LMFDB - Embedded newform 342.4.g.f.163.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,4,Mod(163,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("342.163");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	342.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$20.1786532220$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 64x^{4} + 33x^{3} + 3984x^{2} - 945x + 225 $ x^6 - x^5 + 64x^4 + 33x^3 + 3984x^2 - 945x + 225
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.3
Root			$-3.78825 + 6.56144i$ of defining polynomial
Character	$\chi$	$=$	342.163
Dual form			342.4.g.f.235.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(7.88908 - 13.6643i) q^{5} +16.5765 q^{7} +8.00000 q^{8} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(7.88908 - 13.6643i) q^{5} +16.5765 q^{7} +8.00000 q^{8} +(15.7782 + 27.3286i) q^{10} -16.0285 q^{11} +(33.5522 + 58.1141i) q^{13} +(-16.5765 + 28.7113i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(19.8025 - 34.2989i) q^{17} +(14.7639 - 81.4925i) q^{19} -63.1126 q^{20} +(16.0285 - 27.7621i) q^{22} +(-23.8404 - 41.2928i) q^{23} +(-61.9750 - 107.344i) q^{25} -134.209 q^{26} +(-33.1530 - 57.4227i) q^{28} +(-59.2021 - 102.541i) q^{29} +120.050 q^{31} +(-16.0000 - 27.7128i) q^{32} +(39.6050 + 68.5978i) q^{34} +(130.773 - 226.506i) q^{35} +22.0924 q^{37} +(126.385 + 107.064i) q^{38} +(63.1126 - 109.314i) q^{40} +(54.5508 - 94.4847i) q^{41} +(180.312 - 312.310i) q^{43} +(32.0569 + 55.5242i) q^{44} +95.3617 q^{46} +(96.4726 + 167.095i) q^{47} -68.2197 q^{49} +247.900 q^{50} +(134.209 - 232.456i) q^{52} +(108.922 + 188.659i) q^{53} +(-126.450 + 219.017i) q^{55} +132.612 q^{56} +236.808 q^{58} +(211.595 - 366.493i) q^{59} +(-281.960 - 488.369i) q^{61} +(-120.050 + 207.932i) q^{62} +64.0000 q^{64} +1058.78 q^{65} +(471.426 + 816.534i) q^{67} -158.420 q^{68} +(261.546 + 453.012i) q^{70} +(-332.873 + 576.552i) q^{71} +(93.4728 - 161.900i) q^{73} +(-22.0924 + 38.2652i) q^{74} +(-311.826 + 111.841i) q^{76} -265.696 q^{77} +(438.177 - 758.945i) q^{79} +(126.225 + 218.628i) q^{80} +(109.102 + 188.969i) q^{82} +476.297 q^{83} +(-312.447 - 541.173i) q^{85} +(360.624 + 624.620i) q^{86} -128.228 q^{88} +(-482.370 - 835.489i) q^{89} +(556.177 + 963.328i) q^{91} +(-95.3617 + 165.171i) q^{92} -385.890 q^{94} +(-997.063 - 844.639i) q^{95} +(792.961 - 1373.45i) q^{97} +(68.2197 - 118.160i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 12 q^{4} + q^{5} + 52 q^{7} + 48 q^{8}+O(q^{10}) $ 6 * q - 6 * q^2 - 12 * q^4 + q^5 + 52 * q^7 + 48 * q^8	$ 6 q - 6 q^{2} - 12 q^{4} + q^{5} + 52 q^{7} + 48 q^{8} + 2 q^{10} - 8 q^{11} + 129 q^{13} - 52 q^{14} - 48 q^{16} + 51 q^{17} + 40 q^{19} - 8 q^{20} + 8 q^{22} - 47 q^{23} - 338 q^{25} - 516 q^{26} - 104 q^{28} + 125 q^{29} - 100 q^{31} - 96 q^{32} + 102 q^{34} + 84 q^{35} - 376 q^{37} - 322 q^{38} + 8 q^{40} - 475 q^{41} - 73 q^{43} + 16 q^{44} + 188 q^{46} + 241 q^{47} - 1354 q^{49} + 1352 q^{50} + 516 q^{52} - 29 q^{53} - 1838 q^{55} + 416 q^{56} - 500 q^{58} + 1065 q^{59} - 981 q^{61} + 100 q^{62} + 384 q^{64} - 586 q^{65} + 877 q^{67} - 408 q^{68} + 168 q^{70} - 2135 q^{71} + 667 q^{73} + 376 q^{74} + 484 q^{76} + 492 q^{77} + 1671 q^{79} + 16 q^{80} - 950 q^{82} - 1176 q^{83} - 1929 q^{85} - 146 q^{86} - 64 q^{88} - 693 q^{89} + 1676 q^{91} - 188 q^{92} - 964 q^{94} - 4489 q^{95} - 985 q^{97} + 1354 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 - 12 * q^4 + q^5 + 52 * q^7 + 48 * q^8 + 2 * q^10 - 8 * q^11 + 129 * q^13 - 52 * q^14 - 48 * q^16 + 51 * q^17 + 40 * q^19 - 8 * q^20 + 8 * q^22 - 47 * q^23 - 338 * q^25 - 516 * q^26 - 104 * q^28 + 125 * q^29 - 100 * q^31 - 96 * q^32 + 102 * q^34 + 84 * q^35 - 376 * q^37 - 322 * q^38 + 8 * q^40 - 475 * q^41 - 73 * q^43 + 16 * q^44 + 188 * q^46 + 241 * q^47 - 1354 * q^49 + 1352 * q^50 + 516 * q^52 - 29 * q^53 - 1838 * q^55 + 416 * q^56 - 500 * q^58 + 1065 * q^59 - 981 * q^61 + 100 * q^62 + 384 * q^64 - 586 * q^65 + 877 * q^67 - 408 * q^68 + 168 * q^70 - 2135 * q^71 + 667 * q^73 + 376 * q^74 + 484 * q^76 + 492 * q^77 + 1671 * q^79 + 16 * q^80 - 950 * q^82 - 1176 * q^83 - 1929 * q^85 - 146 * q^86 - 64 * q^88 - 693 * q^89 + 1676 * q^91 - 188 * q^92 - 964 * q^94 - 4489 * q^95 - 985 * q^97 + 1354 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	7.88908	−	13.6643i	0.705620	−	1.22217i	−0.260847	−	0.965380i	$-0.584002\pi$
$5$	7.88908	−	13.6643i	0.705620	−	1.22217i	0.966467	−	0.256790i	$-0.0826649\pi$
$6$		0			0
$7$	16.5765			0.895047			0.447523	−	0.894272i	$-0.352306\pi$
$7$	16.5765			0.895047			0.447523	+	0.894272i	$0.352306\pi$
$8$	8.00000			0.353553
$9$		0			0
$10$	15.7782	+	27.3286i	0.498949	+	0.864205i
$11$	−16.0285			−0.439342			−0.219671	−	0.975574i	$-0.570498\pi$
$11$	−16.0285			−0.439342			−0.219671	+	0.975574i	$0.570498\pi$
$12$		0			0
$13$	33.5522	+	58.1141i	0.715823	+	1.23984i	0.962641	+	0.270780i	$0.0872815\pi$
$13$	33.5522	+	58.1141i	0.715823	+	1.23984i	−0.246818	+	0.969062i	$0.579385\pi$
$14$	−16.5765	+	28.7113i	−0.316447	+	0.548102i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	19.8025	−	34.2989i	0.282518	−	0.489336i	−0.689486	−	0.724299i	$-0.742164\pi$
$17$	19.8025	−	34.2989i	0.282518	−	0.489336i	0.972004	+	0.234963i	$0.0754969\pi$
$18$		0			0
$19$	14.7639	−	81.4925i	0.178267	−	0.983982i
$19$	14.7639	−	81.4925i	0.178267	−	0.983982i
$20$	−63.1126			−0.705620
$21$		0			0
$22$	16.0285	−	27.7621i	0.155331	−	0.269041i
$23$	−23.8404	−	41.2928i	−0.216133	−	0.374354i	0.737489	−	0.675359i	$-0.236011\pi$
$23$	−23.8404	−	41.2928i	−0.216133	−	0.374354i	−0.953623	+	0.301005i	$0.902678\pi$
$24$		0			0
$25$	−61.9750	−	107.344i	−0.495800	−	0.858751i
$26$	−134.209			−1.01233
$27$		0			0
$28$	−33.1530	−	57.4227i	−0.223762	−	0.387567i
$29$	−59.2021	−	102.541i	−0.379088	−	0.656600i	0.611842	−	0.790980i	$-0.290429\pi$
$29$	−59.2021	−	102.541i	−0.379088	−	0.656600i	−0.990930	+	0.134381i	$0.957096\pi$
$30$		0			0
$31$	120.050			0.695533			0.347767	−	0.937581i	$-0.386940\pi$
$31$	120.050			0.695533			0.347767	+	0.937581i	$0.386940\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$		0			0
$34$	39.6050	+	68.5978i	0.199770	+	0.346013i
$35$	130.773	−	226.506i	0.631563	−	1.09390i
$36$		0			0
$37$	22.0924			0.0981614			0.0490807	−	0.998795i	$-0.484371\pi$
$37$	22.0924			0.0981614			0.0490807	+	0.998795i	$0.484371\pi$
$38$	126.385	+	107.064i	0.539537	+	0.457056i
$39$		0			0
$40$	63.1126	−	109.314i	0.249474	−	0.432102i
$41$	54.5508	−	94.4847i	0.207790	−	0.359903i	−0.743228	−	0.669038i	$-0.766706\pi$
$41$	54.5508	−	94.4847i	0.207790	−	0.359903i	0.951018	+	0.309135i	$0.100040\pi$
$42$		0			0
$43$	180.312	−	312.310i	0.639473	−	1.10760i	−0.346075	−	0.938207i	$-0.612486\pi$
$43$	180.312	−	312.310i	0.639473	−	1.10760i	0.985548	−	0.169394i	$-0.0541809\pi$
$44$	32.0569	+	55.5242i	0.109836	+	0.190241i
$45$		0			0
$46$	95.3617			0.305659
$47$	96.4726	+	167.095i	0.299404	+	0.518582i	0.976000	−	0.217772i	$-0.0698789\pi$
$47$	96.4726	+	167.095i	0.299404	+	0.518582i	−0.676596	+	0.736354i	$0.736546\pi$
$48$		0			0
$49$	−68.2197			−0.198891
$50$	247.900			0.701168
$51$		0			0
$52$	134.209	−	232.456i	0.357911	−	0.619921i
$53$	108.922	+	188.659i	0.282294	+	0.488948i	0.971949	−	0.235190i	$-0.0755712\pi$
$53$	108.922	+	188.659i	0.282294	+	0.488948i	−0.689655	+	0.724138i	$0.742238\pi$
$54$		0			0
$55$	−126.450	+	219.017i	−0.310009	+	0.536951i
$56$	132.612			0.316447
