LMFDB - Embedded newform 930.2.br.b.11.12

Newspace parameters

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (of order $30$, degree $8$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	930.11
Dual form			930.2.br.b.761.12

$q$-expansion

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(-1.71718 - 0.226496i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.70312 + 0.315227i) q^{6} +(0.394896 + 3.75719i) q^{7} +(0.587785 - 0.809017i) q^{8} +(2.89740 + 0.777866i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(-1.71718 - 0.226496i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.70312 + 0.315227i) q^{6} +(0.394896 + 3.75719i) q^{7} +(0.587785 - 0.809017i) q^{8} +(2.89740 + 0.777866i) q^{9} +(0.669131 - 0.743145i) q^{10} +(-3.73016 - 1.66078i) q^{11} +(-1.52236 + 0.826093i) q^{12} +(1.26376 + 5.94554i) q^{13} +(1.53660 + 3.45127i) q^{14} +(-1.60037 + 0.662438i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-6.25944 + 2.78688i) q^{17} +(2.99596 - 0.155551i) q^{18} +(0.190708 + 0.0405362i) q^{19} +(0.406737 - 0.913545i) q^{20} +(0.172879 - 6.54120i) q^{21} +(-4.06080 - 0.426808i) q^{22} +(2.56858 + 1.86618i) q^{23} +(-1.19257 + 1.25610i) q^{24} +(0.500000 - 0.866025i) q^{25} +(3.03918 + 5.26402i) q^{26} +(-4.79917 - 1.99198i) q^{27} +(2.52790 + 2.80751i) q^{28} +(-0.716520 - 2.20522i) q^{29} +(-1.31734 + 1.12456i) q^{30} +(-5.12643 + 2.17250i) q^{31} -1.00000i q^{32} +(6.02920 + 3.69671i) q^{33} +(-5.09189 + 4.58476i) q^{34} +(2.22058 + 3.05637i) q^{35} +(2.80126 - 1.07374i) q^{36} +(9.35934 + 5.40362i) q^{37} +(0.193900 - 0.0203797i) q^{38} +(-0.823468 - 10.4958i) q^{39} +(0.104528 - 0.994522i) q^{40} +(8.44129 + 7.60057i) q^{41} +(-1.85693 - 6.27448i) q^{42} +(0.0402884 - 0.189542i) q^{43} +(-3.99395 + 0.848939i) q^{44} +(2.89815 - 0.775048i) q^{45} +(3.01955 + 0.981111i) q^{46} +(4.66582 + 1.51602i) q^{47} +(-0.746047 + 1.56314i) q^{48} +(-7.11349 + 1.51202i) q^{49} +(0.207912 - 0.978148i) q^{50} +(11.3798 - 3.36784i) q^{51} +(4.51710 + 4.06722i) q^{52} +(0.349345 - 3.32380i) q^{53} +(-5.17984 - 0.411464i) q^{54} +(-4.06080 + 0.426808i) q^{55} +(3.27174 + 1.88894i) q^{56} +(-0.318298 - 0.112802i) q^{57} +(-1.36290 - 1.87587i) q^{58} +(-8.33435 + 7.50428i) q^{59} +(-0.905353 + 1.47660i) q^{60} +7.43838i q^{61} +(-4.20418 + 3.65032i) q^{62} +(-1.77842 + 11.1933i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(4.06722 + 4.51710i) q^{65} +(6.87645 + 1.65266i) q^{66} +(-4.90224 - 8.49093i) q^{67} +(-3.42591 + 5.93384i) q^{68} +(-3.98803 - 3.78634i) q^{69} +(3.05637 + 2.22058i) q^{70} +(3.03894 + 0.319405i) q^{71} +(2.33236 - 1.88683i) q^{72} +(-2.09217 + 4.69909i) q^{73} +(10.5711 + 2.24695i) q^{74} +(-1.05474 + 1.37387i) q^{75} +(0.178112 - 0.0793007i) q^{76} +(4.76682 - 14.6708i) q^{77} +(-4.02654 - 9.72762i) q^{78} +(-2.51209 - 5.64224i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(7.78985 + 4.50758i) q^{81} +(10.3769 + 4.62007i) q^{82} +(8.97420 - 9.96686i) q^{83} +(-3.70496 - 5.39356i) q^{84} +(-4.02739 + 5.54323i) q^{85} +(-0.0202552 - 0.192715i) q^{86} +(0.730920 + 3.94905i) q^{87} +(-3.53613 + 2.04159i) q^{88} +(-4.69447 + 3.41073i) q^{89} +(2.51681 - 1.63269i) q^{90} +(-21.8394 + 7.09607i) q^{91} +3.17494 q^{92} +(9.29505 - 2.56946i) q^{93} +4.90593 q^{94} +(0.185426 - 0.0602485i) q^{95} +(-0.226496 + 1.71718i) q^{96} +(10.5103 - 7.63620i) q^{97} +(-6.29809 + 3.63620i) q^{98} +(-9.51591 - 7.71350i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176q + 44q^{4} + 4q^{7} + 4q^{9} + O(q^{10}) $	$ 176q + 44q^{4} + 4q^{7} + 4q^{9} + 22q^{10} + 38q^{13} - 44q^{16} + 4q^{18} + 8q^{19} - 42q^{21} + 4q^{22} + 88q^{25} + 30q^{27} + 36q^{28} + 32q^{31} - 70q^{33} + 14q^{34} - 4q^{36} + 42q^{37} + 58q^{39} - 22q^{40} - 12q^{42} - 46q^{43} + 16q^{45} + 10q^{46} + 38q^{49} + 38q^{51} + 2q^{52} + 4q^{55} + 78q^{57} - 40q^{58} + 16q^{63} + 44q^{64} + 34q^{66} - 76q^{67} + 148q^{69} - 8q^{70} - 4q^{72} - 52q^{73} + 12q^{76} + 60q^{78} + 8q^{79} - 108q^{81} - 40q^{82} - 8q^{84} + 28q^{87} + 6q^{88} + 24q^{90} - 20q^{91} - 28q^{93} - 20q^{94} - 112q^{97} - 132q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{23}{30}\right)$

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 $

$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$3$	−1.71718	−	0.226496i	−0.991413	−	0.130767i
$3$	−1.71718	−	0.226496i	−0.991413	−	0.130767i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	−1.70312	+	0.315227i	−0.695298	+	0.128691i
$7$	0.394896	+	3.75719i	0.149257	+	1.42008i	0.770986	+	0.636852i	$0.219764\pi$
$7$	0.394896	+	3.75719i	0.149257	+	1.42008i	−0.621730	+	0.783232i	$0.713570\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	2.89740	+	0.777866i	0.965800	+	0.259289i
$10$	0.669131	−	0.743145i	0.211598	−	0.235003i
$11$	−3.73016	−	1.66078i	−1.12469	−	0.500743i	−0.241799	−	0.970326i	$-0.577737\pi$
$11$	−3.73016	−	1.66078i	−1.12469	−	0.500743i	−0.882888	+	0.469584i	$0.844404\pi$
$12$	−1.52236	+	0.826093i	−0.439467	+	0.238473i
$13$	1.26376	+	5.94554i	0.350505	+	1.64900i	0.701538	+	0.712632i	$0.252497\pi$
$13$	1.26376	+	5.94554i	0.350505	+	1.64900i	−0.351033	+	0.936363i	$0.614170\pi$
$14$	1.53660	+	3.45127i	0.410675	+	0.922390i
$15$	−1.60037	+	0.662438i	−0.413213	+	0.171041i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−6.25944	+	2.78688i	−1.51814	+	0.675918i	−0.985383	−	0.170352i	$-0.945510\pi$
$17$	−6.25944	+	2.78688i	−1.51814	+	0.675918i	−0.532754	+	0.846270i	$0.678843\pi$
$18$	2.99596	−	0.155551i	0.706156	−	0.0366637i
$19$	0.190708	+	0.0405362i	0.0437513	+	0.00929964i	0.229735	−	0.973253i	$-0.426214\pi$
$19$	0.190708	+	0.0405362i	0.0437513	+	0.00929964i	−0.185984	+	0.982553i	$0.559547\pi$
$20$	0.406737	−	0.913545i	0.0909491	−	0.204275i
$21$	0.172879	−	6.54120i	0.0377253	−	1.42741i
$22$	−4.06080	−	0.426808i	−0.865766	−	0.0909957i
$23$	2.56858	+	1.86618i	0.535586	+	0.389126i	0.822443	−	0.568847i	$-0.192610\pi$
$23$	2.56858	+	1.86618i	0.535586	+	0.389126i	−0.286857	+	0.957973i	$0.592610\pi$
$24$	−1.19257	+	1.25610i	−0.243432	+	0.256399i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	3.03918	+	5.26402i	0.596033	+	1.03236i
$27$	−4.79917	−	1.99198i	−0.923600	−	0.383357i
$28$	2.52790	+	2.80751i	0.477728	+	0.530570i
$29$	−0.716520	−	2.20522i	−0.133054	−	0.409500i	0.862228	−	0.506521i	$-0.169069\pi$
$29$	−0.716520	−	2.20522i	−0.133054	−	0.409500i	−0.995282	+	0.0970211i	$0.969069\pi$
$30$	−1.31734	+	1.12456i	−0.240511	+	0.205315i
$31$	−5.12643	+	2.17250i	−0.920733	+	0.390193i
$31$	−5.12643	+	2.17250i	−0.920733	+	0.390193i
$32$		−	1.00000i		−	0.176777i
$33$	6.02920	+	3.69671i	1.04955	+	0.643515i
$34$	−5.09189	+	4.58476i	−0.873252	+	0.786279i
$35$	2.22058	+	3.05637i	0.375347	+	0.516621i
$36$	2.80126	−	1.07374i	0.466877	−	0.178957i
$37$	9.35934	+	5.40362i	1.53867	+	0.888349i	0.998917	+	0.0465234i	$0.0148142\pi$
$37$	9.35934	+	5.40362i	1.53867	+	0.888349i	0.539749	+	0.841826i	$0.318519\pi$
$38$	0.193900	−	0.0203797i	0.0314548	−	0.00330603i
$39$	−0.823468	−	10.4958i	−0.131860	−	1.68067i
$40$	0.104528	−	0.994522i	0.0165274	−	0.157248i
$41$	8.44129	+	7.60057i	1.31831	+	1.18701i	0.968165	+	0.250314i	$0.0805339\pi$
$41$	8.44129	+	7.60057i	1.31831	+	1.18701i	0.350144	+	0.936696i	$0.386133\pi$
$42$	−1.85693	−	6.27448i	−0.286530	−	0.968173i
$43$	0.0402884	−	0.189542i	0.00614393	−	0.0289049i	−0.974969	−	0.222341i	$-0.928630\pi$
$43$	0.0402884	−	0.189542i	0.00614393	−	0.0289049i	0.981113	+	0.193437i	$0.0619634\pi$
$44$	−3.99395	+	0.848939i	−0.602110	+	0.127982i
$45$	2.89815	−	0.775048i	0.432031	−	0.115537i
