LMFDB - Embedded newform 168.4.q.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,4,Mod(25,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("168.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.q (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:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	168.25
Dual form			168.4.q.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{3} +(-3.50000 - 6.06218i) q^{5} +(-17.5000 + 6.06218i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 - 2.59808i) q^{3} +(-3.50000 - 6.06218i) q^{5} +(-17.5000 + 6.06218i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(-3.50000 + 6.06218i) q^{11} -52.0000 q^{13} -21.0000 q^{15} +(-36.0000 + 62.3538i) q^{17} +(-10.0000 - 17.3205i) q^{19} +(-10.5000 + 54.5596i) q^{21} +(24.0000 + 41.5692i) q^{23} +(38.0000 - 65.8179i) q^{25} -27.0000 q^{27} -243.000 q^{29} +(-47.5000 + 82.2724i) q^{31} +(10.5000 + 18.1865i) q^{33} +(98.0000 + 84.8705i) q^{35} +(-176.000 - 304.841i) q^{37} +(-78.0000 + 135.100i) q^{39} -296.000 q^{41} +158.000 q^{43} +(-31.5000 + 54.5596i) q^{45} +(71.0000 + 122.976i) q^{47} +(269.500 - 212.176i) q^{49} +(108.000 + 187.061i) q^{51} +(187.500 - 324.760i) q^{53} +49.0000 q^{55} -60.0000 q^{57} +(-139.500 + 241.621i) q^{59} +(-123.000 - 213.042i) q^{61} +(126.000 + 109.119i) q^{63} +(182.000 + 315.233i) q^{65} +(365.000 - 632.199i) q^{67} +144.000 q^{69} +338.000 q^{71} +(271.000 - 469.386i) q^{73} +(-114.000 - 197.454i) q^{75} +(24.5000 - 127.306i) q^{77} +(152.500 + 264.138i) q^{79} +(-40.5000 + 70.1481i) q^{81} +1123.00 q^{83} +504.000 q^{85} +(-364.500 + 631.333i) q^{87} +(213.000 + 368.927i) q^{89} +(910.000 - 315.233i) q^{91} +(142.500 + 246.817i) q^{93} +(-70.0000 + 121.244i) q^{95} -369.000 q^{97} +63.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} - 7 q^{5} - 35 q^{7} - 9 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 - 7 * q^5 - 35 * q^7 - 9 * q^9	$ 2 q + 3 q^{3} - 7 q^{5} - 35 q^{7} - 9 q^{9} - 7 q^{11} - 104 q^{13} - 42 q^{15} - 72 q^{17} - 20 q^{19} - 21 q^{21} + 48 q^{23} + 76 q^{25} - 54 q^{27} - 486 q^{29} - 95 q^{31} + 21 q^{33} + 196 q^{35} - 352 q^{37} - 156 q^{39} - 592 q^{41} + 316 q^{43} - 63 q^{45} + 142 q^{47} + 539 q^{49} + 216 q^{51} + 375 q^{53} + 98 q^{55} - 120 q^{57} - 279 q^{59} - 246 q^{61} + 252 q^{63} + 364 q^{65} + 730 q^{67} + 288 q^{69} + 676 q^{71} + 542 q^{73} - 228 q^{75} + 49 q^{77} + 305 q^{79} - 81 q^{81} + 2246 q^{83} + 1008 q^{85} - 729 q^{87} + 426 q^{89} + 1820 q^{91} + 285 q^{93} - 140 q^{95} - 738 q^{97} + 126 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 - 7 * q^5 - 35 * q^7 - 9 * q^9 - 7 * q^11 - 104 * q^13 - 42 * q^15 - 72 * q^17 - 20 * q^19 - 21 * q^21 + 48 * q^23 + 76 * q^25 - 54 * q^27 - 486 * q^29 - 95 * q^31 + 21 * q^33 + 196 * q^35 - 352 * q^37 - 156 * q^39 - 592 * q^41 + 316 * q^43 - 63 * q^45 + 142 * q^47 + 539 * q^49 + 216 * q^51 + 375 * q^53 + 98 * q^55 - 120 * q^57 - 279 * q^59 - 246 * q^61 + 252 * q^63 + 364 * q^65 + 730 * q^67 + 288 * q^69 + 676 * q^71 + 542 * q^73 - 228 * q^75 + 49 * q^77 + 305 * q^79 - 81 * q^81 + 2246 * q^83 + 1008 * q^85 - 729 * q^87 + 426 * q^89 + 1820 * q^91 + 285 * q^93 - 140 * q^95 - 738 * q^97 + 126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$		0			0
$5$	−3.50000	−	6.06218i	−0.313050	−	0.542218i	0.665971	−	0.745977i	$-0.268017\pi$
$5$	−3.50000	−	6.06218i	−0.313050	−	0.542218i	−0.979021	+	0.203760i	$0.934684\pi$
$6$		0			0
$7$	−17.5000	+	6.06218i	−0.944911	+	0.327327i
$7$	−17.5000	+	6.06218i	−0.944911	+	0.327327i
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$		0			0
$11$	−3.50000	+	6.06218i	−0.0959354	+	0.166165i	−0.909999	−	0.414611i	$-0.863918\pi$
$11$	−3.50000	+	6.06218i	−0.0959354	+	0.166165i	0.814063	+	0.580776i	$0.197251\pi$
$12$		0			0
$13$	−52.0000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−52.0000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$		0			0
$15$	−21.0000			−0.361478
$16$		0			0
$17$	−36.0000	+	62.3538i	−0.513605	+	0.889590i	0.486271	+	0.873808i	$0.338357\pi$
$17$	−36.0000	+	62.3538i	−0.513605	+	0.889590i	−0.999875	+	0.0157814i	$0.994976\pi$
$18$		0			0
$19$	−10.0000	−	17.3205i	−0.120745	−	0.209137i	0.799317	−	0.600910i	$-0.205195\pi$
$19$	−10.0000	−	17.3205i	−0.120745	−	0.209137i	−0.920062	+	0.391773i	$0.871862\pi$
$20$		0			0
$21$	−10.5000	+	54.5596i	−0.109109	+	0.566947i
$22$		0			0
$23$	24.0000	+	41.5692i	0.217580	+	0.376860i	0.954068	−	0.299591i	$-0.0968503\pi$
$23$	24.0000	+	41.5692i	0.217580	+	0.376860i	−0.736487	+	0.676451i	$0.763517\pi$
$24$		0			0
$25$	38.0000	−	65.8179i	0.304000	−	0.526543i
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−243.000			−1.55600			−0.777999	−	0.628265i	$-0.783765\pi$
$29$	−243.000			−1.55600			−0.777999	+	0.628265i	$0.783765\pi$
$30$		0			0
$31$	−47.5000	+	82.2724i	−0.275202	+	0.476663i	−0.970186	−	0.242362i	$-0.922078\pi$
$31$	−47.5000	+	82.2724i	−0.275202	+	0.476663i	0.694984	+	0.719025i	$0.255411\pi$
$32$		0			0
$33$	10.5000	+	18.1865i	0.0553883	+	0.0959354i
$34$		0			0
$35$	98.0000	+	84.8705i	0.473286	+	0.409878i
$36$		0			0
$37$	−176.000	−	304.841i	−0.782006	−	1.35447i	−0.930771	−	0.365602i	$-0.880863\pi$
$37$	−176.000	−	304.841i	−0.782006	−	1.35447i	0.148765	−	0.988873i	$-0.452470\pi$
$38$		0			0
$39$	−78.0000	+	135.100i	−0.320256	+	0.554700i
$40$		0			0
$41$	−296.000			−1.12750			−0.563749	−	0.825946i	$-0.690642\pi$
$41$	−296.000			−1.12750			−0.563749	+	0.825946i	$0.690642\pi$
$42$		0			0
$43$	158.000			0.560344			0.280172	−	0.959950i	$-0.409609\pi$
$43$	158.000			0.560344			0.280172	+	0.959950i	$0.409609\pi$
$44$		0			0
$45$	−31.5000	+	54.5596i	−0.104350	+	0.180739i
$46$		0			0
$47$	71.0000	+	122.976i	0.220349	+	0.381656i	0.954914	−	0.296882i	$-0.0959470\pi$
$47$	71.0000	+	122.976i	0.220349	+	0.381656i	−0.734565	+	0.678539i	$0.762614\pi$
$48$		0			0
$49$	269.500	−	212.176i	0.785714	−	0.618590i
$50$		0			0
$51$	108.000	+	187.061i	0.296530	+	0.513605i
$52$		0			0
$53$	187.500	−	324.760i	0.485945	−	0.841682i	−0.513924	−	0.857836i	$-0.671809\pi$
$53$	187.500	−	324.760i	0.485945	−	0.841682i	0.999870	+	0.0161535i	$0.00514205\pi$
$54$		0			0
$55$	49.0000			0.120130
$56$		0			0
$57$	−60.0000			−0.139424
$58$		0			0
$59$	−139.500	+	241.621i	−0.307820	+	0.533159i	−0.977885	−	0.209143i	$-0.932933\pi$
$59$	−139.500	+	241.621i	−0.307820	+	0.533159i	0.670066	+	0.742302i	$0.266266\pi$
$60$		0			0
$61$	−123.000	−	213.042i	−0.258173	−	0.447168i	0.707580	−	0.706634i	$-0.249787\pi$
$61$	−123.000	−	213.042i	−0.258173	−	0.447168i	−0.965752	+	0.259465i	$0.916454\pi$
$62$		0			0
$63$	126.000	+	109.119i	0.251976	+	0.218218i
$64$		0			0
