LMFDB - Embedded newform 300.2.r.a.59.4

Newspace parameters

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.r (of order $10$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			59.4
Character	$\chi$	$=$	300.59
Dual form			300.2.r.a.239.4

$q$-expansion

$f(q)$	$=$	$q+(-1.37885 - 0.314289i) q^{2} +(1.03587 - 1.38816i) q^{3} +(1.80244 + 0.866714i) q^{4} +(1.94623 - 1.10099i) q^{5} +(-1.86458 + 1.58850i) q^{6} +2.63015 q^{7} +(-2.21290 - 1.76156i) q^{8} +(-0.853964 - 2.87589i) q^{9} +O(q^{10})$	\(q+(-1.37885 - 0.314289i) q^{2} +(1.03587 - 1.38816i) q^{3} +(1.80244 + 0.866714i) q^{4} +(1.94623 - 1.10099i) q^{5} +(-1.86458 + 1.58850i) q^{6} +2.63015 q^{7} +(-2.21290 - 1.76156i) q^{8} +(-0.853964 - 2.87589i) q^{9} +(-3.02959 + 0.906413i) q^{10} +(-0.908434 - 0.660016i) q^{11} +(3.07023 - 1.60428i) q^{12} +(4.15899 + 5.72437i) q^{13} +(-3.62658 - 0.826628i) q^{14} +(0.487695 - 3.84215i) q^{15} +(2.49761 + 3.12441i) q^{16} +(-1.53447 + 4.72262i) q^{17} +(0.273625 + 4.23381i) q^{18} +(-6.71489 - 2.18180i) q^{19} +(4.46222 - 0.297638i) q^{20} +(2.72448 - 3.65107i) q^{21} +(1.04516 + 1.19557i) q^{22} +(1.81587 - 2.49933i) q^{23} +(-4.73758 + 1.24712i) q^{24} +(2.57566 - 4.28556i) q^{25} +(-3.93552 - 9.20016i) q^{26} +(-4.87678 - 1.79360i) q^{27} +(4.74070 + 2.27959i) q^{28} +(-0.240777 + 0.0782332i) q^{29} +(-1.88000 + 5.14447i) q^{30} +(-4.71722 - 1.53272i) q^{31} +(-2.46186 - 5.09306i) q^{32} +(-1.85722 + 0.577362i) q^{33} +(3.60007 - 6.02951i) q^{34} +(5.11889 - 2.89576i) q^{35} +(0.953352 - 5.92378i) q^{36} +(-2.57019 - 3.53756i) q^{37} +(8.57310 + 5.11879i) q^{38} +(12.2545 + 0.156333i) q^{39} +(-6.24627 - 0.992030i) q^{40} +(2.13451 + 2.93790i) q^{41} +(-4.90414 + 4.17799i) q^{42} +7.40077 q^{43} +(-1.06536 - 1.97699i) q^{44} +(-4.82833 - 4.65695i) q^{45} +(-3.28932 + 2.87549i) q^{46} +(-9.30818 + 3.02441i) q^{47} +(6.92436 - 0.230613i) q^{48} -0.0823015 q^{49} +(-4.89834 + 5.09963i) q^{50} +(4.96624 + 7.02209i) q^{51} +(2.53497 + 13.9225i) q^{52} +(0.355319 + 1.09356i) q^{53} +(6.16063 + 4.00582i) q^{54} +(-2.49469 - 0.284372i) q^{55} +(-5.82026 - 4.63316i) q^{56} +(-9.98440 + 7.06127i) q^{57} +(0.356583 - 0.0321981i) q^{58} +(1.37468 - 0.998760i) q^{59} +(4.20909 - 6.50258i) q^{60} +(-3.31802 - 2.41068i) q^{61} +(6.02261 + 3.59595i) q^{62} +(-2.24605 - 7.56403i) q^{63} +(1.79384 + 7.79629i) q^{64} +(14.3968 + 6.56196i) q^{65} +(2.74228 - 0.212389i) q^{66} +(-0.555298 + 1.70903i) q^{67} +(-6.85897 + 7.18232i) q^{68} +(-1.58847 - 5.10969i) q^{69} +(-7.96828 + 2.38400i) q^{70} +(2.17375 + 6.69012i) q^{71} +(-3.17631 + 7.86836i) q^{72} +(-1.35514 + 1.86519i) q^{73} +(2.43208 + 5.68554i) q^{74} +(-3.28099 - 8.01468i) q^{75} +(-10.2122 - 9.75246i) q^{76} +(-2.38932 - 1.73594i) q^{77} +(-16.8479 - 4.06701i) q^{78} +(-5.36703 + 1.74385i) q^{79} +(8.30087 + 3.33099i) q^{80} +(-7.54149 + 4.91181i) q^{81} +(-2.01981 - 4.72177i) q^{82} +(8.73160 + 2.83707i) q^{83} +(8.07516 - 4.21949i) q^{84} +(2.21310 + 10.8808i) q^{85} +(-10.2045 - 2.32598i) q^{86} +(-0.140813 + 0.415276i) q^{87} +(0.847617 + 3.06080i) q^{88} +(-7.11762 + 9.79656i) q^{89} +(5.19390 + 7.93873i) q^{90} +(10.9388 + 15.0559i) q^{91} +(5.43921 - 2.93107i) q^{92} +(-7.01406 + 4.96055i) q^{93} +(13.7851 - 1.24474i) q^{94} +(-15.4709 + 3.14671i) q^{95} +(-9.62013 - 1.85827i) q^{96} +(1.59344 - 0.517741i) q^{97} +(0.113481 + 0.0258665i) q^{98} +(-1.12236 + 3.17619i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224q - 6q^{4} - 7q^{6} - 6q^{9} + O(q^{10}) $	$ 224q - 6q^{4} - 7q^{6} - 6q^{9} - 5q^{12} - 20q^{13} + 6q^{16} - 24q^{21} - 10q^{22} - 28q^{24} - 20q^{25} - 50q^{28} - 25q^{30} - 10q^{33} - 14q^{34} - 25q^{36} - 60q^{37} - 20q^{40} - 85q^{42} - 30q^{45} + 6q^{46} - 70q^{48} + 88q^{49} + 40q^{52} - 46q^{54} + 50q^{58} + 10q^{60} - 28q^{61} + 18q^{64} + 64q^{66} - 42q^{69} - 40q^{70} - 5q^{72} - 20q^{73} - 80q^{76} - 85q^{78} + 18q^{81} - 48q^{84} - 20q^{85} + 50q^{88} - 60q^{90} + 60q^{94} + 44q^{96} - 120q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−1.37885	−	0.314289i	−0.974993	−	0.222236i
$2$	−1.37885	−	0.314289i	−0.974993	−	0.222236i
$3$	1.03587	−	1.38816i	0.598057	−	0.801453i
$3$	1.03587	−	1.38816i	0.598057	−	0.801453i
$4$	1.80244	+	0.866714i	0.901222	+	0.433357i
$5$	1.94623	−	1.10099i	0.870383	−	0.492376i
$5$	1.94623	−	1.10099i	0.870383	−	0.492376i
$6$	−1.86458	+	1.58850i	−0.761214	+	0.648501i
$7$	2.63015			0.994104			0.497052	−	0.867721i	$-0.334416\pi$
$7$	2.63015			0.994104			0.497052	+	0.867721i	$0.334416\pi$
$8$	−2.21290	−	1.76156i	−0.782378	−	0.622804i
$9$	−0.853964	−	2.87589i	−0.284655	−	0.958630i
$10$	−3.02959	+	0.906413i	−0.958040	+	0.286633i
$11$	−0.908434	−	0.660016i	−0.273903	−	0.199002i	0.442351	−	0.896842i	$-0.354145\pi$
$11$	−0.908434	−	0.660016i	−0.273903	−	0.199002i	−0.716254	+	0.697840i	$0.754145\pi$
$12$	3.07023	−	1.60428i	0.886298	−	0.463115i
$13$	4.15899	+	5.72437i	1.15350	+	1.58765i	0.732787	+	0.680459i	$0.238219\pi$
$13$	4.15899	+	5.72437i	1.15350	+	1.58765i	0.420711	+	0.907195i	$0.361781\pi$
$14$	−3.62658	−	0.826628i	−0.969244	−	0.220926i
$15$	0.487695	−	3.84215i	0.125922	−	0.992040i
$16$	2.49761	+	3.12441i	0.624403	+	0.781102i
$17$	−1.53447	+	4.72262i	−0.372164	+	1.14540i	0.573207	+	0.819410i	$0.305699\pi$
$17$	−1.53447	+	4.72262i	−0.372164	+	1.14540i	−0.945372	+	0.325994i	$0.894301\pi$
$18$	0.273625	+	4.23381i	0.0644941	+	0.997918i
$19$	−6.71489	−	2.18180i	−1.54050	−	0.500539i	−0.588986	−	0.808143i	$-0.700473\pi$
$19$	−6.71489	−	2.18180i	−1.54050	−	0.500539i	−0.951515	+	0.307604i	$0.900473\pi$
$20$	4.46222	−	0.297638i	0.997783	−	0.0665539i
$21$	2.72448	−	3.65107i	0.594531	−	0.796728i
$22$	1.04516	+	1.19557i	0.222828	+	0.254897i
$23$	1.81587	−	2.49933i	0.378635	−	0.521147i	−0.576587	−	0.817036i	$-0.695616\pi$
$23$	1.81587	−	2.49933i	0.378635	−	0.521147i	0.955222	+	0.295889i	$0.0956159\pi$
$24$	−4.73758	+	1.24712i	−0.967055	+	0.254567i
$25$	2.57566	−	4.28556i	0.515131	−	0.857111i
$26$	−3.93552	−	9.20016i	−0.771818	−	1.80430i
$27$	−4.87678	−	1.79360i	−0.938537	−	0.345178i
$28$	4.74070	+	2.27959i	0.895909	+	0.430802i
$29$	−0.240777	+	0.0782332i	−0.0447112	+	0.0145275i	−0.331287	−	0.943530i	$-0.607483\pi$
$29$	−0.240777	+	0.0782332i	−0.0447112	+	0.0145275i	0.286576	+	0.958058i	$0.407483\pi$
$30$	−1.88000	+	5.14447i	−0.343240	+	0.939248i
$31$	−4.71722	−	1.53272i	−0.847237	−	0.275284i	−0.146949	−	0.989144i	$-0.546945\pi$
$31$	−4.71722	−	1.53272i	−0.847237	−	0.275284i	−0.700288	+	0.713860i	$0.746945\pi$
$32$	−2.46186	−	5.09306i	−0.435200	−	0.900334i
$33$	−1.85722	+	0.577362i	−0.323301	+	0.100506i
$34$	3.60007	−	6.02951i	0.617408	−	1.03405i
$35$	5.11889	−	2.89576i	0.865251	−	0.489473i
$36$	0.953352	−	5.92378i	0.158892	−	0.987296i
$37$	−2.57019	−	3.53756i	−0.422536	−	0.581571i	0.543684	−	0.839290i	$-0.317029\pi$
$37$	−2.57019	−	3.53756i	−0.422536	−	0.581571i	−0.966220	+	0.257719i	$0.917029\pi$
$38$	8.57310	+	5.11879i	1.39074	+	0.830377i
$39$	12.2545	+	0.156333i	1.96229	+	0.0250334i
$40$	−6.24627	−	0.992030i	−0.987622	−	0.156854i
$41$	2.13451	+	2.93790i	0.333354	+	0.458823i	0.942486	−	0.334247i	$-0.108482\pi$
$41$	2.13451	+	2.93790i	0.333354	+	0.458823i	−0.609131	+	0.793069i	$0.708482\pi$
$42$	−4.90414	+	4.17799i	−0.756725	+	0.644678i
$43$	7.40077			1.12861			0.564303	−	0.825567i	$-0.309145\pi$
$43$	7.40077			1.12861			0.564303	+	0.825567i	$0.309145\pi$
$44$	−1.06536	−	1.97699i	−0.160609	−	0.298043i
$45$	−4.82833	−	4.65695i	−0.719765	−	0.694218i