$46$	3.01955	+	0.981111i	0.445208	+	0.144657i
$47$	4.66582	+	1.51602i	0.680579	+	0.221134i	0.628849	−	0.777527i	$-0.283526\pi$
$47$	4.66582	+	1.51602i	0.680579	+	0.221134i	0.0517303	+	0.998661i	$0.483526\pi$
$48$	−0.746047	+	1.56314i	−0.107683	+	0.225620i
$49$	−7.11349	+	1.51202i	−1.01621	+	0.216003i
$50$	0.207912	−	0.978148i	0.0294032	−	0.138331i
$51$	11.3798	−	3.36784i	1.59349	−	0.471592i
$52$	4.51710	+	4.06722i	0.626410	+	0.564022i
$53$	0.349345	−	3.32380i	0.0479863	−	0.456559i	−0.943975	−	0.330017i	$-0.892946\pi$
$53$	0.349345	−	3.32380i	0.0479863	−	0.456559i	0.991961	−	0.126542i	$-0.0403878\pi$
$54$	−5.17984	−	0.411464i	−0.704886	−	0.0559932i
$55$	−4.06080	+	0.426808i	−0.547559	+	0.0575507i
$56$	3.27174	+	1.88894i	0.437205	+	0.252420i
$57$	−0.318298	−	0.112802i	−0.0421596	−	0.0149410i
$58$	−1.36290	−	1.87587i	−0.178958	−	0.246314i
$59$	−8.33435	+	7.50428i	−1.08504	+	0.976974i	−0.999812	−	0.0193875i	$-0.993828\pi$
$59$	−8.33435	+	7.50428i	−1.08504	+	0.976974i	−0.0852275	+	0.996362i	$0.527162\pi$
$60$	−0.905353	+	1.47660i	−0.116881	+	0.190628i
$61$			7.43838i			0.952387i	0.879340	+	0.476194i	$0.157984\pi$
$61$			7.43838i			0.952387i	−0.879340	+	0.476194i	$0.842016\pi$
$62$	−4.20418	+	3.65032i	−0.533932	+	0.463591i
$63$	−1.77842	+	11.1933i	−0.224060	+	1.41022i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	4.06722	+	4.51710i	0.504476	+	0.560278i
$66$	6.87645	+	1.65266i	0.846433	+	0.203428i
$67$	−4.90224	−	8.49093i	−0.598904	−	1.03733i	−0.992983	−	0.118256i	$-0.962270\pi$
$67$	−4.90224	−	8.49093i	−0.598904	−	1.03733i	0.394079	−	0.919077i	$-0.371064\pi$
$68$	−3.42591	+	5.93384i	−0.415452	+	0.719584i
$69$	−3.98803	−	3.78634i	−0.480102	−	0.455822i
$70$	3.05637	+	2.22058i	0.365306	+	0.265411i
$71$	3.03894	+	0.319405i	0.360655	+	0.0379064i	0.283123	−	0.959083i	$-0.408629\pi$
$71$	3.03894	+	0.319405i	0.360655	+	0.0379064i	0.0775319	+	0.996990i	$0.475296\pi$
$72$	2.33236	−	1.88683i	0.274871	−	0.222365i
$73$	−2.09217	+	4.69909i	−0.244870	+	0.549986i	−0.993609	−	0.112878i	$-0.963993\pi$
$73$	−2.09217	+	4.69909i	−0.244870	+	0.549986i	0.748739	+	0.662865i	$0.230660\pi$
$74$	10.5711	+	2.24695i	1.22886	+	0.261203i
$75$	−1.05474	+	1.37387i	−0.121791	+	0.158641i
$76$	0.178112	−	0.0793007i	0.0204309	−	0.00909642i
$77$	4.76682	−	14.6708i	0.543229	−	1.67189i
$78$	−4.02654	−	9.72762i	−0.455916	−	1.10144i
$79$	−2.51209	−	5.64224i	−0.282632	−	0.634802i	0.715318	−	0.698799i	$-0.246282\pi$
$79$	−2.51209	−	5.64224i	−0.282632	−	0.634802i	−0.997950	+	0.0639971i	$0.979615\pi$
$80$	−0.207912	−	0.978148i	−0.0232452	−	0.109360i
$81$	7.78985	+	4.50758i	0.865539	+	0.500842i
$82$	10.3769	+	4.62007i	1.14593	+	0.510202i
$83$	8.97420	−	9.96686i	0.985046	−	1.09400i	−0.0105201	−	0.999945i	$-0.503349\pi$
$83$	8.97420	−	9.96686i	0.985046	−	1.09400i	0.995567	−	0.0940602i	$-0.0299846\pi$
$84$	−3.70496	−	5.39356i	−0.404244	−	0.588486i
$85$	−4.02739	+	5.54323i	−0.436832	+	0.601248i
$86$	−0.0202552	−	0.192715i	−0.00218417	−	0.0207810i
$87$	0.730920	+	3.94905i	0.0783628	+	0.423382i
$88$	−3.53613	+	2.04159i	−0.376953	+	0.217634i
$89$	−4.69447	+	3.41073i	−0.497613	+	0.361537i	−0.808104	−	0.589039i	$-0.799506\pi$
$89$	−4.69447	+	3.41073i	−0.497613	+	0.361537i	0.310492	+	0.950576i	$0.399506\pi$
$90$	2.51681	−	1.63269i	0.265295	−	0.172101i
$91$	−21.8394	+	7.09607i	−2.28940	+	0.743870i
$92$	3.17494			0.331011
$93$	9.29505	−	2.56946i	0.963851	−	0.266440i
$94$	4.90593			0.506008
$95$	0.185426	−	0.0602485i	0.0190243	−	0.00618137i
$96$	−0.226496	+	1.71718i	−0.0231166	+	0.175259i
$97$	10.5103	−	7.63620i	1.06716	−	0.775339i	0.0917622	−	0.995781i	$-0.470750\pi$
$97$	10.5103	−	7.63620i	1.06716	−	0.775339i	0.975400	+	0.220442i	$0.0707500\pi$
$98$	−6.29809	+	3.63620i	−0.636203	+	0.367312i
$99$	−9.51591	−	7.71350i	−0.956385	−	0.775236i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	6.13507	−	8.44420i	0.610462	−	0.840229i	−0.386153	−	0.922435i	$-0.626196\pi$
$101$	6.13507	−	8.44420i	0.610462	−	0.840229i	0.996615	+	0.0822054i	$0.0261964\pi$
$102$	9.78210	−	6.71955i	0.968573	−	0.665335i
$103$	6.45892	−	7.17335i	0.636416	−	0.706811i	−0.335526	−	0.942031i	$-0.608914\pi$
$103$	6.45892	−	7.17335i	0.636416	−	0.706811i	0.971942	+	0.235219i	$0.0755809\pi$
$104$	5.55286	+	2.47229i	0.544503	+	0.242428i
$105$	−3.12088	−	5.75129i	−0.304567	−	0.561268i
$106$	−0.694863	−	3.26907i	−0.0674911	−	0.317521i
$107$	4.84209	+	10.8755i	0.468103	+	1.05138i	0.981191	+	0.193040i	$0.0618346\pi$
$107$	4.84209	+	10.8755i	0.468103	+	1.05138i	−0.513088	+	0.858336i	$0.671499\pi$
$108$	−5.05347	+	1.20933i	−0.486270	+	0.116368i
$109$	3.27050	−	10.0656i	0.313257	−	0.964107i	−0.663209	−	0.748435i	$-0.730806\pi$
$109$	3.27050	−	10.0656i	0.313257	−	0.964107i	0.976466	−	0.215672i	$-0.0691942\pi$
$110$	−3.73016	+	1.66078i	−0.355657	+	0.158349i
$111$	−14.8478	−	11.3988i	−1.40929	−	1.08193i
$112$	3.69533	+	0.785466i	0.349176	+	0.0742196i
$113$	−0.197367	+	0.443294i	−0.0185668	+	0.0417016i	−0.922591	−	0.385780i	$-0.873932\pi$
$113$	−0.197367	+	0.443294i	−0.0185668	+	0.0417016i	0.904024	+	0.427481i	$0.140599\pi$
$114$	−0.337577	−	0.00892191i	−0.0316170	−	0.000835613i
$115$	3.15755	+	0.331872i	0.294443	+	0.0309472i
$116$	−1.87587	−	1.36290i	−0.174171	−	0.126542i
$117$	−0.963207	+	18.2096i	−0.0890485	+	1.68348i
$118$	−5.60748	+	9.71245i	−0.516211	+	0.894103i
$119$	−12.9427	−	22.4174i	−1.18645	−	2.05500i
$120$	−0.404749	+	1.68410i	−0.0369483	+	0.153736i
$121$	3.79551	+	4.21534i	0.345046	+	0.383212i
$122$	2.29859	+	7.07432i	0.208104	+	0.640479i
$123$	−12.7737	−	14.9635i	−1.15177	−	1.34921i
$124$	−2.87040	+	4.77083i	−0.257770	+	0.428433i
$125$		−	1.00000i		−	0.0894427i
$126$	1.76753	+	11.1950i	0.157464	+	0.997328i
$127$	−11.7669	+	10.5950i	−1.04414	+	0.940150i	−0.998270	−	0.0587972i	$-0.981273\pi$
$127$	−11.7669	+	10.5950i	−1.04414	+	0.940150i	−0.0458725	+	0.998947i	$0.514607\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	−0.112113	+	0.316353i	−0.00987099	+	0.0278533i
$130$	5.26402	+	3.03918i	0.461685	+	0.266554i
$131$	−3.79841	+	0.399229i	−0.331868	+	0.0348808i	−0.268997	−	0.963141i	$-0.586692\pi$
$131$	−3.79841	+	0.399229i	−0.331868	+	0.0348808i	−0.0628709	+	0.998022i	$0.520026\pi$
$132$	7.05059	−	0.553169i	0.613676	−	0.0481472i
$133$	−0.0769923	+	0.732532i	−0.00667607	+	0.0635186i
$134$	−7.28615	−	6.56048i	−0.629428	−	0.566739i
$135$	−5.15219	+	0.674476i	−0.443430	+	0.0580496i
$136$	−1.42457	+	6.70208i	−0.122156	+	0.574699i
$137$	−16.5513	+	3.51810i	−1.41408	+	0.300571i	−0.850710	−	0.525636i	$-0.823827\pi$
$137$	−16.5513	+	3.51810i	−1.41408	+	0.300571i	−0.563367	+	0.826207i	$0.690494\pi$
$138$	−4.96288	−	2.36866i	−0.422469	−	0.201633i
$139$	−6.52978	−	2.12165i	−0.553849	−	0.179956i	0.0187029	−	0.999825i	$-0.494046\pi$
$139$	−6.52978	−	2.12165i	−0.553849	−	0.179956i	−0.572551	+	0.819869i	$0.694046\pi$
$140$	3.59298	+	1.16743i	0.303662	+	0.0986659i
$141$	−7.66867	−	3.66005i	−0.645818	−	0.308232i
$142$	2.98890	−	0.635311i	0.250823	−	0.0533141i
$143$	5.16016	−	24.2767i	0.431514	−	2.03012i
$144$	1.63514	−	2.51522i	0.136262	−	0.209601i
$145$	−1.72314	−	1.55152i	−0.143099	−	0.128847i
$146$	−0.537672	+	5.11561i	−0.0444981	+	0.423371i
$147$	12.5576	−	0.985231i	1.03573	−	0.0812605i
$148$	10.7480	−	1.12966i	0.883483	−	0.0928578i
$149$	−3.30591	−	1.90867i	−0.270831	−	0.156364i	0.358434	−	0.933555i	$-0.383311\pi$
$149$	−3.30591	−	1.90867i	−0.270831	−	0.156364i	−0.629265	+	0.777191i	$0.716644\pi$
$150$	−0.578567	+	1.63256i	−0.0472398	+	0.133298i
$151$	2.32612	+	3.20162i	0.189297	+	0.260544i	0.893108	−	0.449843i	$-0.148520\pi$
