LMFDB - Embedded newform 273.2.cd.e.242.2

Newspace parameters

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cd (of order $12$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			242.2
Character	$\chi$	$=$	273.242
Dual form			273.2.cd.e.44.2

$q$-expansion

$f(q)$	$=$	$q+(-2.42391 - 0.649484i) q^{2} +(-1.28483 + 1.16155i) q^{3} +(3.72144 + 2.14858i) q^{4} +(3.58252 + 0.959933i) q^{5} +(3.86873 - 1.98102i) q^{6} +(1.55291 + 2.14207i) q^{7} +(-4.07612 - 4.07612i) q^{8} +(0.301593 - 2.98480i) q^{9} +O(q^{10})$	\(q+(-2.42391 - 0.649484i) q^{2} +(-1.28483 + 1.16155i) q^{3} +(3.72144 + 2.14858i) q^{4} +(3.58252 + 0.959933i) q^{5} +(3.86873 - 1.98102i) q^{6} +(1.55291 + 2.14207i) q^{7} +(-4.07612 - 4.07612i) q^{8} +(0.301593 - 2.98480i) q^{9} +(-8.06023 - 4.65358i) q^{10} +(-2.52674 + 0.677038i) q^{11} +(-7.27712 + 1.56209i) q^{12} +(3.59741 + 0.242118i) q^{13} +(-2.37286 - 6.20077i) q^{14} +(-5.71795 + 2.92793i) q^{15} +(2.93561 + 5.08463i) q^{16} +(-0.358785 + 0.621434i) q^{17} +(-2.66961 + 7.03900i) q^{18} +(1.19661 - 4.46581i) q^{19} +(11.2697 + 11.2697i) q^{20} +(-4.48336 - 0.948423i) q^{21} +6.56431 q^{22} +(2.80909 + 4.86549i) q^{23} +(9.97177 + 0.502509i) q^{24} +(7.58284 + 4.37795i) q^{25} +(-8.56254 - 2.92333i) q^{26} +(3.07951 + 4.18529i) q^{27} +(1.17665 + 11.3081i) q^{28} -1.19958i q^{29} +(15.7614 - 3.38331i) q^{30} +(-3.93812 + 1.05522i) q^{31} +(-0.829338 - 3.09513i) q^{32} +(2.46003 - 3.80482i) q^{33} +(1.27327 - 1.27327i) q^{34} +(3.50707 + 9.16470i) q^{35} +(7.53544 - 10.4598i) q^{36} +(-5.34024 - 1.43091i) q^{37} +(-5.80094 + 10.0475i) q^{38} +(-4.90331 + 3.86750i) q^{39} +(-10.6900 - 18.5156i) q^{40} +(3.34101 - 3.34101i) q^{41} +(10.2513 + 5.21076i) q^{42} +4.83534i q^{43} +(-10.8578 - 2.90934i) q^{44} +(3.94567 - 10.4036i) q^{45} +(-3.64892 - 13.6179i) q^{46} +(-0.235612 + 0.879316i) q^{47} +(-9.67784 - 3.12304i) q^{48} +(-2.17695 + 6.65288i) q^{49} +(-15.5367 - 15.5367i) q^{50} +(-0.260849 - 1.21519i) q^{51} +(12.8674 + 8.63035i) q^{52} +(2.40005 + 1.38567i) q^{53} +(-4.74616 - 12.1448i) q^{54} -9.70201 q^{55} +(2.40151 - 15.0612i) q^{56} +(3.64983 + 7.12775i) q^{57} +(-0.779109 + 2.90768i) q^{58} +(-8.51651 + 2.28199i) q^{59} +(-27.5699 - 1.38934i) q^{60} +(5.31781 + 9.21071i) q^{61} +10.2310 q^{62} +(6.86201 - 3.98909i) q^{63} -3.70150i q^{64} +(12.6554 + 4.32067i) q^{65} +(-8.43405 + 7.62479i) q^{66} +(-3.15045 + 0.844160i) q^{67} +(-2.67040 + 1.54176i) q^{68} +(-9.26073 - 2.98843i) q^{69} +(-2.54850 - 24.4922i) q^{70} +(7.32763 - 7.32763i) q^{71} +(-13.3958 + 10.9371i) q^{72} +(-1.53552 - 5.73065i) q^{73} +(12.0149 + 6.93680i) q^{74} +(-14.8279 + 3.18292i) q^{75} +(14.0483 - 14.0483i) q^{76} +(-5.37406 - 4.36109i) q^{77} +(14.3970 - 6.18984i) q^{78} +(-1.74363 - 3.02006i) q^{79} +(5.63598 + 21.0338i) q^{80} +(-8.81808 - 1.80039i) q^{81} +(-10.2682 + 5.92837i) q^{82} +(-1.93496 + 1.93496i) q^{83} +(-14.6468 - 13.1623i) q^{84} +(-1.88189 + 1.88189i) q^{85} +(3.14048 - 11.7204i) q^{86} +(1.39338 + 1.54126i) q^{87} +(13.0590 + 7.53962i) q^{88} +(-2.74480 + 10.2437i) q^{89} +(-16.3209 + 22.6547i) q^{90} +(5.06782 + 8.08191i) q^{91} +24.1422i q^{92} +(3.83414 - 5.93011i) q^{93} +(1.14220 - 1.97835i) q^{94} +(8.57375 - 14.8502i) q^{95} +(4.66072 + 3.01341i) q^{96} +(-13.6182 - 13.6182i) q^{97} +(9.59767 - 14.7121i) q^{98} +(1.25878 + 7.74601i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−2.42391	−	0.649484i	−1.71396	−	0.459254i	−0.737571	−	0.675270i	$-0.764027\pi$
$2$	−2.42391	−	0.649484i	−1.71396	−	0.459254i	−0.976390	+	0.216015i	$0.930694\pi$
$3$	−1.28483	+	1.16155i	−0.741799	+	0.670622i
$3$	−1.28483	+	1.16155i	−0.741799	+	0.670622i
$4$	3.72144	+	2.14858i	1.86072	+	1.07429i
$5$	3.58252	+	0.959933i	1.60215	+	0.429295i	0.945691	−	0.325066i	$-0.105387\pi$
$5$	3.58252	+	0.959933i	1.60215	+	0.429295i	0.656459	+	0.754361i	$0.272053\pi$
$6$	3.86873	−	1.98102i	1.57940	−	0.808746i
$7$	1.55291	+	2.14207i	0.586944	+	0.809627i
$7$	1.55291	+	2.14207i	0.586944	+	0.809627i
$8$	−4.07612	−	4.07612i	−1.44113	−	1.44113i
$9$	0.301593	−	2.98480i	0.100531	−	0.994934i
$10$	−8.06023	−	4.65358i	−2.54887	−	1.47159i
$11$	−2.52674	+	0.677038i	−0.761841	+	0.204135i	−0.618764	−	0.785577i	$-0.712366\pi$
$11$	−2.52674	+	0.677038i	−0.761841	+	0.204135i	−0.143077	+	0.989712i	$0.545700\pi$
$12$	−7.27712	+	1.56209i	−2.10072	+	0.450936i
$13$	3.59741	+	0.242118i	0.997743	+	0.0671514i
$13$	3.59741	+	0.242118i	0.997743	+	0.0671514i
$14$	−2.37286	−	6.20077i	−0.634174	−	1.65723i
$15$	−5.71795	+	2.92793i	−1.47637	+	0.755988i
$16$	2.93561	+	5.08463i	0.733903	+	1.27116i
$17$	−0.358785	+	0.621434i	−0.0870182	+	0.150720i	−0.906249	−	0.422743i	$-0.861067\pi$
$17$	−0.358785	+	0.621434i	−0.0870182	+	0.150720i	0.819231	+	0.573463i	$0.194401\pi$
$18$	−2.66961	+	7.03900i	−0.629234	+	1.65911i
$19$	1.19661	−	4.46581i	0.274521	−	1.02453i	−0.681640	−	0.731687i	$-0.738733\pi$
$19$	1.19661	−	4.46581i	0.274521	−	1.02453i	0.956162	−	0.292840i	$-0.0946002\pi$
$20$	11.2697	+	11.2697i	2.51997	+	2.51997i
$21$	−4.48336	−	0.948423i	−0.978349	−	0.206963i
$22$	6.56431			1.39952
$23$	2.80909	+	4.86549i	0.585736	+	1.01452i	0.994783	+	0.102011i	$0.0325276\pi$
$23$	2.80909	+	4.86549i	0.585736	+	1.01452i	−0.409048	+	0.912513i	$0.634139\pi$
$24$	9.97177	+	0.502509i	2.03548	+	0.102574i
$25$	7.58284	+	4.37795i	1.51657	+	0.875590i
$26$	−8.56254	−	2.92333i	−1.67925	−	0.573313i
$27$	3.07951	+	4.18529i	0.592651	+	0.805459i
$28$	1.17665	+	11.3081i	0.222366	+	2.13704i
$29$		−	1.19958i		−	0.222757i	−0.993778	−	0.111378i	$-0.964473\pi$
$29$		−	1.19958i		−	0.222757i	0.993778	−	0.111378i	$-0.0355266\pi$
$30$	15.7614	−	3.38331i	2.87763	−	0.617705i
$31$	−3.93812	+	1.05522i	−0.707307	+	0.189522i	−0.594501	−	0.804095i	$-0.702650\pi$
$31$	−3.93812	+	1.05522i	−0.707307	+	0.189522i	−0.112806	+	0.993617i	$0.535984\pi$
$32$	−0.829338	−	3.09513i	−0.146608	−	0.547147i
$33$	2.46003	−	3.80482i	0.428236	−	0.662335i
$34$	1.27327	−	1.27327i	0.218365	−	0.218365i
$35$	3.50707	+	9.16470i	0.592804	+	1.54912i
$36$	7.53544	−	10.4598i	1.25591	−	1.74330i
$37$	−5.34024	−	1.43091i	−0.877930	−	0.235241i	−0.208416	−	0.978040i	$-0.566831\pi$
$37$	−5.34024	−	1.43091i	−0.877930	−	0.235241i	−0.669514	+	0.742800i	$0.733497\pi$
$38$	−5.80094	+	10.0475i	−0.941037	+	1.62992i
$39$	−4.90331	+	3.86750i	−0.785158	+	0.619296i
$40$	−10.6900	−	18.5156i	−1.69023	−	2.92757i
$41$	3.34101	−	3.34101i	0.521779	−	0.521779i	−0.396330	−	0.918108i	$-0.629716\pi$
$41$	3.34101	−	3.34101i	0.521779	−	0.521779i	0.918108	+	0.396330i	$0.129716\pi$
$42$	10.2513	+	5.21076i	1.58180	+	0.804037i
$43$			4.83534i			0.737383i	0.929552	+	0.368691i	$0.120194\pi$
$43$			4.83534i			0.737383i	−0.929552	+	0.368691i	$0.879806\pi$
$44$	−10.8578	−	2.90934i	−1.63687	−	0.438599i
$45$	3.94567	−	10.4036i	0.588186	−	1.55088i
$46$	−3.64892	−	13.6179i	−0.538003	−	2.00786i
$47$	−0.235612	+	0.879316i	−0.0343675	+	0.128261i	−0.980978	−	0.194117i	$-0.937816\pi$
$47$	−0.235612	+	0.879316i	−0.0343675	+	0.128261i	0.946611	+	0.322379i	$0.104482\pi$
$48$	−9.67784	−	3.12304i	−1.39688	−	0.450771i
$49$	−2.17695	+	6.65288i	−0.310993	+	0.950412i
$50$	−15.5367	−	15.5367i	−2.19722	−	2.19722i
$51$	−0.260849	−	1.21519i	−0.0365262	−	0.170160i