$46$	−3.28932	+	2.87549i	−0.484984	+	0.423968i
$47$	−9.30818	+	3.02441i	−1.35774	+	0.441156i	−0.895287	−	0.445489i	$-0.853030\pi$
$47$	−9.30818	+	3.02441i	−1.35774	+	0.441156i	−0.462451	+	0.886645i	$0.653030\pi$
$48$	6.92436	−	0.230613i	0.999446	−	0.0332861i
$49$	−0.0823015			−0.0117574
$50$	−4.89834	+	5.09963i	−0.692730	+	0.721197i
$51$	4.96624	+	7.02209i	0.695412	+	0.983290i
$52$	2.53497	+	13.9225i	0.351537	+	1.93070i
$53$	0.355319	+	1.09356i	0.0488068	+	0.150212i	0.972490	−	0.232946i	$-0.0748366\pi$
$53$	0.355319	+	1.09356i	0.0488068	+	0.150212i	−0.923683	+	0.383158i	$0.874837\pi$
$54$	6.16063	+	4.00582i	0.838356	+	0.545123i
$55$	−2.49469	−	0.284372i	−0.336384	−	0.0383447i
$56$	−5.82026	−	4.63316i	−0.777765	−	0.619132i
$57$	−9.98440	+	7.06127i	−1.32247	+	0.935288i
$58$	0.356583	−	0.0321981i	0.0468216	−	0.00422782i
$59$	1.37468	−	0.998760i	0.178967	−	0.130027i	−0.494695	−	0.869067i	$-0.664720\pi$
$59$	1.37468	−	0.998760i	0.178967	−	0.130027i	0.673662	+	0.739039i	$0.264720\pi$
$60$	4.20909	−	6.50258i	0.543392	−	0.839479i
$61$	−3.31802	−	2.41068i	−0.424829	−	0.308656i	0.354749	−	0.934962i	$-0.384566\pi$
$61$	−3.31802	−	2.41068i	−0.424829	−	0.308656i	−0.779578	+	0.626305i	$0.784566\pi$
$62$	6.02261	+	3.59595i	0.764872	+	0.456687i
$63$	−2.24605	−	7.56403i	−0.282976	−	0.952978i
$64$	1.79384	+	7.79629i	0.224230	+	0.974536i
$65$	14.3968	+	6.56196i	1.78571	+	0.813911i
$66$	2.74228	−	0.212389i	0.337552	−	0.0261433i
$67$	−0.555298	+	1.70903i	−0.0678404	+	0.208791i	−0.979230	−	0.202754i	$-0.935011\pi$
$67$	−0.555298	+	1.70903i	−0.0678404	+	0.208791i	0.911389	+	0.411545i	$0.135011\pi$
$68$	−6.85897	+	7.18232i	−0.831772	+	0.870984i
$69$	−1.58847	−	5.10969i	−0.191229	−	0.615134i
$70$	−7.96828	+	2.38400i	−0.952392	+	0.284943i
$71$	2.17375	+	6.69012i	0.257977	+	0.793971i	0.993229	+	0.116177i	$0.0370639\pi$
$71$	2.17375	+	6.69012i	0.257977	+	0.793971i	−0.735252	+	0.677794i	$0.762936\pi$
$72$	−3.17631	+	7.86836i	−0.374331	+	0.927295i
$73$	−1.35514	+	1.86519i	−0.158607	+	0.218304i	−0.880924	−	0.473259i	$-0.843078\pi$
$73$	−1.35514	+	1.86519i	−0.158607	+	0.218304i	0.722316	+	0.691563i	$0.243078\pi$
$74$	2.43208	+	5.68554i	0.282724	+	0.660931i
$75$	−3.28099	−	8.01468i	−0.378856	−	0.925455i
$76$	−10.2122	−	9.75246i	−1.17142	−	1.11868i
$77$	−2.38932	−	1.73594i	−0.272288	−	0.197829i
$78$	−16.8479	−	4.06701i	−1.90765	−	0.460498i
$79$	−5.36703	+	1.74385i	−0.603838	+	0.196199i	−0.594951	−	0.803762i	$-0.702829\pi$
$79$	−5.36703	+	1.74385i	−0.603838	+	0.196199i	−0.00888659	+	0.999961i	$0.502829\pi$
$80$	8.30087	+	3.33099i	0.928066	+	0.372416i
$81$	−7.54149	+	4.91181i	−0.837943	+	0.545757i
$82$	−2.01981	−	4.72177i	−0.223051	−	0.521432i
$83$	8.73160	+	2.83707i	0.958418	+	0.311409i	0.746131	−	0.665799i	$-0.231909\pi$
$83$	8.73160	+	2.83707i	0.958418	+	0.311409i	0.212286	+	0.977208i	$0.431909\pi$
$84$	8.07516	−	4.21949i	0.881072	−	0.460385i
$85$	2.21310	+	10.8808i	0.240044	+	1.18018i
$86$	−10.2045	−	2.32598i	−1.10038	−	0.250817i
$87$	−0.140813	+	0.415276i	−0.0150967	+	0.0445222i
$88$	0.847617	+	3.06080i	0.0903563	+	0.326283i
$89$	−7.11762	+	9.79656i	−0.754466	+	1.03843i	0.243188	+	0.969979i	$0.421807\pi$
$89$	−7.11762	+	9.79656i	−0.754466	+	1.03843i	−0.997654	+	0.0684541i	$0.978193\pi$
$90$	5.19390	+	7.93873i	0.547486	+	0.836815i
$91$	10.9388	+	15.0559i	1.14670	+	1.57829i
$92$	5.43921	−	2.93107i	0.567077	−	0.305585i
$93$	−7.01406	+	4.96055i	−0.727324	+	0.514385i
$94$	13.7851	−	1.24474i	1.42183	−	0.128386i
$95$	−15.4709	+	3.14671i	−1.58728	+	0.322845i
$96$	−9.62013	−	1.85827i	−0.981850	−	0.189659i
$97$	1.59344	−	0.517741i	0.161790	−	0.0525686i	−0.227002	−	0.973894i	$-0.572892\pi$
$97$	1.59344	−	0.517741i	0.161790	−	0.0525686i	0.388792	+	0.921326i	$0.372892\pi$
$98$	0.113481	+	0.0258665i	0.0114633	+	0.00261291i
$99$	−1.12236	+	3.17619i	−0.112802	+	0.319219i
$100$	8.35683	−	5.49212i	0.835683	−	0.549212i
$101$			1.05180i			0.104658i	0.998630	+	0.0523288i	$0.0166644\pi$
$101$			1.05180i			0.104658i	−0.998630	+	0.0523288i	$0.983336\pi$
$102$	−4.64072	−	11.2432i	−0.459500	−	1.11325i
$103$	1.57304	+	4.84133i	0.154997	+	0.477030i	0.998161	−	0.0606261i	$-0.0193097\pi$
$103$	1.57304	+	4.84133i	0.154997	+	0.477030i	−0.843164	+	0.537657i	$0.819310\pi$
$104$	0.880357	−	19.9937i	0.0863261	−	1.96055i
$105$	1.28271	−	10.1055i	0.125180	−	0.986191i
$106$	−0.146237	−	1.61952i	−0.0142038	−	0.157302i
$107$			11.2872i			1.09117i	0.838054	+	0.545587i	$0.183693\pi$
$107$			11.2872i			1.09117i	−0.838054	+	0.545587i	$0.816307\pi$
$108$	−7.23559	−	7.45964i	−0.696245	−	0.717804i
$109$	11.8212	−	8.58863i	1.13227	−	0.822642i	0.146246	−	0.989248i	$-0.453281\pi$
$109$	11.8212	−	8.58863i	1.13227	−	0.822642i	0.986023	+	0.166606i	$0.0532809\pi$
$110$	3.35043	+	1.17616i	0.319451	+	0.112143i
$111$	−7.57306	−	0.0966114i	−0.718803	−	0.00916995i
$112$	6.56910	+	8.21767i	0.620722	+	0.776497i
$113$	−0.338001	+	0.245572i	−0.0317964	+	0.0231015i	−0.603570	−	0.797310i	$-0.706256\pi$
$113$	−0.338001	+	0.245572i	−0.0317964	+	0.0231015i	0.571774	+	0.820411i	$0.306256\pi$
$114$	15.9863	−	6.59843i	1.49725	−	0.618000i
$115$	0.782380	−	6.86353i	0.0729573	−	0.640028i
$116$	−0.501793	−	0.0676739i	−0.0465903	−	0.00628336i
$117$	12.9110	−	16.8492i	1.19362	−	1.55771i
$118$	−2.20937	+	0.945093i	−0.203389	+	0.0870028i
$119$	−4.03590	+	12.4212i	−0.369970	+	1.13865i
$120$	−7.84739	+	7.64320i	−0.716365	+	0.697725i
$121$	−3.00956	−	9.26246i	−0.273596	−	0.842042i
$122$	3.81740	+	4.36678i	0.345611	+	0.395350i
$123$	6.28933	+	0.0802346i	0.567090	+	0.00723451i
$124$	−7.17409	−	6.85111i	−0.644253	−	0.615248i
$125$	0.294494	−	11.1765i	0.0263403	−	0.999653i
$126$	0.719676	+	11.1356i	0.0641138	+	0.992034i
$127$	4.02987	+	2.92787i	0.357593	+	0.259806i	0.752047	−	0.659109i	$-0.229066\pi$
$127$	4.02987	+	2.92787i	0.357593	+	0.259806i	−0.394455	+	0.918915i	$0.629066\pi$
$128$	−0.0231433	−	11.3137i	−0.00204560	−	0.999998i
$129$	7.66620	−	10.2734i	0.674972	−	0.904526i
$130$	−17.7887	−	13.5727i	−1.56017	−	1.19041i
$131$	3.79895	−	11.6920i	0.331916	−	1.02153i	−0.636305	−	0.771438i	$-0.719538\pi$
$131$	3.79895	−	11.6920i	0.331916	−	1.02153i	0.968221	−	0.250095i	$-0.0804620\pi$
$132$	−3.84795	−	0.569018i	−0.334921	−	0.0495266i
$133$	−17.6612	−	5.73846i	−1.53142	−	0.497588i
$134$	1.30280	−	2.18197i	0.112545	−	0.188494i
$135$	−11.4661	+	1.87850i	−0.986844	+	0.161676i
$136$	11.7148	−	7.74762i	1.00454	−	0.664353i
$137$	9.02585	−	6.55766i	0.771131	−	0.560259i	−0.131174	−	0.991359i	$-0.541874\pi$
$137$	9.02585	−	6.55766i	0.771131	−	0.560259i	0.902304	+	0.431100i	$0.141874\pi$
$138$	0.584337	+	7.54472i	0.0497421	+	0.642249i
$139$	−5.92738	+	8.15834i	−0.502754	+	0.691982i	−0.982676	−	0.185329i	$-0.940665\pi$
$139$	−5.92738	+	8.15834i	−0.502754	+	0.691982i	0.479922	+	0.877311i	$0.340665\pi$
$140$	11.7363	−	0.782834i	0.991900	−	0.0661615i
$141$	−5.44367	+	16.0541i	−0.458440	+	1.35200i
$142$	−0.894641	−	9.90784i	−0.0750766	−	0.831448i
$143$		−	7.94521i		−	0.664412i
$144$	6.85259	−	9.85099i	0.571049	−	0.820916i
$145$	−0.382475	+	0.417352i	−0.0317628	+	0.0346592i
$146$	2.45475	−	2.14591i	0.203156	−	0.177597i
$147$	−0.0852534	+	0.114248i	−0.00703158	+	0.00942298i
$148$	−1.56657	−	8.60388i	−0.128771	−	0.707234i
$149$			1.07076i			0.0877200i	0.999038	+	0.0438600i	$0.0139656\pi$
$149$			1.07076i			0.0877200i	−0.999038	+	0.0438600i	$0.986034\pi$
$150$	2.00506	+	12.0822i	0.163713	+	0.986508i
$151$		−	8.74944i		−	0.712019i	−0.934482	−	0.356010i	$-0.884137\pi$
$151$		−	8.74944i		−	0.712019i	0.934482	−	0.356010i	$-0.115863\pi$