$65$	182.000	+	315.233i	0.347297	+	0.601536i
$66$		0			0
$67$	365.000	−	632.199i	0.665550	−	1.15277i	−0.313586	−	0.949560i	$-0.601530\pi$
$67$	365.000	−	632.199i	0.665550	−	1.15277i	0.979136	−	0.203207i	$-0.0651363\pi$
$68$		0			0
$69$	144.000			0.251240
$70$		0			0
$71$	338.000			0.564975			0.282487	−	0.959271i	$-0.408840\pi$
$71$	338.000			0.564975			0.282487	+	0.959271i	$0.408840\pi$
$72$		0			0
$73$	271.000	−	469.386i	0.434495	−	0.752568i	−0.562759	−	0.826621i	$-0.690260\pi$
$73$	271.000	−	469.386i	0.434495	−	0.752568i	0.997254	+	0.0740532i	$0.0235935\pi$
$74$		0			0
$75$	−114.000	−	197.454i	−0.175514	−	0.304000i
$76$		0			0
$77$	24.5000	−	127.306i	0.0362602	−	0.188413i
$78$		0			0
$79$	152.500	+	264.138i	0.217185	+	0.376175i	0.953946	−	0.299978i	$-0.0969793\pi$
$79$	152.500	+	264.138i	0.217185	+	0.376175i	−0.736761	+	0.676153i	$0.763646\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	1123.00			1.48512			0.742562	−	0.669778i	$-0.233611\pi$
$83$	1123.00			1.48512			0.742562	+	0.669778i	$0.233611\pi$
$84$		0			0
$85$	504.000			0.643135
$86$		0			0
$87$	−364.500	+	631.333i	−0.449178	+	0.777999i
$88$		0			0
$89$	213.000	+	368.927i	0.253685	+	0.439395i	0.964537	−	0.263946i	$-0.0850240\pi$
$89$	213.000	+	368.927i	0.253685	+	0.439395i	−0.710853	+	0.703341i	$0.751691\pi$
$90$		0			0
$91$	910.000	−	315.233i	1.04828	−	0.363137i
$92$		0			0
$93$	142.500	+	246.817i	0.158888	+	0.275202i
$94$		0			0
$95$	−70.0000	+	121.244i	−0.0755984	+	0.130940i
$96$		0			0
$97$	−369.000			−0.386250			−0.193125	−	0.981174i	$-0.561862\pi$
$97$	−369.000			−0.386250			−0.193125	+	0.981174i	$0.561862\pi$
$98$		0			0
$99$	63.0000			0.0639570
$100$		0			0
$101$	−635.000	+	1099.85i	−0.625593	+	1.08356i	0.362833	+	0.931854i	$0.381809\pi$
$101$	−635.000	+	1099.85i	−0.625593	+	1.08356i	−0.988426	+	0.151704i	$0.951524\pi$
$102$		0			0
$103$	−916.000	−	1586.56i	−0.876273	−	1.51775i	−0.855400	−	0.517968i	$-0.826689\pi$
$103$	−916.000	−	1586.56i	−0.876273	−	1.51775i	−0.0208734	−	0.999782i	$-0.506645\pi$
$104$		0			0
$105$	367.500	−	127.306i	0.341565	−	0.118322i
$106$		0			0
$107$	499.500	+	865.159i	0.451294	+	0.781665i	0.998467	−	0.0553553i	$-0.0176291\pi$
$107$	499.500	+	865.159i	0.451294	+	0.781665i	−0.547172	+	0.837020i	$0.684296\pi$
$108$		0			0
$109$	833.000	−	1442.80i	0.731990	−	1.26784i	−0.224041	−	0.974580i	$-0.571925\pi$
$109$	833.000	−	1442.80i	0.731990	−	1.26784i	0.956031	−	0.293264i	$-0.0947417\pi$
$110$		0			0
$111$	−1056.00			−0.902983
$112$		0			0
$113$	−1832.00			−1.52513			−0.762567	−	0.646910i	$-0.776061\pi$
$113$	−1832.00			−1.52513			−0.762567	+	0.646910i	$0.776061\pi$
$114$		0			0
$115$	168.000	−	290.985i	0.136227	−	0.235952i
$116$		0			0
$117$	234.000	+	405.300i	0.184900	+	0.320256i
$118$		0			0
$119$	252.000	−	1309.43i	0.194124	−	1.00870i
$120$		0			0
$121$	641.000	+	1110.24i	0.481593	+	0.834143i
$122$		0			0
$123$	−444.000	+	769.031i	−0.325481	+	0.563749i
$124$		0			0
$125$	−1407.00			−1.00677
$126$		0			0
$127$	−1931.00			−1.34920			−0.674601	−	0.738183i	$-0.735684\pi$
$127$	−1931.00			−1.34920			−0.674601	+	0.738183i	$0.735684\pi$
$128$		0			0
$129$	237.000	−	410.496i	0.161757	−	0.280172i
$130$		0			0
$131$	−489.500	−	847.839i	−0.326472	−	0.565466i	0.655337	−	0.755336i	$-0.272527\pi$
$131$	−489.500	−	847.839i	−0.326472	−	0.565466i	−0.981809	+	0.189871i	$0.939193\pi$
$132$		0			0
$133$	280.000	+	242.487i	0.182549	+	0.158092i
$134$		0			0
$135$	94.5000	+	163.679i	0.0602464	+	0.104350i
$136$		0			0
$137$	243.000	−	420.888i	0.151539	−	0.262474i	−0.780254	−	0.625463i	$-0.784910\pi$
$137$	243.000	−	420.888i	0.151539	−	0.262474i	0.931794	+	0.362989i	$0.118244\pi$
$138$		0			0
$139$	−2630.00			−1.60485			−0.802423	−	0.596755i	$-0.796456\pi$
$139$	−2630.00			−1.60485			−0.802423	+	0.596755i	$0.796456\pi$
$140$		0			0
$141$	426.000			0.254437
$142$		0			0
$143$	182.000	−	315.233i	0.106431	−	0.184344i
$144$		0			0
$145$	850.500	+	1473.11i	0.487105	+	0.843690i
$146$		0			0
$147$	−147.000	−	1018.45i	−0.0824786	−	0.571429i
$148$		0			0
$149$	939.000	+	1626.40i	0.516281	+	0.894225i	0.999821	+	0.0189029i	$0.00601734\pi$
$149$	939.000	+	1626.40i	0.516281	+	0.894225i	−0.483540	+	0.875322i	$0.660649\pi$
$150$		0			0
$151$	−1051.50	+	1821.25i	−0.566688	+	0.981532i	0.430203	+	0.902732i	$0.358442\pi$
$151$	−1051.50	+	1821.25i	−0.566688	+	0.981532i	−0.996890	+	0.0787997i	$0.974891\pi$
$152$		0			0
$153$	648.000			0.342403
$154$		0			0
$155$	665.000			0.344607
$156$		0			0
$157$	−702.000	+	1215.90i	−0.356852	+	0.618085i	−0.987433	−	0.158038i	$-0.949483\pi$
$157$	−702.000	+	1215.90i	−0.356852	+	0.618085i	0.630581	+	0.776123i	$0.282816\pi$
$158$		0			0
$159$	−562.500	−	974.279i	−0.280561	−	0.485945i
$160$		0			0
$161$	−672.000	−	581.969i	−0.328950	−	0.284879i
$162$		0			0
$163$	768.000	+	1330.22i	0.369045	+	0.639205i	0.989417	−	0.145103i	$-0.0463513\pi$
$163$	768.000	+	1330.22i	0.369045	+	0.639205i	−0.620371	+	0.784308i	$0.713018\pi$
$164$		0			0
$165$	73.5000	−	127.306i	0.0346786	−	0.0600651i
$166$		0			0
$167$	−3634.00			−1.68388			−0.841938	−	0.539574i	$-0.818585\pi$
$167$	−3634.00			−1.68388			−0.841938	+	0.539574i	$0.818585\pi$
$168$		0			0
$169$	507.000			0.230769
$170$		0			0
$171$	−90.0000	+	155.885i	−0.0402484	+	0.0697122i
$172$		0			0
$173$	−429.000	−	743.050i	−0.188533	−	0.326549i	0.756228	−	0.654308i	$-0.227040\pi$
$173$	−429.000	−	743.050i	−0.188533	−	0.326549i	−0.944761	+	0.327759i	$0.893707\pi$
$174$		0			0
$175$	−266.000	+	1382.18i	−0.114901	+	0.597044i
$176$		0			0
$177$	418.500	+	724.863i	0.177720	+	0.307820i
$178$		0			0
$179$	1210.00	−	2095.78i	0.505249	−	0.875118i	−0.494732	−	0.869046i	$-0.664734\pi$
$179$	1210.00	−	2095.78i	0.505249	−	0.875118i	0.999982	−	0.00607215i	$-0.00193284\pi$
$180$		0			0
$181$	−2672.00			−1.09728			−0.548641	−	0.836058i	$-0.684855\pi$
$181$	−2672.00			−1.09728			−0.548641	+	0.836058i	$0.684855\pi$
$182$		0			0
$183$	−738.000			−0.298112
$184$		0			0
$185$	−1232.00	+	2133.89i	−0.489613	+	0.848035i
$186$		0			0
$187$	−252.000	−	436.477i	−0.0985458	−	0.170686i
$188$		0			0
$189$	472.500	−	163.679i	0.181848	−	0.0629941i
$190$		0			0
$191$	856.000	+	1482.64i	0.324283	+	0.561674i	0.981367	−	0.192143i	$-0.0615438\pi$
$191$	856.000	+	1482.64i	0.324283	+	0.561674i	−0.657084	+	0.753817i	$0.728210\pi$
$192$		0			0
$193$	1697.50	−	2940.16i	0.633102	−	1.09657i	−0.353812	−	0.935317i	$-0.615115\pi$
$193$	1697.50	−	2940.16i	0.633102	−	1.09657i	0.986914	−	0.161248i	$-0.0515521\pi$
$194$		0			0
$195$	1092.00			0.401024
$196$		0			0
$197$	510.000			0.184447			0.0922233	−	0.995738i	$-0.470603\pi$
$197$	510.000			0.184447			0.0922233	+	0.995738i	$0.470603\pi$