$151$	2.32612	+	3.20162i	0.189297	+	0.260544i	−0.703811	+	0.710387i	$0.748520\pi$
$152$	0.144890	−	0.130459i	0.0117521	−	0.0105816i
$153$	−20.3039	+	3.20570i	−1.64147	+	0.259166i
$154$		−	15.4258i		−	1.24304i
$155$	−3.35337	+	4.44465i	−0.269349	+	0.357003i
$156$	−6.83546	−	8.00724i	−0.547275	−	0.641093i
$157$	−5.24995	−	16.1577i	−0.418992	−	1.28952i	−0.908632	−	0.417599i	$-0.862872\pi$
$157$	−5.24995	−	16.1577i	−0.418992	−	1.28952i	0.489640	−	0.871925i	$-0.337128\pi$
$158$	−4.13269	−	4.58981i	−0.328779	−	0.365146i
$159$	−1.35271	+	5.62843i	−0.107277	+	0.446363i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−5.99728	+	10.3876i	−0.472652	+	0.818657i
$162$	8.80150	+	1.87977i	0.691511	+	0.147688i
$163$	8.15832	+	5.92737i	0.639009	+	0.464267i	0.859510	−	0.511120i	$-0.170769\pi$
$163$	8.15832	+	5.92737i	0.639009	+	0.464267i	−0.220501	+	0.975387i	$0.570769\pi$
$164$	11.2967	+	1.18733i	0.882120	+	0.0927146i
$165$	7.06979	+	0.186849i	0.550383	+	0.0145462i
$166$	5.45504	−	12.2522i	0.423393	−	0.950957i
$167$	−10.1106	−	2.14907i	−0.782380	−	0.166300i	−0.200629	−	0.979667i	$-0.564299\pi$
$167$	−10.1106	−	2.14907i	−0.782380	−	0.166300i	−0.581750	+	0.813367i	$0.697632\pi$
$168$	−5.19033	−	3.98468i	−0.400443	−	0.307425i
$169$	−21.8762	+	9.73992i	−1.68279	+	0.749225i
$170$	−2.11733	+	6.51646i	−0.162392	+	0.499790i
$171$	0.521025	+	0.265795i	0.0398438	+	0.0203258i
$172$	−0.0788161	−	0.177024i	−0.00600967	−	0.0134979i
$173$	0.311118	+	1.46369i	0.0236538	+	0.111283i	0.988391	−	0.151934i	$-0.0485500\pi$
$173$	0.311118	+	1.46369i	0.0236538	+	0.111283i	−0.964737	+	0.263216i	$0.915217\pi$
$174$	1.91547	+	3.52990i	0.145211	+	0.267601i
$175$	3.45127	+	1.53660i	0.260891	+	0.116156i
$176$	−2.73218	+	3.03439i	−0.205945	+	0.228726i
$177$	16.0112	−	10.9985i	1.20348	−	0.826697i
$178$	−3.41073	+	4.69447i	−0.255645	+	0.351865i
$179$	−1.56340	−	14.8748i	−0.116854	−	1.11179i	−0.883080	−	0.469222i	$-0.844534\pi$
$179$	−1.56340	−	14.8748i	−0.116854	−	1.11179i	0.766226	−	0.642571i	$-0.222132\pi$
$180$	1.88909	−	2.33052i	0.140805	−	0.173707i
$181$	15.1547	−	8.74960i	1.12644	−	0.650352i	0.183405	−	0.983037i	$-0.441288\pi$
$181$	15.1547	−	8.74960i	1.12644	−	0.650352i	0.943038	+	0.332685i	$0.107955\pi$
$182$	−18.5777	+	13.4975i	−1.37707	+	1.00050i
$183$	1.68476	−	12.7730i	0.124541	−	0.944209i
$184$	3.01955	−	0.981111i	0.222604	−	0.0723285i
$185$	10.8072			0.794564
$186$	8.04611	−	5.31603i	0.589969	−	0.389790i
$187$	27.9771			2.04589
$188$	4.66582	−	1.51602i	0.340290	−	0.110567i
$189$	5.58908	−	18.8180i	0.406546	−	1.36881i
$190$	0.157733	−	0.114599i	0.0114431	−	0.00831392i
$191$	−9.86557	+	5.69589i	−0.713848	+	0.412140i	−0.812484	−	0.582983i	$-0.801885\pi$
$191$	−9.86557	+	5.69589i	−0.713848	+	0.412140i	0.0986365	+	0.995124i	$0.468552\pi$
$192$	0.315227	+	1.70312i	0.0227496	+	0.122912i
$193$	2.24885	+	21.3964i	0.161876	+	1.54015i	0.710272	+	0.703928i	$0.248572\pi$
$193$	2.24885	+	21.3964i	0.161876	+	1.54015i	−0.548396	+	0.836219i	$0.684761\pi$
$194$	7.63620	−	10.5103i	0.548247	−	0.754598i
$195$	−5.96103	−	8.67788i	−0.426879	−	0.621436i
$196$	−4.86619	+	5.40445i	−0.347585	+	0.386032i
$197$	3.01017	+	1.34021i	0.214466	+	0.0954862i	0.511158	−	0.859487i	$-0.329217\pi$
$197$	3.01017	+	1.34021i	0.214466	+	0.0954862i	−0.296692	+	0.954973i	$0.595883\pi$
$198$	−11.4338	−	4.39540i	−0.812563	−	0.312367i
$199$	0.0158454	+	0.0745467i	0.00112325	+	0.00528448i	0.978706	−	0.205269i	$-0.0658068\pi$
$199$	0.0158454	+	0.0745467i	0.00112325	+	0.00528448i	−0.977582	+	0.210553i	$0.932473\pi$
$200$	−0.406737	−	0.913545i	−0.0287606	−	0.0645974i
$201$	6.49486	+	15.6908i	0.458112	+	1.10674i
$202$	3.22540	−	9.92675i	0.226938	−	0.698444i
$203$	8.00248	−	3.56294i	0.561664	−	0.250069i
$204$	7.22688	−	9.41351i	0.505983	−	0.659078i
$205$	11.1107	+	2.36164i	0.776002	+	0.164944i
$206$	3.92611	−	8.81818i	0.273545	−	0.614392i
$207$	5.99057	+	7.40509i	0.416373	+	0.514690i
$208$	6.04507	+	0.635362i	0.419150	+	0.0440544i
$209$	−0.644049	−	0.467929i	−0.0445498	−	0.0323673i
$210$	−4.74538	−	4.50539i	−0.327462	−	0.310902i
$211$	0.953391	−	1.65132i	0.0656342	−	0.113682i	−0.831341	−	0.555763i	$-0.812426\pi$
$211$	0.953391	−	1.65132i	0.0656342	−	0.113682i	0.896975	+	0.442081i	$0.145760\pi$
$212$	−1.67105	−	2.89435i	−0.114768	−	0.198785i
$213$	−5.14605	−	1.23678i	−0.352602	−	0.0847428i
$214$	7.96582	+	8.84694i	0.544532	+	0.604764i
$215$	−0.0598803	−	0.184293i	−0.00408380	−	0.0125687i
$216$	−4.43243	+	2.71175i	−0.301588	+	0.184511i
$217$	−10.1869	−	18.4030i	−0.691532	−	1.24928i
$218$		−	10.5836i		−	0.716810i
$219$	4.65695	−	7.59530i	0.314687	−	0.513243i
$220$	−3.03439	+	2.73218i	−0.204578	+	0.184203i
$221$	−24.4800	−	33.6938i	−1.64670	−	2.26649i
$222$	−17.6435	−	6.25271i	−1.18415	−	0.419655i
$223$	15.7342	+	9.08415i	1.05364	+	0.608319i	0.923666	−	0.383198i	$-0.125177\pi$
$223$	15.7342	+	9.08415i	1.05364	+	0.608319i	0.129974	+	0.991517i	$0.458511\pi$
$224$	3.75719	−	0.394896i	0.251038	−	0.0263851i
$225$	2.12235	−	2.12029i	0.141490	−	0.141353i
$226$	−0.0507220	+	0.482588i	−0.00337398	+	0.0321013i
$227$	−9.30484	−	8.37812i	−0.617584	−	0.556075i	0.299838	−	0.953990i	$-0.403067\pi$
$227$	−9.30484	−	8.37812i	−0.617584	−	0.556075i	−0.917422	+	0.397915i	$0.869734\pi$
$228$	−0.323812	+	0.0958318i	−0.0214450	+	0.00634662i
$229$	3.32576	−	15.6465i	0.219772	−	1.03395i	−0.720482	−	0.693474i	$-0.756079\pi$
$229$	3.32576	−	15.6465i	0.219772	−	1.03395i	0.940254	−	0.340473i	$-0.110587\pi$
$230$	3.10556	−	0.660107i	0.204775	−	0.0435262i
$231$	−11.5083	+	24.1126i	−0.757193	+	1.58650i
$232$	−2.20522	−	0.716520i	−0.144780	−	0.0470419i
$233$	−9.99918	−	3.24893i	−0.655068	−	0.212845i	−0.0374207	−	0.999300i	$-0.511914\pi$
$233$	−9.99918	−	3.24893i	−0.655068	−	0.212845i	−0.617648	+	0.786455i	$0.711914\pi$
$234$	4.71102	+	17.6160i	0.307969	+	1.15160i
$235$	4.79872	−	1.02000i	0.313034	−	0.0665375i
$236$	−2.33172	+	10.9699i	−0.151782	+	0.714079i
$237$	3.03576	+	10.2577i	0.197194	+	0.666310i
$238$	−19.2366	−	17.3207i	−1.24692	−	1.12273i
$239$	2.10919	−	20.0676i	0.136432	−	1.29806i	−0.685330	−	0.728233i	$-0.740342\pi$
$239$	2.10919	−	20.0676i	0.136432	−	1.29806i	0.821762	−	0.569831i	$-0.192991\pi$
$240$	0.135475	+	1.72674i	0.00874489	+	0.111461i
$241$	10.7058	−	1.12523i	0.689624	−	0.0724824i	0.246767	−	0.969075i	$-0.420632\pi$
$241$	10.7058	−	1.12523i	0.689624	−	0.0724824i	0.442857	+	0.896592i	$0.353965\pi$
$242$	4.91235	+	2.83615i	0.315778	+	0.182314i
$243$	−12.3556	−	9.50468i	−0.792613	−	0.609726i
$244$	4.37217	+	6.01778i	0.279900	+	0.385249i
$245$	−5.40445	+	4.86619i	−0.345278	+	0.310889i
$246$	−16.7725	−	10.2838i	−1.06937	−	0.655671i
$247$			1.18509i			0.0754053i
$248$	−1.25565	+	5.42433i	−0.0797337	+	0.344445i
$249$	−17.6677	+	15.0823i	−1.11965	+	0.955799i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	17.7783	+	19.7448i	1.12215	+	1.24628i	0.965999	+	0.258546i	$0.0832433\pi$
$251$	17.7783	+	19.7448i	1.12215	+	1.24628i	0.156155	+	0.987733i	$0.450090\pi$
$252$	5.14046	+	10.1009i	0.323818	+	0.636294i
$253$	−6.48192	−	11.2270i	−0.407515	−	0.705836i
$254$	−7.91695	+	13.7126i	−0.496754	+	0.860403i
$255$	8.17127	−	8.60653i	0.511705	−	0.538962i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−11.3314	−	1.19098i	−0.706832	−	0.0742910i	−0.255710	−	0.966754i	$-0.582309\pi$
$257$	−11.3314	−	1.19098i	−0.706832	−	0.0742910i	−0.451122	+	0.892463i	$0.648976\pi$
$258$	−0.00886738	+	0.335514i	−0.000552059	+	0.0208882i
$259$	−16.6064	+	37.2987i	−1.03187	+	2.31763i
$260$	5.94554	+	1.26376i	0.368727	+	0.0783752i
$261$	−0.360677	−	6.94677i	−0.0223254	−	0.429994i