$152$	11.0160	+	16.6568i	0.893516	+	1.35104i
$153$	14.8921	+	0.380027i	1.20396	+	0.0307234i
$154$	2.74892	+	3.14454i	0.221514	+	0.253394i
$155$	−10.8683	+	2.21057i	−0.872964	+	0.177557i
$156$	21.9525	+	10.9029i	1.75761	+	0.872932i
$157$			2.09182i			0.166945i	0.996510	+	0.0834727i	$0.0266011\pi$
$157$			2.09182i			0.166945i	−0.996510	+	0.0834727i	$0.973399\pi$
$158$	7.94839	−	0.717710i	0.632340	−	0.0570979i
$159$	1.88609	+	0.639541i	0.149577	+	0.0507189i
$160$	−10.3987	−	7.20181i	−0.822093	−	0.569353i
$161$	4.77602	−	6.57362i	0.376403	−	0.518074i
$162$	11.9423	−	4.40244i	0.938276	−	0.345888i
$163$	8.04275	−	5.84340i	0.629957	−	0.457691i	−0.226428	−	0.974028i	$-0.572705\pi$
$163$	8.04275	−	5.84340i	0.629957	−	0.457691i	0.856385	+	0.516337i	$0.172705\pi$
$164$	1.30101	+	7.14541i	0.101592	+	0.557963i
$165$	−2.97892	+	3.16846i	−0.231909	+	0.246664i
$166$	−11.1479	−	6.65613i	−0.865244	−	0.516616i
$167$	−19.9594	−	6.48519i	−1.54450	−	0.501839i	−0.591888	−	0.806020i	$-0.701617\pi$
$167$	−19.9594	−	6.48519i	−1.54450	−	0.501839i	−0.952614	+	0.304180i	$0.901617\pi$
$168$	−12.4606	+	3.28011i	−0.961353	+	0.253066i
$169$	−11.4539	+	35.2515i	−0.881069	+	2.71165i
$170$	0.368179	−	15.6985i	0.0282380	−	1.20402i
$171$	−0.540344	+	21.1745i	−0.0413211	+	1.61925i
$172$	13.3395	+	6.41435i	1.01713	+	0.489090i
$173$	7.84149	+	5.69717i	0.596177	+	0.433148i	0.844520	−	0.535524i	$-0.179886\pi$
$173$	7.84149	+	5.69717i	0.596177	+	0.433148i	−0.248343	+	0.968672i	$0.579886\pi$
$174$	0.324676	−	0.528346i	0.0246136	−	0.0400538i
$175$	6.77437	−	11.2717i	0.512094	−	0.852058i
$176$	−0.206757	−	4.48678i	−0.0155849	−	0.338204i
$177$	0.0375426	−	2.94285i	0.00282188	−	0.221198i
$178$	12.8931	−	11.2710i	0.966376	−	0.844796i
$179$	1.49678	+	4.60660i	0.111874	+	0.344314i	0.991282	−	0.131755i	$-0.0420613\pi$
$179$	1.49678	+	4.60660i	0.111874	+	0.344314i	−0.879408	+	0.476069i	$0.842061\pi$
$180$	−4.66655	−	12.5787i	−0.347824	−	0.937560i
$181$	3.10362	−	9.55197i	0.230691	−	0.709993i	−0.766973	−	0.641679i	$-0.778238\pi$
$181$	3.10362	−	9.55197i	0.230691	−	0.709993i	0.997664	−	0.0683137i	$-0.0217619\pi$
$182$	−10.3510	−	24.1978i	−0.767268	−	1.79366i
$183$	−6.78343	+	2.10879i	−0.501446	+	0.155886i
$184$	−8.42105	+	2.33201i	−0.620808	+	0.171918i
$185$	−8.89700	−	4.05518i	−0.654120	−	0.298143i
$186$	11.2304	−	4.63541i	0.823450	−	0.339884i
$187$	4.51097	−	3.27741i	0.329875	−	0.239668i
$188$	−19.3988	−	2.61620i	−1.41480	−	0.190806i
$189$	−12.8267	−	4.71744i	−0.933003	−	0.343143i
$190$	22.3210	+	0.523497i	1.61933	+	0.0379785i
$191$	15.7612	−	11.4511i	1.14044	−	0.828576i	0.153257	−	0.988186i	$-0.451024\pi$
$191$	15.7612	−	11.4511i	1.14044	−	0.828576i	0.987180	+	0.159610i	$0.0510238\pi$
$192$	12.6807	+	5.58578i	0.915148	+	0.403119i
$193$			3.72982i			0.268478i	0.990949	+	0.134239i	$0.0428590\pi$
$193$			3.72982i			0.268478i	−0.990949	+	0.134239i	$0.957141\pi$
$194$	−2.35984	+	0.213084i	−0.169426	+	0.0152986i
$195$	24.0222	−	13.1878i	1.72027	−	0.944395i
$196$	−0.148344	−	0.0713319i	−0.0105960	−	0.00509514i
$197$	1.87126	+	5.75914i	0.133322	+	0.410322i	0.995325	−	0.0965806i	$-0.0307906\pi$
$197$	1.87126	+	5.75914i	0.133322	+	0.410322i	−0.862004	+	0.506902i	$0.830791\pi$
$198$	2.54581	−	4.02673i	0.180923	−	0.286167i
$199$			4.07539i			0.288896i	0.989512	+	0.144448i	$0.0461407\pi$
$199$			4.07539i			0.288896i	−0.989512	+	0.144448i	$0.953859\pi$
$200$	−13.2489	+	4.94634i	−0.936840	+	0.349759i
$201$	1.79719	+	2.54117i	0.126764	+	0.179240i
$202$	0.330568	−	1.45027i	0.0232587	−	0.102040i
$203$	−0.633280	+	0.205765i	−0.0444476	+	0.0144419i
$204$	2.86522	+	16.9612i	0.200605	+	1.18752i
$205$	7.38884	+	3.36777i	0.516059	+	0.235216i
$206$	−0.647410	−	7.16985i	−0.0451072	−	0.499547i
$207$	−8.73849	−	3.08791i	−0.607367	−	0.214624i
$208$	−7.49770	+	27.2916i	−0.519872	+	1.89234i
$209$	4.66001	+	6.41395i	0.322340	+	0.443662i
$210$	−4.94470	+	13.5307i	−0.341217	+	0.933710i
$211$	−5.14590	+	7.08272i	−0.354258	+	0.487594i	−0.948538	−	0.316664i	$-0.897437\pi$
$211$	−5.14590	+	7.08272i	−0.354258	+	0.487594i	0.594280	+	0.804258i	$0.297437\pi$
$212$	−0.307360	+	2.27904i	−0.0211096	+	0.156525i
$213$	11.5387	+	3.91256i	0.790616	+	0.268084i
$214$	3.54745	−	15.5633i	0.242498	−	1.06389i
$215$	14.4036	−	8.14815i	0.982320	−	0.555699i
$216$	7.63230	+	12.5598i	0.519312	+	0.854585i
$217$	−12.4070	−	4.03128i	−0.842242	−	0.273661i
$218$	−18.9990	+	8.12713i	−1.28678	+	0.550439i
$219$	1.18544	+	3.81324i	0.0801044	+	0.257675i
$220$	−4.25008	−	2.67475i	−0.286540	−	0.180332i
$221$	−33.4159	+	10.8575i	−2.24780	+	0.730353i
$222$	10.4117	+	2.51334i	0.698790	+	0.168685i
$223$	−2.60197	−	1.89044i	−0.174241	−	0.126593i	0.497247	−	0.867609i	$-0.334344\pi$
$223$	−2.60197	−	1.89044i	−0.174241	−	0.126593i	−0.671488	+	0.741016i	$0.734344\pi$
$224$	−6.47507	−	13.3955i	−0.432634	−	0.895026i
$225$	−14.5243	−	3.74760i	−0.968287	−	0.249840i
$226$	0.543232	−	0.232376i	0.0361353	−	0.0154574i
$227$	−6.51885	+	8.97243i	−0.432671	+	0.595521i	−0.968564	−	0.248765i	$-0.919975\pi$
$227$	−6.51885	+	8.97243i	−0.432671	+	0.595521i	0.535893	+	0.844286i	$0.319975\pi$
$228$	−24.1164	+	4.07393i	−1.59715	+	0.269802i
$229$	−2.00759	−	6.17873i	−0.132665	−	0.408302i	0.862554	−	0.505965i	$-0.168863\pi$
$229$	−2.00759	−	6.17873i	−0.132665	−	0.408302i	−0.995220	+	0.0976628i	$0.968863\pi$
$230$	−3.23592	+	9.21788i	−0.213370	+	0.607809i
$231$	−4.88477	+	1.51855i	−0.321395	+	0.0999132i
$232$	0.670627	+	0.251020i	0.0440288	+	0.0164803i
$233$	5.04864	−	15.5381i	0.330748	−	1.01794i	−0.638031	−	0.770010i	$-0.720251\pi$
$233$	5.04864	−	15.5381i	0.330748	−	1.01794i	0.968779	−	0.247926i	$-0.0797491\pi$
$234$	−23.0979	+	19.1747i	−1.50995	+	1.25349i
$235$	−14.7861	+	16.1344i	−0.964537	+	1.05249i
$236$	3.34342	−	0.608759i	0.217638	−	0.0396268i
$237$	−3.13878	+	9.25668i	−0.203886	+	0.601286i
$238$	9.46874	−	15.8585i	0.613767	−	1.02796i
$239$	−15.0252	−	10.9165i	−0.971902	−	0.706128i	−0.0160176	−	0.999872i	$-0.505099\pi$
$239$	−15.0252	−	10.9165i	−0.971902	−	0.706128i	−0.955884	+	0.293744i	$0.905099\pi$
$240$	13.2225	−	8.07246i	0.853511	−	0.521075i
$241$	−8.82348	+	6.41063i	−0.568370	+	0.412945i	−0.834513	−	0.550988i	$-0.814251\pi$
$241$	−8.82348	+	6.41063i	−0.568370	+	0.412945i	0.266143	+	0.963934i	$0.414251\pi$
$242$	1.23863	+	13.7174i	0.0796221	+	0.881788i
$243$	−0.993601	+	15.5568i	−0.0637396	+	0.997967i
$244$	−3.89118	−	7.22090i	−0.249107	−	0.462271i
$245$	−0.160178	+	0.0906129i	−0.0102334	+	0.00578905i
$246$	−8.64682	−	2.08730i	−0.551301	−	0.133081i
$247$	−15.4378	−	47.5126i	−0.982282	−	3.02315i
$248$	7.73875	+	11.7014i	0.491411	+	0.743039i
$249$	12.9831	−	9.18202i	0.822768	−	0.581887i
$250$	−3.91870	+	15.3181i	−0.247841	+	0.968801i
$251$	14.4760			0.913715			0.456858	−	0.889540i	$-0.348975\pi$
$251$	14.4760			0.913715			0.456858	+	0.889540i	$0.348975\pi$
$252$	2.50746	−	15.5804i	0.157955	−	0.981475i
$253$	−3.29920	+	1.07197i	−0.207419	+	0.0673944i
$254$	−4.63638	−	5.30363i	−0.290912	−	0.332779i
$255$	17.3967	+	8.19888i	1.08942	+	0.513434i
$256$	−3.52386	+	15.6071i	−0.220241	+	0.975445i
$257$	3.60686			0.224989			0.112495	−	0.993652i	$-0.464116\pi$
$257$	3.60686			0.224989			0.112495	+	0.993652i	$0.464116\pi$
$258$	−13.7994	+	11.7561i	−0.859111	+	0.731903i
$259$	−6.75999	−	9.30432i	−0.420045	−	0.578142i
$260$	20.2621	+	24.3055i	1.25660	+	1.50736i
$261$	0.430605	+	0.625640i	0.0266538	+	0.0387262i
$262$	−8.91284	+	14.9275i	−0.550637	+	0.922224i