$198$		0			0
$199$	−138.000	+	239.023i	−0.0491586	+	0.0851452i	−0.889558	−	0.456823i	$-0.848987\pi$
$199$	−138.000	+	239.023i	−0.0491586	+	0.0851452i	0.840399	+	0.541968i	$0.182321\pi$
$200$		0			0
$201$	−1095.00	−	1896.60i	−0.384255	−	0.665550i
$202$		0			0
$203$	4252.50	−	1473.11i	1.47028	−	0.509320i
$204$		0			0
$205$	1036.00	+	1794.40i	0.352963	+	0.611350i
$206$		0			0
$207$	216.000	−	374.123i	0.0725268	−	0.125620i
$208$		0			0
$209$	140.000			0.0463349
$210$		0			0
$211$	3198.00			1.04341			0.521705	−	0.853126i	$-0.325296\pi$
$211$	3198.00			1.04341			0.521705	+	0.853126i	$0.325296\pi$
$212$		0			0
$213$	507.000	−	878.150i	0.163094	−	0.282487i
$214$		0			0
$215$	−553.000	−	957.824i	−0.175415	−	0.303828i
$216$		0			0
$217$	332.500	−	1727.72i	0.104016	−	0.540485i
$218$		0			0
$219$	−813.000	−	1408.16i	−0.250856	−	0.434495i
$220$		0			0
$221$	1872.00	−	3242.40i	0.569793	−	0.986911i
$222$		0			0
$223$	−5091.00			−1.52878			−0.764391	−	0.644752i	$-0.776960\pi$
$223$	−5091.00			−1.52878			−0.764391	+	0.644752i	$0.776960\pi$
$224$		0			0
$225$	−684.000			−0.202667
$226$		0			0
$227$	1947.50	−	3373.17i	0.569428	−	0.986278i	−0.427195	−	0.904160i	$-0.640498\pi$
$227$	1947.50	−	3373.17i	0.569428	−	0.986278i	0.996623	−	0.0821183i	$-0.0261685\pi$
$228$		0			0
$229$	3214.00	+	5566.81i	0.927455	+	1.60640i	0.787565	+	0.616231i	$0.211341\pi$
$229$	3214.00	+	5566.81i	0.927455	+	1.60640i	0.139889	+	0.990167i	$0.455325\pi$
$230$		0			0
$231$	−294.000	−	254.611i	−0.0837393	−	0.0725204i
$232$		0			0
$233$	1912.00	+	3311.68i	0.537593	+	0.931139i	0.999033	+	0.0439676i	$0.0139998\pi$
$233$	1912.00	+	3311.68i	0.537593	+	0.931139i	−0.461439	+	0.887172i	$0.652667\pi$
$234$		0			0
$235$	497.000	−	860.829i	0.137960	−	0.238955i
$236$		0			0
$237$	915.000			0.250783
$238$		0			0
$239$	568.000			0.153727			0.0768637	−	0.997042i	$-0.475509\pi$
$239$	568.000			0.153727			0.0768637	+	0.997042i	$0.475509\pi$
$240$		0			0
$241$	−1767.50	+	3061.40i	−0.472426	+	0.818266i	−0.999502	−	0.0315522i	$-0.989955\pi$
$241$	−1767.50	+	3061.40i	−0.472426	+	0.818266i	0.527076	+	0.849818i	$0.323288\pi$
$242$		0			0
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$		0			0
$245$	−2229.50	−	891.140i	−0.581378	−	0.232379i
$246$		0			0
$247$	520.000	+	900.666i	0.133955	+	0.232016i
$248$		0			0
$249$	1684.50	−	2917.64i	0.428718	−	0.742562i
$250$		0			0
$251$	4335.00			1.09013			0.545065	−	0.838394i	$-0.316505\pi$
$251$	4335.00			1.09013			0.545065	+	0.838394i	$0.316505\pi$
$252$		0			0
$253$	−336.000			−0.0834946
$254$		0			0
$255$	756.000	−	1309.43i	0.185657	−	0.321568i
$256$		0			0
$257$	−1787.00	−	3095.17i	−0.433735	−	0.751252i	0.563456	−	0.826146i	$-0.309471\pi$
$257$	−1787.00	−	3095.17i	−0.433735	−	0.751252i	−0.997191	+	0.0748943i	$0.976138\pi$
$258$		0			0
$259$	4928.00	+	4267.77i	1.18228	+	1.02389i
$260$		0			0
$261$	1093.50	+	1894.00i	0.259333	+	0.449178i
$262$		0			0
$263$	−2733.00	+	4733.69i	−0.640776	+	1.10986i	0.344484	+	0.938792i	$0.388054\pi$
$263$	−2733.00	+	4733.69i	−0.640776	+	1.10986i	−0.985260	+	0.171064i	$0.945280\pi$
$264$		0			0
$265$	−2625.00			−0.608500
$266$		0			0
$267$	1278.00			0.292930
$268$		0			0
$269$	2907.50	−	5035.94i	0.659009	−	1.14144i	−0.321864	−	0.946786i	$-0.604309\pi$
$269$	2907.50	−	5035.94i	0.659009	−	1.14144i	0.980873	−	0.194651i	$-0.0623574\pi$
$270$		0			0
$271$	1618.50	+	2803.32i	0.362793	+	0.628376i	0.988419	−	0.151747i	$-0.0484899\pi$
$271$	1618.50	+	2803.32i	0.362793	+	0.628376i	−0.625626	+	0.780123i	$0.715157\pi$
$272$		0			0
$273$	546.000	−	2837.10i	0.121046	−	0.628971i
$274$		0			0
$275$	266.000	+	460.726i	0.0583287	+	0.101028i
$276$		0			0
$277$	1588.00	−	2750.50i	0.344454	−	0.596611i	−0.640801	−	0.767707i	$-0.721397\pi$
$277$	1588.00	−	2750.50i	0.344454	−	0.596611i	0.985254	+	0.171096i	$0.0547308\pi$
$278$		0			0
$279$	855.000			0.183468
$280$		0			0
$281$	−3282.00			−0.696753			−0.348377	−	0.937355i	$-0.613267\pi$
$281$	−3282.00			−0.696753			−0.348377	+	0.937355i	$0.613267\pi$
$282$		0			0
$283$	−1091.00	+	1889.67i	−0.229163	+	0.396923i	−0.957560	−	0.288233i	$-0.906932\pi$
$283$	−1091.00	+	1889.67i	−0.229163	+	0.396923i	0.728397	+	0.685155i	$0.240266\pi$
$284$		0			0
$285$	210.000	+	363.731i	0.0436468	+	0.0755984i
$286$		0			0
$287$	5180.00	−	1794.40i	1.06539	−	0.369060i
$288$		0			0
$289$	−135.500	−	234.693i	−0.0275799	−	0.0477698i
$290$		0			0
$291$	−553.500	+	958.690i	−0.111501	+	0.193125i
$292$		0			0
$293$	3021.00			0.602351			0.301175	−	0.953569i	$-0.402621\pi$
$293$	3021.00			0.602351			0.301175	+	0.953569i	$0.402621\pi$
$294$		0			0
$295$	1953.00			0.385451
$296$		0			0
$297$	94.5000	−	163.679i	0.0184628	−	0.0319785i
$298$		0			0
$299$	−1248.00	−	2161.60i	−0.241384	−	0.418089i
$300$		0			0
$301$	−2765.00	+	957.824i	−0.529475	+	0.183415i
$302$		0			0
$303$	1905.00	+	3299.56i	0.361186	+	0.625593i
$304$		0			0
$305$	−861.000	+	1491.30i	−0.161642	+	0.279972i
$306$		0			0
$307$	−1304.00			−0.242421			−0.121210	−	0.992627i	$-0.538678\pi$
$307$	−1304.00			−0.242421			−0.121210	+	0.992627i	$0.538678\pi$
$308$		0			0
$309$	−5496.00			−1.01183
$310$		0			0
$311$	−3104.00	+	5376.29i	−0.565954	+	0.980261i	0.431006	+	0.902349i	$0.358159\pi$
$311$	−3104.00	+	5376.29i	−0.565954	+	0.980261i	−0.996960	+	0.0779121i	$0.975175\pi$
$312$		0			0
$313$	−1668.50	−	2889.93i	−0.301307	−	0.521880i	0.675125	−	0.737703i	$-0.264090\pi$
$313$	−1668.50	−	2889.93i	−0.301307	−	0.521880i	−0.976432	+	0.215824i	$0.930756\pi$
$314$		0			0
$315$	220.500	−	1145.75i	0.0394405	−	0.204939i
$316$		0			0
$317$	−4318.50	−	7479.86i	−0.765146	−	1.32527i	−0.940170	−	0.340707i	$-0.889334\pi$
$317$	−4318.50	−	7479.86i	−0.765146	−	1.32527i	0.175024	−	0.984564i	$-0.444000\pi$
$318$		0			0
$319$	850.500	−	1473.11i	0.149275	−	0.258553i
$320$		0			0
$321$	2997.00			0.521110
$322$		0			0
$323$	1440.00			0.248061
$324$		0			0
$325$	−1976.00	+	3422.53i	−0.337258	+	0.584148i
$326$		0			0
$327$	−2499.00	−	4328.39i	−0.422615	−	0.731990i
$328$		0			0
$329$	−1988.00	−	1721.66i	−0.333137	−	0.288505i
$330$		0			0
$331$	−970.000	−	1680.09i	−0.161076	−	0.278991i	0.774179	−	0.632967i	$-0.218163\pi$
$331$	−970.000	−	1680.09i	−0.161076	−	0.278991i	−0.935255	+	0.353975i	$0.884830\pi$
$332$		0			0
$333$	−1584.00	+	2743.57i	−0.260669	+	0.451491i
$334$		0			0
$335$	−5110.00			−0.833400
$336$		0			0
$337$	−5527.00			−0.893397			−0.446699	−	0.894684i	$-0.647400\pi$
$337$	−5527.00			−0.893397			−0.446699	+	0.894684i	$0.647400\pi$
$338$		0			0
$339$	−2748.00	+	4759.68i	−0.440268	+	0.762567i
$340$		0			0
$341$	−332.500	−	575.907i	−0.0528032	−	0.0914578i
$342$		0			0
$343$	−3430.00	+	5346.84i	−0.539949	+	0.841698i