$262$	−3.48913	+	1.55346i	−0.215559	+	0.0959731i
$263$	−1.31834	+	4.05744i	−0.0812925	+	0.250193i	−0.983440	−	0.181236i	$-0.941990\pi$
$263$	−1.31834	+	4.05744i	−0.0812925	+	0.250193i	0.902147	+	0.431428i	$0.141990\pi$
$264$	6.53458	−	2.70485i	0.402175	−	0.166472i
$265$	−1.35936	−	3.05317i	−0.0835047	−	0.187555i
$266$	0.153141	+	0.720472i	0.00938967	+	0.0441749i
$267$	8.83376	−	4.79356i	0.540617	−	0.293361i
$268$	−8.95684	−	3.98784i	−0.547126	−	0.243596i
$269$	2.08755	−	2.31846i	0.127280	−	0.141359i	−0.676136	−	0.736777i	$-0.736347\pi$
$269$	2.08755	−	2.31846i	0.127280	−	0.141359i	0.803416	+	0.595418i	$0.203013\pi$
$270$	−4.69160	+	2.23358i	−0.285522	+	0.135931i
$271$	5.68849	−	7.82954i	0.345551	−	0.475611i	−0.600501	−	0.799624i	$-0.705032\pi$
$271$	5.68849	−	7.82954i	0.345551	−	0.475611i	0.946053	+	0.324013i	$0.105032\pi$
$272$	0.716209	+	6.81428i	0.0434266	+	0.413176i
$273$	39.1094	−	7.23867i	2.36701	−	0.438104i
$274$	−14.6541	+	8.46055i	−0.885287	+	0.511121i
$275$	−3.30336	+	2.40003i	−0.199200	+	0.144727i
$276$	−5.45194	−	0.719110i	−0.328168	−	0.0432853i
$277$	30.5934	−	9.94039i	1.83818	−	0.597260i	0.839644	−	0.543137i	$-0.182763\pi$
$277$	30.5934	−	9.94039i	1.83818	−	0.597260i	0.998534	−	0.0541239i	$-0.0172366\pi$
$278$	−6.86581			−0.411784
$279$	−16.5432	+	2.30693i	−0.990417	+	0.138112i
$280$	3.77788			0.225772
$281$	24.6990	−	8.02520i	1.47342	−	0.478743i	0.541280	−	0.840842i	$-0.317940\pi$
$281$	24.6990	−	8.02520i	1.47342	−	0.478743i	0.932140	+	0.362099i	$0.117940\pi$
$282$	−8.42435	−	1.11117i	−0.501663	−	0.0661693i
$283$	−6.84152	+	4.97065i	−0.406686	+	0.295475i	−0.772259	−	0.635308i	$-0.780873\pi$
$283$	−6.84152	+	4.97065i	−0.406686	+	0.295475i	0.365573	+	0.930783i	$0.380873\pi$
$284$	2.64629	−	1.52784i	0.157029	−	0.0906605i
$285$	−0.332055	+	0.0614593i	−0.0196692	+	0.00364053i
$286$	−2.59429	−	24.6830i	−0.153404	−	1.45954i
$287$	−25.2234	+	34.7170i	−1.48889	+	2.04928i
$288$	0.777866	−	2.89740i	0.0458362	−	0.170731i
$289$	20.0387	−	22.2552i	1.17875	−	1.30913i
$290$	−2.11825	−	0.943104i	−0.124388	−	0.0553809i
$291$	−19.7777	+	10.7322i	−1.15939	+	0.629131i
$292$	1.06945	+	5.03139i	0.0625851	+	0.294440i
$293$	3.56007	+	7.99605i	0.207982	+	0.467135i	0.987174	−	0.159651i	$-0.0510369\pi$
$293$	3.56007	+	7.99605i	0.207982	+	0.467135i	−0.779192	+	0.626786i	$0.784370\pi$
$294$	11.6385	−	4.81752i	0.678772	−	0.280963i
$295$	−3.46562	+	10.6661i	−0.201776	+	0.621003i
$296$	9.87290	−	4.39570i	0.573851	−	0.255495i
$297$	14.5934	+	15.4008i	0.846797	+	0.893643i
$298$	−3.73392	−	0.793670i	−0.216300	−	0.0459760i
$299$	−7.84939	+	17.6300i	−0.453942	+	1.01957i
$300$	−0.0457608	+	1.73145i	−0.00264200	+	0.0999651i
$301$	0.728056	+	0.0765217i	0.0419644	+	0.00441064i
$302$	3.20162	+	2.32612i	0.184233	+	0.133853i
$303$	−12.4476	+	13.1106i	−0.715095	+	0.753186i
$304$	0.0974841	−	0.168847i	0.00559110	−	0.00968406i
$305$	3.71919	+	6.44183i	0.212960	+	0.368858i
$306$	−18.3196	+	9.32306i	−1.04726	+	0.532964i
$307$	3.86841	+	4.29630i	0.220782	+	0.245203i	0.843353	−	0.537360i	$-0.180578\pi$
$307$	3.86841	+	4.29630i	0.220782	+	0.245203i	−0.622571	+	0.782563i	$0.713912\pi$
$308$	−4.76682	−	14.6708i	−0.271615	−	0.835944i
$309$	−12.7158	+	10.8550i	−0.723379	+	0.617520i
$310$	−1.81577	+	5.26336i	−0.103129	+	0.298939i
$311$			23.3649i			1.32490i	0.749105	+	0.662451i	$0.230484\pi$
$311$			23.3649i			1.32490i	−0.749105	+	0.662451i	$0.769516\pi$
$312$	−8.97529	−	5.50307i	−0.508126	−	0.311550i
$313$	−4.09463	+	3.68682i	−0.231442	+	0.208391i	−0.776689	−	0.629884i	$-0.783102\pi$
$313$	−4.09463	+	3.68682i	−0.231442	+	0.208391i	0.545247	+	0.838275i	$0.316436\pi$
$314$	−9.98600	−	13.7445i	−0.563542	−	0.775650i
$315$	4.05647	+	10.5828i	0.228556	+	0.596276i
$316$	−5.34875	−	3.08810i	−0.300891	−	0.173719i
$317$	12.6596	−	1.33058i	0.711034	−	0.0747327i	0.257895	−	0.966173i	$-0.416971\pi$
$317$	12.6596	−	1.33058i	0.711034	−	0.0747327i	0.453138	+	0.891440i	$0.350304\pi$
$318$	0.452773	+	5.77097i	0.0253902	+	0.323620i
$319$	−0.989643	+	9.41582i	−0.0554093	+	0.527185i
$320$	−0.743145	−	0.669131i	−0.0415431	−	0.0374055i
$321$	−5.85148	−	19.7719i	−0.326597	−	1.10356i
$322$	−2.49381	+	11.7325i	−0.138975	+	0.653824i
$323$	−1.30669	+	0.277746i	−0.0727064	+	0.0154542i
$324$	8.95161	−	0.932050i	0.497312	−	0.0517806i
$325$	5.78087	+	1.87832i	0.320665	+	0.104190i
$326$	9.59068	+	3.11620i	0.531179	+	0.172590i
$327$	−7.89584	+	16.5436i	−0.436641	+	0.914864i
$328$	11.1107	−	2.36164i	0.613484	−	0.130400i
$329$	−3.85344	+	18.1290i	−0.212447	+	0.999485i
$330$	6.78151	−	2.00698i	0.373310	−	0.110481i
$331$	15.1960	+	13.6826i	0.835249	+	0.752062i	0.971101	−	0.238667i	$-0.0767105\pi$
$331$	15.1960	+	13.6826i	0.835249	+	0.752062i	−0.135852	+	0.990729i	$0.543377\pi$
$332$	1.40191	−	13.3383i	0.0769397	−	0.732032i
$333$	22.9145	+	22.9368i	1.25570	+	1.25693i
$334$	−10.2798	+	1.08045i	−0.562487	+	0.0591198i
$335$	−8.49093	−	4.90224i	−0.463909	−	0.267838i
$336$	−6.16763	−	2.18576i	−0.336472	−	0.119243i
$337$	9.56303	+	13.1624i	0.520932	+	0.717001i	0.985715	−	0.168424i	$-0.0538677\pi$
$337$	9.56303	+	13.1624i	0.520932	+	0.717001i	−0.464783	+	0.885425i	$0.653868\pi$
$338$	−17.7957	+	16.0233i	−0.967960	+	0.871555i
$339$	0.439319	−	0.716512i	0.0238605	−	0.0389156i
$340$			6.85181i			0.371592i
$341$	22.7304	+	0.410064i	1.23092	+	0.0222062i
$342$	0.577659	+	0.0917802i	0.0312362	+	0.00496290i
$343$	−0.318016	−	0.978754i	−0.0171713	−	0.0528477i
$344$	−0.129662	−	0.144004i	−0.00699090	−	0.00776418i
$345$	−5.34691	−	1.28505i	−0.287868	−	0.0691850i
$346$	0.748196	+	1.29591i	0.0402233	+	0.0696688i
$347$	10.2753	−	17.7974i	0.551609	−	0.955415i	−0.446550	−	0.894759i	$-0.647347\pi$
$347$	10.2753	−	17.7974i	0.551609	−	0.955415i	0.998159	−	0.0606558i	$-0.0193192\pi$
$348$	2.91252	+	2.76522i	0.156127	+	0.148232i
$349$	18.6496	+	13.5497i	0.998289	+	0.725299i	0.961721	−	0.274032i	$-0.0883573\pi$
$349$	18.6496	+	13.5497i	0.998289	+	0.725299i	0.0365684	+	0.999331i	$0.488357\pi$
$350$	3.75719	+	0.394896i	0.200830	+	0.0211081i
$351$	5.77840	−	31.0510i	0.308428	−	1.65738i
$352$	−1.66078	+	3.73016i	−0.0885196	+	0.198818i
$353$	10.1179	+	2.15063i	0.538521	+	0.114466i	0.469140	−	0.883124i	$-0.344564\pi$
$353$	10.1179	+	2.15063i	0.538521	+	0.114466i	0.0693816	+	0.997590i	$0.477897\pi$
$354$	11.8289	−	15.4079i	0.628698	−	0.818922i
$355$	2.79150	−	1.24286i	0.148157	−	0.0659639i
$356$	−1.79313	+	5.51868i	−0.0950356	+	0.292489i
$357$	17.1474	+	41.4261i	0.907539	+	2.19250i
$358$	−6.08345	−	13.6636i	−0.321520	−	0.722146i
$359$	−3.01548	−	14.1867i	−0.159151	−	0.748746i	−0.983244	−	0.182292i	$-0.941648\pi$
$359$	−3.01548	−	14.1867i	−0.159151	−	0.748746i	0.824093	−	0.566454i	$-0.191685\pi$
$360$	1.07647	−	2.80022i	0.0567347	−	0.147584i
$361$	−17.3226	−	7.71254i	−0.911718	−	0.405923i
$362$	11.7092	−	13.0044i	0.615424	−	0.683498i
$363$	−5.56280	−	8.09815i	−0.291972	−	0.425043i
$364$	−13.4975	+	18.5777i	−0.707462	+	0.973738i
$365$	0.537672	+	5.11561i	0.0281431	+	0.267763i
$366$	−2.34478	−	12.6685i	−0.122564	−	0.662192i
$367$	−18.6210	+	10.7509i	−0.972011	+	0.561191i	−0.899849	−	0.436202i	$-0.856323\pi$
$367$	−18.6210	+	10.7509i	−0.972011	+	0.561191i	−0.0721622	+	0.997393i	$0.522990\pi$
$368$	2.56858	−	1.86618i	0.133897	−	0.0972816i
$369$	18.5456	+	28.5881i	0.965444	+	1.48824i
$370$	10.2783	−	3.33962i	0.534343	−	0.173619i
$371$	12.6261			0.655514
$372$	6.00956	−	7.54223i	0.311581	−	0.391046i
$373$	−21.6657			−1.12181			−0.560904	−	0.827881i	$-0.689546\pi$
$373$	−21.6657			−1.12181			−0.560904	+	0.827881i	$0.689546\pi$
$374$	26.6078	−	8.64541i	1.37586	−	0.447043i
