LMFDB - Embedded newform 690.2.q.a.11.15

Newspace parameters

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.q (of order $22$, degree $10$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.15
Character	$\chi$	$=$	690.11
Dual form			690.2.q.a.251.15

$q$-expansion

$f(q)$	$=$	$q+(0.540641 + 0.841254i) q^{2} +(1.37259 - 1.05641i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(1.63079 + 0.583554i) q^{6} +(2.43170 - 2.10708i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(0.767988 - 2.90003i) q^{9} +O(q^{10})$	\(q+(0.540641 + 0.841254i) q^{2} +(1.37259 - 1.05641i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(1.63079 + 0.583554i) q^{6} +(2.43170 - 2.10708i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(0.767988 - 2.90003i) q^{9} +(-0.755750 - 0.654861i) q^{10} +(-1.55820 - 1.00139i) q^{11} +(0.390753 + 1.68740i) q^{12} +(2.29242 - 2.64559i) q^{13} +(3.08727 + 0.906504i) q^{14} +(-1.01936 + 1.40032i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-1.24449 - 2.72506i) q^{17} +(2.85487 - 0.921804i) q^{18} +(5.86887 + 2.68022i) q^{19} +(0.142315 - 0.989821i) q^{20} +(1.11178 - 5.46103i) q^{21} -1.85223i q^{22} +(-1.94424 + 4.38405i) q^{23} +(-1.20827 + 1.24100i) q^{24} +(0.841254 - 0.540641i) q^{25} +(3.46499 + 0.498190i) q^{26} +(-2.00950 - 4.79186i) q^{27} +(0.906504 + 3.08727i) q^{28} +(2.52496 - 1.15311i) q^{29} +(-1.72913 - 0.100470i) q^{30} +(0.0402751 + 0.280119i) q^{31} +(0.281733 - 0.959493i) q^{32} +(-3.19664 + 0.271600i) q^{33} +(1.61964 - 2.52022i) q^{34} +(-1.73957 + 2.70682i) q^{35} +(2.31893 + 1.90330i) q^{36} +(-0.359153 + 1.22316i) q^{37} +(0.918203 + 6.38624i) q^{38} +(0.351709 - 6.05304i) q^{39} +(0.909632 - 0.415415i) q^{40} +(3.28080 + 11.1734i) q^{41} +(5.19519 - 2.01717i) q^{42} +(-4.25540 - 0.611834i) q^{43} +(1.55820 - 1.00139i) q^{44} +(0.0801545 + 2.99893i) q^{45} +(-4.73924 + 0.734595i) q^{46} -5.38966i q^{47} +(-1.69724 - 0.345529i) q^{48} +(0.477179 - 3.31885i) q^{49} +(0.909632 + 0.415415i) q^{50} +(-4.58697 - 2.42569i) q^{51} +(1.45421 + 3.18428i) q^{52} +(4.11043 + 4.74369i) q^{53} +(2.94475 - 4.28117i) q^{54} +(1.77720 + 0.521834i) q^{55} +(-2.10708 + 2.43170i) q^{56} +(10.8869 - 2.52110i) q^{57} +(2.33515 + 1.50071i) q^{58} +(3.68683 + 3.19466i) q^{59} +(-0.850320 - 1.50896i) q^{60} +(-8.76249 + 1.25986i) q^{61} +(-0.213877 + 0.185326i) q^{62} +(-4.24309 - 8.67024i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-1.45421 + 3.18428i) q^{65} +(-1.95672 - 2.54235i) q^{66} +(-3.59050 - 5.58693i) q^{67} +2.99579 q^{68} +(1.96272 + 8.07141i) q^{69} -3.21761 q^{70} +(-2.11429 - 3.28990i) q^{71} +(-0.347453 + 2.97981i) q^{72} +(2.20194 - 4.82158i) q^{73} +(-1.22316 + 0.359153i) q^{74} +(0.583554 - 1.63079i) q^{75} +(-4.87603 + 4.22510i) q^{76} +(-5.89909 + 0.848161i) q^{77} +(5.28229 - 2.97665i) q^{78} +(4.05792 + 3.51621i) q^{79} +(0.841254 + 0.540641i) q^{80} +(-7.82039 - 4.45438i) q^{81} +(-7.62591 + 8.80077i) q^{82} +(-11.1958 - 3.28739i) q^{83} +(4.50568 + 3.27990i) q^{84} +(1.96182 + 2.26406i) q^{85} +(-1.78593 - 3.91065i) q^{86} +(2.24756 - 4.25014i) q^{87} +(1.68485 + 0.769445i) q^{88} +(0.253774 - 1.76504i) q^{89} +(-2.47952 + 1.68877i) q^{90} -11.2636i q^{91} +(-3.18021 - 3.58975i) q^{92} +(0.351203 + 0.341941i) q^{93} +(4.53407 - 2.91387i) q^{94} +(-6.38624 - 0.918203i) q^{95} +(-0.626917 - 1.61461i) q^{96} +(2.61240 + 8.89702i) q^{97} +(3.04998 - 1.39288i) q^{98} +(-4.10075 + 3.74976i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160q + 16q^{4} - 16q^{5} - 2q^{6} + 42q^{9} + O(q^{10}) $	$ 160q + 16q^{4} - 16q^{5} - 2q^{6} + 42q^{9} - 12q^{11} - 12q^{14} - 16q^{16} - 8q^{18} + 16q^{20} + 62q^{21} + 4q^{23} + 2q^{24} - 16q^{25} + 42q^{27} - 2q^{30} - 4q^{31} + 16q^{33} + 2q^{36} + 72q^{38} - 124q^{39} + 44q^{41} + 44q^{43} + 12q^{44} - 2q^{45} + 4q^{46} + 70q^{49} - 2q^{51} - 52q^{53} + 92q^{54} + 10q^{55} - 54q^{56} - 38q^{57} - 36q^{58} - 44q^{61} - 220q^{63} + 16q^{64} - 34q^{66} - 44q^{67} + 22q^{69} - 12q^{70} - 36q^{72} - 28q^{73} - 24q^{74} - 88q^{77} - 54q^{78} - 44q^{79} - 16q^{80} - 66q^{81} - 28q^{82} + 4q^{83} - 18q^{84} + 158q^{86} - 64q^{87} + 80q^{89} - 8q^{90} - 4q^{92} + 4q^{93} + 24q^{94} - 2q^{96} - 88q^{98} + 190q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{22}\right)$

Coefficient data

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

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

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

$2$	0.540641	+	0.841254i	0.382291	+	0.594856i
$2$	0.540641	+	0.841254i	0.382291	+	0.594856i
$3$	1.37259	−	1.05641i	0.792463	−	0.609920i
$3$	1.37259	−	1.05641i	0.792463	−	0.609920i
$4$	−0.415415	+	0.909632i	−0.207708	+	0.454816i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	1.63079	+	0.583554i	0.665766	+	0.238235i
$7$	2.43170	−	2.10708i	0.919098	−	0.796403i	−0.0603342	−	0.998178i	$-0.519217\pi$
$7$	2.43170	−	2.10708i	0.919098	−	0.796403i	0.979432	+	0.201776i	$0.0646712\pi$
$8$	−0.989821	+	0.142315i	−0.349955	+	0.0503159i
$9$	0.767988	−	2.90003i	0.255996	−	0.966678i
$10$	−0.755750	−	0.654861i	−0.238989	−	0.207085i
$11$	−1.55820	−	1.00139i	−0.469814	−	0.301931i	0.284229	−	0.958756i	$-0.408262\pi$
$11$	−1.55820	−	1.00139i	−0.469814	−	0.301931i	−0.754043	+	0.656825i	$0.771899\pi$
$12$	0.390753	+	1.68740i	0.112801	+	0.487110i
$13$	2.29242	−	2.64559i	0.635803	−	0.733755i	−0.342824	−	0.939400i	$-0.611384\pi$
$13$	2.29242	−	2.64559i	0.635803	−	0.733755i	0.978627	+	0.205644i	$0.0659290\pi$
$14$	3.08727	+	0.906504i	0.825107	+	0.242273i
$15$	−1.01936	+	1.40032i	−0.263198	+	0.361562i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−1.24449	−	2.72506i	−0.301834	−	0.660925i	0.696564	−	0.717494i	$-0.254711\pi$
$17$	−1.24449	−	2.72506i	−0.301834	−	0.660925i	−0.998399	+	0.0565694i	$0.981984\pi$
$18$	2.85487	−	0.921804i	0.672899	−	0.217271i
$19$	5.86887	+	2.68022i	1.34641	+	0.614885i	0.952577	−	0.304297i	$-0.0984215\pi$
$19$	5.86887	+	2.68022i	1.34641	+	0.614885i	0.393833	+	0.919182i	$0.371149\pi$
$20$	0.142315	−	0.989821i	0.0318226	−	0.221331i
$21$	1.11178	−	5.46103i	0.242610	−	1.19170i
$22$		−	1.85223i		−	0.394897i
$23$	−1.94424	+	4.38405i	−0.405403	+	0.914138i
$23$	−1.94424	+	4.38405i	−0.405403	+	0.914138i
$24$	−1.20827	+	1.24100i	−0.246638	+	0.253318i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	3.46499	+	0.498190i	0.679540	+	0.0977031i
$27$	−2.00950	−	4.79186i	−0.386728	−	0.922194i
$28$	0.906504	+	3.08727i	0.171313	+	0.583439i
$29$	2.52496	−	1.15311i	0.468873	−	0.214127i	−0.166945	−	0.985966i	$-0.553390\pi$
$29$	2.52496	−	1.15311i	0.468873	−	0.214127i	0.635818	+	0.771839i	$0.280663\pi$
$30$	−1.72913	−	0.100470i	−0.315695	−	0.0183433i
$31$	0.0402751	+	0.280119i	0.00723362	+	0.0503109i	0.993119	−	0.117113i	$-0.0373641\pi$
$31$	0.0402751	+	0.280119i	0.00723362	+	0.0503109i	−0.985885	+	0.167424i	$0.946455\pi$
$32$	0.281733	−	0.959493i	0.0498038	−	0.169616i
$33$	−3.19664	+	0.271600i	−0.556464	+	0.0472794i
$34$	1.61964	−	2.52022i	0.277767	−	0.432213i
$35$	−1.73957	+	2.70682i	−0.294041	+	0.457536i
$36$	2.31893	+	1.90330i	0.386488	+	0.317217i
$37$	−0.359153	+	1.22316i	−0.0590443	+	0.201087i	−0.983733	−	0.179638i	$-0.942507\pi$
$37$	−0.359153	+	1.22316i	−0.0590443	+	0.201087i	0.924688	+	0.380725i	$0.124325\pi$
$38$	0.918203	+	6.38624i	0.148952	+	1.03599i
$39$	0.351709	−	6.05304i	0.0563184	−	0.969263i
$40$	0.909632	−	0.415415i	0.143825	−	0.0656829i
$41$	3.28080	+	11.1734i	0.512375	+	1.74499i	0.655412	+	0.755272i	$0.272495\pi$
$41$	3.28080	+	11.1734i	0.512375	+	1.74499i	−0.143037	+	0.989717i	$0.545687\pi$
$42$	5.19519	−	2.01717i	0.801635	−	0.311256i