$344$		0			0
$345$	−504.000	−	872.954i	−0.0786506	−	0.136227i
$346$		0			0
$347$	−4782.00	+	8282.67i	−0.739802	+	1.28137i	0.212783	+	0.977100i	$0.431747\pi$
$347$	−4782.00	+	8282.67i	−0.739802	+	1.28137i	−0.952584	+	0.304275i	$0.901586\pi$
$348$		0			0
$349$	−918.000			−0.140801			−0.0704003	−	0.997519i	$-0.522428\pi$
$349$	−918.000			−0.140801			−0.0704003	+	0.997519i	$0.522428\pi$
$350$		0			0
$351$	1404.00			0.213504
$352$		0			0
$353$	−5740.00	+	9941.97i	−0.865466	+	1.49903i	0.00111843	+	0.999999i	$0.499644\pi$
$353$	−5740.00	+	9941.97i	−0.865466	+	1.49903i	−0.866584	+	0.499031i	$0.833689\pi$
$354$		0			0
$355$	−1183.00	−	2049.02i	−0.176865	−	0.306339i
$356$		0			0
$357$	−3024.00	−	2618.86i	−0.448311	−	0.388249i
$358$		0			0
$359$	−1827.00	−	3164.46i	−0.268594	−	0.465219i	0.699905	−	0.714236i	$-0.253226\pi$
$359$	−1827.00	−	3164.46i	−0.268594	−	0.465219i	−0.968499	+	0.249017i	$0.919892\pi$
$360$		0			0
$361$	3229.50	−	5593.66i	0.470841	−	0.815521i
$362$		0			0
$363$	3846.00			0.556095
$364$		0			0
$365$	−3794.00			−0.544074
$366$		0			0
$367$	5033.50	−	8718.28i	0.715931	−	1.24003i	−0.246669	−	0.969100i	$-0.579336\pi$
$367$	5033.50	−	8718.28i	0.715931	−	1.24003i	0.962599	−	0.270928i	$-0.0873307\pi$
$368$		0			0
$369$	1332.00	+	2307.09i	0.187916	+	0.325481i
$370$		0			0
$371$	−1312.50	+	6819.95i	−0.183670	+	0.954378i
$372$		0			0
$373$	−4400.00	−	7621.02i	−0.610786	−	1.05791i	−0.991108	−	0.133059i	$-0.957520\pi$
$373$	−4400.00	−	7621.02i	−0.610786	−	1.05791i	0.380322	−	0.924854i	$-0.375813\pi$
$374$		0			0
$375$	−2110.50	+	3655.49i	−0.290629	+	0.503384i
$376$		0			0
$377$	12636.0			1.72623
$378$		0			0
$379$	1136.00			0.153964			0.0769821	−	0.997032i	$-0.475472\pi$
$379$	1136.00			0.153964			0.0769821	+	0.997032i	$0.475472\pi$
$380$		0			0
$381$	−2896.50	+	5016.89i	−0.389481	+	0.674601i
$382$		0			0
$383$	−2145.00	−	3715.25i	−0.286173	−	0.495667i	0.686720	−	0.726922i	$-0.259050\pi$
$383$	−2145.00	−	3715.25i	−0.286173	−	0.495667i	−0.972893	+	0.231256i	$0.925717\pi$
$384$		0			0
$385$	−857.500	+	297.047i	−0.113512	+	0.0393218i
$386$		0			0
$387$	−711.000	−	1231.49i	−0.0933906	−	0.161757i
$388$		0			0
$389$	431.000	−	746.514i	0.0561763	−	0.0973001i	−0.836570	−	0.547861i	$-0.815442\pi$
$389$	431.000	−	746.514i	0.0561763	−	0.0973001i	0.892746	+	0.450560i	$0.148776\pi$
$390$		0			0
$391$	−3456.00			−0.447001
$392$		0			0
$393$	−2937.00			−0.376977
$394$		0			0
$395$	1067.50	−	1848.96i	0.135979	−	0.235523i
$396$		0			0
$397$	4570.00	+	7915.47i	0.577737	+	1.00067i	0.995738	+	0.0922238i	$0.0293975\pi$
$397$	4570.00	+	7915.47i	0.577737	+	1.00067i	−0.418001	+	0.908447i	$0.637269\pi$
$398$		0			0
$399$	1050.00	−	363.731i	0.131744	−	0.0456374i
$400$		0			0
$401$	7116.00	+	12325.3i	0.886175	+	1.53490i	0.844361	+	0.535774i	$0.179980\pi$
$401$	7116.00	+	12325.3i	0.886175	+	1.53490i	0.0418135	+	0.999125i	$0.486686\pi$
$402$		0			0
$403$	2470.00	−	4278.17i	0.305309	−	0.528810i
$404$		0			0
$405$	567.000			0.0695666
$406$		0			0
$407$	2464.00			0.300088
$408$		0			0
$409$	5000.50	−	8661.12i	0.604545	−	1.04710i	−0.387578	−	0.921837i	$-0.626688\pi$
$409$	5000.50	−	8661.12i	0.604545	−	1.04710i	0.992123	−	0.125266i	$-0.0399783\pi$
$410$		0			0
$411$	−729.000	−	1262.67i	−0.0874913	−	0.151539i
$412$		0			0
$413$	976.500	−	5074.04i	0.116345	−	0.604546i
$414$		0			0
$415$	−3930.50	−	6807.83i	−0.464917	−	0.805260i
$416$		0			0
$417$	−3945.00	+	6832.94i	−0.463279	+	0.802423i
$418$		0			0
$419$	−10256.0			−1.19580			−0.597898	−	0.801572i	$-0.703997\pi$
$419$	−10256.0			−1.19580			−0.597898	+	0.801572i	$0.703997\pi$
$420$		0			0
$421$	−4502.00			−0.521174			−0.260587	−	0.965450i	$-0.583916\pi$
$421$	−4502.00			−0.521174			−0.260587	+	0.965450i	$0.583916\pi$
$422$		0			0
$423$	639.000	−	1106.78i	0.0734497	−	0.127219i
$424$		0			0
$425$	2736.00	+	4738.89i	0.312272	+	0.540871i
$426$		0			0
$427$	3444.00	+	2982.59i	0.390320	+	0.338027i
$428$		0			0
$429$	−546.000	−	945.700i	−0.0614479	−	0.106431i
$430$		0			0
$431$	−6178.00	+	10700.6i	−0.690450	+	1.19589i	0.281241	+	0.959637i	$0.409254\pi$
$431$	−6178.00	+	10700.6i	−0.690450	+	1.19589i	−0.971691	+	0.236257i	$0.924079\pi$
$432$		0			0
$433$	862.000			0.0956699			0.0478350	−	0.998855i	$-0.484768\pi$
$433$	862.000			0.0956699			0.0478350	+	0.998855i	$0.484768\pi$
$434$		0			0
$435$	5103.00			0.562460
$436$		0			0
$437$	480.000	−	831.384i	0.0525435	−	0.0910080i
$438$		0			0
$439$	682.500	+	1182.12i	0.0742003	+	0.128519i	0.900738	−	0.434362i	$-0.143026\pi$
$439$	682.500	+	1182.12i	0.0742003	+	0.128519i	−0.826538	+	0.562881i	$0.809693\pi$
$440$		0			0
$441$	−2866.50	−	1145.75i	−0.309524	−	0.123718i
$442$		0			0
$443$	−4465.50	−	7734.47i	−0.478922	−	0.829517i	0.520786	−	0.853687i	$-0.325639\pi$
$443$	−4465.50	−	7734.47i	−0.478922	−	0.829517i	−0.999708	+	0.0241705i	$0.992306\pi$
$444$		0			0
$445$	1491.00	−	2582.49i	0.158832	−	0.275105i
$446$		0			0
$447$	5634.00			0.596150
$448$		0			0
$449$	11228.0			1.18014			0.590069	−	0.807353i	$-0.299100\pi$
$449$	11228.0			1.18014			0.590069	+	0.807353i	$0.299100\pi$
$450$		0			0
$451$	1036.00	−	1794.40i	0.108167	−	0.187351i
$452$		0			0
$453$	3154.50	+	5463.75i	0.327177	+	0.566688i
$454$		0			0
$455$	−5096.00	−	4413.27i	−0.525064	−	0.454719i
$456$		0			0
$457$	−6075.50	−	10523.1i	−0.621882	−	1.07713i	−0.989135	−	0.147010i	$-0.953035\pi$
$457$	−6075.50	−	10523.1i	−0.621882	−	1.07713i	0.367253	−	0.930121i	$-0.380298\pi$
$458$		0			0
$459$	972.000	−	1683.55i	0.0988433	−	0.171202i
$460$		0			0
$461$	18534.0			1.87248			0.936241	−	0.351358i	$-0.114280\pi$
$461$	18534.0			1.87248			0.936241	+	0.351358i	$0.114280\pi$
$462$		0			0
$463$	17096.0			1.71602			0.858011	−	0.513631i	$-0.171700\pi$
$463$	17096.0			1.71602			0.858011	+	0.513631i	$0.171700\pi$
$464$		0			0
$465$	997.500	−	1727.72i	0.0994795	−	0.172304i
$466$		0			0
$467$	1070.00	+	1853.29i	0.106025	+	0.183641i	0.914157	−	0.405361i	$-0.132854\pi$
$467$	1070.00	+	1853.29i	0.106025	+	0.183641i	−0.808131	+	0.589002i	$0.799521\pi$
$468$		0			0
$469$	−2555.00	+	13276.2i	−0.251554	+	1.30711i
$470$		0			0
$471$	2106.00	+	3647.70i	0.206028	+	0.356852i
$472$		0			0
$473$	−553.000	+	957.824i	−0.0537568	+	0.0931095i
$474$		0			0
$475$	−1520.00			−0.146826
$476$		0			0
$477$	−3375.00			−0.323964
$478$		0			0
$479$	6633.00	−	11488.7i	0.632713	−	1.09589i	−0.354282	−	0.935139i	$-0.615275\pi$
$479$	6633.00	−	11488.7i	0.632713	−	1.09589i	0.986995	−	0.160752i	$-0.0513920\pi$
$480$		0			0
$481$	9152.00	+	15851.7i	0.867558	+	1.50265i
$482$		0			0
$483$	−2520.00	+	872.954i	−0.237400	+	0.0822376i
$484$		0			0
$485$	1291.50	+	2236.94i	0.120915	+	0.209432i
$486$		0			0