$375$	−0.226496	+	1.71718i	−0.0116962	+	0.0886747i
$376$	3.96898	−	2.88363i	0.204685	−	0.148712i
$377$	12.2057	−	7.04698i	0.628627	−	0.362938i
$378$	−0.499551	−	19.6241i	−0.0256941	−	1.00935i
$379$	1.92563	+	18.3211i	0.0989128	+	0.941092i	0.925619	+	0.378458i	$0.123546\pi$
$379$	1.92563	+	18.3211i	0.0989128	+	0.941092i	−0.826706	+	0.562635i	$0.809788\pi$
$380$	0.114599	−	0.157733i	0.00587883	−	0.00809151i
$381$	22.6055	−	15.5283i	1.15812	−	0.795537i
$382$	−7.62259	+	8.46574i	−0.390005	+	0.433145i
$383$	14.4436	+	6.43069i	0.738032	+	0.328593i	0.741093	−	0.671402i	$-0.234308\pi$
$383$	14.4436	+	6.43069i	0.738032	+	0.328593i	−0.00306103	+	0.999995i	$0.500974\pi$
$384$	0.826093	+	1.52236i	0.0421564	+	0.0776874i
$385$	−3.20719	−	15.0887i	−0.163454	−	0.768989i
$386$	8.75064	+	19.6542i	0.445396	+	1.00037i
$387$	0.264170	−	0.517841i	0.0134285	−	0.0263233i
$388$	4.01459	−	12.3556i	0.203810	−	0.627262i
$389$	−8.96023	+	3.98935i	−0.454302	+	0.202268i	−0.621114	−	0.783721i	$-0.713319\pi$
$389$	−8.96023	+	3.98935i	−0.454302	+	0.202268i	0.166812	+	0.985989i	$0.446653\pi$
$390$	−8.35089	−	6.41109i	−0.422864	−	0.324638i
$391$	−21.2787	−	4.52293i	−1.07611	−	0.228734i
$392$	−2.95795	+	6.64367i	−0.149399	+	0.335556i
$393$	6.61296	+	0.174776i	0.333580	+	0.00881626i
$394$	3.27699	+	0.344425i	0.165092	+	0.0173519i
$395$	−4.99665	−	3.63028i	−0.251409	−	0.182659i
$396$	−12.2324	−	0.647039i	−0.614702	−	0.0325149i
$397$	−7.77524	+	13.4671i	−0.390228	+	0.675895i	−0.992479	−	0.122411i	$-0.960937\pi$
$397$	−7.77524	+	13.4671i	−0.390228	+	0.675895i	0.602251	+	0.798307i	$0.294271\pi$
$398$	0.0381061	+	0.0660017i	0.00191008	+	0.00330836i
$399$	0.298125	−	1.24045i	0.0149249	−	0.0621002i
$400$	−0.669131	−	0.743145i	−0.0334565	−	0.0371572i
$401$	−11.4336	−	35.1889i	−0.570964	−	1.75725i	−0.649527	−	0.760338i	$-0.725033\pi$
$401$	−11.4336	−	35.1889i	−0.570964	−	1.75725i	0.0785627	−	0.996909i	$-0.474967\pi$
$402$	11.0257	+	12.9158i	0.549912	+	0.644181i
$403$	−19.3953	−	27.7338i	−0.966147	−	1.38152i
$404$		−	10.4376i		−	0.519290i
$405$	9.00000	+	0.00875358i	0.447213	+	0.000434969i
$406$	6.50981	−	5.86146i	0.323076	−	0.290899i
$407$	−25.9377	−	35.7001i	−1.28568	−	1.76959i
$408$	3.96423	−	11.1860i	0.196259	−	0.553790i
$409$	−23.2365	−	13.4156i	−1.14897	−	0.663359i	−0.200335	−	0.979727i	$-0.564203\pi$
$409$	−23.2365	−	13.4156i	−1.14897	−	0.663359i	−0.948636	+	0.316368i	$0.897536\pi$
$410$	11.2967	−	1.18733i	0.557902	−	0.0586379i
$411$	29.2184	−	2.29239i	1.44124	−	0.113075i
$412$	1.00898	−	9.59982i	0.0497090	−	0.472949i
$413$	−31.4862	−	28.3503i	−1.54933	−	1.39503i
$414$	7.98567	+	5.19148i	0.392474	+	0.255147i
$415$	2.78846	−	13.1187i	0.136880	−	0.643969i
$416$	5.94554	−	1.26376i	0.291504	−	0.0619611i
$417$	10.7322	+	5.12222i	0.525560	+	0.250836i
$418$	−0.757125	−	0.246005i	−0.0370322	−	0.0120325i
$419$	11.1334	+	3.61746i	0.543903	+	0.176725i	0.568065	−	0.822983i	$-0.307692\pi$
$419$	11.1334	+	3.61746i	0.543903	+	0.176725i	−0.0241629	+	0.999708i	$0.507692\pi$
$420$	−5.90537	−	2.81848i	−0.288153	−	0.137528i
$421$	10.1854	−	2.16498i	0.496408	−	0.105515i	0.0470974	−	0.998890i	$-0.485003\pi$
$421$	10.1854	−	2.16498i	0.496408	−	0.105515i	0.449311	+	0.893375i	$0.351670\pi$
$422$	0.396442	−	1.86512i	0.0192985	−	0.0907924i
$423$	12.3395	+	8.02188i	0.599966	+	0.390037i
$424$	−2.48367	−	2.23631i	−0.120618	−	0.108605i
$425$	−0.716209	+	6.81428i	−0.0347413	+	0.330541i
$426$	−5.27637	+	0.413969i	−0.255641	+	0.0200568i
$427$	−27.9474	+	2.93739i	−1.35247	+	0.142150i
$428$	10.3098	+	5.95237i	0.498343	+	0.287718i
$429$	−14.3595	+	40.5186i	−0.693282	+	1.95626i
$430$	−0.113899	−	0.156769i	−0.00549270	−	0.00756006i
$431$	13.8086	−	12.4333i	0.665136	−	0.598891i	−0.265820	−	0.964023i	$-0.585643\pi$
$431$	13.8086	−	12.4333i	0.665136	−	0.598891i	0.930956	+	0.365131i	$0.118976\pi$
$432$	−3.37751	+	3.94872i	−0.162501	+	0.189983i
$433$			33.7931i			1.62399i	0.583662	+	0.811997i	$0.301619\pi$
$433$			33.7931i			1.62399i	−0.583662	+	0.811997i	$0.698381\pi$
$434$	−15.3752	−	14.3544i	−0.738032	−	0.689033i
$435$	2.60752	+	3.05452i	0.125021	+	0.146453i
$436$	−3.27050	−	10.0656i	−0.156629	−	0.482053i
$437$	0.414200	+	0.460016i	0.0198139	+	0.0220056i
$438$	2.08194	−	8.66264i	0.0994791	−	0.413917i
$439$	−4.75560	−	8.23694i	−0.226973	−	0.393128i	0.729937	−	0.683515i	$-0.239549\pi$
$439$	−4.75560	−	8.23694i	−0.226973	−	0.393128i	−0.956909	+	0.290387i	$0.906216\pi$
$440$	−2.04159	+	3.53613i	−0.0973288	+	0.168578i
$441$	−21.7868	−	1.15242i	−1.03746	−	0.0548772i
$442$	−33.6938	−	24.4800i	−1.60265	−	1.16439i
$443$	−22.7744	−	2.39368i	−1.08204	−	0.113727i	−0.453313	−	0.891351i	$-0.649758\pi$
$443$	−22.7744	−	2.39368i	−1.08204	−	0.113727i	−0.628730	+	0.777624i	$0.716425\pi$
$444$	−18.7121	−	0.494548i	−0.888039	−	0.0234702i
$445$	−2.36016	+	5.30102i	−0.111883	+	0.251292i
$446$	17.7713	+	3.77740i	0.841494	+	0.178865i
$447$	5.24454	+	4.02630i	0.248058	+	0.190437i
$448$	3.45127	−	1.53660i	0.163057	−	0.0725977i
$449$	4.86519	−	14.9735i	0.229602	−	0.706644i	−0.768189	−	0.640223i	$-0.778842\pi$
$449$	4.86519	−	14.9735i	0.229602	−	0.706644i	0.997792	−	0.0664209i	$-0.0211580\pi$
$450$	1.36327	−	2.67236i	0.0642652	−	0.125976i
$451$	−18.8646	−	42.3705i	−0.888297	−	1.99515i
$452$	0.100888	+	0.474642i	0.00474539	+	0.0223253i
$453$	−3.26920	−	6.02461i	−0.153600	−	0.283061i
$454$	−11.4384	−	5.09271i	−0.536831	−	0.239013i
$455$	−15.3655	+	17.0651i	−0.720345	+	0.800024i
$456$	−0.278350	+	0.191205i	−0.0130349	+	0.00895399i
$457$	1.44637	−	1.99076i	0.0676584	−	0.0931238i	−0.773847	−	0.633373i	$-0.781670\pi$
$457$	1.44637	−	1.99076i	0.0676584	−	0.0931238i	0.841505	+	0.540249i	$0.181670\pi$
$458$	−1.67204	−	15.9084i	−0.0781292	−	0.743350i
$459$	35.5915	−	0.906017i	1.66127	−	0.0422892i
$460$	2.74958	−	1.58747i	0.128200	−	0.0740162i
$461$	−20.9869	+	15.2478i	−0.977456	+	0.710163i	−0.957139	−	0.289630i	$-0.906468\pi$
$461$	−20.9869	+	15.2478i	−0.977456	+	0.710163i	−0.0203171	+	0.999794i	$0.506468\pi$
$462$	−3.49386	+	26.4888i	−0.162549	+	1.23237i
$463$	−25.5865	+	8.31357i	−1.18911	+	0.386364i	−0.835742	−	0.549122i	$-0.814962\pi$
$463$	−25.5865	+	8.31357i	−1.18911	+	0.386364i	−0.353364	+	0.935486i	$0.614962\pi$
$464$	−2.31871			−0.107643
$465$	6.76502	−	6.87274i	0.313720	−	0.318716i
$466$	−10.5138			−0.487041
$467$	18.6040	−	6.04482i	0.860892	−	0.279721i	0.154891	−	0.987932i	$-0.450497\pi$
$467$	18.6040	−	6.04482i	0.860892	−	0.279721i	0.706001	+	0.708211i	$0.250497\pi$
$468$	9.92410	+	15.2981i	0.458742	+	0.707153i
$469$	29.9662	−	21.7717i	1.38371	−	1.00532i
$470$	4.24866	−	2.45296i	0.195976	−	0.113147i
$471$	5.35545	+	28.9347i	0.246766	+	1.33324i
$472$	1.17228	+	11.1535i	0.0539587	+	0.513383i
$473$	−0.465070	+	0.640113i	−0.0213839	+	0.0294324i
$474$	6.05699	+	8.81756i	0.278207	+	0.405004i
$475$	0.130459	−	0.144890i	0.00598588	−	0.00664799i
$476$	−23.6474	−	10.5285i	−1.08388	−	0.482574i
$477$	3.59766	−	9.35863i	0.164726	−	0.428502i
$478$	−4.19526	−	19.7372i	−0.191887	−	0.902757i
$479$	15.1451	+	34.0165i	0.691998	+	1.55425i	0.826249	+	0.563305i	$0.190470\pi$
$479$	15.1451	+	34.0165i	0.691998	+	1.55425i	−0.134251	+	0.990947i	$0.542863\pi$
$480$	0.662438	+	1.60037i	0.0302360	+	0.0730464i
$481$	−20.2994	+	62.4752i	−0.925574	+	2.84862i
$482$	9.83415	−	4.37844i	0.447933	−	0.199433i
$483$	12.6511	−	16.4790i	0.575647	−	0.749820i
$484$	5.54834	+	1.17934i	0.252197	+	0.0536062i
$485$	5.28411	−	11.8683i	0.239939	−	0.538912i
$486$	−14.6880	−	5.22140i	−0.666261	−	0.236847i
$487$	40.8665	+	4.29524i	1.85184	+	0.194636i	0.964069	−	0.265652i	$-0.0855872\pi$
