	0.889325i	$0.348826\pi$
$252$		0			0
$253$	−1717.60			−0.426817
$254$	721.240	+	1249.22i	0.178168	+	0.308596i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−1204.55	+	2086.34i	−0.292364	+	0.506390i	−0.974368	−	0.224959i	$-0.927775\pi$
$257$	−1204.55	+	2086.34i	−0.292364	+	0.506390i	0.682004	+	0.731348i	$0.261109\pi$
$258$		0			0
$259$	6247.94	+	10821.7i	1.49895	+	2.59626i
$260$	365.068			0.0870790
$261$		0			0
$262$	−4290.27			−1.01166
$263$	−1944.35	−	3367.72i	−0.455871	−	0.789591i	0.542867	−	0.839818i	$-0.317339\pi$
$263$	−1944.35	−	3367.72i	−0.455871	−	0.789591i	−0.998738	+	0.0502276i	$0.984005\pi$
$264$		0			0
$265$	−1449.43	+	2510.49i	−0.335993	+	0.581956i
$266$	2163.32	−	3746.98i	0.498653	−	0.863692i
$267$		0			0
$268$	−1783.04	−	3088.32i	−0.406405	−	0.703914i
$269$	−1253.01			−0.284005			−0.142003	−	0.989866i	$-0.545354\pi$
$269$	−1253.01			−0.284005			−0.142003	+	0.989866i	$0.545354\pi$
$270$		0			0
$271$	−3356.72			−0.752422			−0.376211	−	0.926534i	$-0.622773\pi$
$271$	−3356.72			−0.752422			−0.376211	+	0.926534i	$0.622773\pi$
$272$	708.054	+	1226.39i	0.157839	+	0.273384i
$273$		0			0
$274$	−22.4797	+	38.9360i	−0.00495639	+	0.00858472i
$275$	665.667	−	1152.97i	0.145968	−	0.252824i
$276$		0			0
$277$	−2337.21	−	4048.17i	−0.506965	−	0.878090i	−0.999968	−	0.00806167i	$-0.997434\pi$
$277$	−2337.21	−	4048.17i	−0.506965	−	0.878090i	0.493002	−	0.870028i	$-0.335899\pi$
$278$	−2983.12			−0.643582
$279$		0			0
$280$	−1210.14			−0.258284
$281$	650.769	+	1127.16i	0.138155	+	0.239292i	0.926798	−	0.375559i	$-0.122549\pi$
$281$	650.769	+	1127.16i	0.138155	+	0.239292i	−0.788643	+	0.614851i	$0.789216\pi$
$282$		0			0
$283$	1973.65	−	3418.47i	0.414563	−	0.718045i	−0.580819	−	0.814033i	$-0.697268\pi$
$283$	1973.65	−	3418.47i	0.414563	−	0.718045i	0.995383	+	0.0959878i	$0.0306010\pi$
$284$	1987.52	−	3442.49i	0.415273	−	0.719275i
$285$		0			0
$286$	972.054	+	1683.65i	0.200975	+	0.348098i
$287$	2315.00			0.476132
$288$		0			0
$289$	2920.45			0.594432
$290$	1331.33	+	2305.94i	0.269582	+	0.466929i
$291$		0			0
$292$	233.122	−	403.778i	0.0467206	−	0.0809224i
$293$	3133.98	−	5428.22i	0.624878	−	1.08232i	−0.363687	−	0.931521i	$-0.618482\pi$
$293$	3133.98	−	5428.22i	0.624878	−	1.08232i	0.988565	−	0.150799i	$-0.0481845\pi$
$294$		0			0
$295$	−401.368	−	695.190i	−0.0792155	−	0.137205i
$296$	−3304.32			−0.648851
$297$		0			0
$298$	2934.57			0.570453
$299$	294.367	+	509.858i	0.0569353	+	0.0986148i
$300$		0			0
$301$	−83.0946	+	143.924i	−0.0159119	+	0.0275603i
$302$	1336.32	−	2314.58i	0.254625	−	0.441023i
$303$		0			0
$304$	572.054	+	990.827i	0.107926	+	0.186934i
$305$	2517.60			0.472647
$306$		0			0
$307$	−6482.89			−1.20520			−0.602602	−	0.798042i	$-0.705869\pi$
$307$	−6482.89			−1.20520			−0.602602	+	0.798042i	$0.705869\pi$
$308$	−3222.19	−	5581.00i	−0.596108	−	1.03249i
$309$		0			0
$310$	391.334	−	677.811i	0.0716978	−	0.124184i
$311$	1907.90	−	3304.57i	0.347868	−	0.602525i	−0.638003	−	0.770034i	$-0.720239\pi$
$311$	1907.90	−	3304.57i	0.347868	−	0.602525i	0.985870	+	0.167509i	$0.0535724\pi$
$312$		0			0
$313$	2711.01	+	4695.61i	0.489570	+	0.847961i	0.999928	−	0.0120015i	$-0.00382027\pi$
$313$	2711.01	+	4695.61i	0.489570	+	0.847961i	−0.510358	+	0.859962i	$0.670487\pi$
$314$	−2996.45			−0.538534
$315$		0			0
$316$	4010.57			0.713962
$317$	−132.596	−	229.663i	−0.0234932	−	0.0406914i	0.854040	−	0.520208i	$-0.174145\pi$
$317$	−132.596	−	229.663i	−0.0234932	−	0.0406914i	−0.877533	+	0.479516i	$0.840812\pi$
$318$		0			0
$319$	−7089.81	+	12279.9i	−1.24437	+	2.15531i
$320$	160.000	−	277.128i	0.0279508	−	0.0484123i
$321$		0			0
$322$	−975.774	−	1690.09i	−0.168875	−	0.292500i
$323$	6328.83			1.09023
$324$		0			0
$325$	−456.334			−0.0778858
$326$	1604.05	+	2778.30i	0.272516	+	0.472012i
$327$		0			0
$328$	−306.081	+	530.148i	−0.0515259	+	0.0892455i
$329$	3914.59	−	6780.27i	0.655983	−	1.13620i
$330$		0			0
$331$	823.640	+	1426.59i	0.136771	+	0.236895i	0.926273	−	0.376854i	$-0.122994\pi$
$331$	823.640	+	1426.59i	0.136771	+	0.236895i	−0.789501	+	0.613749i	$0.789661\pi$
$332$	2063.89			0.341177
$333$		0			0
$334$	−29.5406			−0.00483949
$335$	2228.80	+	3860.40i	0.363500	+	0.629600i
$336$		0			0
$337$	3994.50	−	6918.67i	0.645680	−	1.11835i	−0.338464	−	0.940979i	$-0.609907\pi$
$337$	3994.50	−	6918.67i	0.645680	−	1.11835i	0.984144	−	0.177371i	$-0.0567592\pi$
$338$	−1863.81	+	3228.22i	−0.299935	+	0.519503i
$339$		0			0
$340$	−885.068	−	1532.98i	−0.141175	−	0.244522i
$341$	4167.98			0.661902
$342$		0			0
$343$	−6936.10			−1.09188
$344$	−21.9730	−	38.0583i	−0.00344391	−	0.00596502i
$345$		0			0
$346$	−455.456	+	788.873i	−0.0707673	+	0.122572i
$347$	1449.72	−	2510.99i	0.224280	−	0.388464i	−0.731823	−	0.681494i	$-0.761330\pi$
$347$	1449.72	−	2510.99i	0.224280	−	0.388464i	0.956103	+	0.293031i	$0.0946638\pi$
$348$		0			0
$349$	1908.64	+	3305.86i	0.292742	+	0.507044i	0.974457	−	0.224574i	$-0.0720989\pi$
$349$	1908.64	+	3305.86i	0.292742	+	0.507044i	−0.681715	+	0.731618i	$0.738766\pi$