$487$	9591.50	−	16613.0i	0.892469	−	1.54580i	0.0555627	−	0.998455i	$-0.482305\pi$
$487$	9591.50	−	16613.0i	0.892469	−	1.54580i	0.836906	−	0.547346i	$-0.184362\pi$
$488$		0			0
$489$	4608.00			0.426137
$490$		0			0
$491$	−21693.0			−1.99387			−0.996936	−	0.0782185i	$-0.975077\pi$
$491$	−21693.0			−1.99387			−0.996936	+	0.0782185i	$0.975077\pi$
$492$		0			0
$493$	8748.00	−	15152.0i	0.799169	−	1.38420i
$494$		0			0
$495$	−220.500	−	381.917i	−0.0200217	−	0.0346786i
$496$		0			0
$497$	−5915.00	+	2049.02i	−0.533851	+	0.184931i
$498$		0			0
$499$	−9829.00	−	17024.3i	−0.881776	−	1.52728i	−0.849364	−	0.527807i	$-0.823014\pi$
$499$	−9829.00	−	17024.3i	−0.881776	−	1.52728i	−0.0324122	−	0.999475i	$-0.510319\pi$
$500$		0			0
$501$	−5451.00	+	9441.41i	−0.486093	+	0.841938i
$502$		0			0
$503$	19436.0			1.72288			0.861440	−	0.507860i	$-0.169563\pi$
$503$	19436.0			1.72288			0.861440	+	0.507860i	$0.169563\pi$
$504$		0			0
$505$	8890.00			0.783366
$506$		0			0
$507$	760.500	−	1317.22i	0.0666173	−	0.115385i
$508$		0			0
$509$	−1544.50	−	2675.15i	−0.134497	−	0.232955i	0.790908	−	0.611934i	$-0.209608\pi$
$509$	−1544.50	−	2675.15i	−0.134497	−	0.232955i	−0.925405	+	0.378980i	$0.876275\pi$
$510$		0			0
$511$	−1897.00	+	9857.10i	−0.164224	+	0.853332i
$512$		0			0
$513$	270.000	+	467.654i	0.0232374	+	0.0402484i
$514$		0			0
$515$	−6412.00	+	11105.9i	−0.548634	+	0.950262i
$516$		0			0
$517$	−994.000			−0.0845572
$518$		0			0
$519$	−2574.00			−0.217700
$520$		0			0
$521$	−975.000	+	1688.75i	−0.0819876	+	0.142007i	−0.904104	−	0.427313i	$-0.859460\pi$
$521$	−975.000	+	1688.75i	−0.0819876	+	0.142007i	0.822116	+	0.569320i	$0.192793\pi$
$522$		0			0
$523$	−6566.00	−	11372.6i	−0.548970	−	0.950843i	−0.998345	−	0.0575005i	$-0.981687\pi$
$523$	−6566.00	−	11372.6i	−0.548970	−	0.950843i	0.449376	−	0.893343i	$-0.351646\pi$
$524$		0			0
$525$	3192.00	+	2764.35i	0.265353	+	0.229802i
$526$		0			0
$527$	−3420.00	−	5923.61i	−0.282690	−	0.489633i
$528$		0			0
$529$	4931.50	−	8541.61i	0.405318	−	0.702031i
$530$		0			0
$531$	2511.00			0.205213
$532$		0			0
$533$	15392.0			1.25085
$534$		0			0
$535$	3496.50	−	6056.12i	0.282555	−	0.489399i
$536$		0			0
$537$	−3630.00	−	6287.34i	−0.291706	−	0.505249i
$538$		0			0
$539$	343.000	+	2376.37i	0.0274101	+	0.189903i
$540$		0			0
$541$	−1465.00	−	2537.45i	−0.116424	−	0.201652i	0.801924	−	0.597426i	$-0.203810\pi$
$541$	−1465.00	−	2537.45i	−0.116424	−	0.201652i	−0.918348	+	0.395774i	$0.870476\pi$
$542$		0			0
$543$	−4008.00	+	6942.06i	−0.316758	+	0.548641i
$544$		0			0
$545$	−11662.0			−0.916597
$546$		0			0
$547$	19824.0			1.54957			0.774783	−	0.632227i	$-0.217859\pi$
$547$	19824.0			1.54957			0.774783	+	0.632227i	$0.217859\pi$
$548$		0			0
$549$	−1107.00	+	1917.38i	−0.0860576	+	0.149056i
$550$		0			0
$551$	2430.00	+	4208.88i	0.187879	+	0.325416i
$552$		0			0
$553$	−4270.00	−	3697.93i	−0.328352	−	0.284362i
$554$		0			0
$555$	3696.00	+	6401.66i	0.282678	+	0.489613i
$556$		0			0
$557$	9584.50	−	16600.8i	0.729099	−	1.26284i	−0.228165	−	0.973622i	$-0.573273\pi$
$557$	9584.50	−	16600.8i	0.729099	−	1.26284i	0.957264	−	0.289215i	$-0.0933941\pi$
$558$		0			0
$559$	−8216.00			−0.621645
$560$		0			0
$561$	−1512.00			−0.113791
$562$		0			0
$563$	−3633.50	+	6293.41i	−0.271996	+	0.471111i	−0.969373	−	0.245594i	$-0.921017\pi$
$563$	−3633.50	+	6293.41i	−0.271996	+	0.471111i	0.697377	+	0.716705i	$0.254350\pi$
$564$		0			0
$565$	6412.00	+	11105.9i	0.477442	+	0.826954i
$566$		0			0
$567$	283.500	−	1473.11i	0.0209980	−	0.109109i
$568$		0			0
$569$	2446.00	+	4236.60i	0.180214	+	0.312139i	0.941953	−	0.335744i	$-0.108988\pi$
$569$	2446.00	+	4236.60i	0.180214	+	0.312139i	−0.761739	+	0.647883i	$0.775654\pi$
$570$		0			0
$571$	−11063.0	+	19161.7i	−0.810809	+	1.40436i	0.101489	+	0.994837i	$0.467639\pi$
$571$	−11063.0	+	19161.7i	−0.810809	+	1.40436i	−0.912298	+	0.409526i	$0.865694\pi$
$572$		0			0
$573$	5136.00			0.374449
$574$		0			0
$575$	3648.00			0.264578
$576$		0			0
$577$	548.500	−	950.030i	0.0395743	−	0.0685446i	−0.845560	−	0.533881i	$-0.820733\pi$
$577$	548.500	−	950.030i	0.0395743	−	0.0685446i	0.885134	+	0.465336i	$0.154066\pi$
$578$		0			0
$579$	−5092.50	−	8820.47i	−0.365522	−	0.633102i
$580$		0			0
$581$	−19652.5	+	6807.83i	−1.40331	+	0.486121i
$582$		0			0
$583$	1312.50	+	2273.32i	0.0932388	+	0.161494i
$584$		0			0
$585$	1638.00	−	2837.10i	0.115766	−	0.200512i
$586$		0			0
$587$	9969.00			0.700962			0.350481	−	0.936570i	$-0.386018\pi$
$587$	9969.00			0.700962			0.350481	+	0.936570i	$0.386018\pi$
$588$		0			0
$589$	1900.00			0.132917
$590$		0			0
$591$	765.000	−	1325.02i	0.0532452	−	0.0922233i
$592$		0			0
$593$	3212.00	+	5563.35i	0.222430	+	0.385260i	0.955545	−	0.294844i	$-0.0952678\pi$
$593$	3212.00	+	5563.35i	0.222430	+	0.385260i	−0.733115	+	0.680104i	$0.761934\pi$
$594$		0			0
$595$	−8820.00	+	3055.34i	−0.607705	+	0.210515i
$596$		0			0
$597$	414.000	+	717.069i	0.0283817	+	0.0491586i
$598$		0			0
$599$	−8523.00	+	14762.3i	−0.581370	+	1.00696i	0.413948	+	0.910301i	$0.364150\pi$
$599$	−8523.00	+	14762.3i	−0.581370	+	1.00696i	−0.995317	+	0.0966609i	$0.969184\pi$
$600$		0			0
$601$	−18877.0			−1.28121			−0.640606	−	0.767869i	$-0.721317\pi$
$601$	−18877.0			−1.28121			−0.640606	+	0.767869i	$0.721317\pi$
$602$		0			0
$603$	−6570.00			−0.443700
$604$		0			0
$605$	4487.00	−	7771.71i	0.301525	−	0.522256i
$606$		0			0
$607$	6891.50	+	11936.4i	0.460819	+	0.798163i	0.999002	−	0.0446657i	$-0.0142223\pi$
$607$	6891.50	+	11936.4i	0.460819	+	0.798163i	−0.538183	+	0.842828i	$0.680889\pi$
$608$		0			0
$609$	2551.50	−	13258.0i	0.169773	−	0.882168i
$610$		0			0
$611$	−3692.00	−	6394.73i	−0.244456	−	0.423409i
$612$		0			0
$613$	−9096.00	+	15754.7i	−0.599321	+	1.03806i	0.393600	+	0.919282i	$0.371229\pi$
$613$	−9096.00	+	15754.7i	−0.599321	+	1.03806i	−0.992921	+	0.118773i	$0.962104\pi$
$614$		0			0
$615$	6216.00			0.407566
$616$		0			0
$617$	−13054.0			−0.851757			−0.425879	−	0.904780i	$-0.640035\pi$
$617$	−13054.0			−0.851757			−0.425879	+	0.904780i	$0.640035\pi$
$618$		0			0
$619$	−3623.00	+	6275.22i	−0.235251	+	0.407468i	−0.959346	−	0.282234i	$-0.908925\pi$
$619$	−3623.00	+	6275.22i	−0.235251	+	0.407468i	0.724094	+	0.689701i	$0.242258\pi$
$620$		0			0
$621$	−648.000	−	1122.37i	−0.0418733	−	0.0725268i
$622$		0			0
$623$	−5964.00	−	5164.98i	−0.383535	−	0.332151i
$624$		0			0
$625$	174.500	+	302.243i	0.0111680	+	0.0193435i
$626$		0			0
$627$	210.000	−	363.731i	0.0133757	−	0.0231675i
$628$		0			0
$629$	25344.0			1.60657
$630$		0			0
$631$	2817.00			0.177723			0.0888613	−	0.996044i	$-0.471677\pi$
$631$	2817.00			0.177723			0.0888613	+	0.996044i	$0.471677\pi$
$632$		0			0