$57$		0			0
$58$	236.808			0.536111
$59$	211.595	−	366.493i	0.466903	−	0.808701i	−0.532382	−	0.846504i	$-0.678703\pi$
$59$	211.595	−	366.493i	0.466903	−	0.808701i	0.999285	+	0.0378039i	$0.0120362\pi$
$60$		0			0
$61$	−281.960	−	488.369i	−0.591824	−	1.02507i	−0.993987	−	0.109501i	$-0.965075\pi$
$61$	−281.960	−	488.369i	−0.591824	−	1.02507i	0.402162	−	0.915568i	$-0.368259\pi$
$62$	−120.050	+	207.932i	−0.245908	+	0.425925i
$63$		0			0
$64$	64.0000			0.125000
$65$	1058.78			2.02040
$66$		0			0
$67$	471.426	+	816.534i	0.859610	+	1.48889i	0.872302	+	0.488968i	$0.162627\pi$
$67$	471.426	+	816.534i	0.859610	+	1.48889i	−0.0126922	+	0.999919i	$0.504040\pi$
$68$	−158.420			−0.282518
$69$		0			0
$70$	261.546	+	453.012i	0.446583	+	0.773504i
$71$	−332.873	+	576.552i	−0.556404	+	0.963721i	0.441388	+	0.897316i	$0.354486\pi$
$71$	−332.873	+	576.552i	−0.556404	+	0.963721i	−0.997793	+	0.0664045i	$0.978847\pi$
$72$		0			0
$73$	93.4728	−	161.900i	0.149865	−	0.259574i	−0.781312	−	0.624140i	$-0.785449\pi$
$73$	93.4728	−	161.900i	0.149865	−	0.259574i	0.931178	+	0.364566i	$0.118783\pi$
$74$	−22.0924	+	38.2652i	−0.0347053	+	0.0601113i
$75$		0			0
$76$	−311.826	+	111.841i	−0.470644	+	0.168804i
$77$	−265.696			−0.393232
$78$		0			0
$79$	438.177	−	758.945i	0.624035	−	1.08086i	−0.364692	−	0.931128i	$-0.618826\pi$
$79$	438.177	−	758.945i	0.624035	−	1.08086i	0.988727	−	0.149732i	$-0.0478410\pi$
$80$	126.225	+	218.628i	0.176405	+	0.305543i
$81$		0			0
$82$	109.102	+	188.969i	0.146930	+	0.254490i
$83$	476.297			0.629885			0.314942	−	0.949111i	$-0.398015\pi$
$83$	476.297			0.629885			0.314942	+	0.949111i	$0.398015\pi$
$84$		0			0
$85$	−312.447	−	541.173i	−0.398701	−	0.690570i
$86$	360.624	+	624.620i	0.452176	+	0.783192i
$87$		0			0
$88$	−128.228			−0.155331
$89$	−482.370	−	835.489i	−0.574507	−	0.995075i	−0.996095	−	0.0882878i	$-0.971860\pi$
$89$	−482.370	−	835.489i	−0.574507	−	0.995075i	0.421588	−	0.906787i	$-0.361473\pi$
$90$		0			0
$91$	556.177	+	963.328i	0.640695	+	1.10972i
$92$	−95.3617	+	165.171i	−0.108067	+	0.187177i
$93$		0			0
$94$	−385.890			−0.423421
$95$	−997.063	−	844.639i	−1.07680	−	0.912191i
$96$		0			0
$97$	792.961	−	1373.45i	0.830031	−	1.43766i	−0.0679822	−	0.997687i	$-0.521656\pi$
$97$	792.961	−	1373.45i	0.830031	−	1.43766i	0.898013	−	0.439969i	$-0.145011\pi$
$98$	68.2197	−	118.160i	0.0703187	−	0.121796i
$99$		0			0
$100$	−247.900	+	429.376i	−0.247900	+	0.429376i
$101$	−521.913	−	903.980i	−0.514181	−	0.890588i	−0.999865	−	0.0164532i	$-0.994763\pi$
$101$	−521.913	−	903.980i	−0.514181	−	0.890588i	0.485683	−	0.874135i	$-0.338571\pi$
$102$		0			0
$103$	1427.83			1.36591			0.682954	−	0.730461i	$-0.260695\pi$
$103$	1427.83			1.36591			0.682954	+	0.730461i	$0.260695\pi$
$104$	268.417	+	464.912i	0.253082	+	0.438350i
$105$		0			0
$106$	−435.688			−0.399225
$107$	−500.924			−0.452581			−0.226290	−	0.974060i	$-0.572660\pi$
$107$	−500.924			−0.452581			−0.226290	+	0.974060i	$0.572660\pi$
$108$		0			0
$109$	−606.462	+	1050.42i	−0.532922	+	0.923048i	0.466339	+	0.884606i	$0.345573\pi$
$109$	−606.462	+	1050.42i	−0.532922	+	0.923048i	−0.999261	+	0.0384417i	$0.987761\pi$
$110$	−252.900	−	438.035i	−0.219209	−	0.379682i
$111$		0			0
$112$	−132.612	+	229.691i	−0.111881	+	0.193783i
$113$	−738.956			−0.615178			−0.307589	−	0.951519i	$-0.599522\pi$
$113$	−738.956			−0.615178			−0.307589	+	0.951519i	$0.599522\pi$
$114$		0			0
$115$	−752.315			−0.610033
$116$	−236.808	+	410.164i	−0.189544	+	0.328300i
$117$		0			0
$118$	423.190	+	732.986i	0.330151	+	0.571838i
$119$	328.256	−	568.556i	0.252867	−	0.437978i
$120$		0			0
$121$	−1074.09			−0.806978
$122$	1127.84			0.836966
$123$		0			0
$124$	−240.099	−	415.864i	−0.173883	−	0.301175i
$125$	16.5658			0.0118535
$126$		0			0
$127$	−119.454	−	206.900i	−0.0834632	−	0.144563i	0.821272	−	0.570537i	$-0.193265\pi$
$127$	−119.454	−	206.900i	−0.0834632	−	0.144563i	−0.904735	+	0.425974i	$0.859931\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−1058.78	+	1833.86i	−0.714318	+	1.23724i
$131$	132.624	−	229.712i	0.0884537	−	0.153206i	−0.818404	−	0.574643i	$-0.805141\pi$
$131$	132.624	−	229.712i	0.0884537	−	0.153206i	0.906858	+	0.421437i	$0.138474\pi$
$132$		0			0
$133$	244.734	−	1350.86i	0.159557	−	0.880710i
$134$	−1885.70			−1.21567
$135$		0			0
$136$	158.420	−	274.391i	0.0998852	−	0.173006i
$137$	1219.22	+	2111.76i	0.760331	+	1.31693i	0.942680	+	0.333698i	$0.108297\pi$
$137$	1219.22	+	2111.76i	0.760331	+	1.31693i	−0.182349	+	0.983234i	$0.558370\pi$
$138$		0			0
$139$	183.397	+	317.653i	0.111910	+	0.193835i	0.916541	−	0.399942i	$-0.130970\pi$
$139$	183.397	+	317.653i	0.111910	+	0.193835i	−0.804630	+	0.593776i	$0.797636\pi$
$140$	−1046.19			−0.631563
$141$		0			0
$142$	−665.745	−	1153.10i	−0.393437	−	0.681453i
$143$	−537.790	−	931.479i	−0.314491	−	0.544715i
$144$		0			0
$145$	−1868.20			−1.06997
$146$	186.946	+	323.799i	0.105971	+	0.183547i
$147$		0			0
$148$	−44.1848	−	76.5304i	−0.0245403	−	0.0425051i
$149$	−1120.88	+	1941.42i	−0.616281	+	1.06743i	0.373877	+	0.927478i	$0.378028\pi$
$149$	−1120.88	+	1941.42i	−0.616281	+	1.06743i	−0.990158	+	0.139952i	$0.955305\pi$
$150$		0			0
$151$	−638.195			−0.343944			−0.171972	−	0.985102i	$-0.555014\pi$
$151$	−638.195			−0.343944			−0.171972	+	0.985102i	$0.555014\pi$
$152$	118.111	−	651.940i	0.0630269	−	0.347890i
$153$		0			0
$154$	265.696	−	460.199i	0.139028	−	0.240804i
$155$	947.080	−	1640.39i	0.490782	−	0.850060i
$156$		0			0
$157$	−1063.00	+	1841.16i	−0.540358	+	0.935928i	0.458525	+	0.888682i	$0.348378\pi$
$157$	−1063.00	+	1841.16i	−0.540358	+	0.935928i	−0.998883	+	0.0472466i	$0.984955\pi$
$158$	876.354	+	1517.89i	0.441259	+	0.764283i
$159$		0			0
$160$	−504.901			−0.249474
$161$	−395.191	−	684.490i	−0.193450	−	0.335064i
$162$		0			0
$163$	−160.043			−0.0769053			−0.0384526	−	0.999260i	$-0.512243\pi$
$163$	−160.043			−0.0769053			−0.0384526	+	0.999260i	$0.512243\pi$
$164$	−436.406			−0.207790
$165$		0			0
$166$	−476.297	+	824.971i	−0.222698	+	0.385724i
$167$	1051.08	+	1820.52i	0.487036	+	0.843571i	0.999889	−	0.0149055i	$-0.00474476\pi$
$167$	1051.08	+	1820.52i	0.487036	+	0.843571i	−0.512853	+	0.858476i	$0.671411\pi$
$168$		0			0
$169$	−1153.00	+	1997.05i	−0.524805	+	0.908988i
$170$	1249.79			0.563848
$171$		0			0
$172$	−1442.50			−0.639473
$173$	−202.732	+	351.142i	−0.0890949	+	0.154317i	−0.907129	−	0.420853i	$-0.861731\pi$
$173$	−202.732	+	351.142i	−0.0890949	+	0.154317i	0.818034	+	0.575170i	$0.195064\pi$
$174$		0			0
$175$	−1027.33	−	1779.39i	−0.443764	−	0.768623i
$176$	128.228	−	222.097i	0.0549178	−	0.0951204i
$177$		0			0
$178$	1929.48			0.812476
$179$	1628.76			0.680107			0.340053	−	0.940406i	$-0.389555\pi$
$179$	1628.76			0.680107			0.340053	+	0.940406i	$0.389555\pi$
$180$		0			0
$181$	−1418.42	−	2456.77i	−0.582487	−	1.00890i	−0.995184	−	0.0980291i	$-0.968746\pi$
$181$	−1418.42	−	2456.77i	−0.582487	−	1.00890i	0.412696	−	0.910869i	$-0.364587\pi$
$182$	−2224.71			−0.906079
$183$		0			0
$184$	−190.723	−	330.342i	−0.0764147	−	0.132354i
$185$	174.289	−	301.877i	0.0692647	−	0.119970i
$186$		0			0
$187$	−317.403	+	549.759i	−0.124122	+	0.214986i
$188$	385.890	−	668.382i	0.149702	−	0.259291i
$189$		0			0
$190$	2460.02	−	882.324i	0.939308	−	0.336898i
$191$	−3521.85			−1.33420			−0.667099	−	0.744969i	$-0.732464\pi$
$191$	−3521.85			−1.33420			−0.667099	+	0.744969i	$0.732464\pi$
$192$		0			0
