LMFDB - Embedded newform 336.4.bl.j.31.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,4,Mod(31,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.31"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bl (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,12,0,18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 23x^{6} + 48x^{5} + 422x^{4} + 384x^{3} + 1247x^{2} - 637x + 2401 $ x^8 - x^7 + 23x^6 + 48x^5 + 422x^4 + 384x^3 + 1247x^2 - 637x + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.3
Root			$2.64566 + 4.58242i$ of defining polynomial
Character	$\chi$	$=$	336.31
Dual form			336.4.bl.j.271.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 - 2.59808i) q^{3} +(11.0480 - 6.37855i) q^{5} +(17.4241 + 6.27712i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(37.8201 + 21.8355i) q^{11} +83.9138i q^{13} -38.2713i q^{15} +(71.7005 + 41.3963i) q^{17} +(-38.8686 - 67.3223i) q^{19} +(42.4445 - 35.8534i) q^{21} +(-3.93978 + 2.27463i) q^{23} +(18.8717 - 32.6868i) q^{25} -27.0000 q^{27} -120.805 q^{29} +(15.9132 - 27.5625i) q^{31} +(113.460 - 65.5064i) q^{33} +(232.539 - 41.7908i) q^{35} +(38.1272 + 66.0382i) q^{37} +(218.015 + 125.871i) q^{39} +264.843i q^{41} -391.848i q^{43} +(-99.4317 - 57.4069i) q^{45} +(-147.029 - 254.662i) q^{47} +(264.196 + 218.746i) q^{49} +(215.101 - 124.189i) q^{51} +(192.305 - 333.081i) q^{53} +557.114 q^{55} -233.211 q^{57} +(370.142 - 641.105i) q^{59} +(-179.037 + 103.367i) q^{61} +(-29.4830 - 164.054i) q^{63} +(535.248 + 927.077i) q^{65} +(172.423 + 99.5486i) q^{67} +13.6478i q^{69} +508.919i q^{71} +(-936.719 - 540.815i) q^{73} +(-56.6152 - 98.0604i) q^{75} +(521.917 + 617.864i) q^{77} +(1105.44 - 638.226i) q^{79} +(-40.5000 + 70.1481i) q^{81} -966.467 q^{83} +1056.19 q^{85} +(-181.208 + 313.861i) q^{87} +(-626.787 + 361.876i) q^{89} +(-526.737 + 1462.12i) q^{91} +(-47.7396 - 82.6875i) q^{93} +(-858.838 - 495.850i) q^{95} -1763.41i q^{97} -393.038i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{3} + 18 q^{5} + 12 q^{7} - 36 q^{9} - 150 q^{11} + 192 q^{17} + 66 q^{19} + 90 q^{21} + 492 q^{23} + 322 q^{25} - 216 q^{27} - 372 q^{29} - 156 q^{31} - 450 q^{33} - 36 q^{35} + 554 q^{37} + 198 q^{39}+ \cdots - 108 q^{95}+O(q^{100}) $ 8 * q + 12 * q^3 + 18 * q^5 + 12 * q^7 - 36 * q^9 - 150 * q^11 + 192 * q^17 + 66 * q^19 + 90 * q^21 + 492 * q^23 + 322 * q^25 - 216 * q^27 - 372 * q^29 - 156 * q^31 - 450 * q^33 - 36 * q^35 + 554 * q^37 + 198 * q^39 - 162 * q^45 - 840 * q^47 - 340 * q^49 + 576 * q^51 + 186 * q^53 - 156 * q^55 + 396 * q^57 + 126 * q^59 + 1632 * q^61 + 162 * q^63 + 936 * q^65 - 582 * q^67 - 1386 * q^73 - 966 * q^75 + 3030 * q^77 + 1260 * q^79 - 324 * q^81 - 756 * q^83 - 5688 * q^85 - 558 * q^87 + 948 * q^89 + 4074 * q^91 + 468 * q^93 - 108 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$		0			0
$5$	11.0480	−	6.37855i	0.988160	−	0.570515i	0.0834364	−	0.996513i	$-0.473410\pi$
$5$	11.0480	−	6.37855i	0.988160	−	0.570515i	0.904724	+	0.425998i	$0.140077\pi$
$6$		0			0
$7$	17.4241	+	6.27712i	0.940811	+	0.338933i
$7$	17.4241	+	6.27712i	0.940811	+	0.338933i
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$		0			0
$11$	37.8201	+	21.8355i	1.03665	+	0.598513i	0.918884	−	0.394528i	$-0.129092\pi$
$11$	37.8201	+	21.8355i	1.03665	+	0.598513i	0.117771	+	0.993041i	$0.462425\pi$
$12$		0			0
$13$			83.9138i			1.79027i	0.445795	+	0.895135i	$0.352921\pi$
$13$			83.9138i			1.79027i	−0.445795	+	0.895135i	$0.647079\pi$
$14$		0			0
$15$		−	38.2713i		−	0.658774i
$16$		0			0
$17$	71.7005	+	41.3963i	1.02294	+	0.590593i	0.914953	−	0.403560i	$-0.132227\pi$
$17$	71.7005	+	41.3963i	1.02294	+	0.590593i	0.107984	+	0.994153i	$0.465561\pi$
$18$		0			0
$19$	−38.8686	−	67.3223i	−0.469319	−	0.812885i	0.530066	−	0.847957i	$-0.322167\pi$
$19$	−38.8686	−	67.3223i	−0.469319	−	0.812885i	−0.999385	+	0.0350721i	$0.988834\pi$
$20$		0			0
$21$	42.4445	−	35.8534i	0.441055	−	0.372564i
$22$		0			0
$23$	−3.93978	+	2.27463i	−0.0357175	+	0.0206215i	−0.517752	−	0.855531i	$-0.673231\pi$
$23$	−3.93978	+	2.27463i	−0.0357175	+	0.0206215i	0.482035	+	0.876152i	$0.339898\pi$
$24$		0			0
$25$	18.8717	−	32.6868i	0.150974	−	0.261494i
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	−120.805			−0.773551			−0.386776	−	0.922174i	$-0.626411\pi$
$29$	−120.805			−0.773551			−0.386776	+	0.922174i	$0.626411\pi$
$30$		0			0
$31$	15.9132	−	27.5625i	0.0921967	−	0.159689i	−0.816239	−	0.577715i	$-0.803944\pi$
$31$	15.9132	−	27.5625i	0.0921967	−	0.159689i	0.908435	+	0.418026i	$0.137278\pi$
$32$		0			0
$33$	113.460	−	65.5064i	0.598513	−	0.345552i
$34$		0			0
$35$	232.539	−	41.7908i	1.12304	−	0.201827i
$36$		0			0
$37$	38.1272	+	66.0382i	0.169407	+	0.293422i	0.938212	−	0.346062i	$-0.112481\pi$
$37$	38.1272	+	66.0382i	0.169407	+	0.293422i	−0.768804	+	0.639484i	$0.779148\pi$
$38$		0			0
$39$	218.015	+	125.871i	0.895135	+	0.516806i
$40$		0			0
$41$			264.843i			1.00882i	0.863465	+	0.504408i	$0.168289\pi$
$41$			264.843i			1.00882i	−0.863465	+	0.504408i	$0.831711\pi$
$42$		0			0
$43$		−	391.848i		−	1.38968i	−0.719164	−	0.694840i	$-0.755475\pi$
$43$		−	391.848i		−	1.38968i	0.719164	−	0.694840i	$-0.244525\pi$
$44$		0			0
$45$	−99.4317	−	57.4069i	−0.329387	−	0.190172i
$46$		0			0
$47$	−147.029	−	254.662i	−0.456306	−	0.790345i	0.542456	−	0.840084i	$-0.317494\pi$
$47$	−147.029	−	254.662i	−0.456306	−	0.790345i	−0.998762	+	0.0497387i	$0.984161\pi$
$48$		0			0
$49$	264.196	+	218.746i	0.770249	+	0.637743i
$50$		0			0
$51$	215.101	−	124.189i	0.590593	−	0.340979i
$52$		0			0
$53$	192.305	−	333.081i	0.498398	−	0.863250i	−0.501601	−	0.865099i	$-0.667255\pi$
$53$	192.305	−	333.081i	0.498398	−	0.863250i	0.999998	+	0.00184939i	$0.000588679\pi$
$54$		0			0
$55$	557.114			1.36584
$56$		0			0
$57$	−233.211			−0.541923
$58$		0			0
$59$	370.142	−	641.105i	0.816752	−	1.41466i	−0.0913106	−	0.995822i	$-0.529106\pi$
$59$	370.142	−	641.105i	0.816752	−	1.41466i	0.908063	−	0.418834i	$-0.137561\pi$
$60$		0			0
$61$	−179.037	+	103.367i	−0.375793	+	0.216964i	−0.675986	−	0.736914i	$-0.736282\pi$
$61$	−179.037	+	103.367i	−0.375793	+	0.216964i	0.300193	+	0.953878i	$0.402949\pi$
$62$		0			0
$63$	−29.4830	−	164.054i	−0.0589604	−	0.328077i
$64$		0			0
$65$	535.248	+	927.077i	1.02138	+	1.76907i
$66$		0			0
$67$	172.423	+	99.5486i	0.314401	+	0.181519i	0.648894	−	0.760879i	$-0.275232\pi$
$67$	172.423	+	99.5486i	0.314401	+	0.181519i	−0.334493	+	0.942398i	$0.608565\pi$
$68$		0			0
$69$			13.6478i			0.0238116i
$70$		0			0
