LMFDB - Embedded newform 63.4.o.a.20.15

Newspace parameters

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.o (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			20.15
Character	$\chi$	$=$	63.20
Dual form			63.4.o.a.41.15

$q$-expansion

$f(q)$	$=$	$q+(1.93743 + 1.11857i) q^{2} +(-5.00204 - 1.40697i) q^{3} +(-1.49759 - 2.59390i) q^{4} +(-2.75758 - 4.77627i) q^{5} +(-8.11730 - 8.32104i) q^{6} +(-17.8859 - 4.80585i) q^{7} -24.5978i q^{8} +(23.0409 + 14.0754i) q^{9} +O(q^{10})$	\(q+(1.93743 + 1.11857i) q^{2} +(-5.00204 - 1.40697i) q^{3} +(-1.49759 - 2.59390i) q^{4} +(-2.75758 - 4.77627i) q^{5} +(-8.11730 - 8.32104i) q^{6} +(-17.8859 - 4.80585i) q^{7} -24.5978i q^{8} +(23.0409 + 14.0754i) q^{9} -12.3382i q^{10} +(-30.2441 - 17.4614i) q^{11} +(3.84148 + 15.0818i) q^{12} +(23.1532 - 13.3675i) q^{13} +(-29.2768 - 29.3176i) q^{14} +(7.07349 + 27.7709i) q^{15} +(15.5338 - 26.9053i) q^{16} +35.9093 q^{17} +(28.8957 + 53.0430i) q^{18} +78.0198i q^{19} +(-8.25943 + 14.3058i) q^{20} +(82.7042 + 49.2038i) q^{21} +(-39.0638 - 67.6605i) q^{22} +(-50.1284 + 28.9416i) q^{23} +(-34.6083 + 123.039i) q^{24} +(47.2915 - 81.9113i) q^{25} +59.8102 q^{26} +(-95.4480 - 102.824i) q^{27} +(14.3198 + 53.5913i) q^{28} +(-192.066 - 110.889i) q^{29} +(-17.3594 + 61.7163i) q^{30} +(126.002 - 72.7471i) q^{31} +(-110.228 + 63.6400i) q^{32} +(126.715 + 129.895i) q^{33} +(69.5717 + 40.1672i) q^{34} +(26.3676 + 98.6801i) q^{35} +(2.00440 - 80.8449i) q^{36} +290.956 q^{37} +(-87.2708 + 151.158i) q^{38} +(-134.621 + 34.2892i) q^{39} +(-117.486 + 67.8304i) q^{40} +(-54.0606 - 93.6357i) q^{41} +(105.195 + 187.839i) q^{42} +(174.061 - 301.482i) q^{43} +104.600i q^{44} +(3.69080 - 148.863i) q^{45} -129.493 q^{46} +(125.545 - 217.450i) q^{47} +(-115.555 + 112.726i) q^{48} +(296.808 + 171.913i) q^{49} +(183.248 - 105.798i) q^{50} +(-179.620 - 50.5232i) q^{51} +(-69.3480 - 40.0381i) q^{52} +160.173i q^{53} +(-69.9077 - 305.979i) q^{54} +192.605i q^{55} +(-118.213 + 439.953i) q^{56} +(109.771 - 390.258i) q^{57} +(-248.076 - 429.680i) q^{58} +(-367.425 - 636.398i) q^{59} +(61.4417 - 59.9373i) q^{60} +(-581.350 - 335.643i) q^{61} +325.492 q^{62} +(-344.462 - 362.482i) q^{63} -533.284 q^{64} +(-127.694 - 73.7240i) q^{65} +(100.203 + 393.402i) q^{66} +(344.364 + 596.455i) q^{67} +(-53.7774 - 93.1452i) q^{68} +(291.464 - 74.2385i) q^{69} +(-59.2956 + 220.680i) q^{70} -577.396i q^{71} +(346.224 - 566.756i) q^{72} -37.4543i q^{73} +(563.705 + 325.455i) q^{74} +(-351.801 + 343.187i) q^{75} +(202.375 - 116.841i) q^{76} +(457.025 + 457.661i) q^{77} +(-299.173 - 84.1509i) q^{78} +(-428.000 + 741.317i) q^{79} -171.342 q^{80} +(332.766 + 648.620i) q^{81} -241.883i q^{82} +(-616.129 + 1067.17i) q^{83} +(3.77299 - 288.213i) q^{84} +(-99.0228 - 171.513i) q^{85} +(674.460 - 389.400i) q^{86} +(804.705 + 824.903i) q^{87} +(-429.513 + 743.939i) q^{88} +1505.64 q^{89} +(173.665 - 284.284i) q^{90} +(-478.358 + 127.819i) q^{91} +(150.143 + 86.6853i) q^{92} +(-732.619 + 186.604i) q^{93} +(486.467 - 280.862i) q^{94} +(372.643 - 215.146i) q^{95} +(640.903 - 163.243i) q^{96} +(1002.35 + 578.705i) q^{97} +(382.745 + 665.071i) q^{98} +(-451.074 - 828.025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44q - 6q^{2} + 78q^{4} + 5q^{7} + O(q^{10}) $	$ 44q - 6q^{2} + 78q^{4} + 5q^{7} - 18q^{11} + 204q^{14} + 66q^{15} - 242q^{16} - 210q^{18} - 57q^{21} - 34q^{22} - 102q^{23} - 352q^{25} + 300q^{28} + 246q^{29} - 144q^{30} + 1068q^{32} - 1818q^{36} + 328q^{37} - 798q^{39} - 1158q^{42} - 170q^{43} + 968q^{46} - 79q^{49} + 288q^{50} - 204q^{51} + 1212q^{56} + 324q^{57} - 538q^{58} + 5316q^{60} + 783q^{63} - 808q^{64} + 4350q^{65} - 590q^{67} + 384q^{70} + 4284q^{72} - 5304q^{74} - 2787q^{77} + 612q^{78} - 302q^{79} - 3720q^{81} + 7050q^{84} - 612q^{85} - 13692q^{86} + 1294q^{88} + 210q^{91} - 10194q^{92} - 4266q^{93} + 6336q^{95} + 1014q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.93743	+	1.11857i	0.684983	+	0.395475i	0.801730	−	0.597686i	$-0.203913\pi$
$2$	1.93743	+	1.11857i	0.684983	+	0.395475i	−0.116747	+	0.993162i	$0.537247\pi$
$3$	−5.00204	−	1.40697i	−0.962644	−	0.270771i
$3$	−5.00204	−	1.40697i	−0.962644	−	0.270771i
$4$	−1.49759	−	2.59390i	−0.187198	−	0.324237i
$5$	−2.75758	−	4.77627i	−0.246645	−	0.427202i	0.715948	−	0.698154i	$-0.245995\pi$
$5$	−2.75758	−	4.77627i	−0.246645	−	0.427202i	−0.962593	+	0.270952i	$0.912662\pi$
$6$	−8.11730	−	8.32104i	−0.552312	−	0.566175i
$7$	−17.8859	−	4.80585i	−0.965745	−	0.259491i
$7$	−17.8859	−	4.80585i	−0.965745	−	0.259491i
$8$		−	24.5978i		−	1.08708i
$9$	23.0409	+	14.0754i	0.853367	+	0.521311i
$10$		−	12.3382i		−	0.390169i
$11$	−30.2441	−	17.4614i	−0.828995	−	0.478620i	0.0245137	−	0.999699i	$-0.492196\pi$
$11$	−30.2441	−	17.4614i	−0.828995	−	0.478620i	−0.853508	+	0.521079i	$0.825530\pi$
$12$	3.84148	+	15.0818i	0.0924115	+	0.362813i
$13$	23.1532	−	13.3675i	0.493965	−	0.285191i	−0.232253	−	0.972656i	$-0.574610\pi$
$13$	23.1532	−	13.3675i	0.493965	−	0.285191i	0.726218	+	0.687464i	$0.241276\pi$
$14$	−29.2768	−	29.3176i	−0.558897	−	0.559676i
$15$	7.07349	+	27.7709i	0.121758	+	0.478028i
$16$	15.5338	−	26.9053i	0.242715	−	0.420395i
$17$	35.9093			0.512311			0.256156	−	0.966636i	$-0.417544\pi$
$17$	35.9093			0.512311			0.256156	+	0.966636i	$0.417544\pi$
$18$	28.8957	+	53.0430i	0.378376	+	0.694575i
$19$			78.0198i			0.942051i	0.882120	+	0.471025i	$0.156116\pi$
$19$			78.0198i			0.942051i	−0.882120	+	0.471025i	$0.843884\pi$
$20$	−8.25943	+	14.3058i	−0.0923432	+	0.159943i
$21$	82.7042	+	49.2038i	0.859406	+	0.511293i
$22$	−39.0638	−	67.6605i	−0.378565	−	0.655694i
$23$	−50.1284	+	28.9416i	−0.454456	+	0.262380i	−0.709710	−	0.704494i	$-0.751174\pi$
$23$	−50.1284	+	28.9416i	−0.454456	+	0.262380i	0.255254	+	0.966874i	$0.417841\pi$
$24$	−34.6083	+	123.039i	−0.294349	+	1.04647i
$25$	47.2915	−	81.9113i	0.378332	−	0.655291i
$26$	59.8102			0.451144
$27$	−95.4480	−	102.824i	−0.680332	−	0.732904i
$28$	14.3198	+	53.5913i	0.0966493	+	0.361707i
$29$	−192.066	−	110.889i	−1.22985	−	0.710056i	−0.262854	−	0.964836i	$-0.584664\pi$
$29$	−192.066	−	110.889i	−1.22985	−	0.710056i	−0.966999	+	0.254779i	$0.917997\pi$
$30$	−17.3594	+	61.7163i	−0.105646	+	0.375593i
$31$	126.002	−	72.7471i	0.730018	−	0.421476i	−0.0884105	−	0.996084i	$-0.528179\pi$
$31$	126.002	−	72.7471i	0.730018	−	0.421476i	0.818429	+	0.574608i	$0.194845\pi$
$32$	−110.228	+	63.6400i	−0.608928	+	0.351564i
$33$	126.715	+	129.895i	0.668430	+	0.685208i
$34$	69.5717	+	40.1672i	0.350925	+	0.202607i
$35$	26.3676	+	98.6801i	0.127341	+	0.476571i
$36$	2.00440	−	80.8449i	0.00927964	−	0.374282i
$37$	290.956			1.29278			0.646390	−	0.763008i	$-0.276278\pi$
$37$	290.956			1.29278			0.646390	+	0.763008i	$0.276278\pi$
$38$	−87.2708	+	151.158i	−0.372558	+	0.645289i
$39$	−134.621	+	34.2892i	−0.552734	+	0.140786i
$40$	−117.486	+	67.8304i	−0.464403	+	0.268123i
$41$	−54.0606	−	93.6357i	−0.205923	−	0.356669i	0.744503	−	0.667619i	$-0.232686\pi$
$41$	−54.0606	−	93.6357i	−0.205923	−	0.356669i	−0.950426	+	0.310949i	$0.899353\pi$
$42$	105.195	+	187.839i	0.386475	+	0.690101i
$43$	174.061	−	301.482i	0.617303	−	1.06920i	−0.372673	−	0.927963i	$-0.621559\pi$