$193$	−2367.70	+	4100.97i	−0.883060	+	1.52950i	−0.0351378	+	0.999382i	$0.511187\pi$
$193$	−2367.70	+	4100.97i	−0.883060	+	1.52950i	−0.847922	+	0.530121i	$0.822146\pi$
$194$	1585.92	+	2746.90i	0.586920	+	1.01658i
$195$		0			0
$196$	136.439	+	236.320i	0.0497228	+	0.0861225i
$197$	−2357.30			−0.852541			−0.426270	−	0.904596i	$-0.640173\pi$
$197$	−2357.30			−0.852541			−0.426270	+	0.904596i	$0.640173\pi$
$198$		0			0
$199$	−342.578	−	593.362i	−0.122034	−	0.211369i	0.798536	−	0.601947i	$-0.205608\pi$
$199$	−342.578	−	593.362i	−0.122034	−	0.211369i	−0.920570	+	0.390579i	$0.872275\pi$
$200$	−495.800	−	858.751i	−0.175292	−	0.303614i
$201$		0			0
$202$	2087.65			0.727162
$203$	−981.363	−	1699.77i	−0.339301	−	0.587687i
$204$		0			0
$205$	−860.710	−	1490.79i	−0.293242	−	0.507910i
$206$	−1427.83	+	2473.08i	−0.482922	+	0.836445i
$207$		0			0
$208$	−1073.67			−0.357911
$209$	−236.643	+	1306.20i	−0.0783203	+	0.432305i
$210$		0			0
$211$	265.510	−	459.876i	0.0866277	−	0.150044i	−0.819456	−	0.573142i	$-0.805724\pi$
$211$	265.510	−	459.876i	0.0866277	−	0.150044i	0.906084	+	0.423099i	$0.139058\pi$
$212$	435.688	−	754.634i	0.141147	−	0.244474i
$213$		0			0
$214$	500.924	−	867.626i	0.160012	−	0.277148i
$215$	−2844.99	−	4927.67i	−0.902451	−	1.56309i
$216$		0			0
$217$	1990.00			0.622535
$218$	−1212.92	−	2100.84i	−0.376833	−	0.652693i
$219$		0			0
$220$	1011.60			0.310009
$221$	2657.66			0.808932
$222$		0			0
$223$	−2425.86	+	4201.71i	−0.728463	+	1.26174i	0.229069	+	0.973410i	$0.426432\pi$
$223$	−2425.86	+	4201.71i	−0.728463	+	1.26174i	−0.957533	+	0.288325i	$0.906902\pi$
$224$	−265.224	−	459.381i	−0.0791117	−	0.137025i
$225$		0			0
$226$	738.956	−	1279.91i	0.217498	−	0.376718i
$227$	3971.88			1.16134			0.580668	−	0.814141i	$-0.302792\pi$
$227$	3971.88			1.16134			0.580668	+	0.814141i	$0.302792\pi$
$228$		0			0
$229$	−78.9844			−0.0227923			−0.0113961	−	0.999935i	$-0.503628\pi$
$229$	−78.9844			−0.0227923			−0.0113961	+	0.999935i	$0.503628\pi$
$230$	752.315	−	1303.05i	0.215679	−	0.373567i
$231$		0			0
$232$	−473.617	−	820.328i	−0.134028	−	0.232143i
$233$	−821.646	+	1423.13i	−0.231021	+	0.400140i	−0.958109	−	0.286405i	$-0.907540\pi$
$233$	−821.646	+	1423.13i	−0.231021	+	0.400140i	0.727088	+	0.686544i	$0.240873\pi$
$234$		0			0
$235$	3044.32			0.845061
$236$	−1692.76			−0.466903
$237$		0			0
$238$	656.512	+	1137.11i	0.178804	+	0.309697i
$239$	6316.74			1.70961			0.854803	−	0.518952i	$-0.173678\pi$
$239$	6316.74			1.70961			0.854803	+	0.518952i	$0.173678\pi$
$240$		0			0
$241$	1747.33	+	3026.46i	0.467034	+	0.808927i	0.999291	−	0.0376561i	$-0.0119891\pi$
$241$	1747.33	+	3026.46i	0.467034	+	0.808927i	−0.532257	+	0.846583i	$0.678656\pi$
$242$	1074.09	−	1860.38i	0.285310	−	0.494171i
$243$		0			0
$244$	−1127.84	+	1953.48i	−0.295912	+	0.512535i
$245$	−538.191	+	932.174i	−0.140342	+	0.243079i
$246$		0			0
$247$	5231.22	−	1876.26i	1.34759	−	0.483334i
$248$	960.396			0.245908
$249$		0			0
$250$	−16.5658	+	28.6928i	−0.00419086	+	0.00725878i
$251$	1815.19	+	3143.99i	0.456468	+	0.790626i	0.998771	−	0.0495570i	$-0.0157809\pi$
$251$	1815.19	+	3143.99i	0.456468	+	0.790626i	−0.542303	+	0.840183i	$0.682448\pi$
$252$		0			0
$253$	382.125	+	661.860i	0.0949566	+	0.164470i
$254$	477.816			0.118035
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−774.708	−	1341.83i	−0.188035	−	0.325686i	0.756560	−	0.653924i	$-0.226878\pi$
$257$	−774.708	−	1341.83i	−0.188035	−	0.325686i	−0.944595	+	0.328238i	$0.893545\pi$
$258$		0			0
$259$	366.215			0.0878590
$260$	−2117.56	−	3667.73i	−0.505099	−	0.874857i
$261$		0			0
$262$	265.249	+	459.424i	0.0625462	+	0.108333i
$263$	−1904.91	+	3299.39i	−0.446622	+	0.773571i	−0.998164	−	0.0605757i	$-0.980706\pi$
$263$	−1904.91	+	3299.39i	−0.446622	+	0.773571i	0.551542	+	0.834147i	$0.314040\pi$
$264$		0			0
$265$	3437.18			0.796771
$266$	2095.02	+	1774.75i	0.482910	+	0.409087i
$267$		0			0
$268$	1885.70	−	3266.13i	0.429805	−	0.744444i
$269$	−1688.20	+	2924.05i	−0.382644	+	0.662759i	−0.991439	−	0.130568i	$-0.958320\pi$
$269$	−1688.20	+	2924.05i	−0.382644	+	0.662759i	0.608795	+	0.793328i	$0.291653\pi$
$270$		0			0
$271$	1762.75	−	3053.17i	0.395127	−	0.684380i	−0.597991	−	0.801503i	$-0.704034\pi$
$271$	1762.75	−	3053.17i	0.395127	−	0.684380i	0.993117	+	0.117123i	$0.0373673\pi$
$272$	316.840	+	548.782i	0.0706295	+	0.122334i
$273$		0			0
$274$	−4876.90			−1.07527
$275$	993.365	+	1720.56i	0.217826	+	0.377286i
$276$		0			0
$277$	6557.88			1.42247			0.711236	−	0.702953i	$-0.248136\pi$
$277$	6557.88			1.42247			0.711236	+	0.702953i	$0.248136\pi$
$278$	−733.589			−0.158265
$279$		0			0
$280$	1046.19	−	1812.05i	0.223291	−	0.386752i
$281$	3943.90	+	6831.04i	0.837272	+	1.45020i	0.892167	+	0.451705i	$0.149184\pi$
$281$	3943.90	+	6831.04i	0.837272	+	1.45020i	−0.0548952	+	0.998492i	$0.517482\pi$
$282$		0			0
$283$	−1036.37	+	1795.04i	−0.217687	+	0.377046i	−0.954101	−	0.299486i	$-0.903185\pi$
$283$	−1036.37	+	1795.04i	−0.217687	+	0.377046i	0.736413	+	0.676532i	$0.236518\pi$
$284$	2662.98			0.556404
$285$		0			0
$286$	2151.16			0.444758
$287$	904.261	−	1566.23i	0.185982	−	0.322130i
$288$		0			0
$289$	1672.22	+	2896.38i	0.340367	+	0.589533i
$290$	1868.20	−	3235.82i	0.378291	−	0.655219i
$291$		0			0
$292$	−747.782			−0.149865
$293$	7820.84			1.55938			0.779690	−	0.626165i	$-0.215376\pi$
$293$	7820.84			1.55938			0.779690	+	0.626165i	$0.215376\pi$
$294$		0			0
$295$	−3338.58	−	5782.58i	−0.658913	−	1.14127i
$296$	176.739			0.0347053
$297$		0			0
$298$	−2241.76	−	3882.84i	−0.435777	−	0.754787i
$299$	1599.80	−	2770.93i	0.309427	−	0.535943i
$300$		0			0
$301$	2988.95	−	5177.00i	0.572359	−	0.991354i
$302$	638.195	−	1105.39i	0.121603	−	0.210622i
$303$		0			0
$304$	1011.08	+	856.515i	0.190755	+	0.161594i
$305$	−8897.62			−1.67041
$306$		0			0
$307$	2968.90	−	5142.28i	0.551934	−	0.955978i	−0.446201	−	0.894933i	$-0.647223\pi$
$307$	2968.90	−	5142.28i	0.551934	−	0.955978i	0.998135	−	0.0610453i	$-0.0194434\pi$
$308$	531.392	+	920.397i	0.0983080	+	0.170274i
$309$		0			0
$310$	1894.16	+	3280.78i	0.347036	+	0.601083i
$311$	−1832.63			−0.334145			−0.167073	−	0.985945i	$-0.553431\pi$
$311$	−1832.63			−0.334145			−0.167073	+	0.985945i	$0.553431\pi$
$312$		0			0
$313$	469.166	+	812.619i	0.0847247	+	0.146747i	0.905274	−	0.424828i	$-0.139666\pi$
$313$	469.166	+	812.619i	0.0847247	+	0.146747i	−0.820549	+	0.571576i	$0.806332\pi$
$314$	−2125.99	−	3682.32i	−0.382091	−	0.661801i
$315$		0			0
$316$	−3505.42			−0.624035
$317$	−3705.73	−	6418.51i	−0.656576	−	1.13722i	−0.981496	−	0.191481i	$-0.938671\pi$
$317$	−3705.73	−	6418.51i	−0.656576	−	1.13722i	0.324920	−	0.945741i	$-0.394663\pi$
$318$		0			0
$319$	948.919	+	1643.58i	0.166549	+	0.288472i
$320$	504.901	−	874.514i	0.0882026	−	0.152771i
$321$		0			0
$322$	1580.76			0.273579
$323$	−2502.74	−	2120.14i	−0.431134	−	0.365225i
$324$		0			0
$325$	4158.79	−	7203.24i	0.709810	−	1.22943i
$326$	160.043	−	277.203i	0.0271901	−	0.0470947i
$327$		0			0
$328$	436.406	−	755.878i	0.0734649	−	0.127245i
$329$	1599.18	+	2769.86i	0.267980	+	0.464155i
$330$		0			0
$331$	−5412.69			−0.898817			−0.449408	−	0.893326i	$-0.648365\pi$
$331$	−5412.69			−0.898817			−0.449408	+	0.893326i	$0.648365\pi$
$332$	−952.595	−	1649.94i	−0.157471	−	0.272748i
$333$		0			0
$334$	−4204.32			−0.688773
$335$	14876.5			2.42623
$336$		0			0
$337$	−4636.79	+	8031.15i	−0.749501	+	1.29817i	0.198561	+	0.980088i	$0.436373\pi$