$263$	0.296395	+	0.407953i	0.0182765	+	0.0251555i	0.818057	−	0.575136i	$-0.195051\pi$
$263$	0.296395	+	0.407953i	0.0182765	+	0.0251555i	−0.799781	+	0.600292i	$0.795051\pi$
$264$	5.12690	+	1.99396i	0.315539	+	0.122720i
$265$	1.89553	+	1.73712i	0.116441	+	0.106710i
$266$	22.5485	+	13.4632i	1.38254	+	0.825481i
$267$	6.22627	+	20.0283i	0.381042	+	1.22571i
$268$	−2.48214	+	2.59915i	−0.151621	+	0.158768i
$269$	−0.145643	−	0.0473224i	−0.00888003	−	0.00288530i	0.304574	−	0.952489i	$-0.401486\pi$
$269$	−0.145643	−	0.0473224i	−0.00888003	−	0.00288530i	−0.313454	+	0.949604i	$0.601486\pi$
$270$	16.4004	+	1.01350i	0.998096	+	0.0616794i
$271$	12.7960	−	4.15766i	0.777299	−	0.252560i	0.106612	−	0.994301i	$-0.466000\pi$
$271$	12.7960	−	4.15766i	0.777299	−	0.252560i	0.670686	+	0.741741i	$0.266000\pi$
$272$	−18.5879	+	7.00096i	−1.12706	+	0.424496i
$273$	32.2311	+	0.411181i	1.95072	+	0.0248858i
$274$	−14.5063	+	6.20530i	−0.876357	+	0.374876i
$275$	−5.16835	+	2.19317i	−0.311663	+	0.132253i
$276$	1.56551	−	10.5867i	0.0942328	−	0.637243i
$277$	16.9554	−	23.3371i	1.01875	−	1.40219i	0.105672	−	0.994401i	$-0.466301\pi$
$277$	16.9554	−	23.3371i	1.01875	−	1.40219i	0.913077	−	0.407787i	$-0.133699\pi$
$278$	10.7370	−	9.38620i	0.643965	−	0.562947i
$279$	−0.379592	+	14.8751i	−0.0227256	+	0.890548i
$280$	−16.4286	−	2.60919i	−0.981799	−	0.155929i
$281$	−0.565777	−	0.183832i	−0.0337514	−	0.0109665i	0.292093	−	0.956390i	$-0.405648\pi$
$281$	−0.565777	−	0.183832i	−0.0337514	−	0.0109665i	−0.325844	+	0.945424i	$0.605648\pi$
$282$	12.5516	−	20.4253i	0.747438	−	1.21631i
$283$	−5.89041	+	18.1288i	−0.350149	+	1.07765i	0.608620	+	0.793461i	$0.291723\pi$
$283$	−5.89041	+	18.1288i	−0.350149	+	1.07765i	−0.958769	+	0.284186i	$0.908277\pi$
$284$	−1.88035	+	13.9426i	−0.111578	+	0.827340i
$285$	−11.6576	+	24.7356i	−0.690538	+	1.46521i
$286$	−2.49709	+	10.9552i	−0.147656	+	0.647797i
$287$	5.61408	+	7.72712i	0.331389	+	0.456117i
$288$	−12.5447	+	11.4293i	−0.739206	+	0.673480i
$289$	−6.19527	−	4.50113i	−0.364428	−	0.264772i
$290$	0.658544	−	0.455258i	0.0386710	−	0.0267337i
$291$	0.931887	−	2.74826i	0.0546282	−	0.161106i
$292$	−4.05916	+	2.18739i	−0.237544	+	0.128007i
$293$	7.03851			0.411194			0.205597	−	0.978637i	$-0.434086\pi$
$293$	7.03851			0.411194			0.205597	+	0.978637i	$0.434086\pi$
$294$	0.153458	−	0.130736i	0.00894986	−	0.00762467i
$295$	1.57582	−	3.45732i	0.0917477	−	0.201293i
$296$	−0.544046	+	12.3558i	−0.0316220	+	0.718166i
$297$	3.24643	+	4.84812i	0.188377	+	0.281316i
$298$	0.336528	−	1.47641i	0.0194946	−	0.0855264i
$299$	21.8593			1.26415
$300$	1.03263	−	17.2897i	0.0596189	−	0.998221i
$301$	19.4651			1.12195
$302$	−2.74985	+	12.0641i	−0.158236	+	0.694214i
$303$	1.46006	+	1.08952i	0.0838782	+	0.0625912i
$304$	−9.95436	−	26.4293i	−0.570922	−	1.51583i
$305$	−9.11178	−	1.03866i	−0.521739	−	0.0594734i
$306$	−20.4145	−	5.20444i	−1.16702	−	0.297518i
$307$	23.4386			1.33771			0.668854	−	0.743393i	$-0.266785\pi$
$307$	23.4386			1.33771			0.668854	+	0.743393i	$0.266785\pi$
$308$	−2.80205	−	5.19979i	−0.159662	−	0.296286i
$309$	8.34999	+	2.83134i	0.475014	+	0.161069i
$310$	15.6805	+	0.367757i	0.890593	+	0.0208872i
$311$	−2.01775	−	1.46598i	−0.114416	−	0.0831280i	0.529106	−	0.848556i	$-0.322527\pi$
$311$	−2.01775	−	1.46598i	−0.114416	−	0.0831280i	−0.643522	+	0.765428i	$0.722527\pi$
$312$	−26.8425	−	21.9329i	−1.51966	−	1.24171i
$313$	−12.8727	−	17.7178i	−0.727609	−	1.00147i	−0.999237	−	0.0390656i	$-0.987562\pi$
$313$	−12.8727	−	17.7178i	−0.727609	−	1.00147i	0.271627	−	0.962402i	$-0.412438\pi$
$314$	0.657436	−	2.88430i	0.0371013	−	0.162771i
$315$	−12.6992	−	12.2485i	−0.715521	−	0.690125i
$316$	−11.1852	−	1.50848i	−0.629216	−	0.0848587i
$317$	1.52336	−	4.68843i	0.0855606	−	0.263328i	−0.899118	−	0.437706i	$-0.855791\pi$
$317$	1.52336	−	4.68843i	0.0855606	−	0.263328i	0.984679	+	0.174377i	$0.0557912\pi$
$318$	−2.39964	−	1.47461i	−0.134565	−	0.0826920i
$319$	0.270365	+	0.0878470i	0.0151375	+	0.00491849i
$320$	12.0748	+	13.1984i	0.675004	+	0.737814i
$321$	15.6684	+	11.6920i	0.874526	+	0.652585i
$322$	−8.65142	+	7.56298i	−0.482125	+	0.421468i
$323$	20.6076	−	28.3640i	1.14664	−	1.57821i
$324$	−17.8503	+	2.31695i	−0.991681	+	0.128720i
$325$	35.2442	−	3.07960i	1.95500	−	0.170826i
$326$	−12.9263	+	5.52941i	−0.715919	+	0.306246i
$327$	0.322840	−	25.3064i	0.0178531	−	1.39945i
$328$	0.451823	−	10.2613i	0.0249477	−	0.566587i
$329$	−24.4819	+	7.95466i	−1.34973	+	0.438555i
$330$	5.10329	−	3.43258i	0.280927	−	0.188957i
$331$	−6.52289	−	2.11942i	−0.358530	−	0.116494i	0.124213	−	0.992256i	$-0.460360\pi$
$331$	−6.52289	−	2.11942i	−0.358530	−	0.116494i	−0.482743	+	0.875762i	$0.660360\pi$
$332$	13.2793	+	12.6815i	0.728796	+	0.695986i
$333$	−7.97879	+	10.4125i	−0.437235	+	0.570603i
$334$	25.4827	+	15.2151i	1.39435	+	0.832534i
$335$	0.800881	+	3.93755i	0.0437568	+	0.215131i
$336$	18.2121	−	0.606547i	0.993553	−	0.0330898i
$337$	−16.5443	−	22.7713i	−0.901225	−	1.24043i	−0.970076	−	0.242803i	$-0.921933\pi$
$337$	−16.5443	−	22.7713i	−0.901225	−	1.24043i	0.0688506	−	0.997627i	$-0.478067\pi$
$338$	26.8723	−	45.0066i	1.46166	−	2.44804i
$339$	−0.00923086	+	0.723578i	−0.000501352	+	0.0392993i
$340$	−5.44152	+	21.5301i	−0.295108	+	1.16763i
$341$	3.27366	+	4.50581i	0.177279	+	0.244003i
$342$	7.39996	−	29.0265i	0.400144	−	1.56958i
$343$	−18.6275			−1.00579
$344$	−16.3772	−	13.0369i	−0.882997	−	0.702901i
$345$	−8.71723	−	8.19577i	−0.469320	−	0.441245i
$346$	−9.02166	−	10.3200i	−0.485007	−	0.554808i
$347$	34.9390	−	11.3524i	1.87562	−	0.609426i	0.886417	−	0.462888i	$-0.153187\pi$
$347$	34.9390	−	11.3524i	1.87562	−	0.609426i	0.989205	−	0.146538i	$-0.0468132\pi$
$348$	−0.613732	+	0.626467i	−0.0328995	+	0.0335822i
$349$	2.33175			0.124816			0.0624078	−	0.998051i	$-0.480122\pi$
$349$	2.33175			0.124816			0.0624078	+	0.998051i	$0.480122\pi$
$350$	−12.8834	+	13.4128i	−0.688646	+	0.716944i
$351$	−10.0153	−	35.3761i	−0.534577	−	1.88823i
$352$	−1.12506	+	6.25157i	−0.0599659	+	0.333210i
$353$	−7.50581	−	23.1005i	−0.399494	−	1.22952i	−0.925406	−	0.378977i	$-0.876276\pi$
$353$	−7.50581	−	23.1005i	−0.399494	−	1.22952i	0.525912	−	0.850539i	$-0.323724\pi$
$354$	−0.976671	+	4.04594i	−0.0519095	+	0.215039i
$355$	11.5964	+	10.6273i	0.615471	+	0.564037i
$356$	−21.3199	+	11.4888i	−1.12995	+	0.608906i
$357$	13.0620	+	18.4692i	0.691312	+	0.977492i
$358$	−0.616021	−	6.82222i	−0.0325577	−	0.360566i
$359$	−19.4805	+	14.1534i	−1.02814	+	0.746988i	−0.967936	−	0.251198i	$-0.919175\pi$
$359$	−19.4805	+	14.1534i	−1.02814	+	0.746988i	−0.0602046	+	0.998186i	$0.519175\pi$
$360$	2.48112	+	18.8107i	0.130766	+	0.991413i
$361$	24.9581	+	18.1332i	1.31359	+	0.954377i
$362$	−7.28151	+	12.1953i	−0.382708	+	0.640970i
$363$	−15.9753	−	5.41693i	−0.838483	−	0.284315i
$364$	6.66735	+	36.6183i	0.349464	+	1.91932i
$365$	−0.583872	+	5.12210i	−0.0305613	+	0.268103i
$366$	10.0161	−	0.775744i	0.523550	−	0.0405488i
$367$	−7.51175	+	23.1188i	−0.392110	+	1.20679i	0.539079	+	0.842255i	$0.318772\pi$
$367$	−7.51175	+	23.1188i	−0.392110	+	1.20679i	−0.931189	+	0.364536i	$0.881228\pi$
$368$	12.3443	−	0.568841i	0.643490	−	0.0296529i
$369$	6.62628	−	8.64747i	0.344950	−	0.450169i
$370$	10.9931	+	8.38771i	0.571504	+	0.436056i
$371$	0.934542	+	2.87622i	0.0485190	+	0.149326i
$372$	−16.9418	+	2.86194i	−0.878393	+	0.148385i
$373$	−12.8117	+	17.6338i	−0.663363	+	0.913041i	−0.999587	−	0.0287408i	$-0.990850\pi$
$373$	−12.8117	+	17.6338i	−0.663363	+	0.913041i	0.336223	+	0.941782i	$0.390850\pi$
$374$	−7.25000	+	3.10131i	−0.374889	+	0.160365i