$487$	40.8665	+	4.29524i	1.85184	+	0.194636i	0.887770	+	0.460288i	$0.152254\pi$
$488$	6.01778	+	4.37217i	0.272412	+	0.197919i
$489$	−12.6668	−	12.0262i	−0.572811	−	0.543842i
$490$	−3.63620	+	6.29809i	−0.164267	+	0.284519i
$491$	4.84079	+	8.38450i	0.218462	+	0.378387i	0.954338	−	0.298729i	$-0.0965627\pi$
$491$	4.84079	+	8.38450i	0.218462	+	0.378387i	−0.735876	+	0.677116i	$0.763229\pi$
$492$	−19.1294	−	4.59749i	−0.862422	−	0.207271i
$493$	10.6307	+	11.8066i	0.478783	+	0.531743i
$494$	0.366212	+	1.12709i	0.0164767	+	0.0507100i
$495$	−12.0978	−	1.92213i	−0.543754	−	0.0863933i
$496$	0.482017	+	5.54686i	0.0216432	+	0.249061i
$497$			11.5440i			0.517819i
$498$	−12.1424	+	19.8037i	−0.544112	+	0.887425i
$499$	26.1329	−	23.5301i	1.16987	−	1.05335i	0.172202	−	0.985062i	$-0.444912\pi$
$499$	26.1329	−	23.5301i	1.16987	−	1.05335i	0.997665	−	0.0682915i	$-0.0217548\pi$
$500$	−0.587785	−	0.809017i	−0.0262866	−	0.0361803i
$501$	16.8749	+	5.98033i	0.753915	+	0.267182i
$502$	23.0096	+	13.2846i	1.02697	+	0.592921i
$503$	39.5009	−	4.15172i	1.76126	−	0.185116i	0.832058	−	0.554689i	$-0.187163\pi$
$503$	39.5009	−	4.15172i	1.76126	−	0.185116i	0.929202	+	0.369573i	$0.120496\pi$
$504$	8.01020	+	8.01800i	0.356803	+	0.357150i
$505$	1.09103	−	10.3804i	0.0485501	−	0.461923i
$506$	−9.63400	−	8.67450i	−0.428284	−	0.385628i
$507$	39.7714	−	11.7703i	1.76631	−	0.522738i
$508$	−3.29205	+	15.4879i	−0.146061	+	0.687164i
$509$	−19.8189	+	4.21264i	−0.878457	+	0.186722i	−0.625000	−	0.780625i	$-0.714901\pi$
$509$	−19.8189	+	4.21264i	−0.878457	+	0.186722i	−0.253457	+	0.967347i	$0.581568\pi$
$510$	5.11177	−	10.7104i	0.226353	−	0.474263i
$511$	−18.4815	−	6.00502i	−0.817575	−	0.265646i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	−0.834491	−	0.574426i	−0.0368437	−	0.0253615i
$514$	−11.1448	+	2.36890i	−0.491576	+	0.104488i
$515$	2.00691	−	9.44176i	0.0884350	−	0.416054i
$516$	0.0952461	+	0.321833i	0.00419298	+	0.0141679i
$517$	−14.8865	−	13.4039i	−0.654707	−	0.589501i
$518$	−4.26774	+	40.6048i	−0.187514	+	1.78407i
$519$	−0.202724	−	2.58389i	−0.00889861	−	0.113420i
$520$	6.04507	−	0.635362i	0.265094	−	0.0278625i
$521$	17.2505	+	9.95960i	0.755759	+	0.436338i	0.827771	−	0.561066i	$-0.189609\pi$
$521$	17.2505	+	9.95960i	0.755759	+	0.436338i	−0.0720117	+	0.997404i	$0.522942\pi$
$522$	−2.48969	−	6.49531i	−0.108971	−	0.284292i
$523$	11.9938	+	16.5080i	0.524452	+	0.721846i	0.986272	−	0.165127i	$-0.0528035\pi$
$523$	11.9938	+	16.5080i	0.524452	+	0.721846i	−0.461820	+	0.886974i	$0.652803\pi$
$524$	−2.83831	+	2.55563i	−0.123992	+	0.111643i
$525$	−5.57841	−	3.42032i	−0.243462	−	0.149275i
$526$			4.26625i			0.186017i
$527$	26.0341	−	27.8854i	1.13406	−	1.21471i
$528$	5.37891	−	4.59176i	0.234087	−	0.199831i
$529$	−3.99242	−	12.2874i	−0.173584	−	0.534235i
$530$	−2.23631	−	2.48367i	−0.0971389	−	0.107884i
$531$	−29.9853	+	15.2599i	−1.30125	+	0.662223i
$532$	0.368284	+	0.637886i	0.0159671	+	0.0276559i
$533$	−34.5217	+	59.7933i	−1.49530	+	2.58994i
$534$	6.92011	−	7.28872i	0.299462	−	0.315414i
$535$	9.63113	+	6.99743i	0.416390	+	0.302525i
$536$	−9.75078	−	1.02485i	−0.421169	−	0.0442667i
$537$	−0.684432	+	25.8968i	−0.0295354	+	1.11753i
$538$	1.26894	−	2.85008i	0.0547077	−	0.122875i
$539$	29.0456	+	6.17383i	1.25108	+	0.265926i
$540$	−3.77176	+	3.57404i	−0.162311	+	0.153802i
$541$	24.6729	−	10.9851i	1.06077	−	0.472286i	0.199219	−	0.979955i	$-0.436159\pi$
$541$	24.6729	−	10.9851i	1.06077	−	0.472286i	0.861552	+	0.507669i	$0.169493\pi$
$542$	2.99062	−	9.20418i	0.128458	−	0.395353i
$543$	−28.0051	+	11.5921i	−1.20182	+	0.497466i
$544$	2.78688	+	6.25944i	0.119487	+	0.268371i
$545$	−2.20045	−	10.3523i	−0.0942568	−	0.443443i
$546$	34.9584	−	18.9699i	1.49608	−	0.811835i
$547$	−6.60600	−	2.94118i	−0.282452	−	0.125756i	0.260621	−	0.965441i	$-0.416073\pi$
$547$	−6.60600	−	2.94118i	−0.282452	−	0.125756i	−0.543073	+	0.839685i	$0.682739\pi$
$548$	−11.3224	+	12.5748i	−0.483670	+	0.537170i
$549$	−5.78607	+	21.5520i	−0.246943	+	0.919815i
$550$	−2.40003	+	3.30336i	−0.102338	+	0.140856i
$551$	−0.0472546	−	0.449598i	−0.00201312	−	0.0191535i
$552$	−5.40732	+	1.00083i	−0.230151	+	0.0425980i
$553$	20.2070	−	11.6665i	0.859287	−	0.496110i
$554$	26.0243	−	18.9078i	1.10567	−	0.803314i
$555$	−18.5579	−	2.44779i	−0.787741	−	0.103903i
$556$	−6.52978	+	2.12165i	−0.276924	+	0.0899781i
$557$	31.5183			1.33547			0.667737	−	0.744397i	$-0.267263\pi$
$557$	31.5183			1.33547			0.667737	+	0.744397i	$0.267263\pi$
$558$	−15.0207	+	7.30615i	−0.635875	+	0.309294i
$559$	1.17785			0.0498175
$560$	3.59298	−	1.16743i	0.151831	−	0.0493329i
$561$	−48.0417	−	6.33669i	−2.02832	−	0.267535i
$562$	21.0102	−	15.2648i	0.886264	−	0.643908i
$563$	1.09405	−	0.631649i	0.0461086	−	0.0266208i	−0.476768	−	0.879029i	$-0.658192\pi$
$563$	1.09405	−	0.631649i	0.0461086	−	0.0266208i	0.522877	+	0.852408i	$0.324859\pi$
$564$	−8.35541	+	1.54648i	−0.351826	+	0.0651186i
$565$	0.0507220	+	0.482588i	0.00213389	+	0.0203026i
$566$	−4.97065	+	6.84152i	−0.208932	+	0.287570i
$567$	−13.8596	+	31.0480i	−0.582050	+	1.30389i
$568$	2.04465	−	2.27081i	0.0857914	−	0.0952811i
$569$	−2.09538	−	0.932923i	−0.0878429	−	0.0391102i	0.362345	−	0.932044i	$-0.381976\pi$
$569$	−2.09538	−	0.932923i	−0.0878429	−	0.0391102i	−0.450188	+	0.892934i	$0.648643\pi$
$570$	−0.296811	+	0.161062i	−0.0124321	+	0.00674614i
$571$	−1.50969	−	7.10253i	−0.0631785	−	0.297231i	0.935202	−	0.354114i	$-0.115217\pi$
$571$	−1.50969	−	7.10253i	−0.0631785	−	0.297231i	−0.998381	+	0.0568822i	$0.981884\pi$
$572$	−10.0948	−	22.6733i	−0.422085	−	0.948018i
$573$	18.2310	−	7.54635i	0.761612	−	0.315253i
$574$	−13.2607	+	40.8122i	−0.553491	+	1.70347i
$575$	2.90045	−	1.29136i	0.120957	−	0.0538536i
$576$	−0.155551	−	2.99596i	−0.00648129	−	0.124832i
$577$	−26.5290	−	5.63891i	−1.10442	−	0.234751i	−0.380598	−	0.924741i	$-0.624282\pi$
$577$	−26.5290	−	5.63891i	−1.10442	−	0.234751i	−0.723819	+	0.689990i	$0.757615\pi$
$578$	12.1807	−	27.3582i	0.506649	−	1.13795i
$579$	0.984510	−	37.2508i	0.0409148	−	1.54809i
$580$	−2.30601	−	0.242371i	−0.0957517	−	0.0100639i
$581$	40.9912	+	29.7819i	1.70060	+	1.23556i
$582$	−15.4933	+	16.3185i	−0.642216	+	0.676425i
$583$	−6.82320	+	11.8181i	−0.282588	+	0.489457i
$584$	2.57190	+	4.45465i	0.106426	+	0.184335i
$585$	8.27066	+	16.2516i	0.341950	+	0.671921i
$586$	5.85675	+	6.50458i	0.241940	+	0.268702i
$587$	−1.88101	−	5.78914i	−0.0776375	−	0.238944i	0.904704	−	0.426041i	$-0.140092\pi$
$587$	−1.88101	−	5.78914i	−0.0776375	−	0.238944i	−0.982341	+	0.187097i	$0.940092\pi$
$588$	9.58020	−	8.17823i	0.395081	−	0.337265i
$589$	−1.06571	+	0.206507i	−0.0439120	+	0.00850896i
$590$			11.2150i			0.461713i
$591$	−4.86544	−	2.98317i	−0.200138	−	0.122711i
$592$	8.03134	−	7.23145i	0.330086	−	0.297211i
$593$	12.9128	+	17.7730i	0.530266	+	0.729849i	0.987171	−	0.159667i	$-0.0510420\pi$
$593$	12.9128	+	17.7730i	0.530266	+	0.729849i	−0.456905	+	0.889516i	$0.651042\pi$
$594$	18.6383	+	10.1374i	0.764738	+	0.415941i
$595$	−22.4174	−	12.9427i	−0.919023	−	0.530598i
$596$	−3.79643	+	0.399021i	−0.155508	+	0.0163445i
$597$	−0.0103249	−	0.131599i	−0.000422568	−	0.00538598i
$598$	−2.01724	+	19.1927i	−0.0824910	+	0.784849i
$599$	−5.43492	−	4.89363i	−0.222065	−	0.199948i	0.550587	−	0.834777i	$-0.314404\pi$
$599$	−5.43492	−	4.89363i	−0.222065	−	0.199948i	−0.772652	+	0.634829i	$0.781070\pi$
$600$	0.491525	+	1.66084i	0.0200664	+	0.0678037i
$601$	4.38550	−	20.6321i	0.178888	−	0.841602i	−0.793562	−	0.608490i	$-0.791776\pi$
$601$	4.38550	−	20.6321i	0.178888	−	0.841602i	0.972450	−	0.233113i	$-0.0748910\pi$
$602$	0.716069	−	0.152205i	0.0291848	−	0.00620342i