$337$	−4636.79	+	8031.15i	−0.749501	+	1.29817i	−0.948062	+	0.318085i	$0.896960\pi$
$338$	−2305.99	−	3994.09i	−0.371093	−	0.642752i
$339$		0			0
$340$	−1249.79	+	2164.69i	−0.199351	+	0.345285i
$341$	−1924.21			−0.305577
$342$		0			0
$343$	−6816.58			−1.07306
$344$	1442.50	−	2498.48i	0.226088	−	0.391596i
$345$		0			0
$346$	−405.464	−	702.284i	−0.0629996	−	0.109119i
$347$	−4837.24	+	8378.35i	−0.748348	+	1.29618i	0.200266	+	0.979741i	$0.435819\pi$
$347$	−4837.24	+	8378.35i	−0.748348	+	1.29618i	−0.948614	+	0.316435i	$0.897514\pi$
$348$		0			0
$349$	1300.56			0.199477			0.0997387	−	0.995014i	$-0.468199\pi$
$349$	1300.56			0.199477			0.0997387	+	0.995014i	$0.468199\pi$
$350$	4109.32			0.627578
$351$		0			0
$352$	256.455	+	444.194i	0.0388327	+	0.0672603i
$353$	−11985.4			−1.80713			−0.903564	−	0.428454i	$-0.859058\pi$
$353$	−11985.4			−1.80713			−0.903564	+	0.428454i	$0.859058\pi$
$354$		0			0
$355$	5252.11	+	9096.93i	0.785221	+	1.36004i
$356$	−1929.48	+	3341.96i	−0.287253	+	0.497538i
$357$		0			0
$358$	−1628.76	+	2821.09i	−0.240454	+	0.416478i
$359$	−2203.95	+	3817.35i	−0.324011	+	0.561204i	−0.981312	−	0.192425i	$-0.938365\pi$
$359$	−2203.95	+	3817.35i	−0.324011	+	0.561204i	0.657301	+	0.753628i	$0.271698\pi$
$360$		0			0
$361$	−6423.05	−	2406.30i	−0.936442	−	0.350823i
$362$	5673.68			0.823762
$363$		0			0
$364$	2224.71	−	3853.31i	0.320347	−	0.554858i
$365$	−1474.83	−	2554.48i	−0.211496	−	0.366322i
$366$		0			0
$367$	−3130.04	−	5421.39i	−0.445196	−	0.771102i	0.552870	−	0.833267i	$-0.313533\pi$
$367$	−3130.04	−	5421.39i	−0.445196	−	0.771102i	−0.998066	+	0.0621658i	$0.980199\pi$
$368$	762.893			0.108067
$369$		0			0
$370$	348.577	+	603.754i	0.0489775	+	0.0848315i
$371$	1805.55	+	3127.30i	0.252667	+	0.437631i
$372$		0			0
$373$	−2745.24			−0.381081			−0.190541	−	0.981679i	$-0.561024\pi$
$373$	−2745.24			−0.381081			−0.190541	+	0.981679i	$0.561024\pi$
$374$	−634.807	−	1099.52i	−0.0877676	−	0.152018i
$375$		0			0
$376$	771.781	+	1336.76i	0.105855	+	0.183347i
$377$	3972.72	−	6880.95i	0.542720	−	0.940018i
$378$		0			0
$379$	10772.3			1.45998			0.729992	−	0.683455i	$-0.239524\pi$
$379$	10772.3			1.45998			0.729992	+	0.683455i	$0.239524\pi$
$380$	−931.789	+	5143.20i	−0.125789	+	0.694318i
$381$		0			0
$382$	3521.85	−	6100.02i	0.471711	−	0.817027i
$383$	−1689.97	+	2927.12i	−0.225466	+	0.390519i	−0.956459	−	0.291866i	$-0.905724\pi$
$383$	−1689.97	+	2927.12i	−0.225466	+	0.390519i	0.730993	+	0.682385i	$0.239057\pi$
$384$		0			0
$385$	−2096.09	+	3630.54i	−0.277472	+	0.480596i
$386$	−4735.39	−	8201.94i	−0.624417	−	1.08152i
$387$		0			0
$388$	−6343.69			−0.830031
$389$	2351.28	+	4072.54i	0.306464	+	0.530812i	0.977586	−	0.210535i	$-0.0675206\pi$
$389$	2351.28	+	4072.54i	0.306464	+	0.530812i	−0.671122	+	0.741347i	$0.734187\pi$
$390$		0			0
$391$	−1888.40			−0.244246
$392$	−545.758			−0.0703187
$393$		0			0
$394$	2357.30	−	4082.96i	0.301419	−	0.522073i
$395$	−6913.62	−	11974.7i	−0.880663	−	1.52535i
$396$		0			0
$397$	−125.749	+	217.804i	−0.0158972	+	0.0275347i	−0.873865	−	0.486169i	$-0.838394\pi$
$397$	−125.749	+	217.804i	−0.0158972	+	0.0275347i	0.857967	+	0.513704i	$0.171727\pi$
$398$	1370.31			0.172582
$399$		0			0
$400$	1983.20			0.247900
$401$	−3225.16	+	5586.15i	−0.401638	+	0.695658i	−0.993924	−	0.110070i	$-0.964892\pi$
$401$	−3225.16	+	5586.15i	−0.401638	+	0.695658i	0.592285	+	0.805728i	$0.298226\pi$
$402$		0			0
$403$	4027.92	+	6976.56i	0.497879	+	0.862351i
$404$	−2087.65	+	3615.92i	−0.257091	+	0.445294i
$405$		0			0
$406$	3925.45			0.479845
$407$	−354.108			−0.0431264
$408$		0			0
$409$	−1007.96	−	1745.84i	−0.121859	−	0.211066i	0.798642	−	0.601807i	$-0.205552\pi$
$409$	−1007.96	−	1745.84i	−0.121859	−	0.211066i	−0.920501	+	0.390741i	$0.872219\pi$
$410$	3442.84			0.414707
$411$		0			0
$412$	−2855.67	−	4946.16i	−0.341477	−	0.591456i
$413$	3507.50	−	6075.17i	0.417900	−	0.723825i
$414$		0			0
$415$	3757.55	−	6508.26i	0.444460	−	0.769827i
$416$	1073.67	−	1859.65i	0.126541	−	0.219175i
$417$		0			0
$418$	−2025.76	−	1716.08i	−0.237041	−	0.200804i
$419$	10124.5			1.18046			0.590232	−	0.807234i	$-0.299036\pi$
$419$	10124.5			1.18046			0.590232	+	0.807234i	$0.299036\pi$
$420$		0			0
$421$	−1573.13	+	2724.75i	−0.182114	+	0.315430i	−0.942600	−	0.333924i	$-0.891627\pi$
$421$	−1573.13	+	2724.75i	−0.182114	+	0.315430i	0.760487	+	0.649354i	$0.224961\pi$
$422$	531.020	+	919.753i	0.0612550	+	0.106097i
$423$		0			0
$424$	871.377	+	1509.27i	0.0998061	+	0.172869i
$425$	−4909.04			−0.560290
$426$		0			0
$427$	−4673.91	−	8095.45i	−0.529710	−	0.917485i
$428$	1001.85	+	1735.25i	0.113145	+	0.195973i
$429$		0			0
$430$	11380.0			1.27626
$431$	5831.16	+	10099.9i	0.651687	+	1.12875i	0.982713	+	0.185133i	$0.0592717\pi$
$431$	5831.16	+	10099.9i	0.651687	+	1.12875i	−0.331027	+	0.943621i	$0.607395\pi$
$432$		0			0
$433$	4484.52	+	7767.42i	0.497719	+	0.862074i	0.999997	−	0.00263209i	$-0.000837820\pi$
$433$	4484.52	+	7767.42i	0.497719	+	0.862074i	−0.502278	+	0.864706i	$0.667504\pi$
$434$	−1990.00	+	3446.78i	−0.220099	+	0.381223i
$435$		0			0
$436$	4851.69			0.532922
$437$	−3717.03	+	1333.17i	−0.406887	+	0.145936i
$438$		0			0
$439$	−49.1536	+	85.1366i	−0.00534391	+	0.00925592i	−0.868685	−	0.495365i	$-0.835034\pi$
$439$	−49.1536	+	85.1366i	−0.00534391	+	0.00925592i	0.863341	+	0.504621i	$0.168368\pi$
$440$	−1011.60	+	1752.14i	−0.109605	+	0.189841i
$441$		0			0
$442$	−2657.66	+	4603.21i	−0.286000	+	0.495367i
$443$	−4660.23	−	8071.75i	−0.499806	−	0.865690i	0.500194	−	0.865914i	$-0.333262\pi$
$443$	−4660.23	−	8071.75i	−0.499806	−	0.865690i	−1.00000		0.000223670i	$0.999929\pi$
$444$		0			0
$445$	−15221.8			−1.62154
$446$	−4851.71	−	8403.41i	−0.515101	−	0.892182i
$447$		0			0
$448$	1060.90			0.111881
$449$	−9992.53			−1.05028			−0.525141	−	0.851015i	$-0.675987\pi$
$449$	−9992.53			−1.05028			−0.525141	+	0.851015i	$0.675987\pi$
$450$		0			0
$451$	−874.365	+	1514.44i	−0.0912910	+	0.158121i
$452$	1477.91	+	2559.82i	0.153795	+	0.266380i
$453$		0			0
$454$	−3971.88	+	6879.50i	−0.410594	+	0.711170i
$455$	17550.9			1.80835
$456$		0			0
$457$	−1536.89			−0.157314			−0.0786572	−	0.996902i	$-0.525063\pi$
$457$	−1536.89			−0.157314			−0.0786572	+	0.996902i	$0.525063\pi$
$458$	78.9844	−	136.805i	0.00805829	−	0.0139574i
$459$		0			0
$460$	1504.63	+	2606.10i	0.152508	+	0.264152i
$461$	−8312.46	+	14397.6i	−0.839804	+	1.45458i	0.0502537	+	0.998736i	$0.483997\pi$
$461$	−8312.46	+	14397.6i	−0.839804	+	1.45458i	−0.890058	+	0.455847i	$0.849336\pi$
$462$		0			0
$463$	7191.48			0.721850			0.360925	−	0.932595i	$-0.382461\pi$
$463$	7191.48			0.721850			0.360925	+	0.932595i	$0.382461\pi$
$464$	1894.47			0.189544
$465$		0			0
$466$	−1643.29	−	2846.27i	−0.163356	−	0.282942i
$467$	7001.51			0.693772			0.346886	−	0.937907i	$-0.387239\pi$
$467$	7001.51			0.693772			0.346886	+	0.937907i	$0.387239\pi$
$468$		0			0
$469$	7814.59	+	13535.3i	0.769391	+	1.33262i
$470$	−3044.32	+	5272.91i	−0.298774	+	0.517492i
$471$		0			0
$472$	1692.76	−	2931.94i	0.165075	−	0.285919i
$473$	−2890.13	+	5005.85i	−0.280948	+	0.486616i
$474$		0			0
$475$	−9662.72	+	3465.68i	−0.933381	+	0.334772i
$476$	−2626.05			−0.252867
$477$		0			0
$478$	−6316.74	+	10940.9i	−0.604437	+	1.04692i
$479$	955.918	+	1655.70i	0.0911837	+	0.157935i	0.908009	−	0.418950i	$-0.137602\pi$
$479$	955.918	+	1655.70i	0.0911837	+	0.157935i	−0.816826	+	0.576884i	$0.804268\pi$
$480$		0			0
$481$	741.248	+	1283.88i	0.0702661	+	0.121705i
