LMFDB - Embedded newform 375.2.l.a.107.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [375,2,Mod(32,375)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("375.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(375, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.l (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [64,0,0,20,0,-6,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			107.4
Character	$\chi$	$=$	375.107
Dual form			375.2.l.a.368.4

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0455229 - 0.0231951i) q^{2} +(-1.41200 + 1.00313i) q^{3} +(-1.17404 - 1.61592i) q^{4} +(0.0875458 - 0.0129140i) q^{6} +(1.44136 + 1.44136i) q^{7} +(0.0319491 + 0.201718i) q^{8} +(0.987463 - 2.83283i) q^{9} +(-2.86751 + 0.931709i) q^{11} +(3.27871 + 1.10396i) q^{12} +(1.42294 + 2.79268i) q^{13} +(-0.0321825 - 0.0990475i) q^{14} +(-1.23123 + 3.78934i) q^{16} +(-6.01096 + 0.952042i) q^{17} +(-0.110660 + 0.106054i) q^{18} +(-1.91085 + 2.63007i) q^{19} +(-3.48107 - 0.589324i) q^{21} +(0.152148 + 0.0240979i) q^{22} +(-2.61153 + 5.12542i) q^{23} +(-0.247462 - 0.252776i) q^{24} -0.160136i q^{26} +(1.44740 + 4.99049i) q^{27} +(0.636918 - 4.02134i) q^{28} +(-0.976916 + 0.709771i) q^{29} +(-0.0161330 - 0.0117213i) q^{31} +(0.432772 - 0.432772i) q^{32} +(3.11428 - 4.19205i) q^{33} +(0.295719 + 0.0960849i) q^{34} +(-5.73695 + 1.73018i) q^{36} +(-2.44005 + 1.24327i) q^{37} +(0.147992 - 0.0754058i) q^{38} +(-4.81061 - 2.51586i) q^{39} +(10.1904 + 3.31106i) q^{41} +(0.144799 + 0.107571i) q^{42} +(-3.91319 + 3.91319i) q^{43} +(4.87212 + 3.53981i) q^{44} +(0.237769 - 0.172749i) q^{46} +(0.575694 - 3.63479i) q^{47} +(-2.06270 - 6.58561i) q^{48} -2.84495i q^{49} +(7.53242 - 7.37405i) q^{51} +(2.84217 - 5.57807i) q^{52} +(-4.01189 - 0.635421i) q^{53} +(0.0498650 - 0.260754i) q^{54} +(-0.244699 + 0.336799i) q^{56} +(0.0598219 - 5.63047i) q^{57} +(0.0609353 - 0.00965120i) q^{58} +(-1.33548 + 4.11017i) q^{59} +(-3.99489 - 12.2950i) q^{61} +(0.000462544 + 0.000907794i) q^{62} +(5.50642 - 2.65984i) q^{63} +(7.54893 - 2.45280i) q^{64} +(-0.239006 + 0.118598i) q^{66} +(-0.145768 - 0.920343i) q^{67} +(8.59551 + 8.59551i) q^{68} +(-1.45399 - 9.85678i) q^{69} +(5.79154 + 7.97137i) q^{71} +(0.602982 + 0.108683i) q^{72} +(-0.0348503 - 0.0177571i) q^{73} +0.139916 q^{74} +6.49339 q^{76} +(-5.47604 - 2.79018i) q^{77} +(0.160637 + 0.226112i) q^{78} +(6.00647 + 8.26720i) q^{79} +(-7.04983 - 5.59463i) q^{81} +(-0.387096 - 0.387096i) q^{82} +(-0.344039 - 2.17217i) q^{83} +(3.13460 + 6.31702i) q^{84} +(0.268906 - 0.0873730i) q^{86} +(0.667409 - 1.98217i) q^{87} +(-0.279557 - 0.548661i) q^{88} +(4.18096 + 12.8677i) q^{89} +(-1.97429 + 6.07624i) q^{91} +(11.3483 - 1.79740i) q^{92} +(0.0345377 + 0.000366951i) q^{93} +(-0.110516 + 0.152113i) q^{94} +(-0.176946 + 1.04520i) q^{96} +(-5.29507 - 0.838657i) q^{97} +(-0.0659889 + 0.129510i) q^{98} +(-0.192183 + 9.04318i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 20 q^{4} - 6 q^{6} - 20 q^{7} + 10 q^{9} - 40 q^{12} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 30 q^{27} + 80 q^{28} - 12 q^{31} + 50 q^{33} - 20 q^{34} - 22 q^{36} + 120 q^{37} - 30 q^{39} - 60 q^{42}+ \cdots + 42 q^{96}+O(q^{100}) $ 64 * q + 20 * q^4 - 6 * q^6 - 20 * q^7 + 10 * q^9 - 40 * q^12 - 8 * q^16 - 10 * q^18 - 6 * q^21 + 30 * q^27 + 80 * q^28 - 12 * q^31 + 50 * q^33 - 20 * q^34 - 22 * q^36 + 120 * q^37 - 30 * q^39 - 60 * q^42 - 20 * q^43 - 12 * q^46 - 100 * q^48 - 16 * q^51 - 100 * q^52 - 120 * q^54 + 70 * q^57 - 120 * q^58 - 12 * q^61 + 70 * q^63 + 100 * q^64 - 30 * q^66 + 60 * q^67 + 80 * q^69 + 40 * q^72 + 80 * q^73 - 64 * q^76 - 70 * q^78 + 60 * q^79 + 14 * q^81 - 60 * q^82 + 130 * q^84 - 100 * q^87 - 60 * q^88 - 12 * q^91 - 20 * q^93 - 260 * q^94 + 42 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$-1$

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 $

$2$	−0.0455229	−	0.0231951i	−0.0321896	−	0.0164014i	0.437822	−	0.899062i	$-0.355750\pi$
$2$	−0.0455229	−	0.0231951i	−0.0321896	−	0.0164014i	−0.470011	+	0.882660i	$0.655750\pi$
$3$	−1.41200	+	1.00313i	−0.815216	+	0.579157i
$3$	−1.41200	+	1.00313i	−0.815216	+	0.579157i
$4$	−1.17404	−	1.61592i	−0.587018	−	0.807961i
$5$		0			0
$5$		0			0
$6$	0.0875458	−	0.0129140i	0.0357404	−	0.00527213i
$7$	1.44136	+	1.44136i	0.544784	+	0.544784i	0.924927	−	0.380144i	$-0.124125\pi$
$7$	1.44136	+	1.44136i	0.544784	+	0.544784i	−0.380144	+	0.924927i	$0.624125\pi$
$8$	0.0319491	+	0.201718i	0.0112957	+	0.0713182i
$9$	0.987463	−	2.83283i	0.329154	−	0.944276i
$10$		0			0
$11$	−2.86751	+	0.931709i	−0.864586	+	0.280921i	−0.707542	−	0.706671i	$-0.750196\pi$
$11$	−2.86751	+	0.931709i	−0.864586	+	0.280921i	−0.157043	+	0.987592i	$0.550196\pi$
$12$	3.27871	+	1.10396i	0.946483	+	0.318687i
$13$	1.42294	+	2.79268i	0.394653	+	0.774551i	0.999767	−	0.0215884i	$-0.00687233\pi$
$13$	1.42294	+	2.79268i	0.394653	+	0.774551i	−0.605114	+	0.796139i	$0.706872\pi$
$14$	−0.0321825	−	0.0990475i	−0.00860113	−	0.0264716i
$15$		0			0
$16$	−1.23123	+	3.78934i	−0.307808	+	0.947334i
$17$	−6.01096	+	0.952042i	−1.45787	+	0.230904i	−0.834494	−	0.551017i	$-0.814240\pi$
$17$	−6.01096	+	0.952042i	−1.45787	+	0.230904i	−0.623377	+	0.781921i	$0.714240\pi$
$18$	−0.110660	+	0.106054i	−0.0260828	+	0.0249972i
$19$	−1.91085	+	2.63007i	−0.438380	+	0.603378i	−0.969851	−	0.243698i	$-0.921639\pi$
$19$	−1.91085	+	2.63007i	−0.438380	+	0.603378i	0.531471	+	0.847076i	$0.321639\pi$
$20$		0			0
$21$	−3.48107	−	0.589324i	−0.759632	−	0.128601i
$22$	0.152148	+	0.0240979i	0.0324381	+	0.00513769i
$23$	−2.61153	+	5.12542i	−0.544542	+	1.06872i	0.440716	+	0.897647i	$0.354725\pi$
$23$	−2.61153	+	5.12542i	−0.544542	+	1.06872i	−0.985258	+	0.171077i	$0.945275\pi$
$24$	−0.247462	−	0.252776i	−0.0505129	−	0.0515978i
$25$		0			0
$26$		−	0.160136i		−	0.0314053i
$27$	1.44740	+	4.99049i	0.278552	+	0.960421i
$28$	0.636918	−	4.02134i	0.120366	−	0.759962i
$29$	−0.976916	+	0.709771i	−0.181409	+	0.131801i	−0.674784	−	0.738016i	$-0.735763\pi$
$29$	−0.976916	+	0.709771i	−0.181409	+	0.131801i	0.493375	+	0.869817i	$0.335763\pi$
$30$		0			0
$31$	−0.0161330	−	0.0117213i	−0.00289757	−	0.00210521i	0.586336	−	0.810068i	$-0.300570\pi$
$31$	−0.0161330	−	0.0117213i	−0.00289757	−	0.00210521i	−0.589233	+	0.807963i	$0.700570\pi$
$32$	0.432772	−	0.432772i	0.0765040	−	0.0765040i
$33$	3.11428	−	4.19205i	0.542127	−	0.729742i
$34$	0.295719	+	0.0960849i	0.0507154	+	0.0164784i
$35$		0			0
$36$	−5.73695	+	1.73018i	−0.956158	+	0.288363i
$37$	−2.44005	+	1.24327i	−0.401142	+	0.204392i	−0.642910	−	0.765942i	$-0.722273\pi$
$37$	−2.44005	+	1.24327i	−0.401142	+	0.204392i	0.241767	+	0.970334i	$0.422273\pi$
$38$	0.147992	−	0.0754058i	0.0240075	−	0.0122324i
$39$	−4.81061	−	2.51586i	−0.770314	−	0.402860i
$40$		0			0
$41$	10.1904	+	3.31106i	1.59147	+	0.517100i	0.964979	−	0.262328i	$-0.0844903\pi$
$41$	10.1904	+	3.31106i	1.59147	+	0.517100i	0.626491	+	0.779428i	$0.284490\pi$
$42$	0.144799	+	0.107571i	0.0223430	+	0.0165986i
$43$	−3.91319	+	3.91319i	−0.596755	+	0.596755i	−0.939448	−	0.342692i	$-0.888661\pi$
$43$	−3.91319	+	3.91319i	−0.596755	+	0.596755i	0.342692	+	0.939448i	$0.388661\pi$
$44$	4.87212	+	3.53981i	0.734500	+	0.533646i
$45$		0			0
$46$	0.237769	−	0.172749i	0.0350571	−	0.0254705i
$47$	0.575694	−	3.63479i	0.0839735	−	0.530188i	−0.909461	−	0.415789i	$-0.863506\pi$
$47$	0.575694	−	3.63479i	0.0839735	−	0.530188i	0.993435	−	0.114399i	$-0.0364944\pi$
$48$	−2.06270	−	6.58561i	−0.297726	−	0.950551i
$49$		−	2.84495i		−	0.406422i
$50$		0			0
$51$	7.53242	−	7.37405i	1.05475	−	1.03257i
$52$	2.84217	−	5.57807i	0.394138	−	0.773540i
$53$	−4.01189	−	0.635421i	−0.551075	−	0.0872818i	−0.125314	−	0.992117i	$-0.539994\pi$
$53$	−4.01189	−	0.635421i	−0.551075	−	0.0872818i	−0.425762	+	0.904835i	$0.639994\pi$
$54$	0.0498650	−	0.260754i	0.00678577	−	0.0354842i
$55$		0			0
$56$	−0.244699	+	0.336799i	−0.0326993	+	0.0450067i
$57$	0.0598219	−	5.63047i	0.00792360	−	0.745775i
$58$	0.0609353	−	0.00965120i	0.00800119	−	0.00126726i
$59$	−1.33548	+	4.11017i	−0.173864	+	0.535099i	−0.999580	−	0.0289879i	$-0.990772\pi$
$59$	−1.33548	+	4.11017i	−0.173864	+	0.535099i	0.825716	+	0.564087i	$0.190772\pi$
$60$		0			0
$61$	−3.99489	−	12.2950i	−0.511493	−	1.57421i	−0.789574	−	0.613656i	$-0.789698\pi$
$61$	−3.99489	−	12.2950i	−0.511493	−	1.57421i	0.278081	−	0.960558i	$-0.410302\pi$
$62$	0.000462544	0	0.000907794i	5.87432e−5	0	0.000115290i
$63$	5.50642	−	2.65984i	0.693744	−	0.335108i
$64$	7.54893	−	2.45280i	0.943617	−	0.306600i
$65$		0			0
$66$	−0.239006	+	0.118598i	−0.0294196	+	0.0145984i
$67$	−0.145768	−	0.920343i	−0.0178084	−	0.112438i	0.977183	−	0.212400i	$-0.0681279\pi$