$52$	12.8674	+	8.63035i	1.78438	+	1.19681i
$53$	2.40005	+	1.38567i	0.329672	+	0.190336i	0.655695	−	0.755026i	$-0.272376\pi$
$53$	2.40005	+	1.38567i	0.329672	+	0.190336i	−0.326024	+	0.945362i	$0.605709\pi$
$54$	−4.74616	−	12.1448i	−0.645870	−	1.65270i
$55$	−9.70201			−1.30822
$56$	2.40151	−	15.0612i	0.320915	−	2.01264i
$57$	3.64983	+	7.12775i	0.483431	+	0.944093i
$58$	−0.779109	+	2.90768i	−0.102302	+	0.381797i
$59$	−8.51651	+	2.28199i	−1.10875	+	0.297090i	−0.766325	−	0.642453i	$-0.777917\pi$
$59$	−8.51651	+	2.28199i	−1.10875	+	0.297090i	−0.342430	+	0.939543i	$0.611250\pi$
$60$	−27.5699	−	1.38934i	−3.55926	−	0.179362i
$61$	5.31781	+	9.21071i	0.680876	+	1.17931i	0.974714	+	0.223456i	$0.0717339\pi$
$61$	5.31781	+	9.21071i	0.680876	+	1.17931i	−0.293838	+	0.955855i	$0.594933\pi$
$62$	10.2310			1.29934
$63$	6.86201	−	3.98909i	0.864532	−	0.502578i
$64$		−	3.70150i		−	0.462688i
$65$	12.6554	+	4.32067i	1.56971	+	0.535913i
$66$	−8.43405	+	7.62479i	−1.03816	+	0.938547i
$67$	−3.15045	+	0.844160i	−0.384888	+	0.103131i	−0.446074	−	0.894996i	$-0.647178\pi$
$67$	−3.15045	+	0.844160i	−0.384888	+	0.103131i	0.0611861	+	0.998126i	$0.480512\pi$
$68$	−2.67040	+	1.54176i	−0.323833	+	0.186965i
$69$	−9.26073	−	2.98843i	−1.11486	−	0.359765i
$70$	−2.54850	−	24.4922i	−0.304604	−	2.92737i
$71$	7.32763	−	7.32763i	0.869629	−	0.869629i	−0.122802	−	0.992431i	$-0.539188\pi$
$71$	7.32763	−	7.32763i	0.869629	−	0.869629i	0.992431	+	0.122802i	$0.0391880\pi$
$72$	−13.3958	+	10.9371i	−1.57870	+	1.28895i
$73$	−1.53552	−	5.73065i	−0.179719	−	0.670722i	−0.995699	−	0.0926420i	$-0.970469\pi$
$73$	−1.53552	−	5.73065i	−0.179719	−	0.670722i	0.815980	−	0.578080i	$-0.196198\pi$
$74$	12.0149	+	6.93680i	1.39670	+	0.806386i
$75$	−14.8279	+	3.18292i	−1.71218	+	0.367532i
$76$	14.0483	−	14.0483i	1.61145	−	1.61145i
$77$	−5.37406	−	4.36109i	−0.612431	−	0.496992i
$78$	14.3970	−	6.18984i	1.63014	−	0.700862i
$79$	−1.74363	−	3.02006i	−0.196174	−	0.339784i	0.751111	−	0.660176i	$-0.229518\pi$
$79$	−1.74363	−	3.02006i	−0.196174	−	0.339784i	−0.947285	+	0.320393i	$0.896185\pi$
$80$	5.63598	+	21.0338i	0.630122	+	2.35165i
$81$	−8.81808	−	1.80039i	−0.979787	−	0.200044i
$82$	−10.2682	+	5.92837i	−1.13394	+	0.654679i
$83$	−1.93496	+	1.93496i	−0.212390	+	0.212390i	−0.805282	−	0.592892i	$-0.797986\pi$
$83$	−1.93496	+	1.93496i	−0.212390	+	0.212390i	0.592892	+	0.805282i	$0.297986\pi$
$84$	−14.6468	−	13.1623i	−1.59810	−	1.43613i
$85$	−1.88189	+	1.88189i	−0.204120	+	0.204120i
$86$	3.14048	−	11.7204i	0.338646	−	1.26385i
$87$	1.39338	+	1.54126i	0.149386	+	0.165241i
$88$	13.0590	+	7.53962i	1.39209	+	0.803726i
$89$	−2.74480	+	10.2437i	−0.290948	+	1.08583i	0.653435	+	0.756983i	$0.273327\pi$
$89$	−2.74480	+	10.2437i	−0.290948	+	1.08583i	−0.944382	+	0.328849i	$0.893339\pi$
$90$	−16.3209	+	22.6547i	−1.72037	+	2.38801i
$91$	5.06782	+	8.08191i	0.531252	+	0.847214i
$92$			24.1422i			2.51700i
$93$	3.83414	−	5.93011i	0.397582	−	0.614924i
$94$	1.14220	−	1.97835i	0.117809	−	0.204052i
$95$	8.57375	−	14.8502i	0.879649	−	1.52360i
$96$	4.66072	+	3.01341i	0.475683	+	0.307555i
$97$	−13.6182	−	13.6182i	−1.38272	−	1.38272i	−0.839749	−	0.542975i	$-0.817298\pi$
$97$	−13.6182	−	13.6182i	−1.38272	−	1.38272i	−0.542975	−	0.839749i	$-0.682702\pi$
$98$	9.59767	−	14.7121i	0.969511	−	1.48614i
$99$	1.25878	+	7.74601i	0.126512	+	0.778504i
$100$	18.8127	+	32.5846i	1.88127	+	3.25846i
$101$	8.22476	−	14.2457i	0.818394	−	1.41750i	−0.0884712	−	0.996079i	$-0.528198\pi$
$101$	8.22476	−	14.2457i	0.818394	−	1.41750i	0.906865	−	0.421421i	$-0.138469\pi$
$102$	−0.156971	+	3.11492i	−0.0155424	+	0.308423i
$103$	−1.66310	+	0.960190i	−0.163870	+	0.0946103i	−0.579692	−	0.814836i	$-0.696827\pi$
$103$	−1.66310	+	0.960190i	−0.163870	+	0.0946103i	0.415822	+	0.909446i	$0.363494\pi$
$104$	−13.6766	−	15.6504i	−1.34110	−	1.53465i
$105$	−15.1513	−	7.70146i	−1.47861	−	0.751586i
$106$	−4.91752	−	4.91752i	−0.477632	−	0.477632i
$107$	6.59999	−	3.81051i	0.638045	−	0.368375i	−0.145816	−	0.989312i	$-0.546581\pi$
$107$	6.59999	−	3.81051i	0.638045	−	0.368375i	0.783861	+	0.620936i	$0.213247\pi$
$108$	2.46780	+	22.1919i	0.237464	+	2.13541i
$109$	15.5683	−	4.17150i	1.49117	−	0.399557i	0.581037	−	0.813877i	$-0.302647\pi$
$109$	15.5683	−	4.17150i	1.49117	−	0.399557i	0.910131	+	0.414320i	$0.135980\pi$
$110$	23.5168	+	6.30130i	2.24224	+	0.600805i
$111$	8.52340	−	4.36448i	0.809005	−	0.414258i
$112$	−6.33291	+	14.1843i	−0.598404	+	1.34029i
$113$			9.44516i			0.888526i	0.895897	+	0.444263i	$0.146534\pi$
$113$			9.44516i			0.888526i	−0.895897	+	0.444263i	$0.853466\pi$
$114$	−4.21748	−	19.6475i	−0.395003	−	1.84016i
$115$	5.39307	+	20.1272i	0.502907	+	1.87687i
$116$	2.57740	−	4.46418i	0.239305	−	0.414489i
$117$	1.80763	−	10.6645i	0.167115	−	0.985937i
$118$	22.1253			2.03680
$119$	−1.88832	+	0.196486i	−0.173102	+	0.0180119i
$120$	35.2417	+	11.3725i	3.21711	+	1.03816i
$121$	−3.60024	+	2.07860i	−0.327294	+	0.188963i
$122$	−6.90766	−	25.7797i	−0.625390	−	2.33399i
$123$	−0.411884	+	8.17341i	−0.0371383	+	0.736971i
$124$	−16.9227	−	4.53443i	−1.51970	−	0.407203i
$125$	9.85018	+	9.85018i	0.881027	+	0.881027i
$126$	−19.2237	+	5.21241i	−1.71259	+	0.464359i
$127$		−	5.13993i		−	0.456095i	−0.973650	−	0.228048i	$-0.926766\pi$
$127$		−	5.13993i		−	0.456095i	0.973650	−	0.228048i	$-0.0732342\pi$
$128$	−4.06274	+	15.1624i	−0.359099	+	1.34018i
$129$	−5.61650	−	6.21261i	−0.494505	−	0.546990i
$130$	−27.8693	−	18.6924i	−2.44430	−	1.63943i
$131$	8.70090	−	5.02346i	0.760201	−	0.438902i	−0.0691670	−	0.997605i	$-0.522034\pi$
$131$	8.70090	−	5.02346i	0.760201	−	0.438902i	0.829368	+	0.558703i	$0.188701\pi$
$132$	17.3298	−	8.87389i	1.50837	−	0.772373i
$133$	11.4243	−	4.37177i	0.990614	−	0.379080i
$134$	8.18466			0.707047
$135$	7.01479	+	17.9500i	0.603737	+	1.54489i
$136$	3.99550	−	1.07059i	0.342611	−	0.0918023i
$137$	−4.27489	+	1.14545i	−0.365228	+	0.0978626i	−0.436766	−	0.899575i	$-0.643876\pi$
$137$	−4.27489	+	1.14545i	−0.365228	+	0.0978626i	0.0715375	+	0.997438i	$0.477209\pi$
$138$	20.5062	+	13.2584i	1.74560	+	1.12863i
$139$	−2.12187			−0.179975			−0.0899875	−	0.995943i	$-0.528683\pi$
$139$	−2.12187			−0.179975			−0.0899875	+	0.995943i	$0.528683\pi$
$140$	−6.63968	+	41.6412i	−0.561156	+	3.51932i
$141$	−0.718649	−	1.40345i	−0.0605212	−	0.118192i
$142$	−22.5207	+	13.0023i	−1.88989	+	1.09113i
$143$	−9.25366	+	1.82382i	−0.773830	+	0.152515i
$144$	16.0620	−	7.22873i	1.33850	−	0.602395i
$145$	1.15152	−	4.29752i	0.0956284	−	0.356890i
$146$			14.8879i			1.23213i
$147$	−4.93065	−	11.0765i	−0.406673	−	0.913574i
$148$	−16.7990	−	16.7990i	−1.38087	−	1.38087i
$149$	−16.0468	−	4.29972i	−1.31460	−	0.352247i	−0.467650	−	0.883914i	$-0.654899\pi$
$149$	−16.0468	−	4.29972i	−1.31460	−	0.352247i	−0.846954	+	0.531667i	$0.821566\pi$
$150$	38.0087	+	1.91538i	3.10340	+	0.156390i
$151$	−2.70205	−	10.0842i	−0.219890	−	0.820640i	−0.984388	−	0.176014i	$-0.943680\pi$
$151$	−2.70205	−	10.0842i	−0.219890	−	0.820640i	0.764498	−	0.644626i	$-0.222987\pi$
$152$	−23.0807	+	13.3257i	−1.87209	+	1.08085i
$153$	1.74665	+	1.25832i	0.141208	+	0.101729i
$154$	10.1938	+	14.0612i	0.821438	+	1.13309i
$155$	−15.1213			−1.21457
$156$	−26.5570	+	3.85756i	−2.12626	+	0.308852i