$482$	−6989.31			−0.660486
$483$		0			0
$484$	2148.18	+	3720.75i	0.201745	+	0.349432i
$485$	−12511.5	−	21670.5i	−1.17137	−	2.02888i
$486$		0			0
$487$	−6061.32			−0.563993			−0.281997	−	0.959415i	$-0.590997\pi$
$487$	−6061.32			−0.563993			−0.281997	+	0.959415i	$0.590997\pi$
$488$	−2255.68	−	3906.95i	−0.209241	−	0.362417i
$489$		0			0
$490$	−1076.38	−	1864.35i	−0.0992366	−	0.171883i
$491$	3219.51	−	5576.36i	0.295916	−	0.512541i	−0.679282	−	0.733877i	$-0.737709\pi$
$491$	3219.51	−	5576.36i	0.295916	−	0.512541i	0.975197	+	0.221337i	$0.0710420\pi$
$492$		0			0
$493$	−4689.39			−0.428397
$494$	−1981.45	+	10937.0i	−0.180464	+	0.996111i
$495$		0			0
$496$	−960.396	+	1663.45i	−0.0869416	+	0.150587i
$497$	−5517.86	+	9557.22i	−0.498008	+	0.862575i
$498$		0			0
$499$	−8229.07	+	14253.2i	−0.738244	+	1.27868i	0.215041	+	0.976605i	$0.431011\pi$
$499$	−8229.07	+	14253.2i	−0.738244	+	1.27868i	−0.953285	+	0.302071i	$0.902322\pi$
$500$	−33.1316	−	57.3857i	−0.00296338	−	0.00513273i
$501$		0			0
$502$	−7260.74			−0.645543
$503$	−1362.42	−	2359.78i	−0.120770	−	0.209179i	0.799302	−	0.600930i	$-0.205203\pi$
$503$	−1362.42	−	2359.78i	−0.120770	−	0.209179i	−0.920071	+	0.391751i	$0.871870\pi$
$504$		0			0
$505$	−16469.7			−1.45127
$506$	−1528.50			−0.134289
$507$		0			0
$508$	−477.816	+	827.602i	−0.0417316	+	0.0722813i
$509$	2730.41	+	4729.20i	0.237767	+	0.411824i	0.960073	−	0.279749i	$-0.0902513\pi$
$509$	2730.41	+	4729.20i	0.237767	+	0.411824i	−0.722307	+	0.691573i	$0.756918\pi$
$510$		0			0
$511$	1549.45	−	2683.73i	0.134136	−	0.232331i
$512$	512.000			0.0441942
$513$		0			0
$514$	3098.83			0.265921
$515$	11264.3	−	19510.3i	0.963813	−	1.66937i
$516$		0			0
$517$	−1546.31	−	2678.28i	−0.131541	−	0.227835i
$518$	−366.215	+	634.303i	−0.0310629	+	0.0538024i
$519$		0			0
$520$	8470.26			0.714318
$521$	−7411.04			−0.623193			−0.311596	−	0.950215i	$-0.600864\pi$
$521$	−7411.04			−0.623193			−0.311596	+	0.950215i	$0.600864\pi$
$522$		0			0
$523$	399.710	+	692.318i	0.0334189	+	0.0578833i	0.882251	−	0.470779i	$-0.156027\pi$
$523$	399.710	+	692.318i	0.0334189	+	0.0578833i	−0.848832	+	0.528662i	$0.822694\pi$
$524$	−1060.99			−0.0884537
$525$		0			0
$526$	−3809.81	−	6598.79i	−0.315809	−	0.546998i
$527$	2377.28	−	4117.57i	0.196501	−	0.340349i
$528$		0			0
$529$	4946.77	−	8568.06i	0.406573	−	0.704204i
$530$	−3437.18	+	5953.37i	−0.281701	+	0.487920i
$531$		0			0
$532$	−5168.98	+	1853.94i	−0.421248	+	0.151087i
$533$	7321.19			0.594964
$534$		0			0
$535$	−3951.83	+	6844.77i	−0.319350	+	0.553131i
$536$	3771.41	+	6532.27i	0.303918	+	0.526401i
$537$		0			0
$538$	−3376.40	−	5848.09i	−0.270570	−	0.468642i
$539$	1093.46			0.0873814
$540$		0			0
$541$	−2947.56	−	5105.33i	−0.234243	−	0.405721i	0.724809	−	0.688950i	$-0.241928\pi$
$541$	−2947.56	−	5105.33i	−0.234243	−	0.405721i	−0.959052	+	0.283228i	$0.908595\pi$
$542$	3525.50	+	6106.34i	0.279397	+	0.483930i
$543$		0			0
$544$	−1267.36			−0.0998852
$545$	9568.84	+	16573.7i	0.752081	+	1.30264i
$546$		0			0
$547$	−5745.64	−	9951.74i	−0.449115	−	0.777890i	0.549214	−	0.835682i	$-0.314927\pi$
$547$	−5745.64	−	9951.74i	−0.449115	−	0.777890i	−0.998329	+	0.0577920i	$0.981594\pi$
$548$	4876.90	−	8447.03i	0.380166	−	0.658466i
$549$		0			0
$550$	−3973.46			−0.308053
$551$	−9230.38	+	3310.62i	−0.713661	+	0.255966i
$552$		0			0
$553$	7263.44	−	12580.6i	0.558540	−	0.967420i
$554$	−6557.88	+	11358.6i	−0.502920	+	0.871083i
$555$		0			0
$556$	733.589	−	1270.61i	0.0559552	−	0.0969173i
$557$	−1122.30	−	1943.88i	−0.0853740	−	0.147872i	0.820176	−	0.572111i	$-0.193875\pi$
$557$	−1122.30	−	1943.88i	−0.0853740	−	0.147872i	−0.905551	+	0.424238i	$0.860542\pi$
$558$		0			0
$559$	24199.5			1.83100
$560$	2092.37	+	3624.09i	0.157891	+	0.273475i
$561$		0			0
$562$	−15775.6			−1.18408
$563$	19529.8			1.46196			0.730978	−	0.682401i	$-0.239064\pi$
$563$	19529.8			1.46196			0.730978	+	0.682401i	$0.239064\pi$
$564$		0			0
$565$	−5829.68	+	10097.3i	−0.434082	+	0.751853i
$566$	−2072.73	−	3590.08i	−0.153928	−	0.266612i
$567$		0			0
$568$	−2662.98	+	4612.42i	−0.196719	+	0.340727i
$569$	3300.68			0.243184			0.121592	−	0.992580i	$-0.461200\pi$
$569$	3300.68			0.243184			0.121592	+	0.992580i	$0.461200\pi$
$570$		0			0
$571$	3080.76			0.225789			0.112895	−	0.993607i	$-0.463988\pi$
$571$	3080.76			0.225789			0.112895	+	0.993607i	$0.463988\pi$
$572$	−2151.16	+	3725.92i	−0.157246	+	0.272357i
$573$		0			0
$574$	1808.52	+	3132.45i	0.131509	+	0.227780i
$575$	−2955.02	+	5118.25i	−0.214318	+	0.371210i
$576$		0			0
$577$	4946.52			0.356892			0.178446	−	0.983950i	$-0.442893\pi$
$577$	4946.52			0.356892			0.178446	+	0.983950i	$0.442893\pi$
$578$	−6688.89			−0.481352
$579$		0			0
$580$	3736.40	+	6471.63i	0.267492	+	0.463310i
$581$	7895.34			0.563776
$582$		0			0
$583$	−1745.85	−	3023.91i	−0.124024	−	0.214816i
$584$	747.782	−	1295.20i	0.0529854	−	0.0917733i
$585$		0			0
$586$	−7820.84	+	13546.1i	−0.551324	+	0.954922i
$587$	7278.01	−	12605.9i	0.511748	−	0.886373i	−0.488160	−	0.872754i	$-0.662332\pi$
$587$	7278.01	−	12605.9i	0.511748	−	0.886373i	0.999907	−	0.0136184i	$-0.00433502\pi$
$588$		0			0
$589$	1772.40	−	9783.13i	0.123991	−	0.684392i
$590$	13354.3			0.931844
$591$		0			0
$592$	−176.739	+	306.121i	−0.0122702	+	0.0212526i
$593$	−10308.6	−	17855.1i	−0.713869	−	1.23646i	−0.963394	−	0.268089i	$-0.913608\pi$
$593$	−10308.6	−	17855.1i	−0.713869	−	1.23646i	0.249525	−	0.968368i	$-0.419725\pi$
$594$		0			0
$595$	−5179.27	−	8970.76i	−0.356856	−	0.618093i
$596$	8967.02			0.616281
$597$		0			0
$598$	3199.59	+	5541.85i	0.218798	+	0.378969i
$599$	10652.2	+	18450.2i	0.726608	+	1.25852i	0.958309	+	0.285735i	$0.0922378\pi$
$599$	10652.2	+	18450.2i	0.726608	+	1.25852i	−0.231700	+	0.972787i	$0.574429\pi$
$600$		0			0
$601$	−26351.4			−1.78852			−0.894258	−	0.447553i	$-0.852296\pi$
$601$	−26351.4			−1.78852			−0.894258	+	0.447553i	$0.852296\pi$
$602$	5977.89	+	10354.0i	0.404719	+	0.700993i
$603$		0			0
$604$	1276.39	+	2210.77i	0.0859860	+	0.148932i
$605$	−8473.56	+	14676.6i	−0.569420	+	0.986265i
$606$		0			0
$607$	24027.8			1.60669			0.803344	−	0.595516i	$-0.203052\pi$
$607$	24027.8			1.60669			0.803344	+	0.595516i	$0.203052\pi$
$608$	−2494.61	+	894.730i	−0.166398	+	0.0596811i
$609$		0			0
$610$	8897.62	−	15411.1i	0.590580	−	1.02292i
$611$	−6473.73	+	11212.8i	−0.428640	+	0.742426i
$612$		0			0
$613$	−7619.00	+	13196.5i	−0.502004	+	0.869497i	0.497993	+	0.867181i	$0.334070\pi$
$613$	−7619.00	+	13196.5i	−0.502004	+	0.869497i	−0.999997	+	0.00231571i	$0.999263\pi$
$614$	5937.79	+	10284.6i	0.390276	+	0.675979i
$615$		0			0
$616$	−2125.57			−0.139028
$617$	−14065.4	−	24362.0i	−0.917751	−	1.58959i	−0.802822	−	0.596218i	$-0.796669\pi$
$617$	−14065.4	−	24362.0i	−0.917751	−	1.58959i	−0.114929	−	0.993374i	$-0.536664\pi$
$618$		0			0
$619$	9482.23			0.615708			0.307854	−	0.951434i	$-0.400389\pi$
$619$	9482.23			0.615708			0.307854	+	0.951434i	$0.400389\pi$
$620$	−7576.64			−0.490782
$621$		0			0
$622$	1832.63	−	3174.21i	0.118138	−	0.204621i
$623$	−7996.01	−	13849.5i	−0.514211	−	0.890639i
$624$		0			0
$625$	7877.57	−	13644.3i	0.504164	−	0.873238i
$626$	−1876.66			−0.119819
$627$		0			0
$628$	8503.96			0.540358
$629$	437.485	−	757.746i	0.0277324	−	0.0480339i
$630$		0			0
$631$	850.702	+	1473.46i	0.0536702	+	0.0929595i	0.891612	−	0.452800i	$-0.149575\pi$
$631$	850.702	+	1473.46i	0.0536702	+	0.0929595i	−0.837942	+	0.545759i	$0.816241\pi$