$350$	1512.67			0.231016
$351$		0			0
$352$	1704.11			0.258038
$353$	−4949.01	−	8571.93i	−0.746201	−	1.29246i	−0.949631	−	0.313369i	$-0.898542\pi$
$353$	−4949.01	−	8571.93i	−0.746201	−	1.29246i	0.203430	−	0.979089i	$-0.434791\pi$
$354$		0			0
$355$	−2484.40	+	4303.11i	−0.371432	+	0.643339i
$356$	1915.52	−	3317.78i	0.285175	−	0.493938i
$357$		0			0
$358$	−2766.07	−	4790.97i	−0.408355	−	0.707292i
$359$	8828.92			1.29797			0.648987	−	0.760800i	$-0.275193\pi$
$359$	8828.92			1.29797			0.648987	+	0.760800i	$0.275193\pi$
$360$		0			0
$361$	−1745.78			−0.254525
$362$	4154.77	+	7196.28i	0.603232	+	1.04483i
$363$		0			0
$364$	−1104.45	+	1912.97i	−0.159036	+	0.275458i
$365$	−291.402	+	504.723i	−0.0417882	+	0.0723792i
$366$		0			0
$367$	1910.80	+	3309.60i	0.271779	+	0.470735i	0.969318	−	0.245812i	$-0.0790546\pi$
$367$	1910.80	+	3309.60i	0.271779	+	0.470735i	−0.697538	+	0.716548i	$0.745721\pi$
$368$	516.054			0.0731010
$369$		0			0
$370$	4130.41			0.580350
$371$	−8770.06	−	15190.2i	−1.22727	−	2.12570i
$372$		0			0
$373$	5186.81	−	8983.83i	0.720008	−	1.24709i	−0.240988	−	0.970528i	$-0.577471\pi$
$373$	5186.81	−	8983.83i	0.720008	−	1.24709i	0.960996	−	0.276563i	$-0.0891953\pi$
$374$	4713.28	−	8163.65i	0.651653	−	1.12870i
$375$		0			0
$376$	1035.15	+	1792.93i	0.141978	+	0.245913i
$377$	4860.27			0.663970
$378$		0			0
$379$	−8312.15			−1.12656			−0.563280	−	0.826266i	$-0.690461\pi$
$379$	−8312.15			−1.12656			−0.563280	+	0.826266i	$0.690461\pi$
$380$	−715.068	−	1238.53i	−0.0965321	−	0.167198i
$381$		0			0
$382$	2778.85	−	4813.12i	0.372195	−	0.644661i
$383$	5037.00	−	8724.34i	0.672007	−	1.16395i	−0.305327	−	0.952247i	$-0.598766\pi$
$383$	5037.00	−	8724.34i	0.672007	−	1.16395i	0.977334	−	0.211702i	$-0.0679008\pi$
$384$		0			0
$385$	4027.74	+	6976.24i	0.533175	+	0.923487i
$386$	2764.80			0.364571
$387$		0			0
$388$	−6934.84			−0.907379
$389$	4178.37	+	7237.16i	0.544607	+	0.943287i	0.998632	+	0.0522975i	$0.0166544\pi$
$389$	4178.37	+	7237.16i	0.544607	+	0.943287i	−0.454025	+	0.890989i	$0.650012\pi$
$390$		0			0
$391$	1427.32	−	2472.19i	0.184611	−	0.319755i
$392$	2289.07	−	3964.78i	0.294937	−	0.510846i
$393$		0			0
$394$	2733.58	+	4734.71i	0.349533	+	0.605409i
$395$	−5013.21			−0.638587
$396$		0			0
$397$	14024.3			1.77295			0.886473	−	0.462781i	$-0.153148\pi$
$397$	14024.3			1.77295			0.886473	+	0.462781i	$0.153148\pi$
$398$	3371.47	+	5839.56i	0.424615	+	0.735454i
$399$		0			0
$400$	−200.000	+	346.410i	−0.0250000	+	0.0433013i
$401$	−5497.03	+	9521.13i	−0.684560	+	1.18569i	0.289015	+	0.957325i	$0.406672\pi$
$401$	−5497.03	+	9521.13i	−0.684560	+	1.18569i	−0.973575	+	0.228368i	$0.926661\pi$
$402$		0			0
$403$	−714.318	−	1237.23i	−0.0882945	−	0.152931i
$404$	−3963.42			−0.488088
$405$		0			0
$406$	−16110.9			−1.96939
$407$	10997.9	+	19048.9i	1.33942	+	2.31995i
$408$		0			0
$409$	1997.20	−	3459.25i	0.241455	−	0.418213i	−0.719674	−	0.694312i	$-0.755709\pi$
$409$	1997.20	−	3459.25i	0.241455	−	0.418213i	0.961129	+	0.276100i	$0.0890419\pi$
$410$	382.601	−	662.685i	0.0460862	−	0.0798236i
$411$		0			0
$412$	2550.80	+	4418.12i	0.305022	+	0.528314i
$413$	4857.10			0.578698
$414$		0			0
$415$	−2579.86			−0.305158
$416$	−292.054	−	505.852i	−0.0344210	−	0.0596189i
$417$		0			0
$418$	3807.98	−	6595.61i	0.445584	−	0.771775i
$419$	1328.85	−	2301.64i	0.154937	−	0.268359i	−0.778099	−	0.628142i	$-0.783816\pi$
$419$	1328.85	−	2301.64i	0.154937	−	0.268359i	0.933036	+	0.359783i	$0.117149\pi$
$420$		0			0
$421$	−7406.89	−	12829.1i	−0.857458	−	1.48516i	−0.874346	−	0.485303i	$-0.838709\pi$
$421$	−7406.89	−	12829.1i	−0.857458	−	1.48516i	0.0168882	−	0.999857i	$-0.494624\pi$
$422$	11375.9			1.31225
$423$		0			0
$424$	4638.19			0.531251
$425$	1106.33	+	1916.23i	0.126271	+	0.218707i
$426$		0			0
$427$	−7616.59	+	13192.3i	−0.863215	+	1.49513i
$428$	−906.189	+	1569.57i	−0.102342	+	0.177261i
$429$		0			0
$430$	27.4662	+	47.5729i	0.00308032	+	0.00533528i
$431$	−4219.77			−0.471599			−0.235800	−	0.971802i	$-0.575771\pi$
$431$	−4219.77			−0.471599			−0.235800	+	0.971802i	$0.575771\pi$
$432$		0			0
$433$	11227.5			1.24609			0.623046	−	0.782185i	$-0.285895\pi$
$433$	11227.5			1.24609			0.623046	+	0.782185i	$0.285895\pi$
$434$	2367.84	+	4101.22i	0.261889	+	0.453605i
$435$		0			0
$436$	1077.71	−	1866.65i	0.118378	−	0.205037i
$437$	1153.17	−	1997.34i	0.126232	−	0.218641i
$438$		0			0
$439$	7841.52	+	13581.9i	0.852518	+	1.47660i	0.878929	+	0.476953i	$0.158259\pi$
$439$	7841.52	+	13581.9i	0.852518	+	1.47660i	−0.0264105	+	0.999651i	$0.508408\pi$
$440$	−2130.14			−0.230796
$441$		0			0
$442$	−3231.09			−0.347709
$443$	2103.62	+	3643.58i	0.225612	+	0.390771i	0.956503	−	0.291723i	$-0.0942285\pi$
$443$	2103.62	+	3643.58i	0.225612	+	0.390771i	−0.730891	+	0.682494i	$0.760895\pi$
$444$		0			0
$445$	−2394.40	+	4147.22i	−0.255068	+	0.441792i
$446$	−5425.39	+	9397.05i	−0.576008	+	0.997676i
$447$		0			0
$448$	968.108	+	1676.81i	0.102096	+	0.176835i
$449$	−16724.0			−1.75781			−0.878903	−	0.477000i	$-0.841724\pi$