$43$	−4.25540	−	0.611834i	−0.648942	−	0.0933038i	−0.190020	−	0.981780i	$-0.560855\pi$
$43$	−4.25540	−	0.611834i	−0.648942	−	0.0933038i	−0.458922	+	0.888476i	$0.651764\pi$
$44$	1.55820	−	1.00139i	0.234907	−	0.150966i
$45$	0.0801545	+	2.99893i	0.0119487	+	0.447054i
$46$	−4.73924	+	0.734595i	−0.698762	+	0.108310i
$47$		−	5.38966i		−	0.786162i	−0.919504	−	0.393081i	$-0.871409\pi$
$47$		−	5.38966i		−	0.786162i	0.919504	−	0.393081i	$-0.128591\pi$
$48$	−1.69724	−	0.345529i	−0.244975	−	0.0498728i
$49$	0.477179	−	3.31885i	0.0681685	−	0.474122i
$50$	0.909632	+	0.415415i	0.128641	+	0.0587486i
$51$	−4.58697	−	2.42569i	−0.642304	−	0.339664i
$52$	1.45421	+	3.18428i	0.201663	+	0.441580i
$53$	4.11043	+	4.74369i	0.564611	+	0.651595i	0.964224	−	0.265088i	$-0.0854011\pi$
$53$	4.11043	+	4.74369i	0.564611	+	0.651595i	−0.399614	+	0.916684i	$0.630856\pi$
$54$	2.94475	−	4.28117i	0.400730	−	0.582594i
$55$	1.77720	+	0.521834i	0.239638	+	0.0703641i
$56$	−2.10708	+	2.43170i	−0.281571	+	0.324950i
$57$	10.8869	−	2.52110i	1.44201	−	0.333928i
$58$	2.33515	+	1.50071i	0.306621	+	0.197053i
$59$	3.68683	+	3.19466i	0.479985	+	0.415909i	0.860957	−	0.508677i	$-0.169865\pi$
$59$	3.68683	+	3.19466i	0.479985	+	0.415909i	−0.380972	+	0.924586i	$0.624411\pi$
$60$	−0.850320	−	1.50896i	−0.109776	−	0.194806i
$61$	−8.76249	+	1.25986i	−1.12192	+	0.161308i	−0.678215	−	0.734864i	$-0.737246\pi$
$61$	−8.76249	+	1.25986i	−1.12192	+	0.161308i	−0.443707	+	0.896172i	$0.646337\pi$
$62$	−0.213877	+	0.185326i	−0.0271624	+	0.0235364i
$63$	−4.24309	−	8.67024i	−0.534579	−	1.09235i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	−1.45421	+	3.18428i	−0.180373	+	0.394961i
$66$	−1.95672	−	2.54235i	−0.240856	−	0.312941i
$67$	−3.59050	−	5.58693i	−0.438650	−	0.682553i	0.549595	−	0.835431i	$-0.314782\pi$
$67$	−3.59050	−	5.58693i	−0.438650	−	0.682553i	−0.988245	+	0.152879i	$0.951146\pi$
$68$	2.99579			0.363292
$69$	1.96272	+	8.07141i	0.236284	+	0.971684i
$70$	−3.21761			−0.384577
$71$	−2.11429	−	3.28990i	−0.250920	−	0.390439i	0.692829	−	0.721102i	$-0.256364\pi$
$71$	−2.11429	−	3.28990i	−0.250920	−	0.390439i	−0.943749	+	0.330663i	$0.892728\pi$
$72$	−0.347453	+	2.97981i	−0.0409478	+	0.351174i
$73$	2.20194	−	4.82158i	0.257718	−	0.564323i	−0.735904	−	0.677086i	$-0.763243\pi$
$73$	2.20194	−	4.82158i	0.257718	−	0.564323i	0.993622	+	0.112763i	$0.0359700\pi$
$74$	−1.22316	+	0.359153i	−0.142190	+	0.0417506i
$75$	0.583554	−	1.63079i	0.0673830	−	0.188307i
$76$	−4.87603	+	4.22510i	−0.559319	+	0.484653i
$77$	−5.89909	+	0.848161i	−0.672264	+	0.0966569i
$78$	5.28229	−	2.97665i	0.598102	−	0.337039i
$79$	4.05792	+	3.51621i	0.456552	+	0.395604i	0.852549	−	0.522647i	$-0.175056\pi$
$79$	4.05792	+	3.51621i	0.456552	+	0.395604i	−0.395997	+	0.918252i	$0.629601\pi$
$80$	0.841254	+	0.540641i	0.0940550	+	0.0604455i
$81$	−7.82039	−	4.45438i	−0.868932	−	0.494931i
$82$	−7.62591	+	8.80077i	−0.842141	+	0.971883i
$83$	−11.1958	−	3.28739i	−1.22890	−	0.360838i	−0.398067	−	0.917356i	$-0.630319\pi$
$83$	−11.1958	−	3.28739i	−1.22890	−	0.360838i	−0.830835	+	0.556518i	$0.812137\pi$
$84$	4.50568	+	3.27990i	0.491610	+	0.357867i
$85$	1.96182	+	2.26406i	0.212790	+	0.245572i
$86$	−1.78593	−	3.91065i	−0.192582	−	0.421696i
$87$	2.24756	−	4.25014i	0.240964	−	0.455663i
$88$	1.68485	+	0.769445i	0.179606	+	0.0820231i
$89$	0.253774	−	1.76504i	0.0269000	−	0.187094i	−0.971941	−	0.235225i	$-0.924417\pi$
$89$	0.253774	−	1.76504i	0.0269000	−	0.187094i	0.998841	+	0.0481310i	$0.0153265\pi$
$90$	−2.47952	+	1.68877i	−0.261365	+	0.178012i
$91$		−	11.2636i		−	1.18075i
$92$	−3.18021	−	3.58975i	−0.331559	−	0.374257i
$93$	0.351203	+	0.341941i	0.0364180	+	0.0354576i
$94$	4.53407	−	2.91387i	0.467654	−	0.300543i
$95$	−6.38624	−	0.918203i	−0.655215	−	0.0942056i
$96$	−0.626917	−	1.61461i	−0.0639845	−	0.164791i
$97$	2.61240	+	8.89702i	0.265249	+	0.903355i	0.979155	+	0.203114i	$0.0651061\pi$
$97$	2.61240	+	8.89702i	0.265249	+	0.903355i	−0.713906	+	0.700241i	$0.753076\pi$
$98$	3.04998	−	1.39288i	0.308095	−	0.140702i
$99$	−4.10075	+	3.74976i	−0.412141	+	0.376866i
$100$	0.142315	+	0.989821i	0.0142315	+	0.0989821i
$101$	−2.65537	+	9.04335i	−0.264219	+	0.899847i	0.715355	+	0.698761i	$0.246265\pi$
$101$	−2.65537	+	9.04335i	−0.264219	+	0.899847i	−0.979574	+	0.201085i	$0.935553\pi$
$102$	−0.439283	−	5.17023i	−0.0434955	−	0.511929i
$103$	−8.93699	+	13.9062i	−0.880587	+	1.37022i	0.0478983	+	0.998852i	$0.484748\pi$
$103$	−8.93699	+	13.9062i	−0.880587	+	1.37022i	−0.928486	+	0.371368i	$0.878889\pi$
$104$	−1.89258	+	2.94491i	−0.185583	+	0.288772i
$105$	0.471810	+	5.55305i	0.0460439	+	0.541922i
$106$	−1.76838	+	6.02254i	−0.171760	+	0.584961i
$107$	1.25334	+	8.71717i	0.121165	+	0.842721i	0.956240	+	0.292584i	$0.0945152\pi$
$107$	1.25334	+	8.71717i	0.121165	+	0.842721i	−0.835075	+	0.550136i	$0.814576\pi$
$108$	5.19360	+	0.162706i	0.499755	+	0.0156564i
$109$	−7.90549	+	3.61032i	−0.757209	+	0.345806i	−0.756327	−	0.654194i	$-0.773008\pi$
$109$	−7.90549	+	3.61032i	−0.757209	+	0.345806i	−0.000882083		1.00000i	$0.500281\pi$
$110$	0.521834	+	1.77720i	0.0497549	+	0.169450i
$111$	0.799194	+	2.05831i	0.0758562	+	0.195366i
$112$	−3.18485	−	0.457913i	−0.300940	−	0.0432687i
$113$	4.90479	−	3.15212i	0.461404	−	0.296527i	−0.289212	−	0.957265i	$-0.593393\pi$
$113$	4.90479	−	3.15212i	0.461404	−	0.296527i	0.750616	+	0.660739i	$0.229757\pi$
$114$	8.00681	+	7.79567i	0.749907	+	0.730131i
$115$	0.630358	−	4.75422i	0.0587812	−	0.443334i
$116$			2.77580i			0.257727i
$117$	−5.91176	−	8.67988i	−0.546542	−	0.802455i
$118$	−0.694266	+	4.82873i	−0.0639124	+	0.444520i
$119$	−8.76818	−	4.00429i	−0.803777	−	0.367073i
$120$	0.809699	−	1.53114i	0.0739151	−	0.139773i
$121$	−3.14437	−	6.88522i	−0.285852	−	0.625929i
$122$	−5.79722	−	6.69035i	−0.524855	−	0.605716i
$123$	16.3069	+	11.8706i	1.47034	+	1.07033i
$124$	−0.271536	−	0.0797303i	−0.0243847	−	0.00715999i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	4.99988	−	8.25700i	0.445425	−	0.735592i
$127$	8.38053	+	5.38584i	0.743652	+	0.477916i	0.856792	−	0.515663i	$-0.172454\pi$
$127$	8.38053	+	5.38584i	0.743652	+	0.477916i	−0.113139	+	0.993579i	$0.536091\pi$
$128$	0.755750	+	0.654861i	0.0667995	+	0.0578821i
$129$	−6.48725	+	3.65566i	−0.571171	+	0.321863i
$130$	−3.46499	+	0.498190i	−0.303900	+	0.0436942i
$131$	−8.04636	+	6.97221i	−0.703014	+	0.609165i	−0.931224	−	0.364447i	$-0.881258\pi$
$131$	−8.04636	+	6.97221i	−0.703014	+	0.609165i	0.228210	+	0.973612i	$0.426713\pi$
$132$	1.08088	−	3.02059i	0.0940783	−	0.262909i
$133$	19.9188	−	5.84869i	1.72718	−	0.507145i
$134$	2.75885	−	6.04105i	0.238329	−	0.521867i
$135$	3.27812	+	4.03161i	0.282136	+	0.346986i
$136$	1.61964	+	2.52022i	0.138883	+	0.216107i
$137$	−5.12402			−0.437774			−0.218887	−	0.975750i	$-0.570243\pi$
$137$	−5.12402			−0.437774			−0.218887	+	0.975750i	$0.570243\pi$
$138$	−5.72898	+	6.01488i	−0.487683	+	0.512021i
$139$	21.7568			1.84539			0.922695	−	0.385532i	$-0.125982\pi$
$139$	21.7568			1.84539			0.922695	+	0.385532i	$0.125982\pi$
$140$	−1.73957	−	2.70682i	−0.147020	−	0.228768i
$141$	−5.69370	−	7.39777i	−0.479496	−	0.623005i
$142$	1.62457	−	3.55731i	0.136331	−	0.298523i
$143$	−6.22131	+	1.82674i	−0.520252	+	0.152760i
$144$	−2.69462	+	1.31871i	−0.224552	+	0.109893i
$145$	−2.09781	+	1.81776i	−0.174214	+	0.150957i
$146$	5.24663	−	0.754351i	0.434214	−	0.0624305i
$147$	−2.85111	−	5.05951i	−0.235155	−	0.417302i
$148$	−0.963429	−	0.834816i	−0.0791934	−	0.0686215i
$149$	−15.1470	−	9.73438i	−1.24089	−	0.797471i	−0.255339	−	0.966852i	$-0.582187\pi$
$149$	−15.1470	−	9.73438i	−1.24089	−	0.797471i	−0.985551	+	0.169380i	$0.945823\pi$