$632$	3505.42	−	6071.56i	0.220630	−	0.382142i
$633$		0			0
$634$	14822.9			0.928539
$635$	−3769.53			−0.235573
$636$		0			0
$637$	−2288.92	−	3964.53i	−0.142371	−	0.246594i
$638$	−3795.67			−0.235536
$639$		0			0
$640$	1009.80	+	1749.03i	0.0623686	+	0.108026i
$641$	10815.8	−	18733.5i	0.666454	−	1.15433i	−0.312435	−	0.949939i	$-0.601145\pi$
$641$	10815.8	−	18733.5i	0.666454	−	1.15433i	0.978889	−	0.204393i	$-0.0655221\pi$
$642$		0			0
$643$	2722.31	−	4715.17i	0.166963	−	0.289189i	−0.770388	−	0.637576i	$-0.779937\pi$
$643$	2722.31	−	4715.17i	0.166963	−	0.289189i	0.937351	+	0.348387i	$0.113271\pi$
$644$	−1580.76	+	2737.96i	−0.0967248	+	0.167532i
$645$		0			0
$646$	6174.93	−	2214.73i	0.376083	−	0.134888i
$647$	−27393.8			−1.66454			−0.832272	−	0.554367i	$-0.812960\pi$
$647$	−27393.8			−1.66454			−0.832272	+	0.554367i	$0.812960\pi$
$648$		0			0
$649$	−3391.54	+	5874.32i	−0.205130	+	0.355296i
$650$	8317.59	+	14406.5i	0.501912	+	0.869337i
$651$		0			0
$652$	320.087	+	554.406i	0.0192263	+	0.0333010i
$653$	23390.6			1.40175			0.700875	−	0.713284i	$-0.252793\pi$
$653$	23390.6			1.40175			0.700875	+	0.713284i	$0.252793\pi$
$654$		0			0
$655$	−2092.57	−	3624.43i	−0.124830	−	0.216211i
$656$	872.812	+	1511.76i	0.0519476	+	0.0899758i
$657$		0			0
$658$	−6396.71			−0.378981
$659$	−10029.5	−	17371.6i	−0.592860	−	1.02686i	−0.993845	−	0.110779i	$-0.964666\pi$
$659$	−10029.5	−	17371.6i	−0.592860	−	1.02686i	0.400985	−	0.916084i	$-0.368668\pi$
$660$		0			0
$661$	−11618.9	−	20124.5i	−0.683696	−	1.18420i	−0.973845	−	0.227214i	$-0.927038\pi$
$661$	−11618.9	−	20124.5i	−0.683696	−	1.18420i	0.290149	−	0.956981i	$-0.406295\pi$
$662$	5412.69	−	9375.05i	0.317780	−	0.550410i
$663$		0			0
$664$	3810.38			0.222698
$665$	−16527.8	−	14001.2i	−0.963791	−	0.816453i
$666$		0			0
$667$	−2822.80	+	4889.24i	−0.163867	+	0.283826i
$668$	4204.32	−	7282.09i	0.243518	−	0.421785i
$669$		0			0
$670$	−14876.5	+	25766.8i	−0.857803	+	1.48576i
$671$	4519.39	+	7827.81i	0.260013	+	0.450356i
$672$		0			0
$673$	−10185.3			−0.583378			−0.291689	−	0.956513i	$-0.594217\pi$
$673$	−10185.3			−0.583378			−0.291689	+	0.956513i	$0.594217\pi$
$674$	−9273.57	−	16062.3i	−0.529977	−	0.917947i
$675$		0			0
$676$	9223.97			0.524805
$677$	−3202.89			−0.181827			−0.0909136	−	0.995859i	$-0.528979\pi$
$677$	−3202.89			−0.181827			−0.0909136	+	0.995859i	$0.528979\pi$
$678$		0			0
$679$	13144.5	−	22767.0i	0.742916	−	1.28677i
$680$	−2499.57	−	4329.39i	−0.140962	−	0.244154i
$681$		0			0
$682$	1924.21	−	3332.83i	0.108038	−	0.187127i
$683$	−1625.51			−0.0910662			−0.0455331	−	0.998963i	$-0.514499\pi$
$683$	−1625.51			−0.0910662			−0.0455331	+	0.998963i	$0.514499\pi$
$684$		0			0
$685$	38474.2			2.14602
$686$	6816.58	−	11806.7i	0.379385	−	0.657115i
$687$		0			0
$688$	2885.00	+	4996.96i	0.159868	+	0.276900i
$689$	−7309.15	+	12659.8i	−0.404146	+	0.700001i
$690$		0			0
$691$	839.130			0.0461968			0.0230984	−	0.999733i	$-0.492647\pi$
$691$	839.130			0.0461968			0.0230984	+	0.999733i	$0.492647\pi$
$692$	1621.85			0.0890949
$693$		0			0
$694$	−9674.48	−	16756.7i	−0.529162	−	0.916535i
$695$	5787.34			0.315865
$696$		0			0
$697$	−2160.48	−	3742.06i	−0.117409	−	0.203358i
$698$	−1300.56	+	2252.64i	−0.0705259	+	0.122154i
$699$		0			0
$700$	−4109.32	+	7117.54i	−0.221882	+	0.384311i
$701$	−729.064	+	1262.78i	−0.0392816	+	0.0680377i	−0.884998	−	0.465595i	$-0.845840\pi$
$701$	−729.064	+	1262.78i	−0.0392816	+	0.0680377i	0.845716	+	0.533633i	$0.179174\pi$
$702$		0			0
$703$	326.171	−	1800.37i	0.0174989	−	0.0965890i
$704$	−1025.82			−0.0549178
$705$		0			0
$706$	11985.4	−	20759.2i	0.638916	−	1.10663i
$707$	−8651.49	−	14984.8i	−0.460216	−	0.797118i
$708$		0			0
$709$	16159.9	+	27989.8i	0.855993	+	1.48262i	0.875721	+	0.482818i	$0.160387\pi$
$709$	16159.9	+	27989.8i	0.855993	+	1.48262i	−0.0197278	+	0.999805i	$0.506280\pi$
$710$	−21008.5			−1.11047
$711$		0			0
$712$	−3858.96	−	6683.91i	−0.203119	−	0.351812i
$713$	−2862.03	−	4957.18i	−0.150328	−	0.260376i
$714$		0			0
$715$	−16970.7			−0.887646
$716$	−3257.52	−	5642.18i	−0.170027	−	0.294495i
$717$		0			0
$718$	−4407.90	−	7634.70i	−0.229110	−	0.396831i
$719$	−2885.84	+	4998.42i	−0.149685	+	0.259262i	−0.931111	−	0.364736i	$-0.881159\pi$
$719$	−2885.84	+	4998.42i	−0.149685	+	0.259262i	0.781426	+	0.623998i	$0.214493\pi$
$720$		0			0
$721$	23668.5			1.22255
$722$	10590.9	−	8718.76i	0.545917	−	0.449416i
$723$		0			0
$724$	−5673.68	+	9827.09i	−0.291244	+	0.504449i
$725$	−7338.10	+	12710.0i	−0.375904	+	0.651085i
$726$		0			0
$727$	−2726.16	+	4721.84i	−0.139075	+	0.240885i	−0.927147	−	0.374698i	$-0.877746\pi$
$727$	−2726.16	+	4721.84i	−0.139075	+	0.240885i	0.788072	+	0.615583i	$0.211080\pi$
$728$	4449.42	+	7706.62i	0.226520	+	0.392344i
$729$		0			0
$730$	5899.31			0.299100
$731$	−7141.26	−	12369.0i	−0.361326	−	0.625834i
$732$		0			0
$733$	9558.30			0.481643			0.240821	−	0.970569i	$-0.422583\pi$
$733$	9558.30			0.481643			0.240821	+	0.970569i	$0.422583\pi$
$734$	12520.2			0.629602
$735$		0			0
$736$	−762.893	+	1321.37i	−0.0382074	+	0.0661771i
$737$	−7556.23	−	13087.8i	−0.377663	−	0.654131i
$738$		0			0
$739$	−6476.74	+	11218.0i	−0.322396	+	0.558406i	−0.980982	−	0.194099i	$-0.937822\pi$
$739$	−6476.74	+	11218.0i	−0.322396	+	0.558406i	0.658586	+	0.752506i	$0.271155\pi$
$740$	−1394.31			−0.0692647
$741$		0			0
$742$	−7222.19			−0.357325
$743$	−91.9794	+	159.313i	−0.00454158	+	0.00786625i	−0.868287	−	0.496062i	$-0.834779\pi$
$743$	−91.9794	+	159.313i	−0.00454158	+	0.00786625i	0.863746	+	0.503928i	$0.168112\pi$
$744$		0			0
$745$	17685.4	+	30632.0i	0.869721	+	1.50640i
$746$	2745.24	−	4754.90i	0.134733	−	0.233364i
$747$		0			0
$748$	2539.23			0.124122
$749$	−8303.57			−0.405081
$750$		0			0
$751$	−5247.19	−	9088.39i	−0.254957	−	0.441598i	0.709927	−	0.704275i	$-0.248728\pi$
$751$	−5247.19	−	9088.39i	−0.254957	−	0.441598i	−0.964884	+	0.262677i	$0.915395\pi$
$752$	−3087.12			−0.149702
$753$		0			0
$754$	7945.43	+	13761.9i	0.383761	+	0.664693i
$755$	−5034.77	+	8720.47i	−0.242694	+	0.420358i
$756$		0			0
$757$	4731.24	−	8194.75i	0.227160	−	0.393452i	−0.729805	−	0.683655i	$-0.760389\pi$
$757$	4731.24	−	8194.75i	0.227160	−	0.393452i	0.956965	+	0.290203i	$0.0937227\pi$
$758$	−10772.3	+	18658.1i	−0.516183	+	0.894054i
$759$		0			0
$760$	−7976.50	−	6757.11i	−0.380708	−	0.322508i
$761$	38400.1			1.82918			0.914588	−	0.404388i	$-0.132515\pi$
$761$	38400.1			1.82918			0.914588	+	0.404388i	$0.132515\pi$
$762$		0			0
$763$	−10053.0	+	17412.3i	−0.476990	+	0.826171i
$764$	7043.70	+	12200.0i	0.333550	+	0.577725i
$765$		0			0
$766$	−3379.95	−	5854.24i	−0.159429	−	0.276139i
$767$	28397.9			1.33688
$768$		0			0
$769$	1535.93	+	2660.31i	0.0720249	+	0.124751i	0.899789	−	0.436326i	$-0.143721\pi$
$769$	1535.93	+	2660.31i	0.0720249	+	0.124751i	−0.827764	+	0.561077i	$0.810387\pi$
$770$	−4192.19	−	7261.08i	−0.196203	−	0.339833i
$771$		0			0
$772$	18941.6			0.883060
$773$	3588.67	+	6215.75i	0.166980	+	0.289218i	0.937357	−	0.348371i	$-0.113265\pi$
$773$	3588.67	+	6215.75i	0.166980	+	0.289218i	−0.770377	+	0.637589i	$0.779932\pi$
$774$		0			0
$775$	−7440.07	−	12886.6i	−0.344846	−	0.597290i
$776$	6343.69	−	10987.6i	0.293460	−	0.508288i
$777$		0			0
$778$	−9405.12			−0.433406
$779$	−6894.41	−	5840.44i	−0.317096	−	0.268621i
$780$		0			0
$781$	5335.44	−	9241.25i	0.244452	−	0.423403i
$782$	1888.40	−	3270.80i	0.0863542	−	0.149570i
$783$		0			0
$784$	545.758	−	945.280i	0.0248614	−	0.0430612i