$157$	−0.902803	+	1.56370i	−0.0720516	+	0.124797i	−0.899800	−	0.436302i	$-0.856288\pi$
$157$	−0.902803	+	1.56370i	−0.0720516	+	0.124797i	0.827749	+	0.561099i	$0.189621\pi$
$158$	2.26492	+	8.45281i	0.180188	+	0.672470i
$159$	−4.69319	+	1.00743i	−0.372194	+	0.0798942i
$160$		−	11.8845i		−	0.939550i
$161$	−6.05997	+	13.5729i	−0.477592	+	1.06970i
$162$	20.2049	+	10.0912i	1.58745	+	0.792838i
$163$	8.58348	+	2.29994i	0.672310	+	0.180145i	0.578795	−	0.815473i	$-0.303523\pi$
$163$	8.58348	+	2.29994i	0.672310	+	0.180145i	0.0935151	+	0.995618i	$0.470190\pi$
$164$	19.6118	−	5.25497i	1.53143	−	0.410345i
$165$	12.4655	−	11.2694i	0.970435	−	0.877321i
$166$	5.94690	−	3.43345i	0.461569	−	0.266487i
$167$	−15.1062	−	15.1062i	−1.16895	−	1.16895i	−0.982456	−	0.186495i	$-0.940287\pi$
$167$	−15.1062	−	15.1062i	−1.16895	−	1.16895i	−0.186495	−	0.982456i	$-0.559713\pi$
$168$	14.4088	+	22.1406i	1.11167	+	1.70819i
$169$	12.8828	+	1.74199i	0.990981	+	0.134000i
$170$	5.78378	−	3.33927i	0.443596	−	0.256110i
$171$	−12.9687	−	4.91850i	−0.991739	−	0.376127i
$172$	−10.3891	+	17.9945i	−0.792162	+	1.37206i
$173$	−6.29273	−	10.8993i	−0.478428	−	0.828661i	0.521267	−	0.853394i	$-0.325460\pi$
$173$	−6.29273	−	10.8993i	−0.478428	−	0.828661i	−0.999694	+	0.0247331i	$0.992126\pi$
$174$	−2.37639	−	4.64086i	−0.180154	−	0.351822i
$175$	2.39755	+	23.0415i	0.181238	+	1.74178i
$176$	−10.8600	−	10.8600i	−0.818605	−	0.818605i
$177$	8.29164	−	12.8243i	0.623238	−	0.963937i
$178$	13.3063	−	23.0471i	0.997347	−	1.72746i
$179$	2.00334	−	3.46988i	0.149736	−	0.259351i	−0.781394	−	0.624039i	$-0.785491\pi$
$179$	2.00334	−	3.46988i	0.149736	−	0.259351i	0.931130	+	0.364687i	$0.118824\pi$
$180$	37.0365	−	30.2388i	2.76054	−	2.25387i
$181$			4.67555i			0.347531i	0.984787	+	0.173766i	$0.0555935\pi$
$181$			4.67555i			0.347531i	−0.984787	+	0.173766i	$0.944407\pi$
$182$	−7.03485	−	22.8813i	−0.521458	−	1.69607i
$183$	−17.5312	−	5.65732i	−1.29595	−	0.418201i
$184$	8.38212	−	31.2825i	0.617938	−	2.30618i
$185$	−17.7579	−	10.2525i	−1.30559	−	0.753782i
$186$	−13.1451	+	11.8838i	−0.963846	+	0.871364i
$187$	0.485823	−	1.81312i	0.0355269	−	0.132588i
$188$	−2.76610	+	2.76610i	−0.201738	+	0.201738i
$189$	−4.18300	+	13.0959i	−0.304269	+	0.952586i
$190$	−30.4269	+	30.4269i	−2.20740	+	2.20740i
$191$	13.1603	−	7.59811i	0.952247	−	0.549780i	0.0584690	−	0.998289i	$-0.481378\pi$
$191$	13.1603	−	7.59811i	0.952247	−	0.549780i	0.893778	+	0.448509i	$0.148045\pi$
$192$	4.29949	+	4.75581i	0.310289	+	0.343221i
$193$	−0.511449	−	1.90875i	−0.0368149	−	0.137395i	0.945072	−	0.326861i	$-0.105991\pi$
$193$	−0.511449	−	1.90875i	−0.0368149	−	0.137395i	−0.981887	+	0.189466i	$0.939324\pi$
$194$	24.1645	+	41.8542i	1.73491	+	3.00496i
$195$	−21.2787	+	9.14855i	−1.52380	+	0.655141i
$196$	−22.3956	+	20.0810i	−1.59969	+	1.43436i
$197$	14.6269	−	14.6269i	1.04213	−	1.04213i	0.0430522	−	0.999073i	$-0.486292\pi$
$197$	14.6269	−	14.6269i	1.04213	−	1.04213i	0.999073	−	0.0430522i	$-0.0137082\pi$
$198$	1.97975	−	19.5932i	0.140695	−	1.39243i
$199$	−6.35018	−	3.66628i	−0.450152	−	0.259895i	0.257742	−	0.966214i	$-0.417021\pi$
$199$	−6.35018	−	3.66628i	−0.450152	−	0.259895i	−0.707894	+	0.706318i	$0.750355\pi$
$200$	−13.0635	−	48.7537i	−0.923729	−	3.44740i
$201$	3.06726	−	4.74401i	0.216348	−	0.334617i
$202$	−29.1884	+	29.1884i	−2.05369	+	2.05369i
$203$	2.56959	−	1.86284i	0.180350	−	0.130746i
$204$	1.64019	−	5.08271i	0.114836	−	0.355861i
$205$	15.1764	−	8.76209i	1.05997	−	0.611971i
$206$	4.65482	−	1.24726i	0.324317	−	0.0869004i
$207$	15.3697	−	6.91718i	1.06827	−	0.480777i
$208$	9.32954	+	19.0023i	0.646887	+	1.31757i
$209$			12.0941i			0.836566i
$210$	31.7233	+	28.5081i	2.18912	+	1.96725i
$211$	12.5260			0.862325			0.431163	−	0.902274i	$-0.358104\pi$
$211$	12.5260			0.862325			0.431163	+	0.902274i	$0.358104\pi$
$212$	5.95443	+	10.3134i	0.408952	+	0.708325i
$213$	−0.903358	+	17.9262i	−0.0618971	+	1.22828i
$214$	−18.4726	+	4.94972i	−1.26276	+	0.338356i
$215$	−4.64160	+	17.3227i	−0.316555	+	1.18140i
$216$	4.50731	−	29.6122i	0.306683	−	2.01486i
$217$	−8.37589	−	6.79709i	−0.568592	−	0.461416i
$218$	−40.4453			−2.73930
$219$	8.62934	+	5.57934i	0.583117	+	0.377017i
$220$	−36.1055	−	20.8455i	−2.43423	−	1.40540i
$221$	−1.44116	+	2.14869i	−0.0969429	+	0.144536i
$222$	−23.4946	+	5.04329i	−1.57685	+	0.338483i
$223$	−3.17920	−	3.17920i	−0.212895	−	0.212895i	0.592601	−	0.805496i	$-0.298101\pi$
$223$	−3.17920	−	3.17920i	−0.212895	−	0.212895i	−0.805496	+	0.592601i	$0.798101\pi$
$224$	5.34211	−	6.58296i	0.356935	−	0.439842i
$225$	15.3543	−	21.3129i	1.02362	−	1.42086i
$226$	6.13448	−	22.8942i	0.408059	−	1.52290i
$227$	2.93970	+	10.9711i	0.195115	+	0.728179i	0.992237	+	0.124361i	$0.0396880\pi$
$227$	2.93970	+	10.9711i	0.195115	+	0.728179i	−0.797122	+	0.603818i	$0.793645\pi$
$228$	−1.73188	+	34.3674i	−0.114697	+	2.27604i
$229$	17.7017	+	4.74317i	1.16976	+	0.313437i	0.790859	−	0.611998i	$-0.209634\pi$
$229$	17.7017	+	4.74317i	1.16976	+	0.313437i	0.378905	+	0.925436i	$0.376301\pi$
$230$		−	52.2892i		−	3.44785i
$231$	11.9704	−	0.638986i	0.787595	−	0.0420422i
$232$	−4.88965	+	4.88965i	−0.321021	+	0.321021i
$233$	−2.40978	−	4.17387i	−0.157870	−	0.273439i	0.776230	−	0.630449i	$-0.217129\pi$
$233$	−2.40978	−	4.17387i	−0.157870	−	0.273439i	−0.934100	+	0.357010i	$0.883796\pi$
$234$	−11.3080	+	24.6758i	−0.739225	+	1.61311i
$235$	−1.68817	+	2.92399i	−0.110124	+	0.190740i
$236$	−36.5967	−	9.80607i	−2.38225	−	0.638321i
$237$	5.74824	+	1.85496i	0.373388	+	0.120492i
$238$	4.70472	+	0.750168i	0.304962	+	0.0486262i
$239$	12.6692	−	12.6692i	0.819500	−	0.819500i	−0.166535	−	0.986036i	$-0.553258\pi$
$239$	12.6692	−	12.6692i	0.819500	−	0.819500i	0.986036	+	0.166535i	$0.0532579\pi$
$240$	−31.6731	−	20.4784i	−2.04449	−	1.32188i
$241$	−3.25905	−	12.1629i	−0.209934	−	0.783484i	−0.987889	−	0.155164i	$-0.950410\pi$
$241$	−3.25905	−	12.1629i	−0.209934	−	0.783484i	0.777955	−	0.628320i	$-0.216257\pi$
$242$	10.0767	−	2.70003i	0.647752	−	0.173565i
$243$	13.4210	−	7.92946i	0.860959	−	0.508675i
$244$			45.7029i			2.92583i
$245$	−14.1853	+	21.7443i	−0.906265	+	1.38920i
$246$	6.30687	−	19.5441i	0.402111	−	1.24608i
$247$	5.38595	−	15.7756i	0.342700	−	1.00378i
$248$	20.3535	+	11.7511i	1.29245	+	0.746194i
$249$	0.238545	−	4.73367i	0.0151172	−	0.299984i
$250$	−17.4784	−	30.2734i	−1.10543	−	1.91466i
$251$	−18.7701			−1.18476			−0.592379	−	0.805660i	$-0.701811\pi$
$251$	−18.7701			−1.18476			−0.592379	+	0.805660i	$0.701811\pi$
$252$	34.1075	−	0.101615i	2.14857	−	0.00640112i
$253$	−10.3920	−	10.3920i	−0.653337	−	0.653337i
$254$	−3.33830	+	12.4587i	−0.209464	+	0.781729i
$255$	0.232002	−	4.60383i	0.0145285	−	0.288303i
$256$	15.9939	−	27.7023i	0.999620	−	1.73139i
$257$	−5.88351	−	10.1905i	−0.367003	−	0.635668i	0.622092	−	0.782944i	$-0.286283\pi$
$257$	−5.88351	−	10.1905i	−0.367003	−	0.635668i	−0.989095	+	0.147276i	$0.952950\pi$
$258$	9.57889	+	18.7066i	0.596356	+	1.16462i
$259$	−5.22778	−	13.6613i	−0.324838	−	0.848869i
$260$	37.8130	+	43.2702i	2.34506	+	2.68350i
$261$	−3.58052	−	0.361786i	−0.221628	−	0.0223940i
$262$	−24.3528	+	6.52532i	−1.50452	+	0.403136i
$263$	12.2786	+	7.08907i	0.757133	+	0.437131i	0.828265	−	0.560336i	$-0.189328\pi$