$43$	174.061	−	301.482i	0.617303	−	1.06920i	0.989976	−	0.141238i	$-0.0451082\pi$
$44$			104.600i			0.358388i
$45$	3.69080	−	148.863i	0.0122265	−	0.493139i
$46$	−129.493			−0.415060
$47$	125.545	−	217.450i	0.389630	−	0.674858i	−0.602770	−	0.797915i	$-0.705936\pi$
$47$	125.545	−	217.450i	0.389630	−	0.674858i	0.992400	+	0.123057i	$0.0392697\pi$
$48$	−115.555	+	112.726i	−0.347479	+	0.338970i
$49$	296.808	+	171.913i	0.865328	+	0.501205i
$50$	183.248	−	105.798i	0.518303	−	0.299242i
$51$	−179.620	−	50.5232i	−0.493173	−	0.138719i
$52$	−69.3480	−	40.0381i	−0.184939	−	0.106775i
$53$			160.173i			0.415122i	0.978222	+	0.207561i	$0.0665525\pi$
$53$			160.173i			0.415122i	−0.978222	+	0.207561i	$0.933448\pi$
$54$	−69.9077	−	305.979i	−0.176171	−	0.771082i
$55$			192.605i			0.472198i
$56$	−118.213	+	439.953i	−0.282088	+	1.04984i
$57$	109.771	−	390.258i	0.255080	−	0.906859i
$58$	−248.076	−	429.680i	−0.561620	−	0.972754i
$59$	−367.425	−	636.398i	−0.810756	−	1.40427i	−0.912336	−	0.409443i	$-0.865723\pi$
$59$	−367.425	−	636.398i	−0.810756	−	1.40427i	0.101580	−	0.994827i	$-0.467610\pi$
$60$	61.4417	−	59.9373i	0.132202	−	0.128964i
$61$	−581.350	−	335.643i	−1.22023	−	0.704502i	−0.255266	−	0.966871i	$-0.582163\pi$
$61$	−581.350	−	335.643i	−1.22023	−	0.704502i	−0.964968	+	0.262368i	$0.915496\pi$
$62$	325.492			0.666734
$63$	−344.462	−	362.482i	−0.688859	−	0.724895i
$64$	−533.284			−1.04157
$65$	−127.694	−	73.7240i	−0.243669	−	0.140682i
$66$	100.203	+	393.402i	0.186881	+	0.733704i
$67$	344.364	+	596.455i	0.627921	+	1.08759i	0.987968	+	0.154657i	$0.0494273\pi$
$67$	344.364	+	596.455i	0.627921	+	1.08759i	−0.360047	+	0.932934i	$0.617239\pi$
$68$	−53.7774	−	93.1452i	−0.0959039	−	0.166110i
$69$	291.464	−	74.2385i	0.508524	−	0.129526i
$70$	−59.2956	+	220.680i	−0.101245	+	0.376804i
$71$		−	577.396i		−	0.965130i	−0.875860	−	0.482565i	$-0.839705\pi$
$71$		−	577.396i		−	0.965130i	0.875860	−	0.482565i	$-0.160295\pi$
$72$	346.224	−	566.756i	0.566707	−	0.927678i
$73$		−	37.4543i		−	0.0600506i	−0.999549	−	0.0300253i	$-0.990441\pi$
$73$		−	37.4543i		−	0.0600506i	0.999549	−	0.0300253i	$-0.00955879\pi$
$74$	563.705	+	325.455i	0.885532	+	0.511262i
$75$	−351.801	+	343.187i	−0.541633	+	0.528370i
$76$	202.375	−	116.841i	0.305448	−	0.176350i
$77$	457.025	+	457.661i	0.676400	+	0.677342i
$78$	−299.173	−	84.1509i	−0.434291	−	0.122157i
$79$	−428.000	+	741.317i	−0.609541	+	1.05576i	0.381775	+	0.924255i	$0.375313\pi$
$79$	−428.000	+	741.317i	−0.609541	+	1.05576i	−0.991316	+	0.131501i	$0.958020\pi$
$80$	−171.342			−0.239458
$81$	332.766	+	648.620i	0.456469	+	0.889739i
$82$		−	241.883i		−	0.325750i
$83$	−616.129	+	1067.17i	−0.814806	+	1.41129i	0.0946603	+	0.995510i	$0.469824\pi$
$83$	−616.129	+	1067.17i	−0.814806	+	1.41129i	−0.909467	+	0.415777i	$0.863510\pi$
$84$	3.77299	−	288.213i	0.00490079	−	0.374365i
$85$	−99.0228	−	171.513i	−0.126359	−	0.218861i
$86$	674.460	−	389.400i	0.845685	−	0.488256i
$87$	804.705	+	824.903i	0.991649	+	1.01654i
$88$	−429.513	+	743.939i	−0.520299	+	0.901184i
$89$	1505.64			1.79323			0.896615	−	0.442811i	$-0.146019\pi$
$89$	1505.64			1.79323			0.896615	+	0.442811i	$0.146019\pi$
$90$	173.665	−	284.284i	0.203399	−	0.332957i
$91$	−478.358	+	127.819i	−0.551050	+	0.147242i
$92$	150.143	+	86.6853i	0.170147	+	0.0982344i
$93$	−732.619	+	186.604i	−0.816871	+	0.208064i
$94$	486.467	−	280.862i	0.533780	−	0.308178i
$95$	372.643	−	215.146i	0.402446	−	0.232352i
$96$	640.903	−	163.243i	0.681374	−	0.173552i
$97$	1002.35	+	578.705i	1.04921	+	0.605759i	0.922427	−	0.386172i	$-0.126203\pi$
$97$	1002.35	+	578.705i	1.04921	+	0.605759i	0.126778	+	0.991931i	$0.459536\pi$
$98$	382.745	+	665.071i	0.394521	+	0.685533i
$99$	−451.074	−	828.025i	−0.457926	−	0.840603i
$100$	−283.293			−0.283293
$101$	77.7834	−	134.725i	0.0766311	−	0.132729i	−0.825163	−	0.564894i	$-0.808917\pi$
$101$	77.7834	−	134.725i	0.0766311	−	0.132729i	0.901794	+	0.432165i	$0.142250\pi$
$102$	−291.487	−	298.803i	−0.282956	−	0.290058i
$103$	−1640.73	+	947.276i	−1.56957	+	0.906193i	−0.573354	+	0.819307i	$0.694358\pi$
$103$	−1640.73	+	947.276i	−1.56957	+	0.906193i	−0.996218	+	0.0868857i	$0.972309\pi$
$104$	−328.812	−	569.519i	−0.310026	−	0.536980i
$105$	6.94737	−	530.701i	0.00645709	−	0.493248i
$106$	−179.165	+	310.323i	−0.164170	+	0.284351i
$107$		−	507.467i		−	0.458492i	−0.973369	−	0.229246i	$-0.926374\pi$
$107$		−	507.467i		−	0.458492i	0.973369	−	0.229246i	$-0.0736260\pi$
$108$	−123.772	+	401.570i	−0.110278	+	0.357787i
$109$	298.426			0.262239			0.131119	−	0.991367i	$-0.458143\pi$
$109$	298.426			0.262239			0.131119	+	0.991367i	$0.458143\pi$
$110$	−215.443	+	373.158i	−0.186743	+	0.323448i
$111$	−1455.37	−	409.365i	−1.24449	−	0.350047i
$112$	−407.137	+	406.571i	−0.343490	+	0.343012i
$113$	216.173	−	124.808i	0.179964	−	0.103902i	−0.407312	−	0.913289i	$-0.633534\pi$
$113$	216.173	−	124.808i	0.179964	−	0.103902i	0.587276	+	0.809387i	$0.300200\pi$
$114$	649.206	−	633.310i	0.533366	−	0.520306i
$115$	276.466	+	159.618i	0.224179	+	0.129430i
$116$			664.266i			0.531686i
$117$	721.625	+	17.8914i	0.570207	+	0.0141373i
$118$		−	1643.97i		−	1.28254i
$119$	−642.269	−	172.575i	−0.494762	−	0.132940i
$120$	683.104	−	173.992i	0.519655	−	0.132360i
$121$	−55.6960	−	96.4683i	−0.0418452	−	0.0724781i
$122$	−750.882	−	1300.57i	−0.557227	−	0.965145i
$123$	138.671	+	544.431i	0.101655	+	0.399103i
$124$	−377.397	−	217.890i	−0.273317	−	0.157799i
$125$	−1211.03			−0.866546
$126$	−261.907	−	1087.59i	−0.185179	−	0.768968i
$127$	1942.24			1.35706			0.678528	−	0.734574i	$-0.262618\pi$
$127$	1942.24			1.35706			0.678528	+	0.734574i	$0.262618\pi$
$128$	−151.377	−	87.3976i	−0.104531	−	0.0603510i
$129$	−1294.84	+	1263.13i	−0.883751	+	0.862112i
$130$	−164.931	−	285.670i	−0.111273	−	0.192730i
$131$	−13.2642	−	22.9743i	−0.00884655	−	0.0153227i	0.861568	−	0.507642i	$-0.169483\pi$
$131$	−13.2642	−	22.9743i	−0.00884655	−	0.0153227i	−0.870415	+	0.492319i	$0.836149\pi$
$132$	147.169	−	523.215i	0.0970409	−	0.345000i
$133$	374.951	−	1395.45i	0.244454	−	0.909781i
$134$			1540.78i			0.993309i
$135$	−227.907	+	739.429i	−0.145297	+	0.471407i
$136$		−	883.291i		−	0.556924i
$137$	−230.946	−	133.337i	−0.144023	−	0.0831515i	0.426257	−	0.904602i	$-0.359832\pi$
$137$	−230.946	−	133.337i	−0.144023	−	0.0831515i	−0.570280	+	0.821451i	$0.693165\pi$
$138$	647.732	+	182.193i	0.399555	+	0.112386i
$139$	444.807	−	256.810i	0.271425	−	0.156707i	−0.358110	−	0.933679i	$-0.616579\pi$
$139$	444.807	−	256.810i	0.271425	−	0.156707i	0.629535	+	0.776972i	$0.283245\pi$
$140$	216.478	−	216.177i	0.130684	−	0.130502i
$141$	−933.925	+	911.057i	−0.557806	+	0.544148i
$142$	645.859	−	1118.66i	0.381685	−	0.661098i
$143$	−933.665			−0.545993
$144$	736.614	−	401.277i	0.426281	−	0.232221i
$145$			1223.14i			0.700528i
$146$	41.8954	−	72.5650i	0.0237486	−	0.0411337i
$147$	−1242.77	−	1277.52i	−0.697291	−	0.716788i
$148$	−435.732	−	754.709i	−0.242006	−	0.419167i
$149$	−1835.58	+	1059.77i	−1.00924	+	0.582683i	−0.910968	−	0.412477i	$-0.864664\pi$
$149$	−1835.58	+	1059.77i	−1.00924	+	0.582683i	−0.0982688	+	0.995160i	$0.531331\pi$
$150$	−1065.47	+	271.384i	−0.579967	+	0.147723i