$71$			508.919i			0.850670i	0.905036	+	0.425335i	$0.139844\pi$
$71$			508.919i			0.850670i	−0.905036	+	0.425335i	$0.860156\pi$
$72$		0			0
$73$	−936.719	−	540.815i	−1.50184	−	0.867091i	−0.999998	−	0.00213422i	$-0.999321\pi$
$73$	−936.719	−	540.815i	−1.50184	−	0.867091i	−0.501847	−	0.864956i	$-0.667346\pi$
$74$		0			0
$75$	−56.6152	−	98.0604i	−0.0871648	−	0.150974i
$76$		0			0
$77$	521.917	+	617.864i	0.772440	+	0.914443i
$78$		0			0
$79$	1105.44	−	638.226i	1.57433	−	0.908937i	0.578696	−	0.815543i	$-0.303562\pi$
$79$	1105.44	−	638.226i	1.57433	−	0.908937i	0.995629	−	0.0933936i	$-0.0297715\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−966.467			−1.27811			−0.639057	−	0.769159i	$-0.720675\pi$
$83$	−966.467			−1.27811			−0.639057	+	0.769159i	$0.720675\pi$
$84$		0			0
$85$	1056.19			1.34777
$86$		0			0
$87$	−181.208	+	313.861i	−0.223305	+	0.386776i
$88$		0			0
$89$	−626.787	+	361.876i	−0.746509	+	0.430997i	−0.824431	−	0.565962i	$-0.808505\pi$
$89$	−626.787	+	361.876i	−0.746509	+	0.430997i	0.0779219	+	0.996959i	$0.475172\pi$
$90$		0			0
$91$	−526.737	+	1462.12i	−0.606781	+	1.68430i
$92$		0			0
$93$	−47.7396	−	82.6875i	−0.0532298	−	0.0921967i
$94$		0			0
$95$	−858.838	−	495.850i	−0.927525	−	0.535507i
$96$		0			0
$97$		−	1763.41i		−	1.84584i	−0.384986	−	0.922922i	$-0.625794\pi$
$97$		−	1763.41i		−	1.84584i	0.384986	−	0.922922i	$-0.374206\pi$
$98$		0			0
$99$		−	393.038i		−	0.399009i
$100$		0			0
$101$	838.138	+	483.899i	0.825721	+	0.476730i	0.852385	−	0.522914i	$-0.175155\pi$
$101$	838.138	+	483.899i	0.825721	+	0.476730i	−0.0266642	+	0.999644i	$0.508488\pi$
$102$		0			0
$103$	−133.523	−	231.269i	−0.127733	−	0.221239i	0.795065	−	0.606524i	$-0.207437\pi$
$103$	−133.523	−	231.269i	−0.127733	−	0.221239i	−0.922798	+	0.385285i	$0.874103\pi$
$104$		0			0
$105$	240.233	−	666.841i	0.223280	−	0.619781i
$106$		0			0
$107$	−1182.50	+	682.719i	−1.06838	+	0.616832i	−0.927739	−	0.373229i	$-0.878251\pi$
$107$	−1182.50	+	682.719i	−1.06838	+	0.616832i	−0.140644	+	0.990060i	$0.544917\pi$
$108$		0			0
$109$	482.433	−	835.598i	0.423933	−	0.734273i	−0.572387	−	0.819984i	$-0.693983\pi$
$109$	482.433	−	835.598i	0.423933	−	0.734273i	0.996320	+	0.0857100i	$0.0273159\pi$
$110$		0			0
$111$	228.763			0.195615
$112$		0			0
$113$	−1492.35			−1.24238			−0.621190	−	0.783660i	$-0.713350\pi$
$113$	−1492.35			−1.24238			−0.621190	+	0.783660i	$0.713350\pi$
$114$		0			0
$115$	−29.0177	+	50.2602i	−0.0235297	+	0.0407547i
$116$		0			0
$117$	654.044	−	377.612i	0.516806	−	0.298378i
$118$		0			0
$119$	989.464	+	1171.36i	0.762219	+	0.902343i
$120$		0			0
$121$	288.075	+	498.961i	0.216435	+	0.374877i
$122$		0			0
$123$	688.081	+	397.264i	0.504408	+	0.291220i
$124$		0			0
$125$			1113.14i			0.796498i
$126$		0			0
$127$			48.9270i			0.0341856i	0.999854	+	0.0170928i	$0.00544107\pi$
$127$			48.9270i			0.0341856i	−0.999854	+	0.0170928i	$0.994559\pi$
$128$		0			0
$129$	−1018.05	−	587.772i	−0.694840	−	0.401166i
$130$		0			0
$131$	−202.141	−	350.118i	−0.134818	−	0.233511i	0.790710	−	0.612191i	$-0.209712\pi$
$131$	−202.141	−	350.118i	−0.134818	−	0.233511i	−0.925528	+	0.378680i	$0.876378\pi$
$132$		0			0
$133$	−254.658	−	1417.01i	−0.166027	−	0.923838i
$134$		0			0
$135$	−298.295	+	172.221i	−0.190172	+	0.109796i
$136$		0			0
$137$	−1302.03	+	2255.19i	−0.811972	+	1.40638i	0.0995107	+	0.995036i	$0.468272\pi$
$137$	−1302.03	+	2255.19i	−0.811972	+	1.40638i	−0.911482	+	0.411339i	$0.865061\pi$
$138$		0			0
$139$	−598.627			−0.365287			−0.182643	−	0.983179i	$-0.558465\pi$
$139$	−598.627			−0.365287			−0.182643	+	0.983179i	$0.558465\pi$
$140$		0			0
$141$	−882.174			−0.526897
$142$		0			0
$143$	−1832.30	+	3173.63i	−1.07150	+	1.85589i
$144$		0			0
$145$	−1334.65	+	770.563i	−0.764393	+	0.441322i
$146$		0			0
$147$	964.611	−	358.282i	0.541223	−	0.201024i
$148$		0			0
$149$	316.337	+	547.912i	0.173929	+	0.301253i	0.939790	−	0.341753i	$-0.111020\pi$
$149$	316.337	+	547.912i	0.173929	+	0.301253i	−0.765861	+	0.643006i	$0.777687\pi$
$150$		0			0
$151$	−1969.82	−	1137.28i	−1.06160	−	0.612917i	−0.135728	−	0.990746i	$-0.543337\pi$
$151$	−1969.82	−	1137.28i	−1.06160	−	0.612917i	−0.925875	+	0.377829i	$0.876671\pi$
$152$		0			0
$153$		−	745.133i		−	0.393729i
$154$		0			0
$155$		−	406.013i		−	0.210398i
$156$		0			0
$157$	90.6457	+	52.3343i	0.0460784	+	0.0266034i	0.522862	−	0.852417i	$-0.324864\pi$
$157$	90.6457	+	52.3343i	0.0460784	+	0.0266034i	−0.476784	+	0.879021i	$0.658198\pi$
$158$		0			0
$159$	−576.914	−	999.244i	−0.287750	−	0.498398i
$160$		0			0
$161$	−82.9252	+	14.9029i	−0.0405927	+	0.00729510i
$162$		0			0
$163$	−240.337	+	138.759i	−0.115489	+	0.0666775i	−0.556632	−	0.830759i	$-0.687907\pi$
$163$	−240.337	+	138.759i	−0.115489	+	0.0666775i	0.441143	+	0.897437i	$0.354573\pi$
$164$		0			0
$165$	835.671	−	1447.43i	0.394284	−	0.682921i
$166$		0			0
$167$	−682.244			−0.316130			−0.158065	−	0.987429i	$-0.550525\pi$
$167$	−682.244			−0.316130			−0.158065	+	0.987429i	$0.550525\pi$
$168$		0			0
$169$	−4844.53			−2.20507
$170$		0			0
$171$	−349.817	+	605.901i	−0.156440	+	0.270962i
$172$		0			0
$173$	3792.47	−	2189.59i	1.66668	−	0.962261i	0.697277	−	0.716802i	$-0.254395\pi$
$173$	3792.47	−	2189.59i	1.66668	−	0.962261i	0.969407	−	0.245459i	$-0.0789386\pi$
$174$		0			0
$175$	534.001	−	451.077i	0.230667	−	0.194847i
$176$		0			0
$177$	−1110.43	−	1923.31i	−0.471552	−	0.816752i
$178$		0			0
$179$	−109.563	−	63.2560i	−0.0457491	−	0.0264133i	0.476951	−	0.878930i	$-0.341742\pi$
$179$	−109.563	−	63.2560i	−0.0457491	−	0.0264133i	−0.522700	+	0.852517i	$0.675075\pi$
$180$		0			0
$181$		−	3978.09i		−	1.63364i	−0.576892	−	0.816820i	$-0.695735\pi$
$181$		−	3978.09i		−	1.63364i	0.576892	−	0.816820i	$-0.304265\pi$
$182$		0			0
$183$			620.204i			0.250529i
$184$		0			0
$185$	842.455	+	486.392i	0.334803	+	0.193299i
$186$		0			0
$187$	1807.82	+	3131.23i	0.706955	+	1.22448i
$188$		0			0
$189$	−470.450	−	169.482i	−0.181059	−	0.0652276i
$190$		0			0
$191$	−3431.93	+	1981.43i	−1.30013	+	0.750633i	−0.980427	−	0.196883i	$-0.936918\pi$
$191$	−3431.93	+	1981.43i	−1.30013	+	0.750633i	−0.319708	+	0.947516i	$0.603585\pi$
$192$		0			0
$193$	−598.539	+	1036.70i	−0.223232	+	0.386649i	−0.955788	−	0.294058i	$-0.904994\pi$
$193$	−598.539	+	1036.70i	−0.223232	+	0.386649i	0.732555	+	0.680707i	$0.238327\pi$
$194$		0			0
$195$	3211.49			1.17938
$196$		0			0
$197$	−1156.54			−0.418276			−0.209138	−	0.977886i	$-0.567066\pi$
$197$	−1156.54			−0.418276			−0.209138	+	0.977886i	$0.567066\pi$
$198$		0			0