$263$	12.2786	+	7.08907i	0.757133	+	0.437131i	−0.0711324	+	0.997467i	$0.522661\pi$
$264$	−25.5363	+	5.48156i	−1.57165	+	0.337367i
$265$	7.26806	+	7.26806i	0.446474	+	0.446474i
$266$	−30.5309	+	3.17684i	−1.87197	+	0.194785i
$267$	−8.37201	−	16.3497i	−0.512359	−	1.00059i
$268$	−13.5380	−	3.62748i	−0.826962	−	0.221584i
$269$	2.26549	+	1.30798i	0.138129	+	0.0797490i	0.567472	−	0.823393i	$-0.307921\pi$
$269$	2.26549	+	1.30798i	0.138129	+	0.0797490i	−0.429343	+	0.903142i	$0.641255\pi$
$270$	−5.34497	−	48.0651i	−0.325284	−	2.92515i
$271$	−22.9213	−	6.14174i	−1.39237	−	0.373084i	−0.516770	−	0.856124i	$-0.672866\pi$
$271$	−22.9213	−	6.14174i	−1.39237	−	0.373084i	−0.875598	+	0.483040i	$0.839533\pi$
$272$	−4.21302			−0.255452
$273$	−15.8989	−	4.49737i	−0.962243	−	0.272193i
$274$	11.1059			0.670931
$275$	−22.1239	−	5.92808i	−1.33412	−	0.357477i
$276$	−28.0424	−	31.0187i	−1.68795	−	1.86710i
$277$	1.85506	+	1.07102i	0.111460	+	0.0643514i	0.554694	−	0.832055i	$-0.312835\pi$
$277$	1.85506	+	1.07102i	0.111460	+	0.0643514i	−0.443234	+	0.896406i	$0.646169\pi$
$278$	5.14323	+	1.37812i	0.308470	+	0.0826544i
$279$	1.96190	+	12.0728i	0.117456	+	0.722777i
$280$	23.0612	−	51.6517i	1.37817	−	3.08678i
$281$	−10.3426	−	10.3426i	−0.616987	−	0.616987i	0.327770	−	0.944758i	$-0.393703\pi$
$281$	−10.3426	−	10.3426i	−0.616987	−	0.616987i	−0.944758	+	0.327770i	$0.893703\pi$
$282$	0.830421	+	3.86858i	0.0494508	+	0.230371i
$283$	−0.330377	−	0.190743i	−0.0196389	−	0.0113385i	0.490148	−	0.871639i	$-0.336943\pi$
$283$	−0.330377	−	0.190743i	−0.0196389	−	0.0113385i	−0.509787	+	0.860300i	$0.670276\pi$
$284$	43.0133	−	11.5254i	2.55237	−	0.683906i
$285$	6.23341	+	29.0389i	0.369235	+	1.72011i
$286$	23.6145	+	1.58934i	1.39636	+	0.0939794i
$287$	12.3450	+	1.96841i	0.728701	+	0.116191i
$288$	−9.48848	+	1.54194i	−0.559114	+	0.0908596i
$289$	8.24255	+	14.2765i	0.484856	+	0.839795i
$290$	−5.58235	+	9.66891i	−0.327807	+	0.567778i
$291$	33.3155	+	1.67887i	1.95299	+	0.0984173i
$292$	6.59838	−	24.6255i	0.386141	−	1.44110i
$293$	9.54534	+	9.54534i	0.557645	+	0.557645i	0.928636	−	0.370992i	$-0.120982\pi$
$293$	9.54534	+	9.54534i	0.557645	+	0.557645i	−0.370992	+	0.928636i	$0.620982\pi$
$294$	4.75744	+	30.0508i	0.277459	+	1.75260i
$295$	−32.7011			−1.90393
$296$	15.9349	+	27.6000i	0.926197	+	1.60422i
$297$	−10.6147	−	8.49020i	−0.615928	−	0.492651i
$298$	36.1033	+	20.8443i	2.09141	+	1.20748i
$299$	8.92743	+	18.1833i	0.516287	+	1.05157i
$300$	−62.0200	−	20.0138i	−3.58072	−	1.15550i
$301$	−10.3577	+	7.50884i	−0.597005	+	0.432802i
$302$			26.1981i			1.50753i
$303$	5.97968	+	27.8568i	0.343524	+	1.60033i
$304$	26.2198	−	7.02557i	1.50381	−	0.402944i
$305$	10.2095	+	38.1023i	0.584593	+	2.18173i
$306$	−3.41646	−	4.18448i	−0.195306	−	0.239211i
$307$	22.5415	−	22.5415i	1.28651	−	1.28651i	0.349620	−	0.936892i	$-0.386311\pi$
$307$	22.5415	−	22.5415i	1.28651	−	1.28651i	0.936892	−	0.349620i	$-0.113689\pi$
$308$	−10.6291	−	27.7761i	−0.605652	−	1.58269i
$309$	1.02149	−	3.16546i	0.0581107	−	0.180077i
$310$	36.6527	+	9.82105i	2.08173	+	0.557798i
$311$	5.70705	−	9.88490i	0.323617	−	0.560522i	−0.657614	−	0.753355i	$-0.728434\pi$
$311$	5.70705	−	9.88490i	0.323617	−	0.560522i	0.981232	+	0.192833i	$0.0617677\pi$
$312$	35.7509	+	4.22208i	2.02400	+	0.239028i
$313$	10.4355	+	18.0749i	0.589852	+	1.02165i	0.994251	+	0.107071i	$0.0341472\pi$
$313$	10.4355	+	18.0749i	0.589852	+	1.02165i	−0.404400	+	0.914582i	$0.632519\pi$
$314$	3.20391	−	3.20391i	0.180807	−	0.180807i
$315$	28.4125	−	7.70391i	1.60086	−	0.434066i
$316$		−	14.9853i		−	0.842991i
$317$	2.30184	+	0.616776i	0.129284	+	0.0346416i	0.322881	−	0.946440i	$-0.395349\pi$
$317$	2.30184	+	0.616776i	0.129284	+	0.0346416i	−0.193597	+	0.981081i	$0.562015\pi$
$318$	12.0302	+	0.606238i	0.674617	+	0.0339961i
$319$	0.812163	+	3.03103i	0.0454724	+	0.169705i
$320$	3.55319	−	13.2607i	0.198629	−	0.741295i
$321$	−4.05379	+	12.5621i	−0.226260	+	0.701148i
$322$	23.5042	−	28.9637i	1.30984	−	1.61408i
$323$	2.34588	+	2.34588i	0.130528	+	0.130528i
$324$	−28.9477	−	25.6464i	−1.60821	−	1.42480i
$325$	26.2186	+	17.5852i	1.45435	+	0.975454i
$326$	−19.3118	−	11.1497i	−1.06958	−	0.617523i
$327$	−15.1572	+	23.4430i	−0.838195	+	1.29640i
$328$	−27.2368			−1.50390
$329$	−2.24944	+	0.860799i	−0.124016	+	0.0474574i
$330$	−37.5344	+	19.2198i	−2.06620	+	1.05802i
$331$	2.10669	−	7.86228i	0.115794	−	0.432150i	−0.883551	−	0.468335i	$-0.844854\pi$
$331$	2.10669	−	7.86228i	0.115794	−	0.432150i	0.999345	+	0.0361852i	$0.0115206\pi$
$332$	−11.3583	+	3.04344i	−0.623367	+	0.167031i
$333$	−5.88157	+	15.5080i	−0.322308	+	0.849833i
$334$	26.8048	+	46.4272i	1.46669	+	2.54038i
$335$	−12.0969			−0.660922
$336$	−8.33902	−	25.5804i	−0.454931	−	1.39553i
$337$			17.1778i			0.935733i	0.883799	+	0.467867i	$0.154977\pi$
$337$			17.1778i			0.935733i	−0.883799	+	0.467867i	$0.845023\pi$
$338$	−30.0952	−	12.5896i	−1.63696	−	0.684783i
$339$	−10.9710	−	12.1355i	−0.595865	−	0.659107i
$340$	−11.0467	+	2.95996i	−0.599093	+	0.160527i
$341$	9.23619	−	5.33252i	0.500168	−	0.288772i
$342$	28.2404	+	20.3449i	1.52706	+	1.10013i
$343$	−17.6316	+	5.66813i	−0.952015	+	0.306050i
$344$	19.7095	−	19.7095i	1.06266	−	1.06266i
$345$	−30.3080	−	19.5958i	−1.63173	−	1.05500i
$346$	8.17406	+	30.5060i	0.439440	+	1.64001i
$347$	8.99067	+	5.19077i	0.482645	+	0.278655i	0.721518	−	0.692396i	$-0.243445\pi$
$347$	8.99067	+	5.19077i	0.482645	+	0.278655i	−0.238873	+	0.971051i	$0.576778\pi$
$348$	1.87385	+	8.72951i	0.100449	+	0.467951i
$349$	−1.14175	+	1.14175i	−0.0611163	+	0.0611163i	−0.737004	−	0.675888i	$-0.763760\pi$
$349$	−1.14175	+	1.14175i	−0.0611163	+	0.0611163i	0.675888	+	0.737004i	$0.263760\pi$
$350$	9.15366	−	57.4077i	0.489284	−	3.06857i
$351$	10.0649	+	15.8018i	0.537226	+	0.843438i
$352$	4.19105	+	7.25911i	0.223384	+	0.386912i
$353$	2.65621	+	9.91309i	0.141376	+	0.527621i	0.999890	+	0.0148314i	$0.00472114\pi$
$353$	2.65621	+	9.91309i	0.141376	+	0.527621i	−0.858514	+	0.512789i	$0.828612\pi$
$354$	−28.4274	+	25.6997i	−1.51090	+	1.36593i
$355$	33.2854	−	19.2173i	1.76660	−	1.01995i
$356$	−32.2240	+	32.2240i	−1.70787	+	1.70787i
$357$	2.19795	−	2.44583i	0.116328	−	0.129447i
$358$	−7.10954	+	7.10954i	−0.375751	+	0.375751i
$359$	−7.24828	+	27.0510i	−0.382550	+	1.42769i	0.459444	+	0.888207i	$0.348049\pi$
$359$	−7.24828	+	27.0510i	−0.382550	+	1.42769i	−0.841993	+	0.539488i	$0.818618\pi$
$360$	−58.4894	+	26.3233i	−3.08266	+	1.38736i
$361$	−2.05710	−	1.18767i	−0.108268	−	0.0625087i
$362$	3.03670	−	11.3331i	0.159605	−	0.595655i
$363$	2.21130	−	6.85251i	0.116063	−	0.359664i
$364$	1.49500	+	40.9650i	0.0783595	+	2.14715i
$365$		−	22.0042i		−	1.15175i
$366$	38.8197	+	25.0991i	2.02914	+	1.31195i
$367$	5.92235	−	10.2578i	0.309144	−	0.535453i	−0.669031	−	0.743234i	$-0.733291\pi$
$367$	5.92235	−	10.2578i	0.309144	−	0.535453i	0.978175	+	0.207781i	$0.0666242\pi$
$368$	−16.4928	+	28.5664i	−0.859747	+	1.48913i
$369$	−8.96464	−	10.9799i	−0.466680	−	0.571590i
$370$	36.3847	+	36.3847i	1.89155	+	1.89155i
$371$	0.758851	+	7.29289i	0.0393976	+	0.378628i
$372$	27.0098	−	13.8306i	1.40039	−	0.717085i
$373$	−13.3628	−	23.1451i	−0.691902	−	1.19841i	−0.971214	−	0.238208i	$-0.923440\pi$
$373$	−13.3628	−	23.1451i	−0.691902	−	1.19841i	0.279313	−	0.960200i	$-0.409893\pi$