$67$	−0.145768	−	0.920343i	−0.0178084	−	0.112438i	−0.994991	+	0.0999620i	$0.968128\pi$
$68$	8.59551	+	8.59551i	1.04236	+	1.04236i
$69$	−1.45399	−	9.85678i	−0.175040	−	1.18662i
$70$		0			0
$71$	5.79154	+	7.97137i	0.687329	+	0.946028i	0.999993	−	0.00383630i	$-0.00122113\pi$
$71$	5.79154	+	7.97137i	0.687329	+	0.946028i	−0.312663	+	0.949864i	$0.601221\pi$
$72$	0.602982	+	0.108683i	0.0710621	+	0.0128084i
$73$	−0.0348503	−	0.0177571i	−0.00407891	−	0.00207831i	0.451950	−	0.892043i	$-0.350729\pi$
$73$	−0.0348503	−	0.0177571i	−0.00407891	−	0.00207831i	−0.456029	+	0.889965i	$0.650729\pi$
$74$	0.139916			0.0162649
$75$		0			0
$76$	6.49339			0.744843
$77$	−5.47604	−	2.79018i	−0.624053	−	0.317971i
$78$	0.160637	+	0.226112i	0.0181886	+	0.0256021i
$79$	6.00647	+	8.26720i	0.675781	+	0.930133i	0.999874	−	0.0158924i	$-0.00505893\pi$
$79$	6.00647	+	8.26720i	0.675781	+	0.930133i	−0.324093	+	0.946025i	$0.605059\pi$
$80$		0			0
$81$	−7.04983	−	5.59463i	−0.783315	−	0.621625i
$82$	−0.387096	−	0.387096i	−0.0427476	−	0.0427476i
$83$	−0.344039	−	2.17217i	−0.0377632	−	0.238427i	0.961586	−	0.274504i	$-0.0885138\pi$
$83$	−0.344039	−	2.17217i	−0.0377632	−	0.238427i	−0.999349	+	0.0360772i	$0.988514\pi$
$84$	3.13460	+	6.31702i	0.342013	+	0.689244i
$85$		0			0
$86$	0.268906	−	0.0873730i	0.0289969	−	0.00942167i
$87$	0.667409	−	1.98217i	0.0715538	−	0.212511i
$88$	−0.279557	−	0.548661i	−0.0298009	−	0.0584875i
$89$	4.18096	+	12.8677i	0.443181	+	1.36397i	0.884466	+	0.466604i	$0.154523\pi$
$89$	4.18096	+	12.8677i	0.443181	+	1.36397i	−0.441285	+	0.897367i	$0.645477\pi$
$90$		0			0
$91$	−1.97429	+	6.07624i	−0.206962	+	0.636963i
$92$	11.3483	−	1.79740i	1.18314	−	0.187392i
$93$	0.0345377		0.000366951i	0.00358139		3.80511e-5i
$94$	−0.110516	+	0.152113i	−0.0113989	+	0.0156892i
$95$		0			0
$96$	−0.176946	+	1.04520i	−0.0180595	+	0.106675i
$97$	−5.29507	−	0.838657i	−0.537633	−	0.0851527i	−0.118287	−	0.992979i	$-0.537740\pi$
$97$	−5.29507	−	0.838657i	−0.537633	−	0.0851527i	−0.419346	+	0.907827i	$0.637740\pi$
$98$	−0.0659889	+	0.129510i	−0.00666588	+	0.0130825i
$99$	−0.192183	+	9.04318i	−0.0193151	+	0.908874i
$100$		0			0
$101$		−	12.2476i		−	1.21869i	−0.792907	−	0.609343i	$-0.791433\pi$
$101$		−	12.2476i		−	1.21869i	0.792907	−	0.609343i	$-0.208567\pi$
$102$	−0.513939	+	0.160973i	−0.0508876	+	0.0159387i
$103$	2.62854	−	16.5959i	0.258998	−	1.63525i	−0.424596	−	0.905383i	$-0.639584\pi$
$103$	2.62854	−	16.5959i	0.258998	−	1.63525i	0.683593	−	0.729863i	$-0.260416\pi$
$104$	−0.517874	+	0.376257i	−0.0507817	+	0.0368951i
$105$		0			0
$106$	0.167894	+	0.121982i	0.0163073	+	0.0118480i
$107$	−3.55622	+	3.55622i	−0.343793	+	0.343793i	−0.857791	−	0.513998i	$-0.828164\pi$
$107$	−3.55622	+	3.55622i	−0.343793	+	0.343793i	0.513998	+	0.857791i	$0.328164\pi$
$108$	6.36495	−	8.19791i	0.612468	−	0.788844i
$109$	−9.79911	−	3.18392i	−0.938585	−	0.304965i	−0.200516	−	0.979690i	$-0.564262\pi$
$109$	−9.79911	−	3.18392i	−0.938585	−	0.304965i	−0.738069	+	0.674726i	$0.764262\pi$
$110$		0			0
$111$	2.19818	−	4.20318i	0.208642	−	0.398948i
$112$	−7.23645	+	3.68716i	−0.683781	+	0.348404i
$113$	7.79680	−	3.97267i	0.733462	−	0.373717i	−0.0470217	−	0.998894i	$-0.514973\pi$
$113$	7.79680	−	3.97267i	0.733462	−	0.373717i	0.780483	+	0.625176i	$0.214973\pi$
$114$	−0.133323	+	0.254928i	−0.0124868	+	0.0238762i
$115$		0			0
$116$	2.29387	+	0.745324i	0.212980	+	0.0692016i
$117$	9.31629	−	1.27328i	0.861292	−	0.117715i
$118$	0.156130	−	0.156130i	0.0143730	−	0.0143730i
$119$	−10.0362	−	7.29173i	−0.920017	−	0.668432i
$120$		0			0
$121$	−1.54468	+	1.12228i	−0.140425	+	0.102025i
$122$	−0.103325	+	0.652366i	−0.00935457	+	0.0590624i
$123$	−17.7102	+	5.54708i	−1.59687	+	0.500163i
$124$			0.0398309i			0.00357692i
$125$		0			0
$126$	−0.312364	−	0.00663826i	−0.0278276	−	0.000591383i
$127$	−1.58496	+	3.11066i	−0.140642	+	0.276026i	−0.950574	−	0.310498i	$-0.899504\pi$
$127$	−1.58496	+	3.11066i	−0.140642	+	0.276026i	0.809932	+	0.586524i	$0.199504\pi$
$128$	−1.60954	−	0.254925i	−0.142264	−	0.0225324i
$129$	1.59997	−	9.45084i	0.140869	−	0.832100i
$130$		0			0
$131$	−4.58971	+	6.31720i	−0.401005	+	0.551936i	−0.960996	−	0.276563i	$-0.910805\pi$
$131$	−4.58971	+	6.31720i	−0.401005	+	0.551936i	0.559991	+	0.828499i	$0.310805\pi$
$132$	−10.4303	−	0.110818i	−0.907841	−	0.00964550i
$133$	−6.54511	+	1.03664i	−0.567533	+	0.0898884i
$134$	−0.0147116	+	0.0452778i	−0.00127089	+	0.00391140i
$135$		0			0
$136$	−0.384089	−	1.18210i	−0.0329353	−	0.101365i
$137$	−4.50142	−	8.83454i	−0.384583	−	0.754786i	0.614844	−	0.788649i	$-0.289219\pi$
$137$	−4.50142	−	8.83454i	−0.384583	−	0.754786i	−0.999426	+	0.0338629i	$0.989219\pi$
$138$	−0.162439	+	0.482434i	−0.0138277	+	0.0410675i
$139$	−4.81723	+	1.56521i	−0.408592	+	0.132760i	−0.506100	−	0.862475i	$-0.668913\pi$
$139$	−4.81723	+	1.56521i	−0.408592	+	0.132760i	0.0975070	+	0.995235i	$0.468913\pi$
$140$		0			0
$141$	2.83328	+	5.70980i	0.238606	+	0.480852i
$142$	−0.0787512	−	0.497215i	−0.00660865	−	0.0417254i
$143$	−6.68226	−	6.68226i	−0.558799	−	0.558799i
$144$	9.51875	+	7.22969i	0.793229	+	0.602474i
$145$		0			0
$146$	0.00117461	+	0.00161671i	9.72113e−5	+	0.000133800i
$147$	2.85385	+	4.01706i	0.235382	+	0.331321i
$148$	4.87374	+	2.48329i	0.400619	+	0.204125i
$149$	2.08572			0.170869			0.0854344	−	0.996344i	$-0.472772\pi$
$149$	2.08572			0.170869			0.0854344	+	0.996344i	$0.472772\pi$
$150$		0			0
$151$	3.13158			0.254844			0.127422	−	0.991849i	$-0.459330\pi$
$151$	3.13158			0.254844			0.127422	+	0.991849i	$0.459330\pi$
$152$	−0.591583	−	0.301426i	−0.0479837	−	0.0244489i
$153$	−3.23862	+	17.9681i	−0.261827	+	1.45264i
$154$	0.184567	+	0.254035i	0.0148728	+	0.0204707i
$155$		0			0
$156$	1.58240	+	10.7273i	0.126693	+	0.858870i
$157$	4.55824	+	4.55824i	0.363787	+	0.363787i	0.865205	−	0.501418i	$-0.167188\pi$
$157$	4.55824	+	4.55824i	0.363787	+	0.363787i	−0.501418	+	0.865205i	$0.667188\pi$
$158$	−0.0816737	−	0.515668i	−0.00649761	−	0.0410243i
$159$	6.30218	−	3.12723i	0.499795	−	0.248006i
$160$		0			0
$161$	−11.1517	+	3.62342i	−0.878881	+	0.285566i
$162$	0.191161	+	0.418205i	0.0150190	+	0.0328573i
$163$	8.30047	+	16.2906i	0.650143	+	1.27598i	0.947055	+	0.321072i	$0.104043\pi$
$163$	8.30047	+	16.2906i	0.650143	+	1.27598i	−0.296912	+	0.954905i	$0.595957\pi$
$164$	−6.61347	−	20.3542i	−0.516425	−	1.58939i
$165$		0			0
$166$	−0.0347221	+	0.106864i	−0.00269496	+	0.00829423i
$167$	−1.24845	+	0.197736i	−0.0966082	+	0.0153012i	−0.204551	−	0.978856i	$-0.565574\pi$
$167$	−1.24845	+	0.197736i	−0.0966082	+	0.0153012i	0.107943	+	0.994157i	$0.465574\pi$
$168$	0.00766063	−	0.721024i	0.000591031	−	0.0556282i
$169$	1.86690	−	2.56957i	0.143608	−	0.197659i
$170$		0			0
$171$	5.56363	+	8.01021i	0.425461	+	0.612556i
$172$	10.9176	+	1.72918i	0.832461	+	0.131849i
$173$	0.940691	−	1.84621i	0.0715194	−	0.140365i	−0.852478	−	0.522762i	$-0.824902\pi$
$173$	0.940691	−	1.84621i	0.0715194	−	0.140365i	0.923998	+	0.382398i	$0.124902\pi$
$174$	−0.0763589	+	0.0747534i	−0.00578876	+	0.00566704i
$175$		0			0
$176$		−	12.0131i		−	0.905521i
$177$	−2.23735	−	7.14320i	−0.168169	−	0.536916i
$178$	0.108137	−	0.682752i	0.00810523	−	0.0511744i
$179$	4.10633	−	2.98343i	0.306922	−	0.222992i	−0.423653	−	0.905825i	$-0.639252\pi$
$179$	4.10633	−	2.98343i	0.306922	−	0.222992i	0.730575	+	0.682833i	$0.239252\pi$
$180$		0			0
$181$	0.846389	+	0.614938i	0.0629116	+	0.0457080i	0.618797	−	0.785551i	$-0.287621\pi$
$181$	0.846389	+	0.614938i	0.0629116	+	0.0457080i	−0.555885	+	0.831259i	$0.687621\pi$
$182$	0.230814	−	0.230814i	0.0171091	−	0.0171091i
$183$	17.9742	+	13.3531i	1.32869	+	0.987089i
$184$	−1.11733	−	0.363042i	−0.0823705	−	0.0267638i
$185$		0			0
$186$	−0.00156374		0.000817809i	−0.000114659		5.99647e-5i
$187$	16.3494	−	8.33045i	1.19559	−	0.609183i
$188$	−6.54942	+	3.33709i	−0.477665	+	0.243383i
$189$	−5.10688	+	9.27934i	−0.371471	+	0.674972i
$190$		0			0
$191$	−18.0007	−	5.84879i	−1.30249	−	0.423204i	−0.426041	−	0.904704i	$-0.640092\pi$
$191$	−18.0007	−	5.84879i	−1.30249	−	0.423204i	−0.876446	+	0.481500i	$0.840092\pi$
$192$	−8.19859	+	11.0359i	−0.591682	+	0.796447i
$193$	−7.84492	+	7.84492i	−0.564690	+	0.564690i	−0.930636	−	0.365946i	$-0.880745\pi$
$193$	−7.84492	+	7.84492i	−0.564690	+	0.564690i	0.365946	+	0.930636i	$0.380745\pi$
$194$	0.221594	+	0.160998i	0.0159095	+	0.0115590i
$195$		0			0
$196$	−4.59722	+	3.34008i	−0.328373	+	0.238577i
$197$	−3.94049	+	24.8793i	−0.280748	+	1.77257i	0.295543	+	0.955329i	$0.404499\pi$
$197$	−3.94049	+	24.8793i	−0.280748	+	1.77257i	−0.576291	+	0.817244i	$0.695501\pi$
$198$	0.218506	−	0.407214i	0.0155285	−	0.0289394i
$199$		−	16.1153i		−	1.14238i	−0.820817	−	0.571191i	$-0.806482\pi$
$199$		−	16.1153i		−	1.14238i	0.820817	−	0.571191i	$-0.193518\pi$