$785$	16772.1	+	29050.1i	0.762576	+	1.32082i
$786$		0			0
$787$	40299.0			1.82529			0.912645	−	0.408754i	$-0.134037\pi$
$787$	40299.0			1.82529			0.912645	+	0.408754i	$0.134037\pi$
$788$	4714.60	+	8165.92i	0.213135	+	0.369161i
$789$		0			0
$790$	27654.5			1.24545
$791$	−12249.3			−0.550613
$792$		0			0
$793$	18920.7	−	32771.7i	0.847283	−	1.46754i
$794$	−251.499	−	435.608i	−0.0112410	−	0.0194700i
$795$		0			0
$796$	−1370.31	+	2373.45i	−0.0610168	+	0.105684i
$797$	33505.8			1.48913			0.744565	−	0.667550i	$-0.232657\pi$
$797$	33505.8			1.48913			0.744565	+	0.667550i	$0.232657\pi$
$798$		0			0
$799$	7641.59			0.338348
$800$	−1983.20	+	3435.01i	−0.0876459	+	0.151807i
$801$		0			0
$802$	−6450.33	−	11172.3i	−0.284001	−	0.491905i
$803$	−1498.23	+	2595.00i	−0.0658421	+	0.114042i
$804$		0			0
$805$	−12470.8			−0.546008
$806$	−16111.7			−0.704107
$807$		0			0
$808$	−4175.31	−	7231.84i	−0.181791	−	0.314870i
$809$	20863.7			0.906710			0.453355	−	0.891330i	$-0.350227\pi$
$809$	20863.7			0.906710			0.453355	+	0.891330i	$0.350227\pi$
$810$		0			0
$811$	−8728.82	−	15118.8i	−0.377941	−	0.654613i	0.612821	−	0.790221i	$-0.290034\pi$
$811$	−8728.82	−	15118.8i	−0.377941	−	0.654613i	−0.990763	+	0.135608i	$0.956701\pi$
$812$	−3925.45	+	6799.08i	−0.169651	+	0.293844i
$813$		0			0
$814$	354.108	−	613.332i	0.0152475	−	0.0264094i
$815$	−1262.59	+	2186.88i	−0.0542659	+	0.0939914i
$816$		0			0
$817$	−22788.8	−	19305.0i	−0.975862	−	0.826679i
$818$	4031.84			0.172335
$819$		0			0
$820$	−3442.84	+	5963.18i	−0.146621	+	0.253955i
$821$	14635.8	+	25349.9i	0.622158	+	1.07761i	0.989083	+	0.147359i	$0.0470773\pi$
$821$	14635.8	+	25349.9i	0.622158	+	1.07761i	−0.366925	+	0.930251i	$0.619589\pi$
$822$		0			0
$823$	−19338.7	−	33495.5i	−0.819080	−	1.41869i	−0.906361	−	0.422505i	$-0.861151\pi$
$823$	−19338.7	−	33495.5i	−0.819080	−	1.41869i	0.0872806	−	0.996184i	$-0.472182\pi$
$824$	11422.7			0.482922
$825$		0			0
$826$	7015.00	+	12150.3i	0.295500	+	0.511821i
$827$	2321.06	+	4020.19i	0.0975951	+	0.169040i	0.910689	−	0.413093i	$-0.135552\pi$
$827$	2321.06	+	4020.19i	0.0975951	+	0.169040i	−0.813094	+	0.582133i	$0.802218\pi$
$828$		0			0
$829$	−7918.14			−0.331735			−0.165868	−	0.986148i	$-0.553042\pi$
$829$	−7918.14			−0.331735			−0.165868	+	0.986148i	$0.553042\pi$
$830$	7515.09	+	13016.5i	0.314280	+	0.544350i
$831$		0			0
$832$	2147.34	+	3719.30i	0.0894779	+	0.154980i
$833$	−1350.92	+	2339.86i	−0.0561904	+	0.0973246i
$834$		0			0
$835$	33168.2			1.37465
$836$	4998.09	−	1792.64i	0.206774	−	0.0741626i
$837$		0			0
$838$	−10124.5	+	17536.1i	−0.417357	+	0.722883i
$839$	4061.92	−	7035.45i	0.167143	−	0.289500i	−0.770271	−	0.637716i	$-0.779879\pi$
$839$	4061.92	−	7035.45i	0.167143	−	0.289500i	0.937414	+	0.348216i	$0.113212\pi$
$840$		0			0
$841$	5184.73	−	8980.21i	0.212585	−	0.368207i
$842$	−3146.27	−	5449.49i	−0.128774	−	0.223043i
$843$		0			0
$844$	−2124.08			−0.0866277
$845$	18192.1	+	31509.7i	0.740626	+	1.28280i
$846$		0			0
$847$	−17804.6			−0.722283
$848$	−3485.51			−0.141147
$849$		0			0
$850$	4909.04	−	8502.70i	0.198093	−	0.343106i
$851$	−526.692	−	912.258i	−0.0212160	−	0.0367471i
$852$		0			0
$853$	−22594.4	+	39134.7i	−0.906938	+	1.57086i	−0.0886427	+	0.996063i	$0.528253\pi$
$853$	−22594.4	+	39134.7i	−0.906938	+	1.57086i	−0.818295	+	0.574799i	$0.805080\pi$
$854$	18695.6			0.749124
$855$		0			0
$856$	−4007.39			−0.160012
$857$	15246.2	−	26407.1i	0.607700	−	1.05257i	−0.383918	−	0.923367i	$-0.625426\pi$
$857$	15246.2	−	26407.1i	0.607700	−	1.05257i	0.991618	−	0.129201i	$-0.0412411\pi$
$858$		0			0
$859$	19527.3	+	33822.2i	0.775625	+	1.34342i	0.934443	+	0.356113i	$0.115898\pi$
$859$	19527.3	+	33822.2i	0.775625	+	1.34342i	−0.158818	+	0.987308i	$0.550768\pi$
$860$	−11380.0	+	19710.7i	−0.451226	+	0.781545i
$861$		0			0
$862$	−23324.6			−0.921624
$863$	21510.4			0.848461			0.424230	−	0.905554i	$-0.360545\pi$
$863$	21510.4			0.848461			0.424230	+	0.905554i	$0.360545\pi$
$864$		0			0
$865$	3198.73	+	5540.37i	0.125734	+	0.217778i
$866$	−17938.1			−0.703881
$867$		0			0
$868$	−3980.00	−	6893.56i	−0.155634	−	0.269565i
$869$	−7023.30	+	12164.7i	−0.274165	+	0.474867i
$870$		0			0
$871$	−31634.7	+	54792.9i	−1.23066	+	2.13156i
$872$	−4851.69	+	8403.38i	−0.188416	+	0.326347i
$873$		0			0
$874$	1407.91	−	7771.26i	0.0544889	−	0.300763i
$875$	274.603			0.0106095
$876$		0			0
$877$	−4199.45	+	7273.66i	−0.161694	+	0.280062i	−0.935476	−	0.353390i	$-0.885029\pi$
$877$	−4199.45	+	7273.66i	−0.161694	+	0.280062i	0.773783	+	0.633451i	$0.218362\pi$
$878$	−98.3073	−	170.273i	−0.00377871	−	0.00654492i
$879$		0			0
$880$	−2023.20	−	3504.28i	−0.0775022	−	0.134238i
$881$	46320.2			1.77136			0.885679	−	0.464298i	$-0.153693\pi$
$881$	46320.2			1.77136			0.885679	+	0.464298i	$0.153693\pi$
$882$		0			0
$883$	−16002.0	−	27716.2i	−0.609863	−	1.05631i	−0.991262	−	0.131904i	$-0.957891\pi$
$883$	−16002.0	−	27716.2i	−0.609863	−	1.05631i	0.381399	−	0.924411i	$-0.375442\pi$
$884$	−5315.33	−	9206.42i	−0.202233	−	0.350278i
$885$		0			0
$886$	18640.9			0.706833
$887$	−16782.7	−	29068.6i	−0.635298	−	1.10037i	−0.986452	−	0.164051i	$-0.947544\pi$
$887$	−16782.7	−	29068.6i	−0.635298	−	1.10037i	0.351154	−	0.936318i	$-0.385789\pi$
$888$		0			0
$889$	−1980.13	−	3429.68i	−0.0747035	−	0.129390i
$890$	15221.8	−	26365.0i	0.573299	−	0.992984i
$891$		0			0
$892$	19406.8			0.728463
$893$	15041.3	−	5394.81i	0.563650	−	0.202162i
$894$		0			0
$895$	12849.4	−	22255.8i	0.479897	−	0.831206i
$896$	−1060.90	+	1837.53i	−0.0395559	+	0.0685127i
$897$		0			0
$898$	9992.53	−	17307.6i	0.371331	−	0.643164i
$899$	−7107.18	−	12310.0i	−0.263668	−	0.456687i
$900$		0			0
$901$	8627.71			0.319013
$902$	−1748.73	−	3028.89i	−0.0645525	−	0.111808i
$903$		0			0
$904$	−5911.65			−0.217498
$905$	−44760.1			−1.64406
$906$		0			0
$907$	−19984.2	+	34613.7i	−0.731604	+	1.26718i	0.224593	+	0.974453i	$0.427895\pi$
$907$	−19984.2	+	34613.7i	−0.731604	+	1.26718i	−0.956197	+	0.292723i	$0.905439\pi$
$908$	−7943.77	−	13759.0i	−0.290334	−	0.502873i
$909$		0			0
$910$	−17550.9	+	30399.1i	−0.639348	+	1.10738i
$911$	−38734.2			−1.40869			−0.704347	−	0.709855i	$-0.748760\pi$
$911$	−38734.2			−1.40869			−0.704347	+	0.709855i	$0.748760\pi$
$912$		0			0
$913$	−7634.32			−0.276735
$914$	1536.89	−	2661.97i	0.0556190	−	0.0963350i
$915$		0			0
$916$	157.969	+	273.610i	0.00569807	+	0.00986935i
$917$	2198.45	−	3807.82i	0.0791702	−	0.137127i
$918$		0			0
$919$	7565.87			0.271572			0.135786	−	0.990738i	$-0.456644\pi$
$919$	7565.87			0.271572			0.135786	+	0.990738i	$0.456644\pi$
$920$	−6018.52			−0.215679
$921$		0			0
$922$	−16624.9	−	28795.2i	−0.593831	−	1.02855i
$923$	−44674.4			−1.59315
$924$		0			0
$925$	−1369.18	−	2371.49i	−0.0486684	−	0.0842962i
$926$	−7191.48	+	12456.0i	−0.255212	+	0.442041i
$927$		0			0
$928$	−1894.47	+	3281.31i	−0.0670139	+	0.116071i
$929$	−11858.4	+	20539.3i	−0.418796	+	0.725376i	−0.995819	−	0.0913524i	$-0.970881\pi$
$929$	−11858.4	+	20539.3i	−0.418796	+	0.725376i	0.577023	+	0.816728i	$0.304214\pi$
$930$		0			0
$931$	−1007.19	+	5559.40i	−0.0354558	+	0.195706i
$932$	6573.17			0.231021
$933$		0			0
$934$	−7001.51	+	12127.0i	−0.245285	+	0.424847i
$935$	5008.04	+	8674.18i	0.175166	+	0.303397i
$936$		0			0
$937$	−22291.9	−	38610.8i	−0.777210	−	1.34617i	−0.933544	−	0.358463i	$-0.883301\pi$
$937$	−22291.9	−	38610.8i	−0.777210	−	1.34617i	0.156334	−	0.987704i	$-0.450032\pi$
$938$	−31258.4			−1.08808