$199$	−1365.38	+	2364.90i	−0.486377	+	0.842430i	−0.999877	−	0.0156593i	$-0.995015\pi$
$199$	−1365.38	+	2364.90i	−0.486377	+	0.842430i	0.513500	+	0.858090i	$0.328349\pi$
$200$		0			0
$201$	517.270	−	298.646i	0.181519	−	0.104800i
$202$		0			0
$203$	−2104.92	−	758.309i	−0.727765	−	0.262182i
$204$		0			0
$205$	1689.31	+	2925.97i	0.575544	+	0.996872i
$206$		0			0
$207$	35.4580	+	20.4717i	0.0119058	+	0.00687383i
$208$		0			0
$209$		−	3394.85i		−	1.12357i
$210$		0			0
$211$		−	84.4515i		−	0.0275539i	−0.999905	−	0.0137770i	$-0.995615\pi$
$211$		−	84.4515i		−	0.0275539i	0.999905	−	0.0137770i	$-0.00438549\pi$
$212$		0			0
$213$	1322.21	+	763.378i	0.425335	+	0.245567i
$214$		0			0
$215$	−2499.42	−	4329.12i	−0.792833	−	1.37323i
$216$		0			0
$217$	450.286	−	380.361i	0.140863	−	0.118989i
$218$		0			0
$219$	−2810.16	+	1622.45i	−0.867091	+	0.500615i
$220$		0			0
$221$	−3473.72	+	6016.66i	−1.05732	+	1.83133i
$222$		0			0
$223$	1329.75			0.399313			0.199656	−	0.979866i	$-0.436017\pi$
$223$	1329.75			0.399313			0.199656	+	0.979866i	$0.436017\pi$
$224$		0			0
$225$	−339.691			−0.100649
$226$		0			0
$227$	−273.008	+	472.864i	−0.0798246	+	0.138260i	−0.903174	−	0.429274i	$-0.858769\pi$
$227$	−273.008	+	472.864i	−0.0798246	+	0.138260i	0.823350	+	0.567535i	$0.192103\pi$
$228$		0			0
$229$	631.143	−	364.391i	0.182127	−	0.105151i	−0.406165	−	0.913800i	$-0.633134\pi$
$229$	631.143	−	364.391i	0.182127	−	0.105151i	0.588292	+	0.808649i	$0.299801\pi$
$230$		0			0
$231$	2388.13	−	429.183i	0.680206	−	0.122243i
$232$		0			0
$233$	1655.87	+	2868.05i	0.465577	+	0.806403i	0.999227	−	0.0393019i	$-0.0125134\pi$
$233$	1655.87	+	2868.05i	0.465577	+	0.806403i	−0.533650	+	0.845705i	$0.679180\pi$
$234$		0			0
$235$	−3248.74	−	1875.66i	−0.901807	−	0.520659i
$236$		0			0
$237$		−	3829.36i		−	1.04955i
$238$		0			0
$239$		−	3516.68i		−	0.951778i	−0.879505	−	0.475889i	$-0.842126\pi$
$239$		−	3516.68i		−	0.951778i	0.879505	−	0.475889i	$-0.157874\pi$
$240$		0			0
$241$	4731.01	+	2731.45i	1.26453	+	0.730076i	0.973947	−	0.226775i	$-0.0728181\pi$
$241$	4731.01	+	2731.45i	1.26453	+	0.730076i	0.290581	+	0.956850i	$0.406151\pi$
$242$		0			0
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$		0			0
$245$	4314.10	+	731.512i	1.12497	+	0.190753i
$246$		0			0
$247$	5649.28	−	3261.61i	1.45528	−	0.840208i
$248$		0			0
$249$	−1449.70	+	2510.95i	−0.368960	+	0.639057i
$250$		0			0
$251$	6658.12			1.67433			0.837165	−	0.546951i	$-0.184211\pi$
$251$	6658.12			1.67433			0.837165	+	0.546951i	$0.184211\pi$
$252$		0			0
$253$	−198.671			−0.0493689
$254$		0			0
$255$	1584.29	−	2744.07i	0.389067	−	0.673884i
$256$		0			0
$257$	−6153.56	+	3552.76i	−1.49357	+	0.862316i	−0.999973	−	0.00737241i	$-0.997653\pi$
$257$	−6153.56	+	3552.76i	−1.49357	+	0.862316i	−0.493602	+	0.869688i	$0.664320\pi$
$258$		0			0
$259$	249.800	+	1389.98i	0.0599299	+	0.333472i
$260$		0			0
$261$	543.624	+	941.584i	0.128925	+	0.223305i
$262$		0			0
$263$	6125.14	+	3536.35i	1.43609	+	0.829128i	0.997575	−	0.0695950i	$-0.0221707\pi$
$263$	6125.14	+	3536.35i	1.43609	+	0.829128i	0.438517	+	0.898723i	$0.355504\pi$
$264$		0			0
$265$		−	4906.50i		−	1.13737i
$266$		0			0
$267$			2171.26i			0.497673i
$268$		0			0
$269$	4478.18	+	2585.48i	1.01502	+	0.586021i	0.912657	−	0.408727i	$-0.134027\pi$
$269$	4478.18	+	2585.48i	1.01502	+	0.586021i	0.102361	+	0.994747i	$0.467360\pi$
$270$		0			0
$271$	1699.20	+	2943.11i	0.380883	+	0.659709i	0.991189	−	0.132457i	$-0.0422867\pi$
$271$	1699.20	+	2943.11i	0.380883	+	0.659709i	−0.610306	+	0.792166i	$0.708953\pi$
$272$		0			0
$273$	3008.59	+	3561.68i	0.666990	+	0.789607i
$274$		0			0
$275$	1427.46	−	824.146i	0.313015	−	0.180720i
$276$		0			0
$277$	1036.24	−	1794.82i	0.224772	−	0.389316i	−0.731479	−	0.681864i	$-0.761170\pi$
$277$	1036.24	−	1794.82i	0.224772	−	0.389316i	0.956251	+	0.292548i	$0.0945031\pi$
$278$		0			0
$279$	−286.438			−0.0614644
$280$		0			0
$281$	3189.71			0.677161			0.338580	−	0.940937i	$-0.390053\pi$
$281$	3189.71			0.677161			0.338580	+	0.940937i	$0.390053\pi$
$282$		0			0
$283$	3711.47	−	6428.45i	0.779590	−	1.35029i	−0.152589	−	0.988290i	$-0.548761\pi$
$283$	3711.47	−	6428.45i	0.779590	−	1.35029i	0.932178	−	0.361999i	$-0.117906\pi$
$284$		0			0
$285$	−2576.51	+	1487.55i	−0.535507	+	0.309175i
$286$		0			0
$287$	−1662.45	+	4614.63i	−0.341921	+	0.949105i
$288$		0			0
$289$	970.808	+	1681.49i	0.197600	+	0.342253i
$290$		0			0
$291$	−4581.47	−	2645.11i	−0.922922	−	0.532849i
$292$		0			0
$293$		−	5969.48i		−	1.19024i	−0.803636	−	0.595121i	$-0.797104\pi$
$293$		−	5969.48i		−	1.19024i	0.803636	−	0.595121i	$-0.202896\pi$
$294$		0			0
$295$		−	9443.87i		−	1.86388i
$296$		0			0
$297$	−1021.14	−	589.558i	−0.199504	−	0.115184i
$298$		0			0
$299$	−190.873	−	330.602i	−0.0369180	−	0.0639439i
$300$		0			0
$301$	2459.68	−	6827.58i	0.471008	−	1.30743i
$302$		0			0
$303$	2514.41	−	1451.70i	0.476730	−	0.275240i
$304$		0			0
$305$	−1318.67	+	2284.00i	−0.247563	+	0.428791i
$306$		0			0
$307$	7160.29			1.33114			0.665569	−	0.746337i	$-0.268189\pi$
$307$	7160.29			1.33114			0.665569	+	0.746337i	$0.268189\pi$
$308$		0			0
$309$	−801.141			−0.147493
$310$		0			0
$311$	1363.69	−	2361.98i	0.248642	−	0.430660i	−0.714507	−	0.699628i	$-0.753349\pi$
$311$	1363.69	−	2361.98i	0.248642	−	0.430660i	0.963149	+	0.268967i	$0.0866824\pi$
$312$		0			0
$313$	−3402.40	+	1964.38i	−0.614425	+	0.354739i	−0.774695	−	0.632335i	$-0.782097\pi$
$313$	−3402.40	+	1964.38i	−0.614425	+	0.354739i	0.160270	+	0.987073i	$0.448763\pi$
$314$		0			0
$315$	−1372.15	−	1624.41i	−0.245435	−	0.290555i
$316$		0			0
$317$	1683.01	+	2915.06i	0.298193	+	0.516486i	0.975723	−	0.219010i	$-0.0702826\pi$
$317$	1683.01	+	2915.06i	0.298193	+	0.516486i	−0.677529	+	0.735496i	$0.736949\pi$
$318$		0			0
$319$	−4568.87	−	2637.84i	−0.801906	−	0.462980i
$320$		0			0
$321$			4096.32i			0.712256i
$322$		0			0
$323$		−	6436.06i		−	1.10871i
$324$		0			0
$325$	2742.87	+	1583.60i	0.468145	+	0.270284i
$326$		0			0
$327$	−1447.30	−	2506.80i	−0.244758	−	0.423933i
$328$		0			0
$329$	−963.301	−	5360.16i	−0.161424	−	0.898222i
$330$		0			0
$331$	−7043.99	+	4066.85i	−1.16971	+	0.675330i	−0.953611	−	0.301043i	$-0.902665\pi$
$331$	−7043.99	+	4066.85i	−1.16971	+	0.675330i	−0.216095	+	0.976372i	$0.569332\pi$
$332$		0			0
$333$	343.144	−	594.344i	0.0564691	−	0.0978073i
$334$		0			0
$335$	2539.90			0.414238
$336$		0			0
$337$	−8055.00			−1.30203			−0.651015	−	0.759065i	$-0.725656\pi$
$337$	−8055.00			−1.30203			−0.651015	+	0.759065i	$0.725656\pi$