$151$	1141.85	−	1977.74i	0.615380	−	1.06587i	−0.374937	−	0.927050i	$-0.622336\pi$
$151$	1141.85	−	1977.74i	0.615380	−	1.06587i	0.990318	−	0.138820i	$-0.0443309\pi$
$152$	1919.12			1.02408
$153$	827.383	+	505.439i	0.437189	+	0.267074i
$154$	373.524	+	1397.90i	0.195451	+	0.731468i
$155$	−694.919	−	401.212i	−0.360111	−	0.207910i
$156$	290.549	+	297.842i	0.149119	+	0.152862i
$157$	3179.20	−	1835.51i	1.61610	−	0.933057i	0.628186	−	0.778063i	$-0.283798\pi$
$157$	3179.20	−	1835.51i	1.61610	−	0.933057i	0.987916	−	0.154993i	$-0.0495356\pi$
$158$	−1658.44	+	957.498i	−0.835051	+	0.482117i
$159$	225.358	−	801.192i	0.112403	−	0.399614i
$160$	607.923	+	350.984i	0.300378	+	0.173423i
$161$	1035.68	−	276.737i	0.506974	−	0.135465i
$162$	−80.8198	+	1628.88i	−0.0391963	+	0.789979i
$163$	169.826			0.0816063			0.0408032	−	0.999167i	$-0.487008\pi$
$163$	169.826			0.0816063			0.0408032	+	0.999167i	$0.487008\pi$
$164$	−161.921	+	280.455i	−0.0770970	+	0.133536i
$165$	270.989	−	963.420i	0.127857	−	0.454558i
$166$	−2387.41	+	1378.37i	−1.11626	+	0.644472i
$167$	218.313	+	378.129i	0.101159	+	0.175213i	0.912162	−	0.409829i	$-0.134412\pi$
$167$	218.313	+	378.129i	0.101159	+	0.175213i	−0.811003	+	0.585041i	$0.801078\pi$
$168$	1210.31	−	2034.34i	0.555817	−	0.934244i
$169$	−741.119	+	1283.66i	−0.337332	+	0.584276i
$170$		−	443.057i		−	0.199888i
$171$	−1098.16	+	1797.65i	−0.491102	+	0.803915i
$172$	−1042.69			−0.462233
$173$	827.732	−	1433.67i	0.363765	−	0.630059i	−0.624812	−	0.780775i	$-0.714825\pi$
$173$	827.732	−	1433.67i	0.363765	−	0.630059i	0.988577	+	0.150716i	$0.0481579\pi$
$174$	636.341	+	2498.31i	0.277247	+	1.08849i
$175$	−1239.50	+	1237.78i	−0.535415	+	0.534670i
$176$	−939.610	+	542.484i	−0.402419	+	0.232337i
$177$	942.484	+	3700.24i	0.400234	+	1.57134i
$178$	2917.07	+	1684.17i	1.22833	+	0.709178i
$179$		−	4545.28i		−	1.89793i	−0.315376	−	0.948967i	$-0.602131\pi$
$179$		−	4545.28i		−	1.89793i	0.315376	−	0.948967i	$-0.397869\pi$
$180$	−391.664	+	213.363i	−0.162183	+	0.0883506i
$181$			69.4780i			0.0285318i	0.999898	+	0.0142659i	$0.00454113\pi$
$181$			69.4780i			0.0285318i	−0.999898	+	0.0142659i	$0.995459\pi$
$182$	−1069.76	−	287.439i	−0.435690	−	0.117068i
$183$	2435.70	+	2496.84i	0.983892	+	1.00859i
$184$	711.901	+	1233.05i	0.285229	+	0.494030i
$185$	−802.333	−	1389.68i	−0.318858	−	0.552278i
$186$	−1628.12	−	457.956i	−0.641827	−	0.180532i
$187$	−1086.05	−	627.029i	−0.424703	−	0.245203i
$188$	−752.057			−0.291752
$189$	1213.01	+	2297.80i	0.466846	+	0.884339i
$190$	962.625			0.367559
$191$	1216.59	+	702.396i	0.460885	+	0.266092i	0.712416	−	0.701757i	$-0.247601\pi$
$191$	1216.59	+	702.396i	0.460885	+	0.266092i	−0.251531	+	0.967849i	$0.580934\pi$
$192$	2667.51	+	750.312i	1.00266	+	0.282027i
$193$	−1156.04	−	2002.32i	−0.431158	−	0.746787i	0.565815	−	0.824532i	$-0.308561\pi$
$193$	−1156.04	−	2002.32i	−0.431158	−	0.746787i	−0.996973	+	0.0777446i	$0.975228\pi$
$194$	1294.65	+	2242.40i	0.479125	+	0.829870i
$195$	535.002	+	548.431i	0.196473	+	0.201405i
$196$	1.43036	−	1027.34i	0.000521267	−	0.374397i
$197$			1556.72i			0.563005i	0.959561	+	0.281502i	$0.0908327\pi$
$197$			1556.72i			0.563005i	−0.959561	+	0.281502i	$0.909167\pi$
$198$	52.2838	−	2108.80i	0.0187659	−	0.756898i
$199$		−	1187.87i		−	0.423146i	−0.977362	−	0.211573i	$-0.932141\pi$
$199$		−	1187.87i		−	0.423146i	0.977362	−	0.211573i	$-0.0678585\pi$
$200$	−2014.84	−	1163.27i	−0.712353	−	0.411277i
$201$	−883.330	−	3468.00i	−0.309977	−	1.21699i
$202$	301.399	−	174.013i	0.104982	−	0.0606114i
$203$	2902.35	+	2906.39i	1.00347	+	1.00487i
$204$	137.945	+	541.579i	0.0473435	+	0.185873i
$205$	−298.153	+	516.416i	−0.101580	+	0.175942i
$206$	−4238.39			−1.43351
$207$	−1562.37	−	38.7361i	−0.524600	−	0.0130065i
$208$		−	830.592i		−	0.276881i
$209$	1362.34	−	2359.64i	0.450885	−	0.780955i
$210$	607.088	−	1020.42i	0.199491	−	0.335313i
$211$	−122.996	−	213.035i	−0.0401298	−	0.0695069i	0.845263	−	0.534351i	$-0.179444\pi$
$211$	−122.996	−	213.035i	−0.0401298	−	0.0695069i	−0.885393	+	0.464844i	$0.846110\pi$
$212$	415.472	−	239.873i	0.134598	−	0.0777101i
$213$	−812.376	+	2888.16i	−0.261329	+	0.929077i
$214$	567.639	−	983.179i	0.181322	−	0.314059i
$215$	−1919.95			−0.609020
$216$	−2529.24	+	2347.81i	−0.796725	+	0.739576i
$217$	−2603.26	+	695.599i	−0.814381	+	0.217605i
$218$	578.178	+	333.811i	0.179629	+	0.103709i
$219$	−52.6969	+	187.348i	−0.0162600	+	0.0578074i
$220$	499.598	−	288.443i	0.153104	−	0.0883947i
$221$	831.417	−	480.019i	0.253064	−	0.146107i
$222$	−2361.77	−	2421.06i	−0.714018	−	0.731940i
$223$	−951.393	−	549.287i	−0.285695	−	0.164946i	0.350304	−	0.936636i	$-0.386078\pi$
$223$	−951.393	−	549.287i	−0.285695	−	0.164946i	−0.635999	+	0.771690i	$0.719412\pi$
$224$	2277.36	−	608.518i	0.679297	−	0.181510i
$225$	2242.57	−	1221.66i	0.664466	−	0.361974i
$226$	558.427			0.164363
$227$	2151.95	−	3727.29i	0.629208	−	1.08982i	−0.358503	−	0.933528i	$-0.616713\pi$
$227$	2151.95	−	3727.29i	0.629208	−	1.08982i	0.987711	−	0.156291i	$-0.0499539\pi$
$228$	−1176.68	+	299.711i	−0.341788	+	0.0870564i
$229$	2476.51	−	1429.81i	0.714639	−	0.412597i	−0.0981371	−	0.995173i	$-0.531288\pi$
$229$	2476.51	−	1429.81i	0.714639	−	0.412597i	0.812776	+	0.582576i	$0.197955\pi$
$230$	357.088	+	618.495i	0.102373	+	0.177315i
$231$	−1642.14	−	2932.26i	−0.467728	−	0.835189i
$232$	−2727.64	+	4724.40i	−0.771888	+	1.33695i
$233$			2256.65i			0.634497i	0.948342	+	0.317249i	$0.102759\pi$
$233$			2256.65i			0.634497i	−0.948342	+	0.317249i	$0.897241\pi$
$234$	1378.08	+	841.853i	0.384991	+	0.235187i
$235$	−1384.80			−0.384401
$236$	−1100.50	+	1906.12i	−0.303545	+	0.525755i
$237$	3183.88	−	3105.92i	0.872639	−	0.851271i
$238$	−1051.31	−	1052.78i	−0.286329	−	0.286728i
$239$	1367.09	−	789.292i	0.370000	−	0.213620i	−0.303458	−	0.952845i	$-0.598141\pi$
$239$	1367.09	−	789.292i	0.370000	−	0.213620i	0.673458	+	0.739225i	$0.264808\pi$
$240$	857.062	+	241.073i	0.230513	+	0.0648382i
$241$	−1248.30	−	720.708i	−0.333652	−	0.192634i	0.323809	−	0.946122i	$-0.395036\pi$
$241$	−1248.30	−	720.708i	−0.333652	−	0.192634i	−0.657461	+	0.753488i	$0.728370\pi$
$242$		−	249.200i		−	0.0661951i
$243$	−751.924	−	3712.62i	−0.198502	−	0.980101i
$244$			2010.62i			0.527527i
$245$	2.63378	−	1891.70i	0.000686801	−	0.493290i
$246$	−340.321	+	1209.91i	−0.0882035	+	0.313581i
$247$	1042.93	+	1806.41i	0.268664	+	0.465341i
$248$	−1789.42	−	3099.37i	−0.458179	−	0.793589i
$249$	4583.37	−	4471.14i	1.16650	−	1.13794i
$250$	−2346.29	−	1354.63i	−0.593570	−	0.342698i
$251$	−2935.90			−0.738296			−0.369148	−	0.929371i	$-0.620350\pi$
$251$	−2935.90			−0.738296			−0.369148	+	0.929371i	$0.620350\pi$
$252$	−424.379	+	1436.35i	−0.106085	+	0.359053i
$253$	2021.45			0.502322
$254$	3762.95	+	2172.54i	0.929562	+	0.536683i
$255$	254.004	+	997.235i	0.0623779	+	0.244899i
$256$	1937.62	+	3356.05i	0.473051	+	0.819348i
$257$	3638.04	+	6301.27i	0.883015	+	1.52943i	0.847973	+	0.530040i	$0.177823\pi$
$257$	3638.04	+	6301.27i	0.883015	+	1.52943i	0.0350420	+	0.999386i	$0.488843\pi$
$258$	−3921.55	+	998.853i	−0.946299	+	0.241030i
$259$	−5203.99	−	1398.29i	−1.24850	−	0.335465i
$260$			441.632i			0.105342i
$261$	−2864.56	−	5258.40i	−0.679355	−	1.24707i