$200$		0			0
$201$	1.12905	+	1.15330i	0.0796368	+	0.0813472i
$202$	−0.284085	+	0.557548i	−0.0199882	+	0.0392290i
$203$	−2.43113	−	0.385053i	−0.170632	−	0.0270254i
$204$	−20.7592	−	3.51441i	−1.45344	−	0.246058i
$205$		0			0
$206$	−0.504603	+	0.694526i	−0.0351573	+	0.0483899i
$207$	11.9406	+	12.4592i	0.829932	+	0.865973i
$208$	−12.3344	+	1.95357i	−0.855236	+	0.135456i
$209$	3.02893	−	9.32209i	0.209515	−	0.644822i
$210$		0			0
$211$	4.91691	+	15.1327i	0.338494	+	1.04178i	0.964975	+	0.262341i	$0.0844944\pi$
$211$	4.91691	+	15.1327i	0.338494	+	1.04178i	−0.626481	+	0.779436i	$0.715506\pi$
$212$	3.68331	+	7.22891i	0.252971	+	0.496484i
$213$	−16.1739	−	5.44588i	−1.10822	−	0.373145i
$214$	0.244376	−	0.0794027i	0.0167052	−	0.00542786i
$215$		0			0
$216$	−0.960431	+	0.451409i	−0.0653491	+	0.0307145i
$217$	−0.00635884	−	0.0401481i	−0.000431666	−	0.00272543i
$218$	0.372233	+	0.372233i	0.0252108	+	0.0252108i
$219$	0.0670211	−	0.00988638i	0.00452887	−	0.000668060i
$220$		0			0
$221$	−11.2120	−	15.4320i	−0.754201	−	1.03807i
$222$	−0.197561	+	0.140354i	−0.0132594	+	0.00941994i
$223$	19.3939	+	9.88171i	1.29871	+	0.661728i	0.960221	−	0.279240i	$-0.0900827\pi$
$223$	19.3939	+	9.88171i	1.29871	+	0.661728i	0.338494	+	0.940969i	$0.390083\pi$
$224$	1.24756			0.0833563
$225$		0			0
$226$	−0.447080			−0.0297393
$227$	19.1146	+	9.73935i	1.26868	+	0.646423i	0.953151	−	0.302493i	$-0.0978191\pi$
$227$	19.1146	+	9.73935i	1.26868	+	0.646423i	0.315526	+	0.948917i	$0.397819\pi$
$228$	−9.16864	+	6.51371i	−0.607208	+	0.431381i
$229$	6.79217	+	9.34861i	0.448839	+	0.617774i	0.972148	−	0.234369i	$-0.0753025\pi$
$229$	6.79217	+	9.34861i	0.448839	+	0.617774i	−0.523309	+	0.852143i	$0.675303\pi$
$230$		0			0
$231$	10.5311	−	1.55345i	0.692893	−	0.102210i
$232$	−0.174385	−	0.174385i	−0.0114490	−	0.0114490i
$233$	−2.28650	−	14.4364i	−0.149793	−	0.945759i	−0.942026	−	0.335540i	$-0.891081\pi$
$233$	−2.28650	−	14.4364i	−0.149793	−	0.945759i	0.792233	−	0.610219i	$-0.208919\pi$
$234$	−0.453639	−	0.158129i	−0.0296553	−	0.0103372i
$235$		0			0
$236$	8.20961	−	2.66746i	0.534400	−	0.173637i
$237$	−16.7742	−	5.64798i	−1.08960	−	0.366876i
$238$	0.287745	+	0.564731i	0.0186517	+	0.0366061i
$239$	−1.25167	−	3.85226i	−0.0809640	−	0.249182i	0.902378	−	0.430945i	$-0.141820\pi$
$239$	−1.25167	−	3.85226i	−0.0809640	−	0.249182i	−0.983342	+	0.181763i	$0.941820\pi$
$240$		0			0
$241$	−0.611740	+	1.88274i	−0.0394057	+	0.121278i	−0.968824	−	0.247749i	$-0.920309\pi$
$241$	−0.611740	+	1.88274i	−0.0394057	+	0.121278i	0.929419	+	0.369027i	$0.120309\pi$
$242$	0.0963496	−	0.0152603i	0.00619358	−	0.000980967i
$243$	15.5665	+	0.827690i	0.998589	+	0.0530963i
$244$	−15.1776	+	20.8902i	−0.971648	+	1.33736i
$245$		0			0
$246$	0.934884	+	0.158270i	0.0596060	+	0.0100909i
$247$	−10.0640	−	1.59398i	−0.640355	−	0.101422i
$248$	0.00184897	−	0.00362881i	0.000117410	−	0.000230429i
$249$	2.66475	+	2.72199i	0.168872	+	0.172499i
$250$		0			0
$251$			27.0328i			1.70629i	0.521671	+	0.853147i	$0.325309\pi$
$251$			27.0328i			1.70629i	−0.521671	+	0.853147i	$0.674691\pi$
$252$	−10.7628	−	5.77520i	−0.677995	−	0.363804i
$253$	2.71318	−	17.1304i	0.170576	−	1.07698i
$254$	0.144304	−	0.104843i	0.00905443	−	0.00657843i
$255$		0			0
$256$	−12.7757	−	9.28206i	−0.798479	−	0.580129i
$257$	8.81239	−	8.81239i	0.549701	−	0.549701i	−0.376653	−	0.926354i	$-0.622925\pi$
$257$	8.81239	−	8.81239i	0.549701	−	0.549701i	0.926354	+	0.376653i	$0.122925\pi$
$258$	−0.292048	+	0.393118i	−0.0181821	+	0.0244745i
$259$	−5.30900	−	1.72500i	−0.329885	−	0.107186i
$260$		0			0
$261$	1.04599	+	3.46831i	0.0647453	+	0.214683i
$262$	0.355465	−	0.181119i	0.0219607	−	0.0111895i
$263$	3.21164	−	1.63641i	0.198038	−	0.100906i	−0.352159	−	0.935940i	$-0.614552\pi$
$263$	3.21164	−	1.63641i	0.198038	−	0.100906i	0.550198	+	0.835035i	$0.314552\pi$
$264$	0.945112	+	0.494276i	0.0581676	+	0.0304206i
$265$		0			0
$266$	0.321997	+	0.104623i	0.0197429	+	0.00641487i
$267$	−18.8115	−	13.9751i	−1.15124	−	0.855260i
$268$	−1.31607	+	1.31607i	−0.0803915	+	0.0803915i
$269$	10.9791	+	7.97680i	0.669409	+	0.486354i	0.869827	−	0.493356i	$-0.164230\pi$
$269$	10.9791	+	7.97680i	0.669409	+	0.486354i	−0.200418	+	0.979710i	$0.564230\pi$
$270$		0			0
$271$	6.66756	−	4.84427i	0.405026	−	0.294268i	−0.366559	−	0.930395i	$-0.619464\pi$
$271$	6.66756	−	4.84427i	0.405026	−	0.294268i	0.771585	+	0.636126i	$0.219464\pi$
$272$	3.79326	−	23.9497i	0.230000	−	1.45217i
$273$	−3.30757	−	10.5601i	−0.200183	−	0.639126i
$274$			0.506585i			0.0306039i
$275$		0			0
$276$	−14.2207	+	13.9217i	−0.855988	+	0.837990i
$277$	−8.76768	+	17.2075i	−0.526799	+	1.03390i	0.462311	+	0.886718i	$0.347020\pi$
$277$	−8.76768	+	17.2075i	−0.526799	+	1.03390i	−0.989109	+	0.147182i	$0.952980\pi$
$278$	0.255600	+	0.0404830i	0.0153299	+	0.00242801i
$279$	−0.0491352	+	0.0341276i	−0.00294165	+	0.00204317i
$280$		0			0
$281$	6.10119	−	8.39756i	0.363966	−	0.500957i	−0.587282	−	0.809382i	$-0.699802\pi$
$281$	6.10119	−	8.39756i	0.363966	−	0.500957i	0.951248	+	0.308426i	$0.0998021\pi$
$282$	0.00345987	−	0.325645i	0.000206032	−	0.0193919i
$283$	−9.52247	+	1.50821i	−0.566052	+	0.0896539i	−0.432900	−	0.901442i	$-0.642510\pi$
$283$	−9.52247	+	1.50821i	−0.566052	+	0.0896539i	−0.133152	+	0.991096i	$0.542510\pi$
$284$	6.08164	−	18.7174i	0.360879	−	1.11067i
$285$		0			0
$286$	0.149200	+	0.459192i	0.00882241	+	0.0271526i
$287$	9.91560	+	19.4605i	0.585299	+	1.14871i
$288$	−0.798623	−	1.65332i	−0.0470593	−	0.0974225i
$289$	19.0573	−	6.19208i	1.12102	−	0.364240i
$290$		0			0
$291$	8.31790	−	4.12746i	0.487604	−	0.241956i
$292$	0.0122214	+	0.0771628i	0.000715202	+	0.00451561i
$293$	−7.74605	−	7.74605i	−0.452529	−	0.452529i	0.443664	−	0.896193i	$-0.353678\pi$
$293$	−7.74605	−	7.74605i	−0.452529	−	0.452529i	−0.896193	+	0.443664i	$0.853678\pi$
$294$	−0.0367398	−	0.249064i	−0.00214271	−	0.0145257i
$295$		0			0
$296$	−0.328748	−	0.452482i	−0.0191081	−	0.0263000i
$297$	−8.80012	−	12.9617i	−0.510635	−	0.752115i
$298$	−0.0949480	−	0.0483784i	−0.00550019	−	0.00280249i
$299$	−18.0297			−1.04269
$300$		0			0
$301$	−11.2806			−0.650205
$302$	−0.142558	−	0.0726372i	−0.00820332	−	0.00417980i
$303$	12.2860	+	17.2936i	0.705811	+	0.993492i
$304$	−7.61350	−	10.4791i	−0.436664	−	0.601017i
$305$		0			0
$306$	0.564204	−	0.742841i	0.0322534	−	0.0424654i
$307$	−17.8437	−	17.8437i	−1.01839	−	1.01839i	−0.999828	−	0.0185640i	$-0.994091\pi$
$307$	−17.8437	−	17.8437i	−1.01839	−	1.01839i	−0.0185640	−	0.999828i	$-0.505909\pi$
$308$	1.92035	+	12.1246i	0.109422	+	0.690865i
$309$	12.9364	+	26.0701i	0.735925	+	1.48308i
$310$		0			0
$311$	4.51681	−	1.46760i	0.256125	−	0.0832199i	−0.178140	−	0.984005i	$-0.557008\pi$
$311$	4.51681	−	1.46760i	0.256125	−	0.0832199i	0.434265	+	0.900785i	$0.357008\pi$
$312$	0.353801	−	1.05077i	0.0200300	−	0.0594880i
$313$	−12.2599	−	24.0613i	−0.692968	−	1.36003i	−0.922222	−	0.386660i	$-0.873629\pi$
$313$	−12.2599	−	24.0613i	−0.692968	−	1.36003i	0.229254	−	0.973367i	$-0.426371\pi$
$314$	−0.101776	−	0.313233i	−0.00574353	−	0.0176768i
$315$		0			0
$316$	6.30734	−	19.4120i	0.354815	−	1.09201i
$317$	−3.83042	+	0.606678i	−0.215138	+	0.0340745i	−0.263073	−	0.964776i	$-0.584736\pi$
$317$	−3.83042	+	0.606678i	−0.215138	+	0.0340745i	0.0479351	+	0.998850i	$0.484736\pi$
$318$	−0.359430	−	0.00381882i	−0.0201558	−	0.000214149i
$319$	2.14001	−	2.94547i	0.119818	−	0.164915i
$320$		0			0
$321$	1.45402	−	8.58872i	0.0811554	−	0.479376i
$322$	0.591706	+	0.0937170i	0.0329745	+	0.00522264i
$323$	8.98213	−	17.6284i	0.499779	−	0.980872i
$324$	−0.763718	+	17.9603i	−0.0424288	+	0.997793i
$325$		0			0
$326$		−	0.934125i		−	0.0517364i
$327$	17.0302	−	5.33409i	0.941772	−	0.294976i
$328$	−0.342328	+	2.16137i	−0.0189019	+	0.119342i
$329$	6.06883	−	4.40926i	0.334585	−	0.243090i
$330$		0			0
$331$	14.0789	+	10.2289i	0.773845	+	0.562232i	0.903126	−	0.429377i	$-0.141267\pi$
$331$	14.0789	+	10.2289i	0.773845	+	0.562232i	−0.129280	+	0.991608i	$0.541267\pi$
$332$	−3.10615	+	3.10615i	−0.170472	+	0.170472i
$333$	1.11251	+	8.13994i	0.0609650	+	0.446066i
$334$	0.0614197	+	0.0199565i	0.00336074	+	0.00109197i
$335$		0			0
$336$	6.51915	−	12.4654i	0.355649	−	0.680041i
$337$	12.4373	−	6.33712i	0.677503	−	0.345205i	−0.0811484	−	0.996702i	$-0.525859\pi$
$337$	12.4373	−	6.33712i	0.677503	−	0.345205i	0.758651	+	0.651497i	$0.225859\pi$
$338$	−0.144588	+	0.0736713i	−0.00786455	+	0.00400719i
$339$	−7.02395	+	13.4306i	−0.381489	+	0.729450i
$340$		0			0
$341$	0.0571823	+	0.0185797i	0.00309659	+	0.00100614i
$342$	−0.0674749	−	0.493697i	−0.00364862	−	0.0266961i
$343$	14.1901	−	14.1901i	0.766195	−	0.766195i
$344$	−0.914384	−	0.664339i	−0.0493003	−	0.0358188i
$345$		0			0
$346$	−0.0856460	+	0.0622255i	−0.00460436	+	0.00334526i