$338$		0			0
$339$	−2238.53	+	3877.25i	−0.358644	+	0.621190i
$340$		0			0
$341$	1203.68	−	694.945i	0.191152	−	0.110362i
$342$		0			0
$343$	3230.27	+	5469.83i	0.508507	+	0.861058i
$344$		0			0
$345$	87.0532	+	150.781i	0.0135849	+	0.0235297i
$346$		0			0
$347$	−1010.15	−	583.211i	−0.156276	−	0.0902259i	0.419823	−	0.907606i	$-0.362092\pi$
$347$	−1010.15	−	583.211i	−0.156276	−	0.0902259i	−0.576099	+	0.817380i	$0.695426\pi$
$348$		0			0
$349$			10232.0i			1.56936i	0.619898	+	0.784682i	$0.287174\pi$
$349$			10232.0i			1.56936i	−0.619898	+	0.784682i	$0.712826\pi$
$350$		0			0
$351$		−	2265.67i		−	0.344538i
$352$		0			0
$353$	−3494.85	−	2017.76i	−0.526947	−	0.304233i	0.212825	−	0.977090i	$-0.431733\pi$
$353$	−3494.85	−	2017.76i	−0.526947	−	0.304233i	−0.739772	+	0.672857i	$0.765067\pi$
$354$		0			0
$355$	3246.16	+	5622.52i	0.485320	+	0.840598i
$356$		0			0
$357$	4527.49	−	813.657i	0.671205	−	0.120626i
$358$		0			0
$359$	−2424.44	+	1399.75i	−0.356426	+	0.205783i	−0.667512	−	0.744599i	$-0.732641\pi$
$359$	−2424.44	+	1399.75i	−0.356426	+	0.205783i	0.311086	+	0.950382i	$0.399307\pi$
$360$		0			0
$361$	407.968	−	706.621i	0.0594792	−	0.103021i
$362$		0			0
$363$	1728.45			0.249918
$364$		0			0
$365$	−13798.5			−1.97875
$366$		0			0
$367$	−2637.37	+	4568.05i	−0.375121	+	0.649728i	−0.990345	−	0.138624i	$-0.955732\pi$
$367$	−2637.37	+	4568.05i	−0.375121	+	0.649728i	0.615224	+	0.788352i	$0.289065\pi$
$368$		0			0
$369$	2064.24	−	1191.79i	0.291220	−	0.168136i
$370$		0			0
$371$	5441.52	−	4596.51i	0.761481	−	0.643232i
$372$		0			0
$373$	5577.61	+	9660.71i	0.774257	+	1.34105i	0.935211	+	0.354090i	$0.115209\pi$
$373$	5577.61	+	9660.71i	0.774257	+	1.34105i	−0.160955	+	0.986962i	$0.551457\pi$
$374$		0			0
$375$	2892.02	+	1669.71i	0.398249	+	0.229929i
$376$		0			0
$377$		−	10137.2i		−	1.38487i
$378$		0			0
$379$		−	10145.3i		−	1.37501i	−0.726180	−	0.687504i	$-0.758706\pi$
$379$		−	10145.3i		−	1.37501i	0.726180	−	0.687504i	$-0.241294\pi$
$380$		0			0
$381$	127.116	+	73.3905i	0.0170928	+	0.00986853i
$382$		0			0
$383$	1600.44	+	2772.05i	0.213522	+	0.369831i	0.952814	−	0.303554i	$-0.0981732\pi$
$383$	1600.44	+	2772.05i	0.213522	+	0.369831i	−0.739292	+	0.673385i	$0.764840\pi$
$384$		0			0
$385$	9707.19	+	3497.07i	1.28500	+	0.462928i
$386$		0			0
$387$	−3054.15	+	1763.32i	−0.401166	+	0.231613i
$388$		0			0
$389$	2376.25	−	4115.79i	0.309719	−	0.536450i	−0.668581	−	0.743639i	$-0.733098\pi$
$389$	2376.25	−	4115.79i	0.309719	−	0.536450i	0.978301	+	0.207189i	$0.0664315\pi$
$390$		0			0
$391$	−376.646			−0.0487156
$392$		0			0
$393$	−1212.84			−0.155674
$394$		0			0
$395$	8141.91	−	14102.2i	1.03712	−	1.79635i
$396$		0			0
$397$	1259.19	−	726.995i	0.159186	−	0.0919064i	−0.418291	−	0.908313i	$-0.637371\pi$
$397$	1259.19	−	726.995i	0.159186	−	0.0919064i	0.577477	+	0.816407i	$0.304037\pi$
$398$		0			0
$399$	−4063.49	−	1463.90i	−0.509847	−	0.183675i
$400$		0			0
$401$	310.342	+	537.528i	0.0386477	+	0.0669399i	0.884702	−	0.466157i	$-0.154362\pi$
$401$	310.342	+	537.528i	0.0386477	+	0.0669399i	−0.846055	+	0.533096i	$0.821028\pi$
$402$		0			0
$403$	2312.87	+	1335.34i	0.285887	+	0.165057i
$404$		0			0
$405$			1033.32i			0.126781i
$406$		0			0
$407$			3330.10i			0.405570i
$408$		0			0
$409$	−4375.16	−	2526.00i	−0.528943	−	0.305386i	0.211643	−	0.977347i	$-0.432119\pi$
$409$	−4375.16	−	2526.00i	−0.528943	−	0.305386i	−0.740586	+	0.671962i	$0.765452\pi$
$410$		0			0
$411$	3906.10	+	6765.56i	0.468792	+	0.811972i
$412$		0			0
$413$	10473.7	−	8847.22i	1.24788	−	1.05410i
$414$		0			0
$415$	−10677.5	+	6164.66i	−1.26298	+	0.729183i
$416$		0			0
$417$	−897.941	+	1555.28i	−0.105449	+	0.182643i
$418$		0			0
$419$	−3832.00			−0.446791			−0.223395	−	0.974728i	$-0.571714\pi$
$419$	−3832.00			−0.446791			−0.223395	+	0.974728i	$0.571714\pi$
$420$		0			0
$421$	−9483.96			−1.09791			−0.548955	−	0.835852i	$-0.684974\pi$
$421$	−9483.96			−1.09791			−0.548955	+	0.835852i	$0.684974\pi$
$422$		0			0
$423$	−1323.26	+	2291.96i	−0.152102	+	0.263448i
$424$		0			0
$425$	2706.23	−	1562.44i	0.308873	−	0.178328i
$426$		0			0
$427$	−3768.41	+	677.239i	−0.427087	+	0.0767538i
$428$		0			0
$429$	5496.89	+	9520.90i	0.618631	+	1.07150i
$430$		0			0
$431$	10181.6	+	5878.32i	1.13788	+	0.656958i	0.945906	−	0.324441i	$-0.105176\pi$
$431$	10181.6	+	5878.32i	1.13788	+	0.656958i	0.191979	+	0.981399i	$0.438509\pi$
$432$		0			0
$433$			806.702i			0.0895326i	0.998997	+	0.0447663i	$0.0142543\pi$
$433$			806.702i			0.0895326i	−0.998997	+	0.0447663i	$0.985746\pi$
$434$		0			0
$435$			4623.38i			0.509595i
$436$		0			0
$437$	306.267	+	176.824i	0.0335258	+	0.0193561i
$438$		0			0
$439$	−6152.35	−	10656.2i	−0.668874	−	1.15852i	−0.978219	−	0.207574i	$-0.933443\pi$
$439$	−6152.35	−	10656.2i	−0.668874	−	1.15852i	0.309345	−	0.950950i	$-0.399890\pi$
$440$		0			0
$441$	516.074	−	3043.56i	0.0557255	−	0.328642i
$442$		0			0
$443$	−13244.5	+	7646.70i	−1.42046	+	0.820103i	−0.996338	−	0.0855016i	$-0.972751\pi$
$443$	−13244.5	+	7646.70i	−1.42046	+	0.820103i	−0.424122	+	0.905605i	$0.639417\pi$
$444$		0			0
$445$	−4616.49	+	7995.99i	−0.491781	+	0.851789i
$446$		0			0
$447$	1898.02			0.200835
$448$		0			0
$449$	−4118.02			−0.432832			−0.216416	−	0.976301i	$-0.569437\pi$
$449$	−4118.02			−0.432832			−0.216416	+	0.976301i	$0.569437\pi$
$450$		0			0
$451$	−5782.96	+	10016.4i	−0.603789	+	1.04579i
$452$		0			0
$453$	−5909.47	+	3411.84i	−0.612917	+	0.353868i
$454$		0			0
$455$	3506.82	+	19513.3i	0.361324	+	2.01054i
$456$		0			0
$457$	1179.13	+	2042.31i	0.120694	+	0.209049i	0.920042	−	0.391820i	$-0.128155\pi$
$457$	1179.13	+	2042.31i	0.120694	+	0.209049i	−0.799347	+	0.600869i	$0.794821\pi$
$458$		0			0
$459$	−1935.91	−	1117.70i	−0.196864	−	0.113660i
$460$		0			0
$461$		−	16195.4i		−	1.63622i	−0.575063	−	0.818109i	$-0.695023\pi$
$461$		−	16195.4i		−	1.63622i	0.575063	−	0.818109i	$-0.304977\pi$
$462$		0			0
$463$			11212.8i			1.12550i	0.826629	+	0.562748i	$0.190256\pi$
$463$			11212.8i			1.12550i	−0.826629	+	0.562748i	$0.809744\pi$
$464$		0			0
$465$	−1054.85	−	609.019i	−0.105199	−	0.0607367i
$466$		0			0
$467$	−2028.44	−	3513.36i	−0.200995	−	0.348134i	0.747854	−	0.663863i	$-0.231084\pi$
$467$	−2028.44	−	3513.36i	−0.200995	−	0.348134i	−0.948849	+	0.315729i	$0.897751\pi$
$468$		0			0
$469$	2379.43	+	2816.86i	0.234269	+	0.277336i
$470$		0			0
$471$	271.937	−	157.003i	0.0266034	−	0.0153595i
$472$		0			0
$473$	8556.18	−	14819.7i	0.831742	−	1.44062i
$474$		0			0
$475$	−2934.07			−0.283420
$476$		0			0