$449$	−16724.0			−1.75781			−0.878903	+	0.477000i	$0.841724\pi$
$450$		0			0
$451$	4074.96			0.425460
$452$	−2709.07	−	4692.24i	−0.281911	−	0.488284i
$453$		0			0
$454$	−3966.41	+	6870.02i	−0.410028	+	0.710189i
$455$	1380.57	−	2391.21i	0.142246	−	0.246377i
$456$		0			0
$457$	7737.77	+	13402.2i	0.792030	+	1.37184i	0.924708	+	0.380677i	$0.124309\pi$
$457$	7737.77	+	13402.2i	0.792030	+	1.37184i	−0.132678	+	0.991159i	$0.542358\pi$
$458$	1193.18			0.121732
$459$		0			0
$460$	−645.068			−0.0653835
$461$	8719.25	+	15102.2i	0.880902	+	1.52577i	0.850339	+	0.526235i	$0.176397\pi$
$461$	8719.25	+	15102.2i	0.880902	+	1.52577i	0.0305633	+	0.999533i	$0.490270\pi$
$462$		0			0
$463$	2221.62	−	3847.96i	0.222997	−	0.386241i	−0.732720	−	0.680530i	$-0.761749\pi$
$463$	2221.62	−	3847.96i	0.222997	−	0.386241i	0.955717	+	0.294289i	$0.0950828\pi$
$464$	2130.14	−	3689.50i	0.213123	−	0.369140i
$465$		0			0
$466$	1330.40	+	2304.32i	0.132252	+	0.229068i
$467$	12491.1			1.23773			0.618866	−	0.785497i	$-0.287593\pi$
$467$	12491.1			1.23773			0.618866	+	0.785497i	$0.287593\pi$
$468$		0			0
$469$	−26971.5			−2.65550
$470$	−1293.94	−	2241.16i	−0.126989	−	0.219951i
$471$		0			0
$472$	−642.189	+	1112.30i	−0.0626253	+	0.108470i
$473$	−146.267	+	253.342i	−0.0142185	+	0.0246272i
$474$		0			0
$475$	893.834	+	1548.17i	0.0863409	+	0.149547i
$476$	10710.5			1.03134
$477$		0			0
$478$	−669.500			−0.0640632
$479$	3693.98	+	6398.16i	0.352364	+	0.610312i	0.986663	−	0.162775i	$-0.0520446\pi$
$479$	3693.98	+	6398.16i	0.352364	+	0.610312i	−0.634299	+	0.773088i	$0.718711\pi$
$480$		0			0
$481$	3769.69	−	6529.30i	0.357346	−	0.618941i
$482$	−3788.11	+	6561.20i	−0.357975	+	0.620030i
$483$		0			0
$484$	−3009.84	−	5213.20i	−0.282668	−	0.489595i
$485$	8668.55			0.811584
$486$		0			0
$487$	11726.6			1.09114			0.545570	−	0.838065i	$-0.316313\pi$
$487$	11726.6			1.09114			0.545570	+	0.838065i	$0.316313\pi$
$488$	−2014.08	−	3488.49i	−0.186830	−	0.323600i
$489$		0			0
$490$	−2861.33	+	4955.98i	−0.263800	+	0.456915i
$491$	−3549.35	+	6147.65i	−0.326232	+	0.565050i	−0.981761	−	0.190120i	$-0.939112\pi$
$491$	−3549.35	+	6147.65i	−0.326232	+	0.565050i	0.655529	+	0.755170i	$0.272446\pi$
$492$		0			0
$493$	−11783.2	−	20409.1i	−1.07645	−	1.86446i
$494$	−2610.48			−0.237755
$495$		0			0
$496$	−1252.27			−0.113364
$497$	−15032.3	−	26036.7i	−1.35672	−	2.34991i
$498$		0			0
$499$	−96.5744	+	167.272i	−0.00866385	+	0.0150062i	−0.870325	−	0.492478i	$-0.836091\pi$
$499$	−96.5744	+	167.272i	−0.00866385	+	0.0150062i	0.861661	+	0.507484i	$0.169424\pi$
$500$	250.000	−	433.013i	0.0223607	−	0.0387298i
$501$		0			0
$502$	3636.79	+	6299.10i	0.323342	+	0.560045i
$503$	12473.5			1.10570			0.552848	−	0.833282i	$-0.313541\pi$
$503$	12473.5			1.10570			0.552848	+	0.833282i	$0.313541\pi$
$504$		0			0
$505$	4954.27			0.436559
$506$	−1717.60	−	2974.97i	−0.150903	−	0.261371i
$507$		0			0
$508$	−1442.48	+	2498.45i	−0.125984	+	0.218210i
$509$	5895.08	−	10210.6i	0.513349	−	0.889147i	−0.486531	−	0.873664i	$-0.661738\pi$
$509$	5895.08	−	10210.6i	0.513349	−	0.889147i	0.999880	−	0.0154838i	$-0.00492886\pi$
$510$		0			0
$511$	−1763.18	−	3053.92i	−0.152639	−	0.264378i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−4818.19			−0.413465
$515$	−3188.51	−	5522.65i	−0.272820	−	0.472538i
$516$		0			0
$517$	6890.65	−	11934.9i	0.586171	−	1.01528i
$518$	−12495.9	+	21643.5i	−1.05992	+	1.83583i
$519$		0			0
$520$	365.068	+	632.316i	0.0307871	+	0.0533248i
$521$	10577.1			0.889426			0.444713	−	0.895673i	$-0.353306\pi$
$521$	10577.1			0.889426			0.444713	+	0.895673i	$0.353306\pi$
$522$		0			0
$523$	3634.17			0.303845			0.151923	−	0.988392i	$-0.451454\pi$
$523$	3634.17			0.303845			0.151923	+	0.988392i	$0.451454\pi$
$524$	−4290.27	−	7430.97i	−0.357674	−	0.619510i
$525$		0			0
$526$	3888.71	−	6735.44i	0.322349	−	0.558325i
$527$	−3463.57	+	5999.09i	−0.286292	+	0.495872i
$528$		0			0
$529$	5563.36	+	9636.02i	0.457250	+	0.791980i
$530$	−5797.74			−0.475165
$531$		0			0
$532$	8653.28			0.705202
$533$	−698.377	−	1209.62i	−0.0567543	−	0.0983014i
$534$		0			0
$535$	1132.74	−	1961.96i	0.0915373	−	0.158547i
$536$	3566.08	−	6176.63i	0.287372	−	0.497742i
$537$		0			0
$538$	−1253.01	−	2170.28i	−0.100411	−	0.173917i
$539$	−30475.1			−2.43536
$540$		0			0
$541$	6353.00			0.504874			0.252437	−	0.967613i	$-0.418768\pi$
$541$	6353.00			0.504874			0.252437	+	0.967613i	$0.418768\pi$
$542$	−3356.72	−	5814.01i	−0.266021	−	0.460763i
$543$		0			0
$544$	−1416.11	+	2452.77i	−0.111609	+	0.193312i
$545$	−1347.14	+	2333.31i	−0.105881	+	0.183391i
$546$		0			0
$547$	−11851.4	−	20527.2i	−0.926376	−	1.60453i	−0.789333	−	0.613966i	$-0.789573\pi$
$547$	−11851.4	−	20527.2i	−0.926376	−	1.60453i	−0.137043	−	0.990565i	$-0.543760\pi$
$548$	−89.9189			−0.00700939
$549$		0			0
$550$	2662.67			0.206430
$551$	−9519.94	−	16489.0i	−0.736049	−	1.27487i
$552$		0			0
$553$	15166.7	−	26269.4i	1.16628	−	2.02005i
$554$	4674.42	−	8096.34i	0.358479	−	0.620903i
$555$		0			0
$556$	−2983.12	−	5166.92i	−0.227541	−	0.394112i