$603$	−7.59895	−	28.4149i	−0.309453	−	1.15714i
$604$	3.76373	+	1.22291i	0.153144	+	0.0497596i
$605$	5.39467	+	1.75284i	0.219325	+	0.0712629i
$606$	−7.78695	+	16.3155i	−0.316323	+	0.662770i
$607$	8.16587	−	1.73571i	0.331442	−	0.0704503i	−0.0391847	−	0.999232i	$-0.512476\pi$
$607$	8.16587	−	1.73571i	0.331442	−	0.0704503i	0.370627	+	0.928782i	$0.379143\pi$
$608$	0.0405362	−	0.190708i	0.00164396	−	0.00773422i
$609$	−14.5487	+	4.30567i	−0.589542	+	0.174474i
$610$	5.52779	+	4.97725i	0.223814	+	0.201523i
$611$	−3.11704	+	29.6567i	−0.126102	+	1.19978i
$612$	−14.5420	+	14.5278i	−0.587824	+	0.587252i
$613$	28.6072	−	3.00674i	1.15544	−	0.121441i	0.492634	−	0.870237i	$-0.336034\pi$
$613$	28.6072	−	3.00674i	1.15544	−	0.121441i	0.662801	+	0.748795i	$0.269367\pi$
$614$	5.00671	+	2.89062i	0.202054	+	0.116656i
$615$	−18.5441	−	6.57188i	−0.747769	−	0.265004i
$616$	−9.06703	−	12.4797i	−0.365321	−	0.502821i
$617$	−27.2062	+	24.4966i	−1.09528	+	0.986196i	−0.999957	−	0.00925034i	$-0.997055\pi$
$617$	−27.2062	+	24.4966i	−1.09528	+	0.986196i	−0.0953243	+	0.995446i	$0.530389\pi$
$618$	−8.73910	+	14.2531i	−0.351538	+	0.573345i
$619$		−	30.5542i		−	1.22808i	−0.789276	−	0.614038i	$-0.789544\pi$
$619$		−	30.5542i		−	1.22808i	0.789276	−	0.614038i	$-0.210456\pi$
$620$	−0.100428	+	5.56686i	−0.00403328	+	0.223570i
$621$	−8.60965	−	14.0727i	−0.345493	−	0.564718i
$622$	7.22015	+	22.2213i	0.289502	+	0.890995i
$623$	−14.6686	−	16.2911i	−0.587685	−	0.652690i
$624$	−10.2365	−	2.46021i	−0.409790	−	0.0984872i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−2.75493	+	4.77168i	−0.110109	+	0.190715i
$627$	0.999963	+	0.949392i	0.0399347	+	0.0379151i
$628$	−13.7445	−	9.98600i	−0.548467	−	0.398485i
$629$	−73.6435	−	7.74024i	−2.93636	−	0.308624i
$630$	7.12821	+	8.81137i	0.283995	+	0.351053i
$631$	8.15980	−	18.3272i	0.324836	−	0.729595i	−0.675131	−	0.737698i	$-0.735913\pi$
$631$	8.15980	−	18.3272i	0.324836	−	0.729595i	0.999967	+	0.00810345i	$0.00257944\pi$
$632$	−6.04124	−	1.28410i	−0.240308	−	0.0510790i
$633$	−2.01116	+	2.61968i	−0.0799364	+	0.104123i
$634$	11.6288	−	5.17749i	0.461840	−	0.205624i
$635$	−4.89295	+	15.0589i	−0.194171	+	0.597596i
$636$	2.21394	+	5.34860i	0.0877884	+	0.212086i
$637$	−17.9795	−	40.3827i	−0.712375	−	1.60002i
$638$	1.96844	+	9.26079i	0.0779314	+	0.366638i
$639$	8.55656	+	3.28933i	0.338492	+	0.130124i
$640$	−0.913545	−	0.406737i	−0.0361111	−	0.0160777i
$641$	−16.7323	+	18.5831i	−0.660887	+	0.733989i	−0.976647	−	0.214850i	$-0.931074\pi$
$641$	−16.7323	+	18.5831i	−0.660887	+	0.733989i	0.315760	+	0.948839i	$0.397740\pi$
$642$	−11.6749	−	16.9960i	−0.460773	−	0.670778i
$643$	14.1651	−	19.4966i	0.558616	−	0.768869i	−0.432534	−	0.901618i	$-0.642380\pi$
$643$	14.1651	−	19.4966i	0.558616	−	0.768869i	0.991150	+	0.132749i	$0.0423803\pi$
$644$	1.25377	+	11.9289i	0.0494056	+	0.470063i
$645$	0.0610837	+	0.330026i	0.00240517	+	0.0129948i
$646$	−1.15691	+	0.667943i	−0.0455180	+	0.0262799i
$647$	−14.2925	+	10.3841i	−0.561895	+	0.408241i	−0.832152	−	0.554548i	$-0.812891\pi$
$647$	−14.2925	+	10.3841i	−0.561895	+	0.408241i	0.270257	+	0.962788i	$0.412891\pi$
$648$	8.22547	−	3.65263i	0.323127	−	0.143489i
$649$	43.5514	−	14.1507i	1.70954	−	0.555464i
$650$	6.07836			0.238413
$651$	13.3245	+	33.9086i	0.522229	+	1.32898i
$652$	10.0842			0.394929
$653$	5.75041	−	1.86842i	0.225031	−	0.0731169i	−0.194331	−	0.980936i	$-0.562254\pi$
$653$	5.75041	−	1.86842i	0.225031	−	0.0731169i	0.419362	+	0.907819i	$0.362254\pi$
$654$	−2.39713	+	18.1739i	−0.0937352	+	0.710654i
$655$	−3.08990	+	2.24495i	−0.120732	+	0.0877173i
$656$	9.83708	−	5.67944i	0.384073	−	0.221745i
$657$	−9.71711	+	11.9877i	−0.379100	+	0.467685i
$658$	1.93733	+	18.4325i	0.0755251	+	0.718574i
$659$	6.02205	−	8.28864i	0.234586	−	0.322880i	−0.675453	−	0.737403i	$-0.736052\pi$
$659$	6.02205	−	8.28864i	0.234586	−	0.322880i	0.910039	+	0.414524i	$0.136052\pi$
$660$	5.82941	−	4.00436i	0.226909	−	0.155869i
$661$	−12.3972	+	13.7685i	−0.482195	+	0.535531i	−0.934326	−	0.356420i	$-0.883997\pi$
$661$	−12.3972	+	13.7685i	−0.482195	+	0.535531i	0.452131	+	0.891951i	$0.350664\pi$
$662$	18.6804	+	8.31706i	0.726036	+	0.323252i
$663$	34.4050	+	63.4028i	1.33618	+	2.46236i
$664$	−2.78846	−	13.1187i	−0.108213	−	0.509102i
$665$	0.299589	+	0.672888i	0.0116176	+	0.0260935i
$666$	28.8808	+	14.7332i	1.11911	+	0.570900i
$667$	2.27491	−	7.00145i	0.0880849	−	0.271097i
$668$	−9.44282	+	4.20421i	−0.365353	+	0.162666i
$669$	−24.9609	−	19.1628i	−0.965044	−	0.740878i
$670$	−9.59023	−	2.03847i	−0.370503	−	0.0787529i
$671$	12.3535	−	27.7464i	0.476901	−	1.07114i
$672$	−6.54120	−	0.172879i	−0.252332	−	0.00666895i
$673$	28.3449	+	2.97917i	1.09261	+	0.114838i	0.633653	−	0.773618i	$-0.281555\pi$
$673$	28.3449	+	2.97917i	1.09261	+	0.114838i	0.458962	+	0.888456i	$0.348222\pi$
$674$	13.1624	+	9.56303i	0.506996	+	0.368354i
$675$	−4.12469	+	3.16021i	−0.158759	+	0.121637i
$676$	−11.9733	+	20.7383i	−0.460510	+	0.797626i
$677$	6.01713	+	10.4220i	0.231257	+	0.400549i	0.958178	−	0.286172i	$-0.0923828\pi$
$677$	6.01713	+	10.4220i	0.231257	+	0.400549i	−0.726921	+	0.686721i	$0.759049\pi$
$678$	0.196403	−	0.817201i	0.00754280	−	0.0313844i
$679$	32.8411	+	36.4738i	1.26033	+	1.39974i
$680$	2.11733	+	6.51646i	0.0811958	+	0.249895i
$681$	14.0805	+	16.4942i	0.539564	+	0.632060i
$682$	21.7447	−	6.63410i	0.832646	−	0.254033i
$683$			20.8488i			0.797758i	0.917003	+	0.398879i	$0.130601\pi$
$683$			20.8488i			0.797758i	−0.917003	+	0.398879i	$0.869399\pi$
$684$	0.577748	−	0.0912183i	0.0220907	−	0.00348782i
$685$	−12.5748	+	11.3224i	−0.480460	+	0.432608i
$686$	−0.604903	−	0.832578i	−0.0230953	−	0.0317880i
$687$	−9.25477	+	26.1145i	−0.353091	+	0.996330i
$688$	−0.167816	−	0.0968884i	−0.00639791	−	0.00369383i
$689$	20.2033	−	2.12345i	0.769683	−	0.0808969i
$690$	−5.48231	+	0.430126i	−0.208708	+	0.0163746i
$691$	0.706793	−	6.72469i	0.0268877	−	0.255819i	−0.972818	−	0.231570i	$-0.925614\pi$
$691$	0.706793	−	6.72469i	0.0268877	−	0.255819i	0.999706	−	0.0242493i	$-0.00771954\pi$
$692$	1.11204	+	1.00128i	0.0422733	+	0.0380630i
$693$	25.2233	−	38.7991i	0.958153	−	1.47386i
$694$	4.27272	−	20.1016i	0.162190	−	0.763046i
$695$	−6.71578	+	1.42748i	−0.254744	+	0.0541475i
$696$	3.62447	+	1.72987i	0.137385	+	0.0655704i
$697$	−74.0197	−	24.0505i	−2.80370	−	0.910976i
$698$	21.9239	+	7.12351i	0.829832	+	0.269629i
$699$	16.4345	+	7.84376i	0.621610	+	0.296678i
$700$	3.69533	−	0.785466i	0.139670	−	0.0296878i
$701$	4.20247	−	19.7711i	0.158725	−	0.746743i	−0.824721	−	0.565540i	$-0.808668\pi$
$701$	4.20247	−	19.7711i	0.158725	−	0.746743i	0.983446	−	0.181203i	$-0.0579990\pi$
$702$	−4.09971	−	31.3169i	−0.154734	−	1.18198i
$703$	1.56586	+	1.40990i	0.0590574	+	0.0531755i
$704$	−0.426808	+	4.06080i	−0.0160859	+	0.153047i
$705$	−8.47129	+	0.664632i	−0.319047	+	0.0250315i
$706$	10.2873	−	1.08124i	0.387167	−	0.0406928i
$707$	34.1492	+	19.7160i	1.28431	+	0.741498i
$708$	6.48862	−	18.3091i	0.243857	−	0.688100i
$709$	−9.12653	−	12.5616i	−0.342754	−	0.471760i	0.602489	−	0.798127i	$-0.294176\pi$
$709$	−9.12653	−	12.5616i	−0.342754	−	0.471760i	−0.945243	+	0.326367i	$0.894176\pi$
$710$	2.27081	−	2.04465i	0.0852220	−	0.0767342i
$711$	−2.88961	−	18.3019i	−0.108369	−	0.686375i
$712$			5.80268i			0.217465i
$713$	−17.2219	−	3.98661i	−0.644966	−	0.149300i
$714$	29.1095	+	34.0997i	1.08940	+	1.27615i
$715$	−7.66949	−	23.6043i	−0.286823	−	0.882750i
$716$	−10.0080	−	11.1150i	−0.374017	−	0.415387i
$717$	−8.16706	+	33.9819i	−0.305005	+	1.26908i
$718$	−7.25183	−	12.5605i	−0.270636	−	0.468755i
$719$	19.8713	−	34.4182i	0.741076	−	1.28358i	−0.210930	−	0.977501i	$-0.567649\pi$