$375$	−15.2096	−	11.9861i	−0.785422	−	0.618960i
$376$	25.9257	+	9.70417i	1.33702	+	0.500454i
$377$	−1.44923	−	1.05292i	−0.0746389	−	0.0542284i
$378$	16.2034	+	10.5359i	0.833413	+	0.541909i
$379$	12.7016	−	4.12699i	0.652435	−	0.211989i	0.0359475	−	0.999354i	$-0.488555\pi$
$379$	12.7016	−	4.12699i	0.652435	−	0.211989i	0.616488	+	0.787365i	$0.288555\pi$
$380$	−30.6127	−	7.73706i	−1.57040	−	0.396903i
$381$	8.23874	−	2.56121i	0.422084	−	0.131215i
$382$	−25.3312	+	10.8358i	−1.29606	+	0.554410i
$383$	−2.52358	−	0.819961i	−0.128949	−	0.0418981i	0.243832	−	0.969818i	$-0.421596\pi$
$383$	−2.52358	−	0.819961i	−0.128949	−	0.0418981i	−0.372781	+	0.927920i	$0.621596\pi$
$384$	−15.7292	−	11.6873i	−0.802675	−	0.596417i
$385$	−6.56142	−	0.747942i	−0.334401	−	0.0381186i
$386$	1.17224	−	5.14286i	0.0596656	−	0.261765i
$387$	−6.31999	−	21.2838i	−0.321263	−	1.08192i
$388$	3.32083	+	0.447860i	0.168589	+	0.0227367i
$389$	7.01879	−	9.66053i	0.355867	−	0.489808i	−0.593125	−	0.805111i	$-0.702106\pi$
$389$	7.01879	−	9.66053i	0.355867	−	0.489808i	0.948991	+	0.315302i	$0.102106\pi$
$390$	−37.2678	+	10.6340i	−1.88713	+	0.538473i
$391$	9.01700	+	12.4108i	0.456009	+	0.627643i
$392$	0.182125	+	0.144979i	0.00919870	+	0.00732253i
$393$	−12.2951	−	17.3849i	−0.620206	−	0.876951i
$394$	−0.770145	−	8.52909i	−0.0387993	−	0.429689i
$395$	−8.52554	+	9.30298i	−0.428966	+	0.468084i
$396$	−4.77584	+	4.75213i	−0.239995	+	0.238804i
$397$	−0.770649	+	0.250399i	−0.0386778	+	0.0125672i	−0.328292	−	0.944576i	$-0.606473\pi$
$397$	−0.770649	+	0.250399i	−0.0386778	+	0.0125672i	0.289614	+	0.957143i	$0.406473\pi$
$398$	1.28085	−	5.61934i	0.0642032	−	0.281672i
$399$	−26.2605	+	18.5722i	−1.31467	+	0.929774i
$400$	19.8228	−	2.65625i	0.991141	−	0.132813i
$401$		−	19.9527i		−	0.996388i	−0.867065	−	0.498194i	$-0.833997\pi$
$401$		−	19.9527i		−	0.996388i	0.867065	−	0.498194i	$-0.166003\pi$
$402$	−1.67939	−	4.06872i	−0.0837605	−	0.202929i
$403$	−10.8450	−	33.3776i	−0.540230	−	1.66266i
$404$	−0.911606	+	1.89580i	−0.0453541	+	0.0943197i
$405$	−9.26967	+	17.8626i	−0.460614	+	0.887601i
$406$	0.937867	−	0.0846859i	0.0465456	−	0.00420289i
$407$			4.91000i			0.243380i
$408$	1.38003	−	24.2875i	0.0683219	−	1.20241i
$409$	−17.5507	+	12.7514i	−0.867829	+	0.630514i	−0.930003	−	0.367551i	$-0.880196\pi$
$409$	−17.5507	+	12.7514i	−0.867829	+	0.630514i	0.0621747	+	0.998065i	$0.480196\pi$
$410$	−9.12963	−	6.96588i	−0.450880	−	0.344020i
$411$	0.246498	−	19.3222i	0.0121588	−	0.953092i
$412$	−1.36073	+	10.0896i	−0.0670381	+	0.497079i
$413$	3.61560	−	2.62689i	0.177912	−	0.129261i
$414$	11.0786	+	7.00417i	0.544481	+	0.344236i
$415$	20.1173	−	4.09177i	0.987520	−	0.200857i
$416$	18.9157	−	35.2746i	0.927416	−	1.72948i
$417$	5.18509	+	16.6791i	0.253915	+	0.816779i
$418$	−4.40961	−	10.3085i	−0.215681	−	0.504203i
$419$	4.46197	−	13.7325i	0.217981	−	0.670877i	−0.780947	−	0.624597i	$-0.785263\pi$
$419$	4.46197	−	13.7325i	0.217981	−	0.670877i	0.998928	−	0.0462804i	$-0.0147368\pi$
$420$	11.0706	−	17.1028i	0.540188	−	0.834530i
$421$	−0.913465	−	2.81136i	−0.0445195	−	0.137017i	0.926326	−	0.376723i	$-0.122949\pi$
$421$	−0.913465	−	2.81136i	−0.0445195	−	0.137017i	−0.970846	+	0.239706i	$0.922949\pi$
$422$	9.32143	−	8.14869i	0.453760	−	0.396672i
$423$	16.6467	+	24.1866i	0.809392	+	1.17599i
$424$	1.14008	−	3.04585i	0.0553672	−	0.147919i
$425$	16.2868	+	18.7399i	0.790025	+	0.909020i
$426$	−14.6804	−	9.02129i	−0.711267	−	0.437083i
$427$	−8.72690	−	6.34046i	−0.422324	−	0.306837i
$428$	−9.78278	+	20.3446i	−0.472868	+	0.983391i
$429$	−11.0292	−	8.23017i	−0.532495	−	0.397356i
$430$	−22.4213	+	6.70815i	−1.08125	+	0.323496i
$431$	−1.95432	+	6.01477i	−0.0941362	+	0.289721i	−0.987028	−	0.160551i	$-0.948673\pi$
$431$	−1.95432	+	6.01477i	−0.0941362	+	0.289721i	0.892891	+	0.450272i	$0.148673\pi$
$432$	−6.57637	−	19.7168i	−0.316406	−	0.948624i
$433$	12.8774	+	4.18412i	0.618849	+	0.201076i	0.601629	−	0.798776i	$-0.294519\pi$
$433$	12.8774	+	4.18412i	0.618849	+	0.201076i	0.0172196	+	0.999852i	$0.494519\pi$
$434$	15.8404	+	9.45790i	0.760362	+	0.453994i
$435$	0.183158	+	0.963257i	0.00878177	+	0.0461846i
$436$	28.7510	−	5.23490i	1.37692	−	0.250706i
$437$	−17.6464	+	12.8209i	−0.844142	+	0.613305i
$438$	−0.436077	−	5.63045i	−0.0208366	−	0.269033i
$439$	8.27611	−	11.3911i	0.394997	−	0.543667i	−0.564482	−	0.825445i	$-0.690924\pi$
$439$	8.27611	−	11.3911i	0.394997	−	0.543667i	0.959480	+	0.281778i	$0.0909242\pi$
$440$	5.01957	+	5.02383i	0.239298	+	0.239502i
$441$	0.0702825	+	0.236690i	0.00334679	+	0.0112710i
$442$	49.4878	−	4.46856i	2.35390	−	0.212548i
$443$			17.7380i			0.842758i	0.906885	+	0.421379i	$0.138454\pi$
$443$			17.7380i			0.842758i	−0.906885	+	0.421379i	$0.861546\pi$
$444$	−13.5663	−	6.73782i	−0.643828	−	0.319763i
$445$	−3.06667	+	26.9028i	−0.145374	+	1.27532i
$446$	2.99358	+	3.42441i	0.141750	+	0.162150i
$447$	1.48638	+	1.10916i	0.0703035	+	0.0524616i
$448$	4.71807	+	20.5054i	0.222908	+	0.968790i
$449$		−	28.2843i		−	1.33482i	−0.744691	−	0.667410i	$-0.767403\pi$
$449$		−	28.2843i		−	1.33482i	0.744691	−	0.667410i	$-0.232597\pi$
$450$	18.8490	+	9.73220i	0.888550	+	0.458780i
$451$		−	4.07769i		−	0.192011i
$452$	−0.822068	+	0.149680i	−0.0386668	+	0.00704034i
$453$	−12.1456	−	9.06325i	−0.570650	−	0.425828i
$454$	11.8084	−	10.3228i	0.554198	−	0.484473i
$455$	37.8658	+	17.2589i	1.77518	+	0.809112i
$456$	34.5333	+	1.96221i	1.61717	+	0.0918889i
$457$			5.94526i			0.278107i	0.990285	+	0.139054i	$0.0444061\pi$
$457$			5.94526i			0.278107i	−0.990285	+	0.139054i	$0.955594\pi$
$458$	0.826255	+	9.15049i	0.0386084	+	0.427574i
$459$	15.9538	−	20.2790i	0.744659	−	0.946541i
$460$	7.35892	−	11.6930i	0.343111	−	0.545191i
$461$	17.8555	−	24.5760i	0.831615	−	1.14462i	−0.156005	−	0.987756i	$-0.549862\pi$
$461$	17.8555	−	24.5760i	0.831615	−	1.14462i	0.987620	−	0.156863i	$-0.0501383\pi$
$462$	7.21262	−	0.558616i	0.335562	−	0.0259892i
$463$	9.77952	−	7.10524i	0.454493	−	0.330209i	−0.336874	−	0.941550i	$-0.609370\pi$
$463$	9.77952	−	7.10524i	0.454493	−	0.330209i	0.791367	+	0.611341i	$0.209370\pi$
$464$	−0.845800	−	0.556890i	−0.0392653	−	0.0258530i
$465$	−8.18950	+	17.3768i	−0.379779	+	0.805829i
$466$	−11.8448	+	19.8380i	−0.548699	+	0.918977i
$467$	−19.8940	−	6.46396i	−0.920585	−	0.299116i	−0.189879	−	0.981808i	$-0.560809\pi$
$467$	−19.8940	−	6.46396i	−0.920585	−	0.299116i	−0.730707	+	0.682691i	$0.760809\pi$
$468$	37.8748	−	19.1796i	1.75077	−	0.886578i
$469$	−1.46052	+	4.49501i	−0.0674405	+	0.207560i
$470$	25.4586	−	17.5998i	1.17432	−	0.811818i
$471$	2.90377	+	2.16684i	0.133799	+	0.0998429i
$472$	−4.80139	−	0.211413i	−0.221002	−	0.00973107i
$473$	−6.72311	−	4.88462i	−0.309129	−	0.224595i
$474$	7.23717	−	11.7771i	0.332414	−	0.540939i
$475$	−26.6455	+	23.1575i	−1.22258	+	1.06254i
$476$	−18.0401	+	18.8906i	−0.826868	+	0.865848i
$477$	2.84152	−	1.95572i	0.130104	−	0.0895461i
$478$	17.2866	+	19.7744i	0.790670	+	0.904461i
$479$	−11.0543	−	34.0217i	−0.505084	−	1.55449i	−0.800629	−	0.599160i	$-0.795501\pi$
$479$	−11.0543	−	34.0217i	−0.505084	−	1.55449i	0.295545	−	0.955329i	$-0.404499\pi$
$480$	−20.7690	+	6.97499i	−0.947969	+	0.318364i
$481$	9.56089	−	29.4254i	0.435939	−	1.34168i
$482$	14.1810	−	6.06617i	0.645928	−	0.276306i
$483$	−4.17791	−	13.4393i	−0.190102	−	0.611507i
$484$	2.60335	−	19.3035i	0.118334	−	0.877432i
$485$	2.53119	−	2.76201i	0.114935	−	0.125416i
$486$	6.25935	−	21.1381i	0.283930	−	0.958845i
$487$	−33.7319	+	24.5077i	−1.52854	+	1.11055i	−0.571495	+	0.820606i	$0.693636\pi$