$262$		−	59.3479i		−	0.0139944i
$263$	5830.68	+	3366.35i	1.36705	+	0.789269i	0.990551	−	0.137146i	$-0.0437930\pi$
$263$	5830.68	+	3366.35i	1.36705	+	0.789269i	0.376503	+	0.926415i	$0.377126\pi$
$264$	3195.14	−	3116.91i	0.744876	−	0.726637i
$265$	765.029	−	441.689i	0.177341	−	0.102388i
$266$	2287.35	−	2284.17i	0.527243	−	0.526509i
$267$	−7531.28	−	2118.38i	−1.72624	−	0.485554i
$268$	1031.43	−	1786.49i	0.235092	−	0.407191i
$269$	−7501.34			−1.70024			−0.850121	−	0.526588i	$-0.823471\pi$
$269$	−7501.34			−1.70024			−0.850121	+	0.526588i	$0.823471\pi$
$270$	−1268.66	+	1177.66i	−0.285956	+	0.265444i
$271$			4621.90i			1.03602i	0.855376	+	0.518008i	$0.173326\pi$
$271$			4621.90i			1.03602i	−0.855376	+	0.518008i	$0.826674\pi$
$272$	557.807	−	966.150i	0.124346	−	0.215373i
$273$	2572.60	+	33.6778i	0.570333	+	0.00746620i
$274$	−298.294	−	516.661i	−0.0657687	−	0.113915i
$275$	−2860.58	+	1651.56i	−0.627271	+	0.362155i
$276$	−629.060	−	644.850i	−0.137192	−	0.140636i
$277$	982.366	−	1701.51i	0.213085	−	0.369075i	−0.739593	−	0.673054i	$-0.764982\pi$
$277$	982.366	−	1701.51i	0.213085	−	0.369075i	0.952679	+	0.303980i	$0.0983154\pi$
$278$	1149.04			0.247895
$279$	3927.14	+	97.3663i	0.842694	+	0.0208931i
$280$	2427.32	−	648.586i	0.518071	−	0.138430i
$281$	1702.23	+	982.785i	0.361376	+	0.208641i	0.669684	−	0.742646i	$-0.266429\pi$
$281$	1702.23	+	982.785i	0.361376	+	0.208641i	−0.308308	+	0.951287i	$0.599763\pi$
$282$	−2828.50	+	720.442i	−0.597285	+	0.152134i
$283$	4621.27	−	2668.09i	0.970692	−	0.560429i	0.0712447	−	0.997459i	$-0.477303\pi$
$283$	4621.27	−	2668.09i	0.970692	−	0.560429i	0.899447	+	0.437030i	$0.143970\pi$
$284$	−1497.71	+	864.701i	−0.312931	+	0.180671i
$285$	−2166.68	+	551.872i	−0.450327	+	0.114702i
$286$	−1808.91	−	1044.37i	−0.373996	−	0.215927i
$287$	516.921	+	1934.56i	0.106317	+	0.397887i
$288$	−3435.50	−	85.1771i	−0.702913	−	0.0174275i
$289$	−3623.52			−0.737537
$290$	−1368.18	+	2369.75i	−0.277042	+	0.479850i
$291$	−4199.57	−	4304.98i	−0.845989	−	0.867224i
$292$	−97.1527	+	56.0911i	−0.0194707	+	0.0112414i
$293$	−1032.50	−	1788.34i	−0.205867	−	0.356572i	0.744542	−	0.667576i	$-0.232668\pi$
$293$	−1032.50	−	1788.34i	−0.205867	−	0.356572i	−0.950409	+	0.311004i	$0.899335\pi$
$294$	−978.776	−	3865.22i	−0.194161	−	0.766749i
$295$	−2026.40	+	3509.83i	−0.399938	+	0.692713i
$296$		−	7156.88i		−	1.40535i
$297$	1091.29	+	4776.47i	0.213209	+	0.933194i
$298$	−4741.73			−0.921748
$299$	−773.756	+	1340.18i	−0.149657	+	0.259214i
$300$	1417.04	+	398.583i	0.272710	+	0.0767074i
$301$	−4562.11	+	4555.76i	−0.873606	+	0.872391i
$302$	4424.50	−	2554.49i	0.843051	−	0.486736i
$303$	−578.629	+	564.461i	−0.109708	+	0.107021i
$304$	2099.14	+	1211.94i	0.396033	+	0.228650i
$305$			3702.24i			0.695049i
$306$	1037.62	+	1904.74i	0.193846	+	0.355839i
$307$			395.602i			0.0735446i	0.999324	+	0.0367723i	$0.0117076\pi$
$307$			395.602i			0.0735446i	−0.999324	+	0.0367723i	$0.988292\pi$
$308$	502.692	−	1870.86i	0.0929986	−	0.346111i
$309$	9539.79	−	2429.87i	1.75631	−	0.447347i
$310$	−897.569	−	1554.64i	−0.164447	−	0.284830i
$311$	3155.13	+	5464.85i	0.575277	+	0.996409i	0.996011	+	0.0892250i	$0.0284390\pi$
$311$	3155.13	+	5464.85i	0.575277	+	0.996409i	−0.420735	+	0.907184i	$0.638228\pi$
$312$	843.438	+	3311.39i	0.153046	+	0.600866i
$313$	8787.97	+	5073.73i	1.58698	+	0.916244i	0.993801	+	0.111175i	$0.0354613\pi$
$313$	8787.97	+	5073.73i	1.58698	+	0.916244i	0.593180	+	0.805070i	$0.297872\pi$
$314$	8212.62			1.47600
$315$	−781.428	+	2644.81i	−0.139773	+	0.473074i
$316$	2563.87			0.456421
$317$	1537.07	+	887.426i	0.272335	+	0.157233i	0.629948	−	0.776637i	$-0.283076\pi$
$317$	1537.07	+	887.426i	0.272335	+	0.157233i	−0.357613	+	0.933870i	$0.616409\pi$
$318$	1332.81	−	1300.17i	0.235032	−	0.229277i
$319$	3872.58	+	6707.50i	0.679695	+	1.17727i
$320$	1470.57	+	2547.11i	0.256898	+	0.444961i
$321$	−713.988	+	2538.37i	−0.124146	+	0.441365i
$322$	2316.10	+	622.325i	0.400842	+	0.107704i
$323$			2801.64i			0.482623i
$324$	1184.11	−	1834.53i	0.203036	−	0.314562i
$325$		−	2528.68i		−	0.431588i
$326$	329.026	+	189.963i	0.0558990	+	0.0322733i
$327$	−1492.74	−	419.875i	−0.252443	−	0.0710065i
$328$	−2303.23	+	1329.77i	−0.387728	+	0.223855i
$329$	−3290.51	+	3285.93i	−0.551403	+	0.550636i
$330$	1602.68	−	1563.43i	0.267347	−	0.260801i
$331$	−2397.72	+	4152.98i	−0.398160	+	0.689633i	−0.993499	−	0.113842i	$-0.963684\pi$
$331$	−2397.72	+	4152.98i	−0.398160	+	0.689633i	0.595339	+	0.803474i	$0.297018\pi$
$332$	3690.83			0.610122
$333$	6703.88	+	4095.32i	1.10321	+	0.673940i
$334$			976.796i			0.160024i
$335$	1899.22	−	3289.54i	0.309748	−	0.536498i
$336$	2608.55	−	1460.86i	0.423536	−	0.237191i
$337$	−3694.91	−	6399.77i	−0.597253	−	1.03447i	−0.993225	−	0.116210i	$-0.962925\pi$
$337$	−3694.91	−	6399.77i	−0.597253	−	1.03447i	0.395971	−	0.918263i	$-0.370408\pi$
$338$	−2871.72	+	1657.99i	−0.462134	+	0.266813i
$339$	−1256.91	+	320.146i	−0.201374	+	0.0512918i
$340$	−296.591	+	513.710i	−0.0473085	+	0.0819407i
$341$	−5081.08			−0.806908
$342$	−4138.40	+	2254.43i	−0.654325	+	0.356450i
$343$	−4482.47	−	4501.23i	−0.705628	−	0.708582i
$344$	−7415.81	−	4281.52i	−1.16231	−	0.671058i
$345$	−1158.32	−	1187.39i	−0.180759	−	0.185296i
$346$	3207.34	−	1851.76i	0.498346	−	0.287720i
$347$	1565.28	−	903.715i	0.242157	−	0.139810i	−0.374010	−	0.927424i	$-0.622018\pi$
$347$	1565.28	−	903.715i	0.242157	−	0.139810i	0.616168	+	0.787615i	$0.288684\pi$
$348$	934.599	−	3322.69i	0.143965	−	0.511824i
$349$	−5094.40	−	2941.25i	−0.781367	−	0.451122i	0.0555477	−	0.998456i	$-0.482310\pi$
$349$	−5094.40	−	2941.25i	−0.781367	−	0.451122i	−0.836914	+	0.547334i	$0.815643\pi$
$350$	−3785.99	+	1011.63i	−0.578199	+	0.154497i
$351$	−3584.43	−	1104.79i	−0.545078	−	0.168004i
$352$	4444.98			0.673064
$353$	−1196.54	+	2072.48i	−0.180413	+	0.312484i	−0.942021	−	0.335554i	$-0.891077\pi$
$353$	−1196.54	+	2072.48i	−0.180413	+	0.312484i	0.761609	+	0.648037i	$0.224410\pi$
$354$	−2313.00	+	8223.19i	−0.347273	+	1.23463i
$355$	−2757.80	+	1592.21i	−0.412306	+	0.238045i
$356$	−2254.83	−	3905.48i	−0.335690	−	0.581432i
$357$	2969.85	+	1766.88i	0.440284	+	0.261941i
$358$	5084.23	−	8806.14i	0.750586	−	1.30005i
$359$		−	10728.4i		−	1.57723i	−0.614887	−	0.788615i	$-0.710798\pi$
$359$		−	10728.4i		−	1.57723i	0.614887	−	0.788615i	$-0.289202\pi$
$360$	−3661.72	−	90.7857i	−0.536082	−	0.0132912i
$361$	771.915			0.112540
$362$	−77.7162	+	134.608i	−0.0112836	+	0.0195438i
$363$	142.866	+	560.901i	0.0206571	+	0.0811011i
$364$	1047.93	+	1049.39i	0.150897	+	0.151107i
$365$	−178.892	+	103.283i	−0.0256538	+	0.0148112i
$366$	1926.09	+	7561.95i	0.275078	+	1.07997i
$367$	4743.12	+	2738.44i	0.674630	+	0.389498i	0.797829	−	0.602884i	$-0.205982\pi$
$367$	4743.12	+	2738.44i	0.674630	+	0.389498i	−0.123199	+	0.992382i	$0.539315\pi$
$368$			1798.29i			0.254735i
$369$	72.3559	−	2918.38i	0.0102078	−	0.411720i
$370$		−	3589.87i		−	0.504402i
$371$	769.767	−	2864.83i	0.107721	−	0.400902i
$372$	1581.19	+	1620.88i	0.220379	+	0.225911i
$373$	−6052.38	−	10483.0i	−0.840162	−	1.45520i	−0.889757	−	0.456434i	$-0.849127\pi$
$373$	−6052.38	−	10483.0i	−0.840162	−	1.45520i	0.0495956	−	0.998769i	$-0.484207\pi$