$557$	−9740.28			−0.740950			−0.370475	−	0.928843i	$-0.620805\pi$
$557$	−9740.28			−0.740950			−0.370475	+	0.928843i	$0.620805\pi$
$558$		0			0
$559$	100.270			0.00758673
$560$	−1210.14	−	2096.02i	−0.0913170	−	0.158166i
$561$		0			0
$562$	−1301.54	+	2254.33i	−0.0976904	+	0.169205i
$563$	5329.72	−	9231.35i	0.398971	−	0.691039i	−0.594628	−	0.804001i	$-0.702701\pi$
$563$	5329.72	−	9231.35i	0.398971	−	0.691039i	0.993599	+	0.112962i	$0.0360339\pi$
$564$		0			0
$565$	3386.33	+	5865.30i	0.252149	+	0.436735i
$566$	7894.61			0.586281
$567$		0			0
$568$	7950.08			0.587285
$569$	8073.77	+	13984.2i	0.594850	+	1.03031i	0.993568	+	0.113237i	$0.0361221\pi$
$569$	8073.77	+	13984.2i	0.594850	+	1.03031i	−0.398717	+	0.917074i	$0.630545\pi$
$570$		0			0
$571$	−10400.6	+	18014.3i	−0.762260	+	1.32027i	0.179422	+	0.983772i	$0.442577\pi$
$571$	−10400.6	+	18014.3i	−0.762260	+	1.32027i	−0.941683	+	0.336502i	$0.890756\pi$
$572$	−1944.11	+	3367.29i	−0.142111	+	0.246143i
$573$		0			0
$574$	2315.00	+	4009.69i	0.168338	+	0.291570i
$575$	806.334			0.0584808
$576$		0			0
$577$	3290.24			0.237391			0.118696	−	0.992931i	$-0.462129\pi$
$577$	3290.24			0.237391			0.118696	+	0.992931i	$0.462129\pi$
$578$	2920.45	+	5058.36i	0.210164	+	0.364014i
$579$		0			0
$580$	−2662.67	+	4611.88i	−0.190623	+	0.330169i
$581$	7804.96	−	13518.6i	0.557323	−	0.965311i
$582$		0			0
$583$	−15437.5	−	26738.5i	−1.09666	−	1.89947i
$584$	932.486			0.0660729
$585$		0			0
$586$	12535.9			0.883710
$587$	−4475.96	−	7752.59i	−0.314723	−	0.545117i	0.664655	−	0.747150i	$-0.268578\pi$
$587$	−4475.96	−	7752.59i	−0.314723	−	0.545117i	−0.979379	+	0.202033i	$0.935245\pi$
$588$		0			0
$589$	−2798.31	+	4846.81i	−0.195759	+	0.339065i
$590$	802.736	−	1390.38i	0.0560138	−	0.0970187i
$591$		0			0
$592$	−3304.32	−	5723.26i	−0.229404	−	0.397339i
$593$	11821.6			0.818646			0.409323	−	0.912390i	$-0.365765\pi$
$593$	11821.6			0.818646			0.409323	+	0.912390i	$0.365765\pi$
$594$		0			0
$595$	−13388.1			−0.922454
$596$	2934.57	+	5082.82i	0.201686	+	0.349330i
$597$		0			0
$598$	−588.733	+	1019.72i	−0.0402593	+	0.0697312i
$599$	−2114.33	+	3662.12i	−0.144222	+	0.249800i	−0.929082	−	0.369873i	$-0.879401\pi$
$599$	−2114.33	+	3662.12i	−0.144222	+	0.249800i	0.784860	+	0.619673i	$0.212735\pi$
$600$		0			0
$601$	−9092.64	−	15748.9i	−0.617132	−	1.06890i	−0.990006	−	0.141022i	$-0.954961\pi$
$601$	−9092.64	−	15748.9i	−0.617132	−	1.06890i	0.372874	−	0.927882i	$-0.378372\pi$
$602$	−332.378			−0.0225029
$603$		0			0
$604$	5345.28			0.360094
$605$	3762.31	+	6516.50i	0.252826	+	0.437907i
$606$		0			0
$607$	3551.60	−	6151.55i	0.237488	−	0.411340i	−0.722505	−	0.691366i	$-0.757009\pi$
$607$	3551.60	−	6151.55i	0.237488	−	0.411340i	0.959993	+	0.280025i	$0.0903428\pi$
$608$	−1144.11	+	1981.65i	−0.0763153	+	0.132182i
$609$		0			0
$610$	2517.60	+	4360.61i	0.167106	+	0.289436i
$611$	−4723.74			−0.312769
$612$		0			0
$613$	−4161.02			−0.274163			−0.137081	−	0.990560i	$-0.543772\pi$
$613$	−4161.02			−0.274163			−0.137081	+	0.990560i	$0.543772\pi$
$614$	−6482.89	−	11228.7i	−0.426104	−	0.738034i
$615$		0			0
$616$	6444.38	−	11162.0i	0.421512	−	0.730080i
$617$	−3028.12	+	5244.87i	−0.197581	+	0.342221i	−0.947744	−	0.319033i	$-0.896642\pi$
$617$	−3028.12	+	5244.87i	−0.197581	+	0.342221i	0.750162	+	0.661254i	$0.229975\pi$
$618$		0			0
$619$	−8526.27	−	14767.9i	−0.553634	−	0.958922i	−0.998008	−	0.0630812i	$-0.979907\pi$
$619$	−8526.27	−	14767.9i	−0.553634	−	0.958922i	0.444374	−	0.895841i	$-0.353426\pi$
$620$	1565.34			0.101396
$621$		0			0
$622$	7631.59			0.491959
$623$	−14487.7	−	25093.5i	−0.931684	−	1.61372i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−5422.03	+	9391.23i	−0.346179	+	0.599599i
$627$		0			0
$628$	−2996.45	−	5190.01i	−0.190400	−	0.329783i
$629$	−36556.9			−2.31736
$630$		0			0
$631$	−22606.8			−1.42625			−0.713123	−	0.701039i	$-0.752720\pi$
$631$	−22606.8			−1.42625			−0.713123	+	0.701039i	$0.752720\pi$
$632$	4010.57	+	6946.51i	0.252424	+	0.437211i
$633$		0			0
$634$	265.193	−	459.327i	0.0166122	−	0.0287732i
$635$	1803.10	−	3123.06i	0.112683	−	0.195173i
$636$		0			0
$637$	5222.90	+	9046.33i	0.324865	+	0.562682i
$638$	−28359.2			−1.75980
$639$		0			0
$640$	640.000			0.0395285
$641$	2153.37	+	3729.74i	0.132688	+	0.229822i	0.924712	−	0.380668i	$-0.124306\pi$
$641$	2153.37	+	3729.74i	0.132688	+	0.229822i	−0.792024	+	0.610490i	$0.790973\pi$
$642$		0			0
$643$	1200.79	−	2079.84i	0.0736465	−	0.127559i	−0.826850	−	0.562422i	$-0.809870\pi$
$643$	1200.79	−	2079.84i	0.0736465	−	0.127559i	0.900497	+	0.434862i	$0.143203\pi$
$644$	1951.55	−	3380.18i	0.119413	−	0.206829i
$645$		0			0
$646$	6328.83	+	10961.9i	0.385456	+	0.667629i
$647$	−15391.0			−0.935212			−0.467606	−	0.883937i	$-0.654883\pi$
$647$	−15391.0			−0.935212			−0.467606	+	0.883937i	$0.654883\pi$
$648$		0			0
$649$	8549.69			0.517110
$650$	−456.334	−	790.394i	−0.0275368	−	0.0476951i
$651$		0			0
$652$	−3208.11	+	5556.61i	−0.192698	+	0.333763i