$487$	−33.7319	+	24.5077i	−1.52854	+	1.11055i	−0.957044	+	0.289943i	$0.906364\pi$
$488$	3.09589	+	11.1795i	0.140144	+	0.506071i
$489$	0.219649	−	17.2176i	0.00993288	−	0.778606i
$490$	0.249340	−	0.0745992i	0.0112640	−	0.00337005i
$491$	−26.9448	+	19.5765i	−1.21600	+	0.883476i	−0.995762	−	0.0919695i	$-0.970684\pi$
$491$	−26.9448	+	19.5765i	−1.21600	+	0.883476i	−0.220239	+	0.975446i	$0.570684\pi$
$492$	11.2666	+	5.59567i	0.507939	+	0.252272i
$493$		−	1.25715i		−	0.0566190i
$494$	6.35365	+	70.3645i	0.285864	+	3.16585i
$495$	1.31256	+	7.41731i	0.0589950	+	0.333383i
$496$	−6.99295	−	18.5666i	−0.313993	−	0.833667i
$497$	5.71730	+	17.5960i	0.256456	+	0.789290i
$498$	−20.7875	+	8.58017i	−0.931509	+	0.384487i
$499$		−	2.95347i		−	0.132215i	−0.997812	−	0.0661077i	$-0.978942\pi$
$499$		−	2.95347i		−	0.132215i	0.997812	−	0.0661077i	$-0.0210581\pi$
$500$	10.2176	−	19.8897i	0.456945	−	0.889495i
$501$	−29.6777	+	20.9890i	−1.32590	+	0.937718i
$502$	−19.9602	−	4.54964i	−0.890866	−	0.203060i
$503$	−40.1948	+	13.0601i	−1.79220	+	0.582320i	−0.999623	−	0.0274568i	$-0.991259\pi$
$503$	−40.1948	+	13.0601i	−1.79220	+	0.582320i	−0.792573	+	0.609777i	$0.791259\pi$
$504$	−8.35417	+	20.6950i	−0.372124	+	0.921828i
$505$	1.15801	+	2.04704i	0.0515309	+	0.0910921i
$506$	4.88600	−	0.441187i	0.217209	−	0.0196132i
$507$	37.0699	+	52.4156i	1.64633	+	2.32786i
$508$	4.72598	+	8.77006i	0.209682	+	0.389109i
$509$	−20.6474	−	28.4187i	−0.915179	−	1.25964i	−0.965367	−	0.260897i	$-0.915982\pi$
$509$	−20.6474	−	28.4187i	−0.915179	−	1.25964i	0.0501873	−	0.998740i	$-0.484018\pi$
$510$	−21.4106	−	16.7726i	−0.948076	−	0.742704i
$511$	−3.56423	+	4.90574i	−0.157672	+	0.217017i
$512$	9.76402	−	20.4123i	0.431513	−	0.902107i
$513$	28.8338	+	22.6840i	1.27304	+	1.00152i
$514$	−4.97331	−	1.13360i	−0.219363	−	0.0500008i
$515$	8.39175	+	7.69046i	0.369785	+	0.338882i
$516$	22.7220	−	11.8729i	1.00028	−	0.522675i
$517$	10.4520	+	3.39607i	0.459680	+	0.149359i
$518$	6.39675	+	14.9538i	0.281057	+	0.657034i
$519$	16.0313	−	4.98371i	0.703696	−	0.218761i
$520$	−20.2995	−	39.8818i	−0.890190	−	1.74893i
$521$	−23.1218	+	7.51272i	−1.01298	+	0.329138i	−0.768042	−	0.640400i	$-0.778769\pi$
$521$	−23.1218	+	7.51272i	−1.01298	+	0.329138i	−0.244942	+	0.969538i	$0.578769\pi$
$522$	−0.397107	−	0.997997i	−0.0173809	−	0.0436812i
$523$	−17.9226	−	13.0215i	−0.783700	−	0.569391i	0.122387	−	0.992482i	$-0.460945\pi$
$523$	−17.9226	−	13.0215i	−0.783700	−	0.569391i	−0.906087	+	0.423091i	$0.860945\pi$
$524$	16.9810	−	17.7815i	0.741819	−	0.776790i
$525$	−8.62951	−	21.0798i	−0.376623	−	0.919999i
$526$	−0.280469	−	0.655659i	−0.0122290	−	0.0285881i
$527$	14.4769	−	19.9257i	0.630623	−	0.867978i
$528$	−6.44253	−	4.36069i	−0.280375	−	0.189775i
$529$	4.15812	+	12.7974i	0.180788	+	0.556408i
$530$	−2.06768	−	2.99097i	−0.0898145	−	0.129919i
$531$	−4.04625	−	3.10051i	−0.175592	−	0.134551i
$532$	−26.8597	−	25.6505i	−1.16451	−	1.11209i
$533$	−7.94020	+	24.4374i	−0.343928	+	1.05850i
$534$	−2.29041	−	29.5728i	−0.0991157	−	1.27974i
$535$	12.4271	+	21.9675i	0.537269	+	0.949740i
$536$	4.23937	−	2.80372i	0.183113	−	0.121102i
$537$	7.94515	+	2.69406i	0.342858	+	0.116257i
$538$	0.185947	+	0.111024i	0.00801675	+	0.00478661i
$539$	0.0747655	+	0.0543203i	0.00322038	+	0.00233974i
$540$	−22.2951	−	6.55192i	−0.959429	−	0.281950i
$541$	18.3219	−	13.3117i	0.787721	−	0.572313i	−0.119565	−	0.992826i	$-0.538150\pi$
$541$	18.3219	−	13.3117i	0.787721	−	0.572313i	0.907286	+	0.420514i	$0.138150\pi$
$542$	−18.9504	+	1.71115i	−0.813988	+	0.0735001i
$543$	−10.0447	−	14.2029i	−0.431060	−	0.609504i
$544$	27.8303	−	3.81128i	1.19321	−	0.163407i
$545$	13.5509	−	29.7305i	0.580458	−	1.27352i
$546$	−44.3126	−	10.6969i	−1.89641	−	0.457783i
$547$	8.57610	+	26.3945i	0.366688	+	1.12855i	0.948917	+	0.315524i	$0.102180\pi$
$547$	8.57610	+	26.3945i	0.366688	+	1.12855i	−0.582230	+	0.813024i	$0.697820\pi$
$548$	21.9522	−	3.99699i	0.937752	−	0.170743i
$549$	−4.09939	+	11.6009i	−0.174958	+	0.495114i
$550$	7.81566	−	1.39969i	0.333261	−	0.0596830i
$551$	1.78748			0.0761492
$552$	−5.48588	+	14.1054i	−0.233495	+	0.600365i
$553$	−14.1161	+	4.58660i	−0.600278	+	0.195042i
$554$	−30.7135	+	26.8494i	−1.30489	+	1.14072i
$555$	−14.8453	+	8.14981i	−0.630149	+	0.345940i
$556$	−17.7547	+	9.56761i	−0.752968	+	0.405757i
$557$	−19.3275			−0.818933			−0.409467	−	0.912325i	$-0.634285\pi$
$557$	−19.3275			−0.818933			−0.409467	+	0.912325i	$0.634285\pi$
$558$	5.19848	−	20.3912i	0.220069	−	0.863227i
$559$	30.7798	+	42.3647i	1.30185	+	1.79184i
$560$	21.8326	+	8.76102i	0.922594	+	0.370221i
$561$	0.123196	−	9.65690i	0.00520132	−	0.407715i
$562$	0.722344	+	0.431294i	0.0304703	+	0.0181930i
$563$	7.76254	+	10.6842i	0.327152	+	0.450286i	0.940634	−	0.339423i	$-0.110232\pi$
$563$	7.76254	+	10.6842i	0.327152	+	0.450286i	−0.613482	+	0.789709i	$0.710232\pi$
$564$	−23.7262	+	24.2185i	−0.999055	+	1.01978i
$565$	−0.387457	+	0.850075i	−0.0163004	+	0.0357629i
$566$	13.8197	−	23.1456i	0.580885	−	0.972883i
$567$	−19.8353	+	12.9188i	−0.833003	+	0.542539i
$568$	6.97473	−	18.6337i	0.292653	−	0.781854i
$569$	27.7963	+	9.03155i	1.16528	+	0.378622i	0.826879	−	0.562380i	$-0.190114\pi$
$569$	27.7963	+	9.03155i	1.16528	+	0.378622i	0.338401	+	0.941002i	$0.390114\pi$
$570$	23.8482	−	30.4428i	0.998892	−	1.27511i
$571$	6.44362	−	2.09366i	0.269657	−	0.0876169i	−0.171067	−	0.985259i	$-0.554722\pi$
$571$	6.44362	−	2.09366i	0.269657	−	0.0876169i	0.440724	+	0.897642i	$0.354722\pi$
$572$	6.88622	−	14.3208i	0.287927	−	0.598783i
$573$	0.430440	−	33.7408i	0.0179819	−	1.40954i
$574$	−5.31241	−	12.4190i	−0.221736	−	0.518358i
$575$	−6.03396	−	14.2194i	−0.251634	−	0.592992i
$576$	20.8894	−	11.8166i	0.870392	−	0.492360i
$577$	−13.7634	+	18.9437i	−0.572977	+	0.788636i	−0.992904	−	0.118923i	$-0.962056\pi$
$577$	−13.7634	+	18.9437i	−0.572977	+	0.788636i	0.419926	+	0.907558i	$0.362056\pi$
$578$	7.12768	+	8.15348i	0.296472	+	0.339140i
$579$	5.17758	+	3.86359i	0.215173	+	0.160565i
$580$	−1.05112	+	0.420758i	−0.0436452	+	0.0174710i
$581$	22.9654	+	7.46192i	0.952767	+	0.309573i
$582$	−2.14868	+	3.49655i	−0.0890656	+	0.144937i
$583$	0.398982	−	1.22794i	0.0165242	−	0.0508561i
$584$	6.28444	−	1.74033i	0.260052	−	0.0720152i
$585$	6.57710	−	47.0074i	0.271930	−	1.94352i
$586$	−9.70503	−	2.21213i	−0.400911	−	0.0913821i
$587$	−13.5473	−	18.6462i	−0.559156	−	0.769612i	0.432063	−	0.901843i	$-0.357786\pi$
$587$	−13.5473	−	18.6462i	−0.559156	−	0.769612i	−0.991219	+	0.132231i	$0.957786\pi$
$588$	−0.252684	+	0.132035i	−0.0104205	+	0.00544501i
$589$	28.3315	+	20.5840i	1.16738	+	0.848151i
$590$	−3.25941	+	4.27186i	−0.134188	+	0.175870i
$591$	9.93296	+	3.36809i	0.408587	+	0.138545i
$592$	4.63345	−	16.8658i	0.190434	−	0.693179i
$593$	−35.4686			−1.45652			−0.728261	−	0.685300i	$-0.759671\pi$
$593$	−35.4686			−1.45652			−0.728261	+	0.685300i	$0.759671\pi$
$594$	−2.95262	−	7.70514i	−0.121147	−	0.316146i
$595$	5.82079	+	28.6181i	0.238629	+	1.17323i
$596$	−0.928042	+	1.92998i	−0.0380141	+	0.0790552i
$597$	5.65728	+	4.22155i	0.231537	+	0.172777i
$598$	−30.1406	−	6.87014i	−1.23254	−	0.280941i
$599$	15.4349			0.630652			0.315326	−	0.948983i	$-0.397886\pi$
$599$	15.4349			0.630652			0.315326	+	0.948983i	$0.397886\pi$
$600$	−6.85780	+	23.5153i	−0.279969	+	0.960009i
$601$	15.2326			0.621350			0.310675	−	0.950516i	$-0.399445\pi$
$601$	15.2326			0.621350			0.310675	+	0.950516i	$0.399445\pi$
$602$	−26.8395	−	6.11769i	−1.09390	−	0.249338i
$603$	5.38919	+	0.137525i	0.219465	+	0.00560045i
$604$	7.58326	−	15.7704i	0.308559	−	0.641688i