$150$	1.68740	−	0.390753i	0.137775	−	0.0319048i
$151$	−12.8464	+	14.8255i	−1.04542	+	1.20648i	−0.0674548	+	0.997722i	$0.521488\pi$
$151$	−12.8464	+	14.8255i	−1.04542	+	1.20648i	−0.977967	+	0.208759i	$0.933058\pi$
$152$	−6.19057	−	1.81771i	−0.502121	−	0.147436i
$153$	−8.85853	+	1.51626i	−0.716170	+	0.122582i
$154$	−3.90281	−	4.50408i	−0.314497	−	0.362949i
$155$	−0.117562	−	0.257426i	−0.00944284	−	0.0206769i
$156$	5.35994	+	2.83445i	0.429138	+	0.226938i
$157$	12.1514	+	5.54934i	0.969783	+	0.442885i	0.836364	−	0.548174i	$-0.184677\pi$
$157$	12.1514	+	5.54934i	0.969783	+	0.442885i	0.133419	+	0.991060i	$0.457404\pi$
$158$	−0.764145	+	5.31475i	−0.0607921	+	0.422818i
$159$	10.6532	+	2.16882i	0.844854	+	0.171998i
$160$			1.00000i			0.0790569i
$161$	4.50974	+	14.7574i	0.355417	+	1.16305i
$162$	−0.480755	−	8.98715i	−0.0377717	−	0.706097i
$163$	19.6150	−	12.6058i	1.53637	−	0.987363i	0.547795	−	0.836613i	$-0.315467\pi$
$163$	19.6150	−	12.6058i	1.53637	−	0.987363i	0.988572	−	0.150750i	$-0.0481689\pi$
$164$	−11.5266	−	1.65727i	−0.900073	−	0.129411i
$165$	2.99064	−	1.16120i	0.232821	−	0.0903990i
$166$	−3.28739	−	11.1958i	−0.255151	−	0.868965i
$167$	6.44543	−	2.94353i	0.498762	−	0.227777i	−0.150117	−	0.988668i	$-0.547965\pi$
$167$	6.44543	−	2.94353i	0.498762	−	0.227777i	0.648880	+	0.760891i	$0.275238\pi$
$168$	−0.323274	+	5.56367i	−0.0249411	+	0.429247i
$169$	0.106118	+	0.738066i	0.00816292	+	0.0567743i
$170$	−0.844010	+	2.87444i	−0.0647326	+	0.220459i
$171$	12.2800	−	14.9615i	0.939072	−	1.14414i
$172$	2.32430	−	3.61668i	0.177226	−	0.275769i
$173$	−5.60048	+	8.71452i	−0.425797	+	0.662552i	−0.986179	−	0.165681i	$-0.947018\pi$
$173$	−5.60048	+	8.71452i	−0.425797	+	0.662552i	0.560383	+	0.828234i	$0.310654\pi$
$174$	4.79057	−	0.407026i	0.363172	−	0.0308566i
$175$	0.906504	−	3.08727i	0.0685253	−	0.233376i
$176$	0.263600	+	1.83338i	0.0198696	+	0.138196i
$177$	8.43538	+	0.490133i	0.634042	+	0.0368406i
$178$	1.62204	−	0.740763i	0.121577	−	0.0555225i
$179$	−5.17490	−	17.6241i	−0.386790	−	1.31729i	−0.891117	−	0.453773i	$-0.850078\pi$
$179$	−5.17490	−	17.6241i	−0.386790	−	1.31729i	0.504327	−	0.863513i	$-0.331741\pi$
$180$	−2.76122	−	1.17289i	−0.205809	−	0.0874220i
$181$	−16.9589	−	2.43832i	−1.26055	−	0.181239i	−0.520539	−	0.853838i	$-0.674269\pi$
$181$	−16.9589	−	2.43832i	−1.26055	−	0.181239i	−0.740007	+	0.672599i	$0.765178\pi$
$182$	9.47556	−	6.08957i	0.702375	−	0.451389i
$183$	−10.6964	+	10.9861i	−0.790697	+	0.812113i
$184$	1.30054	−	4.61612i	0.0958770	−	0.340305i
$185$		−	1.27480i		−	0.0937252i
$186$	−0.0977847	+	0.480318i	−0.00716993	+	0.0352186i
$187$	−0.789689	+	5.49241i	−0.0577478	+	0.401645i
$188$	4.90261	+	2.23894i	0.357559	+	0.163292i
$189$	−14.9834	−	7.41820i	−1.08988	−	0.539595i
$190$	−2.68022	−	5.86887i	−0.194444	−	0.425772i
$191$	2.50095	+	2.88625i	0.180963	+	0.208842i	0.838982	−	0.544159i	$-0.183151\pi$
$191$	2.50095	+	2.88625i	0.180963	+	0.208842i	−0.658020	+	0.753001i	$0.728606\pi$
$192$	1.01936	−	1.40032i	0.0735661	−	0.101060i
$193$	−19.2116	−	5.64103i	−1.38288	−	0.406051i	−0.496110	−	0.868260i	$-0.665239\pi$
$193$	−19.2116	−	5.64103i	−1.38288	−	0.406051i	−0.886771	+	0.462209i	$0.847057\pi$
$194$	−6.07228	+	7.00778i	−0.435964	+	0.503129i
$195$	1.36788	+	5.90694i	0.0979557	+	0.423005i
$196$	2.82071	+	1.81276i	0.201479	+	0.129483i
$197$	16.1402	+	13.9856i	1.14994	+	0.996430i	0.999970	+	0.00774023i	$0.00246382\pi$
$197$	16.1402	+	13.9856i	1.14994	+	0.996430i	0.149972	+	0.988690i	$0.452082\pi$
$198$	−5.37153	−	1.42249i	−0.381738	−	0.101092i
$199$	−16.1046	+	2.31549i	−1.14162	+	0.164141i	−0.687079	−	0.726583i	$-0.741107\pi$
$199$	−16.1046	+	2.31549i	−1.14162	+	0.164141i	−0.454546	+	0.890723i	$0.650198\pi$
$200$	−0.755750	+	0.654861i	−0.0534396	+	0.0463056i
$201$	−10.8304	−	3.87550i	−0.763916	−	0.273357i
$202$	−9.04335	+	2.65537i	−0.636288	+	0.186831i
$203$	3.71025	−	8.12432i	0.260409	−	0.570215i
$204$	4.11198	−	3.16478i	0.287896	−	0.221579i
$205$	−6.29581	−	9.79647i	−0.439718	−	0.684215i
$206$	−16.5304			−1.15172
$207$	11.2207	+	9.00527i	0.779895	+	0.625910i
$208$	−3.50062			−0.242724
$209$	−6.46090	−	10.0533i	−0.446909	−	0.695405i
$210$	−4.41644	+	3.39912i	−0.304763	+	0.234561i
$211$	−3.07953	+	6.74322i	−0.212003	+	0.464222i	−0.985521	−	0.169552i	$-0.945768\pi$
$211$	−3.07953	+	6.74322i	−0.212003	+	0.464222i	0.773518	+	0.633774i	$0.218495\pi$
$212$	−6.02254	+	1.76838i	−0.413630	+	0.121453i
$213$	−6.37754	−	2.28211i	−0.436982	−	0.156368i
$214$	−6.65574	+	5.76723i	−0.454977	+	0.394240i
$215$	4.25540	−	0.611834i	0.290216	−	0.0417267i
$216$	2.67100	+	4.45710i	0.181738	+	0.303267i
$217$	0.688172	+	0.596304i	0.0467162	+	0.0404798i
$218$	−7.31123	−	4.69864i	−0.495179	−	0.318232i
$219$	−2.07122	−	8.94419i	−0.139960	−	0.604392i
$220$	−1.21295	+	1.39982i	−0.0817773	+	0.0943761i
$221$	−10.0623	−	2.95456i	−0.676864	−	0.198745i
$222$	−1.29948	+	1.78513i	−0.0872155	+	0.119810i
$223$	−7.65776	−	8.83752i	−0.512801	−	0.591804i	0.439012	−	0.898481i	$-0.355328\pi$
$223$	−7.65776	−	8.83752i	−0.512801	−	0.591804i	−0.951814	+	0.306677i	$0.900783\pi$
$224$	−1.33664	−	2.92684i	−0.0893081	−	0.195557i
$225$	−0.921804	−	2.85487i	−0.0614536	−	0.190325i
$226$	5.30346	+	2.42201i	0.352781	+	0.161110i
$227$	3.25752	−	22.6565i	0.216209	−	1.50377i	−0.535649	−	0.844441i	$-0.679933\pi$
$227$	3.25752	−	22.6565i	0.216209	−	1.50377i	0.751858	−	0.659326i	$-0.229158\pi$
$228$	−2.22932	+	10.9504i	−0.147641	+	0.725209i
$229$			10.8505i			0.717018i	0.933526	+	0.358509i	$0.116715\pi$
$229$			10.8505i			0.717018i	−0.933526	+	0.358509i	$0.883285\pi$
$230$	4.34031	−	2.04004i	0.286191	−	0.134516i
$231$	−7.20100	+	7.39604i	−0.473791	+	0.486624i
$232$	−2.33515	+	1.50071i	−0.153310	+	0.0985265i
$233$	−3.56986	−	0.513268i	−0.233869	−	0.0336253i	0.0243836	−	0.999703i	$-0.492238\pi$
$233$	−3.56986	−	0.513268i	−0.233869	−	0.0336253i	−0.258253	+	0.966077i	$0.583147\pi$
$234$	4.10584	−	9.66598i	0.268407	−	0.631885i
$235$	1.51844	+	5.17134i	0.0990522	+	0.337341i
$236$	−4.43753	+	2.02655i	−0.288859	+	0.131917i
$237$	9.28441	+	0.539465i	0.603087	+	0.0350420i
$238$	−1.37181	−	9.54114i	−0.0889212	−	0.618460i
$239$	1.15914	−	3.94767i	0.0749785	−	0.255353i	−0.913471	−	0.406904i	$-0.866608\pi$
$239$	1.15914	−	3.94767i	0.0749785	−	0.255353i	0.988450	+	0.151550i	$0.0484266\pi$
$240$	1.72583	−	0.146634i	0.111402	−	0.00946517i
$241$	−15.3411	+	23.8712i	−0.988208	+	1.53768i	−0.152650	+	0.988280i	$0.548781\pi$
$241$	−15.3411	+	23.8712i	−0.988208	+	1.53768i	−0.835558	+	0.549402i	$0.814856\pi$
$242$	4.09224	−	6.36765i	0.263059	−	0.409328i
$243$	−15.4398	+	2.14752i	−0.990465	+	0.137764i
$244$	2.49406	−	8.49400i	0.159666	−	0.543773i
$245$	0.477179	+	3.31885i	0.0304859	+	0.212034i
$246$	−1.16999	+	20.1359i	−0.0745956	+	1.28382i
$247$	20.5447	−	9.38244i	1.30723	−	0.596990i
$248$	−0.0797303	−	0.271536i	−0.00506288	−	0.0172426i
$249$	−18.8401	+	7.31518i	−1.19394	+	0.463581i
$250$	−0.989821	−	0.142315i	−0.0626018	−	0.00900078i
$251$	20.1980	−	12.9805i	1.27489	−	0.819321i	0.284640	−	0.958634i	$-0.408126\pi$
$251$	20.1980	−	12.9805i	1.27489	−	0.819321i	0.990248	+	0.139313i	$0.0444894\pi$
$252$	9.64937	−	0.257905i	0.607853	−	0.0162465i
$253$	7.41967	−	4.88426i	0.466471	−	0.307071i
$254$			9.96196i			0.625069i
$255$	5.08456	+	1.03513i	0.318407	+	0.0648225i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	23.1145	+	10.5561i	1.44185	+	0.658469i	0.974249	−	0.225474i	$-0.0723929\pi$
$257$	23.1145	+	10.5561i	1.44185	+	0.658469i	0.467596	+	0.883942i	$0.345120\pi$
$258$	−6.58261	−	3.48103i	−0.409815	−	0.216719i
$259$	1.70395	+	3.73113i	0.105878	+	0.231841i
$260$	−2.29242	−	2.64559i	−0.142170	−	0.164073i