$477$	−3461.48			−0.332265
$478$		0			0
$479$	2759.51	−	4779.61i	0.263226	−	0.455920i	−0.703872	−	0.710327i	$-0.748547\pi$
$479$	2759.51	−	4779.61i	0.263226	−	0.455920i	0.967097	+	0.254407i	$0.0818803\pi$
$480$		0			0
$481$	−5541.52	+	3199.40i	−0.525304	+	0.303285i
$482$		0			0
$483$	−85.6689	+	237.800i	−0.00807054	+	0.0224022i
$484$		0			0
$485$	−11248.0	−	19482.1i	−1.05308	−	1.82399i
$486$		0			0
$487$	−1286.31	−	742.651i	−0.119688	−	0.0691021i	0.438961	−	0.898506i	$-0.355347\pi$
$487$	−1286.31	−	742.651i	−0.119688	−	0.0691021i	−0.558649	+	0.829404i	$0.688680\pi$
$488$		0			0
$489$			832.553i			0.0769925i
$490$		0			0
$491$		−	1233.26i		−	0.113352i	−0.998393	−	0.0566762i	$-0.981950\pi$
$491$		−	1233.26i		−	0.113352i	0.998393	−	0.0566762i	$-0.0180503\pi$
$492$		0			0
$493$	−8661.80	−	5000.89i	−0.791294	−	0.456854i
$494$		0			0
$495$	−2507.01	−	4342.28i	−0.227640	−	0.394284i
$496$		0			0
$497$	−3194.54	+	8867.43i	−0.288320	+	0.800319i
$498$		0			0
$499$	−9573.75	+	5527.41i	−0.858878	+	0.495873i	−0.863636	−	0.504115i	$-0.831819\pi$
$499$	−9573.75	+	5527.41i	−0.858878	+	0.495873i	0.00475846	+	0.999989i	$0.498485\pi$
$500$		0			0
$501$	−1023.37	+	1772.52i	−0.0912587	+	0.158065i
$502$		0			0
$503$	−12446.0			−1.10326			−0.551630	−	0.834089i	$-0.685994\pi$
$503$	−12446.0			−1.10326			−0.551630	+	0.834089i	$0.685994\pi$
$504$		0			0
$505$	12346.3			1.08793
$506$		0			0
$507$	−7266.79	+	12586.5i	−0.636548	+	1.10253i
$508$		0			0
$509$	−3244.49	+	1873.21i	−0.282534	+	0.163121i	−0.634570	−	0.772866i	$-0.718823\pi$
$509$	−3244.49	+	1873.21i	−0.282534	+	0.163121i	0.352036	+	0.935986i	$0.385489\pi$
$510$		0			0
$511$	−12926.7	−	15303.1i	−1.11907	−	1.32479i
$512$		0			0
$513$	1049.45	+	1817.70i	0.0903205	+	0.156440i
$514$		0			0
$515$	−2950.33	−	1703.37i	−0.252440	−	0.145747i
$516$		0			0
$517$		−	12841.8i		−	1.09242i
$518$		0			0
$519$		−	13137.5i		−	1.11112i
$520$		0			0
$521$	4299.89	+	2482.54i	0.361577	+	0.208756i	0.669772	−	0.742567i	$-0.266392\pi$
$521$	4299.89	+	2482.54i	0.361577	+	0.208756i	−0.308195	+	0.951323i	$0.599725\pi$
$522$		0			0
$523$	−6050.05	−	10479.0i	−0.505832	−	0.876127i	−0.999977	−	0.00674731i	$-0.997852\pi$
$523$	−6050.05	−	10479.0i	−0.505832	−	0.876127i	0.494145	−	0.869379i	$-0.335481\pi$
$524$		0			0
$525$	−370.930	−	2063.99i	−0.0308356	−	0.171581i
$526$		0			0
$527$	2281.97	−	1317.50i	0.188623	−	0.108901i
$528$		0			0
$529$	−6073.15	+	10519.0i	−0.499150	+	0.864552i
$530$		0			0
$531$	−6662.56			−0.544501
$532$		0			0
$533$	−22223.9			−1.80605
$534$		0			0
$535$	−8709.52	+	15085.3i	−0.703823	+	1.21906i
$536$		0			0
$537$	−328.688	+	189.768i	−0.0264133	+	0.0152497i
$538$		0			0
$539$	5215.50	+	14041.8i	0.416786	+	1.12212i
$540$		0			0
$541$	−3750.69	−	6496.38i	−0.298068	−	0.516269i	0.677626	−	0.735407i	$-0.263009\pi$
$541$	−3750.69	−	6496.38i	−0.298068	−	0.516269i	−0.975694	+	0.219138i	$0.929676\pi$
$542$		0			0
$543$	−10335.4	−	5967.13i	−0.816820	−	0.471591i
$544$		0			0
$545$		−	12308.9i		−	0.967440i
$546$		0			0
$547$			19340.6i			1.51178i	0.654699	+	0.755889i	$0.272795\pi$
$547$			19340.6i			1.51178i	−0.654699	+	0.755889i	$0.727205\pi$
$548$		0			0
$549$	1611.34	+	930.306i	0.125264	+	0.0723215i
$550$		0			0
$551$	4695.53	+	8132.90i	0.363042	+	0.628808i
$552$		0			0
$553$	23267.5	−	4181.51i	1.78921	−	0.321548i
$554$		0			0
$555$	2527.37	−	1459.18i	0.193299	−	0.111601i
$556$		0			0
$557$	−10442.9	+	18087.6i	−0.794396	+	1.37593i	0.128826	+	0.991667i	$0.458879\pi$
$557$	−10442.9	+	18087.6i	−0.794396	+	1.37593i	−0.923222	+	0.384267i	$0.874454\pi$
$558$		0			0
$559$	32881.5			2.48790
$560$		0			0
$561$	10846.9			0.816321
$562$		0			0
$563$	11303.0	−	19577.3i	0.846115	−	1.46551i	−0.0385346	−	0.999257i	$-0.512269\pi$
$563$	11303.0	−	19577.3i	0.846115	−	1.46551i	0.884649	−	0.466257i	$-0.154398\pi$
$564$		0			0
$565$	−16487.5	+	9519.06i	−1.22767	+	0.708796i
$566$		0			0
$567$	−1146.00	+	968.041i	−0.0848811	+	0.0717000i
$568$		0			0
$569$	210.319	+	364.283i	0.0154956	+	0.0268392i	0.873669	−	0.486520i	$-0.161734\pi$
$569$	210.319	+	364.283i	0.0154956	+	0.0268392i	−0.858174	+	0.513360i	$0.828401\pi$
$570$		0			0
$571$	1009.41	+	582.783i	0.0739799	+	0.0427123i	0.536534	−	0.843879i	$-0.319733\pi$
$571$	1009.41	+	582.783i	0.0739799	+	0.0427123i	−0.462554	+	0.886591i	$0.653067\pi$
$572$		0			0
$573$			11888.6i			0.866756i
$574$		0			0
$575$			171.705i			0.0124532i
$576$		0			0
$577$	2682.59	+	1548.79i	0.193549	+	0.111745i	0.593643	−	0.804729i	$-0.297689\pi$
$577$	2682.59	+	1548.79i	0.193549	+	0.111745i	−0.400094	+	0.916474i	$0.631023\pi$
$578$		0			0
$579$	1795.62	+	3110.10i	0.128883	+	0.223232i
$580$		0			0
$581$	−16839.8	−	6066.63i	−1.20246	−	0.433195i
$582$		0			0
$583$	14546.0	−	8398.12i	1.03333	−	0.596595i
$584$		0			0
$585$	4817.23	−	8343.70i	0.340458	−	0.589691i
$586$		0			0
$587$	8108.04			0.570110			0.285055	−	0.958511i	$-0.407988\pi$
$587$	8108.04			0.570110			0.285055	+	0.958511i	$0.407988\pi$
$588$		0			0
$589$	−2474.09			−0.173079
$590$		0			0
$591$	−1734.82	+	3004.79i	−0.120746	+	0.209138i
$592$		0			0
$593$	5174.34	−	2987.41i	0.358322	−	0.206877i	−0.310023	−	0.950729i	$-0.600337\pi$
$593$	5174.34	−	2987.41i	0.358322	−	0.206877i	0.668344	+	0.743852i	$0.267003\pi$
$594$		0			0
$595$	18403.2	+	6629.85i	1.26799	+	0.456802i
$596$		0			0
$597$	4096.13	+	7094.71i	0.280810	+	0.486377i
$598$		0			0
$599$	−7433.56	−	4291.77i	−0.507057	−	0.292749i	0.224566	−	0.974459i	$-0.427903\pi$
$599$	−7433.56	−	4291.77i	−0.507057	−	0.292749i	−0.731623	+	0.681709i	$0.761237\pi$
$600$		0			0
$601$		−	26516.8i		−	1.79974i	−0.436159	−	0.899870i	$-0.643662\pi$
$601$		−	26516.8i		−	1.79974i	0.436159	−	0.899870i	$-0.356338\pi$
$602$		0			0
$603$		−	1791.88i		−	0.121013i
$604$		0			0
$605$	6365.30	+	3675.00i	0.427746	+	0.246959i
$606$		0			0
$607$	90.0198	+	155.919i	0.00601942	+	0.0104259i	0.869019	−	0.494778i	$-0.164751\pi$
$607$	90.0198	+	155.919i	0.00601942	+	0.0104259i	−0.863000	+	0.505204i	$0.831417\pi$
$608$		0			0
$609$	−5127.52	+	4331.28i	−0.341179	+	0.288197i
$610$		0			0
$611$	21369.6	−	12337.8i	1.41493	−	0.816911i
$612$		0			0
$613$	11987.9	−	20763.7i	0.789866	−	1.36809i	−0.136183	−	0.990684i	$-0.543483\pi$
$613$	11987.9	−	20763.7i	0.789866	−	1.36809i	0.926049	−	0.377404i	$-0.123183\pi$
$614$		0			0
$615$	10135.9			0.664581
$616$		0			0
$617$	21357.3			1.39354			0.696768	−	0.717296i	$-0.254621\pi$
$617$	21357.3			1.39354			0.696768	+	0.717296i	$0.254621\pi$
$618$		0			0