$347$	2.53725	−	16.0196i	0.136207	−	0.859977i	−0.821075	−	0.570820i	$-0.806625\pi$
$347$	2.53725	−	16.0196i	0.136207	−	0.859977i	0.957282	−	0.289156i	$-0.0933747\pi$
$348$	−3.98659	+	1.24866i	−0.213704	+	0.0669349i
$349$		−	3.27425i		−	0.175267i	−0.996153	−	0.0876333i	$-0.972070\pi$
$349$		−	3.27425i		−	0.175267i	0.996153	−	0.0876333i	$-0.0279304\pi$
$350$		0			0
$351$	−11.8773	+	11.1433i	−0.633963	+	0.594786i
$352$	−0.837759	+	1.64419i	−0.0446527	+	0.0876358i
$353$	28.8857	+	4.57504i	1.53743	+	0.243505i	0.866939	−	0.498414i	$-0.166084\pi$
$353$	28.8857	+	4.57504i	1.53743	+	0.243505i	0.670490	+	0.741919i	$0.266084\pi$
$354$	−0.0638365	+	0.377075i	−0.00339287	+	0.0200413i
$355$		0			0
$356$	15.8846	−	21.8632i	0.841881	−	1.15875i
$357$	21.4856	+	0.228277i	1.13714	+	0.0120817i
$358$	−0.256133	+	0.0405675i	−0.0135371	+	0.00214406i
$359$	−8.54970	+	26.3133i	−0.451236	+	1.38876i	0.424262	+	0.905540i	$0.360534\pi$
$359$	−8.54970	+	26.3133i	−0.451236	+	1.38876i	−0.875498	+	0.483222i	$0.839466\pi$
$360$		0			0
$361$	2.60544	+	8.01873i	0.137129	+	0.422038i
$362$	−0.0242666	−	0.0476258i	−0.00127542	−	0.00250316i
$363$	1.05529	−	3.13416i	0.0553885	−	0.164501i
$364$	12.1366	−	3.94343i	0.636132	−	0.206692i
$365$		0			0
$366$	−0.508514	−	1.02479i	−0.0265804	−	0.0535664i
$367$	0.859901	+	5.42920i	0.0448865	+	0.283402i	0.999914	−	0.0131151i	$-0.00417478\pi$
$367$	0.859901	+	5.42920i	0.0448865	+	0.283402i	−0.955028	+	0.296517i	$0.904175\pi$
$368$	−16.2065	−	16.2065i	−0.844825	−	0.844825i
$369$	19.4423	−	25.5981i	1.01212	−	1.33258i
$370$		0			0
$371$	−4.86671	−	6.69846i	−0.252667	−	0.347767i
$372$	−0.0399555	−	0.0562410i	−0.00207160	−	0.00291596i
$373$	6.70992	+	3.41888i	0.347427	+	0.177023i	0.618992	−	0.785397i	$-0.287541\pi$
$373$	6.70992	+	3.41888i	0.347427	+	0.177023i	−0.271565	+	0.962420i	$0.587541\pi$
$374$	−0.937499			−0.0484769
$375$		0			0
$376$	0.751596			0.0387606
$377$	−3.37226	−	1.71825i	−0.173680	−	0.0884945i
$378$	0.447715	−	0.303968i	0.0230280	−	0.0156344i
$379$	13.4955	+	18.5749i	0.693216	+	0.954130i	0.999997	+	0.00234966i	$0.000747920\pi$
$379$	13.4955	+	18.5749i	0.693216	+	0.954130i	−0.306781	+	0.951780i	$0.599252\pi$
$380$		0			0
$381$	−0.882436	−	5.98215i	−0.0452086	−	0.306475i
$382$	0.683782	+	0.683782i	0.0349853	+	0.0349853i
$383$	1.20753	+	7.62404i	0.0617019	+	0.389570i	0.999142	+	0.0414229i	$0.0131891\pi$
$383$	1.20753	+	7.62404i	0.0617019	+	0.389570i	−0.937440	+	0.348147i	$0.886811\pi$
$384$	2.52838	−	1.25462i	0.129026	−	0.0640245i
$385$		0			0
$386$	0.539087	−	0.175160i	0.0274388	−	0.00891542i
$387$	7.22126	+	14.9495i	0.367077	+	0.759926i
$388$	4.86140	+	9.54104i	0.246800	+	0.484373i
$389$	5.38913	+	16.5860i	0.273240	+	0.840945i	0.989680	+	0.143297i	$0.0457703\pi$
$389$	5.38913	+	16.5860i	0.273240	+	0.840945i	−0.716440	+	0.697649i	$0.754230\pi$
$390$		0			0
$391$	10.8182	−	33.2950i	0.547099	−	1.68380i
$392$	0.573879	−	0.0908935i	0.0289853	−	0.00459082i
$393$	0.143687	−	13.5239i	0.00724806	−	0.682192i
$394$	0.756459	−	1.04118i	0.0381098	−	0.0524537i
$395$		0			0
$396$	14.8387	−	10.3065i	0.745673	−	0.517919i
$397$	10.2495	+	1.62336i	0.514407	+	0.0814741i	0.408241	−	0.912874i	$-0.366142\pi$
$397$	10.2495	+	1.62336i	0.514407	+	0.0814741i	0.106167	+	0.994348i	$0.466142\pi$
$398$	−0.373795	+	0.733615i	−0.0187367	+	0.0367728i
$399$	8.20178	−	8.02933i	0.410602	−	0.401969i
$400$		0			0
$401$			14.7017i			0.734168i	0.930188	+	0.367084i	$0.119644\pi$
$401$			14.7017i			0.734168i	−0.930188	+	0.367084i	$0.880356\pi$
$402$	−0.0246467	−	0.0786897i	−0.00122927	−	0.00392468i
$403$	0.00977756	−	0.0617331i	0.000487055	−	0.00307514i
$404$	−19.7912	+	14.3792i	−0.984651	+	0.715391i
$405$		0			0
$406$	0.101741	+	0.0739189i	0.00504930	+	0.00366853i
$407$	5.83850	−	5.83850i	0.289404	−	0.289404i
$408$	1.72813	+	1.28383i	0.0855554	+	0.0635593i
$409$	−4.73536	−	1.53861i	−0.234148	−	0.0760794i	0.189593	−	0.981863i	$-0.439283\pi$
$409$	−4.73536	−	1.53861i	−0.234148	−	0.0760794i	−0.423741	+	0.905783i	$0.639283\pi$
$410$		0			0
$411$	15.2182	+	7.95882i	0.750658	+	0.392580i
$412$	−29.9037	+	15.2367i	−1.47325	+	0.750659i
$413$	−7.84915	+	3.99934i	−0.386231	+	0.196795i
$414$	−0.254581	−	0.844143i	−0.0125120	−	0.0414873i
$415$		0			0
$416$	1.82440	+	0.592785i	0.0894488	+	0.0290637i
$417$	5.23180	−	7.04239i	0.256202	−	0.344867i
$418$	−0.354112	+	0.354112i	−0.0173202	+	0.0173202i
$419$	−19.7469	−	14.3470i	−0.964699	−	0.700895i	−0.0104616	−	0.999945i	$-0.503330\pi$
$419$	−19.7469	−	14.3470i	−0.964699	−	0.700895i	−0.954237	+	0.299051i	$0.903330\pi$
$420$		0			0
$421$	−2.27800	+	1.65506i	−0.111023	+	0.0806628i	−0.641911	−	0.766779i	$-0.721858\pi$
$421$	−2.27800	+	1.65506i	−0.111023	+	0.0806628i	0.530889	+	0.847442i	$0.321858\pi$
$422$	0.127172	−	0.802932i	0.00619063	−	0.0390861i
$423$	−9.72825	−	5.22006i	−0.473004	−	0.253808i
$424$		−	0.829573i		−	0.0402876i
$425$		0			0
$426$	0.609968	+	0.623068i	0.0295530	+	0.0301877i
$427$	11.9635	−	23.4796i	0.578953	−	1.13626i
$428$	9.92171	+	1.57144i	0.479584	+	0.0759586i
$429$	16.1385	+	2.73215i	0.779174	+	0.131910i
$430$		0			0
$431$	−12.9674	+	17.8481i	−0.624617	+	0.859712i	−0.997679	−	0.0680947i	$-0.978308\pi$
$431$	−12.9674	+	17.8481i	−0.624617	+	0.859712i	0.373062	+	0.927807i	$0.378308\pi$
$432$	−20.6927	−	0.659759i	−0.995580	−	0.0317427i
$433$	−39.8312	+	6.30865i	−1.91417	+	0.303174i	−0.995724	−	0.0923805i	$-0.970552\pi$
$433$	−39.8312	+	6.30865i	−1.91417	+	0.303174i	−0.918442	+	0.395555i	$0.870552\pi$
$434$	−0.000641766		0.00197515i	−3.08058e−5		9.48104e-5i
$435$		0			0
$436$	6.35954	+	19.5726i	0.304567	+	0.937360i
$437$	−8.48993	−	16.6624i	−0.406129	−	0.797072i
$438$	−0.00328031	−	0.00110450i	−0.000156739	−	5.27752e-5i
$439$	−12.3771	+	4.02156i	−0.590727	+	0.191939i	−0.589100	−	0.808060i	$-0.700518\pi$
$439$	−12.3771	+	4.02156i	−0.590727	+	0.191939i	−0.00162635	+	0.999999i	$0.500518\pi$
$440$		0			0
$441$	−8.05926	−	2.80928i	−0.383774	−	0.133775i
$442$	0.152456	+	0.962572i	0.00725162	+	0.0457849i
$443$	20.7027	+	20.7027i	0.983613	+	0.983613i	0.999868	−	0.0162549i	$-0.00517433\pi$
$443$	20.7027	+	20.7027i	0.983613	+	0.983613i	−0.0162549	+	0.999868i	$0.505174\pi$
$444$	−9.37276	+	1.38259i	−0.444812	+	0.0656148i
$445$		0			0
$446$	−0.653662	−	0.899688i	−0.0309518	−	0.0426015i
$447$	−2.94503	+	2.09225i	−0.139295	+	0.0989599i
$448$	14.4161	+	7.34538i	0.681097	+	0.347037i
$449$	27.3773			1.29201			0.646007	−	0.763332i	$-0.276438\pi$
$449$	27.3773			1.29201			0.646007	+	0.763332i	$0.276438\pi$
$450$		0			0
$451$	−32.3059			−1.52123
$452$	−15.5733	−	7.93497i	−0.732504	−	0.373230i
$453$	−4.42177	+	3.14138i	−0.207753	+	0.147595i
$454$	−0.644245	−	0.886727i	−0.0302359	−	0.0416162i
$455$		0			0
$456$	1.13768	−	0.167821i	0.0532768	−	0.00785895i
$457$	−9.58199	−	9.58199i	−0.448227	−	0.448227i	0.446538	−	0.894765i	$-0.352657\pi$
$457$	−9.58199	−	9.58199i	−0.448227	−	0.448227i	−0.894765	+	0.446538i	$0.852657\pi$
$458$	−0.0923573	−	0.583121i	−0.00431557	−	0.0272475i
$459$	−13.4514	−	28.6197i	−0.627859	−	1.33585i
$460$		0			0
$461$	27.6032	−	8.96881i	1.28561	−	0.417719i	0.415056	−	0.909796i	$-0.363762\pi$
$461$	27.6032	−	8.96881i	1.28561	−	0.417719i	0.870552	+	0.492077i	$0.163762\pi$
$462$	−0.515437	−	0.173551i	−0.0239803	−	0.00807433i
$463$	−3.25207	−	6.38255i	−0.151137	−	0.296622i	0.803008	−	0.595968i	$-0.203232\pi$
$463$	−3.25207	−	6.38255i	−0.151137	−	0.296622i	−0.954145	+	0.299346i	$0.903232\pi$
$464$	−1.48675	−	4.57576i	−0.0690208	−	0.212424i
$465$		0			0
$466$	−0.230765	+	0.710222i	−0.0106900	+	0.0329004i
$467$	−8.42928	+	1.33507i	−0.390061	+	0.0617795i	−0.348385	−	0.937352i	$-0.613270\pi$
$467$	−8.42928	+	1.33507i	−0.390061	+	0.0617795i	−0.0416760	+	0.999131i	$0.513270\pi$
$468$	−12.9952	−	13.5595i	−0.600703	−	0.626789i
$469$	1.11644	−	1.53665i	0.0515525	−	0.0709560i
$470$		0			0
$471$	−11.0087	−	1.86371i	−0.507255	−	0.0858752i
$472$	−0.871764	−	0.138074i	−0.0401262	−	0.00635537i
$473$	7.57513	−	14.8670i	0.348305	−	0.683587i
$474$	0.632604	+	0.646191i	0.0290565	+	0.0296805i
$475$		0			0
$476$			24.7785i			1.13572i
$477$	−5.76163	+	10.7375i	−0.263807	+	0.491638i
$478$	−0.0323735	+	0.204399i	−0.00148073	+	0.00934897i
$479$	11.8446	−	8.60560i	0.541193	−	0.393200i	−0.283335	−	0.959021i	$-0.591441\pi$
$479$	11.8446	−	8.60560i	0.541193	−	0.393200i	0.824528	+	0.565821i	$0.191441\pi$
$480$		0			0
$481$	−6.94411	−	5.04519i	−0.316624	−	0.230041i
$482$	0.0715186	−	0.0715186i	0.00325758	−	0.00325758i
$483$	12.1115	−	16.3029i	0.551090	−	0.741808i
$484$	3.62702	+	1.17849i	0.164865	+	0.0535677i
$485$		0			0
$486$	−0.689433	−	0.398744i	−0.0312733	−	0.0180874i