$653$	−12364.6	+	21416.0i	−0.740984	+	1.28342i	0.211064	+	0.977472i	$0.432307\pi$
$653$	−12364.6	+	21416.0i	−0.740984	+	1.28342i	−0.952048	+	0.305950i	$0.901026\pi$
$654$		0			0
$655$	5362.84	+	9288.71i	0.319914	+	0.554107i
$656$	−1224.32			−0.0728686
$657$		0			0
$658$	15658.4			0.927700
$659$	9298.44	+	16105.4i	0.549644	+	0.952012i	0.998299	+	0.0583067i	$0.0185701\pi$
$659$	9298.44	+	16105.4i	0.549644	+	0.952012i	−0.448654	+	0.893705i	$0.648097\pi$
$660$		0			0
$661$	2254.19	−	3904.38i	0.132644	−	0.229747i	−0.792051	−	0.610455i	$-0.790986\pi$
$661$	2254.19	−	3904.38i	0.132644	−	0.229747i	0.924695	+	0.380708i	$0.124320\pi$
$662$	−1647.28	+	2853.17i	−0.0967120	+	0.167510i
$663$		0			0
$664$	2063.89	+	3574.77i	0.120624	+	0.208927i
$665$	−10816.6			−0.630752
$666$		0			0
$667$	−8588.01			−0.498544
$668$	−29.5406	−	51.1658i	−0.00171102	−	0.00296357i
$669$		0			0
$670$	−4457.60	+	7720.79i	−0.257033	+	0.445194i
$671$	−13407.1	+	23221.7i	−0.771348	+	1.33601i
$672$		0			0
$673$	−4216.83	−	7303.77i	−0.241526	−	0.418335i	0.719623	−	0.694365i	$-0.244315\pi$
$673$	−4216.83	−	7303.77i	−0.241526	−	0.418335i	−0.961149	+	0.276030i	$0.910981\pi$
$674$	15978.0			0.913129
$675$		0			0
$676$	−7455.26			−0.424173
$677$	9163.33	+	15871.3i	0.520200	+	0.901012i	0.999724	+	0.0234839i	$0.00747584\pi$
$677$	9163.33	+	15871.3i	0.520200	+	0.901012i	−0.479524	+	0.877529i	$0.659191\pi$
$678$		0			0
$679$	−26225.3	+	45423.5i	−1.48223	+	2.56730i
$680$	1770.14	−	3065.96i	0.0998259	−	0.172903i
$681$		0			0
$682$	4167.98	+	7219.15i	0.234018	+	0.405331i
$683$	31446.2			1.76172			0.880861	−	0.473374i	$-0.156964\pi$
$683$	31446.2			1.76172			0.880861	+	0.473374i	$0.156964\pi$
$684$		0			0
$685$	112.399			0.00626939
$686$	−6936.10	−	12013.7i	−0.386037	−	0.668636i
$687$		0			0
$688$	43.9459	−	76.1166i	0.00243521	−	0.00421791i
$689$	−5291.41	+	9165.00i	−0.292579	+	0.506761i
$690$		0			0
$691$	394.752	+	683.730i	0.0217324	+	0.0376415i	0.876687	−	0.481061i	$-0.159748\pi$
$691$	394.752	+	683.730i	0.0217324	+	0.0376415i	−0.854955	+	0.518703i	$0.826415\pi$
$692$	−1821.82			−0.100080
$693$		0			0
$694$	5798.88			0.317179
$695$	3728.90	+	6458.65i	0.203518	+	0.352504i
$696$		0			0
$697$	−3386.28	+	5865.21i	−0.184024	+	0.318738i
$698$	−3817.27	+	6611.71i	−0.207000	+	0.358534i
$699$		0			0
$700$	1512.67	+	2620.02i	0.0816764	+	0.141468i
$701$	−33721.0			−1.81687			−0.908435	−	0.418027i	$-0.862722\pi$
$701$	−33721.0			−1.81687			−0.908435	+	0.418027i	$0.862722\pi$
$702$		0			0
$703$	−29535.2			−1.58455
$704$	1704.11	+	2951.60i	0.0912301	+	0.158015i
$705$		0			0
$706$	9898.01	−	17143.9i	0.527644	−	0.913906i
$707$	−14988.4	+	25960.6i	−0.797305	+	1.38097i
$708$		0			0
$709$	3463.06	+	5998.20i	0.183439	+	0.317725i	0.943049	−	0.332653i	$-0.107944\pi$
$709$	3463.06	+	5998.20i	0.183439	+	0.317725i	−0.759611	+	0.650378i	$0.774610\pi$
$710$	−9937.60			−0.525284
$711$		0			0
$712$	7662.08			0.403299
$713$	1262.19	+	2186.17i	0.0662963	+	0.114828i
$714$		0			0
$715$	2430.14	−	4209.12i	0.127108	−	0.220157i
$716$	5532.14	−	9581.94i	0.288751	−	0.500131i
$717$		0			0
$718$	8828.92	+	15292.1i	0.458903	+	0.794843i
$719$	33919.7			1.75938			0.879689	−	0.475550i	$-0.157751\pi$
$719$	33919.7			1.75938			0.879689	+	0.475550i	$0.157751\pi$
$720$		0			0
$721$	38585.2			1.99305
$722$	−1745.78	−	3023.79i	−0.0899880	−	0.155864i
$723$		0			0
$724$	−8309.55	+	14392.6i	−0.426550	+	0.738806i
$725$	3328.34	−	5764.85i	0.170498	−	0.295312i
$726$		0			0
$727$	−17487.4	−	30289.1i	−0.892123	−	1.54520i	−0.837326	−	0.546704i	$-0.815882\pi$
$727$	−17487.4	−	30289.1i	−0.892123	−	1.54520i	−0.0547968	−	0.998498i	$-0.517451\pi$
$728$	−4417.81			−0.224911
$729$		0			0
$730$	−1165.61			−0.0590974
$731$	−243.095	−	421.052i	−0.0122998	−	0.0213039i
$732$		0			0
$733$	5612.04	−	9720.34i	0.282791	−	0.489808i	−0.689280	−	0.724495i	$-0.742073\pi$
$733$	5612.04	−	9720.34i	0.282791	−	0.489808i	0.972071	+	0.234687i	$0.0754065\pi$
$734$	−3821.60	+	6619.21i	−0.192177	+	0.332860i
$735$		0			0
$736$	516.054	+	893.832i	0.0258451	+	0.0447651i
$737$	−47476.5			−2.37289
$738$		0			0
$739$	18324.6			0.912153			0.456076	−	0.889941i	$-0.349254\pi$
$739$	18324.6			0.912153			0.456076	+	0.889941i	$0.349254\pi$
$740$	4130.41	+	7154.07i	0.205185	+	0.355390i
$741$		0			0
$742$	17540.1	−	30380.4i	0.867814	−	1.50310i
$743$	−16267.2	+	28175.6i	−0.803212	+	1.39120i	0.114280	+	0.993449i	$0.463544\pi$
$743$	−16267.2	+	28175.6i	−0.803212	+	1.39120i	−0.917492	+	0.397755i	$0.869789\pi$
$744$		0			0
$745$	−3668.21	−	6353.53i	−0.180393	−	0.312450i
$746$	20747.3			1.01825
$747$		0			0
$748$	18853.1			0.921576
$749$	6853.82	+	11871.2i	0.334357	+	0.579123i
$750$		0			0
$751$	8626.30	−	14941.2i	0.419145	−	0.725981i	−0.576708	−	0.816950i	$-0.695663\pi$
$751$	8626.30	−	14941.2i	0.419145	−	0.725981i	0.995854	+	0.0909690i	$0.0289964\pi$
$752$	−2070.30	+	3585.86i	−0.100394	+	0.173887i
$753$		0			0
$754$	4860.27	+	8418.24i	0.234749	+	0.406597i
$755$	−6681.60			−0.322077
$756$		0			0