$374$	−2.35518	+	4.07929i	−0.121783	+	0.210935i
$375$	−24.0973	−	1.21434i	−1.24438	−	0.0627083i
$376$	4.54458	−	2.62382i	0.234369	−	0.135313i
$377$	0.290440	−	4.31539i	0.0149584	−	0.222254i
$378$	18.6448	−	29.0264i	0.958984	−	1.49296i
$379$	8.27837	+	8.27837i	0.425231	+	0.425231i	0.887000	−	0.461769i	$-0.152785\pi$
$379$	8.27837	+	8.27837i	0.425231	+	0.425231i	−0.461769	+	0.887000i	$0.652785\pi$
$380$	63.8135	−	36.8427i	3.27356	−	1.88999i
$381$	5.97030	+	6.60395i	0.305868	+	0.338331i
$382$	−36.8342	+	9.86971i	−1.88460	+	0.504978i
$383$	−4.88230	−	1.30821i	−0.249474	−	0.0668463i	0.131915	−	0.991261i	$-0.457887\pi$
$383$	−4.88230	−	1.30821i	−0.249474	−	0.0668463i	−0.381389	+	0.924415i	$0.624554\pi$
$384$	−12.3919	−	24.2002i	−0.632373	−	1.23496i
$385$	−15.0663	−	20.7824i	−0.767851	−	1.05917i
$386$			4.95882i			0.252397i
$387$	14.4325	+	1.45831i	0.733647	+	0.0741299i
$388$	−21.4197	−	79.9394i	−1.08742	−	4.05831i
$389$	6.23093	−	10.7923i	0.315921	−	0.547191i	−0.663712	−	0.747988i	$-0.731020\pi$
$389$	6.23093	−	10.7923i	0.315921	−	0.547191i	0.979633	+	0.200797i	$0.0643533\pi$
$390$	57.5195	−	8.35504i	2.91261	−	0.423074i
$391$	−4.03144			−0.203879
$392$	35.9915	−	18.2445i	1.81785	−	0.921484i
$393$	−5.34418	+	16.5609i	−0.269578	+	0.835385i
$394$	−44.9542	+	25.9543i	−2.26476	+	1.30756i
$395$	−3.34754	−	12.4932i	−0.168433	−	0.628601i
$396$	−11.9584	+	31.5309i	−0.600934	+	1.58449i
$397$	−32.1566	−	8.61633i	−1.61389	−	0.432441i	−0.664694	−	0.747116i	$-0.731438\pi$
$397$	−32.1566	−	8.61633i	−1.61389	−	0.432441i	−0.949200	+	0.314674i	$0.898105\pi$
$398$	13.0111	+	13.0111i	0.652185	+	0.652185i
$399$	−9.60031	+	18.8869i	−0.480616	+	0.945529i
$400$			51.4079i			2.57040i
$401$	−1.74637	+	6.51755i	−0.0872097	+	0.325471i	−0.995723	−	0.0923840i	$-0.970551\pi$
$401$	−1.74637	+	6.51755i	−0.0872097	+	0.325471i	0.908514	+	0.417855i	$0.137218\pi$
$402$	−10.5159	+	9.50691i	−0.524486	+	0.474161i
$403$	−14.4225	+	2.84256i	−0.718437	+	0.141598i
$404$	61.2160	−	35.3431i	3.04561	−	1.75838i
$405$	−29.8627	−	14.9147i	−1.48389	−	0.741118i
$406$	−7.43834	+	2.84644i	−0.369159	+	0.141267i
$407$	14.4622			0.716864
$408$	−3.89000	+	6.01651i	−0.192584	+	0.297862i
$409$	21.3966	−	5.73320i	1.05799	−	0.283488i	0.312442	−	0.949937i	$-0.398853\pi$
$409$	21.3966	−	5.73320i	1.05799	−	0.283488i	0.745551	+	0.666449i	$0.232186\pi$
$410$	−42.4770	+	11.3817i	−2.09779	+	0.562101i
$411$	4.16201	−	6.43722i	0.205297	−	0.317525i
$412$	−8.25217			−0.406555
$413$	−18.1135	−	14.6993i	−0.891309	−	0.723303i
$414$	−41.7473	+	6.78421i	−2.05177	+	0.333426i
$415$	−8.78948	+	5.07461i	−0.431459	+	0.249103i
$416$	−2.23409	−	11.3353i	−0.109535	−	0.555757i
$417$	2.72626	−	2.46467i	0.133505	−	0.120695i
$418$	7.85492	−	29.3150i	0.384197	−	1.43384i
$419$		−	19.3975i		−	0.947628i	−0.880625	−	0.473814i	$-0.842877\pi$
$419$		−	19.3975i		−	0.947628i	0.880625	−	0.473814i	$-0.157123\pi$
$420$	−39.8375	−	61.2143i	−1.94387	−	2.98695i
$421$	18.5575	+	18.5575i	0.904435	+	0.904435i	0.995816	−	0.0913811i	$-0.0291281\pi$
$421$	18.5575	+	18.5575i	0.904435	+	0.904435i	−0.0913811	+	0.995816i	$0.529128\pi$
$422$	−30.3619	−	8.13544i	−1.47799	−	0.396027i
$423$	2.55353	+	0.968451i	0.124157	+	0.0470877i
$424$	−4.13473	−	15.4310i	−0.200800	−	0.749398i
$425$	−5.44122	+	3.14149i	−0.263938	+	0.152385i
$426$	13.8324	−	42.8647i	0.670184	−	2.07680i
$427$	−11.4720	+	25.6945i	−0.555167	+	1.24345i
$428$	32.7487			1.58297
$429$	9.77095	−	13.0919i	0.471746	−	0.632083i
$430$	22.5016	−	38.9740i	1.08512	−	1.87949i
$431$	−0.947166	−	3.53487i	−0.0456234	−	0.170269i	0.939355	−	0.342946i	$-0.111425\pi$
$431$	−0.947166	−	3.53487i	−0.0456234	−	0.170269i	−0.984978	+	0.172677i	$0.944758\pi$
$432$	−12.2404	+	27.9445i	−0.588917	+	1.34448i
$433$		−	12.2523i		−	0.588807i	−0.955681	−	0.294403i	$-0.904879\pi$
$433$		−	12.2523i		−	0.588807i	0.955681	−	0.294403i	$-0.0951209\pi$
$434$	15.8878	+	21.9155i	0.762638	+	1.05198i
$435$	3.51229	+	6.85915i	0.168401	+	0.328871i
$436$	66.8992	+	17.9256i	3.20389	+	0.858480i
$437$	25.0897	−	6.72277i	1.20020	−	0.321594i
$438$	−17.2930	−	19.1284i	−0.826293	−	0.913991i
$439$	−32.7391	+	18.9019i	−1.56255	+	0.902140i	−0.565555	+	0.824711i	$0.691338\pi$
$439$	−32.7391	+	18.9019i	−1.56255	+	0.902140i	−0.996998	+	0.0774293i	$0.975329\pi$
$440$	39.5466	+	39.5466i	1.88531	+	1.88531i
$441$	19.2010	+	8.50424i	0.914333	+	0.404964i
$442$	4.88877	−	4.27221i	0.232535	−	0.203208i
$443$	−23.7495	+	13.7118i	−1.12837	+	0.651467i	−0.943525	−	0.331300i	$-0.892513\pi$
$443$	−23.7495	+	13.7118i	−1.12837	+	0.651467i	−0.184849	+	0.982767i	$0.559179\pi$
$444$	41.0968	+	2.07100i	1.95037	+	0.0982852i
$445$	−19.6666	+	34.0635i	−0.932285	+	1.61476i
$446$	5.64125	+	9.77093i	0.267121	+	0.462667i
$447$	25.6118	−	13.1147i	1.21140	−	0.620306i
$448$	7.92889	−	5.74809i	0.374605	−	0.271572i
$449$	−21.3150	−	21.3150i	−1.00592	−	1.00592i	−0.999982	−	0.00593671i	$-0.998110\pi$
$449$	−21.3150	−	21.3150i	−1.00592	−	1.00592i	−0.00593671	−	0.999982i	$-0.501890\pi$
$450$	−51.0597	+	41.6881i	−2.40698	+	1.96520i
$451$	−6.17989	+	10.7039i	−0.290999	+	0.504026i
$452$	−20.2936	+	35.1496i	−0.954533	+	1.65330i
$453$	15.1850	+	9.81793i	0.713453	+	0.461287i
$454$		−	28.5023i		−	1.33768i
$455$	10.3975	+	33.8183i	0.487440	+	1.58543i
$456$	14.1764	−	43.9307i	0.663872	−	2.05724i
$457$	−4.17516	+	15.5819i	−0.195306	+	0.728890i	0.796882	+	0.604135i	$0.206481\pi$
$457$	−4.17516	+	15.5819i	−0.195306	+	0.728890i	−0.992188	+	0.124755i	$0.960185\pi$
$458$	−39.8268	−	22.9940i	−1.86098	−	1.07444i
$459$	−3.70576	+	0.412091i	−0.172970	+	0.0192347i
$460$	−23.1749	+	86.4898i	−1.08053	+	4.03261i
$461$	0.939708	−	0.939708i	0.0437665	−	0.0437665i	−0.684885	−	0.728651i	$-0.740147\pi$
$461$	0.939708	−	0.939708i	0.0437665	−	0.0437665i	0.728651	+	0.684885i	$0.240147\pi$
$462$	−29.4302	−	6.22574i	−1.36921	−	0.289648i
$463$	−28.7736	+	28.7736i	−1.33722	+	1.33722i	−0.438483	+	0.898740i	$0.644484\pi$
$463$	−28.7736	+	28.7736i	−1.33722	+	1.33722i	−0.898740	+	0.438483i	$0.855516\pi$
$464$	6.09943	−	3.52151i	0.283159	−	0.163482i
$465$	19.4284	−	17.5642i	0.900969	−	0.814520i
$466$	3.13023	+	11.6822i	0.145005	+	0.541167i
$467$	−13.7213	−	23.7659i	−0.634945	−	1.09976i	−0.986527	−	0.163600i	$-0.947689\pi$
$467$	−13.7213	−	23.7659i	−0.634945	−	1.09976i	0.351582	−	0.936157i	$-0.385644\pi$
$468$	29.6406	−	35.8037i	1.37014	−	1.65503i
$469$	−6.70061	−	5.43758i	−0.309405	−	0.251084i
$470$	5.99105	−	5.99105i	0.276347	−	0.276347i
$471$	−0.656369	−	3.05775i	−0.0302439	−	0.140894i
$472$	44.0160	+	25.4127i	2.02600	+	1.16971i
$473$	−3.27371	−	12.2177i	−0.150525	−	0.561769i
$474$	−12.7284	−	8.22963i	−0.584636	−	0.377999i
$475$	28.6248	−	28.6248i	1.31340	−	1.31340i
$476$	−7.44944	−	3.32599i	−0.341444	−	0.152446i
$477$	4.85978	−	6.74576i	0.222514	−	0.308867i
$478$	−38.9373	+	22.4805i	−1.78095	+	1.02823i
$479$	9.97919	−	2.67392i	0.455961	−	0.122174i	−0.0235263	−	0.999723i	$-0.507489\pi$
$479$	9.97919	−	2.67392i	0.455961	−	0.122174i	0.479487	+	0.877549i	$0.340823\pi$
$480$	13.8044	+	15.2696i	0.630083	+	0.696957i
$481$	−18.8646	−	6.44055i	−0.860151	−	0.293664i
$482$			31.5985i			1.43927i
$483$	−7.97961	−	24.4779i	−0.363085	−	1.11378i