$487$	11.1635	−	5.68806i	0.505864	−	0.257751i	−0.182382	−	0.983228i	$-0.558381\pi$
$487$	11.1635	−	5.68806i	0.505864	−	0.257751i	0.688246	+	0.725477i	$0.258381\pi$
$488$	2.35250	−	1.19866i	0.106492	−	0.0542606i
$489$	−28.0618	−	14.6758i	−1.26900	−	0.663662i
$490$		0			0
$491$	−34.7580	−	11.2936i	−1.56861	−	0.509672i	−0.609518	−	0.792772i	$-0.708637\pi$
$491$	−34.7580	−	11.2936i	−1.56861	−	0.509672i	−0.959090	+	0.283101i	$0.908637\pi$
$492$	29.7560	+	22.1058i	1.34151	+	0.996607i
$493$	5.19647	−	5.19647i	0.234037	−	0.234037i
$494$	0.421169	+	0.305997i	0.0189493	+	0.0137675i
$495$		0			0
$496$	0.0642794	−	0.0467017i	0.00288623	−	0.00209697i
$497$	−3.14193	+	19.8373i	−0.140935	+	0.889826i
$498$	−0.0581706	−	0.185722i	−0.00260669	−	0.00832240i
$499$			8.39246i			0.375698i	0.982198	+	0.187849i	$0.0601515\pi$
$499$			8.39246i			0.375698i	−0.982198	+	0.187849i	$0.939848\pi$
$500$		0			0
$501$	1.56446	−	1.53156i	0.0698948	−	0.0684251i
$502$	0.627027	−	1.23061i	0.0279856	−	0.0549248i
$503$	−37.1261	−	5.88019i	−1.65537	−	0.262185i	−0.742323	−	0.670042i	$-0.766276\pi$
$503$	−37.1261	−	5.88019i	−1.65537	−	0.262185i	−0.913046	+	0.407857i	$0.866276\pi$
$504$	0.712464	+	1.02577i	0.0317357	+	0.0456913i
$505$		0			0
$506$	−0.520852	+	0.716891i	−0.0231547	+	0.0318697i
$507$	−0.0584458	+	5.50096i	−0.00259567	+	0.244306i
$508$	6.88738	−	1.09085i	0.305578	−	0.0483988i
$509$	−4.05260	+	12.4726i	−0.179628	+	0.552839i	−0.999815	−	0.0192578i	$-0.993870\pi$
$509$	−4.05260	+	12.4726i	−0.179628	+	0.552839i	0.820186	+	0.572096i	$0.193870\pi$
$510$		0			0
$511$	−0.0246374	−	0.0758262i	−0.00108990	−	0.00335436i
$512$	1.84593	+	3.62285i	0.0815794	+	0.160109i
$513$	−15.8911	−	5.72935i	−0.701609	−	0.252957i
$514$	−0.605569	+	0.196761i	−0.0267105	+	0.00867877i
$515$		0			0
$516$	−17.1502	+	8.51020i	−0.754997	+	0.374640i
$517$	1.73576	+	10.9592i	0.0763386	+	0.481983i
$518$	0.201670	+	0.201670i	0.00886086	+	0.00886086i
$519$	0.523736	+	3.55048i	0.0229895	+	0.155849i
$520$		0			0
$521$	10.1668	+	13.9934i	0.445415	+	0.613061i	0.971405	−	0.237430i	$-0.0763049\pi$
$521$	10.1668	+	13.9934i	0.445415	+	0.613061i	−0.525990	+	0.850491i	$0.676305\pi$
$522$	0.0328311	−	0.182149i	0.00143698	−	0.00797246i
$523$	10.0784	+	5.13521i	0.440698	+	0.224547i	0.660238	−	0.751057i	$-0.270455\pi$
$523$	10.0784	+	5.13521i	0.440698	+	0.224547i	−0.219540	+	0.975604i	$0.570455\pi$
$524$	15.5966			0.681340
$525$		0			0
$526$	−0.184160			−0.00802976
$527$	0.108134	+	0.0550970i	0.00471039	+	0.00240006i
$528$	12.0507	+	16.9624i	0.524439	+	0.738195i
$529$	−5.93077	−	8.16301i	−0.257860	−	0.354913i
$530$		0			0
$531$	10.3247	+	7.84181i	0.448053	+	0.340306i
$532$	9.35933	+	9.35933i	0.405778	+	0.405778i
$533$	5.25360	+	33.1699i	0.227559	+	1.43675i
$534$	0.532199	+	1.07252i	0.0230305	+	0.0464124i
$535$		0			0
$536$	0.180993	−	0.0588082i	0.00781770	−	0.00254013i
$537$	−2.80536	+	8.33177i	−0.121060	+	0.359542i
$538$	−0.314779	−	0.617789i	−0.0135711	−	0.0266348i
$539$	2.65067	+	8.15791i	0.114172	+	0.351386i
$540$		0			0
$541$	−9.85115	+	30.3187i	−0.423534	+	1.30350i	0.480857	+	0.876799i	$0.340326\pi$
$541$	−9.85115	+	30.3187i	−0.423534	+	1.30350i	−0.904391	+	0.426705i	$0.859674\pi$
$542$	−0.415890	+	0.0658705i	−0.0178640	+	0.00282938i
$543$	−1.81196	−	0.0192515i	−0.0777586	−	0.000826159i
$544$	−2.18936	+	3.01339i	−0.0938679	+	0.129198i
$545$		0			0
$546$	−0.0943722	+	0.557446i	−0.00403876	+	0.0238565i
$547$	18.6875	+	2.95981i	0.799020	+	0.126552i	0.542576	−	0.840007i	$-0.317449\pi$
$547$	18.6875	+	2.95981i	0.799020	+	0.126552i	0.256444	+	0.966559i	$0.417449\pi$
$548$	−8.99110	+	17.6460i	−0.384081	+	0.753801i
$549$	−38.7744	−	0.824023i	−1.65485	−	0.0351685i
$550$		0			0
$551$		−	3.92562i		−	0.167237i
$552$	1.94184	−	0.608211i	0.0826502	−	0.0258872i
$553$	−3.25853	+	20.5735i	−0.138567	+	0.874876i
$554$	0.798260	−	0.579970i	0.0339148	−	0.0246406i
$555$		0			0
$556$	8.18487	+	5.94666i	0.347116	+	0.252194i
$557$	−27.8152	+	27.8152i	−1.17857	+	1.17857i	−0.198459	+	0.980109i	$0.563594\pi$
$557$	−27.8152	+	27.8152i	−1.17857	+	1.17857i	−0.980109	+	0.198459i	$0.936406\pi$
$558$	0.00302837		0.000413895i	0.000128201		1.75216e-5i
$559$	−16.4965	−	5.36005i	−0.697729	−	0.226706i
$560$		0			0
$561$	−14.7288	+	28.1631i	−0.621850	+	1.18905i
$562$	−0.472526	+	0.240764i	−0.0199323	+	0.0101560i
$563$	−36.6601	+	18.6793i	−1.54504	+	0.787237i	−0.998732	−	0.0503464i	$-0.983967\pi$
$563$	−36.6601	+	18.6793i	−1.54504	+	0.787237i	−0.546309	+	0.837584i	$0.683967\pi$
$564$	5.90021	−	11.2819i	0.248444	−	0.475053i
$565$		0			0
$566$	0.468474	+	0.152216i	0.0196914	+	0.00639813i
$567$	−2.09748	−	18.2252i	−0.0880860	−	0.765388i
$568$	−1.42294	+	1.42294i	−0.0597052	+	0.0597052i
$569$	7.49851	+	5.44798i	0.314354	+	0.228391i	0.733762	−	0.679406i	$-0.237763\pi$
$569$	7.49851	+	5.44798i	0.314354	+	0.228391i	−0.419409	+	0.907798i	$0.637763\pi$
$570$		0			0
$571$	6.86662	−	4.98889i	0.287359	−	0.208779i	−0.434762	−	0.900545i	$-0.643167\pi$
$571$	6.86662	−	4.98889i	0.287359	−	0.208779i	0.722121	+	0.691767i	$0.243167\pi$
$572$	−2.95280	+	18.6432i	−0.123463	+	0.779513i
$573$	31.2840	−	9.79859i	1.30691	−	0.409342i
$574$		−	1.11589i		−	0.0465763i
$575$		0			0
$576$	0.505937	−	23.8069i	0.0210807	−	0.991953i
$577$	−11.9271	+	23.4083i	−0.496532	+	0.974498i	0.497711	+	0.867343i	$0.334174\pi$
$577$	−11.9271	+	23.4083i	−0.496532	+	0.974498i	−0.994242	+	0.107155i	$0.965826\pi$
$578$	−1.01117	−	0.160153i	−0.0420590	−	0.00666150i
$579$	3.20752	−	18.9465i	0.133300	−	0.787389i
$580$		0			0
$581$	2.63501	−	3.62677i	0.109318	−	0.150464i
$582$	−0.474392	−	0.00504025i	−0.0196642	−	0.000208925i
$583$	12.0961	−	1.91584i	0.500971	−	0.0793460i
$584$	0.00246850	−	0.00759726i	0.000102147	−	0.000314377i
$585$		0			0
$586$	0.172952	+	0.532293i	0.00714460	+	0.0219888i
$587$	−14.8371	−	29.1195i	−0.612395	−	1.20189i	−0.964040	−	0.265759i	$-0.914378\pi$
$587$	−14.8371	−	29.1195i	−0.612395	−	1.20189i	0.351645	−	0.936133i	$-0.385622\pi$
$588$	3.14073	−	9.32778i	0.129521	−	0.384671i
$589$	0.0616556	−	0.0200331i	0.00254047	−	0.000825450i
$590$		0			0
$591$	−19.3932	−	39.0822i	−0.797728	−	1.60763i
$592$	−1.70690	−	10.7769i	−0.0701531	−	0.442929i
$593$	−4.77949	−	4.77949i	−0.196270	−	0.196270i	0.602129	−	0.798399i	$-0.294319\pi$
$593$	−4.77949	−	4.77949i	−0.196270	−	0.196270i	−0.798399	+	0.602129i	$0.794319\pi$
$594$	0.0999590	+	0.794174i	0.00410137	+	0.0325854i
$595$		0			0
$596$	−2.44871	−	3.37036i	−0.100303	−	0.138055i
$597$	16.1657	+	22.7547i	0.661619	+	0.931288i
$598$	0.820766	+	0.418201i	0.0335636	+	0.0171015i
$599$	−26.7065			−1.09120			−0.545598	−	0.838047i	$-0.683697\pi$
$599$	−26.7065			−1.09120			−0.545598	+	0.838047i	$0.683697\pi$
$600$		0			0
$601$	12.6263			0.515039			0.257520	−	0.966273i	$-0.417095\pi$
$601$	12.6263			0.515039			0.257520	+	0.966273i	$0.417095\pi$
$602$	0.513527	+	0.261655i	0.0209298	+	0.0106643i
$603$	−2.75111	−	0.495868i	−0.112034	−	0.0201933i
$604$	−3.67658	−	5.06038i	−0.149598	−	0.205904i
$605$		0			0
$606$	−0.158166	−	1.07223i	−0.00642507	−	0.0435564i
$607$	27.3885	+	27.3885i	1.11167	+	1.11167i	0.992925	+	0.118742i	$0.0378861\pi$
$607$	27.3885	+	27.3885i	1.11167	+	1.11167i	0.118742	+	0.992925i	$0.462114\pi$
$608$	0.311254	+	1.96518i	0.0126230	+	0.0796987i
$609$	3.81900	−	1.89504i	0.154754	−	0.0767910i
$610$		0			0
$611$	10.9700	−	3.56436i	0.443798	−	0.144199i
$612$	32.8373	−	15.8619i	1.32737	−	0.641177i
$613$	15.4155	+	30.2547i	0.622628	+	1.22198i	0.959840	+	0.280547i	$0.0905160\pi$
$613$	15.4155	+	30.2547i	0.622628	+	1.22198i	−0.337212	+	0.941429i	$0.609484\pi$
$614$	0.398410	+	1.22618i	0.0160785	+	0.0494846i
$615$		0			0
$616$	0.387877	−	1.19376i	0.0156280	−	0.0480981i
$617$	18.1501	−	2.87470i	0.730697	−	0.115731i	0.220010	−	0.975498i	$-0.429391\pi$
$617$	18.1501	−	2.87470i	0.730697	−	0.115731i	0.510687	+	0.859767i	$0.329391\pi$
$618$	0.0157973	−	1.48685i	0.000635459	−	0.0598099i
$619$	−1.95042	+	2.68452i	−0.0783938	+	0.107900i	−0.846413	−	0.532527i	$-0.821243\pi$
$619$	−1.95042	+	2.68452i	−0.0783938	+	0.107900i	0.768019	+	0.640427i	$0.221243\pi$
$620$		0			0
$621$	−29.3583	−	5.61430i	−1.17811	−	0.225294i
$622$	−0.239659	−	0.0379583i	−0.00960946	−	0.00152199i
$623$	−12.5207	+	24.5733i	−0.501631	+	0.984507i
$624$	15.4564	−	15.1314i	0.618752	−	0.605742i
$625$		0			0
$626$			1.37971i			0.0551443i
$627$	5.07443	+	16.2012i	0.202653	+	0.647012i
$628$	2.01422	−	12.7173i	0.0803763	−	0.507476i
$629$	13.4834	−	9.79627i	0.537619	−	0.390603i
$630$		0			0
$631$	16.0880	+	11.6886i	0.640454	+	0.465317i	0.860006	−	0.510284i	$-0.170460\pi$
$631$	16.0880	+	11.6886i	0.640454	+	0.465317i	−0.219552	+	0.975601i	$0.570460\pi$
$632$	−1.47575	+	1.47575i	−0.0587020	+	0.0587020i