$374$	−1402.76	−	2429.64i	−0.193943	−	0.335920i
$375$	6057.65	+	1703.88i	0.834175	+	0.234635i
$376$	−5348.80	−	3088.13i	−0.733625	−	0.423559i
$377$	−5929.26			−0.810007
$378$	−220.127	+	5808.65i	−0.0299527	+	0.790383i
$379$	2.33509			0.000316479			0.000158240	−	1.00000i	$-0.499950\pi$
$379$	2.33509			0.000316479			0.000158240		1.00000i	$0.499950\pi$
$380$	−1116.13	−	644.399i	−0.150675	−	0.0869920i
$381$	−9715.19	−	2732.67i	−1.30636	−	0.367451i
$382$	1571.36	+	2721.68i	0.210466	+	0.364537i
$383$	−4098.57	−	7098.93i	−0.546807	−	0.947097i	−0.998491	−	0.0549191i	$-0.982510\pi$
$383$	−4098.57	−	7098.93i	−0.546807	−	0.947097i	0.451684	−	0.892178i	$-0.350823\pi$
$384$	634.230	+	650.149i	0.0842849	+	0.0864005i
$385$	925.631	−	3444.91i	0.122531	−	0.456023i
$386$		−	5172.45i		−	0.682049i
$387$	8254.01	−	4496.45i	1.08417	−	0.590613i
$388$		−	3466.65i		−	0.453588i
$389$	−4487.63	−	2590.94i	−0.584915	−	0.337701i	0.178169	−	0.984000i	$-0.442983\pi$
$389$	−4487.63	−	2590.94i	−0.584915	−	0.337701i	−0.763084	+	0.646299i	$0.776316\pi$
$390$	423.067	+	1660.98i	0.0549303	+	0.215660i
$391$	−1800.08	+	1039.28i	−0.232823	+	0.134420i
$392$	4228.69	−	7300.82i	0.544850	−	0.940681i
$393$	34.0241	+	133.580i	0.00436715	+	0.0171457i
$394$	−1741.31	+	3016.04i	−0.222655	+	0.385649i
$395$	4720.97			0.601362
$396$	−1472.29	+	2410.08i	−0.186832	+	0.305836i
$397$		−	6757.41i		−	0.854269i	−0.904188	−	0.427135i	$-0.859523\pi$
$397$		−	6757.41i		−	0.854269i	0.904188	−	0.427135i	$-0.140477\pi$
$398$	1328.72	−	2301.41i	0.167344	−	0.289848i
$399$	−3838.87	+	6452.56i	−0.481664	+	0.809604i
$400$	−1469.23	−	2544.78i	−0.183654	−	0.318098i
$401$	−7670.47	+	4428.55i	−0.955225	+	0.551499i	−0.894700	−	0.446667i	$-0.852611\pi$
$401$	−7670.47	+	4428.55i	−0.955225	+	0.551499i	−0.0605248	+	0.998167i	$0.519277\pi$
$402$	2167.83	−	7707.07i	0.268959	−	0.956203i
$403$	1944.90	−	3368.66i	0.240403	−	0.416389i
$404$	−465.950			−0.0573809
$405$	2180.35	−	3378.00i	0.267513	−	0.414455i
$406$	2372.07	+	8877.40i	0.289960	+	1.08517i
$407$	−8799.70	−	5080.51i	−1.07171	−	0.618750i
$408$	−1242.76	+	4418.26i	−0.150799	+	0.536119i
$409$	−9564.59	+	5522.12i	−1.15633	+	0.667607i	−0.950421	−	0.310965i	$-0.899348\pi$
$409$	−9564.59	+	5522.12i	−1.15633	+	0.667607i	−0.205907	+	0.978571i	$0.566015\pi$
$410$	−1155.30	+	667.011i	−0.139161	+	0.0803447i
$411$	967.604	+	991.891i	0.116127	+	0.119042i
$412$	4914.28	+	2837.26i	0.587643	+	0.339276i
$413$	3513.27	+	13148.3i	0.418588	+	1.56655i
$414$	−2983.64	−	1822.67i	−0.354198	−	0.216375i
$415$	6796.10			0.803873
$416$	−1701.42	+	2946.94i	−0.200526	+	0.347321i
$417$	−2586.27	+	658.745i	−0.303717	+	0.0773594i
$418$	5278.86	−	3047.75i	0.617697	−	0.356628i
$419$	4827.28	+	8361.09i	0.562835	+	0.974859i	0.997247	+	0.0741448i	$0.0236227\pi$
$419$	4827.28	+	8361.09i	0.562835	+	0.974859i	−0.434412	+	0.900714i	$0.643044\pi$
$420$	−1386.99	+	776.750i	−0.161138	+	0.0902417i
$421$	1311.18	−	2271.02i	0.151788	−	0.262905i	−0.780097	−	0.625659i	$-0.784830\pi$
$421$	1311.18	−	2271.02i	0.151788	−	0.262905i	0.931885	+	0.362754i	$0.118164\pi$
$422$		−	550.320i		−	0.0634814i
$423$	5953.36	−	3243.15i	0.684308	−	0.372783i
$424$	3939.91			0.451271
$425$	1698.21	−	2941.38i	0.193824	−	0.335713i
$426$	−4804.53	+	4686.89i	−0.546433	+	0.533053i
$427$	8784.90	+	8797.14i	0.995623	+	0.997010i
$428$	−1316.32	+	759.976i	−0.148660	+	0.0858290i
$429$	4670.23	+	1313.63i	0.525597	+	0.147839i
$430$	−3719.75	−	2147.60i	−0.417168	−	0.240852i
$431$		−	2142.38i		−	0.239431i	−0.992808	−	0.119716i	$-0.961802\pi$
$431$		−	2142.38i		−	0.239431i	0.992808	−	0.119716i	$-0.0381983\pi$
$432$	−4249.16	+	970.817i	−0.473236	+	0.108121i
$433$			8576.98i			0.951925i	0.879466	+	0.475962i	$0.157900\pi$
$433$			8576.98i			0.951925i	−0.879466	+	0.475962i	$0.842100\pi$
$434$	−5821.70	−	1564.26i	−0.643895	−	0.173012i
$435$	1720.92	−	6118.22i	0.189682	−	0.674359i
$436$	−446.919	−	774.086i	−0.0490907	−	0.0850276i
$437$	−2258.02	−	3911.01i	−0.247176	−	0.428121i
$438$	−311.659	+	304.028i	−0.0339992	+	0.0331667i
$439$	6408.01	+	3699.67i	0.696669	+	0.402222i	0.806106	−	0.591772i	$-0.201571\pi$
$439$	6408.01	+	3699.67i	0.696669	+	0.402222i	−0.109437	+	0.993994i	$0.534905\pi$
$440$	4737.67			0.513317
$441$	4418.96	+	8138.73i	0.477158	+	0.878817i
$442$	2147.75			0.231126
$443$	12279.2	+	7089.41i	1.31694	+	0.760334i	0.983235	−	0.182345i	$-0.0583687\pi$
$443$	12279.2	+	7089.41i	1.31694	+	0.760334i	0.333702	+	0.942679i	$0.391702\pi$
$444$	1117.70	+	4388.15i	0.119468	+	0.469037i
$445$	−4151.92	−	7191.33i	−0.442292	−	0.766072i
$446$	−1228.84	−	2128.41i	−0.130464	−	0.225971i
$447$	10672.7	−	2718.43i	1.12931	−	0.287645i
$448$	9538.24	+	2562.88i	1.00589	+	0.270279i
$449$			6800.58i			0.714787i	0.933954	+	0.357393i	$0.116334\pi$
$449$			6800.58i			0.714787i	−0.933954	+	0.357393i	$0.883666\pi$
$450$	5711.34	+	141.602i	0.598300	+	0.0148338i
$451$			3775.90i			0.394236i
$452$	−647.477	−	373.821i	−0.0673778	−	0.0389006i
$453$	−8494.20	+	8286.21i	−0.880998	+	0.859426i
$454$	8338.50	−	4814.23i	0.861994	−	0.497672i
$455$	1929.60	+	1932.29i	0.198816	+	0.199093i
$456$	−9599.50	−	2700.13i	−0.985829	−	0.277292i
$457$	1885.91	−	3266.49i	0.193040	−	0.334355i	−0.753216	−	0.657773i	$-0.771499\pi$
$457$	1885.91	−	3266.49i	0.193040	−	0.334355i	0.946256	+	0.323418i	$0.104832\pi$
$458$	6397.41			0.652688
$459$	−3427.47	−	3692.33i	−0.348542	−	0.375475i
$460$		−	956.166i		−	0.0969162i
$461$	−7807.12	+	13522.3i	−0.788750	+	1.36616i	0.137983	+	0.990435i	$0.455938\pi$
$461$	−7807.12	+	13522.3i	−0.788750	+	1.36616i	−0.926733	+	0.375721i	$0.877395\pi$
$462$	98.4164	−	7517.90i	0.00991070	−	0.757065i
$463$	−4055.66	−	7024.62i	−0.407090	−	0.705101i	0.587472	−	0.809244i	$-0.300123\pi$
$463$	−4055.66	−	7024.62i	−0.407090	−	0.705101i	−0.994562	+	0.104144i	$0.966790\pi$
$464$	−5967.01	+	3445.06i	−0.597008	+	0.344683i
$465$	2911.52	+	2984.61i	0.290363	+	0.297651i
$466$	−2524.23	+	4372.09i	−0.250928	+	0.434620i
$467$	6607.80			0.654759			0.327380	−	0.944893i	$-0.393834\pi$
$467$	6607.80			0.654759			0.327380	+	0.944893i	$0.393834\pi$
$468$	−1034.29	−	1898.61i	−0.102158	−	0.187529i
$469$	−3292.76	−	12323.1i	−0.324191	−	1.21328i
$470$	−2682.94	−	1549.00i	−0.263309	−	0.152021i
$471$	−18485.0	+	4708.29i	−1.80837	+	0.460608i
$472$	−15654.0	+	9037.84i	−1.52655	+	0.881357i
$473$	−10528.6	+	6078.71i	−1.02348	+	0.590908i
$474$	9642.74	−	2456.09i	0.934400	−	0.238000i
$475$	6390.70	+	3689.67i	0.617317	+	0.356408i
$476$	514.213	+	1924.43i	0.0495145	+	0.185307i
$477$	−2254.50	+	3690.53i	−0.216408	+	0.354251i
$478$	3531.53			0.337925
$479$	4138.13	−	7167.45i	0.394731	−	0.683694i	−0.598336	−	0.801245i	$-0.704171\pi$
$479$	4138.13	−	7167.45i	0.394731	−	0.683694i	0.993067	+	0.117552i	$0.0375045\pi$
$480$	−2547.03	−	2610.97i	−0.242199	−	0.248279i
$481$	6736.57	−	3889.36i	0.638588	−	0.368689i
$482$	−1612.33	−	2792.64i	−0.152364	−	0.263903i
$483$	−5569.87	−	72.9149i	−0.524716	−	0.00686903i
$484$	−166.819	+	288.940i	−0.0156667	+	0.0271356i
$485$		−	6383.30i		−	0.597630i
$486$	2696.04	−	8034.00i	0.251635	−	0.749855i
$487$	229.243			0.0213306			0.0106653	−	0.999943i	$-0.496605\pi$