$619$	565.488	−	979.454i	0.0367187	−	0.0635987i	−0.847082	−	0.531462i	$-0.821643\pi$
$619$	565.488	−	979.454i	0.0367187	−	0.0635987i	0.883801	+	0.467863i	$0.154976\pi$
$620$		0			0
$621$	106.374	−	61.4151i	0.00687383	−	0.00396861i
$622$		0			0
$623$	−13192.7	+	2370.93i	−0.848403	+	0.152471i
$624$		0			0
$625$	9459.18	+	16383.8i	0.605388	+	1.04856i
$626$		0			0
$627$	−8820.09	−	5092.28i	−0.561787	−	0.324348i
$628$		0			0
$629$			6313.29i			0.400203i
$630$		0			0
$631$		−	21331.4i		−	1.34579i	−0.739740	−	0.672893i	$-0.765052\pi$
$631$		−	21331.4i		−	1.34579i	0.739740	−	0.672893i	$-0.234948\pi$
$632$		0			0
$633$	−219.411	−	126.677i	−0.0137770	−	0.00795414i
$634$		0			0
$635$	312.083	+	540.544i	0.0195034	+	0.0337808i
$636$		0			0
$637$	−18355.8	+	22169.7i	−1.14173	+	1.37895i
$638$		0			0
$639$	3966.63	−	2290.14i	0.245567	−	0.141778i
$640$		0			0
$641$	−7215.00	+	12496.7i	−0.444579	+	0.770034i	−0.998023	−	0.0628529i	$-0.979980\pi$
$641$	−7215.00	+	12496.7i	−0.444579	+	0.770034i	0.553444	+	0.832887i	$0.313313\pi$
$642$		0			0
$643$	−19538.7			−1.19834			−0.599170	−	0.800622i	$-0.704503\pi$
$643$	−19538.7			−1.19834			−0.599170	+	0.800622i	$0.704503\pi$
$644$		0			0
$645$	−14996.5			−0.915485
$646$		0			0
$647$	−13576.4	+	23515.1i	−0.824953	+	1.42886i	0.0770024	+	0.997031i	$0.475465\pi$
$647$	−13576.4	+	23515.1i	−0.824953	+	1.42886i	−0.901955	+	0.431829i	$0.857868\pi$
$648$		0			0
$649$	27997.6	−	16164.4i	1.69338	−	0.977673i
$650$		0			0
$651$	−312.779	−	1740.42i	−0.0188307	−	0.104781i
$652$		0			0
$653$	12093.9	+	20947.3i	0.724766	+	1.25533i	0.959070	+	0.283168i	$0.0913855\pi$
$653$	12093.9	+	20947.3i	0.724766	+	1.25533i	−0.234304	+	0.972163i	$0.575281\pi$
$654$		0			0
$655$	−4466.49	−	2578.73i	−0.266443	−	0.153831i
$656$		0			0
$657$			9734.67i			0.578060i
$658$		0			0
$659$		−	32707.6i		−	1.93340i	−0.255918	−	0.966699i	$-0.582378\pi$
$659$		−	32707.6i		−	1.93340i	0.255918	−	0.966699i	$-0.417622\pi$
$660$		0			0
$661$	3022.47	+	1745.02i	0.177852	+	0.102683i	0.586283	−	0.810106i	$-0.300591\pi$
$661$	3022.47	+	1745.02i	0.177852	+	0.102683i	−0.408431	+	0.912789i	$0.633924\pi$
$662$		0			0
$663$	10421.2	+	18050.0i	0.610444	+	1.05732i
$664$		0			0
$665$	−11851.9	−	14030.7i	−0.691125	−	0.818179i
$666$		0			0
$667$	475.947	−	274.788i	0.0276293	−	0.0159518i
$668$		0			0
$669$	1994.63	−	3454.79i	0.115272	−	0.199656i
$670$		0			0
$671$	−9028.30			−0.519424
$672$		0			0
$673$	−12215.6			−0.699667			−0.349834	−	0.936812i	$-0.613762\pi$
$673$	−12215.6			−0.699667			−0.349834	+	0.936812i	$0.613762\pi$
$674$		0			0
$675$	−509.537	+	882.543i	−0.0290549	+	0.0503246i
$676$		0			0
$677$	19115.3	−	11036.2i	1.08517	−	0.626525i	0.152885	−	0.988244i	$-0.451143\pi$
$677$	19115.3	−	11036.2i	1.08517	−	0.626525i	0.932287	+	0.361719i	$0.117810\pi$
$678$		0			0
$679$	11069.1	−	30725.7i	0.625617	−	1.73659i
$680$		0			0
$681$	819.024	+	1418.59i	0.0460867	+	0.0798246i
$682$		0			0
$683$	11877.9	+	6857.71i	0.665440	+	0.384192i	0.794347	−	0.607465i	$-0.207813\pi$
$683$	11877.9	+	6857.71i	0.665440	+	0.384192i	−0.128907	+	0.991657i	$0.541147\pi$
$684$		0			0
$685$			33220.3i			1.85297i
$686$		0			0
$687$		−	2186.34i		−	0.121418i
$688$		0			0
$689$	27950.1	+	16137.0i	1.54545	+	0.892266i
$690$		0			0
$691$	−2105.60	−	3647.01i	−0.115920	−	0.200780i	0.802227	−	0.597019i	$-0.203648\pi$
$691$	−2105.60	−	3647.01i	−0.115920	−	0.200780i	−0.918147	+	0.396239i	$0.870315\pi$
$692$		0			0
$693$	2467.15	−	6848.32i	0.135237	−	0.375392i
$694$		0			0
$695$	−6613.61	+	3818.37i	−0.360962	+	0.208402i
$696$		0			0
$697$	−10963.5	+	18989.3i	−0.595799	+	1.03195i
$698$		0			0
$699$	9935.21			0.537602
$700$		0			0
$701$	17197.5			0.926592			0.463296	−	0.886204i	$-0.346667\pi$
$701$	17197.5			0.926592			0.463296	+	0.886204i	$0.346667\pi$
$702$		0			0
$703$	2963.90	−	5133.62i	0.159012	−	0.275417i
$704$		0			0
$705$	−9746.23	+	5626.99i	−0.520659	+	0.300602i
$706$		0			0
$707$	11566.3	+	13692.6i	0.615268	+	0.728377i
$708$		0			0
$709$	−10033.9	−	17379.2i	−0.531497	−	0.920579i	−0.999324	−	0.0367592i	$-0.988297\pi$
$709$	−10033.9	−	17379.2i	−0.531497	−	0.920579i	0.467828	−	0.883820i	$-0.345037\pi$
$710$		0			0
$711$	−9948.96	−	5744.03i	−0.524775	−	0.302979i
$712$		0			0
$713$			144.787i			0.00760493i
$714$		0			0
$715$			46749.6i			2.44522i
$716$		0			0
$717$	−9136.59	−	5275.02i	−0.475889	−	0.274755i
$718$		0			0
$719$	−8577.09	−	14856.0i	−0.444884	−	0.770561i	0.553160	−	0.833075i	$-0.313422\pi$
$719$	−8577.09	−	14856.0i	−0.444884	−	0.770561i	−0.998044	+	0.0625134i	$0.980088\pi$
$720$		0			0
$721$	−874.815	−	4867.79i	−0.0451870	−	0.251437i
$722$		0			0
$723$	14193.0	−	8194.35i	0.730076	−	0.421509i
$724$		0			0
$725$	−2279.81	+	3948.74i	−0.116786	+	0.202279i
$726$		0			0
$727$	4014.26			0.204788			0.102394	−	0.994744i	$-0.467350\pi$
$727$	4014.26			0.204788			0.102394	+	0.994744i	$0.467350\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	16221.1	−	28095.7i	0.820735	−	1.42156i
$732$		0			0
$733$	22785.7	−	13155.3i	1.14817	−	0.662897i	0.199730	−	0.979851i	$-0.435993\pi$
$733$	22785.7	−	13155.3i	1.14817	−	0.662897i	0.948441	+	0.316954i	$0.102660\pi$
$734$		0			0
$735$	8371.68	−	10111.1i	0.420128	−	0.507420i
$736$		0			0
$737$	4347.38	+	7529.89i	0.217283	+	0.376346i
$738$		0			0
$739$	−11093.7	−	6404.97i	−0.552219	−	0.318824i	0.197798	−	0.980243i	$-0.436621\pi$
$739$	−11093.7	−	6404.97i	−0.552219	−	0.318824i	−0.750016	+	0.661419i	$0.769954\pi$
$740$		0			0
$741$		−	19569.7i		−	0.970188i
$742$		0			0
$743$		−	4199.36i		−	0.207348i	−0.994611	−	0.103674i	$-0.966940\pi$
$743$		−	4199.36i		−	0.207348i	0.994611	−	0.103674i	$-0.0330599\pi$
$744$		0			0
$745$	6989.77	+	4035.54i	0.343739	+	0.198458i
$746$		0			0
$747$	4349.10	+	7532.86i	0.213019	+	0.368960i
$748$		0			0
$749$	−24889.5	+	4473.02i	−1.21421	+	0.218212i
$750$		0			0
$751$	12052.1	−	6958.30i	0.585603	−	0.338098i	−0.177754	−	0.984075i	$-0.556883\pi$
$751$	12052.1	−	6958.30i	0.585603	−	0.338098i	0.763357	+	0.645977i	$0.223550\pi$
$752$		0			0
$753$	9987.18	−	17298.3i	0.483337	−	0.837165i
$754$		0			0
$755$	−29016.7			−1.39871
$756$		0			0
$757$	15356.4			0.737301			0.368650	−	0.929568i	$-0.379820\pi$
$757$	15356.4			0.737301			0.368650	+	0.929568i	$0.379820\pi$
$758$		0			0
$759$	−298.006	+	516.162i	−0.0142516	+	0.0246844i
$760$		0			0
$761$	11619.3	−	6708.43i	0.553483	−	0.319554i	−0.197043	−	0.980395i	$-0.563134\pi$
$761$	11619.3	−	6708.43i	0.553483	−	0.319554i	0.750526	+	0.660841i	$0.229800\pi$
$762$		0			0