$633$	−22.1227	−	16.4350i	−0.879298	−	0.653232i
$634$	0.188444	+	0.0612291i	0.00748405	+	0.00243172i
$635$		0			0
$636$	−12.4524	−	6.51235i	−0.493768	−	0.258231i
$637$	7.94505	−	4.04820i	0.314794	−	0.160396i
$638$	−0.165740	+	0.0844488i	−0.00656171	+	0.00334336i
$639$	28.3005	−	8.53501i	1.11955	−	0.337640i
$640$		0			0
$641$	39.9060	+	12.9663i	1.57619	+	0.512136i	0.961072	−	0.276296i	$-0.0891072\pi$
$641$	39.9060	+	12.9663i	1.57619	+	0.512136i	0.615121	+	0.788433i	$0.289107\pi$
$642$	−0.265407	+	0.357257i	−0.0104748	+	0.0140998i
$643$	−18.4566	+	18.4566i	−0.727857	+	0.727857i	−0.970193	−	0.242335i	$-0.922087\pi$
$643$	−18.4566	+	18.4566i	−0.727857	+	0.727857i	0.242335	+	0.970193i	$0.422087\pi$
$644$	18.9477	+	13.7663i	0.746645	+	0.542469i
$645$		0			0
$646$	−0.817785	+	0.594156i	−0.0321753	+	0.0233768i
$647$	−0.113401	+	0.715984i	−0.00445824	+	0.0281482i	−0.989817	−	0.142344i	$-0.954536\pi$
$647$	−0.113401	+	0.715984i	−0.00445824	+	0.0281482i	0.985359	+	0.170493i	$0.0545359\pi$
$648$	0.903303	−	1.60082i	0.0354851	−	0.0628863i
$649$		−	13.0302i		−	0.511481i
$650$		0			0
$651$	0.0492524	+	0.0503102i	0.00193035	+	0.00197181i
$652$	16.5793	−	32.5386i	0.649294	−	1.27431i
$653$	22.6537	+	3.58799i	0.886507	+	0.140409i	0.583050	−	0.812436i	$-0.301859\pi$
$653$	22.6537	+	3.58799i	0.886507	+	0.140409i	0.303457	+	0.952845i	$0.401859\pi$
$654$	−0.898989	−	0.152193i	−0.0351532	−	0.00595123i
$655$		0			0
$656$	−25.0934	+	34.5381i	−0.979733	+	1.34849i
$657$	−0.0847161	+	0.0811904i	−0.00330509	+	0.00316754i
$658$	−0.378544	+	0.0599554i	−0.0147572	+	0.00233731i
$659$	6.79306	−	20.9069i	0.264620	−	0.814416i	−0.727161	−	0.686467i	$-0.759161\pi$
$659$	6.79306	−	20.9069i	0.264620	−	0.814416i	0.991781	−	0.127949i	$-0.0408395\pi$
$660$		0			0
$661$	−3.85456	−	11.8631i	−0.149925	−	0.461421i	0.847687	−	0.530497i	$-0.177995\pi$
$661$	−3.85456	−	11.8631i	−0.149925	−	0.461421i	−0.997611	+	0.0690762i	$0.977995\pi$
$662$	−0.403651	−	0.792210i	−0.0156884	−	0.0307901i
$663$	31.3116	+	10.5428i	1.21604	+	0.409449i
$664$	0.427176	−	0.138798i	0.0165776	−	0.00538640i
$665$		0			0
$666$	0.138162	−	0.396358i	0.00535367	−	0.0153586i
$667$	−1.08663	−	6.86070i	−0.0420744	−	0.265647i
$668$	1.78525	+	1.78525i	0.0690736	+	0.0690736i
$669$	−37.2968	+	5.50171i	−1.44198	+	0.212708i
$670$		0			0
$671$	22.9107	+	31.5339i	0.884459	+	1.21735i
$672$	−1.76155	+	1.25147i	−0.0679534	+	0.0482764i
$673$	−11.4552	−	5.83674i	−0.441567	−	0.224990i	0.219048	−	0.975714i	$-0.429705\pi$
$673$	−11.4552	−	5.83674i	−0.441567	−	0.224990i	−0.660616	+	0.750724i	$0.729705\pi$
$674$	−0.713172			−0.0274704
$675$		0			0
$676$	−6.34403			−0.244001
$677$	−25.7050	−	13.0973i	−0.987922	−	0.503371i	−0.116123	−	0.993235i	$-0.537047\pi$
$677$	−25.7050	−	13.0973i	−0.987922	−	0.503371i	−0.871799	+	0.489863i	$0.837047\pi$
$678$	0.631274	−	0.448479i	0.0242439	−	0.0172237i
$679$	−6.42331	−	8.84092i	−0.246504	−	0.339283i
$680$		0			0
$681$	−36.7595	+	5.42245i	−1.40863	+	0.207789i
$682$	−0.00217215	−	0.00217215i	−8.31758e−5	−	8.31758e-5i
$683$	−3.25897	−	20.5763i	−0.124701	−	0.787331i	−0.968196	−	0.250194i	$-0.919506\pi$
$683$	−3.25897	−	20.5763i	−0.124701	−	0.787331i	0.843495	−	0.537137i	$-0.180494\pi$
$684$	6.41198	−	18.3947i	0.245168	−	0.703338i
$685$		0			0
$686$	−0.975118	+	0.316835i	−0.0372302	+	0.0120968i
$687$	−18.9684	−	6.38678i	−0.723689	−	0.243671i
$688$	−10.0103	−	19.6464i	−0.381641	−	0.749013i
$689$	−3.93416	−	12.1081i	−0.149880	−	0.461282i
$690$		0			0
$691$	−3.21593	+	9.89763i	−0.122340	+	0.376524i	−0.993407	−	0.114640i	$-0.963428\pi$
$691$	−3.21593	+	9.89763i	−0.122340	+	0.376524i	0.871067	+	0.491164i	$0.163428\pi$
$692$	−4.08774	+	0.647434i	−0.155392	+	0.0246117i
$693$	−13.3115	+	12.7575i	−0.505662	+	0.484617i
$694$	−0.487079	+	0.670407i	−0.0184893	+	0.0254483i
$695$		0			0
$696$	0.421163	+	0.0713003i	0.0159641	+	0.00270263i
$697$	−64.4062	−	10.2009i	−2.43956	−	0.386388i
$698$	−0.0759465	+	0.149053i	−0.00287462	+	0.00564175i
$699$	17.7101	+	18.0905i	0.669857	+	0.684244i
$700$		0			0
$701$		−	29.3464i		−	1.10840i	−0.832384	−	0.554199i	$-0.813025\pi$
$701$		−	29.3464i		−	1.10840i	0.832384	−	0.554199i	$-0.186975\pi$
$702$	0.799159	−	0.231781i	0.0301623	−	0.00874802i
$703$	1.39271	−	8.79321i	0.0525270	−	0.331642i
$704$	−19.3613	+	14.0668i	−0.729707	+	0.530163i
$705$		0			0
$706$	−1.20884	−	0.878275i	−0.0454953	−	0.0330543i
$707$	17.6533	−	17.6533i	0.663920	−	0.663920i
$708$	−8.91612	+	12.0018i	−0.335088	+	0.451053i
$709$	18.4297	+	5.98817i	0.692141	+	0.224890i	0.633903	−	0.773412i	$-0.281452\pi$
$709$	18.4297	+	5.98817i	0.692141	+	0.224890i	0.0582380	+	0.998303i	$0.481452\pi$
$710$		0			0
$711$	29.3507	−	8.85176i	1.10074	−	0.331967i
$712$	−2.46207	+	1.25449i	−0.0922700	+	0.0470139i
$713$	0.102208	−	0.0520778i	0.00382774	−	0.00195033i
$714$	−0.972793	−	0.508752i	−0.0364059	−	0.0190396i
$715$		0			0
$716$	−9.64197	−	3.13287i	−0.360337	−	0.117081i
$717$	5.63167	+	4.18378i	0.210319	+	0.156246i
$718$	0.999546	−	0.999546i	0.0373027	−	0.0373027i
$719$	23.3742	+	16.9824i	0.871712	+	0.633336i	0.931046	−	0.364903i	$-0.118898\pi$
$719$	23.3742	+	16.9824i	0.871712	+	0.633336i	−0.0593341	+	0.998238i	$0.518898\pi$
$720$		0			0
$721$	27.7094	−	20.1321i	1.03195	−	0.749758i
$722$	0.0673877	−	0.425469i	0.00250791	−	0.0158343i
$723$	−1.02486	−	3.27208i	−0.0381150	−	0.121690i
$724$		−	2.08966i		−	0.0776615i
$725$		0			0
$726$	−0.120737	+	0.118199i	−0.00448097	+	0.00438676i
$727$	−11.8992	+	23.3536i	−0.441318	+	0.866136i	0.558022	+	0.829826i	$0.311560\pi$
$727$	−11.8992	+	23.3536i	−0.441318	+	0.866136i	−0.999341	+	0.0363101i	$0.988440\pi$
$728$	−1.28877	−	0.204121i	−0.0477649	−	0.00756521i
$729$	−22.8101	+	14.4465i	−0.844817	+	0.535055i
$730$		0			0
$731$	19.7965	−	27.2475i	0.732199	−	1.00779i
$732$	0.475156	−	44.7220i	0.0175623	−	1.65297i
$733$	39.8719	−	6.31509i	1.47270	−	0.233253i	0.632092	−	0.774893i	$-0.282196\pi$
$733$	39.8719	−	6.31509i	1.47270	−	0.233253i	0.840610	+	0.541640i	$0.182196\pi$
$734$	0.0867856	−	0.267099i	0.00320332	−	0.00985879i
$735$		0			0
$736$	1.08794	+	3.34834i	0.0401020	+	0.123421i
$737$	1.27548	+	2.50327i	0.0469830	+	0.0922093i
$738$	−1.47882	+	0.714333i	−0.0544360	+	0.0262950i
$739$	−15.4065	+	5.00589i	−0.566739	+	0.184145i	−0.578351	−	0.815788i	$-0.696304\pi$
$739$	−15.4065	+	5.00589i	−0.566739	+	0.184145i	0.0116122	+	0.999933i	$0.496304\pi$
$740$		0			0
$741$	15.8093	−	7.84478i	0.580767	−	0.288185i
$742$	0.0661757	+	0.417817i	0.00242939	+	0.0153385i
$743$	3.57440	+	3.57440i	0.131132	+	0.131132i	0.769626	−	0.638494i	$-0.220442\pi$
$743$	3.57440	+	3.57440i	0.131132	+	0.131132i	−0.638494	+	0.769626i	$0.720442\pi$
$744$	0.00102943	+	0.00697861i	3.77406e−5	+	0.000255848i
$745$		0			0
$746$	−0.226154	−	0.311274i	−0.00828009	−	0.0113966i
$747$	−6.49312	−	1.17034i	−0.237571	−	0.0428205i
$748$	−32.6562	−	16.6392i	−1.19403	−	0.608388i
$749$	−10.2516			−0.374585
$750$		0			0
$751$	5.81393			0.212153			0.106077	−	0.994358i	$-0.466171\pi$
$751$	5.81393			0.212153			0.106077	+	0.994358i	$0.466171\pi$
$752$	13.0646	+	6.65676i	0.476418	+	0.242747i
$753$	−27.1174	−	38.1702i	−0.988212	−	1.39100i
$754$	0.113660	+	0.156440i	0.00413926	+	0.00569720i
$755$		0			0
$756$	20.9903	−	2.64196i	0.763412	−	0.0960870i
$757$	−3.51235	−	3.51235i	−0.127658	−	0.127658i	0.640391	−	0.768049i	$-0.278772\pi$
$757$	−3.51235	−	3.51235i	−0.127658	−	0.127658i	−0.768049	+	0.640391i	$0.778772\pi$
$758$	−0.183506	−	1.15861i	−0.00666525	−	0.0420827i
$759$	13.3530	+	26.9097i	0.484682	+	0.976759i
$760$		0			0
$761$	−16.5920	+	5.39106i	−0.601459	+	0.195426i	−0.593891	−	0.804546i	$-0.702409\pi$
$761$	−16.5920	+	5.39106i	−0.601459	+	0.195426i	−0.00756785	+	0.999971i	$0.502409\pi$
$762$	−0.0985854	+	0.292793i	−0.00357137	+	0.0106068i
$763$	−9.53488	−	18.7133i	−0.345186	−	0.677465i
$764$	11.6823	+	35.9545i	0.422651	+	1.30079i
$765$		0			0
$766$	0.121870	−	0.375077i	0.00440334	−	0.0135521i
$767$	−13.3787	+	2.11898i	−0.483077	+	0.0765119i
$768$	27.3503	+	0.290587i	0.986918	+	0.0104857i
$769$	−2.97500	+	4.09474i	−0.107281	+	0.147660i	−0.859282	−	0.511502i	$-0.829089\pi$
$769$	−2.97500	+	4.09474i	−0.107281	+	0.147660i	0.752000	+	0.659163i	$0.229089\pi$
$770$		0			0
$771$	−3.60309	+	21.2830i	−0.129762	+	0.766489i
$772$	21.8870	+	3.46656i	0.787731	+	0.124764i
$773$	2.40071	−	4.71165i	0.0863474	−	0.169466i	−0.843795	−	0.536666i	$-0.819683\pi$
$773$	2.40071	−	4.71165i	0.0863474	−	0.169466i	0.930142	+	0.367200i	$0.119683\pi$
$774$	0.0180224	−	0.848043i	0.000647801	−	0.0304823i
$775$		0			0
$776$		−	1.09491i		−	0.0393049i
$777$	9.22668	−	2.88992i	0.331005	−	0.103675i
$778$	0.139386	−	0.880046i	0.00499722	−	0.0315512i
$779$	−28.1806	+	20.4744i	−1.00968	+	0.733572i