$757$	−21199.3			−1.01783			−0.508917	−	0.860815i	$-0.669954\pi$
$757$	−21199.3			−1.01783			−0.508917	+	0.860815i	$0.669954\pi$
$758$	−8312.15	−	14397.1i	−0.398299	−	0.689875i
$759$		0			0
$760$	1430.14	−	2477.07i	0.0682585	−	0.118227i
$761$	−3090.85	+	5353.51i	−0.147231	+	0.255012i	−0.930203	−	0.367045i	$-0.880370\pi$
$761$	−3090.85	+	5353.51i	−0.147231	+	0.255012i	0.782972	+	0.622057i	$0.213703\pi$
$762$		0			0
$763$	−8151.09	−	14118.1i	−0.386749	−	0.669868i
$764$	11115.4			0.526364
$765$		0			0
$766$	20148.0			0.950361
$767$	−1465.27	−	2537.91i	−0.0689800	−	0.119477i
$768$		0			0
$769$	−16770.2	+	29046.9i	−0.786411	+	1.36210i	0.141742	+	0.989904i	$0.454730\pi$
$769$	−16770.2	+	29046.9i	−0.786411	+	1.36210i	−0.928153	+	0.372200i	$0.878604\pi$
$770$	−8055.47	+	13952.5i	−0.377012	+	0.653004i
$771$		0			0
$772$	2764.80	+	4788.77i	0.128895	+	0.223253i
$773$	−26574.6			−1.23651			−0.618256	−	0.785977i	$-0.712160\pi$
$773$	−26574.6			−1.23651			−0.618256	+	0.785977i	$0.712160\pi$
$774$		0			0
$775$	−1956.67			−0.0906913
$776$	−6934.84	−	12011.5i	−0.320807	−	0.555654i
$777$		0			0
$778$	−8356.75	+	14474.3i	−0.385095	+	0.667004i
$779$	−2735.86	+	4738.65i	−0.125831	+	0.217946i
$780$		0			0
$781$	−26460.5	−	45831.0i	−1.21233	−	2.09982i
$782$	5709.28			0.261079
$783$		0			0
$784$	9156.27			0.417104
$785$	3745.57	+	6487.51i	0.170299	+	0.294967i
$786$		0			0
$787$	−7354.19	+	12737.8i	−0.333099	+	0.576944i	−0.983118	−	0.182974i	$-0.941428\pi$
$787$	−7354.19	+	12737.8i	−0.333099	+	0.576944i	0.650019	+	0.759918i	$0.274761\pi$
$788$	−5467.17	+	9469.41i	−0.247157	+	0.428089i
$789$		0			0
$790$	−5013.21	−	8683.13i	−0.225775	−	0.391053i
$791$	−40979.2			−1.84204
$792$		0			0
$793$	9190.95			0.411576
$794$	14024.3	+	24290.8i	0.626831	+	1.08570i
$795$		0			0
$796$	−6742.95	+	11679.1i	−0.300248	+	0.520045i
$797$	19144.1	−	33158.5i	0.850839	−	1.47370i	−0.0296136	−	0.999561i	$-0.509428\pi$
$797$	19144.1	−	33158.5i	0.850839	−	1.47370i	0.880452	−	0.474135i	$-0.157239\pi$
$798$		0			0
$799$	11452.2	+	19835.8i	0.507071	+	0.878273i
$800$	−800.000			−0.0353553
$801$		0			0
$802$	−21988.1			−0.968114
$803$	−3103.63	−	5375.64i	−0.136394	−	0.236242i
$804$		0			0
$805$	−2439.43	+	4225.22i	−0.106806	+	0.184993i
$806$	1428.64	−	2474.47i	0.0624337	−	0.108138i
$807$		0			0
$808$	−3963.42	−	6864.84i	−0.172565	−	0.298891i
$809$	1761.26			0.0765423			0.0382712	−	0.999267i	$-0.487815\pi$
$809$	1761.26			0.0765423			0.0382712	+	0.999267i	$0.487815\pi$
$810$		0			0
$811$	−7347.55			−0.318135			−0.159067	−	0.987268i	$-0.550849\pi$
$811$	−7347.55			−0.318135			−0.159067	+	0.987268i	$0.550849\pi$
$812$	−16110.9	−	27905.0i	−0.696285	−	1.20600i
$813$		0			0
$814$	−21995.8	+	38097.9i	−0.947116	+	1.64045i
$815$	4010.14	−	6945.76i	0.172354	−	0.298527i
$816$		0			0
$817$	−196.402	−	340.178i	−0.00841033	−	0.0145671i
$818$	7988.80			0.341469
$819$		0			0
$820$	1530.41			0.0651757
$821$	−4744.70	−	8218.06i	−0.201695	−	0.349345i	0.747380	−	0.664397i	$-0.231311\pi$
$821$	−4744.70	−	8218.06i	−0.201695	−	0.349345i	−0.949075	+	0.315052i	$0.897978\pi$
$822$		0			0
$823$	14232.6	−	24651.6i	0.602816	−	1.04411i	−0.389577	−	0.920994i	$-0.627379\pi$
$823$	14232.6	−	24651.6i	0.602816	−	1.04411i	0.992393	−	0.123113i	$-0.0392878\pi$
$824$	−5101.61	+	8836.24i	−0.215683	+	0.373574i
$825$		0			0
$826$	4857.10	+	8412.74i	0.204601	+	0.354379i
$827$	5990.54			0.251888			0.125944	−	0.992037i	$-0.459804\pi$
$827$	5990.54			0.251888			0.125944	+	0.992037i	$0.459804\pi$
$828$		0			0
$829$	27736.9			1.16205			0.581027	−	0.813885i	$-0.302651\pi$
$829$	27736.9			1.16205			0.581027	+	0.813885i	$0.302651\pi$
$830$	−2579.86	−	4468.46i	−0.107890	−	0.186870i
$831$		0			0
$832$	584.108	−	1011.70i	0.0243393	−	0.0421569i
$833$	25324.7	−	43863.7i	1.05336	−	1.82448i
$834$		0			0
$835$	36.9257	+	63.9572i	0.00153038	+	0.00265070i
$836$	15231.9			0.630151
$837$		0			0
$838$	5315.41			0.219114
$839$	6554.11	+	11352.1i	0.269694	+	0.467123i	0.968783	−	0.247911i	$-0.0797442\pi$
$839$	6554.11	+	11352.1i	0.269694	+	0.467123i	−0.699089	+	0.715035i	$0.746411\pi$
$840$		0			0
$841$	−23254.5	+	40278.0i	−0.953484	+	1.65148i
$842$	14813.8	−	25658.2i	0.606314	−	1.05017i
$843$		0			0
$844$	11375.9	+	19703.6i	0.463950	+	0.803585i
$845$	9319.07			0.379391
$846$		0			0
$847$	−45529.0			−1.84698
$848$	4638.19	+	8033.58i	0.187826	+	0.325323i
$849$		0			0
$850$	−2212.67	+	3832.45i	−0.0892870	+	0.154650i
$851$	−6660.98	+	11537.1i	−0.268314	+	0.464734i
$852$		0			0
$853$	20612.5	+	35701.8i	0.827382	+	1.43307i	0.900085	+	0.435714i	$0.143504\pi$
$853$	20612.5	+	35701.8i	0.827382	+	1.43307i	−0.0727027	+	0.997354i	$0.523162\pi$
$854$	−30466.4			−1.22077
$855$		0			0
$856$	−3624.76			−0.144733
$857$	−8832.73	−	15298.7i	−0.352066	−	0.609796i	0.634545	−	0.772886i	$-0.281187\pi$
$857$	−8832.73	−	15298.7i	−0.352066	−	0.609796i	−0.986611	+	0.163090i	$0.947854\pi$
$858$		0			0
$859$	−5844.43	+	10122.8i	−0.232141	+	0.402080i	−0.958438	−	0.285301i	$-0.907906\pi$