$605$	−16.0551	−	14.7134i	−0.652735	−	0.598186i
$606$	−1.67077	−	1.96116i	−0.0678706	−	0.0796668i
$607$	34.7595			1.41085			0.705423	−	0.708787i	$-0.250757\pi$
$607$	34.7595			1.41085			0.705423	+	0.708787i	$0.250757\pi$
$608$	5.41909	+	39.5706i	0.219773	+	1.60480i
$609$	−0.370359	+	1.09224i	−0.0150077	+	0.0442597i
$610$	12.2373	+	4.29589i	0.495475	+	0.173935i
$611$	−56.0255	−	40.7049i	−2.26655	−	1.64675i
$612$	26.5129	+	13.5922i	1.07172	+	0.549432i
$613$	−13.5100	−	18.5950i	−0.545665	−	0.751043i	0.443751	−	0.896150i	$-0.353647\pi$
$613$	−13.5100	−	18.5950i	−0.545665	−	0.751043i	−0.989416	+	0.145107i	$0.953647\pi$
$614$	−32.3182	−	7.36648i	−1.30426	−	0.297287i
$615$	12.3288	−	6.76831i	0.497147	−	0.272925i
$616$	2.22936	+	8.05038i	0.0898235	+	0.324359i
$617$	4.54521	−	13.9887i	0.182983	−	0.563164i	−0.816925	−	0.576745i	$-0.804323\pi$
$617$	4.54521	−	13.9887i	0.182983	−	0.563164i	0.999908	+	0.0135801i	$0.00432281\pi$
$618$	−10.6235	−	6.52829i	−0.427340	−	0.262607i
$619$	−31.5383	−	10.2474i	−1.26763	−	0.411879i	−0.403424	−	0.915013i	$-0.632180\pi$
$619$	−31.5383	−	10.2474i	−1.26763	−	0.411879i	−0.864208	+	0.503134i	$0.832180\pi$
$620$	−21.5055	−	5.43529i	−0.863680	−	0.218287i
$621$	−13.3384	+	8.93175i	−0.535252	+	0.358419i
$622$	2.32143	+	2.65552i	0.0930807	+	0.106477i
$623$	−18.7204	+	25.7664i	−0.750018	+	1.03231i
$624$	30.1185	+	38.6785i	1.20571	+	1.54838i
$625$	−11.7320	−	22.0762i	−0.469279	−	0.883050i
$626$	12.1810	+	28.4759i	0.486851	+	1.13813i
$627$	13.7307	+	0.175166i	0.548352	+	0.00699547i
$628$	−1.81301	+	3.77039i	−0.0723469	+	0.150455i
$629$	20.6504	−	6.70974i	0.823387	−	0.267535i
$630$	13.6608	+	20.8801i	0.544258	+	0.831881i
$631$	−20.3437	−	6.61008i	−0.809871	−	0.263143i	−0.125328	−	0.992115i	$-0.539998\pi$
$631$	−20.3437	−	6.61008i	−0.809871	−	0.263143i	−0.684543	+	0.728972i	$0.739998\pi$
$632$	14.9486	+	5.59535i	0.594623	+	0.222571i
$633$	4.50147	+	14.4801i	0.178917	+	0.575531i
$634$	−3.57401	+	5.98586i	−0.141942	+	0.237729i
$635$	11.0666	+	1.26149i	0.439165	+	0.0500608i
$636$	2.84528	+	2.78744i	0.112823	+	0.110529i
$637$	−0.342292	−	0.471124i	−0.0135621	−	0.0186666i
$638$	−0.345183	−	0.206100i	−0.0136659	−	0.00815960i
$639$	17.3837	−	11.9646i	0.687690	−	0.473312i
$640$	−12.5013	−	21.9936i	−0.494156	−	0.869373i
$641$	20.8420	+	28.6865i	0.823208	+	1.13305i	0.989149	+	0.146913i	$0.0469336\pi$
$641$	20.8420	+	28.6865i	0.823208	+	1.13305i	−0.165942	+	0.986136i	$0.553066\pi$
$642$	−17.9297	−	21.0459i	−0.707628	−	0.830617i
$643$	−1.63973			−0.0646648			−0.0323324	−	0.999477i	$-0.510294\pi$
$643$	−1.63973			−0.0646648			−0.0323324	+	0.999477i	$0.510294\pi$
$644$	14.3060	−	7.70915i	0.563734	−	0.303783i
$645$	3.60932	−	28.4349i	0.142117	−	1.11962i
$646$	−37.3293	+	32.6329i	−1.46870	+	1.28392i
$647$	41.1106	−	13.3577i	1.61623	−	0.525144i	0.645178	−	0.764032i	$-0.276783\pi$
$647$	41.1106	−	13.3577i	1.61623	−	0.525144i	0.971047	+	0.238888i	$0.0767830\pi$
$648$	25.3410	+	2.41542i	0.995488	+	0.0948865i
$649$	−1.90800			−0.0748955
$650$	−49.5643	−	6.83058i	−1.94407	−	0.267917i
$651$	−18.4480	+	13.0470i	−0.723035	+	0.511352i
$652$	19.5612	−	3.56164i	0.766075	−	0.139485i
$653$	4.92751	+	15.1653i	0.192828	+	0.593464i	0.999995	+	0.00314086i	$0.000999769\pi$
$653$	4.92751	+	15.1653i	0.192828	+	0.593464i	−0.807167	+	0.590323i	$0.799000\pi$
$654$	−8.39868	+	34.7922i	−0.328414	+	1.36048i
$655$	−5.47906	−	26.9379i	−0.214084	−	1.05255i
$656$	−3.84802	+	14.0068i	−0.150240	+	0.546874i
$657$	6.52134	+	2.30443i	0.254422	+	0.0899045i
$658$	36.2569	−	3.27386i	1.41344	−	0.127629i
$659$	1.82519	−	1.32608i	0.0710992	−	0.0516566i	−0.551668	−	0.834064i	$-0.686008\pi$
$659$	1.82519	−	1.32608i	0.0710992	−	0.0516566i	0.622767	+	0.782407i	$0.286008\pi$
$660$	−8.11549	+	3.12909i	−0.315895	+	0.121800i
$661$	−33.6669	−	24.4604i	−1.30949	−	0.951400i	−1.00000		0.000496742i	$-0.999842\pi$
$661$	−33.6669	−	24.4604i	−1.30949	−	0.951400i	−0.309489	−	0.950903i	$-0.600158\pi$
$662$	8.32797	+	4.97243i	0.323676	+	0.193259i
$663$	−19.5425	+	57.6334i	−0.758967	+	2.23830i
$664$	−14.3245	−	21.6593i	−0.555898	−	0.840546i
$665$	−40.6908	+	8.27632i	−1.57792	+	0.320942i
$666$	14.2741	−	11.8496i	0.553109	−	0.459165i
$667$	−0.241689	+	0.743843i	−0.00935825	+	0.0288017i
$668$	−30.3549	−	28.9883i	−1.17446	−	1.12159i
$669$	−5.31953	+	1.65370i	−0.205665	+	0.0639358i
$670$	0.133237	−	5.68099i	0.00514740	−	0.219476i
$671$	1.42311	+	4.37989i	0.0549387	+	0.169084i
$672$	−25.3024	−	4.88754i	−0.976061	−	0.188541i
$673$	−24.8246	+	34.1682i	−0.956920	+	1.31709i	−0.00853574	+	0.999964i	$0.502717\pi$
$673$	−24.8246	+	34.1682i	−0.956920	+	1.31709i	−0.948384	+	0.317124i	$0.897283\pi$
$674$	15.6553	+	36.5978i	0.603020	+	1.40969i
$675$	−20.2475	+	16.2800i	−0.779326	+	0.626618i
$676$	−51.1980	+	53.6116i	−1.96915	+	2.06198i
$677$	35.8387	+	26.0384i	1.37739	+	1.00074i	0.997118	+	0.0758625i	$0.0241710\pi$
$677$	35.8387	+	26.0384i	1.37739	+	1.00074i	0.380276	+	0.924873i	$0.375829\pi$
$678$	0.240141	−	0.994803i	0.00922254	−	0.0382052i
$679$	4.19100	−	1.36174i	0.160836	−	0.0522587i
$680$	14.2697	−	27.9765i	0.547219	−	1.07285i
$681$	5.70249	+	18.3434i	0.218520	+	0.702921i
$682$	−3.09775	−	7.24170i	−0.118619	−	0.277299i
$683$	36.2387	+	11.7747i	1.38663	+	0.450545i	0.904844	−	0.425742i	$-0.139987\pi$
$683$	36.2387	+	11.7747i	1.38663	+	0.450545i	0.481789	+	0.876287i	$0.339987\pi$
$684$	−19.3261	+	37.6975i	−0.738954	+	1.44140i
$685$	10.3465	−	22.7001i	0.395320	−	0.867326i
$686$	25.6845	+	5.85443i	0.980640	+	0.223523i
$687$	−10.6566	−	3.61348i	−0.406576	−	0.137863i
$688$	18.4843	+	23.1230i	0.704706	+	0.881557i
$689$	−4.78216	+	6.58207i	−0.182186	+	0.250757i
$690$	9.44389	+	14.0404i	0.359523	+	0.534511i
$691$	20.6338	+	28.4000i	0.784948	+	1.08039i	0.994719	+	0.102637i	$0.0327281\pi$
$691$	20.6338	+	28.4000i	0.784948	+	1.08039i	−0.209771	+	0.977751i	$0.567272\pi$
$692$	9.19602	+	17.0652i	0.349580	+	0.648720i
$693$	−2.95199	+	8.35385i	−0.112137	+	0.317336i
$694$	−51.7434	+	4.67224i	−1.96415	+	0.177356i
$695$	−2.55385	+	22.4040i	−0.0968731	+	0.849833i
$696$	1.04314	−	0.670913i	0.0395400	−	0.0254309i
$697$	−17.1499	+	5.57235i	−0.649600	+	0.211068i
$698$	−3.21513	−	0.732844i	−0.121694	−	0.0277385i
$699$	−16.3397	−	23.1037i	−0.618023	−	0.873863i
$700$	21.9797	−	14.4451i	0.830756	−	0.545974i
$701$		−	24.1415i		−	0.911812i	−0.890028	−	0.455906i	$-0.849315\pi$
$701$		−	24.1415i		−	0.911812i	0.890028	−	0.455906i	$-0.150685\pi$
$702$	2.69125	+	51.9259i	0.101575	+	1.95982i
$703$	9.54028	+	29.3620i	0.359818	+	1.10741i
$704$	3.51609	−	8.26637i	0.132518	−	0.311551i
$705$	7.08071	+	37.2385i	0.266675	+	1.40248i
$706$	3.08913	+	34.2111i	0.116261	+	1.28755i
$707$			2.76638i			0.104041i
$708$	2.61828	−	5.27178i	0.0984008	−	0.198126i
$709$	−12.4837	+	9.06991i	−0.468834	+	0.340628i	−0.796987	−	0.603997i	$-0.793574\pi$
$709$	−12.4837	+	9.06991i	−0.468834	+	0.340628i	0.328153	+	0.944625i	$0.393574\pi$
$710$	−12.6496	−	18.2980i	−0.474730	−	0.686712i
$711$	9.59838	+	13.9458i	0.359967	+	0.523008i
$712$	33.0078	−	9.14071i	1.23702	−	0.342563i
$713$	−12.3966	+	9.00667i	−0.464257	+	0.337303i
$714$	−12.2058	−	29.5714i	−0.456790	−	1.10668i
$715$	−8.74757	−	15.4632i	−0.327140	−	0.578292i
$716$	−1.29475	+	9.60042i	−0.0483871	+	0.358785i
$717$	−30.7179	+	9.54940i	−1.14718	+	0.356629i
$718$	31.3089	−	13.3929i	1.16844	−	0.499818i
$719$	−0.511996	+	1.57576i	−0.0190942	+	0.0587659i	−0.960150	−	0.279487i	$-0.909836\pi$