$780$		0			0
$781$	−24.0343	−	17.4619i	−0.860014	−	0.624837i
$782$	−1.26476	+	1.26476i	−0.0452275	+	0.0452275i
$783$	−4.95610	−	3.84797i	−0.177117	−	0.137515i
$784$	10.7805	+	3.50279i	0.385017	+	0.125100i
$785$		0			0
$786$	−0.320230	+	0.612316i	−0.0114222	+	0.0218406i
$787$	−28.7152	+	14.6311i	−1.02359	+	0.521543i	−0.883418	−	0.468585i	$-0.844764\pi$
$787$	−28.7152	+	14.6311i	−1.02359	+	0.521543i	−0.140167	+	0.990128i	$0.544764\pi$
$788$	44.8292	−	22.8416i	1.59697	−	0.813699i
$789$	−2.89329	+	5.53230i	−0.103004	+	0.196955i
$790$		0			0
$791$	16.9641	+	5.51196i	0.603173	+	0.195983i
$792$	−1.83032	+	0.250154i	−0.0650374	+	0.00888884i
$793$	28.6515	−	28.6515i	1.01745	−	1.01745i
$794$	−0.428933	−	0.311638i	−0.0152223	−	0.0110596i
$795$		0			0
$796$	−26.0410	+	18.9199i	−0.923000	+	0.670599i
$797$	4.29713	−	27.1310i	0.152212	−	0.961030i	−0.786816	−	0.617188i	$-0.788272\pi$
$797$	4.29713	−	27.1310i	0.152212	−	0.961030i	0.939028	−	0.343841i	$-0.111728\pi$
$798$	−0.559610	+	0.175277i	−0.0198100	+	0.00620475i
$799$			22.3966i			0.792336i
$800$		0			0
$801$	40.5805	+	0.862405i	1.43384	+	0.0304716i
$802$	0.341007	−	0.669264i	0.0120414	−	0.0236325i
$803$	0.116478	+	0.0184483i	0.00411041	+	0.000651025i
$804$	0.538094	−	3.17846i	0.0189771	−	0.112096i
$805$		0			0
$806$	−0.00187701	+	0.00258348i	−6.61147e−5	+	9.09991e-5i
$807$	−23.5042	−	0.249724i	−0.827388	−	0.00879072i
$808$	2.47057	−	0.391301i	0.0869145	−	0.0137659i
$809$	−1.47285	+	4.53298i	−0.0517828	+	0.159371i	−0.973604	−	0.228245i	$-0.926701\pi$
$809$	−1.47285	+	4.53298i	−0.0517828	+	0.159371i	0.921821	+	0.387616i	$0.126701\pi$
$810$		0			0
$811$	−17.2310	−	53.0316i	−0.605062	−	1.86219i	−0.496363	−	0.868115i	$-0.665331\pi$
$811$	−17.2310	−	53.0316i	−0.605062	−	1.86219i	−0.108700	−	0.994075i	$-0.534669\pi$
$812$	2.23202	+	4.38058i	0.0783284	+	0.153728i
$813$	−4.55514	+	13.5285i	−0.159756	+	0.474466i
$814$	−0.401210	+	0.130361i	−0.0140624	+	0.00456915i
$815$		0			0
$816$	18.6686	+	37.6220i	0.653532	+	1.31703i
$817$	−2.81441	−	17.7695i	−0.0984636	−	0.621675i
$818$	0.179879	+	0.179879i	0.00628932	+	0.00628932i
$819$	15.2634	+	11.5929i	0.533347	+	0.405088i
$820$		0			0
$821$	−11.9603	−	16.4619i	−0.417416	−	0.574524i	0.547591	−	0.836746i	$-0.315545\pi$
$821$	−11.9603	−	16.4619i	−0.417416	−	0.574524i	−0.965008	+	0.262222i	$0.915545\pi$
$822$	−0.508170	−	0.715296i	−0.0177245	−	0.0249488i
$823$	−23.9846	−	12.2207i	−0.836050	−	0.425989i	−0.0170998	−	0.999854i	$-0.505443\pi$
$823$	−23.9846	−	12.2207i	−0.836050	−	0.425989i	−0.818950	+	0.573865i	$0.805443\pi$
$824$	3.43168			0.119548
$825$		0			0
$826$	0.450081			0.0156603
$827$	16.6109	+	8.46369i	0.577618	+	0.294311i	0.718289	−	0.695745i	$-0.244926\pi$
$827$	16.6109	+	8.46369i	0.577618	+	0.294311i	−0.140670	+	0.990057i	$0.544926\pi$
$828$	6.11432	−	33.9227i	0.212487	−	1.17889i
$829$	20.7919	+	28.6176i	0.722132	+	0.993930i	0.999450	+	0.0331514i	$0.0105544\pi$
$829$	20.7919	+	28.6176i	0.722132	+	0.993930i	−0.277318	+	0.960778i	$0.589446\pi$
$830$		0			0
$831$	−4.88146	−	33.0921i	−0.169336	−	1.14795i
$832$	17.5916	+	17.5916i	0.609879	+	0.609879i
$833$	2.70851	+	17.1009i	0.0938444	+	0.592510i
$834$	−0.401515	+	0.199238i	−0.0139033	+	0.00689904i
$835$		0			0
$836$	−18.6198	+	6.04995i	−0.643981	+	0.209242i
$837$	0.0351442	−	0.0974770i	0.00121476	−	0.00336930i
$838$	0.566157	+	1.11115i	0.0195576	+	0.0383839i
$839$	−8.42816	−	25.9392i	−0.290972	−	0.895520i	−0.984545	−	0.175134i	$-0.943964\pi$
$839$	−8.42816	−	25.9392i	−0.290972	−	0.895520i	0.693572	−	0.720387i	$-0.256036\pi$
$840$		0			0
$841$	−8.51090	+	26.1939i	−0.293479	+	0.903237i
$842$	0.142090	−	0.0225049i	0.00489676	−	0.000775570i
$843$	−0.191006	+	17.9776i	−0.00657859	+	0.619182i
$844$	18.6806	−	25.7117i	0.643013	−	0.885032i
$845$		0			0
$846$	0.321779	+	0.463280i	0.0110630	+	0.0159279i
$847$	−3.84405	−	0.608837i	−0.132083	−	0.0209199i
$848$	7.34738	−	14.4201i	0.252310	−	0.495187i
$849$	11.9328	−	11.6819i	0.409531	−	0.400920i
$850$		0			0
$851$		−	15.7531i		−	0.540011i
$852$	10.1887	+	32.5295i	0.349059	+	1.11444i
$853$	−7.57479	+	47.8254i	−0.259356	+	1.63751i	0.422743	+	0.906250i	$0.361067\pi$
$853$	−7.57479	+	47.8254i	−0.259356	+	1.63751i	−0.682099	+	0.731260i	$0.738933\pi$
$854$	−1.08922	+	0.791367i	−0.0372725	+	0.0270800i
$855$		0			0
$856$	−0.830973	−	0.603737i	−0.0284021	−	0.0206353i
$857$	27.4824	−	27.4824i	0.938780	−	0.938780i	−0.0594514	−	0.998231i	$-0.518935\pi$
$857$	27.4824	−	27.4824i	0.938780	−	0.938780i	0.998231	+	0.0594514i	$0.0189351\pi$
$858$	−0.671299	−	0.498709i	−0.0229178	−	0.0170257i
$859$	28.7211	+	9.33206i	0.979953	+	0.318406i	0.754827	−	0.655924i	$-0.227721\pi$
$859$	28.7211	+	9.33206i	0.979953	+	0.318406i	0.225126	+	0.974330i	$0.427721\pi$
$860$		0			0
$861$	−33.5221	−	17.5314i	−1.14243	−	0.597470i
$862$	1.00430	−	0.511717i	0.0342066	−	0.0174291i
$863$	32.1153	−	16.3635i	1.09322	−	0.557021i	0.188085	−	0.982153i	$-0.439772\pi$
$863$	32.1153	−	16.3635i	1.09322	−	0.557021i	0.905132	+	0.425131i	$0.139772\pi$
$864$	2.78614	+	1.53335i	0.0947864	+	0.0521657i
$865$		0			0
$866$	1.95956	+	0.636700i	0.0665886	+	0.0216360i
$867$	−20.6973	+	27.8601i	−0.702917	+	0.946178i
$868$	−0.0574107	+	0.0574107i	−0.00194865	+	0.00194865i
$869$	−24.9262	−	18.1100i	−0.845564	−	0.614338i
$870$		0			0
$871$	2.36280	−	1.71668i	0.0800606	−	0.0581674i
$872$	0.329184	−	2.07838i	0.0111476	−	0.0703830i
$873$	−7.60446	+	14.1719i	−0.257372	+	0.479646i
$874$			0.955447i			0.0323185i
$875$		0			0
$876$	−0.0946608	−	0.0966939i	−0.00319829	−	0.00326698i
$877$	18.8108	−	36.9183i	0.635195	−	1.24664i	−0.319085	−	0.947726i	$-0.603375\pi$
$877$	18.8108	−	36.9183i	0.635195	−	1.24664i	0.954280	−	0.298915i	$-0.0966246\pi$
$878$	0.656722	+	0.104015i	0.0221633	+	0.00351032i
$879$	18.7077	+	3.16710i	0.630994	+	0.106824i
$880$		0			0
$881$	7.72042	−	10.6262i	0.260107	−	0.358007i	−0.658912	−	0.752220i	$-0.728983\pi$
$881$	7.72042	−	10.6262i	0.260107	−	0.358007i	0.919019	+	0.394213i	$0.128983\pi$
$882$	0.301719	+	0.314822i	0.0101594	+	0.0106006i
$883$	8.14408	−	1.28990i	0.274070	−	0.0434084i	−0.0178865	−	0.999840i	$-0.505694\pi$
$883$	8.14408	−	1.28990i	0.274070	−	0.0434084i	0.291957	+	0.956432i	$0.405694\pi$
$884$	−11.7736	+	36.2354i	−0.395989	+	1.21873i
$885$		0			0
$886$	−0.462245	−	1.42265i	−0.0155294	−	0.0477947i
$887$	3.97322	+	7.79789i	0.133408	+	0.261827i	0.948040	−	0.318150i	$-0.103061\pi$
$887$	3.97322	+	7.79789i	0.133408	+	0.261827i	−0.814633	+	0.579977i	$0.803061\pi$
$888$	0.918089	+	0.309127i	0.0308090	+	0.0103736i
$889$	−6.76808	+	2.19908i	−0.226994	+	0.0737548i
$890$		0			0
$891$	25.4280	+	9.47423i	0.851870	+	0.317398i
$892$	−6.80112	−	42.9406i	−0.227718	−	1.43776i
$893$	8.45966	+	8.45966i	0.283092	+	0.283092i
$894$	0.182596	−	0.0269350i	0.00610692	−	0.000900842i
$895$		0			0
$896$	−1.95248	−	2.68736i	−0.0652279	−	0.0897785i
$897$	25.4579	−	18.0862i	0.850015	−	0.603879i
$898$	−1.24629	−	0.635018i	−0.0415893	−	0.0211908i
$899$	0.0240800			0.000803114
$900$		0			0
$901$	24.7202			0.823551
$902$	1.47066	+	0.749338i	0.0489676	+	0.0249502i
$903$	15.9282	−	11.3159i	0.530058	−	0.376571i
$904$	1.05046	+	1.44584i	0.0349378	+	0.0480878i
$905$		0			0
$906$	0.274156	−	0.0404412i	0.00910823	−	0.00134357i
$907$	−22.7174	−	22.7174i	−0.754317	−	0.754317i	0.220964	−	0.975282i	$-0.429080\pi$
$907$	−22.7174	−	22.7174i	−0.754317	−	0.754317i	−0.975282	+	0.220964i	$0.929080\pi$
$908$	−6.70314	−	42.3220i	−0.222452	−	1.40450i
$909$	−34.6955	−	12.0941i	−1.15078	−	0.401136i
$910$		0			0
$911$	−32.0727	+	10.4210i	−1.06262	+	0.345265i	−0.787607	−	0.616177i	$-0.788680\pi$
$911$	−32.0727	+	10.4210i	−1.06262	+	0.345265i	−0.275008	+	0.961442i	$0.588680\pi$
$912$	21.2621	+	7.15910i	0.704059	+	0.237061i
$913$	3.01037	+	5.90818i	0.0996286	+	0.195532i
$914$	0.213945	+	0.658455i	0.00707667	+	0.0217798i
$915$		0			0
$916$	7.13239	−	21.9512i	0.235661	−	0.725289i
$917$	−15.7208	+	2.48993i	−0.519147	+	0.0822248i
$918$	−0.0514874	+	1.61486i	−0.00169934	+	0.0532982i
$919$	21.7602	−	29.9504i	0.717804	−	0.987972i	−0.281790	−	0.959476i	$-0.590928\pi$
$919$	21.7602	−	29.9504i	0.717804	−	0.987972i	0.999594	−	0.0284959i	$-0.00907174\pi$
$920$		0			0
$921$	43.0947	+	7.29567i	1.42002	+	0.240400i
$922$	−1.46461	−	0.231971i	−0.0482343	−	0.00763956i
$923$	−14.0205	+	27.5167i	−0.461490	+	0.905724i
$924$	−14.8741	−	15.1936i	−0.489322	−	0.499832i
$925$		0			0
$926$			0.365984i			0.0120270i
$927$	−44.4178	−	23.8341i	−1.45887	−	0.782813i
$928$	−0.115613	+	0.729951i	−0.00379518	+	0.0239618i
$929$	21.0087	−	15.2637i	0.689272	−	0.500785i	−0.187149	−	0.982332i	$-0.559925\pi$
$929$	21.0087	−	15.2637i	0.689272	−	0.500785i	0.876421	+	0.481546i	$0.159925\pi$