$487$	229.243			0.0213306			0.0106653	+	0.999943i	$0.496605\pi$
$488$	−8256.08	+	14299.9i	−0.765851	+	1.32649i
$489$	−849.479	−	238.940i	−0.0785578	−	0.0220966i
$490$	2121.10	−	3662.08i	0.195555	−	0.337624i
$491$	17923.6	−	10348.2i	1.64742	−	0.951138i	0.669326	−	0.742969i	$-0.266583\pi$
$491$	17923.6	−	10348.2i	1.64742	−	0.951138i	0.978093	−	0.208169i	$-0.0667505\pi$
$492$	1204.53	−	1175.03i	0.110375	−	0.107672i
$493$	−6896.96	−	3981.96i	−0.630068	−	0.363770i
$494$			4666.38i			0.425001i
$495$	−2711.00	+	4437.80i	−0.246162	+	0.402958i
$496$		−	4520.14i		−	0.409195i
$497$	−2774.88	+	10327.2i	−0.250443	+	0.932070i
$498$	13881.2	−	3535.67i	1.24906	−	0.318147i
$499$	6552.36	+	11349.0i	0.587824	+	1.01814i	0.994517	+	0.104576i	$0.0333485\pi$
$499$	6552.36	+	11349.0i	0.587824	+	1.01814i	−0.406693	+	0.913565i	$0.633318\pi$
$500$	1813.63	+	3141.30i	0.162216	+	0.280966i
$501$	−559.997	−	2198.58i	−0.0499377	−	0.196058i
$502$	−5688.08	−	3284.02i	−0.505720	−	0.291978i
$503$	−7415.97			−0.657379			−0.328690	−	0.944438i	$-0.606607\pi$
$503$	−7415.97			−0.657379			−0.328690	+	0.944438i	$0.606607\pi$
$504$	−8916.26	+	8473.01i	−0.788019	+	0.748845i
$505$	−857.975			−0.0756028
$506$	3916.41	+	2261.14i	0.344082	+	0.198656i
$507$	5513.17	−	5378.17i	0.482936	−	0.471110i
$508$	−2908.68	−	5037.98i	−0.254039	−	0.440008i
$509$	−10536.9	−	18250.5i	−0.917565	−	1.58927i	−0.803103	−	0.595841i	$-0.796819\pi$
$509$	−10536.9	−	18250.5i	−0.917565	−	1.58927i	−0.114462	−	0.993428i	$-0.536514\pi$
$510$	−623.366	+	2216.19i	−0.0541237	+	0.192421i
$511$	−180.000	+	669.903i	−0.0155826	+	0.0579936i
$512$			10067.8i			0.869021i
$513$	8022.27	−	7446.83i	0.690433	−	0.640908i
$514$			16277.7i			1.39684i
$515$	9048.89	+	5224.38i	0.774255	+	0.447017i
$516$	5215.56	+	1467.02i	0.444966	+	0.125159i
$517$	−7593.98	+	4384.39i	−0.646002	+	0.372969i
$518$	−8518.26	−	8530.13i	−0.722531	−	0.723537i
$519$	−6157.48	+	6006.71i	−0.520777	+	0.508026i
$520$	−1813.45	+	3140.99i	−0.152933	+	0.264887i
$521$	19991.7			1.68110			0.840548	−	0.541736i	$-0.182233\pi$
$521$	19991.7			1.68110			0.840548	+	0.541736i	$0.182233\pi$
$522$	332.030	−	13392.0i	0.0278401	−	1.12289i
$523$		−	3604.15i		−	0.301336i	−0.988584	−	0.150668i	$-0.951858\pi$
$523$		−	3604.15i		−	0.301336i	0.988584	−	0.150668i	$-0.0481424\pi$
$524$	−39.7286	+	68.8119i	−0.00331212	+	0.00573676i
$525$	7941.56	−	4447.48i	0.660187	−	0.369722i
$526$	7531.01	+	13044.1i	0.624273	+	1.08127i
$527$	4524.64	−	2612.30i	0.373997	−	0.215927i
$528$	5463.22	−	1391.53i	0.450296	−	0.114694i
$529$	−4408.26	+	7635.34i	−0.362313	+	0.627545i
$530$	1976.25			0.161967
$531$	491.769	−	19834.8i	0.0401901	−	1.62101i
$532$	−4181.18	+	1117.22i	−0.340746	+	0.0910485i
$533$	−2503.35	−	1445.31i	−0.203438	−	0.117455i
$534$	−12221.7	−	12528.5i	−0.990423	−	1.01528i
$535$	−2423.80	+	1399.38i	−0.195869	+	0.113085i
$536$	14671.5	−	8470.59i	1.18230	−	0.682601i
$537$	−6395.05	+	22735.7i	−0.513905	+	1.82703i
$538$	−14533.3	−	8390.80i	−1.16464	−	0.672404i
$539$	−5974.83	−	10382.1i	−0.477466	−	0.829660i
$540$	2259.31	−	516.191i	0.180047	−	0.0411358i
$541$	−13211.0			−1.04988			−0.524939	−	0.851140i	$-0.675912\pi$
$541$	−13211.0			−1.04988			−0.524939	+	0.851140i	$0.675912\pi$
$542$	−5169.93	+	8954.58i	−0.409719	+	0.709654i
$543$	97.7531	−	347.532i	0.00772557	−	0.0274660i
$544$	−3958.20	+	2285.27i	−0.311961	+	0.180111i
$545$	−822.933	−	1425.36i	−0.0646799	−	0.112029i
$546$	4946.56	+	2942.89i	0.387716	+	0.230667i
$547$	−8858.54	+	15343.4i	−0.692439	+	1.19934i	0.278598	+	0.960408i	$0.410130\pi$
$547$	−8858.54	+	15343.4i	−0.692439	+	1.19934i	−0.971037	+	0.238931i	$0.923203\pi$
$548$			798.735i			0.0622633i
$549$	−8670.52	−	15916.3i	−0.674042	−	1.23732i
$550$	−7389.55			−0.572893
$551$	8651.56	−	14984.9i	0.668909	−	1.15858i
$552$	−1826.10	−	7169.39i	−0.140805	−	0.552807i
$553$	11217.8	−	11202.2i	0.862621	−	0.861421i
$554$	3806.52	−	2197.70i	0.291920	−	0.168540i
$555$	2058.07	+	8080.11i	0.157406	+	0.617984i
$556$	−1332.28	−	769.190i	−0.101621	−	0.0586707i
$557$		−	13013.3i		−	0.989933i	−0.868912	−	0.494966i	$-0.835180\pi$
$557$		−	13013.3i		−	0.989933i	0.868912	−	0.494966i	$-0.164820\pi$
$558$	7499.62	+	4581.43i	0.568968	+	0.347576i
$559$		−	9307.05i		−	0.704198i
$560$	3064.60	+	823.445i	0.231256	+	0.0621373i
$561$	4550.24	+	4664.46i	0.342445	+	0.351040i
$562$	2198.63	+	3808.14i	0.165024	+	0.285831i
$563$	7866.96	+	13626.0i	0.588904	+	1.02001i	0.994376	+	0.105904i	$0.0337736\pi$
$563$	7866.96	+	13626.0i	0.588904	+	1.02001i	−0.405473	+	0.914107i	$0.632893\pi$
$564$	3761.82	+	1058.12i	0.280854	+	0.0789979i
$565$	−1192.23	−	688.335i	−0.0887744	−	0.0512539i
$566$	11937.8			0.886544
$567$	−2834.63	−	13200.3i	−0.209953	−	0.977711i
$568$	−14202.7			−1.04917
$569$	5395.51	+	3115.10i	0.397524	+	0.229511i	0.685415	−	0.728152i	$-0.259621\pi$
$569$	5395.51	+	3115.10i	0.397524	+	0.229511i	−0.287891	+	0.957663i	$0.592954\pi$
$570$	−4815.09	−	1354.38i	−0.353828	−	0.0995241i
$571$	1182.19	+	2047.62i	0.0866432	+	0.150070i	0.906090	−	0.423084i	$-0.139053\pi$
$571$	1182.19	+	2047.62i	0.0866432	+	0.150070i	−0.819447	+	0.573155i	$0.805719\pi$
$572$	1398.25	+	2421.83i	0.102209	+	0.177031i
$573$	−5097.17	−	5225.11i	−0.371618	−	0.380946i
$574$	−1162.45	+	4326.28i	−0.0845293	+	0.314592i
$575$			5474.78i			0.397068i
$576$	−12287.3	−	7506.19i	−0.888841	−	0.542983i
$577$		−	4194.43i		−	0.302628i	−0.988486	−	0.151314i	$-0.951650\pi$
$577$		−	4194.43i		−	0.302628i	0.988486	−	0.151314i	$-0.0483505\pi$
$578$	−7020.30	−	4053.17i	−0.505201	−	0.291678i
$579$	2965.36	+	11642.2i	0.212843	+	0.835635i
$580$	3172.71	−	1831.77i	0.227137	−	0.131138i
$581$	16148.6	−	16126.2i	1.15311	−	1.15151i
$582$	−3320.91	−	13038.1i	−0.236523	−	0.928602i
$583$	2796.85	−	4844.29i	0.198686	−	0.344134i
$584$	−921.295			−0.0652799
$585$	−1904.48	−	3496.01i	−0.134599	−	0.247081i
$586$		−	4619.69i		−	0.325662i
$587$	−6703.36	+	11610.6i	−0.471341	+	0.816387i	−0.999463	−	0.0327817i	$-0.989563\pi$
$587$	−6703.36	+	11610.6i	−0.471341	+	0.816387i	0.528121	+	0.849169i	$0.322897\pi$
$588$	−1452.59	+	5136.81i	−0.101877	+	0.360269i
$589$	5675.71	+	9830.62i	0.397052	+	0.687714i
$590$	−7852.01	+	4533.36i	−0.547902	+	0.316332i
$591$	2190.26	−	7786.80i	0.152445	−	0.541973i
$592$	4519.64	−	7828.24i	0.313777	−	0.543478i
$593$	−4672.62			−0.323577			−0.161789	−	0.986825i	$-0.551726\pi$
$593$	−4672.62			−0.323577			−0.161789	+	0.986825i	$0.551726\pi$
$594$	−3228.53	+	10474.7i	−0.223010	+	0.723542i
$595$	946.845	+	3543.54i	0.0652384	+	0.244153i
$596$	5497.87	+	3174.20i	0.377855	+	0.218155i
$597$	−1671.29	+	5941.79i	−0.114575	+	0.407339i
$598$	−2998.19	+	1731.01i	−0.205025	+	0.118371i
$599$	5611.71	−	3239.92i	0.382785	−	0.221001i	−0.296244	−	0.955112i	$-0.595734\pi$
$599$	5611.71	−	3239.92i	0.382785	−	0.221001i	0.679029	+	0.734111i	$0.262401\pi$
$600$	8441.64	+	8653.53i	0.574381	+	0.588798i
$601$	2243.61	+	1295.35i	0.152277	+	0.0879174i	0.574203	−	0.818713i	$-0.305312\pi$
$601$	2243.61	+	1295.35i	0.152277	+	0.0879174i	−0.421925	+	0.906631i	$0.638646\pi$
$602$	−13934.7	+	3723.39i	−0.943415	+	0.252083i
$603$	−460.904	+	18589.9i	−0.0311268	+	1.25546i