$484$	−17.8641			−0.812005
$485$	−35.7150	−	61.8602i	−1.62174	−	2.80893i
$486$	−37.6814	+	10.5035i	−1.70926	+	0.476450i
$487$	21.6658	−	5.80535i	0.981773	−	0.263065i	0.267982	−	0.963424i	$-0.413643\pi$
$487$	21.6658	−	5.80535i	0.981773	−	0.263065i	0.713791	+	0.700359i	$0.246977\pi$
$488$	15.8680	−	59.2201i	0.718309	−	2.68077i
$489$	−13.6998	+	7.01513i	−0.619528	+	0.317235i
$490$	48.5064	−	43.4932i	2.19130	−	1.96482i
$491$	10.5715			0.477083			0.238542	−	0.971132i	$-0.423331\pi$
$491$	10.5715			0.477083			0.238542	+	0.971132i	$0.423331\pi$
$492$	−19.0940	+	29.5319i	−0.860824	+	1.33140i
$493$	0.745462	+	0.430392i	0.0335739	+	0.0193839i
$494$	−23.3011	+	34.7406i	−1.04836	+	1.56305i
$495$	−2.92606	+	28.9586i	−0.131517	+	1.30159i
$496$	−16.9262	−	16.9262i	−0.760008	−	0.760008i
$497$	27.0754	+	4.31718i	1.21450	+	0.193652i
$498$	−3.65265	+	11.3190i	−0.163679	+	0.507218i
$499$	2.11971	−	7.91086i	0.0948912	−	0.354139i	−0.902112	−	0.431502i	$-0.857984\pi$
$499$	2.11971	−	7.91086i	0.0948912	−	0.354139i	0.997003	+	0.0773638i	$0.0246503\pi$
$500$	15.4930	+	57.8208i	0.692869	+	2.58582i
$501$	36.9555	+	1.86231i	1.65105	+	0.0832017i
$502$	45.4969	+	12.1909i	2.03063	+	0.544105i
$503$		−	11.3010i		−	0.503885i	−0.967742	−	0.251943i	$-0.918931\pi$
$503$		−	11.3010i		−	0.503885i	0.967742	−	0.251943i	$-0.0810694\pi$
$504$	−44.2304	−	11.7104i	−1.97018	−	0.521622i
$505$	43.1402	−	43.1402i	1.91972	−	1.91972i
$506$	18.4397	+	31.9386i	0.819746	+	1.41984i
$507$	−18.5756	+	12.7258i	−0.824972	+	0.565174i
$508$	11.0435	−	19.1280i	0.489978	−	0.848666i
$509$	−10.5043	−	2.81462i	−0.465595	−	0.124756i	0.0183923	−	0.999831i	$-0.494145\pi$
$509$	−10.5043	−	2.81462i	−0.465595	−	0.124756i	−0.483987	+	0.875075i	$0.660812\pi$
$510$	−3.55246	+	11.0086i	−0.157306	+	0.487468i
$511$	9.89095	−	12.1884i	0.437550	−	0.539182i
$512$	−34.5607	+	34.5607i	−1.52738	+	1.52738i
$513$	22.3757	−	8.74433i	0.987910	−	0.386072i
$514$	7.64249	+	28.5222i	0.337096	+	1.25806i
$515$	−6.87979	+	1.84344i	−0.303160	+	0.0812315i
$516$	−7.55323	−	35.1874i	−0.332513	−	1.54904i
$517$		−	2.38132i		−	0.104730i
$518$	3.79889	+	36.5090i	0.166914	+	1.60411i
$519$	20.7453	+	6.69449i	0.910616	+	0.293855i
$520$	−33.9733	−	69.1965i	−1.48983	−	3.03447i
$521$	−30.7947	−	17.7793i	−1.34914	−	0.778926i	−0.361012	−	0.932561i	$-0.617569\pi$
$521$	−30.7947	−	17.7793i	−1.34914	−	0.778926i	−0.988128	+	0.153635i	$0.950902\pi$
$522$	8.44386	+	3.20242i	0.369578	+	0.140166i
$523$	9.50808	+	16.4685i	0.415759	+	0.720116i	0.995508	−	0.0946792i	$-0.0301825\pi$
$523$	9.50808	+	16.4685i	0.415759	+	0.720116i	−0.579748	+	0.814796i	$0.696849\pi$
$524$	43.1732			1.88603
$525$	−29.8444	−	26.8197i	−1.30252	−	1.17051i
$526$	−25.1580	−	25.1580i	−1.09694	−	1.09694i
$527$	0.757192	−	2.82588i	0.0329838	−	0.123097i
$528$	26.5678	+	1.33884i	1.15622	+	0.0582654i
$529$	−4.28196	+	7.41658i	−0.186172	+	0.322460i
$530$	−12.8966	−	22.3376i	−0.560193	−	0.970283i
$531$	4.24277	+	26.1083i	0.184121	+	1.13300i
$532$	51.9080	+	8.27674i	2.25050	+	0.358842i
$533$	12.8279	−	11.2101i	0.555639	−	0.485563i
$534$	9.67411	+	45.0676i	0.418640	+	1.95027i
$535$	27.3024	−	7.31566i	1.18039	−	0.316283i
$536$	16.2825	+	9.40071i	0.703297	+	0.406049i
$537$	1.45649	+	6.78520i	0.0628524	+	0.292803i
$538$	−4.64182	−	4.64182i	−0.200123	−	0.200123i
$539$	0.996339	−	18.2840i	0.0429154	−	0.787548i
$540$	−12.4618	+	81.8717i	−0.536270	+	3.52320i
$541$	14.0981	+	3.77756i	0.606123	+	0.162410i	0.548811	−	0.835946i	$-0.315081\pi$
$541$	14.0981	+	3.77756i	0.606123	+	0.162410i	0.0573115	+	0.998356i	$0.481747\pi$
$542$	51.5701	+	29.7740i	2.21513	+	1.27890i
$543$	−5.43090	−	6.00731i	−0.233062	−	0.257798i
$544$	2.22098	+	0.595109i	0.0952236	+	0.0255151i
$545$	59.7779			2.56060
$546$	35.6164	+	21.2273i	1.52424	+	0.908443i
$547$	−14.8115			−0.633294			−0.316647	−	0.948543i	$-0.602557\pi$
$547$	−14.8115			−0.633294			−0.316647	+	0.948543i	$0.602557\pi$
$548$	−18.3698	−	4.92219i	−0.784721	−	0.210265i
$549$	29.0960	−	13.0947i	1.24179	−	0.558869i
$550$	49.7761	+	28.7382i	2.12246	+	1.22540i
$551$	−5.35711	−	1.43543i	−0.228220	−	0.0611515i
$552$	25.5666	+	49.9291i	1.08819	+	2.12512i
$553$	3.76149	−	8.42487i	0.159955	−	0.358262i
$554$	−3.80089	−	3.80089i	−0.161484	−	0.161484i
$555$	34.7248	−	7.45394i	1.47399	−	0.316402i
$556$	−7.89644	−	4.55901i	−0.334884	−	0.193345i
$557$	−27.4039	+	7.34285i	−1.16114	+	0.311127i	−0.787421	−	0.616415i	$-0.788584\pi$
$557$	−27.4039	+	7.34285i	−1.16114	+	0.311127i	−0.373719	+	0.927542i	$0.621918\pi$
$558$	3.08559	−	30.5375i	0.130624	−	1.29275i
$559$	−1.17072	+	17.3947i	−0.0495163	+	0.735718i
$560$	−36.3037	+	44.7362i	−1.53411	+	1.89045i
$561$	1.48183	+	2.89386i	0.0625628	+	0.122179i
$562$	18.3521	+	31.7868i	0.774138	+	1.34085i
$563$	2.87990	−	4.98814i	0.121373	−	0.210225i	−0.798936	−	0.601416i	$-0.794603\pi$
$563$	2.87990	−	4.98814i	0.121373	−	0.210225i	0.920310	+	0.391191i	$0.127937\pi$
$564$	0.341007	−	6.76694i	0.0143590	−	0.284939i
$565$	−9.06671	+	33.8374i	−0.381440	+	1.42355i
$566$	0.676918	+	0.676918i	0.0284530	+	0.0284530i
$567$	−9.83710	−	21.6848i	−0.413119	−	0.910677i
$568$	−59.7366			−2.50649
$569$	13.6368	+	23.6197i	0.571686	+	0.990189i	0.996393	+	0.0848585i	$0.0270438\pi$
$569$	13.6368	+	23.6197i	0.571686	+	0.990189i	−0.424707	+	0.905331i	$0.639623\pi$
$570$	3.75107	−	74.4360i	0.157115	−	3.11778i
$571$	−19.1573	−	11.0605i	−0.801707	−	0.462866i	0.0423609	−	0.999102i	$-0.486512\pi$
$571$	−19.1573	−	11.0605i	−0.801707	−	0.462866i	−0.844068	+	0.536237i	$0.819845\pi$
$572$	−38.3556	−	13.0950i	−1.60373	−	0.547528i
$573$	−8.08321	+	25.0487i	−0.337681	+	1.04642i
$574$	−28.6446	−	12.7891i	−1.19560	−	0.533807i
$575$			49.1922i			2.05146i
$576$	−11.0482	−	1.11635i	−0.460344	−	0.0465145i
$577$	−25.4078	+	6.80800i	−1.05774	+	0.283421i	−0.745447	−	0.666565i	$-0.767764\pi$
$577$	−25.4078	+	6.80800i	−1.05774	+	0.283421i	−0.312294	+	0.949986i	$0.601097\pi$
$578$	−10.7068	−	39.9583i	−0.445344	−	1.66205i
$579$	2.87424	+	1.85835i	0.119449	+	0.0772306i
$580$	13.5189	−	13.5189i	0.561341	−	0.561341i
$581$	−7.14966	−	1.14001i	−0.296618	−	0.0472957i
$582$	−79.6632	−	25.7073i	−3.30215	−	1.06560i
$583$	−7.00245	−	1.87630i	−0.290012	−	0.0777084i
$584$	−17.0999	+	29.6178i	−0.707597	+	1.22559i
$585$	16.7131	−	36.4707i	0.691002	−	1.50788i
$586$	−16.9375	−	29.3366i	−0.699680	−	1.21188i
$587$	10.0075	−	10.0075i	0.413052	−	0.413052i	−0.469748	−	0.882801i	$-0.655655\pi$
$587$	10.0075	−	10.0075i	0.413052	−	0.413052i	0.882801	+	0.469748i	$0.155655\pi$
$588$	5.44955	−	51.8144i	0.224736	−	2.13679i
$589$			18.8496i			0.776683i
$590$	79.2644	+	21.2388i	3.26326	+	0.874389i
$591$	−1.80322	+	35.7831i	−0.0741747	+	1.47192i
$592$	−8.40121	−	31.3538i	−0.345288	−	1.28863i
$593$	3.76514	−	14.0517i	0.154616	−	0.577034i	−0.844522	−	0.535521i	$-0.820115\pi$
$593$	3.76514	−	14.0517i	0.154616	−	0.577034i	0.999138	−	0.0415135i	$-0.0132180\pi$
$594$	20.2148	+	27.4735i	0.829425	+	1.12725i
$595$	−6.95355	−	1.10874i	−0.285068	−	0.0454540i
$596$	−50.4789	−	50.4789i	−2.06770	−	2.06770i
$597$	12.4175	−	2.66551i	0.508214	−	0.109092i
$598$	−9.82951	−	49.8728i	−0.401959	−	2.03945i
$599$	−4.28171	−	2.47204i	−0.174946	−	0.101005i	0.409970	−	0.912099i	$-0.365539\pi$