$939$		0			0
$940$	−6088.64	−	10545.8i	−0.211265	−	0.365922i
$941$	−20086.2	−	34790.3i	−0.695846	−	1.20524i	−0.969895	−	0.243525i	$-0.921696\pi$
$941$	−20086.2	−	34790.3i	−0.695846	−	1.20524i	0.274049	−	0.961716i	$-0.411637\pi$
$942$		0			0
$943$	−5202.05			−0.179642
$944$	3385.52	+	5863.89i	0.116726	+	0.202175i
$945$		0			0
$946$	−5780.26	−	10011.7i	−0.198660	−	0.344089i
$947$	−21487.4	+	37217.2i	−0.737324	+	1.27708i	0.216372	+	0.976311i	$0.430577\pi$
$947$	−21487.4	+	37217.2i	−0.737324	+	1.27708i	−0.953696	+	0.300772i	$0.902756\pi$
$948$		0			0
$949$	12544.9			0.429108
$950$	3659.98	−	20202.0i	0.124995	−	0.689936i
$951$		0			0
$952$	2626.05	−	4548.45i	0.0894019	−	0.154849i
$953$	16391.0	−	28390.0i	0.557141	−	0.964997i	−0.440592	−	0.897707i	$-0.645231\pi$
$953$	16391.0	−	28390.0i	0.557141	−	0.964997i	0.997733	−	0.0672898i	$-0.0214352\pi$
$954$		0			0
$955$	−27784.1	+	48123.5i	−0.941438	+	1.63062i
$956$	−12633.5	−	21881.8i	−0.427402	−	0.740281i
$957$		0			0
$958$	−3823.67			−0.128953
$959$	20210.5	+	35005.6i	0.680532	+	1.17872i
$960$		0			0
$961$	−15379.1			−0.516234
$962$	−2964.99			−0.0993713
$963$		0			0
$964$	6989.31	−	12105.8i	0.233517	−	0.404464i
$965$	37357.9	+	64705.7i	1.24621	+	2.15850i
$966$		0			0
$967$	−9881.92	+	17116.0i	−0.328626	+	0.569196i	−0.982239	−	0.187632i	$-0.939919\pi$
$967$	−9881.92	+	17116.0i	−0.328626	+	0.569196i	0.653614	+	0.756828i	$0.273252\pi$
$968$	−8592.71			−0.285310
$969$		0			0
$970$	50045.8			1.65657
$971$	6926.88	−	11997.7i	0.228933	−	0.396524i	−0.728559	−	0.684983i	$-0.759810\pi$
$971$	6926.88	−	11997.7i	0.228933	−	0.396524i	0.957492	+	0.288459i	$0.0931429\pi$
$972$		0			0
$973$	3040.08	+	5265.58i	0.100165	+	0.173491i
$974$	6061.32	−	10498.5i	0.199402	−	0.345374i
$975$		0			0
$976$	9022.72			0.295912
$977$	−53113.0			−1.73924			−0.869620	−	0.493722i	$-0.835636\pi$
$977$	−53113.0			−1.73924			−0.869620	+	0.493722i	$0.835636\pi$
$978$		0			0
$979$	7731.65	+	13391.6i	0.252405	+	0.437179i
$980$	4305.53			0.140342
$981$		0			0
$982$	6439.02	+	11152.7i	0.209244	+	0.362421i
$983$	−8672.89	+	15021.9i	−0.281406	+	0.487410i	−0.971731	−	0.236090i	$-0.924134\pi$
$983$	−8672.89	+	15021.9i	−0.281406	+	0.487410i	0.690325	+	0.723499i	$0.257467\pi$
$984$		0			0
$985$	−18596.9	+	32210.8i	−0.601570	+	1.04195i
$986$	4689.39	−	8122.27i	0.151461	−	0.262338i
$987$		0			0
$988$	−16962.0	−	14369.0i	−0.546187	−	0.462690i
$989$	−17194.9			−0.552847
$990$		0			0
$991$	3316.70	−	5744.69i	0.106315	−	0.184143i	−0.807960	−	0.589238i	$-0.799428\pi$
$991$	3316.70	−	5744.69i	0.106315	−	0.184143i	0.914275	+	0.405095i	$0.132761\pi$
$992$	−1920.79	−	3326.91i	−0.0614770	−	0.106481i
$993$		0			0
$994$	−11035.7	−	19114.4i	−0.352145	−	0.609933i
$995$	−10810.5			−0.344438
$996$		0			0
$997$	10306.3	+	17851.0i	0.327386	+	0.567049i	0.981992	−	0.188921i	$-0.0604989\pi$
$997$	10306.3	+	17851.0i	0.327386	+	0.567049i	−0.654606	+	0.755970i	$0.727166\pi$
$998$	−16458.1	−	28506.3i	−0.522017	−	0.904161i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.4.g.f.163.3		6
3.2	odd	2		38.4.c.c.11.1	yes	6
12.11	even	2		304.4.i.e.49.3		6
19.7	even	3	inner	342.4.g.f.235.3		6
57.8	even	6		722.4.a.k.1.1		3
57.11	odd	6		722.4.a.j.1.3		3
57.26	odd	6		38.4.c.c.7.1	✓	6
228.83	even	6		304.4.i.e.273.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.c.c.7.1	✓	6	57.26	odd	6
38.4.c.c.11.1	yes	6	3.2	odd	2
304.4.i.e.49.3		6	12.11	even	2
304.4.i.e.273.3		6	228.83	even	6
342.4.g.f.163.3		6	1.1	even	1	trivial
342.4.g.f.235.3		6	19.7	even	3	inner
722.4.a.j.1.3		3	57.11	odd	6
722.4.a.k.1.1		3	57.8	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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	342.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(7.88908 - 13.6643i) q^{5} +16.5765 q^{7} +8.00000 q^{8} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(7.88908 - 13.6643i) q^{5} +16.5765 q^{7} +8.00000 q^{8} +(15.7782 + 27.3286i) q^{10} -16.0285 q^{11} +(33.5522 + 58.1141i) q^{13} +(-16.5765 + 28.7113i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(19.8025 - 34.2989i) q^{17} +(14.7639 - 81.4925i) q^{19} -63.1126 q^{20} +(16.0285 - 27.7621i) q^{22} +(-23.8404 - 41.2928i) q^{23} +(-61.9750 - 107.344i) q^{25} -134.209 q^{26} +(-33.1530 - 57.4227i) q^{28} +(-59.2021 - 102.541i) q^{29} +120.050 q^{31} +(-16.0000 - 27.7128i) q^{32} +(39.6050 + 68.5978i) q^{34} +(130.773 - 226.506i) q^{35} +22.0924 q^{37} +(126.385 + 107.064i) q^{38} +(63.1126 - 109.314i) q^{40} +(54.5508 - 94.4847i) q^{41} +(180.312 - 312.310i) q^{43} +(32.0569 + 55.5242i) q^{44} +95.3617 q^{46} +(96.4726 + 167.095i) q^{47} -68.2197 q^{49} +247.900 q^{50} +(134.209 - 232.456i) q^{52} +(108.922 + 188.659i) q^{53} +(-126.450 + 219.017i) q^{55} +132.612 q^{56} +236.808 q^{58} +(211.595 - 366.493i) q^{59} +(-281.960 - 488.369i) q^{61} +(-120.050 + 207.932i) q^{62} +64.0000 q^{64} +1058.78 q^{65} +(471.426 + 816.534i) q^{67} -158.420 q^{68} +(261.546 + 453.012i) q^{70} +(-332.873 + 576.552i) q^{71} +(93.4728 - 161.900i) q^{73} +(-22.0924 + 38.2652i) q^{74} +(-311.826 + 111.841i) q^{76} -265.696 q^{77} +(438.177 - 758.945i) q^{79} +(126.225 + 218.628i) q^{80} +(109.102 + 188.969i) q^{82} +476.297 q^{83} +(-312.447 - 541.173i) q^{85} +(360.624 + 624.620i) q^{86} -128.228 q^{88} +(-482.370 - 835.489i) q^{89} +(556.177 + 963.328i) q^{91} +(-95.3617 + 165.171i) q^{92} -385.890 q^{94} +(-997.063 - 844.639i) q^{95} +(792.961 - 1373.45i) q^{97} +(68.2197 - 118.160i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 12 q^{4} + q^{5} + 52 q^{7} + 48 q^{8}+O(q^{10}) \) 6 * q - 6 * q^2 - 12 * q^4 + q^5 + 52 * q^7 + 48 * q^8	\( 6 q - 6 q^{2} - 12 q^{4} + q^{5} + 52 q^{7} + 48 q^{8} + 2 q^{10} - 8 q^{11} + 129 q^{13} - 52 q^{14} - 48 q^{16} + 51 q^{17} + 40 q^{19} - 8 q^{20} + 8 q^{22} - 47 q^{23} - 338 q^{25} - 516 q^{26} - 104 q^{28} + 125 q^{29} - 100 q^{31} - 96 q^{32} + 102 q^{34} + 84 q^{35} - 376 q^{37} - 322 q^{38} + 8 q^{40} - 475 q^{41} - 73 q^{43} + 16 q^{44} + 188 q^{46} + 241 q^{47} - 1354 q^{49} + 1352 q^{50} + 516 q^{52} - 29 q^{53} - 1838 q^{55} + 416 q^{56} - 500 q^{58} + 1065 q^{59} - 981 q^{61} + 100 q^{62} + 384 q^{64} - 586 q^{65} + 877 q^{67} - 408 q^{68} + 168 q^{70} - 2135 q^{71} + 667 q^{73} + 376 q^{74} + 484 q^{76} + 492 q^{77} + 1671 q^{79} + 16 q^{80} - 950 q^{82} - 1176 q^{83} - 1929 q^{85} - 146 q^{86} - 64 q^{88} - 693 q^{89} + 1676 q^{91} - 188 q^{92} - 964 q^{94} - 4489 q^{95} - 985 q^{97} + 1354 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 - 12 * q^4 + q^5 + 52 * q^7 + 48 * q^8 + 2 * q^10 - 8 * q^11 + 129 * q^13 - 52 * q^14 - 48 * q^16 + 51 * q^17 + 40 * q^19 - 8 * q^20 + 8 * q^22 - 47 * q^23 - 338 * q^25 - 516 * q^26 - 104 * q^28 + 125 * q^29 - 100 * q^31 - 96 * q^32 + 102 * q^34 + 84 * q^35 - 376 * q^37 - 322 * q^38 + 8 * q^40 - 475 * q^41 - 73 * q^43 + 16 * q^44 + 188 * q^46 + 241 * q^47 - 1354 * q^49 + 1352 * q^50 + 516 * q^52 - 29 * q^53 - 1838 * q^55 + 416 * q^56 - 500 * q^58 + 1065 * q^59 - 981 * q^61 + 100 * q^62 + 384 * q^64 - 586 * q^65 + 877 * q^67 - 408 * q^68 + 168 * q^70 - 2135 * q^71 + 667 * q^73 + 376 * q^74 + 484 * q^76 + 492 * q^77 + 1671 * q^79 + 16 * q^80 - 950 * q^82 - 1176 * q^83 - 1929 * q^85 - 146 * q^86 - 64 * q^88 - 693 * q^89 + 1676 * q^91 - 188 * q^92 - 964 * q^94 - 4489 * q^95 - 985 * q^97 + 1354 * q^98

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