$633$	4797.00	−	8308.65i	0.301206	−	0.521705i
$634$		0			0
$635$	6758.50	+	11706.1i	0.422367	+	0.731561i
$636$		0			0
$637$	−14014.0	+	11033.2i	−0.871672	+	0.686264i
$638$		0			0
$639$	−1521.00	−	2634.45i	−0.0941625	−	0.163094i
$640$		0			0
$641$	−7893.00	+	13671.1i	−0.486357	+	0.842395i	−0.999877	−	0.0156827i	$-0.995008\pi$
$641$	−7893.00	+	13671.1i	−0.486357	+	0.842395i	0.513520	+	0.858078i	$0.328341\pi$
$642$		0			0
$643$	−17426.0			−1.06876			−0.534381	−	0.845244i	$-0.679455\pi$
$643$	−17426.0			−1.06876			−0.534381	+	0.845244i	$0.679455\pi$
$644$		0			0
$645$	−3318.00			−0.202552
$646$		0			0
$647$	12917.0	−	22372.9i	0.784884	−	1.35946i	−0.144185	−	0.989551i	$-0.546056\pi$
$647$	12917.0	−	22372.9i	0.784884	−	1.35946i	0.929069	−	0.369907i	$-0.120611\pi$
$648$		0			0
$649$	−976.500	−	1691.35i	−0.0590616	−	0.102298i
$650$		0			0
$651$	−3990.00	−	3455.44i	−0.240216	−	0.208033i
$652$		0			0
$653$	−13991.5	−	24234.0i	−0.838483	−	1.45230i	−0.891162	−	0.453684i	$-0.850109\pi$
$653$	−13991.5	−	24234.0i	−0.838483	−	1.45230i	0.0526789	−	0.998612i	$-0.483224\pi$
$654$		0			0
$655$	−3426.50	+	5934.87i	−0.204404	+	0.354038i
$656$		0			0
$657$	−4878.00			−0.289663
$658$		0			0
$659$	−28296.0			−1.67262			−0.836309	−	0.548258i	$-0.815291\pi$
$659$	−28296.0			−1.67262			−0.836309	+	0.548258i	$0.815291\pi$
$660$		0			0
$661$	−10627.0	+	18406.5i	−0.625329	+	1.08310i	0.363148	+	0.931731i	$0.381702\pi$
$661$	−10627.0	+	18406.5i	−0.625329	+	1.08310i	−0.988477	+	0.151370i	$0.951631\pi$
$662$		0			0
$663$	−5616.00	−	9727.20i	−0.328970	−	0.569793i
$664$		0			0
$665$	490.000	−	2546.11i	0.0285735	−	0.148472i
$666$		0			0
$667$	−5832.00	−	10101.3i	−0.338555	−	0.586394i
$668$		0			0
$669$	−7636.50	+	13226.8i	−0.441322	+	0.764391i
$670$		0			0
$671$	1722.00			0.0990716
$672$		0			0
$673$	−28259.0			−1.61858			−0.809290	−	0.587409i	$-0.800148\pi$
$673$	−28259.0			−1.61858			−0.809290	+	0.587409i	$0.800148\pi$
$674$		0			0
$675$	−1026.00	+	1777.08i	−0.0585048	+	0.101333i
$676$		0			0
$677$	−15889.5	−	27521.4i	−0.902043	−	1.56238i	−0.824838	−	0.565369i	$-0.808734\pi$
$677$	−15889.5	−	27521.4i	−0.902043	−	1.56238i	−0.0772049	−	0.997015i	$-0.524600\pi$
$678$		0			0
$679$	6457.50	−	2236.94i	0.364972	−	0.126430i
$680$		0			0
$681$	−5842.50	−	10119.5i	−0.328759	−	0.569428i
$682$		0			0
$683$	4873.50	−	8441.15i	0.273030	−	0.472901i	−0.696606	−	0.717453i	$-0.745308\pi$
$683$	4873.50	−	8441.15i	0.273030	−	0.472901i	0.969636	+	0.244552i	$0.0786409\pi$
$684$		0			0
$685$	−3402.00			−0.189757
$686$		0			0
$687$	19284.0			1.07093
$688$		0			0
$689$	−9750.00	+	16887.5i	−0.539108	+	0.933762i
$690$		0			0
$691$	12256.0	+	21228.0i	0.674733	+	1.16867i	0.976547	+	0.215304i	$0.0690744\pi$
$691$	12256.0	+	21228.0i	0.674733	+	1.16867i	−0.301814	+	0.953367i	$0.597592\pi$
$692$		0			0
$693$	−1102.50	+	381.917i	−0.0604336	+	0.0209348i
$694$		0			0
$695$	9205.00	+	15943.5i	0.502396	+	0.870176i
$696$		0			0
$697$	10656.0	−	18456.7i	0.579089	−	1.00301i
$698$		0			0
$699$	11472.0			0.620760
$700$		0			0
$701$	14325.0			0.771823			0.385911	−	0.922536i	$-0.373887\pi$
$701$	14325.0			0.771823			0.385911	+	0.922536i	$0.373887\pi$
$702$		0			0
$703$	−3520.00	+	6096.82i	−0.188847	+	0.327092i
$704$		0			0
$705$	−1491.00	−	2582.49i	−0.0796515	−	0.137960i
$706$		0			0
$707$	4445.00	−	23096.9i	0.236452	−	1.22864i
$708$		0			0
$709$	−6039.00	−	10459.9i	−0.319886	−	0.554059i	0.660578	−	0.750758i	$-0.270311\pi$
$709$	−6039.00	−	10459.9i	−0.319886	−	0.554059i	−0.980464	+	0.196698i	$0.936978\pi$
$710$		0			0
$711$	1372.50	−	2377.24i	0.0723949	−	0.125392i
$712$		0			0
$713$	−4560.00			−0.239514
$714$		0			0
$715$	−2548.00			−0.133272
$716$		0			0
$717$	852.000	−	1475.71i	0.0443773	−	0.0768637i
$718$		0			0
$719$	5329.00	+	9230.10i	0.276409	+	0.478755i	0.970490	−	0.241143i	$-0.0775222\pi$
$719$	5329.00	+	9230.10i	0.276409	+	0.478755i	−0.694081	+	0.719897i	$0.744189\pi$
$720$		0			0
$721$	25648.0	+	22211.8i	1.32480	+	1.14731i
$722$		0			0
$723$	5302.50	+	9184.20i	0.272755	+	0.472426i
$724$		0			0
$725$	−9234.00	+	15993.8i	−0.473024	+	0.819301i
$726$		0			0
$727$	19099.0			0.974337			0.487168	−	0.873308i	$-0.338030\pi$
$727$	19099.0			0.974337			0.487168	+	0.873308i	$0.338030\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−5688.00	+	9851.90i	−0.287795	+	0.498476i
$732$		0			0
$733$	−703.000	−	1217.63i	−0.0354241	−	0.0613564i	0.847770	−	0.530364i	$-0.177945\pi$
$733$	−703.000	−	1217.63i	−0.0354241	−	0.0613564i	−0.883194	+	0.469008i	$0.844612\pi$
$734$		0			0
$735$	−5659.50	+	4455.70i	−0.284019	+	0.223607i
$736$		0			0
$737$	2555.00	+	4425.39i	0.127700	+	0.221182i
$738$		0			0
$739$	−3365.00	+	5828.35i	−0.167501	+	0.290121i	−0.937541	−	0.347875i	$-0.886903\pi$
$739$	−3365.00	+	5828.35i	−0.167501	+	0.290121i	0.770039	+	0.637996i	$0.220237\pi$
$740$		0			0
$741$	3120.00			0.154678
$742$		0			0
$743$	−1166.00			−0.0575725			−0.0287863	−	0.999586i	$-0.509164\pi$
$743$	−1166.00			−0.0575725			−0.0287863	+	0.999586i	$0.509164\pi$
$744$		0			0
$745$	6573.00	−	11384.8i	0.323243	−	0.559873i
$746$		0			0
$747$	−5053.50	−	8752.92i	−0.247521	−	0.428718i
$748$		0			0
$749$	−13986.0	−	12112.2i	−0.682293	−	0.590883i
$750$		0			0
$751$	8483.50	+	14693.9i	0.412207	+	0.713963i	0.995131	−	0.0985636i	$-0.0314248\pi$
$751$	8483.50	+	14693.9i	0.412207	+	0.713963i	−0.582924	+	0.812527i	$0.698091\pi$
$752$		0			0
$753$	6502.50	−	11262.7i	0.314694	−	0.545065i
$754$		0			0
$755$	14721.0			0.709605
$756$		0			0
$757$	11878.0			0.570295			0.285147	−	0.958484i	$-0.407957\pi$
$757$	11878.0			0.570295			0.285147	+	0.958484i	$0.407957\pi$
$758$		0			0
$759$	−504.000	+	872.954i	−0.0241028	+	0.0417473i
$760$		0			0
$761$	−13662.0	−	23663.3i	−0.650785	−	1.12719i	−0.982933	−	0.183965i	$-0.941107\pi$
$761$	−13662.0	−	23663.3i	−0.650785	−	1.12719i	0.332148	−	0.943227i	$-0.392227\pi$
$762$		0			0
$763$	−5831.00	+	30298.8i	−0.276666	+	1.43760i
$764$		0			0
$765$	−2268.00	−	3928.29i	−0.107189	−	0.185657i
$766$		0			0
$767$	7254.00	−	12564.3i	0.341495	−	0.591487i
$768$		0			0
$769$	−11971.0			−0.561359			−0.280680	−	0.959802i	$-0.590560\pi$
$769$	−11971.0			−0.561359			−0.280680	+	0.959802i	$0.590560\pi$
$770$		0			0
$771$	−10722.0			−0.500834
$772$		0			0
$773$	169.000	−	292.717i	0.00786353	−	0.0136200i	−0.862067	−	0.506795i	$-0.830830\pi$
$773$	169.000	−	292.717i	0.00786353	−	0.0136200i	0.869930	+	0.493175i	$0.164164\pi$
$774$		0			0
$775$	3610.00	+	6252.70i	0.167323	+	0.289811i
$776$		0			0
$777$	18480.0	−	6401.66i	0.853238	−	0.295570i
$778$		0			0
$779$	2960.00	+	5126.87i	0.136140	+	0.235801i
$780$		0			0
$781$	−1183.00	+	2049.02i	−0.0542011	+	0.0938791i
$782$		0			0