$261$	−1.40492	−	8.20804i	−0.0869623	−	0.508065i
$262$	−10.2156	−	2.99957i	−0.631121	−	0.185314i
$263$	3.84446	−	4.43674i	0.237060	−	0.273581i	−0.624737	−	0.780835i	$-0.714794\pi$
$263$	3.84446	−	4.43674i	0.237060	−	0.273581i	0.861797	+	0.507254i	$0.169339\pi$
$264$	3.12545	−	0.723765i	0.192358	−	0.0445446i
$265$	−5.28038	−	3.39349i	−0.324371	−	0.208461i
$266$	15.6891	+	13.5947i	0.961963	+	0.833546i
$267$	−1.51628	−	2.69076i	−0.0927948	−	0.164672i
$268$	6.57360	−	0.945141i	0.401547	−	0.0577337i
$269$	6.79932	−	5.89164i	0.414562	−	0.359220i	−0.422467	−	0.906378i	$-0.638836\pi$
$269$	6.79932	−	5.89164i	0.414562	−	0.359220i	0.837029	+	0.547158i	$0.184290\pi$
$270$	−1.61932	+	4.93739i	−0.0985488	+	0.300480i
$271$	26.0003	−	7.63438i	1.57941	−	0.463756i	0.629685	−	0.776850i	$-0.283184\pi$
$271$	26.0003	−	7.63438i	1.57941	−	0.463756i	0.949722	+	0.313095i	$0.101366\pi$
$272$	−1.24449	+	2.72506i	−0.0754586	+	0.165231i
$273$	−11.8990	−	15.4603i	−0.720161	−	0.935699i
$274$	−2.77025	−	4.31060i	−0.167357	−	0.260413i
$275$	−1.85223			−0.111694
$276$	−8.15736	−	1.56763i	−0.491015	−	0.0943604i
$277$	16.3447			0.982055			0.491028	−	0.871144i	$-0.336621\pi$
$277$	16.3447			0.982055			0.491028	+	0.871144i	$0.336621\pi$
$278$	11.7626	+	18.3030i	0.705475	+	1.09774i
$279$	0.843286	+	0.0983293i	0.0504862	+	0.00588682i
$280$	1.33664	−	2.92684i	0.0798796	−	0.174912i
$281$	−17.2277	+	5.05852i	−1.02772	+	0.301766i	−0.751784	−	0.659410i	$-0.770806\pi$
$281$	−17.2277	+	5.05852i	−1.02772	+	0.301766i	−0.275937	+	0.961176i	$0.588988\pi$
$282$	3.14516	−	8.78938i	0.187291	−	0.523400i
$283$	11.2533	−	9.75107i	0.668941	−	0.579641i	−0.252766	−	0.967527i	$-0.581340\pi$
$283$	11.2533	−	9.75107i	0.668941	−	0.579641i	0.921707	+	0.387887i	$0.126795\pi$
$284$	3.87091	−	0.556552i	0.229696	−	0.0330253i
$285$	−9.73567	+	5.48619i	−0.576691	+	0.324974i
$286$	−4.90025	−	4.24609i	−0.289758	−	0.251077i
$287$	31.5212	+	20.2574i	1.86064	+	1.19576i
$288$	−2.56619	−	1.55391i	−0.151214	−	0.0915652i
$289$	5.25543	−	6.06509i	0.309143	−	0.356770i
$290$	−2.66336	−	0.782034i	−0.156398	−	0.0459226i
$291$	12.9847	+	9.45216i	0.761174	+	0.554095i
$292$	3.47114	+	4.00591i	0.203133	+	0.234428i
$293$	−3.17818	−	6.95924i	−0.185671	−	0.406563i	0.793791	−	0.608190i	$-0.208104\pi$
$293$	−3.17818	−	6.95924i	−0.185671	−	0.406563i	−0.979462	+	0.201627i	$0.935377\pi$
$294$	2.71491	−	5.13388i	0.158337	−	0.299414i
$295$	−4.43753	−	2.02655i	−0.258363	−	0.117990i
$296$	0.181423	−	1.26182i	0.0105450	−	0.0733420i
$297$	−1.66734	+	9.47895i	−0.0967486	+	0.550025i
$298$		−	18.0053i		−	1.04302i
$299$	7.14139	+	15.1938i	0.412997	+	0.878678i
$300$	1.24100	+	1.20827i	0.0716491	+	0.0697597i
$301$	−11.6371	+	7.47868i	−0.670749	+	0.431064i
$302$	−19.4173	−	2.79178i	−1.11734	−	0.160649i
$303$	5.90878	+	15.2179i	0.339450	+	0.874248i
$304$	−1.81771	−	6.19057i	−0.104253	−	0.355053i
$305$	8.05261	−	3.67750i	0.461091	−	0.210573i
$306$	−6.06484	−	6.63252i	−0.346704	−	0.379156i
$307$	−3.78724	−	26.3408i	−0.216149	−	1.50335i	−0.752071	−	0.659082i	$-0.770945\pi$
$307$	−3.78724	−	26.3408i	−0.216149	−	1.50335i	0.535922	−	0.844267i	$-0.319964\pi$
$308$	1.67906	−	5.71834i	0.0956731	−	0.325833i
$309$	2.42391	+	28.5286i	0.137891	+	1.62294i
$310$	0.153001	−	0.238075i	0.00868989	−	0.0135217i
$311$	2.31236	−	3.59810i	0.131122	−	0.204029i	−0.769484	−	0.638666i	$-0.779487\pi$
$311$	2.31236	−	3.59810i	0.131122	−	0.204029i	0.900606	+	0.434636i	$0.143123\pi$
$312$	0.513309	+	6.04149i	0.0290604	+	0.342032i
$313$	−1.71466	+	5.83958i	−0.0969181	+	0.330073i	−0.993652	−	0.112497i	$-0.964115\pi$
$313$	−1.71466	+	5.83958i	−0.0969181	+	0.330073i	0.896734	+	0.442570i	$0.145933\pi$
$314$	1.90112	+	13.2226i	0.107286	+	0.746192i
$315$	6.51391	+	7.12361i	0.367017	+	0.401370i
$316$	−4.88418	+	2.23053i	−0.274756	+	0.125477i
$317$	−2.97046	−	10.1165i	−0.166838	−	0.568196i	−0.999888	−	0.0149987i	$-0.995226\pi$
$317$	−2.97046	−	10.1165i	−0.166838	−	0.568196i	0.833050	−	0.553198i	$-0.186593\pi$
$318$	3.93503	+	10.1346i	0.220666	+	0.568320i
$319$	−5.08910	−	0.731701i	−0.284935	−	0.0409674i
$320$	−0.841254	+	0.540641i	−0.0470275	+	0.0302227i
$321$	10.9292	+	10.6410i	0.610011	+	0.593924i
$322$	−9.97657	+	11.7723i	−0.555972	+	0.656044i
$323$		−	19.3286i		−	1.07547i
$324$	7.30056	−	5.26326i	0.405586	−	0.292403i
$325$	0.498190	−	3.46499i	0.0276346	−	0.192203i
$326$	21.2094	+	9.68599i	1.17468	+	0.536457i
$327$	−7.03699	+	13.3069i	−0.389147	+	0.735875i
$328$	−4.83754	−	10.5927i	−0.267109	−	0.584887i
$329$	−11.3565	−	13.1061i	−0.626102	−	0.722560i
$330$	2.59372	+	1.88809i	0.142780	+	0.103936i
$331$	19.3628	+	5.68543i	1.06427	+	0.312499i	0.766571	−	0.642159i	$-0.221961\pi$
$331$	19.3628	+	5.68543i	1.06427	+	0.312499i	0.297703	+	0.954658i	$0.403779\pi$
$332$	7.64123	−	8.81845i	0.419367	−	0.483976i
$333$	3.27138	+	1.98093i	0.179271	+	0.108554i
$334$	5.96092	+	3.83085i	0.326167	+	0.209615i
$335$	5.01908	+	4.34906i	0.274222	+	0.237615i
$336$	−4.85523	+	2.73599i	−0.264875	+	0.149261i
$337$	6.56404	−	0.943767i	0.357566	−	0.0514102i	0.0388089	−	0.999247i	$-0.487644\pi$
$337$	6.56404	−	0.943767i	0.357566	−	0.0514102i	0.318757	+	0.947836i	$0.396735\pi$
$338$	−0.563529	+	0.488301i	−0.0306519	+	0.0265601i
$339$	3.40232	−	9.50804i	0.184789	−	0.516406i
$340$	−2.87444	+	0.844010i	−0.155888	+	0.0457729i
$341$	0.217753	−	0.476812i	0.0117920	−	0.0258208i
$342$	19.2255	+	2.24174i	1.03960	+	0.121219i
$343$	6.34424	+	9.87183i	0.342557	+	0.533028i
$344$	4.29916			0.231795
$345$	−4.15720	−	7.19150i	−0.223816	−	0.387177i
$346$	−10.3590			−0.556902
$347$	8.69112	+	13.5237i	0.466564	+	0.725988i	0.992191	−	0.124727i	$-0.0398056\pi$
$347$	8.69112	+	13.5237i	0.466564	+	0.725988i	−0.525627	+	0.850715i	$0.676169\pi$
$348$	2.93239	+	3.81003i	0.157193	+	0.204239i
$349$	−10.3720	+	22.7116i	−0.555202	+	1.21572i	0.399107	+	0.916904i	$0.369320\pi$
$349$	−10.3720	+	22.7116i	−0.555202	+	1.21572i	−0.954310	+	0.298820i	$0.903407\pi$
$350$	3.08727	−	0.906504i	0.165021	−	0.0484547i
$351$	−17.2839	−	5.66863i	−0.922547	−	0.302569i
$352$	−1.39982	+	1.21295i	−0.0746108	+	0.0646507i
$353$	31.4976	−	4.52868i	1.67645	−	0.241037i	0.762536	−	0.646945i	$-0.223954\pi$
$353$	31.4976	−	4.52868i	1.67645	−	0.241037i	0.913914	+	0.405908i	$0.133045\pi$
$354$	4.14818	+	7.36128i	0.220473	+	0.391247i
$355$	2.95552	+	2.56097i	0.156863	+	0.135922i
$356$	1.50011	+	0.964064i	0.0795058	+	0.0510953i
$357$	−16.2653	+	3.76657i	−0.860849	+	0.199348i
$358$	12.0286	−	13.8817i	0.635729	−	0.733671i
$359$	30.1194	+	8.84385i	1.58964	+	0.466761i	0.952639	−	0.304102i	$-0.0983564\pi$
$359$	30.1194	+	8.84385i	1.58964	+	0.466761i	0.637001	+	0.770863i	$0.280175\pi$
$360$	−0.506131	−	2.95700i	−0.0266754	−	0.155847i
$361$	14.8177	+	17.1005i	0.779877	+	0.900026i
$362$	−7.11743	−	15.5850i	−0.374084	−	0.819130i
$363$	−11.5896	−	6.12881i	−0.608294	−	0.321679i
$364$	10.2457	+	4.67907i	0.537023	+	0.245250i
$365$	−0.754351	+	5.24663i	−0.0394845	+	0.274621i
$366$	−15.0249	−	3.05883i	−0.785366	−	0.159888i
$367$			1.34419i			0.0701661i	0.999384	+	0.0350831i	$0.0111696\pi$
$367$			1.34419i			0.0701661i	−0.999384	+	0.0350831i	$0.988830\pi$
$368$	4.58645	−	1.40158i	0.239085	−	0.0730625i
$369$	34.9228	−	0.933406i	1.81801	−	0.0485912i
$370$	1.07243	−	0.689209i	0.0557530	−	0.0358303i
$371$	19.9907	+	2.87423i	1.03786	+	0.149222i
$372$	−0.456935	+	0.177418i	−0.0236910	+	0.00919867i
$373$	−7.67790	−	26.1485i	−0.397547	−	1.35392i	−0.878738	−	0.477304i	$-0.841614\pi$
$373$	−7.67790	−	26.1485i	−0.397547	−	1.35392i	0.481191	−	0.876616i	$-0.340204\pi$
$374$	−5.04745	+	2.30509i	−0.260997	+	0.119193i