$859$	−5844.43	+	10122.8i	−0.232141	+	0.402080i	0.726297	+	0.687381i	$0.241240\pi$
$860$	−54.9324	+	95.1458i	−0.00217812	+	0.00377261i
$861$		0			0
$862$	−4219.77	−	7308.86i	−0.166736	−	0.288794i
$863$	18801.0			0.741591			0.370795	−	0.928715i	$-0.379085\pi$
$863$	18801.0			0.741591			0.370795	+	0.928715i	$0.379085\pi$
$864$		0			0
$865$	2277.28			0.0895143
$866$	11227.5	+	19446.6i	0.440560	+	0.763073i
$867$		0			0
$868$	−4735.68	+	8202.43i	−0.185184	+	0.320747i
$869$	26697.0	−	46240.6i	1.04216	−	1.80507i
$870$		0			0
$871$	8136.63	+	14093.1i	0.316532	+	0.548249i
$872$	4310.84			0.167412
$873$		0			0
$874$	4612.67			0.178519
$875$	−1890.84	−	3275.02i	−0.0730536	−	0.126533i
$876$		0			0
$877$	−3677.53	+	6369.67i	−0.141598	+	0.245255i	−0.928098	−	0.372335i	$-0.878557\pi$
$877$	−3677.53	+	6369.67i	−0.141598	+	0.245255i	0.786501	+	0.617589i	$0.211891\pi$
$878$	−15683.0	+	27163.8i	−0.602821	+	1.04412i
$879$		0			0
$880$	−2130.14	−	3689.50i	−0.0815987	−	0.141333i
$881$	23538.6			0.900155			0.450077	−	0.892990i	$-0.351396\pi$
$881$	23538.6			0.900155			0.450077	+	0.892990i	$0.351396\pi$
$882$		0			0
$883$	33937.6			1.29342			0.646711	−	0.762735i	$-0.276144\pi$
$883$	33937.6			1.29342			0.646711	+	0.762735i	$0.276144\pi$
$884$	−3231.09	−	5596.42i	−0.122934	−	0.212928i
$885$		0			0
$886$	−4207.24	+	7287.16i	−0.159532	+	0.276317i
$887$	12708.0	−	22010.8i	0.481051	−	0.833204i	−0.518713	−	0.854948i	$-0.673589\pi$
$887$	12708.0	−	22010.8i	0.481051	−	0.833204i	0.999764	+	0.0217445i	$0.00692203\pi$
$888$		0			0
$889$	10910.0	+	18896.6i	0.411596	+	0.712905i
$890$	−9577.60			−0.360721
$891$		0			0
$892$	−21701.6			−0.814599
$893$	9252.52	+	16025.8i	0.346723	+	0.600542i
$894$		0			0
$895$	−6915.17	+	11977.4i	−0.258267	+	0.447331i
$896$	−1936.22	+	3353.62i	−0.0721925	+	0.125041i
$897$		0			0
$898$	−16724.0	−	28966.9i	−0.621479	−	1.07643i
$899$	20839.9			0.773136
$900$		0			0
$901$	51313.9			1.89735
$902$	4074.96	+	7058.04i	0.150423	+	0.260540i
$903$		0			0
$904$	5418.14	−	9384.49i	0.199341	−	0.345269i
$905$	10386.9	−	17990.7i	0.381518	−	0.660808i
$906$		0			0
$907$	−4586.22	−	7943.56i	−0.167897	−	0.290807i	0.769783	−	0.638306i	$-0.220364\pi$
$907$	−4586.22	−	7943.56i	−0.167897	−	0.290807i	−0.937680	+	0.347499i	$0.887031\pi$
$908$	−15865.6			−0.579867
$909$		0			0
$910$	5522.26			0.201166
$911$	3344.15	+	5792.24i	0.121621	+	0.210654i	0.920407	−	0.390961i	$-0.127857\pi$
$911$	3344.15	+	5792.24i	0.121621	+	0.210654i	−0.798786	+	0.601615i	$0.794524\pi$
$912$		0			0
$913$	13738.7	−	23796.0i	0.498010	−	0.862578i
$914$	−15475.5	+	26804.4i	−0.560050	+	0.970035i
$915$		0			0
$916$	1193.18	+	2066.64i	0.0430389	+	0.0745456i
$917$	−64897.6			−2.33709
$918$		0			0
$919$	−19386.0			−0.695848			−0.347924	−	0.937523i	$-0.613113\pi$
$919$	−19386.0			−0.695848			−0.347924	+	0.937523i	$0.613113\pi$
$920$	−645.068	−	1117.29i	−0.0231166	−	0.0400391i
$921$		0			0
$922$	−17438.5	+	30204.4i	−0.622892	+	1.07888i
$923$	−9069.74	+	15709.3i	−0.323439	+	0.560213i
$924$		0			0
$925$	−5163.01	−	8942.59i	−0.183523	−	0.317871i
$926$	8886.48			0.315365
$927$		0			0
$928$	8520.54			0.301401
$929$	12812.3	+	22191.5i	0.452484	+	0.783725i	0.998540	−	0.0540237i	$-0.0172047\pi$
$929$	12812.3	+	22191.5i	0.452484	+	0.783725i	−0.546056	+	0.837749i	$0.683871\pi$
$930$		0			0
$931$	20460.5	−	35438.6i	0.720263	−	1.24753i
$932$	−2660.80	+	4608.64i	−0.0935164	+	0.161975i
$933$		0			0
$934$	12491.1	+	21635.3i	0.437604	+	0.757952i
$935$	−23566.4			−0.824283
$936$		0			0
$937$	12320.7			0.429563			0.214782	−	0.976662i	$-0.431096\pi$
$937$	12320.7			0.429563			0.214782	+	0.976662i	$0.431096\pi$
$938$	−26971.5	−	46716.0i	−0.938860	−	1.62615i
$939$		0			0
$940$	2587.87	−	4482.33i	0.0897947	−	0.155529i
$941$	−12542.8	+	21724.8i	−0.434520	+	0.752611i	−0.997256	−	0.0740253i	$-0.976415\pi$
$941$	−12542.8	+	21724.8i	−0.434520	+	0.752611i	0.562736	+	0.826637i	$0.309749\pi$
$942$		0			0
$943$	1234.02	+	2137.38i	0.0426142	+	0.0738099i
$944$	−2568.76			−0.0885656
$945$		0			0
$946$	−585.068			−0.0201080
$947$	−2117.64	−	3667.86i	−0.0726653	−	0.125860i	0.827403	−	0.561608i	$-0.189817\pi$
$947$	−2117.64	−	3667.86i	−0.0726653	−	0.125860i	−0.900069	+	0.435748i	$0.856484\pi$
$948$		0			0
$949$	−1063.81	+	1842.58i	−0.0363887	+	0.0630271i
$950$	−1787.67	+	3096.33i	−0.0610523	+	0.105746i
$951$		0			0
$952$	10710.5	+	18551.2i	0.364632	+	0.631561i
$953$	34165.2			1.16130			0.580650	−	0.814153i	$-0.302798\pi$
$953$	34165.2			1.16130			0.580650	+	0.814153i	$0.302798\pi$
$954$		0			0
$955$	−13894.3			−0.470794
$956$	−669.500	−	1159.61i	−0.0226498	−	0.0392305i
$957$		0			0
$958$	−7387.96	+	12796.3i	−0.249159	+	0.431556i
$959$	−340.044	+	588.973i	−0.0114500	+	0.0198321i
$960$		0			0
$961$	11832.6	+	20494.7i	0.397189	+	0.687951i
$962$	15078.8			0.505363
$963$		0			0
$964$	−15152.4			−0.506253
$965$	−3456.00	−	5985.96i	−0.115288	−	0.199684i
$966$		0			0
$967$	5939.53	−	10287.6i	0.197520	−	0.342116i	−0.750203	−	0.661207i	$-0.770044\pi$