$930$		0			0
$931$	7.48241	+	5.43629i	0.245226	+	0.178167i
$932$	−20.6436	+	20.6436i	−0.676205	+	0.676205i
$933$	−4.90552	+	6.60318i	−0.160599	+	0.216179i
$934$	0.414692	+	0.134742i	0.0135692	+	0.00440888i
$935$		0			0
$936$	0.554491	+	1.83859i	0.0181241	+	0.0600961i
$937$	22.3857	−	11.4061i	0.731310	−	0.372621i	−0.0483450	−	0.998831i	$-0.515395\pi$
$937$	22.3857	−	11.4061i	0.731310	−	0.372621i	0.779655	+	0.626210i	$0.215395\pi$
$938$	−0.0864664	+	0.0440569i	−0.00282323	+	0.00143851i
$939$	41.4475	+	21.6763i	1.35259	+	0.707378i
$940$		0			0
$941$	37.5058	+	12.1864i	1.22265	+	0.397264i	0.848047	−	0.529920i	$-0.177778\pi$
$941$	37.5058	+	12.1864i	1.22265	+	0.397264i	0.374606	+	0.927184i	$0.377778\pi$
$942$	0.457920	+	0.340190i	0.0149198	+	0.0110840i
$943$	−43.5831	+	43.5831i	−1.41926	+	1.41926i
$944$	−13.9305	−	10.1211i	−0.453401	−	0.329415i
$945$		0			0
$946$	−0.689684	+	0.501085i	−0.0224236	+	0.0162917i
$947$	4.35156	−	27.4747i	0.141407	−	0.892808i	−0.810348	−	0.585949i	$-0.800722\pi$
$947$	4.35156	−	27.4747i	0.141407	−	0.892808i	0.951755	−	0.306859i	$-0.0992780\pi$
$948$	10.5668	+	33.7367i	0.343194	+	1.09572i
$949$		−	0.122593i		−	0.00397954i
$950$		0			0
$951$	4.79995	−	4.69903i	0.155649	−	0.152377i
$952$	1.15023	−	2.25745i	0.0372791	−	0.0731644i
$953$	−9.41698	−	1.49150i	−0.305046	−	0.0483145i	0.00203511	−	0.999998i	$-0.499352\pi$
$953$	−9.41698	−	1.49150i	−0.305046	−	0.0483145i	−0.307081	+	0.951683i	$0.599352\pi$
$954$	0.511344	−	0.355163i	0.0165554	−	0.0114988i
$955$		0			0
$956$	−4.75543	+	6.54529i	−0.153802	+	0.211690i
$957$	−0.0669960	+	6.30571i	−0.00216567	+	0.203835i
$958$	−0.738808	+	0.117016i	−0.0238698	+	0.00378060i
$959$	6.24559	−	19.2220i	0.201681	−	0.620709i
$960$		0			0
$961$	−9.57940	−	29.4824i	−0.309013	−	0.951044i
$962$	0.199093	+	0.390741i	0.00641900	+	0.0125980i
$963$	6.56253	+	13.5858i	0.211475	+	0.437796i
$964$	3.76057	−	1.22188i	0.121120	−	0.0393542i
$965$		0			0
$966$	−0.929496	+	0.461229i	−0.0299060	+	0.0148398i
$967$	9.67859	+	61.1082i	0.311242	+	1.96511i	0.256201	+	0.966624i	$0.417529\pi$
$967$	9.67859	+	61.1082i	0.311242	+	1.96511i	0.0550419	+	0.998484i	$0.482471\pi$
$968$	−0.275735	−	0.275735i	−0.00886245	−	0.00886245i
$969$	5.00086	+	33.9015i	0.160651	+	1.08907i
$970$		0			0
$971$	−15.4537	−	21.2702i	−0.495933	−	0.682594i	0.485535	−	0.874217i	$-0.338625\pi$
$971$	−15.4537	−	21.2702i	−0.495933	−	0.682594i	−0.981469	+	0.191623i	$0.938625\pi$
$972$	−16.9381	−	26.1259i	−0.543290	−	0.837990i
$973$	−9.19942	−	4.68734i	−0.294920	−	0.150269i
$974$	−0.640128			−0.0205110
$975$		0			0
$976$	51.5085			1.64875
$977$	17.3791	+	8.85510i	0.556007	+	0.283300i	0.709330	−	0.704876i	$-0.248998\pi$
$977$	17.3791	+	8.85510i	0.556007	+	0.283300i	−0.153323	+	0.988176i	$0.548998\pi$
$978$	0.937048	+	1.31898i	0.0299635	+	0.0421763i
$979$	−23.9779	−	33.0027i	−0.766336	−	1.05477i
$980$		0			0
$981$	−18.6958	+	24.6152i	−0.596910	+	0.785903i
$982$	1.32033	+	1.32033i	0.0421335	+	0.0421335i
$983$	−8.67590	−	54.7775i	−0.276718	−	1.74713i	−0.599241	−	0.800569i	$-0.704531\pi$
$983$	−8.67590	−	54.7775i	−0.276718	−	1.74713i	0.322523	−	0.946562i	$-0.395469\pi$
$984$	−1.68477	−	3.39525i	−0.0537085	−	0.108237i
$985$		0			0
$986$	−0.357091	+	0.116026i	−0.0113721	+	0.00369502i
$987$	−4.14610	+	12.3137i	−0.131972	+	0.391949i
$988$	9.23973	+	18.1340i	0.293955	+	0.576919i
$989$	−9.83731	−	30.2761i	−0.312808	−	0.962725i
$990$		0			0
$991$	−8.12909	+	25.0188i	−0.258229	+	0.794748i	0.734947	+	0.678124i	$0.237207\pi$
$991$	−8.12909	+	25.0188i	−0.258229	+	0.794748i	−0.993176	+	0.116623i	$0.962793\pi$
$992$	−0.0120546	+	0.00190925i	−0.000382733	+	6.06189e-5i
$993$	−30.1402	−	0.320230i	−0.956471	−	0.0101622i
$994$	0.603158	−	0.830176i	0.0191310	−	0.0263316i
$995$		0			0
$996$	1.27000	−	7.50174i	0.0402415	−	0.237702i
$997$	25.0233	+	3.96330i	0.792496	+	0.125519i	0.539541	−	0.841959i	$-0.318598\pi$
$997$	25.0233	+	3.96330i	0.792496	+	0.125519i	0.252955	+	0.967478i	$0.418598\pi$
$998$	0.194664	−	0.382049i	0.00616197	−	0.0120935i
$999$	−9.73626	−	10.3776i	−0.308042	−	0.328332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.l.a.107.4		64
3.2	odd	2	inner	375.2.l.a.107.5		64
5.2	odd	4		375.2.l.c.143.5		64
5.3	odd	4		75.2.l.a.8.4	✓	64
5.4	even	2		375.2.l.b.107.5		64
15.2	even	4		375.2.l.c.143.4		64
15.8	even	4		75.2.l.a.8.5	yes	64
15.14	odd	2		375.2.l.b.107.4		64
25.3	odd	20	inner	375.2.l.a.368.5		64
25.4	even	10		375.2.l.c.257.4		64
25.21	even	5		75.2.l.a.47.5	yes	64
25.22	odd	20		375.2.l.b.368.4		64
75.29	odd	10		375.2.l.c.257.5		64
75.47	even	20		375.2.l.b.368.5		64
75.53	even	20	inner	375.2.l.a.368.4		64
75.71	odd	10		75.2.l.a.47.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.l.a.8.4	✓	64	5.3	odd	4
75.2.l.a.8.5	yes	64	15.8	even	4
75.2.l.a.47.4	yes	64	75.71	odd	10
75.2.l.a.47.5	yes	64	25.21	even	5
375.2.l.a.107.4		64	1.1	even	1	trivial
375.2.l.a.107.5		64	3.2	odd	2	inner
375.2.l.a.368.4		64	75.53	even	20	inner
375.2.l.a.368.5		64	25.3	odd	20	inner
375.2.l.b.107.4		64	15.14	odd	2
375.2.l.b.107.5		64	5.4	even	2
375.2.l.b.368.4		64	25.22	odd	20
375.2.l.b.368.5		64	75.47	even	20
375.2.l.c.143.4		64	15.2	even	4
375.2.l.c.143.5		64	5.2	odd	4
375.2.l.c.257.4		64	25.4	even	10
375.2.l.c.257.5		64	75.29	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0455229 - 0.0231951i) q^{2} +(-1.41200 + 1.00313i) q^{3} +(-1.17404 - 1.61592i) q^{4} +(0.0875458 - 0.0129140i) q^{6} +(1.44136 + 1.44136i) q^{7} +(0.0319491 + 0.201718i) q^{8} +(0.987463 - 2.83283i) q^{9} +(-2.86751 + 0.931709i) q^{11} +(3.27871 + 1.10396i) q^{12} +(1.42294 + 2.79268i) q^{13} +(-0.0321825 - 0.0990475i) q^{14} +(-1.23123 + 3.78934i) q^{16} +(-6.01096 + 0.952042i) q^{17} +(-0.110660 + 0.106054i) q^{18} +(-1.91085 + 2.63007i) q^{19} +(-3.48107 - 0.589324i) q^{21} +(0.152148 + 0.0240979i) q^{22} +(-2.61153 + 5.12542i) q^{23} +(-0.247462 - 0.252776i) q^{24} -0.160136i q^{26} +(1.44740 + 4.99049i) q^{27} +(0.636918 - 4.02134i) q^{28} +(-0.976916 + 0.709771i) q^{29} +(-0.0161330 - 0.0117213i) q^{31} +(0.432772 - 0.432772i) q^{32} +(3.11428 - 4.19205i) q^{33} +(0.295719 + 0.0960849i) q^{34} +(-5.73695 + 1.73018i) q^{36} +(-2.44005 + 1.24327i) q^{37} +(0.147992 - 0.0754058i) q^{38} +(-4.81061 - 2.51586i) q^{39} +(10.1904 + 3.31106i) q^{41} +(0.144799 + 0.107571i) q^{42} +(-3.91319 + 3.91319i) q^{43} +(4.87212 + 3.53981i) q^{44} +(0.237769 - 0.172749i) q^{46} +(0.575694 - 3.63479i) q^{47} +(-2.06270 - 6.58561i) q^{48} -2.84495i q^{49} +(7.53242 - 7.37405i) q^{51} +(2.84217 - 5.57807i) q^{52} +(-4.01189 - 0.635421i) q^{53} +(0.0498650 - 0.260754i) q^{54} +(-0.244699 + 0.336799i) q^{56} +(0.0598219 - 5.63047i) q^{57} +(0.0609353 - 0.00965120i) q^{58} +(-1.33548 + 4.11017i) q^{59} +(-3.99489 - 12.2950i) q^{61} +(0.000462544 + 0.000907794i) q^{62} +(5.50642 - 2.65984i) q^{63} +(7.54893 - 2.45280i) q^{64} +(-0.239006 + 0.118598i) q^{66} +(-0.145768 - 0.920343i) q^{67} +(8.59551 + 8.59551i) q^{68} +(-1.45399 - 9.85678i) q^{69} +(5.79154 + 7.97137i) q^{71} +(0.602982 + 0.108683i) q^{72} +(-0.0348503 - 0.0177571i) q^{73} +0.139916 q^{74} +6.49339 q^{76} +(-5.47604 - 2.79018i) q^{77} +(0.160637 + 0.226112i) q^{78} +(6.00647 + 8.26720i) q^{79} +(-7.04983 - 5.59463i) q^{81} +(-0.387096 - 0.387096i) q^{82} +(-0.344039 - 2.17217i) q^{83} +(3.13460 + 6.31702i) q^{84} +(0.268906 - 0.0873730i) q^{86} +(0.667409 - 1.98217i) q^{87} +(-0.279557 - 0.548661i) q^{88} +(4.18096 + 12.8677i) q^{89} +(-1.97429 + 6.07624i) q^{91} +(11.3483 - 1.79740i) q^{92} +(0.0345377 + 0.000366951i) q^{93} +(-0.110516 + 0.152113i) q^{94} +(-0.176946 + 1.04520i) q^{96} +(-5.29507 - 0.838657i) q^{97} +(-0.0659889 + 0.129510i) q^{98} +(-0.192183 + 9.04318i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 20 q^{4} - 6 q^{6} - 20 q^{7} + 10 q^{9} - 40 q^{12} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 30 q^{27} + 80 q^{28} - 12 q^{31} + 50 q^{33} - 20 q^{34} - 22 q^{36} + 120 q^{37} - 30 q^{39} - 60 q^{42}+ \cdots + 42 q^{96}+O(q^{100}) \) 64 * q + 20 * q^4 - 6 * q^6 - 20 * q^7 + 10 * q^9 - 40 * q^12 - 8 * q^16 - 10 * q^18 - 6 * q^21 + 30 * q^27 + 80 * q^28 - 12 * q^31 + 50 * q^33 - 20 * q^34 - 22 * q^36 + 120 * q^37 - 30 * q^39 - 60 * q^42 - 20 * q^43 - 12 * q^46 - 100 * q^48 - 16 * q^51 - 100 * q^52 - 120 * q^54 + 70 * q^57 - 120 * q^58 - 12 * q^61 + 70 * q^63 + 100 * q^64 - 30 * q^66 + 60 * q^67 + 80 * q^69 + 40 * q^72 + 80 * q^73 - 64 * q^76 - 70 * q^78 + 60 * q^79 + 14 * q^81 - 60 * q^82 + 130 * q^84 - 100 * q^87 - 60 * q^88 - 12 * q^91 - 20 * q^93 - 260 * q^94 + 42 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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