$763$	13651.1	−	11531.2i	0.647710	−	0.547128i
$764$		0			0
$765$	−4752.87	−	8232.21i	−0.224628	−	0.389067i
$766$		0			0
$767$	53797.5	+	31060.0i	2.53262	+	1.46221i
$768$		0			0
$769$			6362.25i			0.298347i	0.988811	+	0.149173i	$0.0476612\pi$
$769$			6362.25i			0.298347i	−0.988811	+	0.149173i	$0.952339\pi$
$770$		0			0
$771$			21316.6i			0.995716i
$772$		0			0
$773$	683.703	+	394.736i	0.0318125	+	0.0183670i	0.515822	−	0.856696i	$-0.327487\pi$
$773$	683.703	+	394.736i	0.0318125	+	0.0183670i	−0.484009	+	0.875063i	$0.660820\pi$
$774$		0			0
$775$	−600.620	−	1040.30i	−0.0278386	−	0.0482178i
$776$		0			0
$777$	3985.98	+	1435.97i	0.184036	+	0.0663001i
$778$		0			0
$779$	17829.8	−	10294.1i	0.820051	−	0.473457i
$780$		0			0
$781$	−11112.5	+	19247.4i	−0.509137	+	0.881851i
$782$		0			0
$783$	3261.74			0.148870
$784$		0			0
$785$	1335.27			0.0607105
$786$		0			0
$787$	1637.91	−	2836.94i	0.0741869	−	0.128495i	−0.826546	−	0.562870i	$-0.809697\pi$
$787$	1637.91	−	2836.94i	0.0741869	−	0.128495i	0.900732	+	0.434374i	$0.143031\pi$
$788$		0			0
$789$	18375.4	−	10609.0i	0.829128	−	0.478697i
$790$		0			0
$791$	−26002.9	−	9367.69i	−1.16884	−	0.421083i
$792$		0			0
$793$	−8673.95	−	15023.7i	−0.388425	−	0.672772i
$794$		0			0
$795$	−12747.5	−	7359.74i	−0.568686	−	0.328331i
$796$		0			0
$797$			2241.13i			0.0996045i	0.998759	+	0.0498023i	$0.0158591\pi$
$797$			2241.13i			0.0996045i	−0.998759	+	0.0498023i	$0.984141\pi$
$798$		0			0
$799$		−	24345.8i		−	1.07796i
$800$		0			0
$801$	5641.09	+	3256.88i	0.248836	+	0.143666i
$802$		0			0
$803$	−23617.9	−	40907.4i	−1.03793	−	1.79775i
$804$		0			0
$805$	−821.096	+	693.589i	−0.0359501	+	0.0303674i
$806$		0			0
$807$	13434.6	−	7756.44i	0.586021	−	0.338339i
$808$		0			0
$809$	−12640.5	+	21894.0i	−0.549340	+	0.951486i	0.448979	+	0.893542i	$0.351788\pi$
$809$	−12640.5	+	21894.0i	−0.549340	+	0.951486i	−0.998320	+	0.0579435i	$0.981546\pi$
$810$		0			0
$811$	34777.3			1.50579			0.752894	−	0.658141i	$-0.228657\pi$
$811$	34777.3			1.50579			0.752894	+	0.658141i	$0.228657\pi$
$812$		0			0
$813$	10195.2			0.439806
$814$		0			0
$815$	−1770.16	+	3066.01i	−0.0760809	+	0.131776i
$816$		0			0
$817$	−26380.1	+	15230.6i	−1.12965	+	0.652204i
$818$		0			0
$819$	13766.4	−	2474.03i	0.587347	−	0.105555i
$820$		0			0
$821$	9958.23	+	17248.2i	0.423319	+	0.733209i	0.996262	−	0.0863857i	$-0.0275317\pi$
$821$	9958.23	+	17248.2i	0.423319	+	0.733209i	−0.572943	+	0.819595i	$0.694198\pi$
$822$		0			0
$823$	16066.6	+	9276.03i	0.680492	+	0.392882i	0.800040	−	0.599946i	$-0.204811\pi$
$823$	16066.6	+	9276.03i	0.680492	+	0.392882i	−0.119548	+	0.992828i	$0.538145\pi$
$824$		0			0
$825$		−	4944.88i		−	0.208677i
$826$		0			0
$827$			18820.5i			0.791358i	0.918389	+	0.395679i	$0.129491\pi$
$827$			18820.5i			0.791358i	−0.918389	+	0.395679i	$0.870509\pi$
$828$		0			0
$829$	−16671.9	−	9625.55i	−0.698481	−	0.403268i	0.108301	−	0.994118i	$-0.465459\pi$
$829$	−16671.9	−	9625.55i	−0.698481	−	0.403268i	−0.806781	+	0.590850i	$0.798792\pi$
$830$		0			0
$831$	−3108.73	−	5384.47i	−0.129772	−	0.224772i
$832$		0			0
$833$	9887.69	+	26620.9i	0.411270	+	1.10727i
$834$		0			0
$835$	−7537.41	+	4351.73i	−0.312387	+	0.180357i
$836$		0			0
$837$	−429.657	+	744.187i	−0.0177433	+	0.0307322i
$838$		0			0
$839$	−31608.3			−1.30064			−0.650321	−	0.759660i	$-0.725366\pi$
$839$	−31608.3			−1.30064			−0.650321	+	0.759660i	$0.725366\pi$
$840$		0			0
$841$	−9795.07			−0.401618
$842$		0			0
$843$	4784.57	−	8287.11i	0.195480	−	0.338580i
$844$		0			0
$845$	−53522.2	+	30901.1i	−2.17896	+	1.25802i
$846$		0			0
$847$	1887.40	+	10502.2i	0.0765667	+	0.426045i
$848$		0			0
$849$	−11134.4	−	19285.4i	−0.450096	−	0.779590i
$850$		0			0
$851$	−300.425	−	173.451i	−0.0121016	−	0.00698685i
$852$		0			0
$853$			43451.9i			1.74416i	0.489366	+	0.872079i	$0.337228\pi$
$853$			43451.9i			1.74416i	−0.489366	+	0.872079i	$0.662772\pi$
$854$		0			0
$855$			8925.30i			0.357005i
$856$		0			0
$857$	−23342.8	−	13476.9i	−0.930424	−	0.537180i	−0.0434783	−	0.999054i	$-0.513844\pi$
$857$	−23342.8	−	13476.9i	−0.930424	−	0.537180i	−0.886946	+	0.461874i	$0.847177\pi$
$858$		0			0
$859$	−2904.53	−	5030.79i	−0.115368	−	0.199824i	0.802559	−	0.596573i	$-0.203471\pi$
$859$	−2904.53	−	5030.79i	−0.115368	−	0.199824i	−0.917927	+	0.396750i	$0.870138\pi$
$860$		0			0
$861$	9495.49	+	11241.1i	0.375848	+	0.444943i
$862$		0			0
$863$	−9823.54	+	5671.62i	−0.387482	+	0.223713i	−0.681069	−	0.732220i	$-0.738484\pi$
$863$	−9823.54	+	5671.62i	−0.387482	+	0.223713i	0.293586	+	0.955933i	$0.405151\pi$
$864$		0			0
$865$	27932.7	−	48380.9i	1.09797	−	1.90174i
$866$		0			0
$867$	5824.85			0.228169
$868$		0			0
$869$	55743.8			2.17604
$870$		0			0
$871$	−8353.51	+	14468.7i	−0.324969	+	0.562862i
$872$		0			0
$873$	−13744.4	+	7935.34i	−0.532849	+	0.307641i
$874$		0			0
$875$	−6987.31	+	19395.4i	−0.269959	+	0.749354i
$876$		0			0
$877$	−21412.5	−	37087.5i	−0.824455	−	1.42800i	−0.902335	−	0.431036i	$-0.858148\pi$
$877$	−21412.5	−	37087.5i	−0.824455	−	1.42800i	0.0778794	−	0.996963i	$-0.475185\pi$
$878$		0			0
$879$	−15509.2	−	8954.22i	−0.595121	−	0.343593i
$880$		0			0
$881$			24785.0i			0.947818i	0.880574	+	0.473909i	$0.157157\pi$
$881$			24785.0i			0.947818i	−0.880574	+	0.473909i	$0.842843\pi$
$882$		0			0
$883$			3938.21i			0.150092i	0.997180	+	0.0750460i	$0.0239104\pi$
$883$			3938.21i			0.150092i	−0.997180	+	0.0750460i	$0.976090\pi$
$884$		0			0
$885$	−24535.9	−	14165.8i	−0.931938	−	0.538055i
$886$		0			0
$887$	12558.0	+	21751.2i	0.475375	+	0.823374i	0.999602	−	0.0282048i	$-0.00897905\pi$
$887$	12558.0	+	21751.2i	0.475375	+	0.823374i	−0.524227	+	0.851578i	$0.675646\pi$
$888$		0			0
$889$	−307.121	+	852.507i	−0.0115866	+	0.0321622i
$890$		0			0
$891$	−3063.43	+	1768.67i	−0.115184	+	0.0665014i
$892$		0			0
$893$	−11429.6	+	19796.7i	−0.428306	+	0.741848i
$894$		0			0
$895$	−1613.93			−0.0602767
$896$		0			0
$897$	−1145.24			−0.0426293
$898$		0			0
$899$	−1922.40	+	3329.69i	−0.0713188	+	0.123528i
$900$		0			0
$901$	27576.7	−	15921.4i	1.01966	−	0.588700i
$902$		0			0
$903$	−14049.1	−	16631.8i	−0.517745	−	0.612925i
$904$		0			0
$905$	−25374.4	−	43949.8i	−0.932016	−	1.61430i
$906$		0			0
$907$	−47018.2	−	27146.0i	−1.72129	−	0.993789i	−0.916287	−	0.400522i	$-0.868829\pi$
$907$	−47018.2	−	27146.0i	−1.72129	−	0.993789i	−0.805006	−	0.593267i	$-0.797838\pi$
$908$		0			0
$909$		−	8710.18i		−	0.317820i
$910$		0			0
$911$			32933.0i			1.19772i	0.800855	+	0.598858i	$0.204379\pi$