$604$	−6840.08			−0.460793
$605$	−307.172	+	532.038i	−0.0206419	+	0.0357528i
$606$	−1752.44	+	446.362i	−0.117472	+	0.0299211i
$607$	1869.60	−	1079.41i	0.125016	−	0.0721781i	−0.436188	−	0.899856i	$-0.643672\pi$
$607$	1869.60	−	1079.41i	0.125016	−	0.0721781i	0.561204	+	0.827678i	$0.310338\pi$
$608$	−4965.18	−	8599.94i	−0.331192	−	0.573641i
$609$	−10428.5	−	18621.4i	−0.693897	−	1.23904i
$610$	−4141.23	+	7172.82i	−0.274875	+	0.476097i
$611$		−	6712.89i		−	0.444476i
$612$	71.9768	−	2903.09i	0.00475407	−	0.191749i
$613$	6333.20			0.417285			0.208642	−	0.977992i	$-0.433096\pi$
$613$	6333.20			0.417285			0.208642	+	0.977992i	$0.433096\pi$
$614$	−442.510	+	766.449i	−0.0290851	+	0.0503768i
$615$	2217.95	−	2163.64i	0.145425	−	0.141864i
$616$	11257.5	−	11241.8i	0.736325	−	0.735301i
$617$	1802.84	−	1040.87i	0.117633	−	0.0679157i	−0.440029	−	0.897984i	$-0.645032\pi$
$617$	1802.84	−	1040.87i	0.117633	−	0.0679157i	0.557662	+	0.830068i	$0.311698\pi$
$618$	21200.6	+	5963.27i	1.37996	+	0.388152i
$619$	−20384.1	−	11768.8i	−1.32360	−	0.764179i	−0.339296	−	0.940680i	$-0.610189\pi$
$619$	−20384.1	−	11768.8i	−1.32360	−	0.764179i	−0.984301	+	0.176501i	$0.943522\pi$
$620$			2403.40i			0.155682i
$621$	7760.54	+	2391.96i	0.501481	+	0.154567i
$622$			14117.0i			0.910031i
$623$	−26929.7	−	7235.88i	−1.73180	−	0.465328i
$624$	−1168.61	+	4154.66i	−0.0749711	+	0.266537i
$625$	−2571.92	−	4454.69i	−0.164603	−	0.285100i
$626$	11350.7	+	19660.0i	0.724704	+	1.25522i
$627$	−10134.4	+	9886.25i	−0.645501	+	0.629695i
$628$	−9522.27	−	5497.68i	−0.605063	−	0.349333i
$629$	10448.0			0.662306
$630$	−4472.38	+	4250.04i	−0.282831	+	0.268771i
$631$	13465.2			0.849510			0.424755	−	0.905308i	$-0.360360\pi$
$631$	13465.2			0.849510			0.424755	+	0.905308i	$0.360360\pi$
$632$	18234.8	+	10527.9i	1.14769	+	0.662620i
$633$	315.498	+	1238.66i	0.0198103	+	0.0777763i
$634$	1985.30	+	3438.64i	0.124363	+	0.215404i
$635$	−5355.89	−	9276.67i	−0.334712	−	0.579738i
$636$	−2415.70	+	615.300i	−0.150611	+	0.0383620i
$637$	9170.11	+	12.7674i	0.570382	+	0.000794135i
$638$			17327.0i			1.07521i
$639$	8127.08	−	13303.7i	0.503133	−	0.823610i
$640$			964.023i			0.0595412i
$641$	−2697.97	−	1557.67i	−0.166246	−	0.0959819i	0.414569	−	0.910018i	$-0.363932\pi$
$641$	−2697.97	−	1557.67i	−0.166246	−	0.0959819i	−0.580814	+	0.814036i	$0.697266\pi$
$642$	−4222.65	+	4119.26i	−0.259587	+	0.253231i
$643$	−138.508	+	79.9675i	−0.00849489	+	0.00490452i	−0.504241	−	0.863563i	$-0.668228\pi$
$643$	−138.508	+	79.9675i	−0.00849489	+	0.00490452i	0.495747	+	0.868467i	$0.334894\pi$
$644$	−2268.85	−	2272.01i	−0.138828	−	0.139021i
$645$	9603.66	+	2701.30i	0.586269	+	0.164905i
$646$	−3133.84	+	5427.97i	−0.190866	+	0.330589i
$647$	11705.0			0.711239			0.355619	−	0.934631i	$-0.384270\pi$
$647$	11705.0			0.711239			0.355619	+	0.934631i	$0.384270\pi$
$648$	15954.6	−	8185.31i	0.967218	−	0.496218i
$649$			25663.1i			1.55218i
$650$	2828.52	−	4899.13i	0.170682	−	0.295631i
$651$	14000.3	+	183.277i	0.842880	+	0.0110341i
$652$	−254.330	−	440.512i	−0.0152766	−	0.0264598i
$653$	−23280.1	+	13440.8i	−1.39513	+	0.805479i	−0.993878	−	0.110487i	$-0.964759\pi$
$653$	−23280.1	+	13440.8i	−1.39513	+	0.805479i	−0.401254	+	0.915967i	$0.631425\pi$
$654$	−2422.41	−	2483.22i	−0.144838	−	0.148473i
$655$	−73.1541	+	126.707i	−0.00436392	+	0.00755853i
$656$	−3359.06			−0.199923
$657$	527.185	−	862.981i	0.0313051	−	0.0512452i
$658$	−10050.7	+	2685.57i	−0.595465	+	0.159110i
$659$	−7188.85	−	4150.48i	−0.424943	−	0.245341i	0.272247	−	0.962227i	$-0.412233\pi$
$659$	−7188.85	−	4150.48i	−0.424943	−	0.245341i	−0.697190	+	0.716886i	$0.745567\pi$
$660$	−2904.84	+	739.888i	−0.171319	+	0.0436365i
$661$	−1248.35	+	720.734i	−0.0734571	+	0.0424105i	−0.536279	−	0.844041i	$-0.680170\pi$
$661$	−1248.35	+	720.734i	−0.0734571	+	0.0424105i	0.462822	+	0.886451i	$0.346837\pi$
$662$	−9290.83	+	5364.06i	−0.545466	+	0.314925i
$663$	−4834.16	+	1231.30i	−0.283172	+	0.0721264i
$664$	26250.0	+	15155.4i	1.53418	+	0.885760i
$665$	−7699.00	+	2057.20i	−0.448954	+	0.119962i
$666$	8407.36	+	15433.2i	0.489157	+	0.897932i
$667$	12837.3			0.745219
$668$	653.886	−	1132.56i	0.0378736	−	0.0655991i
$669$	3986.08	+	4086.13i	0.230360	+	0.236142i
$670$	7359.19	−	4248.83i	0.424344	−	0.244995i
$671$	11721.6	+	20302.4i	0.674378	+	1.16806i
$672$	−12247.6	−	160.333i	−0.703069	−	0.00920384i
$673$	8012.16	−	13877.5i	0.458909	−	0.794854i	−0.539994	−	0.841669i	$-0.681574\pi$
$673$	8012.16	−	13877.5i	0.458909	−	0.794854i	0.998904	+	0.0468146i	$0.0149070\pi$
$674$		−	16532.1i		−	0.944796i
$675$	−12936.3	+	2955.59i	−0.737657	+	0.168534i
$676$	4439.56			0.252592
$677$	13755.2	−	23824.7i	0.780880	−	1.35252i	−0.150549	−	0.988602i	$-0.548104\pi$
$677$	13755.2	−	23824.7i	0.780880	−	1.35252i	0.931430	−	0.363922i	$-0.118562\pi$
$678$	−2793.28	−	785.687i	−0.158223	−	0.0445046i
$679$	−15146.7	−	15167.8i	−0.856076	−	0.857269i
$680$	−4218.83	+	2435.75i	−0.237919	+	0.137363i
$681$	−16008.3	+	15616.4i	−0.900794	+	0.878737i
$682$	−9844.21	−	5683.56i	−0.552719	−	0.319112i
$683$			2208.68i			0.123738i	0.998084	+	0.0618688i	$0.0197060\pi$
$683$			2208.68i			0.123738i	−0.998084	+	0.0618688i	$0.980294\pi$
$684$	6307.50	+	156.383i	0.352592	+	0.00874190i
$685$			1470.75i			0.0820357i
$686$	−3649.49	−	13734.8i	−0.203117	−	0.764426i
$687$	−14399.3	+	3667.63i	−0.799662	+	0.203681i
$688$	−5407.64	−	9366.31i	−0.299658	−	0.519022i
$689$	2141.12	+	3708.52i	0.118389	+	0.205056i
$690$	−915.970	−	3596.15i	−0.0505368	−	0.198410i
$691$	20410.4	+	11784.0i	1.12366	+	0.648746i	0.942333	−	0.334676i	$-0.108627\pi$
$691$	20410.4	+	11784.0i	1.12366	+	0.648746i	0.181328	+	0.983423i	$0.441960\pi$
$692$	−4958.40			−0.272385
$693$	4088.49	+	16977.7i	0.224111	+	0.930636i
$694$	4043.48			0.221165
$695$	−2453.18	−	1416.35i	−0.133891	−	0.0773022i
$696$	20290.8	−	19794.0i	1.10506	−	1.07800i
$697$	−1941.28	−	3362.40i	−0.105497	−	0.182726i
$698$	−6580.02	−	11396.9i	−0.356816	−	0.618023i
$699$	3175.03	−	11287.9i	0.171803	−	0.610795i
$700$	5066.93	+	1361.46i	0.273589	+	0.0735120i
$701$			18383.9i			0.990516i	0.868746	+	0.495258i	$0.164926\pi$
$701$			18383.9i			0.990516i	−0.868746	+	0.495258i	$0.835074\pi$
$702$	−5708.77	−	6149.90i	−0.306928	−	0.330645i
$703$			22700.3i			1.21786i
$704$	16128.7	+	9311.91i	0.863456	+	0.498517i
$705$	6926.82	+	1948.36i	0.370042	+	0.104085i
$706$	−4636.43	+	2676.85i	−0.247159	+	0.142697i
$707$	−2038.69	+	2035.85i	−0.108448	+	0.108297i
$708$	8186.60	−	7986.15i	0.434564	−	0.423923i
$709$	11608.4	−	20106.3i	0.614895	−	1.06503i	−0.375508	−	0.926819i	$-0.622532\pi$
$709$	11608.4	−	20106.3i	0.614895	−	1.06503i	0.990403	−	0.138211i	$-0.0441351\pi$
$710$	−7124.03			−0.376564
$711$	−20295.8	+	11056.3i	−1.07054	+	0.583186i
$712$		−	37035.5i		−	1.94939i
$713$	−4210.84	+	7293.39i	−0.221174	+	0.383085i
$714$	3777.49	+	6745.19i	0.197996	+	0.353547i
$715$	2574.65	+	4459.43i	0.134667	+	0.233249i
$716$	−11790.0	+	6806.95i	−0.615381	+	0.355290i
$717$	−7948.77	+	2024.62i	−0.414020	+	0.105454i
$718$	12000.6	−	20785.6i	0.623756	−	1.08038i
$719$	−24589.3			−1.27542			−0.637709	−	0.770278i	$-0.720118\pi$
$719$	−24589.3			−1.27542			−0.637709	+	0.770278i	$0.720118\pi$