$719$	19.8713	−	34.4182i	0.741076	−	1.28358i	0.952006	−	0.306080i	$-0.0990175\pi$
$720$	0.158465	−	2.99581i	0.00590563	−	0.111647i
$721$	29.5022	+	21.4346i	1.09872	+	0.798267i
$722$	−18.8581	−	1.98207i	−0.701826	−	0.0737649i
$723$	−18.6387	−	0.492607i	−0.693181	−	0.0183202i
$724$	7.11756	−	15.9863i	0.264522	−	0.594126i
$725$	−2.26804	−	0.482087i	−0.0842328	−	0.0179042i
$726$	−7.79301	−	5.98280i	−0.289226	−	0.222042i
$727$	−3.78705	+	1.68610i	−0.140454	+	0.0625340i	−0.475760	−	0.879575i	$-0.657827\pi$
$727$	−3.78705	+	1.68610i	−0.140454	+	0.0625340i	0.335306	+	0.942109i	$0.391160\pi$
$728$	−7.09607	+	21.8394i	−0.262998	+	0.809424i
$729$	19.0640	+	19.1197i	0.706074	+	0.708138i
$730$	2.09217	+	4.69909i	0.0774346	+	0.173921i
$731$	0.276049	+	1.29871i	0.0102100	+	0.0480344i
$732$	−6.14480	−	11.3239i	−0.227118	−	0.418542i
$733$	22.8799	+	10.1868i	0.845088	+	0.376257i	0.783158	−	0.621823i	$-0.213608\pi$
$733$	22.8799	+	10.1868i	0.845088	+	0.376257i	0.0619303	+	0.998080i	$0.480274\pi$
$734$	−14.3875	+	15.9789i	−0.531051	+	0.589792i
$735$	10.3826	−	7.13203i	0.382967	−	0.263069i
$736$	1.86618	−	2.56858i	0.0687884	−	0.0946792i
$737$	4.18463	+	39.8141i	0.154143	+	1.46657i
$738$	26.4721	+	21.4580i	0.974451	+	0.789880i
$739$	−10.0653	+	5.81119i	−0.370257	+	0.213768i	−0.673571	−	0.739123i	$-0.735240\pi$
$739$	−10.0653	+	5.81119i	−0.370257	+	0.213768i	0.303314	+	0.952891i	$0.401907\pi$
$740$	8.74324	−	6.35233i	0.321408	−	0.233516i
$741$	0.268417	−	2.03501i	0.00986055	−	0.0747578i
$742$	12.0081	−	3.90168i	0.440832	−	0.143235i
$743$	13.7011			0.502645			0.251323	−	0.967903i	$-0.419134\pi$
$743$	13.7011			0.502645			0.251323	+	0.967903i	$0.419134\pi$
$744$	3.38476	−	9.03014i	0.124091	−	0.331061i
$745$	−3.81734			−0.139857
$746$	−20.6053	+	6.69507i	−0.754414	+	0.245124i
$747$	33.7547	−	21.8972i	1.23502	−	0.801178i
$748$	22.6340	−	16.4445i	0.827580	−	0.601272i
$749$	−38.9492	+	22.4873i	−1.42317	+	0.821670i
$750$	0.315227	+	1.70312i	0.0115105	+	0.0621893i
$751$	−3.15257	−	29.9947i	−0.115039	−	1.09452i	−0.887929	−	0.459981i	$-0.847856\pi$
$751$	−3.15257	−	29.9947i	−0.115039	−	1.09452i	0.772890	−	0.634540i	$-0.218810\pi$
$752$	2.88363	−	3.96898i	0.105155	−	0.144734i
$753$	−26.0563	−	37.9320i	−0.949546	−	1.38232i
$754$	9.43069	−	10.4738i	0.343446	−	0.381435i
$755$	3.61529	+	1.60963i	0.131574	+	0.0585804i
$756$	−6.53928	−	18.5093i	−0.237831	−	0.673175i
$757$	2.50848	+	11.8015i	0.0911724	+	0.428932i	0.999933	+	0.0116136i	$0.00369681\pi$
$757$	2.50848	+	11.8015i	0.0911724	+	0.428932i	−0.908760	+	0.417319i	$0.862970\pi$
$758$	7.49292	+	16.8294i	0.272155	+	0.611270i
$759$	8.58774	+	20.7469i	0.311715	+	0.753065i
$760$	0.0602485	−	0.185426i	0.00218544	−	0.00672610i
$761$	−18.7679	+	8.35601i	−0.680336	+	0.302905i	−0.717656	−	0.696398i	$-0.754785\pi$
$761$	−18.7679	+	8.35601i	−0.680336	+	0.302905i	0.0373193	+	0.999303i	$0.488118\pi$
$762$	16.7007	−	21.7538i	0.605001	−	0.788056i
$763$	39.1097	+	8.31303i	1.41587	+	0.300952i
$764$	−4.63345	+	10.4069i	−0.167632	+	0.376509i
$765$	−15.9809	+	12.9282i	−0.577789	+	0.467419i
$766$	15.7238	+	1.65264i	0.568126	+	0.0597124i
$767$	−55.1496	−	40.0685i	−1.99134	−	1.44679i
$768$	1.25610	+	1.19257i	0.0453254	+	0.0430332i
$769$	−1.01455	+	1.75725i	−0.0365855	+	0.0633680i	−0.883738	−	0.467981i	$-0.844981\pi$
$769$	−1.01455	+	1.75725i	−0.0365855	+	0.0633680i	0.847153	+	0.531349i	$0.178315\pi$
$770$	−7.71288	−	13.3591i	−0.277953	−	0.481428i
$771$	19.1882	+	4.61162i	0.691047	+	0.166084i
$772$	14.3958	+	15.9882i	0.518118	+	0.575428i
$773$	−5.59205	−	17.2106i	−0.201132	−	0.619021i	−0.999850

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(-1.71718 - 0.226496i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.70312 + 0.315227i) q^{6} +(0.394896 + 3.75719i) q^{7} +(0.587785 - 0.809017i) q^{8} +(2.89740 + 0.777866i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(-1.71718 - 0.226496i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.70312 + 0.315227i) q^{6} +(0.394896 + 3.75719i) q^{7} +(0.587785 - 0.809017i) q^{8} +(2.89740 + 0.777866i) q^{9} +(0.669131 - 0.743145i) q^{10} +(-3.73016 - 1.66078i) q^{11} +(-1.52236 + 0.826093i) q^{12} +(1.26376 + 5.94554i) q^{13} +(1.53660 + 3.45127i) q^{14} +(-1.60037 + 0.662438i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-6.25944 + 2.78688i) q^{17} +(2.99596 - 0.155551i) q^{18} +(0.190708 + 0.0405362i) q^{19} +(0.406737 - 0.913545i) q^{20} +(0.172879 - 6.54120i) q^{21} +(-4.06080 - 0.426808i) q^{22} +(2.56858 + 1.86618i) q^{23} +(-1.19257 + 1.25610i) q^{24} +(0.500000 - 0.866025i) q^{25} +(3.03918 + 5.26402i) q^{26} +(-4.79917 - 1.99198i) q^{27} +(2.52790 + 2.80751i) q^{28} +(-0.716520 - 2.20522i) q^{29} +(-1.31734 + 1.12456i) q^{30} +(-5.12643 + 2.17250i) q^{31} -1.00000i q^{32} +(6.02920 + 3.69671i) q^{33} +(-5.09189 + 4.58476i) q^{34} +(2.22058 + 3.05637i) q^{35} +(2.80126 - 1.07374i) q^{36} +(9.35934 + 5.40362i) q^{37} +(0.193900 - 0.0203797i) q^{38} +(-0.823468 - 10.4958i) q^{39} +(0.104528 - 0.994522i) q^{40} +(8.44129 + 7.60057i) q^{41} +(-1.85693 - 6.27448i) q^{42} +(0.0402884 - 0.189542i) q^{43} +(-3.99395 + 0.848939i) q^{44} +(2.89815 - 0.775048i) q^{45} +(3.01955 + 0.981111i) q^{46} +(4.66582 + 1.51602i) q^{47} +(-0.746047 + 1.56314i) q^{48} +(-7.11349 + 1.51202i) q^{49} +(0.207912 - 0.978148i) q^{50} +(11.3798 - 3.36784i) q^{51} +(4.51710 + 4.06722i) q^{52} +(0.349345 - 3.32380i) q^{53} +(-5.17984 - 0.411464i) q^{54} +(-4.06080 + 0.426808i) q^{55} +(3.27174 + 1.88894i) q^{56} +(-0.318298 - 0.112802i) q^{57} +(-1.36290 - 1.87587i) q^{58} +(-8.33435 + 7.50428i) q^{59} +(-0.905353 + 1.47660i) q^{60} +7.43838i q^{61} +(-4.20418 + 3.65032i) q^{62} +(-1.77842 + 11.1933i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(4.06722 + 4.51710i) q^{65} +(6.87645 + 1.65266i) q^{66} +(-4.90224 - 8.49093i) q^{67} +(-3.42591 + 5.93384i) q^{68} +(-3.98803 - 3.78634i) q^{69} +(3.05637 + 2.22058i) q^{70} +(3.03894 + 0.319405i) q^{71} +(2.33236 - 1.88683i) q^{72} +(-2.09217 + 4.69909i) q^{73} +(10.5711 + 2.24695i) q^{74} +(-1.05474 + 1.37387i) q^{75} +(0.178112 - 0.0793007i) q^{76} +(4.76682 - 14.6708i) q^{77} +(-4.02654 - 9.72762i) q^{78} +(-2.51209 - 5.64224i) q^{79} +(-0.207912 - 0.978148i) q^{80} +(7.78985 + 4.50758i) q^{81} +(10.3769 + 4.62007i) q^{82} +(8.97420 - 9.96686i) q^{83} +(-3.70496 - 5.39356i) q^{84} +(-4.02739 + 5.54323i) q^{85} +(-0.0202552 - 0.192715i) q^{86} +(0.730920 + 3.94905i) q^{87} +(-3.53613 + 2.04159i) q^{88} +(-4.69447 + 3.41073i) q^{89} +(2.51681 - 1.63269i) q^{90} +(-21.8394 + 7.09607i) q^{91} +3.17494 q^{92} +(9.29505 - 2.56946i) q^{93} +4.90593 q^{94} +(0.185426 - 0.0602485i) q^{95} +(-0.226496 + 1.71718i) q^{96} +(10.5103 - 7.63620i) q^{97} +(-6.29809 + 3.63620i) q^{98} +(-9.51591 - 7.71350i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176q + 44q^{4} + 4q^{7} + 4q^{9} + O(q^{10}) \)	\( 176q + 44q^{4} + 4q^{7} + 4q^{9} + 22q^{10} + 38q^{13} - 44q^{16} + 4q^{18} + 8q^{19} - 42q^{21} + 4q^{22} + 88q^{25} + 30q^{27} + 36q^{28} + 32q^{31} - 70q^{33} + 14q^{34} - 4q^{36} + 42q^{37} + 58q^{39} - 22q^{40} - 12q^{42} - 46q^{43} + 16q^{45} + 10q^{46} + 38q^{49} + 38q^{51} + 2q^{52} + 4q^{55} + 78q^{57} - 40q^{58} + 16q^{63} + 44q^{64} + 34q^{66} - 76q^{67} + 148q^{69} - 8q^{70} - 4q^{72} - 52q^{73} + 12q^{76} + 60q^{78} + 8q^{79} - 108q^{81} - 40q^{82} - 8q^{84} + 28q^{87} + 6q^{88} + 24q^{90} - 20q^{91} - 28q^{93} - 20q^{94} - 112q^{97} - 132q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

Downloads

Learn more about