$375$	−0.100470	+	1.72913i	−0.00518827	+	0.0892921i
$376$	0.767028	+	5.33480i	0.0395565	+	0.275121i
$377$	2.73760	−	9.32342i	0.140994	−	0.480181i
$378$	−1.86002	−	16.6154i	−0.0956694	−	0.854603i
$379$	7.50693	−	11.6810i	0.385605	−	0.600014i	−0.593138	−	0.805100i	$-0.702111\pi$
$379$	7.50693	−	11.6810i	0.385605	−	0.600014i	0.978744	+	0.205087i	$0.0657477\pi$
$380$	3.48817	−	5.42770i	0.178939	−	0.278435i
$381$	17.1927	−	1.46076i	0.880808	−	0.0748370i
$382$	−1.07595	+	3.66436i	−0.0550506	+	0.187485i
$383$	4.19607	+	29.1843i	0.214409	+	1.49125i	0.758196	+	0.652027i	$0.226081\pi$
$383$	4.19607	+	29.1843i	0.214409	+	1.49125i	−0.543787	+	0.839223i	$0.683010\pi$
$384$	1.72913	+	0.100470i	0.0882395	+	0.00512711i
$385$	5.42118	−	2.47577i	0.276289	−	0.126177i
$386$	−5.64103	−	19.2116i	−0.287121	−	0.977845i
$387$	−5.04244	+	11.8709i	−0.256321	+	0.603433i
$388$	−9.17824	−	1.31963i	−0.465955	−	0.0669942i
$389$	3.94054	−	2.53243i	0.199793	−	0.128399i	−0.436919	−	0.899501i	$-0.643930\pi$
$389$	3.94054	−	2.53243i	0.199793	−	0.128399i	0.636712	+	0.771102i	$0.280294\pi$
$390$	−4.22970	+	4.34426i	−0.214179	+	0.219980i
$391$	14.3664	−	0.157741i	0.726541	−	0.00797733i
$392$			3.35298i			0.169351i
$393$	−3.67880	+	18.0702i	−0.185571	+	0.911523i
$394$	−3.03935	+	21.1392i	−0.153120	+	1.06498i
$395$	−4.88418	−	2.23053i	−0.245750	−	0.112230i
$396$	−1.70739	−	5.28788i	−0.0857998	−	0.265726i
$397$	1.61145	+	3.52859i	0.0808766	+	0.177095i	0.945750	−	0.324895i	$-0.105329\pi$
$397$	1.61145	+	3.52859i	0.0808766	+	0.177095i	−0.864874	+	0.501990i	$0.832602\pi$
$398$	−10.6547	−	12.2962i	−0.534073	−	0.616353i
$399$	21.1617	−	29.0703i	1.05941	−	1.45533i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	−21.6275	+	24.9594i	−1.08002	+	1.24642i	−0.112497	+	0.993652i	$0.535885\pi$
$401$	−21.6275	+	24.9594i	−1.08002	+	1.24642i	−0.967528	+	0.252763i	$0.918661\pi$
$402$	−2.59507	−	11.2063i	−0.129430	−	0.558922i
$403$	0.833409	+	0.535600i	0.0415151	+	0.0266801i
$404$	−7.12304	−	6.17215i	−0.354384	−	0.307076i
$405$	8.75855	+	2.07069i	0.435216	+	0.102894i
$406$	8.84052	−	1.27108i	0.438748	−	0.0630824i
$407$	1.78449	−	1.54627i	0.0884541	−	0.0766459i
$408$	4.88549	+	1.74820i	0.241868	+	0.0865490i
$409$	−3.62942	+	1.06569i	−0.179463	+	0.0526951i	−0.370229	−	0.928940i	$-0.620721\pi$
$409$	−3.62942	+	1.06569i	−0.179463	+	0.0526951i	0.190766	+	0.981635i	$0.438903\pi$
$410$	4.83754	−	10.5927i	0.238909	−	0.523138i
$411$	−7.03316	+	5.41307i	−0.346920	+	0.267007i
$412$	−8.93699	−	13.9062i	−0.440294	−	0.685110i
$413$	15.6967			0.772384
$414$	−1.50933	+	14.3081i	−0.0741794	+	0.703205i
$415$	11.6685			0.572784
$416$	−1.89258	−	2.94491i	−0.0927913	−	0.144386i
$417$	29.8631	−	22.9842i	1.46240	−	1.12554i
$418$	4.96439	−	10.8705i	0.242816	−	0.531694i
$419$	−20.5903	+	6.04585i	−1.00590	+	0.295359i	−0.742875	−	0.669430i	$-0.766539\pi$
$419$	−20.5903	+	6.04585i	−1.00590	+	0.295359i	−0.263025	+	0.964789i	$0.584720\pi$
$420$	−5.24723	−	1.87765i	−0.256038	−	0.0916198i
$421$	−17.3805	+	15.0603i	−0.847075	+	0.733995i	−0.965899	−	0.258921i	$-0.916633\pi$
$421$	−17.3805	+	15.0603i	−0.847075	+	0.733995i	0.118823	+	0.992915i	$0.462088\pi$
$422$	−7.33768	+	1.05500i	−0.357192	+	0.0513565i
$423$	−15.6302	−	4.13919i	−0.759966	−	0.201255i
$424$	−4.74369	−	4.11043i	−0.230374	−	0.199620i
$425$	−2.52022	−	1.61964i	−0.122248	−	0.0785643i
$426$	−1.52812	−	6.59893i	−0.0740378	−	0.319719i
$427$	−18.6532	+	21.5269i	−0.902690	+	1.04176i
$428$	−8.45007	−	2.48117i	−0.408450	−	0.119932i
$429$	−6.60950	+	9.07963i	−0.319110	+	0.438369i
$430$	2.81535	+	3.24909i	0.135768	+	0.156685i
$431$	−1.23148	−	2.69657i	−0.0593184	−	0.129889i	0.877651	−	0.479299i	$-0.159109\pi$
$431$	−1.23148	−	2.69657i	−0.0593184	−	0.129889i	−0.936970	+	0.349410i	$0.886382\pi$
$432$	−2.30550	+	4.65668i	−0.110924	+	0.224045i
$433$	−2.50438	−	1.14371i	−0.120353	−	0.0549634i	0.354328	−	0.935121i	$-0.384709\pi$
$433$	−2.50438	−	1.14371i	−0.120353	−	0.0549634i	−0.474682	+	0.880158i	$0.657437\pi$
$434$	−0.129589	+	0.901314i	−0.00622049	+	0.0432644i
$435$	−0.959120	+	4.71119i	−0.0459863	+	0.225884i
$436$		−	8.69087i		−	0.416217i
$437$	−23.1607	+	20.5184i	−1.10793	+	0.981529i
$438$	6.40454	−	6.57801i	0.306021	−	0.314310i
$439$	−16.1449	+	10.3757i	−0.770555	+	0.495205i	−0.865887	−	0.500240i	$-0.833245\pi$
$439$	−16.1449	+	10.3757i	−0.770555	+	0.495205i	0.0953320	+	0.995446i	$0.469609\pi$
$440$	−1.83338	−	0.263600i	−0.0874029	−	0.0125666i
$441$	−9.25832	−	3.93268i	−0.440872	−	0.187270i
$442$	−2.95456	−	10.0623i	−0.140534	−	0.478615i
$443$	−3.47705	+	1.58791i	−0.165199	+	0.0754441i	−0.496299	−	0.868152i	$-0.665308\pi$
$443$	−3.47705	+	1.58791i	−0.165199	+	0.0754441i	0.331099	+	0.943596i	$0.392581\pi$
$444$	−2.20430	−	0.128080i	−0.104611	−	0.00607839i
$445$	0.253774	+	1.76504i	0.0120300	+	0.0836708i
$446$	3.29450	−	11.2200i	0.155999	−	0.531284i
$447$	−31.0741	+	2.64018i	−1.46975	+	0.124876i
$448$	1.73957	−	2.70682i	0.0821869	−	0.127885i
$449$	15.1631	−	23.5942i	0.715589	−	1.11348i	−0.272879	−	0.962048i	$-0.587976\pi$
$449$	15.1631	−	23.5942i	0.715589	−	1.11348i	0.988468	−	0.151430i	$-0.0483879\pi$
$450$	1.90330	−	2.31893i	0.0897226	−	0.109315i
$451$	6.07680	−	20.6957i	0.286145	−	0.974522i
$452$	0.829744	+	5.77100i	0.0390279	+	0.271445i
$453$	−1.97092	+	33.9203i	−0.0926019	+	1.59372i
$454$	20.8210	−	9.50865i	0.977179	−	0.446263i
$455$	3.17333	+	10.8074i	0.148768	+	0.506657i
$456$	−10.4173	+	4.04482i	−0.487837	+	0.189416i
$457$	18.9753	+	2.72823i	0.887626	+	0.127621i	0.571021	−	0.820936i	$-0.306548\pi$
$457$	18.9753	+	2.72823i	0.887626	+	0.127621i	0.316606	+	0.948557i	$0.397457\pi$
$458$	−9.12798	+	5.86620i	−0.426523	+	0.274109i
$459$	−10.5573	+	11.4395i	−0.492773	+	0.533948i
$460$	4.06273	+	2.54837i	0.189426	+	0.118818i
$461$		−	20.8925i		−	0.973060i	−0.873664	−	0.486530i	$-0.838262\pi$
$461$		−	20.8925i		−	0.973060i	0.873664	−	0.486530i	$-0.161738\pi$
$462$	−10.1151	−	2.05927i	−0.470597	−	0.0958058i
$463$	−1.57042	+	10.9225i	−0.0729834	+	0.507611i	0.920237	+	0.391362i	$0.127996\pi$
$463$	−1.57042	+	10.9225i	−0.0729834	+	0.507611i	−0.993220	+	0.116249i	$0.962913\pi$
$464$	−2.52496	−	1.15311i	−0.117218	−	0.0535318i
$465$	−0.433312	−	0.229145i	−0.0200944	−	0.0106263i
$466$	−1.49822	−	3.28065i	−0.0694038	−	0.151973i
$467$	−11.0966	−	12.8062i	−0.513490	−	0.592599i	0.438499	−	0.898732i	$-0.355510\pi$
$467$	−11.0966	−	12.8062i	−0.513490	−	0.592599i	−0.951989	+	0.306133i	$0.900965\pi$
$468$	10.3513	−	1.77177i	0.478490	−	0.0819002i
$469$	−20.5032	−	6.02028i	−0.946749	−	0.277990i
$470$	−3.52948	+	4.07323i	−0.162803	+	0.187884i
$471$	22.5412	−	5.21989i	1.03864	−	0.240520i
$472$	−4.10396	−	2.63745i	−0.188900	−	0.121399i
$473$	6.01806	+	5.21468i	0.276711	+	0.239771i
$474$	4.56570	+	8.10220i	0.209710	+	0.372146i
$475$	6.38624	−	0.918203i	0.293021	−	0.0421300i
$476$	7.28486	−	6.31237i	0.333901	−	0.289327i
$477$	16.9136	−	8.27728i	0.774421	−	0.378991i
$478$	3.94767	−	1.15914i	0.180562	−	0.0530178i
$479$	3.00865	−	6.58802i	0.137469	−	0.301014i	−0.828360	−	0.560196i	$-0.810726\pi$
$479$	3.00865	−	6.58802i	0.137469	−	0.301014i	0.965828	+	0.259182i	$0.0834530\pi$
$480$	1.05641	+	1.37259i	0.0482184	+	0.0626497i
$481$	2.41266	+	3.75417i	0.110008	+	0.171175i
$482$	−28.3758			−1.29248
$483$	21.7799	+	15.4917i	0.991020	+	0.704895i
$484$	7.56924			0.344056
$485$	−5.01316	−	7.80063i	−0.227636	−	0.354208i
$486$	−10.1540	−	11.8278i	−0.460595	−	0.536518i
$487$	−14.1895	+	31.0706i	−0.642986	+	1.40794i	0.254576	+	0.967053i	$0.418064\pi$
$487$	−14.1895	+	31.0706i	−0.642986	+	1.40794i	−0.897562	+	0.440889i	$0.854663\pi$
$488$	8.49400	−	2.49406i	0.384506	−	0.112901i