$967$	5939.53	−	10287.6i	0.197520	−	0.342116i	0.947724	+	0.319092i	$0.103378\pi$
$968$	6019.69	−	10426.4i	0.199876	−	0.346196i
$969$		0			0
$970$	8668.55	+	15014.4i	0.286938	+	0.496992i
$971$	−48679.3			−1.60885			−0.804425	−	0.594054i	$-0.797527\pi$
$971$	−48679.3			−1.60885			−0.804425	+	0.594054i	$0.797527\pi$
$972$		0			0
$973$	−45124.8			−1.48678
$974$	11726.6	+	20311.1i	0.385776	+	0.668184i
$975$		0			0
$976$	4028.16	−	6976.98i	0.132109	−	0.228819i
$977$	1601.79	−	2774.38i	0.0524521	−	0.0908497i	−0.838607	−	0.544737i	$-0.816630\pi$
$977$	1601.79	−	2774.38i	0.0524521	−	0.0908497i	0.891059	+	0.453887i	$0.149963\pi$
$978$		0			0
$979$	−25502.0	−	44170.7i	−0.832530	−	1.44198i
$980$	−11445.3			−0.373069
$981$		0			0
$982$	−14197.4			−0.461361
$983$	13592.4	+	23542.7i	0.441028	+	0.763883i	0.997766	−	0.0668054i	$-0.0212807\pi$
$983$	13592.4	+	23542.7i	0.441028	+	0.763883i	−0.556738	+	0.830688i	$0.687947\pi$
$984$		0			0
$985$	6833.96	−	11836.8i	0.221064	−	0.382894i
$986$	23566.4	−	40818.2i	0.761164	−	1.31837i
$987$		0			0
$988$	−2610.48	−	4521.48i	−0.0840591	−	0.145595i
$989$	−177.176			−0.00569652
$990$		0			0
$991$	−37424.6			−1.19963			−0.599815	−	0.800139i	$-0.704759\pi$
$991$	−37424.6			−1.19963			−0.599815	+	0.800139i	$0.704759\pi$
$992$	−1252.27	−	2169.00i	−0.0400803	−	0.0694211i
$993$		0			0
$994$	30064.6	−	52073.4i	0.959347	−	1.66164i
$995$	8428.68	−	14598.9i	0.268550	−	0.465142i
$996$		0			0
$997$	−10540.7	−	18257.0i	−0.334831	−	0.579944i	0.648622	−	0.761111i	$-0.275346\pi$
$997$	−10540.7	−	18257.0i	−0.334831	−	0.579944i	−0.983452	+	0.181167i	$0.942012\pi$
$998$	−386.297			−0.0122525
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.4.e.be.271.2		4
3.2	odd	2		810.4.e.ba.271.2		4
9.2	odd	6		810.4.e.ba.541.2		4
9.4	even	3		810.4.a.h.1.1	✓	2
9.5	odd	6		810.4.a.n.1.1	yes	2
9.7	even	3	inner	810.4.e.be.541.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
810.4.a.h.1.1	✓	2	9.4	even	3
810.4.a.n.1.1	yes	2	9.5	odd	6
810.4.e.ba.271.2		4	3.2	odd	2
810.4.e.ba.541.2		4	9.2	odd	6
810.4.e.be.271.2		4	1.1	even	1	trivial
810.4.e.be.541.2		4	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	810.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(15.1267 + 26.2002i) q^{7} -8.00000 q^{8} +10.0000 q^{10} +(26.6267 + 46.1188i) q^{11} +(9.12669 - 15.8079i) q^{13} +(-30.2534 + 52.4004i) q^{14} +(-8.00000 - 13.8564i) q^{16} -88.5068 q^{17} -71.5068 q^{19} +(10.0000 + 17.3205i) q^{20} +(-53.2534 + 92.2376i) q^{22} +(-16.1267 + 27.9322i) q^{23} +(-12.5000 - 21.6506i) q^{25} +36.5068 q^{26} -121.014 q^{28} +(133.133 + 230.594i) q^{29} +(39.1334 - 67.7811i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-88.5068 - 153.298i) q^{34} +151.267 q^{35} +413.041 q^{37} +(-71.5068 - 123.853i) q^{38} +(-20.0000 + 34.6410i) q^{40} +(38.2601 - 66.2685i) q^{41} +(2.74662 + 4.75729i) q^{43} -213.014 q^{44} -64.5068 q^{46} +(-129.394 - 224.116i) q^{47} +(-286.133 + 495.598i) q^{49} +(25.0000 - 43.3013i) q^{50} +(36.5068 + 63.2316i) q^{52} -579.774 q^{53} +266.267 q^{55} +(-121.014 - 209.602i) q^{56} +(-266.267 + 461.188i) q^{58} +(80.2736 - 139.038i) q^{59} +(251.760 + 436.061i) q^{61} +156.534 q^{62} +64.0000 q^{64} +(-45.6334 - 79.0394i) q^{65} +(-445.760 + 772.079i) q^{67} +(177.014 - 306.596i) q^{68} +(151.267 + 262.002i) q^{70} -993.760 q^{71} -116.561 q^{73} +(413.041 + 715.407i) q^{74} +(143.014 - 247.707i) q^{76} +(-805.547 + 1395.25i) q^{77} +(-501.321 - 868.313i) q^{79} -80.0000 q^{80} +153.041 q^{82} +(-257.986 - 446.846i) q^{83} +(-221.267 + 383.245i) q^{85} +(-5.49324 + 9.51458i) q^{86} +(-213.014 - 368.950i) q^{88} -957.760 q^{89} +552.226 q^{91} +(-64.5068 - 111.729i) q^{92} +(258.787 - 448.233i) q^{94} +(-178.767 + 309.633i) q^{95} +(866.855 + 1501.44i) q^{97} -1144.53 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{4} + 10 q^{5} + 5 q^{7} - 32 q^{8} + 40 q^{10} + 51 q^{11} - 19 q^{13} - 10 q^{14} - 32 q^{16} - 132 q^{17} - 64 q^{19} + 40 q^{20} - 102 q^{22} - 9 q^{23} - 50 q^{25} - 76 q^{26} - 40 q^{28}+ \cdots - 3468 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^4 + 10 * q^5 + 5 * q^7 - 32 * q^8 + 40 * q^10 + 51 * q^11 - 19 * q^13 - 10 * q^14 - 32 * q^16 - 132 * q^17 - 64 * q^19 + 40 * q^20 - 102 * q^22 - 9 * q^23 - 50 * q^25 - 76 * q^26 - 40 * q^28 + 255 * q^29 - 121 * q^31 + 64 * q^32 - 132 * q^34 + 50 * q^35 + 320 * q^37 - 64 * q^38 - 80 * q^40 - 180 * q^41 + 122 * q^43 - 408 * q^44 - 36 * q^46 + 93 * q^47 - 867 * q^49 + 100 * q^50 - 76 * q^52 - 1542 * q^53 + 510 * q^55 - 40 * q^56 - 510 * q^58 - 456 * q^59 + 674 * q^61 - 484 * q^62 + 256 * q^64 + 95 * q^65 - 1450 * q^67 + 264 * q^68 + 50 * q^70 - 3642 * q^71 + 1532 * q^73 + 320 * q^74 + 128 * q^76 - 1668 * q^77 + 326 * q^79 - 320 * q^80 - 720 * q^82 - 1476 * q^83 - 330 * q^85 - 244 * q^86 - 408 * q^88 - 3498 * q^89 + 2986 * q^91 - 36 * q^92 - 186 * q^94 - 160 * q^95 + 26 * q^97 - 3468 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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