$599$	−4.28171	−	2.47204i	−0.174946	−	0.101005i	−0.584916	+	0.811094i	$0.698872\pi$
$600$	73.4143	+	47.4664i	2.99713	+	1.93781i
$601$	−14.4246			−0.588392			−0.294196	−	0.955745i	$-0.595052\pi$
$601$	−14.4246			−0.588392			−0.294196	+	0.955745i	$0.595052\pi$
$602$	29.9829	−	11.4736i	1.22201	−	0.467629i
$603$	1.56950	+	9.65805i	0.0639148	+	0.393306i
$604$	11.6111	−	43.3333i	0.472450	−	1.76321i
$605$	−14.8932	+	3.99063i	−0.605496	+	0.162242i
$606$	3.59838	−	71.4061i	0.146174	−	2.90067i
$607$	−12.9626	−	22.4520i	−0.526138	−	0.911297i	−0.999536	−	0.0304489i	$-0.990306\pi$
$607$	−12.9626	−	22.4520i	−0.526138	−	0.911297i	0.473399	−	0.880848i	$-0.343027\pi$
$608$	−14.8147			−0.600814
$609$	−1.13771	+	5.37816i	−0.0461024	+	0.217934i
$610$		−	98.9873i		−	4.00788i
$611$	−1.06049	+	3.10622i	−0.0429029	+	0.125664i
$612$	3.79646	+	8.43560i	0.153463	+	0.340989i
$613$	−9.97821	+	2.67365i	−0.403016	+	0.107988i	−0.454632	−	0.890679i	$-0.650229\pi$
$613$	−9.97821	+	2.67365i	−0.403016	+	0.107988i	0.0516164	+	0.998667i	$0.483563\pi$
$614$	−69.2788	+	39.9982i	−2.79587	+	1.61419i
$615$	−9.32150	+	28.8860i	−0.375879	+	1.16480i
$616$	4.12902	+	39.6817i	0.166363	+	1.59882i
$617$	−21.0842	+	21.0842i	−0.848818	+	0.848818i	−0.989986	−	0.141168i	$-0.954914\pi$
$617$	−21.0842	+	21.0842i	−0.848818	+	0.848818i	0.141168	+	0.989986i	$0.454914\pi$
$618$	−4.53192	+	7.00933i	−0.182300	+	0.281957i
$619$	−3.41253	−	12.7357i	−0.137161	−	0.511893i	−0.999980	−	0.00637874i	$-0.997970\pi$
$619$	−3.41253	−	12.7357i	−0.137161	−	0.511893i	0.862818	−	0.505514i	$-0.168697\pi$
$620$	−56.2732	−	32.4893i	−2.25998	−	1.30480i
$621$	−11.7129	+	26.7401i	−0.470021	+	1.07304i
$622$	−20.2535	+	20.2535i	−0.812089	+	0.812089i
$623$	−26.2052	+	10.0280i	−1.04989	+	0.401763i
$624$	−34.0590	−	13.5780i	−1.36345	−	0.543556i
$625$	3.94317	+	6.82976i	0.157727	+	0.273191i
$626$	−13.5554	−	50.5896i	−0.541784	−	2.02197i
$627$	−14.0479	−	15.5389i	−0.561020	−	0.620564i
$628$	−6.71947	+	3.87949i	−0.268136	+	0.154808i
$629$	2.80522	−	2.80522i	0.111851	−	0.111851i
$630$	−73.8729	+	0.220086i	−2.94317	+	0.00876842i
$631$	12.2359	−	12.2359i	0.487104	−	0.487104i	−0.420287	−	0.907391i	$-0.638071\pi$
$631$	12.2359	−	12.2359i	0.487104	−	0.487104i	0.907391	+	0.420287i	$0.138071\pi$
$632$	−5.20288	+	19.4174i	−0.206959	+	0.772383i
$633$	−16.0938	+	14.5496i	−0.639672	+	0.578295i
$634$	−5.17886	−	2.99002i	−0.205679	−	0.118749i
$635$	4.93399	−	18.4139i	0.195799	−	0.730733i
$636$	−19.6300	−	6.33458i	−0.778379	−	0.251183i
$637$	−9.44218	+	23.4061i	−0.374113	+	0.927383i
$638$		−	7.87443i		−	0.311752i
$639$	−19.6616	−	24.0815i	−0.777799	−	0.952648i
$640$	−29.1097	+	50.4195i	−1.15066	+	1.99300i
$641$	−20.3458	+	35.2400i	−0.803612	+	1.39190i	0.113612	+	0.993525i	$0.463758\pi$
$641$	−20.3458	+	35.2400i	−0.803612	+	1.39190i	−0.917224	+	0.398372i	$0.869575\pi$
$642$	17.9849	−	27.8165i	0.709806	−	1.09783i
$643$	−17.8828	−	17.8828i	−0.705229	−	0.705229i	0.260299	−	0.965528i	$-0.416179\pi$
$643$	−17.8828	−	17.8828i	−0.705229	−	0.705229i	−0.965528	+	0.260299i	$0.916179\pi$
$644$	−51.7143	+	37.4906i	−2.03783	+	1.47734i
$645$	−14.1575	−	27.6482i	−0.557452	−	1.08865i
$646$	−4.16259	−	7.20981i	−0.163775	−	0.283666i
$647$	7.90638	−	13.6943i	0.310832	−	0.538377i	−0.667711	−	0.744421i	$-0.732726\pi$
$647$	7.90638	−	13.6943i	0.310832	−	0.538377i	0.978543	+	0.206044i	$0.0660591\pi$
$648$	28.6050	+	43.2822i	1.12371	+	1.70029i
$649$	19.9740	−	11.5320i	0.784049	−	0.452671i
$650$	−52.1301	−	59.6535i	−2.04471	−	2.33980i
$651$	18.6568	−	0.995908i	0.731217	−	0.0390327i
$652$	27.0014	+	27.0014i	1.05746	+	1.05746i
$653$	−43.4808	+	25.1036i	−1.70153	+	0.982381i	−0.757322	+	0.653041i	$0.773493\pi$
$653$	−43.4808	+	25.1036i	−1.70153	+	0.982381i	−0.944212	+	0.329340i	$0.893174\pi$
$654$	51.9655	−	46.9794i	2.03201	−	1.83704i
$655$	35.9933	−	9.64438i	1.40637	−	0.376837i
$656$	26.7958	+	7.17990i	1.04620	+	0.280328i
$657$	−17.5680	+	2.85491i	−0.685391	+	0.111381i
$658$	6.01152	−	0.625519i	0.234353	−	0.0243853i
$659$			41.1531i			1.60310i	0.597930	+	0.801548i	$0.295990\pi$
$659$			41.1531i			1.60310i	−0.597930	+	0.801548i	$0.704010\pi$
$660$	70.6027	−	15.1554i	2.74821	−	0.589923i
$661$	3.36505	+	12.5585i	0.130885	+	0.488470i	0.999981	−	0.00617374i	$-0.00196518\pi$
$661$	3.36505	+	12.5585i	0.130885	+	0.488470i	−0.869096	+	0.494644i	$0.835299\pi$
$662$	−10.2129	+	17.6892i	−0.396934	+	0.687509i
$663$	−0.644164	−	4.43469i	−0.0250172	−	0.172229i
$664$	15.7743			0.612162
$665$	45.1244	−	4.69535i	1.74985	−	0.182078i
$666$	24.3286	−	33.7700i	0.942713	−	1.30856i
$667$	5.83655	−	3.36973i	0.225992	−	0.130477i
$668$	−23.7600	−	88.6736i	−0.919303	−	3.43088i
$669$	7.77755	+	0.391936i	0.300698	+	0.0151531i
$670$	29.3217	+	7.85672i	1.13280	+	0.303532i
$671$	−19.6727	−	19.6727i	−0.759458	−	0.759458i
$672$	0.782725	+	14.6631i	0.0301943	+	0.565643i
$673$			50.2523i			1.93709i	0.248847	+	0.968543i	$0.419948\pi$
$673$			50.2523i			1.93709i	−0.248847	+	0.968543i	$0.580052\pi$
$674$	11.1567	−	41.6373i	0.429740	−	1.60381i
$675$	5.02839	+	45.2183i	0.193543	+	1.74045i
$676$	44.1997	+	34.1623i	1.69999	+	1.31394i
$677$	32.2713	−	18.6318i	1.24029	−	0.716080i	0.271134	−	0.962542i	$-0.412601\pi$
$677$	32.2713	−	18.6318i	1.24029	−	0.716080i	0.969152	+	0.246462i	$0.0792680\pi$
$678$	18.7110	+	36.5407i	0.718592	+	1.40334i
$679$	8.02339	−	50.3192i	0.307910	−	1.93107i
$680$	15.3416			0.588325
$681$	−16.5206	−	10.6814i	−0.633069	−	0.409314i
$682$	−25.8510	+	6.92677i	−0.989888	+	0.265240i
$683$	41.3864	−	11.0895i	1.58361	−	0.424326i	0.643567	−	0.765390i	$-0.277454\pi$
$683$	41.3864	−	11.0895i	1.58361	−	0.424326i	0.940040	+	0.341064i	$0.110787\pi$
$684$	−37.6944	−	46.1681i	−1.44128	−	1.76528i
$685$	−16.4144			−0.627162
$686$	46.4186	−	2.28759i	1.77227	−	0.0873406i
$687$	−28.2532	+	14.4673i	−1.07793	+	0.551962i
$688$	−24.5859	+	14.1947i	−0.937330	+	0.541168i
$689$	8.29846	+	5.56591i	0.316146	+	0.212044i
$690$	60.7367	+	67.1829i	2.31221	+	2.55761i
$691$	12.4091	−	46.3114i	0.472064	−	1.76177i	−0.160270	−	0.987073i	$-0.551237\pi$
$691$	12.4091	−	46.3114i	0.472064	−	1.76177i	0.632335	−	0.774695i	$-0.282097\pi$
$692$		−	54.0817i		−	2.05588i
$693$	−14.6378	+	14.7252i	−0.556043	+	0.559366i
$694$	−18.4212	−	18.4212i	−0.699261	−	0.699261i
$695$	−7.60165	−	2.03686i	−0.288347	−	0.0772624i
$696$	0.602801	−	11.9620i	0.0228491	−	0.453417i
$697$	0.877514	+	3.27493i	0.0332382	+	0.124047i
$698$	3.50903	−	2.02594i	0.132819	−	0.0766830i
$699$	7.94433	+	2.56363i	0.300482	+	0.0969656i
$700$	−40.5842	+	90.8992i	−1.53394	+	3.43567i
$701$	6.76669			0.255574			0.127787	−	0.991802i	$-0.459213\pi$
$701$	6.76669			0.255574			0.127787	+	0.991802i	$0.459213\pi$
$702$	−14.1334	−	44.8391i	−0.533431	−	1.69234i
$703$	−12.7804	+	22.1362i	−0.482021	+	0.834884i
$704$	2.50606	+	9.35274i	0.0944506	+	0.352495i
$705$	−1.22736	−	5.71774i	−0.0462249	−	0.215343i
$706$		−	25.7536i		−	0.969249i
$707$	43.2876	−	4.50423i	1.62800	−	0.169399i
$708$	58.4110	−	29.9099i	2.19522	−	1.12408i
$709$	44.6938	+	11.9757i	1.67851	+	0.449755i	0.967385	−	0.253311i	$-0.0815195\pi$
$709$	44.6938	+	11.9757i	1.67851	+	0.449755i	0.711125	+	0.703066i	$0.248186\pi$
$710$	−93.1620	+	24.9627i	−3.49631	+	0.936833i