$489$	13.6064	−	38.0241i	0.615302	−	1.71951i
$490$	−2.53402	+	2.19574i	−0.114475	+	0.0991933i
$491$	−30.4032	+	4.37133i	−1.37208	+	0.197275i	−0.788627	−	0.614872i	$-0.789208\pi$
$491$	−30.4032	+	4.37133i	−1.37208	+	0.197275i	−0.583452	+	0.812147i	$0.698299\pi$
$492$	−17.5720	+	9.90205i	−0.792205	+	0.446419i
$493$	−6.28459	−	5.44563i	−0.283044	−	0.245259i
$494$	19.0003	+	12.2108i	0.854864	+	0.549388i
$495$	2.87821	−	4.75319i	0.129366	−	0.213640i
$496$	0.185326	−	0.213877i	0.00832136	−	0.00960336i
$497$	−12.0734	−	3.54508i	−0.541567	−	0.159018i
$498$	−16.3396	−	11.8944i	−0.732197	−	0.533001i
$499$	−20.7977	−	24.0018i	−0.931034	−	1.07447i	−0.997058	−	0.0766519i	$-0.975577\pi$
$499$	−20.7977	−	24.0018i	−0.931034	−	1.07447i	0.0660244	−	0.997818i	$-0.478968\pi$
$500$	−0.415415	−	0.909632i	−0.0185779	−	0.0406800i
$501$	5.73733	−	10.8493i	0.256325	−	0.484710i
$502$	21.8398	+	9.97389i	0.974757	+	0.445156i
$503$	3.09338	−	21.5149i	0.137927	−	0.959302i	−0.796878	−	0.604140i	$-0.793517\pi$
$503$	3.09338	−	21.5149i	0.137927	−	0.959302i	0.934805	−	0.355162i	$-0.115574\pi$
$504$	5.43381	+	7.97813i	0.242041	+	0.355374i
$505$		−	9.42513i		−	0.419413i
$506$	8.12028	+	3.60119i	0.360991	+	0.160092i
$507$	0.925358	+	0.900956i	0.0410966	+	0.0400128i
$508$	−8.38053	+	5.38584i	−0.371826	+	0.238958i
$509$	−6.55957	−	0.943123i	−0.290748	−	0.0418032i	−0.00460223	−	0.999989i	$-0.501465\pi$
$509$	−6.55957	−	0.943123i	−0.290748	−	0.0418032i	−0.286145	+	0.958186i	$0.592374\pi$
$510$	1.87811	+	4.83703i	0.0831641	+	0.214188i
$511$	−4.80500	−	16.3643i	−0.212561	−	0.723915i
$512$	−0.909632	+	0.415415i	−0.0402004	+	0.0183589i
$513$	1.04976	−	33.5087i	0.0463482	−	1.47944i
$514$	3.61634	+	25.1522i	0.159510	+	1.10942i
$515$	4.65714	−	15.8608i	0.205218	−	0.698909i
$516$	−0.630402	−	7.41963i	−0.0277519	−	0.326631i
$517$	−5.39716	+	8.39815i	−0.237367	+	0.369350i
$518$	−2.21760	+	3.45066i	−0.0974358	+	0.151613i
$519$	1.51897	+	17.8778i	0.0666756	+	0.784750i
$520$	0.986239	−	3.35882i	0.0432494	−	0.147294i
$521$	−6.11680	−	42.5433i	−0.267982	−	1.86386i	−0.467543	−	0.883970i	$-0.654861\pi$
$521$	−6.11680	−	42.5433i	−0.267982	−	1.86386i	0.199561	−	0.979885i	$-0.436048\pi$
$522$	6.14548	−	5.61949i	0.268981	−	0.245958i
$523$	21.7057	−	9.91265i	0.949123	−	0.433450i	0.120161	−	0.992754i	$-0.461659\pi$
$523$	21.7057	−	9.91265i	0.949123	−	0.433450i	0.828962	+	0.559304i	$0.188932\pi$
$524$	−2.99957	−	10.2156i	−0.131037	−	0.446270i
$525$	−2.01717	−	5.19519i	−0.0880366	−	0.226737i
$526$	5.81090	+	0.835481i	0.253367	+	0.0364287i
$527$	0.713221	−	0.458359i	0.0310684	−	0.0199664i
$528$	2.29862	+	2.23800i	0.100034	+	0.0973965i
$529$	−15.4398	−	17.0473i	−0.671297	−	0.741189i
$530$		−	6.27680i		−	0.272647i
$531$	12.0961	−	8.23848i	0.524925	−	0.357520i
$532$	−2.95441	+	20.5484i	−0.128090	+	0.890886i
$533$	37.0812	+	16.9344i	1.60616	+	0.733511i
$534$	1.44385	−	2.73031i	0.0624813	−	0.118152i
$535$	−3.65848	−	8.01096i	−0.158170	−	0.346344i
$536$	4.34906	+	5.01908i	0.187851	+	0.216791i
$537$	−25.7213	−	18.7238i	−1.10996	−	0.807990i
$538$	8.63236	+	2.53469i	0.372167	+	0.109278i
$539$	−4.06701	+	4.69358i	−0.175179	+	0.202167i
$540$	−5.02907	+	1.30709i	−0.216417	+	0.0562483i
$541$	3.29222	+	2.11578i	0.141544	+	0.0909646i	0.609496	−	0.792789i	$-0.291372\pi$
$541$	3.29222	+	2.11578i	0.141544	+	0.0909646i	−0.467952	+	0.883754i	$0.655008\pi$
$542$	20.4793	+	17.7454i	0.879661	+	0.762230i
$543$	−25.8535	+	14.5688i	−1.10948	+	0.625207i
$544$	−2.96529	+	0.426345i	−0.127136	+	0.0182794i
$545$	6.56812	−	5.69131i	0.281347	−	0.243789i
$546$	6.57293	−	18.3686i	0.281295	−	0.786101i
$547$	28.3335	−	8.31947i	1.21145	−	0.355715i	0.387232	−	0.921982i	$-0.373431\pi$
$547$	28.3335	−	8.31947i	1.21145	−	0.355715i	0.824221	+	0.566268i	$0.191613\pi$
$548$	2.12859	−	4.66097i	0.0909290	−	0.199107i
$549$	−3.07587	+	26.3791i	−0.131275	+	1.12583i
$550$	−1.00139	−	1.55820i	−0.0426995	−	0.0664417i
$551$	17.9092			0.762959
$552$	−3.09143	−	7.70993i	−0.131580	−	0.328157i
$553$	17.2766			0.734676
$554$	8.83659	+	13.7500i	0.375431	+	0.584181i
$555$	−1.34671	−	1.74977i	−0.0571648	−	0.0742737i
$556$	−9.03811	+	19.7907i	−0.383301	+	0.839313i
$557$	−25.8082	+	7.57797i	−1.09353	+	0.321089i	−0.778278	−	0.627920i	$-0.783907\pi$
$557$	−25.8082	+	7.57797i	−1.09353	+	0.321089i	−0.315250	+	0.949009i	$0.602088\pi$
$558$	0.373195	+	0.762579i	0.0157986	+	0.0322825i
$559$	−11.3738	+	9.85547i	−0.481061	+	0.416842i
$560$	3.18485	−	0.457913i	0.134585	−	0.0193504i
$561$	4.71833	+	8.37305i	0.199208	+	0.353510i
$562$	−13.5695	−	11.7581i	−0.572396	−	0.495984i
$563$	−36.9815	−	23.7665i	−1.55858	−	1.00164i	−0.982937	−	0.183941i	$-0.941114\pi$
$563$	−36.9815	−	23.7665i	−1.55858	−	1.00164i	−0.575646	−	0.817699i	$-0.695249\pi$
$564$	9.09450	−	2.10602i	0.382947	−	0.0886796i
$565$	−3.81806	+	4.40628i	−0.160627	+	0.185373i
$566$	14.2871	+	4.19508i	0.600533	+	0.176332i
$567$	−28.4026	+	5.64647i	−1.19280	+	0.237129i
$568$	2.56097	+	2.95552i	0.107456	+	0.124011i
$569$	6.18389	+	13.5408i	0.259242	+	0.567661i	0.993838	−	0.110844i	$-0.0353554\pi$
$569$	6.18389	+	13.5408i	0.259242	+	0.567661i	−0.734596	+	0.678505i	$0.762628\pi$
$570$	−9.87878	−	5.22411i	−0.413776	−	0.218814i
$571$	26.9649	+	12.3145i	1.12845	+	0.515344i	0.890068	−	0.455828i	$-0.150657\pi$
$571$	26.9649	+	12.3145i	1.12845	+	0.515344i	0.238379	+	0.971172i	$0.423384\pi$
$572$	0.922764	−	6.41796i	0.0385827	−	0.268349i
$573$	6.48184	+	1.31960i	0.270783	+	0.0551269i
$574$			37.4693i			1.56394i
$575$	0.734595	+	4.73924i	0.0306347	+	0.197640i
$576$	−0.0801545	−	2.99893i	−0.00333977	−	0.124955i
$577$	−38.2047	+	24.5527i	−1.59048	+	1.02214i	−0.618890	+	0.785477i	$0.712418\pi$
$577$	−38.2047	+	24.5527i	−1.59048	+	1.02214i	−0.971592	+	0.236663i	$0.923946\pi$
$578$	7.94358	+	1.14211i	0.330409	+	0.0475057i
$579$	−32.3288	+	12.5526i	−1.34354	+	0.521666i
$580$	−0.782034	−	2.66336i	−0.0324722	−	0.110590i
$581$	−34.1518	+	15.5966i	−1.41685	+	0.647055i
$582$	−0.931624	+	16.0336i	−0.0386170	+	0.664615i
$583$	−1.65456	−	11.5077i	−0.0685250	−	0.476602i
$584$	−1.49335	+	5.08587i	−0.0617951	+	0.210455i
$585$	8.11769	+	6.66275i	0.335625	+	0.275471i
$586$	4.13623	−	6.43610i	0.170866	−	0.265873i
$587$	23.3269	−	36.2974i	0.962804	−	1.49815i	0.0985288	−	0.995134i	$-0.468586\pi$
$587$	23.3269	−	36.2974i	0.962804	−	1.49815i	0.864276	−	0.503019i	$-0.167777\pi$
$588$	5.78669	−	0.491661i	0.238639	−	0.0202757i
$589$	−0.514413	+	1.75193i	−0.0211960	+	0.0721870i
$590$	−0.694266	−	4.82873i	−0.0285825	−	0.198796i
$591$	36.9284	+	2.14570i	1.51903	+	0.0882623i
$592$	1.15960	−	0.529571i	0.0476592	−	0.0217652i
$593$	2.04630	+	6.96905i	0.0840313	+	0.286184i	0.990779	−	0.135490i	$-0.0432608\pi$
$593$	2.04630	+	6.96905i	0.0840313	+	0.286184i	−0.906747	+	0.421674i	$0.861443\pi$
$594$	−8.87563	+	3.72206i	−0.364172	+	0.152718i
$595$	9.54114	+	1.37181i	0.391149	+	0.0562387i
$596$	15.1470	−	9.73438i	0.620445	−	0.398736i
$597$	−19.6588	+	20.1913i	−0.804583	+	0.826375i
$598$	−8.92088	+	14.2221i	−0.364802	+	0.581585i
$599$		−	27.6259i		−	1.12876i	−0.825514	−	0.564381i	$-0.809115\pi$
$599$		−	27.6259i		−	1.12876i	0.825514	−	0.564381i	$-0.190885\pi$
$600$	−0.345529	+	1.69724i	−0.0141062	+	0.0692894i
$601$	−2.35312	+	16.3663i	−0.0959857	+	0.667595i	0.883847	+	0.467776i	$0.154945\pi$
$601$	−2.35312	+	16.3663i	−0.0959857	+	0.667595i	−0.979833	+	0.199819i	$0.935965\pi$
$602$	−12.5829	−	5.74643i	−0.512842	−	0.234207i
$603$	−18.9598	+	6.12188i	−0.772101	+	0.249302i
$604$	−8.14917	−	17.8442i	−0.331585	−	0.726070i
$605$	4.95680	+	5.72045i	0.201522	+	0.232569i
$606$	−9.60762	+	13.1982i	−0.390283	+	0.536141i