$783$	6561.00			0.299452
$784$		0			0
$785$	9828.00			0.446849
$786$		0			0
$787$	−7057.00	+	12223.1i	−0.319638	+	0.553629i	−0.980412	−	0.196956i	$-0.936895\pi$
$787$	−7057.00	+	12223.1i	−0.319638	+	0.553629i	0.660775	+	0.750584i	$0.270228\pi$
$788$		0			0
$789$	8199.00	+	14201.1i	0.369952	+	0.640776i
$790$		0			0
$791$	32060.0	−	11105.9i	1.44112	−	0.499217i
$792$		0			0
$793$	6396.00	+	11078.2i	0.286417	+	0.496089i
$794$		0			0
$795$	−3937.50	+	6819.95i	−0.175659	+	0.304250i
$796$		0			0
$797$	1563.00			0.0694659			0.0347329	−	0.999397i	$-0.488942\pi$
$797$	1563.00			0.0694659			0.0347329	+	0.999397i	$0.488942\pi$
$798$		0			0
$799$	−10224.0			−0.452690
$800$		0			0
$801$	1917.00	−	3320.34i	0.0845616	−	0.146465i
$802$		0			0
$803$	1897.00	+	3285.70i	0.0833670	+	0.144396i
$804$		0			0
$805$	−1176.00	+	6110.68i	−0.0514889	+	0.267544i
$806$		0			0
$807$	−8722.50	−	15107.8i	−0.380479	−	0.659009i
$808$		0			0
$809$	15784.0	−	27338.7i	0.685953	−	1.18811i	−0.287183	−	0.957876i	$-0.592719\pi$
$809$	15784.0	−	27338.7i	0.685953	−	1.18811i	0.973136	−	0.230230i	$-0.0739477\pi$
$810$		0			0
$811$	2626.00			0.113701			0.0568504	−	0.998383i	$-0.481894\pi$
$811$	2626.00			0.113701			0.0568504	+	0.998383i	$0.481894\pi$
$812$		0			0
$813$	9711.00			0.418917
$814$		0			0
$815$	5376.00	−	9311.51i	0.231059	−	0.400206i
$816$		0			0
$817$	−1580.00	−	2736.64i	−0.0676588	−	0.117188i
$818$		0			0
$819$	−6552.00	−	5674.20i	−0.279543	−	0.242091i
$820$		0			0
$821$	−180.500	−	312.635i	−0.00767295	−	0.0132899i	0.862163	−	0.506630i	$-0.169109\pi$
$821$	−180.500	−	312.635i	−0.00767295	−	0.0132899i	−0.869836	+	0.493340i	$0.835776\pi$
$822$		0			0
$823$	14772.0	−	25585.9i	0.625662	−	1.08368i	−0.362751	−	0.931886i	$-0.618162\pi$
$823$	14772.0	−	25585.9i	0.625662	−	1.08368i	0.988413	−	0.151792i	$-0.0485043\pi$
$824$		0			0
$825$	1596.00			0.0673522
$826$		0			0
$827$	24163.0			1.01600			0.507999	−	0.861358i	$-0.330385\pi$
$827$	24163.0			1.01600			0.507999	+	0.861358i	$0.330385\pi$
$828$		0			0
$829$	19598.0	−	33944.7i	0.821070	−	1.42213i	−0.0838169	−	0.996481i	$-0.526711\pi$
$829$	19598.0	−	33944.7i	0.821070	−	1.42213i	0.904886	−	0.425653i	$-0.139956\pi$
$830$		0			0
$831$	−4764.00	−	8251.49i	−0.198870	−	0.344454i
$832$		0			0
$833$	3528.00	+	24442.7i	0.146744	+	1.01667i
$834$		0			0
$835$	12719.0	+	22030.0i	0.527137	+	0.913028i
$836$		0			0
$837$	1282.50	−	2221.36i	0.0529626	−	0.0917339i
$838$		0			0
$839$	6528.00			0.268619			0.134310	−	0.990939i	$-0.457118\pi$
$839$	6528.00			0.268619			0.134310	+	0.990939i	$0.457118\pi$
$840$		0			0
$841$	34660.0			1.42113
$842$		0			0
$843$	−4923.00	+	8526.89i	−0.201135	+	0.348377i
$844$		0			0
$845$	−1774.50	−	3073.52i	−0.0722422	−	0.125127i
$846$		0			0
$847$	−17948.0	−	15543.4i	−0.728100	−	0.630553i
$848$		0			0
$849$	3273.00	+	5669.00i	0.132308	+	0.229163i
$850$		0			0
$851$	8448.00	−	14632.4i	0.340298	−	0.589414i
$852$		0			0
$853$	1046.00			0.0419864			0.0209932	−	0.999780i	$-0.493317\pi$
$853$	1046.00			0.0419864			0.0209932	+	0.999780i	$0.493317\pi$
$854$		0			0
$855$	1260.00			0.0503989
$856$		0			0
$857$	−16455.0	+	28500.9i	−0.655883	+	1.13602i	0.325788	+	0.945443i	$0.394370\pi$
$857$	−16455.0	+	28500.9i	−0.655883	+	1.13602i	−0.981672	+	0.190581i	$0.938963\pi$
$858$		0			0
$859$	−11341.0	−	19643.2i	−0.450466	−	0.780229i	0.547949	−	0.836512i	$-0.315409\pi$
$859$	−11341.0	−	19643.2i	−0.450466	−	0.780229i	−0.998415	+	0.0562823i	$0.982075\pi$
$860$		0			0
$861$	3108.00	−	16149.6i	0.123020	−	0.639231i
$862$		0			0
$863$	3725.00	+	6451.89i	0.146930	+	0.254490i	0.930091	−	0.367328i	$-0.119728\pi$
$863$	3725.00	+	6451.89i	0.146930	+	0.254490i	−0.783161	+	0.621818i	$0.786394\pi$
$864$		0			0
$865$	−3003.00	+	5201.35i	−0.118041	+	0.204452i
$866$		0			0
$867$	−813.000			−0.0318465
$868$		0			0
$869$	−2135.00			−0.0833428
$870$		0			0
$871$	−18980.0	+	32874.3i	−0.738361	+	1.27888i
$872$		0			0
$873$	1660.50	+	2876.07i	0.0643750	+	0.111501i
$874$		0			0
$875$	24622.5	−	8529.48i	0.951306	−	0.329542i
$876$		0			0
$877$	−5040.00	−	8729.54i	−0.194058	−	0.336118i	0.752533	−	0.658554i	$-0.228832\pi$
$877$	−5040.00	−	8729.54i	−0.194058	−	0.336118i	−0.946591	+	0.322436i	$0.895498\pi$
$878$		0			0
$879$	4531.50	−	7848.79i	0.173884	−	0.301175i
$880$		0			0
$881$	−32958.0			−1.26037			−0.630183	−	0.776446i	$-0.717020\pi$
$881$	−32958.0			−1.26037			−0.630183	+	0.776446i	$0.717020\pi$
$882$		0			0
$883$	−19784.0			−0.754003			−0.377001	−	0.926213i	$-0.623045\pi$
$883$	−19784.0			−0.754003			−0.377001	+	0.926213i	$0.623045\pi$
$884$		0			0
$885$	2929.50	−	5074.04i	0.111270	−	0.192726i
$886$		0			0
$887$	5740.00	+	9941.97i	0.217283	+	0.376346i	0.953976	−	0.299881i	$-0.0969471\pi$
$887$	5740.00	+	9941.97i	0.217283	+	0.376346i	−0.736693	+	0.676227i	$0.763614\pi$
$888$		0			0
$889$	33792.5	−	11706.1i	1.27488	−	0.441630i
$890$		0			0
$891$	−283.500	−	491.036i	−0.0106595	−	0.0184628i
$892$		0			0
$893$	1420.00	−	2459.51i	0.0532122	−	0.0921662i
$894$		0			0
$895$	−16940.0			−0.632672
$896$		0			0
$897$	−7488.00			−0.278726
$898$		0			0
$899$	11542.5	−	19992.2i	0.428213	−	0.741688i
$900$		0			0
$901$	13500.0	+	23382.7i	0.499168	+	0.864584i
$902$		0			0
$903$	−1659.00	+	8620.42i	−0.0611385	+	0.317685i
$904$		0			0
$905$	9352.00	+	16198.1i	0.343504	+	0.594966i
$906$		0			0
$907$	22676.0	−	39276.0i	0.830148	−	1.43786i	−0.0677725	−	0.997701i	$-0.521589\pi$
$907$	22676.0	−	39276.0i	0.830148	−	1.43786i	0.897920	−	0.440158i	$-0.145077\pi$
$908$		0			0
$909$	11430.0			0.417062
$910$		0			0
$911$	−39906.0			−1.45131			−0.725656	−	0.688058i	$-0.758463\pi$
$911$	−39906.0			−1.45131			−0.725656	+	0.688058i	$0.758463\pi$
$912$		0			0
$913$	−3930.50	+	6807.83i	−0.142476	+	0.246776i
$914$		0			0
$915$	2583.00	+	4473.89i	0.0933239	+	0.161642i
$916$		0			0
$917$	13706.0	+	11869.7i	0.493579	+	0.427452i
$918$		0			0
$919$	−8764.00	−	15179.7i	−0.314579	−	0.544866i	0.664769	−	0.747049i	$-0.268530\pi$
$919$	−8764.00	−	15179.7i	−0.314579	−	0.544866i	−0.979348	+	0.202183i	$0.935197\pi$
$920$		0			0
$921$	−1956.00	+	3387.89i	−0.0699809	+	0.121210i
$922$		0			0
$923$	−17576.0			−0.626783
$924$		0			0
$925$	−26752.0			−0.950919
$926$		0			0
$927$	−8244.00	+	14279.0i	−0.292091	+	0.505917i
$928$		0			0
$929$	−8533.00	−	14779.6i	−0.301355	−	0.521962i	0.675088	−	0.737737i	$-0.264106\pi$
$929$	−8533.00	−	14779.6i	−0.301355	−	0.521962i	−0.976443	+	0.215775i	$0.930772\pi$
$930$		0			0
$931$	−6370.00	−	2546.11i	−0.224241	−	0.0896300i
$932$		0			0
$933$	9312.00	+	16128.9i	0.326754	+	0.565954i
$934$		0			0
$935$	−1764.00	+	3055.34i	−0.0616994	+	0.106867i
$936$		0			0
$937$	−30821.0			−1.07458			−0.537288	−	0.843399i	$-0.680551\pi$