$720$	−3947.88	−	2411.71i	−0.204346	−	0.124832i
$721$	33898.3	−	9057.74i	1.75096	−	0.467861i
$722$	1495.53	+	863.443i	0.0770883	+	0.0445070i
$723$	5230.05	+	5361.33i	0.269029	+	0.275781i
$724$	180.219	−	104.049i	0.00925107	−	0.00534111i
$725$	−18166.2	+	10488.3i	−0.930586	+	0.537274i
$726$	−350.616	+	1246.51i	−0.0179237	+	0.0637223i
$727$	−14219.3	−	8209.54i	−0.725400	−	0.418810i	0.0913367	−	0.995820i	$-0.470886\pi$
$727$	−14219.3	−	8209.54i	−0.725400	−	0.418810i	−0.816737	+	0.577010i	$0.804219\pi$
$728$	3144.06	+	11766.6i	0.160064	+	0.599035i
$729$	−1462.36	+	19628.6i	−0.0742958	+	0.997236i
$730$	−462.119			−0.0234299
$731$	6250.41	−	10826.0i	0.316252	−	0.547764i
$732$	2828.87	−	10057.2i	0.142839	−	0.507821i
$733$	−1654.43	+	955.186i	−0.0833667	+	0.0481318i	−0.541104	−	0.840956i	$-0.681993\pi$
$733$	−1654.43	+	955.186i	−0.0833667	+	0.0481318i	0.457737	+	0.889088i	$0.348660\pi$
$734$	6126.30	+	10611.1i	0.308073	+	0.533599i
$735$	−2674.73	+	9458.65i	−0.134230	+	0.474677i
$736$	3683.69	−	6380.34i	0.184487	−	0.319541i
$737$		−	24052.3i		−	1.20214i
$738$	3404.60	−	5573.20i	0.169817	−	0.277984i
$739$	10538.9			0.524601			0.262300	−	0.964986i	$-0.415519\pi$
$739$	10538.9			0.524601			0.262300	+	0.964986i	$0.415519\pi$
$740$	−2403.13	+	4162.34i	−0.119379	+	0.206771i
$741$	−2675.23	−	10503.1i	−0.132628	−	0.520704i
$742$	4695.89	−	4689.36i	0.232334	−	0.232010i
$743$	−9283.92	+	5360.07i	−0.458404	+	0.264660i	−0.711373	−	0.702815i	$-0.751926\pi$
$743$	−9283.92	+	5360.07i	−0.458404	+	0.264660i	0.252969	+	0.967474i	$0.418593\pi$
$744$	4590.06	+	18020.8i	0.226182	+	0.888004i
$745$	10123.5	+	5844.80i	0.497847	+	0.287432i
$746$		−	27080.1i		−	1.32905i
$747$	−29217.0	+	15916.2i	−1.43105	+	0.779577i
$748$			3756.12i			0.183606i
$749$	−2438.81	+	9076.47i	−0.118975	+	0.442787i
$750$	9830.33	+	10077.1i	0.478604	+	0.490617i
$751$	16974.5	+	29400.7i	0.824779	+	1.42856i	0.902088	+	0.431552i	$0.142034\pi$
$751$	16974.5	+	29400.7i	0.824779	+	1.42856i	−0.0773094	+	0.997007i	$0.524633\pi$
$752$	−3900.37	−	6755.63i	−0.189138	−	0.327597i
$753$	14685.5	+	4130.71i	0.710716	+	0.199909i
$754$	−11487.5	−	6632.32i	−0.554841	−	0.320338i
$755$	−12595.0			−0.607123
$756$	4143.65	−	6587.59i	0.199343	−	0.316916i
$757$	−4201.14			−0.201708			−0.100854	−	0.994901i	$-0.532158\pi$
$757$	−4201.14			−0.201708			−0.100854	+	0.994901i	$0.532158\pi$
$758$	4.52407	+	2.61197i	0.000216783	+	0.000125160i
$759$	−10111.4	−	2844.11i	−0.483557	−	0.136014i
$760$	−5292.11	−	9166.21i	−0.252586	−	0.437491i
$761$	−1844.61	−	3194.96i	−0.0878674	−	0.152191i	0.818742	−	0.574161i	$-0.194672\pi$
$761$	−1844.61	−	3194.96i	−0.0878674	−	0.152191i	−0.906609	+	0.421971i	$0.861339\pi$
$762$	−15765.8	−	16161.5i	−0.749519	−	0.768332i
$763$	−5337.60	−	1434.19i	−0.253256	−	0.0680487i
$764$		−	4207.60i		−	0.199248i
$765$	132.534	−	5345.59i	0.00626377	−	0.252641i
$766$		−	18338.2i		−	0.864994i
$767$	−17014.1	−	9823.11i	−0.800971	−	0.462441i
$768$	−4970.19	−	19513.3i	−0.233524	−	0.916828i
$769$	−2527.18	+	1459.07i	−0.118508	+	0.0684204i	−0.558082	−	0.829786i	$-0.688463\pi$
$769$	−2527.18	+	1459.07i	−0.118508	+	0.0684204i	0.439574	+	0.898206i	$0.355129\pi$
$770$	5646.72	−	5638.87i	0.264278	−	0.263910i
$771$	−9331.97	−	36637.8i	−0.435905	−	1.71139i
$772$	−3462.54	+	5997.29i	−0.161424	+	0.279595i
$773$	6902.85			0.321188			0.160594	−	0.987021i

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.93743 + 1.11857i) q^{2} +(-5.00204 - 1.40697i) q^{3} +(-1.49759 - 2.59390i) q^{4} +(-2.75758 - 4.77627i) q^{5} +(-8.11730 - 8.32104i) q^{6} +(-17.8859 - 4.80585i) q^{7} -24.5978i q^{8} +(23.0409 + 14.0754i) q^{9} +O(q^{10})\)	\(q+(1.93743 + 1.11857i) q^{2} +(-5.00204 - 1.40697i) q^{3} +(-1.49759 - 2.59390i) q^{4} +(-2.75758 - 4.77627i) q^{5} +(-8.11730 - 8.32104i) q^{6} +(-17.8859 - 4.80585i) q^{7} -24.5978i q^{8} +(23.0409 + 14.0754i) q^{9} -12.3382i q^{10} +(-30.2441 - 17.4614i) q^{11} +(3.84148 + 15.0818i) q^{12} +(23.1532 - 13.3675i) q^{13} +(-29.2768 - 29.3176i) q^{14} +(7.07349 + 27.7709i) q^{15} +(15.5338 - 26.9053i) q^{16} +35.9093 q^{17} +(28.8957 + 53.0430i) q^{18} +78.0198i q^{19} +(-8.25943 + 14.3058i) q^{20} +(82.7042 + 49.2038i) q^{21} +(-39.0638 - 67.6605i) q^{22} +(-50.1284 + 28.9416i) q^{23} +(-34.6083 + 123.039i) q^{24} +(47.2915 - 81.9113i) q^{25} +59.8102 q^{26} +(-95.4480 - 102.824i) q^{27} +(14.3198 + 53.5913i) q^{28} +(-192.066 - 110.889i) q^{29} +(-17.3594 + 61.7163i) q^{30} +(126.002 - 72.7471i) q^{31} +(-110.228 + 63.6400i) q^{32} +(126.715 + 129.895i) q^{33} +(69.5717 + 40.1672i) q^{34} +(26.3676 + 98.6801i) q^{35} +(2.00440 - 80.8449i) q^{36} +290.956 q^{37} +(-87.2708 + 151.158i) q^{38} +(-134.621 + 34.2892i) q^{39} +(-117.486 + 67.8304i) q^{40} +(-54.0606 - 93.6357i) q^{41} +(105.195 + 187.839i) q^{42} +(174.061 - 301.482i) q^{43} +104.600i q^{44} +(3.69080 - 148.863i) q^{45} -129.493 q^{46} +(125.545 - 217.450i) q^{47} +(-115.555 + 112.726i) q^{48} +(296.808 + 171.913i) q^{49} +(183.248 - 105.798i) q^{50} +(-179.620 - 50.5232i) q^{51} +(-69.3480 - 40.0381i) q^{52} +160.173i q^{53} +(-69.9077 - 305.979i) q^{54} +192.605i q^{55} +(-118.213 + 439.953i) q^{56} +(109.771 - 390.258i) q^{57} +(-248.076 - 429.680i) q^{58} +(-367.425 - 636.398i) q^{59} +(61.4417 - 59.9373i) q^{60} +(-581.350 - 335.643i) q^{61} +325.492 q^{62} +(-344.462 - 362.482i) q^{63} -533.284 q^{64} +(-127.694 - 73.7240i) q^{65} +(100.203 + 393.402i) q^{66} +(344.364 + 596.455i) q^{67} +(-53.7774 - 93.1452i) q^{68} +(291.464 - 74.2385i) q^{69} +(-59.2956 + 220.680i) q^{70} -577.396i q^{71} +(346.224 - 566.756i) q^{72} -37.4543i q^{73} +(563.705 + 325.455i) q^{74} +(-351.801 + 343.187i) q^{75} +(202.375 - 116.841i) q^{76} +(457.025 + 457.661i) q^{77} +(-299.173 - 84.1509i) q^{78} +(-428.000 + 741.317i) q^{79} -171.342 q^{80} +(332.766 + 648.620i) q^{81} -241.883i q^{82} +(-616.129 + 1067.17i) q^{83} +(3.77299 - 288.213i) q^{84} +(-99.0228 - 171.513i) q^{85} +(674.460 - 389.400i) q^{86} +(804.705 + 824.903i) q^{87} +(-429.513 + 743.939i) q^{88} +1505.64 q^{89} +(173.665 - 284.284i) q^{90} +(-478.358 + 127.819i) q^{91} +(150.143 + 86.6853i) q^{92} +(-732.619 + 186.604i) q^{93} +(486.467 - 280.862i) q^{94} +(372.643 - 215.146i) q^{95} +(640.903 - 163.243i) q^{96} +(1002.35 + 578.705i) q^{97} +(382.745 + 665.071i) q^{98} +(-451.074 - 828.025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44q - 6q^{2} + 78q^{4} + 5q^{7} + O(q^{10}) \)	\( 44q - 6q^{2} + 78q^{4} + 5q^{7} - 18q^{11} + 204q^{14} + 66q^{15} - 242q^{16} - 210q^{18} - 57q^{21} - 34q^{22} - 102q^{23} - 352q^{25} + 300q^{28} + 246q^{29} - 144q^{30} + 1068q^{32} - 1818q^{36} + 328q^{37} - 798q^{39} - 1158q^{42} - 170q^{43} + 968q^{46} - 79q^{49} + 288q^{50} - 204q^{51} + 1212q^{56} + 324q^{57} - 538q^{58} + 5316q^{60} + 783q^{63} - 808q^{64} + 4350q^{65} - 590q^{67} + 384q^{70} + 4284q^{72} - 5304q^{74} - 2787q^{77} + 612q^{78} - 302q^{79} - 3720q^{81} + 7050q^{84} - 612q^{85} - 13692q^{86} + 1294q^{88} + 210q^{91} - 10194q^{92} - 4266q^{93} + 6336q^{95} + 1014q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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