$911$			32933.0i			1.19772i	−0.800855	+	0.598858i	$0.795621\pi$
$912$		0			0
$913$	−36551.9	−	21103.3i	−1.32496	−	0.764968i
$914$		0			0
$915$	3956.00	+	6851.99i	0.142930	+	0.247563i
$916$		0			0
$917$	−1324.38	−	7369.34i	−0.0476934	−	0.265384i
$918$		0			0
$919$	−23666.0	+	13663.5i	−0.849476	+	0.490445i	−0.860474	−	0.509495i	$-0.829832\pi$
$919$	−23666.0	+	13663.5i	−0.849476	+	0.490445i	0.0109983	+	0.999940i	$0.496499\pi$
$920$		0			0
$921$	10740.4	−	18603.0i	0.384266	−	0.665569i
$922$		0			0
$923$	−42705.3			−1.52293
$924$		0			0
$925$	2878.10			0.102304
$926$		0			0
$927$	−1201.71	+	2081.42i	−0.0425775	+	0.0737464i
$928$		0			0
$929$	21572.8	−	12455.1i	0.761875	−	0.439869i	−0.0680933	−	0.997679i	$-0.521692\pi$
$929$	21572.8	−	12455.1i	0.761875	−	0.439869i	0.829969	+	0.557810i	$0.188358\pi$
$930$		0			0
$931$	4457.57	−	26288.6i	0.156918	−	0.925429i
$932$		0			0
$933$	−4091.06	−	7085.93i	−0.143553	−	0.248642i
$934$		0			0
$935$	39945.4	+	23062.5i	1.39717	+	0.806656i
$936$		0			0
$937$		−	10564.4i		−	0.368328i	−0.982896	−	0.184164i	$-0.941042\pi$
$937$		−	10564.4i		−	0.368328i	0.982896	−	0.184164i	$-0.0589578\pi$
$938$		0			0
$939$			11786.3i			0.409617i
$940$		0			0
$941$	28671.9	+	16553.7i	0.993281	+	0.573471i	0.906254	−	0.422735i	$-0.138930\pi$
$941$	28671.9	+	16553.7i	0.993281	+	0.573471i	0.0870279	+	0.996206i	$0.472263\pi$
$942$		0			0
$943$	−602.420	−	1043.42i	−0.0208033	−	0.0360323i
$944$		0			0
$945$	−6278.56	+	1128.35i	−0.216129	+	0.0388415i
$946$		0			0
$947$	−38030.2	+	21956.8i	−1.30498	+	0.753431i	−0.981254	−	0.192720i	$-0.938269\pi$
$947$	−38030.2	+	21956.8i	−1.30498	+	0.753431i	−0.323726	+	0.946151i	$0.604936\pi$
$948$		0			0
$949$	45381.9	−	78603.7i	1.55233	−	2.68871i
$950$		0			0
$951$	10098.1			0.344324
$952$		0			0
$953$	28321.2			0.962660			0.481330	−	0.876539i	$-0.340154\pi$
$953$	28321.2			0.962660			0.481330	+	0.876539i	$0.340154\pi$
$954$		0			0
$955$	−25277.2	+	43781.4i	−0.856494	+	1.48349i
$956$		0			0
$957$	−13706.6	+	7913.52i	−0.462980	+	0.267302i
$958$		0			0
$959$	−36842.7	+	31121.5i	−1.24058	+	1.04793i
$960$		0			0
$961$	14389.0	+	24922.5i	0.483000	+	0.836580i
$962$		0			0
$963$	10642.5	+	6144.48i	0.356128	+	0.205611i
$964$		0			0
$965$			15271.2i			0.509429i
$966$		0			0
$967$			11889.1i			0.395375i	0.980265	+	0.197688i	$0.0633431\pi$
$967$			11889.1i			0.395375i	−0.980265	+	0.197688i	$0.936657\pi$
$968$		0			0
$969$	−16721.4	−	9654.09i	−0.554353	−	0.320056i
$970$		0			0
$971$	−8075.19	−	13986.6i	−0.266885	−	0.462258i	0.701171	−	0.712993i	$-0.252661\pi$
$971$	−8075.19	−	13986.6i	−0.266885	−	0.462258i	−0.968056	+	0.250735i	$0.919328\pi$
$972$		0			0
$973$	−10430.5	−	3757.65i	−0.343666	−	0.123808i
$974$		0			0
$975$	8228.62	−	4750.80i	0.270284	−	0.156048i
$976$		0			0
$977$	−5607.74	+	9712.90i	−0.183631	+	0.318058i	−0.943114	−	0.332468i	$-0.892119\pi$
$977$	−5607.74	+	9712.90i	−0.183631	+	0.318058i	0.759483	+	0.650527i	$0.225452\pi$
$978$		0			0
$979$	−31606.9			−1.03183
$980$		0			0
$981$	−8683.79			−0.282622
$982$		0			0
$983$	25317.0	−	43850.3i	0.821451	−	1.42280i	−0.0831503	−	0.996537i	$-0.526498\pi$
$983$	25317.0	−	43850.3i	0.821451	−	1.42280i	0.904602	−	0.426258i	$-0.140169\pi$
$984$		0			0
$985$	−12777.5	+	7377.07i	−0.413324	+	0.238632i
$986$		0			0
$987$	−15371.1	−	5537.51i	−0.495710	−	0.178583i
$988$		0			0
$989$	891.311	+	1543.80i	0.0286573	+	0.0496358i
$990$		0			0
$991$	34579.1	+	19964.3i	1.10842	+	0.639945i	0.938419	−	0.345499i	$-0.112290\pi$
$991$	34579.1	+	19964.3i	1.10842	+	0.639945i	0.169998	+	0.985444i	$0.445624\pi$
$992$		0			0
$993$			24401.1i			0.779804i
$994$		0			0
$995$			34836.5i			1.10994i
$996$		0			0
$997$	−34285.4	−	19794.7i	−1.08910	−	0.628790i	−0.155761	−	0.987795i	$-0.549783\pi$
$997$	−34285.4	−	19794.7i	−1.08910	−	0.628790i	−0.933336	+	0.359005i	$0.883116\pi$
$998$		0			0
$999$	−1029.43	−	1783.03i	−0.0326024	−	0.0564691i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bl.j.31.3	yes	8
4.3	odd	2		336.4.bl.i.31.3	✓	8
7.5	odd	6		336.4.bl.i.271.3	yes	8
28.19	even	6	inner	336.4.bl.j.271.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.4.bl.i.31.3	✓	8	4.3	odd	2
336.4.bl.i.271.3	yes	8	7.5	odd	6
336.4.bl.j.31.3	yes	8	1.1	even	1	trivial
336.4.bl.j.271.3	yes	8	28.19	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{3} +(11.0480 - 6.37855i) q^{5} +(17.4241 + 6.27712i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(37.8201 + 21.8355i) q^{11} +83.9138i q^{13} -38.2713i q^{15} +(71.7005 + 41.3963i) q^{17} +(-38.8686 - 67.3223i) q^{19} +(42.4445 - 35.8534i) q^{21} +(-3.93978 + 2.27463i) q^{23} +(18.8717 - 32.6868i) q^{25} -27.0000 q^{27} -120.805 q^{29} +(15.9132 - 27.5625i) q^{31} +(113.460 - 65.5064i) q^{33} +(232.539 - 41.7908i) q^{35} +(38.1272 + 66.0382i) q^{37} +(218.015 + 125.871i) q^{39} +264.843i q^{41} -391.848i q^{43} +(-99.4317 - 57.4069i) q^{45} +(-147.029 - 254.662i) q^{47} +(264.196 + 218.746i) q^{49} +(215.101 - 124.189i) q^{51} +(192.305 - 333.081i) q^{53} +557.114 q^{55} -233.211 q^{57} +(370.142 - 641.105i) q^{59} +(-179.037 + 103.367i) q^{61} +(-29.4830 - 164.054i) q^{63} +(535.248 + 927.077i) q^{65} +(172.423 + 99.5486i) q^{67} +13.6478i q^{69} +508.919i q^{71} +(-936.719 - 540.815i) q^{73} +(-56.6152 - 98.0604i) q^{75} +(521.917 + 617.864i) q^{77} +(1105.44 - 638.226i) q^{79} +(-40.5000 + 70.1481i) q^{81} -966.467 q^{83} +1056.19 q^{85} +(-181.208 + 313.861i) q^{87} +(-626.787 + 361.876i) q^{89} +(-526.737 + 1462.12i) q^{91} +(-47.7396 - 82.6875i) q^{93} +(-858.838 - 495.850i) q^{95} -1763.41i q^{97} -393.038i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{3} + 18 q^{5} + 12 q^{7} - 36 q^{9} - 150 q^{11} + 192 q^{17} + 66 q^{19} + 90 q^{21} + 492 q^{23} + 322 q^{25} - 216 q^{27} - 372 q^{29} - 156 q^{31} - 450 q^{33} - 36 q^{35} + 554 q^{37} + 198 q^{39}+ \cdots - 108 q^{95}+O(q^{100}) \) 8 * q + 12 * q^3 + 18 * q^5 + 12 * q^7 - 36 * q^9 - 150 * q^11 + 192 * q^17 + 66 * q^19 + 90 * q^21 + 492 * q^23 + 322 * q^25 - 216 * q^27 - 372 * q^29 - 156 * q^31 - 450 * q^33 - 36 * q^35 + 554 * q^37 + 198 * q^39 - 162 * q^45 - 840 * q^47 - 340 * q^49 + 576 * q^51 + 186 * q^53 - 156 * q^55 + 396 * q^57 + 126 * q^59 + 1632 * q^61 + 162 * q^63 + 936 * q^65 - 582 * q^67 - 1386 * q^73 - 966 * q^75 + 3030 * q^77 + 1260 * q^79 - 324 * q^81 - 756 * q^83 - 5688 * q^85 - 558 * q^87 + 948 * q^89 + 4074 * q^91 + 468 * q^93 - 108 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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