$607$	−22.4737	−	6.59887i	−0.912179	−	0.267840i	−0.208221	−	0.978082i	$-0.566767\pi$
$607$	−22.4737	−	6.59887i	−0.912179	−	0.267840i	−0.703958	+	0.710242i	$0.748585\pi$
$608$	4.22510	−	4.87603i	0.171351	−	0.197749i
$609$	−3.48998	−	15.0709i	−0.141421	−	0.610703i
$610$	7.44728	+	4.78608i	0.301532	+	0.193783i
$611$	−14.2588	−	12.3554i	−0.576851	−	0.499844i
$612$	2.30073	−	8.68788i	0.0930014	−	0.351187i
$613$	−18.4769	+	2.65657i	−0.746273	+	0.107298i	−0.504952	−	0.863147i	$-0.668490\pi$
$613$	−18.4769	+	2.65657i	−0.746273	+	0.107298i	−0.241321	+	0.970445i	$0.577581\pi$
$614$	20.1118	−	17.4269i	0.811645	−	0.703294i
$615$	−18.9907	−	6.79554i	−0.765777	−	0.274023i
$616$	5.71834	−	1.67906i	0.230398	−	0.0676511i
$617$	3.85720	−	8.44608i	0.155285	−	0.340026i	−0.815960	−	0.578108i	$-0.803791\pi$
$617$	3.85720	−	8.44608i	0.155285	−	0.340026i	0.971245	+	0.238081i	$0.0765185\pi$
$618$	−22.6893	+	17.4629i	−0.912699	+	0.702459i
$619$	−15.2782	−	23.7734i	−0.614084	−	0.955534i	−0.999463	−	0.0327750i	$-0.989566\pi$
$619$	−15.2782	−	23.7734i	−0.614084	−	0.955534i	0.385379	−	0.922759i	$-0.374071\pi$
$620$	0.283000			0.0113656
$621$	24.9147	+	0.506795i	0.999793	+	0.0203370i
$622$	4.27707			0.171495
$623$	−3.10198	−	4.82677i	−0.124278	−	0.193380i
$624$	−4.80491	+	3.69810i	−0.192350	+	0.148042i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−5.83958	+	1.71466i	−0.233397	+	0.0685315i
$627$	−19.4886	−	6.97373i	−0.778300	−	0.278504i
$628$	−10.0957	+	8.74798i	−0.402863	+	0.349082i
$629$	3.78016	−	0.543504i	0.150725	−	0.0216709i
$630$	−2.47108	+	9.33116i	−0.0984503	+	0.371762i
$631$	33.5801	+	29.0973i	1.33680	+	1.15834i	0.974018	+	0.226471i	$0.0727190\pi$
$631$	33.5801	+	29.0973i	1.33680	+	1.15834i	0.362783	+	0.931873i	$0.381826\pi$
$632$	−4.51703	−	2.90292i	−0.179678	−	0.115472i
$633$	2.89670	+	12.5089i	0.115134	+	0.497184i
$634$	6.90455	−	7.96827i	0.274215	−	0.316461i
$635$	−9.55843	−	2.80661i	−0.379315	−	0.111377i
$636$	−6.39833	+	8.78954i	−0.253710	+	0.348528i
$637$	−7.68644	−	8.87063i	−0.304548	−	0.351467i
$638$	−2.13583	−	4.67681i	−0.0845582	−	0.185157i
$639$	−11.1646	+	3.60491i	−0.441664	+	0.142608i
$640$	−0.909632	−	0.415415i	−0.0359564	−	0.0164207i
$641$	1.55617	−	10.8234i	0.0614648	−	0.427497i	−0.935734	−	0.352706i	$-0.885262\pi$
$641$	1.55617	−	10.8234i	0.0614648	−	0.427497i	0.997199	−	0.0747917i	$-0.0238292\pi$
$642$	−3.04301	+	14.9472i	−0.120098	+	0.589920i
$643$		−	36.3973i		−	1.43537i	−0.696369	−	0.717684i	$-0.745202\pi$
$643$		−	36.3973i		−	1.43537i	0.696369	−	0.717684i	$-0.254798\pi$
$644$	−15.2972	−	2.02824i	−0.602795	−	0.0799240i
$645$	5.19455	−	5.33525i	0.204535	−	0.210075i
$646$	16.2602	−	10.4498i	0.639750	−	0.411142i
$647$	6.01170	+	0.864351i	0.236344	+	0.0339812i	0.259469	−	0.965751i	$-0.416452\pi$
$647$	6.01170	+	0.864351i	0.236344	+	0.0339812i	−0.0231249	+	0.999733i	$0.507362\pi$
$648$	8.37471	+	3.29609i	0.328990	+	0.129483i
$649$	−2.54571	−	8.66988i	−0.0999277	−	0.340322i
$650$	3.18428	−	1.45421i	0.124898	−	0.0570388i
$651$	1.57452	+	0.0914865i	0.0617103	+	0.00358564i
$652$	3.31827	+	23.0791i	0.129954	+	0.903847i
$653$	−1.77051	+	6.02981i	−0.0692855	+	0.235965i	−0.986854	−	0.161612i	$-0.948331\pi$
$653$	−1.77051	+	6.02981i	−0.0692855	+	0.235965i	0.917569	+	0.397577i	$0.130149\pi$
$654$	−14.9990	+	1.27438i	−0.586507	+	0.0498320i
$655$	5.75613	−	8.95671i	0.224910	−	0.349968i
$656$	6.29581	−	9.79647i	0.245810	−	0.382488i
$657$	−12.2917	−	10.0886i	−0.479544	−	0.393594i
$658$	4.88575	−	16.6393i	0.190466	−	0.648669i
$659$	−5.50163	−	38.2647i	−0.214313	−	1.49058i	−0.758531	−	0.651636i	$-0.774083\pi$
$659$	−5.50163	−	38.2647i	−0.214313	−	1.49058i	0.544218	−	0.838944i	$-0.316826\pi$
$660$	−0.186094	+	3.20276i	−0.00724371	+	0.124667i
$661$	−29.9231	+	13.6654i	−1.16387	+	0.531524i	−0.901218	−	0.433366i	$-0.857326\pi$
$661$	−29.9231	+	13.6654i	−1.16387	+	0.531524i	−0.262657	+	0.964889i	$0.584599\pi$
$662$	5.68543	+	19.3628i	0.220970	+	0.752556i
$663$	−16.9326	+	6.57455i	−0.657609	+	0.255334i
$664$	11.5497	+	1.66060i	0.448216	+	0.0644437i
$665$	−17.4642	+	11.2235i	−0.677232	+	0.435230i
$666$	0.102181	+	3.82303i	0.00395943	+	0.148140i
$667$	0.146158	+	13.3115i	0.00565927	+	0.515422i
$668$			7.08575i			0.274156i
$669$	−19.8470	−	4.04052i	−0.767329	−	0.156216i
$670$	−0.945141	+	6.57360i	−0.0365140	+	0.253960i
$671$	14.9153	+	6.81159i	0.575798	+	0.262958i
$672$	−4.92660	−	2.60529i	−0.190048	−	0.100501i
$673$	−0.408509	−	0.894510i	−0.0157469	−	0.0344808i	0.901595	−	0.432581i	$-0.142397\pi$
$673$	−0.408509	−	0.894510i	−0.0157469	−	0.0344808i	−0.917342	+	0.398100i	$0.869670\pi$
$674$	4.34274	+	5.01178i	0.167276	+	0.193047i
$675$	−4.28117	−	2.94475i	−0.164782	−	0.113344i
$676$	−0.715452	−	0.210076i	−0.0275174	−	0.00807983i
$677$	−25.5626	+	29.5008i	−0.982451	+	1.13381i	0.00855155	+	0.999963i	$0.497278\pi$
$677$	−25.5626	+	29.5008i	−0.982451	+	1.13381i	−0.991002	+	0.133845i	$0.957268\pi$
$678$	9.83810	−	2.27822i	0.377830	−	0.0874946i
$679$	25.0993	+	16.1304i	0.963224	+	0.619027i
$680$	−2.26406	−	1.96182i	−0.0868229	−	0.0752325i
$681$	−19.4634	−	34.5393i	−0.745839	−	1.32355i
$682$	0.518846	−	0.0745988i	0.0198676	−	0.00285654i
$683$	11.9537	−	10.3580i	0.457396	−	0.396336i	−0.395459	−	0.918484i	$-0.629414\pi$
$683$	11.9537	−	10.3580i	0.457396	−	0.396336i	0.852855	+	0.522148i	$0.174869\pi$
$684$	8.50821	+	17.3855i	0.325320	+	0.664751i
$685$	4.91646	−	1.44360i	0.187848	−	0.0551572i
$686$	−4.87475	+	10.6742i	−0.186119	+	0.407544i
$687$	11.4625	+	14.8932i	0.437323	+	0.568211i
$688$	2.32430	+	3.61668i	0.0886131	+	0.137885i
$689$	21.9727			0.837092
$690$	3.80233	−	7.38528i	0.144752	−	0.281153i
$691$	−27.8791			−1.06057			−0.530285	−	0.847819i	$-0.677915\pi$
$691$	−27.8791			−1.06057			−0.530285	+	0.847819i	$0.677915\pi$
$692$	−5.60048	−	8.71452i	−0.212898	−	0.331276i
$693$	−2.07074	+	17.7589i	−0.0786608	+	0.674606i
$694$	−6.67804	+	14.6229i	−0.253495	+	0.555077i
$695$	−20.8755	+	6.12960i	−0.791853	+	0.232509i
$696$	−1.61983	+	4.52674i	−0.0613995	+	0.171586i
$697$	26.3652	−	22.8456i	0.998654	−	0.865339i
$698$	−24.7138	+	3.55330i	−0.935430	+	0.134494i
$699$	−5.44216	+	3.06674i	−0.205841	+	0.115995i
$700$	2.43170	+	2.10708i	0.0919098	+	0.0796403i
$701$	−1.53942	−	0.989324i	−0.0581430	−	0.0373663i	0.511246	−	0.859434i	$-0.329184\pi$
$701$	−1.53942	−	0.989324i	−0.0581430	−	0.0373663i	−0.569389	+	0.822068i	$0.692820\pi$
$702$	−4.57563	−	17.6049i	−0.172696	−	0.664452i
$703$	−5.38616	+	6.21596i	−0.203143	+	0.234440i
$704$	−1.77720	−	0.521834i	−0.0669809	−	0.0196674i
$705$	7.54726	+	5.49401i	0.284246	+	0.206916i
$706$	20.8387	+	24.0491i	0.784274	+	0.905100i
$707$	12.5980	+	27.5858i	0.473797	+	1.03747i
$708$	−3.95002	+	7.46948i	−0.148451	+	0.280720i
$709$	42.3102	+	19.3224i	1.58899	+	0.725669i	0.996786	−	0.0801156i	$-0.0255289\pi$
$709$	42.3102	+	19.3224i	1.58899	+	0.725669i	0.592208	+	0.805785i	$0.298256\pi$
$710$	−0.556552	+	3.87091i	−0.0208870	+	0.145273i
$711$	13.3136	−	9.06770i	0.499297	−	0.340065i
$712$			1.78319i			0.0668278i
$713$	−1.30636	−	0.368052i	−0.0489237	−	0.0137837i
$714$	−11.9623	−	11.6469i	−0.447678	−	0.435872i
$715$	5.45465	−	3.50549i	0.203993	−	0.131098i
$716$	18.1812	+	2.61406i	0.679462	+	0.0976919i
$717$	−2.57934	−	6.64305i	−0.0963274	−	0.248089i
$718$	8.84385	+	30.1194i	0.330050	+	1.12405i
$719$	−35.5667	+	16.2428i	−1.32642	+	0.605754i	−0.947523	−	0.319687i	$-0.896422\pi$
$719$	−35.5667	+	16.2428i	−1.32642	+	0.605754i	−0.378893	+	0.925441i	$0.623695\pi$
$720$	2.21395	−	2.02446i	0.0825090	−	0.0754471i
$721$	7.56946	+	52.6468i	0.281902	+	1.96067i
$722$	−6.37482	+	21.7106i	−0.237246	+	0.807986i