$719$	−0.511996	+	1.57576i	−0.0190942	+	0.0587659i	0.941055	+	0.338252i	$0.109836\pi$
$720$	2.49093	−	26.7169i	0.0928313	−	0.995682i
$721$	4.13734	+	12.7334i	0.154083	+	0.474218i
$722$	−28.7144	−	32.8469i	−1.06864	−	1.22244i
$723$	−0.240971	+	18.8889i	−0.00896181	+	0.702487i
$724$	13.8729	−	14.5270i	0.515584	−	0.539890i
$725$	−0.284886	+	1.23337i	−0.0105804	+	0.0458060i
$726$	20.3250	+	12.4900i	0.754330	+	0.463546i
$727$	9.30425	+	6.75993i	0.345076	+	0.250712i	0.746800	−	0.665048i	$-0.231589\pi$
$727$	9.30425	+	6.75993i	0.345076	+	0.250712i	−0.401725	+	0.915760i	$0.631589\pi$
$728$	2.31547	−	52.5866i	0.0858171	−	1.94899i
$729$	20.5660	+	17.4940i	0.761704	+	0.647926i
$730$	2.41489	−	6.87909i	0.0893791	−	0.254607i
$731$	−11.3563	+	34.9510i	−0.420027	+	1.29271i
$732$	−14.0545	−	2.07832i	−0.519469	−	0.0768168i
$733$	11.8534	+	3.85140i	0.437815	+	0.142255i	0.519627	−	0.854393i	$-0.326071\pi$
$733$	11.8534	+	3.85140i	0.437815	+	0.142255i	−0.0818124	+	0.996648i	$0.526071\pi$
$734$	17.6235	−	29.5164i	0.650497	−	1.08947i
$735$	−0.0401380	+	0.316215i	−0.00148051	+	0.0116638i
$736$	−17.1997	−	3.09533i	−0.633988	−	0.114095i
$737$	1.63244	−	1.18604i	0.0601317	−	0.0436882i
$738$	−11.8544	+	9.84098i	−0.436368	+	0.362252i
$739$	3.08442	−	4.24534i	0.113462	−	0.156167i	−0.748509	−	0.663125i	$-0.769230\pi$
$739$	3.08442	−	4.24534i	0.113462	−	0.156167i	0.861971	+	0.506957i	$0.169230\pi$
$740$	−12.5217	−	15.0204i	−0.460305	−	0.552160i
$741$	−81.9464	−	27.7866i	−3.01038	−	1.02077i
$742$	−0.384625	−	4.25959i	−0.0141200	−	0.156375i
$743$			19.7148i			0.723266i	0.932320	+	0.361633i	$0.117781\pi$
$743$			19.7148i			0.723266i	−0.932320	+	0.361633i	$0.882219\pi$
$744$	24.2597	+	1.37845i	0.889403	+	0.0505366i
$745$	1.17889	+	2.08395i	0.0431913	+	0.0763500i
$746$	23.2075	−	20.2877i	0.849685	−	0.742786i
$747$	0.702628	−	27.5339i	0.0257078	−	1.00741i
$748$	10.9714	−	1.99763i	0.401153	−	0.0730407i
$749$			29.6871i			1.08474i
$750$	17.2047	+	21.3073i	0.628226	+	0.778031i
$751$		−	43.6176i		−	1.59163i	−0.605540	−	0.795815i	$-0.707043\pi$
$751$		−	43.6176i		−	1.59163i	0.605540	−	0.795815i	$-0.292957\pi$
$752$	−32.6977	−	21.5288i	−1.19236	−	0.785073i
$753$	14.9952	−	20.0949i	0.546454	−	0.732300i
$754$	1.66734	+	1.90730i	0.0607209	+	0.0694597i
$755$	−9.63302	−	17.0285i	−0.350581	−	0.619729i
$756$	−19.0307	−	19.6200i	−0.692140	−	0.713572i
$757$			13.1585i			0.478255i	0.970988	+	0.239127i	$0.0768613\pi$
$757$			13.1585i			0.478255i	−0.970988	+	0.239127i	$0.923139\pi$
$758$	−18.8106	+	1.69852i	−0.683231	+	0.0616932i
$759$	−1.92946	+	5.69023i	−0.0700348	+	0.206542i
$760$	39.7786	+	20.2895i	1.44292	+	0.735977i
$761$	−8.19231	+	11.2758i	−0.296971	+	0.408746i	−0.931263	−	0.364348i	$-0.881292\pi$
$761$	−8.19231	+	11.2758i	−0.296971	+	0.408746i	0.634292	+	0.773094i	$0.281292\pi$
$762$	−12.1649	+	0.942172i	−0.440689	+	0.0341313i
$763$	31.0917	−	22.5894i	1.12559	−	0.817791i
$764$	38.3335	−	6.97965i	1.38686	−	0.252515i
$765$	29.4020	−	15.6564i	1.06303	−	0.566059i
$766$	3.22193	+	1.92374i	0.116413	+	0.0695074i
$767$	11.4345	+	3.71531i	0.412877	+	0.134152i
$768$	18.0149	+	21.0586i	0.650057	+	0.759885i
$769$	10.7577	−	33.1089i	0.387933	−	1.19394i	−0.546397	−	0.837526i	$-0.684001\pi$
$769$	10.7577	−	33.1089i	0.387933	−	1.19394i	0.934330	−	0.356409i	$-0.115999\pi$
$770$	8.81213	+	3.09348i	0.317567	+	0.111481i
$771$	3.73622	−	5.00688i	0.134557	−	0.180319i
$772$	−3.23269	+	6.72280i	−0.116347	+	0.241959i
$773$	−26.9509	−	19.5810i	−0.969357	−	0.704279i	−0.0140523	−	0.999901i	$-0.504473\pi$
$773$	−26.9509	−	19.5810i	−0.969357	−	0.704279i	−0.955305	+	0.295622i	$0.904473\pi$
$774$	2.02504	+	31.3334i

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37885 - 0.314289i) q^{2} +(1.03587 - 1.38816i) q^{3} +(1.80244 + 0.866714i) q^{4} +(1.94623 - 1.10099i) q^{5} +(-1.86458 + 1.58850i) q^{6} +2.63015 q^{7} +(-2.21290 - 1.76156i) q^{8} +(-0.853964 - 2.87589i) q^{9} +O(q^{10})\)	\(q+(-1.37885 - 0.314289i) q^{2} +(1.03587 - 1.38816i) q^{3} +(1.80244 + 0.866714i) q^{4} +(1.94623 - 1.10099i) q^{5} +(-1.86458 + 1.58850i) q^{6} +2.63015 q^{7} +(-2.21290 - 1.76156i) q^{8} +(-0.853964 - 2.87589i) q^{9} +(-3.02959 + 0.906413i) q^{10} +(-0.908434 - 0.660016i) q^{11} +(3.07023 - 1.60428i) q^{12} +(4.15899 + 5.72437i) q^{13} +(-3.62658 - 0.826628i) q^{14} +(0.487695 - 3.84215i) q^{15} +(2.49761 + 3.12441i) q^{16} +(-1.53447 + 4.72262i) q^{17} +(0.273625 + 4.23381i) q^{18} +(-6.71489 - 2.18180i) q^{19} +(4.46222 - 0.297638i) q^{20} +(2.72448 - 3.65107i) q^{21} +(1.04516 + 1.19557i) q^{22} +(1.81587 - 2.49933i) q^{23} +(-4.73758 + 1.24712i) q^{24} +(2.57566 - 4.28556i) q^{25} +(-3.93552 - 9.20016i) q^{26} +(-4.87678 - 1.79360i) q^{27} +(4.74070 + 2.27959i) q^{28} +(-0.240777 + 0.0782332i) q^{29} +(-1.88000 + 5.14447i) q^{30} +(-4.71722 - 1.53272i) q^{31} +(-2.46186 - 5.09306i) q^{32} +(-1.85722 + 0.577362i) q^{33} +(3.60007 - 6.02951i) q^{34} +(5.11889 - 2.89576i) q^{35} +(0.953352 - 5.92378i) q^{36} +(-2.57019 - 3.53756i) q^{37} +(8.57310 + 5.11879i) q^{38} +(12.2545 + 0.156333i) q^{39} +(-6.24627 - 0.992030i) q^{40} +(2.13451 + 2.93790i) q^{41} +(-4.90414 + 4.17799i) q^{42} +7.40077 q^{43} +(-1.06536 - 1.97699i) q^{44} +(-4.82833 - 4.65695i) q^{45} +(-3.28932 + 2.87549i) q^{46} +(-9.30818 + 3.02441i) q^{47} +(6.92436 - 0.230613i) q^{48} -0.0823015 q^{49} +(-4.89834 + 5.09963i) q^{50} +(4.96624 + 7.02209i) q^{51} +(2.53497 + 13.9225i) q^{52} +(0.355319 + 1.09356i) q^{53} +(6.16063 + 4.00582i) q^{54} +(-2.49469 - 0.284372i) q^{55} +(-5.82026 - 4.63316i) q^{56} +(-9.98440 + 7.06127i) q^{57} +(0.356583 - 0.0321981i) q^{58} +(1.37468 - 0.998760i) q^{59} +(4.20909 - 6.50258i) q^{60} +(-3.31802 - 2.41068i) q^{61} +(6.02261 + 3.59595i) q^{62} +(-2.24605 - 7.56403i) q^{63} +(1.79384 + 7.79629i) q^{64} +(14.3968 + 6.56196i) q^{65} +(2.74228 - 0.212389i) q^{66} +(-0.555298 + 1.70903i) q^{67} +(-6.85897 + 7.18232i) q^{68} +(-1.58847 - 5.10969i) q^{69} +(-7.96828 + 2.38400i) q^{70} +(2.17375 + 6.69012i) q^{71} +(-3.17631 + 7.86836i) q^{72} +(-1.35514 + 1.86519i) q^{73} +(2.43208 + 5.68554i) q^{74} +(-3.28099 - 8.01468i) q^{75} +(-10.2122 - 9.75246i) q^{76} +(-2.38932 - 1.73594i) q^{77} +(-16.8479 - 4.06701i) q^{78} +(-5.36703 + 1.74385i) q^{79} +(8.30087 + 3.33099i) q^{80} +(-7.54149 + 4.91181i) q^{81} +(-2.01981 - 4.72177i) q^{82} +(8.73160 + 2.83707i) q^{83} +(8.07516 - 4.21949i) q^{84} +(2.21310 + 10.8808i) q^{85} +(-10.2045 - 2.32598i) q^{86} +(-0.140813 + 0.415276i) q^{87} +(0.847617 + 3.06080i) q^{88} +(-7.11762 + 9.79656i) q^{89} +(5.19390 + 7.93873i) q^{90} +(10.9388 + 15.0559i) q^{91} +(5.43921 - 2.93107i) q^{92} +(-7.01406 + 4.96055i) q^{93} +(13.7851 - 1.24474i) q^{94} +(-15.4709 + 3.14671i) q^{95} +(-9.62013 - 1.85827i) q^{96} +(1.59344 - 0.517741i) q^{97} +(0.113481 + 0.0258665i) q^{98} +(-1.12236 + 3.17619i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224q - 6q^{4} - 7q^{6} - 6q^{9} + O(q^{10}) \)	\( 224q - 6q^{4} - 7q^{6} - 6q^{9} - 5q^{12} - 20q^{13} + 6q^{16} - 24q^{21} - 10q^{22} - 28q^{24} - 20q^{25} - 50q^{28} - 25q^{30} - 10q^{33} - 14q^{34} - 25q^{36} - 60q^{37} - 20q^{40} - 85q^{42} - 30q^{45} + 6q^{46} - 70q^{48} + 88q^{49} + 40q^{52} - 46q^{54} + 50q^{58} + 10q^{60} - 28q^{61} + 18q^{64} + 64q^{66} - 42q^{69} - 40q^{70} - 5q^{72} - 20q^{73} - 80q^{76} - 85q^{78} + 18q^{81} - 48q^{84} - 20q^{85} + 50q^{88} - 60q^{90} + 60q^{94} + 44q^{96} - 120q^{97} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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