$711$	−9.54016	+	4.29357i	−0.357784	+	0.161021i
$712$	52.9428	−	30.5665i	1.98412	−	1.14553i
$713$	−16.1967	−	16.1967i	−0.606570	−	0.606570i
$714$	−6.91614	+	4.50094i	−0.258830	+	0.168443i
$715$	−34.9021	−	2.34903i	−1.30527	−	0.0878487i
$716$	14.9106	−	8.60865i	0.557236	−	0.321720i
$717$	−1.56187	+	30.9937i	−0.0583291	+	1.15748i
$718$	35.1383	−	60.8614i	1.31135	−	2.27133i
$719$	17.7507	+	30.7452i	0.661990	+	1.14660i	0.980092	+	0.198544i	$0.0636214\pi$
$719$	17.7507	+	30.7452i	0.661990	+	1.14660i	−0.318101	+	0.948057i	$0.603045\pi$
$720$	64.4814	−	10.4786i	2.40308	−	0.390516i
$721$	−4.63943	−	2.07139i	−0.172782	−	0.0771426i
$722$	4.21484	+	4.21484i	0.156860	+	0.156860i
$723$	18.3152	+	11.8418i	0.681150	+	0.440401i
$724$	−10.0458	+	17.3998i	−0.373349	+	0.646659i
$725$	5.25171	−	9.09623i	0.195044	−	0.337826i
$726$	−9.81059	+	15.1737i	−0.364105	+	0.563147i
$727$			11.8237i			0.438518i	0.975667	+	0.219259i	$0.0703640\pi$
$727$			11.8237i			0.438518i	−0.975667	+	0.219259i	$0.929636\pi$
$728$	12.2858	−	53.5999i	0.455342	−	1.98654i
$729$	−8.03329	+	25.7772i	−0.297529	+	0.954713i
$730$	−14.2913	+	53.3360i	−0.528947	+	1.97406i
$731$	−3.00485	−	1.73485i	−0.111138	−	0.0641657i
$732$	−53.0863	−	58.7206i	−1.96213	−	2.17038i
$733$	1.34969	−	5.03711i	0.0498519	−	0.186050i	−0.936510	−	0.350641i	$-0.885964\pi$
$733$	1.34969	−	5.03711i	0.0498519	−	0.186050i	0.986362	+	0.164591i	$0.0526304\pi$
$734$	−21.0175	+	21.0175i	−0.775770	+	0.775770i
$735$	−7.03146	−	44.4148i	−0.259359	−	1.63827i
$736$	12.7296	−	12.7296i	0.469221	−	0.469221i
$737$	7.38884	−	4.26595i	0.272171	−	0.157138i
$738$	14.5982	+	32.4366i	0.537367	+	1.19401i
$739$	−4.85016	−	18.1010i	−0.178416	−	0.665858i	−0.995945	−	0.0899695i	$-0.971323\pi$
$739$	−4.85016	−	18.1010i	−0.178416	−	0.665858i	0.817529	−	0.575888i	$-0.195344\pi$
$740$	−44.0567	−	76.3085i	−1.61956	−	2.80516i
$741$	11.4042	+	26.5251i	0.418943	+	0.974425i
$742$	2.89723	−	18.1701i	0.106361	−	0.667047i
$743$	−34.5937	+	34.5937i	−1.26912	+	1.26912i	−0.322578	+	0.946543i	$0.604550\pi$
$743$	−34.5937	+	34.5937i	−1.26912	+	1.26912i	−0.946543	+	0.322578i	$0.895450\pi$
$744$	−39.8003	+	8.54343i	−1.45915	+	0.313217i
$745$	−53.3604	−	30.8077i	−1.95497	−	1.12871i
$746$	17.3579	+	64.7806i	0.635518	+	2.37178i
$747$	5.19191	+	6.35906i	0.189962	+	0.232666i
$748$	5.70358	−	5.70358i	0.208544	−	0.208544i
$749$	18.4116	+	8.22029i	0.672744	+	0.300363i
$750$	57.6210	+	18.5943i	2.10402	+	0.678967i
$751$	−7.42934	+	4.28933i	−0.271100	+	0.156520i	−0.629388	−	0.777092i	$-0.716694\pi$
$751$	−7.42934	+	4.28933i	−0.271100	+	0.156520i	0.358287	+	0.933611i	$0.383361\pi$
$752$	−5.16266	+	1.38333i	−0.188263	+	0.0504449i
$753$	24.1164	−	21.8024i	0.878852	−	0.794525i
$754$	−3.50678	+	10.2715i	−0.127709	+	0.374065i
$755$		−	38.7206i		−	1.40919i
$756$	−43.7044	+	39.7481i	−1.58951	+	1.44563i
$757$	40.1392			1.45889			0.729443	−	0.684042i	$-0.239779\pi$
$757$	40.1392			1.45889			0.729443	+	0.684042i	$0.239779\pi$
$758$	−14.6893	−	25.4427i	−0.533541	−	0.924120i
$759$	25.4227	+	1.28113i	0.922787	+	0.0465022i
$760$	−95.4788	+	25.5835i	−3.46338	+	0.928010i
$761$	−3.29654	+	12.3028i	−0.119499	+	0.445978i	−0.999584	−	0.0288391i	$-0.990819\pi$
$761$	−3.29654	+	12.3028i	−0.119499	+	0.445978i	0.880085	+	0.474817i	$0.157486\pi$
$762$	−10.1823	−	19.8850i	−0.368865	−	0.720357i
$763$	33.1117	+	26.8704i	1.19873	+	0.972773i
$764$	65.3005			2.36249
$765$	5.04950	+	6.18463i	0.182565	+	0.223606i
$766$	10.9846	+	6.34195i	0.396889	+	0.229144i
$767$	−31.1899	+	6.14727i	−1.12620	+	0.221965i
$768$	11.6281	+	54.1706i	0.419594	+	1.95471i
$769$	−13.5525	−	13.5525i	−0.488714	−	0.488714i	0.419186	−	0.907900i	$-0.362316\pi$
$769$	−13.5525	−	13.5525i	−0.488714	−	0.488714i	−0.907900	+	0.419186i	$0.862316\pi$
$770$	23.0215	+	60.1600i	0.829639	+	2.16801i
$771$	19.3962	+	6.25914i	0.698536	+	0.225417i
$772$	2.19777	−	8.20220i	0.0790996	−	0.295204i
$773$	6.54075	+	24.4104i	0.235254	+

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.42391 - 0.649484i) q^{2} +(-1.28483 + 1.16155i) q^{3} +(3.72144 + 2.14858i) q^{4} +(3.58252 + 0.959933i) q^{5} +(3.86873 - 1.98102i) q^{6} +(1.55291 + 2.14207i) q^{7} +(-4.07612 - 4.07612i) q^{8} +(0.301593 - 2.98480i) q^{9} +O(q^{10})\)	\(q+(-2.42391 - 0.649484i) q^{2} +(-1.28483 + 1.16155i) q^{3} +(3.72144 + 2.14858i) q^{4} +(3.58252 + 0.959933i) q^{5} +(3.86873 - 1.98102i) q^{6} +(1.55291 + 2.14207i) q^{7} +(-4.07612 - 4.07612i) q^{8} +(0.301593 - 2.98480i) q^{9} +(-8.06023 - 4.65358i) q^{10} +(-2.52674 + 0.677038i) q^{11} +(-7.27712 + 1.56209i) q^{12} +(3.59741 + 0.242118i) q^{13} +(-2.37286 - 6.20077i) q^{14} +(-5.71795 + 2.92793i) q^{15} +(2.93561 + 5.08463i) q^{16} +(-0.358785 + 0.621434i) q^{17} +(-2.66961 + 7.03900i) q^{18} +(1.19661 - 4.46581i) q^{19} +(11.2697 + 11.2697i) q^{20} +(-4.48336 - 0.948423i) q^{21} +6.56431 q^{22} +(2.80909 + 4.86549i) q^{23} +(9.97177 + 0.502509i) q^{24} +(7.58284 + 4.37795i) q^{25} +(-8.56254 - 2.92333i) q^{26} +(3.07951 + 4.18529i) q^{27} +(1.17665 + 11.3081i) q^{28} -1.19958i q^{29} +(15.7614 - 3.38331i) q^{30} +(-3.93812 + 1.05522i) q^{31} +(-0.829338 - 3.09513i) q^{32} +(2.46003 - 3.80482i) q^{33} +(1.27327 - 1.27327i) q^{34} +(3.50707 + 9.16470i) q^{35} +(7.53544 - 10.4598i) q^{36} +(-5.34024 - 1.43091i) q^{37} +(-5.80094 + 10.0475i) q^{38} +(-4.90331 + 3.86750i) q^{39} +(-10.6900 - 18.5156i) q^{40} +(3.34101 - 3.34101i) q^{41} +(10.2513 + 5.21076i) q^{42} +4.83534i q^{43} +(-10.8578 - 2.90934i) q^{44} +(3.94567 - 10.4036i) q^{45} +(-3.64892 - 13.6179i) q^{46} +(-0.235612 + 0.879316i) q^{47} +(-9.67784 - 3.12304i) q^{48} +(-2.17695 + 6.65288i) q^{49} +(-15.5367 - 15.5367i) q^{50} +(-0.260849 - 1.21519i) q^{51} +(12.8674 + 8.63035i) q^{52} +(2.40005 + 1.38567i) q^{53} +(-4.74616 - 12.1448i) q^{54} -9.70201 q^{55} +(2.40151 - 15.0612i) q^{56} +(3.64983 + 7.12775i) q^{57} +(-0.779109 + 2.90768i) q^{58} +(-8.51651 + 2.28199i) q^{59} +(-27.5699 - 1.38934i) q^{60} +(5.31781 + 9.21071i) q^{61} +10.2310 q^{62} +(6.86201 - 3.98909i) q^{63} -3.70150i q^{64} +(12.6554 + 4.32067i) q^{65} +(-8.43405 + 7.62479i) q^{66} +(-3.15045 + 0.844160i) q^{67} +(-2.67040 + 1.54176i) q^{68} +(-9.26073 - 2.98843i) q^{69} +(-2.54850 - 24.4922i) q^{70} +(7.32763 - 7.32763i) q^{71} +(-13.3958 + 10.9371i) q^{72} +(-1.53552 - 5.73065i) q^{73} +(12.0149 + 6.93680i) q^{74} +(-14.8279 + 3.18292i) q^{75} +(14.0483 - 14.0483i) q^{76} +(-5.37406 - 4.36109i) q^{77} +(14.3970 - 6.18984i) q^{78} +(-1.74363 - 3.02006i) q^{79} +(5.63598 + 21.0338i) q^{80} +(-8.81808 - 1.80039i) q^{81} +(-10.2682 + 5.92837i) q^{82} +(-1.93496 + 1.93496i) q^{83} +(-14.6468 - 13.1623i) q^{84} +(-1.88189 + 1.88189i) q^{85} +(3.14048 - 11.7204i) q^{86} +(1.39338 + 1.54126i) q^{87} +(13.0590 + 7.53962i) q^{88} +(-2.74480 + 10.2437i) q^{89} +(-16.3209 + 22.6547i) q^{90} +(5.06782 + 8.08191i) q^{91} +24.1422i q^{92} +(3.83414 - 5.93011i) q^{93} +(1.14220 - 1.97835i) q^{94} +(8.57375 - 14.8502i) q^{95} +(4.66072 + 3.01341i) q^{96} +(-13.6182 - 13.6182i) q^{97} +(9.59767 - 14.7121i) q^{98} +(1.25878 + 7.74601i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

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