$723$	4.16085	+	48.9719i	0.154744	+	1.82128i
$724$	9.26297	−	14.4135i	0.344255	−	0.535672i
$725$	1.50071	−	2.33515i	0.0557350	−	0.0867254i
$726$	−1.10991	−	13.0632i	−0.0411925	−	0.484822i
$727$	2.64046	−	8.99258i	0.0979292	−	0.333516i	−0.895926	−	0.444203i	$-0.853487\pi$
$727$	2.64046	−	8.99258i	0.0979292	−	0.333516i	0.993855	+	0.110687i	$0.0353051\pi$
$728$	1.60298	+	11.1490i	0.0594104	+	0.413208i
$729$	−18.9238	+	19.2585i	−0.700883	+	0.713277i
$730$	−4.82158	+	2.20194i	−0.178455	+	0.0814975i
$731$	3.62853	+	12.3577i	0.134206	+	0.457064i
$732$	−5.54985	−	14.2935i	−0.205128	−	0.528304i
$733$	−44.7129	−	6.42874i	−1.65151	−	0.237451i	−0.747283	−	0.664506i	$-0.768642\pi$
$733$	−44.7129	−	6.42874i	−1.65151	−	0.237451i	−0.904226	+	0.427055i	$0.859551\pi$
$734$	−1.13080	+	0.726724i	−0.0417388	+	0.0268239i
$735$	4.16105	+	4.05132i	0.153483	+	0.149435i
$736$	3.65871	+	3.10062i	0.134862	+	0.114290i
$737$			12.3010i			0.453115i
$738$	19.6659	+	28.8743i	0.723913	+	1.06288i
$739$	−1.98415	+	13.8001i	−0.0729881	+	0.507644i	0.920230	+	0.391378i	$0.128002\pi$
$739$	−1.98415	+	13.8001i	−0.0729881	+	0.507644i	−0.993218	+	0.116266i	$0.962908\pi$
$740$	1.15960	+	0.529571i	0.0426277	+	0.0194674i
$741$	18.2876	−	34.5818i	0.671813	−	1.27040i
$742$	8.38983	+	18.3712i	0.308000	+	0.674426i
$743$	10.4268	+	12.0331i	0.382521	+	0.441453i	0.914059	−	0.405582i	$-0.132931\pi$
$743$	10.4268	+	12.0331i	0.382521	+	0.441453i	−0.531538	+	0.847035i	$0.678386\pi$
$744$	−0.396291	−	0.288479i	−0.0145287	−	0.0105762i
$745$	17.2759	+	5.07267i	0.632941	+	0.185848i
$746$	17.8466	−	20.5960i	0.653409	−	0.754074i
$747$	−18.1318	+	29.9436i	−0.663408	+	1.09558i
$748$	−4.66802	−	2.99996i	−0.170680	−	0.109689i
$749$	21.4156	+	18.5567i	0.782507	+	0.678046i
$750$	−1.50896	+	0.850320i	−0.0550994	+	0.0310493i
$751$	−10.6831	+	1.53599i	−0.389831	+	0.0560492i	−0.334444	−	0.942416i	$-0.608548\pi$
$751$	−10.6831	+	1.53599i	−0.389831	+	0.0560492i	−0.0553871	+	0.998465i	$0.517639\pi$
$752$	−4.07323	+	3.52948i	−0.148535	+	0.128707i
$753$	14.0108	−	39.1543i	0.510582	−	1.42686i
$754$	9.32342	−	2.73760i	0.339539	−	0.0996976i
$755$	8.14917	−	17.8442i	0.296579	−	0.649417i
$756$	12.9721	−	10.5477i	0.471792	−	0.383616i
$757$	−9.15386	−	14.2437i	−0.332703	−	0.517696i	0.634089	−	0.773260i	$-0.281375\pi$
$757$	−9.15386	−	14.2437i	−0.332703	−	0.517696i	−0.966792	+	0.255564i	$0.917739\pi$
$758$	13.8853			0.504335
$759$	5.02435	−	14.5423i	0.182372	−	0.527852i
$760$	6.45191			0.234036
$761$	−20.0180	−	31.1486i	−0.725651	−	1.12914i	−0.986501	−	0.163756i	$-0.947639\pi$
$761$	−20.0180	−	31.1486i	−0.725651	−	1.12914i	0.260849	−	0.965380i	$-0.415997\pi$
$762$	10.5239	+	13.6737i	0.381242	+	0.495344i
$763$	−11.6166	+	25.4368i	−0.420548	+	0.920872i
$764$	−3.66436	+	1.07595i	−0.132572	+	0.0389266i
$765$	8.07252	−	3.95058i	0.291863	−	0.142833i
$766$	−22.2829	+	19.3082i	−0.805112	+	0.697634i
$767$	16.9035	−	2.43036i	0.610351	−	0.0877553i
$768$	0.850320	+	1.50896i	0.0306833	+	0.0544499i
$769$	−11.3795	−	9.86042i	−0.410357	−	0.355576i	0.425087	−	0.905153i	$-0.360244\pi$
$769$	−11.3795	−	9.86042i	−0.410357	−	0.355576i	−0.835443	+	0.549577i	$0.814789\pi$
$770$	5.01366	+	3.22208i	0.180680	+	0.116116i
$771$	42.8782	−	9.92937i	1.54422	−	0.357597i
$772$	13.1121	−	15.1321i	0.471913	−	0.544617i
$773$	−36.8057	−	10.8071i	−1.32381	−	0.388706i	−0.457943	−	0.888981i	$-0.651414\pi$
$773$	−36.8057	−	10.8071i	−1.32381	−	0.388706i	−0.865866

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.q (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540641 + 0.841254i) q^{2} +(1.37259 - 1.05641i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(1.63079 + 0.583554i) q^{6} +(2.43170 - 2.10708i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(0.767988 - 2.90003i) q^{9} +O(q^{10})\)	\(q+(0.540641 + 0.841254i) q^{2} +(1.37259 - 1.05641i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(1.63079 + 0.583554i) q^{6} +(2.43170 - 2.10708i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(0.767988 - 2.90003i) q^{9} +(-0.755750 - 0.654861i) q^{10} +(-1.55820 - 1.00139i) q^{11} +(0.390753 + 1.68740i) q^{12} +(2.29242 - 2.64559i) q^{13} +(3.08727 + 0.906504i) q^{14} +(-1.01936 + 1.40032i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-1.24449 - 2.72506i) q^{17} +(2.85487 - 0.921804i) q^{18} +(5.86887 + 2.68022i) q^{19} +(0.142315 - 0.989821i) q^{20} +(1.11178 - 5.46103i) q^{21} -1.85223i q^{22} +(-1.94424 + 4.38405i) q^{23} +(-1.20827 + 1.24100i) q^{24} +(0.841254 - 0.540641i) q^{25} +(3.46499 + 0.498190i) q^{26} +(-2.00950 - 4.79186i) q^{27} +(0.906504 + 3.08727i) q^{28} +(2.52496 - 1.15311i) q^{29} +(-1.72913 - 0.100470i) q^{30} +(0.0402751 + 0.280119i) q^{31} +(0.281733 - 0.959493i) q^{32} +(-3.19664 + 0.271600i) q^{33} +(1.61964 - 2.52022i) q^{34} +(-1.73957 + 2.70682i) q^{35} +(2.31893 + 1.90330i) q^{36} +(-0.359153 + 1.22316i) q^{37} +(0.918203 + 6.38624i) q^{38} +(0.351709 - 6.05304i) q^{39} +(0.909632 - 0.415415i) q^{40} +(3.28080 + 11.1734i) q^{41} +(5.19519 - 2.01717i) q^{42} +(-4.25540 - 0.611834i) q^{43} +(1.55820 - 1.00139i) q^{44} +(0.0801545 + 2.99893i) q^{45} +(-4.73924 + 0.734595i) q^{46} -5.38966i q^{47} +(-1.69724 - 0.345529i) q^{48} +(0.477179 - 3.31885i) q^{49} +(0.909632 + 0.415415i) q^{50} +(-4.58697 - 2.42569i) q^{51} +(1.45421 + 3.18428i) q^{52} +(4.11043 + 4.74369i) q^{53} +(2.94475 - 4.28117i) q^{54} +(1.77720 + 0.521834i) q^{55} +(-2.10708 + 2.43170i) q^{56} +(10.8869 - 2.52110i) q^{57} +(2.33515 + 1.50071i) q^{58} +(3.68683 + 3.19466i) q^{59} +(-0.850320 - 1.50896i) q^{60} +(-8.76249 + 1.25986i) q^{61} +(-0.213877 + 0.185326i) q^{62} +(-4.24309 - 8.67024i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-1.45421 + 3.18428i) q^{65} +(-1.95672 - 2.54235i) q^{66} +(-3.59050 - 5.58693i) q^{67} +2.99579 q^{68} +(1.96272 + 8.07141i) q^{69} -3.21761 q^{70} +(-2.11429 - 3.28990i) q^{71} +(-0.347453 + 2.97981i) q^{72} +(2.20194 - 4.82158i) q^{73} +(-1.22316 + 0.359153i) q^{74} +(0.583554 - 1.63079i) q^{75} +(-4.87603 + 4.22510i) q^{76} +(-5.89909 + 0.848161i) q^{77} +(5.28229 - 2.97665i) q^{78} +(4.05792 + 3.51621i) q^{79} +(0.841254 + 0.540641i) q^{80} +(-7.82039 - 4.45438i) q^{81} +(-7.62591 + 8.80077i) q^{82} +(-11.1958 - 3.28739i) q^{83} +(4.50568 + 3.27990i) q^{84} +(1.96182 + 2.26406i) q^{85} +(-1.78593 - 3.91065i) q^{86} +(2.24756 - 4.25014i) q^{87} +(1.68485 + 0.769445i) q^{88} +(0.253774 - 1.76504i) q^{89} +(-2.47952 + 1.68877i) q^{90} -11.2636i q^{91} +(-3.18021 - 3.58975i) q^{92} +(0.351203 + 0.341941i) q^{93} +(4.53407 - 2.91387i) q^{94} +(-6.38624 - 0.918203i) q^{95} +(-0.626917 - 1.61461i) q^{96} +(2.61240 + 8.89702i) q^{97} +(3.04998 - 1.39288i) q^{98} +(-4.10075 + 3.74976i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160q + 16q^{4} - 16q^{5} - 2q^{6} + 42q^{9} + O(q^{10}) \)	\( 160q + 16q^{4} - 16q^{5} - 2q^{6} + 42q^{9} - 12q^{11} - 12q^{14} - 16q^{16} - 8q^{18} + 16q^{20} + 62q^{21} + 4q^{23} + 2q^{24} - 16q^{25} + 42q^{27} - 2q^{30} - 4q^{31} + 16q^{33} + 2q^{36} + 72q^{38} - 124q^{39} + 44q^{41} + 44q^{43} + 12q^{44} - 2q^{45} + 4q^{46} + 70q^{49} - 2q^{51} - 52q^{53} + 92q^{54} + 10q^{55} - 54q^{56} - 38q^{57} - 36q^{58} - 44q^{61} - 220q^{63} + 16q^{64} - 34q^{66} - 44q^{67} + 22q^{69} - 12q^{70} - 36q^{72} - 28q^{73} - 24q^{74} - 88q^{77} - 54q^{78} - 44q^{79} - 16q^{80} - 66q^{81} - 28q^{82} + 4q^{83} - 18q^{84} + 158q^{86} - 64q^{87} + 80q^{89} - 8q^{90} - 4q^{92} + 4q^{93} + 24q^{94} - 2q^{96} - 88q^{98} + 190q^{99} + O(q^{100}) \)

Introduction

L-functions

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