$937$	−30821.0			−1.07458			−0.537288	+	0.843399i	$0.680551\pi$
$938$		0			0
$939$	−10011.0			−0.347920
$940$		0			0
$941$	−2089.50	+	3619.12i	−0.0723866	+	0.125377i	−0.899947	−	0.436000i	$-0.856395\pi$
$941$	−2089.50	+	3619.12i	−0.0723866	+	0.125377i	0.827560	+	0.561377i	$0.189728\pi$
$942$		0			0
$943$	−7104.00	−	12304.5i	−0.245321	−	0.424909i
$944$		0			0
$945$	−2646.00	−	2291.50i	−0.0910840	−	0.0788811i
$946$		0			0
$947$	−4888.00	−	8466.26i	−0.167728	−	0.290514i	0.769893	−	0.638174i	$-0.220310\pi$
$947$	−4888.00	−	8466.26i	−0.167728	−	0.290514i	−0.937621	+	0.347660i	$0.886976\pi$
$948$		0			0
$949$	−14092.0	+	24408.1i	−0.482029	+	0.834899i
$950$		0			0
$951$	−25911.0			−0.883514
$952$		0			0
$953$	14778.0			0.502315			0.251158	−	0.967946i	$-0.419189\pi$
$953$	14778.0			0.502315			0.251158	+	0.967946i	$0.419189\pi$
$954$		0			0
$955$	5992.00	−	10378.4i	0.203033	−	0.351664i
$956$		0			0
$957$	−2551.50	−	4419.33i	−0.0861842	−	0.149275i
$958$		0			0
$959$	−1701.00	+	8838.66i	−0.0572765	+	0.297617i
$960$		0			0
$961$	10383.0	+	17983.9i	0.348528	+	0.603668i
$962$		0			0
$963$	4495.50	−	7786.43i	0.150431	−	0.260555i
$964$		0			0
$965$	−23765.0			−0.792769
$966$		0			0
$967$	8759.00			0.291283			0.145641	−	0.989337i	$-0.453475\pi$
$967$	8759.00			0.291283			0.145641	+	0.989337i	$0.453475\pi$
$968$		0			0
$969$	2160.00	−	3741.23i	0.0716091	−	0.124031i
$970$		0			0
$971$	16789.5	+	29080.3i	0.554893	+	0.961102i	0.997912	+	0.0645901i	$0.0205740\pi$
$971$	16789.5	+	29080.3i	0.554893	+	0.961102i	−0.443019	+	0.896512i	$0.646093\pi$
$972$		0			0
$973$	46025.0	−	15943.5i	1.51644	−	0.525309i
$974$		0			0
$975$	5928.00	+	10267.6i	0.194716	+	0.337258i
$976$		0			0
$977$	−21317.0	+	36922.1i	−0.698046	+	1.20905i	0.271097	+	0.962552i	$0.412614\pi$
$977$	−21317.0	+	36922.1i	−0.698046	+	1.20905i	−0.969143	+	0.246500i	$0.920720\pi$
$978$		0			0
$979$	−2982.00			−0.0973495
$980$		0			0
$981$	−14994.0			−0.487993
$982$		0			0
$983$	−14574.0	+	25242.9i	−0.472877	+	0.819048i	−0.999518	−	0.0310404i	$-0.990118\pi$
$983$	−14574.0	+	25242.9i	−0.472877	+	0.819048i	0.526641	+	0.850088i	$0.323451\pi$
$984$		0			0
$985$	−1785.00	−	3091.71i	−0.0577409	−	0.100010i
$986$		0			0
$987$	−7455.00	+	2582.49i	−0.240421	+	0.0832842i
$988$		0			0
$989$	3792.00	+	6567.94i	0.121920	+	0.211171i
$990$		0			0
$991$	22398.5	−	38795.3i	0.717974	−	1.24357i	−0.243828	−	0.969819i	$-0.578403\pi$
$991$	22398.5	−	38795.3i	0.717974	−	1.24357i	0.961801	−	0.273748i	$-0.0882635\pi$
$992$		0			0
$993$	−5820.00			−0.185994
$994$		0			0
$995$	1932.00			0.0615563
$996$		0			0
$997$	−5327.00	+	9226.63i	−0.169215	+	0.293090i	−0.938144	−	0.346245i	$-0.887457\pi$
$997$	−5327.00	+	9226.63i	−0.169215	+	0.293090i	0.768929	+	0.639334i	$0.220790\pi$
$998$		0			0
$999$	4752.00	+	8230.71i	0.150497	+	0.260669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.q.a.25.1	✓	2
3.2	odd	2		504.4.s.e.361.1		2
4.3	odd	2		336.4.q.a.193.1		2
7.2	even	3	inner	168.4.q.a.121.1	yes	2
7.3	odd	6		1176.4.a.i.1.1		1
7.4	even	3		1176.4.a.f.1.1		1
21.2	odd	6		504.4.s.e.289.1		2
28.3	even	6		2352.4.a.c.1.1		1
28.11	odd	6		2352.4.a.bg.1.1		1
28.23	odd	6		336.4.q.a.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.q.a.25.1	✓	2	1.1	even	1	trivial
168.4.q.a.121.1	yes	2	7.2	even	3	inner
336.4.q.a.193.1		2	4.3	odd	2
336.4.q.a.289.1		2	28.23	odd	6
504.4.s.e.289.1		2	21.2	odd	6
504.4.s.e.361.1		2	3.2	odd	2
1176.4.a.f.1.1		1	7.4	even	3
1176.4.a.i.1.1		1	7.3	odd	6
2352.4.a.c.1.1		1	28.3	even	6
2352.4.a.bg.1.1		1	28.11	odd	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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{3} +(-3.50000 - 6.06218i) q^{5} +(-17.5000 + 6.06218i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 2.59808i) q^{3} +(-3.50000 - 6.06218i) q^{5} +(-17.5000 + 6.06218i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(-3.50000 + 6.06218i) q^{11} -52.0000 q^{13} -21.0000 q^{15} +(-36.0000 + 62.3538i) q^{17} +(-10.0000 - 17.3205i) q^{19} +(-10.5000 + 54.5596i) q^{21} +(24.0000 + 41.5692i) q^{23} +(38.0000 - 65.8179i) q^{25} -27.0000 q^{27} -243.000 q^{29} +(-47.5000 + 82.2724i) q^{31} +(10.5000 + 18.1865i) q^{33} +(98.0000 + 84.8705i) q^{35} +(-176.000 - 304.841i) q^{37} +(-78.0000 + 135.100i) q^{39} -296.000 q^{41} +158.000 q^{43} +(-31.5000 + 54.5596i) q^{45} +(71.0000 + 122.976i) q^{47} +(269.500 - 212.176i) q^{49} +(108.000 + 187.061i) q^{51} +(187.500 - 324.760i) q^{53} +49.0000 q^{55} -60.0000 q^{57} +(-139.500 + 241.621i) q^{59} +(-123.000 - 213.042i) q^{61} +(126.000 + 109.119i) q^{63} +(182.000 + 315.233i) q^{65} +(365.000 - 632.199i) q^{67} +144.000 q^{69} +338.000 q^{71} +(271.000 - 469.386i) q^{73} +(-114.000 - 197.454i) q^{75} +(24.5000 - 127.306i) q^{77} +(152.500 + 264.138i) q^{79} +(-40.5000 + 70.1481i) q^{81} +1123.00 q^{83} +504.000 q^{85} +(-364.500 + 631.333i) q^{87} +(213.000 + 368.927i) q^{89} +(910.000 - 315.233i) q^{91} +(142.500 + 246.817i) q^{93} +(-70.0000 + 121.244i) q^{95} -369.000 q^{97} +63.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} - 7 q^{5} - 35 q^{7} - 9 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 - 7 * q^5 - 35 * q^7 - 9 * q^9	\( 2 q + 3 q^{3} - 7 q^{5} - 35 q^{7} - 9 q^{9} - 7 q^{11} - 104 q^{13} - 42 q^{15} - 72 q^{17} - 20 q^{19} - 21 q^{21} + 48 q^{23} + 76 q^{25} - 54 q^{27} - 486 q^{29} - 95 q^{31} + 21 q^{33} + 196 q^{35} - 352 q^{37} - 156 q^{39} - 592 q^{41} + 316 q^{43} - 63 q^{45} + 142 q^{47} + 539 q^{49} + 216 q^{51} + 375 q^{53} + 98 q^{55} - 120 q^{57} - 279 q^{59} - 246 q^{61} + 252 q^{63} + 364 q^{65} + 730 q^{67} + 288 q^{69} + 676 q^{71} + 542 q^{73} - 228 q^{75} + 49 q^{77} + 305 q^{79} - 81 q^{81} + 2246 q^{83} + 1008 q^{85} - 729 q^{87} + 426 q^{89} + 1820 q^{91} + 285 q^{93} - 140 q^{95} - 738 q^{97} + 126 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 - 7 * q^5 - 35 * q^7 - 9 * q^9 - 7 * q^11 - 104 * q^13 - 42 * q^15 - 72 * q^17 - 20 * q^19 - 21 * q^21 + 48 * q^23 + 76 * q^25 - 54 * q^27 - 486 * q^29 - 95 * q^31 + 21 * q^33 + 196 * q^35 - 352 * q^37 - 156 * q^39 - 592 * q^41 + 316 * q^43 - 63 * q^45 + 142 * q^47 + 539 * q^49 + 216 * q^51 + 375 * q^53 + 98 * q^55 - 120 * q^57 - 279 * q^59 - 246 * q^61 + 252 * q^63 + 364 * q^65 + 730 * q^67 + 288 * q^69 + 676 * q^71 + 542 * q^73 - 228 * q^75 + 49 * q^77 + 305 * q^79 - 81 * q^81 + 2246 * q^83 + 1008 * q^85 - 729 * q^87 + 426 * q^89 + 1820 * q^91 + 285 * q^93 - 140 * q^95 - 738 * q^97 + 126 * q^99

Introduction

L-functions

Modular forms

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Database

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